LMFDB - Embedded newform 1638.2.y.d.1331.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1638,2,Mod(827,1638)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1638, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([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("1638.827"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.y (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 20 x^{14} - 12 x^{13} + 40 x^{12} + 40 x^{11} + 82 x^{10} + 104 x^{9} + 537 x^{8} + \cdots + 16 $ x^16 - 8x^15 + 20x^14 - 12x^13 + 40x^12 + 40x^11 + 82x^10 + 104x^9 + 537x^8 - 2528x^7 + 5494x^6 - 7284x^5 + 6002x^4 - 2984x^3 + 1000x^2 - 192*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1331.1
Root			$0.838459 + 0.347301i$ of defining polynomial
Character	$\chi$	$=$	1638.1331
Dual form			1638.2.y.d.827.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.64304 - 1.64304i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.32362i q^{10} +(1.53031 - 1.53031i) q^{11} +(-0.148739 + 3.60248i) q^{13} +1.00000i q^{14} -1.00000 q^{16} +5.58470 q^{17} +(-0.269765 + 0.269765i) q^{19} +(1.64304 - 1.64304i) q^{20} -2.16419 q^{22} +4.44768 q^{23} +0.399189i q^{25} +(2.65251 - 2.44217i) q^{26} +(0.707107 - 0.707107i) q^{28} -6.10807i q^{29} +(-0.476750 + 0.476750i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.94898 - 3.94898i) q^{34} +2.32362i q^{35} +(2.38034 + 2.38034i) q^{37} +0.381505 q^{38} -2.32362 q^{40} +(-7.88217 - 7.88217i) q^{41} -4.01105i q^{43} +(1.53031 + 1.53031i) q^{44} +(-3.14498 - 3.14498i) q^{46} +(-1.17580 + 1.17580i) q^{47} +1.00000i q^{49} +(0.282269 - 0.282269i) q^{50} +(-3.60248 - 0.148739i) q^{52} +2.66798i q^{53} -5.02874 q^{55} -1.00000 q^{56} +(-4.31906 + 4.31906i) q^{58} +(1.84687 - 1.84687i) q^{59} -1.03753 q^{61} +0.674226 q^{62} -1.00000i q^{64} +(6.16342 - 5.67465i) q^{65} +(-2.08222 + 2.08222i) q^{67} +5.58470i q^{68} +(1.64304 - 1.64304i) q^{70} +(-5.32146 - 5.32146i) q^{71} +(-5.80507 - 5.80507i) q^{73} -3.36631i q^{74} +(-0.269765 - 0.269765i) q^{76} -2.16419 q^{77} -2.05100 q^{79} +(1.64304 + 1.64304i) q^{80} +11.1471i q^{82} +(-8.82822 - 8.82822i) q^{83} +(-9.17590 - 9.17590i) q^{85} +(-2.83624 + 2.83624i) q^{86} -2.16419i q^{88} +(4.84471 - 4.84471i) q^{89} +(2.65251 - 2.44217i) q^{91} +4.44768i q^{92} +1.66284 q^{94} +0.886471 q^{95} +(0.753379 - 0.753379i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{5} - 8 q^{11} + 4 q^{13} - 16 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{20} - 8 q^{22} + 24 q^{23} + 8 q^{26} - 8 q^{31} + 4 q^{34} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 8 q^{44} + 4 q^{47} - 16 q^{50}+ \cdots - 28 q^{97}+O(q^{100}) $ 16 * q + 4 * q^5 - 8 * q^11 + 4 * q^13 - 16 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^20 - 8 * q^22 + 24 * q^23 + 8 * q^26 - 8 * q^31 + 4 * q^34 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 8 * q^44 + 4 * q^47 - 16 * q^50 - 16 * q^55 - 16 * q^56 + 4 * q^58 - 8 * q^59 - 40 * q^61 + 24 * q^62 + 56 * q^65 - 4 * q^67 - 4 * q^70 - 24 * q^71 - 12 * q^73 + 16 * q^76 - 8 * q^77 + 16 * q^79 - 4 * q^80 + 8 * q^85 + 24 * q^86 + 16 * q^89 + 8 * q^91 - 8 * q^94 - 40 * q^95 - 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−1.64304	−	1.64304i	−0.734792	−	0.734792i	0.236773	−	0.971565i	$-0.423910\pi$
$5$	−1.64304	−	1.64304i	−0.734792	−	0.734792i	−0.971565	+	0.236773i	$0.923910\pi$
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$			2.32362i			0.734792i
$11$	1.53031	−	1.53031i	0.461406	−	0.461406i	−0.437710	−	0.899116i	$-0.644210\pi$
$11$	1.53031	−	1.53031i	0.461406	−	0.461406i	0.899116	+	0.437710i	$0.144210\pi$
$12$		0			0
$13$	−0.148739	+	3.60248i	−0.0412526	+	0.999149i
$13$	−0.148739	+	3.60248i	−0.0412526	+	0.999149i
$14$			1.00000i			0.267261i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	5.58470			1.35449			0.677244	−	0.735759i	$-0.263174\pi$
$17$	5.58470			1.35449			0.677244	+	0.735759i	$0.263174\pi$
$18$		0			0
$19$	−0.269765	+	0.269765i	−0.0618883	+	0.0618883i	−0.737374	−	0.675485i	$-0.763934\pi$
$19$	−0.269765	+	0.269765i	−0.0618883	+	0.0618883i	0.675485	+	0.737374i	$0.263934\pi$
$20$	1.64304	−	1.64304i	0.367396	−	0.367396i
$21$		0			0
$22$	−2.16419			−0.461406
$23$	4.44768			0.927405			0.463702	−	0.885991i	$-0.346521\pi$
$23$	4.44768			0.927405			0.463702	+	0.885991i	$0.346521\pi$
$24$		0			0
$25$			0.399189i			0.0798378i
$26$	2.65251	−	2.44217i	0.520201	−	0.478948i
$27$		0			0
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$		−	6.10807i		−	1.13424i	−0.823635	−	0.567120i	$-0.808058\pi$
$29$		−	6.10807i		−	1.13424i	0.823635	−	0.567120i	$-0.191942\pi$
$30$		0			0
$31$	−0.476750	+	0.476750i	−0.0856267	+	0.0856267i	−0.748623	−	0.662996i	$-0.769285\pi$
$31$	−0.476750	+	0.476750i	−0.0856267	+	0.0856267i	0.662996	+	0.748623i	$0.269285\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	−3.94898	−	3.94898i	−0.677244	−	0.677244i
$35$			2.32362i			0.392763i
$36$		0			0
$37$	2.38034	+	2.38034i	0.391325	+	0.391325i	0.875160	−	0.483834i	$-0.160756\pi$
$37$	2.38034	+	2.38034i	0.391325	+	0.391325i	−0.483834	+	0.875160i	$0.660756\pi$
$38$	0.381505			0.0618883
$39$		0			0
$40$	−2.32362			−0.367396
$41$	−7.88217	−	7.88217i	−1.23099	−	1.23099i	−0.963585	−	0.267404i	$-0.913834\pi$
$41$	−7.88217	−	7.88217i	−1.23099	−	1.23099i	−0.267404	−	0.963585i	$-0.586166\pi$
$42$		0			0
$43$		−	4.01105i		−	0.611680i	−0.952083	−	0.305840i	$-0.901063\pi$
$43$		−	4.01105i		−	0.611680i	0.952083	−	0.305840i	$-0.0989372\pi$
$44$	1.53031	+	1.53031i	0.230703	+	0.230703i
$45$		0			0
$46$	−3.14498	−	3.14498i	−0.463702	−	0.463702i
$47$	−1.17580	+	1.17580i	−0.171509	+	0.171509i	−0.787642	−	0.616133i	$-0.788698\pi$
$47$	−1.17580	+	1.17580i	−0.171509	+	0.171509i	0.616133	+	0.787642i	$0.288698\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	0.282269	−	0.282269i	0.0399189	−	0.0399189i
$51$		0			0
$52$	−3.60248	−	0.148739i	−0.499574	−	0.0206263i
$53$			2.66798i			0.366475i	0.983069	+	0.183238i	$0.0586577\pi$
$53$			2.66798i			0.366475i	−0.983069	+	0.183238i	$0.941342\pi$
$54$		0			0
$55$	−5.02874			−0.678075
$56$	−1.00000			−0.133631
$57$		0			0
$58$	−4.31906	+	4.31906i	−0.567120	+	0.567120i
$59$	1.84687	−	1.84687i	0.240441	−	0.240441i	−0.576591	−	0.817033i	$-0.695617\pi$
$59$	1.84687	−	1.84687i	0.240441	−	0.240441i	0.817033	+	0.576591i	$0.195617\pi$
$60$		0			0
$61$	−1.03753			−0.132842			−0.0664209	−	0.997792i	$-0.521158\pi$
$61$	−1.03753			−0.132842			−0.0664209	+	0.997792i	$0.521158\pi$
$62$	0.674226			0.0856267
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	6.16342	−	5.67465i	0.764478	−	0.703854i
$66$		0			0
$67$	−2.08222	+	2.08222i	−0.254384	+	0.254384i	−0.822765	−	0.568381i	$-0.807570\pi$
$67$	−2.08222	+	2.08222i	−0.254384	+	0.254384i	0.568381	+	0.822765i	$0.307570\pi$
$68$			5.58470i			0.677244i
$69$		0			0
