LMFDB - Embedded newform 637.2.u.c.30.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(30,637)] 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("637.30"); 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([2, 1])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [2,3,4,1,3] 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:	$0$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			30.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.c.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50000 - 0.866025i) q^{2} +2.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +(3.00000 - 1.73205i) q^{6} +1.73205i q^{8} +1.00000 q^{9} +3.00000 q^{10} +(1.00000 - 1.73205i) q^{12} +(-2.50000 - 2.59808i) q^{13} +(3.00000 + 1.73205i) q^{15} +(2.50000 + 4.33013i) q^{16} +(1.50000 - 2.59808i) q^{17} +(1.50000 - 0.866025i) q^{18} -3.46410i q^{19} +(1.50000 - 0.866025i) q^{20} +(3.00000 + 5.19615i) q^{23} +3.46410i q^{24} +(-1.00000 - 1.73205i) q^{25} +(-6.00000 - 1.73205i) q^{26} -4.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} +6.00000 q^{30} +(3.00000 - 1.73205i) q^{31} +(4.50000 + 2.59808i) q^{32} -5.19615i q^{34} +(0.500000 - 0.866025i) q^{36} +(-7.50000 + 4.33013i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-5.00000 - 5.19615i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(-4.50000 - 2.59808i) q^{41} +(-4.00000 - 6.92820i) q^{43} +(1.50000 + 0.866025i) q^{45} +(9.00000 + 5.19615i) q^{46} +(3.00000 + 1.73205i) q^{47} +(5.00000 + 8.66025i) q^{48} +(-3.00000 - 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(-3.50000 + 0.866025i) q^{52} +(1.50000 + 2.59808i) q^{53} +(-6.00000 + 3.46410i) q^{54} -6.92820i q^{57} +5.19615i q^{58} +(-6.00000 - 3.46410i) q^{59} +(3.00000 - 1.73205i) q^{60} +1.00000 q^{61} +(3.00000 - 5.19615i) q^{62} -1.00000 q^{64} +(-1.50000 - 6.06218i) q^{65} -3.46410i q^{67} +(-1.50000 - 2.59808i) q^{68} +(6.00000 + 10.3923i) q^{69} +(3.00000 - 1.73205i) q^{71} +1.73205i q^{72} +(1.50000 - 0.866025i) q^{73} +(-7.50000 + 12.9904i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(-3.00000 - 1.73205i) q^{76} +(-12.0000 - 3.46410i) q^{78} +(-2.00000 + 3.46410i) q^{79} +8.66025i q^{80} -11.0000 q^{81} -9.00000 q^{82} +13.8564i q^{83} +(4.50000 - 2.59808i) q^{85} +(-12.0000 - 6.92820i) q^{86} +(-3.00000 + 5.19615i) q^{87} +(6.00000 - 3.46410i) q^{89} +3.00000 q^{90} +6.00000 q^{92} +(6.00000 - 3.46410i) q^{93} +6.00000 q^{94} +(3.00000 - 5.19615i) q^{95} +(9.00000 + 5.19615i) q^{96} +(6.00000 - 3.46410i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 4 q^{3} + q^{4} + 3 q^{5} + 6 q^{6} + 2 q^{9} + 6 q^{10} + 2 q^{12} - 5 q^{13} + 6 q^{15} + 5 q^{16} + 3 q^{17} + 3 q^{18} + 3 q^{20} + 6 q^{23} - 2 q^{25} - 12 q^{26} - 8 q^{27} - 3 q^{29}+ \cdots + 12 q^{97}+O(q^{100}) $ 2 * q + 3 * q^2 + 4 * q^3 + q^4 + 3 * q^5 + 6 * q^6 + 2 * q^9 + 6 * q^10 + 2 * q^12 - 5 * q^13 + 6 * q^15 + 5 * q^16 + 3 * q^17 + 3 * q^18 + 3 * q^20 + 6 * q^23 - 2 * q^25 - 12 * q^26 - 8 * q^27 - 3 * q^29 + 12 * q^30 + 6 * q^31 + 9 * q^32 + q^36 - 15 * q^37 - 6 * q^38 - 10 * q^39 - 3 * q^40 - 9 * q^41 - 8 * q^43 + 3 * q^45 + 18 * q^46 + 6 * q^47 + 10 * q^48 - 6 * q^50 + 6 * q^51 - 7 * q^52 + 3 * q^53 - 12 * q^54 - 12 * q^59 + 6 * q^60 + 2 * q^61 + 6 * q^62 - 2 * q^64 - 3 * q^65 - 3 * q^68 + 12 * q^69 + 6 * q^71 + 3 * q^73 - 15 * q^74 - 4 * q^75 - 6 * q^76 - 24 * q^78 - 4 * q^79 - 22 * q^81 - 18 * q^82 + 9 * q^85 - 24 * q^86 - 6 * q^87 + 12 * q^89 + 6 * q^90 + 12 * q^92 + 12 * q^93 + 12 * q^94 + 6 * q^95 + 18 * q^96 + 12 * q^97

Character values

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

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

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 $

$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.135045	−	0.990839i	$-0.456882\pi$
$2$	1.50000	−	0.866025i	1.06066	−	0.612372i	0.925615	+	0.378467i	$0.123549\pi$
$3$	2.00000			1.15470			0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000			1.15470			0.577350	+	0.816497i	$0.304087\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	0.796387	−	0.604787i	$-0.206742\pi$
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	−0.125567	+	0.992085i	$0.540075\pi$
$6$	3.00000	−	1.73205i	1.22474	−	0.707107i
$7$		0			0
$7$		0			0
$8$			1.73205i			0.612372i
$9$	1.00000			0.333333
$10$	3.00000			0.948683
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$	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
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	1.50000	−	0.866025i	0.353553	−	0.204124i
$19$		−	3.46410i		−	0.794719i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$		−	3.46410i		−	0.794719i	0.917663	−	0.397360i	$-0.130073\pi$
$20$	1.50000	−	0.866025i	0.335410	−	0.193649i
$21$		0			0
$22$		0			0
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$			3.46410i			0.707107i
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	−6.00000	−	1.73205i	−1.17670	−	0.339683i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$	6.00000			1.09545
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	−0.205783	−	0.978598i	$-0.565974\pi$
$31$	3.00000	−	1.73205i	0.538816	−	0.311086i	0.744599	+	0.667512i	$0.232641\pi$
$32$	4.50000	+	2.59808i	0.795495	+	0.459279i
$33$		0			0
$34$		−	5.19615i		−	0.891133i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−7.50000	+	4.33013i	−1.23299	+	0.711868i	−0.967653	−	0.252286i	$-0.918817\pi$
$37$	−7.50000	+	4.33013i	−1.23299	+	0.711868i	−0.265340	+	0.964155i	$0.585484\pi$
$38$	−3.00000	−	5.19615i	−0.486664	−	0.842927i
$39$	−5.00000	−	5.19615i	−0.800641	−	0.832050i
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	−4.50000	−	2.59808i	−0.702782	−	0.405751i	0.105601	−	0.994409i	$-0.466323\pi$
$41$	−4.50000	−	2.59808i	−0.702782	−	0.405751i	−0.808383	+	0.588657i	$0.799657\pi$
$42$		0			0
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$		0			0
$45$	1.50000	+	0.866025i	0.223607	+	0.129099i
$46$	9.00000	+	5.19615i	1.32698	+	0.766131i
$47$	3.00000	+	1.73205i	0.437595	+	0.252646i	0.702577	−	0.711608i	$-0.252033\pi$
$47$	3.00000	+	1.73205i	0.437595	+	0.252646i	−0.264982	+	0.964253i	$0.585366\pi$
$48$	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
$52$	−3.50000	+	0.866025i	−0.485363	+	0.120096i
$53$	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	$0.767275\pi$
$54$	−6.00000	+	3.46410i	−0.816497	+	0.471405i
$55$		0			0
$56$		0			0
$57$		−	6.92820i		−	0.917663i
$58$			5.19615i			0.682288i
$59$	−6.00000	−	3.46410i	−0.781133	−	0.450988i	0.0556984	−	0.998448i	$-0.482261\pi$
$59$	−6.00000	−	3.46410i	−0.781133	−	0.450988i	−0.836832	+	0.547460i	$0.815595\pi$
$60$	3.00000	−	1.73205i	0.387298	−	0.223607i
$61$	1.00000			0.128037			0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000			0.128037			0.0640184	+	0.997949i	$0.479608\pi$
$62$	3.00000	−	5.19615i	0.381000	−	0.659912i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.50000	−	6.06218i	−0.186052	−	0.751921i
