LMFDB - Embedded newform 216.2.n.b.37.7

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			37.7
Root			$-0.179748 - 1.40274i$ of defining polynomial
Character	$\chi$	$=$	216.37
Dual form			216.2.n.b.181.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12494 + 0.857038i) q^{2} +(0.530970 + 1.92823i) q^{4} +(-1.19115 - 0.687709i) q^{5} +(1.80469 + 3.12581i) q^{7} +(-1.05526 + 2.62420i) q^{8} +O(q^{10})$	\(q+(1.12494 + 0.857038i) q^{2} +(0.530970 + 1.92823i) q^{4} +(-1.19115 - 0.687709i) q^{5} +(1.80469 + 3.12581i) q^{7} +(-1.05526 + 2.62420i) q^{8} +(-0.750573 - 1.79449i) q^{10} +(1.83294 - 1.05825i) q^{11} +(0.887751 + 0.512543i) q^{13} +(-0.648778 + 5.06302i) q^{14} +(-3.43614 + 2.04766i) q^{16} -0.808822 q^{17} -7.43122i q^{19} +(0.693598 - 2.66196i) q^{20} +(2.96890 + 0.380437i) q^{22} +(1.65498 - 2.86652i) q^{23} +(-1.55411 - 2.69180i) q^{25} +(0.559395 + 1.33742i) q^{26} +(-5.06904 + 5.13956i) q^{28} +(-7.71083 + 4.45185i) q^{29} +(3.26436 - 5.65403i) q^{31} +(-5.62037 - 0.641410i) q^{32} +(-0.909875 - 0.693192i) q^{34} -4.96439i q^{35} +4.01531i q^{37} +(6.36884 - 8.35966i) q^{38} +(3.06165 - 2.40010i) q^{40} +(3.45852 - 5.99034i) q^{41} +(0.245957 - 0.142003i) q^{43} +(3.01378 + 2.97243i) q^{44} +(4.31847 - 1.80627i) q^{46} +(3.61351 + 6.25878i) q^{47} +(-3.01378 + 5.22003i) q^{49} +(0.558698 - 4.36005i) q^{50} +(-0.516932 + 1.98393i) q^{52} -3.86330i q^{53} -2.91107 q^{55} +(-10.1072 + 1.43732i) q^{56} +(-12.4896 - 1.60042i) q^{58} +(7.06904 + 4.08131i) q^{59} +(-6.31237 + 3.64445i) q^{61} +(8.51792 - 3.56275i) q^{62} +(-5.77286 - 5.53842i) q^{64} +(-0.704961 - 1.22103i) q^{65} +(2.43973 + 1.40858i) q^{67} +(-0.429460 - 1.55960i) q^{68} +(4.25468 - 5.58463i) q^{70} -4.69830 q^{71} +0.409922 q^{73} +(-3.44128 + 4.51698i) q^{74} +(14.3291 - 3.94576i) q^{76} +(6.61576 + 3.81961i) q^{77} +(-0.0456121 - 0.0790024i) q^{79} +(5.50115 - 0.0760042i) q^{80} +(9.02458 - 3.77467i) q^{82} +(-2.40891 + 1.39079i) q^{83} +(0.963426 + 0.556234i) q^{85} +(0.398389 + 0.0510497i) q^{86} +(0.842830 + 5.92673i) q^{88} -8.91934 q^{89} +3.69992i q^{91} +(6.40605 + 1.66916i) q^{92} +(-1.29904 + 10.1377i) q^{94} +(-5.11052 + 8.85168i) q^{95} +(-2.76022 - 4.78084i) q^{97} +(-7.86408 + 3.28928i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.12494	+	0.857038i	0.795451	+	0.606018i
$2$	1.12494	+	0.857038i	0.795451	+	0.606018i
$3$		0			0
$3$		0			0
$4$	0.530970	+	1.92823i	0.265485	+	0.964115i
$5$	−1.19115	−	0.687709i	−0.532697	−	0.307553i	0.209417	−	0.977826i	$-0.432843\pi$
$5$	−1.19115	−	0.687709i	−0.532697	−	0.307553i	−0.742114	+	0.670274i	$0.766177\pi$
$6$		0			0
$7$	1.80469	+	3.12581i	0.682107	+	1.18144i	0.974337	+	0.225096i	$0.0722696\pi$
$7$	1.80469	+	3.12581i	0.682107	+	1.18144i	−0.292229	+	0.956348i	$0.594397\pi$
$8$	−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	$-0.563295\pi$
$11$	1.83294	−	1.05825i	0.552652	−	0.319074i	0.750191	+	0.661221i	$0.229961\pi$
$12$		0			0
$13$	0.887751	+	0.512543i	0.246218	+	0.142154i	0.618031	−	0.786154i	$-0.287931\pi$
$13$	0.887751	+	0.512543i	0.246218	+	0.142154i	−0.371813	+	0.928307i	$0.621264\pi$
$14$	−0.648778	+	5.06302i	−0.173393	+	1.35315i
$15$		0			0
$16$	−3.43614	+	2.04766i	−0.859035	+	0.511916i
$17$	−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	$-0.324866\pi$
$20$	0.693598	−	2.66196i	0.155093	−	0.595232i
$21$		0			0
$22$	2.96890	+	0.380437i	0.632972	+	0.0811093i
$23$	1.65498	−	2.86652i	0.345088	−	0.597710i	−0.640282	−	0.768140i	$-0.721182\pi$
$23$	1.65498	−	2.86652i	0.345088	−	0.597710i	0.985370	+	0.170430i	$0.0545157\pi$
$24$		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	$-0.976444\pi$
$29$	−7.71083	+	4.45185i	−1.43187	+	0.826688i	−0.434603	+	0.900622i	$0.643111\pi$
$30$		0			0
$31$	3.26436	−	5.65403i	0.586296	−	1.01549i	−0.408417	−	0.912796i	$-0.633919\pi$
$31$	3.26436	−	5.65403i	0.586296	−	1.01549i	0.994713	−	0.102698i	$-0.0327476\pi$
$32$	−5.62037	−	0.641410i	−0.993551	−	0.113386i
$33$		0			0
$34$	−0.909875	−	0.693192i	−0.156042	−	0.118881i
$35$		−	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	$0.892932\pi$
$38$	6.36884	−	8.35966i	1.03316	−	1.35612i
$39$		0			0
$40$	3.06165	−	2.40010i	0.484090	−	0.379489i
$41$	3.45852	−	5.99034i	0.540131	−	0.935534i	−0.458765	−	0.888557i	$-0.651708\pi$
$41$	3.45852	−	5.99034i	0.540131	−	0.935534i	0.998896	−	0.0469764i	$-0.0149585\pi$
$42$		0			0
$43$	0.245957	−	0.142003i	0.0375081	−	0.0216553i	−0.481129	−	0.876650i	$-0.659773\pi$
$43$	0.245957	−	0.142003i	0.0375081	−	0.0216553i	0.518637	+	0.854995i	$0.326440\pi$
$44$	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	0.999502	+	0.0315619i	$0.0100481\pi$
$47$	3.61351	+	6.25878i	0.527084	+	0.912937i	−0.472417	+	0.881375i	$0.656619\pi$
$48$		0			0
$49$	−3.01378	+	5.22003i	−0.430540	+	0.745718i
$50$	0.558698	−	4.36005i	0.0790118	−	0.616604i
$51$		0			0
$52$	−0.516932	+	1.98393i	−0.0716856	+	0.275122i
$53$		−	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
$56$	−10.1072	+	1.43732i	−1.35063	+	0.192070i
$57$		0			0
$58$	−12.4896	−	1.60042i	−1.63997	−	0.210146i
$59$	7.06904	+	4.08131i	0.920310	+	0.531341i	0.883734	−	0.467989i	$-0.155021\pi$
$59$	7.06904	+	4.08131i	0.920310	+	0.531341i	0.0365764	+	0.999331i	$0.488355\pi$
$60$		0			0
$61$	−6.31237	+	3.64445i	−0.808216	+	0.466624i	−0.846336	−	0.532650i	$-0.821196\pi$
