LMFDB - Embedded newform 900.2.bj.f.163.7

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			163.7
Character	$\chi$	$=$	900.163
Dual form			900.2.bj.f.127.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17502 + 0.786967i) q^{2} +(0.761365 - 1.84941i) q^{4} +(0.0577937 - 2.23532i) q^{5} +(0.0211854 + 0.0211854i) q^{7} +(0.560803 + 2.77227i) q^{8} +O(q^{10})$	\(q+(-1.17502 + 0.786967i) q^{2} +(0.761365 - 1.84941i) q^{4} +(0.0577937 - 2.23532i) q^{5} +(0.0211854 + 0.0211854i) q^{7} +(0.560803 + 2.77227i) q^{8} +(1.69122 + 2.67204i) q^{10} +(-1.52583 + 2.10012i) q^{11} +(3.59397 + 0.569229i) q^{13} +(-0.0415656 - 0.00822116i) q^{14} +(-2.84065 - 2.81616i) q^{16} +(1.43409 + 2.81456i) q^{17} +(-1.41553 + 4.35657i) q^{19} +(-4.09003 - 1.80878i) q^{20} +(0.140158 - 3.66847i) q^{22} +(5.82595 - 0.922739i) q^{23} +(-4.99332 - 0.258375i) q^{25} +(-4.67097 + 2.15948i) q^{26} +(0.0553104 - 0.0230507i) q^{28} +(7.62028 - 2.47598i) q^{29} +(1.76558 + 0.573671i) q^{31} +(5.55405 + 1.07356i) q^{32} +(-3.90006 - 2.17860i) q^{34} +(0.0485806 - 0.0461318i) q^{35} +(1.30788 - 8.25760i) q^{37} +(-1.76519 - 6.23305i) q^{38} +(6.22933 - 1.09336i) q^{40} +(0.210898 - 0.153226i) q^{41} +(1.26128 - 1.26128i) q^{43} +(2.72228 + 4.42084i) q^{44} +(-6.11947 + 5.66907i) q^{46} +(5.36731 - 10.5339i) q^{47} -6.99910i q^{49} +(6.07061 - 3.62598i) q^{50} +(3.78906 - 6.21334i) q^{52} +(1.61963 - 3.17871i) q^{53} +(4.60626 + 3.53209i) q^{55} +(-0.0468509 + 0.0706126i) q^{56} +(-7.00551 + 8.90625i) q^{58} +(-0.594783 + 0.432135i) q^{59} +(3.96742 + 2.88250i) q^{61} +(-2.52606 + 0.715375i) q^{62} +(-7.37100 + 3.10940i) q^{64} +(1.48012 - 8.00078i) q^{65} +(2.97451 - 1.51559i) q^{67} +(6.29715 - 0.509314i) q^{68} +(-0.0207792 + 0.0924374i) q^{70} +(-10.8065 + 3.51125i) q^{71} +(-1.68398 - 10.6322i) q^{73} +(4.96167 + 10.7321i) q^{74} +(6.97935 + 5.93485i) q^{76} +(-0.0768172 + 0.0121667i) q^{77} +(4.55633 + 14.0229i) q^{79} +(-6.45918 + 6.18700i) q^{80} +(-0.127226 + 0.346014i) q^{82} +(5.86554 + 11.5118i) q^{83} +(6.37433 - 3.04299i) q^{85} +(-0.489447 + 2.47461i) q^{86} +(-6.67780 - 3.05226i) q^{88} +(5.58568 - 7.68803i) q^{89} +(0.0640804 + 0.0881991i) q^{91} +(2.72915 - 11.4771i) q^{92} +(1.98314 + 16.6015i) q^{94} +(9.65652 + 3.41596i) q^{95} +(5.72355 + 2.91630i) q^{97} +(5.50806 + 8.22412i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−1.17502	+	0.786967i	−0.830868	+	0.556470i
$2$	−1.17502	+	0.786967i	−0.830868	+	0.556470i
$3$		0			0
$3$		0			0
$4$	0.761365	−	1.84941i	0.380683	−	0.924706i
$5$	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	$-0.248198\pi$
$7$	0.0211854	+	0.0211854i	0.00800734	+	0.00800734i	−0.703092	+	0.711099i	$0.748198\pi$
$8$	0.560803	+	2.77227i	0.198274	+	0.980147i
$9$		0			0
$10$	1.69122	+	2.67204i	0.534809	+	0.844973i
$11$	−1.52583	+	2.10012i	−0.460054	+	0.633210i	−0.974520	−	0.224301i	$-0.927990\pi$
$11$	−1.52583	+	2.10012i	−0.460054	+	0.633210i	0.514466	+	0.857511i	$0.327990\pi$
$12$		0			0
$13$	3.59397	+	0.569229i	0.996788	+	0.157876i	0.633452	−	0.773782i	$-0.281638\pi$
$13$	3.59397	+	0.569229i	0.996788	+	0.157876i	0.363336	+	0.931658i	$0.381638\pi$
$14$	−0.0415656	−	0.00822116i	−0.0111089	−	0.00219720i
$15$		0			0
$16$	−2.84065	−	2.81616i	−0.710161	−	0.704039i
$17$	1.43409	+	2.81456i	0.347818	+	0.682632i	0.996950	−	0.0780444i	$-0.0248676\pi$
$17$	1.43409	+	2.81456i	0.347818	+	0.682632i	−0.649132	+	0.760676i	$0.724868\pi$
$18$		0			0
$19$	−1.41553	+	4.35657i	−0.324746	+	0.999465i	0.646809	+	0.762652i	$0.276103\pi$
$19$	−1.41553	+	4.35657i	−0.324746	+	0.999465i	−0.971555	+	0.236813i	$0.923897\pi$
$20$	−4.09003	−	1.80878i	−0.914558	−	0.404456i
$21$		0			0
$22$	0.140158	−	3.66847i	0.0298818	−	0.782120i
$23$	5.82595	−	0.922739i	1.21479	−	0.192404i	0.484040	−	0.875046i	$-0.339169\pi$
$23$	5.82595	−	0.922739i	1.21479	−	0.192404i	0.730754	+	0.682641i	$0.239169\pi$
$24$		0			0
$25$	−4.99332	−	0.258375i	−0.998664	−	0.0516749i
$26$	−4.67097	+	2.15948i	−0.916052	+	0.423509i
$27$		0			0
$28$	0.0553104	−	0.0230507i	0.0104527	−	0.00435618i
$29$	7.62028	−	2.47598i	1.41505	−	0.459778i	0.501025	−	0.865433i	$-0.332957\pi$
$29$	7.62028	−	2.47598i	1.41505	−	0.459778i	0.914026	+	0.405655i	$0.132957\pi$
$30$		0			0
$31$	1.76558	+	0.573671i	0.317107	+	0.103034i	0.463246	−	0.886230i	$-0.346685\pi$
$31$	1.76558	+	0.573671i	0.317107	+	0.103034i	−0.146139	+	0.989264i	$0.546685\pi$
$32$	5.55405	+	1.07356i	0.981827	+	0.189780i
$33$		0			0
$34$	−3.90006	−	2.17860i	−0.668855	−	0.373626i
$35$	0.0485806	−	0.0461318i	0.00821162	−	0.00779770i
$36$		0			0
$37$	1.30788	−	8.25760i	0.215013	−	1.35754i	−0.609988	−	0.792410i	$-0.708826\pi$
$37$	1.30788	−	8.25760i	0.215013	−	1.35754i	0.825002	−	0.565130i	$-0.191174\pi$
$38$	−1.76519	−	6.23305i	−0.286351	−	1.01113i
$39$		0			0
$40$	6.22933	−	1.09336i	0.984944	−	0.172875i
$41$	0.210898	−	0.153226i	0.0329367	−	0.0239299i	−0.571195	−	0.820814i	$-0.693520\pi$
$41$	0.210898	−	0.153226i	0.0329367	−	0.0239299i	0.604132	+	0.796884i	$0.293520\pi$
$42$		0			0
$43$	1.26128	−	1.26128i	0.192343	−	0.192343i	−0.604365	−	0.796708i	$-0.706573\pi$
$43$	1.26128	−	1.26128i	0.192343	−	0.192343i	0.796708	+	0.604365i	$0.206573\pi$
$44$	2.72228	+	4.42084i	0.410399	+	0.666467i
$45$		0			0
$46$	−6.11947	+	5.66907i	−0.902266	+	0.835859i
$47$	5.36731	−	10.5339i	0.782903	−	1.53653i	−0.0598348	−	0.998208i	$-0.519057\pi$
$47$	5.36731	−	10.5339i	0.782903	−	1.53653i	0.842737	−	0.538325i	$-0.180943\pi$
$48$		0			0
$49$		−	6.99910i		−	0.999872i
$50$	6.07061	−	3.62598i	0.858513	−	0.512791i
$51$		0			0
$52$	3.78906	−	6.21334i	0.525449	−	0.861635i
$53$	1.61963	−	3.17871i	0.222474	−	0.436629i	−0.752610	−	0.658466i	$-0.771205\pi$
$53$	1.61963	−	3.17871i	0.222474	−	0.436629i	0.975084	+	0.221837i	$0.0712054\pi$
$54$		0			0
$55$	4.60626	+	3.53209i	0.621108	+	0.476267i
$56$	−0.0468509	+	0.0706126i	−0.00626072	+	0.00943601i
$57$		0			0
$58$	−7.00551	+	8.90625i	−0.919868	+	1.16945i
$59$	−0.594783	+	0.432135i	−0.0774341	+	0.0562592i	−0.625829	−	0.779960i	$-0.715239\pi$
$59$	−0.594783	+	0.432135i	−0.0774341	+	0.0562592i	0.548395	+	0.836220i	$0.315239\pi$
$60$		0			0
$61$	3.96742	+	2.88250i	0.507976	+	0.369066i	0.812055	−	0.583581i	$-0.198349\pi$
$61$	3.96742	+	2.88250i	0.507976	+	0.369066i	−0.304079	+	0.952647i	$0.598349\pi$
$62$	−2.52606	+	0.715375i	−0.320810	+	0.0908527i
$63$		0			0
$64$	−7.37100	+	3.10940i	−0.921375	+	0.388675i
$65$	1.48012	−	8.00078i	0.183586	−	0.992375i
$66$		0			0
$67$	2.97451	−	1.51559i	0.363394	−	0.185158i	−0.262754	−	0.964863i	$-0.584631\pi$
$67$	2.97451	−	1.51559i	0.363394	−	0.185158i	0.626148	+	0.779705i	$0.284631\pi$
$68$	6.29715	−	0.509314i	0.763642	−	0.0617634i
$69$		0			0
$70$	−0.0207792	+	0.0924374i	−0.00248358	+	0.0110484i
$71$	−10.8065	+	3.51125i	−1.28250	+	0.416709i	−0.869459	−	0.494005i	$-0.835532\pi$
$71$	−10.8065	+	3.51125i	−1.28250	+	0.416709i	−0.413038	+	0.910714i	$0.635532\pi$
$72$		0			0
$73$	−1.68398	−	10.6322i	−0.197094	−	1.24441i	−0.865614	−	0.500711i	$-0.833072\pi$
$73$	−1.68398	−	10.6322i	−0.197094	−	1.24441i	0.668520	−	0.743694i	$-0.266928\pi$
$74$	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	0.787558	+	0.616240i	$0.211345\pi$
$79$	4.55633	+	14.0229i	0.512627	+	1.57770i	−0.274931	+	0.961464i	$0.588655\pi$
