LMFDB - Embedded newform 847.2.l.g.118.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(118,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("847.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.l (of order $10$, degree $4$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{4} $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			118.3
Root			$0.891007 - 0.453990i$ of defining polynomial
Character	$\chi$	$=$	847.118
Dual form			847.2.l.g.524.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.831254 + 1.14412i) q^{2} +(-2.12663 + 0.690983i) q^{3} +(-1.31433 + 1.80902i) q^{5} +(-2.55834 - 1.85874i) q^{6} +(2.50609 - 0.848228i) q^{7} +(2.68999 - 0.874032i) q^{8} +(1.61803 - 1.17557i) q^{9} +O(q^{10})$	\(q+(0.831254 + 1.14412i) q^{2} +(-2.12663 + 0.690983i) q^{3} +(-1.31433 + 1.80902i) q^{5} +(-2.55834 - 1.85874i) q^{6} +(2.50609 - 0.848228i) q^{7} +(2.68999 - 0.874032i) q^{8} +(1.61803 - 1.17557i) q^{9} -3.16228 q^{10} +(5.11667 - 3.71748i) q^{13} +(3.05368 + 2.16219i) q^{14} +(1.54508 - 4.75528i) q^{15} +(3.23607 + 2.35114i) q^{16} +(2.68999 + 0.874032i) q^{18} +(0.977198 + 3.00750i) q^{19} +(-4.74342 + 3.53553i) q^{21} -3.00000 q^{23} +(-5.11667 + 3.71748i) q^{24} +(8.50651 + 2.76393i) q^{26} +(1.31433 - 1.80902i) q^{27} +(-1.34500 - 0.437016i) q^{29} +(6.72499 - 2.18508i) q^{30} +(3.94298 + 5.42705i) q^{31} +(-1.75937 + 5.64842i) q^{35} +(-0.309017 + 0.951057i) q^{37} +(-2.62866 + 3.61803i) q^{38} +(-8.31254 + 11.4412i) q^{39} +(-1.95440 + 6.01501i) q^{40} +(2.93159 + 9.02251i) q^{41} +(-7.98807 - 2.48812i) q^{42} +4.24264i q^{43} +4.47214i q^{45} +(-2.49376 - 3.43237i) q^{46} +(-4.25325 + 1.38197i) q^{47} +(-8.50651 - 2.76393i) q^{48} +(5.56102 - 4.25148i) q^{49} +3.16228 q^{54} +(6.00000 - 4.47214i) q^{56} +(-4.15627 - 5.72061i) q^{57} +(-0.618034 - 1.90211i) q^{58} +(-2.12663 - 0.690983i) q^{59} +(-2.55834 - 1.85874i) q^{61} +(-2.93159 + 9.02251i) q^{62} +(3.05779 - 4.31855i) q^{63} +(6.47214 - 4.70228i) q^{64} +14.1421i q^{65} +11.0000 q^{67} +(6.37988 - 2.07295i) q^{69} +(-7.92497 + 2.68233i) q^{70} +(-7.28115 - 5.29007i) q^{71} +(3.32502 - 4.57649i) q^{72} +(0.977198 - 3.00750i) q^{73} +(-1.34500 + 0.437016i) q^{74} -20.0000 q^{78} +(4.98752 + 6.86474i) q^{79} +(-8.50651 + 2.76393i) q^{80} +(-3.39919 + 10.4616i) q^{81} +(-7.88597 + 10.8541i) q^{82} +(7.67501 + 5.57622i) q^{83} +(-4.85410 + 3.52671i) q^{86} +3.16228 q^{87} -2.23607i q^{89} +(-5.11667 + 3.71748i) q^{90} +(9.66959 - 13.6565i) q^{91} +(-12.1353 - 8.81678i) q^{93} +(-5.11667 - 3.71748i) q^{94} +(-6.72499 - 2.18508i) q^{95} +(-3.94298 - 5.42705i) q^{97} +(9.48683 + 2.82843i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^9	$ 16 q + 8 q^{9} - 12 q^{14} - 20 q^{15} + 16 q^{16} - 48 q^{23} + 4 q^{37} - 20 q^{42} + 8 q^{49} + 96 q^{56} + 8 q^{58} + 32 q^{64} + 176 q^{67} + 20 q^{70} - 36 q^{71} - 320 q^{78} + 44 q^{81} - 24 q^{86} + 40 q^{91} - 60 q^{93}+O(q^{100}) $ 16 * q + 8 * q^9 - 12 * q^14 - 20 * q^15 + 16 * q^16 - 48 * q^23 + 4 * q^37 - 20 * q^42 + 8 * q^49 + 96 * q^56 + 8 * q^58 + 32 * q^64 + 176 * q^67 + 20 * q^70 - 36 * q^71 - 320 * q^78 + 44 * q^81 - 24 * q^86 + 40 * q^91 - 60 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.831254	+	1.14412i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$2$	0.831254	+	1.14412i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$3$	−2.12663	+	0.690983i	−1.22781	+	0.398939i	−0.849920	−	0.526912i	$-0.823350\pi$
$3$	−2.12663	+	0.690983i	−1.22781	+	0.398939i	−0.377889	+	0.925851i	$0.623350\pi$
$4$		0			0
$5$	−1.31433	+	1.80902i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$5$	−1.31433	+	1.80902i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$6$	−2.55834	−	1.85874i	−1.04444	−	0.758827i
$7$	2.50609	−	0.848228i	0.947215	−	0.320600i
$7$	2.50609	−	0.848228i	0.947215	−	0.320600i
$8$	2.68999	−	0.874032i	0.951057	−	0.309017i
$9$	1.61803	−	1.17557i	0.539345	−	0.391857i
$10$	−3.16228			−1.00000
$11$		0			0
$11$		0			0
$12$		0			0
$13$	5.11667	−	3.71748i	1.41911	−	1.03104i	0.427192	−	0.904161i	$-0.359503\pi$
$13$	5.11667	−	3.71748i	1.41911	−	1.03104i	0.991918	−	0.126883i	$-0.0404971\pi$
$14$	3.05368	+	2.16219i	0.816130	+	0.577869i
$15$	1.54508	−	4.75528i	0.398939	−	1.22781i
$16$	3.23607	+	2.35114i	0.809017	+	0.587785i
$17$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$17$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$18$	2.68999	+	0.874032i	0.634038	+	0.206011i
$19$	0.977198	+	3.00750i	0.224184	+	0.689969i	0.998373	+	0.0570143i	$0.0181581\pi$
$19$	0.977198	+	3.00750i	0.224184	+	0.689969i	−0.774189	+	0.632955i	$0.781842\pi$
$20$		0			0
$21$	−4.74342	+	3.53553i	−1.03510	+	0.771517i
$22$		0			0
$23$	−3.00000			−0.625543			−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000			−0.625543			−0.312772	+	0.949828i	$0.601257\pi$
$24$	−5.11667	+	3.71748i	−1.04444	+	0.758827i
$25$		0			0
$26$	8.50651	+	2.76393i	1.66826	+	0.542052i
$27$	1.31433	−	1.80902i	0.252942	−	0.348145i
$28$		0			0
$29$	−1.34500	−	0.437016i	−0.249760	−	0.0811518i	0.181462	−	0.983398i	$-0.441917\pi$
$29$	−1.34500	−	0.437016i	−0.249760	−	0.0811518i	−0.431221	+	0.902246i	$0.641917\pi$
$30$	6.72499	−	2.18508i	1.22781	−	0.398939i
$31$	3.94298	+	5.42705i	0.708181	+	0.974727i	0.999834	+	0.0182031i	$0.00579455\pi$
$31$	3.94298	+	5.42705i	0.708181	+	0.974727i	−0.291654	+	0.956524i	$0.594205\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.75937	+	5.64842i	−0.297388	+	0.954757i
$36$		0			0
$37$	−0.309017	+	0.951057i	−0.0508021	+	0.156353i	−0.973239	−	0.229795i	$-0.926194\pi$
$37$	−0.309017	+	0.951057i	−0.0508021	+	0.156353i	0.922437	+	0.386148i	$0.126194\pi$
$38$	−2.62866	+	3.61803i	−0.426424	+	0.586923i
$39$	−8.31254	+	11.4412i	−1.33107	+	1.83206i
$40$	−1.95440	+	6.01501i	−0.309017	+	0.951057i
$41$	2.93159	+	9.02251i	0.457838	+	1.40908i	0.867771	+	0.496964i	$0.165552\pi$
$41$	2.93159	+	9.02251i	0.457838	+	1.40908i	−0.409933	+	0.912116i	$0.634448\pi$
$42$	−7.98807	−	2.48812i	−1.23259	−	0.383926i
$43$			4.24264i			0.646997i	0.946229	+	0.323498i	$0.104859\pi$
$43$			4.24264i			0.646997i	−0.946229	+	0.323498i	$0.895141\pi$
$44$		0			0
$45$			4.47214i			0.666667i
$46$	−2.49376	−	3.43237i	−0.367685	−	0.506075i
$47$	−4.25325	+	1.38197i	−0.620401	+	0.201580i	−0.602318	−	0.798256i	$-0.705756\pi$
$47$	−4.25325	+	1.38197i	−0.620401	+	0.201580i	−0.0180826	+	0.999836i	$0.505756\pi$
$48$	−8.50651	−	2.76393i	−1.22781	−	0.398939i
$49$	5.56102	−	4.25148i	0.794431	−	0.607354i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$53$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$54$	3.16228			0.430331
$55$		0			0
$56$	6.00000	−	4.47214i	0.801784	−	0.597614i
$57$	−4.15627	−	5.72061i	−0.550511	−	0.757714i
$58$	−0.618034	−	1.90211i	−0.0811518	−	0.249760i
$59$	−2.12663	−	0.690983i	−0.276863	−	0.0899583i	0.167294	−	0.985907i	$-0.446497\pi$
$59$	−2.12663	−	0.690983i	−0.276863	−	0.0899583i	−0.444158	+	0.895949i	$0.646497\pi$
$60$		0			0
$61$	−2.55834	−	1.85874i	−0.327561	−	0.237987i	0.411834	−	0.911259i	$-0.364888\pi$
$61$	−2.55834	−	1.85874i	−0.327561	−	0.237987i	−0.739395	+	0.673272i	$0.764888\pi$
$62$	−2.93159	+	9.02251i	−0.372313	+	1.14586i
$63$	3.05779	−	4.31855i	0.385246	−	0.544087i
$64$	6.47214	−	4.70228i	0.809017	−	0.587785i
$65$			14.1421i			1.75412i
$66$		0			0
$67$	11.0000			1.34386			0.671932	−	0.740613i	$-0.265465\pi$
$67$	11.0000			1.34386			0.671932	+	0.740613i	$0.265465\pi$
$68$		0			0
$69$	6.37988	−	2.07295i	0.768047	−	0.249554i
$70$	−7.92497	+	2.68233i	−0.947215	+	0.320600i
$71$	−7.28115	−	5.29007i	−0.864114	−	0.627815i	0.0648872	−	0.997893i	$-0.479331\pi$
$71$	−7.28115	−	5.29007i	−0.864114	−	0.627815i	−0.929001	+	0.370077i	$0.879331\pi$
$72$	3.32502	−	4.57649i	0.391857	−	0.539345i
$73$	0.977198	−	3.00750i	0.114372	−	0.352002i	−0.877443	−	0.479680i	$-0.840753\pi$
