LMFDB - Embedded newform 735.2.s.b.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:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 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.b.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	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$	−4.50000	−	2.59808i	−1.06066	−	0.612372i
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	0.114708	+	0.993399i	$0.463407\pi$
$20$	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	0.205783	−	0.978598i	$-0.434026\pi$
$31$	−3.00000	−	1.73205i	−0.538816	−	0.311086i	−0.744599	+	0.667512i	$0.767359\pi$
$32$	−4.50000	−	2.59808i	−0.795495	−	0.459279i
$33$	−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	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		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	$0.172597\pi$
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.0186297	+	0.999826i	$0.494070\pi$
$48$			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	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$	1.50000	+	0.866025i	0.193649	+	0.111803i
$61$	6.00000	−	3.46410i	0.768221	−	0.443533i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.00000	−	3.46410i	0.768221	−	0.443533i	0.832240	+	0.554416i	$0.187058\pi$
$62$	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	0.808184	−	0.588930i	$-0.200451\pi$
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	−0.105937	+	0.994373i	$0.533784\pi$
$74$	−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	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		−	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	$-0.885595\pi$
$97$		−	6.92820i		−	0.703452i	0.936103	−	0.351726i	$-0.114405\pi$
$98$		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	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$	9.00000	−	15.5885i	0.891133	−	1.54349i
$103$	3.00000	−	1.73205i	0.295599	−	0.170664i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	3.00000	−	1.73205i	0.295599	−	0.170664i	0.640464	+	0.767988i	$0.278742\pi$
$104$		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	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$	−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	$-0.737392\pi$
$139$		−	17.3205i		−	1.46911i	0.678551	−	0.734553i	$-0.262608\pi$
$140$		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	0.895466	−	0.445130i	$-0.146843\pi$
$157$	12.0000	+	6.92820i	0.957704	+	0.552931i	0.0622385	+	0.998061i	$0.480176\pi$
$158$	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	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		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	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$		−	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	$0.280971\pi$
$181$			20.7846i			1.54491i	−0.635071	+	0.772454i	$0.719029\pi$
$182$		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	0.783841	−	0.620962i	$-0.213258\pi$
$199$	9.00000	+	5.19615i	0.637993	+	0.368345i	−0.145848	+	0.989307i	$0.546591\pi$
$200$	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	$0.196921\pi$
$223$			17.3205i			1.15987i	−0.814664	+	0.579934i	$0.803079\pi$
$224$		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	$-0.540033\pi$
$227$	12.0000	−	20.7846i	0.796468	−	1.37952i	0.921903	−	0.387421i	$-0.126634\pi$
$228$	−3.00000	+	5.19615i	−0.198680	+	0.344124i
$229$	6.00000	−	3.46410i	0.396491	−	0.228914i	−0.288478	−	0.957487i	$-0.593149\pi$
$229$	6.00000	−	3.46410i	0.396491	−	0.228914i	0.684969	+	0.728572i	$0.259816\pi$
$230$	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	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		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	0.757159	−	0.653231i	$-0.226587\pi$
$257$	−3.00000	−	5.19615i	−0.187135	−	0.324127i	−0.944294	+	0.329104i	$0.893253\pi$
$258$	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	$0.351559\pi$
$269$	−9.00000	+	15.5885i	−0.548740	+	0.950445i	−0.998361	+	0.0572259i	$0.981774\pi$
$270$	4.50000	−	7.79423i	0.273861	−	0.474342i
$271$	−21.0000	+	12.1244i	−1.27566	+	0.736502i	−0.976047	−	0.217559i	$-0.930191\pi$
