LMFDB - Embedded newform 637.2.k.b.569.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

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

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.73205i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-4.50000 - 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.00000 + 3.46410i) q^{13} +(1.50000 - 0.866025i) q^{15} -5.00000 q^{16} -6.00000 q^{17} +(-3.00000 + 1.73205i) q^{18} +(1.50000 - 0.866025i) q^{19} +(1.50000 + 0.866025i) q^{20} +(4.50000 - 7.79423i) q^{22} +(-1.50000 - 0.866025i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-6.00000 + 1.73205i) q^{26} -5.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(1.50000 + 2.59808i) q^{30} +(1.50000 - 0.866025i) q^{31} -5.19615i q^{32} +(4.50000 - 2.59808i) q^{33} -10.3923i q^{34} +(-1.00000 - 1.73205i) q^{36} +(1.50000 + 2.59808i) q^{38} +(-3.50000 - 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{40} +(4.50000 - 2.59808i) q^{41} +(-5.50000 + 9.52628i) q^{43} +(4.50000 + 2.59808i) q^{44} -3.46410i q^{45} +(-7.50000 - 4.33013i) q^{47} +(2.50000 - 4.33013i) q^{48} +(3.00000 - 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(-1.00000 - 3.46410i) q^{52} +(4.50000 + 7.79423i) q^{53} -8.66025i q^{54} +(4.50000 + 7.79423i) q^{55} +1.73205i q^{57} +(4.50000 - 2.59808i) q^{58} +3.46410i q^{59} +(-1.50000 + 0.866025i) q^{60} +(3.50000 + 6.06218i) q^{61} +(1.50000 + 2.59808i) q^{62} -1.00000 q^{64} +(1.50000 - 6.06218i) q^{65} +(4.50000 + 7.79423i) q^{66} +(7.50000 + 4.33013i) q^{67} +6.00000 q^{68} +(1.50000 + 0.866025i) q^{71} +(-3.00000 + 1.73205i) q^{72} +(-7.50000 + 4.33013i) q^{73} +2.00000 q^{75} +(-1.50000 + 0.866025i) q^{76} +(1.50000 - 6.06218i) q^{78} +(2.50000 - 4.33013i) q^{79} +(7.50000 + 4.33013i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} -3.46410i q^{83} +(9.00000 + 5.19615i) q^{85} +(-16.5000 - 9.52628i) q^{86} +3.00000 q^{87} +(4.50000 - 7.79423i) q^{88} -6.92820i q^{89} +6.00000 q^{90} +1.73205i q^{93} +(7.50000 - 12.9904i) q^{94} -3.00000 q^{95} +(4.50000 + 2.59808i) q^{96} +(4.50000 + 2.59808i) q^{97} -10.3923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} - 2 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{9} + 3 q^{10} - 9 q^{11} + q^{12} + 2 q^{13} + 3 q^{15} - 10 q^{16} - 12 q^{17} - 6 q^{18} + 3 q^{19} + 3 q^{20} + 9 q^{22} - 3 q^{24} - 2 q^{25} - 12 q^{26}+ \cdots + 9 q^{97}+O(q^{100}) $ 2 * q - q^3 - 2 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^9 + 3 * q^10 - 9 * q^11 + q^12 + 2 * q^13 + 3 * q^15 - 10 * q^16 - 12 * q^17 - 6 * q^18 + 3 * q^19 + 3 * q^20 + 9 * q^22 - 3 * q^24 - 2 * q^25 - 12 * q^26 - 10 * q^27 - 3 * q^29 + 3 * q^30 + 3 * q^31 + 9 * q^33 - 2 * q^36 + 3 * q^38 - 7 * q^39 + 3 * q^40 + 9 * q^41 - 11 * q^43 + 9 * q^44 - 15 * q^47 + 5 * q^48 + 6 * q^50 + 6 * q^51 - 2 * q^52 + 9 * q^53 + 9 * q^55 + 9 * q^58 - 3 * q^60 + 7 * q^61 + 3 * q^62 - 2 * q^64 + 3 * q^65 + 9 * q^66 + 15 * q^67 + 12 * q^68 + 3 * q^71 - 6 * q^72 - 15 * q^73 + 4 * q^75 - 3 * q^76 + 3 * q^78 + 5 * q^79 + 15 * q^80 - q^81 + 9 * q^82 + 18 * q^85 - 33 * q^86 + 6 * q^87 + 9 * q^88 + 12 * q^90 + 15 * q^94 - 6 * q^95 + 9 * q^96 + 9 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$			1.73205i			1.22474i	0.790569	+	0.612372i	$0.209785\pi$
$2$			1.73205i			1.22474i	−0.790569	+	0.612372i	$0.790215\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	−1.00000			−0.500000
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	0.125567	−	0.992085i	$-0.459925\pi$
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$		0			0
$7$		0			0
$8$			1.73205i			0.612372i
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	1.50000	−	2.59808i	0.474342	−	0.821584i
$11$	−4.50000	−	2.59808i	−1.35680	−	0.783349i	−0.367610	−	0.929980i	$-0.619824\pi$
$11$	−4.50000	−	2.59808i	−1.35680	−	0.783349i	−0.989191	+	0.146631i	$0.953157\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$		0			0
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	−5.00000			−1.25000
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$	−3.00000	+	1.73205i	−0.707107	+	0.408248i
$19$	1.50000	−	0.866025i	0.344124	−	0.198680i	−0.317970	−	0.948101i	$-0.603001\pi$
$19$	1.50000	−	0.866025i	0.344124	−	0.198680i	0.662094	+	0.749421i	$0.269668\pi$
$20$	1.50000	+	0.866025i	0.335410	+	0.193649i
$21$		0			0
$22$	4.50000	−	7.79423i	0.959403	−	1.66174i
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	−6.00000	+	1.73205i	−1.17670	+	0.339683i
$27$	−5.00000			−0.962250
$28$		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	$0.923185\pi$
$30$	1.50000	+	2.59808i	0.273861	+	0.474342i
$31$	1.50000	−	0.866025i	0.269408	−	0.155543i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	1.50000	−	0.866025i	0.269408	−	0.155543i	0.628619	+	0.777714i	$0.283621\pi$
$32$		−	5.19615i		−	0.918559i
$33$	4.50000	−	2.59808i	0.783349	−	0.452267i
$34$		−	10.3923i		−	1.78227i
$35$		0			0
$36$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	1.50000	+	2.59808i	0.243332	+	0.421464i
$39$	−3.50000	−	0.866025i	−0.560449	−	0.138675i
$40$	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
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	0.0522047	+	0.998636i	$0.483375\pi$
$43$	−5.50000	+	9.52628i	−0.838742	+	1.45274i	−0.890947	+	0.454108i	$0.849958\pi$
$44$	4.50000	+	2.59808i	0.678401	+	0.391675i
$45$		−	3.46410i		−	0.516398i
$46$		0			0
$47$	−7.50000	−	4.33013i	−1.09399	−	0.631614i	−0.159352	−	0.987222i	$-0.550941\pi$
$47$	−7.50000	−	4.33013i	−1.09399	−	0.631614i	−0.934635	+	0.355608i	$0.884274\pi$
$48$	2.50000	−	4.33013i	0.360844	−	0.625000i
$49$		0			0
$50$	3.00000	−	1.73205i	0.424264	−	0.244949i
$51$	3.00000	−	5.19615i	0.420084	−	0.727607i
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$		−	8.66025i		−	1.17851i
$55$	4.50000	+	7.79423i	0.606780	+	1.05097i
$56$		0			0
$57$			1.73205i			0.229416i
$58$	4.50000	−	2.59808i	0.590879	−	0.341144i
$59$			3.46410i			0.450988i	0.974245	+	0.225494i	$0.0723995\pi$
$59$			3.46410i			0.450988i	−0.974245	+	0.225494i	$0.927600\pi$
$60$	−1.50000	+	0.866025i	−0.193649	+	0.111803i
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$	1.50000	+	2.59808i	0.190500	+	0.329956i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.50000	−	6.06218i	0.186052	−	0.751921i
$66$	4.50000	+	7.79423i	0.553912	+	0.959403i
$67$	7.50000	+	4.33013i	0.916271	+	0.529009i	0.882443	−	0.470418i	$-0.155897\pi$
$67$	7.50000	+	4.33013i	0.916271	+	0.529009i	0.0338274	+	0.999428i	$0.489230\pi$
$68$	6.00000			0.727607
$69$		0			0
$70$		0			0
$71$	1.50000	+	0.866025i	0.178017	+	0.102778i	0.586361	−	0.810050i	$-0.300560\pi$
$71$	1.50000	+	0.866025i	0.178017	+	0.102778i	−0.408344	+	0.912828i	$0.633893\pi$
$72$	−3.00000	+	1.73205i	−0.353553	+	0.204124i
$73$	−7.50000	+	4.33013i	−0.877809	+	0.506803i	−0.869935	−	0.493166i	$-0.835840\pi$
$73$	−7.50000	+	4.33013i	−0.877809	+	0.506803i	−0.00787336	+	0.999969i	$0.502506\pi$
$74$		0			0
$75$	2.00000			0.230940
$76$	−1.50000	+	0.866025i	−0.172062	+	0.0993399i
$77$		0			0
$78$	1.50000	−	6.06218i	0.169842	−	0.686406i
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	−0.690426	−	0.723403i	$-0.742577\pi$
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	0.971698	+	0.236225i	$0.0759104\pi$
$80$	7.50000	+	4.33013i	0.838525	+	0.484123i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$		−	3.46410i		−	0.380235i	−0.981761	−	0.190117i	$-0.939113\pi$
$83$		−	3.46410i		−	0.380235i	0.981761	−	0.190117i	$-0.0608868\pi$
$84$		0			0
$85$	9.00000	+	5.19615i	0.976187	+	0.563602i
