LMFDB - Embedded newform 576.2.y.a.335.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			335.20
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65298 - 0.517369i) q^{3} +(-1.94452 - 0.521033i) q^{5} +(0.322227 - 0.558114i) q^{7} +(2.46466 - 1.71040i) q^{9} +O(q^{10})$	\(q+(1.65298 - 0.517369i) q^{3} +(-1.94452 - 0.521033i) q^{5} +(0.322227 - 0.558114i) q^{7} +(2.46466 - 1.71040i) q^{9} +(5.59477 - 1.49911i) q^{11} +(-1.97877 - 0.530209i) q^{13} +(-3.48381 + 0.144781i) q^{15} +3.05892i q^{17} +(-4.11098 - 4.11098i) q^{19} +(0.243883 - 1.08926i) q^{21} +(7.05832 - 4.07512i) q^{23} +(-0.820436 - 0.473679i) q^{25} +(3.18911 - 4.10239i) q^{27} +(4.49126 - 1.20343i) q^{29} +(-0.147988 + 0.0854411i) q^{31} +(8.47242 - 5.37256i) q^{33} +(-0.917373 + 0.917373i) q^{35} +(-2.65918 - 2.65918i) q^{37} +(-3.54517 + 0.147331i) q^{39} +(0.983212 + 1.70297i) q^{41} +(0.220196 + 0.821783i) q^{43} +(-5.68376 + 2.04174i) q^{45} +(-4.02475 + 6.97107i) q^{47} +(3.29234 + 5.70250i) q^{49} +(1.58259 + 5.05632i) q^{51} +(-3.25765 + 3.25765i) q^{53} -11.6602 q^{55} +(-8.92225 - 4.66846i) q^{57} +(-0.135818 + 0.506879i) q^{59} +(-0.805675 - 3.00682i) q^{61} +(-0.160417 - 1.92670i) q^{63} +(3.57150 + 2.06201i) q^{65} +(-0.583631 + 2.17814i) q^{67} +(9.55889 - 10.3878i) q^{69} +15.3137i q^{71} +9.33784i q^{73} +(-1.60123 - 0.358511i) q^{75} +(0.966110 - 3.60557i) q^{77} +(9.44301 + 5.45193i) q^{79} +(3.14908 - 8.43109i) q^{81} +(-3.31253 - 12.3625i) q^{83} +(1.59380 - 5.94814i) q^{85} +(6.80132 - 4.31288i) q^{87} -3.86733 q^{89} +(-0.933529 + 0.933529i) q^{91} +(-0.200417 + 0.217797i) q^{93} +(5.85194 + 10.1359i) q^{95} +(-7.33044 + 12.6967i) q^{97} +(11.2251 - 13.2641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	1.65298	−	0.517369i	0.954346	−	0.298703i
$3$	1.65298	−	0.517369i	0.954346	−	0.298703i
$4$		0			0
$5$	−1.94452	−	0.521033i	−0.869617	−	0.233013i	−0.203695	−	0.979034i	$-0.565295\pi$
$5$	−1.94452	−	0.521033i	−0.869617	−	0.233013i	−0.665922	+	0.746021i	$0.731962\pi$
$6$		0			0
$7$	0.322227	−	0.558114i	0.121790	−	0.210947i	−0.798683	−	0.601751i	$-0.794470\pi$
$7$	0.322227	−	0.558114i	0.121790	−	0.210947i	0.920474	+	0.390804i	$0.127803\pi$
$8$		0			0
$9$	2.46466	−	1.71040i	0.821553	−	0.570133i
$10$		0			0
$11$	5.59477	−	1.49911i	1.68689	−	0.452000i	0.717303	−	0.696762i	$-0.245377\pi$
$11$	5.59477	−	1.49911i	1.68689	−	0.452000i	0.969583	+	0.244762i	$0.0787099\pi$
$12$		0			0
$13$	−1.97877	−	0.530209i	−0.548811	−	0.147054i	−0.0262502	−	0.999655i	$-0.508357\pi$
$13$	−1.97877	−	0.530209i	−0.548811	−	0.147054i	−0.522561	+	0.852602i	$0.675023\pi$
$14$		0			0
$15$	−3.48381	+	0.144781i	−0.899517	+	0.0373823i
$16$		0			0
$17$			3.05892i			0.741898i	0.928653	+	0.370949i	$0.120967\pi$
$17$			3.05892i			0.741898i	−0.928653	+	0.370949i	$0.879033\pi$
$18$		0			0
$19$	−4.11098	−	4.11098i	−0.943124	−	0.943124i	0.0553434	−	0.998467i	$-0.482375\pi$
$19$	−4.11098	−	4.11098i	−0.943124	−	0.943124i	−0.998467	+	0.0553434i	$0.982375\pi$
$20$		0			0
$21$	0.243883	−	1.08926i	0.0532196	−	0.237696i
$22$		0			0
$23$	7.05832	−	4.07512i	1.47176	−	0.849722i	0.472266	−	0.881456i	$-0.343436\pi$
$23$	7.05832	−	4.07512i	1.47176	−	0.849722i	0.999496	+	0.0317341i	$0.0101030\pi$
$24$		0			0
$25$	−0.820436	−	0.473679i	−0.164087	−	0.0947357i
$26$		0			0
$27$	3.18911	−	4.10239i	0.613745	−	0.789504i
$28$		0			0
$29$	4.49126	−	1.20343i	0.834006	−	0.223471i	0.183545	−	0.983011i	$-0.441243\pi$
$29$	4.49126	−	1.20343i	0.834006	−	0.223471i	0.650460	+	0.759540i	$0.274576\pi$
$30$		0			0
$31$	−0.147988	+	0.0854411i	−0.0265795	+	0.0153457i	−0.513231	−	0.858251i	$-0.671552\pi$
$31$	−0.147988	+	0.0854411i	−0.0265795	+	0.0153457i	0.486651	+	0.873596i	$0.338218\pi$
$32$		0			0
$33$	8.47242	−	5.37256i	1.47486	−	0.935242i
$34$		0			0
$35$	−0.917373	+	0.917373i	−0.155064	+	0.155064i
$36$		0			0
$37$	−2.65918	−	2.65918i	−0.437167	−	0.437167i	0.453891	−	0.891057i	$-0.350036\pi$
$37$	−2.65918	−	2.65918i	−0.437167	−	0.437167i	−0.891057	+	0.453891i	$0.850036\pi$
$38$		0			0
$39$	−3.54517	+	0.147331i	−0.567681	+	0.0235918i
$40$		0			0
$41$	0.983212	+	1.70297i	0.153552	+	0.265960i	0.932531	−	0.361090i	$-0.117595\pi$
$41$	0.983212	+	1.70297i	0.153552	+	0.265960i	−0.778979	+	0.627050i	$0.784262\pi$
$42$		0			0
$43$	0.220196	+	0.821783i	0.0335796	+	0.125321i	0.980681	−	0.195614i	$-0.0626698\pi$
$43$	0.220196	+	0.821783i	0.0335796	+	0.125321i	−0.947101	+	0.320934i	$0.896003\pi$
$44$		0			0
$45$	−5.68376	+	2.04174i	−0.847284	+	0.304364i
$46$		0			0
$47$	−4.02475	+	6.97107i	−0.587070	+	1.01684i	0.407544	+	0.913186i	$0.366385\pi$
$47$	−4.02475	+	6.97107i	−0.587070	+	1.01684i	−0.994614	+	0.103650i	$0.966948\pi$
$48$		0			0
$49$	3.29234	+	5.70250i	0.470334	+	0.814643i
$50$		0			0
$51$	1.58259	+	5.05632i	0.221607	+	0.708027i
$52$		0			0
$53$	−3.25765	+	3.25765i	−0.447473	+	0.447473i	−0.894514	−	0.447041i	$-0.852478\pi$
$53$	−3.25765	+	3.25765i	−0.447473	+	0.447473i	0.447041	+	0.894514i	$0.352478\pi$
$54$		0			0
$55$	−11.6602			−1.57227
$56$		0			0
$57$	−8.92225	−	4.66846i	−1.18178	−	0.618352i
$58$		0			0
$59$	−0.135818	+	0.506879i	−0.0176820	+	0.0659900i	−0.974203	−	0.225673i	$-0.927542\pi$
$59$	−0.135818	+	0.506879i	−0.0176820	+	0.0659900i	0.956521	+	0.291663i	$0.0942086\pi$
$60$		0			0
$61$	−0.805675	−	3.00682i	−0.103156	−	0.384984i	0.894973	−	0.446120i	$-0.147194\pi$
$61$	−0.805675	−	3.00682i	−0.103156	−	0.384984i	−0.998129	+	0.0611358i	$0.980528\pi$
$62$		0			0
$63$	−0.160417	−	1.92670i	−0.0202106	−	0.242741i
$64$		0			0
$65$	3.57150	+	2.06201i	0.442990	+	0.255760i
$66$		0			0
$67$	−0.583631	+	2.17814i	−0.0713019	+	0.266102i	−0.992369	−	0.123301i	$-0.960652\pi$
$67$	−0.583631	+	2.17814i	−0.0713019	+	0.266102i	0.921067	+	0.389403i	$0.127319\pi$
$68$		0			0
$69$	9.55889	−	10.3878i	1.15076	−	1.25055i
$70$		0			0
$71$			15.3137i			1.81741i	0.417442	+	0.908704i	$0.362927\pi$
$71$			15.3137i			1.81741i	−0.417442	+	0.908704i	$0.637073\pi$
$72$		0			0
$73$			9.33784i			1.09291i	0.837488	+	0.546456i	$0.184023\pi$
$73$			9.33784i			1.09291i	−0.837488	+	0.546456i	$0.815977\pi$
$74$		0			0
$75$	−1.60123	−	0.358511i	−0.184894	−	0.0413973i
$76$		0			0
$77$	0.966110	−	3.60557i	0.110098	−	0.410893i
$78$		0			0
$79$	9.44301	+	5.45193i	1.06242	+	0.613390i	0.926101	−	0.377275i	$-0.123139\pi$
$79$	9.44301	+	5.45193i	1.06242	+	0.613390i	0.136321	+	0.990665i	$0.456472\pi$
$80$		0			0
$81$	3.14908	−	8.43109i	0.349897	−	0.936788i
$82$		0			0
$83$	−3.31253	−	12.3625i	−0.363598	−	1.35697i	−0.869312	−	0.494264i	$-0.835437\pi$
$83$	−3.31253	−	12.3625i	−0.363598	−	1.35697i	0.505714	−	0.862701i	$-0.331229\pi$
$84$		0			0
$85$	1.59380	−	5.94814i	0.172872	−	0.645167i
$86$		0			0
$87$	6.80132	−	4.31288i	0.729178	−	0.462389i