$73$	0.977198	−	3.00750i	0.114372	−	0.352002i	0.991816	+	0.127679i	$0.0407526\pi$
$74$	−1.34500	+	0.437016i	−0.156353	+	0.0508021i
$75$		0			0
$76$		0			0
$77$		0			0
$78$	−20.0000			−2.26455
$79$	4.98752	+	6.86474i	0.561140	+	0.772343i	0.991471	−	0.130328i	$-0.0416031\pi$
$79$	4.98752	+	6.86474i	0.561140	+	0.772343i	−0.430331	+	0.902671i	$0.641603\pi$
$80$	−8.50651	+	2.76393i	−0.951057	+	0.309017i
$81$	−3.39919	+	10.4616i	−0.377687	+	1.16240i
$82$	−7.88597	+	10.8541i	−0.870859	+	1.19864i
$83$	7.67501	+	5.57622i	0.842442	+	0.612070i	0.923052	−	0.384676i	$-0.125687\pi$
$83$	7.67501	+	5.57622i	0.842442	+	0.612070i	−0.0806100	+	0.996746i	$0.525687\pi$
$84$		0			0
$85$		0			0
$86$	−4.85410	+	3.52671i	−0.523431	+	0.380295i
$87$	3.16228			0.339032
$88$		0			0
$89$		−	2.23607i		−	0.237023i	−0.992953	−	0.118511i	$-0.962188\pi$
$89$		−	2.23607i		−	0.237023i	0.992953	−	0.118511i	$-0.0378122\pi$
$90$	−5.11667	+	3.71748i	−0.539345	+	0.391857i
$91$	9.66959	−	13.6565i	1.01365	−	1.43159i
$92$		0			0
$93$	−12.1353	−	8.81678i	−1.25837	−	0.914257i
$94$	−5.11667	−	3.71748i	−0.527744	−	0.383429i
$95$	−6.72499	−	2.18508i	−0.689969	−	0.224184i
$96$		0			0
$97$	−3.94298	−	5.42705i	−0.400349	−	0.551034i	0.560482	−	0.828166i	$-0.310616\pi$
$97$	−3.94298	−	5.42705i	−0.400349	−	0.551034i	−0.960832	+	0.277133i	$0.910616\pi$
$98$	9.48683	+	2.82843i	0.958315	+	0.285714i
$99$		0			0
$100$		0			0
$101$	7.67501	−	5.57622i	0.763692	−	0.554855i	−0.136349	−	0.990661i	$-0.543537\pi$
$101$	7.67501	−	5.57622i	0.763692	−	0.554855i	0.900041	+	0.435806i	$0.143537\pi$
$102$		0			0
$103$	12.7598	+	4.14590i	1.25726	+	0.408507i	0.860516	−	0.509423i	$-0.170141\pi$
$103$	12.7598	+	4.14590i	1.25726	+	0.408507i	0.396741	+	0.917931i	$0.370141\pi$
$104$	10.5146	−	14.4721i	1.03104	−	1.41911i
$105$	−0.161437	−	13.2278i	−0.0157546	−	1.29090i
$106$		0			0
$107$	−2.68999	+	0.874032i	−0.260052	+	0.0844959i	−0.436141	−	0.899878i	$-0.643655\pi$
$107$	−2.68999	+	0.874032i	−0.260052	+	0.0844959i	0.176090	+	0.984374i	$0.443655\pi$
$108$		0			0
$109$		−	12.7279i		−	1.21911i	−0.792742	−	0.609557i	$-0.791347\pi$
$109$		−	12.7279i		−	1.21911i	0.792742	−	0.609557i	$-0.208653\pi$
$110$		0			0
$111$		−	2.23607i		−	0.212238i
$112$	10.1042	+	3.14726i	0.954757	+	0.297388i
$113$	−0.927051	−	2.85317i	−0.0872096	−	0.268404i	0.897936	−	0.440127i	$-0.145067\pi$
$113$	−0.927051	−	2.85317i	−0.0872096	−	0.268404i	−0.985145	+	0.171723i	$0.945067\pi$
$114$	3.09017	−	9.51057i	0.289421	−	0.890746i
$115$	3.94298	−	5.42705i	0.367685	−	0.506075i
$116$		0			0
$117$	3.90879	−	12.0300i	0.361368	−	1.11218i
$118$	−0.977198	−	3.00750i	−0.0899583	−	0.276863i
$119$		0			0
$120$		−	14.1421i		−	1.29099i
$121$		0			0
$122$		−	4.47214i		−	0.404888i
$123$	−12.4688	−	17.1618i	−1.12427	−	1.54743i
$124$		0			0
$125$	−10.6331	−	3.45492i	−0.951057	−	0.309017i
$126$	7.48276	−	0.0913225i	0.666617	−	0.00813565i
$127$	−7.48128	+	10.2971i	−0.663857	+	0.913720i	−0.999601	−	0.0282327i	$-0.991012\pi$
$127$	−7.48128	+	10.2971i	−0.663857	+	0.913720i	0.335745	+	0.941953i	$0.391012\pi$
$128$	10.7600	+	3.49613i	0.951057	+	0.309017i
$129$	−2.93159	−	9.02251i	−0.258112	−	0.794388i
$130$	−16.1803	+	11.7557i	−1.41911	+	1.03104i
$131$	−18.9737			−1.65774			−0.828868	−	0.559444i	$-0.811015\pi$
$131$	−18.9737			−1.65774			−0.828868	+	0.559444i	$0.811015\pi$
$132$		0			0
$133$	5.00000	+	6.70820i	0.433555	+	0.581675i
$134$	9.14379	+	12.5854i	0.789903	+	1.08721i
$135$	1.54508	+	4.75528i	0.132980	+	0.409270i
$136$		0			0
$137$	12.1353	+	8.81678i	1.03678	+	0.753268i	0.969655	−	0.244476i	$-0.0786159\pi$
$137$	12.1353	+	8.81678i	1.03678	+	0.753268i	0.0671295	+	0.997744i	$0.478616\pi$
$138$	7.67501	+	5.57622i	0.653340	+	0.474679i
$139$	3.90879	−	12.0300i	0.331539	−	1.02037i	−0.636862	−	0.770977i	$-0.719768\pi$
$139$	3.90879	−	12.0300i	0.331539	−	1.02037i	0.968402	−	0.249395i	$-0.0802319\pi$
$140$		0			0
$141$	8.09017	−	5.87785i	0.681315	−	0.495004i
$142$		−	12.7279i		−	1.06810i
$143$		0			0
$144$	8.00000			0.666667
$145$	2.55834	−	1.85874i	0.212458	−	0.154360i
$146$	4.25325	−	1.38197i	0.352002	−	0.114372i
$147$	−8.88851	+	12.8839i	−0.733112	+	1.06264i
$148$		0			0
$149$	11.6376	−	16.0177i	0.953386	−	1.31222i	0.00337853	−	0.999994i	$-0.498925\pi$
$149$	11.6376	−	16.0177i	0.953386	−	1.31222i	0.950007	−	0.312228i	$-0.101075\pi$
$150$		0			0
$151$	−16.1400	+	5.24419i	−1.31345	+	0.426766i	−0.880241	−	0.474526i	$-0.842619\pi$
$151$	−16.1400	+	5.24419i	−1.31345	+	0.426766i	−0.433210	+	0.901293i	$0.642619\pi$
$152$	5.25731	+	7.23607i	0.426424	+	0.586923i
$153$		0			0
$154$		0			0
$155$	−15.0000			−1.20483
$156$		0			0
$157$	6.37988	−	2.07295i	0.509170	−	0.165439i	−0.0431548	−	0.999068i	$-0.513741\pi$
$157$	6.37988	−	2.07295i	0.509170	−	0.165439i	0.552325	+	0.833629i	$0.313741\pi$
$158$	−3.70820	+	11.4127i	−0.295009	+	0.907944i
$159$		0			0
$160$		0			0
$161$	−7.51828	+	2.54469i	−0.592524	+	0.200549i
$162$	−14.7950	+	4.80718i	−1.16240	+	0.377687i
$163$	8.09017	−	5.87785i	0.633671	−	0.460389i	−0.223999	−	0.974589i	$-0.571911\pi$
$163$	8.09017	−	5.87785i	0.633671	−	0.460389i	0.857670	+	0.514200i	$0.171911\pi$
$164$		0			0
$165$		0			0
$166$			13.4164i			1.04132i
$167$	−7.67501	+	5.57622i	−0.593910	+	0.431501i	−0.843712	−	0.536796i	$-0.819634\pi$
$167$	−7.67501	+	5.57622i	−0.593910	+	0.431501i	0.249802	+	0.968297i	$0.419634\pi$
$168$	−9.66959	+	13.6565i	−0.746025	+	1.05362i
$169$	8.34346	−	25.6785i	0.641805	−	1.97527i
$170$		0			0
$171$	5.11667	+	3.71748i	0.391282	+	0.284283i
$172$		0			0
$173$	−2.93159	−	9.02251i	−0.222885	−	0.685969i	−0.998499	−	0.0547622i	$-0.982560\pi$
$173$	−2.93159	−	9.02251i	−0.222885	−	0.685969i	0.775615	−	0.631207i	$-0.217440\pi$
$174$	2.62866	+	3.61803i	0.199278	+	0.274282i
$175$		0			0
$176$		0			0
$177$	5.00000			0.375823
$178$	2.55834	−	1.85874i	0.191755	−	0.139318i
$179$	2.78115	+	8.55951i	0.207873	+	0.639768i	0.999583	+	0.0288706i	$0.00919109\pi$
$179$	2.78115	+	8.55951i	0.207873	+	0.639768i	−0.791710	+	0.610897i	$0.790809\pi$
$180$		0			0
$181$	−11.8290	+	16.2812i	−0.879239	+	1.21017i	0.0973922	+	0.995246i	$0.468950\pi$
$181$	−11.8290	+	16.2812i	−0.879239	+	1.21017i	−0.976631	+	0.214922i	$0.931050\pi$
$182$	23.6626	−	0.288787i	1.75399	−	0.0214063i
$183$	6.72499	+	2.18508i	0.497125	+	0.161526i
$184$	−8.06998	+	2.62210i	−0.594927	+	0.193303i
$185$	−1.31433	−	1.80902i	−0.0966313	−	0.133002i
$186$		−	21.2132i		−	1.55543i
$187$		0			0
$188$		0			0
$189$	1.75937	−	5.64842i	0.127975	−	0.410862i
$190$	−3.09017	−	9.51057i	−0.224184	−	0.689969i
$191$	0.927051	−	2.85317i	0.0670791	−	0.206448i	−0.911899	−	0.410416i	$-0.865384\pi$
$191$	0.927051	−	2.85317i	0.0670791	−	0.206448i	0.978978	+	0.203967i	$0.0653837\pi$
$192$	−10.5146	+	14.4721i	−0.758827	+	1.04444i
$193$	−2.49376	+	3.43237i	−0.179505	+	0.247067i	−0.889282	−	0.457359i	$-0.848796\pi$
$193$	−2.49376	+	3.43237i	−0.179505	+	0.247067i	0.709777	+	0.704426i	$0.248796\pi$
$194$	2.93159	−	9.02251i	0.210476	−	0.647779i
$195$	−9.77198	−	30.0750i	−0.699786	−	2.15372i
$196$		0			0
$197$		−	5.65685i		−	0.403034i	−0.979485	−	0.201517i	$-0.935413\pi$
$197$		−	5.65685i		−	0.403034i	0.979485	−	0.201517i	$-0.0645872\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$		0			0
$201$	−23.3929	+	7.60081i	−1.65001	+	0.536120i
$202$	12.7598	+	4.14590i	0.897774	+	0.291704i
$203$	−3.74138	+	0.0456612i	−0.262593	+	0.00320479i
$204$		0			0
$205$	−20.1750	−	6.55524i	−1.40908	−	0.457838i
$206$	5.86319	+	18.0450i	0.408507	+	1.25726i
$207$	−4.85410	+	3.52671i	−0.337383	+	0.245123i
$208$	25.2982			1.75412
$209$		0			0
$210$	15.0000	−	11.1803i	1.03510	−	0.771517i
$211$	−12.4688	−	17.1618i	−0.858388	−	1.18147i	−0.981951	−	0.189133i	$-0.939432\pi$
$211$	−12.4688	−	17.1618i	−0.858388	−	1.18147i	0.123563	−	0.992337i	$-0.460568\pi$
$212$		0			0
$213$	19.1396	+	6.21885i	1.31143	+	0.426108i
