LMFDB - Embedded newform 637.2.r.a.324.1

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			324.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	637.324
Dual form			637.2.r.a.116.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 - 1.00000i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.866025 + 0.500000i) q^{5} +4.00000i q^{6} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-0.464102 - 7.19615i) 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} +(3.19615 - 6.46410i) 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} +(-3.19615 + 6.46410i) 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} +(0.232051 + 3.59808i) 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	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	−1.73205	−	1.00000i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$	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	−0.215615	−	0.976478i	$-0.569176\pi$
$11$	1.73205	−	1.00000i	0.522233	−	0.301511i	0.737848	+	0.674967i	$0.235842\pi$
$12$	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	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	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
$26$	−0.464102	−	7.19615i	−0.0910178	−	1.41128i
$27$	−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	0.862080	−	0.506772i	$-0.169162\pi$
$37$	5.19615	+	3.00000i	0.854242	+	0.493197i	−0.00783774	+	0.999969i	$0.502495\pi$
$38$	3.00000	+	5.19615i	0.486664	+	0.842927i
$39$	3.19615	−	6.46410i	0.511794	−	1.03508i
$40$		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
$52$	−3.19615	+	6.46410i	−0.443227	+	0.896410i
$53$	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	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	8.00000			1.00000
$65$	0.232051	+	3.59808i	0.0287824	+	0.446286i
$66$	4.00000	+	6.92820i	0.492366	+	0.852803i
$67$	−10.3923	+	6.00000i	−1.26962	+	0.733017i	−0.974916	−	0.222571i	$-0.928555\pi$
$67$	−10.3923	+	6.00000i	−1.26962	+	0.733017i	−0.294706	+	0.955588i	$0.595222\pi$
$68$	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	$-0.687914\pi$
$71$		−	14.0000i		−	1.66149i	0.556650	−	0.830747i	$-0.312086\pi$
$72$		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	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$	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	0.493135	−	0.869953i	$-0.335851\pi$
$109$	15.5885	−	9.00000i	1.49310	−	0.862044i	0.999969	+	0.00790932i	$0.00251764\pi$
$110$	−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
$117$	−3.59808	+	0.232051i	−0.332642	+	0.0214531i
$118$	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
$130$	3.19615	−	6.46410i	0.280321	−	0.566939i
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		−	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	−0.572161	−	0.820141i	$-0.693895\pi$
$137$	−1.73205	+	1.00000i	−0.147979	+	0.0854358i	0.424182	+	0.905577i	$0.360562\pi$
$138$	10.3923	+	6.00000i	0.884652	+	0.510754i
$139$	18.0000			1.52674			0.763370	−	0.645961i	$-0.223543\pi$
$139$	18.0000			1.52674			0.763370	+	0.645961i	$0.223543\pi$
$140$		0			0
$141$			22.0000i			1.85273i
$142$	−14.0000	+	24.2487i	−1.17485	+	2.03491i
$143$	6.46410	+	3.19615i	0.540555	+	0.267276i
$144$	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	0.101391	−	0.994847i	$-0.467671\pi$
$149$	−8.66025	−	5.00000i	−0.709476	−	0.409616i	−0.810867	+	0.585231i	$0.801004\pi$
$150$	13.8564	−	8.00000i	1.13137	−	0.653197i
$151$	−5.19615	+	3.00000i	−0.422857	+	0.244137i	−0.696299	−	0.717752i	$-0.745171\pi$
$151$	−5.19615	+	3.00000i	−0.422857	+	0.244137i	0.273442	+	0.961888i	$0.411838\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$		0			0
$155$	3.00000			0.240966
$156$	14.3923	−	0.928203i	1.15231	−	0.0743157i
