LMFDB - Embedded newform 216.2.n.b.181.7

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			181.7
Root			$-0.179748 + 1.40274i$ of defining polynomial
Character	$\chi$	$=$	216.181
Dual form			216.2.n.b.37.7

$q$-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 $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

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

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 $

$2$	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	−0.742114	−	0.670274i	$-0.766177\pi$
$5$	−1.19115	+	0.687709i	−0.532697	+	0.307553i	0.209417	+	0.977826i	$0.432843\pi$
$6$		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	0.750191	−	0.661221i	$-0.229961\pi$
$11$	1.83294	+	1.05825i	0.552652	+	0.319074i	−0.197539	+	0.980295i	$0.563295\pi$
$12$		0			0
$13$	0.887751	−	0.512543i	0.246218	−	0.142154i	−0.371813	−	0.928307i	$-0.621264\pi$
$13$	0.887751	−	0.512543i	0.246218	−	0.142154i	0.618031	+	0.786154i	$0.287931\pi$
$14$	−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	$0.324866\pi$
$19$			7.43122i			1.70484i	−0.522858	+	0.852420i	$0.675134\pi$
$20$	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	0.985370	−	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	−0.434603	−	0.900622i	$-0.643111\pi$
$29$	−7.71083	−	4.45185i	−1.43187	−	0.826688i	−0.997263	+	0.0739344i	$0.976444\pi$
$30$		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	$0.633919\pi$
$32$	−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	$-0.892932\pi$
$37$		−	4.01531i		−	0.660113i	0.943961	−	0.330057i	$-0.107068\pi$
$38$	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	0.998896	+	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	0.518637	−	0.854995i	$-0.326440\pi$
$43$	0.245957	+	0.142003i	0.0375081	+	0.0216553i	−0.481129	+	0.876650i	$0.659773\pi$
$44$	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
$50$	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	$0.0854818\pi$
$53$			3.86330i			0.530666i	−0.964157	+	0.265333i	$0.914518\pi$
$54$		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	0.0365764	−	0.999331i	$-0.488355\pi$
$59$	7.06904	−	4.08131i	0.920310	−	0.531341i	0.883734	+	0.467989i	$0.155021\pi$
$60$		0			0
$61$	−6.31237	−	3.64445i	−0.808216	−	0.466624i	0.0381201	−	0.999273i	$-0.487863\pi$
$61$	−6.31237	−	3.64445i	−0.808216	−	0.466624i	−0.846336	+	0.532650i	$0.821196\pi$
$62$	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	−0.343511	−	0.939149i	$-0.611616\pi$
$67$	2.43973	−	1.40858i	0.298061	−	0.172085i	0.641571	+	0.767063i	$0.278283\pi$
$68$	−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	−0.868580	−	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	0.361933	−	0.932204i	$-0.382117\pi$
$83$	−2.40891	−	1.39079i	−0.264412	−	0.152659i	−0.626346	+	0.779545i	$0.715450\pi$
$84$		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	−0.971448	−	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	0.753305	−	0.657671i	$-0.228458\pi$
$101$	5.63193	+	3.25160i	0.560398	+	0.323546i	−0.192907	+	0.981217i	$0.561792\pi$
$102$		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	$0.880720\pi$
$104$	−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	$0.00688417\pi$
$107$			0.447393i			0.0432511i	−0.999766	+	0.0216256i	$0.993116\pi$
$108$		0			0
$109$		−	9.36497i		−	0.897002i	−0.893782	−	0.448501i	$-0.851958\pi$
$109$		−	9.36497i		−	0.897002i	0.893782	−	0.448501i	$-0.148042\pi$
$110$	−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	−0.999267	−	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
$122$	−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	−0.391061	−	0.920365i	$-0.627892\pi$
$131$	2.40891	−	1.39079i	0.210468	−	0.121514i	0.601529	+	0.798851i	$0.294559\pi$
$132$		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	−0.551247	−	0.834342i	$-0.685848\pi$
