LMFDB - Embedded newform 432.2.be.c.335.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,2,Mod(47,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("432.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,0,0,3,0,0,0,6,0,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			335.4
Character	$\chi$	$=$	432.335
Dual form			432.2.be.c.383.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.796460 - 1.53807i) q^{3} +(1.12266 - 3.08448i) q^{5} +(3.05005 + 0.537806i) q^{7} +(-1.73130 - 2.45002i) q^{9} +(1.75059 - 0.637162i) q^{11} +(-3.44119 + 2.88750i) q^{13} +(-3.84999 - 4.18339i) q^{15} +(-5.33058 + 3.07761i) q^{17} +(5.61763 + 3.24334i) q^{19} +(3.25643 - 4.26285i) q^{21} +(0.0995927 + 0.564818i) q^{23} +(-4.42344 - 3.71171i) q^{25} +(-5.14721 + 0.711524i) q^{27} +(5.05288 - 6.02179i) q^{29} +(-6.55127 + 1.15517i) q^{31} +(0.414275 - 3.20000i) q^{33} +(5.08302 - 8.80406i) q^{35} +(-2.51317 - 4.35293i) q^{37} +(1.70040 + 7.59256i) q^{39} +(4.01288 + 4.78237i) q^{41} +(3.06074 + 8.40931i) q^{43} +(-9.50070 + 2.58964i) q^{45} +(1.29158 - 7.32493i) q^{47} +(2.43573 + 0.886535i) q^{49} +(0.487984 + 10.6500i) q^{51} +4.40691i q^{53} -6.11498i q^{55} +(9.46269 - 6.05710i) q^{57} +(1.19847 + 0.436209i) q^{59} +(0.757644 - 4.29681i) q^{61} +(-3.96293 - 8.40379i) q^{63} +(5.04316 + 13.8560i) q^{65} +(3.35363 + 3.99670i) q^{67} +(0.948051 + 0.296675i) q^{69} +(-2.77247 - 4.80206i) q^{71} +(-5.12137 + 8.87047i) q^{73} +(-9.23195 + 3.84733i) q^{75} +(5.68206 - 1.00190i) q^{77} +(0.530104 - 0.631754i) q^{79} +(-3.00517 + 8.48345i) q^{81} +(5.90712 + 4.95666i) q^{83} +(3.50841 + 19.8972i) q^{85} +(-5.23750 - 12.5678i) q^{87} +(-2.31943 - 1.33912i) q^{89} +(-12.0487 + 6.95633i) q^{91} +(-3.44110 + 10.9963i) q^{93} +(16.3107 - 13.6863i) q^{95} +(9.55043 - 3.47607i) q^{97} +(-4.59186 - 3.18585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9} + 18 q^{11} - 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} - 27 q^{31} + 27 q^{33} - 27 q^{35} + 45 q^{39} + 18 q^{41} + 27 q^{45} - 45 q^{47} + 63 q^{51} - 9 q^{57} - 54 q^{59}+ \cdots - 99 q^{99}+O(q^{100}) $ 36 * q + 3 * q^5 + 6 * q^9 + 18 * q^11 - 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 - 27 * q^31 + 27 * q^33 - 27 * q^35 + 45 * q^39 + 18 * q^41 + 27 * q^45 - 45 * q^47 + 63 * q^51 - 9 * q^57 - 54 * q^59 + 63 * q^63 - 57 * q^65 - 63 * q^69 - 36 * q^71 + 9 * q^73 + 45 * q^75 - 81 * q^77 - 54 * q^81 + 27 * q^83 - 36 * q^85 - 45 * q^87 - 63 * q^89 - 27 * q^91 - 63 * q^93 + 72 * q^95 - 99 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.796460	−	1.53807i	0.459836	−	0.888004i
$3$	0.796460	−	1.53807i	0.459836	−	0.888004i
$4$		0			0
$5$	1.12266	−	3.08448i	0.502069	−	1.37942i	−0.387183	−	0.922003i	$-0.626552\pi$
$5$	1.12266	−	3.08448i	0.502069	−	1.37942i	0.889251	−	0.457419i	$-0.151226\pi$
$6$		0			0
$7$	3.05005	+	0.537806i	1.15281	+	0.203272i	0.717203	−	0.696864i	$-0.245422\pi$
$7$	3.05005	+	0.537806i	1.15281	+	0.203272i	0.435609	+	0.900136i	$0.356533\pi$
$8$		0			0
$9$	−1.73130	−	2.45002i	−0.577101	−	0.816672i
$10$		0			0
$11$	1.75059	−	0.637162i	0.527822	−	0.192112i	−0.0643433	−	0.997928i	$-0.520495\pi$
$11$	1.75059	−	0.637162i	0.527822	−	0.192112i	0.592166	+	0.805816i	$0.298273\pi$
$12$		0			0
$13$	−3.44119	+	2.88750i	−0.954414	+	0.800848i	−0.980035	−	0.198823i	$-0.936288\pi$
$13$	−3.44119	+	2.88750i	−0.954414	+	0.800848i	0.0256213	+	0.999672i	$0.491844\pi$
$14$		0			0
$15$	−3.84999	−	4.18339i	−0.994063	−	1.08015i
$16$		0			0
$17$	−5.33058	+	3.07761i	−1.29286	+	0.746430i	−0.979159	−	0.203093i	$-0.934901\pi$
$17$	−5.33058	+	3.07761i	−1.29286	+	0.746430i	−0.313696	+	0.949524i	$0.601567\pi$
$18$		0			0
$19$	5.61763	+	3.24334i	1.28877	+	0.744073i	0.978435	−	0.206554i	$-0.0662249\pi$
$19$	5.61763	+	3.24334i	1.28877	+	0.744073i	0.310337	+	0.950627i	$0.399558\pi$
$20$		0			0
$21$	3.25643	−	4.26285i	0.710610	−	0.930229i
$22$		0			0
$23$	0.0995927	+	0.564818i	0.0207665	+	0.117773i	0.993429	−	0.114451i	$-0.0365109\pi$
$23$	0.0995927	+	0.564818i	0.0207665	+	0.117773i	−0.972662	+	0.232224i	$0.925400\pi$
$24$		0			0
$25$	−4.42344	−	3.71171i	−0.884688	−	0.742342i
$26$		0			0
$27$	−5.14721	+	0.711524i	−0.990580	+	0.136933i
$28$		0			0
$29$	5.05288	−	6.02179i	0.938296	−	1.11822i	−0.0545130	−	0.998513i	$-0.517361\pi$
$29$	5.05288	−	6.02179i	0.938296	−	1.11822i	0.992809	−	0.119705i	$-0.0381949\pi$
$30$		0			0
$31$	−6.55127	+	1.15517i	−1.17664	+	0.207474i	−0.727578	−	0.686025i	$-0.759354\pi$
$31$	−6.55127	+	1.15517i	−1.17664	+	0.207474i	−0.449065	+	0.893499i	$0.648243\pi$
$32$		0			0
$33$	0.414275	−	3.20000i	0.0721160	−	0.557048i
$34$		0			0
$35$	5.08302	−	8.80406i	0.859188	−	1.48816i
$36$		0			0
$37$	−2.51317	−	4.35293i	−0.413162	−	0.715618i	0.582071	−	0.813138i	$-0.302242\pi$
$37$	−2.51317	−	4.35293i	−0.413162	−	0.715618i	−0.995234	+	0.0975198i	$0.968909\pi$
$38$		0			0
$39$	1.70040	+	7.59256i	0.272282	+	1.21578i
$40$		0			0
$41$	4.01288	+	4.78237i	0.626707	+	0.746880i	0.982208	−	0.187796i	$-0.0601343\pi$
$41$	4.01288	+	4.78237i	0.626707	+	0.746880i	−0.355501	+	0.934676i	$0.615690\pi$
$42$		0			0
$43$	3.06074	+	8.40931i	0.466758	+	1.28241i	0.920314	+	0.391180i	$0.127933\pi$
$43$	3.06074	+	8.40931i	0.466758	+	1.28241i	−0.453556	+	0.891228i	$0.649845\pi$
$44$		0			0
$45$	−9.50070	+	2.58964i	−1.41628	+	0.386041i
$46$		0			0
$47$	1.29158	−	7.32493i	0.188397	−	1.06845i	−0.733116	−	0.680103i	$-0.761935\pi$
$47$	1.29158	−	7.32493i	0.188397	−	1.06845i	0.921513	−	0.388347i	$-0.126954\pi$
$48$		0			0
$49$	2.43573	+	0.886535i	0.347962	+	0.126648i
$50$		0			0
$51$	0.487984	+	10.6500i	0.0683314	+	1.49130i
$52$		0			0
$53$			4.40691i			0.605335i	0.953096	+	0.302668i	$0.0978772\pi$
$53$			4.40691i			0.605335i	−0.953096	+	0.302668i	$0.902123\pi$
$54$		0			0
$55$		−	6.11498i		−	0.824543i
$56$		0			0
$57$	9.46269	−	6.05710i	1.25336	−	0.802283i
$58$		0			0
$59$	1.19847	+	0.436209i	0.156028	+	0.0567896i	0.418853	−	0.908054i	$-0.362432\pi$
$59$	1.19847	+	0.436209i	0.156028	+	0.0567896i	−0.262825	+	0.964843i	$0.584654\pi$
$60$		0			0
$61$	0.757644	−	4.29681i	0.0970064	−	0.550151i	−0.897108	−	0.441812i	$-0.854336\pi$
$61$	0.757644	−	4.29681i	0.0970064	−	0.550151i	0.994114	−	0.108339i	$-0.0345531\pi$
$62$		0			0
$63$	−3.96293	−	8.40379i	−0.499283	−	1.05878i
$64$		0			0
$65$	5.04316	+	13.8560i	0.625527	+	1.71862i
$66$		0			0
$67$	3.35363	+	3.99670i	0.409711	+	0.488275i	0.930955	−	0.365133i	$-0.118976\pi$
$67$	3.35363	+	3.99670i	0.409711	+	0.488275i	−0.521244	+	0.853407i	$0.674532\pi$
$68$		0			0
$69$	0.948051	+	0.296675i	0.114132	+	0.0357154i
$70$		0			0
$71$	−2.77247	−	4.80206i	−0.329032	−	0.569900i	0.653288	−	0.757109i	$-0.273389\pi$
$71$	−2.77247	−	4.80206i	−0.329032	−	0.569900i	−0.982320	+	0.187210i	$0.940056\pi$
$72$		0			0