$86$	−16.5000	−	9.52628i	−1.77924	−	1.02725i
$87$	3.00000			0.321634
$88$	4.50000	−	7.79423i	0.479702	−	0.830868i
$89$		−	6.92820i		−	0.734388i	−0.930144	−	0.367194i	$-0.880318\pi$
$89$		−	6.92820i		−	0.734388i	0.930144	−	0.367194i	$-0.119682\pi$
$90$	6.00000			0.632456
$91$		0			0
$92$		0			0
$93$			1.73205i			0.179605i
$94$	7.50000	−	12.9904i	0.773566	−	1.33986i
$95$	−3.00000			−0.307794
$96$	4.50000	+	2.59808i	0.459279	+	0.265165i
$97$	4.50000	+	2.59808i	0.456906	+	0.263795i	0.710742	−	0.703452i	$-0.248359\pi$
$97$	4.50000	+	2.59808i	0.456906	+	0.263795i	−0.253837	+	0.967247i	$0.581693\pi$
$98$		0			0
$99$		−	10.3923i		−	1.04447i
$100$	1.00000	+	1.73205i	0.100000	+	0.173205i
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	−0.998240	−	0.0592978i	$-0.981114\pi$
$101$	−4.50000	+	7.79423i	−0.447767	+	0.775555i	0.550474	+	0.834853i	$0.314447\pi$
$102$	9.00000	+	5.19615i	0.891133	+	0.514496i
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	0.344865	+	0.938652i	$0.387925\pi$
$103$	−6.50000	+	11.2583i	−0.640464	+	1.10932i	−0.985329	+	0.170664i	$0.945409\pi$
$104$	−6.00000	+	1.73205i	−0.588348	+	0.169842i
$105$		0			0
$106$	−13.5000	+	7.79423i	−1.31124	+	0.757042i
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	5.00000			0.481125
$109$	−4.50000	+	2.59808i	−0.431022	+	0.248851i	−0.699782	−	0.714357i	$-0.746719\pi$
$109$	−4.50000	+	2.59808i	−0.431022	+	0.248851i	0.268760	+	0.963207i	$0.413386\pi$
$110$	−13.5000	+	7.79423i	−1.28717	+	0.743151i
$111$		0			0
$112$		0			0
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	0.260955	+	0.965351i	$0.415962\pi$
$113$	−7.50000	+	12.9904i	−0.705541	+	1.22203i	−0.966496	+	0.256681i	$0.917371\pi$
$114$	−3.00000			−0.280976
$115$		0			0
$116$	1.50000	+	2.59808i	0.139272	+	0.241225i
$117$	−5.00000	+	5.19615i	−0.462250	+	0.480384i
$118$	−6.00000			−0.552345
$119$		0			0
$120$	1.50000	+	2.59808i	0.136931	+	0.237171i
$121$	8.00000	+	13.8564i	0.727273	+	1.25967i
$122$	−10.5000	+	6.06218i	−0.950625	+	0.548844i
$123$			5.19615i			0.468521i
$124$	−1.50000	+	0.866025i	−0.134704	+	0.0777714i
$125$			12.1244i			1.08444i
$126$		0			0
$127$	−6.50000	−	11.2583i	−0.576782	−	0.999015i	−0.995846	−	0.0910585i	$-0.970975\pi$
$127$	−6.50000	−	11.2583i	−0.576782	−	0.999015i	0.419064	−	0.907957i	$-0.362358\pi$
$128$		−	12.1244i		−	1.07165i
$129$	−5.50000	−	9.52628i	−0.484248	−	0.838742i
$130$	10.5000	+	2.59808i	0.920911	+	0.227866i
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	−0.326546	−	0.945181i	$-0.605885\pi$
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	0.981824	−	0.189794i	$-0.0607819\pi$
$132$	−4.50000	+	2.59808i	−0.391675	+	0.226134i
$133$		0			0
$134$	−7.50000	+	12.9904i	−0.647901	+	1.12220i
$135$	7.50000	+	4.33013i	0.645497	+	0.372678i
$136$		−	10.3923i		−	0.891133i
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$		0			0
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	0.446857	+	0.894606i	$0.352543\pi$
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	−0.998179	+	0.0603135i	$0.980790\pi$
$140$		0			0
$141$	7.50000	−	4.33013i	0.631614	−	0.364662i
$142$	−1.50000	+	2.59808i	−0.125877	+	0.218026i
$143$	4.50000	−	18.1865i	0.376309	−	1.52083i
$144$	−5.00000	−	8.66025i	−0.416667	−	0.721688i
$145$			5.19615i			0.431517i
$146$	−7.50000	−	12.9904i	−0.620704	−	1.07509i
$147$		0			0
$148$		0			0
$149$	−16.5000	+	9.52628i	−1.35173	+	0.780423i	−0.988492	−	0.151272i	$-0.951663\pi$
$149$	−16.5000	+	9.52628i	−1.35173	+	0.780423i	−0.363241	+	0.931695i	$0.618330\pi$
$150$			3.46410i			0.282843i
$151$	10.5000	−	6.06218i	0.854478	−	0.493333i	−0.00768132	−	0.999970i	$-0.502445\pi$
$151$	10.5000	−	6.06218i	0.854478	−	0.493333i	0.862159	+	0.506637i	$0.169112\pi$
$152$	1.50000	+	2.59808i	0.121666	+	0.210732i
$153$	−6.00000	−	10.3923i	−0.485071	−	0.840168i
$154$		0			0
$155$	−3.00000			−0.240966
$156$	3.50000	+	0.866025i	0.280224	+	0.0693375i
$157$	11.5000	+	19.9186i	0.917800	+	1.58968i	0.802749	+	0.596316i	$0.203370\pi$
$157$	11.5000	+	19.9186i	0.917800	+	1.58968i	0.115050	+	0.993360i	$0.463297\pi$
$158$	7.50000	+	4.33013i	0.596668	+	0.344486i
$159$	−9.00000			−0.713746
$160$	−4.50000	+	7.79423i	−0.355756	+	0.616188i
$161$		0			0
$162$	−1.50000	−	0.866025i	−0.117851	−	0.0680414i
$163$	10.5000	−	6.06218i	0.822423	−	0.474826i	−0.0288280	−	0.999584i	$-0.509178\pi$
$163$	10.5000	−	6.06218i	0.822423	−	0.474826i	0.851251	+	0.524758i	$0.175844\pi$
$164$	−4.50000	+	2.59808i	−0.351391	+	0.202876i
$165$	−9.00000			−0.700649
$166$	6.00000			0.465690
$167$	1.50000	−	0.866025i	0.116073	−	0.0670151i	−0.440839	−	0.897586i	$-0.645319\pi$
$167$	1.50000	−	0.866025i	0.116073	−	0.0670151i	0.556913	+	0.830571i	$0.311986\pi$
$168$		0			0
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$	−9.00000	+	15.5885i	−0.690268	+	1.19558i
$171$	3.00000	+	1.73205i	0.229416	+	0.132453i
$172$	5.50000	−	9.52628i	0.419371	−	0.726372i
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	0.996544	+	0.0830722i	$0.0264732\pi$
$173$	7.50000	+	12.9904i	0.570214	+	0.987640i	−0.426329	+	0.904568i	$0.640193\pi$
$174$			5.19615i			0.393919i
$175$		0			0
$176$	22.5000	+	12.9904i	1.69600	+	0.979187i
$177$	−3.00000	−	1.73205i	−0.225494	−	0.130189i
$178$	12.0000			0.899438
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	−0.916623	−	0.399753i	$-0.869096\pi$
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	0.804508	+	0.593942i	$0.202429\pi$
$180$			3.46410i			0.258199i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	−7.00000			−0.517455
$184$		0			0
$185$		0			0
$186$	−3.00000			−0.219971
$187$	27.0000	+	15.5885i	1.97444	+	1.13994i
$188$	7.50000	+	4.33013i	0.546994	+	0.315807i
$189$		0			0
$190$		−	5.19615i		−	0.376969i
$191$	7.50000	+	12.9904i	0.542681	+	0.939951i	0.998749	+	0.0500060i	$0.0159241\pi$
$191$	7.50000	+	12.9904i	0.542681	+	0.939951i	−0.456068	+	0.889945i	$0.650743\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	1.50000	+	0.866025i	0.107972	+	0.0623379i	0.553014	−	0.833172i	$-0.313478\pi$
$193$	1.50000	+	0.866025i	0.107972	+	0.0623379i	−0.445041	+	0.895510i	$0.646811\pi$
$194$	−4.50000	+	7.79423i	−0.323081	+	0.559593i
$195$	4.50000	+	4.33013i	0.322252	+	0.310087i
$196$		0			0
$197$	19.5000	−	11.2583i	1.38932	−	0.802123i	0.396079	−	0.918216i	$-0.370371\pi$
$197$	19.5000	−	11.2583i	1.38932	−	0.802123i	0.993238	+	0.116094i	$0.0370372\pi$
$198$	18.0000			1.27920
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$	3.00000	−	1.73205i	0.212132	−	0.122474i
$201$	−7.50000	+	4.33013i	−0.529009	+	0.305424i
$202$	−13.5000	−	7.79423i	−0.949857	−	0.548400i
$203$		0			0
$204$	−3.00000	+	5.19615i	−0.210042	+	0.363803i
$205$	−9.00000			−0.628587
$206$	−19.5000	−	11.2583i	−1.35863	−	0.784405i
$207$		0			0
$208$	−5.00000	−	17.3205i	−0.346688	−	1.20096i
$209$	−9.00000			−0.622543
$210$		0			0
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	0.550743	−	0.834675i	$-0.314345\pi$
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	−4.50000	−	7.79423i	−0.309061	−	0.535310i
$213$	−1.50000	+	0.866025i	−0.102778	+	0.0593391i
$214$		0			0
$215$	16.5000	−	9.52628i	1.12529	−	0.649687i
$216$		−	8.66025i		−	0.589256i
$217$		0			0
$218$	−4.50000	−	7.79423i	−0.304778	−	0.527892i
$219$		−	8.66025i		−	0.585206i
$220$	−4.50000	−	7.79423i	−0.303390	−	0.525487i
$221$	−6.00000	−	20.7846i	−0.403604	−	1.39812i
$222$		0			0
$223$	−4.50000	+	2.59808i	−0.301342	+	0.173980i	−0.643046	−	0.765828i	$-0.722329\pi$
$223$	−4.50000	+	2.59808i	−0.301342	+	0.173980i	0.341703	+	0.939808i	$0.388996\pi$