$88$		0			0
$89$	−3.86733			−0.409936			−0.204968	−	0.978769i	$-0.565709\pi$
$89$	−3.86733			−0.409936			−0.204968	+	0.978769i	$0.565709\pi$
$90$		0			0
$91$	−0.933529	+	0.933529i	−0.0978604	+	0.0978604i
$92$		0			0
$93$	−0.200417	+	0.217797i	−0.0207822	+	0.0225845i
$94$		0			0
$95$	5.85194	+	10.1359i	0.600396	+	1.03992i
$96$		0			0
$97$	−7.33044	+	12.6967i	−0.744293	+	1.28915i	0.206231	+	0.978503i	$0.433880\pi$
$97$	−7.33044	+	12.6967i	−0.744293	+	1.28915i	−0.950524	+	0.310650i	$0.899453\pi$
$98$		0			0
$99$	11.2251	−	13.2641i	1.12817	−	1.33309i
$100$		0			0
$101$	−0.631544	−	2.35695i	−0.0628410	−	0.234526i	0.927361	−	0.374168i	$-0.122072\pi$
$101$	−0.631544	−	2.35695i	−0.0628410	−	0.234526i	−0.990202	+	0.139642i	$0.955405\pi$
$102$		0			0
$103$	−2.00255	−	3.46852i	−0.197317	−	0.341763i	0.750341	−	0.661051i	$-0.229890\pi$
$103$	−2.00255	−	3.46852i	−0.197317	−	0.341763i	−0.947658	+	0.319288i	$0.896556\pi$
$104$		0			0
$105$	−1.04178	+	1.99102i	−0.101667	+	0.194303i
$106$		0			0
$107$	1.96059	+	1.96059i	0.189537	+	0.189537i	0.795496	−	0.605959i	$-0.207210\pi$
$107$	1.96059	+	1.96059i	0.189537	+	0.189537i	−0.605959	+	0.795496i	$0.707210\pi$
$108$		0			0
$109$	−10.8066	+	10.8066i	−1.03509	+	1.03509i	−0.0357265	+	0.999362i	$0.511375\pi$
$109$	−10.8066	+	10.8066i	−1.03509	+	1.03509i	−0.999362	+	0.0357265i	$0.988625\pi$
$110$		0			0
$111$	−5.77134	−	3.01978i	−0.547791	−	0.286625i
$112$		0			0
$113$	−5.23197	+	3.02068i	−0.492183	+	0.284162i	−0.725479	−	0.688244i	$-0.758382\pi$
$113$	−5.23197	+	3.02068i	−0.492183	+	0.284162i	0.233297	+	0.972406i	$0.425049\pi$
$114$		0			0
$115$	−15.8483	+	4.24655i	−1.47787	+	0.395993i
$116$		0			0
$117$	−5.78385	+	2.07770i	−0.534717	+	0.192083i
$118$		0			0
$119$	1.70723	+	0.985668i	0.156501	+	0.0903560i
$120$		0			0
$121$	19.5278	−	11.2744i	1.77525	−	1.02494i
$122$		0			0
$123$	2.50629	+	2.30629i	0.225985	+	0.207951i
$124$		0			0
$125$	8.46600	+	8.46600i	0.757222	+	0.757222i
$126$		0			0
$127$		−	5.90485i		−	0.523971i	−0.965072	−	0.261985i	$-0.915623\pi$
$127$		−	5.90485i		−	0.523971i	0.965072	−	0.261985i	$-0.0843772\pi$
$128$		0			0
$129$	0.789144	+	1.24446i	0.0694802	+	0.109569i
$130$		0			0
$131$	1.55900	+	0.417733i	0.136211	+	0.0364975i	0.326280	−	0.945273i	$-0.394205\pi$
$131$	1.55900	+	0.417733i	0.136211	+	0.0364975i	−0.190070	+	0.981771i	$0.560871\pi$
$132$		0			0
$133$	−3.61906	+	0.969725i	−0.313813	+	0.0840859i
$134$		0			0
$135$	−8.33878	+	6.31555i	−0.717688	+	0.543556i
$136$		0			0
$137$	−5.55314	+	9.61831i	−0.474436	+	0.821748i	−0.999572	−	0.0292708i	$-0.990681\pi$
$137$	−5.55314	+	9.61831i	−0.474436	+	0.821748i	0.525135	+	0.851019i	$0.324015\pi$
$138$		0			0
$139$	−11.1674	−	2.99230i	−0.947207	−	0.253803i	−0.248030	−	0.968752i	$-0.579783\pi$
$139$	−11.1674	−	2.99230i	−0.947207	−	0.253803i	−0.699177	+	0.714949i	$0.746450\pi$
$140$		0			0
$141$	−3.04620	+	13.6053i	−0.256536	+	1.14577i
$142$		0			0
$143$	−11.8656			−0.992250
$144$		0			0
$145$	−9.36038			−0.777337
$146$		0			0
$147$	8.39246	+	7.72274i	0.692198	+	0.636961i
$148$		0			0
$149$	21.2808	+	5.70216i	1.74339	+	0.467139i	0.983195	−	0.182558i	$-0.0584378\pi$
$149$	21.2808	+	5.70216i	1.74339	+	0.467139i	0.760193	+	0.649698i	$0.225104\pi$
$150$		0			0
$151$	8.13154	−	14.0842i	0.661735	−	1.14616i	−0.318425	−	0.947948i	$-0.603154\pi$
$151$	8.13154	−	14.0842i	0.661735	−	1.14616i	0.980160	−	0.198210i	$-0.0635129\pi$
$152$		0			0
$153$	5.23197	+	7.53920i	0.422980	+	0.609508i
$154$		0			0
$155$	0.332284	−	0.0890353i	0.0266897	−	0.00715149i
$156$		0			0
$157$	−22.9837	−	6.15846i	−1.83430	−	0.491499i	−0.835942	−	0.548817i	$-0.815078\pi$
$157$	−22.9837	−	6.15846i	−1.83430	−	0.491499i	−0.998356	+	0.0573183i	$0.981745\pi$
$158$		0			0
$159$	−3.69941	+	7.07023i	−0.293382	+	0.560705i
$160$		0			0
$161$		−	5.25246i		−	0.413952i
$162$		0			0
$163$	11.4188	+	11.4188i	0.894390	+	0.894390i	0.994933	−	0.100543i	$-0.0320579\pi$
$163$	11.4188	+	11.4188i	0.894390	+	0.894390i	−0.100543	+	0.994933i	$0.532058\pi$
$164$		0			0
$165$	−19.2741	+	6.03265i	−1.50049	+	0.469641i
$166$		0			0
$167$	−0.427233	+	0.246663i	−0.0330603	+	0.0190874i	−0.516439	−	0.856324i	$-0.672743\pi$
$167$	−0.427233	+	0.246663i	−0.0330603	+	0.0190874i	0.483379	+	0.875411i	$0.339409\pi$
$168$		0			0
$169$	−7.62393	−	4.40168i	−0.586456	−	0.338591i
$170$		0			0
$171$	−17.1636	−	3.10075i	−1.31253	−	0.237120i
$172$		0			0
$173$	19.8154	−	5.30952i	1.50654	−	0.403675i	0.591254	−	0.806486i	$-0.298633\pi$
$173$	19.8154	−	5.30952i	1.50654	−	0.403675i	0.915284	+	0.402810i	$0.131967\pi$
$174$		0			0
$175$	−0.528733	+	0.305264i	−0.0399685	+	0.0230758i
$176$		0			0
$177$	0.0377401	+	0.908126i	0.00283672	+	0.0682590i
$178$		0			0
$179$	−7.49467	+	7.49467i	−0.560178	+	0.560178i	−0.929358	−	0.369180i	$-0.879639\pi$
$179$	−7.49467	+	7.49467i	−0.560178	+	0.560178i	0.369180	+	0.929358i	$0.379639\pi$
$180$		0			0
$181$	0.879477	+	0.879477i	0.0653710	+	0.0653710i	0.739036	−	0.673665i	$-0.235281\pi$
$181$	0.879477	+	0.879477i	0.0653710	+	0.0653710i	−0.673665	+	0.739036i	$0.735281\pi$
$182$		0			0
$183$	−2.88740	−	4.55337i	−0.213443	−	0.336595i
$184$		0			0
$185$	3.78532	+	6.55636i	0.278302	+	0.482033i
$186$		0			0
$187$	4.58567	+	17.1140i	0.335337	+	1.25150i
$188$		0			0
$189$	−1.26198	−	3.10179i	−0.0917954	−	0.225622i
$190$		0			0
$191$	3.97558	−	6.88590i	0.287663	−	0.498246i	−0.685589	−	0.727989i	$-0.740455\pi$
$191$	3.97558	−	6.88590i	0.287663	−	0.498246i	0.973251	+	0.229743i	$0.0737885\pi$
$192$		0			0
$193$	−2.95444	−	5.11723i	−0.212665	−	0.368346i	0.739883	−	0.672736i	$-0.234881\pi$
$193$	−2.95444	−	5.11723i	−0.212665	−	0.368346i	−0.952548	+	0.304389i	$0.901548\pi$
$194$		0			0
$195$	6.97042	+	1.56066i	0.499162	+	0.111761i
$196$		0			0
$197$	−11.6691	+	11.6691i	−0.831390	+	0.831390i	−0.987707	−	0.156317i	$-0.950038\pi$
$197$	−11.6691	+	11.6691i	−0.831390	+	0.831390i	0.156317	+	0.987707i	$0.450038\pi$
$198$		0			0
$199$	−0.633451			−0.0449041			−0.0224521	−	0.999748i	$-0.507147\pi$
$199$	−0.633451			−0.0449041			−0.0224521	+	0.999748i	$0.507147\pi$
$200$		0			0
$201$	0.162175	+	3.90237i	0.0114390	+	0.275252i
$202$		0			0
$203$	0.775555	−	2.89441i	0.0544333	−	0.203148i
$204$		0			0
$205$	−1.02457	−	3.82376i	−0.0715592	−	0.267063i
$206$		0			0
$207$	10.4263	−	22.1163i	0.724676	−	1.53719i
$208$		0			0
$209$	−29.1628	−	16.8372i	−2.01723	−	1.16465i
$210$		0			0
$211$	−5.54263	+	20.6854i	−0.381570	+	1.42404i	0.461932	+	0.886915i	$0.347156\pi$
$211$	−5.54263	+	20.6854i	−0.381570	+	1.42404i	−0.843503	+	0.537125i	$0.819510\pi$
$212$		0			0
$213$	7.92286	+	25.3133i	0.542866	+	1.73444i
$214$		0			0
$215$		−	1.71270i		−	0.116805i
$216$		0			0
$217$			0.110126i			0.00747582i
$218$		0			0
