LMFDB - Embedded newform 936.2.w.k.307.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(307,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.3
Character	$\chi$	$=$	936.307
Dual form			936.2.w.k.811.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20976 - 0.732456i) q^{2} +(0.927017 + 1.77218i) q^{4} +(-0.232047 + 0.232047i) q^{5} +(-1.32779 - 1.32779i) q^{7} +(0.176583 - 2.82291i) q^{8} +(0.450684 - 0.110756i) q^{10} +(-0.693922 + 0.693922i) q^{11} +(3.60100 - 0.181078i) q^{13} +(0.633752 + 2.57884i) q^{14} +(-2.28128 + 3.28569i) q^{16} -6.65027i q^{17} +(3.67982 + 3.67982i) q^{19} +(-0.626342 - 0.196119i) q^{20} +(1.34774 - 0.331209i) q^{22} -8.15485 q^{23} +4.89231i q^{25} +(-4.48896 - 2.41851i) q^{26} +(1.12220 - 3.58396i) q^{28} -5.34245i q^{29} +(2.87096 - 2.87096i) q^{31} +(5.16641 - 2.30395i) q^{32} +(-4.87103 + 8.04520i) q^{34} +0.616217 q^{35} +(-7.85762 - 7.85762i) q^{37} +(-1.75638 - 7.14700i) q^{38} +(0.614072 + 0.696023i) q^{40} +(5.49860 + 5.49860i) q^{41} -6.91010i q^{43} +(-1.87303 - 0.586480i) q^{44} +(9.86538 + 5.97307i) q^{46} +(4.22794 + 4.22794i) q^{47} -3.47397i q^{49} +(3.58340 - 5.91850i) q^{50} +(3.65909 + 6.21378i) q^{52} -10.9391i q^{53} -0.322045i q^{55} +(-3.98268 + 3.51375i) q^{56} +(-3.91311 + 6.46306i) q^{58} +(7.51705 - 7.51705i) q^{59} -6.47155i q^{61} +(-5.57601 + 1.37031i) q^{62} +(-7.93764 - 0.996957i) q^{64} +(-0.793583 + 0.877620i) q^{65} +(3.34449 + 3.34449i) q^{67} +(11.7855 - 6.16491i) q^{68} +(-0.745472 - 0.451352i) q^{70} +(-7.22680 + 7.22680i) q^{71} +(9.22075 - 9.22075i) q^{73} +(3.75044 + 15.2612i) q^{74} +(-3.11007 + 9.93259i) q^{76} +1.84276 q^{77} -13.9125i q^{79} +(-0.233071 - 1.29180i) q^{80} +(-2.62448 - 10.6794i) q^{82} +(-4.01110 - 4.01110i) q^{83} +(1.54318 + 1.54318i) q^{85} +(-5.06135 + 8.35954i) q^{86} +(1.83634 + 2.08141i) q^{88} +(1.32098 - 1.32098i) q^{89} +(-5.02179 - 4.54092i) q^{91} +(-7.55969 - 14.4519i) q^{92} +(-2.01799 - 8.21154i) q^{94} -1.70778 q^{95} +(-4.77810 - 4.77810i) q^{97} +(-2.54453 + 4.20266i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 40 q^{16} - 8 q^{19} - 32 q^{22} + 24 q^{28} + 8 q^{34} + 16 q^{40} - 8 q^{46} + 24 q^{52} - 24 q^{58} + 40 q^{67} - 24 q^{70} + 56 q^{76} + 104 q^{91} - 64 q^{94} - 32 q^{97}+O(q^{100}) $ 48 * q - 40 * q^16 - 8 * q^19 - 32 * q^22 + 24 * q^28 + 8 * q^34 + 16 * q^40 - 8 * q^46 + 24 * q^52 - 24 * q^58 + 40 * q^67 - 24 * q^70 + 56 * q^76 + 104 * q^91 - 64 * q^94 - 32 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−1.20976	−	0.732456i	−0.855426	−	0.517924i
$2$	−1.20976	−	0.732456i	−0.855426	−	0.517924i
$3$		0			0
$3$		0			0
$4$	0.927017	+	1.77218i	0.463508	+	0.886092i
$5$	−0.232047	+	0.232047i	−0.103775	+	0.103775i	−0.757088	−	0.653313i	$-0.773378\pi$
$5$	−0.232047	+	0.232047i	−0.103775	+	0.103775i	0.653313	+	0.757088i	$0.273378\pi$
$6$		0			0
$7$	−1.32779	−	1.32779i	−0.501856	−	0.501856i	0.410159	−	0.912014i	$-0.365473\pi$
$7$	−1.32779	−	1.32779i	−0.501856	−	0.501856i	−0.912014	+	0.410159i	$0.865473\pi$
$8$	0.176583	−	2.82291i	0.0624316	−	0.998049i
$9$		0			0
$10$	0.450684	−	0.110756i	0.142519	−	0.0350241i
$11$	−0.693922	+	0.693922i	−0.209225	+	0.209225i	−0.803938	−	0.594713i	$-0.797266\pi$
$11$	−0.693922	+	0.693922i	−0.209225	+	0.209225i	0.594713	+	0.803938i	$0.297266\pi$
$12$		0			0
$13$	3.60100	−	0.181078i	0.998738	−	0.0502220i
$13$	3.60100	−	0.181078i	0.998738	−	0.0502220i
$14$	0.633752	+	2.57884i	0.169377	+	0.689224i
$15$		0			0
$16$	−2.28128	+	3.28569i	−0.570320	+	0.821423i
$17$		−	6.65027i		−	1.61293i	−0.591283	−	0.806464i	$-0.701378\pi$
$17$		−	6.65027i		−	1.61293i	0.591283	−	0.806464i	$-0.298622\pi$
$18$		0			0
$19$	3.67982	+	3.67982i	0.844210	+	0.844210i	0.989403	−	0.145194i	$-0.0463805\pi$
$19$	3.67982	+	3.67982i	0.844210	+	0.844210i	−0.145194	+	0.989403i	$0.546380\pi$
$20$	−0.626342	−	0.196119i	−0.140054	−	0.0438535i
$21$		0			0
$22$	1.34774	−	0.331209i	0.287340	−	0.0706139i
$23$	−8.15485			−1.70040			−0.850202	−	0.526457i	$-0.823520\pi$
$23$	−8.15485			−1.70040			−0.850202	+	0.526457i	$0.823520\pi$
$24$		0			0
$25$			4.89231i			0.978462i
$26$	−4.48896	−	2.41851i	−0.880358	−	0.474310i
$27$		0			0
$28$	1.12220	−	3.58396i	0.212076	−	0.677305i
$29$		−	5.34245i		−	0.992069i	−0.868303	−	0.496034i	$-0.834789\pi$
$29$		−	5.34245i		−	0.992069i	0.868303	−	0.496034i	$-0.165211\pi$
$30$		0			0
$31$	2.87096	−	2.87096i	0.515640	−	0.515640i	−0.400609	−	0.916249i	$-0.631202\pi$
$31$	2.87096	−	2.87096i	0.515640	−	0.515640i	0.916249	+	0.400609i	$0.131202\pi$
$32$	5.16641	−	2.30395i	0.913302	−	0.407284i
$33$		0			0
$34$	−4.87103	+	8.04520i	−0.835375	+	1.37974i
$35$	0.616217			0.104160
$36$		0			0
$37$	−7.85762	−	7.85762i	−1.29178	−	1.29178i	−0.933682	−	0.358103i	$-0.883424\pi$
$37$	−7.85762	−	7.85762i	−1.29178	−	1.29178i	−0.358103	−	0.933682i	$-0.616576\pi$
$38$	−1.75638	−	7.14700i	−0.284922	−	1.15940i
$39$		0			0
$40$	0.614072	+	0.696023i	0.0970933	+	0.110051i
$41$	5.49860	+	5.49860i	0.858737	+	0.858737i	0.991189	−	0.132452i	$-0.0422852\pi$
$41$	5.49860	+	5.49860i	0.858737	+	0.858737i	−0.132452	+	0.991189i	$0.542285\pi$
$42$		0			0
$43$		−	6.91010i		−	1.05378i	−0.849933	−	0.526891i	$-0.823358\pi$
$43$		−	6.91010i		−	1.05378i	0.849933	−	0.526891i	$-0.176642\pi$
$44$	−1.87303	−	0.586480i	−0.282371	−	0.0884152i
$45$		0			0
$46$	9.86538	+	5.97307i	1.45457	+	0.880681i
$47$	4.22794	+	4.22794i	0.616708	+	0.616708i	0.944685	−	0.327978i	$-0.106367\pi$
$47$	4.22794	+	4.22794i	0.616708	+	0.616708i	−0.327978	+	0.944685i	$0.606367\pi$
$48$		0			0
$49$		−	3.47397i		−	0.496282i
$50$	3.58340	−	5.91850i	0.506769	−	0.837002i
$51$		0			0
$52$	3.65909	+	6.21378i	0.507425	+	0.861696i
$53$		−	10.9391i		−	1.50261i	−0.659957	−	0.751304i	$-0.729425\pi$
$53$		−	10.9391i		−	1.50261i	0.659957	−	0.751304i	$-0.270575\pi$
$54$		0			0
$55$		−	0.322045i		−	0.0434245i
$56$	−3.98268	+	3.51375i	−0.532208	+	0.469545i
$57$		0			0
$58$	−3.91311	+	6.46306i	−0.513817	+	0.848642i
$59$	7.51705	−	7.51705i	0.978637	−	0.978637i	−0.0211400	−	0.999777i	$-0.506730\pi$
$59$	7.51705	−	7.51705i	0.978637	−	0.978637i	0.999777	+	0.0211400i	$0.00672956\pi$
$60$		0			0
$61$		−	6.47155i		−	0.828597i	−0.910141	−	0.414299i	$-0.864027\pi$
$61$		−	6.47155i		−	0.828597i	0.910141	−	0.414299i	$-0.135973\pi$
$62$	−5.57601	+	1.37031i	−0.708154	+	0.174029i
$63$		0			0
$64$	−7.93764	−	0.996957i	−0.992205	−	0.124620i
$65$	−0.793583	+	0.877620i	−0.0984318	+	0.108855i
$66$		0			0
$67$	3.34449	+	3.34449i	0.408595	+	0.408595i	0.881248	−	0.472654i	$-0.156704\pi$
$67$	3.34449	+	3.34449i	0.408595	+	0.408595i	−0.472654	+	0.881248i	$0.656704\pi$
$68$	11.7855	−	6.16491i	1.42920	−	0.747606i
$69$		0			0
$70$	−0.745472	−	0.451352i	−0.0891009	−	0.0539469i
$71$	−7.22680	+	7.22680i	−0.857663	+	0.857663i	−0.991062	−	0.133399i	$-0.957411\pi$
$71$	−7.22680	+	7.22680i	−0.857663	+	0.857663i	0.133399	+	0.991062i	$0.457411\pi$
$72$		0			0
$73$	9.22075	−	9.22075i	1.07921	−	1.07921i	0.0826264	−	0.996581i	$-0.473669\pi$
$73$	9.22075	−	9.22075i	1.07921	−	1.07921i	0.996581	−	0.0826264i	$-0.0263308\pi$
$74$	3.75044	+	15.2612i	0.435980	+	1.77407i
$75$		0			0
$76$	−3.11007	+	9.93259i	−0.356750	+	1.13935i
