LMFDB - Embedded newform 432.2.be.b.383.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
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			383.3
Character	$\chi$	$=$	432.383
Dual form			432.2.be.b.335.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.796460 - 1.53807i) q^{3} +(1.12266 + 3.08448i) q^{5} +(-3.05005 + 0.537806i) q^{7} +(-1.73130 + 2.45002i) q^{9} +O(q^{10})$	\(q+(-0.796460 - 1.53807i) q^{3} +(1.12266 + 3.08448i) q^{5} +(-3.05005 + 0.537806i) q^{7} +(-1.73130 + 2.45002i) q^{9} +(-1.75059 - 0.637162i) q^{11} +(-3.44119 - 2.88750i) q^{13} +(3.84999 - 4.18339i) q^{15} +(-5.33058 - 3.07761i) q^{17} +(-5.61763 + 3.24334i) q^{19} +(3.25643 + 4.26285i) q^{21} +(-0.0995927 + 0.564818i) q^{23} +(-4.42344 + 3.71171i) q^{25} +(5.14721 + 0.711524i) q^{27} +(5.05288 + 6.02179i) q^{29} +(6.55127 + 1.15517i) q^{31} +(0.414275 + 3.20000i) q^{33} +(-5.08302 - 8.80406i) q^{35} +(-2.51317 + 4.35293i) q^{37} +(-1.70040 + 7.59256i) q^{39} +(4.01288 - 4.78237i) q^{41} +(-3.06074 + 8.40931i) q^{43} +(-9.50070 - 2.58964i) q^{45} +(-1.29158 - 7.32493i) q^{47} +(2.43573 - 0.886535i) q^{49} +(-0.487984 + 10.6500i) q^{51} -4.40691i q^{53} -6.11498i q^{55} +(9.46269 + 6.05710i) q^{57} +(-1.19847 + 0.436209i) q^{59} +(0.757644 + 4.29681i) q^{61} +(3.96293 - 8.40379i) q^{63} +(5.04316 - 13.8560i) q^{65} +(-3.35363 + 3.99670i) q^{67} +(0.948051 - 0.296675i) q^{69} +(2.77247 - 4.80206i) q^{71} +(-5.12137 - 8.87047i) q^{73} +(9.23195 + 3.84733i) q^{75} +(5.68206 + 1.00190i) q^{77} +(-0.530104 - 0.631754i) q^{79} +(-3.00517 - 8.48345i) q^{81} +(-5.90712 + 4.95666i) q^{83} +(3.50841 - 19.8972i) q^{85} +(5.23750 - 12.5678i) q^{87} +(-2.31943 + 1.33912i) q^{89} +(12.0487 + 6.95633i) q^{91} +(-3.44110 - 10.9963i) q^{93} +(-16.3107 - 13.6863i) q^{95} +(9.55043 + 3.47607i) q^{97} +(4.59186 - 3.18585i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 36 * q + 3 * q^5 + 6 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{18}\right)$

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	0.889251	+	0.457419i	$0.151226\pi$
$5$	1.12266	+	3.08448i	0.502069	+	1.37942i	−0.387183	+	0.922003i	$0.626552\pi$
$6$		0			0
$7$	−3.05005	+	0.537806i	−1.15281	+	0.203272i	−0.717203	−	0.696864i	$-0.754578\pi$
$7$	−3.05005	+	0.537806i	−1.15281	+	0.203272i	−0.435609	+	0.900136i	$0.643467\pi$
$8$		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	$-0.479505\pi$
$11$	−1.75059	−	0.637162i	−0.527822	−	0.192112i	−0.592166	+	0.805816i	$0.701727\pi$
$12$		0			0
$13$	−3.44119	−	2.88750i	−0.954414	−	0.800848i	0.0256213	−	0.999672i	$-0.491844\pi$
$13$	−3.44119	−	2.88750i	−0.954414	−	0.800848i	−0.980035	+	0.198823i	$0.936288\pi$
$14$		0			0
$15$	3.84999	−	4.18339i	0.994063	−	1.08015i
$16$		0			0
$17$	−5.33058	−	3.07761i	−1.29286	−	0.746430i	−0.313696	−	0.949524i	$-0.601567\pi$
$17$	−5.33058	−	3.07761i	−1.29286	−	0.746430i	−0.979159	+	0.203093i	$0.934901\pi$
$18$		0			0
$19$	−5.61763	+	3.24334i	−1.28877	+	0.744073i	−0.978435	−	0.206554i	$-0.933775\pi$
$19$	−5.61763	+	3.24334i	−1.28877	+	0.744073i	−0.310337	+	0.950627i	$0.600442\pi$
$20$		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	$-0.963489\pi$
$23$	−0.0995927	+	0.564818i	−0.0207665	+	0.117773i	0.972662	+	0.232224i	$0.0746002\pi$
$24$		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	0.992809	+	0.119705i	$0.0381949\pi$
$29$	5.05288	+	6.02179i	0.938296	+	1.11822i	−0.0545130	+	0.998513i	$0.517361\pi$
$30$		0			0
$31$	6.55127	+	1.15517i	1.17664	+	0.207474i	0.727578	−	0.686025i	$-0.240646\pi$
$31$	6.55127	+	1.15517i	1.17664	+	0.207474i	0.449065	+	0.893499i	$0.351757\pi$
$32$		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	−0.995234	−	0.0975198i	$-0.968909\pi$
$37$	−2.51317	+	4.35293i	−0.413162	+	0.715618i	0.582071	+	0.813138i	$0.302242\pi$
$38$		0			0
$39$	−1.70040	+	7.59256i	−0.272282	+	1.21578i
$40$		0			0
$41$	4.01288	−	4.78237i	0.626707	−	0.746880i	−0.355501	−	0.934676i	$-0.615690\pi$
$41$	4.01288	−	4.78237i	0.626707	−	0.746880i	0.982208	+	0.187796i	$0.0601343\pi$
$42$		0			0
$43$	−3.06074	+	8.40931i	−0.466758	+	1.28241i	0.453556	+	0.891228i	$0.350155\pi$