$214$	−3.23607	−	2.35114i	−0.221213	−	0.160721i
$215$	−7.67501	−	5.57622i	−0.523431	−	0.380295i
$216$	1.95440	−	6.01501i	0.132980	−	0.409270i
$217$	14.4849	+	10.2562i	0.983297	+	0.696233i
$218$	14.5623	−	10.5801i	0.986284	−	0.716577i
$219$			7.07107i			0.477818i
$220$		0			0
$221$		0			0
$222$	2.55834	−	1.85874i	0.171704	−	0.124750i
$223$	−6.37988	+	2.07295i	−0.427228	+	0.138815i	−0.514736	−	0.857349i	$-0.672110\pi$
$223$	−6.37988	+	2.07295i	−0.427228	+	0.138815i	0.0875072	+	0.996164i	$0.472110\pi$
$224$		0			0
$225$		0			0
$226$	2.49376	−	3.43237i	0.165883	−	0.228318i
$227$	−2.93159	+	9.02251i	−0.194577	+	0.598845i	0.805405	+	0.592725i	$0.201948\pi$
$227$	−2.93159	+	9.02251i	−0.194577	+	0.598845i	−0.999981	+	0.00611993i	$0.998052\pi$
$228$		0			0
$229$	3.94298	+	5.42705i	0.260560	+	0.358630i	0.919174	−	0.393851i	$-0.128857\pi$
$229$	3.94298	+	5.42705i	0.260560	+	0.358630i	−0.658615	+	0.752480i	$0.728857\pi$
$230$	9.48683			0.625543
$231$		0			0
$232$	−4.00000			−0.262613
$233$	10.8063	+	14.8736i	0.707944	+	0.974402i	0.999839	+	0.0179512i	$0.00571435\pi$
$233$	10.8063	+	14.8736i	0.707944	+	0.974402i	−0.291895	+	0.956450i	$0.594286\pi$
$234$	17.0130	−	5.52786i	1.11218	−	0.361368i
$235$	3.09017	−	9.51057i	0.201580	−	0.620401i
$236$		0			0
$237$	−15.3500	−	11.1524i	−0.997091	−	0.724429i
$238$		0			0
$239$	−6.72499	+	2.18508i	−0.435003	+	0.141341i	−0.518329	−	0.855181i	$-0.673446\pi$
$239$	−6.72499	+	2.18508i	−0.435003	+	0.141341i	0.0833259	+	0.996522i	$0.473446\pi$
$240$	16.1803	−	11.7557i	1.04444	−	0.758827i
$241$	12.6491			0.814801			0.407400	−	0.913250i	$-0.366435\pi$
$241$	12.6491			0.814801			0.407400	+	0.913250i	$0.366435\pi$
$242$		0			0
$243$		−	17.8885i		−	1.14755i
$244$		0			0
$245$	0.382001	+	15.6478i	0.0244051	+	0.999702i
$246$	9.27051	−	28.5317i	0.591066	−	1.81911i
$247$	16.1803	+	11.7557i	1.02953	+	0.747998i
$248$	15.3500	+	11.1524i	0.974727	+	0.708181i
$249$	−20.1750	−	6.55524i	−1.27854	−	0.415421i
$250$	−4.88599	−	15.0375i	−0.309017	−	0.951057i
$251$	−6.57164	−	9.04508i	−0.414798	−	0.570921i	0.549582	−	0.835440i	$-0.314787\pi$
$251$	−6.57164	−	9.04508i	−0.414798	−	0.570921i	−0.964381	+	0.264519i	$0.914787\pi$
$252$		0			0
$253$		0			0
$254$	−18.0000			−1.12942
$255$		0			0
$256$		0			0
$257$	−21.2663	−	6.90983i	−1.32655	−	0.431023i	−0.441813	−	0.897107i	$-0.645665\pi$
$257$	−21.2663	−	6.90983i	−1.32655	−	0.431023i	−0.884741	+	0.466084i	$0.845665\pi$
$258$	7.88597	−	10.8541i	0.490959	−	0.675747i
$259$	0.0322874	+	2.64555i	0.00200624	+	0.164387i
$260$		0			0
$261$	−2.68999	+	0.874032i	−0.166506	+	0.0541012i
$262$	−15.7719	−	21.7082i	−0.974393	−	1.34114i
$263$			11.3137i			0.697633i	0.937191	+	0.348817i	$0.113416\pi$
$263$			11.3137i			0.697633i	−0.937191	+	0.348817i	$0.886584\pi$
$264$		0			0
$265$		0			0
$266$	−3.51874	+	11.2968i	−0.215748	+	0.692653i
$267$	1.54508	+	4.75528i	0.0945577	+	0.291019i
$268$		0			0
$269$	10.5146	−	14.4721i	0.641088	−	0.882382i	−0.357585	−	0.933881i	$-0.616400\pi$
$269$	10.5146	−	14.4721i	0.641088	−	0.882382i	0.998673	+	0.0514988i	$0.0163998\pi$
$270$	−4.15627	+	5.72061i	−0.252942	+	0.348145i
$271$	−7.81758	+	24.0600i	−0.474884	+	1.46154i	0.371230	+	0.928541i	$0.378936\pi$
$271$	−7.81758	+	24.0600i	−0.474884	+	1.46154i	−0.846114	+	0.533002i	$0.821064\pi$
$272$		0			0
$273$	−11.1272	+	35.7237i	−0.673451	+	2.16210i
$274$			21.2132i			1.28154i
$275$		0			0
$276$		0			0
$277$	−2.49376	−	3.43237i	−0.149836	−	0.206231i	0.727501	−	0.686107i	$-0.240682\pi$
$277$	−2.49376	−	3.43237i	−0.149836	−	0.206231i	−0.877336	+	0.479876i	$0.840682\pi$
$278$	17.0130	−	5.52786i	1.02037	−	0.331539i
$279$	12.7598	+	4.14590i	0.763907	+	0.248208i
$280$	0.204203	+	16.7320i	0.0122035	+	0.999926i
$281$	14.1313	−	19.4501i	0.843004	−	1.16029i	−0.142358	−	0.989815i	$-0.545468\pi$
$281$	14.1313	−	19.4501i	0.843004	−	1.16029i	0.985361	−	0.170480i	$-0.0545317\pi$
$282$	13.4500	+	4.37016i	0.800934	+	0.260239i
$283$	−1.95440	−	6.01501i	−0.116177	−	0.357555i	0.876014	−	0.482286i	$-0.160193\pi$
$283$	−1.95440	−	6.01501i	−0.116177	−	0.357555i	−0.992191	+	0.124731i	$0.960193\pi$
$284$		0			0
$285$	15.8114			0.936586
$286$		0			0
$287$	15.0000	+	20.1246i	0.885422	+	1.18792i
$288$		0			0
$289$	−5.25329	−	16.1680i	−0.309017	−	0.951057i
$290$	4.25325	+	1.38197i	0.249760	+	0.0811518i
$291$	12.1353	+	8.81678i	0.711381	+	0.516849i
$292$		0			0
$293$	2.93159	−	9.02251i	0.171265	−	0.527101i	−0.828178	−	0.560465i	$-0.810622\pi$
$293$	2.93159	−	9.02251i	0.171265	−	0.527101i	0.999443	+	0.0333646i	$0.0106222\pi$
$294$	−22.1294	+	0.540231i	−1.29061	+	0.0315069i
$295$	4.04508	−	2.93893i	0.235514	−	0.171111i
$296$			2.82843i			0.164399i
$297$		0			0
$298$	28.0000			1.62200
$299$	−15.3500	+	11.1524i	−0.887714	+	0.644962i
$300$		0			0
$301$	3.59873	+	10.6325i	0.207427	+	0.612845i
$302$	−19.4164	−	14.1068i	−1.11729	−	0.811758i
$303$	−12.4688	+	17.1618i	−0.716314	+	0.985922i
$304$	−3.90879	+	12.0300i	−0.224184	+	0.689969i
$305$	6.72499	−	2.18508i	0.385072	−	0.125117i
$306$		0			0
$307$	−6.32456			−0.360961			−0.180481	−	0.983579i	$-0.557765\pi$
$307$	−6.32456			−0.360961			−0.180481	+	0.983579i	$0.557765\pi$
$308$		0			0
$309$	−30.0000			−1.70664
$310$	−12.4688	−	17.1618i	−0.708181	−	0.974727i
$311$	−4.25325	+	1.38197i	−0.241180	+	0.0783641i	−0.427113	−	0.904198i	$-0.640469\pi$
$311$	−4.25325	+	1.38197i	−0.241180	+	0.0783641i	0.185933	+	0.982562i	$0.440469\pi$
$312$	−12.3607	+	38.0423i	−0.699786	+	2.15372i
$313$	3.94298	−	5.42705i	0.222871	−	0.306755i	−0.682910	−	0.730503i	$-0.739286\pi$
$313$	3.94298	−	5.42705i	0.222871	−	0.306755i	0.905780	+	0.423748i	$0.139286\pi$
$314$	7.67501	+	5.57622i	0.433126	+	0.314684i
$315$	3.79339	+	11.2076i	0.213733	+	0.631476i
$316$		0			0
$317$	−16.9894	+	12.3435i	−0.954217	+	0.693279i	−0.951801	−	0.306718i	$-0.900769\pi$
$317$	−16.9894	+	12.3435i	−0.954217	+	0.693279i	−0.00241678	+	0.999997i	$0.500769\pi$
$318$		0			0
$319$		0			0
$320$			17.8885i			1.00000i
$321$	5.11667	−	3.71748i	0.285585	−	0.207490i
$322$	−9.16103	−	6.48656i	−0.510524	−	0.361482i
$323$		0			0
$324$		0			0
$325$		0			0
$326$	13.4500	+	4.37016i	0.744925	+	0.242041i
$327$	8.79478	+	27.0675i	0.486352	+	1.49684i
$328$	15.7719	+	21.7082i	0.870859	+	1.19864i
$329$	−9.48683	+	7.07107i	−0.523026	+	0.389841i
$330$		0			0
$331$	−19.0000			−1.04433			−0.522167	−	0.852843i	$-0.674876\pi$
$331$	−19.0000			−1.04433			−0.522167	+	0.852843i	$0.674876\pi$
$332$		0			0
$333$	0.618034	+	1.90211i	0.0338681	+	0.104235i
$334$	−12.7598	−	4.14590i	−0.698183	−	0.226853i
$335$	−14.4576	+	19.8992i	−0.789903	+	1.08721i
$336$	−23.6626	+	0.288787i	−1.29090	+	0.0157546i
$337$	−16.1400	−	5.24419i	−0.879200	−	0.285669i	−0.165575	−	0.986197i	$-0.552948\pi$
$337$	−16.1400	−	5.24419i	−0.879200	−	0.285669i	−0.713625	+	0.700528i	$0.752948\pi$
$338$	36.3149	−	11.7994i	1.97527	−	0.641805i
$339$	3.94298	+	5.42705i	0.214153	+	0.294757i
$340$		0			0
$341$		0			0
$342$			8.94427i			0.483651i
$343$	10.3302	−	15.3716i	0.557779	−	0.829990i
$344$	3.70820	+	11.4127i	0.199933	+	0.615330i
$345$	−4.63525	+	14.2658i	−0.249554	+	0.768047i
$346$	7.88597	−	10.8541i	0.423952	−	0.583520i
$347$	−0.831254	+	1.14412i	−0.0446240	+	0.0614197i	−0.830746	−	0.556652i	$-0.812086\pi$
$347$	−0.831254	+	1.14412i	−0.0446240	+	0.0614197i	0.786122	+	0.618071i	$0.212086\pi$
$348$		0			0
$349$	3.90879	+	12.0300i	0.209233	+	0.643952i	0.999513	+	0.0312066i	$0.00993497\pi$
$349$	3.90879	+	12.0300i	0.209233	+	0.643952i	−0.790280	+	0.612746i	$0.790065\pi$
$350$		0			0
$351$		−	14.1421i		−	0.754851i
$352$		0			0
$353$		−	15.6525i		−	0.833097i	−0.909113	−	0.416549i	$-0.863240\pi$
$353$		−	15.6525i		−	0.833097i	0.909113	−	0.416549i	$-0.136760\pi$
$354$	4.15627	+	5.72061i	0.220903	+	0.304047i
$355$	19.1396	−	6.21885i	1.01583	−	0.330062i
$356$		0			0
$357$		0			0