$73$	−5.12137	+	8.87047i	−0.599411	+	1.03821i	0.393497	+	0.919326i	$0.371265\pi$
$73$	−5.12137	+	8.87047i	−0.599411	+	1.03821i	−0.992908	+	0.118884i	$0.962068\pi$
$74$		0			0
$75$	−9.23195	+	3.84733i	−1.06601	+	0.444251i
$76$		0			0
$77$	5.68206	−	1.00190i	0.647531	−	0.114177i
$78$		0			0
$79$	0.530104	−	0.631754i	0.0596414	−	0.0710778i	−0.735399	−	0.677634i	$-0.763005\pi$
$79$	0.530104	−	0.631754i	0.0596414	−	0.0710778i	0.795040	+	0.606557i	$0.207450\pi$
$80$		0			0
$81$	−3.00517	+	8.48345i	−0.333908	+	0.942606i
$82$		0			0
$83$	5.90712	+	4.95666i	0.648391	+	0.544065i	0.906582	−	0.422029i	$-0.138682\pi$
$83$	5.90712	+	4.95666i	0.648391	+	0.544065i	−0.258191	+	0.966094i	$0.583126\pi$
$84$		0			0
$85$	3.50841	+	19.8972i	0.380540	+	2.15815i
$86$		0			0
$87$	−5.23750	−	12.5678i	−0.561519	−	1.34741i
$88$		0			0
$89$	−2.31943	−	1.33912i	−0.245859	−	0.141947i	0.372008	−	0.928230i	$-0.378670\pi$
$89$	−2.31943	−	1.33912i	−0.245859	−	0.141947i	−0.617867	+	0.786283i	$0.712003\pi$
$90$		0			0
$91$	−12.0487	+	6.95633i	−1.26305	+	0.729222i
$92$		0			0
$93$	−3.44110	+	10.9963i	−0.356825	+	1.14027i
$94$		0			0
$95$	16.3107	−	13.6863i	1.67344	−	1.40419i
$96$		0			0
$97$	9.55043	−	3.47607i	0.969699	−	0.352942i	0.191872	−	0.981420i	$-0.438544\pi$
$97$	9.55043	−	3.47607i	0.969699	−	0.352942i	0.777827	+	0.628478i	$0.216322\pi$
$98$		0			0
$99$	−4.59186	−	3.18585i	−0.461499	−	0.320190i
$100$		0			0
$101$	6.42237	+	1.13244i	0.639050	+	0.112682i	0.483779	−	0.875190i	$-0.339264\pi$
$101$	6.42237	+	1.13244i	0.639050	+	0.112682i	0.155271	+	0.987872i	$0.450375\pi$
$102$		0			0
$103$	−3.66572	+	10.0715i	−0.361194	+	0.992372i	0.617414	+	0.786638i	$0.288180\pi$
$103$	−3.66572	+	10.0715i	−0.361194	+	0.992372i	−0.978608	+	0.205734i	$0.934042\pi$
$104$		0			0
$105$	−9.49281	−	14.8301i	−0.926404	−	1.44727i
$106$		0			0
$107$	−8.80586			−0.851295			−0.425647	−	0.904889i	$-0.639954\pi$
$107$	−8.80586			−0.851295			−0.425647	+	0.904889i	$0.639954\pi$
$108$		0			0
$109$	−9.44106			−0.904290			−0.452145	−	0.891944i	$-0.649341\pi$
$109$	−9.44106			−0.904290			−0.452145	+	0.891944i	$0.649341\pi$
$110$		0			0
$111$	−8.69674	+	0.398486i	−0.825458	+	0.0378226i
$112$		0			0
$113$	4.23372	−	11.6321i	0.398275	−	1.09425i	−0.564849	−	0.825194i	$-0.691065\pi$
$113$	4.23372	−	11.6321i	0.398275	−	1.09425i	0.963124	−	0.269058i	$-0.0867123\pi$
$114$		0			0
$115$	1.85398	+	0.326907i	0.172885	+	0.0304842i
$116$		0			0
$117$	13.0322	+	3.43183i	1.20482	+	0.317273i
$118$		0			0
$119$	−17.9137	+	6.52005i	−1.64215	+	0.597692i
$120$		0			0
$121$	−5.76790	+	4.83984i	−0.524355	+	0.439986i
$122$		0			0
$123$	10.5517	−	2.36312i	0.951415	−	0.213076i
$124$		0			0
$125$	−2.20134	+	1.27095i	−0.196894	+	0.113677i
$126$		0			0
$127$	12.5683	+	7.25630i	1.11525	+	0.643893i	0.940185	−	0.340663i	$-0.110652\pi$
$127$	12.5683	+	7.25630i	1.11525	+	0.643893i	0.175070	+	0.984556i	$0.443985\pi$
$128$		0			0
$129$	15.3718	+	1.99005i	1.35342	+	0.175214i
$130$		0			0
$131$	2.42294	+	13.7412i	0.211693	+	1.20057i	0.886553	+	0.462627i	$0.153093\pi$
$131$	2.42294	+	13.7412i	0.211693	+	1.20057i	−0.674860	+	0.737946i	$0.735796\pi$
$132$		0			0
$133$	15.3898	+	12.9135i	1.33446	+	1.11975i
$134$		0			0
$135$	−3.58388	+	16.6753i	−0.308451	+	1.43518i
$136$		0			0
$137$	−6.55243	+	7.80889i	−0.559812	+	0.667158i	−0.969507	−	0.245065i	$-0.921191\pi$
$137$	−6.55243	+	7.80889i	−0.559812	+	0.667158i	0.409695	+	0.912223i	$0.365635\pi$
$138$		0			0
$139$	14.0879	−	2.48408i	1.19492	−	0.210697i	0.459418	−	0.888220i	$-0.348058\pi$
$139$	14.0879	−	2.48408i	1.19492	−	0.210697i	0.735501	+	0.677523i	$0.236947\pi$
$140$		0			0
$141$	−10.2375	−	7.82055i	−0.862156	−	0.658609i
$142$		0			0
$143$	−4.18430	+	7.24742i	−0.349909	+	0.606060i
$144$		0			0
$145$	−12.9014	−	22.3459i	−1.07141	−	1.85573i
$146$		0			0
$147$	3.30351	−	3.04024i	0.272469	−	0.250754i
$148$		0			0
$149$	−14.2222	−	16.9494i	−1.16513	−	1.38855i	−0.906305	−	0.422624i	$-0.861109\pi$
$149$	−14.2222	−	16.9494i	−1.16513	−	1.38855i	−0.258825	−	0.965924i	$-0.583335\pi$
$150$		0			0
$151$	0.795084	+	2.18447i	0.0647030	+	0.177770i	0.967831	−	0.251602i	$-0.0809573\pi$
$151$	0.795084	+	2.18447i	0.0647030	+	0.177770i	−0.903128	+	0.429372i	$0.858735\pi$
$152$		0			0
$153$	16.7691	+	7.73173i	1.35570	+	0.625073i
$154$		0			0
$155$	−3.79176	+	21.5041i	−0.304561	+	1.72725i
$156$		0			0
$157$	2.76548	+	1.00655i	0.220709	+	0.0803317i	0.450008	−	0.893024i	$-0.351421\pi$
$157$	2.76548	+	1.00655i	0.220709	+	0.0803317i	−0.229299	+	0.973356i	$0.573643\pi$
$158$		0			0
$159$	6.77812	+	3.50992i	0.537540	+	0.278355i
$160$		0			0
$161$			1.77629i			0.139991i
$162$		0			0
$163$		−	24.7290i		−	1.93692i	−0.249167	−	0.968461i	$-0.580157\pi$
$163$		−	24.7290i		−	1.93692i	0.249167	−	0.968461i	$-0.419843\pi$
$164$		0			0
$165$	−9.40525	−	4.87033i	−0.732198	−	0.379155i
$166$		0			0
$167$	−9.45713	−	3.44211i	−0.731814	−	0.266359i	−0.0508817	−	0.998705i	$-0.516203\pi$
$167$	−9.45713	−	3.44211i	−0.731814	−	0.266359i	−0.680933	+	0.732346i	$0.738425\pi$
$168$		0			0
$169$	1.24670	−	7.07037i	0.0958997	−	0.543874i
$170$		0			0
$171$	−1.77959	−	19.3785i	−0.136088	−	1.48191i
$172$		0			0
$173$	6.32967	+	17.3906i	0.481236	+	1.32218i	0.908435	+	0.418027i	$0.137278\pi$
$173$	6.32967	+	17.3906i	0.481236	+	1.32218i	−0.427199	+	0.904158i	$0.640500\pi$
$174$		0			0
$175$	−11.4955	−	13.6999i	−0.868982	−	1.03561i
$176$		0			0
$177$	1.62546	−	1.49591i	0.122177	−	0.112440i
$178$		0			0
$179$	−8.14426	−	14.1063i	−0.608731	−	1.05435i	−0.991450	−	0.130488i	$-0.958346\pi$
$179$	−8.14426	−	14.1063i	−0.608731	−	1.05435i	0.382719	−	0.923865i	$-0.374988\pi$
$180$		0			0
$181$	−5.29198	+	9.16598i	−0.393350	+	0.681302i	−0.992889	−	0.119043i	$-0.962017\pi$
$181$	−5.29198	+	9.16598i	−0.393350	+	0.681302i	0.599539	+	0.800345i	$0.295351\pi$
$182$		0			0
$183$	−6.00536	−	4.58755i	−0.443929	−	0.339121i
$184$		0			0
$185$	−16.2480	+	2.86496i	−1.19457	+	0.210636i
$186$		0			0
$187$	−7.37071	+	8.78408i	−0.539000	+	0.642355i
$188$		0			0
$189$	−16.0819	−	0.598017i	−1.16979	−	0.0434993i
$190$		0			0
$191$	−8.48829	−	7.12252i	−0.614191	−	0.515367i	0.281781	−	0.959479i	$-0.409075\pi$
$191$	−8.48829	−	7.12252i	−0.614191	−	0.515367i	−0.895972	+	0.444112i	$0.853519\pi$
$192$		0			0
$193$	−2.72887	−	15.4762i	−0.196429	−	1.11400i	−0.910370	−	0.413796i	$-0.864203\pi$
$193$	−2.72887	−	15.4762i	−0.196429	−	1.11400i	0.713941	−	0.700206i	$-0.246908\pi$
$194$		0			0
$195$	25.3281	+	3.27900i	1.81378	+	0.234814i
$196$		0			0
$197$	−11.8949	−	6.86752i	−0.847476	−	0.489291i	0.0123223	−	0.999924i	$-0.496078\pi$
$197$	−11.8949	−	6.86752i	−0.847476	−	0.489291i	−0.859799	+	0.510633i	$0.829411\pi$
$198$		0			0
$199$	13.3305	−	7.69637i	0.944974	−	0.545581i	0.0534579	−	0.998570i	$-0.482976\pi$
$199$	13.3305	−	7.69637i	0.944974	−	0.545581i	0.891516	+	0.452989i	$0.149642\pi$
