LMFDB - Embedded newform 931.2.f.e.704.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(324,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("931.324");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.f (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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			704.1
Root			$0.809017 + 1.40126i$ of defining polynomial
Character	$\chi$	$=$	931.704
Dual form			931.2.f.e.324.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 1.40126i) q^{2} +(0.190983 - 0.330792i) q^{3} +(-0.309017 + 0.535233i) q^{4} +(0.500000 + 0.866025i) q^{5} -0.618034 q^{6} -2.23607 q^{8} +(1.42705 + 2.47172i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 1.40126i) q^{2} +(0.190983 - 0.330792i) q^{3} +(-0.309017 + 0.535233i) q^{4} +(0.500000 + 0.866025i) q^{5} -0.618034 q^{6} -2.23607 q^{8} +(1.42705 + 2.47172i) q^{9} +(0.809017 - 1.40126i) q^{10} +(-0.309017 + 0.535233i) q^{11} +(0.118034 + 0.204441i) q^{12} +1.00000 q^{13} +0.381966 q^{15} +(2.42705 + 4.20378i) q^{16} +(1.92705 - 3.33775i) q^{17} +(2.30902 - 3.99933i) q^{18} +(-0.500000 - 0.866025i) q^{19} -0.618034 q^{20} +1.00000 q^{22} +(2.73607 + 4.73901i) q^{23} +(-0.427051 + 0.739674i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-0.809017 - 1.40126i) q^{26} +2.23607 q^{27} +1.38197 q^{29} +(-0.309017 - 0.535233i) q^{30} +(4.78115 - 8.28120i) q^{31} +(1.69098 - 2.92887i) q^{32} +(0.118034 + 0.204441i) q^{33} -6.23607 q^{34} -1.76393 q^{36} +(1.26393 + 2.18919i) q^{37} +(-0.809017 + 1.40126i) q^{38} +(0.190983 - 0.330792i) q^{39} +(-1.11803 - 1.93649i) q^{40} +1.09017 q^{41} +8.47214 q^{43} +(-0.190983 - 0.330792i) q^{44} +(-1.42705 + 2.47172i) q^{45} +(4.42705 - 7.66788i) q^{46} +(3.73607 + 6.47106i) q^{47} +1.85410 q^{48} -6.47214 q^{50} +(-0.736068 - 1.27491i) q^{51} +(-0.309017 + 0.535233i) q^{52} +(-2.42705 + 4.20378i) q^{53} +(-1.80902 - 3.13331i) q^{54} -0.618034 q^{55} -0.381966 q^{57} +(-1.11803 - 1.93649i) q^{58} +(3.88197 - 6.72376i) q^{59} +(-0.118034 + 0.204441i) q^{60} +(-5.97214 - 10.3440i) q^{61} -15.4721 q^{62} +4.23607 q^{64} +(0.500000 + 0.866025i) q^{65} +(0.190983 - 0.330792i) q^{66} +(1.16312 - 2.01458i) q^{67} +(1.19098 + 2.06284i) q^{68} +2.09017 q^{69} +8.70820 q^{71} +(-3.19098 - 5.52694i) q^{72} +(-5.66312 + 9.80881i) q^{73} +(2.04508 - 3.54219i) q^{74} +(-0.763932 - 1.32317i) q^{75} +0.618034 q^{76} -0.618034 q^{78} +(2.23607 + 3.87298i) q^{79} +(-2.42705 + 4.20378i) q^{80} +(-3.85410 + 6.67550i) q^{81} +(-0.881966 - 1.52761i) q^{82} -3.14590 q^{83} +3.85410 q^{85} +(-6.85410 - 11.8717i) q^{86} +(0.263932 - 0.457144i) q^{87} +(0.690983 - 1.19682i) q^{88} +(1.38197 + 2.39364i) q^{89} +4.61803 q^{90} -3.38197 q^{92} +(-1.82624 - 3.16314i) q^{93} +(6.04508 - 10.4704i) q^{94} +(0.500000 - 0.866025i) q^{95} +(-0.645898 - 1.11873i) q^{96} -7.47214 q^{97} -1.76393 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 3 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - q^{9}+O(q^{10}) $ 4 * q - q^2 + 3 * q^3 + q^4 + 2 * q^5 + 2 * q^6 - q^9	$ 4 q - q^{2} + 3 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - q^{9} + q^{10} + q^{11} - 4 q^{12} + 4 q^{13} + 6 q^{15} + 3 q^{16} + q^{17} + 7 q^{18} - 2 q^{19} + 2 q^{20} + 4 q^{22} + 2 q^{23} + 5 q^{24} + 8 q^{25} - q^{26} + 10 q^{29} + q^{30} - q^{31} + 9 q^{32} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 14 q^{37} - q^{38} + 3 q^{39} - 18 q^{41} + 16 q^{43} - 3 q^{44} + q^{45} + 11 q^{46} + 6 q^{47} - 6 q^{48} - 8 q^{50} + 6 q^{51} + q^{52} - 3 q^{53} - 5 q^{54} + 2 q^{55} - 6 q^{57} + 20 q^{59} + 4 q^{60} - 6 q^{61} - 44 q^{62} + 8 q^{64} + 2 q^{65} + 3 q^{66} - 11 q^{67} + 7 q^{68} - 14 q^{69} + 8 q^{71} - 15 q^{72} - 7 q^{73} - 3 q^{74} - 12 q^{75} - 2 q^{76} + 2 q^{78} - 3 q^{80} - 2 q^{81} - 8 q^{82} - 26 q^{83} + 2 q^{85} - 14 q^{86} + 10 q^{87} + 5 q^{88} + 10 q^{89} + 14 q^{90} - 18 q^{92} + 24 q^{93} + 13 q^{94} + 2 q^{95} - 16 q^{96} - 12 q^{97} - 16 q^{99}+O(q^{100}) $ 4 * q - q^2 + 3 * q^3 + q^4 + 2 * q^5 + 2 * q^6 - q^9 + q^10 + q^11 - 4 * q^12 + 4 * q^13 + 6 * q^15 + 3 * q^16 + q^17 + 7 * q^18 - 2 * q^19 + 2 * q^20 + 4 * q^22 + 2 * q^23 + 5 * q^24 + 8 * q^25 - q^26 + 10 * q^29 + q^30 - q^31 + 9 * q^32 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 14 * q^37 - q^38 + 3 * q^39 - 18 * q^41 + 16 * q^43 - 3 * q^44 + q^45 + 11 * q^46 + 6 * q^47 - 6 * q^48 - 8 * q^50 + 6 * q^51 + q^52 - 3 * q^53 - 5 * q^54 + 2 * q^55 - 6 * q^57 + 20 * q^59 + 4 * q^60 - 6 * q^61 - 44 * q^62 + 8 * q^64 + 2 * q^65 + 3 * q^66 - 11 * q^67 + 7 * q^68 - 14 * q^69 + 8 * q^71 - 15 * q^72 - 7 * q^73 - 3 * q^74 - 12 * q^75 - 2 * q^76 + 2 * q^78 - 3 * q^80 - 2 * q^81 - 8 * q^82 - 26 * q^83 + 2 * q^85 - 14 * q^86 + 10 * q^87 + 5 * q^88 + 10 * q^89 + 14 * q^90 - 18 * q^92 + 24 * q^93 + 13 * q^94 + 2 * q^95 - 16 * q^96 - 12 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.809017	−	1.40126i	−0.572061	−	0.990839i	−0.996354	−	0.0853143i	$-0.972811\pi$
$2$	−0.809017	−	1.40126i	−0.572061	−	0.990839i	0.424293	−	0.905525i	$-0.360523\pi$
$3$	0.190983	−	0.330792i	0.110264	−	0.190983i	−0.805613	−	0.592443i	$-0.798164\pi$
$3$	0.190983	−	0.330792i	0.110264	−	0.190983i	0.915877	+	0.401460i	$0.131497\pi$
$4$	−0.309017	+	0.535233i	−0.154508	+	0.267617i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$	−0.618034			−0.252311
$7$		0			0
$7$		0			0
$8$	−2.23607			−0.790569
$9$	1.42705	+	2.47172i	0.475684	+	0.823908i
$10$	0.809017	−	1.40126i	0.255834	−	0.443117i
$11$	−0.309017	+	0.535233i	−0.0931721	+	0.161379i	−0.908844	−	0.417136i	$-0.863034\pi$
$11$	−0.309017	+	0.535233i	−0.0931721	+	0.161379i	0.815672	+	0.578514i	$0.196367\pi$
$12$	0.118034	+	0.204441i	0.0340735	+	0.0590170i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$		0			0
$15$	0.381966			0.0986232
$16$	2.42705	+	4.20378i	0.606763	+	1.05094i
$17$	1.92705	−	3.33775i	0.467379	−	0.809523i	−0.531927	−	0.846790i	$-0.678532\pi$
$17$	1.92705	−	3.33775i	0.467379	−	0.809523i	0.999305	+	0.0372670i	$0.0118652\pi$
$18$	2.30902	−	3.99933i	0.544241	−	0.942652i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$20$	−0.618034			−0.138197
$21$		0			0
$22$	1.00000			0.213201
$23$	2.73607	+	4.73901i	0.570510	+	0.988152i	0.996514	+	0.0834304i	$0.0265876\pi$
$23$	2.73607	+	4.73901i	0.570510	+	0.988152i	−0.426004	+	0.904721i	$0.640079\pi$
$24$	−0.427051	+	0.739674i	−0.0871714	+	0.150985i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−0.809017	−	1.40126i	−0.158661	−	0.274809i
$27$	2.23607			0.430331
$28$		0			0
$29$	1.38197			0.256625			0.128312	−	0.991734i	$-0.459044\pi$
$29$	1.38197			0.256625			0.128312	+	0.991734i	$0.459044\pi$
$30$	−0.309017	−	0.535233i	−0.0564185	−	0.0977198i
$31$	4.78115	−	8.28120i	0.858720	−	1.48735i	−0.0144296	−	0.999896i	$-0.504593\pi$
$31$	4.78115	−	8.28120i	0.858720	−	1.48735i	0.873150	−	0.487452i	$-0.162073\pi$
$32$	1.69098	−	2.92887i	0.298926	−	0.517756i
$33$	0.118034	+	0.204441i	0.0205471	+	0.0355886i
$34$	−6.23607			−1.06948
$35$		0			0
$36$	−1.76393			−0.293989
$37$	1.26393	+	2.18919i	0.207789	+	0.359901i	0.951018	−	0.309136i	$-0.100040\pi$
$37$	1.26393	+	2.18919i	0.207789	+	0.359901i	−0.743229	+	0.669037i	$0.766707\pi$
$38$	−0.809017	+	1.40126i	−0.131240	+	0.227314i
$39$	0.190983	−	0.330792i	0.0305818	−	0.0529692i
$40$	−1.11803	−	1.93649i	−0.176777	−	0.306186i
$41$	1.09017			0.170256			0.0851280	−	0.996370i	$-0.472870\pi$
$41$	1.09017			0.170256			0.0851280	+	0.996370i	$0.472870\pi$
$42$		0			0
$43$	8.47214			1.29199			0.645994	−	0.763342i	$-0.276443\pi$
$43$	8.47214			1.29199			0.645994	+	0.763342i	$0.276443\pi$
$44$	−0.190983	−	0.330792i	−0.0287918	−	0.0498688i
$45$	−1.42705	+	2.47172i	−0.212732	+	0.368463i
$46$	4.42705	−	7.66788i	0.652733	−	1.13057i
$47$	3.73607	+	6.47106i	0.544962	+	0.943901i	0.998609	+	0.0527200i	$0.0167891\pi$
$47$	3.73607	+	6.47106i	0.544962	+	0.943901i	−0.453648	+	0.891181i	$0.649878\pi$
$48$	1.85410			0.267617
$49$		0			0
$50$	−6.47214			−0.915298
$51$	−0.736068	−	1.27491i	−0.103070	−	0.178523i
$52$	−0.309017	+	0.535233i	−0.0428529	+	0.0742235i
$53$	−2.42705	+	4.20378i	−0.333381	+	0.577433i	−0.983173	−	0.182680i	$-0.941523\pi$
$53$	−2.42705	+	4.20378i	−0.333381	+	0.577433i	0.649791	+	0.760113i	$0.274856\pi$