$43$	−3.06074	+	8.40931i	−0.466758	+	1.28241i	−0.920314	+	0.391180i	$0.872067\pi$
$44$		0			0
$45$	−9.50070	−	2.58964i	−1.41628	−	0.386041i
$46$		0			0
$47$	−1.29158	−	7.32493i	−0.188397	−	1.06845i	−0.921513	−	0.388347i	$-0.873046\pi$
$47$	−1.29158	−	7.32493i	−0.188397	−	1.06845i	0.733116	−	0.680103i	$-0.238065\pi$
$48$		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	$-0.902123\pi$
$53$		−	4.40691i		−	0.605335i	0.953096	−	0.302668i	$-0.0978772\pi$
$54$		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	$-0.637568\pi$
$59$	−1.19847	+	0.436209i	−0.156028	+	0.0567896i	0.262825	+	0.964843i	$0.415346\pi$
$60$		0			0
$61$	0.757644	+	4.29681i	0.0970064	+	0.550151i	0.994114	+	0.108339i	$0.0345531\pi$
$61$	0.757644	+	4.29681i	0.0970064	+	0.550151i	−0.897108	+	0.441812i	$0.854336\pi$
$62$		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	$-0.881024\pi$
$67$	−3.35363	+	3.99670i	−0.409711	+	0.488275i	0.521244	+	0.853407i	$0.325468\pi$
$68$		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	$-0.726611\pi$
$71$	2.77247	−	4.80206i	0.329032	−	0.569900i	0.982320	+	0.187210i	$0.0599444\pi$
$72$		0			0
$73$	−5.12137	−	8.87047i	−0.599411	−	1.03821i	−0.992908	−	0.118884i	$-0.962068\pi$
$73$	−5.12137	−	8.87047i	−0.599411	−	1.03821i	0.393497	−	0.919326i	$-0.371265\pi$
$74$		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	$-0.236995\pi$
$79$	−0.530104	−	0.631754i	−0.0596414	−	0.0710778i	−0.795040	+	0.606557i	$0.792550\pi$
$80$		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	$-0.861318\pi$
$83$	−5.90712	+	4.95666i	−0.648391	+	0.544065i	0.258191	+	0.966094i	$0.416874\pi$
$84$		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	−0.617867	−	0.786283i	$-0.712003\pi$
$89$	−2.31943	+	1.33912i	−0.245859	+	0.141947i	0.372008	+	0.928230i	$0.378670\pi$
$90$		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	0.777827	−	0.628478i	$-0.216322\pi$
$97$	9.55043	+	3.47607i	0.969699	+	0.352942i	0.191872	+	0.981420i	$0.438544\pi$
$98$		0			0
$99$	4.59186	−	3.18585i	0.461499	−	0.320190i
$100$		0			0
$101$	6.42237	−	1.13244i	0.639050	−	0.112682i	0.155271	−	0.987872i	$-0.450375\pi$
$101$	6.42237	−	1.13244i	0.639050	−	0.112682i	0.483779	+	0.875190i	$0.339264\pi$
$102$		0			0
$103$	3.66572	+	10.0715i	0.361194	+	0.992372i	0.978608	+	0.205734i	$0.0659581\pi$
$103$	3.66572	+	10.0715i	0.361194	+	0.992372i	−0.617414	+	0.786638i	$0.711820\pi$
$104$		0			0
$105$	−9.49281	+	14.8301i	−0.926404	+	1.44727i
$106$		0			0
$107$	8.80586			0.851295			0.425647	−	0.904889i	$-0.360046\pi$
$107$	8.80586			0.851295			0.425647	+	0.904889i	$0.360046\pi$
$108$		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	0.963124	+	0.269058i	$0.0867123\pi$
$113$	4.23372	+	11.6321i	0.398275	+	1.09425i	−0.564849	+	0.825194i	$0.691065\pi$
$114$		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	$-0.889348\pi$
$127$	−12.5683	+	7.25630i	−1.11525	+	0.643893i	−0.175070	+	0.984556i	$0.556015\pi$
$128$		0			0
$129$	15.3718	−	1.99005i	1.35342	−	0.175214i
$130$		0			0
$131$	−2.42294	+	13.7412i	−0.211693	+	1.20057i	0.674860	+	0.737946i	$0.264204\pi$
$131$	−2.42294	+	13.7412i	−0.211693	+	1.20057i	−0.886553	+	0.462627i	$0.846907\pi$
$132$		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	0.409695	−	0.912223i	$-0.365635\pi$
$137$	−6.55243	−	7.80889i	−0.559812	−	0.667158i	−0.969507	+	0.245065i	$0.921191\pi$
$138$		0			0
$139$	−14.0879	−	2.48408i	−1.19492	−	0.210697i	−0.459418	−	0.888220i	$-0.651942\pi$
$139$	−14.0879	−	2.48408i	−1.19492	−	0.210697i	−0.735501	+	0.677523i	$0.763053\pi$
$140$		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	−0.258825	+	0.965924i	$0.583335\pi$
$149$	−14.2222	+	16.9494i	−1.16513	+	1.38855i	−0.906305	+	0.422624i	$0.861109\pi$
$150$		0			0
$151$	−0.795084	+	2.18447i	−0.0647030	+	0.177770i	−0.967831	−	0.251602i	$-0.919043\pi$
$151$	−0.795084	+	2.18447i	−0.0647030	+	0.177770i	0.903128	+	0.429372i	$0.141265\pi$
$152$		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	−0.229299	−	0.973356i	$-0.573643\pi$
$157$	2.76548	−	1.00655i	0.220709	−	0.0803317i	0.450008	+	0.893024i	$0.351421\pi$
