LMFDB - Embedded newform 2888.1.bb.a.419.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2888,1,Mod(115,2888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2888, base_ring=CyclotomicField(38))

chi = DirichletCharacter(H, H._module([19, 19, 4]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2888.115");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2888 = 2^{3} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2888.bb (of order $38$, degree $18$, 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:	$1.44129975648$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\Q(\zeta_{38})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} + \cdots + 1 $ x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{19}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{19} - \cdots)$

Embedding invariants

Embedding label			419.1
Root			$-0.546948 + 0.837166i$ of defining polynomial
Character	$\chi$	$=$	2888.419
Dual form			2888.1.bb.a.1027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.986361 - 0.164595i) q^{2} +(0.598305 + 0.915773i) q^{3} +(0.945817 + 0.324699i) q^{4} +(-0.439413 - 1.00176i) q^{6} +(-0.879474 - 0.475947i) q^{8} +(-0.0789770 + 0.180049i) q^{9} +O(q^{10})$	\(q+(-0.986361 - 0.164595i) q^{2} +(0.598305 + 0.915773i) q^{3} +(0.945817 + 0.324699i) q^{4} +(-0.439413 - 1.00176i) q^{6} +(-0.879474 - 0.475947i) q^{8} +(-0.0789770 + 0.180049i) q^{9} +(-0.759861 - 1.73231i) q^{11} +(0.268536 + 1.06042i) q^{12} +(0.789141 + 0.614213i) q^{16} +(1.49277 - 0.512467i) q^{17} +(0.107535 - 0.164595i) q^{18} +(-0.986361 + 0.164595i) q^{19} +(0.464369 + 1.83375i) q^{22} +(-0.0903332 - 1.09016i) q^{24} +(0.245485 + 0.969400i) q^{25} +(0.866840 - 0.144650i) q^{27} +(-0.677282 - 0.735724i) q^{32} +(1.13177 - 1.73231i) q^{33} +(-1.55676 + 0.259777i) q^{34} +(-0.133160 + 0.144650i) q^{36} +1.00000 q^{38} +(-0.0903332 + 1.09016i) q^{41} +(1.33609 - 1.45138i) q^{43} +(-0.156210 - 1.88517i) q^{44} +(-0.0903332 + 1.09016i) q^{48} +(0.789141 - 0.614213i) q^{49} +(-0.0825793 - 0.996584i) q^{50} +(1.36243 + 1.06042i) q^{51} -0.878826 q^{54} +(-0.740876 - 0.804806i) q^{57} +(0.162906 - 1.96598i) q^{59} +(0.546948 + 0.837166i) q^{64} +(-1.40147 + 1.52240i) q^{66} +(0.706561 + 0.382372i) q^{67} +1.57828 q^{68} +(0.155152 - 0.120760i) q^{72} +(-0.156210 + 0.0536269i) q^{73} +(-0.740876 + 0.804806i) q^{75} +(-0.986361 - 0.164595i) q^{76} +(0.784261 + 0.851934i) q^{81} +(0.268536 - 1.06042i) q^{82} +(1.24549 - 0.969400i) q^{83} +(-1.55676 + 1.21167i) q^{86} +(-0.156210 + 1.88517i) q^{88} +(1.49277 + 0.512467i) q^{89} +(0.268536 - 1.06042i) q^{96} +(-1.75895 + 0.951895i) q^{97} +(-0.879474 + 0.475947i) q^{98} +0.371913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9}+O(q^{10}) $ 18 * q - q^2 + 17 * q^3 - q^4 - 2 * q^6 - q^8 + 16 * q^9	$ 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9} - 2 q^{11} - 2 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} - q^{19} - 2 q^{22} - 2 q^{24} - q^{25} + 15 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} + 18 q^{38} - 2 q^{41} - 2 q^{43} - 2 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} - 4 q^{54} - 2 q^{57} - 2 q^{59} - q^{64} - 4 q^{66} - 2 q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} - 2 q^{75} - q^{76} + 14 q^{81} - 2 q^{82} + 17 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} - 2 q^{97} - q^{98} - 6 q^{99}+O(q^{100}) $ 18 * q - q^2 + 17 * q^3 - q^4 - 2 * q^6 - q^8 + 16 * q^9 - 2 * q^11 - 2 * q^12 - q^16 - 2 * q^17 - 3 * q^18 - q^19 - 2 * q^22 - 2 * q^24 - q^25 + 15 * q^27 - q^32 - 4 * q^33 - 2 * q^34 - 3 * q^36 + 18 * q^38 - 2 * q^41 - 2 * q^43 - 2 * q^44 - 2 * q^48 - q^49 - q^50 - 4 * q^51 - 4 * q^54 - 2 * q^57 - 2 * q^59 - q^64 - 4 * q^66 - 2 * q^67 - 2 * q^68 - 3 * q^72 - 2 * q^73 - 2 * q^75 - q^76 + 14 * q^81 - 2 * q^82 + 17 * q^83 - 2 * q^86 - 2 * q^88 - 2 * q^89 - 2 * q^96 - 2 * q^97 - q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times$.

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{19}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.986361	−	0.164595i	−0.986361	−	0.164595i
$2$	−0.986361	−	0.164595i	−0.986361	−	0.164595i
$3$	0.598305	+	0.915773i	0.598305	+	0.915773i	1.00000			$0$
$3$	0.598305	+	0.915773i	0.598305	+	0.915773i	−0.401695	+	0.915773i	$0.631579\pi$
$4$	0.945817	+	0.324699i	0.945817	+	0.324699i
$5$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$5$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$6$	−0.439413	−	1.00176i	−0.439413	−	1.00176i
$7$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$7$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$8$	−0.879474	−	0.475947i	−0.879474	−	0.475947i
$9$	−0.0789770	+	0.180049i	−0.0789770	+	0.180049i
$10$		0			0
$11$	−0.759861	−	1.73231i	−0.759861	−	1.73231i	−0.677282	−	0.735724i	$-0.736842\pi$
$11$	−0.759861	−	1.73231i	−0.759861	−	1.73231i	−0.0825793	−	0.996584i	$-0.526316\pi$
$12$	0.268536	+	1.06042i	0.268536	+	1.06042i
$13$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$13$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$14$		0			0
$15$		0			0
$16$	0.789141	+	0.614213i	0.789141	+	0.614213i
$17$	1.49277	−	0.512467i	1.49277	−	0.512467i	0.546948	−	0.837166i	$-0.315789\pi$
$17$	1.49277	−	0.512467i	1.49277	−	0.512467i	0.945817	+	0.324699i	$0.105263\pi$
$18$	0.107535	−	0.164595i	0.107535	−	0.164595i
$19$	−0.986361	+	0.164595i	−0.986361	+	0.164595i
$19$	−0.986361	+	0.164595i	−0.986361	+	0.164595i
$20$		0			0
$21$		0			0
$22$	0.464369	+	1.83375i	0.464369	+	1.83375i
$23$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$23$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$24$	−0.0903332	−	1.09016i	−0.0903332	−	1.09016i
$25$	0.245485	+	0.969400i	0.245485	+	0.969400i
$26$		0			0
$27$	0.866840	−	0.144650i	0.866840	−	0.144650i
$28$		0			0
$29$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$29$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$30$		0			0
$31$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$31$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$32$	−0.677282	−	0.735724i	−0.677282	−	0.735724i
$33$	1.13177	−	1.73231i	1.13177	−	1.73231i
$34$	−1.55676	+	0.259777i	−1.55676	+	0.259777i
$35$		0			0
