LMFDB - Embedded newform 637.2.bd.b.293.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(97,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 5]))

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

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

chi := DirichletCharacter("637.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.4
Character	$\chi$	$=$	637.293
Dual form			637.2.bd.b.587.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.474142 - 0.127046i) q^{2} +(2.11812 + 1.22290i) q^{3} +(-1.52338 + 0.879524i) q^{4} +(2.54420 - 2.54420i) q^{5} +(1.15965 + 0.310728i) q^{6} +(-1.30475 + 1.30475i) q^{8} +(1.49096 + 2.58241i) q^{9} +O(q^{10})$	\(q+(0.474142 - 0.127046i) q^{2} +(2.11812 + 1.22290i) q^{3} +(-1.52338 + 0.879524i) q^{4} +(2.54420 - 2.54420i) q^{5} +(1.15965 + 0.310728i) q^{6} +(-1.30475 + 1.30475i) q^{8} +(1.49096 + 2.58241i) q^{9} +(0.883082 - 1.52954i) q^{10} +(0.547609 + 2.04371i) q^{11} -4.30227 q^{12} +(0.582584 + 3.55817i) q^{13} +(8.50022 - 2.27763i) q^{15} +(1.30618 - 2.26236i) q^{16} +(-0.572121 - 0.990942i) q^{17} +(1.03501 + 1.03501i) q^{18} +(4.40387 + 1.18001i) q^{19} +(-1.63810 + 6.11348i) q^{20} +(0.519289 + 0.899435i) q^{22} +(1.28375 + 0.741175i) q^{23} +(-4.35920 + 1.16804i) q^{24} -7.94593i q^{25} +(0.728279 + 1.61306i) q^{26} -0.0442386i q^{27} +(2.75801 - 4.77701i) q^{29} +(3.74095 - 2.15984i) q^{30} +(-4.28712 + 4.28712i) q^{31} +(1.28703 - 4.80327i) q^{32} +(-1.33934 + 4.99849i) q^{33} +(-0.397162 - 0.397162i) q^{34} +(-4.54259 - 2.62266i) q^{36} +(-0.700045 - 2.61260i) q^{37} +2.23797 q^{38} +(-3.11730 + 8.24908i) q^{39} +6.63910i q^{40} +(-1.21867 - 4.54813i) q^{41} +(-4.55704 + 2.63101i) q^{43} +(-2.63171 - 2.63171i) q^{44} +(10.3635 + 2.77688i) q^{45} +(0.702845 + 0.188327i) q^{46} +(-4.77175 - 4.77175i) q^{47} +(5.53327 - 3.19464i) q^{48} +(-1.00950 - 3.76750i) q^{50} -2.79858i q^{51} +(-4.01700 - 4.90806i) q^{52} +3.48778 q^{53} +(-0.00562033 - 0.0209754i) q^{54} +(6.59283 + 3.80637i) q^{55} +(7.88489 + 7.88489i) q^{57} +(0.700787 - 2.61537i) q^{58} +(-2.95801 + 11.0394i) q^{59} +(-10.9458 + 10.9458i) q^{60} +(-8.20082 + 4.73474i) q^{61} +(-1.48804 + 2.57737i) q^{62} +2.78376i q^{64} +(10.5349 + 7.57050i) q^{65} +2.54015i q^{66} +(-7.43875 + 1.99321i) q^{67} +(1.74312 + 1.00639i) q^{68} +(1.81276 + 3.13980i) q^{69} +(1.74779 - 6.52285i) q^{71} +(-5.31473 - 1.42408i) q^{72} +(-4.00398 - 4.00398i) q^{73} +(-0.663841 - 1.14981i) q^{74} +(9.71705 - 16.8304i) q^{75} +(-7.74662 + 2.07570i) q^{76} +(-0.430029 + 4.30727i) q^{78} -11.8232 q^{79} +(-2.43273 - 9.07908i) q^{80} +(4.52697 - 7.84094i) q^{81} +(-1.15564 - 2.00163i) q^{82} +(5.06789 - 5.06789i) q^{83} +(-3.97675 - 1.06557i) q^{85} +(-1.82642 + 1.82642i) q^{86} +(11.6836 - 6.74552i) q^{87} +(-3.38102 - 1.95203i) q^{88} +(-9.63048 + 2.58048i) q^{89} +5.26655 q^{90} -2.60753 q^{92} +(-14.3234 + 3.83793i) q^{93} +(-2.86872 - 1.65626i) q^{94} +(14.2065 - 8.20214i) q^{95} +(8.60000 - 8.60000i) q^{96} +(-13.1665 - 3.52795i) q^{97} +(-4.46123 + 4.46123i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$-1$

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 $

$2$	0.474142	−	0.127046i	0.335269	−	0.0898350i	−0.0872571	−	0.996186i	$-0.527810\pi$
$2$	0.474142	−	0.127046i	0.335269	−	0.0898350i	0.422526	+	0.906351i	$0.361143\pi$
$3$	2.11812	+	1.22290i	1.22290	+	0.706040i	0.965535	−	0.260275i	$-0.0838131\pi$
$3$	2.11812	+	1.22290i	1.22290	+	0.706040i	0.257363	+	0.966315i	$0.417146\pi$
$4$	−1.52338	+	0.879524i	−0.761690	+	0.439762i
$5$	2.54420	−	2.54420i	1.13780	−	1.13780i	0.148958	−	0.988844i	$-0.452408\pi$
$5$	2.54420	−	2.54420i	1.13780	−	1.13780i	0.988844	−	0.148958i	$-0.0475920\pi$
$6$	1.15965	+	0.310728i	0.473427	+	0.126854i
$7$		0			0
$7$		0			0
$8$	−1.30475	+	1.30475i	−0.461299	+	0.461299i
$9$	1.49096	+	2.58241i	0.496985	+	0.860804i
$10$	0.883082	−	1.52954i	0.279255	−	0.483684i
$11$	0.547609	+	2.04371i	0.165110	+	0.616201i	0.998026	+	0.0628007i	$0.0200032\pi$
$11$	0.547609	+	2.04371i	0.165110	+	0.616201i	−0.832916	+	0.553400i	$0.813330\pi$
$12$	−4.30227			−1.24196
$13$	0.582584	+	3.55817i	0.161580	+	0.986860i
$13$	0.582584	+	3.55817i	0.161580	+	0.986860i
$14$		0			0
$15$	8.50022	−	2.27763i	2.19475	−	0.588081i
$16$	1.30618	−	2.26236i	0.326544	−	0.565590i
$17$	−0.572121	−	0.990942i	−0.138760	−	0.240339i	0.788268	−	0.615332i	$-0.210978\pi$
$17$	−0.572121	−	0.990942i	−0.138760	−	0.240339i	−0.927027	+	0.374994i	$0.877645\pi$
$18$	1.03501	+	1.03501i	0.243954	+	0.243954i
$19$	4.40387	+	1.18001i	1.01032	+	0.270713i	0.725762	−	0.687946i	$-0.241488\pi$
$19$	4.40387	+	1.18001i	1.01032	+	0.270713i	0.284555	+	0.958660i	$0.408154\pi$
$20$	−1.63810	+	6.11348i	−0.366291	+	1.36701i
$21$		0			0
$22$	0.519289	+	0.899435i	0.110713	+	0.191760i
$23$	1.28375	+	0.741175i	0.267681	+	0.154546i	0.627833	−	0.778348i	$-0.283942\pi$
$23$	1.28375	+	0.741175i	0.267681	+	0.154546i	−0.360152	+	0.932894i	$0.617275\pi$
$24$	−4.35920	+	1.16804i	−0.889817	+	0.238426i
$25$		−	7.94593i		−	1.58919i
$26$	0.728279	+	1.61306i	0.142827	+	0.316348i
$27$		−	0.0442386i		−	0.00851372i
$28$		0			0
$29$	2.75801	−	4.77701i	0.512149	−	0.887068i	−0.487752	−	0.872982i	$-0.662183\pi$
$29$	2.75801	−	4.77701i	0.512149	−	0.887068i	0.999901	−	0.0140858i	$-0.00448381\pi$
$30$	3.74095	−	2.15984i	0.683001	−	0.394331i
$31$	−4.28712	+	4.28712i	−0.769990	+	0.769990i	−0.978105	−	0.208114i	$-0.933267\pi$
$31$	−4.28712	+	4.28712i	−0.769990	+	0.769990i	0.208114	+	0.978105i	$0.433267\pi$
$32$	1.28703	−	4.80327i	0.227517	−	0.849106i
$33$	−1.33934	+	4.99849i	−0.233149	+	0.870125i
$34$	−0.397162	−	0.397162i	−0.0681127	−	0.0681127i
$35$		0			0
$36$	−4.54259	−	2.62266i	−0.757098	−	0.437111i
$37$	−0.700045	−	2.61260i	−0.115087	−	0.429509i	0.884207	−	0.467096i	$-0.154700\pi$
$37$	−0.700045	−	2.61260i	−0.115087	−	0.429509i	−0.999293	+	0.0375866i	$0.988033\pi$
$38$	2.23797			0.363047
$39$	−3.11730	+	8.24908i	−0.499167	+	1.32091i
$40$			6.63910i			1.04973i
$41$	−1.21867	−	4.54813i	−0.190324	−	0.710299i	−0.993428	−	0.114460i	$-0.963486\pi$
$41$	−1.21867	−	4.54813i	−0.190324	−	0.710299i	0.803104	−	0.595839i	$-0.203180\pi$
$42$		0			0
$43$	−4.55704	+	2.63101i	−0.694942	+	0.401225i	−0.805461	−	0.592649i	$-0.798082\pi$
$43$	−4.55704	+	2.63101i	−0.694942	+	0.401225i	0.110519	+	0.993874i	$0.464749\pi$
$44$	−2.63171	−	2.63171i	−0.396745	−	0.396745i
$45$	10.3635	+	2.77688i	1.54489	+	0.413953i
$46$	0.702845	+	0.188327i	0.103629	+	0.0277673i
$47$	−4.77175	−	4.77175i	−0.696032	−	0.696032i	0.267520	−	0.963552i	$-0.413796\pi$
$47$	−4.77175	−	4.77175i	−0.696032	−	0.696032i	−0.963552	+	0.267520i	$0.913796\pi$
$48$	5.53327	−	3.19464i	0.798659	−	0.461106i
$49$		0			0
$50$	−1.00950	−	3.76750i	−0.142765	−	0.532804i
$51$		−	2.79858i		−	0.391880i
$52$	−4.01700	−	4.90806i	−0.557057	−	0.680625i
$53$	3.48778			0.479084			0.239542	−	0.970886i	$-0.423003\pi$
$53$	3.48778			0.479084			0.239542	+	0.970886i	$0.423003\pi$
$54$	−0.00562033	−	0.0209754i	−0.000764830	−	0.00285439i
$55$	6.59283	+	3.80637i	0.888977	+	0.513251i
$56$		0			0
$57$	7.88489	+	7.88489i	1.04438	+	1.04438i
$58$	0.700787	−	2.61537i	0.0920179	−	0.343415i
$59$	−2.95801	+	11.0394i	−0.385100	+	1.43721i	0.452909	+	0.891557i	$0.350386\pi$
$59$	−2.95801	+	11.0394i	−0.385100	+	1.43721i	−0.838009	+	0.545656i	$0.816280\pi$
$60$	−10.9458	+	10.9458i	−1.41310	+	1.41310i
$61$	−8.20082	+	4.73474i	−1.05001	+	0.606222i	−0.922651	−	0.385635i	$-0.873982\pi$
$61$	−8.20082	+	4.73474i	−1.05001	+	0.606222i	−0.127356	+	0.991857i	$0.540649\pi$
$62$	−1.48804	+	2.57737i	−0.188982	+	0.327326i
$63$		0			0
$64$			2.78376i			0.347970i
$65$	10.5349	+	7.57050i	1.30670	+	0.939005i
$66$			2.54015i			0.312671i
$67$	−7.43875	+	1.99321i	−0.908788	+	0.243509i	−0.682786	−	0.730618i	$-0.739232\pi$
$67$	−7.43875	+	1.99321i	−0.908788	+	0.243509i	−0.226001	+	0.974127i	$0.572565\pi$
$68$	1.74312	+	1.00639i	0.211384	+	0.122043i
$69$	1.81276	+	3.13980i	0.218231	+	0.377987i
$70$		0			0
$71$	1.74779	−	6.52285i	0.207425	−	0.774120i	−0.781272	−	0.624191i	$-0.785429\pi$
$71$	1.74779	−	6.52285i	0.207425	−	0.774120i	0.988697	−	0.149929i	$-0.0479045\pi$
$72$	−5.31473	−	1.42408i	−0.626347	−	0.167829i
$73$	−4.00398	−	4.00398i	−0.468630	−	0.468630i	0.432840	−	0.901471i	$-0.357511\pi$
$73$	−4.00398	−	4.00398i	−0.468630	−	0.468630i	−0.901471	+	0.432840i	$0.857511\pi$
$74$	−0.663841	−	1.14981i	−0.0771699	−	0.133662i
$75$	9.71705	−	16.8304i	1.12203	−	1.94341i
$76$	−7.74662	+	2.07570i	−0.888598	+	0.238099i
$77$		0			0
$78$	−0.430029	+	4.30727i	−0.0486912	+	0.487703i
$79$	−11.8232			−1.33021			−0.665107	−	0.746748i	$-0.731614\pi$