$61$	−6.31237	+	3.64445i	−0.808216	+	0.466624i	0.0381201	+	0.999273i	$0.487863\pi$
$62$	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	$-0.278283\pi$
$67$	2.43973	+	1.40858i	0.298061	+	0.172085i	−0.343511	+	0.939149i	$0.611616\pi$
$68$	−0.429460	−	1.55960i	−0.0520797	−	0.189129i
$69$		0			0
$70$	4.25468	−	5.58463i	0.508531	−	0.667492i
$71$	−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	$0.492363\pi$
$74$	−3.44128	+	4.51698i	−0.400040	+	0.525088i
$75$		0			0
$76$	14.3291	−	3.94576i	1.64366	−	0.452609i
$77$	6.61576	+	3.81961i	0.753936	+	0.435285i
$78$		0			0
$79$	−0.0456121	−	0.0790024i	−0.00513176	−	0.00888847i	0.863448	−	0.504438i	$-0.168300\pi$
$79$	−0.0456121	−	0.0790024i	−0.00513176	−	0.00888847i	−0.868580	+	0.495549i	$0.834967\pi$
$80$	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	$-0.715450\pi$
$83$	−2.40891	+	1.39079i	−0.264412	+	0.152659i	0.361933	+	0.932204i	$0.382117\pi$
$84$		0			0
$85$	0.963426	+	0.556234i	0.104498	+	0.0603321i
$86$	0.398389	+	0.0510497i	0.0429594	+	0.00550483i
$87$		0			0
$88$	0.842830	+	5.92673i	0.0898460	+	0.631791i
$89$	−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
$92$	6.40605	+	1.66916i	0.667877	+	0.174021i
$93$		0			0
$94$	−1.29904	+	10.1377i	−0.133986	+	1.04562i
$95$	−5.11052	+	8.85168i	−0.524328	+	0.908163i
$96$		0			0
$97$	−2.76022	−	4.78084i	−0.280258	−	0.485421i	0.691190	−	0.722673i	$-0.257087\pi$
$97$	−2.76022	−	4.78084i	−0.280258	−	0.485421i	−0.971448	+	0.237252i	$0.923753\pi$
$98$	−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	$-0.561792\pi$
$101$	5.63193	−	3.25160i	0.560398	−	0.323546i	0.753305	+	0.657671i	$0.228458\pi$
$102$		0			0
$103$	−1.50528	+	2.60723i	−0.148320	+	0.256898i	−0.930607	−	0.366021i	$-0.880720\pi$
$103$	−1.50528	+	2.60723i	−0.148320	+	0.256898i	0.782287	+	0.622918i	$0.214053\pi$
$104$	−2.28182	+	1.78877i	−0.223751	+	0.175403i
$105$		0			0
$106$	3.31100	−	4.34598i	0.321593	−	0.422119i
$107$		−	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	$0.851958\pi$
$110$	−3.27477	−	2.49490i	−0.312237	−	0.237879i
$111$		0			0
$112$	−12.6018	−	7.04533i	−1.19075	−	0.665721i
$113$	−5.66349	+	9.80944i	−0.532776	+	0.922795i	0.466492	+	0.884526i	$0.345518\pi$
$113$	−5.66349	+	9.80944i	−0.532776	+	0.922795i	−0.999267	+	0.0382692i	$0.987816\pi$
$114$		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
$122$	−10.2245	−	1.31017i	−0.925678	−	0.118617i
$123$		0			0
$124$	12.6355	+	3.29231i	1.13471	+	0.295658i
$125$			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	$0.675955\pi$
$128$	−1.74746	−	11.1779i	−0.154455	−	0.988000i
$129$		0			0
$130$	0.253431	−	1.97776i	0.0222274	−	0.173461i
$131$	2.40891	+	1.39079i	0.210468	+	0.121514i	0.601529	−	0.798851i	$-0.294559\pi$
$131$	2.40891	+	1.39079i	0.210468	+	0.121514i	−0.391061	+	0.920365i	$0.627892\pi$
$132$		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	0.968907	+	0.247424i	$0.0795840\pi$
$137$	8.17841	+	14.1654i	0.698729	+	1.21023i	−0.270178	+	0.962810i	$0.587083\pi$
$138$		0			0
$139$	−1.22979	−	0.710017i	−0.104309	−	0.0602229i	0.446938	−	0.894565i	$-0.352514\pi$
$139$	−1.22979	−	0.710017i	−0.104309	−	0.0602229i	−0.551247	+	0.834342i	$0.685848\pi$
$140$	9.57249	−	2.63594i	0.809023	−	0.222778i
$141$		0			0
$142$	−5.28530	−	4.02663i	−0.443533	−	0.337907i
$143$	2.16959			0.181430
$144$		0			0
$145$	12.2463			1.01700
$146$	0.461137	+	0.351319i	0.0381639	+	0.0290753i
$147$		0			0
$148$	−7.74245	+	2.13201i	−0.636425	+	0.175250i
$149$	−4.91390	−	2.83704i	−0.402563	−	0.232420i	0.285027	−	0.958520i	$-0.407998\pi$
$149$	−4.91390	−	2.83704i	−0.402563	−	0.232420i	−0.687589	+	0.726100i	$0.741331\pi$
$150$		0			0
$151$	7.07318	+	12.2511i	0.575607	+	0.996981i	0.995975	+	0.0896271i	$0.0285675\pi$
$151$	7.07318	+	12.2511i	0.575607	+	0.996981i	−0.420368	+	0.907354i	$0.638099\pi$
$152$	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	$-0.663075\pi$
$157$	−18.6713	−	10.7799i	−1.49013	−	0.860328i	−0.999936	+	0.0112838i	$0.996408\pi$
$158$	0.0163974	−	0.127964i	0.00130451	−	0.0101803i
$159$		0			0
$160$	6.25359	+	4.62919i	0.494389	+	0.365970i
$161$	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	$0.801304\pi$
$164$	13.3871	+	3.48814i	1.04536	+	0.272378i
$165$		0			0
$166$	−3.90183	−	0.499983i	−0.302841	−	0.0388062i
$167$	11.0234	−	19.0931i	0.853019	−	1.47747i	−0.0254524	−	0.999676i	$-0.508103\pi$
$167$	11.0234	−	19.0931i	0.853019	−	1.47747i	0.878471	−	0.477796i	$-0.158564\pi$
$168$		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	$-0.507780\pi$
$173$	10.9052	−	6.29612i	0.829107	−	0.478685i	0.853547	+	0.521016i	$0.174447\pi$
$174$		0			0
$175$	5.60937	−	9.71572i	0.424029	−	0.734439i
$176$	−4.13130	+	7.38954i	−0.311409	+	0.557007i
$177$		0			0
$178$	−10.0337	−	7.64422i	−0.752058	−	0.572958i
$179$			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	$-0.228189\pi$
$182$	−3.17097	+	4.16218i	−0.235048	+	0.308521i
$183$		0			0
$184$	5.77588	+	7.36793i	0.425803	+	0.543171i
$185$	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	−0.967252	−	0.253820i	$-0.918313\pi$
$191$	−9.72173	−	16.8385i	−0.703440	−	1.21839i	0.263812	−	0.964574i	$-0.415020\pi$
$192$		0			0
$193$	0.159120	−	0.275604i	0.0114537	−	0.0198384i	−0.860242	−	0.509886i	$-0.829687\pi$
$193$	0.159120	−	0.275604i	0.0114537	−	0.0198384i	0.871695	+	0.490048i	$0.163021\pi$
$194$	0.992289	−	7.74376i	0.0712422	−	0.555970i
$195$		0			0