$158$		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	$-0.483797\pi$
$167$	9.45713	−	3.44211i	0.731814	−	0.266359i	0.680933	+	0.732346i	$0.261575\pi$
$168$		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	−0.427199	−	0.904158i	$-0.640500\pi$
$173$	6.32967	−	17.3906i	0.481236	−	1.32218i	0.908435	−	0.418027i	$-0.137278\pi$
$174$		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	−0.382719	−	0.923865i	$-0.625012\pi$
$179$	8.14426	−	14.1063i	0.608731	−	1.05435i	0.991450	−	0.130488i	$-0.0416544\pi$
$180$		0			0
$181$	−5.29198	−	9.16598i	−0.393350	−	0.681302i	0.599539	−	0.800345i	$-0.295351\pi$
$181$	−5.29198	−	9.16598i	−0.393350	−	0.681302i	−0.992889	+	0.119043i	$0.962017\pi$
$182$		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	$-0.590925\pi$
$191$	8.48829	−	7.12252i	0.614191	−	0.515367i	0.895972	+	0.444112i	$0.146481\pi$
$192$		0			0
$193$	−2.72887	+	15.4762i	−0.196429	+	1.11400i	0.713941	+	0.700206i	$0.246908\pi$
$193$	−2.72887	+	15.4762i	−0.196429	+	1.11400i	−0.910370	+	0.413796i	$0.864203\pi$
$194$		0			0
$195$	−25.3281	+	3.27900i	−1.81378	+	0.234814i
$196$		0			0
$197$	−11.8949	+	6.86752i	−0.847476	+	0.489291i	−0.859799	−	0.510633i	$-0.829411\pi$
$197$	−11.8949	+	6.86752i	−0.847476	+	0.489291i	0.0123223	+	0.999924i	$0.496078\pi$
$198$		0			0
$199$	−13.3305	−	7.69637i	−0.944974	−	0.545581i	−0.0534579	−	0.998570i	$-0.517024\pi$
$199$	−13.3305	−	7.69637i	−0.944974	−	0.545581i	−0.891516	+	0.452989i	$0.850358\pi$
$200$		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	$-0.130087\pi$
$211$	−0.592005	−	1.62652i	−0.0407553	−	0.111974i	−0.958401	+	0.285425i	$0.907865\pi$
$212$		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	$-0.630914\pi$
$223$	−6.89847	+	1.21639i	−0.461956	+	0.0814552i	−0.0621733	+	0.998065i	$0.519803\pi$
$224$		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	$-0.394016\pi$
$227$	−0.456091	−	0.166003i	−0.0302718	−	0.0110180i	−0.357112	+	0.934062i	$0.616238\pi$
$228$		0			0
$229$	18.7833	+	15.7611i	1.24124	+	1.04152i	0.997426	+	0.0717003i	$0.0228425\pi$
$229$	18.7833	+	15.7611i	1.24124	+	1.04152i	0.243812	+	0.969822i	$0.421602\pi$
$230$		0			0
$231$	−2.98454	−	9.53736i	−0.196368	−	0.627512i
$232$		0			0
$233$	−7.90560	−	4.56430i	−0.517913	−	0.299017i	0.218167	−	0.975911i	$-0.429992\pi$
$233$	−7.90560	−	4.56430i	−0.517913	−	0.299017i	−0.736081	+	0.676894i	$0.763326\pi$
$234$		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	0.591475	+	0.806323i	$0.298546\pi$
$239$	−3.71199	+	21.0517i	−0.240108	+	1.36172i	−0.831584	+	0.555399i	$0.812565\pi$
$240$		0			0
$241$	−6.62233	+	5.55679i	−0.426582	+	0.357945i	−0.830660	−	0.556780i	$-0.812037\pi$
$241$	−6.62233	+	5.55679i	−0.426582	+	0.357945i	0.404078	+	0.914724i	$0.367592\pi$
$242$		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	$-0.125013\pi$
$251$	2.06728	+	3.58063i	0.130485	+	0.226007i	−0.793378	+	0.608729i	$0.791680\pi$
$252$		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	−0.623213	−	0.782052i	$-0.714173\pi$
$257$	4.09081	−	4.87523i	0.255178	−	0.304109i	0.878391	+	0.477943i	$0.158618\pi$
$258$		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	$-0.0410973\pi$
$263$	0.255737	+	1.45036i	0.0157694	+	0.0894328i	−0.975907	+	0.218185i	$0.929986\pi$
$264$		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	$0.0784635\pi$
$269$			8.00417i			0.488023i	−0.969772	+	0.244011i	$0.921537\pi$
$270$		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	0.949082	+	0.315029i	$0.102014\pi$
$277$	2.74587	+	15.5726i	0.164983	+	0.935665i	−0.784099	+	0.620636i	$0.786874\pi$
$278$		0			0
$279$	−14.1724	+	14.0508i	−0.848480	+	0.841198i
$280$		0			0
$281$	−6.37720	+	17.5212i	−0.380432	+	1.04523i	0.590743	+	0.806859i	$0.298835\pi$
$281$	−6.37720	+	17.5212i	−0.380432	+	1.04523i	−0.971175	+	0.238368i	$0.923388\pi$
$282$		0			0
$283$	0.664710	−	0.792171i	0.0395129	−	0.0470897i	−0.745926	−	0.666029i	$-0.767993\pi$
$283$	0.664710	−	0.792171i	0.0395129	−	0.0470897i	0.785439	+	0.618939i	$0.212437\pi$
$284$		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	−0.229047	−	0.973415i	$-0.573561\pi$