$79$	−11.8232			−1.33021			−0.665107	+	0.746748i	$0.731614\pi$
$80$	−2.43273	−	9.07908i	−0.271988	−	1.01507i
$81$	4.52697	−	7.84094i	0.502996	−	0.871215i
$82$	−1.15564	−	2.00163i	−0.127619	−	0.221043i
$83$	5.06789	−	5.06789i	0.556274	−	0.556274i	−0.371971	−	0.928244i	$-0.621318\pi$
$83$	5.06789	−	5.06789i	0.556274	−	0.556274i	0.928244	+	0.371971i	$0.121318\pi$
$84$		0			0
$85$	−3.97675	−	1.06557i	−0.431339	−	0.115577i
$86$	−1.82642	+	1.82642i	−0.196948	+	0.196948i
$87$	11.6836	−	6.74552i	1.25261	−	0.723196i
$88$	−3.38102	−	1.95203i	−0.360418	−	0.208087i
$89$	−9.63048	+	2.58048i	−1.02083	+	0.273530i	−0.730147	−	0.683290i	$-0.760549\pi$
$89$	−9.63048	+	2.58048i	−1.02083	+	0.273530i	−0.290681	+	0.956820i	$0.593882\pi$
$90$	5.26655			0.555143
$91$		0			0
$92$	−2.60753			−0.271854
$93$	−14.3234	+	3.83793i	−1.48526	+	0.397975i
$94$	−2.86872	−	1.65626i	−0.295886	−	0.170830i
$95$	14.2065	−	8.20214i	1.45756	−	0.841521i
$96$	8.60000	−	8.60000i	0.877733	−	0.877733i
$97$	−13.1665	−	3.52795i	−1.33685	−	0.358209i	−0.481587	−	0.876398i	$-0.659939\pi$
$97$	−13.1665	−	3.52795i	−1.33685	−	0.358209i	−0.855266	+	0.518190i	$0.826606\pi$
$98$		0			0
$99$	−4.46123	+	4.46123i	−0.448370	+	0.448370i
$100$	6.98864	+	12.1047i	0.698864	+	1.21047i
$101$	4.87153	−	8.43773i	0.484735	−	0.839586i	−0.515111	−	0.857123i	$-0.672249\pi$
$101$	4.87153	−	8.43773i	0.484735	−	0.839586i	0.999846	+	0.0175378i	$0.00558274\pi$
$102$	−0.355548	−	1.32692i	−0.0352045	−	0.131385i
$103$	12.3673			1.21858			0.609291	−	0.792947i	$-0.291454\pi$
$103$	12.3673			1.21858			0.609291	+	0.792947i	$0.291454\pi$
$104$	−5.40266	−	3.88240i	−0.529774	−	0.380701i
$105$		0			0
$106$	1.65370	−	0.443108i	0.160622	−	0.0430385i
$107$	4.09359	−	7.09030i	0.395742	−	0.685446i	−0.597453	−	0.801904i	$-0.703821\pi$
$107$	4.09359	−	7.09030i	0.395742	−	0.685446i	0.993196	+	0.116458i	$0.0371541\pi$
$108$	0.0389089	+	0.0673922i	0.00374401	+	0.00648482i
$109$	2.10702	+	2.10702i	0.201816	+	0.201816i	0.800778	−	0.598962i	$-0.204420\pi$
$109$	2.10702	+	2.10702i	0.201816	+	0.201816i	−0.598962	+	0.800778i	$0.704420\pi$
$110$	3.60952	+	0.967168i	0.344154	+	0.0922159i
$111$	1.71217	−	6.38989i	0.162512	−	0.606501i
$112$		0			0
$113$	−8.19898	−	14.2011i	−0.771295	−	1.33592i	−0.936853	−	0.349723i	$-0.886276\pi$
$113$	−8.19898	−	14.2011i	−0.771295	−	1.33592i	0.165558	−	0.986200i	$-0.447057\pi$
$114$	4.74030	+	2.73681i	0.443970	+	0.256326i
$115$	5.15183	−	1.38043i	0.480410	−	0.128726i
$116$			9.70294i			0.900895i
$117$	−8.32006	+	6.80955i	−0.769190	+	0.629543i
$118$			5.61007i			0.516448i
$119$		0			0
$120$	−8.11894	+	14.0624i	−0.741154	+	1.28372i
$121$	5.64942	−	3.26169i	0.513584	−	0.296518i
$122$	−3.28682	+	3.28682i	−0.297575	+	0.297575i
$123$	2.98061	−	11.1238i	0.268753	−	1.00300i
$124$	2.76029	−	10.3016i	0.247882	−	0.925107i
$125$	−7.49503	−	7.49503i	−0.670376	−	0.670376i
$126$		0			0
$127$	7.41767	+	4.28259i	0.658212	+	0.380019i	0.791595	−	0.611046i	$-0.209251\pi$
$127$	7.41767	+	4.28259i	0.658212	+	0.380019i	−0.133384	+	0.991064i	$0.542584\pi$
$128$	2.92773	+	10.9264i	0.258777	+	0.965770i
$129$	−12.8698			−1.13312
$130$	5.95685	+	2.25107i	0.522450	+	0.197432i
$131$			14.6866i			1.28317i	0.767050	+	0.641587i	$0.221724\pi$
$131$			14.6866i			1.28317i	−0.767050	+	0.641587i	$0.778276\pi$
$132$	−2.35597	−	8.79258i	−0.205060	−	0.765296i
$133$		0			0
$134$	−3.27379	+	1.89013i	−0.282813	+	0.163282i
$135$	−0.112552	−	0.112552i	−0.00968692	−	0.00968692i
$136$	2.03941	+	0.546458i	0.174878	+	0.0468583i
$137$	−2.19784	−	0.588910i	−0.187774	−	0.0503140i	0.163706	−	0.986509i	$-0.447655\pi$
$137$	−2.19784	−	0.588910i	−0.187774	−	0.0503140i	−0.351481	+	0.936195i	$0.614322\pi$
$138$	1.25841	+	1.25841i	0.107123	+	0.107123i
$139$	−4.23236	+	2.44355i	−0.358984	+	0.207259i	−0.668635	−	0.743591i	$-0.733121\pi$
$139$	−4.23236	+	2.44355i	−0.358984	+	0.207259i	0.309651	+	0.950850i	$0.399788\pi$
$140$		0			0
$141$	−4.27178	−	15.9425i	−0.359749	−	1.34260i
$142$		−	3.31481i		−	0.278172i
$143$	−6.95283	+	3.13912i	−0.581425	+	0.262506i
$144$	7.78980			0.649150
$145$	−5.13675	−	19.1706i	−0.426584	−	1.59203i
$146$	−2.40714	−	1.38976i	−0.199217	−	0.115018i
$147$		0			0
$148$	3.36428	+	3.36428i	0.276542	+	0.276542i
$149$	0.717149	−	2.67644i	0.0587512	−	0.219262i	−0.930309	−	0.366778i	$-0.880461\pi$
$149$	0.717149	−	2.67644i	0.0587512	−	0.219262i	0.989060	+	0.147515i	$0.0471276\pi$
$150$	2.46902	−	9.21452i	0.201595	−	0.752363i
$151$	4.46455	−	4.46455i	0.363320	−	0.363320i	−0.501714	−	0.865034i	$-0.667297\pi$
$151$	4.46455	−	4.46455i	0.363320	−	0.363320i	0.865034	+	0.501714i	$0.167297\pi$
$152$	−7.28557	+	4.20633i	−0.590938	+	0.341178i
$153$	1.70601	−	2.95490i	0.137923	−	0.238890i
$154$		0			0
$155$			21.8146i			1.75219i
$156$	−2.50644	−	15.3082i	−0.200676	−	1.22564i
$157$			1.90887i			0.152345i	0.997095	+	0.0761723i	$0.0242699\pi$
$157$			1.90887i			0.152345i	−0.997095	+	0.0761723i	$0.975730\pi$
$158$	−5.60588	+	1.50209i	−0.445980	+	0.119500i
$159$	7.38754	+	4.26520i	0.585870	+	0.338252i
$160$	−8.94602	−	15.4950i	−0.707245	−	1.22498i
$161$		0			0
$162$	1.15027	−	4.29285i	0.0903734	−	0.337278i
$163$	−5.96280	−	1.59773i	−0.467043	−	0.125144i	0.0176201	−	0.999845i	$-0.494391\pi$
$163$	−5.96280	−	1.59773i	−0.467043	−	0.125144i	−0.484663	+	0.874701i	$0.661058\pi$
$164$	5.85669	+	5.85669i	0.457330	+	0.457330i
$165$	9.30961	+	16.1247i	0.724752	+	1.25531i
$166$	1.75905	−	3.04676i	0.136528	−	0.236474i
$167$	2.11863	−	0.567684i	0.163944	−	0.0439287i	−0.175913	−	0.984406i	$-0.556288\pi$
$167$	2.11863	−	0.567684i	0.163944	−	0.0439287i	0.339857	+	0.940477i	$0.389621\pi$
$168$		0			0
$169$	−12.3212	+	4.14587i	−0.947784	+	0.318913i
$170$	−2.02092			−0.154997
$171$	3.51869	+	13.1319i	0.269081	+	1.00422i
$172$	4.62807	−	8.01605i	0.352887	−	0.611218i
$173$	9.47370	+	16.4089i	0.720272	+	1.24755i	0.960891	+	0.276928i	$0.0893164\pi$
$173$	9.47370	+	16.4089i	0.720272	+	1.24755i	−0.240618	+	0.970620i	$0.577350\pi$
$174$	4.68269	−	4.68269i	0.354993	−	0.354993i
$175$		0			0
$176$	5.33888	+	1.43055i	0.402433	+	0.107832i
$177$	−19.7655	+	19.7655i	−1.48567	+	1.48567i
$178$	−4.23837	+	2.44703i	−0.317680	+	0.183412i
$179$	−10.2742	−	5.93179i	−0.767926	−	0.443363i	0.0642080	−	0.997937i	$-0.479548\pi$
$179$	−10.2742	−	5.93179i	−0.767926	−	0.443363i	−0.832134	+	0.554574i	$0.812881\pi$
$180$	−18.2299	+	4.88467i	−1.35877	+	0.364082i
$181$	10.2064			0.758635			0.379317	−	0.925267i	$-0.376159\pi$
$181$	10.2064			0.758635			0.379317	+	0.925267i	$0.376159\pi$
$182$		0			0
$183$	−23.1604			−1.71207
$184$	−2.64203	+	0.707929i	−0.194773	+	0.0521892i
$185$	−8.42804	−	4.86593i	−0.619642	−	0.357750i
$186$	−6.30371	+	3.63945i	−0.462210	+	0.266857i
$187$	1.71190	−	1.71190i	0.125186	−	0.125186i
$188$	11.4661	+	3.07232i	0.836249	+	0.224072i
$189$		0			0
$190$	5.69386	−	5.69386i	0.413076	−	0.413076i
$191$	2.98574	+	5.17145i	0.216040	+	0.374193i	0.953594	−	0.301096i	$-0.0973524\pi$
$191$	2.98574	+	5.17145i	0.216040	+	0.374193i	−0.737553	+	0.675289i	$0.764019\pi$
$192$	−3.40425	+	5.89633i	−0.245681	+	0.425531i
$193$	−0.259754	−	0.969416i	−0.0186975	−	0.0697801i	0.955947	−	0.293540i	$-0.0948335\pi$
$193$	−0.259754	−	0.969416i	−0.0186975	−	0.0697801i	−0.974644	+	0.223760i	$0.928167\pi$
$194$	−6.69099			−0.480385
$195$	13.0563	+	28.9184i	0.934981	+	2.07089i
$196$		0			0
$197$	−4.08621	+	1.09490i	−0.291130	+	0.0780081i	−0.401428	−	0.915890i	$-0.631486\pi$
$197$	−4.08621	+	1.09490i	−0.291130	+	0.0780081i	0.110298	+	0.993899i	$0.464819\pi$
$198$	−1.54847	+	2.68204i	−0.110045	+	0.190604i
$199$	7.52706	+	13.0372i	0.533579	+	0.924186i	0.999231	+	0.0392178i	$0.0124866\pi$
$199$	7.52706	+	13.0372i	0.533579	+	0.924186i	−0.465652	+	0.884968i	$0.654180\pi$
$200$	10.3675	+	10.3675i	0.733090	+	0.733090i
$201$	−18.1937	−	4.87498i	−1.28328	−	0.343854i
$202$	1.23782	−	4.61959i	0.0870924	−	0.325033i
$203$		0			0
$204$	2.46142	+	4.26330i	0.172334	+	0.298491i
$205$	−14.6719	−	8.47082i	−1.02473	−	0.591628i
$206$	5.86383	−	1.57121i	0.408553	−	0.109471i
$207$			4.42024i			0.307228i
$208$	8.81083	+	3.32958i	0.610921	+	0.230865i
$209$			9.64640i			0.667255i
$210$		0			0
$211$	12.3556	−	21.4005i	0.850592	−	1.47327i	−0.0300832	−	0.999547i	$-0.509577\pi$
$211$	12.3556	−	21.4005i	0.850592	−	1.47327i	0.880675	−	0.473721i	$-0.157089\pi$
$212$	−5.31322	+	3.06759i	−0.364913	+	0.210683i
$213$	11.6788	−	11.6788i	0.800219	−	0.800219i
$214$	1.04015	−	3.88188i	0.0711030	−	0.265360i
$215$	−4.90021	+	18.2878i	−0.334192	+	1.24722i
$216$	0.0577203	+	0.0577203i	0.00392737	+	0.00392737i
$217$		0			0
$218$	1.26672	+	0.731339i	0.0857929	+	0.0495325i