$224$		0			0
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$	−22.5000	−	12.9904i	−1.49668	−	0.864107i
$227$			17.3205i			1.14960i	0.818293	+	0.574801i	$0.194921\pi$
$227$			17.3205i			1.14960i	−0.818293	+	0.574801i	$0.805079\pi$
$228$		−	1.73205i		−	0.114708i
$229$	10.5000	+	6.06218i	0.693860	+	0.400600i	0.805056	−	0.593198i	$-0.202135\pi$
$229$	10.5000	+	6.06218i	0.693860	+	0.400600i	−0.111197	+	0.993798i	$0.535468\pi$
$230$		0			0
$231$		0			0
$232$	4.50000	−	2.59808i	0.295439	−	0.170572i
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	−0.910968	−	0.412477i	$-0.864664\pi$
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	0.812700	+	0.582683i	$0.197997\pi$
$234$	−9.00000	−	8.66025i	−0.588348	−	0.566139i
$235$	7.50000	+	12.9904i	0.489246	+	0.847399i
$236$		−	3.46410i		−	0.225494i
$237$	2.50000	+	4.33013i	0.162392	+	0.281272i
$238$		0			0
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$	−7.50000	+	4.33013i	−0.484123	+	0.279508i
$241$			6.92820i			0.446285i	0.974786	+	0.223142i	$0.0716315\pi$
$241$			6.92820i			0.446285i	−0.974786	+	0.223142i	$0.928369\pi$
$242$	−24.0000	+	13.8564i	−1.54278	+	0.890724i
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−3.50000	−	6.06218i	−0.224065	−	0.388091i
$245$		0			0
$246$	−9.00000			−0.573819
$247$	4.50000	+	4.33013i	0.286328	+	0.275519i
$248$	1.50000	+	2.59808i	0.0952501	+	0.164978i
$249$	3.00000	+	1.73205i	0.190117	+	0.109764i
$250$	−21.0000			−1.32816
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	−0.814795	−	0.579748i	$-0.803151\pi$
$251$	1.50000	−	2.59808i	0.0946792	−	0.163989i	0.909475	+	0.415759i	$0.136484\pi$
$252$		0			0
$253$		0			0
$254$	19.5000	−	11.2583i	1.22354	−	0.706410i
$255$	−9.00000	+	5.19615i	−0.563602	+	0.325396i
$256$	19.0000			1.18750
$257$	−30.0000			−1.87135			−0.935674	−	0.352865i	$-0.885208\pi$
$257$	−30.0000			−1.87135			−0.935674	+	0.352865i	$0.885208\pi$
$258$	16.5000	−	9.52628i	1.02725	−	0.593080i
$259$		0			0
$260$	−1.50000	+	6.06218i	−0.0930261	+	0.375960i
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	22.5000	+	12.9904i	1.39005	+	0.802548i
$263$	−1.50000	+	2.59808i	−0.0924940	+	0.160204i	−0.908560	−	0.417755i	$-0.862817\pi$
$263$	−1.50000	+	2.59808i	−0.0924940	+	0.160204i	0.816066	+	0.577959i	$0.196151\pi$
$264$	4.50000	+	7.79423i	0.276956	+	0.479702i
$265$		−	15.5885i		−	0.957591i
$266$		0			0
$267$	6.00000	+	3.46410i	0.367194	+	0.212000i
$268$	−7.50000	−	4.33013i	−0.458135	−	0.264505i
$269$	6.00000			0.365826			0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000			0.365826			0.182913	+	0.983129i	$0.441447\pi$
$270$	−7.50000	+	12.9904i	−0.456435	+	0.790569i
$271$		−	17.3205i		−	1.05215i	−0.850439	−	0.526073i	$-0.823664\pi$
$271$		−	17.3205i		−	1.05215i	0.850439	−	0.526073i	$-0.176336\pi$
$272$	30.0000			1.81902
$273$		0			0
$274$		0			0
$275$			10.3923i			0.626680i
$276$		0			0
$277$	−10.0000			−0.600842			−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000			−0.600842			−0.300421	+	0.953807i	$0.597127\pi$
$278$	−19.5000	−	11.2583i	−1.16953	−	0.675230i
$279$	3.00000	+	1.73205i	0.179605	+	0.103695i
$280$		0			0
$281$		−	6.92820i		−	0.413302i	−0.978415	−	0.206651i	$-0.933744\pi$
$281$		−	6.92820i		−	0.413302i	0.978415	−	0.206651i	$-0.0662565\pi$
$282$	7.50000	+	12.9904i	0.446619	+	0.773566i
$283$	9.50000	−	16.4545i	0.564716	−	0.978117i	−0.432360	−	0.901701i	$-0.642319\pi$
$283$	9.50000	−	16.4545i	0.564716	−	0.978117i	0.997076	−	0.0764162i	$-0.0243478\pi$
$284$	−1.50000	−	0.866025i	−0.0890086	−	0.0513892i
$285$	1.50000	−	2.59808i	0.0888523	−	0.153897i
$286$	31.5000	+	7.79423i	1.86263	+	0.460882i
$287$		0			0
$288$	9.00000	−	5.19615i	0.530330	−	0.306186i
$289$	19.0000			1.11765
$290$	−9.00000			−0.528498
$291$	−4.50000	+	2.59808i	−0.263795	+	0.152302i
$292$	7.50000	−	4.33013i	0.438904	−	0.253402i
$293$	22.5000	+	12.9904i	1.31446	+	0.758906i	0.982832	−	0.184503i	$-0.0590674\pi$
$293$	22.5000	+	12.9904i	1.31446	+	0.758906i	0.331632	+	0.943409i	$0.392401\pi$
$294$		0			0
$295$	3.00000	−	5.19615i	0.174667	−	0.302532i
$296$		0			0
$297$	22.5000	+	12.9904i	1.30558	+	0.753778i
$298$	−16.5000	−	28.5788i	−0.955819	−	1.65553i
$299$		0			0
$300$	−2.00000			−0.115470
$301$		0			0
$302$	10.5000	+	18.1865i	0.604207	+	1.04652i
$303$	−4.50000	−	7.79423i	−0.258518	−	0.447767i
$304$	−7.50000	+	4.33013i	−0.430155	+	0.248350i
$305$		−	12.1244i		−	0.694239i
$306$	18.0000	−	10.3923i	1.02899	−	0.594089i
$307$		−	24.2487i		−	1.38395i	−0.721923	−	0.691974i	$-0.756741\pi$
$307$		−	24.2487i		−	1.38395i	0.721923	−	0.691974i	$-0.243259\pi$
$308$		0			0
$309$	−6.50000	−	11.2583i	−0.369772	−	0.640464i
$310$		−	5.19615i		−	0.295122i
$311$	−7.50000	−	12.9904i	−0.425286	−	0.736617i	0.571161	−	0.820838i	$-0.306493\pi$
$311$	−7.50000	−	12.9904i	−0.425286	−	0.736617i	−0.996447	+	0.0842210i	$0.973160\pi$
$312$	1.50000	−	6.06218i	0.0849208	−	0.343203i
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	−0.462093	−	0.886831i	$-0.652902\pi$
$313$	9.50000	−	16.4545i	0.536972	−	0.930062i	0.999065	−	0.0432311i	$-0.0137652\pi$
$314$	−34.5000	+	19.9186i	−1.94695	+	1.12407i
$315$		0			0
$316$	−2.50000	+	4.33013i	−0.140636	+	0.243589i
$317$	−4.50000	−	2.59808i	−0.252745	−	0.145922i	0.368275	−	0.929717i	$-0.379948\pi$
$317$	−4.50000	−	2.59808i	−0.252745	−	0.145922i	−0.621021	+	0.783794i	$0.713282\pi$
$318$		−	15.5885i		−	0.874157i
$319$			15.5885i			0.872786i
$320$	1.50000	+	0.866025i	0.0838525	+	0.0484123i
$321$		0			0
$322$		0			0
$323$	−9.00000	+	5.19615i	−0.500773	+	0.289122i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	5.00000	−	5.19615i	0.277350	−	0.288231i
$326$	10.5000	+	18.1865i	0.581541	+	1.00726i
$327$		−	5.19615i		−	0.287348i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$		−	15.5885i		−	0.858116i
$331$	28.5000	−	16.4545i	1.56650	−	0.904420i	0.569929	−	0.821694i	$-0.306971\pi$
$331$	28.5000	−	16.4545i	1.56650	−	0.904420i	0.996572	−	0.0827265i	$-0.0263628\pi$
$332$			3.46410i			0.190117i
$333$		0			0
$334$	1.50000	+	2.59808i	0.0820763	+	0.142160i
$335$	−7.50000	−	12.9904i	−0.409769	−	0.709740i
$336$		0			0
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$	−12.0000	−	19.0526i	−0.652714	−	1.03632i
$339$	−7.50000	−	12.9904i	−0.407344	−	0.705541i
$340$	−9.00000	−	5.19615i	−0.488094	−	0.281801i
$341$	−9.00000			−0.487377
$342$	−3.00000	+	5.19615i	−0.162221	+	0.280976i
$343$		0			0
$344$	−16.5000	−	9.52628i	−0.889620	−	0.513623i
$345$		0			0
$346$	−22.5000	+	12.9904i	−1.20961	+	0.698367i
$347$		0			0			−	1.00000i	$-0.5\pi$
$347$		0			0				1.00000i	$0.5\pi$
$348$	−3.00000			−0.160817
$349$	4.50000	−	2.59808i	0.240879	−	0.139072i	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	4.50000	−	2.59808i	0.240879	−	0.139072i	0.615581	+	0.788074i	$0.288921\pi$
$350$		0			0
$351$	−5.00000	−	17.3205i	−0.266880	−	0.924500i
$352$	−13.5000	+	23.3827i	−0.719552	+	1.24630i
$353$	−1.50000	−	0.866025i	−0.0798369	−	0.0460939i	0.459550	−	0.888152i	$-0.348011\pi$
$353$	−1.50000	−	0.866025i	−0.0798369	−	0.0460939i	−0.539387	+	0.842058i	$0.681344\pi$
$354$	3.00000	−	5.19615i	0.159448	−	0.276172i
$355$	−1.50000	−	2.59808i	−0.0796117	−	0.137892i
$356$			6.92820i			0.367194i
$357$		0			0
$358$	−4.50000	−	2.59808i	−0.237832	−	0.137313i
$359$	−16.5000	−	9.52628i	−0.870837	−	0.502778i	−0.00321050	−	0.999995i	$-0.501022\pi$
$359$	−16.5000	−	9.52628i	−0.870837	−	0.502778i	−0.867626	+	0.497217i	$0.834355\pi$
$360$	6.00000			0.316228
$361$	−8.00000	+	13.8564i	−0.421053	+	0.729285i
$362$		−	3.46410i		−	0.182069i