$139$	−1.22979	+	0.710017i	−0.104309	+	0.0602229i	0.446938	+	0.894565i	$0.352514\pi$
$140$	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	−0.687589	−	0.726100i	$-0.741331\pi$
$149$	−4.91390	+	2.83704i	−0.402563	+	0.232420i	0.285027	+	0.958520i	$0.407998\pi$
$150$		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	−0.999936	−	0.0112838i	$-0.996408\pi$
$157$	−18.6713	+	10.7799i	−1.49013	+	0.860328i	−0.490196	+	0.871612i	$0.663075\pi$
$158$	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	$-0.801304\pi$
$163$		−	14.9239i		−	1.16893i	0.811418	−	0.584466i	$-0.198696\pi$
$164$	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	0.878471	+	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	0.853547	−	0.521016i	$-0.174447\pi$
$173$	10.9052	+	6.29612i	0.829107	+	0.478685i	−0.0244397	+	0.999701i	$0.507780\pi$
$174$		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	$-0.850485\pi$
$179$		−	12.1116i		−	0.905264i	0.891697	−	0.452632i	$-0.149515\pi$
$180$		0			0
$181$			17.6790i			1.31407i	0.753862	+	0.657033i	$0.228189\pi$
$181$			17.6790i			1.31407i	−0.753862	+	0.657033i	$0.771811\pi$
$182$	−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	0.263812	+	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	$0.829687\pi$
$194$	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	$0.337836\pi$
$197$			24.5066i			1.74602i	−0.487701	+	0.873011i	$0.662164\pi$
$198$		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	−0.239238	−	0.970961i	$-0.576898\pi$
$211$	7.00175	−	4.04246i	0.482020	−	0.278294i	0.721258	+	0.692667i	$0.243564\pi$
$212$	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	−0.928044	−	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	0.535882	−	0.844293i	$-0.319979\pi$
$227$	1.09451	+	0.631913i	0.0726449	+	0.0419415i	−0.463238	+	0.886234i	$0.653312\pi$
$228$		0			0
$229$	6.29196	−	3.63267i	0.415785	−	0.240053i	−0.277487	−	0.960729i	$-0.589502\pi$
$229$	6.29196	−	3.63267i	0.415785	−	0.240053i	0.693272	+	0.720676i	$0.256168\pi$
$230$	−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	0.606173	−	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
$248$	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	$-0.993555\pi$
$251$		−	0.641516i		−	0.0404922i	0.999795	−	0.0202461i	$-0.00644497\pi$
$252$		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	0.921610	−	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
$266$	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	$-0.734887\pi$
$269$		−	24.2695i		−	1.47974i	0.672750	−	0.739870i	$-0.265113\pi$
$270$		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	0.790909	−	0.611933i	$-0.209608\pi$
$277$	10.9249	+	6.30750i	0.656414	+	0.378981i	−0.134495	+	0.990914i	$0.542941\pi$
$278$	−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	−0.469667	−	0.882844i	$-0.655626\pi$
$283$	1.01045	−	0.583382i	0.0600649	−	0.0346785i	0.529732	+	0.848165i	$0.322293\pi$
$284$	−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	−0.436963	−	0.899480i	$-0.643946\pi$
$293$	2.11446	−	1.22079i	0.123528	−	0.0713191i	0.560491	+	0.828161i	$0.310612\pi$
$294$		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	$0.148331\pi$
$307$			15.7452i			0.898626i	−0.893374	+	0.449313i	$0.851669\pi$
$308$	−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	−0.997370	−	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	0.0549932	−	0.998487i	$-0.482486\pi$
$317$	−13.9271	−	8.04083i	−0.782225	−	0.451618i	−0.837218	+	0.546869i	$0.815820\pi$
$318$		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	0.901063	−	0.433688i	$-0.142788\pi$
$331$	17.7569	+	10.2520i	0.976010	+	0.563499i	0.0749465	+	0.997188i	$0.476121\pi$
$332$	−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	$0.723348\pi$
$338$	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	0.316873	−	0.948468i	$-0.397367\pi$
