LMFDB - Embedded newform 637.2.u.b.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.b.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	$-0.695913\pi$
$3$	−2.00000			−1.15470			−0.577350	+	0.816497i	$0.695913\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−1.50000	+	0.866025i	−0.670820	+	0.387298i	0.125567	+	0.992085i	$0.459925\pi$
$6$	−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	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	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	−0.362892	−	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	0.205783	−	0.978598i	$-0.434026\pi$
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	−0.744599	+	0.667512i	$0.767359\pi$
$32$	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	−0.105601	−	0.994409i	$-0.533677\pi$
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	0.808383	+	0.588657i	$0.200343\pi$
$42$		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	−0.702577	−	0.711608i	$-0.747967\pi$
$47$	−3.00000	+	1.73205i	−0.437595	+	0.252646i	0.264982	+	0.964253i	$0.414634\pi$
$48$	−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	−0.0556984	−	0.998448i	$-0.517739\pi$
$59$	6.00000	−	3.46410i	0.781133	−	0.450988i	0.836832	+	0.547460i	$0.184405\pi$
$60$	3.00000	+	1.73205i	0.387298	+	0.223607i
$61$	−1.00000			−0.128037			−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000			−0.128037			−0.0640184	+	0.997949i	$0.520392\pi$
$62$	−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	0.409644	−	0.912245i	$-0.365653\pi$
$73$	−1.50000	−	0.866025i	−0.175562	−	0.101361i	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−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	$0.275031\pi$
$83$			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	$-0.453015\pi$
$89$	−6.00000	−	3.46410i	−0.635999	−	0.367194i	−0.783072	+	0.621932i	$0.786348\pi$
$90$	−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	$-0.447739\pi$
$97$	−6.00000	−	3.46410i	−0.609208	−	0.351726i	−0.772655	+	0.634826i	$0.781072\pi$
$98$		0			0
$99$		0			0
$100$	−2.00000			−0.200000
$101$	3.00000			0.298511			0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000			0.298511			0.149256	+	0.988799i	$0.452312\pi$
$102$			10.3923i			1.02899i
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	0.507300	−	0.861770i	$-0.330644\pi$
$103$	−5.00000	−	8.66025i	−0.492665	−	0.853320i	−0.999964	+	0.00844953i	$0.997310\pi$
$104$	−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	$0.121357\pi$
$131$	9.00000	+	15.5885i	0.786334	+	1.36197i	−0.141865	+	0.989886i	$0.545310\pi$
$132$		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	−0.938293	−	0.345843i	$-0.887593\pi$
$139$	−2.00000	+	3.46410i	−0.169638	+	0.293821i	0.768655	+	0.639664i	$0.220926\pi$
$140$		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	$0.340272\pi$
$157$	−6.50000	+	11.2583i	−0.518756	+	0.898513i	−0.999762	+	0.0217953i	$0.993062\pi$
$158$		−	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	0.0422232	−	0.999108i	$-0.486556\pi$
$167$	12.0000	−	6.92820i	0.928588	−	0.536120i	0.886365	+	0.462988i	$0.153223\pi$
$168$		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	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$			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	$-0.634057\pi$
$181$	−11.0000			−0.817624			−0.408812	+	0.912619i	$0.634057\pi$
$182$		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	0.828403	−	0.560133i	$-0.189250\pi$
$199$	−1.00000	−	1.73205i	−0.0708881	−	0.122782i	−0.899291	+	0.437351i	$0.855917\pi$
$200$	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	−0.167412	−	0.985887i	$-0.553541\pi$
$223$	9.00000	−	5.19615i	0.602685	−	0.347960i	0.770097	+	0.637927i	$0.220208\pi$
$224$		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	$-0.368981\pi$
$227$	21.0000	−	12.1244i	1.39382	−	0.804722i	0.993736	+	0.111757i	$0.0356478\pi$
$228$	−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	−0.547533	−	0.836784i	$-0.684433\pi$
