LMFDB - Embedded newform 360.2.bs.a.113.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(113,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("360.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bs (of order $12$, degree $4$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			113.18
Character	$\chi$	$=$	360.113
Dual form			360.2.bs.a.137.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73052 + 0.0727431i) q^{3} +(0.484586 + 2.18293i) q^{5} +(-1.02200 - 0.273845i) q^{7} +(2.98942 + 0.251767i) q^{9} +O(q^{10})$	\(q+(1.73052 + 0.0727431i) q^{3} +(0.484586 + 2.18293i) q^{5} +(-1.02200 - 0.273845i) q^{7} +(2.98942 + 0.251767i) q^{9} +(3.03367 - 1.75149i) q^{11} +(-2.02133 + 0.541614i) q^{13} +(0.679794 + 3.81286i) q^{15} +(2.34785 + 2.34785i) q^{17} +5.86265i q^{19} +(-1.74868 - 0.548238i) q^{21} +(-1.43580 - 5.35848i) q^{23} +(-4.53035 + 2.11563i) q^{25} +(5.15494 + 0.653149i) q^{27} +(-2.81857 - 4.88191i) q^{29} +(2.56785 - 4.44765i) q^{31} +(5.37724 - 2.81031i) q^{33} +(0.102535 - 2.36366i) q^{35} +(-4.29278 + 4.29278i) q^{37} +(-3.53736 + 0.790237i) q^{39} +(-1.24185 - 0.716981i) q^{41} +(0.884185 - 3.29982i) q^{43} +(0.899040 + 6.64769i) q^{45} +(2.17240 - 8.10751i) q^{47} +(-5.09268 - 2.94026i) q^{49} +(3.89221 + 4.23379i) q^{51} +(-5.20169 + 5.20169i) q^{53} +(5.29345 + 5.77353i) q^{55} +(-0.426468 + 10.1455i) q^{57} +(6.57205 - 11.3831i) q^{59} +(3.79591 + 6.57471i) q^{61} +(-2.98625 - 1.07594i) q^{63} +(-2.16181 - 4.14996i) q^{65} +(-0.881854 - 3.29112i) q^{67} +(-2.09489 - 9.37741i) q^{69} +4.66179i q^{71} +(-8.77780 - 8.77780i) q^{73} +(-7.99378 + 3.33160i) q^{75} +(-3.58005 + 0.959272i) q^{77} +(-8.87983 + 5.12677i) q^{79} +(8.87323 + 1.50527i) q^{81} +(-15.1755 - 4.06625i) q^{83} +(-3.98744 + 6.26291i) q^{85} +(-4.52248 - 8.65330i) q^{87} +10.3392 q^{89} +2.21412 q^{91} +(4.76727 - 7.50997i) q^{93} +(-12.7978 + 2.84096i) q^{95} +(-14.6693 - 3.93063i) q^{97} +(9.50986 - 4.47215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) $ 72 * q + 12 * q^15 + 16 * q^21 + 24 * q^23 - 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 - 36 * q^47 + 24 * q^51 - 40 * q^57 + 12 * q^61 - 44 * q^63 - 72 * q^65 - 36 * q^75 - 48 * q^77 - 20 * q^81 - 60 * q^83 + 24 * q^85 - 40 * q^87 - 84 * q^93 - 60 * q^95 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	1.73052	+	0.0727431i	0.999118	+	0.0419983i
$3$	1.73052	+	0.0727431i	0.999118	+	0.0419983i
$4$		0			0
$5$	0.484586	+	2.18293i	0.216713	+	0.976235i
$5$	0.484586	+	2.18293i	0.216713	+	0.976235i
$6$		0			0
$7$	−1.02200	−	0.273845i	−0.386281	−	0.103504i	0.0604520	−	0.998171i	$-0.480746\pi$
$7$	−1.02200	−	0.273845i	−0.386281	−	0.103504i	−0.446733	+	0.894668i	$0.647412\pi$
$8$		0			0
$9$	2.98942	+	0.251767i	0.996472	+	0.0839224i
$10$		0			0
$11$	3.03367	−	1.75149i	0.914685	−	0.528094i	0.0327495	−	0.999464i	$-0.489574\pi$
$11$	3.03367	−	1.75149i	0.914685	−	0.528094i	0.881936	+	0.471370i	$0.156240\pi$
$12$		0			0
$13$	−2.02133	+	0.541614i	−0.560616	+	0.150217i	−0.527989	−	0.849251i	$-0.677054\pi$
$13$	−2.02133	+	0.541614i	−0.560616	+	0.150217i	−0.0326268	+	0.999468i	$0.510387\pi$
$14$		0			0
$15$	0.679794	+	3.81286i	0.175522	+	0.984475i
$16$		0			0
$17$	2.34785	+	2.34785i	0.569436	+	0.569436i	0.931970	−	0.362534i	$-0.118088\pi$
$17$	2.34785	+	2.34785i	0.569436	+	0.569436i	−0.362534	+	0.931970i	$0.618088\pi$
$18$		0			0
$19$			5.86265i			1.34499i	0.740104	+	0.672493i	$0.234776\pi$
$19$			5.86265i			1.34499i	−0.740104	+	0.672493i	$0.765224\pi$
$20$		0			0
$21$	−1.74868	−	0.548238i	−0.381593	−	0.119635i
$22$		0			0
$23$	−1.43580	−	5.35848i	−0.299385	−	1.11732i	−0.937672	−	0.347522i	$-0.887023\pi$
$23$	−1.43580	−	5.35848i	−0.299385	−	1.11732i	0.638287	−	0.769798i	$-0.279643\pi$
$24$		0			0
$25$	−4.53035	+	2.11563i	−0.906071	+	0.423127i
$26$		0			0
$27$	5.15494	+	0.653149i	0.992068	+	0.125699i
$28$		0			0
$29$	−2.81857	−	4.88191i	−0.523396	−	0.906549i	−0.999629	−	0.0272297i	$-0.991331\pi$
$29$	−2.81857	−	4.88191i	−0.523396	−	0.906549i	0.476233	−	0.879319i	$-0.342002\pi$
$30$		0			0
$31$	2.56785	−	4.44765i	0.461200	−	0.798822i	−0.537821	−	0.843059i	$-0.680752\pi$
$31$	2.56785	−	4.44765i	0.461200	−	0.798822i	0.999021	+	0.0442369i	$0.0140856\pi$
$32$		0			0
$33$	5.37724	−	2.81031i	0.936057	−	0.489213i
$34$		0			0
$35$	0.102535	−	2.36366i	0.0173316	−	0.399531i
$36$		0			0
$37$	−4.29278	+	4.29278i	−0.705729	+	0.705729i	−0.965634	−	0.259905i	$-0.916309\pi$
$37$	−4.29278	+	4.29278i	−0.705729	+	0.705729i	0.259905	+	0.965634i	$0.416309\pi$
$38$		0			0
$39$	−3.53736	+	0.790237i	−0.566430	+	0.126539i
$40$		0			0
$41$	−1.24185	−	0.716981i	−0.193944	−	0.111974i	0.399884	−	0.916566i	$-0.369051\pi$
$41$	−1.24185	−	0.716981i	−0.193944	−	0.111974i	−0.593828	+	0.804592i	$0.702384\pi$
$42$		0			0
$43$	0.884185	−	3.29982i	0.134837	−	0.503219i	−0.865162	−	0.501493i	$-0.832784\pi$
$43$	0.884185	−	3.29982i	0.134837	−	0.503219i	0.999999	−	0.00172520i	$-0.000549147\pi$
$44$		0			0
$45$	0.899040	+	6.64769i	0.134021	+	0.990979i
$46$		0			0
$47$	2.17240	−	8.10751i	0.316877	−	1.18260i	−0.605352	−	0.795958i	$-0.706968\pi$
$47$	2.17240	−	8.10751i	0.316877	−	1.18260i	0.922229	−	0.386644i	$-0.126366\pi$
$48$		0			0
$49$	−5.09268	−	2.94026i	−0.727526	−	0.420037i
$50$		0			0
$51$	3.89221	+	4.23379i	0.545018	+	0.592849i
$52$		0			0
$53$	−5.20169	+	5.20169i	−0.714507	+	0.714507i	−0.967475	−	0.252968i	$-0.918593\pi$
$53$	−5.20169	+	5.20169i	−0.714507	+	0.714507i	0.252968	+	0.967475i	$0.418593\pi$
$54$		0			0
$55$	5.29345	+	5.77353i	0.713768	+	0.778503i
$56$		0			0
$57$	−0.426468	+	10.1455i	−0.0564871	+	1.34380i
$58$		0			0
$59$	6.57205	−	11.3831i	0.855608	−	1.48196i	−0.0204713	−	0.999790i	$-0.506517\pi$
$59$	6.57205	−	11.3831i	0.855608	−	1.48196i	0.876080	−	0.482167i	$-0.160150\pi$
$60$		0			0
$61$	3.79591	+	6.57471i	0.486017	+	0.841806i	0.999871	−	0.0160720i	$-0.00511611\pi$
$61$	3.79591	+	6.57471i	0.486017	+	0.841806i	−0.513854	+	0.857878i	$0.671783\pi$
$62$		0			0
$63$	−2.98625	−	1.07594i	−0.376232	−	0.135556i
$64$		0			0
$65$	−2.16181	−	4.14996i	−0.268140	−	0.514739i
$66$		0			0
$67$	−0.881854	−	3.29112i	−0.107736	−	0.402075i	0.890906	−	0.454189i	$-0.150071\pi$
$67$	−0.881854	−	3.29112i	−0.107736	−	0.402075i	−0.998641	+	0.0521139i	$0.983404\pi$
$68$		0			0
$69$	−2.09489	−	9.37741i	−0.252195	−	1.12891i
$70$		0			0
$71$			4.66179i			0.553252i	0.960978	+	0.276626i	$0.0892164\pi$
$71$			4.66179i			0.553252i	−0.960978	+	0.276626i	$0.910784\pi$
$72$		0			0
$73$	−8.77780	−	8.77780i	−1.02736	−	1.02736i	−0.999615	−	0.0277492i	$-0.991166\pi$
$73$	−8.77780	−	8.77780i	−1.02736	−	1.02736i	−0.0277492	−	0.999615i	$-0.508834\pi$
$74$		0			0
$75$	−7.99378	+	3.33160i	−0.923042	+	0.384700i
$76$		0			0
$77$	−3.58005	+	0.959272i	−0.407985	+	0.109319i
$78$		0			0
$79$	−8.87983	+	5.12677i	−0.999059	+	0.576807i	−0.907970	−	0.419036i	$-0.862368\pi$
