LMFDB - Embedded newform 637.2.k.a.569.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(459,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.459"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-2,-2,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			569.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	637.569
Dual form			637.2.k.a.459.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.73205i q^{2} +(-1.00000 + 1.73205i) q^{3} -1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(3.00000 + 1.73205i) q^{6} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(1.00000 - 1.73205i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(3.00000 - 1.73205i) q^{15} -5.00000 q^{16} -3.00000 q^{17} +(-1.50000 + 0.866025i) q^{18} +(3.00000 - 1.73205i) q^{19} +(1.50000 + 0.866025i) q^{20} -6.00000 q^{23} +(3.00000 + 1.73205i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(4.50000 + 4.33013i) q^{26} -4.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(-3.00000 - 5.19615i) q^{30} +(-3.00000 + 1.73205i) q^{31} +5.19615i q^{32} +5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +8.66025i q^{37} +(-3.00000 - 5.19615i) q^{38} +(-2.00000 - 6.92820i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(-4.50000 + 2.59808i) q^{41} +(-4.00000 + 6.92820i) q^{43} +1.73205i q^{45} +10.3923i q^{46} +(-3.00000 - 1.73205i) q^{47} +(5.00000 - 8.66025i) q^{48} +(-3.00000 + 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(2.50000 - 2.59808i) q^{52} +(1.50000 + 2.59808i) q^{53} +6.92820i q^{54} +6.92820i q^{57} +(-4.50000 + 2.59808i) q^{58} -6.92820i q^{59} +(-3.00000 + 1.73205i) q^{60} +(-0.500000 - 0.866025i) q^{61} +(3.00000 + 5.19615i) q^{62} -1.00000 q^{64} +(6.00000 - 1.73205i) q^{65} +(-3.00000 - 1.73205i) q^{67} +3.00000 q^{68} +(6.00000 - 10.3923i) q^{69} +(3.00000 + 1.73205i) q^{71} +(-1.50000 + 0.866025i) q^{72} +(-1.50000 + 0.866025i) q^{73} +15.0000 q^{74} +4.00000 q^{75} +(-3.00000 + 1.73205i) q^{76} +(-12.0000 + 3.46410i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(7.50000 + 4.33013i) q^{80} +(5.50000 - 9.52628i) q^{81} +(4.50000 + 7.79423i) q^{82} -13.8564i q^{83} +(4.50000 + 2.59808i) q^{85} +(12.0000 + 6.92820i) q^{86} +6.00000 q^{87} -6.92820i q^{89} +3.00000 q^{90} +6.00000 q^{92} -6.92820i q^{93} +(-3.00000 + 5.19615i) q^{94} -6.00000 q^{95} +(-9.00000 - 5.19615i) q^{96} +(6.00000 + 3.46410i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 2 q^{4} - 3 q^{5} + 6 q^{6} - q^{9} - 3 q^{10} + 2 q^{12} - 5 q^{13} + 6 q^{15} - 10 q^{16} - 6 q^{17} - 3 q^{18} + 6 q^{19} + 3 q^{20} - 12 q^{23} + 6 q^{24} - 2 q^{25} + 9 q^{26} - 8 q^{27}+ \cdots + 12 q^{97}+O(q^{100}) $ 2 * q - 2 * q^3 - 2 * q^4 - 3 * q^5 + 6 * q^6 - q^9 - 3 * q^10 + 2 * q^12 - 5 * q^13 + 6 * q^15 - 10 * q^16 - 6 * q^17 - 3 * q^18 + 6 * q^19 + 3 * q^20 - 12 * q^23 + 6 * q^24 - 2 * q^25 + 9 * q^26 - 8 * q^27 - 3 * q^29 - 6 * q^30 - 6 * q^31 + q^36 - 6 * q^38 - 4 * q^39 - 3 * q^40 - 9 * q^41 - 8 * q^43 - 6 * q^47 + 10 * q^48 - 6 * q^50 + 6 * q^51 + 5 * q^52 + 3 * q^53 - 9 * q^58 - 6 * q^60 - q^61 + 6 * q^62 - 2 * q^64 + 12 * q^65 - 6 * q^67 + 6 * q^68 + 12 * q^69 + 6 * q^71 - 3 * q^72 - 3 * q^73 + 30 * q^74 + 8 * q^75 - 6 * q^76 - 24 * q^78 - 4 * q^79 + 15 * q^80 + 11 * q^81 + 9 * q^82 + 9 * q^85 + 24 * q^86 + 12 * q^87 + 6 * q^90 + 12 * q^92 - 6 * q^94 - 12 * q^95 - 18 * q^96 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	1.73205i		−	1.22474i	−0.790569	−	0.612372i	$-0.790215\pi$
$2$		−	1.73205i		−	1.22474i	0.790569	−	0.612372i	$-0.209785\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	−1.00000			−0.500000
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	0.125567	−	0.992085i	$-0.459925\pi$
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$6$	3.00000	+	1.73205i	1.22474	+	0.707107i
$7$		0			0
$7$		0			0
$8$		−	1.73205i		−	0.612372i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	1.00000	−	1.73205i	0.288675	−	0.500000i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$13$	−2.50000	+	2.59808i	−0.693375	+	0.720577i
$14$		0			0
$15$	3.00000	−	1.73205i	0.774597	−	0.447214i
$16$	−5.00000			−1.25000
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$	−1.50000	+	0.866025i	−0.353553	+	0.204124i
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	0.802955	+	0.596040i	$0.203260\pi$
$20$	1.50000	+	0.866025i	0.335410	+	0.193649i
$21$		0			0
$22$		0			0
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$	3.00000	+	1.73205i	0.612372	+	0.353553i
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	4.50000	+	4.33013i	0.882523	+	0.849208i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$	−3.00000	−	5.19615i	−0.547723	−	0.948683i
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	−0.744599	−	0.667512i	$-0.767359\pi$
$31$	−3.00000	+	1.73205i	−0.538816	+	0.311086i	0.205783	+	0.978598i	$0.434026\pi$
$32$			5.19615i			0.918559i
$33$		0			0
$34$			5.19615i			0.891133i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$			8.66025i			1.42374i	0.702313	+	0.711868i	$0.252151\pi$
$37$			8.66025i			1.42374i	−0.702313	+	0.711868i	$0.747849\pi$
$38$	−3.00000	−	5.19615i	−0.486664	−	0.842927i
$39$	−2.00000	−	6.92820i	−0.320256	−	1.10940i
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	−0.808383	−	0.588657i	$-0.799657\pi$
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	0.105601	+	0.994409i	$0.466323\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$		0			0
$45$			1.73205i			0.258199i
$46$			10.3923i			1.53226i
$47$	−3.00000	−	1.73205i	−0.437595	−	0.252646i	0.264982	−	0.964253i	$-0.414634\pi$
$47$	−3.00000	−	1.73205i	−0.437595	−	0.252646i	−0.702577	+	0.711608i	$0.747967\pi$
$48$	5.00000	−	8.66025i	0.721688	−	1.25000i
$49$		0			0
$50$	−3.00000	+	1.73205i	−0.424264	+	0.244949i
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	2.50000	−	2.59808i	0.346688	−	0.360288i
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$			6.92820i			0.942809i
$55$		0			0
$56$		0			0
$57$			6.92820i			0.917663i
$58$	−4.50000	+	2.59808i	−0.590879	+	0.341144i
$59$		−	6.92820i		−	0.901975i	−0.892530	−	0.450988i	$-0.851072\pi$
$59$		−	6.92820i		−	0.901975i	0.892530	−	0.450988i	$-0.148928\pi$
$60$	−3.00000	+	1.73205i	−0.387298	+	0.223607i
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	3.00000	+	5.19615i	0.381000	+	0.659912i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	6.00000	−	1.73205i	0.744208	−	0.214834i
$66$		0			0
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	0.305424	−	0.952217i	$-0.401202\pi$
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	3.00000			0.363803
$69$	6.00000	−	10.3923i	0.722315	−	1.25109i
$70$		0			0
$71$	3.00000	+	1.73205i	0.356034	+	0.205557i	0.667340	−	0.744753i	$-0.267433\pi$
$71$	3.00000	+	1.73205i	0.356034	+	0.205557i	−0.311305	+	0.950310i	$0.600766\pi$
$72$	−1.50000	+	0.866025i	−0.176777	+	0.102062i
$73$	−1.50000	+	0.866025i	−0.175562	+	0.101361i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−1.50000	+	0.866025i	−0.175562	+	0.101361i	0.409644	+	0.912245i	$0.365653\pi$
$74$	15.0000			1.74371
$75$	4.00000			0.461880
$76$	−3.00000	+	1.73205i	−0.344124	+	0.198680i
$77$		0			0
$78$	−12.0000	+	3.46410i	−1.35873	+	0.392232i
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$	7.50000	+	4.33013i	0.838525	+	0.484123i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$		−	13.8564i		−	1.52094i	−0.649374	−	0.760469i	$-0.724969\pi$
$83$		−	13.8564i		−	1.52094i	0.649374	−	0.760469i	$-0.275031\pi$
$84$		0			0
$85$	4.50000	+	2.59808i	0.488094	+	0.281801i
$86$	12.0000	+	6.92820i	1.29399	+	0.747087i
$87$	6.00000			0.643268
$88$		0			0
$89$		−	6.92820i		−	0.734388i	−0.930144	−	0.367194i	$-0.880318\pi$
