LMFDB - Embedded newform 637.2.r.c.324.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(116,637)]

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([4, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.r (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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			324.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	637.324
Dual form			637.2.r.c.116.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 + 1.00000i) q^{2} +(1.00000 + 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.866025 + 0.500000i) q^{5} +4.00000i q^{6} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.73205 + 1.00000i) q^{2} +(1.00000 + 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.866025 + 0.500000i) q^{5} +4.00000i q^{6} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-1.73205 + 1.00000i) q^{11} +(-2.00000 + 3.46410i) q^{12} +(-2.00000 + 3.00000i) q^{13} +2.00000i q^{15} +(2.00000 - 3.46410i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-1.73205 + 1.00000i) q^{18} +(-2.59808 - 1.50000i) q^{19} +2.00000i q^{20} -4.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-6.46410 + 3.19615i) q^{26} +4.00000 q^{27} +3.00000 q^{29} +(-2.00000 + 3.46410i) q^{30} +(2.59808 - 1.50000i) q^{31} +(6.92820 - 4.00000i) q^{32} +(-3.46410 - 2.00000i) q^{33} +12.0000i q^{34} -2.00000 q^{36} +(-5.19615 - 3.00000i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-7.19615 - 0.464102i) q^{39} -10.0000i q^{41} +1.00000 q^{43} +(-3.46410 - 2.00000i) q^{44} +(-0.866025 + 0.500000i) q^{45} +(5.19615 - 3.00000i) q^{46} +(-9.52628 - 5.50000i) q^{47} +8.00000 q^{48} -8.00000i q^{50} +(-6.00000 + 10.3923i) q^{51} +(-7.19615 - 0.464102i) q^{52} +(4.50000 + 7.79423i) q^{53} +(6.92820 + 4.00000i) q^{54} -2.00000 q^{55} -6.00000i q^{57} +(5.19615 + 3.00000i) q^{58} +(-6.92820 + 4.00000i) q^{59} +(-3.46410 + 2.00000i) q^{60} +(4.00000 - 6.92820i) q^{61} +6.00000 q^{62} +8.00000 q^{64} +(-3.23205 + 1.59808i) q^{65} +(-4.00000 - 6.92820i) q^{66} +(10.3923 - 6.00000i) q^{67} +(-6.00000 + 10.3923i) q^{68} +6.00000 q^{69} +14.0000i q^{71} +(-7.79423 + 4.50000i) q^{73} +(-6.00000 - 10.3923i) q^{74} +(4.00000 - 6.92820i) q^{75} -6.00000i q^{76} +(-12.0000 - 8.00000i) q^{78} +(4.50000 - 7.79423i) q^{79} +(3.46410 - 2.00000i) q^{80} +(5.50000 + 9.52628i) q^{81} +(10.0000 - 17.3205i) q^{82} -11.0000i q^{83} +6.00000i q^{85} +(1.73205 + 1.00000i) q^{86} +(3.00000 + 5.19615i) q^{87} +(4.33013 + 2.50000i) q^{89} -2.00000 q^{90} +6.00000 q^{92} +(5.19615 + 3.00000i) q^{93} +(-11.0000 - 19.0526i) q^{94} +(-1.50000 - 2.59808i) q^{95} +(13.8564 + 8.00000i) q^{96} +9.00000i q^{97} -2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} + 4 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 + 4 * q^4 - 2 * q^9	$ 4 q + 4 q^{3} + 4 q^{4} - 2 q^{9} + 4 q^{10} - 8 q^{12} - 8 q^{13} + 8 q^{16} + 12 q^{17} - 16 q^{22} + 6 q^{23} - 8 q^{25} - 12 q^{26} + 16 q^{27} + 12 q^{29} - 8 q^{30} - 8 q^{36} - 12 q^{38} - 8 q^{39} + 4 q^{43} + 32 q^{48} - 24 q^{51} - 8 q^{52} + 18 q^{53} - 8 q^{55} + 16 q^{61} + 24 q^{62} + 32 q^{64} - 6 q^{65} - 16 q^{66} - 24 q^{68} + 24 q^{69} - 24 q^{74} + 16 q^{75} - 48 q^{78} + 18 q^{79} + 22 q^{81} + 40 q^{82} + 12 q^{87} - 8 q^{90} + 24 q^{92} - 44 q^{94} - 6 q^{95}+O(q^{100}) $ 4 * q + 4 * q^3 + 4 * q^4 - 2 * q^9 + 4 * q^10 - 8 * q^12 - 8 * q^13 + 8 * q^16 + 12 * q^17 - 16 * q^22 + 6 * q^23 - 8 * q^25 - 12 * q^26 + 16 * q^27 + 12 * q^29 - 8 * q^30 - 8 * q^36 - 12 * q^38 - 8 * q^39 + 4 * q^43 + 32 * q^48 - 24 * q^51 - 8 * q^52 + 18 * q^53 - 8 * q^55 + 16 * q^61 + 24 * q^62 + 32 * q^64 - 6 * q^65 - 16 * q^66 - 24 * q^68 + 24 * q^69 - 24 * q^74 + 16 * q^75 - 48 * q^78 + 18 * q^79 + 22 * q^81 + 40 * q^82 + 12 * q^87 - 8 * q^90 + 24 * q^92 - 44 * q^94 - 6 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.73205	+	1.00000i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$2$	1.73205	+	1.00000i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	0.995782	+	0.0917517i	$0.0292466\pi$
$3$	1.00000	+	1.73205i	0.577350	+	1.00000i	−0.418432	+	0.908248i	$0.637420\pi$
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i	0.680989	−	0.732294i	$-0.261550\pi$
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i	−0.293691	+	0.955901i	$0.594884\pi$
$6$			4.00000i			1.63299i
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	−1.73205	+	1.00000i	−0.522233	+	0.301511i	−0.737848	−	0.674967i	$-0.764158\pi$
$11$	−1.73205	+	1.00000i	−0.522233	+	0.301511i	0.215615	+	0.976478i	$0.430824\pi$
$12$	−2.00000	+	3.46410i	−0.577350	+	1.00000i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$13$	−2.00000	+	3.00000i	−0.554700	+	0.832050i
$14$		0			0
$15$			2.00000i			0.516398i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	−1.73205	+	1.00000i	−0.408248	+	0.235702i
$19$	−2.59808	−	1.50000i	−0.596040	−	0.344124i	0.171442	−	0.985194i	$-0.445157\pi$
$19$	−2.59808	−	1.50000i	−0.596040	−	0.344124i	−0.767482	+	0.641071i	$0.778491\pi$
$20$			2.00000i			0.447214i
$21$		0			0
$22$	−4.00000			−0.852803
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−6.46410	+	3.19615i	−1.26771	+	0.626817i
$27$	4.00000			0.769800
$28$		0			0
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	−2.00000	+	3.46410i	−0.365148	+	0.632456i
$31$	2.59808	−	1.50000i	0.466628	−	0.269408i	−0.248199	−	0.968709i	$-0.579839\pi$
$31$	2.59808	−	1.50000i	0.466628	−	0.269408i	0.714827	+	0.699301i	$0.246505\pi$
$32$	6.92820	−	4.00000i	1.22474	−	0.707107i
$33$	−3.46410	−	2.00000i	−0.603023	−	0.348155i
$34$			12.0000i			2.05798i
$35$		0			0
$36$	−2.00000			−0.333333
$37$	−5.19615	−	3.00000i	−0.854242	−	0.493197i	0.00783774	−	0.999969i	$-0.497505\pi$
$37$	−5.19615	−	3.00000i	−0.854242	−	0.493197i	−0.862080	+	0.506772i	$0.830838\pi$
$38$	−3.00000	−	5.19615i	−0.486664	−	0.842927i
$39$	−7.19615	−	0.464102i	−1.15231	−	0.0743157i
$40$		0			0
$41$		−	10.0000i		−	1.56174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$		−	10.0000i		−	1.56174i	0.624695	−	0.780869i	$-0.285223\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	−3.46410	−	2.00000i	−0.522233	−	0.301511i
$45$	−0.866025	+	0.500000i	−0.129099	+	0.0745356i
$46$	5.19615	−	3.00000i	0.766131	−	0.442326i
$47$	−9.52628	−	5.50000i	−1.38955	−	0.802257i	−0.396286	−	0.918127i	$-0.629701\pi$
$47$	−9.52628	−	5.50000i	−1.38955	−	0.802257i	−0.993264	+	0.115870i	$0.963035\pi$
$48$	8.00000			1.15470
$49$		0			0
$50$		−	8.00000i		−	1.13137i
$51$	−6.00000	+	10.3923i	−0.840168	+	1.45521i
$52$	−7.19615	−	0.464102i	−0.997927	−	0.0643593i
$53$	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	$0.621227\pi$
$54$	6.92820	+	4.00000i	0.942809	+	0.544331i
$55$	−2.00000			−0.269680
$56$		0			0
$57$		−	6.00000i		−	0.794719i
$58$	5.19615	+	3.00000i	0.682288	+	0.393919i
$59$	−6.92820	+	4.00000i	−0.901975	+	0.520756i	−0.877841	−	0.478953i	$-0.841016\pi$
$59$	−6.92820	+	4.00000i	−0.901975	+	0.520756i	−0.0241347	+	0.999709i	$0.507683\pi$
$60$	−3.46410	+	2.00000i	−0.447214	+	0.258199i
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	8.00000			1.00000
$65$	−3.23205	+	1.59808i	−0.400887	+	0.198217i
$66$	−4.00000	−	6.92820i	−0.492366	−	0.852803i
$67$	10.3923	−	6.00000i	1.26962	−	0.733017i	0.294706	−	0.955588i	$-0.404778\pi$
$67$	10.3923	−	6.00000i	1.26962	−	0.733017i	0.974916	+	0.222571i	$0.0714450\pi$
$68$	−6.00000	+	10.3923i	−0.727607	+	1.26025i
$69$	6.00000			0.722315
$70$		0			0
$71$			14.0000i			1.66149i	0.556650	+	0.830747i	$0.312086\pi$