$358$	−7.48128	+	10.2971i	−0.395398	+	0.544219i
$359$	−5.37999	−	1.74806i	−0.283945	−	0.0922593i	0.163582	−	0.986530i	$-0.447695\pi$
$359$	−5.37999	−	1.74806i	−0.283945	−	0.0922593i	−0.447527	+	0.894270i	$0.647695\pi$
$360$	3.90879	+	12.0300i	0.206011	+	0.634038i
$361$	7.28115	−	5.29007i	0.383219	−	0.278425i
$362$	−28.4605			−1.49585
$363$		0			0
$364$		0			0
$365$	4.15627	+	5.72061i	0.217549	+	0.299431i
$366$	3.09017	+	9.51057i	0.161526	+	0.497125i
$367$	−31.8994	−	10.3647i	−1.66514	−	0.541035i	−0.683197	−	0.730234i	$-0.739411\pi$
$367$	−31.8994	−	10.3647i	−1.66514	−	0.541035i	−0.981939	+	0.189199i	$0.939411\pi$
$368$	−9.70820	−	7.05342i	−0.506075	−	0.367685i
$369$	15.3500	+	11.1524i	0.799090	+	0.580573i
$370$	0.977198	−	3.00750i	0.0508021	−	0.156353i
$371$		0			0
$372$		0			0
$373$		−	4.24264i		−	0.219676i	−0.993950	−	0.109838i	$-0.964967\pi$
$373$		−	4.24264i		−	0.219676i	0.993950	−	0.109838i	$-0.0350331\pi$
$374$		0			0
$375$	25.0000			1.29099
$376$	−10.2333	+	7.43496i	−0.527744	+	0.383429i
$377$	−8.50651	+	2.76393i	−0.438107	+	0.142350i
$378$	7.92497	−	2.68233i	0.407616	−	0.137964i
$379$	−13.7533	−	9.99235i	−0.706459	−	0.513273i	0.175570	−	0.984467i	$-0.443823\pi$
$379$	−13.7533	−	9.99235i	−0.706459	−	0.513273i	−0.882029	+	0.471194i	$0.843823\pi$
$380$		0			0
$381$	8.79478	−	27.0675i	0.450570	−	1.38671i
$382$	4.03499	−	1.31105i	0.206448	−	0.0670791i
$383$	−14.4576	−	19.8992i	−0.738749	−	1.01680i	−0.998690	−	0.0511763i	$-0.983703\pi$
$383$	−14.4576	−	19.8992i	−0.738749	−	1.01680i	0.259940	−	0.965625i	$-0.416297\pi$
$384$	−25.2982			−1.29099
$385$		0			0
$386$	−6.00000			−0.305392
$387$	4.98752	+	6.86474i	0.253530	+	0.348954i
$388$		0			0
$389$	0.927051	−	2.85317i	0.0470034	−	0.144661i	−0.924800	−	0.380453i	$-0.875768\pi$
$389$	0.927051	−	2.85317i	0.0470034	−	0.144661i	0.971804	+	0.235791i	$0.0757682\pi$
$390$	26.2866	−	36.1803i	1.33107	−	1.83206i
$391$		0			0
$392$	11.2432	−	16.2970i	0.567866	−	0.823121i
$393$	40.3499	−	13.1105i	2.03538	−	0.661336i
$394$	6.47214	−	4.70228i	0.326061	−	0.236898i
$395$	−18.9737			−0.954669
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$	−15.2684	−	10.8109i	−0.764376	−	0.541224i
$400$		0			0
$401$	−19.4164	−	14.1068i	−0.969609	−	0.704462i	−0.0142467	−	0.999899i	$-0.504535\pi$
$401$	−19.4164	−	14.1068i	−0.969609	−	0.704462i	−0.955362	+	0.295436i	$0.904535\pi$
$402$	−28.1417	−	20.4461i	−1.40358	−	1.01976i
$403$	40.3499	+	13.1105i	2.00997	+	0.653080i
$404$		0			0
$405$	−14.4576	−	19.8992i	−0.718404	−	0.988799i
$406$	−3.16228	−	4.24264i	−0.156941	−	0.210559i
$407$		0			0
$408$		0			0
$409$	−10.2333	+	7.43496i	−0.506006	+	0.367635i	−0.811307	−	0.584621i	$-0.801243\pi$
$409$	−10.2333	+	7.43496i	−0.506006	+	0.367635i	0.305300	+	0.952256i	$0.401243\pi$
$410$	−9.27051	−	28.5317i	−0.457838	−	1.40908i
$411$	−31.8994	−	10.3647i	−1.57348	−	0.511255i
$412$		0			0
$413$	−5.91564	+	0.0721968i	−0.291090	+	0.00355257i
$414$	−8.06998	−	2.62210i	−0.396618	−	0.128869i
$415$	−20.1750	+	6.55524i	−0.990350	+	0.321784i
$416$		0			0
$417$			28.2843i			1.38509i
$418$		0			0
$419$		−	22.3607i		−	1.09239i	−0.837658	−	0.546195i	$-0.816076\pi$
$419$		−	22.3607i		−	1.09239i	0.837658	−	0.546195i	$-0.183924\pi$
$420$		0			0
$421$	−1.23607	−	3.80423i	−0.0602423	−	0.185407i	0.916407	−	0.400249i	$-0.131076\pi$
$421$	−1.23607	−	3.80423i	−0.0602423	−	0.185407i	−0.976649	+	0.214842i	$0.931076\pi$
$422$	9.27051	−	28.5317i	0.451281	−	1.38890i
$423$	−5.25731	+	7.23607i	−0.255619	+	0.351830i
$424$		0			0
$425$		0			0
$426$	8.79478	+	27.0675i	0.426108	+	1.31143i
$427$	−7.98807	−	2.48812i	−0.386570	−	0.120409i
$428$		0			0
$429$		0			0
$430$		−	13.4164i		−	0.646997i
$431$	20.7813	+	28.6031i	1.00100	+	1.37776i	0.924708	+	0.380676i	$0.124309\pi$
$431$	20.7813	+	28.6031i	1.00100	+	1.37776i	0.0762938	+	0.997085i	$0.475691\pi$
$432$	8.50651	−	2.76393i	0.409270	−	0.132980i
$433$	19.1396	+	6.21885i	0.919793	+	0.298859i	0.730382	−	0.683039i	$-0.239342\pi$
$433$	19.1396	+	6.21885i	0.919793	+	0.298859i	0.189411	+	0.981898i	$0.439342\pi$
$434$	0.306305	+	25.0979i	0.0147031	+	1.20474i
$435$	−4.15627	+	5.72061i	−0.199278	+	0.274282i
$436$		0			0
$437$	−2.93159	−	9.02251i	−0.140237	−	0.431605i
$438$	−8.09017	+	5.87785i	−0.386563	+	0.280855i
$439$	−15.8114			−0.754636			−0.377318	−	0.926084i	$-0.623154\pi$
$439$	−15.8114			−0.754636			−0.377318	+	0.926084i	$0.623154\pi$
$440$		0			0
$441$	4.00000	−	13.4164i	0.190476	−	0.638877i
$442$		0			0
$443$	−4.63525	−	14.2658i	−0.220228	−	0.677791i	−0.998741	−	0.0501629i	$-0.984026\pi$
$443$	−4.63525	−	14.2658i	−0.220228	−	0.677791i	0.778513	−	0.627628i	$-0.215974\pi$
$444$		0			0
$445$	4.04508	+	2.93893i	0.191755	+	0.139318i
$446$	−7.67501	−	5.57622i	−0.363422	−	0.264042i
$447$	−13.6808	+	42.1051i	−0.647078	+	1.99150i
$448$	12.2312	−	17.2742i	0.577869	−	0.816130i
$449$	21.8435	−	15.8702i	1.03086	−	0.748961i	0.0623766	−	0.998053i	$-0.480132\pi$
$449$	21.8435	−	15.8702i	1.03086	−	0.748961i	0.968480	+	0.249092i	$0.0801320\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	30.7000	−	22.3049i	1.44241	−	1.04797i
$454$	−12.7598	+	4.14590i	−0.598845	+	0.194577i
$455$	11.9958	+	35.4415i	0.562370	+	1.66152i
$456$	−16.1803	−	11.7557i	−0.757714	−	0.550511i
$457$	−4.98752	+	6.86474i	−0.233306	+	0.321119i	−0.909578	−	0.415534i	$-0.863595\pi$
$457$	−4.98752	+	6.86474i	−0.233306	+	0.321119i	0.676271	+	0.736653i	$0.263595\pi$
$458$	−2.93159	+	9.02251i	−0.136984	+	0.421594i
$459$		0			0
$460$		0			0
$461$	−9.48683			−0.441846			−0.220923	−	0.975291i	$-0.570907\pi$
$461$	−9.48683			−0.441846			−0.220923	+	0.975291i	$0.570907\pi$
$462$		0			0
$463$	−25.0000			−1.16185			−0.580924	−	0.813958i	$-0.697309\pi$
$463$	−25.0000			−1.16185			−0.580924	+	0.813958i	$0.697309\pi$
$464$	−3.32502	−	4.57649i	−0.154360	−	0.212458i
$465$	31.8994	−	10.3647i	1.47930	−	0.480654i
$466$	−8.03444	+	24.7275i	−0.372188	+	1.14548i
$467$	6.57164	−	9.04508i	0.304099	−	0.418557i	−0.629430	−	0.777057i	$-0.716712\pi$
$467$	6.57164	−	9.04508i	0.304099	−	0.418557i	0.933530	+	0.358500i	$0.116712\pi$
$468$		0			0
$469$	27.5670	−	9.33051i	1.27293	−	0.430843i
$470$	13.4500	−	4.37016i	0.620401	−	0.201580i
$471$	−12.1353	+	8.81678i	−0.559163	+	0.406256i
$472$	−6.32456			−0.291111
$473$		0			0
$474$		−	26.8328i		−	1.23247i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−8.09017	−	5.87785i	−0.370036	−	0.268847i
$479$	−15.3500	−	11.1524i	−0.701360	−	0.509568i	0.179015	−	0.983846i	$-0.442709\pi$
$479$	−15.3500	−	11.1524i	−0.701360	−	0.509568i	−0.880375	+	0.474278i	$0.842709\pi$
$480$		0			0
$481$	1.95440	+	6.01501i	0.0891127	+	0.274261i
$482$	10.5146	+	14.4721i	0.478928	+	0.659188i
$483$	14.2302	−	10.6066i	0.647499	−	0.482617i
$484$		0			0
$485$	15.0000			0.681115
$486$	20.4667	−	14.8699i	0.928388	−	0.674513i
$487$	8.96149	+	27.5806i	0.406084	+	1.24980i	0.919987	+	0.391950i	$0.128199\pi$
$487$	8.96149	+	27.5806i	0.406084	+	1.24980i	−0.513903	+	0.857848i	$0.671801\pi$
$488$	−8.50651	−	2.76393i	−0.385072	−	0.125117i
$489$	−13.1433	+	18.0902i	−0.594360	+	0.818066i
$490$	−17.5855	+	13.4444i	−0.794431	+	0.607354i
$491$	30.9349	+	10.0514i	1.39607	+	0.453612i	0.907919	−	0.419145i	$-0.137670\pi$
$491$	30.9349	+	10.0514i	1.39607	+	0.453612i	0.488155	+	0.872757i	$0.337670\pi$
$492$		0			0
$493$		0			0
$494$			28.2843i			1.27257i
$495$		0			0
$496$			26.8328i			1.20483i
$497$	−22.7344	−	7.08133i	−1.01978	−	0.317641i
$498$	−9.27051	−	28.5317i	−0.415421	−	1.27854i
$499$	−4.94427	+	15.2169i	−0.221336	+	0.681202i	0.777307	+	0.629122i	$0.216585\pi$
$499$	−4.94427	+	15.2169i	−0.221336	+	0.681202i	−0.998643	+	0.0520806i	$0.983415\pi$
$500$		0			0
$501$	12.4688	−	17.1618i	0.557065	−	0.766735i
$502$	4.88599	−	15.0375i	0.218072	−	0.671158i
$503$	8.79478	+	27.0675i	0.392140	+	1.20688i	0.931167	+	0.364594i	$0.118792\pi$