$363$	−16.0000			−0.839782
$364$		0			0
$365$	15.0000			0.785136
$366$		−	12.1244i		−	0.633750i
$367$	11.5000	−	19.9186i	0.600295	−	1.03974i	−0.392481	−	0.919760i	$-0.628383\pi$
$367$	11.5000	−	19.9186i	0.600295	−	1.03974i	0.992776	−	0.119982i	$-0.0382835\pi$
$368$		0			0
$369$	9.00000	+	5.19615i	0.468521	+	0.270501i
$370$		0			0
$371$		0			0
$372$		−	1.73205i		−	0.0898027i
$373$	−9.50000	−	16.4545i	−0.491891	−	0.851981i	0.508065	−	0.861319i	$-0.330361\pi$
$373$	−9.50000	−	16.4545i	−0.491891	−	0.851981i	−0.999956	+	0.00933789i	$0.997028\pi$
$374$	−27.0000	+	46.7654i	−1.39614	+	2.41818i
$375$	−10.5000	−	6.06218i	−0.542218	−	0.313050i
$376$	7.50000	−	12.9904i	0.386783	−	0.669928i
$377$	7.50000	−	7.79423i	0.386270	−	0.401423i
$378$		0			0
$379$	−1.50000	+	0.866025i	−0.0770498	+	0.0444847i	−0.538030	−	0.842926i	$-0.680831\pi$
$379$	−1.50000	+	0.866025i	−0.0770498	+	0.0444847i	0.460980	+	0.887410i	$0.347498\pi$
$380$	3.00000			0.153897
$381$	13.0000			0.666010
$382$	−22.5000	+	12.9904i	−1.15120	+	0.664646i
$383$	13.5000	−	7.79423i	0.689818	−	0.398266i	−0.113726	−	0.993512i	$-0.536279\pi$
$383$	13.5000	−	7.79423i	0.689818	−	0.398266i	0.803544	+	0.595246i	$0.202945\pi$
$384$	10.5000	+	6.06218i	0.535826	+	0.309359i
$385$		0			0
$386$	−1.50000	+	2.59808i	−0.0763480	+	0.132239i
$387$	−22.0000			−1.11832
$388$	−4.50000	−	2.59808i	−0.228453	−	0.131897i
$389$	−1.50000	−	2.59808i	−0.0760530	−	0.131728i	0.825491	−	0.564416i	$-0.190898\pi$
$389$	−1.50000	−	2.59808i	−0.0760530	−	0.131728i	−0.901544	+	0.432688i	$0.857565\pi$
$390$	−7.50000	+	7.79423i	−0.379777	+	0.394676i
$391$		0			0
$392$		0			0
$393$	7.50000	+	12.9904i	0.378325	+	0.655278i
$394$	19.5000	+	33.7750i	0.982396	+	1.70156i
$395$	−7.50000	+	4.33013i	−0.377366	+	0.217872i
$396$			10.3923i			0.522233i
$397$	−31.5000	+	18.1865i	−1.58094	+	0.912756i	−0.586217	+	0.810154i	$0.699383\pi$
$397$	−31.5000	+	18.1865i	−1.58094	+	0.912756i	−0.994722	+	0.102602i	$0.967283\pi$
$398$		−	6.92820i		−	0.347279i
$399$		0			0
$400$	5.00000	+	8.66025i	0.250000	+	0.433013i
$401$			6.92820i			0.345978i	0.984924	+	0.172989i	$0.0553425\pi$
$401$			6.92820i			0.345978i	−0.984924	+	0.172989i	$0.944657\pi$
$402$	−7.50000	−	12.9904i	−0.374066	−	0.647901i
$403$	4.50000	+	4.33013i	0.224161	+	0.215699i
$404$	4.50000	−	7.79423i	0.223883	−	0.387777i
$405$	1.50000	−	0.866025i	0.0745356	−	0.0430331i
$406$		0			0
$407$		0			0
$408$	9.00000	+	5.19615i	0.445566	+	0.257248i
$409$		−	6.92820i		−	0.342578i	−0.985221	−	0.171289i	$-0.945207\pi$
$409$		−	6.92820i		−	0.342578i	0.985221	−	0.171289i	$-0.0547931\pi$
$410$		−	15.5885i		−	0.769859i
$411$		0			0
$412$	6.50000	−	11.2583i	0.320232	−	0.554658i
$413$		0			0
$414$		0			0
$415$	−3.00000	+	5.19615i	−0.147264	+	0.255069i
$416$	18.0000	−	5.19615i	0.882523	−	0.254762i
$417$	−6.50000	−	11.2583i	−0.318306	−	0.551323i
$418$		−	15.5885i		−	0.762456i
$419$	10.5000	+	18.1865i	0.512959	+	0.888470i	0.999887	+	0.0150285i	$0.00478389\pi$
$419$	10.5000	+	18.1865i	0.512959	+	0.888470i	−0.486928	+	0.873442i	$0.661883\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	19.5000	−	11.2583i	0.949245	−	0.548047i
$423$		−	17.3205i		−	0.842152i
$424$	−13.5000	+	7.79423i	−0.655618	+	0.378521i
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$	−1.50000	−	2.59808i	−0.0726752	−	0.125877i
$427$		0			0
$428$		0			0
$429$	13.5000	+	12.9904i	0.651786	+	0.627182i
$430$	16.5000	+	28.5788i	0.795701	+	1.37819i
$431$	−28.5000	−	16.4545i	−1.37280	−	0.792585i	−0.381517	−	0.924362i	$-0.624598\pi$
$431$	−28.5000	−	16.4545i	−1.37280	−	0.792585i	−0.991279	+	0.131777i	$0.957932\pi$
$432$	25.0000			1.20281
$433$	9.50000	−	16.4545i	0.456541	−	0.790752i	−0.542234	−	0.840227i	$-0.682422\pi$
$433$	9.50000	−	16.4545i	0.456541	−	0.790752i	0.998775	+	0.0494752i	$0.0157549\pi$
$434$		0			0
$435$	−4.50000	−	2.59808i	−0.215758	−	0.124568i
$436$	4.50000	−	2.59808i	0.215511	−	0.124425i
$437$		0			0
$438$	15.0000			0.716728
$439$	−8.00000			−0.381819			−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000			−0.381819			−0.190910	+	0.981608i	$0.561144\pi$
$440$	−13.5000	+	7.79423i	−0.643587	+	0.371575i
$441$		0			0
$442$	36.0000	−	10.3923i	1.71235	−	0.494312i
$443$	−7.50000	+	12.9904i	−0.356336	+	0.617192i	−0.987346	−	0.158583i	$-0.949307\pi$
$443$	−7.50000	+	12.9904i	−0.356336	+	0.617192i	0.631010	+	0.775775i	$0.282641\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	−4.50000	−	7.79423i	−0.213081	−	0.369067i
$447$		−	19.0526i		−	0.901155i
$448$		0			0
$449$	1.50000	+	0.866025i	0.0707894	+	0.0408703i	0.534977	−	0.844867i	$-0.320320\pi$
$449$	1.50000	+	0.866025i	0.0707894	+	0.0408703i	−0.464188	+	0.885737i	$0.653654\pi$
$450$	6.00000	+	3.46410i	0.282843	+	0.163299i
$451$	−27.0000			−1.27138
$452$	7.50000	−	12.9904i	0.352770	−	0.611016i
$453$			12.1244i			0.569652i
$454$	−30.0000			−1.40797
$455$		0			0
$456$	−3.00000			−0.140488
$457$			34.6410i			1.62044i	0.586127	+	0.810219i	$0.300652\pi$
$457$			34.6410i			1.62044i	−0.586127	+	0.810219i	$0.699348\pi$
$458$	−10.5000	+	18.1865i	−0.490633	+	0.849801i
$459$	30.0000			1.40028
$460$		0			0
$461$	−25.5000	−	14.7224i	−1.18765	−	0.685692i	−0.229881	−	0.973219i	$-0.573834\pi$
$461$	−25.5000	−	14.7224i	−1.18765	−	0.685692i	−0.957773	+	0.287527i	$0.907167\pi$
$462$		0			0
$463$		−	24.2487i		−	1.12693i	−0.826139	−	0.563467i	$-0.809467\pi$
$463$		−	24.2487i		−	1.12693i	0.826139	−	0.563467i	$-0.190533\pi$
$464$	7.50000	+	12.9904i	0.348179	+	0.603063i
$465$	1.50000	−	2.59808i	0.0695608	−	0.120483i
$466$	−4.50000	−	2.59808i	−0.208458	−	0.120354i
$467$	−10.5000	+	18.1865i	−0.485882	+	0.841572i	−0.999868	−	0.0162260i	$-0.994835\pi$
$467$	−10.5000	+	18.1865i	−0.485882	+	0.841572i	0.513986	+	0.857798i	$0.328168\pi$
$468$	5.00000	−	5.19615i	0.231125	−	0.240192i
$469$		0			0
$470$	−22.5000	+	12.9904i	−1.03785	+	0.599202i
$471$	−23.0000			−1.05978
$472$	−6.00000			−0.276172
$473$	49.5000	−	28.5788i	2.27601	−	1.31406i
$474$	−7.50000	+	4.33013i	−0.344486	+	0.198889i
$475$	−3.00000	−	1.73205i	−0.137649	−	0.0794719i
$476$		0			0
$477$	−9.00000	+	15.5885i	−0.412082	+	0.713746i
$478$	−18.0000			−0.823301
$479$	−25.5000	−	14.7224i	−1.16512	−	0.672685i	−0.212598	−	0.977140i	$-0.568192\pi$
$479$	−25.5000	−	14.7224i	−1.16512	−	0.672685i	−0.952527	+	0.304455i	$0.901526\pi$
$480$	−4.50000	−	7.79423i	−0.205396	−	0.355756i
$481$		0			0
$482$	−12.0000			−0.546585
$483$		0			0
$484$	−8.00000	−	13.8564i	−0.363636	−	0.629837i
$485$	−4.50000	−	7.79423i	−0.204334	−	0.353918i
$486$	24.0000	−	13.8564i	1.08866	−	0.628539i
$487$		−	24.2487i		−	1.09881i	−0.835555	−	0.549407i	$-0.814854\pi$
$487$		−	24.2487i		−	1.09881i	0.835555	−	0.549407i	$-0.185146\pi$
$488$	−10.5000	+	6.06218i	−0.475313	+	0.274422i
$489$			12.1244i			0.548282i
$490$		0			0
$491$	13.5000	+	23.3827i	0.609246	+	1.05525i	0.991365	+	0.131132i	$0.0418613\pi$
$491$	13.5000	+	23.3827i	0.609246	+	1.05525i	−0.382118	+	0.924113i	$0.624805\pi$
$492$		−	5.19615i		−	0.234261i
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	−7.50000	+	7.79423i	−0.337441	+	0.350679i
$495$	−9.00000	+	15.5885i	−0.404520	+	0.700649i
$496$	−7.50000	+	4.33013i	−0.336760	+	0.194428i
$497$		0			0
$498$	−3.00000	+	5.19615i	−0.134433	+	0.232845i
$499$	1.50000	+	0.866025i	0.0671492	+	0.0387686i	0.533199	−	0.845990i	$-0.320990\pi$
$499$	1.50000	+	0.866025i	0.0671492	+	0.0387686i	−0.466049	+	0.884759i	$0.654323\pi$
$500$		−	12.1244i		−	0.542218i
$501$			1.73205i			0.0773823i
$502$	4.50000	+	2.59808i	0.200845	+	0.115958i