$80$	−6.45918	+	6.18700i	−0.722159	+	0.691727i
$81$		0			0
$82$	−0.127226	+	0.346014i	−0.0140498	+	0.0382108i
$83$	5.86554	+	11.5118i	0.643826	+	1.26358i	0.950192	+	0.311666i	$0.100887\pi$
$83$	5.86554	+	11.5118i	0.643826	+	1.26358i	−0.306366	+	0.951914i	$0.599113\pi$
$84$		0			0
$85$	6.37433	−	3.04299i	0.691393	−	0.330059i
$86$	−0.489447	+	2.47461i	−0.0527784	+	0.266844i
$87$		0			0
$88$	−6.67780	−	3.05226i	−0.711856	−	0.325372i
$89$	5.58568	−	7.68803i	0.592081	−	0.814930i	−0.402874	−	0.915256i	$-0.631989\pi$
$89$	5.58568	−	7.68803i	0.592081	−	0.814930i	0.994955	+	0.100326i	$0.0319886\pi$
$90$		0			0
$91$	0.0640804	+	0.0881991i	0.00671745	+	0.00924578i
$92$	2.72915	−	11.4771i	0.284534	−	1.19657i
$93$		0			0
$94$	1.98314	+	16.6015i	0.204546	+	1.71232i
$95$	9.65652	+	3.41596i	0.990738	+	0.350470i
$96$		0			0
$97$	5.72355	+	2.91630i	0.581139	+	0.296105i	0.719740	−	0.694243i	$-0.244261\pi$
$97$	5.72355	+	2.91630i	0.581139	+	0.296105i	−0.138602	+	0.990348i	$0.544261\pi$
$98$	5.50806	+	8.22412i	0.556398	+	0.830761i
$99$		0			0
$100$	−4.27958	+	9.03799i	−0.427958	+	0.903799i
$101$	−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	$-0.401727\pi$
$103$	−2.92604	−	1.49089i	−0.288311	−	0.146902i	−0.592165	+	0.805817i	$0.701727\pi$
$104$	0.437451	+	10.2827i	0.0428956	+	1.00830i
$105$		0			0
$106$	0.598431	+	5.00966i	0.0581247	+	0.486581i
$107$	8.49218	+	8.49218i	0.820970	+	0.820970i	0.986247	−	0.165277i	$-0.0528520\pi$
$107$	8.49218	+	8.49218i	0.820970	+	0.820970i	−0.165277	+	0.986247i	$0.552852\pi$
$108$		0			0
$109$	5.49608	+	7.56470i	0.526429	+	0.724567i	0.986581	−	0.163273i	$-0.0522051\pi$
$109$	5.49608	+	7.56470i	0.526429	+	0.724567i	−0.460152	+	0.887840i	$0.652205\pi$
$110$	−8.19211	−	0.525313i	−0.781087	−	0.0500866i
$111$		0			0
$112$	−0.000518830	−	0.119842i	−4.90248e−5	−	0.0113240i
$113$	−1.12540	−	0.178245i	−0.105868	−	0.0167679i	0.103276	−	0.994653i	$-0.467068\pi$
$113$	−1.12540	−	0.178245i	−0.105868	−	0.0167679i	−0.209144	+	0.977885i	$0.567068\pi$
$114$		0			0
$115$	−1.72592	−	13.0762i	−0.160942	−	1.21936i
$116$	1.22271	−	15.9782i	0.113526	−	1.48354i
$117$		0			0
$118$	0.358808	−	0.975844i	0.0330310	−	0.0898337i
$119$	−0.0292459	+	0.0900095i	−0.00268096	+	0.00825116i
$120$		0			0
$121$	1.31683	+	4.05278i	0.119712	+	0.368434i
$122$	−6.93025	−	0.264778i	−0.627435	−	0.0239719i
$123$		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	0.932482	+	0.361215i	$0.117638\pi$
$127$	1.77224	+	11.1895i	0.157261	+	0.992904i	−0.775222	+	0.631689i	$0.782362\pi$
$128$	6.21411	−	9.45436i	0.549255	−	0.835655i
$129$		0			0
$130$	4.55718	+	10.5659i	0.399691	+	0.926692i
$131$	−9.16360	−	2.97743i	−0.800628	−	0.260140i	−0.120004	−	0.992773i	$-0.538291\pi$
$131$	−9.16360	−	2.97743i	−0.800628	−	0.260140i	−0.680623	+	0.732634i	$0.738291\pi$
$132$		0			0
$133$	−0.122284	+	0.0623070i	−0.0106034	+	0.00540270i
$134$	−2.30240	+	4.12169i	−0.198897	+	0.356060i
$135$		0			0
$136$	−6.99849	+	5.55411i	−0.600116	+	0.476261i
$137$	−0.0445855	+	0.281502i	−0.00380919	+	0.0240503i	−0.989520	−	0.144398i	$-0.953876\pi$
$137$	−0.0445855	+	0.281502i	−0.00380919	+	0.0240503i	0.985711	+	0.168448i	$0.0538755\pi$
$138$		0			0
$139$	5.57303	+	4.04904i	0.472698	+	0.343435i	0.798492	−	0.602006i	$-0.205632\pi$
$139$	5.57303	+	4.04904i	0.472698	+	0.343435i	−0.325794	+	0.945441i	$0.605632\pi$
$140$	−0.0483292	−	0.124969i	−0.00408456	−	0.0105618i
$141$		0			0
$142$	9.93468	−	12.6302i	0.833700	−	1.05990i
$143$	−6.67923	+	6.67923i	−0.558545	+	0.558545i
$144$		0			0
$145$	−5.09421	−	17.1769i	−0.423051	−	1.42646i
$146$	10.3459	+	11.1679i	0.856233	+	0.924259i
$147$		0			0
$148$	−14.2759	−	8.70585i	−1.17347	−	0.715616i
$149$		−	8.23987i		−	0.675036i	−0.941319	−	0.337518i	$-0.890413\pi$
$149$		−	8.23987i		−	0.675036i	0.941319	−	0.337518i	$-0.109587\pi$
$150$		0			0
$151$		−	22.2516i		−	1.81081i	−0.424548	−	0.905406i	$-0.639567\pi$
$151$		−	22.2516i		−	1.81081i	0.424548	−	0.905406i	$-0.360433\pi$
$152$	−12.8714	−	1.48107i	−1.04401	−	0.120131i
$153$		0			0
$154$	0.0806874	−	0.0747488i	0.00650198	−	0.00602343i
$155$	1.38438	−	3.91348i	0.111196	−	0.314338i
$156$		0			0
$157$	5.82859	−	5.82859i	0.465172	−	0.465172i	−0.435174	−	0.900346i	$-0.643313\pi$
$157$	5.82859	−	5.82859i	0.465172	−	0.465172i	0.900346	+	0.435174i	$0.143313\pi$
$158$	−16.3894	−	12.8916i	−1.30387	−	1.02560i
$159$		0			0
$160$	2.72073	−	12.3530i	0.215093	−	0.976594i
$161$	0.142974	+	0.103877i	0.0112679	+	0.00818662i
$162$		0			0
$163$	3.20813	−	20.2553i	0.251280	−	1.58652i	−0.462805	−	0.886460i	$-0.653157\pi$
$163$	3.20813	−	20.2553i	0.251280	−	1.58652i	0.714085	−	0.700059i	$-0.246843\pi$
$164$	−0.122808	−	0.506697i	−0.00958969	−	0.0395664i
$165$		0			0
$166$	−15.9515	−	8.91062i	−1.23808	−	0.691598i
$167$	−10.1310	+	5.16198i	−0.783957	+	0.399446i	−0.799677	−	0.600430i	$-0.794996\pi$
$167$	−10.1310	+	5.16198i	−0.783957	+	0.399446i	0.0157198	+	0.999876i	$0.494996\pi$
$168$		0			0
$169$	0.228867	+	0.0743633i	0.0176051	+	0.00572025i
$170$	−5.09526	+	8.59198i	−0.390789	+	0.658975i
$171$		0			0
$172$	−1.37233	−	3.29291i	−0.104639	−	0.251082i
$173$	3.10093	+	19.5785i	0.235759	+	1.48852i	0.767188	+	0.641422i	$0.221655\pi$
$173$	3.10093	+	19.5785i	0.235759	+	1.48852i	−0.531429	+	0.847103i	$0.678345\pi$
$174$		0			0
$175$	−0.100312	−	0.111259i	−0.00758286	−	0.00841042i
$176$	10.2486	−	1.66873i	0.772518	−	0.125785i
$177$		0			0
$178$	−0.513085	+	13.4294i	−0.0384573	+	1.00657i
$179$	4.56995	+	14.0649i	0.341574	+	1.05126i	0.963392	+	0.268095i	$0.0863942\pi$
$179$	4.56995	+	14.0649i	0.341574	+	1.05126i	−0.621818	+	0.783162i	$0.713606\pi$
$180$		0			0
$181$	−4.73402	+	14.5698i	−0.351877	+	1.08297i	0.605921	+	0.795525i	$0.292805\pi$
$181$	−4.73402	+	14.5698i	−0.351877	+	1.08297i	−0.957798	+	0.287442i	$0.907195\pi$
$182$	−0.144706	−	0.0532070i	−0.0107263	−	0.00394396i
$183$		0			0
$184$	5.82530	+	15.6336i	0.429446	+	1.15253i
$185$	−18.3828	−	3.40076i	−1.35153	−	0.250029i
$186$		0			0
$187$	−8.09910	−	1.28277i	−0.592265	−	0.0938055i
$188$	−15.3951	−	17.9465i	−1.12280	−	1.30889i
$189$		0			0
$190$	−14.0349	+	3.58553i	−1.01820	+	0.260122i
$191$	−13.5147	−	18.6014i	−0.977888	−	1.34595i	−0.937959	−	0.346745i	$-0.887287\pi$
$191$	−13.5147	−	18.6014i	−0.977888	−	1.34595i	−0.0399290	−	0.999203i	$-0.512713\pi$
$192$		0			0
$193$	8.41078	+	8.41078i	0.605421	+	0.605421i	0.941746	−	0.336325i	$-0.109184\pi$
$193$	8.41078	+	8.41078i	0.605421	+	0.605421i	−0.336325	+	0.941746i	$0.609184\pi$
$194$	−9.02034	+	1.07753i	−0.647623	+	0.0773621i
$195$		0			0
$196$	−12.9442	−	5.32887i	−0.924587	−	0.380634i
$197$	13.3126	+	6.78313i	0.948486	+	0.483278i	0.858584	−	0.512673i	$-0.171345\pi$
$197$	13.3126	+	6.78313i	0.948486	+	0.483278i	0.0899021	+	0.995951i	$0.471345\pi$
$198$		0			0
$199$	17.0769			1.21055			0.605276	−	0.796016i	$-0.293063\pi$
$199$	17.0769			1.21055			0.605276	+	0.796016i	$0.293063\pi$
$200$	−2.08398	−	13.9877i	−0.147360	−	0.989083i
$201$		0			0
$202$	18.4573	−	12.3617i	1.29865	−	0.869767i
$203$	0.213894	+	0.108984i	0.0150124	+	0.00764919i
$204$		0			0
$205$	−0.330321	−	0.480279i	−0.0230706	−	0.0335442i
$206$	4.61145	−	0.550863i	0.321295	−	0.0383805i
$207$		0			0
$208$	−8.60616	−	11.7382i	−0.596730	−	0.813895i
$209$	−6.98946	−	9.62017i	−0.483471	−	0.665441i
$210$		0			0