$271$	−21.0000	+	12.1244i	−1.27566	+	0.736502i	−0.299612	+	0.954061i	$0.596857\pi$
$272$	−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	0.874484	−	0.485054i	$-0.161200\pi$
$283$	15.0000	+	8.66025i	0.891657	+	0.514799i	0.0171732	+	0.999853i	$0.494533\pi$
$284$	−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	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		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	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$		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	0.104065	−	0.994571i	$-0.466815\pi$
$313$	18.0000	−	10.3923i	1.01742	−	0.587408i	0.913356	+	0.407163i	$0.133482\pi$
$314$	−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	$-0.940632\pi$
$349$		−	6.92820i		−	0.370858i	0.982658	−	0.185429i	$-0.0593675\pi$
$350$		0			0
$351$		0			0
$352$	9.00000	+	15.5885i	0.479702	+	0.830868i
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$	−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	0.716154	−	0.697942i	$-0.245901\pi$
$367$	9.00000	+	5.19615i	0.469796	+	0.271237i	−0.246358	+	0.969179i	$0.579234\pi$
$368$	−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	0.671027	−	0.741433i	$-0.265853\pi$
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	−0.977613	+	0.210411i	$0.932520\pi$
$384$	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	−0.769931	−	0.638127i	$-0.779710\pi$
$397$	−12.0000	+	6.92820i	−0.602263	+	0.347717i	0.167668	+	0.985843i	$0.446376\pi$
$398$	−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	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		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	$0.0532382\pi$
$433$			6.92820i			0.332948i	−0.986046	+	0.166474i	$0.946762\pi$
$434$		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	−0.0973349	−	0.995252i	$-0.531032\pi$
$439$	15.0000	−	8.66025i	0.715911	−	0.413331i	0.813246	+	0.581920i	$0.197698\pi$
$440$	−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	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		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	$-0.979272\pi$
$467$	−12.0000	−	20.7846i	−0.555294	−	0.961797i	0.442587	−	0.896726i	$-0.354061\pi$
$468$		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	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		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	$0.0648436\pi$
$509$	15.0000	+	25.9808i	0.664863	+	1.15158i	−0.314459	+	0.949271i	$0.601823\pi$
$510$	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	−0.924229	−	0.381839i	$-0.875291\pi$
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	0.792797	+	0.609486i	$0.208624\pi$
$522$	18.0000	−	31.1769i	0.787839	−	1.36458i
$523$	−15.0000	+	8.66025i	−0.655904	+	0.378686i	−0.790715	−	0.612185i	$-0.790291\pi$
$523$	−15.0000	+	8.66025i	−0.655904	+	0.378686i	0.134810	+	0.990871i	$0.456957\pi$
$524$	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	0.970893	−	0.239512i	$-0.0769875\pi$
$577$	30.0000	+	17.3205i	1.24892	+	0.721062i	0.278023	+	0.960574i	$0.410321\pi$
$578$	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	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$			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	$-0.908801\pi$
$601$		−	13.8564i		−	0.565215i	0.959236	−	0.282607i	$-0.0911993\pi$
$602$		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	−0.163677	−	0.986514i	$-0.552335\pi$
$607$	15.0000	−	8.66025i	0.608831	−	0.351509i	0.772508	+	0.635005i	$0.219002\pi$
$608$	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	0.770182	−	0.637824i	$-0.220165\pi$
$619$	15.0000	+	8.66025i	0.602901	+	0.348085i	−0.167281	+	0.985909i	$0.553499\pi$
$620$	−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	$-0.789257\pi$
$643$		−	31.1769i		−	1.22950i	0.788723	−	0.614749i	$-0.210743\pi$
$644$		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	−0.959529	−	0.281609i	$-0.909132\pi$
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	0.723645	+	0.690172i	$0.242465\pi$
$648$	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	$-0.941166\pi$
$661$	−42.0000	−	24.2487i	−1.63361	−	0.943166i	−0.650644	−	0.759383i	$-0.725501\pi$
