LMFDB - Embedded newform 2888.1.bs.a.291.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2888,1,Mod(35,2888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2888, base_ring=CyclotomicField(342))

chi = DirichletCharacter(H, H._module([171, 171, 40]))

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

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

chi := DirichletCharacter("2888.35");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2888 = 2^{3} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2888.bs (of order $342$, degree $108$, 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:	$108$
Coefficient field:	$\Q(\zeta_{171})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{108} - x^{105} + x^{99} - x^{96} + x^{90} - x^{87} + x^{81} - x^{78} + x^{72} - x^{69} + x^{63} + \cdots + 1 $ x^108 - x^105 + x^99 - x^96 + x^90 - x^87 + x^81 - x^78 + x^72 - x^69 + x^63 - x^60 + x^54 - x^48 + x^45 - x^39 + x^36 - x^30 + x^27 - x^21 + x^18 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{171}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{171} - \cdots)$

Embedding invariants

Embedding label			291.1
Root			$0.418451 - 0.908239i$ of defining polynomial
Character	$\chi$	$=$	2888.291
Dual form			2888.1.bs.a.1707.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.367783 + 0.929912i) q^{2} +(-1.13140 - 0.639431i) q^{3} +(-0.729471 - 0.684011i) q^{4} +(1.01073 - 0.816933i) q^{6} +(0.904357 - 0.426776i) q^{8} +(0.355376 + 0.590216i) q^{9} +O(q^{10})$	\(q+(-0.367783 + 0.929912i) q^{2} +(-1.13140 - 0.639431i) q^{3} +(-0.729471 - 0.684011i) q^{4} +(1.01073 - 0.816933i) q^{6} +(0.904357 - 0.426776i) q^{8} +(0.355376 + 0.590216i) q^{9} +(1.20701 + 1.05119i) q^{11} +(0.387948 + 1.24034i) q^{12} +(0.0642573 + 0.997933i) q^{16} +(-1.13366 - 0.343183i) q^{17} +(-0.679549 + 0.113397i) q^{18} +(-0.621436 + 0.783465i) q^{19} +(-1.42143 + 0.735804i) q^{22} +(-1.29609 - 0.0954181i) q^{24} +(0.384804 - 0.922998i) q^{25} +(0.0111387 + 0.404091i) q^{27} +(-0.951623 - 0.307269i) q^{32} +(-0.693453 - 1.96111i) q^{33} +(0.736072 - 0.927991i) q^{34} +(0.144478 - 0.673626i) q^{36} +(-0.500000 - 0.866025i) q^{38} +(-0.0672572 + 0.663347i) q^{41} +(0.0408859 + 0.0369501i) q^{43} +(-0.161456 - 1.59242i) q^{44} +(0.565409 - 1.17015i) q^{48} +(0.993931 - 0.110008i) q^{49} +(0.716783 + 0.697297i) q^{50} +(1.06319 + 1.11318i) q^{51} +(-0.379865 - 0.138260i) q^{54} +(1.20407 - 0.489050i) q^{57} +(1.07667 + 0.776218i) q^{59} +(0.635724 - 0.771917i) q^{64} +(2.07870 + 0.0764138i) q^{66} +(-0.681337 + 0.687624i) q^{67} +(0.592235 + 1.02578i) q^{68} +(0.573277 + 0.382100i) q^{72} +(-0.0459248 - 0.196450i) q^{73} +(-1.02556 + 0.798227i) q^{75} +(0.989219 - 0.146447i) q^{76} +(0.568108 - 1.07321i) q^{81} +(-0.592118 - 0.306511i) q^{82} +(1.15085 + 1.56579i) q^{83} +(-0.0493975 + 0.0244307i) q^{86} +(1.54019 + 0.435524i) q^{88} +(-0.452508 + 1.93567i) q^{89} +(0.880191 + 0.956143i) q^{96} +(-0.244445 - 0.246701i) q^{97} +(-0.263253 + 0.964727i) q^{98} +(-0.191484 + 1.08596i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 108 * q + 3 * q^3 + 3 * q^6 + 3 * q^8 + 3 * q^9	$ 108 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9} - 6 q^{18} - 6 q^{22} + 3 q^{24} - 60 q^{27} + 3 q^{33} + 3 q^{36} - 54 q^{38} + 3 q^{41} - 6 q^{44} - 6 q^{48} + 3 q^{49} + 3 q^{50} - 3 q^{51} + 3 q^{54} + 3 q^{59} + 3 q^{64} + 3 q^{66} + 3 q^{67} - 3 q^{68} - 6 q^{72} - 6 q^{73} - 3 q^{81} + 3 q^{82} + 3 q^{97} - 3 q^{99}+O(q^{100}) $ 108 * q + 3 * q^3 + 3 * q^6 + 3 * q^8 + 3 * q^9 - 6 * q^18 - 6 * q^22 + 3 * q^24 - 60 * q^27 + 3 * q^33 + 3 * q^36 - 54 * q^38 + 3 * q^41 - 6 * q^44 - 6 * q^48 + 3 * q^49 + 3 * q^50 - 3 * q^51 + 3 * q^54 + 3 * q^59 + 3 * q^64 + 3 * q^66 + 3 * q^67 - 3 * q^68 - 6 * q^72 - 6 * q^73 - 3 * q^81 + 3 * q^82 + 3 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{106}{171}\right)$

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 $

$2$	−0.367783	+	0.929912i	−0.367783	+	0.929912i
$2$	−0.367783	+	0.929912i	−0.367783	+	0.929912i
$3$	−1.13140	−	0.639431i	−1.13140	−	0.639431i	−0.191711	−	0.981451i	$-0.561404\pi$
$3$	−1.13140	−	0.639431i	−1.13140	−	0.639431i	−0.939693	+	0.342020i	$0.888889\pi$
$4$	−0.729471	−	0.684011i	−0.729471	−	0.684011i
$5$		0			0		0.832107	−	0.554615i	$-0.187135\pi$
$5$		0			0		−0.832107	+	0.554615i	$0.812865\pi$
$6$	1.01073	−	0.816933i	1.01073	−	0.816933i
$7$		0			0		0.998482	−	0.0550878i	$-0.0175439\pi$
$7$		0			0		−0.998482	+	0.0550878i	$0.982456\pi$
$8$	0.904357	−	0.426776i	0.904357	−	0.426776i
$9$	0.355376	+	0.590216i	0.355376	+	0.590216i
$10$		0			0
$11$	1.20701	+	1.05119i	1.20701	+	1.05119i	0.997301	+	0.0734214i	$0.0233918\pi$
$11$	1.20701	+	1.05119i	1.20701	+	1.05119i	0.209708	+	0.977764i	$0.432749\pi$
$12$	0.387948	+	1.24034i	0.387948	+	1.24034i
$13$		0			0		0.983171	−	0.182687i	$-0.0584795\pi$
$13$		0			0		−0.983171	+	0.182687i	$0.941520\pi$
$14$		0			0
$15$		0			0
$16$	0.0642573	+	0.997933i	0.0642573	+	0.997933i
$17$	−1.13366	−	0.343183i	−1.13366	−	0.343183i	−0.333374	−	0.942795i	$-0.608187\pi$
$17$	−1.13366	−	0.343183i	−1.13366	−	0.343183i	−0.800291	+	0.599612i	$0.795322\pi$
$18$	−0.679549	+	0.113397i	−0.679549	+	0.113397i
$19$	−0.621436	+	0.783465i	−0.621436	+	0.783465i
$19$	−0.621436	+	0.783465i	−0.621436	+	0.783465i
$20$		0			0
$21$		0			0
$22$	−1.42143	+	0.735804i	−1.42143	+	0.735804i
$23$		0			0		0.00918581	−	0.999958i	$-0.497076\pi$
$23$		0			0		−0.00918581	+	0.999958i	$0.502924\pi$
$24$	−1.29609	−	0.0954181i	−1.29609	−	0.0954181i
$25$	0.384804	−	0.922998i	0.384804	−	0.922998i
$26$		0			0
$27$	0.0111387	+	0.404091i	0.0111387	+	0.404091i
$28$		0			0
$29$		0			0		0.119134	−	0.992878i	$-0.461988\pi$
$29$		0			0		−0.119134	+	0.992878i	$0.538012\pi$
$30$		0			0
$31$		0			0		0.851919	−	0.523673i	$-0.175439\pi$