$219$	−3.58445	−	13.3774i	−0.242215	−	0.903958i
$220$	−13.3912			−0.902834
$221$	3.19264	−	2.61301i	0.214760	−	0.175770i
$222$		−	3.24724i		−	0.217940i
$223$	0.193376	+	0.721689i	0.0129494	+	0.0483279i	0.972098	−	0.234574i	$-0.0753696\pi$
$223$	0.193376	+	0.721689i	0.0129494	+	0.0483279i	−0.959149	+	0.282902i	$0.908703\pi$
$224$		0			0
$225$	20.5197	−	11.8470i	1.36798	−	0.789802i
$226$	−5.69167	−	5.69167i	−0.378604	−	0.378604i
$227$	10.0184	+	2.68443i	0.664946	+	0.178172i	0.575477	−	0.817818i	$-0.304816\pi$
$227$	10.0184	+	2.68443i	0.664946	+	0.178172i	0.0894687	+	0.995990i	$0.471483\pi$
$228$	−18.9466	−	5.07674i	−1.25477	−	0.336215i
$229$	1.21458	+	1.21458i	0.0802616	+	0.0802616i	0.746098	−	0.665836i	$-0.231925\pi$
$229$	1.21458	+	1.21458i	0.0802616	+	0.0802616i	−0.665836	+	0.746098i	$0.731925\pi$
$230$	2.26732	−	1.30904i	0.149503	−	0.0863154i
$231$		0			0
$232$	2.63429	+	9.83132i	0.172950	+	0.645458i
$233$			8.31061i			0.544446i	0.962234	+	0.272223i	$0.0877589\pi$
$233$			8.31061i			0.544446i	−0.962234	+	0.272223i	$0.912241\pi$
$234$	−3.07976	+	4.28572i	−0.201330	+	0.280167i
$235$	−24.2806			−1.58389
$236$	−5.20328	−	19.4189i	−0.338705	−	1.26406i
$237$	−25.0430	−	14.4586i	−1.62672	−	0.939185i
$238$		0			0
$239$	5.13978	+	5.13978i	0.332465	+	0.332465i	0.853522	−	0.521057i	$-0.174462\pi$
$239$	5.13978	+	5.13978i	0.332465	+	0.332465i	−0.521057	+	0.853522i	$0.674462\pi$
$240$	5.94996	−	22.2056i	0.384068	−	1.43336i
$241$	2.00591	−	7.48614i	0.129212	−	0.482225i	−0.870743	−	0.491738i	$-0.836362\pi$
$241$	2.00591	−	7.48614i	0.129212	−	0.482225i	0.999955	+	0.00951360i	$0.00302832\pi$
$242$	2.26424	−	2.26424i	0.145551	−	0.145551i
$243$	19.0624	−	11.0057i	1.22285	−	0.706014i
$244$	8.32864	−	14.4256i	0.533187	−	0.923507i
$245$		0			0
$246$		−	5.65293i		−	0.360418i
$247$	−1.63306	+	16.3572i	−0.103909	+	1.04078i
$248$		−	11.1873i		−	0.710391i
$249$	16.9319	−	4.53689i	1.07302	−	0.287514i
$250$	−4.50592	−	2.60149i	−0.284979	−	0.164533i
$251$	−1.76122	−	3.05052i	−0.111167	−	0.192547i	0.805074	−	0.593174i	$-0.202126\pi$
$251$	−1.76122	−	3.05052i	−0.111167	−	0.192547i	−0.916241	+	0.400627i	$0.868792\pi$
$252$		0			0
$253$	−0.811749	+	3.02949i	−0.0510343	+	0.190462i
$254$	4.06111	+	1.08817i	0.254817	+	0.0682780i
$255$	−7.12015	−	7.12015i	−0.445881	−	0.445881i
$256$	−0.00743845	−	0.0128838i	−0.000464903	−	0.000805236i
$257$	−5.42573	+	9.39764i	−0.338448	+	0.586209i	−0.984141	−	0.177388i	$-0.943235\pi$
$257$	−5.42573	+	9.39764i	−0.338448	+	0.586209i	0.645693	+	0.763597i	$0.276569\pi$
$258$	−6.10211	+	1.63506i	−0.379901	+	0.101794i
$259$		0			0
$260$	−22.7071	−	2.26703i	−1.40824	−	0.140595i
$261$	16.4483			1.01812
$262$	1.86587	+	6.96354i	0.115274	+	0.430209i
$263$	2.34957	−	4.06957i	0.144881	−	0.250940i	−0.784448	−	0.620195i	$-0.787054\pi$
$263$	2.34957	−	4.06957i	0.144881	−	0.250940i	0.929328	+	0.369254i	$0.120387\pi$
$264$	−4.77427	−	8.26928i	−0.293836	−	0.508939i
$265$	8.87362	−	8.87362i	0.545102	−	0.545102i
$266$		0			0
$267$	−23.5542	−	6.31132i	−1.44149	−	0.386247i
$268$	9.57898	−	9.57898i	0.585129	−	0.585129i
$269$	−22.2662	+	12.8554i	−1.35760	+	0.783809i	−0.989299	−	0.145899i	$-0.953393\pi$
$269$	−22.2662	+	12.8554i	−1.35760	+	0.783809i	−0.368298	+	0.929708i	$0.620059\pi$
$270$	−0.0676648	−	0.0390663i	−0.00411795	−	0.00237750i
$271$	−1.28101	+	0.343245i	−0.0778156	+	0.0208506i	−0.297517	−	0.954717i	$-0.596158\pi$
$271$	−1.28101	+	0.343245i	−0.0778156	+	0.0208506i	0.219701	+	0.975567i	$0.429492\pi$
$272$	−2.98916			−0.181244
$273$		0			0
$274$	−1.11691			−0.0674749
$275$	16.2391	−	4.35126i	0.979257	−	0.262391i
$276$	−5.52306	−	3.18874i	−0.332449	−	0.191940i
$277$	0.157067	−	0.0906826i	0.00943723	−	0.00544859i	−0.495274	−	0.868737i	$-0.664932\pi$
$277$	0.157067	−	0.0906826i	0.00943723	−	0.00544859i	0.504711	+	0.863288i	$0.331599\pi$
$278$	−1.69629	+	1.69629i	−0.101737	+	0.101737i
$279$	−17.4630	−	4.67921i	−1.04548	−	0.280137i
$280$		0			0
$281$	5.50563	−	5.50563i	0.328439	−	0.328439i	−0.523554	−	0.851993i	$-0.675394\pi$
$281$	5.50563	−	5.50563i	0.328439	−	0.328439i	0.851993	+	0.523554i	$0.175394\pi$
$282$	−4.05086	−	7.01630i	−0.241225	−	0.417815i
$283$	−3.65425	+	6.32935i	−0.217223	+	0.376241i	−0.953958	−	0.299941i	$-0.903033\pi$
$283$	−3.65425	+	6.32935i	−0.217223	+	0.376241i	0.736735	+	0.676181i	$0.236366\pi$
$284$	3.07445	+	11.4740i	0.182435	+	0.680857i
$285$	40.1215			2.37659
$286$	−2.89782	+	2.37172i	−0.171351	+	0.140243i
$287$		0			0
$288$	14.3229	−	3.83782i	0.843987	−	0.226146i
$289$	7.84536	−	13.5886i	0.461492	−	0.799327i
$290$	−4.87109	−	8.43698i	−0.286040	−	0.495437i
$291$	−23.5739	−	23.5739i	−1.38192	−	1.38192i
$292$	9.62118	+	2.57799i	0.563037	+	0.150865i
$293$	−8.30804	+	31.0060i	−0.485361	+	1.81139i	0.0930708	+	0.995659i	$0.470332\pi$
$293$	−8.30804	+	31.0060i	−0.485361	+	1.81139i	−0.578431	+	0.815731i	$0.696335\pi$
$294$		0			0
$295$	20.5608	+	35.6123i	1.19710	+	2.07343i
$296$	4.32218	+	2.49541i	0.251221	+	0.145043i
$297$	0.0904107	−	0.0242255i	0.00524616	−	0.00140570i
$298$		−	1.36012i		−	0.0787898i
$299$	−1.88934	+	4.99961i	−0.109263	+	0.289135i
$300$			34.1855i			1.97370i
$301$		0			0
$302$	1.54963	−	2.68403i	0.0891709	−	0.154449i
$303$	20.6370	−	11.9148i	1.18556	−	0.684485i
$304$	8.42184	−	8.42184i	0.483025	−	0.483025i
$305$	−8.81839	+	32.9107i	−0.504939	+	1.88446i
$306$	0.433484	−	1.61779i	0.0247806	−	0.0924826i
$307$	9.65602	+	9.65602i	0.551098	+	0.551098i	0.926758	−	0.375659i	$-0.122584\pi$
$307$	9.65602	+	9.65602i	0.551098	+	0.551098i	−0.375659	+	0.926758i	$0.622584\pi$
$308$		0			0
$309$	26.1953	+	15.1239i	1.49020	+	0.860368i
$310$	2.77146	+	10.3432i	0.157408	+	0.587456i
$311$	16.5874			0.940584			0.470292	−	0.882511i	$-0.344149\pi$
$311$	16.5874			0.940584			0.470292	+	0.882511i	$0.344149\pi$
$312$	−6.69570	−	14.8303i	−0.379069	−	0.839600i
$313$		−	9.30989i		−	0.526226i	−0.964765	−	0.263113i	$-0.915251\pi$
$313$		−	9.30989i		−	0.526226i	0.964765	−	0.263113i	$-0.0847493\pi$
$314$	0.242514	+	0.905076i	0.0136859	+	0.0510764i
$315$		0			0
$316$	18.0112	−	10.3988i	1.01321	−	0.584978i
$317$	23.4352	+	23.4352i	1.31625	+	1.31625i	0.916719	+	0.399533i	$0.130828\pi$
$317$	23.4352	+	23.4352i	1.31625	+	1.31625i	0.399533	+	0.916719i	$0.369172\pi$
$318$	4.04462	+	1.08375i	0.226811	+	0.0607738i
$319$	11.2731	+	3.02062i	0.631173	+	0.169122i
$320$	7.08244	+	7.08244i	0.395920	+	0.395920i
$321$	17.3414	−	10.0121i	0.967904	−	0.558820i
$322$		0			0
$323$	−1.35022	−	5.03909i	−0.0751282	−	0.280382i
$324$			15.9263i			0.884795i
$325$	28.2730	−	4.62917i	1.56830	−	0.256780i
$326$	−3.03020			−0.167827
$327$	1.88626	+	7.03960i	0.104310	+	0.389291i
$328$	7.52423	+	4.34412i	0.415456	+	0.239864i
$329$		0			0
$330$	6.46265	+	6.46265i	0.355757	+	0.355757i
$331$	−6.09453	+	22.7451i	−0.334985	+	1.25018i	0.568900	+	0.822407i	$0.307369\pi$
$331$	−6.09453	+	22.7451i	−0.334985	+	1.25018i	−0.903885	+	0.427776i	$0.859297\pi$
$332$	−3.26300	+	12.1777i	−0.179080	+	0.668336i
$333$	5.70308	−	5.70308i	0.312527	−	0.312527i
$334$	0.932407	−	0.538326i	0.0510191	−	0.0294559i
$335$	−13.8546	+	23.9968i	−0.756955	+	1.31109i
$336$		0			0
$337$		−	24.5958i		−	1.33982i	−0.742442	−	0.669911i	$-0.766332\pi$
$337$		−	24.5958i		−	1.33982i	0.742442	−	0.669911i	$-0.233668\pi$
$338$	−5.31528	+	3.53109i	−0.289113	+	0.192066i
$339$		−	40.1061i		−	2.17826i
$340$	6.99529	−	1.87438i	0.379373	−	0.101653i
$341$	−11.1093	−	6.41395i	−0.601602	−	0.347335i
$342$	3.33672	+	5.77937i	0.180429	+	0.312512i
$343$		0			0
$344$	2.51299	−	9.37860i	0.135491	−	0.505660i
$345$	12.6003	+	3.37624i	0.678378	+	0.181771i
$346$	6.57657	+	6.57657i	0.353558	+	0.353558i
$347$	16.6796	+	28.8899i	0.895406	+	1.55089i	0.833301	+	0.552819i	$0.186448\pi$
$347$	16.6796	+	28.8899i	0.895406	+	1.55089i	0.0621044	+	0.998070i	$0.480219\pi$
$348$	−11.8657	+	20.5520i	−0.636068	+	1.10170i
$349$	5.28189	−	1.41528i	0.282733	−	0.0757580i	−0.114666	−	0.993404i	$-0.536580\pi$
$349$	5.28189	−	1.41528i	0.282733	−	0.0757580i	0.397399	+	0.917646i	$0.369913\pi$
$350$		0			0
$351$	0.157409	−	0.0257727i	0.00840184	−	0.00137564i
$352$	10.5213			0.560785
$353$	−1.14383	−	4.26881i	−0.0608797	−	0.227206i	0.928782	−	0.370626i	$-0.120857\pi$
$353$	−1.14383	−	4.26881i	−0.0608797	−	0.227206i	−0.989662	+	0.143420i	$0.954190\pi$
$354$	−6.86054	+	11.8828i	−0.364633	+	0.631563i
$355$	−12.1487	−	21.0422i	−0.644787	−	1.11680i
$356$	12.4013	−	12.4013i	0.657267	−	0.657267i
$357$		0			0
$358$	−5.62502	−	1.50722i	−0.297291	−	0.0796590i
$359$	19.6363	−	19.6363i	1.03636	−	1.03636i	0.0370502	−	0.999313i	$-0.488204\pi$
$359$	19.6363	−	19.6363i	1.03636	−	1.03636i	0.999313	−	0.0370502i	$-0.0117961\pi$