$200$		0			0
$201$	8.81822	−	1.97490i	0.621990	−	0.139299i
$202$		0			0
$203$	18.6501	−	15.6493i	1.30898	−	1.09837i
$204$		0			0
$205$	19.2562	−	7.00869i	1.34491	−	0.489508i
$206$		0			0
$207$	1.21139	−	1.22188i	0.0841974	−	0.0849263i
$208$		0			0
$209$	11.9007	+	2.09841i	0.823188	+	0.145150i
$210$		0			0
$211$	0.592005	−	1.62652i	0.0407553	−	0.111974i	−0.917646	−	0.397400i	$-0.869913\pi$
$211$	0.592005	−	1.62652i	0.0407553	−	0.111974i	0.958401	+	0.285425i	$0.0921349\pi$
$212$		0			0
$213$	−9.59405	+	0.439601i	−0.657374	+	0.0301210i
$214$		0			0
$215$	29.3745			2.00333
$216$		0			0
$217$	−20.6030			−1.39862
$218$		0			0
$219$	9.56442	+	14.9420i	0.646304	+	1.00969i
$220$		0			0
$221$	9.45692	−	25.9827i	0.636142	−	1.74778i
$222$		0			0
$223$	6.89847	+	1.21639i	0.461956	+	0.0814552i	0.399782	−	0.916610i	$-0.369086\pi$
$223$	6.89847	+	1.21639i	0.461956	+	0.0814552i	0.0621733	+	0.998065i	$0.480197\pi$
$224$		0			0
$225$	−1.43543	+	17.2636i	−0.0956950	+	1.15091i
$226$		0			0
$227$	0.456091	−	0.166003i	0.0302718	−	0.0110180i	−0.326840	−	0.945080i	$-0.605984\pi$
$227$	0.456091	−	0.166003i	0.0302718	−	0.0110180i	0.357112	+	0.934062i	$0.383762\pi$
$228$		0			0
$229$	18.7833	−	15.7611i	1.24124	−	1.04152i	0.243812	−	0.969822i	$-0.421602\pi$
$229$	18.7833	−	15.7611i	1.24124	−	1.04152i	0.997426	−	0.0717003i	$-0.0228425\pi$
$230$		0			0
$231$	2.98454	−	9.53736i	0.196368	−	0.627512i
$232$		0			0
$233$	−7.90560	+	4.56430i	−0.517913	+	0.299017i	−0.736081	−	0.676894i	$-0.763326\pi$
$233$	−7.90560	+	4.56430i	−0.517913	+	0.299017i	0.218167	+	0.975911i	$0.429992\pi$
$234$		0			0
$235$	−21.1436	−	12.2073i	−1.37926	−	0.796314i
$236$		0			0
$237$	−0.549473	−	1.31850i	−0.0356921	−	0.0856459i
$238$		0			0
$239$	3.71199	+	21.0517i	0.240108	+	1.36172i	0.831584	+	0.555399i	$0.187435\pi$
$239$	3.71199	+	21.0517i	0.240108	+	1.36172i	−0.591475	+	0.806323i	$0.701454\pi$
$240$		0			0
$241$	−6.62233	−	5.55679i	−0.426582	−	0.357945i	0.404078	−	0.914724i	$-0.367592\pi$
$241$	−6.62233	−	5.55679i	−0.426582	−	0.357945i	−0.830660	+	0.556780i	$0.812037\pi$
$242$		0			0
$243$	10.6546	+	11.3789i	0.683495	+	0.729956i
$244$		0			0
$245$	5.46900	−	6.51770i	0.349402	−	0.416401i
$246$		0			0
$247$	−28.6965	+	5.05996i	−1.82591	+	0.321958i
$248$		0			0
$249$	12.3285	−	5.13777i	0.781285	−	0.325593i
$250$		0			0
$251$	−2.06728	+	3.58063i	−0.130485	+	0.226007i	−0.923864	−	0.382721i	$-0.874987\pi$
$251$	−2.06728	+	3.58063i	−0.130485	+	0.226007i	0.793378	+	0.608729i	$0.208320\pi$
$252$		0			0
$253$	0.534227	+	0.925308i	0.0335866	+	0.0581736i
$254$		0			0
$255$	33.3975	+	10.4511i	2.09143	+	0.654475i
$256$		0			0
$257$	4.09081	+	4.87523i	0.255178	+	0.304109i	0.878391	−	0.477943i	$-0.158618\pi$
$257$	4.09081	+	4.87523i	0.255178	+	0.304109i	−0.623213	+	0.782052i	$0.714173\pi$
$258$		0			0
$259$	−5.32426	−	14.6283i	−0.330833	−	0.908957i
$260$		0			0
$261$	−23.5016	−	1.95410i	−1.45471	−	0.120956i
$262$		0			0
$263$	−0.255737	+	1.45036i	−0.0157694	+	0.0894328i	−0.991677	−	0.128753i	$-0.958903\pi$
$263$	−0.255737	+	1.45036i	−0.0157694	+	0.0894328i	0.975907	+	0.218185i	$0.0700138\pi$
$264$		0			0
$265$	13.5930	+	4.94746i	0.835013	+	0.303920i
$266$		0			0
$267$	−3.90699	+	2.50088i	−0.239104	+	0.153051i
$268$		0			0
$269$		−	8.00417i		−	0.488023i	−0.969772	−	0.244011i	$-0.921537\pi$
$269$		−	8.00417i		−	0.488023i	0.969772	−	0.244011i	$-0.0784635\pi$
$270$		0			0
$271$		−	12.8446i		−	0.780254i	−0.920761	−	0.390127i	$-0.872431\pi$
$271$		−	12.8446i		−	0.780254i	0.920761	−	0.390127i	$-0.127569\pi$
$272$		0			0
$273$	1.10299	+	24.0722i	0.0667561	+	1.45692i
$274$		0			0
$275$	−10.1086	−	3.67923i	−0.609571	−	0.221866i
$276$		0			0
$277$	2.74587	−	15.5726i	0.164983	−	0.935665i	−0.784099	−	0.620636i	$-0.786874\pi$
$277$	2.74587	−	15.5726i	0.164983	−	0.935665i	0.949082	−	0.315029i	$-0.102014\pi$
$278$		0			0
$279$	14.1724	+	14.0508i	0.848480	+	0.841198i
$280$		0			0
$281$	−6.37720	−	17.5212i	−0.380432	−	1.04523i	−0.971175	−	0.238368i	$-0.923388\pi$
$281$	−6.37720	−	17.5212i	−0.380432	−	1.04523i	0.590743	−	0.806859i	$-0.298835\pi$
$282$		0			0
$283$	−0.664710	−	0.792171i	−0.0395129	−	0.0470897i	0.745926	−	0.666029i	$-0.232007\pi$
$283$	−0.664710	−	0.792171i	−0.0395129	−	0.0470897i	−0.785439	+	0.618939i	$0.787563\pi$
$284$		0			0
$285$	−8.05965	−	35.9875i	−0.477412	−	2.13172i
$286$		0			0
$287$	9.66751	+	16.7446i	0.570655	+	0.988403i
$288$		0			0
$289$	10.4434	−	18.0885i	0.614316	−	1.06403i
$290$		0			0
$291$	2.26010	−	17.4578i	0.132489	−	1.02339i
$292$		0			0
$293$	−13.3037	+	2.34580i	−0.777208	+	0.137043i	−0.548161	−	0.836373i	$-0.684672\pi$
$293$	−13.3037	+	2.34580i	−0.777208	+	0.137043i	−0.229047	+	0.973415i	$0.573561\pi$
$294$		0			0
$295$	2.69096	−	3.20696i	0.156674	−	0.186716i
$296$		0			0
$297$	−8.55729	+	4.52519i	−0.496544	+	0.262578i
$298$		0			0
$299$	−1.97363	−	1.65607i	−0.114138	−	0.0957732i
$300$		0			0
$301$	4.81283	+	27.2949i	0.277407	+	1.57325i
$302$		0			0
$303$	6.85693	−	8.97611i	0.393920	−	0.515664i
$304$		0			0
$305$	−12.4029	−	7.16080i	−0.710186	−	0.410026i
$306$		0			0
$307$	5.44502	−	3.14368i	0.310763	−	0.179419i	−0.336505	−	0.941682i	$-0.609245\pi$
$307$	5.44502	−	3.14368i	0.310763	−	0.179419i	0.647268	+	0.762262i	$0.275911\pi$
$308$		0			0
$309$	12.5710	+	13.6596i	0.715140	+	0.777070i
$310$		0			0
$311$	−24.7245	+	20.7464i	−1.40200	+	1.17642i	−0.441797	+	0.897115i	$0.645659\pi$
$311$	−24.7245	+	20.7464i	−1.40200	+	1.17642i	−0.960203	+	0.279303i	$0.909897\pi$
$312$		0			0
$313$	−7.70071	+	2.80283i	−0.435270	+	0.158425i	−0.550356	−	0.834930i	$-0.685508\pi$
$313$	−7.70071	+	2.80283i	−0.435270	+	0.158425i	0.115086	+	0.993356i	$0.463286\pi$
$314$		0			0
$315$	−30.3704	+	2.78900i	−1.71118	+	0.157143i
$316$		0			0
$317$	−0.256610	−	0.0452473i	−0.0144127	−	0.00254134i	0.166437	−	0.986052i	$-0.446774\pi$
$317$	−0.256610	−	0.0452473i	−0.0144127	−	0.00254134i	−0.180850	+	0.983511i	$0.557885\pi$
$318$		0			0
$319$	5.00866	−	13.7612i	0.280431	−	0.770478i
$320$		0			0
$321$	−7.01351	+	13.5440i	−0.391456	+	0.755953i
$322$		0			0
$323$	−39.9269			−2.22159
$324$		0			0
$325$	25.9395			1.43886
$326$		0			0
$327$	−7.51943	+	14.5210i	−0.415825	+	0.803013i
$328$		0			0
$329$	7.87879	−	21.6468i	0.434372	−	1.19343i
$330$		0			0
$331$	−0.525724	−	0.0926993i	−0.0288964	−	0.00509521i	0.159181	−	0.987249i	$-0.449115\pi$
$331$	−0.525724	−	0.0926993i	−0.0288964	−	0.00509521i	−0.188078	+	0.982154i	$0.560226\pi$
$332$		0			0
$333$	−6.31371	+	13.6936i	−0.345989	+	0.750402i
$334$		0			0
$335$	16.0927	−	5.85727i	0.879240	−	0.320017i
$336$		0			0
$337$	−23.8983	+	20.0530i	−1.30182	+	1.09236i	−0.311996	+	0.950083i	$0.600998\pi$
$337$	−23.8983	+	20.0530i	−1.30182	+	1.09236i	−0.989827	+	0.142276i	$0.954558\pi$
$338$		0			0
$339$	−14.5189	−	15.7762i	−0.788559	−	0.856847i
$340$		0			0