$293$	−13.3037	−	2.34580i	−0.777208	−	0.137043i	−0.548161	+	0.836373i	$0.684672\pi$
$294$		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	$-0.390755\pi$
$307$	−5.44502	−	3.14368i	−0.310763	−	0.179419i	−0.647268	+	0.762262i	$0.724089\pi$
$308$		0			0
$309$	12.5710	−	13.6596i	0.715140	−	0.777070i
$310$		0			0
$311$	24.7245	+	20.7464i	1.40200	+	1.17642i	0.960203	+	0.279303i	$0.0901032\pi$
$311$	24.7245	+	20.7464i	1.40200	+	1.17642i	0.441797	+	0.897115i	$0.354341\pi$
$312$		0			0
$313$	−7.70071	−	2.80283i	−0.435270	−	0.158425i	0.115086	−	0.993356i	$-0.463286\pi$
$313$	−7.70071	−	2.80283i	−0.435270	−	0.158425i	−0.550356	+	0.834930i	$0.685508\pi$
$314$		0			0
$315$	30.3704	+	2.78900i	1.71118	+	0.157143i
$316$		0			0
$317$	−0.256610	+	0.0452473i	−0.0144127	+	0.00254134i	−0.180850	−	0.983511i	$-0.557885\pi$
$317$	−0.256610	+	0.0452473i	−0.0144127	+	0.00254134i	0.166437	+	0.986052i	$0.446774\pi$
$318$		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	$-0.550885\pi$
$331$	0.525724	−	0.0926993i	0.0288964	−	0.00509521i	0.188078	+	0.982154i	$0.439774\pi$
$332$		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	−0.989827	−	0.142276i	$-0.954558\pi$
$337$	−23.8983	−	20.0530i	−1.30182	−	1.09236i	−0.311996	−	0.950083i	$-0.600998\pi$
$338$		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	0.689818	+	0.723983i	$0.257691\pi$
$347$	−3.83765	+	21.7644i	−0.206016	+	1.16837i	−0.895833	+	0.444390i	$0.853420\pi$
$348$		0			0
$349$	−1.37320	+	1.15226i	−0.0735059	+	0.0616788i	−0.678800	−	0.734323i	$-0.737500\pi$
$349$	−1.37320	+	1.15226i	−0.0735059	+	0.0616788i	0.605294	+	0.796002i	$0.293055\pi$
$350$		0			0
$351$	−15.6580	−	17.3110i	−0.835761	−	0.923995i
$352$		0			0
$353$	−16.2088	−	19.3168i	−0.862705	−	1.02813i	−0.999296	−	0.0375040i	$-0.988059\pi$
$353$	−16.2088	−	19.3168i	−0.862705	−	1.02813i	0.136592	−	0.990627i	$-0.456385\pi$
$354$		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	$-0.0614511\pi$
$359$	6.14950	+	10.6512i	0.324558	+	0.562151i	−0.656865	+	0.754008i	$0.728118\pi$
$360$		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	0.326956	+	0.945039i	$0.393977\pi$
$367$	−10.1719	+	27.9469i	−0.530966	+	1.45882i	−0.857923	+	0.513779i	$0.828245\pi$
$368$		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	−0.493508	−	0.869741i	$-0.664286\pi$
$373$	−6.03535	+	2.19669i	−0.312499	+	0.113740i	0.181010	+	0.983481i	$0.442063\pi$
$374$		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	$-0.438170\pi$
$383$	19.0144	−	6.92069i	0.971593	−	0.353631i	0.778566	+	0.627563i	$0.215947\pi$
$384$		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	0.500473	+	0.865752i	$0.333159\pi$
$389$	−8.66645	+	23.8109i	−0.439406	+	1.20726i	−0.939879	+	0.341507i	$0.889063\pi$
$390$		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	0.943347	−	0.331808i	$-0.107659\pi$
$397$	3.67253	+	6.36102i	0.184319	+	0.319250i	−0.759028	+	0.651058i	$0.774325\pi$
$398$		0			0
$399$	−32.1192	−	13.3854i	−1.60797	−	0.670107i
$400$		0			0
$401$	−9.92983	−	1.75090i	−0.495872	−	0.0874356i	−0.0798812	−	0.996804i	$-0.525454\pi$
$401$	−9.92983	−	1.75090i	−0.495872	−	0.0874356i	−0.415991	+	0.909369i	$0.636565\pi$
$402$		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	−0.987840	−	0.155477i	$-0.950309\pi$
$409$	−0.129387	+	0.733791i	−0.00639778	+	0.0362836i	0.981442	+	0.191761i	$0.0614197\pi$
$410$		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	−0.960128	−	0.279561i	$-0.909811\pi$
$419$	−28.7016	−	24.0835i	−1.40217	−	1.17656i	−0.442039	−	0.896996i	$-0.645745\pi$
$420$		0			0
$421$	−13.2383	−	4.81836i	−0.645197	−	0.234832i	−0.00136448	−	0.999999i	$-0.500434\pi$
$421$	−13.2383	−	4.81836i	−0.645197	−	0.234832i	−0.643832	+	0.765167i	$0.722657\pi$
$422$		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	$-0.436308\pi$
$431$	8.25286			0.397526			0.198763	+	0.980048i	$0.436308\pi$
$432$		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	$-0.499284\pi$
$439$	7.25755	−	1.27970i	0.346384	−	0.0610768i	0.344134	+	0.938921i	$0.388173\pi$
$440$		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	$-0.128557\pi$