$157$	−9.00000	−	15.5885i	−0.718278	−	1.24409i	−0.961681	−	0.274169i	$-0.911597\pi$
$157$	−9.00000	−	15.5885i	−0.718278	−	1.24409i	0.243403	−	0.969925i	$-0.421736\pi$
$158$	−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	0.0343508	−	0.999410i	$-0.489064\pi$
$163$	−10.3923	−	6.00000i	−0.813988	−	0.469956i	−0.848339	+	0.529454i	$0.822397\pi$
$164$	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	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$			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	$-0.266738\pi$
$181$	18.0000			1.33793			0.668965	+	0.743294i	$0.266738\pi$
$182$		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	−0.0769360	−	0.997036i	$-0.524514\pi$
$193$	10.3923	−	6.00000i	0.748054	−	0.431889i	0.824991	+	0.565147i	$0.191180\pi$
$194$	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	$-0.954488\pi$
$197$		−	4.00000i		−	0.284988i	0.989796	−	0.142494i	$-0.0455122\pi$
$198$	2.00000	−	3.46410i	0.142134	−	0.246183i
$199$	1.00000	+	1.73205i	0.0708881	+	0.122782i	0.899291	−	0.437351i	$-0.144083\pi$
$199$	1.00000	+	1.73205i	0.0708881	+	0.122782i	−0.828403	+	0.560133i	$0.810750\pi$
$200$		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
$208$	14.3923	−	0.928203i	0.997927	−	0.0643593i
$209$	−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
$221$	9.58846	−	19.3923i	0.644989	−	1.30447i
$222$	−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	$0.135336\pi$
$234$	6.46410	+	3.19615i	0.422572	+	0.208939i
$235$	−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	$0.0833068\pi$
$239$			8.00000i			0.517477i	−0.965947	+	0.258738i	$0.916693\pi$
$240$	−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
$247$	−0.696152	−	10.7942i	−0.0442951	−	0.686820i
$248$		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	$-0.439359\pi$
$251$	6.00000			0.378717			0.189358	+	0.981908i	$0.439359\pi$
$252$		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	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$			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	$0.0945841\pi$
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	−0.224523	+	0.974469i	$0.572083\pi$
$270$	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	$-0.981000\pi$
$281$		−	2.00000i		−	0.119310i	0.998219	−	0.0596550i	$-0.0190001\pi$
$282$	22.0000	−	38.1051i	1.31008	−	2.26913i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	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
$299$	10.7942	−	0.696152i	0.624246	−	0.0402595i
$300$	−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	$0.157077\pi$
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	−0.0301210	+	0.999546i	$0.509589\pi$
$312$		0			0
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	0.972028	+	0.234863i	$0.0754642\pi$
$314$			36.0000i			2.03160i
$315$		0			0
$316$	18.0000			1.01258
$317$	−17.3205	−	10.0000i	−0.972817	−	0.561656i	−0.0727229	−	0.997352i	$-0.523169\pi$
$317$	−17.3205	−	10.0000i	−0.972817	−	0.561656i	−0.900094	+	0.435696i	$0.856502\pi$
$318$	−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
$325$	6.39230	−	12.9282i	0.354581	−	0.717128i
$326$	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	0.186421	−	0.982470i	$-0.440311\pi$
$331$	−10.3923	−	6.00000i	−0.571213	−	0.329790i	−0.757634	+	0.652680i	$0.773645\pi$
$332$	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	$0.236998\pi$
$338$	20.6603	−	15.7846i	1.12377	−	0.858570i
$339$	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	0.909887	−	0.414855i	$-0.136168\pi$
$359$	19.0526	+	11.0000i	1.00556	+	0.580558i	0.0956683	+	0.995413i	$0.469501\pi$
$360$		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	0.529607	−	0.848243i	$-0.322339\pi$
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	−0.999404	+	0.0345320i	$0.989006\pi$