$503$	−4.50000	+	7.79423i	−0.200645	+	0.347527i	−0.948736	−	0.316068i	$-0.897637\pi$
$503$	−4.50000	+	7.79423i	−0.200645	+	0.347527i	0.748091	+	0.663596i	$0.230970\pi$
$504$		0			0
$505$	13.5000	−	7.79423i	0.600742	−	0.346839i
$506$		0			0
$507$	−0.500000	−	12.9904i	−0.0222058	−	0.576923i
$508$	6.50000	+	11.2583i	0.288391	+	0.499508i
$509$		−	6.92820i		−	0.307087i	−0.988142	−	0.153544i	$-0.950931\pi$
$509$		−	6.92820i		−	0.307087i	0.988142	−	0.153544i	$-0.0490686\pi$
$510$	−9.00000	−	15.5885i	−0.398527	−	0.690268i
$511$		0			0
$512$			8.66025i			0.382733i
$513$	−7.50000	+	4.33013i	−0.331133	+	0.191180i
$514$		−	51.9615i		−	2.29192i
$515$	19.5000	−	11.2583i	0.859273	−	0.496101i
$516$	5.50000	+	9.52628i	0.242124	+	0.419371i
$517$	22.5000	+	38.9711i	0.989549	+	1.71395i
$518$		0			0
$519$	−15.0000			−0.658427
$520$	10.5000	+	2.59808i	0.460455	+	0.113933i
$521$	19.5000	+	33.7750i	0.854311	+	1.47971i	0.877283	+	0.479973i	$0.159354\pi$
$521$	19.5000	+	33.7750i	0.854311	+	1.47971i	−0.0229727	+	0.999736i	$0.507313\pi$
$522$	9.00000	+	5.19615i	0.393919	+	0.227429i
$523$	4.00000			0.174908			0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000			0.174908			0.0874539	+	0.996169i	$0.472127\pi$
$524$	−7.50000	+	12.9904i	−0.327639	+	0.567487i
$525$		0			0
$526$	−4.50000	−	2.59808i	−0.196209	−	0.113282i
$527$	−9.00000	+	5.19615i	−0.392046	+	0.226348i
$528$	−22.5000	+	12.9904i	−0.979187	+	0.565334i
$529$	−23.0000			−1.00000
$530$	27.0000			1.17281
$531$	−6.00000	+	3.46410i	−0.260378	+	0.150329i
$532$		0			0
$533$	13.5000	+	12.9904i	0.584750	+	0.562676i
$534$	−6.00000	+	10.3923i	−0.259645	+	0.449719i
$535$		0			0
$536$	−7.50000	+	12.9904i	−0.323951	+	0.561099i
$537$	−1.50000	−	2.59808i	−0.0647298	−	0.112115i
$538$			10.3923i			0.448044i
$539$		0			0
$540$	−7.50000	−	4.33013i	−0.322749	−	0.186339i
$541$	−10.5000	−	6.06218i	−0.451430	−	0.260633i	0.257004	−	0.966410i	$-0.417265\pi$
$541$	−10.5000	−	6.06218i	−0.451430	−	0.260633i	−0.708434	+	0.705777i	$0.750598\pi$
$542$	30.0000			1.28861
$543$	1.00000	−	1.73205i	0.0429141	−	0.0743294i
$544$			31.1769i			1.33670i
$545$	9.00000			0.385518
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$	−7.00000	+	12.1244i	−0.298753	+	0.517455i
$550$	−18.0000			−0.767523
$551$	−4.50000	−	2.59808i	−0.191706	−	0.110682i
$552$		0			0
$553$		0			0
$554$		−	17.3205i		−	0.735878i
$555$		0			0
$556$	6.50000	−	11.2583i	0.275661	−	0.477460i
$557$	13.5000	+	7.79423i	0.572013	+	0.330252i	0.757953	−	0.652309i	$-0.226200\pi$
$557$	13.5000	+	7.79423i	0.572013	+	0.330252i	−0.185940	+	0.982561i	$0.559533\pi$
$558$	−3.00000	+	5.19615i	−0.127000	+	0.219971i
$559$	−38.5000	−	9.52628i	−1.62838	−	0.402919i
$560$		0			0
$561$	−27.0000	+	15.5885i	−1.13994	+	0.658145i
$562$	12.0000			0.506189
$563$	36.0000			1.51722			0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000			1.51722			0.758610	+	0.651546i	$0.225879\pi$
$564$	−7.50000	+	4.33013i	−0.315807	+	0.182331i
$565$	22.5000	−	12.9904i	0.946582	−	0.546509i
$566$	28.5000	+	16.4545i	1.19794	+	0.691633i
$567$		0			0
$568$	−1.50000	+	2.59808i	−0.0629386	+	0.109013i
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$	4.50000	+	2.59808i	0.188484	+	0.108821i
$571$	11.5000	+	19.9186i	0.481260	+	0.833567i	0.999769	−	0.0215055i	$-0.00684595\pi$
$571$	11.5000	+	19.9186i	0.481260	+	0.833567i	−0.518509	+	0.855072i	$0.673513\pi$
$572$	−4.50000	+	18.1865i	−0.188154	+	0.760417i
$573$	−15.0000			−0.626634
$574$		0			0
$575$		0			0
$576$	−1.00000	−	1.73205i	−0.0416667	−	0.0721688i
$577$	−13.5000	+	7.79423i	−0.562012	+	0.324478i	−0.753953	−	0.656929i	$-0.771855\pi$
$577$	−13.5000	+	7.79423i	−0.562012	+	0.324478i	0.191940	+	0.981407i	$0.438522\pi$
$578$			32.9090i			1.36883i
$579$	−1.50000	+	0.866025i	−0.0623379	+	0.0359908i
$580$		−	5.19615i		−	0.215758i
$581$		0			0
$582$	−4.50000	−	7.79423i	−0.186531	−	0.323081i
$583$		−	46.7654i		−	1.93682i
$584$	−7.50000	−	12.9904i	−0.310352	−	0.537546i
$585$	12.0000	−	3.46410i	0.496139	−	0.143223i
$586$	−22.5000	+	38.9711i	−0.929466	+	1.60988i
$587$	13.5000	−	7.79423i	0.557205	−	0.321702i	−0.194818	−	0.980839i	$-0.562412\pi$
$587$	13.5000	−	7.79423i	0.557205	−	0.321702i	0.752023	+	0.659137i	$0.229078\pi$
$588$		0			0
$589$	1.50000	−	2.59808i	0.0618064	−	0.107052i
$590$	9.00000	+	5.19615i	0.370524	+	0.213922i
$591$			22.5167i			0.926212i
$592$		0			0
$593$	4.50000	+	2.59808i	0.184793	+	0.106690i	0.589543	−	0.807737i	$-0.299308\pi$
$593$	4.50000	+	2.59808i	0.184793	+	0.106690i	−0.404750	+	0.914428i	$0.632641\pi$
$594$	−22.5000	+	38.9711i	−0.923186	+	1.59901i
$595$		0			0
$596$	16.5000	−	9.52628i	0.675866	−	0.390212i
$597$	2.00000	−	3.46410i	0.0818546	−	0.141776i
$598$		0			0
$599$	−4.50000	−	7.79423i	−0.183865	−	0.318464i	0.759328	−	0.650708i	$-0.225528\pi$
$599$	−4.50000	−	7.79423i	−0.183865	−	0.318464i	−0.943193	+	0.332244i	$0.892194\pi$
$600$			3.46410i			0.141421i
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	0.992114	−	0.125336i	$-0.0400009\pi$
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	−0.604601	+	0.796528i	$0.706668\pi$
$602$		0			0
$603$			17.3205i			0.705346i
$604$	−10.5000	+	6.06218i	−0.427239	+	0.246667i
$605$		−	27.7128i		−	1.12669i
$606$	13.5000	−	7.79423i	0.548400	−	0.316619i
$607$	−21.5000	−	37.2391i	−0.872658	−	1.51149i	−0.859237	−	0.511578i	$-0.829061\pi$
$607$	−21.5000	−	37.2391i	−0.872658	−	1.51149i	−0.0134214	−	0.999910i	$-0.504272\pi$
$608$	−4.50000	−	7.79423i	−0.182499	−	0.316098i
$609$		0			0
$610$	21.0000			0.850265
$611$	7.50000	−	30.3109i	0.303418	−	1.22625i
$612$	6.00000	+	10.3923i	0.242536	+	0.420084i
$613$	31.5000	+	18.1865i	1.27227	+	0.734547i	0.975415	−	0.220375i	$-0.0707280\pi$
$613$	31.5000	+	18.1865i	1.27227	+	0.734547i	0.296858	+	0.954922i	$0.404061\pi$
$614$	42.0000			1.69498
$615$	4.50000	−	7.79423i	0.181458	−	0.314294i
$616$		0			0
$617$	37.5000	+	21.6506i	1.50969	+	0.871622i	0.999936	+	0.0113033i	$0.00359804\pi$
$617$	37.5000	+	21.6506i	1.50969	+	0.871622i	0.509757	+	0.860318i	$0.329735\pi$
$618$	19.5000	−	11.2583i	0.784405	−	0.452876i
$619$	−16.5000	+	9.52628i	−0.663191	+	0.382893i	−0.793492	−	0.608581i	$-0.791739\pi$
$619$	−16.5000	+	9.52628i	−0.663191	+	0.382893i	0.130301	+	0.991475i	$0.458406\pi$
$620$	3.00000			0.120483
$621$		0			0
$622$	22.5000	−	12.9904i	0.902168	−	0.520867i
$623$		0			0
$624$	17.5000	+	4.33013i	0.700561	+	0.173344i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	28.5000	+	16.4545i	1.13909	+	0.657653i
$627$	4.50000	−	7.79423i	0.179713	−	0.311272i
$628$	−11.5000	−	19.9186i	−0.458900	−	0.794838i
$629$		0			0
$630$		0			0
$631$	−40.5000	−	23.3827i	−1.61228	−	0.930850i	−0.988841	−	0.148978i	$-0.952402\pi$
$631$	−40.5000	−	23.3827i	−1.61228	−	0.930850i	−0.623439	−	0.781872i	$-0.714265\pi$
$632$	7.50000	+	4.33013i	0.298334	+	0.172243i
$633$	13.0000			0.516704
$634$	4.50000	−	7.79423i	0.178718	−	0.309548i
$635$			22.5167i			0.893546i
$636$	9.00000			0.356873
$637$		0			0
$638$	−27.0000			−1.06894
$639$			3.46410i			0.137038i
$640$	−10.5000	+	18.1865i	−0.415049	+	0.718886i
$641$	30.0000			1.18493			0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000			1.18493			0.592464	+	0.805597i	$0.298155\pi$
$642$		0			0
$643$	4.50000	+	2.59808i	0.177463	+	0.102458i	0.586100	−	0.810239i	$-0.300663\pi$
$643$	4.50000	+	2.59808i	0.177463	+	0.102458i	−0.408637	+	0.912697i	$0.633996\pi$
$644$		0			0
$645$			19.0526i			0.750194i
$646$	−9.00000	−	15.5885i	−0.354100	−	0.613320i
$647$	−4.50000	+	7.79423i	−0.176913	+	0.306423i	−0.940822	−	0.338902i	$-0.889945\pi$
