LMFDB - Embedded newform 931.2.f.d.324.1

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			324.1
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	931.324
Dual form			931.2.f.d.704.1

$q$-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 $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.809017	+	1.40126i	−0.572061	+	0.990839i	0.424293	+	0.905525i	$0.360523\pi$
$2$	−0.809017	+	1.40126i	−0.572061	+	0.990839i	−0.996354	+	0.0853143i	$0.972811\pi$
$3$	−0.190983	−	0.330792i	−0.110264	−	0.190983i	0.805613	−	0.592443i	$-0.201836\pi$
$3$	−0.190983	−	0.330792i	−0.110264	−	0.190983i	−0.915877	+	0.401460i	$0.868503\pi$
$4$	−0.309017	−	0.535233i	−0.154508	−	0.267617i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	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	0.815672	−	0.578514i	$-0.196367\pi$
$11$	−0.309017	−	0.535233i	−0.0931721	−	0.161379i	−0.908844	+	0.417136i	$0.863034\pi$
$12$	−0.118034	+	0.204441i	−0.0340735	+	0.0590170i
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$		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	$-0.321468\pi$
$17$	−1.92705	−	3.33775i	−0.467379	−	0.809523i	−0.999305	+	0.0372670i	$0.988135\pi$
$18$	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	−0.426004	−	0.904721i	$-0.640079\pi$
$23$	2.73607	−	4.73901i	0.570510	−	0.988152i	0.996514	−	0.0834304i	$-0.0265876\pi$
$24$	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	−0.873150	−	0.487452i	$-0.837927\pi$
$31$	−4.78115	−	8.28120i	−0.858720	−	1.48735i	0.0144296	−	0.999896i	$-0.495407\pi$
$32$	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	−0.743229	−	0.669037i	$-0.766707\pi$
$37$	1.26393	−	2.18919i	0.207789	−	0.359901i	0.951018	+	0.309136i	$0.100040\pi$
$38$	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	$-0.527130\pi$
$41$	−1.09017			−0.170256			−0.0851280	+	0.996370i	$0.527130\pi$
$42$		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	0.453648	+	0.891181i	$0.350122\pi$
$47$	−3.73607	+	6.47106i	−0.544962	+	0.943901i	−0.998609	+	0.0527200i	$0.983211\pi$
$48$	−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	0.649791	−	0.760113i	$-0.274856\pi$
$53$	−2.42705	−	4.20378i	−0.333381	−	0.577433i	−0.983173	+	0.182680i	$0.941523\pi$
$54$	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	−0.999981	−	0.00623382i	$-0.998016\pi$
$59$	−3.88197	−	6.72376i	−0.505389	−	0.875359i	0.494592	−	0.869125i	$-0.335318\pi$
$60$	−0.118034	−	0.204441i	−0.0152381	−	0.0263932i
$61$	5.97214	−	10.3440i	0.764654	−	1.32442i	−0.175776	−	0.984430i	$-0.556243\pi$
$61$	5.97214	−	10.3440i	0.764654	−	1.32442i	0.940429	−	0.339989i	$-0.110423\pi$
$62$	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	0.928286	−	0.371866i	$-0.121282\pi$
$67$	1.16312	+	2.01458i	0.142098	+	0.246120i	−0.786189	+	0.617986i	$0.787949\pi$
$68$	−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	0.979872	+	0.199627i	$0.0639730\pi$
$73$	5.66312	+	9.80881i	0.662818	+	1.14803i	−0.317054	+	0.948407i	$0.602694\pi$
$74$	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	−0.712383	−	0.701791i	$-0.752384\pi$
$79$	2.23607	−	3.87298i	0.251577	−	0.435745i	0.963960	+	0.266046i	$0.0857174\pi$
