LMFDB - Embedded newform 600.2.bq.a.403.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(67,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 10, 0, 13]))

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

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

chi := DirichletCharacter("600.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bq (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$60$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			403.32
Character	$\chi$	$=$	600.403
Dual form			600.2.bq.a.67.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.137625 - 1.40750i) q^{2} +(-0.156434 - 0.987688i) q^{3} +(-1.96212 - 0.387414i) q^{4} +(-1.86666 + 1.23110i) q^{5} +(-1.41170 + 0.0842514i) q^{6} +(2.13082 + 2.13082i) q^{7} +(-0.815321 + 2.70837i) q^{8} +(-0.951057 + 0.309017i) q^{9} +O(q^{10})$	\(q+(0.137625 - 1.40750i) q^{2} +(-0.156434 - 0.987688i) q^{3} +(-1.96212 - 0.387414i) q^{4} +(-1.86666 + 1.23110i) q^{5} +(-1.41170 + 0.0842514i) q^{6} +(2.13082 + 2.13082i) q^{7} +(-0.815321 + 2.70837i) q^{8} +(-0.951057 + 0.309017i) q^{9} +(1.47587 + 2.79675i) q^{10} +(-0.0873587 + 0.268863i) q^{11} +(-0.0757011 + 1.99857i) q^{12} +(2.99402 + 1.52553i) q^{13} +(3.29239 - 2.70588i) q^{14} +(1.50795 + 1.65109i) q^{15} +(3.69982 + 1.52030i) q^{16} +(-0.216929 + 1.36963i) q^{17} +(0.304053 + 1.38114i) q^{18} +(-0.0549118 - 0.0755796i) q^{19} +(4.13954 - 1.69239i) q^{20} +(1.77125 - 2.43792i) q^{21} +(0.366402 + 0.159960i) q^{22} +(1.84517 + 3.62135i) q^{23} +(2.80257 + 0.381601i) q^{24} +(1.96881 - 4.59606i) q^{25} +(2.55923 - 4.00413i) q^{26} +(0.453990 + 0.891007i) q^{27} +(-3.35542 - 5.00644i) q^{28} +(-2.28992 - 1.66373i) q^{29} +(2.53144 - 1.89521i) q^{30} +(5.56242 + 7.65602i) q^{31} +(2.64902 - 4.99827i) q^{32} +(0.279218 + 0.0442238i) q^{33} +(1.89790 + 0.493822i) q^{34} +(-6.60076 - 1.35427i) q^{35} +(1.98580 - 0.237876i) q^{36} +(0.630361 - 1.23715i) q^{37} +(-0.113936 + 0.0668868i) q^{38} +(1.03838 - 3.19580i) q^{39} +(-1.81233 - 6.05933i) q^{40} +(2.92379 + 8.99849i) q^{41} +(-3.18761 - 2.82856i) q^{42} +(-5.49497 - 5.49497i) q^{43} +(0.275569 - 0.493696i) q^{44} +(1.39487 - 1.74767i) q^{45} +(5.35099 - 2.09869i) q^{46} +(-0.289550 - 1.82814i) q^{47} +(0.922807 - 3.89210i) q^{48} +2.08080i q^{49} +(-6.19801 - 3.40363i) q^{50} +1.38671 q^{51} +(-5.28361 - 4.15319i) q^{52} +(0.674962 - 0.106904i) q^{53} +(1.31657 - 0.516368i) q^{54} +(-0.167927 - 0.609421i) q^{55} +(-7.50835 + 4.03374i) q^{56} +(-0.0660590 + 0.0660590i) q^{57} +(-2.65685 + 2.99410i) q^{58} +(-2.89245 + 0.939813i) q^{59} +(-2.31912 - 3.82383i) q^{60} +(11.1166 + 3.61199i) q^{61} +(11.5414 - 6.77546i) q^{62} +(-2.68499 - 1.36807i) q^{63} +(-6.67050 - 4.41638i) q^{64} +(-7.46687 + 0.838285i) q^{65} +(0.100672 - 0.386914i) q^{66} +(-2.31795 + 14.6350i) q^{67} +(0.956254 - 2.60334i) q^{68} +(3.28811 - 2.38895i) q^{69} +(-2.81456 + 9.10419i) q^{70} +(-5.56713 + 7.66249i) q^{71} +(-0.0615147 - 2.82776i) q^{72} +(7.54080 - 3.84223i) q^{73} +(-1.65454 - 1.05750i) q^{74} +(-4.84747 - 1.22559i) q^{75} +(0.0784629 + 0.169570i) q^{76} +(-0.759044 + 0.386752i) q^{77} +(-4.35519 - 1.90134i) q^{78} +(2.61351 + 1.89883i) q^{79} +(-8.77793 + 1.71695i) q^{80} +(0.809017 - 0.587785i) q^{81} +(13.0678 - 2.87682i) q^{82} +(-16.3194 - 2.58475i) q^{83} +(-4.41989 + 4.09728i) q^{84} +(-1.28122 - 2.82369i) q^{85} +(-8.49042 + 6.97793i) q^{86} +(-1.28502 + 2.52199i) q^{87} +(-0.656953 - 0.455809i) q^{88} +(5.80221 + 1.88525i) q^{89} +(-2.26788 - 2.20380i) q^{90} +(3.12909 + 9.63034i) q^{91} +(-2.21748 - 7.82036i) q^{92} +(6.69161 - 6.69161i) q^{93} +(-2.61296 + 0.155944i) q^{94} +(0.195547 + 0.0734795i) q^{95} +(-5.35113 - 1.83450i) q^{96} +(4.23446 - 0.670672i) q^{97} +(2.92873 + 0.286370i) q^{98} -0.282699i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 12 q^{8}+O(q^{10}) $ 480 * q + 12 * q^8	$ 480 q + 12 q^{8} - 8 q^{10} + 8 q^{12} - 8 q^{17} + 20 q^{20} + 28 q^{22} + 8 q^{25} - 4 q^{28} - 8 q^{30} - 20 q^{32} + 48 q^{35} + 20 q^{38} - 108 q^{40} - 20 q^{42} + 32 q^{43} - 140 q^{44} - 16 q^{48} + 124 q^{50} - 132 q^{52} + 152 q^{58} - 20 q^{60} + 116 q^{62} - 60 q^{64} + 8 q^{65} - 48 q^{67} - 72 q^{68} - 4 q^{70} - 12 q^{72} + 40 q^{73} + 24 q^{78} - 76 q^{80} + 120 q^{81} - 64 q^{82} - 80 q^{83} - 80 q^{84} - 132 q^{88} + 200 q^{89} - 48 q^{90} - 216 q^{92} - 40 q^{94} + 20 q^{96} - 56 q^{97} - 192 q^{98}+O(q^{100}) $ 480 * q + 12 * q^8 - 8 * q^10 + 8 * q^12 - 8 * q^17 + 20 * q^20 + 28 * q^22 + 8 * q^25 - 4 * q^28 - 8 * q^30 - 20 * q^32 + 48 * q^35 + 20 * q^38 - 108 * q^40 - 20 * q^42 + 32 * q^43 - 140 * q^44 - 16 * q^48 + 124 * q^50 - 132 * q^52 + 152 * q^58 - 20 * q^60 + 116 * q^62 - 60 * q^64 + 8 * q^65 - 48 * q^67 - 72 * q^68 - 4 * q^70 - 12 * q^72 + 40 * q^73 + 24 * q^78 - 76 * q^80 + 120 * q^81 - 64 * q^82 - 80 * q^83 - 80 * q^84 - 132 * q^88 + 200 * q^89 - 48 * q^90 - 216 * q^92 - 40 * q^94 + 20 * q^96 - 56 * q^97 - 192 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	0.137625	−	1.40750i	0.0973153	−	0.995254i
$2$	0.137625	−	1.40750i	0.0973153	−	0.995254i
$3$	−0.156434	−	0.987688i	−0.0903175	−	0.570242i
$3$	−0.156434	−	0.987688i	−0.0903175	−	0.570242i
$4$	−1.96212	−	0.387414i	−0.981059	−	0.193707i
$5$	−1.86666	+	1.23110i	−0.834794	+	0.550563i
$5$	−1.86666	+	1.23110i	−0.834794	+	0.550563i
$6$	−1.41170	+	0.0842514i	−0.576325	+	0.0343955i
$7$	2.13082	+	2.13082i	0.805375	+	0.805375i	0.983930	−	0.178555i	$-0.0571423\pi$
$7$	2.13082	+	2.13082i	0.805375	+	0.805375i	−0.178555	+	0.983930i	$0.557142\pi$
$8$	−0.815321	+	2.70837i	−0.288260	+	0.957552i
$9$	−0.951057	+	0.309017i	−0.317019	+	0.103006i
$10$	1.47587	+	2.79675i	0.466711	+	0.884410i
$11$	−0.0873587	+	0.268863i	−0.0263397	+	0.0810651i	−0.963362	−	0.268204i	$-0.913570\pi$
$11$	−0.0873587	+	0.268863i	−0.0263397	+	0.0810651i	0.937023	+	0.349269i	$0.113570\pi$
$12$	−0.0757011	+	1.99857i	−0.0218530	+	0.576937i
$13$	2.99402	+	1.52553i	0.830391	+	0.423105i	0.816883	−	0.576803i	$-0.195700\pi$
$13$	2.99402	+	1.52553i	0.830391	+	0.423105i	0.0135080	+	0.999909i	$0.495700\pi$
$14$	3.29239	−	2.70588i	0.879928	−	0.723177i
$15$	1.50795	+	1.65109i	0.389350	+	0.426309i
$16$	3.69982	+	1.52030i	0.924955	+	0.380076i
$17$	−0.216929	+	1.36963i	−0.0526129	+	0.332185i	0.947316	+	0.320299i	$0.103783\pi$
$17$	−0.216929	+	1.36963i	−0.0526129	+	0.332185i	−0.999929	+	0.0118856i	$0.996217\pi$
$18$	0.304053	+	1.38114i	0.0716660	+	0.325538i
$19$	−0.0549118	−	0.0755796i	−0.0125976	−	0.0173392i	0.802672	−	0.596421i	$-0.203411\pi$
$19$	−0.0549118	−	0.0755796i	−0.0125976	−	0.0173392i	−0.815269	+	0.579082i	$0.803411\pi$
$20$	4.13954	−	1.69239i	0.925630	−	0.378429i
$21$	1.77125	−	2.43792i	0.386519	−	0.531998i
$22$	0.366402	+	0.159960i	0.0781171	+	0.0341035i
$23$	1.84517	+	3.62135i	0.384744	+	0.755103i	0.999433	−	0.0336667i	$-0.0107185\pi$
$23$	1.84517	+	3.62135i	0.384744	+	0.755103i	−0.614689	+	0.788770i	$0.710718\pi$
$24$	2.80257	+	0.381601i	0.572072	+	0.0778941i
$25$	1.96881	−	4.59606i	0.393762	−	0.919213i
$26$	2.55923	−	4.00413i	0.501907	−	0.785275i
$27$	0.453990	+	0.891007i	0.0873705	+	0.171474i
$28$	−3.35542	−	5.00644i	−0.634114	−	0.946127i
$29$	−2.28992	−	1.66373i	−0.425228	−	0.308946i	0.354510	−	0.935052i	$-0.384648\pi$
$29$	−2.28992	−	1.66373i	−0.425228	−	0.308946i	−0.779738	+	0.626106i	$0.784648\pi$
$30$	2.53144	−	1.89521i	0.462176	−	0.346016i
$31$	5.56242	+	7.65602i	0.999041	+	1.37506i	0.925912	+	0.377739i	$0.123298\pi$
$31$	5.56242	+	7.65602i	0.999041	+	1.37506i	0.0731285	+	0.997323i	$0.476702\pi$
$32$	2.64902	−	4.99827i	0.468284	−	0.883578i
$33$	0.279218	+	0.0442238i	0.0486057	+	0.00769838i
$34$	1.89790	+	0.493822i	0.325488	+	0.0846898i
$35$	−6.60076	−	1.35427i	−1.11573	−	0.228913i
$36$	1.98580	−	0.237876i	0.330967	−	0.0396459i
$37$	0.630361	−	1.23715i	0.103631	−	0.203387i	−0.833369	−	0.552717i	$-0.813591\pi$
$37$	0.630361	−	1.23715i	0.103631	−	0.203387i	0.937000	+	0.349331i	$0.113591\pi$
$38$	−0.113936	+	0.0668868i	−0.0184828	+	0.0108505i
$39$	1.03838	−	3.19580i	0.166274	−	0.511738i
$40$	−1.81233	−	6.05933i	−0.286555	−	0.958064i
$41$	2.92379	+	8.99849i	0.456619	+	1.40533i	0.869224	+	0.494418i	$0.164619\pi$
$41$	2.92379	+	8.99849i	0.456619	+	1.40533i	−0.412605	+	0.910910i	$0.635381\pi$
$42$	−3.18761	−	2.82856i	−0.491859	−	0.436456i
$43$	−5.49497	−	5.49497i	−0.837975	−	0.837975i	0.150617	−	0.988592i	$-0.451874\pi$
$43$	−5.49497	−	5.49497i	−0.837975	−	0.837975i	−0.988592	+	0.150617i	$0.951874\pi$
$44$	0.275569	−	0.493696i	0.0415436	−	0.0744275i
$45$	1.39487	−	1.74767i	0.207934	−	0.260527i
$46$	5.35099	−	2.09869i	0.788960	−	0.309435i
$47$	−0.289550	−	1.82814i	−0.0422352	−	0.266662i	0.957530	−	0.288334i	$-0.0931012\pi$
$47$	−0.289550	−	1.82814i	−0.0422352	−	0.266662i	−0.999765	+	0.0216714i	$0.993101\pi$
$48$	0.922807	−	3.89210i	0.133196	−	0.561776i
$49$			2.08080i			0.297257i
$50$	−6.19801	−	3.40363i	−0.876531	−	0.481346i
$51$	1.38671			0.194178
$52$	−5.28361	−	4.15319i	−0.732704	−	0.575944i
$53$	0.674962	−	0.106904i	0.0927132	−	0.0146843i	−0.109905	−	0.993942i	$-0.535055\pi$
$53$	0.674962	−	0.106904i	0.0927132	−	0.0146843i	0.202619	+	0.979258i	$0.435055\pi$
$54$	1.31657	−	0.516368i	0.179163	−	0.0702687i
$55$	−0.167927	−	0.609421i	−0.0226432	−	0.0821743i
$56$	−7.50835	+	4.03374i	−1.00335	+	0.539032i
$57$	−0.0660590	+	0.0660590i	−0.00874973	+	0.00874973i
$58$	−2.65685	+	2.99410i	−0.348861	+	0.393144i
$59$	−2.89245	+	0.939813i	−0.376565	+	0.122353i	−0.491183	−	0.871056i	$-0.663435\pi$
$59$	−2.89245	+	0.939813i	−0.376565	+	0.122353i	0.114619	+	0.993410i	$0.463435\pi$
$60$	−2.31912	−	3.82383i	−0.299397	−	0.493655i
$61$	11.1166	+	3.61199i	1.42333	+	0.462468i	0.916658	−	0.399672i	$-0.130876\pi$