$341$	−10.7326	+	6.19644i	−0.581200	+	0.335556i
$342$		0			0
$343$	−11.8229	−	6.82593i	−0.638375	−	0.368566i
$344$		0			0
$345$	1.97943	−	2.59118i	0.106569	−	0.139504i
$346$		0			0
$347$	3.83765	+	21.7644i	0.206016	+	1.16837i	0.895833	+	0.444390i	$0.146580\pi$
$347$	3.83765	+	21.7644i	0.206016	+	1.16837i	−0.689818	+	0.723983i	$0.742309\pi$
$348$		0			0
$349$	−1.37320	−	1.15226i	−0.0735059	−	0.0616788i	0.605294	−	0.796002i	$-0.293055\pi$
$349$	−1.37320	−	1.15226i	−0.0735059	−	0.0616788i	−0.678800	+	0.734323i	$0.737500\pi$
$350$		0			0
$351$	15.6580	−	17.3110i	0.835761	−	0.923995i
$352$		0			0
$353$	−16.2088	+	19.3168i	−0.862705	+	1.02813i	0.136592	+	0.990627i	$0.456385\pi$
$353$	−16.2088	+	19.3168i	−0.862705	+	1.02813i	−0.999296	+	0.0375040i	$0.988059\pi$
$354$		0			0
$355$	−17.9244	+	3.16056i	−0.951329	+	0.167745i
$356$		0			0
$357$	−4.23925	+	32.7454i	−0.224365	+	1.73307i
$358$		0			0
$359$	−6.14950	+	10.6512i	−0.324558	+	0.562151i	−0.981423	−	0.191857i	$-0.938549\pi$
$359$	−6.14950	+	10.6512i	−0.324558	+	0.562151i	0.656865	+	0.754008i	$0.271882\pi$
$360$		0			0
$361$	11.5385	+	19.9852i	0.607289	+	1.05186i
$362$		0			0
$363$	2.85011	+	12.7262i	0.149592	+	0.667950i
$364$		0			0
$365$	21.6113	+	25.7553i	1.13118	+	1.34809i
$366$		0			0
$367$	10.1719	+	27.9469i	0.530966	+	1.45882i	0.857923	+	0.513779i	$0.171755\pi$
$367$	10.1719	+	27.9469i	0.530966	+	1.45882i	−0.326956	+	0.945039i	$0.606023\pi$
$368$		0			0
$369$	4.76936	−	18.1114i	0.248283	−	0.942840i
$370$		0			0
$371$	−2.37006	+	13.4413i	−0.123048	+	0.697837i
$372$		0			0
$373$	−6.03535	−	2.19669i	−0.312499	−	0.113740i	0.181010	−	0.983481i	$-0.442063\pi$
$373$	−6.03535	−	2.19669i	−0.312499	−	0.113740i	−0.493508	+	0.869741i	$0.664286\pi$
$374$		0			0
$375$	0.201520	+	4.39807i	0.0104065	+	0.227116i
$376$		0			0
$377$			35.3123i			1.81868i
$378$		0			0
$379$			32.5133i			1.67009i	0.550178	+	0.835047i	$0.314560\pi$
$379$			32.5133i			1.67009i	−0.550178	+	0.835047i	$0.685440\pi$
$380$		0			0
$381$	21.1708	−	13.5515i	1.08461	−	0.694265i
$382$		0			0
$383$	−19.0144	−	6.92069i	−0.971593	−	0.353631i	−0.193027	−	0.981194i	$-0.561830\pi$
$383$	−19.0144	−	6.92069i	−0.971593	−	0.353631i	−0.778566	+	0.627563i	$0.784053\pi$
$384$		0			0
$385$	3.28867	−	18.6510i	0.167606	−	0.950543i
$386$		0			0
$387$	15.3039	−	22.0579i	0.777940	−	1.12127i
$388$		0			0
$389$	−8.66645	−	23.8109i	−0.439406	−	1.20726i	−0.939879	−	0.341507i	$-0.889063\pi$
$389$	−8.66645	−	23.8109i	−0.439406	−	1.20726i	0.500473	−	0.865752i	$-0.333159\pi$
$390$		0			0
$391$	−2.26918	−	2.70430i	−0.114757	−	0.136762i
$392$		0			0
$393$	23.0646	+	7.21765i	1.16346	+	0.364082i
$394$		0			0
$395$	−1.35351	−	2.34434i	−0.0681023	−	0.117957i
$396$		0			0
$397$	3.67253	−	6.36102i	0.184319	−	0.319250i	−0.759028	−	0.651058i	$-0.774325\pi$
$397$	3.67253	−	6.36102i	0.184319	−	0.319250i	0.943347	+	0.331808i	$0.107659\pi$
$398$		0			0
$399$	32.1192	−	13.3854i	1.60797	−	0.670107i
$400$		0			0
$401$	−9.92983	+	1.75090i	−0.495872	+	0.0874356i	−0.415991	−	0.909369i	$-0.636565\pi$
$401$	−9.92983	+	1.75090i	−0.495872	+	0.0874356i	−0.0798812	+	0.996804i	$0.525454\pi$
$402$		0			0
$403$	19.2086	−	22.8919i	0.956849	−	1.14033i
$404$		0			0
$405$	22.7933	+	18.7934i	1.13261	+	0.933853i
$406$		0			0
$407$	−7.17305	−	6.01890i	−0.355555	−	0.298346i
$408$		0			0
$409$	−0.129387	−	0.733791i	−0.00639778	−	0.0362836i	0.981442	−	0.191761i	$-0.0614197\pi$
$409$	−0.129387	−	0.733791i	−0.00639778	−	0.0362836i	−0.987840	+	0.155477i	$0.950309\pi$
$410$		0			0
$411$	6.79185	+	16.2975i	0.335017	+	0.803899i
$412$		0			0
$413$	3.42081	+	1.97501i	0.168327	+	0.0971838i
$414$		0			0
$415$	21.9204	−	12.6558i	1.07603	−	0.621247i
$416$		0			0
$417$	7.39976	−	23.6466i	0.362368	−	1.15798i
$418$		0			0
$419$	28.7016	−	24.0835i	1.40217	−	1.17656i	0.442039	−	0.896996i	$-0.354255\pi$
$419$	28.7016	−	24.0835i	1.40217	−	1.17656i	0.960128	−	0.279561i	$-0.0901891\pi$
$420$		0			0
$421$	−13.2383	+	4.81836i	−0.645197	+	0.234832i	−0.643832	−	0.765167i	$-0.722657\pi$
$421$	−13.2383	+	4.81836i	−0.645197	+	0.234832i	−0.00136448	+	0.999999i	$0.500434\pi$
$422$		0			0
$423$	−20.1823	+	9.51728i	−0.981298	+	0.462746i
$424$		0			0
$425$	35.0027	+	6.17192i	1.69788	+	0.299382i
$426$		0			0
$427$	4.62171	−	12.6980i	0.223660	−	0.614501i
$428$		0			0
$429$	7.81440	+	12.2080i	0.377283	+	0.589409i
$430$		0			0
$431$	−8.25286			−0.397526			−0.198763	−	0.980048i	$-0.563692\pi$
$431$	−8.25286			−0.397526			−0.198763	+	0.980048i	$0.563692\pi$
$432$		0			0
$433$	−3.81968			−0.183562			−0.0917812	−	0.995779i	$-0.529256\pi$
$433$	−3.81968			−0.183562			−0.0917812	+	0.995779i	$0.529256\pi$
$434$		0			0
$435$	−44.6450	+	2.04564i	−2.14057	+	0.0980810i
$436$		0			0
$437$	−1.27242	+	3.49595i	−0.0608682	+	0.167234i
$438$		0			0
$439$	−7.25755	−	1.27970i	−0.346384	−	0.0610768i	−0.00225021	−	0.999997i	$-0.500716\pi$
$439$	−7.25755	−	1.27970i	−0.346384	−	0.0610768i	−0.344134	+	0.938921i	$0.611827\pi$
$440$		0			0
$441$	−2.04497	−	7.50245i	−0.0973796	−	0.357260i
$442$		0			0
$443$	−28.8637	+	10.5055i	−1.37136	+	0.499133i	−0.919546	−	0.392982i	$-0.871443\pi$
$443$	−28.8637	+	10.5055i	−1.37136	+	0.499133i	−0.451809	+	0.892115i	$0.649221\pi$
$444$		0			0
$445$	−6.73443	+	5.65086i	−0.319242	+	0.267876i
$446$		0			0
$447$	−37.3967	+	8.37524i	−1.76880	+	0.396135i
$448$		0			0
$449$	−21.4724	+	12.3971i	−1.01334	+	0.585055i	−0.912169	−	0.409814i	$-0.865594\pi$
$449$	−21.4724	+	12.3971i	−1.01334	+	0.585055i	−0.101176	+	0.994869i	$0.532260\pi$
$450$		0			0
$451$	10.0720	+	5.81510i	0.474274	+	0.273822i
$452$		0			0
$453$	3.99312	+	0.516953i	0.187613	+	0.0242886i
$454$		0			0
$455$	7.93007	+	44.9737i	0.371767	+	2.10840i
$456$		0			0
$457$	5.08205	+	4.26434i	0.237728	+	0.199478i	0.753866	−	0.657028i	$-0.228187\pi$
$457$	5.08205	+	4.26434i	0.237728	+	0.199478i	−0.516138	+	0.856505i	$0.672631\pi$
$458$		0			0
$459$	25.2478	−	19.6339i	1.17847	−	0.916433i
$460$		0			0
$461$	4.80345	−	5.72452i	0.223719	−	0.266618i	−0.642497	−	0.766289i	$-0.722101\pi$
$461$	4.80345	−	5.72452i	0.223719	−	0.266618i	0.866215	+	0.499671i	$0.166546\pi$
$462$		0			0
$463$	12.6122	−	2.22387i	0.586139	−	0.103352i	0.127288	−	0.991866i	$-0.459373\pi$
$463$	12.6122	−	2.22387i	0.586139	−	0.103352i	0.458850	+	0.888514i	$0.348261\pi$
$464$		0			0
$465$	30.0548	+	22.9591i	1.39376	+	1.06470i
$466$		0			0
$467$	21.2201	−	36.7544i	0.981951	−	1.70079i	0.327180	−	0.944962i	$-0.393902\pi$
$467$	21.2201	−	36.7544i	0.981951	−	1.70079i	0.654771	−	0.755827i	$-0.272765\pi$
$468$		0			0
$469$	8.07929	+	13.9937i	0.373067	+	0.646171i
$470$		0			0
$471$	3.75074	−	3.45182i	0.172825	−	0.159051i
$472$		0			0
$473$	10.7162	+	12.7711i	0.492731	+	0.587214i
$474$		0			0
$475$	−12.8109	−	35.1977i	−0.587805	−	1.61498i
$476$		0			0
$477$	10.7970	−	7.62970i	0.494361	−	0.349340i