$77$	1.84276			0.210002
$78$		0			0
$79$		−	13.9125i		−	1.56528i	−0.622475	−	0.782640i	$-0.713873\pi$
$79$		−	13.9125i		−	1.56528i	0.622475	−	0.782640i	$-0.286127\pi$
$80$	−0.233071	−	1.29180i	−0.0260581	−	0.144427i
$81$		0			0
$82$	−2.62448	−	10.6794i	−0.289825	−	1.17935i
$83$	−4.01110	−	4.01110i	−0.440275	−	0.440275i	0.451829	−	0.892104i	$-0.350772\pi$
$83$	−4.01110	−	4.01110i	−0.440275	−	0.440275i	−0.892104	+	0.451829i	$0.850772\pi$
$84$		0			0
$85$	1.54318	+	1.54318i	0.167381	+	0.167381i
$86$	−5.06135	+	8.35954i	−0.545779	+	0.901432i
$87$		0			0
$88$	1.83634	+	2.08141i	0.195755	+	0.221879i
$89$	1.32098	−	1.32098i	0.140024	−	0.140024i	−0.633620	−	0.773644i	$-0.718432\pi$
$89$	1.32098	−	1.32098i	0.140024	−	0.140024i	0.773644	+	0.633620i	$0.218432\pi$
$90$		0			0
$91$	−5.02179	−	4.54092i	−0.526427	−	0.476018i
$92$	−7.55969	−	14.4519i	−0.788152	−	1.50672i
$93$		0			0
$94$	−2.01799	−	8.21154i	−0.208140	−	0.846956i
$95$	−1.70778			−0.175215
$96$		0			0
$97$	−4.77810	−	4.77810i	−0.485142	−	0.485142i	0.421627	−	0.906769i	$-0.361459\pi$
$97$	−4.77810	−	4.77810i	−0.485142	−	0.485142i	−0.906769	+	0.421627i	$0.861459\pi$
$98$	−2.54453	+	4.20266i	−0.257037	+	0.424533i
$99$		0			0
$100$	−8.67008	+	4.53525i	−0.867008	+	0.453525i
$101$	4.90646			0.488211			0.244106	−	0.969749i	$-0.421506\pi$
$101$	4.90646			0.488211			0.244106	+	0.969749i	$0.421506\pi$
$102$		0			0
$103$	−9.68894			−0.954680			−0.477340	−	0.878719i	$-0.658399\pi$
$103$	−9.68894			−0.954680			−0.477340	+	0.878719i	$0.658399\pi$
$104$	0.124710	−	10.1973i	0.0122289	−	0.999925i
$105$		0			0
$106$	−8.01244	+	13.2337i	−0.778237	+	1.28537i
$107$	−7.23790			−0.699714			−0.349857	−	0.936803i	$-0.613770\pi$
$107$	−7.23790			−0.699714			−0.349857	+	0.936803i	$0.613770\pi$
$108$		0			0
$109$	−3.80269	+	3.80269i	−0.364232	+	0.364232i	−0.865368	−	0.501137i	$-0.832915\pi$
$109$	−3.80269	+	3.80269i	−0.364232	+	0.364232i	0.501137	+	0.865368i	$0.332915\pi$
$110$	−0.235884	+	0.389595i	−0.0224906	+	0.0371465i
$111$		0			0
$112$	7.39174	−	1.33364i	0.698454	−	0.126017i
$113$	1.22553			0.115288			0.0576440	−	0.998337i	$-0.481641\pi$
$113$	1.22553			0.115288			0.0576440	+	0.998337i	$0.481641\pi$
$114$		0			0
$115$	1.89231	−	1.89231i	0.176459	−	0.176459i
$116$	9.46782	−	4.95255i	0.879065	−	0.459832i
$117$		0			0
$118$	−14.5997	+	3.58789i	−1.34401	+	0.330292i
$119$	−8.83013	+	8.83013i	−0.809457	+	0.809457i
$120$		0			0
$121$			10.0369i			0.912450i
$122$	−4.74012	+	7.82899i	−0.429151	+	0.708804i
$123$		0			0
$124$	7.74930	+	2.42644i	0.695908	+	0.217901i
$125$	−2.29548	−	2.29548i	−0.205314	−	0.205314i
$126$		0			0
$127$	−11.2982			−1.00255			−0.501275	−	0.865288i	$-0.667135\pi$
$127$	−11.2982			−1.00255			−0.501275	+	0.865288i	$0.667135\pi$
$128$	8.87237	+	7.02004i	0.784214	+	0.620490i
$129$		0			0
$130$	1.60286	−	0.480441i	0.140580	−	0.0421375i
$131$	−11.6351			−1.01656			−0.508282	−	0.861191i	$-0.669719\pi$
$131$	−11.6351			−1.01656			−0.508282	+	0.861191i	$0.669719\pi$
$132$		0			0
$133$		−	9.77203i		−	0.847343i
$134$	−1.59633	−	6.49571i	−0.137902	−	0.561144i
$135$		0			0
$136$	−18.7731	−	1.17433i	−1.60978	−	0.100698i
$137$	−6.64576	+	6.64576i	−0.567786	+	0.567786i	−0.931508	−	0.363722i	$-0.881506\pi$
$137$	−6.64576	+	6.64576i	−0.567786	+	0.567786i	0.363722	+	0.931508i	$0.381506\pi$
$138$		0			0
$139$	12.0057			1.01831			0.509157	−	0.860674i	$-0.329957\pi$
$139$	12.0057			1.01831			0.509157	+	0.860674i	$0.329957\pi$
$140$	0.571244	+	1.09205i	0.0482789	+	0.0922951i
$141$		0			0
$142$	14.0360	−	3.44935i	1.17787	−	0.289463i
$143$	−2.37316	+	2.62447i	−0.198454	+	0.219469i
$144$		0			0
$145$	1.23970	+	1.23970i	0.102952	+	0.102952i
$146$	−17.9086	+	4.40106i	−1.48213	+	0.364234i
$147$		0			0
$148$	6.64101	−	21.2093i	0.545888	−	1.74339i
$149$	15.0395	−	15.0395i	1.23208	−	1.23208i	0.268920	−	0.963162i	$-0.413333\pi$
$149$	15.0395	−	15.0395i	1.23208	−	1.23208i	0.963162	−	0.268920i	$-0.0866668\pi$
$150$		0			0
$151$	2.14133	+	2.14133i	0.174259	+	0.174259i	0.788848	−	0.614589i	$-0.210678\pi$
$151$	2.14133	+	2.14133i	0.174259	+	0.174259i	−0.614589	+	0.788848i	$0.710678\pi$
$152$	11.0376	−	9.73802i	0.895268	−	0.789857i
$153$		0			0
$154$	−2.22929	−	1.34974i	−0.179641	−	0.108765i
$155$			1.33240i			0.107021i
$156$		0			0
$157$		−	1.56379i		−	0.124804i	−0.998051	−	0.0624018i	$-0.980124\pi$
$157$		−	1.56379i		−	0.124804i	0.998051	−	0.0624018i	$-0.0198760\pi$
$158$	−10.1903	+	16.8307i	−0.810696	+	1.33898i
$159$		0			0
$160$	−0.664227	+	1.73347i	−0.0525117	+	0.137043i
$161$	10.8279	+	10.8279i	0.853357	+	0.853357i
$162$		0			0
$163$	3.34449	−	3.34449i	0.261961	−	0.261961i	−0.563889	−	0.825850i	$-0.690696\pi$
$163$	3.34449	−	3.34449i	0.261961	−	0.261961i	0.825850	+	0.563889i	$0.190696\pi$
$164$	−4.64724	+	14.8418i	−0.362889	+	1.15895i
$165$		0			0
$166$	1.91449	+	7.79040i	0.148594	+	0.604652i
$167$	12.1201	+	12.1201i	0.937882	+	0.937882i	0.998180	−	0.0602983i	$-0.0192052\pi$
$167$	12.1201	+	12.1201i	0.937882	+	0.937882i	−0.0602983	+	0.998180i	$0.519205\pi$
$168$		0			0
$169$	12.9344	−	1.30412i	0.994956	−	0.100317i
$170$	−0.736557	−	2.99717i	−0.0564914	−	0.229873i
$171$		0			0
$172$	12.2460	−	6.40578i	0.933747	−	0.488436i
$173$	17.4010			1.32297			0.661485	−	0.749958i	$-0.269926\pi$
$173$	17.4010			1.32297			0.661485	+	0.749958i	$0.269926\pi$
$174$		0			0
$175$	6.49593	−	6.49593i	0.491047	−	0.491047i
$176$	−0.696983	−	3.86304i	−0.0525371	−	0.291188i
$177$		0			0
$178$	−2.56562	+	0.630503i	−0.192302	+	0.0472582i
$179$			3.61291i			0.270041i	0.990843	+	0.135021i	$0.0431101\pi$
$179$			3.61291i			0.270041i	−0.990843	+	0.135021i	$0.956890\pi$
$180$		0			0
$181$	−1.37454			−0.102169			−0.0510845	−	0.998694i	$-0.516268\pi$
$181$	−1.37454			−0.102169			−0.0510845	+	0.998694i	$0.516268\pi$
$182$	2.74911	+	9.17165i	0.203778	+	0.679848i
$183$		0			0
$184$	−1.44001	+	23.0204i	−0.106159	+	1.69709i
$185$	3.64667			0.268109
$186$		0			0
$187$	4.61477	+	4.61477i	0.337465	+	0.337465i
$188$	−3.57332	+	11.4121i	−0.260611	+	0.832309i
$189$		0			0
$190$	2.06600	+	1.25088i	0.149883	+	0.0907481i
$191$			15.9525i			1.15428i	0.816645	+	0.577140i	$0.195832\pi$
$191$			15.9525i			1.15428i	−0.816645	+	0.577140i	$0.804168\pi$
$192$		0			0
$193$	−2.65778	+	2.65778i	−0.191311	+	0.191311i	−0.796262	−	0.604951i	$-0.793193\pi$
$193$	−2.65778	+	2.65778i	−0.191311	+	0.191311i	0.604951	+	0.796262i	$0.293193\pi$
$194$	2.28058	+	9.28007i	0.163736	+	0.666270i
$195$		0			0
$196$	6.15652	−	3.22043i	0.439752	−	0.230031i
$197$	−0.232047	+	0.232047i	−0.0165327	+	0.0165327i	−0.715325	−	0.698792i	$-0.753721\pi$
$197$	−0.232047	+	0.232047i	−0.0165327	+	0.0165327i	0.698792	+	0.715325i	$0.253721\pi$
$198$		0			0
$199$	18.9301			1.34192			0.670960	−	0.741493i	$-0.265882\pi$
$199$	18.9301			1.34192			0.670960	+	0.741493i	$0.265882\pi$
$200$	13.8105	+	0.863900i	0.976553	+	0.0610870i
$201$		0			0
$202$	−5.93562	−	3.59377i	−0.417629	−	0.252857i
$203$	−7.09363	+	7.09363i	−0.497875	+	0.497875i
$204$		0			0
$205$	−2.55187			−0.178230
$206$	11.7212	+	7.09672i	0.816658	+	0.494452i
$207$		0			0
$208$	−7.61992	+	12.2449i	−0.528347	+	0.849029i
$209$	−5.10702			−0.353260
$210$		0			0