$360$	−17.1449	+	9.89860i	−0.903615	+	0.521702i
$361$	1.54713	+	0.893234i	0.0814278	+	0.0470123i
$362$	4.83927	−	1.29668i	0.254347	−	0.0681520i
$363$	15.9549			0.837413
$364$		0			0
$365$	−20.3739			−1.06642
$366$	−10.9813	+	2.94244i	−0.574003	+	0.153804i
$367$	14.5923	+	8.42486i	0.761711	+	0.439774i	0.829910	−	0.557898i	$-0.188392\pi$
$367$	14.5923	+	8.42486i	0.761711	+	0.439774i	−0.0681985	+	0.997672i	$0.521725\pi$
$368$	3.35361	−	1.93621i	0.174819	−	0.100932i
$369$	9.92816	−	9.92816i	0.516840	−	0.516840i
$370$	−4.61428	−	1.23639i	−0.239885	−	0.0642770i
$371$		0			0
$372$	18.4444	−	18.4444i	0.956296	−	0.956296i
$373$	−1.39145	−	2.41007i	−0.0720466	−	0.124788i	0.827752	−	0.561095i	$-0.189620\pi$
$373$	−1.39145	−	2.41007i	−0.0720466	−	0.124788i	−0.899798	+	0.436306i	$0.856286\pi$
$374$	0.594192	−	1.02917i	0.0307250	−	0.0532172i
$375$	−6.70972	−	25.0410i	−0.346489	−	1.29311i
$376$	12.4519			0.642158
$377$	18.6042	+	7.03046i	0.958165	+	0.362087i
$378$		0			0
$379$	0.734071	−	0.196694i	0.0377067	−	0.0101035i	−0.239916	−	0.970794i	$-0.577120\pi$
$379$	0.734071	−	0.196694i	0.0377067	−	0.0101035i	0.277623	+	0.960690i	$0.410453\pi$
$380$	−14.4280	+	24.9900i	−0.740139	+	1.28196i
$381$	10.4743	+	18.1421i	0.536617	+	0.929448i
$382$	2.07268	+	2.07268i	0.106047	+	0.106047i
$383$	−30.3934	−	8.14389i	−1.55303	−	0.416134i	−0.622582	−	0.782554i	$-0.713916\pi$
$383$	−30.3934	−	8.14389i	−1.55303	−	0.416134i	−0.930449	+	0.366421i	$0.880583\pi$
$384$	−7.16063	+	26.7238i	−0.365414	+	1.36374i
$385$		0			0
$386$	−0.246321	−	0.426640i	−0.0125374	−	0.0217154i
$387$	−13.5887	−	7.84543i	−0.690752	−	0.398806i
$388$	23.1605	−	6.20583i	1.17579	−	0.315053i
$389$			27.0602i			1.37201i	0.727599	+	0.686003i	$0.240636\pi$
$389$			27.0602i			1.37201i	−0.727599	+	0.686003i	$0.759364\pi$
$390$	9.86449	+	12.0527i	0.499508	+	0.610310i
$391$		−	1.69617i		−	0.0857789i
$392$		0			0
$393$	−17.9602	+	31.1080i	−0.905973	+	1.56919i
$394$	−1.79834	+	1.03827i	−0.0905991	+	0.0523074i
$395$	−30.0806	+	30.0806i	−1.51352	+	1.51352i
$396$	2.87239	−	10.7199i	0.144343	−	0.538696i
$397$	−0.0590847	+	0.220507i	−0.00296537	+	0.0110669i	−0.967393	−	0.253281i	$-0.918490\pi$
$397$	−0.0590847	+	0.220507i	−0.00296537	+	0.0110669i	0.964427	+	0.264348i	$0.0851568\pi$
$398$	5.22522	+	5.22522i	0.261917	+	0.261917i
$399$		0			0
$400$	−17.9766	−	10.3788i	−0.898828	−	0.518939i
$401$	−6.65077	−	24.8210i	−0.332124	−	1.23950i	−0.906954	−	0.421230i	$-0.861599\pi$
$401$	−6.65077	−	24.8210i	−0.332124	−	1.23950i	0.574830	−	0.818273i	$-0.305068\pi$
$402$	−9.24572			−0.461135
$403$	−17.7519	−	12.7567i	−0.884287	−	0.635457i
$404$			17.1385i			0.852672i
$405$	−8.43141	−	31.4664i	−0.418960	−	1.56358i
$406$		0			0
$407$	4.95604	−	2.86137i	0.245662	−	0.141833i
$408$	3.65145	+	3.65145i	0.180774	+	0.180774i
$409$	−28.8314	−	7.72535i	−1.42562	−	0.381994i	−0.538147	−	0.842851i	$-0.680876\pi$
$409$	−28.8314	−	7.72535i	−1.42562	−	0.381994i	−0.887475	+	0.460857i	$0.847542\pi$
$410$	−8.03274	−	2.15237i	−0.396709	−	0.106298i
$411$	−3.93512	−	3.93512i	−0.194105	−	0.194105i
$412$	−18.8400	+	10.8773i	−0.928182	+	0.535886i
$413$		0			0
$414$	0.561574	+	2.09582i	0.0275998	+	0.103004i
$415$		−	25.7875i		−	1.26586i
$416$	17.8407	+	1.78117i	0.874711	+	0.0873292i
$417$	−11.9529			−0.585334
$418$	1.22554	+	4.57376i	0.0599429	+	0.223710i
$419$	7.72615	+	4.46069i	0.377447	+	0.217919i	0.676707	−	0.736253i	$-0.263406\pi$
$419$	7.72615	+	4.46069i	0.377447	+	0.217919i	−0.299260	+	0.954172i	$0.596740\pi$
$420$		0			0
$421$	18.1408	+	18.1408i	0.884130	+	0.884130i	0.993951	−	0.109821i	$-0.0350278\pi$
$421$	18.1408	+	18.1408i	0.884130	+	0.884130i	−0.109821	+	0.993951i	$0.535028\pi$
$422$	3.13945	−	11.7166i	0.152826	−	0.570354i
$423$	5.20816	−	19.4371i	0.253229	−	0.945065i
$424$	−4.55068	+	4.55068i	−0.221001	+	0.221001i
$425$	−7.87395	+	4.54603i	−0.381943	+	0.220515i
$426$	4.05367	−	7.02116i	0.196401	−	0.340176i
$427$		0			0
$428$			14.4016i			0.696130i
$429$	−18.5658	−	1.85357i	−0.896363	−	0.0894910i
$430$			9.29358i			0.448176i
$431$	11.3663	−	3.04559i	0.547496	−	0.146701i	0.0255403	−	0.999674i	$-0.491869\pi$
$431$	11.3663	−	3.04559i	0.547496	−	0.146701i	0.521955	+	0.852973i	$0.325203\pi$
$432$	−0.100084	−	0.0577833i	−0.00481528	−	0.00278010i
$433$	6.26407	+	10.8497i	0.301032	+	0.521403i	0.976370	−	0.216106i	$-0.0693356\pi$
$433$	6.26407	+	10.8497i	0.301032	+	0.521403i	−0.675338	+	0.737508i	$0.736002\pi$
$434$		0			0
$435$	12.5634	−	46.8874i	0.602370	−	2.24808i
$436$	−5.06298	−	1.35662i	−0.242473	−	0.0649703i
$437$	4.77888	+	4.77888i	0.228605	+	0.228605i
$438$	−3.39908	−	5.88738i	−0.162414	−	0.281310i
$439$	−8.88189	+	15.3839i	−0.423910	+	0.734233i	−0.996318	−	0.0857358i	$-0.972676\pi$
$439$	−8.88189	+	15.3839i	−0.423910	+	0.734233i	0.572408	+	0.819969i	$0.306009\pi$
$440$	−13.5684	+	3.63563i	−0.646847	+	0.173322i
$441$		0			0
$442$	1.18179	−	1.64455i	0.0562120	−	0.0782233i
$443$	−6.69890			−0.318274			−0.159137	−	0.987256i	$-0.550871\pi$
$443$	−6.69890			−0.318274			−0.159137	+	0.987256i	$0.550871\pi$
$444$	3.01178	+	11.2401i	0.142933	+	0.533433i
$445$	−17.9366	+	31.0671i	−0.850278	+	1.47272i
$446$	0.183375	+	0.317615i	0.00868307	+	0.0150395i
$447$	4.79202	−	4.79202i	0.226655	−	0.226655i
$448$		0			0
$449$	22.8700	+	6.12801i	1.07930	+	0.289199i	0.754311	−	0.656518i	$-0.227971\pi$
$449$	22.8700	+	6.12801i	1.07930	+	0.289199i	0.324993	+	0.945716i	$0.394638\pi$
$450$	8.22411	−	8.22411i	0.387688	−	0.387688i
$451$	8.62769	−	4.98120i	0.406262	−	0.234555i
$452$	24.9803	+	14.4224i	1.17498	+	0.678373i
$453$	14.9161	−	3.99676i	0.700821	−	0.187784i
$454$	5.09120			0.238942
$455$		0			0
$456$	−20.5756			−0.963542
$457$	30.8488	−	8.26591i	1.44305	−	0.386663i	0.549447	−	0.835528i	$-0.314838\pi$
$457$	30.8488	−	8.26591i	1.44305	−	0.386663i	0.893599	+	0.448865i	$0.148172\pi$
$458$	0.730190	+	0.421575i	0.0341195	+	0.0196989i
$459$	−0.0438379	+	0.0253098i	−0.00204618	+	0.00118136i
$460$	−6.63408	+	6.63408i	−0.309315	+	0.309315i
$461$	−36.7537	−	9.84812i	−1.71179	−	0.458673i	−0.735927	−	0.677060i	$-0.763254\pi$
$461$	−36.7537	−	9.84812i	−1.71179	−	0.458673i	−0.975862	+	0.218388i	$0.929920\pi$
$462$		0			0
$463$	−9.11397	+	9.11397i	−0.423562	+	0.423562i	−0.886428	−	0.462866i	$-0.846821\pi$
$463$	−9.11397	+	9.11397i	−0.423562	+	0.423562i	0.462866	+	0.886428i	$0.346821\pi$
$464$	−7.20488	−	12.4792i	−0.334478	−	0.579333i
$465$	−26.6770	+	46.2060i	−1.23712	+	2.14275i
$466$	1.05583	+	3.94041i	0.0489104	+	0.182536i
$467$	−17.8406			−0.825565			−0.412783	−	0.910830i	$-0.635443\pi$
$467$	−17.8406			−0.825565			−0.412783	+	0.910830i	$0.635443\pi$
$468$	6.68545	−	17.6912i	0.309035	−	0.817778i
$469$		0			0
$470$	−11.5125	+	3.08475i	−0.531030	+	0.142289i
$471$	−2.33435	+	4.04322i	−0.107561	+	0.186302i
$472$	−10.5443	−	18.2632i	−0.485339	−	0.840631i
$473$	−7.87248	−	7.87248i	−0.361977	−	0.361977i
$474$	−13.7108	−	3.67380i	−0.629759	−	0.168743i
$475$	9.37629	−	34.9928i	0.430214	−	1.60558i
$476$		0			0
$477$	5.20013	+	9.00689i	0.238098	+	0.412397i
$478$	3.08997	+	1.78400i	0.141332	+	0.0815981i
$479$	−8.87813	+	2.37889i	−0.405652	+	0.108694i	−0.455875	−	0.890044i	$-0.650674\pi$
$479$	−8.87813	+	2.37889i	−0.405652	+	0.108694i	0.0502226	+	0.998738i	$0.484007\pi$
$480$		−	43.7602i		−	1.99737i
$481$	8.88825	−	4.01294i	0.405270	−	0.182974i
$482$		−	3.80434i		−	0.173283i
$483$		0			0
$484$	−5.73748	+	9.93760i	−0.260794	+	0.451709i
$485$	−42.4740	+	24.5224i	−1.92864	+	1.11350i
$486$	7.64005	−	7.64005i	0.346560	−	0.346560i
$487$	2.86354	−	10.6869i	0.129759	−	0.484269i	−0.870205	−	0.492690i	$-0.836014\pi$
$487$	2.86354	−	10.6869i	0.129759	−	0.484269i	0.999965	+	0.00842076i	$0.00268044\pi$
$488$	4.52236	−	16.8777i	0.204718	−	0.764017i
$489$	−10.6761	−	10.6761i	−0.482789	−	0.482789i
$490$		0			0
$491$	2.45531	+	1.41757i	0.110807	+	0.0639743i	0.554379	−	0.832264i	$-0.312956\pi$
$491$	2.45531	+	1.41757i	0.110807	+	0.0639743i	−0.443572	+	0.896239i	$0.646289\pi$
$492$	5.24304	+	19.5673i	0.236375	+	0.882162i
$493$	−6.31165			−0.284263
$494$	1.30381	+	7.96310i	0.0586611	+	0.358277i
$495$			22.7005i			1.02031i
$496$	4.09929	+	15.2988i	0.184064	+	0.686935i
$497$		0			0
$498$	7.45174	−	4.30226i	0.333920	−	0.192789i
$499$	−27.1221	−	27.1221i	−1.21415	−	1.21415i	−0.969648	−	0.244505i	$-0.921375\pi$
$499$	−27.1221	−	27.1221i	−1.21415	−	1.21415i	−0.244505	−	0.969648i	$-0.578625\pi$
$500$	18.0098	+	4.82572i	0.805425	+	0.215813i
$501$	5.18172	+	1.38844i	0.231502	+	0.0620309i
$502$	−1.22262	−	1.22262i	−0.0545684	−	0.0545684i
$503$	25.0453	−	14.4599i	1.11672	−	0.644736i	0.176155	−	0.984362i	$-0.443634\pi$