$70$	1.64304	−	1.64304i	0.196381	−	0.196381i
$71$	−5.32146	−	5.32146i	−0.631541	−	0.631541i	0.316914	−	0.948454i	$-0.397353\pi$
$71$	−5.32146	−	5.32146i	−0.631541	−	0.631541i	−0.948454	+	0.316914i	$0.897353\pi$
$72$		0			0
$73$	−5.80507	−	5.80507i	−0.679432	−	0.679432i	0.280439	−	0.959872i	$-0.409520\pi$
$73$	−5.80507	−	5.80507i	−0.679432	−	0.679432i	−0.959872	+	0.280439i	$0.909520\pi$
$74$		−	3.36631i		−	0.391325i
$75$		0			0
$76$	−0.269765	−	0.269765i	−0.0309441	−	0.0309441i
$77$	−2.16419			−0.246632
$78$		0			0
$79$	−2.05100			−0.230755			−0.115378	−	0.993322i	$-0.536808\pi$
$79$	−2.05100			−0.230755			−0.115378	+	0.993322i	$0.536808\pi$
$80$	1.64304	+	1.64304i	0.183698	+	0.183698i
$81$		0			0
$82$			11.1471i			1.23099i
$83$	−8.82822	−	8.82822i	−0.969023	−	0.969023i	0.0305119	−	0.999534i	$-0.490286\pi$
$83$	−8.82822	−	8.82822i	−0.969023	−	0.969023i	−0.999534	+	0.0305119i	$0.990286\pi$
$84$		0			0
$85$	−9.17590	−	9.17590i	−0.995266	−	0.995266i
$86$	−2.83624	+	2.83624i	−0.305840	+	0.305840i
$87$		0			0
$88$		−	2.16419i		−	0.230703i
$89$	4.84471	−	4.84471i	0.513538	−	0.513538i	−0.402071	−	0.915609i	$-0.631709\pi$
$89$	4.84471	−	4.84471i	0.513538	−	0.513538i	0.915609	+	0.402071i	$0.131709\pi$
$90$		0			0
$91$	2.65251	−	2.44217i	0.278059	−	0.256009i
$92$			4.44768i			0.463702i
$93$		0			0
$94$	1.66284			0.171509
$95$	0.886471			0.0909500
$96$		0			0
$97$	0.753379	−	0.753379i	0.0764941	−	0.0764941i	−0.667825	−	0.744319i	$-0.732774\pi$
$97$	0.753379	−	0.753379i	0.0764941	−	0.0764941i	0.744319	+	0.667825i	$0.232774\pi$
$98$	0.707107	−	0.707107i	0.0714286	−	0.0714286i
$99$		0			0
$100$	−0.399189			−0.0399189
$101$	1.48794			0.148056			0.0740280	−	0.997256i	$-0.476415\pi$
$101$	1.48794			0.148056			0.0740280	+	0.997256i	$0.476415\pi$
$102$		0			0
$103$		−	3.36590i		−	0.331652i	−0.986155	−	0.165826i	$-0.946971\pi$
$103$		−	3.36590i		−	0.331652i	0.986155	−	0.165826i	$-0.0530290\pi$
$104$	2.44217	+	2.65251i	0.239474	+	0.260100i
$105$		0			0
$106$	1.88655	−	1.88655i	0.183238	−	0.183238i
$107$		−	1.38366i		−	0.133764i	−0.997761	−	0.0668819i	$-0.978695\pi$
$107$		−	1.38366i		−	0.133764i	0.997761	−	0.0668819i	$-0.0213051\pi$
$108$		0			0
$109$	4.22721	−	4.22721i	0.404893	−	0.404893i	−0.475060	−	0.879953i	$-0.657574\pi$
$109$	4.22721	−	4.22721i	0.404893	−	0.404893i	0.879953	+	0.475060i	$0.157574\pi$
$110$	3.55585	+	3.55585i	0.339037	+	0.339037i
$111$		0			0
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$		−	16.5111i		−	1.55323i	−0.629976	−	0.776615i	$-0.716935\pi$
$113$		−	16.5111i		−	1.55323i	0.629976	−	0.776615i	$-0.283065\pi$
$114$		0			0
$115$	−7.30773	−	7.30773i	−0.681449	−	0.681449i
$116$	6.10807			0.567120
$117$		0			0
$118$	−2.61186			−0.240441
$119$	−3.94898	−	3.94898i	−0.362002	−	0.362002i
$120$		0			0
$121$			6.31630i			0.574209i
$122$	0.733642	+	0.733642i	0.0664209	+	0.0664209i
$123$		0			0
$124$	−0.476750	−	0.476750i	−0.0428134	−	0.0428134i
$125$	−7.55934	+	7.55934i	−0.676128	+	0.676128i
$126$		0			0
$127$		−	19.9525i		−	1.77050i	−0.465116	−	0.885250i	$-0.653987\pi$
$127$		−	19.9525i		−	1.77050i	0.465116	−	0.885250i	$-0.346013\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−8.37078	−	0.345611i	−0.734166	−	0.0303121i
$131$			12.1986i			1.06580i	0.846180	+	0.532898i	$0.178897\pi$
$131$			12.1986i			1.06580i	−0.846180	+	0.532898i	$0.821103\pi$
$132$		0			0
$133$	0.381505			0.0330807
$134$	2.94471			0.254384
$135$		0			0
$136$	3.94898	−	3.94898i	0.338622	−	0.338622i
$137$	4.13022	−	4.13022i	0.352868	−	0.352868i	−0.508307	−	0.861176i	$-0.669729\pi$
$137$	4.13022	−	4.13022i	0.352868	−	0.352868i	0.861176	+	0.508307i	$0.169729\pi$
$138$		0			0
$139$	12.9729			1.10035			0.550173	−	0.835051i	$-0.314562\pi$
$139$	12.9729			1.10035			0.550173	+	0.835051i	$0.314562\pi$
$140$	−2.32362			−0.196381
$141$		0			0
$142$			7.52568i			0.631541i
$143$	5.28530	+	5.74053i	0.441979	+	0.480047i
$144$		0			0
$145$	−10.0358	+	10.0358i	−0.833430	+	0.833430i
$146$			8.20961i			0.679432i
$147$		0			0
$148$	−2.38034	+	2.38034i	−0.195663	+	0.195663i
$149$	−8.89445	−	8.89445i	−0.728662	−	0.728662i	0.241691	−	0.970353i	$-0.422298\pi$
$149$	−8.89445	−	8.89445i	−0.728662	−	0.728662i	−0.970353	+	0.241691i	$0.922298\pi$
$150$		0			0
$151$	−4.19184	−	4.19184i	−0.341127	−	0.341127i	0.515664	−	0.856791i	$-0.327545\pi$
$151$	−4.19184	−	4.19184i	−0.341127	−	0.341127i	−0.856791	+	0.515664i	$0.827545\pi$
$152$			0.381505i			0.0309441i
$153$		0			0
$154$	1.53031	+	1.53031i	0.123316	+	0.123316i
$155$	1.56664			0.125836
$156$		0			0
$157$	19.1147			1.52552			0.762760	−	0.646682i	$-0.223844\pi$
$157$	19.1147			1.52552			0.762760	+	0.646682i	$0.223844\pi$
$158$	1.45027	+	1.45027i	0.115378	+	0.115378i
$159$		0			0
$160$		−	2.32362i		−	0.183698i
$161$	−3.14498	−	3.14498i	−0.247859	−	0.247859i
$162$		0			0
$163$	−13.3438	−	13.3438i	−1.04516	−	1.04516i	−0.998931	−	0.0462337i	$-0.985278\pi$
$163$	−13.3438	−	13.3438i	−1.04516	−	1.04516i	−0.0462337	−	0.998931i	$-0.514722\pi$
$164$	7.88217	−	7.88217i	0.615494	−	0.615494i
$165$		0			0
$166$			12.4850i			0.969023i
$167$	−6.12142	+	6.12142i	−0.473690	+	0.473690i	−0.903106	−	0.429417i	$-0.858719\pi$
$167$	−6.12142	+	6.12142i	−0.473690	+	0.473690i	0.429417	+	0.903106i	$0.358719\pi$
$168$		0			0
$169$	−12.9558	−	1.07166i	−0.996596	−	0.0824350i
$170$			12.9767i			0.995266i
$171$		0			0
$172$	4.01105			0.305840
$173$	4.73310			0.359851			0.179925	−	0.983680i	$-0.442414\pi$
$173$	4.73310			0.359851			0.179925	+	0.983680i	$0.442414\pi$
$174$		0			0
$175$	0.282269	−	0.282269i	0.0213375	−	0.0213375i
$176$	−1.53031	+	1.53031i	−0.115351	+	0.115351i
$177$		0			0
$178$	−6.85145			−0.513538
$179$	6.35128			0.474717			0.237359	−	0.971422i	$-0.423718\pi$
$179$	6.35128			0.474717			0.237359	+	0.971422i	$0.423718\pi$
$180$		0			0
$181$			12.9313i			0.961173i	0.876947	+	0.480586i	$0.159576\pi$
$181$			12.9313i			0.961173i	−0.876947	+	0.480586i	$0.840424\pi$
$182$	−3.60248	−	0.148739i	−0.267034	−	0.0110252i
$183$		0			0
$184$	3.14498	−	3.14498i	0.231851	−	0.231851i
$185$		−	7.82201i		−	0.575085i
$186$		0			0
$187$	8.54632	−	8.54632i	0.624969	−	0.624969i
$188$	−1.17580	−	1.17580i	−0.0857543	−	0.0857543i
$189$		0			0
$190$	−0.626830	−	0.626830i	−0.0454750	−	0.0454750i
$191$		−	16.8092i		−	1.21627i	−0.793832	−	0.608137i	$-0.791917\pi$
$191$		−	16.8092i		−	1.21627i	0.793832	−	0.608137i	$-0.208083\pi$
$192$		0			0
$193$	5.83733	+	5.83733i	0.420180	+	0.420180i	0.885266	−	0.465086i	$-0.153976\pi$
$193$	5.83733	+	5.83733i	0.420180	+	0.420180i	−0.465086	+	0.885266i	$0.653976\pi$
$194$	−1.06544			−0.0764941
$195$		0			0
$196$	−1.00000			−0.0714286
$197$	−3.11368	−	3.11368i	−0.221841	−	0.221841i	0.587432	−	0.809273i	$-0.300139\pi$
$197$	−3.11368	−	3.11368i	−0.221841	−	0.221841i	−0.809273	+	0.587432i	$0.800139\pi$
$198$		0			0