$80$	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	$-0.444766\pi$
$83$	3.14590			0.345307			0.172654	+	0.984983i	$0.444766\pi$
$84$		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	$-0.880130\pi$
$89$	−1.38197	+	2.39364i	−0.146488	+	0.253725i	0.783439	+	0.621469i	$0.213464\pi$
$90$	−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	$-0.376151\pi$
$97$	7.47214			0.758680			0.379340	+	0.925257i	$0.376151\pi$
$98$		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	$-0.217245\pi$
$101$	−1.59017	−	2.75426i	−0.158228	−	0.274059i	−0.934230	+	0.356672i	$0.883911\pi$
$102$	−1.19098	−	2.06284i	−0.117925	−	0.204252i
$103$	6.35410	−	11.0056i	0.626088	−	1.08442i	−0.362241	−	0.932084i	$-0.617988\pi$
$103$	6.35410	−	11.0056i	0.626088	−	1.08442i	0.988329	−	0.152332i	$-0.0486784\pi$
$104$	2.23607			0.219265
$105$		0			0
$106$	7.85410			0.762858
$107$	−2.88197	+	4.99171i	−0.278610	+	0.482567i	−0.971040	−	0.238919i	$-0.923207\pi$
$107$	−2.88197	+	4.99171i	−0.278610	+	0.482567i	0.692429	+	0.721486i	$0.256540\pi$
$108$	0.690983	+	1.19682i	0.0664899	+	0.115164i
$109$	6.11803	+	10.5967i	0.586001	+	1.01498i	0.994750	+	0.102337i	$0.0326320\pi$
$109$	6.11803	+	10.5967i	0.586001	+	1.01498i	−0.408748	+	0.912647i	$0.634035\pi$
$110$	−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	$-0.755205\pi$
$131$	2.78115	−	4.81710i	0.242990	−	0.420872i	0.961565	+	0.274578i	$0.0885383\pi$
$132$	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	0.678722	−	0.734396i	$-0.262534\pi$
$137$	−3.47214	−	6.01392i	−0.296645	−	0.513804i	−0.975366	+	0.220592i	$0.929201\pi$
$138$	1.69098	−	2.92887i	0.143946	−	0.249322i
$139$	−9.47214			−0.803416			−0.401708	−	0.915768i	$-0.631583\pi$
$139$	−9.47214			−0.803416			−0.401708	+	0.915768i	$0.631583\pi$
$140$		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	−0.565742	−	0.824582i	$-0.691410\pi$
$149$	5.26393	−	9.11740i	0.431238	−	0.746926i	0.996980	+	0.0776559i	$0.0247436\pi$
$150$	1.23607	+	2.14093i	0.100925	+	0.174806i
$151$	5.01722	+	8.69008i	0.408296	+	0.707189i	0.994699	−	0.102830i	$-0.0327899\pi$
$151$	5.01722	+	8.69008i	0.408296	+	0.707189i	−0.586403	+	0.810019i	$0.699457\pi$
$152$	−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	$-0.00298003\pi$
$157$	6.16312	+	10.6748i	0.491870	+	0.851945i	−0.508086	+	0.861306i	$0.669647\pi$
$158$	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	−0.930768	−	0.365611i	$-0.880860\pi$
$163$	−1.89919	+	3.28949i	−0.148756	+	0.257653i	0.782012	+	0.623263i	$0.214194\pi$
$164$	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	$-0.406642\pi$
$167$	7.47214			0.578211			0.289106	+	0.957297i	$0.406642\pi$
$168$		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	0.107471	+	0.994208i	$0.465725\pi$
$173$	−10.6180	+	18.3910i	−0.807274	+	1.39824i	−0.914745	+	0.404032i	$0.867609\pi$
$174$	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	−0.843050	−	0.537836i	$-0.819242\pi$
$179$	−11.8713	−	20.5617i	−0.887304	−	1.53686i	−0.0442548	−	0.999020i	$-0.514091\pi$
$180$	0.881966	−	1.52761i	0.0657379	−	0.113861i
$181$	−4.90983			−0.364945			−0.182472	−	0.983211i	$-0.558410\pi$
$181$	−4.90983			−0.364945			−0.182472	+	0.983211i	$0.558410\pi$