$211$	−5.30779	+	7.30555i	−0.365404	+	0.502935i	−0.951644	−	0.307202i	$-0.900607\pi$
$211$	−5.30779	+	7.30555i	−0.365404	+	0.502935i	0.586241	+	0.810137i	$0.300607\pi$
$212$	−4.64561	−	5.41552i	−0.319061	−	0.371940i
$213$		0			0
$214$	−16.6616	−	3.29545i	−1.13896	−	0.225272i
$215$	−2.74646	−	2.89225i	−0.187307	−	0.197250i
$216$		0			0
$217$	0.0252511	+	0.0495580i	0.00171415	+	0.00336422i
$218$	−12.4112	−	4.56348i	−0.840593	−	0.309078i
$219$		0			0
$220$	10.0393	−	5.82966i	0.676852	−	0.393036i
$221$	3.55195	+	10.9318i	0.238930	+	0.735351i
$222$		0			0
$223$	−9.74743	+	1.54384i	−0.652736	+	0.103383i	−0.474015	−	0.880517i	$-0.657196\pi$
$223$	−9.74743	+	1.54384i	−0.652736	+	0.103383i	−0.178721	+	0.983900i	$0.557196\pi$
$224$	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	−0.673461	−	0.739223i	$-0.735193\pi$
$227$	−3.93830	−	24.8654i	−0.261394	−	1.65038i	0.412067	−	0.911154i	$-0.364807\pi$
$228$		0			0
$229$	9.35273	−	3.03889i	0.618046	−	0.200815i	0.0167733	−	0.999859i	$-0.494661\pi$
$229$	9.35273	−	3.03889i	0.618046	−	0.200815i	0.601272	+	0.799044i	$0.294661\pi$
$230$	12.3185	+	14.0066i	0.812260	+	0.923568i
$231$		0			0
$232$	11.1376	+	19.7370i	0.731218	+	1.29580i
$233$	10.0980	−	5.14520i	0.661543	−	0.337073i	−0.0907764	−	0.995871i	$-0.528935\pi$
$233$	10.0980	−	5.14520i	0.661543	−	0.337073i	0.752320	+	0.658798i	$0.228935\pi$
$234$		0			0
$235$	−23.2365	−	12.6065i	−1.51578	−	0.822355i
$236$	0.346348	+	1.42901i	0.0225454	+	0.0930207i
$237$		0			0
$238$	−0.0364699	−	0.128779i	−0.00236399	−	0.00834750i
$239$	−16.1051	−	11.7010i	−1.04175	−	0.756877i	−0.0711251	−	0.997467i	$-0.522659\pi$
$239$	−16.1051	−	11.7010i	−1.04175	−	0.756877i	−0.970627	+	0.240590i	$0.922659\pi$
$240$		0			0
$241$	−14.9844	+	10.8868i	−0.965232	+	0.701282i	−0.954360	−	0.298659i	$-0.903461\pi$
$241$	−14.9844	+	10.8868i	−0.965232	+	0.701282i	−0.0108717	+	0.999941i	$0.503461\pi$
$242$	−4.73671	−	3.72581i	−0.304487	−	0.239504i
$243$		0			0
$244$	8.35158	−	5.14276i	0.534655	−	0.329231i
$245$	−15.6452	−	0.404504i	−0.999538	−	0.0258428i
$246$		0			0
$247$	−7.56727	+	14.8516i	−0.481494	+	0.944985i
$248$	−0.600232	+	5.21638i	−0.0381147	+	0.331241i
$249$		0			0
$250$	−7.75439	−	13.7793i	−0.490431	−	0.871480i
$251$			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
$254$	−10.8882	−	11.7532i	−0.683184	−	0.737461i
$255$		0			0
$256$	0.138535	+	15.9994i	0.00865842	+	0.999963i
$257$	−7.29636	+	7.29636i	−0.455134	+	0.455134i	−0.897054	−	0.441920i	$-0.854297\pi$
$257$	−7.29636	+	7.29636i	−0.455134	+	0.455134i	0.441920	+	0.897054i	$0.354297\pi$
$258$		0			0
$259$	0.202649	−	0.147233i	0.0125920	−	0.00914860i
$260$	−13.6698	−	8.82886i	−0.847766	−	0.547543i
$261$		0			0
$262$	13.1106	−	3.71289i	0.809976	−	0.229383i
$263$	1.98412	−	12.5273i	0.122346	−	0.772464i	−0.847866	−	0.530210i	$-0.822113\pi$
$263$	1.98412	−	12.5273i	0.122346	−	0.772464i	0.970213	−	0.242254i	$-0.0778869\pi$
$264$		0			0
$265$	−7.01183	−	3.80411i	−0.430733	−	0.233684i
$266$	0.0946536	−	0.169446i	0.00580359	−	0.0103894i
$267$		0			0
$268$	−0.538257	−	6.65500i	−0.0328793	−	0.406519i
$269$	18.1138	+	5.88553i	1.10442	+	0.358847i	0.803801	−	0.594898i	$-0.202808\pi$
$269$	18.1138	+	5.88553i	1.10442	+	0.358847i	0.300617	+	0.953745i	$0.402808\pi$
$270$		0			0
$271$	−17.6810	+	5.74491i	−1.07404	+	0.348978i	−0.792062	−	0.610441i	$-0.790992\pi$
$271$	−17.6810	+	5.74491i	−1.07404	+	0.348978i	−0.281983	+	0.959419i	$0.590992\pi$
$272$	3.85250	−	12.0338i	0.233592	−	0.729656i
$273$		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	−0.919199	−	0.393793i	$-0.871163\pi$
$277$	−27.8230	+	4.40673i	−1.67172	+	0.264774i	−0.752521	+	0.658568i	$0.771163\pi$
$278$	−9.73491	−	0.371934i	−0.583861	−	0.0223071i
$279$		0			0
$280$	0.155134	+	0.108808i	0.00927104	+	0.00650251i
$281$	−4.15266	+	12.7806i	−0.247727	+	0.762425i	0.747449	+	0.664319i	$0.231278\pi$
$281$	−4.15266	+	12.7806i	−0.247727	+	0.762425i	−0.995176	+	0.0981057i	$0.968722\pi$
$282$		0			0
$283$	−4.92195	−	9.65986i	−0.292579	−	0.574219i	0.697192	−	0.716885i	$-0.254433\pi$
$283$	−4.92195	−	9.65986i	−0.292579	−	0.574219i	−0.989771	+	0.142666i	$0.954433\pi$
$284$	−1.73396	+	22.6590i	−0.102892	+	1.34457i
$285$		0			0
$286$	2.59192	−	13.1046i	0.153264	−	0.774891i
$287$	0.00771411	+	0.00122180i	0.000455350	+	7.21203e-5i
$288$		0			0
$289$	4.12720	−	5.68061i	0.242777	−	0.334153i
$290$	19.5035	+	16.1743i	1.14528	+	0.949786i
$291$		0			0
$292$	−20.9454	−	4.98063i	−1.22574	−	0.291469i
$293$	−0.921753	−	0.921753i	−0.0538494	−	0.0538494i	0.679669	−	0.733519i	$-0.262123\pi$
$293$	−0.921753	−	0.921753i	−0.0538494	−	0.0538494i	−0.733519	+	0.679669i	$0.762123\pi$
$294$		0			0
$295$	0.931586	+	1.35451i	0.0542390	+	0.0788623i
$296$	23.6258	−	1.00510i	1.37322	−	0.0584202i
$297$		0			0
$298$	6.48451	+	9.68205i	0.375637	+	0.560866i
$299$	21.4635			1.24127
$300$		0			0
$301$	0.0534413			0.00308030
$302$	17.5113	+	26.1462i	1.00766	+	1.50454i
$303$		0			0
$304$	16.2898	−	8.38910i	0.934284	−	0.481148i
$305$	6.67260	−	8.70187i	0.382072	−	0.498267i
$306$		0			0
$307$	15.8559	+	15.8559i	0.904945	+	0.904945i	0.995859	−	0.0909141i	$-0.0289789\pi$
$307$	15.8559	+	15.8559i	0.904945	+	0.904945i	−0.0909141	+	0.995859i	$0.528979\pi$
$308$	−0.0359848	+	0.151330i	−0.00205043	+	0.00862283i
$309$		0			0
$310$	1.45310	+	5.68790i	0.0825306	+	0.323051i
$311$	10.3201	−	14.2044i	0.585200	−	0.805458i	−0.409054	−	0.912510i	$-0.634141\pi$
$311$	10.3201	−	14.2044i	0.585200	−	0.805458i	0.994253	+	0.107052i	$0.0341411\pi$
$312$		0			0
$313$	−12.9632	−	2.05317i	−0.732722	−	0.116052i	−0.221086	−	0.975254i	$-0.570960\pi$
$313$	−12.9632	−	2.05317i	−0.732722	−	0.116052i	−0.511636	+	0.859202i	$0.670960\pi$
$314$	−2.26183	+	11.4356i	−0.127642	+	0.645351i
$315$		0			0
$316$	29.4032	+	2.25005i	1.65406	+	0.126575i
$317$	3.09677	+	6.07775i	0.173932	+	0.341360i	0.961472	−	0.274903i	$-0.0886457\pi$
$317$	3.09677	+	6.07775i	0.173932	+	0.341360i	−0.787540	+	0.616263i	$0.788646\pi$
$318$		0			0
$319$	−6.42738	+	19.7814i	−0.359864	+	1.10755i
$320$	6.52451	+	16.6563i	0.364731	+	0.931113i
$321$		0			0
$322$	−0.249745	−	0.00954180i	−0.0139177	−	0.000531744i
$323$	−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
$328$	0.543057	+	0.498736i	0.0299853	+	0.0275381i
$329$	0.336875	−	0.109457i	0.0185725	−	0.00603457i
$330$		0			0
$331$	−6.17995	−	2.00799i	−0.339681	−	0.110369i	0.134209	−	0.990953i	$-0.457151\pi$
$331$	−6.17995	−	2.00799i	−0.339681	−	0.110369i	−0.473890	+	0.880584i	$0.657151\pi$
$332$	25.7558	−	2.08313i	1.41353	−	0.114327i
$333$		0			0
$334$	7.84182	−	14.0382i	0.429085	−	0.768136i
$335$	−3.21591	−	6.73657i	−0.175704	−	0.368058i
$336$		0			0
$337$	−4.19864	+	26.5091i	−0.228714	+	1.44405i	0.559595	+	0.828766i	$0.310957\pi$
$337$	−4.19864	+	26.5091i	−0.228714	+	1.44405i	−0.788309	+	0.615279i	$0.789043\pi$
$338$	−0.327445	+	0.0927319i	−0.0178107	+	0.00504395i
$339$		0			0
$340$	−0.774546	−	14.1056i	−0.0420056	−	0.764983i
$341$	−3.89875	+	2.83261i	−0.211129	+	0.153394i
$342$		0			0
$343$	0.296577	−	0.296577i	0.0160136	−	0.0160136i
$344$	4.20393	+	2.78927i	0.226661	+	0.150387i
$345$		0			0
$346$	−19.0513	−	20.5649i	−1.02420	−	1.10557i
$347$	−5.17054	+	10.1478i	−0.277569	+	0.544760i	−0.987137	−	0.159877i	$-0.948890\pi$
