LMFDB - Embedded newform 380.2.bb.a.59.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(59,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 1]))

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

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

chi := DirichletCharacter("380.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bb (of order $18$, degree $6$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$56$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.5
Character	$\chi$	$=$	380.59
Dual form			380.2.bb.a.219.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34415 - 0.439613i) q^{2} +(-1.17302 + 1.39795i) q^{3} +(1.61348 + 1.18181i) q^{4} +(0.426294 + 2.19506i) q^{5} +(2.19126 - 1.36338i) q^{6} +(1.36812 + 2.36965i) q^{7} +(-1.64922 - 2.29784i) q^{8} +(-0.0573416 - 0.325200i) q^{9} +O(q^{10})$	\(q+(-1.34415 - 0.439613i) q^{2} +(-1.17302 + 1.39795i) q^{3} +(1.61348 + 1.18181i) q^{4} +(0.426294 + 2.19506i) q^{5} +(2.19126 - 1.36338i) q^{6} +(1.36812 + 2.36965i) q^{7} +(-1.64922 - 2.29784i) q^{8} +(-0.0573416 - 0.325200i) q^{9} +(0.391971 - 3.13789i) q^{10} +(2.24016 + 1.29335i) q^{11} +(-3.54475 + 0.869277i) q^{12} +(0.527993 - 0.443038i) q^{13} +(-0.797230 - 3.78661i) q^{14} +(-3.56862 - 1.97890i) q^{15} +(1.20665 + 3.81366i) q^{16} +(-0.544629 - 0.0960328i) q^{17} +(-0.0658864 + 0.462326i) q^{18} +(1.26967 - 4.16989i) q^{19} +(-1.90632 + 4.04548i) q^{20} +(-4.91747 - 0.867083i) q^{21} +(-2.44253 - 2.72326i) q^{22} +(0.366941 + 0.133555i) q^{23} +(5.14682 + 0.389876i) q^{24} +(-4.63655 + 1.87148i) q^{25} +(-0.904467 + 0.363398i) q^{26} +(-4.21932 - 2.43603i) q^{27} +(-0.593046 + 5.44025i) q^{28} +(-8.63898 + 1.52328i) q^{29} +(3.92681 + 4.22875i) q^{30} +(4.91391 + 8.51114i) q^{31} +(0.0546187 - 5.65659i) q^{32} +(-4.43578 + 1.61449i) q^{33} +(0.689846 + 0.368508i) q^{34} +(-4.61830 + 4.01327i) q^{35} +(0.291806 - 0.592472i) q^{36} +9.48947 q^{37} +(-3.53976 + 5.04679i) q^{38} +1.25780i q^{39} +(4.34083 - 4.59969i) q^{40} +(-3.19809 + 3.81133i) q^{41} +(6.22864 + 3.32727i) q^{42} +(-2.46866 + 0.898519i) q^{43} +(2.08595 + 4.73425i) q^{44} +(0.689389 - 0.264499i) q^{45} +(-0.434511 - 0.340830i) q^{46} +(-0.347487 - 1.97070i) q^{47} +(-6.74670 - 2.78666i) q^{48} +(-0.243505 + 0.421764i) q^{49} +(7.05494 - 0.477266i) q^{50} +(0.773107 - 0.648714i) q^{51} +(1.37549 - 0.0908469i) q^{52} +(-9.32287 - 3.39325i) q^{53} +(4.60050 + 5.12926i) q^{54} +(-1.88402 + 5.46862i) q^{55} +(3.18875 - 7.05181i) q^{56} +(4.33993 + 6.66626i) q^{57} +(12.2817 + 1.75028i) q^{58} +(1.22506 - 6.94767i) q^{59} +(-3.41922 - 7.41035i) q^{60} +(-1.23607 - 0.449894i) q^{61} +(-2.86343 - 13.6005i) q^{62} +(0.692162 - 0.580793i) q^{63} +(-2.56012 + 7.57930i) q^{64} +(1.19757 + 0.970109i) q^{65} +(6.67210 - 0.220096i) q^{66} +(3.08193 - 0.543427i) q^{67} +(-0.765256 - 0.798596i) q^{68} +(-0.617130 + 0.356300i) q^{69} +(7.97198 - 3.36418i) q^{70} +(3.62520 - 1.31947i) q^{71} +(-0.652689 + 0.668090i) q^{72} +(5.31372 - 6.33264i) q^{73} +(-12.7553 - 4.17169i) q^{74} +(2.82251 - 8.67691i) q^{75} +(6.97660 - 5.22753i) q^{76} +7.07786i q^{77} +(0.552943 - 1.69067i) q^{78} +(-9.44434 - 7.92474i) q^{79} +(-7.85681 + 4.27440i) q^{80} +(9.28567 - 3.37971i) q^{81} +(5.97422 - 3.71709i) q^{82} +(-0.643215 - 1.11408i) q^{83} +(-6.90952 - 7.21055i) q^{84} +(-0.0213748 - 1.23643i) q^{85} +(3.71325 - 0.122491i) q^{86} +(8.00419 - 13.8637i) q^{87} +(-0.722598 - 7.28055i) q^{88} +(7.29789 + 8.69728i) q^{89} +(-1.04292 + 0.0524626i) q^{90} +(1.77221 + 0.645030i) q^{91} +(0.434215 + 0.649144i) q^{92} +(-17.6622 - 3.11432i) q^{93} +(-0.399268 + 2.80167i) q^{94} +(9.69439 + 1.00939i) q^{95} +(7.84354 + 6.71162i) q^{96} +(-1.36674 + 7.75117i) q^{97} +(0.512720 - 0.459866i) q^{98} +(0.292145 - 0.802662i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	$ 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) $ 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.34415	−	0.439613i	−0.950458	−	0.310853i
$2$	−1.34415	−	0.439613i	−0.950458	−	0.310853i
$3$	−1.17302	+	1.39795i	−0.677241	+	0.807104i	−0.989750	−	0.142811i	$-0.954386\pi$
$3$	−1.17302	+	1.39795i	−0.677241	+	0.807104i	0.312509	+	0.949915i	$0.398830\pi$
$4$	1.61348	+	1.18181i	0.806741	+	0.590905i
$5$	0.426294	+	2.19506i	0.190645	+	0.981659i
$5$	0.426294	+	2.19506i	0.190645	+	0.981659i
$6$	2.19126	−	1.36338i	0.894580	−	0.556596i
$7$	1.36812	+	2.36965i	0.517101	+	0.895645i	0.999803	+	0.0198602i	$0.00632211\pi$
$7$	1.36812	+	2.36965i	0.517101	+	0.895645i	−0.482702	+	0.875785i	$0.660345\pi$
$8$	−1.64922	−	2.29784i	−0.583089	−	0.812409i
$9$	−0.0573416	−	0.325200i	−0.0191139	−	0.108400i
$10$	0.391971	−	3.13789i	0.123952	−	0.992288i
$11$	2.24016	+	1.29335i	0.675433	+	0.389961i	0.798132	−	0.602483i	$-0.205822\pi$
$11$	2.24016	+	1.29335i	0.675433	+	0.389961i	−0.122699	+	0.992444i	$0.539155\pi$
$12$	−3.54475	+	0.869277i	−1.02328	+	0.250939i
$13$	0.527993	−	0.443038i	0.146439	−	0.122877i	−0.566625	−	0.823976i	$-0.691751\pi$
$13$	0.527993	−	0.443038i	0.146439	−	0.122877i	0.713064	+	0.701099i	$0.247307\pi$
$14$	−0.797230	−	3.78661i	−0.213069	−	1.01202i
$15$	−3.56862	−	1.97890i	−0.921413	−	0.510950i
$16$	1.20665	+	3.81366i	0.301662	+	0.953415i
$17$	−0.544629	−	0.0960328i	−0.132092	−	0.0232914i	0.107211	−	0.994236i	$-0.465808\pi$
$17$	−0.544629	−	0.0960328i	−0.132092	−	0.0232914i	−0.239303	+	0.970945i	$0.576919\pi$
$18$	−0.0658864	+	0.462326i	−0.0155296	+	0.108971i
$19$	1.26967	−	4.16989i	0.291281	−	0.956637i
$19$	1.26967	−	4.16989i	0.291281	−	0.956637i
$20$	−1.90632	+	4.04548i	−0.426267	+	0.904597i
$21$	−4.91747	−	0.867083i	−1.07308	−	0.189213i
$22$	−2.44253	−	2.72326i	−0.520750	−	0.580602i
$23$	0.366941	+	0.133555i	0.0765124	+	0.0278482i	0.379993	−	0.924989i	$-0.375926\pi$
$23$	0.366941	+	0.133555i	0.0765124	+	0.0278482i	−0.303480	+	0.952838i	$0.598149\pi$
$24$	5.14682	+	0.389876i	1.05059	+	0.0795831i
$25$	−4.63655	+	1.87148i	−0.927309	+	0.374296i
$26$	−0.904467	+	0.363398i	−0.177381	+	0.0712683i
$27$	−4.21932	−	2.43603i	−0.812009	−	0.468814i
$28$	−0.593046	+	5.44025i	−0.112075	+	1.02811i
$29$	−8.63898	+	1.52328i	−1.60422	+	0.282867i	−0.902857	−	0.429940i	$-0.858535\pi$
$29$	−8.63898	+	1.52328i	−1.60422	+	0.282867i	−0.701360	+	0.712807i	$0.747424\pi$
$30$	3.92681	+	4.22875i	0.716935	+	0.772060i
$31$	4.91391	+	8.51114i	0.882564	+	1.52865i	0.848481	+	0.529226i	$0.177518\pi$
$31$	4.91391	+	8.51114i	0.882564	+	1.52865i	0.0340829	+	0.999419i	$0.489149\pi$
$32$	0.0546187	−	5.65659i	0.00965531	−	0.999953i
$33$	−4.43578	+	1.61449i	−0.772170	+	0.281047i
$34$	0.689846	+	0.368508i	0.118308	+	0.0631987i
$35$	−4.61830	+	4.01327i	−0.780636	+	0.678367i
$36$	0.291806	−	0.592472i	0.0486343	−	0.0987453i
$37$	9.48947			1.56006			0.780030	−	0.625743i	$-0.215204\pi$
$37$	9.48947			1.56006			0.780030	+	0.625743i	$0.215204\pi$
$38$	−3.53976	+	5.04679i	−0.574224	+	0.818698i
$39$			1.25780i			0.201409i
$40$	4.34083	−	4.59969i	0.686346	−	0.727275i
$41$	−3.19809	+	3.81133i	−0.499457	+	0.595230i	−0.955596	−	0.294678i	$-0.904787\pi$
$41$	−3.19809	+	3.81133i	−0.499457	+	0.595230i	0.456139	+	0.889908i	$0.349232\pi$
$42$	6.22864	+	3.32727i	0.961101	+	0.513409i
$43$	−2.46866	+	0.898519i	−0.376467	+	0.137023i	−0.523322	−	0.852135i	$-0.675307\pi$
$43$	−2.46866	+	0.898519i	−0.376467	+	0.137023i	0.146854	+	0.989158i	$0.453085\pi$
$44$	2.08595	+	4.73425i	0.314469	+	0.713714i
$45$	0.689389	−	0.264499i	0.102768	−	0.0394292i
$46$	−0.434511	−	0.340830i	−0.0640651	−	0.0502527i
$47$	−0.347487	−	1.97070i	−0.0506862	−	0.287456i	0.948920	−	0.315517i	$-0.102178\pi$
$47$	−0.347487	−	1.97070i	−0.0506862	−	0.287456i	−0.999606	+	0.0280610i	$0.991067\pi$
$48$	−6.74670	−	2.78666i	−0.973803	−	0.402219i
$49$	−0.243505	+	0.421764i	−0.0347865	+	0.0602519i
$50$	7.05494	−	0.477266i	0.997720	−	0.0674957i
$51$	0.773107	−	0.648714i	0.108257	−	0.0908381i
$52$	1.37549	−	0.0908469i	0.190747	−	0.0125982i
$53$	−9.32287	−	3.39325i	−1.28059	−	0.466098i	−0.389966	−	0.920829i	$-0.627513\pi$
$53$	−9.32287	−	3.39325i	−1.28059	−	0.466098i	−0.890629	+	0.454731i	$0.849735\pi$
$54$	4.60050	+	5.12926i	0.626049	+	0.698003i
$55$	−1.88402	+	5.46862i	−0.254041	+	0.737388i
$56$	3.18875	−	7.05181i	0.426114	−	0.942337i
$57$	4.33993	+	6.66626i	0.574838	+	0.882968i
$58$	12.2817	+	1.75028i	1.61267	+	0.229823i
$59$	1.22506	−	6.94767i	0.159490	−	0.904510i	−0.795076	−	0.606510i	$-0.792569\pi$
$59$	1.22506	−	6.94767i	0.159490	−	0.904510i	0.954566	−	0.298000i	$-0.0963197\pi$
$60$	−3.41922	−	7.41035i	−0.441419	−	0.956672i
$61$	−1.23607	−	0.449894i	−0.158263	−	0.0576031i	0.261674	−	0.965156i	$-0.415726\pi$
$61$	−1.23607	−	0.449894i	−0.158263	−	0.0576031i	−0.419937	+	0.907553i	$0.637948\pi$
$62$	−2.86343	−	13.6005i	−0.363656	−	1.72726i
$63$	0.692162	−	0.580793i	0.0872042	−	0.0731730i
$64$	−2.56012	+	7.57930i	−0.320015	+	0.947412i
$65$	1.19757	+	0.970109i	0.148541	+	0.120327i
$66$	6.67210	−	0.220096i	0.821279	−	0.0270919i
$67$	3.08193	−	0.543427i	0.376518	−	0.0663902i	0.0178130	−	0.999841i	$-0.494330\pi$
$67$	3.08193	−	0.543427i	0.376518	−	0.0663902i	0.358705	+	0.933451i	$0.383219\pi$
$68$	−0.765256	−	0.798596i	−0.0928010	−	0.0968440i
$69$	−0.617130	+	0.356300i	−0.0742938	+	0.0428935i
$70$	7.97198	−	3.36418i	0.952834	−	0.402096i
$71$	3.62520	−	1.31947i	0.430233	−	0.156592i	−0.117821	−	0.993035i	$-0.537591\pi$
$71$	3.62520	−	1.31947i	0.430233	−	0.156592i	0.548054	+	0.836443i	$0.315369\pi$
$72$	−0.652689	+	0.668090i	−0.0769201	+	0.0787351i
$73$	5.31372	−	6.33264i	0.621924	−	0.741180i	−0.359476	−	0.933154i	$-0.617045\pi$
