LMFDB - Embedded newform 900.2.bj.f.127.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.3
Character	$\chi$	$=$	900.127
Dual form			900.2.bj.f.163.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36070 + 0.385348i) q^{2} +(1.70301 - 1.04869i) q^{4} +(0.0577937 + 2.23532i) q^{5} +(-0.0211854 + 0.0211854i) q^{7} +(-1.91318 + 2.08320i) q^{8} +O(q^{10})$	\(q+(-1.36070 + 0.385348i) q^{2} +(1.70301 - 1.04869i) q^{4} +(0.0577937 + 2.23532i) q^{5} +(-0.0211854 + 0.0211854i) q^{7} +(-1.91318 + 2.08320i) q^{8} +(-0.940016 - 3.01933i) q^{10} +(1.52583 + 2.10012i) q^{11} +(3.59397 - 0.569229i) q^{13} +(0.0206633 - 0.0369908i) q^{14} +(1.80052 - 3.57185i) q^{16} +(1.43409 - 2.81456i) q^{17} +(1.41553 + 4.35657i) q^{19} +(2.44257 + 3.74618i) q^{20} +(-2.88547 - 2.26966i) q^{22} +(-5.82595 - 0.922739i) q^{23} +(-4.99332 + 0.258375i) q^{25} +(-4.67097 + 2.15948i) q^{26} +(-0.0138622 + 0.0582959i) q^{28} +(7.62028 + 2.47598i) q^{29} +(-1.76558 + 0.573671i) q^{31} +(-1.07356 + 5.55405i) q^{32} +(-0.866784 + 4.38240i) q^{34} +(-0.0485806 - 0.0461318i) q^{35} +(1.30788 + 8.25760i) q^{37} +(-3.60491 - 5.38251i) q^{38} +(-4.76719 - 4.15619i) q^{40} +(0.210898 + 0.153226i) q^{41} +(-1.26128 - 1.26128i) q^{43} +(4.80087 + 1.97642i) q^{44} +(8.28295 - 0.989443i) q^{46} +(-5.36731 - 10.5339i) q^{47} +6.99910i q^{49} +(6.69485 - 2.27574i) q^{50} +(5.52364 - 4.73835i) q^{52} +(1.61963 + 3.17871i) q^{53} +(-4.60626 + 3.53209i) q^{55} +(-0.00360186 - 0.0846651i) q^{56} +(-11.3230 - 0.432610i) q^{58} +(0.594783 + 0.432135i) q^{59} +(3.96742 - 2.88250i) q^{61} +(2.18136 - 1.46096i) q^{62} +(-0.679450 - 7.97109i) q^{64} +(1.48012 + 8.00078i) q^{65} +(-2.97451 - 1.51559i) q^{67} +(-0.509314 - 6.29715i) q^{68} +(0.0838805 + 0.0440512i) q^{70} +(10.8065 + 3.51125i) q^{71} +(-1.68398 + 10.6322i) q^{73} +(-4.96167 - 10.7321i) q^{74} +(6.97935 + 5.93485i) q^{76} +(-0.0768172 - 0.0121667i) q^{77} +(-4.55633 + 14.0229i) q^{79} +(8.08830 + 3.81830i) q^{80} +(-0.346014 - 0.127226i) q^{82} +(-5.86554 + 11.5118i) q^{83} +(6.37433 + 3.04299i) q^{85} +(2.20225 + 1.23019i) q^{86} +(-7.29416 - 0.839315i) q^{88} +(5.58568 + 7.68803i) q^{89} +(-0.0640804 + 0.0881991i) q^{91} +(-10.8893 + 4.53815i) q^{92} +(11.3625 + 12.2653i) q^{94} +(-9.65652 + 3.41596i) q^{95} +(5.72355 - 2.91630i) q^{97} +(-2.69709 - 9.52369i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8}+O(q^{10}) $ 240 * q - 12 * q^8	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{20}\right)$

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 $

$2$	−1.36070	+	0.385348i	−0.962161	+	0.272482i
$2$	−1.36070	+	0.385348i	−0.962161	+	0.272482i
$3$		0			0
$3$		0			0
$4$	1.70301	−	1.04869i	0.851507	−	0.524343i
$5$	0.0577937	+	2.23532i	0.0258461	+	0.999666i
$5$	0.0577937	+	2.23532i	0.0258461	+	0.999666i
$6$		0			0
$7$	−0.0211854	+	0.0211854i	−0.00800734	+	0.00800734i	−0.711099	−	0.703092i	$-0.751802\pi$
$7$	−0.0211854	+	0.0211854i	−0.00800734	+	0.00800734i	0.703092	+	0.711099i	$0.251802\pi$
$8$	−1.91318	+	2.08320i	−0.676413	+	0.736523i
$9$		0			0
$10$	−0.940016	−	3.01933i	−0.297259	−	0.954797i
$11$	1.52583	+	2.10012i	0.460054	+	0.633210i	0.974520	−	0.224301i	$-0.0720097\pi$
$11$	1.52583	+	2.10012i	0.460054	+	0.633210i	−0.514466	+	0.857511i	$0.672010\pi$
$12$		0			0
$13$	3.59397	−	0.569229i	0.996788	−	0.157876i	0.363336	−	0.931658i	$-0.381638\pi$
$13$	3.59397	−	0.569229i	0.996788	−	0.157876i	0.633452	+	0.773782i	$0.281638\pi$
$14$	0.0206633	−	0.0369908i	0.00552249	−	0.00988620i
$15$		0			0
$16$	1.80052	−	3.57185i	0.450129	−	0.892964i
$17$	1.43409	−	2.81456i	0.347818	−	0.682632i	−0.649132	−	0.760676i	$-0.724868\pi$
$17$	1.43409	−	2.81456i	0.347818	−	0.682632i	0.996950	+	0.0780444i	$0.0248676\pi$
$18$		0			0
$19$	1.41553	+	4.35657i	0.324746	+	0.999465i	0.971555	+	0.236813i	$0.0761030\pi$
$19$	1.41553	+	4.35657i	0.324746	+	0.999465i	−0.646809	+	0.762652i	$0.723897\pi$
$20$	2.44257	+	3.74618i	0.546176	+	0.837670i
$21$		0			0
$22$	−2.88547	−	2.26966i	−0.615185	−	0.483894i
$23$	−5.82595	−	0.922739i	−1.21479	−	0.192404i	−0.484040	−	0.875046i	$-0.660831\pi$
$23$	−5.82595	−	0.922739i	−1.21479	−	0.192404i	−0.730754	+	0.682641i	$0.760831\pi$
$24$		0			0
$25$	−4.99332	+	0.258375i	−0.998664	+	0.0516749i
$26$	−4.67097	+	2.15948i	−0.916052	+	0.423509i
$27$		0			0
$28$	−0.0138622	+	0.0582959i	−0.00261971	+	0.0110169i
$29$	7.62028	+	2.47598i	1.41505	+	0.459778i	0.914026	−	0.405655i	$-0.132957\pi$
$29$	7.62028	+	2.47598i	1.41505	+	0.459778i	0.501025	+	0.865433i	$0.332957\pi$
$30$		0			0
$31$	−1.76558	+	0.573671i	−0.317107	+	0.103034i	−0.463246	−	0.886230i	$-0.653315\pi$
$31$	−1.76558	+	0.573671i	−0.317107	+	0.103034i	0.146139	+	0.989264i	$0.453315\pi$
$32$	−1.07356	+	5.55405i	−0.189780	+	0.981827i
$33$		0			0
$34$	−0.866784	+	4.38240i	−0.148652	+	0.751576i
$35$	−0.0485806	−	0.0461318i	−0.00821162	−	0.00779770i
$36$		0			0
$37$	1.30788	+	8.25760i	0.215013	+	1.35754i	0.825002	+	0.565130i	$0.191174\pi$
$37$	1.30788	+	8.25760i	0.215013	+	1.35754i	−0.609988	+	0.792410i	$0.708826\pi$
$38$	−3.60491	−	5.38251i	−0.584794	−	0.873159i
$39$		0			0
$40$	−4.76719	−	4.15619i	−0.753759	−	0.657151i
$41$	0.210898	+	0.153226i	0.0329367	+	0.0239299i	0.604132	−	0.796884i	$-0.293520\pi$
$41$	0.210898	+	0.153226i	0.0329367	+	0.0239299i	−0.571195	+	0.820814i	$0.693520\pi$
$42$		0			0
$43$	−1.26128	−	1.26128i	−0.192343	−	0.192343i	0.604365	−	0.796708i	$-0.293427\pi$
$43$	−1.26128	−	1.26128i	−0.192343	−	0.192343i	−0.796708	+	0.604365i	$0.793427\pi$
$44$	4.80087	+	1.97642i	0.723759	+	0.297957i
$45$		0			0
$46$	8.28295	−	0.989443i	1.22125	−	0.145885i
$47$	−5.36731	−	10.5339i	−0.782903	−	1.53653i	−0.842737	−	0.538325i	$-0.819057\pi$
$47$	−5.36731	−	10.5339i	−0.782903	−	1.53653i	0.0598348	−	0.998208i	$-0.480943\pi$
$48$		0			0
$49$			6.99910i			0.999872i
$50$	6.69485	−	2.27574i	0.946795	−	0.321838i
$51$		0			0
$52$	5.52364	−	4.73835i	0.765991	−	0.657091i
$53$	1.61963	+	3.17871i	0.222474	+	0.436629i	0.975084	−	0.221837i	$-0.0712054\pi$
$53$	1.61963	+	3.17871i	0.222474	+	0.436629i	−0.752610	+	0.658466i	$0.771205\pi$
$54$		0			0
$55$	−4.60626	+	3.53209i	−0.621108	+	0.476267i
$56$	−0.00360186	−	0.0846651i	−0.000481319	−	0.0113139i
$57$		0			0
$58$	−11.3230	−	0.432610i	−1.48679	−	0.0568045i
$59$	0.594783	+	0.432135i	0.0774341	+	0.0562592i	0.625829	−	0.779960i	$-0.284761\pi$
$59$	0.594783	+	0.432135i	0.0774341	+	0.0562592i	−0.548395	+	0.836220i	$0.684761\pi$
$60$		0			0
$61$	3.96742	−	2.88250i	0.507976	−	0.369066i	−0.304079	−	0.952647i	$-0.598349\pi$
$61$	3.96742	−	2.88250i	0.507976	−	0.369066i	0.812055	+	0.583581i	$0.198349\pi$
$62$	2.18136	−	1.46096i	0.277033	−	0.185542i
$63$		0			0
$64$	−0.679450	−	7.97109i	−0.0849313	−	0.996387i
$65$	1.48012	+	8.00078i	0.183586	+	0.992375i
$66$		0			0
$67$	−2.97451	−	1.51559i	−0.363394	−	0.185158i	0.262754	−	0.964863i	$-0.415369\pi$
$67$	−2.97451	−	1.51559i	−0.363394	−	0.185158i	−0.626148	+	0.779705i	$0.715369\pi$
$68$	−0.509314	−	6.29715i	−0.0617634	−	0.763642i
$69$		0			0
$70$	0.0838805	+	0.0440512i	0.0100256	+	0.00526513i
$71$	10.8065	+	3.51125i	1.28250	+	0.416709i	0.869459	−	0.494005i	$-0.164468\pi$
$71$	10.8065	+	3.51125i	1.28250	+	0.416709i	0.413038	+	0.910714i	$0.364468\pi$
$72$		0			0
$73$	−1.68398	+	10.6322i	−0.197094	+	1.24441i	0.668520	+	0.743694i	$0.266928\pi$
$73$	−1.68398	+	10.6322i	−0.197094	+	1.24441i	−0.865614	+	0.500711i	$0.833072\pi$
$74$	−4.96167	−	10.7321i	−0.576783	−	1.24759i
$75$		0			0
$76$	6.97935	+	5.93485i	0.800586	+	0.680774i
$77$	−0.0768172	−	0.0121667i	−0.00875414	−	0.00138652i
$78$		0			0
$79$	−4.55633	+	14.0229i	−0.512627	+	1.57770i	0.274931	+	0.961464i	$0.411345\pi$
$79$	−4.55633	+	14.0229i	−0.512627	+	1.57770i	−0.787558	+	0.616240i	$0.788655\pi$