$196$	−11.6656	−	3.03959i	−0.833260	−	0.217114i
$197$		−	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	$0.581391\pi$
$200$	8.70382	−	1.23776i	0.615453	−	0.0875225i
$201$		0			0
$202$	9.12232	+	1.16894i	0.641844	+	0.0822462i
$203$	−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	$-0.243564\pi$
$211$	7.00175	+	4.04246i	0.482020	+	0.278294i	−0.239238	+	0.970961i	$0.576898\pi$
$212$	7.44934	−	2.05130i	0.511623	−	0.140884i
$213$		0			0
$214$	0.383433	−	0.503289i	0.0262109	−	0.0344042i
$215$	−0.390628			−0.0266406
$216$		0			0
$217$	23.5646			1.59967
$218$	−8.02614	+	10.5350i	−0.543599	+	0.713521i
$219$		0			0
$220$	−1.54569	−	5.61321i	−0.104210	−	0.378442i
$221$	−0.718032	−	0.414556i	−0.0483001	−	0.0278861i
$222$		0			0
$223$	−2.11236	−	3.65872i	−0.141454	−	0.245006i	0.786590	−	0.617475i	$-0.211844\pi$
$223$	−2.11236	−	3.65872i	−0.141454	−	0.245006i	−0.928044	+	0.372469i	$0.878511\pi$
$224$	−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	$-0.653312\pi$
$227$	1.09451	−	0.631913i	0.0726449	−	0.0419415i	0.535882	+	0.844293i	$0.319979\pi$
$228$		0			0
$229$	6.29196	+	3.63267i	0.415785	+	0.240053i	0.693272	−	0.720676i	$-0.256168\pi$
$229$	6.29196	+	3.63267i	0.415785	+	0.240053i	−0.277487	+	0.960729i	$0.589502\pi$
$230$	−6.38612	−	0.818320i	−0.421088	−	0.0539584i
$231$		0			0
$232$	−3.54563	−	24.9326i	−0.232782	−	1.63691i
$233$	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
$236$	−4.11626	+	15.7978i	−0.267946	+	1.02835i
$237$		0			0
$238$	0.524746	−	4.09509i	0.0340142	−	0.265445i
$239$	−5.96266	+	10.3276i	−0.385692	+	0.668039i	−0.991865	−	0.127294i	$-0.959371\pi$
$239$	−5.96266	+	10.3276i	−0.385692	+	0.668039i	0.606173	+	0.795333i	$0.292704\pi$
$240$		0			0
$241$	1.80170	+	3.12063i	0.116057	+	0.201017i	0.918202	−	0.396113i	$-0.129641\pi$
$241$	1.80170	+	3.12063i	0.116057	+	0.201017i	−0.802145	+	0.597130i	$0.796308\pi$
$242$	−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
$248$	11.3926	+	14.5328i	0.723429	+	0.922833i
$249$		0			0
$250$	−9.55786	+	12.5455i	−0.604492	+	0.793449i
$251$			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
$254$	−13.3126	−	10.1423i	−0.835308	−	0.636383i
$255$		0			0
$256$	7.61414	−	14.0721i	0.475884	−	0.879508i
$257$	1.99885	−	3.46212i	0.124685	−	0.215961i	−0.796925	−	0.604079i	$-0.793541\pi$
$257$	1.99885	−	3.46212i	0.124685	−	0.215961i	0.921610	+	0.388118i	$0.126875\pi$
$258$		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	0.985928	−	0.167169i	$-0.0534627\pi$
$263$	5.64671	+	9.78039i	0.348191	+	0.603085i	−0.637737	+	0.770254i	$0.720129\pi$
$264$		0			0
$265$	−2.65683	+	4.60176i	−0.163208	+	0.282684i
$266$	37.6245	+	4.82121i	2.30690	+	0.295608i
$267$		0			0
$268$	−1.42064	+	5.45228i	−0.0867795	+	0.333051i
$269$			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	$0.378826\pi$
$272$	2.77923	−	1.65620i	0.168515	−	0.100422i
$273$		0			0
$274$	−2.94011	+	22.9444i	−0.177619	+	1.38612i
$275$	−5.69719	−	3.28928i	−0.343554	−	0.198351i
$276$		0			0
$277$	10.9249	−	6.30750i	0.656414	−	0.378981i	−0.134495	−	0.990914i	$-0.542941\pi$
$277$	10.9249	−	6.30750i	0.656414	−	0.378981i	0.790909	+	0.611933i	$0.209608\pi$
$278$	−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	−0.996633	−	0.0819947i	$-0.973871\pi$
$281$	−9.54364	−	16.5301i	−0.569326	−	0.986101i	0.427307	−	0.904107i	$-0.359462\pi$
$282$		0			0
$283$	1.01045	+	0.583382i	0.0600649	+	0.0346785i	0.529732	−	0.848165i	$-0.322293\pi$
$283$	1.01045	+	0.583382i	0.0600649	+	0.0346785i	−0.469667	+	0.882844i	$0.655626\pi$
$284$	−2.49466	−	9.05941i	−0.148031	−	0.537577i
$285$		0			0
$286$	2.44066	+	1.85942i	0.144319	+	0.109950i
$287$	24.9662			1.47371
$288$		0			0
$289$	−16.3458			−0.961518
$290$	13.7763	+	10.4956i	0.808974	+	0.616320i
$291$		0			0
$292$	0.217656	+	0.790423i	0.0127374	+	0.0462560i
$293$	2.11446	+	1.22079i	0.123528	+	0.0713191i	0.560491	−	0.828161i	$-0.310612\pi$
$293$	2.11446	+	1.22079i	0.123528	+	0.0713191i	−0.436963	+	0.899480i	$0.643946\pi$
$294$		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
$302$	−2.54278	+	19.8437i	−0.146321	+	1.14188i
$303$		0			0
$304$	15.2167	+	25.5347i	0.872735	+	1.46452i
$305$	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	$-0.148331\pi$
$308$	−3.85232	+	14.7848i	−0.219506	+	0.842443i
$309$		0			0
$310$	−12.5962	−	1.61409i	−0.715418	−	0.0916739i
$311$	−9.90129	+	17.1495i	−0.561451	+	0.972461i	0.435919	+	0.899986i	$0.356423\pi$
$311$	−9.90129	+	17.1495i	−0.561451	+	0.972461i	−0.997370	+	0.0724757i	$0.976910\pi$
$312$		0			0
$313$	16.2557	+	28.1557i	0.918828	+	1.59146i	0.801198	+	0.598399i	$0.204196\pi$
$313$	16.2557	+	28.1557i	0.918828	+	1.59146i	0.117630	+	0.993057i	$0.462470\pi$
$314$	−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	$-0.815820\pi$
$317$	−13.9271	+	8.04083i	−0.782225	+	0.451618i	0.0549932	+	0.998487i	$0.482486\pi$
$318$		0			0
$319$	−9.42233	+	16.3200i	−0.527549	+	0.913742i
$320$	3.06750	+	10.5671i	0.171478	+	0.590720i
$321$		0			0
$322$	13.4395	+	10.2390i	0.748956	+	0.570595i
$323$			6.01054i			0.334435i
$324$		0			0
$325$		−	3.18620i		−	0.176739i
$326$	−12.7904	+	16.7885i	−0.708393	+	0.929828i
$327$		0			0
$328$	12.0702	+	15.3972i	0.666466	+	0.850169i
$329$	−13.0425	+	22.5903i	−0.719056	+	1.24544i
$330$		0			0
$331$	17.7569	−	10.2520i	0.976010	−	0.563499i	0.0749465	−	0.997188i	$-0.476121\pi$
$331$	17.7569	−	10.2520i	0.976010	−	0.563499i	0.901063	+	0.433688i	$0.142788\pi$