$368$	−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	$-0.847025\pi$
$379$		−	18.0000i		−	0.924598i	0.886724	−	0.462299i	$-0.152975\pi$
$380$	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	$0.558272\pi$
$390$	−14.3923	+	0.928203i	−0.728783	+	0.0470014i
$391$	−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	0.962960	−	0.269643i	$-0.0869057\pi$
$401$	24.2487	+	14.0000i	1.21092	+	0.699127i	0.247962	+	0.968770i	$0.420239\pi$
$402$	−24.0000	−	41.5692i	−1.19701	−	2.07328i
$403$	9.69615	+	4.79423i	0.483000	+	0.238818i
$404$	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
$416$	−25.8564	−	12.7846i	−1.26771	−	0.626817i
$417$	−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	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$		−	30.0000i		−	1.46211i	−0.682318	−	0.731055i	$-0.739028\pi$
$421$		−	30.0000i		−	1.46211i	0.682318	−	0.731055i	$-0.260972\pi$
$422$	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
$429$	−0.928203	−	14.3923i	−0.0448141	−	0.694867i
$430$	−1.00000	−	1.73205i	−0.0482243	−	0.0835269i
$431$	3.46410	−	2.00000i	0.166860	−	0.0963366i	−0.414244	−	0.910166i	$-0.635954\pi$
$431$	3.46410	−	2.00000i	0.166860	−	0.0963366i	0.581104	+	0.813829i	$0.302621\pi$
$432$	−8.00000	+	13.8564i	−0.384900	+	0.666667i
$433$	20.0000			0.961139			0.480569	−	0.876957i	$-0.340430\pi$
$433$	20.0000			0.961139			0.480569	+	0.876957i	$0.340430\pi$
$434$		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	$-0.504362\pi$
$439$	18.0000	−	31.1769i	0.859093	−	1.48799i	0.872795	−	0.488087i	$-0.162305\pi$
$440$		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	$-0.969911\pi$
$449$		−	4.00000i		−	0.188772i	0.995536	−	0.0943858i	$-0.0300887\pi$
$450$	−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	$0.106754\pi$
$457$	36.3731	+	21.0000i	1.70146	+	0.982339i	0.757174	+	0.653213i	$0.226579\pi$
$458$	−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	$0.245531\pi$
$463$			30.0000i			1.39422i	−0.716965	+	0.697109i	$0.754469\pi$
$464$	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	$0.590845\pi$
$467$	−21.0000	+	36.3731i	−0.971764	+	1.68314i	−0.690225	+	0.723595i	$0.742488\pi$
$468$	−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
$481$	1.39230	+	21.5885i	0.0634836	+	0.984349i
$482$	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	−0.245705	−	0.969345i	$-0.579019\pi$
$487$	10.3923	−	6.00000i	0.470920	−	0.271886i	0.716625	+	0.697459i	$0.245686\pi$
$488$		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
$494$	−9.58846	+	19.3923i	−0.431405	+	0.872501i
$495$	−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	0.379165	−	0.925329i	$-0.376211\pi$
$499$	−5.19615	−	3.00000i	−0.232612	−	0.134298i	−0.611776	+	0.791031i	$0.709545\pi$
$500$	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	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$		−	6.00000i		−	0.266996i
$506$	−6.00000	+	10.3923i	−0.266733	+	0.461994i
$507$	25.7846	−	3.33975i	1.14513	−	0.148323i
$508$		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	$-0.990459\pi$
$521$	−12.0000	−	20.7846i	−0.525730	−	0.910590i	0.473821	−	0.880621i	$-0.342874\pi$
$522$	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	0.125952	−	0.992036i	$-0.459801\pi$
$541$	−15.5885	−	9.00000i	−0.670200	−	0.386940i	−0.796152	+	0.605096i	$0.793135\pi$
$542$		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	−0.954673	−	0.297658i	$-0.903795\pi$
$557$	−27.7128	+	16.0000i	−1.17423	+	0.677942i	−0.219557	+	0.975600i	$0.570461\pi$
$558$	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	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$	−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	$0.893637\pi$
$572$	0.928203	+	14.3923i	0.0388101	+	0.601772i