$347$	−5.17054	+	10.1478i	−0.277569	+	0.544760i	0.709568	+	0.704637i	$0.248890\pi$
$348$		0			0
$349$		−	3.75104i		−	0.200789i	−0.994948	−	0.100394i	$-0.967990\pi$
$349$		−	3.75104i		−	0.200789i	0.994948	−	0.100394i	$-0.0320104\pi$
$350$	0.205426	+	0.0517904i	0.0109805	+	0.00276831i
$351$		0			0
$352$	−10.7291	+	10.0261i	−0.571864	+	0.534394i
$353$	13.7908	−	27.0659i	0.734008	−	1.44057i	−0.157478	−	0.987522i	$-0.550336\pi$
$353$	13.7908	−	27.0659i	0.734008	−	1.44057i	0.891486	−	0.453049i	$-0.149664\pi$
$354$		0			0
$355$	7.22422	+	24.3590i	0.383422	+	1.29284i
$356$	−9.96559	−	16.1836i	−0.528175	−	0.857730i
$357$		0			0
$358$	−16.4384	−	12.9302i	−0.868796	−	0.683380i
$359$	1.82816	−	1.32824i	0.0964867	−	0.0701017i	−0.538496	−	0.842628i	$-0.681007\pi$
$359$	1.82816	−	1.32824i	0.0964867	−	0.0701017i	0.634983	+	0.772526i	$0.281007\pi$
$360$		0			0
$361$	−1.60462	−	1.16583i	−0.0844538	−	0.0613593i
$362$	−5.90338	−	20.8454i	−0.310275	−	1.09561i
$363$		0			0
$364$	0.211905	−	0.0513593i	0.0111068	−	0.00269196i
$365$	−23.8637	+	3.14975i	−1.24908	+	0.164866i
$366$		0			0
$367$	22.5340	−	11.4816i	1.17627	−	0.599337i	0.247096	−	0.968991i	$-0.420524\pi$
$367$	22.5340	−	11.4816i	1.17627	−	0.599337i	0.929169	+	0.369654i	$0.120524\pi$
$368$	−19.1480	−	13.7856i	−0.998160	−	0.718624i
$369$		0			0
$370$	24.2765	−	10.4707i	1.26208	−	0.544345i
$371$	0.101655	−	0.0330297i	0.00527766	−	0.00171481i
$372$		0			0
$373$	2.74365	+	17.3227i	0.142061	+	0.896935i	0.951033	+	0.309089i	$0.100024\pi$
$373$	2.74365	+	17.3227i	0.142061	+	0.896935i	−0.808973	+	0.587846i	$0.799976\pi$
$374$	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	−0.943435	−	0.331557i	$-0.892426\pi$
$379$	−7.30173	−	22.4724i	−0.375065	−	1.15433i	0.568371	−	0.822773i	$-0.307574\pi$
$380$	13.6696	−	15.2581i	0.701238	−	0.782723i
$381$		0			0
$382$	30.5188	+	11.2215i	1.56148	+	0.574139i
$383$	−2.62572	−	5.15327i	−0.134168	−	0.263320i	0.814141	−	0.580667i	$-0.197208\pi$
$383$	−2.62572	−	5.15327i	−0.134168	−	0.263320i	−0.948310	+	0.317347i	$0.897208\pi$
$384$		0			0
$385$	0.0227568	+	0.172414i	0.00115980	+	0.00878705i
$386$	−16.5019	−	3.26387i	−0.839924	−	0.166126i
$387$		0			0
$388$	9.75115	−	8.36484i	0.495039	−	0.424660i
$389$	−12.5726	+	17.3047i	−0.637456	+	0.877382i	−0.998477	−	0.0551754i	$-0.982428\pi$
$389$	−12.5726	+	17.3047i	−0.637456	+	0.877382i	0.361021	+	0.932558i	$0.382428\pi$
$390$		0			0
$391$	10.9520	+	15.0742i	0.553869	+	0.762335i
$392$	19.4034	−	3.92512i	0.980021	−	0.198248i
$393$		0			0
$394$	−20.9808	+	2.50627i	−1.05700	+	0.126264i
$395$	31.6091	−	9.37442i	1.59043	−	0.471678i
$396$		0			0
$397$	6.27013	+	3.19479i	0.314689	+	0.160342i	0.604200	−	0.796833i	$-0.293493\pi$
$397$	6.27013	+	3.19479i	0.314689	+	0.160342i	−0.289511	+	0.957175i	$0.593493\pi$
$398$	−20.0658	+	13.4390i	−1.00581	+	0.673636i
$399$		0			0
$400$	13.4566	+	14.7959i	0.672831	+	0.739796i
$401$	−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
$404$	−11.9596	+	29.0506i	−0.595010	+	1.44532i
$405$		0			0
$406$	−0.337097	+	0.0402681i	−0.0167299	+	0.00199847i
$407$	15.3464	+	15.3464i	0.760691	+	0.760691i
$408$		0			0
$409$	−0.908588	−	1.25056i	−0.0449268	−	0.0618364i	0.785963	−	0.618274i	$-0.212168\pi$
$409$	−0.908588	−	1.25056i	−0.0449268	−	0.0618364i	−0.830889	+	0.556438i	$0.812168\pi$
$410$	0.766099	+	0.304388i	0.0378349	+	0.0150327i
$411$		0			0
$412$	−4.98506	+	4.27634i	−0.245596	+	0.210680i
$413$	−0.0217557	−	0.00344576i	−0.00107053	−	0.000169555i
$414$		0			0
$415$	26.0715	−	12.4460i	1.27980	−	0.610952i
$416$	19.3500	+	7.01986i	0.948711	+	0.344177i
$417$		0			0
$418$	15.7835	+	5.80346i	0.771998	+	0.283856i
$419$	−4.92418	+	15.1551i	−0.240562	+	0.740373i	0.755773	+	0.654834i	$0.227261\pi$
$419$	−4.92418	+	15.1551i	−0.240562	+	0.740373i	−0.996335	+	0.0855393i	$0.972739\pi$
$420$		0			0
$421$	0.995697	+	3.06444i	0.0485273	+	0.149352i	0.972384	−	0.233387i	$-0.0749809\pi$
$421$	0.995697	+	3.06444i	0.0485273	+	0.149352i	−0.923857	+	0.382739i	$0.874981\pi$
$422$	0.487559	−	12.7613i	0.0237340	−	0.621209i
$423$		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
$428$	22.1712	−	9.23988i	1.07168	−	0.446626i
$429$		0			0
$430$	5.50326	+	1.23709i	0.265391	+	0.0596577i
$431$	29.8166	+	9.68800i	1.43621	+	0.466654i	0.920715	−	0.390235i	$-0.127606\pi$
$431$	29.8166	+	9.68800i	1.43621	+	0.466654i	0.515499	+	0.856890i	$0.327606\pi$
$432$		0			0
$433$	25.0873	−	12.7826i	1.20562	−	0.614293i	0.268491	−	0.963282i	$-0.413475\pi$
$433$	25.0873	−	12.7826i	1.20562	−	0.614293i	0.937127	+	0.348990i	$0.113475\pi$
$434$	−0.0686711	−	0.0383601i	−0.00329632	−	0.00184134i
$435$		0			0
$436$	18.1748	−	4.40501i	0.870414	−	0.210962i
$437$	−4.22685	+	26.6873i	−0.202198	+	1.27663i
$438$		0			0
$439$	−25.3167	−	18.3936i	−1.20830	−	0.877881i	−0.213224	−	0.977003i	$-0.568396\pi$
$439$	−25.3167	−	18.3936i	−1.20830	−	0.877881i	−0.995075	+	0.0991225i	$0.968396\pi$
$440$	−7.20871	+	14.7506i	−0.343662	+	0.703208i
$441$		0			0
$442$	−12.7766	−	10.0498i	−0.607720	−	0.478022i
$443$	−27.6411	+	27.6411i	−1.31327	+	1.31327i	−0.394278	+	0.918991i	$0.629005\pi$
$443$	−27.6411	+	27.6411i	−1.31327	+	1.31327i	−0.918991	+	0.394278i	$0.870995\pi$
$444$		0			0
$445$	−16.8624	−	12.9301i	−0.799354	−	0.612946i
$446$	10.2385	−	9.48496i	0.484808	−	0.449126i
$447$		0			0
$448$	−0.222032	−	0.0902838i	−0.0104900	−	0.00426551i
$449$		−	32.7243i		−	1.54436i	−0.635406	−	0.772178i	$-0.719167\pi$
$449$		−	32.7243i		−	1.54436i	0.635406	−	0.772178i	$-0.280833\pi$
$450$		0			0
$451$			0.676707i			0.0318649i
$452$	−1.18649	+	1.94561i	−0.0558076	+	0.0915137i
$453$		0			0
$454$	24.1959	+	26.1182i	1.13557	+	1.22579i
$455$	0.200857	−	0.138143i	0.00941631	−	0.00647624i
$456$		0			0
$457$	7.11038	−	7.11038i	0.332610	−	0.332610i	−0.520967	−	0.853577i	$-0.674429\pi$
$457$	7.11038	−	7.11038i	0.332610	−	0.332610i	0.853577	+	0.520967i	$0.174429\pi$
$458$	−8.59818	+	10.9311i	−0.401767	+	0.510775i
$459$		0			0
$460$	−25.4973	−	6.76383i	−1.18882	−	0.315365i
$461$	20.0752	+	14.5855i	0.934994	+	0.679313i	0.947210	−	0.320613i	$-0.103889\pi$
$461$	20.0752	+	14.5855i	0.934994	+	0.679313i	−0.0122168	+	0.999925i	$0.503889\pi$
$462$		0			0
$463$	−4.64024	+	29.2973i	−0.215650	+	1.36156i	0.607763	+	0.794119i	$0.292067\pi$
$463$	−4.64024	+	29.2973i	−0.215650	+	1.36156i	−0.823413	+	0.567443i	$0.807933\pi$
$464$	−28.6193	−	14.4265i	−1.32862	−	0.669735i
$465$		0			0
$466$	−7.81632	+	13.9925i	−0.362084	+	0.648192i
$467$	−35.6038	+	18.1410i	−1.64755	+	0.839468i	−0.650768	+	0.759276i	$0.725553\pi$
$467$	−35.6038	+	18.1410i	−1.64755	+	0.839468i	−0.996779	+	0.0801913i	$0.974447\pi$
$468$		0			0
$469$	0.0951245	+	0.0309078i	0.00439244	+	0.00142719i
$470$	37.2244	−	3.47350i	1.71703	−	0.160221i
$471$		0			0
$472$	−1.53155	−	1.40656i	−0.0704954	−	0.0647421i
$473$	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
$478$	28.1322	+	1.07482i	1.28674	+	0.0491613i
$479$	−1.67227	−	5.14672i	−0.0764080	−	0.235160i	0.905556	−	0.424226i	$-0.139454\pi$
$479$	−1.67227	−	5.14672i	−0.0764080	−	0.235160i	−0.981964	+	0.189067i	$0.939454\pi$
$480$		0			0
$481$	9.40093	−	28.9331i	0.428645	−	1.31923i
$482$	9.03949	−	24.5845i	0.411738	−	1.11979i
$483$		0			0
$484$	8.49784	+	0.650289i	0.386265	+	0.0295586i
$485$	6.84964	−	12.6254i	0.311026	−	0.573291i
$486$		0			0