$347$	24.1550	−	13.9459i	1.29671	−	0.748654i	0.979834	+	0.199814i	$0.0640339\pi$
$348$		0			0
$349$	−26.0103	−	15.0171i	−1.39230	−	0.803846i	−0.398732	−	0.917068i	$-0.630550\pi$
$349$	−26.0103	−	15.0171i	−1.39230	−	0.803846i	−0.993570	+	0.113222i	$0.963883\pi$
$350$	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
$356$	−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	−0.675155	−	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	0.0960206	−	0.995379i	$-0.469389\pi$
$373$	19.4301	−	11.2180i	1.00605	−	0.580846i	0.910034	+	0.414533i	$0.136055\pi$
$374$	−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	$-0.802209\pi$
$379$		−	22.6668i		−	1.16431i	0.813077	−	0.582157i	$-0.197791\pi$
$380$	−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	0.911383	−	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	0.771282	−	0.636494i	$-0.219616\pi$
$389$	11.9463	+	6.89722i	0.605703	+	0.349703i	−0.165579	+	0.986197i	$0.552949\pi$
$390$		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	$-0.796581\pi$
$397$		−	23.7680i		−	1.19288i	0.802657	−	0.596441i	$-0.203419\pi$
$398$	−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	0.955902	−	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	$0.661092\pi$
$410$	−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	−0.270977	−	0.962586i	$-0.587347\pi$
$419$	8.74372	−	5.04819i	0.427159	−	0.246620i	0.698135	+	0.715966i	$0.254013\pi$
$420$		0			0
$421$	−20.2218	−	11.6751i	−0.985551	−	0.569008i	−0.0816096	−	0.996664i	$-0.526006\pi$
$421$	−20.2218	−	11.6751i	−0.985551	−	0.569008i	−0.903941	+	0.427656i	$0.859339\pi$
$422$	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	0.403081	+	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	0.941140	−	0.338016i	$-0.109756\pi$
$443$	23.5518	+	13.5976i	1.11898	+	0.646044i	0.177840	+	0.984059i	$0.443089\pi$
$444$		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	−0.999860	−	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	$-0.995438\pi$
$461$	−32.4695	−	18.7463i	−1.51226	−	0.873101i	−0.512359	−	0.858771i	$-0.671228\pi$
$462$		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	$0.954207\pi$
$464$	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	$0.215230\pi$
$467$			27.0476i			1.25161i	−0.779979	+	0.625806i	$0.784770\pi$
$468$		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	0.364838	+	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
$482$	−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	−0.227817	−	0.973704i	$-0.573159\pi$
$491$	11.1131	−	6.41614i	0.501526	−	0.289556i	0.729344	+	0.684147i	$0.239826\pi$
$492$		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	−0.803129	−	0.595805i	$-0.796833\pi$
$499$	−15.3846	+	8.88232i	−0.688711	+	0.397627i	0.114418	+	0.993433i	$0.463500\pi$
$500$	−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	−0.338756	−	0.940874i	$-0.610006\pi$
$509$	6.91916	−	3.99478i	0.306686	−	0.177065i	0.645443	+	0.763809i	$0.276673\pi$
$510$		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	$0.131950\pi$
$523$			18.4217i			0.805526i	−0.915304	+	0.402763i	$0.868050\pi$
$524$	−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	$-0.906253\pi$
$541$		−	13.5032i		−	0.580549i	0.956943	−	0.290275i	$-0.0937467\pi$
$542$	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	0.991900	−	0.127019i	$-0.0405410\pi$
$547$	32.2252	+	18.6052i	1.37785	+	0.795501i	0.385948	+	0.922520i	$0.373874\pi$
$548$	−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	$0.116989\pi$
$557$			16.9602i			0.718628i	−0.933217	+	0.359314i	$0.883011\pi$
$558$		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	−0.923759	−	0.382974i	$-0.874900\pi$
$563$	−25.0083	+	14.4385i	−1.05397	+	0.608512i	−0.130214	+	0.991486i	$0.541566\pi$
$564$		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	0.239390	−	0.970924i	$-0.423053\pi$