$79$	−8.87983	+	5.12677i	−0.999059	+	0.576807i	−0.0910891	+	0.995843i	$0.529035\pi$
$80$		0			0
$81$	8.87323	+	1.50527i	0.985914	+	0.167253i
$82$		0			0
$83$	−15.1755	−	4.06625i	−1.66572	−	0.446329i	−0.701770	−	0.712404i	$-0.747607\pi$
$83$	−15.1755	−	4.06625i	−1.66572	−	0.446329i	−0.963952	+	0.266075i	$0.914273\pi$
$84$		0			0
$85$	−3.98744	+	6.26291i	−0.432499	+	0.679308i
$86$		0			0
$87$	−4.52248	−	8.65330i	−0.484861	−	0.927731i
$88$		0			0
$89$	10.3392			1.09595			0.547977	−	0.836494i	$-0.315398\pi$
$89$	10.3392			1.09595			0.547977	+	0.836494i	$0.315398\pi$
$90$		0			0
$91$	2.21412			0.232103
$92$		0			0
$93$	4.76727	−	7.50997i	0.494342	−	0.778748i
$94$		0			0
$95$	−12.7978	+	2.84096i	−1.31302	+	0.291476i
$96$		0			0
$97$	−14.6693	−	3.93063i	−1.48944	−	0.399095i	−0.579894	−	0.814692i	$-0.696906\pi$
$97$	−14.6693	−	3.93063i	−1.48944	−	0.399095i	−0.909549	+	0.415597i	$0.863573\pi$
$98$		0			0
$99$	9.50986	−	4.47215i	0.955777	−	0.449468i
$100$		0			0
$101$	14.5015	−	8.37245i	1.44295	−	0.833090i	0.444909	−	0.895576i	$-0.353236\pi$
$101$	14.5015	−	8.37245i	1.44295	−	0.833090i	0.998046	+	0.0624854i	$0.0199027\pi$
$102$		0			0
$103$	−4.85603	+	1.30117i	−0.478478	+	0.128208i	−0.489994	−	0.871726i	$-0.663001\pi$
$103$	−4.85603	+	1.30117i	−0.478478	+	0.128208i	0.0115156	+	0.999934i	$0.496334\pi$
$104$		0			0
$105$	0.349380	−	4.08291i	0.0340960	−	0.398451i
$106$		0			0
$107$	9.14988	+	9.14988i	0.884552	+	0.884552i	0.993993	−	0.109441i	$-0.0349061\pi$
$107$	9.14988	+	9.14988i	0.884552	+	0.884552i	−0.109441	+	0.993993i	$0.534906\pi$
$108$		0			0
$109$		−	11.5964i		−	1.11073i	−0.831607	−	0.555365i	$-0.812579\pi$
$109$		−	11.5964i		−	1.11073i	0.831607	−	0.555365i	$-0.187421\pi$
$110$		0			0
$111$	−7.74103	+	7.11648i	−0.734746	+	0.675467i
$112$		0			0
$113$	3.58782	+	13.3899i	0.337513	+	1.25962i	0.901119	+	0.433573i	$0.142747\pi$
$113$	3.58782	+	13.3899i	0.337513	+	1.25962i	−0.563605	+	0.826044i	$0.690586\pi$
$114$		0			0
$115$	11.0014	−	5.73089i	1.02589	−	0.534408i
$116$		0			0
$117$	−6.17896	+	1.11020i	−0.571245	+	0.102638i
$118$		0			0
$119$	−1.75656	−	3.04245i	−0.161023	−	0.278901i
$120$		0			0
$121$	0.635424	−	1.10059i	0.0577658	−	0.100053i
$122$		0			0
$123$	−2.09689	−	1.33109i	−0.189070	−	0.120020i
$124$		0			0
$125$	−6.81362	−	8.86423i	−0.609429	−	0.792841i
$126$		0			0
$127$	−6.76760	+	6.76760i	−0.600528	+	0.600528i	−0.940453	−	0.339925i	$-0.889598\pi$
$127$	−6.76760	+	6.76760i	−0.600528	+	0.600528i	0.339925	+	0.940453i	$0.389598\pi$
$128$		0			0
$129$	1.77014	−	5.64610i	0.155852	−	0.497112i
$130$		0			0
$131$	−5.85971	−	3.38311i	−0.511965	−	0.295583i	0.221676	−	0.975120i	$-0.428847\pi$
$131$	−5.85971	−	3.38311i	−0.511965	−	0.295583i	−0.733641	+	0.679537i	$0.762181\pi$
$132$		0			0
$133$	1.60546	−	5.99165i	0.139211	−	0.519542i
$134$		0			0
$135$	1.07223	+	11.5694i	0.0922833	+	0.995733i
$136$		0			0
$137$	−1.16745	+	4.35697i	−0.0997417	+	0.372241i	−0.997696	−	0.0678483i	$-0.978387\pi$
$137$	−1.16745	+	4.35697i	−0.0997417	+	0.372241i	0.897954	+	0.440089i	$0.145053\pi$
$138$		0			0
$139$	10.6952	+	6.17490i	0.907159	+	0.523748i	0.879516	−	0.475870i	$-0.157867\pi$
$139$	10.6952	+	6.17490i	0.907159	+	0.523748i	0.0276427	+	0.999618i	$0.491200\pi$
$140$		0			0
$141$	4.34915	−	13.8722i	0.366265	−	1.16825i
$142$		0			0
$143$	−5.18341	+	5.18341i	−0.433459	+	0.433459i
$144$		0			0
$145$	9.29103	−	8.51845i	0.771578	−	0.707419i
$146$		0			0
$147$	−8.59911	−	5.45864i	−0.709243	−	0.450221i
$148$		0			0
$149$	−4.76198	+	8.24799i	−0.390116	+	0.675701i	−0.992465	−	0.122532i	$-0.960899\pi$
$149$	−4.76198	+	8.24799i	−0.390116	+	0.675701i	0.602348	+	0.798233i	$0.294232\pi$
$150$		0			0
$151$	4.67021	+	8.08905i	0.380057	+	0.658277i	0.991070	−	0.133343i	$-0.0425712\pi$
$151$	4.67021	+	8.08905i	0.380057	+	0.658277i	−0.611013	+	0.791620i	$0.709238\pi$
$152$		0			0
$153$	6.42758	+	7.60980i	0.519639	+	0.615216i
$154$		0			0
$155$	10.9533	+	3.45017i	0.879787	+	0.277124i
$156$		0			0
$157$	2.48856	+	9.28742i	0.198608	+	0.741217i	0.991303	+	0.131598i	$0.0420108\pi$
$157$	2.48856	+	9.28742i	0.198608	+	0.741217i	−0.792695	+	0.609619i	$0.791323\pi$
$158$		0			0
$159$	−9.38003	+	8.62325i	−0.743885	+	0.683868i
$160$		0			0
$161$			5.86956i			0.462586i
$162$		0			0
$163$	−2.93054	−	2.93054i	−0.229538	−	0.229538i	0.582962	−	0.812499i	$-0.301894\pi$
$163$	−2.93054	−	2.93054i	−0.229538	−	0.229538i	−0.812499	+	0.582962i	$0.801894\pi$
$164$		0			0
$165$	8.74044	+	10.3763i	0.680443	+	0.807793i
$166$		0			0
$167$	−7.73934	+	2.07375i	−0.598888	+	0.160472i	−0.545512	−	0.838103i	$-0.683665\pi$
$167$	−7.73934	+	2.07375i	−0.598888	+	0.160472i	−0.0533758	+	0.998574i	$0.516998\pi$
$168$		0			0
$169$	−7.46590	+	4.31044i	−0.574300	+	0.331572i
$170$		0			0
$171$	−1.47602	+	17.5259i	−0.112874	+	1.34024i
$172$		0			0
$173$	13.4780	+	3.61143i	1.02472	+	0.274572i	0.731766	−	0.681556i	$-0.238696\pi$
$173$	13.4780	+	3.61143i	1.02472	+	0.274572i	0.292950	+	0.956128i	$0.405363\pi$
$174$		0			0
$175$	5.20939	−	0.921569i	0.393793	−	0.0696641i
$176$		0			0
$177$	12.2011	−	19.2207i	0.917093	−	1.44472i
$178$		0			0
$179$	11.3858			0.851018			0.425509	−	0.904954i	$-0.360095\pi$
$179$	11.3858			0.851018			0.425509	+	0.904954i	$0.360095\pi$
$180$		0			0
$181$	21.2179			1.57711			0.788556	−	0.614963i	$-0.210829\pi$
$181$	21.2179			1.57711			0.788556	+	0.614963i	$0.210829\pi$
$182$		0			0
$183$	6.09065	+	11.6538i	0.450233	+	0.861475i
$184$		0			0
$185$	−11.4511	−	7.29061i	−0.841898	−	0.536016i
$186$		0			0
$187$	11.2348	+	3.01036i	0.821570	+	0.220139i
$188$		0			0
$189$	−5.08950	−	2.07917i	−0.370207	−	0.151238i
$190$		0			0
$191$	7.13978	−	4.12215i	0.516616	−	0.298269i	−0.218933	−	0.975740i	$-0.570258\pi$
$191$	7.13978	−	4.12215i	0.516616	−	0.298269i	0.735549	+	0.677471i	$0.236924\pi$
$192$		0			0
$193$	17.1032	−	4.58279i	1.23112	−	0.329877i	0.416103	−	0.909318i	$-0.363396\pi$
$193$	17.1032	−	4.58279i	1.23112	−	0.329877i	0.815014	+	0.579441i	$0.196729\pi$
$194$		0			0
$195$	−3.43919	−	7.33886i	−0.246285	−	0.525547i
$196$		0			0
$197$	11.1977	+	11.1977i	0.797802	+	0.797802i	0.982749	−	0.184946i	$-0.0592111\pi$
$197$	11.1977	+	11.1977i	0.797802	+	0.797802i	−0.184946	+	0.982749i	$0.559211\pi$
$198$		0			0
$199$			3.35600i			0.237901i	0.992900	+	0.118950i	$0.0379529\pi$
$199$			3.35600i			0.237901i	−0.992900	+	0.118950i	$0.962047\pi$
$200$		0			0
$201$	−1.28666	−	5.75951i	−0.0907541	−	0.406245i
$202$		0			0
$203$	1.54370	+	5.76118i	0.108347	+	0.404356i
$204$		0			0
$205$	0.963336	−	3.05830i	0.0672823	−	0.213601i
$206$		0			0
$207$	−2.94312	−	16.3802i	−0.204561	−	1.13850i
$208$		0			0
$209$	10.2684	+	17.7853i	0.710278	+	1.23024i
$210$		0			0
$211$	0.857665	−	1.48552i	0.0590441	−	0.102267i	−0.834992	−	0.550261i	$-0.814528\pi$