$71$			14.0000i			1.66149i	−0.556650	+	0.830747i	$0.687914\pi$
$72$		0			0
$73$	−7.79423	+	4.50000i	−0.912245	+	0.526685i	−0.881153	−	0.472831i	$-0.843232\pi$
$73$	−7.79423	+	4.50000i	−0.912245	+	0.526685i	−0.0310925	+	0.999517i	$0.509899\pi$
$74$	−6.00000	−	10.3923i	−0.697486	−	1.20808i
$75$	4.00000	−	6.92820i	0.461880	−	0.800000i
$76$		−	6.00000i		−	0.688247i
$77$		0			0
$78$	−12.0000	−	8.00000i	−1.35873	−	0.905822i
$79$	4.50000	−	7.79423i	0.506290	−	0.876919i	−0.493684	−	0.869641i	$-0.664350\pi$
$79$	4.50000	−	7.79423i	0.506290	−	0.876919i	0.999974	−	0.00727784i	$-0.00231663\pi$
$80$	3.46410	−	2.00000i	0.387298	−	0.223607i
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	10.0000	−	17.3205i	1.10432	−	1.91273i
$83$		−	11.0000i		−	1.20741i	−0.797209	−	0.603703i	$-0.793691\pi$
$83$		−	11.0000i		−	1.20741i	0.797209	−	0.603703i	$-0.206309\pi$
$84$		0			0
$85$			6.00000i			0.650791i
$86$	1.73205	+	1.00000i	0.186772	+	0.107833i
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$		0			0
$89$	4.33013	+	2.50000i	0.458993	+	0.264999i	0.711621	−	0.702564i	$-0.247962\pi$
$89$	4.33013	+	2.50000i	0.458993	+	0.264999i	−0.252628	+	0.967563i	$0.581295\pi$
$90$	−2.00000			−0.210819
$91$		0			0
$92$	6.00000			0.625543
$93$	5.19615	+	3.00000i	0.538816	+	0.311086i
$94$	−11.0000	−	19.0526i	−1.13456	−	1.96512i
$95$	−1.50000	−	2.59808i	−0.153897	−	0.266557i
$96$	13.8564	+	8.00000i	1.41421	+	0.816497i
$97$			9.00000i			0.913812i	0.889515	+	0.456906i	$0.151042\pi$
$97$			9.00000i			0.913812i	−0.889515	+	0.456906i	$0.848958\pi$
$98$		0			0
$99$		−	2.00000i		−	0.201008i
$100$	4.00000	−	6.92820i	0.400000	−	0.692820i
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$	−20.7846	+	12.0000i	−2.05798	+	1.18818i
$103$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$103$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$104$		0			0
$105$		0			0
$106$			18.0000i			1.74831i
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	4.00000	+	6.92820i	0.384900	+	0.666667i
$109$	−15.5885	+	9.00000i	−1.49310	+	0.862044i	−0.999969	−	0.00790932i	$-0.997482\pi$
$109$	−15.5885	+	9.00000i	−1.49310	+	0.862044i	−0.493135	+	0.869953i	$0.664149\pi$
$110$	−3.46410	−	2.00000i	−0.330289	−	0.190693i
$111$		−	12.0000i		−	1.13899i
$112$		0			0
$113$	−15.0000			−1.41108			−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000			−1.41108			−0.705541	+	0.708669i	$0.749296\pi$
$114$	6.00000	−	10.3923i	0.561951	−	0.973329i
$115$	2.59808	−	1.50000i	0.242272	−	0.139876i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	−1.59808	−	3.23205i	−0.147742	−	0.298803i
$118$	−16.0000			−1.47292
$119$		0			0
$120$		0			0
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$	13.8564	−	8.00000i	1.25450	−	0.724286i
$123$	17.3205	−	10.0000i	1.56174	−	0.901670i
$124$	5.19615	+	3.00000i	0.466628	+	0.269408i
$125$		−	9.00000i		−	0.804984i
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$	1.00000	+	1.73205i	0.0880451	+	0.152499i
$130$	−7.19615	−	0.464102i	−0.631144	−	0.0407044i
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$		−	8.00000i		−	0.696311i
$133$		0			0
$134$	24.0000			2.07328
$135$	3.46410	+	2.00000i	0.298142	+	0.172133i
$136$		0			0
$137$	1.73205	−	1.00000i	0.147979	−	0.0854358i	−0.424182	−	0.905577i	$-0.639438\pi$
$137$	1.73205	−	1.00000i	0.147979	−	0.0854358i	0.572161	+	0.820141i	$0.306105\pi$
$138$	10.3923	+	6.00000i	0.884652	+	0.510754i
$139$	−18.0000			−1.52674			−0.763370	−	0.645961i	$-0.776457\pi$
$139$	−18.0000			−1.52674			−0.763370	+	0.645961i	$0.776457\pi$
$140$		0			0
$141$		−	22.0000i		−	1.85273i
$142$	−14.0000	+	24.2487i	−1.17485	+	2.03491i
$143$	0.464102	−	7.19615i	0.0388101	−	0.601772i
$144$	2.00000	+	3.46410i	0.166667	+	0.288675i
$145$	2.59808	+	1.50000i	0.215758	+	0.124568i
$146$	−18.0000			−1.48969
$147$		0			0
$148$		−	12.0000i		−	0.986394i
$149$	8.66025	+	5.00000i	0.709476	+	0.409616i	0.810867	−	0.585231i	$-0.198996\pi$
$149$	8.66025	+	5.00000i	0.709476	+	0.409616i	−0.101391	+	0.994847i	$0.532329\pi$
$150$	13.8564	−	8.00000i	1.13137	−	0.653197i
$151$	5.19615	−	3.00000i	0.422857	−	0.244137i	−0.273442	−	0.961888i	$-0.588162\pi$
$151$	5.19615	−	3.00000i	0.422857	−	0.244137i	0.696299	+	0.717752i	$0.254829\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$		0			0
$155$	3.00000			0.240966
$156$	−6.39230	−	12.9282i	−0.511794	−	1.03508i
$157$	9.00000	+	15.5885i	0.718278	+	1.24409i	0.961681	+	0.274169i	$0.0884028\pi$
$157$	9.00000	+	15.5885i	0.718278	+	1.24409i	−0.243403	+	0.969925i	$0.578264\pi$
$158$	15.5885	−	9.00000i	1.24015	−	0.716002i
$159$	−9.00000	+	15.5885i	−0.713746	+	1.23625i
$160$	8.00000			0.632456
$161$		0			0
$162$			22.0000i			1.72848i
$163$	10.3923	+	6.00000i	0.813988	+	0.469956i	0.848339	−	0.529454i	$-0.177603\pi$
$163$	10.3923	+	6.00000i	0.813988	+	0.469956i	−0.0343508	+	0.999410i	$0.510936\pi$
$164$	17.3205	−	10.0000i	1.35250	−	0.780869i
$165$	−2.00000	−	3.46410i	−0.155700	−	0.269680i
$166$	11.0000	−	19.0526i	0.853766	−	1.47877i
$167$			1.00000i			0.0773823i	0.999251	+	0.0386912i	$0.0123189\pi$
$167$			1.00000i			0.0773823i	−0.999251	+	0.0386912i	$0.987681\pi$
$168$		0			0
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$	−6.00000	+	10.3923i	−0.460179	+	0.797053i
$171$	2.59808	−	1.50000i	0.198680	−	0.114708i
$172$	1.00000	+	1.73205i	0.0762493	+	0.132068i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$			12.0000i			0.909718i
$175$		0			0
$176$			8.00000i			0.603023i
$177$	−13.8564	−	8.00000i	−1.04151	−	0.601317i
$178$	5.00000	+	8.66025i	0.374766	+	0.649113i
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	0.647397	−	0.762153i	$-0.275858\pi$
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	−0.983742	+	0.179585i	$0.942524\pi$
$180$	−1.73205	−	1.00000i	−0.129099	−	0.0745356i
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$	16.0000			1.18275
$184$		0			0
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$	6.00000	+	10.3923i	0.439941	+	0.762001i
$187$	−10.3923	−	6.00000i	−0.759961	−	0.438763i
$188$		−	22.0000i		−	1.60451i
$189$		0			0
$190$		−	6.00000i		−	0.435286i
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	8.00000	+	13.8564i	0.577350	+	1.00000i
$193$	−10.3923	+	6.00000i	−0.748054	+	0.431889i	−0.824991	−	0.565147i	$-0.808820\pi$
$193$	−10.3923	+	6.00000i	−0.748054	+	0.431889i	0.0769360	+	0.997036i	$0.475486\pi$
$194$	−9.00000	+	15.5885i	−0.646162	+	1.11919i
$195$	−6.00000	−	4.00000i	−0.429669	−	0.286446i
$196$		0			0
$197$			4.00000i			0.284988i	0.989796	+	0.142494i	$0.0455122\pi$
$197$			4.00000i			0.284988i	−0.989796	+	0.142494i	$0.954488\pi$
$198$	2.00000	−	3.46410i	0.142134	−	0.246183i
$199$	−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	$0.855917\pi$
$200$		0			0
$201$	20.7846	+	12.0000i	1.46603	+	0.846415i
$202$			12.0000i			0.844317i
$203$		0			0
$204$	−24.0000			−1.68034
$205$	5.00000	−	8.66025i	0.349215	−	0.604858i
$206$		0			0
$207$	1.50000	+	2.59808i	0.104257	+	0.180579i
$208$	6.39230	+	12.9282i	0.443227	+	0.896410i
$209$	6.00000			0.415029
$210$		0			0
$211$	−9.00000			−0.619586			−0.309793	−	0.950804i	$-0.600260\pi$
$211$	−9.00000			−0.619586			−0.309793	+	0.950804i	$0.600260\pi$
$212$	−9.00000	+	15.5885i	−0.618123	+	1.07062i
$213$	−24.2487	+	14.0000i	−1.66149	+	0.959264i
$214$	20.7846	−	12.0000i	1.42081	−	0.820303i
$215$	0.866025	+	0.500000i	0.0590624	+	0.0340997i
$216$		0			0
$217$		0			0
$218$	−36.0000			−2.43823
$219$	−15.5885	−	9.00000i	−1.05337	−	0.608164i
$220$	−2.00000	−	3.46410i	−0.134840	−	0.233550i