$182$		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	−0.454747	−	0.890621i	$-0.650270\pi$
$191$	7.51722	−	13.0202i	0.543927	−	0.942109i	0.998674	−	0.0514883i	$-0.0163965\pi$
$192$	−0.809017	−	1.40126i	−0.0583858	−	0.101127i
$193$	−8.54508	−	14.8005i	−0.615089	−	1.06536i	−0.990369	−	0.138453i	$-0.955787\pi$
$193$	−8.54508	−	14.8005i	−0.615089	−	1.06536i	0.375280	−	0.926911i	$-0.377546\pi$
$194$	−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	−0.971781	−	0.235883i	$-0.924202\pi$
$199$	−9.73607	−	16.8634i	−0.690172	−	1.19541i	0.281610	−	0.959529i	$-0.409132\pi$
$200$	−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	$-0.804653\pi$
$223$	−24.4164			−1.63504			−0.817522	+	0.575898i	$0.804653\pi$
$224$		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	−0.882711	−	0.469916i	$-0.844284\pi$
$227$	−12.7812	−	22.1376i	−0.848315	−	1.46932i	0.0343961	−	0.999408i	$-0.489049\pi$
$228$	0.118034	+	0.204441i	0.00781699	+	0.0135394i
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$	−8.85410			−0.583822
$231$		0			0
$232$	−3.09017			−0.202880
$233$	6.78115	−	11.7453i	0.444248	−	0.769460i	−0.553751	−	0.832682i	$-0.686804\pi$
$233$	6.78115	−	11.7453i	0.444248	−	0.769460i	0.998000	+	0.0632218i	$0.0201375\pi$
$234$	−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	−0.957058	−	0.289897i	$-0.906379\pi$
$241$	−11.3262	−	19.6176i	−0.729587	−	1.26368i	0.227471	−	0.973785i	$-0.426954\pi$
$242$	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	$-0.573694\pi$
$251$	−7.27051			−0.458911			−0.229455	+	0.973319i	$0.573694\pi$
$252$		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	$-0.969774\pi$
$257$	−6.66312	+	11.5409i	−0.415634	+	0.719899i	0.579861	+	0.814716i	$0.303107\pi$
$258$	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	−0.999924	−	0.0123273i	$-0.996076\pi$
$263$	−8.28115	−	14.3434i	−0.510638	−	0.884451i	0.489286	−	0.872123i	$-0.337257\pi$
$264$	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	0.924742	+	0.380594i	$0.124280\pi$
$269$	12.9894	+	22.4982i	0.791975	+	1.37174i	−0.132767	+	0.991147i	$0.542386\pi$
$270$	1.80902	+	3.13331i	0.110093	+	0.190687i
$271$	12.7812	−	22.1376i	0.776400	−	1.34476i	−0.157605	−	0.987502i	$-0.550377\pi$
$271$	12.7812	−	22.1376i	0.776400	−	1.34476i	0.934004	−	0.357262i	$-0.116290\pi$
$272$	−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	0.999859	+	0.0167772i	$0.00534060\pi$
$277$	8.56231	+	14.8303i	0.514459	+	0.891069i	−0.485400	+	0.874292i	$0.661326\pi$
$278$	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	$-0.323449\pi$
$283$	−7.95492	−	13.7783i	−0.472871	−	0.819036i	−0.999518	+	0.0310480i	$0.990116\pi$
$284$	−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	$-0.222064\pi$
$293$	26.2361			1.53273			0.766364	+	0.642407i	$0.222064\pi$
$294$		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	$-0.139253\pi$
$307$	31.7426			1.81165			0.905824	+	0.423654i	$0.139253\pi$
$308$		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	0.748771	+	0.662828i	$0.230644\pi$
$311$	16.7254	+	28.9693i	0.948412	+	1.64270i	0.199640	+	0.979869i	$0.436023\pi$
$312$	−0.427051	−	0.739674i	−0.0241770	−	0.0418758i
