LMFDB - Embedded newform 735.2.s.a.521.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(521,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("735.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.s (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:	$5.86900454856$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	735.521
Dual form			735.2.s.a.656.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.00000 q^{6} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.00000 q^{6} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 + 0.866025i) q^{10} +(-3.00000 - 1.73205i) q^{11} +(-1.50000 + 0.866025i) q^{12} +1.73205i q^{15} +(2.50000 + 4.33013i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-4.50000 - 2.59808i) q^{18} +(3.00000 - 1.73205i) q^{19} -1.00000 q^{20} +6.00000 q^{22} +(-3.00000 + 1.73205i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +6.92820i q^{29} +(-1.50000 - 2.59808i) q^{30} +(3.00000 + 1.73205i) q^{31} +(-4.50000 - 2.59808i) q^{32} +(3.00000 + 5.19615i) q^{33} +10.3923i q^{34} +3.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(-1.50000 + 0.866025i) q^{40} -6.00000 q^{41} -8.00000 q^{43} +(-3.00000 + 1.73205i) q^{44} +(1.50000 - 2.59808i) q^{45} +(3.00000 - 5.19615i) q^{46} +(-6.00000 - 10.3923i) q^{47} -8.66025i q^{48} -1.73205i q^{50} +(-9.00000 + 5.19615i) q^{51} +(4.50000 + 7.79423i) q^{54} +3.46410i q^{55} -6.00000 q^{57} +(-6.00000 - 10.3923i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(1.50000 + 0.866025i) q^{60} +(-6.00000 + 3.46410i) q^{61} -6.00000 q^{62} -1.00000 q^{64} +(-9.00000 - 5.19615i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(-3.00000 - 5.19615i) q^{68} +6.00000 q^{69} -3.46410i q^{71} +(4.50000 - 2.59808i) q^{72} +(-6.00000 - 3.46410i) q^{73} +(-3.00000 - 1.73205i) q^{74} +(1.50000 - 0.866025i) q^{75} -3.46410i q^{76} +(-4.00000 - 6.92820i) q^{79} +(2.50000 - 4.33013i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(9.00000 - 5.19615i) q^{82} -6.00000 q^{85} +(12.0000 - 6.92820i) q^{86} +(6.00000 - 10.3923i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(3.00000 + 5.19615i) q^{89} +5.19615i q^{90} +3.46410i q^{92} +(-3.00000 - 5.19615i) q^{93} +(18.0000 + 10.3923i) q^{94} +(-3.00000 - 1.73205i) q^{95} +(4.50000 + 7.79423i) q^{96} +6.92820i q^{97} -10.3923i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 3 q^{3} + q^{4} - q^{5} + 6 q^{6} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 3 * q^3 + q^4 - q^5 + 6 * q^6 + 3 * q^9	$ 2 q - 3 q^{2} - 3 q^{3} + q^{4} - q^{5} + 6 q^{6} + 3 q^{9} + 3 q^{10} - 6 q^{11} - 3 q^{12} + 5 q^{16} + 6 q^{17} - 9 q^{18} + 6 q^{19} - 2 q^{20} + 12 q^{22} - 6 q^{23} - 3 q^{24} - q^{25} - 3 q^{30} + 6 q^{31} - 9 q^{32} + 6 q^{33} + 6 q^{36} + 2 q^{37} - 6 q^{38} - 3 q^{40} - 12 q^{41} - 16 q^{43} - 6 q^{44} + 3 q^{45} + 6 q^{46} - 12 q^{47} - 18 q^{51} + 9 q^{54} - 12 q^{57} - 12 q^{58} - 12 q^{59} + 3 q^{60} - 12 q^{61} - 12 q^{62} - 2 q^{64} - 18 q^{66} - 8 q^{67} - 6 q^{68} + 12 q^{69} + 9 q^{72} - 12 q^{73} - 6 q^{74} + 3 q^{75} - 8 q^{79} + 5 q^{80} - 9 q^{81} + 18 q^{82} - 12 q^{85} + 24 q^{86} + 12 q^{87} - 6 q^{88} + 6 q^{89} - 6 q^{93} + 36 q^{94} - 6 q^{95} + 9 q^{96}+O(q^{100}) $ 2 * q - 3 * q^2 - 3 * q^3 + q^4 - q^5 + 6 * q^6 + 3 * q^9 + 3 * q^10 - 6 * q^11 - 3 * q^12 + 5 * q^16 + 6 * q^17 - 9 * q^18 + 6 * q^19 - 2 * q^20 + 12 * q^22 - 6 * q^23 - 3 * q^24 - q^25 - 3 * q^30 + 6 * q^31 - 9 * q^32 + 6 * q^33 + 6 * q^36 + 2 * q^37 - 6 * q^38 - 3 * q^40 - 12 * q^41 - 16 * q^43 - 6 * q^44 + 3 * q^45 + 6 * q^46 - 12 * q^47 - 18 * q^51 + 9 * q^54 - 12 * q^57 - 12 * q^58 - 12 * q^59 + 3 * q^60 - 12 * q^61 - 12 * q^62 - 2 * q^64 - 18 * q^66 - 8 * q^67 - 6 * q^68 + 12 * q^69 + 9 * q^72 - 12 * q^73 - 6 * q^74 + 3 * q^75 - 8 * q^79 + 5 * q^80 - 9 * q^81 + 18 * q^82 - 12 * q^85 + 24 * q^86 + 12 * q^87 - 6 * q^88 + 6 * q^89 - 6 * q^93 + 36 * q^94 - 6 * q^95 + 9 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.135045	+	0.990839i	$0.543118\pi$
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	3.00000			1.22474
$7$		0			0
$7$		0			0
$8$		−	1.73205i		−	0.612372i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	1.50000	+	0.866025i	0.474342	+	0.273861i
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.0258656	−	0.999665i	$-0.508234\pi$
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.878668	+	0.477432i	$0.841568\pi$
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		0			0
$15$			1.73205i			0.447214i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$	−4.50000	−	2.59808i	−1.06066	−	0.612372i
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.00000	−	1.73205i	0.688247	−	0.397360i	0.802955	+	0.596040i	$0.203260\pi$
$20$	−1.00000			−0.223607
$21$		0			0
$22$	6.00000			1.27920
$23$	−3.00000	+	1.73205i	−0.625543	+	0.361158i	−0.779024	−	0.626994i	$-0.784285\pi$
$23$	−3.00000	+	1.73205i	−0.625543	+	0.361158i	0.153481	+	0.988152i	$0.450952\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$			6.92820i			1.28654i	0.765641	+	0.643268i	$0.222422\pi$
$29$			6.92820i			1.28654i	−0.765641	+	0.643268i	$0.777578\pi$
$30$	−1.50000	−	2.59808i	−0.273861	−	0.474342i
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	0.744599	−	0.667512i	$-0.232641\pi$
$31$	3.00000	+	1.73205i	0.538816	+	0.311086i	−0.205783	+	0.978598i	$0.565974\pi$
$32$	−4.50000	−	2.59808i	−0.795495	−	0.459279i
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$			10.3923i			1.78227i
$35$		0			0
$36$	3.00000			0.500000
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$	−3.00000	+	5.19615i	−0.486664	+	0.842927i
$39$		0			0
$40$	−1.50000	+	0.866025i	−0.237171	+	0.136931i
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	−3.00000	+	1.73205i	−0.452267	+	0.261116i
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	−6.00000	−	10.3923i	−0.875190	−	1.51587i	−0.856560	−	0.516047i	$-0.827403\pi$
$47$	−6.00000	−	10.3923i	−0.875190	−	1.51587i	−0.0186297	−	0.999826i	$-0.505930\pi$
$48$		−	8.66025i		−	1.25000i
$49$		0			0
$50$		−	1.73205i		−	0.244949i
$51$	−9.00000	+	5.19615i	−1.26025	+	0.727607i
$52$		0			0
$53$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$53$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$54$	4.50000	+	7.79423i	0.612372	+	1.06066i
$55$			3.46410i			0.467099i
$56$		0			0
$57$	−6.00000			−0.794719
$58$	−6.00000	−	10.3923i	−0.787839	−	1.36458i
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$	1.50000	+	0.866025i	0.193649	+	0.111803i
$61$	−6.00000	+	3.46410i	−0.768221	+	0.443533i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−6.00000	+	3.46410i	−0.768221	+	0.443533i	0.0640184	+	0.997949i	$0.479608\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−9.00000	−	5.19615i	−1.10782	−	0.639602i
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	−0.999915	−	0.0130248i	$-0.995854\pi$
$67$	−4.00000	+	6.92820i	−0.488678	+	0.846415i	0.511237	+	0.859440i	$0.329187\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$	6.00000			0.722315
$70$		0			0
$71$		−	3.46410i		−	0.411113i	−0.978645	−	0.205557i	$-0.934100\pi$
$71$		−	3.46410i		−	0.411113i	0.978645	−	0.205557i	$-0.0659005\pi$