$80$	8.08830	+	3.81830i	0.904299	+	0.426899i
$81$		0			0
$82$	−0.346014	−	0.127226i	−0.0382108	−	0.0140498i
$83$	−5.86554	+	11.5118i	−0.643826	+	1.26358i	0.306366	+	0.951914i	$0.400887\pi$
$83$	−5.86554	+	11.5118i	−0.643826	+	1.26358i	−0.950192	+	0.311666i	$0.899113\pi$
$84$		0			0
$85$	6.37433	+	3.04299i	0.691393	+	0.330059i
$86$	2.20225	+	1.23019i	0.237474	+	0.132655i
$87$		0			0
$88$	−7.29416	−	0.839315i	−0.777560	−	0.0894713i
$89$	5.58568	+	7.68803i	0.592081	+	0.814930i	0.994955	−	0.100326i	$-0.0319886\pi$
$89$	5.58568	+	7.68803i	0.592081	+	0.814930i	−0.402874	+	0.915256i	$0.631989\pi$
$90$		0			0
$91$	−0.0640804	+	0.0881991i	−0.00671745	+	0.00924578i
$92$	−10.8893	+	4.53815i	−1.13529	+	0.473135i
$93$		0			0
$94$	11.3625	+	12.2653i	1.17196	+	1.26507i
$95$	−9.65652	+	3.41596i	−0.990738	+	0.350470i
$96$		0			0
$97$	5.72355	−	2.91630i	0.581139	−	0.296105i	−0.138602	−	0.990348i	$-0.544261\pi$
$97$	5.72355	−	2.91630i	0.581139	−	0.296105i	0.719740	+	0.694243i	$0.244261\pi$
$98$	−2.69709	−	9.52369i	−0.272447	−	0.962038i
$99$		0			0
$100$	−8.23274	+	5.67644i	−0.823274	+	0.567644i
$101$	−15.7080			−1.56301			−0.781505	−	0.623900i	$-0.785547\pi$
$101$	−15.7080			−1.56301			−0.781505	+	0.623900i	$0.785547\pi$
$102$		0			0
$103$	2.92604	−	1.49089i	0.288311	−	0.146902i	−0.303854	−	0.952719i	$-0.598273\pi$
$103$	2.92604	−	1.49089i	0.288311	−	0.146902i	0.592165	+	0.805817i	$0.298273\pi$
$104$	−5.69011	+	8.57600i	−0.557961	+	0.840946i
$105$		0			0
$106$	−3.42874	−	3.70115i	−0.333029	−	0.359487i
$107$	−8.49218	+	8.49218i	−0.820970	+	0.820970i	−0.986247	−	0.165277i	$-0.947148\pi$
$107$	−8.49218	+	8.49218i	−0.820970	+	0.820970i	0.165277	+	0.986247i	$0.447148\pi$
$108$		0			0
$109$	5.49608	−	7.56470i	0.526429	−	0.724567i	−0.460152	−	0.887840i	$-0.652205\pi$
$109$	5.49608	−	7.56470i	0.526429	−	0.724567i	0.986581	+	0.163273i	$0.0522051\pi$
$110$	4.90666	−	6.58113i	0.467832	−	0.627486i
$111$		0			0
$112$	0.0375266	+	0.113816i	0.00354593	+	0.0107546i
$113$	−1.12540	+	0.178245i	−0.105868	+	0.0167679i	−0.209144	−	0.977885i	$-0.567068\pi$
$113$	−1.12540	+	0.178245i	−0.105868	+	0.0167679i	0.103276	+	0.994653i	$0.467068\pi$
$114$		0			0
$115$	1.72592	−	13.0762i	0.160942	−	1.21936i
$116$	15.5740	−	3.77466i	1.44601	−	0.350468i
$117$		0			0
$118$	−0.975844	−	0.358808i	−0.0898337	−	0.0330310i
$119$	0.0292459	+	0.0900095i	0.00268096	+	0.00825116i
$120$		0			0
$121$	1.31683	−	4.05278i	0.119712	−	0.368434i
$122$	−4.28771	+	5.45106i	−0.388191	+	0.493515i
$123$		0			0
$124$	−2.40520	+	2.82851i	−0.215994	+	0.254008i
$125$	−0.866133	−	11.1467i	−0.0774693	−	0.996995i
$126$		0			0
$127$	−1.77224	+	11.1895i	−0.157261	+	0.992904i	0.775222	+	0.631689i	$0.217638\pi$
$127$	−1.77224	+	11.1895i	−0.157261	+	0.992904i	−0.932482	+	0.361215i	$0.882362\pi$
$128$	3.99617	+	10.5845i	0.353215	+	0.935542i
$129$		0			0
$130$	−5.09708	−	10.3163i	−0.447044	−	0.904800i
$131$	9.16360	−	2.97743i	0.800628	−	0.260140i	0.120004	−	0.992773i	$-0.461709\pi$
$131$	9.16360	−	2.97743i	0.800628	−	0.260140i	0.680623	+	0.732634i	$0.261709\pi$
$132$		0			0
$133$	−0.122284	−	0.0623070i	−0.0106034	−	0.00540270i
$134$	4.63144	+	0.916041i	0.400096	+	0.0791339i
$135$		0			0
$136$	3.11962	+	8.37228i	0.267505	+	0.717917i
$137$	−0.0445855	−	0.281502i	−0.00380919	−	0.0240503i	0.985711	−	0.168448i	$-0.0538755\pi$
$137$	−0.0445855	−	0.281502i	−0.00380919	−	0.0240503i	−0.989520	+	0.144398i	$0.953876\pi$
$138$		0			0
$139$	−5.57303	+	4.04904i	−0.472698	+	0.343435i	−0.798492	−	0.602006i	$-0.794368\pi$
$139$	−5.57303	+	4.04904i	−0.472698	+	0.343435i	0.325794	+	0.945441i	$0.394368\pi$
$140$	−0.131111	−	0.0276174i	−0.0110809	−	0.00233409i
$141$		0			0
$142$	−16.0575	−	0.613495i	−1.34751	−	0.0514833i
$143$	6.67923	+	6.67923i	0.558545	+	0.558545i
$144$		0			0
$145$	−5.09421	+	17.1769i	−0.423051	+	1.42646i
$146$	−1.80571	−	15.1162i	−0.149441	−	1.25102i
$147$		0			0
$148$	10.8870	+	12.6913i	0.894902	+	1.04321i
$149$			8.23987i			0.675036i	0.941319	+	0.337518i	$0.109587\pi$
$149$			8.23987i			0.675036i	−0.941319	+	0.337518i	$0.890413\pi$
$150$		0			0
$151$		−	22.2516i		−	1.81081i	−0.424548	−	0.905406i	$-0.639567\pi$
$151$		−	22.2516i		−	1.81081i	0.424548	−	0.905406i	$-0.360433\pi$
$152$	−11.7838	−	5.38608i	−0.955791	−	0.436868i
$153$		0			0
$154$	0.109214	−	0.0130462i	0.00880069	−	0.00105129i
$155$	−1.38438	−	3.91348i	−0.111196	−	0.314338i
$156$		0			0
$157$	5.82859	+	5.82859i	0.465172	+	0.465172i	0.900346	−	0.435174i	$-0.143313\pi$
$157$	5.82859	+	5.82859i	0.465172	+	0.465172i	−0.435174	+	0.900346i	$0.643313\pi$
$158$	0.796094	−	20.8368i	0.0633339	−	1.65769i
$159$		0			0
$160$	−12.4771	−	2.07876i	−0.986404	−	0.164340i
$161$	0.142974	−	0.103877i	0.0112679	−	0.00818662i
$162$		0			0
$163$	−3.20813	−	20.2553i	−0.251280	−	1.58652i	−0.714085	−	0.700059i	$-0.753157\pi$
$163$	−3.20813	−	20.2553i	−0.251280	−	1.58652i	0.462805	−	0.886460i	$-0.346843\pi$
$164$	0.519848	+	0.0397808i	0.0405933	+	0.00310636i
$165$		0			0
$166$	3.54521	−	17.9243i	0.275162	−	1.39120i
$167$	10.1310	+	5.16198i	0.783957	+	0.399446i	0.799677	−	0.600430i	$-0.205004\pi$
$167$	10.1310	+	5.16198i	0.783957	+	0.399446i	−0.0157198	+	0.999876i	$0.505004\pi$
$168$		0			0
$169$	0.228867	−	0.0743633i	0.0176051	−	0.00572025i
$170$	−9.84617	−	1.68427i	−0.755167	−	0.129177i
$171$		0			0
$172$	−3.47065	−	0.825288i	−0.264635	−	0.0629276i
$173$	3.10093	−	19.5785i	0.235759	−	1.48852i	−0.531429	−	0.847103i	$-0.678345\pi$
$173$	3.10093	−	19.5785i	0.235759	−	1.48852i	0.767188	−	0.641422i	$-0.221655\pi$
$174$		0			0
$175$	0.100312	−	0.111259i	0.00758286	−	0.00841042i
$176$	10.2486	−	1.66873i	0.772518	−	0.125785i
$177$		0			0
$178$	−10.5630	−	8.30868i	−0.791731	−	0.622762i
$179$	−4.56995	+	14.0649i	−0.341574	+	1.05126i	0.621818	+	0.783162i	$0.286394\pi$
$179$	−4.56995	+	14.0649i	−0.341574	+	1.05126i	−0.963392	+	0.268095i	$0.913606\pi$
$180$		0			0
$181$	−4.73402	−	14.5698i	−0.351877	−	1.08297i	−0.957798	−	0.287442i	$-0.907195\pi$
$181$	−4.73402	−	14.5698i	−0.351877	−	1.08297i	0.605921	−	0.795525i	$-0.292805\pi$
$182$	0.0532070	−	0.144706i	0.00394396	−	0.0107263i
$183$		0			0
$184$	13.0684	−	10.3712i	0.963412	−	0.764578i
$185$	−18.3828	+	3.40076i	−1.35153	+	0.250029i
$186$		0			0
$187$	8.09910	−	1.28277i	0.592265	−	0.0938055i
$188$	−20.1874	−	12.3108i	−1.47232	−	0.897859i
$189$		0			0
$190$	11.8233	−	8.36921i	0.857753	−	0.607166i
$191$	13.5147	−	18.6014i	0.977888	−	1.34595i	0.0399290	−	0.999203i	$-0.487287\pi$
$191$	13.5147	−	18.6014i	0.977888	−	1.34595i	0.937959	−	0.346745i	$-0.112713\pi$
$192$		0			0
$193$	8.41078	−	8.41078i	0.605421	−	0.605421i	−0.336325	−	0.941746i	$-0.609184\pi$
$193$	8.41078	−	8.41078i	0.605421	−	0.605421i	0.941746	+	0.336325i	$0.109184\pi$
$194$	−6.66426	+	6.17376i	−0.478466	+	0.443250i
$195$		0			0
$196$	7.33986	+	11.9196i	0.524276	+	0.851398i
$197$	13.3126	−	6.78313i	0.948486	−	0.483278i	0.0899021	−	0.995951i	$-0.471345\pi$
$197$	13.3126	−	6.78313i	0.948486	−	0.483278i	0.858584	+	0.512673i	$0.171345\pi$
$198$		0			0
$199$	−17.0769			−1.21055			−0.605276	−	0.796016i	$-0.706937\pi$
$199$	−17.0769			−1.21055			−0.605276	+	0.796016i	$0.706937\pi$
$200$	9.01490	−	10.8964i	0.637449	−	0.770492i
$201$		0			0
$202$	21.3740	−	6.05306i	1.50387	−	0.425892i
$203$	−0.213894	+	0.108984i	−0.0150124	+	0.00764919i
$204$		0			0
$205$	−0.330321	+	0.480279i	−0.0230706	+	0.0335442i
$206$	−3.40696	+	3.15620i	−0.237374	+	0.219903i
$207$		0			0
$208$	4.43780	−	13.8620i	0.307706	−	0.961160i
$209$	−6.98946	+	9.62017i	−0.483471	+	0.665441i
$210$		0			0
$211$	5.30779	+	7.30555i	0.365404	+	0.502935i	0.951644	−	0.307202i	$-0.0993927\pi$