$36$	−0.133160	+	0.144650i	−0.133160	+	0.144650i
$37$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$37$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$38$	1.00000			1.00000
$39$		0			0
$40$		0			0
$41$	−0.0903332	+	1.09016i	−0.0903332	+	1.09016i	0.789141	+	0.614213i	$0.210526\pi$
$41$	−0.0903332	+	1.09016i	−0.0903332	+	1.09016i	−0.879474	+	0.475947i	$0.842105\pi$
$42$		0			0
$43$	1.33609	−	1.45138i	1.33609	−	1.45138i	0.546948	−	0.837166i	$-0.315789\pi$
$43$	1.33609	−	1.45138i	1.33609	−	1.45138i	0.789141	−	0.614213i	$-0.210526\pi$
$44$	−0.156210	−	1.88517i	−0.156210	−	1.88517i
$45$		0			0
$46$		0			0
$47$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$47$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$48$	−0.0903332	+	1.09016i	−0.0903332	+	1.09016i
$49$	0.789141	−	0.614213i	0.789141	−	0.614213i
$50$	−0.0825793	−	0.996584i	−0.0825793	−	0.996584i
$51$	1.36243	+	1.06042i	1.36243	+	1.06042i
$52$		0			0
$53$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$53$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$54$	−0.878826			−0.878826
$55$		0			0
$56$		0			0
$57$	−0.740876	−	0.804806i	−0.740876	−	0.804806i
$58$		0			0
$59$	0.162906	−	1.96598i	0.162906	−	1.96598i	−0.0825793	−	0.996584i	$-0.526316\pi$
$59$	0.162906	−	1.96598i	0.162906	−	1.96598i	0.245485	−	0.969400i	$-0.421053\pi$
$60$		0			0
$61$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$61$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$62$		0			0
$63$		0			0
$64$	0.546948	+	0.837166i	0.546948	+	0.837166i
$65$		0			0
$66$	−1.40147	+	1.52240i	−1.40147	+	1.52240i
$67$	0.706561	+	0.382372i	0.706561	+	0.382372i	0.789141	−	0.614213i	$-0.210526\pi$
$67$	0.706561	+	0.382372i	0.706561	+	0.382372i	−0.0825793	+	0.996584i	$0.526316\pi$
$68$	1.57828			1.57828
$69$		0			0
$70$		0			0
$71$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$71$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$72$	0.155152	−	0.120760i	0.155152	−	0.120760i
$73$	−0.156210	+	0.0536269i	−0.156210	+	0.0536269i	−0.401695	−	0.915773i	$-0.631579\pi$
$73$	−0.156210	+	0.0536269i	−0.156210	+	0.0536269i	0.245485	+	0.969400i	$0.421053\pi$
$74$		0			0
$75$	−0.740876	+	0.804806i	−0.740876	+	0.804806i
$76$	−0.986361	−	0.164595i	−0.986361	−	0.164595i
$77$		0			0
$78$		0			0
$79$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$79$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$80$		0			0
$81$	0.784261	+	0.851934i	0.784261	+	0.851934i
$82$	0.268536	−	1.06042i	0.268536	−	1.06042i
$83$	1.24549	−	0.969400i	1.24549	−	0.969400i	0.245485	−	0.969400i	$-0.421053\pi$
$83$	1.24549	−	0.969400i	1.24549	−	0.969400i	1.00000			$0$
$84$		0			0
$85$		0			0
$86$	−1.55676	+	1.21167i	−1.55676	+	1.21167i
$87$		0			0
$88$	−0.156210	+	1.88517i	−0.156210	+	1.88517i
$89$	1.49277	+	0.512467i	1.49277	+	0.512467i	0.945817	−	0.324699i	$-0.105263\pi$
$89$	1.49277	+	0.512467i	1.49277	+	0.512467i	0.546948	+	0.837166i	$0.315789\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.268536	−	1.06042i	0.268536	−	1.06042i
$97$	−1.75895	+	0.951895i	−1.75895	+	0.951895i	−0.879474	+	0.475947i	$0.842105\pi$
$97$	−1.75895	+	0.951895i	−1.75895	+	0.951895i	−0.879474	+	0.475947i	$0.842105\pi$
$98$	−0.879474	+	0.475947i	−0.879474	+	0.475947i
$99$	0.371913			0.371913
$100$	−0.0825793	+	0.996584i	−0.0825793	+	0.996584i
$101$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$101$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$102$	−1.16931	−	1.27021i	−1.16931	−	1.27021i
$103$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$103$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.162906	+	0.0271842i	0.162906	+	0.0271842i	0.245485	−	0.969400i	$-0.421053\pi$
$107$	0.162906	+	0.0271842i	0.162906	+	0.0271842i	−0.0825793	+	0.996584i	$0.526316\pi$
$108$	0.866840	+	0.144650i	0.866840	+	0.144650i
$109$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$109$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.86584	−	0.640542i	−1.86584	−	0.640542i	−0.986361	−	0.164595i	$-0.947368\pi$
$113$	−1.86584	−	0.640542i	−1.86584	−	0.640542i	−0.879474	−	0.475947i	$-0.842105\pi$
$114$	0.598305	+	0.915773i	0.598305	+	0.915773i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.484275	+	1.91236i	−0.484275	+	1.91236i
$119$		0			0
$120$		0			0
$121$	−1.74622	+	1.89690i	−1.74622	+	1.89690i
$122$		0			0
$123$	−1.05239	+	0.569523i	−1.05239	+	0.569523i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−0.401695	−	0.915773i	−0.401695	−	0.915773i
$129$	2.12852	+	0.355188i	2.12852	+	0.355188i
$130$		0			0
$131$	−1.55676	+	0.259777i	−1.55676	+	0.259777i	−0.879474	−	0.475947i	$-0.842105\pi$
$131$	−1.55676	+	0.259777i	−1.55676	+	0.259777i	−0.677282	+	0.735724i	$0.736842\pi$
$132$	1.63293	−	1.27096i	1.63293	−	1.27096i
$133$		0			0
$134$	−0.633988	−	0.493453i	−0.633988	−	0.493453i
$135$		0			0
$136$	−1.55676	−	0.259777i	−1.55676	−	0.259777i
$137$	1.19130	+	0.644701i	1.19130	+	0.644701i	0.945817	−	0.324699i	$-0.105263\pi$
$137$	1.19130	+	0.644701i	1.19130	+	0.644701i	0.245485	+	0.969400i	$0.421053\pi$
$138$		0			0
$139$	−0.332526	+	0.361219i	−0.332526	+	0.361219i	−0.879474	−	0.475947i	$-0.842105\pi$
$139$	−0.332526	+	0.361219i	−0.332526	+	0.361219i	0.546948	+	0.837166i	$0.315789\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.172913	+	0.0935756i	−0.172913	+	0.0935756i
$145$		0			0
$146$	0.162906	−	0.0271842i	0.162906	−	0.0271842i
$147$	1.03463	+	0.355188i	1.03463	+	0.355188i
$148$		0			0
$149$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$149$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$150$	0.863238	−	0.671885i	0.863238	−	0.671885i
$151$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$151$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$152$	0.945817	+	0.324699i	0.945817	+	0.324699i
$153$	−0.0256247	+	0.309245i	−0.0256247	+	0.309245i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$157$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.633341	−	0.969400i	−0.633341	−	0.969400i
$163$	−0.484275	−	0.0808112i	−0.484275	−	0.0808112i	−0.0825793	−	0.996584i	$-0.526316\pi$
$163$	−0.484275	−	0.0808112i	−0.484275	−	0.0808112i	−0.401695	+	0.915773i	$0.631579\pi$
$164$	−0.439413	+	1.00176i	−0.439413	+	1.00176i
