LMFDB - Embedded newform 539.2.e.g.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(67,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("539.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.e (of order $3$, 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:	$4.30393666895$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	539.177
Dual form			539.2.e.g.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} +(1.00000 - 1.73205i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.00000 + 1.73205i) q^{12} -4.00000 q^{13} -1.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-2.00000 - 3.46410i) q^{18} -2.00000 q^{20} -2.00000 q^{22} +(0.500000 - 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-4.00000 + 6.92820i) q^{26} -5.00000 q^{27} +(-1.00000 + 1.73205i) q^{30} +(3.50000 + 6.06218i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(-0.500000 + 0.866025i) q^{33} -4.00000 q^{34} -4.00000 q^{36} +(-1.50000 + 2.59808i) q^{37} +(2.00000 + 3.46410i) q^{39} +8.00000 q^{41} -6.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(-1.00000 - 1.73205i) q^{46} +(4.00000 - 6.92820i) q^{47} -4.00000 q^{48} +8.00000 q^{50} +(-1.00000 + 1.73205i) q^{51} +(4.00000 + 6.92820i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-5.00000 + 8.66025i) q^{54} -1.00000 q^{55} +(2.50000 + 4.33013i) q^{59} +(1.00000 + 1.73205i) q^{60} +(6.00000 - 10.3923i) q^{61} +14.0000 q^{62} -8.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(1.00000 + 1.73205i) q^{66} +(3.50000 + 6.06218i) q^{67} +(-2.00000 + 3.46410i) q^{68} -1.00000 q^{69} -3.00000 q^{71} +(2.00000 + 3.46410i) q^{73} +(3.00000 + 5.19615i) q^{74} +(2.00000 - 3.46410i) q^{75} +8.00000 q^{78} +(5.00000 - 8.66025i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.00000 - 13.8564i) q^{82} +6.00000 q^{83} -2.00000 q^{85} +(-6.00000 + 10.3923i) q^{86} +(7.50000 - 12.9904i) q^{89} -4.00000 q^{90} -2.00000 q^{92} +(3.50000 - 6.06218i) q^{93} +(-8.00000 - 13.8564i) q^{94} +(-4.00000 + 6.92820i) q^{96} +7.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 - 2 * q^4 + q^5 - 4 * q^6 + 2 * q^9	$ 2 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 4 q^{6} + 2 q^{9} - 2 q^{10} - q^{11} - 2 q^{12} - 8 q^{13} - 2 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} - 4 q^{20} - 4 q^{22} + q^{23} + 4 q^{25} - 8 q^{26} - 10 q^{27} - 2 q^{30} + 7 q^{31} - 8 q^{32} - q^{33} - 8 q^{34} - 8 q^{36} - 3 q^{37} + 4 q^{39} + 16 q^{41} - 12 q^{43} - 2 q^{44} - 2 q^{45} - 2 q^{46} + 8 q^{47} - 8 q^{48} + 16 q^{50} - 2 q^{51} + 8 q^{52} + 6 q^{53} - 10 q^{54} - 2 q^{55} + 5 q^{59} + 2 q^{60} + 12 q^{61} + 28 q^{62} - 16 q^{64} - 4 q^{65} + 2 q^{66} + 7 q^{67} - 4 q^{68} - 2 q^{69} - 6 q^{71} + 4 q^{73} + 6 q^{74} + 4 q^{75} + 16 q^{78} + 10 q^{79} - 4 q^{80} - q^{81} + 16 q^{82} + 12 q^{83} - 4 q^{85} - 12 q^{86} + 15 q^{89} - 8 q^{90} - 4 q^{92} + 7 q^{93} - 16 q^{94} - 8 q^{96} + 14 q^{97} - 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - q^3 - 2 * q^4 + q^5 - 4 * q^6 + 2 * q^9 - 2 * q^10 - q^11 - 2 * q^12 - 8 * q^13 - 2 * q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 - 4 * q^20 - 4 * q^22 + q^23 + 4 * q^25 - 8 * q^26 - 10 * q^27 - 2 * q^30 + 7 * q^31 - 8 * q^32 - q^33 - 8 * q^34 - 8 * q^36 - 3 * q^37 + 4 * q^39 + 16 * q^41 - 12 * q^43 - 2 * q^44 - 2 * q^45 - 2 * q^46 + 8 * q^47 - 8 * q^48 + 16 * q^50 - 2 * q^51 + 8 * q^52 + 6 * q^53 - 10 * q^54 - 2 * q^55 + 5 * q^59 + 2 * q^60 + 12 * q^61 + 28 * q^62 - 16 * q^64 - 4 * q^65 + 2 * q^66 + 7 * q^67 - 4 * q^68 - 2 * q^69 - 6 * q^71 + 4 * q^73 + 6 * q^74 + 4 * q^75 + 16 * q^78 + 10 * q^79 - 4 * q^80 - q^81 + 16 * q^82 + 12 * q^83 - 4 * q^85 - 12 * q^86 + 15 * q^89 - 8 * q^90 - 4 * q^92 + 7 * q^93 - 16 * q^94 - 8 * q^96 + 14 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	−0.732294	−	0.680989i	$-0.761550\pi$
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i	0.955901	+	0.293691i	$0.0948835\pi$
$6$	−2.00000			−0.816497
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	−1.00000	−	1.73205i	−0.316228	−	0.547723i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$	−1.00000	+	1.73205i	−0.288675	+	0.500000i
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	−2.00000	−	3.46410i	−0.471405	−	0.816497i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	−2.00000			−0.447214
$21$		0			0
$22$	−2.00000			−0.426401
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−4.00000	+	6.92820i	−0.784465	+	1.35873i
$27$	−5.00000			−0.962250
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	0.987829	+	0.155543i	$0.0497126\pi$
$31$	3.50000	+	6.06218i	0.628619	+	1.08880i	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−4.00000	−	6.92820i	−0.707107	−	1.22474i
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$	−4.00000			−0.685994
$35$		0			0
$36$	−4.00000			−0.666667
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	−0.962580	−	0.270998i	$-0.912646\pi$
$37$	−1.50000	+	2.59808i	−0.246598	+	0.427121i	0.715981	+	0.698119i	$0.245980\pi$
$38$		0			0
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$		0			0
$41$	8.00000			1.24939			0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000			1.24939			0.624695	+	0.780869i	$0.285223\pi$
$42$		0			0
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	−1.00000	−	1.73205i	−0.149071	−	0.258199i
$46$	−1.00000	−	1.73205i	−0.147442	−	0.255377i
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	−0.411606	−	0.911362i	$-0.635032\pi$
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	0.995066	−	0.0992202i	$-0.0316348\pi$
$48$	−4.00000			−0.577350
$49$		0			0
$50$	8.00000			1.13137
$51$	−1.00000	+	1.73205i	−0.140028	+	0.242536i
$52$	4.00000	+	6.92820i	0.554700	+	0.960769i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	−5.00000	+	8.66025i	−0.680414	+	1.17851i
$55$	−1.00000			−0.134840
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	0.981608	−	0.190909i	$-0.0611434\pi$
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	−0.656136	+	0.754643i	$0.727810\pi$
$60$	1.00000	+	1.73205i	0.129099	+	0.223607i
$61$	6.00000	−	10.3923i	0.768221	−	1.33060i	−0.170305	−	0.985391i	$-0.554475\pi$
$61$	6.00000	−	10.3923i	0.768221	−	1.33060i	0.938527	−	0.345207i	$-0.112191\pi$
$62$	14.0000			1.77800
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$	1.00000	+	1.73205i	0.123091	+	0.213201i
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$	−1.00000			−0.120386
$70$		0			0
$71$	−3.00000			−0.356034			−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000			−0.356034			−0.178017	+	0.984027i	$0.556968\pi$
$72$		0			0
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	0.959006	−	0.283387i	$-0.0914581\pi$
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	−0.724923	+	0.688830i	$0.758125\pi$
$74$	3.00000	+	5.19615i	0.348743	+	0.604040i
$75$	2.00000	−	3.46410i	0.230940	−	0.400000i
$76$		0			0
$77$		0			0
$78$	8.00000			0.905822
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$	−2.00000	−	3.46410i	−0.223607	−	0.387298i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	8.00000	−	13.8564i	0.883452	−	1.53018i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$	−2.00000			−0.216930
