LMFDB - Embedded newform 507.2.j.a.316.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(316,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("507.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.j (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:	$4.04841538248$
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 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	507.316
Dual form			507.2.j.a.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +(-3.00000 + 1.73205i) q^{7} +1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +(-3.00000 + 1.73205i) q^{7} +1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.00000 + 1.73205i) q^{11} +1.00000 q^{12} +6.00000 q^{14} +(2.50000 - 4.33013i) q^{16} +(3.00000 + 5.19615i) q^{17} +1.73205i q^{18} +(3.00000 - 1.73205i) q^{19} +3.46410i q^{21} +(-3.00000 - 5.19615i) q^{22} +(1.50000 + 0.866025i) q^{24} +5.00000 q^{25} -1.00000 q^{27} +(-3.00000 - 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} -3.46410i q^{31} +(-4.50000 + 2.59808i) q^{32} +(3.00000 - 1.73205i) q^{33} -10.3923i q^{34} +(0.500000 - 0.866025i) q^{36} +(-6.00000 - 3.46410i) q^{37} -6.00000 q^{38} +(6.00000 + 3.46410i) q^{41} +(3.00000 - 5.19615i) q^{42} +(2.00000 + 3.46410i) q^{43} +3.46410i q^{44} +3.46410i q^{47} +(-2.50000 - 4.33013i) q^{48} +(2.50000 - 4.33013i) q^{49} +(-7.50000 - 4.33013i) q^{50} +6.00000 q^{51} +6.00000 q^{53} +(1.50000 + 0.866025i) q^{54} +(-3.00000 - 5.19615i) q^{56} -3.46410i q^{57} +(9.00000 - 5.19615i) q^{58} +(9.00000 - 5.19615i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-3.00000 + 5.19615i) q^{62} +(3.00000 + 1.73205i) q^{63} -1.00000 q^{64} -6.00000 q^{66} +(9.00000 + 5.19615i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(3.00000 - 1.73205i) q^{71} +(1.50000 - 0.866025i) q^{72} +(6.00000 + 10.3923i) q^{74} +(2.50000 - 4.33013i) q^{75} +(3.00000 + 1.73205i) q^{76} -12.0000 q^{77} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-6.00000 - 10.3923i) q^{82} -3.46410i q^{83} +(-3.00000 + 1.73205i) q^{84} -6.92820i q^{86} +(3.00000 + 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(6.00000 + 3.46410i) q^{89} +(-3.00000 - 1.73205i) q^{93} +(3.00000 - 5.19615i) q^{94} +5.19615i q^{96} +(-12.0000 + 6.92820i) q^{97} +(-7.50000 + 4.33013i) q^{98} -3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + q^{3} + q^{4} - 3 q^{6} - 6 q^{7} - q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 + q^3 + q^4 - 3 * q^6 - 6 * q^7 - q^9	$ 2 q - 3 q^{2} + q^{3} + q^{4} - 3 q^{6} - 6 q^{7} - q^{9} + 6 q^{11} + 2 q^{12} + 12 q^{14} + 5 q^{16} + 6 q^{17} + 6 q^{19} - 6 q^{22} + 3 q^{24} + 10 q^{25} - 2 q^{27} - 6 q^{28} - 6 q^{29} - 9 q^{32} + 6 q^{33} + q^{36} - 12 q^{37} - 12 q^{38} + 12 q^{41} + 6 q^{42} + 4 q^{43} - 5 q^{48} + 5 q^{49} - 15 q^{50} + 12 q^{51} + 12 q^{53} + 3 q^{54} - 6 q^{56} + 18 q^{58} + 18 q^{59} + 2 q^{61} - 6 q^{62} + 6 q^{63} - 2 q^{64} - 12 q^{66} + 18 q^{67} - 6 q^{68} + 6 q^{71} + 3 q^{72} + 12 q^{74} + 5 q^{75} + 6 q^{76} - 24 q^{77} - 16 q^{79} - q^{81} - 12 q^{82} - 6 q^{84} + 6 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{93} + 6 q^{94} - 24 q^{97} - 15 q^{98}+O(q^{100}) $ 2 * q - 3 * q^2 + q^3 + q^4 - 3 * q^6 - 6 * q^7 - q^9 + 6 * q^11 + 2 * q^12 + 12 * q^14 + 5 * q^16 + 6 * q^17 + 6 * q^19 - 6 * q^22 + 3 * q^24 + 10 * q^25 - 2 * q^27 - 6 * q^28 - 6 * q^29 - 9 * q^32 + 6 * q^33 + q^36 - 12 * q^37 - 12 * q^38 + 12 * q^41 + 6 * q^42 + 4 * q^43 - 5 * q^48 + 5 * q^49 - 15 * q^50 + 12 * q^51 + 12 * q^53 + 3 * q^54 - 6 * q^56 + 18 * q^58 + 18 * q^59 + 2 * q^61 - 6 * q^62 + 6 * q^63 - 2 * q^64 - 12 * q^66 + 18 * q^67 - 6 * q^68 + 6 * q^71 + 3 * q^72 + 12 * q^74 + 5 * q^75 + 6 * q^76 - 24 * q^77 - 16 * q^79 - q^81 - 12 * q^82 - 6 * q^84 + 6 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^93 + 6 * q^94 - 24 * q^97 - 15 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.50000	−	0.866025i	−1.06066	−	0.612372i	−0.135045	−	0.990839i	$-0.543118\pi$
$2$	−1.50000	−	0.866025i	−1.06066	−	0.612372i	−0.925615	+	0.378467i	$0.876451\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0		1.00000			$0$
$5$		0			0		−1.00000			$\pi$
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−3.00000	+	1.73205i	−1.13389	+	0.654654i	−0.188982	+	0.981981i	$0.560519\pi$
$8$			1.73205i			0.612372i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.878668	−	0.477432i	$-0.158432\pi$
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.0258656	+	0.999665i	$0.491766\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	6.00000			1.60357
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$			1.73205i			0.408248i
$19$	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	$0.203260\pi$
$20$		0			0
$21$			3.46410i			0.755929i
$22$	−3.00000	−	5.19615i	−0.639602	−	1.10782i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	5.00000			1.00000
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−3.00000	−	1.73205i	−0.566947	−	0.327327i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$	−4.50000	+	2.59808i	−0.795495	+	0.459279i
$33$	3.00000	−	1.73205i	0.522233	−	0.301511i
$34$		−	10.3923i		−	1.78227i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−6.00000	−	3.46410i	−0.986394	−	0.569495i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−6.00000	−	3.46410i	−0.986394	−	0.569495i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	−6.00000			−0.973329
$39$		0			0
$40$		0			0
$41$	6.00000	+	3.46410i	0.937043	+	0.541002i	0.889032	−	0.457845i	$-0.151379\pi$
$41$	6.00000	+	3.46410i	0.937043	+	0.541002i	0.0480106	+	0.998847i	$0.484712\pi$
$42$	3.00000	−	5.19615i	0.462910	−	0.801784i
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$			3.46410i			0.522233i
$45$		0			0
$46$		0			0
$47$			3.46410i			0.505291i	0.967559	+	0.252646i	$0.0813007\pi$
$47$			3.46410i			0.505291i	−0.967559	+	0.252646i	$0.918699\pi$
$48$	−2.50000	−	4.33013i	−0.360844	−	0.625000i
$49$	2.50000	−	4.33013i	0.357143	−	0.618590i
$50$	−7.50000	−	4.33013i	−1.06066	−	0.612372i
$51$	6.00000			0.840168
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$	1.50000	+	0.866025i	0.204124	+	0.117851i
$55$		0			0
$56$	−3.00000	−	5.19615i	−0.400892	−	0.694365i
$57$		−	3.46410i		−	0.458831i
$58$	9.00000	−	5.19615i	1.18176	−	0.682288i
$59$	9.00000	−	5.19615i	1.17170	−	0.676481i	0.217620	−	0.976034i	$-0.430171\pi$
$59$	9.00000	−	5.19615i	1.17170	−	0.676481i	0.954080	+	0.299552i	$0.0968372\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	−3.00000	+	5.19615i	−0.381000	+	0.659912i
$63$	3.00000	+	1.73205i	0.377964	+	0.218218i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−6.00000			−0.738549
$67$	9.00000	+	5.19615i	1.09952	+	0.634811i	0.936096	−	0.351744i	$-0.114411\pi$
$67$	9.00000	+	5.19615i	1.09952	+	0.634811i	0.163429	+	0.986555i	$0.447745\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$		0			0
$70$		0			0
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	−0.311305	−	0.950310i	$-0.600766\pi$