$211$	0.857665	−	1.48552i	0.0590441	−	0.102267i	0.894037	+	0.447994i	$0.147861\pi$
$212$		0			0
$213$	−0.339113	+	8.06733i	−0.0232356	+	0.552764i
$214$		0			0
$215$	7.63174	+	0.331064i	0.520481	+	0.0225784i
$216$		0			0
$217$	−3.84232	+	3.84232i	−0.260834	+	0.260834i
$218$		0			0
$219$	−14.5517	−	15.8287i	−0.983310	−	1.06961i
$220$		0			0
$221$	−6.01740	−	3.47415i	−0.404774	−	0.233696i
$222$		0			0
$223$	5.74149	−	21.4275i	0.384479	−	1.43489i	−0.454508	−	0.890743i	$-0.650185\pi$
$223$	5.74149	−	21.4275i	0.384479	−	1.43489i	0.838987	−	0.544152i	$-0.183148\pi$
$224$		0			0
$225$	−14.0758	+	5.18391i	−0.938384	+	0.345594i
$226$		0			0
$227$	−1.91144	+	7.13360i	−0.126867	+	0.473474i	−0.999899	−	0.0141884i	$-0.995484\pi$
$227$	−1.91144	+	7.13360i	−0.126867	+	0.473474i	0.873032	+	0.487662i	$0.162150\pi$
$228$		0			0
$229$	24.0687	+	13.8961i	1.59051	+	0.918279i	0.993220	+	0.116252i	$0.0370879\pi$
$229$	24.0687	+	13.8961i	1.59051	+	0.918279i	0.597287	+	0.802028i	$0.296245\pi$
$230$		0			0
$231$	−6.26514	+	1.39962i	−0.412216	+	0.0920881i
$232$		0			0
$233$	−6.28622	+	6.28622i	−0.411824	+	0.411824i	−0.882373	−	0.470550i	$-0.844056\pi$
$233$	−6.28622	+	6.28622i	−0.411824	+	0.411824i	0.470550	+	0.882373i	$0.344056\pi$
$234$		0			0
$235$	18.7508	+	0.813409i	1.22317	+	0.0530610i
$236$		0			0
$237$	−15.7397	+	8.22605i	−1.02240	+	0.534339i
$238$		0			0
$239$	−5.12635	+	8.87910i	−0.331596	+	0.574341i	−0.982825	−	0.184540i	$-0.940920\pi$
$239$	−5.12635	+	8.87910i	−0.331596	+	0.574341i	0.651229	+	0.758881i	$0.274254\pi$
$240$		0			0
$241$	4.65400	+	8.06097i	0.299791	+	0.519253i	0.976088	−	0.217376i	$-0.0697498\pi$
$241$	4.65400	+	8.06097i	0.299791	+	0.519253i	−0.676297	+	0.736629i	$0.736416\pi$
$242$		0			0
$243$	15.2458	+	3.25038i	0.978020	+	0.208512i
$244$		0			0
$245$	3.95054	−	12.5418i	0.252390	−	0.801264i
$246$		0			0
$247$	−3.17530	−	11.8504i	−0.202039	−	0.754021i
$248$		0			0
$249$	−25.9657	−	8.14065i	−1.64551	−	0.515893i
$250$		0			0
$251$		−	14.5314i		−	0.917213i	−0.888639	−	0.458607i	$-0.848349\pi$
$251$		−	14.5314i		−	0.917213i	0.888639	−	0.458607i	$-0.151651\pi$
$252$		0			0
$253$	−13.7411	−	13.7411i	−0.863893	−	0.863893i
$254$		0			0
$255$	−7.35595	+	10.5480i	−0.460647	+	0.660544i
$256$		0			0
$257$	−7.01406	+	1.87941i	−0.437525	+	0.117234i	−0.470856	−	0.882210i	$-0.656055\pi$
$257$	−7.01406	+	1.87941i	−0.437525	+	0.117234i	0.0333314	+	0.999444i	$0.489388\pi$
$258$		0			0
$259$	5.56279	−	3.21168i	0.345655	−	0.199564i
$260$		0			0
$261$	−7.19679	−	15.3037i	−0.445470	−	0.947275i
$262$		0			0
$263$	−6.40762	−	1.71692i	−0.395111	−	0.105870i	0.0557925	−	0.998442i	$-0.482231\pi$
$263$	−6.40762	−	1.71692i	−0.395111	−	0.105870i	−0.450904	+	0.892573i	$0.648898\pi$
$264$		0			0
$265$	−13.8756	−	8.83425i	−0.852370	−	0.542684i
$266$		0			0
$267$	17.8922	+	0.752106i	1.09499	+	0.0460281i
$268$		0			0
$269$	6.93929			0.423096			0.211548	−	0.977368i	$-0.432149\pi$
$269$	6.93929			0.423096			0.211548	+	0.977368i	$0.432149\pi$
$270$		0			0
$271$	−29.3283			−1.78157			−0.890783	−	0.454429i	$-0.849843\pi$
$271$	−29.3283			−1.78157			−0.890783	+	0.454429i	$0.849843\pi$
$272$		0			0
$273$	3.83159	+	0.161062i	0.231898	+	0.00974793i
$274$		0			0
$275$	−10.0381	+	14.3530i	−0.605319	+	0.865518i
$276$		0			0
$277$	19.6330	+	5.26065i	1.17963	+	0.316082i	0.794781	−	0.606897i	$-0.207586\pi$
$277$	19.6330	+	5.26065i	1.17963	+	0.316082i	0.384852	+	0.922978i	$0.374252\pi$
$278$		0			0
$279$	8.79616	−	12.6494i	0.526612	−	0.757299i
$280$		0			0
$281$	−26.7865	+	15.4652i	−1.59795	+	0.922576i	−0.606067	+	0.795414i	$0.707254\pi$
$281$	−26.7865	+	15.4652i	−1.59795	+	0.922576i	−0.991882	+	0.127162i	$0.959413\pi$
$282$		0			0
$283$	−28.2345	+	7.56542i	−1.67837	+	0.449718i	−0.967348	−	0.253453i	$-0.918434\pi$
$283$	−28.2345	+	7.56542i	−1.67837	+	0.449718i	−0.711021	+	0.703171i	$0.751767\pi$
$284$		0			0
$285$	−22.3535	+	3.98540i	−1.32410	+	0.236075i
$286$		0			0
$287$	1.07283	+	1.07283i	0.0633271	+	0.0633271i
$288$		0			0
$289$		−	5.97525i		−	0.351485i
$290$		0			0
$291$	−25.0996	−	7.86913i	−1.47137	−	0.461297i
$292$		0			0
$293$	0.103790	+	0.387349i	0.00606346	+	0.0226292i	0.968891	−	0.247487i	$-0.0796047\pi$
$293$	0.103790	+	0.387349i	0.00606346	+	0.0226292i	−0.962828	+	0.270116i	$0.912938\pi$
$294$		0			0
$295$	28.0333	+	8.83021i	1.63216	+	0.514115i
$296$		0			0
$297$	16.7824	−	7.04738i	0.973811	−	0.408931i
$298$		0			0
$299$	5.80445	+	10.0536i	0.335680	+	0.581415i
$300$		0			0
$301$	−1.80728	+	3.13030i	−0.104170	+	0.180427i
$302$		0			0
$303$	25.7042	−	13.4338i	1.47667	−	0.771754i
$304$		0			0
$305$	−12.5127	+	11.4722i	−0.716474	+	0.656897i
$306$		0			0
$307$	0.0650929	−	0.0650929i	0.00371505	−	0.00371505i	−0.705247	−	0.708962i	$-0.749164\pi$
$307$	0.0650929	−	0.0650929i	0.00371505	−	0.00371505i	0.708962	+	0.705247i	$0.249164\pi$
$308$		0			0
$309$	−8.49811	+	1.89846i	−0.483441	+	0.108000i
$310$		0			0
$311$	−0.404598	−	0.233595i	−0.0229427	−	0.0132460i	0.488485	−	0.872572i	$-0.337550\pi$
$311$	−0.404598	−	0.233595i	−0.0229427	−	0.0132460i	−0.511427	+	0.859326i	$0.670883\pi$
$312$		0			0
$313$	5.41656	−	20.2149i	0.306162	−	1.14261i	−0.625779	−	0.780001i	$-0.715219\pi$
$313$	5.41656	−	20.2149i	0.306162	−	1.14261i	0.931941	−	0.362611i	$-0.118115\pi$
$314$		0			0
$315$	0.901613	−	7.04015i	0.0508001	−	0.396667i
$316$		0			0
$317$	3.78998	−	14.1444i	0.212867	−	0.794429i	−0.774040	−	0.633137i	$-0.781767\pi$
$317$	3.78998	−	14.1444i	0.212867	−	0.794429i	0.986907	−	0.161293i	$-0.0515663\pi$
$318$		0			0
$319$	−17.1012	−	9.87340i	−0.957485	−	0.552804i
$320$		0			0
$321$	15.1685	+	16.4997i	0.846622	+	0.920921i
$322$		0			0
$323$	−13.7646	+	13.7646i	−0.765883	+	0.765883i
$324$		0			0
$325$	8.01148	−	6.73010i	0.444397	−	0.373319i
$326$		0			0
$327$	0.843556	−	20.0678i	0.0466487	−	1.10975i
$328$		0			0
$329$	−4.44040	+	7.69099i	−0.244807	+	0.424018i
$330$		0			0
$331$	−11.7882	−	20.4178i	−0.647940	−	1.12227i	−0.983614	−	0.180287i	$-0.942297\pi$
$331$	−11.7882	−	20.4178i	−0.647940	−	1.12227i	0.335674	−	0.941978i	$-0.391036\pi$
$332$		0			0
$333$	−13.9137	+	11.7521i	−0.762466	+	0.644013i
$334$		0			0
$335$	6.75695	−	3.51986i	0.369172	−	0.192310i
$336$		0			0
$337$	−0.410471	−	1.53190i	−0.0223598	−	0.0834478i	0.953844	−	0.300301i	$-0.0970873\pi$
$337$	−0.410471	−	1.53190i	−0.0223598	−	0.0834478i	−0.976204	+	0.216854i	$0.930421\pi$
$338$		0			0
$339$	5.23477	+	23.4325i	0.284314	+	1.27268i
$340$		0			0
$341$		−	17.9903i		−	0.974228i
$342$		0			0
$343$	9.63666	+	9.63666i	0.520331	+	0.520331i
$344$		0			0
$345$	19.4551	−	9.11716i	1.04743	−	0.490852i
$346$		0			0
$347$	15.5464	−	4.16564i	0.834573	−	0.223623i	0.183865	−	0.982951i	$-0.441139\pi$
$347$	15.5464	−	4.16564i	0.834573	−	0.223623i	0.650708	+	0.759328i	$0.274472\pi$
$348$		0			0
$349$	−22.2777	+	12.8621i	−1.19250	+	0.688490i	−0.958873	−	0.283837i	$-0.908393\pi$