$199$			18.0613i			1.28033i	0.768238	+	0.640165i	$0.221134\pi$
$199$			18.0613i			1.28033i	−0.768238	+	0.640165i	$0.778866\pi$
$200$	0.282269	+	0.282269i	0.0199594	+	0.0199594i
$201$		0			0
$202$	−1.05214	−	1.05214i	−0.0740280	−	0.0740280i
$203$	−4.31906	+	4.31906i	−0.303138	+	0.303138i
$204$		0			0
$205$			25.9015i			1.80904i
$206$	−2.38005	+	2.38005i	−0.165826	+	0.165826i
$207$		0			0
$208$	0.148739	−	3.60248i	0.0103132	−	0.249787i
$209$			0.825648i			0.0571112i
$210$		0			0
$211$	−4.56632			−0.314358			−0.157179	−	0.987570i	$-0.550240\pi$
$211$	−4.56632			−0.314358			−0.157179	+	0.987570i	$0.550240\pi$
$212$	−2.66798			−0.183238
$213$		0			0
$214$	−0.978398	+	0.978398i	−0.0668819	+	0.0668819i
$215$	−6.59034	+	6.59034i	−0.449457	+	0.449457i
$216$		0			0
$217$	0.674226			0.0457694
$218$	−5.97817			−0.404893
$219$		0			0
$220$		−	5.02874i		−	0.339037i
$221$	−0.830659	+	20.1188i	−0.0558762	+	1.35333i
$222$		0			0
$223$	12.2953	−	12.2953i	0.823354	−	0.823354i	−0.163234	−	0.986587i	$-0.552192\pi$
$223$	12.2953	−	12.2953i	0.823354	−	0.823354i	0.986587	+	0.163234i	$0.0521924\pi$
$224$		−	1.00000i		−	0.0668153i
$225$		0			0
$226$	−11.6751	+	11.6751i	−0.776615	+	0.776615i
$227$	−13.2910	−	13.2910i	−0.882153	−	0.882153i	0.111600	−	0.993753i	$-0.464402\pi$
$227$	−13.2910	−	13.2910i	−0.882153	−	0.882153i	−0.993753	+	0.111600i	$0.964402\pi$
$228$		0			0
$229$	8.61423	+	8.61423i	0.569244	+	0.569244i	0.931917	−	0.362672i	$-0.118136\pi$
$229$	8.61423	+	8.61423i	0.569244	+	0.569244i	−0.362672	+	0.931917i	$0.618136\pi$
$230$			10.3347i			0.681449i
$231$		0			0
$232$	−4.31906	−	4.31906i	−0.283560	−	0.283560i
$233$	−2.94207			−0.192742			−0.0963708	−	0.995346i	$-0.530723\pi$
$233$	−2.94207			−0.192742			−0.0963708	+	0.995346i	$0.530723\pi$
$234$		0			0
$235$	3.86379			0.252046
$236$	1.84687	+	1.84687i	0.120221	+	0.120221i
$237$		0			0
$238$			5.58470i			0.362002i
$239$	11.1260	+	11.1260i	0.719682	+	0.719682i	0.968540	−	0.248858i	$-0.0800552\pi$
$239$	11.1260	+	11.1260i	0.719682	+	0.719682i	−0.248858	+	0.968540i	$0.580055\pi$
$240$		0			0
$241$	−8.50173	−	8.50173i	−0.547644	−	0.547644i	0.378115	−	0.925759i	$-0.376573\pi$
$241$	−8.50173	−	8.50173i	−0.547644	−	0.547644i	−0.925759	+	0.378115i	$0.876573\pi$
$242$	4.46630	−	4.46630i	0.287105	−	0.287105i
$243$		0			0
$244$		−	1.03753i		−	0.0664209i
$245$	1.64304	−	1.64304i	0.104970	−	0.104970i
$246$		0			0
$247$	−0.931698	−	1.01195i	−0.0592825	−	0.0643886i
$248$			0.674226i			0.0428134i
$249$		0			0
$250$	10.6905			0.676128
$251$	−23.1026			−1.45822			−0.729110	−	0.684396i	$-0.760066\pi$
$251$	−23.1026			−1.45822			−0.729110	+	0.684396i	$0.760066\pi$
$252$		0			0
$253$	6.80633	−	6.80633i	0.427910	−	0.427910i
$254$	−14.1086	+	14.1086i	−0.885250	+	0.885250i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−2.22951			−0.139073			−0.0695365	−	0.997579i	$-0.522152\pi$
$257$	−2.22951			−0.139073			−0.0695365	+	0.997579i	$0.522152\pi$
$258$		0			0
$259$		−	3.36631i		−	0.209172i
$260$	5.67465	+	6.16342i	0.351927	+	0.382239i
$261$		0			0
$262$	8.62570	−	8.62570i	0.532898	−	0.532898i
$263$		−	27.0080i		−	1.66538i	−0.553738	−	0.832691i	$-0.686799\pi$
$263$		−	27.0080i		−	1.66538i	0.553738	−	0.832691i	$-0.313201\pi$
$264$		0			0
$265$	4.38361	−	4.38361i	0.269283	−	0.269283i
$266$	−0.269765	−	0.269765i	−0.0165403	−	0.0165403i
$267$		0			0
$268$	−2.08222	−	2.08222i	−0.127192	−	0.127192i
$269$			19.9009i			1.21338i	0.794938	+	0.606690i	$0.207503\pi$
$269$			19.9009i			1.21338i	−0.794938	+	0.606690i	$0.792497\pi$
$270$		0			0
$271$	13.6851	+	13.6851i	0.831308	+	0.831308i	0.987696	−	0.156388i	$-0.0499850\pi$
$271$	13.6851	+	13.6851i	0.831308	+	0.831308i	−0.156388	+	0.987696i	$0.549985\pi$
$272$	−5.58470			−0.338622
$273$		0			0
$274$	−5.84101			−0.352868
$275$	0.610883	+	0.610883i	0.0368376	+	0.0368376i
$276$		0			0
$277$			8.95516i			0.538064i	0.963131	+	0.269032i	$0.0867037\pi$
$277$			8.95516i			0.538064i	−0.963131	+	0.269032i	$0.913296\pi$
$278$	−9.17321	−	9.17321i	−0.550173	−	0.550173i
$279$		0			0
$280$	1.64304	+	1.64304i	0.0981907	+	0.0981907i
$281$	12.4026	−	12.4026i	0.739878	−	0.739878i	−0.232676	−	0.972554i	$-0.574748\pi$
$281$	12.4026	−	12.4026i	0.739878	−	0.739878i	0.972554	+	0.232676i	$0.0747483\pi$
$282$		0			0
$283$		−	22.8552i		−	1.35860i	−0.733862	−	0.679299i	$-0.762284\pi$
$283$		−	22.8552i		−	1.35860i	0.733862	−	0.679299i	$-0.237716\pi$
$284$	5.32146	−	5.32146i	0.315770	−	0.315770i
$285$		0			0
$286$	0.321898	−	7.79644i	0.0190342	−	0.461013i
$287$			11.1471i			0.657991i
$288$		0			0
$289$	14.1888			0.834636
$290$	14.1928			0.833430
$291$		0			0
$292$	5.80507	−	5.80507i	0.339716	−	0.339716i
$293$	−5.96950	+	5.96950i	−0.348742	+	0.348742i	−0.859641	−	0.510899i	$-0.829313\pi$
$293$	−5.96950	+	5.96950i	−0.348742	+	0.348742i	0.510899	+	0.859641i	$0.329313\pi$
$294$		0			0
$295$	−6.06897			−0.353349
$296$	3.36631			0.195663
$297$		0			0
$298$			12.5787i			0.728662i
$299$	−0.661541	+	16.0227i	−0.0382579	+	0.926615i
$300$		0			0
$301$	−2.83624	+	2.83624i	−0.163478	+	0.163478i
$302$			5.92816i			0.341127i
$303$		0			0
$304$	0.269765	−	0.269765i	0.0154721	−	0.0154721i
$305$	1.70470	+	1.70470i	0.0976110	+	0.0976110i
$306$		0			0
$307$	17.1095	+	17.1095i	0.976492	+	0.976492i	0.999730	−	0.0232379i	$-0.00739751\pi$
$307$	17.1095	+	17.1095i	0.976492	+	0.976492i	−0.0232379	+	0.999730i	$0.507398\pi$
$308$		−	2.16419i		−	0.123316i
$309$		0			0
$310$	−1.10778	−	1.10778i	−0.0629178	−	0.0629178i
$311$	−25.7952			−1.46271			−0.731356	−	0.681996i	$-0.761112\pi$
$311$	−25.7952			−1.46271			−0.731356	+	0.681996i	$0.761112\pi$
$312$		0			0
$313$	21.9022			1.23798			0.618992	−	0.785397i	$-0.287541\pi$
$313$	21.9022			1.23798			0.618992	+	0.785397i	$0.287541\pi$
$314$	−13.5161	−	13.5161i	−0.762760	−	0.762760i
$315$		0			0
$316$		−	2.05100i		−	0.115378i
$317$	13.6891	+	13.6891i	0.768855	+	0.768855i	0.977905	−	0.209050i	$-0.0670371\pi$
$317$	13.6891	+	13.6891i	0.768855	+	0.768855i	−0.209050	+	0.977905i	$0.567037\pi$
$318$		0			0
$319$	−9.34724	−	9.34724i	−0.523345	−	0.523345i
$320$	−1.64304	+	1.64304i	−0.0918490	+	0.0918490i
$321$		0			0
$322$			4.44768i			0.247859i
$323$	−1.50655	+	1.50655i	−0.0838269	+	0.0838269i
$324$		0			0
$325$	−1.43807	−	0.0593748i	−0.0797698	−	0.00329352i
$326$			18.8709i			1.04516i
$327$		0			0
$328$	−11.1471			−0.615494
$329$	1.66284			0.0916752
$330$		0			0
$331$	1.71263	−	1.71263i	0.0941344	−	0.0941344i	−0.658471	−	0.752606i	$-0.728797\pi$
$331$	1.71263	−	1.71263i	0.0941344	−	0.0941344i	0.752606	+	0.658471i	$0.228797\pi$
$332$	8.82822	−	8.82822i	0.484511	−	0.484511i
$333$		0			0
$334$	8.65699			0.473690
$335$	6.84237			0.373839
$336$		0			0
$337$		−	34.4232i		−	1.87515i	−0.347783	−	0.937575i	$-0.613065\pi$
$337$		−	34.4232i		−	1.87515i	0.347783	−	0.937575i	$-0.386935\pi$
$338$	8.40333	+	9.91888i	0.457081	+	0.539516i