$54$	−1.80902	−	3.13331i	−0.246176	−	0.426389i
$55$	−0.618034			−0.0833357
$56$		0			0
$57$	−0.381966			−0.0505926
$58$	−1.11803	−	1.93649i	−0.146805	−	0.254274i
$59$	3.88197	−	6.72376i	0.505389	−	0.875359i	−0.494592	−	0.869125i	$-0.664682\pi$
$59$	3.88197	−	6.72376i	0.505389	−	0.875359i	0.999981	−	0.00623382i	$-0.00198430\pi$
$60$	−0.118034	+	0.204441i	−0.0152381	+	0.0263932i
$61$	−5.97214	−	10.3440i	−0.764654	−	1.32442i	−0.940429	−	0.339989i	$-0.889577\pi$
$61$	−5.97214	−	10.3440i	−0.764654	−	1.32442i	0.175776	−	0.984430i	$-0.443757\pi$
$62$	−15.4721			−1.96496
$63$		0			0
$64$	4.23607			0.529508
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$	0.190983	−	0.330792i	0.0235084	−	0.0407177i
$67$	1.16312	−	2.01458i	0.142098	−	0.246120i	−0.786189	−	0.617986i	$-0.787949\pi$
$67$	1.16312	−	2.01458i	0.142098	−	0.246120i	0.928286	+	0.371866i	$0.121282\pi$
$68$	1.19098	+	2.06284i	0.144428	+	0.250156i
$69$	2.09017			0.251627
$70$		0			0
$71$	8.70820			1.03347			0.516737	−	0.856144i	$-0.327147\pi$
$71$	8.70820			1.03347			0.516737	+	0.856144i	$0.327147\pi$
$72$	−3.19098	−	5.52694i	−0.376061	−	0.651357i
$73$	−5.66312	+	9.80881i	−0.662818	+	1.14803i	0.317054	+	0.948407i	$0.397306\pi$
$73$	−5.66312	+	9.80881i	−0.662818	+	1.14803i	−0.979872	+	0.199627i	$0.936027\pi$
$74$	2.04508	−	3.54219i	0.237736	−	0.411771i
$75$	−0.763932	−	1.32317i	−0.0882113	−	0.152786i
$76$	0.618034			0.0708934
$77$		0			0
$78$	−0.618034			−0.0699786
$79$	2.23607	+	3.87298i	0.251577	+	0.435745i	0.963960	−	0.266046i	$-0.0857174\pi$
$79$	2.23607	+	3.87298i	0.251577	+	0.435745i	−0.712383	+	0.701791i	$0.752384\pi$
$80$	−2.42705	+	4.20378i	−0.271353	+	0.469996i
$81$	−3.85410	+	6.67550i	−0.428234	+	0.741722i
$82$	−0.881966	−	1.52761i	−0.0973969	−	0.168696i
$83$	−3.14590			−0.345307			−0.172654	−	0.984983i	$-0.555234\pi$
$83$	−3.14590			−0.345307			−0.172654	+	0.984983i	$0.555234\pi$
$84$		0			0
$85$	3.85410			0.418036
$86$	−6.85410	−	11.8717i	−0.739097	−	1.28015i
$87$	0.263932	−	0.457144i	0.0282965	−	0.0490109i
$88$	0.690983	−	1.19682i	0.0736590	−	0.127581i
$89$	1.38197	+	2.39364i	0.146488	+	0.253725i	0.929927	−	0.367744i	$-0.119870\pi$
$89$	1.38197	+	2.39364i	0.146488	+	0.253725i	−0.783439	+	0.621469i	$0.786536\pi$
$90$	4.61803			0.486784
$91$		0			0
$92$	−3.38197			−0.352594
$93$	−1.82624	−	3.16314i	−0.189372	−	0.328002i
$94$	6.04508	−	10.4704i	0.623503	−	1.07994i
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$	−0.645898	−	1.11873i	−0.0659217	−	0.114180i
$97$	−7.47214			−0.758680			−0.379340	−	0.925257i	$-0.623849\pi$
$97$	−7.47214			−0.758680			−0.379340	+	0.925257i	$0.623849\pi$
$98$		0			0
$99$	−1.76393			−0.177282
$100$	1.23607	+	2.14093i	0.123607	+	0.214093i
$101$	1.59017	−	2.75426i	0.158228	−	0.274059i	−0.776002	−	0.630731i	$-0.782755\pi$
$101$	1.59017	−	2.75426i	0.158228	−	0.274059i	0.934230	+	0.356672i	$0.116089\pi$
$102$	−1.19098	+	2.06284i	−0.117925	+	0.204252i
$103$	−6.35410	−	11.0056i	−0.626088	−	1.08442i	−0.988329	−	0.152332i	$-0.951322\pi$
$103$	−6.35410	−	11.0056i	−0.626088	−	1.08442i	0.362241	−	0.932084i	$-0.382012\pi$
$104$	−2.23607			−0.219265
$105$		0			0
$106$	7.85410			0.762858
$107$	−2.88197	−	4.99171i	−0.278610	−	0.482567i	0.692429	−	0.721486i	$-0.256540\pi$
$107$	−2.88197	−	4.99171i	−0.278610	−	0.482567i	−0.971040	+	0.238919i	$0.923207\pi$
$108$	−0.690983	+	1.19682i	−0.0664899	+	0.115164i
$109$	6.11803	−	10.5967i	0.586001	−	1.01498i	−0.408748	−	0.912647i	$-0.634035\pi$
$109$	6.11803	−	10.5967i	0.586001	−	1.01498i	0.994750	−	0.102337i	$-0.0326320\pi$
$110$	0.500000	+	0.866025i	0.0476731	+	0.0825723i
$111$	0.965558			0.0916467
$112$		0			0
$113$	−20.2705			−1.90689			−0.953445	−	0.301568i	$-0.902490\pi$
$113$	−20.2705			−1.90689			−0.953445	+	0.301568i	$0.902490\pi$
$114$	0.309017	+	0.535233i	0.0289421	+	0.0501292i
$115$	−2.73607	+	4.73901i	−0.255140	+	0.441915i
$116$	−0.427051	+	0.739674i	−0.0396507	+	0.0686770i
$117$	1.42705	+	2.47172i	0.131931	+	0.228511i
$118$	−12.5623			−1.15645
$119$		0			0
$120$	−0.854102			−0.0779685
$121$	5.30902	+	9.19549i	0.482638	+	0.835953i
$122$	−9.66312	+	16.7370i	−0.874858	+	1.51530i
$123$	0.208204	−	0.360620i	0.0187731	−	0.0325160i
$124$	2.95492	+	5.11806i	0.265359	+	0.459616i
$125$	9.00000			0.804984
$126$		0			0
$127$	−3.70820			−0.329050			−0.164525	−	0.986373i	$-0.552609\pi$
$127$	−3.70820			−0.329050			−0.164525	+	0.986373i	$0.552609\pi$
$128$	−6.80902	−	11.7936i	−0.601838	−	1.04241i
$129$	1.61803	−	2.80252i	0.142460	−	0.246748i
$130$	0.809017	−	1.40126i	0.0709555	−	0.122899i
$131$	−2.78115	−	4.81710i	−0.242990	−	0.420872i	0.718574	−	0.695450i	$-0.244795\pi$
$131$	−2.78115	−	4.81710i	−0.242990	−	0.420872i	−0.961565	+	0.274578i	$0.911462\pi$
$132$	−0.145898			−0.0126988
$133$		0			0
$134$	−3.76393			−0.325154
$135$	1.11803	+	1.93649i	0.0962250	+	0.166667i
$136$	−4.30902	+	7.46344i	−0.369495	+	0.639984i
$137$	−3.47214	+	6.01392i	−0.296645	+	0.513804i	−0.975366	−	0.220592i	$-0.929201\pi$
$137$	−3.47214	+	6.01392i	−0.296645	+	0.513804i	0.678722	+	0.734396i	$0.262534\pi$
$138$	−1.69098	−	2.92887i	−0.143946	−	0.249322i
$139$	9.47214			0.803416			0.401708	−	0.915768i	$-0.368417\pi$
$139$	9.47214			0.803416			0.401708	+	0.915768i	$0.368417\pi$
$140$		0			0
$141$	2.85410			0.240359
$142$	−7.04508	−	12.2024i	−0.591210	−	1.02401i
$143$	−0.309017	+	0.535233i	−0.0258413	+	0.0447584i
$144$	−6.92705	+	11.9980i	−0.577254	+	0.999834i
$145$	0.690983	+	1.19682i	0.0573830	+	0.0993903i
$146$	18.3262			1.51669
$147$		0			0
$148$	−1.56231			−0.128421
$149$	5.26393	+	9.11740i	0.431238	+	0.746926i	0.996980	−	0.0776559i	$-0.0247436\pi$
$149$	5.26393	+	9.11740i	0.431238	+	0.746926i	−0.565742	+	0.824582i	$0.691410\pi$
$150$	−1.23607	+	2.14093i	−0.100925	+	0.174806i
$151$	5.01722	−	8.69008i	0.408296	−	0.707189i	−0.586403	−	0.810019i	$-0.699457\pi$
$151$	5.01722	−	8.69008i	0.408296	−	0.707189i	0.994699	+	0.102830i	$0.0327899\pi$
$152$	1.11803	+	1.93649i	0.0906845	+	0.157070i
$153$	11.0000			0.889297
$154$		0			0
$155$	9.56231			0.768063
$156$	0.118034	+	0.204441i	0.00945028	+	0.0163684i
$157$	−6.16312	+	10.6748i	−0.491870	+	0.851945i	−0.999956	−	0.00936190i	$-0.997020\pi$
$157$	−6.16312	+	10.6748i	−0.491870	+	0.851945i	0.508086	+	0.861306i	$0.330353\pi$
$158$	3.61803	−	6.26662i	0.287835	−	0.498545i
$159$	0.927051	+	1.60570i	0.0735199	+	0.127340i
$160$	3.38197			0.267368
$161$		0			0
$162$	12.4721			0.979904
$163$	−1.89919	−	3.28949i	−0.148756	−	0.257653i	0.782012	−	0.623263i	$-0.214194\pi$
$163$	−1.89919	−	3.28949i	−0.148756	−	0.257653i	−0.930768	+	0.365611i	$0.880860\pi$
$164$	−0.336881	+	0.583495i	−0.0263060	+	0.0455633i
$165$	−0.118034	+	0.204441i	−0.00918893	+	0.0159157i
$166$	2.54508	+	4.40822i	0.197537	+	0.342144i
$167$	−7.47214			−0.578211			−0.289106	−	0.957297i	$-0.593358\pi$
$167$	−7.47214			−0.578211			−0.289106	+	0.957297i	$0.593358\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	−3.11803	−	5.40059i	−0.239142	−	0.414207i
$171$	1.42705	−	2.47172i	0.109129	−	0.189018i
$172$	−2.61803	+	4.53457i	−0.199623	+	0.345758i
$173$	10.6180	+	18.3910i	0.807274	+	1.39824i	0.914745	+	0.404032i	$0.132391\pi$
$173$	10.6180	+	18.3910i	0.807274	+	1.39824i	−0.107471	+	0.994208i	$0.534275\pi$
$174$	−0.854102			−0.0647493
$175$		0			0
$176$	−3.00000			−0.226134
$177$	−1.48278	−	2.56825i	−0.111453	−	0.193041i
$178$	2.23607	−	3.87298i	0.167600	−	0.290292i
$179$	−11.8713	+	20.5617i	−0.887304	+	1.53686i	−0.0442548	+	0.999020i	$0.514091\pi$
$179$	−11.8713	+	20.5617i	−0.887304	+	1.53686i	−0.843050	+	0.537836i	$0.819242\pi$
$180$	−0.881966	−	1.52761i	−0.0657379	−	0.113861i
$181$	4.90983			0.364945			0.182472	−	0.983211i	$-0.441590\pi$
$181$	4.90983			0.364945			0.182472	+	0.983211i	$0.441590\pi$
$182$		0			0
$183$	−4.56231			−0.337255
$184$	−6.11803	−	10.5967i	−0.451027	−	0.781202i
$185$	−1.26393	+	2.18919i	−0.0929261	+	0.160953i
$186$	−2.95492	+	5.11806i	−0.216665	+	0.375275i
$187$	1.19098	+	2.06284i	0.0870933	+	0.150850i
$188$	−4.61803			−0.336805
$189$		0			0
$190$	−1.61803			−0.117385
$191$	7.51722	+	13.0202i	0.543927	+	0.942109i	0.998674	+	0.0514883i	$0.0163965\pi$
$191$	7.51722	+	13.0202i	0.543927	+	0.942109i	−0.454747	+	0.890621i	$0.650270\pi$