$219$	4.83111	+	15.4352i	0.326456	+	1.04302i
$220$		0			0
$221$	1.62187	−	6.05289i	0.109099	−	0.407162i
$222$		0			0
$223$	13.1779	+	7.60824i	0.882455	+	0.509485i	0.871467	−	0.490454i	$-0.163169\pi$
$223$	13.1779	+	7.60824i	0.882455	+	0.509485i	0.0109877	+	0.999940i	$0.496502\pi$
$224$		0			0
$225$	−2.83227	+	0.235815i	−0.188818	+	0.0157210i
$226$		0			0
$227$	−3.90123	−	14.5596i	−0.258934	−	0.966353i	−0.965860	−	0.259066i	$-0.916585\pi$
$227$	−3.90123	−	14.5596i	−0.258934	−	0.966353i	0.706926	−	0.707287i	$-0.250081\pi$
$228$		0			0
$229$	−2.78483	+	10.3931i	−0.184026	+	0.686796i	0.810810	+	0.585309i	$0.199027\pi$
$229$	−2.78483	+	10.3931i	−0.184026	+	0.686796i	−0.994837	+	0.101487i	$0.967640\pi$
$230$		0			0
$231$	−0.268456	−	6.45976i	−0.0176631	−	0.425021i
$232$		0			0
$233$	−2.05717			−0.134770			−0.0673848	−	0.997727i	$-0.521466\pi$
$233$	−2.05717			−0.134770			−0.0673848	+	0.997727i	$0.521466\pi$
$234$		0			0
$235$	11.4584	−	11.4584i	0.747462	−	0.747462i
$236$		0			0
$237$	18.4297	+	4.12638i	1.19714	+	0.268037i
$238$		0			0
$239$	−4.07795	−	7.06322i	−0.263781	−	0.456882i	0.703463	−	0.710732i	$-0.251636\pi$
$239$	−4.07795	−	7.06322i	−0.263781	−	0.456882i	−0.967243	+	0.253851i	$0.918303\pi$
$240$		0			0
$241$	5.82747	−	10.0935i	0.375380	−	0.650178i	−0.615003	−	0.788524i	$-0.710845\pi$
$241$	5.82747	−	10.0935i	0.375380	−	0.650178i	0.990384	+	0.138346i	$0.0441787\pi$
$242$		0			0
$243$	0.843360	−	15.5656i	0.0541015	−	0.998535i
$244$		0			0
$245$	−3.43084	−	12.8041i	−0.219188	−	0.818021i
$246$		0			0
$247$	5.95500	+	10.3144i	0.378907	+	0.656287i
$248$		0			0
$249$	−11.8715	−	18.7212i	−0.752328	−	1.18641i
$250$		0			0
$251$	0.0658814	+	0.0658814i	0.00415840	+	0.00415840i	0.709183	−	0.705025i	$-0.249064\pi$
$251$	0.0658814	+	0.0658814i	0.00415840	+	0.00415840i	−0.705025	+	0.709183i	$0.749064\pi$
$252$		0			0
$253$	33.3806	−	33.3806i	2.09862	−	2.09862i
$254$		0			0
$255$	−0.442874	−	10.6567i	−0.0277338	−	0.667350i
$256$		0			0
$257$	14.7849	−	8.53605i	0.922255	−	0.532464i	0.0379016	−	0.999281i	$-0.487933\pi$
$257$	14.7849	−	8.53605i	0.922255	−	0.532464i	0.884354	+	0.466817i	$0.154599\pi$
$258$		0			0
$259$	−2.34099	+	0.627265i	−0.145462	+	0.0389764i
$260$		0			0
$261$	9.01107	−	10.6479i	0.557771	−	0.659087i
$262$		0			0
$263$	6.39765	+	3.69369i	0.394496	+	0.227762i	0.684106	−	0.729382i	$-0.260192\pi$
$263$	6.39765	+	3.69369i	0.394496	+	0.227762i	−0.289610	+	0.957145i	$0.593526\pi$
$264$		0			0
$265$	8.03192	−	4.63723i	0.493397	−	0.284863i
$266$		0			0
$267$	−6.39260	+	2.00084i	−0.391221	+	0.122449i
$268$		0			0
$269$	−7.77076	−	7.77076i	−0.473792	−	0.473792i	0.429348	−	0.903139i	$-0.358744\pi$
$269$	−7.77076	−	7.77076i	−0.473792	−	0.473792i	−0.903139	+	0.429348i	$0.858744\pi$
$270$		0			0
$271$		−	15.0480i		−	0.914103i	−0.889440	−	0.457052i	$-0.848905\pi$
$271$		−	15.0480i		−	0.914103i	0.889440	−	0.457052i	$-0.151095\pi$
$272$		0			0
$273$	−1.06012	+	2.02608i	−0.0641615	+	0.122624i
$274$		0			0
$275$	−5.30024	−	1.42020i	−0.319617	−	0.0856410i
$276$		0			0
$277$	13.5306	−	3.62552i	0.812976	−	0.217836i	0.171702	−	0.985149i	$-0.445073\pi$
$277$	13.5306	−	3.62552i	0.812976	−	0.217836i	0.641273	+	0.767313i	$0.278407\pi$
$278$		0			0
$279$	−0.218602	+	0.463702i	−0.0130874	+	0.0277611i
$280$		0			0
$281$	7.72501	−	13.3801i	0.460835	−	0.798190i	−0.538167	−	0.842838i	$-0.680883\pi$
$281$	7.72501	−	13.3801i	0.460835	−	0.798190i	0.999003	+	0.0446477i	$0.0142165\pi$
$282$		0			0
$283$	−6.38640	−	1.71123i	−0.379632	−	0.101722i	0.0639565	−	0.997953i	$-0.479628\pi$
$283$	−6.38640	−	1.71123i	−0.379632	−	0.101722i	−0.443588	+	0.896231i	$0.646295\pi$
$284$		0			0
$285$	14.9171	+	13.7267i	0.883612	+	0.813100i
$286$		0			0
$287$	1.26727			0.0748046
$288$		0			0
$289$	7.64299			0.449588
$290$		0			0
$291$	−5.54816	+	24.7799i	−0.325239	+	1.45262i
$292$		0			0
$293$	15.6194	+	4.18520i	0.912493	+	0.244502i	0.684374	−	0.729131i	$-0.260076\pi$
$293$	15.6194	+	4.18520i	0.912493	+	0.244502i	0.228119	+	0.973633i	$0.426742\pi$
$294$		0			0
$295$	0.528201	−	0.914872i	0.0307531	−	0.0532659i
$296$		0			0
$297$	11.6924	−	27.7327i	0.678462	−	1.60922i
$298$		0			0
$299$	−16.1274	+	4.32134i	−0.932674	+	0.249909i
$300$		0			0
$301$	0.529601	+	0.141906i	0.0305257	+	0.00817934i
$302$		0			0
$303$	−2.26334	−	3.56925i	−0.130026	−	0.205048i
$304$		0			0
$305$			6.26661i			0.358825i
$306$		0			0
$307$	7.76011	+	7.76011i	0.442893	+	0.442893i	0.892983	−	0.450090i	$-0.148608\pi$
$307$	7.76011	+	7.76011i	0.442893	+	0.442893i	−0.450090	+	0.892983i	$0.648608\pi$
$308$		0			0
$309$	−5.10467	−	4.69732i	−0.290395	−	0.267221i
$310$		0			0
$311$	3.77550	−	2.17978i	0.214089	−	0.123604i	−0.389121	−	0.921186i	$-0.627221\pi$
$311$	3.77550	−	2.17978i	0.214089	−	0.123604i	0.603210	+	0.797582i	$0.293888\pi$
$312$		0			0
$313$	2.20758	+	1.27455i	0.124780	+	0.0720416i	0.561091	−	0.827754i	$-0.310382\pi$
$313$	2.20758	+	1.27455i	0.124780	+	0.0720416i	−0.436311	+	0.899796i	$0.643715\pi$
$314$		0			0
$315$	−0.691938	+	3.83009i	−0.0389863	+	0.215801i
$316$		0			0
$317$	−18.3388	+	4.91388i	−1.03001	+	0.275991i	−0.733969	−	0.679183i	$-0.762334\pi$
$317$	−18.3388	+	4.91388i	−1.03001	+	0.275991i	−0.296044	+	0.955174i	$0.595667\pi$
$318$		0			0
$319$	23.3235	−	13.4658i	1.30586	−	0.753941i
$320$		0			0
$321$	4.25515	+	2.22646i	0.237500	+	0.124269i
$322$		0			0
$323$	12.5752	−	12.5752i	0.699701	−	0.699701i
$324$		0			0
$325$	1.37230	+	1.37230i	0.0761216	+	0.0761216i
$326$		0			0
$327$	−12.2721	+	23.4541i	−0.678648	+	1.29702i
$328$		0			0
$329$	2.59377	+	4.49254i	0.142999	+	0.247681i
$330$		0			0
$331$	−5.58231	−	20.8335i	−0.306831	−	1.14511i	−0.931357	−	0.364106i	$-0.881374\pi$
$331$	−5.58231	−	20.8335i	−0.306831	−	1.14511i	0.624526	−	0.781004i	$-0.285292\pi$
$332$		0			0
$333$	−11.1022	−	2.00571i	−0.608398	−	0.109912i
$334$		0			0
$335$	2.26977	−	3.93135i	0.124011	−	0.214793i
$336$		0			0
$337$	8.17417	+	14.1581i	0.445275	+	0.771239i	0.998071	−	0.0620772i	$-0.0197725\pi$
$337$	8.17417	+	14.1581i	0.445275	+	0.771239i	−0.552796	+	0.833317i	$0.686439\pi$
$338$		0			0
$339$	−7.08552	+	7.69997i	−0.384832	+	0.418205i
$340$		0			0
$341$	−0.699874	+	0.699874i	−0.0379003	+	0.0379003i
$342$		0			0
$343$	8.75470			0.472709
$344$		0			0
$345$	−23.9999	+	15.2189i	−1.29211	+	0.819358i
$346$		0			0
$347$	−2.09454	+	7.81694i	−0.112441	+	0.419635i	−0.999083	−	0.0428214i	$-0.986365\pi$
$347$	−2.09454	+	7.81694i	−0.112441	+	0.419635i	0.886642	+	0.462457i	$0.153032\pi$
$348$		0			0
$349$	4.31180	+	16.0919i	0.230806	+	0.861378i	0.979995	+	0.199022i	$0.0637767\pi$
$349$	4.31180	+	16.0919i	0.230806	+	0.861378i	−0.749189	+	0.662356i	$0.769557\pi$
$350$		0			0
$351$	−8.48563	+	6.42677i	−0.452930	+	0.343035i