$647$	−4.50000	+	7.79423i	−0.176913	+	0.306423i	0.763908	+	0.645325i	$0.223278\pi$
$648$	−1.50000	−	0.866025i	−0.0589256	−	0.0340207i
$649$	9.00000	−	15.5885i	0.353281	−	0.611900i
$650$	9.00000	+	8.66025i	0.353009	+	0.339683i
$651$		0			0
$652$	−10.5000	+	6.06218i	−0.411212	+	0.237413i
$653$	−30.0000			−1.17399			−0.586995	−	0.809590i	$-0.699689\pi$
$653$	−30.0000			−1.17399			−0.586995	+	0.809590i	$0.699689\pi$
$654$	9.00000			0.351928
$655$	−22.5000	+	12.9904i	−0.879148	+	0.507576i
$656$	−22.5000	+	12.9904i	−0.878477	+	0.507189i
$657$	−15.0000	−	8.66025i	−0.585206	−	0.337869i
$658$		0			0
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	−0.974320	−	0.225168i	$-0.927707\pi$
$659$	−7.50000	+	12.9904i	−0.292159	+	0.506033i	0.682161	+	0.731202i	$0.261040\pi$
$660$	9.00000			0.350325
$661$	−31.5000	−	18.1865i	−1.22521	−	0.707374i	−0.259184	−	0.965828i	$-0.583454\pi$
$661$	−31.5000	−	18.1865i	−1.22521	−	0.707374i	−0.966024	+	0.258454i	$0.916787\pi$
$662$	28.5000	+	49.3634i	1.10768	+	1.91856i
$663$	21.0000	+	5.19615i	0.815572	+	0.201802i
$664$	6.00000			0.232845
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−1.50000	+	0.866025i	−0.0580367	+	0.0335075i
$669$		−	5.19615i		−	0.200895i
$670$	22.5000	−	12.9904i	0.869251	−	0.501862i
$671$		−	36.3731i		−	1.40417i
$672$		0			0
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	0.875501	−	0.483216i	$-0.160531\pi$
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	−0.856228	+	0.516599i	$0.827198\pi$
$674$			38.1051i			1.46775i
$675$	5.00000	+	8.66025i	0.192450	+	0.333333i
$676$	11.0000	−	6.92820i	0.423077	−	0.266469i
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	−0.480913	−	0.876768i	$-0.659695\pi$
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	0.999760	−	0.0219013i	$-0.00697196\pi$
$678$	22.5000	−	12.9904i	0.864107	−	0.498893i
$679$		0			0
$680$	−9.00000	+	15.5885i	−0.345134	+	0.597790i
$681$	−15.0000	−	8.66025i	−0.574801	−	0.331862i
$682$		−	15.5885i		−	0.596913i
$683$			24.2487i			0.927851i	0.885874	+	0.463926i	$0.153559\pi$
$683$			24.2487i			0.927851i	−0.885874	+	0.463926i	$0.846441\pi$
$684$	−3.00000	−	1.73205i	−0.114708	−	0.0662266i
$685$		0			0
$686$		0			0
$687$	−10.5000	+	6.06218i	−0.400600	+	0.231287i
$688$	27.5000	−	47.6314i	1.04843	−	1.81593i
$689$	−22.5000	+	23.3827i	−0.857182	+	0.890809i
$690$		0			0
$691$			31.1769i			1.18603i	0.805193	+	0.593013i	$0.202062\pi$
$691$			31.1769i			1.18603i	−0.805193	+	0.593013i	$0.797938\pi$
$692$	−7.50000	−	12.9904i	−0.285107	−	0.493820i
$693$		0			0
$694$		0			0
$695$	19.5000	−	11.2583i	0.739677	−	0.427053i
$696$			5.19615i			0.196960i
$697$	−27.0000	+	15.5885i	−1.02270	+	0.590455i
$698$	4.50000	+	7.79423i	0.170328	+	0.295016i
$699$	−1.50000	−	2.59808i	−0.0567352	−	0.0982683i
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$	30.0000	−	8.66025i	1.13228	−	0.326860i
$703$		0			0
$704$	4.50000	+	2.59808i	0.169600	+	0.0979187i
$705$	−15.0000			−0.564933
$706$	1.50000	−	2.59808i	0.0564532	−	0.0977799i
$707$		0			0
$708$	3.00000	+	1.73205i	0.112747	+	0.0650945i
$709$	−10.5000	+	6.06218i	−0.394336	+	0.227670i	−0.684037	−	0.729447i	$-0.739777\pi$
$709$	−10.5000	+	6.06218i	−0.394336	+	0.227670i	0.289701	+	0.957117i	$0.406444\pi$
$710$	4.50000	−	2.59808i	0.168882	−	0.0975041i
$711$	10.0000			0.375029
$712$	12.0000			0.449719
$713$		0			0
$714$		0			0
$715$	−22.5000	+	23.3827i	−0.841452	+	0.874463i
$716$	1.50000	−	2.59808i	0.0560576	−	0.0970947i
$717$	−9.00000	−	5.19615i	−0.336111	−	0.194054i
$718$	16.5000	−	28.5788i	0.615775	−	1.06655i
$719$	−7.50000	−	12.9904i	−0.279703	−	0.484459i	0.691608	−	0.722273i	$-0.256903\pi$
$719$	−7.50000	−	12.9904i	−0.279703	−	0.484459i	−0.971311	+	0.237814i	$0.923569\pi$
$720$			17.3205i			0.645497i
$721$		0			0
$722$	−24.0000	−	13.8564i	−0.893188	−	0.515682i
$723$	−6.00000	−	3.46410i	−0.223142	−	0.128831i
$724$	2.00000			0.0743294
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		−	27.7128i		−	1.02852i
$727$	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
$730$			25.9808i			0.961591i
$731$	33.0000	−	57.1577i	1.22055	−	2.11405i
$732$	7.00000			0.258727
$733$	−43.5000	−	25.1147i	−1.60671	−	0.927634i	−0.990100	−	0.140365i	$-0.955173\pi$
$733$	−43.5000	−	25.1147i	−1.60671	−	0.927634i	−0.616609	−	0.787269i	$-0.711494\pi$
$734$	34.5000	+	19.9186i	1.27342	+	0.735208i
$735$		0			0
$736$		0			0
$737$	−22.5000	−	38.9711i	−0.828798	−	1.43552i
$738$	−9.00000	+	15.5885i	−0.331295	+	0.573819i
$739$	−34.5000	−	19.9186i	−1.26910	−	0.732717i	−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−34.5000	−	19.9186i	−1.26910	−	0.732717i	−0.974818	+	0.223001i	$0.928415\pi$
$740$		0			0
$741$	−6.00000	+	1.73205i	−0.220416	+	0.0636285i
$742$		0			0
$743$	−1.50000	+	0.866025i	−0.0550297	+	0.0317714i	−0.527262	−	0.849703i	$-0.676782\pi$
$743$	−1.50000	+	0.866025i	−0.0550297	+	0.0317714i	0.472233	+	0.881474i	$0.343448\pi$
$744$	−3.00000			−0.109985
$745$	33.0000			1.20903
$746$	28.5000	−	16.4545i	1.04346	−	0.602441i
$747$	6.00000	−	3.46410i	0.219529	−	0.126745i
$748$	−27.0000	−	15.5885i	−0.987218	−	0.569970i
$749$		0			0
$750$	10.5000	−	18.1865i	0.383406	−	0.664078i
$751$	20.0000			0.729810			0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000			0.729810			0.364905	+	0.931045i	$0.381101\pi$
$752$	37.5000	+	21.6506i	1.36748	+	0.789517i
$753$	1.50000	+	2.59808i	0.0546630	+	0.0946792i
$754$	13.5000	+	12.9904i	0.491641	+	0.473082i
$755$	−21.0000			−0.764268
$756$		0			0
$757$	8.50000	+	14.7224i	0.308938	+	0.535096i	0.978130	−	0.207993i	$-0.0666932\pi$
$757$	8.50000	+	14.7224i	0.308938	+	0.535096i	−0.669193	+	0.743089i	$0.733360\pi$
$758$	−1.50000	−	2.59808i	−0.0544825	−	0.0943664i
$759$		0			0
$760$		−	5.19615i		−	0.188484i
$761$	−25.5000	+	14.7224i	−0.924374	+	0.533688i	−0.885028	−	0.465538i	$-0.845861\pi$
$761$	−25.5000	+	14.7224i	−0.924374	+	0.533688i	−0.0393463	+	0.999226i	$0.512528\pi$
$762$			22.5167i			0.815693i
$763$		0			0
$764$	−7.50000	−	12.9904i	−0.271340	−	0.469975i
$765$			20.7846i			0.751469i
$766$	13.5000	+	23.3827i	0.487775	+	0.844851i
$767$	−12.0000	+	3.46410i	−0.433295	+	0.125081i
$768$	−9.50000	+	16.4545i	−0.342802	+	0.593750i
$769$	16.5000	−	9.52628i	0.595005	−	0.343526i	−0.172069	−	0.985085i	$-0.555045\pi$
$769$	16.5000	−	9.52628i	0.595005	−	0.343526i	0.767074	+	0.641558i	$0.221712\pi$
$770$		0			0
$771$	15.0000	−	25.9808i	0.540212	−	0.935674i
$772$	−1.50000	−	0.866025i	−0.0539862	−	0.0311689i
$773$			13.8564i			0.498380i	0.968455	+	0.249190i	$0.0801644\pi$
$773$			13.8564i			0.498380i	−0.968455	+	0.249190i	$0.919836\pi$
$774$		−	38.1051i		−	1.36966i
$775$	−3.00000	−	1.73205i	−0.107763	−	0.0622171i
$776$	−4.50000	+	7.79423i	−0.161541	+	0.279797i
$777$		0			0
$778$	4.50000	−	2.59808i	0.161333	−	0.0931455i
$779$	4.50000	−	7.79423i	0.161229	−	0.279257i
$780$	−4.50000	−	4.33013i	−0.161126	−	0.155043i
$781$	−4.50000	−	7.79423i	−0.161023	−	0.278899i
$782$		0			0
$783$	7.50000	+	12.9904i	0.268028	+	0.464238i
$784$		0			0
$785$		−	39.8372i		−	1.42185i
$786$	−22.5000	+	12.9904i	−0.802548	+	0.463352i
$787$			31.1769i			1.11134i	0.831404	+	0.555668i	$0.187538\pi$
$787$			31.1769i			1.11134i	−0.831404	+	0.555668i	$0.812462\pi$
$788$	−19.5000	+	11.2583i	−0.694659	+	0.401061i
$789$	−1.50000	−	2.59808i	−0.0534014	−	0.0924940i
$790$	−7.50000	−	12.9904i	−0.266838	−	0.462177i
$791$		0			0
$792$	18.0000			0.639602
$793$	−17.5000	+	18.1865i	−0.621443	+	0.645823i
$794$	−31.5000	−	54.5596i	−1.11789	−	1.93625i
$795$	13.5000	+	7.79423i	0.478796	+	0.276433i
$796$	4.00000			0.141776