$332$	−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	−0.645493	−	0.763766i	$-0.723348\pi$
$337$	6.21760	−	10.7692i	0.338694	−	0.586635i	0.984187	+	0.177131i	$0.0566815\pi$
$338$	2.14785	−	16.7617i	0.116827	−	0.911714i
$339$		0			0
$340$	−0.560997	+	2.15305i	−0.0304243	+	0.116766i
$341$		−	13.8180i		−	0.748287i
$342$		0			0
$343$	3.50988			0.189515
$344$	0.113097	+	0.795291i	0.00609778	+	0.0428792i
$345$		0			0
$346$	17.6637	+	2.26343i	0.949606	+	0.121683i
$347$	24.1550	+	13.9459i	1.29671	+	0.748654i	0.979834	−	0.199814i	$-0.0640339\pi$
$347$	24.1550	+	13.9459i	1.29671	+	0.748654i	0.316873	+	0.948468i	$0.397367\pi$
$348$		0			0
$349$	−26.0103	+	15.0171i	−1.39230	+	0.803846i	−0.993570	−	0.113222i	$-0.963883\pi$
$349$	−26.0103	+	15.0171i	−1.39230	+	0.803846i	−0.398732	+	0.917068i	$0.630550\pi$
$350$	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	0.999986	+	0.00529122i	$0.00168426\pi$
$353$	9.48011	+	16.4200i	0.504575	+	0.873950i	−0.495411	+	0.868659i	$0.664982\pi$
$354$		0			0
$355$	5.59637	+	3.23107i	0.297024	+	0.171487i
$356$	−4.73590	−	17.1985i	−0.251002	−	0.911521i
$357$		0			0
$358$	−10.3801	+	13.6248i	−0.548606	+	0.720093i
$359$	−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
$362$	15.1515	−	19.8877i	0.796348	−	1.04528i
$363$		0			0
$364$	−7.13429	+	1.96455i	−0.373938	+	0.102970i
$365$	−0.488277	−	0.281907i	−0.0255576	−	0.0147557i
$366$		0			0
$367$	5.77148	+	9.99650i	0.301269	+	0.521813i	0.976424	−	0.215863i	$-0.0692565\pi$
$367$	5.77148	+	9.99650i	0.301269	+	0.521813i	−0.675155	+	0.737676i	$0.735923\pi$
$368$	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	$-0.136055\pi$
$373$	19.4301	+	11.2180i	1.00605	+	0.580846i	0.0960206	+	0.995379i	$0.469389\pi$
$374$	−2.40132	−	0.307706i	−0.124169	−	0.0159111i
$375$		0			0
$376$	−20.2375	+	2.87794i	−1.04367	+	0.148418i
$377$	−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	$0.802209\pi$
$380$	−19.7816	−	5.15428i	−1.01477	−	0.264409i
$381$		0			0
$382$	3.49493	−	27.2742i	0.178816	−	1.39547i
$383$	1.94277	−	3.36498i	0.0992709	−	0.171942i	−0.812112	−	0.583501i	$-0.801682\pi$
$383$	1.94277	−	3.36498i	0.0992709	−	0.171942i	0.911383	+	0.411559i	$0.135016\pi$
$384$		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	$-0.552949\pi$
$389$	11.9463	−	6.89722i	0.605703	−	0.349703i	0.771282	+	0.636494i	$0.219616\pi$
$390$		0			0
$391$	−1.33859	+	2.31850i	−0.0676953	+	0.117252i
$392$	−10.5181	−	13.4172i	−0.531243	−	0.677673i
$393$		0			0
$394$	21.0031	−	27.5684i	1.05812	−	1.38887i
$395$			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	$0.796581\pi$
$398$	−8.02732	−	6.11565i	−0.402373	−	0.306550i
$399$		0			0
$400$	10.8521	+	6.06711i	0.542603	+	0.303356i
$401$	4.47782	−	7.75581i	0.223612	−	0.387307i	−0.732290	−	0.680992i	$-0.761549\pi$
$401$	4.47782	−	7.75581i	0.223612	−	0.387307i	0.955902	+	0.293686i	$0.0948820\pi$
$402$		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	−0.484757	−	0.874649i	$-0.661092\pi$
$409$	10.4170	−	18.0429i	0.515090	−	0.892162i	0.999847	−	0.0175128i	$-0.00557480\pi$
$410$	−13.3455	−	1.71009i	−0.659086	−	0.0844555i
$411$		0			0
$412$	−5.82659	−	1.51817i	−0.287055	−	0.0747949i
$413$			29.4619i			1.44973i
$414$		0			0
$415$	3.82582			0.187802
$416$	−4.66074	−	3.45010i	−0.228512	−	0.169155i
$417$		0			0
$418$	2.82711	−	22.0626i	0.138278	−	1.07912i
$419$	8.74372	+	5.04819i	0.427159	+	0.246620i	0.698135	−	0.715966i	$-0.254013\pi$
$419$	8.74372	+	5.04819i	0.427159	+	0.246620i	−0.270977	+	0.962586i	$0.587347\pi$
$420$		0			0
$421$	−20.2218	+	11.6751i	−0.985551	+	0.569008i	−0.903941	−	0.427656i	$-0.859339\pi$
$421$	−20.2218	+	11.6751i	−0.985551	+	0.569008i	−0.0816096	+	0.996664i	$0.526006\pi$
$422$	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
$428$	0.862677	−	0.237552i	0.0416991	−	0.0114825i
$429$		0			0
$430$	−0.439432	−	0.334783i	−0.0211913	−	0.0161447i
$431$	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	$0.575891\pi$
$434$	26.5087	+	20.1957i	1.27246	+	0.969426i
$435$		0			0
$436$	−18.0578	+	4.97252i	−0.864813	+	0.238141i
$437$	−21.3017	−	12.2986i	−1.01900	−	0.588320i
$438$		0			0
$439$	−12.3831	−	21.4482i	−0.591015	−	1.02367i	−0.994096	−	0.108504i	$-0.965394\pi$
$439$	−12.3831	−	21.4482i	−0.591015	−	1.02367i	0.403081	−	0.915164i	$-0.367939\pi$
$440$	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	$-0.443089\pi$
$443$	23.5518	−	13.5976i	1.11898	−	0.646044i	0.941140	+	0.338016i	$0.109756\pi$
$444$		0			0
$445$	10.6242	+	6.13391i	0.503637	+	0.290775i
$446$	0.759387	−	5.92621i	0.0359580	−	0.280614i
$447$		0			0
$448$	6.89385	−	28.0400i	0.325704	−	1.32476i
$449$	−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
$452$	−21.9220	−	5.71198i	−1.03112	−	0.268669i
$453$		0			0
$454$	1.77282	+	0.227170i	0.0832028	+	0.0106616i
$455$	2.54447	−	4.40714i	0.119286	−	0.206610i
$456$		0			0
$457$	−10.3779	−	17.9750i	−0.485456	−	0.840834i	0.514404	−	0.857548i	$-0.328013\pi$
$457$	−10.3779	−	17.9750i	−0.485456	−	0.840834i	−0.999860	+	0.0167133i	$0.994680\pi$
$458$	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	−0.512359	+	0.858771i	$0.671228\pi$
$461$	−32.4695	+	18.7463i	−1.51226	+	0.873101i	−0.999897	+	0.0143300i	$0.995438\pi$
$462$		0			0
$463$	−7.97597	+	13.8148i	−0.370675	+	0.642028i	−0.989670	−	0.143367i	$-0.954207\pi$
$463$	−7.97597	+	13.8148i	−0.370675	+	0.642028i	0.618995	+	0.785395i	$0.287540\pi$