$211$	5.30779	+	7.30555i	0.365404	+	0.502935i	−0.586241	+	0.810137i	$0.699393\pi$
$212$	6.09172	+	3.71490i	0.418381	+	0.255140i
$213$		0			0
$214$	8.28287	−	14.8278i	0.566205	−	1.01360i
$215$	2.74646	−	2.89225i	0.187307	−	0.197250i
$216$		0			0
$217$	0.0252511	−	0.0495580i	0.00171415	−	0.00336422i
$218$	−4.56348	+	12.4112i	−0.309078	+	0.840593i
$219$		0			0
$220$	−4.14048	+	10.8457i	−0.279151	+	0.731218i
$221$	3.55195	−	10.9318i	0.238930	−	0.735351i
$222$		0			0
$223$	9.74743	+	1.54384i	0.652736	+	0.103383i	0.474015	−	0.880517i	$-0.342804\pi$
$223$	9.74743	+	1.54384i	0.652736	+	0.103383i	0.178721	+	0.983900i	$0.442804\pi$
$224$	−0.0949211	−	0.140409i	−0.00634218	−	0.00938145i
$225$		0			0
$226$	1.46264	−	0.676207i	0.0972934	−	0.0449806i
$227$	3.93830	−	24.8654i	0.261394	−	1.65038i	−0.412067	−	0.911154i	$-0.635193\pi$
$227$	3.93830	−	24.8654i	0.261394	−	1.65038i	0.673461	−	0.739223i	$-0.264807\pi$
$228$		0			0
$229$	9.35273	+	3.03889i	0.618046	+	0.200815i	0.601272	−	0.799044i	$-0.294661\pi$
$229$	9.35273	+	3.03889i	0.618046	+	0.200815i	0.0167733	+	0.999859i	$0.494661\pi$
$230$	2.69042	+	18.4579i	0.177401	+	1.21708i
$231$		0			0
$232$	−19.7370	+	11.1376i	−1.29580	+	0.731218i
$233$	10.0980	+	5.14520i	0.661543	+	0.337073i	0.752320	−	0.658798i	$-0.228935\pi$
$233$	10.0980	+	5.14520i	0.661543	+	0.337073i	−0.0907764	+	0.995871i	$0.528935\pi$
$234$		0			0
$235$	23.2365	−	12.6065i	1.51578	−	0.822355i
$236$	1.46610	+	0.112192i	0.0954348	+	0.00730306i
$237$		0			0
$238$	−0.0744798	−	0.111206i	−0.00482781	−	0.00720843i
$239$	16.1051	−	11.7010i	1.04175	−	0.756877i	0.0711251	−	0.997467i	$-0.477341\pi$
$239$	16.1051	−	11.7010i	1.04175	−	0.756877i	0.970627	+	0.240590i	$0.0773410\pi$
$240$		0			0
$241$	−14.9844	−	10.8868i	−0.965232	−	0.701282i	−0.0108717	−	0.999941i	$-0.503461\pi$
$241$	−14.9844	−	10.8868i	−0.965232	−	0.701282i	−0.954360	+	0.298659i	$0.903461\pi$
$242$	−0.230080	+	6.02205i	−0.0147901	+	0.387112i
$243$		0			0
$244$	3.73374	−	9.06952i	0.239028	−	0.580616i
$245$	−15.6452	+	0.404504i	−0.999538	+	0.0258428i
$246$		0			0
$247$	7.56727	+	14.8516i	0.481494	+	0.944985i
$248$	2.18281	−	4.77559i	0.138608	−	0.303251i
$249$		0			0
$250$	5.47392	+	14.8336i	0.346201	+	0.938160i
$251$			11.5425i			0.728554i	0.931291	+	0.364277i	$0.118684\pi$
$251$			11.5425i			0.728554i	−0.931291	+	0.364277i	$0.881316\pi$
$252$		0			0
$253$	−6.95153	−	13.6431i	−0.437039	−	0.857737i
$254$	−1.90035	−	15.9084i	−0.119239	−	0.998184i
$255$		0			0
$256$	−9.51629	−	12.8624i	−0.594768	−	0.803897i
$257$	−7.29636	−	7.29636i	−0.455134	−	0.455134i	0.441920	−	0.897054i	$-0.354297\pi$
$257$	−7.29636	−	7.29636i	−0.455134	−	0.455134i	−0.897054	+	0.441920i	$0.854297\pi$
$258$		0			0
$259$	−0.202649	−	0.147233i	−0.0125920	−	0.00914860i
$260$	10.9110	+	12.0733i	0.676669	+	0.748752i
$261$		0			0
$262$	−11.3216	+	7.58257i	−0.699449	+	0.468453i
$263$	−1.98412	−	12.5273i	−0.122346	−	0.772464i	−0.970213	−	0.242254i	$-0.922113\pi$
$263$	−1.98412	−	12.5273i	−0.122346	−	0.772464i	0.847866	−	0.530210i	$-0.177887\pi$
$264$		0			0
$265$	−7.01183	+	3.80411i	−0.430733	+	0.233684i
$266$	0.190402	+	0.0376592i	0.0116743	+	0.00230903i
$267$		0			0
$268$	−6.65500	+	0.538257i	−0.406519	+	0.0328793i
$269$	18.1138	−	5.88553i	1.10442	−	0.358847i	0.300617	−	0.953745i	$-0.402808\pi$
$269$	18.1138	−	5.88553i	1.10442	−	0.358847i	0.803801	+	0.594898i	$0.202808\pi$
$270$		0			0
$271$	17.6810	+	5.74491i	1.07404	+	0.348978i	0.792062	−	0.610441i	$-0.209008\pi$
$271$	17.6810	+	5.74491i	1.07404	+	0.348978i	0.281983	+	0.959419i	$0.409008\pi$
$272$	−7.47110	−	10.1900i	−0.453002	−	0.617861i
$273$		0			0
$274$	0.169143	+	0.365859i	0.0102183	+	0.0221023i
$275$	−8.16156	−	10.0923i	−0.492161	−	0.608591i
$276$		0			0
$277$	−27.8230	−	4.40673i	−1.67172	−	0.264774i	−0.752521	−	0.658568i	$-0.771163\pi$
$277$	−27.8230	−	4.40673i	−1.67172	−	0.264774i	−0.919199	+	0.393793i	$0.871163\pi$
$278$	6.02294	−	7.65709i	0.361232	−	0.459242i
$279$		0			0
$280$	0.189046	−	0.0129444i	0.0112976	−	0.000773578i
$281$	−4.15266	−	12.7806i	−0.247727	−	0.762425i	−0.995176	−	0.0981057i	$-0.968722\pi$
$281$	−4.15266	−	12.7806i	−0.247727	−	0.762425i	0.747449	−	0.664319i	$-0.231278\pi$
$282$		0			0
$283$	4.92195	−	9.65986i	0.292579	−	0.574219i	−0.697192	−	0.716885i	$-0.745567\pi$
$283$	4.92195	−	9.65986i	0.292579	−	0.574219i	0.989771	+	0.142666i	$0.0455673\pi$
$284$	22.0858	−	5.35293i	1.31055	−	0.317638i
$285$		0			0
$286$	−11.6623	−	6.51461i	−0.689604	−	0.385217i
$287$	−0.00771411	+	0.00122180i	−0.000455350	+	7.21203e-5i
$288$		0			0
$289$	4.12720	+	5.68061i	0.242777	+	0.334153i
$290$	0.312622	−	25.3356i	0.0183578	−	1.48776i
$291$		0			0
$292$	8.28201	+	19.8728i	0.484668	+	1.16296i
$293$	−0.921753	+	0.921753i	−0.0538494	+	0.0538494i	−0.733519	−	0.679669i	$-0.762123\pi$
$293$	−0.921753	+	0.921753i	−0.0538494	+	0.0538494i	0.679669	+	0.733519i	$0.262123\pi$
$294$		0			0
$295$	−0.931586	+	1.35451i	−0.0542390	+	0.0788623i
$296$	−19.7044	−	13.0737i	−1.14530	−	0.759896i
$297$		0			0
$298$	−3.17521	−	11.2120i	−0.183935	−	0.649494i
$299$	−21.4635			−1.24127
$300$		0			0
$301$	0.0534413			0.00308030
$302$	8.57461	+	30.2778i	0.493413	+	1.74229i
$303$		0			0
$304$	18.1097	+	2.78798i	1.03866	+	0.159902i
$305$	6.67260	+	8.70187i	0.382072	+	0.498267i
$306$		0			0
$307$	−15.8559	+	15.8559i	−0.904945	+	0.904945i	−0.995859	−	0.0909141i	$-0.971021\pi$
$307$	−15.8559	+	15.8559i	−0.904945	+	0.904945i	0.0909141	+	0.995859i	$0.471021\pi$
$308$	−0.143580	+	0.0598372i	−0.00818122	+	0.00340954i
$309$		0			0
$310$	3.39178	+	4.79161i	0.192640	+	0.272145i
$311$	−10.3201	−	14.2044i	−0.585200	−	0.805458i	0.409054	−	0.912510i	$-0.365859\pi$
$311$	−10.3201	−	14.2044i	−0.585200	−	0.805458i	−0.994253	+	0.107052i	$0.965859\pi$
$312$		0			0
$313$	−12.9632	+	2.05317i	−0.732722	+	0.116052i	−0.511636	−	0.859202i	$-0.670960\pi$
$313$	−12.9632	+	2.05317i	−0.732722	+	0.116052i	−0.221086	+	0.975254i	$0.570960\pi$
$314$	−10.1770	−	5.68493i	−0.574321	−	0.320819i
$315$		0			0
$316$	6.94617	+	28.6594i	0.390752	+	1.61222i
$317$	3.09677	−	6.07775i	0.173932	−	0.341360i	−0.787540	−	0.616263i	$-0.788646\pi$
$317$	3.09677	−	6.07775i	0.173932	−	0.341360i	0.961472	+	0.274903i	$0.0886457\pi$
$318$		0			0
$319$	6.42738	+	19.7814i	0.359864	+	1.10755i
$320$	17.7787	−	1.97947i	0.993859	−	0.110656i
$321$		0			0
$322$	−0.154516	+	0.196439i	−0.00861084	+	0.0109471i
$323$	14.2918	+	2.26360i	0.795219	+	0.125950i
$324$		0			0
$325$	−17.7988	+	3.77093i	−0.987298	+	0.209174i
$326$	12.1706	+	26.3252i	0.674069	+	1.45802i
$327$		0			0
$328$	−0.722687	+	0.146192i	−0.0399037	+	0.00807212i
$329$	0.336875	+	0.109457i	0.0185725	+	0.00603457i
$330$		0			0
$331$	6.17995	−	2.00799i	0.339681	−	0.110369i	−0.134209	−	0.990953i	$-0.542849\pi$
$331$	6.17995	−	2.00799i	0.339681	−	0.110369i	0.473890	+	0.880584i	$0.342849\pi$
$332$	2.08313	+	25.7558i	0.114327	+	1.41353i
$333$		0			0
$334$	−15.7744	−	3.11997i	−0.863135	−	0.170717i
$335$	3.21591	−	6.73657i	0.175704	−	0.368058i
$336$		0			0
$337$	−4.19864	−	26.5091i	−0.228714	−	1.44405i	−0.788309	−	0.615279i	$-0.789043\pi$
$337$	−4.19864	−	26.5091i	−0.228714	−	1.44405i	0.559595	−	0.828766i	$-0.310957\pi$
$338$	−0.282763	+	0.189379i	−0.0153803	+	0.0103009i
$339$		0			0
$340$	14.0467	−	1.50242i	0.761790	−	0.0814800i
$341$	−3.89875	−	2.83261i	−0.211129	−	0.153394i
$342$		0			0
$343$	−0.296577	−	0.296577i	−0.0160136	−	0.0160136i
$344$	5.04054	−	0.214437i	0.271768	−	0.0115617i
$345$		0			0
$346$	3.32509	+	27.8354i	0.178758	+	1.49644i
$347$	5.17054	+	10.1478i	0.277569	+	0.544760i	0.987137	−	0.159877i	$-0.0511098\pi$
$347$	5.17054	+	10.1478i	0.277569	+	0.544760i	−0.709568	+	0.704637i	$0.751110\pi$
$348$		0			0
$349$			3.75104i			0.200789i	0.994948	+	0.100394i	$0.0320104\pi$