$443$	28.8637	+	10.5055i	1.37136	+	0.499133i	0.451809	+	0.892115i	$0.350779\pi$
$444$		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	−0.101176	−	0.994869i	$-0.532260\pi$
$449$	−21.4724	−	12.3971i	−1.01334	−	0.585055i	−0.912169	+	0.409814i	$0.865594\pi$
$450$		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	−0.516138	−	0.856505i	$-0.672631\pi$
$457$	5.08205	−	4.26434i	0.237728	−	0.199478i	0.753866	+	0.657028i	$0.228187\pi$
$458$		0			0
$459$	−25.2478	−	19.6339i	−1.17847	−	0.916433i
$460$		0			0
$461$	4.80345	+	5.72452i	0.223719	+	0.266618i	0.866215	−	0.499671i	$-0.166546\pi$
$461$	4.80345	+	5.72452i	0.223719	+	0.266618i	−0.642497	+	0.766289i	$0.722101\pi$
$462$		0			0
$463$	−12.6122	−	2.22387i	−0.586139	−	0.103352i	−0.127288	−	0.991866i	$-0.540627\pi$
$463$	−12.6122	−	2.22387i	−0.586139	−	0.103352i	−0.458850	+	0.888514i	$0.651739\pi$
$464$		0			0
$465$	30.0548	−	22.9591i	1.39376	−	1.06470i
$466$		0			0
$467$	−21.2201	−	36.7544i	−0.981951	−	1.70079i	−0.654771	−	0.755827i	$-0.727235\pi$
$467$	−21.2201	−	36.7544i	−0.981951	−	1.70079i	−0.327180	−	0.944962i	$-0.606098\pi$
$468$		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	0.999999	+	0.00137483i	$0.000437621\pi$
$479$	1.33018	+	7.54383i	0.0607775	+	0.344687i	−0.939222	+	0.343312i	$0.888451\pi$
$480$		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	$-0.371457\pi$
$491$	28.4746	−	10.3639i	1.28504	−	0.467716i	0.892096	+	0.451846i	$0.149234\pi$
$492$		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	$-0.830604\pi$
$499$	−4.74411	+	5.65381i	−0.212376	+	0.253099i	0.649331	+	0.760506i	$0.275049\pi$
$500$		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	$-0.701915\pi$
$503$	8.99874	−	15.5863i	0.401234	−	0.694958i	0.993875	+	0.110509i	$0.0352480\pi$
$504$		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	0.477252	−	0.878766i	$-0.341633\pi$
$509$	14.1044	+	2.48699i	0.625167	+	0.110234i	0.147915	+	0.989000i	$0.452744\pi$
$510$		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	0.0142531	−	0.999898i	$-0.495463\pi$
$521$	20.2534	−	11.6933i	0.887317	−	0.512293i	0.873064	+	0.487606i	$0.162130\pi$
$522$		0			0
$523$	18.5635	+	10.7177i	0.811726	+	0.468650i	0.847555	−	0.530708i	$-0.178074\pi$
$523$	18.5635	+	10.7177i	0.811726	+	0.468650i	−0.0358289	+	0.999358i	$0.511407\pi$
$524$		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	$-0.400180\pi$
$547$	21.6034	−	3.80927i	0.923696	−	0.162873i	0.615216	+	0.788358i	$0.289069\pi$
$548$		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	0.940816	−	0.338918i	$-0.110061\pi$
$557$	26.3790	+	15.2299i	1.11771	+	0.645311i	0.176896	+	0.984230i	$0.443394\pi$
$558$		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	−0.688740	−	0.725008i	$-0.741836\pi$
$563$	4.89813	−	27.7786i	0.206431	−	1.17073i	0.895171	−	0.445722i	$-0.147053\pi$
$564$		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	0.841054	−	0.540951i	$-0.181935\pi$
$569$	3.87085	+	4.61310i	0.162274	+	0.193391i	−0.678780	+	0.734342i	$0.737491\pi$
$570$		0			0
$571$	−34.8030	−	6.13671i	−1.45646	−	0.256814i	−0.611332	−	0.791374i	$-0.709366\pi$
$571$	−34.8030	−	6.13671i	−1.45646	−	0.256814i	−0.845130	+	0.534561i	$0.820477\pi$
$572$		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	−0.947426	−	0.319973i	$-0.896326\pi$
$577$	−4.72269	+	8.17994i	−0.196608	+	0.340535i	0.750818	+	0.660509i	$0.229659\pi$
$578$		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	−0.856325	−	0.516438i	$-0.827258\pi$
$587$	−5.53066	−	31.3659i	−0.228275	−	1.29461i	0.628050	−	0.778173i	$-0.283853\pi$
$588$		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	$0.183422\pi$
$593$			26.5370i			1.08975i	−0.838519	+	0.544873i	$0.816578\pi$
$594$		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	$-0.376620\pi$
$599$	30.9021	−	11.2474i	1.26262	−	0.459558i	0.884649	+	0.466258i	$0.154398\pi$
$600$		0			0
$601$	−1.31366	−	7.45015i	−0.0535854	−	0.303898i	0.946222	−	0.323518i	$-0.104866\pi$
$601$	−1.31366	−	7.45015i	−0.0535854	−	0.303898i	−0.999808	+	0.0196197i	$0.993754\pi$