$503$	8.79478	+	27.0675i	0.392140	+	1.20688i	−0.539027	+	0.842288i	$0.681208\pi$
$504$	4.45089	−	14.2895i	0.198259	−	0.636505i
$505$			21.2132i			0.943975i
$506$		0			0
$507$			60.3738i			2.68130i
$508$		0			0
$509$	14.8864	−	4.83688i	0.659828	−	0.214391i	0.0400852	−	0.999196i	$-0.487237\pi$
$509$	14.8864	−	4.83688i	0.659828	−	0.214391i	0.619742	+	0.784805i	$0.287237\pi$
$510$		0			0
$511$	−0.102102	−	8.36598i	−0.00451671	−	0.370089i
$512$	13.3001	−	18.3060i	0.587785	−	0.809017i
$513$	6.72499	+	2.18508i	0.296915	+	0.0964736i
$514$	−9.77198	−	30.0750i	−0.431023	−	1.32655i
$515$	−24.2705	+	17.6336i	−1.06949	+	0.777027i
$516$		0			0
$517$		0			0
$518$	−3.00000	+	2.23607i	−0.131812	+	0.0982472i
$519$	12.4688	+	17.1618i	0.547320	+	0.753321i
$520$	12.3607	+	38.0423i	0.542052	+	1.66826i
$521$	10.6331	+	3.45492i	0.465846	+	0.151363i	0.532529	−	0.846412i	$-0.321242\pi$
$521$	10.6331	+	3.45492i	0.465846	+	0.151363i	−0.0666831	+	0.997774i	$0.521242\pi$
$522$	−3.23607	−	2.35114i	−0.141639	−	0.102907i
$523$	−25.5834	−	18.5874i	−1.11868	−	0.812770i	−0.134674	−	0.990890i	$-0.542999\pi$
$523$	−25.5834	−	18.5874i	−1.11868	−	0.812770i	−0.984009	+	0.178120i	$0.942999\pi$
$524$		0			0
$525$		0			0
$526$	−12.9443	+	9.40456i	−0.564397	+	0.410058i
$527$		0			0
$528$		0			0
$529$	−14.0000			−0.608696
$530$		0			0
$531$	−4.25325	+	1.38197i	−0.184576	+	0.0599722i
$532$		0			0
$533$	48.5410	+	35.2671i	2.10254	+	1.52759i
$534$	−4.15627	+	5.72061i	−0.179859	+	0.247555i
$535$	1.95440	−	6.01501i	0.0844959	−	0.260052i
$536$	29.5899	−	9.61435i	1.27809	−	0.415277i
$537$	−11.8290	−	16.2812i	−0.510457	−	0.702584i
$538$	25.2982			1.09068
$539$		0			0
$540$		0			0
$541$	−14.9626	−	20.5942i	−0.643291	−	0.885414i	0.355495	−	0.934678i	$-0.384312\pi$
$541$	−14.9626	−	20.5942i	−0.643291	−	0.885414i	−0.998786	+	0.0492640i	$0.984312\pi$
$542$	−34.0260	+	11.0557i	−1.46154	+	0.474884i
$543$	13.9058	−	42.7975i	0.596753	−	1.83662i
$544$		0			0
$545$	23.0250	+	16.7287i	0.986284	+	0.716577i
$546$	−50.1219	+	16.9646i	−2.14502	+	0.726016i
$547$	8.06998	−	2.62210i	0.345048	−	0.112113i	−0.131366	−	0.991334i	$-0.541936\pi$
$547$	8.06998	−	2.62210i	0.345048	−	0.112113i	0.476414	+	0.879221i	$0.341936\pi$
$548$		0			0
$549$	−6.32456			−0.269925
$550$		0			0
$551$		−	4.47214i		−	0.190519i
$552$	15.3500	−	11.1524i	0.653340	−	0.474679i
$553$	18.3221	+	12.9731i	0.779134	+	0.551673i
$554$	1.85410	−	5.70634i	0.0787732	−	0.242439i
$555$	4.04508	+	2.93893i	0.171704	+	0.124750i
$556$		0			0
$557$	−21.5200	−	6.99226i	−0.911830	−	0.296271i	−0.184719	−	0.982791i	$-0.559137\pi$
$557$	−21.5200	−	6.99226i	−0.911830	−	0.296271i	−0.727111	+	0.686520i	$0.759137\pi$
$558$	5.86319	+	18.0450i	0.248208	+	0.763907i
$559$	15.7719	+	21.7082i	0.667082	+	0.918159i
$560$	−18.9737	+	14.1421i	−0.801784	+	0.597614i
$561$		0			0
$562$	34.0000			1.43420
$563$	−30.7000	+	22.3049i	−1.29385	+	0.940039i	−0.999876	−	0.0157739i	$-0.994979\pi$
$563$	−30.7000	+	22.3049i	−1.29385	+	0.940039i	−0.293977	+	0.955813i	$0.594979\pi$
$564$		0			0
$565$	6.37988	+	2.07295i	0.268404	+	0.0872096i
$566$	5.25731	−	7.23607i	0.220981	−	0.304155i
$567$	0.355161	+	29.1011i	0.0149154	+	1.22213i
$568$	−24.2099	−	7.86629i	−1.01583	−	0.330062i
$569$	−14.7950	+	4.80718i	−0.620237	+	0.201527i	−0.602246	−	0.798311i	$-0.705727\pi$
$569$	−14.7950	+	4.80718i	−0.620237	+	0.201527i	−0.0179916	+	0.999838i	$0.505727\pi$
$570$	13.1433	+	18.0902i	0.550511	+	0.757714i
$571$		−	16.9706i		−	0.710196i	−0.934829	−	0.355098i	$-0.884448\pi$
$571$		−	16.9706i		−	0.710196i	0.934829	−	0.355098i	$-0.115552\pi$
$572$		0			0
$573$			6.70820i			0.280239i
$574$	−10.5562	+	33.8905i	−0.440608	+	1.41456i
$575$		0			0
$576$	4.94427	−	15.2169i	0.206011	−	0.634038i
$577$	11.8290	−	16.2812i	0.492446	−	0.677793i	−0.488391	−	0.872625i	$-0.662416\pi$
$577$	11.8290	−	16.2812i	0.492446	−	0.677793i	0.980837	+	0.194832i	$0.0624160\pi$
$578$	14.1313	−	19.4501i	0.587785	−	0.809017i
$579$	2.93159	−	9.02251i	0.121833	−	0.374963i
$580$		0			0
$581$	23.9642	+	7.46437i	0.994203	+	0.309674i
$582$			21.2132i			0.879316i
$583$		0			0
$584$		−	8.94427i		−	0.370117i
$585$	16.6251	+	22.8825i	0.687362	+	0.946073i
$586$	12.7598	−	4.14590i	0.527101	−	0.171265i
$587$	4.25325	+	1.38197i	0.175551	+	0.0570398i	0.395473	−	0.918477i	$-0.370581\pi$
$587$	4.25325	+	1.38197i	0.175551	+	0.0570398i	−0.219923	+	0.975517i	$0.570581\pi$
$588$		0			0
$589$	−12.4688	+	17.1618i	−0.513768	+	0.707141i
$590$	6.72499	+	2.18508i	0.276863	+	0.0899583i
$591$	3.90879	+	12.0300i	0.160786	+	0.494849i
$592$	−3.23607	+	2.35114i	−0.133002	+	0.0966313i
$593$	28.4605			1.16873			0.584366	−	0.811490i	$-0.301343\pi$
$593$	28.4605			1.16873			0.584366	+	0.811490i	$0.301343\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−25.5195	−	8.29180i	−1.04357	−	0.339077i
$599$	9.70820	+	7.05342i	0.396666	+	0.288195i	0.768182	−	0.640232i	$-0.221162\pi$
$599$	9.70820	+	7.05342i	0.396666	+	0.288195i	−0.371515	+	0.928427i	$0.621162\pi$
$600$		0			0
$601$	−4.88599	+	15.0375i	−0.199304	+	0.613393i	0.800596	+	0.599205i	$0.204517\pi$
$601$	−4.88599	+	15.0375i	−0.199304	+	0.613393i	−0.999899	+	0.0141885i	$0.995483\pi$
$602$	−9.17338	+	12.9557i	−0.373879	+	0.528033i
$603$	17.7984	−	12.9313i	0.724806	−	0.526602i
$604$		0			0
$605$		0			0
$606$	−30.0000			−1.21867
$607$	5.11667	−	3.71748i	0.207679	−	0.150888i	−0.479084	−	0.877769i	$-0.659031\pi$
$607$	5.11667	−	3.71748i	0.207679	−	0.150888i	0.686763	+	0.726881i	$0.259031\pi$
$608$		0			0
$609$	7.92497	−	2.68233i	0.321136	−	0.108694i
$610$	8.09017	+	5.87785i	0.327561	+	0.237987i
$611$	−16.6251	+	22.8825i	−0.672579	+	0.925725i
$612$		0			0
$613$	24.2099	−	7.86629i	0.977831	−	0.317716i	0.223858	−	0.974622i	$-0.428135\pi$
$613$	24.2099	−	7.86629i	0.977831	−	0.317716i	0.753973	+	0.656905i	$0.228135\pi$
$614$	−5.25731	−	7.23607i	−0.212168	−	0.292024i
$615$	47.4342			1.91273
$616$		0			0
$617$	24.0000			0.966204			0.483102	−	0.875564i	$-0.339510\pi$
$617$	24.0000			0.966204			0.483102	+	0.875564i	$0.339510\pi$
$618$	−24.9376	−	34.3237i	−1.00314	−	1.38070i
$619$	−44.6592	+	14.5106i	−1.79500	+	0.583232i	−0.999735	−	0.0230252i	$-0.992670\pi$
$619$	−44.6592	+	14.5106i	−1.79500	+	0.583232i	−0.795269	+	0.606257i	$0.792670\pi$
$620$		0			0
$621$	−3.94298	+	5.42705i	−0.158226	+	0.217780i
$622$	−5.11667	−	3.71748i	−0.205160	−	0.149057i
$623$	−1.89670	−	5.60380i	−0.0759895	−	0.224511i
$624$	−53.7999	+	17.4806i	−2.15372	+	0.699786i
$625$	20.2254	−	14.6946i	0.809017	−	0.587785i
$626$	9.48683			0.379170
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−9.66959	+	13.6565i	−0.385246	+	0.544087i
$631$	3.39919	−	10.4616i	0.135319	−	0.416471i	−0.860320	−	0.509754i	$-0.829736\pi$
$631$	3.39919	−	10.4616i	0.135319	−	0.416471i	0.995640	+	0.0932836i	$0.0297363\pi$
$632$	19.4164	+	14.1068i	0.772343	+	0.561140i
$633$	38.3750	+	27.8811i	1.52527	+	1.10817i
$634$	−28.2449	−	9.17734i	−1.12175	−	0.364479i
$635$	−8.79478	−	27.0675i	−0.349010	−	1.07414i
$636$		0			0
$637$	12.6491	−	42.4264i	0.501176	−	1.68100i
$638$		0			0
$639$	−18.0000			−0.712069
$640$	−20.4667	+	14.8699i	−0.809017	+	0.587785i
$641$	6.48936	+	19.9722i	0.256314	+	0.788854i	0.993568	+	0.113238i	$0.0361222\pi$
$641$	6.48936	+	19.9722i	0.256314	+	0.788854i	−0.737254	+	0.675616i	$0.763878\pi$
$642$	8.50651	+	2.76393i	0.335725	+	0.109084i
$643$	−3.94298	+	5.42705i	−0.155496	+	0.214022i	−0.879656	−	0.475610i	$-0.842228\pi$
$643$	−3.94298	+	5.42705i	−0.155496	+	0.214022i	0.724160	+	0.689632i	$0.242228\pi$
$644$		0			0
$645$	20.1750	+	6.55524i	0.794388	+	0.258112i
$646$		0			0
$647$	17.0863	+	23.5172i	0.671730	+	0.924557i	0.999798	−	0.0200968i	$-0.00639745\pi$
$647$	17.0863	+	23.5172i	0.671730	+	0.924557i	−0.328068	+	0.944654i	$0.606397\pi$
$648$			31.1127i			1.22222i
$649$		0			0
$650$		0			0
$651$	−37.8907	−	11.8022i	−1.48505	−	0.462565i