$352$		0			0
$353$	−11.3077	−	6.52852i	−0.601849	−	0.347478i	0.167919	−	0.985801i	$-0.446295\pi$
$353$	−11.3077	−	6.52852i	−0.601849	−	0.347478i	−0.769769	+	0.638323i	$0.779628\pi$
$354$		0			0
$355$	7.97897	−	29.7779i	0.423480	−	1.58045i
$356$		0			0
$357$	3.33196	+	0.746018i	0.176346	+	0.0394835i
$358$		0			0
$359$		−	21.1411i		−	1.11578i	−0.829914	−	0.557892i	$-0.811610\pi$
$359$		−	21.1411i		−	1.11578i	0.829914	−	0.557892i	$-0.188390\pi$
$360$		0			0
$361$			14.8003i			0.778966i
$362$		0			0
$363$	26.4460	−	28.7394i	1.38805	−	1.50843i
$364$		0			0
$365$	4.86533	−	18.1576i	0.254663	−	0.950415i
$366$		0			0
$367$	−27.7535	−	16.0235i	−1.44872	−	0.836419i	−0.450315	−	0.892870i	$-0.648688\pi$
$367$	−27.7535	−	16.0235i	−1.44872	−	0.836419i	−0.998405	+	0.0564512i	$0.982021\pi$
$368$		0			0
$369$	5.33604	+	2.51556i	0.277783	+	0.130955i
$370$		0			0
$371$	0.768436	+	2.86784i	0.0398952	+	0.148891i
$372$		0			0
$373$	−0.185580	+	0.692592i	−0.00960894	+	0.0358611i	−0.970564	−	0.240844i	$-0.922576\pi$
$373$	−0.185580	+	0.692592i	−0.00960894	+	0.0358611i	0.960955	+	0.276705i	$0.0892425\pi$
$374$		0			0
$375$	18.3741	+	9.61404i	0.948836	+	0.496467i
$376$		0			0
$377$	−9.52522			−0.490574
$378$		0			0
$379$	3.65005	−	3.65005i	0.187491	−	0.187491i	−0.607120	−	0.794610i	$-0.707675\pi$
$379$	3.65005	−	3.65005i	0.187491	−	0.187491i	0.794610	+	0.607120i	$0.207675\pi$
$380$		0			0
$381$	−3.05499	−	9.76057i	−0.156512	−	0.500049i
$382$		0			0
$383$	9.73635	+	16.8639i	0.497504	+	0.861703i	0.999996	−	0.00287933i	$-0.000916521\pi$
$383$	9.73635	+	16.8639i	0.497504	+	0.861703i	−0.502492	+	0.864582i	$0.667583\pi$
$384$		0			0
$385$	−3.75724	+	6.50774i	−0.191487	+	0.331665i
$386$		0			0
$387$	1.94828	+	1.64879i	0.0990368	+	0.0838127i
$388$		0			0
$389$	0.0834155	+	0.311311i	0.00422934	+	0.0157841i	0.968008	−	0.250918i	$-0.0807326\pi$
$389$	0.0834155	+	0.311311i	0.00422934	+	0.0157841i	−0.963779	+	0.266702i	$0.914066\pi$
$390$		0			0
$391$	12.4655	+	21.5909i	0.630407	+	1.09190i
$392$		0			0
$393$	2.79311	−	0.116077i	0.140894	−	0.00585530i
$394$		0			0
$395$	−15.5215	−	15.5215i	−0.780972	−	0.780972i
$396$		0			0
$397$	3.56364	−	3.56364i	0.178854	−	0.178854i	−0.612002	−	0.790856i	$-0.709636\pi$
$397$	3.56364	−	3.56364i	0.178854	−	0.178854i	0.790856	+	0.612002i	$0.209636\pi$
$398$		0			0
$399$	−5.48052	+	3.47533i	−0.274369	+	0.173984i
$400$		0			0
$401$	−16.5507	+	9.55556i	−0.826503	+	0.477182i	−0.852654	−	0.522476i	$-0.825008\pi$
$401$	−16.5507	+	9.55556i	−0.826503	+	0.477182i	0.0261506	+	0.999658i	$0.491675\pi$
$402$		0			0
$403$	0.338136	−	0.0906033i	0.0168438	−	0.00451327i
$404$		0			0
$405$	−10.5163	+	14.7537i	−0.522561	+	0.733116i
$406$		0			0
$407$	−18.8639	−	10.8911i	−0.935049	−	0.539851i
$408$		0			0
$409$	−11.7821	+	6.80241i	−0.582589	+	0.336358i	−0.762161	−	0.647387i	$-0.775862\pi$
$409$	−11.7821	+	6.80241i	−0.582589	+	0.336358i	0.179573	+	0.983745i	$0.442528\pi$
$410$		0			0
$411$	−4.20298	+	18.7719i	−0.207318	+	0.925948i
$412$		0			0
$413$	0.239132	+	0.239132i	0.0117669	+	0.0117669i
$414$		0			0
$415$			25.7652i			1.26476i
$416$		0			0
$417$	−20.0076	+	0.831479i	−0.979775	+	0.0407177i
$418$		0			0
$419$	7.80143	+	2.09039i	0.381125	+	0.102122i	0.444295	−	0.895881i	$-0.353454\pi$
$419$	7.80143	+	2.09039i	0.381125	+	0.102122i	−0.0631698	+	0.998003i	$0.520121\pi$
$420$		0			0
$421$	15.3973	−	4.12570i	0.750419	−	0.201074i	0.136715	−	0.990610i	$-0.456345\pi$
$421$	15.3973	−	4.12570i	0.750419	−	0.201074i	0.613704	+	0.789536i	$0.289679\pi$
$422$		0			0
$423$	2.00367	+	24.0652i	0.0974220	+	1.17009i
$424$		0			0
$425$	1.44895	−	2.50965i	0.0702842	−	0.121736i
$426$		0			0
$427$	−1.93776	−	0.519221i	−0.0937747	−	0.0251268i
$428$		0			0
$429$	−19.6135	+	6.13889i	−0.946950	+	0.296388i
$430$		0			0
$431$	0.112162			0.00540266			0.00270133	−	0.999996i	$-0.499140\pi$
$431$	0.112162			0.00540266			0.00270133	+	0.999996i	$0.499140\pi$
$432$		0			0
$433$	20.7054			0.995038			0.497519	−	0.867453i	$-0.334244\pi$
$433$	20.7054			0.995038			0.497519	+	0.867453i	$0.334244\pi$
$434$		0			0
$435$	−15.4725	+	4.84277i	−0.741849	+	0.232193i
$436$		0			0
$437$	−45.7694	−	12.2639i	−2.18945	−	0.586661i
$438$		0			0
$439$	19.9756	−	34.5988i	0.953384	−	1.65131i	0.215361	−	0.976534i	$-0.430907\pi$
$439$	19.9756	−	34.5988i	0.953384	−	1.65131i	0.738023	−	0.674776i	$-0.235760\pi$
$440$		0			0
$441$	17.8680	+	8.42350i	0.850859	+	0.401119i
$442$		0			0
$443$	−4.52965	+	1.21372i	−0.215210	+	0.0576654i	−0.364813	−	0.931081i	$-0.618867\pi$
$443$	−4.52965	+	1.21372i	−0.215210	+	0.0576654i	0.149603	+	0.988746i	$0.452200\pi$
$444$		0			0
$445$	7.52010	+	2.01501i	0.356487	+	0.0955204i
$446$		0			0
$447$	38.1267	−	1.58448i	1.80333	−	0.0749432i
$448$		0			0
$449$			0.895625i			0.0422672i	0.999777	+	0.0211336i	$0.00672753\pi$
$449$			0.895625i			0.0422672i	−0.999777	+	0.0211336i	$0.993272\pi$
$450$		0			0
$451$	8.05379	+	8.05379i	0.379238	+	0.379238i
$452$		0			0
$453$	6.15448	−	27.4879i	0.289163	−	1.29149i
$454$		0			0
$455$	2.30167	−	1.32887i	0.107904	−	0.0622983i
$456$		0			0
$457$	−28.9564	−	16.7180i	−1.35453	−	0.782036i	−0.365646	−	0.930754i	$-0.619152\pi$
$457$	−28.9564	−	16.7180i	−1.35453	−	0.782036i	−0.988880	+	0.148719i	$0.952485\pi$
$458$		0			0
$459$	12.5489	+	9.75525i	0.585731	+	0.455336i
$460$		0			0
$461$	−4.83893	+	1.29659i	−0.225371	+	0.0603881i	−0.369738	−	0.929136i	$-0.620552\pi$
$461$	−4.83893	+	1.29659i	−0.225371	+	0.0603881i	0.144366	+	0.989524i	$0.453886\pi$
$462$		0			0
$463$	−16.0584	+	9.27134i	−0.746299	+	0.430876i	−0.824355	−	0.566073i	$-0.808462\pi$
$463$	−16.0584	+	9.27134i	−0.746299	+	0.430876i	0.0780562	+	0.996949i	$0.475129\pi$
$464$		0			0
$465$	0.503194	−	0.319087i	0.0233351	−	0.0147973i
$466$		0			0
$467$	−13.6565	+	13.6565i	−0.631948	+	0.631948i	−0.948556	−	0.316608i	$-0.897456\pi$
$467$	−13.6565	+	13.6565i	−0.631948	+	0.631948i	0.316608	+	0.948556i	$0.397456\pi$
$468$		0			0
$469$	1.02759	+	1.02759i	0.0474497	+	0.0474497i
$470$		0			0
$471$	−41.1777	+	1.71127i	−1.89737	+	0.0788512i
$472$		0			0
$473$	2.46389	+	4.26758i	0.113290	+	0.196224i
$474$		0			0
$475$	1.42551	+	5.32008i	0.0654069	+	0.244102i
$476$		0			0
$477$	−2.45712	+	13.6009i	−0.112504	+	0.622741i
$478$		0			0
$479$	1.37861	−	2.38783i	0.0629904	−	0.109103i	−0.832810	−	0.553558i	$-0.813270\pi$
$479$	1.37861	−	2.38783i	0.0629904	−	0.109103i	0.895801	+	0.444456i	$0.146603\pi$
$480$		0			0
$481$	3.85198	+	6.67182i	0.175635	+	0.304209i
$482$		0			0
$483$	−2.71746	−	8.68219i	−0.123649	−	0.395053i
$484$		0			0
$485$	20.8696	−	20.8696i	0.947639	−	0.947639i
$486$		0			0
$487$	−17.4202			−0.789383			−0.394692	−	0.918814i	$-0.629149\pi$
$487$	−17.4202			−0.789383			−0.394692	+	0.918814i	$0.629149\pi$