$86$	−6.00000	+	10.3923i	−0.646997	+	1.12063i
$87$		0			0
$88$		0			0
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	−0.127842	−	0.991795i	$-0.540805\pi$
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	0.922840	−	0.385183i	$-0.125862\pi$
$90$	−4.00000			−0.421637
$91$		0			0
$92$	−2.00000			−0.208514
$93$	3.50000	−	6.06218i	0.362933	−	0.628619i
$94$	−8.00000	−	13.8564i	−0.825137	−	1.42918i
$95$		0			0
$96$	−4.00000	+	6.92820i	−0.408248	+	0.707107i
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$		0			0
$99$	−2.00000			−0.201008
$100$	4.00000	−	6.92820i	0.400000	−	0.692820i
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$	2.00000	+	3.46410i	0.198030	+	0.342997i
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	0.138767	+	0.990325i	$0.455686\pi$
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	−0.927030	+	0.374987i	$0.877647\pi$
$104$		0			0
$105$		0			0
$106$	12.0000			1.16554
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$	5.00000	+	8.66025i	0.481125	+	0.833333i
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	0.520794	−	0.853682i	$-0.325636\pi$
$109$	−5.00000	−	8.66025i	−0.478913	−	0.829502i	−0.999708	+	0.0241802i	$0.992302\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$	3.00000			0.284747
$112$		0			0
$113$	9.00000			0.846649			0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000			0.846649			0.423324	+	0.905978i	$0.360863\pi$
$114$		0			0
$115$	−0.500000	−	0.866025i	−0.0466252	−	0.0807573i
$116$		0			0
$117$	−4.00000	+	6.92820i	−0.369800	+	0.640513i
$118$	10.0000			0.920575
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−12.0000	−	20.7846i	−1.08643	−	1.88175i
$123$	−4.00000	−	6.92820i	−0.360668	−	0.624695i
$124$	7.00000	−	12.1244i	0.628619	−	1.08880i
$125$	9.00000			0.804984
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	3.00000	+	5.19615i	0.264135	+	0.457496i
$130$	4.00000	+	6.92820i	0.350823	+	0.607644i
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	0.141865	+	0.989886i	$0.454690\pi$
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	−0.928199	+	0.372084i	$0.878643\pi$
$132$	2.00000			0.174078
$133$		0			0
$134$	14.0000			1.20942
$135$	−2.50000	+	4.33013i	−0.215166	+	0.372678i
$136$		0			0
$137$	3.50000	+	6.06218i	0.299025	+	0.517927i	0.975913	−	0.218159i	$-0.0700052\pi$
$137$	3.50000	+	6.06218i	0.299025	+	0.517927i	−0.676888	+	0.736086i	$0.736672\pi$
$138$	−1.00000	+	1.73205i	−0.0851257	+	0.147442i
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$		0			0
$141$	−8.00000			−0.673722
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$	−4.00000	−	6.92820i	−0.333333	−	0.577350i
$145$		0			0
$146$	8.00000			0.662085
$147$		0			0
$148$	6.00000			0.493197
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	−4.00000	−	6.92820i	−0.326599	−	0.565685i
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	0.822464	−	0.568818i	$-0.192599\pi$
$151$	−1.00000	−	1.73205i	−0.0813788	−	0.140952i	−0.903842	+	0.427865i	$0.859266\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$		0			0
$155$	7.00000			0.562254
$156$	4.00000	−	6.92820i	0.320256	−	0.554700i
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$	−10.0000	−	17.3205i	−0.795557	−	1.37795i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$	−8.00000			−0.632456
$161$		0			0
$162$	−2.00000			−0.157135
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$	−8.00000	−	13.8564i	−0.624695	−	1.08200i
$165$	0.500000	+	0.866025i	0.0389249	+	0.0674200i
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	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
$169$	3.00000			0.230769
$170$	−2.00000	+	3.46410i	−0.153393	+	0.265684i
$171$		0			0
$172$	6.00000	+	10.3923i	0.457496	+	0.792406i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$		0			0
$176$	−4.00000			−0.301511
$177$	2.50000	−	4.33013i	0.187912	−	0.325472i
$178$	−15.0000	−	25.9808i	−1.12430	−	1.94734i
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	0.997446	+	0.0714220i	$0.0227537\pi$
$179$	7.50000	+	12.9904i	0.560576	+	0.970947i	−0.436870	+	0.899525i	$0.643913\pi$
$180$	−2.00000	+	3.46410i	−0.149071	+	0.258199i
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$	−12.0000			−0.887066
$184$		0			0
$185$	1.50000	+	2.59808i	0.110282	+	0.191014i
$186$	−7.00000	−	12.1244i	−0.513265	−	0.889001i
$187$	−1.00000	+	1.73205i	−0.0731272	+	0.126660i
$188$	−16.0000			−1.16692
$189$		0			0
$190$		0			0
$191$	−8.50000	+	14.7224i	−0.615038	+	1.06528i	0.375339	+	0.926887i	$0.377526\pi$
$191$	−8.50000	+	14.7224i	−0.615038	+	1.06528i	−0.990378	+	0.138390i	$0.955807\pi$
$192$	4.00000	+	6.92820i	0.288675	+	0.500000i
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	0.785022	−	0.619467i	$-0.212651\pi$
$193$	−2.00000	−	3.46410i	−0.143963	−	0.249351i	−0.928986	+	0.370116i	$0.879318\pi$
$194$	7.00000	−	12.1244i	0.502571	−	0.870478i
$195$	4.00000			0.286446
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$	−2.00000	+	3.46410i	−0.142134	+	0.246183i
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$		0			0
$201$	3.50000	−	6.06218i	0.246871	−	0.427593i
$202$	4.00000			0.281439
$203$		0			0
$204$	4.00000			0.280056
$205$	4.00000	−	6.92820i	0.279372	−	0.483887i
$206$	16.0000	+	27.7128i	1.11477	+	1.93084i
$207$	−1.00000	−	1.73205i	−0.0695048	−	0.120386i
$208$	−8.00000	+	13.8564i	−0.554700	+	0.960769i
$209$		0			0
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$	1.50000	+	2.59808i	0.102778	+	0.178017i
$214$	18.0000	+	31.1769i	1.23045	+	2.13121i
$215$	−3.00000	+	5.19615i	−0.204598	+	0.354375i
$216$		0			0
$217$		0			0
$218$	−20.0000			−1.35457
$219$	2.00000	−	3.46410i	0.135147	−	0.234082i
$220$	1.00000	+	1.73205i	0.0674200	+	0.116775i
$221$	4.00000	+	6.92820i	0.269069	+	0.466041i
$222$	3.00000	−	5.19615i	0.201347	−	0.348743i
$223$	−19.0000			−1.27233			−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000			−1.27233			−0.636167	+	0.771551i	$0.719481\pi$
$224$		0			0
$225$	8.00000			0.533333
$226$	9.00000	−	15.5885i	0.598671	−	1.03693i
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$		0			0
$229$	7.50000	−	12.9904i	0.495614	−	0.858429i	−0.504373	−	0.863486i	$-0.668276\pi$
$229$	7.50000	−	12.9904i	0.495614	−	0.858429i	0.999987	+	0.00505719i	$0.00160976\pi$
$230$	−2.00000			−0.131876
$231$		0			0
$232$		0			0
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	0.142166	+	0.989843i	$0.454593\pi$
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	−0.928312	+	0.371802i	$0.878740\pi$
$234$	8.00000	+	13.8564i	0.522976	+	0.905822i
$235$	−4.00000	−	6.92820i	−0.260931	−	0.451946i
$236$	5.00000	−	8.66025i	0.325472	−	0.563735i
$237$	−10.0000			−0.649570
$238$		0			0
$239$	−30.0000			−1.94054			−0.970269	−	0.242028i	$-0.922188\pi$
$239$	−30.0000			−1.94054			−0.970269	+	0.242028i	$0.922188\pi$
$240$	−2.00000	+	3.46410i	−0.129099	+	0.223607i
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	0.707953	−	0.706260i	$-0.249619\pi$