$61$	11.1166	+	3.61199i	1.42333	+	0.462468i	0.506671	+	0.862139i	$0.330876\pi$
$62$	11.5414	−	6.77546i	1.46576	−	0.860484i
$63$	−2.68499	−	1.36807i	−0.338277	−	0.172361i
$64$	−6.67050	−	4.41638i	−0.833813	−	0.552047i
$65$	−7.46687	+	0.838285i	−0.926151	+	0.103976i
$66$	0.100672	−	0.386914i	0.0123919	−	0.0476258i
$67$	−2.31795	+	14.6350i	−0.283183	+	1.78795i	0.278336	+	0.960484i	$0.410217\pi$
$67$	−2.31795	+	14.6350i	−0.283183	+	1.78795i	−0.561519	+	0.827464i	$0.689783\pi$
$68$	0.956254	−	2.60334i	0.115963	−	0.315701i
$69$	3.28811	−	2.38895i	0.395842	−	0.287596i
$70$	−2.81456	+	9.10419i	−0.336404	+	1.08816i
$71$	−5.56713	+	7.66249i	−0.660697	+	0.909371i	−0.999504	−	0.0314849i	$-0.989976\pi$
$71$	−5.56713	+	7.66249i	−0.660697	+	0.909371i	0.338808	+	0.940856i	$0.389976\pi$
$72$	−0.0615147	−	2.82776i	−0.00724958	−	0.333254i
$73$	7.54080	−	3.84223i	0.882584	−	0.449699i	0.0468933	−	0.998900i	$-0.485068\pi$
$73$	7.54080	−	3.84223i	0.882584	−	0.449699i	0.835690	+	0.549201i	$0.185068\pi$
$74$	−1.65454	−	1.05750i	−0.192336	−	0.122931i
$75$	−4.84747	−	1.22559i	−0.559737	−	0.141519i
$76$	0.0784629	+	0.169570i	0.00900032	+	0.0194510i
$77$	−0.759044	+	0.386752i	−0.0865011	+	0.0440745i
$78$	−4.35519	−	1.90134i	−0.493128	−	0.215284i
$79$	2.61351	+	1.89883i	0.294043	+	0.213635i	0.725019	−	0.688728i	$-0.241831\pi$
$79$	2.61351	+	1.89883i	0.294043	+	0.213635i	−0.430976	+	0.902363i	$0.641831\pi$
$80$	−8.77793	+	1.71695i	−0.981403	+	0.191961i
$81$	0.809017	−	0.587785i	0.0898908	−	0.0653095i
$82$	13.0678	−	2.87682i	1.44309	−	0.317691i
$83$	−16.3194	−	2.58475i	−1.79129	−	0.283713i	−0.829703	−	0.558205i	$-0.811490\pi$
$83$	−16.3194	−	2.58475i	−1.79129	−	0.283713i	−0.961589	+	0.274492i	$0.911490\pi$
$84$	−4.41989	+	4.09728i	−0.482250	+	0.447050i
$85$	−1.28122	−	2.82369i	−0.138968	−	0.306272i
$86$	−8.49042	+	6.97793i	−0.915546	+	0.752450i
$87$	−1.28502	+	2.52199i	−0.137769	+	0.270386i
$88$	−0.656953	−	0.455809i	−0.0700314	−	0.0485894i
$89$	5.80221	+	1.88525i	0.615033	+	0.199836i	0.599934	−	0.800050i	$-0.295194\pi$
$89$	5.80221	+	1.88525i	0.615033	+	0.199836i	0.0150992	+	0.999886i	$0.495194\pi$
$90$	−2.26788	−	2.20380i	−0.239055	−	0.232301i
$91$	3.12909	+	9.63034i	0.328018	+	1.00953i
$92$	−2.21748	−	7.82036i	−0.231188	−	0.815328i
$93$	6.69161	−	6.69161i	0.693887	−	0.693887i
$94$	−2.61296	+	0.155944i	−0.269507	+	0.0160844i
$95$	0.195547	+	0.0734795i	0.0200627	+	0.00753884i
$96$	−5.35113	−	1.83450i	−0.546148	−	0.187233i
$97$	4.23446	−	0.670672i	0.429944	−	0.0680965i	0.0622879	−	0.998058i	$-0.480160\pi$
$97$	4.23446	−	0.670672i	0.429944	−	0.0680965i	0.367656	+	0.929962i	$0.380160\pi$
$98$	2.92873	+	0.286370i	0.295847	+	0.0289277i
$99$		−	0.282699i		−	0.0284123i
$100$	−5.64361	+	8.25528i	−0.564361	+	0.825528i
$101$		−	1.64913i		−	0.164095i	−0.996628	−	0.0820474i	$-0.973854\pi$
$101$		−	1.64913i		−	0.164095i	0.996628	−	0.0820474i	$-0.0261459\pi$
$102$	0.190845	−	1.95179i	0.0188965	−	0.193256i
$103$	−12.5396	+	1.98607i	−1.23556	+	0.195693i	−0.739836	−	0.672787i	$-0.765097\pi$
$103$	−12.5396	+	1.98607i	−1.23556	+	0.195693i	−0.495723	+	0.868481i	$0.665097\pi$
$104$	−6.57278	+	6.86510i	−0.644514	+	0.673179i
$105$	−0.305007	+	6.73134i	−0.0297657	+	0.656912i
$106$	−0.0575754	−	0.964723i	−0.00559221	−	0.0937022i
$107$	9.25644	−	9.25644i	0.894854	−	0.894854i	−0.100121	−	0.994975i	$-0.531923\pi$
$107$	9.25644	−	9.25644i	0.894854	−	0.894854i	0.994975	+	0.100121i	$0.0319230\pi$
$108$	−0.545595	−	1.92414i	−0.0524999	−	0.185151i
$109$	4.61422	+	14.2011i	0.441962	+	1.36022i	0.885781	+	0.464103i	$0.153623\pi$
$109$	4.61422	+	14.2011i	0.441962	+	1.36022i	−0.443819	+	0.896117i	$0.646377\pi$
$110$	−0.880871	+	0.152486i	−0.0839878	+	0.0145389i
$111$	−1.32053	−	0.429067i	−0.125339	−	0.0407252i
$112$	4.64416	+	11.1232i	0.438832	+	1.05104i
$113$	6.57508	−	12.9043i	0.618532	−	1.21394i	−0.343024	−	0.939327i	$-0.611451\pi$
$113$	6.57508	−	12.9043i	0.618532	−	1.21394i	0.961556	−	0.274610i	$-0.0885488\pi$
$114$	0.0838868	+	0.102070i	0.00785672	+	0.00955969i
$115$	−7.90252	−	4.48823i	−0.736913	−	0.418530i
$116$	3.84855	+	4.15157i	0.357329	+	0.385464i
$117$	−3.31889	−	0.525661i	−0.306832	−	0.0485974i
$118$	0.924716	+	4.20046i	0.0851270	+	0.386684i
$119$	−3.38068	+	2.45621i	−0.309906	+	0.225160i
$120$	−5.70122	+	2.73791i	−0.520447	+	0.249936i
$121$	8.83453	+	6.41866i	0.803139	+	0.583515i
$122$	6.61379	−	15.1495i	0.598785	−	1.37157i
$123$	8.43032	−	4.29546i	0.760137	−	0.387309i
$124$	−7.94809	−	17.1770i	−0.713759	−	1.54254i
$125$	1.98310	+	11.0031i	0.177374	+	0.984143i
$126$	−2.29508	+	3.59085i	−0.204462	+	0.319898i
$127$	4.17261	−	2.12605i	0.370259	−	0.188656i	−0.258953	−	0.965890i	$-0.583378\pi$
$127$	4.17261	−	2.12605i	0.370259	−	0.188656i	0.629212	+	0.777233i	$0.283378\pi$
$128$	−7.13408	+	8.78094i	−0.630570	+	0.776132i
$129$	−4.56772	+	6.28692i	−0.402165	+	0.553532i
$130$	0.152261	+	10.6250i	0.0133542	+	0.931874i
$131$	13.9354	−	10.1246i	1.21754	−	0.884594i	0.221646	−	0.975127i	$-0.428857\pi$
$131$	13.9354	−	10.1246i	1.21754	−	0.884594i	0.995893	+	0.0905335i	$0.0288572\pi$
$132$	−0.530727	−	0.194945i	−0.0461938	−	0.0169678i
$133$	0.0440394	−	0.278054i	0.00381870	−	0.0241103i
$134$	20.2797	+	5.27666i	1.75190	+	0.455834i
$135$	−1.94436	−	1.10430i	−0.167344	−	0.0950428i
$136$	−3.53260	−	1.70421i	−0.302918	−	0.146135i
$137$	1.13994	+	0.580827i	0.0973914	+	0.0496234i	0.502008	−	0.864863i	$-0.332595\pi$
$137$	1.13994	+	0.580827i	0.0973914	+	0.0496234i	−0.404616	+	0.914487i	$0.632595\pi$
$138$	−2.90993	−	4.95680i	−0.247710	−	0.421951i
$139$	−6.67343	−	2.16833i	−0.566033	−	0.183915i	0.0120011	−	0.999928i	$-0.496180\pi$
$139$	−6.67343	−	2.16833i	−0.566033	−	0.183915i	−0.578034	+	0.816013i	$0.696180\pi$
$140$	12.4268	+	5.21445i	1.05026	+	0.440702i
$141$	−1.76034	+	0.571970i	−0.148247	+	0.0481685i
$142$	10.0188	+	8.89029i	0.840759	+	0.746056i
$143$	−0.671711	+	0.671711i	−0.0561713	+	0.0561713i
$144$	−3.98854	−	0.302587i	−0.332378	−	0.0252156i
$145$	6.32270	+	0.286491i	0.525072	+	0.0237918i
$146$	−4.37014	−	11.1425i	−0.361675	−	0.922157i
$147$	2.05518	−	0.325509i	0.169509	−	0.0268475i
$148$	−1.71613	+	2.18323i	−0.141065	+	0.179460i
$149$	−9.66403			−0.791708			−0.395854	−	0.918313i	$-0.629551\pi$
$149$	−9.66403			−0.791708			−0.395854	+	0.918313i	$0.629551\pi$
$150$	−2.39215	+	6.65414i	−0.195318	+	0.543309i
$151$			7.38361i			0.600869i	0.953802	+	0.300435i	$0.0971318\pi$
$151$			7.38361i			0.600869i	−0.953802	+	0.300435i	$0.902868\pi$
$152$	0.249468	−	0.0870997i	0.0202345	−	0.00706472i
$153$	−0.216929	−	1.36963i	−0.0175376	−	0.110728i
$154$	0.439891	+	1.12158i	0.0354474	+	0.0903797i
$155$	−19.8084	−	7.44328i	−1.59105	−	0.597859i
$156$	−3.27552	+	5.86826i	−0.262251	+	0.469837i
$157$	−10.7431	−	10.7431i	−0.857392	−	0.857392i	0.133638	−	0.991030i	$-0.457334\pi$
$157$	−10.7431	−	10.7431i	−0.857392	−	0.857392i	−0.991030	+	0.133638i	$0.957334\pi$
$158$	3.03229	−	3.41720i	0.241236	−	0.271858i
$159$	−0.211175	−	0.649929i	−0.0167472	−	0.0515427i
$160$	1.20855	+	12.5912i	0.0955440	+	0.995425i
$161$	−3.78472	+	11.6482i	−0.298278	+	0.918004i
$162$	−0.715968	−	1.21959i	−0.0562517	−	0.0958197i
$163$	−2.37169	+	4.65471i	−0.185765	+	0.364585i	−0.965042	−	0.262095i	$-0.915587\pi$
$163$	−2.37169	+	4.65471i	−0.185765	+	0.364585i	0.779277	+	0.626680i	$0.215587\pi$
$164$	−2.25068	−	18.7888i	−0.175748	−	1.46716i
$165$	−0.575648	+	0.261194i	−0.0448142	+	0.0203339i
$166$	−5.88399	+	22.6139i	−0.456686	+	1.75518i
$167$	−23.4952	−	3.72127i	−1.81811	−	0.287961i	−0.847889	−	0.530174i	$-0.822127\pi$
$167$	−23.4952	−	3.72127i	−1.81811	−	0.287961i	−0.970223	+	0.242213i	$0.922127\pi$
$168$	5.15865	+	6.78489i	0.397998	+	0.523466i
$169$	−1.00431	−	1.38231i	−0.0772542	−	0.106331i
$170$	−4.15068	+	1.41471i	−0.318342	+	0.108503i
$171$	0.0755796	+	0.0549118i	0.00577972	+	0.00419921i
$172$	8.65296	+	12.9106i	0.659782	+	0.984425i
$173$	7.29157	+	14.3105i	0.554368	+	1.08801i	0.982841	+	0.184454i	$0.0590516\pi$
$173$	7.29157	+	14.3105i	0.554368	+	1.08801i	−0.428473	+	0.903554i	$0.640948\pi$
$174$	3.37286	+	2.15576i	0.255696	+	0.163427i
$175$	13.9886	−	5.59821i	1.05744	−	0.423185i
$176$	−0.731965	+	0.861932i	−0.0551739	+	0.0649705i
$177$	1.38072	+	2.70982i	0.103781	+	0.203682i
$178$	3.45202	−	7.90716i	0.258740	−	0.592667i
$179$	2.17494	−	2.99355i	0.162563	−	0.223748i	−0.719963	−	0.694012i	$-0.755841\pi$
$179$	2.17494	−	2.99355i	0.162563	−	0.223748i	0.882526	+	0.470264i	$0.155841\pi$
$180$	−3.41396	+	2.88875i	−0.254462	+	0.215314i
$181$	−14.1867	−	19.5263i	−1.05449	−	1.45138i	−0.884853	−	0.465869i	$-0.845742\pi$
$181$	−14.1867	−	19.5263i	−1.05449	−	1.45138i	−0.169633	−	0.985507i	$-0.554258\pi$
$182$	13.9854	−	3.07882i	1.03666	−	0.228218i
$183$	1.82851	−	11.5447i	0.135167	−	0.853411i
$184$	−11.3123	+	2.04483i	−0.833957	+	0.150747i
$185$	0.346386	+	3.08537i	0.0254668	+	0.226841i
$186$	−8.49751	−	10.3394i	−0.623068	−	0.758120i
$187$	−0.349292	−	0.177973i	−0.0255428	−	0.0130147i
$188$	−0.140118	+	3.69921i	−0.0102191	+	0.269793i
$189$	−0.931203	+	2.86595i	−0.0677351	+	0.208467i
$190$	0.130335	−	0.265120i	0.00945546	−	0.0192339i
$191$	−11.7919	+	3.83142i	−0.853232	+	0.277232i	−0.702799	−	0.711388i	$-0.748067\pi$
$191$	−11.7919	+	3.83142i	−0.853232	+	0.277232i	−0.150433	+	0.988620i	$0.548067\pi$
$192$	−3.31851	+	7.27925i	−0.239493	+	0.525335i
$193$	−12.4507	−	12.4507i	−0.896217	−	0.896217i	0.0988817	−	0.995099i	$-0.468473\pi$
$193$	−12.4507	−	12.4507i	−0.896217	−	0.896217i	−0.995099	+	0.0988817i	$0.968473\pi$
$194$	−0.361206	−	6.05231i	−0.0259331	−	0.434530i
$195$	1.99604	+	7.24380i	0.142939	+	0.518740i
$196$	0.806131	−	4.08278i	0.0575808	−	0.291627i