$339$		0			0
$340$	9.17590	−	9.17590i	0.497633	−	0.497633i
$341$			1.45915i			0.0790174i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−2.83624	−	2.83624i	−0.152920	−	0.152920i
$345$		0			0
$346$	−3.34680	−	3.34680i	−0.179925	−	0.179925i
$347$			29.9057i			1.60542i	0.596369	+	0.802710i	$0.296610\pi$
$347$			29.9057i			1.60542i	−0.596369	+	0.802710i	$0.703390\pi$
$348$		0			0
$349$	8.82539	+	8.82539i	0.472412	+	0.472412i	0.902694	−	0.430282i	$-0.141586\pi$
$349$	8.82539	+	8.82539i	0.472412	+	0.472412i	−0.430282	+	0.902694i	$0.641586\pi$
$350$	−0.399189			−0.0213375
$351$		0			0
$352$	2.16419			0.115351
$353$	−1.90896	−	1.90896i	−0.101603	−	0.101603i	0.654478	−	0.756081i	$-0.272889\pi$
$353$	−1.90896	−	1.90896i	−0.101603	−	0.101603i	−0.756081	+	0.654478i	$0.772889\pi$
$354$		0			0
$355$			17.4868i			0.928102i
$356$	4.84471	+	4.84471i	0.256769	+	0.256769i
$357$		0			0
$358$	−4.49104	−	4.49104i	−0.237359	−	0.237359i
$359$	−23.8347	+	23.8347i	−1.25795	+	1.25795i	−0.305880	+	0.952070i	$0.598951\pi$
$359$	−23.8347	+	23.8347i	−1.25795	+	1.25795i	−0.952070	+	0.305880i	$0.901049\pi$
$360$		0			0
$361$			18.8545i			0.992340i
$362$	9.14378	−	9.14378i	0.480586	−	0.480586i
$363$		0			0
$364$	2.44217	+	2.65251i	0.128004	+	0.139029i
$365$			19.0760i			0.998482i
$366$		0			0
$367$	−11.6160			−0.606351			−0.303176	−	0.952935i	$-0.598047\pi$
$367$	−11.6160			−0.606351			−0.303176	+	0.952935i	$0.598047\pi$
$368$	−4.44768			−0.231851
$369$		0			0
$370$	−5.53099	+	5.53099i	−0.287543	+	0.287543i
$371$	1.88655	−	1.88655i	0.0979446	−	0.0979446i
$372$		0			0
$373$	35.3238			1.82900			0.914498	−	0.404591i	$-0.132586\pi$
$373$	35.3238			1.82900			0.914498	+	0.404591i	$0.132586\pi$
$374$	−12.0863			−0.624969
$375$		0			0
$376$			1.66284i			0.0857543i
$377$	22.0042	+	0.908505i	1.13327	+	0.0467904i
$378$		0			0
$379$	17.0162	−	17.0162i	0.874061	−	0.874061i	−0.118851	−	0.992912i	$-0.537921\pi$
$379$	17.0162	−	17.0162i	0.874061	−	0.874061i	0.992912	+	0.118851i	$0.0379210\pi$
$380$			0.886471i			0.0454750i
$381$		0			0
$382$	−11.8859	+	11.8859i	−0.608137	+	0.608137i
$383$	−6.96996	−	6.96996i	−0.356149	−	0.356149i	0.506243	−	0.862391i	$-0.331034\pi$
$383$	−6.96996	−	6.96996i	−0.356149	−	0.356149i	−0.862391	+	0.506243i	$0.831034\pi$
$384$		0			0
$385$	3.55585	+	3.55585i	0.181223	+	0.181223i
$386$		−	8.25523i		−	0.420180i
$387$		0			0
$388$	0.753379	+	0.753379i	0.0382470	+	0.0382470i
$389$	31.0858			1.57611			0.788055	−	0.615605i	$-0.211088\pi$
$389$	31.0858			1.57611			0.788055	+	0.615605i	$0.211088\pi$
$390$		0			0
$391$	24.8389			1.25616
$392$	0.707107	+	0.707107i	0.0357143	+	0.0357143i
$393$		0			0
$394$			4.40341i			0.221841i
$395$	3.36988	+	3.36988i	0.169557	+	0.169557i
$396$		0			0
$397$	−0.920019	−	0.920019i	−0.0461744	−	0.0461744i	0.683643	−	0.729817i	$-0.260395\pi$
$397$	−0.920019	−	0.920019i	−0.0461744	−	0.0461744i	−0.729817	+	0.683643i	$0.760395\pi$
$398$	12.7712	−	12.7712i	0.640165	−	0.640165i
$399$		0			0
$400$		−	0.399189i		−	0.0199594i
$401$	4.80873	−	4.80873i	0.240137	−	0.240137i	−0.576770	−	0.816907i	$-0.695687\pi$
$401$	4.80873	−	4.80873i	0.240137	−	0.240137i	0.816907	+	0.576770i	$0.195687\pi$
$402$		0			0
$403$	−1.64657	−	1.78839i	−0.0820215	−	0.0890862i
$404$			1.48794i			0.0740280i
$405$		0			0
$406$	6.10807			0.303138
$407$	7.28532			0.361120
$408$		0			0
$409$	12.9718	−	12.9718i	0.641413	−	0.641413i	−0.309490	−	0.950903i	$-0.600158\pi$
$409$	12.9718	−	12.9718i	0.641413	−	0.641413i	0.950903	+	0.309490i	$0.100158\pi$
$410$	18.3151	−	18.3151i	0.904520	−	0.904520i
$411$		0			0
$412$	3.36590			0.165826
$413$	−2.61186			−0.128521
$414$		0			0
$415$			29.0103i			1.42406i
$416$	−2.65251	+	2.44217i	−0.130050	+	0.119737i
$417$		0			0
$418$	0.583821	−	0.583821i	0.0285556	−	0.0285556i
$419$		−	3.44464i		−	0.168282i	−0.996454	−	0.0841408i	$-0.973185\pi$
$419$		−	3.44464i		−	0.168282i	0.996454	−	0.0841408i	$-0.0268145\pi$
$420$		0			0
$421$	4.79318	−	4.79318i	0.233605	−	0.233605i	−0.580591	−	0.814196i	$-0.697178\pi$
$421$	4.79318	−	4.79318i	0.233605	−	0.233605i	0.814196	+	0.580591i	$0.197178\pi$
$422$	3.22888	+	3.22888i	0.157179	+	0.157179i
$423$		0			0
$424$	1.88655	+	1.88655i	0.0916188	+	0.0916188i
$425$			2.22935i			0.108139i
$426$		0			0
$427$	0.733642	+	0.733642i	0.0355034	+	0.0355034i
$428$	1.38366			0.0668819
$429$		0			0
$430$	9.32014			0.449457
$431$	15.4940	+	15.4940i	0.746318	+	0.746318i	0.973786	−	0.227467i	$-0.0730445\pi$
$431$	15.4940	+	15.4940i	0.746318	+	0.746318i	−0.227467	+	0.973786i	$0.573044\pi$
$432$		0			0
$433$			41.1947i			1.97969i	0.142147	+	0.989846i	$0.454599\pi$
$433$			41.1947i			1.97969i	−0.142147	+	0.989846i	$0.545401\pi$
$434$	−0.476750	−	0.476750i	−0.0228847	−	0.0228847i
$435$		0			0
$436$	4.22721	+	4.22721i	0.202446	+	0.202446i
$437$	−1.19983	+	1.19983i	−0.0573955	+	0.0573955i
$438$		0			0
$439$			16.2888i			0.777421i	0.921360	+	0.388710i	$0.127079\pi$
$439$			16.2888i			0.777421i	−0.921360	+	0.388710i	$0.872921\pi$
$440$	−3.55585	+	3.55585i	−0.169519	+	0.169519i
$441$		0			0
$442$	14.8135	−	13.6387i	0.704605	−	0.648729i
$443$		−	30.0869i		−	1.42947i	−0.699395	−	0.714735i	$-0.746547\pi$
$443$		−	30.0869i		−	1.42947i	0.699395	−	0.714735i	$-0.253453\pi$
$444$		0			0
$445$	−15.9201			−0.754687
$446$	−17.3882			−0.823354
$447$		0			0
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	22.6406	−	22.6406i	1.06848	−	1.06848i	0.0710006	−	0.997476i	$-0.477381\pi$
$449$	22.6406	−	22.6406i	1.06848	−	1.06848i	0.997476	−	0.0710006i	$-0.0226192\pi$
$450$		0			0
$451$	−24.1243			−1.13597
$452$	16.5111			0.776615
$453$		0			0
$454$			18.7963i			0.882153i
$455$	−8.37078	−	0.345611i	−0.392428	−	0.0162025i
$456$		0			0
$457$	21.8016	−	21.8016i	1.01983	−	1.01983i	0.0200351	−	0.999799i	$-0.493622\pi$
$457$	21.8016	−	21.8016i	1.01983	−	1.01983i	0.999799	−	0.0200351i	$-0.00637779\pi$
$458$		−	12.1824i		−	0.569244i
$459$		0			0
$460$	7.30773	−	7.30773i	0.340725	−	0.340725i
$461$	−14.3854	−	14.3854i	−0.669994	−	0.669994i	0.287720	−	0.957714i	$-0.407103\pi$
$461$	−14.3854	−	14.3854i	−0.669994	−	0.669994i	−0.957714	+	0.287720i	$0.907103\pi$
$462$		0			0
$463$	2.64406	+	2.64406i	0.122880	+	0.122880i	0.765872	−	0.642993i	$-0.222307\pi$
$463$	2.64406	+	2.64406i	0.122880	+	0.122880i	−0.642993	+	0.765872i	$0.722307\pi$
$464$			6.10807i			0.283560i
$465$		0			0
$466$	2.08036	+	2.08036i	0.0963708	+	0.0963708i
$467$	−26.6599			−1.23367			−0.616837	−	0.787091i	$-0.711586\pi$
$467$	−26.6599			−1.23367			−0.616837	+	0.787091i	$0.711586\pi$
$468$		0			0
$469$	2.94471			0.135974
$470$	−2.73212	−	2.73212i	−0.126023	−	0.126023i
$471$		0			0
$472$		−	2.61186i		−	0.120221i
$473$	−6.13816	−	6.13816i	−0.282233	−	0.282233i
$474$		0			0
$475$	−0.107687	−	0.107687i	−0.00494102	−	0.00494102i
$476$	3.94898	−	3.94898i	0.181001	−	0.181001i