$89$		−	6.92820i		−	0.734388i	0.930144	−	0.367194i	$-0.119682\pi$
$90$	3.00000			0.316228
$91$		0			0
$92$	6.00000			0.625543
$93$		−	6.92820i		−	0.718421i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$	−6.00000			−0.615587
$96$	−9.00000	−	5.19615i	−0.918559	−	0.530330i
$97$	6.00000	+	3.46410i	0.609208	+	0.351726i	0.772655	−	0.634826i	$-0.218928\pi$
$97$	6.00000	+	3.46410i	0.609208	+	0.351726i	−0.163448	+	0.986552i	$0.552261\pi$
$98$		0			0
$99$		0			0
$100$	1.00000	+	1.73205i	0.100000	+	0.173205i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$	−9.00000	−	5.19615i	−0.891133	−	0.514496i
$103$	5.00000	−	8.66025i	0.492665	−	0.853320i	−0.507300	−	0.861770i	$-0.669356\pi$
$103$	5.00000	−	8.66025i	0.492665	−	0.853320i	0.999964	+	0.00844953i	$0.00268960\pi$
$104$	4.50000	+	4.33013i	0.441261	+	0.424604i
$105$		0			0
$106$	4.50000	−	2.59808i	0.437079	−	0.252347i
$107$	6.00000			0.580042			0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000			0.580042			0.290021	+	0.957020i	$0.406338\pi$
$108$	4.00000			0.384900
$109$	12.0000	−	6.92820i	1.14939	−	0.663602i	0.200653	−	0.979662i	$-0.435694\pi$
$109$	12.0000	−	6.92820i	1.14939	−	0.663602i	0.948739	+	0.316061i	$0.102360\pi$
$110$		0			0
$111$	−15.0000	−	8.66025i	−1.42374	−	0.821995i
$112$		0			0
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	−0.260955	−	0.965351i	$-0.584038\pi$
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	0.966496	−	0.256681i	$-0.0826291\pi$
$114$	12.0000			1.12390
$115$	9.00000	+	5.19615i	0.839254	+	0.484544i
$116$	1.50000	+	2.59808i	0.139272	+	0.241225i
$117$	3.50000	+	0.866025i	0.323575	+	0.0800641i
$118$	−12.0000			−1.10469
$119$		0			0
$120$	−3.00000	−	5.19615i	−0.273861	−	0.474342i
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$	−1.50000	+	0.866025i	−0.135804	+	0.0784063i
$123$		−	10.3923i		−	0.937043i
$124$	3.00000	−	1.73205i	0.269408	−	0.155543i
$125$			12.1244i			1.08444i
$126$		0			0
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	0.906977	−	0.421180i	$-0.138384\pi$
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	−0.818241	+	0.574875i	$0.805051\pi$
$128$			12.1244i			1.07165i
$129$	−8.00000	−	13.8564i	−0.704361	−	1.21999i
$130$	−3.00000	−	10.3923i	−0.263117	−	0.911465i
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	0.141865	+	0.989886i	$0.454690\pi$
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	−0.928199	+	0.372084i	$0.878643\pi$
$132$		0			0
$133$		0			0
$134$	−3.00000	+	5.19615i	−0.259161	+	0.448879i
$135$	6.00000	+	3.46410i	0.516398	+	0.298142i
$136$			5.19615i			0.445566i
$137$			15.5885i			1.33181i	0.746036	+	0.665906i	$0.231955\pi$
$137$			15.5885i			1.33181i	−0.746036	+	0.665906i	$0.768045\pi$
$138$	−18.0000	−	10.3923i	−1.53226	−	0.884652i
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$		0			0
$141$	6.00000	−	3.46410i	0.505291	−	0.291730i
$142$	3.00000	−	5.19615i	0.251754	−	0.436051i
$143$		0			0
$144$	2.50000	+	4.33013i	0.208333	+	0.360844i
$145$			5.19615i			0.431517i
$146$	1.50000	+	2.59808i	0.124141	+	0.215018i
$147$		0			0
$148$		−	8.66025i		−	0.711868i
$149$	16.5000	−	9.52628i	1.35173	−	0.780423i	0.363241	−	0.931695i	$-0.381670\pi$
$149$	16.5000	−	9.52628i	1.35173	−	0.780423i	0.988492	+	0.151272i	$0.0483370\pi$
$150$		−	6.92820i		−	0.565685i
$151$	−15.0000	+	8.66025i	−1.22068	+	0.704761i	−0.965064	−	0.262016i	$-0.915613\pi$
$151$	−15.0000	+	8.66025i	−1.22068	+	0.704761i	−0.255619	+	0.966778i	$0.582279\pi$
$152$	−3.00000	−	5.19615i	−0.243332	−	0.421464i
$153$	1.50000	+	2.59808i	0.121268	+	0.210042i
$154$		0			0
$155$	6.00000			0.481932
$156$	2.00000	+	6.92820i	0.160128	+	0.554700i
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$	6.00000	+	3.46410i	0.477334	+	0.275589i
$159$	−6.00000			−0.475831
$160$	4.50000	−	7.79423i	0.355756	−	0.616188i
$161$		0			0
$162$	−16.5000	−	9.52628i	−1.29636	−	0.748455i
$163$	−18.0000	+	10.3923i	−1.40987	+	0.813988i	−0.995375	−	0.0960641i	$-0.969375\pi$
$163$	−18.0000	+	10.3923i	−1.40987	+	0.813988i	−0.414494	+	0.910052i	$0.636041\pi$
$164$	4.50000	−	2.59808i	0.351391	−	0.202876i
$165$		0			0
$166$	−24.0000			−1.86276
$167$	−12.0000	+	6.92820i	−0.928588	+	0.536120i	−0.886365	−	0.462988i	$-0.846777\pi$
$167$	−12.0000	+	6.92820i	−0.928588	+	0.536120i	−0.0422232	+	0.999108i	$0.513444\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	4.50000	−	7.79423i	0.345134	−	0.597790i
$171$	−3.00000	−	1.73205i	−0.229416	−	0.132453i
$172$	4.00000	−	6.92820i	0.304997	−	0.528271i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		−	10.3923i		−	0.787839i
$175$		0			0
$176$		0			0
$177$	12.0000	+	6.92820i	0.901975	+	0.520756i
$178$	−12.0000			−0.899438
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$		−	1.73205i		−	0.129099i
$181$	11.0000			0.817624			0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000			0.817624			0.408812	+	0.912619i	$0.365943\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$			10.3923i			0.766131i
$185$	7.50000	−	12.9904i	0.551411	−	0.955072i
$186$	−12.0000			−0.879883
$187$		0			0
$188$	3.00000	+	1.73205i	0.218797	+	0.126323i
$189$		0			0
$190$			10.3923i			0.753937i
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$	1.00000	−	1.73205i	0.0721688	−	0.125000i
$193$	4.50000	+	2.59808i	0.323917	+	0.187014i	0.653137	−	0.757240i	$-0.273452\pi$
$193$	4.50000	+	2.59808i	0.323917	+	0.187014i	−0.329220	+	0.944253i	$0.606786\pi$
$194$	6.00000	−	10.3923i	0.430775	−	0.746124i
$195$	−3.00000	+	12.1244i	−0.214834	+	0.868243i
$196$		0			0
$197$	12.0000	−	6.92820i	0.854965	−	0.493614i	−0.00735824	−	0.999973i	$-0.502342\pi$
$197$	12.0000	−	6.92820i	0.854965	−	0.493614i	0.862323	+	0.506359i	$0.169009\pi$
$198$		0			0
$199$	−2.00000			−0.141776			−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000			−0.141776			−0.0708881	+	0.997484i	$0.522583\pi$
$200$	−3.00000	+	1.73205i	−0.212132	+	0.122474i
$201$	6.00000	−	3.46410i	0.423207	−	0.244339i
$202$	−4.50000	−	2.59808i	−0.316619	−	0.182800i
$203$		0			0
$204$	−3.00000	+	5.19615i	−0.210042	+	0.363803i
$205$	9.00000			0.628587
$206$	−15.0000	−	8.66025i	−1.04510	−	0.603388i
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	12.5000	−	12.9904i	0.866719	−	0.900721i
$209$		0			0
$210$		0			0
$211$	−5.00000	−	8.66025i	−0.344214	−	0.596196i	0.640996	−	0.767544i	$-0.278521\pi$
$211$	−5.00000	−	8.66025i	−0.344214	−	0.596196i	−0.985211	+	0.171347i	$0.945188\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$	−6.00000	+	3.46410i	−0.411113	+	0.237356i
$214$		−	10.3923i		−	0.710403i
$215$	12.0000	−	6.92820i	0.818393	−	0.472500i
$216$			6.92820i			0.471405i
$217$		0			0
$218$	−12.0000	−	20.7846i	−0.812743	−	1.40771i
$219$		−	3.46410i		−	0.234082i
$220$		0			0
$221$	7.50000	−	7.79423i	0.504505	−	0.524297i
$222$	−15.0000	+	25.9808i	−1.00673	+	1.74371i
$223$	−9.00000	+	5.19615i	−0.602685	+	0.347960i	−0.770097	−	0.637927i	$-0.779792\pi$
$223$	−9.00000	+	5.19615i	−0.602685	+	0.347960i	0.167412	+	0.985887i	$0.446459\pi$
$224$		0			0
$225$	−1.00000	+	1.73205i	−0.0666667	+	0.115470i
$226$	−22.5000	−	12.9904i	−1.49668	−	0.864107i
$227$		−	24.2487i		−	1.60944i	−0.593652	−	0.804722i	$-0.702314\pi$
$227$		−	24.2487i		−	1.60944i	0.593652	−	0.804722i	$-0.297686\pi$
$228$		−	6.92820i		−	0.458831i
$229$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$229$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$230$	9.00000	−	15.5885i	0.593442	−	1.02787i
$231$		0			0
$232$	−4.50000	+	2.59808i	−0.295439	+	0.170572i
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	1.50000	−	6.06218i	0.0980581	−	0.396297i
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$			6.92820i			0.450988i