$487$	−33.8274	−	5.35774i	−1.53287	−	0.242782i	−0.667763	−	0.744374i	$-0.732748\pi$
$487$	−33.8274	−	5.35774i	−1.53287	−	0.242782i	−0.865105	+	0.501591i	$0.832748\pi$
$488$	−5.76613	+	12.6153i	−0.261021	+	0.571067i
$489$		0			0
$490$	18.7019	−	11.8370i	0.844864	−	0.534741i
$491$	−8.94325	−	12.3093i	−0.403603	−	0.555512i	0.558041	−	0.829814i	$-0.311553\pi$
$491$	−8.94325	−	12.3093i	−0.403603	−	0.555512i	−0.961644	+	0.274302i	$0.911553\pi$
$492$		0			0
$493$	17.8970	+	17.8970i	0.806040	+	0.806040i
$494$	−2.79600	−	23.4062i	−0.125798	−	1.05309i
$495$		0			0
$496$	−3.39984	−	6.60174i	−0.152657	−	0.296427i
$497$	−0.303328	−	0.154553i	−0.0136061	−	0.00693266i
$498$		0			0
$499$	−2.90097			−0.129865			−0.0649327	−	0.997890i	$-0.520683\pi$
$499$	−2.90097			−0.129865			−0.0649327	+	0.997890i	$0.520683\pi$
$500$	19.9555	+	10.0886i	0.892436	+	0.451175i
$501$		0			0
$502$	−9.08354	−	13.5627i	−0.405418	−	0.605332i
$503$	7.33460	+	3.73716i	0.327034	+	0.166632i	0.609797	−	0.792558i	$-0.291251\pi$
$503$	7.33460	+	3.73716i	0.327034	+	0.166632i	−0.282763	+	0.959190i	$0.591251\pi$
$504$		0			0
$505$	−0.907825	+	35.1125i	−0.0403977	+	1.56249i
$506$	−2.56849	−	21.5016i	−0.114183	−	0.955865i
$507$		0			0
$508$	22.0432	+	5.24167i	0.978011	+	0.232562i
$509$	−3.84108	−	5.28680i	−0.170253	−	0.234333i	0.715361	−	0.698755i	$-0.246262\pi$
$509$	−3.84108	−	5.28680i	−0.170253	−	0.234333i	−0.885614	+	0.464422i	$0.846262\pi$
$510$		0			0
$511$	0.189572	−	0.260923i	0.00838617	−	0.0115426i
$512$	−12.7538	−	18.6907i	−0.563643	−	0.826019i
$513$		0			0
$514$	2.83141	−	14.3154i	0.124888	−	0.631425i
$515$	−3.50173	+	6.45448i	−0.154305	+	0.284418i
$516$		0			0
$517$	13.9330	+	27.3450i	0.612771	+	1.20263i
$518$	−0.122250	+	0.332480i	−0.00537134	+	0.0146083i
$519$		0			0
$520$	23.0104	−	0.383570i	1.00907	−	0.0168207i
$521$	5.29421	+	16.2939i	0.231944	+	0.713849i	0.997512	+	0.0704945i	$0.0224577\pi$
$521$	5.29421	+	16.2939i	0.231944	+	0.713849i	−0.765569	+	0.643354i	$0.777542\pi$
$522$		0			0
$523$	6.28174	−	0.994930i	0.274681	−	0.0435053i	−0.0175740	−	0.999846i	$-0.505594\pi$
$523$	6.28174	−	0.994930i	0.274681	−	0.0435053i	0.292255	+	0.956340i	$0.405594\pi$
$524$	−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
$530$	11.2328	−	1.04816i	0.487921	−	0.0455291i
$531$		0			0
$532$	0.0221282	+	0.273593i	0.000959379	+	0.0118617i
$533$	0.845180	−	0.430641i	0.0366088	−	0.0186531i
$534$		0			0
$535$	19.4735	−	18.4919i	0.841914	−	0.799477i
$536$	5.86973	+	7.39620i	0.253534	+	0.319467i
$537$		0			0
$538$	−25.9159	+	7.33932i	−1.11731	+	0.316421i
$539$	14.6990	+	10.6794i	0.633129	+	0.459995i
$540$		0			0
$541$	−22.6575	+	16.4616i	−0.974122	+	0.707741i	−0.956387	−	0.292102i	$-0.905645\pi$
$541$	−22.6575	+	16.4616i	−0.974122	+	0.707741i	−0.0177348	+	0.999843i	$0.505645\pi$
$542$	16.2546	−	20.6648i	0.698193	−	0.887628i
$543$		0			0
$544$	4.94342	+	17.1718i	0.211947	+	0.736235i
$545$	17.2272	−	11.8483i	0.737931	−	0.507526i
$546$		0			0
$547$	1.24110	−	2.43580i	0.0530657	−	0.104147i	−0.862951	−	0.505288i	$-0.831386\pi$
$547$	1.24110	−	2.43580i	0.0530657	−	0.104147i	0.916016	+	0.401141i	$0.131386\pi$
$548$	0.486666	+	0.296782i	0.0207894	+	0.0126779i
$549$		0			0
$550$	−1.64769	+	18.2816i	−0.0702579	+	0.779531i
$551$			36.7031i			1.56361i
$552$		0			0
$553$	−0.200554	+	0.393610i	−0.00852843	+	0.0167380i
$554$	29.2247	−	27.0738i	1.24164	−	1.15025i
$555$		0			0
$556$	11.7315	−	7.22402i	0.497525	−	0.306367i
$557$	−14.0130	+	14.0130i	−0.593751	+	0.593751i	−0.938643	−	0.344891i	$-0.887916\pi$
$557$	−14.0130	+	14.0130i	−0.593751	+	0.593751i	0.344891	+	0.938643i	$0.387916\pi$
$558$		0			0
$559$	5.25094	−	3.81503i	0.222091	−	0.161359i
$560$	−0.267915	−	0.00576634i	−0.0113215	−	0.000243672i
$561$		0			0
$562$	−5.17841	−	18.2855i	−0.218438	−	0.771327i
$563$	2.73526	−	17.2697i	0.115277	−	0.727832i	−0.860562	−	0.509345i	$-0.829888\pi$
$563$	2.73526	−	17.2697i	0.115277	−	0.727832i	0.975840	−	0.218487i	$-0.0701123\pi$
$564$		0			0
$565$	−0.463476	+	2.50532i	−0.0194986	+	0.105400i
$566$	13.3854	+	7.47717i	0.562630	+	0.314289i
$567$		0			0
$568$	−15.7945	−	27.9895i	−0.662721	−	1.17441i
$569$	−27.6880	−	8.99636i	−1.16074	−	0.377147i	−0.335561	−	0.942019i	$-0.608926\pi$
$569$	−27.6880	−	8.99636i	−1.16074	−	0.377147i	−0.825179	+	0.564871i	$0.808926\pi$
$570$		0			0
$571$	−1.78586	+	0.580261i	−0.0747358	+	0.0242831i	−0.346146	−	0.938181i	$-0.612510\pi$
$571$	−1.78586	+	0.580261i	−0.0747358	+	0.0242831i	0.271410	+	0.962464i	$0.412510\pi$
$572$	7.26731	+	17.4380i	0.303861	+	0.729118i
$573$		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	0.392231	−	0.919867i	$-0.371703\pi$
$577$	25.2103	−	3.99292i	1.04952	−	0.166227i	0.657288	+	0.753639i	$0.271703\pi$
$578$	−0.379113	+	9.92283i	−0.0157690	+	0.412735i
$579$		0			0
$580$	−35.6457	−	3.65659i	−1.48011	−	0.151832i
$581$	−0.119618	+	0.368145i	−0.00496258	+	0.0152732i
$582$		0			0
$583$	4.20439	+	8.25158i	0.174128	+	0.341746i
$584$	28.5310	−	10.6310i	1.18062	−	0.439914i
$585$		0			0
$586$	1.80847	+	0.357693i	0.0747073	+	0.0147762i
$587$	−13.7586	−	2.17915i	−0.567879	−	0.0899432i	−0.134109	−	0.990967i	$-0.542817\pi$
$587$	−13.7586	−	2.17915i	−0.567879	−	0.0899432i	−0.433771	+	0.901023i	$0.642817\pi$
$588$		0			0
$589$	−4.99848	+	6.87981i	−0.205959	+	0.283478i
$590$	−2.16059	−	0.858449i	−0.0889500	−	0.0353418i
$591$		0			0
$592$	−26.9699	+	19.7737i	−1.10846	+	0.812695i
$593$	30.4927	+	30.4927i	1.25219	+	1.25219i	0.954738	+	0.297448i	$0.0961356\pi$
$593$	30.4927	+	30.4927i	1.25219	+	1.25219i	0.297448	+	0.954738i	$0.403864\pi$
$594$		0			0
$595$	0.199510	+	0.0705759i	0.00817911	+	0.00289333i
$596$	−15.2389	−	6.27355i	−0.624210	−	0.256975i
$597$		0			0
$598$	−25.2202	+	16.8911i	−1.03133	+	0.690728i
$599$	20.9517			0.856063			0.428032	−	0.903764i	$-0.359207\pi$
$599$	20.9517			0.856063			0.428032	+	0.903764i	$0.359207\pi$
$600$		0			0
$601$	−34.4158			−1.40385			−0.701925	−	0.712251i	$-0.747676\pi$
$601$	−34.4158			−1.40385			−0.701925	+	0.712251i	$0.747676\pi$
$602$	−0.0627948	+	0.0420565i	−0.00255933	+	0.00171410i
$603$		0			0
$604$	−41.1524	−	16.9416i	−1.67447	−	0.689344i
$605$	9.13536	−	2.70931i	0.371405	−	0.110149i
$606$		0			0
$607$	−30.1682	−	30.1682i	−1.22449	−	1.22449i	−0.966020	−	0.258469i	$-0.916782\pi$
$607$	−30.1682	−	30.1682i	−1.22449	−	1.22449i	−0.258469	−	0.966020i	$-0.583218\pi$
$608$	−12.5390	+	22.6769i	−0.508523	+	0.919671i
$609$		0			0
$610$	−0.992389	+	15.4760i	−0.0401806	+	0.626606i
$611$	25.2862	−	34.8034i	1.02297	−	1.40800i
$612$		0			0
$613$	−32.0453	−	5.07547i	−1.29430	−	0.204996i	−0.528971	−	0.848640i	$-0.677422\pi$
$613$	−32.0453	−	5.07547i	−1.29430	−	0.204996i	−0.765326	+	0.643643i	$0.777422\pi$
$614$	−31.1092	−	6.15300i	−1.25546	−	0.248315i
$615$		0			0
$616$	−0.0768087	−	0.206135i	−0.00309471	−	0.00830543i
$617$	−5.54357	−	10.8799i	−0.223176	−	0.438007i	0.752085	−	0.659067i	$-0.229048\pi$
$617$	−5.54357	−	10.8799i	−0.223176	−	0.438007i	−0.975260	+	0.221060i	$0.929048\pi$
$618$		0			0
$619$	2.03053	−	6.24934i	0.0816140	−	0.251182i	−0.901921	−	0.431902i	$-0.857843\pi$
$619$	2.03053	−	6.24934i	0.0816140	−	0.251182i	0.983535	+	0.180720i	$0.0578427\pi$
$620$	−6.18362	−	5.53987i	−0.248340	−	0.222487i
$621$		0			0
$622$	−0.947976	+	24.8121i	−0.0380104	+	0.994876i