$477$		0			0
$478$		−	15.7346i		−	0.719682i
$479$	−7.79650	+	7.79650i	−0.356231	+	0.356231i	−0.862422	−	0.506190i	$-0.831053\pi$
$479$	−7.79650	+	7.79650i	−0.356231	+	0.356231i	0.506190	+	0.862422i	$0.331053\pi$
$480$		0			0
$481$	−8.92918	+	8.22108i	−0.407136	+	0.374849i
$482$			12.0233i			0.547644i
$483$		0			0
$484$	−6.31630			−0.287105
$485$	−2.47567			−0.112414
$486$		0			0
$487$	−12.0844	+	12.0844i	−0.547595	+	0.547595i	−0.925744	−	0.378150i	$-0.876560\pi$
$487$	−12.0844	+	12.0844i	−0.547595	+	0.547595i	0.378150	+	0.925744i	$0.376560\pi$
$488$	−0.733642	+	0.733642i	−0.0332104	+	0.0332104i
$489$		0			0
$490$	−2.32362			−0.104970
$491$	43.7467			1.97426			0.987131	−	0.159911i	$-0.0511207\pi$
$491$	43.7467			1.97426			0.987131	+	0.159911i	$0.0511207\pi$
$492$		0			0
$493$		−	34.1117i		−	1.53631i
$494$	−0.0567445	+	1.37436i	−0.00255305	+	0.0618356i
$495$		0			0
$496$	0.476750	−	0.476750i	0.0214067	−	0.0214067i
$497$			7.52568i			0.337573i
$498$		0			0
$499$	6.66476	−	6.66476i	0.298356	−	0.298356i	−0.542014	−	0.840370i	$-0.682338\pi$
$499$	6.66476	−	6.66476i	0.298356	−	0.298356i	0.840370	+	0.542014i	$0.182338\pi$
$500$	−7.55934	−	7.55934i	−0.338064	−	0.338064i
$501$		0			0
$502$	16.3360	+	16.3360i	0.729110	+	0.729110i
$503$			13.8865i			0.619167i	0.950872	+	0.309584i	$0.100190\pi$
$503$			13.8865i			0.619167i	−0.950872	+	0.309584i	$0.899810\pi$
$504$		0			0
$505$	−2.44476	−	2.44476i	−0.108790	−	0.108790i
$506$	−9.62560			−0.427910
$507$		0			0
$508$	19.9525			0.885250
$509$	26.3768	+	26.3768i	1.16913	+	1.16913i	0.982413	+	0.186719i	$0.0597855\pi$
$509$	26.3768	+	26.3768i	1.16913	+	1.16913i	0.186719	+	0.982413i	$0.440214\pi$
$510$		0			0
$511$			8.20961i			0.363172i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	1.57650	+	1.57650i	0.0695365	+	0.0695365i
$515$	−5.53032	+	5.53032i	−0.243695	+	0.243695i
$516$		0			0
$517$			3.59869i			0.158270i
$518$	−2.38034	+	2.38034i	−0.104586	+	0.104586i
$519$		0			0
$520$	0.345611	−	8.37078i	0.0151560	−	0.367083i
$521$			8.95627i			0.392381i	0.980566	+	0.196191i	$0.0628572\pi$
$521$			8.95627i			0.392381i	−0.980566	+	0.196191i	$0.937143\pi$
$522$		0			0
$523$	−0.956586			−0.0418286			−0.0209143	−	0.999781i	$-0.506658\pi$
$523$	−0.956586			−0.0418286			−0.0209143	+	0.999781i	$0.506658\pi$
$524$	−12.1986			−0.532898
$525$		0			0
$526$	−19.0975	+	19.0975i	−0.832691	+	0.832691i
$527$	−2.66250	+	2.66250i	−0.115980	+	0.115980i
$528$		0			0
$529$	−3.21817			−0.139920
$530$	−6.19936			−0.269283
$531$		0			0
$532$			0.381505i			0.0165403i
$533$	29.5678	−	27.2230i	1.28072	−	1.17916i
$534$		0			0
$535$	−2.27342	+	2.27342i	−0.0982886	+	0.0982886i
$536$			2.94471i			0.127192i
$537$		0			0
$538$	14.0721	−	14.0721i	0.606690	−	0.606690i
$539$	1.53031	+	1.53031i	0.0659151	+	0.0659151i
$540$		0			0
$541$	30.1258	+	30.1258i	1.29521	+	1.29521i	0.931522	+	0.363686i	$0.118482\pi$
$541$	30.1258	+	30.1258i	1.29521	+	1.29521i	0.363686	+	0.931522i	$0.381518\pi$
$542$		−	19.3536i		−	0.831308i
$543$		0			0
$544$	3.94898	+	3.94898i	0.169311	+	0.169311i
$545$	−13.8910			−0.595024
$546$		0			0
$547$	−33.0740			−1.41414			−0.707071	−	0.707143i	$-0.749984\pi$
$547$	−33.0740			−1.41414			−0.707071	+	0.707143i	$0.749984\pi$
$548$	4.13022	+	4.13022i	0.176434	+	0.176434i
$549$		0			0
$550$		−	0.863919i		−	0.0368376i
$551$	1.64774	+	1.64774i	0.0701962	+	0.0701962i
$552$		0			0
$553$	1.45027	+	1.45027i	0.0616719	+	0.0616719i
$554$	6.33226	−	6.33226i	0.269032	−	0.269032i
$555$		0			0
$556$			12.9729i			0.550173i
$557$	19.4197	−	19.4197i	0.822841	−	0.822841i	−0.163674	−	0.986515i	$-0.552334\pi$
$557$	19.4197	−	19.4197i	0.822841	−	0.822841i	0.986515	+	0.163674i	$0.0523344\pi$
$558$		0			0
$559$	14.4497	+	0.596598i	0.611159	+	0.0252334i
$560$		−	2.32362i		−	0.0981907i
$561$		0			0
$562$	−17.5399			−0.739878
$563$	−3.91292			−0.164910			−0.0824550	−	0.996595i	$-0.526276\pi$
$563$	−3.91292			−0.164910			−0.0824550	+	0.996595i	$0.526276\pi$
$564$		0			0
$565$	−27.1284	+	27.1284i	−1.14130	+	1.14130i
$566$	−16.1610	+	16.1610i	−0.679299	+	0.679299i
$567$		0			0
$568$	−7.52568			−0.315770
$569$	14.2555			0.597620			0.298810	−	0.954313i	$-0.403410\pi$
$569$	14.2555			0.597620			0.298810	+	0.954313i	$0.403410\pi$
$570$		0			0
$571$			9.15631i			0.383180i	0.981475	+	0.191590i	$0.0613643\pi$
$571$			9.15631i			0.383180i	−0.981475	+	0.191590i	$0.938636\pi$
$572$	−5.74053	+	5.28530i	−0.240024	+	0.220990i
$573$		0			0
$574$	7.88217	−	7.88217i	0.328996	−	0.328996i
$575$			1.77546i			0.0740420i
$576$		0			0
$577$	8.79359	−	8.79359i	0.366082	−	0.366082i	−0.499964	−	0.866046i	$-0.666653\pi$
$577$	8.79359	−	8.79359i	0.366082	−	0.366082i	0.866046	+	0.499964i	$0.166653\pi$
$578$	−10.0330	−	10.0330i	−0.417318	−	0.417318i
$579$		0			0
$580$	−10.0358	−	10.0358i	−0.416715	−	0.416715i
$581$			12.4850i			0.517964i
$582$		0			0
$583$	4.08284	+	4.08284i	0.169094	+	0.169094i
$584$	−8.20961			−0.339716
$585$		0			0
$586$	8.44214			0.348742
$587$	−9.59316	−	9.59316i	−0.395952	−	0.395952i	0.480850	−	0.876803i	$-0.340328\pi$
$587$	−9.59316	−	9.59316i	−0.395952	−	0.395952i	−0.876803	+	0.480850i	$0.840328\pi$
$588$		0			0
$589$		−	0.257220i		−	0.0105986i
$590$	4.29141	+	4.29141i	0.176674	+	0.176674i
$591$		0			0
$592$	−2.38034	−	2.38034i	−0.0978314	−	0.0978314i
$593$	10.1705	−	10.1705i	0.417651	−	0.417651i	−0.466742	−	0.884393i	$-0.654572\pi$
$593$	10.1705	−	10.1705i	0.417651	−	0.417651i	0.884393	+	0.466742i	$0.154572\pi$
$594$		0			0
$595$			12.9767i			0.531992i
$596$	8.89445	−	8.89445i	0.364331	−	0.364331i
$597$		0			0
$598$	11.7975	−	10.8620i	0.482437	−	0.444179i
$599$			8.66779i			0.354156i	0.984197	+	0.177078i	$0.0566645\pi$
$599$			8.66779i			0.354156i	−0.984197	+	0.177078i	$0.943335\pi$
$600$		0			0
$601$	−23.5504			−0.960642			−0.480321	−	0.877093i	$-0.659480\pi$
$601$	−23.5504			−0.960642			−0.480321	+	0.877093i	$0.659480\pi$
$602$	4.01105			0.163478
$603$		0			0
$604$	4.19184	−	4.19184i	0.170564	−	0.170564i
$605$	10.3780	−	10.3780i	0.421924	−	0.421924i
$606$		0			0
$607$	−47.7045			−1.93626			−0.968132	−	0.250439i	$-0.919425\pi$
$607$	−47.7045			−1.93626			−0.968132	+	0.250439i	$0.919425\pi$
$608$	−0.381505			−0.0154721
$609$		0			0
$610$		−	2.41081i		−	0.0976110i
$611$	−4.06092	−	4.41070i	−0.164287	−	0.178438i
$612$		0			0
$613$	−15.2912	+	15.2912i	−0.617604	+	0.617604i	−0.944916	−	0.327312i	$-0.893857\pi$
$613$	−15.2912	+	15.2912i	−0.617604	+	0.617604i	0.327312	+	0.944916i	$0.393857\pi$
$614$		−	24.1965i		−	0.976492i
$615$		0			0
$616$	−1.53031	+	1.53031i	−0.0616580	+	0.0616580i
$617$	−0.424342	−	0.424342i	−0.0170834	−	0.0170834i	0.698514	−	0.715597i	$-0.253845\pi$
$617$	−0.424342	−	0.424342i	−0.0170834	−	0.0170834i	−0.715597	+	0.698514i	$0.753845\pi$
$618$		0			0
$619$	−8.73769	−	8.73769i	−0.351197	−	0.351197i	0.509358	−	0.860555i	$-0.329883\pi$