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$		0			0
$239$			20.7846i			1.34444i	0.740349	+	0.672222i	$0.234660\pi$
$239$			20.7846i			1.34444i	−0.740349	+	0.672222i	$0.765340\pi$
$240$	−15.0000	+	8.66025i	−0.968246	+	0.559017i
$241$			1.73205i			0.111571i	0.998443	+	0.0557856i	$0.0177663\pi$
$241$			1.73205i			0.111571i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	−16.5000	+	9.52628i	−1.06066	+	0.612372i
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	0.500000	+	0.866025i	0.0320092	+	0.0554416i
$245$		0			0
$246$	−18.0000			−1.14764
$247$	−3.00000	+	12.1244i	−0.190885	+	0.771454i
$248$	3.00000	+	5.19615i	0.190500	+	0.329956i
$249$	24.0000	+	13.8564i	1.52094	+	0.878114i
$250$	21.0000			1.32816
$251$	9.00000	−	15.5885i	0.568075	−	0.983935i	−0.428681	−	0.903456i	$-0.641022\pi$
$251$	9.00000	−	15.5885i	0.568075	−	0.983935i	0.996756	−	0.0804789i	$-0.0256450\pi$
$252$		0			0
$253$		0			0
$254$	3.00000	−	1.73205i	0.188237	−	0.108679i
$255$	−9.00000	+	5.19615i	−0.563602	+	0.325396i
$256$	19.0000			1.18750
$257$	3.00000			0.187135			0.0935674	−	0.995613i	$-0.470173\pi$
$257$	3.00000			0.187135			0.0935674	+	0.995613i	$0.470173\pi$
$258$	−24.0000	+	13.8564i	−1.49417	+	0.862662i
$259$		0			0
$260$	−6.00000	+	1.73205i	−0.372104	+	0.107417i
$261$	−1.50000	+	2.59808i	−0.0928477	+	0.160817i
$262$	27.0000	+	15.5885i	1.66807	+	0.963058i
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	−0.989561	−	0.144112i	$-0.953967\pi$
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	0.619586	+	0.784929i	$0.287301\pi$
$264$		0			0
$265$		−	5.19615i		−	0.319197i
$266$		0			0
$267$	12.0000	+	6.92820i	0.734388	+	0.423999i
$268$	3.00000	+	1.73205i	0.183254	+	0.105802i
$269$	−6.00000			−0.365826			−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000			−0.365826			−0.182913	+	0.983129i	$0.558553\pi$
$270$	6.00000	−	10.3923i	0.365148	−	0.632456i
$271$			20.7846i			1.26258i	0.775549	+	0.631288i	$0.217473\pi$
$271$			20.7846i			1.26258i	−0.775549	+	0.631288i	$0.782527\pi$
$272$	15.0000			0.909509
$273$		0			0
$274$	27.0000			1.63113
$275$		0			0
$276$	−6.00000	+	10.3923i	−0.361158	+	0.625543i
$277$	−7.00000			−0.420589			−0.210295	−	0.977638i	$-0.567442\pi$
$277$	−7.00000			−0.420589			−0.210295	+	0.977638i	$0.567442\pi$
$278$	−6.00000	−	3.46410i	−0.359856	−	0.207763i
$279$	3.00000	+	1.73205i	0.179605	+	0.103695i
$280$		0			0
$281$			22.5167i			1.34323i	0.740900	+	0.671616i	$0.234399\pi$
$281$			22.5167i			1.34323i	−0.740900	+	0.671616i	$0.765601\pi$
$282$	−6.00000	−	10.3923i	−0.357295	−	0.618853i
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	−3.00000	−	1.73205i	−0.178017	−	0.102778i
$285$	6.00000	−	10.3923i	0.355409	−	0.615587i
$286$		0			0
$287$		0			0
$288$	4.50000	−	2.59808i	0.265165	−	0.153093i
$289$	−8.00000			−0.470588
$290$	9.00000			0.528498
$291$	−12.0000	+	6.92820i	−0.703452	+	0.406138i
$292$	1.50000	−	0.866025i	0.0877809	−	0.0506803i
$293$	4.50000	+	2.59808i	0.262893	+	0.151781i	0.625653	−	0.780101i	$-0.284832\pi$
$293$	4.50000	+	2.59808i	0.262893	+	0.151781i	−0.362761	+	0.931882i	$0.618166\pi$
$294$		0			0
$295$	−6.00000	+	10.3923i	−0.349334	+	0.605063i
$296$	15.0000			0.871857
$297$		0			0
$298$	−16.5000	−	28.5788i	−0.955819	−	1.65553i
$299$	15.0000	−	15.5885i	0.867472	−	0.901504i
$300$	−4.00000			−0.230940
$301$		0			0
$302$	15.0000	+	25.9808i	0.863153	+	1.49502i
$303$	3.00000	+	5.19615i	0.172345	+	0.298511i
$304$	−15.0000	+	8.66025i	−0.860309	+	0.496700i
$305$			1.73205i			0.0991769i
$306$	4.50000	−	2.59808i	0.257248	−	0.148522i
$307$			17.3205i			0.988534i	0.869310	+	0.494267i	$0.164563\pi$
$307$			17.3205i			0.988534i	−0.869310	+	0.494267i	$0.835437\pi$
$308$		0			0
$309$	10.0000	+	17.3205i	0.568880	+	0.985329i
$310$		−	10.3923i		−	0.590243i
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	0.880693	+	0.473688i	$0.157077\pi$
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	−0.0301210	+	0.999546i	$0.509589\pi$
$312$	−12.0000	+	3.46410i	−0.679366	+	0.196116i
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	−0.972028	−	0.234863i	$-0.924536\pi$
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	0.689412	+	0.724370i	$0.257869\pi$
$314$	19.5000	−	11.2583i	1.10045	−	0.635344i
$315$		0			0
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	−4.50000	−	2.59808i	−0.252745	−	0.145922i	0.368275	−	0.929717i	$-0.379948\pi$
$317$	−4.50000	−	2.59808i	−0.252745	−	0.145922i	−0.621021	+	0.783794i	$0.713282\pi$
$318$			10.3923i			0.582772i
$319$		0			0
$320$	1.50000	+	0.866025i	0.0838525	+	0.0484123i
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$		0			0
$323$	−9.00000	+	5.19615i	−0.500773	+	0.289122i
$324$	−5.50000	+	9.52628i	−0.305556	+	0.529238i
$325$	7.00000	+	1.73205i	0.388290	+	0.0960769i
$326$	18.0000	+	31.1769i	0.996928	+	1.72673i
$327$			27.7128i			1.53252i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$		0			0
$331$	24.0000	−	13.8564i	1.31916	−	0.761617i	0.335566	−	0.942017i	$-0.391072\pi$
$331$	24.0000	−	13.8564i	1.31916	−	0.761617i	0.983593	+	0.180400i	$0.0577391\pi$
$332$			13.8564i			0.760469i
$333$	7.50000	−	4.33013i	0.410997	−	0.237289i
$334$	12.0000	+	20.7846i	0.656611	+	1.13728i
$335$	3.00000	+	5.19615i	0.163908	+	0.283896i
$336$		0			0
$337$	−23.0000			−1.25289			−0.626445	−	0.779466i	$-0.715491\pi$
$337$	−23.0000			−1.25289			−0.626445	+	0.779466i	$0.715491\pi$
$338$	−22.5000	+	0.866025i	−1.22384	+	0.0471056i
$339$	15.0000	+	25.9808i	0.814688	+	1.41108i
$340$	−4.50000	−	2.59808i	−0.244047	−	0.140900i
$341$		0			0
$342$	−3.00000	+	5.19615i	−0.162221	+	0.280976i
$343$		0			0
$344$	12.0000	+	6.92820i	0.646997	+	0.373544i
$345$	−18.0000	+	10.3923i	−0.969087	+	0.559503i
$346$	−9.00000	+	5.19615i	−0.483843	+	0.279347i
$347$	−30.0000			−1.61048			−0.805242	−	0.592946i	$-0.797965\pi$
$347$	−30.0000			−1.61048			−0.805242	+	0.592946i	$0.797965\pi$
$348$	−6.00000			−0.321634
$349$	12.0000	−	6.92820i	0.642345	−	0.370858i	−0.143172	−	0.989698i	$-0.545730\pi$
$349$	12.0000	−	6.92820i	0.642345	−	0.370858i	0.785517	+	0.618840i	$0.212397\pi$
$350$		0			0
$351$	10.0000	−	10.3923i	0.533761	−	0.554700i
$352$		0			0
$353$	−28.5000	−	16.4545i	−1.51690	−	0.875784i	−0.999803	−	0.0198582i	$-0.993679\pi$
$353$	−28.5000	−	16.4545i	−1.51690	−	0.875784i	−0.517099	−	0.855926i	$-0.672988\pi$
$354$	12.0000	−	20.7846i	0.637793	−	1.10469i
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$			6.92820i			0.367194i
$357$		0			0
$358$		0			0
$359$	−6.00000	−	3.46410i	−0.316668	−	0.182828i	0.333238	−	0.942843i	$-0.391859\pi$
$359$	−6.00000	−	3.46410i	−0.316668	−	0.182828i	−0.649906	+	0.760014i	$0.725192\pi$
$360$	3.00000			0.158114
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$		−	19.0526i		−	1.00138i
$363$	22.0000			1.15470
$364$		0			0
$365$	3.00000			0.157027
$366$		−	3.46410i		−	0.181071i
$367$	11.0000	−	19.0526i	0.574195	−	0.994535i	−0.421933	−	0.906627i	$-0.638648\pi$
$367$	11.0000	−	19.0526i	0.574195	−	0.994535i	0.996129	−	0.0879086i	$-0.0280183\pi$
$368$	30.0000			1.56386
$369$	4.50000	+	2.59808i	0.234261	+	0.135250i
$370$	−22.5000	−	12.9904i	−1.16972	−	0.675338i
$371$		0			0
$372$			6.92820i			0.359211i
$373$	−9.50000	−	16.4545i	−0.491891	−	0.851981i	0.508065	−	0.861319i	$-0.330361\pi$
$373$	−9.50000	−	16.4545i	−0.491891	−	0.851981i	−0.999956	+	0.00933789i	$0.997028\pi$
$374$		0			0
$375$	−21.0000	−	12.1244i	−1.08444	−	0.626099i
$376$	−3.00000	+	5.19615i	−0.154713	+	0.267971i
$377$	10.5000	+	2.59808i	0.540778	+	0.133808i
$378$		0			0
$379$	−21.0000	+	12.1244i	−1.07870	+	0.622786i	−0.930545	−	0.366178i	$-0.880666\pi$
$379$	−21.0000	+	12.1244i	−1.07870	+	0.622786i	−0.148153	+	0.988964i	$0.547333\pi$
