LMFDB - Embedded newform 637.2.u.c.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			361.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	637.361
Dual form			637.2.u.c.30.1

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.925615	−	0.378467i	$-0.123549\pi$
$2$	1.50000	+	0.866025i	1.06066	+	0.612372i	0.135045	+	0.990839i	$0.456882\pi$
$3$	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	−0.125567	−	0.992085i	$-0.540075\pi$
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	0.796387	+	0.604787i	$0.206742\pi$
$6$	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	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$	1.50000	+	0.866025i	0.353553	+	0.204124i
$19$			3.46410i			0.794719i	0.917663	+	0.397360i	$0.130073\pi$
$19$			3.46410i			0.794719i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	1.50000	+	0.866025i	0.335410	+	0.193649i
$21$		0			0
$22$		0			0
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		−	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	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$	6.00000			1.09545
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	0.744599	−	0.667512i	$-0.232641\pi$
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	−0.205783	+	0.978598i	$0.565974\pi$
$32$	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	−0.265340	−	0.964155i	$-0.585484\pi$
$37$	−7.50000	−	4.33013i	−1.23299	−	0.711868i	−0.967653	+	0.252286i	$0.918817\pi$
$38$	−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	−0.808383	−	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
$45$	1.50000	−	0.866025i	0.223607	−	0.129099i
$46$	9.00000	−	5.19615i	1.32698	−	0.766131i
$47$	3.00000	−	1.73205i	0.437595	−	0.252646i	−0.264982	−	0.964253i	$-0.585366\pi$
$47$	3.00000	−	1.73205i	0.437595	−	0.252646i	0.702577	+	0.711608i	$0.252033\pi$
$48$	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	−0.744423	−	0.667708i	$-0.767275\pi$
$53$	1.50000	−	2.59808i	0.206041	−	0.356873i	0.950464	+	0.310835i	$0.100609\pi$
$54$	−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	−0.836832	−	0.547460i	$-0.815595\pi$
$59$	−6.00000	+	3.46410i	−0.781133	+	0.450988i	0.0556984	+	0.998448i	$0.482261\pi$
$60$	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	$0.0678686\pi$
$67$			3.46410i			0.423207i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−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	0.667340	−	0.744753i	$-0.267433\pi$
$71$	3.00000	+	1.73205i	0.356034	+	0.205557i	−0.311305	+	0.950310i	$0.600766\pi$
$72$		−	1.73205i		−	0.204124i
$73$	1.50000	+	0.866025i	0.175562	+	0.101361i	0.585206	−	0.810885i	$-0.301014\pi$
$73$	1.50000	+	0.866025i	0.175562	+	0.101361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$	−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	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		−	8.66025i		−	0.968246i
$81$	−11.0000			−1.22222
$82$	−9.00000			−0.993884
$83$		−	13.8564i		−	1.52094i	−0.649374	−	0.760469i	$-0.724969\pi$
$83$		−	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
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$		0			0
$89$	6.00000	+	3.46410i	0.635999	+	0.367194i	0.783072	−	0.621932i	$-0.213652\pi$
$89$	6.00000	+	3.46410i	0.635999	+	0.367194i	−0.147073	+	0.989126i	$0.546985\pi$
$90$	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	0.772655	−	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
$100$	−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	0.999964	−	0.00844953i	$-0.00268960\pi$
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	−0.507300	+	0.861770i	$0.669356\pi$