$503$	25.0453	−	14.4599i	1.11672	−	0.644736i	0.940561	+	0.339626i	$0.110301\pi$
$504$		0			0
$505$	−9.07314	−	33.8614i	−0.403750	−	1.50681i
$506$			1.53954i			0.0684408i
$507$	−31.1677	−	6.28610i	−1.38421	−	0.279175i
$508$	−15.0666			−0.668471
$509$	3.31260	+	12.3628i	0.146829	+	0.547972i	0.999667	+	0.0257972i	$0.00821241\pi$
$509$	3.31260	+	12.3628i	0.146829	+	0.547972i	−0.852839	+	0.522175i	$0.825121\pi$
$510$	−4.28055	−	2.47138i	−0.189546	−	0.109434i
$511$		0			0
$512$	−16.0026	−	16.0026i	−0.707221	−	0.707221i
$513$	0.0522021	−	0.194821i	0.00230478	−	0.00860155i
$514$	−1.37863	+	5.14513i	−0.0608089	+	0.226942i
$515$	31.4648	−	31.4648i	1.38650	−	1.38650i
$516$	19.6056	−	11.3193i	0.863089	−	0.498305i
$517$	7.13901	−	12.3651i	0.313973	−	0.543817i
$518$		0			0
$519$			46.3415i			2.03416i
$520$	−23.6231	+	3.86783i	−1.03594	+	0.169616i
$521$		−	16.1503i		−	0.707557i	−0.935329	−	0.353779i	$-0.884897\pi$
$521$		−	16.1503i		−	0.707557i	0.935329	−	0.353779i	$-0.115103\pi$
$522$	7.79881	−	2.08969i	0.341345	−	0.0914631i
$523$	31.2872	+	18.0636i	1.36809	+	0.789868i	0.990684	−	0.136179i	$-0.0434823\pi$
$523$	31.2872	+	18.0636i	1.36809	+	0.789868i	0.377407	+	0.926047i	$0.376816\pi$
$524$	−12.9172	−	22.3733i	−0.564292	−	0.977382i
$525$		0			0
$526$	0.597006	−	2.22806i	0.0260307	−	0.0971479i
$527$	6.70104	+	1.79554i	0.291902	+	0.0782149i
$528$	9.55897	+	9.55897i	0.416001	+	0.416001i
$529$	−10.4013	−	18.0156i	−0.452231	−	0.783287i
$530$	3.08000	−	5.33471i	0.133787	−	0.231725i
$531$	−32.9187	+	8.82053i	−1.42855	+	0.382778i
$532$		0			0
$533$	15.4731	−	6.98590i	0.670212	−	0.302593i
$534$	−11.9699			−0.517986
$535$	−7.62425	−	28.4541i	−0.329625	−	1.23018i
$536$	7.10508	−	12.3064i	0.306893	−	0.531553i
$537$	−14.5079	−	25.1285i	−0.626063	−	1.08437i
$538$	−8.92413	+	8.92413i	−0.384747	+	0.384747i
$539$		0			0
$540$	0.270451	+	0.0724673i	0.0116384	+	0.00311849i
$541$	−18.4157	+	18.4157i	−0.791753	+	0.791753i	−0.981779	−	0.190026i	$-0.939143\pi$
$541$	−18.4157	+	18.4157i	−0.791753	+	0.791753i	0.190026	+	0.981779i	$0.439143\pi$
$542$	−0.563771	+	0.325493i	−0.0242160	+	0.0139811i
$543$	21.6184	+	12.4814i	0.927732	+	0.535627i
$544$	−5.49610	+	1.47268i	−0.235643	+	0.0631404i
$545$	10.7214			0.459254
$546$		0			0
$547$	−21.3472			−0.912739			−0.456369	−	0.889790i	$-0.650850\pi$
$547$	−21.3472			−0.912739			−0.456369	+	0.889790i	$0.650850\pi$
$548$	3.86611	−	1.03592i	0.165152	−	0.0442524i
$549$	−24.4541	−	14.1186i	−1.04368	−	0.602567i
$550$	7.14685	−	4.12623i	0.304743	−	0.175943i
$551$	17.7828	−	17.7828i	0.757574	−	0.757574i
$552$	−6.46186	−	1.73145i	−0.275035	−	0.0736954i
$553$		0			0
$554$	0.0629511	−	0.0629511i	0.00267454	−	0.00267454i
$555$	−11.9011	−	20.6133i	−0.505172	−	0.874984i
$556$	4.29833	−	7.44492i	0.182290	−	0.315735i
$557$	−1.69776	−	6.33615i	−0.0719366	−	0.268471i	0.920585	−	0.390543i	$-0.127713\pi$
$557$	−1.69776	−	6.33615i	−0.0719366	−	0.268471i	−0.992521	+	0.122072i	$0.961046\pi$
$558$	−8.87443			−0.375685
$559$	−12.0164	−	14.6819i	−0.508241	−	0.620980i
$560$		0			0
$561$	5.71948	−	1.53253i	0.241476	−	0.0647034i
$562$	1.91098	−	3.30992i	0.0806100	−	0.139621i
$563$	5.04580	+	8.73958i	0.212655	+	0.368329i	0.952545	−	0.304399i	$-0.0984556\pi$
$563$	5.04580	+	8.73958i	0.212655	+	0.368329i	−0.739890	+	0.672728i	$0.765122\pi$
$564$	20.5294	+	20.5294i	0.864443	+	0.864443i
$565$	−56.9902	−	15.2705i	−2.39760	−	0.642434i
$566$	−0.928516	+	3.46527i	−0.0390284	+	0.145656i
$567$		0			0
$568$	6.23026	+	10.7911i	0.261416	+	0.452786i
$569$	27.1118	+	15.6530i	1.13658	+	0.656207i	0.945582	−	0.325383i	$-0.105493\pi$
$569$	27.1118	+	15.6530i	1.13658	+	0.656207i	0.191001	+	0.981590i	$0.438826\pi$
$570$	19.0233	−	5.09727i	0.796797	−	0.213501i
$571$			9.30555i			0.389425i	0.980860	+	0.194713i	$0.0623774\pi$
$571$			9.30555i			0.389425i	−0.980860	+	0.194713i	$0.937623\pi$
$572$	7.83088	−	10.8973i	0.327426	−	0.455637i
$573$			14.6050i			0.610133i
$574$		0			0
$575$	5.88933	−	10.2006i	0.245602	−	0.425395i
$576$	−7.18881	+	4.15046i	−0.299534	+	0.172936i
$577$	−12.1536	+	12.1536i	−0.505963	+	0.505963i	−0.913285	−	0.407322i	$-0.866463\pi$
$577$	−12.1536	+	12.1536i	−0.505963	+	0.505963i	0.407322	+	0.913285i	$0.366463\pi$
$578$	1.99344	−	7.43962i	0.0829162	−	0.309448i
$579$	0.635306	−	2.37099i	0.0264024	−	0.0985351i
$580$	24.6862	+	24.6862i	1.02504	+	1.02504i
$581$		0			0
$582$	−14.1723	−	8.18239i	−0.587461	−	0.339171i
$583$	1.90994	+	7.12800i	0.0791017	+	0.295212i
$584$	10.4484			0.432357
$585$	−3.84304	+	38.4928i	−0.158890	+	1.59148i
$586$			15.7568i			0.650905i
$587$	5.01190	+	18.7047i	0.206863	+	0.772025i	0.988873	+	0.148759i	$0.0475278\pi$
$587$	5.01190	+	18.7047i	0.206863	+	0.772025i	−0.782010	+	0.623266i	$0.785805\pi$
$588$		0			0
$589$	−23.9388	+	13.8211i	−0.986380	+	0.569487i
$590$	14.2731	+	14.2731i	0.587616	+	0.587616i
$591$	−9.99403	−	2.67789i	−0.411099	−	0.110154i
$592$	−6.82503	−	1.82876i	−0.280507	−	0.0751616i
$593$	−7.16008	−	7.16008i	−0.294029	−	0.294029i	0.544640	−	0.838670i	$-0.316666\pi$
$593$	−7.16008	−	7.16008i	−0.294029	−	0.294029i	−0.838670	+	0.544640i	$0.816666\pi$
$594$	0.0397897	−	0.0229726i	0.00163259	−	0.000942578i
$595$		0			0
$596$	1.26150	+	4.70799i	0.0516731	+	0.192847i
$597$			36.8193i			1.50691i
$598$	−0.260633	+	2.61056i	−0.0106581	+	0.106754i
$599$	17.9346			0.732786			0.366393	−	0.930460i	$-0.380593\pi$
$599$	17.9346			0.732786			0.366393	+	0.930460i	$0.380593\pi$
$600$	9.28118	+	34.6378i	0.378903	+	1.41408i
$601$	29.5092	+	17.0372i	1.20371	+	0.694960i	0.961377	−	0.275234i	$-0.0887552\pi$
$601$	29.5092	+	17.0372i	1.20371	+	0.694960i	0.242329	+	0.970194i	$0.422089\pi$
$602$		0			0
$603$	−16.2381	−	16.2381i	−0.661268	−	0.661268i
$604$	−2.87453	+	10.7279i	−0.116963	+	0.436511i
$605$	6.07486	−	22.6717i	0.246978	−	0.921734i
$606$	8.27112	−	8.27112i	0.335991	−	0.335991i
$607$	27.7235	−	16.0061i	1.12526	−	0.649669i	0.182522	−	0.983202i	$-0.441574\pi$
$607$	27.7235	−	16.0061i	1.12526	−	0.649669i	0.942739	+	0.333533i	$0.108241\pi$
$608$	11.3358	−	19.6342i	0.459729	−	0.796274i
$609$		0			0
$610$			16.7247i			0.677162i
$611$	14.1988	−	19.7587i	0.574421	−	0.799350i
$612$			6.00192i			0.242613i
$613$	−16.7504	+	4.48824i	−0.676541	+	0.181279i	−0.580699	−	0.814118i	$-0.697221\pi$
$613$	−16.7504	+	4.48824i	−0.676541	+	0.181279i	−0.0958413	+	0.995397i	$0.530554\pi$
$614$	5.80508	+	3.35157i	0.234274	+	0.135258i
$615$	−20.7179	−	35.8845i	−0.835426	−	1.44700i
$616$		0			0
$617$	−4.46908	+	16.6788i	−0.179918	+	0.671464i	0.815743	+	0.578414i	$0.196328\pi$
$617$	−4.46908	+	16.6788i	−0.179918	+	0.671464i	−0.995661	+	0.0930497i	$0.970338\pi$
$618$	14.3417	+	3.84286i	0.576909	+	0.154582i
$619$	2.14560	+	2.14560i	0.0862390	+	0.0862390i	0.748910	−	0.662671i	$-0.230577\pi$
$619$	2.14560	+	2.14560i	0.0862390	+	0.0862390i	−0.662671	+	0.748910i	$0.730577\pi$
$620$	−19.1865	−	33.2320i	−0.770548	−	1.33463i
$621$	0.0327885	−	0.0567914i	0.00131576	−	0.00227896i
$622$	7.86477	−	2.10736i	0.315349	−	0.0844974i
$623$		0			0
$624$	14.5907	+	17.8272i	0.584094	+	0.713659i
$625$	1.59189			0.0636757
$626$	−1.18278	−	4.41421i	−0.0472736	−	0.176427i
$627$	−11.7966	+	20.4322i	−0.471109	+	0.815985i
$628$	−1.67890	−	2.90794i	−0.0669954	−	0.116039i
$629$	−2.18843	+	2.18843i	−0.0872583	+	0.0872583i
$630$		0			0
$631$	−46.4748	−	12.4529i	−1.85013	−	0.495742i	−0.850587	−	0.525834i	$-0.823753\pi$
$631$	−46.4748	−	12.4529i	−1.85013	−	0.495742i	−0.999547	+	0.0300916i	$0.990420\pi$
$632$	15.4263	−	15.4263i	0.613627	−	0.613627i
$633$	52.3411	−	30.2192i	2.08037	−	1.20110i
$634$	14.0890	+	8.13426i	0.559544	+	0.323053i
$635$	29.7678	−	7.97626i	1.18130	−	0.316528i
$636$	−15.0054			−0.595002
$637$		0			0
$638$	5.72881			0.226806
$639$	19.4506	−	5.21176i	0.769452	−	0.206174i
$640$	35.2478	+	20.3503i	1.39329	+	0.804417i
$641$	−43.6877	+	25.2231i	−1.72556	+	0.996253i	−0.819537	+	0.573026i	$0.805769\pi$
$641$	−43.6877	+	25.2231i	−1.72556	+	0.996253i	−0.906024	+	0.423227i	$0.860897\pi$
$642$	6.95030	−	6.95030i	0.274307	−	0.274307i
$643$	−23.5329	−	6.30561i	−0.928046	−	0.248669i	−0.237025	−	0.971504i	$-0.576172\pi$
$643$	−23.5329	−	6.30561i	−0.928046	−	0.248669i	−0.691021	+	0.722834i	$0.742839\pi$
$644$		0			0
$645$	−32.7434	+	32.7434i	−1.28927	+	1.28927i
$646$	−1.28039	−	2.21770i	−0.0503763	−	0.0872543i
$647$	21.8129	−	37.7811i	0.857554	−	1.48533i	−0.0167008	−	0.999861i	$-0.505316\pi$
$647$	21.8129	−	37.7811i	0.857554	−	1.48533i	0.874255	−	0.485467i	$-0.161350\pi$
$648$	4.32391	+	16.1370i	0.169859	+	0.633923i
$649$	−24.1812			−0.949196
$650$	12.8173	−	5.78685i	0.502735	−	0.226979i