$66$		0			0
$67$		−	3.46410i		−	0.423207i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$		−	3.46410i		−	0.423207i	0.977356	−	0.211604i	$-0.0678686\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	6.00000	+	10.3923i	0.722315	+	1.25109i
$70$		0			0
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	−0.311305	−	0.950310i	$-0.600766\pi$
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	0.667340	+	0.744753i	$0.267433\pi$
$72$			1.73205i			0.204124i
$73$	1.50000	−	0.866025i	0.175562	−	0.101361i	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	1.50000	−	0.866025i	0.175562	−	0.101361i	0.585206	+	0.810885i	$0.301014\pi$
$74$	−7.50000	+	12.9904i	−0.871857	+	1.51010i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	−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	$0.238911\pi$
$80$			8.66025i			0.968246i
$81$	−11.0000			−1.22222
$82$	−9.00000			−0.993884
$83$			13.8564i			1.52094i	0.649374	+	0.760469i	$0.275031\pi$
$83$			13.8564i			1.52094i	−0.649374	+	0.760469i	$0.724969\pi$
$84$		0			0
$85$	4.50000	−	2.59808i	0.488094	−	0.281801i
$86$	−12.0000	−	6.92820i	−1.29399	−	0.747087i
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$		0			0
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	−0.147073	−	0.989126i	$-0.546985\pi$
$89$	6.00000	−	3.46410i	0.635999	−	0.367194i	0.783072	+	0.621932i	$0.213652\pi$
$90$	3.00000			0.316228
$91$		0			0
$92$	6.00000			0.625543
$93$	6.00000	−	3.46410i	0.622171	−	0.359211i
$94$	6.00000			0.618853
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$	9.00000	+	5.19615i	0.918559	+	0.530330i
$97$	6.00000	−	3.46410i	0.609208	−	0.351726i	−0.163448	−	0.986552i	$-0.552261\pi$
$97$	6.00000	−	3.46410i	0.609208	−	0.351726i	0.772655	+	0.634826i	$0.218928\pi$
$98$		0			0
$99$		0			0
$100$	−2.00000			−0.200000
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$		−	10.3923i		−	1.02899i
$103$	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
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$	−2.00000	+	3.46410i	−0.192450	+	0.333333i
$109$	−12.0000	+	6.92820i	−1.14939	+	0.663602i	−0.948739	−	0.316061i	$-0.897640\pi$
$109$	−12.0000	+	6.92820i	−1.14939	+	0.663602i	−0.200653	+	0.979662i	$0.564306\pi$
$110$		0			0
$111$	−15.0000	+	8.66025i	−1.42374	+	0.821995i
$112$		0			0
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$	−6.00000	−	10.3923i	−0.561951	−	0.973329i
$115$			10.3923i			0.969087i
$116$	1.50000	+	2.59808i	0.139272	+	0.241225i
$117$	−2.50000	−	2.59808i	−0.231125	−	0.240192i
$118$	−12.0000			−1.10469
$119$		0			0
$120$	−3.00000	+	5.19615i	−0.273861	+	0.474342i
$121$	11.0000			1.00000
$122$	1.50000	−	0.866025i	0.135804	−	0.0784063i
$123$	−9.00000	−	5.19615i	−0.811503	−	0.468521i
$124$		−	3.46410i		−	0.311086i
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	−0.818241	−	0.574875i	$-0.805051\pi$
$127$	1.00000	−	1.73205i	0.0887357	−	0.153695i	0.906977	+	0.421180i	$0.138384\pi$
$128$	−10.5000	+	6.06218i	−0.928078	+	0.535826i
$129$	−8.00000	−	13.8564i	−0.704361	−	1.21999i
$130$	−7.50000	−	7.79423i	−0.657794	−	0.683599i
$131$	−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
$136$	4.50000	+	2.59808i	0.385872	+	0.222783i
$137$	13.5000	+	7.79423i	1.15338	+	0.665906i	0.949709	−	0.313133i	$-0.101379\pi$
$137$	13.5000	+	7.79423i	1.15338	+	0.665906i	0.203674	+	0.979039i	$0.434712\pi$
$138$	18.0000	+	10.3923i	1.53226	+	0.884652i
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$		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
$145$	−4.50000	+	2.59808i	−0.373705	+	0.215758i
$146$	1.50000	−	2.59808i	0.124141	−	0.215018i
$147$		0			0
$148$			8.66025i			0.711868i
$149$		−	19.0526i		−	1.56085i	−0.625252	−	0.780423i	$-0.715004\pi$
$149$		−	19.0526i		−	1.56085i	0.625252	−	0.780423i	$-0.284996\pi$
$150$	−6.00000	−	3.46410i	−0.489898	−	0.282843i
$151$	15.0000	−	8.66025i	1.22068	−	0.704761i	0.255619	−	0.966778i	$-0.417721\pi$
$151$	15.0000	−	8.66025i	1.22068	−	0.704761i	0.965064	+	0.262016i	$0.0843873\pi$
$152$	6.00000			0.486664
$153$	1.50000	−	2.59808i	0.121268	−	0.210042i
$154$		0			0
$155$	6.00000			0.481932
$156$	−7.00000	+	1.73205i	−0.560449	+	0.138675i
$157$	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	$0.659728\pi$
$158$			6.92820i			0.551178i
$159$	3.00000	+	5.19615i	0.237915	+	0.412082i
$160$	4.50000	+	7.79423i	0.355756	+	0.616188i
$161$		0			0
$162$	−16.5000	+	9.52628i	−1.29636	+	0.748455i
$163$			20.7846i			1.62798i	0.580881	+	0.813988i	$0.302708\pi$
$163$			20.7846i			1.62798i	−0.580881	+	0.813988i	$0.697292\pi$
$164$	−4.50000	+	2.59808i	−0.351391	+	0.202876i
$165$		0			0
$166$	12.0000	+	20.7846i	0.931381	+	1.61320i
$167$	−12.0000	−	6.92820i	−0.928588	−	0.536120i	−0.0422232	−	0.999108i	$-0.513444\pi$
$167$	−12.0000	−	6.92820i	−0.928588	−	0.536120i	−0.886365	+	0.462988i	$0.846777\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	4.50000	−	7.79423i	0.345134	−	0.597790i
$171$		−	3.46410i		−	0.264906i
$172$	−8.00000			−0.609994
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$			10.3923i			0.787839i
$175$		0			0
$176$		0			0
$177$	−12.0000	−	6.92820i	−0.901975	−	0.520756i
$178$	6.00000	−	10.3923i	0.449719	−	0.778936i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	1.50000	−	0.866025i	0.111803	−	0.0645497i
$181$	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
$184$	−9.00000	+	5.19615i	−0.663489	+	0.383065i
$185$	−15.0000			−1.10282
$186$	6.00000	−	10.3923i	0.439941	−	0.762001i
$187$		0			0
$188$	3.00000	−	1.73205i	0.218797	−	0.126323i
$189$		0			0
$190$		−	10.3923i		−	0.753937i
$191$	18.0000			1.30243			0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000			1.30243			0.651217	+	0.758891i	$0.274259\pi$
$192$	−2.00000			−0.144338
$193$			5.19615i			0.374027i	0.982357	+	0.187014i	$0.0598809\pi$
$193$			5.19615i			0.374027i	−0.982357	+	0.187014i	$0.940119\pi$
$194$	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	0.862323	−	0.506359i	$-0.169009\pi$
$197$	12.0000	+	6.92820i	0.854965	+	0.493614i	−0.00735824	+	0.999973i	$0.502342\pi$
$198$		0			0
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	−0.828403	−	0.560133i	$-0.810750\pi$
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	0.899291	+	0.437351i	$0.144083\pi$
$200$	3.00000	−	1.73205i	0.212132	−	0.122474i
$201$		−	6.92820i		−	0.488678i
$202$	−4.50000	+	2.59808i	−0.316619	+	0.182800i
$203$		0			0
$204$	−3.00000	−	5.19615i	−0.210042	−	0.363803i
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$		−	17.3205i		−	1.20678i
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	5.00000	−	17.3205i	0.346688	−	1.20096i
$209$		0			0
$210$		0			0
$211$	−5.00000	+	8.66025i	−0.344214	+	0.596196i	−0.985211	−	0.171347i	$-0.945188\pi$
$211$	−5.00000	+	8.66025i	−0.344214	+	0.596196i	0.640996	+	0.767544i	$0.278521\pi$
$212$	3.00000			0.206041
$213$	6.00000	−	3.46410i	0.411113	−	0.237356i
$214$	−9.00000	−	5.19615i	−0.615227	−	0.355202i