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	−0.965615	+	0.259975i	$0.916286\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	−24.0000			−1.53644
$245$		0			0
$246$	−16.0000			−1.02012
$247$		0			0
$248$		0			0
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$	9.00000	−	15.5885i	0.569210	−	0.985901i
$251$	23.0000			1.45175			0.725874	−	0.687828i	$-0.241436\pi$
$251$	23.0000			1.45175			0.725874	+	0.687828i	$0.241436\pi$
$252$		0			0
$253$	−1.00000			−0.0628695
$254$	8.00000	−	13.8564i	0.501965	−	0.869428i
$255$	1.00000	+	1.73205i	0.0626224	+	0.108465i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	−0.895528	−	0.445005i	$-0.853202\pi$
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	0.833150	+	0.553047i	$0.186535\pi$
$258$	12.0000			0.747087
$259$		0			0
$260$	8.00000			0.496139
$261$		0			0
$262$	18.0000	+	31.1769i	1.11204	+	1.92612i
$263$	−7.00000	−	12.1244i	−0.431638	−	0.747620i	0.565376	−	0.824833i	$-0.308731\pi$
$263$	−7.00000	−	12.1244i	−0.431638	−	0.747620i	−0.997015	+	0.0772134i	$0.975398\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$	−15.0000			−0.917985
$268$	7.00000	−	12.1244i	0.427593	−	0.740613i
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	0.977229	−	0.212187i	$-0.0680585\pi$
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	−0.672374	+	0.740212i	$0.734725\pi$
$270$	5.00000	+	8.66025i	0.304290	+	0.527046i
$271$	−14.0000	+	24.2487i	−0.850439	+	1.47300i	0.0303728	+	0.999539i	$0.490331\pi$
$271$	−14.0000	+	24.2487i	−0.850439	+	1.47300i	−0.880812	+	0.473466i	$0.843003\pi$
$272$	−8.00000			−0.485071
$273$		0			0
$274$	14.0000			0.845771
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$	1.00000	+	1.73205i	0.0601929	+	0.104257i
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	−10.0000	+	17.3205i	−0.599760	+	1.03882i
$279$	14.0000			0.838158
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$	−8.00000	+	13.8564i	−0.476393	+	0.825137i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	8.00000			0.473050
$287$		0			0
$288$	−16.0000			−0.942809
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	−3.50000	−	6.06218i	−0.205174	−	0.355371i
$292$	4.00000	−	6.92820i	0.234082	−	0.405442i
$293$	−24.0000			−1.40209			−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000			−1.40209			−0.701047	+	0.713115i	$0.747284\pi$
$294$		0			0
$295$	5.00000			0.291111
$296$		0			0
$297$	2.50000	+	4.33013i	0.145065	+	0.251259i
$298$	−10.0000	−	17.3205i	−0.579284	−	1.00335i
$299$	−2.00000	+	3.46410i	−0.115663	+	0.200334i
$300$	−8.00000			−0.461880
$301$		0			0
$302$	−4.00000			−0.230174
$303$	1.00000	−	1.73205i	0.0574485	−	0.0995037i
$304$		0			0
$305$	−6.00000	−	10.3923i	−0.343559	−	0.595062i
$306$	−4.00000	+	6.92820i	−0.228665	+	0.396059i
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$	7.00000	−	12.1244i	0.397573	−	0.688617i
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$		0			0
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	−20.0000			−1.12509
$317$	−6.50000	+	11.2583i	−0.365076	+	0.632331i	−0.988788	−	0.149323i	$-0.952290\pi$
$317$	−6.50000	+	11.2583i	−0.365076	+	0.632331i	0.623712	+	0.781654i	$0.285624\pi$
$318$	−6.00000	−	10.3923i	−0.336463	−	0.582772i
$319$		0			0
$320$	−4.00000	+	6.92820i	−0.223607	+	0.387298i
$321$	18.0000			1.00466
$322$		0			0
$323$		0			0
$324$	−1.00000	+	1.73205i	−0.0555556	+	0.0962250i
$325$	−8.00000	−	13.8564i	−0.443760	−	0.768615i
$326$	4.00000	+	6.92820i	0.221540	+	0.383718i
$327$	−5.00000	+	8.66025i	−0.276501	+	0.478913i
$328$		0			0
$329$		0			0
$330$	2.00000			0.110096
$331$	−3.50000	+	6.06218i	−0.192377	+	0.333207i	−0.946038	−	0.324057i	$-0.894953\pi$
$331$	−3.50000	+	6.06218i	−0.192377	+	0.333207i	0.753660	+	0.657264i	$0.228286\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$	3.00000	+	5.19615i	0.164399	+	0.284747i
$334$	12.0000	−	20.7846i	0.656611	−	1.13728i
$335$	7.00000			0.382451
$336$		0			0
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$	3.00000	−	5.19615i	0.163178	−	0.282633i
$339$	−4.50000	−	7.79423i	−0.244406	−	0.423324i
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	3.50000	−	6.06218i	0.189536	−	0.328285i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.500000	+	0.866025i	−0.0269191	+	0.0466252i
$346$	6.00000	+	10.3923i	0.322562	+	0.558694i
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	−0.947067	−	0.321037i	$-0.895969\pi$
$347$	−14.0000	−	24.2487i	−0.751559	−	1.30174i	0.195507	−	0.980702i	$-0.437365\pi$
$348$		0			0
$349$	−30.0000			−1.60586			−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000			−1.60586			−0.802932	+	0.596071i	$0.796728\pi$
$350$		0			0
$351$	20.0000			1.06752
$352$	−4.00000	+	6.92820i	−0.213201	+	0.369274i
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	−0.997592	−	0.0693543i	$-0.977906\pi$
$353$	−10.5000	−	18.1865i	−0.558859	−	0.967972i	0.438733	−	0.898617i	$-0.355427\pi$
$354$	−5.00000	−	8.66025i	−0.265747	−	0.460287i
$355$	−1.50000	+	2.59808i	−0.0796117	+	0.137892i
$356$	−30.0000			−1.59000
$357$		0			0
$358$	30.0000			1.58555
$359$	10.0000	−	17.3205i	0.527780	−	0.914141i	−0.471696	−	0.881761i	$-0.656358\pi$
$359$	10.0000	−	17.3205i	0.527780	−	0.914141i	0.999476	−	0.0323801i	$-0.0103087\pi$
$360$		0			0
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	−7.00000	+	12.1244i	−0.367912	+	0.637242i
$363$	1.00000			0.0524864
$364$		0			0
$365$	4.00000			0.209370
$366$	−12.0000	+	20.7846i	−0.627250	+	1.08643i
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	−0.997960	+	0.0638362i	$0.979666\pi$
$368$	−2.00000	−	3.46410i	−0.104257	−	0.180579i
$369$	8.00000	−	13.8564i	0.416463	−	0.721336i
$370$	6.00000			0.311925
$371$		0			0
$372$	−14.0000			−0.725866
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	−0.303902	−	0.952703i	$-0.598289\pi$
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	0.977016	−	0.213165i	$-0.0683772\pi$
$374$	2.00000	+	3.46410i	0.103418	+	0.179124i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−5.00000			−0.256833			−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000			−0.256833			−0.128416	+	0.991720i	$0.540989\pi$
$380$		0			0
$381$	−4.00000	−	6.92820i	−0.204926	−	0.354943i
$382$	17.0000	+	29.4449i	0.869796	+	1.50653i
$383$	−0.500000	+	0.866025i	−0.0255488	+	0.0442518i	−0.878517	−	0.477711i	$-0.841467\pi$
$383$	−0.500000	+	0.866025i	−0.0255488	+	0.0442518i	0.852968	+	0.521963i	$0.174800\pi$
$384$		0			0
$385$		0			0
$386$	−8.00000			−0.407189
$387$	−6.00000	+	10.3923i	−0.304997	+	0.528271i
$388$	−7.00000	−	12.1244i	−0.355371	−	0.615521i
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	0.991100	−	0.133120i	$-0.0424994\pi$
$389$	7.50000	+	12.9904i	0.380265	+	0.658638i	−0.610835	+	0.791758i	$0.709166\pi$
$390$	4.00000	−	6.92820i	0.202548	−	0.350823i
$391$	−2.00000			−0.101144
$392$		0			0
$393$	18.0000			0.907980
$394$	−2.00000	+	3.46410i	−0.100759	+	0.174519i
$395$	−5.00000	−	8.66025i	−0.251577	−	0.435745i
$396$	2.00000	+	3.46410i	0.100504	+	0.174078i