$72$	4.50000	−	2.59808i	0.530330	−	0.306186i
$73$	−6.00000	−	3.46410i	−0.702247	−	0.405442i	0.105937	−	0.994373i	$-0.466216\pi$
$73$	−6.00000	−	3.46410i	−0.702247	−	0.405442i	−0.808184	+	0.588930i	$0.799549\pi$
$74$	−3.00000	−	1.73205i	−0.348743	−	0.201347i
$75$	1.50000	−	0.866025i	0.173205	−	0.100000i
$76$		−	3.46410i		−	0.397360i
$77$		0			0
$78$		0			0
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	2.50000	−	4.33013i	0.279508	−	0.484123i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	9.00000	−	5.19615i	0.993884	−	0.573819i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−6.00000			−0.650791
$86$	12.0000	−	6.92820i	1.29399	−	0.747087i
$87$	6.00000	−	10.3923i	0.643268	−	1.11417i
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$			5.19615i			0.547723i
$91$		0			0
$92$			3.46410i			0.361158i
$93$	−3.00000	−	5.19615i	−0.311086	−	0.538816i
$94$	18.0000	+	10.3923i	1.85656	+	1.07188i
$95$	−3.00000	−	1.73205i	−0.307794	−	0.177705i
$96$	4.50000	+	7.79423i	0.459279	+	0.795495i
$97$			6.92820i			0.703452i	0.936103	+	0.351726i	$0.114405\pi$
$97$			6.92820i			0.703452i	−0.936103	+	0.351726i	$0.885595\pi$
$98$		0			0
$99$		−	10.3923i		−	1.04447i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$	9.00000	−	15.5885i	0.891133	−	1.54349i
$103$	−3.00000	+	1.73205i	−0.295599	+	0.170664i	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	−3.00000	+	1.73205i	−0.295599	+	0.170664i	0.344865	+	0.938652i	$0.387925\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.00000	+	5.19615i	−0.870063	+	0.502331i	−0.867369	−	0.497665i	$-0.834191\pi$
$107$	−9.00000	+	5.19615i	−0.870063	+	0.502331i	−0.00269372	+	0.999996i	$0.500857\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$	−3.00000	−	5.19615i	−0.286039	−	0.495434i
$111$		−	3.46410i		−	0.328798i
$112$		0			0
$113$			6.92820i			0.651751i	0.945413	+	0.325875i	$0.105659\pi$
$113$			6.92820i			0.651751i	−0.945413	+	0.325875i	$0.894341\pi$
$114$	9.00000	−	5.19615i	0.842927	−	0.486664i
$115$	3.00000	+	1.73205i	0.279751	+	0.161515i
$116$	6.00000	+	3.46410i	0.557086	+	0.321634i
$117$		0			0
$118$		−	20.7846i		−	1.91338i
$119$		0			0
$120$	3.00000			0.273861
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	6.00000	−	10.3923i	0.543214	−	0.940875i
$123$	9.00000	+	5.19615i	0.811503	+	0.468521i
$124$	3.00000	−	1.73205i	0.269408	−	0.155543i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	10.5000	−	6.06218i	0.928078	−	0.535826i
$129$	12.0000	+	6.92820i	1.05654	+	0.609994i
$130$		0			0
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$	6.00000			0.522233
$133$		0			0
$134$		−	13.8564i		−	1.19701i
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$	−9.00000	−	5.19615i	−0.771744	−	0.445566i
$137$	18.0000	+	10.3923i	1.53784	+	0.887875i	0.998965	+	0.0454914i	$0.0144854\pi$
$137$	18.0000	+	10.3923i	1.53784	+	0.887875i	0.538879	+	0.842383i	$0.318848\pi$
$138$	−9.00000	+	5.19615i	−0.766131	+	0.442326i
$139$			17.3205i			1.46911i	0.678551	+	0.734553i	$0.262608\pi$
$139$			17.3205i			1.46911i	−0.678551	+	0.734553i	$0.737392\pi$
$140$		0			0
$141$			20.7846i			1.75038i
$142$	3.00000	+	5.19615i	0.251754	+	0.436051i
$143$		0			0
$144$	−7.50000	+	12.9904i	−0.625000	+	1.08253i
$145$	6.00000	−	3.46410i	0.498273	−	0.287678i
$146$	12.0000			0.993127
$147$		0			0
$148$	2.00000			0.164399
$149$	−6.00000	+	3.46410i	−0.491539	+	0.283790i	−0.725213	−	0.688525i	$-0.758259\pi$
$149$	−6.00000	+	3.46410i	−0.491539	+	0.283790i	0.233674	+	0.972315i	$0.424925\pi$
$150$	−1.50000	+	2.59808i	−0.122474	+	0.212132i
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$	−3.00000	−	5.19615i	−0.243332	−	0.421464i
$153$	18.0000			1.45521
$154$		0			0
$155$		−	3.46410i		−	0.278243i
$156$		0			0
$157$	−12.0000	−	6.92820i	−0.957704	−	0.552931i	−0.0622385	−	0.998061i	$-0.519824\pi$
$157$	−12.0000	−	6.92820i	−0.957704	−	0.552931i	−0.895466	+	0.445130i	$0.853157\pi$
$158$	12.0000	+	6.92820i	0.954669	+	0.551178i
$159$		0			0
$160$			5.19615i			0.410792i
$161$		0			0
$162$		−	15.5885i		−	1.22474i
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$	−3.00000	+	5.19615i	−0.234261	+	0.405751i
$165$	3.00000	−	5.19615i	0.233550	−	0.404520i
$166$		0			0
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$	9.00000	−	5.19615i	0.690268	−	0.398527i
$171$	9.00000	+	5.19615i	0.688247	+	0.397360i
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$			20.7846i			1.57568i
$175$		0			0
$176$		−	17.3205i		−	1.30558i
$177$	18.0000	−	10.3923i	1.35296	−	0.781133i
$178$	−9.00000	−	5.19615i	−0.674579	−	0.389468i
$179$	9.00000	+	5.19615i	0.672692	+	0.388379i	0.797096	−	0.603853i	$-0.206369\pi$
$179$	9.00000	+	5.19615i	0.672692	+	0.388379i	−0.124404	+	0.992232i	$0.539702\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$		−	20.7846i		−	1.54491i	−0.635071	−	0.772454i	$-0.719029\pi$
$181$		−	20.7846i		−	1.54491i	0.635071	−	0.772454i	$-0.280971\pi$
$182$		0			0
$183$	12.0000			0.887066
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$	1.00000	−	1.73205i	0.0735215	−	0.127343i
$186$	9.00000	+	5.19615i	0.659912	+	0.381000i
$187$	−18.0000	+	10.3923i	−1.31629	+	0.759961i
$188$	−12.0000			−0.875190
$189$		0			0
$190$	6.00000			0.435286
$191$	9.00000	−	5.19615i	0.651217	−	0.375980i	−0.137705	−	0.990473i	$-0.543973\pi$
$191$	9.00000	−	5.19615i	0.651217	−	0.375980i	0.788922	+	0.614493i	$0.210639\pi$
$192$	1.50000	+	0.866025i	0.108253	+	0.0625000i
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	−6.00000	−	10.3923i	−0.430775	−	0.746124i
$195$		0			0
$196$		0			0
$197$			13.8564i			0.987228i	0.869681	+	0.493614i	$0.164324\pi$
$197$			13.8564i			0.987228i	−0.869681	+	0.493614i	$0.835676\pi$
$198$	9.00000	+	15.5885i	0.639602	+	1.10782i
$199$	−9.00000	−	5.19615i	−0.637993	−	0.368345i	0.145848	−	0.989307i	$-0.453409\pi$
$199$	−9.00000	−	5.19615i	−0.637993	−	0.368345i	−0.783841	+	0.620962i	$0.786742\pi$
$200$	1.50000	+	0.866025i	0.106066	+	0.0612372i
$201$	12.0000	−	6.92820i	0.846415	−	0.488678i
$202$		−	10.3923i		−	0.731200i
$203$		0			0
$204$			10.3923i			0.727607i
$205$	3.00000	+	5.19615i	0.209529	+	0.362915i
$206$	3.00000	−	5.19615i	0.209020	−	0.362033i
$207$	−9.00000	−	5.19615i	−0.625543	−	0.361158i
$208$		0			0
$209$	−12.0000			−0.830057
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$		0			0
$213$	−3.00000	+	5.19615i	−0.205557	+	0.356034i
$214$	9.00000	−	15.5885i	0.615227	−	1.06561i
$215$	4.00000	+	6.92820i	0.272798	+	0.472500i
$216$	−9.00000			−0.612372
$217$		0			0
$218$			3.46410i			0.234619i
$219$	6.00000	+	10.3923i	0.405442	+	0.702247i
$220$	3.00000	+	1.73205i	0.202260	+	0.116775i
$221$		0			0
$222$	3.00000	+	5.19615i	0.201347	+	0.348743i
$223$		−	17.3205i		−	1.15987i	−0.814664	−	0.579934i	$-0.803079\pi$
$223$		−	17.3205i		−	1.15987i	0.814664	−	0.579934i	$-0.196921\pi$
$224$		0			0
$225$	−3.00000			−0.200000
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	0.125435	+	0.992102i	$0.459967\pi$
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	−0.921903	+	0.387421i	$0.873366\pi$
$228$	−3.00000	+	5.19615i	−0.198680	+	0.344124i
$229$	−6.00000	+	3.46410i	−0.396491	+	0.228914i	−0.684969	−	0.728572i	$-0.740184\pi$