$651$		0			0
$652$	10.4889	−	2.81048i	0.410776	−	0.110067i
$653$	−24.0057	+	41.5791i	−0.939416	+	1.62712i	−0.172852	+	0.984948i	$0.555298\pi$
$653$	−24.0057	+	41.5791i	−0.939416	+	1.62712i	−0.766564	+	0.642168i	$0.778035\pi$
$654$	1.78871	+	3.09813i	0.0699439	+	0.121146i
$655$	37.3657	+	37.3657i	1.46000	+	1.46000i
$656$	−11.8813	−	3.18359i	−0.463887	−	0.124298i
$657$	4.37016	−	16.3097i	0.170496	−	0.636301i
$658$		0			0
$659$	2.00241	+	3.46828i	0.0780030	+	0.135105i	0.902388	−	0.430924i	$-0.141812\pi$
$659$	2.00241	+	3.46828i	0.0780030	+	0.135105i	−0.824385	+	0.566029i	$0.808479\pi$
$660$	−28.3642	−	16.3761i	−1.10407	−	0.637437i
$661$	−20.3607	+	5.45564i	−0.791941	+	0.212200i	−0.632043	−	0.774934i	$-0.717783\pi$
$661$	−20.3607	+	5.45564i	−0.791941	+	0.212200i	−0.159898	+	0.987134i	$0.551117\pi$
$662$			11.5587i			0.449241i
$663$	9.95783	−	1.63041i	0.386730	−	0.0633198i
$664$			13.2247i			0.513217i
$665$		0			0
$666$	1.97952	−	3.42862i	0.0767047	−	0.132856i
$667$	7.08120	−	4.08833i	0.274185	−	0.158301i
$668$	−2.72818	+	2.72818i	−0.105557	+	0.105557i
$669$	−0.472958	+	1.76510i	−0.0182856	+	0.0682428i
$670$	−3.52033	+	13.1381i	−0.136002	+	0.507567i
$671$	−14.1673	−	14.1673i	−0.546921	−	0.546921i
$672$		0			0
$673$	−39.2951	−	22.6870i	−1.51471	−	0.874521i	−0.999851	−	0.0172480i	$-0.994510\pi$
$673$	−39.2951	−	22.6870i	−1.51471	−	0.874521i	−0.514863	−	0.857273i	$-0.672157\pi$
$674$	−3.12480	−	11.6619i	−0.120363	−	0.449200i
$675$	−0.351516			−0.0135299
$676$	15.1235	−	17.1525i	0.581672	−	0.659713i
$677$		−	14.1282i		−	0.542992i	−0.962440	−	0.271496i	$-0.912482\pi$
$677$		−	14.1282i		−	0.542992i	0.962440	−	0.271496i	$-0.0875184\pi$
$678$	−5.09531	−	19.0160i	−0.195684	−	0.730304i
$679$		0			0
$680$	6.57896	−	3.79837i	0.252292	−	0.145661i
$681$	17.9374	+	17.9374i	0.687364	+	0.687364i
$682$	−6.08225	−	1.62973i	−0.232901	−	0.0624057i
$683$	0.234842	+	0.0629256i	0.00898597	+	0.00240778i	0.263309	−	0.964711i	$-0.415186\pi$
$683$	0.234842	+	0.0629256i	0.00898597	+	0.00240778i	−0.254323	+	0.967119i	$0.581853\pi$
$684$	−16.9102	−	16.9102i	−0.646577	−	0.646577i
$685$	−7.09006	+	4.09345i	−0.270897	+	0.156403i
$686$		0			0
$687$	1.08732	+	4.05793i	0.0414838	+	0.154820i
$688$			13.7462i			0.524070i
$689$	2.03193	+	12.4101i	0.0774102	+	0.472788i
$690$	6.40328			0.243769
$691$	9.34895	+	34.8908i	0.355651	+	1.32731i	0.879664	+	0.475597i	$0.157768\pi$
$691$	9.34895	+	34.8908i	0.355651	+	1.32731i	−0.524013	+	0.851710i	$0.675566\pi$
$692$	−28.8641	−	16.6647i	−1.09725	−	0.633497i
$693$		0			0
$694$	11.5788	+	11.5788i	0.439526	+	0.439526i
$695$	−4.55108	+	16.9849i	−0.172632	+	0.644273i
$696$	−6.44294	+	24.0454i	−0.244219	+	0.911438i
$697$	−3.80971	+	3.80971i	−0.144303	+	0.144303i
$698$	2.32456	−	1.34208i	0.0879858	−	0.0507986i
$699$	−10.1630	+	17.6029i	−0.384401	+	0.665802i
$700$		0			0
$701$			26.1953i			0.989383i	0.869069	+	0.494691i	$0.164719\pi$
$701$			26.1953i			0.989383i	−0.869069	+	0.494691i	$0.835281\pi$
$702$	0.0713596	−	0.0322180i	0.00269330	−	0.00121599i
$703$		−	12.3316i		−	0.465096i
$704$	−5.68918	+	1.52441i	−0.214419	+	0.0574534i
$705$	−51.4293	−	29.6927i	−1.93694	−	1.11829i
$706$	−1.08467	−	1.87871i	−0.0408221	−	0.0707060i
$707$		0			0
$708$	12.7262	−	47.4947i	0.478279	−	1.78496i
$709$	−15.0889	−	4.04305i	−0.566674	−	0.151840i	−0.0359035	−	0.999355i	$-0.511431\pi$
$709$	−15.0889	−	4.04305i	−0.566674	−	0.151840i	−0.530771	+	0.847515i	$0.678098\pi$
$710$	−8.43354	−	8.43354i	−0.316505	−	0.316505i
$711$	−17.6279	−	30.5324i	−0.661097	−	1.14505i
$712$	9.19849	−	15.9323i	0.344728	−	0.597087i
$713$	−8.68112	+	2.32610i	−0.325111	+	0.0871131i
$714$		0			0
$715$	−9.70285	+	25.6760i	−0.362866	+	0.960227i
$716$	20.8686			0.779896
$717$	4.60125	+	17.1721i	0.171837	+	0.641304i
$718$	6.81568	−	11.8051i	0.254359	−	0.440562i
$719$	−0.698769	−	1.21030i	−0.0260597	−	0.0451367i	0.852701	−	0.522399i	$-0.174963\pi$
$719$	−0.698769	−	1.21030i	−0.0260597	−	0.0451367i	−0.878761	+	0.477262i	$0.841629\pi$
$720$	19.8188	−	19.8188i	0.738604	−	0.738604i
$721$		0			0
$722$	0.847040	+	0.226964i	0.0315236	+	0.00844671i
$723$	13.4035	−	13.4035i	0.498483	−	0.498483i
$724$	−15.5482	+	8.97676i	−0.577845	+	0.333619i
$725$	−37.9578	−	21.9149i	−1.40972	−	0.813900i
$726$	7.56487	−	2.02700i	0.280759	−	0.0752291i
$727$	8.63150			0.320124			0.160062	−	0.987107i	$-0.448831\pi$
$727$	8.63150			0.320124			0.160062	+	0.987107i	$0.448831\pi$
$728$		0			0
$729$	26.6734			0.987905
$730$	−9.66010	+	2.58842i	−0.357536	+	0.0958015i
$731$	5.21435	+	3.01051i	0.192860	+	0.111348i
$732$	35.2821	−	20.3702i	1.30407	−	0.752903i
$733$	−0.574095	+	0.574095i	−0.0212047	+	0.0212047i	−0.717630	−	0.696425i	$-0.754773\pi$
$733$	−0.574095	+	0.574095i	−0.0212047	+	0.0212047i	0.696425	+	0.717630i	$0.254773\pi$
$734$	7.98916	+	2.14069i	0.294885	+	0.0790143i
$735$		0			0
$736$	5.21230	−	5.21230i	0.192128	−	0.192128i
$737$	−8.14706	−	14.1111i	−0.300101	−	0.519790i
$738$	3.44603	−	5.96869i	0.126850	−	0.219711i
$739$	−5.79070	−	21.6112i	−0.213014	−	0.794981i	−0.986856	−	0.161601i	$-0.948334\pi$
$739$	−5.79070	−	21.6112i	−0.213014	−	0.794981i	0.773842	−	0.633379i	$-0.218333\pi$
$740$	17.1188			0.629300
$741$	−23.4622	+	32.6494i	−0.861905	+	1.19941i
$742$		0			0
$743$	21.2232	−	5.68675i	0.778605	−	0.208627i	0.152436	−	0.988313i	$-0.451288\pi$
$743$	21.2232	−	5.68675i	0.778605	−	0.208627i	0.626170	+	0.779687i	$0.284622\pi$
$744$	13.6809	−	23.6960i	0.501565	−	0.868736i
$745$	−4.98483	−	8.63397i	−0.182630	−	0.316324i
$746$	−0.965935	−	0.965935i	−0.0353654	−	0.0353654i
$747$	20.6434	+	5.53138i	0.755302	+	0.202383i
$748$	−1.10222	+	4.11352i	−0.0403010	+	0.150405i
$749$		0			0
$750$	−6.36272	−	11.0206i	−0.232334	−	0.402414i
$751$	22.0152	+	12.7105i	0.803347	+	0.463813i	0.844640	−	0.535334i	$-0.179814\pi$
$751$	22.0152	+	12.7105i	0.803347	+	0.463813i	−0.0412930	+	0.999147i	$0.513148\pi$
$752$	−17.0282	+	4.56269i	−0.620954	+	0.166384i
$753$		−	8.61516i		−	0.313954i
$754$	9.71422	+	0.969847i	0.353771	+	0.0353197i
$755$		−	22.7174i		−	0.826771i
$756$		0			0
$757$	19.9731	−	34.5945i	0.725936	−	1.25736i	−0.232651	−	0.972560i	$-0.574740\pi$
$757$	19.9731	−	34.5945i	0.725936	−	1.25736i	0.958587	−	0.284799i	$-0.0919267\pi$
$758$	0.323065	−	0.186521i	0.0117342	−	0.00677476i
$759$	−5.42414	+	5.42414i	−0.196884	+	0.196884i
$760$	−7.83422	+	29.2377i	−0.284177	+	1.06056i
$761$	−4.51324	+	16.8436i	−0.163605	+	0.610581i	0.834609	+	0.550842i	$0.185693\pi$
$761$	−4.51324	+	16.8436i	−0.163605	+	0.610581i	−0.998214	+	0.0597387i	$0.980973\pi$
$762$	7.27120	+	7.27120i	0.263408	+	0.263408i
$763$		0			0
$764$	−9.09684	−	5.25206i	−0.329112	−	0.190013i
$765$	−3.17743	−	11.8583i	−0.114880	−	0.428738i
$766$	−15.4454			−0.558067
$767$	−41.0035	−	4.09370i	−1.48055	−	0.147815i
$768$		−	0.0363858i		−	0.00131296i
$769$	0.710240	+	2.65065i	0.0256119	+	0.0955849i	0.977549	−	0.210710i	$-0.0675774\pi$
$769$	0.710240	+	2.65065i	0.0256119	+	0.0955849i	−0.951937	+	0.306295i	$0.900911\pi$
$770$		0			0
$771$	−22.9847	+	13.2702i	−0.827774	+	0.477915i
$772$	1.24833	+	1.24833i	0.0449284	+	0.0449284i
$773$	12.8420	+	3.44100i	0.461894	+	0.123764i	0.482259	−	0.876029i	$-0.339816\pi$
$773$	12.8420	+	3.44100i	0.461894	+	0.123764i	−0.0203654	+	0.999793i	$0.506483\pi$
$774$	−7.43969	−	1.99346i	−0.267414	−	0.0716534i
$775$	34.0652	+	34.0652i	1.22366	+	1.22366i
$776$	21.7820	−	12.5759i	0.781930	−	0.451448i
$777$		0			0
$778$	3.43789	+	12.8304i	0.123254	+	0.459991i
$779$		−	21.4674i		−	0.769149i
$780$	−45.3241	−	32.5703i	−1.62286	−	1.16621i
$781$	14.2879			0.511261
$782$	−0.215491	−	0.804224i	−0.00770595	−	0.0287590i
$783$	−0.211328	−	0.122010i	−0.00755225	−	0.00436029i
$784$		0			0
$785$	4.85655	+	4.85655i	0.173338	+	0.173338i
$786$	−4.56354	+	17.0314i	−0.162776	+	0.607489i
$787$	5.67760	−	21.1891i	0.202385	−	0.755309i	−0.787846	−	0.615872i	$-0.788804\pi$
$787$	5.67760	−	21.1891i	0.202385	−	0.755309i	0.990231	−	0.139437i	$-0.0445294\pi$
$788$	5.26186	−	5.26186i	0.187446	−	0.187446i
$789$	9.95333	−	5.74656i	0.354348	−	0.204583i
$790$	−10.4409	+	18.0841i	−0.371469	+	0.643403i
$791$		0			0
$792$		−	11.6416i		−	0.413666i
$793$	−21.6247	−	26.4215i	−0.767916	−	0.938256i
$794$			0.112058i			0.00397679i
$795$	29.6469	−	7.94387i	1.05147	−	0.281740i
$796$	−22.9332	−	13.2405i	−0.812844	−	0.469296i
$797$	23.0740	+	39.9654i	0.817324	+	1.41565i	0.907647	+	0.419735i	$0.137877\pi$
$797$	23.0740	+	39.9654i	0.817324	+	1.41565i	−0.0903225	+	0.995913i	$0.528790\pi$
$798$		0			0
$799$	−1.99851	+	7.45855i	−0.0707023	+	0.263865i
$800$	−38.1664	−	10.2267i	−1.34939	−	0.361567i