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	−0.890028	−	0.455905i	$-0.849316\pi$
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	0.839840	+	0.542834i	$0.182649\pi$
$398$		0			0
$399$		0			0
$400$	16.0000			0.800000
$401$	−1.00000	+	1.73205i	−0.0499376	+	0.0864945i	−0.889914	−	0.456129i	$-0.849236\pi$
$401$	−1.00000	+	1.73205i	−0.0499376	+	0.0864945i	0.839976	+	0.542623i	$0.182569\pi$
$402$	−7.00000	−	12.1244i	−0.349128	−	0.604708i
$403$	−14.0000	−	24.2487i	−0.697390	−	1.20791i
$404$	2.00000	−	3.46410i	0.0995037	−	0.172345i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	3.00000			0.148704
$408$		0			0
$409$	−15.0000	−	25.9808i	−0.741702	−	1.28467i	−0.951720	−	0.306968i	$-0.900685\pi$
$409$	−15.0000	−	25.9808i	−0.741702	−	1.28467i	0.210017	−	0.977698i	$-0.432648\pi$
$410$	−8.00000	−	13.8564i	−0.395092	−	0.684319i
$411$	3.50000	−	6.06218i	0.172642	−	0.299025i
$412$	32.0000			1.57653
$413$		0			0
$414$	−4.00000			−0.196589
$415$	3.00000	−	5.19615i	0.147264	−	0.255069i
$416$	16.0000	+	27.7128i	0.784465	+	1.35873i
$417$	5.00000	+	8.66025i	0.244851	+	0.424094i
$418$		0			0
$419$	−20.0000			−0.977064			−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000			−0.977064			−0.488532	+	0.872546i	$0.662467\pi$
$420$		0			0
$421$	22.0000			1.07221			0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000			1.07221			0.536107	+	0.844150i	$0.319894\pi$
$422$	12.0000	−	20.7846i	0.584151	−	1.01178i
$423$	−8.00000	−	13.8564i	−0.388973	−	0.673722i
$424$		0			0
$425$	4.00000	−	6.92820i	0.194029	−	0.336067i
$426$	6.00000			0.290701
$427$		0			0
$428$	36.0000			1.74013
$429$	2.00000	−	3.46410i	0.0965609	−	0.167248i
$430$	6.00000	+	10.3923i	0.289346	+	0.501161i
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	0.997173	−	0.0751385i	$-0.0239399\pi$
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	−0.563658	+	0.826008i	$0.690607\pi$
$432$	−10.0000	+	17.3205i	−0.481125	+	0.833333i
$433$	11.0000			0.528626			0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000			0.528626			0.264313	+	0.964437i	$0.414855\pi$
$434$		0			0
$435$		0			0
$436$	−10.0000	+	17.3205i	−0.478913	+	0.829502i
$437$		0			0
$438$	−4.00000	−	6.92820i	−0.191127	−	0.331042i
$439$	20.0000	−	34.6410i	0.954548	−	1.65333i	0.219149	−	0.975691i	$-0.429672\pi$
$439$	20.0000	−	34.6410i	0.954548	−	1.65333i	0.735399	−	0.677634i	$-0.236995\pi$
$440$		0			0
$441$		0			0
$442$	16.0000			0.761042
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	−0.705278	−	0.708931i	$-0.749178\pi$
$443$	5.50000	−	9.52628i	0.261313	−	0.452607i	0.966591	+	0.256323i	$0.0825112\pi$
$444$	−3.00000	−	5.19615i	−0.142374	−	0.246598i
$445$	−7.50000	−	12.9904i	−0.355534	−	0.615803i
$446$	−19.0000	+	32.9090i	−0.899676	+	1.55828i
$447$	−10.0000			−0.472984
$448$		0			0
$449$	35.0000			1.65175			0.825876	−	0.563852i	$-0.190681\pi$
$449$	35.0000			1.65175			0.825876	+	0.563852i	$0.190681\pi$
$450$	8.00000	−	13.8564i	0.377124	−	0.653197i
$451$	−4.00000	−	6.92820i	−0.188353	−	0.326236i
$452$	−9.00000	−	15.5885i	−0.423324	−	0.733219i
$453$	−1.00000	+	1.73205i	−0.0469841	+	0.0813788i
$454$	36.0000			1.68956
$455$		0			0
$456$		0			0
$457$	6.00000	−	10.3923i	0.280668	−	0.486132i	−0.690881	−	0.722968i	$-0.742777\pi$
$457$	6.00000	−	10.3923i	0.280668	−	0.486132i	0.971549	+	0.236837i	$0.0761106\pi$
$458$	−15.0000	−	25.9808i	−0.700904	−	1.21400i
$459$	5.00000	+	8.66025i	0.233380	+	0.404226i
$460$	−1.00000	+	1.73205i	−0.0466252	+	0.0807573i
$461$	−12.0000			−0.558896			−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000			−0.558896			−0.279448	+	0.960161i	$0.590151\pi$
$462$		0			0
$463$	−11.0000			−0.511213			−0.255607	−	0.966781i	$-0.582275\pi$
$463$	−11.0000			−0.511213			−0.255607	+	0.966781i	$0.582275\pi$
$464$		0			0
$465$	−3.50000	−	6.06218i	−0.162309	−	0.281127i
$466$	24.0000	+	41.5692i	1.11178	+	1.92566i
$467$	−13.5000	+	23.3827i	−0.624705	+	1.08202i	0.363892	+	0.931441i	$0.381448\pi$
$467$	−13.5000	+	23.3827i	−0.624705	+	1.08202i	−0.988598	+	0.150581i	$0.951886\pi$
$468$	16.0000			0.739600
$469$		0			0
$470$	−16.0000			−0.738025
$471$	−3.50000	+	6.06218i	−0.161271	+	0.279330i
$472$		0			0
$473$	3.00000	+	5.19615i	0.137940	+	0.238919i
$474$	−10.0000	+	17.3205i	−0.459315	+	0.795557i
$475$		0			0
$476$		0			0
$477$	12.0000			0.549442
$478$	−30.0000	+	51.9615i	−1.37217	+	2.37666i
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	0.998796	−	0.0490589i	$-0.0156222\pi$
$479$	10.0000	+	17.3205i	0.456912	+	0.791394i	−0.541884	+	0.840453i	$0.682289\pi$
$480$	4.00000	+	6.92820i	0.182574	+	0.316228i
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$	−16.0000			−0.728780
$483$		0			0
$484$	2.00000			0.0909091
$485$	3.50000	−	6.06218i	0.158927	−	0.275269i
$486$	16.0000	+	27.7128i	0.725775	+	1.25708i
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	−0.999698	−	0.0245553i	$-0.992183\pi$
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	0.478584	−	0.878042i	$-0.341150\pi$
$488$		0			0
$489$	4.00000			0.180886
$490$		0			0
$491$	−8.00000			−0.361035			−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000			−0.361035			−0.180517	+	0.983572i	$0.557777\pi$
$492$	−8.00000	+	13.8564i	−0.360668	+	0.624695i
$493$		0			0
$494$		0			0
$495$	−1.00000	+	1.73205i	−0.0449467	+	0.0778499i
$496$	28.0000			1.25724
$497$		0			0
$498$	−12.0000			−0.537733
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	−0.998233	−	0.0594153i	$-0.981076\pi$
$499$	−10.0000	+	17.3205i	−0.447661	+	0.775372i	0.550572	+	0.834788i	$0.314410\pi$
$500$	−9.00000	−	15.5885i	−0.402492	−	0.697137i
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$	23.0000	−	39.8372i	1.02654	−	1.77802i
$503$	26.0000			1.15928			0.579641	−	0.814872i	$-0.303193\pi$
$503$	26.0000			1.15928			0.579641	+	0.814872i	$0.303193\pi$
$504$		0			0
$505$	2.00000			0.0889988
$506$	−1.00000	+	1.73205i	−0.0444554	+	0.0769991i
$507$	−1.50000	−	2.59808i	−0.0666173	−	0.115385i
$508$	−8.00000	−	13.8564i	−0.354943	−	0.614779i
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$	4.00000			0.177123
$511$		0			0
$512$	−32.0000			−1.41421
$513$		0			0
$514$	2.00000	+	3.46410i	0.0882162	+	0.152795i
$515$	8.00000	+	13.8564i	0.352522	+	0.610586i
$516$	6.00000	−	10.3923i	0.264135	−	0.457496i
$517$	−8.00000			−0.351840
$518$		0			0
$519$	6.00000			0.263371
$520$		0			0
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	0.831295	−	0.555831i	$-0.187600\pi$
$521$	−1.50000	−	2.59808i	−0.0657162	−	0.113824i	−0.897011	+	0.442007i	$0.854267\pi$
$522$		0			0
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$	36.0000			1.57267
$525$		0			0
$526$	−28.0000			−1.22086
$527$	7.00000	−	12.1244i	0.304925	−	0.528145i
$528$	2.00000	+	3.46410i	0.0870388	+	0.150756i
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	6.00000	−	10.3923i	0.260623	−	0.451413i
$531$	10.0000			0.433963
$532$		0			0
$533$	−32.0000			−1.38607
$534$	−15.0000	+	25.9808i	−0.649113	+	1.12430i
$535$	9.00000	+	15.5885i	0.389104	+	0.673948i
$536$		0			0
$537$	7.50000	−	12.9904i	0.323649	−	0.560576i
$538$	20.0000			0.862261
$539$		0			0