$165$		0			0
$166$	−1.38806	+	0.751179i	−1.38806	+	0.751179i
$167$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$167$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$168$		0			0
$169$	−0.401695	+	0.915773i	−0.401695	+	0.915773i
$170$		0			0
$171$	0.0482647	−	0.190593i	0.0482647	−	0.190593i
$172$	1.73496	−	0.938912i	1.73496	−	0.938912i
$173$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$173$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$174$		0			0
$175$		0			0
$176$	0.464369	−	1.83375i	0.464369	−	1.83375i
$177$	1.89786	−	1.02707i	1.89786	−	1.02707i
$178$	−1.38806	−	0.751179i	−1.38806	−	0.751179i
$179$	1.33609	+	1.45138i	1.33609	+	1.45138i	0.789141	+	0.614213i	$0.210526\pi$
$179$	1.33609	+	1.45138i	1.33609	+	1.45138i	0.546948	+	0.837166i	$0.315789\pi$
$180$		0			0
$181$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$181$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.02204	−	2.19653i	−2.02204	−	2.19653i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$191$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$192$	−0.439413	+	1.00176i	−0.439413	+	1.00176i
$193$	0.322718	+	0.735724i	0.322718	+	0.735724i	1.00000			$0$
$193$	0.322718	+	0.735724i	0.322718	+	0.735724i	−0.677282	+	0.735724i	$0.736842\pi$
$194$	1.89163	−	0.649399i	1.89163	−	0.649399i
$195$		0			0
$196$	0.945817	−	0.324699i	0.945817	−	0.324699i
$197$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$197$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$198$	−0.366840	−	0.0612148i	−0.366840	−	0.0612148i
$199$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$199$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$200$	0.245485	−	0.969400i	0.245485	−	0.969400i
$201$	0.0725729	+	0.875825i	0.0725729	+	0.875825i
$202$		0			0
$203$		0			0
$204$	0.944293	+	1.44535i	0.944293	+	1.44535i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.03463	+	1.58361i	1.03463	+	1.58361i
$210$		0			0
$211$	−1.38806	+	1.08037i	−1.38806	+	1.08037i	−0.401695	+	0.915773i	$0.631579\pi$
$211$	−1.38806	+	1.08037i	−1.38806	+	1.08037i	−0.986361	+	0.164595i	$0.947368\pi$
$212$		0			0
$213$		0			0
$214$	−0.156210	−	0.0536269i	−0.156210	−	0.0536269i
$215$		0			0
$216$	−0.831209	−	0.285354i	−0.831209	−	0.285354i
$217$		0			0
$218$		0			0
$219$	−0.142571	−	0.110968i	−0.142571	−	0.110968i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$223$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$224$		0			0
$225$	−0.193928	−	0.0323608i	−0.193928	−	0.0323608i
$226$	1.73496	+	0.938912i	1.73496	+	0.938912i
$227$	−1.38806	−	1.08037i	−1.38806	−	1.08037i	−0.986361	−	0.164595i	$-0.947368\pi$
$227$	−1.38806	−	1.08037i	−1.38806	−	1.08037i	−0.401695	−	0.915773i	$-0.631579\pi$
$228$	−0.439413	−	1.00176i	−0.439413	−	1.00176i
$229$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$229$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.803391	−	1.83155i	−0.803391	−	1.83155i	−0.401695	−	0.915773i	$-0.631579\pi$
$233$	−0.803391	−	1.83155i	−0.803391	−	1.83155i	−0.401695	−	0.915773i	$-0.631579\pi$
$234$		0			0
$235$		0			0
$236$	0.792434	−	1.80657i	0.792434	−	1.80657i
$237$		0			0
$238$		0			0
$239$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$239$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$240$		0			0
$241$	−0.0903332	+	0.138265i	−0.0903332	+	0.138265i	−0.879474	−	0.475947i	$-0.842105\pi$
$241$	−0.0903332	+	0.138265i	−0.0903332	+	0.138265i	0.789141	+	0.614213i	$0.210526\pi$
$242$	2.03463	−	1.58361i	2.03463	−	1.58361i
$243$	−0.0952129	+	0.375987i	−0.0952129	+	0.375987i
$244$		0			0
$245$		0			0
$246$	1.13177	−	0.388538i	1.13177	−	0.388538i
$247$		0			0
$248$		0			0
$249$	1.63293	+	0.560586i	1.63293	+	0.560586i
$250$		0			0
$251$	−0.759861	+	1.73231i	−0.759861	+	1.73231i	−0.0825793	+	0.996584i	$0.526316\pi$
$251$	−0.759861	+	1.73231i	−0.759861	+	1.73231i	−0.677282	+	0.735724i	$0.736842\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.245485	+	0.969400i	0.245485	+	0.969400i
$257$	0.0663435	+	0.800647i	0.0663435	+	0.800647i	0.945817	+	0.324699i	$0.105263\pi$
$257$	0.0663435	+	0.800647i	0.0663435	+	0.800647i	−0.879474	+	0.475947i	$0.842105\pi$
$258$	−2.04103	−	0.700687i	−2.04103	−	0.700687i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.57828			1.57828
$263$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$263$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$264$	−1.81985	+	0.984855i	−1.81985	+	0.984855i
$265$		0			0
$266$		0			0
$267$	0.423825	+	1.67365i	0.423825	+	1.67365i
$268$	0.544122	+	0.591074i	0.544122	+	0.591074i
$269$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$269$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$270$		0			0
$271$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$271$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$272$	1.49277	+	0.512467i	1.49277	+	0.512467i
$273$		0			0
$274$	−1.06894	−	0.831990i	−1.06894	−	0.831990i
$275$	1.49277	−	1.16187i	1.49277	−	1.16187i
$276$		0			0
$277$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$277$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$278$	0.387445	−	0.301561i	0.387445	−	0.301561i
$279$		0			0
$280$		0			0
$281$	−0.431796	−	1.70512i	−0.431796	−	1.70512i	−0.677282	−	0.735724i	$-0.736842\pi$
$281$	−0.431796	−	1.70512i	−0.431796	−	1.70512i	0.245485	−	0.969400i	$-0.421053\pi$
$282$		0			0
$283$	1.09390	−	1.67433i	1.09390	−	1.67433i	0.546948	−	0.837166i	$-0.315789\pi$
$283$	1.09390	−	1.67433i	1.09390	−	1.67433i	0.546948	−	0.837166i	$-0.315789\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.185956	−	0.0638389i	0.185956	−	0.0638389i
$289$	1.17659	−	0.915773i	1.17659	−	0.915773i
$290$		0			0
$291$	−1.92411	−	1.04127i	−1.92411	−	1.04127i
$292$	−0.165159			−0.165159
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	−0.962053	−	0.520637i	−0.962053	−	0.520637i
$295$		0			0
$296$		0			0
$297$	−0.909257	−	1.39172i	−0.909257	−	1.39172i
$298$		0			0
$299$		0			0
$300$	−0.962053	+	0.520637i	−0.962053	+	0.520637i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.879474	−	0.475947i	−0.879474	−	0.475947i
$305$		0			0
$306$	0.0761752	−	0.300809i	0.0761752	−	0.300809i
$307$	1.09390			1.09390			0.546948	−	0.837166i	$-0.315789\pi$