$211$	−28.2261			−1.94317			−0.971583	−	0.236699i	$-0.923934\pi$
$211$	−28.2261			−1.94317			−0.971583	+	0.236699i	$0.923934\pi$
$212$	19.3862	−	10.1408i	1.33145	−	0.696471i
$213$		0			0
$214$	8.75609	+	5.30144i	0.598554	+	0.362399i
$215$	1.60347	+	1.60347i	0.109356	+	0.109356i
$216$		0			0
$217$	−7.62404			−0.517553
$218$	7.38563	−	1.81502i	0.500218	−	0.122929i
$219$		0			0
$220$	0.570723	−	0.298541i	0.0384781	−	0.0201276i
$221$	−1.20422	−	23.9476i	−0.0810044	−	1.61089i
$222$		0			0
$223$	−8.36647	+	8.36647i	−0.560260	+	0.560260i	−0.929381	−	0.369121i	$-0.879659\pi$
$223$	−8.36647	+	8.36647i	−0.560260	+	0.560260i	0.369121	+	0.929381i	$0.379659\pi$
$224$	−9.91903	−	3.80074i	−0.662743	−	0.253948i
$225$		0			0
$226$	−1.48259	−	0.897645i	−0.0986204	−	0.0597105i
$227$	15.1395	+	15.1395i	1.00484	+	1.00484i	0.999988	+	0.00485599i	$0.00154572\pi$
$227$	15.1395	+	15.1395i	1.00484	+	1.00484i	0.00485599	+	0.999988i	$0.498454\pi$
$228$		0			0
$229$	7.68899	+	7.68899i	0.508103	+	0.508103i	0.913944	−	0.405841i	$-0.133021\pi$
$229$	7.68899	+	7.68899i	0.508103	+	0.508103i	−0.405841	+	0.913944i	$0.633021\pi$
$230$	−3.67526	+	0.903198i	−0.242340	+	0.0595551i
$231$		0			0
$232$	−15.0813	−	0.943388i	−0.990134	−	0.0619365i
$233$		−	14.6667i		−	0.960848i	−0.877036	−	0.480424i	$-0.840483\pi$
$233$		−	14.6667i		−	0.960848i	0.877036	−	0.480424i	$-0.159517\pi$
$234$		0			0
$235$	−1.96216			−0.127997
$236$	20.2900	+	6.35317i	1.32077	+	0.413556i
$237$		0			0
$238$	17.1500	−	4.21462i	1.11167	−	0.273193i
$239$	−14.6118	+	14.6118i	−0.945160	+	0.945160i	−0.998573	−	0.0534121i	$-0.982990\pi$
$239$	−14.6118	+	14.6118i	−0.945160	+	0.945160i	0.0534121	+	0.998573i	$0.482990\pi$
$240$		0			0
$241$	4.71367	−	4.71367i	0.303634	−	0.303634i	−0.538800	−	0.842434i	$-0.681122\pi$
$241$	4.71367	−	4.71367i	0.303634	−	0.303634i	0.842434	+	0.538800i	$0.181122\pi$
$242$	7.35162	−	12.1423i	0.472580	−	0.780533i
$243$		0			0
$244$	11.4688	−	5.99924i	0.734214	−	0.384062i
$245$	0.806125	+	0.806125i	0.0515014	+	0.0515014i
$246$		0			0
$247$	13.9174	+	12.5847i	0.885542	+	0.800746i
$248$	−7.59750	−	8.61143i	−0.482442	−	0.546826i
$249$		0			0
$250$	1.09563	+	4.45831i	0.0692938	+	0.281968i
$251$		−	2.84128i		−	0.179340i	−0.995972	−	0.0896701i	$-0.971419\pi$
$251$		−	2.84128i		−	0.179340i	0.995972	−	0.0896701i	$-0.0285813\pi$
$252$		0			0
$253$	5.65883	−	5.65883i	0.355767	−	0.355767i
$254$	13.6680	+	8.27540i	0.857607	+	0.519245i
$255$		0			0
$256$	−5.59153	−	14.9912i	−0.349471	−	0.936947i
$257$			18.5254i			1.15558i	0.816185	+	0.577790i	$0.196085\pi$
$257$			18.5254i			1.15558i	−0.816185	+	0.577790i	$0.803915\pi$
$258$		0			0
$259$			20.8665i			1.29658i
$260$	−2.29097	−	0.592807i	−0.142080	−	0.0367643i
$261$		0			0
$262$	14.0756	+	8.52220i	0.869595	+	0.526503i
$263$			3.70928i			0.228724i	0.993439	+	0.114362i	$0.0364824\pi$
$263$			3.70928i			0.228724i	−0.993439	+	0.114362i	$0.963518\pi$
$264$		0			0
$265$	2.53840	+	2.53840i	0.155932	+	0.155932i
$266$	−7.15758	+	11.8218i	−0.438860	+	0.724839i
$267$		0			0
$268$	−2.82666	+	9.02746i	−0.172666	+	0.551440i
$269$			15.5582i			0.948601i	0.880363	+	0.474300i	$0.157299\pi$
$269$			15.5582i			0.948601i	−0.880363	+	0.474300i	$0.842701\pi$
$270$		0			0
$271$	−7.90807	−	7.90807i	−0.480381	−	0.480381i	0.424872	−	0.905253i	$-0.360319\pi$
$271$	−7.90807	−	7.90807i	−0.480381	−	0.480381i	−0.905253	+	0.424872i	$0.860319\pi$
$272$	21.8507	+	15.1711i	1.32490	+	0.919885i
$273$		0			0
$274$	12.9075	−	3.17202i	0.779769	−	0.191629i
$275$	−3.39488	−	3.39488i	−0.204719	−	0.204719i
$276$		0			0
$277$	10.4041			0.625122			0.312561	−	0.949898i	$-0.398813\pi$
$277$	10.4041			0.625122			0.312561	+	0.949898i	$0.398813\pi$
$278$	−14.5240	−	8.79367i	−0.871092	−	0.527409i
$279$		0			0
$280$	0.108814	−	1.73952i	0.00650286	−	0.103956i
$281$	−9.28915	+	9.28915i	−0.554144	+	0.554144i	−0.927634	−	0.373490i	$-0.878161\pi$
$281$	−9.28915	+	9.28915i	−0.554144	+	0.554144i	0.373490	+	0.927634i	$0.378161\pi$
$282$		0			0
$283$			14.0298i			0.833985i	0.908910	+	0.416992i	$0.136916\pi$
$283$			14.0298i			0.833985i	−0.908910	+	0.416992i	$0.863084\pi$
$284$	−19.5066	−	6.10786i	−1.15750	−	0.362435i
$285$		0			0
$286$	4.79325	−	1.43673i	0.283431	−	0.0849556i
$287$		−	14.6019i		−	0.861924i
$288$		0			0
$289$	−27.2261			−1.60154
$290$	−0.591709	−	2.40776i	−0.0347463	−	0.141389i
$291$		0			0
$292$	24.8887	+	7.79308i	1.45650	+	0.456056i
$293$	5.13851	+	5.13851i	0.300195	+	0.300195i	0.841090	−	0.540895i	$-0.181914\pi$
$293$	5.13851	+	5.13851i	0.300195	+	0.300195i	−0.540895	+	0.841090i	$0.681914\pi$
$294$		0			0
$295$			3.48862i			0.203115i
$296$	−23.5689	+	20.7938i	−1.36991	+	1.20862i
$297$		0			0
$298$	−29.2099	+	7.17834i	−1.69208	+	0.415830i
$299$	−29.3656	+	1.47666i	−1.69826	+	0.0853976i
$300$		0			0
$301$	−9.17513	+	9.17513i	−0.528846	+	0.528846i
$302$	−1.02206	−	4.15892i	−0.0588128	−	0.239319i
$303$		0			0
$304$	−20.4855	+	3.69606i	−1.17492	+	0.211984i
$305$	1.50170	+	1.50170i	0.0859873	+	0.0859873i
$306$		0			0
$307$	15.9650	−	15.9650i	0.911170	−	0.911170i	−0.0851939	−	0.996364i	$-0.527151\pi$
$307$	15.9650	−	15.9650i	0.911170	−	0.911170i	0.996364	+	0.0851939i	$0.0271510\pi$
$308$	1.70827	+	3.26571i	0.0973376	+	0.186081i
$309$		0			0
$310$	0.975921	−	1.61187i	0.0554286	−	0.0915482i
$311$	11.8644			0.672769			0.336384	−	0.941725i	$-0.390796\pi$
$311$	11.8644			0.672769			0.336384	+	0.941725i	$0.390796\pi$
$312$		0			0
$313$	2.08900			0.118077			0.0590386	−	0.998256i	$-0.481196\pi$
$313$	2.08900			0.118077			0.0590386	+	0.998256i	$0.481196\pi$
$314$	−1.14540	+	1.89180i	−0.0646389	+	0.106760i
$315$		0			0
$316$	24.6555	−	12.8971i	1.38698	−	0.725520i
$317$	17.2819	−	17.2819i	0.970647	−	0.970647i	−0.0289346	−	0.999581i	$-0.509211\pi$
$317$	17.2819	−	17.2819i	0.970647	−	0.970647i	0.999581	+	0.0289346i	$0.00921146\pi$
$318$		0			0
$319$	3.70724	+	3.70724i	0.207566	+	0.207566i
$320$	2.07325	−	1.61056i	0.115898	−	0.0900332i
$321$		0			0
$322$	−5.16815	−	21.0301i	−0.288010	−	1.17196i
$323$	24.4718	−	24.4718i	1.36165	−	1.36165i
$324$		0			0
$325$	0.885889	+	17.6172i	0.0491403	+	0.977227i
$326$	−6.49571	+	1.59633i	−0.359764	+	0.0884123i
$327$		0			0
$328$	16.4930	−	14.5511i	0.910674	−	0.803449i
$329$		−	11.2276i		−	0.618996i
$330$		0			0
$331$	−5.85157	−	5.85157i	−0.321631	−	0.321631i	0.527761	−	0.849393i	$-0.323032\pi$
$331$	−5.85157	−	5.85157i	−0.321631	−	0.321631i	−0.849393	+	0.527761i	$0.823032\pi$
$332$	3.39005	−	10.8268i	0.186053	−	0.594195i
$333$		0			0
$334$	−5.78492	−	23.5398i	−0.316537	−	1.28804i
$335$	−1.55216			−0.0848035
$336$		0			0
$337$			19.6314i			1.06939i	0.845045	+	0.534695i	$0.179574\pi$
$337$			19.6314i			1.06939i	−0.845045	+	0.534695i	$0.820426\pi$
$338$	−16.6027	−	7.89622i	−0.903068	−	0.429498i
$339$		0			0
$340$	−1.30424	+	4.16534i	−0.0707325	+	0.225897i
$341$			3.98444i			0.215770i
$342$		0			0
$343$	−13.9072	+	13.9072i	−0.750917	+	0.750917i
$344$	−19.5066	−	1.22021i	−1.05173	−	0.0657893i
$345$		0			0
$346$	−21.0509	−	12.7454i	−1.13170	−	0.685199i
$347$	18.5916			0.998047			0.499024	−	0.866588i	$-0.333692\pi$
$347$	18.5916			0.998047			0.499024	+	0.866588i	$0.333692\pi$
$348$		0			0