$313$	−11.7984	+	20.4354i	−0.666884	+	1.15508i	0.311887	+	0.950119i	$0.399039\pi$
$313$	−11.7984	+	20.4354i	−0.666884	+	1.15508i	−0.978771	+	0.204957i	$0.934295\pi$
$314$	−19.9443			−1.12552
$315$		0			0
$316$	−2.76393			−0.155483
$317$	−10.7082	+	18.5472i	−0.601433	+	1.04171i	0.391172	+	0.920318i	$0.372070\pi$
$317$	−10.7082	+	18.5472i	−0.601433	+	1.04171i	−0.992604	+	0.121394i	$0.961263\pi$
$318$	−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	−0.881342	−	0.472479i	$-0.843359\pi$
$331$	−0.572949	+	0.992377i	−0.0314921	+	0.0545460i	0.849850	+	0.527025i	$0.176693\pi$
$332$	−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	0.889151	−	0.457613i	$-0.151296\pi$
$347$	0.899187	+	1.55744i	0.0482709	+	0.0836076i	−0.840880	+	0.541221i	$0.817962\pi$
$348$	−0.163119	+	0.282530i	−0.00874409	+	0.0151452i
$349$	35.9787			1.92590			0.962948	−	0.269686i	$-0.0869200\pi$
$349$	35.9787			1.92590			0.962948	+	0.269686i	$0.0869200\pi$
$350$		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	$-0.281559\pi$
$353$	−6.63525	−	11.4926i	−0.353159	−	0.611689i	−0.986801	+	0.161937i	$0.948226\pi$
$354$	−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	−0.832068	−	0.554674i	$-0.812843\pi$
$359$	1.21885	−	2.11111i	0.0643283	−	0.111420i	0.896396	+	0.443254i	$0.146176\pi$
$360$	−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	$-0.0846450\pi$
$367$	4.88197	+	8.45581i	0.254837	+	0.441390i	−0.710015	+	0.704187i	$0.751312\pi$
$368$	−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	−0.998751	−	0.0499548i	$-0.984092\pi$
$373$	−8.80902	+	15.2577i	−0.456114	+	0.790012i	0.542638	+	0.839967i	$0.317426\pi$
$374$	−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	$-0.839093\pi$
$383$	−0.354102	+	0.613323i	−0.0180938	+	0.0313393i	0.856837	+	0.515588i	$0.172426\pi$
$384$	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	0.740556	+	0.671994i	$0.234562\pi$
$389$	18.7812	+	32.5299i	0.952242	+	1.64933i	0.211686	+	0.977338i	$0.432105\pi$
$390$	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	$-0.758881\pi$
$397$	4.61803	−	7.99867i	0.231772	−	0.401442i	0.958330	+	0.285664i	$0.0922142\pi$
$398$	31.5066			1.57928
$399$		0			0
$400$	19.4164			0.970820
$401$	−11.4894	+	19.9001i	−0.573751	+	0.993766i	0.422425	+	0.906398i	$0.361179\pi$
$401$	−11.4894	+	19.9001i	−0.573751	+	0.993766i	−0.996176	+	0.0873682i	$0.972154\pi$
$402$	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	0.996155	+	0.0876083i	$0.0279224\pi$
$409$	11.6074	+	20.1046i	0.573949	+	0.994108i	−0.422206	+	0.906500i	$0.638744\pi$
$410$	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	$-0.425679\pi$
$419$	9.47214			0.462744			0.231372	+	0.972865i	$0.425679\pi$
$420$		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	0.930737	+	0.365688i	$0.119166\pi$
$431$	16.2361	+	28.1217i	0.782064	+	1.35457i	−0.148674	+	0.988886i	$0.547500\pi$
$432$	−5.42705	+	9.39993i	−0.261109	+	0.452254i
$433$	−16.1246			−0.774899			−0.387450	−	0.921891i	$-0.626644\pi$
$433$	−16.1246			−0.774899			−0.387450	+	0.921891i	$0.626644\pi$
$434$		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	$-0.859313\pi$
$439$	−1.70820	+	2.95870i	−0.0815281	+	0.141211i	0.822378	+	0.568941i	$0.192647\pi$