$73$	5.31372	−	6.33264i	0.621924	−	0.741180i	0.981400	+	0.191974i	$0.0614890\pi$
$74$	−12.7553	−	4.17169i	−1.48277	−	0.484949i
$75$	2.82251	−	8.67691i	0.325916	−	1.00192i
$76$	6.97660	−	5.22753i	0.800271	−	0.599639i
$77$			7.07786i			0.806597i
$78$	0.552943	−	1.69067i	0.0626084	−	0.191430i
$79$	−9.44434	−	7.92474i	−1.06257	−	0.891603i	−0.0682124	−	0.997671i	$-0.521730\pi$
$79$	−9.44434	−	7.92474i	−1.06257	−	0.891603i	−0.994359	+	0.106068i	$0.966174\pi$
$80$	−7.85681	+	4.27440i	−0.878419	+	0.477892i
$81$	9.28567	−	3.37971i	1.03174	−	0.375523i
$82$	5.97422	−	3.71709i	0.659742	−	0.410483i
$83$	−0.643215	−	1.11408i	−0.0706020	−	0.122286i	0.828563	−	0.559895i	$-0.189159\pi$
$83$	−0.643215	−	1.11408i	−0.0706020	−	0.122286i	−0.899165	+	0.437609i	$0.855825\pi$
$84$	−6.90952	−	7.21055i	−0.753891	−	0.786735i
$85$	−0.0213748	−	1.23643i	−0.00231842	−	0.134110i
$86$	3.71325	−	0.122491i	0.400410	−	0.0132085i
$87$	8.00419	−	13.8637i	0.858139	−	1.48634i
$88$	−0.722598	−	7.28055i	−0.0770292	−	0.776109i
$89$	7.29789	+	8.69728i	0.773574	+	0.921910i	0.998624	−	0.0524373i	$-0.0166990\pi$
$89$	7.29789	+	8.69728i	0.773574	+	0.921910i	−0.225050	+	0.974347i	$0.572255\pi$
$90$	−1.04292	+	0.0524626i	−0.109933	+	0.00553004i
$91$	1.77221	+	0.645030i	0.185778	+	0.0676175i
$92$	0.434215	+	0.649144i	0.0452700	+	0.0676779i
$93$	−17.6622	−	3.11432i	−1.83148	−	0.322940i
$94$	−0.399268	+	2.80167i	−0.0411814	+	0.288971i
$95$	9.69439	+	1.00939i	0.994623	+	0.103561i
$96$	7.84354	+	6.71162i	0.800528	+	0.685002i
$97$	−1.36674	+	7.75117i	−0.138772	+	0.787012i	0.833387	+	0.552689i	$0.186398\pi$
$97$	−1.36674	+	7.75117i	−0.138772	+	0.787012i	−0.972159	+	0.234323i	$0.924713\pi$
$98$	0.512720	−	0.459866i	0.0517926	−	0.0464535i
$99$	0.292145	−	0.802662i	0.0293617	−	0.0806706i
$100$	−9.69272	−	2.45992i	−0.969272	−	0.245992i
$101$	5.70389	−	4.78613i	0.567558	−	0.476238i	−0.313276	−	0.949662i	$-0.601427\pi$
$101$	5.70389	−	4.78613i	0.567558	−	0.476238i	0.880835	+	0.473424i	$0.156982\pi$
$102$	−1.32435	+	0.532101i	−0.131131	+	0.0526859i
$103$	9.76852	+	5.63986i	0.962521	+	0.555712i	0.896948	−	0.442136i	$-0.145779\pi$
$103$	9.76852	+	5.63986i	0.962521	+	0.555712i	0.0655730	+	0.997848i	$0.479112\pi$
$104$	−1.88881	−	0.482572i	−0.185213	−	0.0473201i
$105$	−0.192993	−	11.1638i	−0.0188342	−	1.08947i
$106$	11.0396	+	8.65949i	1.07226	+	0.841084i
$107$	−8.30629	+	4.79564i	−0.802999	+	0.463612i	−0.844519	−	0.535526i	$-0.820113\pi$
$107$	−8.30629	+	4.79564i	−0.802999	+	0.463612i	0.0415197	+	0.999138i	$0.486780\pi$
$108$	−3.92888	−	8.91693i	−0.378056	−	0.858032i
$109$	−4.54408	−	12.4848i	−0.435244	−	1.19582i	−0.942552	−	0.334059i	$-0.891582\pi$
$109$	−4.54408	−	12.4848i	−0.435244	−	1.19582i	0.507308	−	0.861765i	$-0.330641\pi$
$110$	4.93648	−	6.52241i	0.470675	−	0.621887i
$111$	−11.1313	+	13.2658i	−1.05654	+	1.25913i
$112$	−7.38622	+	8.07688i	−0.697932	+	0.763193i
$113$	16.7648			1.57710			0.788551	−	0.614970i	$-0.210832\pi$
$113$	16.7648			1.57710			0.788551	+	0.614970i	$0.210832\pi$
$114$	−2.90295	−	10.8684i	−0.271886	−	1.01791i
$115$	−0.136737	+	0.862390i	−0.0127508	+	0.0804182i
$116$	−15.7391	−	7.75184i	−1.46134	−	0.719741i
$117$	−0.174352	−	0.146299i	−0.0161189	−	0.0135253i
$118$	−4.70095	+	8.80017i	−0.432758	+	0.810121i
$119$	−0.517554	−	1.42197i	−0.0474441	−	0.130351i
$120$	1.33826	+	11.4638i	0.122166	+	1.04649i
$121$	−2.15447	−	3.73165i	−0.195861	−	0.339241i
$122$	1.46369	+	1.14812i	0.132516	+	0.103946i
$123$	−1.57663	−	8.94150i	−0.142160	−	0.806228i
$124$	−2.13005	+	19.5399i	−0.191285	+	1.75473i
$125$	−6.08454	−	9.37968i	−0.544217	−	0.838944i
$126$	−1.18569	+	0.476390i	−0.105630	+	0.0424402i
$127$	13.1642	+	15.6884i	1.16813	+	1.39212i	0.903944	+	0.427651i	$0.140659\pi$
$127$	13.1642	+	15.6884i	1.16813	+	1.39212i	0.264186	+	0.964472i	$0.414897\pi$
$128$	6.77315	−	9.06226i	0.598667	−	0.800998i
$129$	1.63970	−	4.50503i	0.144367	−	0.396646i
$130$	−1.18325	−	1.83044i	−0.103778	−	0.160540i
$131$	0.182318	+	0.0321476i	0.0159292	+	0.00280875i	0.181607	−	0.983371i	$-0.441870\pi$
$131$	0.182318	+	0.0321476i	0.0159292	+	0.00280875i	−0.165678	+	0.986180i	$0.552981\pi$
$132$	−9.06507	−	2.63730i	−0.789013	−	0.229547i
$133$	11.6182	−	2.69624i	1.00743	−	0.233793i
$134$	−4.38147	−	0.624407i	−0.378502	−	0.0539405i
$135$	3.54855	−	10.3001i	0.305410	−	0.886493i
$136$	0.677547	+	1.40985i	0.0580992	+	0.120894i
$137$	0.245425	−	0.674299i	0.0209681	−	0.0576092i	−0.928767	−	0.370664i	$-0.879130\pi$
$137$	0.245425	−	0.674299i	0.0209681	−	0.0576092i	0.949735	+	0.313055i	$0.101352\pi$
$138$	0.986150	−	0.207623i	0.0839467	−	0.0176741i
$139$	−2.54609	−	3.03431i	−0.215956	−	0.257367i	0.647180	−	0.762337i	$-0.275948\pi$
$139$	−2.54609	−	3.03431i	−0.215956	−	0.257367i	−0.863137	+	0.504970i	$0.831504\pi$
$140$	−12.1945	+	1.01738i	−1.03062	+	0.0859842i
$141$	3.16254	+	1.82589i	0.266334	+	0.153768i
$142$	−5.45287	+	0.179876i	−0.457595	+	0.0150949i
$143$	1.75579	−	0.309593i	0.146827	−	0.0258895i
$144$	1.17101	−	0.611083i	0.0975844	−	0.0509236i
$145$	−7.02644	−	18.3137i	−0.583514	−	1.52087i
$146$	−9.92635	+	6.17605i	−0.821510	+	0.511134i
$147$	−0.303967	−	0.835142i	−0.0250708	−	0.0688814i
$148$	15.3111	+	11.2148i	1.25856	+	0.921847i
$149$	10.7942	+	9.05743i	0.884297	+	0.742013i	0.967058	−	0.254556i	$-0.0819293\pi$
$149$	10.7942	+	9.05743i	0.884297	+	0.742013i	−0.0827608	+	0.996569i	$0.526374\pi$
$150$	−7.60836	+	10.4223i	−0.621220	+	0.850974i
$151$	15.0663			1.22608			0.613038	−	0.790054i	$-0.289947\pi$
$151$	15.0663			1.22608			0.613038	+	0.790054i	$0.289947\pi$
$152$	−11.6757	+	3.95959i	−0.947023	+	0.321165i
$153$			0.182620i			0.0147640i
$154$	3.11152	−	9.51371i	0.250733	−	0.766636i
$155$	−16.5877	+	14.4146i	−1.33235	+	1.15780i
$156$	−1.48648	+	2.02943i	−0.119013	+	0.162484i
$157$	6.52871	+	17.9375i	0.521048	+	1.43157i	0.869355	+	0.494187i	$0.164534\pi$
$157$	6.52871	+	17.9375i	0.521048	+	1.43157i	−0.348307	+	0.937380i	$0.613243\pi$
$158$	9.21080	+	14.8039i	0.732772	+	1.17773i
$159$	15.6794	−	9.05253i	1.24346	−	0.717913i
$160$	12.4398	−	2.29148i	0.983454	−	0.181157i
$161$	0.185539	+	1.05224i	0.0146225	+	0.0829283i
$162$	−13.9671	+	0.460739i	−1.09736	+	0.0361991i
$163$	−7.60887	+	13.1789i	−0.595972	+	1.03225i	0.397437	+	0.917630i	$0.369900\pi$
$163$	−7.60887	+	13.1789i	−0.595972	+	1.03225i	−0.993409	+	0.114625i	$0.963433\pi$
$164$	−9.66433	+	2.36998i	−0.754657	+	0.185064i
$165$	−5.43484	−	9.04853i	−0.423102	−	0.704427i
$166$	0.374814	+	1.78026i	0.0290912	+	0.138175i
$167$	−1.44630	+	3.97367i	−0.111918	+	0.307492i	−0.982989	−	0.183665i	$-0.941204\pi$
$167$	−1.44630	+	3.97367i	−0.111918	+	0.307492i	0.871071	+	0.491157i	$0.163426\pi$
$168$	6.11759	+	12.7296i	0.471983	+	0.982108i
$169$	−2.17493	+	12.3347i	−0.167303	+	0.948820i
$170$	−0.514819	+	1.67134i	−0.0394848	+	0.128186i
$171$	−1.42885	−	0.173788i	−0.109267	−	0.0132899i
$172$	−5.04502	−	1.46775i	−0.384679	−	0.111915i
$173$	0.635695	−	3.60521i	0.0483310	−	0.274099i	−0.951060	−	0.309008i	$-0.900003\pi$
$173$	0.635695	−	3.60521i	0.0483310	−	0.274099i	0.999390	+	0.0349091i	$0.0111142\pi$
$174$	−16.8535	+	15.1161i	−1.27766	+	1.14595i
$175$	−10.7781	−	8.42660i	−0.814749	−	0.636991i
$176$	−2.22934	+	10.1038i	−0.168043	+	0.761604i
$177$	8.27545	+	9.86230i	0.622021	+	0.741296i
$178$	−5.98602	−	14.8987i	−0.448671	−	1.11670i
$179$	−10.1085	+	17.5085i	−0.755546	+	1.30864i	0.189556	+	0.981870i	$0.439295\pi$
$179$	−10.1085	+	17.5085i	−0.755546	+	1.30864i	−0.945102	+	0.326775i	$0.894038\pi$
$180$	1.42490	+	0.387963i	0.106206	+	0.0289170i
$181$	21.1624	−	3.73150i	1.57299	−	0.277360i	0.681987	−	0.731364i	$-0.261116\pi$
$181$	21.1624	−	3.73150i	1.57299	−	0.277360i	0.891000	+	0.454004i	$0.150005\pi$
$182$	−2.09855	−	1.64610i	−0.155555	−	0.122017i
$183$	2.07886	−	1.20023i	0.153674	−	0.0887237i
$184$	−0.298278	−	1.06343i	−0.0219894	−	0.0783973i
$185$	4.04531	+	20.8299i	0.297417	+	1.53145i
$186$	22.3716	+	11.9506i	1.64036	+	0.876263i
$187$	−1.09585	−	0.919527i	−0.0801365	−	0.0672425i
$188$	1.76833	−	3.59035i	0.128969	−	0.261853i
$189$		−	13.3311i		−	0.969696i
$190$	−12.5870	−	5.61855i	−0.913155	−	0.407612i
$191$			6.21850i			0.449955i	0.974364	+	0.224977i	$0.0722308\pi$
$191$			6.21850i			0.449955i	−0.974364	+	0.224977i	$0.927769\pi$
$192$	−7.59238	−	12.4695i	−0.547933	−	0.899912i
$193$	−10.5116	−	8.82024i	−0.756638	−	0.634895i	0.180611	−	0.983555i	$-0.442192\pi$
$193$	−10.5116	−	8.82024i	−0.756638	−	0.634895i	−0.937249	+	0.348660i	$0.886637\pi$
$194$	5.24462	−	9.81791i	0.376542	−	0.704885i
$195$	−2.76093	+	0.536191i	−0.197715	+	0.0383974i
$196$	−0.891336	+	0.392731i	−0.0636669	+	0.0280522i
$197$	11.8514	−	6.84239i	0.844375	−	0.487500i	−0.0143741	−	0.999897i	$-0.504576\pi$
$197$	11.8514	−	6.84239i	0.844375	−	0.487500i	0.858749	+	0.512397i	$0.171242\pi$
$198$	−0.745548	+	0.950468i	−0.0529838	+	0.0675468i
$199$	−10.4631	+	1.84493i	−0.741709	+	0.130783i	−0.531720	−	0.846920i	$-0.678454\pi$
$199$	−10.4631	+	1.84493i	−0.741709	+	0.130783i	−0.209990	+	0.977704i	$0.567343\pi$
$200$	11.9471	+	7.56755i	0.844785	+	0.535106i
$201$	−2.85547	+	4.94582i	−0.201409	+	0.348851i
$202$	−9.77093	+	3.92578i	−0.687480	+	0.276217i
$203$	−15.4288	−	18.3873i	−1.08289	−	1.29054i
$204$	2.01405	−	0.133022i	0.141012	−	0.00931337i
$205$	−9.72942	−	5.39523i	−0.679532	−	0.376820i
$206$	−10.6510	−	11.8752i	−0.742091	−	0.827383i
$207$	0.0223913	−	0.126987i	0.00155630	−	0.00882624i
$208$	2.32670	+	1.47899i	0.161328	+	0.102550i
$209$	8.23739	−	7.69907i	0.569792	−	0.532556i
$210$	−4.64832	+	15.0906i	−0.320764	+	1.04135i