$215$		−	13.8564i		−	0.944999i
$216$		−	6.92820i		−	0.471405i
$217$		0			0
$218$	−12.0000	+	20.7846i	−0.812743	+	1.40771i
$219$	3.00000	−	1.73205i	0.202721	−	0.117041i
$220$		0			0
$221$	−10.5000	+	2.59808i	−0.706306	+	0.174766i
$222$	−15.0000	+	25.9808i	−1.00673	+	1.74371i
$223$	−9.00000	−	5.19615i	−0.602685	−	0.347960i	0.167412	−	0.985887i	$-0.446459\pi$
$223$	−9.00000	−	5.19615i	−0.602685	−	0.347960i	−0.770097	+	0.637927i	$0.779792\pi$
$224$		0			0
$225$	−1.00000	−	1.73205i	−0.0666667	−	0.115470i
$226$	22.5000	+	12.9904i	1.49668	+	0.864107i
$227$	−21.0000	−	12.1244i	−1.39382	−	0.804722i	−0.400083	−	0.916479i	$-0.631019\pi$
$227$	−21.0000	−	12.1244i	−1.39382	−	0.804722i	−0.993736	+	0.111757i	$0.964352\pi$
$228$	−6.00000	−	3.46410i	−0.397360	−	0.229416i
$229$		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	$0.229636\pi$
$234$	−6.00000	−	1.73205i	−0.392232	−	0.113228i
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	−6.00000	+	3.46410i	−0.390567	+	0.225494i
$237$	−4.00000	+	6.92820i	−0.259828	+	0.450035i
$238$		0			0
$239$		−	20.7846i		−	1.34444i	−0.740349	−	0.672222i	$-0.765340\pi$
$239$		−	20.7846i		−	1.34444i	0.740349	−	0.672222i	$-0.234660\pi$
$240$			17.3205i			1.11803i
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	1.50000	+	0.866025i	0.0966235	+	0.0557856i	−0.450910	+	0.892570i	$0.648900\pi$
$242$	16.5000	−	9.52628i	1.06066	−	0.612372i
$243$	−10.0000			−0.641500
$244$	0.500000	−	0.866025i	0.0320092	−	0.0554416i
$245$		0			0
$246$	−18.0000			−1.14764
$247$	−9.00000	+	8.66025i	−0.572656	+	0.551039i
$248$	3.00000	+	5.19615i	0.190500	+	0.329956i
$249$			27.7128i			1.75623i
$250$	−10.5000	−	18.1865i	−0.664078	−	1.15022i
$251$	9.00000	+	15.5885i	0.568075	+	0.983935i	0.996756	+	0.0804789i	$0.0256450\pi$
$251$	9.00000	+	15.5885i	0.568075	+	0.983935i	−0.428681	+	0.903456i	$0.641022\pi$
$252$		0			0
$253$		0			0
$254$		−	3.46410i		−	0.217357i
$255$	9.00000	−	5.19615i	0.563602	−	0.325396i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	0.815442	−	0.578838i	$-0.196494\pi$
$257$	−1.50000	−	2.59808i	−0.0935674	−	0.162064i	−0.909010	+	0.416775i	$0.863160\pi$
$258$	−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
$262$			31.1769i			1.92612i
$263$	12.0000			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$264$		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
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	−0.759958	−	0.649972i	$-0.774781\pi$
$269$	3.00000	−	5.19615i	0.182913	−	0.316815i	0.942871	+	0.333157i	$0.108114\pi$
$270$	−12.0000			−0.730297
$271$	−18.0000	+	10.3923i	−1.09342	+	0.631288i	−0.934485	−	0.356001i	$-0.884140\pi$
$271$	−18.0000	+	10.3923i	−1.09342	+	0.631288i	−0.158937	+	0.987289i	$0.550807\pi$
$272$	15.0000			0.909509
$273$		0			0
$274$	27.0000			1.63113
$275$		0			0
$276$	12.0000			0.722315
$277$	3.50000	−	6.06218i	0.210295	−	0.364241i	−0.741512	−	0.670940i	$-0.765891\pi$
$277$	3.50000	−	6.06218i	0.210295	−	0.364241i	0.951807	+	0.306699i	$0.0992243\pi$
$278$	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	$-0.765601\pi$
$281$		−	22.5167i		−	1.34323i	0.740900	−	0.671616i	$-0.234399\pi$
$282$	12.0000			0.714590
$283$	4.00000			0.237775			0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000			0.237775			0.118888	+	0.992908i	$0.462067\pi$
$284$		−	3.46410i		−	0.205557i
$285$	6.00000	−	10.3923i	0.355409	−	0.615587i
$286$		0			0
$287$		0			0
$288$	4.50000	+	2.59808i	0.265165	+	0.153093i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$	12.0000	−	6.92820i	0.703452	−	0.406138i
$292$		−	1.73205i		−	0.101361i
$293$	4.50000	−	2.59808i	0.262893	−	0.151781i	−0.362761	−	0.931882i	$-0.618166\pi$
$293$	4.50000	−	2.59808i	0.262893	−	0.151781i	0.625653	+	0.780101i	$0.284832\pi$
$294$		0			0
$295$	−6.00000	−	10.3923i	−0.349334	−	0.605063i
$296$	−7.50000	−	12.9904i	−0.435929	−	0.755051i
$297$		0			0
$298$	−16.5000	−	28.5788i	−0.955819	−	1.65553i
$299$	6.00000	−	20.7846i	0.346989	−	1.20201i
$300$	−4.00000			−0.230940
$301$		0			0
$302$	15.0000	−	25.9808i	0.863153	−	1.49502i
$303$	−6.00000			−0.344691
$304$	15.0000	−	8.66025i	0.860309	−	0.496700i
$305$	1.50000	+	0.866025i	0.0858898	+	0.0495885i
$306$		−	5.19615i		−	0.297044i
$307$		−	17.3205i		−	0.988534i	−0.869310	−	0.494267i	$-0.835437\pi$
$307$		−	17.3205i		−	0.988534i	0.869310	−	0.494267i	$-0.164563\pi$
$308$		0			0
$309$	10.0000	−	17.3205i	0.568880	−	0.985329i
$310$	9.00000	−	5.19615i	0.511166	−	0.295122i
$311$	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	$0.509589\pi$
$312$	9.00000	−	8.66025i	0.509525	−	0.490290i
$313$	−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	0.621021	−	0.783794i	$-0.286718\pi$
$317$	4.50000	+	2.59808i	0.252745	+	0.145922i	−0.368275	+	0.929717i	$0.620052\pi$
$318$	9.00000	+	5.19615i	0.504695	+	0.291386i
$319$		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
$325$	−2.00000	+	6.92820i	−0.110940	+	0.384308i
$326$	18.0000	+	31.1769i	0.996928	+	1.72673i
$327$	−24.0000	+	13.8564i	−1.32720	+	0.766261i
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$		0			0
$330$		0			0
$331$		−	27.7128i		−	1.52323i	−0.648027	−	0.761617i	$-0.724406\pi$
$331$		−	27.7128i		−	1.52323i	0.648027	−	0.761617i	$-0.275594\pi$
$332$	12.0000	+	6.92820i	0.658586	+	0.380235i
$333$	−7.50000	+	4.33013i	−0.410997	+	0.237289i
$334$	−24.0000			−1.31322
$335$	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	$0.715491\pi$
$338$	10.5000	+	19.9186i	0.571125	+	1.08343i
$339$	15.0000	+	25.9808i	0.814688	+	1.41108i
$340$		−	5.19615i		−	0.281801i
$341$		0			0
$342$	−3.00000	−	5.19615i	−0.162221	−	0.280976i
$343$		0			0
$344$	12.0000	−	6.92820i	0.646997	−	0.373544i
$345$			20.7846i			1.11901i
$346$	9.00000	−	5.19615i	0.483843	−	0.279347i
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	−0.110885	−	0.993833i	$-0.535369\pi$
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	0.916127	−	0.400887i	$-0.131298\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	12.0000	+	6.92820i	0.642345	+	0.370858i	0.785517	−	0.618840i	$-0.212397\pi$
$349$	12.0000	+	6.92820i	0.642345	+	0.370858i	−0.143172	+	0.989698i	$0.545730\pi$
$350$		0			0
$351$	10.0000	+	10.3923i	0.533761	+	0.554700i
$352$		0			0
$353$		−	32.9090i		−	1.75157i	−0.482704	−	0.875784i	$-0.660345\pi$
$353$		−	32.9090i		−	1.75157i	0.482704	−	0.875784i	$-0.339655\pi$
$354$	−24.0000			−1.27559
$355$	6.00000			0.318447
$356$		−	6.92820i		−	0.367194i
$357$		0			0
$358$		0			0
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	0.649906	−	0.760014i	$-0.274808\pi$
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	−0.333238	+	0.942843i	$0.608141\pi$
$360$	−1.50000	+	2.59808i	−0.0790569	+	0.136931i
$361$	7.00000			0.368421
$362$	16.5000	−	9.52628i	0.867221	−	0.500690i
$363$	22.0000			1.15470
$364$		0			0
$365$	3.00000			0.157027
$366$	3.00000	−	1.73205i	0.156813	−	0.0905357i
$367$	−22.0000			−1.14839			−0.574195	−	0.818718i	$-0.694685\pi$