$192$	0.809017	−	1.40126i	0.0583858	−	0.101127i
$193$	−8.54508	+	14.8005i	−0.615089	+	1.06536i	0.375280	+	0.926911i	$0.377546\pi$
$193$	−8.54508	+	14.8005i	−0.615089	+	1.06536i	−0.990369	+	0.138453i	$0.955787\pi$
$194$	6.04508	+	10.4704i	0.434012	+	0.751731i
$195$	0.381966			0.0273532
$196$		0			0
$197$	0.562306			0.0400626			0.0200313	−	0.999799i	$-0.493623\pi$
$197$	0.562306			0.0400626			0.0200313	+	0.999799i	$0.493623\pi$
$198$	1.42705	+	2.47172i	0.101416	+	0.175658i
$199$	9.73607	−	16.8634i	0.690172	−	1.19541i	−0.281610	−	0.959529i	$-0.590868\pi$
$199$	9.73607	−	16.8634i	0.690172	−	1.19541i	0.971781	−	0.235883i	$-0.0757983\pi$
$200$	−4.47214	+	7.74597i	−0.316228	+	0.547723i
$201$	−0.444272	−	0.769502i	−0.0313365	−	0.0542765i
$202$	−5.14590			−0.362064
$203$		0			0
$204$	0.909830			0.0637008
$205$	0.545085	+	0.944115i	0.0380704	+	0.0659398i
$206$	−10.2812	+	17.8075i	−0.716322	+	1.24071i
$207$	−7.80902	+	13.5256i	−0.542764	+	0.940095i
$208$	2.42705	+	4.20378i	0.168286	+	0.291479i
$209$	0.618034			0.0427503
$210$		0			0
$211$	17.3262			1.19279			0.596394	−	0.802692i	$-0.296600\pi$
$211$	17.3262			1.19279			0.596394	+	0.802692i	$0.296600\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$	1.66312	−	2.88061i	0.113955	−	0.197376i
$214$	−4.66312	+	8.07676i	−0.318764	+	0.552116i
$215$	4.23607	+	7.33708i	0.288897	+	0.500385i
$216$	−5.00000			−0.340207
$217$		0			0
$218$	−19.7984			−1.34092
$219$	2.16312	+	3.74663i	0.146170	+	0.253174i
$220$	0.190983	−	0.330792i	0.0128761	−	0.0223020i
$221$	1.92705	−	3.33775i	0.129627	−	0.224521i
$222$	−0.781153	−	1.35300i	−0.0524276	−	0.0908072i
$223$	24.4164			1.63504			0.817522	−	0.575898i	$-0.195347\pi$
$223$	24.4164			1.63504			0.817522	+	0.575898i	$0.195347\pi$
$224$		0			0
$225$	11.4164			0.761094
$226$	16.3992	+	28.4042i	1.09086	+	1.88942i
$227$	12.7812	−	22.1376i	0.848315	−	1.46932i	−0.0343961	−	0.999408i	$-0.510951\pi$
$227$	12.7812	−	22.1376i	0.848315	−	1.46932i	0.882711	−	0.469916i	$-0.155716\pi$
$228$	0.118034	−	0.204441i	0.00781699	−	0.0135394i
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$	8.85410			0.583822
$231$		0			0
$232$	−3.09017			−0.202880
$233$	6.78115	+	11.7453i	0.444248	+	0.769460i	0.998000	−	0.0632218i	$-0.0201375\pi$
$233$	6.78115	+	11.7453i	0.444248	+	0.769460i	−0.553751	+	0.832682i	$0.686804\pi$
$234$	2.30902	−	3.99933i	0.150945	−	0.261445i
$235$	−3.73607	+	6.47106i	−0.243714	+	0.422125i
$236$	2.39919	+	4.15551i	0.156174	+	0.270501i
$237$	1.70820			0.110960
$238$		0			0
$239$	−25.0000			−1.61712			−0.808558	−	0.588417i	$-0.799751\pi$
$239$	−25.0000			−1.61712			−0.808558	+	0.588417i	$0.799751\pi$
$240$	0.927051	+	1.60570i	0.0598409	+	0.103647i
$241$	11.3262	−	19.6176i	0.729587	−	1.26368i	−0.227471	−	0.973785i	$-0.573046\pi$
$241$	11.3262	−	19.6176i	0.729587	−	1.26368i	0.957058	−	0.289897i	$-0.0936211\pi$
$242$	8.59017	−	14.8786i	0.552197	−	0.956433i
$243$	4.82624	+	8.35929i	0.309603	+	0.536249i
$244$	7.38197			0.472582
$245$		0			0
$246$	−0.673762			−0.0429575
$247$	−0.500000	−	0.866025i	−0.0318142	−	0.0551039i
$248$	−10.6910	+	18.5173i	−0.678878	+	1.17585i
$249$	−0.600813	+	1.04064i	−0.0380750	+	0.0659478i
$250$	−7.28115	−	12.6113i	−0.460501	−	0.797610i
$251$	7.27051			0.458911			0.229455	−	0.973319i	$-0.426306\pi$
$251$	7.27051			0.458911			0.229455	+	0.973319i	$0.426306\pi$
$252$		0			0
$253$	−3.38197			−0.212622
$254$	3.00000	+	5.19615i	0.188237	+	0.326036i
$255$	0.736068	−	1.27491i	0.0460944	−	0.0798378i
$256$	−6.78115	+	11.7453i	−0.423822	+	0.734081i
$257$	6.66312	+	11.5409i	0.415634	+	0.719899i	0.995495	−	0.0948164i	$-0.0302264\pi$
$257$	6.66312	+	11.5409i	0.415634	+	0.719899i	−0.579861	+	0.814716i	$0.696893\pi$
$258$	−5.23607			−0.325983
$259$		0			0
$260$	−0.618034			−0.0383288
$261$	1.97214	+	3.41584i	0.122072	+	0.211435i
$262$	−4.50000	+	7.79423i	−0.278011	+	0.481529i
$263$	−8.28115	+	14.3434i	−0.510638	+	0.884451i	0.489286	+	0.872123i	$0.337257\pi$
$263$	−8.28115	+	14.3434i	−0.510638	+	0.884451i	−0.999924	+	0.0123273i	$0.996076\pi$
$264$	−0.263932	−	0.457144i	−0.0162439	−	0.0281352i
$265$	−4.85410			−0.298185
$266$		0			0
$267$	1.05573			0.0646095
$268$	0.718847	+	1.24508i	0.0439106	+	0.0760553i
$269$	−12.9894	+	22.4982i	−0.791975	+	1.37174i	0.132767	+	0.991147i	$0.457614\pi$
$269$	−12.9894	+	22.4982i	−0.791975	+	1.37174i	−0.924742	+	0.380594i	$0.875720\pi$
$270$	1.80902	−	3.13331i	0.110093	−	0.190687i
$271$	−12.7812	−	22.1376i	−0.776400	−	1.34476i	−0.934004	−	0.357262i	$-0.883710\pi$
$271$	−12.7812	−	22.1376i	−0.776400	−	1.34476i	0.157605	−	0.987502i	$-0.449623\pi$
$272$	18.7082			1.13435
$273$		0			0
$274$	11.2361			0.678796
$275$	1.23607	+	2.14093i	0.0745377	+	0.129103i
$276$	−0.645898	+	1.11873i	−0.0388785	+	0.0673395i
$277$	8.56231	−	14.8303i	0.514459	−	0.891069i	−0.485400	−	0.874292i	$-0.661326\pi$
$277$	8.56231	−	14.8303i	0.514459	−	0.891069i	0.999859	−	0.0167772i	$-0.00534060\pi$
$278$	−7.66312	−	13.2729i	−0.459603	−	0.796056i
$279$	27.2918			1.63392
$280$		0			0
$281$	−11.2918			−0.673612			−0.336806	−	0.941574i	$-0.609347\pi$
$281$	−11.2918			−0.673612			−0.336806	+	0.941574i	$0.609347\pi$
$282$	−2.30902	−	3.99933i	−0.137500	−	0.238157i
$283$	7.95492	−	13.7783i	0.472871	−	0.819036i	−0.526647	−	0.850084i	$-0.676551\pi$
$283$	7.95492	−	13.7783i	0.472871	−	0.819036i	0.999518	+	0.0310480i	$0.00988446\pi$
$284$	−2.69098	+	4.66092i	−0.159680	+	0.276575i
$285$	−0.190983	−	0.330792i	−0.0113129	−	0.0195944i
$286$	1.00000			0.0591312
$287$		0			0
$288$	9.65248			0.568778
$289$	1.07295	+	1.85840i	0.0631146	+	0.109318i
$290$	1.11803	−	1.93649i	0.0656532	−	0.113715i
$291$	−1.42705	+	2.47172i	−0.0836552	+	0.144895i
$292$	−3.50000	−	6.06218i	−0.204822	−	0.354762i
$293$	−26.2361			−1.53273			−0.766364	−	0.642407i	$-0.777936\pi$
$293$	−26.2361			−1.53273			−0.766364	+	0.642407i	$0.777936\pi$
$294$		0			0
$295$	7.76393			0.452034
$296$	−2.82624	−	4.89519i	−0.164272	−	0.284527i
$297$	−0.690983	+	1.19682i	−0.0400949	+	0.0694464i
$298$	8.51722	−	14.7523i	0.493389	−	0.854575i
$299$	2.73607	+	4.73901i	0.158231	+	0.274064i
$300$	0.944272			0.0545176
$301$		0			0
$302$	−16.2361			−0.934281
$303$	−0.607391	−	1.05203i	−0.0348937	−	0.0604377i
$304$	2.42705	−	4.20378i	0.139201	−	0.241103i
$305$	5.97214	−	10.3440i	0.341964	−	0.592298i
$306$	−8.89919	−	15.4138i	−0.508733	−	0.881151i
$307$	−31.7426			−1.81165			−0.905824	−	0.423654i	$-0.860747\pi$
$307$	−31.7426			−1.81165			−0.905824	+	0.423654i	$0.860747\pi$
$308$		0			0
$309$	−4.85410			−0.276140
$310$	−7.73607	−	13.3993i	−0.439379	−	0.761027i
$311$	−16.7254	+	28.9693i	−0.948412	+	1.64270i	−0.199640	+	0.979869i	$0.563977\pi$
$311$	−16.7254	+	28.9693i	−0.948412	+	1.64270i	−0.748771	+	0.662828i	$0.769356\pi$
$312$	−0.427051	+	0.739674i	−0.0241770	+	0.0418758i
$313$	11.7984	+	20.4354i	0.666884	+	1.15508i	0.978771	+	0.204957i	$0.0657055\pi$
$313$	11.7984	+	20.4354i	0.666884	+	1.15508i	−0.311887	+	0.950119i	$0.600961\pi$
$314$	19.9443			1.12552
$315$		0			0
$316$	−2.76393			−0.155483
$317$	−10.7082	−	18.5472i	−0.601433	−	1.04171i	−0.992604	−	0.121394i	$-0.961263\pi$
$317$	−10.7082	−	18.5472i	−0.601433	−	1.04171i	0.391172	−	0.920318i	$-0.372070\pi$
$318$	1.50000	−	2.59808i	0.0841158	−	0.145693i
$319$	−0.427051	+	0.739674i	−0.0239103	+	0.0414138i
$320$	2.11803	+	3.66854i	0.118402	+	0.205078i
$321$	−2.20163			−0.122883
$322$		0			0
$323$	−3.85410			−0.214448
$324$	−2.38197	−	4.12569i	−0.132331	−	0.229205i
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$	−3.07295	+	5.32250i	−0.170195	+	0.294786i
$327$	−2.33688	−	4.04760i	−0.129230	−	0.223833i
$328$	−2.43769			−0.134599
$329$		0			0
$330$	0.381966			0.0210265
$331$	−0.572949	−	0.992377i	−0.0314921	−	0.0545460i	0.849850	−	0.527025i	$-0.176693\pi$
$331$	−0.572949	−	0.992377i	−0.0314921	−	0.0545460i	−0.881342	+	0.472479i	$0.843359\pi$
$332$	0.972136	−	1.68379i	0.0533529	−	0.0924099i
$333$	−3.60739	+	6.24818i	−0.197684	+	0.342398i
$334$	6.04508	+	10.4704i	0.330772	+	0.572914i
$335$	2.32624			0.127096
$336$		0			0
$337$	−6.79837			−0.370331			−0.185166	−	0.982707i	$-0.559282\pi$
$337$	−6.79837			−0.370331			−0.185166	+	0.982707i	$0.559282\pi$
$338$	9.70820	+	16.8151i	0.528057	+	0.914621i
$339$	−3.87132	+	6.70533i	−0.210261	+	0.364183i