$197$	−2.04993	−	12.9427i	−0.146051	−	0.922133i	−0.946494	−	0.322723i	$-0.895402\pi$
$197$	−2.04993	−	12.9427i	−0.146051	−	0.922133i	0.800442	−	0.599410i	$-0.204598\pi$
$198$	−0.397899	−	0.0389063i	−0.0282774	−	0.00276495i
$199$	−0.793485			−0.0562487			−0.0281243	−	0.999604i	$-0.508953\pi$
$199$	−0.793485			−0.0562487			−0.0281243	+	0.999604i	$0.508953\pi$
$200$	10.8426	+	9.07952i	0.766688	+	0.642019i
$201$	14.8174			1.04514
$202$	−2.32116	−	0.226961i	−0.163316	−	0.0159689i
$203$	−1.33431	−	8.42452i	−0.0936504	−	0.591285i
$204$	−2.72088	−	0.537229i	−0.190500	−	0.0376135i
$205$	−16.5357	−	13.1976i	−1.15490	−	0.921762i
$206$	1.06964	+	17.9228i	0.0745256	+	1.24874i
$207$	−2.87392	−	2.87392i	−0.199751	−	0.199751i
$208$	8.75806	+	10.1960i	0.607262	+	0.706965i
$209$	0.0251176	−	0.00816119i	0.00173742	−	0.000564521i
$210$	9.43240	+	1.35570i	0.650897	+	0.0935520i
$211$	0.737794	−	2.27070i	0.0507919	−	0.156321i	−0.922443	−	0.386132i	$-0.873811\pi$
$211$	0.737794	−	2.27070i	0.0507919	−	0.156321i	0.973235	+	0.229811i	$0.0738108\pi$
$212$	−1.36577	−	0.0517323i	−0.0938016	−	0.00355299i
$213$	8.43905	+	4.29991i	0.578234	+	0.294625i
$214$	−11.7545	−	14.3024i	−0.803524	−	0.977690i
$215$	17.0220	+	3.49239i	1.16089	+	0.238179i
$216$	−2.78332	+	0.503116i	−0.189381	+	0.0342327i
$217$	−4.46108	+	28.1661i	−0.302838	+	1.91204i
$218$	20.6231	−	4.54010i	1.39677	−	0.307494i
$219$	−4.97456	−	6.84690i	−0.336150	−	0.462671i
$220$	0.0933942	+	1.26081i	0.00629664	+	0.0850040i
$221$	−2.73890	+	3.76977i	−0.184238	+	0.253582i
$222$	−0.785649	+	1.79960i	−0.0527293	+	0.120781i
$223$	3.18349	+	6.24794i	0.213182	+	0.418393i	0.972691	−	0.232103i	$-0.0745608\pi$
$223$	3.18349	+	6.24794i	0.213182	+	0.418393i	−0.759509	+	0.650497i	$0.774561\pi$
$224$	16.2950	−	5.00584i	1.08876	−	0.334467i
$225$	−0.452187	+	4.97951i	−0.0301458	+	0.331967i
$226$	−17.2580	−	11.0304i	−1.14798	−	0.733731i
$227$	−1.04374	−	2.04845i	−0.0692754	−	0.135961i	0.853772	−	0.520648i	$-0.174309\pi$
$227$	−1.04374	−	2.04845i	−0.0692754	−	0.135961i	−0.923047	+	0.384687i	$0.874309\pi$
$228$	0.155208	−	0.104023i	0.0102789	−	0.00688912i
$229$	−6.71009	−	4.87517i	−0.443415	−	0.322160i	0.343575	−	0.939125i	$-0.388362\pi$
$229$	−6.71009	−	4.87517i	−0.443415	−	0.322160i	−0.786991	+	0.616965i	$0.788362\pi$
$230$	−7.40477	+	10.5051i	−0.488256	+	0.692686i
$231$	0.500731	+	0.689198i	0.0329457	+	0.0453459i
$232$	6.37300	−	4.84548i	0.418408	−	0.318121i
$233$	−2.30467	−	0.365023i	−0.150984	−	0.0239135i	0.0804850	−	0.996756i	$-0.474353\pi$
$233$	−2.30467	−	0.365023i	−0.150984	−	0.0239135i	−0.231469	+	0.972842i	$0.574353\pi$
$234$	−1.19663	+	4.59900i	−0.0782262	+	0.300646i
$235$	2.79111	+	3.05605i	0.182072	+	0.199355i
$236$	6.03942	−	0.723451i	0.393133	−	0.0470927i
$237$	1.46661	−	2.87838i	0.0952664	−	0.186971i
$238$	2.99185	+	5.09634i	0.193933	+	0.330347i
$239$	0.820128	−	2.52409i	0.0530497	−	0.163270i	−0.921022	−	0.389512i	$-0.872644\pi$
$239$	0.820128	−	2.52409i	0.0530497	−	0.163270i	0.974071	+	0.226241i	$0.0726438\pi$
$240$	3.06898	+	8.40127i	0.198102	+	0.542300i
$241$	−7.98863	−	24.5865i	−0.514593	−	1.58375i	−0.784021	−	0.620734i	$-0.786835\pi$
$241$	−7.98863	−	24.5865i	−0.514593	−	1.58375i	0.269428	−	0.963021i	$-0.413165\pi$
$242$	10.2501	−	11.5512i	0.658903	−	0.742542i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−20.4127	−	11.3939i	−1.30679	−	0.729417i
$245$	−2.56167	−	3.88414i	−0.163659	−	0.248149i
$246$	−4.88565	−	12.4569i	−0.311498	−	0.794220i
$247$	−0.0491081	−	0.310056i	−0.00312467	−	0.0197284i
$248$	−25.2705	+	8.82297i	−1.60468	+	0.560259i
$249$			16.5229i			1.04709i
$250$	15.7597	−	1.27693i	0.996734	−	0.0807600i
$251$	28.6590			1.80894			0.904471	−	0.426535i	$-0.140266\pi$
$251$	28.6590			1.80894			0.904471	+	0.426535i	$0.140266\pi$
$252$	4.73826	+	3.72452i	0.298483	+	0.234623i
$253$	−1.13484	+	0.179740i	−0.0713465	+	0.0113002i
$254$	−2.41816	−	6.16555i	−0.151729	−	0.386861i
$255$	−2.58850	+	1.70717i	−0.162098	+	0.106907i
$256$	11.3774	+	11.2497i	0.711085	+	0.703107i
$257$	12.1532	−	12.1532i	0.758095	−	0.758095i	−0.217881	−	0.975975i	$-0.569914\pi$
$257$	12.1532	−	12.1532i	0.758095	−	0.758095i	0.975975	+	0.217881i	$0.0699144\pi$
$258$	8.22022	+	7.29430i	0.511768	+	0.454123i
$259$	3.97934	−	1.29297i	0.247264	−	0.0803409i
$260$	14.9756	+	1.24795i	0.928750	+	0.0773948i
$261$	2.69196	+	0.874672i	0.166628	+	0.0541409i
$262$	−12.3326	−	21.0074i	−0.761910	−	1.29784i
$263$	−16.9128	−	8.61750i	−1.04289	−	0.531378i	−0.153318	−	0.988177i	$-0.548996\pi$
$263$	−16.9128	−	8.61750i	−1.04289	−	0.531378i	−0.889570	+	0.456799i	$0.848996\pi$
$264$	−0.347427	+	0.720169i	−0.0213827	+	0.0443233i
$265$	−1.12831	+	1.03050i	−0.0693118	+	0.0633028i
$266$	−0.385300	−	0.100253i	−0.0236243	−	0.00614688i
$267$	0.954376	−	6.02569i	0.0584069	−	0.368766i
$268$	10.2179	−	27.8176i	0.624157	−	1.69923i
$269$	−2.54733	+	1.85075i	−0.155314	+	0.112842i	−0.662728	−	0.748860i	$-0.730601\pi$
$269$	−2.54733	+	1.85075i	−0.155314	+	0.112842i	0.507414	+	0.861702i	$0.330601\pi$
$270$	−1.82189	+	2.58471i	−0.110877	+	0.157300i
$271$	9.04482	−	12.4491i	0.549434	−	0.756231i	−0.440502	−	0.897752i	$-0.645199\pi$
$271$	9.04482	−	12.4491i	0.549434	−	0.756231i	0.989935	+	0.141521i	$0.0451994\pi$
$272$	−2.88485	+	4.73760i	−0.174920	+	0.287259i
$273$	9.02228	−	4.59708i	0.546053	−	0.278228i
$274$	0.974398	−	1.52453i	0.0588655	−	0.0921000i
$275$	1.06372	+	0.930845i	0.0641445	+	0.0561321i
$276$	−7.37718	+	3.41355i	−0.444054	+	0.205472i
$277$	9.22022	−	4.69794i	0.553989	−	0.282272i	−0.154500	−	0.987993i	$-0.549377\pi$
$277$	9.22022	−	4.69794i	0.553989	−	0.282272i	0.708490	+	0.705721i	$0.249377\pi$
$278$	−3.97035	+	9.09444i	−0.238126	+	0.545448i
$279$	−7.65602	−	5.56242i	−0.458354	−	0.333014i
$280$	9.04959	−	16.7731i	0.540816	−	1.00238i
$281$	−2.89362	+	2.10234i	−0.172619	+	0.125415i	−0.670740	−	0.741692i	$-0.734023\pi$
$281$	−2.89362	+	2.10234i	−0.172619	+	0.125415i	0.498121	+	0.867107i	$0.334023\pi$
$282$	0.562781	+	2.55640i	0.0335131	+	0.152231i
$283$	20.7906	+	3.29291i	1.23588	+	0.195743i	0.739974	−	0.672636i	$-0.234838\pi$
$283$	20.7906	+	3.29291i	1.23588	+	0.195743i	0.495901	+	0.868379i	$0.334838\pi$
$284$	13.8919	−	12.8779i	0.824334	−	0.764165i
$285$	0.0419845	−	0.204634i	0.00248695	−	0.0121215i
$286$	0.852990	+	1.03788i	0.0504383	+	0.0613710i
$287$	−12.9441	+	25.4042i	−0.764067	+	1.49957i
$288$	−0.974813	+	5.57223i	−0.0574414	+	0.328347i
$289$	14.3391	+	4.65906i	0.843478	+	0.274063i
$290$	1.27340	−	8.85978i	0.0747764	−	0.520264i
$291$	−1.32483	−	4.07741i	−0.0776629	−	0.239022i
$292$	−16.2845	+	4.61750i	−0.952977	+	0.270219i
$293$	16.4570	−	16.4570i	0.961431	−	0.961431i	−0.0378525	−	0.999283i	$-0.512052\pi$
$293$	16.4570	−	16.4570i	0.961431	−	0.961431i	0.999283	+	0.0378525i	$0.0120517\pi$
$294$	−0.175310	−	2.93747i	−0.0102243	−	0.171317i
$295$	4.24220	−	5.31519i	0.246991	−	0.309462i
$296$	2.83672	+	2.71592i	0.164881	+	0.157860i
$297$	−0.279218	+	0.0442238i	−0.0162019	+	0.00256613i
$298$	−1.33001	+	13.6021i	−0.0770454	+	0.787951i
$299$			13.6572i			0.789818i
$300$	9.03650	+	4.28272i	0.521722	+	0.247263i
$301$		−	23.4176i		−	1.34977i
$302$	10.3924	+	1.01617i	0.598017	+	0.0584738i
$303$	−1.62883	+	0.257981i	−0.0935738	+	0.0148206i
$304$	−0.0882599	−	0.363114i	−0.00506205	−	0.0208260i
$305$	−25.1975	+	6.94320i	−1.44280	+	0.397567i
$306$	−1.95761	+	0.116832i	−0.111909	+	0.00667883i
$307$	−20.6531	+	20.6531i	−1.17873	+	1.17873i	−0.198664	+	0.980068i	$0.563660\pi$
$307$	−20.6531	+	20.6531i	−1.17873	+	1.17873i	−0.980068	+	0.198664i	$0.936340\pi$
$308$	1.63917	−	0.464790i	0.0934003	−	0.0264839i
$309$	3.92324	+	12.0745i	0.223185	+	0.686893i
$310$	−13.2026	+	26.8560i	−0.749854	+	1.52532i
$311$	18.3590	+	5.96519i	1.04104	+	0.338255i	0.779147	−	0.626841i	$-0.215653\pi$
$311$	18.3590	+	5.96519i	1.04104	+	0.338255i	0.261895	+	0.965096i	$0.415653\pi$
$312$	7.80879	+	5.41792i	0.442086	+	0.306729i
$313$	13.9124	−	27.3046i	0.786375	−	1.54335i	−0.0522469	−	0.998634i	$-0.516638\pi$
$313$	13.9124	−	27.3046i	0.786375	−	1.54335i	0.838622	−	0.544714i	$-0.183362\pi$
$314$	−16.5994	+	13.6424i	−0.936760	+	0.769885i
$315$	6.69618	−	0.751762i	0.377287	−	0.0423570i
$316$	−4.39239	−	4.73824i	−0.247091	−	0.266547i
$317$	24.5629	+	3.89038i	1.37959	+	0.218506i	0.801758	−	0.597649i	$-0.203898\pi$
$317$	24.5629	+	3.89038i	1.37959	+	0.218506i	0.577833	+	0.816155i	$0.303898\pi$
$318$	−0.943839	+	0.207782i	−0.0529278	+	0.0116519i
$319$	0.647358	−	0.470333i	0.0362451	−	0.0263336i
$320$	17.8885	+	0.0318349i	0.999998	+	0.00177962i
$321$	−10.5905	−	7.69446i	−0.591105	−	0.429463i
$322$	15.8739	+	6.93007i	0.884620	+	0.386198i
$323$	0.115428	−	0.0588137i	0.00642260	−	0.00327248i
$324$	−1.81510	+	0.839880i	−0.100839	+	0.0466600i
$325$	12.9061	−	10.7572i	0.715900	−	0.596703i
$326$	6.22511	+	3.97877i	0.344777	+	0.220363i
$327$	13.3045	−	6.77896i	0.735738	−	0.374877i
$328$	−26.7550	+	0.582026i	−1.47730	+	0.0321370i
$329$	3.27847	−	4.51243i	0.180748	−	0.248778i
$330$	0.288407	+	0.846172i	0.0158763	+	0.0465803i
$331$	5.36622	−	3.89879i	0.294954	−	0.214297i	−0.430459	−	0.902610i	$-0.641648\pi$
$331$	5.36622	−	3.89879i	0.294954	−	0.214297i	0.725414	+	0.688313i	$0.241648\pi$
$332$	31.0193	+	11.3940i	1.70241	+	0.625325i
$333$	−0.217207	+	1.37139i	−0.0119029	+	0.0751519i
$334$	−8.47121	+	32.5574i	−0.463524	+	1.78146i
$335$	−13.6902	−	30.1721i	−0.747978	−	1.64848i
$336$	10.2597	−	6.32703i	0.559713	−	0.345168i
$337$	−27.0765	−	13.7961i	−1.47495	−	0.751524i	−0.482699	−	0.875786i	$-0.660344\pi$
$337$	−27.0765	−	13.7961i	−1.47495	−	0.751524i	−0.992249	+	0.124262i	$0.960344\pi$
$338$	−2.08382	+	1.22332i	−0.113345	+	0.0665399i
$339$	−13.7740	−	4.47545i	−0.748102	−	0.243073i