$652$		0			0
$653$	4.63525	−	14.2658i	0.181392	−	0.558266i	−0.818476	−	0.574541i	$-0.805181\pi$
$653$	4.63525	−	14.2658i	0.181392	−	0.558266i	0.999868	+	0.0162749i	$0.00518070\pi$
$654$	−23.6579	+	32.5623i	−0.925097	+	1.27329i
$655$	24.9376	−	34.3237i	0.974393	−	1.34114i
$656$	−11.7264	+	36.0901i	−0.457838	+	1.40908i
$657$	−1.95440	−	6.01501i	−0.0762482	−	0.234668i
$658$	−15.9761	−	4.97625i	−0.622815	−	0.193994i
$659$		−	14.1421i		−	0.550899i	−0.961315	−	0.275450i	$-0.911173\pi$
$659$		−	14.1421i		−	0.550899i	0.961315	−	0.275450i	$-0.0888267\pi$
$660$		0			0
$661$		−	46.9574i		−	1.82643i	−0.407476	−	0.913216i	$-0.633591\pi$
$661$		−	46.9574i		−	1.82643i	0.407476	−	0.913216i	$-0.366409\pi$
$662$	−15.7938	−	21.7383i	−0.613844	−	0.844884i
$663$		0			0
$664$	25.5195	+	8.29180i	0.990350	+	0.321784i
$665$	−18.7069	+	0.228306i	−0.725422	+	0.00885333i
$666$	−1.66251	+	2.28825i	−0.0644209	+	0.0886677i
$667$	4.03499	+	1.31105i	0.156235	+	0.0507640i
$668$		0			0
$669$	12.1353	−	8.81678i	0.469176	−	0.340876i
$670$	−34.7851			−1.34386
$671$		0			0
$672$		0			0
$673$	−17.4563	−	24.0266i	−0.672892	−	0.926157i	0.326929	−	0.945049i	$-0.393986\pi$
$673$	−17.4563	−	24.0266i	−0.672892	−	0.926157i	−0.999822	+	0.0188922i	$0.993986\pi$
$674$	−7.41641	−	22.8254i	−0.285669	−	0.879200i
$675$		0			0
$676$		0			0
$677$	30.7000	+	22.3049i	1.17990	+	0.857246i	0.992160	−	0.124973i	$-0.0398844\pi$
$677$	30.7000	+	22.3049i	1.17990	+	0.857246i	0.187738	+	0.982219i	$0.439884\pi$
$678$	−2.93159	+	9.02251i	−0.112587	+	0.346508i
$679$	−14.4849	−	10.2562i	−0.555878	−	0.393595i
$680$		0			0
$681$		−	21.2132i		−	0.812892i
$682$		0			0
$683$	18.0000			0.688751			0.344375	−	0.938832i	$-0.388091\pi$
$683$	18.0000			0.688751			0.344375	+	0.938832i	$0.388091\pi$
$684$		0			0
$685$	−31.8994	+	10.3647i	−1.21881	+	0.396017i
$686$	26.1741	−	0.958696i	0.999330	−	0.0366032i
$687$	−12.1353	−	8.81678i	−0.462989	−	0.336381i
$688$	−9.97505	+	13.7295i	−0.380295	+	0.523431i
$689$		0			0
$690$	−20.1750	+	6.55524i	−0.768047	+	0.249554i
$691$	−3.94298	−	5.42705i	−0.149998	−	0.206455i	0.727405	−	0.686208i	$-0.240726\pi$
$691$	−3.94298	−	5.42705i	−0.149998	−	0.206455i	−0.877403	+	0.479753i	$0.840726\pi$
$692$		0			0
$693$		0			0
$694$	−2.00000			−0.0759190
$695$	16.6251	+	22.8825i	0.630625	+	0.867981i
$696$	8.50651	−	2.76393i	0.322438	−	0.104767i
$697$		0			0
$698$	−10.5146	+	14.4721i	−0.397984	+	0.547778i
$699$	−33.2584	−	24.1636i	−1.25795	−	0.913952i
$700$		0			0
$701$	−6.72499	+	2.18508i	−0.253999	+	0.0825293i	−0.433249	−	0.901274i	$-0.642633\pi$
$701$	−6.72499	+	2.18508i	−0.253999	+	0.0825293i	0.179250	+	0.983804i	$0.442633\pi$
$702$	16.1803	−	11.7557i	0.610688	−	0.443690i
$703$	−3.16228			−0.119268
$704$		0			0
$705$			22.3607i			0.842152i
$706$	17.9084	−	13.0112i	0.673990	−	0.489682i
$707$	14.5044	−	20.4847i	0.545494	−	0.770406i
$708$		0			0
$709$	−33.1697	−	24.0992i	−1.24571	−	0.905064i	−0.247749	−	0.968824i	$-0.579691\pi$
$709$	−33.1697	−	24.0992i	−1.24571	−	0.905064i	−0.997965	+	0.0637600i	$0.979691\pi$
$710$	23.0250	+	16.7287i	0.864114	+	0.627815i
$711$	16.1400	+	5.24419i	0.605296	+	0.196673i
$712$	−1.95440	−	6.01501i	−0.0732441	−	0.225422i
$713$	−11.8290	−	16.2812i	−0.442998	−	0.609734i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	12.7917	−	9.29370i	0.477714	−	0.347080i
$718$	−2.47214	−	7.60845i	−0.0922593	−	0.283945i
$719$	48.9124	+	15.8926i	1.82413	+	0.592694i	0.999641	+	0.0268105i	$0.00853506\pi$
$719$	48.9124	+	15.8926i	1.82413	+	0.592694i	0.824485	+	0.565884i	$0.191465\pi$
$720$	−10.5146	+	14.4721i	−0.391857	+	0.539345i
$721$	35.4938	−	0.433181i	1.32186	−	0.0161325i
$722$	12.1050	+	3.93314i	0.450500	+	0.146376i
$723$	−26.8999	+	8.74032i	−1.00042	+	0.325056i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	33.5410i		−	1.24397i	−0.783030	−	0.621984i	$-0.786327\pi$
$727$		−	33.5410i		−	1.24397i	0.783030	−	0.621984i	$-0.213673\pi$
$728$	14.0750	−	45.1873i	0.521653	−	1.67475i
$729$	2.16312	+	6.65740i	0.0801155	+	0.246570i
$730$	−3.09017	+	9.51057i	−0.114372	+	0.352002i
$731$		0			0
$732$		0			0
$733$	3.90879	−	12.0300i	0.144374	−	0.444339i	−0.852556	−	0.522637i	$-0.824948\pi$
$733$	3.90879	−	12.0300i	0.144374	−	0.444339i	0.996930	+	0.0782977i	$0.0249485\pi$
$734$	−14.6580	−	45.1126i	−0.541035	−	1.66514i
$735$	−11.6247	−	33.0131i	−0.428785	−	1.21771i
$736$		0			0
$737$		0			0
$738$			26.8328i			0.987730i
$739$	29.9251	+	41.1884i	1.10081	+	1.51514i	0.834301	+	0.551309i	$0.185872\pi$
$739$	29.9251	+	41.1884i	1.10081	+	1.51514i	0.266513	+	0.963831i	$0.414128\pi$
$740$		0			0
$741$	−42.5325	−	13.8197i	−1.56247	−	0.507678i
$742$		0			0
$743$	11.6376	−	16.0177i	0.426940	−	0.587633i	−0.540307	−	0.841468i	$-0.681692\pi$
$743$	11.6376	−	16.0177i	0.426940	−	0.587633i	0.967248	+	0.253835i	$0.0816919\pi$
$744$	−40.3499	−	13.1105i	−1.47930	−	0.480654i
$745$	13.6808	+	42.1051i	0.501224	+	1.54261i
$746$	4.85410	−	3.52671i	0.177721	−	0.129122i
$747$	18.9737			0.694210
$748$		0			0
$749$	−6.00000	+	4.47214i	−0.219235	+	0.163408i
$750$	20.7813	+	28.6031i	0.758827	+	1.04444i
$751$	−2.16312	−	6.65740i	−0.0789333	−	0.242932i	0.903801	−	0.427952i	$-0.140765\pi$
$751$	−2.16312	−	6.65740i	−0.0789333	−	0.242932i	−0.982735	+	0.185020i	$0.940765\pi$
$752$	−17.0130	−	5.52786i	−0.620401	−	0.201580i
$753$	20.2254	+	14.6946i	0.737055	+	0.535502i
$754$	−10.2333	−	7.43496i	−0.372676	−	0.270765i
$755$	11.7264	−	36.0901i	0.426766	−	1.31345i
$756$		0			0
$757$	−35.5967	+	25.8626i	−1.29379	+	0.939990i	−0.999875	−	0.0158423i	$-0.994957\pi$
$757$	−35.5967	+	25.8626i	−1.29379	+	0.939990i	−0.293911	+	0.955833i	$0.594957\pi$
$758$		−	24.0416i		−	0.873231i
$759$		0			0
$760$	−20.0000			−0.725476
$761$	−30.7000	+	22.3049i	−1.11288	+	0.808551i	−0.983114	−	0.182994i	$-0.941421\pi$
$761$	−30.7000	+	22.3049i	−1.11288	+	0.808551i	−0.129761	+	0.991545i	$0.541421\pi$
$762$	38.2793	−	12.4377i	1.38671	−	0.450570i
$763$	−10.7962	−	31.8974i	−0.390848	−	1.15476i
$764$		0			0
$765$		0			0
$766$	10.7492	−	33.0826i	0.388383	−	1.19532i
$767$	−13.4500	+	4.37016i	−0.485650	+	0.157797i
$768$		0			0
$769$	−6.32456			−0.228069			−0.114035	−	0.993477i	$-0.536377\pi$
$769$	−6.32456			−0.228069			−0.114035	+	0.993477i	$0.536377\pi$
$770$		0			0
$771$	50.0000			1.80071
$772$		0			0
$773$	8.50651	−	2.76393i	0.305958	−	0.0994117i	−0.152014	−	0.988378i	$-0.548576\pi$
$773$	8.50651	−	2.76393i	0.305958	−	0.0994117i	0.457972	+	0.888967i	$0.348576\pi$
$774$	−3.70820	+	11.4127i	−0.133289	+	0.410220i
$775$		0			0
$776$	−15.3500	−	11.1524i	−0.551034	−	0.400349i
$777$	−1.89670	−	5.60380i	−0.0680436	−	0.201035i
$778$	4.03499	−	1.31105i	0.144661	−	0.0470034i
$779$	−24.2705	+	17.6336i	−0.869581	+	0.631788i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−2.55834	+	1.85874i	−0.0914275	+	0.0664260i
$784$	27.9917	−	0.683344i	0.999702	−	0.0244051i
$785$	−4.63525	+	14.2658i	−0.165439	+	0.509170i
$786$	48.5410	+	35.2671i	1.73140	+	1.25794i
$787$	−17.9084	−	13.0112i	−0.638364	−	0.463799i	0.220924	−	0.975291i	$-0.429093\pi$
$787$	−17.9084	−	13.0112i	−0.638364	−	0.463799i	−0.859288	+	0.511493i	$0.829093\pi$
$788$		0			0
$789$	−7.81758	−	24.0600i	−0.278313	−	0.856560i
$790$	−15.7719	−	21.7082i	−0.561140	−	0.772343i
$791$	−4.74342	−	6.36396i	−0.168656	−	0.226276i
$792$		0			0
$793$	−20.0000			−0.710221
$794$		0			0
$795$		0			0
$796$		0			0
$797$	22.3436	−	30.7533i	0.791450	−	1.08934i	−0.202476	−	0.979287i	$-0.564899\pi$
$797$	22.3436	−	30.7533i	0.791450	−	1.08934i	0.993926	−	0.110050i	$-0.0351012\pi$
$798$	−0.322874	−	26.4555i	−0.0114296	−	0.936516i
$799$		0			0
$800$		0			0
$801$	−2.62866	−	3.61803i	−0.0928790	−	0.127837i
$802$		−	33.9411i		−	1.19850i
$803$		0			0
$804$		0			0
$805$	5.27811	−	16.9453i	0.186029	−	0.597242i
$806$	18.5410	+	57.0634i	0.653080	+	2.00997i
$807$	−12.3607	+	38.0423i	−0.435117	+	1.33915i