$307$	1.09390			1.09390			0.546948	+	0.837166i	$0.315789\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$311$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$312$		0			0
$313$	0.111859	−	1.34994i	0.111859	−	1.34994i	−0.677282	−	0.735724i	$-0.736842\pi$
$313$	0.111859	−	1.34994i	0.111859	−	1.34994i	0.789141	−	0.614213i	$-0.210526\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$317$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.0725729	+	0.165450i	0.0725729	+	0.165450i
$322$		0			0
$323$	−1.38806	+	0.751179i	−1.38806	+	0.751179i
$324$	0.465145	+	1.06042i	0.465145	+	1.06042i
$325$		0			0
$326$	0.464369	+	0.159418i	0.464369	+	0.159418i
$327$		0			0
$328$	0.598305	−	0.915773i	0.598305	−	0.915773i
$329$		0			0
$330$		0			0
$331$	−0.431796	+	1.70512i	−0.431796	+	1.70512i	0.245485	+	0.969400i	$0.421053\pi$
$331$	−0.431796	+	1.70512i	−0.431796	+	1.70512i	−0.677282	+	0.735724i	$0.736842\pi$
$332$	1.49277	−	0.512467i	1.49277	−	0.512467i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.0405441	−	0.489294i	−0.0405441	−	0.489294i	−0.986361	−	0.164595i	$-0.947368\pi$
$337$	−0.0405441	−	0.489294i	−0.0405441	−	0.489294i	0.945817	−	0.324699i	$-0.105263\pi$
$338$	0.546948	−	0.837166i	0.546948	−	0.837166i
$339$	−0.529746	−	2.09192i	−0.529746	−	2.09192i
$340$		0			0
$341$		0			0
$342$	−0.0789770	+	0.180049i	−0.0789770	+	0.180049i
$343$		0			0
$344$	−1.86584	+	0.640542i	−1.86584	+	0.640542i
$345$		0			0
$346$		0			0
$347$	−1.86584	+	0.311353i	−1.86584	+	0.311353i	−0.986361	−	0.164595i	$-0.947368\pi$
$347$	−1.86584	+	0.311353i	−1.86584	+	0.311353i	−0.879474	+	0.475947i	$0.842105\pi$
$348$		0			0
$349$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$349$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$350$		0			0
$351$		0			0
$352$	−0.759861	+	1.73231i	−0.759861	+	1.73231i
$353$	−0.431796	−	0.233676i	−0.431796	−	0.233676i	0.245485	−	0.969400i	$-0.421053\pi$
$353$	−0.431796	−	0.233676i	−0.431796	−	0.233676i	−0.677282	+	0.735724i	$0.736842\pi$
$354$	−2.04103	+	0.700687i	−2.04103	+	0.700687i
$355$		0			0
$356$	1.24549	+	0.969400i	1.24549	+	0.969400i
$357$		0			0
$358$	−1.07898	−	1.65150i	−1.07898	−	1.65150i
$359$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$359$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$360$		0			0
$361$	0.945817	−	0.324699i	0.945817	−	0.324699i
$362$		0			0
$363$	−2.78191	−	0.464218i	−2.78191	−	0.464218i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$367$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$368$		0			0
$369$	−0.189148	−	0.102362i	−0.189148	−	0.102362i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$373$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$374$	1.63293	+	2.49939i	1.63293	+	2.49939i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.439413	+	0.672572i	−0.439413	+	0.672572i	−0.986361	−	0.164595i	$-0.947368\pi$
$379$	−0.439413	+	0.672572i	−0.439413	+	0.672572i	0.546948	+	0.837166i	$0.315789\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$383$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$384$	0.598305	−	0.915773i	0.598305	−	0.915773i
$385$		0			0
$386$	−0.197221	−	0.778807i	−0.197221	−	0.778807i
$387$	0.155800	+	0.355188i	0.155800	+	0.355188i
$388$	−1.97272	+	0.329189i	−1.97272	+	0.329189i
$389$		0			0		1.00000			$0$
$389$		0			0		−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$	−0.986361	+	0.164595i	−0.986361	+	0.164595i
$393$	−1.16931	−	1.27021i	−1.16931	−	1.27021i
$394$		0			0
$395$		0			0
$396$	0.351761	+	0.120760i	0.351761	+	0.120760i
$397$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$397$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$398$		0			0
$399$		0			0
$400$	−0.401695	+	0.915773i	−0.401695	+	0.915773i
$401$	0.544122	+	1.24047i	0.544122	+	1.24047i	0.945817	+	0.324699i	$0.105263\pi$
$401$	0.544122	+	1.24047i	0.544122	+	1.24047i	−0.401695	+	0.915773i	$0.631579\pi$
$402$	0.0725729	−	0.875825i	0.0725729	−	0.875825i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.693517	−	1.58106i	−0.693517	−	1.58106i
$409$	0.145253	−	1.75294i	0.145253	−	1.75294i	−0.401695	−	0.915773i	$-0.631579\pi$
$409$	0.145253	−	1.75294i	0.145253	−	1.75294i	0.546948	−	0.837166i	$-0.315789\pi$
$410$		0			0
$411$	0.122362	+	1.47669i	0.122362	+	1.47669i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.529746	−	0.0883990i	−0.529746	−	0.0883990i
$418$	−0.759861	−	1.73231i	−0.759861	−	1.73231i
$419$	−1.86584	+	0.311353i	−1.86584	+	0.311353i	−0.986361	−	0.164595i	$-0.947368\pi$
$419$	−1.86584	+	0.311353i	−1.86584	+	0.311353i	−0.879474	+	0.475947i	$0.842105\pi$
$420$		0			0
$421$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$421$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$422$	1.54695	−	0.837166i	1.54695	−	0.837166i
$423$		0			0
$424$		0			0
$425$	0.863238	+	1.32128i	0.863238	+	1.32128i
$426$		0			0
$427$		0			0
$428$	0.145253	+	0.0786068i	0.145253	+	0.0786068i
$429$		0			0
$430$		0			0
$431$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$431$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$432$	0.772905	+	0.418275i	0.772905	+	0.418275i
$433$	0.863238	−	0.671885i	0.863238	−	0.671885i	−0.0825793	−	0.996584i	$-0.526316\pi$
$433$	0.863238	−	0.671885i	0.863238	−	0.671885i	0.945817	+	0.324699i	$0.105263\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.122362	+	0.132921i	0.122362	+	0.132921i
$439$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$439$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$440$		0			0
$441$	0.0482647	+	0.190593i	0.0482647	+	0.190593i
$442$		0			0
$443$	−0.484275	+	1.91236i	−0.484275	+	1.91236i	−0.0825793	+	0.996584i	$0.526316\pi$
$443$	−0.484275	+	1.91236i	−0.484275	+	1.91236i	−0.401695	+	0.915773i	$0.631579\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.0903332	+	1.09016i	−0.0903332	+	1.09016i	0.789141	+	0.614213i	$0.210526\pi$
$449$	−0.0903332	+	1.09016i	−0.0903332	+	1.09016i	−0.879474	+	0.475947i	$0.842105\pi$
$450$	0.185956	+	0.0638389i	0.185956	+	0.0638389i
$451$	1.95713	−	0.671885i	1.95713	−	0.671885i
$452$	−1.55676	−	1.21167i	−1.55676	−	1.21167i
$453$		0			0
$454$	1.19130	+	1.29410i	1.19130	+	1.29410i
$455$		0			0