$104$	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	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$	−2.00000	−	3.46410i	−0.192450	−	0.333333i
$109$	−12.0000	−	6.92820i	−1.14939	−	0.663602i	−0.200653	−	0.979662i	$-0.564306\pi$
$109$	−12.0000	−	6.92820i	−1.14939	−	0.663602i	−0.948739	+	0.316061i	$0.897640\pi$
$110$		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	$-0.0826291\pi$
$114$	−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	0.906977	−	0.421180i	$-0.138384\pi$
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	−0.818241	+	0.574875i	$0.805051\pi$
$128$	−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	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$		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	0.203674	−	0.979039i	$-0.434712\pi$
$137$	13.5000	−	7.79423i	1.15338	−	0.665906i	0.949709	+	0.313133i	$0.101379\pi$
$138$	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
$145$	−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	$0.284996\pi$
$149$			19.0526i			1.56085i	−0.625252	+	0.780423i	$0.715004\pi$
$150$	−6.00000	+	3.46410i	−0.489898	+	0.282843i
$151$	15.0000	+	8.66025i	1.22068	+	0.704761i	0.965064	−	0.262016i	$-0.0843873\pi$
$151$	15.0000	+	8.66025i	1.22068	+	0.704761i	0.255619	+	0.966778i	$0.417721\pi$
$152$	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	−0.481006	−	0.876717i	$-0.659728\pi$
$157$	6.50000	−	11.2583i	0.518756	−	0.898513i	0.999762	−	0.0217953i	$-0.00693820\pi$
$158$		−	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	$-0.697292\pi$
$163$		−	20.7846i		−	1.62798i	0.580881	−	0.813988i	$-0.302708\pi$
$164$	−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	−0.886365	−	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
$171$			3.46410i			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	$-0.940119\pi$
$193$		−	5.19615i		−	0.374027i	0.982357	−	0.187014i	$-0.0598809\pi$
$194$	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
$199$	1.00000	+	1.73205i	0.0708881	+	0.122782i	0.899291	−	0.437351i	$-0.144083\pi$
$199$	1.00000	+	1.73205i	0.0708881	+	0.122782i	−0.828403	+	0.560133i	$0.810750\pi$
$200$	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	0.640996	−	0.767544i	$-0.278521\pi$
$211$	−5.00000	−	8.66025i	−0.344214	−	0.596196i	−0.985211	+	0.171347i	$0.945188\pi$
$212$	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	−0.770097	−	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
$227$	−21.0000	+	12.1244i	−1.39382	+	0.804722i	−0.993736	−	0.111757i	$-0.964352\pi$
$227$	−21.0000	+	12.1244i	−1.39382	+	0.804722i	−0.400083	+	0.916479i	$0.631019\pi$
$228$	−6.00000	+	3.46410i	−0.397360	+	0.229416i
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$	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	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$	−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	$0.234660\pi$
$239$			20.7846i			1.34444i	−0.740349	+	0.672222i	$0.765340\pi$
$240$		−	17.3205i		−	1.11803i
$241$	1.50000	−	0.866025i	0.0966235	−	0.0557856i	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	1.50000	−	0.866025i	0.0966235	−	0.0557856i	0.547533	+	0.836784i	$0.315567\pi$
$242$	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	−0.428681	−	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
$254$			3.46410i			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	−0.909010	−	0.416775i	$-0.863160\pi$
$257$	−1.50000	+	2.59808i	−0.0935674	+	0.162064i	0.815442	+	0.578838i	$0.196494\pi$