$602$		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	$-0.853267\pi$
$607$	−7.44129	+	8.86819i	−0.302033	+	0.359949i	0.593586	+	0.804770i	$0.297712\pi$
$608$		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	0.861603	−	0.507582i	$-0.169461\pi$
$613$	−0.217321	−	0.376411i	−0.00877751	−	0.0152031i	−0.870381	+	0.492379i	$0.836127\pi$
$614$		0			0
$615$	−4.55696	−	35.1995i	−0.183754	−	1.41938i
$616$		0			0
$617$	−8.52403	−	1.50302i	−0.343165	−	0.0605092i	−0.000590102	−	1.00000i	$-0.500188\pi$
$617$	−8.52403	−	1.50302i	−0.343165	−	0.0605092i	−0.342575	+	0.939491i	$0.611299\pi$
$618$		0			0
$619$	−15.5425	−	18.5228i	−0.624704	−	0.744494i	0.357167	−	0.934040i	$-0.383743\pi$
$619$	−15.5425	−	18.5228i	−0.624704	−	0.744494i	−0.981872	+	0.189547i	$0.939298\pi$
$620$		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	$-0.440226\pi$
$631$	−14.3376	−	8.27784i	−0.570773	−	0.329536i	−0.757458	+	0.652884i	$0.773559\pi$
$632$		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	−0.929593	−	0.368588i	$-0.879841\pi$
$641$	−42.4598	+	7.48680i	−1.67706	+	0.295711i	−0.747467	+	0.664299i	$0.768730\pi$
$642$		0			0
$643$	8.45774	+	23.2375i	0.333541	+	0.916396i	0.987183	+	0.159592i	$0.0510179\pi$
$643$	8.45774	+	23.2375i	0.333541	+	0.916396i	−0.653642	+	0.756804i	$0.726760\pi$
$644$		0			0
$645$	23.3956	+	45.1800i	0.921202	+	1.77896i
$646$		0			0
$647$	−35.4946			−1.39544			−0.697718	−	0.716372i	$-0.745801\pi$
$647$	−35.4946			−1.39544			−0.697718	+	0.716372i	$0.745801\pi$
$648$		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	0.999912	−	0.0132637i	$-0.00422210\pi$
$653$	5.76008	+	15.8257i	0.225409	+	0.619307i	−0.774503	+	0.632570i	$0.782000\pi$
$654$		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	$-0.440544\pi$
$659$	−7.79491	−	2.83712i	−0.303647	−	0.110518i	−0.489350	+	0.872088i	$0.662766\pi$
$660$		0			0
$661$	33.9315	+	28.4719i	1.31978	+	1.10743i	0.986351	+	0.164657i	$0.0526517\pi$
$661$	33.9315	+	28.4719i	1.31978	+	1.10743i	0.333433	+	0.942774i	$0.391793\pi$
$662$		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	−0.245193	−	0.969474i	$-0.578851\pi$
$673$	17.3028	−	14.5188i	0.666975	−	0.559658i	0.912168	+	0.409816i	$0.134407\pi$
$674$		0			0
$675$	−25.4093	+	15.9575i	−0.978006	+	0.614206i
$676$		0			0
$677$	−5.67582	−	6.76418i	−0.218139	−	0.259968i	0.645866	−	0.763451i	$-0.276496\pi$
$677$	−5.67582	−	6.76418i	−0.218139	−	0.259968i	−0.864006	+	0.503482i	$0.832052\pi$
$678$		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	0.852622	+	0.522528i	$0.175011\pi$
$683$	22.9677	+	39.7812i	0.878834	+	1.52218i	0.0262119	+	0.999656i	$0.491656\pi$
$684$		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	$-0.864798\pi$
$691$	1.35958	−	3.73542i	0.0517209	−	0.142102i	0.962863	+	0.269990i	$0.0870204\pi$
$692$		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	$-0.878040\pi$
$701$		−	19.7960i		−	0.747684i	0.927492	−	0.373842i	$-0.121960\pi$
$702$		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	0.995360	−	0.0962195i	$-0.0306751\pi$
$709$	0.722087	+	4.09516i	0.0271185	+	0.153797i	−0.968242	+	0.250016i	$0.919564\pi$
$710$		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	$-0.843153\pi$
$719$	−0.827080	+	1.43254i	−0.0308449	+	0.0534249i	0.850191	+	0.526475i	$0.176486\pi$
$720$		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	$-0.117454\pi$
$727$	11.2040	+	13.3525i	0.415535	+	0.495215i	−0.517156	+	0.855891i	$0.673009\pi$
$728$		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	0.921665	+	0.387987i	$0.126830\pi$
$733$	−2.08784	+	11.8408i	−0.0771163	+	0.437348i	−0.998781	+	0.0493610i	$0.984282\pi$
$734$		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	$-0.472129\pi$
$739$	−19.8865	−	11.4815i	−0.731538	−	0.422354i	−0.818984	+	0.573816i	$0.805463\pi$
$740$		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	$-0.154638\pi$
$743$	15.7558	+	13.2207i	0.578023	+	0.485019i	−0.306274	+	0.951943i	$0.599082\pi$
$744$		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	−0.921570	−	0.388213i	$-0.873093\pi$
$751$	−12.7470	−	35.0221i	−0.465145	−	1.27797i	0.456425	−	0.889762i	$-0.349130\pi$