$456$	0.268536	+	1.06042i	0.268536	+	1.06042i
$457$	−0.431796	+	1.70512i	−0.431796	+	1.70512i	0.245485	+	0.969400i	$0.421053\pi$
$457$	−0.431796	+	1.70512i	−0.431796	+	1.70512i	−0.677282	+	0.735724i	$0.736842\pi$
$458$		0			0
$459$	1.21986	−	0.660156i	1.21986	−	0.660156i
$460$		0			0
$461$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$461$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$462$		0			0
$463$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$463$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$464$		0			0
$465$		0			0
$466$	0.490971	+	1.93880i	0.490971	+	1.93880i
$467$	−0.0405441	−	0.160105i	−0.0405441	−	0.160105i	0.945817	−	0.324699i	$-0.105263\pi$
$467$	−0.0405441	−	0.160105i	−0.0405441	−	0.160105i	−0.986361	+	0.164595i	$0.947368\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.07898	+	1.65150i	−1.07898	+	1.65150i
$473$	−3.52948	−	1.21167i	−3.52948	−	1.21167i
$474$		0			0
$475$	−0.401695	−	0.915773i	−0.401695	−	0.915773i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$479$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$480$		0			0
$481$		0			0
$482$	0.111859	−	0.121511i	0.111859	−	0.121511i
$483$		0			0
$484$	−2.26753	+	1.22713i	−2.26753	+	1.22713i
$485$		0			0
$486$	0.155800	−	0.355188i	0.155800	−	0.355188i
$487$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$487$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$488$		0			0
$489$	−0.215739	−	0.491836i	−0.215739	−	0.491836i
$490$		0			0
$491$	−0.332526	+	1.31311i	−0.332526	+	1.31311i	0.546948	+	0.837166i	$0.315789\pi$
$491$	−0.332526	+	1.31311i	−0.332526	+	1.31311i	−0.879474	+	0.475947i	$0.842105\pi$
$492$	−1.18029	+	0.196955i	−1.18029	+	0.196955i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.51839	−	0.821712i	−1.51839	−	0.821712i
$499$	1.73496	+	0.289513i	1.73496	+	0.289513i	0.945817	−	0.324699i	$-0.105263\pi$
$499$	1.73496	+	0.289513i	1.73496	+	0.289513i	0.789141	+	0.614213i	$0.210526\pi$
$500$		0			0
$501$		0			0
$502$	1.03463	−	1.58361i	1.03463	−	1.58361i
$503$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$503$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.07898	+	0.180049i	−1.07898	+	0.180049i
$508$		0			0
$509$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$509$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$510$		0			0
$511$		0			0
$512$	−0.0825793	−	0.996584i	−0.0825793	−	0.996584i
$513$	−0.831209	+	0.285354i	−0.831209	+	0.285354i
$514$	0.0663435	−	0.800647i	0.0663435	−	0.800647i
$515$		0			0
$516$	1.89786	+	1.02707i	1.89786	+	1.02707i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.156210	−	1.88517i	−0.156210	−	1.88517i	−0.401695	−	0.915773i	$-0.631579\pi$
$521$	−0.156210	−	1.88517i	−0.156210	−	1.88517i	0.245485	−	0.969400i	$-0.421053\pi$
$522$		0			0
$523$	0.863238	+	1.32128i	0.863238	+	1.32128i	0.945817	+	0.324699i	$0.105263\pi$
$523$	0.863238	+	1.32128i	0.863238	+	1.32128i	−0.0825793	+	0.996584i	$0.526316\pi$
$524$	−1.55676	−	0.259777i	−1.55676	−	0.259777i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.95713	−	0.671885i	1.95713	−	0.671885i
$529$	−0.401695	−	0.915773i	−0.401695	−	0.915773i
$530$		0			0
$531$	0.341109	+	0.184599i	0.341109	+	0.184599i
$532$		0			0
$533$		0			0
$534$	−0.142571	−	1.72058i	−0.142571	−	1.72058i
$535$		0			0
$536$	−0.439413	−	0.672572i	−0.439413	−	0.672572i
$537$	−0.529746	+	2.09192i	−0.529746	+	2.09192i
$538$		0			0
$539$	−1.66364	−	0.900319i	−1.66364	−	0.900319i
$540$		0			0
$541$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$541$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$542$		0			0
$543$		0			0
$544$	−1.38806	−	0.751179i	−1.38806	−	0.751179i
$545$		0			0
$546$		0			0
$547$	−0.439413	−	0.672572i	−0.439413	−	0.672572i	0.546948	−	0.837166i	$-0.315789\pi$
$547$	−0.439413	−	0.672572i	−0.439413	−	0.672572i	−0.986361	+	0.164595i	$0.947368\pi$
$548$	0.917421	+	0.996584i	0.917421	+	0.996584i
$549$		0			0
$550$	−1.66364	+	0.900319i	−1.66364	+	0.900319i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.431796	+	0.233676i	−0.431796	+	0.233676i
$557$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$557$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.801722	−	3.16593i	0.801722	−	3.16593i
$562$	0.145253	+	1.75294i	0.145253	+	1.75294i
$563$	−0.0903332	+	0.138265i	−0.0903332	+	0.138265i	−0.879474	−	0.475947i	$-0.842105\pi$
$563$	−0.0903332	+	0.138265i	−0.0903332	+	0.138265i	0.789141	+	0.614213i	$0.210526\pi$
$564$		0			0
$565$		0			0
$566$	−1.35456	+	1.47145i	−1.35456	+	1.47145i
$567$		0			0
$568$		0			0
$569$	0.111859	−	1.34994i	0.111859	−	1.34994i	−0.677282	−	0.735724i	$-0.736842\pi$
$569$	0.111859	−	1.34994i	0.111859	−	1.34994i	0.789141	−	0.614213i	$-0.210526\pi$
$570$		0			0
$571$	0.0136387	+	0.164595i	0.0136387	+	0.164595i	1.00000			$0$
$571$	0.0136387	+	0.164595i	0.0136387	+	0.164595i	−0.986361	+	0.164595i	$0.947368\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.193928	+	0.0323608i	−0.193928	+	0.0323608i
$577$	1.03463	+	0.355188i	1.03463	+	0.355188i	0.789141	−	0.614213i	$-0.210526\pi$
$577$	1.03463	+	0.355188i	1.03463	+	0.355188i	0.245485	+	0.969400i	$0.421053\pi$
$578$	−1.31127	+	0.709624i	−1.31127	+	0.709624i
$579$	−0.480672	+	0.735724i	−0.480672	+	0.735724i
$580$		0			0
$581$		0			0
$582$	1.72648	+	1.34377i	1.72648	+	1.34377i
$583$		0			0
$584$	0.162906	+	0.0271842i	0.162906	+	0.0271842i
$585$		0			0
$586$		0			0
$587$	−1.66364	−	0.900319i	−1.66364	−	0.900319i	−0.986361	−	0.164595i	$-0.947368\pi$
$587$	−1.66364	−	0.900319i	−1.66364	−	0.900319i	−0.677282	−	0.735724i	$-0.736842\pi$
$588$	0.863238	+	0.671885i	0.863238	+	0.671885i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.484275	−	0.0808112i	−0.484275	−	0.0808112i	−0.0825793	−	0.996584i	$-0.526316\pi$
$593$	−0.484275	−	0.0808112i	−0.484275	−	0.0808112i	−0.401695	+	0.915773i	$0.631579\pi$
$594$	0.667786	+	1.52240i	0.667786	+	1.52240i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$599$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$600$	1.03463	−	0.355188i	1.03463	−	0.355188i
$601$	−1.35456	+	1.47145i	−1.35456	+	1.47145i	−0.677282	+	0.735724i	$0.736842\pi$
$601$	−1.35456	+	1.47145i	−1.35456	+	1.47145i	−0.677282	+	0.735724i	$0.736842\pi$
$602$		0			0