$464$	17.3796	−	31.0864i	0.806828	−	1.44315i
$465$		0			0
$466$	6.64907	+	5.06562i	0.308012	+	0.234660i
$467$		−	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
$470$	8.51911	−	11.1821i	0.392957	−	0.515790i
$471$		0			0
$472$	−18.1698	+	14.2437i	−0.836335	+	0.655621i
$473$	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	−0.988750	−	0.149577i	$-0.952209\pi$
$479$	−13.6550	−	23.6511i	−0.623912	−	1.08065i	0.364838	−	0.931071i	$-0.381124\pi$
$480$		0			0
$481$	−2.05802	+	3.56460i	−0.0938377	+	0.162532i
$482$	−0.647703	+	5.05464i	−0.0295021	+	0.230232i
$483$		0			0
$484$	−12.6195	−	3.28814i	−0.573615	−	0.149461i
$485$			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	$0.357442\pi$
$488$	−2.90258	−	20.4108i	−0.131394	−	0.923951i
$489$		0			0
$490$	11.6293	+	1.49019i	0.525360	+	0.0673198i
$491$	11.1131	+	6.41614i	0.501526	+	0.289556i	0.729344	−	0.684147i	$-0.239826\pi$
$491$	11.1131	+	6.41614i	0.501526	+	0.289556i	−0.227817	+	0.973704i	$0.573159\pi$
$492$		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	$-0.463500\pi$
$499$	−15.3846	−	8.88232i	−0.688711	−	0.397627i	−0.803129	+	0.595805i	$0.796833\pi$
$500$	−21.5040	+	5.92148i	−0.961688	+	0.264817i
$501$		0			0
$502$	−0.549804	+	0.721666i	−0.0245390	+	0.0322095i
$503$	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
$506$	6.00402	−	7.88079i	0.266911	−	0.350344i
$507$		0			0
$508$	−6.28355	−	22.8189i	−0.278787	−	1.01242i
$509$	6.91916	+	3.99478i	0.306686	+	0.177065i	0.645443	−	0.763809i	$-0.276673\pi$
$509$	6.91916	+	3.99478i	0.306686	+	0.177065i	−0.338756	+	0.940874i	$0.610006\pi$
$510$		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
$518$	−20.3296	−	2.60505i	−0.893232	−	0.114459i
$519$		0			0
$520$	3.94814	−	0.561458i	0.173137	−	0.0246216i
$521$	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	$-0.131950\pi$
$524$	−1.40270	+	5.38340i	−0.0612770	+	0.235175i
$525$		0			0
$526$	−2.02997	+	15.8418i	−0.0885110	+	0.690734i
$527$	−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
$536$	−6.27095	+	4.91593i	−0.270864	+	0.212336i
$537$		0			0
$538$	−20.7999	+	27.3017i	−0.896748	+	1.17706i
$539$			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	$0.906253\pi$
$542$	13.7614	+	10.4841i	0.591101	+	0.450333i
$543$		0			0
$544$	4.54588	+	0.518787i	0.194903	+	0.0222428i
$545$	6.44038	−	11.1551i	0.275875	−	0.477830i
$546$		0			0
$547$	32.2252	−	18.6052i	1.37785	−	0.795501i	0.385948	−	0.922520i	$-0.373874\pi$
$547$	32.2252	−	18.6052i	1.37785	−	0.795501i	0.991900	+	0.127019i	$0.0405410\pi$
$548$	−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
$554$	17.6956	+	2.26752i	0.751815	+	0.0963378i
$555$		0			0
$556$	0.716097	−	2.74831i	0.0303693	−	0.116554i
$557$		−	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
$560$	10.1654	+	17.0584i	0.429567	+	0.720847i
$561$		0			0
$562$	3.43090	−	26.7746i	0.144724	−	1.12942i
$563$	−25.0083	−	14.4385i	−1.05397	−	0.608512i	−0.130214	−	0.991486i	$-0.541566\pi$
$563$	−25.0083	−	14.4385i	−1.05397	−	0.608512i	−0.923759	+	0.382974i	$0.874900\pi$
$564$		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	0.816205	−	0.577762i	$-0.196074\pi$
$569$	−2.20060	−	3.81154i	−0.0922538	−	0.159788i	−0.908459	+	0.417974i	$0.862740\pi$
$570$		0			0
$571$	28.6730	+	16.5544i	1.19993	+	0.692779i	0.960539	−	0.278144i	$-0.0897193\pi$
$571$	28.6730	+	16.5544i	1.19993	+	0.692779i	0.239390	+	0.970924i	$0.423053\pi$
$572$	1.15199	+	4.18347i	0.0481671	+	0.174920i
$573$		0			0
$574$	28.0854	+	21.3970i	1.17226	+	0.893093i
$575$	−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	$0.423656\pi$
$578$	−18.3880	−	14.0090i	−0.764841	−	0.582697i
$579$		0			0
$580$	6.50242	+	23.6137i	0.269998	+	0.980506i
$581$	−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	$-0.847257\pi$
$587$	−22.5512	+	13.0200i	−0.930788	+	0.537391i	−0.0437275	+	0.999043i	$0.513923\pi$
$588$		0			0
$589$	−42.0164	−	24.2582i	−1.73125	−	0.999540i
$590$	2.01804	−	15.7486i	0.0830812	−	0.648361i
$591$		0			0
$592$	−8.22201	−	13.7972i	−0.337923	−	0.567061i
$593$	−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
$596$	2.86134	−	10.9815i	0.117205	−	0.449821i
$597$		0			0
$598$	4.75951	+	0.609886i	0.194631	+	0.0249401i
$599$	8.10409	−	14.0367i	0.331124	−	0.573524i	−0.651608	−	0.758556i	$-0.725905\pi$
$599$	8.10409	−	14.0367i	0.331124	−	0.573524i	0.982733	+	0.185032i	$0.0592388\pi$
$600$		0			0
$601$	9.78181	+	16.9426i	0.399008	+	0.691102i	0.993604	−	0.112922i	$-0.0360212\pi$
$601$	9.78181	+	16.9426i	0.399008	+	0.691102i	−0.594596	+	0.804025i	$0.702688\pi$
$602$	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	−0.933170	−	0.359437i	$-0.882969\pi$
$607$	−3.82627	+	6.62730i	−0.155304	+	0.268994i	0.777866	+	0.628430i	$0.216302\pi$
$608$	−4.76646	+	41.7662i	−0.193306	+	1.69384i
$609$		0			0
$610$	11.2778	+	8.59205i	0.456625	+	0.347882i
$611$			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	$-0.188588\pi$
$614$	13.4942	−	17.7124i	0.544583	−	0.714813i
$615$		0			0
$616$	−17.0048	+	13.3304i	−0.685142	+	0.537097i
$617$	12.6938	−	21.9863i	0.511034	−	0.885136i	−0.488885	−	0.872348i	$-0.662596\pi$
$617$	12.6938	−	21.9863i	0.511034	−	0.885136i	0.999918	−	0.0127878i	$-0.00407059\pi$
$618$		0			0
$619$	19.8583	−	11.4652i	0.798171	−	0.460824i	−0.0446605	−	0.999002i	$-0.514221\pi$
$619$	19.8583	−	11.4652i	0.798171	−	0.460824i	0.842831	+	0.538178i	$0.180887\pi$