$540$	10.0000			0.430331
$541$	4.00000	−	6.92820i	0.171973	−	0.297867i	−0.767136	−	0.641484i	$-0.778319\pi$
$541$	4.00000	−	6.92820i	0.171973	−	0.297867i	0.939110	+	0.343617i	$0.111652\pi$
$542$	28.0000	+	48.4974i	1.20270	+	2.08314i
$543$	3.50000	+	6.06218i	0.150199	+	0.260153i
$544$	−8.00000	+	13.8564i	−0.342997	+	0.594089i
$545$	−10.0000			−0.428353
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	7.00000	−	12.1244i	0.299025	−	0.517927i
$549$	−12.0000	−	20.7846i	−0.512148	−	0.887066i
$550$	−4.00000	−	6.92820i	−0.170561	−	0.295420i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	4.00000			0.169944
$555$	1.50000	−	2.59808i	0.0636715	−	0.110282i
$556$	10.0000	+	17.3205i	0.424094	+	0.734553i
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	0.886433	−	0.462856i	$-0.153175\pi$
$557$	1.00000	+	1.73205i	0.0423714	+	0.0733893i	−0.844062	+	0.536246i	$0.819842\pi$
$558$	14.0000	−	24.2487i	0.592667	−	1.02653i
$559$	24.0000			1.01509
$560$		0			0
$561$	2.00000			0.0844401
$562$	−18.0000	+	31.1769i	−0.759284	+	1.31512i
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	0.905088	−	0.425223i	$-0.139804\pi$
$563$	2.00000	+	3.46410i	0.0842900	+	0.145994i	−0.820798	+	0.571218i	$0.806471\pi$
$564$	8.00000	+	13.8564i	0.336861	+	0.583460i
$565$	4.50000	−	7.79423i	0.189316	−	0.327906i
$566$	8.00000			0.336265
$567$		0			0
$568$		0			0
$569$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$569$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$570$		0			0
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	0.994765	+	0.102190i	$0.0325850\pi$
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	−0.408883	+	0.912587i	$0.634082\pi$
$572$	4.00000	−	6.92820i	0.167248	−	0.289683i
$573$	17.0000			0.710185
$574$		0			0
$575$	4.00000			0.166812
$576$	−8.00000	+	13.8564i	−0.333333	+	0.577350i
$577$	16.5000	+	28.5788i	0.686904	+	1.18975i	0.972834	+	0.231502i	$0.0743641\pi$
$577$	16.5000	+	28.5788i	0.686904	+	1.18975i	−0.285930	+	0.958250i	$0.592303\pi$
$578$	−13.0000	−	22.5167i	−0.540729	−	0.936570i
$579$	−2.00000	+	3.46410i	−0.0831172	+	0.143963i
$580$		0			0
$581$		0			0
$582$	−14.0000			−0.580319
$583$	3.00000	−	5.19615i	0.124247	−	0.215203i
$584$		0			0
$585$	4.00000	+	6.92820i	0.165380	+	0.286446i
$586$	−24.0000	+	41.5692i	−0.991431	+	1.71721i
$587$	−28.0000			−1.15568			−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000			−1.15568			−0.577842	+	0.816149i	$0.696105\pi$
$588$		0			0
$589$		0			0
$590$	5.00000	−	8.66025i	0.205847	−	0.356537i
$591$	1.00000	+	1.73205i	0.0411345	+	0.0712470i
$592$	6.00000	+	10.3923i	0.246598	+	0.427121i
$593$	22.0000	−	38.1051i	0.903432	−	1.56479i	0.0804231	−	0.996761i	$-0.474373\pi$
$593$	22.0000	−	38.1051i	0.903432	−	1.56479i	0.823009	−	0.568029i	$-0.192294\pi$
$594$	10.0000			0.410305
$595$		0			0
$596$	−20.0000			−0.819232
$597$		0			0
$598$	4.00000	+	6.92820i	0.163572	+	0.283315i
$599$	−20.0000	−	34.6410i	−0.817178	−	1.41539i	−0.907754	−	0.419504i	$-0.862204\pi$
$599$	−20.0000	−	34.6410i	−0.817178	−	1.41539i	0.0905757	−	0.995890i	$-0.471129\pi$
$600$		0			0
$601$	−2.00000			−0.0815817			−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000			−0.0815817			−0.0407909	+	0.999168i	$0.512988\pi$
$602$		0			0
$603$	14.0000			0.570124
$604$	−2.00000	+	3.46410i	−0.0813788	+	0.140952i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	−2.00000	−	3.46410i	−0.0812444	−	0.140720i
$607$	−11.0000	+	19.0526i	−0.446476	+	0.773320i	−0.998154	−	0.0607380i	$-0.980655\pi$
$607$	−11.0000	+	19.0526i	−0.446476	+	0.773320i	0.551678	+	0.834058i	$0.313988\pi$
$608$		0			0
$609$		0			0
$610$	−24.0000			−0.971732
$611$	−16.0000	+	27.7128i	−0.647291	+	1.12114i
$612$	4.00000	+	6.92820i	0.161690	+	0.280056i
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	−8.00000	+	13.8564i	−0.322854	+	0.559199i
$615$	−8.00000			−0.322591
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$	16.0000	−	27.7128i	0.643614	−	1.11477i
$619$	−12.5000	−	21.6506i	−0.502417	−	0.870212i	−0.999996	−	0.00279365i	$-0.999111\pi$
$619$	−12.5000	−	21.6506i	−0.502417	−	0.870212i	0.497579	−	0.867419i	$-0.334223\pi$
$620$	−7.00000	−	12.1244i	−0.281127	−	0.486926i
$621$	−2.50000	+	4.33013i	−0.100322	+	0.173762i
$622$	24.0000			0.962312
$623$		0			0
$624$	16.0000			0.640513
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	1.00000	+	1.73205i	0.0399680	+	0.0692267i
$627$		0			0
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	6.00000			0.239236
$630$		0			0
$631$	7.00000			0.278666			0.139333	−	0.990246i	$-0.455504\pi$
$631$	7.00000			0.278666			0.139333	+	0.990246i	$0.455504\pi$
$632$		0			0
$633$	−6.00000	−	10.3923i	−0.238479	−	0.413057i
$634$	13.0000	+	22.5167i	0.516296	+	0.894251i
$635$	4.00000	−	6.92820i	0.158735	−	0.274937i
$636$	−12.0000			−0.475831
$637$		0			0
$638$		0			0
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$	18.0000	−	31.1769i	0.710403	−	1.23045i
$643$	−29.0000			−1.14365			−0.571824	−	0.820376i	$-0.693764\pi$
$643$	−29.0000			−1.14365			−0.571824	+	0.820376i	$0.693764\pi$
$644$		0			0
$645$	6.00000			0.236250
$646$		0			0
$647$	−3.50000	−	6.06218i	−0.137599	−	0.238329i	0.788988	−	0.614408i	$-0.210605\pi$
$647$	−3.50000	−	6.06218i	−0.137599	−	0.238329i	−0.926587	+	0.376080i	$0.877272\pi$
$648$		0			0
$649$	2.50000	−	4.33013i	0.0981336	−	0.169972i
$650$	−32.0000			−1.25514
$651$		0			0
$652$	8.00000			0.313304
$653$	20.5000	−	35.5070i	0.802227	−	1.38950i	−0.115920	−	0.993259i	$-0.536982\pi$
$653$	20.5000	−	35.5070i	0.802227	−	1.38950i	0.918147	−	0.396239i	$-0.129685\pi$
$654$	10.0000	+	17.3205i	0.391031	+	0.677285i
$655$	9.00000	+	15.5885i	0.351659	+	0.609091i
$656$	16.0000	−	27.7128i	0.624695	−	1.08200i
$657$	8.00000			0.312110
$658$		0			0
$659$	10.0000			0.389545			0.194772	−	0.980848i	$-0.437603\pi$
$659$	10.0000			0.389545			0.194772	+	0.980848i	$0.437603\pi$
$660$	1.00000	−	1.73205i	0.0389249	−	0.0674200i
$661$	18.5000	+	32.0429i	0.719567	+	1.24633i	0.961172	+	0.275951i	$0.0889928\pi$
$661$	18.5000	+	32.0429i	0.719567	+	1.24633i	−0.241605	+	0.970375i	$0.577674\pi$
$662$	7.00000	+	12.1244i	0.272063	+	0.471226i
$663$	4.00000	−	6.92820i	0.155347	−	0.269069i
$664$		0			0
$665$		0			0
$666$	12.0000			0.464991
$667$		0			0
$668$	−12.0000	−	20.7846i	−0.464294	−	0.804181i
$669$	9.50000	+	16.4545i	0.367291	+	0.636167i
$670$	7.00000	−	12.1244i	0.270434	−	0.468405i
$671$	−12.0000			−0.463255
$672$		0			0
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$	−22.0000	+	38.1051i	−0.847408	+	1.46775i
$675$	−10.0000	−	17.3205i	−0.384900	−	0.666667i
$676$	−3.00000	−	5.19615i	−0.115385	−	0.199852i
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	0.107772	+	0.994176i	$0.465628\pi$
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	−0.914867	+	0.403755i	$0.867705\pi$
$678$	−18.0000			−0.691286
$679$		0			0
$680$		0			0
$681$	9.00000	−	15.5885i	0.344881	−	0.597351i
$682$	−7.00000	−	12.1244i	−0.268044	−	0.464266i
$683$	8.00000	+	13.8564i	0.306111	+	0.530201i	0.977508	−	0.210898i	$-0.0676386\pi$