$258$	−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	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$	−12.0000			−0.730297
$271$	−18.0000	−	10.3923i	−1.09342	−	0.631288i	−0.158937	−	0.987289i	$-0.550807\pi$
$271$	−18.0000	−	10.3923i	−1.09342	−	0.631288i	−0.934485	+	0.356001i	$0.884140\pi$
$272$	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	0.951807	−	0.306699i	$-0.0992243\pi$
$277$	3.50000	+	6.06218i	0.210295	+	0.364241i	−0.741512	+	0.670940i	$0.765891\pi$
$278$	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	$0.765601\pi$
$282$	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	0.625653	−	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
$296$	−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	$0.164563\pi$
$307$			17.3205i			0.988534i	−0.869310	+	0.494267i	$0.835437\pi$
$308$		0			0
$309$	10.0000	+	17.3205i	0.568880	+	0.985329i
$310$	9.00000	+	5.19615i	0.511166	+	0.295122i
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	−0.0301210	−	0.999546i	$-0.509589\pi$
$311$	15.0000	−	25.9808i	0.850572	−	1.47323i	0.880693	−	0.473688i	$-0.157077\pi$
$312$	9.00000	+	8.66025i	0.509525	+	0.490290i
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	0.689412	−	0.724370i	$-0.257869\pi$
$313$	−5.00000	−	8.66025i	−0.282617	−	0.489506i	−0.972028	+	0.234863i	$0.924536\pi$
$314$	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	$-0.620052\pi$
$317$	4.50000	−	2.59808i	0.252745	−	0.145922i	0.621021	+	0.783794i	$0.286718\pi$
$318$	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	$0.275594\pi$
$331$			27.7128i			1.52323i	−0.648027	+	0.761617i	$0.724406\pi$
$332$	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	0.916127	+	0.400887i	$0.131298\pi$
$347$	15.0000	+	25.9808i	0.805242	+	1.39472i	−0.110885	+	0.993833i	$0.535369\pi$
$348$	3.00000	−	5.19615i	0.160817	−	0.278543i
$349$	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
$353$			32.9090i			1.75157i	0.482704	+	0.875784i	$0.339655\pi$
$353$			32.9090i			1.75157i	−0.482704	+	0.875784i	$0.660345\pi$
$354$	−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	−0.333238	−	0.942843i	$-0.608141\pi$
$359$	6.00000	−	3.46410i	0.316668	−	0.182828i	0.649906	+	0.760014i	$0.274808\pi$
$360$	−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	−0.930545	−	0.366178i	$-0.880666\pi$
$379$	−21.0000	+	12.1244i	−1.07870	+	0.622786i	−0.148153	+	0.988964i	$0.547333\pi$
$380$	−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	$0.178192\pi$
$383$			20.7846i			1.06204i	−0.847358	+	0.531022i	$0.821808\pi$
$384$	−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	−0.729103	−	0.684403i	$-0.760063\pi$
$389$	4.50000	−	7.79423i	0.228159	−	0.395183i	0.957263	+	0.289220i	$0.0933960\pi$
$390$	−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	$0.113043\pi$
$397$			13.8564i			0.695433i	−0.937600	+	0.347717i	$0.886957\pi$
$398$			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	0.536985	−	0.843592i	$-0.319563\pi$
$401$	1.50000	+	0.866025i	0.0749064	+	0.0432472i	−0.462079	+	0.886839i	$0.652896\pi$
$402$	−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	−0.795141	−	0.606425i	$-0.792603\pi$
$409$	−13.5000	+	7.79423i	−0.667532	+	0.385400i	0.127609	+	0.991825i	$0.459270\pi$
$410$	−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	0.557986	−	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	$-0.124030\pi$
$422$		−	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	$-0.946637\pi$
$431$		−	6.92820i		−	0.333720i	0.985981	−	0.166860i	$-0.0533628\pi$
$432$	−10.0000	+	17.3205i	−0.481125	+	0.833333i
$433$	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