$620$	−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
$626$	−5.84388	+	45.6052i	−0.233568	+	1.82275i
$627$		0			0
$628$	10.8722	−	41.7264i	0.433848	−	1.66506i
$629$		−	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	$0.346647\pi$
$632$	0.255451	−	0.0363272i	0.0101613	−	0.00144502i
$633$		0			0
$634$	−22.5584	−	2.89065i	−0.895910	−	0.114802i
$635$	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	0.972506	+	0.232879i	$0.0748146\pi$
$641$	17.4170	+	30.1672i	0.687932	+	1.19153i	−0.284574	+	0.958654i	$0.591852\pi$
$642$		0			0
$643$	−34.0047	−	19.6326i	−1.34102	−	0.774236i	−0.354059	−	0.935223i	$-0.615199\pi$
$643$	−34.0047	−	19.6326i	−1.34102	−	0.774236i	−0.986956	+	0.160987i	$0.948532\pi$
$644$	6.34345	+	23.0364i	0.249967	+	0.907761i
$645$		0			0
$646$	−5.15126	+	6.76148i	−0.202674	+	0.266027i
$647$	−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
$650$	2.73070	−	3.58428i	0.107107	−	0.140587i
$651$		0			0
$652$	−28.7767	+	7.92415i	−1.12698	+	0.310334i
$653$	15.7763	+	9.10843i	0.617373	+	0.356440i	0.775845	−	0.630923i	$-0.217324\pi$
$653$	15.7763	+	9.10843i	0.617373	+	0.356440i	−0.158473	+	0.987363i	$0.550657\pi$
$654$		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	$-0.969569\pi$
$659$	−36.2085	+	20.9050i	−1.41048	+	0.814343i	−0.415049	+	0.909799i	$0.636236\pi$
$660$		0			0
$661$	−9.78973	−	5.65210i	−0.380776	−	0.219841i	0.297380	−	0.954759i	$-0.403887\pi$
$661$	−9.78973	−	5.65210i	−0.380776	−	0.219841i	−0.678156	+	0.734918i	$0.737221\pi$
$662$	28.7618	+	3.68555i	1.11786	+	0.143243i
$663$		0			0
$664$	−1.10768	−	7.78911i	−0.0429861	−	0.302276i
$665$	−36.8915			−1.43059
$666$		0			0
$667$			29.4710i			1.14112i
$668$	42.6691	+	11.1178i	1.65092	+	0.430161i
$669$		0			0
$670$	0.696483	−	5.43531i	0.0269075	−	0.209984i
$671$	−7.71346	+	13.3601i	−0.297775	+	0.515761i
$672$		0			0
$673$	17.6390	+	30.5517i	0.679934	+	1.17768i	0.975000	+	0.222203i	$0.0713249\pi$
$673$	17.6390	+	30.5517i	0.679934	+	1.17768i	−0.295066	+	0.955477i	$0.595342\pi$
$674$	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	$-0.793629\pi$
$677$	−17.5026	+	10.1051i	−0.672679	+	0.388372i	0.124412	+	0.992231i	$0.460296\pi$
$678$		0			0
$679$	9.96266	−	17.2558i	0.382332	−	0.662218i
$680$	−2.47633	+	1.94125i	−0.0949631	+	0.0744436i
$681$		0			0
$682$	11.8426	−	15.5444i	0.453475	−	0.595226i
$683$		−	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
$686$	3.94839	+	3.00810i	0.150750	+	0.114850i
$687$		0			0
$688$	−0.554368	+	0.991582i	−0.0211351	+	0.0378037i
$689$	1.98011	−	3.42965i	0.0754362	−	0.130659i
$690$		0			0
$691$	7.91193	−	4.56796i	0.300984	−	0.173773i	−0.341901	−	0.939736i	$-0.611071\pi$
$691$	7.91193	−	4.56796i	0.300984	−	0.173773i	0.642885	+	0.765963i	$0.277737\pi$
$692$	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
$698$	−42.1302	−	5.39859i	−1.59465	−	0.204339i
$699$		0			0
$700$	21.7125	+	5.65740i	0.820657	+	0.213830i
$701$		−	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
$704$	−16.4423	−	4.04248i	−0.619694	−	0.152357i
$705$		0			0
$706$	−3.40807	+	26.5963i	−0.128264	+	1.00097i
$707$	20.3277	+	11.7362i	0.764504	+	0.441386i
$708$		0			0
$709$	23.1529	−	13.3673i	0.869525	−	0.502021i	0.00233491	−	0.999997i	$-0.499257\pi$
$709$	23.1529	−	13.3673i	0.869525	−	0.502021i	0.867190	+	0.497977i	$0.165923\pi$
$710$	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
$716$	−23.3540	+	6.43090i	−0.872779	+	0.240334i
$717$		0			0
$718$	−32.2204	−	24.5473i	−1.20246	−	0.916096i
$719$	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
$722$	−40.7487	−	31.0446i	−1.51651	−	1.15536i
$723$		0			0
$724$	34.0891	−	9.38700i	1.26691	−	0.348865i
$725$	23.9670	+	13.8374i	0.890112	+	0.513907i
$726$		0			0
$727$	−9.18140	−	15.9027i	−0.340519	−	0.589797i	0.644010	−	0.765017i	$-0.277270\pi$
$727$	−9.18140	−	15.9027i	−0.340519	−	0.589797i	−0.984529	+	0.175220i	$0.943936\pi$
$728$	−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	$-0.0584100\pi$
$733$	35.6508	+	20.5830i	1.31679	+	0.760249i	0.333580	+	0.942722i	$0.391743\pi$
$734$	−2.07483	+	16.1918i	−0.0765833	+	0.597651i
$735$		0			0
$736$	−11.1402	+	15.0494i	−0.410635	+	0.554727i
$737$	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	$0.688613\pi$
$740$	10.6886	+	2.78501i	0.392920	+	0.102379i
$741$		0			0
$742$	19.5600	+	2.50643i	0.718070	+	0.0920138i
$743$	21.7217	−	37.6231i	0.796893	−	1.38026i	−0.124737	−	0.992190i	$-0.539809\pi$
$743$	21.7217	−	37.6231i	0.796893	−	1.38026i	0.921630	−	0.388070i	$-0.126858\pi$
$744$		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	0.437776	+	0.899084i	$0.355766\pi$
$751$	−15.3394	+	26.5686i	−0.559742	+	0.969501i	−0.997518	+	0.0704172i	$0.977567\pi$
$752$	−25.2324	−	14.1068i	−0.920131	−	0.514422i
$753$		0			0
$754$	−10.2674	−	7.82224i	−0.373916	−	0.284869i
$755$		−	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	$-0.0164435\pi$
$758$	−19.4263	+	25.4987i	−0.705594	+	0.926154i
$759$		0			0
$760$	−17.8357	−	22.7518i	−0.646967	−	0.825296i
$761$	−6.52480	+	11.3013i	−0.236524	+	0.409672i	−0.959714	−	0.280977i	$-0.909342\pi$
$761$	−6.52480	+	11.3013i	−0.236524	+	0.409672i	0.723191	+	0.690649i	$0.242675\pi$
$762$		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	−0.502910	−	0.864339i	$-0.667737\pi$
$769$	13.7846	−	23.8756i	0.497084	−	0.860975i	0.999994	+	0.00336360i	$0.00107067\pi$