$367$	−22.0000			−1.14839			−0.574195	+	0.818718i	$0.694685\pi$
$368$	−15.0000	+	25.9808i	−0.781929	+	1.35434i
$369$	−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
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$		0			0
$375$		−	24.2487i		−	1.25220i
$376$	−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	−0.148153	−	0.988964i	$-0.547333\pi$
$379$	−21.0000	−	12.1244i	−1.07870	−	0.622786i	−0.930545	+	0.366178i	$0.880666\pi$
$380$	−3.00000	−	5.19615i	−0.153897	−	0.266557i
$381$	2.00000	−	3.46410i	0.102463	−	0.177471i
$382$	27.0000	−	15.5885i	1.38144	−	0.797575i
$383$		−	20.7846i		−	1.06204i	−0.847358	−	0.531022i	$-0.821808\pi$
$383$		−	20.7846i		−	1.06204i	0.847358	−	0.531022i	$-0.178192\pi$
$384$	−21.0000	+	12.1244i	−1.07165	+	0.618718i
$385$		0			0
$386$	4.50000	+	7.79423i	0.229044	+	0.396716i
$387$	−4.00000	−	6.92820i	−0.203331	−	0.352180i
$388$		−	6.92820i		−	0.351726i
$389$	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	$0.760063\pi$
$390$	−15.0000	−	15.5885i	−0.759555	−	0.789352i
$391$	18.0000			0.910299
$392$		0			0
$393$	−18.0000	+	31.1769i	−0.907980	+	1.57267i
$394$	24.0000			1.20910
$395$	−6.00000	+	3.46410i	−0.301893	+	0.174298i
$396$		0			0
$397$		−	13.8564i		−	0.695433i	−0.937600	−	0.347717i	$-0.886957\pi$
$397$		−	13.8564i		−	0.695433i	0.937600	−	0.347717i	$-0.113043\pi$
$398$		−	3.46410i		−	0.173640i
$399$		0			0
$400$	5.00000	−	8.66025i	0.250000	−	0.433013i
$401$	1.50000	−	0.866025i	0.0749064	−	0.0432472i	−0.462079	−	0.886839i	$-0.652896\pi$
$401$	1.50000	−	0.866025i	0.0749064	−	0.0432472i	0.536985	+	0.843592i	$0.319563\pi$
$402$	−6.00000	−	10.3923i	−0.299253	−	0.518321i
$403$	−12.0000	−	3.46410i	−0.597763	−	0.172559i
$404$	−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
$409$	−13.5000	−	7.79423i	−0.667532	−	0.385400i	0.127609	−	0.991825i	$-0.459270\pi$
$409$	−13.5000	−	7.79423i	−0.667532	−	0.385400i	−0.795141	+	0.606425i	$0.792603\pi$
$410$	−13.5000	−	7.79423i	−0.666717	−	0.384930i
$411$	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
$416$	−4.50000	−	18.1865i	−0.220631	−	0.891668i
$417$	4.00000	+	6.92820i	0.195881	+	0.339276i
$418$		0			0
$419$	−9.00000	+	15.5885i	−0.439679	+	0.761546i	−0.997665	−	0.0683046i	$-0.978241\pi$
$419$	−9.00000	+	15.5885i	−0.439679	+	0.761546i	0.557986	+	0.829851i	$0.311574\pi$
$420$		0			0
$421$			15.5885i			0.759735i	0.925041	+	0.379867i	$0.124030\pi$
$421$			15.5885i			0.759735i	−0.925041	+	0.379867i	$0.875970\pi$
$422$			17.3205i			0.843149i
$423$	3.00000	+	1.73205i	0.145865	+	0.0842152i
$424$	−4.50000	+	2.59808i	−0.218539	+	0.126174i
$425$	−6.00000			−0.291043
$426$	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
$431$			6.92820i			0.333720i	0.985981	+	0.166860i	$0.0533628\pi$
$431$			6.92820i			0.333720i	−0.985981	+	0.166860i	$0.946637\pi$
$432$	−10.0000	−	17.3205i	−0.481125	−	0.833333i
$433$	8.50000	+	14.7224i	0.408484	+	0.707515i	0.994720	−	0.102625i	$-0.0327243\pi$
$433$	8.50000	+	14.7224i	0.408484	+	0.707515i	−0.586236	+	0.810140i	$0.699391\pi$
$434$		0			0
$435$	−9.00000	+	5.19615i	−0.431517	+	0.249136i
$436$			13.8564i			0.663602i
$437$	18.0000	−	10.3923i	0.861057	−	0.497131i
$438$	3.00000	−	5.19615i	0.143346	−	0.248282i
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		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	$0.0746503\pi$
$444$			17.3205i			0.821995i
$445$	12.0000			0.568855
$446$	−18.0000			−0.852325
$447$		−	38.1051i		−	1.80231i
$448$		0			0
$449$	−6.00000	+	3.46410i	−0.283158	+	0.163481i	−0.634852	−	0.772634i	$-0.718939\pi$
$449$	−6.00000	+	3.46410i	−0.283158	+	0.163481i	0.351694	+	0.936115i	$0.385606\pi$
$450$	−3.00000	−	1.73205i	−0.141421	−	0.0816497i
$451$		0			0
$452$	15.0000			0.705541
$453$	30.0000	−	17.3205i	1.40952	−	0.813788i
$454$	−42.0000			−1.97116
$455$		0			0
$456$	12.0000			0.561951
$457$	−1.50000	+	0.866025i	−0.0701670	+	0.0405110i	−0.534673	−	0.845059i	$-0.679565\pi$
$457$	−1.50000	+	0.866025i	−0.0701670	+	0.0405110i	0.464506	+	0.885570i	$0.346232\pi$
$458$		0			0
$459$	−6.00000	+	10.3923i	−0.280056	+	0.485071i
$460$	9.00000	+	5.19615i	0.419627	+	0.242272i
$461$	19.5000	−	11.2583i	0.908206	−	0.524353i	0.0283522	−	0.999598i	$-0.490974\pi$
$461$	19.5000	−	11.2583i	0.908206	−	0.524353i	0.879853	+	0.475245i	$0.157641\pi$
$462$		0			0
$463$			13.8564i			0.643962i	0.946746	+	0.321981i	$0.104349\pi$
$463$			13.8564i			0.643962i	−0.946746	+	0.321981i	$0.895651\pi$
$464$	−15.0000			−0.696358
$465$	12.0000			0.556487
$466$			10.3923i			0.481414i
$467$	−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
$471$	13.0000	+	22.5167i	0.599008	+	1.03751i
$472$	6.00000	−	10.3923i	0.276172	−	0.478345i
$473$		0			0
$474$			13.8564i			0.636446i
$475$	−6.00000	+	3.46410i	−0.275299	+	0.158944i
$476$		0			0
$477$	1.50000	+	2.59808i	0.0686803	+	0.118958i
$478$	−18.0000	−	31.1769i	−0.823301	−	1.42600i
$479$		−	24.2487i		−	1.10795i	−0.832533	−	0.553976i	$-0.813110\pi$
$479$		−	24.2487i		−	1.10795i	0.832533	−	0.553976i	$-0.186890\pi$
$480$	9.00000	+	15.5885i	0.410792	+	0.711512i
$481$	30.0000	+	8.66025i	1.36788	+	0.394874i
$482$	3.00000			0.136646
$483$		0			0
$484$	5.50000	−	9.52628i	0.250000	−	0.433013i
$485$	12.0000			0.544892
$486$	−15.0000	+	8.66025i	−0.680414	+	0.392837i
$487$	6.00000	+	3.46410i	0.271886	+	0.156973i	0.629744	−	0.776802i	$-0.283160\pi$
$487$	6.00000	+	3.46410i	0.271886	+	0.156973i	−0.357858	+	0.933776i	$0.616493\pi$
$488$			1.73205i			0.0784063i
$489$			41.5692i			1.87983i
$490$		0			0
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	−0.969061	−	0.246822i	$-0.920614\pi$
$491$	−6.00000	+	10.3923i	−0.270776	+	0.468998i	0.698285	+	0.715820i	$0.253947\pi$
$492$	−9.00000	+	5.19615i	−0.405751	+	0.234261i
$493$	4.50000	+	7.79423i	0.202670	+	0.351034i
$494$	−6.00000	+	20.7846i	−0.269953	+	0.935144i
$495$		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	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	−27.0000	−	15.5885i	−1.20869	−	0.697835i	−0.962472	+	0.271380i	$0.912520\pi$
$500$	−10.5000	−	6.06218i	−0.469574	−	0.271109i
$501$	−24.0000	−	13.8564i	−1.07224	−	0.619059i
$502$	27.0000	+	15.5885i	1.20507	+	0.695747i
$503$	−18.0000	−	31.1769i	−0.802580	−	1.39011i	−0.917912	−	0.396783i	$-0.870127\pi$
$503$	−18.0000	−	31.1769i	−0.802580	−	1.39011i	0.115332	−	0.993327i	$-0.463207\pi$
$504$		0			0
$505$	−4.50000	−	2.59808i	−0.200247	−	0.115613i
$506$		0			0
$507$	−1.00000	+	25.9808i	−0.0444116	+	1.15385i
$508$	−1.00000	−	1.73205i	−0.0443678	−	0.0768473i
$509$	−16.5000	+	9.52628i	−0.731350	+	0.422245i	−0.818916	−	0.573914i	$-0.805424\pi$
$509$	−16.5000	+	9.52628i	−0.731350	+	0.422245i	0.0875661	+	0.996159i	$0.472091\pi$
$510$	9.00000	−	15.5885i	0.398527	−	0.690268i
$511$		0			0
$512$			8.66025i			0.382733i
$513$			13.8564i			0.611775i
$514$	−4.50000	−	2.59808i	−0.198486	−	0.114596i
$515$	15.0000	−	8.66025i	0.660979	−	0.381616i
$516$	−16.0000			−0.704361
$517$		0			0
$518$		0			0