$752$		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	−0.993190	−	0.116510i	$-0.962829\pi$
$761$	−8.47595	−	23.2875i	−0.307253	−	0.844171i	0.685936	−	0.727661i	$-0.259393\pi$
$762$		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	0.887091	−	0.461595i	$-0.152723\pi$
$769$	16.2655	+	13.6484i	0.586550	+	0.492174i	−0.300541	+	0.953769i	$0.597167\pi$
$770$		0			0
$771$	−10.7566	−	2.40901i	−0.387390	−	0.0867584i
$772$		0			0
$773$	12.2938	+	7.09780i	0.442176	+	0.255290i	0.704520	−	0.709684i	$-0.251162\pi$
$773$	12.2938	+	7.09780i	0.442176	+	0.255290i	−0.262344	+	0.964974i	$0.584496\pi$
$774$		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	$-0.608942\pi$
$787$	−27.3006	−	4.81383i	−0.973160	−	0.171594i	−0.637552	+	0.770407i	$0.720053\pi$
$788$		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	−0.480345	−	0.877080i	$-0.659488\pi$
$797$	13.1789	−	15.7060i	0.466821	−	0.556336i	0.947166	+	0.320744i	$0.103933\pi$
$798$		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	$0.0630628\pi$
$809$			11.1965i			0.393648i	−0.980439	+	0.196824i	$0.936937\pi$
$810$		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	−0.480455	−	0.877020i	$-0.659528\pi$
$821$	12.9321	−	35.5306i	0.451332	−	1.24003i	0.931787	−	0.363006i	$-0.118249\pi$
$822$		0			0
$823$	−1.68950	+	2.01347i	−0.0588923	+	0.0701851i	−0.794686	−	0.607020i	$-0.792365\pi$
$823$	−1.68950	+	2.01347i	−0.0588923	+	0.0701851i	0.735794	+	0.677205i	$0.236809\pi$
$824$		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	$-0.847946\pi$
$827$	−1.31968	+	2.28576i	−0.0458899	+	0.0794836i	0.842168	+	0.539215i	$0.181279\pi$
$828$		0			0
$829$	5.69261	+	9.85989i	0.197713	+	0.342448i	0.947786	−	0.318906i	$-0.103315\pi$
$829$	5.69261	+	9.85989i	0.197713	+	0.342448i	−0.750074	+	0.661354i	$0.769982\pi$
$830$		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	$-0.825482\pi$
$839$	−14.1450	+	11.8690i	−0.488338	+	0.409765i	0.365092	+	0.930971i	$0.381038\pi$
$840$		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	0.124268	−	0.992249i	$-0.460342\pi$
$853$	−12.2182	−	4.44706i	−0.418343	−	0.152264i	−0.542611	+	0.839984i	$0.682564\pi$
$854$		0			0
$855$	61.7705	−	16.2663i	2.11251	−	0.556297i
$856$		0			0
$857$	44.4317	−	7.83451i	1.51776	−	0.267622i	0.648207	−	0.761464i	$-0.275519\pi$
$857$	44.4317	−	7.83451i	1.51776	−	0.267622i	0.869551	+	0.493843i	$0.164408\pi$
$858$		0			0
$859$	1.21631	+	3.34179i	0.0415001	+	0.114021i	0.958712	−	0.284380i	$-0.0917877\pi$
$859$	1.21631	+	3.34179i	0.0415001	+	0.114021i	−0.917212	+	0.398400i	$0.869565\pi$
$860$		0			0
$861$	33.4541	+	1.53287i	1.14011	+	0.0522402i
$862$		0			0
$863$	−25.1350			−0.855605			−0.427802	−	0.903872i	$-0.640712\pi$
$863$	−25.1350			−0.855605			−0.427802	+	0.903872i	$0.640712\pi$
$864$		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	0.757774	−	0.652517i	$-0.226287\pi$
$877$	7.30747	+	6.13169i	0.246756	+	0.207053i	−0.511018	+	0.859570i	$0.670732\pi$
$878$		0			0
$879$	6.98784	+	22.3303i	0.235694	+	0.753181i
$880$		0			0
$881$	23.3602	+	13.4870i	0.787027	+	0.454390i	0.838915	−	0.544263i	$-0.183191\pi$
$881$	23.3602	+	13.4870i	0.787027	+	0.454390i	−0.0518881	+	0.998653i	$0.516524\pi$
$882$		0			0
$883$	−3.96969	+	2.29190i	−0.133591	+	0.0771286i	−0.565306	−	0.824881i	$-0.691242\pi$
$883$	−3.96969	+	2.29190i	−0.133591	+	0.0771286i	0.431715	+	0.902010i	$0.357909\pi$
$884$		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	$-0.960362\pi$
$887$	−0.517007	+	2.93209i	−0.0173594	+	0.0984501i	0.974897	+	0.222656i	$0.0714727\pi$
$888$		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	$-0.903411\pi$
$907$	−0.939557	+	2.58141i	−0.0311975	+	0.0857144i	0.923116	+	0.384521i	$0.125634\pi$
$908$		0			0
$909$	−8.34459	+	17.6955i	−0.276773	+	0.586923i
$910$		0			0
$911$	−7.45754	−	42.2938i	−0.247079	−	1.40126i	−0.815613	−	0.578597i	$-0.803600\pi$
$911$	−7.45754	−	42.2938i	−0.247079	−	1.40126i	0.568534	−	0.822660i	$-0.307511\pi$
$912$		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	0.540281	+	0.841485i	$0.318318\pi$
$929$	−12.6336	+	34.7105i	−0.414494	+	1.13881i	−0.954775	+	0.297329i	$0.903904\pi$