$623$	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
$628$	−6.34177	−	15.2171i	−0.253064	−	0.607230i
$629$	25.1171	−	8.16105i	1.00149	−	0.325402i
$630$		0			0
$631$	−12.7502	−	4.14278i	−0.507576	−	0.164921i	0.0440238	−	0.999030i	$-0.485982\pi$
$631$	−12.7502	−	4.14278i	−0.507576	−	0.164921i	−0.551599	+	0.834109i	$0.685982\pi$
$632$	−36.3202	+	20.4955i	−1.44474	+	0.815267i
$633$		0			0
$634$	−8.42177	−	4.70445i	−0.334471	−	0.186838i
$635$	25.1145	−	3.31484i	0.996637	−	0.131545i
$636$		0			0
$637$	3.98409	−	25.1546i	0.157855	−	0.996660i
$638$	−8.01501	−	28.3018i	−0.317317	−	1.12048i
$639$		0			0
$640$	−20.7744	−	14.4369i	−0.821180	−	0.570670i
$641$	5.26652	−	3.82635i	0.208015	−	0.151132i	−0.478900	−	0.877869i	$-0.658964\pi$
$641$	5.26652	−	3.82635i	0.208015	−	0.151132i	0.686915	+	0.726738i	$0.258964\pi$
$642$		0			0
$643$	−24.1498	+	24.1498i	−0.952377	+	0.952377i	−0.998916	−	0.0465397i	$-0.985181\pi$
$643$	−24.1498	+	24.1498i	−0.952377	+	0.952377i	0.0465397	+	0.998916i	$0.485181\pi$
$644$	0.300966	−	0.185329i	0.0118597	−	0.00730300i
$645$		0			0
$646$	15.0119	−	13.9070i	0.590634	−	0.547164i
$647$	−16.9157	+	33.1990i	−0.665026	+	1.30519i	0.274129	+	0.961693i	$0.411611\pi$
$647$	−16.9157	+	33.1990i	−0.665026	+	1.30519i	−0.939155	+	0.343494i	$0.888389\pi$
$648$		0			0
$649$		−	1.90848i		−	0.0749144i
$650$	23.8816	−	9.57611i	0.936713	−	0.375606i
$651$		0			0
$652$	−35.0179	−	21.3548i	−1.37141	−	0.836320i
$653$	−1.60583	+	3.15162i	−0.0628409	+	0.123332i	−0.920290	−	0.391236i	$-0.872048\pi$
$653$	−1.60583	+	3.15162i	−0.0628409	+	0.123332i	0.857450	+	0.514568i	$0.172048\pi$
$654$		0			0
$655$	−7.18512	+	20.3115i	−0.280746	+	0.793636i
$656$	−1.03059	−	0.158660i	−0.0402379	−	0.00619461i
$657$		0			0
$658$	−0.309697	+	0.393724i	−0.0120732	+	0.0153490i
$659$	0.360535	−	0.261944i	0.0140445	−	0.0102039i	−0.580741	−	0.814088i	$-0.697237\pi$
$659$	0.360535	−	0.261944i	0.0140445	−	0.0102039i	0.594785	+	0.803885i	$0.297237\pi$
$660$		0			0
$661$	12.6735	+	9.20784i	0.492942	+	0.358144i	0.806315	−	0.591487i	$-0.201459\pi$
$661$	12.6735	+	9.20784i	0.492942	+	0.358144i	−0.313372	+	0.949630i	$0.601459\pi$
$662$	8.84181	−	2.50398i	0.343647	−	0.0973200i
$663$		0			0
$664$	−28.6243	+	22.7167i	−1.11084	+	0.881579i
$665$	0.132209	+	0.276946i	0.00512684	+	0.0107395i
$666$		0			0
$667$	42.1107	−	21.4565i	1.63053	−	0.830798i
$668$	1.83327	+	22.6665i	0.0709312	+	0.876992i
$669$		0			0
$670$	9.08023	+	5.38481i	0.350800	+	0.208033i
$671$	−12.1072	+	3.93387i	−0.467393	+	0.151865i
$672$		0			0
$673$	−5.14603	−	32.4907i	−0.198365	−	1.25243i	−0.862979	−	0.505240i	$-0.831404\pi$
$673$	−5.14603	−	32.4907i	−0.198365	−	1.25243i	0.664614	−	0.747187i	$-0.268596\pi$
$674$	−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	−0.337062	−	0.941482i	$-0.609433\pi$
$677$	−9.54108	+	1.51116i	−0.366693	+	0.0580785i	−0.0296312	+	0.999561i	$0.509433\pi$
$678$		0			0
$679$	0.0594729	+	0.183039i	0.00228236	+	0.00702439i
$680$	12.0107	+	15.9649i	0.460591	+	0.612225i
$681$		0			0
$682$	2.35196	−	6.39657i	0.0900611	−	0.244937i
$683$	−0.657454	−	1.29033i	−0.0251568	−	0.0493729i	0.878086	−	0.478503i	$-0.158820\pi$
$683$	−0.657454	−	1.29033i	−0.0251568	−	0.0493729i	−0.903243	+	0.429130i	$0.858820\pi$
$684$		0			0
$685$	0.626670	+	0.115932i	0.0239438	+	0.00442953i
$686$	−0.115089	+	0.581881i	−0.00439411	+	0.0222163i
$687$		0			0
$688$	−7.13478	+	0.0308885i	−0.272011	+	0.00117761i
$689$	7.63032	−	10.5022i	0.290692	−	0.400103i
$690$		0			0
$691$	8.30255	+	11.4275i	0.315844	+	0.434722i	0.937193	−	0.348812i	$-0.113415\pi$
$691$	8.30255	+	11.4275i	0.315844	+	0.434722i	−0.621349	+	0.783534i	$0.713415\pi$
$692$	38.5696	+	9.17149i	1.46620	+	0.348648i
$693$		0			0
$694$	−1.91044	−	15.9929i	−0.0725193	−	0.607082i
$695$	9.37299	−	12.2235i	0.355538	−	0.463664i
$696$		0			0
$697$	0.733711	+	0.373844i	0.0277913	+	0.0141604i
$698$	2.95195	+	4.40756i	0.111733	+	0.166829i
$699$		0			0
$700$	−0.282138	+	0.100809i	−0.0106638	+	0.00381021i
$701$	−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
$704$	4.71676	−	20.2244i	0.177770	−	0.762236i
$705$		0			0
$706$	5.09548	+	42.6559i	0.191771	+	1.60538i
$707$	−0.332782	−	0.332782i	−0.0125155	−	0.0125155i
$708$		0			0
$709$	−12.7559	−	17.5570i	−0.479057	−	0.659366i	0.499266	−	0.866449i	$-0.333603\pi$
$709$	−12.7559	−	17.5570i	−0.479057	−	0.659366i	−0.978323	+	0.207083i	$0.933603\pi$
$710$	−27.6583	−	22.9371i	−1.03800	−	0.860816i
$711$		0			0
$712$	24.4458	+	11.1736i	0.916145	+	0.418747i
$713$	10.8155	+	1.71301i	0.405044	+	0.0641527i
$714$		0			0
$715$	14.5442	+	15.3162i	0.543922	+	0.572795i
$716$	29.4911	+	2.25678i	1.10213	+	0.0843398i
$717$		0			0
$718$	−1.10286	+	2.99941i	−0.0411582	+	0.111937i
$719$	6.74838	−	20.7694i	0.251672	−	0.774567i	−0.742795	−	0.669519i	$-0.766500\pi$
$719$	6.74838	−	20.7694i	0.251672	−	0.774567i	0.994467	−	0.105048i	$-0.0334997\pi$
$720$		0			0
$721$	−0.0304042	−	0.0935746i	−0.00113231	−	0.00348490i
$722$	2.80294	+	0.107089i	0.104315	+	0.00398546i
$723$		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	−0.999345	−	0.0361826i	$-0.988480\pi$
$727$	−1.62027	−	10.2300i	−0.0600925	−	0.379409i	0.939253	−	0.343226i	$-0.111520\pi$
$728$	−0.208576	+	0.227111i	−0.00773033	+	0.00841729i
$729$		0			0
$730$	25.5617	−	22.4810i	0.946081	−	0.832059i
$731$	5.35872	+	1.74115i	0.198199	+	0.0643989i
$732$		0			0
$733$	7.04429	−	3.58925i	0.260187	−	0.132572i	−0.319032	−	0.947744i	$-0.603358\pi$
$733$	7.04429	−	3.58925i	0.260187	−	0.132572i	0.579219	+	0.815172i	$0.303358\pi$
$734$	−17.4423	+	31.2247i	−0.643808	+	1.15253i
$735$		0			0
$736$	33.3482	+	1.12955i	1.22923	+	0.0416356i
$737$	−1.35567	+	8.55935i	−0.0499366	+	0.315288i
$738$		0			0
$739$	−39.2364	−	28.5069i	−1.44334	−	1.04864i	−0.987332	−	0.158666i	$-0.949281\pi$
$739$	−39.2364	−	28.5069i	−1.44334	−	1.04864i	−0.456003	−	0.889978i	$-0.650719\pi$
$740$	−20.2854	+	31.4081i	−0.745707	+	1.15459i
$741$		0			0
$742$	−0.0934537	+	0.118810i	−0.00343079	+	0.00436164i
$743$	22.8092	−	22.8092i	0.836787	−	0.836787i	−0.151648	−	0.988435i	$-0.548458\pi$
$743$	22.8092	−	22.8092i	0.836787	−	0.836787i	0.988435	+	0.151648i	$0.0484580\pi$
$744$		0			0
$745$	−18.4188	−	0.476212i	−0.674811	−	0.0174471i
$746$	−16.8562	−	18.1954i	−0.617151	−	0.666182i
$747$		0			0
$748$	−8.53874	+	14.0019i	−0.312207	+	0.511960i
$749$			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	$-0.319104\pi$
$752$	−44.9118	+	14.8080i	−1.63777	+	0.539993i
$753$		0			0
$754$	−30.2473	+	28.0211i	−1.10154	+	1.02047i
$755$	−49.7395	−	1.28600i	−1.81021	−	0.0468024i
$756$		0			0
$757$	−8.32615	+	8.32615i	−0.302619	+	0.302619i	−0.842038	−	0.539419i	$-0.818644\pi$
$757$	−8.32615	+	8.32615i	−0.302619	+	0.302619i	0.539419	+	0.842038i	$0.318644\pi$
$758$	26.2648	+	20.6594i	0.953979	+	0.750383i
$759$		0			0
$760$	−4.05456	+	28.6862i	−0.147074	+	1.04056i
$761$	−29.2453	−	21.2480i	−1.06014	−	0.770239i	−0.0860281	−	0.996293i	$-0.527417\pi$
$761$	−29.2453	−	21.2480i	−1.06014	−	0.770239i	−0.974115	+	0.226054i	$0.927417\pi$
$762$		0			0
$763$	−0.0438247	+	0.276698i	−0.00158656	+	0.0100171i
$764$	−44.6912	+	10.8318i	−1.61687	+	0.391880i
$765$		0			0
$766$	7.14075	+	3.98887i	0.258006	+	0.144124i
$767$	−2.38362	+	1.21451i	−0.0860674	+	0.0438535i
$768$		0			0