$211$	0.507885	−	2.88036i	0.0349643	−	0.198292i	−0.962322	−	0.271912i	$-0.912344\pi$
$211$	0.507885	−	2.88036i	0.0349643	−	0.198292i	0.997286	+	0.0736198i	$0.0234551\pi$
$212$	−11.0321	−	16.4928i	−0.757688	−	1.13273i
$213$	−2.40788	+	6.61559i	−0.164985	+	0.453293i
$214$	13.2731	−	2.79451i	0.907332	−	0.191029i
$215$	−3.02467	−	5.03581i	−0.206281	−	0.343440i
$216$	1.36101	+	13.7129i	0.0926050	+	0.933043i
$217$	−13.4456	+	23.2885i	−0.912749	+	1.58093i
$218$	0.619473	+	18.7790i	0.0419560	+	1.27188i
$219$	2.61962	+	14.8566i	0.177017	+	1.00391i
$220$	−9.50271	+	6.59696i	−0.640672	+	0.444767i
$221$	−0.330106	+	0.190587i	−0.0222054	+	0.0128203i
$222$	20.7939	−	12.9377i	1.39560	−	0.868323i
$223$	−0.702531	−	1.93019i	−0.0470450	−	0.129255i	0.913945	−	0.405838i	$-0.133020\pi$
$223$	−0.702531	−	1.93019i	−0.0470450	−	0.129255i	−0.960990	+	0.276583i	$0.910798\pi$
$224$	13.4789	−	7.60947i	0.900596	−	0.508429i
$225$	0.874472	+	1.40049i	0.0582982	+	0.0933662i
$226$	−22.5344	−	7.37002i	−1.49897	−	0.490247i
$227$		−	12.0059i		−	0.796857i	−0.917199	−	0.398428i	$-0.869556\pi$
$227$		−	12.0059i		−	0.796857i	0.917199	−	0.398428i	$-0.130444\pi$
$228$	−0.875859	+	15.8849i	−0.0580052	+	1.05200i
$229$	14.3495			0.948243			0.474122	−	0.880459i	$-0.342766\pi$
$229$	14.3495			0.948243			0.474122	+	0.880459i	$0.342766\pi$
$230$	0.562913	−	1.09907i	0.0371174	−	0.0724705i
$231$	−9.89446	−	8.30244i	−0.651008	−	0.546260i
$232$	17.7479	+	17.3387i	1.16520	+	1.13834i
$233$	3.31500	+	9.10788i	0.217173	+	0.596677i	0.999662	−	0.0259867i	$-0.00827274\pi$
$233$	3.31500	+	9.10788i	0.217173	+	0.596677i	−0.782490	+	0.622664i	$0.786051\pi$
$234$	0.170041	+	0.273295i	0.0111159	+	0.0178659i
$235$	4.17766	−	1.60285i	0.272521	−	0.104558i
$236$	10.1875	−	9.76215i	0.663147	−	0.635462i
$237$	22.1567	−	3.90683i	1.43923	−	0.253776i
$238$	0.0705555	+	2.13886i	0.00457344	+	0.138642i
$239$	7.14550	+	4.12545i	0.462204	+	0.266853i	0.712970	−	0.701194i	$-0.247349\pi$
$239$	7.14550	+	4.12545i	0.462204	+	0.266853i	−0.250767	+	0.968048i	$0.580683\pi$
$240$	3.24079	−	15.9973i	0.209192	−	1.03262i
$241$	−9.16260	−	10.9196i	−0.590215	−	0.703391i	0.385432	−	0.922736i	$-0.374052\pi$
$241$	−9.16260	−	10.9196i	−0.590215	−	0.703391i	−0.975647	+	0.219345i	$0.929608\pi$
$242$	1.25545	+	5.96302i	0.0807034	+	0.383318i
$243$	−1.16857	+	3.21061i	−0.0749636	+	0.205961i
$244$	−1.46269	−	2.18670i	−0.0936394	−	0.139989i
$245$	−1.02960	−	0.354713i	−0.0657787	−	0.0226618i
$246$	−1.81157	+	12.7118i	−0.115502	+	0.810477i
$247$	−1.17705	−	2.76418i	−0.0748936	−	0.175881i
$248$	11.4531	−	25.3281i	0.727272	−	1.60834i
$249$	2.31192	+	0.407655i	0.146512	+	0.0258341i
$250$	4.05511	+	15.2825i	0.256468	+	0.966553i
$251$	4.54394	−	12.4844i	0.286811	−	0.788007i	−0.709697	−	0.704507i	$-0.751168\pi$
$251$	4.54394	−	12.4844i	0.286811	−	0.788007i	0.996508	−	0.0834994i	$-0.0266097\pi$
$252$	1.80318	−	0.119094i	0.113589	−	0.00750222i
$253$	0.649270	+	0.773770i	0.0408192	+	0.0486465i
$254$	−10.7978	−	26.8747i	−0.677513	−	1.68627i
$255$	1.75353	+	1.42047i	0.109811	+	0.0889533i
$256$	−13.0880	+	9.20348i	−0.818001	+	0.575217i
$257$	−0.0276182	−	0.156631i	−0.00172278	−	0.00977034i	0.983934	−	0.178531i	$-0.0571345\pi$
$257$	−0.0276182	−	0.156631i	−0.00172278	−	0.00977034i	−0.985657	+	0.168761i	$0.946023\pi$
$258$	−4.18446	+	5.33460i	−0.260513	+	0.332118i
$259$	12.9827	+	22.4868i	0.806708	+	1.39726i
$260$	0.785779	+	2.98056i	0.0487320	+	0.184846i
$261$	0.990745	+	2.72205i	0.0613256	+	0.168491i
$262$	−0.230931	−	0.123361i	−0.0142669	−	0.00762124i
$263$	5.37382	+	4.50917i	0.331364	+	0.278047i	0.793255	−	0.608889i	$-0.208385\pi$
$263$	5.37382	+	4.50917i	0.331364	+	0.278047i	−0.461891	+	0.886936i	$0.652829\pi$
$264$	11.0254	+	7.53004i	0.678568	+	0.463442i
$265$	3.47409	−	21.9108i	0.213411	−	1.34597i
$266$	−16.8020	−	1.48338i	−1.03019	−	0.0909517i
$267$	−20.7189			−1.26797
$268$	5.61487	+	2.76545i	0.342982	+	0.168927i
$269$	4.32068	−	5.14918i	0.263436	−	0.313951i	−0.618070	−	0.786123i	$-0.712085\pi$
$269$	4.32068	−	5.14918i	0.263436	−	0.313951i	0.881507	+	0.472172i	$0.156530\pi$
$270$	−9.29784	+	12.2849i	−0.565849	+	0.747637i
$271$	−5.61426	−	15.4251i	−0.341042	−	0.937006i	−0.985093	−	0.172023i	$-0.944970\pi$
$271$	−5.61426	−	15.4251i	−0.341042	−	0.937006i	0.644051	−	0.764983i	$-0.277253\pi$
$272$	−0.290938	−	2.19291i	−0.0176407	−	0.132965i
$273$	−2.98054	+	1.72082i	−0.180391	+	0.104149i
$274$	−0.626318	+	0.798468i	−0.0378373	+	0.0482372i
$275$	−12.8071	−	1.80429i	−0.772296	−	0.108803i
$276$	−1.41681	−	0.154447i	−0.0852818	−	0.00929663i
$277$	−17.2303	−	9.94792i	−1.03527	−	0.597713i	−0.116779	−	0.993158i	$-0.537257\pi$
$277$	−17.2303	−	9.94792i	−1.03527	−	0.597713i	−0.918490	+	0.395445i	$0.870590\pi$
$278$	2.08841	+	5.19786i	0.125254	+	0.311747i
$279$	2.48605	−	2.08605i	0.148836	−	0.124888i
$280$	16.8385	+	3.99333i	1.00629	+	0.238647i
$281$	−7.32284	+	20.1193i	−0.436844	+	1.20022i	0.504689	+	0.863301i	$0.331607\pi$
$281$	−7.32284	+	20.1193i	−0.436844	+	1.20022i	−0.941534	+	0.336919i	$0.890615\pi$
$282$	−3.44824	−	3.84456i	−0.205340	−	0.228940i
$283$	0.697814	−	3.95750i	0.0414808	−	0.235249i	−0.957018	−	0.290030i	$-0.906335\pi$
$283$	0.697814	−	3.95750i	0.0414808	−	0.235249i	0.998498	+	0.0547806i	$0.0174459\pi$
$284$	7.40856	+	2.15537i	0.439617	+	0.127898i
$285$	−12.7827	+	12.3682i	−0.757184	+	0.732628i
$286$	−2.49615	−	0.355728i	−0.147600	−	0.0210346i
$287$	−13.4069	−	2.36400i	−0.791385	−	0.139542i
$288$	−1.84266	+	0.306596i	−0.108580	+	0.0180663i
$289$	−15.6874	−	5.70974i	−0.922787	−	0.335867i
$290$	1.39367	+	27.7052i	0.0818394	+	1.62691i
$291$	−9.23251	−	11.0029i	−0.541219	−	0.645000i
$292$	16.0576	−	3.93779i	0.939699	−	0.230442i
$293$	−12.0729	+	20.9108i	−0.705305	+	1.22162i	0.261277	+	0.965264i	$0.415857\pi$
$293$	−12.0729	+	20.9108i	−0.705305	+	1.22162i	−0.966581	+	0.256360i	$0.917477\pi$
$294$	0.0414383	+	1.25618i	0.00241673	+	0.0732622i
$295$	15.7728	−	0.272672i	0.918326	−	0.0158755i
$296$	−15.6503	−	21.8053i	−0.909653	−	1.26741i
$297$	−6.30130	−	10.9142i	−0.365638	−	0.633304i
$298$	−10.5273	−	16.9198i	−0.609830	−	0.980139i
$299$	0.252912	−	0.0920525i	0.0146263	−	0.00532353i
$300$	14.8085	−	10.6644i	0.854972	−	0.615707i
$301$	−5.50660	−	4.62059i	−0.317395	−	0.266326i
$302$	−20.2513	−	6.62332i	−1.16533	−	0.381129i
$303$			13.5879i			0.780607i
$304$	17.4346	−	0.189501i	0.999941	−	0.0108686i
$305$	0.460612	−	2.90504i	0.0263746	−	0.166342i
$306$	0.0802821	−	0.245469i	0.00458942	−	0.0140325i
$307$	−4.07184	+	4.85263i	−0.232392	+	0.276954i	−0.869620	−	0.493721i	$-0.835636\pi$
$307$	−4.07184	+	4.85263i	−0.232392	+	0.276954i	0.637228	+	0.770675i	$0.280081\pi$
$308$	−8.36469	+	11.4200i	−0.476622	+	0.650715i
$309$	−19.3428	+	7.04022i	−1.10038	+	0.400504i
$310$	28.6331	−	12.0832i	1.62625	−	0.686279i
$311$	24.9320	−	14.3945i	1.41376	−	0.816236i	0.418022	−	0.908437i	$-0.362724\pi$
$311$	24.9320	−	14.3945i	1.41376	−	0.816236i	0.995740	+	0.0922011i	$0.0293903\pi$
$312$	2.89021	−	2.07439i	0.163626	−	0.117439i
$313$	31.2411	−	5.50865i	1.76585	−	0.311367i	0.806009	−	0.591903i	$-0.201623\pi$
$313$	31.2411	−	5.50865i	1.76585	−	0.311367i	0.959844	+	0.280536i	$0.0905122\pi$
$314$	−0.890028	−	26.9808i	−0.0502272	−	1.52261i
$315$	1.56994	+	1.27175i	0.0884559	+	0.0716547i
$316$	−5.87272	−	23.9479i	−0.330367	−	1.34717i
$317$	22.2893	−	18.7029i	1.25189	−	1.05046i	0.255392	−	0.966838i	$-0.417796\pi$
$317$	22.2893	−	18.7029i	1.25189	−	1.05046i	0.996498	−	0.0836220i	$-0.0266488\pi$
$318$	−25.0551	+	5.27509i	−1.40502	+	0.295812i
$319$	−21.3228	−	7.76087i	−1.19385	−	0.434525i
$320$	−17.7284	−	2.38861i	−0.991045	−	0.133527i
$321$	3.03936	−	17.2371i	0.169641	−	0.962081i
$322$	0.213187	−	1.49594i	0.0118804	−	0.0833653i
$323$	−1.09194	+	2.14911i	−0.0607573	+	0.119580i
$324$	18.9764	+	5.52081i	1.05425	+	0.306712i
$325$	−1.61893	+	3.04230i	−0.0898018	+	0.168756i
$326$	16.0211	−	14.3695i	0.887326	−	0.795855i
$327$	22.7833	+	8.29244i	1.25992	+	0.458573i
$328$	14.0322	+	1.06295i	0.774798	+	0.0586916i
$329$	4.19447	−	3.51958i	0.231248	−	0.194040i
$330$	3.32740	+	14.5518i	0.183167	+	0.801051i
$331$	−9.41823	+	16.3128i	−0.517673	+	0.896635i	0.482117	+	0.876107i	$0.339868\pi$
$331$	−9.41823	+	16.3128i	−0.517673	+	0.896635i	−0.999789	+	0.0205282i	$0.993465\pi$
$332$	0.278817	−	2.55771i	0.0153021	−	0.140372i
$333$	−0.544141	−	3.08598i	−0.0298187	−	0.169111i
$334$	3.69092	−	4.70540i	0.201958	−	0.257468i
$335$	2.50666	+	6.53335i	0.136954	+	0.356955i
$336$	−2.62689	−	19.7998i	−0.143309	−	1.08017i
$337$	−11.2305	+	4.08757i	−0.611764	+	0.222664i	−0.629275	−	0.777183i	$-0.716648\pi$
$337$	−11.2305	+	4.08757i	−0.611764	+	0.222664i	0.0175107	+	0.999847i	$0.494426\pi$
$338$	8.34591	−	15.6235i	0.453958	−	0.849807i
$339$	−19.6654	+	23.4363i	−1.06808	+	1.27289i
$340$	1.42674	−	2.02022i	0.0773758	−	0.109562i
$341$			25.4217i			1.37666i
$342$	1.84419	+	0.861739i	0.0997226	+	0.0465975i
$343$	17.8211			0.962249
$344$	6.13602	+	4.19072i	0.330832	+	0.225949i
$345$	−1.04518	−	1.20275i	−0.0562705	−	0.0647537i
$346$	−2.43936	+	4.56648i	−0.131141	+	0.245495i
$347$	7.72163	−	2.81044i	0.414519	−	0.150872i	−0.126338	−	0.991987i	$-0.540322\pi$
$347$	7.72163	−	2.81044i	0.414519	−	0.150872i	0.540857	+	0.841115i	$0.318100\pi$
$348$	29.2988	−	12.9093i	1.57058	−	0.692012i
$349$	−1.88320	−	3.26180i	−0.100805	−	0.174600i	0.811211	−	0.584753i	$-0.198809\pi$
$349$	−1.88320	−	3.26180i	−0.100805	−	0.174600i	−0.912017	+	0.410153i	$0.865475\pi$
$350$	10.7830	+	16.0648i	0.576374	+	0.858700i
$351$	−3.30703	+	0.583118i	−0.176516	+	0.0311245i