$770$	1.88864	−	14.7388i	0.0680618	−	0.531150i
$771$		0			0
$772$	0.615917	+	0.160483i	0.0221673	+	0.00577590i
$773$		−	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
$776$	15.4586	−	2.19835i	0.554933	−	0.0789160i
$777$		0			0
$778$	19.3501	+	2.47953i	0.693734	+	0.0888953i
$779$	−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	$-0.252454\pi$
$787$	12.2138	+	7.05164i	0.435375	+	0.251364i	−0.266259	+	0.963902i	$0.585788\pi$
$788$	47.2543	−	13.0123i	1.68337	−	0.463543i
$789$		0			0
$790$	−0.107534	+	0.141147i	−0.00382588	+	0.00502180i
$791$	−40.8832			−1.45364
$792$		0			0
$793$	−7.47175			−0.265329
$794$	−20.3701	+	26.7375i	−0.722907	+	0.948879i
$795$		0			0
$796$	−3.78889	−	13.7594i	−0.134294	−	0.487691i
$797$	22.7555	+	13.1379i	0.806040	+	0.465367i	0.845579	−	0.533851i	$-0.179256\pi$
$797$	22.7555	+	13.1379i	0.806040	+	0.465367i	−0.0395390	+	0.999218i	$0.512589\pi$
$798$		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
$806$	9.38785	+	1.20296i	0.330673	+	0.0423726i
$807$		0			0
$808$	2.58970	+	18.2106i	0.0911053	+	0.640647i
$809$	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	$-0.230425\pi$
$812$	16.2060	−	62.1969i	0.568718	−	2.18268i
$813$		0			0
$814$	−1.52757	+	11.9211i	−0.0535414	+	0.417833i
$815$	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	$-0.659840\pi$
$821$	1.06427	−	0.614456i	0.0371432	−	0.0214446i	0.518457	+	0.855104i	$0.326507\pi$
$822$		0			0
$823$	−17.4937	+	30.2999i	−0.609791	+	1.05619i	0.381484	+	0.924376i	$0.375413\pi$
$823$	−17.4937	+	30.2999i	−0.609791	+	1.05619i	−0.991275	+	0.131813i	$0.957920\pi$
$824$	−5.25342	−	6.70146i	−0.183012	−	0.233456i
$825$		0			0
$826$	−25.2500	+	33.1429i	−0.878561	+	1.15319i
$827$			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	$-0.167720\pi$
$830$	4.30381	+	3.27888i	0.149388	+	0.113812i
$831$		0			0
$832$	−2.28618	−	7.87558i	−0.0792590	−	0.273036i
$833$	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	0.702958	−	0.711231i	$-0.251862\pi$
$839$	−7.66037	−	13.2681i	−0.264465	−	0.458067i	−0.967423	+	0.253164i	$0.918529\pi$
$840$		0			0
$841$	25.1380	−	43.5402i	0.866826	−	1.50139i
$842$	−32.7543	−	4.19715i	−1.12879	−	0.144643i
$843$		0			0
$844$	−4.07707	+	15.6474i	−0.140339	+	0.538606i
$845$			16.4351i			0.565386i
$846$		0			0
$847$	−23.5347			−0.808662
$848$	7.91075	+	13.2749i	0.271656	+	0.455861i
$849$		0			0
$850$	−0.451887	+	3.52650i	−0.0154996	+	0.120958i
$851$	11.5100	+	6.64528i	0.394556	+	0.227797i
$852$		0			0
$853$	−5.67204	+	3.27476i	−0.194207	+	0.112126i	−0.593951	−	0.804502i	$-0.702433\pi$
$853$	−5.67204	+	3.27476i	−0.194207	+	0.112126i	0.399743	+	0.916627i	$0.369099\pi$
$854$	−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	0.957583	−	0.288156i	$-0.0930421\pi$
$857$	6.71094	+	11.6237i	0.229241	+	0.397058i	−0.728342	+	0.685214i	$0.759709\pi$
$858$		0			0
$859$	2.57865	+	1.48878i	0.0879824	+	0.0507967i	0.543346	−	0.839509i	$-0.317157\pi$
$859$	2.57865	+	1.48878i	0.0879824	+	0.0507967i	−0.455363	+	0.890306i	$0.650491\pi$
$860$	−0.207412	−	0.753221i	−0.00707268	−	0.0256846i
$861$		0			0
$862$	7.20352	+	5.48803i	0.245353	+	0.186923i
$863$	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
$866$	−11.0565	−	8.42347i	−0.375716	−	0.286241i
$867$		0			0
$868$	12.5121	+	45.4379i	0.424687	+	1.54226i
$869$	−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	$-0.360582\pi$
$877$	−4.38552	−	2.53198i	−0.148088	−	0.0854988i	−0.572213	+	0.820105i	$0.693915\pi$
$878$	4.45170	−	34.7408i	0.150237	−	1.17244i
$879$		0			0
$880$	10.0028	−	5.96089i	0.337196	−	0.200942i
$881$	−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	$0.843240\pi$
$884$	0.418106	−	1.60465i	0.0140624	−	0.0539702i
$885$		0			0
$886$	38.1480	+	4.88830i	1.28161	+	0.164226i
$887$	−0.666005	+	1.15356i	−0.0223623	+	0.0387326i	−0.876990	−	0.480509i	$-0.840452\pi$
$887$	−0.666005	+	1.15356i	−0.0223623	+	0.0387326i	0.854628	+	0.519241i	$0.173785\pi$
$888$		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
$896$	31.7865	−	25.6349i	1.06191	−	0.856402i
$897$		0			0
$898$	−36.7698	−	28.0132i	−1.22702	−	0.934814i
$899$			58.1297i			1.93873i
$900$		0			0
$901$			3.12473i			0.104100i
$902$	12.5470	−	16.4690i	0.417768	−	0.548357i
$903$		0			0
$904$	−19.7655	−	25.2136i	−0.657391	−	0.838593i
$905$	−12.1580	+	21.0582i	−0.404145	+	0.699999i
$906$		0			0
$907$	−0.778677	+	0.449569i	−0.0258555	+	0.0149277i	−0.512872	−	0.858465i	$-0.671418\pi$
$907$	−0.778677	+	0.449569i	−0.0258555	+	0.0149277i	0.487017	+	0.873393i	$0.338085\pi$
$908$	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	0.713808	−	0.700341i	$-0.246969\pi$
$911$	−7.53390	−	13.0491i	−0.249609	−	0.432336i	−0.963417	+	0.268005i	$0.913636\pi$
$912$		0			0
$913$	−2.94360	+	5.09846i	−0.0974188	+	0.168734i
$914$	3.73080	−	29.1150i	0.123404	−	0.963038i
$915$		0			0
$916$	−3.66377	+	14.0612i	−0.121054	+	0.464595i
$917$			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	$0.655627\pi$
$920$	−1.81293	−	12.7484i	−0.0597705	−	0.420302i
$921$		0			0
$922$	−52.5925	−	6.73922i	−1.73204	−	0.221944i
$923$	−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	0.829135	−	0.559049i	$-0.188834\pi$
$929$	−2.12086	−	3.67344i	−0.0695833	−	0.120522i	−0.898718	+	0.438527i	$0.855500\pi$
$930$		0			0
$931$	38.7912	+	22.3961i	1.27133	+	0.734002i
$932$	3.13836	+	11.3970i	0.102800	+	0.373322i
$933$		0			0
$934$	23.1808	−	30.4268i	0.758499	−	0.995596i