$31$		0			0		−0.851919	+	0.523673i	$0.824561\pi$
$32$	−0.951623	−	0.307269i	−0.951623	−	0.307269i
$33$	−0.693453	−	1.96111i	−0.693453	−	1.96111i
$34$	0.736072	−	0.927991i	0.736072	−	0.927991i
$35$		0			0
$36$	0.144478	−	0.673626i	0.144478	−	0.673626i
$37$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$37$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$38$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$39$		0			0
$40$		0			0
$41$	−0.0672572	+	0.663347i	−0.0672572	+	0.663347i	0.904357	+	0.426776i	$0.140351\pi$
$41$	−0.0672572	+	0.663347i	−0.0672572	+	0.663347i	−0.971614	+	0.236570i	$0.923977\pi$
$42$		0			0
$43$	0.0408859	+	0.0369501i	0.0408859	+	0.0369501i	0.690683	−	0.723158i	$-0.257310\pi$
$43$	0.0408859	+	0.0369501i	0.0408859	+	0.0369501i	−0.649797	+	0.760108i	$0.725146\pi$
$44$	−0.161456	−	1.59242i	−0.161456	−	1.59242i
$45$		0			0
$46$		0			0
$47$		0			0		−0.933251	−	0.359225i	$-0.883041\pi$
$47$		0			0		0.933251	+	0.359225i	$0.116959\pi$
$48$	0.565409	−	1.17015i	0.565409	−	1.17015i
$49$	0.993931	−	0.110008i	0.993931	−	0.110008i
$50$	0.716783	+	0.697297i	0.716783	+	0.697297i
$51$	1.06319	+	1.11318i	1.06319	+	1.11318i
$52$		0			0
$53$		0			0		−0.155527	−	0.987832i	$-0.549708\pi$
$53$		0			0		0.155527	+	0.987832i	$0.450292\pi$
$54$	−0.379865	−	0.138260i	−0.379865	−	0.138260i
$55$		0			0
$56$		0			0
$57$	1.20407	−	0.489050i	1.20407	−	0.489050i
$58$		0			0
$59$	1.07667	+	0.776218i	1.07667	+	0.776218i	0.975796	−	0.218681i	$-0.0701754\pi$
$59$	1.07667	+	0.776218i	1.07667	+	0.776218i	0.100874	+	0.994899i	$0.467836\pi$
$60$		0			0
$61$		0			0		−0.995784	−	0.0917303i	$-0.970760\pi$
$61$		0			0		0.995784	+	0.0917303i	$0.0292398\pi$
$62$		0			0
$63$		0			0
$64$	0.635724	−	0.771917i	0.635724	−	0.771917i
$65$		0			0
$66$	2.07870	+	0.0764138i	2.07870	+	0.0764138i
$67$	−0.681337	+	0.687624i	−0.681337	+	0.687624i	−0.962268	−	0.272103i	$-0.912281\pi$
$67$	−0.681337	+	0.687624i	−0.681337	+	0.687624i	0.280931	+	0.959728i	$0.409357\pi$
$68$	0.592235	+	1.02578i	0.592235	+	1.02578i
$69$		0			0
$70$		0			0
$71$		0			0		0.995784	−	0.0917303i	$-0.0292398\pi$
$71$		0			0		−0.995784	+	0.0917303i	$0.970760\pi$
$72$	0.573277	+	0.382100i	0.573277	+	0.382100i
$73$	−0.0459248	−	0.196450i	−0.0459248	−	0.196450i	0.945817	−	0.324699i	$-0.105263\pi$
$73$	−0.0459248	−	0.196450i	−0.0459248	−	0.196450i	−0.991742	+	0.128249i	$0.959064\pi$
$74$		0			0
$75$	−1.02556	+	0.798227i	−1.02556	+	0.798227i
$76$	0.989219	−	0.146447i	0.989219	−	0.146447i
$77$		0			0
$78$		0			0
$79$		0			0		0.951623	−	0.307269i	$-0.0994152\pi$
$79$		0			0		−0.951623	+	0.307269i	$0.900585\pi$
$80$		0			0
$81$	0.568108	−	1.07321i	0.568108	−	1.07321i
$82$	−0.592118	−	0.306511i	−0.592118	−	0.306511i
$83$	1.15085	+	1.56579i	1.15085	+	1.56579i	0.766044	+	0.642788i	$0.222222\pi$
$83$	1.15085	+	1.56579i	1.15085	+	1.56579i	0.384804	+	0.922998i	$0.374269\pi$
$84$		0			0
$85$		0			0
$86$	−0.0493975	+	0.0244307i	−0.0493975	+	0.0244307i
$87$		0			0
$88$	1.54019	+	0.435524i	1.54019	+	0.435524i
$89$	−0.452508	+	1.93567i	−0.452508	+	1.93567i	−0.119134	+	0.992878i	$0.538012\pi$
$89$	−0.452508	+	1.93567i	−0.452508	+	1.93567i	−0.333374	+	0.942795i	$0.608187\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.880191	+	0.956143i	0.880191	+	0.956143i
$97$	−0.244445	−	0.246701i	−0.244445	−	0.246701i	0.577333	−	0.816509i	$-0.304094\pi$
$97$	−0.244445	−	0.246701i	−0.244445	−	0.246701i	−0.821778	+	0.569808i	$0.807018\pi$
$98$	−0.263253	+	0.964727i	−0.263253	+	0.964727i
$99$	−0.191484	+	1.08596i	−0.191484	+	1.08596i
$100$	−0.912045	+	0.410091i	−0.912045	+	0.410091i
$101$		0			0		0.999831	−	0.0183709i	$-0.00584795\pi$
$101$		0			0		−0.999831	+	0.0183709i	$0.994152\pi$
$102$	−1.42618	+	0.579265i	−1.42618	+	0.579265i
$103$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$103$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.0530293	+	1.92381i	−0.0530293	+	1.92381i	0.245485	+	0.969400i	$0.421053\pi$
$107$	−0.0530293	+	1.92381i	−0.0530293	+	1.92381i	−0.298515	+	0.954405i	$0.596491\pi$
$108$	0.268277	−	0.302392i	0.268277	−	0.302392i
$109$		0			0		0.155527	−	0.987832i	$-0.450292\pi$
$109$		0			0		−0.155527	+	0.987832i	$0.549708\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.08210	−	1.65628i	1.08210	−	1.65628i	0.418451	−	0.908239i	$-0.362573\pi$
$113$	1.08210	−	1.65628i	1.08210	−	1.65628i	0.663651	−	0.748042i	$-0.269006\pi$
$114$	0.0119378	+	1.29954i	0.0119378	+	1.29954i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.11780	+	0.715728i	−1.11780	+	0.715728i
$119$		0			0
$120$		0			0
$121$	0.214527	+	1.54706i	0.214527	+	1.54706i
$122$		0			0
$123$	0.500260	−	0.707506i	0.500260	−	0.707506i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$127$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$128$	0.484006	+	0.875065i	0.484006	+	0.875065i
$129$	−0.0226314	−	0.0679492i	−0.0226314	−	0.0679492i
$130$		0			0
$131$	1.75624	−	0.359833i	1.75624	−	0.359833i	0.789141	−	0.614213i	$-0.210526\pi$
$131$	1.75624	−	0.359833i	1.75624	−	0.359833i	0.967104	+	0.254380i	$0.0818713\pi$
$132$	−0.835570	+	1.90491i	−0.835570	+	1.90491i
$133$		0			0
$134$	−0.388846	−	0.886480i	−0.388846	−	0.886480i
$135$		0			0
$136$	−1.17170	+	0.173462i	−1.17170	+	0.173462i
$137$	1.93290	+	0.508416i	1.93290	+	0.508416i	0.975796	+	0.218681i	$0.0701754\pi$
$137$	1.93290	+	0.508416i	1.93290	+	0.508416i	0.957107	+	0.289735i	$0.0935673\pi$
$138$		0			0
$139$	−0.645146	+	1.02824i	−0.645146	+	1.02824i	0.350638	+	0.936511i	$0.385965\pi$
$139$	−0.645146	+	1.02824i	−0.645146	+	1.02824i	−0.995784	+	0.0917303i	$0.970760\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.566160	+	0.392567i	−0.566160	+	0.392567i
$145$		0			0
$146$	0.199572	+	0.0295452i	0.199572	+	0.0295452i
$147$	−1.19488	−	0.511087i	−1.19488	−	0.511087i