$349$			3.75104i			0.200789i	−0.994948	+	0.100394i	$0.967990\pi$
$350$	−0.0936208	+	0.190046i	−0.00500424	+	0.0101584i
$351$		0			0
$352$	−13.3022	+	6.21992i	−0.709012	+	0.331523i
$353$	13.7908	+	27.0659i	0.734008	+	1.44057i	0.891486	+	0.453049i	$0.149664\pi$
$353$	13.7908	+	27.0659i	0.734008	+	1.44057i	−0.157478	+	0.987522i	$0.550336\pi$
$354$		0			0
$355$	−7.22422	+	24.3590i	−0.383422	+	1.29284i
$356$	17.5748	+	7.23520i	0.931464	+	0.383465i
$357$		0			0
$358$	0.798474	−	20.8991i	0.0422007	−	1.10455i
$359$	−1.82816	−	1.32824i	−0.0964867	−	0.0701017i	0.538496	−	0.842628i	$-0.318993\pi$
$359$	−1.82816	−	1.32824i	−0.0964867	−	0.0701017i	−0.634983	+	0.772526i	$0.718993\pi$
$360$		0			0
$361$	−1.60462	+	1.16583i	−0.0844538	+	0.0613593i
$362$	12.0560	+	18.0009i	0.633652	+	0.946108i
$363$		0			0
$364$	−0.0166367	+	0.217405i	−0.000871999	+	0.0113951i
$365$	−23.8637	−	3.14975i	−1.24908	−	0.164866i
$366$		0			0
$367$	−22.5340	−	11.4816i	−1.17627	−	0.599337i	−0.247096	−	0.968991i	$-0.579476\pi$
$367$	−22.5340	−	11.4816i	−1.17627	−	0.599337i	−0.929169	+	0.369654i	$0.879476\pi$
$368$	−13.7856	+	19.1480i	−0.718624	+	0.998160i
$369$		0			0
$370$	23.7030	−	11.7112i	1.23226	−	0.608835i
$371$	−0.101655	−	0.0330297i	−0.00527766	−	0.00171481i
$372$		0			0
$373$	2.74365	−	17.3227i	0.142061	−	0.896935i	−0.808973	−	0.587846i	$-0.799976\pi$
$373$	2.74365	−	17.3227i	0.142061	−	0.896935i	0.951033	−	0.309089i	$-0.100024\pi$
$374$	−10.5261	+	4.86644i	−0.544294	+	0.251637i
$375$		0			0
$376$	32.2130	+	8.97219i	1.66126	+	0.462705i
$377$	28.7965	+	4.56091i	1.48309	+	0.234899i
$378$		0			0
$379$	7.30173	−	22.4724i	0.375065	−	1.15433i	−0.568371	−	0.822773i	$-0.692426\pi$
$379$	7.30173	−	22.4724i	0.375065	−	1.15433i	0.943435	−	0.331557i	$-0.107574\pi$
$380$	−12.8629	+	15.9441i	−0.659854	+	0.817914i
$381$		0			0
$382$	−11.2215	+	30.5188i	−0.574139	+	1.56148i
$383$	2.62572	−	5.15327i	0.134168	−	0.263320i	−0.814141	−	0.580667i	$-0.802792\pi$
$383$	2.62572	−	5.15327i	0.134168	−	0.263320i	0.948310	+	0.317347i	$0.102792\pi$
$384$		0			0
$385$	0.0227568	−	0.172414i	0.00115980	−	0.00878705i
$386$	−8.20348	+	14.6856i	−0.417546	+	0.747479i
$387$		0			0
$388$	6.68901	−	10.9687i	0.339583	−	0.556852i
$389$	−12.5726	−	17.3047i	−0.637456	−	0.877382i	0.361021	−	0.932558i	$-0.382428\pi$
$389$	−12.5726	−	17.3047i	−0.637456	−	0.877382i	−0.998477	+	0.0551754i	$0.982428\pi$
$390$		0			0
$391$	−10.9520	+	15.0742i	−0.553869	+	0.762335i
$392$	−14.5805	−	13.3906i	−0.736428	−	0.676326i
$393$		0			0
$394$	−15.5007	+	14.3598i	−0.780912	+	0.723436i
$395$	−31.6091	−	9.37442i	−1.59043	−	0.471678i
$396$		0			0
$397$	6.27013	−	3.19479i	0.314689	−	0.160342i	−0.289511	−	0.957175i	$-0.593493\pi$
$397$	6.27013	−	3.19479i	0.314689	−	0.160342i	0.604200	+	0.796833i	$0.293493\pi$
$398$	23.2366	−	6.58056i	1.16475	−	0.329854i
$399$		0			0
$400$	−8.06767	+	18.3006i	−0.403384	+	0.915031i
$401$	−30.8073			−1.53844			−0.769221	−	0.638983i	$-0.779355\pi$
$401$	−30.8073			−1.53844			−0.769221	+	0.638983i	$0.779355\pi$
$402$		0			0
$403$	−6.01889	+	3.06678i	−0.299822	+	0.152767i
$404$	−26.7510	+	16.4728i	−1.33091	+	0.819553i
$405$		0			0
$406$	0.249048	−	0.230718i	0.0123601	−	0.0114504i
$407$	−15.3464	+	15.3464i	−0.760691	+	0.760691i
$408$		0			0
$409$	−0.908588	+	1.25056i	−0.0449268	+	0.0618364i	−0.830889	−	0.556438i	$-0.812168\pi$
$409$	−0.908588	+	1.25056i	−0.0449268	+	0.0618364i	0.785963	+	0.618274i	$0.212168\pi$
$410$	0.264393	−	0.780805i	0.0130575	−	0.0385612i
$411$		0			0
$412$	3.41961	−	5.60751i	0.168472	−	0.276262i
$413$	−0.0217557	+	0.00344576i	−0.00107053	+	0.000169555i
$414$		0			0
$415$	−26.0715	−	12.4460i	−1.27980	−	0.610952i
$416$	−0.696806	+	20.5722i	−0.0341637	+	1.00863i
$417$		0			0
$418$	5.80346	−	15.7835i	0.283856	−	0.771998i
$419$	4.92418	+	15.1551i	0.240562	+	0.740373i	0.996335	+	0.0855393i	$0.0272613\pi$
$419$	4.92418	+	15.1551i	0.240562	+	0.740373i	−0.755773	+	0.654834i	$0.772739\pi$
$420$		0			0
$421$	0.995697	−	3.06444i	0.0485273	−	0.149352i	−0.923857	−	0.382739i	$-0.874981\pi$
$421$	0.995697	−	3.06444i	0.0485273	−	0.149352i	0.972384	+	0.233387i	$0.0749809\pi$
$422$	−10.0375	−	7.89533i	−0.488618	−	0.384338i
$423$		0			0
$424$	−9.72054	−	2.70743i	−0.472071	−	0.131485i
$425$	−6.43366	+	14.4245i	−0.312079	+	0.699693i
$426$		0			0
$427$	−0.0229845	+	0.145118i	−0.00111230	+	0.00702277i
$428$	−5.55667	+	23.3679i	−0.268592	+	1.12953i
$429$		0			0
$430$	−2.62259	+	4.99383i	−0.126473	+	0.240824i
$431$	−29.8166	+	9.68800i	−1.43621	+	0.466654i	−0.920715	−	0.390235i	$-0.872394\pi$
$431$	−29.8166	+	9.68800i	−1.43621	+	0.466654i	−0.515499	+	0.856890i	$0.672394\pi$
$432$		0			0
$433$	25.0873	+	12.7826i	1.20562	+	0.614293i	0.937127	−	0.348990i	$-0.113475\pi$
$433$	25.0873	+	12.7826i	1.20562	+	0.614293i	0.268491	+	0.963282i	$0.413475\pi$
$434$	−0.0152621	+	0.0771640i	−0.000732603	+	0.00370399i
$435$		0			0
$436$	1.42690	−	18.6465i	0.0683362	−	0.893003i
$437$	−4.22685	−	26.6873i	−0.202198	−	1.27663i
$438$		0			0
$439$	25.3167	−	18.3936i	1.20830	−	0.877881i	0.213224	−	0.977003i	$-0.431604\pi$
$439$	25.3167	−	18.3936i	1.20830	−	0.877881i	0.995075	+	0.0991225i	$0.0316036\pi$
$440$	1.45458	−	16.3533i	0.0693445	−	0.779613i
$441$		0			0
$442$	−0.620606	+	16.2436i	−0.0295192	+	0.772630i
$443$	27.6411	+	27.6411i	1.31327	+	1.31327i	0.918991	+	0.394278i	$0.129005\pi$
$443$	27.6411	+	27.6411i	1.31327	+	1.31327i	0.394278	+	0.918991i	$0.370995\pi$
$444$		0			0
$445$	−16.8624	+	12.9301i	−0.799354	+	0.612946i
$446$	−13.8583	+	1.65544i	−0.656207	+	0.0783875i
$447$		0			0
$448$	0.183265	+	0.154477i	0.00865848	+	0.00729833i
$449$			32.7243i			1.54436i	0.635406	+	0.772178i	$0.280833\pi$
$449$			32.7243i			1.54436i	−0.635406	+	0.772178i	$0.719167\pi$
$450$		0			0
$451$			0.676707i			0.0318649i
$452$	−1.72964	+	1.48374i	−0.0813555	+	0.0697893i
$453$		0			0
$454$	4.22299	+	35.3520i	0.198195	+	1.65915i
$455$	−0.200857	−	0.138143i	−0.00941631	−	0.00647624i
$456$		0			0
$457$	7.11038	+	7.11038i	0.332610	+	0.332610i	0.853577	−	0.520967i	$-0.174429\pi$
$457$	7.11038	+	7.11038i	0.332610	+	0.332610i	−0.520967	+	0.853577i	$0.674429\pi$
$458$	−13.8973	−	0.530962i	−0.649378	−	0.0248102i
$459$		0			0
$460$	−10.7736	−	24.0789i	−0.502320	−	1.12268i
$461$	20.0752	−	14.5855i	0.934994	−	0.679313i	−0.0122168	−	0.999925i	$-0.503889\pi$
$461$	20.0752	−	14.5855i	0.934994	−	0.679313i	0.947210	+	0.320613i	$0.103889\pi$
$462$		0			0
$463$	4.64024	+	29.2973i	0.215650	+	1.36156i	0.823413	+	0.567443i	$0.192067\pi$
$463$	4.64024	+	29.2973i	0.215650	+	1.36156i	−0.607763	+	0.794119i	$0.707933\pi$
$464$	22.5643	−	22.7605i	1.04752	−	1.05663i
$465$		0			0
$466$	−15.7231	−	3.10983i	−0.728358	−	0.144060i
$467$	35.6038	+	18.1410i	1.64755	+	0.839468i	0.996779	+	0.0801913i	$0.0255531\pi$
$467$	35.6038	+	18.1410i	1.64755	+	0.839468i	0.650768	+	0.759276i	$0.274447\pi$
$468$		0			0
$469$	0.0951245	−	0.0309078i	0.00439244	−	0.00142719i
$470$	−26.7601	+	26.1078i	−1.23435	+	1.20426i
$471$		0			0
$472$	−2.03815	+	0.412298i	−0.0938136	+	0.0189776i
$473$	0.724343	−	4.57332i	0.0333053	−	0.210281i
$474$		0			0
$475$	−8.19384	−	21.3880i	−0.375959	−	0.981349i
$476$	0.144198	+	0.122618i	0.00660930	+	0.00562018i
$477$		0			0
$478$	−17.4052	+	22.1277i	−0.796098	+	1.01210i
$479$	1.67227	−	5.14672i	0.0764080	−	0.235160i	−0.905556	−	0.424226i	$-0.860546\pi$
$479$	1.67227	−	5.14672i	0.0764080	−	0.235160i	0.981964	+	0.189067i	$0.0605462\pi$
$480$		0			0
$481$	9.40093	+	28.9331i	0.428645	+	1.31923i
$482$	24.5845	+	9.03949i	1.11979	+	0.411738i
$483$		0			0
$484$	−2.00751	−	8.28287i	−0.0912507	−	0.376494i
$485$	6.84964	+	12.6254i	0.311026	+	0.573291i
$486$		0			0