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	0.667340	+	0.744753i	$0.267433\pi$
$72$	1.50000	−	0.866025i	0.176777	−	0.102062i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	6.00000	+	10.3923i	0.697486	+	1.20808i
$75$	2.50000	−	4.33013i	0.288675	−	0.500000i
$76$	3.00000	+	1.73205i	0.344124	+	0.198680i
$77$	−12.0000			−1.36753
$78$		0			0
$79$	−8.00000			−0.900070			−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000			−0.900070			−0.450035	+	0.893011i	$0.648589\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−6.00000	−	10.3923i	−0.662589	−	1.14764i
$83$		−	3.46410i		−	0.380235i	−0.981761	−	0.190117i	$-0.939113\pi$
$83$		−	3.46410i		−	0.380235i	0.981761	−	0.190117i	$-0.0608868\pi$
$84$	−3.00000	+	1.73205i	−0.327327	+	0.188982i
$85$		0			0
$86$		−	6.92820i		−	0.747087i
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$	6.00000	+	3.46410i	0.635999	+	0.367194i	0.783072	−	0.621932i	$-0.213652\pi$
$89$	6.00000	+	3.46410i	0.635999	+	0.367194i	−0.147073	+	0.989126i	$0.546985\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−3.00000	−	1.73205i	−0.311086	−	0.179605i
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$		0			0
$96$			5.19615i			0.530330i
$97$	−12.0000	+	6.92820i	−1.21842	+	0.703452i	−0.964579	−	0.263795i	$-0.915026\pi$
$97$	−12.0000	+	6.92820i	−1.21842	+	0.703452i	−0.253837	+	0.967247i	$0.581693\pi$
$98$	−7.50000	+	4.33013i	−0.757614	+	0.437409i
$99$		−	3.46410i		−	0.348155i
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$	−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	−	5.19615i	−0.891133	−	0.514496i
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$		0			0
$105$		0			0
$106$	−9.00000	−	5.19615i	−0.874157	−	0.504695i
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$			6.92820i			0.663602i	0.943349	+	0.331801i	$0.107656\pi$
$109$			6.92820i			0.663602i	−0.943349	+	0.331801i	$0.892344\pi$
$110$		0			0
$111$	−6.00000	+	3.46410i	−0.569495	+	0.328798i
$112$			17.3205i			1.63663i
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$	−3.00000	+	5.19615i	−0.280976	+	0.486664i
$115$		0			0
$116$	−6.00000			−0.557086
$117$		0			0
$118$	−18.0000			−1.65703
$119$	−18.0000	−	10.3923i	−1.65006	−	0.952661i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$		−	3.46410i		−	0.313625i
$123$	6.00000	−	3.46410i	0.541002	−	0.312348i
$124$	3.00000	−	1.73205i	0.269408	−	0.155543i
$125$		0			0
$126$	−3.00000	−	5.19615i	−0.267261	−	0.462910i
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	−0.632166	−	0.774833i	$-0.717834\pi$
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	0.987108	+	0.160055i	$0.0511671\pi$
$128$	10.5000	+	6.06218i	0.928078	+	0.535826i
$129$	4.00000			0.352180
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	3.00000	+	1.73205i	0.261116	+	0.150756i
$133$	−6.00000	+	10.3923i	−0.520266	+	0.901127i
$134$	−9.00000	−	15.5885i	−0.777482	−	1.34664i
$135$		0			0
$136$	−9.00000	+	5.19615i	−0.771744	+	0.445566i
$137$	−18.0000	+	10.3923i	−1.53784	+	0.887875i	−0.538879	+	0.842383i	$0.681152\pi$
$137$	−18.0000	+	10.3923i	−1.53784	+	0.887875i	−0.998965	+	0.0454914i	$0.985515\pi$
$138$		0			0
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$		0			0
$141$	3.00000	+	1.73205i	0.252646	+	0.145865i
$142$	−6.00000			−0.503509
$143$		0			0
$144$	−5.00000			−0.416667
$145$		0			0
$146$		0			0
$147$	−2.50000	−	4.33013i	−0.206197	−	0.357143i
$148$		−	6.92820i		−	0.569495i
$149$	12.0000	−	6.92820i	0.983078	−	0.567581i	0.0798802	−	0.996804i	$-0.474546\pi$
$149$	12.0000	−	6.92820i	0.983078	−	0.567581i	0.903198	+	0.429224i	$0.141213\pi$
$150$	−7.50000	+	4.33013i	−0.612372	+	0.353553i
$151$			10.3923i			0.845714i	0.906196	+	0.422857i	$0.138973\pi$
$151$			10.3923i			0.845714i	−0.906196	+	0.422857i	$0.861027\pi$
$152$	3.00000	+	5.19615i	0.243332	+	0.421464i
$153$	3.00000	−	5.19615i	0.242536	−	0.420084i
$154$	18.0000	+	10.3923i	1.45048	+	0.837436i
$155$		0			0
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	12.0000	+	6.92820i	0.954669	+	0.551178i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$		0			0
$161$		0			0
$162$	1.50000	−	0.866025i	0.117851	−	0.0680414i
$163$	3.00000	−	1.73205i	0.234978	−	0.135665i	−0.377888	−	0.925851i	$-0.623350\pi$
$163$	3.00000	−	1.73205i	0.234978	−	0.135665i	0.612866	+	0.790186i	$0.290016\pi$
$164$			6.92820i			0.541002i
$165$		0			0
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	−15.0000	−	8.66025i	−1.16073	−	0.670151i	−0.209255	−	0.977861i	$-0.567104\pi$
$167$	−15.0000	−	8.66025i	−1.16073	−	0.670151i	−0.951480	+	0.307711i	$0.900437\pi$
$168$	−6.00000			−0.462910
$169$		0			0
$170$		0			0
$171$	−3.00000	−	1.73205i	−0.229416	−	0.132453i
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	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	$0.593460\pi$
$174$		−	10.3923i		−	0.787839i
$175$	−15.0000	+	8.66025i	−1.13389	+	0.654654i
$176$	15.0000	−	8.66025i	1.13067	−	0.652791i
$177$		−	10.3923i		−	0.781133i
$178$	−6.00000	−	10.3923i	−0.449719	−	0.778936i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$		0			0
$186$	3.00000	+	5.19615i	0.219971	+	0.381000i
$187$			20.7846i			1.51992i
$188$	−3.00000	+	1.73205i	−0.218797	+	0.126323i
$189$	3.00000	−	1.73205i	0.218218	−	0.125988i
$190$		0			0
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.863743	−	0.503932i	$-0.831886\pi$
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.00454614	−	0.999990i	$-0.501447\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$193$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$194$	24.0000			1.72310
$195$		0			0
$196$	5.00000			0.357143
$197$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$197$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$198$	−3.00000	+	5.19615i	−0.213201	+	0.369274i
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$			8.66025i			0.612372i
$201$	9.00000	−	5.19615i	0.634811	−	0.366508i
$202$	9.00000	−	5.19615i	0.633238	−	0.365600i
$203$		−	20.7846i		−	1.45879i
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$		0			0
$206$	−12.0000	−	6.92820i	−0.836080	−	0.482711i
$207$		0			0
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	−0.283918	−	0.958849i	$-0.591634\pi$
$211$	10.0000	−	17.3205i	0.688428	−	1.19239i	0.972346	−	0.233544i	$-0.0750324\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		−	3.46410i		−	0.237356i
$214$	18.0000	−	10.3923i	1.23045	−	0.710403i
$215$		0			0
$216$		−	1.73205i		−	0.117851i
$217$	6.00000	+	10.3923i	0.407307	+	0.705476i
$218$	6.00000	−	10.3923i	0.406371	−	0.703856i
$219$		0			0
$220$		0			0
$221$		0			0
$222$	12.0000			0.805387
$223$	3.00000	+	1.73205i	0.200895	+	0.115987i	0.597073	−	0.802187i	$-0.296330\pi$
$223$	3.00000	+	1.73205i	0.200895	+	0.115987i	−0.396178	+	0.918174i	$0.629664\pi$
$224$	9.00000	−	15.5885i	0.601338	−	1.04155i
$225$	−2.50000	−	4.33013i	−0.166667	−	0.288675i
$226$		−	10.3923i		−	0.691286i
$227$	−15.0000	+	8.66025i	−0.995585	+	0.574801i	−0.906939	−	0.421262i	$-0.861587\pi$
$227$	−15.0000	+	8.66025i	−0.995585	+	0.574801i	−0.0886460	+	0.996063i	$0.528254\pi$
