LMFDB - Embedded newform 576.2.y.a.47.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [576,2,Mod(47,576)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			47.10
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.517369	−	1.65298i	−0.298703	−	0.954346i
$3$	−0.517369	−	1.65298i	−0.298703	−	0.954346i
$4$		0			0
$5$	−0.521033	+	1.94452i	−0.233013	+	0.869617i	0.746021	+	0.665922i	$0.231962\pi$
$5$	−0.521033	+	1.94452i	−0.233013	+	0.869617i	−0.979034	+	0.203695i	$0.934705\pi$
$6$		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
$11$	1.49911	+	5.59477i	0.452000	+	1.68689i	0.696762	+	0.717303i	$0.254623\pi$
$11$	1.49911	+	5.59477i	0.452000	+	1.68689i	−0.244762	+	0.969583i	$0.578710\pi$
$12$		0			0
$13$	0.530209	−	1.97877i	0.147054	−	0.548811i	−0.852602	−	0.522561i	$-0.824977\pi$
$13$	0.530209	−	1.97877i	0.147054	−	0.548811i	0.999655	−	0.0262502i	$-0.00835665\pi$
$14$		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	−0.998467	−	0.0553434i	$-0.982375\pi$
$19$	−4.11098	+	4.11098i	−0.943124	+	0.943124i	0.0553434	+	0.998467i	$0.482375\pi$
$20$		0			0
$21$	−1.08926	−	0.243883i	−0.237696	−	0.0532196i
$22$		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
$27$	4.10239	+	3.18911i	0.789504	+	0.613745i
$28$		0			0
$29$	1.20343	+	4.49126i	0.223471	+	0.834006i	0.983011	+	0.183545i	$0.0587574\pi$
$29$	1.20343	+	4.49126i	0.223471	+	0.834006i	−0.759540	+	0.650460i	$0.774576\pi$
$30$		0			0
$31$	0.147988	−	0.0854411i	0.0265795	−	0.0153457i	−0.486651	−	0.873596i	$-0.661782\pi$
$31$	0.147988	−	0.0854411i	0.0265795	−	0.0153457i	0.513231	+	0.858251i	$0.328448\pi$
$32$		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	−0.891057	−	0.453891i	$-0.850036\pi$
$37$	−2.65918	+	2.65918i	−0.437167	+	0.437167i	0.453891	+	0.891057i	$0.350036\pi$
$38$		0			0
$39$	−3.54517	+	0.147331i	−0.567681	+	0.0235918i
$40$		0			0
$41$	−0.983212	−	1.70297i	−0.153552	−	0.265960i	0.778979	−	0.627050i	$-0.215738\pi$
$41$	−0.983212	−	1.70297i	−0.153552	−	0.265960i	−0.932531	+	0.361090i	$0.882405\pi$
$42$		0			0
$43$	−0.821783	+	0.220196i	−0.125321	+	0.0335796i	−0.320934	−	0.947101i	$-0.603997\pi$
$43$	−0.821783	+	0.220196i	−0.125321	+	0.0335796i	0.195614	+	0.980681i	$0.437330\pi$
$44$		0			0
$45$	−2.04174	−	5.68376i	−0.304364	−	0.847284i
$46$		0			0
$47$	4.02475	−	6.97107i	0.587070	−	1.01684i	−0.407544	−	0.913186i	$-0.633615\pi$
$47$	4.02475	−	6.97107i	0.587070	−	1.01684i	0.994614	−	0.103650i	$-0.0330520\pi$
$48$		0			0
$49$	3.29234	+	5.70250i	0.470334	+	0.814643i
$50$		0			0
$51$	5.05632	−	1.58259i	0.708027	−	0.221607i
$52$		0			0
$53$	3.25765	+	3.25765i	0.447473	+	0.447473i	0.894514	−	0.447041i	$-0.147522\pi$
$53$	3.25765	+	3.25765i	0.447473	+	0.447473i	−0.447041	+	0.894514i	$0.647522\pi$
$54$		0			0
$55$	−11.6602			−1.57227
$56$		0			0
$57$	8.92225	+	4.66846i	1.18178	+	0.618352i
$58$		0			0
$59$	−0.506879	−	0.135818i	−0.0659900	−	0.0176820i	0.225673	−	0.974203i	$-0.427542\pi$
$59$	−0.506879	−	0.135818i	−0.0659900	−	0.0176820i	−0.291663	+	0.956521i	$0.594209\pi$
$60$		0			0
$61$	3.00682	−	0.805675i	0.384984	−	0.103156i	−0.0611358	−	0.998129i	$-0.519472\pi$
$61$	3.00682	−	0.805675i	0.384984	−	0.103156i	0.446120	+	0.894973i	$0.352806\pi$
$62$		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
$67$	2.17814	+	0.583631i	0.266102	+	0.0713019i	0.389403	−	0.921067i	$-0.372681\pi$
$67$	2.17814	+	0.583631i	0.266102	+	0.0713019i	−0.123301	+	0.992369i	$0.539348\pi$
$68$		0			0
$69$	−10.3878	−	9.55889i	−1.25055	−	1.15076i
$70$		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	$-0.815977\pi$
$73$		−	9.33784i		−	1.09291i	0.837488	−	0.546456i	$-0.184023\pi$
$74$		0			0
$75$	0.358511	−	1.60123i	0.0413973	−	0.184894i
$76$		0			0
$77$	3.60557	+	0.966110i	0.410893	+	0.110098i
$78$		0			0
$79$	−9.44301	−	5.45193i	−1.06242	−	0.613390i	−0.136321	−	0.990665i	$-0.543528\pi$
$79$	−9.44301	−	5.45193i	−1.06242	−	0.613390i	−0.926101	+	0.377275i	$0.876861\pi$
$80$		0			0
$81$	3.14908	−	8.43109i	0.349897	−	0.936788i
$82$		0			0
$83$	−12.3625	+	3.31253i	−1.35697	+	0.363598i	−0.862701	−	0.505714i	$-0.831229\pi$
$83$	−12.3625	+	3.31253i	−1.35697	+	0.363598i	−0.494264	+	0.869312i	$0.664563\pi$
$84$		0			0
$85$	−5.94814	−	1.59380i	−0.645167	−	0.172872i
$86$		0			0
$87$	6.80132	−	4.31288i	0.729178	−	0.462389i
$88$		0			0
$89$	3.86733			0.409936			0.204968	−	0.978769i	$-0.434291\pi$
$89$	3.86733			0.409936			0.204968	+	0.978769i	$0.434291\pi$
$90$		0			0
$91$	−0.933529	−	0.933529i	−0.0978604	−	0.0978604i
$92$		0			0
$93$	−0.217797	−	0.200417i	−0.0225845	−	0.0207822i
$94$		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
$99$	−13.2641	−	11.2251i	−1.33309	−	1.12817i
$100$		0			0