$349$	−22.2777	+	12.8621i	−1.19250	+	0.688490i	−0.233627	+	0.972326i	$0.575059\pi$
$350$		0			0
$351$	−10.7736	+	1.47176i	−0.575052	+	0.0785566i
$352$		0			0
$353$	13.0783	+	3.50432i	0.696087	+	0.186516i	0.589477	−	0.807785i	$-0.299334\pi$
$353$	13.0783	+	3.50432i	0.696087	+	0.186516i	0.106610	+	0.994301i	$0.466000\pi$
$354$		0			0
$355$	−10.1763	+	2.25904i	−0.540105	+	0.119897i
$356$		0			0
$357$	−2.81845	−	5.39280i	−0.149168	−	0.285417i
$358$		0			0
$359$	7.72953			0.407949			0.203975	−	0.978976i	$-0.434614\pi$
$359$	7.72953			0.407949			0.203975	+	0.978976i	$0.434614\pi$
$360$		0			0
$361$	−15.3707			−0.808985
$362$		0			0
$363$	1.17968	−	1.85837i	0.0619169	−	0.0975390i
$364$		0			0
$365$	14.9077	−	23.4149i	0.780305	−	1.22559i
$366$		0			0
$367$	12.9841	+	3.47907i	0.677764	+	0.181606i	0.581250	−	0.813725i	$-0.302564\pi$
$367$	12.9841	+	3.47907i	0.677764	+	0.181606i	0.0965141	+	0.995332i	$0.469231\pi$
$368$		0			0
$369$	−3.53189	−	2.45601i	−0.183863	−	0.127855i
$370$		0			0
$371$	6.74059	−	3.89168i	0.349954	−	0.202046i
$372$		0			0
$373$	−14.5120	+	3.88848i	−0.751403	+	0.201338i	−0.614140	−	0.789197i	$-0.710497\pi$
$373$	−14.5120	+	3.88848i	−0.751403	+	0.201338i	−0.137263	+	0.990535i	$0.543830\pi$
$374$		0			0
$375$	−11.1463	−	15.8354i	−0.575593	−	0.817736i
$376$		0			0
$377$	8.34138	+	8.34138i	0.429603	+	0.429603i
$378$		0			0
$379$			15.6332i			0.803025i	0.915854	+	0.401512i	$0.131515\pi$
$379$			15.6332i			0.803025i	−0.915854	+	0.401512i	$0.868485\pi$
$380$		0			0
$381$	−12.2038	+	11.2192i	−0.625219	+	0.574777i
$382$		0			0
$383$	4.33075	+	16.1626i	0.221291	+	0.825868i	0.983857	+	0.178958i	$0.0572726\pi$
$383$	4.33075	+	16.1626i	0.221291	+	0.825868i	−0.762566	+	0.646910i	$0.776061\pi$
$384$		0			0
$385$	−3.82886	−	7.35015i	−0.195137	−	0.374598i
$386$		0			0
$387$	3.47399	−	9.64194i	0.176593	−	0.490127i
$388$		0			0
$389$	−12.3166	−	21.3329i	−0.624475	−	1.08162i	−0.988642	−	0.150289i	$-0.951979\pi$
$389$	−12.3166	−	21.3329i	−0.624475	−	1.08162i	0.364167	−	0.931334i	$-0.381354\pi$
$390$		0			0
$391$	9.20984	−	15.9519i	0.465762	−	0.806723i
$392$		0			0
$393$	−9.89426	−	6.28079i	−0.499100	−	0.316824i
$394$		0			0
$395$	−15.4944	−	16.8997i	−0.779609	−	0.850315i
$396$		0			0
$397$	−6.17732	+	6.17732i	−0.310031	+	0.310031i	−0.844921	−	0.534891i	$-0.820353\pi$
$397$	−6.17732	+	6.17732i	−0.310031	+	0.310031i	0.534891	+	0.844921i	$0.320353\pi$
$398$		0			0
$399$	3.21413	−	10.2519i	0.160908	−	0.513237i
$400$		0			0
$401$	−23.9759	−	13.8425i	−1.19730	−	0.691262i	−0.237349	−	0.971425i	$-0.576278\pi$
$401$	−23.9759	−	13.8425i	−1.19730	−	0.691262i	−0.959953	+	0.280162i	$0.909612\pi$
$402$		0			0
$403$	−2.78157	+	10.3810i	−0.138560	+	0.517113i
$404$		0			0
$405$	1.01393	+	20.0991i	0.0503828	+	0.998730i
$406$		0			0
$407$	−5.50411	+	20.5416i	−0.272829	+	1.01821i
$408$		0			0
$409$	24.6405	+	14.2262i	1.21840	+	0.703441i	0.964575	−	0.263810i	$-0.0849793\pi$
$409$	24.6405	+	14.2262i	1.21840	+	0.703441i	0.253821	+	0.967251i	$0.418313\pi$
$410$		0			0
$411$	−2.33723	+	7.45491i	−0.115287	+	0.367724i
$412$		0			0
$413$	−9.83386	+	9.83386i	−0.483893	+	0.483893i
$414$		0			0
$415$	1.52252	−	35.0974i	0.0747376	−	1.72286i
$416$		0			0
$417$	18.0592	+	11.4638i	0.884362	+	0.561385i
$418$		0			0
$419$	4.56092	−	7.89974i	0.222815	−	0.385928i	−0.732846	−	0.680394i	$-0.761809\pi$
$419$	4.56092	−	7.89974i	0.222815	−	0.385928i	0.955662	+	0.294466i	$0.0951419\pi$
$420$		0			0
$421$	16.0489	+	27.7976i	0.782177	+	1.35477i	0.930671	+	0.365856i	$0.119224\pi$
$421$	16.0489	+	27.7976i	0.782177	+	1.35477i	−0.148495	+	0.988913i	$0.547443\pi$
$422$		0			0
$423$	8.53542	−	23.6898i	0.415006	−	1.15184i
$424$		0			0
$425$	−15.6037	−	5.66939i	−0.756893	−	0.275006i
$426$		0			0
$427$	−2.07898	−	7.75886i	−0.100609	−	0.375478i
$428$		0			0
$429$	−9.34707	+	8.59296i	−0.451281	+	0.414872i
$430$		0			0
$431$			10.1750i			0.490115i	0.969509	+	0.245057i	$0.0788068\pi$
$431$			10.1750i			0.490115i	−0.969509	+	0.245057i	$0.921193\pi$
$432$		0			0
$433$	13.3799	+	13.3799i	0.642996	+	0.642996i	0.951291	−	0.308295i	$-0.0997584\pi$
$433$	13.3799	+	13.3799i	0.642996	+	0.642996i	−0.308295	+	0.951291i	$0.599758\pi$
$434$		0			0
$435$	16.6980	−	14.0655i	0.800607	−	0.674390i
$436$		0			0
$437$	31.4149	−	8.41760i	1.50278	−	0.402668i
$438$		0			0
$439$	−24.6956	+	14.2580i	−1.17866	+	0.680499i	−0.955704	−	0.294330i	$-0.904904\pi$
$439$	−24.6956	+	14.2580i	−1.17866	+	0.680499i	−0.222955	+	0.974829i	$0.571570\pi$
$440$		0			0
$441$	−14.4839	−	10.0718i	−0.689709	−	0.479611i
$442$		0			0
$443$	−3.75037	−	1.00491i	−0.178185	−	0.0477446i	0.168623	−	0.985681i	$-0.446068\pi$
$443$	−3.75037	−	1.00491i	−0.178185	−	0.0477446i	−0.346808	+	0.937936i	$0.612735\pi$
$444$		0			0
$445$	5.01023	+	22.5697i	0.237508	+	1.06991i
$446$		0			0
$447$	−8.84069	+	13.9269i	−0.418150	+	0.658721i
$448$		0			0
$449$	21.0261			0.992281			0.496140	−	0.868242i	$-0.334750\pi$
$449$	21.0261			0.992281			0.496140	+	0.868242i	$0.334750\pi$
$450$		0			0
$451$	−5.02313			−0.236530
$452$		0			0
$453$	7.49349	+	14.3380i	0.352075	+	0.673658i
$454$		0			0
$455$	1.07293	+	4.83327i	0.0502999	+	0.226587i
$456$		0			0
$457$	−38.6217	−	10.3487i	−1.80665	−	0.484090i	−0.811664	−	0.584125i	$-0.801438\pi$
$457$	−38.6217	−	10.3487i	−1.80665	−	0.484090i	−0.994984	+	0.100035i	$0.968105\pi$
$458$		0			0
$459$	10.5695	+	13.6365i	0.493342	+	0.636497i
$460$		0			0
$461$	−31.5555	+	18.2186i	−1.46968	+	0.848523i	−0.999422	−	0.0340040i	$-0.989174\pi$
$461$	−31.5555	+	18.2186i	−1.46968	+	0.848523i	−0.470263	+	0.882527i	$0.655841\pi$
$462$		0			0
$463$	18.8704	−	5.05632i	0.876984	−	0.234987i	0.207878	−	0.978155i	$-0.433344\pi$
$463$	18.8704	−	5.05632i	0.876984	−	0.234987i	0.669105	+	0.743168i	$0.266677\pi$
$464$		0			0
$465$	18.7039	+	6.76737i	0.867372	+	0.313829i
$466$		0			0
$467$	−12.2353	−	12.2353i	−0.566183	−	0.566183i	0.364874	−	0.931057i	$-0.381112\pi$
$467$	−12.2353	−	12.2353i	−0.566183	−	0.566183i	−0.931057	+	0.364874i	$0.881112\pi$
$468$		0			0
$469$			3.60503i			0.166465i
$470$		0			0
$471$	3.63091	+	16.2531i	0.167303	+	0.748904i
$472$		0			0
$473$	−3.09728	−	11.5592i	−0.142413	−	0.531493i
$474$		0			0
$475$	−12.4032	−	26.5599i	−0.569099	−	1.21865i
$476$		0			0
$477$	−16.8596	+	14.2404i	−0.771949	+	0.652023i
$478$		0			0
$479$	−5.47597	−	9.48465i	−0.250203	−	0.433365i	0.713378	−	0.700779i	$-0.247164\pi$
$479$	−5.47597	−	9.48465i	−0.250203	−	0.433365i	−0.963582	+	0.267414i	$0.913831\pi$
$480$		0			0
$481$	6.35210	−	11.0022i	0.289631	−	0.501655i
$482$		0			0
$483$	−0.426971	+	10.1574i	−0.0194278	+	0.462178i
$484$		0			0
$485$	1.47174	−	33.9268i	0.0668283	−	1.54054i
$486$		0			0
$487$	−7.74120	+	7.74120i	−0.350787	+	0.350787i	−0.860402	−	0.509615i	$-0.829788\pi$
$487$	−7.74120	+	7.74120i	−0.350787	+	0.350787i	0.509615	+	0.860402i	$0.329788\pi$