$349$	4.63491	+	4.63491i	0.248101	+	0.248101i	0.820191	−	0.572090i	$-0.193867\pi$
$349$	4.63491	+	4.63491i	0.248101	+	0.248101i	−0.572090	+	0.820191i	$0.693867\pi$
$350$	−12.6165	+	3.10051i	−0.674379	+	0.165729i
$351$		0			0
$352$	−1.98633	+	5.18384i	−0.105872	+	0.276300i
$353$	−9.42145	−	9.42145i	−0.501453	−	0.501453i	0.410436	−	0.911889i	$-0.365376\pi$
$353$	−9.42145	−	9.42145i	−0.501453	−	0.501453i	−0.911889	+	0.410436i	$0.865376\pi$
$354$		0			0
$355$		−	3.35391i		−	0.178007i
$356$	3.56559	+	1.11645i	0.188976	+	0.0591717i
$357$		0			0
$358$	2.64630	−	4.37074i	0.139861	−	0.231001i
$359$	−14.5075	−	14.5075i	−0.765677	−	0.765677i	0.211665	−	0.977342i	$-0.432111\pi$
$359$	−14.5075	−	14.5075i	−0.765677	−	0.765677i	−0.977342	+	0.211665i	$0.932111\pi$
$360$		0			0
$361$			8.08222i			0.425380i
$362$	1.66286	+	1.00679i	0.0873980	+	0.0529158i
$363$		0			0
$364$	3.39207	−	13.1091i	0.177793	−	0.687101i
$365$			4.27929i			0.223988i
$366$		0			0
$367$		−	28.8535i		−	1.50614i	−0.657940	−	0.753070i	$-0.728572\pi$
$367$		−	28.8535i		−	1.50614i	0.657940	−	0.753070i	$-0.271428\pi$
$368$	18.6035	−	26.7943i	0.969774	−	1.39675i
$369$		0			0
$370$	−4.41158	−	2.67103i	−0.229347	−	0.138860i
$371$	−14.5248	+	14.5248i	−0.754092	+	0.754092i
$372$		0			0
$373$			29.6380i			1.53460i	0.641290	+	0.767299i	$0.278400\pi$
$373$			29.6380i			1.53460i	−0.641290	+	0.767299i	$0.721600\pi$
$374$	−2.20263	−	8.96285i	−0.113895	−	0.463458i
$375$		0			0
$376$	12.6817	−	11.1885i	0.654007	−	0.577003i
$377$	−0.967400	−	19.2382i	−0.0498236	−	0.990817i
$378$		0			0
$379$	−13.5358	−	13.5358i	−0.695285	−	0.695285i	0.268105	−	0.963390i	$-0.413603\pi$
$379$	−13.5358	−	13.5358i	−0.695285	−	0.695285i	−0.963390	+	0.268105i	$0.913603\pi$
$380$	−1.58314	−	3.02651i	−0.0812136	−	0.155257i
$381$		0			0
$382$	11.6845	−	19.2986i	0.597830	−	0.987402i
$383$	−25.6471	+	25.6471i	−1.31051	+	1.31051i	−0.389465	+	0.921041i	$0.627340\pi$
$383$	−25.6471	+	25.6471i	−1.31051	+	1.31051i	−0.921041	+	0.389465i	$0.872660\pi$
$384$		0			0
$385$	−0.427606	+	0.427606i	−0.0217928	+	0.0217928i
$386$	5.16196	−	1.26856i	0.262737	−	0.0645678i
$387$		0			0
$388$	4.03829	−	12.8970i	0.205013	−	0.654748i
$389$	−2.59961			−0.131806			−0.0659028	−	0.997826i	$-0.520993\pi$
$389$	−2.59961			−0.131806			−0.0659028	+	0.997826i	$0.520993\pi$
$390$		0			0
$391$			54.2320i			2.74263i
$392$	−9.80671	−	0.613446i	−0.495314	−	0.0309837i
$393$		0			0
$394$	0.450684	−	0.110756i	0.0227051	−	0.00557980i
$395$	3.22835	+	3.22835i	0.162436	+	0.162436i
$396$		0			0
$397$	−0.396880	−	0.396880i	−0.0199188	−	0.0199188i	0.697077	−	0.716996i	$-0.254483\pi$
$397$	−0.396880	−	0.396880i	−0.0199188	−	0.0199188i	−0.716996	+	0.697077i	$0.754483\pi$
$398$	−22.9008	−	13.8655i	−1.14791	−	0.695013i
$399$		0			0
$400$	−16.0746	−	11.1607i	−0.803731	−	0.558036i
$401$	−1.18544	+	1.18544i	−0.0591979	+	0.0591979i	−0.736086	−	0.676888i	$-0.763328\pi$
$401$	−1.18544	+	1.18544i	−0.0591979	+	0.0591979i	0.676888	+	0.736086i	$0.263328\pi$
$402$		0			0
$403$	9.81847	−	10.8582i	0.489093	−	0.540885i
$404$	4.54837	+	8.69516i	0.226290	+	0.432600i
$405$		0			0
$406$	13.7773	−	3.38579i	0.683758	−	0.168034i
$407$	10.9051			0.540548
$408$		0			0
$409$	−3.20321	−	3.20321i	−0.158389	−	0.158389i	0.623464	−	0.781852i	$-0.285725\pi$
$409$	−3.20321	−	3.20321i	−0.158389	−	0.158389i	−0.781852	+	0.623464i	$0.785725\pi$
$410$	3.08713	+	1.86913i	0.152463	+	0.0923097i
$411$		0			0
$412$	−8.98181	−	17.1706i	−0.442502	−	0.845934i
$413$	−19.9621			−0.982269
$414$		0			0
$415$	1.86152			0.0913787
$416$	18.1871	−	9.23204i	0.891694	−	0.452638i
$417$		0			0
$418$	6.17825	+	3.74067i	0.302188	+	0.182962i
$419$	−26.8342			−1.31094			−0.655468	−	0.755223i	$-0.727528\pi$
$419$	−26.8342			−1.31094			−0.655468	+	0.755223i	$0.727528\pi$
$420$		0			0
$421$	1.67708	−	1.67708i	0.0817361	−	0.0817361i	−0.665057	−	0.746793i	$-0.731593\pi$
$421$	1.67708	−	1.67708i	0.0817361	−	0.0817361i	0.746793	+	0.665057i	$0.231593\pi$
$422$	34.1467	+	20.6744i	1.66224	+	1.00641i
$423$		0			0
$424$	−30.8802	−	1.93167i	−1.49968	−	0.0938102i
$425$	32.5352			1.57819
$426$		0			0
$427$	−8.59283	+	8.59283i	−0.415836	+	0.415836i
$428$	−6.70966	−	12.8269i	−0.324323	−	0.620011i
$429$		0			0
$430$	−0.765335	−	3.11428i	−0.0369077	−	0.150184i
$431$	12.1299	−	12.1299i	0.584276	−	0.584276i	−0.351800	−	0.936075i	$-0.614430\pi$
$431$	12.1299	−	12.1299i	0.584276	−	0.584276i	0.936075	+	0.351800i	$0.114430\pi$
$432$		0			0
$433$		−	22.8756i		−	1.09933i	−0.835384	−	0.549666i	$-0.814755\pi$
$433$		−	22.8756i		−	1.09933i	0.835384	−	0.549666i	$-0.185245\pi$
$434$	9.22322	+	5.58427i	0.442729	+	0.268054i
$435$		0			0
$436$	−10.2642	−	3.21391i	−0.491567	−	0.153918i
$437$	−30.0084	−	30.0084i	−1.43550	−	1.43550i
$438$		0			0
$439$	17.4118			0.831018			0.415509	−	0.909589i	$-0.363604\pi$
$439$	17.4118			0.831018			0.415509	+	0.909589i	$0.363604\pi$
$440$	−0.909103	−	0.0568677i	−0.0433398	−	0.00271106i
$441$		0			0
$442$	−16.0838	+	29.8528i	−0.765027	+	1.41995i
$443$	23.8279			1.13210			0.566049	−	0.824371i	$-0.308471\pi$
$443$	23.8279			1.13210			0.566049	+	0.824371i	$0.308471\pi$
$444$		0			0
$445$			0.613059i			0.0290618i
$446$	16.2495	−	3.99332i	0.769434	−	0.189089i
$447$		0			0
$448$	9.21573	+	11.8632i	0.435402	+	0.560485i
$449$	8.40224	−	8.40224i	0.396526	−	0.396526i	−0.480480	−	0.877006i	$-0.659537\pi$
$449$	8.40224	−	8.40224i	0.396526	−	0.396526i	0.877006	+	0.480480i	$0.159537\pi$
$450$		0			0
$451$	−7.63119			−0.359339
$452$	1.13609	+	2.17186i	0.0534370	+	0.102156i
$453$		0			0
$454$	−7.22608	−	29.4041i	−0.339137	−	1.38000i
$455$	2.21900	−	0.111583i	0.104028	−	0.00523110i
$456$		0			0
$457$	−7.98105	−	7.98105i	−0.373338	−	0.373338i	0.495354	−	0.868691i	$-0.335038\pi$
$457$	−7.98105	−	7.98105i	−0.373338	−	0.373338i	−0.868691	+	0.495354i	$0.835038\pi$
$458$	−3.66995	−	14.9336i	−0.171486	−	0.697803i
$459$		0			0
$460$	5.10772	+	1.59932i	0.238149	+	0.0745686i
$461$	−17.2976	+	17.2976i	−0.805629	+	0.805629i	−0.983969	−	0.178340i	$-0.942927\pi$
$461$	−17.2976	+	17.2976i	−0.805629	+	0.805629i	0.178340	+	0.983969i	$0.442927\pi$
$462$		0			0
$463$	17.9414	+	17.9414i	0.833806	+	0.833806i	0.988035	−	0.154229i	$-0.0492895\pi$
$463$	17.9414	+	17.9414i	0.833806	+	0.833806i	−0.154229	+	0.988035i	$0.549289\pi$
$464$	17.5537	+	12.1876i	0.814908	+	0.565797i
$465$		0			0
$466$	−10.7427	+	17.7431i	−0.497647	+	0.821934i
$467$			4.30932i			0.199412i	0.995017	+	0.0997058i	$0.0317902\pi$
$467$			4.30932i			0.199412i	−0.995017	+	0.0997058i	$0.968210\pi$
$468$		0			0
$469$		−	8.88154i		−	0.410111i
$470$	2.37373	+	1.43719i	0.109492	+	0.0662928i
$471$		0			0
$472$	−19.8926	−	22.5473i	−0.915630	−	1.03783i
$473$	4.79507	+	4.79507i	0.220478	+	0.220478i
$474$		0			0
$475$	−18.0028	+	18.0028i	−0.826027	+	0.826027i
$476$	−23.8343	−	7.46295i	−1.09244	−	0.342064i
$477$		0			0
$478$	28.3793	−	6.97422i	1.29804	−	0.318993i
$479$	4.44410	+	4.44410i	0.203056	+	0.203056i	0.801308	−	0.598252i	$-0.204138\pi$
$479$	4.44410	+	4.44410i	0.203056	+	0.203056i	−0.598252	+	0.801308i	$0.704138\pi$
$480$		0			0
$481$	−29.7181	−	26.8725i	−1.35503	−	1.22528i
$482$	−9.15495	+	2.24983i	−0.416997	+	0.102477i
$483$		0			0
$484$	−17.7873	+	9.30442i	−0.808515	+	0.422928i