$683$	8.00000	+	13.8564i	0.306111	+	0.530201i	−0.671397	+	0.741098i	$0.734305\pi$
$684$		0			0
$685$	7.00000			0.267456
$686$		0			0
$687$	−15.0000			−0.572286
$688$	−12.0000	+	20.7846i	−0.457496	+	0.792406i
$689$	−12.0000	−	20.7846i	−0.457164	−	0.791831i
$690$	1.00000	+	1.73205i	0.0380693	+	0.0659380i
$691$	8.50000	−	14.7224i	0.323355	−	0.560068i	−0.657823	−	0.753173i	$-0.728522\pi$
$691$	8.50000	−	14.7224i	0.323355	−	0.560068i	0.981178	+	0.193105i	$0.0618558\pi$
$692$	12.0000			0.456172
$693$		0			0
$694$	−56.0000			−2.12573
$695$	−5.00000	+	8.66025i	−0.189661	+	0.328502i
$696$		0			0
$697$	−8.00000	−	13.8564i	−0.303022	−	0.524849i
$698$	−30.0000	+	51.9615i	−1.13552	+	1.96677i
$699$	24.0000			0.907763
$700$		0			0
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$	20.0000	−	34.6410i	0.754851	−	1.30744i
$703$		0			0
$704$	4.00000	+	6.92820i	0.150756	+	0.261116i
$705$	−4.00000	+	6.92820i	−0.150649	+	0.260931i
$706$	−42.0000			−1.58069
$707$		0			0
$708$	−10.0000			−0.375823
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	−0.529943	−	0.848034i	$-0.677787\pi$
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	0.999390	+	0.0349269i	$0.0111198\pi$
$710$	3.00000	+	5.19615i	0.112588	+	0.195008i
$711$	−10.0000	−	17.3205i	−0.375029	−	0.649570i
$712$		0			0
$713$	7.00000			0.262152
$714$		0			0
$715$	4.00000			0.149592
$716$	15.0000	−	25.9808i	0.560576	−	0.970947i
$717$	15.0000	+	25.9808i	0.560185	+	0.970269i
$718$	−20.0000	−	34.6410i	−0.746393	−	1.29279i
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	−0.691608	−	0.722273i	$-0.743097\pi$
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	0.971311	+	0.237814i	$0.0764307\pi$
$720$	−8.00000			−0.298142
$721$		0			0
$722$	38.0000			1.41421
$723$	−4.00000	+	6.92820i	−0.148762	+	0.257663i
$724$	7.00000	+	12.1244i	0.260153	+	0.450598i
$725$		0			0
$726$	1.00000	−	1.73205i	0.0371135	−	0.0642824i
$727$	−3.00000			−0.111264			−0.0556319	−	0.998451i	$-0.517717\pi$
$727$	−3.00000			−0.111264			−0.0556319	+	0.998451i	$0.517717\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	4.00000	−	6.92820i	0.148047	−	0.256424i
$731$	6.00000	+	10.3923i	0.221918	+	0.384373i
$732$	12.0000	+	20.7846i	0.443533	+	0.768221i
$733$	−18.0000	+	31.1769i	−0.664845	+	1.15155i	0.314482	+	0.949263i	$0.398169\pi$
$733$	−18.0000	+	31.1769i	−0.664845	+	1.15155i	−0.979327	+	0.202282i	$0.935164\pi$
$734$	−34.0000			−1.25496
$735$		0			0
$736$	−8.00000			−0.294884
$737$	3.50000	−	6.06218i	0.128924	−	0.223303i
$738$	−16.0000	−	27.7128i	−0.588968	−	1.02012i
$739$	−25.0000	−	43.3013i	−0.919640	−	1.59286i	−0.799962	−	0.600050i	$-0.795147\pi$
$739$	−25.0000	−	43.3013i	−0.919640	−	1.59286i	−0.119677	−	0.992813i	$-0.538186\pi$
$740$	3.00000	−	5.19615i	0.110282	−	0.191014i
$741$		0			0
$742$		0			0
$743$	4.00000			0.146746			0.0733729	−	0.997305i	$-0.476624\pi$
$743$	4.00000			0.146746			0.0733729	+	0.997305i	$0.476624\pi$
$744$		0			0
$745$	−5.00000	−	8.66025i	−0.183186	−	0.317287i
$746$	−26.0000	−	45.0333i	−0.951928	−	1.64879i
$747$	6.00000	−	10.3923i	0.219529	−	0.380235i
$748$	4.00000			0.146254
$749$		0			0
$750$	−18.0000			−0.657267
$751$	11.5000	−	19.9186i	0.419641	−	0.726839i	−0.576262	−	0.817265i	$-0.695489\pi$
$751$	11.5000	−	19.9186i	0.419641	−	0.726839i	0.995903	+	0.0904254i	$0.0288227\pi$
$752$	−16.0000	−	27.7128i	−0.583460	−	1.01058i
$753$	−11.5000	−	19.9186i	−0.419083	−	0.725874i
$754$		0			0
$755$	−2.00000			−0.0727875
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	−5.00000	+	8.66025i	−0.181608	+	0.314555i
$759$	0.500000	+	0.866025i	0.0181489	+	0.0314347i
$760$		0			0
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$	−16.0000			−0.579619
$763$		0			0
$764$	34.0000			1.23008
$765$	−2.00000	+	3.46410i	−0.0723102	+	0.125245i
$766$	1.00000	+	1.73205i	0.0361315	+	0.0625815i
$767$	−10.0000	−	17.3205i	−0.361079	−	0.625407i
$768$	−8.00000	+	13.8564i	−0.288675	+	0.500000i
$769$	−20.0000			−0.721218			−0.360609	−	0.932717i	$-0.617431\pi$
$769$	−20.0000			−0.721218			−0.360609	+	0.932717i	$0.617431\pi$
$770$		0			0
$771$	2.00000			0.0720282
$772$	−4.00000	+	6.92820i	−0.143963	+	0.249351i
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	0.807018	−	0.590527i	$-0.201080\pi$
$773$	−3.00000	−	5.19615i	−0.107903	−	0.186893i	−0.914920	+	0.403634i	$0.867747\pi$
$774$	12.0000	+	20.7846i	0.431331	+	0.747087i
$775$	−14.0000	+	24.2487i	−0.502895	+	0.871039i
$776$		0			0
$777$		0			0
$778$	30.0000			1.07555
$779$		0			0
$780$	−4.00000	−	6.92820i	−0.143223	−	0.248069i
$781$	1.50000	+	2.59808i	0.0536742	+	0.0929665i
$782$	−2.00000	+	3.46410i	−0.0715199	+	0.123876i
$783$		0			0
$784$		0			0
$785$	−7.00000			−0.249841
$786$	18.0000	−	31.1769i	0.642039	−	1.11204i
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	−0.996531	−	0.0832226i	$-0.973479\pi$
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	0.426193	−	0.904632i	$-0.359855\pi$
$788$	2.00000	+	3.46410i	0.0712470	+	0.123404i
$789$	−7.00000	+	12.1244i	−0.249207	+	0.431638i
$790$	−20.0000			−0.711568
$791$		0			0
$792$		0			0
$793$	−24.0000	+	41.5692i	−0.852265	+	1.47617i
$794$	2.00000	+	3.46410i	0.0709773	+	0.122936i
$795$	−3.00000	−	5.19615i	−0.106399	−	0.184289i
$796$		0			0
$797$	−53.0000			−1.87736			−0.938678	−	0.344795i	$-0.887949\pi$
$797$	−53.0000			−1.87736			−0.938678	+	0.344795i	$0.887949\pi$
$798$		0			0
$799$	−16.0000			−0.566039
$800$	16.0000	−	27.7128i	0.565685	−	0.979796i
$801$	−15.0000	−	25.9808i	−0.529999	−	0.917985i
$802$	2.00000	+	3.46410i	0.0706225	+	0.122322i
$803$	2.00000	−	3.46410i	0.0705785	−	0.122245i
$804$	−14.0000			−0.493742
$805$		0			0
$806$	−56.0000			−1.97252
$807$	5.00000	−	8.66025i	0.176008	−	0.304855i
$808$		0			0
$809$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$809$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$810$	−1.00000	+	1.73205i	−0.0351364	+	0.0608581i
$811$	38.0000			1.33436			0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000			1.33436			0.667180	+	0.744896i	$0.267501\pi$
$812$		0			0
$813$	28.0000			0.982003
$814$	3.00000	−	5.19615i	0.105150	−	0.182125i
$815$	2.00000	+	3.46410i	0.0700569	+	0.121342i
$816$	4.00000	+	6.92820i	0.140028	+	0.242536i
$817$		0			0
$818$	−60.0000			−2.09785
$819$		0			0
$820$	−16.0000			−0.558744
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$	−7.00000	−	12.1244i	−0.244153	−	0.422885i
$823$	−19.5000	−	33.7750i	−0.679727	−	1.17732i	−0.975063	−	0.221929i	$-0.928765\pi$
$823$	−19.5000	−	33.7750i	−0.679727	−	1.17732i	0.295336	−	0.955394i	$-0.404569\pi$
$824$		0			0
$825$	−4.00000			−0.139262
$826$		0			0
$827$	−52.0000			−1.80822			−0.904109	−	0.427303i	$-0.859464\pi$
$827$	−52.0000			−1.80822			−0.904109	+	0.427303i	$0.859464\pi$
$828$	−2.00000	+	3.46410i	−0.0695048	+	0.120386i
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$	−6.00000	−	10.3923i	−0.208263	−	0.360722i
$831$	1.00000	−	1.73205i	0.0346896	−	0.0600842i
$832$	32.0000			1.10940
$833$		0			0
$834$	20.0000			0.692543
$835$	6.00000	−	10.3923i	0.207639	−	0.359641i
$836$		0			0
$837$	−17.5000	−	30.3109i	−0.604888	−	1.04770i