$436$		−	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	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$		0			0
$441$		0			0
$442$	−13.5000	−	12.9904i	−0.642130	−	0.617889i
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	0.972626	−	0.232377i	$-0.0746503\pi$
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	−0.687557	+	0.726130i	$0.741317\pi$
$444$		−	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	0.351694	−	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
$452$	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	0.464506	−	0.885570i	$-0.346232\pi$
$457$	−1.50000	−	0.866025i	−0.0701670	−	0.0405110i	−0.534673	+	0.845059i	$0.679565\pi$
$458$		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	0.879853	−	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	$-0.104349\pi$
$464$	−15.0000			−0.696358
$465$	12.0000			0.556487
$466$		−	10.3923i		−	0.481414i
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	0.693153	−	0.720791i	$-0.256221\pi$
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	−0.970799	+	0.239892i	$0.922888\pi$
$468$	−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	$0.186890\pi$
$479$			24.2487i			1.10795i	−0.832533	+	0.553976i	$0.813110\pi$
$480$	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	−0.357858	−	0.933776i	$-0.616493\pi$
$487$	6.00000	−	3.46410i	0.271886	−	0.156973i	0.629744	+	0.776802i	$0.283160\pi$
$488$		−	1.73205i		−	0.0784063i
$489$		−	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	$0.920614\pi$
$492$	−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	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−27.0000	+	15.5885i	−1.20869	+	0.697835i	−0.246214	+	0.969216i	$0.579187\pi$
$500$	−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	0.115332	+	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
$507$	−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	0.0875661	−	0.996159i	$-0.472091\pi$
$509$	−16.5000	−	9.52628i	−0.731350	−	0.422245i	−0.818916	+	0.573914i	$0.805424\pi$
$510$	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	−0.947603	−	0.319451i	$-0.896501\pi$
$521$	−4.50000	+	7.79423i	−0.197149	+	0.341471i	0.750454	+	0.660922i	$0.229835\pi$
$522$		−	5.19615i		−	0.227429i
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	−0.636401	−	0.771358i	$-0.719578\pi$
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	0.986216	+	0.165460i	$0.0529109\pi$
$524$	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	−0.935255	−	0.353975i	$-0.884830\pi$
$541$	−25.5000	+	14.7224i	−1.09633	+	0.632967i	−0.161076	+	0.986942i	$0.551496\pi$
$542$	−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	$-0.892866\pi$
$557$		−	15.5885i		−	0.660504i	0.943893	−	0.330252i	$-0.107134\pi$
$558$	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	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$	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	0.0294311	−	0.999567i	$-0.490630\pi$
$569$	21.0000	−	36.3731i	0.880366	−	1.52484i	0.850935	−	0.525271i	$-0.176036\pi$
$570$			20.7846i			0.870572i
$571$	−20.0000	+	34.6410i	−0.836974	+	1.44968i	0.0554391	+	0.998462i	$0.482344\pi$
$571$	−20.0000	+	34.6410i	−0.836974	+	1.44968i	−0.892413	+	0.451219i	$0.850989\pi$
$572$		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	0.115547	−	0.993302i	$-0.463138\pi$
$577$	−16.5000	−	9.52628i	−0.686904	−	0.396584i	−0.802451	+	0.596718i	$0.796471\pi$
$578$	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	−0.823137	−	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