$221$	−21.5885	−	1.39230i	−1.45220	−	0.0936566i
$222$	12.0000	−	20.7846i	0.805387	−	1.39497i
$223$			21.0000i			1.40626i	0.711059	+	0.703132i	$0.248216\pi$
$223$			21.0000i			1.40626i	−0.711059	+	0.703132i	$0.751784\pi$
$224$		0			0
$225$	4.00000			0.266667
$226$	−25.9808	−	15.0000i	−1.72821	−	0.997785i
$227$	17.3205	−	10.0000i	1.14960	−	0.663723i	0.200812	−	0.979630i	$-0.435642\pi$
$227$	17.3205	−	10.0000i	1.14960	−	0.663723i	0.948790	+	0.315906i	$0.102309\pi$
$228$	10.3923	−	6.00000i	0.688247	−	0.397360i
$229$	5.19615	+	3.00000i	0.343371	+	0.198246i	0.661762	−	0.749714i	$-0.269809\pi$
$229$	5.19615	+	3.00000i	0.343371	+	0.198246i	−0.318390	+	0.947960i	$0.603142\pi$
$230$	6.00000			0.395628
$231$		0			0
$232$		0			0
$233$	1.50000	−	2.59808i	0.0982683	−	0.170206i	−0.812700	−	0.582683i	$-0.802003\pi$
$233$	1.50000	−	2.59808i	0.0982683	−	0.170206i	0.910968	+	0.412477i	$0.135336\pi$
$234$	0.464102	−	7.19615i	0.0303393	−	0.470427i
$235$	−5.50000	−	9.52628i	−0.358780	−	0.621426i
$236$	−13.8564	−	8.00000i	−0.901975	−	0.520756i
$237$	18.0000			1.16923
$238$		0			0
$239$		−	8.00000i		−	0.517477i	−0.965947	−	0.258738i	$-0.916693\pi$
$239$		−	8.00000i		−	0.517477i	0.965947	−	0.258738i	$-0.0833068\pi$
$240$	6.92820	+	4.00000i	0.447214	+	0.258199i
$241$	−18.1865	+	10.5000i	−1.17150	+	0.676364i	−0.954032	−	0.299704i	$-0.903112\pi$
$241$	−18.1865	+	10.5000i	−1.17150	+	0.676364i	−0.217465	+	0.976068i	$0.569779\pi$
$242$	−12.1244	+	7.00000i	−0.779383	+	0.449977i
$243$	−5.00000	+	8.66025i	−0.320750	+	0.555556i
$244$	16.0000			1.02430
$245$		0			0
$246$	40.0000			2.55031
$247$	9.69615	−	4.79423i	0.616951	−	0.305049i
$248$		0			0
$249$	19.0526	−	11.0000i	1.20741	−	0.697097i
$250$	9.00000	−	15.5885i	0.569210	−	0.985901i
$251$	−6.00000			−0.378717			−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000			−0.378717			−0.189358	+	0.981908i	$0.560641\pi$
$252$		0			0
$253$			6.00000i			0.377217i
$254$		0			0
$255$	−10.3923	+	6.00000i	−0.650791	+	0.375735i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$			4.00000i			0.249029i
$259$		0			0
$260$	−6.00000	−	4.00000i	−0.372104	−	0.248069i
$261$	−1.50000	+	2.59808i	−0.0928477	+	0.160817i
$262$	−20.7846	+	12.0000i	−1.28408	+	0.741362i
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$		0			0
$265$			9.00000i			0.552866i
$266$		0			0
$267$			10.0000i			0.611990i
$268$	20.7846	+	12.0000i	1.26962	+	0.733017i
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	−0.956176	−	0.292791i	$-0.905416\pi$
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	0.224523	−	0.974469i	$-0.427917\pi$
$270$	4.00000	+	6.92820i	0.243432	+	0.421637i
$271$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$271$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$272$	24.0000			1.45521
$273$		0			0
$274$	4.00000			0.241649
$275$	6.92820	+	4.00000i	0.417786	+	0.241209i
$276$	6.00000	+	10.3923i	0.361158	+	0.625543i
$277$	8.50000	+	14.7224i	0.510716	+	0.884585i	0.999923	+	0.0124177i	$0.00395278\pi$
$277$	8.50000	+	14.7224i	0.510716	+	0.884585i	−0.489207	+	0.872167i	$0.662714\pi$
$278$	−31.1769	−	18.0000i	−1.86987	−	1.07957i
$279$			3.00000i			0.179605i
$280$		0			0
$281$			2.00000i			0.119310i	0.998219	+	0.0596550i	$0.0190001\pi$
$281$			2.00000i			0.119310i	−0.998219	+	0.0596550i	$0.981000\pi$
$282$	22.0000	−	38.1051i	1.31008	−	2.26913i
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	−24.2487	+	14.0000i	−1.43890	+	0.830747i
$285$	3.00000	−	5.19615i	0.177705	−	0.307794i
$286$	8.00000	−	12.0000i	0.473050	−	0.709575i
$287$		0			0
$288$			8.00000i			0.471405i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	3.00000	+	5.19615i	0.176166	+	0.305129i
$291$	−15.5885	+	9.00000i	−0.913812	+	0.527589i
$292$	−15.5885	−	9.00000i	−0.912245	−	0.526685i
$293$			1.00000i			0.0584206i	0.999573	+	0.0292103i	$0.00929925\pi$
$293$			1.00000i			0.0584206i	−0.999573	+	0.0292103i	$0.990701\pi$
$294$		0			0
$295$	−8.00000			−0.465778
$296$		0			0
$297$	−6.92820	+	4.00000i	−0.402015	+	0.232104i
$298$	10.0000	+	17.3205i	0.579284	+	1.00335i
$299$	4.79423	+	9.69615i	0.277257	+	0.560743i
$300$	16.0000			0.923760
$301$		0			0
$302$	12.0000			0.690522
$303$	−6.00000	+	10.3923i	−0.344691	+	0.597022i
$304$	−10.3923	+	6.00000i	−0.596040	+	0.344124i
$305$	6.92820	−	4.00000i	0.396708	−	0.229039i
$306$	−10.3923	−	6.00000i	−0.594089	−	0.342997i
$307$		−	33.0000i		−	1.88341i	−0.336440	−	0.941705i	$-0.609223\pi$
$307$		−	33.0000i		−	1.88341i	0.336440	−	0.941705i	$-0.390777\pi$
$308$		0			0
$309$		0			0
$310$	5.19615	+	3.00000i	0.295122	+	0.170389i
$311$	−15.0000	−	25.9808i	−0.850572	−	1.47323i	−0.880693	−	0.473688i	$-0.842923\pi$
$311$	−15.0000	−	25.9808i	−0.850572	−	1.47323i	0.0301210	−	0.999546i	$-0.490411\pi$
$312$		0			0
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	−0.972028	−	0.234863i	$-0.924536\pi$
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	0.689412	+	0.724370i	$0.257869\pi$
$314$			36.0000i			2.03160i
$315$		0			0
$316$	18.0000			1.01258
$317$	17.3205	+	10.0000i	0.972817	+	0.561656i	0.900094	−	0.435696i	$-0.143498\pi$
$317$	17.3205	+	10.0000i	0.972817	+	0.561656i	0.0727229	+	0.997352i	$0.476831\pi$
$318$	−31.1769	+	18.0000i	−1.74831	+	1.00939i
$319$	−5.19615	+	3.00000i	−0.290929	+	0.167968i
$320$	6.92820	+	4.00000i	0.387298	+	0.223607i
$321$	24.0000			1.33955
$322$		0			0
$323$		−	18.0000i		−	1.00155i
$324$	−11.0000	+	19.0526i	−0.611111	+	1.05848i
$325$	14.3923	+	0.928203i	0.798341	+	0.0514875i
$326$	12.0000	+	20.7846i	0.664619	+	1.15115i
$327$	−31.1769	−	18.0000i	−1.72409	−	0.995402i
$328$		0			0
$329$		0			0
$330$		−	8.00000i		−	0.440386i
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	0.757634	−	0.652680i	$-0.226355\pi$
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	−0.186421	+	0.982470i	$0.559689\pi$
$332$	19.0526	−	11.0000i	1.04565	−	0.603703i
$333$	5.19615	−	3.00000i	0.284747	−	0.164399i
$334$	−1.00000	+	1.73205i	−0.0547176	+	0.0947736i
$335$	12.0000			0.655630
$336$		0			0
$337$	27.0000			1.47078			0.735392	−	0.677642i	$-0.236998\pi$
$337$	27.0000			1.47078			0.735392	+	0.677642i	$0.236998\pi$
$338$	3.33975	−	25.7846i	0.181658	−	1.40250i
$339$	−15.0000	−	25.9808i	−0.814688	−	1.41108i
$340$	−10.3923	+	6.00000i	−0.563602	+	0.325396i
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$	6.00000			0.324443
$343$		0			0
$344$		0			0
$345$	5.19615	+	3.00000i	0.279751	+	0.161515i
$346$	10.3923	−	6.00000i	0.558694	−	0.322562i
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	0.984487	+	0.175457i	$0.0561403\pi$
$347$	12.0000	+	20.7846i	0.644194	+	1.11578i	−0.340293	+	0.940319i	$0.610526\pi$
$348$	−6.00000	+	10.3923i	−0.321634	+	0.557086i
$349$			27.0000i			1.44528i	0.691226	+	0.722638i	$0.257071\pi$
$349$			27.0000i			1.44528i	−0.691226	+	0.722638i	$0.742929\pi$
$350$		0			0
$351$	−8.00000	+	12.0000i	−0.427008	+	0.640513i
$352$	−8.00000	+	13.8564i	−0.426401	+	0.738549i
$353$	−1.73205	+	1.00000i	−0.0921878	+	0.0532246i	−0.545385	−	0.838186i	$-0.683617\pi$
$353$	−1.73205	+	1.00000i	−0.0921878	+	0.0532246i	0.453197	+	0.891410i	$0.350283\pi$
$354$	−16.0000	−	27.7128i	−0.850390	−	1.47292i
$355$	−7.00000	+	12.1244i	−0.371521	+	0.643494i
$356$			10.0000i			0.529999i
$357$		0			0
$358$		−	18.0000i		−	0.951330i
$359$	−19.0526	−	11.0000i	−1.00556	−	0.580558i	−0.0956683	−	0.995413i	$-0.530499\pi$
$359$	−19.0526	−	11.0000i	−1.00556	−	0.580558i	−0.909887	+	0.414855i	$0.863832\pi$
$360$		0			0
$361$	−5.00000	−	8.66025i	−0.263158	−	0.455803i