$440$	−1.38197			−0.0658826
$441$		0			0
$442$	−6.23607			−0.296620
$443$	−11.0451	+	19.1306i	−0.524768	+	0.908925i	0.474816	+	0.880085i	$0.342515\pi$
$443$	−11.0451	+	19.1306i	−0.524768	+	0.908925i	−0.999584	+	0.0288396i	$0.990819\pi$
$444$	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	0.380979	+	0.924584i	$0.375587\pi$
$457$	−13.0451	+	22.5947i	−0.610223	+	1.05694i	−0.991202	+	0.132354i	$0.957746\pi$
$458$	−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	$-0.222697\pi$
$461$	32.8541			1.53017			0.765084	+	0.643930i	$0.222697\pi$
$462$		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	$-0.679448\pi$
$467$	10.0451	−	17.3986i	0.464831	−	0.805111i	0.999194	+	0.0401441i	$0.0127817\pi$
$468$	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	$-0.0568901\pi$
$479$	7.39919	+	12.8158i	0.338077	+	0.585567i	−0.645994	+	0.763343i	$0.723557\pi$
$480$	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	0.955180	−	0.296027i	$-0.0956618\pi$
$487$	4.88197	+	8.45581i	0.221223	+	0.383169i	−0.733957	+	0.679196i	$0.762328\pi$
$488$	−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	−0.403654	−	0.914912i	$-0.632260\pi$
$499$	13.1910	−	22.8475i	0.590509	−	1.02279i	0.994164	−	0.107881i	$-0.0344065\pi$
$500$	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	$-0.406817\pi$
$503$	12.9443			0.577157			0.288578	+	0.957456i	$0.406817\pi$
$504$		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	$-0.762199\pi$
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	0.955300	+	0.295637i	$0.0955319\pi$
$510$	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	$-0.259897\pi$
$521$	−6.59017	−	11.4145i	−0.288721	−	0.500079i	−0.973505	+	0.228667i	$0.926563\pi$
$522$	3.19098	+	5.52694i	0.139666	+	0.241908i
$523$	19.4443	−	33.6785i	0.850239	−	1.47266i	−0.0307542	−	0.999527i	$-0.509791\pi$
$523$	19.4443	−	33.6785i	0.850239	−	1.47266i	0.880993	−	0.473130i	$-0.156876\pi$
$524$	−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	−0.864825	−	0.502074i	$-0.832571\pi$
$541$	0.0557281	−	0.0965239i	0.00239594	−	0.00414989i	0.867221	+	0.497924i	$0.165904\pi$
$542$	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	0.932173	+	0.362012i	$0.117910\pi$
$557$	18.3992	+	31.8683i	0.779599	+	1.35030i	−0.152575	+	0.988292i	$0.548756\pi$
$558$	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	$-0.277816\pi$
$563$	−8.11803	−	14.0608i	−0.342134	−	0.592594i	−0.984829	+	0.173528i	$0.944483\pi$
$564$	−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	−0.605883	−	0.795554i	$-0.707180\pi$
$569$	9.20820	−	15.9491i	0.386028	−	0.668620i	0.991911	+	0.126933i	$0.0405135\pi$
$570$	0.309017	+	0.535233i	0.0129433	+	0.0224184i
$571$	−13.8262	−	23.9477i	−0.578610	−	1.00218i	−0.995639	−	0.0932888i	$-0.970262\pi$
$571$	−13.8262	−	23.9477i	−0.578610	−	1.00218i	0.417029	−	0.908893i	$-0.363071\pi$
$572$	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	0.714549	+	0.699585i	$0.246632\pi$
$577$	23.1353	+	40.0714i	0.963133	+	1.66820i	0.248584	+	0.968610i	$0.420035\pi$
$578$	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	$-0.213066\pi$
$587$	38.0000			1.56843			0.784214	+	0.620491i	$0.213066\pi$