$352$	7.43833	−	12.6010i	0.396464	−	0.671636i
$353$	−15.3251	−	8.84794i	−0.815672	−	0.470928i	0.0332500	−	0.999447i	$-0.489414\pi$
$353$	−15.3251	−	8.84794i	−0.815672	−	0.470928i	−0.848922	+	0.528519i	$0.822748\pi$
$354$	−6.78786	−	16.8944i	−0.360771	−	0.897928i
$355$	4.44171	+	7.39505i	0.235741	+	0.392488i
$356$	1.49646	+	22.6576i	0.0793124	+	1.20085i
$357$	2.59493	+	0.944477i	0.137338	+	0.0499870i
$358$	21.2843	−	19.0902i	1.12491	−	1.00895i
$359$	27.0391	+	4.76772i	1.42707	+	0.251631i	0.833218	−	0.552945i	$-0.186496\pi$
$359$	27.0391	+	4.76772i	1.42707	+	0.251631i	0.593850	+	0.804576i	$0.297607\pi$
$360$	−1.74473	−	1.14789i	−0.0919554	−	0.0604989i
$361$	−15.7759	−	10.5887i	−0.830310	−	0.557301i
$362$	−30.0858	−	4.28755i	−1.58128	−	0.225349i
$363$	7.74386	+	1.36545i	0.406447	+	0.0716676i
$364$	2.09712	+	3.13515i	0.109919	+	0.164327i
$365$	16.1657	+	8.96435i	0.846152	+	0.469215i
$366$	−3.32194	+	0.699398i	−0.173641	+	0.0365581i
$367$	19.3104	−	16.2034i	1.00800	−	0.845809i	0.0199242	−	0.999801i	$-0.493658\pi$
$367$	19.3104	−	16.2034i	1.00800	−	0.845809i	0.988072	+	0.153992i	$0.0492131\pi$
$368$	−0.0665677	+	1.56054i	−0.00347008	+	0.0813488i
$369$	1.42283	+	0.821471i	0.0740695	+	0.0427641i
$370$	3.71959	−	29.7769i	0.193373	−	1.54803i
$371$	−4.71399	−	26.7343i	−0.244738	−	1.38798i
$372$	−24.8171	−	25.8983i	−1.28671	−	1.34276i
$373$	−13.7616	−	23.8359i	−0.712551	−	1.23417i	−0.963897	−	0.266277i	$-0.914206\pi$
$373$	−13.7616	−	23.8359i	−0.712551	−	1.23417i	0.251345	−	0.967897i	$-0.419127\pi$
$374$	1.06875	+	1.71773i	0.0552638	+	0.0888218i
$375$	20.2495	+	2.49666i	1.04568	+	0.128927i
$376$	−3.95526	+	4.04859i	−0.203977	+	0.208790i
$377$	−3.88644	+	4.63168i	−0.200162	+	0.238544i
$378$	−5.86052	+	17.9190i	−0.301433	+	0.921655i
$379$	10.8427			0.556952			0.278476	−	0.960443i	$-0.410171\pi$
$379$	10.8427			0.556952			0.278476	+	0.960443i	$0.410171\pi$
$380$	14.4488	+	13.0856i	0.741208	+	0.671275i
$381$	−37.3733			−1.91469
$382$	2.73373	−	8.35860i	0.139870	−	0.427663i
$383$	20.9261	−	24.9387i	1.06927	−	1.27431i	0.109361	−	0.994002i	$-0.465120\pi$
$383$	20.9261	−	24.9387i	1.06927	−	1.27431i	0.959911	−	0.280306i	$-0.0904359\pi$
$384$	4.72353	+	20.0987i	0.241047	+	1.02566i
$385$	−15.5363	+	3.01725i	−0.791803	+	0.153773i
$386$	10.2516	+	16.4767i	0.521794	+	0.838644i
$387$	0.433755	+	0.751286i	0.0220490	+	0.0381900i
$388$	−11.3656	+	10.8911i	−0.577003	+	0.552914i
$389$	5.36751	+	30.4407i	0.272144	+	1.54340i	0.747891	+	0.663821i	$0.231066\pi$
$389$	5.36751	+	30.4407i	0.272144	+	1.54340i	−0.475748	+	0.879582i	$0.657823\pi$
$390$	3.94683	+	0.493019i	0.199855	+	0.0249650i
$391$	−0.187021	−	0.107977i	−0.00945805	−	0.00546061i
$392$	1.37074	−	0.136047i	0.0692328	−	0.00687139i
$393$	−0.258803	+	0.217161i	−0.0130549	+	0.0109543i
$394$	−18.9380	+	3.98719i	−0.954084	+	0.200872i
$395$	13.3692	−	24.1091i	0.672677	−	1.21306i
$396$	1.41997	−	0.949821i	0.0713560	−	0.0477303i
$397$	−3.15781	−	0.556807i	−0.158486	−	0.0279453i	0.0938422	−	0.995587i	$-0.470085\pi$
$397$	−3.15781	−	0.556807i	−0.158486	−	0.0279453i	−0.252328	+	0.967642i	$0.581196\pi$
$398$	14.8750	+	2.11985i	0.745618	+	0.106258i
$399$	−9.85919	+	19.4044i	−0.493577	+	0.971435i
$400$	−12.7319	−	15.4240i	−0.636593	−	0.771200i
$401$	7.29685	+	1.28663i	0.364387	+	0.0642513i	0.352844	−	0.935682i	$-0.385215\pi$
$401$	7.29685	+	1.28663i	0.364387	+	0.0642513i	0.0115431	+	0.999933i	$0.496326\pi$
$402$	6.01242	−	5.39262i	0.299872	−	0.268960i
$403$	6.36527	+	2.31677i	0.317077	+	0.115406i
$404$	14.8594	−	0.981417i	0.739284	−	0.0488273i
$405$	11.3771	+	18.9418i	0.565332	+	0.941227i
$406$	12.6553	+	31.4981i	0.628074	+	1.56322i
$407$	21.2579	+	12.2732i	1.05371	+	0.608362i
$408$	−2.76567	−	0.706601i	−0.136921	−	0.0349820i
$409$	−15.8416	+	2.79329i	−0.783315	+	0.138119i	−0.550982	−	0.834517i	$-0.685747\pi$
$409$	−15.8416	+	2.79329i	−0.783315	+	0.138119i	−0.232332	+	0.972636i	$0.574636\pi$
$410$	10.7060	+	11.5292i	0.528731	+	0.569386i
$411$	0.654746	+	1.13405i	0.0322962	+	0.0559387i
$412$	9.09608	+	20.6444i	0.448132	+	1.01707i
$413$	18.1396	−	6.60228i	0.892592	−	0.324877i
$414$	−0.0859226	+	0.160847i	−0.00422287	+	0.00790519i
$415$	2.17127	−	1.88682i	0.106583	−	0.0926203i
$416$	−2.47725	−	3.01084i	−0.121457	−	0.147618i
$417$	7.22840			0.353976
$418$	−14.4569	+	6.72744i	−0.707110	+	0.329050i
$419$		−	33.7665i		−	1.64960i	−0.565424	−	0.824801i	$-0.691287\pi$
$419$		−	33.7665i		−	1.64960i	0.565424	−	0.824801i	$-0.308713\pi$
$420$	12.8821	−	18.2406i	0.628580	−	0.890051i
$421$	−23.2641	+	27.7250i	−1.13382	+	1.35124i	−0.205850	+	0.978584i	$0.565996\pi$
$421$	−23.2641	+	27.7250i	−1.13382	+	1.35124i	−0.927971	+	0.372652i	$0.878449\pi$
$422$	−1.94892	+	3.64837i	−0.0948718	+	0.177600i
$423$	−0.620946	+	0.226006i	−0.0301914	+	0.0109888i
$424$	7.57836	+	27.0187i	0.368038	+	1.31214i
$425$	2.70492	−	0.574002i	0.131208	−	0.0278432i
$426$	6.14485	−	7.83382i	0.297719	−	0.379550i
$427$	−0.625005	−	3.54458i	−0.0302461	−	0.171534i
$428$	−19.0696	−	2.07879i	−0.921763	−	0.100482i
$429$	−1.62678	+	2.81766i	−0.0785415	+	0.136038i
$430$	1.85181	+	8.09858i	0.0893022	+	0.390548i
$431$	−18.8061	+	15.7802i	−0.905858	+	0.760105i	−0.971327	−	0.237749i	$-0.923590\pi$
$431$	−18.8061	+	15.7802i	−0.905858	+	0.760105i	0.0654684	+	0.997855i	$0.479146\pi$
$432$	4.19895	−	19.0305i	0.202022	−	0.915605i
$433$	4.83707	+	1.76055i	0.232455	+	0.0846067i	0.455621	−	0.890174i	$-0.349417\pi$
$433$	4.83707	+	1.76055i	0.232455	+	0.0846067i	−0.223166	+	0.974780i	$0.571639\pi$
$434$	28.3109	−	25.3924i	1.35897	−	1.21887i
$435$	33.8436	+	11.6596i	1.62268	+	0.559037i
$436$	7.42284	−	25.5142i	0.355489	−	1.22191i
$437$	1.02280	−	1.36053i	0.0489273	−	0.0650830i
$438$	3.00998	−	21.1211i	0.143822	−	1.00921i
$439$	−2.13084	+	12.0846i	−0.101700	+	0.576767i	0.890788	+	0.454419i	$0.150153\pi$
$439$	−2.13084	+	12.0846i	−0.101700	+	0.576767i	−0.992487	+	0.122347i	$0.960958\pi$
$440$	15.6732	−	4.68980i	0.747189	−	0.223577i
$441$	0.151121	+	0.0550034i	0.00719622	+	0.00261921i
$442$	0.527497	−	0.111059i	0.0250905	−	0.00528253i
$443$	−20.1188	+	16.8817i	−0.955872	+	0.802072i	−0.980277	−	0.197631i	$-0.936675\pi$
$443$	−20.1188	+	16.8817i	−0.955872	+	0.802072i	0.0244049	+	0.999702i	$0.492231\pi$
$444$	−33.6378	+	8.24898i	−1.59638	+	0.391479i
$445$	−15.9800	+	19.7269i	−0.757524	+	0.935143i
$446$	0.0957727	+	2.90331i	0.00453497	+	0.137476i
$447$	−25.3236	+	4.46523i	−1.19776	+	0.211198i
$448$	−21.4629	+	4.30278i	−1.01403	+	0.203287i
$449$	−20.9114	+	12.0732i	−0.986869	+	0.569769i	−0.904337	−	0.426820i	$-0.859634\pi$
$449$	−20.9114	+	12.0732i	−0.986869	+	0.569769i	−0.0825318	+	0.996588i	$0.526301\pi$
$450$	−0.559749	−	2.26690i	−0.0263868	−	0.106863i
$451$	−12.0936	+	4.40172i	−0.569466	+	0.207269i
$452$	27.0497	+	19.8128i	1.27231	+	0.931918i
$453$	−17.6730	+	21.0618i	−0.830349	+	0.989571i
$454$	−5.27792	+	16.1377i	−0.247705	+	0.757379i
$455$	−0.660396	+	4.16506i	−0.0309599	+	0.195261i
$456$	8.16048	−	20.9666i	0.382149	−	0.981852i
$457$			24.6991i			1.15538i	0.816257	+	0.577689i	$0.196045\pi$
$457$			24.6991i			1.15538i	−0.816257	+	0.577689i	$0.803955\pi$
$458$	−19.2879	−	6.30823i	−0.901265	−	0.294764i
$459$	2.06403	+	1.73192i	0.0963406	+	0.0808393i
$460$	−1.23980	+	1.22985i	−0.0578062	+	0.0573422i
$461$	18.0400	−	6.56603i	0.840207	−	0.305810i	0.114166	−	0.993462i	$-0.463580\pi$
$461$	18.0400	−	6.56603i	0.840207	−	0.305810i	0.726041	+	0.687651i	$0.241358\pi$
$462$	9.64979	+	15.5095i	0.448949	+	0.721565i
$463$	−12.5649	−	21.7630i	−0.583939	−	1.01141i	−0.995007	−	0.0998074i	$-0.968177\pi$
$463$	−12.5649	−	21.7630i	−0.583939	−	1.01141i	0.411068	−	0.911605i	$-0.365156\pi$
$464$	−16.2335	−	31.1081i	−0.753620	−	1.44416i
$465$	−0.693178	−	40.0971i	−0.0321454	−	1.85946i
$466$	−0.451917	−	13.6997i	−0.0209347	−	0.634625i
$467$	0.475449	−	0.823502i	0.0220012	−	0.0381071i	−0.854815	−	0.518933i	$-0.826330\pi$
$467$	0.475449	−	0.823502i	0.0220012	−	0.0381071i	0.876816	+	0.480825i	$0.159663\pi$
$468$	−0.108416	−	0.442102i	−0.00501155	−	0.0204362i
$469$	5.50418	+	6.55963i	0.254160	+	0.302896i
$470$	−6.32004	+	0.317921i	−0.291522	+	0.0146646i
$471$	−32.7339	−	11.9142i	−1.50830	−	0.548976i
$472$	−17.9850	+	8.64327i	−0.827828	+	0.397839i
$473$	−6.69229	−	1.18003i	−0.307712	−	0.0542579i
$474$	−31.4995	−	4.48901i	−1.44682	−	0.206187i
$475$	1.91699	+	21.7100i	0.0879575	+	0.996124i
$476$	0.845432	−	2.90597i	0.0387503	−	0.133195i
$477$	−0.568897	+	3.22637i	−0.0260480	+	0.147726i
$478$	−7.79102	−	8.68648i	−0.356353	−	0.397310i
$479$	8.95565	−	24.6055i	0.409194	−	1.12425i	−0.548421	−	0.836202i	$-0.684771\pi$
$479$	8.95565	−	24.6055i	0.409194	−	1.12425i	0.957615	−	0.288050i	$-0.0930068\pi$
$480$	−11.3887	+	20.0781i	−0.519822	+	0.916437i
$481$	5.01037	−	4.20420i	0.228453	−	0.191695i
$482$	7.51554	+	18.7055i	0.342323	+	0.852014i
$483$	−1.68862	−	0.974924i	−0.0768347	−	0.0443606i
$484$	0.933907	−	8.56711i	0.0424503	−	0.389414i
$485$	−17.5969	+	0.304206i	−0.799034	+	0.0138133i
$486$	2.98216	−	3.80183i	0.135273	−	0.172455i
$487$	−6.80434	+	3.92849i	−0.308334	+	0.178017i	−0.646181	−	0.763184i	$-0.723635\pi$
$487$	−6.80434	+	3.92849i	−0.308334	+	0.178017i	0.337847	+	0.941201i	$0.390301\pi$
$488$	1.00478	+	3.58228i	0.0454842	+	0.162162i
$489$	−9.49812	−	26.0959i	−0.429520	−	1.18010i
$490$	1.22800	+	0.929412i	0.0554754	+	0.0419866i
$491$	−6.11989	+	7.29341i	−0.276187	+	0.329147i	−0.886251	−	0.463205i	$-0.846699\pi$
$491$	−6.11989	+	7.29341i	−0.276187	+	0.329147i	0.610064	+	0.792352i	$0.291144\pi$
$492$	8.02331	−	16.2902i	0.361719	−	0.734420i