$619$	−8.73769	−	8.73769i	−0.351197	−	0.351197i	−0.860555	+	0.509358i	$0.829883\pi$
$620$			1.56664i			0.0629178i
$621$		0			0
$622$	18.2400	+	18.2400i	0.731356	+	0.731356i
$623$	−6.85145			−0.274498
$624$		0			0
$625$	26.8366			1.07346
$626$	−15.4872	−	15.4872i	−0.618992	−	0.618992i
$627$		0			0
$628$			19.1147i			0.762760i
$629$	13.2935	+	13.2935i	0.530045	+	0.530045i
$630$		0			0
$631$	−28.1191	−	28.1191i	−1.11940	−	1.11940i	−0.991829	−	0.127574i	$-0.959281\pi$
$631$	−28.1191	−	28.1191i	−1.11940	−	1.11940i	−0.127574	−	0.991829i	$-0.540719\pi$
$632$	−1.45027	+	1.45027i	−0.0576888	+	0.0576888i
$633$		0			0
$634$		−	19.3593i		−	0.768855i
$635$	−32.7829	+	32.7829i	−1.30095	+	1.30095i
$636$		0			0
$637$	−3.60248	−	0.148739i	−0.142736	−	0.00589323i
$638$			13.2190i			0.523345i
$639$		0			0
$640$	2.32362			0.0918490
$641$	−23.4505			−0.926239			−0.463120	−	0.886296i	$-0.653270\pi$
$641$	−23.4505			−0.926239			−0.463120	+	0.886296i	$0.653270\pi$
$642$		0			0
$643$	−14.1136	+	14.1136i	−0.556586	+	0.556586i	−0.928334	−	0.371748i	$-0.878759\pi$
$643$	−14.1136	+	14.1136i	−0.556586	+	0.556586i	0.371748	+	0.928334i	$0.378759\pi$
$644$	3.14498	−	3.14498i	0.123930	−	0.123930i
$645$		0			0
$646$	2.13059			0.0838269
$647$	16.5537			0.650794			0.325397	−	0.945578i	$-0.394502\pi$
$647$	16.5537			0.650794			0.325397	+	0.945578i	$0.394502\pi$
$648$		0			0
$649$		−	5.65256i		−	0.221882i
$650$	0.974886	+	1.05885i	0.0382382	+	0.0415317i
$651$		0			0
$652$	13.3438	−	13.3438i	0.522582	−	0.522582i
$653$		−	25.6224i		−	1.00268i	−0.865250	−	0.501341i	$-0.832840\pi$
$653$		−	25.6224i		−	1.00268i	0.865250	−	0.501341i	$-0.167160\pi$
$654$		0			0
$655$	20.0428	−	20.0428i	0.783138	−	0.783138i
$656$	7.88217	+	7.88217i	0.307747	+	0.307747i
$657$		0			0
$658$	−1.17580	−	1.17580i	−0.0458376	−	0.0458376i
$659$			11.5715i			0.450762i	0.974271	+	0.225381i	$0.0723626\pi$
$659$			11.5715i			0.450762i	−0.974271	+	0.225381i	$0.927637\pi$
$660$		0			0
$661$	−23.5822	−	23.5822i	−0.917243	−	0.917243i	0.0795854	−	0.996828i	$-0.474640\pi$
$661$	−23.5822	−	23.5822i	−0.917243	−	0.917243i	−0.996828	+	0.0795854i	$0.974640\pi$
$662$	−2.42202			−0.0941344
$663$		0			0
$664$	−12.4850			−0.484511
$665$	−0.626830	−	0.626830i	−0.0243074	−	0.0243074i
$666$		0			0
$667$		−	27.1667i		−	1.05190i
$668$	−6.12142	−	6.12142i	−0.236845	−	0.236845i
$669$		0			0
$670$	−4.83829	−	4.83829i	−0.186919	−	0.186919i
$671$	−1.58774	+	1.58774i	−0.0612940	+	0.0612940i
$672$		0			0
$673$			46.1492i			1.77892i	0.457012	+	0.889461i	$0.348920\pi$
$673$			46.1492i			1.77892i	−0.457012	+	0.889461i	$0.651080\pi$
$674$	−24.3409	+	24.3409i	−0.937575	+	0.937575i
$675$		0			0
$676$	1.07166	−	12.9558i	0.0412175	−	0.498298i
$677$			5.39786i			0.207457i	0.994606	+	0.103728i	$0.0330772\pi$
$677$			5.39786i			0.207457i	−0.994606	+	0.103728i	$0.966923\pi$
$678$		0			0
$679$	−1.06544			−0.0408878
$680$	−12.9767			−0.497633
$681$		0			0
$682$	1.03177	−	1.03177i	0.0395087	−	0.0395087i
$683$	−10.3603	+	10.3603i	−0.396425	+	0.396425i	−0.876970	−	0.480545i	$-0.840439\pi$
$683$	−10.3603	+	10.3603i	−0.396425	+	0.396425i	0.480545	+	0.876970i	$0.340439\pi$
$684$		0			0
$685$	−13.5723			−0.518569
$686$	−1.00000			−0.0381802
$687$		0			0
$688$			4.01105i			0.152920i
$689$	−9.61134	−	0.396831i	−0.366163	−	0.0151181i
$690$		0			0
$691$	−13.8730	+	13.8730i	−0.527753	+	0.527753i	−0.919902	−	0.392149i	$-0.871732\pi$
$691$	−13.8730	+	13.8730i	−0.527753	+	0.527753i	0.392149	+	0.919902i	$0.371732\pi$
$692$			4.73310i			0.179925i
$693$		0			0
$694$	21.1465	−	21.1465i	0.802710	−	0.802710i
$695$	−21.3150	−	21.3150i	−0.808525	−	0.808525i
$696$		0			0
$697$	−44.0195	−	44.0195i	−1.66736	−	1.66736i
$698$		−	12.4810i		−	0.472412i
$699$		0			0
$700$	0.282269	+	0.282269i	0.0106688	+	0.0106688i
$701$	−3.76297			−0.142126			−0.0710628	−	0.997472i	$-0.522639\pi$
$701$	−3.76297			−0.142126			−0.0710628	+	0.997472i	$0.522639\pi$
$702$		0			0
$703$	−1.28426			−0.0484369
$704$	−1.53031	−	1.53031i	−0.0576757	−	0.0576757i
$705$		0			0
$706$			2.69967i			0.101603i
$707$	−1.05214	−	1.05214i	−0.0395696	−	0.0395696i
$708$		0			0
$709$	−33.9937	−	33.9937i	−1.27666	−	1.27666i	−0.942526	−	0.334134i	$-0.891556\pi$
$709$	−33.9937	−	33.9937i	−1.27666	−	1.27666i	−0.334134	−	0.942526i	$-0.608444\pi$
$710$	12.3650	−	12.3650i	0.464051	−	0.464051i
$711$		0			0
$712$		−	6.85145i		−	0.256769i
$713$	−2.12043	+	2.12043i	−0.0794106	+	0.0794106i
$714$		0			0
$715$	0.747967	−	18.1159i	0.0279724	−	0.677497i
$716$			6.35128i			0.237359i
$717$		0			0
$718$	33.7074			1.25795
$719$	−37.8616			−1.41200			−0.706001	−	0.708211i	$-0.749502\pi$
$719$	−37.8616			−1.41200			−0.706001	+	0.708211i	$0.749502\pi$
$720$		0			0
$721$	−2.38005	+	2.38005i	−0.0886377	+	0.0886377i
$722$	13.3321	−	13.3321i	0.496170	−	0.496170i
$723$		0			0
$724$	−12.9313			−0.480586
$725$	2.43827			0.0905552
$726$		0			0
$727$		−	26.5558i		−	0.984899i	−0.870341	−	0.492449i	$-0.836102\pi$
$727$		−	26.5558i		−	0.984899i	0.870341	−	0.492449i	$-0.163898\pi$
$728$	0.148739	−	3.60248i	0.00551262	−	0.133517i
$729$		0			0
$730$	13.4888	−	13.4888i	0.499241	−	0.499241i
$731$		−	22.4005i		−	0.828512i
$732$		0			0
$733$	16.9806	−	16.9806i	0.627193	−	0.627193i	−0.320168	−	0.947361i	$-0.603739\pi$
$733$	16.9806	−	16.9806i	0.627193	−	0.627193i	0.947361	+	0.320168i	$0.103739\pi$
$734$	8.21377	+	8.21377i	0.303176	+	0.303176i
$735$		0			0
$736$	3.14498	+	3.14498i	0.115926	+	0.115926i
$737$			6.37290i			0.234749i
$738$		0			0
$739$	13.4039	+	13.4039i	0.493070	+	0.493070i	0.909272	−	0.416202i	$-0.136639\pi$
$739$	13.4039	+	13.4039i	0.493070	+	0.493070i	−0.416202	+	0.909272i	$0.636639\pi$
$740$	7.82201			0.287543
$741$		0			0
$742$	−2.66798			−0.0979446
$743$	17.6664	+	17.6664i	0.648116	+	0.648116i	0.952537	−	0.304421i	$-0.0984631\pi$
$743$	17.6664	+	17.6664i	0.648116	+	0.648116i	−0.304421	+	0.952537i	$0.598463\pi$
$744$		0			0
$745$			29.2279i			1.07083i
$746$	−24.9777	−	24.9777i	−0.914498	−	0.914498i
$747$		0			0
$748$	8.54632	+	8.54632i	0.312484	+	0.312484i
$749$	−0.978398	+	0.978398i	−0.0357499	+	0.0357499i
$750$		0			0
$751$			33.6709i			1.22867i	0.789045	+	0.614335i	$0.210576\pi$
$751$			33.6709i			1.22867i	−0.789045	+	0.614335i	$0.789424\pi$
$752$	1.17580	−	1.17580i	0.0428771	−	0.0428771i
$753$		0			0
$754$	−14.9169	−	16.2017i	−0.543242	−	0.590033i
$755$			13.7748i			0.501315i
$756$		0			0
$757$	−25.3843			−0.922607			−0.461304	−	0.887242i	$-0.652618\pi$
$757$	−25.3843			−0.922607			−0.461304	+	0.887242i	$0.652618\pi$
$758$	−24.0645			−0.874061
$759$		0			0
$760$	0.626830	−	0.626830i	0.0227375	−	0.0227375i
$761$	−14.0445	+	14.0445i	−0.509114	+	0.509114i	−0.914254	−	0.405140i	$-0.867223\pi$
$761$	−14.0445	+	14.0445i	−0.509114	+	0.509114i	0.405140	+	0.914254i	$0.367223\pi$
$762$		0			0