$340$	1.41996	+	6.03678i	0.0770083	+	0.327390i
$341$	−2.54434	+	0.826707i	−0.137784	+	0.0447687i
$342$	0.0876901	−	0.0988212i	0.00474174	−	0.00534364i
$343$	10.4819	−	10.4819i	0.565971	−	0.565971i
$344$	19.3626	−	10.4022i	1.04396	−	0.560851i
$345$	−3.19675	+	8.50734i	−0.172107	+	0.458020i
$346$	21.1456	−	8.29341i	1.13679	−	0.445857i
$347$	−12.3965	+	1.96342i	−0.665480	+	0.105402i	−0.480030	−	0.877252i	$-0.659374\pi$
$347$	−12.3965	+	1.96342i	−0.665480	+	0.105402i	−0.185450	+	0.982654i	$0.559374\pi$
$348$	3.49842	−	4.45062i	0.187535	−	0.238578i
$349$	−16.1106			−0.862380			−0.431190	−	0.902261i	$-0.641906\pi$
$349$	−16.1106			−0.862380			−0.431190	+	0.902261i	$0.641906\pi$
$350$	−5.95432	−	20.4594i	−0.318272	−	1.09360i
$351$			3.36026i			0.179358i
$352$	1.11243	+	1.14886i	0.0592929	+	0.0612347i
$353$	0.0487602	+	0.307859i	0.00259524	+	0.0163857i	0.988952	−	0.148236i	$-0.0473596\pi$
$353$	0.0487602	+	0.307859i	0.00259524	+	0.0163857i	−0.986357	+	0.164622i	$0.947360\pi$
$354$	4.00409	−	1.57043i	0.212815	−	0.0834673i
$355$	0.958651	−	21.1569i	0.0508799	−	1.12289i
$356$	−10.6543	−	5.94695i	−0.564674	−	0.315187i
$357$	2.95482	+	2.95482i	0.156386	+	0.156386i
$358$	−3.91410	−	3.47322i	−0.206867	−	0.183565i
$359$	3.85088	+	11.8518i	0.203242	+	0.625514i	0.999781	+	0.0209270i	$0.00666176\pi$
$359$	3.85088	+	11.8518i	0.203242	+	0.625514i	−0.796539	+	0.604587i	$0.793338\pi$
$360$	3.59607	+	5.20272i	0.189529	+	0.274207i
$361$	5.86863	−	18.0618i	0.308875	−	0.950620i
$362$	−29.4357	+	17.2805i	−1.54711	+	0.908241i
$363$	4.95761	−	9.72986i	0.260207	−	0.510685i
$364$	−2.40872	−	20.1081i	−0.126251	−	1.05395i
$365$	−9.34592	+	16.4556i	−0.489188	+	0.861323i
$366$	−15.9976	−	4.16247i	−0.836207	−	0.217576i
$367$	0.0371810	+	0.00588889i	0.00194083	+	0.000307397i	0.157405	−	0.987534i	$-0.449687\pi$
$367$	0.0371810	+	0.00588889i	0.00194083	+	0.000307397i	−0.155464	+	0.987842i	$0.549687\pi$
$368$	1.32125	+	16.2035i	0.0688747	+	0.844668i
$369$	−5.56137	−	7.65457i	−0.289513	−	0.398481i
$370$	4.39034	−	0.0629156i	0.228243	−	0.00327083i
$371$	1.66602	+	1.21043i	0.0864953	+	0.0628425i
$372$	−15.7221	+	10.5373i	−0.815155	+	0.546334i
$373$	10.7737	+	21.1446i	0.557843	+	1.09483i	0.981937	+	0.189210i	$0.0605925\pi$
$373$	10.7737	+	21.1446i	0.557843	+	1.09483i	−0.424094	+	0.905618i	$0.639407\pi$
$374$	−0.298569	+	0.467136i	−0.0154386	+	0.0241550i
$375$	10.5574	−	3.67995i	0.545180	−	0.190032i
$376$	5.18736	+	0.706319i	0.267518	+	0.0364256i
$377$	−4.31801	−	8.47456i	−0.222389	−	0.436462i
$378$	3.90567	+	1.70509i	0.200886	+	0.0877006i
$379$	3.25104	−	4.47467i	0.166995	−	0.229848i	−0.717315	−	0.696749i	$-0.754629\pi$
$379$	3.25104	−	4.47467i	0.166995	−	0.229848i	0.884310	+	0.466900i	$0.154629\pi$
$380$	−0.355220	−	0.219933i	−0.0182224	−	0.0112823i
$381$	−2.75261	−	3.78865i	−0.141021	−	0.194098i
$382$	3.76987	+	17.1244i	0.192884	+	0.876161i
$383$	3.34339	−	21.1093i	0.170839	−	1.07864i	−0.742025	−	0.670372i	$-0.766135\pi$
$383$	3.34339	−	21.1093i	0.170839	−	1.07864i	0.912864	−	0.408263i	$-0.133865\pi$
$384$	9.78885	+	5.67261i	0.499535	+	0.289479i
$385$	0.940745	−	1.65639i	0.0479448	−	0.0844174i
$386$	−19.2378	+	15.8108i	−0.979179	+	0.804748i
$387$	6.92407	+	3.52799i	0.351970	+	0.179338i
$388$	−8.56834	−	0.324549i	−0.434991	−	0.0164765i
$389$	4.14873	−	12.7685i	0.210349	−	0.647387i	−0.789102	−	0.614262i	$-0.789454\pi$
$389$	4.14873	−	12.7685i	0.210349	−	0.647387i	0.999451	−	0.0331256i	$-0.0105461\pi$
$390$	10.4704	−	1.81250i	0.530188	−	0.0917796i
$391$	−5.36018	+	1.74163i	−0.271076	+	0.0880780i
$392$	−5.63557	−	1.69652i	−0.284640	−	0.0856873i
$393$	−12.1800	−	12.1800i	−0.614398	−	0.614398i
$394$	−18.4991	+	1.10404i	−0.931969	+	0.0556206i
$395$	−7.21617	−	0.326975i	−0.363085	−	0.0164519i
$396$	−0.109521	+	0.554689i	−0.00550366	+	0.0278742i
$397$	−0.543516	−	3.43163i	−0.0272783	−	0.172228i	0.970288	−	0.241953i	$-0.0777880\pi$
$397$	−0.543516	−	3.43163i	−0.0272783	−	0.172228i	−0.997566	+	0.0697245i	$0.977788\pi$
$398$	−0.109203	+	1.11683i	−0.00547386	+	0.0559817i
$399$	−0.281520			−0.0140936
$400$	14.2717	−	14.0114i	0.713583	−	0.700571i
$401$	−15.6586			−0.781955			−0.390978	−	0.920400i	$-0.627863\pi$
$401$	−15.6586			−0.781955			−0.390978	+	0.920400i	$0.627863\pi$
$402$	2.03924	−	20.8555i	0.101708	−	1.04018i
$403$	4.97452	+	31.4079i	0.247798	+	1.56454i
$404$	−0.638897	+	3.23579i	−0.0317863	+	0.160987i
$405$	−0.786537	+	2.09317i	−0.0390833	+	0.104010i
$406$	−12.0412	+	0.718625i	−0.597592	+	0.0356648i
$407$	0.277556	+	0.277556i	0.0137580	+	0.0137580i
$408$	−1.13061	+	3.75571i	−0.0559736	+	0.185935i
$409$	34.6398	−	11.2552i	1.71283	−	0.556532i	0.722028	−	0.691864i	$-0.243210\pi$
$409$	34.6398	−	11.2552i	1.71283	−	0.556532i	0.990800	+	0.135333i	$0.0432103\pi$
$410$	−20.8514	+	21.4577i	−1.02978	+	1.05972i
$411$	0.395351	−	1.21676i	0.0195012	−	0.0600185i
$412$	25.3735	+	0.961090i	1.25006	+	0.0473495i
$413$	−8.16586	−	4.16072i	−0.401816	−	0.204735i
$414$	−4.44056	+	3.64952i	−0.218242	+	0.179364i
$415$	33.6449	−	15.2660i	1.65156	−	0.749377i
$416$	15.5562	−	10.9238i	0.762706	−	0.535581i
$417$	−1.09768	+	6.93047i	−0.0537535	+	0.339386i
$418$	−0.00803009	−	0.0364762i	−0.000392764	−	0.00178411i
$419$	15.5333	+	21.3797i	0.758850	+	1.04447i	0.997309	+	0.0733144i	$0.0233577\pi$
$419$	15.5333	+	21.3797i	0.758850	+	1.04447i	−0.238459	+	0.971153i	$0.576642\pi$
$420$	3.20628	−	13.0895i	0.156450	−	0.638704i
$421$	−10.6122	+	14.6064i	−0.517207	+	0.711874i	−0.985114	−	0.171903i	$-0.945008\pi$
$421$	−10.6122	+	14.6064i	−0.517207	+	0.711874i	0.467907	+	0.883778i	$0.345008\pi$
$422$	−3.09447	−	1.35095i	−0.150636	−	0.0657632i
$423$	0.840306	+	1.64919i	0.0408571	+	0.0801865i
$424$	−0.260777	+	1.91521i	−0.0126645	+	0.0930106i
$425$	5.86783	+	3.69356i	0.284631	+	0.179164i
$426$	7.21355	−	11.2862i	0.349498	−	0.546818i
$427$	15.9909	+	31.3839i	0.773854	+	1.51877i
$428$	−21.7483	+	14.5762i	−1.05124	+	0.704566i
$429$	0.768520	+	0.558362i	0.0371045	+	0.0269580i
$430$	7.25819	−	23.4779i	0.350021	−	1.13221i
$431$	23.2147	+	31.9523i	1.11821	+	1.53909i	0.808727	+	0.588184i	$0.200157\pi$
$431$	23.2147	+	31.9523i	1.11821	+	1.53909i	0.309485	+	0.950904i	$0.399843\pi$
$432$	0.325083	+	3.98677i	0.0156406	+	0.191813i
$433$	14.4130	+	2.28280i	0.692646	+	0.109704i	0.492825	−	0.870128i	$-0.335964\pi$
$433$	14.4130	+	2.28280i	0.692646	+	0.109704i	0.199820	+	0.979833i	$0.435964\pi$
$434$	39.0299	+	10.1553i	1.87350	+	0.487471i
$435$	−0.706124	−	6.28968i	−0.0338561	−	0.301567i
$436$	−3.55194	−	29.6519i	−0.170107	−	1.42007i
$437$	0.172378	−	0.338312i	0.00824598	−	0.0161837i
$438$	−10.3216	+	6.05940i	−0.493187	+	0.289529i
$439$	3.39101	−	10.4365i	0.161844	−	0.498105i	−0.836946	−	0.547286i	$-0.815661\pi$
$439$	3.39101	−	10.4365i	0.161844	−	0.498105i	0.998790	+	0.0491807i	$0.0156610\pi$
$440$	1.78745	+	0.0420666i	0.0852133	+	0.00200545i
$441$	−0.643003	−	1.97896i	−0.0306192	−	0.0942362i
$442$	4.92902	+	4.37382i	0.234450	+	0.208041i
$443$	−4.16873	−	4.16873i	−0.198063	−	0.198063i	0.601106	−	0.799169i	$-0.294727\pi$
$443$	−4.16873	−	4.16873i	−0.198063	−	0.198063i	−0.799169	+	0.601106i	$0.794727\pi$
$444$	2.42481	+	1.35347i	0.115077	+	0.0642329i
$445$	−13.1517	+	3.62396i	−0.623448	+	0.171792i
$446$	9.23212	−	3.62089i	0.437153	−	0.171454i
$447$	1.51179	+	9.54505i	0.0715051	+	0.451465i
$448$	−4.80314	−	23.6242i	−0.226927	−	1.11614i
$449$			4.78534i			0.225834i	0.993604	+	0.112917i	$0.0360195\pi$
$449$			4.78534i			0.225834i	−0.993604	+	0.112917i	$0.963981\pi$
$450$	6.94643	+	1.32176i	0.327458	+	0.0623082i
$451$	−2.67478			−0.125950
$452$	−17.9004	+	22.7725i	−0.841964	+	1.07113i
$453$	7.29270	−	1.15505i	0.342641	−	0.0542690i
$454$	−3.02685	+	1.18715i	−0.142057	+	0.0557156i
$455$	−17.6968	−	14.1243i	−0.829639	−	0.662159i
$456$	−0.125053	−	0.232771i	−0.00585613	−	0.0109005i
$457$	−16.6177	+	16.6177i	−0.777342	+	0.777342i	−0.979378	−	0.202036i	$-0.935244\pi$
$457$	−16.6177	+	16.6177i	−0.777342	+	0.777342i	0.202036	+	0.979378i	$0.435244\pi$
$458$	−7.78528	+	8.77352i	−0.363782	+	0.409960i
$459$	−1.31884	+	0.428516i	−0.0615580	+	0.0200014i
$460$	13.7669	+	11.8680i	0.641884	+	0.553348i
$461$	2.70116	+	0.877660i	0.125806	+	0.0408767i	0.371243	−	0.928536i	$-0.378932\pi$
$461$	2.70116	+	0.877660i	0.125806	+	0.0408767i	−0.245438	+	0.969412i	$0.578932\pi$
$462$	1.03896	−	0.609929i	0.0483368	−	0.0283765i
$463$	−31.8297	−	16.2180i	−1.47925	−	0.753716i	−0.486475	−	0.873694i	$-0.661718\pi$
$463$	−31.8297	−	16.2180i	−1.47925	−	0.753716i	−0.992777	+	0.119978i	$0.961718\pi$
$464$	−5.94293	−	9.63686i	−0.275894	−	0.447380i
$465$	−4.25292	+	20.7289i	−0.197224	+	0.961281i
$466$	−0.830949	+	3.19358i	−0.0384930	+	0.147940i
$467$	2.26802	−	14.3197i	0.104951	−	0.662636i	−0.877985	−	0.478689i	$-0.841112\pi$
$467$	2.26802	−	14.3197i	0.104951	−	0.662636i	0.982936	−	0.183948i	$-0.0588877\pi$
$468$	6.30842	+	2.31719i	0.291607	+	0.107112i
$469$	−36.1237	+	26.2454i	−1.66804	+	1.21190i
$470$	4.68552	−	3.50790i	0.216127	−	0.161807i
$471$	−8.93024	+	12.2914i	−0.411484	+	0.566359i
$472$	−0.187085	−	8.60006i	−0.00861127	−	0.395850i
$473$	1.95743	−	0.997358i	0.0900025	−	0.0458586i
$474$	−3.84948	−	2.46039i	−0.176812	−	0.113009i
$475$	−0.455480	+	0.103576i	−0.0208988	+	0.00475241i
$476$	7.58486	−	3.50965i	0.347652	−	0.160864i
$477$	−0.608892	+	0.310246i	−0.0278793	+	0.0142052i
$478$	−3.43980	−	1.50171i	−0.157333	−	0.0686866i
$479$	−22.7636	−	16.5387i	−1.04009	−	0.755673i	−0.0697901	−	0.997562i	$-0.522233\pi$
$479$	−22.7636	−	16.5387i	−1.04009	−	0.755673i	−0.970304	+	0.241889i	$0.922233\pi$
$480$	12.2472	−	3.16337i	0.559004	−	0.144388i
$481$	3.77462	−	2.74242i	0.172108	−	0.125044i
$482$	−35.7049	+	7.86030i	−1.62632	+	0.358027i