$478$		0			0
$479$	−1.33018	+	7.54383i	−0.0607775	+	0.344687i	0.939222	+	0.343312i	$0.111549\pi$
$479$	−1.33018	+	7.54383i	−0.0607775	+	0.344687i	−0.999999	+	0.00137483i	$0.999562\pi$
$480$		0			0
$481$	21.2174	+	7.72250i	0.967429	+	0.352115i
$482$		0			0
$483$	2.73205	+	1.41474i	0.124313	+	0.0643729i
$484$		0			0
$485$		−	33.3606i		−	1.51483i
$486$		0			0
$487$			26.7514i			1.21222i	0.795380	+	0.606111i	$0.207271\pi$
$487$			26.7514i			1.21222i	−0.795380	+	0.606111i	$0.792729\pi$
$488$		0			0
$489$	−38.0348	−	19.6956i	−1.71999	−	0.890666i
$490$		0			0
$491$	−28.4746	−	10.3639i	−1.28504	−	0.467716i	−0.392944	−	0.919562i	$-0.628543\pi$
$491$	−28.4746	−	10.3639i	−1.28504	−	0.467716i	−0.892096	+	0.451846i	$0.850766\pi$
$492$		0			0
$493$	−8.40206	+	47.6504i	−0.378410	+	2.14607i
$494$		0			0
$495$	−14.9818	+	10.5869i	−0.673382	+	0.475845i
$496$		0			0
$497$	−5.87360	−	16.1376i	−0.263467	−	0.723870i
$498$		0			0
$499$	4.74411	+	5.65381i	0.212376	+	0.253099i	0.861707	−	0.507406i	$-0.169396\pi$
$499$	4.74411	+	5.65381i	0.212376	+	0.253099i	−0.649331	+	0.760506i	$0.724951\pi$
$500$		0			0
$501$	−12.8264	+	11.8042i	−0.573042	+	0.527373i
$502$		0			0
$503$	−8.99874	−	15.5863i	−0.401234	−	0.694958i	0.592641	−	0.805467i	$-0.298085\pi$
$503$	−8.99874	−	15.5863i	−0.401234	−	0.694958i	−0.993875	+	0.110509i	$0.964752\pi$
$504$		0			0
$505$	10.7031	−	18.5384i	0.476283	−	0.824946i
$506$		0			0
$507$	−9.88176	−	7.54876i	−0.438864	−	0.335252i
$508$		0			0
$509$	14.1044	−	2.48699i	0.625167	−	0.110234i	0.147915	−	0.989000i	$-0.452744\pi$
$509$	14.1044	−	2.48699i	0.625167	−	0.110234i	0.477252	+	0.878766i	$0.341633\pi$
$510$		0			0
$511$	−20.3910	+	24.3011i	−0.902047	+	1.07502i
$512$		0			0
$513$	−31.2228	−	12.6971i	−1.37852	−	0.560589i
$514$		0			0
$515$	26.9499	+	22.6137i	1.18756	+	0.996478i
$516$		0			0
$517$	−2.40614	−	13.6459i	−0.105822	−	0.600145i
$518$		0			0
$519$	31.7893	+	4.11547i	1.39539	+	0.180649i
$520$		0			0
$521$	20.2534	+	11.6933i	0.887317	+	0.512293i	0.873064	−	0.487606i	$-0.162130\pi$
$521$	20.2534	+	11.6933i	0.887317	+	0.512293i	0.0142531	+	0.999898i	$0.495463\pi$
$522$		0			0
$523$	−18.5635	+	10.7177i	−0.811726	+	0.468650i	−0.847555	−	0.530708i	$-0.821926\pi$
$523$	−18.5635	+	10.7177i	−0.811726	+	0.468650i	0.0358289	+	0.999358i	$0.488593\pi$
$524$		0			0
$525$	−30.2270	+	6.76954i	−1.31922	+	0.295447i
$526$		0			0
$527$	31.3669	−	26.3200i	1.36636	−	1.14652i
$528$		0			0
$529$	21.3038	−	7.75396i	0.926253	−	0.337129i
$530$		0			0
$531$	−1.00620	−	3.69149i	−0.0436656	−	0.160197i
$532$		0			0
$533$	−27.6182	−	4.86983i	−1.19628	−	0.210936i
$534$		0			0
$535$	−9.88599	+	27.1615i	−0.427408	+	1.17429i
$536$		0			0
$537$	−28.1830	+	1.29135i	−1.21619	+	0.0557258i
$538$		0			0
$539$	4.82884			0.207993
$540$		0			0
$541$	−23.8755			−1.02649			−0.513245	−	0.858242i	$-0.671557\pi$
$541$	−23.8755			−1.02649			−0.513245	+	0.858242i	$0.671557\pi$
$542$		0			0
$543$	9.88305	+	15.4398i	0.424122	+	0.662583i
$544$		0			0
$545$	−10.5991	+	29.1208i	−0.454016	+	1.24740i
$546$		0			0
$547$	−21.6034	−	3.80927i	−0.923696	−	0.162873i	−0.308480	−	0.951231i	$-0.599820\pi$
$547$	−21.6034	−	3.80927i	−0.923696	−	0.162873i	−0.615216	+	0.788358i	$0.710931\pi$
$548$		0			0
$549$	−11.8390	+	5.58285i	−0.505275	+	0.238270i
$550$		0			0
$551$	47.9159	−	17.4400i	2.04129	−	0.742967i
$552$		0			0
$553$	1.95661	−	1.64179i	0.0832034	−	0.0698159i
$554$		0			0
$555$	−8.53436	+	27.2723i	−0.362263	+	1.15765i
$556$		0			0
$557$	26.3790	−	15.2299i	1.11771	−	0.645311i	0.176896	−	0.984230i	$-0.443394\pi$
$557$	26.3790	−	15.2299i	1.11771	−	0.645311i	0.940816	+	0.338918i	$0.110061\pi$
$558$		0			0
$559$	−34.8145	−	20.1001i	−1.47249	−	0.850145i
$560$		0			0
$561$	7.64003	+	18.3328i	0.322562	+	0.774012i
$562$		0			0
$563$	−4.89813	−	27.7786i	−0.206431	−	1.17073i	−0.895171	−	0.445722i	$-0.852947\pi$
$563$	−4.89813	−	27.7786i	−0.206431	−	1.17073i	0.688740	−	0.725008i	$-0.258164\pi$
$564$		0			0
$565$	−31.1259	−	26.1177i	−1.30947	−	1.09878i
$566$		0			0
$567$	−13.7284	+	24.2588i	−0.576538	+	1.01877i
$568$		0			0
$569$	3.87085	−	4.61310i	0.162274	−	0.193391i	−0.678780	−	0.734342i	$-0.737491\pi$
$569$	3.87085	−	4.61310i	0.162274	−	0.193391i	0.841054	+	0.540951i	$0.181935\pi$
$570$		0			0
$571$	34.8030	−	6.13671i	1.45646	−	0.256814i	0.611332	−	0.791374i	$-0.290634\pi$
$571$	34.8030	−	6.13671i	1.45646	−	0.256814i	0.845130	+	0.534561i	$0.179523\pi$
$572$		0			0
$573$	−17.7155	+	7.38276i	−0.740075	+	0.308419i
$574$		0			0
$575$	1.65590	−	2.86810i	0.0690557	−	0.119608i
$576$		0			0
$577$	−4.72269	−	8.17994i	−0.196608	−	0.340535i	0.750818	−	0.660509i	$-0.229659\pi$
$577$	−4.72269	−	8.17994i	−0.196608	−	0.340535i	−0.947426	+	0.319973i	$0.896326\pi$
$578$		0			0
$579$	−25.9769	−	8.12898i	−1.07956	−	0.337829i
$580$		0			0
$581$	15.3513	+	18.2950i	0.636879	+	0.759003i
$582$		0			0
$583$	2.80792	+	7.71469i	0.116292	+	0.319510i
$584$		0			0
$585$	25.2161	−	36.3447i	1.04256	−	1.50267i
$586$		0			0
$587$	5.53066	−	31.3659i	0.228275	−	1.29461i	−0.628050	−	0.778173i	$-0.716147\pi$
$587$	5.53066	−	31.3659i	0.228275	−	1.29461i	0.856325	−	0.516438i	$-0.172742\pi$
$588$		0			0
$589$	−40.5492	−	14.7587i	−1.67080	−	0.608121i
$590$		0			0
$591$	−20.0365	+	12.8255i	−0.824192	+	0.527569i
$592$		0			0
$593$		−	26.5370i		−	1.08975i	−0.838519	−	0.544873i	$-0.816578\pi$
$593$		−	26.5370i		−	1.08975i	0.838519	−	0.544873i	$-0.183422\pi$
$594$		0			0
$595$			62.5743i			2.56530i
$596$		0			0
$597$	−1.22033	−	26.6331i	−0.0499448	−	1.09002i
$598$		0			0
$599$	−30.9021	−	11.2474i	−1.26262	−	0.459558i	−0.377976	−	0.925816i	$-0.623380\pi$
$599$	−30.9021	−	11.2474i	−1.26262	−	0.459558i	−0.884649	+	0.466258i	$0.845602\pi$
$600$		0			0
$601$	−1.31366	+	7.45015i	−0.0535854	+	0.303898i	−0.999808	−	0.0196197i	$-0.993754\pi$
$601$	−1.31366	+	7.45015i	−0.0535854	+	0.303898i	0.946222	+	0.323518i	$0.104866\pi$
$602$		0			0
$603$	3.98583	−	15.1360i	0.162316	−	0.616384i
$604$		0			0
$605$	8.45302	+	23.2245i	0.343664	+	0.944210i
$606$		0			0
$607$	7.44129	+	8.86819i	0.302033	+	0.359949i	0.895619	−	0.444822i	$-0.146733\pi$
$607$	7.44129	+	8.86819i	0.302033	+	0.359949i	−0.593586	+	0.804770i	$0.702288\pi$
$608$		0			0
$609$	−9.21562	−	41.1492i	−0.373436	−	1.66745i
$610$		0			0
$611$	16.7062	+	28.9359i	0.675859	+	1.17062i
$612$		0			0
$613$	−0.217321	+	0.376411i	−0.00877751	+	0.0152031i	−0.870381	−	0.492379i	$-0.836127\pi$
$613$	−0.217321	+	0.376411i	−0.00877751	+	0.0152031i	0.861603	+	0.507582i	$0.169461\pi$
$614$		0			0
$615$	4.55696	−	35.1995i	0.183754	−	1.41938i
$616$		0			0
$617$	−8.52403	+	1.50302i	−0.343165	+	0.0605092i	−0.342575	−	0.939491i	$-0.611299\pi$
$617$	−8.52403	+	1.50302i	−0.343165	+	0.0605092i	−0.000590102		1.00000i	$0.500188\pi$
$618$		0			0