$588$		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	$-0.867255\pi$
$593$	−2.59017	+	4.48631i	−0.106366	+	0.184231i	0.807930	+	0.589279i	$0.200588\pi$
$594$	−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	0.954712	+	0.297531i	$0.0961630\pi$
$599$	17.9894	+	31.1585i	0.735025	+	1.27310i	−0.219687	+	0.975570i	$0.570504\pi$
$600$	−1.70820	+	2.95870i	−0.0697371	+	0.120788i
$601$	34.5623			1.40983			0.704913	−	0.709294i	$-0.250986\pi$
$601$	34.5623			1.40983			0.704913	+	0.709294i	$0.250986\pi$
$602$		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	$-0.769839\pi$
$607$	4.88197	−	8.45581i	0.198153	−	0.343211i	0.947930	+	0.318480i	$0.103172\pi$
$608$	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	0.519149	−	0.854684i	$-0.326249\pi$
$613$	−11.8992	−	20.6100i	−0.480604	−	0.832430i	−0.999752	+	0.0222540i	$0.992916\pi$
$614$	−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	$-0.189832\pi$
$619$	−1.80902	−	3.13331i	−0.0727105	−	0.125938i	−0.900088	+	0.435707i	$0.856498\pi$
$620$	−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	−0.958260	−	0.285897i	$-0.907709\pi$
$641$	−18.3992	−	31.8683i	−0.726724	−	1.25872i	0.231536	−	0.972826i	$-0.425625\pi$
$642$	−1.78115	+	3.08505i	−0.0702965	+	0.121757i
$643$	−11.6525			−0.459529			−0.229764	−	0.973246i	$-0.573796\pi$
$643$	−11.6525			−0.459529			−0.229764	+	0.973246i	$0.573796\pi$
$644$		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	$-0.271256\pi$
$647$	−8.20820	−	14.2170i	−0.322698	−	0.558929i	−0.981044	+	0.193787i	$0.937923\pi$
$648$	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	0.0325486	−	0.999470i	$-0.489638\pi$
$653$	22.5344	−	39.0308i	0.881841	−	1.52739i	0.849292	−	0.527923i	$-0.177029\pi$
$654$	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	$-0.179051\pi$
$661$	−1.00000	−	1.73205i	−0.0388955	−	0.0673690i	−0.884818	+	0.465937i	$0.845717\pi$
$662$	−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	0.415977	+	0.909375i	$0.363440\pi$
$677$	−15.0795	+	26.1185i	−0.579553	+	1.00382i	−0.995530	+	0.0944407i	$0.969894\pi$
$678$	−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	−0.963548	−	0.267534i	$-0.913791\pi$
$683$	−18.6459	−	32.2956i	−0.713465	−	1.23576i	0.250083	−	0.968224i	$-0.419542\pi$
$684$	−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	$-0.961103\pi$
$691$	−10.2705	+	17.7890i	−0.390709	+	0.676727i	0.601835	+	0.798621i	$0.294437\pi$
$692$	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	−0.178114	+	0.984010i	$0.557000\pi$
$709$	−25.0623	+	43.4092i	−0.941235	+	1.63027i	−0.763120	+	0.646256i	$0.776334\pi$
$710$	−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	−0.259645	−	0.965704i	$-0.583605\pi$
$719$	18.9443	−	32.8124i	0.706502	−	1.22370i	0.966147	−	0.257993i	$-0.0830613\pi$
$720$	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	$-0.362369\pi$
$727$	22.5967			0.838067			0.419033	+	0.907971i	$0.362369\pi$
$728$		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	0.493649	+	0.869661i	$0.335663\pi$
$733$	−13.7082	+	23.7433i	−0.506324	+	0.876979i	−0.999973	+	0.00731786i	$0.997671\pi$
$734$	−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	0.613143	−	0.789972i	$-0.289905\pi$