$148$		0			0
$149$		0			0		0.562235	−	0.826977i	$-0.309942\pi$
$149$		0			0		−0.562235	+	0.826977i	$0.690058\pi$
$150$	−0.365097	−	1.24726i	−0.365097	−	1.24726i
$151$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$151$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$152$	−0.227635	+	0.973746i	−0.227635	+	0.973746i
$153$	−0.200325	−	0.791065i	−0.200325	−	0.791065i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.00918581	−	0.999958i	$-0.502924\pi$
$157$		0			0		0.00918581	+	0.999958i	$0.497076\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.789048	+	0.922998i	0.789048	+	0.922998i
$163$	−0.0782293	−	0.0480874i	−0.0782293	−	0.0480874i	0.484006	−	0.875065i	$-0.339181\pi$
$163$	−0.0782293	−	0.0480874i	−0.0782293	−	0.0480874i	−0.562235	+	0.826977i	$0.690058\pi$
$164$	0.502799	−	0.437888i	0.502799	−	0.437888i
$165$		0			0
$166$	−1.87930	+	0.494318i	−1.87930	+	0.494318i
$167$		0			0		0.919425	−	0.393266i	$-0.128655\pi$
$167$		0			0		−0.919425	+	0.393266i	$0.871345\pi$
$168$		0			0
$169$	0.933251	−	0.359225i	0.933251	−	0.359225i
$170$		0			0
$171$	−0.683256	−	0.0883566i	−0.683256	−	0.0883566i
$172$	−0.00455084	−	0.0549205i	−0.00455084	−	0.0549205i
$173$		0			0		−0.435066	−	0.900399i	$-0.643275\pi$
$173$		0			0		0.435066	+	0.900399i	$0.356725\pi$
$174$		0			0
$175$		0			0
$176$	−0.971454	+	1.27206i	−0.971454	+	1.27206i
$177$	−0.721810	−	1.56667i	−0.721810	−	1.56667i
$178$	−1.63358	−	1.13270i	−1.63358	−	1.13270i
$179$	0.0868068	−	0.626005i	0.0868068	−	0.626005i	−0.896364	−	0.443318i	$-0.853801\pi$
$179$	0.0868068	−	0.626005i	0.0868068	−	0.626005i	0.983171	−	0.182687i	$-0.0584795\pi$
$180$		0			0
$181$		0			0		−0.367783	−	0.929912i	$-0.619883\pi$
$181$		0			0		0.367783	+	0.929912i	$0.380117\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.00760	−	1.60592i	−1.00760	−	1.60592i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$191$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$192$	−1.21285	+	0.466847i	−1.21285	+	0.466847i
$193$	0.383357	+	0.00704378i	0.383357	+	0.00704378i	0.209708	−	0.977764i	$-0.432749\pi$
$193$	0.383357	+	0.00704378i	0.383357	+	0.00704378i	0.173648	+	0.984808i	$0.444444\pi$
$194$	0.319313	−	0.136580i	0.319313	−	0.136580i
$195$		0			0
$196$	−0.800291	−	0.599612i	−0.800291	−	0.599612i
$197$		0			0		0.754107	−	0.656752i	$-0.228070\pi$
$197$		0			0		−0.754107	+	0.656752i	$0.771930\pi$
$198$	−0.939424	−	0.577462i	−0.939424	−	0.577462i
$199$		0			0		−0.649797	−	0.760108i	$-0.725146\pi$
$199$		0			0		0.649797	+	0.760108i	$0.274854\pi$
$200$	−0.0459136	−	0.998945i	−0.0459136	−	0.998945i
$201$	1.21056	−	0.342312i	1.21056	−	0.342312i
$202$		0			0
$203$		0			0
$204$	−0.0141400	−	1.53927i	−0.0141400	−	1.53927i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.57365	+	0.292406i	−1.57365	+	0.292406i
$210$		0			0
$211$	0.508124	+	1.73587i	0.508124	+	1.73587i	0.663651	+	0.748042i	$0.269006\pi$
$211$	0.508124	+	1.73587i	0.508124	+	1.73587i	−0.155527	+	0.987832i	$0.549708\pi$
$212$		0			0
$213$		0			0
$214$	−1.76947	−	0.756855i	−1.76947	−	0.756855i
$215$		0			0
$216$	0.182530	+	0.360689i	0.182530	+	0.360689i
$217$		0			0
$218$		0			0
$219$	−0.0736572	+	0.251630i	−0.0736572	+	0.251630i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.621436	−	0.783465i	$-0.713450\pi$
$223$		0			0		0.621436	+	0.783465i	$0.286550\pi$
$224$		0			0
$225$	0.681518	−	0.100894i	0.681518	−	0.100894i
$226$	1.14222	+	1.61541i	1.14222	+	1.61541i
$227$	−0.776963	−	1.77130i	−0.776963	−	1.77130i	−0.621436	−	0.783465i	$-0.713450\pi$
$227$	−0.776963	−	1.77130i	−0.776963	−	1.77130i	−0.155527	−	0.987832i	$-0.549708\pi$
$228$	−1.21285	−	0.466847i	−1.21285	−	0.466847i
$229$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$229$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.741540	+	1.34068i	0.741540	+	1.34068i	0.933251	+	0.359225i	$0.116959\pi$
$233$	0.741540	+	1.34068i	0.741540	+	1.34068i	−0.191711	+	0.981451i	$0.561404\pi$
$234$		0			0
$235$		0			0
$236$	−0.254458	−	1.30268i	−0.254458	−	1.30268i
$237$		0			0
$238$		0			0
$239$		0			0		0.451533	−	0.892254i	$-0.350877\pi$
$239$		0			0		−0.451533	+	0.892254i	$0.649123\pi$
$240$		0			0
$241$	−0.757521	+	0.428125i	−0.757521	+	0.428125i	−0.821778	−	0.569808i	$-0.807018\pi$
$241$	−0.757521	+	0.428125i	−0.757521	+	0.428125i	0.0642573	+	0.997933i	$0.479532\pi$
$242$	−1.51753	−	0.369490i	−1.51753	−	0.369490i
$243$	−0.988566	+	0.632982i	−0.988566	+	0.632982i
$244$		0			0
$245$		0			0
$246$	0.473931	+	0.725406i	0.473931	+	0.725406i
$247$		0			0
$248$		0			0
$249$	−0.300861	−	2.50742i	−0.300861	−	2.50742i
$250$		0			0
$251$	−0.115323	+	0.208499i	−0.115323	+	0.208499i	−0.926494	−	0.376309i	$-0.877193\pi$
$251$	−0.115323	+	0.208499i	−0.115323	+	0.208499i	0.811171	+	0.584809i	$0.198830\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.991742	+	0.128249i	−0.991742	+	0.128249i
$257$	0.836845	−	0.603318i	0.836845	−	0.603318i	−0.0825793	−	0.996584i	$-0.526316\pi$
$257$	0.836845	−	0.603318i	0.836845	−	0.603318i	0.919425	+	0.393266i	$0.128655\pi$
$258$	0.0715102	+	0.00394533i	0.0715102	+	0.00394533i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.311304	+	1.76549i	−0.311304	+	1.76549i
$263$		0			0		0.263253	−	0.964727i	$-0.415205\pi$
$263$		0			0		−0.263253	+	0.964727i	$0.584795\pi$
$264$	−1.46409	−	1.47760i	−1.46409	−	1.47760i
$265$		0			0
$266$		0			0
$267$	1.74970	−	1.90068i	1.74970	−	1.90068i
$268$	0.967359	−	0.0355604i	0.967359	−	0.0355604i
$269$		0			0		0.690683	−	0.723158i	$-0.257310\pi$
$269$		0			0		−0.690683	+	0.723158i	$0.742690\pi$
$270$		0			0
$271$		0			0		0.729471	−	0.684011i	$-0.239766\pi$
$271$		0			0		−0.729471	+	0.684011i	$0.760234\pi$
$272$	0.269627	−	1.15337i	0.269627	−	1.15337i
$273$		0			0
$274$	−1.18367	+	1.61044i	−1.18367	+	1.61044i
$275$	1.43470	−	0.709567i	1.43470	−	0.709567i