$488$		0			0
$489$	24.7828	+	12.9673i	1.12071	+	0.586400i
$490$		0			0
$491$	4.32873	−	16.1550i	0.195353	−	0.729066i	−0.796822	−	0.604213i	$-0.793487\pi$
$491$	4.32873	−	16.1550i	0.195353	−	0.729066i	0.992175	−	0.124853i	$-0.0398459\pi$
$492$		0			0
$493$	3.68120	+	13.7384i	0.165793	+	0.618747i
$494$		0			0
$495$	−28.7385	+	19.9436i	−1.29170	+	0.896400i
$496$		0			0
$497$	8.54681	+	4.93450i	0.383377	+	0.221343i
$498$		0			0
$499$	8.60246	−	32.1048i	0.385099	−	1.43721i	−0.452911	−	0.891556i	$-0.649615\pi$
$499$	8.60246	−	32.1048i	0.385099	−	1.43721i	0.838011	−	0.545654i	$-0.183719\pi$
$500$		0			0
$501$	−0.578590	+	0.628765i	−0.0258495	+	0.0280912i
$502$		0			0
$503$		−	5.04620i		−	0.224999i	−0.993652	−	0.112499i	$-0.964114\pi$
$503$		−	5.04620i		−	0.224999i	0.993652	−	0.112499i	$-0.0358857\pi$
$504$		0			0
$505$			4.91221i			0.218590i
$506$		0			0
$507$	−14.8795	−	3.33148i	−0.660821	−	0.147956i
$508$		0			0
$509$	−10.6205	+	39.6362i	−0.470745	+	1.75684i	0.166360	+	0.986065i	$0.446799\pi$
$509$	−10.6205	+	39.6362i	−0.470745	+	1.75684i	−0.637105	+	0.770777i	$0.719868\pi$
$510$		0			0
$511$	5.21158	+	3.00891i	0.230547	+	0.133106i
$512$		0			0
$513$	−29.9752	+	3.75445i	−1.32344	+	0.165763i
$514$		0			0
$515$	2.08679	+	7.78801i	0.0919549	+	0.343181i
$516$		0			0
$517$	−12.0671	+	45.0351i	−0.530711	+	1.98064i
$518$		0			0
$519$	30.0074	−	19.0284i	1.31718	−	0.835254i
$520$		0			0
$521$	−10.9553			−0.479963			−0.239981	−	0.970778i	$-0.577141\pi$
$521$	−10.9553			−0.479963			−0.239981	+	0.970778i	$0.577141\pi$
$522$		0			0
$523$	−8.18896	+	8.18896i	−0.358078	+	0.358078i	−0.863104	−	0.505026i	$-0.831483\pi$
$523$	−8.18896	+	8.18896i	−0.358078	+	0.358078i	0.505026	+	0.863104i	$0.331483\pi$
$524$		0			0
$525$	−0.716049	+	0.778145i	−0.0312509	+	0.0339610i
$526$		0			0
$527$	−0.261358	−	0.452685i	−0.0113849	−	0.0197193i
$528$		0			0
$529$	21.7133	−	37.6085i	0.944056	−	1.63515i
$530$		0			0
$531$	0.532220	+	1.48159i	0.0230964	+	0.0642953i
$532$		0			0
$533$	−1.04262	−	3.89110i	−0.0451607	−	0.168542i
$534$		0			0
$535$	−2.79088	−	4.83394i	−0.120660	−	0.208989i
$536$		0			0
$537$	−8.51100	+	16.2660i	−0.367277	+	0.701931i
$538$		0			0
$539$	26.9686	+	26.9686i	1.16162	+	1.16162i
$540$		0			0
$541$	−16.3651	+	16.3651i	−0.703590	+	0.703590i	−0.965179	−	0.261589i	$-0.915753\pi$
$541$	−16.3651	+	16.3651i	−0.703590	+	0.703590i	0.261589	+	0.965179i	$0.415753\pi$
$542$		0			0
$543$	1.90877	+	0.998740i	0.0819131	+	0.0428600i
$544$		0			0
$545$	26.6444	−	15.3831i	1.14132	−	0.658941i
$546$		0			0
$547$	−23.6196	+	6.32886i	−1.00990	+	0.270603i	−0.725589	−	0.688129i	$-0.758432\pi$
$547$	−23.6196	+	6.32886i	−1.00990	+	0.270603i	−0.284314	+	0.958731i	$0.591766\pi$
$548$		0			0
$549$	−7.12857	−	6.03276i	−0.304240	−	0.257472i
$550$		0			0
$551$	−23.4108	−	13.5162i	−0.997332	−	0.575810i
$552$		0			0
$553$	6.08559	−	3.51352i	0.258786	−	0.149410i
$554$		0			0
$555$	9.64909	+	8.87910i	0.409581	+	0.376897i
$556$		0			0
$557$	−1.55709	−	1.55709i	−0.0659760	−	0.0659760i	0.673349	−	0.739325i	$-0.264855\pi$
$557$	−1.55709	−	1.55709i	−0.0659760	−	0.0659760i	−0.739325	+	0.673349i	$0.764855\pi$
$558$		0			0
$559$		−	1.74287i		−	0.0737154i
$560$		0			0
$561$	16.4342	+	25.9165i	0.693854	+	1.09419i
$562$		0			0
$563$	29.3036	+	7.85187i	1.23500	+	0.330917i	0.816524	−	0.577311i	$-0.195898\pi$
$563$	29.3036	+	7.85187i	1.23500	+	0.330917i	0.418475	+	0.908228i	$0.362565\pi$
$564$		0			0
$565$	11.7476	−	3.14775i	0.494224	−	0.132427i
$566$		0			0
$567$	−3.69079	−	4.47427i	−0.154999	−	0.187902i
$568$		0			0
$569$	11.5050	−	19.9273i	0.482316	−	0.835395i	−0.517478	−	0.855696i	$-0.673129\pi$
$569$	11.5050	−	19.9273i	0.482316	−	0.835395i	0.999794	+	0.0203012i	$0.00646252\pi$
$570$		0			0
$571$	14.1061	+	3.77973i	0.590324	+	0.158177i	0.541601	−	0.840636i	$-0.317818\pi$
$571$	14.1061	+	3.77973i	0.590324	+	0.158177i	0.0487226	+	0.998812i	$0.484485\pi$
$572$		0			0
$573$	3.00898	−	13.4391i	0.125702	−	0.561425i
$574$		0			0
$575$	−7.72120			−0.321996
$576$		0			0
$577$	−18.7394			−0.780130			−0.390065	−	0.920787i	$-0.627548\pi$
$577$	−18.7394			−0.780130			−0.390065	+	0.920787i	$0.627548\pi$
$578$		0			0
$579$	−7.53111	−	6.93013i	−0.312982	−	0.288006i
$580$		0			0
$581$	−7.96709	−	2.13478i	−0.330531	−	0.0885654i
$582$		0			0
$583$	−13.3422	+	23.1094i	−0.552578	+	0.957093i
$584$		0			0
$585$	12.3294	−	1.02655i	0.509757	−	0.0424425i
$586$		0			0
$587$	13.9200	−	3.72984i	0.574538	−	0.153947i	0.0401610	−	0.999193i	$-0.487213\pi$
$587$	13.9200	−	3.72984i	0.574538	−	0.153947i	0.534377	+	0.845246i	$0.320546\pi$
$588$		0			0
$589$	0.959624	+	0.257131i	0.0395406	+	0.0105949i
$590$		0			0
$591$	−13.2515	+	25.3260i	−0.545095	+	1.04177i
$592$		0			0
$593$			11.6038i			0.476512i	0.971202	+	0.238256i	$0.0765758\pi$
$593$			11.6038i			0.476512i	−0.971202	+	0.238256i	$0.923424\pi$
$594$		0			0
$595$	−2.80617	−	2.80617i	−0.115042	−	0.115042i
$596$		0			0
$597$	−1.04708	+	0.327728i	−0.0428541	+	0.0134130i
$598$		0			0
$599$	2.74819	−	1.58667i	0.112288	−	0.0648294i	−0.442804	−	0.896618i	$-0.646016\pi$
$599$	2.74819	−	1.58667i	0.112288	−	0.0648294i	0.555092	+	0.831789i	$0.312683\pi$
$600$		0			0
$601$	29.2389	+	16.8811i	1.19268	+	0.688593i	0.958913	−	0.283700i	$-0.0915620\pi$
$601$	29.2389	+	16.8811i	1.19268	+	0.688593i	0.233765	+	0.972293i	$0.424895\pi$
$602$		0			0
$603$	2.28704	+	6.36662i	0.0931354	+	0.259269i
$604$		0			0
$605$	−43.8466	+	11.7487i	−1.78262	+	0.477651i
$606$		0			0
$607$	−26.7618	+	15.4509i	−1.08623	+	0.627133i	−0.932569	−	0.360991i	$-0.882438\pi$
$607$	−26.7618	+	15.4509i	−1.08623	+	0.627133i	−0.153657	+	0.988124i	$0.549105\pi$
$608$		0			0
$609$	−0.215506	−	5.18564i	−0.00873273	−	0.210133i
$610$		0			0
$611$	11.6602	−	11.6602i	0.471720	−	0.471720i
$612$		0			0
$613$	−27.1318	−	27.1318i	−1.09584	−	1.09584i	−0.994891	−	0.100951i	$-0.967811\pi$
$613$	−27.1318	−	27.1318i	−1.09584	−	1.09584i	−0.100951	−	0.994891i	$-0.532189\pi$
$614$		0			0
$615$	−3.67189	−	5.79049i	−0.148065	−	0.233495i
$616$		0			0
$617$	4.23780	+	7.34009i	0.170607	+	0.295501i	0.938632	−	0.344919i	$-0.112094\pi$
$617$	4.23780	+	7.34009i	0.170607	+	0.295501i	−0.768025	+	0.640420i	$0.778760\pi$
$618$		0			0
$619$	6.55190	+	24.4520i	0.263343	+	0.982810i	0.963257	+	0.268582i	$0.0865552\pi$
$619$	6.55190	+	24.4520i	0.263343	+	0.982810i	−0.699914	+	0.714228i	$0.746778\pi$
$620$		0			0
$621$	5.79205	−	41.9520i	0.232427	−	1.68348i
$622$		0			0
$623$	−1.24616	+	2.15841i	−0.0499262	+	0.0864748i
$624$		0			0
$625$	−9.68286	−	16.7712i	−0.387315	−	0.670848i
$626$		0			0
$627$	−56.9165	−	12.7435i	−2.27302	−	0.508925i
$628$		0			0
$629$	8.13423	−	8.13423i	0.324333	−	0.324333i
$630$		0			0