$838$	−20.0000	+	34.6410i	−0.690889	+	1.19665i
$839$	5.00000			0.172619			0.0863096	−	0.996268i	$-0.472493\pi$
$839$	5.00000			0.172619			0.0863096	+	0.996268i	$0.472493\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	22.0000	−	38.1051i	0.758170	−	1.31319i
$843$	9.00000	+	15.5885i	0.309976	+	0.536895i
$844$	−12.0000	−	20.7846i	−0.413057	−	0.715436i
$845$	1.50000	−	2.59808i	0.0516016	−	0.0893765i
$846$	−32.0000			−1.10018
$847$		0			0
$848$	24.0000			0.824163
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$	−8.00000	−	13.8564i	−0.274398	−	0.475271i
$851$	1.50000	+	2.59808i	0.0514193	+	0.0890609i
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.00000	+	6.92820i	0.136637	+	0.236663i	0.926222	−	0.376979i	$-0.123037\pi$
$857$	4.00000	+	6.92820i	0.136637	+	0.236663i	−0.789584	+	0.613642i	$0.789704\pi$
$858$	−4.00000	−	6.92820i	−0.136558	−	0.236525i
$859$	−7.50000	+	12.9904i	−0.255897	+	0.443226i	−0.965139	−	0.261739i	$-0.915704\pi$
$859$	−7.50000	+	12.9904i	−0.255897	+	0.443226i	0.709242	+	0.704965i	$0.249037\pi$
$860$	12.0000			0.409197
$861$		0			0
$862$	36.0000			1.22616
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$	20.0000	+	34.6410i	0.680414	+	1.17851i
$865$	3.00000	+	5.19615i	0.102003	+	0.176674i
$866$	11.0000	−	19.0526i	0.373795	−	0.647432i
$867$	−13.0000			−0.441503
$868$		0			0
$869$	−10.0000			−0.339227
$870$		0			0
$871$	−14.0000	−	24.2487i	−0.474372	−	0.821636i
$872$		0			0
$873$	7.00000	−	12.1244i	0.236914	−	0.410347i
$874$		0			0
$875$		0			0
$876$	−8.00000			−0.270295
$877$	6.00000	−	10.3923i	0.202606	−	0.350923i	−0.746762	−	0.665092i	$-0.768392\pi$
$877$	6.00000	−	10.3923i	0.202606	−	0.350923i	0.949367	+	0.314169i	$0.101726\pi$
$878$	−40.0000	−	69.2820i	−1.34993	−	2.33816i
$879$	12.0000	+	20.7846i	0.404750	+	0.701047i
$880$	−2.00000	+	3.46410i	−0.0674200	+	0.116775i
$881$	43.0000			1.44871			0.724353	−	0.689429i	$-0.242138\pi$
$881$	43.0000			1.44871			0.724353	+	0.689429i	$0.242138\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$	8.00000	−	13.8564i	0.269069	−	0.466041i
$885$	−2.50000	−	4.33013i	−0.0840366	−	0.145556i
$886$	−11.0000	−	19.0526i	−0.369552	−	0.640083i
$887$	−11.0000	+	19.0526i	−0.369344	+	0.639722i	−0.989463	−	0.144785i	$-0.953751\pi$
$887$	−11.0000	+	19.0526i	−0.369344	+	0.639722i	0.620119	+	0.784508i	$0.287084\pi$
$888$		0			0
$889$		0			0
$890$	−30.0000			−1.00560
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$	19.0000	+	32.9090i	0.636167	+	1.10187i
$893$		0			0
$894$	−10.0000	+	17.3205i	−0.334450	+	0.579284i
$895$	15.0000			0.501395
$896$		0			0
$897$	4.00000			0.133556
$898$	35.0000	−	60.6218i	1.16797	−	2.02297i
$899$		0			0
$900$	−8.00000	−	13.8564i	−0.266667	−	0.461880i
$901$	6.00000	−	10.3923i	0.199889	−	0.346218i
$902$	−16.0000			−0.532742
$903$		0			0
$904$		0			0
$905$	−3.50000	+	6.06218i	−0.116344	+	0.201514i
$906$	2.00000	+	3.46410i	0.0664455	+	0.115087i
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$	18.0000	−	31.1769i	0.597351	−	1.03464i
$909$	4.00000			0.132672
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$	−3.00000	−	5.19615i	−0.0992855	−	0.171968i
$914$	−12.0000	−	20.7846i	−0.396925	−	0.687494i
$915$	−6.00000	+	10.3923i	−0.198354	+	0.343559i
$916$	−30.0000			−0.991228
$917$		0			0
$918$	20.0000			0.660098
$919$	−5.00000	+	8.66025i	−0.164935	+	0.285675i	−0.936632	−	0.350315i	$-0.886075\pi$
$919$	−5.00000	+	8.66025i	−0.164935	+	0.285675i	0.771697	+	0.635990i	$0.219408\pi$
$920$		0			0
$921$	4.00000	+	6.92820i	0.131804	+	0.228292i
$922$	−12.0000	+	20.7846i	−0.395199	+	0.684505i
$923$	12.0000			0.394985
$924$		0			0
$925$	−12.0000			−0.394558
$926$	−11.0000	+	19.0526i	−0.361482	+	0.626106i
$927$	16.0000	+	27.7128i	0.525509	+	0.910208i
$928$		0			0
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$	−14.0000			−0.459078
$931$		0			0
$932$	48.0000			1.57229
$933$	6.00000	−	10.3923i	0.196431	−	0.340229i
$934$	27.0000	+	46.7654i	0.883467	+	1.53021i
$935$	1.00000	+	1.73205i	0.0327035	+	0.0566441i
$936$		0			0
$937$	−8.00000			−0.261349			−0.130674	−	0.991425i	$-0.541714\pi$
$937$	−8.00000			−0.261349			−0.130674	+	0.991425i	$0.541714\pi$
$938$		0			0
$939$	1.00000			0.0326338
$940$	−8.00000	+	13.8564i	−0.260931	+	0.451946i
$941$	21.0000	+	36.3731i	0.684580	+	1.18573i	0.973568	+	0.228395i	$0.0733479\pi$
$941$	21.0000	+	36.3731i	0.684580	+	1.18573i	−0.288988	+	0.957333i	$0.593319\pi$
$942$	7.00000	+	12.1244i	0.228072	+	0.395033i
$943$	4.00000	−	6.92820i	0.130258	−	0.225613i
$944$	20.0000			0.650945
$945$		0			0
$946$	12.0000			0.390154
$947$	13.5000	−	23.3827i	0.438691	−	0.759835i	−0.558898	−	0.829237i	$-0.688776\pi$
$947$	13.5000	−	23.3827i	0.438691	−	0.759835i	0.997589	+	0.0694014i	$0.0221089\pi$
$948$	10.0000	+	17.3205i	0.324785	+	0.562544i
$949$	−8.00000	−	13.8564i	−0.259691	−	0.449798i
$950$		0			0
$951$	13.0000			0.421554
$952$		0			0
$953$	34.0000			1.10137			0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000			1.10137			0.550684	+	0.834714i	$0.314367\pi$
$954$	12.0000	−	20.7846i	0.388514	−	0.672927i
$955$	8.50000	+	14.7224i	0.275054	+	0.476407i
$956$	30.0000	+	51.9615i	0.970269	+	1.68056i
$957$		0			0
$958$	40.0000			1.29234
$959$		0			0
$960$	8.00000			0.258199
$961$	−9.00000	+	15.5885i	−0.290323	+	0.502853i
$962$	−12.0000	−	20.7846i	−0.386896	−	0.670123i
$963$	18.0000	+	31.1769i	0.580042	+	1.00466i
$964$	−8.00000	+	13.8564i	−0.257663	+	0.446285i
$965$	−4.00000			−0.128765
$966$		0			0
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$		0			0
$969$		0			0
$970$	−7.00000	−	12.1244i	−0.224756	−	0.389290i
$971$	23.5000	−	40.7032i	0.754151	−	1.30623i	−0.191644	−	0.981464i	$-0.561382\pi$
$971$	23.5000	−	40.7032i	0.754151	−	1.30623i	0.945795	−	0.324763i	$-0.105285\pi$
$972$	32.0000			1.02640
$973$		0			0
$974$	−46.0000			−1.47394
$975$	−8.00000	+	13.8564i	−0.256205	+	0.443760i
$976$	−24.0000	−	41.5692i	−0.768221	−	1.33060i
$977$	13.5000	+	23.3827i	0.431903	+	0.748078i	0.997037	−	0.0769208i	$-0.0245089\pi$
$977$	13.5000	+	23.3827i	0.431903	+	0.748078i	−0.565134	+	0.824999i	$0.691176\pi$
$978$	4.00000	−	6.92820i	0.127906	−	0.221540i
$979$	−15.0000			−0.479402
$980$		0			0
$981$	−20.0000			−0.638551
$982$	−8.00000	+	13.8564i	−0.255290	+	0.442176i
$983$	19.5000	+	33.7750i	0.621953	+	1.07725i	0.989122	+	0.147100i	$0.0469940\pi$
$983$	19.5000	+	33.7750i	0.621953	+	1.07725i	−0.367168	+	0.930155i	$0.619673\pi$
$984$		0			0
$985$	−1.00000	+	1.73205i	−0.0318626	+	0.0551877i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.00000	+	5.19615i	−0.0953945	+	0.165228i
$990$	2.00000	+	3.46410i	0.0635642	+	0.110096i
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	0.922538	−	0.385906i	$-0.126111\pi$
$991$	4.00000	+	6.92820i	0.127064	+	0.220082i	−0.795474	+	0.605988i	$0.792778\pi$
$992$	28.0000	−	48.4974i	0.889001	−	1.53979i
$993$	7.00000			0.222138
$994$		0			0
$995$		0			0
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	19.0000	+	32.9090i	0.601736	+	1.04224i	0.992558	+	0.121771i	$0.0388574\pi$