$930$		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	0.548294	−	0.836285i	$-0.315277\pi$
$937$	−13.7777	−	23.8636i	−0.450097	−	0.779591i	−0.998392	+	0.0566942i	$0.981944\pi$
$938$		0			0
$939$	1.82236	+	14.0766i	0.0594706	+	0.459371i
$940$		0			0
$941$	−51.2999	−	9.04556i	−1.67233	−	0.294877i	−0.744428	−	0.667703i	$-0.767278\pi$
$941$	−51.2999	−	9.04556i	−1.67233	−	0.294877i	−0.927901	+	0.372826i	$0.878389\pi$
$942$		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	−0.341427	+	0.939908i	$0.610910\pi$
$947$	−40.8161	+	34.2488i	−1.32634	+	1.11294i	−0.984917	+	0.173027i	$0.944645\pi$
$948$		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	−0.121768	−	0.992559i	$-0.538856\pi$
$953$	20.8973	−	12.0650i	0.676929	−	0.390825i	0.798697	+	0.601733i	$0.205523\pi$
$954$		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	$-0.0590851\pi$
$967$	3.46122	+	9.50964i	0.111305	+	0.305809i	−0.871516	+	0.490367i	$0.836863\pi$
$968$		0			0
$969$	−31.8002	−	61.4103i	−1.02157	−	1.97278i
$970$		0			0
$971$	−16.3688			−0.525299			−0.262649	−	0.964891i	$-0.584596\pi$
$971$	−16.3688			−0.525299			−0.262649	+	0.964891i	$0.584596\pi$
$972$		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	0.933058	+	0.359725i	$0.117129\pi$
$977$	14.0507	+	38.6039i	0.449521	+	1.23505i	−0.483538	+	0.875324i	$0.660648\pi$
$978$		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	$-0.347796\pi$
$983$	7.58582	+	2.76101i	0.241950	+	0.0880626i	−0.218199	+	0.975904i	$0.570018\pi$
$984$		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	$-0.677228\pi$
$991$	−1.80881	+	1.04432i	−0.0574589	+	0.0331739i	0.470995	+	0.882136i	$0.343895\pi$
$992$		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	−0.220343	−	0.975422i	$-0.570718\pi$
$997$	22.1658	−	18.5993i	0.701998	−	0.589046i	0.922341	+	0.386376i	$0.126273\pi$
$998$		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.b.383.3	yes	36
4.3	odd	2		432.2.be.c.383.4	yes	36
27.11	odd	18		432.2.be.c.335.4	yes	36
108.11	even	18	inner	432.2.be.b.335.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.b.335.3	✓	36	108.11	even	18	inner
432.2.be.b.383.3	yes	36	1.1	even	1	trivial
432.2.be.c.335.4	yes	36	27.11	odd	18
432.2.be.c.383.4	yes	36	4.3	odd	2

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

\(f(q)\)	\(=\)	\(q+(-0.796460 - 1.53807i) q^{3} +(1.12266 + 3.08448i) q^{5} +(-3.05005 + 0.537806i) q^{7} +(-1.73130 + 2.45002i) q^{9} +O(q^{10})\)	\(q+(-0.796460 - 1.53807i) q^{3} +(1.12266 + 3.08448i) q^{5} +(-3.05005 + 0.537806i) q^{7} +(-1.73130 + 2.45002i) q^{9} +(-1.75059 - 0.637162i) q^{11} +(-3.44119 - 2.88750i) q^{13} +(3.84999 - 4.18339i) q^{15} +(-5.33058 - 3.07761i) q^{17} +(-5.61763 + 3.24334i) q^{19} +(3.25643 + 4.26285i) q^{21} +(-0.0995927 + 0.564818i) q^{23} +(-4.42344 + 3.71171i) q^{25} +(5.14721 + 0.711524i) q^{27} +(5.05288 + 6.02179i) q^{29} +(6.55127 + 1.15517i) q^{31} +(0.414275 + 3.20000i) q^{33} +(-5.08302 - 8.80406i) q^{35} +(-2.51317 + 4.35293i) q^{37} +(-1.70040 + 7.59256i) q^{39} +(4.01288 - 4.78237i) q^{41} +(-3.06074 + 8.40931i) q^{43} +(-9.50070 - 2.58964i) q^{45} +(-1.29158 - 7.32493i) q^{47} +(2.43573 - 0.886535i) q^{49} +(-0.487984 + 10.6500i) q^{51} -4.40691i q^{53} -6.11498i q^{55} +(9.46269 + 6.05710i) q^{57} +(-1.19847 + 0.436209i) q^{59} +(0.757644 + 4.29681i) q^{61} +(3.96293 - 8.40379i) q^{63} +(5.04316 - 13.8560i) q^{65} +(-3.35363 + 3.99670i) q^{67} +(0.948051 - 0.296675i) q^{69} +(2.77247 - 4.80206i) q^{71} +(-5.12137 - 8.87047i) q^{73} +(9.23195 + 3.84733i) q^{75} +(5.68206 + 1.00190i) q^{77} +(-0.530104 - 0.631754i) q^{79} +(-3.00517 - 8.48345i) q^{81} +(-5.90712 + 4.95666i) q^{83} +(3.50841 - 19.8972i) q^{85} +(5.23750 - 12.5678i) q^{87} +(-2.31943 + 1.33912i) q^{89} +(12.0487 + 6.95633i) q^{91} +(-3.44110 - 10.9963i) q^{93} +(-16.3107 - 13.6863i) q^{95} +(9.55043 + 3.47607i) q^{97} +(4.59186 - 3.18585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 36 * q + 3 * q^5 + 6 * q^9	\( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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