$808$	15.7719	−	21.7082i	0.554855	−	0.763692i
$809$	24.1064	−	33.1796i	0.847535	−	1.16653i	−0.136866	−	0.990590i	$-0.543703\pi$
$809$	24.1064	−	33.1796i	0.847535	−	1.16653i	0.984401	−	0.175942i	$-0.0562970\pi$
$810$	10.7492	−	33.0826i	0.377687	−	1.16240i
$811$	−7.81758	−	24.0600i	−0.274512	−	0.844862i	−0.989348	−	0.145570i	$-0.953498\pi$
$811$	−7.81758	−	24.0600i	−0.274512	−	0.844862i	0.714836	−	0.699293i	$-0.246502\pi$
$812$		0			0
$813$		−	56.5685i		−	1.98395i
$814$		0			0
$815$			22.3607i			0.783260i
$816$		0			0
$817$	−12.7598	+	4.14590i	−0.446408	+	0.145047i
$818$	−17.0130	−	5.52786i	−0.594846	−	0.193277i
$819$	−0.408407	−	33.4639i	−0.0142709	−	1.16932i
$820$		0			0
$821$	−13.4500	−	4.37016i	−0.469407	−	0.152520i	0.0647558	−	0.997901i	$-0.479373\pi$
$821$	−13.4500	−	4.37016i	−0.469407	−	0.152520i	−0.534163	+	0.845381i	$0.679373\pi$
$822$	−14.6580	−	45.1126i	−0.511255	−	1.57348i
$823$	34.7877	−	25.2748i	1.21262	−	0.881023i	0.217158	−	0.976137i	$-0.430321\pi$
$823$	34.7877	−	25.2748i	1.21262	−	0.881023i	0.995466	+	0.0951136i	$0.0303214\pi$
$824$	37.9473			1.32196
$825$		0			0
$826$	−5.00000	−	6.70820i	−0.173972	−	0.233408i
$827$	13.3001	+	18.3060i	0.462488	+	0.636561i	0.975022	−	0.222106i	$-0.0712932\pi$
$827$	13.3001	+	18.3060i	0.462488	+	0.636561i	−0.512534	+	0.858667i	$0.671293\pi$
$828$		0			0
$829$	19.1396	+	6.21885i	0.664747	+	0.215989i	0.621905	−	0.783092i	$-0.286359\pi$
$829$	19.1396	+	6.21885i	0.664747	+	0.215989i	0.0428419	+	0.999082i	$0.486359\pi$
$830$	−24.2705	−	17.6336i	−0.842442	−	0.612070i
$831$	7.67501	+	5.57622i	0.266243	+	0.193437i
$832$	15.6352	−	48.1201i	0.542052	−	1.66826i
$833$		0			0
$834$	−32.3607	+	23.5114i	−1.12056	+	0.814134i
$835$		−	21.2132i		−	0.734113i
$836$		0			0
$837$	15.0000			0.518476
$838$	25.5834	−	18.5874i	0.883763	−	0.642091i
$839$	14.8864	−	4.83688i	0.513935	−	0.166988i	−0.0405560	−	0.999177i	$-0.512913\pi$
$839$	14.8864	−	4.83688i	0.513935	−	0.166988i	0.554491	+	0.832190i	$0.312913\pi$
$840$	−11.9958	−	35.4415i	−0.413893	−	1.22285i
$841$	−21.8435	−	15.8702i	−0.753223	−	0.547248i
$842$	3.32502	−	4.57649i	0.114588	−	0.157716i
$843$	−16.6124	+	51.1276i	−0.572160	+	1.76093i
$844$		0			0
$845$	35.4869	+	48.8435i	1.22078	+	1.68027i
$846$	−12.6491			−0.434885
$847$		0			0
$848$		0			0
$849$	8.31254	+	11.4412i	0.285286	+	0.392662i
$850$		0			0
$851$	0.927051	−	2.85317i	0.0317789	−	0.0978054i
$852$		0			0
$853$	20.4667	+	14.8699i	0.700766	+	0.509136i	0.880182	−	0.474637i	$-0.157421\pi$
$853$	20.4667	+	14.8699i	0.700766	+	0.509136i	−0.179416	+	0.983773i	$0.557421\pi$
$854$	−3.79339	−	11.2076i	−0.129807	−	0.383516i
$855$	−13.4500	+	4.37016i	−0.459979	+	0.149456i
$856$	−6.47214	+	4.70228i	−0.221213	+	0.160721i
$857$	18.9737			0.648128			0.324064	−	0.946035i	$-0.394951\pi$
$857$	18.9737			0.648128			0.324064	+	0.946035i	$0.394951\pi$
$858$		0			0
$859$		−	6.70820i		−	0.228881i	−0.993430	−	0.114440i	$-0.963492\pi$
$859$		−	6.70820i		−	0.228881i	0.993430	−	0.114440i	$-0.0365075\pi$
$860$		0			0
$861$	−45.8052	−	32.4328i	−1.56104	−	1.10531i
$862$	−15.4508	+	47.5528i	−0.526258	+	1.61966i
$863$	−14.5623	−	10.5801i	−0.495707	−	0.360152i	0.311668	−	0.950191i	$-0.399112\pi$
$863$	−14.5623	−	10.5801i	−0.495707	−	0.360152i	−0.807375	+	0.590039i	$0.799112\pi$
$864$		0			0
$865$	20.1750	+	6.55524i	0.685969	+	0.222885i
$866$	8.79478	+	27.0675i	0.298859	+	0.919793i
$867$	22.3436	+	30.7533i	0.758827	+	1.04444i
$868$		0			0
$869$		0			0
$870$	−10.0000			−0.339032
$871$	56.2834	−	40.8923i	1.90709	−	1.38558i
$872$	−11.1246	−	34.2380i	−0.376727	−	1.15945i
$873$	−12.7598	−	4.14590i	−0.431853	−	0.140317i
$874$	7.88597	−	10.8541i	0.266747	−	0.367145i
$875$	−29.5782	+	0.360984i	−0.999926	+	0.0122035i
$876$		0			0
$877$	4.03499	−	1.31105i	0.136252	−	0.0442709i	−0.240097	−	0.970749i	$-0.577179\pi$
$877$	4.03499	−	1.31105i	0.136252	−	0.0442709i	0.376349	+	0.926478i	$0.377179\pi$
$878$	−13.1433	−	18.0902i	−0.443564	−	0.610514i
$879$			21.2132i			0.715504i
$880$		0			0
$881$			51.4296i			1.73271i	0.499432	+	0.866353i	$0.333542\pi$
$881$			51.4296i			1.73271i	−0.499432	+	0.866353i	$0.666458\pi$
$882$	18.6750	−	6.57595i	0.628821	−	0.221424i
$883$	2.47214	+	7.60845i	0.0831940	+	0.256045i	0.983998	−	0.178182i	$-0.0570216\pi$
$883$	2.47214	+	7.60845i	0.0831940	+	0.256045i	−0.900804	+	0.434227i	$0.857022\pi$
$884$		0			0
$885$	−6.57164	+	9.04508i	−0.220903	+	0.304047i
$886$	12.4688	−	17.1618i	0.418898	−	0.576563i
$887$	−5.86319	+	18.0450i	−0.196866	+	0.605893i	0.803083	+	0.595867i	$0.203191\pi$
$887$	−5.86319	+	18.0450i	−0.196866	+	0.605893i	−0.999950	+	0.0100259i	$0.996809\pi$
$888$	−1.95440	−	6.01501i	−0.0655852	−	0.201851i
$889$	−10.0145	+	32.1514i	−0.335876	+	1.07832i
$890$			7.07107i			0.237023i
$891$		0			0
$892$		0			0
$893$	−8.31254	−	11.4412i	−0.278169	−	0.382866i
$894$	−59.5456	+	19.3475i	−1.99150	+	0.647078i
$895$	−19.1396	−	6.21885i	−0.639768	−	0.207873i
$896$	29.9310	−	0.365290i	0.999926	−	0.0122035i
$897$	24.9376	−	34.3237i	0.832643	−	1.14603i
$898$	36.3149	+	11.7994i	1.21184	+	0.393752i
$899$	−2.93159	−	9.02251i	−0.0977741	−	0.300918i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−15.0000	−	20.1246i	−0.499169	−	0.669705i
$904$	−4.98752	−	6.86474i	−0.165883	−	0.228318i
$905$	−13.9058	−	42.7975i	−0.462243	−	1.42264i
$906$	51.0390	+	16.5836i	1.69566	+	0.550953i
$907$	8.09017	+	5.87785i	0.268630	+	0.195171i	0.713943	−	0.700204i	$-0.246908\pi$
$907$	8.09017	+	5.87785i	0.268630	+	0.195171i	−0.445313	+	0.895375i	$0.646908\pi$
$908$		0			0
$909$	5.86319	−	18.0450i	0.194470	−	0.598516i
$910$	−30.5779	+	43.1855i	−1.01365	+	1.43159i
$911$	4.85410	−	3.52671i	0.160824	−	0.116845i	−0.504463	−	0.863433i	$-0.668309\pi$
$911$	4.85410	−	3.52671i	0.160824	−	0.116845i	0.665286	+	0.746588i	$0.268309\pi$
$912$		−	28.2843i		−	0.936586i
$913$		0			0
$914$	−12.0000			−0.396925
$915$	−12.7917	+	9.29370i	−0.422880	+	0.307240i
$916$		0			0
$917$	−47.5498	+	16.0940i	−1.57023	+	0.531471i
$918$		0			0
$919$	7.48128	−	10.2971i	0.246785	−	0.339670i	−0.667597	−	0.744523i	$-0.732677\pi$
$919$	7.48128	−	10.2971i	0.246785	−	0.339670i	0.914382	+	0.404853i	$0.132677\pi$
$920$	5.86319	−	18.0450i	0.193303	−	0.594927i
$921$	13.4500	−	4.37016i	0.443192	−	0.144002i
$922$	−7.88597	−	10.8541i	−0.259710	−	0.357461i
$923$	−56.9210			−1.87358
$924$		0			0
$925$		0			0
$926$	−20.7813	−	28.6031i	−0.682917	−	0.939955i
$927$	25.5195	−	8.29180i	0.838171	−	0.272338i
$928$		0			0
$929$	−21.0292	+	28.9443i	−0.689947	+	0.949631i	−0.999999	−	0.00108875i	$-0.999653\pi$
$929$	−21.0292	+	28.9443i	−0.689947	+	0.949631i	0.310052	+	0.950720i	$0.399653\pi$
$930$	38.3750	+	27.8811i	1.25837	+	0.914257i
$931$	18.2206	+	12.5702i	0.597155	+	0.411973i
$932$		0			0
$933$	8.09017	−	5.87785i	0.264860	−	0.192432i
$934$	15.8114			0.517364
$935$		0			0
$936$		−	35.7771i		−	1.16941i
$937$	−40.9334	+	29.7398i	−1.33724	+	0.971558i	−0.337695	+	0.941256i	$0.609647\pi$
$937$	−40.9334	+	29.7398i	−1.33724	+	0.971558i	−0.999541	+	0.0303026i	$0.990353\pi$
$938$	33.5905	+	23.7841i	1.09677	+	0.776577i
$939$	−4.63525	+	14.2658i	−0.151266	+	0.465548i
$940$		0			0
$941$	−30.7000	−	22.3049i	−1.00079	−	0.727118i	−0.0385346	−	0.999257i	$-0.512269\pi$
$941$	−30.7000	−	22.3049i	−1.00079	−	0.727118i	−0.962258	+	0.272139i	$0.912269\pi$
$942$	−20.1750	−	6.55524i	−0.657336	−	0.213581i
$943$	−8.79478	−	27.0675i	−0.286397	−	0.881440i
$944$	−5.25731	−	7.23607i	−0.171111	−	0.235514i
$945$	7.90569	+	10.6066i	0.257172	+	0.345033i
$946$		0			0
$947$	−15.0000			−0.487435			−0.243717	−	0.969846i	$-0.578367\pi$
$947$	−15.0000			−0.487435			−0.243717	+	0.969846i	$0.578367\pi$
$948$		0			0
$949$	−6.18034	−	19.0211i	−0.200622	−	0.617452i
$950$		0			0
$951$	27.6009	−	37.9894i	0.895020	−	1.23189i
$952$		0			0
$953$	−9.41498	−	3.05911i	−0.304981	−	0.0990944i	0.152528	−	0.988299i	$-0.451258\pi$