$519$	12.0000			0.526742
$520$	10.5000	−	2.59808i	0.460455	−	0.113933i
$521$	−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	$0.896501\pi$
$522$			5.19615i			0.227429i
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	0.986216	−	0.165460i	$-0.0529109\pi$
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	−0.636401	+	0.771358i	$0.719578\pi$
$524$	9.00000	+	15.5885i	0.393167	+	0.680985i
$525$		0			0
$526$	18.0000	−	10.3923i	0.784837	−	0.453126i
$527$		−	10.3923i		−	0.452696i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	4.50000	+	7.79423i	0.195468	+	0.338560i
$531$	−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
$535$		−	10.3923i		−	0.449299i
$536$	6.00000			0.259161
$537$		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	−0.161076	−	0.986942i	$-0.551496\pi$
$541$	−25.5000	−	14.7224i	−1.09633	−	0.632967i	−0.935255	+	0.353975i	$0.884830\pi$
$542$	−18.0000	+	31.1769i	−0.773166	+	1.33916i
$543$	22.0000			0.944110
$544$	13.5000	−	7.79423i	0.578808	−	0.334175i
$545$	−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	$0.655864\pi$
$548$	13.5000	−	7.79423i	0.576691	−	0.332953i
$549$	1.00000			0.0426790
$550$		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
$555$	−30.0000			−1.27343
$556$	4.00000			0.169638
$557$			15.5885i			0.660504i	0.943893	+	0.330252i	$0.107134\pi$
$557$			15.5885i			0.660504i	−0.943893	+	0.330252i	$0.892866\pi$
$558$	3.00000	−	5.19615i	0.127000	−	0.219971i
$559$	−8.00000	+	27.7128i	−0.338364	+	1.17213i
$560$		0			0
$561$		0			0
$562$	−19.5000	−	33.7750i	−0.822558	−	1.42471i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	6.00000	−	3.46410i	0.252646	−	0.145865i
$565$			25.9808i			1.09302i
$566$	6.00000	−	3.46410i	0.252199	−	0.145607i
$567$		0			0
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	21.0000	+	36.3731i	0.880366	+	1.52484i	0.850935	+	0.525271i	$0.176036\pi$
$569$	21.0000	+	36.3731i	0.880366	+	1.52484i	0.0294311	+	0.999567i	$0.490630\pi$
$570$		−	20.7846i		−	0.870572i
$571$	−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
$576$	−1.00000			−0.0416667
$577$	−16.5000	+	9.52628i	−0.686904	+	0.396584i	−0.802451	−	0.596718i	$-0.796471\pi$
$577$	−16.5000	+	9.52628i	−0.686904	+	0.396584i	0.115547	+	0.993302i	$0.463138\pi$
$578$	12.0000	+	6.92820i	0.499134	+	0.288175i
$579$			10.3923i			0.431889i
$580$			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
$585$	−1.50000	−	6.06218i	−0.0620174	−	0.250640i
$586$	4.50000	−	7.79423i	0.185893	−	0.321977i
$587$	−18.0000	−	10.3923i	−0.742940	−	0.428936i	0.0801976	−	0.996779i	$-0.474445\pi$
$587$	−18.0000	−	10.3923i	−0.742940	−	0.428936i	−0.823137	+	0.567843i	$0.807778\pi$
$588$		0			0
$589$	−6.00000	−	10.3923i	−0.247226	−	0.428207i
$590$	−18.0000	−	10.3923i	−0.741048	−	0.427844i
$591$	24.0000	+	13.8564i	0.987228	+	0.569976i
$592$	−37.5000	−	21.6506i	−1.54124	−	0.889836i
$593$	22.5000	+	12.9904i	0.923964	+	0.533451i	0.884898	−	0.465786i	$-0.154228\pi$
$593$	22.5000	+	12.9904i	0.923964	+	0.533451i	0.0390666	+	0.999237i	$0.487562\pi$
$594$		0			0
$595$		0			0
$596$	−16.5000	−	9.52628i	−0.675866	−	0.390212i
$597$	2.00000	−	3.46410i	0.0818546	−	0.141776i
$598$	−9.00000	−	36.3731i	−0.368037	−	1.48741i
$599$	−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	$-0.376657\pi$
$600$	6.00000	−	3.46410i	0.244949	−	0.141421i
$601$	−12.5000	+	21.6506i	−0.509886	+	0.883148i	0.490049	+	0.871695i	$0.336979\pi$
$601$	−12.5000	+	21.6506i	−0.509886	+	0.883148i	−0.999934	+	0.0114528i	$0.996354\pi$
$602$		0			0
$603$		−	3.46410i		−	0.141069i
$604$		−	17.3205i		−	0.704761i
$605$	16.5000	+	9.52628i	0.670820	+	0.387298i
$606$	−9.00000	+	5.19615i	−0.365600	+	0.211079i
$607$	−34.0000			−1.38002			−0.690009	−	0.723801i	$-0.742393\pi$
$607$	−34.0000			−1.38002			−0.690009	+	0.723801i	$0.742393\pi$
$608$	9.00000	−	15.5885i	0.364998	−	0.632195i
$609$		0			0
$610$	3.00000			0.121466
$611$	−3.00000	−	12.1244i	−0.121367	−	0.490499i
$612$	−1.50000	−	2.59808i	−0.0606339	−	0.105021i
$613$			12.1244i			0.489698i	0.969561	+	0.244849i	$0.0787384\pi$
$613$			12.1244i			0.489698i	−0.969561	+	0.244849i	$0.921262\pi$
$614$	−15.0000	−	25.9808i	−0.605351	−	1.04850i
$615$	−9.00000	−	15.5885i	−0.362915	−	0.628587i
$616$		0			0
$617$	−19.5000	+	11.2583i	−0.785040	+	0.453243i	−0.838214	−	0.545342i	$-0.816400\pi$
$617$	−19.5000	+	11.2583i	−0.785040	+	0.453243i	0.0531732	+	0.998585i	$0.483066\pi$
$618$		−	34.6410i		−	1.39347i
$619$	−18.0000	+	10.3923i	−0.723481	+	0.417702i	−0.816033	−	0.578006i	$-0.803831\pi$
$619$	−18.0000	+	10.3923i	−0.723481	+	0.417702i	0.0925515	+	0.995708i	$0.470498\pi$
$620$	3.00000	−	5.19615i	0.120483	−	0.208683i
$621$	−12.0000	−	20.7846i	−0.481543	−	0.834058i
$622$	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
$626$			17.3205i			0.692267i
$627$		0			0
$628$	13.0000			0.518756
$629$			25.9808i			1.03592i
$630$		0			0
$631$	−42.0000	+	24.2487i	−1.67199	+	0.965326i	−0.705473	+	0.708737i	$0.749265\pi$
$631$	−42.0000	+	24.2487i	−1.67199	+	0.965326i	−0.966521	+	0.256589i	$0.917401\pi$
$632$	−6.00000	−	3.46410i	−0.238667	−	0.137795i
$633$	−10.0000	+	17.3205i	−0.397464	+	0.688428i
$634$	9.00000			0.357436
$635$	3.00000	−	1.73205i	0.119051	−	0.0687343i
$636$	6.00000			0.237915
$637$		0			0
$638$		0			0
$639$	3.00000	−	1.73205i	0.118678	−	0.0685189i
$640$	−21.0000			−0.830098
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$	−18.0000	−	10.3923i	−0.710403	−	0.410152i
$643$	12.0000	−	6.92820i	0.473234	−	0.273222i	−0.244359	−	0.969685i	$-0.578577\pi$
$643$	12.0000	−	6.92820i	0.473234	−	0.273222i	0.717592	+	0.696463i	$0.245244\pi$
$644$		0			0
$645$		−	27.7128i		−	1.09119i
$646$	−18.0000			−0.708201
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$		−	19.0526i		−	0.748455i
$649$		0			0
$650$	3.00000	+	12.1244i	0.117670	+	0.475556i
$651$		0			0
$652$	18.0000	+	10.3923i	0.704934	+	0.406994i
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	0.994623	+	0.103558i	$0.0330227\pi$
$653$	15.0000	+	25.9808i	0.586995	+	1.01671i	−0.407628	+	0.913148i	$0.633644\pi$
$654$	−24.0000	+	41.5692i	−0.938474	+	1.62549i
$655$	−27.0000	+	15.5885i	−1.05498	+	0.609091i
$656$		−	25.9808i		−	1.01438i
$657$	1.50000	−	0.866025i	0.0585206	−	0.0337869i
$658$		0			0
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	0.958902	−	0.283738i	$-0.0915745\pi$
$659$	6.00000	+	10.3923i	0.233727	+	0.404827i	−0.725175	+	0.688565i	$0.758241\pi$
$660$		0			0
$661$			46.7654i			1.81896i	0.415745	+	0.909481i	$0.363521\pi$
$661$			46.7654i			1.81896i	−0.415745	+	0.909481i	$0.636479\pi$
$662$	−24.0000	−	41.5692i	−0.932786	−	1.61563i
$663$	−21.0000	+	5.19615i	−0.815572	+	0.201802i
$664$	−24.0000			−0.931381
$665$		0			0
$666$	−7.50000	+	12.9904i	−0.290619	+	0.503367i
$667$	−18.0000			−0.696963
$668$	−12.0000	+	6.92820i	−0.464294	+	0.268060i
$669$	−18.0000	−	10.3923i	−0.695920	−	0.401790i
$670$		−	10.3923i		−	0.401490i
$671$		0			0
$672$		0			0