$362$	−31.1769	−	18.0000i	−1.63862	−	0.946059i
$363$	−14.0000			−0.734809
$364$		0			0
$365$	−9.00000			−0.471082
$366$	27.7128	+	16.0000i	1.44857	+	0.836333i
$367$	9.00000	+	15.5885i	0.469796	+	0.813711i	0.999404	−	0.0345320i	$-0.0109941\pi$
$367$	9.00000	+	15.5885i	0.469796	+	0.813711i	−0.529607	+	0.848243i	$0.677661\pi$
$368$	−6.00000	−	10.3923i	−0.312772	−	0.541736i
$369$	8.66025	+	5.00000i	0.450835	+	0.260290i
$370$		−	12.0000i		−	0.623850i
$371$		0			0
$372$			12.0000i			0.622171i
$373$	9.00000	−	15.5885i	0.466002	−	0.807140i	−0.533244	−	0.845962i	$-0.679027\pi$
$373$	9.00000	−	15.5885i	0.466002	−	0.807140i	0.999246	+	0.0388219i	$0.0123605\pi$
$374$	−12.0000	−	20.7846i	−0.620505	−	1.07475i
$375$	15.5885	−	9.00000i	0.804984	−	0.464758i
$376$		0			0
$377$	−6.00000	+	9.00000i	−0.309016	+	0.463524i
$378$		0			0
$379$			18.0000i			0.924598i	0.886724	+	0.462299i	$0.152975\pi$
$379$			18.0000i			0.924598i	−0.886724	+	0.462299i	$0.847025\pi$
$380$	3.00000	−	5.19615i	0.153897	−	0.266557i
$381$		0			0
$382$		0			0
$383$	−6.92820	−	4.00000i	−0.354015	−	0.204390i	0.312437	−	0.949938i	$-0.398855\pi$
$383$	−6.92820	−	4.00000i	−0.354015	−	0.204390i	−0.666452	+	0.745548i	$0.732188\pi$
$384$		0			0
$385$		0			0
$386$	−24.0000			−1.22157
$387$	−0.500000	+	0.866025i	−0.0254164	+	0.0440225i
$388$	−15.5885	+	9.00000i	−0.791384	+	0.456906i
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	0.942578	+	0.333987i	$0.108394\pi$
$389$	15.0000	+	25.9808i	0.760530	+	1.31728i	−0.182047	+	0.983290i	$0.558272\pi$
$390$	−6.39230	−	12.9282i	−0.323687	−	0.654645i
$391$	18.0000			0.910299
$392$		0			0
$393$	−24.0000			−1.21064
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$	7.79423	−	4.50000i	0.392170	−	0.226420i
$396$	3.46410	−	2.00000i	0.174078	−	0.100504i
$397$	18.1865	+	10.5000i	0.912756	+	0.526980i	0.881317	−	0.472526i	$-0.156658\pi$
$397$	18.1865	+	10.5000i	0.912756	+	0.526980i	0.0314391	+	0.999506i	$0.489991\pi$
$398$		−	4.00000i		−	0.200502i
$399$		0			0
$400$	−16.0000			−0.800000
$401$	−24.2487	−	14.0000i	−1.21092	−	0.699127i	−0.247962	−	0.968770i	$-0.579761\pi$
$401$	−24.2487	−	14.0000i	−1.21092	−	0.699127i	−0.962960	+	0.269643i	$0.913094\pi$
$402$	24.0000	+	41.5692i	1.19701	+	2.07328i
$403$	−0.696152	+	10.7942i	−0.0346778	+	0.537699i
$404$	−6.00000	+	10.3923i	−0.298511	+	0.517036i
$405$			11.0000i			0.546594i
$406$		0			0
$407$	12.0000			0.594818
$408$		0			0
$409$	7.79423	−	4.50000i	0.385400	−	0.222511i	−0.294765	−	0.955570i	$-0.595241\pi$
$409$	7.79423	−	4.50000i	0.385400	−	0.222511i	0.680165	+	0.733059i	$0.261908\pi$
$410$	17.3205	−	10.0000i	0.855399	−	0.493865i
$411$	3.46410	+	2.00000i	0.170872	+	0.0986527i
$412$		0			0
$413$		0			0
$414$			6.00000i			0.294884i
$415$	5.50000	−	9.52628i	0.269984	−	0.467627i
$416$	−1.85641	+	28.7846i	−0.0910178	+	1.41128i
$417$	−18.0000	−	31.1769i	−0.881464	−	1.52674i
$418$	10.3923	+	6.00000i	0.508304	+	0.293470i
$419$	6.00000			0.293119			0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000			0.293119			0.146560	+	0.989202i	$0.453180\pi$
$420$		0			0
$421$			30.0000i			1.46211i	0.682318	+	0.731055i	$0.260972\pi$
$421$			30.0000i			1.46211i	−0.682318	+	0.731055i	$0.739028\pi$
$422$	−15.5885	−	9.00000i	−0.758834	−	0.438113i
$423$	9.52628	−	5.50000i	0.463184	−	0.267419i
$424$		0			0
$425$	12.0000	−	20.7846i	0.582086	−	1.00820i
$426$	−56.0000			−2.71321
$427$		0			0
$428$	24.0000			1.16008
$429$	12.9282	−	6.39230i	0.624180	−	0.308623i
$430$	1.00000	+	1.73205i	0.0482243	+	0.0835269i
$431$	−3.46410	+	2.00000i	−0.166860	+	0.0963366i	−0.581104	−	0.813829i	$-0.697379\pi$
$431$	−3.46410	+	2.00000i	−0.166860	+	0.0963366i	0.414244	+	0.910166i	$0.364046\pi$
$432$	8.00000	−	13.8564i	0.384900	−	0.666667i
$433$	−20.0000			−0.961139			−0.480569	−	0.876957i	$-0.659570\pi$
$433$	−20.0000			−0.961139			−0.480569	+	0.876957i	$0.659570\pi$
$434$		0			0
$435$			6.00000i			0.287678i
$436$	−31.1769	−	18.0000i	−1.49310	−	0.862044i
$437$	−7.79423	+	4.50000i	−0.372849	+	0.215264i
$438$	−18.0000	−	31.1769i	−0.860073	−	1.48969i
$439$	−18.0000	+	31.1769i	−0.859093	+	1.48799i	0.0137020	+	0.999906i	$0.495638\pi$
$439$	−18.0000	+	31.1769i	−0.859093	+	1.48799i	−0.872795	+	0.488087i	$0.837695\pi$
$440$		0			0
$441$		0			0
$442$	−36.0000	−	24.0000i	−1.71235	−	1.14156i
$443$	−13.5000	+	23.3827i	−0.641404	+	1.11094i	0.343715	+	0.939074i	$0.388315\pi$
$443$	−13.5000	+	23.3827i	−0.641404	+	1.11094i	−0.985119	+	0.171871i	$0.945019\pi$
$444$	20.7846	−	12.0000i	0.986394	−	0.569495i
$445$	2.50000	+	4.33013i	0.118511	+	0.205268i
$446$	−21.0000	+	36.3731i	−0.994379	+	1.72231i
$447$			20.0000i			0.945968i
$448$		0			0
$449$			4.00000i			0.188772i	0.995536	+	0.0943858i	$0.0300887\pi$
$449$			4.00000i			0.188772i	−0.995536	+	0.0943858i	$0.969911\pi$
$450$	6.92820	+	4.00000i	0.326599	+	0.188562i
$451$	10.0000	+	17.3205i	0.470882	+	0.815591i
$452$	−15.0000	−	25.9808i	−0.705541	−	1.22203i
$453$	10.3923	+	6.00000i	0.488273	+	0.281905i
$454$	40.0000			1.87729
$455$		0			0
$456$		0			0
$457$	−36.3731	−	21.0000i	−1.70146	−	0.982339i	−0.944286	−	0.329125i	$-0.893246\pi$
$457$	−36.3731	−	21.0000i	−1.70146	−	0.982339i	−0.757174	−	0.653213i	$-0.773421\pi$
$458$	6.00000	+	10.3923i	0.280362	+	0.485601i
$459$	12.0000	+	20.7846i	0.560112	+	0.970143i
$460$	5.19615	+	3.00000i	0.242272	+	0.139876i
$461$		−	2.00000i		−	0.0931493i	−0.998915	−	0.0465746i	$-0.985169\pi$
$461$		−	2.00000i		−	0.0931493i	0.998915	−	0.0465746i	$-0.0148305\pi$
$462$		0			0
$463$		−	30.0000i		−	1.39422i	−0.716965	−	0.697109i	$-0.754469\pi$
$463$		−	30.0000i		−	1.39422i	0.716965	−	0.697109i	$-0.245531\pi$
$464$	6.00000	−	10.3923i	0.278543	−	0.482451i
$465$	3.00000	+	5.19615i	0.139122	+	0.240966i
$466$	5.19615	−	3.00000i	0.240707	−	0.138972i
$467$	21.0000	−	36.3731i	0.971764	−	1.68314i	0.281539	−	0.959550i	$-0.409155\pi$
$467$	21.0000	−	36.3731i	0.971764	−	1.68314i	0.690225	−	0.723595i	$-0.257512\pi$
$468$	4.00000	−	6.00000i	0.184900	−	0.277350i
$469$		0			0
$470$		−	22.0000i		−	1.01478i
$471$	−18.0000	+	31.1769i	−0.829396	+	1.43656i
$472$		0			0
$473$	−1.73205	+	1.00000i	−0.0796398	+	0.0459800i
$474$	31.1769	+	18.0000i	1.43200	+	0.826767i
$475$			12.0000i			0.550598i
$476$		0			0
$477$	−9.00000			−0.412082
$478$	8.00000	−	13.8564i	0.365911	−	0.633777i
$479$	25.1147	−	14.5000i	1.14752	−	0.662522i	0.199240	−	0.979951i	$-0.436153\pi$
$479$	25.1147	−	14.5000i	1.14752	−	0.662522i	0.948282	+	0.317429i	$0.102819\pi$
$480$	8.00000	+	13.8564i	0.365148	+	0.632456i
$481$	19.3923	−	9.58846i	0.884213	−	0.437196i
$482$	−42.0000			−1.91305
$483$		0			0
$484$	−14.0000			−0.636364
$485$	−4.50000	+	7.79423i	−0.204334	+	0.353918i
$486$	−17.3205	+	10.0000i	−0.785674	+	0.453609i
$487$	−10.3923	+	6.00000i	−0.470920	+	0.271886i	−0.716625	−	0.697459i	$-0.754314\pi$
$487$	−10.3923	+	6.00000i	−0.470920	+	0.271886i	0.245705	+	0.969345i	$0.420981\pi$
$488$		0			0
$489$			24.0000i			1.08532i
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$	34.6410	+	20.0000i	1.56174	+	0.901670i
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	21.5885	+	1.39230i	0.971311	+	0.0626428i
$495$	1.00000	−	1.73205i	0.0449467	−	0.0778499i
$496$		−	12.0000i		−	0.538816i
$497$		0			0
$498$	44.0000			1.97169
$499$	5.19615	+	3.00000i	0.232612	+	0.134298i	0.611776	−	0.791031i	$-0.290455\pi$
$499$	5.19615	+	3.00000i	0.232612	+	0.134298i	−0.379165	+	0.925329i	$0.623789\pi$
$500$	15.5885	−	9.00000i	0.697137	−	0.402492i
$501$	−1.73205	+	1.00000i	−0.0773823	+	0.0446767i