$487$	33.8274	−	5.35774i	1.53287	−	0.242782i	0.667763	−	0.744374i	$-0.267252\pi$
$487$	33.8274	−	5.35774i	1.53287	−	0.242782i	0.865105	+	0.501591i	$0.167252\pi$
$488$	−1.58558	+	13.7797i	−0.0717759	+	0.623777i
$489$		0			0
$490$	21.1326	−	6.57927i	0.954674	−	0.297221i
$491$	8.94325	−	12.3093i	0.403603	−	0.555512i	−0.558041	−	0.829814i	$-0.688447\pi$
$491$	8.94325	−	12.3093i	0.403603	−	0.555512i	0.961644	+	0.274302i	$0.0884467\pi$
$492$		0			0
$493$	17.8970	−	17.8970i	0.806040	−	0.806040i
$494$	−16.0198	−	17.2926i	−0.720766	−	0.778030i
$495$		0			0
$496$	−1.12988	+	7.33929i	−0.0507332	+	0.329544i
$497$	−0.303328	+	0.154553i	−0.0136061	+	0.00693266i
$498$		0			0
$499$	2.90097			0.129865			0.0649327	−	0.997890i	$-0.479317\pi$
$499$	2.90097			0.129865			0.0649327	+	0.997890i	$0.479317\pi$
$500$	−13.1645	−	18.0748i	−0.588733	−	0.808328i
$501$		0			0
$502$	−4.44786	−	15.7058i	−0.198518	−	0.700986i
$503$	−7.33460	+	3.73716i	−0.327034	+	0.166632i	−0.609797	−	0.792558i	$-0.708749\pi$
$503$	−7.33460	+	3.73716i	−0.327034	+	0.166632i	0.282763	+	0.959190i	$0.408749\pi$
$504$		0			0
$505$	−0.907825	−	35.1125i	−0.0403977	−	1.56249i
$506$	14.7163	+	15.8855i	0.654219	+	0.706195i
$507$		0			0
$508$	8.71609	+	20.9143i	0.386714	+	0.927924i
$509$	−3.84108	+	5.28680i	−0.170253	+	0.234333i	−0.885614	−	0.464422i	$-0.846262\pi$
$509$	−3.84108	+	5.28680i	−0.170253	+	0.234333i	0.715361	+	0.698755i	$0.246262\pi$
$510$		0			0
$511$	−0.189572	−	0.260923i	−0.00838617	−	0.0115426i
$512$	17.9053	+	13.8347i	0.791310	+	0.611415i
$513$		0			0
$514$	12.7398	+	7.11653i	0.561928	+	0.313897i
$515$	3.50173	+	6.45448i	0.154305	+	0.284418i
$516$		0			0
$517$	13.9330	−	27.3450i	0.612771	−	1.20263i
$518$	0.332480	+	0.122250i	0.0146083	+	0.00537134i
$519$		0			0
$520$	−19.4990	−	12.2236i	−0.855086	−	0.536040i
$521$	5.29421	−	16.2939i	0.231944	−	0.713849i	−0.765569	−	0.643354i	$-0.777542\pi$
$521$	5.29421	−	16.2939i	0.231944	−	0.713849i	0.997512	−	0.0704945i	$-0.0224577\pi$
$522$		0			0
$523$	−6.28174	−	0.994930i	−0.274681	−	0.0435053i	0.0175740	−	0.999846i	$-0.494406\pi$
$523$	−6.28174	−	0.994930i	−0.274681	−	0.0435053i	−0.292255	+	0.956340i	$0.594406\pi$
$524$	12.4833	−	14.6804i	0.545338	−	0.641314i
$525$		0			0
$526$	7.52715	+	16.2813i	0.328199	+	0.709898i
$527$	−0.917367	+	5.79203i	−0.0399611	+	0.252305i
$528$		0			0
$529$	11.2159	+	3.64427i	0.487648	+	0.158447i
$530$	8.07509	−	7.87824i	0.350760	−	0.342209i
$531$		0			0
$532$	−0.273593	+	0.0221282i	−0.0118617	+	0.000959379i
$533$	0.845180	+	0.430641i	0.0366088	+	0.0186531i
$534$		0			0
$535$	−19.4735	−	18.4919i	−0.841914	−	0.799477i
$536$	8.84805	−	3.29690i	0.382177	−	0.142404i
$537$		0			0
$538$	−22.3795	+	14.9886i	−0.964848	+	0.646203i
$539$	−14.6990	+	10.6794i	−0.633129	+	0.459995i
$540$		0			0
$541$	−22.6575	−	16.4616i	−0.974122	−	0.707741i	−0.0177348	−	0.999843i	$-0.505645\pi$
$541$	−22.6575	−	16.4616i	−0.974122	−	0.707741i	−0.956387	+	0.292102i	$0.905645\pi$
$542$	−26.2723	−	1.00377i	−1.12849	−	0.0431154i
$543$		0			0
$544$	14.0926	+	10.9866i	0.604217	+	0.471047i
$545$	17.2272	+	11.8483i	0.737931	+	0.507526i
$546$		0			0
$547$	−1.24110	−	2.43580i	−0.0530657	−	0.104147i	0.862951	−	0.505288i	$-0.168614\pi$
$547$	−1.24110	−	2.43580i	−0.0530657	−	0.104147i	−0.916016	+	0.401141i	$0.868614\pi$
$548$	−0.371136	−	0.432645i	−0.0158542	−	0.0184817i
$549$		0			0
$550$	14.9945	+	10.5876i	0.639368	+	0.451458i
$551$			36.7031i			1.56361i
$552$		0			0
$553$	−0.200554	−	0.393610i	−0.00852843	−	0.0167380i
$554$	39.5569	−	4.72528i	1.68061	−	0.200758i
$555$		0			0
$556$	−5.24477	+	12.7399i	−0.222428	+	0.540294i
$557$	−14.0130	−	14.0130i	−0.593751	−	0.593751i	0.344891	−	0.938643i	$-0.387916\pi$
$557$	−14.0130	−	14.0130i	−0.593751	−	0.593751i	−0.938643	+	0.344891i	$0.887916\pi$
$558$		0			0
$559$	−5.25094	−	3.81503i	−0.222091	−	0.161359i
$560$	−0.252246	+	0.0904618i	−0.0106594	+	0.00382271i
$561$		0			0
$562$	10.5755	+	15.7903i	0.446100	+	0.666074i
$563$	−2.73526	−	17.2697i	−0.115277	−	0.727832i	−0.975840	−	0.218487i	$-0.929888\pi$
$563$	−2.73526	−	17.2697i	−0.115277	−	0.727832i	0.860562	−	0.509345i	$-0.170112\pi$
$564$		0			0
$565$	−0.463476	−	2.50532i	−0.0194986	−	0.105400i
$566$	−2.97489	+	15.0408i	−0.125044	+	0.632214i
$567$		0			0
$568$	−27.9895	+	15.7945i	−1.17441	+	0.662721i
$569$	−27.6880	+	8.99636i	−1.16074	+	0.377147i	−0.825179	−	0.564871i	$-0.808926\pi$
$569$	−27.6880	+	8.99636i	−1.16074	+	0.377147i	−0.335561	+	0.942019i	$0.608926\pi$
$570$		0			0
$571$	1.78586	+	0.580261i	0.0747358	+	0.0242831i	0.346146	−	0.938181i	$-0.387490\pi$
$571$	1.78586	+	0.580261i	0.0747358	+	0.0242831i	−0.271410	+	0.962464i	$0.587490\pi$
$572$	18.3792	+	4.37041i	0.768474	+	0.182736i
$573$		0			0
$574$	0.0100258	−	0.00463511i	0.000418468	−	0.000193466i
$575$	29.3292	+	3.10226i	1.22311	+	0.129373i
$576$		0			0
$577$	25.2103	+	3.99292i	1.04952	+	0.166227i	0.657288	−	0.753639i	$-0.271703\pi$
$577$	25.2103	+	3.99292i	1.04952	+	0.166227i	0.392231	+	0.919867i	$0.371703\pi$
$578$	−7.80490	−	6.13920i	−0.324641	−	0.255357i
$579$		0			0
$580$	9.33764	+	34.5947i	0.387725	+	1.43647i
$581$	−0.119618	−	0.368145i	−0.00496258	−	0.0152732i
$582$		0			0
$583$	−4.20439	+	8.25158i	−0.174128	+	0.341746i
$584$	−18.9273	−	23.8494i	−0.783215	−	0.986896i
$585$		0			0
$586$	0.899035	−	1.60943i	0.0371388	−	0.0664848i
$587$	13.7586	−	2.17915i	0.567879	−	0.0899432i	0.134109	−	0.990967i	$-0.457183\pi$
$587$	13.7586	−	2.17915i	0.567879	−	0.0899432i	0.433771	+	0.901023i	$0.357183\pi$
$588$		0			0
$589$	−4.99848	−	6.87981i	−0.205959	−	0.283478i
$590$	0.745654	−	2.20206i	0.0306981	−	0.0906574i
$591$		0			0
$592$	31.8498	+	10.1964i	1.30902	+	0.419069i
$593$	30.4927	−	30.4927i	1.25219	−	1.25219i	0.297448	−	0.954738i	$-0.403864\pi$
$593$	30.4927	−	30.4927i	1.25219	−	1.25219i	0.954738	−	0.297448i	$-0.0961356\pi$
$594$		0			0
$595$	−0.199510	+	0.0705759i	−0.00817911	+	0.00289333i
$596$	8.64104	+	14.0326i	0.353951	+	0.574798i
$597$		0			0
$598$	29.2054	−	8.27092i	1.19430	−	0.338223i
$599$	−20.9517			−0.856063			−0.428032	−	0.903764i	$-0.640793\pi$
$599$	−20.9517			−0.856063			−0.428032	+	0.903764i	$0.640793\pi$
$600$		0			0
$601$	−34.4158			−1.40385			−0.701925	−	0.712251i	$-0.747676\pi$
$601$	−34.4158			−1.40385			−0.701925	+	0.712251i	$0.747676\pi$
$602$	−0.0727176	+	0.0205935i	−0.00296375	+	0.000839327i
$603$		0			0
$604$	−23.3350	−	37.8948i	−0.949486	−	1.54192i
$605$	9.13536	+	2.70931i	0.371405	+	0.110149i
$606$		0			0
$607$	30.1682	−	30.1682i	1.22449	−	1.22449i	0.258469	−	0.966020i	$-0.416782\pi$
$607$	30.1682	−	30.1682i	1.22449	−	1.22449i	0.966020	−	0.258469i	$-0.0832180\pi$
$608$	−25.7163	+	3.18493i	−1.04293	+	0.129166i
$609$		0			0
$610$	−12.4327	−	9.26937i	−0.503384	−	0.375306i
$611$	−25.2862	−	34.8034i	−1.02297	−	1.40800i
$612$		0			0
$613$	−32.0453	+	5.07547i	−1.29430	+	0.204996i	−0.765326	−	0.643643i	$-0.777422\pi$
$613$	−32.0453	+	5.07547i	−1.29430	+	0.204996i	−0.528971	+	0.848640i	$0.677422\pi$
$614$	15.4651	−	27.6852i	0.624121	−	1.11728i
$615$		0			0
$616$	0.172311	−	0.136749i	0.00694261	−	0.00550976i
$617$	−5.54357	+	10.8799i	−0.223176	+	0.438007i	−0.975260	−	0.221060i	$-0.929048\pi$
$617$	−5.54357	+	10.8799i	−0.223176	+	0.438007i	0.752085	+	0.659067i	$0.229048\pi$
$618$		0			0
$619$	−2.03053	−	6.24934i	−0.0816140	−	0.251182i	0.901921	−	0.431902i	$-0.142157\pi$
$619$	−2.03053	−	6.24934i	−0.0816140	−	0.251182i	−0.983535	+	0.180720i	$0.942157\pi$
$620$	−6.46163	−	5.21293i	−0.259505	−	0.209356i
$621$		0			0
$622$	19.5162	+	15.3511i	0.782529	+	0.615524i
$623$	−0.281209	−	0.0445392i	−0.0112664	−	0.00178442i
$624$		0			0
$625$	24.8665	−	2.58030i	0.994659	−	0.103212i
$626$	16.8478	−	7.78908i	0.673375	−	0.311314i