$228$	3.00000	−	1.73205i	0.198680	−	0.114708i
$229$		−	6.92820i		−	0.457829i	−0.973447	−	0.228914i	$-0.926482\pi$
$229$		−	6.92820i		−	0.457829i	0.973447	−	0.228914i	$-0.0735176\pi$
$230$		0			0
$231$	−6.00000	+	10.3923i	−0.394771	+	0.683763i
$232$	−9.00000	−	5.19615i	−0.590879	−	0.341144i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$		0			0
$236$	9.00000	+	5.19615i	0.585850	+	0.338241i
$237$	−4.00000	+	6.92820i	−0.259828	+	0.450035i
$238$	18.0000	+	31.1769i	1.16677	+	2.02090i
$239$		−	10.3923i		−	0.672222i	−0.941822	−	0.336111i	$-0.890888\pi$
$239$		−	10.3923i		−	0.672222i	0.941822	−	0.336111i	$-0.109112\pi$
$240$		0			0
$241$	12.0000	−	6.92820i	0.772988	−	0.446285i	−0.0609515	−	0.998141i	$-0.519414\pi$
$241$	12.0000	−	6.92820i	0.772988	−	0.446285i	0.833939	+	0.551856i	$0.186080\pi$
$242$		−	1.73205i		−	0.111340i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$		0			0
$246$	−12.0000			−0.765092
$247$		0			0
$248$	6.00000			0.381000
$249$	−3.00000	−	1.73205i	−0.190117	−	0.109764i
$250$		0			0
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$			3.46410i			0.218218i
$253$		0			0
$254$	−12.0000	+	6.92820i	−0.752947	+	0.434714i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$	−6.00000	−	3.46410i	−0.373544	−	0.215666i
$259$	24.0000			1.49129
$260$		0			0
$261$	6.00000			0.371391
$262$	18.0000	+	10.3923i	1.11204	+	0.642039i
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	−0.212565	−	0.977147i	$-0.568182\pi$
$263$	12.0000	−	20.7846i	0.739952	−	1.28163i	0.952517	−	0.304487i	$-0.0984850\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$		0			0
$266$	18.0000	−	10.3923i	1.10365	−	0.637193i
$267$	6.00000	−	3.46410i	0.367194	−	0.212000i
$268$			10.3923i			0.634811i
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$	−9.00000	−	5.19615i	−0.546711	−	0.315644i	0.201083	−	0.979574i	$-0.435554\pi$
$271$	−9.00000	−	5.19615i	−0.546711	−	0.315644i	−0.747794	+	0.663930i	$0.768887\pi$
$272$	30.0000			1.81902
$273$		0			0
$274$	36.0000			2.17484
$275$	15.0000	+	8.66025i	0.904534	+	0.522233i
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$		−	6.92820i		−	0.415526i
$279$	−3.00000	+	1.73205i	−0.179605	+	0.103695i
$280$		0			0
$281$			6.92820i			0.413302i	0.978415	+	0.206651i	$0.0662565\pi$
$281$			6.92820i			0.413302i	−0.978415	+	0.206651i	$0.933744\pi$
$282$	−3.00000	−	5.19615i	−0.178647	−	0.309426i
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	3.00000	+	1.73205i	0.178017	+	0.102778i
$285$		0			0
$286$		0			0
$287$	−24.0000			−1.41668
$288$	4.50000	+	2.59808i	0.265165	+	0.153093i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$			13.8564i			0.812277i
$292$		0			0
$293$	24.0000	−	13.8564i	1.40209	−	0.809500i	0.407487	−	0.913211i	$-0.366405\pi$
$293$	24.0000	−	13.8564i	1.40209	−	0.809500i	0.994607	+	0.103711i	$0.0330717\pi$
$294$			8.66025i			0.505076i
$295$		0			0
$296$	6.00000	−	10.3923i	0.348743	−	0.604040i
$297$	−3.00000	−	1.73205i	−0.174078	−	0.100504i
$298$	−24.0000			−1.39028
$299$		0			0
$300$	5.00000			0.288675
$301$	−12.0000	−	6.92820i	−0.691669	−	0.399335i
$302$	9.00000	−	15.5885i	0.517892	−	0.897015i
$303$	3.00000	+	5.19615i	0.172345	+	0.298511i
$304$		−	17.3205i		−	0.993399i
$305$		0			0
$306$	−9.00000	+	5.19615i	−0.514496	+	0.297044i
$307$		−	10.3923i		−	0.593120i	−0.955014	−	0.296560i	$-0.904160\pi$
$307$		−	10.3923i		−	0.593120i	0.955014	−	0.296560i	$-0.0958395\pi$
$308$	−6.00000	−	10.3923i	−0.341882	−	0.592157i
$309$	4.00000	−	6.92820i	0.227552	−	0.394132i
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	10.0000			0.565233			0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000			0.565233			0.282617	+	0.959233i	$0.408798\pi$
$314$	−21.0000	−	12.1244i	−1.18510	−	0.684217i
$315$		0			0
$316$	−4.00000	−	6.92820i	−0.225018	−	0.389742i
$317$			13.8564i			0.778253i	0.921184	+	0.389127i	$0.127223\pi$
$317$			13.8564i			0.778253i	−0.921184	+	0.389127i	$0.872777\pi$
$318$	−9.00000	+	5.19615i	−0.504695	+	0.291386i
$319$	−18.0000	+	10.3923i	−1.00781	+	0.581857i
$320$		0			0
$321$	6.00000	+	10.3923i	0.334887	+	0.580042i
$322$		0			0
$323$	18.0000	+	10.3923i	1.00155	+	0.578243i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−6.00000			−0.332309
$327$	6.00000	+	3.46410i	0.331801	+	0.191565i
$328$	−6.00000	+	10.3923i	−0.331295	+	0.573819i
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$		0			0
$331$	3.00000	−	1.73205i	0.164895	−	0.0952021i	−0.415282	−	0.909693i	$-0.636317\pi$
$331$	3.00000	−	1.73205i	0.164895	−	0.0952021i	0.580176	+	0.814491i	$0.302984\pi$
$332$	3.00000	−	1.73205i	0.164646	−	0.0950586i
$333$			6.92820i			0.379663i
$334$	15.0000	+	25.9808i	0.820763	+	1.42160i
$335$		0			0
$336$	15.0000	+	8.66025i	0.818317	+	0.472456i
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$		0			0
$339$	6.00000			0.325875
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	3.00000	+	5.19615i	0.162221	+	0.280976i
$343$		−	6.92820i		−	0.374088i
$344$	−6.00000	+	3.46410i	−0.323498	+	0.186772i
$345$		0			0
$346$		−	31.1769i		−	1.67608i
$347$	−18.0000	−	31.1769i	−0.966291	−	1.67366i	−0.706107	−	0.708105i	$-0.749550\pi$
$347$	−18.0000	−	31.1769i	−0.966291	−	1.67366i	−0.260184	−	0.965559i	$-0.583783\pi$
$348$	−3.00000	+	5.19615i	−0.160817	+	0.278543i
$349$	6.00000	+	3.46410i	0.321173	+	0.185429i	0.651915	−	0.758292i	$-0.273966\pi$
$349$	6.00000	+	3.46410i	0.321173	+	0.185429i	−0.330743	+	0.943721i	$0.607299\pi$
$350$	30.0000			1.60357
$351$		0			0
$352$	−18.0000			−0.959403
$353$	−30.0000	−	17.3205i	−1.59674	−	0.921878i	−0.992110	−	0.125370i	$-0.959988\pi$
$353$	−30.0000	−	17.3205i	−1.59674	−	0.921878i	−0.604629	−	0.796507i	$-0.706679\pi$
$354$	−9.00000	+	15.5885i	−0.478345	+	0.828517i
$355$		0			0
$356$			6.92820i			0.367194i
$357$	−18.0000	+	10.3923i	−0.952661	+	0.550019i
$358$	−18.0000	+	10.3923i	−0.951330	+	0.549250i
$359$			17.3205i			0.914141i	0.889430	+	0.457071i	$0.151101\pi$
$359$			17.3205i			0.914141i	−0.889430	+	0.457071i	$0.848899\pi$
$360$		0			0
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$	15.0000	+	8.66025i	0.788382	+	0.455173i
$363$	1.00000			0.0524864
$364$		0			0
$365$		0			0
$366$	−3.00000	−	1.73205i	−0.156813	−	0.0905357i
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	−0.578101	−	0.815966i	$-0.696206\pi$
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	0.995697	+	0.0926670i	$0.0295392\pi$
$368$		0			0
$369$		−	6.92820i		−	0.360668i
$370$		0			0
$371$	−18.0000	+	10.3923i	−0.934513	+	0.539542i
$372$		−	3.46410i		−	0.179605i
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	−0.996610	−	0.0822766i	$-0.973781\pi$
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	0.427051	−	0.904227i	$-0.359552\pi$
$374$	18.0000	−	31.1769i	0.930758	−	1.61212i
$375$		0			0
$376$	−6.00000			−0.309426
$377$		0			0
$378$	−6.00000			−0.308607
$379$	−15.0000	−	8.66025i	−0.770498	−	0.444847i	0.0625541	−	0.998042i	$-0.480075\pi$
$379$	−15.0000	−	8.66025i	−0.770498	−	0.444847i	−0.833052	+	0.553194i	$0.813409\pi$