$380$	6.00000			0.307794
$381$	−4.00000			−0.204926
$382$	−27.0000	+	15.5885i	−1.38144	+	0.797575i
$383$	18.0000	−	10.3923i	0.919757	−	0.531022i	0.0361995	−	0.999345i	$-0.488475\pi$
$383$	18.0000	−	10.3923i	0.919757	−	0.531022i	0.883558	+	0.468323i	$0.155141\pi$
$384$	−21.0000	−	12.1244i	−1.07165	−	0.618718i
$385$		0			0
$386$	4.50000	−	7.79423i	0.229044	−	0.396716i
$387$	8.00000			0.406663
$388$	−6.00000	−	3.46410i	−0.304604	−	0.175863i
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	0.957263	−	0.289220i	$-0.0933960\pi$
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	−0.729103	+	0.684403i	$0.760063\pi$
$390$	21.0000	+	5.19615i	1.06338	+	0.263117i
$391$	18.0000			0.910299
$392$		0			0
$393$	−18.0000	−	31.1769i	−0.907980	−	1.57267i
$394$	−12.0000	−	20.7846i	−0.604551	−	1.04711i
$395$	6.00000	−	3.46410i	0.301893	−	0.174298i
$396$		0			0
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	−0.167668	−	0.985843i	$-0.553624\pi$
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	0.769931	+	0.638127i	$0.220290\pi$
$398$			3.46410i			0.173640i
$399$		0			0
$400$	5.00000	+	8.66025i	0.250000	+	0.433013i
$401$		−	1.73205i		−	0.0864945i	−0.999064	−	0.0432472i	$-0.986230\pi$
$401$		−	1.73205i		−	0.0864945i	0.999064	−	0.0432472i	$-0.0137703\pi$
$402$	−6.00000	−	10.3923i	−0.299253	−	0.518321i
$403$	3.00000	−	12.1244i	0.149441	−	0.603957i
$404$	−1.50000	+	2.59808i	−0.0746278	+	0.129259i
$405$	−16.5000	+	9.52628i	−0.819892	+	0.473365i
$406$		0			0
$407$		0			0
$408$	−9.00000	−	5.19615i	−0.445566	−	0.257248i
$409$		−	15.5885i		−	0.770800i	−0.922750	−	0.385400i	$-0.874064\pi$
$409$		−	15.5885i		−	0.770800i	0.922750	−	0.385400i	$-0.125936\pi$
$410$		−	15.5885i		−	0.769859i
$411$	−27.0000	−	15.5885i	−1.33181	−	0.768922i
$412$	−5.00000	+	8.66025i	−0.246332	+	0.426660i
$413$		0			0
$414$	9.00000	−	5.19615i	0.442326	−	0.255377i
$415$	−12.0000	+	20.7846i	−0.589057	+	1.02028i
$416$	−13.5000	−	12.9904i	−0.661892	−	0.636906i
$417$	4.00000	+	6.92820i	0.195881	+	0.339276i
$418$		0			0
$419$	−9.00000	−	15.5885i	−0.439679	−	0.761546i	0.557986	−	0.829851i	$-0.311574\pi$
$419$	−9.00000	−	15.5885i	−0.439679	−	0.761546i	−0.997665	+	0.0683046i	$0.978241\pi$
$420$		0			0
$421$		−	15.5885i		−	0.759735i	−0.925041	−	0.379867i	$-0.875970\pi$
$421$		−	15.5885i		−	0.759735i	0.925041	−	0.379867i	$-0.124030\pi$
$422$	−15.0000	+	8.66025i	−0.730189	+	0.421575i
$423$			3.46410i			0.168430i
$424$	4.50000	−	2.59808i	0.218539	−	0.126174i
$425$	3.00000	+	5.19615i	0.145521	+	0.252050i
$426$	6.00000	+	10.3923i	0.290701	+	0.503509i
$427$		0			0
$428$	−6.00000			−0.290021
$429$		0			0
$430$	−12.0000	−	20.7846i	−0.578691	−	1.00232i
$431$	6.00000	+	3.46410i	0.289010	+	0.166860i	0.637495	−	0.770454i	$-0.279971\pi$
$431$	6.00000	+	3.46410i	0.289010	+	0.166860i	−0.348485	+	0.937314i	$0.613304\pi$
$432$	20.0000			0.962250
$433$	8.50000	−	14.7224i	0.408484	−	0.707515i	−0.586236	−	0.810140i	$-0.699391\pi$
$433$	8.50000	−	14.7224i	0.408484	−	0.707515i	0.994720	+	0.102625i	$0.0327243\pi$
$434$		0			0
$435$	−9.00000	−	5.19615i	−0.431517	−	0.249136i
$436$	−12.0000	+	6.92820i	−0.574696	+	0.331801i
$437$	−18.0000	+	10.3923i	−0.861057	+	0.497131i
$438$	−6.00000			−0.286691
$439$	−28.0000			−1.33637			−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000			−1.33637			−0.668184	+	0.743996i	$0.732928\pi$
$440$		0			0
$441$		0			0
$442$	−13.5000	−	12.9904i	−0.642130	−	0.617889i
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	−0.687557	−	0.726130i	$-0.741317\pi$
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	0.972626	+	0.232377i	$0.0746503\pi$
$444$	15.0000	+	8.66025i	0.711868	+	0.410997i
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	9.00000	+	15.5885i	0.426162	+	0.738135i
$447$			38.1051i			1.80231i
$448$		0			0
$449$	−6.00000	−	3.46410i	−0.283158	−	0.163481i	0.351694	−	0.936115i	$-0.385606\pi$
$449$	−6.00000	−	3.46410i	−0.283158	−	0.163481i	−0.634852	+	0.772634i	$0.718939\pi$
$450$	3.00000	+	1.73205i	0.141421	+	0.0816497i
$451$		0			0
$452$	−7.50000	+	12.9904i	−0.352770	+	0.611016i
$453$		−	34.6410i		−	1.62758i
$454$	−42.0000			−1.97116
$455$		0			0
$456$	12.0000			0.561951
$457$			1.73205i			0.0810219i	0.999179	+	0.0405110i	$0.0128986\pi$
$457$			1.73205i			0.0810219i	−0.999179	+	0.0405110i	$0.987101\pi$
$458$		0			0
$459$	12.0000			0.560112
$460$	−9.00000	−	5.19615i	−0.419627	−	0.242272i
$461$	19.5000	+	11.2583i	0.908206	+	0.524353i	0.879853	−	0.475245i	$-0.157641\pi$
$461$	19.5000	+	11.2583i	0.908206	+	0.524353i	0.0283522	+	0.999598i	$0.490974\pi$
$462$		0			0
$463$		−	13.8564i		−	0.643962i	−0.946746	−	0.321981i	$-0.895651\pi$
$463$		−	13.8564i		−	0.643962i	0.946746	−	0.321981i	$-0.104349\pi$
$464$	7.50000	+	12.9904i	0.348179	+	0.603063i
$465$	−6.00000	+	10.3923i	−0.278243	+	0.481932i
$466$	9.00000	+	5.19615i	0.416917	+	0.240707i
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$	−3.50000	−	0.866025i	−0.161788	−	0.0400320i
$469$		0			0
$470$	9.00000	−	5.19615i	0.415139	−	0.239681i
$471$	−26.0000			−1.19802
$472$	−12.0000			−0.552345
$473$		0			0
$474$	−12.0000	+	6.92820i	−0.551178	+	0.318223i
$475$	−6.00000	−	3.46410i	−0.275299	−	0.158944i
$476$		0			0
$477$	1.50000	−	2.59808i	0.0686803	−	0.118958i
$478$	36.0000			1.64660
$479$	−21.0000	−	12.1244i	−0.959514	−	0.553976i	−0.0634909	−	0.997982i	$-0.520223\pi$
$479$	−21.0000	−	12.1244i	−0.959514	−	0.553976i	−0.896024	+	0.444006i	$0.853557\pi$
$480$	9.00000	+	15.5885i	0.410792	+	0.711512i
$481$	−22.5000	−	21.6506i	−1.02591	−	0.987184i
$482$	3.00000			0.136646
$483$		0			0
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	−6.00000	−	10.3923i	−0.272446	−	0.471890i
$486$	15.0000	−	8.66025i	0.680414	−	0.392837i
$487$			6.92820i			0.313947i	0.987603	+	0.156973i	$0.0501737\pi$
$487$			6.92820i			0.313947i	−0.987603	+	0.156973i	$0.949826\pi$
$488$	−1.50000	+	0.866025i	−0.0679018	+	0.0392031i
$489$		−	41.5692i		−	1.87983i
$490$		0			0
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	0.698285	−	0.715820i	$-0.253947\pi$
$491$	−6.00000	−	10.3923i	−0.270776	−	0.468998i	−0.969061	+	0.246822i	$0.920614\pi$
$492$			10.3923i			0.468521i
$493$	4.50000	+	7.79423i	0.202670	+	0.351034i
$494$	21.0000	+	5.19615i	0.944835	+	0.233786i
$495$		0			0
$496$	15.0000	−	8.66025i	0.673520	−	0.388857i
$497$		0			0
$498$	24.0000	−	41.5692i	1.07547	−	1.86276i
$499$	27.0000	+	15.5885i	1.20869	+	0.697835i	0.962472	−	0.271380i	$-0.0874801\pi$
$499$	27.0000	+	15.5885i	1.20869	+	0.697835i	0.246214	+	0.969216i	$0.420813\pi$
$500$		−	12.1244i		−	0.542218i
$501$		−	27.7128i		−	1.23812i
$502$	−27.0000	−	15.5885i	−1.20507	−	0.695747i
$503$	−18.0000	+	31.1769i	−0.802580	+	1.39011i	0.115332	+	0.993327i	$0.463207\pi$
$503$	−18.0000	+	31.1769i	−0.802580	+	1.39011i	−0.917912	+	0.396783i	$0.870127\pi$
$504$		0			0
$505$	−4.50000	+	2.59808i	−0.200247	+	0.115613i
$506$		0			0
$507$	23.0000	+	12.1244i	1.02147	+	0.538462i
$508$	−1.00000	−	1.73205i	−0.0443678	−	0.0768473i
$509$			19.0526i			0.844490i	0.906482	+	0.422245i	$0.138758\pi$
$509$			19.0526i			0.844490i	−0.906482	+	0.422245i	$0.861242\pi$
$510$	9.00000	+	15.5885i	0.398527	+	0.690268i
$511$		0			0
$512$		−	8.66025i		−	0.382733i
$513$	−12.0000	+	6.92820i	−0.529813	+	0.305888i
$514$		−	5.19615i		−	0.229192i
$515$	−15.0000	+	8.66025i	−0.660979	+	0.381616i
$516$	8.00000	+	13.8564i	0.352180	+	0.609994i
$517$		0			0
$518$		0			0
$519$	12.0000			0.526742
$520$	−3.00000	−	10.3923i	−0.131559	−	0.455733i
$521$	−4.50000	−	7.79423i	−0.197149	−	0.341471i	0.750454	−	0.660922i	$-0.229835\pi$
$521$	−4.50000	−	7.79423i	−0.197149	−	0.341471i	−0.947603	+	0.319451i	$0.896501\pi$
$522$	4.50000	+	2.59808i	0.196960	+	0.113715i