$229$	−6.00000	+	3.46410i	−0.396491	+	0.228914i	0.288478	+	0.957487i	$0.406851\pi$
$230$	−6.00000			−0.395628
$231$		0			0
$232$	12.0000			0.787839
$233$	−6.00000	+	3.46410i	−0.393073	+	0.226941i	−0.683491	−	0.729959i	$-0.739539\pi$
$233$	−6.00000	+	3.46410i	−0.393073	+	0.226941i	0.290418	+	0.956900i	$0.406206\pi$
$234$		0			0
$235$	−6.00000	+	10.3923i	−0.391397	+	0.677919i
$236$	6.00000	+	10.3923i	0.390567	+	0.676481i
$237$			13.8564i			0.900070i
$238$		0			0
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$	−7.50000	+	4.33013i	−0.484123	+	0.279508i
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	−1.50000	−	0.866025i	−0.0964237	−	0.0556702i
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$			6.92820i			0.443533i
$245$		0			0
$246$	−18.0000			−1.14764
$247$		0			0
$248$	3.00000	−	5.19615i	0.190500	−	0.329956i
$249$		0			0
$250$	−1.50000	+	0.866025i	−0.0948683	+	0.0547723i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	12.0000			0.754434
$254$	6.00000	−	3.46410i	0.376473	−	0.217357i
$255$	9.00000	+	5.19615i	0.563602	+	0.325396i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$	−24.0000			−1.49417
$259$		0			0
$260$		0			0
$261$	−18.0000	+	10.3923i	−1.11417	+	0.643268i
$262$	18.0000	+	10.3923i	1.11204	+	0.642039i
$263$	−21.0000	−	12.1244i	−1.29492	−	0.747620i	−0.315394	−	0.948961i	$-0.602137\pi$
$263$	−21.0000	−	12.1244i	−1.29492	−	0.747620i	−0.979521	+	0.201341i	$0.935470\pi$
$264$	9.00000	−	5.19615i	0.553912	−	0.319801i
$265$		0			0
$266$		0			0
$267$		−	10.3923i		−	0.635999i
$268$	4.00000	+	6.92820i	0.244339	+	0.423207i
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	−0.449622	−	0.893219i	$-0.648441\pi$
$269$	9.00000	−	15.5885i	0.548740	−	0.950445i	0.998361	−	0.0572259i	$-0.0182255\pi$
$270$	4.50000	−	7.79423i	0.273861	−	0.474342i
$271$	21.0000	−	12.1244i	1.27566	−	0.736502i	0.299612	−	0.954061i	$-0.403143\pi$
$271$	21.0000	−	12.1244i	1.27566	−	0.736502i	0.976047	+	0.217559i	$0.0698094\pi$
$272$	30.0000			1.81902
$273$		0			0
$274$	−36.0000			−2.17484
$275$	3.00000	−	1.73205i	0.180907	−	0.104447i
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	−0.995997	−	0.0893846i	$-0.971510\pi$
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	0.575408	+	0.817867i	$0.304843\pi$
$278$	−15.0000	−	25.9808i	−0.899640	−	1.55822i
$279$			10.3923i			0.622171i
$280$		0			0
$281$		−	13.8564i		−	0.826604i	−0.910594	−	0.413302i	$-0.864375\pi$
$281$		−	13.8564i		−	0.826604i	0.910594	−	0.413302i	$-0.135625\pi$
$282$	−18.0000	−	31.1769i	−1.07188	−	1.85656i
$283$	−15.0000	−	8.66025i	−0.891657	−	0.514799i	−0.0171732	−	0.999853i	$-0.505467\pi$
$283$	−15.0000	−	8.66025i	−0.891657	−	0.514799i	−0.874484	+	0.485054i	$0.838800\pi$
$284$	−3.00000	−	1.73205i	−0.178017	−	0.102778i
$285$	3.00000	+	5.19615i	0.177705	+	0.307794i
$286$		0			0
$287$		0			0
$288$		−	15.5885i		−	0.918559i
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−6.00000	+	10.3923i	−0.352332	+	0.610257i
$291$	6.00000	−	10.3923i	0.351726	−	0.609208i
$292$	−6.00000	+	3.46410i	−0.351123	+	0.202721i
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$		0			0
$295$	12.0000			0.698667
$296$	3.00000	−	1.73205i	0.174371	−	0.100673i
$297$	−9.00000	+	15.5885i	−0.522233	+	0.904534i
$298$	6.00000	−	10.3923i	0.347571	−	0.602010i
$299$		0			0
$300$		−	1.73205i		−	0.100000i
$301$		0			0
$302$			13.8564i			0.797347i
$303$	9.00000	−	5.19615i	0.517036	−	0.298511i
$304$	15.0000	+	8.66025i	0.860309	+	0.496700i
$305$	6.00000	+	3.46410i	0.343559	+	0.198354i
$306$	−27.0000	+	15.5885i	−1.54349	+	0.891133i
$307$		−	24.2487i		−	1.38395i	−0.721923	−	0.691974i	$-0.756741\pi$
$307$		−	24.2487i		−	1.38395i	0.721923	−	0.691974i	$-0.243259\pi$
$308$		0			0
$309$	6.00000			0.341328
$310$	3.00000	+	5.19615i	0.170389	+	0.295122i
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$	−18.0000	+	10.3923i	−1.01742	+	0.587408i	−0.913356	−	0.407163i	$-0.866518\pi$
$313$	−18.0000	+	10.3923i	−1.01742	+	0.587408i	−0.104065	+	0.994571i	$0.533185\pi$
$314$	24.0000			1.35440
$315$		0			0
$316$	−8.00000			−0.450035
$317$	−24.0000	+	13.8564i	−1.34797	+	0.778253i	−0.987962	−	0.154694i	$-0.950561\pi$
$317$	−24.0000	+	13.8564i	−1.34797	+	0.778253i	−0.360012	+	0.932948i	$0.617227\pi$
$318$		0			0
$319$	12.0000	−	20.7846i	0.671871	−	1.16371i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	18.0000			1.00466
$322$		0			0
$323$		−	20.7846i		−	1.15649i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$		0			0
$326$	−24.0000	−	13.8564i	−1.32924	−	0.767435i
$327$	−3.00000	+	1.73205i	−0.165900	+	0.0957826i
$328$			10.3923i			0.573819i
$329$		0			0
$330$			10.3923i			0.572078i
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	−0.937829	−	0.347097i	$-0.887167\pi$
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	0.168320	−	0.985732i	$-0.446166\pi$
$332$		0			0
$333$	−3.00000	+	5.19615i	−0.164399	+	0.284747i
$334$	18.0000	−	10.3923i	0.984916	−	0.568642i
$335$	8.00000			0.437087
$336$		0			0
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	−19.5000	+	11.2583i	−1.06066	+	0.612372i
$339$	6.00000	−	10.3923i	0.325875	−	0.564433i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$	−18.0000			−0.973329
$343$		0			0
$344$			13.8564i			0.747087i
$345$	−3.00000	−	5.19615i	−0.161515	−	0.279751i
$346$	−27.0000	−	15.5885i	−1.45153	−	0.838041i
$347$	−15.0000	−	8.66025i	−0.805242	−	0.464907i	0.0400587	−	0.999197i	$-0.487246\pi$
$347$	−15.0000	−	8.66025i	−0.805242	−	0.464907i	−0.845301	+	0.534291i	$0.820579\pi$
$348$	−6.00000	−	10.3923i	−0.321634	−	0.557086i
$349$			6.92820i			0.370858i	0.982658	+	0.185429i	$0.0593675\pi$
$349$			6.92820i			0.370858i	−0.982658	+	0.185429i	$0.940632\pi$
$350$		0			0
$351$		0			0
$352$	9.00000	+	15.5885i	0.479702	+	0.830868i
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$	−18.0000	+	31.1769i	−0.956689	+	1.65703i
$355$	−3.00000	+	1.73205i	−0.159223	+	0.0919277i
$356$	6.00000			0.317999
$357$		0			0
$358$	−18.0000			−0.951330
$359$	−3.00000	+	1.73205i	−0.158334	+	0.0914141i	−0.577073	−	0.816692i	$-0.695805\pi$
$359$	−3.00000	+	1.73205i	−0.158334	+	0.0914141i	0.418740	+	0.908106i	$0.362472\pi$
$360$	−4.50000	−	2.59808i	−0.237171	−	0.136931i
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	18.0000	+	31.1769i	0.946059	+	1.63862i
$363$		−	1.73205i		−	0.0909091i
$364$		0			0
$365$			6.92820i			0.362639i
$366$	−18.0000	+	10.3923i	−0.940875	+	0.543214i
$367$	−9.00000	−	5.19615i	−0.469796	−	0.271237i	0.246358	−	0.969179i	$-0.420766\pi$
$367$	−9.00000	−	5.19615i	−0.469796	−	0.271237i	−0.716154	+	0.697942i	$0.754099\pi$
$368$	−15.0000	−	8.66025i	−0.781929	−	0.451447i
$369$	−9.00000	−	15.5885i	−0.468521	−	0.811503i
$370$			3.46410i			0.180090i
$371$		0			0
$372$	−6.00000			−0.311086
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	0.625917	−	0.779890i	$-0.284725\pi$
$373$	−7.00000	−	12.1244i	−0.362446	−	0.627775i	−0.988363	+	0.152115i	$0.951392\pi$
$374$	18.0000	−	31.1769i	0.930758	−	1.61212i
$375$	−1.50000	−	0.866025i	−0.0774597	−	0.0447214i
$376$	−18.0000	+	10.3923i	−0.928279	+	0.535942i
$377$		0			0
$378$		0			0