$631$	−32.2960			−1.28568			−0.642842	−	0.765999i	$-0.722245\pi$
$631$	−32.2960			−1.28568			−0.642842	+	0.765999i	$0.722245\pi$
$632$		0			0
$633$	1.54015	+	37.0600i	0.0612153	+	1.47300i
$634$		0			0
$635$	−3.07662	+	11.4821i	−0.122092	+	0.455654i
$636$		0			0
$637$	−3.49126	−	13.0295i	−0.138329	−	0.516249i
$638$		0			0
$639$	26.1926	+	37.7432i	1.03616	+	1.49310i
$640$		0			0
$641$	27.0376	+	15.6102i	1.06792	+	0.616564i	0.927613	−	0.373544i	$-0.121857\pi$
$641$	27.0376	+	15.6102i	1.06792	+	0.616564i	0.140308	+	0.990108i	$0.455191\pi$
$642$		0			0
$643$	4.88530	−	18.2322i	0.192657	−	0.719007i	−0.800204	−	0.599728i	$-0.795275\pi$
$643$	4.88530	−	18.2322i	0.192657	−	0.719007i	0.992861	−	0.119278i	$-0.0380581\pi$
$644$		0			0
$645$	−0.886101	−	2.83106i	−0.0348902	−	0.111473i
$646$		0			0
$647$			25.7862i			1.01376i	0.862017	+	0.506879i	$0.169201\pi$
$647$			25.7862i			1.01376i	−0.862017	+	0.506879i	$0.830799\pi$
$648$		0			0
$649$			3.03948i			0.119310i
$650$		0			0
$651$	0.0569757	+	0.182035i	0.00223305	+	0.00713452i
$652$		0			0
$653$	−2.62920	+	9.81233i	−0.102889	+	0.383986i	−0.998097	−	0.0616618i	$-0.980360\pi$
$653$	−2.62920	+	9.81233i	−0.102889	+	0.383986i	0.895208	+	0.445648i	$0.147027\pi$
$654$		0			0
$655$	−2.81386	−	1.62458i	−0.109947	−	0.0634777i
$656$		0			0
$657$	15.9714	+	23.0146i	0.623105	+	0.897885i
$658$		0			0
$659$	−2.84300	−	10.6102i	−0.110748	−	0.413316i	0.888186	−	0.459484i	$-0.151966\pi$
$659$	−2.84300	−	10.6102i	−0.110748	−	0.413316i	−0.998934	+	0.0461683i	$0.985299\pi$
$660$		0			0
$661$	5.96571	−	22.2643i	0.232039	−	0.865982i	−0.747422	−	0.664350i	$-0.768709\pi$
$661$	5.96571	−	22.2643i	0.232039	−	0.865982i	0.979461	−	0.201633i	$-0.0646247\pi$
$662$		0			0
$663$	−0.450673	−	10.8444i	−0.0175027	−	0.421161i
$664$		0			0
$665$	7.54261			0.292490
$666$		0			0
$667$	26.7966	−	26.7966i	1.03757	−	1.03757i
$668$		0			0
$669$	25.7190	+	5.75842i	0.994352	+	0.222633i
$670$		0			0
$671$	−9.01513	−	15.6147i	−0.348025	−	0.602797i
$672$		0			0
$673$	−0.408559	+	0.707645i	−0.0157488	+	0.0272777i	−0.873792	−	0.486299i	$-0.838347\pi$
$673$	−0.408559	+	0.707645i	−0.0157488	+	0.0272777i	0.858044	+	0.513577i	$0.171680\pi$
$674$		0			0
$675$	−4.55967	+	1.85513i	−0.175502	+	0.0714039i
$676$		0			0
$677$	8.56517	+	31.9657i	0.329186	+	1.22854i	0.910036	+	0.414529i	$0.136054\pi$
$677$	8.56517	+	31.9657i	0.329186	+	1.22854i	−0.580850	+	0.814011i	$0.697280\pi$
$678$		0			0
$679$	4.72413	+	8.18243i	0.181295	+	0.314013i
$680$		0			0
$681$	−13.9813	−	22.0483i	−0.535765	−	0.844891i
$682$		0			0
$683$	−21.1555	−	21.1555i	−0.809494	−	0.809494i	0.175063	−	0.984557i	$-0.443987\pi$
$683$	−21.1555	−	21.1555i	−0.809494	−	0.809494i	−0.984557	+	0.175063i	$0.943987\pi$
$684$		0			0
$685$	15.8097	−	15.8097i	0.604056	−	0.604056i
$686$		0			0
$687$	0.773828	+	18.6203i	0.0295234	+	0.710410i
$688$		0			0
$689$	8.17337	−	4.71890i	0.311381	−	0.179776i
$690$		0			0
$691$	24.5275	−	6.57213i	0.933071	−	0.250016i	0.239908	−	0.970796i	$-0.422883\pi$
$691$	24.5275	−	6.57213i	0.933071	−	0.250016i	0.693164	+	0.720780i	$0.256216\pi$
$692$		0			0
$693$	−3.78583	−	10.5389i	−0.143812	−	0.400341i
$694$		0			0
$695$	20.1562	+	11.6372i	0.764568	+	0.441423i
$696$		0			0
$697$	−5.20926	+	3.00757i	−0.197315	+	0.113920i
$698$		0			0
$699$	−3.40045	+	1.06432i	−0.128617	+	0.0402561i
$700$		0			0
$701$	−15.7130	−	15.7130i	−0.593472	−	0.593472i	0.345096	−	0.938568i	$-0.387847\pi$
$701$	−15.7130	−	15.7130i	−0.593472	−	0.593472i	−0.938568	+	0.345096i	$0.887847\pi$
$702$		0			0
$703$			21.8637i			0.824605i
$704$		0			0
$705$	13.0122	−	24.8686i	0.490068	−	0.936607i
$706$		0			0
$707$	−1.51895	−	0.407001i	−0.0571260	−	0.0153069i
$708$		0			0
$709$	−4.97496	+	1.33304i	−0.186838	+	0.0500632i	−0.351025	−	0.936366i	$-0.614167\pi$
$709$	−4.97496	+	1.33304i	−0.186838	+	0.0500632i	0.164187	+	0.986429i	$0.447500\pi$
$710$		0			0
$711$	32.5988	−	2.71418i	1.22255	−	0.101790i
$712$		0			0
$713$	−0.696366	+	1.20614i	−0.0260791	+	0.0451704i
$714$		0			0
$715$	23.0729	+	6.18236i	0.862877	+	0.231207i
$716$		0			0
$717$	−10.3950	−	9.56552i	−0.388210	−	0.357231i
$718$		0			0
$719$	21.0741			0.785932			0.392966	−	0.919553i	$-0.371449\pi$
$719$	21.0741			0.785932			0.392966	+	0.919553i	$0.371449\pi$
$720$		0			0
$721$	−2.58110			−0.0961253
$722$		0			0
$723$	4.41061	−	19.6992i	0.164032	−	0.732622i
$724$		0			0
$725$	−4.25483	−	1.14008i	−0.158020	−	0.0423414i
$726$		0			0
$727$	−6.94402	+	12.0274i	−0.257539	+	0.446071i	−0.965582	−	0.260098i	$-0.916245\pi$
$727$	−6.94402	+	12.0274i	−0.257539	+	0.446071i	0.708043	+	0.706169i	$0.249578\pi$
$728$		0			0
$729$	−6.65913	−	26.1659i	−0.246634	−	0.969109i
$730$		0			0
$731$	−2.51377	+	0.673562i	−0.0929751	+	0.0249126i
$732$		0			0
$733$	−33.3201	−	8.92809i	−1.23071	−	0.329767i	−0.415851	−	0.909433i	$-0.636516\pi$
$733$	−33.3201	−	8.92809i	−1.23071	−	0.329767i	−0.814854	+	0.579666i	$0.803183\pi$
$734$		0			0
$735$	−12.2955	−	19.3898i	−0.453527	−	0.715203i
$736$		0			0
$737$			13.0611i			0.481113i
$738$		0			0
$739$	14.5953	+	14.5953i	0.536895	+	0.536895i	0.922616	−	0.385721i	$-0.126047\pi$
$739$	14.5953	+	14.5953i	0.536895	+	0.536895i	−0.385721	+	0.922616i	$0.626047\pi$
$740$		0			0
$741$	15.1798	+	13.9684i	0.557644	+	0.513144i
$742$		0			0
$743$	−45.2494	+	26.1248i	−1.66004	+	0.958424i	−0.687347	+	0.726330i	$0.741225\pi$
$743$	−45.2494	+	26.1248i	−1.66004	+	0.958424i	−0.972693	+	0.232095i	$0.925442\pi$
$744$		0			0
$745$	−38.4099	−	22.1760i	−1.40723	−	0.812464i
$746$		0			0
$747$	−29.3091	−	24.8037i	−1.07237	−	0.907520i
$748$		0			0
$749$	1.72599	−	0.462476i	0.0630661	−	0.0168985i
$750$		0			0
$751$	−12.4720	+	7.20072i	−0.455110	+	0.262758i	−0.709986	−	0.704216i	$-0.751299\pi$
$751$	−12.4720	+	7.20072i	−0.455110	+	0.262758i	0.254876	+	0.966974i	$0.417965\pi$
$752$		0			0
$753$	0.142985	+	0.0748154i	0.00521068	+	0.00272642i
$754$		0			0
$755$	−23.1503	+	23.1503i	−0.842526	+	0.842526i
$756$		0			0
$757$	−18.7302	−	18.7302i	−0.680761	−	0.680761i	0.279411	−	0.960172i	$-0.409861\pi$
$757$	−18.7302	−	18.7302i	−0.680761	−	0.680761i	−0.960172	+	0.279411i	$0.909861\pi$
$758$		0			0
$759$	37.9072	−	72.4474i	1.37594	−	2.62967i
$760$		0			0
$761$	−22.9842	−	39.8099i	−0.833178	−	1.44311i	−0.895505	−	0.445050i	$-0.853186\pi$
$761$	−22.9842	−	39.8099i	−0.833178	−	1.44311i	0.0623277	−	0.998056i	$-0.480148\pi$
$762$		0			0
$763$	2.54914	+	9.51352i	0.0922851	+	0.344413i
$764$		0			0
$765$	−6.24552	−	17.3862i	−0.225807	−	0.628598i
$766$		0			0
$767$	0.537503	−	0.930983i	0.0194081	−	0.0336159i
$768$		0			0
$769$	8.08642	+	14.0061i	0.291604	+	0.505072i	0.974189	−	0.225733i	$-0.0724778\pi$
$769$	8.08642	+	14.0061i	0.291604	+	0.505072i	−0.682585	+	0.730806i	$0.739144\pi$
$770$		0			0