$276$		0			0
$277$		0			0		−0.350638	−	0.936511i	$-0.614035\pi$
$277$		0			0		0.350638	+	0.936511i	$0.385965\pi$
$278$	−0.718900	−	0.978099i	−0.718900	−	0.978099i
$279$		0			0
$280$		0			0
$281$	0.700810	+	0.917669i	0.700810	+	0.917669i	0.999325	−	0.0367355i	$-0.0116959\pi$
$281$	0.700810	+	0.917669i	0.700810	+	0.917669i	−0.298515	+	0.954405i	$0.596491\pi$
$282$		0			0
$283$	1.22122	−	1.42853i	1.22122	−	1.42853i	0.350638	−	0.936511i	$-0.385965\pi$
$283$	1.22122	−	1.42853i	1.22122	−	1.42853i	0.870582	−	0.492024i	$-0.163743\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.156828	−	0.670858i	−0.156828	−	0.670858i
$289$	0.335314	+	0.223493i	0.335314	+	0.223493i
$290$		0			0
$291$	0.118818	+	0.435424i	0.118818	+	0.435424i
$292$	−0.100874	+	0.174718i	−0.100874	+	0.174718i
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	0.914722	−	0.923163i	0.914722	−	0.923163i
$295$		0			0
$296$		0			0
$297$	−0.411330	+	0.499450i	−0.411330	+	0.499450i
$298$		0			0
$299$		0			0
$300$	1.29412	+	0.119212i	1.29412	+	0.119212i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.821778	−	0.569808i	−0.821778	−	0.569808i
$305$		0			0
$306$	0.809297	+	0.104656i	0.809297	+	0.104656i
$307$	−1.63616	−	0.595513i	−1.63616	−	0.595513i	−0.649797	−	0.760108i	$-0.725146\pi$
$307$	−1.63616	−	0.595513i	−1.63616	−	0.595513i	−0.986361	+	0.164595i	$0.947368\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.716783	−	0.697297i	$-0.754386\pi$
$311$		0			0		0.716783	+	0.697297i	$0.245614\pi$
$312$		0			0
$313$	−0.182474	+	0.377642i	−0.182474	+	0.377642i	−0.971614	−	0.236570i	$-0.923977\pi$
$313$	−0.182474	+	0.377642i	−0.182474	+	0.377642i	0.789141	+	0.614213i	$0.210526\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.100874	−	0.994899i	$-0.532164\pi$
$317$		0			0		0.100874	+	0.994899i	$0.467836\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	1.29014	−	2.14269i	1.29014	−	2.14269i
$322$		0			0
$323$	0.973372	−	0.674921i	0.973372	−	0.674921i
$324$	−1.14851	+	0.394282i	−1.14851	+	0.394282i
$325$		0			0
$326$	0.0734884	−	0.0550606i	0.0734884	−	0.0550606i
$327$		0			0
$328$	0.222276	+	0.628606i	0.222276	+	0.628606i
$329$		0			0
$330$		0			0
$331$	0.157170	−	0.502500i	0.157170	−	0.502500i	−0.842155	−	0.539235i	$-0.818713\pi$
$331$	0.157170	−	0.502500i	0.157170	−	0.502500i	0.999325	+	0.0367355i	$0.0116959\pi$
$332$	0.231504	−	1.92939i	0.231504	−	1.92939i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.97813	−	0.145630i	−1.97813	−	0.145630i	−0.979649	−	0.200718i	$-0.935673\pi$
$337$	−1.97813	−	0.145630i	−1.97813	−	0.145630i	−0.998482	+	0.0550878i	$0.982456\pi$
$338$	−0.00918581	+	0.999958i	−0.00918581	+	0.999958i
$339$	−2.28337	+	1.18199i	−2.28337	+	1.18199i
$340$		0			0
$341$		0			0
$342$	0.333454	−	0.602872i	0.333454	−	0.602872i
$343$		0			0
$344$	0.0527449	+	0.0159669i	0.0527449	+	0.0159669i
$345$		0			0
$346$		0			0
$347$	0.581072	−	1.74463i	0.581072	−	1.74463i	−0.0825793	−	0.996584i	$-0.526316\pi$
$347$	0.581072	−	1.74463i	0.581072	−	1.74463i	0.663651	−	0.748042i	$-0.269006\pi$
$348$		0			0
$349$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$349$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$350$		0			0
$351$		0			0
$352$	−0.825621	−	1.37121i	−0.825621	−	1.37121i
$353$	−1.52322	+	0.718824i	−1.52322	+	0.718824i	−0.991742	−	0.128249i	$-0.959064\pi$
$353$	−1.52322	+	0.718824i	−1.52322	+	0.718824i	−0.531476	+	0.847073i	$0.678363\pi$
$354$	1.72234	−	0.0950239i	1.72234	−	0.0950239i
$355$		0			0
$356$	1.65411	−	1.10250i	1.65411	−	1.10250i
$357$		0			0
$358$	0.550204	+	0.310957i	0.550204	+	0.310957i
$359$		0			0		0.367783	−	0.929912i	$-0.380117\pi$
$359$		0			0		−0.367783	+	0.929912i	$0.619883\pi$
$360$		0			0
$361$	−0.227635	−	0.973746i	−0.227635	−	0.973746i
$362$		0			0
$363$	0.746521	−	1.88752i	0.746521	−	1.88752i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.777724	−	0.628606i	$-0.216374\pi$
$367$		0			0		−0.777724	+	0.628606i	$0.783626\pi$
$368$		0			0
$369$	−0.415419	+	0.196041i	−0.415419	+	0.196041i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$373$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$374$	1.86394	−	0.346346i	1.86394	−	0.346346i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.86584	+	0.311353i	−1.86584	+	0.311353i	−0.986361	−	0.164595i	$-0.947368\pi$
$379$	−1.86584	+	0.311353i	−1.86584	+	0.311353i	−0.879474	+	0.475947i	$0.842105\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.888069	−	0.459710i	$-0.152047\pi$
$383$		0			0		−0.888069	+	0.459710i	$0.847953\pi$
$384$	0.0119378	−	1.29954i	0.0119378	−	1.29954i
$385$		0			0
$386$	−0.147542	+	0.353897i	−0.147542	+	0.353897i
$387$	−0.00727866	+	0.0372627i	−0.00727866	+	0.0372627i
$388$	0.00956952	+	0.347164i	0.00956952	+	0.347164i
$389$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$389$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$390$		0			0
$391$		0			0
$392$	0.851919	−	0.523673i	0.851919	−	0.523673i
$393$	−2.21711	−	0.715882i	−2.21711	−	0.715882i
$394$		0			0
$395$		0			0
$396$	0.882492	−	0.661200i	0.882492	−	0.661200i
$397$		0			0		0.209708	−	0.977764i	$-0.432749\pi$
$397$		0			0		−0.209708	+	0.977764i	$0.567251\pi$
$398$		0			0
$399$		0			0
$400$	0.945817	+	0.324699i	0.945817	+	0.324699i
$401$	−0.548298	+	0.910625i	−0.548298	+	0.910625i	0.451533	+	0.892254i	$0.350877\pi$
$401$	−0.548298	+	0.910625i	−0.548298	+	0.910625i	−0.999831	+	0.0183709i	$0.994152\pi$
$402$	−0.126901	+	1.25161i	−0.126901	+	1.25161i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.43658	+	0.552967i	1.43658	+	0.552967i
$409$	−0.364107	+	0.753546i	−0.364107	+	0.753546i	−0.999831	−	0.0183709i	$-0.994152\pi$
$409$	−0.364107	+	0.753546i	−0.364107	+	0.753546i	0.635724	+	0.771917i	$0.280702\pi$
$410$		0			0