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$	−3.00000	+	1.73205i	−0.153897	+	0.0888523i
$381$	6.00000	+	3.46410i	0.307389	+	0.177471i
$382$	−9.00000	+	15.5885i	−0.460480	+	0.797575i
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$	−21.0000			−1.07165
$385$		0			0
$386$			24.2487i			1.23423i
$387$	−12.0000	−	20.7846i	−0.609994	−	1.05654i
$388$	6.00000	+	3.46410i	0.304604	+	0.175863i
$389$	6.00000	+	3.46410i	0.304212	+	0.175637i	0.644334	−	0.764745i	$-0.277135\pi$
$389$	6.00000	+	3.46410i	0.304212	+	0.175637i	−0.340121	+	0.940382i	$0.610468\pi$
$390$		0			0
$391$			20.7846i			1.05112i
$392$		0			0
$393$			20.7846i			1.04844i
$394$	−12.0000	−	20.7846i	−0.604551	−	1.04711i
$395$	−4.00000	+	6.92820i	−0.201262	+	0.348596i
$396$	−9.00000	−	5.19615i	−0.452267	−	0.261116i
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	−0.167668	−	0.985843i	$-0.553624\pi$
$397$	12.0000	−	6.92820i	0.602263	−	0.347717i	0.769931	+	0.638127i	$0.220290\pi$
$398$	18.0000			0.902258
$399$		0			0
$400$	−5.00000			−0.250000
$401$	24.0000	−	13.8564i	1.19850	−	0.691956i	0.238282	−	0.971196i	$-0.423416\pi$
$401$	24.0000	−	13.8564i	1.19850	−	0.691956i	0.960221	+	0.279240i	$0.0900826\pi$
$402$	−12.0000	+	20.7846i	−0.598506	+	1.03664i
$403$		0			0
$404$	3.00000	+	5.19615i	0.149256	+	0.258518i
$405$	9.00000			0.447214
$406$		0			0
$407$		−	6.92820i		−	0.343418i
$408$	9.00000	+	15.5885i	0.445566	+	0.771744i
$409$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$409$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$410$	−9.00000	−	5.19615i	−0.444478	−	0.256620i
$411$	−18.0000	−	31.1769i	−0.887875	−	1.53784i
$412$			3.46410i			0.170664i
$413$		0			0
$414$	18.0000			0.884652
$415$		0			0
$416$		0			0
$417$	15.0000	−	25.9808i	0.734553	−	1.27228i
$418$	18.0000	−	10.3923i	0.880409	−	0.508304i
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−6.00000	+	3.46410i	−0.292075	+	0.168630i
$423$	18.0000	−	31.1769i	0.875190	−	1.51587i
$424$		0			0
$425$	3.00000	+	5.19615i	0.145521	+	0.252050i
$426$		−	10.3923i		−	0.503509i
$427$		0			0
$428$			10.3923i			0.502331i
$429$		0			0
$430$	−12.0000	−	6.92820i	−0.578691	−	0.334108i
$431$	−9.00000	−	5.19615i	−0.433515	−	0.250290i	0.267328	−	0.963606i	$-0.413859\pi$
$431$	−9.00000	−	5.19615i	−0.433515	−	0.250290i	−0.700843	+	0.713316i	$0.747193\pi$
$432$	22.5000	−	12.9904i	1.08253	−	0.625000i
$433$		−	6.92820i		−	0.332948i	−0.986046	−	0.166474i	$-0.946762\pi$
$433$		−	6.92820i		−	0.332948i	0.986046	−	0.166474i	$-0.0532382\pi$
$434$		0			0
$435$	−12.0000			−0.575356
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−6.00000	+	10.3923i	−0.287019	+	0.497131i
$438$	−18.0000	−	10.3923i	−0.860073	−	0.496564i
$439$	−15.0000	+	8.66025i	−0.715911	+	0.413331i	−0.813246	−	0.581920i	$-0.802302\pi$
$439$	−15.0000	+	8.66025i	−0.715911	+	0.413331i	0.0973349	+	0.995252i	$0.468968\pi$
$440$	6.00000			0.286039
$441$		0			0
$442$		0			0
$443$	−9.00000	+	5.19615i	−0.427603	+	0.246877i	−0.698325	−	0.715781i	$-0.746071\pi$
$443$	−9.00000	+	5.19615i	−0.427603	+	0.246877i	0.270722	+	0.962658i	$0.412738\pi$
$444$	−3.00000	−	1.73205i	−0.142374	−	0.0821995i
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$	15.0000	+	25.9808i	0.710271	+	1.23022i
$447$	12.0000			0.567581
$448$		0			0
$449$			13.8564i			0.653924i	0.945037	+	0.326962i	$0.106025\pi$
$449$			13.8564i			0.653924i	−0.945037	+	0.326962i	$0.893975\pi$
$450$	4.50000	−	2.59808i	0.212132	−	0.122474i
$451$	18.0000	+	10.3923i	0.847587	+	0.489355i
$452$	6.00000	+	3.46410i	0.282216	+	0.162938i
$453$	−12.0000	+	6.92820i	−0.563809	+	0.325515i
$454$		−	41.5692i		−	1.95094i
$455$		0			0
$456$			10.3923i			0.486664i
$457$	19.0000	+	32.9090i	0.888783	+	1.53942i	0.841316	+	0.540544i	$0.181781\pi$
$457$	19.0000	+	32.9090i	0.888783	+	1.53942i	0.0474665	+	0.998873i	$0.484885\pi$
$458$	6.00000	−	10.3923i	0.280362	−	0.485601i
$459$	−27.0000	−	15.5885i	−1.26025	−	0.727607i
$460$	3.00000	−	1.73205i	0.139876	−	0.0807573i
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	20.0000			0.929479			0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000			0.929479			0.464739	+	0.885448i	$0.346148\pi$
$464$	−30.0000	+	17.3205i	−1.39272	+	0.804084i
$465$	−3.00000	+	5.19615i	−0.139122	+	0.240966i
$466$	6.00000	−	10.3923i	0.277945	−	0.481414i
$467$	12.0000	+	20.7846i	0.555294	+	0.961797i	0.997881	+	0.0650714i	$0.0207275\pi$
$467$	12.0000	+	20.7846i	0.555294	+	0.961797i	−0.442587	+	0.896726i	$0.645939\pi$
$468$		0			0
$469$		0			0
$470$		−	20.7846i		−	0.958723i
$471$	12.0000	+	20.7846i	0.552931	+	0.957704i
$472$	18.0000	+	10.3923i	0.828517	+	0.478345i
$473$	24.0000	+	13.8564i	1.10352	+	0.637118i
$474$	−12.0000	−	20.7846i	−0.551178	−	0.954669i
$475$			3.46410i			0.158944i
$476$		0			0
$477$		0			0
$478$	−9.00000	−	15.5885i	−0.411650	−	0.712999i
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	4.50000	−	7.79423i	0.205396	−	0.355756i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.00000			0.0454545
$485$	6.00000	−	3.46410i	0.272446	−	0.157297i
$486$	−13.5000	+	23.3827i	−0.612372	+	1.06066i
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	−0.907776	−	0.419456i	$-0.862221\pi$
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	0.817147	+	0.576429i	$0.195554\pi$
$488$	6.00000	+	10.3923i	0.271607	+	0.470438i
$489$		−	27.7128i		−	1.25322i
$490$		0			0
$491$		−	24.2487i		−	1.09433i	−0.837025	−	0.547165i	$-0.815707\pi$
$491$		−	24.2487i		−	1.09433i	0.837025	−	0.547165i	$-0.184293\pi$
$492$	9.00000	−	5.19615i	0.405751	−	0.234261i
$493$	36.0000	+	20.7846i	1.62136	+	0.936092i
$494$		0			0
$495$	−9.00000	+	5.19615i	−0.404520	+	0.233550i
$496$			17.3205i			0.777714i
$497$		0			0
$498$		0			0
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	0.998233	−	0.0594153i	$-0.0189236\pi$
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	−0.550572	+	0.834788i	$0.685590\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	18.0000	+	10.3923i	0.804181	+	0.464294i
$502$	18.0000	−	10.3923i	0.803379	−	0.463831i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$	−18.0000	+	10.3923i	−0.800198	+	0.461994i
$507$	−19.5000	−	11.2583i	−0.866025	−	0.500000i
$508$	−2.00000	+	3.46410i	−0.0887357	+	0.153695i
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$	−18.0000			−0.797053
$511$		0			0
$512$		−	8.66025i		−	0.382733i
$513$	−9.00000	−	15.5885i	−0.397360	−	0.688247i
$514$	−9.00000	−	5.19615i	−0.396973	−	0.229192i
$515$	3.00000	+	1.73205i	0.132196	+	0.0763233i
$516$	12.0000	−	6.92820i	0.528271	−	0.304997i
$517$			41.5692i			1.82821i
$518$		0			0
$519$		−	31.1769i		−	1.36851i
$520$		0			0
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	−0.792797	−	0.609486i	$-0.791376\pi$
$521$	3.00000	−	5.19615i	0.131432	−	0.227648i	0.924229	+	0.381839i	$0.124709\pi$
$522$	18.0000	−	31.1769i	0.787839	−	1.36458i
$523$	15.0000	−	8.66025i	0.655904	−	0.378686i	−0.134810	−	0.990871i	$-0.543043\pi$
$523$	15.0000	−	8.66025i	0.655904	−	0.378686i	0.790715	+	0.612185i	$0.209709\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	42.0000			1.83129
$527$	18.0000	−	10.3923i	0.784092	−	0.452696i
$528$	−15.0000	+	25.9808i	−0.652791	+	1.13067i