$771$	20.0228	−	21.7591i	0.721102	−	0.783636i
$772$		0			0
$773$	−3.33435	+	3.33435i	−0.119928	+	0.119928i	−0.764524	−	0.644596i	$-0.777026\pi$
$773$	−3.33435	+	3.33435i	−0.119928	+	0.119928i	0.644596	+	0.764524i	$0.277026\pi$
$774$		0			0
$775$	0.161887			0.00581514
$776$		0			0
$777$	−3.54506	+	2.24801i	−0.127178	+	0.0806468i
$778$		0			0
$779$	2.95893	−	11.0429i	0.106015	−	0.395652i
$780$		0			0
$781$	22.9570	+	85.6769i	0.821468	+	3.06576i
$782$		0			0
$783$	9.38620	−	22.2627i	0.335435	−	0.795605i
$784$		0			0
$785$	41.4835	+	23.9505i	1.48061	+	0.854831i
$786$		0			0
$787$	−0.0125528	+	0.0468477i	−0.000447460	+	0.00166994i	−0.966149	−	0.257984i	$-0.916942\pi$
$787$	−0.0125528	+	0.0468477i	−0.000447460	+	0.00166994i	0.965702	+	0.259654i	$0.0836085\pi$
$788$		0			0
$789$	12.4862	+	2.79562i	0.444519	+	0.0995269i
$790$		0			0
$791$			3.89338i			0.138433i
$792$		0			0
$793$			6.37697i			0.226453i
$794$		0			0
$795$	10.8774	−	11.8207i	0.385782	−	0.419237i
$796$		0			0
$797$	−5.10564	+	19.0545i	−0.180851	+	0.674945i	0.814630	+	0.579981i	$0.196940\pi$
$797$	−5.10564	+	19.0545i	−0.180851	+	0.674945i	−0.995481	+	0.0949636i	$0.969727\pi$
$798$		0			0
$799$	−21.3240	−	12.3114i	−0.754388	−	0.435546i
$800$		0			0
$801$	−9.53164	+	6.61467i	−0.336784	+	0.233718i
$802$		0			0
$803$	13.9985	+	52.2431i	0.493996	+	1.84362i
$804$		0			0
$805$	−2.73671	+	10.2135i	−0.0964562	+	0.359980i
$806$		0			0
$807$	−16.8652	−	8.82453i	−0.593685	−	0.310638i
$808$		0			0
$809$	20.7043			0.727925			0.363963	−	0.931414i	$-0.381424\pi$
$809$	20.7043			0.727925			0.363963	+	0.931414i	$0.381424\pi$
$810$		0			0
$811$	−14.8452	+	14.8452i	−0.521285	+	0.521285i	−0.917959	−	0.396675i	$-0.870164\pi$
$811$	−14.8452	+	14.8452i	−0.521285	+	0.521285i	0.396675	+	0.917959i	$0.370164\pi$
$812$		0			0
$813$	−7.78540	−	24.8740i	−0.273046	−	0.872371i
$814$		0			0
$815$	−16.2545	−	28.1537i	−0.569372	−	0.986181i
$816$		0			0
$817$	2.47311	−	4.28356i	0.0865232	−	0.149863i
$818$		0			0
$819$	−0.704124	+	3.89754i	−0.0246041	+	0.136191i
$820$		0			0
$821$	−7.48593	−	27.9379i	−0.261261	−	0.975038i	−0.964500	−	0.264084i	$-0.914930\pi$
$821$	−7.48593	−	27.9379i	−0.261261	−	0.975038i	0.703239	−	0.710954i	$-0.251736\pi$
$822$		0			0
$823$	21.2527	+	36.8108i	0.740823	+	1.28314i	0.952121	+	0.305722i	$0.0988978\pi$
$823$	21.2527	+	36.8108i	0.740823	+	1.28314i	−0.211297	+	0.977422i	$0.567769\pi$
$824$		0			0
$825$	−9.49594	+	0.394634i	−0.330606	+	0.0137394i
$826$		0			0
$827$	11.9196	+	11.9196i	0.414485	+	0.414485i	0.883298	−	0.468812i	$-0.155318\pi$
$827$	11.9196	+	11.9196i	0.414485	+	0.414485i	−0.468812	+	0.883298i	$0.655318\pi$
$828$		0			0
$829$	9.25865	−	9.25865i	0.321566	−	0.321566i	−0.527801	−	0.849368i	$-0.676983\pi$
$829$	9.25865	−	9.25865i	0.321566	−	0.321566i	0.849368	+	0.527801i	$0.176983\pi$
$830$		0			0
$831$	20.4900	−	12.9932i	0.710792	−	0.450730i
$832$		0			0
$833$	−17.4435	+	10.0710i	−0.604382	+	0.348940i
$834$		0			0
$835$	0.959284	−	0.257039i	0.0331974	−	0.00889521i
$836$		0			0
$837$	−0.121439	+	0.879586i	−0.00419755	+	0.0304030i
$838$		0			0
$839$	21.0564	+	12.1569i	0.726947	+	0.419703i	0.817304	−	0.576206i	$-0.195467\pi$
$839$	21.0564	+	12.1569i	0.726947	+	0.419703i	−0.0903570	+	0.995909i	$0.528801\pi$
$840$		0			0
$841$	−6.39158	+	3.69018i	−0.220399	+	0.127248i
$842$		0			0
$843$	5.84679	−	26.1137i	0.201374	−	0.899403i
$844$		0			0
$845$	12.5315	+	12.5315i	0.431096	+	0.431096i
$846$		0			0
$847$		−	14.5316i		−	0.499313i
$848$		0			0
$849$	−11.4419	+	0.475504i	−0.392685	+	0.0163193i
$850$		0			0
$851$	−29.6059	−	7.93286i	−1.01488	−	0.271935i
$852$		0			0
$853$	1.86281	−	0.499139i	0.0637814	−	0.0170902i	−0.226787	−	0.973944i	$-0.572822\pi$
$853$	1.86281	−	0.499139i	0.0637814	−	0.0170902i	0.290569	+	0.956854i	$0.406156\pi$
$854$		0			0
$855$	31.7594	+	14.9723i	1.08615	+	0.512041i
$856$		0			0
$857$	−15.0498	+	26.0670i	−0.514090	+	0.890431i	0.485776	+	0.874083i	$0.338537\pi$
$857$	−15.0498	+	26.0670i	−0.514090	+	0.890431i	−0.999866	+	0.0163473i	$0.994796\pi$
$858$		0			0
$859$	−45.9807	−	12.3205i	−1.56884	−	0.420370i	−0.633392	−	0.773831i	$-0.718338\pi$
$859$	−45.9807	−	12.3205i	−1.56884	−	0.420370i	−0.935449	+	0.353462i	$0.885004\pi$
$860$		0			0
$861$	2.09477	−	0.655647i	0.0713895	−	0.0223444i
$862$		0			0
$863$	−4.03429			−0.137329			−0.0686644	−	0.997640i	$-0.521874\pi$
$863$	−4.03429			−0.137329			−0.0686644	+	0.997640i	$0.521874\pi$
$864$		0			0
$865$	−41.2979			−1.40417
$866$		0			0
$867$	12.6337	−	3.95425i	0.429062	−	0.134293i
$868$		0			0
$869$	61.0045	+	16.3461i	2.06944	+	0.554504i
$870$		0			0
$871$	2.30974	−	4.00059i	0.0782626	−	0.135555i
$872$		0			0
$873$	3.64937	+	43.8310i	0.123513	+	1.48345i
$874$		0			0
$875$	7.45296	−	1.99702i	0.251956	−	0.0675114i
$876$		0			0
$877$	38.9169	+	10.4278i	1.31413	+	0.352120i	0.846776	−	0.531949i	$-0.178540\pi$
$877$	38.9169	+	10.4278i	1.31413	+	0.352120i	0.467355	+	0.884070i	$0.345207\pi$
$878$		0			0
$879$	27.9837	−	1.16295i	0.943868	−	0.0392254i
$880$		0			0
$881$		−	35.0413i		−	1.18057i	−0.807195	−	0.590285i	$-0.799015\pi$
$881$		−	35.0413i		−	1.18057i	0.807195	−	0.590285i	$-0.200985\pi$
$882$		0			0
$883$	−4.73704	−	4.73704i	−0.159414	−	0.159414i	0.622893	−	0.782307i	$-0.285957\pi$
$883$	−4.73704	−	4.73704i	−0.159414	−	0.159414i	−0.782307	+	0.622893i	$0.785957\pi$
$884$		0			0
$885$	0.399778	−	1.78554i	0.0134384	−	0.0600201i
$886$		0			0
$887$	12.6364	−	7.29561i	0.424288	−	0.244963i	−0.272623	−	0.962121i	$-0.587891\pi$
$887$	12.6364	−	7.29561i	0.424288	−	0.244963i	0.696910	+	0.717159i	$0.254558\pi$
$888$		0			0
$889$	−3.29558	−	1.90270i	−0.110530	−	0.0638146i
$890$		0			0
$891$	4.97919	−	51.8908i	0.166809	−	1.73841i
$892$		0			0
$893$	45.2036	−	12.1123i	1.51268	−	0.405322i
$894$		0			0
$895$	18.4785	−	10.6686i	0.617669	−	0.356612i
$896$		0			0
$897$	−24.4225	+	15.4869i	−0.815445	+	0.517093i
$898$		0			0
$899$	−0.561832	+	0.561832i	−0.0187381	+	0.0187381i
$900$		0			0
$901$	−9.96490	−	9.96490i	−0.331979	−	0.331979i
$902$		0			0
$903$	0.948836	−	0.0394319i	0.0315753	−	0.00131221i
$904$		0			0
$905$	−1.25193	−	2.16840i	−0.0416154	−	0.0720801i
$906$		0			0
$907$	−9.59805	−	35.8204i	−0.318698	−	1.18940i	−0.920497	−	0.390750i	$-0.872216\pi$
$907$	−9.59805	−	35.8204i	−0.318698	−	1.18940i	0.601799	−	0.798648i	$-0.294451\pi$
$908$		0			0
$909$	−5.58787	−	4.72889i	−0.185338	−	0.156848i
$910$		0			0
$911$	18.5603	−	32.1474i	0.614931	−	1.06509i	−0.375465	−	0.926837i	$-0.622517\pi$
$911$	18.5603	−	32.1474i	0.614931	−	1.06509i	0.990397	−	0.138256i	$-0.0441497\pi$
$912$		0			0
$913$	−37.0657	−	64.1997i	−1.22670	−	2.12470i
$914$		0			0
$915$	3.24215	+	10.3586i	0.107182	+	0.342443i
$916$		0			0
$917$	0.735495	−	0.735495i	0.0242882	−	0.0242882i