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	9.00000	−	15.5885i	0.393167	−	0.680985i
$525$		0			0
$526$	18.0000	+	10.3923i	0.784837	+	0.453126i
$527$	9.00000	−	5.19615i	0.392046	−	0.226348i
$528$		0			0
$529$	13.0000			0.565217
$530$	−9.00000			−0.390935
$531$	−6.00000	+	3.46410i	−0.260378	+	0.150329i
$532$		0			0
$533$	4.50000	−	18.1865i	0.194917	−	0.787746i
$534$	12.0000	−	20.7846i	0.519291	−	0.899438i
$535$	−9.00000	−	5.19615i	−0.389104	−	0.224649i
$536$	−3.00000	+	5.19615i	−0.129580	+	0.224440i
$537$		0			0
$538$			10.3923i			0.448044i
$539$		0			0
$540$	−6.00000	−	3.46410i	−0.258199	−	0.149071i
$541$	25.5000	+	14.7224i	1.09633	+	0.632967i	0.935255	−	0.353975i	$-0.115170\pi$
$541$	25.5000	+	14.7224i	1.09633	+	0.632967i	0.161076	+	0.986942i	$0.448504\pi$
$542$	36.0000			1.54633
$543$	−11.0000	+	19.0526i	−0.472055	+	0.817624i
$544$		−	15.5885i		−	0.668350i
$545$	−24.0000			−1.02805
$546$		0			0
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$		−	15.5885i		−	0.665906i
$549$	−0.500000	+	0.866025i	−0.0213395	+	0.0369611i
$550$		0			0
$551$	−9.00000	−	5.19615i	−0.383413	−	0.221364i
$552$	−18.0000	−	10.3923i	−0.766131	−	0.442326i
$553$		0			0
$554$			12.1244i			0.515115i
$555$	15.0000	+	25.9808i	0.636715	+	1.10282i
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	13.5000	+	7.79423i	0.572013	+	0.330252i	0.757953	−	0.652309i	$-0.226200\pi$
$557$	13.5000	+	7.79423i	0.572013	+	0.330252i	−0.185940	+	0.982561i	$0.559533\pi$
$558$	3.00000	−	5.19615i	0.127000	−	0.219971i
$559$	−8.00000	−	27.7128i	−0.338364	−	1.17213i
$560$		0			0
$561$		0			0
$562$	39.0000			1.64512
$563$		0			0			−	1.00000i	$-0.5\pi$
$563$		0			0				1.00000i	$0.5\pi$
$564$	−6.00000	+	3.46410i	−0.252646	+	0.145865i
$565$	−22.5000	+	12.9904i	−0.946582	+	0.546509i
$566$	6.00000	+	3.46410i	0.252199	+	0.145607i
$567$		0			0
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	−42.0000			−1.76073			−0.880366	−	0.474295i	$-0.842703\pi$
$569$	−42.0000			−1.76073			−0.880366	+	0.474295i	$0.842703\pi$
$570$	−18.0000	−	10.3923i	−0.753937	−	0.435286i
$571$	−20.0000	−	34.6410i	−0.836974	−	1.44968i	−0.892413	−	0.451219i	$-0.850989\pi$
$571$	−20.0000	−	34.6410i	−0.836974	−	1.44968i	0.0554391	−	0.998462i	$-0.482344\pi$
$572$		0			0
$573$	36.0000			1.50392
$574$		0			0
$575$	6.00000	+	10.3923i	0.250217	+	0.433389i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	16.5000	−	9.52628i	0.686904	−	0.396584i	−0.115547	−	0.993302i	$-0.536862\pi$
$577$	16.5000	−	9.52628i	0.686904	−	0.396584i	0.802451	+	0.596718i	$0.203529\pi$
$578$			13.8564i			0.576351i
$579$	−9.00000	+	5.19615i	−0.374027	+	0.215945i
$580$		−	5.19615i		−	0.215758i
$581$		0			0
$582$	12.0000	+	20.7846i	0.497416	+	0.861550i
$583$		0			0
$584$	1.50000	+	2.59808i	0.0620704	+	0.107509i
$585$	−4.50000	−	4.33013i	−0.186052	−	0.179029i
$586$	4.50000	−	7.79423i	0.185893	−	0.321977i
$587$	−18.0000	+	10.3923i	−0.742940	+	0.428936i	−0.823137	−	0.567843i	$-0.807778\pi$
$587$	−18.0000	+	10.3923i	−0.742940	+	0.428936i	0.0801976	+	0.996779i	$0.474445\pi$
$588$		0			0
$589$	−6.00000	+	10.3923i	−0.247226	+	0.428207i
$590$	18.0000	+	10.3923i	0.741048	+	0.427844i
$591$			27.7128i			1.13995i
$592$		−	43.3013i		−	1.77967i
$593$	−22.5000	−	12.9904i	−0.923964	−	0.533451i	−0.0390666	−	0.999237i	$-0.512438\pi$
$593$	−22.5000	−	12.9904i	−0.923964	−	0.533451i	−0.884898	+	0.465786i	$0.845772\pi$
$594$		0			0
$595$		0			0
$596$	−16.5000	+	9.52628i	−0.675866	+	0.390212i
$597$	2.00000	−	3.46410i	0.0818546	−	0.141776i
$598$	−27.0000	−	25.9808i	−1.10411	−	1.06243i
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	−0.990752	−	0.135686i	$-0.956676\pi$
$599$	−15.0000	−	25.9808i	−0.612883	−	1.06155i	0.377869	−	0.925859i	$-0.376657\pi$
$600$		−	6.92820i		−	0.282843i
$601$	−12.5000	−	21.6506i	−0.509886	−	0.883148i	−0.999934	−	0.0114528i	$-0.996354\pi$
$601$	−12.5000	−	21.6506i	−0.509886	−	0.883148i	0.490049	−	0.871695i	$-0.336979\pi$
$602$		0			0
$603$			3.46410i			0.141069i
$604$	15.0000	−	8.66025i	0.610341	−	0.352381i
$605$			19.0526i			0.774597i
$606$	9.00000	−	5.19615i	0.365600	−	0.211079i
$607$	17.0000	+	29.4449i	0.690009	+	1.19513i	0.971834	+	0.235665i	$0.0757267\pi$
$607$	17.0000	+	29.4449i	0.690009	+	1.19513i	−0.281826	+	0.959466i	$0.590940\pi$
$608$	9.00000	+	15.5885i	0.364998	+	0.632195i
$609$		0			0
$610$	3.00000			0.121466
$611$	12.0000	−	3.46410i	0.485468	−	0.140143i
$612$	−1.50000	−	2.59808i	−0.0606339	−	0.105021i
$613$	10.5000	+	6.06218i	0.424091	+	0.244849i	0.696826	−	0.717240i	$-0.254595\pi$
$613$	10.5000	+	6.06218i	0.424091	+	0.244849i	−0.272735	+	0.962089i	$0.587928\pi$
$614$	30.0000			1.21070
$615$	−9.00000	+	15.5885i	−0.362915	+	0.628587i
$616$		0			0
$617$	−19.5000	−	11.2583i	−0.785040	−	0.453243i	0.0531732	−	0.998585i	$-0.483066\pi$
$617$	−19.5000	−	11.2583i	−0.785040	−	0.453243i	−0.838214	+	0.545342i	$0.816400\pi$
$618$	30.0000	−	17.3205i	1.20678	−	0.696733i
$619$	18.0000	−	10.3923i	0.723481	−	0.417702i	−0.0925515	−	0.995708i	$-0.529502\pi$
$619$	18.0000	−	10.3923i	0.723481	−	0.417702i	0.816033	+	0.578006i	$0.196169\pi$
$620$	−6.00000			−0.240966
$621$	24.0000			0.963087
$622$	45.0000	−	25.9808i	1.80434	−	1.04173i
$623$		0			0
$624$	10.0000	+	34.6410i	0.400320	+	1.38675i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	15.0000	+	8.66025i	0.599521	+	0.346133i
$627$		0			0
$628$	−6.50000	−	11.2583i	−0.259378	−	0.449256i
$629$		−	25.9808i		−	1.03592i
$630$		0			0
$631$	−42.0000	−	24.2487i	−1.67199	−	0.965326i	−0.966521	−	0.256589i	$-0.917401\pi$
$631$	−42.0000	−	24.2487i	−1.67199	−	0.965326i	−0.705473	−	0.708737i	$-0.749265\pi$
$632$	6.00000	+	3.46410i	0.238667	+	0.137795i
$633$	20.0000			0.794929
$634$	−4.50000	+	7.79423i	−0.178718	+	0.309548i
$635$		−	3.46410i		−	0.137469i
$636$	6.00000			0.237915
$637$		0			0
$638$		0			0
$639$		−	3.46410i		−	0.137038i
$640$	10.5000	−	18.1865i	0.415049	−	0.718886i
$641$	33.0000			1.30342			0.651711	−	0.758468i	$-0.274052\pi$
$641$	33.0000			1.30342			0.651711	+	0.758468i	$0.274052\pi$
$642$	18.0000	+	10.3923i	0.710403	+	0.410152i
$643$	12.0000	+	6.92820i	0.473234	+	0.273222i	0.717592	−	0.696463i	$-0.245244\pi$
$643$	12.0000	+	6.92820i	0.473234	+	0.273222i	−0.244359	+	0.969685i	$0.578577\pi$
$644$		0			0
$645$			27.7128i			1.09119i
$646$	9.00000	+	15.5885i	0.354100	+	0.613320i
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	−0.986916	−	0.161233i	$-0.948453\pi$
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	0.633090	+	0.774078i	$0.281786\pi$
$648$	−16.5000	−	9.52628i	−0.648181	−	0.374228i
$649$		0			0
$650$	3.00000	−	12.1244i	0.117670	−	0.475556i
$651$		0			0
$652$	18.0000	−	10.3923i	0.704934	−	0.406994i
$653$	−30.0000			−1.17399			−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000			−1.17399			−0.586995	+	0.809590i	$0.699689\pi$
$654$	48.0000			1.87695
$655$	27.0000	−	15.5885i	1.05498	−	0.609091i
$656$	22.5000	−	12.9904i	0.878477	−	0.507189i
$657$	1.50000	+	0.866025i	0.0585206	+	0.0337869i
$658$		0			0
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	−0.725175	−	0.688565i	$-0.758241\pi$
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	0.958902	+	0.283738i	$0.0915745\pi$
$660$		0			0
$661$	40.5000	+	23.3827i	1.57527	+	0.909481i	0.995506	+	0.0946945i	$0.0301874\pi$
$661$	40.5000	+	23.3827i	1.57527	+	0.909481i	0.579761	+	0.814787i	$0.303146\pi$
$662$	−24.0000	−	41.5692i	−0.932786	−	1.61563i
$663$	6.00000	+	20.7846i	0.233021	+	0.807207i
$664$	−24.0000			−0.931381
$665$		0			0
$666$	−7.50000	−	12.9904i	−0.290619	−	0.503367i
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$	12.0000	−	6.92820i	0.464294	−	0.268060i
$669$		−	20.7846i		−	0.803579i