$485$	2.21749			0.100691
$486$		0			0
$487$	−14.5302	+	14.5302i	−0.658424	+	0.658424i	−0.955007	−	0.296583i	$-0.904153\pi$
$487$	−14.5302	+	14.5302i	−0.658424	+	0.658424i	0.296583	+	0.955007i	$0.404153\pi$
$488$	−18.2686	−	1.14277i	−0.826981	−	0.0517307i
$489$		0			0
$490$	−0.384763	−	1.56566i	−0.0173818	−	0.0707295i
$491$		−	43.8723i		−	1.97993i	−0.141310	−	0.989965i	$-0.545131\pi$
$491$		−	43.8723i		−	1.97993i	0.141310	−	0.989965i	$-0.454869\pi$
$492$		0			0
$493$	−35.5288			−1.60014
$494$	−7.61889	−	25.4183i	−0.342790	−	1.14362i
$495$		0			0
$496$	2.88363	+	15.9826i	0.129479	+	0.717638i
$497$	19.1913			0.860846
$498$		0			0
$499$	−0.806097	−	0.806097i	−0.0360858	−	0.0360858i	0.688834	−	0.724919i	$-0.258123\pi$
$499$	−0.806097	−	0.806097i	−0.0360858	−	0.0360858i	−0.724919	+	0.688834i	$0.758123\pi$
$500$	1.94007	−	6.19596i	0.0867624	−	0.277092i
$501$		0			0
$502$	−2.08111	+	3.43726i	−0.0928847	+	0.153412i
$503$		−	24.9180i		−	1.11104i	−0.831504	−	0.555519i	$-0.812519\pi$
$503$		−	24.9180i		−	1.11104i	0.831504	−	0.555519i	$-0.187481\pi$
$504$		0			0
$505$	−1.13853	+	1.13853i	−0.0506639	+	0.0506639i
$506$	−10.9906	+	2.70096i	−0.488593	+	0.120072i
$507$		0			0
$508$	−10.4736	−	20.0224i	−0.464690	−	0.888351i
$509$	−2.52753	+	2.52753i	−0.112031	+	0.112031i	−0.760900	−	0.648869i	$-0.775242\pi$
$509$	−2.52753	+	2.52753i	−0.112031	+	0.112031i	0.648869	+	0.760900i	$0.275242\pi$
$510$		0			0
$511$	−24.4863			−1.08321
$512$	−4.21597	+	22.2312i	−0.186322	+	0.982489i
$513$		0			0
$514$	13.5690	−	22.4112i	0.598503	−	0.988514i
$515$	2.24829	−	2.24829i	0.0990714	−	0.0990714i
$516$		0			0
$517$	−5.86771			−0.258062
$518$	15.2838	−	25.2433i	0.671530	−	1.10913i
$519$		0			0
$520$	2.33731	+	2.39519i	0.102498	+	0.105036i
$521$	−29.1489			−1.27703			−0.638517	−	0.769607i	$-0.720452\pi$
$521$	−29.1489			−1.27703			−0.638517	+	0.769607i	$0.720452\pi$
$522$		0			0
$523$	3.00463			0.131383			0.0656916	−	0.997840i	$-0.479075\pi$
$523$	3.00463			0.131383			0.0656916	+	0.997840i	$0.479075\pi$
$524$	−10.7859	−	20.6195i	−0.471186	−	0.900769i
$525$		0			0
$526$	2.71689	−	4.48733i	0.118462	−	0.195657i
$527$	−19.0927	−	19.0927i	−0.831690	−	0.831690i
$528$		0			0
$529$	43.5016			1.89137
$530$	−1.21158	−	4.93010i	−0.0526275	−	0.214150i
$531$		0			0
$532$	17.3179	−	9.05884i	0.750824	−	0.392751i
$533$	20.7961	+	18.8048i	0.900781	+	0.814526i
$534$		0			0
$535$	1.67953	−	1.67953i	0.0726125	−	0.0726125i
$536$	10.0318	−	8.85062i	0.433307	−	0.382288i
$537$		0			0
$538$	11.3957	−	18.8216i	0.491304	−	0.811458i
$539$	2.41066	+	2.41066i	0.103835	+	0.103835i
$540$		0			0
$541$	24.7845	+	24.7845i	1.06557	+	1.06557i	0.997694	+	0.0678735i	$0.0216214\pi$
$541$	24.7845	+	24.7845i	1.06557	+	1.06557i	0.0678735	+	0.997694i	$0.478379\pi$
$542$	3.77452	+	15.3591i	0.162130	+	0.659732i
$543$		0			0
$544$	−15.3219	−	34.3581i	−0.656920	−	1.47309i
$545$		−	1.76481i		−	0.0755959i
$546$		0			0
$547$	−1.61287			−0.0689615			−0.0344807	−	0.999405i	$-0.510978\pi$
$547$	−1.61287			−0.0689615			−0.0344807	+	0.999405i	$0.510978\pi$
$548$	−17.9383	−	5.61679i	−0.766284	−	0.239937i
$549$		0			0
$550$	1.62037	+	6.59357i	0.0690930	+	0.281151i
$551$	19.6593	−	19.6593i	0.837514	−	0.837514i
$552$		0			0
$553$	−18.4728	+	18.4728i	−0.785544	+	0.785544i
$554$	−12.5864	−	7.62054i	−0.534746	−	0.323766i
$555$		0			0
$556$	11.1295	+	21.2764i	0.471997	+	0.902320i
$557$	−1.31897	−	1.31897i	−0.0558867	−	0.0558867i	0.678611	−	0.734498i	$-0.262582\pi$
$557$	−1.31897	−	1.31897i	−0.0558867	−	0.0558867i	−0.734498	+	0.678611i	$0.762582\pi$
$558$		0			0
$559$	−1.25127	−	24.8833i	−0.0529229	−	1.05245i
$560$	−1.40576	+	2.02470i	−0.0594043	+	0.0855591i
$561$		0			0
$562$	18.0415	−	4.43371i	0.761034	−	0.187025i
$563$		−	18.4845i		−	0.779029i	−0.921020	−	0.389514i	$-0.872643\pi$
$563$		−	18.4845i		−	0.779029i	0.921020	−	0.389514i	$-0.127357\pi$
$564$		0			0
$565$	−0.284380	+	0.284380i	−0.0119640	+	0.0119640i
$566$	10.2762	−	16.9726i	0.431941	−	0.713412i
$567$		0			0
$568$	19.1245	+	21.6767i	0.802445	+	0.909535i
$569$			29.8587i			1.25174i	0.779927	+	0.625871i	$0.215256\pi$
$569$			29.8587i			1.25174i	−0.779927	+	0.625871i	$0.784744\pi$
$570$		0			0
$571$			11.4747i			0.480202i	0.970748	+	0.240101i	$0.0771805\pi$
$571$			11.4747i			0.480202i	−0.970748	+	0.240101i	$0.922819\pi$
$572$	−6.85100	−	1.77275i	−0.286455	−	0.0741225i
$573$		0			0
$574$	−10.6953	+	17.6648i	−0.446412	+	0.737313i
$575$		−	39.8960i		−	1.66378i
$576$		0			0
$577$	25.9864	+	25.9864i	1.08183	+	1.08183i	0.996339	+	0.0854895i	$0.0272454\pi$
$577$	25.9864	+	25.9864i	1.08183	+	1.08183i	0.0854895	+	0.996339i	$0.472755\pi$
$578$	32.9369	+	19.9419i	1.37000	+	0.829475i
$579$		0			0
$580$	−1.04775	+	3.34620i	−0.0435057	+	0.138943i
$581$			10.6517i			0.441909i
$582$		0			0
$583$	7.59091	+	7.59091i	0.314383	+	0.314383i
$584$	−24.4011	−	27.6576i	−1.00973	−	1.14448i
$585$		0			0
$586$	−2.45261	−	9.98007i	−0.101316	−	0.412273i
$587$	25.5226	+	25.5226i	1.05343	+	1.05343i	0.998490	+	0.0549413i	$0.0174972\pi$
$587$	25.5226	+	25.5226i	1.05343	+	1.05343i	0.0549413	+	0.998490i	$0.482503\pi$
$588$		0			0
$589$	21.1293			0.870616
$590$	2.55526	−	4.22037i	0.105198	−	0.173750i
$591$		0			0
$592$	43.7431	−	7.89229i	1.79783	−	0.324371i
$593$	−22.7163	+	22.7163i	−0.932847	+	0.932847i	−0.997883	−	0.0650355i	$-0.979284\pi$
$593$	−22.7163	+	22.7163i	−0.932847	+	0.932847i	0.0650355	+	0.997883i	$0.479284\pi$
$594$		0			0
$595$		−	4.09801i		−	0.168002i
$596$	40.5946	+	12.7109i	1.66282	+	0.520658i
$597$		0			0
$598$	36.6068	+	19.7226i	1.49696	+	0.806518i
$599$			8.61150i			0.351856i	0.984403	+	0.175928i	$0.0562926\pi$
$599$			8.61150i			0.351856i	−0.984403	+	0.175928i	$0.943707\pi$
$600$		0			0
$601$	−28.8742			−1.17780			−0.588902	−	0.808205i	$-0.700439\pi$
$601$	−28.8742			−1.17780			−0.588902	+	0.808205i	$0.700439\pi$
$602$	17.8201	−	4.37929i	0.726291	−	0.178487i
$603$		0			0
$604$	−1.80978	+	5.77989i	−0.0736391	+	0.235180i
$605$	−2.32904	−	2.32904i	−0.0946890	−	0.0946890i
$606$		0			0
$607$		−	13.3771i		−	0.542962i	−0.962444	−	0.271481i	$-0.912487\pi$
$607$		−	13.3771i		−	0.542962i	0.962444	−	0.271481i	$-0.0875134\pi$
$608$	27.4896	+	10.5334i	1.11485	+	0.427185i
$609$		0			0
$610$	−0.716763	−	2.91663i	−0.0290209	−	0.118091i
$611$	15.9904	+	14.4592i	0.646902	+	0.584957i
$612$		0			0
$613$	7.77290	−	7.77290i	0.313945	−	0.313945i	−0.532491	−	0.846436i	$-0.678744\pi$
$613$	7.77290	−	7.77290i	0.313945	−	0.313945i	0.846436	+	0.532491i	$0.178744\pi$
$614$	−31.0074	+	7.62009i	−1.25136	+	0.307522i
$615$		0			0
$616$	0.325400	−	5.20194i	0.0131107	−	0.209592i
$617$	−2.02065	−	2.02065i	−0.0813483	−	0.0813483i	0.665262	−	0.746610i	$-0.268320\pi$
$617$	−2.02065	−	2.02065i	−0.0813483	−	0.0813483i	−0.746610	+	0.665262i	$0.768320\pi$
$618$		0			0
$619$	31.3058	−	31.3058i	1.25829	−	1.25829i	0.306376	−	0.951911i	$-0.400884\pi$
$619$	31.3058	−	31.3058i	1.25829	−	1.25829i	0.951911	−	0.306376i	$-0.0991165\pi$
$620$	−2.36125	+	1.23515i	−0.0948301	+	0.0496049i
$621$		0			0
$622$	−14.3530	−	8.69015i	−0.575504	−	0.348443i
$623$	−3.50796			−0.140543
$624$		0			0
$625$	−23.3962			−0.935849