$571$	28.6730	−	16.5544i	1.19993	−	0.692779i	0.960539	+	0.278144i	$0.0897193\pi$
$572$	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	−0.0437275	−	0.999043i	$-0.513923\pi$
$587$	−22.5512	−	13.0200i	−0.930788	−	0.537391i	−0.887061	+	0.461653i	$0.847257\pi$
$588$		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	0.982733	−	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	$0.882969\pi$
$608$	−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	$0.188588\pi$
$613$			27.6512i			1.11682i	−0.829565	+	0.558410i	$0.811412\pi$
$614$	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	0.999918	+	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	0.842831	−	0.538178i	$-0.180887\pi$
$619$	19.8583	+	11.4652i	0.798171	+	0.460824i	−0.0446605	+	0.999002i	$0.514221\pi$
$620$	−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	−0.284574	−	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	−0.986956	−	0.160987i	$-0.948532\pi$
$643$	−34.0047	+	19.6326i	−1.34102	+	0.774236i	−0.354059	+	0.935223i	$0.615199\pi$
$644$	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	−0.158473	−	0.987363i	$-0.550657\pi$
$653$	15.7763	−	9.10843i	0.617373	−	0.356440i	0.775845	+	0.630923i	$0.217324\pi$
$654$		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	−0.415049	−	0.909799i	$-0.636236\pi$
$659$	−36.2085	−	20.9050i	−1.41048	−	0.814343i	−0.995434	+	0.0954566i	$0.969569\pi$
$660$		0			0
$661$	−9.78973	+	5.65210i	−0.380776	+	0.219841i	−0.678156	−	0.734918i	$-0.737221\pi$
$661$	−9.78973	+	5.65210i	−0.380776	+	0.219841i	0.297380	+	0.954759i	$0.403887\pi$
$662$	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	−0.295066	−	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	0.124412	−	0.992231i	$-0.460296\pi$
$677$	−17.5026	−	10.1051i	−0.672679	−	0.388372i	−0.797091	+	0.603859i	$0.793629\pi$
$678$		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	$0.314772\pi$
$683$			43.6659i			1.67083i	−0.549621	+	0.835414i	$0.685228\pi$
$684$		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	0.642885	−	0.765963i	$-0.277737\pi$
$691$	7.91193	+	4.56796i	0.300984	+	0.173773i	−0.341901	+	0.939736i	$0.611071\pi$
$692$	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	$0.321769\pi$
$701$			44.8665i			1.69458i	−0.531127	+	0.847292i	$0.678231\pi$
$702$		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	0.867190	−	0.497977i	$-0.165923\pi$
$709$	23.1529	+	13.3673i	0.869525	+	0.502021i	0.00233491	+	0.999997i	$0.499257\pi$
$710$	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	−0.984529	−	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	0.333580	−	0.942722i	$-0.391743\pi$
$733$	35.6508	−	20.5830i	1.31679	−	0.760249i	0.983211	+	0.182472i	$0.0584100\pi$
$734$	−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	$-0.688613\pi$
$739$		−	45.1004i		−	1.65905i	0.558473	−	0.829523i	$-0.311387\pi$
$740$	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	0.921630	+	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	$-0.355766\pi$
$752$	−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	$0.0164435\pi$
$757$			2.84137i			0.103271i	−0.998666	+	0.0516357i	$0.983557\pi$
$758$	−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	0.723191	−	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	$0.667737\pi$
$770$	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	$0.0911774\pi$
$773$			15.7109i			0.565082i	−0.959255	+	0.282541i	$0.908823\pi$
$774$		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	−0.266259	−	0.963902i	$-0.585788\pi$
$787$	12.2138	−	7.05164i	0.435375	−	0.251364i	0.701634	+	0.712538i	$0.252454\pi$
$788$	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	−0.0395390	−	0.999218i	$-0.512589\pi$
$797$	22.7555	−	13.1379i	0.806040	−	0.465367i	0.845579	+	0.533851i	$0.179256\pi$
$798$		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	$0.230425\pi$