$627$		0			0
$628$	16.0385	+	3.81381i	0.640007	+	0.152188i
$629$	25.1171	+	8.16105i	1.00149	+	0.325402i
$630$		0			0
$631$	12.7502	−	4.14278i	0.507576	−	0.164921i	−0.0440238	−	0.999030i	$-0.514018\pi$
$631$	12.7502	−	4.14278i	0.507576	−	0.164921i	0.551599	+	0.834109i	$0.314018\pi$
$632$	−20.4955	−	36.3202i	−0.815267	−	1.44474i
$633$		0			0
$634$	−1.87173	+	9.46333i	−0.0743358	+	0.375837i
$635$	−25.1145	−	3.31484i	−0.996637	−	0.131545i
$636$		0			0
$637$	3.98409	+	25.1546i	0.157855	+	0.996660i
$638$	−16.3685	−	24.4398i	−0.648034	−	0.967583i
$639$		0			0
$640$	−23.4287	+	9.54444i	−0.926100	+	0.377277i
$641$	5.26652	+	3.82635i	0.208015	+	0.151132i	0.686915	−	0.726738i	$-0.258964\pi$
$641$	5.26652	+	3.82635i	0.208015	+	0.151132i	−0.478900	+	0.877869i	$0.658964\pi$
$642$		0			0
$643$	24.1498	+	24.1498i	0.952377	+	0.952377i	0.998916	−	0.0465397i	$-0.0148194\pi$
$643$	24.1498	+	24.1498i	0.952377	+	0.952377i	−0.0465397	+	0.998916i	$0.514819\pi$
$644$	0.134553	−	0.326838i	0.00530211	−	0.0128792i
$645$		0			0
$646$	−20.3192	+	2.42724i	−0.799448	+	0.0954984i
$647$	16.9157	+	33.1990i	0.665026	+	1.30519i	0.939155	+	0.343494i	$0.111611\pi$
$647$	16.9157	+	33.1990i	0.665026	+	1.30519i	−0.274129	+	0.961693i	$0.588389\pi$
$648$		0			0
$649$			1.90848i			0.0749144i
$650$	22.7657	−	11.9898i	0.892944	−	0.470280i
$651$		0			0
$652$	−26.7050	−	31.1308i	−1.04585	−	1.21918i
$653$	−1.60583	−	3.15162i	−0.0628409	−	0.123332i	0.857450	−	0.514568i	$-0.172048\pi$
$653$	−1.60583	−	3.15162i	−0.0628409	−	0.123332i	−0.920290	+	0.391236i	$0.872048\pi$
$654$		0			0
$655$	7.18512	+	20.3115i	0.280746	+	0.793636i
$656$	0.927026	−	0.477410i	0.0361943	−	0.0186397i
$657$		0			0
$658$	−0.500565	−	0.0191247i	−0.0195140	−	0.000745557i
$659$	−0.360535	−	0.261944i	−0.0140445	−	0.0102039i	0.580741	−	0.814088i	$-0.302763\pi$
$659$	−0.360535	−	0.261944i	−0.0140445	−	0.0102039i	−0.594785	+	0.803885i	$0.702763\pi$
$660$		0			0
$661$	12.6735	−	9.20784i	0.492942	−	0.358144i	−0.313372	−	0.949630i	$-0.601459\pi$
$661$	12.6735	−	9.20784i	0.492942	−	0.358144i	0.806315	+	0.591487i	$0.201459\pi$
$662$	−7.63529	+	5.11370i	−0.296754	+	0.198750i
$663$		0			0
$664$	−12.7595	−	34.2432i	−0.495163	−	1.32889i
$665$	0.132209	−	0.276946i	0.00512684	−	0.0107395i
$666$		0			0
$667$	−42.1107	−	21.4565i	−1.63053	−	0.830798i
$668$	22.6665	−	1.83327i	0.876992	−	0.0709312i
$669$		0			0
$670$	−1.77998	+	10.4057i	−0.0687665	+	0.402007i
$671$	12.1072	+	3.93387i	0.467393	+	0.151865i
$672$		0			0
$673$	−5.14603	+	32.4907i	−0.198365	+	1.25243i	0.664614	+	0.747187i	$0.268596\pi$
$673$	−5.14603	+	32.4907i	−0.198365	+	1.25243i	−0.862979	+	0.505240i	$0.831404\pi$
$674$	15.9283	+	34.4531i	0.613536	+	1.32708i
$675$		0			0
$676$	0.311779	−	0.366651i	0.0119915	−	0.0141020i
$677$	−9.54108	−	1.51116i	−0.366693	−	0.0580785i	−0.0296312	−	0.999561i	$-0.509433\pi$
$677$	−9.54108	−	1.51116i	−0.366693	−	0.0580785i	−0.337062	+	0.941482i	$0.609433\pi$
$678$		0			0
$679$	−0.0594729	+	0.183039i	−0.00228236	+	0.00702439i
$680$	−18.5344	+	7.45721i	−0.710763	+	0.285971i
$681$		0			0
$682$	6.39657	+	2.35196i	0.244937	+	0.0900611i
$683$	0.657454	−	1.29033i	0.0251568	−	0.0493729i	−0.878086	−	0.478503i	$-0.841180\pi$
$683$	0.657454	−	1.29033i	0.0251568	−	0.0493729i	0.903243	+	0.429130i	$0.141180\pi$
$684$		0			0
$685$	0.626670	−	0.115932i	0.0239438	−	0.00442953i
$686$	0.517838	+	0.289267i	0.0197711	+	0.0110443i
$687$		0			0
$688$	−6.77604	+	2.23415i	−0.258334	+	0.0851760i
$689$	7.63032	+	10.5022i	0.290692	+	0.400103i
$690$		0			0
$691$	−8.30255	+	11.4275i	−0.315844	+	0.434722i	−0.937193	−	0.348812i	$-0.886585\pi$
$691$	−8.30255	+	11.4275i	−0.315844	+	0.434722i	0.621349	+	0.783534i	$0.286585\pi$
$692$	−15.2508	−	36.5943i	−0.579747	−	1.39111i
$693$		0			0
$694$	−10.9460	−	11.8156i	−0.415503	−	0.448514i
$695$	−9.37299	−	12.2235i	−0.355538	−	0.463664i
$696$		0			0
$697$	0.733711	−	0.373844i	0.0277913	−	0.0141604i
$698$	−1.44545	−	5.10404i	−0.0547113	−	0.193191i
$699$		0			0
$700$	0.0541563	−	0.294672i	0.00204692	−	0.0111375i
$701$	−21.3510			−0.806416			−0.403208	−	0.915108i	$-0.632105\pi$
$701$	−21.3510			−0.806416			−0.403208	+	0.915108i	$0.632105\pi$
$702$		0			0
$703$	−34.1234	+	17.3868i	−1.28699	+	0.655754i
$704$	15.7035	−	13.5894i	0.591849	−	0.512171i
$705$		0			0
$706$	−29.1949	−	31.5143i	−1.09876	−	1.18606i
$707$	0.332782	−	0.332782i	0.0125155	−	0.0125155i
$708$		0			0
$709$	−12.7559	+	17.5570i	−0.479057	+	0.659366i	−0.978323	−	0.207083i	$-0.933603\pi$
$709$	−12.7559	+	17.5570i	−0.479057	+	0.659366i	0.499266	+	0.866449i	$0.333603\pi$
$710$	0.443337	−	35.9291i	0.0166382	−	1.34839i
$711$		0			0
$712$	−26.7022	−	3.07253i	−1.00071	−	0.115148i
$713$	10.8155	−	1.71301i	0.405044	−	0.0641527i
$714$		0			0
$715$	−14.5442	+	15.3162i	−0.543922	+	0.572795i
$716$	6.96693	+	28.7451i	0.260366	+	1.07425i
$717$		0			0
$718$	2.99941	+	1.10286i	0.111937	+	0.0411582i
$719$	−6.74838	−	20.7694i	−0.251672	−	0.774567i	−0.994467	−	0.105048i	$-0.966500\pi$
$719$	−6.74838	−	20.7694i	−0.251672	−	0.774567i	0.742795	−	0.669519i	$-0.233500\pi$
$720$		0			0
$721$	−0.0304042	+	0.0935746i	−0.00113231	+	0.00348490i
$722$	1.73416	−	2.20468i	0.0645388	−	0.0820496i
$723$		0			0
$724$	−23.3413	−	19.8481i	−0.867472	−	0.737650i
$725$	−38.6902	−	10.3945i	−1.43692	−	0.386041i
$726$		0			0
$727$	1.62027	−	10.2300i	0.0600925	−	0.379409i	−0.939253	−	0.343226i	$-0.888480\pi$
$727$	1.62027	−	10.2300i	0.0600925	−	0.379409i	0.999345	−	0.0361826i	$-0.0115198\pi$
$728$	−0.0611388	−	0.302234i	−0.00226596	−	0.0112015i
$729$		0			0
$730$	33.6851	−	4.90995i	1.24674	−	0.181726i
$731$	−5.35872	+	1.74115i	−0.198199	+	0.0643989i
$732$		0			0
$733$	7.04429	+	3.58925i	0.260187	+	0.132572i	0.579219	−	0.815172i	$-0.303358\pi$
$733$	7.04429	+	3.58925i	0.260187	+	0.132572i	−0.319032	+	0.947744i	$0.603358\pi$
$734$	35.0865	+	6.93966i	1.29506	+	0.256148i
$735$		0			0
$736$	11.3794	−	31.3670i	0.419451	−	1.15620i
$737$	−1.35567	−	8.55935i	−0.0499366	−	0.315288i
$738$		0			0
$739$	39.2364	−	28.5069i	1.44334	−	1.04864i	0.456003	−	0.889978i	$-0.349281\pi$
$739$	39.2364	−	28.5069i	1.44334	−	1.04864i	0.987332	−	0.158666i	$-0.0507195\pi$
$740$	−27.7398	+	25.0693i	−1.01974	+	0.921566i
$741$		0			0
$742$	0.151050	+	0.00577103i	0.00554521	+	0.000211861i
$743$	−22.8092	−	22.8092i	−0.836787	−	0.836787i	0.151648	−	0.988435i	$-0.451542\pi$
$743$	−22.8092	−	22.8092i	−0.836787	−	0.836787i	−0.988435	+	0.151648i	$0.951542\pi$
$744$		0			0
$745$	−18.4188	+	0.476212i	−0.674811	+	0.0174471i
$746$	2.94198	+	24.6283i	0.107714	+	0.901705i
$747$		0			0
$748$	12.4477	−	10.6780i	0.455131	−	0.390426i
$749$		−	0.359821i		−	0.0131476i
$750$		0			0
$751$		−	46.1937i		−	1.68563i	−0.538201	−	0.842816i	$-0.680896\pi$
$751$		−	46.1937i		−	1.68563i	0.538201	−	0.842816i	$-0.319104\pi$
$752$	−47.2896	+	0.204731i	−1.72448	+	0.00746575i
$753$		0			0
$754$	−40.9409	+	4.89062i	−1.49098	+	0.178106i
$755$	49.7395	−	1.28600i	1.81021	−	0.0468024i
$756$		0			0
$757$	−8.32615	−	8.32615i	−0.302619	−	0.302619i	0.539419	−	0.842038i	$-0.318644\pi$
$757$	−8.32615	−	8.32615i	−0.302619	−	0.302619i	−0.842038	+	0.539419i	$0.818644\pi$
$758$	−1.27578	+	33.3919i	−0.0463383	+	1.21285i
$759$		0			0
$760$	11.3586	−	26.6518i	0.412019	−	0.966763i
$761$	−29.2453	+	21.2480i	−1.06014	+	0.770239i	−0.974115	−	0.226054i	$-0.927417\pi$
$761$	−29.2453	+	21.2480i	−1.06014	+	0.770239i	−0.0860281	+	0.996293i	$0.527417\pi$
$762$		0			0
$763$	0.0438247	+	0.276698i	0.00158656	+	0.0100171i
$764$	3.50871	−	45.8511i	0.126941	−	1.65883i
$765$		0			0
$766$	−1.58702	+	8.02388i	−0.0573415	+	0.289915i
$767$	2.38362	+	1.21451i	0.0860674	+	0.0438535i
$768$		0			0