$488$		0			0
$489$	−4.85819	−	5.28454i	−0.219695	−	0.238975i
$490$		0			0
$491$	10.3601	+	5.98141i	0.467545	+	0.269937i	0.715212	−	0.698908i	$-0.246330\pi$
$491$	10.3601	+	5.98141i	0.467545	+	0.269937i	−0.247666	+	0.968845i	$0.579664\pi$
$492$		0			0
$493$	4.84440	−	18.0796i	0.218181	−	0.814262i
$494$		0			0
$495$	14.3707	+	18.5922i	0.645916	+	0.835658i
$496$		0			0
$497$	1.27661	−	4.76436i	0.0572636	−	0.213711i
$498$		0			0
$499$	−6.46929	−	3.73505i	−0.289605	−	0.167204i	0.348158	−	0.937436i	$-0.386807\pi$
$499$	−6.46929	−	3.73505i	−0.289605	−	0.167204i	−0.637764	+	0.770232i	$0.720140\pi$
$500$		0			0
$501$	−13.5439	+	3.02569i	−0.605099	+	0.135178i
$502$		0			0
$503$	14.0162	−	14.0162i	0.624953	−	0.624953i	−0.321841	−	0.946794i	$-0.604302\pi$
$503$	14.0162	−	14.0162i	0.624953	−	0.624953i	0.946794	+	0.321841i	$0.104302\pi$
$504$		0			0
$505$	25.3037	+	27.5986i	1.12600	+	1.22812i
$506$		0			0
$507$	−13.2335	+	6.91622i	−0.587719	+	0.307160i
$508$		0			0
$509$	5.03740	−	8.72503i	0.223279	−	0.386730i	−0.732523	−	0.680742i	$-0.761657\pi$
$509$	5.03740	−	8.72503i	0.223279	−	0.386730i	0.955802	+	0.294012i	$0.0949906\pi$
$510$		0			0
$511$	6.56718	+	11.3747i	0.290515	+	0.503187i
$512$		0			0
$513$	−3.82918	+	30.2216i	−0.169063	+	1.33432i
$514$		0			0
$515$	−5.19352	−	9.96983i	−0.228854	−	0.439323i
$516$		0			0
$517$	−7.60987	−	28.4004i	−0.334682	−	1.24905i
$518$		0			0
$519$	23.0613	+	7.23010i	1.01228	+	0.317366i
$520$		0			0
$521$		−	22.0900i		−	0.967778i	−0.875129	−	0.483889i	$-0.839224\pi$
$521$		−	22.0900i		−	0.967778i	0.875129	−	0.483889i	$-0.160776\pi$
$522$		0			0
$523$	11.5971	+	11.5971i	0.507106	+	0.507106i	0.913637	−	0.406531i	$-0.133262\pi$
$523$	11.5971	+	11.5971i	0.507106	+	0.507106i	−0.406531	+	0.913637i	$0.633262\pi$
$524$		0			0
$525$	9.08200	−	1.21585i	0.396371	−	0.0530640i
$526$		0			0
$527$	16.4713	−	4.41348i	0.717502	−	0.192254i
$528$		0			0
$529$	−6.73319	+	3.88741i	−0.292747	+	0.169018i
$530$		0			0
$531$	22.5125	−	32.3743i	0.976959	−	1.40492i
$532$		0			0
$533$	2.89851	+	0.776654i	0.125548	+	0.0336406i
$534$		0			0
$535$	−15.5396	+	24.4074i	−0.671837	+	1.05523i
$536$		0			0
$537$	19.7035	+	0.828242i	0.850267	+	0.0357413i
$538$		0			0
$539$	−20.5993			−0.887276
$540$		0			0
$541$	3.09474			0.133053			0.0665266	−	0.997785i	$-0.478808\pi$
$541$	3.09474			0.133053			0.0665266	+	0.997785i	$0.478808\pi$
$542$		0			0
$543$	36.7180	+	1.54345i	1.57572	+	0.0662360i
$544$		0			0
$545$	25.3140	−	5.61944i	1.08433	−	0.240710i
$546$		0			0
$547$	5.49927	+	1.47353i	0.235132	+	0.0630034i	0.374461	−	0.927243i	$-0.377828\pi$
$547$	5.49927	+	1.47353i	0.235132	+	0.0630034i	−0.139329	+	0.990246i	$0.544495\pi$
$548$		0			0
$549$	9.69226	+	20.6102i	0.413656	+	0.879624i
$550$		0			0
$551$	28.6210	−	16.5243i	1.21929	−	0.703960i
$552$		0			0
$553$	10.4791	−	2.80788i	0.445619	−	0.119403i
$554$		0			0
$555$	−19.2860	−	13.4496i	−0.818644	−	0.570902i
$556$		0			0
$557$	−16.3849	−	16.3849i	−0.694250	−	0.694250i	0.268914	−	0.963164i	$-0.413335\pi$
$557$	−16.3849	−	16.3849i	−0.694250	−	0.694250i	−0.963164	+	0.268914i	$0.913335\pi$
$558$		0			0
$559$			7.14892i			0.302367i
$560$		0			0
$561$	19.2231	+	6.02675i	0.811600	+	0.254449i
$562$		0			0
$563$	7.31313	+	27.2930i	0.308212	+	1.15026i	0.930145	+	0.367192i	$0.119681\pi$
$563$	7.31313	+	27.2930i	0.308212	+	1.15026i	−0.621933	+	0.783070i	$0.713653\pi$
$564$		0			0
$565$	−27.4906	+	14.3205i	−1.15654	+	0.602468i
$566$		0			0
$567$	−8.65625	−	3.96828i	−0.363528	−	0.166652i
$568$		0			0
$569$	10.8959	+	18.8722i	0.456778	+	0.791164i	0.998789	−	0.0492085i	$-0.0156699\pi$
$569$	10.8959	+	18.8722i	0.456778	+	0.791164i	−0.542010	+	0.840372i	$0.682337\pi$
$570$		0			0
$571$	−5.87084	+	10.1686i	−0.245687	+	0.425543i	−0.962325	−	0.271903i	$-0.912347\pi$
$571$	−5.87084	+	10.1686i	−0.245687	+	0.425543i	0.716637	+	0.697446i	$0.245680\pi$
$572$		0			0
$573$	12.6554	−	6.61411i	0.528687	−	0.276308i
$574$		0			0
$575$	17.8413	+	21.2382i	0.744032	+	0.885693i
$576$		0			0
$577$	−15.4625	+	15.4625i	−0.643711	+	0.643711i	−0.951466	−	0.307755i	$-0.900422\pi$
$577$	−15.4625	+	15.4625i	−0.643711	+	0.643711i	0.307755	+	0.951466i	$0.400422\pi$
$578$		0			0
$579$	29.9309	−	6.68649i	1.24388	−	0.277881i
$580$		0			0
$581$	14.3958	+	8.31143i	0.597240	+	0.344816i
$582$		0			0
$583$	−6.66949	+	24.8909i	−0.276222	+	1.03088i
$584$		0			0
$585$	−5.41774	−	12.9502i	−0.223996	−	0.535427i
$586$		0			0
$587$	−3.21285	+	11.9905i	−0.132608	+	0.494901i	−0.999996	−	0.00273128i	$-0.999131\pi$
$587$	−3.21285	+	11.9905i	−0.132608	+	0.494901i	0.867388	+	0.497633i	$0.165797\pi$
$588$		0			0
$589$	26.0751	+	15.0544i	1.07440	+	0.620307i
$590$		0			0
$591$	18.5633	+	20.1924i	0.763592	+	0.830605i
$592$		0			0
$593$	−11.6248	+	11.6248i	−0.477374	+	0.477374i	−0.904291	−	0.426917i	$-0.859600\pi$
$593$	−11.6248	+	11.6248i	−0.477374	+	0.477374i	0.426917	+	0.904291i	$0.359600\pi$
$594$		0			0
$595$	5.79024	−	5.30877i	0.237377	−	0.217638i
$596$		0			0
$597$	−0.244126	+	5.80764i	−0.00999142	+	0.237691i
$598$		0			0
$599$	16.0973	−	27.8814i	0.657719	−	1.13920i	−0.323486	−	0.946233i	$-0.604855\pi$
$599$	16.0973	−	27.8814i	0.657719	−	1.13920i	0.981205	−	0.192969i	$-0.0618118\pi$
$600$		0			0
$601$	−2.93479	−	5.08320i	−0.119712	−	0.207348i	0.799941	−	0.600078i	$-0.204864\pi$
$601$	−2.93479	−	5.08320i	−0.119712	−	0.207348i	−0.919654	+	0.392730i	$0.871531\pi$
$602$		0			0
$603$	−1.80763	−	10.0606i	−0.0736124	−	0.409698i
$604$		0			0
$605$	2.71042	+	0.853756i	0.110194	+	0.0347101i
$606$		0			0
$607$	−4.65927	−	17.3886i	−0.189114	−	0.705783i	−0.993712	−	0.111964i	$-0.964286\pi$
$607$	−4.65927	−	17.3886i	−0.189114	−	0.705783i	0.804598	−	0.593819i	$-0.202381\pi$
$608$		0			0
$609$	2.25233	+	10.0821i	0.0912689	+	0.408549i
$610$		0			0
$611$			17.5646i			0.710586i
$612$		0			0
$613$	17.1936	+	17.1936i	0.694444	+	0.694444i	0.963206	−	0.268763i	$-0.0866148\pi$
$613$	17.1936	+	17.1936i	0.694444	+	0.694444i	−0.268763	+	0.963206i	$0.586615\pi$
$614$		0			0
$615$	1.88955	−	5.22239i	0.0761938	−	0.210587i
$616$		0			0
$617$	9.10738	−	2.44031i	0.366649	−	0.0982434i	−0.0707902	−	0.997491i	$-0.522552\pi$
$617$	9.10738	−	2.44031i	0.366649	−	0.0982434i	0.437439	+	0.899248i	$0.355885\pi$
$618$		0			0
$619$	−40.5913	+	23.4354i	−1.63150	+	0.941949i	−0.647874	+	0.761748i	$0.724342\pi$
$619$	−40.5913	+	23.4354i	−1.63150	+	0.941949i	−0.983630	+	0.180201i	$0.942325\pi$
$620$		0			0
$621$	−3.90158	−	28.5604i	−0.156565	−	1.14609i
$622$		0			0
$623$	−10.5667	−	2.83134i	−0.423346	−	0.113435i
$624$		0			0
$625$	16.0482	−	19.1691i	0.641928	−	0.766765i
$626$		0			0
$627$	16.4759	+	31.5249i	0.657984	+	1.25898i
$628$		0			0
$629$	−20.1576			−0.803735
$630$		0			0
$631$	−22.7433			−0.905396			−0.452698	−	0.891664i	$-0.649538\pi$