$340$	−1.19098	+	2.06284i	−0.0645901	+	0.111873i
$341$	2.95492	+	5.11806i	0.160018	+	0.277159i
$342$	−4.61803			−0.249715
$343$		0			0
$344$	−18.9443			−1.02141
$345$	1.04508	+	1.81014i	0.0562655	+	0.0974547i
$346$	17.1803	−	29.7572i	0.923621	−	1.59976i
$347$	0.899187	−	1.55744i	0.0482709	−	0.0836076i	−0.840880	−	0.541221i	$-0.817962\pi$
$347$	0.899187	−	1.55744i	0.0482709	−	0.0836076i	0.889151	+	0.457613i	$0.151296\pi$
$348$	0.163119	+	0.282530i	0.00874409	+	0.0151452i
$349$	−35.9787			−1.92590			−0.962948	−	0.269686i	$-0.913080\pi$
$349$	−35.9787			−1.92590			−0.962948	+	0.269686i	$0.913080\pi$
$350$		0			0
$351$	2.23607			0.119352
$352$	1.04508	+	1.81014i	0.0557032	+	0.0964808i
$353$	6.63525	−	11.4926i	0.353159	−	0.611689i	−0.633642	−	0.773626i	$-0.718441\pi$
$353$	6.63525	−	11.4926i	0.353159	−	0.611689i	0.986801	+	0.161937i	$0.0517741\pi$
$354$	−2.39919	+	4.15551i	−0.127515	+	0.220863i
$355$	4.35410	+	7.54153i	0.231092	+	0.400263i
$356$	−1.70820			−0.0905346
$357$		0			0
$358$	38.4164			2.03037
$359$	1.21885	+	2.11111i	0.0643283	+	0.111420i	0.896396	−	0.443254i	$-0.146176\pi$
$359$	1.21885	+	2.11111i	0.0643283	+	0.111420i	−0.832068	+	0.554674i	$0.812843\pi$
$360$	3.19098	−	5.52694i	0.168180	−	0.291296i
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$	−3.97214	−	6.87994i	−0.208771	−	0.361602i
$363$	4.05573			0.212871
$364$		0			0
$365$	−11.3262			−0.592842
$366$	3.69098	+	6.39297i	0.192931	+	0.334166i
$367$	−4.88197	+	8.45581i	−0.254837	+	0.441390i	−0.964851	−	0.262797i	$-0.915355\pi$
$367$	−4.88197	+	8.45581i	−0.254837	+	0.441390i	0.710015	+	0.704187i	$0.248688\pi$
$368$	−13.2812	+	23.0036i	−0.692328	+	1.19915i
$369$	1.55573	+	2.69460i	0.0809880	+	0.140275i
$370$	4.09017			0.212638
$371$		0			0
$372$	2.25735			0.117038
$373$	−8.80902	−	15.2577i	−0.456114	−	0.790012i	0.542638	−	0.839967i	$-0.317426\pi$
$373$	−8.80902	−	15.2577i	−0.456114	−	0.790012i	−0.998751	+	0.0499548i	$0.984092\pi$
$374$	1.92705	−	3.33775i	0.0996454	−	0.172591i
$375$	1.71885	−	2.97713i	0.0887609	−	0.153738i
$376$	−8.35410	−	14.4697i	−0.430830	−	0.746219i
$377$	1.38197			0.0711749
$378$		0			0
$379$	−15.0000			−0.770498			−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000			−0.770498			−0.385249	+	0.922813i	$0.625884\pi$
$380$	0.309017	+	0.535233i	0.0158522	+	0.0274569i
$381$	−0.708204	+	1.22665i	−0.0362824	+	0.0628429i
$382$	12.1631	−	21.0671i	0.622319	−	1.07789i
$383$	0.354102	+	0.613323i	0.0180938	+	0.0313393i	0.874931	−	0.484248i	$-0.160907\pi$
$383$	0.354102	+	0.613323i	0.0180938	+	0.0313393i	−0.856837	+	0.515588i	$0.827574\pi$
$384$	−5.20163			−0.265444
$385$		0			0
$386$	27.6525			1.40747
$387$	12.0902	+	20.9408i	0.614578	+	1.06448i
$388$	2.30902	−	3.99933i	0.117223	−	0.203035i
$389$	18.7812	−	32.5299i	0.952242	−	1.64933i	0.211686	−	0.977338i	$-0.432105\pi$
$389$	18.7812	−	32.5299i	0.952242	−	1.64933i	0.740556	−	0.671994i	$-0.234562\pi$
$390$	−0.309017	−	0.535233i	−0.0156477	−	0.0271026i
$391$	21.0902			1.06658
$392$		0			0
$393$	−2.12461			−0.107172
$394$	−0.454915	−	0.787936i	−0.0229183	−	0.0396956i
$395$	−2.23607	+	3.87298i	−0.112509	+	0.194871i
$396$	0.545085	−	0.944115i	0.0273916	−	0.0474436i
$397$	−4.61803	−	7.99867i	−0.231772	−	0.401442i	0.726557	−	0.687106i	$-0.241119\pi$
$397$	−4.61803	−	7.99867i	−0.231772	−	0.401442i	−0.958330	+	0.285664i	$0.907786\pi$
$398$	−31.5066			−1.57928
$399$		0			0
$400$	19.4164			0.970820
$401$	−11.4894	−	19.9001i	−0.573751	−	0.993766i	−0.996176	−	0.0873682i	$-0.972154\pi$
$401$	−11.4894	−	19.9001i	−0.573751	−	0.993766i	0.422425	−	0.906398i	$-0.361179\pi$
$402$	−0.718847	+	1.24508i	−0.0358528	+	0.0620989i
$403$	4.78115	−	8.28120i	0.238166	−	0.412516i
$404$	0.982779	+	1.70222i	0.0488951	+	0.0846888i
$405$	−7.70820			−0.383024
$406$		0			0
$407$	−1.56231			−0.0774406
$408$	1.64590	+	2.85078i	0.0814841	+	0.141135i
$409$	−11.6074	+	20.1046i	−0.573949	+	0.994108i	0.422206	+	0.906500i	$0.361256\pi$
$409$	−11.6074	+	20.1046i	−0.573949	+	0.994108i	−0.996155	+	0.0876083i	$0.972078\pi$
$410$	0.881966	−	1.52761i	0.0435572	−	0.0754433i
$411$	1.32624	+	2.29711i	0.0654185	+	0.113308i
$412$	7.85410			0.386944
$413$		0			0
$414$	25.2705			1.24198
$415$	−1.57295	−	2.72443i	−0.0772130	−	0.133737i
$416$	1.69098	−	2.92887i	0.0829073	−	0.143600i
$417$	1.80902	−	3.13331i	0.0885879	−	0.153439i
$418$	−0.500000	−	0.866025i	−0.0244558	−	0.0423587i
$419$	−9.47214			−0.462744			−0.231372	−	0.972865i	$-0.574321\pi$
$419$	−9.47214			−0.462744			−0.231372	+	0.972865i	$0.574321\pi$
$420$		0			0
$421$	3.58359			0.174654			0.0873268	−	0.996180i	$-0.472168\pi$
$421$	3.58359			0.174654			0.0873268	+	0.996180i	$0.472168\pi$
$422$	−14.0172	−	24.2785i	−0.682348	−	1.18186i
$423$	−10.6631	+	18.4691i	−0.518459	+	0.897997i
$424$	5.42705	−	9.39993i	0.263561	−	0.456501i
$425$	−7.70820	−	13.3510i	−0.373903	−	0.647619i
$426$	−5.38197			−0.260757
$427$		0			0
$428$	3.56231			0.172191
$429$	0.118034	+	0.204441i	0.00569873	+	0.00987050i
$430$	6.85410	−	11.8717i	0.330534	−	0.572502i
$431$	16.2361	−	28.1217i	0.782064	−	1.35457i	−0.148674	−	0.988886i	$-0.547500\pi$
$431$	16.2361	−	28.1217i	0.782064	−	1.35457i	0.930737	−	0.365688i	$-0.119166\pi$
$432$	5.42705	+	9.39993i	0.261109	+	0.452254i
$433$	16.1246			0.774899			0.387450	−	0.921891i	$-0.373356\pi$
$433$	16.1246			0.774899			0.387450	+	0.921891i	$0.373356\pi$
$434$		0			0
$435$	0.527864			0.0253091
$436$	3.78115	+	6.54915i	0.181084	+	0.313647i
$437$	2.73607	−	4.73901i	0.130884	−	0.226698i
$438$	3.50000	−	6.06218i	0.167236	−	0.289662i
$439$	1.70820	+	2.95870i	0.0815281	+	0.141211i	0.903907	−	0.427730i	$-0.140687\pi$
$439$	1.70820	+	2.95870i	0.0815281	+	0.141211i	−0.822378	+	0.568941i	$0.807353\pi$
$440$	1.38197			0.0658826
$441$		0			0
$442$	−6.23607			−0.296620
$443$	−11.0451	−	19.1306i	−0.524768	−	0.908925i	−0.999584	−	0.0288396i	$-0.990819\pi$
$443$	−11.0451	−	19.1306i	−0.524768	−	0.908925i	0.474816	−	0.880085i	$-0.342515\pi$
$444$	−0.298374	+	0.516799i	−0.0141602	+	0.0245262i
$445$	−1.38197	+	2.39364i	−0.0655115	+	0.113469i
$446$	−19.7533	−	34.2137i	−0.935345	−	1.62007i
$447$	4.02129			0.190200
$448$		0			0
$449$	−13.6180			−0.642675			−0.321337	−	0.946965i	$-0.604132\pi$
$449$	−13.6180			−0.642675			−0.321337	+	0.946965i	$0.604132\pi$
$450$	−9.23607	−	15.9973i	−0.435392	−	0.754122i
$451$	−0.336881	+	0.583495i	−0.0158631	+	0.0274757i
$452$	6.26393	−	10.8494i	0.294631	−	0.510315i
$453$	−1.91641	−	3.31932i	−0.0900407	−	0.155955i
$454$	−41.3607			−1.94115
$455$		0			0
$456$	0.854102			0.0399970
$457$	−13.0451	−	22.5947i	−0.610223	−	1.05694i	−0.991202	−	0.132354i	$-0.957746\pi$
$457$	−13.0451	−	22.5947i	−0.610223	−	1.05694i	0.380979	−	0.924584i	$-0.375587\pi$
$458$	8.09017	−	14.0126i	0.378029	−	0.654765i
$459$	4.30902	−	7.46344i	0.201128	−	0.348363i
$460$	−1.69098	−	2.92887i	−0.0788425	−	0.136559i
$461$	−32.8541			−1.53017			−0.765084	−	0.643930i	$-0.777303\pi$
$461$	−32.8541			−1.53017			−0.765084	+	0.643930i	$0.777303\pi$
$462$		0			0
$463$	23.0689			1.07210			0.536051	−	0.844186i	$-0.319915\pi$
$463$	23.0689			1.07210			0.536051	+	0.844186i	$0.319915\pi$
$464$	3.35410	+	5.80948i	0.155710	+	0.269698i
$465$	1.82624	−	3.16314i	0.0846898	−	0.146687i
$466$	10.9721	−	19.0043i	0.508274	−	0.880357i
$467$	−10.0451	−	17.3986i	−0.464831	−	0.805111i	0.534363	−	0.845255i	$-0.320552\pi$
$467$	−10.0451	−	17.3986i	−0.464831	−	0.805111i	−0.999194	+	0.0401441i	$0.987218\pi$
$468$	−1.76393			−0.0815378
$469$		0			0
$470$	12.0902			0.557678
$471$	2.35410	+	4.07742i	0.108471	+	0.187878i
$472$	−8.68034	+	15.0348i	−0.399545	+	0.692032i
$473$	−2.61803	+	4.53457i	−0.120377	+	0.208500i
$474$	−1.38197	−	2.39364i	−0.0634758	−	0.109943i
$475$	−4.00000			−0.183533
$476$		0			0
$477$	−13.8541			−0.634336
$478$	20.2254	+	35.0315i	0.925089	+	1.60230i
$479$	−7.39919	+	12.8158i	−0.338077	+	0.585567i	−0.984071	−	0.177775i	$-0.943110\pi$
$479$	−7.39919	+	12.8158i	−0.338077	+	0.585567i	0.645994	+	0.763343i	$0.276443\pi$
$480$	0.645898	−	1.11873i	0.0294811	−	0.0510627i
$481$	1.26393	+	2.18919i	0.0576303	+	0.0998187i
$482$	−36.6525			−1.66947
$483$		0			0
$484$	−6.56231			−0.298287
$485$	−3.73607	−	6.47106i	−0.169646	−	0.293836i
$486$	7.80902	−	13.5256i	0.354224	−	0.613534i