$801$	−21.0225	−	21.0225i	−0.742793	−	0.742793i
$802$	−6.30682	−	10.9237i	−0.222702	−	0.385730i
$803$	5.99034	−	10.3756i	0.211394	−	0.366146i
$804$	32.0035	−	8.57532i	1.12868	−	0.302428i
$805$		0			0
$806$	−10.0376	−	3.79318i	−0.353560	−	0.133609i
$807$	−62.8835			−2.21360
$808$	4.65301	+	17.3653i	0.163692	+	0.610908i
$809$	18.6015	−	32.2188i	0.653994	−	1.13275i	−0.328151	−	0.944625i	$-0.606425\pi$
$809$	18.6015	−	32.2188i	0.653994	−	1.13275i	0.982145	−	0.188126i	$-0.0602413\pi$
$810$	−7.99537	−	13.8484i	−0.280929	−	0.486583i
$811$	5.71666	−	5.71666i	0.200739	−	0.200739i	−0.599578	−	0.800317i	$-0.704665\pi$
$811$	5.71666	−	5.71666i	0.200739	−	0.200739i	0.800317	+	0.599578i	$0.204665\pi$
$812$		0			0
$813$	−3.13308	−	0.839506i	−0.109882	−	0.0294427i
$814$	1.98634	−	1.98634i	0.0696212	−	0.0696212i
$815$	−19.2355	+	11.1056i	−0.673791	+	0.389013i
$816$	−6.33140	−	3.65544i	−0.221643	−	0.127966i
$817$	−23.1732	+	6.20924i	−0.810728	+	0.217234i
$818$	−14.6517			−0.512283
$819$		0			0
$820$	29.8012			1.04070
$821$	−6.20586	+	1.66286i	−0.216586	+	0.0580341i	−0.365480	−	0.930819i	$-0.619095\pi$
$821$	−6.20586	+	1.66286i	−0.216586	+	0.0580341i	0.148894	+	0.988853i	$0.452429\pi$
$822$	−2.36575	−	1.36586i	−0.0825149	−	0.0476400i
$823$	−7.71255	+	4.45284i	−0.268843	+	0.155216i	−0.628362	−	0.777921i	$-0.716274\pi$
$823$	−7.71255	+	4.45284i	−0.268843	+	0.155216i	0.359519	+	0.933138i	$0.382941\pi$
$824$	−16.1362	+	16.1362i	−0.562131	+	0.562131i
$825$	39.7176	+	10.6423i	1.38279	+	0.370517i
$826$		0			0
$827$	−0.00569088	+	0.00569088i	−0.000197891	+	0.000197891i	−0.707206	−	0.707008i	$-0.750045\pi$
$827$	−0.00569088	+	0.00569088i	−0.000197891	+	0.000197891i	0.707008	+	0.707206i	$0.250045\pi$
$828$	−3.88771	−	6.73371i	−0.135107	−	0.234013i
$829$	−8.36149	+	14.4825i	−0.290407	+	0.502999i	−0.973906	−	0.226952i	$-0.927124\pi$
$829$	−8.36149	+	14.4825i	−0.290407	+	0.502999i	0.683499	+	0.729951i	$0.260457\pi$
$830$	−3.27620	−	12.2269i	−0.113718	−	0.424403i
$831$	0.443582			0.0153877
$832$	−9.90509	+	1.62177i	−0.343397	+	0.0562249i
$833$		0			0
$834$	−5.66735	+	1.51856i	−0.196244	+	0.0525835i
$835$	3.94591	−	6.83451i	0.136554	−	0.236518i
$836$	−8.48424	−	14.6951i	−0.293434	−	0.508242i
$837$	0.189656	+	0.189656i	0.00655548	+	0.00655548i
$838$	4.23000	+	1.13343i	0.146123	+	0.0391535i
$839$	−5.65746	+	21.1139i	−0.195317	+	0.728934i	0.796867	+	0.604154i	$0.206489\pi$
$839$	−5.65746	+	21.1139i	−0.195317	+	0.728934i	−0.992185	+	0.124779i	$0.960178\pi$
$840$		0			0
$841$	−0.713208	−	1.23531i	−0.0245934	−	0.0425970i
$842$	10.9060	+	6.29661i	0.375847	+	0.216996i
$843$	18.3944	−	4.92877i	0.633538	−	0.169756i
$844$			43.4681i			1.49623i
$845$	−20.7997	+	41.8955i	−0.715530	+	1.44125i
$846$		−	9.87762i		−	0.339600i
$847$		0			0
$848$	4.55565	−	7.89062i	0.156442	−	0.270965i
$849$	−15.4803	+	8.93755i	−0.531282	+	0.306736i
$850$	−3.15582	+	3.15582i	−0.108244	+	0.108244i
$851$	1.03771	−	3.87279i	0.0355723	−	0.132758i
$852$	−7.51948	+	28.0631i	−0.257613	+	0.961425i
$853$	−34.9450	−	34.9450i	−1.19649	−	1.19649i	−0.975209	−	0.221284i	$-0.928975\pi$
$853$	−34.9450	−	34.9450i	−1.19649	−	1.19649i	−0.221284	−	0.975209i	$-0.571025\pi$
$854$		0			0
$855$	42.3626	+	24.4580i	1.44877	+	0.836448i
$856$	3.90997	+	14.5922i	0.133640	+	0.498751i
$857$	24.8386			0.848469			0.424235	−	0.905552i	$-0.360543\pi$
$857$	24.8386			0.848469			0.424235	+	0.905552i	$0.360543\pi$
$858$	−9.03829	+	1.47985i	−0.308562	+	0.0505213i
$859$		−	20.6295i		−	0.703869i	−0.936025	−	0.351935i	$-0.885524\pi$
$859$		−	20.6295i		−	0.703869i	0.936025	−	0.351935i	$-0.114476\pi$
$860$	−8.61971	−	32.1692i	−0.293930	−	1.09696i
$861$		0			0
$862$	5.00231	−	2.88809i	0.170379	−	0.0983686i
$863$	−15.9482	−	15.9482i	−0.542884	−	0.542884i	0.381490	−	0.924373i	$-0.375411\pi$
$863$	−15.9482	−	15.9482i	−0.542884	−	0.542884i	−0.924373	+	0.381490i	$0.875411\pi$
$864$	−0.212490	−	0.0569365i	−0.00722905	−	0.00193702i
$865$	65.8506	+	17.6446i	2.23899	+	0.599935i
$866$	4.34847	+	4.34847i	0.147767	+	0.147767i
$867$	33.2348	−	19.1881i	1.12871	−	0.651663i
$868$		0			0
$869$	−6.47450	−	24.1632i	−0.219632	−	0.819679i
$870$		−	23.8274i		−	0.807824i
$871$	−11.4259	−	25.3071i	−0.387151	−	0.857500i
$872$	−5.49828			−0.186195
$873$	−10.5200	−	39.2613i	−0.356049	−	1.32879i
$874$	2.87301	+	1.65873i	0.0971809	+	0.0561074i
$875$		0			0
$876$	17.2262	+	17.2262i	0.582019	+	0.582019i
$877$	3.33311	−	12.4394i	0.112551	−	0.420047i	−0.886541	−	0.462650i	$-0.846899\pi$
$877$	3.33311	−	12.4394i	0.112551	−	0.420047i	0.999092	+	0.0426034i	$0.0135652\pi$
$878$	−2.25682	+	8.42255i	−0.0761639	+	0.284247i
$879$	−55.5146	+	55.5146i	−1.87246	+	1.87246i
$880$	17.2228	−	9.94358i	0.580580	−	0.335198i
$881$	−3.52615	+	6.10747i	−0.118799	+	0.205766i	−0.919292	−	0.393576i	$-0.871238\pi$
$881$	−3.52615	+	6.10747i	−0.118799	+	0.205766i	0.800493	+	0.599342i	$0.204571\pi$
$882$		0			0
$883$		−	55.6508i		−	1.87280i	−0.350938	−	0.936399i	$-0.614137\pi$
$883$		−	55.6508i		−	1.87280i	0.350938	−	0.936399i	$-0.385863\pi$
$884$	−2.56539	+	6.78861i	−0.0862835	+	0.228326i
$885$			100.575i			3.38079i
$886$	−3.17623	+	0.851068i	−0.106708	+	0.0285922i
$887$	12.9108	+	7.45405i	0.433502	+	0.250282i	0.700837	−	0.713321i	$-0.252810\pi$
$887$	12.9108	+	7.45405i	0.433502	+	0.250282i	−0.267335	+	0.963604i	$0.586143\pi$
$888$	6.10326	+	10.5712i	0.204812	+	0.354745i
$889$		0			0
$890$	−4.55755	+	17.0090i	−0.152769	+	0.570143i
$891$	18.5036	+	4.95802i	0.619893	+	0.166100i
$892$	−0.929328	−	0.929328i	−0.0311162	−	0.0311162i
$893$	−15.3834	−	26.6449i	−0.514787	−	0.891637i
$894$	1.66329	−	2.88090i	0.0556287	−	0.0963518i
$895$	−41.2312	+	11.0479i	−1.37821	+	0.369289i
$896$		0			0
$897$	−10.1159	+	8.27932i	−0.337759	+	0.276439i
$898$	11.6222			0.387837
$899$	8.65571	+	32.3035i	0.288684	+	1.07738i
$900$	−20.8395	+	36.0951i	−0.694650	+	1.20317i
$901$	−1.99543	−	3.45619i	−0.0664775	−	0.115142i
$902$	3.45791	−	3.45791i	0.115136	−	0.115136i
$903$		0			0
$904$	29.2265	+	7.83121i	0.972058	+	0.260462i
$905$	25.9671	−	25.9671i	0.863176	−	0.863176i
$906$	6.56459	−	3.79007i	0.218094	−	0.125917i
$907$	1.94216	+	1.12131i	0.0644883	+	0.0372324i	0.531897	−	0.846809i	$-0.321479\pi$
$907$	1.94216	+	1.12131i	0.0644883	+	0.0372324i	−0.467409	+	0.884041i	$0.654813\pi$
$908$	−17.6229	+	4.72204i	−0.584836	+	0.156706i
$909$	29.0529			0.963625
$910$		0			0
$911$	−22.3252			−0.739667			−0.369834	−	0.929098i	$-0.620585\pi$
$911$	−22.3252			−0.739667			−0.369834	+	0.929098i	$0.620585\pi$
$912$	28.1375	−	7.53942i	0.931726	−	0.249655i
$913$	13.1325	+	7.58206i	0.434623	+	0.250930i
$914$	13.5766	−	7.83843i	0.449073	−	0.259272i
$915$	−58.9248	+	58.9248i	−1.94799	+	1.94799i
$916$	−2.91852	−	0.782015i	−0.0964305	−	0.0258385i
$917$		0			0
$918$	−0.0175699	+	0.0175699i	−0.000579892	+	0.000579892i
$919$	20.7445	+	35.9305i	0.684297	+	1.18524i	0.973657	+	0.228017i	$0.0732240\pi$
$919$	20.7445	+	35.9305i	0.684297	+	1.18524i	−0.289361	+	0.957220i	$0.593443\pi$
$920$	−4.92074	+	8.52297i	−0.162232	+	0.280994i
$921$	8.64429	+	32.2609i	0.284839	+	1.06303i
$922$	−18.6776			−0.615115
$923$	24.2277	+	2.41884i	0.797463	+	0.0796170i
$924$		0			0
$925$	−20.7595	+	5.56250i	−0.682569	+	0.182894i
$926$	−3.16342	+	5.47921i	−0.103956	+	0.180058i
$927$	18.4390	+	31.9373i	0.605617	+	1.04896i
$928$	−19.3956	−	19.3956i	−0.636692	−	0.636692i
$929$	47.9399	+	12.8455i	1.57286	+	0.421446i	0.936706	−	0.350117i	$-0.113858\pi$
$929$	47.9399	+	12.8455i	1.57286	+	0.421446i	0.636152	+	0.771563i	$0.280525\pi$
$930$	−6.77842	+	25.2974i	−0.222273	+	0.829534i
$931$		0			0
$932$	−7.30938	−	12.6602i	−0.239427	−	0.414699i
$933$	35.1341	+	20.2847i	1.15024	+	0.664090i
$934$	−8.45898	+	2.26658i	−0.276786	+	0.0741647i
$935$		−	8.71082i		−	0.284874i
$936$	1.97084	−	19.7404i	0.0644188	−	0.645234i
$937$			47.8712i			1.56388i	0.623352	+	0.781942i	$0.285771\pi$
$937$			47.8712i			1.56388i	−0.623352	+	0.781942i	$0.714229\pi$
$938$		0			0
$939$	11.3850	−	19.7195i	0.371537	−	0.643521i
$940$	36.9886	−	21.3554i	1.20644	−	0.696536i
$941$	5.38352	−	5.38352i	0.175498	−	0.175498i	−0.613892	−	0.789390i	$-0.710397\pi$
$941$	5.38352	−	5.38352i	0.175498	−	0.175498i	0.789390	+	0.613892i	$0.210397\pi$
$942$	−0.593140	+	2.21363i	−0.0193256	+	0.0721240i
$943$	1.80649	−	6.74192i	0.0588275	−	0.219547i
$944$	21.1115	+	21.1115i	0.687122	+	0.687122i
$945$		0			0
$946$	−4.73284	−	2.73251i	−0.153878	−	0.0888414i
$947$	−1.83209	−	6.83743i	−0.0595348	−	0.222187i	0.929749	−	0.368195i	$-0.120024\pi$
$947$	−1.83209	−	6.83743i	−0.0595348	−	0.222187i	−0.989283	+	0.146008i	$0.953357\pi$
$948$	50.8666			1.65207
$949$	11.9142	−	16.5795i	0.386751	−	0.538193i