$483$	12.0968	+	1.91595i	0.550424	+	0.0871786i
$484$	−14.8477	−	16.0168i	−0.674896	−	0.728036i
$485$	−7.07862	+	6.46494i	−0.321423	+	0.293558i
$486$	−1.09257	+	0.897938i	−0.0495599	+	0.0407313i
$487$	−1.64612	+	3.23070i	−0.0745930	+	0.146397i	−0.925291	−	0.379257i	$-0.876179\pi$
$487$	−1.64612	+	3.23070i	−0.0745930	+	0.146397i	0.850698	+	0.525654i	$0.176179\pi$
$488$	−18.8462	+	27.1628i	−0.853126	+	1.22960i
$489$	4.96842	+	1.61434i	0.224680	+	0.0730029i
$490$	−5.81948	+	3.07099i	−0.262897	+	0.138733i
$491$	6.24832	+	19.2304i	0.281983	+	0.867854i	0.987287	+	0.158949i	$0.0508105\pi$
$491$	6.24832	+	19.2304i	0.281983	+	0.867854i	−0.705304	+	0.708905i	$0.749189\pi$
$492$	−18.2054	+	5.16219i	−0.820764	+	0.232729i
$493$	2.77544	−	2.77544i	0.125000	−	0.125000i
$494$	−0.443163	+	0.0264483i	−0.0199388	+	0.00118996i
$495$	0.348029	+	0.527701i	0.0156427	+	0.0237184i
$496$	8.94050	+	36.7825i	0.401440	+	1.65158i
$497$	−28.1900	+	4.46485i	−1.26449	+	0.200276i
$498$	23.2560	+	2.27396i	1.04212	+	0.101898i
$499$			38.3720i			1.71777i	0.512171	+	0.858883i	$0.328841\pi$
$499$			38.3720i			1.71777i	−0.512171	+	0.858883i	$0.671159\pi$
$500$	0.371652	−	22.3576i	0.0166208	−	0.999862i
$501$			23.7881i			1.06277i
$502$	3.94419	−	40.3376i	0.176038	−	1.80036i
$503$	19.0365	−	3.01509i	0.848797	−	0.134436i	0.283142	−	0.959078i	$-0.408623\pi$
$503$	19.0365	−	3.01509i	0.848797	−	0.134436i	0.565655	+	0.824642i	$0.308623\pi$
$504$	5.89437	−	6.15653i	0.262556	−	0.274233i
$505$	2.03024	+	3.07836i	0.0903444	+	0.136985i
$506$	0.0968033	+	1.62202i	0.00430343	+	0.0721076i
$507$	−1.20818	+	1.20818i	−0.0536572	+	0.0536572i
$508$	−9.01081	+	2.55504i	−0.399790	+	0.113361i
$509$	8.91678	+	27.4430i	0.395229	+	1.21639i	0.928783	+	0.370624i	$0.120856\pi$
$509$	8.91678	+	27.4430i	0.395229	+	1.21639i	−0.533553	+	0.845766i	$0.679144\pi$
$510$	2.04660	+	3.87827i	0.0906248	+	0.171733i
$511$	24.2552	+	7.88099i	1.07299	+	0.348635i
$512$	17.3998	−	14.4654i	0.768969	−	0.639286i
$513$	0.0424125	−	0.0832392i	0.00187256	−	0.00367510i
$514$	−15.4330	−	18.7782i	−0.680722	−	0.828271i
$515$	20.9620	−	19.1447i	0.923696	−	0.843616i
$516$	11.3980	−	10.5661i	0.501771	−	0.465146i
$517$	0.516814	+	0.0818553i	0.0227295	+	0.00359999i
$518$	−1.27219	−	5.77887i	−0.0558970	−	0.253909i
$519$	12.9937	−	9.44046i	0.570359	−	0.414390i
$520$	3.81752	−	20.9065i	0.167409	−	0.916810i
$521$	20.3759	+	14.8040i	0.892686	+	0.648575i	0.936577	−	0.350462i	$-0.113975\pi$
$521$	20.3759	+	14.8040i	0.892686	+	0.648575i	−0.0438908	+	0.999036i	$0.513975\pi$
$522$	1.60158	−	3.66857i	0.0700994	−	0.160569i
$523$	−1.71718	+	0.874949i	−0.0750872	+	0.0382589i	−0.491131	−	0.871086i	$-0.663416\pi$
$523$	−1.71718	+	0.874949i	−0.0750872	+	0.0382589i	0.416044	+	0.909345i	$0.363416\pi$
$524$	−31.2653	+	14.4670i	−1.36583	+	0.631993i
$525$	−7.71758	−	12.9406i	−0.336823	−	0.564774i
$526$	−14.4568	+	22.6188i	−0.630345	+	0.986227i
$527$	−11.6926	+	5.95767i	−0.509337	+	0.259520i
$528$	0.965824	+	0.588117i	0.0420321	+	0.0255945i
$529$	3.80956	−	5.24341i	0.165633	−	0.227974i
$530$	1.29514	+	1.72992i	0.0562572	+	0.0751431i
$531$	2.46046	−	1.78763i	0.106775	−	0.0775766i
$532$	−0.194133	+	0.528514i	−0.00841671	+	0.0229140i
$533$	−4.97358	+	31.4020i	−0.215430	+	1.36017i
$534$	−8.34982	−	2.17257i	−0.361332	−	0.0940163i
$535$	−5.88303	+	28.6742i	−0.254346	+	1.23969i
$536$	−37.7470	−	18.2101i	−1.63042	−	0.786556i
$537$	−3.29693	−	1.67987i	−0.142273	−	0.0724917i
$538$	2.25435	+	3.84008i	0.0971920	+	0.165558i
$539$	−0.559450	−	0.181776i	−0.0240972	−	0.00782966i
$540$	3.38724	+	2.92003i	0.145764	+	0.125658i
$541$	−3.83258	+	1.24528i	−0.164775	+	0.0535388i	−0.390243	−	0.920712i	$-0.627609\pi$
$541$	−3.83258	+	1.24528i	−0.164775	+	0.0535388i	0.225468	+	0.974251i	$0.427609\pi$
$542$	−16.2774	−	14.4439i	−0.699173	−	0.620419i
$543$	−17.0666	+	17.0666i	−0.732398	+	0.732398i
$544$	6.27115	+	4.71245i	0.268873	+	0.202044i
$545$	−26.0961	−	20.8280i	−1.11783	−	0.892176i
$546$	−5.22871	−	13.3315i	−0.223768	−	0.570537i
$547$	−26.4425	+	4.18808i	−1.13060	+	0.179069i	−0.693578	−	0.720382i	$-0.743967\pi$
$547$	−26.4425	+	4.18808i	−1.13060	+	0.179069i	−0.437021	+	0.899451i	$0.643967\pi$
$548$	−2.01167	−	1.58128i	−0.0859343	−	0.0675489i
$549$	−11.6886			−0.498859
$550$	1.45656	−	1.36908i	0.0621079	−	0.0583776i
$551$			0.264430i			0.0112651i
$552$	3.78930	+	10.8532i	0.161283	+	0.461942i
$553$	1.52287	+	9.61500i	0.0647588	+	0.408871i
$554$	−5.34342	−	13.6240i	−0.227020	−	0.578829i
$555$	2.99320	−	0.824780i	0.127054	−	0.0350100i
$556$	12.2540	+	6.83990i	0.519686	+	0.290076i
$557$	17.7123	+	17.7123i	0.750494	+	0.750494i	0.974571	−	0.224078i	$-0.0719369\pi$
$557$	17.7123	+	17.7123i	0.750494	+	0.750494i	−0.224078	+	0.974571i	$0.571937\pi$
$558$	−8.88277	+	10.0103i	−0.376038	+	0.423771i
$559$	−8.06930	−	24.8348i	−0.341295	−	1.05040i
$560$	−22.3627	−	15.0457i	−0.944997	−	0.635797i
$561$	−0.121141	+	0.372833i	−0.00511457	+	0.0157410i
$562$	2.56081	+	4.36210i	0.108021	+	0.184004i
$563$	−2.30556	+	4.52492i	−0.0971678	+	0.190703i	−0.934474	−	0.356032i	$-0.884129\pi$
$563$	−2.30556	+	4.52492i	−0.0971678	+	0.190703i	0.837306	+	0.546735i	$0.184129\pi$
$564$	3.67559	−	0.440292i	0.154770	−	0.0185396i
$565$	3.61304	+	32.1825i	0.152002	+	1.35393i
$566$	7.49608	−	28.8097i	0.315084	−	1.21096i
$567$	2.97634	+	0.471405i	0.124994	+	0.0197972i
$568$	−16.2138	−	21.3252i	−0.680318	−	0.894786i
$569$	19.5402	+	26.8947i	0.819167	+	1.12749i	0.989844	+	0.142159i	$0.0454045\pi$
$569$	19.5402	+	26.8947i	0.819167	+	1.12749i	−0.170677	+	0.985327i	$0.554595\pi$
$570$	−0.282245	−	0.0872560i	−0.0118219	−	0.00365475i
$571$	−25.9184	−	18.8308i	−1.08465	−	0.788046i	−0.106164	−	0.994349i	$-0.533857\pi$
$571$	−25.9184	−	18.8308i	−1.08465	−	0.788046i	−0.978488	+	0.206303i	$0.933857\pi$
$572$	1.57821	−	1.05775i	0.0659881	−	0.0442266i
$573$	5.62891	+	11.0474i	0.235151	+	0.461510i
$574$	33.9751	+	21.7151i	1.41809	+	0.906371i
$575$	20.2767	−	1.35077i	0.845598	−	0.0563311i
$576$	7.70876	+	2.13893i	0.321198	+	0.0891220i
$577$	−16.7127	−	32.8004i	−0.695757	−	1.36550i	−0.920369	−	0.391051i	$-0.872112\pi$
$577$	−16.7127	−	32.8004i	−0.695757	−	1.36550i	0.224612	−	0.974448i	$-0.427888\pi$
$578$	8.53106	−	19.5411i	0.354845	−	0.812804i
$579$	−10.3497	+	14.2451i	−0.430117	+	0.592005i
$580$	−12.2949	−	3.01163i	−0.510518	−	0.125051i
$581$	−29.2662	−	40.2815i	−1.21417	−	1.67116i
$582$	−5.92129	+	1.30355i	−0.245445	+	0.0540338i
$583$	−0.0302215	+	0.190811i	−0.00125165	+	0.00790259i
$584$	4.25799	+	23.5559i	0.176197	+	0.974750i
$585$	6.84237	−	3.10465i	0.282897	−	0.128361i
$586$	−20.8984	−	25.4282i	−0.863306	−	1.05043i
$587$	23.4414	+	11.9440i	0.967528	+	0.492980i	0.865012	−	0.501751i	$-0.167311\pi$
$587$	23.4414	+	11.9440i	0.967528	+	0.492980i	0.102516	+	0.994731i	$0.467311\pi$
$588$	−4.15862	−	0.157519i	−0.171499	−	0.00649597i
$589$	0.273196	−	0.840812i	0.0112569	−	0.0346450i
$590$	−6.89730	−	6.70241i	−0.283957	−	0.275934i
$591$	−12.4627	+	4.04938i	−0.512648	+	0.166569i
$592$	4.21307	−	3.61890i	0.173156	−	0.148736i
$593$	−4.43203	−	4.43203i	−0.182002	−	0.182002i	0.610226	−	0.792228i	$-0.291079\pi$
$593$	−4.43203	−	4.43203i	−0.182002	−	0.182002i	−0.792228	+	0.610226i	$0.791079\pi$
$594$	0.0238178	+	0.399086i	0.000977255	+	0.0163747i
$595$	3.28674	−	8.74683i	0.134743	−	0.358585i
$596$	18.9620	+	3.74398i	0.776713	+	0.153359i
$597$	0.124128	+	0.783716i	0.00508024	+	0.0320754i
$598$	19.2226	+	1.87957i	0.786069	+	0.0768614i
$599$	29.7462			1.21540			0.607699	−	0.794168i	$-0.292093\pi$
$599$	29.7462			1.21540			0.607699	+	0.794168i	$0.292093\pi$
$600$	7.27158	−	12.1295i	0.296861	−	0.495184i
$601$	−40.3102			−1.64429			−0.822143	−	0.569281i	$-0.807222\pi$
$601$	−40.3102			−1.64429			−0.822143	+	0.569281i	$0.807222\pi$
$602$	−32.9603	−	3.22284i	−1.34336	−	0.131353i
$603$	−2.31795	−	14.6350i	−0.0943944	−	0.595983i
$604$	2.86051	−	14.4875i	0.116393	−	0.589489i
$605$	−24.3930	−	1.10528i	−0.991717	−	0.0449362i
$606$	0.138942	+	2.32808i	0.00564412	+	0.0945719i
$607$	−7.71252	−	7.71252i	−0.313042	−	0.313042i	0.533045	−	0.846087i	$-0.321048\pi$
$607$	−7.71252	−	7.71252i	−0.313042	−	0.313042i	−0.846087	+	0.533045i	$0.821048\pi$
$608$	−0.523230	+	0.0742525i	−0.0212198	+	0.00301134i
$609$	−8.11207	+	2.63577i	−0.328717	+	0.106807i
$610$	6.30477	+	36.4211i	0.255273	+	1.47465i
$611$	1.92197	−	5.91521i	0.0777545	−	0.239304i
$612$	−0.104975	+	2.77142i	−0.00424337	+	0.112028i
$613$	12.0458	+	6.13766i	0.486527	+	0.247898i	0.680006	−	0.733207i	$-0.261977\pi$
$613$	12.0458	+	6.13766i	0.486527	+	0.247898i	−0.193479	+	0.981104i	$0.561977\pi$
$614$	26.2268	+	31.9116i	1.05843	+	1.28785i
$615$	−10.4484	+	18.3967i	−0.421320	+	0.741826i
$616$	−0.428602	−	2.37110i	−0.0172689	−	0.0955342i
$617$	2.61995	−	16.5417i	0.105475	−	0.665945i	−0.877132	−	0.480250i	$-0.840546\pi$
$617$	2.61995	−	16.5417i	0.105475	−	0.665945i	0.982607	−	0.185696i	$-0.0594539\pi$
$618$	17.5348	−	3.86021i	0.705352	−	0.155281i
$619$	−8.12418	−	11.1820i	−0.326538	−	0.449441i	0.613911	−	0.789375i	$-0.289595\pi$
$619$	−8.12418	−	11.1820i	−0.326538	−	0.449441i	−0.940449	+	0.339934i	$0.889595\pi$
$620$	35.9828	+	22.2787i	1.44511	+	0.894732i
$621$	−2.38895	+	3.28811i	−0.0958654	+	0.131947i
$622$	10.9227	−	25.0193i	0.437959	−	1.00318i
$623$	8.34634	+	16.3806i	0.334389	+	0.656275i
$624$	8.70040	−	10.2452i	0.348295	−	0.410138i
$625$	−17.2476	−	18.0975i	−0.689903	−	0.723901i
$626$	−36.5166	−	23.3395i	−1.45950	−	0.932834i
$627$	−0.0119900	−	0.0235316i	−0.000478833	−	0.000939763i
$628$	16.9172	+	25.2412i	0.675070	+	1.00724i
$629$	1.55770	+	1.13174i	0.0621096	+	0.0451253i
$630$	−0.136546	−	9.52835i	−0.00544011	−	0.379618i