$769$	−16.5650	−	5.38228i	−0.597348	−	0.194090i	−0.00529061	−	0.999986i	$-0.501684\pi$
$769$	−16.5650	−	5.38228i	−0.597348	−	0.194090i	−0.592057	+	0.805896i	$0.701684\pi$
$770$	−0.162424	−	0.184682i	−0.00585336	−	0.00665549i
$771$		0			0
$772$	21.9587	−	9.15132i	0.790310	−	0.329363i
$773$	−0.778227	−	4.91353i	−0.0279909	−	0.176728i	0.969732	−	0.244171i	$-0.0785158\pi$
$773$	−0.778227	−	4.91353i	−0.0279909	−	0.176728i	−0.997723	+	0.0674434i	$0.978516\pi$
$774$		0			0
$775$	−8.66788	−	3.32071i	−0.311359	−	0.119283i
$776$	−4.87498	+	17.5027i	−0.175002	+	0.628311i
$777$		0			0
$778$	1.15488	−	30.2276i	0.0414045	−	1.08371i
$779$	0.369007	+	1.13569i	0.0132210	+	0.0406902i
$780$		0			0
$781$	9.11482	−	28.0525i	0.326154	−	1.00380i
$782$	−24.7318	−	9.09365i	−0.884408	−	0.325188i
$783$		0			0
$784$	−19.7106	+	19.8820i	−0.703949	+	0.710070i
$785$	−12.6919	−	13.3656i	−0.452994	−	0.477039i
$786$		0			0
$787$	−17.8401	−	2.82559i	−0.635930	−	0.100721i	−0.169858	−	0.985468i	$-0.554331\pi$
$787$	−17.8401	−	2.82559i	−0.635930	−	0.100721i	−0.466071	+	0.884747i	$0.654331\pi$
$788$	22.6806	−	19.4561i	0.807962	−	0.693095i
$789$		0			0
$790$	−29.7641	+	35.8905i	−1.05896	+	1.27693i
$791$	−0.0200658	−	0.0276182i	−0.000713457	−	0.000981989i
$792$		0			0
$793$	12.6180	+	12.6180i	0.448078	+	0.448078i
$794$	−9.88176	+	1.18043i	−0.350690	+	0.0418919i
$795$		0			0
$796$	13.0018	−	31.5823i	0.460836	−	1.11940i
$797$	−11.5754	−	5.89797i	−0.410022	−	0.208917i	0.236799	−	0.971559i	$-0.423902\pi$
$797$	−11.5754	−	5.89797i	−0.410022	−	0.208917i	−0.646821	+	0.762642i	$0.723902\pi$
$798$		0			0
$799$	37.3456			1.32119
$800$	−27.4558	−	6.79564i	−0.970708	−	0.240262i
$801$		0			0
$802$	36.1993	−	24.2443i	1.27824	−	0.856097i
$803$	24.8984	+	12.6864i	0.878644	+	0.447692i
$804$		0			0
$805$	0.240460	−	0.313589i	0.00847511	−	0.0110526i
$806$	−9.48579	+	1.13313i	−0.334123	+	0.0399128i
$807$		0			0
$808$	−8.80912	−	43.5470i	−0.309904	−	1.53198i
$809$	21.2576	+	29.2586i	0.747379	+	1.02868i	0.998160	+	0.0606351i	$0.0193126\pi$
$809$	21.2576	+	29.2586i	0.747379	+	1.02868i	−0.250781	+	0.968044i	$0.580687\pi$
$810$		0			0
$811$	−30.8598	+	42.4749i	−1.08364	+	1.49150i	−0.228180	+	0.973619i	$0.573277\pi$
$811$	−30.8598	+	42.4749i	−1.08364	+	1.49150i	−0.855455	+	0.517877i	$0.826723\pi$
$812$	0.364408	−	0.312600i	0.0127882	−	0.0109701i
$813$		0			0
$814$	−30.1094	−	5.95527i	−1.05534	−	0.208732i
$815$	−45.0917	−	8.34182i	−1.57949	−	0.292201i
$816$		0			0
$817$	3.70945	+	7.28021i	0.129777	+	0.254702i
$818$	2.05177	+	0.754415i	0.0717383	+	0.0263775i
$819$		0			0
$820$	−1.13973	+	0.245231i	−0.0398011	+	0.00856385i
$821$	2.47595	+	7.62021i	0.0864114	+	0.265947i	0.984920	−	0.173008i	$-0.0553487\pi$
$821$	2.47595	+	7.62021i	0.0864114	+	0.265947i	−0.898509	+	0.438955i	$0.855349\pi$
$822$		0			0
$823$	−33.6993	+	5.33745i	−1.17468	+	0.186052i	−0.713111	−	0.701051i	$-0.752715\pi$
$823$	−33.6993	+	5.33745i	−1.17468	+	0.186052i	−0.461573	+	0.887102i	$0.652715\pi$
$824$	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	−0.995156	−	0.0983080i	$-0.968657\pi$
$827$	−2.27430	−	14.3594i	−0.0790852	−	0.499325i	0.916071	−	0.401017i	$-0.131343\pi$
$828$		0			0
$829$	−9.98390	+	3.24396i	−0.346755	+	0.112668i	−0.477216	−	0.878786i	$-0.658354\pi$
$829$	−9.98390	+	3.24396i	−0.346755	+	0.112668i	0.130461	+	0.991453i	$0.458354\pi$
$830$	−20.8400	+	35.1418i	−0.723367	+	1.21979i
$831$		0			0
$832$	−28.2611	+	6.97930i	−0.979778	+	0.241964i
$833$	19.6994	−	10.0374i	0.682544	−	0.347774i
$834$		0			0
$835$	10.9532	+	22.9443i	0.379051	+	0.794020i
$836$	−23.1132	+	5.60193i	−0.799386	+	0.193747i
$837$		0			0
$838$	−6.14050	−	21.6827i	−0.212120	−	0.749017i
$839$	−22.2107	−	16.1370i	−0.766797	−	0.557111i	0.134191	−	0.990956i	$-0.457157\pi$
$839$	−22.2107	−	16.1370i	−0.766797	−	0.557111i	−0.900988	+	0.433845i	$0.857157\pi$
$840$		0			0
$841$	28.4768	−	20.6896i	0.981957	−	0.713434i
$842$	−3.58158	−	2.81721i	−0.123429	−	0.0970875i
$843$		0			0
$844$	9.46980	+	15.3785i	0.325964	+	0.529350i
$845$	0.179453	−	0.507293i	0.00617337	−	0.0174514i
$846$		0			0
$847$	−0.0579622	+	0.113757i	−0.00199161	+	0.00390875i
$848$	−13.5525	+	4.46844i	−0.465396	+	0.153447i
$849$		0			0
$850$	18.9114	+	11.8861i	0.648654	+	0.407690i
$851$		−	49.3152i		−	1.69050i
$852$		0			0
$853$	10.4218	−	20.4539i	0.356836	−	0.700329i	−0.640897	−	0.767627i	$-0.721438\pi$
$853$	10.4218	−	20.4539i	0.356836	−	0.700329i	0.997733	+	0.0672973i	$0.0214376\pi$
$854$	−0.141211	−	0.152430i	−0.00483213	−	0.00521604i
$855$		0			0
$856$	−18.7802	+	28.3051i	−0.641894	+	0.967447i
$857$	−7.96786	+	7.96786i	−0.272177	+	0.272177i	−0.829976	−	0.557799i	$-0.811646\pi$
$857$	−7.96786	+	7.96786i	−0.272177	+	0.272177i	0.557799	+	0.829976i	$0.311646\pi$
$858$		0			0
$859$	9.67439	−	7.02885i	0.330086	−	0.239821i	−0.410381	−	0.911914i	$-0.634604\pi$
$859$	9.67439	−	7.02885i	0.330086	−	0.239821i	0.740467	+	0.672093i	$0.234604\pi$
$860$	−7.44002	+	2.87728i	−0.253702	+	0.0981144i
$861$		0			0
$862$	−42.6594	+	12.0810i	−1.45298	+	0.411482i
$863$	6.25940	−	39.5203i	0.213073	−	1.34529i	−0.616706	−	0.787194i	$-0.711533\pi$
$863$	6.25940	−	39.5203i	0.213073	−	1.34529i	0.829778	−	0.558093i	$-0.188467\pi$
$864$		0			0
$865$	43.9434	−	5.80005i	1.49412	−	0.197208i
$866$	−19.4187	+	34.7627i	−0.659873	+	1.18129i
$867$		0			0
$868$	0.110878	−	0.00896786i	0.00376346	−	0.000304389i
$869$	−36.4021	−	11.8277i	−1.23486	−	0.401229i
$870$		0			0
$871$	11.5530	−	3.75380i	0.391458	−	0.127193i
$872$	−17.8892	+	19.4789i	−0.605805	+	0.659640i
$873$		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	−0.0645431	−	0.997915i	$-0.520559\pi$
$877$	5.40297	−	0.855747i	0.182445	−	0.0288965i	0.246989	+	0.969018i	$0.420559\pi$
$878$	44.2229	+	1.68959i	1.49245	+	0.0570208i
$879$		0			0
$880$	−3.13785	−	23.0054i	−0.105777	−	0.775511i
$881$	16.7420	−	51.5264i	0.564051	−	1.73597i	−0.106705	−	0.994291i	$-0.534030\pi$
$881$	16.7420	−	51.5264i	0.564051	−	1.73597i	0.670755	−	0.741679i	$-0.265970\pi$
$882$		0			0
$883$	20.7386	+	40.7019i	0.697911	+	1.36973i	0.918916	+	0.394454i	$0.129066\pi$
$883$	20.7386	+	40.7019i	0.697911	+	1.36973i	−0.221005	+	0.975273i	$0.570934\pi$
$884$	22.9217	+	1.75406i	0.770940	+	0.0589954i
$885$		0			0
$886$	10.7263	−	54.2316i	0.360358	−	1.82195i
$887$	26.6295	+	4.21771i	0.894133	+	0.141617i	0.586558	−	0.809907i	$-0.300483\pi$
$887$	26.6295	+	4.21771i	0.894133	+	0.141617i	0.307575	+	0.951524i	$0.400483\pi$
$888$		0			0
$889$	−0.199508	+	0.274599i	−0.00669128	+	0.00920976i
$890$	29.9893	+	1.92304i	1.00524	+	0.0644605i
$891$		0			0
$892$	−4.56616	+	19.2024i	−0.152886	+	0.642945i
$893$	38.2942	+	38.2942i	1.28147	+	1.28147i
$894$		0			0
$895$	31.7036	−	9.40244i	1.05973	−	0.314289i
$896$	0.331943	−	0.0686459i	0.0110894	−	0.00229330i
$897$		0			0
$898$	25.7530	+	38.4519i	0.859388	+	1.28316i
$899$	14.8746			0.496096
$900$		0			0
$901$	11.2694			0.375437
$902$	−0.532546	−	0.795147i	−0.0177319	−	0.0264755i
$903$		0			0
$904$	−0.136981	−	3.21986i	−0.00455592	−	0.107091i
$905$	32.2946	+	11.4241i	1.07351	+	0.379750i
$906$		0			0
$907$	−8.52774	−	8.52774i	−0.283159	−	0.283159i	0.551209	−	0.834368i	$-0.314167\pi$
$907$	−8.52774	−	8.52774i	−0.283159	−	0.283159i	−0.834368	+	0.551209i	$0.814167\pi$
$908$	−48.9849	−	11.6481i	−1.62562	−	0.386557i