$591$	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	0.0390666	−	0.999237i	$-0.487562\pi$
$593$	22.5000	−	12.9904i	0.923964	−	0.533451i	0.884898	+	0.465786i	$0.154228\pi$
$594$		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	0.377869	+	0.925859i	$0.376657\pi$
$599$	−15.0000	+	25.9808i	−0.612883	+	1.06155i	−0.990752	+	0.135686i	$0.956676\pi$
$600$	6.00000	+	3.46410i	0.244949	+	0.141421i
$601$	−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
$604$			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	$-0.921262\pi$
$613$		−	12.1244i		−	0.489698i	0.969561	−	0.244849i	$-0.0787384\pi$
$614$	−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	0.0531732	−	0.998585i	$-0.483066\pi$
$617$	−19.5000	−	11.2583i	−0.785040	−	0.453243i	−0.838214	+	0.545342i	$0.816400\pi$
$618$			34.6410i			1.39347i
$619$	−18.0000	−	10.3923i	−0.723481	−	0.417702i	0.0925515	−	0.995708i	$-0.470498\pi$
$619$	−18.0000	−	10.3923i	−0.723481	−	0.417702i	−0.816033	+	0.578006i	$0.803831\pi$
$620$	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	−0.966521	−	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
$633$	−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	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$	−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
$646$	−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	−0.407628	−	0.913148i	$-0.633644\pi$
$653$	15.0000	−	25.9808i	0.586995	−	1.01671i	0.994623	−	0.103558i	$-0.0330227\pi$
$654$	−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	−0.725175	−	0.688565i	$-0.758241\pi$
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	0.958902	+	0.283738i	$0.0915745\pi$
$660$		0			0
$661$		−	46.7654i		−	1.81896i	−0.415745	−	0.909481i	$-0.636479\pi$
$661$		−	46.7654i		−	1.81896i	0.415745	−	0.909481i	$-0.363521\pi$
$662$	−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	0.988968	−	0.148132i	$-0.0473259\pi$
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	−0.622770	+	0.782405i	$0.713993\pi$
$674$	−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	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$	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	−0.844708	−	0.535227i	$-0.820226\pi$
$683$	−21.0000	+	12.1244i	−0.803543	+	0.463926i	0.0411658	+	0.999152i	$0.486893\pi$
$684$	−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	0.254071	−	0.967186i	$-0.418230\pi$
$691$	−12.0000	−	6.92820i	−0.456502	−	0.263561i	−0.710572	+	0.703624i	$0.751564\pi$
$692$	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	$0.0311079\pi$
$709$			5.19615i			0.195146i	−0.995228	+	0.0975728i	$0.968892\pi$
$710$	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	−0.681218	−	0.732081i	$-0.738549\pi$
$733$	−10.5000	+	6.06218i	−0.387826	+	0.223912i	0.293392	+	0.955992i	$0.405216\pi$
$734$	−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	$-0.875137\pi$
$739$		−	20.7846i		−	0.764574i	0.924044	−	0.382287i	$-0.124863\pi$
$740$	−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	$0.552510\pi$
$744$	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	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$		−	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	0.999505	−	0.0314762i	$-0.0100208\pi$
$757$	13.0000	+	22.5167i	0.472493	+	0.818382i	−0.527011	+	0.849858i	$0.676688\pi$
$758$	−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	$-0.783928\pi$
$761$		−	34.6410i		−	1.25574i	0.778320	−	0.627868i	$-0.216072\pi$
$762$			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	−0.387901	−	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