$739$	−10.2639	−	17.7777i	−0.377565	−	0.653961i	−0.990707	+	0.136011i	$0.956572\pi$
$740$	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	−0.860850	−	0.508859i	$-0.830068\pi$
$751$	0.281153	−	0.486971i	0.0102594	−	0.0177698i	0.871110	+	0.491089i	$0.163401\pi$
$752$	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	0.426089	+	0.904681i	$0.359891\pi$
$761$	−15.7361	+	27.2557i	−0.570432	+	0.988017i	−0.996521	+	0.0833362i	$0.973442\pi$
$762$	−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	$-0.638745\pi$
$769$	−23.4164			−0.844417			−0.422209	+	0.906499i	$0.638745\pi$
$770$		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	$-0.0211701\pi$
$773$	12.2705	+	21.2531i	0.441340	+	0.764423i	−0.556450	+	0.830881i	$0.687837\pi$
$774$	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	0.879823	+	0.475301i	$0.157661\pi$
$787$	23.8885	+	41.3762i	0.851535	+	1.47490i	−0.0282884	+	0.999600i	$0.509006\pi$
$788$	−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	$-0.307201\pi$
$797$	32.1459			1.13867			0.569333	+	0.822107i	$0.307201\pi$
$798$		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	0.926163	−	0.377124i	$-0.123087\pi$
$809$	3.88197	+	6.72376i	0.136483	+	0.236395i	−0.789680	+	0.613519i	$0.789754\pi$
$810$	−6.23607	+	10.8012i	−0.219113	+	0.379515i
$811$	−38.0000			−1.33436			−0.667180	−	0.744896i	$-0.732499\pi$
$811$	−38.0000			−1.33436			−0.667180	+	0.744896i	$0.732499\pi$
$812$		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	−0.810063	−	0.586342i	$-0.800567\pi$
$821$	2.94427	−	5.09963i	0.102756	−	0.177978i	0.912819	+	0.408364i	$0.133901\pi$
$822$	−2.14590	−	3.71680i	−0.0748468	−	0.129638i
$823$	−14.5623	−	25.2227i	−0.507610	−	0.879206i	−0.999961	−	0.00880976i	$-0.997196\pi$
$823$	−14.5623	−	25.2227i	−0.507610	−	0.879206i	0.492351	−	0.870397i	$-0.336138\pi$
$824$	−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	$-0.216309\pi$
$829$	−4.47214	−	7.74597i	−0.155324	−	0.269029i	−0.933177	+	0.359418i	$0.882975\pi$
$830$	−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	$-0.542098\pi$
$839$	−7.63932			−0.263739			−0.131869	+	0.991267i	$0.542098\pi$
$840$		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	$-0.380383\pi$
$853$	21.4377			0.734013			0.367006	+	0.930218i	$0.380383\pi$
$854$		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	0.966732	+	0.255790i	$0.0823356\pi$
$857$	20.6353	+	35.7413i	0.704887	+	1.22090i	−0.261845	+	0.965110i	$0.584331\pi$
$858$	0.190983	+	0.330792i	0.00652005	+	0.0112931i
$859$	−7.39919	+	12.8158i	−0.252457	+	0.437268i	−0.964202	−	0.265170i	$-0.914572\pi$
$859$	−7.39919	+	12.8158i	−0.252457	+	0.437268i	0.711745	+	0.702438i	$0.247905\pi$
$860$	5.23607			0.178548
$861$		0			0
$862$	−52.5410			−1.78955
$863$	8.75329	−	15.1611i	0.297965	−	0.516091i	−0.677705	−	0.735334i	$-0.737025\pi$
$863$	8.75329	−	15.1611i	0.297965	−	0.516091i	0.975670	+	0.219243i	$0.0703587\pi$
$864$	−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	0.278572	+	0.960415i	$0.410139\pi$
$877$	−20.5066	+	35.5184i	−0.692458	+	1.19937i	−0.971030	+	0.238957i	$0.923194\pi$