$380$		0			0
$381$	−4.00000	−	6.92820i	−0.204926	−	0.354943i
$382$			41.5692i			2.12687i
$383$	3.00000	−	1.73205i	0.153293	−	0.0885037i	−0.421392	−	0.906879i	$-0.638458\pi$
$383$	3.00000	−	1.73205i	0.153293	−	0.0885037i	0.574684	+	0.818375i	$0.305125\pi$
$384$	10.5000	−	6.06218i	0.535826	−	0.309359i
$385$		0			0
$386$		0			0
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$	−12.0000	−	6.92820i	−0.609208	−	0.351726i
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$		0			0
$391$		0			0
$392$	7.50000	+	4.33013i	0.378807	+	0.218704i
$393$	−6.00000	+	10.3923i	−0.302660	+	0.524222i
$394$		0			0
$395$		0			0
$396$	3.00000	−	1.73205i	0.150756	−	0.0870388i
$397$	−30.0000	+	17.3205i	−1.50566	+	0.869291i	−0.505678	+	0.862722i	$0.668758\pi$
$397$	−30.0000	+	17.3205i	−1.50566	+	0.869291i	−0.999978	+	0.00656933i	$0.997909\pi$
$398$			27.7128i			1.38912i
$399$	6.00000	+	10.3923i	0.300376	+	0.520266i
$400$	12.5000	−	21.6506i	0.625000	−	1.08253i
$401$	−6.00000	−	3.46410i	−0.299626	−	0.172989i	0.342649	−	0.939463i	$-0.388676\pi$
$401$	−6.00000	−	3.46410i	−0.299626	−	0.172989i	−0.642275	+	0.766475i	$0.722009\pi$
$402$	−18.0000			−0.897758
$403$		0			0
$404$	−6.00000			−0.298511
$405$		0			0
$406$	−18.0000	+	31.1769i	−0.893325	+	1.54728i
$407$	−12.0000	−	20.7846i	−0.594818	−	1.03025i
$408$			10.3923i			0.514496i
$409$	24.0000	−	13.8564i	1.18672	−	0.685155i	0.229163	−	0.973388i	$-0.426401\pi$
$409$	24.0000	−	13.8564i	1.18672	−	0.685155i	0.957560	+	0.288233i	$0.0930677\pi$
$410$		0			0
$411$			20.7846i			1.02523i
$412$	4.00000	+	6.92820i	0.197066	+	0.341328i
$413$	−18.0000	+	31.1769i	−0.885722	+	1.53412i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	4.00000			0.195881
$418$	−18.0000	−	10.3923i	−0.880409	−	0.508304i
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	−0.681426	−	0.731887i	$-0.738640\pi$
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	0.974546	+	0.224189i	$0.0719734\pi$
$420$		0			0
$421$		−	34.6410i		−	1.68830i	−0.536107	−	0.844150i	$-0.680106\pi$
$421$		−	34.6410i		−	1.68830i	0.536107	−	0.844150i	$-0.319894\pi$
$422$	−30.0000	+	17.3205i	−1.46038	+	0.843149i
$423$	3.00000	−	1.73205i	0.145865	−	0.0842152i
$424$			10.3923i			0.504695i
$425$	15.0000	+	25.9808i	0.727607	+	1.26025i
$426$	−3.00000	+	5.19615i	−0.145350	+	0.251754i
$427$	−6.00000	−	3.46410i	−0.290360	−	0.167640i
$428$	−12.0000			−0.580042
$429$		0			0
$430$		0			0
$431$	21.0000	+	12.1244i	1.01153	+	0.584010i	0.911641	−	0.410988i	$-0.134816\pi$
$431$	21.0000	+	12.1244i	1.01153	+	0.584010i	0.0998939	+	0.994998i	$0.468150\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	−17.0000	−	29.4449i	−0.816968	−	1.41503i	−0.907906	−	0.419173i	$-0.862320\pi$
$433$	−17.0000	−	29.4449i	−0.816968	−	1.41503i	0.0909384	−	0.995857i	$-0.471013\pi$
$434$		−	20.7846i		−	0.997693i
$435$		0			0
$436$	−6.00000	+	3.46410i	−0.287348	+	0.165900i
$437$		0			0
$438$		0			0
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$		0			0
$441$	−5.00000			−0.238095
$442$		0			0
$443$	−36.0000			−1.71041			−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000			−1.71041			−0.855206	+	0.518289i	$0.826569\pi$
$444$	−6.00000	−	3.46410i	−0.284747	−	0.164399i
$445$		0			0
$446$	−3.00000	−	5.19615i	−0.142054	−	0.246045i
$447$		−	13.8564i		−	0.655386i
$448$	3.00000	−	1.73205i	0.141737	−	0.0818317i
$449$	6.00000	−	3.46410i	0.283158	−	0.163481i	−0.351694	−	0.936115i	$-0.614394\pi$
$449$	6.00000	−	3.46410i	0.283158	−	0.163481i	0.634852	+	0.772634i	$0.281061\pi$
$450$			8.66025i			0.408248i
$451$	12.0000	+	20.7846i	0.565058	+	0.978709i
$452$	−3.00000	+	5.19615i	−0.141108	+	0.244406i
$453$	9.00000	+	5.19615i	0.422857	+	0.244137i
$454$	30.0000			1.40797
$455$		0			0
$456$	6.00000			0.280976
$457$	24.0000	+	13.8564i	1.12267	+	0.648175i	0.942082	−	0.335383i	$-0.108866\pi$
$457$	24.0000	+	13.8564i	1.12267	+	0.648175i	0.180591	+	0.983558i	$0.442199\pi$
$458$	−6.00000	+	10.3923i	−0.280362	+	0.485601i
$459$	−3.00000	−	5.19615i	−0.140028	−	0.242536i
$460$		0			0
$461$	−12.0000	+	6.92820i	−0.558896	+	0.322679i	−0.752702	−	0.658361i	$-0.771250\pi$
$461$	−12.0000	+	6.92820i	−0.558896	+	0.322679i	0.193806	+	0.981040i	$0.437917\pi$
$462$	18.0000	−	10.3923i	0.837436	−	0.483494i
$463$		−	17.3205i		−	0.804952i	−0.915430	−	0.402476i	$-0.868150\pi$
$463$		−	17.3205i		−	0.804952i	0.915430	−	0.402476i	$-0.131850\pi$
$464$	15.0000	+	25.9808i	0.696358	+	1.20613i
$465$		0			0
$466$	9.00000	+	5.19615i	0.416917	+	0.240707i
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$	−36.0000			−1.66233
$470$		0			0
$471$	7.00000	−	12.1244i	0.322543	−	0.558661i
$472$	9.00000	+	15.5885i	0.414259	+	0.717517i
$473$			13.8564i			0.637118i
$474$	12.0000	−	6.92820i	0.551178	−	0.318223i
$475$	15.0000	−	8.66025i	0.688247	−	0.397360i
$476$		−	20.7846i		−	0.952661i
$477$	−3.00000	−	5.19615i	−0.137361	−	0.237915i
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	9.00000	+	5.19615i	0.411220	+	0.237418i	0.691314	−	0.722554i	$-0.257032\pi$
$479$	9.00000	+	5.19615i	0.411220	+	0.237418i	−0.280094	+	0.959973i	$0.590365\pi$
$480$		0			0
$481$		0			0
$482$	−24.0000			−1.09317
$483$		0			0
$484$	−0.500000	+	0.866025i	−0.0227273	+	0.0393648i
$485$		0			0
$486$		−	1.73205i		−	0.0785674i
$487$	33.0000	−	19.0526i	1.49537	−	0.863354i	0.495387	−	0.868672i	$-0.335026\pi$
$487$	33.0000	−	19.0526i	1.49537	−	0.863354i	0.999986	+	0.00531860i	$0.00169297\pi$
$488$	−3.00000	+	1.73205i	−0.135804	+	0.0784063i
$489$		−	3.46410i		−	0.156652i
$490$		0			0
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	−0.698285	−	0.715820i	$-0.746053\pi$
$491$	6.00000	−	10.3923i	0.270776	−	0.468998i	0.969061	+	0.246822i	$0.0793863\pi$
$492$	6.00000	+	3.46410i	0.270501	+	0.156174i
$493$	−36.0000			−1.62136
$494$		0			0
$495$		0			0
$496$	−15.0000	−	8.66025i	−0.673520	−	0.388857i
$497$	−6.00000	+	10.3923i	−0.269137	+	0.466159i
$498$	3.00000	+	5.19615i	0.134433	+	0.232845i
$499$		−	10.3923i		−	0.465223i	−0.972570	−	0.232612i	$-0.925273\pi$
$499$		−	10.3923i		−	0.465223i	0.972570	−	0.232612i	$-0.0747271\pi$
$500$		0			0
$501$	−15.0000	+	8.66025i	−0.670151	+	0.386912i
$502$		−	20.7846i		−	0.927663i
$503$	−12.0000	−	20.7846i	−0.535054	−	0.926740i	−0.999161	−	0.0409609i	$-0.986958\pi$
$503$	−12.0000	−	20.7846i	−0.535054	−	0.926740i	0.464107	−	0.885779i	$-0.346375\pi$
$504$	−3.00000	+	5.19615i	−0.133631	+	0.231455i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	8.00000			0.354943
$509$	36.0000	+	20.7846i	1.59567	+	0.921262i	0.992308	+	0.123796i	$0.0395068\pi$
$509$	36.0000	+	20.7846i	1.59567	+	0.921262i	0.603364	+	0.797466i	$0.293827\pi$
$510$		0			0
$511$		0			0
$512$			8.66025i			0.382733i
$513$	−3.00000	+	1.73205i	−0.132453	+	0.0764719i
$514$	27.0000	−	15.5885i	1.19092	−	0.687577i
$515$		0			0
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$	−6.00000	+	10.3923i	−0.263880	+	0.457053i
$518$	−36.0000	−	20.7846i	−1.58175	−	0.913223i
$519$	18.0000			0.790112