$493$	4.85132			0.218493
$494$	0.366958	+	4.23292i	0.0165102	+	0.190448i
$495$	1.88643	+	0.299105i	0.0847887	+	0.0134438i
$496$	−26.5292	+	29.0099i	−1.19120	+	1.30258i
$497$	8.08639	+	6.78529i	0.362724	+	0.304362i
$498$	−2.92836	−	1.56430i	−0.131223	−	0.0700980i
$499$	−3.92539	−	10.7849i	−0.175724	−	0.482799i	0.820294	−	0.571941i	$-0.193810\pi$
$499$	−3.92539	−	10.7849i	−0.175724	−	0.482799i	−0.996019	+	0.0891426i	$0.971587\pi$
$500$	1.26772	−	22.3247i	0.0566942	−	0.998392i
$501$	−3.85844	−	6.68302i	−0.172383	−	0.298575i
$502$	−11.5960	+	14.7833i	−0.517556	+	0.659811i
$503$	3.92980	+	22.2870i	0.175221	+	0.993728i	0.937888	+	0.346937i	$0.112778\pi$
$503$	3.92980	+	22.2870i	0.175221	+	0.993728i	−0.762667	+	0.646791i	$0.776111\pi$
$504$	−2.47610	−	0.632619i	−0.110294	−	0.0281791i
$505$	12.9374	+	10.4801i	0.575705	+	0.466357i
$506$	−0.532558	−	1.32549i	−0.0236751	−	0.0589252i
$507$	−14.6919	−	17.5092i	−0.652492	−	0.777610i
$508$	2.69937	+	40.8705i	0.119765	+	1.81334i
$509$	−3.07492	+	8.44829i	−0.136294	+	0.374464i	−0.988998	−	0.147930i	$-0.952739\pi$
$509$	−3.07492	+	8.44829i	−0.136294	+	0.374464i	0.852704	+	0.522394i	$0.174961\pi$
$510$	−1.73256	−	2.68020i	−0.0767189	−	0.118681i
$511$	22.2760	+	3.92786i	0.985431	+	0.173758i
$512$	21.6382	−	6.61721i	0.956283	−	0.292442i
$513$	−15.5151	+	14.5012i	−0.685008	+	0.640242i
$514$	−0.0317337	+	0.222676i	−0.00139972	+	0.00982183i
$515$	−8.21555	+	23.8467i	−0.362020	+	1.05081i
$516$	7.96971	−	5.33097i	0.350847	−	0.234683i
$517$	1.77039	−	4.86410i	0.0778615	−	0.213923i
$518$	−7.56529	−	35.9330i	−0.332400	−	1.57880i
$519$	4.29420	+	5.11763i	0.188494	+	0.224639i
$520$	0.254086	−	4.35176i	0.0111424	−	0.190837i
$521$	28.9479	+	16.7131i	1.26823	+	0.732213i	0.974653	−	0.223722i	$-0.0718207\pi$
$521$	28.9479	+	16.7131i	1.26823	+	0.732213i	0.293578	+	0.955935i	$0.405154\pi$
$522$	−0.135063	−	4.09439i	−0.00591157	−	0.179207i
$523$	−35.3296	+	6.22956i	−1.54485	+	0.272399i	−0.880146	−	0.474704i	$-0.842555\pi$
$523$	−35.3296	+	6.22956i	−1.54485	+	0.272399i	−0.664708	+	0.747103i	$0.731444\pi$
$524$	0.256175	+	0.267335i	0.0111910	+	0.0116786i
$525$	24.4228	−	5.18268i	1.06590	−	0.226191i
$526$	−5.24093	−	8.42340i	−0.228516	−	0.367278i
$527$	−1.85891	−	5.10731i	−0.0809753	−	0.222478i
$528$	−11.5095	−	14.9684i	−0.500888	−	0.651417i
$529$	−17.5022	−	14.6861i	−0.760966	−	0.638526i
$530$	−14.3019	+	27.9241i	−0.621236	+	1.21295i
$531$	−2.32963			−0.101097
$532$	21.9323	+	9.38024i	0.950884	+	0.406685i
$533$			3.42923i			0.148536i
$534$	27.8493	+	9.10827i	1.20516	+	0.394153i
$535$	−14.0676	−	16.1884i	−0.608196	−	0.699886i
$536$	−6.33150	−	6.18554i	−0.273479	−	0.267175i
$537$	−12.6184	−	34.6689i	−0.544526	−	1.49607i
$538$	−8.07129	+	5.02185i	−0.347978	+	0.216508i
$539$	−1.09098	+	0.629878i	−0.0469918	+	0.0271307i
$540$	17.8983	−	12.4253i	0.770220	−	0.534702i
$541$	−0.791281	−	4.48758i	−0.0340198	−	0.192936i	0.963062	−	0.269281i	$-0.0867861\pi$
$541$	−0.791281	−	4.48758i	−0.0340198	−	0.192936i	−0.997081	+	0.0763450i	$0.975675\pi$
$542$	0.765365	+	23.2017i	0.0328752	+	0.996598i
$543$	−19.6074	+	33.9610i	−0.841433	+	1.45740i
$544$	−0.572965	+	3.07550i	−0.0245657	+	0.131861i
$545$	25.4676	−	15.2967i	1.09091	−	0.655239i
$546$	4.76279	−	1.00275i	0.203828	−	0.0429139i
$547$	−11.2318	+	30.8590i	−0.480235	+	1.31944i	0.429057	+	0.903278i	$0.358846\pi$
$547$	−11.2318	+	30.8590i	−0.480235	+	1.31944i	−0.909292	+	0.416158i	$0.863376\pi$
$548$	1.19288	−	0.797923i	0.0509574	−	0.0340856i
$549$	−0.0754273	+	0.427769i	−0.00321916	+	0.0182568i
$550$	16.4214	+	8.05539i	0.700213	+	0.343483i
$551$	−4.61669	+	37.9576i	−0.196678	+	1.61705i
$552$	1.83651	+	0.830447i	0.0781669	+	0.0353462i
$553$	5.85790	−	33.2218i	0.249103	−	1.41274i
$554$	18.7869	+	20.9462i	0.798179	+	0.889917i
$555$	−33.8643	−	18.7787i	−1.43746	−	0.797112i
$556$	−0.522087	−	7.90480i	−0.0221414	−	0.335238i
$557$	1.32626	+	1.58057i	0.0561953	+	0.0669710i	0.793410	−	0.608688i	$-0.208304\pi$
$557$	1.32626	+	1.58057i	0.0561953	+	0.0669710i	−0.737215	+	0.675659i	$0.763859\pi$
$558$	−4.25868	+	1.71106i	−0.180284	+	0.0724349i
$559$	−0.905356	+	1.56812i	−0.0382925	+	0.0663245i
$560$	−20.8779	−	12.7700i	−0.882253	−	0.539633i
$561$	2.57090	−	0.453319i	0.108543	−	0.0191391i
$562$	18.6877	−	23.8242i	0.788294	−	1.00496i
$563$	26.4632	−	15.2786i	1.11529	−	0.643915i	0.175098	−	0.984551i	$-0.443976\pi$
$563$	26.4632	−	15.2786i	1.11529	−	0.643915i	0.940195	+	0.340636i	$0.110642\pi$
$564$	2.94484	+	6.68356i	0.124000	+	0.281429i
$565$	7.14674	+	36.7997i	0.300666	+	1.54818i
$566$	−2.67773	+	5.01271i	−0.112554	+	0.210700i
$567$	20.7127	+	17.3800i	0.869850	+	0.729891i
$568$	−9.01069	−	6.15404i	−0.378080	−	0.258218i
$569$		−	7.97165i		−	0.334189i	−0.985941	−	0.167094i	$-0.946562\pi$
$569$		−	7.97165i		−	0.334189i	0.985941	−	0.167094i	$-0.0534385\pi$
$570$	22.6191	−	11.0053i	0.947411	−	0.460960i
$571$		−	42.2091i		−	1.76640i	−0.468999	−	0.883199i	$-0.655385\pi$
$571$		−	42.2091i		−	1.76640i	0.468999	−	0.883199i	$-0.344615\pi$
$572$	3.19882	+	1.57549i	0.133749	+	0.0658746i
$573$	−8.69312	−	7.29439i	−0.363160	−	0.304728i
$574$	16.9817	+	9.07141i	0.708801	+	0.378634i
$575$	−1.95128	+	0.0674857i	−0.0813742	+	0.00281435i
$576$	2.61159	+	0.397944i	0.108816	+	0.0165810i
$577$	−16.5669	+	9.56489i	−0.689688	+	0.398192i	−0.803495	−	0.595311i	$-0.797029\pi$
$577$	−16.5669	+	9.56489i	−0.689688	+	0.398192i	0.113807	+	0.993503i	$0.463695\pi$
$578$	18.5761	+	14.5711i	0.772665	+	0.606078i
$579$	24.6604	−	4.34830i	1.02485	−	0.180709i
$580$	10.3063	−	37.8527i	0.427944	−	1.57175i
$581$	1.75999	−	3.04839i	0.0730167	−	0.126469i
$582$	7.57288	+	18.8482i	0.313906	+	0.781285i
$583$	−16.4960	−	19.6592i	−0.683195	−	0.814200i
$584$	−23.3149	−	1.76612i	−0.964778	−	0.0730827i
$585$	0.246809	−	0.445079i	0.0102043	−	0.0184018i
$586$	25.4204	−	22.7999i	1.05011	−	0.941856i
$587$	3.85916	−	21.8864i	0.159285	−	0.903348i	−0.795479	−	0.605982i	$-0.792781\pi$
$587$	3.85916	−	21.8864i	0.159285	−	0.903348i	0.954763	−	0.297367i	$-0.0961084\pi$
$588$	0.496535	−	1.70672i	0.0204768	−	0.0703839i
$589$	41.7295	−	9.68413i	1.71943	−	0.399028i
$590$	−21.3209	−	6.56740i	−0.877766	−	0.270375i
$591$	−4.33655	+	24.5938i	−0.178382	+	1.01165i
$592$	11.4504	+	36.1896i	0.470610	+	1.48738i
$593$	−6.68355	+	18.3629i	−0.274461	+	0.754074i	0.723505	+	0.690319i	$0.242530\pi$
$593$	−6.68355	+	18.3629i	−0.274461	+	0.754074i	−0.997966	+	0.0637551i	$0.979692\pi$
$594$	3.67189	+	17.4404i	0.150659	+	0.715589i
$595$	2.90067	−	1.74224i	0.118916	−	0.0714247i
$596$	6.71211	+	27.3707i	0.274939	+	1.12115i
$597$	9.69427	−	16.7910i	0.396760	−	0.687209i
$598$	−0.380420	+	0.0125491i	−0.0155565	+	0.000513170i
$599$	−3.71618	−	21.0755i	−0.151839	−	0.861122i	−0.961619	−	0.274388i	$-0.911525\pi$
$599$	−3.71618	−	21.0755i	−0.151839	−	0.861122i	0.809780	−	0.586734i	$-0.199586\pi$
$600$	−24.5931	+	7.82449i	−1.00401	+	0.319433i
$601$	−2.22870	+	1.28674i	−0.0909104	+	0.0524871i	−0.544766	−	0.838588i	$-0.683382\pi$
$601$	−2.22870	+	1.28674i	−0.0909104	+	0.0524871i	0.453856	+	0.891075i	$0.350048\pi$
$602$	5.37043	+	8.63153i	0.218882	+	0.351795i
$603$	−0.353445	−	0.971083i	−0.0143934	−	0.0395456i
$604$	24.3092	+	17.8055i	0.989125	+	0.724495i
$605$	7.27274	−	6.31996i	0.295679	−	0.256943i
$606$	5.97343	−	18.2642i	0.242654	−	0.741934i
$607$		−	41.1646i		−	1.67082i	−0.549629	−	0.835409i	$-0.685231\pi$
$607$		−	41.1646i		−	1.67082i	0.549629	−	0.835409i	$-0.314769\pi$
$608$	−23.5180	−	7.40974i	−0.953780	−	0.300504i
$609$	43.8027			1.77498
$610$	−1.89622	+	3.70232i	−0.0767759	+	0.149903i
$611$	−1.05657	−	0.886564i	−0.0427441	−	0.0358665i
$612$	−0.215823	+	0.294654i	−0.00872411	+	0.0119107i
$613$	−0.358494	−	0.984953i	−0.0144794	−	0.0397819i	0.932242	−	0.361834i	$-0.117849\pi$
$613$	−0.358494	−	0.984953i	−0.0144794	−	0.0397819i	−0.946722	+	0.322053i	$0.895627\pi$
$614$	7.60644	−	4.73263i	0.306971	−	0.190994i
$615$	18.9550	−	7.27250i	0.764339	−	0.293255i
$616$	16.2638	−	11.6730i	0.655286	−	0.470317i
$617$	−23.3255	+	4.11292i	−0.939050	+	0.165580i	−0.622167	−	0.782885i	$-0.713747\pi$
$617$	−23.3255	+	4.11292i	−0.939050	+	0.165580i	−0.316883	+	0.948465i	$0.602636\pi$
$618$	29.0947	−	0.959759i	1.17036	−	0.0386072i
$619$	−3.88344	−	2.24210i	−0.156089	−	0.0901178i	0.419921	−	0.907561i	$-0.362058\pi$
$619$	−3.88344	−	2.24210i	−0.156089	−	0.0901178i	−0.576010	+	0.817443i	$0.695391\pi$
$620$	−43.7992	+	3.65414i	−1.75902	+	0.146754i
$621$	−1.22290	−	1.45739i	−0.0490732	−	0.0584831i
$622$	−39.8403	+	8.38794i	−1.59745	+	0.336326i
$623$	−10.6252	+	29.1924i	−0.425688	+	1.16957i
$624$	−4.79681	+	1.51771i	−0.192026	+	0.0607572i
$625$	17.9951	−	17.3544i	0.719805	−	0.694176i
$626$	−44.4144	−	6.32953i	−1.77516	−	0.252979i
$627$	1.10029	+	20.5466i	0.0439412	+	0.820550i
$628$	−10.6648	+	36.6575i	−0.425570	+	1.46279i
$629$	−5.16824	−	0.911300i	−0.206071	−	0.0363359i
$630$	−1.55116	−	2.39958i	−0.0617996	−	0.0956016i
$631$	−5.62826	+	15.4635i	−0.224057	+	0.615592i	−0.999882	−	0.0153560i	$-0.995112\pi$
$631$	−5.62826	+	15.4635i	−0.224057	+	0.615592i	0.775825	+	0.630948i	$0.217334\pi$
$632$	−2.63395	+	34.7712i	−0.104773	+	1.38313i
$633$	3.43083	+	4.08870i	0.136363	+	0.162511i
$634$	−38.1821	+	15.3409i	−1.51641	+	0.609264i
$635$	−28.8252	+	35.5840i	−1.14389	+	1.41211i
$636$	35.9969	+	3.92405i	1.42737	+	0.155599i
$637$	0.0582885	+	0.330570i	0.00230947	+	0.0130977i
$638$	25.2493	+	19.8055i	0.999629	+	0.784109i
$639$	−0.636966	−	1.10326i	−0.0251980	−	0.0436442i
$640$	22.7795	+	11.0043i	0.900439	+	0.434981i