$631$	−22.7433			−0.905396			−0.452698	+	0.891664i	$0.649538\pi$
$632$		0			0
$633$	1.59227	−	2.50834i	0.0632871	−	0.0996974i
$634$		0			0
$635$	−18.0527	−	11.4937i	−0.716399	−	0.456114i
$636$		0			0
$637$	11.8865	+	3.18497i	0.470959	+	0.126193i
$638$		0			0
$639$	−1.17369	+	13.9360i	−0.0464303	+	0.551301i
$640$		0			0
$641$	−1.02228	+	0.590214i	−0.0403777	+	0.0233121i	−0.520053	−	0.854134i	$-0.674088\pi$
$641$	−1.02228	+	0.590214i	−0.0403777	+	0.0233121i	0.479675	+	0.877446i	$0.340754\pi$
$642$		0			0
$643$	−44.1803	+	11.8381i	−1.74230	+	0.466848i	−0.982956	−	0.183842i	$-0.941146\pi$
$643$	−44.1803	+	11.8381i	−1.74230	+	0.466848i	−0.759344	+	0.650690i	$0.774480\pi$
$644$		0			0
$645$	13.1828	+	1.12807i	0.519073	+	0.0444178i
$646$		0			0
$647$	−23.7783	−	23.7783i	−0.934823	−	0.934823i	0.0631795	−	0.998002i	$-0.479876\pi$
$647$	−23.7783	−	23.7783i	−0.934823	−	0.934823i	−0.998002	+	0.0631795i	$0.979876\pi$
$648$		0			0
$649$		−	46.0435i		−	1.80737i
$650$		0			0
$651$	−6.92872	+	6.36972i	−0.271558	+	0.249649i
$652$		0			0
$653$	−1.03616	−	3.86700i	−0.0405480	−	0.151327i	0.942684	−	0.333687i	$-0.108293\pi$
$653$	−1.03616	−	3.86700i	−0.0405480	−	0.151327i	−0.983232	+	0.182360i	$0.941626\pi$
$654$		0			0
$655$	4.54554	−	14.4307i	0.177609	−	0.563855i
$656$		0			0
$657$	−24.0305	−	28.4505i	−0.937521	−	1.10996i
$658$		0			0
$659$	7.02187	+	12.1622i	0.273533	+	0.473773i	0.969764	−	0.244045i	$-0.0784744\pi$
$659$	7.02187	+	12.1622i	0.273533	+	0.473773i	−0.696231	+	0.717818i	$0.745141\pi$
$660$		0			0
$661$	−1.19797	+	2.07494i	−0.0465955	+	0.0807057i	−0.888382	−	0.459104i	$-0.848170\pi$
$661$	−1.19797	+	2.07494i	−0.0465955	+	0.0807057i	0.841787	+	0.539810i	$0.181504\pi$
$662$		0			0
$663$	−10.1605	−	6.44981i	−0.394602	−	0.250490i
$664$		0			0
$665$	13.8573	+	0.601129i	0.537364	+	0.0233108i
$666$		0			0
$667$	−22.1127	+	22.1127i	−0.856208	+	0.856208i
$668$		0			0
$669$	11.4945	−	36.6632i	0.444403	−	1.41748i
$670$		0			0
$671$	23.0311	+	13.2970i	0.889104	+	0.513325i
$672$		0			0
$673$	−5.28589	+	19.7272i	−0.203756	+	0.760428i	0.786069	+	0.618139i	$0.212113\pi$
$673$	−5.28589	+	19.7272i	−0.203756	+	0.760428i	−0.989825	+	0.142289i	$0.954554\pi$
$674$		0			0
$675$	−24.7355	+	7.94697i	−0.952070	+	0.305879i
$676$		0			0
$677$	5.91922	−	22.0908i	0.227494	−	0.849019i	−0.753896	−	0.656994i	$-0.771828\pi$
$677$	5.91922	−	22.0908i	0.227494	−	0.849019i	0.981390	−	0.192026i	$-0.0615056\pi$
$678$		0			0
$679$	13.9157	+	8.03423i	0.534035	+	0.308325i
$680$		0			0
$681$	−3.82672	+	12.2058i	−0.146640	+	0.467728i
$682$		0			0
$683$	13.4305	−	13.4305i	0.513903	−	0.513903i	−0.401817	−	0.915720i	$-0.631621\pi$
$683$	13.4305	−	13.4305i	0.513903	−	0.513903i	0.915720	+	0.401817i	$0.131621\pi$
$684$		0			0
$685$	−10.0767	−	0.437126i	−0.385010	−	0.0167017i
$686$		0			0
$687$	40.6406	+	25.7983i	1.55054	+	0.984268i
$688$		0			0
$689$	7.69703	−	13.3316i	0.293233	−	0.507895i
$690$		0			0
$691$	−13.8183	−	23.9340i	−0.525673	−	0.910492i	−0.999553	−	0.0299024i	$-0.990480\pi$
$691$	−13.8183	−	23.9340i	−0.525673	−	0.910492i	0.473880	−	0.880589i	$-0.342853\pi$
$692$		0			0
$693$	−10.9438	+	1.96632i	−0.415720	+	0.0746945i
$694$		0			0
$695$	−8.29660	+	26.3392i	−0.314708	+	0.999103i
$696$		0			0
$697$	−1.23231	−	4.59902i	−0.0466769	−	0.174200i
$698$		0			0
$699$	−11.3357	+	10.4212i	−0.428756	+	0.394164i
$700$		0			0
$701$			9.61048i			0.362983i	0.983393	+	0.181491i	$0.0580925\pi$
$701$			9.61048i			0.362983i	−0.983393	+	0.181491i	$0.941908\pi$
$702$		0			0
$703$	−25.1671	−	25.1671i	−0.949195	−	0.949195i
$704$		0			0
$705$	32.3896	+	2.77162i	1.21986	+	0.104385i
$706$		0			0
$707$	−17.1133	+	4.58551i	−0.643613	+	0.172456i
$708$		0			0
$709$	8.73819	−	5.04499i	0.328170	−	0.189469i	−0.326859	−	0.945073i	$-0.605990\pi$
$709$	8.73819	−	5.04499i	0.328170	−	0.189469i	0.655028	+	0.755604i	$0.272657\pi$
$710$		0			0
$711$	−27.8363	+	13.0904i	−1.04394	+	0.490929i
$712$		0			0
$713$	−27.5196	−	7.37385i	−1.03062	−	0.276153i
$714$		0			0
$715$	−13.8268	−	8.80321i	−0.517094	−	0.329221i
$716$		0			0
$717$	−9.51716	+	14.9926i	−0.355425	+	0.559908i
$718$		0			0
$719$	−47.9590			−1.78857			−0.894285	−	0.447498i	$-0.852315\pi$
$719$	−47.9590			−1.78857			−0.894285	+	0.447498i	$0.852315\pi$
$720$		0			0
$721$	5.31919			0.198097
$722$		0			0
$723$	7.46748	+	14.2882i	0.277718	+	0.531385i
$724$		0			0
$725$	23.0975	+	16.1537i	0.857819	+	0.599934i
$726$		0			0
$727$	23.7888	+	6.37418i	0.882276	+	0.236405i	0.671389	−	0.741105i	$-0.265698\pi$
$727$	23.7888	+	6.37418i	0.882276	+	0.236405i	0.210887	+	0.977510i	$0.432365\pi$
$728$		0			0
$729$	26.1468	+	6.73388i	0.968400	+	0.249403i
$730$		0			0
$731$	9.82341	−	5.67155i	0.363332	−	0.209770i
$732$		0			0
$733$	8.09901	−	2.17012i	0.299144	−	0.0801553i	−0.106125	−	0.994353i	$-0.533845\pi$
$733$	8.09901	−	2.17012i	0.299144	−	0.0801553i	0.405269	+	0.914197i	$0.367178\pi$
$734$		0			0
$735$	7.74882	−	21.4164i	0.285819	−	0.789957i
$736$		0			0
$737$	−8.43962	−	8.43962i	−0.310877	−	0.310877i
$738$		0			0
$739$		−	47.7351i		−	1.75596i	−0.478695	−	0.877981i	$-0.658890\pi$
$739$		−	47.7351i		−	1.75596i	0.478695	−	0.877981i	$-0.341110\pi$
$740$		0			0
$741$	−4.63289	−	20.7383i	−0.170193	−	0.761841i
$742$		0			0
$743$	−10.9431	−	40.8401i	−0.401463	−	1.49828i	−0.810488	−	0.585756i	$-0.800798\pi$
$743$	−10.9431	−	40.8401i	−0.401463	−	1.49828i	0.409025	−	0.912523i	$-0.365869\pi$
$744$		0			0
$745$	−20.3123	−	6.39820i	−0.744187	−	0.234412i
$746$		0			0
$747$	−44.3420	−	15.9764i	−1.62239	−	0.584546i
$748$		0			0
$749$	−6.84555	−	11.8568i	−0.250131	−	0.433240i
$750$		0			0
$751$	2.98283	−	5.16642i	0.108845	−	0.188525i	−0.806458	−	0.591292i	$-0.798618\pi$
$751$	2.98283	−	5.16642i	0.108845	−	0.188525i	0.915303	+	0.402767i	$0.131951\pi$
$752$		0			0
$753$	1.05706	−	25.1469i	0.0385214	−	0.916404i
$754$		0			0
$755$	−15.3947	+	14.1146i	−0.560270	+	0.513682i
$756$		0			0
$757$	13.4661	−	13.4661i	0.489435	−	0.489435i	−0.418693	−	0.908128i	$-0.637512\pi$
$757$	13.4661	−	13.4661i	0.489435	−	0.489435i	0.908128	+	0.418693i	$0.137512\pi$
$758$		0			0
$759$	−22.7796	−	24.7788i	−0.826848	−	0.899412i
$760$		0			0
$761$	1.84492	+	1.06516i	0.0668782	+	0.0386121i	0.533066	−	0.846074i	$-0.321040\pi$
$761$	1.84492	+	1.06516i	0.0668782	+	0.0386121i	−0.466188	+	0.884686i	$0.654373\pi$
$762$		0			0
$763$	−3.17560	+	11.8515i	−0.114965	+	0.429054i
$764$		0			0
$765$	−13.4969	+	17.7185i	−0.487983	+	0.640615i
$766$		0			0
$767$	−7.11903	+	26.5686i	−0.257053	+	0.959336i
$768$		0			0
$769$	−27.7015	−	15.9935i	−0.998941	−	0.576739i	−0.0910060	−	0.995850i	$-0.529008\pi$
$769$	−27.7015	−	15.9935i	−0.998941	−	0.576739i	−0.907935	+	0.419112i	$0.862342\pi$
$770$		0			0
$771$	−12.2747	+	2.74214i	−0.442062	+	0.0987557i
$772$		0			0
$773$	32.0937	−	32.0937i	1.15433	−	1.15433i	0.168656	−	0.985675i	$-0.446057\pi$