$670$	9.00000	−	5.19615i	0.347700	−	0.200745i
$671$		0			0
$672$		0			0
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	0.988968	−	0.148132i	$-0.0473259\pi$
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	−0.622770	+	0.782405i	$0.713993\pi$
$674$			39.8372i			1.53447i
$675$	4.00000	+	6.92820i	0.153960	+	0.266667i
$676$	0.500000	+	12.9904i	0.0192308	+	0.499630i
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$	45.0000	−	25.9808i	1.72821	−	0.997785i
$679$		0			0
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$	42.0000	+	24.2487i	1.60944	+	0.929213i
$682$		0			0
$683$		−	24.2487i		−	0.927851i	−0.885874	−	0.463926i	$-0.846441\pi$
$683$		−	24.2487i		−	0.927851i	0.885874	−	0.463926i	$-0.153559\pi$
$684$	3.00000	+	1.73205i	0.114708	+	0.0662266i
$685$	13.5000	−	23.3827i	0.515808	−	0.893407i
$686$		0			0
$687$		0			0
$688$	20.0000	−	34.6410i	0.762493	−	1.32068i
$689$	−10.5000	−	2.59808i	−0.400018	−	0.0989788i
$690$	18.0000	+	31.1769i	0.685248	+	1.18688i
$691$			13.8564i			0.527123i	0.964643	+	0.263561i	$0.0848971\pi$
$691$			13.8564i			0.527123i	−0.964643	+	0.263561i	$0.915103\pi$
$692$	3.00000	+	5.19615i	0.114043	+	0.197528i
$693$		0			0
$694$			51.9615i			1.97243i
$695$	−6.00000	+	3.46410i	−0.227593	+	0.131401i
$696$		−	10.3923i		−	0.393919i
$697$	13.5000	−	7.79423i	0.511349	−	0.295227i
$698$	−12.0000	−	20.7846i	−0.454207	−	0.786709i
$699$	−6.00000	−	10.3923i	−0.226941	−	0.393073i
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$	−18.0000	−	17.3205i	−0.679366	−	0.653720i
$703$	15.0000	+	25.9808i	0.565736	+	0.979883i
$704$		0			0
$705$	−12.0000			−0.451946
$706$	−28.5000	+	49.3634i	−1.07261	+	1.85782i
$707$		0			0
$708$	−12.0000	−	6.92820i	−0.450988	−	0.260378i
$709$	4.50000	−	2.59808i	0.169001	−	0.0975728i	−0.413114	−	0.910679i	$-0.635559\pi$
$709$	4.50000	−	2.59808i	0.169001	−	0.0975728i	0.582115	+	0.813107i	$0.302225\pi$
$710$	−9.00000	+	5.19615i	−0.337764	+	0.195008i
$711$	4.00000			0.150012
$712$	−12.0000			−0.449719
$713$	18.0000	−	10.3923i	0.674105	−	0.389195i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−36.0000	−	20.7846i	−1.34444	−	0.776215i
$718$	−6.00000	+	10.3923i	−0.223918	+	0.387837i
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.833744	+	0.552151i	$0.186193\pi$
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.0613050	+	0.998119i	$0.480474\pi$
$720$		−	8.66025i		−	0.322749i
$721$		0			0
$722$	10.5000	+	6.06218i	0.390770	+	0.225611i
$723$	−3.00000	−	1.73205i	−0.111571	−	0.0644157i
$724$	−11.0000			−0.408812
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		−	38.1051i		−	1.41421i
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		−	5.19615i		−	0.192318i
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$	−2.00000			−0.0739221
$733$	10.5000	+	6.06218i	0.387826	+	0.223912i	0.681218	−	0.732081i	$-0.261451\pi$
$733$	10.5000	+	6.06218i	0.387826	+	0.223912i	−0.293392	+	0.955992i	$0.594784\pi$
$734$	−33.0000	−	19.0526i	−1.21805	−	0.703243i
$735$		0			0
$736$		−	31.1769i		−	1.14920i
$737$		0			0
$738$	4.50000	−	7.79423i	0.165647	−	0.286910i
$739$	18.0000	+	10.3923i	0.662141	+	0.382287i	0.793092	−	0.609102i	$-0.208470\pi$
$739$	18.0000	+	10.3923i	0.662141	+	0.382287i	−0.130951	+	0.991389i	$0.541803\pi$
$740$	−7.50000	+	12.9904i	−0.275705	+	0.477536i
$741$	−18.0000	−	17.3205i	−0.661247	−	0.636285i
$742$		0			0
$743$	−30.0000	+	17.3205i	−1.10059	+	0.635428i	−0.936377	−	0.350997i	$-0.885843\pi$
$743$	−30.0000	+	17.3205i	−1.10059	+	0.635428i	−0.164216	+	0.986424i	$0.552510\pi$
$744$	−12.0000			−0.439941
$745$	−33.0000			−1.20903
$746$	−28.5000	+	16.4545i	−1.04346	+	0.602441i
$747$	−12.0000	+	6.92820i	−0.439057	+	0.253490i
$748$		0			0
$749$		0			0
$750$	−21.0000	+	36.3731i	−0.766812	+	1.32816i
$751$	−16.0000			−0.583848			−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000			−0.583848			−0.291924	+	0.956441i	$0.594295\pi$
$752$	15.0000	+	8.66025i	0.546994	+	0.315807i
$753$	18.0000	+	31.1769i	0.655956	+	1.13615i
$754$	4.50000	−	18.1865i	0.163880	−	0.662314i
$755$	30.0000			1.09181
$756$		0			0
$757$	13.0000	+	22.5167i	0.472493	+	0.818382i	0.999505	−	0.0314762i	$-0.0100208\pi$
$757$	13.0000	+	22.5167i	0.472493	+	0.818382i	−0.527011	+	0.849858i	$0.676688\pi$
$758$	21.0000	+	36.3731i	0.762754	+	1.32113i
$759$		0			0
$760$			10.3923i			0.376969i
$761$	−30.0000	+	17.3205i	−1.08750	+	0.627868i	−0.932910	−	0.360111i	$-0.882739\pi$
$761$	−30.0000	+	17.3205i	−1.08750	+	0.627868i	−0.154590	+	0.987979i	$0.549406\pi$
$762$			6.92820i			0.250982i
$763$		0			0
$764$	9.00000	+	15.5885i	0.325609	+	0.563971i
$765$		−	5.19615i		−	0.187867i
$766$	−18.0000	−	31.1769i	−0.650366	−	1.12647i
$767$	18.0000	+	17.3205i	0.649942	+	0.625407i
$768$	−19.0000	+	32.9090i	−0.685603	+	1.18750i
$769$	6.00000	−	3.46410i	0.216366	−	0.124919i	−0.387901	−	0.921701i	$-0.626800\pi$
$769$	6.00000	−	3.46410i	0.216366	−	0.124919i	0.604266	+	0.796782i	$0.293466\pi$
$770$		0			0
$771$	−3.00000	+	5.19615i	−0.108042	+	0.187135i
$772$	−4.50000	−	2.59808i	−0.161959	−	0.0935068i
$773$			34.6410i			1.24595i	0.782241	+	0.622975i	$0.214076\pi$
$773$			34.6410i			1.24595i	−0.782241	+	0.622975i	$0.785924\pi$
$774$		−	13.8564i		−	0.498058i
$775$	6.00000	+	3.46410i	0.215526	+	0.124434i
$776$	6.00000	−	10.3923i	0.215387	−	0.373062i
$777$		0			0
$778$	13.5000	−	7.79423i	0.483998	−	0.279437i
$779$	−9.00000	+	15.5885i	−0.322458	+	0.558514i
$780$	3.00000	−	12.1244i	0.107417	−	0.434122i
$781$		0			0
$782$		−	31.1769i		−	1.11488i
$783$	6.00000	+	10.3923i	0.214423	+	0.371391i
$784$		0			0
$785$		−	22.5167i		−	0.803654i
$786$	−54.0000	+	31.1769i	−1.92612	+	1.11204i
$787$		−	38.1051i		−	1.35830i	−0.733999	−	0.679150i	$-0.762348\pi$
$787$		−	38.1051i		−	1.35830i	0.733999	−	0.679150i	$-0.237652\pi$
$788$	−12.0000	+	6.92820i	−0.427482	+	0.246807i
$789$	−12.0000	−	20.7846i	−0.427211	−	0.739952i
$790$	−6.00000	−	10.3923i	−0.213470	−	0.369742i
$791$		0			0
$792$		0			0
$793$	3.50000	+	0.866025i	0.124289	+	0.0307535i
$794$	−12.0000	−	20.7846i	−0.425864	−	0.737618i
$795$	9.00000	+	5.19615i	0.319197	+	0.184289i
$796$	2.00000			0.0708881
$797$	−21.0000	+	36.3731i	−0.743858	+	1.28840i	0.206868	+	0.978369i	$0.433673\pi$
$797$	−21.0000	+	36.3731i	−0.743858	+	1.28840i	−0.950726	+	0.310031i	$0.899660\pi$
$798$		0			0
$799$	9.00000	+	5.19615i	0.318397	+	0.183827i
$800$	9.00000	−	5.19615i	0.318198	−	0.183712i
$801$	−6.00000	+	3.46410i	−0.212000	+	0.122398i
$802$	−3.00000			−0.105934
$803$		0			0
$804$	−6.00000	+	3.46410i	−0.211604	+	0.122169i
$805$		0			0
$806$	−21.0000	−	5.19615i	−0.739693	−	0.183027i
$807$	6.00000	−	10.3923i	0.211210	−	0.365826i
$808$	−4.50000	−	2.59808i	−0.158309	−	0.0914000i
$809$	−16.5000	+	28.5788i	−0.580109	+	1.00478i	0.415357	+	0.909659i	$0.363657\pi$
$809$	−16.5000	+	28.5788i	−0.580109	+	1.00478i	−0.995466	+	0.0951198i	$0.969677\pi$
$810$	16.5000	+	28.5788i	0.579751	+	1.00416i
$811$			38.1051i			1.33805i	0.743239	+	0.669026i	$0.233288\pi$
$811$			38.1051i			1.33805i	−0.743239	+	0.669026i	$0.766712\pi$
$812$		0			0
$813$	−36.0000	−	20.7846i	−1.26258	−	0.728948i
$814$		0			0
$815$	36.0000			1.26102
$816$	−15.0000	+	25.9808i	−0.525105	+	0.909509i
$817$			27.7128i			0.969549i
$818$	−27.0000			−0.944033
$819$		0			0
$820$	−9.00000			−0.314294
$821$		−	41.5692i		−	1.45078i	−0.688340	−	0.725388i	$-0.741660\pi$
$821$		−	41.5692i		−	1.45078i	0.688340	−	0.725388i	$-0.258340\pi$
$822$	−27.0000	+	46.7654i	−0.941733	+	1.63113i
$823$	−4.00000			−0.139431			−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000			−0.139431			−0.0697156	+	0.997567i	$0.522209\pi$
$824$	−15.0000	−	8.66025i	−0.522550	−	0.301694i
$825$		0			0
$826$		0			0
$827$		−	20.7846i		−	0.722752i	−0.932420	−	0.361376i	$-0.882307\pi$