$626$	−2.52718	−	1.53010i	−0.101006	−	0.0611551i
$627$		0			0
$628$	2.77132	−	1.44966i	0.110588	−	0.0578476i
$629$	−52.2553	+	52.2553i	−2.08356	+	2.08356i
$630$		0			0
$631$	16.2286	+	16.2286i	0.646051	+	0.646051i	0.952036	−	0.305985i	$-0.0989859\pi$
$631$	16.2286	+	16.2286i	0.646051	+	0.646051i	−0.305985	+	0.952036i	$0.598986\pi$
$632$	−39.2737	−	2.45672i	−1.56223	−	0.0977229i
$633$		0			0
$634$	−33.5651	+	8.24863i	−1.33304	+	0.327595i
$635$	2.62170	−	2.62170i	0.104039	−	0.104039i
$636$		0			0
$637$	−0.629059	−	12.5098i	−0.0249242	−	0.495656i
$638$	−1.76947	−	7.20025i	−0.0700539	−	0.285061i
$639$		0			0
$640$	−3.68779	+	0.429828i	−0.145773	+	0.0169904i
$641$		−	42.7819i		−	1.68978i	−0.534939	−	0.844891i	$-0.679665\pi$
$641$		−	42.7819i		−	1.68978i	0.534939	−	0.844891i	$-0.320335\pi$
$642$		0			0
$643$	−26.4945	−	26.4945i	−1.04484	−	1.04484i	−0.998946	−	0.0458946i	$-0.985386\pi$
$643$	−26.4945	−	26.4945i	−1.04484	−	1.04484i	−0.0458946	−	0.998946i	$-0.514614\pi$
$644$	−9.15139	+	29.2267i	−0.360615	+	1.15169i
$645$		0			0
$646$	−47.5295	+	11.6804i	−1.87002	+	0.459559i
$647$	4.44940			0.174924			0.0874620	−	0.996168i	$-0.472124\pi$
$647$	4.44940			0.174924			0.0874620	+	0.996168i	$0.472124\pi$
$648$		0			0
$649$			10.4325i			0.409511i
$650$	11.8321	−	21.9614i	0.464094	−	0.861397i
$651$		0			0
$652$	9.02746	+	2.82666i	0.353543	+	0.110700i
$653$			14.3860i			0.562968i	0.959566	+	0.281484i	$0.0908267\pi$
$653$			14.3860i			0.562968i	−0.959566	+	0.281484i	$0.909173\pi$
$654$		0			0
$655$	2.69989	−	2.69989i	0.105493	−	0.105493i
$656$	−30.6105	+	5.52286i	−1.19514	+	0.215631i
$657$		0			0
$658$	−8.22371	+	13.5826i	−0.320593	+	0.529506i
$659$	−14.3624			−0.559481			−0.279741	−	0.960076i	$-0.590248\pi$
$659$	−14.3624			−0.559481			−0.279741	+	0.960076i	$0.590248\pi$
$660$		0			0
$661$	13.4958	+	13.4958i	0.524927	+	0.524927i	0.919055	−	0.394128i	$-0.128953\pi$
$661$	13.4958	+	13.4958i	0.524927	+	0.524927i	−0.394128	+	0.919055i	$0.628953\pi$
$662$	2.79295	+	11.3650i	0.108551	+	0.441713i
$663$		0			0
$664$	−12.0313	+	10.6147i	−0.466903	+	0.411929i
$665$	2.26757	+	2.26757i	0.0879326	+	0.0879326i
$666$		0			0
$667$			43.5669i			1.68692i
$668$	−10.2435	+	32.7146i	−0.396334	+	1.26577i
$669$		0			0
$670$	1.87773	+	1.13689i	0.0725431	+	0.0439218i
$671$	4.49075	+	4.49075i	0.173363	+	0.173363i
$672$		0			0
$673$			27.3845i			1.05560i	0.849370	+	0.527798i	$0.176982\pi$
$673$			27.3845i			1.05560i	−0.849370	+	0.527798i	$0.823018\pi$
$674$	14.3791	−	23.7492i	0.553864	−	0.914785i
$675$		0			0
$676$	14.3016	+	21.7132i	0.550061	+	0.835125i
$677$		−	13.2247i		−	0.508265i	−0.967169	−	0.254132i	$-0.918210\pi$
$677$		−	13.2247i		−	0.508265i	0.967169	−	0.254132i	$-0.0817899\pi$
$678$		0			0
$679$			12.6886i			0.486943i
$680$	4.62874	−	4.08375i	0.177504	−	0.156604i
$681$		0			0
$682$	2.91843	−	4.82020i	0.111752	−	0.184575i
$683$	22.8160	−	22.8160i	0.873029	−	0.873029i	−0.119772	−	0.992801i	$-0.538216\pi$
$683$	22.8160	−	22.8160i	0.873029	−	0.873029i	0.992801	+	0.119772i	$0.0382164\pi$
$684$		0			0
$685$		−	3.08426i		−	0.117843i
$686$	27.0107	−	6.63790i	1.03127	−	0.253436i
$687$		0			0
$688$	22.7045	+	15.7639i	0.865600	+	0.600992i
$689$	−1.98084	−	39.3919i	−0.0754639	−	1.50071i
$690$		0			0
$691$	7.60424	+	7.60424i	0.289279	+	0.289279i	0.836795	−	0.547516i	$-0.184427\pi$
$691$	7.60424	+	7.60424i	0.289279	+	0.289279i	−0.547516	+	0.836795i	$0.684427\pi$
$692$	16.1310	+	30.8377i	0.613208	+	1.17227i
$693$		0			0
$694$	−22.4912	−	13.6175i	−0.853756	−	0.516913i
$695$	−2.78589	+	2.78589i	−0.105675	+	0.105675i
$696$		0			0
$697$	36.5672	−	36.5672i	1.38508	−	1.38508i
$698$	−2.21224	−	9.00198i	−0.0837346	−	0.340730i
$699$		0			0
$700$	17.5338	+	5.49016i	0.662717	+	0.207508i
$701$	−23.0640			−0.871115			−0.435557	−	0.900161i	$-0.643449\pi$
$701$	−23.0640			−0.871115			−0.435557	+	0.900161i	$0.643449\pi$
$702$		0			0
$703$		−	57.8293i		−	2.18107i
$704$	6.19991	−	4.81629i	0.233668	−	0.181521i
$705$		0			0
$706$	4.49686	+	18.2984i	0.169241	+	0.688671i
$707$	−6.51473	−	6.51473i	−0.245012	−	0.245012i
$708$		0			0
$709$	−6.22100	−	6.22100i	−0.233635	−	0.233635i	0.580573	−	0.814208i	$-0.302828\pi$
$709$	−6.22100	−	6.22100i	−0.233635	−	0.233635i	−0.814208	+	0.580573i	$0.802828\pi$
$710$	−2.45659	+	4.05741i	−0.0921943	+	0.152272i
$711$		0			0
$712$	−3.49574	−	3.96227i	−0.131009	−	0.148492i
$713$	−23.4123	+	23.4123i	−0.876796	+	0.876796i
$714$		0			0
$715$	−0.0583152	−	1.15968i	−0.00218086	−	0.0433697i
$716$	−6.40274	+	3.34923i	−0.239282	+	0.125167i
$717$		0			0
$718$	6.92443	+	28.1767i	0.258417	+	1.05154i
$719$	45.2323			1.68688			0.843441	−	0.537222i	$-0.180526\pi$
$719$	45.2323			1.68688			0.843441	+	0.537222i	$0.180526\pi$
$720$		0			0
$721$	12.8648	+	12.8648i	0.479111	+	0.479111i
$722$	5.91987	−	9.77751i	0.220315	−	0.363881i
$723$		0			0
$724$	−1.27422	−	2.43594i	−0.0473562	−	0.0905311i
$725$	26.1369			0.970701
$726$		0			0
$727$	−17.5545			−0.651059			−0.325530	−	0.945532i	$-0.605543\pi$
$727$	−17.5545			−0.651059			−0.325530	+	0.945532i	$0.605543\pi$
$728$	−13.7054	+	13.3742i	−0.507955	+	0.495681i
$729$		0			0
$730$	3.13439	−	5.17690i	0.116009	−	0.191606i
$731$	−45.9541			−1.69967
$732$		0			0
$733$	−7.39588	+	7.39588i	−0.273173	+	0.273173i	−0.830376	−	0.557203i	$-0.811874\pi$
$733$	−7.39588	+	7.39588i	−0.273173	+	0.273173i	0.557203	+	0.830376i	$0.311874\pi$
$734$	−21.1339	+	34.9057i	−0.780067	+	1.28839i
$735$		0			0
$736$	−42.1313	+	18.7883i	−1.55298	+	0.692548i
$737$	−4.64163			−0.170977
$738$		0			0
$739$	−8.24932	+	8.24932i	−0.303456	+	0.303456i	−0.842364	−	0.538908i	$-0.818837\pi$
$739$	−8.24932	+	8.24932i	−0.303456	+	0.303456i	0.538908	+	0.842364i	$0.318837\pi$
$740$	3.38053	+	6.46258i	0.124271	+	0.237569i
$741$		0			0
$742$	28.2103	−	6.93270i	1.03563	−	0.254507i
$743$	5.93732	−	5.93732i	0.217819	−	0.217819i	−0.589760	−	0.807579i	$-0.700778\pi$
$743$	5.93732	−	5.93732i	0.217819	−	0.217819i	0.807579	+	0.589760i	$0.200778\pi$
$744$		0			0
$745$			6.97973i			0.255718i
$746$	21.7085	−	35.8547i	0.794806	−	1.31274i
$747$		0			0
$748$	−3.90025	+	12.4562i	−0.142607	+	0.455443i
$749$	9.61038	+	9.61038i	0.351155	+	0.351155i
$750$		0			0
$751$	−18.4552			−0.673439			−0.336719	−	0.941605i	$-0.609317\pi$
$751$	−18.4552			−0.673439			−0.336719	+	0.941605i	$0.609317\pi$
$752$	−23.5368	+	4.24659i	−0.858298	+	0.154857i
$753$		0			0
$754$	−12.9208	+	23.9821i	−0.470548	+	0.873376i
$755$	−0.993779			−0.0361673
$756$		0			0
$757$		−	34.1220i		−	1.24018i	−0.784529	−	0.620092i	$-0.787095\pi$
$757$		−	34.1220i		−	1.24018i	0.784529	−	0.620092i	$-0.212905\pi$
$758$	6.46061	+	26.2893i	0.234660	+	0.954870i
$759$		0			0
$760$	−0.301566	+	4.82092i	−0.0109390	+	0.174873i
$761$	−0.883636	+	0.883636i	−0.0320318	+	0.0320318i	−0.722941	−	0.690909i	$-0.757210\pi$
$761$	−0.883636	+	0.883636i	−0.0320318	+	0.0320318i	0.690909	+	0.722941i	$0.257210\pi$
$762$		0			0
$763$	10.0983			0.365583
$764$	−28.2707	+	14.7882i	−1.02280	+	0.535019i
$765$		0			0
$766$	49.8121	−	12.2414i	1.79978	−	0.442298i
$767$	25.7077	−	28.4301i	0.928253	−	1.02655i
$768$		0			0
$769$	0.187906	+	0.187906i	0.00677607	+	0.00677607i	0.710487	−	0.703711i	$-0.248475\pi$