$529$	−5.50000	+	9.52628i	−0.239130	+	0.414186i
$530$		0			0
$531$	−36.0000			−1.56227
$532$		0			0
$533$		0			0
$534$	9.00000	+	15.5885i	0.389468	+	0.674579i
$535$	9.00000	+	5.19615i	0.389104	+	0.224649i
$536$	12.0000	+	6.92820i	0.518321	+	0.299253i
$537$	−9.00000	−	15.5885i	−0.388379	−	0.672692i
$538$			31.1769i			1.34413i
$539$		0			0
$540$			5.19615i			0.223607i
$541$	17.0000	+	29.4449i	0.730887	+	1.26593i	0.956504	+	0.291718i	$0.0942267\pi$
$541$	17.0000	+	29.4449i	0.730887	+	1.26593i	−0.225617	+	0.974216i	$0.572440\pi$
$542$	−21.0000	+	36.3731i	−0.902027	+	1.56236i
$543$	−18.0000	+	31.1769i	−0.772454	+	1.33793i
$544$	−27.0000	+	15.5885i	−1.15762	+	0.668350i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	18.0000	−	10.3923i	0.768922	−	0.443937i
$549$	−18.0000	−	10.3923i	−0.768221	−	0.443533i
$550$	−3.00000	+	5.19615i	−0.127920	+	0.221565i
$551$	12.0000	+	20.7846i	0.511217	+	0.885454i
$552$		−	10.3923i		−	0.442326i
$553$		0			0
$554$		−	24.2487i		−	1.03023i
$555$	−3.00000	+	1.73205i	−0.127343	+	0.0735215i
$556$	15.0000	+	8.66025i	0.636142	+	0.367277i
$557$	−24.0000	−	13.8564i	−1.01691	−	0.587115i	−0.103704	−	0.994608i	$-0.533070\pi$
$557$	−24.0000	−	13.8564i	−1.01691	−	0.587115i	−0.913208	+	0.407493i	$0.866403\pi$
$558$	−9.00000	−	15.5885i	−0.381000	−	0.659912i
$559$		0			0
$560$		0			0
$561$	36.0000			1.51992
$562$	12.0000	+	20.7846i	0.506189	+	0.876746i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$	18.0000	+	10.3923i	0.757937	+	0.437595i
$565$	6.00000	−	3.46410i	0.252422	−	0.145736i
$566$	30.0000			1.26099
$567$		0			0
$568$	−6.00000			−0.251754
$569$	24.0000	−	13.8564i	1.00613	−	0.580891i	0.0960754	−	0.995374i	$-0.469371\pi$
$569$	24.0000	−	13.8564i	1.00613	−	0.580891i	0.910057	+	0.414483i	$0.136038\pi$
$570$	−9.00000	−	5.19615i	−0.376969	−	0.217643i
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$		0			0
$573$	−18.0000			−0.751961
$574$		0			0
$575$		−	3.46410i		−	0.144463i
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$	−30.0000	−	17.3205i	−1.24892	−	0.721062i	−0.278023	−	0.960574i	$-0.589679\pi$
$577$	−30.0000	−	17.3205i	−1.24892	−	0.721062i	−0.970893	+	0.239512i	$0.923012\pi$
$578$	28.5000	+	16.4545i	1.18544	+	0.684416i
$579$	−21.0000	+	12.1244i	−0.872730	+	0.503871i
$580$		−	6.92820i		−	0.287678i
$581$		0			0
$582$			20.7846i			0.861550i
$583$		0			0
$584$	−6.00000	+	10.3923i	−0.248282	+	0.430037i
$585$		0			0
$586$	−9.00000	+	5.19615i	−0.371787	+	0.214651i
$587$		0			0			−	1.00000i	$-0.5\pi$
$587$		0			0				1.00000i	$0.5\pi$
$588$		0			0
$589$	12.0000			0.494451
$590$	−18.0000	+	10.3923i	−0.741048	+	0.427844i
$591$	12.0000	−	20.7846i	0.493614	−	0.854965i
$592$	−5.00000	+	8.66025i	−0.205499	+	0.355934i
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	0.921026	−	0.389501i	$-0.127353\pi$
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	−0.797831	+	0.602881i	$0.794019\pi$
$594$		−	31.1769i		−	1.27920i
$595$		0			0
$596$			6.92820i			0.283790i
$597$	9.00000	+	15.5885i	0.368345	+	0.637993i
$598$		0			0
$599$	−21.0000	−	12.1244i	−0.858037	−	0.495388i	0.00531761	−	0.999986i	$-0.498307\pi$
$599$	−21.0000	−	12.1244i	−0.858037	−	0.495388i	−0.863354	+	0.504598i	$0.831641\pi$
$600$	−1.50000	−	2.59808i	−0.0612372	−	0.106066i
$601$			13.8564i			0.565215i	0.959236	+	0.282607i	$0.0911993\pi$
$601$			13.8564i			0.565215i	−0.959236	+	0.282607i	$0.908801\pi$
$602$		0			0
$603$	−24.0000			−0.977356
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$	0.500000	−	0.866025i	0.0203279	−	0.0352089i
$606$	−9.00000	+	15.5885i	−0.365600	+	0.633238i
$607$	−15.0000	+	8.66025i	−0.608831	+	0.351509i	−0.772508	−	0.635005i	$-0.780998\pi$
$607$	−15.0000	+	8.66025i	−0.608831	+	0.351509i	0.163677	+	0.986514i	$0.447665\pi$
$608$	−18.0000			−0.729996
$609$		0			0
$610$	−12.0000			−0.485866
$611$		0			0
$612$	9.00000	−	15.5885i	0.363803	−	0.630126i
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	−0.286300	−	0.958140i	$-0.592425\pi$
$613$	17.0000	−	29.4449i	0.686624	−	1.18927i	0.972924	−	0.231127i	$-0.0742412\pi$
$614$	21.0000	+	36.3731i	0.847491	+	1.46790i
$615$		−	10.3923i		−	0.419058i
$616$		0			0
$617$			6.92820i			0.278919i	0.990228	+	0.139459i	$0.0445365\pi$
$617$			6.92820i			0.278919i	−0.990228	+	0.139459i	$0.955464\pi$
$618$	−9.00000	+	5.19615i	−0.362033	+	0.209020i
$619$	−15.0000	−	8.66025i	−0.602901	−	0.348085i	0.167281	−	0.985909i	$-0.446501\pi$
$619$	−15.0000	−	8.66025i	−0.602901	−	0.348085i	−0.770182	+	0.637824i	$0.779835\pi$
$620$	−3.00000	−	1.73205i	−0.120483	−	0.0695608i
$621$	9.00000	+	15.5885i	0.361158	+	0.625543i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	18.0000	−	31.1769i	0.719425	−	1.24608i
$627$	18.0000	+	10.3923i	0.718851	+	0.415029i
$628$	−12.0000	+	6.92820i	−0.478852	+	0.276465i
$629$	12.0000			0.478471
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	−12.0000	+	6.92820i	−0.477334	+	0.275589i
$633$	−6.00000	−	3.46410i	−0.238479	−	0.137686i
$634$	24.0000	−	41.5692i	0.953162	−	1.65092i
$635$	2.00000	+	3.46410i	0.0793676	+	0.137469i
$636$		0			0
$637$		0			0
$638$			41.5692i			1.64574i
$639$	9.00000	−	5.19615i	0.356034	−	0.205557i
$640$	−10.5000	−	6.06218i	−0.415049	−	0.239629i
$641$	24.0000	+	13.8564i	0.947943	+	0.547295i	0.892441	−	0.451163i	$-0.148991\pi$
$641$	24.0000	+	13.8564i	0.947943	+	0.547295i	0.0555017	+	0.998459i	$0.482324\pi$
$642$	−27.0000	+	15.5885i	−1.06561	+	0.615227i
$643$			31.1769i			1.22950i	0.788723	+	0.614749i	$0.210743\pi$
$643$			31.1769i			1.22950i	−0.788723	+	0.614749i	$0.789257\pi$
$644$		0			0
$645$		−	13.8564i		−	0.545595i
$646$	18.0000	+	31.1769i	0.708201	+	1.22664i
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	−0.723645	−	0.690172i	$-0.757535\pi$
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	0.959529	+	0.281609i	$0.0908680\pi$
$648$	13.5000	+	7.79423i	0.530330	+	0.306186i
$649$	36.0000	−	20.7846i	1.41312	−	0.815867i
$650$		0			0
$651$		0			0
$652$	16.0000			0.626608
$653$	36.0000	−	20.7846i	1.40879	−	0.813365i	0.413517	−	0.910496i	$-0.364300\pi$
$653$	36.0000	−	20.7846i	1.40879	−	0.813365i	0.995272	+	0.0971316i	$0.0309668\pi$
$654$	3.00000	−	5.19615i	0.117309	−	0.203186i
$655$	−6.00000	+	10.3923i	−0.234439	+	0.406061i
$656$	−15.0000	−	25.9808i	−0.585652	−	1.01438i
$657$		−	20.7846i		−	0.810885i
$658$		0			0
$659$		−	10.3923i		−	0.404827i	−0.979300	−	0.202413i	$-0.935122\pi$
$659$		−	10.3923i		−	0.404827i	0.979300	−	0.202413i	$-0.0648785\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	42.0000	+	24.2487i	1.63361	+	0.943166i	0.982967	+	0.183782i	$0.0588342\pi$
$661$	42.0000	+	24.2487i	1.63361	+	0.943166i	0.650644	+	0.759383i	$0.274499\pi$
$662$	42.0000	+	24.2487i	1.63238	+	0.942453i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		−	10.3923i		−	0.402694i
$667$	−12.0000	−	20.7846i	−0.464642	−	0.804783i
$668$	−6.00000	+	10.3923i	−0.232147	+	0.402090i
$669$	−15.0000	+	25.9808i	−0.579934	+	1.00447i
$670$	−12.0000	+	6.92820i	−0.463600	+	0.267660i
$671$	24.0000			0.926510
$672$		0			0
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$	21.0000	−	12.1244i	0.808890	−	0.467013i
$675$	4.50000	+	2.59808i	0.173205	+	0.100000i