$502$	−10.3923	−	6.00000i	−0.463831	−	0.267793i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$			6.00000i			0.266996i
$506$	−6.00000	+	10.3923i	−0.266733	+	0.461994i
$507$	15.7846	−	20.6603i	0.701019	−	0.917554i
$508$		0			0
$509$	32.0429	+	18.5000i	1.42028	+	0.819998i	0.996322	−	0.0856847i	$-0.0273078\pi$
$509$	32.0429	+	18.5000i	1.42028	+	0.819998i	0.423956	+	0.905683i	$0.360641\pi$
$510$	−24.0000			−1.06274
$511$		0			0
$512$		−	32.0000i		−	1.41421i
$513$	−10.3923	−	6.00000i	−0.458831	−	0.264906i
$514$	−10.3923	+	6.00000i	−0.458385	+	0.264649i
$515$		0			0
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$	22.0000			0.967559
$518$		0			0
$519$	12.0000			0.526742
$520$		0			0
$521$	12.0000	+	20.7846i	0.525730	+	0.910590i	0.999551	+	0.0299693i	$0.00954094\pi$
$521$	12.0000	+	20.7846i	0.525730	+	0.910590i	−0.473821	+	0.880621i	$0.657126\pi$
$522$	−5.19615	+	3.00000i	−0.227429	+	0.131306i
$523$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$523$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$524$	−24.0000			−1.04844
$525$		0			0
$526$		−	18.0000i		−	0.784837i
$527$	15.5885	+	9.00000i	0.679044	+	0.392046i
$528$	−13.8564	+	8.00000i	−0.603023	+	0.348155i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	−9.00000	+	15.5885i	−0.390935	+	0.677119i
$531$		−	8.00000i		−	0.347170i
$532$		0			0
$533$	30.0000	+	20.0000i	1.29944	+	0.866296i
$534$	−10.0000	+	17.3205i	−0.432742	+	0.749532i
$535$	10.3923	−	6.00000i	0.449299	−	0.259403i
$536$		0			0
$537$	9.00000	−	15.5885i	0.388379	−	0.672692i
$538$		−	48.0000i		−	2.06943i
$539$		0			0
$540$			8.00000i			0.344265i
$541$	15.5885	+	9.00000i	0.670200	+	0.386940i	0.796152	−	0.605096i	$-0.206865\pi$
$541$	15.5885	+	9.00000i	0.670200	+	0.386940i	−0.125952	+	0.992036i	$0.540199\pi$
$542$		0			0
$543$	−18.0000	−	31.1769i	−0.772454	−	1.33793i
$544$	41.5692	+	24.0000i	1.78227	+	1.02899i
$545$	−18.0000			−0.771035
$546$		0			0
$547$	17.0000			0.726868			0.363434	−	0.931620i	$-0.381604\pi$
$547$	17.0000			0.726868			0.363434	+	0.931620i	$0.381604\pi$
$548$	3.46410	+	2.00000i	0.147979	+	0.0854358i
$549$	4.00000	+	6.92820i	0.170716	+	0.295689i
$550$	8.00000	+	13.8564i	0.341121	+	0.590839i
$551$	−7.79423	−	4.50000i	−0.332045	−	0.191706i
$552$		0			0
$553$		0			0
$554$			34.0000i			1.44452i
$555$	6.00000	−	10.3923i	0.254686	−	0.441129i
$556$	−18.0000	−	31.1769i	−0.763370	−	1.32220i
$557$	27.7128	−	16.0000i	1.17423	−	0.677942i	0.219557	−	0.975600i	$-0.429539\pi$
$557$	27.7128	−	16.0000i	1.17423	−	0.677942i	0.954673	+	0.297658i	$0.0962055\pi$
$558$	−3.00000	+	5.19615i	−0.127000	+	0.219971i
$559$	−2.00000	+	3.00000i	−0.0845910	+	0.126886i
$560$		0			0
$561$		−	24.0000i		−	1.01328i
$562$	−2.00000	+	3.46410i	−0.0843649	+	0.146124i
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	−0.943560	−	0.331202i	$-0.892546\pi$
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	0.184950	−	0.982748i	$-0.440788\pi$
$564$	38.1051	−	22.0000i	1.60451	−	0.926367i
$565$	−12.9904	−	7.50000i	−0.546509	−	0.315527i
$566$		−	8.00000i		−	0.336265i
$567$		0			0
$568$		0			0
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	−0.664897	−	0.746935i	$-0.731525\pi$
$569$	7.50000	−	12.9904i	0.314416	−	0.544585i	0.979313	+	0.202350i	$0.0648579\pi$
$570$	10.3923	−	6.00000i	0.435286	−	0.251312i
$571$	−4.50000	−	7.79423i	−0.188319	−	0.326178i	0.756371	−	0.654143i	$-0.226971\pi$
$571$	−4.50000	−	7.79423i	−0.188319	−	0.326178i	−0.944690	+	0.327965i	$0.893637\pi$
$572$	12.9282	−	6.39230i	0.540555	−	0.267276i
$573$		0			0
$574$		0			0
$575$	−12.0000			−0.500435
$576$	−4.00000	+	6.92820i	−0.166667	+	0.288675i
$577$	36.3731	−	21.0000i	1.51423	−	0.874241i	0.514370	−	0.857569i	$-0.328026\pi$
$577$	36.3731	−	21.0000i	1.51423	−	0.874241i	0.999861	−	0.0166728i	$-0.00530737\pi$
$578$	−32.9090	+	19.0000i	−1.36883	+	0.790296i
$579$	−20.7846	−	12.0000i	−0.863779	−	0.498703i
$580$			6.00000i			0.249136i
$581$		0			0
$582$	−36.0000			−1.49225
$583$	−15.5885	−	9.00000i	−0.645608	−	0.372742i
$584$		0			0
$585$	0.232051	−	3.59808i	0.00959412	−	0.148762i
$586$	−1.00000	+	1.73205i	−0.0413096	+	0.0715504i
$587$		−	43.0000i		−	1.77480i	−0.461000	−	0.887400i	$-0.652509\pi$
$587$		−	43.0000i		−	1.77480i	0.461000	−	0.887400i	$-0.347491\pi$
$588$		0			0
$589$	−9.00000			−0.370839
$590$	−13.8564	−	8.00000i	−0.570459	−	0.329355i
$591$	−6.92820	+	4.00000i	−0.284988	+	0.164538i
$592$	−20.7846	+	12.0000i	−0.854242	+	0.493197i
$593$	−11.2583	−	6.50000i	−0.462324	−	0.266923i	0.250697	−	0.968066i	$-0.419340\pi$
$593$	−11.2583	−	6.50000i	−0.462324	−	0.266923i	−0.713021	+	0.701143i	$0.752674\pi$
$594$	−16.0000			−0.656488
$595$		0			0
$596$			20.0000i			0.819232i
$597$	2.00000	−	3.46410i	0.0818546	−	0.141776i
$598$	−1.39230	+	21.5885i	−0.0569356	+	0.882818i
$599$	10.5000	+	18.1865i	0.429018	+	0.743082i	0.996786	−	0.0801071i	$-0.0255262\pi$
$599$	10.5000	+	18.1865i	0.429018	+	0.743082i	−0.567768	+	0.823189i	$0.692193\pi$
$600$		0			0
$601$	44.0000			1.79480			0.897399	−	0.441221i	$-0.145454\pi$
$601$	44.0000			1.79480			0.897399	+	0.441221i	$0.145454\pi$
$602$		0			0
$603$			12.0000i			0.488678i
$604$	10.3923	+	6.00000i	0.422857	+	0.244137i
$605$	−6.06218	+	3.50000i	−0.246463	+	0.142295i
$606$	−20.7846	+	12.0000i	−0.844317	+	0.487467i
$607$	−9.00000	+	15.5885i	−0.365299	+	0.632716i	−0.988824	−	0.149087i	$-0.952366\pi$
$607$	−9.00000	+	15.5885i	−0.365299	+	0.632716i	0.623525	+	0.781803i	$0.285700\pi$
$608$	−24.0000			−0.973329
$609$		0			0
$610$	16.0000			0.647821
$611$	35.5526	−	17.5788i	1.43830	−	0.711164i
$612$	−6.00000	−	10.3923i	−0.242536	−	0.420084i
$613$	−20.7846	+	12.0000i	−0.839482	+	0.484675i	−0.857088	−	0.515170i	$-0.827729\pi$
$613$	−20.7846	+	12.0000i	−0.839482	+	0.484675i	0.0176058	+	0.999845i	$0.494396\pi$
$614$	33.0000	−	57.1577i	1.33177	−	2.30670i
$615$	20.0000			0.806478
$616$		0			0
$617$		−	8.00000i		−	0.322068i	−0.986949	−	0.161034i	$-0.948517\pi$
$617$		−	8.00000i		−	0.322068i	0.986949	−	0.161034i	$-0.0514829\pi$
$618$		0			0
$619$	31.1769	−	18.0000i	1.25311	−	0.723481i	0.281381	−	0.959596i	$-0.409208\pi$
$619$	31.1769	−	18.0000i	1.25311	−	0.723481i	0.971725	+	0.236115i	$0.0758742\pi$
$620$	3.00000	+	5.19615i	0.120483	+	0.208683i
$621$	6.00000	−	10.3923i	0.240772	−	0.417029i
$622$		−	60.0000i		−	2.40578i
$623$		0			0
$624$	−16.0000	+	24.0000i	−0.640513	+	0.960769i
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−17.3205	+	10.0000i	−0.692267	+	0.399680i
$627$	6.00000	+	10.3923i	0.239617	+	0.415029i
$628$	−18.0000	+	31.1769i	−0.718278	+	1.24409i
$629$		−	36.0000i		−	1.43541i
$630$		0			0
$631$		−	12.0000i		−	0.477712i	−0.971055	−	0.238856i	$-0.923228\pi$
$631$		−	12.0000i		−	0.477712i	0.971055	−	0.238856i	$-0.0767725\pi$
$632$		0			0
$633$	−9.00000	−	15.5885i	−0.357718	−	0.619586i
$634$	20.0000	+	34.6410i	0.794301	+	1.37577i
$635$		0			0
$636$	−36.0000			−1.42749
$637$		0			0
$638$	−12.0000			−0.475085
$639$	−12.1244	−	7.00000i	−0.479632	−	0.276916i
$640$		0			0
$641$	−19.5000	−	33.7750i	−0.770204	−	1.33403i	−0.937451	−	0.348117i	$-0.886821\pi$
$641$	−19.5000	−	33.7750i	−0.770204	−	1.33403i	0.167247	−	0.985915i	$-0.446512\pi$
$642$	41.5692	+	24.0000i	1.64061	+	0.947204i
$643$			12.0000i			0.473234i	0.971603	+	0.236617i	$0.0760386\pi$
$643$			12.0000i			0.473234i	−0.971603	+	0.236617i	$0.923961\pi$
$644$		0			0
$645$			2.00000i			0.0787499i
$646$	18.0000	−	31.1769i	0.708201	−	1.22664i
$647$	−9.00000	−	15.5885i	−0.353827	−	0.612845i	0.633090	−	0.774078i	$-0.281786\pi$