$769$	0.187906	+	0.187906i	0.00677607	+	0.00677607i	−0.703711	+	0.710487i	$0.748475\pi$
$770$	0.830502	−	0.204096i	0.0299292	−	0.00735512i
$771$		0			0
$772$	−7.17387	−	2.24627i	−0.258193	−	0.0808449i
$773$	−20.8118	+	20.8118i	−0.748547	+	0.748547i	−0.974206	−	0.225659i	$-0.927546\pi$
$773$	−20.8118	+	20.8118i	−0.748547	+	0.748547i	0.225659	+	0.974206i	$0.427546\pi$
$774$		0			0
$775$	14.0456	+	14.0456i	0.504534	+	0.504534i
$776$	−14.3319	+	12.6444i	−0.514484	+	0.453908i
$777$		0			0
$778$	3.14489	+	1.90410i	0.112750	+	0.0682653i
$779$			40.4678i			1.44991i
$780$		0			0
$781$		−	10.0297i		−	0.358890i
$782$	39.7225	−	65.6074i	1.42047	−	2.34612i
$783$		0			0
$784$	11.4144	+	7.92510i	0.407657	+	0.283039i
$785$	0.362872	+	0.362872i	0.0129514	+	0.0129514i
$786$		0			0
$787$	4.16069	−	4.16069i	0.148313	−	0.148313i	−0.629051	−	0.777364i	$-0.716556\pi$
$787$	4.16069	−	4.16069i	0.148313	−	0.148313i	0.777364	+	0.629051i	$0.216556\pi$
$788$	−0.626342	−	0.196119i	−0.0223125	−	0.00698644i
$789$		0			0
$790$	−1.54089	−	6.27015i	−0.0548225	−	0.223082i
$791$	−1.62724	−	1.62724i	−0.0578579	−	0.0578579i
$792$		0			0
$793$	−1.17185	−	23.3041i	−0.0416138	−	0.827551i
$794$	0.189431	+	0.770824i	0.00672264	+	0.0273555i
$795$		0			0
$796$	17.5485	+	33.5477i	0.621991	+	1.18907i
$797$	29.4944			1.04475			0.522373	−	0.852717i	$-0.325047\pi$
$797$	29.4944			1.04475			0.522373	+	0.852717i	$0.325047\pi$
$798$		0			0
$799$	28.1169	−	28.1169i	0.994705	−	0.994705i
$800$	11.2716	+	25.2757i	0.398512	+	0.893631i
$801$		0			0
$802$	2.30237	−	0.565809i	0.0812995	−	0.0199794i
$803$			12.7970i			0.451595i
$804$		0			0
$805$	−5.02516			−0.177114
$806$	−19.8311	+	5.94418i	−0.698521	+	0.209375i
$807$		0			0
$808$	0.866399	−	13.8505i	0.0304798	−	0.487259i
$809$	19.5531			0.687450			0.343725	−	0.939070i	$-0.388311\pi$
$809$	19.5531			0.687450			0.343725	+	0.939070i	$0.388311\pi$
$810$		0			0
$811$	27.4702	+	27.4702i	0.964608	+	0.964608i	0.999395	−	0.0347864i	$-0.0110751\pi$
$811$	27.4702	+	27.4702i	0.964608	+	0.964608i	−0.0347864	+	0.999395i	$0.511075\pi$
$812$	−19.1471	−	5.99531i	−0.671933	−	0.210394i
$813$		0			0
$814$	−13.1926	−	7.98754i	−0.462399	−	0.279963i
$815$			1.55216i			0.0543697i
$816$		0			0
$817$	25.4280	−	25.4280i	0.889612	−	0.889612i
$818$	1.52889	+	6.22132i	0.0534565	+	0.217523i
$819$		0			0
$820$	−2.36562	−	4.52238i	−0.0826112	−	0.157928i
$821$	−17.4449	+	17.4449i	−0.608833	+	0.608833i	−0.942641	−	0.333808i	$-0.891666\pi$
$821$	−17.4449	+	17.4449i	−0.608833	+	0.608833i	0.333808	+	0.942641i	$0.391666\pi$
$822$		0			0
$823$	−18.8107			−0.655701			−0.327851	−	0.944730i	$-0.606324\pi$
$823$	−18.8107			−0.655701			−0.327851	+	0.944730i	$0.606324\pi$
$824$	−1.71090	+	27.3510i	−0.0596022	+	0.952817i
$825$		0			0
$826$	24.1492	+	14.6213i	0.840258	+	0.508741i
$827$	−23.3884	+	23.3884i	−0.813293	+	0.813293i	−0.985126	−	0.171833i	$-0.945031\pi$
$827$	−23.3884	+	23.3884i	−0.813293	+	0.813293i	0.171833	+	0.985126i	$0.445031\pi$
$828$		0			0
$829$	19.2767			0.669507			0.334754	−	0.942306i	$-0.391347\pi$
$829$	19.2767			0.669507			0.334754	+	0.942306i	$0.391347\pi$
$830$	−2.25199	−	1.36348i	−0.0781677	−	0.0473272i
$831$		0			0
$832$	−28.7640	−	2.15271i	−0.997211	−	0.0746320i
$833$	−23.1029			−0.800467
$834$		0			0
$835$	−5.62487			−0.194657
$836$	−4.73429	−	9.05058i	−0.163739	−	0.313021i
$837$		0			0
$838$	32.4628	+	19.6548i	1.12141	+	0.678965i
$839$	6.55312	+	6.55312i	0.226239	+	0.226239i	0.811119	−	0.584881i	$-0.198859\pi$
$839$	6.55312	+	6.55312i	0.226239	+	0.226239i	−0.584881	+	0.811119i	$0.698859\pi$
$840$		0			0
$841$	0.458181			0.0157994
$842$	−3.25725	+	0.800472i	−0.112252	+	0.0275861i
$843$		0			0
$844$	−26.1661	−	50.0219i	−0.900674	−	1.72182i
$845$	−2.69878	+	3.30401i	−0.0928407	+	0.113661i
$846$		0			0
$847$	13.3269	−	13.3269i	0.457918	−	0.457918i
$848$	35.9427	+	24.9552i	1.23428	+	0.856967i
$849$		0			0
$850$	−39.3596	−	23.8306i	−1.35002	−	0.817382i
$851$	64.0777	+	64.0777i	2.19656	+	2.19656i
$852$		0			0
$853$	−21.8978	−	21.8978i	−0.749767	−	0.749767i	0.224668	−	0.974435i	$-0.427870\pi$
$853$	−21.8978	−	21.8978i	−0.749767	−	0.749767i	−0.974435	+	0.224668i	$0.927870\pi$
$854$	16.6891	−	4.10135i	0.571089	−	0.140345i
$855$		0			0
$856$	−1.27809	+	20.4319i	−0.0436843	+	0.698349i
$857$		−	7.82287i		−	0.267224i	−0.991034	−	0.133612i	$-0.957342\pi$
$857$		−	7.82287i		−	0.267224i	0.991034	−	0.133612i	$-0.0426576\pi$
$858$		0			0
$859$	16.6431			0.567855			0.283928	−	0.958846i	$-0.408362\pi$
$859$	16.6431			0.567855			0.283928	+	0.958846i	$0.408362\pi$
$860$	−1.35520	+	4.32809i	−0.0462120	+	0.147586i
$861$		0			0
$862$	−23.5588	+	5.78959i	−0.802416	+	0.197194i
$863$	19.6786	−	19.6786i	0.669868	−	0.669868i	−0.287817	−	0.957685i	$-0.592930\pi$
$863$	19.6786	−	19.6786i	0.669868	−	0.669868i	0.957685	+	0.287817i	$0.0929295\pi$
$864$		0			0
$865$	−4.03784	+	4.03784i	−0.137291	+	0.137291i
$866$	−16.7554	+	27.6739i	−0.569371	+	0.940398i
$867$		0			0
$868$	−7.06761	−	13.5112i	−0.239890	−	0.458600i
$869$	9.65419	+	9.65419i	0.327496	+	0.327496i
$870$		0			0
$871$	12.6491	+	11.4379i	0.428600	+	0.387559i
$872$	10.0632	+	11.4061i	0.340782	+	0.386261i
$873$		0			0
$874$	14.3230	+	58.2827i	0.484483	+	1.97144i
$875$			6.09581i			0.206076i
$876$		0			0
$877$	−26.1436	+	26.1436i	−0.882808	+	0.882808i	−0.993819	−	0.111011i	$-0.964591\pi$
$877$	−26.1436	+	26.1436i	−0.882808	+	0.882808i	0.111011	+	0.993819i	$0.464591\pi$
$878$	−21.0640	−	12.7533i	−0.710875	−	0.430404i
$879$		0			0
$880$	1.05814	+	0.734674i	0.0356699	+	0.0247659i
$881$			11.7759i			0.396739i	0.980127	+	0.198370i	$0.0635646\pi$
$881$			11.7759i			0.396739i	−0.980127	+	0.198370i	$0.936435\pi$
$882$		0			0
$883$			31.7284i			1.06775i	0.845565	+	0.533873i	$0.179264\pi$
$883$			31.7284i			1.06775i	−0.845565	+	0.533873i	$0.820736\pi$
$884$	41.3233	−	24.3340i	1.38985	−	0.818440i
$885$		0			0
$886$	−28.8260	−	17.4529i	−0.968427	−	0.586342i
$887$		−	19.6370i		−	0.659346i	−0.944095	−	0.329673i	$-0.893061\pi$
$887$		−	19.6370i		−	0.659346i	0.944095	−	0.329673i	$-0.106939\pi$
$888$		0			0
$889$	15.0015	+	15.0015i	0.503135	+	0.503135i
$890$	0.449039	−	0.741651i	0.0150518	−	0.0248602i
$891$		0			0
$892$	−22.5828	−	7.07108i	−0.756128	−	0.236757i
$893$			31.1161i			1.04126i
$894$		0			0
$895$	−0.838364	−	0.838364i	−0.0280234	−	0.0280234i
$896$	−2.45950	−	21.1017i	−0.0821660	−	0.704959i
$897$		0			0
$898$	−16.3189	+	4.01039i	−0.544569	+	0.133828i
$899$	−15.3380	−	15.3380i	−0.511550	−	0.511550i
$900$		0			0
$901$	−72.7483			−2.42360
$902$	9.23188	+	5.58951i	0.307388	+	0.186110i
$903$		0			0
$904$	0.216408	−	3.45955i	0.00719762	−	0.115063i
$905$	0.318958	−	0.318958i	0.0106025	−	0.0106025i
$906$		0			0
$907$		−	28.2808i		−	0.939048i	−0.882920	−	0.469524i	$-0.844426\pi$
$907$		−	28.2808i		−	0.939048i	0.882920	−	0.469524i	$-0.155574\pi$
$908$	−12.7954	+	40.8646i	−0.424631	+	1.35614i
$909$		0			0
$910$	−2.76618	−	1.49033i	−0.0916978	−	0.0494040i
$911$			9.69423i			0.321184i	0.987021	+	0.160592i	$0.0513404\pi$
$911$			9.69423i			0.321184i	−0.987021	+	0.160592i	$0.948660\pi$
$912$		0			0
$913$	5.56677			0.184233
$914$	3.80935	+	15.5009i	0.126002	+	0.512724i
$915$		0			0