$641$	−3.74903	−	10.3004i	−0.148078	−	0.406840i	0.843372	−	0.537330i	$-0.180567\pi$
$641$	−3.74903	−	10.3004i	−0.148078	−	0.406840i	−0.991450	+	0.130490i	$0.958345\pi$
$642$	−11.6630	+	21.8331i	−0.460302	+	0.861684i
$643$	−20.9035	−	17.5402i	−0.824356	−	0.691716i	0.129632	−	0.991562i	$-0.458620\pi$
$643$	−20.9035	−	17.5402i	−0.824356	−	0.691716i	−0.953988	+	0.299846i	$0.903065\pi$
$644$	−0.944188	+	1.91705i	−0.0372062	+	0.0755422i
$645$	10.5878	+	1.67876i	0.416894	+	0.0661010i
$646$	2.41251	−	2.40870i	0.0949190	−	0.0947689i
$647$	−8.12098			−0.319269			−0.159634	−	0.987176i	$-0.551031\pi$
$647$	−8.12098			−0.319269			−0.159634	+	0.987176i	$0.551031\pi$
$648$	−23.0802	−	15.7631i	−0.906675	−	0.619232i
$649$	11.7301	−	13.9794i	0.460448	−	0.548741i
$650$	3.51351	−	3.37760i	0.137811	−	0.132481i
$651$	−16.7841	−	46.1140i	−0.657822	−	1.80735i
$652$	−27.8518	+	12.2717i	−1.09076	+	0.480598i
$653$	−8.02307	+	4.63212i	−0.313967	+	0.181269i	−0.648700	−	0.761044i	$-0.724687\pi$
$653$	−8.02307	+	4.63212i	−0.313967	+	0.181269i	0.334733	+	0.942313i	$0.391354\pi$
$654$	−26.9787	−	21.1621i	−1.05495	−	0.827504i
$655$	0.00715534	+	0.413903i	0.000279582	+	0.0161725i
$656$	−18.3941	−	7.59749i	−0.718168	−	0.296632i
$657$	−2.36407	−	1.36490i	−0.0922313	−	0.0532498i
$658$	−7.18524	+	2.88690i	−0.280110	+	0.112543i
$659$	20.5268	−	17.2240i	0.799610	−	0.670952i	−0.148494	−	0.988913i	$-0.547443\pi$
$659$	20.5268	−	17.2240i	0.799610	−	0.670952i	0.948104	+	0.317961i	$0.102998\pi$
$660$	1.92463	−	21.0226i	0.0749163	−	0.818304i
$661$	13.9626	−	38.3620i	0.543083	−	1.49211i	−0.299795	−	0.954004i	$-0.596918\pi$
$661$	13.9626	−	38.3620i	0.543083	−	1.49211i	0.842878	−	0.538105i	$-0.180859\pi$
$662$	19.8308	−	17.7866i	0.770748	−	0.691294i
$663$	0.120790	−	0.685032i	0.00469108	−	0.0266044i
$664$	−1.49917	+	3.31537i	−0.0581792	+	0.128661i
$665$	10.8712	+	24.3533i	0.421566	+	0.944381i
$666$	−0.625227	+	4.38723i	−0.0242270	+	0.170002i
$667$	−3.37344	−	0.594828i	−0.130620	−	0.0230318i
$668$	−7.02970	+	4.70219i	−0.271987	+	0.181933i
$669$	3.52238	+	1.28204i	0.136183	+	0.0495666i
$670$	−0.497189	−	9.88377i	−0.0192081	−	0.381843i
$671$	−2.18713	−	2.60652i	−0.0844331	−	0.100623i
$672$	−5.17332	+	27.7688i	−0.199565	+	1.07120i
$673$	9.24882	−	16.0194i	0.356516	−	0.617504i	−0.630860	−	0.775896i	$-0.717298\pi$
$673$	9.24882	−	16.0194i	0.356516	−	0.617504i	0.987376	+	0.158393i	$0.0506313\pi$
$674$	16.8924	−	0.557238i	0.650672	−	0.0214640i
$675$	24.1221	+	3.39838i	0.928459	+	0.130804i
$676$	−18.0864	+	17.3314i	−0.695633	+	0.666592i
$677$	−10.2412	−	17.7383i	−0.393602	−	0.681739i	0.599319	−	0.800510i	$-0.295438\pi$
$677$	−10.2412	−	17.7383i	−0.393602	−	0.681739i	−0.992922	+	0.118771i	$0.962105\pi$
$678$	36.7361	−	22.8568i	1.41084	−	0.877809i
$679$	−20.2375	+	7.36583i	−0.776642	+	0.282675i
$680$	−2.80586	+	2.08826i	−0.107600	+	0.0800813i
$681$	16.7835	+	14.0831i	0.643146	+	0.539664i
$682$	11.1757	−	34.1706i	0.427940	−	1.30846i
$683$			31.6147i			1.20970i	0.796338	+	0.604852i	$0.206768\pi$
$683$			31.6147i			1.20970i	−0.796338	+	0.604852i	$0.793232\pi$
$684$	−2.10004	−	1.96904i	−0.0802971	−	0.0752880i
$685$	1.58475	+	0.251272i	0.0605501	+	0.00960059i
$686$	−23.9542	−	7.83438i	−0.914577	−	0.299118i
$687$	−16.8322	+	20.0598i	−0.642189	+	0.765331i
$688$	−6.40544	−	8.33043i	−0.244205	−	0.317595i
$689$	−6.42575	+	2.33878i	−0.244801	+	0.0891004i
$690$	0.876135	+	2.07615i	0.0333539	+	0.0790376i
$691$	26.0592	−	15.0453i	0.991340	−	0.572350i	0.0856655	−	0.996324i	$-0.472698\pi$
$691$	26.0592	−	15.0453i	0.991340	−	0.572350i	0.905675	+	0.423974i	$0.139365\pi$
$692$	5.28635	−	5.06566i	0.200957	−	0.192568i
$693$	2.30172	−	0.405856i	0.0874352	−	0.0154172i
$694$	−11.6145	+	0.383134i	−0.440882	+	0.0145436i
$695$	5.57510	−	6.88232i	0.211476	−	0.261061i
$696$	−45.0571	+	4.47194i	−1.70789	+	0.169508i
$697$	2.10778	−	1.76864i	0.0798380	−	0.0669921i
$698$	1.09738	+	5.21223i	0.0415364	+	0.197286i
$699$	−16.6209	−	6.04950i	−0.628659	−	0.228813i
$700$	−7.43164	−	26.3339i	−0.280889	−	0.995326i
$701$	−0.447131	+	2.53580i	−0.0168879	+	0.0957760i	−0.992087	−	0.125555i	$-0.959929\pi$
$701$	−0.447131	+	2.53580i	−0.0168879	+	0.0957760i	0.975199	+	0.221331i	$0.0710400\pi$
$702$	4.70149	+	0.670012i	0.177446	+	0.0252880i
$703$	12.0485	−	39.5700i	0.454416	−	1.49241i
$704$	−15.5378	+	13.6677i	−0.585603	+	0.515119i
$705$	−2.65976	+	7.72031i	−0.100172	+	0.290764i
$706$	16.7095	+	18.6301i	0.628872	+	0.701151i
$707$	19.1451	+	6.96824i	0.720025	+	0.262068i
$708$	1.69692	+	25.6927i	0.0637740	+	0.965589i
$709$	−6.24268	+	5.23823i	−0.234449	+	0.196726i	−0.752441	−	0.658659i	$-0.771124\pi$
$709$	−6.24268	+	5.23823i	−0.234449	+	0.196726i	0.517993	+	0.855385i	$0.326679\pi$
$710$	−2.71937	−	11.8927i	−0.102056	−	0.446325i
$711$	−2.03557	+	3.52572i	−0.0763400	+	0.132225i
$712$	7.94910	−	31.1131i	0.297905	−	1.16601i
$713$	0.666403	+	3.77936i	0.0249570	+	0.141538i
$714$	−3.07277	−	2.41028i	−0.114996	−	0.0902026i
$715$	1.42806	+	3.72208i	0.0534064	+	0.139198i
$716$	−37.0016	+	16.3032i	−1.38282	+	0.609281i
$717$	−14.1489	+	5.14979i	−0.528402	+	0.192322i
$718$	−34.2486	−	18.2953i	−1.27815	−	0.682773i
$719$	19.6366	−	23.4020i	0.732322	−	0.872748i	−0.263443	−	0.964675i	$-0.584858\pi$
$719$	19.6366	−	23.4020i	0.732322	−	0.872748i	0.995766	+	0.0919271i	$0.0293027\pi$
$720$	1.84056	+	2.30994i	0.0685935	+	0.0860863i
$721$			30.8640i			1.14944i
$722$	16.5502	+	21.1681i	0.615936	+	0.787796i
$723$	26.0128			0.967427
$724$	38.5550	+	18.9892i	1.43289	+	0.705729i
$725$	37.2042	−	23.2304i	1.38173	−	0.862757i
$726$	−9.80865	−	5.23967i	−0.364033	−	0.194462i
$727$	−17.9504	+	6.53342i	−0.665745	+	0.242311i	−0.652715	−	0.757604i	$-0.726370\pi$
$727$	−17.9504	+	6.53342i	−0.665745	+	0.242311i	−0.0130301	+	0.999915i	$0.504148\pi$
$728$	−1.44059	−	5.13604i	−0.0533917	−	0.190354i
$729$	11.7049	+	20.2735i	0.433515	+	0.750870i
$730$	−17.7883	−	19.1561i	−0.658375	−	0.708998i
$731$	1.43079	−	0.252287i	0.0529197	−	0.00933117i
$732$	4.77265	+	0.520270i	0.176402	+	0.0192297i
$733$	25.3179	+	14.6173i	0.935139	+	0.539903i	0.888433	−	0.459006i	$-0.151794\pi$
$733$	25.3179	+	14.6173i	0.935139	+	0.539903i	0.0467061	+	0.998909i	$0.485128\pi$
$734$	−33.0793	+	13.2907i	−1.22098	+	0.490568i
$735$	1.70361	−	1.02324i	0.0628384	−	0.0377428i
$736$	0.775511	−	2.06834i	0.0285857	−	0.0762400i
$737$	7.60685	+	2.76867i	0.280202	+	0.101985i
$738$	−1.55137	−	1.72967i	−0.0571067	−	0.0636702i
$739$	18.1564	+	3.20146i	0.667894	+	0.117768i	0.497307	−	0.867575i	$-0.334322\pi$
$739$	18.1564	+	3.20146i	0.667894	+	0.117768i	0.170587	+	0.985343i	$0.445433\pi$
$740$	−18.0900	+	38.3895i	−0.665002	+	1.41123i
$741$	5.24487	+	1.59698i	0.192675	+	0.0586666i
$742$	−5.41645	+	38.0073i	−0.198844	+	1.39529i
$743$	37.2186	+	6.56265i	1.36542	+	0.240760i	0.807859	−	0.589376i	$-0.200626\pi$
$743$	37.2186	+	6.56265i	1.36542	+	0.240760i	0.557560	+	0.830137i	$0.311738\pi$
$744$	21.9727	+	45.7211i	0.805558	+	1.67622i
$745$	−15.2801	+	27.5551i	−0.559818	+	1.00954i
$746$	8.01918	+	38.0888i	0.293603	+	1.39453i
$747$	−0.325416	+	0.273057i	−0.0119064	+	0.00999062i
$748$	−0.681426	−	2.77873i	−0.0249154	−	0.101600i
$749$	−22.7280	−	13.1220i	−0.830463	−	0.479468i
$750$	−26.1209	−	12.2578i	−0.953799	−	0.447593i
$751$	6.53721	+	37.0744i	0.238546	+	1.35286i	0.835015	+	0.550227i	$0.185459\pi$
$751$	6.53721	+	37.0744i	0.238546	+	1.35286i	−0.596469	+	0.802636i	$0.703430\pi$
$752$	7.09628	−	3.70313i	0.258775	−	0.135039i
$753$	12.1224	+	20.9965i	0.441763	+	0.765156i
$754$	7.26011	−	4.51715i	0.264398	−	0.164505i
$755$	6.42266	+	33.0713i	0.233745	+	1.20359i
$756$	15.7549	−	21.5095i	0.572999	−	0.782293i
$757$	19.4845	−	23.2207i	0.708175	−	0.843970i	−0.285250	−	0.958453i	$-0.592077\pi$
$757$	19.4845	−	23.2207i	0.708175	−	0.843970i	0.993425	+	0.114483i	$0.0365212\pi$
$758$	−14.5742	−	4.76658i	−0.529359	−	0.173130i
$759$	−1.84329			−0.0669072
$760$	−13.6688	−	23.9408i	−0.495819	−	0.868426i
$761$	−27.9953			−1.01483			−0.507414	−	0.861702i	$-0.669399\pi$
$761$	−27.9953			−1.01483			−0.507414	+	0.861702i	$0.669399\pi$
$762$	50.2354	+	16.4298i	1.81984	+	0.595188i
$763$	23.3677	−	27.8486i	0.845968	−	1.00819i
$764$	−7.34909	+	10.0334i	−0.265881	+	0.362997i
$765$	−0.400862	+	0.0778499i	−0.0144932	+	0.00281467i
$766$	−39.0911	+	24.3220i	−1.41242	+	0.878790i
$767$	−2.43126	−	4.21107i	−0.0877878	−	0.152053i
$768$	2.48648	−	29.0921i	0.0897231	−	1.04977i
$769$	1.49615	+	8.48506i	0.0539524	+	0.305979i	0.999828	−	0.0185504i	$-0.00590512\pi$
$769$	1.49615	+	8.48506i	0.0539524	+	0.305979i	−0.945876	+	0.324530i	$0.894794\pi$
$770$	22.2095	+	2.77431i	0.800377	+	0.0999793i
$771$	0.251357	+	0.145121i	0.00905242	+	0.00522642i
$772$	−6.53634	−	26.6540i	−0.235248	−	0.959297i
$773$	7.60795	−	6.38383i	0.273639	−	0.229610i	−0.495633	−	0.868532i	$-0.665064\pi$
$773$	7.60795	−	6.38383i	0.273639	−	0.229610i	0.769272	+	0.638922i	$0.220619\pi$
$774$	−0.252758	−	1.20053i	−0.00908518	−	0.0431520i
$775$	−38.7120	−	30.2660i	−1.39058	−	1.08719i
$776$	20.0650	−	9.64287i	0.720292	−	0.346159i
$777$	−46.6642	−	8.22816i	−1.67407	−	0.295184i
$778$	6.16735	−	43.2765i	0.221110	−	1.55154i
$779$	11.8323	+	18.1748i	0.423937	+	0.651179i
$780$	−5.08839	−	2.39777i	−0.182194	−	0.0858538i
$781$	9.82756	+	1.73286i	0.351658	+	0.0620068i
$782$	0.203916	+	0.227353i	0.00729203	+	0.00813014i
$783$	40.1614	+	14.6176i	1.43525	+	0.522389i
$784$	−1.90229	−	0.419727i	−0.0679389	−	0.0149903i
$785$	−36.5907	+	21.9775i	−1.30598	+	0.784412i
$786$	0.443337	−	0.178124i	0.0158133	−	0.00635349i
$787$	26.7401	+	15.4384i	0.953182	+	0.550320i	0.894068	−	0.447931i	$-0.147839\pi$