$673$	9.50000	−	16.4545i	0.366198	−	0.634274i	−0.622770	−	0.782405i	$-0.713993\pi$
$673$	9.50000	−	16.4545i	0.366198	−	0.634274i	0.988968	+	0.148132i	$0.0473259\pi$
$674$	−34.5000	+	19.9186i	−1.32889	+	0.767235i
$675$	4.00000	+	6.92820i	0.153960	+	0.266667i
$676$	11.0000	+	6.92820i	0.423077	+	0.266469i
$677$	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
$683$	−21.0000	−	12.1244i	−0.803543	−	0.463926i	0.0411658	−	0.999152i	$-0.486893\pi$
$683$	−21.0000	−	12.1244i	−0.803543	−	0.463926i	−0.844708	+	0.535227i	$0.820226\pi$
$684$	−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
$689$	3.00000	−	10.3923i	0.114291	−	0.395915i
$690$	18.0000	+	31.1769i	0.685248	+	1.18688i
$691$	−12.0000	+	6.92820i	−0.456502	+	0.263561i	−0.710572	−	0.703624i	$-0.751564\pi$
$691$	−12.0000	+	6.92820i	−0.456502	+	0.263561i	0.254071	+	0.967186i	$0.418230\pi$
$692$	3.00000	−	5.19615i	0.114043	−	0.197528i
$693$		0			0
$694$		−	51.9615i		−	1.97243i
$695$			6.92820i			0.262802i
$696$	−9.00000	−	5.19615i	−0.341144	−	0.196960i
$697$	−13.5000	+	7.79423i	−0.511349	+	0.295227i
$698$	24.0000			0.908413
$699$	−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	$0.389598\pi$
$702$	24.0000	+	6.92820i	0.905822	+	0.261488i
$703$	15.0000	+	25.9808i	0.565736	+	0.979883i
$704$		0			0
$705$	6.00000	+	10.3923i	0.225973	+	0.391397i
$706$	−28.5000	−	49.3634i	−1.07261	−	1.85782i
$707$		0			0
$708$	−12.0000	+	6.92820i	−0.450988	+	0.260378i
$709$		−	5.19615i		−	0.195146i	−0.995228	−	0.0975728i	$-0.968892\pi$
$709$		−	5.19615i		−	0.195146i	0.995228	−	0.0975728i	$-0.0311079\pi$
$710$	9.00000	−	5.19615i	0.337764	−	0.195008i
$711$	−2.00000	+	3.46410i	−0.0750059	+	0.129914i
$712$	6.00000	+	10.3923i	0.224860	+	0.389468i
$713$	18.0000	+	10.3923i	0.674105	+	0.389195i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		−	41.5692i		−	1.55243i
$718$	12.0000			0.447836
$719$	−48.0000			−1.79010			−0.895049	−	0.445968i	$-0.852860\pi$
$719$	−48.0000			−1.79010			−0.895049	+	0.445968i	$0.852860\pi$
$720$			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
$724$	5.50000	−	9.52628i	0.204406	−	0.354041i
$725$	6.00000			0.222834
$726$	33.0000	−	19.0526i	1.22474	−	0.707107i
$727$	−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
$730$	4.50000	−	2.59808i	0.166552	−	0.0961591i
$731$	−24.0000			−0.887672
$732$	1.00000	−	1.73205i	0.0369611	−	0.0640184i
$733$	−10.5000	−	6.06218i	−0.387826	−	0.223912i	0.293392	−	0.955992i	$-0.405216\pi$
$733$	−10.5000	−	6.06218i	−0.387826	−	0.223912i	−0.681218	+	0.732081i	$0.738549\pi$
$734$	−33.0000	+	19.0526i	−1.21805	+	0.703243i
$735$		0			0
$736$			31.1769i			1.14920i
$737$		0			0
$738$	−9.00000			−0.331295
$739$			20.7846i			0.764574i	0.924044	+	0.382287i	$0.124863\pi$
$739$			20.7846i			0.764574i	−0.924044	+	0.382287i	$0.875137\pi$
$740$	−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	−0.164216	−	0.986424i	$-0.552510\pi$
$743$	−30.0000	−	17.3205i	−1.10059	−	0.635428i	−0.936377	+	0.350997i	$0.885843\pi$
$744$	6.00000	+	10.3923i	0.219971	+	0.381000i
$745$	16.5000	−	28.5788i	0.604513	−	1.04705i
$746$	28.5000	−	16.4545i	1.04346	−	0.602441i
$747$			13.8564i			0.506979i
$748$		0			0
$749$		0			0
$750$	−21.0000	−	36.3731i	−0.766812	−	1.32816i
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$			17.3205i			0.631614i
$753$	18.0000	+	31.1769i	0.655956	+	1.13615i
$754$	13.5000	−	12.9904i	0.491641	−	0.473082i
$755$	30.0000			1.09181
$756$		0			0
$757$	13.0000	−	22.5167i	0.472493	−	0.818382i	−0.527011	−	0.849858i	$-0.676688\pi$
$757$	13.0000	−	22.5167i	0.472493	−	0.818382i	0.999505	+	0.0314762i	$0.0100208\pi$
$758$	−42.0000			−1.52551
$759$		0			0
$760$	9.00000	+	5.19615i	0.326464	+	0.188484i
$761$			34.6410i			1.25574i	0.778320	+	0.627868i	$0.216072\pi$
$761$			34.6410i			1.25574i	−0.778320	+	0.627868i	$0.783928\pi$
$762$		−	6.92820i		−	0.250982i
$763$		0			0
$764$	9.00000	−	15.5885i	0.325609	−	0.563971i
$765$	4.50000	−	2.59808i	0.162698	−	0.0939336i
$766$	−18.0000	−	31.1769i	−0.650366	−	1.12647i
$767$	6.00000	+	24.2487i	0.216647	+	0.875570i
$768$	−19.0000	+	32.9090i	−0.685603	+	1.18750i
$769$	6.00000	+	3.46410i	0.216366	+	0.124919i	0.604266	−	0.796782i	$-0.293466\pi$
$769$	6.00000	+	3.46410i	0.216366	+	0.124919i	−0.387901	+	0.921701i	$0.626800\pi$
$770$		0			0
$771$	−3.00000	−	5.19615i	−0.108042	−	0.187135i
$772$	4.50000	+	2.59808i	0.161959	+	0.0935068i
$773$	30.0000	+	17.3205i	1.07903	+	0.622975i	0.930633	−	0.365953i	$-0.119257\pi$
$773$	30.0000	+	17.3205i	1.07903	+	0.622975i	0.148392	+	0.988929i	$0.452590\pi$
$774$	−12.0000	−	6.92820i	−0.431331	−	0.249029i
$775$	−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
$780$	−12.0000	−	3.46410i	−0.429669	−	0.124035i
$781$		0			0
$782$	27.0000	−	15.5885i	0.965518	−	0.557442i
$783$	6.00000	−	10.3923i	0.214423	−	0.371391i
$784$		0			0
$785$			22.5167i			0.803654i
$786$			62.3538i			2.22409i
$787$	−33.0000	−	19.0526i	−1.17632	−	0.679150i	−0.221162	−	0.975237i	$-0.570985\pi$
$787$	−33.0000	−	19.0526i	−1.17632	−	0.679150i	−0.955161	+	0.296087i	$0.904318\pi$
$788$	12.0000	−	6.92820i	0.427482	−	0.246807i
$789$	24.0000			0.854423
$790$	−6.00000	+	10.3923i	−0.213470	+	0.369742i
$791$		0			0
$792$		0			0
$793$	−2.50000	−	2.59808i	−0.0887776	−	0.0922604i
$794$	−12.0000	−	20.7846i	−0.425864	−	0.737618i
$795$			10.3923i			0.368577i
$796$	−1.00000	−	1.73205i	−0.0354441	−	0.0613909i
$797$	−21.0000	−	36.3731i	−0.743858	−	1.28840i	−0.950726	−	0.310031i	$-0.899660\pi$
$797$	−21.0000	−	36.3731i	−0.743858	−	1.28840i	0.206868	−	0.978369i	$-0.433673\pi$
$798$		0			0
$799$	9.00000	−	5.19615i	0.318397	−	0.183827i
$800$		−	10.3923i		−	0.367423i
$801$	6.00000	−	3.46410i	0.212000	−	0.122398i
$802$	1.50000	−	2.59808i	0.0529668	−	0.0917413i
$803$		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
$808$		−	5.19615i		−	0.182800i
$809$	33.0000			1.16022			0.580109	−	0.814539i	$-0.303010\pi$
$809$	33.0000			1.16022			0.580109	+	0.814539i	$0.303010\pi$
$810$	−33.0000			−1.15950
$811$		−	38.1051i		−	1.33805i	−0.743239	−	0.669026i	$-0.766712\pi$
$811$		−	38.1051i		−	1.33805i	0.743239	−	0.669026i	$-0.233288\pi$
$812$		0			0
$813$	−36.0000	+	20.7846i	−1.26258	+	0.728948i
$814$		0			0
$815$	−18.0000	+	31.1769i	−0.630512	+	1.09208i
$816$	30.0000			1.05021
$817$	−24.0000	+	13.8564i	−0.839654	+	0.484774i
$818$	−27.0000			−0.944033
$819$		0			0
$820$	−9.00000			−0.314294
$821$	36.0000	−	20.7846i	1.25641	−	0.725388i	0.284034	−	0.958814i	$-0.408327\pi$
$821$	36.0000	−	20.7846i	1.25641	−	0.725388i	0.972375	+	0.233426i	$0.0749938\pi$
$822$	54.0000			1.88347
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	−0.829060	−	0.559159i	$-0.811124\pi$
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	0.898776	+	0.438408i	$0.144457\pi$
$824$	15.0000	+	8.66025i	0.522550	+	0.301694i
$825$		0			0
$826$		0			0
$827$			20.7846i			0.722752i	0.932420	+	0.361376i	$0.117693\pi$
$827$			20.7846i			0.722752i	−0.932420	+	0.361376i	$0.882307\pi$