$619$	15.5425	−	18.5228i	0.624704	−	0.744494i	−0.357167	−	0.934040i	$-0.616257\pi$
$619$	15.5425	−	18.5228i	0.624704	−	0.744494i	0.981872	+	0.189547i	$0.0607018\pi$
$620$		0			0
$621$	−0.914506	−	2.83637i	−0.0366979	−	0.113820i
$622$		0			0
$623$	−6.35419	−	5.33180i	−0.254575	−	0.213614i
$624$		0			0
$625$	−3.56471	−	20.2165i	−0.142588	−	0.808659i
$626$		0			0
$627$	12.7059	−	16.6328i	0.507426	−	0.664249i
$628$		0			0
$629$	26.7933	+	15.4691i	1.06832	+	0.616794i
$630$		0			0
$631$	14.3376	−	8.27784i	0.570773	−	0.329536i	−0.186685	−	0.982420i	$-0.559774\pi$
$631$	14.3376	−	8.27784i	0.570773	−	0.329536i	0.757458	+	0.652884i	$0.226441\pi$
$632$		0			0
$633$	−2.03019	−	2.20600i	−0.0806928	−	0.0876806i
$634$		0			0
$635$	36.4918	−	30.6203i	1.44813	−	1.21513i
$636$		0			0
$637$	−10.9417	+	3.98245i	−0.433526	+	0.157790i
$638$		0			0
$639$	−6.96514	+	15.1064i	−0.275537	+	0.597601i
$640$		0			0
$641$	−42.4598	−	7.48680i	−1.67706	−	0.295711i	−0.747467	−	0.664299i	$-0.768730\pi$
$641$	−42.4598	−	7.48680i	−1.67706	−	0.295711i	−0.929593	+	0.368588i	$0.879841\pi$
$642$		0			0
$643$	−8.45774	+	23.2375i	−0.333541	+	0.916396i	0.653642	+	0.756804i	$0.273240\pi$
$643$	−8.45774	+	23.2375i	−0.333541	+	0.916396i	−0.987183	+	0.159592i	$0.948982\pi$
$644$		0			0
$645$	23.3956	−	45.1800i	0.921202	−	1.77896i
$646$		0			0
$647$	35.4946			1.39544			0.697718	−	0.716372i	$-0.254199\pi$
$647$	35.4946			1.39544			0.697718	+	0.716372i	$0.254199\pi$
$648$		0			0
$649$	2.37597			0.0932651
$650$		0			0
$651$	−16.4094	+	31.6888i	−0.643136	+	1.24198i
$652$		0			0
$653$	5.76008	−	15.8257i	0.225409	−	0.619307i	−0.774503	−	0.632570i	$-0.782000\pi$
$653$	5.76008	−	15.8257i	0.225409	−	0.619307i	0.999912	+	0.0132637i	$0.00422210\pi$
$654$		0			0
$655$	45.1046	+	7.95315i	1.76238	+	0.310755i
$656$		0			0
$657$	30.5995	−	2.81004i	1.19380	−	0.109630i
$658$		0			0
$659$	7.79491	−	2.83712i	0.303647	−	0.110518i	−0.185703	−	0.982606i	$-0.559456\pi$
$659$	7.79491	−	2.83712i	0.303647	−	0.110518i	0.489350	+	0.872088i	$0.337234\pi$
$660$		0			0
$661$	33.9315	−	28.4719i	1.31978	−	1.10743i	0.333433	−	0.942774i	$-0.391793\pi$
$661$	33.9315	−	28.4719i	1.31978	−	1.10743i	0.986351	−	0.164657i	$-0.0526517\pi$
$662$		0			0
$663$	−32.4311	−	35.2395i	−1.25952	−	1.36859i
$664$		0			0
$665$	57.1091	−	32.9719i	2.21459	−	1.27860i
$666$		0			0
$667$	3.90445	+	2.25423i	0.151181	+	0.0872843i
$668$		0			0
$669$	7.36524	−	9.64151i	0.284756	−	0.372762i
$670$		0			0
$671$	−1.41144	−	8.00470i	−0.0544882	−	0.309018i
$672$		0			0
$673$	17.3028	+	14.5188i	0.666975	+	0.559658i	0.912168	−	0.409816i	$-0.134407\pi$
$673$	17.3028	+	14.5188i	0.666975	+	0.559658i	−0.245193	+	0.969474i	$0.578851\pi$
$674$		0			0
$675$	25.4093	+	15.9575i	0.978006	+	0.614206i
$676$		0			0
$677$	−5.67582	+	6.76418i	−0.218139	+	0.259968i	−0.864006	−	0.503482i	$-0.832052\pi$
$677$	−5.67582	+	6.76418i	−0.218139	+	0.259968i	0.645866	+	0.763451i	$0.276496\pi$
$678$		0			0
$679$	30.9988	−	5.46592i	1.18962	−	0.209763i
$680$		0			0
$681$	0.107933	−	0.833714i	0.00413601	−	0.0319480i
$682$		0			0
$683$	−22.9677	+	39.7812i	−0.878834	+	1.52218i	−0.0262119	+	0.999656i	$0.508344\pi$
$683$	−22.9677	+	39.7812i	−0.878834	+	1.52218i	−0.852622	+	0.522528i	$0.824989\pi$
$684$		0			0
$685$	16.7302	+	28.9776i	0.639229	+	1.10718i
$686$		0			0
$687$	−9.28146	−	41.4431i	−0.354110	−	1.58115i
$688$		0			0
$689$	−12.7249	−	15.1650i	−0.484782	−	0.577741i
$690$		0			0
$691$	−1.35958	−	3.73542i	−0.0517209	−	0.142102i	0.911142	−	0.412092i	$-0.135202\pi$
$691$	−1.35958	−	3.73542i	−0.0517209	−	0.142102i	−0.962863	+	0.269990i	$0.912980\pi$
$692$		0			0
$693$	−12.2920	−	12.1865i	−0.466936	−	0.462929i
$694$		0			0
$695$	8.15382	−	46.2426i	0.309292	−	1.75408i
$696$		0			0
$697$	−36.1092	−	13.1427i	−1.36773	−	0.497815i
$698$		0			0
$699$	0.723713	+	15.7946i	0.0273733	+	0.597408i
$700$		0			0
$701$			19.7960i			0.747684i	0.927492	+	0.373842i	$0.121960\pi$
$701$			19.7960i			0.747684i	−0.927492	+	0.373842i	$0.878040\pi$
$702$		0			0
$703$		−	32.6042i		−	1.22969i
$704$		0			0
$705$	−35.6156	+	22.7977i	−1.34136	+	0.858611i
$706$		0			0
$707$	18.9795	+	6.90799i	0.713799	+	0.259802i
$708$		0			0
$709$	0.722087	−	4.09516i	0.0271185	−	0.153797i	−0.968242	−	0.250016i	$-0.919564\pi$
$709$	0.722087	−	4.09516i	0.0271185	−	0.153797i	0.995360	+	0.0962195i	$0.0306751\pi$
$710$		0			0
$711$	−2.46558	−	0.205007i	−0.0924664	−	0.00768835i
$712$		0			0
$713$	−1.30492	−	3.58523i	−0.0488695	−	0.134268i
$714$		0			0
$715$	17.6570	+	21.0428i	0.660334	+	0.786956i
$716$		0			0
$717$	35.3354	+	11.0576i	1.31963	+	0.412952i
$718$		0			0
$719$	0.827080	+	1.43254i	0.0308449	+	0.0534249i	0.881036	−	0.473050i	$-0.156847\pi$
$719$	0.827080	+	1.43254i	0.0308449	+	0.0534249i	−0.850191	+	0.526475i	$0.823514\pi$
$720$		0			0
$721$	−16.5971	+	28.7471i	−0.618110	+	1.07060i
$722$		0			0
$723$	−13.8211	+	5.75983i	−0.514014	+	0.214210i
$724$		0			0
$725$	−44.7022	+	7.88221i	−1.66020	+	0.292738i
$726$		0			0
$727$	−11.2040	+	13.3525i	−0.415535	+	0.495215i	−0.932691	−	0.360676i	$-0.882546\pi$
$727$	−11.2040	+	13.3525i	−0.415535	+	0.495215i	0.517156	+	0.855891i	$0.326991\pi$
$728$		0			0
$729$	25.9875	−	7.32472i	0.962499	−	0.271286i
$730$		0			0
$731$	−42.1961	−	35.4067i	−1.56068	−	1.30956i
$732$		0			0
$733$	−2.08784	−	11.8408i	−0.0771163	−	0.437348i	−0.998781	−	0.0493610i	$-0.984282\pi$
$733$	−2.08784	−	11.8408i	−0.0771163	−	0.437348i	0.921665	−	0.387987i	$-0.126830\pi$
$734$		0			0
$735$	−5.66883	−	13.6028i	−0.209098	−	0.501746i
$736$		0			0
$737$	8.41737	+	4.85977i	0.310058	+	0.179012i
$738$		0			0
$739$	19.8865	−	11.4815i	0.731538	−	0.422354i	−0.0874467	−	0.996169i	$-0.527871\pi$
$739$	19.8865	−	11.4815i	0.731538	−	0.422354i	0.818984	+	0.573816i	$0.194537\pi$
$740$		0			0
$741$	−15.0730	+	48.1671i	−0.553721	+	1.76946i
$742$		0			0
$743$	−15.7558	+	13.2207i	−0.578023	+	0.485019i	−0.884297	−	0.466924i	$-0.845362\pi$
$743$	−15.7558	+	13.2207i	−0.578023	+	0.485019i	0.306274	+	0.951943i	$0.400918\pi$
$744$		0			0
$745$	−68.2468	+	24.8398i	−2.50037	+	0.910060i
$746$		0			0
$747$	1.91689	−	23.0540i	0.0701352	−	0.843503i
$748$		0			0
$749$	−26.8583	−	4.73585i	−0.981382	−	0.173044i
$750$		0			0
$751$	12.7470	−	35.0221i	0.465145	−	1.27797i	−0.456425	−	0.889762i	$-0.650870\pi$
$751$	12.7470	−	35.0221i	0.465145	−	1.27797i	0.921570	−	0.388213i	$-0.126907\pi$
$752$		0			0
$753$	3.86075	+	6.03144i	0.140693	+	0.219798i
$754$		0			0
$755$	7.63058			0.277705
$756$		0			0
$757$	−13.7573			−0.500018			−0.250009	−	0.968244i	$-0.580434\pi$
$757$	−13.7573			−0.500018			−0.250009	+	0.968244i	$0.580434\pi$
$758$		0			0
$759$	1.84868	−	0.0847066i	0.0671027	−	0.00307466i
$760$		0			0
$761$	−8.47595	+	23.2875i	−0.307253	+	0.844171i	0.685936	+	0.727661i	$0.259393\pi$
$761$	−8.47595	+	23.2875i	−0.307253	+	0.844171i	−0.993190	+	0.116510i	$0.962829\pi$