$918$		0			0
$919$	34.5722			1.14043			0.570215	−	0.821495i	$-0.306860\pi$
$919$	34.5722			1.14043			0.570215	+	0.821495i	$0.306860\pi$
$920$		0			0
$921$	16.8421	+	8.81243i	0.554967	+	0.290380i
$922$		0			0
$923$	8.11949	−	30.3023i	0.267256	−	0.997414i
$924$		0			0
$925$	0.922089	+	3.44128i	0.0303181	+	0.113149i
$926$		0			0
$927$	−10.8681	−	5.12355i	−0.356957	−	0.168280i
$928$		0			0
$929$	52.2313	+	30.1558i	1.71365	+	0.989378i	0.929509	+	0.368800i	$0.120231\pi$
$929$	52.2313	+	30.1558i	1.71365	+	0.989378i	0.784145	+	0.620578i	$0.213102\pi$
$930$		0			0
$931$	9.90812	−	36.9776i	0.324726	−	1.21189i
$932$		0			0
$933$	5.11305	−	5.55646i	0.167394	−	0.181910i
$934$		0			0
$935$		−	35.6678i		−	1.16646i
$936$		0			0
$937$		−	35.3168i		−	1.15375i	−0.816833	−	0.576874i	$-0.804272\pi$
$937$		−	35.3168i		−	1.15375i	0.816833	−	0.576874i	$-0.195728\pi$
$938$		0			0
$939$	4.30849	+	0.964660i	0.140602	+	0.0314805i
$940$		0			0
$941$	11.2160	−	41.8587i	0.365632	−	1.36456i	−0.500931	−	0.865487i	$-0.667009\pi$
$941$	11.2160	−	41.8587i	0.365632	−	1.36456i	0.866563	−	0.499069i	$-0.166324\pi$
$942$		0			0
$943$	13.8797	+	8.01342i	0.451984	+	0.260953i
$944$		0			0
$945$	0.837812	+	6.68903i	0.0272540	+	0.217594i
$946$		0			0
$947$	13.1777	+	49.1797i	0.428217	+	1.59813i	0.756797	+	0.653650i	$0.226763\pi$
$947$	13.1777	+	49.1797i	0.428217	+	1.59813i	−0.328581	+	0.944476i	$0.606570\pi$
$948$		0			0
$949$	4.95101	−	18.4774i	0.160717	−	0.599802i
$950$		0			0
$951$	−27.7714	+	17.6105i	−0.900549	+	0.571059i
$952$		0			0
$953$	36.4989			1.18231			0.591157	−	0.806556i	$-0.298671\pi$
$953$	36.4989			1.18231			0.591157	+	0.806556i	$0.298671\pi$
$954$		0			0
$955$	−11.3184	+	11.3184i	−0.366254	+	0.366254i
$956$		0			0
$957$	31.5863	−	34.3255i	1.02104	−	1.10959i
$958$		0			0
$959$	3.57874	+	6.19856i	0.115564	+	0.200162i
$960$		0			0
$961$	−15.4854	+	26.8215i	−0.499529	+	0.865210i
$962$		0			0
$963$	8.18557	+	1.47879i	0.263776	+	0.0476534i
$964$		0			0
$965$	3.07872	+	11.4899i	0.0991074	+	0.369874i
$966$		0			0
$967$	−8.71394	−	15.0930i	−0.280222	−	0.485358i	0.691218	−	0.722647i	$-0.257075\pi$
$967$	−8.71394	−	15.0930i	−0.280222	−	0.485358i	−0.971439	+	0.237289i	$0.923741\pi$
$968$		0			0
$969$	14.2804	−	27.2925i	0.458754	−	0.876760i
$970$		0			0
$971$	28.3062	+	28.3062i	0.908390	+	0.908390i	0.996142	−	0.0877520i	$-0.0279683\pi$
$971$	28.3062	+	28.3062i	0.908390	+	0.908390i	−0.0877520	+	0.996142i	$0.527968\pi$
$972$		0			0
$973$	−5.26848	+	5.26848i	−0.168900	+	0.168900i
$974$		0			0
$975$	2.97837	+	1.55839i	0.0953841	+	0.0499086i
$976$		0			0
$977$	1.76106	−	1.01675i	0.0563414	−	0.0325287i	−0.471565	−	0.881831i	$-0.656311\pi$
$977$	1.76106	−	1.01675i	0.0563414	−	0.0325287i	0.527906	+	0.849303i	$0.322977\pi$
$978$		0			0
$979$	−21.6368	+	5.79756i	−0.691515	+	0.185291i
$980$		0			0
$981$	−8.15101	+	45.1183i	−0.260242	+	1.44052i
$982$		0			0
$983$	−27.8069	−	16.0543i	−0.886903	−	0.512054i	−0.0139748	−	0.999902i	$-0.504448\pi$
$983$	−27.8069	−	16.0543i	−0.886903	−	0.512054i	−0.872928	+	0.487849i	$0.837782\pi$
$984$		0			0
$985$	28.7709	−	16.6109i	0.916716	−	0.529266i
$986$		0			0
$987$	6.61173	+	6.08412i	0.210454	+	0.193660i
$988$		0			0
$989$	4.90308	+	4.90308i	0.155909	+	0.155909i
$990$		0			0
$991$		−	22.8049i		−	0.724420i	−0.932096	−	0.362210i	$-0.882022\pi$
$991$		−	22.8049i		−	0.724420i	0.932096	−	0.362210i	$-0.117978\pi$
$992$		0			0
$993$	−20.0060	−	31.5491i	−0.634872	−	1.00118i
$994$		0			0
$995$	1.23176	+	0.330049i	0.0390494	+	0.0104632i
$996$		0			0
$997$	−35.2150	+	9.43584i	−1.11527	+	0.298836i	−0.768968	−	0.639287i	$-0.779230\pi$
$997$	−35.2150	+	9.43584i	−1.11527	+	0.298836i	−0.346303	+	0.938123i	$0.612563\pi$
$998$		0			0
$999$	−19.3894	+	2.42856i	−0.613454	+	0.0768362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.335.20		88
3.2	odd	2		1728.2.z.a.143.16		88
4.3	odd	2		144.2.u.a.11.13	✓	88
9.4	even	3		1728.2.z.a.719.16		88
9.5	odd	6	inner	576.2.y.a.527.10		88
12.11	even	2		432.2.v.a.251.10		88
16.3	odd	4	inner	576.2.y.a.47.10		88
16.13	even	4		144.2.u.a.83.21	yes	88
36.23	even	6		144.2.u.a.59.21	yes	88
36.31	odd	6		432.2.v.a.395.2		88
48.29	odd	4		432.2.v.a.35.2		88
48.35	even	4		1728.2.z.a.1007.16		88
144.13	even	12		432.2.v.a.179.10		88
144.67	odd	12		1728.2.z.a.1583.16		88
144.77	odd	12		144.2.u.a.131.13	yes	88
144.131	even	12	inner	576.2.y.a.239.20		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.13	✓	88	4.3	odd	2
144.2.u.a.59.21	yes	88	36.23	even	6
144.2.u.a.83.21	yes	88	16.13	even	4
144.2.u.a.131.13	yes	88	144.77	odd	12
432.2.v.a.35.2		88	48.29	odd	4
432.2.v.a.179.10		88	144.13	even	12
432.2.v.a.251.10		88	12.11	even	2
432.2.v.a.395.2		88	36.31	odd	6
576.2.y.a.47.10		88	16.3	odd	4	inner
576.2.y.a.239.20		88	144.131	even	12	inner
576.2.y.a.335.20		88	1.1	even	1	trivial
576.2.y.a.527.10		88	9.5	odd	6	inner
1728.2.z.a.143.16		88	3.2	odd	2
1728.2.z.a.719.16		88	9.4	even	3
1728.2.z.a.1007.16		88	48.35	even	4
1728.2.z.a.1583.16		88	144.67	odd	12

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.65298 - 0.517369i) q^{3} +(-1.94452 - 0.521033i) q^{5} +(0.322227 - 0.558114i) q^{7} +(2.46466 - 1.71040i) q^{9} +O(q^{10})\)	\(q+(1.65298 - 0.517369i) q^{3} +(-1.94452 - 0.521033i) q^{5} +(0.322227 - 0.558114i) q^{7} +(2.46466 - 1.71040i) q^{9} +(5.59477 - 1.49911i) q^{11} +(-1.97877 - 0.530209i) q^{13} +(-3.48381 + 0.144781i) q^{15} +3.05892i q^{17} +(-4.11098 - 4.11098i) q^{19} +(0.243883 - 1.08926i) q^{21} +(7.05832 - 4.07512i) q^{23} +(-0.820436 - 0.473679i) q^{25} +(3.18911 - 4.10239i) q^{27} +(4.49126 - 1.20343i) q^{29} +(-0.147988 + 0.0854411i) q^{31} +(8.47242 - 5.37256i) q^{33} +(-0.917373 + 0.917373i) q^{35} +(-2.65918 - 2.65918i) q^{37} +(-3.54517 + 0.147331i) q^{39} +(0.983212 + 1.70297i) q^{41} +(0.220196 + 0.821783i) q^{43} +(-5.68376 + 2.04174i) q^{45} +(-4.02475 + 6.97107i) q^{47} +(3.29234 + 5.70250i) q^{49} +(1.58259 + 5.05632i) q^{51} +(-3.25765 + 3.25765i) q^{53} -11.6602 q^{55} +(-8.92225 - 4.66846i) q^{57} +(-0.135818 + 0.506879i) q^{59} +(-0.805675 - 3.00682i) q^{61} +(-0.160417 - 1.92670i) q^{63} +(3.57150 + 2.06201i) q^{65} +(-0.583631 + 2.17814i) q^{67} +(9.55889 - 10.3878i) q^{69} +15.3137i q^{71} +9.33784i q^{73} +(-1.60123 - 0.358511i) q^{75} +(0.966110 - 3.60557i) q^{77} +(9.44301 + 5.45193i) q^{79} +(3.14908 - 8.43109i) q^{81} +(-3.31253 - 12.3625i) q^{83} +(1.59380 - 5.94814i) q^{85} +(6.80132 - 4.31288i) q^{87} -3.86733 q^{89} +(-0.933529 + 0.933529i) q^{91} +(-0.200417 + 0.217797i) q^{93} +(5.85194 + 10.1359i) q^{95} +(-7.33044 + 12.6967i) q^{97} +(11.2251 - 13.2641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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