$773$	30.0000	−	17.3205i	1.07903	−	0.622975i	0.148392	−	0.988929i	$-0.452590\pi$
$773$	30.0000	−	17.3205i	1.07903	−	0.622975i	0.930633	+	0.365953i	$0.119257\pi$
$774$	−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	−0.955161	−	0.296087i	$-0.904318\pi$
$787$	−33.0000	+	19.0526i	−1.17632	+	0.679150i	−0.221162	+	0.975237i	$0.570985\pi$
$788$	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	0.206868	+	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
$800$			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	$0.233288\pi$
$811$			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
$815$	−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	0.972375	−	0.233426i	$-0.0749938\pi$
$821$	36.0000	+	20.7846i	1.25641	+	0.725388i	0.284034	+	0.958814i	$0.408327\pi$
$822$	54.0000			1.88347
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	0.898776	−	0.438408i	$-0.144457\pi$
$823$	2.00000	+	3.46410i	0.0697156	+	0.120751i	−0.829060	+	0.559159i	$0.811124\pi$
$824$	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	$-0.117693\pi$
$828$	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	0.987742	−	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
$842$	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	$-0.853281\pi$
$853$		−	25.9808i		−	0.889564i	0.895639	−	0.444782i	$-0.146719\pi$
$854$		0			0
$855$	3.00000	+	5.19615i	0.102598	+	0.177705i
$856$	9.00000	+	5.19615i	0.307614	+	0.177601i
$857$	−1.50000	+	2.59808i	−0.0512390	+	0.0887486i	−0.890507	−	0.454969i	$-0.849650\pi$
$857$	−1.50000	+	2.59808i	−0.0512390	+	0.0887486i	0.839268	+	0.543718i	$0.182984\pi$
$858$		0			0
$859$	7.00000	+	12.1244i	0.238837	+	0.413678i	0.960381	−	0.278691i	$-0.0899005\pi$
$859$	7.00000	+	12.1244i	0.238837	+	0.413678i	−0.721544	+	0.692369i	$0.756567\pi$
$860$	−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	$-0.510315\pi$
$863$	24.0000	−	13.8564i	0.816970	−	0.471678i	0.849370	+	0.527797i	$0.176982\pi$
$864$	−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	$-0.934376\pi$
$877$		−	12.1244i		−	0.409410i	0.978824	−	0.204705i	$-0.0656236\pi$
$878$	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	0.543852	−	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	$0.446184\pi$
$884$	−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	0.387768	+	0.921757i	$0.373246\pi$
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	−0.992149	+	0.125061i	$0.960087\pi$
$888$	−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	$0.278331\pi$
$929$			46.7654i			1.53432i	−0.641455	+	0.767161i	$0.721669\pi$
$930$	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	0.763825	−	0.645424i	$-0.223319\pi$
$941$	18.0000	+	10.3923i	0.586783	+	0.338779i	−0.177041	+	0.984203i	$0.556653\pi$
$942$	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	0.723510	−	0.690314i	$-0.242528\pi$
$947$	15.0000	+	8.66025i	0.487435	+	0.281420i	−0.236075	+	0.971735i	$0.575861\pi$
$948$	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	−0.813337	−	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
$955$	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	$-0.604213\pi$
$967$		−	58.8897i		−	1.89377i	0.321578	−	0.946883i	$-0.395787\pi$
$968$		−	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	$0.243564\pi$
$977$			43.3013i			1.38533i	−0.721259	+	0.692665i	$0.756436\pi$
$978$	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	0.997516	−	0.0704339i	$-0.0224384\pi$
$983$	45.0000	+	25.9808i	1.43528	+	0.828658i	0.437761	+	0.899092i	$0.355772\pi$