$769$	−16.5650	+	5.38228i	−0.597348	+	0.194090i	−0.592057	−	0.805896i	$-0.701684\pi$
$769$	−16.5650	+	5.38228i	−0.597348	+	0.194090i	−0.00529061	+	0.999986i	$0.501684\pi$
$770$	0.0354742	+	0.243374i	0.00127840	+	0.00877058i
$771$		0			0
$772$	5.50341	−	23.1439i	0.198072	−	0.832969i
$773$	−0.778227	+	4.91353i	−0.0279909	+	0.176728i	−0.997723	−	0.0674434i	$-0.978516\pi$
$773$	−0.778227	+	4.91353i	−0.0279909	+	0.176728i	0.969732	+	0.244171i	$0.0785158\pi$
$774$		0			0
$775$	8.66788	−	3.32071i	0.311359	−	0.119283i
$776$	−4.87498	+	17.5027i	−0.175002	+	0.628311i
$777$		0			0
$778$	23.7759	+	18.7017i	0.852406	+	0.670488i
$779$	−0.369007	+	1.13569i	−0.0132210	+	0.0406902i
$780$		0			0
$781$	9.11482	+	28.0525i	0.326154	+	1.00380i
$782$	9.09365	−	24.7318i	0.325188	−	0.884408i
$783$		0			0
$784$	24.9998	+	12.6020i	0.892849	+	0.450071i
$785$	−12.6919	+	13.3656i	−0.452994	+	0.477039i
$786$		0			0
$787$	17.8401	−	2.82559i	0.635930	−	0.100721i	0.169858	−	0.985468i	$-0.445669\pi$
$787$	17.8401	−	2.82559i	0.635930	−	0.100721i	0.466071	+	0.884747i	$0.345669\pi$
$788$	15.5582	−	25.5125i	0.554239	−	0.908847i
$789$		0			0
$790$	46.6230	+	0.575291i	1.65877	+	0.0204679i
$791$	0.0200658	−	0.0276182i	0.000713457	−	0.000981989i
$792$		0			0
$793$	12.6180	−	12.6180i	0.448078	−	0.448078i
$794$	−7.30067	+	6.76334i	−0.259091	+	0.240022i
$795$		0			0
$796$	−29.0823	+	17.9083i	−1.03079	+	0.634745i
$797$	−11.5754	+	5.89797i	−0.410022	+	0.208917i	−0.646821	−	0.762642i	$-0.723902\pi$
$797$	−11.5754	+	5.89797i	−0.410022	+	0.208917i	0.236799	+	0.971559i	$0.423902\pi$
$798$		0			0
$799$	−37.3456			−1.32119
$800$	3.92559	−	28.0105i	0.138790	−	0.990322i
$801$		0			0
$802$	41.9195	−	11.8715i	1.48023	−	0.419198i
$803$	−24.8984	+	12.6864i	−0.878644	+	0.447692i
$804$		0			0
$805$	0.240460	+	0.313589i	0.00847511	+	0.0110526i
$806$	7.00813	−	6.49233i	0.246851	−	0.228683i
$807$		0			0
$808$	30.0524	−	32.7230i	1.05724	−	1.15119i
$809$	21.2576	−	29.2586i	0.747379	−	1.02868i	−0.250781	−	0.968044i	$-0.580687\pi$
$809$	21.2576	−	29.2586i	0.747379	−	1.02868i	0.998160	−	0.0606351i	$-0.0193126\pi$
$810$		0			0
$811$	30.8598	+	42.4749i	1.08364	+	1.49150i	0.855455	+	0.517877i	$0.173277\pi$
$811$	30.8598	+	42.4749i	1.08364	+	1.49150i	0.228180	+	0.973619i	$0.426723\pi$
$812$	−0.249974	+	0.409909i	−0.00877235	+	0.0143850i
$813$		0			0
$814$	14.9681	−	26.7955i	0.524633	−	0.939182i
$815$	45.0917	−	8.34182i	1.57949	−	0.292201i
$816$		0			0
$817$	3.70945	−	7.28021i	0.129777	−	0.254702i
$818$	0.754415	−	2.05177i	0.0263775	−	0.0717383i
$819$		0			0
$820$	−0.0588791	+	1.16433i	−0.00205615	+	0.0406600i
$821$	2.47595	−	7.62021i	0.0864114	−	0.265947i	−0.898509	−	0.438955i	$-0.855349\pi$
$821$	2.47595	−	7.62021i	0.0864114	−	0.265947i	0.984920	+	0.173008i	$0.0553487\pi$
$822$		0			0
$823$	33.6993	+	5.33745i	1.17468	+	0.186052i	0.713111	−	0.701051i	$-0.247285\pi$
$823$	33.6993	+	5.33745i	1.17468	+	0.186052i	0.461573	+	0.887102i	$0.347285\pi$
$824$	−2.49223	+	8.94789i	−0.0868209	+	0.311714i
$825$		0			0
$826$	0.0282752	−	0.0130722i	0.000983819	−	0.000454839i
$827$	2.27430	−	14.3594i	0.0790852	−	0.499325i	−0.916071	−	0.401017i	$-0.868657\pi$
$827$	2.27430	−	14.3594i	0.0790852	−	0.499325i	0.995156	−	0.0983080i	$-0.0313430\pi$
$828$		0			0
$829$	−9.98390	−	3.24396i	−0.346755	−	0.112668i	0.130461	−	0.991453i	$-0.458354\pi$
$829$	−9.98390	−	3.24396i	−0.346755	−	0.112668i	−0.477216	+	0.878786i	$0.658354\pi$
$830$	40.2715	+	6.88877i	1.39785	+	0.239113i
$831$		0			0
$832$	−6.97930	−	28.2611i	−0.241964	−	0.979778i
$833$	19.6994	+	10.0374i	0.682544	+	0.347774i
$834$		0			0
$835$	−10.9532	+	22.9443i	−0.379051	+	0.794020i
$836$	−1.81462	+	23.7130i	−0.0627598	+	0.820132i
$837$		0			0
$838$	−12.5403	−	18.7240i	−0.433197	−	0.646809i
$839$	22.2107	−	16.1370i	0.766797	−	0.557111i	−0.134191	−	0.990956i	$-0.542843\pi$
$839$	22.2107	−	16.1370i	0.766797	−	0.557111i	0.900988	+	0.433845i	$0.142843\pi$
$840$		0			0
$841$	28.4768	+	20.6896i	0.981957	+	0.713434i
$842$	−0.173971	+	4.55348i	−0.00599543	+	0.156923i
$843$		0			0
$844$	16.7005	+	6.87525i	0.574854	+	0.236656i
$845$	0.179453	+	0.507293i	0.00617337	+	0.0174514i
$846$		0			0
$847$	0.0579622	+	0.113757i	0.00199161	+	0.00390875i
$848$	14.2701	−	0.0617792i	0.490036	−	0.00212151i
$849$		0			0
$850$	3.19583	−	22.1067i	0.109616	−	0.758253i
$851$		−	49.3152i		−	1.69050i
$852$		0			0
$853$	10.4218	+	20.4539i	0.356836	+	0.700329i	0.997733	−	0.0672973i	$-0.0214376\pi$
$853$	10.4218	+	20.4539i	0.356836	+	0.700329i	−0.640897	+	0.767627i	$0.721438\pi$
$854$	−0.0246460	−	0.206320i	−0.000843369	−	0.00706012i
$855$		0			0
$856$	−1.44381	−	33.9380i	−0.0493483	−	1.15998i
$857$	−7.96786	−	7.96786i	−0.272177	−	0.272177i	0.557799	−	0.829976i	$-0.311646\pi$
$857$	−7.96786	−	7.96786i	−0.272177	−	0.272177i	−0.829976	+	0.557799i	$0.811646\pi$
$858$		0			0
$859$	−9.67439	−	7.02885i	−0.330086	−	0.239821i	0.410381	−	0.911914i	$-0.365396\pi$
$859$	−9.67439	−	7.02885i	−0.330086	−	0.239821i	−0.740467	+	0.672093i	$0.765396\pi$
$860$	1.64420	−	7.80572i	0.0560668	−	0.266173i
$861$		0			0
$862$	36.8382	−	24.6722i	1.25471	−	0.840339i
$863$	−6.25940	−	39.5203i	−0.213073	−	1.34529i	−0.829778	−	0.558093i	$-0.811533\pi$
$863$	−6.25940	−	39.5203i	−0.213073	−	1.34529i	0.616706	−	0.787194i	$-0.288467\pi$
$864$		0			0
$865$	43.9434	+	5.80005i	1.49412	+	0.197208i
$866$	−39.0620	−	7.72598i	−1.32738	−	0.262539i
$867$		0			0
$868$	−0.00896786	−	0.110878i	−0.000304389	−	0.00376346i
$869$	−36.4021	+	11.8277i	−1.23486	+	0.401229i
$870$		0			0
$871$	−11.5530	−	3.75380i	−0.391458	−	0.127193i
$872$	5.24378	+	25.9221i	0.177577	+	0.877833i
$873$		0			0
$874$	16.0354	+	34.6846i	0.542405	+	1.17323i
$875$	0.254498	+	0.217799i	0.00860359	+	0.00736295i
$876$		0			0
$877$	5.40297	+	0.855747i	0.182445	+	0.0288965i	0.246989	−	0.969018i	$-0.420559\pi$
$877$	5.40297	+	0.855747i	0.182445	+	0.0288965i	−0.0645431	+	0.997915i	$0.520559\pi$
$878$	−27.3605	+	34.7840i	−0.923372	+	1.17390i
$879$		0			0
$880$	4.32246	+	22.8125i	0.145710	+	0.769008i
$881$	16.7420	+	51.5264i	0.564051	+	1.73597i	0.670755	+	0.741679i	$0.265970\pi$
$881$	16.7420	+	51.5264i	0.564051	+	1.73597i	−0.106705	+	0.994291i	$0.534030\pi$
$882$		0			0
$883$	−20.7386	+	40.7019i	−0.697911	+	1.36973i	0.221005	+	0.975273i	$0.429066\pi$
$883$	−20.7386	+	40.7019i	−0.697911	+	1.36973i	−0.918916	+	0.394454i	$0.870934\pi$
$884$	−5.41498	−	22.3419i	−0.182126	−	0.751438i
$885$		0			0
$886$	−48.2627	−	26.9599i	−1.62142	−	0.905734i
$887$	−26.6295	+	4.21771i	−0.894133	+	0.141617i	−0.586558	−	0.809907i	$-0.699517\pi$
$887$	−26.6295	+	4.21771i	−0.894133	+	0.141617i	−0.307575	+	0.951524i	$0.599517\pi$
$888$		0			0
$889$	−0.199508	−	0.274599i	−0.00669128	−	0.00920976i
$890$	17.9621	−	24.0919i	0.602091	−	0.807562i
$891$		0			0
$892$	18.2190	−	7.59281i	0.610018	−	0.254226i
$893$	38.2942	−	38.2942i	1.28147	−	1.28147i
$894$		0			0
$895$	−31.7036	−	9.40244i	−1.05973	−	0.314289i
$896$	−0.308897	−	0.139575i	−0.0103195	−	0.00466289i
$897$		0			0
$898$	−12.6102	−	44.5280i	−0.420809	−	1.48592i
$899$	−14.8746			−0.496096
$900$		0			0
$901$	11.2694			0.375437
$902$	−0.260768	−	0.920796i	−0.00868261	−	0.0306592i
$903$		0			0
$904$	1.78177	−	2.68544i	0.0592607	−	0.0893164i
$905$	32.2946	−	11.4241i	1.07351	−	0.379750i
$906$		0			0
$907$	8.52774	−	8.52774i	0.283159	−	0.283159i	−0.551209	−	0.834368i	$-0.685833\pi$
$907$	8.52774	−	8.52774i	0.283159	−	0.283159i	0.834368	+	0.551209i	$0.185833\pi$
$908$	−19.3691	−	46.4762i	−0.642785	−	1.54237i
$909$		0			0
$910$	0.326539	+	0.110572i	0.0108247	+	0.00366541i
$911$	30.7632	+	42.3419i	1.01923	+	1.40285i	0.912742	+	0.408535i	$0.133960\pi$
$911$	30.7632	+	42.3419i	1.01923	+	1.40285i	0.106487	+	0.994314i	$0.466040\pi$
$912$		0			0