$573$		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
$585$	−3.23205	−	1.59808i	−0.133629	−	0.0660723i
$586$	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
$598$	−19.3923	−	9.58846i	−0.793010	−	0.392101i
$599$	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	$-0.854546\pi$
$601$	−44.0000			−1.79480			−0.897399	+	0.441221i	$0.854546\pi$
$602$		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	−0.623525	−	0.781803i	$-0.714300\pi$
$607$	9.00000	−	15.5885i	0.365299	−	0.632716i	0.988824	+	0.149087i	$0.0476335\pi$
$608$	24.0000			0.973329
$609$		0			0
$610$	16.0000			0.647821
$611$	−2.55256	−	39.5788i	−0.103265	−	1.60119i
$612$	6.00000	+	10.3923i	0.242536	+	0.420084i
$613$	20.7846	−	12.0000i	0.839482	−	0.484675i	−0.0176058	−	0.999845i	$-0.505604\pi$
$613$	20.7846	−	12.0000i	0.839482	−	0.484675i	0.857088	+	0.515170i	$0.172271\pi$
$614$	−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	$0.0514829\pi$
$617$			8.00000i			0.322068i	−0.986949	+	0.161034i	$0.948517\pi$
$618$		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	$0.0767725\pi$
$631$			12.0000i			0.477712i	−0.971055	+	0.238856i	$0.923228\pi$
$632$		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	0.986916	−	0.161233i	$-0.0515470\pi$
$647$	9.00000	+	15.5885i	0.353827	+	0.612845i	−0.633090	+	0.774078i	$0.718214\pi$
$648$		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
$663$	−43.1769	+	2.78461i	−1.67685	+	0.108145i
$664$		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
$676$	−25.7846	+	3.33975i	−0.991716	+	0.128452i
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	−0.985517	−	0.169580i	$-0.945759\pi$
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	0.639618	+	0.768693i	$0.279092\pi$
$678$		−	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	0.340901	−	0.940099i	$-0.389268\pi$
$683$	34.6410	−	20.0000i	1.32550	−	0.765279i	0.984600	+	0.174820i	$0.0559345\pi$
$684$	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
$689$	−14.3827	+	29.0885i	−0.547937	+	1.10818i
$690$	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	$0.408580\pi$
$702$	1.85641	+	28.7846i	0.0700655	+	1.08641i
$703$	−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	−0.0747503	−	0.997202i	$-0.523816\pi$
$709$	−25.9808	−	15.0000i	−0.975728	−	0.563337i	−0.900978	+	0.433865i	$0.857149\pi$
$710$	−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	−0.983608	−	0.180319i	$-0.942287\pi$
$719$	−9.00000	+	15.5885i	−0.335643	+	0.581351i	0.647965	+	0.761670i	$0.275620\pi$
$720$			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	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$		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	−0.894852	−	0.446362i	$-0.852719\pi$
$739$	−25.9808	+	15.0000i	−0.955718	+	0.551784i	−0.0608653	+	0.998146i	$0.519386\pi$
$740$	−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	$0.298965\pi$
$743$			44.0000i			1.61420i	−0.590412	+	0.807102i	$0.701035\pi$
$744$		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
$754$	−1.39230	−	21.5885i	−0.0507048	−	0.786205i
$755$	−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
$767$	−25.8564	−	12.7846i	−0.933621	−	0.461626i
$768$	−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
$780$	12.9282	+	6.39230i	0.462904	+	0.228881i
$781$	−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
$793$	−28.7846	+	1.85641i	−1.02217	+	0.0659229i
$794$	−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	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$		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	0.238320	−	0.971187i	$-0.423403\pi$
$821$	−13.8564	−	8.00000i	−0.483592	−	0.279202i	−0.721912	+	0.691985i	$0.756737\pi$
$822$	−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	$0.0221553\pi$