$631$	−14.5721	−	20.0567i	−0.580104	−	0.798445i	0.413602	−	0.910458i	$-0.364270\pi$
$631$	−14.5721	−	20.0567i	−0.580104	−	0.798445i	−0.993707	+	0.112012i	$0.964270\pi$
$632$	−7.27358	+	5.53020i	−0.289327	+	0.219979i
$633$	−2.35816	−	0.373495i	−0.0937284	−	0.0148451i
$634$	8.85618	−	34.0369i	0.351724	−	1.35178i
$635$	−5.17145	+	9.10548i	−0.205223	+	0.361340i
$636$	0.162558	+	1.35705i	0.00644586	+	0.0538105i
$637$	−3.17432	+	6.22996i	−0.125771	+	0.246840i
$638$	−0.572902	−	0.975887i	−0.0226814	−	0.0386357i
$639$	2.92681	−	9.00780i	0.115783	−	0.356343i
$640$	2.50671	−	25.1737i	0.0990864	−	0.995079i
$641$	−2.94028	−	9.04926i	−0.116134	−	0.357424i	0.876048	−	0.482224i	$-0.160171\pi$
$641$	−2.94028	−	9.04926i	−0.116134	−	0.357424i	−0.992182	+	0.124800i	$0.960171\pi$
$642$	−12.2875	+	13.8472i	−0.484948	+	0.546506i
$643$	17.0309	+	17.0309i	0.671631	+	0.671631i	0.958092	−	0.286461i	$-0.0924788\pi$
$643$	17.0309	+	17.0309i	0.671631	+	0.671631i	−0.286461	+	0.958092i	$0.592479\pi$
$644$	11.9387	−	21.3888i	0.470452	−	0.842838i
$645$	0.786554	−	17.3588i	0.0309705	−	0.683502i
$646$	−0.0668945	−	0.170560i	−0.00263193	−	0.00671058i
$647$	−1.65699	−	10.4619i	−0.0651432	−	0.411298i	−0.998613	−	0.0526429i	$-0.983235\pi$
$647$	−1.65699	−	10.4619i	−0.0651432	−	0.411298i	0.933470	−	0.358655i	$-0.116765\pi$
$648$	0.932329	+	2.67035i	0.0366254	+	0.104901i
$649$		−	0.859772i		−	0.0337490i
$650$	−13.3646	−	19.6458i	−0.524203	−	0.770570i
$651$	28.5172			1.11768
$652$	6.45685	−	8.21427i	0.252870	−	0.321696i
$653$	−0.575286	+	0.0911163i	−0.0225127	+	0.00356566i	−0.167681	−	0.985841i	$-0.553628\pi$
$653$	−0.575286	+	0.0911163i	−0.0225127	+	0.00356566i	0.145168	+	0.989407i	$0.453628\pi$
$654$	−7.71037	−	19.6590i	−0.301499	−	0.768727i
$655$	−13.5481	+	36.0550i	−0.529370	+	1.40878i
$656$	−2.86295	+	37.7378i	−0.111779	+	1.47342i
$657$	−5.98441	+	5.98441i	−0.233474	+	0.233474i
$658$	−5.90005	−	5.23547i	−0.230008	−	0.204100i
$659$	26.2895	−	8.54198i	1.02409	−	0.332748i	0.251641	−	0.967821i	$-0.419030\pi$
$659$	26.2895	−	8.54198i	1.02409	−	0.332748i	0.772453	+	0.635072i	$0.219030\pi$
$660$	1.23068	−	0.289479i	0.0479042	−	0.0112680i
$661$	25.4345	+	8.26418i	0.989289	+	0.321439i	0.758577	−	0.651583i	$-0.225895\pi$
$661$	25.4345	+	8.26418i	0.989289	+	0.321439i	0.230711	+	0.973022i	$0.425895\pi$
$662$	−4.74903	−	8.08953i	−0.184576	−	0.314409i
$663$	4.15182	+	2.11546i	0.161243	+	0.0821576i
$664$	20.3060	−	42.0917i	0.788027	−	1.63347i
$665$	0.260105	+	0.573248i	0.0100864	+	0.0222296i
$666$	1.90035	+	0.494457i	0.0736369	+	0.0191598i
$667$	1.79964	−	11.3625i	0.0696822	−	0.439956i
$668$	44.6587	+	16.4039i	1.72790	+	0.634687i
$669$	5.67301	−	4.12169i	0.219331	−	0.159354i
$670$	−44.3514	+	15.1166i	−1.71344	+	0.584005i
$671$	−1.94226	+	2.67329i	−0.0749800	+	0.103201i
$672$	−7.49331	−	15.3113i	−0.289061	−	0.590646i
$673$	−32.5965	+	16.6088i	−1.25650	+	0.640221i	−0.950179	−	0.311706i	$-0.899100\pi$
$673$	−32.5965	+	16.6088i	−1.25650	+	0.640221i	−0.306326	+	0.951927i	$0.599100\pi$
$674$	−23.1445	+	36.2115i	−0.891492	+	1.39481i
$675$	4.98894	−	0.332348i	0.192024	−	0.0127921i
$676$	1.43504	+	3.10133i	0.0551939	+	0.119282i
$677$	32.8308	−	16.7281i	1.26179	−	0.642913i	0.310312	−	0.950635i	$-0.399566\pi$
$677$	32.8308	−	16.7281i	1.26179	−	0.642913i	0.951476	+	0.307721i	$0.0995665\pi$
$678$	−8.19485	+	18.7710i	−0.314721	+	0.720897i
$679$	10.4520	+	7.59379i	0.401109	+	0.291423i
$680$	8.69220	−	1.16779i	0.333331	−	0.0447827i
$681$	−1.85996	+	1.35134i	−0.0712737	+	0.0517834i
$682$	0.813427	+	3.69494i	0.0311477	+	0.141487i
$683$	−20.2038	−	3.19997i	−0.773078	−	0.122444i	−0.242582	−	0.970131i	$-0.577994\pi$
$683$	−20.2038	−	3.19997i	−0.773078	−	0.122444i	−0.530496	+	0.847687i	$0.677994\pi$
$684$	−0.127023	−	0.137024i	−0.00485683	−	0.00523925i
$685$	−2.84292	+	0.319167i	−0.108623	+	0.0121947i
$686$	−13.3108	−	16.1959i	−0.508207	−	0.618363i
$687$	−3.76546	+	7.39012i	−0.143661	+	0.281951i
$688$	−11.9764	−	28.6844i	−0.456595	−	1.09358i
$689$	2.18393	+	0.709603i	0.0832012	+	0.0270337i
$690$	11.5341	+	5.67024i	0.439097	+	0.215862i
$691$	−1.61527	−	4.97128i	−0.0614476	−	0.189116i	0.915620	−	0.402044i	$-0.131700\pi$
$691$	−1.61527	−	4.97128i	−0.0614476	−	0.189116i	−0.977068	+	0.212928i	$0.931700\pi$
$692$	−8.76284	−	30.9038i	−0.333113	−	1.17479i
$693$	0.602381	−	0.602381i	0.0228826	−	0.0228826i
$694$	1.05744	+	17.7183i	0.0401400	+	0.672579i
$695$	15.1264	−	4.16810i	0.573778	−	0.158105i
$696$	−5.78278	−	5.53654i	−0.219196	−	0.209862i
$697$	−12.9589	+	2.05248i	−0.490853	+	0.0777434i
$698$	−2.21722	+	22.6757i	−0.0839228	+	0.858287i
$699$			2.33339i			0.0882570i
$700$	−29.6161	+	5.56499i	−1.11938	+	0.210337i
$701$		−	29.0077i		−	1.09561i	−0.836607	−	0.547803i	$-0.815464\pi$
$701$		−	29.0077i		−	1.09561i	0.836607	−	0.547803i	$-0.184536\pi$
$702$	4.72958	+	0.462455i	0.178506	+	0.0174542i
$703$	−0.128118	+	0.0202919i	−0.00483205	+	0.000765322i
$704$	1.77013	−	1.40764i	0.0667141	−	0.0530524i
$705$	2.58180	−	3.23482i	0.0972363	−	0.121830i
$706$	0.440023	−	0.0262609i	0.0165605	−	0.000988342i
$707$	3.51401	−	3.51401i	0.132158	−	0.132158i
$708$	−1.65932	−	5.85189i	−0.0623610	−	0.219928i
$709$	9.19960	+	28.3135i	0.345498	+	1.06333i	0.961316	+	0.275446i	$0.0888256\pi$
$709$	9.19960	+	28.3135i	0.345498	+	1.06333i	−0.615818	+	0.787888i	$0.711174\pi$
$710$	−29.6464	−	4.26102i	−1.11261	−	0.159913i
$711$	−3.07237	−	0.998273i	−0.115223	−	0.0374382i
$712$	−9.83662	+	14.1774i	−0.368643	+	0.531322i
$713$	−17.4615	+	34.2701i	−0.653938	+	1.28343i
$714$	4.56557	−	3.75226i	0.170862	−	0.140425i
$715$	0.426913	−	2.08079i	0.0159656	−	0.0778173i
$716$	−5.42724	+	5.03110i	−0.202825	+	0.188021i
$717$	−2.62131	−	0.415175i	−0.0978948	−	0.0155050i
$718$	17.2114	−	3.78902i	0.642323	−	0.141405i
$719$	−3.22089	+	2.34011i	−0.120119	+	0.0872714i	−0.646223	−	0.763149i	$-0.723652\pi$
$719$	−3.22089	+	2.34011i	−0.120119	+	0.0872714i	0.526104	+	0.850420i	$0.323652\pi$
$720$	7.81774	−	4.34545i	0.291350	−	0.161945i
$721$	−30.9515	−	22.4876i	−1.15269	−	0.837482i
$722$	−24.6143	−	10.7458i	−0.916049	−	0.399919i
$723$	−23.0341	+	11.7365i	−0.856647	+	0.436483i
$724$	20.2712	+	43.8090i	0.753373	+	1.62815i
$725$	−12.1550	+	7.24907i	−0.451426	+	0.269224i
$726$	−13.0125	−	8.31692i	−0.482939	−	0.308670i
$727$	−26.6627	+	13.5853i	−0.988866	+	0.503852i	−0.872111	−	0.489309i	$-0.837249\pi$
$727$	−26.6627	+	13.5853i	−0.988866	+	0.503852i	−0.116755	+	0.993161i	$0.537249\pi$
$728$	−28.6337	+	0.622895i	−1.06124	+	0.0230860i
$729$	−0.587785	+	0.809017i	−0.0217698	+	0.0299636i
$730$	21.8750	+	15.4191i	0.809630	+	0.570686i
$731$	8.71811	−	6.33408i	0.322451	−	0.234274i
$732$	−8.06034	+	21.9438i	−0.297919	+	0.811065i
$733$	3.39386	−	21.4280i	0.125355	−	0.791461i	−0.842268	−	0.539060i	$-0.818780\pi$
$733$	3.39386	−	21.4280i	0.125355	−	0.791461i	0.967623	−	0.252401i	$-0.0812203\pi$
$734$	0.0134056	−	0.0515218i	0.000494811	−	0.00190170i
$735$	−3.43559	+	3.13774i	−0.126724	+	0.115737i
$736$	22.9883	+	0.370354i	0.847362	+	0.0136514i
$737$	−3.73231	−	1.90170i	−0.137481	−	0.0700502i
$738$	−11.5392	+	6.77418i	−0.424764	+	0.249361i
$739$	6.09760	+	1.98123i	0.224304	+	0.0728807i	0.419013	−	0.907980i	$-0.362376\pi$
$739$	6.09760	+	1.98123i	0.224304	+	0.0728807i	−0.194709	+	0.980861i	$0.562376\pi$
$740$	0.515665	−	6.18806i	0.0189562	−	0.227478i
$741$	−0.298557	+	0.0970070i	−0.0109678	+	0.00356364i
$742$	1.93297	−	2.17833i	0.0709615	−	0.0799692i
$743$	21.4253	−	21.4253i	0.786019	−	0.786019i	−0.194820	−	0.980839i	$-0.562412\pi$
$743$	21.4253	−	21.4253i	0.786019	−	0.786019i	0.980839	+	0.194820i	$0.0624123\pi$
$744$	12.6675	+	23.5791i	0.464414	+	0.864453i
$745$	18.0394	−	11.8973i	0.660913	−	0.435885i
$746$	31.2438	−	12.2540i	1.14392	−	0.448651i
$747$	16.3194	−	2.58475i	0.597097	−	0.0945709i
$748$	0.616404	+	0.484526i	0.0225380	+	0.0177160i
$749$	39.4477			1.44139
$750$	−3.72657	−	15.3660i	−0.136075	−	0.561085i
$751$		−	4.73646i		−	0.172836i	−0.996259	−	0.0864180i	$-0.972458\pi$
$751$		−	4.73646i		−	0.172836i	0.996259	−	0.0864180i	$-0.0275421\pi$
$752$	1.70805	−	7.20401i	0.0622863	−	0.262703i
$753$	−4.48326	−	28.3062i	−0.163379	−	1.03154i
$754$	−12.5222	+	4.91129i	−0.456032	+	0.178859i
$755$	−9.08992	−	13.7827i	−0.330816	−	0.501602i
$756$	2.93744	−	5.26257i	0.106834	−	0.191398i
$757$	−32.5386	−	32.5386i	−1.18264	−	1.18264i	−0.979059	−	0.203579i	$-0.934743\pi$
$757$	−32.5386	−	32.5386i	−1.18264	−	1.18264i	−0.203579	−	0.979059i	$-0.565257\pi$
$758$	−5.85068	−	5.19166i	−0.212506	−	0.188570i
$759$	0.355055	+	1.09275i	0.0128877	+	0.0396642i
$760$	−0.358443	+	0.469704i	−0.0130021	+	0.0170380i
$761$	−15.6782	+	48.2527i	−0.568336	+	1.74916i	0.0894905	+	0.995988i	$0.471476\pi$
$761$	−15.6782	+	48.2527i	−0.568336	+	1.74916i	−0.657826	+	0.753170i	$0.728524\pi$
$762$	−5.71135	+	3.35290i	−0.206900	+	0.121463i
$763$	−20.4280	+	40.0921i	−0.739542	+	1.45143i
$764$	24.6215	−	2.94936i	0.890773	−	0.106704i
$765$	2.09108	+	2.28957i	0.0756031	+	0.0827797i
$766$	−29.2512	−	7.61098i	−1.05689	−	0.274996i
$767$	−10.0937	−	1.59869i	−0.364464	−	0.0577255i
$768$	9.33139	−	12.9971i	0.336718	−	0.468993i
$769$	16.5014	+	22.7122i	0.595054	+	0.819022i	0.995244	−	0.0974102i	$-0.0310559\pi$
$769$	16.5014	+	22.7122i	0.595054	+	0.819022i	−0.400190	+	0.916432i	$0.631056\pi$
$770$	−2.20190	−	1.55206i	−0.0793510	−	0.0559324i
$771$	−13.9047	−	10.1024i	−0.500767	−	0.363828i
$772$	19.6061	+	29.2532i	0.705639	+	1.05285i
$773$	20.2623	+	39.7669i	0.728783	+	1.43032i	0.895843	+	0.444370i	$0.146573\pi$
$773$	20.2623	+	39.7669i	0.728783	+	1.43032i	−0.167060	+	0.985947i	$0.553427\pi$
$774$	5.91857	−	9.26009i	0.212739	−	0.332847i
$775$	46.1389	−	10.4920i	1.65736	−	0.376884i