$603$	−0.124648	+	0.0970174i	−0.124648	+	0.0970174i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$607$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$608$	0.789141	+	0.614213i	0.789141	+	0.614213i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.124648	+	0.284169i	−0.124648	+	0.284169i
$613$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$613$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$614$	−1.07898	−	0.180049i	−1.07898	−	0.180049i
$615$		0			0
$616$		0			0
$617$	0.387445	+	1.52999i	0.387445	+	1.52999i	0.789141	+	0.614213i	$0.210526\pi$
$617$	0.387445	+	1.52999i	0.387445	+	1.52999i	−0.401695	+	0.915773i	$0.631579\pi$
$618$		0			0
$619$	−1.66364	−	0.571129i	−1.66364	−	0.571129i	−0.677282	−	0.735724i	$-0.736842\pi$
$619$	−1.66364	−	0.571129i	−1.66364	−	0.571129i	−0.986361	+	0.164595i	$0.947368\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.879474	+	0.475947i	−0.879474	+	0.475947i
$626$	−0.332526	+	1.31311i	−0.332526	+	1.31311i
$627$	−0.831209	+	1.89497i	−0.831209	+	1.89497i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$631$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$632$		0			0
$633$	−1.81985	−	0.624756i	−1.81985	−	0.624756i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.33609	+	1.45138i	1.33609	+	1.45138i	0.789141	+	0.614213i	$0.210526\pi$
$641$	1.33609	+	1.45138i	1.33609	+	1.45138i	0.546948	+	0.837166i	$0.315789\pi$
$642$	−0.0443510	−	0.175138i	−0.0443510	−	0.175138i
$643$	0.111859	−	0.121511i	0.111859	−	0.121511i	−0.677282	−	0.735724i	$-0.736842\pi$
$643$	0.111859	−	0.121511i	0.111859	−	0.121511i	0.789141	+	0.614213i	$0.210526\pi$
$644$		0			0
$645$		0			0
$646$	1.49277	−	0.512467i	1.49277	−	0.512467i
$647$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$647$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$648$	−0.284261	−	1.12252i	−0.284261	−	1.12252i
$649$	−3.52948	+	1.21167i	−3.52948	+	1.21167i
$650$		0			0
$651$		0			0
$652$	−0.431796	−	0.233676i	−0.431796	−	0.233676i
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$		0			0
$655$		0			0
$656$	−0.740876	+	0.804806i	−0.740876	+	0.804806i
$657$	0.00268149	−	0.0323608i	0.00268149	−	0.0323608i
$658$		0			0
$659$	−0.156210	+	1.88517i	−0.156210	+	1.88517i	0.245485	+	0.969400i	$0.421053\pi$
$659$	−0.156210	+	1.88517i	−0.156210	+	1.88517i	−0.401695	+	0.915773i	$0.631579\pi$
$660$		0			0
$661$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$661$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$662$	0.706561	−	1.61080i	0.706561	−	1.61080i
$663$		0			0
$664$	−1.55676	+	0.259777i	−1.55676	+	0.259777i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.863238	−	0.671885i	0.863238	−	0.671885i	−0.0825793	−	0.996584i	$-0.526316\pi$
$673$	0.863238	−	0.671885i	0.863238	−	0.671885i	0.945817	+	0.324699i	$0.105263\pi$
$674$	−0.0405441	+	0.489294i	−0.0405441	+	0.489294i
$675$	0.353020	+	0.804806i	0.353020	+	0.804806i
$676$	−0.677282	+	0.735724i	−0.677282	+	0.735724i
$677$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$677$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$678$	0.178202	+	2.15058i	0.178202	+	2.15058i
$679$		0			0
$680$		0			0
$681$	0.158891	−	1.91753i	0.158891	−	1.91753i
$682$		0			0
$683$	−0.439413	+	1.00176i	−0.439413	+	1.00176i	0.546948	+	0.837166i	$0.315789\pi$
$683$	−0.439413	+	1.00176i	−0.439413	+	1.00176i	−0.986361	+	0.164595i	$0.947368\pi$
$684$	0.107535	−	0.164595i	0.107535	−	0.164595i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.94582	−	0.324699i	1.94582	−	0.324699i
$689$		0			0
$690$		0			0
$691$	0.792434	−	0.132234i	0.792434	−	0.132234i	0.245485	−	0.969400i	$-0.421053\pi$
$691$	0.792434	−	0.132234i	0.792434	−	0.132234i	0.546948	+	0.837166i	$0.315789\pi$
$692$		0			0
$693$		0			0
$694$	1.89163			1.89163
$695$		0			0
$696$		0			0
$697$	0.423825	+	1.67365i	0.423825	+	1.67365i
$698$		0			0
$699$	1.19661	−	1.83155i	1.19661	−	1.83155i
$700$		0			0
$701$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$701$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$702$		0			0
$703$		0			0
$704$	1.03463	−	1.58361i	1.03463	−	1.58361i
$705$		0			0
$706$	0.387445	+	0.301561i	0.387445	+	0.301561i
$707$		0			0
$708$	2.12852	−	0.355188i	2.12852	−	0.355188i
$709$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$709$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$710$		0			0
$711$		0			0
$712$	−1.06894	−	1.16118i	−1.06894	−	1.16118i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.792434	+	1.80657i	0.792434	+	1.80657i
$717$		0			0
$718$		0			0
$719$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$719$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$720$		0			0
$721$		0			0
$722$	−0.986361	+	0.164595i	−0.986361	+	0.164595i
$723$	−0.180666			−0.180666
$724$		0			0
$725$		0			0
$726$	2.66756	+	0.915773i	2.66756	+	0.915773i
$727$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$727$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$728$		0			0
$729$	0.693928	−	0.238226i	0.693928	−	0.238226i
$730$		0			0
$731$	1.25068	−	2.85127i	1.25068	−	2.85127i
$732$		0			0
$733$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$733$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.125498	−	1.51453i	0.125498	−	1.51453i
$738$	0.169720	+	0.132099i	0.169720	+	0.132099i
$739$	0.464369	−	0.159418i	0.464369	−	0.159418i	−0.0825793	−	0.996584i	$-0.526316\pi$
$739$	0.464369	−	0.159418i	0.464369	−	0.159418i	0.546948	+	0.837166i	$0.315789\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$743$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.0761752	+	0.300809i	0.0761752	+	0.300809i
$748$	−1.19927	−	2.73407i	−1.19927	−	2.73407i
$749$		0			0
$750$		0			0
$751$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$751$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$752$		0			0
$753$	−2.04103	+	0.340588i	−2.04103	+	0.340588i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$757$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$758$	0.544122	−	0.591074i	0.544122	−	0.591074i
$759$		0			0
$760$		0			0
$761$	0.0663435	−	0.151248i	0.0663435	−	0.151248i	−0.879474	−	0.475947i	$-0.842105\pi$