$828$	6.00000			0.208514
$829$	25.0000			0.868286			0.434143	−	0.900844i	$-0.357051\pi$
$829$	25.0000			0.868286			0.434143	+	0.900844i	$0.357051\pi$
$830$			41.5692i			1.44289i
$831$	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
$835$	−12.0000	−	20.7846i	−0.415277	−	0.719281i
$836$		0			0
$837$	−12.0000	+	6.92820i	−0.414781	+	0.239474i
$838$			31.1769i			1.07699i
$839$	39.0000	−	22.5167i	1.34643	−	0.777361i	0.358688	−	0.933458i	$-0.383224\pi$
$839$	39.0000	−	22.5167i	1.34643	−	0.777361i	0.987742	+	0.156096i	$0.0498910\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	13.5000	+	23.3827i	0.465241	+	0.805821i
$843$		−	45.0333i		−	1.55103i
$844$	5.00000	+	8.66025i	0.172107	+	0.298098i
$845$	−12.0000	+	19.0526i	−0.412813	+	0.655428i
$846$	6.00000			0.206284
$847$		0			0
$848$	−7.50000	+	12.9904i	−0.257551	+	0.446092i
$849$	8.00000			0.274559
$850$	−9.00000	+	5.19615i	−0.308697	+	0.178227i
$851$	−45.0000	−	25.9808i	−1.54258	−	0.890609i
$852$		−	6.92820i		−	0.237356i
$853$			25.9808i			0.889564i	0.895639	+	0.444782i	$0.146719\pi$
$853$			25.9808i			0.889564i	−0.895639	+	0.444782i	$0.853281\pi$
$854$		0			0
$855$	3.00000	−	5.19615i	0.102598	−	0.177705i
$856$	9.00000	−	5.19615i	0.307614	−	0.177601i
$857$	−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	0.849370	−	0.527797i	$-0.176982\pi$
$863$	24.0000	+	13.8564i	0.816970	+	0.471678i	−0.0324008	+	0.999475i	$0.510315\pi$
$864$	−18.0000	−	10.3923i	−0.612372	−	0.353553i
$865$	9.00000	+	5.19615i	0.306009	+	0.176674i
$866$	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
$871$	−9.00000	+	8.66025i	−0.304953	+	0.293442i
$872$	−12.0000	−	20.7846i	−0.406371	−	0.703856i
$873$	6.00000	−	3.46410i	0.203069	−	0.117242i
$874$	18.0000	−	31.1769i	0.608859	−	1.05457i
$875$		0			0
$876$		−	3.46410i		−	0.117041i
$877$			12.1244i			0.409410i	0.978824	+	0.204705i	$0.0656236\pi$
$877$			12.1244i			0.409410i	−0.978824	+	0.204705i	$0.934376\pi$
$878$	42.0000	+	24.2487i	1.41743	+	0.818354i
$879$	9.00000	−	5.19615i	0.303562	−	0.175262i
$880$		0			0
$881$	−13.5000	+	23.3827i	−0.454827	+	0.787783i	−0.998678	−	0.0513987i	$-0.983632\pi$
$881$	−13.5000	+	23.3827i	−0.454827	+	0.787783i	0.543852	+	0.839181i	$0.316965\pi$
$882$		0			0
$883$	10.0000			0.336527			0.168263	−	0.985742i	$-0.446184\pi$
$883$	10.0000			0.336527			0.168263	+	0.985742i	$0.446184\pi$
$884$	−3.00000	+	10.3923i	−0.100901	+	0.349531i
$885$	−12.0000	−	20.7846i	−0.403376	−	0.698667i
$886$		−	20.7846i		−	0.698273i
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	−0.992149	−	0.125061i	$-0.960087\pi$
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	0.387768	−	0.921757i	$-0.373246\pi$
$888$	−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
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$	−33.0000	−	57.1577i	−1.10369	−	1.91164i
$895$		0			0
$896$		0			0
$897$	12.0000	−	41.5692i	0.400668	−	1.38796i
$898$	−6.00000	+	10.3923i	−0.200223	+	0.346796i
$899$			10.3923i			0.346603i
$900$	−2.00000			−0.0666667
$901$	9.00000			0.299833
$902$		0			0
$903$		0			0
$904$	−22.5000	+	12.9904i	−0.748339	+	0.432054i
$905$	16.5000	+	9.52628i	0.548479	+	0.316664i
$906$	30.0000	−	51.9615i	0.996683	−	1.72631i
$907$	28.0000			0.929725			0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000			0.929725			0.464862	+	0.885383i	$0.346104\pi$
$908$	−21.0000	+	12.1244i	−0.696909	+	0.402361i
$909$	−3.00000			−0.0995037
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	30.0000	−	17.3205i	0.993399	−	0.573539i
$913$		0			0
$914$	−1.50000	+	2.59808i	−0.0496156	+	0.0859367i
$915$	3.00000	+	1.73205i	0.0991769	+	0.0572598i
$916$		0			0
$917$		0			0
$918$			20.7846i			0.685994i
$919$	22.0000			0.725713			0.362857	−	0.931845i	$-0.381802\pi$
$919$	22.0000			0.725713			0.362857	+	0.931845i	$0.381802\pi$
$920$	−18.0000			−0.593442
$921$		−	34.6410i		−	1.14146i
$922$	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
$926$	12.0000	+	20.7846i	0.394344	+	0.683025i
$927$	5.00000	−	8.66025i	0.164222	−	0.284440i
$928$	−13.5000	+	7.79423i	−0.443159	+	0.255858i
$929$		−	46.7654i		−	1.53432i	−0.641455	−	0.767161i	$-0.721669\pi$
$929$		−	46.7654i		−	1.53432i	0.641455	−	0.767161i	$-0.278331\pi$
$930$	18.0000	−	10.3923i	0.590243	−	0.340777i
$931$		0			0
$932$	3.00000	+	5.19615i	0.0982683	+	0.170206i
$933$	30.0000	+	51.9615i	0.982156	+	1.70114i
$934$			20.7846i			0.680093i
$935$		0			0
$936$	4.50000	−	4.33013i	0.147087	−	0.141535i
$937$	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
$940$	6.00000			0.195698
$941$	18.0000	−	10.3923i	0.586783	−	0.338779i	−0.177041	−	0.984203i	$-0.556653\pi$
$941$	18.0000	−	10.3923i	0.586783	−	0.338779i	0.763825	+	0.645424i	$0.223319\pi$
$942$	39.0000	+	22.5167i	1.27069	+	0.733632i
$943$		−	31.1769i		−	1.01526i
$944$		−	34.6410i		−	1.12747i
$945$		0			0
$946$		0			0
$947$	15.0000	−	8.66025i	0.487435	−	0.281420i	−0.236075	−	0.971735i	$-0.575861\pi$
$947$	15.0000	−	8.66025i	0.487435	−	0.281420i	0.723510	+	0.690314i	$0.242528\pi$
$948$	4.00000	+	6.92820i	0.129914	+	0.225018i
$949$	−6.00000	−	1.73205i	−0.194768	−	0.0562247i
$950$	−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	0.910516	−	0.413473i	$-0.135685\pi$
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	−0.813337	+	0.581793i	$0.802351\pi$
$954$	4.50000	+	2.59808i	0.145693	+	0.0841158i
$955$	27.0000	+	15.5885i	0.873699	+	0.504431i
$956$	−18.0000	−	10.3923i	−0.582162	−	0.336111i
$957$		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
$962$	52.5000	−	12.9904i	1.69267	−	0.418827i
$963$	−3.00000	−	5.19615i	−0.0966736	−	0.167444i
$964$	1.50000	−	0.866025i	0.0483117	−	0.0278928i
$965$	−4.50000	+	7.79423i	−0.144860	+	0.250905i
$966$		0			0
$967$			58.8897i			1.89377i	0.321578	+	0.946883i	$0.395787\pi$
$967$			58.8897i			1.89377i	−0.321578	+	0.946883i	$0.604213\pi$
$968$			19.0526i			0.612372i
$969$	−18.0000	−	10.3923i	−0.578243	−	0.333849i
$970$	18.0000	−	10.3923i	0.577945	−	0.333677i
$971$	6.00000			0.192549			0.0962746	−	0.995355i	$-0.469307\pi$
$971$	6.00000			0.192549			0.0962746	+	0.995355i	$0.469307\pi$
$972$	−5.00000	+	8.66025i	−0.160375	+	0.277778i
$973$		0			0
$974$	12.0000			0.384505
$975$	−4.00000	+	13.8564i	−0.128103	+	0.443760i
$976$	2.50000	+	4.33013i	0.0800230	+	0.138604i
$977$		−	43.3013i		−	1.38533i	−0.721259	−	0.692665i	$-0.756436\pi$
$977$		−	43.3013i		−	1.38533i	0.721259	−	0.692665i	$-0.243564\pi$
$978$	36.0000	+	62.3538i	1.15115	+	1.99386i
$979$		0			0
$980$		0			0
$981$	−12.0000	+	6.92820i	−0.383131	+	0.221201i
$982$			20.7846i			0.663264i
$983$	45.0000	−	25.9808i	1.43528	−	0.828658i	0.437761	−	0.899092i	$-0.355772\pi$
$983$	45.0000	−	25.9808i	1.43528	−	0.828658i	0.997516	+	0.0704339i	$0.0224384\pi$
$984$	9.00000	−	15.5885i	0.286910	−	0.496942i
$985$	12.0000	+	20.7846i	0.382352	+	0.662253i
$986$	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
$991$	2.00000			0.0635321			0.0317660	−	0.999495i	$-0.489887\pi$