$787$	26.7401	+	15.4384i	0.953182	+	0.550320i	0.0591139	+	0.998251i	$0.481172\pi$
$788$	27.2084	+	2.96600i	0.969258	+	0.105659i
$789$	−12.6071	+	2.22298i	−0.448826	+	0.0791402i
$790$	−28.5689	+	26.5290i	−1.01644	+	0.943861i
$791$	22.9363	+	39.7268i	0.815520	+	1.41252i
$792$	−2.32620	+	0.652467i	−0.0826580	+	0.0231844i
$793$	−0.851959	+	0.310088i	−0.0302540	+	0.0110115i
$794$	3.99979	+	2.13664i	0.141947	+	0.0758266i
$795$	26.5549	+	30.5582i	0.941805	+	1.08379i
$796$	−19.0624	−	9.38865i	−0.675648	−	0.332772i
$797$	−43.7968			−1.55136			−0.775681	−	0.631125i	$-0.782593\pi$
$797$	−43.7968			−1.55136			−0.775681	+	0.631125i	$0.782593\pi$
$798$	21.7826	−	21.7482i	0.771097	−	0.769878i
$799$			1.10667i			0.0391512i
$800$	10.3330	+	26.3293i	0.365325	+	0.930880i
$801$	2.40989	−	2.87199i	0.0851491	−	0.101477i
$802$	−9.24245	−	4.93722i	−0.326362	−	0.174339i
$803$	20.0939	−	7.31359i	0.709099	−	0.258091i
$804$	−10.4523	+	4.60536i	−0.368623	+	0.162419i
$805$	−2.23064	+	0.855833i	−0.0786196	+	0.0301641i
$806$	−7.53740	−	5.91234i	−0.265494	−	0.208253i
$807$	2.13006	+	12.0801i	0.0749815	+	0.425241i
$808$	−20.4048	−	5.21322i	−0.717837	−	0.183400i
$809$	24.0224	−	41.6081i	0.844584	−	1.46286i	−0.0413975	−	0.999143i	$-0.513181\pi$
$809$	24.0224	−	41.6081i	0.844584	−	1.46286i	0.885982	−	0.463720i	$-0.153486\pi$
$810$	−6.96544	−	30.4622i	−0.244741	−	1.07033i
$811$	16.4856	−	13.8330i	0.578887	−	0.485744i	−0.305695	−	0.952130i	$-0.598889\pi$
$811$	16.4856	−	13.8330i	0.578887	−	0.485744i	0.884581	+	0.466386i	$0.154444\pi$
$812$	−3.16375	−	47.9016i	−0.111026	−	1.68102i
$813$	28.1490	+	10.2454i	0.987229	+	0.359322i
$814$	−23.1783	−	25.8423i	−0.812400	−	0.905773i
$815$	−32.1721	−	11.0838i	−1.12694	−	0.388248i
$816$	3.40684	+	2.16560i	0.119263	+	0.0758111i
$817$	0.612346	+	11.4348i	0.0214233	+	0.400055i
$818$	22.5214	+	3.20954i	0.787442	+	0.112219i
$819$	0.108143	−	0.613309i	0.00377882	−	0.0214307i
$820$	−9.32209	−	20.2034i	−0.325541	−	0.705535i
$821$	7.61347	+	2.77108i	0.265712	+	0.0967113i	0.471441	−	0.881898i	$-0.343734\pi$
$821$	7.61347	+	2.77108i	0.265712	+	0.0967113i	−0.205729	+	0.978609i	$0.565956\pi$
$822$	−0.381533	−	1.81217i	−0.0133075	−	0.0632068i
$823$	−12.8774	+	10.8055i	−0.448879	+	0.376654i	−0.839020	−	0.544101i	$-0.816871\pi$
$823$	−12.8774	+	10.8055i	−0.448879	+	0.376654i	0.390140	+	0.920755i	$0.372426\pi$
$824$	−3.15099	−	31.7479i	−0.109770	−	1.10599i
$825$	17.5452	−	15.7871i	0.610846	−	0.549637i
$826$	−27.2848	+	0.900056i	−0.949360	+	0.0313170i
$827$	−17.7356	+	3.12726i	−0.616726	+	0.108745i	−0.473279	−	0.880913i	$-0.656930\pi$
$827$	−17.7356	+	3.12726i	−0.616726	+	0.108745i	−0.143447	+	0.989658i	$0.545819\pi$
$828$	0.186203	−	0.178430i	0.00647101	−	0.00620086i
$829$	21.5482	−	12.4409i	0.748399	−	0.432089i	−0.0767159	−	0.997053i	$-0.524443\pi$
$829$	21.5482	−	12.4409i	0.748399	−	0.432089i	0.825115	+	0.564964i	$0.191110\pi$
$830$	−3.74798	+	1.58165i	−0.130094	+	0.0548999i
$831$	34.1181	−	12.4180i	1.18354	−	0.430774i
$832$	2.00619	+	5.13605i	0.0695523	+	0.178060i
$833$	0.173123	−	0.206320i	0.00599836	−	0.00714857i
$834$	−9.71606	−	3.17770i	−0.336440	−	0.110035i
$835$	−9.33898	−	1.48075i	−0.323189	−	0.0512436i
$836$	22.3897	−	2.68726i	0.774365	−	0.0929409i
$837$		−	47.8817i		−	1.65503i
$838$	−14.8442	+	45.3873i	−0.512783	+	1.56788i
$839$	−9.21482	−	7.73215i	−0.318131	−	0.266943i	0.469712	−	0.882820i	$-0.344358\pi$
$839$	−9.21482	−	7.73215i	−0.318131	−	0.266943i	−0.787843	+	0.615876i	$0.788802\pi$
$840$	−25.3342	+	18.8550i	−0.874114	+	0.650560i
$841$	45.0604	−	16.4007i	1.55381	−	0.565540i
$842$	43.4587	−	27.0394i	1.49769	−	0.931841i
$843$	−19.5359	−	33.8372i	−0.672854	−	1.16542i
$844$	4.22350	−	4.04718i	0.145379	−	0.139310i
$845$	−28.0024	+	0.484092i	−0.963313	+	0.0166533i
$846$	0.934000	−	0.0308103i	0.0321116	−	0.00105928i
$847$	5.89514	−	10.2107i	0.202559	−	0.350843i
$848$	1.69129	−	39.6487i	0.0580790	−	1.36154i
$849$	4.71382	+	5.61772i	0.161778	+	0.192800i
$850$	−3.88816	−	0.417573i	−0.133363	−	0.0143226i
$851$	3.48207	+	1.26737i	0.119364	+	0.0434449i
$852$	−11.7034	+	7.82848i	−0.400953	+	0.268199i
$853$	35.6551	+	6.28695i	1.22081	+	0.215261i	0.746673	−	0.665192i	$-0.231650\pi$
$853$	35.6551	+	6.28695i	1.22081	+	0.215261i	0.474134	+	0.880453i	$0.342761\pi$
$854$	−0.718141	+	5.03921i	−0.0245743	+	0.172438i
$855$	−0.227637	−	3.21050i	−0.00778503	−	0.109797i
$856$	24.7185	+	11.1774i	0.844862	+	0.382037i
$857$	7.03750	−	39.9116i	0.240396	−	1.36336i	−0.590549	−	0.807002i	$-0.701089\pi$
$857$	7.03750	−	39.9116i	0.240396	−	1.36336i	0.830946	−	0.556354i	$-0.187800\pi$
$858$	3.42531	−	3.07221i	0.116938	−	0.104883i
$859$	−8.44644	+	23.2064i	−0.288189	+	0.791793i	0.708131	+	0.706081i	$0.249539\pi$
$859$	−8.44644	+	23.2064i	−0.288189	+	0.791793i	−0.996320	+	0.0857116i	$0.972684\pi$
$860$	1.07112	−	11.6998i	0.0365250	−	0.398959i
$861$	19.0313	−	15.9691i	0.648583	−	0.544226i
$862$	32.2154	−	12.9436i	1.09726	−	0.440859i
$863$	−44.0512	−	25.4330i	−1.49952	−	0.865748i	−0.499520	−	0.866303i	$-0.666490\pi$
$863$	−44.0512	−	25.4330i	−1.49952	−	0.865748i	−1.00000		0.000554480i	$0.999824\pi$
$864$	−14.0101	+	23.7339i	−0.476632	+	0.807445i
$865$	8.18462	−	0.141492i	0.278285	−	0.00481086i
$866$	−5.72779	−	4.49288i	−0.194638	−	0.152674i
$867$	26.3834	−	15.2325i	0.896029	−	0.517322i
$868$	−49.2169	+	21.6854i	−1.67053	+	0.736050i
$869$	−10.9073	−	29.9675i	−0.370005	−	1.01658i
$870$	−40.3652	−	30.5504i	−1.36851	−	1.03576i
$871$	1.38648	−	1.65234i	0.0469790	−	0.0559874i
$872$	−21.1938	+	31.0317i	−0.717711	+	1.05087i
$873$	2.59905			0.0879647
$874$	−1.97291	+	1.37912i	−0.0667346	+	0.0466494i
$875$	13.9022	−	27.2508i	0.469981	−	0.921244i
$876$	−13.3310	+	27.0667i	−0.450412	+	0.914499i
$877$	−43.4600	−	36.4673i	−1.46754	−	1.23141i	−0.918383	−	0.395693i	$-0.870504\pi$
$877$	−43.4600	−	36.4673i	−1.46754	−	1.23141i	−0.549157	−	0.835719i	$-0.685051\pi$
$878$	8.17672	−	15.3068i	0.275951	−	0.516579i
$879$	−15.0705	−	41.4060i	−0.508316	−	1.39659i
$880$	−23.1288	−	0.586330i	−0.779672	−	0.0197652i
$881$	−22.9221	−	39.7023i	−0.772267	−	1.33761i	−0.936318	−	0.351153i	$-0.885790\pi$
$881$	−22.9221	−	39.7023i	−0.772267	−	1.33761i	0.164051	−	0.986452i	$-0.447544\pi$
$882$	−0.178949	−	0.140367i	−0.00602551	−	0.00472642i
$883$	4.60416	+	26.1115i	0.154942	+	0.878721i	0.958839	+	0.283952i	$0.0916455\pi$
$883$	4.60416	+	26.1115i	0.154942	+	0.878721i	−0.803896	+	0.594769i	$0.797243\pi$
$884$	−0.757858	−	0.0826147i	−0.0254895	−	0.00277863i
$885$	−18.1205	+	22.3693i	−0.609115	+	0.751937i
$886$	34.4640	−	13.8470i	1.15784	−	0.465200i
$887$	6.63716	+	7.90985i	0.222854	+	0.265587i	0.865874	−	0.500263i	$-0.166763\pi$
$887$	6.63716	+	7.90985i	0.222854	+	0.265587i	−0.643020	+	0.765849i	$0.722319\pi$
$888$	48.8406	+	3.69971i	1.63898	+	0.124154i
$889$	−19.1660	+	52.6581i	−0.642807	+	1.76610i
$890$	30.1517	−	19.4909i	1.01069	−	0.653336i
$891$	25.1725	+	4.43859i	0.843311	+	0.148699i
$892$	1.14760	−	3.94458i	0.0384244	−	0.132074i
$893$	−8.65878	−	1.05315i	−0.289755	−	0.0352422i
$894$	36.0017	+	5.13062i	1.20408	+	0.171594i
$895$	−42.7413	−	14.7250i	−1.42868	−	0.492203i
$896$	30.7409	+	3.65176i	1.02698	+	0.121997i
$897$	−0.167986	+	0.461537i	−0.00560887	+	0.0154103i
$898$	33.4156	−	7.03528i	1.11509	−	0.234770i
$899$	−55.4160	−	66.0422i	−1.84823	−	2.20263i
$900$	−0.244172	+	3.29313i	−0.00813906	+	0.109771i
$901$	4.75164	+	2.74336i	0.158300	+	0.0913947i
$902$	18.1907	−	0.600065i	0.605684	−	0.0199800i
$903$	12.9187	−	2.27791i	0.429906	−	0.0758040i
$904$	−27.6489	−	38.5228i	−0.919590	−	1.28125i
$905$	17.2122	+	44.8619i	0.572154	+	1.49126i
$906$	33.0142	−	20.5410i	1.09682	−	0.682429i
$907$	−17.0157	−	46.7503i	−0.564998	−	1.55232i	−0.812215	−	0.583359i	$-0.801738\pi$
$907$	−17.0157	−	46.7503i	−0.564998	−	1.55232i	0.247217	−	0.968960i	$-0.420484\pi$
$908$	14.1886	−	19.3712i	0.470867	−	0.642857i
$909$	−1.88352	−	1.58046i	−0.0624725	−	0.0524206i
$910$	2.71869	−	5.30815i	0.0901236	−	0.175964i
$911$	3.84133			0.127269			0.0636344	−	0.997973i	$-0.479731\pi$
$911$	3.84133			0.127269			0.0636344	+	0.997973i	$0.479731\pi$
$912$	−20.1861	+	24.5949i	−0.668429	+	0.814417i
$913$		−	3.32762i		−	0.110128i
$914$	10.8581	−	33.1994i	0.359152	−	1.09814i
$915$	3.52078	+	4.05157i	0.116394	+	0.133941i
$916$	23.1527	+	16.9584i	0.764986	+	0.560322i
$917$	0.173254	+	0.476013i	0.00572137	+	0.0157193i
$918$	−2.01299	−	3.23534i	−0.0664385	−	0.106782i
$919$	33.9448	−	19.5980i	1.11974	−	0.646480i	0.178402	−	0.983958i	$-0.442907\pi$
$919$	33.9448	−	19.5980i	1.11974	−	0.646480i	0.941333	+	0.337478i	$0.109574\pi$
$920$	2.20714	−	1.10807i	0.0727673	−	0.0365321i
$921$	−2.00738	−	11.3844i	−0.0661454	−	0.375129i
$922$	−27.1350	+	0.895114i	−0.893644	+	0.0294790i
$923$	1.32951	−	2.30277i	0.0437613	−	0.0757967i
$924$	−6.15262	−	25.0892i	−0.202406	−	0.825375i
$925$	−43.9984	+	17.7593i	−1.44666	+	0.583924i
$926$	7.32179	+	34.7764i	0.240609	+	1.14282i
$927$	1.27394	−	3.50012i	0.0418417	−	0.114959i
$928$	8.14475	+	48.9504i	0.267364	+	1.60687i
$929$	−5.98718	+	33.9550i	−0.196433	+	1.11403i	0.713931	+	0.700217i	$0.246913\pi$
$929$	−5.98718	+	33.9550i	−0.196433	+	1.11403i	−0.910363	+	0.413810i	$0.864198\pi$
$930$	−16.6955	+	54.2013i	−0.547466	+	1.77733i
$931$	1.44954	+	1.55089i	0.0475066	+	0.0508283i
$932$	−5.41510	+	18.6131i	−0.177378	+	0.609692i
$933$	−9.12289	+	51.7385i	−0.298670	+	1.69384i
$934$	−1.00110	+	0.897898i	−0.0327569	+	0.0293801i
$935$	1.55126	−	2.79744i	0.0507316	−	0.0914861i
$936$	−0.0486254	+	0.641912i	−0.00158937	+	0.0209816i