$909$		0			0
$910$	−0.127298	+	0.320389i	−0.00421988	+	0.0106208i
$911$	−30.7632	+	42.3419i	−1.01923	+	1.40285i	−0.106487	+	0.994314i	$0.533960\pi$
$911$	−30.7632	+	42.3419i	−1.01923	+	1.40285i	−0.912742	+	0.408535i	$0.866040\pi$
$912$		0			0
$913$	−33.1259	−	5.24663i	−1.09631	−	0.173638i
$914$	−2.75924	+	13.9505i	−0.0912674	+	0.461442i
$915$		0			0
$916$	1.50069	−	19.6107i	0.0495843	−	0.647957i
$917$	−0.131057	−	0.257213i	−0.00432787	−	0.00849392i
$918$		0			0
$919$	2.30130	−	7.08267i	0.0759129	−	0.233636i	−0.905898	−	0.423495i	$-0.860803\pi$
$919$	2.30130	−	7.08267i	0.0759129	−	0.233636i	0.981811	+	0.189859i	$0.0608031\pi$
$920$	35.2829	−	12.1179i	1.16324	−	0.399515i
$921$		0			0
$922$	−35.0671	−	1.33978i	−1.15487	−	0.0441233i
$923$	−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
$928$	44.9815	−	5.57091i	1.47659	−	0.182874i
$929$	8.13021	−	2.64167i	0.266744	−	0.0866703i	−0.172592	−	0.984993i	$-0.555214\pi$
$929$	8.13021	−	2.64167i	0.266744	−	0.0866703i	0.439335	+	0.898323i	$0.355214\pi$
$930$		0			0
$931$	30.4921	+	9.90747i	0.999337	+	0.324704i
$932$	−1.82731	−	22.5928i	−0.0598554	−	0.740051i
$933$		0			0
$934$	27.5589	−	49.3352i	0.901756	−	1.61430i
$935$	−3.33548	+	18.0299i	−0.109082	+	0.589642i
$936$		0			0
$937$	−4.86156	+	30.6947i	−0.158820	+	1.00275i	0.771560	+	0.636156i	$0.219477\pi$
$937$	−4.86156	+	30.6947i	−0.158820	+	1.00275i	−0.930381	+	0.366595i	$0.880523\pi$
$938$	−0.136097	+	0.0385424i	−0.00444373	+	0.00125845i
$939$		0			0
$940$	−41.0060	+	33.3758i	−1.33747	+	1.08860i
$941$	−13.4123	+	9.74458i	−0.437227	+	0.317664i	−0.784532	−	0.620088i	$-0.787097\pi$
$941$	−13.4123	+	9.74458i	−0.437227	+	0.317664i	0.347305	+	0.937752i	$0.387097\pi$
$942$		0			0
$943$	1.08729	−	1.08729i	0.0354071	−	0.0354071i
$944$	2.90653	+	0.447459i	0.0945994	+	0.0145635i
$945$		0			0
$946$	−4.45017	−	4.80373i	−0.144688	−	0.156183i
$947$	9.06273	−	17.7866i	0.294499	−	0.577987i	−0.695588	−	0.718441i	$-0.744856\pi$
$947$	9.06273	−	17.7866i	0.294499	−	0.577987i	0.990087	+	0.140454i	$0.0448561\pi$
$948$		0			0
$949$		−	39.1704i		−	1.27152i
$950$	7.20368	+	31.5797i	0.233718	+	1.02458i
$951$		0			0
$952$	−0.265932	−	0.0305999i	−0.00861891	−	0.000991749i
$953$	3.35084	−	6.57639i	0.108544	−	0.213030i	−0.830345	−	0.557250i	$-0.811857\pi$
$953$	3.35084	−	6.57639i	0.108544	−	0.213030i	0.938889	+	0.344220i	$0.111857\pi$
$954$		0			0
$955$	−42.3611	+	29.1346i	−1.37077	+	0.942774i
$956$	−33.9019	+	20.8762i	−1.09647	+	0.675184i
$957$		0			0
$958$	6.01526	+	4.73150i	0.194344	+	0.152868i
$959$	−0.00690829	+	0.00501917i	−0.000223080	+	0.000162077i
$960$		0			0
$961$	−22.2914	−	16.1956i	−0.719076	−	0.522439i
$962$	11.7231	+	41.3953i	0.377967	+	1.33464i
$963$		0			0
$964$	8.72559	+	36.0012i	0.281032	+	1.15952i
$965$	19.2869	−	18.3147i	0.620867	−	0.589571i
$966$		0			0
$967$	−11.2886	+	5.75184i	−0.363018	+	0.184967i	−0.625980	−	0.779839i	$-0.715301\pi$
$967$	−11.2886	+	5.75184i	−0.363018	+	0.184967i	0.262962	+	0.964806i	$0.415301\pi$
$968$	−10.4969	+	5.92341i	−0.337384	+	0.190386i
$969$		0			0
$970$	1.88730	+	20.2256i	0.0605977	+	0.649406i
$971$	22.4953	−	7.30917i	0.721909	−	0.234563i	0.0750585	−	0.997179i	$-0.476086\pi$
$971$	22.4953	−	7.30917i	0.721909	−	0.234563i	0.646851	+	0.762617i	$0.276086\pi$
$972$		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	−0.425767	−	0.904833i	$-0.639996\pi$
$977$	−17.2253	+	2.72822i	−0.551087	+	0.0872836i	−0.125320	+	0.992116i	$0.539996\pi$
$978$		0			0
$979$	7.62301	+	23.4612i	0.243633	+	0.749824i
$980$	−12.6598	+	28.6265i	−0.404404	+	0.914440i
$981$		0			0
$982$	20.1956	+	7.42572i	0.644466	+	0.236964i
$983$	15.5561	+	30.5305i	0.496162	+	0.973773i	0.994294	+	0.106672i	$0.0340195\pi$
$983$	15.5561	+	30.5305i	0.496162	+	0.973773i	−0.498132	+	0.867101i	$0.665981\pi$
$984$		0			0
$985$	15.9319	−	29.3660i	0.507631	−	0.935679i
$986$	−35.1137	−	6.94506i	−1.11825	−	0.221176i
$987$		0			0
$988$	21.7053	+	25.3025i	0.690537	+	0.804980i
$989$	6.18429	−	8.51195i	0.196649	−	0.270664i
$990$		0			0
$991$	6.27760	+	8.64037i	0.199414	+	0.274470i	0.897000	−	0.442032i	$-0.145742\pi$
$991$	6.27760	+	8.64037i	0.199414	+	0.274470i	−0.697585	+	0.716502i	$0.745742\pi$
$992$	9.19024	+	5.08165i	0.291791	+	0.161343i
$993$		0			0
$994$	0.478046	−	0.0571052i	0.0151627	−	0.00181127i
$995$	0.986939	−	38.1724i	0.0312881	−	1.21015i
$996$		0			0
$997$	−8.62027	−	4.39225i	−0.273007	−	0.139104i	0.312128	−	0.950040i	$-0.398958\pi$
$997$	−8.62027	−	4.39225i	−0.273007	−	0.139104i	−0.585135	+	0.810936i	$0.698958\pi$
$998$	3.40871	−	2.28297i	0.107901	−	0.0722661i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.127.24	✓	240	300.227	odd	20
300.2.w.a.127.28	yes	240	75.2	even	20
300.2.w.a.163.24	yes	240	3.2	odd	2
300.2.w.a.163.28	yes	240	12.11	even	2
900.2.bj.f.127.3		240	25.2	odd	20	inner
900.2.bj.f.127.7		240	100.27	even	20	inner
900.2.bj.f.163.3		240	4.3	odd	2	inner
900.2.bj.f.163.7		240	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17502 + 0.786967i) q^{2} +(0.761365 - 1.84941i) q^{4} +(0.0577937 - 2.23532i) q^{5} +(0.0211854 + 0.0211854i) q^{7} +(0.560803 + 2.77227i) q^{8} +O(q^{10})\)	\(q+(-1.17502 + 0.786967i) q^{2} +(0.761365 - 1.84941i) q^{4} +(0.0577937 - 2.23532i) q^{5} +(0.0211854 + 0.0211854i) q^{7} +(0.560803 + 2.77227i) q^{8} +(1.69122 + 2.67204i) q^{10} +(-1.52583 + 2.10012i) q^{11} +(3.59397 + 0.569229i) q^{13} +(-0.0415656 - 0.00822116i) q^{14} +(-2.84065 - 2.81616i) q^{16} +(1.43409 + 2.81456i) q^{17} +(-1.41553 + 4.35657i) q^{19} +(-4.09003 - 1.80878i) q^{20} +(0.140158 - 3.66847i) q^{22} +(5.82595 - 0.922739i) q^{23} +(-4.99332 - 0.258375i) q^{25} +(-4.67097 + 2.15948i) q^{26} +(0.0553104 - 0.0230507i) q^{28} +(7.62028 - 2.47598i) q^{29} +(1.76558 + 0.573671i) q^{31} +(5.55405 + 1.07356i) q^{32} +(-3.90006 - 2.17860i) q^{34} +(0.0485806 - 0.0461318i) q^{35} +(1.30788 - 8.25760i) q^{37} +(-1.76519 - 6.23305i) q^{38} +(6.22933 - 1.09336i) q^{40} +(0.210898 - 0.153226i) q^{41} +(1.26128 - 1.26128i) q^{43} +(2.72228 + 4.42084i) q^{44} +(-6.11947 + 5.66907i) q^{46} +(5.36731 - 10.5339i) q^{47} -6.99910i q^{49} +(6.07061 - 3.62598i) q^{50} +(3.78906 - 6.21334i) q^{52} +(1.61963 - 3.17871i) q^{53} +(4.60626 + 3.53209i) q^{55} +(-0.0468509 + 0.0706126i) q^{56} +(-7.00551 + 8.90625i) q^{58} +(-0.594783 + 0.432135i) q^{59} +(3.96742 + 2.88250i) q^{61} +(-2.52606 + 0.715375i) q^{62} +(-7.37100 + 3.10940i) q^{64} +(1.48012 - 8.00078i) q^{65} +(2.97451 - 1.51559i) q^{67} +(6.29715 - 0.509314i) q^{68} +(-0.0207792 + 0.0924374i) q^{70} +(-10.8065 + 3.51125i) q^{71} +(-1.68398 - 10.6322i) q^{73} +(4.96167 + 10.7321i) q^{74} +(6.97935 + 5.93485i) q^{76} +(-0.0768172 + 0.0121667i) q^{77} +(4.55633 + 14.0229i) q^{79} +(-6.45918 + 6.18700i) q^{80} +(-0.127226 + 0.346014i) q^{82} +(5.86554 + 11.5118i) q^{83} +(6.37433 - 3.04299i) q^{85} +(-0.489447 + 2.47461i) q^{86} +(-6.67780 - 3.05226i) q^{88} +(5.58568 - 7.68803i) q^{89} +(0.0640804 + 0.0881991i) q^{91} +(2.72915 - 11.4771i) q^{92} +(1.98314 + 16.6015i) q^{94} +(9.65652 + 3.41596i) q^{95} +(5.72355 + 2.91630i) q^{97} +(5.50806 + 8.22412i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 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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