$763$	−5.97817			−0.216424
$764$	16.8092			0.608137
$765$		0			0
$766$			9.85702i			0.356149i
$767$	6.37860	+	6.92800i	0.230318	+	0.250156i
$768$		0			0
$769$	16.9392	−	16.9392i	0.610844	−	0.610844i	−0.332322	−	0.943166i	$-0.607832\pi$
$769$	16.9392	−	16.9392i	0.610844	−	0.610844i	0.943166	+	0.332322i	$0.107832\pi$
$770$		−	5.02874i		−	0.181223i
$771$		0			0
$772$	−5.83733	+	5.83733i	−0.210090	+	0.210090i
$773$	7.82875	+	7.82875i	0.281581	+	0.281581i	0.833739	−	0.552158i	$-0.186196\pi$
$773$	7.82875	+	7.82875i	0.281581	+	0.281581i	−0.552158	+	0.833739i	$0.686196\pi$
$774$		0			0
$775$	−0.190313	−	0.190313i	−0.00683625	−	0.00683625i
$776$		−	1.06544i		−	0.0382470i
$777$		0			0
$778$	−21.9809	−	21.9809i	−0.788055	−	0.788055i
$779$	4.25266			0.152368
$780$		0			0
$781$	−16.2870			−0.582793
$782$	−17.5638	−	17.5638i	−0.628079	−	0.628079i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$	−31.4063	−	31.4063i	−1.12094	−	1.12094i
$786$		0			0
$787$	−35.4794	−	35.4794i	−1.26470	−	1.26470i	−0.948787	−	0.315918i	$-0.897688\pi$
$787$	−35.4794	−	35.4794i	−1.26470	−	1.26470i	−0.315918	−	0.948787i	$-0.602312\pi$
$788$	3.11368	−	3.11368i	0.110920	−	0.110920i
$789$		0			0
$790$		−	4.76573i		−	0.169557i
$791$	−11.6751	+	11.6751i	−0.415118	+	0.415118i
$792$		0			0
$793$	0.154320	−	3.73767i	0.00548007	−	0.132729i
$794$			1.30110i			0.0461744i
$795$		0			0
$796$	−18.0613			−0.640165
$797$	42.1947			1.49461			0.747307	−	0.664479i	$-0.231346\pi$
$797$	42.1947			1.49461			0.747307	+	0.664479i	$0.231346\pi$
$798$		0			0
$799$	−6.56650	+	6.56650i	−0.232306	+	0.232306i
$800$	−0.282269	+	0.282269i	−0.00997972	+	0.00997972i
$801$		0			0
$802$	−6.80058			−0.240137
$803$	−17.7671			−0.626988
$804$		0			0
$805$			10.3347i			0.364250i
$806$	−0.100283	+	2.42889i	−0.00353233	+	0.0855538i
$807$		0			0
$808$	1.05214	−	1.05214i	0.0370140	−	0.0370140i
$809$		−	44.4852i		−	1.56402i	−0.623268	−	0.782009i	$-0.714195\pi$
$809$		−	44.4852i		−	1.56402i	0.623268	−	0.782009i	$-0.285805\pi$
$810$		0			0
$811$	−27.3005	+	27.3005i	−0.958652	+	0.958652i	−0.999178	−	0.0405265i	$-0.987096\pi$
$811$	−27.3005	+	27.3005i	−0.958652	+	0.958652i	0.0405265	+	0.999178i	$0.487096\pi$
$812$	−4.31906	−	4.31906i	−0.151569	−	0.151569i
$813$		0			0
$814$	−5.15150	−	5.15150i	−0.180560	−	0.180560i
$815$			43.8488i			1.53596i
$816$		0			0
$817$	1.08204	+	1.08204i	0.0378558	+	0.0378558i
$818$	−18.3449			−0.641413
$819$		0			0
$820$	−25.9015			−0.904520
$821$	21.6541	+	21.6541i	0.755735	+	0.755735i	0.975543	−	0.219808i	$-0.0705431\pi$
$821$	21.6541	+	21.6541i	0.755735	+	0.755735i	−0.219808	+	0.975543i	$0.570543\pi$
$822$		0			0
$823$		−	46.1645i		−	1.60919i	−0.593822	−	0.804596i	$-0.702382\pi$
$823$		−	46.1645i		−	1.60919i	0.593822	−	0.804596i	$-0.297618\pi$
$824$	−2.38005	−	2.38005i	−0.0829130	−	0.0829130i
$825$		0			0
$826$	1.84687	+	1.84687i	0.0642607	+	0.0642607i
$827$	−3.44205	+	3.44205i	−0.119692	+	0.119692i	−0.764416	−	0.644724i	$-0.776972\pi$
$827$	−3.44205	+	3.44205i	−0.119692	+	0.119692i	0.644724	+	0.764416i	$0.276972\pi$
$828$		0			0
$829$		−	0.659377i		−	0.0229011i	−0.999934	−	0.0114506i	$-0.996355\pi$
$829$		−	0.659377i		−	0.0229011i	0.999934	−	0.0114506i	$-0.00364491\pi$
$830$	20.5134	−	20.5134i	0.712030	−	0.712030i
$831$		0			0
$832$	3.60248	+	0.148739i	0.124894	+	0.00515658i
$833$			5.58470i			0.193498i
$834$		0			0
$835$	20.1155			0.696126
$836$	−0.825648			−0.0285556
$837$		0			0
$838$	−2.43573	+	2.43573i	−0.0841408	+	0.0841408i
$839$	4.33493	−	4.33493i	0.149658	−	0.149658i	−0.628307	−	0.777965i	$-0.716252\pi$
$839$	4.33493	−	4.33493i	0.149658	−	0.149658i	0.777965	+	0.628307i	$0.216252\pi$
$840$		0			0
$841$	−8.30852			−0.286501
$842$	−6.77858			−0.233605
$843$		0			0
$844$		−	4.56632i		−	0.157179i
$845$	19.5261	+	23.0477i	0.671718	+	0.792863i
$846$		0			0
$847$	4.46630	−	4.46630i	0.153464	−	0.153464i
$848$		−	2.66798i		−	0.0916188i
$849$		0			0
$850$	1.57639	−	1.57639i	0.0540696	−	0.0540696i
$851$	10.5870	+	10.5870i	0.362917	+	0.362917i
$852$		0			0
$853$	9.33289	+	9.33289i	0.319552	+	0.319552i	0.848595	−	0.529043i	$-0.177449\pi$
$853$	9.33289	+	9.33289i	0.319552	+	0.319552i	−0.529043	+	0.848595i	$0.677449\pi$
$854$		−	1.03753i		−	0.0355034i
$855$		0			0
$856$	−0.978398	−	0.978398i	−0.0334410	−	0.0334410i
$857$	10.9256			0.373211			0.186605	−	0.982435i	$-0.440251\pi$
$857$	10.9256			0.373211			0.186605	+	0.982435i	$0.440251\pi$
$858$		0			0
$859$	35.8523			1.22326			0.611632	−	0.791142i	$-0.290513\pi$
$859$	35.8523			1.22326			0.611632	+	0.791142i	$0.290513\pi$
$860$	−6.59034	−	6.59034i	−0.224729	−	0.224729i
$861$		0			0
$862$		−	21.9118i		−	0.746318i
$863$	6.58473	+	6.58473i	0.224147	+	0.224147i	0.810242	−	0.586095i	$-0.199336\pi$
$863$	6.58473	+	6.58473i	0.224147	+	0.224147i	−0.586095	+	0.810242i	$0.699336\pi$
$864$		0			0
$865$	−7.77669	−	7.77669i	−0.264415	−	0.264415i
$866$	29.1291	−	29.1291i	0.989846	−	0.989846i
$867$		0			0
$868$			0.674226i			0.0228847i
$869$	−3.13866	+	3.13866i	−0.106472	+	0.106472i
$870$		0			0
$871$	−7.19146	−	7.81088i	−0.243673	−	0.264661i
$872$		−	5.97817i		−	0.202446i
$873$		0			0
$874$	1.69681			0.0573955
$875$	10.6905			0.361405
$876$		0			0
$877$	−34.9867	+	34.9867i	−1.18142	+	1.18142i	−0.202040	+	0.979377i	$0.564757\pi$
$877$	−34.9867	+	34.9867i	−1.18142	+	1.18142i	−0.979377	+	0.202040i	$0.935243\pi$
$878$	11.5179	−	11.5179i	0.388710	−	0.388710i
$879$		0			0
$880$	5.02874			0.169519
$881$	23.5610			0.793791			0.396896	−	0.917864i	$-0.370087\pi$
$881$	23.5610			0.793791			0.396896	+	0.917864i	$0.370087\pi$
$882$		0			0
$883$			1.36002i			0.0457684i	0.999738	+	0.0228842i	$0.00728491\pi$
$883$			1.36002i			0.0457684i	−0.999738	+	0.0228842i	$0.992715\pi$
$884$	−20.1188	−	0.830659i	−0.676667	−	0.0279381i
$885$		0			0
$886$	−21.2746	+	21.2746i	−0.714735	+	0.714735i
$887$		−	10.8692i		−	0.364954i	−0.983210	−	0.182477i	$-0.941589\pi$
$887$		−	10.8692i		−	0.364954i	0.983210	−	0.182477i	$-0.0584115\pi$
$888$		0			0
$889$	−14.1086	+	14.1086i	−0.473186	+	0.473186i
$890$	11.2572	+	11.2572i	0.377343	+	0.377343i
$891$		0			0
$892$	12.2953	+	12.2953i	0.411677	+	0.411677i
$893$		−	0.634381i		−	0.0212287i
$894$		0			0
$895$	−10.4354	−	10.4354i	−0.348818	−	0.348818i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−32.0187			−1.06848
$899$	2.91202	+	2.91202i	0.0971213	+	0.0971213i
$900$		0			0
$901$			14.8998i			0.496386i
$902$	17.0585	+	17.0585i	0.567985	+	0.567985i
$903$		0			0
$904$	−11.6751	−	11.6751i	−0.388307	−	0.388307i
$905$	21.2466	−	21.2466i	0.706262	−	0.706262i
$906$		0			0
$907$			12.3624i			0.410487i	0.978711	+	0.205244i	$0.0657986\pi$
$907$			12.3624i			0.410487i	−0.978711	+	0.205244i	$0.934201\pi$
$908$	13.2910	−	13.2910i	0.441077	−	0.441077i
$909$		0			0
$910$	5.67465	+	6.16342i	0.188113	+	0.204315i
$911$		−	22.7992i		−	0.755371i	−0.925934	−	0.377685i	$-0.876720\pi$