$647$	−9.00000	−	15.5885i	−0.353827	−	0.612845i	−0.986916	+	0.161233i	$0.948453\pi$
$648$		0			0
$649$	8.00000	−	13.8564i	0.314027	−	0.543912i
$650$	24.0000	+	16.0000i	0.941357	+	0.627572i
$651$		0			0
$652$			24.0000i			0.939913i
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	−0.634437	−	0.772975i	$-0.718768\pi$
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	0.986634	+	0.162951i	$0.0521013\pi$
$654$	−36.0000	−	62.3538i	−1.40771	−	2.43823i
$655$	−10.3923	+	6.00000i	−0.406061	+	0.234439i
$656$	−34.6410	−	20.0000i	−1.35250	−	0.780869i
$657$		−	9.00000i		−	0.351123i
$658$		0			0
$659$	−39.0000			−1.51922			−0.759612	−	0.650376i	$-0.774611\pi$
$659$	−39.0000			−1.51922			−0.759612	+	0.650376i	$0.774611\pi$
$660$	4.00000	−	6.92820i	0.155700	−	0.269680i
$661$	2.59808	−	1.50000i	0.101053	−	0.0583432i	−0.448622	−	0.893722i	$-0.648085\pi$
$661$	2.59808	−	1.50000i	0.101053	−	0.0583432i	0.549675	+	0.835379i	$0.314752\pi$
$662$	12.0000	+	20.7846i	0.466393	+	0.807817i
$663$	−19.1769	−	38.7846i	−0.744770	−	1.50627i
$664$		0			0
$665$		0			0
$666$	12.0000			0.464991
$667$	4.50000	−	7.79423i	0.174241	−	0.301794i
$668$	−1.73205	+	1.00000i	−0.0670151	+	0.0386912i
$669$	−36.3731	+	21.0000i	−1.40626	+	0.811907i
$670$	20.7846	+	12.0000i	0.802980	+	0.463600i
$671$			16.0000i			0.617673i
$672$		0			0
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$	46.7654	+	27.0000i	1.80133	+	1.04000i
$675$	−8.00000	−	13.8564i	−0.307920	−	0.533333i
$676$	15.7846	−	20.6603i	0.607100	−	0.794625i
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	−0.639618	−	0.768693i	$-0.720908\pi$
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	0.985517	+	0.169580i	$0.0542410\pi$
$678$		−	60.0000i		−	2.30429i
$679$		0			0
$680$		0			0
$681$	34.6410	+	20.0000i	1.32745	+	0.766402i
$682$	−10.3923	+	6.00000i	−0.397942	+	0.229752i
$683$	−34.6410	+	20.0000i	−1.32550	+	0.765279i	−0.984600	−	0.174820i	$-0.944066\pi$
$683$	−34.6410	+	20.0000i	−1.32550	+	0.765279i	−0.340901	+	0.940099i	$0.610732\pi$
$684$	5.19615	+	3.00000i	0.198680	+	0.114708i
$685$	2.00000			0.0764161
$686$		0			0
$687$			12.0000i			0.457829i
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	−32.3827	−	2.08846i	−1.23368	−	0.0795639i
$690$	6.00000	+	10.3923i	0.228416	+	0.395628i
$691$	12.9904	+	7.50000i	0.494177	+	0.285313i	0.726306	−	0.687372i	$-0.241236\pi$
$691$	12.9904	+	7.50000i	0.494177	+	0.285313i	−0.232128	+	0.972685i	$0.574569\pi$
$692$	12.0000			0.456172
$693$		0			0
$694$			48.0000i			1.82206i
$695$	−15.5885	−	9.00000i	−0.591304	−	0.341389i
$696$		0			0
$697$	51.9615	−	30.0000i	1.96818	−	1.13633i
$698$	−27.0000	+	46.7654i	−1.02197	+	1.77010i
$699$	6.00000			0.226941
$700$		0			0
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$	−25.8564	+	12.7846i	−0.975887	+	0.482524i
$703$	9.00000	+	15.5885i	0.339441	+	0.587930i
$704$	−13.8564	+	8.00000i	−0.522233	+	0.301511i
$705$	11.0000	−	19.0526i	0.414284	−	0.717561i
$706$	−4.00000			−0.150542
$707$		0			0
$708$		−	32.0000i		−	1.20263i
$709$	25.9808	+	15.0000i	0.975728	+	0.563337i	0.900978	−	0.433865i	$-0.142851\pi$
$709$	25.9808	+	15.0000i	0.975728	+	0.563337i	0.0747503	+	0.997202i	$0.476184\pi$
$710$	−24.2487	+	14.0000i	−0.910038	+	0.525411i
$711$	4.50000	+	7.79423i	0.168763	+	0.292306i
$712$		0			0
$713$		−	9.00000i		−	0.337053i
$714$		0			0
$715$	4.00000	−	6.00000i	0.149592	−	0.224387i
$716$	9.00000	−	15.5885i	0.336346	−	0.582568i
$717$	13.8564	−	8.00000i	0.517477	−	0.298765i
$718$	−22.0000	−	38.1051i	−0.821033	−	1.42207i
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	−0.647965	−	0.761670i	$-0.724380\pi$
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	0.983608	+	0.180319i	$0.0577130\pi$
$720$			4.00000i			0.149071i
$721$		0			0
$722$		−	20.0000i		−	0.744323i
$723$	−36.3731	−	21.0000i	−1.35273	−	0.780998i
$724$	−18.0000	−	31.1769i	−0.668965	−	1.15868i
$725$	−6.00000	−	10.3923i	−0.222834	−	0.385961i
$726$	−24.2487	−	14.0000i	−0.899954	−	0.519589i
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−15.5885	−	9.00000i	−0.576955	−	0.333105i
$731$	3.00000	+	5.19615i	0.110959	+	0.192187i
$732$	16.0000	+	27.7128i	0.591377	+	1.02430i
$733$	12.9904	+	7.50000i	0.479811	+	0.277019i	0.720338	−	0.693624i	$-0.243987\pi$
$733$	12.9904	+	7.50000i	0.479811	+	0.277019i	−0.240527	+	0.970642i	$0.577320\pi$
$734$			36.0000i			1.32878i
$735$		0			0
$736$		−	24.0000i		−	0.884652i
$737$	−12.0000	+	20.7846i	−0.442026	+	0.765611i
$738$	10.0000	+	17.3205i	0.368105	+	0.637577i
$739$	25.9808	−	15.0000i	0.955718	−	0.551784i	0.0608653	−	0.998146i	$-0.480614\pi$
$739$	25.9808	−	15.0000i	0.955718	−	0.551784i	0.894852	+	0.446362i	$0.147281\pi$
$740$	6.00000	−	10.3923i	0.220564	−	0.382029i
$741$	18.0000	+	12.0000i	0.661247	+	0.440831i
$742$		0			0
$743$		−	44.0000i		−	1.61420i	−0.590412	−	0.807102i	$-0.701035\pi$
$743$		−	44.0000i		−	1.61420i	0.590412	−	0.807102i	$-0.298965\pi$
$744$		0			0
$745$	5.00000	+	8.66025i	0.183186	+	0.317287i
$746$	31.1769	−	18.0000i	1.14147	−	0.659027i
$747$	9.52628	+	5.50000i	0.348548	+	0.201234i
$748$		−	24.0000i		−	0.877527i
$749$		0			0
$750$	36.0000			1.31453
$751$	−6.50000	+	11.2583i	−0.237188	+	0.410822i	−0.959906	−	0.280321i	$-0.909559\pi$
$751$	−6.50000	+	11.2583i	−0.237188	+	0.410822i	0.722718	+	0.691143i	$0.242893\pi$
$752$	−38.1051	+	22.0000i	−1.38955	+	0.802257i
$753$	−6.00000	−	10.3923i	−0.218652	−	0.378717i
$754$	−19.3923	+	9.58846i	−0.706226	+	0.349191i
$755$	6.00000			0.218362
$756$		0			0
$757$	9.00000			0.327111			0.163555	−	0.986534i	$-0.447704\pi$
$757$	9.00000			0.327111			0.163555	+	0.986534i	$0.447704\pi$
$758$	−18.0000	+	31.1769i	−0.653789	+	1.13240i
$759$	−10.3923	+	6.00000i	−0.377217	+	0.217786i
$760$		0			0
$761$	16.4545	+	9.50000i	0.596475	+	0.344375i	0.767653	−	0.640865i	$-0.221424\pi$
$761$	16.4545	+	9.50000i	0.596475	+	0.344375i	−0.171179	+	0.985240i	$0.554758\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−5.19615	−	3.00000i	−0.187867	−	0.108465i
$766$	−8.00000	−	13.8564i	−0.289052	−	0.500652i
$767$	1.85641	−	28.7846i	0.0670310	−	1.03935i
$768$	16.0000	−	27.7128i	0.577350	−	1.00000i
$769$		−	9.00000i		−	0.324548i	−0.986746	−	0.162274i	$-0.948117\pi$
$769$		−	9.00000i		−	0.324548i	0.986746	−	0.162274i	$-0.0518829\pi$
$770$		0			0
$771$	−12.0000			−0.432169
$772$	−20.7846	−	12.0000i	−0.748054	−	0.431889i
$773$	−12.1244	+	7.00000i	−0.436083	+	0.251773i	−0.701935	−	0.712241i	$-0.747680\pi$
$773$	−12.1244	+	7.00000i	−0.436083	+	0.251773i	0.265852	+	0.964014i	$0.414347\pi$
$774$	−1.73205	+	1.00000i	−0.0622573	+	0.0359443i
$775$	−10.3923	−	6.00000i	−0.373303	−	0.215526i
$776$		0			0
$777$		0			0
$778$			60.0000i			2.15110i
$779$	−15.0000	+	25.9808i	−0.537431	+	0.930857i
$780$	0.928203	−	14.3923i	0.0332350	−	0.515327i
$781$	−14.0000	−	24.2487i	−0.500959	−	0.867687i
$782$	31.1769	+	18.0000i	1.11488	+	0.643679i
$783$	12.0000			0.428845
$784$		0			0
$785$			18.0000i			0.642448i
$786$	−41.5692	−	24.0000i	−1.48272	−	0.856052i
$787$	18.1865	−	10.5000i	0.648280	−	0.374285i	−0.139517	−	0.990220i	$-0.544555\pi$
$787$	18.1865	−	10.5000i	0.648280	−	0.374285i	0.787797	+	0.615935i	$0.211222\pi$
$788$	−6.92820	+	4.00000i	−0.246807	+	0.142494i
$789$	9.00000	−	15.5885i	0.320408	−	0.554964i
$790$	18.0000			0.640411
$791$		0			0
$792$		0			0
$793$	12.7846	+	25.8564i	0.453995	+	0.918188i
$794$	21.0000	+	36.3731i	0.745262	+	1.29083i
$795$	−15.5885	+	9.00000i	−0.552866	+	0.319197i