$487$	4.88197	−	8.45581i	0.221223	−	0.383169i	−0.733957	−	0.679196i	$-0.762328\pi$
$487$	4.88197	−	8.45581i	0.221223	−	0.383169i	0.955180	+	0.296027i	$0.0956618\pi$
$488$	13.3541	+	23.1300i	0.604512	+	1.04705i
$489$	−1.45085			−0.0656097
$490$		0			0
$491$	26.4721			1.19467			0.597335	−	0.801992i	$-0.296226\pi$
$491$	26.4721			1.19467			0.597335	+	0.801992i	$0.296226\pi$
$492$	0.128677	+	0.222875i	0.00580121	+	0.0100480i
$493$	2.66312	−	4.61266i	0.119941	−	0.207744i
$494$	−0.809017	+	1.40126i	−0.0363994	+	0.0630456i
$495$	−0.881966	−	1.52761i	−0.0396414	−	0.0686610i
$496$	46.4164			2.08416
$497$		0			0
$498$	1.94427			0.0871249
$499$	13.1910	+	22.8475i	0.590509	+	1.02279i	0.994164	+	0.107881i	$0.0344065\pi$
$499$	13.1910	+	22.8475i	0.590509	+	1.02279i	−0.403654	+	0.914912i	$0.632260\pi$
$500$	−2.78115	+	4.81710i	−0.124377	+	0.215427i
$501$	−1.42705	+	2.47172i	−0.0637559	+	0.110429i
$502$	−5.88197	−	10.1879i	−0.262525	−	0.454707i
$503$	−12.9443			−0.577157			−0.288578	−	0.957456i	$-0.593183\pi$
$503$	−12.9443			−0.577157			−0.288578	+	0.957456i	$0.593183\pi$
$504$		0			0
$505$	3.18034			0.141523
$506$	2.73607	+	4.73901i	0.121633	+	0.210675i
$507$	−2.29180	+	3.96951i	−0.101782	+	0.176292i
$508$	1.14590	−	1.98475i	0.0508410	−	0.0880592i
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	0.733679	−	0.679496i	$-0.237801\pi$
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	−0.955300	+	0.295637i	$0.904468\pi$
$510$	−2.38197			−0.105475
$511$		0			0
$512$	−5.29180			−0.233867
$513$	−1.11803	−	1.93649i	−0.0493624	−	0.0854982i
$514$	10.7812	−	18.6735i	0.475536	−	0.823653i
$515$	6.35410	−	11.0056i	0.279995	−	0.484966i
$516$	1.00000	+	1.73205i	0.0440225	+	0.0762493i
$517$	−4.61803			−0.203101
$518$		0			0
$519$	8.11146			0.356053
$520$	−1.11803	−	1.93649i	−0.0490290	−	0.0849208i
$521$	6.59017	−	11.4145i	0.288721	−	0.500079i	−0.684784	−	0.728746i	$-0.740103\pi$
$521$	6.59017	−	11.4145i	0.288721	−	0.500079i	0.973505	+	0.228667i	$0.0734368\pi$
$522$	3.19098	−	5.52694i	0.139666	−	0.241908i
$523$	−19.4443	−	33.6785i	−0.850239	−	1.47266i	−0.880993	−	0.473130i	$-0.843124\pi$
$523$	−19.4443	−	33.6785i	−0.850239	−	1.47266i	0.0307542	−	0.999527i	$-0.490209\pi$
$524$	3.43769			0.150176
$525$		0			0
$526$	26.7984			1.16846
$527$	−18.4271	−	31.9166i	−0.802695	−	1.39031i
$528$	−0.572949	+	0.992377i	−0.0249344	+	0.0431877i
$529$	−3.47214	+	6.01392i	−0.150962	+	0.261475i
$530$	3.92705	+	6.80185i	0.170580	+	0.295454i
$531$	22.1591			0.961621
$532$		0			0
$533$	1.09017			0.0472205
$534$	−0.854102	−	1.47935i	−0.0369606	−	0.0640176i
$535$	2.88197	−	4.99171i	0.124598	−	0.215811i
$536$	−2.60081	+	4.50474i	−0.112338	+	0.194575i
$537$	4.53444	+	7.85388i	0.195676	+	0.338920i
$538$	42.0344			1.81223
$539$		0			0
$540$	−1.38197			−0.0594703
$541$	0.0557281	+	0.0965239i	0.00239594	+	0.00414989i	0.867221	−	0.497924i	$-0.165904\pi$
$541$	0.0557281	+	0.0965239i	0.00239594	+	0.00414989i	−0.864825	+	0.502074i	$0.832571\pi$
$542$	−20.6803	+	35.8194i	−0.888297	+	1.53857i
$543$	0.937694	−	1.62413i	0.0402403	−	0.0696983i
$544$	−6.51722	−	11.2882i	−0.279424	−	0.483976i
$545$	12.2361			0.524136
$546$		0			0
$547$	−15.6180			−0.667779			−0.333889	−	0.942612i	$-0.608361\pi$
$547$	−15.6180			−0.667779			−0.333889	+	0.942612i	$0.608361\pi$
$548$	−2.14590	−	3.71680i	−0.0916682	−	0.158774i
$549$	17.0451	−	29.5230i	0.727466	−	1.26001i
$550$	2.00000	−	3.46410i	0.0852803	−	0.147710i
$551$	−0.690983	−	1.19682i	−0.0294369	−	0.0509861i
$552$	−4.67376			−0.198929
$553$		0			0
$554$	−27.7082			−1.17721
$555$	0.482779	+	0.836198i	0.0204928	+	0.0354946i
$556$	−2.92705	+	5.06980i	−0.124135	+	0.215007i
$557$	18.3992	−	31.8683i	0.779599	−	1.35030i	−0.152575	−	0.988292i	$-0.548756\pi$
$557$	18.3992	−	31.8683i	0.779599	−	1.35030i	0.932173	−	0.362012i	$-0.117910\pi$
$558$	−22.0795	−	38.2429i	−0.934701	−	1.61895i
$559$	8.47214			0.358333
$560$		0			0
$561$	0.909830			0.0384131
$562$	9.13525	+	15.8227i	0.385347	+	0.667441i
$563$	8.11803	−	14.0608i	0.342134	−	0.592594i	−0.642695	−	0.766123i	$-0.722184\pi$
$563$	8.11803	−	14.0608i	0.342134	−	0.592594i	0.984829	+	0.173528i	$0.0555169\pi$
$564$	−0.881966	+	1.52761i	−0.0371375	+	0.0643240i
$565$	−10.1353	−	17.5548i	−0.426393	−	0.738535i
$566$	−25.7426			−1.08204
$567$		0			0
$568$	−19.4721			−0.817033
$569$	9.20820	+	15.9491i	0.386028	+	0.668620i	0.991911	−	0.126933i	$-0.0405135\pi$
$569$	9.20820	+	15.9491i	0.386028	+	0.668620i	−0.605883	+	0.795554i	$0.707180\pi$
$570$	−0.309017	+	0.535233i	−0.0129433	+	0.0224184i
$571$	−13.8262	+	23.9477i	−0.578610	+	1.00218i	0.417029	+	0.908893i	$0.363071\pi$
$571$	−13.8262	+	23.9477i	−0.578610	+	1.00218i	−0.995639	+	0.0932888i	$0.970262\pi$
$572$	−0.190983	−	0.330792i	−0.00798540	−	0.0138311i
$573$	5.74265			0.239902
$574$		0			0
$575$	21.8885			0.912815
$576$	6.04508	+	10.4704i	0.251879	+	0.436266i
$577$	−23.1353	+	40.0714i	−0.963133	+	1.66820i	−0.248584	+	0.968610i	$0.579965\pi$
$577$	−23.1353	+	40.0714i	−0.963133	+	1.66820i	−0.714549	+	0.699585i	$0.753368\pi$
$578$	1.73607	−	3.00696i	0.0722109	−	0.125073i
$579$	3.26393	+	5.65330i	0.135644	+	0.234943i
$580$	−0.854102			−0.0354647
$581$		0			0
$582$	4.61803			0.191424
$583$	−1.50000	−	2.59808i	−0.0621237	−	0.107601i
$584$	12.6631	−	21.9332i	0.524004	−	0.907601i
$585$	−1.42705	+	2.47172i	−0.0590013	+	0.102193i
$586$	21.2254	+	36.7635i	0.876814	+	1.51869i
$587$	−38.0000			−1.56843			−0.784214	−	0.620491i	$-0.786934\pi$
$587$	−38.0000			−1.56843			−0.784214	+	0.620491i	$0.786934\pi$
$588$		0			0
$589$	−9.56231			−0.394008
$590$	−6.28115	−	10.8793i	−0.258591	−	0.447893i
$591$	0.107391	−	0.186006i	0.00441747	−	0.00765128i
$592$	−6.13525	+	10.6266i	−0.252157	+	0.436749i
$593$	2.59017	+	4.48631i	0.106366	+	0.184231i	0.914295	−	0.405048i	$-0.132745\pi$
$593$	2.59017	+	4.48631i	0.106366	+	0.184231i	−0.807930	+	0.589279i	$0.799412\pi$
$594$	2.23607			0.0917470
$595$		0			0
$596$	−6.50658			−0.266520
$597$	−3.71885	−	6.44123i	−0.152202	−	0.263622i
$598$	4.42705	−	7.66788i	0.181036	−	0.313563i
$599$	17.9894	−	31.1585i	0.735025	−	1.27310i	−0.219687	−	0.975570i	$-0.570504\pi$
$599$	17.9894	−	31.1585i	0.735025	−	1.27310i	0.954712	−	0.297531i	$-0.0961630\pi$
$600$	1.70820	+	2.95870i	0.0697371	+	0.120788i
$601$	−34.5623			−1.40983			−0.704913	−	0.709294i	$-0.749014\pi$
$601$	−34.5623			−1.40983			−0.704913	+	0.709294i	$0.749014\pi$
$602$		0			0
$603$	6.63932			0.270374
$604$	3.10081	+	5.37077i	0.126170	+	0.218533i
$605$	−5.30902	+	9.19549i	−0.215842	+	0.373850i
$606$	−0.982779	+	1.70222i	−0.0399227	+	0.0691481i
$607$	−4.88197	−	8.45581i	−0.198153	−	0.343211i	0.749777	−	0.661691i	$-0.230161\pi$
$607$	−4.88197	−	8.45581i	−0.198153	−	0.343211i	−0.947930	+	0.318480i	$0.896828\pi$
$608$	−3.38197			−0.137157
$609$		0			0
$610$	−19.3262			−0.782497
$611$	3.73607	+	6.47106i	0.151145	+	0.261791i
$612$	−3.39919	+	5.88756i	−0.137404	+	0.237991i
$613$	−11.8992	+	20.6100i	−0.480604	+	0.832430i	−0.999752	−	0.0222540i	$-0.992916\pi$
$613$	−11.8992	+	20.6100i	−0.480604	+	0.832430i	0.519149	+	0.854684i	$0.326249\pi$
$614$	25.6803	+	44.4797i	1.03637	+	1.79505i
$615$	0.416408			0.0167912
$616$		0			0
$617$	−36.1459			−1.45518			−0.727590	−	0.686013i	$-0.759359\pi$
$617$	−36.1459			−1.45518			−0.727590	+	0.686013i	$0.759359\pi$
$618$	3.92705	+	6.80185i	0.157969	+	0.273611i
$619$	1.80902	−	3.13331i	0.0727105	−	0.125938i	−0.827378	−	0.561646i	$-0.810168\pi$
$619$	1.80902	−	3.13331i	0.0727105	−	0.125938i	0.900088	+	0.435707i	$0.143502\pi$
$620$	−2.95492	+	5.11806i	−0.118672	+	0.205546i
$621$	6.11803	+	10.5967i	0.245508	+	0.425233i
$622$	54.1246			2.17020
$623$		0			0
$624$	1.85410			0.0742235
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	19.0902	−	33.0651i	0.762997	−	1.32155i
$627$	0.118034	−	0.204441i	0.00471382	−	0.00816458i
$628$	−3.80902	−	6.59741i	−0.151996	−	0.263265i
$629$	9.74265			0.388465
$630$		0			0
$631$	0.819660			0.0326302			0.0163151	−	0.999867i	$-0.494807\pi$
$631$	0.819660			0.0326302			0.0163151	+	0.999867i	$0.494807\pi$
$632$	−5.00000	−	8.66025i	−0.198889	−	0.344486i
$633$	3.30902	−	5.73139i	0.131522	−	0.227802i
$634$	−17.3262	+	30.0099i	−0.688113	+	1.19185i
$635$	−1.85410	−	3.21140i	−0.0735778	−	0.127440i