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	0.802600	−	0.596518i	$-0.203449\pi$
$677$	−3.00000	−	5.19615i	−0.115299	−	0.199704i	−0.917899	+	0.396813i	$0.870116\pi$
$678$			20.7846i			0.798228i
$679$		0			0
$680$			10.3923i			0.398527i
$681$	36.0000	−	20.7846i	1.37952	−	0.796468i
$682$	18.0000	+	10.3923i	0.689256	+	0.397942i
$683$	−15.0000	−	8.66025i	−0.573959	−	0.331375i	0.184770	−	0.982782i	$-0.440846\pi$
$683$	−15.0000	−	8.66025i	−0.573959	−	0.331375i	−0.758729	+	0.651406i	$0.774179\pi$
$684$	9.00000	−	5.19615i	0.344124	−	0.198680i
$685$		−	20.7846i		−	0.794139i
$686$		0			0
$687$	12.0000			0.457829
$688$	−20.0000	−	34.6410i	−0.762493	−	1.32068i
$689$		0			0
$690$	9.00000	+	5.19615i	0.342624	+	0.197814i
$691$	27.0000	−	15.5885i	1.02713	−	0.593013i	0.110968	−	0.993824i	$-0.464605\pi$
$691$	27.0000	−	15.5885i	1.02713	−	0.593013i	0.916161	+	0.400811i	$0.131272\pi$
$692$	18.0000			0.684257
$693$		0			0
$694$	30.0000			1.13878
$695$	15.0000	−	8.66025i	0.568982	−	0.328502i
$696$	−18.0000	−	10.3923i	−0.682288	−	0.393919i
$697$	−18.0000	+	31.1769i	−0.681799	+	1.18091i
$698$	−6.00000	−	10.3923i	−0.227103	−	0.393355i
$699$	12.0000			0.453882
$700$		0			0
$701$			20.7846i			0.785024i	0.919747	+	0.392512i	$0.128394\pi$
$701$			20.7846i			0.785024i	−0.919747	+	0.392512i	$0.871606\pi$
$702$		0			0
$703$	6.00000	+	3.46410i	0.226294	+	0.130651i
$704$	3.00000	+	1.73205i	0.113067	+	0.0652791i
$705$	18.0000	−	10.3923i	0.677919	−	0.391397i
$706$			10.3923i			0.391120i
$707$		0			0
$708$		−	20.7846i		−	0.781133i
$709$	−11.0000	−	19.0526i	−0.413114	−	0.715534i	0.582115	−	0.813107i	$-0.302225\pi$
$709$	−11.0000	−	19.0526i	−0.413114	−	0.715534i	−0.995228	+	0.0975728i	$0.968892\pi$
$710$	3.00000	−	5.19615i	0.112588	−	0.195008i
$711$	12.0000	−	20.7846i	0.450035	−	0.779484i
$712$	9.00000	−	5.19615i	0.337289	−	0.194734i
$713$	−12.0000			−0.449404
$714$		0			0
$715$		0			0
$716$	9.00000	−	5.19615i	0.336346	−	0.194189i
$717$	9.00000	−	15.5885i	0.336111	−	0.582162i
$718$	3.00000	−	5.19615i	0.111959	−	0.193919i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	15.0000			0.559017
$721$		0			0
$722$		−	12.1244i		−	0.451222i
$723$		0			0
$724$	−18.0000	−	10.3923i	−0.668965	−	0.386227i
$725$	−6.00000	−	3.46410i	−0.222834	−	0.128654i
$726$	1.50000	+	2.59808i	0.0556702	+	0.0964237i
$727$		−	3.46410i		−	0.128476i	−0.997935	−	0.0642382i	$-0.979538\pi$
$727$		−	3.46410i		−	0.128476i	0.997935	−	0.0642382i	$-0.0204617\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−6.00000	−	10.3923i	−0.222070	−	0.384636i
$731$	−24.0000	+	41.5692i	−0.887672	+	1.53749i
$732$	6.00000	−	10.3923i	0.221766	−	0.384111i
$733$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$733$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$734$	18.0000			0.664392
$735$		0			0
$736$	18.0000			0.663489
$737$	24.0000	−	13.8564i	0.884051	−	0.510407i
$738$	27.0000	+	15.5885i	0.993884	+	0.573819i
$739$	2.00000	−	3.46410i	0.0735712	−	0.127429i	−0.826893	−	0.562360i	$-0.809894\pi$
$739$	2.00000	−	3.46410i	0.0735712	−	0.127429i	0.900464	+	0.434930i	$0.143227\pi$
$740$	−1.00000	−	1.73205i	−0.0367607	−	0.0636715i
$741$		0			0
$742$		0			0
$743$		−	31.1769i		−	1.14377i	−0.820334	−	0.571885i	$-0.806212\pi$
$743$		−	31.1769i		−	1.14377i	0.820334	−	0.571885i	$-0.193788\pi$
$744$	−9.00000	+	5.19615i	−0.329956	+	0.190500i
$745$	6.00000	+	3.46410i	0.219823	+	0.126915i
$746$	21.0000	+	12.1244i	0.768865	+	0.443904i
$747$		0			0
$748$			20.7846i			0.759961i
$749$		0			0
$750$	3.00000			0.109545
$751$	−8.00000	−	13.8564i	−0.291924	−	0.505627i	0.682341	−	0.731034i	$-0.260962\pi$
$751$	−8.00000	−	13.8564i	−0.291924	−	0.505627i	−0.974265	+	0.225407i	$0.927629\pi$
$752$	30.0000	−	51.9615i	1.09399	−	1.89484i
$753$	18.0000	+	10.3923i	0.655956	+	0.378717i
$754$		0			0
$755$	−8.00000			−0.291150
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	−6.00000	+	3.46410i	−0.217930	+	0.125822i
$759$	−18.0000	−	10.3923i	−0.653359	−	0.377217i
$760$	−3.00000	+	5.19615i	−0.108821	+	0.188484i
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	−0.942207	−	0.335032i	$-0.891253\pi$
$761$	−21.0000	−	36.3731i	−0.761249	−	1.31852i	0.180957	−	0.983491i	$-0.442080\pi$
$762$	−12.0000			−0.434714
$763$		0			0
$764$		−	10.3923i		−	0.375980i
$765$	−9.00000	−	15.5885i	−0.325396	−	0.563602i
$766$	−18.0000	−	10.3923i	−0.650366	−	0.375489i
$767$		0			0
$768$	28.5000	−	16.4545i	1.02841	−	0.593750i
$769$		−	41.5692i		−	1.49902i	−0.661991	−	0.749512i	$-0.730288\pi$
$769$		−	41.5692i		−	1.49902i	0.661991	−	0.749512i	$-0.269712\pi$
$770$		0			0
$771$		−	10.3923i		−	0.374270i
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	−0.914920	−	0.403634i	$-0.867747\pi$
$773$	−3.00000	+	5.19615i	−0.107903	+	0.186893i	0.807018	+	0.590527i	$0.201080\pi$
$774$	36.0000	+	20.7846i	1.29399	+	0.747087i
$775$	−3.00000	+	1.73205i	−0.107763	+	0.0622171i
$776$	12.0000			0.430775
$777$		0			0
$778$	−12.0000			−0.430221
$779$	−18.0000	+	10.3923i	−0.644917	+	0.372343i
$780$		0			0
$781$	−6.00000	+	10.3923i	−0.214697	+	0.371866i
$782$	−18.0000	−	31.1769i	−0.643679	−	1.11488i
$783$	36.0000			1.28654
$784$		0			0
$785$			13.8564i			0.494556i
$786$	−18.0000	−	31.1769i	−0.642039	−	1.11204i
$787$	21.0000	+	12.1244i	0.748569	+	0.432187i	0.825177	−	0.564875i	$-0.191076\pi$
$787$	21.0000	+	12.1244i	0.748569	+	0.432187i	−0.0766075	+	0.997061i	$0.524409\pi$
$788$	12.0000	+	6.92820i	0.427482	+	0.246807i
$789$	21.0000	+	36.3731i	0.747620	+	1.29492i
$790$		−	13.8564i		−	0.492989i
$791$		0			0
$792$	−18.0000			−0.639602
$793$		0			0
$794$	−12.0000	+	20.7846i	−0.425864	+	0.737618i
$795$		0			0
$796$	−9.00000	+	5.19615i	−0.318997	+	0.184173i
$797$	−18.0000			−0.637593			−0.318796	−	0.947823i	$-0.603279\pi$
$797$	−18.0000			−0.637593			−0.318796	+	0.947823i	$0.603279\pi$
$798$		0			0
$799$	−72.0000			−2.54718
$800$	4.50000	−	2.59808i	0.159099	−	0.0918559i
$801$	−9.00000	+	15.5885i	−0.317999	+	0.550791i
$802$	−24.0000	+	41.5692i	−0.847469	+	1.46786i
$803$	12.0000	+	20.7846i	0.423471	+	0.733473i
$804$		−	13.8564i		−	0.488678i
$805$		0			0
$806$		0			0
$807$	−27.0000	+	15.5885i	−0.950445	+	0.548740i
$808$	9.00000	+	5.19615i	0.316619	+	0.182800i
$809$	48.0000	+	27.7128i	1.68759	+	0.974331i	0.956356	+	0.292204i	$0.0943886\pi$
$809$	48.0000	+	27.7128i	1.68759	+	0.974331i	0.731234	+	0.682127i	$0.238945\pi$
$810$	−13.5000	+	7.79423i	−0.474342	+	0.273861i
$811$		−	38.1051i		−	1.33805i	−0.743239	−	0.669026i	$-0.766712\pi$
$811$		−	38.1051i		−	1.33805i	0.743239	−	0.669026i	$-0.233288\pi$
$812$		0			0
$813$	−42.0000			−1.47300
$814$	6.00000	+	10.3923i	0.210300	+	0.364250i
$815$	8.00000	−	13.8564i	0.280228	−	0.485369i
$816$	−45.0000	−	25.9808i	−1.57532	−	0.909509i
$817$	−24.0000	+	13.8564i	−0.839654	+	0.484774i
$818$		0			0
$819$		0			0
$820$	6.00000			0.209529
$821$	−18.0000	+	10.3923i	−0.628204	+	0.362694i	−0.780056	−	0.625709i	$-0.784810\pi$
$821$	−18.0000	+	10.3923i	−0.628204	+	0.362694i	0.151852	+	0.988403i	$0.451476\pi$
$822$	54.0000	+	31.1769i	1.88347	+	1.08742i
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	0.172379	+	0.985031i	$0.444854\pi$