$991$	2.00000			0.0635321			0.0317660	+	0.999495i	$0.489887\pi$
$992$	18.0000			0.571501
$993$		−	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
$997$	−8.50000	+	14.7224i	−0.269198	+	0.466264i	−0.968655	−	0.248410i	$-0.920092\pi$
$997$	−8.50000	+	14.7224i	−0.269198	+	0.466264i	0.699457	+	0.714675i	$0.253425\pi$
$998$	−54.0000			−1.70934
$999$	30.0000	−	17.3205i	0.949158	−	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.c.30.1		2
7.2	even	3		13.2.e.a.4.1	✓	2
7.3	odd	6		637.2.k.c.459.1		2
7.4	even	3		637.2.k.a.459.1		2
7.5	odd	6		637.2.q.a.589.1		2
7.6	odd	2		637.2.u.b.30.1		2
13.10	even	6		637.2.k.a.569.1		2
21.2	odd	6		117.2.q.c.82.1		2
28.23	odd	6		208.2.w.b.17.1		2
35.2	odd	12		325.2.m.a.199.2		4
35.9	even	6		325.2.n.a.251.1		2
35.23	odd	12		325.2.m.a.199.1		4
56.37	even	6		832.2.w.d.641.1		2
56.51	odd	6		832.2.w.a.641.1		2
84.23	even	6		1872.2.by.d.433.1		2
91.2	odd	12		169.2.c.a.146.1		4
91.9	even	3		169.2.b.a.168.2		2
91.10	odd	6		637.2.u.b.361.1		2
91.16	even	3		169.2.e.a.23.1		2
91.19	even	12		8281.2.a.q.1.2		2
91.23	even	6		13.2.e.a.10.1	yes	2
91.30	even	6		169.2.b.a.168.1		2
91.33	even	12		8281.2.a.q.1.1		2
91.37	odd	12		169.2.c.a.146.2		4
91.44	odd	12		169.2.c.a.22.1		4
91.51	even	6		169.2.e.a.147.1		2
91.58	odd	12		169.2.a.a.1.2		2
91.62	odd	6		637.2.k.c.569.1		2
91.72	odd	12		169.2.a.a.1.1		2
91.75	odd	6		637.2.q.a.491.1		2
91.86	odd	12		169.2.c.a.22.2		4
91.88	even	6	inner	637.2.u.c.361.1		2
273.23	odd	6		117.2.q.c.10.1		2
273.149	even	12		1521.2.a.k.1.1		2
273.191	odd	6		1521.2.b.a.1351.1		2
273.212	odd	6		1521.2.b.a.1351.2		2
273.254	even	12		1521.2.a.k.1.2		2
364.23	odd	6		208.2.w.b.49.1		2
364.163	even	12		2704.2.a.o.1.2		2
364.191	odd	6		2704.2.f.b.337.1		2
364.303	odd	6		2704.2.f.b.337.2		2
364.331	even	12		2704.2.a.o.1.1		2
455.23	odd	12		325.2.m.a.49.2		4
455.114	even	6		325.2.n.a.101.1		2
455.149	odd	12		4225.2.a.v.1.1		2
455.254	odd	12		4225.2.a.v.1.2		2
455.387	odd	12		325.2.m.a.49.1		4
728.205	even	6		832.2.w.d.257.1		2
728.387	odd	6		832.2.w.a.257.1		2
1092.23	even	6		1872.2.by.d.1297.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.2.e.a.4.1	✓	2	7.2	even	3
13.2.e.a.10.1	yes	2	91.23	even	6
117.2.q.c.10.1		2	273.23	odd	6
117.2.q.c.82.1		2	21.2	odd	6
169.2.a.a.1.1		2	91.72	odd	12
169.2.a.a.1.2		2	91.58	odd	12
169.2.b.a.168.1		2	91.30	even	6
169.2.b.a.168.2		2	91.9	even	3
169.2.c.a.22.1		4	91.44	odd	12
169.2.c.a.22.2		4	91.86	odd	12
169.2.c.a.146.1		4	91.2	odd	12
169.2.c.a.146.2		4	91.37	odd	12
169.2.e.a.23.1		2	91.16	even	3
169.2.e.a.147.1		2	91.51	even	6
208.2.w.b.17.1		2	28.23	odd	6
208.2.w.b.49.1		2	364.23	odd	6
325.2.m.a.49.1		4	455.387	odd	12
325.2.m.a.49.2		4	455.23	odd	12
325.2.m.a.199.1		4	35.23	odd	12
325.2.m.a.199.2		4	35.2	odd	12
325.2.n.a.101.1		2	455.114	even	6
325.2.n.a.251.1		2	35.9	even	6
637.2.k.a.459.1		2	7.4	even	3
637.2.k.a.569.1		2	13.10	even	6
637.2.k.c.459.1		2	7.3	odd	6
637.2.k.c.569.1		2	91.62	odd	6
637.2.q.a.491.1		2	91.75	odd	6
637.2.q.a.589.1		2	7.5	odd	6
637.2.u.b.30.1		2	7.6	odd	2
637.2.u.b.361.1		2	91.10	odd	6
637.2.u.c.30.1		2	1.1	even	1	trivial
637.2.u.c.361.1		2	91.88	even	6	inner
832.2.w.a.257.1		2	728.387	odd	6
832.2.w.a.641.1		2	56.51	odd	6
832.2.w.d.257.1		2	728.205	even	6
832.2.w.d.641.1		2	56.37	even	6
1521.2.a.k.1.1		2	273.149	even	12
1521.2.a.k.1.2		2	273.254	even	12
1521.2.b.a.1351.1		2	273.191	odd	6
1521.2.b.a.1351.2		2	273.212	odd	6
1872.2.by.d.433.1		2	84.23	even	6
1872.2.by.d.1297.1		2	1092.23	even	6
2704.2.a.o.1.1		2	364.331	even	12
2704.2.a.o.1.2		2	364.163	even	12
2704.2.f.b.337.1		2	364.191	odd	6
2704.2.f.b.337.2		2	364.303	odd	6
4225.2.a.v.1.1		2	455.149	odd	12
4225.2.a.v.1.2		2	455.254	odd	12
8281.2.a.q.1.1		2	91.33	even	12
8281.2.a.q.1.2		2	91.19	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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{2} +2.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +(3.00000 - 1.73205i) q^{6} +1.73205i q^{8} +1.00000 q^{9} +3.00000 q^{10} +(1.00000 - 1.73205i) q^{12} +(-2.50000 - 2.59808i) q^{13} +(3.00000 + 1.73205i) q^{15} +(2.50000 + 4.33013i) q^{16} +(1.50000 - 2.59808i) q^{17} +(1.50000 - 0.866025i) q^{18} -3.46410i q^{19} +(1.50000 - 0.866025i) q^{20} +(3.00000 + 5.19615i) q^{23} +3.46410i q^{24} +(-1.00000 - 1.73205i) q^{25} +(-6.00000 - 1.73205i) q^{26} -4.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} +6.00000 q^{30} +(3.00000 - 1.73205i) q^{31} +(4.50000 + 2.59808i) q^{32} -5.19615i q^{34} +(0.500000 - 0.866025i) q^{36} +(-7.50000 + 4.33013i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-5.00000 - 5.19615i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(-4.50000 - 2.59808i) q^{41} +(-4.00000 - 6.92820i) q^{43} +(1.50000 + 0.866025i) q^{45} +(9.00000 + 5.19615i) q^{46} +(3.00000 + 1.73205i) q^{47} +(5.00000 + 8.66025i) q^{48} +(-3.00000 - 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(-3.50000 + 0.866025i) q^{52} +(1.50000 + 2.59808i) q^{53} +(-6.00000 + 3.46410i) q^{54} -6.92820i q^{57} +5.19615i q^{58} +(-6.00000 - 3.46410i) q^{59} +(3.00000 - 1.73205i) q^{60} +1.00000 q^{61} +(3.00000 - 5.19615i) q^{62} -1.00000 q^{64} +(-1.50000 - 6.06218i) q^{65} -3.46410i q^{67} +(-1.50000 - 2.59808i) q^{68} +(6.00000 + 10.3923i) q^{69} +(3.00000 - 1.73205i) q^{71} +1.73205i q^{72} +(1.50000 - 0.866025i) q^{73} +(-7.50000 + 12.9904i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(-3.00000 - 1.73205i) q^{76} +(-12.0000 - 3.46410i) q^{78} +(-2.00000 + 3.46410i) q^{79} +8.66025i q^{80} -11.0000 q^{81} -9.00000 q^{82} +13.8564i q^{83} +(4.50000 - 2.59808i) q^{85} +(-12.0000 - 6.92820i) q^{86} +(-3.00000 + 5.19615i) q^{87} +(6.00000 - 3.46410i) q^{89} +3.00000 q^{90} +6.00000 q^{92} +(6.00000 - 3.46410i) q^{93} +6.00000 q^{94} +(3.00000 - 5.19615i) q^{95} +(9.00000 + 5.19615i) q^{96} +(6.00000 - 3.46410i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 4 q^{3} + q^{4} + 3 q^{5} + 6 q^{6} + 2 q^{9} + 6 q^{10} + 2 q^{12} - 5 q^{13} + 6 q^{15} + 5 q^{16} + 3 q^{17} + 3 q^{18} + 3 q^{20} + 6 q^{23} - 2 q^{25} - 12 q^{26} - 8 q^{27} - 3 q^{29}+ \cdots + 12 q^{97}+O(q^{100}) \) 2 * q + 3 * q^2 + 4 * q^3 + q^4 + 3 * q^5 + 6 * q^6 + 2 * q^9 + 6 * q^10 + 2 * q^12 - 5 * q^13 + 6 * q^15 + 5 * q^16 + 3 * q^17 + 3 * q^18 + 3 * q^20 + 6 * q^23 - 2 * q^25 - 12 * q^26 - 8 * q^27 - 3 * q^29 + 12 * q^30 + 6 * q^31 + 9 * q^32 + q^36 - 15 * q^37 - 6 * q^38 - 10 * q^39 - 3 * q^40 - 9 * q^41 - 8 * q^43 + 3 * q^45 + 18 * q^46 + 6 * q^47 + 10 * q^48 - 6 * q^50 + 6 * q^51 - 7 * q^52 + 3 * q^53 - 12 * q^54 - 12 * q^59 + 6 * q^60 + 2 * q^61 + 6 * q^62 - 2 * q^64 - 3 * q^65 - 3 * q^68 + 12 * q^69 + 6 * q^71 + 3 * q^73 - 15 * q^74 - 4 * q^75 - 6 * q^76 - 24 * q^78 - 4 * q^79 - 22 * q^81 - 18 * q^82 + 9 * q^85 - 24 * q^86 - 6 * q^87 + 12 * q^89 + 6 * q^90 + 12 * q^92 + 12 * q^93 + 12 * q^94 + 6 * q^95 + 18 * q^96 + 12 * q^97

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