$636$	−1.14590			−0.0454378
$637$		0			0
$638$	1.38197			0.0547126
$639$	12.4271	+	21.5243i	0.491607	+	0.851488i
$640$	6.80902	−	11.7936i	0.269150	−	0.466182i
$641$	−18.3992	+	31.8683i	−0.726724	+	1.25872i	0.231536	+	0.972826i	$0.425625\pi$
$641$	−18.3992	+	31.8683i	−0.726724	+	1.25872i	−0.958260	+	0.285897i	$0.907709\pi$
$642$	1.78115	+	3.08505i	0.0702965	+	0.121757i
$643$	11.6525			0.459529			0.229764	−	0.973246i	$-0.426204\pi$
$643$	11.6525			0.459529			0.229764	+	0.973246i	$0.426204\pi$
$644$		0			0
$645$	3.23607			0.127420
$646$	3.11803	+	5.40059i	0.122677	+	0.212484i
$647$	8.20820	−	14.2170i	0.322698	−	0.558929i	−0.658346	−	0.752716i	$-0.728744\pi$
$647$	8.20820	−	14.2170i	0.322698	−	0.558929i	0.981044	+	0.193787i	$0.0620769\pi$
$648$	8.61803	−	14.9269i	0.338548	−	0.586383i
$649$	2.39919	+	4.15551i	0.0941763	+	0.163118i
$650$	−6.47214			−0.253858
$651$		0			0
$652$	2.34752			0.0919361
$653$	22.5344	+	39.0308i	0.881841	+	1.52739i	0.849292	+	0.527923i	$0.177029\pi$
$653$	22.5344	+	39.0308i	0.881841	+	1.52739i	0.0325486	+	0.999470i	$0.489638\pi$
$654$	−3.78115	+	6.54915i	−0.147855	+	0.256092i
$655$	2.78115	−	4.81710i	0.108669	−	0.188220i
$656$	2.64590	+	4.58283i	0.103305	+	0.178929i
$657$	−32.3262			−1.26117
$658$		0			0
$659$	10.3262			0.402253			0.201127	−	0.979565i	$-0.435540\pi$
$659$	10.3262			0.402253			0.201127	+	0.979565i	$0.435540\pi$
$660$	−0.0729490	−	0.126351i	−0.00283954	−	0.00491822i
$661$	1.00000	−	1.73205i	0.0388955	−	0.0673690i	−0.845922	−	0.533306i	$-0.820949\pi$
$661$	1.00000	−	1.73205i	0.0388955	−	0.0673690i	0.884818	+	0.465937i	$0.154283\pi$
$662$	−0.927051	+	1.60570i	−0.0360309	+	0.0624073i
$663$	−0.736068	−	1.27491i	−0.0285865	−	0.0495133i
$664$	7.03444			0.272989
$665$		0			0
$666$	11.6738			0.452349
$667$	3.78115	+	6.54915i	0.146407	+	0.253584i
$668$	2.30902	−	3.99933i	0.0893385	−	0.154739i
$669$	4.66312	−	8.07676i	0.180287	−	0.312266i
$670$	−1.88197	−	3.25966i	−0.0727067	−	0.125932i
$671$	7.38197			0.284978
$672$		0			0
$673$	15.5066			0.597735			0.298867	−	0.954295i	$-0.403391\pi$
$673$	15.5066			0.597735			0.298867	+	0.954295i	$0.403391\pi$
$674$	5.50000	+	9.52628i	0.211852	+	0.366939i
$675$	4.47214	−	7.74597i	0.172133	−	0.298142i
$676$	3.70820	−	6.42280i	0.142623	−	0.247031i
$677$	15.0795	+	26.1185i	0.579553	+	1.00382i	0.995530	+	0.0944407i	$0.0301063\pi$
$677$	15.0795	+	26.1185i	0.579553	+	1.00382i	−0.415977	+	0.909375i	$0.636560\pi$
$678$	12.5279			0.481130
$679$		0			0
$680$	−8.61803			−0.330487
$681$	−4.88197	−	8.45581i	−0.187077	−	0.324027i
$682$	4.78115	−	8.28120i	0.183080	−	0.317104i
$683$	−18.6459	+	32.2956i	−0.713465	+	1.23576i	0.250083	+	0.968224i	$0.419542\pi$
$683$	−18.6459	+	32.2956i	−0.713465	+	1.23576i	−0.963548	+	0.267534i	$0.913791\pi$
$684$	0.881966	+	1.52761i	0.0337228	+	0.0584096i
$685$	−6.94427			−0.265327
$686$		0			0
$687$	3.81966			0.145729
$688$	20.5623	+	35.6150i	0.783931	+	1.35781i
$689$	−2.42705	+	4.20378i	−0.0924633	+	0.160151i
$690$	1.69098	−	2.92887i	0.0643746	−	0.111500i
$691$	10.2705	+	17.7890i	0.390709	+	0.676727i	0.992543	−	0.121894i	$-0.0388967\pi$
$691$	10.2705	+	17.7890i	0.390709	+	0.676727i	−0.601835	+	0.798621i	$0.705563\pi$
$692$	−13.1246			−0.498923
$693$		0			0
$694$	−2.90983			−0.110456
$695$	4.73607	+	8.20311i	0.179649	+	0.311162i
$696$	−0.590170	+	1.02220i	−0.0223703	+	0.0387466i
$697$	2.10081	−	3.63871i	0.0795740	−	0.137826i
$698$	29.1074	+	50.4155i	1.10173	+	1.90825i
$699$	5.18034			0.195938
$700$		0			0
$701$	0.944272			0.0356647			0.0178323	−	0.999841i	$-0.494323\pi$
$701$	0.944272			0.0356647			0.0178323	+	0.999841i	$0.494323\pi$
$702$	−1.80902	−	3.13331i	−0.0682769	−	0.118259i
$703$	1.26393	−	2.18919i	0.0476701	−	0.0825670i
$704$	−1.30902	+	2.26728i	−0.0493354	+	0.0854515i
$705$	1.42705	+	2.47172i	0.0537458	+	0.0930905i
$706$	−21.4721			−0.808114
$707$		0			0
$708$	1.83282			0.0688814
$709$	−25.0623	−	43.4092i	−0.941235	−	1.63027i	−0.763120	−	0.646256i	$-0.776334\pi$
$709$	−25.0623	−	43.4092i	−0.941235	−	1.63027i	−0.178114	−	0.984010i	$-0.557000\pi$
$710$	7.04508	−	12.2024i	0.264397	−	0.457950i
$711$	−6.38197	+	11.0539i	−0.239342	+	0.414553i
$712$	−3.09017	−	5.35233i	−0.115809	−	0.200587i
$713$	52.3262			1.95963
$714$		0			0
$715$	−0.618034			−0.0231132
$716$	−7.33688	−	12.7079i	−0.274192	−	0.474915i
$717$	−4.77458	+	8.26981i	−0.178310	+	0.308842i
$718$	1.97214	−	3.41584i	0.0735995	−	0.127478i
$719$	−18.9443	−	32.8124i	−0.706502	−	1.22370i	−0.966147	−	0.257993i	$-0.916939\pi$
$719$	−18.9443	−	32.8124i	−0.706502	−	1.22370i	0.259645	−	0.965704i	$-0.416395\pi$
$720$	−13.8541			−0.516312
$721$		0			0
$722$	1.61803			0.0602170
$723$	−4.32624	−	7.49326i	−0.160895	−	0.278677i
$724$	−1.51722	+	2.62790i	−0.0563871	+	0.0976653i
$725$	2.76393	−	4.78727i	0.102650	−	0.177795i
$726$	−3.28115	−	5.68312i	−0.121775	−	0.210921i
$727$	−22.5967			−0.838067			−0.419033	−	0.907971i	$-0.637631\pi$
$727$	−22.5967			−0.838067			−0.419033	+	0.907971i	$0.637631\pi$
$728$		0			0
$729$	−19.4377			−0.719915
$730$	9.16312	+	15.8710i	0.339142	+	0.587412i
$731$	16.3262	−	28.2779i	0.603848	−	1.04589i
$732$	1.40983	−	2.44190i	0.0521088	−	0.0902551i
$733$	13.7082	+	23.7433i	0.506324	+	0.876979i	0.999973	+	0.00731786i	$0.00232937\pi$
$733$	13.7082	+	23.7433i	0.506324	+	0.876979i	−0.493649	+	0.869661i	$0.664337\pi$
$734$	15.7984			0.583129
$735$		0			0
$736$	18.5066			0.682162
$737$	0.718847	+	1.24508i	0.0264791	+	0.0458631i
$738$	2.51722	−	4.35995i	0.0926602	−	0.160492i
$739$	−10.2639	+	17.7777i	−0.377565	+	0.653961i	−0.990707	−	0.136011i	$-0.956572\pi$
$739$	−10.2639	+	17.7777i	−0.377565	+	0.653961i	0.613143	+	0.789972i	$0.289905\pi$
$740$	−0.781153	−	1.35300i	−0.0287158	−	0.0497371i
$741$	−0.381966			−0.0140319
$742$		0			0
$743$	8.34752			0.306241			0.153120	−	0.988208i	$-0.451068\pi$
$743$	8.34752			0.306241			0.153120	+	0.988208i	$0.451068\pi$
$744$	4.08359	+	7.07299i	0.149712	+	0.259308i
$745$	−5.26393	+	9.11740i	−0.192856	+	0.334036i
$746$	−14.2533	+	24.6874i	−0.521850	+	0.903871i
$747$	−4.48936	−	7.77579i	−0.164257	−	0.284501i
$748$	−1.47214			−0.0538266
$749$		0			0
$750$	−5.56231			−0.203107
$751$	0.281153	+	0.486971i	0.0102594	+	0.0177698i	0.871110	−	0.491089i	$-0.163401\pi$
$751$	0.281153	+	0.486971i	0.0102594	+	0.0177698i	−0.860850	+	0.508859i	$0.830068\pi$
$752$	−18.1353	+	31.4112i	−0.661325	+	1.14545i
$753$	1.38854	−	2.40503i	0.0506013	−	0.0876441i
$754$	−1.11803	−	1.93649i	−0.0407164	−	0.0705229i
$755$	10.0344			0.365191
$756$		0			0
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	12.1353	+	21.0189i	0.440772	+	0.763440i
$759$	−0.645898	+	1.11873i	−0.0234446	+	0.0406073i
$760$	−1.11803	+	1.93649i	−0.0405554	+	0.0702439i
$761$	15.7361	+	27.2557i	0.570432	+	0.988017i	0.996521	+	0.0833362i	$0.0265575\pi$
$761$	15.7361	+	27.2557i	0.570432	+	0.988017i	−0.426089	+	0.904681i	$0.640109\pi$
$762$	2.29180			0.0830230
$763$		0			0
$764$	−9.29180			−0.336165
$765$	5.50000	+	9.52628i	0.198853	+	0.344423i
$766$	0.572949	−	0.992377i	0.0207015	−	0.0358560i
$767$	3.88197	−	6.72376i	0.140170	−	0.242781i
$768$	2.59017	+	4.48631i	0.0934647	+	0.161886i
$769$	23.4164			0.844417			0.422209	−	0.906499i	$-0.361255\pi$
$769$	23.4164			0.844417			0.422209	+	0.906499i	$0.361255\pi$
$770$		0			0
$771$	5.09017			0.183318
$772$	−5.28115	−	9.14723i	−0.190073	−	0.329216i
$773$	−12.2705	+	21.2531i	−0.441340	+	0.764423i	−0.997789	−	0.0664588i	$-0.978830\pi$
$773$	−12.2705	+	21.2531i	−0.441340	+	0.764423i	0.556450	+	0.830881i	$0.312163\pi$
$774$	19.5623	−	33.8829i	0.703153	−	1.21790i
$775$	−19.1246	−	33.1248i	−0.686976	−	1.18988i
$776$	16.7082			0.599790
$777$		0			0
$778$	−60.7771			−2.17896
$779$	−0.545085	−	0.944115i	−0.0195297	−	0.0338264i
$780$	−0.118034	+	0.204441i	−0.00422629	+	0.00732016i
$781$	−2.69098	+	4.66092i	−0.0962909	+	0.166781i
$782$	−17.0623	−	29.5528i	−0.610147	−	1.05681i
$783$	3.09017			0.110434
$784$		0			0
$785$	−12.3262			−0.439942
$786$	1.71885	+	2.97713i	0.0613092	+	0.106191i
$787$	−23.8885	+	41.3762i	−0.851535	+	1.47490i	0.0282884	+	0.999600i	$0.490994\pi$
$787$	−23.8885	+	41.3762i	−0.851535	+	1.47490i	−0.879823	+	0.475301i	$0.842339\pi$
$788$	−0.173762	+	0.300965i	−0.00619002	+	0.0107214i
$789$	3.16312	+	5.47868i	0.112610	+	0.195046i