$762$		0			0
$763$	−28.7957	−	5.07747i	−1.04248	−	0.183817i
$764$		0			0
$765$	42.6743	−	43.0437i	1.54289	−	1.55625i
$766$		0			0
$767$	−5.38373	+	1.95952i	−0.194395	+	0.0707541i
$768$		0			0
$769$	16.2655	−	13.6484i	0.586550	−	0.492174i	−0.300541	−	0.953769i	$-0.597167\pi$
$769$	16.2655	−	13.6484i	0.586550	−	0.492174i	0.887091	+	0.461595i	$0.152723\pi$
$770$		0			0
$771$	10.7566	−	2.40901i	0.387390	−	0.0867584i
$772$		0			0
$773$	12.2938	−	7.09780i	0.442176	−	0.255290i	−0.262344	−	0.964974i	$-0.584496\pi$
$773$	12.2938	−	7.09780i	0.442176	−	0.255290i	0.704520	+	0.709684i	$0.251162\pi$
$774$		0			0
$775$	33.2668	+	19.2066i	1.19498	+	0.689921i
$776$		0			0
$777$	−26.7398	−	3.46176i	−0.959286	−	0.124190i
$778$		0			0
$779$	7.03204	+	39.8807i	0.251949	+	1.42887i
$780$		0			0
$781$	−7.91315	−	6.63992i	−0.283155	−	0.237595i
$782$		0			0
$783$	−21.7236	+	34.5906i	−0.776337	+	1.23617i
$784$		0			0
$785$	6.20939	−	7.40006i	0.221623	−	0.264119i
$786$		0			0
$787$	27.3006	−	4.81383i	0.973160	−	0.171594i	0.335608	−	0.942002i	$-0.391058\pi$
$787$	27.3006	−	4.81383i	0.973160	−	0.171594i	0.637552	+	0.770407i	$0.279947\pi$
$788$		0			0
$789$	2.02706	+	1.54849i	0.0721653	+	0.0551278i
$790$		0			0
$791$	19.1689	−	33.2015i	0.681567	−	1.18051i
$792$		0			0
$793$	9.79985	+	16.9738i	0.348003	+	0.602759i
$794$		0			0
$795$	18.4358	−	16.9665i	0.653851	−	0.601741i
$796$		0			0
$797$	13.1789	+	15.7060i	0.466821	+	0.556336i	0.947166	−	0.320744i	$-0.103933\pi$
$797$	13.1789	+	15.7060i	0.466821	+	0.556336i	−0.480345	+	0.877080i	$0.659488\pi$
$798$		0			0
$799$	15.6584	+	43.0211i	0.553954	+	1.52198i
$800$		0			0
$801$	0.734763	+	8.00107i	0.0259616	+	0.282704i
$802$		0			0
$803$	−3.31348	+	18.7917i	−0.116930	+	0.663145i
$804$		0			0
$805$	5.47893	+	1.99417i	0.193107	+	0.0702851i
$806$		0			0
$807$	−12.3110	−	6.37500i	−0.433366	−	0.224411i
$808$		0			0
$809$		−	11.1965i		−	0.393648i	−0.980439	−	0.196824i	$-0.936937\pi$
$809$		−	11.1965i		−	0.393648i	0.980439	−	0.196824i	$-0.0630628\pi$
$810$		0			0
$811$			12.2038i			0.428533i	0.976775	+	0.214267i	$0.0687361\pi$
$811$			12.2038i			0.428533i	−0.976775	+	0.214267i	$0.931264\pi$
$812$		0			0
$813$	−19.7559	−	10.2302i	−0.692868	−	0.358789i
$814$		0			0
$815$	−76.2760	−	27.7622i	−2.67183	−	0.972467i
$816$		0			0
$817$	−10.0802	+	57.1674i	−0.352660	+	2.00003i
$818$		0			0
$819$	37.9031	+	17.4760i	1.32444	+	0.610663i
$820$		0			0
$821$	12.9321	+	35.5306i	0.451332	+	1.24003i	0.931787	+	0.363006i	$0.118249\pi$
$821$	12.9321	+	35.5306i	0.451332	+	1.24003i	−0.480455	+	0.877020i	$0.659528\pi$
$822$		0			0
$823$	1.68950	+	2.01347i	0.0588923	+	0.0701851i	0.794686	−	0.607020i	$-0.207635\pi$
$823$	1.68950	+	2.01347i	0.0588923	+	0.0701851i	−0.735794	+	0.677205i	$0.763191\pi$
$824$		0			0
$825$	−13.7100	+	12.6173i	−0.477320	+	0.439279i
$826$		0			0
$827$	1.31968	+	2.28576i	0.0458899	+	0.0794836i	0.888058	−	0.459731i	$-0.152054\pi$
$827$	1.31968	+	2.28576i	0.0458899	+	0.0794836i	−0.842168	+	0.539215i	$0.818721\pi$
$828$		0			0
$829$	5.69261	−	9.85989i	0.197713	−	0.342448i	−0.750074	−	0.661354i	$-0.769982\pi$
$829$	5.69261	−	9.85989i	0.197713	−	0.342448i	0.947786	+	0.318906i	$0.103315\pi$
$830$		0			0
$831$	−21.7647	−	16.6263i	−0.755009	−	0.576758i
$832$		0			0
$833$	−15.7123	+	2.77050i	−0.544398	+	0.0959921i
$834$		0			0
$835$	−21.2343	+	25.3060i	−0.734842	+	0.875751i
$836$		0			0
$837$	32.8988	−	10.6073i	1.13715	−	0.366640i
$838$		0			0
$839$	14.1450	+	11.8690i	0.488338	+	0.409765i	0.853430	−	0.521207i	$-0.174518\pi$
$839$	14.1450	+	11.8690i	0.488338	+	0.409765i	−0.365092	+	0.930971i	$0.618962\pi$
$840$		0			0
$841$	−5.69454	−	32.2953i	−0.196363	−	1.11363i
$842$		0			0
$843$	−32.0280	−	4.14637i	−1.10310	−	0.142809i
$844$		0			0
$845$	−20.4088	−	11.7830i	−0.702084	−	0.405348i
$846$		0			0
$847$	−20.1953	+	11.6598i	−0.693919	+	0.400634i
$848$		0			0
$849$	−1.74783	+	0.391437i	−0.0599853	+	0.0134341i
$850$		0			0
$851$	2.20832	−	1.85300i	0.0757004	−	0.0635202i
$852$		0			0
$853$	−12.2182	+	4.44706i	−0.418343	+	0.152264i	−0.542611	−	0.839984i	$-0.682564\pi$
$853$	−12.2182	+	4.44706i	−0.418343	+	0.152264i	0.124268	+	0.992249i	$0.460342\pi$
$854$		0			0
$855$	−61.7705	−	16.2663i	−2.11251	−	0.556297i
$856$		0			0
$857$	44.4317	+	7.83451i	1.51776	+	0.267622i	0.869551	−	0.493843i	$-0.164408\pi$
$857$	44.4317	+	7.83451i	1.51776	+	0.267622i	0.648207	+	0.761464i	$0.275519\pi$
$858$		0			0
$859$	−1.21631	+	3.34179i	−0.0415001	+	0.114021i	−0.958712	−	0.284380i	$-0.908212\pi$
$859$	−1.21631	+	3.34179i	−0.0415001	+	0.114021i	0.917212	+	0.398400i	$0.130435\pi$
$860$		0			0
$861$	33.4541	−	1.53287i	1.14011	−	0.0522402i
$862$		0			0
$863$	25.1350			0.855605			0.427802	−	0.903872i	$-0.359288\pi$
$863$	25.1350			0.855605			0.427802	+	0.903872i	$0.359288\pi$
$864$		0			0
$865$	60.7471			2.06546
$866$		0			0
$867$	−19.5035	−	30.4693i	−0.662375	−	1.03479i
$868$		0			0
$869$	0.525465	−	1.44370i	0.0178252	−	0.0489743i
$870$		0			0
$871$	−23.0809	−	4.06979i	−0.782068	−	0.137900i
$872$		0			0
$873$	−25.0511	−	17.3806i	−0.847853	−	0.588244i
$874$		0			0
$875$	−7.39774	+	2.69256i	−0.250089	+	0.0910250i
$876$		0			0
$877$	7.30747	−	6.13169i	0.246756	−	0.207053i	−0.511018	−	0.859570i	$-0.670732\pi$
$877$	7.30747	−	6.13169i	0.246756	−	0.207053i	0.757774	+	0.652517i	$0.226287\pi$
$878$		0			0
$879$	−6.98784	+	22.3303i	−0.235694	+	0.753181i
$880$		0			0
$881$	23.3602	−	13.4870i	0.787027	−	0.454390i	−0.0518881	−	0.998653i	$-0.516524\pi$
$881$	23.3602	−	13.4870i	0.787027	−	0.454390i	0.838915	+	0.544263i	$0.183191\pi$
$882$		0			0
$883$	3.96969	+	2.29190i	0.133591	+	0.0771286i	0.565306	−	0.824881i	$-0.308758\pi$
$883$	3.96969	+	2.29190i	0.133591	+	0.0771286i	−0.431715	+	0.902010i	$0.642091\pi$
$884$		0			0
$885$	−2.78928	−	6.69309i	−0.0937607	−	0.224986i
$886$		0			0
$887$	0.517007	+	2.93209i	0.0173594	+	0.0984501i	0.992256	−	0.124206i	$-0.0396384\pi$
$887$	0.517007	+	2.93209i	0.0173594	+	0.0984501i	−0.974897	+	0.222656i	$0.928527\pi$
$888$		0			0
$889$	34.4314	+	28.8914i	1.15479	+	0.968987i
$890$		0			0
$891$	0.144517	+	16.7658i	0.00484151	+	0.561676i
$892$		0			0
$893$	31.0128	−	36.9597i	1.03781	−	1.23681i
$894$		0			0
$895$	−52.6538	+	9.28429i	−1.76002	+	0.310339i
$896$		0			0
$897$	−4.11907	+	1.71658i	−0.137532	+	0.0573150i
$898$		0			0
$899$	−26.1466	+	45.2873i	−0.872039	+	1.51042i
$900$		0			0
$901$	−13.5627	−	23.4914i	−0.451841	−	0.782611i
$902$		0			0
$903$	45.8147	+	14.3368i	1.52462	+	0.477100i
$904$		0			0
$905$	22.3312	+	26.6133i	0.742314	+	0.884656i
$906$		0			0
$907$	0.939557	+	2.58141i	0.0311975	+	0.0857144i	0.954314	−	0.298807i	$-0.0965887\pi$
$907$	0.939557	+	2.58141i	0.0311975	+	0.0857144i	−0.923116	+	0.384521i	$0.874366\pi$
$908$		0			0
$909$	−8.34459	−	17.6955i	−0.276773	−	0.586923i
$910$		0			0