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	−9.00000	−	5.19615i	−0.393919	−	0.227429i
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	−0.818980	−	0.573822i	$-0.805460\pi$
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	0.906434	+	0.422347i	$0.138794\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$			17.3205i			0.755929i
$526$	−36.0000	+	20.7846i	−1.56967	+	0.906252i
$527$	18.0000	−	10.3923i	0.784092	−	0.452696i
$528$		−	17.3205i		−	0.753778i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	−9.00000	−	5.19615i	−0.390567	−	0.225494i
$532$	−12.0000			−0.520266
$533$		0			0
$534$	−12.0000			−0.519291
$535$		0			0
$536$	−9.00000	+	15.5885i	−0.388741	+	0.673319i
$537$	−6.00000	−	10.3923i	−0.258919	−	0.448461i
$538$			10.3923i			0.448044i
$539$	15.0000	−	8.66025i	0.646096	−	0.373024i
$540$		0			0
$541$			6.92820i			0.297867i	0.988847	+	0.148933i	$0.0475840\pi$
$541$			6.92820i			0.297867i	−0.988847	+	0.148933i	$0.952416\pi$
$542$	9.00000	+	15.5885i	0.386583	+	0.669582i
$543$	−5.00000	+	8.66025i	−0.214571	+	0.371647i
$544$	−27.0000	−	15.5885i	−1.15762	−	0.668350i
$545$		0			0
$546$		0			0
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$	−18.0000	−	10.3923i	−0.768922	−	0.443937i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$	−15.0000	−	25.9808i	−0.639602	−	1.10782i
$551$			20.7846i			0.885454i
$552$		0			0
$553$	24.0000	−	13.8564i	1.02058	−	0.589234i
$554$		−	17.3205i		−	0.735878i
$555$		0			0
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	−12.0000	−	6.92820i	−0.508456	−	0.293557i	0.223743	−	0.974648i	$-0.428173\pi$
$557$	−12.0000	−	6.92820i	−0.508456	−	0.293557i	−0.732199	+	0.681091i	$0.761506\pi$
$558$	6.00000			0.254000
$559$		0			0
$560$		0			0
$561$	18.0000	+	10.3923i	0.759961	+	0.438763i
$562$	6.00000	−	10.3923i	0.253095	−	0.438373i
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$			3.46410i			0.145865i
$565$		0			0
$566$	6.00000	−	3.46410i	0.252199	−	0.145607i
$567$		−	3.46410i		−	0.145479i
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$		0			0
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$	36.0000	+	20.7846i	1.50261	+	0.867533i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	28.5000	−	16.4545i	1.18544	−	0.684416i
$579$		0			0
$580$		0			0
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$	12.0000	−	20.7846i	0.497416	−	0.861550i
$583$	18.0000	+	10.3923i	0.745484	+	0.430405i
$584$		0			0
$585$		0			0
$586$	−48.0000			−1.98286
$587$	−9.00000	−	5.19615i	−0.371470	−	0.214468i	0.302631	−	0.953108i	$-0.402135\pi$
$587$	−9.00000	−	5.19615i	−0.371470	−	0.214468i	−0.674100	+	0.738640i	$0.735468\pi$
$588$	2.50000	−	4.33013i	0.103098	−	0.178571i
$589$	−6.00000	−	10.3923i	−0.247226	−	0.428207i
$590$		0			0
$591$		0			0
$592$	−30.0000	+	17.3205i	−1.23299	+	0.711868i
$593$			6.92820i			0.284507i	0.989830	+	0.142254i	$0.0454349\pi$
$593$			6.92820i			0.284507i	−0.989830	+	0.142254i	$0.954565\pi$
$594$	3.00000	+	5.19615i	0.123091	+	0.213201i
$595$		0			0
$596$	12.0000	+	6.92820i	0.491539	+	0.283790i
$597$	−16.0000			−0.654836
$598$		0			0
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$	7.50000	+	4.33013i	0.306186	+	0.176777i
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	−0.949799	−	0.312861i	$-0.898713\pi$
$601$	−5.00000	+	8.66025i	−0.203954	+	0.353259i	0.745845	+	0.666120i	$0.232046\pi$
$602$	12.0000	+	20.7846i	0.489083	+	0.847117i
$603$		−	10.3923i		−	0.423207i
$604$	−9.00000	+	5.19615i	−0.366205	+	0.211428i
$605$		0			0
$606$		−	10.3923i		−	0.422159i
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	−0.983262	−	0.182199i	$-0.941678\pi$
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	0.333842	−	0.942629i	$-0.391655\pi$
$608$	−9.00000	+	15.5885i	−0.364998	+	0.632195i
$609$	−18.0000	−	10.3923i	−0.729397	−	0.421117i
$610$		0			0
$611$		0			0
$612$	6.00000			0.242536
$613$	18.0000	+	10.3923i	0.727013	+	0.419741i	0.817328	−	0.576172i	$-0.195454\pi$
$613$	18.0000	+	10.3923i	0.727013	+	0.419741i	−0.0903153	+	0.995913i	$0.528787\pi$
$614$	−9.00000	+	15.5885i	−0.363210	+	0.629099i
$615$		0			0
$616$		−	20.7846i		−	0.837436i
$617$	−6.00000	+	3.46410i	−0.241551	+	0.139459i	−0.615889	−	0.787833i	$-0.711203\pi$
$617$	−6.00000	+	3.46410i	−0.241551	+	0.139459i	0.374338	+	0.927292i	$0.377870\pi$
$618$	−12.0000	+	6.92820i	−0.482711	+	0.278693i
$619$			31.1769i			1.25311i	0.779379	+	0.626553i	$0.215535\pi$
$619$			31.1769i			1.25311i	−0.779379	+	0.626553i	$0.784465\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−24.0000			−0.961540
$624$		0			0
$625$	25.0000			1.00000
$626$	−15.0000	−	8.66025i	−0.599521	−	0.346133i
$627$	6.00000	−	10.3923i	0.239617	−	0.415029i
$628$	7.00000	+	12.1244i	0.279330	+	0.483814i
$629$		−	41.5692i		−	1.65747i
$630$		0			0
$631$	33.0000	−	19.0526i	1.31371	−	0.758470i	0.331001	−	0.943630i	$-0.392614\pi$
$631$	33.0000	−	19.0526i	1.31371	−	0.758470i	0.982708	+	0.185160i	$0.0592804\pi$
$632$		−	13.8564i		−	0.551178i
$633$	−10.0000	−	17.3205i	−0.397464	−	0.688428i
$634$	12.0000	−	20.7846i	0.476581	−	0.825462i
$635$		0			0
$636$	6.00000			0.237915
$637$		0			0
$638$	36.0000			1.42525
$639$	−3.00000	−	1.73205i	−0.118678	−	0.0685189i
$640$		0			0
$641$	3.00000	+	5.19615i	0.118493	+	0.205236i	0.919171	−	0.393860i	$-0.128860\pi$
$641$	3.00000	+	5.19615i	0.118493	+	0.205236i	−0.800678	+	0.599095i	$0.795527\pi$
$642$		−	20.7846i		−	0.820303i
$643$	−9.00000	+	5.19615i	−0.354925	+	0.204916i	−0.666852	−	0.745190i	$-0.732359\pi$
$643$	−9.00000	+	5.19615i	−0.354925	+	0.204916i	0.311927	+	0.950106i	$0.399026\pi$
$644$		0			0
$645$		0			0
$646$	−18.0000	−	31.1769i	−0.708201	−	1.22664i
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	−0.527710	−	0.849425i	$-0.676949\pi$
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	0.999478	+	0.0322975i	$0.0102824\pi$
$648$	−1.50000	−	0.866025i	−0.0589256	−	0.0340207i
$649$	36.0000			1.41312
$650$		0			0
$651$	12.0000			0.470317
$652$	3.00000	+	1.73205i	0.117489	+	0.0678323i
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	−0.918736	−	0.394872i	$-0.870789\pi$
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	0.801337	+	0.598213i	$0.204122\pi$
$654$	−6.00000	−	10.3923i	−0.234619	−	0.406371i
$655$		0			0
$656$	30.0000	−	17.3205i	1.17130	−	0.676252i
$657$		0			0
$658$			20.7846i			0.810268i
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$		0			0
$661$	18.0000	+	10.3923i	0.700119	+	0.404214i	0.807392	−	0.590016i	$-0.200879\pi$
$661$	18.0000	+	10.3923i	0.700119	+	0.404214i	−0.107273	+	0.994230i	$0.534212\pi$
$662$	−6.00000			−0.233197
$663$		0			0
$664$	6.00000			0.232845
$665$		0			0
$666$	6.00000	−	10.3923i	0.232495	−	0.402694i
$667$		0			0
$668$		−	17.3205i		−	0.670151i
$669$	3.00000	−	1.73205i	0.115987	−	0.0669650i
$670$		0			0
$671$			6.92820i			0.267460i
$672$	−9.00000	−	15.5885i	−0.347183	−	0.601338i
$673$	23.0000	−	39.8372i	0.886585	−	1.53561i	0.0426985	−	0.999088i	$-0.486405\pi$
$673$	23.0000	−	39.8372i	0.886585	−	1.53561i	0.843886	−	0.536522i	$-0.180262\pi$