$101$	−2.35695	+	0.631544i	−0.234526	+	0.0628410i	−0.374168	−	0.927361i	$-0.622072\pi$
$101$	−2.35695	+	0.631544i	−0.234526	+	0.0628410i	0.139642	+	0.990202i	$0.455405\pi$
$102$		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	$-0.792790\pi$
$107$	−1.96059	+	1.96059i	−0.189537	+	0.189537i	0.605959	+	0.795496i	$0.292790\pi$
$108$		0			0
$109$	−10.8066	−	10.8066i	−1.03509	−	1.03509i	−0.999362	−	0.0357265i	$-0.988625\pi$
$109$	−10.8066	−	10.8066i	−1.03509	−	1.03509i	−0.0357265	−	0.999362i	$-0.511375\pi$
$110$		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
$115$	4.24655	+	15.8483i	0.395993	+	1.47787i
$116$		0			0
$117$	2.07770	+	5.78385i	0.192083	+	0.534717i
$118$		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
$123$	−2.30629	+	2.50629i	−0.207951	+	0.225985i
$124$		0			0
$125$	−8.46600	+	8.46600i	−0.757222	+	0.757222i
$126$		0			0
$127$			5.90485i			0.523971i	0.965072	+	0.261985i	$0.0843772\pi$
$127$			5.90485i			0.523971i	−0.965072	+	0.261985i	$0.915623\pi$
$128$		0			0
$129$	0.789144	+	1.24446i	0.0694802	+	0.109569i
$130$		0			0
$131$	0.417733	−	1.55900i	0.0364975	−	0.136211i	−0.945273	−	0.326280i	$-0.894205\pi$
$131$	0.417733	−	1.55900i	0.0364975	−	0.136211i	0.981771	+	0.190070i	$0.0608714\pi$
$132$		0			0
$133$	0.969725	+	3.61906i	0.0840859	+	0.313813i
$134$		0			0
$135$	−8.33878	+	6.31555i	−0.717688	+	0.543556i
$136$		0			0
$137$	5.55314	−	9.61831i	0.474436	−	0.821748i	−0.525135	−	0.851019i	$-0.675985\pi$
$137$	5.55314	−	9.61831i	0.474436	−	0.821748i	0.999572	+	0.0292708i	$0.00931852\pi$
$138$		0			0
$139$	2.99230	−	11.1674i	0.253803	−	0.947207i	−0.714949	−	0.699177i	$-0.753550\pi$
$139$	2.99230	−	11.1674i	0.253803	−	0.947207i	0.968752	−	0.248030i	$-0.0797833\pi$
$140$		0			0
$141$	−13.6053	−	3.04620i	−1.14577	−	0.256536i
$142$		0			0
$143$	11.8656			0.992250
$144$		0			0
$145$	−9.36038			−0.777337
$146$		0			0
$147$	7.72274	−	8.39246i	0.636961	−	0.692198i
$148$		0			0
$149$	5.70216	−	21.2808i	0.467139	−	1.74339i	−0.182558	−	0.983195i	$-0.558438\pi$
$149$	5.70216	−	21.2808i	0.467139	−	1.74339i	0.649698	−	0.760193i	$-0.274896\pi$
$150$		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
$155$	0.0890353	+	0.332284i	0.00715149	+	0.0266897i
$156$		0			0
$157$	6.15846	−	22.9837i	0.491499	−	1.83430i	−0.0573183	−	0.998356i	$-0.518255\pi$
$157$	6.15846	−	22.9837i	0.491499	−	1.83430i	0.548817	−	0.835942i	$-0.315078\pi$
$158$		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	−0.100543	−	0.994933i	$-0.532058\pi$
$163$	11.4188	−	11.4188i	0.894390	−	0.894390i	0.994933	+	0.100543i	$0.0320579\pi$
$164$		0			0
$165$	6.03265	+	19.2741i	0.469641	+	1.50049i
$166$		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
$171$	3.10075	−	17.1636i	0.237120	−	1.31253i
$172$		0			0
$173$	5.30952	+	19.8154i	0.403675	+	1.50654i	0.806486	+	0.591254i	$0.201367\pi$
$173$	5.30952	+	19.8154i	0.403675	+	1.50654i	−0.402810	+	0.915284i	$0.631967\pi$
$174$		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	$-0.120361\pi$
$179$	7.49467	+	7.49467i	0.560178	+	0.560178i	−0.369180	+	0.929358i	$0.620361\pi$
$180$		0			0
$181$	0.879477	−	0.879477i	0.0653710	−	0.0653710i	−0.673665	−	0.739036i	$-0.735281\pi$
$181$	0.879477	−	0.879477i	0.0653710	−	0.0653710i	0.739036	+	0.673665i	$0.235281\pi$
$182$		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
$187$	−17.1140	+	4.58567i	−1.25150	+	0.335337i
$188$		0			0
$189$	3.10179	−	1.26198i	0.225622	−	0.0917954i
$190$		0			0
$191$	−3.97558	+	6.88590i	−0.287663	+	0.498246i	−0.973251	−	0.229743i	$-0.926211\pi$
$191$	−3.97558	+	6.88590i	−0.287663	+	0.498246i	0.685589	+	0.727989i	$0.259545\pi$
$192$		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
$195$	1.56066	−	6.97042i	0.111761	−	0.499162i
$196$		0			0
$197$	11.6691	+	11.6691i	0.831390	+	0.831390i	0.987707	−	0.156317i	$-0.0499620\pi$
$197$	11.6691	+	11.6691i	0.831390	+	0.831390i	−0.156317	+	0.987707i	$0.549962\pi$
$198$		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
$203$	2.89441	+	0.775555i	0.203148	+	0.0544333i
$204$		0			0
$205$	3.82376	−	1.02457i	0.267063	−	0.0715592i
$206$		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
$211$	20.6854	+	5.54263i	1.42404	+	0.381570i	0.886915	−	0.461932i	$-0.152844\pi$
$211$	20.6854	+	5.54263i	1.42404	+	0.381570i	0.537125	+	0.843503i	$0.319510\pi$
$212$		0			0
$213$	25.3133	−	7.92286i	1.73444	−	0.542866i
$214$		0			0
$215$		−	1.71270i		−	0.116805i
$216$		0			0
$217$		−	0.110126i		−	0.00747582i
$218$		0			0
$219$	−15.4352	+	4.83111i	−1.04302	+	0.326456i
$220$		0			0
$221$	6.05289	+	1.62187i	0.407162	+	0.109099i
$222$		0			0
$223$	−13.1779	−	7.60824i	−0.882455	−	0.509485i	−0.0109877	−	0.999940i	$-0.503498\pi$