$811$			37.7228i			1.32463i	−0.749227	+	0.662314i	$0.769575\pi$
$812$	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	0.518457	−	0.855104i	$-0.326507\pi$
$821$	1.06427	+	0.614456i	0.0371432	+	0.0214446i	−0.481313	+	0.876549i	$0.659840\pi$
$822$		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	$-0.375413\pi$
$824$	−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	$-0.678243\pi$
$827$		−	48.7311i		−	1.69455i	0.531157	−	0.847273i	$-0.321757\pi$
$828$		0			0
$829$			28.9573i			1.00573i	0.864366	+	0.502863i	$0.167720\pi$
$829$			28.9573i			1.00573i	−0.864366	+	0.502863i	$0.832280\pi$
$830$	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	−0.967423	−	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
$842$	−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	0.399743	−	0.916627i	$-0.369099\pi$
$853$	−5.67204	−	3.27476i	−0.194207	−	0.112126i	−0.593951	+	0.804502i	$0.702433\pi$
$854$	−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	−0.455363	−	0.890306i	$-0.650491\pi$
$859$	2.57865	−	1.48878i	0.0879824	−	0.0507967i	0.543346	+	0.839509i	$0.317157\pi$
$860$	−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	−0.572213	−	0.820105i	$-0.693915\pi$
$877$	−4.38552	+	2.53198i	−0.148088	+	0.0854988i	0.424125	+	0.905604i	$0.360582\pi$
$878$	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	$-0.843240\pi$
$883$		−	28.0994i		−	0.945619i	0.881165	−	0.472809i	$-0.156760\pi$
$884$	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	0.854628	−	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
$896$	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	0.487017	−	0.873393i	$-0.338085\pi$
$907$	−0.778677	−	0.449569i	−0.0258555	−	0.0149277i	−0.512872	+	0.858465i	$0.671418\pi$
$908$	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
$914$	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	−0.898718	−	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
$932$	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	−0.961534	−	0.274686i	$-0.911426\pi$
$941$	−36.9463	+	21.3310i	−1.20442	+	0.695370i	−0.242882	+	0.970056i	$0.578093\pi$
$942$		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	0.845107	−	0.534597i	$-0.179537\pi$
$947$	24.7629	+	14.2969i	0.804686	+	0.464585i	−0.0404213	+	0.999183i	$0.512870\pi$
$948$		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	0.731466	−	0.681878i	$-0.238836\pi$
$967$	−6.99023	−	12.1074i	−0.224791	−	0.389349i	−0.956257	+	0.292529i	$0.905503\pi$
$968$	−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	$0.0908268\pi$
$971$			17.5426i			0.562969i	−0.959566	+	0.281484i	$0.909173\pi$
$972$		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	−0.957956	−	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
$986$	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	0.0257404	−	0.999669i	$-0.491806\pi$
$997$	−26.1168	−	15.0786i	−0.827128	−	0.477543i	−0.852868	+	0.522126i	$0.825139\pi$
$998$	−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.181.7		16
3.2	odd	2		72.2.n.b.61.2	yes	16
4.3	odd	2		864.2.r.b.721.3		16
8.3	odd	2		864.2.r.b.721.6		16
8.5	even	2	inner	216.2.n.b.181.5		16
9.2	odd	6		648.2.d.j.325.8		8
9.4	even	3	inner	216.2.n.b.37.5		16
9.5	odd	6		72.2.n.b.13.4	yes	16
9.7	even	3		648.2.d.k.325.1		8
12.11	even	2		288.2.r.b.241.6		16
24.5	odd	2		72.2.n.b.61.4	yes	16
24.11	even	2		288.2.r.b.241.3		16
36.7	odd	6		2592.2.d.k.1297.3		8
36.11	even	6		2592.2.d.j.1297.6		8
36.23	even	6		288.2.r.b.49.3		16
36.31	odd	6		864.2.r.b.145.6		16
72.5	odd	6		72.2.n.b.13.2	✓	16
72.11	even	6		2592.2.d.j.1297.3		8
72.13	even	6	inner	216.2.n.b.37.7		16
72.29	odd	6		648.2.d.j.325.7		8
72.43	odd	6		2592.2.d.k.1297.6		8
72.59	even	6		288.2.r.b.49.6		16
72.61	even	6		648.2.d.k.325.2		8
72.67	odd	6		864.2.r.b.145.3		16

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