$241$	−1.50000	+	0.866025i	−0.0966235	+	0.0557856i	0.450910	+	0.892570i	$0.351100\pi$
$242$	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	$0.358978\pi$
$251$	−9.00000	+	15.5885i	−0.568075	+	0.983935i	−0.996756	+	0.0804789i	$0.974355\pi$
$252$		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	$-0.803506\pi$
$257$	1.50000	−	2.59808i	0.0935674	−	0.162064i	0.909010	+	0.416775i	$0.136840\pi$
$258$	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	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$	−12.0000			−0.730297
$271$	18.0000	+	10.3923i	1.09342	+	0.631288i	0.934485	−	0.356001i	$-0.115860\pi$
$271$	18.0000	+	10.3923i	1.09342	+	0.631288i	0.158937	+	0.987289i	$0.449193\pi$
$272$	−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	$-0.537933\pi$
$283$	−4.00000			−0.237775			−0.118888	+	0.992908i	$0.537933\pi$
$284$			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	$-0.381834\pi$
$293$	−4.50000	−	2.59808i	−0.262893	−	0.151781i	−0.625653	+	0.780101i	$0.715168\pi$
$294$		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	0.0301210	+	0.999546i	$0.490411\pi$
$311$	−15.0000	+	25.9808i	−0.850572	+	1.47323i	−0.880693	+	0.473688i	$0.842923\pi$
$312$	9.00000	+	8.66025i	0.509525	+	0.490290i
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	0.972028	−	0.234863i	$-0.0754642\pi$
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	−0.689412	+	0.724370i	$0.742131\pi$
$314$	−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	−0.785517	−	0.618840i	$-0.787603\pi$
$349$	−12.0000	+	6.92820i	−0.642345	+	0.370858i	0.143172	+	0.989698i	$0.454270\pi$
$350$		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	−0.333238	−	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	$-0.305315\pi$
$367$	22.0000			1.14839			0.574195	+	0.818718i	$0.305315\pi$
$368$	−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	$-0.821808\pi$
$383$		−	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	−0.729103	−	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	$-0.886957\pi$
$397$		−	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	0.536985	−	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	−0.127609	−	0.991825i	$-0.540730\pi$
$409$	13.5000	−	7.79423i	0.667532	−	0.385400i	0.795141	+	0.606425i	$0.207397\pi$
$410$	−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	$-0.0217590\pi$
$419$	9.00000	+	15.5885i	0.439679	+	0.761546i	−0.557986	+	0.829851i	$0.688426\pi$
$420$		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	−0.994720	−	0.102625i	$-0.967276\pi$
$433$	−8.50000	+	14.7224i	−0.408484	+	0.707515i	0.586236	+	0.810140i	$0.300609\pi$
$434$		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	$0.399595\pi$
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	−0.978412	+	0.206666i	$0.933739\pi$
$440$		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	−0.0283522	−	0.999598i	$-0.509026\pi$
$461$	−19.5000	−	11.2583i	−0.908206	−	0.524353i	−0.879853	+	0.475245i	$0.842359\pi$
$462$		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	0.970799	−	0.239892i	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$	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	−0.357858	−	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	$-0.536793\pi$
$503$	18.0000	−	31.1769i	0.802580	−	1.39011i	0.917912	−	0.396783i	$-0.129873\pi$
$504$		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	$-0.194576\pi$
$509$	16.5000	+	9.52628i	0.731350	+	0.422245i	−0.0875661	+	0.996159i	$0.527909\pi$
$510$	−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	$-0.770165\pi$
$521$	4.50000	−	7.79423i	0.197149	−	0.341471i	0.947603	+	0.319451i	$0.103499\pi$
$522$		−	5.19615i		−	0.227429i
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$	−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	0.802451	−	0.596718i	$-0.203529\pi$
$577$	16.5000	+	9.52628i	0.686904	+	0.396584i	−0.115547	+	0.993302i	$0.536862\pi$
$578$	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	$-0.525555\pi$