$773$	32.0937	−	32.0937i	1.15433	−	1.15433i	0.985675	−	0.168656i	$-0.0539426\pi$
$774$		0			0
$775$	−2.22368	+	25.5821i	−0.0798770	+	0.918935i
$776$		0			0
$777$	9.86016	−	5.15323i	0.353731	−	0.184871i
$778$		0			0
$779$	4.20341	−	7.28052i	0.150603	−	0.260852i
$780$		0			0
$781$	8.16507	+	14.1423i	0.292169	+	0.506052i
$782$		0			0
$783$	−11.3410	−	27.0069i	−0.405293	−	0.965149i
$784$		0			0
$785$	−19.0679	+	9.93289i	−0.680561	+	0.354520i
$786$		0			0
$787$	9.07990	+	33.8866i	0.323663	+	1.20793i	0.915649	+	0.401980i	$0.131678\pi$
$787$	9.07990	+	33.8866i	0.323663	+	1.20793i	−0.591985	+	0.805949i	$0.701656\pi$
$788$		0			0
$789$	−10.9636	−	3.43728i	−0.390316	−	0.122370i
$790$		0			0
$791$		−	14.6670i		−	0.521500i
$792$		0			0
$793$	−11.2337	−	11.2337i	−0.398922	−	0.398922i
$794$		0			0
$795$	−23.3694	−	16.2972i	−0.828826	−	0.578003i
$796$		0			0
$797$	−21.3153	+	5.71142i	−0.755027	+	0.202309i	−0.615747	−	0.787944i	$-0.711146\pi$
$797$	−21.3153	+	5.71142i	−0.755027	+	0.202309i	−0.139280	+	0.990253i	$0.544479\pi$
$798$		0			0
$799$	24.1356	−	13.9347i	0.853857	−	0.492975i
$800$		0			0
$801$	30.9082	+	2.60307i	1.09209	+	0.0919751i
$802$		0			0
$803$	−42.0032	−	11.2547i	−1.48226	−	0.397170i
$804$		0			0
$805$	−12.8128	+	2.84431i	−0.451593	+	0.100249i
$806$		0			0
$807$	12.0086	+	0.504786i	0.422723	+	0.0177693i
$808$		0			0
$809$	4.04754			0.142304			0.0711520	−	0.997465i	$-0.477332\pi$
$809$	4.04754			0.142304			0.0711520	+	0.997465i	$0.477332\pi$
$810$		0			0
$811$	34.5590			1.21353			0.606765	−	0.794882i	$-0.292467\pi$
$811$	34.5590			1.21353			0.606765	+	0.794882i	$0.292467\pi$
$812$		0			0
$813$	−50.7532	−	2.13343i	−1.77999	−	0.0748227i
$814$		0			0
$815$	4.97706	−	7.81726i	0.174339	−	0.273827i
$816$		0			0
$817$	19.3457	+	5.18367i	0.676821	+	0.181354i
$818$		0			0
$819$	6.61894	+	0.557444i	0.231284	+	0.0194787i
$820$		0			0
$821$	−23.8625	+	13.7770i	−0.832807	+	0.480821i	−0.854813	−	0.518937i	$-0.826328\pi$
$821$	−23.8625	+	13.7770i	−0.832807	+	0.480821i	0.0220060	+	0.999758i	$0.492995\pi$
$822$		0			0
$823$	31.3974	−	8.41292i	1.09445	−	0.293256i	0.333945	−	0.942593i	$-0.391620\pi$
$823$	31.3974	−	8.41292i	1.09445	−	0.293256i	0.760501	+	0.649337i	$0.224953\pi$
$824$		0			0
$825$	−18.4152	+	24.1080i	−0.641135	+	0.839332i
$826$		0			0
$827$	29.3910	+	29.3910i	1.02203	+	1.02203i	0.999752	+	0.0222732i	$0.00709038\pi$
$827$	29.3910	+	29.3910i	1.02203	+	1.02203i	0.0222732	+	0.999752i	$0.492910\pi$
$828$		0			0
$829$			10.1087i			0.351091i	0.984471	+	0.175545i	$0.0561688\pi$
$829$			10.1087i			0.351091i	−0.984471	+	0.175545i	$0.943831\pi$
$830$		0			0
$831$	33.5927	+	10.5318i	1.16532	+	0.365345i
$832$		0			0
$833$	−5.05355	−	18.8601i	−0.175095	−	0.653464i
$834$		0			0
$835$	−8.27722	−	15.8895i	−0.286445	−	0.549879i
$836$		0			0
$837$	16.1421	−	21.2502i	0.557953	−	0.734514i
$838$		0			0
$839$	−0.0228131	−	0.0395134i	−0.000787594	−	0.00136415i	0.865631	−	0.500682i	$-0.166917\pi$
$839$	−0.0228131	−	0.0395134i	−0.000787594	−	0.00136415i	−0.866419	+	0.499318i	$0.833584\pi$
$840$		0			0
$841$	−1.38873	+	2.40534i	−0.0478871	+	0.0829429i
$842$		0			0
$843$	−47.4796	+	24.8143i	−1.63529	+	0.854651i
$844$		0			0
$845$	−13.0272	−	14.2087i	−0.448151	−	0.488796i
$846$		0			0
$847$	−0.950795	+	0.950795i	−0.0326697	+	0.0326697i
$848$		0			0
$849$	−49.4108	+	11.0383i	−1.69578	+	0.378832i
$850$		0			0
$851$	29.1664	+	16.8392i	0.999810	+	0.577240i
$852$		0			0
$853$	9.97269	−	37.2186i	0.341458	−	1.27434i	−0.555237	−	0.831692i	$-0.687373\pi$
$853$	9.97269	−	37.2186i	0.341458	−	1.27434i	0.896696	−	0.442648i	$-0.145961\pi$
$854$		0			0
$855$	−38.9731	+	5.27076i	−1.33285	+	0.180256i
$856$		0			0
$857$	1.69965	−	6.34316i	0.0580588	−	0.216678i	−0.930801	−	0.365525i	$-0.880889\pi$
$857$	1.69965	−	6.34316i	0.0580588	−	0.216678i	0.988860	+	0.148847i	$0.0475561\pi$
$858$		0			0
$859$	4.97240	+	2.87082i	0.169656	+	0.0979511i	0.582424	−	0.812885i	$-0.302104\pi$
$859$	4.97240	+	2.87082i	0.169656	+	0.0979511i	−0.412767	+	0.910836i	$0.635438\pi$
$860$		0			0
$861$	1.77851	+	1.93460i	0.0606116	+	0.0659309i
$862$		0			0
$863$	25.6499	−	25.6499i	0.873133	−	0.873133i	−0.119680	−	0.992813i	$-0.538187\pi$
$863$	25.6499	−	25.6499i	0.873133	−	0.873133i	0.992813	+	0.119680i	$0.0381867\pi$
$864$		0			0
$865$	−1.35222	+	31.1717i	−0.0459770	+	1.05987i
$866$		0			0
$867$	0.434658	−	10.3403i	0.0147618	−	0.351175i
$868$		0			0
$869$	−17.9590	+	31.1058i	−0.609216	+	1.05519i
$870$		0			0
$871$	3.56504	+	6.17482i	0.120797	+	0.209226i
$872$		0			0
$873$	−42.8631	−	15.4435i	−1.45070	−	0.522685i
$874$		0			0
$875$	4.53612	+	10.9251i	0.153349	+	0.369337i
$876$		0			0
$877$	−1.62818	−	6.07643i	−0.0549796	−	0.205187i	0.932972	−	0.359948i	$-0.117206\pi$
$877$	−1.62818	−	6.07643i	−0.0549796	−	0.205187i	−0.987952	+	0.154762i	$0.950539\pi$
$878$		0			0
$879$	0.151434	+	0.677866i	0.00510773	+	0.0228638i
$880$		0			0
$881$			4.05072i			0.136472i	0.997669	+	0.0682361i	$0.0217371\pi$
$881$			4.05072i			0.136472i	−0.997669	+	0.0682361i	$0.978263\pi$
$882$		0			0
$883$	33.3454	+	33.3454i	1.12216	+	1.12216i	0.991416	+	0.130745i	$0.0417369\pi$
$883$	33.3454	+	33.3454i	1.12216	+	1.12216i	0.130745	+	0.991416i	$0.458263\pi$
$884$		0			0
$885$	47.8699	+	17.3201i	1.60913	+	0.582209i
$886$		0			0
$887$	23.3378	−	6.25335i	0.783607	−	0.209967i	0.155233	−	0.987878i	$-0.450387\pi$
$887$	23.3378	−	6.25335i	0.783607	−	0.209967i	0.628374	+	0.777911i	$0.283721\pi$
$888$		0			0
$889$	8.76978	−	5.06323i	0.294129	−	0.169815i
$890$		0			0
$891$	29.5549	−	10.9749i	0.990126	−	0.367671i
$892$		0			0
$893$	47.5315	+	12.7360i	1.59058	+	0.426195i
$894$		0			0
$895$	5.51742	+	24.8545i	0.184427	+	0.830793i
$896$		0			0
$897$	9.31341	+	17.8202i	0.310966	+	0.595000i
$898$		0			0
$899$	−28.9508			−0.965562
$900$		0			0
$901$	−24.4255			−0.813732
$902$		0			0
$903$	−3.35525	+	5.28559i	−0.111656	+	0.175893i
$904$		0			0
$905$	10.2819	+	46.3171i	0.341781	+	1.53963i
$906$		0			0
$907$	9.26617	+	2.48286i	0.307678	+	0.0824421i	0.409354	−	0.912375i	$-0.365754\pi$
$907$	9.26617	+	2.48286i	0.307678	+	0.0824421i	−0.101676	+	0.994818i	$0.532421\pi$
$908$		0			0
$909$	45.4590	−	21.3777i	1.50778	−	0.709055i
$910$		0			0
$911$	−29.1002	+	16.8010i	−0.964133	+	0.556643i	−0.897443	−	0.441131i	$-0.854577\pi$
$911$	−29.1002	+	16.8010i	−0.964133	+	0.556643i	−0.0666905	+	0.997774i	$0.521244\pi$
$912$		0			0
$913$	−53.1593	+	14.2440i	−1.75931	+	0.471407i
$914$		0			0
$915$	−22.4880	+	18.9427i	−0.743430	+	0.626227i
$916$		0			0
$917$	5.06219	+	5.06219i	0.167168	+	0.167168i
$918$		0			0
$919$		−	34.0444i		−	1.12302i	−0.827469	−	0.561511i	$-0.810220\pi$
$919$		−	34.0444i		−	1.12302i	0.827469	−	0.561511i	$-0.189780\pi$
$920$		0			0
$921$	0.117380	−	0.107910i	0.00386780	−	0.00355575i
$922$		0			0
$923$	−2.52489	−	9.42302i	−0.0831077	−	0.310162i