$674$	21.0000	+	12.1244i	0.808890	+	0.467013i
$675$	−5.00000			−0.192450
$676$		0			0
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$	−9.00000	−	5.19615i	−0.345643	−	0.199557i
$679$	24.0000	−	41.5692i	0.921035	−	1.59528i
$680$		0			0
$681$			17.3205i			0.663723i
$682$	−18.0000	+	10.3923i	−0.689256	+	0.397942i
$683$	−27.0000	+	15.5885i	−1.03313	+	0.596476i	−0.917879	−	0.396861i	$-0.870099\pi$
$683$	−27.0000	+	15.5885i	−1.03313	+	0.596476i	−0.115248	+	0.993337i	$0.536766\pi$
$684$		−	3.46410i		−	0.132453i
$685$		0			0
$686$	−6.00000	+	10.3923i	−0.229081	+	0.396780i
$687$	−6.00000	−	3.46410i	−0.228914	−	0.132164i
$688$	20.0000			0.762493
$689$		0			0
$690$		0			0
$691$	−39.0000	−	22.5167i	−1.48363	−	0.856574i	−0.483803	−	0.875177i	$-0.660745\pi$
$691$	−39.0000	−	22.5167i	−1.48363	−	0.856574i	−0.999827	+	0.0186028i	$0.994078\pi$
$692$	−9.00000	+	15.5885i	−0.342129	+	0.592584i
$693$	6.00000	+	10.3923i	0.227921	+	0.394771i
$694$			62.3538i			2.36692i
$695$		0			0
$696$	−9.00000	+	5.19615i	−0.341144	+	0.196960i
$697$			41.5692i			1.57455i
$698$	−6.00000	−	10.3923i	−0.227103	−	0.393355i
$699$	−3.00000	+	5.19615i	−0.113470	+	0.196537i
$700$	−15.0000	−	8.66025i	−0.566947	−	0.327327i
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	−24.0000			−0.905177
$704$	−3.00000	−	1.73205i	−0.113067	−	0.0652791i
$705$		0			0
$706$	30.0000	+	51.9615i	1.12906	+	1.95560i
$707$		−	20.7846i		−	0.781686i
$708$	9.00000	−	5.19615i	0.338241	−	0.195283i
$709$	−6.00000	+	3.46410i	−0.225335	+	0.130097i	−0.608418	−	0.793617i	$-0.708196\pi$
$709$	−6.00000	+	3.46410i	−0.225335	+	0.130097i	0.383083	+	0.923714i	$0.374862\pi$
$710$		0			0
$711$	4.00000	+	6.92820i	0.150012	+	0.259828i
$712$	−6.00000	+	10.3923i	−0.224860	+	0.389468i
$713$		0			0
$714$	36.0000			1.34727
$715$		0			0
$716$	12.0000			0.448461
$717$	−9.00000	−	5.19615i	−0.336111	−	0.194054i
$718$	15.0000	−	25.9808i	0.559795	−	0.969593i
$719$	−12.0000	−	20.7846i	−0.447524	−	0.775135i	0.550700	−	0.834703i	$-0.314361\pi$
$719$	−12.0000	−	20.7846i	−0.447524	−	0.775135i	−0.998224	+	0.0595683i	$0.981028\pi$
$720$		0			0
$721$	−24.0000	+	13.8564i	−0.893807	+	0.516040i
$722$	10.5000	−	6.06218i	0.390770	−	0.225611i
$723$		−	13.8564i		−	0.515325i
$724$	−5.00000	−	8.66025i	−0.185824	−	0.321856i
$725$	−15.0000	+	25.9808i	−0.557086	+	0.964901i
$726$	−1.50000	−	0.866025i	−0.0556702	−	0.0321412i
$727$	16.0000			0.593407			0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000			0.593407			0.296704	+	0.954970i	$0.404113\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−12.0000	+	20.7846i	−0.443836	+	0.768747i
$732$	1.00000	+	1.73205i	0.0369611	+	0.0640184i
$733$			34.6410i			1.27950i	0.768585	+	0.639748i	$0.220961\pi$
$733$			34.6410i			1.27950i	−0.768585	+	0.639748i	$0.779039\pi$
$734$	−24.0000	+	13.8564i	−0.885856	+	0.511449i
$735$		0			0
$736$		0			0
$737$	18.0000	+	31.1769i	0.663039	+	1.14842i
$738$	−6.00000	+	10.3923i	−0.220863	+	0.382546i
$739$	33.0000	+	19.0526i	1.21392	+	0.700860i	0.963612	−	0.267305i	$-0.0861332\pi$
$739$	33.0000	+	19.0526i	1.21392	+	0.700860i	0.250313	+	0.968165i	$0.419467\pi$
$740$		0			0
$741$		0			0
$742$	36.0000			1.32160
$743$	−3.00000	−	1.73205i	−0.110059	−	0.0635428i	0.443960	−	0.896047i	$-0.353573\pi$
$743$	−3.00000	−	1.73205i	−0.110059	−	0.0635428i	−0.554019	+	0.832504i	$0.686907\pi$
$744$	3.00000	−	5.19615i	0.109985	−	0.190500i
$745$		0			0
$746$			38.1051i			1.39513i
$747$	−3.00000	+	1.73205i	−0.109764	+	0.0633724i
$748$	−18.0000	+	10.3923i	−0.658145	+	0.379980i
$749$		−	41.5692i		−	1.51891i
$750$		0			0
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$	15.0000	+	8.66025i	0.546994	+	0.315807i
$753$	12.0000			0.437304
$754$		0			0
$755$		0			0
$756$	3.00000	+	1.73205i	0.109109	+	0.0629941i
$757$	−11.0000	+	19.0526i	−0.399802	+	0.692477i	−0.993701	−	0.112062i	$-0.964254\pi$
$757$	−11.0000	+	19.0526i	−0.399802	+	0.692477i	0.593899	+	0.804539i	$0.297588\pi$
$758$	15.0000	+	25.9808i	0.544825	+	0.943664i
$759$		0			0
$760$		0			0
$761$	−42.0000	+	24.2487i	−1.52250	+	0.879015i	−0.522852	+	0.852423i	$0.675132\pi$
$761$	−42.0000	+	24.2487i	−1.52250	+	0.879015i	−0.999646	+	0.0265919i	$0.991535\pi$
$762$			13.8564i			0.501965i
$763$	−12.0000	−	20.7846i	−0.434429	−	0.752453i
$764$	12.0000	−	20.7846i	0.434145	−	0.751961i
$765$		0			0
$766$	−6.00000			−0.216789
$767$		0			0
$768$	−19.0000			−0.685603
$769$	−24.0000	−	13.8564i	−0.865462	−	0.499675i	0.000375472	−	1.00000i	$-0.499880\pi$
$769$	−24.0000	−	13.8564i	−0.865462	−	0.499675i	−0.865838	+	0.500325i	$0.833214\pi$
$770$		0			0
$771$	9.00000	+	15.5885i	0.324127	+	0.561405i
$772$		0			0
$773$	−12.0000	+	6.92820i	−0.431610	+	0.249190i	−0.700032	−	0.714111i	$-0.746831\pi$
$773$	−12.0000	+	6.92820i	−0.431610	+	0.249190i	0.268422	+	0.963301i	$0.413498\pi$
$774$	−6.00000	+	3.46410i	−0.215666	+	0.124515i
$775$		−	17.3205i		−	0.622171i
$776$	−12.0000	−	20.7846i	−0.430775	−	0.746124i
$777$	12.0000	−	20.7846i	0.430498	−	0.745644i
$778$	27.0000	+	15.5885i	0.967997	+	0.558873i
$779$	24.0000			0.859889
$780$		0			0
$781$	12.0000			0.429394
$782$		0			0
$783$	3.00000	−	5.19615i	0.107211	−	0.185695i
$784$	−12.5000	−	21.6506i	−0.446429	−	0.773237i
$785$		0			0
$786$	18.0000	−	10.3923i	0.642039	−	0.370681i
$787$	−9.00000	+	5.19615i	−0.320815	+	0.185223i	−0.651756	−	0.758429i	$-0.725967\pi$
$787$	−9.00000	+	5.19615i	−0.320815	+	0.185223i	0.330941	+	0.943652i	$0.392634\pi$
$788$		0			0
$789$	−12.0000	−	20.7846i	−0.427211	−	0.739952i
$790$		0			0
$791$	−18.0000	−	10.3923i	−0.640006	−	0.369508i
$792$	6.00000			0.213201
$793$		0			0
$794$	60.0000			2.12932
$795$		0			0
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	21.0000	+	36.3731i	0.743858	+	1.28840i	0.950726	+	0.310031i	$0.100340\pi$
$797$	21.0000	+	36.3731i	0.743858	+	1.28840i	−0.206868	+	0.978369i	$0.566327\pi$
$798$		−	20.7846i		−	0.735767i
$799$	−18.0000	+	10.3923i	−0.636794	+	0.367653i
$800$	−22.5000	+	12.9904i	−0.795495	+	0.459279i
$801$		−	6.92820i		−	0.244796i
$802$	6.00000	+	10.3923i	0.211867	+	0.366965i
$803$		0			0
$804$	9.00000	+	5.19615i	0.317406	+	0.183254i
$805$		0			0
$806$		0			0
$807$	−6.00000			−0.211210
$808$	−9.00000	−	5.19615i	−0.316619	−	0.182800i
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$		0			0
$811$		−	38.1051i		−	1.33805i	−0.743239	−	0.669026i	$-0.766712\pi$
$811$		−	38.1051i		−	1.33805i	0.743239	−	0.669026i	$-0.233288\pi$
$812$	18.0000	−	10.3923i	0.631676	−	0.364698i
$813$	−9.00000	+	5.19615i	−0.315644	+	0.182237i
$814$			41.5692i			1.45700i
$815$		0			0
$816$	15.0000	−	25.9808i	0.525105	−	0.909509i
$817$	12.0000	+	6.92820i	0.419827	+	0.242387i
$818$	−48.0000			−1.67828
$819$		0			0
$820$		0			0
$821$	−12.0000	−	6.92820i	−0.418803	−	0.241796i	0.275762	−	0.961226i	$-0.411070\pi$
$821$	−12.0000	−	6.92820i	−0.418803	−	0.241796i	−0.694565	+	0.719430i	$0.744403\pi$
$822$	18.0000	−	31.1769i	0.627822	−	1.08742i
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$			13.8564i			0.482711i
$825$	15.0000	−	8.66025i	0.522233	−	0.301511i