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	−12.0000			−0.425062			−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000			−0.425062			−0.212531	+	0.977154i	$0.568171\pi$
$798$		0			0
$799$		−	66.0000i		−	2.33491i
$800$	−27.7128	−	16.0000i	−0.979796	−	0.565685i
$801$	−4.33013	+	2.50000i	−0.152998	+	0.0883332i
$802$	−28.0000	−	48.4974i	−0.988714	−	1.71250i
$803$	9.00000	−	15.5885i	0.317603	−	0.550105i
$804$			48.0000i			1.69283i
$805$		0			0
$806$	−12.0000	+	18.0000i	−0.422682	+	0.634023i
$807$	24.0000	−	41.5692i	0.844840	−	1.46331i
$808$		0			0
$809$	7.50000	+	12.9904i	0.263686	+	0.456717i	0.967219	−	0.253946i	$-0.0817284\pi$
$809$	7.50000	+	12.9904i	0.263686	+	0.456717i	−0.703533	+	0.710663i	$0.748395\pi$
$810$	−11.0000	+	19.0526i	−0.386501	+	0.669439i
$811$		−	12.0000i		−	0.421377i	−0.977553	−	0.210688i	$-0.932429\pi$
$811$		−	12.0000i		−	0.421377i	0.977553	−	0.210688i	$-0.0675706\pi$
$812$		0			0
$813$		0			0
$814$	20.7846	+	12.0000i	0.728500	+	0.420600i
$815$	6.00000	+	10.3923i	0.210171	+	0.364027i
$816$	24.0000	+	41.5692i	0.840168	+	1.45521i
$817$	−2.59808	−	1.50000i	−0.0908952	−	0.0524784i
$818$	18.0000			0.629355
$819$		0			0
$820$	20.0000			0.698430
$821$	13.8564	+	8.00000i	0.483592	+	0.279202i	0.721912	−	0.691985i	$-0.243263\pi$
$821$	13.8564	+	8.00000i	0.483592	+	0.279202i	−0.238320	+	0.971187i	$0.576597\pi$
$822$	4.00000	+	6.92820i	0.139516	+	0.241649i
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$		0			0
$825$			16.0000i			0.557048i
$826$		0			0
$827$		−	4.00000i		−	0.139094i	−0.997579	−	0.0695468i	$-0.977845\pi$
$827$		−	4.00000i		−	0.139094i	0.997579	−	0.0695468i	$-0.0221553\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	0.848137	−	0.529777i	$-0.177724\pi$
$829$	−1.00000	−	1.73205i	−0.0347314	−	0.0601566i	−0.882869	+	0.469620i	$0.844391\pi$
$830$	19.0526	−	11.0000i	0.661324	−	0.381816i
$831$	−17.0000	+	29.4449i	−0.589723	+	1.02143i
$832$	−16.0000	+	24.0000i	−0.554700	+	0.832050i
$833$		0			0
$834$		−	72.0000i		−	2.49316i
$835$	−0.500000	+	0.866025i	−0.0173032	+	0.0299700i
$836$	6.00000	+	10.3923i	0.207514	+	0.359425i
$837$	10.3923	−	6.00000i	0.359211	−	0.207390i
$838$	10.3923	+	6.00000i	0.358996	+	0.207267i
$839$			16.0000i			0.552381i	0.961103	+	0.276191i	$0.0890721\pi$
$839$			16.0000i			0.552381i	−0.961103	+	0.276191i	$0.910928\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	−30.0000	+	51.9615i	−1.03387	+	1.79071i
$843$	−3.46410	+	2.00000i	−0.119310	+	0.0688837i
$844$	−9.00000	−	15.5885i	−0.309793	−	0.536577i
$845$	1.66987	−	12.8923i	0.0574454	−	0.443509i
$846$	22.0000			0.756376
$847$		0			0
$848$	36.0000			1.23625
$849$	4.00000	−	6.92820i	0.137280	−	0.237775i
$850$	41.5692	−	24.0000i	1.42581	−	0.823193i
$851$	−15.5885	+	9.00000i	−0.534365	+	0.308516i
$852$	−48.4974	−	28.0000i	−1.66149	−	0.959264i
$853$			45.0000i			1.54077i	0.637579	+	0.770385i	$0.279936\pi$
$853$			45.0000i			1.54077i	−0.637579	+	0.770385i	$0.720064\pi$
$854$		0			0
$855$	3.00000			0.102598
$856$		0			0
$857$	18.0000	+	31.1769i	0.614868	+	1.06498i	0.990408	+	0.138177i	$0.0441242\pi$
$857$	18.0000	+	31.1769i	0.614868	+	1.06498i	−0.375539	+	0.926806i	$0.622542\pi$
$858$	28.7846	+	1.85641i	0.982690	+	0.0633767i
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	−0.898126	−	0.439738i	$-0.855071\pi$
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	0.829887	+	0.557931i	$0.188405\pi$
$860$			2.00000i			0.0681994i
$861$		0			0
$862$	−8.00000			−0.272481
$863$	27.7128	+	16.0000i	0.943355	+	0.544646i	0.891010	−	0.453983i	$-0.149997\pi$
$863$	27.7128	+	16.0000i	0.943355	+	0.544646i	0.0523446	+	0.998629i	$0.483331\pi$
$864$	27.7128	−	16.0000i	0.942809	−	0.544331i
$865$	5.19615	−	3.00000i	0.176674	−	0.102003i
$866$	−34.6410	−	20.0000i	−1.17715	−	0.679628i
$867$	−38.0000			−1.29055
$868$		0			0
$869$			18.0000i			0.610608i
$870$	−6.00000	+	10.3923i	−0.203419	+	0.352332i
$871$	−2.78461	+	43.1769i	−0.0943529	+	1.46299i
$872$		0			0
$873$	−7.79423	−	4.50000i	−0.263795	−	0.152302i
$874$	−18.0000			−0.608859
$875$		0			0
$876$		−	36.0000i		−	1.21633i
$877$	15.5885	+	9.00000i	0.526385	+	0.303908i	0.739543	−	0.673109i	$-0.235042\pi$
$877$	15.5885	+	9.00000i	0.526385	+	0.303908i	−0.213158	+	0.977018i	$0.568375\pi$
$878$	−62.3538	+	36.0000i	−2.10434	+	1.21494i
$879$	−1.73205	+	1.00000i	−0.0584206	+	0.0337292i
$880$	−4.00000	+	6.92820i	−0.134840	+	0.233550i
$881$	12.0000			0.404290			0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000			0.404290			0.202145	+	0.979356i	$0.435209\pi$
$882$		0			0
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$	−19.1769	−	38.7846i	−0.644989	−	1.30447i
$885$	−8.00000	−	13.8564i	−0.268917	−	0.465778i
$886$	−46.7654	+	27.0000i	−1.57111	+	0.907083i
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	0.387768	+	0.921757i	$0.373246\pi$
$887$	−18.0000	+	31.1769i	−0.604381	+	1.04682i	−0.992149	+	0.125061i	$0.960087\pi$
$888$		0			0
$889$		0			0
$890$			10.0000i			0.335201i
$891$	−19.0526	−	11.0000i	−0.638285	−	0.368514i
$892$	−36.3731	+	21.0000i	−1.21786	+	0.703132i
$893$	16.5000	+	28.5788i	0.552151	+	0.956354i
$894$	−20.0000	+	34.6410i	−0.668900	+	1.15857i
$895$		−	9.00000i		−	0.300837i
$896$		0			0
$897$	−12.0000	+	18.0000i	−0.400668	+	0.601003i
$898$	−4.00000	+	6.92820i	−0.133482	+	0.231197i
$899$	7.79423	−	4.50000i	0.259952	−	0.150083i
$900$	4.00000	+	6.92820i	0.133333	+	0.230940i
$901$	−27.0000	+	46.7654i	−0.899500	+	1.55798i
$902$			40.0000i			1.33185i
$903$		0			0
$904$		0			0
$905$	−15.5885	−	9.00000i	−0.518178	−	0.299170i
$906$	12.0000	+	20.7846i	0.398673	+	0.690522i
$907$	−4.50000	−	7.79423i	−0.149420	−	0.258803i	0.781593	−	0.623788i	$-0.214407\pi$
$907$	−4.50000	−	7.79423i	−0.149420	−	0.258803i	−0.931013	+	0.364985i	$0.881074\pi$
$908$	34.6410	+	20.0000i	1.14960	+	0.663723i
$909$	−6.00000			−0.199007
$910$		0			0
$911$	−27.0000			−0.894550			−0.447275	−	0.894397i	$-0.647605\pi$
$911$	−27.0000			−0.894550			−0.447275	+	0.894397i	$0.647605\pi$
$912$	−20.7846	−	12.0000i	−0.688247	−	0.397360i
$913$	11.0000	+	19.0526i	0.364047	+	0.630548i
$914$	−42.0000	−	72.7461i	−1.38924	−	2.40623i
$915$	13.8564	+	8.00000i	0.458079	+	0.264472i
$916$			12.0000i			0.396491i
$917$		0			0
$918$			48.0000i			1.58424i
$919$	−18.0000	+	31.1769i	−0.593765	+	1.02843i	0.399955	+	0.916535i	$0.369026\pi$
$919$	−18.0000	+	31.1769i	−0.593765	+	1.02843i	−0.993720	+	0.111897i	$0.964307\pi$
$920$		0			0
$921$	57.1577	−	33.0000i	1.88341	−	1.08739i
$922$	2.00000	−	3.46410i	0.0658665	−	0.114084i
$923$	−42.0000	−	28.0000i	−1.38245	−	0.921631i
$924$		0			0
$925$			24.0000i			0.789115i
$926$	30.0000	−	51.9615i	0.985861	−	1.70756i
$927$		0			0
$928$	20.7846	−	12.0000i	0.682288	−	0.393919i
$929$	−6.06218	−	3.50000i	−0.198894	−	0.114831i	0.397246	−	0.917712i	$-0.369966\pi$
$929$	−6.06218	−	3.50000i	−0.198894	−	0.114831i	−0.596139	+	0.802881i	$0.703299\pi$
$930$			12.0000i			0.393496i
$931$		0			0
$932$	6.00000			0.196537
$933$	30.0000	−	51.9615i	0.982156	−	1.70114i
$934$	72.7461	−	42.0000i	2.38033	−	1.37428i
$935$	−6.00000	−	10.3923i	−0.196221	−	0.339865i
$936$		0			0
$937$	2.00000			0.0653372			0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000			0.0653372			0.0326686	+	0.999466i	$0.489599\pi$
$938$		0			0
$939$	−20.0000			−0.652675
$940$	11.0000	−	19.0526i	0.358780	−	0.621426i
$941$	0.866025	−	0.500000i	0.0282316	−	0.0162995i	−0.485818	−	0.874060i	$-0.661478\pi$
$941$	0.866025	−	0.500000i	0.0282316	−	0.0162995i	0.514049	+	0.857761i	$0.328145\pi$
$942$	−62.3538	+	36.0000i	−2.03160	+	1.17294i
$943$	−25.9808	−	15.0000i	−0.846050	−	0.488467i