$916$	−6.49849	+	20.7541i	−0.214716	+	0.685736i
$917$	15.4489	+	15.4489i	0.510168	+	0.510168i
$918$		0			0
$919$			40.5263i			1.33684i	0.743784	+	0.668420i	$0.233029\pi$
$919$			40.5263i			1.33684i	−0.743784	+	0.668420i	$0.766971\pi$
$920$	−5.00767	−	5.67597i	−0.165098	−	0.187131i
$921$		0			0
$922$	33.5956	−	8.25613i	1.10641	−	0.271901i
$923$	−24.7151	+	27.3323i	−0.813507	+	0.899654i
$924$		0			0
$925$	38.4419	−	38.4419i	1.26396	−	1.26396i
$926$	−8.56341	−	34.8459i	−0.281411	−	1.14511i
$927$		0			0
$928$	−12.3087	−	27.6013i	−0.404054	−	0.906058i
$929$	−9.85386	−	9.85386i	−0.323295	−	0.323295i	0.526735	−	0.850030i	$-0.323416\pi$
$929$	−9.85386	−	9.85386i	−0.323295	−	0.323295i	−0.850030	+	0.526735i	$0.823416\pi$
$930$		0			0
$931$	12.7836	−	12.7836i	0.418966	−	0.418966i
$932$	25.9921	−	13.5963i	0.851400	−	0.445361i
$933$		0			0
$934$	3.15639	−	5.21322i	0.103280	−	0.170582i
$935$	−2.14169			−0.0700406
$936$		0			0
$937$	17.3821			0.567848			0.283924	−	0.958847i	$-0.408364\pi$
$937$	17.3821			0.567848			0.283924	+	0.958847i	$0.408364\pi$
$938$	−6.50533	+	10.7445i	−0.212407	+	0.350820i
$939$		0			0
$940$	−1.81895	−	3.47731i	−0.0593278	−	0.113417i
$941$	3.62696	−	3.62696i	0.118236	−	0.118236i	−0.645513	−	0.763749i	$-0.723357\pi$
$941$	3.62696	−	3.62696i	0.118236	−	0.118236i	0.763749	+	0.645513i	$0.223357\pi$
$942$		0			0
$943$	−44.8403	−	44.8403i	−1.46020	−	1.46020i
$944$	7.55021	+	41.8472i	0.245739	+	1.36201i
$945$		0			0
$946$	−2.28869	−	9.31304i	−0.0744116	−	0.302793i
$947$	39.0436	−	39.0436i	1.26875	−	1.26875i	0.322009	−	0.946737i	$-0.395642\pi$
$947$	39.0436	−	39.0436i	1.26875	−	1.26875i	0.946737	−	0.322009i	$-0.104358\pi$
$948$		0			0
$949$	31.5343	−	34.8736i	1.02365	−	1.13205i
$950$	34.9653	−	8.59275i	1.13442	−	0.278786i
$951$		0			0
$952$	23.3674	+	26.4859i	0.757342	+	0.858414i
$953$		−	37.7512i		−	1.22288i	−0.791291	−	0.611440i	$-0.790590\pi$
$953$		−	37.7512i		−	1.22288i	0.791291	−	0.611440i	$-0.209410\pi$
$954$		0			0
$955$	−3.70172	−	3.70172i	−0.119785	−	0.119785i
$956$	−39.4403	−	12.3494i	−1.27559	−	0.399410i
$957$		0			0
$958$	−2.12117	−	8.63139i	−0.0685318	−	0.278867i
$959$	17.6483			0.569893
$960$		0			0
$961$			14.5152i			0.468231i
$962$	16.2688	+	54.2763i	0.524527	+	1.74994i
$963$		0			0
$964$	12.7232	+	3.98385i	0.409785	+	0.128311i
$965$		−	1.23346i		−	0.0397064i
$966$		0			0
$967$	3.95277	−	3.95277i	0.127113	−	0.127113i	−0.640688	−	0.767801i	$-0.721351\pi$
$967$	3.95277	−	3.95277i	0.127113	−	0.127113i	0.767801	+	0.640688i	$0.221351\pi$
$968$	28.3334	+	1.77236i	0.910670	+	0.0569657i
$969$		0			0
$970$	−2.68261	−	1.62421i	−0.0861336	−	0.0521502i
$971$	34.4354			1.10509			0.552543	−	0.833484i	$-0.313658\pi$
$971$	34.4354			1.10509			0.552543	+	0.833484i	$0.313658\pi$
$972$		0			0
$973$	−15.9410	−	15.9410i	−0.511046	−	0.511046i
$974$	28.2206	−	6.93524i	0.904248	−	0.222219i
$975$		0			0
$976$	21.2635	+	14.7634i	0.680629	+	0.472565i
$977$	23.7209	+	23.7209i	0.758900	+	0.758900i	0.976122	−	0.217222i	$-0.0696997\pi$
$977$	23.7209	+	23.7209i	0.758900	+	0.758900i	−0.217222	+	0.976122i	$0.569700\pi$
$978$		0			0
$979$			1.83331i			0.0585929i
$980$	−0.681311	+	2.17589i	−0.0217637	+	0.0695064i
$981$		0			0
$982$	−32.1345	+	53.0748i	−1.02545	+	1.69368i
$983$	−25.5496	−	25.5496i	−0.814907	−	0.814907i	0.170458	−	0.985365i	$-0.445475\pi$
$983$	−25.5496	−	25.5496i	−0.814907	−	0.814907i	−0.985365	+	0.170458i	$0.945475\pi$
$984$		0			0
$985$		−	0.107692i		−	0.00343134i
$986$	42.9811	+	26.0233i	1.36880	+	0.828749i
$987$		0			0
$988$	−9.40079	+	36.3304i	−0.299079	+	1.15583i
$989$			56.3509i			1.79185i
$990$		0			0
$991$		−	46.5439i		−	1.47852i	−0.673423	−	0.739258i	$-0.735177\pi$
$991$		−	46.5439i		−	1.47852i	0.673423	−	0.739258i	$-0.264823\pi$
$992$	8.21803	−	21.4471i	0.260923	−	0.680946i
$993$		0			0
$994$	−23.2167	−	14.0568i	−0.736390	−	0.445853i
$995$	−4.39268	+	4.39268i	−0.139257	+	0.139257i
$996$		0			0
$997$		−	4.95335i		−	0.156874i	−0.996919	−	0.0784371i	$-0.975007\pi$
$997$		−	4.95335i		−	0.156874i	0.996919	−	0.0784371i	$-0.0249930\pi$
$998$	0.384750	+	1.56561i	0.0121790	+	0.0495585i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.w.k.307.3	✓	48
3.2	odd	2	inner	936.2.w.k.307.22	yes	48
8.3	odd	2	inner	936.2.w.k.307.10	yes	48
13.5	odd	4	inner	936.2.w.k.811.10	yes	48
24.11	even	2	inner	936.2.w.k.307.15	yes	48
39.5	even	4	inner	936.2.w.k.811.15	yes	48
104.83	even	4	inner	936.2.w.k.811.3	yes	48
312.83	odd	4	inner	936.2.w.k.811.22	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.w.k.307.3	✓	48	1.1	even	1	trivial
936.2.w.k.307.10	yes	48	8.3	odd	2	inner
936.2.w.k.307.15	yes	48	24.11	even	2	inner
936.2.w.k.307.22	yes	48	3.2	odd	2	inner
936.2.w.k.811.3	yes	48	104.83	even	4	inner
936.2.w.k.811.10	yes	48	13.5	odd	4	inner
936.2.w.k.811.15	yes	48	39.5	even	4	inner
936.2.w.k.811.22	yes	48	312.83	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20976 - 0.732456i) q^{2} +(0.927017 + 1.77218i) q^{4} +(-0.232047 + 0.232047i) q^{5} +(-1.32779 - 1.32779i) q^{7} +(0.176583 - 2.82291i) q^{8} +(0.450684 - 0.110756i) q^{10} +(-0.693922 + 0.693922i) q^{11} +(3.60100 - 0.181078i) q^{13} +(0.633752 + 2.57884i) q^{14} +(-2.28128 + 3.28569i) q^{16} -6.65027i q^{17} +(3.67982 + 3.67982i) q^{19} +(-0.626342 - 0.196119i) q^{20} +(1.34774 - 0.331209i) q^{22} -8.15485 q^{23} +4.89231i q^{25} +(-4.48896 - 2.41851i) q^{26} +(1.12220 - 3.58396i) q^{28} -5.34245i q^{29} +(2.87096 - 2.87096i) q^{31} +(5.16641 - 2.30395i) q^{32} +(-4.87103 + 8.04520i) q^{34} +0.616217 q^{35} +(-7.85762 - 7.85762i) q^{37} +(-1.75638 - 7.14700i) q^{38} +(0.614072 + 0.696023i) q^{40} +(5.49860 + 5.49860i) q^{41} -6.91010i q^{43} +(-1.87303 - 0.586480i) q^{44} +(9.86538 + 5.97307i) q^{46} +(4.22794 + 4.22794i) q^{47} -3.47397i q^{49} +(3.58340 - 5.91850i) q^{50} +(3.65909 + 6.21378i) q^{52} -10.9391i q^{53} -0.322045i q^{55} +(-3.98268 + 3.51375i) q^{56} +(-3.91311 + 6.46306i) q^{58} +(7.51705 - 7.51705i) q^{59} -6.47155i q^{61} +(-5.57601 + 1.37031i) q^{62} +(-7.93764 - 0.996957i) q^{64} +(-0.793583 + 0.877620i) q^{65} +(3.34449 + 3.34449i) q^{67} +(11.7855 - 6.16491i) q^{68} +(-0.745472 - 0.451352i) q^{70} +(-7.22680 + 7.22680i) q^{71} +(9.22075 - 9.22075i) q^{73} +(3.75044 + 15.2612i) q^{74} +(-3.11007 + 9.93259i) q^{76} +1.84276 q^{77} -13.9125i q^{79} +(-0.233071 - 1.29180i) q^{80} +(-2.62448 - 10.6794i) q^{82} +(-4.01110 - 4.01110i) q^{83} +(1.54318 + 1.54318i) q^{85} +(-5.06135 + 8.35954i) q^{86} +(1.83634 + 2.08141i) q^{88} +(1.32098 - 1.32098i) q^{89} +(-5.02179 - 4.54092i) q^{91} +(-7.55969 - 14.4519i) q^{92} +(-2.01799 - 8.21154i) q^{94} -1.70778 q^{95} +(-4.77810 - 4.77810i) q^{97} +(-2.54453 + 4.20266i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 40 q^{16} - 8 q^{19} - 32 q^{22} + 24 q^{28} + 8 q^{34} + 16 q^{40} - 8 q^{46} + 24 q^{52} - 24 q^{58} + 40 q^{67} - 24 q^{70} + 56 q^{76} + 104 q^{91} - 64 q^{94} - 32 q^{97}+O(q^{100}) \) 48 * q - 40 * q^16 - 8 * q^19 - 32 * q^22 + 24 * q^28 + 8 * q^34 + 16 * q^40 - 8 * q^46 + 24 * q^52 - 24 * q^58 + 40 * q^67 - 24 * q^70 + 56 * q^76 + 104 * q^91 - 64 * q^94 - 32 * q^97

Introduction

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