$776$	−1.63602	+	12.0153i	−0.0587296	+	0.431323i
$777$	−1.89955	−	3.72808i	−0.0681460	−	0.133744i
$778$	−17.4007	−	7.59660i	−0.623844	−	0.272351i
$779$	0.519552	−	0.715102i	0.0186149	−	0.0256212i
$780$	−1.11012	−	14.9865i	−0.0397486	−	0.536603i
$781$	−1.57382	−	2.16618i	−0.0563157	−	0.0775120i
$782$	1.71365	+	7.78416i	0.0612801	+	0.278361i
$783$	0.442788	−	2.79565i	0.0158239	−	0.0999084i
$784$	−3.16345	+	7.69859i	−0.112980	+	0.274950i
$785$	33.2794	+	6.82789i	1.18779	+	0.243698i
$786$	−18.8196	+	15.4670i	−0.671272	+	0.551691i
$787$	−8.99340	−	4.58236i	−0.320580	−	0.163344i	0.286294	−	0.958142i	$-0.407577\pi$
$787$	−8.99340	−	4.58236i	−0.320580	−	0.163344i	−0.606874	+	0.794798i	$0.707577\pi$
$788$	−0.991993	+	26.1894i	−0.0353383	+	0.932958i
$789$	−5.86566	+	18.0526i	−0.208823	+	0.642691i
$790$	−1.45334	+	10.1118i	−0.0517076	+	0.359760i
$791$	41.5071	−	13.4865i	1.47582	−	0.479524i
$792$	0.765652	+	0.230490i	0.0272063	+	0.00819012i
$793$	27.7730	+	27.7730i	0.986247	+	0.986247i
$794$	−4.90482	+	0.292723i	−0.174066	+	0.0103884i
$795$	1.19432	+	0.953218i	0.0423580	+	0.0338071i
$796$	1.55691	+	0.307407i	0.0551833	+	0.0108958i
$797$	−6.71993	−	42.4280i	−0.238032	−	1.50288i	−0.760007	−	0.649915i	$-0.774805\pi$
$797$	−6.71993	−	42.4280i	−0.238032	−	1.50288i	0.521975	−	0.852961i	$-0.325195\pi$
$798$	−0.0387441	+	0.396240i	−0.00137153	+	0.0140267i
$799$	2.56670			0.0908032
$800$	−17.7570	−	22.0157i	−0.627803	−	0.778372i
$801$	−6.10080			−0.215561
$802$	−2.15502	+	22.0396i	−0.0760962	+	0.778244i
$803$	0.374277	+	2.36309i	0.0132079	+	0.0833916i
$804$	−29.0735	−	5.74047i	−1.02534	−	0.202451i
$805$	−7.27524	−	26.4025i	−0.256418	−	0.930565i
$806$	44.8912	−	2.67914i	1.58123	−	0.0943688i
$807$	2.22645	+	2.22645i	0.0783748	+	0.0783748i
$808$	4.46645	+	1.34457i	0.157129	+	0.0473019i
$809$	−27.7947	+	9.03103i	−0.977208	+	0.317514i	−0.753722	−	0.657193i	$-0.771744\pi$
$809$	−27.7947	+	9.03103i	−0.977208	+	0.317514i	−0.223486	+	0.974707i	$0.571744\pi$
$810$	2.83789	+	1.39512i	0.0997134	+	0.0490196i
$811$	7.64133	−	23.5176i	0.268323	−	0.825814i	−0.722586	−	0.691281i	$-0.757047\pi$
$811$	7.64133	−	23.5176i	0.268323	−	0.825814i	0.990909	−	0.134533i	$-0.0429534\pi$
$812$	−0.645695	+	17.0468i	−0.0226594	+	0.598227i
$813$	−13.7108	−	6.98599i	−0.480858	−	0.245009i
$814$	0.428860	−	0.352462i	0.0150315	−	0.0123538i
$815$	−1.30326	−	11.6085i	−0.0456511	−	0.406629i
$816$	5.13056	+	2.10821i	0.179606	+	0.0738022i
$817$	−0.113569	+	0.717047i	−0.00397328	+	0.0250863i
$818$	−11.0744	−	50.3045i	−0.387206	−	1.75886i
$819$	−5.95188	−	8.19206i	−0.207976	−	0.286254i
$820$	27.3321	+	32.3015i	0.954477	+	1.12802i
$821$	−17.8856	+	24.6175i	−0.624213	+	0.859155i	−0.997651	−	0.0684998i	$-0.978179\pi$
$821$	−17.8856	+	24.6175i	−0.624213	+	0.859155i	0.373438	+	0.927655i	$0.378179\pi$
$822$	−1.65819	−	0.723913i	−0.0578359	−	0.0252494i
$823$	20.0687	+	39.3871i	0.699552	+	1.37295i	0.917795	+	0.397054i	$0.129967\pi$
$823$	20.0687	+	39.3871i	0.699552	+	1.37295i	−0.218243	+	0.975894i	$0.570033\pi$
$824$	4.84476	−	35.5810i	0.168775	−	1.23952i
$825$	0.752983	−	1.19624i	0.0262155	−	0.0416476i
$826$	−6.98004	+	10.9208i	−0.242867	+	0.379985i
$827$	21.9177	+	43.0160i	0.762155	+	1.49581i	0.865359	+	0.501152i	$0.167090\pi$
$827$	21.9177	+	43.0160i	0.762155	+	1.49581i	−0.103204	+	0.994660i	$0.532910\pi$
$828$	4.52557	+	6.75236i	0.157274	+	0.234661i
$829$	45.8230	+	33.2923i	1.59150	+	1.15629i	0.901764	+	0.432228i	$0.142272\pi$
$829$	45.8230	+	33.2923i	1.59150	+	1.15629i	0.689734	+	0.724063i	$0.257728\pi$
$830$	−16.8565	−	49.4562i	−0.585098	−	1.71665i
$831$	−6.08246	−	8.37179i	−0.210998	−	0.290414i
$832$	−13.2343	−	23.3988i	−0.458816	−	0.811206i
$833$	−2.84993	−	0.451385i	−0.0987444	−	0.0156396i
$834$	9.60357	+	2.49879i	0.332545	+	0.0865259i
$835$	48.4387	−	21.9785i	1.67629	−	0.760597i
$836$	−0.0524454	+	0.00628234i	−0.00181386	+	0.000217279i
$837$	−4.29628	+	8.43191i	−0.148501	+	0.291450i
$838$	32.2297	−	18.9207i	1.11336	−	0.653605i
$839$	11.0621	−	34.0456i	0.381905	−	1.17538i	−0.556795	−	0.830650i	$-0.687969\pi$
$839$	11.0621	−	34.0456i	0.381905	−	1.17538i	0.938701	−	0.344734i	$-0.112031\pi$
$840$	−17.9823	−	6.31428i	−0.620447	−	0.217863i
$841$	−6.48573	−	19.9610i	−0.223646	−	0.688312i
$842$	19.0981	+	16.9469i	0.658163	+	0.584028i
$843$	2.52912	+	2.52912i	0.0871074	+	0.0871074i
$844$	−2.32734	+	4.16955i	−0.0801103	+	0.143522i
$845$	3.57644	+	1.34390i	0.123033	+	0.0462315i
$846$	2.43689	−	0.955762i	0.0837819	−	0.0328598i
$847$	5.14779	+	32.5018i	0.176880	+	1.11678i
$848$	2.65977	+	0.630624i	0.0913367	+	0.0216557i
$849$		−	21.0498i		−	0.722427i
$850$	6.00625	−	7.75065i	0.206013	−	0.265845i
$851$	5.64328			0.193449
$852$	−14.8926	−	11.7063i	−0.510211	−	0.401052i
$853$	11.8495	−	1.87678i	0.405721	−	0.0642598i	0.0497610	−	0.998761i	$-0.484154\pi$
$853$	11.8495	−	1.87678i	0.405721	−	0.0642598i	0.355960	+	0.934501i	$0.384154\pi$
$854$	46.3736	−	18.1880i	1.58687	−	0.622381i
$855$	−0.208683	−	0.00945573i	−0.00713680	−	0.000323379i
$856$	17.5229	+	32.6168i	0.598919	+	1.11482i
$857$	36.2767	−	36.2767i	1.23919	−	1.23919i	0.278856	−	0.960333i	$-0.410045\pi$
$857$	36.2767	−	36.2767i	1.23919	−	1.23919i	0.960333	−	0.278856i	$-0.0899551\pi$
$858$	0.891663	−	1.00485i	0.0304409	−	0.0343049i
$859$	19.8652	−	6.45461i	0.677793	−	0.220228i	0.0501644	−	0.998741i	$-0.484025\pi$
$859$	19.8652	−	6.45461i	0.677793	−	0.220228i	0.627629	+	0.778513i	$0.284025\pi$
$860$	−32.0463	−	13.4471i	−1.09277	−	0.458541i
$861$	27.1164	+	8.81065i	0.924124	+	0.300266i
$862$	48.1678	−	28.2773i	1.64060	−	0.963128i
$863$	−22.8038	−	11.6191i	−0.776249	−	0.395519i	0.0205299	−	0.999789i	$-0.493465\pi$
$863$	−22.8038	−	11.6191i	−0.776249	−	0.395519i	−0.796779	+	0.604270i	$0.793465\pi$
$864$	5.65612	+	0.0911230i	0.192425	+	0.00310007i
$865$	−31.2285	−	17.7362i	−1.06180	−	0.603048i
$866$	5.19663	−	19.9722i	0.176589	−	0.678682i
$867$	2.35857	−	14.8914i	0.0801012	−	0.505739i
$868$	19.6651	−	53.5370i	0.667478	−	1.81717i
$869$	−0.738837	+	0.536797i	−0.0250633	+	0.0182096i
$870$	−8.94991	+	0.128256i	−0.303430	+	0.00434830i
$871$	−29.2661	+	40.2813i	−0.991643	+	1.36488i
$872$	−42.2239	+	0.918534i	−1.42988	+	0.0311055i
$873$	−3.81996	+	1.94637i	−0.129286	+	0.0658745i
$874$	−0.452451	−	0.289183i	−0.0153044	−	0.00978176i
$875$	−19.2199	+	27.6712i	−0.649752	+	0.935457i
$876$	7.10810	+	15.3616i	0.240161	+	0.519022i
$877$	−19.1884	+	9.77699i	−0.647947	+	0.330145i	−0.746890	−	0.664948i	$-0.768454\pi$
$877$	−19.1884	+	9.77699i	−0.647947	+	0.330145i	0.0989430	+	0.995093i	$0.468454\pi$
$878$	−14.2226	−	6.20917i	−0.479991	−	0.209549i
$879$	−18.8289	−	13.6800i	−0.635082	−	0.461414i
$880$	0.305206	−	2.51005i	0.0102885	−	0.0846137i
$881$	12.0677	−	8.76768i	0.406570	−	0.295391i	−0.365642	−	0.930756i	$-0.619150\pi$
$881$	12.0677	−	8.76768i	0.406570	−	0.295391i	0.772212	+	0.635365i	$0.219150\pi$
$882$	−2.87388	+	0.632674i	−0.0967686	+	0.0213032i
$883$	3.93229	+	0.622813i	0.132332	+	0.0209593i	0.222249	−	0.974990i	$-0.428660\pi$
$883$	3.93229	+	0.622813i	0.132332	+	0.0209593i	−0.0899170	+	0.995949i	$0.528660\pi$
$884$	6.83451	−	6.33566i	0.229869	−	0.213091i
$885$	−5.91338	−	3.35850i	−0.198776	−	0.112895i
$886$	−6.44122	+	5.29378i	−0.216397	+	0.177848i
$887$	3.92853	−	7.71018i	0.131907	−	0.258883i	−0.815600	−	0.578616i	$-0.803593\pi$
$887$	3.92853	−	7.71018i	0.131907	−	0.258883i	0.947508	+	0.319733i	$0.103593\pi$
$888$	2.23873	−	3.22666i	0.0751268	−	0.108279i
$889$	13.4213	+	4.36085i	0.450136	+	0.146258i
$890$	3.29073	+	19.0097i	0.110306	+	0.637207i
$891$	0.0873587	+	0.268863i	0.00292663	+	0.00900723i
$892$	−3.82584	−	13.4925i	−0.128099	−	0.451764i
$893$	−0.122271	+	0.122271i	−0.00409164	+	0.00409164i
$894$	13.6427	−	0.814208i	0.456281	−	0.0272312i
$895$	−0.374522	+	8.26549i	−0.0125189	+	0.276285i
$896$	−33.9121	+	3.50915i	−1.13292	+	0.117232i
$897$	13.4891	−	2.13646i	0.450387	−	0.0713344i
$898$	6.73538	+	0.658582i	0.224762	+	0.0219772i
$899$		−	26.7860i		−	0.893364i
$900$	2.81638	−	9.59521i	0.0938792	−	0.319840i
$901$			0.947641i			0.0315705i
$902$	−0.368115	+	3.76475i	−0.0122569	+	0.125352i
$903$	−23.1293	+	3.66332i	−0.769695	+	0.121908i
$904$	29.5888	+	28.3289i	0.984110	+	0.942206i
$905$	50.5203	+	18.9837i	1.67935	+	0.631039i
$906$	−0.622079	−	10.4235i	−0.0206672	−	0.346296i
$907$	13.7535	−	13.7535i	0.456678	−	0.456678i	−0.440885	−	0.897563i	$-0.645336\pi$
$907$	13.7535	−	13.7535i	0.456678	−	0.456678i	0.897563	+	0.440885i	$0.145336\pi$
$908$	1.25434	+	4.42367i	0.0416268	+	0.146805i
$909$	0.509610	+	1.56842i	0.0169027	+	0.0520211i
$910$	−22.3155	+	22.9644i	−0.739753	+	0.761263i
$911$	17.2226	+	5.59595i	0.570609	+	0.185402i	0.580089	−	0.814553i	$-0.303018\pi$
$911$	17.2226	+	5.59595i	0.570609	+	0.185402i	−0.00948031	+	0.999955i	$0.503018\pi$
$912$	−0.344836	+	0.143977i	−0.0114187	+	0.00476755i
$913$	2.12059	−	4.16189i	0.0701812	−	0.137738i
$914$	21.1024	+	25.6764i	0.698005	+	0.849300i
$915$	10.7995	+	23.8011i	0.357020	+	0.786841i
$916$	11.2773	+	12.1652i	0.372612	+	0.401951i
$917$	51.2676	+	8.11999i	1.69300	+	0.268146i
$918$	0.421632	+	1.91524i	0.0139159	+	0.0632122i
$919$	9.62088	−	6.98998i	0.317364	−	0.230578i	−0.417686	−	0.908591i	$-0.637159\pi$
$919$	9.62088	−	6.98998i	0.317364	−	0.230578i	0.735050	+	0.678013i	$0.237159\pi$
$920$	18.5989	−	17.7436i	0.613186	−	0.584988i
$921$	23.6296	+	17.1679i	0.778623	+	0.565703i
$922$	1.60705	−	3.68110i	0.0529255	−	0.121230i
$923$	−28.3574	+	14.4488i	−0.933396	+	0.475589i
$924$	−0.715490	−	1.54628i	−0.0235379	−	0.0508688i
$925$	−4.44497	−	5.33289i	−0.146150	−	0.175344i
$926$	−27.2075	+	42.5683i	−0.894093	+	1.39888i
$927$	11.3121	−	5.76380i	0.371538	−	0.189308i