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	−0.939251	+	0.343230i	$0.888479\pi$
$824$	3.00000	+	5.19615i	0.104510	+	0.181017i
$825$	−6.00000			−0.208893
$826$		0			0
$827$		−	38.1051i		−	1.32504i	−0.749042	−	0.662522i	$-0.769486\pi$
$827$		−	38.1051i		−	1.32504i	0.749042	−	0.662522i	$-0.230514\pi$
$828$	−9.00000	+	5.19615i	−0.312772	+	0.180579i
$829$	−30.0000	−	17.3205i	−1.04194	−	0.601566i	−0.121560	−	0.992584i	$-0.538790\pi$
$829$	−30.0000	−	17.3205i	−1.04194	−	0.601566i	−0.920383	+	0.391018i	$0.872123\pi$
$830$		0			0
$831$	21.0000	−	12.1244i	0.728482	−	0.420589i
$832$		0			0
$833$		0			0
$834$			51.9615i			1.79928i
$835$	6.00000	+	10.3923i	0.207639	+	0.359641i
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$	9.00000	−	15.5885i	0.311086	−	0.538816i
$838$	18.0000	−	10.3923i	0.621800	−	0.358996i
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	−19.0000			−0.655172
$842$	15.0000	−	8.66025i	0.516934	−	0.298452i
$843$	−12.0000	+	20.7846i	−0.413302	+	0.715860i
$844$	2.00000	−	3.46410i	0.0688428	−	0.119239i
$845$	−6.50000	−	11.2583i	−0.223607	−	0.387298i
$846$			62.3538i			2.14377i
$847$		0			0
$848$		0			0
$849$	15.0000	+	25.9808i	0.514799	+	0.891657i
$850$	−9.00000	−	5.19615i	−0.308697	−	0.178227i
$851$	−6.00000	−	3.46410i	−0.205677	−	0.118748i
$852$	3.00000	+	5.19615i	0.102778	+	0.178017i
$853$			41.5692i			1.42330i	0.702533	+	0.711651i	$0.252052\pi$
$853$			41.5692i			1.42330i	−0.702533	+	0.711651i	$0.747948\pi$
$854$		0			0
$855$		−	10.3923i		−	0.355409i
$856$	9.00000	+	15.5885i	0.307614	+	0.532803i
$857$	15.0000	−	25.9808i	0.512390	−	0.887486i	−0.487507	−	0.873119i	$-0.662093\pi$
$857$	15.0000	−	25.9808i	0.512390	−	0.887486i	0.999897	−	0.0143666i	$-0.00457319\pi$
$858$		0			0
$859$	−33.0000	+	19.0526i	−1.12595	+	0.650065i	−0.942912	−	0.333042i	$-0.891925\pi$
$859$	−33.0000	+	19.0526i	−1.12595	+	0.650065i	−0.183033	+	0.983107i	$0.558592\pi$
$860$	8.00000			0.272798
$861$		0			0
$862$	18.0000			0.613082
$863$	−15.0000	+	8.66025i	−0.510606	+	0.294798i	−0.733083	−	0.680140i	$-0.761919\pi$
$863$	−15.0000	+	8.66025i	−0.510606	+	0.294798i	0.222477	+	0.974938i	$0.428586\pi$
$864$	−13.5000	+	23.3827i	−0.459279	+	0.795495i
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	6.00000	+	10.3923i	0.203888	+	0.353145i
$867$			32.9090i			1.11765i
$868$		0			0
$869$			27.7128i			0.940093i
$870$	18.0000	−	10.3923i	0.610257	−	0.352332i
$871$		0			0
$872$	−3.00000	−	1.73205i	−0.101593	−	0.0586546i
$873$	−18.0000	+	10.3923i	−0.609208	+	0.351726i
$874$		−	20.7846i		−	0.703050i
$875$		0			0
$876$	12.0000			0.405442
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	−0.985079	−	0.172102i	$-0.944944\pi$
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	0.343495	−	0.939155i	$-0.388389\pi$
$878$	15.0000	−	25.9808i	0.506225	−	0.876808i
$879$	−9.00000	−	5.19615i	−0.303562	−	0.175262i
$880$	−15.0000	+	8.66025i	−0.505650	+	0.291937i
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	16.0000			0.538443			0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000			0.538443			0.269221	+	0.963078i	$0.413234\pi$
$884$		0			0
$885$	−18.0000	−	10.3923i	−0.605063	−	0.349334i
$886$	9.00000	−	15.5885i	0.302361	−	0.523704i
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	−0.992149	−	0.125061i	$-0.960087\pi$
$887$	−18.0000	−	31.1769i	−0.604381	−	1.04682i	0.387768	−	0.921757i	$-0.373246\pi$
$888$	−6.00000			−0.201347
$889$		0			0
$890$			10.3923i			0.348351i
$891$	27.0000	−	15.5885i	0.904534	−	0.522233i
$892$	−15.0000	−	8.66025i	−0.502237	−	0.289967i
$893$	−36.0000	−	20.7846i	−1.20469	−	0.695530i
$894$	−18.0000	+	10.3923i	−0.602010	+	0.347571i
$895$		−	10.3923i		−	0.347376i
$896$		0			0
$897$		0			0
$898$	−12.0000	−	20.7846i	−0.400445	−	0.693591i
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$	−1.50000	+	2.59808i	−0.0500000	+	0.0866025i
$901$		0			0
$902$	−36.0000			−1.19867
$903$		0			0
$904$	12.0000			0.399114
$905$	−18.0000	+	10.3923i	−0.598340	+	0.345452i
$906$	12.0000	−	20.7846i	0.398673	−	0.690522i
$907$	16.0000	−	27.7128i	0.531271	−	0.920189i	−0.468063	−	0.883695i	$-0.655048\pi$
$907$	16.0000	−	27.7128i	0.531271	−	0.920189i	0.999334	−	0.0364935i	$-0.0116188\pi$
$908$	12.0000	+	20.7846i	0.398234	+	0.689761i
$909$	−18.0000			−0.597022
$910$		0			0
$911$		−	17.3205i		−	0.573854i	−0.957952	−	0.286927i	$-0.907366\pi$
$911$		−	17.3205i		−	0.573854i	0.957952	−	0.286927i	$-0.0926337\pi$
$912$	−15.0000	−	25.9808i	−0.496700	−	0.860309i
$913$		0			0
$914$	−57.0000	−	32.9090i	−1.88539	−	1.08853i
$915$	−6.00000	−	10.3923i	−0.198354	−	0.343559i
$916$			6.92820i			0.228914i
$917$		0			0
$918$	54.0000			1.78227
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	0.703378	−	0.710816i	$-0.251674\pi$
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	−0.967274	+	0.253735i	$0.918341\pi$
$920$	3.00000	−	5.19615i	0.0989071	−	0.171312i
$921$	−21.0000	+	36.3731i	−0.691974	+	1.19853i
$922$	27.0000	−	15.5885i	0.889198	−	0.513378i
$923$		0			0
$924$		0			0
$925$	−2.00000			−0.0657596
$926$	−30.0000	+	17.3205i	−0.985861	+	0.569187i
$927$	−9.00000	−	5.19615i	−0.295599	−	0.170664i
$928$	18.0000	−	31.1769i	0.590879	−	1.02343i
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	0.999959	−	0.00905914i	$-0.00288365\pi$
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	−0.507825	+	0.861460i	$0.669550\pi$
$930$		−	10.3923i		−	0.340777i
$931$		0			0
$932$			6.92820i			0.226941i
$933$		0			0
$934$	−36.0000	−	20.7846i	−1.17796	−	0.680093i
$935$	18.0000	+	10.3923i	0.588663	+	0.339865i
$936$		0			0
$937$		−	6.92820i		−	0.226335i	−0.993576	−	0.113167i	$-0.963900\pi$
$937$		−	6.92820i		−	0.226335i	0.993576	−	0.113167i	$-0.0360996\pi$
$938$		0			0
$939$	36.0000			1.17482
$940$	6.00000	+	10.3923i	0.195698	+	0.338960i
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	−0.681218	−	0.732081i	$-0.738549\pi$
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	0.974609	+	0.223912i	$0.0718827\pi$
$942$	−36.0000	−	20.7846i	−1.17294	−	0.677199i
$943$	18.0000	−	10.3923i	0.586161	−	0.338420i
$944$	−60.0000			−1.95283
$945$		0			0
$946$	−48.0000			−1.56061
$947$	27.0000	−	15.5885i	0.877382	−	0.506557i	0.00758776	−	0.999971i	$-0.497585\pi$
$947$	27.0000	−	15.5885i	0.877382	−	0.506557i	0.869794	+	0.493414i	$0.164251\pi$
$948$	12.0000	+	6.92820i	0.389742	+	0.225018i
$949$		0			0
$950$	−3.00000	−	5.19615i	−0.0973329	−	0.168585i
$951$	48.0000			1.55651
$952$		0			0
$953$		−	34.6410i		−	1.12213i	−0.827771	−	0.561066i	$-0.810391\pi$
$953$		−	34.6410i		−	1.12213i	0.827771	−	0.561066i	$-0.189609\pi$
$954$		0			0
$955$	−9.00000	−	5.19615i	−0.291233	−	0.168144i
$956$	9.00000	+	5.19615i	0.291081	+	0.168056i
$957$	−36.0000	+	20.7846i	−1.16371	+	0.671871i
$958$		0			0
$959$		0			0
$960$		−	1.73205i		−	0.0559017i
$961$	−9.50000	−	16.4545i	−0.306452	−	0.530790i
$962$		0			0
$963$	−27.0000	−	15.5885i	−0.870063	−	0.502331i
$964$		0			0
$965$	−14.0000			−0.450676
$966$		0			0
$967$	20.0000			0.643157			0.321578	−	0.946883i	$-0.395787\pi$
$967$	20.0000			0.643157			0.321578	+	0.946883i	$0.395787\pi$
$968$	1.50000	−	0.866025i	0.0482118	−	0.0278351i
$969$	−18.0000	+	31.1769i	−0.578243	+	1.00155i