$950$		−	17.7828i		−	0.576949i
$951$	20.9797	+	78.2974i	0.680314	+	2.53897i
$952$		0			0
$953$	41.2624	−	23.8229i	1.33662	−	0.771698i	0.350316	−	0.936632i	$-0.386074\pi$
$953$	41.2624	−	23.8229i	1.33662	−	0.771698i	0.986305	+	0.164933i	$0.0527408\pi$
$954$	3.60989	+	3.60989i	0.116874	+	0.116874i
$955$	20.7535	+	5.56089i	0.671569	+	0.179946i
$956$	−12.3504	−	3.30928i	−0.399441	−	0.107030i
$957$	20.1839	+	20.1839i	0.652453	+	0.652453i
$958$	−3.90727	+	2.25586i	−0.126238	+	0.0728836i
$959$		0			0
$960$	6.34036	+	23.6626i	0.204634	+	0.763706i
$961$		−	5.75886i		−	0.185770i
$962$	3.70447	−	3.03192i	0.119437	−	0.0977530i
$963$	24.4134			0.786712
$964$	3.52849	+	13.1685i	0.113645	+	0.424128i
$965$	−3.12726	−	1.80552i	−0.100670	−	0.0581218i
$966$		0			0
$967$	31.2419	+	31.2419i	1.00467	+	1.00467i	0.999989	+	0.00468303i	$0.00149066\pi$
$967$	31.2419	+	31.2419i	1.00467	+	1.00467i	0.00468303	+	0.999989i	$0.498509\pi$
$968$	−3.11539	+	11.6268i	−0.100132	+	0.373699i
$969$	3.30236	−	12.3246i	0.106087	−	0.395922i
$970$	−17.0232	+	17.0232i	−0.546583	+	0.546583i
$971$	6.43644	−	3.71608i	0.206555	−	0.119255i	−0.393154	−	0.919473i	$-0.628616\pi$
$971$	6.43644	−	3.71608i	0.206555	−	0.119255i	0.599709	+	0.800218i	$0.295283\pi$
$972$	−19.3595	+	33.5317i	−0.620957	+	1.07553i
$973$		0			0
$974$		−	5.43090i		−	0.174017i
$975$	65.5466	+	24.7698i	2.09917	+	0.793269i
$976$			24.7376i			0.791832i
$977$	−36.9665	+	9.90514i	−1.18266	+	0.316893i	−0.795982	−	0.605320i	$-0.793045\pi$
$977$	−36.9665	+	9.90514i	−1.18266	+	0.316893i	−0.386680	+	0.922214i	$0.626378\pi$
$978$	−6.41833	−	3.70562i	−0.205235	−	0.118493i
$979$	−10.5475	−	18.2688i	−0.337099	−	0.583873i
$980$		0			0
$981$	−2.29972	+	8.58268i	−0.0734245	+	0.274024i
$982$	1.34426	+	0.360194i	0.0428972	+	0.0114943i
$983$	−18.1986	−	18.1986i	−0.580445	−	0.580445i	0.354581	−	0.935025i	$-0.384624\pi$
$983$	−18.1986	−	18.1986i	−0.580445	−	0.580445i	−0.935025	+	0.354581i	$0.884624\pi$
$984$	10.6248	+	18.4027i	0.338707	+	0.586658i
$985$	−7.61050	+	13.1818i	−0.242491	+	0.420006i
$986$	−2.99262	+	0.801870i	−0.0953044	+	0.0255367i
$987$		0			0
$988$	−11.8988	−	26.3545i	−0.378550	−	0.838449i
$989$	−7.80015			−0.248030
$990$	2.88401	+	10.7633i	0.0916599	+	0.342079i
$991$	23.4047	−	40.5381i	0.743474	−	1.28774i	−0.207430	−	0.978250i	$-0.566510\pi$
$991$	23.4047	−	40.5381i	0.743474	−	1.28774i	0.950904	−	0.309485i	$-0.100157\pi$
$992$	15.0745	+	26.1099i	0.478617	+	0.828989i
$993$	−40.7238	+	40.7238i	−1.29233	+	1.29233i
$994$		0			0
$995$	52.3197	+	14.0190i	1.65865	+	0.444433i
$996$	−21.8035	+	21.8035i	−0.690869	+	0.690869i
$997$	24.4448	−	14.1132i	0.774174	−	0.446969i	−0.0601878	−	0.998187i	$-0.519170\pi$
$997$	24.4448	−	14.1132i	0.774174	−	0.446969i	0.834361	+	0.551218i	$0.185837\pi$
$998$	−16.3055	−	9.41398i	−0.516141	−	0.297994i
$999$	−0.115578	+	0.0309690i	−0.00365672	+	0.000979815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bd.b.293.4		28
7.2	even	3		91.2.ba.a.59.4	yes	28
7.3	odd	6		91.2.w.a.33.4	✓	28
7.4	even	3		637.2.x.a.215.4		28
7.5	odd	6		637.2.bb.a.423.4		28
7.6	odd	2		637.2.bd.a.293.4		28
13.2	odd	12		637.2.bd.a.587.4		28
21.2	odd	6		819.2.et.b.514.4		28
21.17	even	6		819.2.gh.b.397.4		28
91.2	odd	12		91.2.w.a.80.4	yes	28
91.41	even	12	inner	637.2.bd.b.587.4		28
91.54	even	12		637.2.x.a.80.4		28
91.67	odd	12		637.2.bb.a.509.4		28
91.80	even	12		91.2.ba.a.54.4	yes	28
273.2	even	12		819.2.gh.b.262.4		28
273.80	odd	12		819.2.et.b.145.4		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.4	✓	28	7.3	odd	6
91.2.w.a.80.4	yes	28	91.2	odd	12
91.2.ba.a.54.4	yes	28	91.80	even	12
91.2.ba.a.59.4	yes	28	7.2	even	3
637.2.x.a.80.4		28	91.54	even	12
637.2.x.a.215.4		28	7.4	even	3
637.2.bb.a.423.4		28	7.5	odd	6
637.2.bb.a.509.4		28	91.67	odd	12
637.2.bd.a.293.4		28	7.6	odd	2
637.2.bd.a.587.4		28	13.2	odd	12
637.2.bd.b.293.4		28	1.1	even	1	trivial
637.2.bd.b.587.4		28	91.41	even	12	inner
819.2.et.b.145.4		28	273.80	odd	12
819.2.et.b.514.4		28	21.2	odd	6
819.2.gh.b.262.4		28	273.2	even	12
819.2.gh.b.397.4		28	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.474142 - 0.127046i) q^{2} +(2.11812 + 1.22290i) q^{3} +(-1.52338 + 0.879524i) q^{4} +(2.54420 - 2.54420i) q^{5} +(1.15965 + 0.310728i) q^{6} +(-1.30475 + 1.30475i) q^{8} +(1.49096 + 2.58241i) q^{9} +O(q^{10})\)	\(q+(0.474142 - 0.127046i) q^{2} +(2.11812 + 1.22290i) q^{3} +(-1.52338 + 0.879524i) q^{4} +(2.54420 - 2.54420i) q^{5} +(1.15965 + 0.310728i) q^{6} +(-1.30475 + 1.30475i) q^{8} +(1.49096 + 2.58241i) q^{9} +(0.883082 - 1.52954i) q^{10} +(0.547609 + 2.04371i) q^{11} -4.30227 q^{12} +(0.582584 + 3.55817i) q^{13} +(8.50022 - 2.27763i) q^{15} +(1.30618 - 2.26236i) q^{16} +(-0.572121 - 0.990942i) q^{17} +(1.03501 + 1.03501i) q^{18} +(4.40387 + 1.18001i) q^{19} +(-1.63810 + 6.11348i) q^{20} +(0.519289 + 0.899435i) q^{22} +(1.28375 + 0.741175i) q^{23} +(-4.35920 + 1.16804i) q^{24} -7.94593i q^{25} +(0.728279 + 1.61306i) q^{26} -0.0442386i q^{27} +(2.75801 - 4.77701i) q^{29} +(3.74095 - 2.15984i) q^{30} +(-4.28712 + 4.28712i) q^{31} +(1.28703 - 4.80327i) q^{32} +(-1.33934 + 4.99849i) q^{33} +(-0.397162 - 0.397162i) q^{34} +(-4.54259 - 2.62266i) q^{36} +(-0.700045 - 2.61260i) q^{37} +2.23797 q^{38} +(-3.11730 + 8.24908i) q^{39} +6.63910i q^{40} +(-1.21867 - 4.54813i) q^{41} +(-4.55704 + 2.63101i) q^{43} +(-2.63171 - 2.63171i) q^{44} +(10.3635 + 2.77688i) q^{45} +(0.702845 + 0.188327i) q^{46} +(-4.77175 - 4.77175i) q^{47} +(5.53327 - 3.19464i) q^{48} +(-1.00950 - 3.76750i) q^{50} -2.79858i q^{51} +(-4.01700 - 4.90806i) q^{52} +3.48778 q^{53} +(-0.00562033 - 0.0209754i) q^{54} +(6.59283 + 3.80637i) q^{55} +(7.88489 + 7.88489i) q^{57} +(0.700787 - 2.61537i) q^{58} +(-2.95801 + 11.0394i) q^{59} +(-10.9458 + 10.9458i) q^{60} +(-8.20082 + 4.73474i) q^{61} +(-1.48804 + 2.57737i) q^{62} +2.78376i q^{64} +(10.5349 + 7.57050i) q^{65} +2.54015i q^{66} +(-7.43875 + 1.99321i) q^{67} +(1.74312 + 1.00639i) q^{68} +(1.81276 + 3.13980i) q^{69} +(1.74779 - 6.52285i) q^{71} +(-5.31473 - 1.42408i) q^{72} +(-4.00398 - 4.00398i) q^{73} +(-0.663841 - 1.14981i) q^{74} +(9.71705 - 16.8304i) q^{75} +(-7.74662 + 2.07570i) q^{76} +(-0.430029 + 4.30727i) q^{78} -11.8232 q^{79} +(-2.43273 - 9.07908i) q^{80} +(4.52697 - 7.84094i) q^{81} +(-1.15564 - 2.00163i) q^{82} +(5.06789 - 5.06789i) q^{83} +(-3.97675 - 1.06557i) q^{85} +(-1.82642 + 1.82642i) q^{86} +(11.6836 - 6.74552i) q^{87} +(-3.38102 - 1.95203i) q^{88} +(-9.63048 + 2.58048i) q^{89} +5.26655 q^{90} -2.60753 q^{92} +(-14.3234 + 3.83793i) q^{93} +(-2.86872 - 1.65626i) q^{94} +(14.2065 - 8.20214i) q^{95} +(8.60000 - 8.60000i) q^{96} +(-13.1665 - 3.52795i) q^{97} +(-4.46123 + 4.46123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q + 4 q^{2} + 6 q^{3} + 6 q^{4} - 12 q^{6} - 4 q^{8} + 6 q^{9} - 6 q^{10} - 4 q^{11} + 16 q^{12} + 10 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 22 q^{19} + 36 q^{20} - 8 q^{22} + 6 q^{23} + 30 q^{24} - 8 q^{29} + 30 q^{30} - 34 q^{31} + 10 q^{32} + 30 q^{33} - 12 q^{34} + 54 q^{36} + 26 q^{37} - 8 q^{39} - 18 q^{41} + 48 q^{43} + 12 q^{44} + 18 q^{45} - 42 q^{46} - 36 q^{47} - 12 q^{48} + 10 q^{50} - 2 q^{52} - 24 q^{53} + 6 q^{55} + 12 q^{57} - 16 q^{58} - 48 q^{59} - 26 q^{60} - 30 q^{61} + 36 q^{62} - 26 q^{65} + 14 q^{67} + 30 q^{68} - 42 q^{69} - 42 q^{71} - 8 q^{72} - 26 q^{73} - 6 q^{74} + 20 q^{75} - 52 q^{76} - 62 q^{78} - 8 q^{79} - 18 q^{80} - 6 q^{81} - 54 q^{82} + 66 q^{83} - 54 q^{85} + 48 q^{86} + 42 q^{87} + 6 q^{88} - 30 q^{89} + 72 q^{90} - 156 q^{92} - 34 q^{93} + 18 q^{94} + 6 q^{95} + 84 q^{96} - 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q + 4 * q^2 + 6 * q^3 + 6 * q^4 - 12 * q^6 - 4 * q^8 + 6 * q^9 - 6 * q^10 - 4 * q^11 + 16 * q^12 + 10 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 22 * q^19 + 36 * q^20 - 8 * q^22 + 6 * q^23 + 30 * q^24 - 8 * q^29 + 30 * q^30 - 34 * q^31 + 10 * q^32 + 30 * q^33 - 12 * q^34 + 54 * q^36 + 26 * q^37 - 8 * q^39 - 18 * q^41 + 48 * q^43 + 12 * q^44 + 18 * q^45 - 42 * q^46 - 36 * q^47 - 12 * q^48 + 10 * q^50 - 2 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^57 - 16 * q^58 - 48 * q^59 - 26 * q^60 - 30 * q^61 + 36 * q^62 - 26 * q^65 + 14 * q^67 + 30 * q^68 - 42 * q^69 - 42 * q^71 - 8 * q^72 - 26 * q^73 - 6 * q^74 + 20 * q^75 - 52 * q^76 - 62 * q^78 - 8 * q^79 - 18 * q^80 - 6 * q^81 - 54 * q^82 + 66 * q^83 - 54 * q^85 + 48 * q^86 + 42 * q^87 + 6 * q^88 - 30 * q^89 + 72 * q^90 - 156 * q^92 - 34 * q^93 + 18 * q^94 + 6 * q^95 + 84 * q^96 - 62 * q^97 - 36 * q^99

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