$913$	−33.1259	+	5.24663i	−1.09631	+	0.173638i
$914$	−12.4151	−	6.93513i	−0.410654	−	0.229394i
$915$		0			0
$916$	19.1147	−	4.63281i	0.631567	−	0.153072i
$917$	−0.131057	+	0.257213i	−0.00432787	+	0.00849392i
$918$		0			0
$919$	−2.30130	−	7.08267i	−0.0759129	−	0.233636i	0.905898	−	0.423495i	$-0.139197\pi$
$919$	−2.30130	−	7.08267i	−0.0759129	−	0.233636i	−0.981811	+	0.189859i	$0.939197\pi$
$920$	23.9383	+	28.6126i	0.789223	+	0.943329i
$921$		0			0
$922$	−21.6958	+	27.5824i	−0.714514	+	0.908377i
$923$	40.8370	+	6.46794i	1.34417	+	0.212895i
$924$		0			0
$925$	−8.66419	−	40.8949i	−0.284877	−	1.34462i
$926$	−17.6036	−	38.0768i	−0.578491	−	1.25128i
$927$		0			0
$928$	−21.9325	+	39.6653i	−0.719971	+	1.30208i
$929$	8.13021	+	2.64167i	0.266744	+	0.0866703i	0.439335	−	0.898323i	$-0.355214\pi$
$929$	8.13021	+	2.64167i	0.266744	+	0.0866703i	−0.172592	+	0.984993i	$0.555214\pi$
$930$		0			0
$931$	−30.4921	+	9.90747i	−0.999337	+	0.324704i
$932$	22.5928	−	1.82731i	0.740051	−	0.0598554i
$933$		0			0
$934$	−55.4368	−	10.9647i	−1.81395	−	0.358776i
$935$	3.33548	+	18.0299i	0.109082	+	0.589642i
$936$		0			0
$937$	−4.86156	−	30.6947i	−0.158820	−	1.00275i	−0.930381	−	0.366595i	$-0.880523\pi$
$937$	−4.86156	−	30.6947i	−0.158820	−	1.00275i	0.771560	−	0.636156i	$-0.219477\pi$
$938$	−0.117526	+	0.0787123i	−0.00383735	+	0.00257005i
$939$		0			0
$940$	26.3519	−	45.8368i	0.859506	−	1.49503i
$941$	−13.4123	−	9.74458i	−0.437227	−	0.317664i	0.347305	−	0.937752i	$-0.387097\pi$
$941$	−13.4123	−	9.74458i	−0.437227	−	0.317664i	−0.784532	+	0.620088i	$0.787097\pi$
$942$		0			0
$943$	−1.08729	−	1.08729i	−0.0354071	−	0.0354071i
$944$	2.61444	−	1.34641i	0.0850927	−	0.0438220i
$945$		0			0
$946$	0.776704	+	6.50204i	0.0252528	+	0.211400i
$947$	−9.06273	−	17.7866i	−0.294499	−	0.577987i	0.695588	−	0.718441i	$-0.255144\pi$
$947$	−9.06273	−	17.7866i	−0.294499	−	0.577987i	−0.990087	+	0.140454i	$0.955144\pi$
$948$		0			0
$949$			39.1704i			1.27152i
$950$	19.3912	+	25.9452i	0.629133	+	0.841773i
$951$		0			0
$952$	−0.243461	−	0.111280i	−0.00789060	−	0.00360660i
$953$	3.35084	+	6.57639i	0.108544	+	0.213030i	0.938889	−	0.344220i	$-0.111857\pi$
$953$	3.35084	+	6.57639i	0.108544	+	0.213030i	−0.830345	+	0.557250i	$0.811857\pi$
$954$		0			0
$955$	42.3611	+	29.1346i	1.37077	+	0.942774i
$956$	15.1565	−	36.8162i	0.490196	−	1.19072i
$957$		0			0
$958$	−0.292184	+	7.64755i	−0.00944002	+	0.247081i
$959$	0.00690829	+	0.00501917i	0.000223080	+	0.000162077i
$960$		0			0
$961$	−22.2914	+	16.1956i	−0.719076	+	0.522439i
$962$	−23.9411	−	35.7466i	−0.771894	−	1.15252i
$963$		0			0
$964$	−36.9355	−	2.82646i	−1.18961	−	0.0910340i
$965$	19.2869	+	18.3147i	0.620867	+	0.589571i
$966$		0			0
$967$	11.2886	+	5.75184i	0.363018	+	0.184967i	0.625980	−	0.779839i	$-0.284699\pi$
$967$	11.2886	+	5.75184i	0.363018	+	0.184967i	−0.262962	+	0.964806i	$0.584699\pi$
$968$	5.92341	+	10.4969i	0.190386	+	0.337384i
$969$		0			0
$970$	−14.1855	−	14.5399i	−0.455469	−	0.466850i
$971$	−22.4953	−	7.30917i	−0.721909	−	0.234563i	−0.0750585	−	0.997179i	$-0.523914\pi$
$971$	−22.4953	−	7.30917i	−0.721909	−	0.234563i	−0.646851	+	0.762617i	$0.723914\pi$
$972$		0			0
$973$	0.0322863	−	0.203848i	0.00103505	−	0.00653505i
$974$	−43.9644	+	20.3256i	−1.40871	+	0.651275i
$975$		0			0
$976$	−3.15247	−	19.3610i	−0.100908	−	0.619731i
$977$	−17.2253	−	2.72822i	−0.551087	−	0.0872836i	−0.125320	−	0.992116i	$-0.539996\pi$
$977$	−17.2253	−	2.72822i	−0.551087	−	0.0872836i	−0.425767	+	0.904833i	$0.639996\pi$
$978$		0			0
$979$	−7.62301	+	23.4612i	−0.243633	+	0.749824i
$980$	−26.2199	+	17.0958i	−0.837563	+	0.546106i
$981$		0			0
$982$	−7.42572	+	20.1956i	−0.236964	+	0.644466i
$983$	−15.5561	+	30.5305i	−0.496162	+	0.973773i	0.498132	+	0.867101i	$0.334019\pi$
$983$	−15.5561	+	30.5305i	−0.496162	+	0.973773i	−0.994294	+	0.106672i	$0.965981\pi$
$984$		0			0
$985$	15.9319	+	29.3660i	0.507631	+	0.935679i
$986$	−17.4559	+	31.2490i	−0.555909	+	0.995171i
$987$		0			0
$988$	28.4619	+	17.3568i	0.905492	+	0.552194i
$989$	6.18429	+	8.51195i	0.196649	+	0.270664i
$990$		0			0
$991$	−6.27760	+	8.64037i	−0.199414	+	0.274470i	−0.897000	−	0.442032i	$-0.854258\pi$
$991$	−6.27760	+	8.64037i	−0.199414	+	0.274470i	0.697585	+	0.716502i	$0.254258\pi$
$992$	−1.29075	−	10.4220i	−0.0409813	−	0.330898i
$993$		0			0
$994$	0.353182	−	0.327187i	0.0112022	−	0.0103778i
$995$	−0.986939	−	38.1724i	−0.0312881	−	1.21015i
$996$		0			0
$997$	−8.62027	+	4.39225i	−0.273007	+	0.139104i	−0.585135	−	0.810936i	$-0.698958\pi$
$997$	−8.62027	+	4.39225i	−0.273007	+	0.139104i	0.312128	+	0.950040i	$0.398958\pi$
$998$	−3.94735	+	1.11788i	−0.124951	+	0.0353860i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.127.3		240
3.2	odd	2		300.2.w.a.127.28	yes	240
4.3	odd	2	inner	900.2.bj.f.127.7		240
12.11	even	2		300.2.w.a.127.24	✓	240
25.13	odd	20	inner	900.2.bj.f.163.7		240
75.38	even	20		300.2.w.a.163.24	yes	240
100.63	even	20	inner	900.2.bj.f.163.3		240
300.263	odd	20		300.2.w.a.163.28	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.24	✓	240	12.11	even	2
300.2.w.a.127.28	yes	240	3.2	odd	2
300.2.w.a.163.24	yes	240	75.38	even	20
300.2.w.a.163.28	yes	240	300.263	odd	20
900.2.bj.f.127.3		240	1.1	even	1	trivial
900.2.bj.f.127.7		240	4.3	odd	2	inner
900.2.bj.f.163.3		240	100.63	even	20	inner
900.2.bj.f.163.7		240	25.13	odd	20	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36070 + 0.385348i) q^{2} +(1.70301 - 1.04869i) q^{4} +(0.0577937 + 2.23532i) q^{5} +(-0.0211854 + 0.0211854i) q^{7} +(-1.91318 + 2.08320i) q^{8} +O(q^{10})\)	\(q+(-1.36070 + 0.385348i) q^{2} +(1.70301 - 1.04869i) q^{4} +(0.0577937 + 2.23532i) q^{5} +(-0.0211854 + 0.0211854i) q^{7} +(-1.91318 + 2.08320i) q^{8} +(-0.940016 - 3.01933i) q^{10} +(1.52583 + 2.10012i) q^{11} +(3.59397 - 0.569229i) q^{13} +(0.0206633 - 0.0369908i) q^{14} +(1.80052 - 3.57185i) q^{16} +(1.43409 - 2.81456i) q^{17} +(1.41553 + 4.35657i) q^{19} +(2.44257 + 3.74618i) q^{20} +(-2.88547 - 2.26966i) q^{22} +(-5.82595 - 0.922739i) q^{23} +(-4.99332 + 0.258375i) q^{25} +(-4.67097 + 2.15948i) q^{26} +(-0.0138622 + 0.0582959i) q^{28} +(7.62028 + 2.47598i) q^{29} +(-1.76558 + 0.573671i) q^{31} +(-1.07356 + 5.55405i) q^{32} +(-0.866784 + 4.38240i) q^{34} +(-0.0485806 - 0.0461318i) q^{35} +(1.30788 + 8.25760i) q^{37} +(-3.60491 - 5.38251i) q^{38} +(-4.76719 - 4.15619i) q^{40} +(0.210898 + 0.153226i) q^{41} +(-1.26128 - 1.26128i) q^{43} +(4.80087 + 1.97642i) q^{44} +(8.28295 - 0.989443i) q^{46} +(-5.36731 - 10.5339i) q^{47} +6.99910i q^{49} +(6.69485 - 2.27574i) q^{50} +(5.52364 - 4.73835i) q^{52} +(1.61963 + 3.17871i) q^{53} +(-4.60626 + 3.53209i) q^{55} +(-0.00360186 - 0.0846651i) q^{56} +(-11.3230 - 0.432610i) q^{58} +(0.594783 + 0.432135i) q^{59} +(3.96742 - 2.88250i) q^{61} +(2.18136 - 1.46096i) q^{62} +(-0.679450 - 7.97109i) q^{64} +(1.48012 + 8.00078i) q^{65} +(-2.97451 - 1.51559i) q^{67} +(-0.509314 - 6.29715i) q^{68} +(0.0838805 + 0.0440512i) q^{70} +(10.8065 + 3.51125i) q^{71} +(-1.68398 + 10.6322i) q^{73} +(-4.96167 - 10.7321i) q^{74} +(6.97935 + 5.93485i) q^{76} +(-0.0768172 - 0.0121667i) q^{77} +(-4.55633 + 14.0229i) q^{79} +(8.08830 + 3.81830i) q^{80} +(-0.346014 - 0.127226i) q^{82} +(-5.86554 + 11.5118i) q^{83} +(6.37433 + 3.04299i) q^{85} +(2.20225 + 1.23019i) q^{86} +(-7.29416 - 0.839315i) q^{88} +(5.58568 + 7.68803i) q^{89} +(-0.0640804 + 0.0881991i) q^{91} +(-10.8893 + 4.53815i) q^{92} +(11.3625 + 12.2653i) q^{94} +(-9.65652 + 3.41596i) q^{95} +(5.72355 - 2.91630i) q^{97} +(-2.69709 - 9.52369i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 240 * q - 12 * q^8	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

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