$411$	−1.86180	−	1.81118i	−1.86180	−	1.81118i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.38741	−	0.750829i	1.38741	−	0.750829i
$418$	0.306849	−	1.57089i	0.306849	−	1.57089i
$419$	1.75628	+	0.950449i	1.75628	+	0.950449i	0.904357	+	0.426776i	$0.140351\pi$
$419$	1.75628	+	0.950449i	1.75628	+	0.950449i	0.851919	+	0.523673i	$0.175439\pi$
$420$		0			0
$421$		0			0		−0.777724	−	0.628606i	$-0.783626\pi$
$421$		0			0		0.777724	+	0.628606i	$0.216374\pi$
$422$	−1.80109	−	0.165914i	−1.80109	−	0.165914i
$423$		0			0
$424$		0			0
$425$	−0.752996	+	0.914313i	−0.752996	+	0.914313i
$426$		0			0
$427$		0			0
$428$	1.35459	−	1.36709i	1.35459	−	1.36709i
$429$		0			0
$430$		0			0
$431$		0			0		−0.263253	−	0.964727i	$-0.584795\pi$
$431$		0			0		0.263253	+	0.964727i	$0.415205\pi$
$432$	−0.402540	+	0.0370815i	−0.402540	+	0.0370815i
$433$	−1.64152	−	1.09410i	−1.64152	−	1.09410i	−0.912045	−	0.410091i	$-0.865497\pi$
$433$	−1.64152	−	1.09410i	−1.64152	−	1.09410i	−0.729471	−	0.684011i	$-0.760234\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.206904	−	0.161040i	−0.206904	−	0.161040i
$439$		0			0		0.649797	−	0.760108i	$-0.274854\pi$
$439$		0			0		−0.649797	+	0.760108i	$0.725146\pi$
$440$		0			0
$441$	0.418147	+	0.547539i	0.418147	+	0.547539i
$442$		0			0
$443$	−0.653233	−	0.338147i	−0.653233	−	0.338147i	0.100874	−	0.994899i	$-0.467836\pi$
$443$	−0.653233	−	0.338147i	−0.653233	−	0.338147i	−0.754107	+	0.656752i	$0.771930\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.65779	+	0.468778i	1.65779	+	0.468778i	0.967104	−	0.254380i	$-0.0818713\pi$
$449$	1.65779	+	0.468778i	1.65779	+	0.468778i	0.690683	+	0.723158i	$0.257310\pi$
$450$	−0.156828	+	0.670858i	−0.156828	+	0.670858i
$451$	−0.778481	+	0.729966i	−0.778481	+	0.729966i
$452$	−1.92228	+	0.468040i	−1.92228	+	0.468040i
$453$		0			0
$454$	1.93290	−	0.0710541i	1.93290	−	0.0710541i
$455$		0			0
$456$	0.880191	−	0.956143i	0.880191	−	0.956143i
$457$	1.34885	+	1.46524i	1.34885	+	1.46524i	0.741914	+	0.670495i	$0.233918\pi$
$457$	1.34885	+	1.46524i	1.34885	+	1.46524i	0.606938	+	0.794749i	$0.292398\pi$
$458$		0			0
$459$	0.126050	−	0.461926i	0.126050	−	0.461926i
$460$		0			0
$461$		0			0		0.912045	−	0.410091i	$-0.134503\pi$
$461$		0			0		−0.912045	+	0.410091i	$0.865497\pi$
$462$		0			0
$463$		0			0		0.926494	−	0.376309i	$-0.122807\pi$
$463$		0			0		−0.926494	+	0.376309i	$0.877193\pi$
$464$		0			0
$465$		0			0
$466$	−1.51944	+	0.196489i	−1.51944	+	0.196489i
$467$	−1.77994	−	0.398894i	−1.77994	−	0.398894i	−0.800291	−	0.599612i	$-0.795322\pi$
$467$	−1.77994	−	0.398894i	−1.77994	−	0.398894i	−0.979649	+	0.200718i	$0.935673\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.30497	+	0.242481i	1.30497	+	0.242481i
$473$	0.0105083	+	0.0875778i	0.0105083	+	0.0875778i
$474$		0			0
$475$	0.484006	+	0.875065i	0.484006	+	0.875065i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.842155	−	0.539235i	$-0.181287\pi$
$479$		0			0		−0.842155	+	0.539235i	$0.818713\pi$
$480$		0			0
$481$		0			0
$482$	−0.119516	−	0.861884i	−0.119516	−	0.861884i
$483$		0			0
$484$	0.901714	−	1.27527i	0.901714	−	1.27527i
$485$		0			0
$486$	−0.225040	−	1.15208i	−0.225040	−	1.15208i
$487$		0			0		0.975796	−	0.218681i	$-0.0701754\pi$
$487$		0			0		−0.975796	+	0.218681i	$0.929825\pi$
$488$		0			0
$489$	0.0577603	+	0.104429i	0.0577603	+	0.104429i
$490$		0			0
$491$	−0.713037	−	1.71030i	−0.713037	−	1.71030i	−0.703852	−	0.710347i	$-0.748538\pi$
$491$	−0.713037	−	1.71030i	−0.713037	−	1.71030i	−0.00918581	−	0.999958i	$-0.502924\pi$
$492$	−0.848868	+	0.173922i	−0.848868	+	0.173922i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	2.44233	+	0.642413i	2.44233	+	0.642413i
$499$	0.327189	+	0.412499i	0.327189	+	0.412499i	0.919425	−	0.393266i	$-0.128655\pi$
$499$	0.327189	+	0.412499i	0.327189	+	0.412499i	−0.592235	+	0.805765i	$0.701754\pi$
$500$		0			0
$501$		0			0
$502$	−0.151472	−	0.183922i	−0.151472	−	0.183922i
$503$		0			0		0.280931	−	0.959728i	$-0.409357\pi$
$503$		0			0		−0.280931	+	0.959728i	$0.590643\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.28558	−	0.190321i	−1.28558	−	0.190321i
$508$		0			0
$509$		0			0		−0.912045	−	0.410091i	$-0.865497\pi$
$509$		0			0		0.912045	+	0.410091i	$0.134503\pi$
$510$		0			0
$511$		0			0
$512$	0.245485	−	0.969400i	0.245485	−	0.969400i
$513$	−0.323513	−	0.242390i	−0.323513	−	0.242390i
$514$	0.253255	+	1.00008i	0.253255	+	1.00008i
$515$		0			0
$516$	−0.0299690	+	0.0650471i	−0.0299690	+	0.0650471i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.229277	−	0.0648334i	0.229277	−	0.0648334i	−0.155527	−	0.987832i	$-0.549708\pi$
$521$	0.229277	−	0.0648334i	0.229277	−	0.0648334i	0.384804	+	0.922998i	$0.374269\pi$
$522$		0			0
$523$	0.522041	+	0.610663i	0.522041	+	0.610663i	0.957107	−	0.289735i	$-0.0935673\pi$
$523$	0.522041	+	0.610663i	0.522041	+	0.610663i	−0.435066	+	0.900399i	$0.643275\pi$
$524$	−1.52726	−	0.938803i	−1.52726	−	0.938803i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.91250	−	0.818036i	1.91250	−	0.818036i
$529$	−0.999831	−	0.0183709i	−0.999831	−	0.0183709i
$530$		0			0
$531$	−0.0755138	+	0.911316i	−0.0755138	+	0.911316i
$532$		0			0
$533$		0			0
$534$	1.12395	+	2.32610i	1.12395	+	2.32610i
$535$		0			0
$536$	−0.322710	+	0.912637i	−0.322710	+	0.912637i
$537$	−0.498501	+	0.652757i	−0.498501	+	0.652757i
$538$		0			0
$539$	1.31532	+	0.912024i	1.31532	+	0.912024i
$540$		0			0
$541$		0			0		−0.367783	−	0.929912i	$-0.619883\pi$
$541$		0			0		0.367783	+	0.929912i	$0.380117\pi$
$542$		0			0
$543$		0			0
$544$	0.973372	+	0.674921i	0.973372	+	0.674921i
$545$		0			0
$546$		0			0
$547$	0.502799	−	1.42194i	0.502799	−	1.42194i	−0.367783	−	0.929912i	$-0.619883\pi$
$547$	0.502799	−	1.42194i	0.502799	−	1.42194i	0.870582	−	0.492024i	$-0.163743\pi$
$548$	−1.06224	−	1.69300i	−1.06224	−	1.69300i
$549$		0			0