$223$	−13.1779	−	7.60824i	−0.882455	−	0.509485i	−0.871467	+	0.490454i	$0.836831\pi$
$224$		0			0
$225$	−2.83227	+	0.235815i	−0.188818	+	0.0157210i
$226$		0			0
$227$	−14.5596	+	3.90123i	−0.966353	+	0.258934i	−0.707287	−	0.706926i	$-0.750081\pi$
$227$	−14.5596	+	3.90123i	−0.966353	+	0.258934i	−0.259066	+	0.965860i	$0.583415\pi$
$228$		0			0
$229$	10.3931	+	2.78483i	0.686796	+	0.184026i	0.585309	−	0.810810i	$-0.300973\pi$
$229$	10.3931	+	2.78483i	0.686796	+	0.184026i	0.101487	+	0.994837i	$0.467640\pi$
$230$		0			0
$231$	−0.268456	−	6.45976i	−0.0176631	−	0.425021i
$232$		0			0
$233$	2.05717			0.134770			0.0673848	−	0.997727i	$-0.478534\pi$
$233$	2.05717			0.134770			0.0673848	+	0.997727i	$0.478534\pi$
$234$		0			0
$235$	11.4584	+	11.4584i	0.747462	+	0.747462i
$236$		0			0
$237$	−4.12638	+	18.4297i	−0.268037	+	1.19714i
$238$		0			0
$239$	4.07795	+	7.06322i	0.263781	+	0.456882i	0.967243	−	0.253851i	$-0.0816971\pi$
$239$	4.07795	+	7.06322i	0.263781	+	0.456882i	−0.703463	+	0.710732i	$0.748364\pi$
$240$		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
$243$	−15.5656	−	0.843360i	−0.998535	−	0.0541015i
$244$		0			0
$245$	−12.8041	+	3.43084i	−0.818021	+	0.219188i
$246$		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	$-0.750936\pi$
$251$	−0.0658814	+	0.0658814i	−0.00415840	+	0.00415840i	0.705025	+	0.709183i	$0.250936\pi$
$252$		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
$259$	0.627265	+	2.34099i	0.0389764	+	0.145462i
$260$		0			0
$261$	−10.6479	−	9.01107i	−0.659087	−	0.557771i
$262$		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
$267$	−2.00084	−	6.39260i	−0.122449	−	0.391221i
$268$		0			0
$269$	7.77076	−	7.77076i	0.473792	−	0.473792i	−0.429348	−	0.903139i	$-0.641256\pi$
$269$	7.77076	−	7.77076i	0.473792	−	0.473792i	0.903139	+	0.429348i	$0.141256\pi$
$270$		0			0
$271$			15.0480i			0.914103i	0.889440	+	0.457052i	$0.151095\pi$
$271$			15.0480i			0.914103i	−0.889440	+	0.457052i	$0.848905\pi$
$272$		0			0
$273$	−1.06012	+	2.02608i	−0.0641615	+	0.122624i
$274$		0			0
$275$	−1.42020	+	5.30024i	−0.0856410	+	0.319617i
$276$		0			0
$277$	−3.62552	−	13.5306i	−0.217836	−	0.812976i	−0.985149	−	0.171702i	$-0.945073\pi$
$277$	−3.62552	−	13.5306i	−0.217836	−	0.812976i	0.767313	−	0.641273i	$-0.221593\pi$
$278$		0			0
$279$	−0.218602	+	0.463702i	−0.0130874	+	0.0277611i
$280$		0			0
$281$	−7.72501	+	13.3801i	−0.460835	+	0.798190i	−0.999003	−	0.0446477i	$-0.985783\pi$
$281$	−7.72501	+	13.3801i	−0.460835	+	0.798190i	0.538167	+	0.842838i	$0.319117\pi$
$282$		0			0
$283$	1.71123	−	6.38640i	0.101722	−	0.379632i	−0.896231	−	0.443588i	$-0.853705\pi$
$283$	1.71123	−	6.38640i	0.101722	−	0.379632i	0.997953	+	0.0639565i	$0.0203719\pi$
$284$		0			0
$285$	−13.7267	+	14.9171i	−0.813100	+	0.883612i
$286$		0			0
$287$	−1.26727			−0.0748046
$288$		0			0
$289$	7.64299			0.449588
$290$		0			0
$291$	24.7799	+	5.54816i	1.45262	+	0.325239i
$292$		0			0
$293$	4.18520	−	15.6194i	0.244502	−	0.912493i	−0.729131	−	0.684374i	$-0.760076\pi$
$293$	4.18520	−	15.6194i	0.244502	−	0.912493i	0.973633	−	0.228119i	$-0.0732577\pi$
$294$		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
$299$	−4.32134	−	16.1274i	−0.249909	−	0.932674i
$300$		0			0
$301$	−0.141906	+	0.529601i	−0.00817934	+	0.0305257i
$302$		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	−0.450090	−	0.892983i	$-0.648608\pi$
$307$	7.76011	−	7.76011i	0.442893	−	0.442893i	0.892983	+	0.450090i	$0.148608\pi$
$308$		0			0
$309$	−4.69732	+	5.10467i	−0.267221	+	0.290395i
$310$		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	0.436311	−	0.899796i	$-0.356285\pi$
$313$	−2.20758	−	1.27455i	−0.124780	−	0.0720416i	−0.561091	+	0.827754i	$0.689618\pi$
$314$		0			0
$315$	−3.83009	−	0.691938i	−0.215801	−	0.0389863i
$316$		0			0
$317$	−4.91388	−	18.3388i	−0.275991	−	1.03001i	−0.955174	−	0.296044i	$-0.904333\pi$
$317$	−4.91388	−	18.3388i	−0.275991	−	1.03001i	0.679183	−	0.733969i	$-0.262334\pi$
$318$		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
$331$	20.8335	−	5.58231i	1.14511	−	0.306831i	0.364106	−	0.931357i	$-0.381374\pi$
$331$	20.8335	−	5.58231i	1.14511	−	0.306831i	0.781004	+	0.624526i	$0.214708\pi$
$332$		0			0
$333$	2.00571	−	11.1022i	0.109912	−	0.608398i
$334$		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
$339$	7.69997	+	7.08552i	0.418205	+	0.384832i
$340$		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
$347$	−7.81694	−	2.09454i	−0.419635	−	0.112441i	0.0428214	−	0.999083i	$-0.486365\pi$
$347$	−7.81694	−	2.09454i	−0.419635	−	0.112441i	−0.462457	+	0.886642i	$0.653032\pi$
$348$		0			0
$349$	−16.0919	+	4.31180i	−0.861378	+	0.230806i	−0.662356	−	0.749189i	$-0.730443\pi$