$924$		0			0
$925$	10.3659	−	28.5298i	0.340827	−	0.938053i
$926$		0			0
$927$	−14.8443	+	2.66715i	−0.487550	+	0.0876005i
$928$		0			0
$929$	14.7454	+	25.5398i	0.483782	+	0.837934i	0.999826	−	0.0186272i	$-0.00592956\pi$
$929$	14.7454	+	25.5398i	0.483782	+	0.837934i	−0.516045	+	0.856562i	$0.672596\pi$
$930$		0			0
$931$	17.2377	−	29.8566i	0.564944	−	0.978511i
$932$		0			0
$933$	−0.683174	−	0.433673i	−0.0223661	−	0.0141978i
$934$		0			0
$935$	−1.12716	+	25.9835i	−0.0368622	+	0.849753i
$936$		0			0
$937$	10.6227	−	10.6227i	0.347030	−	0.347030i	−0.511972	−	0.859002i	$-0.671085\pi$
$937$	10.6227	−	10.6227i	0.347030	−	0.347030i	0.859002	+	0.511972i	$0.171085\pi$
$938$		0			0
$939$	10.8440	−	34.5883i	0.353879	−	1.12874i
$940$		0			0
$941$	−1.50561	−	0.869262i	−0.0490814	−	0.0283371i	0.475259	−	0.879846i	$-0.342355\pi$
$941$	−1.50561	−	0.869262i	−0.0490814	−	0.0283371i	−0.524340	+	0.851509i	$0.675688\pi$
$942$		0			0
$943$	−2.05888	+	7.68385i	−0.0670464	+	0.250221i
$944$		0			0
$945$	2.07238	−	12.1176i	0.0674147	−	0.394184i
$946$		0			0
$947$	−1.60318	+	5.98315i	−0.0520964	+	0.194426i	−0.987070	−	0.160292i	$-0.948756\pi$
$947$	−1.60318	+	5.98315i	−0.0520964	+	0.194426i	0.934973	+	0.354718i	$0.115423\pi$
$948$		0			0
$949$	22.4970	+	12.9887i	0.730284	+	0.421630i
$950$		0			0
$951$	7.58756	−	24.2015i	0.246044	−	0.784788i
$952$		0			0
$953$	−6.07936	+	6.07936i	−0.196930	+	0.196930i	−0.798682	−	0.601753i	$-0.794469\pi$
$953$	−6.07936	+	6.07936i	−0.196930	+	0.196930i	0.601753	+	0.798682i	$0.294469\pi$
$954$		0			0
$955$	12.4582	+	13.5881i	0.403138	+	0.439700i
$956$		0			0
$957$	−28.8759	−	18.3301i	−0.933424	−	0.592529i
$958$		0			0
$959$	2.38627	−	4.13314i	0.0770566	−	0.133466i
$960$		0			0
$961$	2.31225	+	4.00493i	0.0745887	+	0.129191i
$962$		0			0
$963$	25.0492	+	29.6564i	0.807198	+	0.955665i
$964$		0			0
$965$	18.2919	+	35.1143i	0.588837	+	1.13037i
$966$		0			0
$967$	−7.29533	−	27.2266i	−0.234602	−	0.875547i	−0.978328	−	0.207062i	$-0.933610\pi$
$967$	−7.29533	−	27.2266i	−0.234602	−	0.875547i	0.743726	−	0.668485i	$-0.233057\pi$
$968$		0			0
$969$	−24.8212	+	22.8187i	−0.797373	+	0.733042i
$970$		0			0
$971$		−	51.6230i		−	1.65666i	−0.560241	−	0.828330i	$-0.689291\pi$
$971$		−	51.6230i		−	1.65666i	0.560241	−	0.828330i	$-0.310709\pi$
$972$		0			0
$973$	−9.23960	−	9.23960i	−0.296208	−	0.296208i
$974$		0			0
$975$	14.3536	−	11.0638i	0.459684	−	0.354325i
$976$		0			0
$977$	−12.3446	+	3.30773i	−0.394939	+	0.105824i	−0.450822	−	0.892614i	$-0.648869\pi$
$977$	−12.3446	+	3.30773i	−0.394939	+	0.105824i	0.0558831	+	0.998437i	$0.482203\pi$
$978$		0			0
$979$	31.3657	−	18.1090i	1.00245	−	0.578766i
$980$		0			0
$981$	2.91959	−	34.6664i	0.0932152	−	1.10681i
$982$		0			0
$983$	42.3618	+	11.3508i	1.35113	+	0.362035i	0.860552	−	0.509362i	$-0.170119\pi$
$983$	42.3618	+	11.3508i	1.35113	+	0.362035i	0.490579	+	0.871397i	$0.336785\pi$
$984$		0			0
$985$	−19.0175	+	29.8700i	−0.605948	+	0.951737i
$986$		0			0
$987$	−8.24367	+	12.9864i	−0.262399	+	0.413363i
$988$		0			0
$989$	−18.9516			−0.602624
$990$		0			0
$991$	18.8860			0.599933			0.299966	−	0.953950i	$-0.403025\pi$
$991$	18.8860			0.599933			0.299966	+	0.953950i	$0.403025\pi$
$992$		0			0
$993$	−18.9146	−	36.1910i	−0.600235	−	1.14849i
$994$		0			0
$995$	−7.32591	+	1.62627i	−0.232247	+	0.0515563i
$996$		0			0
$997$	38.6193	+	10.3480i	1.22309	+	0.327725i	0.811883	−	0.583820i	$-0.198442\pi$
$997$	38.6193	+	10.3480i	1.22309	+	0.327725i	0.411202	+	0.911544i	$0.365109\pi$
$998$		0			0
$999$	−24.9329	+	19.3252i	−0.788840	+	0.611422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bs.a.113.18	✓	72
3.2	odd	2		1080.2.bt.a.233.9		72
4.3	odd	2		720.2.cu.e.113.1		72
5.2	odd	4	inner	360.2.bs.a.257.10	yes	72
9.2	odd	6	inner	360.2.bs.a.353.10	yes	72
9.7	even	3		1080.2.bt.a.953.3		72
15.2	even	4		1080.2.bt.a.17.3		72
20.7	even	4		720.2.cu.e.257.9		72
36.11	even	6		720.2.cu.e.353.9		72
45.2	even	12	inner	360.2.bs.a.137.18	yes	72
45.7	odd	12		1080.2.bt.a.737.9		72
180.47	odd	12		720.2.cu.e.497.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bs.a.113.18	✓	72	1.1	even	1	trivial
360.2.bs.a.137.18	yes	72	45.2	even	12	inner
360.2.bs.a.257.10	yes	72	5.2	odd	4	inner
360.2.bs.a.353.10	yes	72	9.2	odd	6	inner
720.2.cu.e.113.1		72	4.3	odd	2
720.2.cu.e.257.9		72	20.7	even	4
720.2.cu.e.353.9		72	36.11	even	6
720.2.cu.e.497.1		72	180.47	odd	12
1080.2.bt.a.17.3		72	15.2	even	4
1080.2.bt.a.233.9		72	3.2	odd	2
1080.2.bt.a.737.9		72	45.7	odd	12
1080.2.bt.a.953.3		72	9.7	even	3

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.73052 + 0.0727431i) q^{3} +(0.484586 + 2.18293i) q^{5} +(-1.02200 - 0.273845i) q^{7} +(2.98942 + 0.251767i) q^{9} +O(q^{10})\)	\(q+(1.73052 + 0.0727431i) q^{3} +(0.484586 + 2.18293i) q^{5} +(-1.02200 - 0.273845i) q^{7} +(2.98942 + 0.251767i) q^{9} +(3.03367 - 1.75149i) q^{11} +(-2.02133 + 0.541614i) q^{13} +(0.679794 + 3.81286i) q^{15} +(2.34785 + 2.34785i) q^{17} +5.86265i q^{19} +(-1.74868 - 0.548238i) q^{21} +(-1.43580 - 5.35848i) q^{23} +(-4.53035 + 2.11563i) q^{25} +(5.15494 + 0.653149i) q^{27} +(-2.81857 - 4.88191i) q^{29} +(2.56785 - 4.44765i) q^{31} +(5.37724 - 2.81031i) q^{33} +(0.102535 - 2.36366i) q^{35} +(-4.29278 + 4.29278i) q^{37} +(-3.53736 + 0.790237i) q^{39} +(-1.24185 - 0.716981i) q^{41} +(0.884185 - 3.29982i) q^{43} +(0.899040 + 6.64769i) q^{45} +(2.17240 - 8.10751i) q^{47} +(-5.09268 - 2.94026i) q^{49} +(3.89221 + 4.23379i) q^{51} +(-5.20169 + 5.20169i) q^{53} +(5.29345 + 5.77353i) q^{55} +(-0.426468 + 10.1455i) q^{57} +(6.57205 - 11.3831i) q^{59} +(3.79591 + 6.57471i) q^{61} +(-2.98625 - 1.07594i) q^{63} +(-2.16181 - 4.14996i) q^{65} +(-0.881854 - 3.29112i) q^{67} +(-2.09489 - 9.37741i) q^{69} +4.66179i q^{71} +(-8.77780 - 8.77780i) q^{73} +(-7.99378 + 3.33160i) q^{75} +(-3.58005 + 0.959272i) q^{77} +(-8.87983 + 5.12677i) q^{79} +(8.87323 + 1.50527i) q^{81} +(-15.1755 - 4.06625i) q^{83} +(-3.98744 + 6.26291i) q^{85} +(-4.52248 - 8.65330i) q^{87} +10.3392 q^{89} +2.21412 q^{91} +(4.76727 - 7.50997i) q^{93} +(-12.7978 + 2.84096i) q^{95} +(-14.6693 - 3.93063i) q^{97} +(9.50986 - 4.47215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{15} + 16 q^{21} + 24 q^{23} - 12 q^{27} + 12 q^{33} + 12 q^{41} - 16 q^{45} - 36 q^{47} + 24 q^{51} - 40 q^{57} + 12 q^{61} - 44 q^{63} - 72 q^{65} - 36 q^{75} - 48 q^{77} - 20 q^{81} - 60 q^{83} + 24 q^{85} - 40 q^{87} - 84 q^{93} - 60 q^{95} + 24 q^{97}+O(q^{100}) \) 72 * q + 12 * q^15 + 16 * q^21 + 24 * q^23 - 12 * q^27 + 12 * q^33 + 12 * q^41 - 16 * q^45 - 36 * q^47 + 24 * q^51 - 40 * q^57 + 12 * q^61 - 44 * q^63 - 72 * q^65 - 36 * q^75 - 48 * q^77 - 20 * q^81 - 60 * q^83 + 24 * q^85 - 40 * q^87 - 84 * q^93 - 60 * q^95 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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