$550$	0.132175	+	1.59512i	0.132175	+	1.59512i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.17394	−	0.308786i	1.17394	−	0.308786i
$557$		0			0		−0.800291	−	0.599612i	$-0.795322\pi$
$557$		0			0		0.800291	+	0.599612i	$0.204678\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.113123	+	2.46123i	0.113123	+	2.46123i
$562$	−1.11110	+	0.314188i	−1.11110	+	0.314188i
$563$	−0.394282	+	1.05308i	−0.394282	+	1.05308i	0.577333	+	0.816509i	$0.304094\pi$
$563$	−0.394282	+	1.05308i	−0.394282	+	1.05308i	−0.971614	+	0.236570i	$0.923977\pi$
$564$		0			0
$565$		0			0
$566$	0.879268	+	1.66102i	0.879268	+	1.66102i
$567$		0			0
$568$		0			0
$569$	−0.454882	−	1.79629i	−0.454882	−	1.79629i	−0.592235	−	0.805765i	$-0.701754\pi$
$569$	−0.454882	−	1.79629i	−0.454882	−	1.79629i	0.137354	−	0.990522i	$-0.456140\pi$
$570$		0			0
$571$	0.398262	−	1.57270i	0.398262	−	1.57270i	−0.367783	−	0.929912i	$-0.619883\pi$
$571$	0.398262	−	1.57270i	0.398262	−	1.57270i	0.766044	−	0.642788i	$-0.222222\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.681518	+	0.100894i	0.681518	+	0.100894i
$577$	0.786193	+	1.55356i	0.786193	+	1.55356i	0.832107	+	0.554615i	$0.187135\pi$
$577$	0.786193	+	1.55356i	0.786193	+	1.55356i	−0.0459136	+	0.998945i	$0.514620\pi$
$578$	−0.331152	+	0.229616i	−0.331152	+	0.229616i
$579$	−0.429227	−	0.253100i	−0.429227	−	0.253100i
$580$		0			0
$581$		0			0
$582$	−0.448605	−	0.0496516i	−0.448605	−	0.0496516i
$583$		0			0
$584$	−0.125373	−	0.158062i	−0.125373	−	0.158062i
$585$		0			0
$586$		0			0
$587$	0.521370	+	0.737362i	0.521370	+	0.737362i	0.989219	−	0.146447i	$-0.0467836\pi$
$587$	0.521370	+	0.737362i	0.521370	+	0.737362i	−0.467849	+	0.883809i	$0.654971\pi$
$588$	0.522041	+	1.19013i	0.522041	+	1.19013i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.243194	+	0.730173i	0.243194	+	0.730173i	0.997301	+	0.0734214i	$0.0233918\pi$
$593$	0.243194	+	0.730173i	0.243194	+	0.730173i	−0.754107	+	0.656752i	$0.771930\pi$
$594$	−0.313165	−	0.566190i	−0.313165	−	0.566190i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.577333	−	0.816509i	$-0.304094\pi$
$599$		0			0		−0.577333	+	0.816509i	$0.695906\pi$
$600$	−0.586810	+	1.15957i	−0.586810	+	1.15957i
$601$	−0.258140	−	1.86157i	−0.258140	−	1.86157i	−0.467849	−	0.883809i	$-0.654971\pi$
$601$	−0.258140	−	1.86157i	−0.258140	−	1.86157i	0.209708	−	0.977764i	$-0.432749\pi$
$602$		0			0
$603$	−0.647977	−	0.157771i	−0.647977	−	0.157771i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$607$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$608$	0.832107	−	0.554615i	0.832107	−	0.554615i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.394966	+	0.714084i	−0.394966	+	0.714084i
$613$		0			0		0.155527	−	0.987832i	$-0.450292\pi$
$613$		0			0		−0.155527	+	0.987832i	$0.549708\pi$
$614$	1.15553	−	1.30246i	1.15553	−	1.30246i
$615$		0			0
$616$		0			0
$617$	−1.36996	+	0.177159i	−1.36996	+	0.177159i	−0.777724	−	0.628606i	$-0.783626\pi$
$617$	−1.36996	+	0.177159i	−1.36996	+	0.177159i	−0.592235	+	0.805765i	$0.701754\pi$
$618$		0			0
$619$	−1.80597	−	0.0996380i	−1.80597	−	0.0996380i	−0.879474	−	0.475947i	$-0.842105\pi$
$619$	−1.80597	−	0.0996380i	−1.80597	−	0.0996380i	−0.926494	+	0.376309i	$0.877193\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.703852	−	0.710347i	−0.703852	−	0.710347i
$626$	−0.284063	−	0.308575i	−0.284063	−	0.308575i
$627$	1.96740	+	0.675410i	1.96740	+	0.675410i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.971614	−	0.236570i	$-0.0760234\pi$
$631$		0			0		−0.971614	+	0.236570i	$0.923977\pi$
$632$		0			0
$633$	0.535079	−	2.28888i	0.535079	−	2.28888i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.581476	−	1.09846i	0.581476	−	1.09846i	−0.401695	−	0.915773i	$-0.631579\pi$
$641$	0.581476	−	1.09846i	0.581476	−	1.09846i	0.983171	−	0.182687i	$-0.0584795\pi$
$642$	1.51802	+	1.98776i	1.51802	+	1.98776i
$643$	0.828037	−	0.267365i	0.828037	−	0.267365i	0.137354	−	0.990522i	$-0.456140\pi$
$643$	0.828037	−	0.267365i	0.828037	−	0.267365i	0.690683	+	0.723158i	$0.257310\pi$
$644$		0			0
$645$		0			0
$646$	0.269627	+	1.15337i	0.269627	+	1.15337i
$647$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$647$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$648$	0.0557528	−	1.21302i	0.0557528	−	1.21302i
$649$	0.483601	+	2.06868i	0.483601	+	2.06868i
$650$		0			0
$651$		0			0
$652$	0.0241737	+	0.0885881i	0.0241737	+	0.0885881i
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$		0			0
$655$		0			0
$656$	−0.666298	−	0.0244933i	−0.666298	−	0.0244933i
$657$	0.0996276	−	0.0969192i	0.0996276	−	0.0969192i
$658$		0			0
$659$	1.12276	+	1.65144i	1.12276	+	1.65144i	0.606938	+	0.794749i	$0.292398\pi$
$659$	1.12276	+	1.65144i	1.12276	+	1.65144i	0.515825	+	0.856694i	$0.327485\pi$
$660$		0			0
$661$		0			0		−0.995784	−	0.0917303i	$-0.970760\pi$
$661$		0			0		0.995784	+	0.0917303i	$0.0292398\pi$
$662$	0.409476	+	0.330965i	0.409476	+	0.330965i
$663$		0			0
$664$	1.70902	+	0.924875i	1.70902	+	0.924875i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.26373	−	0.139870i	1.26373	−	0.139870i	0.546948	−	0.837166i	$-0.315789\pi$
$673$	1.26373	−	0.139870i	1.26373	−	0.139870i	0.716783	+	0.697297i	$0.245614\pi$
$674$	0.862946	−	1.78593i	0.862946	−	1.78593i
$675$	0.377261	+	0.145215i	0.377261	+	0.145215i
$676$	−0.926494	−	0.376309i	−0.926494	−	0.376309i
$677$		0			0		−0.904357	−	0.426776i	$-0.859649\pi$
$677$		0			0		0.904357	+	0.426776i	$0.140351\pi$
$678$	−0.259363	−	2.55805i	−0.259363	−	2.55805i
$679$		0			0
$680$		0			0
$681$	−0.253564	+	2.50087i	−0.253564	+	2.50087i
$682$		0			0
$683$	0.663278	+	0.227704i	0.663278	+	0.227704i	0.635724	−	0.771917i	$-0.280702\pi$
$683$	0.663278	+	0.227704i	0.663278	+	0.227704i	0.0275543	+	0.999620i	$0.491228\pi$
$684$	0.437979	+	0.531809i	0.437979	+	0.531809i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.0342465	+	0.0431757i	−0.0342465	+	0.0431757i