$826$	54.0000	−	31.1769i	1.87890	−	1.08478i
$827$			24.2487i			0.843210i	0.906780	+	0.421605i	$0.138533\pi$
$827$			24.2487i			0.843210i	−0.906780	+	0.421605i	$0.861467\pi$
$828$		0			0
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	−0.848137	−	0.529777i	$-0.822276\pi$
$829$	1.00000	−	1.73205i	0.0347314	−	0.0601566i	0.882869	+	0.469620i	$0.155609\pi$
$830$		0			0
$831$	10.0000			0.346896
$832$		0			0
$833$	30.0000			1.03944
$834$	−6.00000	−	3.46410i	−0.207763	−	0.119952i
$835$		0			0
$836$	6.00000	+	10.3923i	0.207514	+	0.359425i
$837$			3.46410i			0.119737i
$838$	−18.0000	+	10.3923i	−0.621800	+	0.358996i
$839$	3.00000	−	1.73205i	0.103572	−	0.0597970i	−0.447320	−	0.894374i	$-0.647621\pi$
$839$	3.00000	−	1.73205i	0.103572	−	0.0597970i	0.550891	+	0.834577i	$0.314288\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−30.0000	+	51.9615i	−1.03387	+	1.79071i
$843$	6.00000	+	3.46410i	0.206651	+	0.119310i
$844$	20.0000			0.688428
$845$		0			0
$846$	−6.00000			−0.206284
$847$	−3.00000	−	1.73205i	−0.103081	−	0.0595140i
$848$	15.0000	−	25.9808i	0.515102	−	0.892183i
$849$	2.00000	+	3.46410i	0.0686398	+	0.118888i
$850$		−	51.9615i		−	1.78227i
$851$		0			0
$852$	3.00000	−	1.73205i	0.102778	−	0.0593391i
$853$		−	20.7846i		−	0.711651i	−0.934552	−	0.355826i	$-0.884200\pi$
$853$		−	20.7846i		−	0.711651i	0.934552	−	0.355826i	$-0.115800\pi$
$854$	6.00000	+	10.3923i	0.205316	+	0.355617i
$855$		0			0
$856$	−18.0000	−	10.3923i	−0.615227	−	0.355202i
$857$	42.0000			1.43469			0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000			1.43469			0.717346	+	0.696717i	$0.245357\pi$
$858$		0			0
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$		0			0
$861$	−12.0000	+	20.7846i	−0.408959	+	0.708338i
$862$	−21.0000	−	36.3731i	−0.715263	−	1.23887i
$863$			31.1769i			1.06127i	0.847599	+	0.530637i	$0.178047\pi$
$863$			31.1769i			1.06127i	−0.847599	+	0.530637i	$0.821953\pi$
$864$	4.50000	−	2.59808i	0.153093	−	0.0883883i
$865$		0			0
$866$			58.8897i			2.00115i
$867$	9.50000	+	16.4545i	0.322637	+	0.558824i
$868$	−6.00000	+	10.3923i	−0.203653	+	0.352738i
$869$	−24.0000	−	13.8564i	−0.814144	−	0.470046i
$870$		0			0
$871$		0			0
$872$	−12.0000			−0.406371
$873$	12.0000	+	6.92820i	0.406138	+	0.234484i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	42.0000	−	24.2487i	1.41824	−	0.818821i	0.422095	−	0.906552i	$-0.361295\pi$
$877$	42.0000	−	24.2487i	1.41824	−	0.818821i	0.996144	+	0.0877308i	$0.0279615\pi$
$878$	12.0000	−	6.92820i	0.404980	−	0.233816i
$879$		−	27.7128i		−	0.934730i
$880$		0			0
$881$	−9.00000	+	15.5885i	−0.303218	+	0.525188i	−0.976863	−	0.213866i	$-0.931394\pi$
$881$	−9.00000	+	15.5885i	−0.303218	+	0.525188i	0.673645	+	0.739055i	$0.264728\pi$
$882$	7.50000	+	4.33013i	0.252538	+	0.145803i
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		0			0
$885$		0			0
$886$	54.0000	+	31.1769i	1.81417	+	1.04741i
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	0.109881	+	0.993945i	$0.464953\pi$
$887$	−24.0000	+	41.5692i	−0.805841	+	1.39576i	−0.915722	+	0.401813i	$0.868380\pi$
$888$	−6.00000	−	10.3923i	−0.201347	−	0.348743i
$889$			27.7128i			0.929458i
$890$		0			0
$891$	−3.00000	+	1.73205i	−0.100504	+	0.0580259i
$892$			3.46410i			0.115987i
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$	−12.0000	+	20.7846i	−0.401340	+	0.695141i
$895$		0			0
$896$	−42.0000			−1.40312
$897$		0			0
$898$	−12.0000			−0.400445
$899$	18.0000	+	10.3923i	0.600334	+	0.346603i
$900$	2.50000	−	4.33013i	0.0833333	−	0.144338i
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$		−	41.5692i		−	1.38410i
$903$	−12.0000	+	6.92820i	−0.399335	+	0.230556i
$904$	−9.00000	+	5.19615i	−0.299336	+	0.172821i
$905$		0			0
$906$	−9.00000	−	15.5885i	−0.299005	−	0.517892i
$907$	22.0000	−	38.1051i	0.730498	−	1.26526i	−0.226173	−	0.974087i	$-0.572621\pi$
$907$	22.0000	−	38.1051i	0.730498	−	1.26526i	0.956671	−	0.291172i	$-0.0940453\pi$
$908$	−15.0000	−	8.66025i	−0.497792	−	0.287401i
$909$	6.00000			0.199007
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$	−15.0000	−	8.66025i	−0.496700	−	0.286770i
$913$	6.00000	−	10.3923i	0.198571	−	0.343935i
$914$	−24.0000	−	41.5692i	−0.793849	−	1.37499i
$915$		0			0
$916$	6.00000	−	3.46410i	0.198246	−	0.114457i
$917$	36.0000	−	20.7846i	1.18882	−	0.686368i
$918$			10.3923i			0.342997i
$919$	16.0000	+	27.7128i	0.527791	+	0.914161i	0.999475	+	0.0323936i	$0.0103130\pi$
$919$	16.0000	+	27.7128i	0.527791	+	0.914161i	−0.471684	+	0.881768i	$0.656354\pi$
$920$		0			0
$921$	−9.00000	−	5.19615i	−0.296560	−	0.171219i
$922$	24.0000			0.790398
$923$		0			0
$924$	−12.0000			−0.394771
$925$	−30.0000	−	17.3205i	−0.986394	−	0.569495i
$926$	−15.0000	+	25.9808i	−0.492931	+	0.853781i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$		−	31.1769i		−	1.02343i
$929$	−18.0000	+	10.3923i	−0.590561	+	0.340960i	−0.765319	−	0.643651i	$-0.777419\pi$
$929$	−18.0000	+	10.3923i	−0.590561	+	0.340960i	0.174758	+	0.984611i	$0.444086\pi$
$930$		0			0
$931$		−	17.3205i		−	0.567657i
$932$	−3.00000	−	5.19615i	−0.0982683	−	0.170206i
$933$		0			0
$934$	−18.0000	−	10.3923i	−0.588978	−	0.340047i
$935$		0			0
$936$		0			0
$937$	−38.0000			−1.24141			−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000			−1.24141			−0.620703	+	0.784046i	$0.713153\pi$
$938$	54.0000	+	31.1769i	1.76316	+	1.01796i
$939$	5.00000	−	8.66025i	0.163169	−	0.282617i
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$	−21.0000	+	12.1244i	−0.684217	+	0.395033i
$943$		0			0
$944$		−	51.9615i		−	1.69120i
$945$		0			0
$946$	12.0000	−	20.7846i	0.390154	−	0.675766i
$947$	−45.0000	−	25.9808i	−1.46230	−	0.844261i	−0.463186	−	0.886261i	$-0.653294\pi$
$947$	−45.0000	−	25.9808i	−1.46230	−	0.844261i	−0.999118	+	0.0419998i	$0.986627\pi$
$948$	−8.00000			−0.259828
$949$		0			0
$950$	−30.0000			−0.973329
$951$	12.0000	+	6.92820i	0.389127	+	0.224662i
$952$	18.0000	−	31.1769i	0.583383	−	1.01045i
$953$	−21.0000	−	36.3731i	−0.680257	−	1.17824i	−0.974902	−	0.222633i	$-0.928535\pi$
$953$	−21.0000	−	36.3731i	−0.680257	−	1.17824i	0.294646	−	0.955607i	$-0.404798\pi$
$954$			10.3923i			0.336463i
$955$		0			0
$956$	9.00000	−	5.19615i	0.291081	−	0.168056i
$957$			20.7846i			0.671871i
$958$	−9.00000	−	15.5885i	−0.290777	−	0.503640i
$959$	36.0000	−	62.3538i	1.16250	−	2.01351i
$960$		0			0
$961$	19.0000			0.612903
$962$		0			0
$963$	12.0000			0.386695
$964$	12.0000	+	6.92820i	0.386494	+	0.223142i
$965$		0			0
$966$		0			0
$967$			10.3923i			0.334194i	0.985940	+	0.167097i	$0.0534393\pi$
$967$			10.3923i			0.334194i	−0.985940	+	0.167097i	$0.946561\pi$
$968$	−1.50000	+	0.866025i	−0.0482118	+	0.0278351i
$969$	18.0000	−	10.3923i	0.578243	−	0.333849i
$970$		0			0
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	0.946094	−	0.323891i	$-0.104991\pi$
$971$	6.00000	+	10.3923i	0.192549	+	0.333505i	−0.753545	+	0.657396i	$0.771658\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−12.0000	−	6.92820i	−0.384702	−	0.222108i
$974$	−66.0000			−2.11478
$975$		0			0
$976$	10.0000			0.320092