$349$	−16.0919	+	4.31180i	−0.861378	+	0.230806i	−0.199022	+	0.979995i	$0.563777\pi$
$350$		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
$355$	−29.7779	−	7.97897i	−1.58045	−	0.423480i
$356$		0			0
$357$	0.746018	−	3.33196i	0.0394835	−	0.176346i
$358$		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
$363$	28.7394	+	26.4460i	1.50843	+	1.38805i
$364$		0			0
$365$	18.1576	+	4.86533i	0.950415	+	0.254663i
$366$		0			0
$367$	27.7535	+	16.0235i	1.44872	+	0.836419i	0.998405	−	0.0564512i	$-0.0179785\pi$
$367$	27.7535	+	16.0235i	1.44872	+	0.836419i	0.450315	+	0.892870i	$0.351312\pi$
$368$		0			0
$369$	5.33604	+	2.51556i	0.277783	+	0.130955i
$370$		0			0
$371$	2.86784	−	0.768436i	0.148891	−	0.0398952i
$372$		0			0
$373$	0.692592	+	0.185580i	0.0358611	+	0.00960894i	0.276705	−	0.960955i	$-0.410758\pi$
$373$	0.692592	+	0.185580i	0.0358611	+	0.00960894i	−0.240844	+	0.970564i	$0.577424\pi$
$374$		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	0.794610	−	0.607120i	$-0.207675\pi$
$379$	3.65005	+	3.65005i	0.187491	+	0.187491i	−0.607120	+	0.794610i	$0.707675\pi$
$380$		0			0
$381$	9.76057	−	3.05499i	0.500049	−	0.156512i
$382$		0			0
$383$	−9.73635	−	16.8639i	−0.497504	−	0.861703i	0.502492	−	0.864582i	$-0.332417\pi$
$383$	−9.73635	−	16.8639i	−0.497504	−	0.861703i	−0.999996	+	0.00287933i	$0.999083\pi$
$384$		0			0
$385$	−3.75724	+	6.50774i	−0.191487	+	0.331665i
$386$		0			0
$387$	1.64879	−	1.94828i	0.0838127	−	0.0990368i
$388$		0			0
$389$	0.311311	−	0.0834155i	0.0157841	−	0.00422934i	−0.250918	−	0.968008i	$-0.580733\pi$
$389$	0.311311	−	0.0834155i	0.0157841	−	0.00422934i	0.266702	+	0.963779i	$0.414066\pi$
$390$		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	0.790856	−	0.612002i	$-0.209636\pi$
$397$	3.56364	+	3.56364i	0.178854	+	0.178854i	−0.612002	+	0.790856i	$0.709636\pi$
$398$		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
$403$	−0.0906033	−	0.338136i	−0.00451327	−	0.0168438i
$404$		0			0
$405$	14.7537	+	10.5163i	0.733116	+	0.522561i
$406$		0			0
$407$	−18.8639	−	10.8911i	−0.935049	−	0.539851i
$408$		0			0
$409$	11.7821	−	6.80241i	0.582589	−	0.336358i	−0.179573	−	0.983745i	$-0.557472\pi$
$409$	11.7821	−	6.80241i	0.582589	−	0.336358i	0.762161	+	0.647387i	$0.224138\pi$
$410$		0			0
$411$	−18.7719	−	4.20298i	−0.925948	−	0.207318i
$412$		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
$419$	2.09039	−	7.80143i	0.102122	−	0.381125i	−0.895881	−	0.444295i	$-0.853454\pi$
$419$	2.09039	−	7.80143i	0.102122	−	0.381125i	0.998003	+	0.0631698i	$0.0201210\pi$
$420$		0			0
$421$	−4.12570	−	15.3973i	−0.201074	−	0.750419i	−0.990610	−	0.136715i	$-0.956345\pi$
$421$	−4.12570	−	15.3973i	−0.201074	−	0.750419i	0.789536	−	0.613704i	$-0.210321\pi$
$422$		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
$427$	0.519221	−	1.93776i	0.0251268	−	0.0937747i
$428$		0			0
$429$	−6.13889	−	19.6135i	−0.296388	−	0.946950i
$430$		0			0
$431$	−0.112162			−0.00540266			−0.00270133	−	0.999996i	$-0.500860\pi$
$431$	−0.112162			−0.00540266			−0.00270133	+	0.999996i	$0.500860\pi$
$432$		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
$435$	4.84277	+	15.4725i	0.232193	+	0.741849i
$436$		0			0
$437$	−12.2639	+	45.7694i	−0.586661	+	2.18945i
$438$		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
$443$	−1.21372	−	4.52965i	−0.0576654	−	0.215210i	0.931081	−	0.364813i	$-0.118867\pi$
$443$	−1.21372	−	4.52965i	−0.0576654	−	0.215210i	−0.988746	+	0.149603i	$0.952200\pi$
$444$		0			0
$445$	−2.01501	+	7.52010i	−0.0955204	+	0.356487i
$446$		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
$453$	−27.4879	−	6.15448i	−1.29149	−	0.289163i
$454$		0			0
$455$	2.30167	−	1.32887i	0.107904	−	0.0622983i
$456$		0			0
$457$	28.9564	+	16.7180i	1.35453	+	0.782036i	0.988880	−	0.148719i	$-0.0475148\pi$
$457$	28.9564	+	16.7180i	1.35453	+	0.782036i	0.365646	+	0.930754i	$0.380848\pi$
$458$		0			0
$459$	−9.75525	+	12.5489i	−0.455336	+	0.585731i
$460$		0			0
$461$	−1.29659	−	4.83893i	−0.0603881	−	0.225371i	0.929136	−	0.369738i	$-0.120552\pi$
$461$	−1.29659	−	4.83893i	−0.0603881	−	0.225371i	−0.989524	+	0.144366i	$0.953886\pi$
$462$		0			0
$463$	16.0584	−	9.27134i	0.746299	−	0.430876i	−0.0780562	−	0.996949i	$-0.524871\pi$
$463$	16.0584	−	9.27134i	0.746299	−	0.430876i	0.824355	+	0.566073i	$0.191538\pi$
$464$		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	$-0.102544\pi$
$467$	13.6565	+	13.6565i	0.631948	+	0.631948i	−0.316608	+	0.948556i	$0.602544\pi$
$468$		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
$475$	−5.32008	+	1.42551i	−0.244102	+	0.0654069i
$476$		0			0
$477$	−13.6009	−	2.45712i	−0.622741	−	0.112504i
$478$		0			0
$479$	−1.37861	+	2.38783i	−0.0629904	+	0.109103i	−0.895801	−	0.444456i	$-0.853397\pi$