$790$	7.23607			0.257448
$791$		0			0
$792$	3.94427			0.140154
$793$	−5.97214	−	10.3440i	−0.212077	−	0.367328i
$794$	−7.47214	+	12.9421i	−0.265176	+	0.459299i
$795$	−0.927051	+	1.60570i	−0.0328791	+	0.0569483i
$796$	6.01722	+	10.4221i	0.213275	+	0.369403i
$797$	−32.1459			−1.13867			−0.569333	−	0.822107i	$-0.692799\pi$
$797$	−32.1459			−1.13867			−0.569333	+	0.822107i	$0.692799\pi$
$798$		0			0
$799$	28.7984			1.01881
$800$	−6.76393	−	11.7155i	−0.239141	−	0.414205i
$801$	−3.94427	+	6.83168i	−0.139364	+	0.241386i
$802$	−18.5902	+	32.1991i	−0.656442	+	1.13699i
$803$	−3.50000	−	6.06218i	−0.123512	−	0.213930i
$804$	0.549150			0.0193670
$805$		0			0
$806$	−15.4721			−0.544983
$807$	4.96149	+	8.59356i	0.174653	+	0.302508i
$808$	−3.55573	+	6.15870i	−0.125090	+	0.216662i
$809$	3.88197	−	6.72376i	0.136483	−	0.236395i	−0.789680	−	0.613519i	$-0.789754\pi$
$809$	3.88197	−	6.72376i	0.136483	−	0.236395i	0.926163	+	0.377124i	$0.123087\pi$
$810$	6.23607	+	10.8012i	0.219113	+	0.379515i
$811$	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
$813$	−9.76393			−0.342436
$814$	1.26393	+	2.18919i	0.0443008	+	0.0767312i
$815$	1.89919	−	3.28949i	0.0665256	−	0.115226i
$816$	3.57295	−	6.18853i	0.125078	−	0.216642i
$817$	−4.23607	−	7.33708i	−0.148201	−	0.256692i
$818$	37.5623			1.31334
$819$		0			0
$820$	−0.673762			−0.0235288
$821$	2.94427	+	5.09963i	0.102756	+	0.177978i	0.912819	−	0.408364i	$-0.133901\pi$
$821$	2.94427	+	5.09963i	0.102756	+	0.177978i	−0.810063	+	0.586342i	$0.800567\pi$
$822$	2.14590	−	3.71680i	0.0748468	−	0.129638i
$823$	−14.5623	+	25.2227i	−0.507610	+	0.879206i	0.492351	+	0.870397i	$0.336138\pi$
$823$	−14.5623	+	25.2227i	−0.507610	+	0.879206i	−0.999961	+	0.00880976i	$0.997196\pi$
$824$	14.2082	+	24.6093i	0.494966	+	0.857307i
$825$	0.944272			0.0328753
$826$		0			0
$827$	35.7639			1.24363			0.621817	−	0.783163i	$-0.286395\pi$
$827$	35.7639			1.24363			0.621817	+	0.783163i	$0.286395\pi$
$828$	−4.82624	−	8.35929i	−0.167723	−	0.290505i
$829$	4.47214	−	7.74597i	0.155324	−	0.269029i	−0.777853	−	0.628446i	$-0.783691\pi$
$829$	4.47214	−	7.74597i	0.155324	−	0.269029i	0.933177	+	0.359418i	$0.117025\pi$
$830$	−2.54508	+	4.40822i	−0.0883412	+	0.153011i
$831$	−3.27051	−	5.66469i	−0.113453	−	0.196506i
$832$	4.23607			0.146859
$833$		0			0
$834$	−5.85410			−0.202711
$835$	−3.73607	−	6.47106i	−0.129292	−	0.223940i
$836$	−0.190983	+	0.330792i	−0.00660529	+	0.0114407i
$837$	10.6910	−	18.5173i	0.369534	−	0.640052i
$838$	7.66312	+	13.2729i	0.264718	+	0.458505i
$839$	7.63932			0.263739			0.131869	−	0.991267i	$-0.457902\pi$
$839$	7.63932			0.263739			0.131869	+	0.991267i	$0.457902\pi$
$840$		0			0
$841$	−27.0902			−0.934144
$842$	−2.89919	−	5.02154i	−0.0999126	−	0.173054i
$843$	−2.15654	+	3.73524i	−0.0742752	+	0.128648i
$844$	−5.35410	+	9.27358i	−0.184296	+	0.319210i
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$	34.5066			1.18636
$847$		0			0
$848$	−23.5623			−0.809133
$849$	−3.03851	−	5.26285i	−0.104281	−	0.180621i
$850$	−12.4721	+	21.6024i	−0.427791	+	0.740955i
$851$	−6.91641	+	11.9796i	−0.237091	+	0.410654i
$852$	1.02786	+	1.78031i	0.0352140	+	0.0609925i
$853$	−21.4377			−0.734013			−0.367006	−	0.930218i	$-0.619617\pi$
$853$	−21.4377			−0.734013			−0.367006	+	0.930218i	$0.619617\pi$
$854$		0			0
$855$	2.85410			0.0976082
$856$	6.44427	+	11.1618i	0.220261	+	0.381503i
$857$	−20.6353	+	35.7413i	−0.704887	+	1.22090i	0.261845	+	0.965110i	$0.415669\pi$
$857$	−20.6353	+	35.7413i	−0.704887	+	1.22090i	−0.966732	+	0.255790i	$0.917664\pi$
$858$	0.190983	−	0.330792i	0.00652005	−	0.0112931i
$859$	7.39919	+	12.8158i	0.252457	+	0.437268i	0.964202	−	0.265170i	$-0.0854280\pi$
$859$	7.39919	+	12.8158i	0.252457	+	0.437268i	−0.711745	+	0.702438i	$0.752095\pi$
$860$	−5.23607			−0.178548
$861$		0			0
$862$	−52.5410			−1.78955
$863$	8.75329	+	15.1611i	0.297965	+	0.516091i	0.975670	−	0.219243i	$-0.0703587\pi$
$863$	8.75329	+	15.1611i	0.297965	+	0.516091i	−0.677705	+	0.735334i	$0.737025\pi$
$864$	3.78115	−	6.54915i	0.128637	−	0.222807i
$865$	−10.6180	+	18.3910i	−0.361024	+	0.625312i
$866$	−13.0451	−	22.5947i	−0.443290	−	0.767801i
$867$	0.819660			0.0278371
$868$		0			0
$869$	−2.76393			−0.0937600
$870$	−0.427051	−	0.739674i	−0.0144784	−	0.0250773i
$871$	1.16312	−	2.01458i	0.0394108	−	0.0682615i
$872$	−13.6803	+	23.6950i	−0.463275	+	0.802415i
$873$	−10.6631	−	18.4691i	−0.360892	−	0.625083i
$874$	−8.85410			−0.299494
$875$		0			0
$876$	−2.67376			−0.0903380
$877$	−20.5066	−	35.5184i	−0.692458	−	1.19937i	−0.971030	−	0.238957i	$-0.923194\pi$
$877$	−20.5066	−	35.5184i	−0.692458	−	1.19937i	0.278572	−	0.960415i	$-0.410139\pi$
$878$	2.76393	−	4.78727i	0.0932782	−	0.161563i
$879$	−5.01064	+	8.67869i	−0.169005	+	0.292725i
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	−10.0902			−0.339946			−0.169973	−	0.985449i	$-0.554368\pi$
$881$	−10.0902			−0.339946			−0.169973	+	0.985449i	$0.554368\pi$
$882$		0			0
$883$	13.4721			0.453373			0.226687	−	0.973968i	$-0.427211\pi$
$883$	13.4721			0.453373			0.226687	+	0.973968i	$0.427211\pi$
$884$	1.19098	+	2.06284i	0.0400571	+	0.0693809i
$885$	1.48278	−	2.56825i	0.0498431	−	0.0863307i
$886$	−17.8713	+	30.9540i	−0.600399	+	1.03992i
$887$	0.972136	+	1.68379i	0.0326411	+	0.0565361i	0.881884	−	0.471466i	$-0.156275\pi$
$887$	0.972136	+	1.68379i	0.0326411	+	0.0565361i	−0.849243	+	0.528002i	$0.822941\pi$
$888$	−2.15905			−0.0724531
$889$		0			0
$890$	4.47214			0.149906
$891$	−2.38197	−	4.12569i	−0.0797989	−	0.138216i
$892$	−7.54508	+	13.0685i	−0.252628	+	0.437565i
$893$	3.73607	−	6.47106i	0.125023	−	0.216546i
$894$	−3.25329	−	5.63486i	−0.108806	−	0.188458i
$895$	−23.7426			−0.793629
$896$		0			0
$897$	2.09017			0.0697887
$898$	11.0172	+	19.0824i	0.367649	+	0.636787i
$899$	6.60739	−	11.4443i	0.220369	−	0.381690i
$900$	−3.52786	+	6.11044i	−0.117595	+	0.203681i
$901$	9.35410	+	16.2018i	0.311630	+	0.539760i
$902$	1.09017			0.0362987
$903$		0			0
$904$	45.3262			1.50753
$905$	2.45492	+	4.25204i	0.0816041	+	0.141343i
$906$	−3.10081	+	5.37077i	−0.103018	+	0.178432i
$907$	0.736068	−	1.27491i	0.0244407	−	0.0423326i	−0.853546	−	0.521017i	$-0.825553\pi$
$907$	0.736068	−	1.27491i	0.0244407	−	0.0423326i	0.877987	+	0.478684i	$0.158886\pi$
$908$	7.89919	+	13.6818i	0.262144	+	0.454046i
$909$	9.07701			0.301066
$910$		0			0
$911$	22.0000			0.728893			0.364446	−	0.931224i	$-0.381258\pi$
$911$	22.0000			0.728893			0.364446	+	0.931224i	$0.381258\pi$
$912$	−0.927051	−	1.60570i	−0.0306977	−	0.0531700i
$913$	0.972136	−	1.68379i	0.0321730	−	0.0557253i
$914$	−21.1074	+	36.5591i	−0.698170	+	1.20927i
$915$	−2.28115	−	3.95107i	−0.0754126	−	0.130618i
$916$	−6.18034			−0.204204
$917$		0			0
$918$	−13.9443			−0.460230
$919$	−9.53444	−	16.5141i	−0.314512	−	0.544751i	0.664821	−	0.747002i	$-0.268508\pi$
$919$	−9.53444	−	16.5141i	−0.314512	−	0.544751i	−0.979334	+	0.202251i	$0.935174\pi$
$920$	6.11803	−	10.5967i	0.201706	−	0.349364i
$921$	−6.06231	+	10.5002i	−0.199760	+	0.345994i
$922$	26.5795	+	46.0371i	0.875350	+	1.51615i
$923$	8.70820			0.286634
$924$		0			0
$925$	10.1115			0.332463
$926$	−18.6631	−	32.3255i	−0.613308	−	1.06228i
$927$	18.1353	−	31.4112i	0.595640	−	1.03168i
$928$	2.33688	−	4.04760i	0.0767119	−	0.132869i
$929$	−13.7188	−	23.7617i	−0.450101	−	0.779597i	0.548291	−	0.836288i	$-0.315279\pi$
$929$	−13.7188	−	23.7617i	−0.450101	−	0.779597i	−0.998392	+	0.0566902i	$0.981945\pi$
$930$	−5.90983			−0.193791
$931$		0			0
$932$	−8.38197			−0.274560
$933$	6.38854	+	11.0653i	0.209152	+	0.362261i
$934$	−16.2533	+	28.1515i	−0.531824	+	0.921146i
$935$	−1.19098	+	2.06284i	−0.0389493	+	0.0674622i
$936$	−3.19098	−	5.52694i	−0.104301	−	0.180654i
$937$	51.9230			1.69625			0.848125	−	0.529796i	$-0.177732\pi$
$937$	51.9230			1.69625			0.848125	+	0.529796i	$0.177732\pi$
$938$		0			0
$939$	9.01316			0.294133
$940$	−2.30902	−	3.99933i	−0.0753118	−	0.130444i
$941$	11.6525	−	20.1827i	0.379860	−	0.657937i	−0.611182	−	0.791490i	$-0.709306\pi$
$941$	11.6525	−	20.1827i	0.379860	−	0.657937i	0.991042	+	0.133554i	$0.0426389\pi$
$942$	3.80902	−	6.59741i	0.124104	−	0.214955i
$943$	2.98278	+	5.16632i	0.0971327	+	0.168239i
$944$	37.6869			1.22660
$945$		0			0
$946$	8.47214			0.275453