$944$			32.0000i			1.04151i
$945$		0			0
$946$	−4.00000			−0.130051
$947$	13.8564	+	8.00000i	0.450273	+	0.259965i	0.707945	−	0.706267i	$-0.249622\pi$
$947$	13.8564	+	8.00000i	0.450273	+	0.259965i	−0.257673	+	0.966232i	$0.582956\pi$
$948$	18.0000	+	31.1769i	0.584613	+	1.01258i
$949$	2.08846	−	32.3827i	0.0677942	−	1.05119i
$950$	−12.0000	+	20.7846i	−0.389331	+	0.674342i
$951$			40.0000i			1.29709i
$952$		0			0
$953$	3.00000			0.0971795			0.0485898	−	0.998819i	$-0.484527\pi$
$953$	3.00000			0.0971795			0.0485898	+	0.998819i	$0.484527\pi$
$954$	−15.5885	−	9.00000i	−0.504695	−	0.291386i
$955$		0			0
$956$	13.8564	−	8.00000i	0.448148	−	0.258738i
$957$	−10.3923	−	6.00000i	−0.335936	−	0.193952i
$958$	58.0000			1.87389
$959$		0			0
$960$			16.0000i			0.516398i
$961$	−11.0000	+	19.0526i	−0.354839	+	0.614599i
$962$	43.1769	+	2.78461i	1.39208	+	0.0897794i
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$	−36.3731	−	21.0000i	−1.17150	−	0.676364i
$965$	−12.0000			−0.386294
$966$		0			0
$967$			54.0000i			1.73652i	0.496107	+	0.868261i	$0.334762\pi$
$967$			54.0000i			1.73652i	−0.496107	+	0.868261i	$0.665238\pi$
$968$		0			0
$969$	31.1769	−	18.0000i	1.00155	−	0.578243i
$970$	−15.5885	+	9.00000i	−0.500515	+	0.288973i
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	−0.753545	−	0.657396i	$-0.771658\pi$
$971$	6.00000	−	10.3923i	0.192549	−	0.333505i	0.946094	+	0.323891i	$0.104991\pi$
$972$	−20.0000			−0.641500
$973$		0			0
$974$	−24.0000			−0.769010
$975$	12.7846	+	25.8564i	0.409435	+	0.828068i
$976$	−16.0000	−	27.7128i	−0.512148	−	0.887066i
$977$	8.66025	−	5.00000i	0.277066	−	0.159964i	−0.355028	−	0.934856i	$-0.615529\pi$
$977$	8.66025	−	5.00000i	0.277066	−	0.159964i	0.632094	+	0.774891i	$0.282195\pi$
$978$	−24.0000	+	41.5692i	−0.767435	+	1.32924i
$979$	−10.0000			−0.319601
$980$		0			0
$981$		−	18.0000i		−	0.574696i
$982$	20.7846	+	12.0000i	0.663264	+	0.382935i
$983$	25.1147	−	14.5000i	0.801036	−	0.462478i	−0.0427975	−	0.999084i	$-0.513627\pi$
$983$	25.1147	−	14.5000i	0.801036	−	0.462478i	0.843833	+	0.536606i	$0.180294\pi$
$984$		0			0
$985$	−2.00000	+	3.46410i	−0.0637253	+	0.110375i
$986$			36.0000i			1.14647i
$987$		0			0
$988$	18.0000	+	12.0000i	0.572656	+	0.381771i
$989$	1.50000	−	2.59808i	0.0476972	−	0.0826140i
$990$	3.46410	−	2.00000i	0.110096	−	0.0635642i
$991$	28.0000	+	48.4974i	0.889449	+	1.54057i	0.840528	+	0.541769i	$0.182245\pi$
$991$	28.0000	+	48.4974i	0.889449	+	1.54057i	0.0489218	+	0.998803i	$0.484422\pi$
$992$	12.0000	−	20.7846i	0.381000	−	0.659912i
$993$			24.0000i			0.761617i
$994$		0			0
$995$		−	2.00000i		−	0.0634043i
$996$	38.1051	+	22.0000i	1.20741	+	0.697097i
$997$	−18.0000	−	31.1769i	−0.570066	−	0.987383i	−0.996559	−	0.0828918i	$-0.973584\pi$
$997$	−18.0000	−	31.1769i	−0.570066	−	0.987383i	0.426493	−	0.904491i	$-0.359749\pi$
$998$	6.00000	+	10.3923i	0.189927	+	0.328963i
$999$	−20.7846	−	12.0000i	−0.657596	−	0.379663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.r.c.324.2		4
7.2	even	3		637.2.c.a.246.1	✓	2
7.3	odd	6		637.2.r.a.116.1		4
7.4	even	3	inner	637.2.r.c.116.1		4
7.5	odd	6		637.2.c.c.246.1	yes	2
7.6	odd	2		637.2.r.a.324.2		4
13.12	even	2	inner	637.2.r.c.324.1		4
91.5	even	12		8281.2.a.b.1.1		1
91.12	odd	6		637.2.c.c.246.2	yes	2
91.25	even	6	inner	637.2.r.c.116.2		4
91.38	odd	6		637.2.r.a.116.2		4
91.44	odd	12		8281.2.a.a.1.1		1
91.47	even	12		8281.2.a.m.1.1		1
91.51	even	6		637.2.c.a.246.2	yes	2
91.86	odd	12		8281.2.a.k.1.1		1
91.90	odd	2		637.2.r.a.324.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.a.246.1	✓	2	7.2	even	3
637.2.c.a.246.2	yes	2	91.51	even	6
637.2.c.c.246.1	yes	2	7.5	odd	6
637.2.c.c.246.2	yes	2	91.12	odd	6
637.2.r.a.116.1		4	7.3	odd	6
637.2.r.a.116.2		4	91.38	odd	6
637.2.r.a.324.1		4	91.90	odd	2
637.2.r.a.324.2		4	7.6	odd	2
637.2.r.c.116.1		4	7.4	even	3	inner
637.2.r.c.116.2		4	91.25	even	6	inner
637.2.r.c.324.1		4	13.12	even	2	inner
637.2.r.c.324.2		4	1.1	even	1	trivial
8281.2.a.a.1.1		1	91.44	odd	12
8281.2.a.b.1.1		1	91.5	even	12
8281.2.a.k.1.1		1	91.86	odd	12
8281.2.a.m.1.1		1	91.47	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.00000i) q^{2} +(1.00000 + 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.866025 + 0.500000i) q^{5} +4.00000i q^{6} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.73205 + 1.00000i) q^{2} +(1.00000 + 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.866025 + 0.500000i) q^{5} +4.00000i q^{6} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-1.73205 + 1.00000i) q^{11} +(-2.00000 + 3.46410i) q^{12} +(-2.00000 + 3.00000i) q^{13} +2.00000i q^{15} +(2.00000 - 3.46410i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-1.73205 + 1.00000i) q^{18} +(-2.59808 - 1.50000i) q^{19} +2.00000i q^{20} -4.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-6.46410 + 3.19615i) q^{26} +4.00000 q^{27} +3.00000 q^{29} +(-2.00000 + 3.46410i) q^{30} +(2.59808 - 1.50000i) q^{31} +(6.92820 - 4.00000i) q^{32} +(-3.46410 - 2.00000i) q^{33} +12.0000i q^{34} -2.00000 q^{36} +(-5.19615 - 3.00000i) q^{37} +(-3.00000 - 5.19615i) q^{38} +(-7.19615 - 0.464102i) q^{39} -10.0000i q^{41} +1.00000 q^{43} +(-3.46410 - 2.00000i) q^{44} +(-0.866025 + 0.500000i) q^{45} +(5.19615 - 3.00000i) q^{46} +(-9.52628 - 5.50000i) q^{47} +8.00000 q^{48} -8.00000i q^{50} +(-6.00000 + 10.3923i) q^{51} +(-7.19615 - 0.464102i) q^{52} +(4.50000 + 7.79423i) q^{53} +(6.92820 + 4.00000i) q^{54} -2.00000 q^{55} -6.00000i q^{57} +(5.19615 + 3.00000i) q^{58} +(-6.92820 + 4.00000i) q^{59} +(-3.46410 + 2.00000i) q^{60} +(4.00000 - 6.92820i) q^{61} +6.00000 q^{62} +8.00000 q^{64} +(-3.23205 + 1.59808i) q^{65} +(-4.00000 - 6.92820i) q^{66} +(10.3923 - 6.00000i) q^{67} +(-6.00000 + 10.3923i) q^{68} +6.00000 q^{69} +14.0000i q^{71} +(-7.79423 + 4.50000i) q^{73} +(-6.00000 - 10.3923i) q^{74} +(4.00000 - 6.92820i) q^{75} -6.00000i q^{76} +(-12.0000 - 8.00000i) q^{78} +(4.50000 - 7.79423i) q^{79} +(3.46410 - 2.00000i) q^{80} +(5.50000 + 9.52628i) q^{81} +(10.0000 - 17.3205i) q^{82} -11.0000i q^{83} +6.00000i q^{85} +(1.73205 + 1.00000i) q^{86} +(3.00000 + 5.19615i) q^{87} +(4.33013 + 2.50000i) q^{89} -2.00000 q^{90} +6.00000 q^{92} +(5.19615 + 3.00000i) q^{93} +(-11.0000 - 19.0526i) q^{94} +(-1.50000 - 2.59808i) q^{95} +(13.8564 + 8.00000i) q^{96} +9.00000i q^{97} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} + 4 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 + 4 * q^4 - 2 * q^9	\( 4 q + 4 q^{3} + 4 q^{4} - 2 q^{9} + 4 q^{10} - 8 q^{12} - 8 q^{13} + 8 q^{16} + 12 q^{17} - 16 q^{22} + 6 q^{23} - 8 q^{25} - 12 q^{26} + 16 q^{27} + 12 q^{29} - 8 q^{30} - 8 q^{36} - 12 q^{38} - 8 q^{39} + 4 q^{43} + 32 q^{48} - 24 q^{51} - 8 q^{52} + 18 q^{53} - 8 q^{55} + 16 q^{61} + 24 q^{62} + 32 q^{64} - 6 q^{65} - 16 q^{66} - 24 q^{68} + 24 q^{69} - 24 q^{74} + 16 q^{75} - 48 q^{78} + 18 q^{79} + 22 q^{81} + 40 q^{82} + 12 q^{87} - 8 q^{90} + 24 q^{92} - 44 q^{94} - 6 q^{95}+O(q^{100}) \) 4 * q + 4 * q^3 + 4 * q^4 - 2 * q^9 + 4 * q^10 - 8 * q^12 - 8 * q^13 + 8 * q^16 + 12 * q^17 - 16 * q^22 + 6 * q^23 - 8 * q^25 - 12 * q^26 + 16 * q^27 + 12 * q^29 - 8 * q^30 - 8 * q^36 - 12 * q^38 - 8 * q^39 + 4 * q^43 + 32 * q^48 - 24 * q^51 - 8 * q^52 + 18 * q^53 - 8 * q^55 + 16 * q^61 + 24 * q^62 + 32 * q^64 - 6 * q^65 - 16 * q^66 - 24 * q^68 + 24 * q^69 - 24 * q^74 + 16 * q^75 - 48 * q^78 + 18 * q^79 + 22 * q^81 + 40 * q^82 + 12 * q^87 - 8 * q^90 + 24 * q^92 - 44 * q^94 - 6 * q^95

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