$977$	−42.0000	−	24.2487i	−1.34370	−	0.775785i	−0.356351	−	0.934352i	$-0.615979\pi$
$977$	−42.0000	−	24.2487i	−1.34370	−	0.775785i	−0.987348	+	0.158567i	$0.949313\pi$
$978$	−3.00000	+	5.19615i	−0.0959294	+	0.166155i
$979$	12.0000	+	20.7846i	0.383522	+	0.664279i
$980$		0			0
$981$	6.00000	−	3.46410i	0.191565	−	0.110600i
$982$	−18.0000	+	10.3923i	−0.574403	+	0.331632i
$983$		−	51.9615i		−	1.65732i	−0.559756	−	0.828658i	$-0.689105\pi$
$983$		−	51.9615i		−	1.65732i	0.559756	−	0.828658i	$-0.310895\pi$
$984$	6.00000	+	10.3923i	0.191273	+	0.331295i
$985$		0			0
$986$	54.0000	+	31.1769i	1.71971	+	0.992875i
$987$	−12.0000			−0.381964
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	0.491698	+	0.870766i	$0.336377\pi$
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	−0.999954	+	0.00956046i	$0.996957\pi$
$992$	9.00000	+	15.5885i	0.285750	+	0.494934i
$993$		−	3.46410i		−	0.109930i
$994$	18.0000	−	10.3923i	0.570925	−	0.329624i
$995$		0			0
$996$		−	3.46410i		−	0.109764i
$997$	−19.0000	−	32.9090i	−0.601736	−	1.04224i	−0.992558	−	0.121771i	$-0.961143\pi$
$997$	−19.0000	−	32.9090i	−0.601736	−	1.04224i	0.390822	−	0.920466i	$-0.372191\pi$
$998$	−9.00000	+	15.5885i	−0.284890	+	0.493444i
$999$	6.00000	+	3.46410i	0.189832	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.j.a.316.1		2
13.2	odd	12		507.2.e.e.484.1		4
13.3	even	3		507.2.j.c.361.1		2
13.4	even	6		39.2.b.a.25.1	✓	2
13.5	odd	4		507.2.e.e.22.1		4
13.6	odd	12		507.2.a.f.1.2		2
13.7	odd	12		507.2.a.f.1.1		2
13.8	odd	4		507.2.e.e.22.2		4
13.9	even	3		39.2.b.a.25.2	yes	2
13.10	even	6	inner	507.2.j.a.361.1		2
13.11	odd	12		507.2.e.e.484.2		4
13.12	even	2		507.2.j.c.316.1		2
39.17	odd	6		117.2.b.a.64.2		2
39.20	even	12		1521.2.a.l.1.2		2
39.32	even	12		1521.2.a.l.1.1		2
39.35	odd	6		117.2.b.a.64.1		2
52.7	even	12		8112.2.a.bv.1.2		2
52.19	even	12		8112.2.a.bv.1.1		2
52.35	odd	6		624.2.c.e.337.2		2
52.43	odd	6		624.2.c.e.337.1		2
65.4	even	6		975.2.b.d.376.2		2
65.9	even	6		975.2.b.d.376.1		2
65.17	odd	12		975.2.h.f.649.4		4
65.22	odd	12		975.2.h.f.649.2		4
65.43	odd	12		975.2.h.f.649.1		4
65.48	odd	12		975.2.h.f.649.3		4
91.48	odd	6		1911.2.c.d.883.2		2
91.69	odd	6		1911.2.c.d.883.1		2
104.35	odd	6		2496.2.c.d.961.2		2
104.43	odd	6		2496.2.c.d.961.1		2
104.61	even	6		2496.2.c.k.961.1		2
104.69	even	6		2496.2.c.k.961.2		2
156.35	even	6		1872.2.c.e.1585.2		2
156.95	even	6		1872.2.c.e.1585.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.b.a.25.1	✓	2	13.4	even	6
39.2.b.a.25.2	yes	2	13.9	even	3
117.2.b.a.64.1		2	39.35	odd	6
117.2.b.a.64.2		2	39.17	odd	6
507.2.a.f.1.1		2	13.7	odd	12
507.2.a.f.1.2		2	13.6	odd	12
507.2.e.e.22.1		4	13.5	odd	4
507.2.e.e.22.2		4	13.8	odd	4
507.2.e.e.484.1		4	13.2	odd	12
507.2.e.e.484.2		4	13.11	odd	12
507.2.j.a.316.1		2	1.1	even	1	trivial
507.2.j.a.361.1		2	13.10	even	6	inner
507.2.j.c.316.1		2	13.12	even	2
507.2.j.c.361.1		2	13.3	even	3
624.2.c.e.337.1		2	52.43	odd	6
624.2.c.e.337.2		2	52.35	odd	6
975.2.b.d.376.1		2	65.9	even	6
975.2.b.d.376.2		2	65.4	even	6
975.2.h.f.649.1		4	65.43	odd	12
975.2.h.f.649.2		4	65.22	odd	12
975.2.h.f.649.3		4	65.48	odd	12
975.2.h.f.649.4		4	65.17	odd	12
1521.2.a.l.1.1		2	39.32	even	12
1521.2.a.l.1.2		2	39.20	even	12
1872.2.c.e.1585.1		2	156.95	even	6
1872.2.c.e.1585.2		2	156.35	even	6
1911.2.c.d.883.1		2	91.69	odd	6
1911.2.c.d.883.2		2	91.48	odd	6
2496.2.c.d.961.1		2	104.43	odd	6
2496.2.c.d.961.2		2	104.35	odd	6
2496.2.c.k.961.1		2	104.61	even	6
2496.2.c.k.961.2		2	104.69	even	6
8112.2.a.bv.1.1		2	52.19	even	12
8112.2.a.bv.1.2		2	52.7	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +(-3.00000 + 1.73205i) q^{7} +1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +(-3.00000 + 1.73205i) q^{7} +1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.00000 + 1.73205i) q^{11} +1.00000 q^{12} +6.00000 q^{14} +(2.50000 - 4.33013i) q^{16} +(3.00000 + 5.19615i) q^{17} +1.73205i q^{18} +(3.00000 - 1.73205i) q^{19} +3.46410i q^{21} +(-3.00000 - 5.19615i) q^{22} +(1.50000 + 0.866025i) q^{24} +5.00000 q^{25} -1.00000 q^{27} +(-3.00000 - 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} -3.46410i q^{31} +(-4.50000 + 2.59808i) q^{32} +(3.00000 - 1.73205i) q^{33} -10.3923i q^{34} +(0.500000 - 0.866025i) q^{36} +(-6.00000 - 3.46410i) q^{37} -6.00000 q^{38} +(6.00000 + 3.46410i) q^{41} +(3.00000 - 5.19615i) q^{42} +(2.00000 + 3.46410i) q^{43} +3.46410i q^{44} +3.46410i q^{47} +(-2.50000 - 4.33013i) q^{48} +(2.50000 - 4.33013i) q^{49} +(-7.50000 - 4.33013i) q^{50} +6.00000 q^{51} +6.00000 q^{53} +(1.50000 + 0.866025i) q^{54} +(-3.00000 - 5.19615i) q^{56} -3.46410i q^{57} +(9.00000 - 5.19615i) q^{58} +(9.00000 - 5.19615i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-3.00000 + 5.19615i) q^{62} +(3.00000 + 1.73205i) q^{63} -1.00000 q^{64} -6.00000 q^{66} +(9.00000 + 5.19615i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(3.00000 - 1.73205i) q^{71} +(1.50000 - 0.866025i) q^{72} +(6.00000 + 10.3923i) q^{74} +(2.50000 - 4.33013i) q^{75} +(3.00000 + 1.73205i) q^{76} -12.0000 q^{77} -8.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-6.00000 - 10.3923i) q^{82} -3.46410i q^{83} +(-3.00000 + 1.73205i) q^{84} -6.92820i q^{86} +(3.00000 + 5.19615i) q^{87} +(-3.00000 + 5.19615i) q^{88} +(6.00000 + 3.46410i) q^{89} +(-3.00000 - 1.73205i) q^{93} +(3.00000 - 5.19615i) q^{94} +5.19615i q^{96} +(-12.0000 + 6.92820i) q^{97} +(-7.50000 + 4.33013i) q^{98} -3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + q^{3} + q^{4} - 3 q^{6} - 6 q^{7} - q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 + q^3 + q^4 - 3 * q^6 - 6 * q^7 - q^9	\( 2 q - 3 q^{2} + q^{3} + q^{4} - 3 q^{6} - 6 q^{7} - q^{9} + 6 q^{11} + 2 q^{12} + 12 q^{14} + 5 q^{16} + 6 q^{17} + 6 q^{19} - 6 q^{22} + 3 q^{24} + 10 q^{25} - 2 q^{27} - 6 q^{28} - 6 q^{29} - 9 q^{32} + 6 q^{33} + q^{36} - 12 q^{37} - 12 q^{38} + 12 q^{41} + 6 q^{42} + 4 q^{43} - 5 q^{48} + 5 q^{49} - 15 q^{50} + 12 q^{51} + 12 q^{53} + 3 q^{54} - 6 q^{56} + 18 q^{58} + 18 q^{59} + 2 q^{61} - 6 q^{62} + 6 q^{63} - 2 q^{64} - 12 q^{66} + 18 q^{67} - 6 q^{68} + 6 q^{71} + 3 q^{72} + 12 q^{74} + 5 q^{75} + 6 q^{76} - 24 q^{77} - 16 q^{79} - q^{81} - 12 q^{82} - 6 q^{84} + 6 q^{87} - 6 q^{88} + 12 q^{89} - 6 q^{93} + 6 q^{94} - 24 q^{97} - 15 q^{98}+O(q^{100}) \) 2 * q - 3 * q^2 + q^3 + q^4 - 3 * q^6 - 6 * q^7 - q^9 + 6 * q^11 + 2 * q^12 + 12 * q^14 + 5 * q^16 + 6 * q^17 + 6 * q^19 - 6 * q^22 + 3 * q^24 + 10 * q^25 - 2 * q^27 - 6 * q^28 - 6 * q^29 - 9 * q^32 + 6 * q^33 + q^36 - 12 * q^37 - 12 * q^38 + 12 * q^41 + 6 * q^42 + 4 * q^43 - 5 * q^48 + 5 * q^49 - 15 * q^50 + 12 * q^51 + 12 * q^53 + 3 * q^54 - 6 * q^56 + 18 * q^58 + 18 * q^59 + 2 * q^61 - 6 * q^62 + 6 * q^63 - 2 * q^64 - 12 * q^66 + 18 * q^67 - 6 * q^68 + 6 * q^71 + 3 * q^72 + 12 * q^74 + 5 * q^75 + 6 * q^76 - 24 * q^77 - 16 * q^79 - q^81 - 12 * q^82 - 6 * q^84 + 6 * q^87 - 6 * q^88 + 12 * q^89 - 6 * q^93 + 6 * q^94 - 24 * q^97 - 15 * q^98

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