$911$	7.45754	−	42.2938i	0.247079	−	1.40126i	−0.568534	−	0.822660i	$-0.692489\pi$
$911$	7.45754	−	42.2938i	0.247079	−	1.40126i	0.815613	−	0.578597i	$-0.196400\pi$
$912$		0			0
$913$	13.4991	+	4.91329i	0.446756	+	0.162606i
$914$		0			0
$915$	−20.8922	+	13.3732i	−0.690674	+	0.442103i
$916$		0			0
$917$			43.2144i			1.42706i
$918$		0			0
$919$		−	30.9255i		−	1.02014i	−0.860134	−	0.510069i	$-0.829620\pi$
$919$		−	30.9255i		−	1.02014i	0.860134	−	0.510069i	$-0.170380\pi$
$920$		0			0
$921$	−0.498460	−	10.8786i	−0.0164248	−	0.358463i
$922$		0			0
$923$	23.4065	+	8.51928i	0.770436	+	0.280416i
$924$		0			0
$925$	−5.03997	+	28.5831i	−0.165713	+	0.939806i
$926$		0			0
$927$	31.0218	−	8.45572i	1.01889	−	0.277722i
$928$		0			0
$929$	−12.6336	−	34.7105i	−0.414494	−	1.13881i	−0.954775	−	0.297329i	$-0.903904\pi$
$929$	−12.6336	−	34.7105i	−0.414494	−	1.13881i	0.540281	−	0.841485i	$-0.318318\pi$
$930$		0			0
$931$	10.8077	+	12.8801i	0.354209	+	0.422129i
$932$		0			0
$933$	12.2172	+	54.5516i	0.399973	+	1.78594i
$934$		0			0
$935$	18.8195	+	32.5964i	0.615464	+	1.06602i
$936$		0			0
$937$	−13.7777	+	23.8636i	−0.450097	+	0.779591i	−0.998392	−	0.0566942i	$-0.981944\pi$
$937$	−13.7777	+	23.8636i	−0.450097	+	0.779591i	0.548294	+	0.836285i	$0.315277\pi$
$938$		0			0
$939$	−1.82236	+	14.0766i	−0.0594706	+	0.459371i
$940$		0			0
$941$	−51.2999	+	9.04556i	−1.67233	+	0.294877i	−0.927901	−	0.372826i	$-0.878389\pi$
$941$	−51.2999	+	9.04556i	−1.67233	+	0.294877i	−0.744428	+	0.667703i	$0.767278\pi$
$942$		0			0
$943$	−2.30151	+	2.74284i	−0.0749476	+	0.0893191i
$944$		0			0
$945$	−19.8991	+	48.9330i	−0.647317	+	1.59179i
$946$		0			0
$947$	40.8161	+	34.2488i	1.32634	+	1.11294i	0.984917	+	0.173027i	$0.0553548\pi$
$947$	40.8161	+	34.2488i	1.32634	+	1.11294i	0.341427	+	0.939908i	$0.389090\pi$
$948$		0			0
$949$	−7.98989	−	45.3129i	−0.259363	−	1.47092i
$950$		0			0
$951$	−0.273973	+	0.358646i	−0.00888419	+	0.0116299i
$952$		0			0
$953$	20.8973	+	12.0650i	0.676929	+	0.390825i	0.798697	−	0.601733i	$-0.205523\pi$
$953$	20.8973	+	12.0650i	0.676929	+	0.390825i	−0.121768	+	0.992559i	$0.538856\pi$
$954$		0			0
$955$	−31.4987	+	18.1858i	−1.01928	+	0.588479i
$956$		0			0
$957$	−17.1764	−	18.6639i	−0.555235	−	0.603318i
$958$		0			0
$959$	−24.1849	+	20.2936i	−0.780972	+	0.655313i
$960$		0			0
$961$	12.4542	−	4.53297i	0.401750	−	0.146225i
$962$		0			0
$963$	15.2456	+	21.5745i	0.491283	+	0.695229i
$964$		0			0
$965$	−50.7997	−	8.95735i	−1.63530	−	0.288347i
$966$		0			0
$967$	−3.46122	+	9.50964i	−0.111305	+	0.305809i	−0.982822	−	0.184557i	$-0.940915\pi$
$967$	−3.46122	+	9.50964i	−0.111305	+	0.305809i	0.871516	+	0.490367i	$0.163137\pi$
$968$		0			0
$969$	−31.8002	+	61.4103i	−1.02157	+	1.97278i
$970$		0			0
$971$	16.3688			0.525299			0.262649	−	0.964891i	$-0.415404\pi$
$971$	16.3688			0.525299			0.262649	+	0.964891i	$0.415404\pi$
$972$		0			0
$973$	44.3048			1.42035
$974$		0			0
$975$	20.6597	−	39.8966i	0.661641	−	1.27771i
$976$		0			0
$977$	14.0507	−	38.6039i	0.449521	−	1.23505i	−0.483538	−	0.875324i	$-0.660648\pi$
$977$	14.0507	−	38.6039i	0.449521	−	1.23505i	0.933058	−	0.359725i	$-0.117129\pi$
$978$		0			0
$979$	−4.91360	−	0.866401i	−0.157039	−	0.0276903i
$980$		0			0
$981$	16.3454	+	23.1308i	0.521867	+	0.738509i
$982$		0			0
$983$	−7.58582	+	2.76101i	−0.241950	+	0.0880626i	−0.460149	−	0.887842i	$-0.652204\pi$
$983$	−7.58582	+	2.76101i	−0.241950	+	0.0880626i	0.218199	+	0.975904i	$0.429982\pi$
$984$		0			0
$985$	−34.5367	+	28.9797i	−1.10043	+	0.923370i
$986$		0			0
$987$	−27.0191	−	29.3589i	−0.860027	−	0.934504i
$988$		0			0
$989$	−4.44491	+	2.56627i	−0.141340	+	0.0816026i
$990$		0			0
$991$	1.80881	+	1.04432i	0.0574589	+	0.0331739i	0.528454	−	0.848962i	$-0.322772\pi$
$991$	1.80881	+	1.04432i	0.0574589	+	0.0331739i	−0.470995	+	0.882136i	$0.656105\pi$
$992$		0			0
$993$	−0.561295	+	0.734767i	−0.0178122	+	0.0233171i
$994$		0			0
$995$	−8.77369	−	49.7581i	−0.278145	−	1.57744i
$996$		0			0
$997$	22.1658	+	18.5993i	0.701998	+	0.589046i	0.922341	−	0.386376i	$-0.126273\pi$
$997$	22.1658	+	18.5993i	0.701998	+	0.589046i	−0.220343	+	0.975422i	$0.570718\pi$
$998$		0			0
$999$	16.0330	+	20.6173i	0.507262	+	0.652302i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.c.335.4	yes	36
4.3	odd	2		432.2.be.b.335.3	✓	36
27.5	odd	18		432.2.be.b.383.3	yes	36
108.59	even	18	inner	432.2.be.c.383.4	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.335.3	✓	36	4.3	odd	2
432.2.be.b.383.3	yes	36	27.5	odd	18
432.2.be.c.335.4	yes	36	1.1	even	1	trivial
432.2.be.c.383.4	yes	36	108.59	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.796460 - 1.53807i) q^{3} +(1.12266 - 3.08448i) q^{5} +(3.05005 + 0.537806i) q^{7} +(-1.73130 - 2.45002i) q^{9} +(1.75059 - 0.637162i) q^{11} +(-3.44119 + 2.88750i) q^{13} +(-3.84999 - 4.18339i) q^{15} +(-5.33058 + 3.07761i) q^{17} +(5.61763 + 3.24334i) q^{19} +(3.25643 - 4.26285i) q^{21} +(0.0995927 + 0.564818i) q^{23} +(-4.42344 - 3.71171i) q^{25} +(-5.14721 + 0.711524i) q^{27} +(5.05288 - 6.02179i) q^{29} +(-6.55127 + 1.15517i) q^{31} +(0.414275 - 3.20000i) q^{33} +(5.08302 - 8.80406i) q^{35} +(-2.51317 - 4.35293i) q^{37} +(1.70040 + 7.59256i) q^{39} +(4.01288 + 4.78237i) q^{41} +(3.06074 + 8.40931i) q^{43} +(-9.50070 + 2.58964i) q^{45} +(1.29158 - 7.32493i) q^{47} +(2.43573 + 0.886535i) q^{49} +(0.487984 + 10.6500i) q^{51} +4.40691i q^{53} -6.11498i q^{55} +(9.46269 - 6.05710i) q^{57} +(1.19847 + 0.436209i) q^{59} +(0.757644 - 4.29681i) q^{61} +(-3.96293 - 8.40379i) q^{63} +(5.04316 + 13.8560i) q^{65} +(3.35363 + 3.99670i) q^{67} +(0.948051 + 0.296675i) q^{69} +(-2.77247 - 4.80206i) q^{71} +(-5.12137 + 8.87047i) q^{73} +(-9.23195 + 3.84733i) q^{75} +(5.68206 - 1.00190i) q^{77} +(0.530104 - 0.631754i) q^{79} +(-3.00517 + 8.48345i) q^{81} +(5.90712 + 4.95666i) q^{83} +(3.50841 + 19.8972i) q^{85} +(-5.23750 - 12.5678i) q^{87} +(-2.31943 - 1.33912i) q^{89} +(-12.0487 + 6.95633i) q^{91} +(-3.44110 + 10.9963i) q^{93} +(16.3107 - 13.6863i) q^{95} +(9.55043 - 3.47607i) q^{97} +(-4.59186 - 3.18585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9} + 18 q^{11} - 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} - 27 q^{31} + 27 q^{33} - 27 q^{35} + 45 q^{39} + 18 q^{41} + 27 q^{45} - 45 q^{47} + 63 q^{51} - 9 q^{57} - 54 q^{59}+ \cdots - 99 q^{99}+O(q^{100}) \) 36 * q + 3 * q^5 + 6 * q^9 + 18 * q^11 - 9 * q^15 + 18 * q^21 - 9 * q^25 + 30 * q^29 - 27 * q^31 + 27 * q^33 - 27 * q^35 + 45 * q^39 + 18 * q^41 + 27 * q^45 - 45 * q^47 + 63 * q^51 - 9 * q^57 - 54 * q^59 + 63 * q^63 - 57 * q^65 - 63 * q^69 - 36 * q^71 + 9 * q^73 + 45 * q^75 - 81 * q^77 - 54 * q^81 + 27 * q^83 - 36 * q^85 - 45 * q^87 - 63 * q^89 - 27 * q^91 - 63 * q^93 + 72 * q^95 - 99 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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