$662$	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	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$		−	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	−0.916161	−	0.400811i	$-0.868728\pi$
$691$	−27.0000	+	15.5885i	−1.02713	+	0.593013i	−0.110968	+	0.993824i	$0.535395\pi$
$692$	−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	$0.0204617\pi$
$727$			3.46410i			0.128476i	−0.997935	+	0.0642382i	$0.979538\pi$
$728$		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	$0.108747\pi$
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	−0.180957	+	0.983491i	$0.557920\pi$
$762$	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	$0.269712\pi$
$769$			41.5692i			1.49902i	−0.661991	+	0.749512i	$0.730288\pi$
$770$		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	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$	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	0.0766075	−	0.997061i	$-0.475591\pi$
$787$	−21.0000	−	12.1244i	−0.748569	−	0.432187i	−0.825177	+	0.564875i	$0.808924\pi$
$788$	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	$-0.396721\pi$
$797$	18.0000			0.637593			0.318796	+	0.947823i	$0.396721\pi$
$798$		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	$0.233288\pi$
$811$			38.1051i			1.33805i	−0.743239	+	0.669026i	$0.766712\pi$
$812$		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	0.920383	−	0.391018i	$-0.127877\pi$
$829$	30.0000	+	17.3205i	1.04194	+	0.601566i	0.121560	+	0.992584i	$0.461210\pi$
$830$		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	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		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	$-0.747948\pi$
$853$		−	41.5692i		−	1.42330i	0.702533	−	0.711651i	$-0.252052\pi$
$854$		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	$0.337907\pi$
$857$	−15.0000	+	25.9808i	−0.512390	+	0.887486i	−0.999897	+	0.0143666i	$0.995427\pi$
$858$		0			0
$859$	33.0000	−	19.0526i	1.12595	−	0.650065i	0.183033	−	0.983107i	$-0.441408\pi$
$859$	33.0000	−	19.0526i	1.12595	−	0.650065i	0.942912	+	0.333042i	$0.108075\pi$
$860$	−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	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		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	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$	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	0.507825	−	0.861460i	$-0.330450\pi$
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	−0.999959	+	0.00905914i	$0.997116\pi$
$930$			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	$0.0360996\pi$
$937$			6.92820i			0.226335i	−0.993576	+	0.113167i	$0.963900\pi$
$938$		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	−0.974609	−	0.223912i	$-0.928117\pi$
$941$	−9.00000	+	15.5885i	−0.293392	+	0.508169i	0.681218	+	0.732081i	$0.261451\pi$
$942$	−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	$-0.753825\pi$
$971$	−30.0000	−	51.9615i	−0.962746	−	1.66752i	−0.247193	−	0.968966i	$-0.579508\pi$
$972$			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	$-0.427181\pi$
$983$	30.0000	−	51.9615i	0.956851	−	1.65732i	0.730073	−	0.683369i	$-0.239486\pi$
$984$	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.b.521.1		2
3.2	odd	2		735.2.s.f.521.1		2
7.2	even	3		735.2.s.d.656.1		2
7.3	odd	6		105.2.b.b.41.1	yes	2
7.4	even	3		105.2.b.a.41.1	✓	2
7.5	odd	6		735.2.s.f.656.1		2
7.6	odd	2		735.2.s.a.521.1		2
21.2	odd	6		735.2.s.a.656.1		2
21.5	even	6	inner	735.2.s.b.656.1		2
21.11	odd	6		105.2.b.b.41.2	yes	2
21.17	even	6		105.2.b.a.41.2	yes	2
21.20	even	2		735.2.s.d.521.1		2
28.3	even	6		1680.2.f.c.881.1		2
28.11	odd	6		1680.2.f.b.881.2		2
35.3	even	12		525.2.g.c.524.1		4
35.4	even	6		525.2.b.a.251.2		2
35.17	even	12		525.2.g.c.524.4		4
35.18	odd	12		525.2.g.b.524.1		4
35.24	odd	6		525.2.b.b.251.2		2
35.32	odd	12		525.2.g.b.524.4		4
84.11	even	6		1680.2.f.c.881.2		2
84.59	odd	6		1680.2.f.b.881.1		2
105.17	odd	12		525.2.g.b.524.2		4
105.32	even	12		525.2.g.c.524.2		4
105.38	odd	12		525.2.g.b.524.3		4
105.53	even	12		525.2.g.c.524.3		4
105.59	even	6		525.2.b.a.251.1		2
105.74	odd	6		525.2.b.b.251.1		2

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more