$984$	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	0.699457	−	0.714675i	$-0.253425\pi$
$997$	−8.50000	−	14.7224i	−0.269198	−	0.466264i	−0.968655	+	0.248410i	$0.920092\pi$
$998$	−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.361.1		2
7.2	even	3		637.2.k.a.569.1		2
7.3	odd	6		637.2.q.a.491.1		2
7.4	even	3		13.2.e.a.10.1	yes	2
7.5	odd	6		637.2.k.c.569.1		2
7.6	odd	2		637.2.u.b.361.1		2
13.4	even	6		637.2.k.a.459.1		2
21.11	odd	6		117.2.q.c.10.1		2
28.11	odd	6		208.2.w.b.49.1		2
35.4	even	6		325.2.n.a.101.1		2
35.18	odd	12		325.2.m.a.49.2		4
35.32	odd	12		325.2.m.a.49.1		4
56.11	odd	6		832.2.w.a.257.1		2
56.53	even	6		832.2.w.d.257.1		2
84.11	even	6		1872.2.by.d.1297.1		2
91.4	even	6		13.2.e.a.4.1	✓	2
91.11	odd	12		169.2.a.a.1.2		2
91.17	odd	6		637.2.q.a.589.1		2
91.18	odd	12		169.2.c.a.146.2		4
91.24	even	12		8281.2.a.q.1.2		2
91.25	even	6		169.2.e.a.23.1		2
91.30	even	6	inner	637.2.u.c.30.1		2
91.32	odd	12		169.2.c.a.22.2		4
91.46	odd	12		169.2.c.a.22.1		4
91.60	odd	12		169.2.c.a.146.1		4
91.67	odd	12		169.2.a.a.1.1		2
91.69	odd	6		637.2.k.c.459.1		2
91.74	even	3		169.2.e.a.147.1		2
91.80	even	12		8281.2.a.q.1.1		2
91.81	even	3		169.2.b.a.168.1		2
91.82	odd	6		637.2.u.b.30.1		2
91.88	even	6		169.2.b.a.168.2		2
273.11	even	12		1521.2.a.k.1.1		2
273.95	odd	6		117.2.q.c.82.1		2
273.158	even	12		1521.2.a.k.1.2		2
273.179	odd	6		1521.2.b.a.1351.1		2
273.263	odd	6		1521.2.b.a.1351.2		2
364.11	even	12		2704.2.a.o.1.1		2
364.67	even	12		2704.2.a.o.1.2		2
364.95	odd	6		208.2.w.b.17.1		2
364.179	odd	6		2704.2.f.b.337.1		2
364.263	odd	6		2704.2.f.b.337.2		2
455.4	even	6		325.2.n.a.251.1		2
455.249	odd	12		4225.2.a.v.1.2		2
455.277	odd	12		325.2.m.a.199.2		4
455.284	odd	12		4225.2.a.v.1.1		2
455.368	odd	12		325.2.m.a.199.1		4
728.277	even	6		832.2.w.d.641.1		2
728.459	odd	6		832.2.w.a.641.1		2
1092.95	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	91.4	even	6
13.2.e.a.10.1	yes	2	7.4	even	3
117.2.q.c.10.1		2	21.11	odd	6
117.2.q.c.82.1		2	273.95	odd	6
169.2.a.a.1.1		2	91.67	odd	12
169.2.a.a.1.2		2	91.11	odd	12
169.2.b.a.168.1		2	91.81	even	3
169.2.b.a.168.2		2	91.88	even	6
169.2.c.a.22.1		4	91.46	odd	12
169.2.c.a.22.2		4	91.32	odd	12
169.2.c.a.146.1		4	91.60	odd	12
169.2.c.a.146.2		4	91.18	odd	12
169.2.e.a.23.1		2	91.25	even	6
169.2.e.a.147.1		2	91.74	even	3
208.2.w.b.17.1		2	364.95	odd	6
208.2.w.b.49.1		2	28.11	odd	6
325.2.m.a.49.1		4	35.32	odd	12
325.2.m.a.49.2		4	35.18	odd	12
325.2.m.a.199.1		4	455.368	odd	12
325.2.m.a.199.2		4	455.277	odd	12
325.2.n.a.101.1		2	35.4	even	6
325.2.n.a.251.1		2	455.4	even	6
637.2.k.a.459.1		2	13.4	even	6
637.2.k.a.569.1		2	7.2	even	3
637.2.k.c.459.1		2	91.69	odd	6
637.2.k.c.569.1		2	7.5	odd	6
637.2.q.a.491.1		2	7.3	odd	6
637.2.q.a.589.1		2	91.17	odd	6
637.2.u.b.30.1		2	91.82	odd	6
637.2.u.b.361.1		2	7.6	odd	2
637.2.u.c.30.1		2	91.30	even	6	inner
637.2.u.c.361.1		2	1.1	even	1	trivial
832.2.w.a.257.1		2	56.11	odd	6
832.2.w.a.641.1		2	728.459	odd	6
832.2.w.d.257.1		2	56.53	even	6
832.2.w.d.641.1		2	728.277	even	6
1521.2.a.k.1.1		2	273.11	even	12
1521.2.a.k.1.2		2	273.158	even	12
1521.2.b.a.1351.1		2	273.179	odd	6
1521.2.b.a.1351.2		2	273.263	odd	6
1872.2.by.d.433.1		2	1092.95	even	6
1872.2.by.d.1297.1		2	84.11	even	6
2704.2.a.o.1.1		2	364.11	even	12
2704.2.a.o.1.2		2	364.67	even	12
2704.2.f.b.337.1		2	364.179	odd	6
2704.2.f.b.337.2		2	364.263	odd	6
4225.2.a.v.1.1		2	455.284	odd	12
4225.2.a.v.1.2		2	455.249	odd	12
8281.2.a.q.1.1		2	91.80	even	12
8281.2.a.q.1.2		2	91.24	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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