$479$	−1.37861	+	2.38783i	−0.0629904	+	0.109103i	0.832810	+	0.553558i	$0.186730\pi$
$480$		0			0
$481$	3.85198	+	6.67182i	0.175635	+	0.304209i
$482$		0			0
$483$	−8.68219	+	2.71746i	−0.395053	+	0.123649i
$484$		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
$491$	16.1550	+	4.32873i	0.729066	+	0.195353i	0.604213	−	0.796822i	$-0.293487\pi$
$491$	16.1550	+	4.32873i	0.729066	+	0.195353i	0.124853	+	0.992175i	$0.460154\pi$
$492$		0			0
$493$	−13.7384	+	3.68120i	−0.618747	+	0.165793i
$494$		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
$499$	−32.1048	−	8.60246i	−1.43721	−	0.385099i	−0.545654	−	0.838011i	$-0.683719\pi$
$499$	−32.1048	−	8.60246i	−1.43721	−	0.385099i	−0.891556	+	0.452911i	$0.850385\pi$
$500$		0			0
$501$	0.628765	+	0.578590i	0.0280912	+	0.0258495i
$502$		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
$507$	3.33148	−	14.8795i	0.147956	−	0.660821i
$508$		0			0
$509$	−39.6362	−	10.6205i	−1.75684	−	0.470745i	−0.770777	−	0.637105i	$-0.780132\pi$
$509$	−39.6362	−	10.6205i	−1.75684	−	0.470745i	−0.986065	+	0.166360i	$0.946799\pi$
$510$		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
$515$	7.78801	−	2.08679i	0.343181	−	0.0919549i
$516$		0			0
$517$	45.0351	+	12.0671i	1.98064	+	0.530711i
$518$		0			0
$519$	30.0074	−	19.0284i	1.31718	−	0.835254i
$520$		0			0
$521$	10.9553			0.479963			0.239981	−	0.970778i	$-0.422859\pi$
$521$	10.9553			0.479963			0.239981	+	0.970778i	$0.422859\pi$
$522$		0			0
$523$	−8.18896	−	8.18896i	−0.358078	−	0.358078i	0.505026	−	0.863104i	$-0.331483\pi$
$523$	−8.18896	−	8.18896i	−0.358078	−	0.358078i	−0.863104	+	0.505026i	$0.831483\pi$
$524$		0			0
$525$	−0.778145	−	0.716049i	−0.0339610	−	0.0312509i
$526$		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
$531$	1.48159	−	0.532220i	0.0642953	−	0.0230964i
$532$		0			0
$533$	−3.89110	+	1.04262i	−0.168542	+	0.0451607i
$534$		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	0.261589	−	0.965179i	$-0.415753\pi$
$541$	−16.3651	−	16.3651i	−0.703590	−	0.703590i	−0.965179	+	0.261589i	$0.915753\pi$
$542$		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
$547$	6.32886	+	23.6196i	0.270603	+	1.00990i	0.958731	+	0.284314i	$0.0917658\pi$
$547$	6.32886	+	23.6196i	0.270603	+	1.00990i	−0.688129	+	0.725589i	$0.741568\pi$
$548$		0			0
$549$	−6.03276	+	7.12857i	−0.257472	+	0.304240i
$550$		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
$555$	−8.87910	+	9.64909i	−0.376897	+	0.409581i
$556$		0			0
$557$	1.55709	−	1.55709i	0.0659760	−	0.0659760i	−0.673349	−	0.739325i	$-0.735145\pi$
$557$	1.55709	−	1.55709i	0.0659760	−	0.0659760i	0.739325	+	0.673349i	$0.235145\pi$
$558$		0			0
$559$			1.74287i			0.0737154i
$560$		0			0
$561$	16.4342	+	25.9165i	0.693854	+	1.09419i
$562$		0			0
$563$	7.85187	−	29.3036i	0.330917	−	1.23500i	−0.577311	−	0.816524i	$-0.695898\pi$
$563$	7.85187	−	29.3036i	0.330917	−	1.23500i	0.908228	−	0.418475i	$-0.137435\pi$
$564$		0			0
$565$	−3.14775	−	11.7476i	−0.132427	−	0.494224i
$566$		0			0
$567$	−3.69079	−	4.47427i	−0.154999	−	0.187902i
$568$		0			0
$569$	−11.5050	+	19.9273i	−0.482316	+	0.835395i	−0.999794	−	0.0203012i	$-0.993537\pi$
$569$	−11.5050	+	19.9273i	−0.482316	+	0.835395i	0.517478	+	0.855696i	$0.326871\pi$
$570$		0			0
$571$	−3.77973	+	14.1061i	−0.158177	+	0.590324i	0.840636	+	0.541601i	$0.182182\pi$
$571$	−3.77973	+	14.1061i	−0.158177	+	0.590324i	−0.998812	+	0.0487226i	$0.984485\pi$
$572$		0			0
$573$	13.4391	+	3.00898i	0.561425	+	0.125702i
$574$		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
$579$	−6.93013	+	7.53111i	−0.288006	+	0.312982i
$580$		0			0
$581$	−2.13478	+	7.96709i	−0.0885654	+	0.330531i
$582$		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
$587$	3.72984	+	13.9200i	0.153947	+	0.574538i	0.999193	+	0.0401610i	$0.0127871\pi$
$587$	3.72984	+	13.9200i	0.153947	+	0.574538i	−0.845246	+	0.534377i	$0.820546\pi$
$588$		0			0
$589$	−0.257131	+	0.959624i	−0.0105949	+	0.0395406i
$590$		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
$597$	0.327728	+	1.04708i	0.0134130	+	0.0428541i
$598$		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	−0.233765	−	0.972293i	$-0.575105\pi$
$601$	−29.2389	−	16.8811i	−1.19268	−	0.688593i	−0.958913	+	0.283700i	$0.908438\pi$
$602$		0			0
$603$	−6.36662	+	2.28704i	−0.259269	+	0.0931354i
$604$		0			0
$605$	−11.7487	−	43.8466i	−0.477651	−	1.78262i
$606$		0			0
$607$	26.7618	−	15.4509i	1.08623	−	0.627133i	0.153657	−	0.988124i	$-0.450895\pi$
$607$	26.7618	−	15.4509i	1.08623	−	0.627133i	0.932569	+	0.360991i	$0.117562\pi$
$608$		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	−0.100951	+	0.994891i	$0.532189\pi$