$689$		0			0
$690$		0			0
$691$	−0.326644	+	0.200787i	−0.326644	+	0.200787i	−0.677282	−	0.735724i	$-0.736842\pi$
$691$	−0.326644	+	0.200787i	−0.326644	+	0.200787i	0.350638	+	0.936511i	$0.385965\pi$
$692$		0			0
$693$		0			0
$694$	1.40864	+	1.18199i	1.40864	+	1.18199i
$695$		0			0
$696$		0			0
$697$	0.303896	−	0.728931i	0.303896	−	0.728931i
$698$		0			0
$699$	0.0182898	−	1.99101i	0.0182898	−	1.99101i
$700$		0			0
$701$		0			0		−0.896364	−	0.443318i	$-0.853801\pi$
$701$		0			0		0.896364	+	0.443318i	$0.146199\pi$
$702$		0			0
$703$		0			0
$704$	1.57875	−	0.263447i	1.57875	−	0.263447i
$705$		0			0
$706$	−0.108229	−	1.68083i	−0.108229	−	1.68083i
$707$		0			0
$708$	−0.545082	+	1.63657i	−0.545082	+	1.63657i
$709$		0			0		0.983171	−	0.182687i	$-0.0584795\pi$
$709$		0			0		−0.983171	+	0.182687i	$0.941520\pi$
$710$		0			0
$711$		0			0
$712$	0.416871	+	1.94366i	0.416871	+	1.94366i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.491518	+	0.397276i	−0.491518	+	0.397276i
$717$		0			0
$718$		0			0
$719$		0			0		−0.870582	−	0.492024i	$-0.836257\pi$
$719$		0			0		0.870582	+	0.492024i	$0.163743\pi$
$720$		0			0
$721$		0			0
$722$	0.989219	+	0.146447i	0.989219	+	0.146447i
$723$	1.13082			1.13082
$724$		0			0
$725$		0			0
$726$	1.48067	+	1.38840i	1.48067	+	1.38840i
$727$		0			0		0.832107	−	0.554615i	$-0.187135\pi$
$727$		0			0		−0.832107	+	0.554615i	$0.812865\pi$
$728$		0			0
$729$	0.310760	−	0.0171451i	0.310760	−	0.0171451i
$730$		0			0
$731$	−0.0336703	−	0.0559204i	−0.0336703	−	0.0559204i
$732$		0			0
$733$		0			0		−0.754107	−	0.656752i	$-0.771930\pi$
$733$		0			0		0.754107	+	0.656752i	$0.228070\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.54520	+	0.113758i	−1.54520	+	0.113758i
$738$	−0.0295168	−	0.458404i	−0.0295168	−	0.458404i
$739$	−1.61207	−	0.488004i	−1.61207	−	0.488004i	−0.649797	−	0.760108i	$-0.725146\pi$
$739$	−1.61207	−	0.488004i	−1.61207	−	0.488004i	−0.962268	+	0.272103i	$0.912281\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.896364	−	0.443318i	$-0.853801\pi$
$743$		0			0		0.896364	+	0.443318i	$0.146199\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.515168	+	1.23569i	−0.515168	+	1.23569i
$748$	−0.363453	+	1.86068i	−0.363453	+	1.86068i
$749$		0			0
$750$		0			0
$751$		0			0		0.119134	−	0.992878i	$-0.461988\pi$
$751$		0			0		−0.119134	+	0.992878i	$0.538012\pi$
$752$		0			0
$753$	0.263798	−	0.162156i	0.263798	−	0.162156i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.800291	−	0.599612i	$-0.204678\pi$
$757$		0			0		−0.800291	+	0.599612i	$0.795322\pi$
$758$	0.396692	−	1.84957i	0.396692	−	1.84957i
$759$		0			0
$760$		0			0
$761$	1.53444	+	0.526774i	1.53444	+	0.526774i	0.957107	−	0.289735i	$-0.0935673\pi$
$761$	1.53444	+	0.526774i	1.53444	+	0.526774i	0.577333	+	0.816509i	$0.304094\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.20407	+	0.489050i	1.20407	+	0.489050i
$769$	−1.40754	−	0.541788i	−1.40754	−	0.541788i	−0.467849	−	0.883809i	$-0.654971\pi$
$769$	−1.40754	−	0.541788i	−1.40754	−	0.541788i	−0.939693	+	0.342020i	$0.888889\pi$
$770$		0			0
$771$	−1.33259	+	0.147491i	−1.33259	+	0.147491i
$772$	−0.274830	−	0.267358i	−0.274830	−	0.267358i
$773$		0			0		−0.690683	−	0.723158i	$-0.742690\pi$
$773$		0			0		0.690683	+	0.723158i	$0.257310\pi$
$774$	−0.0319740	−	0.0204731i	−0.0319740	−	0.0204731i
$775$		0			0
$776$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$777$		0			0
$778$		0			0
$779$	−0.477913	−	0.464921i	−0.477913	−	0.464921i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.173648	+	0.984808i	0.173648	+	0.984808i
$785$		0			0
$786$	1.48112	−	1.79843i	1.48112	−	1.79843i
$787$	−1.43332	+	1.39436i	−1.43332	+	1.39436i	−0.703852	+	0.710347i	$0.748538\pi$
$787$	−1.43332	+	1.39436i	−1.43332	+	1.39436i	−0.729471	+	0.684011i	$0.760234\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.290293	+	1.06382i	0.290293	+	1.06382i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$797$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$798$		0			0
$799$		0			0
$800$	−0.649797	+	0.760108i	−0.649797	+	0.760108i
$801$	−1.30327	+	0.420814i	−1.30327	+	0.420814i
$802$	−0.645146	−	0.844781i	−0.645146	−	0.844781i
$803$	0.151074	−	0.285393i	0.151074	−	0.285393i
$804$	−1.11721	−	0.578326i	−1.11721	−	0.578326i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.16454	+	1.58441i	−1.16454	+	1.58441i	−0.435066	+	0.900399i	$0.643275\pi$
$809$	−1.16454	+	1.58441i	−1.16454	+	1.58441i	−0.729471	+	0.684011i	$0.760234\pi$
$810$		0			0
$811$	−0.111762	+	0.478081i	−0.111762	+	0.478081i	0.888069	+	0.459710i	$0.152047\pi$
$811$	−0.111762	+	0.478081i	−0.111762	+	0.478081i	−0.999831	+	0.0183709i	$0.994152\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.04256	+	1.13252i	−1.04256	+	1.13252i
$817$	−0.0543571	+	0.00907059i	−0.0543571	+	0.00907059i
$818$	−0.566819	−	0.615729i	−0.566819	−	0.615729i
$819$		0			0
$820$		0			0
$821$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$821$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$822$	2.36898	−	1.06518i	2.36898	−	1.06518i
$823$		0			0		0.999831	−	0.0183709i	$-0.00584795\pi$
$823$		0			0		−0.999831	+	0.0183709i	$0.994152\pi$
$824$		0			0
$825$	−2.07695	−	0.114588i	−2.07695	−	0.114588i
$826$		0			0
$827$	−1.95010	+	0.252181i	−1.95010	+	0.252181i	−0.998482	−	0.0550878i	$-0.982456\pi$
$827$	−1.95010	+	0.252181i	−1.95010	+	0.252181i	−0.951623	+	0.307269i	$0.900585\pi$
$828$		0			0
$829$		0			0		0.0275543	−	0.999620i	$-0.491228\pi$
$829$		0			0		−0.0275543	+	0.999620i	$0.508772\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.16454	−	0.216387i	−1.16454	−	0.216387i
$834$	0.187939	+	1.56631i	0.187939	+	1.56631i
$835$		0			0
$836$	1.34794	+	0.863090i	1.34794	+	0.863090i
$837$		0			0
$838$	−1.52976	+	1.28362i	−1.52976	+	1.28362i