$970$	−6.00000	+	10.3923i	−0.192648	+	0.333677i
$971$	30.0000	+	51.9615i	0.962746	+	1.66752i	0.715553	+	0.698558i	$0.246175\pi$
$971$	30.0000	+	51.9615i	0.962746	+	1.66752i	0.247193	+	0.968966i	$0.420492\pi$
$972$		−	15.5885i		−	0.500000i
$973$		0			0
$974$		−	6.92820i		−	0.221994i
$975$		0			0
$976$	−30.0000	−	17.3205i	−0.960277	−	0.554416i
$977$	6.00000	+	3.46410i	0.191957	+	0.110826i	0.592898	−	0.805277i	$-0.297984\pi$
$977$	6.00000	+	3.46410i	0.191957	+	0.110826i	−0.400941	+	0.916104i	$0.631317\pi$
$978$	24.0000	+	41.5692i	0.767435	+	1.32924i
$979$		−	20.7846i		−	0.664279i
$980$		0			0
$981$	6.00000			0.191565
$982$	21.0000	+	36.3731i	0.670137	+	1.16071i
$983$	−30.0000	+	51.9615i	−0.956851	+	1.65732i	−0.226778	+	0.973946i	$0.572819\pi$
$983$	−30.0000	+	51.9615i	−0.956851	+	1.65732i	−0.730073	+	0.683369i	$0.760514\pi$
$984$	9.00000	−	15.5885i	0.286910	−	0.496942i
$985$	12.0000	−	6.92820i	0.382352	−	0.220751i
$986$	−72.0000			−2.29295
$987$		0			0
$988$		0			0
$989$	24.0000	−	13.8564i	0.763156	−	0.440608i
$990$	9.00000	−	15.5885i	0.286039	−	0.495434i
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	−0.964658	−	0.263504i	$-0.915122\pi$
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	0.710530	+	0.703667i	$0.248455\pi$
$992$	−9.00000	−	15.5885i	−0.285750	−	0.494934i
$993$			48.4974i			1.53902i
$994$		0			0
$995$			10.3923i			0.329458i
$996$		0			0
$997$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$997$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$998$	−30.0000	−	17.3205i	−0.949633	−	0.548271i
$999$	9.00000	−	5.19615i	0.284747	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.s.a.521.1		2
3.2	odd	2		735.2.s.d.521.1		2
7.2	even	3		735.2.s.f.656.1		2
7.3	odd	6		105.2.b.a.41.1	✓	2
7.4	even	3		105.2.b.b.41.1	yes	2
7.5	odd	6		735.2.s.d.656.1		2
7.6	odd	2		735.2.s.b.521.1		2
21.2	odd	6		735.2.s.b.656.1		2
21.5	even	6	inner	735.2.s.a.656.1		2
21.11	odd	6		105.2.b.a.41.2	yes	2
21.17	even	6		105.2.b.b.41.2	yes	2
21.20	even	2		735.2.s.f.521.1		2
28.3	even	6		1680.2.f.b.881.2		2
28.11	odd	6		1680.2.f.c.881.1		2
35.3	even	12		525.2.g.b.524.1		4
35.4	even	6		525.2.b.b.251.2		2
35.17	even	12		525.2.g.b.524.4		4
35.18	odd	12		525.2.g.c.524.1		4
35.24	odd	6		525.2.b.a.251.2		2
35.32	odd	12		525.2.g.c.524.4		4
84.11	even	6		1680.2.f.b.881.1		2
84.59	odd	6		1680.2.f.c.881.2		2
105.17	odd	12		525.2.g.c.524.2		4
105.32	even	12		525.2.g.b.524.2		4
105.38	odd	12		525.2.g.c.524.3		4
105.53	even	12		525.2.g.b.524.3		4
105.59	even	6		525.2.b.b.251.1		2
105.74	odd	6		525.2.b.a.251.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.b.a.41.1	✓	2	7.3	odd	6
105.2.b.a.41.2	yes	2	21.11	odd	6
105.2.b.b.41.1	yes	2	7.4	even	3
105.2.b.b.41.2	yes	2	21.17	even	6
525.2.b.a.251.1		2	105.74	odd	6
525.2.b.a.251.2		2	35.24	odd	6
525.2.b.b.251.1		2	105.59	even	6
525.2.b.b.251.2		2	35.4	even	6
525.2.g.b.524.1		4	35.3	even	12
525.2.g.b.524.2		4	105.32	even	12
525.2.g.b.524.3		4	105.53	even	12
525.2.g.b.524.4		4	35.17	even	12
525.2.g.c.524.1		4	35.18	odd	12
525.2.g.c.524.2		4	105.17	odd	12
525.2.g.c.524.3		4	105.38	odd	12
525.2.g.c.524.4		4	35.32	odd	12
735.2.s.a.521.1		2	1.1	even	1	trivial
735.2.s.a.656.1		2	21.5	even	6	inner
735.2.s.b.521.1		2	7.6	odd	2
735.2.s.b.656.1		2	21.2	odd	6
735.2.s.d.521.1		2	3.2	odd	2
735.2.s.d.656.1		2	7.5	odd	6
735.2.s.f.521.1		2	21.20	even	2
735.2.s.f.656.1		2	7.2	even	3
1680.2.f.b.881.1		2	84.11	even	6
1680.2.f.b.881.2		2	28.3	even	6
1680.2.f.c.881.1		2	28.11	odd	6
1680.2.f.c.881.2		2	84.59	odd	6

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.00000 q^{6} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.00000 q^{6} -1.73205i q^{8} +(1.50000 + 2.59808i) q^{9} +(1.50000 + 0.866025i) q^{10} +(-3.00000 - 1.73205i) q^{11} +(-1.50000 + 0.866025i) q^{12} +1.73205i q^{15} +(2.50000 + 4.33013i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-4.50000 - 2.59808i) q^{18} +(3.00000 - 1.73205i) q^{19} -1.00000 q^{20} +6.00000 q^{22} +(-3.00000 + 1.73205i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +6.92820i q^{29} +(-1.50000 - 2.59808i) q^{30} +(3.00000 + 1.73205i) q^{31} +(-4.50000 - 2.59808i) q^{32} +(3.00000 + 5.19615i) q^{33} +10.3923i q^{34} +3.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(-1.50000 + 0.866025i) q^{40} -6.00000 q^{41} -8.00000 q^{43} +(-3.00000 + 1.73205i) q^{44} +(1.50000 - 2.59808i) q^{45} +(3.00000 - 5.19615i) q^{46} +(-6.00000 - 10.3923i) q^{47} -8.66025i q^{48} -1.73205i q^{50} +(-9.00000 + 5.19615i) q^{51} +(4.50000 + 7.79423i) q^{54} +3.46410i q^{55} -6.00000 q^{57} +(-6.00000 - 10.3923i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(1.50000 + 0.866025i) q^{60} +(-6.00000 + 3.46410i) q^{61} -6.00000 q^{62} -1.00000 q^{64} +(-9.00000 - 5.19615i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(-3.00000 - 5.19615i) q^{68} +6.00000 q^{69} -3.46410i q^{71} +(4.50000 - 2.59808i) q^{72} +(-6.00000 - 3.46410i) q^{73} +(-3.00000 - 1.73205i) q^{74} +(1.50000 - 0.866025i) q^{75} -3.46410i q^{76} +(-4.00000 - 6.92820i) q^{79} +(2.50000 - 4.33013i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(9.00000 - 5.19615i) q^{82} -6.00000 q^{85} +(12.0000 - 6.92820i) q^{86} +(6.00000 - 10.3923i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(3.00000 + 5.19615i) q^{89} +5.19615i q^{90} +3.46410i q^{92} +(-3.00000 - 5.19615i) q^{93} +(18.0000 + 10.3923i) q^{94} +(-3.00000 - 1.73205i) q^{95} +(4.50000 + 7.79423i) q^{96} +6.92820i q^{97} -10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 3 q^{3} + q^{4} - q^{5} + 6 q^{6} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 3 * q^3 + q^4 - q^5 + 6 * q^6 + 3 * q^9	\( 2 q - 3 q^{2} - 3 q^{3} + q^{4} - q^{5} + 6 q^{6} + 3 q^{9} + 3 q^{10} - 6 q^{11} - 3 q^{12} + 5 q^{16} + 6 q^{17} - 9 q^{18} + 6 q^{19} - 2 q^{20} + 12 q^{22} - 6 q^{23} - 3 q^{24} - q^{25} - 3 q^{30} + 6 q^{31} - 9 q^{32} + 6 q^{33} + 6 q^{36} + 2 q^{37} - 6 q^{38} - 3 q^{40} - 12 q^{41} - 16 q^{43} - 6 q^{44} + 3 q^{45} + 6 q^{46} - 12 q^{47} - 18 q^{51} + 9 q^{54} - 12 q^{57} - 12 q^{58} - 12 q^{59} + 3 q^{60} - 12 q^{61} - 12 q^{62} - 2 q^{64} - 18 q^{66} - 8 q^{67} - 6 q^{68} + 12 q^{69} + 9 q^{72} - 12 q^{73} - 6 q^{74} + 3 q^{75} - 8 q^{79} + 5 q^{80} - 9 q^{81} + 18 q^{82} - 12 q^{85} + 24 q^{86} + 12 q^{87} - 6 q^{88} + 6 q^{89} - 6 q^{93} + 36 q^{94} - 6 q^{95} + 9 q^{96}+O(q^{100}) \) 2 * q - 3 * q^2 - 3 * q^3 + q^4 - q^5 + 6 * q^6 + 3 * q^9 + 3 * q^10 - 6 * q^11 - 3 * q^12 + 5 * q^16 + 6 * q^17 - 9 * q^18 + 6 * q^19 - 2 * q^20 + 12 * q^22 - 6 * q^23 - 3 * q^24 - q^25 - 3 * q^30 + 6 * q^31 - 9 * q^32 + 6 * q^33 + 6 * q^36 + 2 * q^37 - 6 * q^38 - 3 * q^40 - 12 * q^41 - 16 * q^43 - 6 * q^44 + 3 * q^45 + 6 * q^46 - 12 * q^47 - 18 * q^51 + 9 * q^54 - 12 * q^57 - 12 * q^58 - 12 * q^59 + 3 * q^60 - 12 * q^61 - 12 * q^62 - 2 * q^64 - 18 * q^66 - 8 * q^67 - 6 * q^68 + 12 * q^69 + 9 * q^72 - 12 * q^73 - 6 * q^74 + 3 * q^75 - 8 * q^79 + 5 * q^80 - 9 * q^81 + 18 * q^82 - 12 * q^85 + 24 * q^86 + 12 * q^87 - 6 * q^88 + 6 * q^89 - 6 * q^93 + 36 * q^94 - 6 * q^95 + 9 * q^96

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