$613$	−27.1318	+	27.1318i	−1.09584	+	1.09584i	−0.994891	+	0.100951i	$0.967811\pi$
$614$		0			0
$615$	−3.67189	−	5.79049i	−0.148065	−	0.233495i
$616$		0			0
$617$	−4.23780	−	7.34009i	−0.170607	−	0.295501i	0.768025	−	0.640420i	$-0.221240\pi$
$617$	−4.23780	−	7.34009i	−0.170607	−	0.295501i	−0.938632	+	0.344919i	$0.887906\pi$
$618$		0			0
$619$	−24.4520	+	6.55190i	−0.982810	+	0.263343i	−0.714228	−	0.699914i	$-0.753222\pi$
$619$	−24.4520	+	6.55190i	−0.982810	+	0.263343i	−0.268582	+	0.963257i	$0.586555\pi$
$620$		0			0
$621$	41.9520	+	5.79205i	1.68348	+	0.232427i
$622$		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
$627$	−12.7435	+	56.9165i	−0.508925	+	2.27302i
$628$		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
$635$	−11.4821	−	3.07662i	−0.455654	−	0.122092i
$636$		0			0
$637$	13.0295	−	3.49126i	0.516249	−	0.138329i
$638$		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
$643$	−18.2322	−	4.88530i	−0.719007	−	0.192657i	−0.119278	−	0.992861i	$-0.538058\pi$
$643$	−18.2322	−	4.88530i	−0.719007	−	0.192657i	−0.599728	+	0.800204i	$0.704725\pi$
$644$		0			0
$645$	−2.83106	+	0.886101i	−0.111473	+	0.0348902i
$646$		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
$651$	−0.182035	+	0.0569757i	−0.00713452	+	0.00223305i
$652$		0			0
$653$	−9.81233	−	2.62920i	−0.383986	−	0.102889i	0.0616618	−	0.998097i	$-0.480360\pi$
$653$	−9.81233	−	2.62920i	−0.383986	−	0.102889i	−0.445648	+	0.895208i	$0.647027\pi$
$654$		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
$659$	−10.6102	+	2.84300i	−0.413316	+	0.110748i	−0.459484	−	0.888186i	$-0.651966\pi$
$659$	−10.6102	+	2.84300i	−0.413316	+	0.110748i	0.0461683	+	0.998934i	$0.485299\pi$
$660$		0			0
$661$	−22.2643	−	5.96571i	−0.865982	−	0.232039i	−0.201633	−	0.979461i	$-0.564625\pi$
$661$	−22.2643	−	5.96571i	−0.865982	−	0.232039i	−0.664350	+	0.747422i	$0.731291\pi$
$662$		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
$669$	−5.75842	+	25.7190i	−0.222633	+	0.994352i
$670$		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
$675$	1.85513	+	4.55967i	0.0714039	+	0.175502i
$676$		0			0
$677$	31.9657	−	8.56517i	1.22854	−	0.329186i	0.414529	−	0.910036i	$-0.363946\pi$
$677$	31.9657	−	8.56517i	1.22854	−	0.329186i	0.814011	+	0.580850i	$0.197280\pi$
$678$		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	$-0.556013\pi$
$683$	21.1555	−	21.1555i	0.809494	−	0.809494i	0.984557	+	0.175063i	$0.0560130\pi$
$684$		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
$691$	−6.57213	−	24.5275i	−0.250016	−	0.933071i	−0.970796	−	0.239908i	$-0.922883\pi$
$691$	−6.57213	−	24.5275i	−0.250016	−	0.933071i	0.720780	−	0.693164i	$-0.243784\pi$
$692$		0			0
$693$	−10.5389	+	3.78583i	−0.400341	+	0.143812i
$694$		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
$699$	−1.06432	−	3.40045i	−0.0402561	−	0.128617i
$700$		0			0
$701$	15.7130	−	15.7130i	0.593472	−	0.593472i	−0.345096	−	0.938568i	$-0.612153\pi$
$701$	15.7130	−	15.7130i	0.593472	−	0.593472i	0.938568	+	0.345096i	$0.112153\pi$
$702$		0			0
$703$		−	21.8637i		−	0.824605i
$704$		0			0
$705$	13.0122	−	24.8686i	0.490068	−	0.936607i
$706$		0			0
$707$	−0.407001	+	1.51895i	−0.0153069	+	0.0571260i
$708$		0			0
$709$	1.33304	+	4.97496i	0.0500632	+	0.186838i	0.986429	−	0.164187i	$-0.0524999\pi$
$709$	1.33304	+	4.97496i	0.0500632	+	0.186838i	−0.936366	+	0.351025i	$0.885833\pi$
$710$		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
$715$	−6.18236	+	23.0729i	−0.231207	+	0.862877i
$716$		0			0
$717$	9.56552	−	10.3950i	0.357231	−	0.388210i
$718$		0			0
$719$	−21.0741			−0.785932			−0.392966	−	0.919553i	$-0.628551\pi$
$719$	−21.0741			−0.785932			−0.392966	+	0.919553i	$0.628551\pi$
$720$		0			0
$721$	−2.58110			−0.0961253
$722$		0			0
$723$	−19.6992	−	4.41061i	−0.732622	−	0.164032i
$724$		0			0
$725$	−1.14008	+	4.25483i	−0.0423414	+	0.158020i
$726$		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
$731$	−0.673562	−	2.51377i	−0.0249126	−	0.0929751i
$732$		0			0
$733$	8.92809	−	33.3201i	0.329767	−	1.23071i	−0.579666	−	0.814854i	$-0.696817\pi$
$733$	8.92809	−	33.3201i	0.329767	−	1.23071i	0.909433	−	0.415851i	$-0.136516\pi$
$734$		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	−0.385721	−	0.922616i	$-0.626047\pi$
$739$	14.5953	−	14.5953i	0.536895	−	0.536895i	0.922616	+	0.385721i	$0.126047\pi$
$740$		0			0
$741$	13.9684	−	15.1798i	0.513144	−	0.557644i
$742$		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
$747$	24.8037	−	29.3091i	0.907520	−	1.07237i
$748$		0			0
$749$	0.462476	+	1.72599i	0.0168985	+	0.0630661i
$750$		0			0
$751$	12.4720	−	7.20072i	0.455110	−	0.262758i	−0.254876	−	0.966974i	$-0.582035\pi$
$751$	12.4720	−	7.20072i	0.455110	−	0.262758i	0.709986	+	0.704216i	$0.248701\pi$