$911$		−	22.7992i		−	0.755371i	0.925934	−	0.377685i	$-0.123280\pi$
$912$		0			0
$913$	−27.0198			−0.894226
$914$	−30.8321			−1.01983
$915$		0			0
$916$	−8.61423	+	8.61423i	−0.284622	+	0.284622i
$917$	8.62570	−	8.62570i	0.284846	−	0.284846i
$918$		0			0
$919$	−22.8130			−0.752532			−0.376266	−	0.926512i	$-0.622792\pi$
$919$	−22.8130			−0.752532			−0.376266	+	0.926512i	$0.622792\pi$
$920$	−10.3347			−0.340725
$921$		0			0
$922$			20.3440i			0.669994i
$923$	19.9620	−	18.3789i	0.657056	−	0.604950i
$924$		0			0
$925$	−0.950205	+	0.950205i	−0.0312426	+	0.0312426i
$926$		−	3.73926i		−	0.122880i
$927$		0			0
$928$	4.31906	−	4.31906i	0.141780	−	0.141780i
$929$	−27.1722	−	27.1722i	−0.891490	−	0.891490i	0.103173	−	0.994663i	$-0.467100\pi$
$929$	−27.1722	−	27.1722i	−0.891490	−	0.891490i	−0.994663	+	0.103173i	$0.967100\pi$
$930$		0			0
$931$	−0.269765	−	0.269765i	−0.00884118	−	0.00884118i
$932$		−	2.94207i		−	0.0963708i
$933$		0			0
$934$	18.8514	+	18.8514i	0.616837	+	0.616837i
$935$	−28.0840			−0.918444
$936$		0			0
$937$	23.5920			0.770719			0.385359	−	0.922767i	$-0.374078\pi$
$937$	23.5920			0.770719			0.385359	+	0.922767i	$0.374078\pi$
$938$	−2.08222	−	2.08222i	−0.0679870	−	0.0679870i
$939$		0			0
$940$			3.86379i			0.126023i
$941$	33.9675	+	33.9675i	1.10731	+	1.10731i	0.993503	+	0.113805i	$0.0363038\pi$
$941$	33.9675	+	33.9675i	1.10731	+	1.10731i	0.113805	+	0.993503i	$0.463696\pi$
$942$		0			0
$943$	−35.0574	−	35.0574i	−1.14162	−	1.14162i
$944$	−1.84687	+	1.84687i	−0.0601104	+	0.0601104i
$945$		0			0
$946$			8.68066i			0.282233i
$947$	−24.0942	+	24.0942i	−0.782956	+	0.782956i	−0.980329	−	0.197373i	$-0.936759\pi$
$947$	−24.0942	+	24.0942i	−0.782956	+	0.782956i	0.197373	+	0.980329i	$0.436759\pi$
$948$		0			0
$949$	21.7761	−	20.0492i	0.706882	−	0.650825i
$950$			0.152293i			0.00494102i
$951$		0			0
$952$	−5.58470			−0.181001
$953$	−47.4433			−1.53684			−0.768419	−	0.639947i	$-0.778956\pi$
$953$	−47.4433			−1.53684			−0.768419	+	0.639947i	$0.778956\pi$
$954$		0			0
$955$	−27.6183	+	27.6183i	−0.893708	+	0.893708i
$956$	−11.1260	+	11.1260i	−0.359841	+	0.359841i
$957$		0			0
$958$	11.0259			0.356231
$959$	−5.84101			−0.188616
$960$		0			0
$961$			30.5454i			0.985336i
$962$	12.1271	+	0.500700i	0.390992	+	0.0161432i
$963$		0			0
$964$	8.50173	−	8.50173i	0.273822	−	0.273822i
$965$		−	19.1820i		−	0.617490i
$966$		0			0
$967$	35.9011	−	35.9011i	1.15450	−	1.15450i	0.168863	−	0.985640i	$-0.445990\pi$
$967$	35.9011	−	35.9011i	1.15450	−	1.15450i	0.985640	−	0.168863i	$-0.0540095\pi$
$968$	4.46630	+	4.46630i	0.143552	+	0.143552i
$969$		0			0
$970$	1.75056	+	1.75056i	0.0562072	+	0.0562072i
$971$		−	23.9787i		−	0.769512i	−0.923018	−	0.384756i	$-0.874286\pi$
$971$		−	23.9787i		−	0.769512i	0.923018	−	0.384756i	$-0.125714\pi$
$972$		0			0
$973$	−9.17321	−	9.17321i	−0.294080	−	0.294080i
$974$	17.0899			0.547595
$975$		0			0
$976$	1.03753			0.0332104
$977$	8.45109	+	8.45109i	0.270374	+	0.270374i	0.829251	−	0.558876i	$-0.188767\pi$
$977$	8.45109	+	8.45109i	0.270374	+	0.270374i	−0.558876	+	0.829251i	$0.688767\pi$
$978$		0			0
$979$		−	14.8278i		−	0.473899i
$980$	1.64304	+	1.64304i	0.0524851	+	0.0524851i
$981$		0			0
$982$	−30.9336	−	30.9336i	−0.987131	−	0.987131i
$983$	33.2491	−	33.2491i	1.06048	−	1.06048i	0.0624314	−	0.998049i	$-0.480115\pi$
$983$	33.2491	−	33.2491i	1.06048	−	1.06048i	0.998049	−	0.0624314i	$-0.0198855\pi$
$984$		0			0
$985$			10.2318i			0.326014i
$986$	−24.1206	+	24.1206i	−0.768157	+	0.768157i
$987$		0			0
$988$	1.01195	−	0.931698i	0.0321943	−	0.0296413i
$989$		−	17.8399i		−	0.567275i
$990$		0			0
$991$	−18.1429			−0.576327			−0.288164	−	0.957581i	$-0.593045\pi$
$991$	−18.1429			−0.576327			−0.288164	+	0.957581i	$0.593045\pi$
$992$	−0.674226			−0.0214067
$993$		0			0
$994$	5.32146	−	5.32146i	0.168786	−	0.168786i
$995$	29.6755	−	29.6755i	0.940775	−	0.940775i
$996$		0			0
$997$	25.5884			0.810393			0.405197	−	0.914230i	$-0.367203\pi$
$997$	25.5884			0.810393			0.405197	+	0.914230i	$0.367203\pi$
$998$	−9.42540			−0.298356
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.y.d.1331.1	yes	16
3.2	odd	2		1638.2.y.c.1331.8	yes	16
13.8	odd	4		1638.2.y.c.827.8	✓	16
39.8	even	4	inner	1638.2.y.d.827.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.y.c.827.8	✓	16	13.8	odd	4
1638.2.y.c.1331.8	yes	16	3.2	odd	2
1638.2.y.d.827.1	yes	16	39.8	even	4	inner
1638.2.y.d.1331.1	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(-1.64304 - 1.64304i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.32362i q^{10} +(1.53031 - 1.53031i) q^{11} +(-0.148739 + 3.60248i) q^{13} +1.00000i q^{14} -1.00000 q^{16} +5.58470 q^{17} +(-0.269765 + 0.269765i) q^{19} +(1.64304 - 1.64304i) q^{20} -2.16419 q^{22} +4.44768 q^{23} +0.399189i q^{25} +(2.65251 - 2.44217i) q^{26} +(0.707107 - 0.707107i) q^{28} -6.10807i q^{29} +(-0.476750 + 0.476750i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.94898 - 3.94898i) q^{34} +2.32362i q^{35} +(2.38034 + 2.38034i) q^{37} +0.381505 q^{38} -2.32362 q^{40} +(-7.88217 - 7.88217i) q^{41} -4.01105i q^{43} +(1.53031 + 1.53031i) q^{44} +(-3.14498 - 3.14498i) q^{46} +(-1.17580 + 1.17580i) q^{47} +1.00000i q^{49} +(0.282269 - 0.282269i) q^{50} +(-3.60248 - 0.148739i) q^{52} +2.66798i q^{53} -5.02874 q^{55} -1.00000 q^{56} +(-4.31906 + 4.31906i) q^{58} +(1.84687 - 1.84687i) q^{59} -1.03753 q^{61} +0.674226 q^{62} -1.00000i q^{64} +(6.16342 - 5.67465i) q^{65} +(-2.08222 + 2.08222i) q^{67} +5.58470i q^{68} +(1.64304 - 1.64304i) q^{70} +(-5.32146 - 5.32146i) q^{71} +(-5.80507 - 5.80507i) q^{73} -3.36631i q^{74} +(-0.269765 - 0.269765i) q^{76} -2.16419 q^{77} -2.05100 q^{79} +(1.64304 + 1.64304i) q^{80} +11.1471i q^{82} +(-8.82822 - 8.82822i) q^{83} +(-9.17590 - 9.17590i) q^{85} +(-2.83624 + 2.83624i) q^{86} -2.16419i q^{88} +(4.84471 - 4.84471i) q^{89} +(2.65251 - 2.44217i) q^{91} +4.44768i q^{92} +1.66284 q^{94} +0.886471 q^{95} +(0.753379 - 0.753379i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{5} - 8 q^{11} + 4 q^{13} - 16 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{20} - 8 q^{22} + 24 q^{23} + 8 q^{26} - 8 q^{31} + 4 q^{34} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 8 q^{44} + 4 q^{47} - 16 q^{50}+ \cdots - 28 q^{97}+O(q^{100}) \) 16 * q + 4 * q^5 - 8 * q^11 + 4 * q^13 - 16 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^20 - 8 * q^22 + 24 * q^23 + 8 * q^26 - 8 * q^31 + 4 * q^34 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 8 * q^44 + 4 * q^47 - 16 * q^50 - 16 * q^55 - 16 * q^56 + 4 * q^58 - 8 * q^59 - 40 * q^61 + 24 * q^62 + 56 * q^65 - 4 * q^67 - 4 * q^70 - 24 * q^71 - 12 * q^73 + 16 * q^76 - 8 * q^77 + 16 * q^79 - 4 * q^80 + 8 * q^85 + 24 * q^86 + 16 * q^89 + 8 * q^91 - 8 * q^94 - 40 * q^95 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more