$827$		−	20.7846i		−	0.722752i	0.932420	−	0.361376i	$-0.117693\pi$
$828$	−3.00000	−	5.19615i	−0.104257	−	0.180579i
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	−0.997225	−	0.0744432i	$-0.976282\pi$
$829$	−12.5000	+	21.6506i	−0.434143	+	0.751958i	0.563082	+	0.826401i	$0.309615\pi$
$830$	36.0000	+	20.7846i	1.24958	+	0.721444i
$831$	7.00000	−	12.1244i	0.242827	−	0.420589i
$832$	2.50000	−	2.59808i	0.0866719	−	0.0900721i
$833$		0			0
$834$	12.0000	−	6.92820i	0.415526	−	0.239904i
$835$	24.0000			0.830554
$836$		0			0
$837$	12.0000	−	6.92820i	0.414781	−	0.239474i
$838$	−27.0000	+	15.5885i	−0.932700	+	0.538494i
$839$	39.0000	+	22.5167i	1.34643	+	0.777361i	0.987742	−	0.156096i	$-0.0498910\pi$
$839$	39.0000	+	22.5167i	1.34643	+	0.777361i	0.358688	+	0.933458i	$0.383224\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−27.0000			−0.930481
$843$	−39.0000	−	22.5167i	−1.34323	−	0.775515i
$844$	5.00000	+	8.66025i	0.172107	+	0.298098i
$845$	−10.5000	+	19.9186i	−0.361211	+	0.685220i
$846$	6.00000			0.206284
$847$		0			0
$848$	−7.50000	−	12.9904i	−0.257551	−	0.446092i
$849$	−4.00000	−	6.92820i	−0.137280	−	0.237775i
$850$	9.00000	−	5.19615i	0.308697	−	0.178227i
$851$		−	51.9615i		−	1.78122i
$852$	6.00000	−	3.46410i	0.205557	−	0.118678i
$853$		−	25.9808i		−	0.889564i	−0.895639	−	0.444782i	$-0.853281\pi$
$853$		−	25.9808i		−	0.889564i	0.895639	−	0.444782i	$-0.146719\pi$
$854$		0			0
$855$	3.00000	+	5.19615i	0.102598	+	0.177705i
$856$		−	10.3923i		−	0.355202i
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	0.839268	−	0.543718i	$-0.182984\pi$
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	−0.890507	+	0.454969i	$0.849650\pi$
$858$		0			0
$859$	7.00000	−	12.1244i	0.238837	−	0.413678i	−0.721544	−	0.692369i	$-0.756567\pi$
$859$	7.00000	−	12.1244i	0.238837	−	0.413678i	0.960381	+	0.278691i	$0.0899005\pi$
$860$	−12.0000	+	6.92820i	−0.409197	+	0.236250i
$861$		0			0
$862$	6.00000	−	10.3923i	0.204361	−	0.353963i
$863$	−24.0000	−	13.8564i	−0.816970	−	0.471678i	0.0324008	−	0.999475i	$-0.489685\pi$
$863$	−24.0000	−	13.8564i	−0.816970	−	0.471678i	−0.849370	+	0.527797i	$0.823018\pi$
$864$		−	20.7846i		−	0.707107i
$865$			10.3923i			0.353349i
$866$	−25.5000	−	14.7224i	−0.866525	−	0.500289i
$867$	8.00000	−	13.8564i	0.271694	−	0.470588i
$868$		0			0
$869$		0			0
$870$	−9.00000	+	15.5885i	−0.305129	+	0.528498i
$871$	12.0000	−	3.46410i	0.406604	−	0.117377i
$872$	−12.0000	−	20.7846i	−0.406371	−	0.703856i
$873$		−	6.92820i		−	0.234484i
$874$	18.0000	+	31.1769i	0.608859	+	1.05457i
$875$		0			0
$876$			3.46410i			0.117041i
$877$	−10.5000	+	6.06218i	−0.354560	+	0.204705i	−0.666692	−	0.745334i	$-0.732290\pi$
$877$	−10.5000	+	6.06218i	−0.354560	+	0.204705i	0.312132	+	0.950039i	$0.398957\pi$
$878$			48.4974i			1.63671i
$879$	−9.00000	+	5.19615i	−0.303562	+	0.175262i
$880$		0			0
$881$	−13.5000	−	23.3827i	−0.454827	−	0.787783i	0.543852	−	0.839181i	$-0.316965\pi$
$881$	−13.5000	−	23.3827i	−0.454827	−	0.787783i	−0.998678	+	0.0513987i	$0.983632\pi$
$882$		0			0
$883$	10.0000			0.336527			0.168263	−	0.985742i	$-0.446184\pi$
$883$	10.0000			0.336527			0.168263	+	0.985742i	$0.446184\pi$
$884$	−7.50000	+	7.79423i	−0.252252	+	0.262148i
$885$	−12.0000	−	20.7846i	−0.403376	−	0.698667i
$886$	−18.0000	−	10.3923i	−0.604722	−	0.349136i
$887$	36.0000			1.20876			0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000			1.20876			0.604381	+	0.796696i	$0.293421\pi$
$888$	−15.0000	+	25.9808i	−0.503367	+	0.871857i
$889$		0			0
$890$	18.0000	+	10.3923i	0.603361	+	0.348351i
$891$		0			0
$892$	9.00000	−	5.19615i	0.301342	−	0.173980i
$893$	−12.0000			−0.401565
$894$	66.0000			2.20737
$895$		0			0
$896$		0			0
$897$	12.0000	+	41.5692i	0.400668	+	1.38796i
$898$	−6.00000	+	10.3923i	−0.200223	+	0.346796i
$899$	9.00000	+	5.19615i	0.300167	+	0.173301i
$900$	1.00000	−	1.73205i	0.0333333	−	0.0577350i
$901$	−4.50000	−	7.79423i	−0.149917	−	0.259663i
$902$		0			0
$903$		0			0
$904$	−22.5000	−	12.9904i	−0.748339	−	0.432054i
$905$	−16.5000	−	9.52628i	−0.548479	−	0.316664i
$906$	−60.0000			−1.99337
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	−0.999195	−	0.0401089i	$-0.987230\pi$
$907$	−14.0000	+	24.2487i	−0.464862	+	0.805165i	0.534333	+	0.845274i	$0.320563\pi$
$908$			24.2487i			0.804722i
$909$	−3.00000			−0.0995037
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		−	34.6410i		−	1.14708i
$913$		0			0
$914$	3.00000			0.0992312
$915$	−3.00000	−	1.73205i	−0.0991769	−	0.0572598i
$916$		0			0
$917$		0			0
$918$		−	20.7846i		−	0.685994i
$919$	−11.0000	−	19.0526i	−0.362857	−	0.628486i	0.625573	−	0.780165i	$-0.284865\pi$
$919$	−11.0000	−	19.0526i	−0.362857	−	0.628486i	−0.988430	+	0.151680i	$0.951532\pi$
$920$	9.00000	−	15.5885i	0.296721	−	0.513936i
$921$	−30.0000	−	17.3205i	−0.988534	−	0.570730i
$922$	19.5000	−	33.7750i	0.642198	−	1.11232i
$923$	−12.0000	+	3.46410i	−0.394985	+	0.114022i
$924$		0			0
$925$	15.0000	−	8.66025i	0.493197	−	0.284747i
$926$	−24.0000			−0.788689
$927$	−10.0000			−0.328443
$928$	13.5000	−	7.79423i	0.443159	−	0.255858i
$929$	40.5000	−	23.3827i	1.32876	−	0.767161i	0.343654	−	0.939096i	$-0.388335\pi$
$929$	40.5000	−	23.3827i	1.32876	−	0.767161i	0.985108	+	0.171935i	$0.0550020\pi$
$930$	18.0000	+	10.3923i	0.590243	+	0.340777i
$931$		0			0
$932$	3.00000	−	5.19615i	0.0982683	−	0.170206i
$933$	−60.0000			−1.96431
$934$	18.0000	+	10.3923i	0.588978	+	0.340047i
$935$		0			0
$936$	1.50000	−	6.06218i	0.0490290	−	0.198148i
$937$	7.00000			0.228680			0.114340	−	0.993442i	$-0.463525\pi$
$937$	7.00000			0.228680			0.114340	+	0.993442i	$0.463525\pi$
$938$		0			0
$939$	−10.0000	−	17.3205i	−0.326338	−	0.565233i
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	−18.0000	+	10.3923i	−0.586783	+	0.338779i	−0.763825	−	0.645424i	$-0.776681\pi$
$941$	−18.0000	+	10.3923i	−0.586783	+	0.338779i	0.177041	+	0.984203i	$0.443347\pi$
$942$			45.0333i			1.46726i
$943$	27.0000	−	15.5885i	0.879241	−	0.507630i
$944$			34.6410i			1.12747i
$945$		0			0
$946$		0			0
$947$		−	17.3205i		−	0.562841i	−0.959585	−	0.281420i	$-0.909194\pi$
$947$		−	17.3205i		−	0.562841i	0.959585	−	0.281420i	$-0.0908056\pi$
$948$	4.00000	+	6.92820i	0.129914	+	0.225018i
$949$	1.50000	−	6.06218i	0.0486921	−	0.196787i
$950$	−6.00000	+	10.3923i	−0.194666	+	0.337171i
$951$	9.00000	−	5.19615i	0.291845	−	0.168497i
$952$		0			0
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	−0.813337	−	0.581793i	$-0.802351\pi$
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	0.910516	+	0.413473i	$0.135685\pi$
$954$	−4.50000	−	2.59808i	−0.145693	−	0.0841158i
$955$			31.1769i			1.00886i
$956$		−	20.7846i		−	0.672222i
$957$		0			0
$958$	−21.0000	+	36.3731i	−0.678479	+	1.17516i
$959$		0			0
$960$	−3.00000	+	1.73205i	−0.0968246	+	0.0559017i
$961$	−9.50000	+	16.4545i	−0.306452	+	0.530790i
$962$	−37.5000	+	38.9711i	−1.20905	+	1.25648i
$963$	−3.00000	−	5.19615i	−0.0966736	−	0.167444i
$964$		−	1.73205i		−	0.0557856i
$965$	−4.50000	−	7.79423i	−0.144860	−	0.250905i
$966$		0			0
$967$		−	58.8897i		−	1.89377i	−0.321578	−	0.946883i	$-0.604213\pi$
$967$		−	58.8897i		−	1.89377i	0.321578	−	0.946883i	$-0.395787\pi$
$968$	−16.5000	+	9.52628i	−0.530330	+	0.306186i
$969$		−	20.7846i		−	0.667698i
$970$	−18.0000	+	10.3923i	−0.577945	+	0.333677i
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	0.813865	−	0.581054i	$-0.197359\pi$
$971$	−3.00000	−	5.19615i	−0.0962746	−	0.166752i	−0.910140	+	0.414301i	$0.864026\pi$
$972$	−5.00000	−	8.66025i	−0.160375	−	0.277778i
$973$		0			0
$974$	12.0000			0.384505
$975$	−10.0000	+	10.3923i	−0.320256	+	0.332820i
$976$	2.50000	+	4.33013i	0.0800230	+	0.138604i