$761$	0.0663435	−	0.151248i	0.0663435	−	0.151248i	0.945817	+	0.324699i	$0.105263\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.740876	+	0.804806i	−0.740876	+	0.804806i
$769$	0.322718	+	0.735724i	0.322718	+	0.735724i	1.00000			$0$
$769$	0.322718	+	0.735724i	0.322718	+	0.735724i	−0.677282	+	0.735724i	$0.736842\pi$
$770$		0			0
$771$	−0.693517	+	0.539786i	−0.693517	+	0.539786i
$772$	0.0663435	+	0.800647i	0.0663435	+	0.800647i
$773$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$773$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$774$	−0.0952129	−	0.375987i	−0.0952129	−	0.375987i
$775$		0			0
$776$	2.00000			2.00000
$777$		0			0
$778$		0			0
$779$	−0.0903332	−	1.09016i	−0.0903332	−	1.09016i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	1.00000			1.00000
$785$		0			0
$786$	0.944293	+	1.44535i	0.944293	+	1.44535i
$787$	0.0663435	−	0.800647i	0.0663435	−	0.800647i	−0.879474	−	0.475947i	$-0.842105\pi$
$787$	0.0663435	−	0.800647i	0.0663435	−	0.800647i	0.945817	−	0.324699i	$-0.105263\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.327087	−	0.177011i	−0.327087	−	0.177011i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$797$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$798$		0			0
$799$		0			0
$800$	0.546948	−	0.837166i	0.546948	−	0.837166i
$801$	−0.210164	+	0.228298i	−0.210164	+	0.228298i
$802$	−0.332526	−	1.31311i	−0.332526	−	1.31311i
$803$	0.211596	+	0.229855i	0.211596	+	0.229855i
$804$	−0.215739	+	0.851934i	−0.215739	+	0.851934i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.863238	+	0.671885i	0.863238	+	0.671885i	0.945817	−	0.324699i	$-0.105263\pi$
$809$	0.863238	+	0.671885i	0.863238	+	0.671885i	−0.0825793	+	0.996584i	$0.526316\pi$
$810$		0			0
$811$	−0.156210	−	0.0536269i	−0.156210	−	0.0536269i	0.245485	−	0.969400i	$-0.421053\pi$
$811$	−0.156210	−	0.0536269i	−0.156210	−	0.0536269i	−0.401695	+	0.915773i	$0.631579\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.423825	+	1.67365i	0.423825	+	1.67365i
$817$	−1.07898	+	1.65150i	−1.07898	+	1.65150i
$818$	−0.431796	+	1.70512i	−0.431796	+	1.70512i
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$	0.122362	−	1.47669i	0.122362	−	1.47669i
$823$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$823$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$824$		0			0
$825$	1.95713	+	0.671885i	1.95713	+	0.671885i
$826$		0			0
$827$	0.268536	+	1.06042i	0.268536	+	1.06042i	0.945817	+	0.324699i	$0.105263\pi$
$827$	0.268536	+	1.06042i	0.268536	+	1.06042i	−0.677282	+	0.735724i	$0.736842\pi$
$828$		0			0
$829$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$829$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.863238	−	1.32128i	0.863238	−	1.32128i
$834$	0.507971	+	0.174387i	0.507971	+	0.174387i
$835$		0			0
$836$	0.464369	+	1.83375i	0.464369	+	1.83375i
$837$		0			0
$838$	1.89163			1.89163
$839$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$839$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$840$		0			0
$841$	0.789141	−	0.614213i	0.789141	−	0.614213i
$842$		0			0
$843$	1.30316	−	1.41561i	1.30316	−	1.41561i
$844$	−1.66364	+	0.571129i	−1.66364	+	0.571129i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	2.18779			2.18779
$850$	−0.633988	−	1.44535i	−0.633988	−	1.44535i
$851$		0			0
$852$		0			0
$853$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$853$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$854$		0			0
$855$		0			0
$856$	−0.130333	−	0.101443i	−0.130333	−	0.101443i
$857$	1.54695	+	0.837166i	1.54695	+	0.837166i	1.00000			$0$
$857$	1.54695	+	0.837166i	1.54695	+	0.837166i	0.546948	+	0.837166i	$0.315789\pi$
$858$		0			0
$859$	−1.38806	−	0.751179i	−1.38806	−	0.751179i	−0.401695	−	0.915773i	$-0.631579\pi$
$859$	−1.38806	−	0.751179i	−1.38806	−	0.751179i	−0.986361	+	0.164595i	$0.947368\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$863$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$864$	−0.693517	−	0.539786i	−0.693517	−	0.539786i
$865$		0			0
$866$	−0.962053	+	0.520637i	−0.962053	+	0.520637i
$867$	1.54260	+	0.529574i	1.54260	+	0.529574i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.0324717	−	0.391875i	−0.0324717	−	0.391875i
$874$		0			0
$875$		0			0
$876$	−0.0988152	−	0.151248i	−0.0988152	−	0.151248i
$877$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$877$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.07898	+	1.65150i	−1.07898	+	1.65150i	−0.401695	+	0.915773i	$0.631579\pi$
$881$	−1.07898	+	1.65150i	−1.07898	+	1.65150i	−0.677282	+	0.735724i	$0.736842\pi$
$882$	−0.0162359	−	0.195938i	−0.0162359	−	0.195938i
$883$	0.387445	−	1.52999i	0.387445	−	1.52999i	−0.401695	−	0.915773i	$-0.631579\pi$
$883$	0.387445	−	1.52999i	0.387445	−	1.52999i	0.789141	−	0.614213i	$-0.210526\pi$
$884$		0			0
$885$		0			0
$886$	0.792434	−	1.80657i	0.792434	−	1.80657i
$887$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$887$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.879884	−	2.00593i	0.879884	−	2.00593i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.268536	−	1.06042i	0.268536	−	1.06042i
$899$		0			0
$900$	−0.172913	−	0.0935756i	−0.172913	−	0.0935756i
$901$		0			0
$902$	−2.04103	+	0.340588i	−2.04103	+	0.340588i
$903$		0			0
$904$	1.33609	+	1.45138i	1.33609	+	1.45138i
$905$		0			0
$906$		0			0
$907$	0.120526	−	0.475947i	0.120526	−	0.475947i	−0.879474	−	0.475947i	$-0.842105\pi$
$907$	0.120526	−	0.475947i	0.120526	−	0.475947i	1.00000			$0$
$908$	−0.962053	−	1.47253i	−0.962053	−	1.47253i
$909$		0			0
$910$		0			0
$911$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$911$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$912$	−0.0903332	−	1.09016i	−0.0903332	−	1.09016i
$913$	−2.62570	−	1.42096i	−2.62570	−	1.42096i
$914$	0.706561	−	1.61080i	0.706561	−	1.61080i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−1.31188	+	0.450369i	−1.31188	+	0.450369i
$919$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$919$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$920$		0			0
$921$	0.654483	+	1.00176i	0.654483	+	1.00176i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.740876	−	1.13399i	−0.740876	−	1.13399i	−0.986361	−	0.164595i	$-0.947368\pi$
$929$	−0.740876	−	1.13399i	−0.740876	−	1.13399i	0.245485	−	0.969400i	$-0.421053\pi$