$797$	−16.5000	+	28.5788i	−0.584460	+	1.01231i	0.410483	+	0.911868i	$0.365360\pi$
$797$	−16.5000	+	28.5788i	−0.584460	+	1.01231i	−0.994943	+	0.100446i	$0.967973\pi$
$798$		0			0
$799$	45.0000	+	25.9808i	1.59199	+	0.919133i
$800$	−9.00000	+	5.19615i	−0.318198	+	0.183712i
$801$	12.0000	−	6.92820i	0.423999	−	0.244796i
$802$	−12.0000			−0.423735
$803$	45.0000			1.58802
$804$	7.50000	−	4.33013i	0.264505	−	0.152712i
$805$		0			0
$806$	−7.50000	+	7.79423i	−0.264176	+	0.274540i
$807$	−3.00000	+	5.19615i	−0.105605	+	0.182913i
$808$	−13.5000	−	7.79423i	−0.474928	−	0.274200i
$809$	10.5000	−	18.1865i	0.369160	−	0.639404i	−0.620274	−	0.784385i	$-0.712979\pi$
$809$	10.5000	−	18.1865i	0.369160	−	0.639404i	0.989434	+	0.144981i	$0.0463120\pi$
$810$	1.50000	+	2.59808i	0.0527046	+	0.0912871i
$811$			3.46410i			0.121641i	0.998149	+	0.0608205i	$0.0193717\pi$
$811$			3.46410i			0.121641i	−0.998149	+	0.0608205i	$0.980628\pi$
$812$		0			0
$813$	15.0000	+	8.66025i	0.526073	+	0.303728i
$814$		0			0
$815$	−21.0000			−0.735598
$816$	−15.0000	+	25.9808i	−0.525105	+	0.909509i
$817$			19.0526i			0.666565i
$818$	12.0000			0.419570
$819$		0			0
$820$	9.00000			0.314294
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$		0			0
$823$	32.0000			1.11545			0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000			1.11545			0.557725	+	0.830026i	$0.311674\pi$
$824$	−19.5000	−	11.2583i	−0.679315	−	0.392203i
$825$	−9.00000	−	5.19615i	−0.313340	−	0.180907i
$826$		0			0
$827$			10.3923i			0.361376i	0.983540	+	0.180688i	$0.0578324\pi$
$827$			10.3923i			0.361376i	−0.983540	+	0.180688i	$0.942168\pi$
$828$		0			0
$829$	3.50000	−	6.06218i	0.121560	−	0.210548i	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	3.50000	−	6.06218i	0.121560	−	0.210548i	0.920383	+	0.391018i	$0.127877\pi$
$830$	−9.00000	−	5.19615i	−0.312395	−	0.180361i
$831$	5.00000	−	8.66025i	0.173448	−	0.300421i
$832$	−1.00000	−	3.46410i	−0.0346688	−	0.120096i
$833$		0			0
$834$	19.5000	−	11.2583i	0.675230	−	0.389844i
$835$	−3.00000			−0.103819
$836$	9.00000			0.311272
$837$	−7.50000	+	4.33013i	−0.259238	+	0.149671i
$838$	−31.5000	+	18.1865i	−1.08815	+	0.628243i
$839$	−1.50000	−	0.866025i	−0.0517858	−	0.0298985i	0.473884	−	0.880587i	$-0.342852\pi$
$839$	−1.50000	−	0.866025i	−0.0517858	−	0.0298985i	−0.525669	+	0.850689i	$0.676185\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	6.00000	+	3.46410i	0.206651	+	0.119310i
$844$	6.50000	+	11.2583i	0.223739	+	0.387528i
$845$	22.5000	−	0.866025i	0.774024	−	0.0297922i
$846$	30.0000			1.03142
$847$		0			0
$848$	−22.5000	−	38.9711i	−0.772653	−	1.33827i
$849$	9.50000	+	16.4545i	0.326039	+	0.564716i
$850$	−18.0000	+	10.3923i	−0.617395	+	0.356453i
$851$		0			0
$852$	1.50000	−	0.866025i	0.0513892	−	0.0296695i
$853$		−	41.5692i		−	1.42330i	−0.702533	−	0.711651i	$-0.747948\pi$
$853$		−	41.5692i		−	1.42330i	0.702533	−	0.711651i	$-0.252052\pi$
$854$		0			0
$855$	−3.00000	−	5.19615i	−0.102598	−	0.177705i
$856$		0			0
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	−0.997176	−	0.0751033i	$-0.976071\pi$
$857$	−16.5000	−	28.5788i	−0.563629	−	0.976235i	0.433546	−	0.901131i	$-0.357262\pi$
$858$	−22.5000	+	23.3827i	−0.768137	+	0.798272i
$859$	−14.5000	+	25.1147i	−0.494734	+	0.856904i	−0.999982	−	0.00607046i	$-0.998068\pi$
$859$	−14.5000	+	25.1147i	−0.494734	+	0.856904i	0.505248	+	0.862974i	$0.331401\pi$
$860$	−16.5000	+	9.52628i	−0.562645	+	0.324843i
$861$		0			0
$862$	28.5000	−	49.3634i	0.970714	−	1.68133i
$863$	1.50000	+	0.866025i	0.0510606	+	0.0294798i	0.525313	−	0.850909i	$-0.323948\pi$
$863$	1.50000	+	0.866025i	0.0510606	+	0.0294798i	−0.474252	+	0.880389i	$0.657282\pi$
$864$			25.9808i			0.883883i
$865$		−	25.9808i		−	0.883372i
$866$	28.5000	+	16.4545i	0.968469	+	0.559146i
$867$	−9.50000	+	16.4545i	−0.322637	+	0.558824i
$868$		0			0
$869$	−22.5000	+	12.9904i	−0.763260	+	0.440668i
$870$	4.50000	−	7.79423i	0.152564	−	0.264249i
$871$	−7.50000	+	30.3109i	−0.254128	+	1.02705i
$872$	−4.50000	−	7.79423i	−0.152389	−	0.263946i
$873$			10.3923i			0.351726i
$874$		0			0
$875$		0			0
$876$			8.66025i			0.292603i
$877$	1.50000	−	0.866025i	0.0506514	−	0.0292436i	−0.474460	−	0.880277i	$-0.657357\pi$
$877$	1.50000	−	0.866025i	0.0506514	−	0.0292436i	0.525112	+	0.851033i	$0.324023\pi$
$878$		−	13.8564i		−	0.467631i
$879$	−22.5000	+	12.9904i	−0.758906	+	0.438155i
$880$	−22.5000	−	38.9711i	−0.758475	−	1.31372i
$881$	−16.5000	−	28.5788i	−0.555899	−	0.962846i	−0.997833	−	0.0657979i	$-0.979041\pi$
$881$	−16.5000	−	28.5788i	−0.555899	−	0.962846i	0.441934	−	0.897048i	$-0.354293\pi$
$882$		0			0
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$	6.00000	+	20.7846i	0.201802	+	0.699062i
$885$	3.00000	+	5.19615i	0.100844	+	0.174667i
$886$	−22.5000	−	12.9904i	−0.755902	−	0.436420i
$887$	−24.0000			−0.805841			−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000			−0.805841			−0.402921	+	0.915235i	$0.632005\pi$
$888$		0			0
$889$		0			0
$890$	−18.0000	−	10.3923i	−0.603361	−	0.348351i
$891$	4.50000	−	2.59808i	0.150756	−	0.0870388i
$892$	4.50000	−	2.59808i	0.150671	−	0.0869900i
$893$	−15.0000			−0.501956
$894$	33.0000			1.10369
$895$	4.50000	−	2.59808i	0.150418	−	0.0868441i
$896$		0			0
$897$		0			0
$898$	−1.50000	+	2.59808i	−0.0500556	+	0.0866989i
$899$	−4.50000	−	2.59808i	−0.150083	−	0.0866507i
$900$	−2.00000	+	3.46410i	−0.0666667	+	0.115470i
$901$	−27.0000	−	46.7654i	−0.899500	−	1.55798i
$902$		−	46.7654i		−	1.55712i
$903$		0			0
$904$	−22.5000	−	12.9904i	−0.748339	−	0.432054i
$905$	3.00000	+	1.73205i	0.0997234	+	0.0575753i
$906$	−21.0000			−0.697678
$907$	14.5000	−	25.1147i	0.481465	−	0.833921i	−0.518309	−	0.855193i	$-0.673438\pi$
$907$	14.5000	−	25.1147i	0.481465	−	0.833921i	0.999774	+	0.0212722i	$0.00677166\pi$
$908$		−	17.3205i		−	0.574801i
$909$	−18.0000			−0.597022
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		−	8.66025i		−	0.286770i
$913$	−9.00000	+	15.5885i	−0.297857	+	0.515903i
$914$	−60.0000			−1.98462
$915$	10.5000	+	6.06218i	0.347119	+	0.200409i
$916$	−10.5000	−	6.06218i	−0.346930	−	0.200300i
$917$		0			0
$918$			51.9615i			1.71499i
$919$	23.5000	+	40.7032i	0.775193	+	1.34267i	0.934686	+	0.355475i	$0.115681\pi$
$919$	23.5000	+	40.7032i	0.775193	+	1.34267i	−0.159492	+	0.987199i	$0.550986\pi$
$920$		0			0
$921$	21.0000	+	12.1244i	0.691974	+	0.399511i
$922$	25.5000	−	44.1673i	0.839798	−	1.45457i
$923$	−1.50000	+	6.06218i	−0.0493731	+	0.199539i
$924$		0			0
$925$		0			0
$926$	42.0000			1.38021
$927$	−26.0000			−0.853952
$928$	−13.5000	+	7.79423i	−0.443159	+	0.255858i
$929$	40.5000	−	23.3827i	1.32876	−	0.767161i	0.343654	−	0.939096i	$-0.388335\pi$
$929$	40.5000	−	23.3827i	1.32876	−	0.767161i	0.985108	+	0.171935i	$0.0550020\pi$
$930$	4.50000	+	2.59808i	0.147561	+	0.0851943i
$931$		0			0
$932$	1.50000	−	2.59808i	0.0491341	−	0.0851028i
$933$	15.0000			0.491078
$934$	−31.5000	−	18.1865i	−1.03071	−	0.595082i
$935$	−27.0000	−	46.7654i	−0.882994	−	1.52939i
$936$	−9.00000	−	8.66025i	−0.294174	−	0.283069i
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$		0			0
$939$	9.50000	+	16.4545i	0.310021	+	0.536972i
$940$	−7.50000	−	12.9904i	−0.244623	−	0.423700i
$941$	4.50000	−	2.59808i	0.146696	−	0.0846949i	−0.424856	−	0.905261i	$-0.639675\pi$
$941$	4.50000	−	2.59808i	0.146696	−	0.0846949i	0.571551	+	0.820566i	$0.306342\pi$
$942$		−	39.8372i		−	1.29797i
$943$		0			0
$944$		−	17.3205i		−	0.563735i
$945$		0			0
$946$	49.5000	+	85.7365i	1.60938	+	2.78753i
$947$			38.1051i			1.23825i	0.785292	+	0.619125i	$0.212513\pi$
$947$			38.1051i			1.23825i	−0.785292	+	0.619125i	$0.787487\pi$