$587$	18.0000	−	10.3923i	0.742940	−	0.428936i	0.823137	+	0.567843i	$0.192222\pi$
$588$		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	$-0.845772\pi$
$593$	−22.5000	+	12.9904i	−0.923964	+	0.533451i	−0.0390666	+	0.999237i	$0.512438\pi$
$594$		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	$0.00364562\pi$
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	−0.490049	+	0.871695i	$0.663021\pi$
$602$		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	$-0.257607\pi$
$607$	34.0000			1.38002			0.690009	+	0.723801i	$0.257607\pi$
$608$	−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	0.816033	−	0.578006i	$-0.196169\pi$
$619$	18.0000	+	10.3923i	0.723481	+	0.417702i	−0.0925515	+	0.995708i	$0.529502\pi$
$620$	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	0.244359	−	0.969685i	$-0.421423\pi$
$643$	−12.0000	−	6.92820i	−0.473234	−	0.273222i	−0.717592	+	0.696463i	$0.754756\pi$
$644$		0			0
$645$			27.7128i			1.09119i
$646$	−18.0000			−0.708201
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$			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	$0.363521\pi$
$661$			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	0.988968	−	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	0.802600	−	0.596518i	$-0.203449\pi$
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	−0.917899	+	0.396813i	$0.870116\pi$
$678$	−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	0.710572	−	0.703624i	$-0.248436\pi$
$691$	12.0000	+	6.92820i	0.456502	+	0.263561i	−0.254071	+	0.967186i	$0.581770\pi$
$692$	−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	$-0.147140\pi$
$719$	48.0000			1.79010			0.895049	+	0.445968i	$0.147140\pi$
$720$			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	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		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	$-0.594784\pi$
$733$	10.5000	−	6.06218i	0.387826	−	0.223912i	0.681218	+	0.732081i	$0.261451\pi$
$734$	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	$0.216072\pi$
$761$			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	$-0.706534\pi$
$769$	−6.00000	+	3.46410i	−0.216366	+	0.124919i	0.387901	+	0.921701i	$0.373200\pi$
$770$		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	$-0.880743\pi$
$773$	−30.0000	+	17.3205i	−1.07903	+	0.622975i	−0.148392	+	0.988929i	$0.547410\pi$
$774$	−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	$-0.429015\pi$
$787$	33.0000	−	19.0526i	1.17632	−	0.679150i	0.955161	+	0.296087i	$0.0956817\pi$
$788$	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	$-0.566327\pi$
$797$	21.0000	−	36.3731i	0.743858	−	1.28840i	0.950726	−	0.310031i	$-0.100340\pi$
$798$		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	0.972375	−	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	$-0.642949\pi$
$829$	−25.0000			−0.868286			−0.434143	+	0.900844i	$0.642949\pi$
$830$		−	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	$-0.616776\pi$
$839$	−39.0000	−	22.5167i	−1.34643	−	0.777361i	−0.987742	+	0.156096i	$0.950109\pi$
$840$		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	$-0.817016\pi$
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	0.890507	+	0.454969i	$0.150350\pi$
$858$		0			0
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	0.721544	−	0.692369i	$-0.243433\pi$
$859$	−7.00000	−	12.1244i	−0.238837	−	0.413678i	−0.960381	+	0.278691i	$0.910099\pi$
$860$	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	0.998678	−	0.0513987i	$-0.0163679\pi$
$881$	13.5000	+	23.3827i	0.454827	+	0.787783i	−0.543852	+	0.839181i	$0.683035\pi$
$882$		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	$-0.626754\pi$
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	0.992149	−	0.125061i	$-0.0399128\pi$
$888$	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	$-0.536475\pi$
$937$	−7.00000			−0.228680			−0.114340	+	0.993442i	$0.536475\pi$
$938$		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	$-0.443347\pi$