$930$		0			0
$931$	−0.677282	+	0.735724i	−0.677282	+	0.735724i
$932$	−0.165159	−	1.99317i	−0.165159	−	1.99317i
$933$		0			0
$934$	0.0136387	+	0.164595i	0.0136387	+	0.164595i
$935$		0			0
$936$		0			0
$937$	1.94582	−	0.324699i	1.94582	−	0.324699i	0.945817	−	0.324699i	$-0.105263\pi$
$937$	1.94582	−	0.324699i	1.94582	−	0.324699i	1.00000			$0$
$938$		0			0
$939$	1.30316	−	0.705236i	1.30316	−	0.705236i
$940$		0			0
$941$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$941$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$942$		0			0
$943$		0			0
$944$	1.33609	−	1.45138i	1.33609	−	1.45138i
$945$		0			0
$946$	3.28191	+	1.77608i	3.28191	+	1.77608i
$947$	1.94582	+	0.324699i	1.94582	+	0.324699i	1.00000			$0$
$947$	1.94582	+	0.324699i	1.94582	+	0.324699i	0.945817	+	0.324699i	$0.105263\pi$
$948$		0			0
$949$		0			0
$950$	0.245485	+	0.969400i	0.245485	+	0.969400i
$951$		0			0
$952$		0			0
$953$	0.120526	−	0.475947i	0.120526	−	0.475947i	−0.879474	−	0.475947i	$-0.842105\pi$
$953$	0.120526	−	0.475947i	0.120526	−	0.475947i	1.00000			$0$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.945817	−	0.324699i	0.945817	−	0.324699i
$962$		0			0
$963$	−0.0177603	+	0.0271842i	−0.0177603	+	0.0271842i
$964$	−0.130333	+	0.101443i	−0.130333	+	0.101443i
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	2.43858	−	0.837166i	2.43858	−	0.837166i
$969$	−1.51839	−	0.821712i	−1.51839	−	0.821712i
$970$		0			0
$971$	1.89163	+	0.649399i	1.89163	+	0.649399i	0.945817	+	0.324699i	$0.105263\pi$
$971$	1.89163	+	0.649399i	1.89163	+	0.649399i	0.945817	+	0.324699i	$0.105263\pi$
$972$	−0.212137	+	0.324699i	−0.212137	+	0.324699i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.332526	−	1.31311i	−0.332526	−	1.31311i	−0.879474	−	0.475947i	$-0.842105\pi$
$977$	−0.332526	−	1.31311i	−0.332526	−	1.31311i	0.546948	−	0.837166i	$-0.315789\pi$
$978$	0.131843	+	0.520637i	0.131843	+	0.520637i
$979$	−0.246543	−	2.97533i	−0.246543	−	2.97533i
$980$		0			0
$981$		0			0
$982$	0.544122	−	1.24047i	0.544122	−	1.24047i
$983$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$983$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$984$	1.19661			1.19661
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$991$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$992$		0			0
$993$	−1.81985	+	0.624756i	−1.81985	+	0.624756i
$994$		0			0
$995$		0			0
$996$	1.36243	+	1.06042i	1.36243	+	1.06042i
$997$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$997$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$998$	−1.66364	−	0.571129i	−1.66364	−	0.571129i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.bb.a.419.1	✓	18
8.3	odd	2	CM	2888.1.bb.a.419.1	✓	18
361.305	even	19	inner	2888.1.bb.a.1027.1	yes	18
2888.1027	odd	38	inner	2888.1.bb.a.1027.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2888.1.bb.a.419.1	✓	18	1.1	even	1	trivial
2888.1.bb.a.419.1	✓	18	8.3	odd	2	CM
2888.1.bb.a.1027.1	yes	18	361.305	even	19	inner
2888.1.bb.a.1027.1	yes	18	2888.1027	odd	38	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2888 = 2^{3} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2888.bb (of order \(38\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.986361 - 0.164595i) q^{2} +(0.598305 + 0.915773i) q^{3} +(0.945817 + 0.324699i) q^{4} +(-0.439413 - 1.00176i) q^{6} +(-0.879474 - 0.475947i) q^{8} +(-0.0789770 + 0.180049i) q^{9} +O(q^{10})\)	\(q+(-0.986361 - 0.164595i) q^{2} +(0.598305 + 0.915773i) q^{3} +(0.945817 + 0.324699i) q^{4} +(-0.439413 - 1.00176i) q^{6} +(-0.879474 - 0.475947i) q^{8} +(-0.0789770 + 0.180049i) q^{9} +(-0.759861 - 1.73231i) q^{11} +(0.268536 + 1.06042i) q^{12} +(0.789141 + 0.614213i) q^{16} +(1.49277 - 0.512467i) q^{17} +(0.107535 - 0.164595i) q^{18} +(-0.986361 + 0.164595i) q^{19} +(0.464369 + 1.83375i) q^{22} +(-0.0903332 - 1.09016i) q^{24} +(0.245485 + 0.969400i) q^{25} +(0.866840 - 0.144650i) q^{27} +(-0.677282 - 0.735724i) q^{32} +(1.13177 - 1.73231i) q^{33} +(-1.55676 + 0.259777i) q^{34} +(-0.133160 + 0.144650i) q^{36} +1.00000 q^{38} +(-0.0903332 + 1.09016i) q^{41} +(1.33609 - 1.45138i) q^{43} +(-0.156210 - 1.88517i) q^{44} +(-0.0903332 + 1.09016i) q^{48} +(0.789141 - 0.614213i) q^{49} +(-0.0825793 - 0.996584i) q^{50} +(1.36243 + 1.06042i) q^{51} -0.878826 q^{54} +(-0.740876 - 0.804806i) q^{57} +(0.162906 - 1.96598i) q^{59} +(0.546948 + 0.837166i) q^{64} +(-1.40147 + 1.52240i) q^{66} +(0.706561 + 0.382372i) q^{67} +1.57828 q^{68} +(0.155152 - 0.120760i) q^{72} +(-0.156210 + 0.0536269i) q^{73} +(-0.740876 + 0.804806i) q^{75} +(-0.986361 - 0.164595i) q^{76} +(0.784261 + 0.851934i) q^{81} +(0.268536 - 1.06042i) q^{82} +(1.24549 - 0.969400i) q^{83} +(-1.55676 + 1.21167i) q^{86} +(-0.156210 + 1.88517i) q^{88} +(1.49277 + 0.512467i) q^{89} +(0.268536 - 1.06042i) q^{96} +(-1.75895 + 0.951895i) q^{97} +(-0.879474 + 0.475947i) q^{98} +0.371913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9}+O(q^{10}) \) 18 * q - q^2 + 17 * q^3 - q^4 - 2 * q^6 - q^8 + 16 * q^9	\( 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9} - 2 q^{11} - 2 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} - q^{19} - 2 q^{22} - 2 q^{24} - q^{25} + 15 q^{27} - q^{32} - 4 q^{33} - 2 q^{34} - 3 q^{36} + 18 q^{38} - 2 q^{41} - 2 q^{43} - 2 q^{44} - 2 q^{48} - q^{49} - q^{50} - 4 q^{51} - 4 q^{54} - 2 q^{57} - 2 q^{59} - q^{64} - 4 q^{66} - 2 q^{67} - 2 q^{68} - 3 q^{72} - 2 q^{73} - 2 q^{75} - q^{76} + 14 q^{81} - 2 q^{82} + 17 q^{83} - 2 q^{86} - 2 q^{88} - 2 q^{89} - 2 q^{96} - 2 q^{97} - q^{98} - 6 q^{99}+O(q^{100}) \) 18 * q - q^2 + 17 * q^3 - q^4 - 2 * q^6 - q^8 + 16 * q^9 - 2 * q^11 - 2 * q^12 - q^16 - 2 * q^17 - 3 * q^18 - q^19 - 2 * q^22 - 2 * q^24 - q^25 + 15 * q^27 - q^32 - 4 * q^33 - 2 * q^34 - 3 * q^36 + 18 * q^38 - 2 * q^41 - 2 * q^43 - 2 * q^44 - 2 * q^48 - q^49 - q^50 - 4 * q^51 - 4 * q^54 - 2 * q^57 - 2 * q^59 - q^64 - 4 * q^66 - 2 * q^67 - 2 * q^68 - 3 * q^72 - 2 * q^73 - 2 * q^75 - q^76 + 14 * q^81 - 2 * q^82 + 17 * q^83 - 2 * q^86 - 2 * q^88 - 2 * q^89 - 2 * q^96 - 2 * q^97 - q^98 - 6 * q^99

Introduction

L-functions

Modular forms

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Database

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