$953$	−9.41498	−	3.05911i	−0.304981	−	0.0990944i	−0.457510	+	0.889205i	$0.651258\pi$
$954$		0			0
$955$	3.94298	+	5.42705i	0.127592	+	0.175615i
$956$		0			0
$957$		0			0
$958$		−	26.8328i		−	0.866929i
$959$	37.8907	+	11.8022i	1.22356	+	0.381113i
$960$	−12.3607	−	38.0423i	−0.398939	−	1.22781i
$961$	−4.32624	+	13.3148i	−0.139556	+	0.429509i
$962$	−5.25731	+	7.23607i	−0.169503	+	0.233300i
$963$	−3.32502	+	4.57649i	−0.107147	+	0.147475i
$964$		0			0
$965$	−2.93159	−	9.02251i	−0.0943713	−	0.290445i
$966$	23.9642	+	7.46437i	0.771036	+	0.240162i
$967$			46.6690i			1.50078i	0.660998	+	0.750388i	$0.270133\pi$
$967$			46.6690i			1.50078i	−0.660998	+	0.750388i	$0.729867\pi$
$968$		0			0
$969$		0			0
$970$	12.4688	+	17.1618i	0.400349	+	0.551034i
$971$	27.6462	−	8.98278i	0.887207	−	0.288271i	0.170261	−	0.985399i	$-0.445539\pi$
$971$	27.6462	−	8.98278i	0.887207	−	0.288271i	0.716947	+	0.697128i	$0.245539\pi$
$972$		0			0
$973$	−0.408407	−	33.4639i	−0.0130929	−	1.07280i
$974$	−24.1064	+	33.1796i	−0.772418	+	1.06314i
$975$		0			0
$976$	−3.90879	−	12.0300i	−0.125117	−	0.385072i
$977$	16.9894	−	12.3435i	0.543538	−	0.394903i	−0.281860	−	0.959456i	$-0.590951\pi$
$977$	16.9894	−	12.3435i	0.543538	−	0.394903i	0.825397	+	0.564552i	$0.190951\pi$
$978$	−31.6228			−1.01118
$979$		0			0
$980$		0			0
$981$	−14.9626	−	20.5942i	−0.477718	−	0.657523i
$982$	14.2148	+	43.7486i	0.453612	+	1.39607i
$983$	−27.6462	−	8.98278i	−0.881775	−	0.286506i	−0.167081	−	0.985943i	$-0.553434\pi$
$983$	−27.6462	−	8.98278i	−0.881775	−	0.286506i	−0.714694	+	0.699437i	$0.753434\pi$
$984$	−48.5410	−	35.2671i	−1.54743	−	1.12427i
$985$	10.2333	+	7.43496i	0.326061	+	0.236898i
$986$		0			0
$987$	15.2890	−	21.5928i	0.486653	−	0.687305i
$988$		0			0
$989$		−	12.7279i		−	0.404724i
$990$		0			0
$991$	−46.0000			−1.46124			−0.730619	−	0.682785i	$-0.760768\pi$
$991$	−46.0000			−1.46124			−0.730619	+	0.682785i	$0.760768\pi$
$992$		0			0
$993$	40.4059	−	13.1287i	1.28224	−	0.416626i
$994$	−10.7962	−	31.8974i	−0.342434	−	1.01172i
$995$		0			0
$996$		0			0
$997$	−16.6124	+	51.1276i	−0.526119	+	1.61923i	0.235974	+	0.971759i	$0.424172\pi$
$997$	−16.6124	+	51.1276i	−0.526119	+	1.61923i	−0.762093	+	0.647467i	$0.775828\pi$
$998$	−21.5200	+	6.99226i	−0.681202	+	0.221336i
$999$	1.31433	+	1.80902i	0.0415835	+	0.0572348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.l.g.118.3		16
7.6	odd	2	inner	847.2.l.g.118.4		16
11.2	odd	10		77.2.b.b.76.4	yes	4
11.3	even	5	inner	847.2.l.g.699.4		16
11.4	even	5	inner	847.2.l.g.524.2		16
11.5	even	5	inner	847.2.l.g.475.1		16
11.6	odd	10	inner	847.2.l.g.475.3		16
11.7	odd	10	inner	847.2.l.g.524.4		16
11.8	odd	10	inner	847.2.l.g.699.2		16
11.9	even	5		77.2.b.b.76.2	yes	4
11.10	odd	2	inner	847.2.l.g.118.1		16
33.2	even	10		693.2.c.b.307.2		4
33.20	odd	10		693.2.c.b.307.4		4
44.31	odd	10		1232.2.e.c.769.1		4
44.35	even	10		1232.2.e.c.769.2		4
77.2	odd	30		539.2.i.b.472.3		8
77.6	even	10	inner	847.2.l.g.475.4		16
77.9	even	15		539.2.i.b.472.1		8
77.13	even	10		77.2.b.b.76.3	yes	4
77.20	odd	10		77.2.b.b.76.1	✓	4
77.24	even	30		539.2.i.b.362.1		8
77.27	odd	10	inner	847.2.l.g.475.2		16
77.31	odd	30		539.2.i.b.362.3		8
77.41	even	10	inner	847.2.l.g.699.1		16
77.46	odd	30		539.2.i.b.362.2		8
77.48	odd	10	inner	847.2.l.g.524.1		16
77.53	even	15		539.2.i.b.362.4		8
77.62	even	10	inner	847.2.l.g.524.3		16
77.68	even	30		539.2.i.b.472.4		8
77.69	odd	10	inner	847.2.l.g.699.3		16
77.75	odd	30		539.2.i.b.472.2		8
77.76	even	2	inner	847.2.l.g.118.2		16
231.20	even	10		693.2.c.b.307.3		4
231.167	odd	10		693.2.c.b.307.1		4
308.167	odd	10		1232.2.e.c.769.3		4
308.251	even	10		1232.2.e.c.769.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.b.b.76.1	✓	4	77.20	odd	10
77.2.b.b.76.2	yes	4	11.9	even	5
77.2.b.b.76.3	yes	4	77.13	even	10
77.2.b.b.76.4	yes	4	11.2	odd	10
539.2.i.b.362.1		8	77.24	even	30
539.2.i.b.362.2		8	77.46	odd	30
539.2.i.b.362.3		8	77.31	odd	30
539.2.i.b.362.4		8	77.53	even	15
539.2.i.b.472.1		8	77.9	even	15
539.2.i.b.472.2		8	77.75	odd	30
539.2.i.b.472.3		8	77.2	odd	30
539.2.i.b.472.4		8	77.68	even	30
693.2.c.b.307.1		4	231.167	odd	10
693.2.c.b.307.2		4	33.2	even	10
693.2.c.b.307.3		4	231.20	even	10
693.2.c.b.307.4		4	33.20	odd	10
847.2.l.g.118.1		16	11.10	odd	2	inner
847.2.l.g.118.2		16	77.76	even	2	inner
847.2.l.g.118.3		16	1.1	even	1	trivial
847.2.l.g.118.4		16	7.6	odd	2	inner
847.2.l.g.475.1		16	11.5	even	5	inner
847.2.l.g.475.2		16	77.27	odd	10	inner
847.2.l.g.475.3		16	11.6	odd	10	inner
847.2.l.g.475.4		16	77.6	even	10	inner
847.2.l.g.524.1		16	77.48	odd	10	inner
847.2.l.g.524.2		16	11.4	even	5	inner
847.2.l.g.524.3		16	77.62	even	10	inner
847.2.l.g.524.4		16	11.7	odd	10	inner
847.2.l.g.699.1		16	77.41	even	10	inner
847.2.l.g.699.2		16	11.8	odd	10	inner
847.2.l.g.699.3		16	77.69	odd	10	inner
847.2.l.g.699.4		16	11.3	even	5	inner
1232.2.e.c.769.1		4	44.31	odd	10
1232.2.e.c.769.2		4	44.35	even	10
1232.2.e.c.769.3		4	308.167	odd	10
1232.2.e.c.769.4		4	308.251	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.l (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.831254 + 1.14412i) q^{2} +(-2.12663 + 0.690983i) q^{3} +(-1.31433 + 1.80902i) q^{5} +(-2.55834 - 1.85874i) q^{6} +(2.50609 - 0.848228i) q^{7} +(2.68999 - 0.874032i) q^{8} +(1.61803 - 1.17557i) q^{9} +O(q^{10})\)	\(q+(0.831254 + 1.14412i) q^{2} +(-2.12663 + 0.690983i) q^{3} +(-1.31433 + 1.80902i) q^{5} +(-2.55834 - 1.85874i) q^{6} +(2.50609 - 0.848228i) q^{7} +(2.68999 - 0.874032i) q^{8} +(1.61803 - 1.17557i) q^{9} -3.16228 q^{10} +(5.11667 - 3.71748i) q^{13} +(3.05368 + 2.16219i) q^{14} +(1.54508 - 4.75528i) q^{15} +(3.23607 + 2.35114i) q^{16} +(2.68999 + 0.874032i) q^{18} +(0.977198 + 3.00750i) q^{19} +(-4.74342 + 3.53553i) q^{21} -3.00000 q^{23} +(-5.11667 + 3.71748i) q^{24} +(8.50651 + 2.76393i) q^{26} +(1.31433 - 1.80902i) q^{27} +(-1.34500 - 0.437016i) q^{29} +(6.72499 - 2.18508i) q^{30} +(3.94298 + 5.42705i) q^{31} +(-1.75937 + 5.64842i) q^{35} +(-0.309017 + 0.951057i) q^{37} +(-2.62866 + 3.61803i) q^{38} +(-8.31254 + 11.4412i) q^{39} +(-1.95440 + 6.01501i) q^{40} +(2.93159 + 9.02251i) q^{41} +(-7.98807 - 2.48812i) q^{42} +4.24264i q^{43} +4.47214i q^{45} +(-2.49376 - 3.43237i) q^{46} +(-4.25325 + 1.38197i) q^{47} +(-8.50651 - 2.76393i) q^{48} +(5.56102 - 4.25148i) q^{49} +3.16228 q^{54} +(6.00000 - 4.47214i) q^{56} +(-4.15627 - 5.72061i) q^{57} +(-0.618034 - 1.90211i) q^{58} +(-2.12663 - 0.690983i) q^{59} +(-2.55834 - 1.85874i) q^{61} +(-2.93159 + 9.02251i) q^{62} +(3.05779 - 4.31855i) q^{63} +(6.47214 - 4.70228i) q^{64} +14.1421i q^{65} +11.0000 q^{67} +(6.37988 - 2.07295i) q^{69} +(-7.92497 + 2.68233i) q^{70} +(-7.28115 - 5.29007i) q^{71} +(3.32502 - 4.57649i) q^{72} +(0.977198 - 3.00750i) q^{73} +(-1.34500 + 0.437016i) q^{74} -20.0000 q^{78} +(4.98752 + 6.86474i) q^{79} +(-8.50651 + 2.76393i) q^{80} +(-3.39919 + 10.4616i) q^{81} +(-7.88597 + 10.8541i) q^{82} +(7.67501 + 5.57622i) q^{83} +(-4.85410 + 3.52671i) q^{86} +3.16228 q^{87} -2.23607i q^{89} +(-5.11667 + 3.71748i) q^{90} +(9.66959 - 13.6565i) q^{91} +(-12.1353 - 8.81678i) q^{93} +(-5.11667 - 3.71748i) q^{94} +(-6.72499 - 2.18508i) q^{95} +(-3.94298 - 5.42705i) q^{97} +(9.48683 + 2.82843i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^9	\( 16 q + 8 q^{9} - 12 q^{14} - 20 q^{15} + 16 q^{16} - 48 q^{23} + 4 q^{37} - 20 q^{42} + 8 q^{49} + 96 q^{56} + 8 q^{58} + 32 q^{64} + 176 q^{67} + 20 q^{70} - 36 q^{71} - 320 q^{78} + 44 q^{81} - 24 q^{86} + 40 q^{91} - 60 q^{93}+O(q^{100}) \) 16 * q + 8 * q^9 - 12 * q^14 - 20 * q^15 + 16 * q^16 - 48 * q^23 + 4 * q^37 - 20 * q^42 + 8 * q^49 + 96 * q^56 + 8 * q^58 + 32 * q^64 + 176 * q^67 + 20 * q^70 - 36 * q^71 - 320 * q^78 + 44 * q^81 - 24 * q^86 + 40 * q^91 - 60 * q^93

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