$878$	−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	$-0.445632\pi$
$881$	10.0902			0.339946			0.169973	+	0.985449i	$0.445632\pi$
$882$		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	$-0.843725\pi$
$887$	−0.972136	+	1.68379i	−0.0326411	+	0.0565361i	0.849243	+	0.528002i	$0.177059\pi$
$888$	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	0.877987	−	0.478684i	$-0.158886\pi$
$907$	0.736068	+	1.27491i	0.0244407	+	0.0423326i	−0.853546	+	0.521017i	$0.825553\pi$
$908$	−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	−0.979334	−	0.202251i	$-0.935174\pi$
$919$	−9.53444	+	16.5141i	−0.314512	+	0.544751i	0.664821	+	0.747002i	$0.268508\pi$
$920$	−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	$-0.684721\pi$
$929$	13.7188	−	23.7617i	0.450101	−	0.779597i	0.998392	+	0.0566902i	$0.0180547\pi$
$930$	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	$-0.822268\pi$
$937$	−51.9230			−1.69625			−0.848125	+	0.529796i	$0.822268\pi$
$938$		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	$-0.290694\pi$
$941$	−11.6525	−	20.1827i	−0.379860	−	0.657937i	−0.991042	+	0.133554i	$0.957361\pi$
$942$	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	0.438979	+	0.898497i	$0.355340\pi$
$947$	−17.1910	+	29.7757i	−0.558632	+	0.967579i	−0.997611	+	0.0690816i	$0.977993\pi$
$948$	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	$-0.837520\pi$
$971$	−0.409830	+	0.709846i	−0.0131521	+	0.0227801i	0.859374	+	0.511347i	$0.170853\pi$
$972$	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	0.943747	−	0.330668i	$-0.107274\pi$
$977$	5.79837	+	10.0431i	0.185506	+	0.321307i	−0.758241	+	0.651975i	$0.773941\pi$
$978$	−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	$-0.0657914\pi$
$983$	9.77051	+	16.9230i	0.311631	+	0.539760i	−0.667085	+	0.744982i	$0.732458\pi$
$984$	−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	0.550640	−	0.834743i	$-0.314384\pi$
$991$	−14.0902	−	24.4049i	−0.447589	−	0.775247i	−0.998229	+	0.0594963i	$0.981051\pi$
$992$	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	0.999871	+	0.0160839i	$0.00511987\pi$
$997$	16.2254	+	28.1033i	0.513864	+	0.890039i	−0.486006	+	0.873955i	$0.661547\pi$
$998$	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.d.324.1		4
7.2	even	3		133.2.a.c.1.2	✓	2
7.3	odd	6		931.2.f.e.704.1		4
7.4	even	3	inner	931.2.f.d.704.1		4
7.5	odd	6		931.2.a.j.1.2		2
7.6	odd	2		931.2.f.e.324.1		4
21.2	odd	6		1197.2.a.g.1.1		2
21.5	even	6		8379.2.a.w.1.1		2
28.23	odd	6		2128.2.a.c.1.2		2
35.9	even	6		3325.2.a.m.1.1		2
56.37	even	6		8512.2.a.f.1.2		2
56.51	odd	6		8512.2.a.bb.1.1		2
133.37	odd	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	7.2	even	3
931.2.a.j.1.2		2	7.5	odd	6
931.2.f.d.324.1		4	1.1	even	1	trivial
931.2.f.d.704.1		4	7.4	even	3	inner
931.2.f.e.324.1		4	7.6	odd	2
931.2.f.e.704.1		4	7.3	odd	6
1197.2.a.g.1.1		2	21.2	odd	6
2128.2.a.c.1.2		2	28.23	odd	6
2527.2.a.a.1.1		2	133.37	odd	6
3325.2.a.m.1.1		2	35.9	even	6
8379.2.a.w.1.1		2	21.5	even	6
8512.2.a.f.1.2		2	56.37	even	6
8512.2.a.bb.1.1		2	56.51	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
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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