$935$	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	$0.579634\pi$
$938$	−8.71452	+	11.4386i	−0.284539	+	0.373483i
$939$		0			0
$940$	19.1669	−	5.27793i	0.625156	−	0.172147i
$941$	−36.9463	−	21.3310i	−1.20442	−	0.695370i	−0.242882	−	0.970056i	$-0.578093\pi$
$941$	−36.9463	−	21.3310i	−1.20442	−	0.695370i	−0.961534	+	0.274686i	$0.911426\pi$
$942$		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	$-0.512870\pi$
$947$	24.7629	−	14.2969i	0.804686	−	0.464585i	0.845107	+	0.534597i	$0.179537\pi$
$948$		0			0
$949$	0.363908	+	0.210103i	0.0118130	+	0.00682022i
$950$	−32.4005	−	4.15181i	−1.05121	−	0.134702i
$951$		0			0
$952$	8.17489	−	1.16254i	0.264950	−	0.0376780i
$953$	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
$956$	−23.0800	−	6.01372i	−0.746462	−	0.194498i
$957$		0			0
$958$	4.90892	−	38.3089i	0.158600	−	1.23770i
$959$	−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	−0.956257	−	0.292529i	$-0.905503\pi$
$967$	−6.99023	+	12.1074i	−0.224791	+	0.389349i	0.731466	+	0.681878i	$0.238836\pi$
$968$	−11.3781	−	14.5144i	−0.365707	−	0.466510i
$969$		0			0
$970$	−6.50742	+	8.54155i	−0.208941	+	0.274253i
$971$		−	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
$974$	21.5004	+	16.3802i	0.688918	+	0.524855i
$975$		0			0
$976$	14.2276	−	25.4484i	0.455414	−	0.814585i
$977$	−22.7380	+	39.3834i	−0.727454	+	1.25999i	0.230502	+	0.973072i	$0.425963\pi$
$977$	−22.7380	+	39.3834i	−0.727454	+	1.25999i	−0.957956	+	0.286916i	$0.907370\pi$
$978$		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	0.935234	−	0.354030i	$-0.115189\pi$
$983$	5.04836	+	8.74402i	0.161018	+	0.278891i	−0.774216	+	0.632921i	$0.781856\pi$
$984$		0			0
$985$	−16.8534	+	29.1909i	−0.536994	+	0.930100i
$986$	10.1019	+	1.29446i	0.321709	+	0.0412240i
$987$		0			0
$988$	14.7430	+	3.84144i	0.469039	+	0.122212i
$989$		−	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	$0.590212\pi$
$992$	−21.9735	+	29.6840i	−0.697658	+	0.942467i
$993$		0			0
$994$	3.04816	−	23.7876i	0.0966817	−	0.754498i
$995$	8.49978	+	4.90735i	0.269461	+	0.155573i
$996$		0			0
$997$	−26.1168	+	15.0786i	−0.827128	+	0.477543i	−0.852868	−	0.522126i	$-0.825139\pi$
$997$	−26.1168	+	15.0786i	−0.827128	+	0.477543i	0.0257404	+	0.999669i	$0.491806\pi$
$998$	−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.37.7		16
3.2	odd	2		72.2.n.b.13.2	✓	16
4.3	odd	2		864.2.r.b.145.3		16
8.3	odd	2		864.2.r.b.145.6		16
8.5	even	2	inner	216.2.n.b.37.5		16
9.2	odd	6		72.2.n.b.61.4	yes	16
9.4	even	3		648.2.d.k.325.2		8
9.5	odd	6		648.2.d.j.325.7		8
9.7	even	3	inner	216.2.n.b.181.5		16
12.11	even	2		288.2.r.b.49.6		16
24.5	odd	2		72.2.n.b.13.4	yes	16
24.11	even	2		288.2.r.b.49.3		16
36.7	odd	6		864.2.r.b.721.6		16
36.11	even	6		288.2.r.b.241.3		16
36.23	even	6		2592.2.d.j.1297.3		8
36.31	odd	6		2592.2.d.k.1297.6		8
72.5	odd	6		648.2.d.j.325.8		8
72.11	even	6		288.2.r.b.241.6		16
72.13	even	6		648.2.d.k.325.1		8
72.29	odd	6		72.2.n.b.61.2	yes	16
72.43	odd	6		864.2.r.b.721.3		16
72.59	even	6		2592.2.d.j.1297.6		8
72.61	even	6	inner	216.2.n.b.181.7		16
72.67	odd	6		2592.2.d.k.1297.3		8

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

\(f(q)\)	\(=\)	\(q+(1.12494 + 0.857038i) q^{2} +(0.530970 + 1.92823i) q^{4} +(-1.19115 - 0.687709i) q^{5} +(1.80469 + 3.12581i) q^{7} +(-1.05526 + 2.62420i) q^{8} +O(q^{10})\)	\(q+(1.12494 + 0.857038i) q^{2} +(0.530970 + 1.92823i) q^{4} +(-1.19115 - 0.687709i) q^{5} +(1.80469 + 3.12581i) q^{7} +(-1.05526 + 2.62420i) q^{8} +(-0.750573 - 1.79449i) q^{10} +(1.83294 - 1.05825i) q^{11} +(0.887751 + 0.512543i) q^{13} +(-0.648778 + 5.06302i) q^{14} +(-3.43614 + 2.04766i) q^{16} -0.808822 q^{17} -7.43122i q^{19} +(0.693598 - 2.66196i) q^{20} +(2.96890 + 0.380437i) q^{22} +(1.65498 - 2.86652i) q^{23} +(-1.55411 - 2.69180i) q^{25} +(0.559395 + 1.33742i) q^{26} +(-5.06904 + 5.13956i) q^{28} +(-7.71083 + 4.45185i) q^{29} +(3.26436 - 5.65403i) q^{31} +(-5.62037 - 0.641410i) q^{32} +(-0.909875 - 0.693192i) q^{34} -4.96439i q^{35} +4.01531i q^{37} +(6.36884 - 8.35966i) q^{38} +(3.06165 - 2.40010i) q^{40} +(3.45852 - 5.99034i) q^{41} +(0.245957 - 0.142003i) q^{43} +(3.01378 + 2.97243i) q^{44} +(4.31847 - 1.80627i) q^{46} +(3.61351 + 6.25878i) q^{47} +(-3.01378 + 5.22003i) q^{49} +(0.558698 - 4.36005i) q^{50} +(-0.516932 + 1.98393i) q^{52} -3.86330i q^{53} -2.91107 q^{55} +(-10.1072 + 1.43732i) q^{56} +(-12.4896 - 1.60042i) q^{58} +(7.06904 + 4.08131i) q^{59} +(-6.31237 + 3.64445i) q^{61} +(8.51792 - 3.56275i) q^{62} +(-5.77286 - 5.53842i) q^{64} +(-0.704961 - 1.22103i) q^{65} +(2.43973 + 1.40858i) q^{67} +(-0.429460 - 1.55960i) q^{68} +(4.25468 - 5.58463i) q^{70} -4.69830 q^{71} +0.409922 q^{73} +(-3.44128 + 4.51698i) q^{74} +(14.3291 - 3.94576i) q^{76} +(6.61576 + 3.81961i) q^{77} +(-0.0456121 - 0.0790024i) q^{79} +(5.50115 - 0.0760042i) q^{80} +(9.02458 - 3.77467i) q^{82} +(-2.40891 + 1.39079i) q^{83} +(0.963426 + 0.556234i) q^{85} +(0.398389 + 0.0510497i) q^{86} +(0.842830 + 5.92673i) q^{88} -8.91934 q^{89} +3.69992i q^{91} +(6.40605 + 1.66916i) q^{92} +(-1.29904 + 10.1377i) q^{94} +(-5.11052 + 8.85168i) q^{95} +(-2.76022 - 4.78084i) q^{97} +(-7.86408 + 3.28928i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - q^{4} + 6 q^{7} + 2 q^{8}+O(q^{10}) \) 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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