$977$	−37.5000	−	21.6506i	−1.19973	−	0.692665i	−0.239236	−	0.970961i	$-0.576897\pi$
$977$	−37.5000	−	21.6506i	−1.19973	−	0.692665i	−0.960495	+	0.278296i	$0.910230\pi$
$978$	−72.0000			−2.30231
$979$		0			0
$980$		0			0
$981$	−12.0000	−	6.92820i	−0.383131	−	0.221201i
$982$	−18.0000	+	10.3923i	−0.574403	+	0.331632i
$983$	−45.0000	+	25.9808i	−1.43528	+	0.828658i	−0.997516	−	0.0704339i	$-0.977562\pi$
$983$	−45.0000	+	25.9808i	−1.43528	+	0.828658i	−0.437761	+	0.899092i	$0.644228\pi$
$984$	−18.0000			−0.573819
$985$	−24.0000			−0.764704
$986$	13.5000	−	7.79423i	0.429928	−	0.248219i
$987$		0			0
$988$	3.00000	−	12.1244i	0.0954427	−	0.385727i
$989$	24.0000	−	41.5692i	0.763156	−	1.32182i
$990$		0			0
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	−0.881471	−	0.472237i	$-0.843446\pi$
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	0.849705	+	0.527258i	$0.176780\pi$
$992$	−9.00000	−	15.5885i	−0.285750	−	0.494934i
$993$			55.4256i			1.75888i
$994$		0			0
$995$	3.00000	+	1.73205i	0.0951064	+	0.0549097i
$996$	−24.0000	−	13.8564i	−0.760469	−	0.439057i
$997$	17.0000			0.538395			0.269198	−	0.963085i	$-0.413241\pi$
$997$	17.0000			0.538395			0.269198	+	0.963085i	$0.413241\pi$
$998$	27.0000	−	46.7654i	0.854670	−	1.48033i
$999$		−	34.6410i		−	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.a.569.1		2
7.2	even	3		13.2.e.a.10.1	yes	2
7.3	odd	6		637.2.u.b.361.1		2
7.4	even	3		637.2.u.c.361.1		2
7.5	odd	6		637.2.q.a.491.1		2
7.6	odd	2		637.2.k.c.569.1		2
13.4	even	6		637.2.u.c.30.1		2
21.2	odd	6		117.2.q.c.10.1		2
28.23	odd	6		208.2.w.b.49.1		2
35.2	odd	12		325.2.m.a.49.1		4
35.9	even	6		325.2.n.a.101.1		2
35.23	odd	12		325.2.m.a.49.2		4
56.37	even	6		832.2.w.d.257.1		2
56.51	odd	6		832.2.w.a.257.1		2
84.23	even	6		1872.2.by.d.1297.1		2
91.2	odd	12		169.2.a.a.1.1		2
91.4	even	6	inner	637.2.k.a.459.1		2
91.9	even	3		169.2.e.a.147.1		2
91.16	even	3		169.2.b.a.168.1		2
91.17	odd	6		637.2.k.c.459.1		2
91.23	even	6		169.2.b.a.168.2		2
91.30	even	6		13.2.e.a.4.1	✓	2
91.37	odd	12		169.2.a.a.1.2		2
91.44	odd	12		169.2.c.a.146.2		4
91.51	even	6		169.2.e.a.23.1		2
91.54	even	12		8281.2.a.q.1.1		2
91.58	odd	12		169.2.c.a.22.2		4
91.69	odd	6		637.2.u.b.30.1		2
91.72	odd	12		169.2.c.a.22.1		4
91.82	odd	6		637.2.q.a.589.1		2
91.86	odd	12		169.2.c.a.146.1		4
91.89	even	12		8281.2.a.q.1.2		2
273.2	even	12		1521.2.a.k.1.2		2
273.23	odd	6		1521.2.b.a.1351.1		2
273.107	odd	6		1521.2.b.a.1351.2		2
273.128	even	12		1521.2.a.k.1.1		2
273.212	odd	6		117.2.q.c.82.1		2
364.23	odd	6		2704.2.f.b.337.1		2
364.107	odd	6		2704.2.f.b.337.2		2
364.219	even	12		2704.2.a.o.1.1		2
364.275	even	12		2704.2.a.o.1.2		2
364.303	odd	6		208.2.w.b.17.1		2
455.184	odd	12		4225.2.a.v.1.2		2
455.212	odd	12		325.2.m.a.199.2		4
455.219	odd	12		4225.2.a.v.1.1		2
455.303	odd	12		325.2.m.a.199.1		4
455.394	even	6		325.2.n.a.251.1		2
728.485	even	6		832.2.w.d.641.1		2
728.667	odd	6		832.2.w.a.641.1		2
1092.1031	even	6		1872.2.by.d.433.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.2.e.a.4.1	✓	2	91.30	even	6
13.2.e.a.10.1	yes	2	7.2	even	3
117.2.q.c.10.1		2	21.2	odd	6
117.2.q.c.82.1		2	273.212	odd	6
169.2.a.a.1.1		2	91.2	odd	12
169.2.a.a.1.2		2	91.37	odd	12
169.2.b.a.168.1		2	91.16	even	3
169.2.b.a.168.2		2	91.23	even	6
169.2.c.a.22.1		4	91.72	odd	12
169.2.c.a.22.2		4	91.58	odd	12
169.2.c.a.146.1		4	91.86	odd	12
169.2.c.a.146.2		4	91.44	odd	12
169.2.e.a.23.1		2	91.51	even	6
169.2.e.a.147.1		2	91.9	even	3
208.2.w.b.17.1		2	364.303	odd	6
208.2.w.b.49.1		2	28.23	odd	6
325.2.m.a.49.1		4	35.2	odd	12
325.2.m.a.49.2		4	35.23	odd	12
325.2.m.a.199.1		4	455.303	odd	12
325.2.m.a.199.2		4	455.212	odd	12
325.2.n.a.101.1		2	35.9	even	6
325.2.n.a.251.1		2	455.394	even	6
637.2.k.a.459.1		2	91.4	even	6	inner
637.2.k.a.569.1		2	1.1	even	1	trivial
637.2.k.c.459.1		2	91.17	odd	6
637.2.k.c.569.1		2	7.6	odd	2
637.2.q.a.491.1		2	7.5	odd	6
637.2.q.a.589.1		2	91.82	odd	6
637.2.u.b.30.1		2	91.69	odd	6
637.2.u.b.361.1		2	7.3	odd	6
637.2.u.c.30.1		2	13.4	even	6
637.2.u.c.361.1		2	7.4	even	3
832.2.w.a.257.1		2	56.51	odd	6
832.2.w.a.641.1		2	728.667	odd	6
832.2.w.d.257.1		2	56.37	even	6
832.2.w.d.641.1		2	728.485	even	6
1521.2.a.k.1.1		2	273.128	even	12
1521.2.a.k.1.2		2	273.2	even	12
1521.2.b.a.1351.1		2	273.23	odd	6
1521.2.b.a.1351.2		2	273.107	odd	6
1872.2.by.d.433.1		2	1092.1031	even	6
1872.2.by.d.1297.1		2	84.23	even	6
2704.2.a.o.1.1		2	364.219	even	12
2704.2.a.o.1.2		2	364.275	even	12
2704.2.f.b.337.1		2	364.23	odd	6
2704.2.f.b.337.2		2	364.107	odd	6
4225.2.a.v.1.1		2	455.219	odd	12
4225.2.a.v.1.2		2	455.184	odd	12
8281.2.a.q.1.1		2	91.54	even	12
8281.2.a.q.1.2		2	91.89	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{2} +(-1.00000 + 1.73205i) q^{3} -1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(3.00000 + 1.73205i) q^{6} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(1.00000 - 1.73205i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(3.00000 - 1.73205i) q^{15} -5.00000 q^{16} -3.00000 q^{17} +(-1.50000 + 0.866025i) q^{18} +(3.00000 - 1.73205i) q^{19} +(1.50000 + 0.866025i) q^{20} -6.00000 q^{23} +(3.00000 + 1.73205i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(4.50000 + 4.33013i) q^{26} -4.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(-3.00000 - 5.19615i) q^{30} +(-3.00000 + 1.73205i) q^{31} +5.19615i q^{32} +5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +8.66025i q^{37} +(-3.00000 - 5.19615i) q^{38} +(-2.00000 - 6.92820i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(-4.50000 + 2.59808i) q^{41} +(-4.00000 + 6.92820i) q^{43} +1.73205i q^{45} +10.3923i q^{46} +(-3.00000 - 1.73205i) q^{47} +(5.00000 - 8.66025i) q^{48} +(-3.00000 + 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(2.50000 - 2.59808i) q^{52} +(1.50000 + 2.59808i) q^{53} +6.92820i q^{54} +6.92820i q^{57} +(-4.50000 + 2.59808i) q^{58} -6.92820i q^{59} +(-3.00000 + 1.73205i) q^{60} +(-0.500000 - 0.866025i) q^{61} +(3.00000 + 5.19615i) q^{62} -1.00000 q^{64} +(6.00000 - 1.73205i) q^{65} +(-3.00000 - 1.73205i) q^{67} +3.00000 q^{68} +(6.00000 - 10.3923i) q^{69} +(3.00000 + 1.73205i) q^{71} +(-1.50000 + 0.866025i) q^{72} +(-1.50000 + 0.866025i) q^{73} +15.0000 q^{74} +4.00000 q^{75} +(-3.00000 + 1.73205i) q^{76} +(-12.0000 + 3.46410i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(7.50000 + 4.33013i) q^{80} +(5.50000 - 9.52628i) q^{81} +(4.50000 + 7.79423i) q^{82} -13.8564i q^{83} +(4.50000 + 2.59808i) q^{85} +(12.0000 + 6.92820i) q^{86} +6.00000 q^{87} -6.92820i q^{89} +3.00000 q^{90} +6.00000 q^{92} -6.92820i q^{93} +(-3.00000 + 5.19615i) q^{94} -6.00000 q^{95} +(-9.00000 - 5.19615i) q^{96} +(6.00000 + 3.46410i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 2 q^{4} - 3 q^{5} + 6 q^{6} - q^{9} - 3 q^{10} + 2 q^{12} - 5 q^{13} + 6 q^{15} - 10 q^{16} - 6 q^{17} - 3 q^{18} + 6 q^{19} + 3 q^{20} - 12 q^{23} + 6 q^{24} - 2 q^{25} + 9 q^{26} - 8 q^{27}+ \cdots + 12 q^{97}+O(q^{100}) \) 2 * q - 2 * q^3 - 2 * q^4 - 3 * q^5 + 6 * q^6 - q^9 - 3 * q^10 + 2 * q^12 - 5 * q^13 + 6 * q^15 - 10 * q^16 - 6 * q^17 - 3 * q^18 + 6 * q^19 + 3 * q^20 - 12 * q^23 + 6 * q^24 - 2 * q^25 + 9 * q^26 - 8 * q^27 - 3 * q^29 - 6 * q^30 - 6 * q^31 + q^36 - 6 * q^38 - 4 * q^39 - 3 * q^40 - 9 * q^41 - 8 * q^43 - 6 * q^47 + 10 * q^48 - 6 * q^50 + 6 * q^51 + 5 * q^52 + 3 * q^53 - 9 * q^58 - 6 * q^60 - q^61 + 6 * q^62 - 2 * q^64 + 12 * q^65 - 6 * q^67 + 6 * q^68 + 12 * q^69 + 6 * q^71 - 3 * q^72 - 3 * q^73 + 30 * q^74 + 8 * q^75 - 6 * q^76 - 24 * q^78 - 4 * q^79 + 15 * q^80 + 11 * q^81 + 9 * q^82 + 9 * q^85 + 24 * q^86 + 12 * q^87 + 6 * q^90 + 12 * q^92 - 6 * q^94 - 12 * q^95 - 18 * q^96 + 12 * q^97

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