$928$	−14.3818	+	7.03841i	−0.472105	+	0.231047i
$929$	−7.42668	+	10.2220i	−0.243662	+	0.335371i	−0.913279	−	0.407335i	$-0.866458\pi$
$929$	−7.42668	+	10.2220i	−0.243662	+	0.335371i	0.669617	+	0.742706i	$0.266458\pi$
$930$	28.5907	+	8.83880i	0.937525	+	0.289836i
$931$	0.157266	−	0.114261i	0.00515419	−	0.00374474i
$932$	4.38061	+	1.60908i	0.143492	+	0.0527071i
$933$	3.01977	−	19.0661i	0.0988630	−	0.624196i
$934$	−19.8429	−	5.16298i	−0.649278	−	0.168938i
$935$	0.871111	−	0.0977972i	0.0284884	−	0.00319831i
$936$	4.12965	−	8.56020i	0.134982	−	0.279799i
$937$	28.6133	+	14.5792i	0.934755	+	0.476282i	0.853896	−	0.520444i	$-0.174234\pi$
$937$	28.6133	+	14.5792i	0.934755	+	0.476282i	0.0808594	+	0.996726i	$0.474234\pi$
$938$	31.9689	+	54.4561i	1.04382	+	1.77806i
$939$	−29.1448	−	9.46973i	−0.951105	−	0.309033i
$940$	−4.29253	−	7.07765i	−0.140007	−	0.230848i
$941$	9.55987	−	3.10619i	0.311643	−	0.101259i	−0.149020	−	0.988834i	$-0.547612\pi$
$941$	9.55987	−	3.10619i	0.311643	−	0.101259i	0.460663	+	0.887575i	$0.347612\pi$
$942$	16.0712	+	14.2609i	0.523627	+	0.464646i
$943$	−27.1918	+	27.1918i	−0.885486	+	0.885486i
$944$	−12.1303	−	0.920259i	−0.394809	−	0.0299519i
$945$	−1.79002	−	6.49614i	−0.0582294	−	0.211319i
$946$	−1.13439	−	2.89234i	−0.0368823	−	0.0940381i
$947$	−18.7753	+	2.97371i	−0.610114	+	0.0966326i	−0.453843	−	0.891082i	$-0.649947\pi$
$947$	−18.7753	+	2.97371i	−0.610114	+	0.0966326i	−0.156271	+	0.987714i	$0.549947\pi$
$948$	−3.99278	+	5.07954i	−0.129680	+	0.164976i
$949$	28.4387			0.923159
$950$	0.0830986	+	0.655343i	0.00269607	+	0.0212621i
$951$		−	24.8691i		−	0.806436i
$952$	−3.89597	−	11.1587i	−0.126269	−	0.361656i
$953$	2.20490	+	13.9212i	0.0714238	+	0.450952i	0.997319	+	0.0731724i	$0.0233123\pi$
$953$	2.20490	+	13.9212i	0.0714238	+	0.450952i	−0.925896	+	0.377780i	$0.876688\pi$
$954$	0.352873	+	0.899714i	0.0114247	+	0.0291293i
$955$	17.2946	−	21.6689i	0.559640	−	0.701189i
$956$	−2.58706	+	4.63484i	−0.0836714	+	0.149902i
$957$	−0.565812	−	0.565812i	−0.0182901	−	0.0182901i
$958$	−26.4111	+	29.7636i	−0.853303	+	0.961619i
$959$	1.19136	+	3.66664i	0.0384711	+	0.118402i
$960$	−2.76694	−	17.6733i	−0.0893025	−	0.570402i
$961$	−18.0945	+	55.6893i	−0.583695	+	1.79643i
$962$	−3.34048	−	5.69021i	−0.107701	−	0.183460i
$963$	−5.94300	+	11.6638i	−0.191511	+	0.375861i
$964$	6.14951	+	51.3365i	0.198062	+	1.65344i
$965$	38.5690	+	7.91314i	1.24158	+	0.254733i
$966$	4.36152	−	16.7626i	0.140330	−	0.539328i
$967$	−23.2805	−	3.68727i	−0.748651	−	0.118575i	−0.229561	−	0.973294i	$-0.573729\pi$
$967$	−23.2805	−	3.68727i	−0.748651	−	0.118575i	−0.519090	+	0.854720i	$0.673729\pi$
$968$	−24.5871	+	18.6939i	−0.790259	+	0.600844i
$969$	−0.0761465	−	0.104807i	−0.00244618	−	0.00336688i
$970$	8.12521	+	10.8529i	0.260885	+	0.348465i
$971$	3.05972	+	2.22302i	0.0981911	+	0.0713400i	0.635797	−	0.771856i	$-0.280671\pi$
$971$	3.05972	+	2.22302i	0.0981911	+	0.0713400i	−0.537606	+	0.843196i	$0.680671\pi$
$972$	1.11348	+	1.66137i	0.0357150	+	0.0532885i
$973$	−9.59956	−	18.8402i	−0.307748	−	0.603989i
$974$	4.32066	+	2.76154i	0.138443	+	0.0884856i
$975$	−12.6437	−	11.0644i	−0.404924	−	0.354344i
$976$	35.6380	+	30.2643i	1.14074	+	0.968735i
$977$	−26.1594	−	51.3408i	−0.836914	−	1.64254i	−0.764016	−	0.645197i	$-0.776775\pi$
$977$	−26.1594	−	51.3408i	−0.836914	−	1.64254i	−0.0728979	−	0.997339i	$-0.523225\pi$
$978$	2.95596	−	6.77088i	0.0945212	−	0.216509i
$979$	−1.01375	+	1.39530i	−0.0323995	+	0.0445941i
$980$	3.52152	+	8.61357i	0.112491	+	0.275150i
$981$	−8.77677	−	12.0802i	−0.280221	−	0.385691i
$982$	27.9267	−	6.14795i	0.891176	−	0.196189i
$983$	3.05428	−	19.2840i	0.0974165	−	0.615063i	−0.889883	−	0.456190i	$-0.849214\pi$
$983$	3.05428	−	19.2840i	0.0974165	−	0.615063i	0.987299	−	0.158873i	$-0.0507862\pi$
$984$	4.76027	+	26.3346i	0.151752	+	0.839516i
$985$	19.7603	+	21.6360i	0.629615	+	0.689380i
$986$	−3.52447	−	4.28841i	−0.112242	−	0.136571i
$987$	−4.96974	−	2.53221i	−0.158189	−	0.0806011i
$988$	−0.0237642	+	0.627392i	−0.000756039	+	0.0199600i
$989$	9.76005	−	30.0383i	0.310351	−	0.955163i
$990$	0.790638	−	0.417227i	0.0251281	−	0.0132603i
$991$	15.0537	−	4.89123i	0.478196	−	0.155375i	−0.0599944	−	0.998199i	$-0.519108\pi$
$991$	15.0537	−	4.89123i	0.478196	−	0.155375i	0.538190	+	0.842824i	$0.319108\pi$
$992$	53.0018	−	7.52158i	1.68281	−	0.238810i
$993$	−4.69025	−	4.69025i	−0.148841	−	0.148841i
$994$	2.40465	+	40.2919i	0.0762708	+	1.27798i
$995$	1.48116	−	0.976856i	0.0469561	−	0.0309684i
$996$	6.40119	−	32.4198i	0.202829	−	1.02726i
$997$	0.876456	+	5.53373i	0.0277577	+	0.175255i	0.997672	−	0.0681901i	$-0.0217224\pi$
$997$	0.876456	+	5.53373i	0.0277577	+	0.175255i	−0.969915	+	0.243445i	$0.921722\pi$
$998$	54.0086	+	5.28093i	1.70961	+	0.167165i
$999$	1.38849			0.0439298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bq.a.403.32	yes	480
8.3	odd	2	inner	600.2.bq.a.403.11	yes	480
25.17	odd	20	inner	600.2.bq.a.67.11	✓	480
200.67	even	20	inner	600.2.bq.a.67.32	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bq.a.67.11	✓	480	25.17	odd	20	inner
600.2.bq.a.67.32	yes	480	200.67	even	20	inner
600.2.bq.a.403.11	yes	480	8.3	odd	2	inner
600.2.bq.a.403.32	yes	480	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.137625 - 1.40750i) q^{2} +(-0.156434 - 0.987688i) q^{3} +(-1.96212 - 0.387414i) q^{4} +(-1.86666 + 1.23110i) q^{5} +(-1.41170 + 0.0842514i) q^{6} +(2.13082 + 2.13082i) q^{7} +(-0.815321 + 2.70837i) q^{8} +(-0.951057 + 0.309017i) q^{9} +O(q^{10})\)	\(q+(0.137625 - 1.40750i) q^{2} +(-0.156434 - 0.987688i) q^{3} +(-1.96212 - 0.387414i) q^{4} +(-1.86666 + 1.23110i) q^{5} +(-1.41170 + 0.0842514i) q^{6} +(2.13082 + 2.13082i) q^{7} +(-0.815321 + 2.70837i) q^{8} +(-0.951057 + 0.309017i) q^{9} +(1.47587 + 2.79675i) q^{10} +(-0.0873587 + 0.268863i) q^{11} +(-0.0757011 + 1.99857i) q^{12} +(2.99402 + 1.52553i) q^{13} +(3.29239 - 2.70588i) q^{14} +(1.50795 + 1.65109i) q^{15} +(3.69982 + 1.52030i) q^{16} +(-0.216929 + 1.36963i) q^{17} +(0.304053 + 1.38114i) q^{18} +(-0.0549118 - 0.0755796i) q^{19} +(4.13954 - 1.69239i) q^{20} +(1.77125 - 2.43792i) q^{21} +(0.366402 + 0.159960i) q^{22} +(1.84517 + 3.62135i) q^{23} +(2.80257 + 0.381601i) q^{24} +(1.96881 - 4.59606i) q^{25} +(2.55923 - 4.00413i) q^{26} +(0.453990 + 0.891007i) q^{27} +(-3.35542 - 5.00644i) q^{28} +(-2.28992 - 1.66373i) q^{29} +(2.53144 - 1.89521i) q^{30} +(5.56242 + 7.65602i) q^{31} +(2.64902 - 4.99827i) q^{32} +(0.279218 + 0.0442238i) q^{33} +(1.89790 + 0.493822i) q^{34} +(-6.60076 - 1.35427i) q^{35} +(1.98580 - 0.237876i) q^{36} +(0.630361 - 1.23715i) q^{37} +(-0.113936 + 0.0668868i) q^{38} +(1.03838 - 3.19580i) q^{39} +(-1.81233 - 6.05933i) q^{40} +(2.92379 + 8.99849i) q^{41} +(-3.18761 - 2.82856i) q^{42} +(-5.49497 - 5.49497i) q^{43} +(0.275569 - 0.493696i) q^{44} +(1.39487 - 1.74767i) q^{45} +(5.35099 - 2.09869i) q^{46} +(-0.289550 - 1.82814i) q^{47} +(0.922807 - 3.89210i) q^{48} +2.08080i q^{49} +(-6.19801 - 3.40363i) q^{50} +1.38671 q^{51} +(-5.28361 - 4.15319i) q^{52} +(0.674962 - 0.106904i) q^{53} +(1.31657 - 0.516368i) q^{54} +(-0.167927 - 0.609421i) q^{55} +(-7.50835 + 4.03374i) q^{56} +(-0.0660590 + 0.0660590i) q^{57} +(-2.65685 + 2.99410i) q^{58} +(-2.89245 + 0.939813i) q^{59} +(-2.31912 - 3.82383i) q^{60} +(11.1166 + 3.61199i) q^{61} +(11.5414 - 6.77546i) q^{62} +(-2.68499 - 1.36807i) q^{63} +(-6.67050 - 4.41638i) q^{64} +(-7.46687 + 0.838285i) q^{65} +(0.100672 - 0.386914i) q^{66} +(-2.31795 + 14.6350i) q^{67} +(0.956254 - 2.60334i) q^{68} +(3.28811 - 2.38895i) q^{69} +(-2.81456 + 9.10419i) q^{70} +(-5.56713 + 7.66249i) q^{71} +(-0.0615147 - 2.82776i) q^{72} +(7.54080 - 3.84223i) q^{73} +(-1.65454 - 1.05750i) q^{74} +(-4.84747 - 1.22559i) q^{75} +(0.0784629 + 0.169570i) q^{76} +(-0.759044 + 0.386752i) q^{77} +(-4.35519 - 1.90134i) q^{78} +(2.61351 + 1.89883i) q^{79} +(-8.77793 + 1.71695i) q^{80} +(0.809017 - 0.587785i) q^{81} +(13.0678 - 2.87682i) q^{82} +(-16.3194 - 2.58475i) q^{83} +(-4.41989 + 4.09728i) q^{84} +(-1.28122 - 2.82369i) q^{85} +(-8.49042 + 6.97793i) q^{86} +(-1.28502 + 2.52199i) q^{87} +(-0.656953 - 0.455809i) q^{88} +(5.80221 + 1.88525i) q^{89} +(-2.26788 - 2.20380i) q^{90} +(3.12909 + 9.63034i) q^{91} +(-2.21748 - 7.82036i) q^{92} +(6.69161 - 6.69161i) q^{93} +(-2.61296 + 0.155944i) q^{94} +(0.195547 + 0.0734795i) q^{95} +(-5.35113 - 1.83450i) q^{96} +(4.23446 - 0.670672i) q^{97} +(2.92873 + 0.286370i) q^{98} -0.282699i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 12 q^{8}+O(q^{10}) \) 480 * q + 12 * q^8	\( 480 q + 12 q^{8} - 8 q^{10} + 8 q^{12} - 8 q^{17} + 20 q^{20} + 28 q^{22} + 8 q^{25} - 4 q^{28} - 8 q^{30} - 20 q^{32} + 48 q^{35} + 20 q^{38} - 108 q^{40} - 20 q^{42} + 32 q^{43} - 140 q^{44} - 16 q^{48} + 124 q^{50} - 132 q^{52} + 152 q^{58} - 20 q^{60} + 116 q^{62} - 60 q^{64} + 8 q^{65} - 48 q^{67} - 72 q^{68} - 4 q^{70} - 12 q^{72} + 40 q^{73} + 24 q^{78} - 76 q^{80} + 120 q^{81} - 64 q^{82} - 80 q^{83} - 80 q^{84} - 132 q^{88} + 200 q^{89} - 48 q^{90} - 216 q^{92} - 40 q^{94} + 20 q^{96} - 56 q^{97} - 192 q^{98}+O(q^{100}) \) 480 * q + 12 * q^8 - 8 * q^10 + 8 * q^12 - 8 * q^17 + 20 * q^20 + 28 * q^22 + 8 * q^25 - 4 * q^28 - 8 * q^30 - 20 * q^32 + 48 * q^35 + 20 * q^38 - 108 * q^40 - 20 * q^42 + 32 * q^43 - 140 * q^44 - 16 * q^48 + 124 * q^50 - 132 * q^52 + 152 * q^58 - 20 * q^60 + 116 * q^62 - 60 * q^64 + 8 * q^65 - 48 * q^67 - 72 * q^68 - 4 * q^70 - 12 * q^72 + 40 * q^73 + 24 * q^78 - 76 * q^80 + 120 * q^81 - 64 * q^82 - 80 * q^83 - 80 * q^84 - 132 * q^88 + 200 * q^89 - 48 * q^90 - 216 * q^92 - 40 * q^94 + 20 * q^96 - 56 * q^97 - 192 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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