$752$		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	−0.960172	−	0.279411i	$-0.909861\pi$
$757$	−18.7302	+	18.7302i	−0.680761	+	0.680761i	0.279411	+	0.960172i	$0.409861\pi$
$758$		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	$0.146814\pi$
$761$	22.9842	+	39.8099i	0.833178	+	1.44311i	−0.0623277	+	0.998056i	$0.519852\pi$
$762$		0			0
$763$	−9.51352	+	2.54914i	−0.344413	+	0.0922851i
$764$		0			0
$765$	17.3862	−	6.24552i	0.628598	−	0.225807i
$766$		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
$771$	−21.7591	−	20.0228i	−0.783636	−	0.721102i
$772$		0			0
$773$	3.33435	+	3.33435i	0.119928	+	0.119928i	0.764524	−	0.644596i	$-0.222974\pi$
$773$	3.33435	+	3.33435i	0.119928	+	0.119928i	−0.644596	+	0.764524i	$0.722974\pi$
$774$		0			0
$775$	0.161887			0.00581514
$776$		0			0
$777$	3.54506	−	2.24801i	0.127178	−	0.0806468i
$778$		0			0
$779$	11.0429	+	2.95893i	0.395652	+	0.106015i
$780$		0			0
$781$	−85.6769	+	22.9570i	−3.06576	+	0.821468i
$782$		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
$787$	0.0468477	+	0.0125528i	0.00166994	+	0.000447460i	0.259654	−	0.965702i	$-0.416392\pi$
$787$	0.0468477	+	0.0125528i	0.00166994	+	0.000447460i	−0.257984	+	0.966149i	$0.583058\pi$
$788$		0			0
$789$	2.79562	−	12.4862i	0.0995269	−	0.444519i
$790$		0			0
$791$			3.89338i			0.138433i
$792$		0			0
$793$		−	6.37697i		−	0.226453i
$794$		0			0
$795$	11.8207	+	10.8774i	0.419237	+	0.385782i
$796$		0			0
$797$	−19.0545	−	5.10564i	−0.674945	−	0.180851i	−0.0949636	−	0.995481i	$-0.530273\pi$
$797$	−19.0545	−	5.10564i	−0.674945	−	0.180851i	−0.579981	+	0.814630i	$0.696940\pi$
$798$		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
$803$	52.2431	−	13.9985i	1.84362	−	0.493996i
$804$		0			0
$805$	10.2135	+	2.73671i	0.359980	+	0.0964562i
$806$		0			0
$807$	−16.8652	−	8.82453i	−0.593685	−	0.310638i
$808$		0			0
$809$	−20.7043			−0.727925			−0.363963	−	0.931414i	$-0.618576\pi$
$809$	−20.7043			−0.727925			−0.363963	+	0.931414i	$0.618576\pi$
$810$		0			0
$811$	−14.8452	−	14.8452i	−0.521285	−	0.521285i	0.396675	−	0.917959i	$-0.370164\pi$
$811$	−14.8452	−	14.8452i	−0.521285	−	0.521285i	−0.917959	+	0.396675i	$0.870164\pi$
$812$		0			0
$813$	24.8740	−	7.78540i	0.872371	−	0.273046i
$814$		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
$819$	3.89754	+	0.704124i	0.136191	+	0.0246041i
$820$		0			0
$821$	−27.9379	+	7.48593i	−0.975038	+	0.261261i	−0.710954	−	0.703239i	$-0.751736\pi$
$821$	−27.9379	+	7.48593i	−0.975038	+	0.261261i	−0.264084	+	0.964500i	$0.585070\pi$
$822$		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	$-0.844682\pi$
$827$	−11.9196	+	11.9196i	−0.414485	+	0.414485i	0.468812	+	0.883298i	$0.344682\pi$
$828$		0			0
$829$	9.25865	+	9.25865i	0.321566	+	0.321566i	0.849368	−	0.527801i	$-0.176983\pi$
$829$	9.25865	+	9.25865i	0.321566	+	0.321566i	−0.527801	+	0.849368i	$0.676983\pi$
$830$		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
$835$	−0.257039	−	0.959284i	−0.00889521	−	0.0331974i
$836$		0			0
$837$	0.879586	+	0.121439i	0.0304030	+	0.00419755i
$838$		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
$843$	26.1137	+	5.84679i	0.899403	+	0.201374i
$844$		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
$851$	−7.93286	+	29.6059i	−0.271935	+	1.01488i
$852$		0			0
$853$	−0.499139	−	1.86281i	−0.0170902	−	0.0637814i	0.956854	−	0.290569i	$-0.0938445\pi$
$853$	−0.499139	−	1.86281i	−0.0170902	−	0.0637814i	−0.973944	+	0.226787i	$0.927178\pi$
$854$		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	$-0.661463\pi$
$857$	15.0498	−	26.0670i	0.514090	−	0.890431i	0.999866	−	0.0163473i	$-0.00520374\pi$
$858$		0			0
$859$	12.3205	−	45.9807i	0.420370	−	1.56884i	−0.353462	−	0.935449i	$-0.614996\pi$
$859$	12.3205	−	45.9807i	0.420370	−	1.56884i	0.773831	−	0.633392i	$-0.218338\pi$
$860$		0			0
$861$	0.655647	+	2.09477i	0.0223444	+	0.0713895i
$862$		0			0
$863$	4.03429			0.137329			0.0686644	−	0.997640i	$-0.478126\pi$
$863$	4.03429			0.137329			0.0686644	+	0.997640i	$0.478126\pi$
$864$		0			0
$865$	−41.2979			−1.40417
$866$		0			0
$867$	−3.95425	−	12.6337i	−0.134293	−	0.429062i
$868$		0			0
$869$	16.3461	−	61.0045i	0.554504	−	2.06944i
$870$		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
$875$	1.99702	+	7.45296i	0.0675114	+	0.251956i
$876$		0			0
$877$	−10.4278	+	38.9169i	−0.352120	+	1.31413i	0.531949	+	0.846776i	$0.321460\pi$
$877$	−10.4278	+	38.9169i	−0.352120	+	1.31413i	−0.884070	+	0.467355i	$0.845207\pi$
$878$		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	−0.782307	−	0.622893i	$-0.785957\pi$
$883$	−4.73704	+	4.73704i	−0.159414	+	0.159414i	0.622893	+	0.782307i	$0.285957\pi$
$884$		0			0