$827$			4.00000i			0.139094i	−0.997579	+	0.0695468i	$0.977845\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$	−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
$845$	−10.3301	+	7.89230i	−0.355367	+	0.271504i
$846$	−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	$-0.955876\pi$
$857$	−18.0000	−	31.1769i	−0.614868	−	1.06498i	0.375539	−	0.926806i	$-0.377458\pi$
$858$	−12.7846	+	25.8564i	−0.436459	+	0.882723i
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$			2.00000i			0.0681994i
$861$		0			0
$862$	−8.00000			−0.272481
$863$	−27.7128	−	16.0000i	−0.943355	−	0.544646i	−0.0523446	−	0.998629i	$-0.516669\pi$
$863$	−27.7128	−	16.0000i	−0.943355	−	0.544646i	−0.891010	+	0.453983i	$0.850003\pi$
$864$	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
$871$	−38.7846	−	19.1769i	−1.31417	−	0.649785i
$872$		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	0.213158	−	0.977018i	$-0.431625\pi$
$877$	−15.5885	−	9.00000i	−0.526385	−	0.303908i	−0.739543	+	0.673109i	$0.764958\pi$
$878$	−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	$-0.564791\pi$
$881$	−12.0000			−0.404290			−0.202145	+	0.979356i	$0.564791\pi$
$882$		0			0
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$	43.1769	−	2.78461i	1.45220	−	0.0936566i
$885$	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	$-0.626754\pi$
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	0.992149	−	0.125061i	$-0.0399128\pi$
$888$		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	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		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	0.257673	−	0.966232i	$-0.417044\pi$
$947$	−13.8564	−	8.00000i	−0.450273	−	0.259965i	−0.707945	+	0.706267i	$0.750378\pi$
$948$	−18.0000	−	31.1769i	−0.584613	−	1.01258i
$949$	−29.0885	−	14.3827i	−0.944251	−	0.466882i
$950$	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
$962$	19.1769	−	38.7846i	0.618289	−	1.25047i
$963$	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	$-0.665238\pi$
$967$		−	54.0000i		−	1.73652i	0.496107	−	0.868261i	$-0.334762\pi$
$968$		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	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$	20.0000			0.641500
$973$		0			0
$974$	−24.0000			−0.769010
$975$	−28.7846	+	1.85641i	−0.921845	+	0.0594526i
$976$	16.0000	+	27.7128i	0.512148	+	0.887066i
$977$	−8.66025	+	5.00000i	−0.277066	+	0.159964i	−0.632094	−	0.774891i	$-0.717805\pi$
$977$	−8.66025	+	5.00000i	−0.277066	+	0.159964i	0.355028	+	0.934856i	$0.384471\pi$
$978$	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	$0.0264156\pi$
$997$	18.0000	+	31.1769i	0.570066	+	0.987383i	−0.426493	+	0.904491i	$0.640251\pi$
$998$	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.a.324.1		4
7.2	even	3		637.2.c.c.246.2	yes	2
7.3	odd	6		637.2.r.c.116.2		4
7.4	even	3	inner	637.2.r.a.116.2		4
7.5	odd	6		637.2.c.a.246.2	yes	2
7.6	odd	2		637.2.r.c.324.1		4
13.12	even	2	inner	637.2.r.a.324.2		4
91.5	even	12		8281.2.a.k.1.1		1
91.12	odd	6		637.2.c.a.246.1	✓	2
91.25	even	6	inner	637.2.r.a.116.1		4
91.38	odd	6		637.2.r.c.116.1		4
91.44	odd	12		8281.2.a.m.1.1		1
91.47	even	12		8281.2.a.a.1.1		1
91.51	even	6		637.2.c.c.246.1	yes	2
91.86	odd	12		8281.2.a.b.1.1		1
91.90	odd	2		637.2.r.c.324.2		4

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

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} +(-0.464102 - 7.19615i) 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} +(3.19615 - 6.46410i) 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} +(-3.19615 + 6.46410i) 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} +(0.232051 + 3.59808i) 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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