$941$	−18.0000	−	10.3923i	−0.586783	−	0.338779i	−0.763825	+	0.645424i	$0.776681\pi$
$942$	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	$-0.530693\pi$
$971$	−6.00000			−0.192549			−0.0962746	+	0.995355i	$0.530693\pi$
$972$	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	−0.437761	−	0.899092i	$-0.644228\pi$
$983$	−45.0000	−	25.9808i	−1.43528	−	0.828658i	−0.997516	+	0.0704339i	$0.977562\pi$
$984$	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	$-0.0799082\pi$
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	−0.699457	+	0.714675i	$0.746575\pi$
$998$	−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.b.361.1		2
7.2	even	3		637.2.k.c.569.1		2
7.3	odd	6		13.2.e.a.10.1	yes	2
7.4	even	3		637.2.q.a.491.1		2
7.5	odd	6		637.2.k.a.569.1		2
7.6	odd	2		637.2.u.c.361.1		2
13.4	even	6		637.2.k.c.459.1		2
21.17	even	6		117.2.q.c.10.1		2
28.3	even	6		208.2.w.b.49.1		2
35.3	even	12		325.2.m.a.49.2		4
35.17	even	12		325.2.m.a.49.1		4
35.24	odd	6		325.2.n.a.101.1		2
56.3	even	6		832.2.w.a.257.1		2
56.45	odd	6		832.2.w.d.257.1		2
84.59	odd	6		1872.2.by.d.1297.1		2
91.3	odd	6		169.2.b.a.168.1		2
91.4	even	6		637.2.q.a.589.1		2
91.10	odd	6		169.2.b.a.168.2		2
91.11	odd	12		8281.2.a.q.1.2		2
91.17	odd	6		13.2.e.a.4.1	✓	2
91.24	even	12		169.2.a.a.1.2		2
91.30	even	6	inner	637.2.u.b.30.1		2
91.31	even	12		169.2.c.a.146.2		4
91.38	odd	6		169.2.e.a.23.1		2
91.45	even	12		169.2.c.a.22.2		4
91.59	even	12		169.2.c.a.22.1		4
91.67	odd	12		8281.2.a.q.1.1		2
91.69	odd	6		637.2.k.a.459.1		2
91.73	even	12		169.2.c.a.146.1		4
91.80	even	12		169.2.a.a.1.1		2
91.82	odd	6		637.2.u.c.30.1		2
91.87	odd	6		169.2.e.a.147.1		2
273.17	even	6		117.2.q.c.82.1		2
273.80	odd	12		1521.2.a.k.1.2		2
273.101	even	6		1521.2.b.a.1351.1		2
273.185	even	6		1521.2.b.a.1351.2		2
273.206	odd	12		1521.2.a.k.1.1		2
364.3	even	6		2704.2.f.b.337.2		2
364.115	odd	12		2704.2.a.o.1.1		2
364.171	odd	12		2704.2.a.o.1.2		2
364.199	even	6		208.2.w.b.17.1		2
364.283	even	6		2704.2.f.b.337.1		2
455.17	even	12		325.2.m.a.199.2		4
455.24	even	12		4225.2.a.v.1.1		2
455.108	even	12		325.2.m.a.199.1		4
455.199	odd	6		325.2.n.a.251.1		2
455.444	even	12		4225.2.a.v.1.2		2
728.381	odd	6		832.2.w.d.641.1		2
728.563	even	6		832.2.w.a.641.1		2
1092.563	odd	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	91.17	odd	6
13.2.e.a.10.1	yes	2	7.3	odd	6
117.2.q.c.10.1		2	21.17	even	6
117.2.q.c.82.1		2	273.17	even	6
169.2.a.a.1.1		2	91.80	even	12
169.2.a.a.1.2		2	91.24	even	12
169.2.b.a.168.1		2	91.3	odd	6
169.2.b.a.168.2		2	91.10	odd	6
169.2.c.a.22.1		4	91.59	even	12
169.2.c.a.22.2		4	91.45	even	12
169.2.c.a.146.1		4	91.73	even	12
169.2.c.a.146.2		4	91.31	even	12
169.2.e.a.23.1		2	91.38	odd	6
169.2.e.a.147.1		2	91.87	odd	6
208.2.w.b.17.1		2	364.199	even	6
208.2.w.b.49.1		2	28.3	even	6
325.2.m.a.49.1		4	35.17	even	12
325.2.m.a.49.2		4	35.3	even	12
325.2.m.a.199.1		4	455.108	even	12
325.2.m.a.199.2		4	455.17	even	12
325.2.n.a.101.1		2	35.24	odd	6
325.2.n.a.251.1		2	455.199	odd	6
637.2.k.a.459.1		2	91.69	odd	6
637.2.k.a.569.1		2	7.5	odd	6
637.2.k.c.459.1		2	13.4	even	6
637.2.k.c.569.1		2	7.2	even	3
637.2.q.a.491.1		2	7.4	even	3
637.2.q.a.589.1		2	91.4	even	6
637.2.u.b.30.1		2	91.30	even	6	inner
637.2.u.b.361.1		2	1.1	even	1	trivial
637.2.u.c.30.1		2	91.82	odd	6
637.2.u.c.361.1		2	7.6	odd	2
832.2.w.a.257.1		2	56.3	even	6
832.2.w.a.641.1		2	728.563	even	6
832.2.w.d.257.1		2	56.45	odd	6
832.2.w.d.641.1		2	728.381	odd	6
1521.2.a.k.1.1		2	273.206	odd	12
1521.2.a.k.1.2		2	273.80	odd	12
1521.2.b.a.1351.1		2	273.101	even	6
1521.2.b.a.1351.2		2	273.185	even	6
1872.2.by.d.433.1		2	1092.563	odd	6
1872.2.by.d.1297.1		2	84.59	odd	6
2704.2.a.o.1.1		2	364.115	odd	12
2704.2.a.o.1.2		2	364.171	odd	12
2704.2.f.b.337.1		2	364.283	even	6
2704.2.f.b.337.2		2	364.3	even	6
4225.2.a.v.1.1		2	455.24	even	12
4225.2.a.v.1.2		2	455.444	even	12
8281.2.a.q.1.1		2	91.67	odd	12
8281.2.a.q.1.2		2	91.11	odd	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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