$937$	−21.2716	−	25.3505i	−0.694911	−	0.828163i	0.297029	−	0.954868i	$-0.404004\pi$
$937$	−21.2716	−	25.3505i	−0.694911	−	0.828163i	−0.991940	+	0.126705i	$0.959560\pi$
$938$	−4.51476	−	11.2368i	−0.147412	−	0.366896i
$939$	−28.9455	+	50.1351i	−0.944601	+	1.63610i
$940$	8.63485	+	2.35103i	0.281638	+	0.0766823i
$941$	38.2758	−	6.74905i	1.24775	−	0.220013i	0.489519	−	0.871993i	$-0.337172\pi$
$941$	38.2758	−	6.74905i	1.24775	−	0.220013i	0.758236	+	0.651980i	$0.226061\pi$
$942$	38.7617	+	30.4047i	1.26292	+	0.990638i
$943$	−1.68253	+	0.971411i	−0.0547908	+	0.0316335i
$944$	27.9743	−	3.71141i	0.910485	−	0.120796i
$945$	29.2626	−	5.68298i	0.951911	−	0.184867i
$946$	8.47668	+	4.52815i	0.275601	+	0.147223i
$947$	−12.4334	−	10.4329i	−0.404033	−	0.339024i	0.418017	−	0.908439i	$-0.362725\pi$
$947$	−12.4334	−	10.4329i	−0.404033	−	0.339024i	−0.822050	+	0.569415i	$0.807170\pi$
$948$	40.3666	+	19.8815i	1.31105	+	0.645720i
$949$		−	5.69777i		−	0.184957i
$950$	6.96728	−	30.0243i	0.226048	−	0.974116i
$951$			53.0980i			1.72182i
$952$	−2.41389	+	3.53440i	−0.0782346	+	0.114550i
$953$	13.2500	+	11.1181i	0.429210	+	0.360150i	0.831654	−	0.555295i	$-0.187395\pi$
$953$	13.2500	+	11.1181i	0.429210	+	0.360150i	−0.402443	+	0.915445i	$0.631839\pi$
$954$	2.18304	−	4.08664i	0.0706784	−	0.132310i
$955$	−13.6500	+	2.65091i	−0.441702	+	0.0857814i
$956$	6.65362	+	15.1010i	0.215193	+	0.488400i
$957$	35.8612	−	20.7045i	1.15923	−	0.669282i
$958$	−22.8546	+	29.1364i	−0.738399	+	0.941355i
$959$	1.93363	−	0.340950i	0.0624400	−	0.0110099i
$960$	24.1348	−	21.9814i	0.778947	−	0.709447i
$961$	−32.7930	+	56.7991i	−1.05784	+	1.83223i
$962$	−8.58291	+	3.44846i	−0.276724	+	0.111183i
$963$	2.03584	+	2.42622i	0.0656040	+	0.0781837i
$964$	−1.87883	−	28.4470i	−0.0605131	−	0.916215i
$965$	14.8799	−	26.8335i	0.479001	−	0.863800i
$966$	1.84117	+	2.05278i	0.0592386	+	0.0660472i
$967$	0.493186	−	2.79699i	0.0158598	−	0.0899453i	−0.975850	−	0.218440i	$-0.929903\pi$
$967$	0.493186	−	2.79699i	0.0158598	−	0.0899453i	0.991710	+	0.128494i	$0.0410144\pi$
$968$	−5.02152	+	11.1049i	−0.161398	+	0.356926i
$969$	−1.72347	−	4.04742i	−0.0553660	−	0.130022i
$970$	23.7866	+	7.32692i	0.763742	+	0.235253i
$971$	−2.47794	+	14.0531i	−0.0795208	+	0.450985i	0.918884	+	0.394527i	$0.129092\pi$
$971$	−2.47794	+	14.0531i	−0.0795208	+	0.450985i	−0.998405	+	0.0564574i	$0.982019\pi$
$972$	−5.67980	+	3.79924i	−0.182180	+	0.121861i
$973$	3.70691	−	10.1846i	0.118838	−	0.326505i
$974$	10.8731	−	2.28921i	0.348396	−	0.0733509i
$975$	−2.35394	−	5.83183i	−0.0753864	−	0.186768i
$976$	0.224240	−	5.25683i	0.00717774	−	0.168267i
$977$	26.4111	−	45.7454i	0.844966	−	1.46352i	−0.0406851	−	0.999172i	$-0.512954\pi$
$977$	26.4111	−	45.7454i	0.844966	−	1.46352i	0.885651	−	0.464352i	$-0.153713\pi$
$978$	1.29483	+	39.2523i	0.0414042	+	1.25515i
$979$	5.09973	+	28.9220i	0.162988	+	0.924352i
$980$	−1.24204	−	1.78911i	−0.0396754	−	0.0571512i
$981$	−3.79948	+	2.19363i	−0.121308	+	0.0700373i
$982$	11.4323	−	7.11305i	0.364820	−	0.226987i
$983$	−6.10489	−	16.7730i	−0.194716	−	0.534977i	0.803460	−	0.595359i	$-0.202990\pi$
$983$	−6.10489	−	16.7730i	−0.194716	−	0.534977i	−0.998175	+	0.0603823i	$0.980768\pi$
$984$	−17.9459	+	18.3694i	−0.572095	+	0.585594i
$985$	20.0716	+	23.0975i	0.639534	+	0.735949i
$986$	−6.52091	−	2.13270i	−0.207668	−	0.0679191i
$987$			9.99215i			0.318054i
$988$	1.36760	−	5.85100i	0.0435091	−	0.186145i
$989$	−1.02585			−0.0326203
$990$	−2.40415	−	1.23134i	−0.0764090	−	0.0391346i
$991$	13.6667	+	11.4677i	0.434137	+	0.364285i	0.833510	−	0.552504i	$-0.186328\pi$
$991$	13.6667	+	11.4677i	0.434137	+	0.364285i	−0.399373	+	0.916789i	$0.630772\pi$
$992$	48.4124	−	27.3311i	1.53710	−	0.867763i
$993$	−11.7567	−	32.3014i	−0.373089	−	1.02505i
$994$	−7.88643	−	12.6753i	−0.250142	−	0.402037i
$995$	−8.51008	−	22.1806i	−0.269788	−	0.703173i
$996$	3.24848	+	3.39000i	0.102932	+	0.107416i
$997$	−31.9997	+	5.64242i	−1.01344	+	0.178697i	−0.655619	−	0.755092i	$-0.727592\pi$
$997$	−31.9997	+	5.64242i	−1.01344	+	0.178697i	−0.357823	+	0.933789i	$0.616481\pi$
$998$	0.535129	+	16.2222i	0.0169392	+	0.513504i
$999$	−40.0391	−	23.1166i	−1.26678	−	0.731377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bb.a.59.5	yes	336
4.3	odd	2	inner	380.2.bb.a.59.56	yes	336
5.4	even	2	inner	380.2.bb.a.59.52	yes	336
19.10	odd	18	inner	380.2.bb.a.219.1	yes	336
20.19	odd	2	inner	380.2.bb.a.59.1	✓	336
76.67	even	18	inner	380.2.bb.a.219.52	yes	336
95.29	odd	18	inner	380.2.bb.a.219.56	yes	336
380.219	even	18	inner	380.2.bb.a.219.5	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bb.a.59.1	✓	336	20.19	odd	2	inner
380.2.bb.a.59.5	yes	336	1.1	even	1	trivial
380.2.bb.a.59.52	yes	336	5.4	even	2	inner
380.2.bb.a.59.56	yes	336	4.3	odd	2	inner
380.2.bb.a.219.1	yes	336	19.10	odd	18	inner
380.2.bb.a.219.5	yes	336	380.219	even	18	inner
380.2.bb.a.219.52	yes	336	76.67	even	18	inner
380.2.bb.a.219.56	yes	336	95.29	odd	18	inner

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34415 - 0.439613i) q^{2} +(-1.17302 + 1.39795i) q^{3} +(1.61348 + 1.18181i) q^{4} +(0.426294 + 2.19506i) q^{5} +(2.19126 - 1.36338i) q^{6} +(1.36812 + 2.36965i) q^{7} +(-1.64922 - 2.29784i) q^{8} +(-0.0573416 - 0.325200i) q^{9} +O(q^{10})\)	\(q+(-1.34415 - 0.439613i) q^{2} +(-1.17302 + 1.39795i) q^{3} +(1.61348 + 1.18181i) q^{4} +(0.426294 + 2.19506i) q^{5} +(2.19126 - 1.36338i) q^{6} +(1.36812 + 2.36965i) q^{7} +(-1.64922 - 2.29784i) q^{8} +(-0.0573416 - 0.325200i) q^{9} +(0.391971 - 3.13789i) q^{10} +(2.24016 + 1.29335i) q^{11} +(-3.54475 + 0.869277i) q^{12} +(0.527993 - 0.443038i) q^{13} +(-0.797230 - 3.78661i) q^{14} +(-3.56862 - 1.97890i) q^{15} +(1.20665 + 3.81366i) q^{16} +(-0.544629 - 0.0960328i) q^{17} +(-0.0658864 + 0.462326i) q^{18} +(1.26967 - 4.16989i) q^{19} +(-1.90632 + 4.04548i) q^{20} +(-4.91747 - 0.867083i) q^{21} +(-2.44253 - 2.72326i) q^{22} +(0.366941 + 0.133555i) q^{23} +(5.14682 + 0.389876i) q^{24} +(-4.63655 + 1.87148i) q^{25} +(-0.904467 + 0.363398i) q^{26} +(-4.21932 - 2.43603i) q^{27} +(-0.593046 + 5.44025i) q^{28} +(-8.63898 + 1.52328i) q^{29} +(3.92681 + 4.22875i) q^{30} +(4.91391 + 8.51114i) q^{31} +(0.0546187 - 5.65659i) q^{32} +(-4.43578 + 1.61449i) q^{33} +(0.689846 + 0.368508i) q^{34} +(-4.61830 + 4.01327i) q^{35} +(0.291806 - 0.592472i) q^{36} +9.48947 q^{37} +(-3.53976 + 5.04679i) q^{38} +1.25780i q^{39} +(4.34083 - 4.59969i) q^{40} +(-3.19809 + 3.81133i) q^{41} +(6.22864 + 3.32727i) q^{42} +(-2.46866 + 0.898519i) q^{43} +(2.08595 + 4.73425i) q^{44} +(0.689389 - 0.264499i) q^{45} +(-0.434511 - 0.340830i) q^{46} +(-0.347487 - 1.97070i) q^{47} +(-6.74670 - 2.78666i) q^{48} +(-0.243505 + 0.421764i) q^{49} +(7.05494 - 0.477266i) q^{50} +(0.773107 - 0.648714i) q^{51} +(1.37549 - 0.0908469i) q^{52} +(-9.32287 - 3.39325i) q^{53} +(4.60050 + 5.12926i) q^{54} +(-1.88402 + 5.46862i) q^{55} +(3.18875 - 7.05181i) q^{56} +(4.33993 + 6.66626i) q^{57} +(12.2817 + 1.75028i) q^{58} +(1.22506 - 6.94767i) q^{59} +(-3.41922 - 7.41035i) q^{60} +(-1.23607 - 0.449894i) q^{61} +(-2.86343 - 13.6005i) q^{62} +(0.692162 - 0.580793i) q^{63} +(-2.56012 + 7.57930i) q^{64} +(1.19757 + 0.970109i) q^{65} +(6.67210 - 0.220096i) q^{66} +(3.08193 - 0.543427i) q^{67} +(-0.765256 - 0.798596i) q^{68} +(-0.617130 + 0.356300i) q^{69} +(7.97198 - 3.36418i) q^{70} +(3.62520 - 1.31947i) q^{71} +(-0.652689 + 0.668090i) q^{72} +(5.31372 - 6.33264i) q^{73} +(-12.7553 - 4.17169i) q^{74} +(2.82251 - 8.67691i) q^{75} +(6.97660 - 5.22753i) q^{76} +7.07786i q^{77} +(0.552943 - 1.69067i) q^{78} +(-9.44434 - 7.92474i) q^{79} +(-7.85681 + 4.27440i) q^{80} +(9.28567 - 3.37971i) q^{81} +(5.97422 - 3.71709i) q^{82} +(-0.643215 - 1.11408i) q^{83} +(-6.90952 - 7.21055i) q^{84} +(-0.0213748 - 1.23643i) q^{85} +(3.71325 - 0.122491i) q^{86} +(8.00419 - 13.8637i) q^{87} +(-0.722598 - 7.28055i) q^{88} +(7.29789 + 8.69728i) q^{89} +(-1.04292 + 0.0524626i) q^{90} +(1.77221 + 0.645030i) q^{91} +(0.434215 + 0.649144i) q^{92} +(-17.6622 - 3.11432i) q^{93} +(-0.399268 + 2.80167i) q^{94} +(9.69439 + 1.00939i) q^{95} +(7.84354 + 6.71162i) q^{96} +(-1.36674 + 7.75117i) q^{97} +(0.512720 - 0.459866i) q^{98} +(0.292145 - 0.802662i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9}+O(q^{10}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9	\( 336 q - 18 q^{4} - 12 q^{5} - 18 q^{6} - 24 q^{9} - 15 q^{10} + 18 q^{14} - 6 q^{16} - 42 q^{20} + 12 q^{21} + 12 q^{24} - 12 q^{25} + 18 q^{26} - 24 q^{29} - 24 q^{30} + 12 q^{34} - 6 q^{36} - 48 q^{40} - 12 q^{41} - 36 q^{44} - 6 q^{45} - 18 q^{46} - 108 q^{49} - 36 q^{50} + 36 q^{54} - 30 q^{60} - 24 q^{61} + 18 q^{64} - 18 q^{65} - 48 q^{66} - 180 q^{69} - 21 q^{70} - 30 q^{74} - 48 q^{76} + 3 q^{80} - 60 q^{81} + 90 q^{84} - 36 q^{85} + 102 q^{86} - 48 q^{89} - 78 q^{90} + 24 q^{96}+O(q^{100}) \) 336 * q - 18 * q^4 - 12 * q^5 - 18 * q^6 - 24 * q^9 - 15 * q^10 + 18 * q^14 - 6 * q^16 - 42 * q^20 + 12 * q^21 + 12 * q^24 - 12 * q^25 + 18 * q^26 - 24 * q^29 - 24 * q^30 + 12 * q^34 - 6 * q^36 - 48 * q^40 - 12 * q^41 - 36 * q^44 - 6 * q^45 - 18 * q^46 - 108 * q^49 - 36 * q^50 + 36 * q^54 - 30 * q^60 - 24 * q^61 + 18 * q^64 - 18 * q^65 - 48 * q^66 - 180 * q^69 - 21 * q^70 - 30 * q^74 - 48 * q^76 + 3 * q^80 - 60 * q^81 + 90 * q^84 - 36 * q^85 + 102 * q^86 - 48 * q^89 - 78 * q^90 + 24 * q^96

Introduction

L-functions

Modular forms

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Representations

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Database

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