$948$	−2.50000	−	4.33013i	−0.0811962	−	0.140636i
$949$	−22.5000	−	21.6506i	−0.730381	−	0.702809i
$950$	3.00000	−	5.19615i	0.0973329	−	0.168585i
$951$	4.50000	−	2.59808i	0.145922	−	0.0842484i
$952$		0			0
$953$	28.5000	−	49.3634i	0.923206	−	1.59904i	0.128784	−	0.991673i	$-0.458893\pi$
$953$	28.5000	−	49.3634i	0.923206	−	1.59904i	0.794422	−	0.607366i	$-0.207774\pi$
$954$	−27.0000	−	15.5885i	−0.874157	−	0.504695i
$955$		−	25.9808i		−	0.840718i
$956$		−	10.3923i		−	0.336111i
$957$	−13.5000	−	7.79423i	−0.436393	−	0.251952i
$958$	25.5000	−	44.1673i	0.823868	−	1.42698i
$959$		0			0
$960$	−1.50000	+	0.866025i	−0.0484123	+	0.0279508i
$961$	−14.0000	+	24.2487i	−0.451613	+	0.782216i
$962$		0			0
$963$		0			0
$964$		−	6.92820i		−	0.223142i
$965$	−1.50000	−	2.59808i	−0.0482867	−	0.0836350i
$966$		0			0
$967$		−	10.3923i		−	0.334194i	−0.985940	−	0.167097i	$-0.946561\pi$
$967$		−	10.3923i		−	0.334194i	0.985940	−	0.167097i	$-0.0534393\pi$
$968$	−24.0000	+	13.8564i	−0.771389	+	0.445362i
$969$		−	10.3923i		−	0.333849i
$970$	13.5000	−	7.79423i	0.433459	−	0.250258i
$971$	10.5000	+	18.1865i	0.336961	+	0.583634i	0.983860	−	0.178942i	$-0.0572676\pi$
$971$	10.5000	+	18.1865i	0.336961	+	0.583634i	−0.646899	+	0.762576i	$0.723934\pi$
$972$	8.00000	+	13.8564i	0.256600	+	0.444444i
$973$		0			0
$974$	42.0000			1.34577
$975$	2.00000	+	6.92820i	0.0640513	+	0.221880i
$976$	−17.5000	−	30.3109i	−0.560161	−	0.970228i
$977$	−16.5000	−	9.52628i	−0.527882	−	0.304773i	0.212272	−	0.977211i	$-0.431914\pi$
$977$	−16.5000	−	9.52628i	−0.527882	−	0.304773i	−0.740153	+	0.672438i	$0.765247\pi$
$978$	−21.0000			−0.671506
$979$	−18.0000	+	31.1769i	−0.575282	+	0.996419i
$980$		0			0
$981$	−9.00000	−	5.19615i	−0.287348	−	0.165900i
$982$	−40.5000	+	23.3827i	−1.29241	+	0.746171i
$983$	31.5000	−	18.1865i	1.00469	−	0.580060i	0.0950602	−	0.995472i	$-0.469696\pi$
$983$	31.5000	−	18.1865i	1.00469	−	0.580060i	0.909634	+	0.415411i	$0.136362\pi$
$984$	−9.00000			−0.286910
$985$	−39.0000			−1.24264
$986$	−27.0000	+	15.5885i	−0.859855	+	0.496438i
$987$		0			0
$988$	−4.50000	−	4.33013i	−0.143164	−	0.137760i
$989$		0			0
$990$	−27.0000	−	15.5885i	−0.858116	−	0.495434i
$991$	−29.5000	+	51.0955i	−0.937098	+	1.62310i	−0.166250	+	0.986084i	$0.553166\pi$
$991$	−29.5000	+	51.0955i	−0.937098	+	1.62310i	−0.770849	+	0.637018i	$0.780168\pi$
$992$	−4.50000	−	7.79423i	−0.142875	−	0.247467i
$993$			32.9090i			1.04433i
$994$		0			0
$995$	6.00000	+	3.46410i	0.190213	+	0.109819i
$996$	−3.00000	−	1.73205i	−0.0950586	−	0.0548821i
$997$	−2.00000			−0.0633406			−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000			−0.0633406			−0.0316703	+	0.999498i	$0.510083\pi$
$998$	−1.50000	+	2.59808i	−0.0474817	+	0.0822407i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.b.569.1		2
7.2	even	3		637.2.q.b.491.1		2
7.3	odd	6		91.2.u.a.88.1	yes	2
7.4	even	3		637.2.u.a.361.1		2
7.5	odd	6		637.2.q.c.491.1		2
7.6	odd	2		91.2.k.a.23.1	yes	2
13.4	even	6		637.2.u.a.30.1		2
21.17	even	6		819.2.do.c.361.1		2
21.20	even	2		819.2.bm.a.478.1		2
91.2	odd	12		8281.2.a.w.1.2		2
91.4	even	6	inner	637.2.k.b.459.1		2
91.17	odd	6		91.2.k.a.4.1	✓	2
91.24	even	12		1183.2.e.e.508.2		4
91.30	even	6		637.2.q.b.589.1		2
91.37	odd	12		8281.2.a.w.1.1		2
91.41	even	12		1183.2.e.e.170.1		4
91.54	even	12		8281.2.a.s.1.2		2
91.69	odd	6		91.2.u.a.30.1	yes	2
91.76	even	12		1183.2.e.e.170.2		4
91.80	even	12		1183.2.e.e.508.1		4
91.82	odd	6		637.2.q.c.589.1		2
91.89	even	12		8281.2.a.s.1.1		2
273.17	even	6		819.2.bm.a.550.1		2
273.251	even	6		819.2.do.c.667.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.k.a.4.1	✓	2	91.17	odd	6
91.2.k.a.23.1	yes	2	7.6	odd	2
91.2.u.a.30.1	yes	2	91.69	odd	6
91.2.u.a.88.1	yes	2	7.3	odd	6
637.2.k.b.459.1		2	91.4	even	6	inner
637.2.k.b.569.1		2	1.1	even	1	trivial
637.2.q.b.491.1		2	7.2	even	3
637.2.q.b.589.1		2	91.30	even	6
637.2.q.c.491.1		2	7.5	odd	6
637.2.q.c.589.1		2	91.82	odd	6
637.2.u.a.30.1		2	13.4	even	6
637.2.u.a.361.1		2	7.4	even	3
819.2.bm.a.478.1		2	21.20	even	2
819.2.bm.a.550.1		2	273.17	even	6
819.2.do.c.361.1		2	21.17	even	6
819.2.do.c.667.1		2	273.251	even	6
1183.2.e.e.170.1		4	91.41	even	12
1183.2.e.e.170.2		4	91.76	even	12
1183.2.e.e.508.1		4	91.80	even	12
1183.2.e.e.508.2		4	91.24	even	12
8281.2.a.s.1.1		2	91.89	even	12
8281.2.a.s.1.2		2	91.54	even	12
8281.2.a.w.1.1		2	91.37	odd	12
8281.2.a.w.1.2		2	91.2	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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.73205i q^{2} +(-0.500000 + 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-4.50000 - 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.00000 + 3.46410i) q^{13} +(1.50000 - 0.866025i) q^{15} -5.00000 q^{16} -6.00000 q^{17} +(-3.00000 + 1.73205i) q^{18} +(1.50000 - 0.866025i) q^{19} +(1.50000 + 0.866025i) q^{20} +(4.50000 - 7.79423i) q^{22} +(-1.50000 - 0.866025i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-6.00000 + 1.73205i) q^{26} -5.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(1.50000 + 2.59808i) q^{30} +(1.50000 - 0.866025i) q^{31} -5.19615i q^{32} +(4.50000 - 2.59808i) q^{33} -10.3923i q^{34} +(-1.00000 - 1.73205i) q^{36} +(1.50000 + 2.59808i) q^{38} +(-3.50000 - 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{40} +(4.50000 - 2.59808i) q^{41} +(-5.50000 + 9.52628i) q^{43} +(4.50000 + 2.59808i) q^{44} -3.46410i q^{45} +(-7.50000 - 4.33013i) q^{47} +(2.50000 - 4.33013i) q^{48} +(3.00000 - 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(-1.00000 - 3.46410i) q^{52} +(4.50000 + 7.79423i) q^{53} -8.66025i q^{54} +(4.50000 + 7.79423i) q^{55} +1.73205i q^{57} +(4.50000 - 2.59808i) q^{58} +3.46410i q^{59} +(-1.50000 + 0.866025i) q^{60} +(3.50000 + 6.06218i) q^{61} +(1.50000 + 2.59808i) q^{62} -1.00000 q^{64} +(1.50000 - 6.06218i) q^{65} +(4.50000 + 7.79423i) q^{66} +(7.50000 + 4.33013i) q^{67} +6.00000 q^{68} +(1.50000 + 0.866025i) q^{71} +(-3.00000 + 1.73205i) q^{72} +(-7.50000 + 4.33013i) q^{73} +2.00000 q^{75} +(-1.50000 + 0.866025i) q^{76} +(1.50000 - 6.06218i) q^{78} +(2.50000 - 4.33013i) q^{79} +(7.50000 + 4.33013i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{82} -3.46410i q^{83} +(9.00000 + 5.19615i) q^{85} +(-16.5000 - 9.52628i) q^{86} +3.00000 q^{87} +(4.50000 - 7.79423i) q^{88} -6.92820i q^{89} +6.00000 q^{90} +1.73205i q^{93} +(7.50000 - 12.9904i) q^{94} -3.00000 q^{95} +(4.50000 + 2.59808i) q^{96} +(4.50000 + 2.59808i) q^{97} -10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} - 2 q^{4} - 3 q^{5} - 3 q^{6} + 2 q^{9} + 3 q^{10} - 9 q^{11} + q^{12} + 2 q^{13} + 3 q^{15} - 10 q^{16} - 12 q^{17} - 6 q^{18} + 3 q^{19} + 3 q^{20} + 9 q^{22} - 3 q^{24} - 2 q^{25} - 12 q^{26}+ \cdots + 9 q^{97}+O(q^{100}) \) 2 * q - q^3 - 2 * q^4 - 3 * q^5 - 3 * q^6 + 2 * q^9 + 3 * q^10 - 9 * q^11 + q^12 + 2 * q^13 + 3 * q^15 - 10 * q^16 - 12 * q^17 - 6 * q^18 + 3 * q^19 + 3 * q^20 + 9 * q^22 - 3 * q^24 - 2 * q^25 - 12 * q^26 - 10 * q^27 - 3 * q^29 + 3 * q^30 + 3 * q^31 + 9 * q^33 - 2 * q^36 + 3 * q^38 - 7 * q^39 + 3 * q^40 + 9 * q^41 - 11 * q^43 + 9 * q^44 - 15 * q^47 + 5 * q^48 + 6 * q^50 + 6 * q^51 - 2 * q^52 + 9 * q^53 + 9 * q^55 + 9 * q^58 - 3 * q^60 + 7 * q^61 + 3 * q^62 - 2 * q^64 + 3 * q^65 + 9 * q^66 + 15 * q^67 + 12 * q^68 + 3 * q^71 - 6 * q^72 - 15 * q^73 + 4 * q^75 - 3 * q^76 + 3 * q^78 + 5 * q^79 + 15 * q^80 - q^81 + 9 * q^82 + 18 * q^85 - 33 * q^86 + 6 * q^87 + 9 * q^88 + 12 * q^90 + 15 * q^94 - 6 * q^95 + 9 * q^96 + 9 * q^97

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