$885$	−1.78554	−	0.399778i	−0.0600201	−	0.0134384i
$886$		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
$891$	51.8908	+	4.97919i	1.73841	+	0.166809i
$892$		0			0
$893$	12.1123	+	45.2036i	0.405322	+	1.51268i
$894$		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
$907$	35.8204	−	9.59805i	1.18940	−	0.318698i	0.390750	−	0.920497i	$-0.372216\pi$
$907$	35.8204	−	9.59805i	1.18940	−	0.318698i	0.798648	+	0.601799i	$0.205549\pi$
$908$		0			0
$909$	4.72889	−	5.58787i	0.156848	−	0.185338i
$910$		0			0
$911$	−18.5603	+	32.1474i	−0.614931	+	1.06509i	0.375465	+	0.926837i	$0.377483\pi$
$911$	−18.5603	+	32.1474i	−0.614931	+	1.06509i	−0.990397	+	0.138256i	$0.955850\pi$
$912$		0			0
$913$	−37.0657	−	64.1997i	−1.22670	−	2.12470i
$914$		0			0
$915$	10.3586	−	3.24215i	0.342443	−	0.107182i
$916$		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
$923$	30.3023	+	8.11949i	0.997414	+	0.267256i
$924$		0			0
$925$	−3.44128	+	0.922089i	−0.113149	+	0.0303181i
$926$		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
$931$	−36.9776	−	9.90812i	−1.21189	−	0.324726i
$932$		0			0
$933$	−5.55646	−	5.11305i	−0.181910	−	0.167394i
$934$		0			0
$935$		−	35.6678i		−	1.16646i
$936$		0			0
$937$			35.3168i			1.15375i	0.816833	+	0.576874i	$0.195728\pi$
$937$			35.3168i			1.15375i	−0.816833	+	0.576874i	$0.804272\pi$
$938$		0			0
$939$	−0.964660	+	4.30849i	−0.0314805	+	0.140602i
$940$		0			0
$941$	41.8587	+	11.2160i	1.36456	+	0.365632i	0.865487	−	0.500931i	$-0.167009\pi$
$941$	41.8587	+	11.2160i	1.36456	+	0.365632i	0.499069	+	0.866563i	$0.333676\pi$
$942$		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
$947$	49.1797	−	13.1777i	1.59813	−	0.428217i	0.653650	−	0.756797i	$-0.273237\pi$
$947$	49.1797	−	13.1777i	1.59813	−	0.428217i	0.944476	+	0.328581i	$0.106570\pi$
$948$		0			0
$949$	−18.4774	−	4.95101i	−0.599802	−	0.160717i
$950$		0			0
$951$	−27.7714	+	17.6105i	−0.900549	+	0.571059i
$952$		0			0
$953$	−36.4989			−1.18231			−0.591157	−	0.806556i	$-0.701329\pi$
$953$	−36.4989			−1.18231			−0.591157	+	0.806556i	$0.701329\pi$
$954$		0			0
$955$	−11.3184	−	11.3184i	−0.366254	−	0.366254i
$956$		0			0
$957$	34.3255	+	31.5863i	1.10959	+	1.02104i
$958$		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
$963$	1.47879	−	8.18557i	0.0476534	−	0.263776i
$964$		0			0
$965$	11.4899	−	3.07872i	0.369874	−	0.0991074i
$966$		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	$-0.972032\pi$
$971$	−28.3062	+	28.3062i	−0.908390	+	0.908390i	0.0877520	+	0.996142i	$0.472032\pi$
$972$		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
$979$	5.79756	+	21.6368i	0.185291	+	0.691515i
$980$		0			0
$981$	45.1183	+	8.15101i	1.44052	+	0.260242i
$982$		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
$987$	−6.08412	+	6.61173i	−0.193660	+	0.210454i
$988$		0			0
$989$	−4.90308	+	4.90308i	−0.155909	+	0.155909i
$990$		0			0
$991$			22.8049i			0.724420i	0.932096	+	0.362210i	$0.117978\pi$
$991$			22.8049i			0.724420i	−0.932096	+	0.362210i	$0.882022\pi$
$992$		0			0
$993$	−20.0060	−	31.5491i	−0.634872	−	1.00118i
$994$		0			0
$995$	0.330049	−	1.23176i	0.0104632	−	0.0390494i
$996$		0			0
$997$	9.43584	+	35.2150i	0.298836	+	1.11527i	0.938123	+	0.346303i	$0.112563\pi$
$997$	9.43584	+	35.2150i	0.298836	+	1.11527i	−0.639287	+	0.768968i	$0.720770\pi$
$998$		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.47.10		88
3.2	odd	2		1728.2.z.a.1007.16		88
4.3	odd	2		144.2.u.a.83.21	yes	88
9.4	even	3		1728.2.z.a.1583.16		88
9.5	odd	6	inner	576.2.y.a.239.20		88
12.11	even	2		432.2.v.a.35.2		88
16.5	even	4		144.2.u.a.11.13	✓	88
16.11	odd	4	inner	576.2.y.a.335.20		88
36.23	even	6		144.2.u.a.131.13	yes	88
36.31	odd	6		432.2.v.a.179.10		88
48.5	odd	4		432.2.v.a.251.10		88
48.11	even	4		1728.2.z.a.143.16		88
144.5	odd	12		144.2.u.a.59.21	yes	88
144.59	even	12	inner	576.2.y.a.527.10		88
144.85	even	12		432.2.v.a.395.2		88
144.139	odd	12		1728.2.z.a.719.16		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.13	✓	88	16.5	even	4
144.2.u.a.59.21	yes	88	144.5	odd	12
144.2.u.a.83.21	yes	88	4.3	odd	2
144.2.u.a.131.13	yes	88	36.23	even	6
432.2.v.a.35.2		88	12.11	even	2
432.2.v.a.179.10		88	36.31	odd	6
432.2.v.a.251.10		88	48.5	odd	4
432.2.v.a.395.2		88	144.85	even	12
576.2.y.a.47.10		88	1.1	even	1	trivial
576.2.y.a.239.20		88	9.5	odd	6	inner
576.2.y.a.335.20		88	16.11	odd	4	inner
576.2.y.a.527.10		88	144.59	even	12	inner
1728.2.z.a.143.16		88	48.11	even	4
1728.2.z.a.719.16		88	144.139	odd	12
1728.2.z.a.1007.16		88	3.2	odd	2
1728.2.z.a.1583.16		88	9.4	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 $\F_{q}$
Belyi maps

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

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