$947$	−17.1910	−	29.7757i	−0.558632	−	0.967579i	−0.997611	−	0.0690816i	$-0.977993\pi$
$947$	−17.1910	−	29.7757i	−0.558632	−	0.967579i	0.438979	−	0.898497i	$-0.355340\pi$
$948$	−0.527864	+	0.914287i	−0.0171442	+	0.0296947i
$949$	−5.66312	+	9.80881i	−0.183833	+	0.318407i
$950$	3.23607	+	5.60503i	0.104992	+	0.181851i
$951$	−8.18034			−0.265266
$952$		0			0
$953$	17.7426			0.574741			0.287370	−	0.957820i	$-0.407219\pi$
$953$	17.7426			0.574741			0.287370	+	0.957820i	$0.407219\pi$
$954$	11.2082	+	19.4132i	0.362879	+	0.628525i
$955$	−7.51722	+	13.0202i	−0.243252	+	0.421324i
$956$	7.72542	−	13.3808i	0.249858	−	0.432767i
$957$	0.163119	+	0.282530i	0.00527289	+	0.00913291i
$958$	23.9443			0.773604
$959$		0			0
$960$	1.61803			0.0522218
$961$	−30.2188	−	52.3406i	−0.974802	−	1.68841i
$962$	2.04508	−	3.54219i	0.0659362	−	0.114205i
$963$	8.22542	−	14.2469i	0.265061	−	0.459098i
$964$	7.00000	+	12.1244i	0.225455	+	0.390499i
$965$	−17.0902			−0.550152
$966$		0			0
$967$	−37.4508			−1.20434			−0.602169	−	0.798369i	$-0.705697\pi$
$967$	−37.4508			−1.20434			−0.602169	+	0.798369i	$0.705697\pi$
$968$	−11.8713	−	20.5617i	−0.381559	−	0.660879i
$969$	−0.736068	+	1.27491i	−0.0236459	+	0.0409559i
$970$	−6.04508	+	10.4704i	−0.194096	+	0.336184i
$971$	0.409830	+	0.709846i	0.0131521	+	0.0227801i	0.872527	−	0.488567i	$-0.162480\pi$
$971$	0.409830	+	0.709846i	0.0131521	+	0.0227801i	−0.859374	+	0.511347i	$0.829147\pi$
$972$	−5.96556			−0.191345
$973$		0			0
$974$	−15.7984			−0.506213
$975$	−0.763932	−	1.32317i	−0.0244654	−	0.0423753i
$976$	28.9894	−	50.2110i	0.927927	−	1.60722i
$977$	5.79837	−	10.0431i	0.185506	−	0.321307i	−0.758241	−	0.651975i	$-0.773941\pi$
$977$	5.79837	−	10.0431i	0.185506	−	0.321307i	0.943747	+	0.330668i	$0.107274\pi$
$978$	1.17376	+	2.03302i	0.0375328	+	0.0650087i
$979$	−1.70820			−0.0545944
$980$		0			0
$981$	34.9230			1.11501
$982$	−21.4164	−	37.0943i	−0.683425	−	1.18373i
$983$	−9.77051	+	16.9230i	−0.311631	+	0.539760i	−0.978716	−	0.205221i	$-0.934209\pi$
$983$	−9.77051	+	16.9230i	−0.311631	+	0.539760i	0.667085	+	0.744982i	$0.267542\pi$
$984$	−0.465558	+	0.806370i	−0.0148415	+	0.0257061i
$985$	0.281153	+	0.486971i	0.00895828	+	0.0155162i
$986$	−8.61803			−0.274454
$987$		0			0
$988$	0.618034			0.0196623
$989$	23.1803	+	40.1495i	0.737092	+	1.27668i
$990$	−1.42705	+	2.47172i	−0.0453547	+	0.0785566i
$991$	−14.0902	+	24.4049i	−0.447589	+	0.775247i	−0.998229	−	0.0594963i	$-0.981051\pi$
$991$	−14.0902	+	24.4049i	−0.447589	+	0.775247i	0.550640	+	0.834743i	$0.314384\pi$
$992$	−16.1697	−	28.0067i	−0.513388	−	0.889215i
$993$	−0.437694			−0.0138898
$994$		0			0
$995$	19.4721			0.617308
$996$	−0.371323	−	0.643150i	−0.0117658	−	0.0203790i
$997$	−16.2254	+	28.1033i	−0.513864	+	0.890039i	0.486006	+	0.873955i	$0.338453\pi$
$997$	−16.2254	+	28.1033i	−0.513864	+	0.890039i	−0.999871	+	0.0160839i	$0.994880\pi$
$998$	21.3435	−	36.9680i	0.675615	−	1.17020i
$999$	2.82624	+	4.89519i	0.0894182	+	0.154877i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.f.e.704.1		4
7.2	even	3	inner	931.2.f.e.324.1		4
7.3	odd	6		133.2.a.c.1.2	✓	2
7.4	even	3		931.2.a.j.1.2		2
7.5	odd	6		931.2.f.d.324.1		4
7.6	odd	2		931.2.f.d.704.1		4
21.11	odd	6		8379.2.a.w.1.1		2
21.17	even	6		1197.2.a.g.1.1		2
28.3	even	6		2128.2.a.c.1.2		2
35.24	odd	6		3325.2.a.m.1.1		2
56.3	even	6		8512.2.a.bb.1.1		2
56.45	odd	6		8512.2.a.f.1.2		2
133.94	even	6		2527.2.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.a.c.1.2	✓	2	7.3	odd	6
931.2.a.j.1.2		2	7.4	even	3
931.2.f.d.324.1		4	7.5	odd	6
931.2.f.d.704.1		4	7.6	odd	2
931.2.f.e.324.1		4	7.2	even	3	inner
931.2.f.e.704.1		4	1.1	even	1	trivial
1197.2.a.g.1.1		2	21.17	even	6
2128.2.a.c.1.2		2	28.3	even	6
2527.2.a.a.1.1		2	133.94	even	6
3325.2.a.m.1.1		2	35.24	odd	6
8379.2.a.w.1.1		2	21.11	odd	6
8512.2.a.f.1.2		2	56.45	odd	6
8512.2.a.bb.1.1		2	56.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 1.40126i) q^{2} +(0.190983 - 0.330792i) q^{3} +(-0.309017 + 0.535233i) q^{4} +(0.500000 + 0.866025i) q^{5} -0.618034 q^{6} -2.23607 q^{8} +(1.42705 + 2.47172i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 1.40126i) q^{2} +(0.190983 - 0.330792i) q^{3} +(-0.309017 + 0.535233i) q^{4} +(0.500000 + 0.866025i) q^{5} -0.618034 q^{6} -2.23607 q^{8} +(1.42705 + 2.47172i) q^{9} +(0.809017 - 1.40126i) q^{10} +(-0.309017 + 0.535233i) q^{11} +(0.118034 + 0.204441i) q^{12} +1.00000 q^{13} +0.381966 q^{15} +(2.42705 + 4.20378i) q^{16} +(1.92705 - 3.33775i) q^{17} +(2.30902 - 3.99933i) q^{18} +(-0.500000 - 0.866025i) q^{19} -0.618034 q^{20} +1.00000 q^{22} +(2.73607 + 4.73901i) q^{23} +(-0.427051 + 0.739674i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-0.809017 - 1.40126i) q^{26} +2.23607 q^{27} +1.38197 q^{29} +(-0.309017 - 0.535233i) q^{30} +(4.78115 - 8.28120i) q^{31} +(1.69098 - 2.92887i) q^{32} +(0.118034 + 0.204441i) q^{33} -6.23607 q^{34} -1.76393 q^{36} +(1.26393 + 2.18919i) q^{37} +(-0.809017 + 1.40126i) q^{38} +(0.190983 - 0.330792i) q^{39} +(-1.11803 - 1.93649i) q^{40} +1.09017 q^{41} +8.47214 q^{43} +(-0.190983 - 0.330792i) q^{44} +(-1.42705 + 2.47172i) q^{45} +(4.42705 - 7.66788i) q^{46} +(3.73607 + 6.47106i) q^{47} +1.85410 q^{48} -6.47214 q^{50} +(-0.736068 - 1.27491i) q^{51} +(-0.309017 + 0.535233i) q^{52} +(-2.42705 + 4.20378i) q^{53} +(-1.80902 - 3.13331i) q^{54} -0.618034 q^{55} -0.381966 q^{57} +(-1.11803 - 1.93649i) q^{58} +(3.88197 - 6.72376i) q^{59} +(-0.118034 + 0.204441i) q^{60} +(-5.97214 - 10.3440i) q^{61} -15.4721 q^{62} +4.23607 q^{64} +(0.500000 + 0.866025i) q^{65} +(0.190983 - 0.330792i) q^{66} +(1.16312 - 2.01458i) q^{67} +(1.19098 + 2.06284i) q^{68} +2.09017 q^{69} +8.70820 q^{71} +(-3.19098 - 5.52694i) q^{72} +(-5.66312 + 9.80881i) q^{73} +(2.04508 - 3.54219i) q^{74} +(-0.763932 - 1.32317i) q^{75} +0.618034 q^{76} -0.618034 q^{78} +(2.23607 + 3.87298i) q^{79} +(-2.42705 + 4.20378i) q^{80} +(-3.85410 + 6.67550i) q^{81} +(-0.881966 - 1.52761i) q^{82} -3.14590 q^{83} +3.85410 q^{85} +(-6.85410 - 11.8717i) q^{86} +(0.263932 - 0.457144i) q^{87} +(0.690983 - 1.19682i) q^{88} +(1.38197 + 2.39364i) q^{89} +4.61803 q^{90} -3.38197 q^{92} +(-1.82624 - 3.16314i) q^{93} +(6.04508 - 10.4704i) q^{94} +(0.500000 - 0.866025i) q^{95} +(-0.645898 - 1.11873i) q^{96} -7.47214 q^{97} -1.76393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 3 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - q^{9}+O(q^{10}) \) 4 * q - q^2 + 3 * q^3 + q^4 + 2 * q^5 + 2 * q^6 - q^9	\( 4 q - q^{2} + 3 q^{3} + q^{4} + 2 q^{5} + 2 q^{6} - q^{9} + q^{10} + q^{11} - 4 q^{12} + 4 q^{13} + 6 q^{15} + 3 q^{16} + q^{17} + 7 q^{18} - 2 q^{19} + 2 q^{20} + 4 q^{22} + 2 q^{23} + 5 q^{24} + 8 q^{25} - q^{26} + 10 q^{29} + q^{30} - q^{31} + 9 q^{32} - 4 q^{33} - 16 q^{34} - 16 q^{36} + 14 q^{37} - q^{38} + 3 q^{39} - 18 q^{41} + 16 q^{43} - 3 q^{44} + q^{45} + 11 q^{46} + 6 q^{47} - 6 q^{48} - 8 q^{50} + 6 q^{51} + q^{52} - 3 q^{53} - 5 q^{54} + 2 q^{55} - 6 q^{57} + 20 q^{59} + 4 q^{60} - 6 q^{61} - 44 q^{62} + 8 q^{64} + 2 q^{65} + 3 q^{66} - 11 q^{67} + 7 q^{68} - 14 q^{69} + 8 q^{71} - 15 q^{72} - 7 q^{73} - 3 q^{74} - 12 q^{75} - 2 q^{76} + 2 q^{78} - 3 q^{80} - 2 q^{81} - 8 q^{82} - 26 q^{83} + 2 q^{85} - 14 q^{86} + 10 q^{87} + 5 q^{88} + 10 q^{89} + 14 q^{90} - 18 q^{92} + 24 q^{93} + 13 q^{94} + 2 q^{95} - 16 q^{96} - 12 q^{97} - 16 q^{99}+O(q^{100}) \) 4 * q - q^2 + 3 * q^3 + q^4 + 2 * q^5 + 2 * q^6 - q^9 + q^10 + q^11 - 4 * q^12 + 4 * q^13 + 6 * q^15 + 3 * q^16 + q^17 + 7 * q^18 - 2 * q^19 + 2 * q^20 + 4 * q^22 + 2 * q^23 + 5 * q^24 + 8 * q^25 - q^26 + 10 * q^29 + q^30 - q^31 + 9 * q^32 - 4 * q^33 - 16 * q^34 - 16 * q^36 + 14 * q^37 - q^38 + 3 * q^39 - 18 * q^41 + 16 * q^43 - 3 * q^44 + q^45 + 11 * q^46 + 6 * q^47 - 6 * q^48 - 8 * q^50 + 6 * q^51 + q^52 - 3 * q^53 - 5 * q^54 + 2 * q^55 - 6 * q^57 + 20 * q^59 + 4 * q^60 - 6 * q^61 - 44 * q^62 + 8 * q^64 + 2 * q^65 + 3 * q^66 - 11 * q^67 + 7 * q^68 - 14 * q^69 + 8 * q^71 - 15 * q^72 - 7 * q^73 - 3 * q^74 - 12 * q^75 - 2 * q^76 + 2 * q^78 - 3 * q^80 - 2 * q^81 - 8 * q^82 - 26 * q^83 + 2 * q^85 - 14 * q^86 + 10 * q^87 + 5 * q^88 + 10 * q^89 + 14 * q^90 - 18 * q^92 + 24 * q^93 + 13 * q^94 + 2 * q^95 - 16 * q^96 - 12 * q^97 - 16 * q^99

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