$997$	19.0000	+	32.9090i	0.601736	+	1.04224i	−0.390822	+	0.920466i	$0.627809\pi$
$998$	20.0000	+	34.6410i	0.633089	+	1.09654i
$999$	7.50000	−	12.9904i	0.237289	−	0.410997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.e.g.177.1		2
7.2	even	3		539.2.a.a.1.1		1
7.3	odd	6		539.2.e.h.67.1		2
7.4	even	3	inner	539.2.e.g.67.1		2
7.5	odd	6		11.2.a.a.1.1	✓	1
7.6	odd	2		539.2.e.h.177.1		2
21.2	odd	6		4851.2.a.t.1.1		1
21.5	even	6		99.2.a.d.1.1		1
28.19	even	6		176.2.a.b.1.1		1
28.23	odd	6		8624.2.a.j.1.1		1
35.12	even	12		275.2.b.a.199.1		2
35.19	odd	6		275.2.a.b.1.1		1
35.33	even	12		275.2.b.a.199.2		2
56.5	odd	6		704.2.a.h.1.1		1
56.19	even	6		704.2.a.c.1.1		1
63.5	even	6		891.2.e.b.298.1		2
63.40	odd	6		891.2.e.k.298.1		2
63.47	even	6		891.2.e.b.595.1		2
63.61	odd	6		891.2.e.k.595.1		2
77.5	odd	30		121.2.c.e.3.1		4
77.19	even	30		121.2.c.a.9.1		4
77.26	odd	30		121.2.c.e.27.1		4
77.40	even	30		121.2.c.a.27.1		4
77.47	odd	30		121.2.c.e.9.1		4
77.54	even	6		121.2.a.d.1.1		1
77.61	even	30		121.2.c.a.3.1		4
77.65	odd	6		5929.2.a.h.1.1		1
77.68	even	30		121.2.c.a.81.1		4
77.75	odd	30		121.2.c.e.81.1		4
84.47	odd	6		1584.2.a.g.1.1		1
91.12	odd	6		1859.2.a.b.1.1		1
105.47	odd	12		2475.2.c.a.199.2		2
105.68	odd	12		2475.2.c.a.199.1		2
105.89	even	6		2475.2.a.a.1.1		1
112.5	odd	12		2816.2.c.j.1409.2		2
112.19	even	12		2816.2.c.f.1409.2		2
112.61	odd	12		2816.2.c.j.1409.1		2
112.75	even	12		2816.2.c.f.1409.1		2
119.33	odd	6		3179.2.a.a.1.1		1
133.75	even	6		3971.2.a.b.1.1		1
140.19	even	6		4400.2.a.i.1.1		1
140.47	odd	12		4400.2.b.h.4049.1		2
140.103	odd	12		4400.2.b.h.4049.2		2
161.68	even	6		5819.2.a.a.1.1		1
168.5	even	6		6336.2.a.br.1.1		1
168.131	odd	6		6336.2.a.bu.1.1		1
203.173	odd	6		9251.2.a.d.1.1		1
231.131	odd	6		1089.2.a.b.1.1		1
308.131	odd	6		1936.2.a.i.1.1		1
385.54	even	6		3025.2.a.a.1.1		1
616.131	odd	6		7744.2.a.k.1.1		1
616.285	even	6		7744.2.a.x.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.2.a.a.1.1	✓	1	7.5	odd	6
99.2.a.d.1.1		1	21.5	even	6
121.2.a.d.1.1		1	77.54	even	6
121.2.c.a.3.1		4	77.61	even	30
121.2.c.a.9.1		4	77.19	even	30
121.2.c.a.27.1		4	77.40	even	30
121.2.c.a.81.1		4	77.68	even	30
121.2.c.e.3.1		4	77.5	odd	30
121.2.c.e.9.1		4	77.47	odd	30
121.2.c.e.27.1		4	77.26	odd	30
121.2.c.e.81.1		4	77.75	odd	30
176.2.a.b.1.1		1	28.19	even	6
275.2.a.b.1.1		1	35.19	odd	6
275.2.b.a.199.1		2	35.12	even	12
275.2.b.a.199.2		2	35.33	even	12
539.2.a.a.1.1		1	7.2	even	3
539.2.e.g.67.1		2	7.4	even	3	inner
539.2.e.g.177.1		2	1.1	even	1	trivial
539.2.e.h.67.1		2	7.3	odd	6
539.2.e.h.177.1		2	7.6	odd	2
704.2.a.c.1.1		1	56.19	even	6
704.2.a.h.1.1		1	56.5	odd	6
891.2.e.b.298.1		2	63.5	even	6
891.2.e.b.595.1		2	63.47	even	6
891.2.e.k.298.1		2	63.40	odd	6
891.2.e.k.595.1		2	63.61	odd	6
1089.2.a.b.1.1		1	231.131	odd	6
1584.2.a.g.1.1		1	84.47	odd	6
1859.2.a.b.1.1		1	91.12	odd	6
1936.2.a.i.1.1		1	308.131	odd	6
2475.2.a.a.1.1		1	105.89	even	6
2475.2.c.a.199.1		2	105.68	odd	12
2475.2.c.a.199.2		2	105.47	odd	12
2816.2.c.f.1409.1		2	112.75	even	12
2816.2.c.f.1409.2		2	112.19	even	12
2816.2.c.j.1409.1		2	112.61	odd	12
2816.2.c.j.1409.2		2	112.5	odd	12
3025.2.a.a.1.1		1	385.54	even	6
3179.2.a.a.1.1		1	119.33	odd	6
3971.2.a.b.1.1		1	133.75	even	6
4400.2.a.i.1.1		1	140.19	even	6
4400.2.b.h.4049.1		2	140.47	odd	12
4400.2.b.h.4049.2		2	140.103	odd	12
4851.2.a.t.1.1		1	21.2	odd	6
5819.2.a.a.1.1		1	161.68	even	6
5929.2.a.h.1.1		1	77.65	odd	6
6336.2.a.br.1.1		1	168.5	even	6
6336.2.a.bu.1.1		1	168.131	odd	6
7744.2.a.k.1.1		1	616.131	odd	6
7744.2.a.x.1.1		1	616.285	even	6
8624.2.a.j.1.1		1	28.23	odd	6
9251.2.a.d.1.1		1	203.173	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} +(1.00000 - 1.73205i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-1.00000 + 1.73205i) q^{12} -4.00000 q^{13} -1.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(-2.00000 - 3.46410i) q^{18} -2.00000 q^{20} -2.00000 q^{22} +(0.500000 - 0.866025i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-4.00000 + 6.92820i) q^{26} -5.00000 q^{27} +(-1.00000 + 1.73205i) q^{30} +(3.50000 + 6.06218i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(-0.500000 + 0.866025i) q^{33} -4.00000 q^{34} -4.00000 q^{36} +(-1.50000 + 2.59808i) q^{37} +(2.00000 + 3.46410i) q^{39} +8.00000 q^{41} -6.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.00000 - 1.73205i) q^{45} +(-1.00000 - 1.73205i) q^{46} +(4.00000 - 6.92820i) q^{47} -4.00000 q^{48} +8.00000 q^{50} +(-1.00000 + 1.73205i) q^{51} +(4.00000 + 6.92820i) q^{52} +(3.00000 + 5.19615i) q^{53} +(-5.00000 + 8.66025i) q^{54} -1.00000 q^{55} +(2.50000 + 4.33013i) q^{59} +(1.00000 + 1.73205i) q^{60} +(6.00000 - 10.3923i) q^{61} +14.0000 q^{62} -8.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(1.00000 + 1.73205i) q^{66} +(3.50000 + 6.06218i) q^{67} +(-2.00000 + 3.46410i) q^{68} -1.00000 q^{69} -3.00000 q^{71} +(2.00000 + 3.46410i) q^{73} +(3.00000 + 5.19615i) q^{74} +(2.00000 - 3.46410i) q^{75} +8.00000 q^{78} +(5.00000 - 8.66025i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.00000 - 13.8564i) q^{82} +6.00000 q^{83} -2.00000 q^{85} +(-6.00000 + 10.3923i) q^{86} +(7.50000 - 12.9904i) q^{89} -4.00000 q^{90} -2.00000 q^{92} +(3.50000 - 6.06218i) q^{93} +(-8.00000 - 13.8564i) q^{94} +(-4.00000 + 6.92820i) q^{96} +7.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 - 2 * q^4 + q^5 - 4 * q^6 + 2 * q^9	\( 2 q + 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 4 q^{6} + 2 q^{9} - 2 q^{10} - q^{11} - 2 q^{12} - 8 q^{13} - 2 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} - 4 q^{20} - 4 q^{22} + q^{23} + 4 q^{25} - 8 q^{26} - 10 q^{27} - 2 q^{30} + 7 q^{31} - 8 q^{32} - q^{33} - 8 q^{34} - 8 q^{36} - 3 q^{37} + 4 q^{39} + 16 q^{41} - 12 q^{43} - 2 q^{44} - 2 q^{45} - 2 q^{46} + 8 q^{47} - 8 q^{48} + 16 q^{50} - 2 q^{51} + 8 q^{52} + 6 q^{53} - 10 q^{54} - 2 q^{55} + 5 q^{59} + 2 q^{60} + 12 q^{61} + 28 q^{62} - 16 q^{64} - 4 q^{65} + 2 q^{66} + 7 q^{67} - 4 q^{68} - 2 q^{69} - 6 q^{71} + 4 q^{73} + 6 q^{74} + 4 q^{75} + 16 q^{78} + 10 q^{79} - 4 q^{80} - q^{81} + 16 q^{82} + 12 q^{83} - 4 q^{85} - 12 q^{86} + 15 q^{89} - 8 q^{90} - 4 q^{92} + 7 q^{93} - 16 q^{94} - 8 q^{96} + 14 q^{97} - 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 - 2 * q^4 + q^5 - 4 * q^6 + 2 * q^9 - 2 * q^10 - q^11 - 2 * q^12 - 8 * q^13 - 2 * q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 - 4 * q^20 - 4 * q^22 + q^23 + 4 * q^25 - 8 * q^26 - 10 * q^27 - 2 * q^30 + 7 * q^31 - 8 * q^32 - q^33 - 8 * q^34 - 8 * q^36 - 3 * q^37 + 4 * q^39 + 16 * q^41 - 12 * q^43 - 2 * q^44 - 2 * q^45 - 2 * q^46 + 8 * q^47 - 8 * q^48 + 16 * q^50 - 2 * q^51 + 8 * q^52 + 6 * q^53 - 10 * q^54 - 2 * q^55 + 5 * q^59 + 2 * q^60 + 12 * q^61 + 28 * q^62 - 16 * q^64 - 4 * q^65 + 2 * q^66 + 7 * q^67 - 4 * q^68 - 2 * q^69 - 6 * q^71 + 4 * q^73 + 6 * q^74 + 4 * q^75 + 16 * q^78 + 10 * q^79 - 4 * q^80 - q^81 + 16 * q^82 + 12 * q^83 - 4 * q^85 - 12 * q^86 + 15 * q^89 - 8 * q^90 - 4 * q^92 + 7 * q^93 - 16 * q^94 - 8 * q^96 + 14 * q^97 - 4 * q^99

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