$839$		0			0		−0.663651	−	0.748042i	$-0.730994\pi$
$839$		0			0		0.663651	+	0.748042i	$0.269006\pi$
$840$		0			0
$841$	−0.971614	−	0.236570i	−0.971614	−	0.236570i
$842$		0			0
$843$	−0.206112	−	1.48637i	−0.206112	−	1.48637i
$844$	0.816695	−	1.61383i	0.816695	−	1.61383i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2.29514	+	0.835363i	−2.29514	+	0.835363i
$850$	−0.573291	−	1.03649i	−0.573291	−	1.03649i
$851$		0			0
$852$		0			0
$853$		0			0		0.979649	−	0.200718i	$-0.0643275\pi$
$853$		0			0		−0.979649	+	0.200718i	$0.935673\pi$
$854$		0			0
$855$		0			0
$856$	0.773077	+	1.76244i	0.773077	+	1.76244i
$857$	−0.812713	−	1.14940i	−0.812713	−	1.14940i	−0.986361	−	0.164595i	$-0.947368\pi$
$857$	−0.812713	−	1.14940i	−0.812713	−	1.14940i	0.173648	−	0.984808i	$-0.444444\pi$
$858$		0			0
$859$	1.33593	+	0.351392i	1.33593	+	0.351392i	0.851919	−	0.523673i	$-0.175439\pi$
$859$	1.33593	+	0.351392i	1.33593	+	0.351392i	0.484006	+	0.875065i	$0.339181\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.635724	−	0.771917i	$-0.719298\pi$
$863$		0			0		0.635724	+	0.771917i	$0.280702\pi$
$864$	0.113565	−	0.387965i	0.113565	−	0.387965i
$865$		0			0
$866$	1.62114	−	1.12407i	1.62114	−	1.12407i
$867$	−0.236467	−	0.467272i	−0.236467	−	0.467272i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.0587369	−	0.231947i	0.0587369	−	0.231947i
$874$		0			0
$875$		0			0
$876$	0.225849	−	0.133175i	0.225849	−	0.133175i
$877$		0			0		0.418451	−	0.908239i	$-0.362573\pi$
$877$		0			0		−0.418451	+	0.908239i	$0.637427\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.221601	−	0.591871i	0.221601	−	0.591871i	−0.777724	−	0.628606i	$-0.783626\pi$
$881$	0.221601	−	0.591871i	0.221601	−	0.591871i	0.999325	+	0.0367355i	$0.0116959\pi$
$882$	−0.662950	+	0.187465i	−0.662950	+	0.187465i
$883$	−0.0764100	−	1.66246i	−0.0764100	−	1.66246i	−0.592235	−	0.805765i	$-0.701754\pi$
$883$	−0.0764100	−	1.66246i	−0.0764100	−	1.66246i	0.515825	−	0.856694i	$-0.327485\pi$
$884$		0			0
$885$		0			0
$886$	0.554695	−	0.483084i	0.554695	−	0.483084i
$887$		0			0		−0.800291	−	0.599612i	$-0.795322\pi$
$887$		0			0		0.800291	+	0.599612i	$0.204678\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.81385	−	0.698185i	1.81385	−	0.698185i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.04563	+	1.36919i	−1.04563	+	1.36919i
$899$		0			0
$900$	−0.566160	−	0.392567i	−0.566160	−	0.392567i
$901$		0			0
$902$	−0.392492	−	0.992387i	−0.392492	−	0.992387i
$903$		0			0
$904$	0.271745	−	1.95969i	0.271745	−	1.95969i
$905$		0			0
$906$		0			0
$907$	1.07801	−	1.41158i	1.07801	−	1.41158i	0.173648	−	0.984808i	$-0.444444\pi$
$907$	1.07801	−	1.41158i	1.07801	−	1.41158i	0.904357	−	0.426776i	$-0.140351\pi$
$908$	−0.644815	+	1.82356i	−0.644815	+	1.82356i
$909$		0			0
$910$		0			0
$911$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$911$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$912$	0.565409	+	1.17015i	0.565409	+	1.17015i
$913$	−0.256846	+	3.09967i	−0.256846	+	3.09967i
$914$	−1.85863	+	0.715422i	−1.85863	+	0.715422i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.383192	+	0.287103i	0.383192	+	0.287103i
$919$		0			0		0.754107	−	0.656752i	$-0.228070\pi$
$919$		0			0		−0.754107	+	0.656752i	$0.771930\pi$
$920$		0			0
$921$	1.47037	+	1.71998i	1.47037	+	1.71998i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.915623	−	0.539910i	0.915623	−	0.539910i	0.0275543	−	0.999620i	$-0.491228\pi$
$929$	0.915623	−	0.539910i	0.915623	−	0.539910i	0.888069	+	0.459710i	$0.152047\pi$
$930$		0			0
$931$	−0.531476	+	0.847073i	−0.531476	+	0.847073i
$932$	0.376106	−	1.48521i	0.376106	−	1.48521i
$933$		0			0
$934$	1.02557	−	1.50848i	1.02557	−	1.50848i
$935$		0			0
$936$		0			0
$937$	−0.727635	−	0.107721i	−0.727635	−	0.107721i	−0.227635	−	0.973746i	$-0.573099\pi$
$937$	−0.727635	−	0.107721i	−0.727635	−	0.107721i	−0.500000	+	0.866025i	$0.666667\pi$
$938$		0			0
$939$	0.447928	−	0.310586i	0.447928	−	0.310586i
$940$		0			0
$941$		0			0		0.280931	−	0.959728i	$-0.409357\pi$
$941$		0			0		−0.280931	+	0.959728i	$0.590643\pi$
$942$		0			0
$943$		0			0
$944$	−0.705430	+	1.12432i	−0.705430	+	1.12432i
$945$		0			0
$946$	−0.0853044	−	0.0224378i	−0.0853044	−	0.0224378i
$947$	−1.73998	+	0.257592i	−1.73998	+	0.257592i	−0.939693	−	0.342020i	$-0.888889\pi$
$947$	−1.73998	+	0.257592i	−1.73998	+	0.257592i	−0.800291	+	0.599612i	$0.795322\pi$
$948$		0			0
$949$		0			0
$950$	−0.991742	+	0.128249i	−0.991742	+	0.128249i
$951$		0			0
$952$		0			0
$953$	0.683465	+	1.63937i	0.683465	+	1.63937i	0.766044	+	0.642788i	$0.222222\pi$
$953$	0.683465	+	1.63937i	0.683465	+	1.63937i	−0.0825793	+	0.996584i	$0.526316\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.451533	−	0.892254i	0.451533	−	0.892254i
$962$		0			0
$963$	−1.15431	+	0.652375i	−1.15431	+	0.652375i
$964$	0.845432	+	0.205847i	0.845432	+	0.205847i
$965$		0			0
$966$		0			0
$967$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$967$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$968$	0.854258	+	1.30754i	0.854258	+	1.30754i
$969$	−1.53284	+	0.141203i	−1.53284	+	0.141203i
$970$		0			0
$971$	−0.182523	−	1.52118i	−0.182523	−	1.52118i	−0.729471	−	0.684011i	$-0.760234\pi$
$971$	−0.182523	−	1.52118i	−0.182523	−	1.52118i	0.546948	−	0.837166i	$-0.315789\pi$
$972$	1.15410	+	0.214448i	1.15410	+	0.214448i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.95028	+	0.437067i	1.95028	+	0.437067i	0.983171	+	0.182687i	$0.0584795\pi$
$977$	1.95028	+	0.437067i	1.95028	+	0.437067i	0.967104	+	0.254380i	$0.0818713\pi$
$978$	−0.118353	+	0.0153050i	−0.118353	+	0.0153050i
$979$	−2.58093	+	1.86071i	−2.58093	+	1.86071i
$980$		0			0
$981$		0			0
$982$	1.85268	−	0.0340410i	1.85268	−	0.0340410i
$983$		0			0		0.912045	−	0.410091i	$-0.134503\pi$
$983$		0			0		−0.912045	+	0.410091i	$0.865497\pi$
$984$	0.150466	−	0.853338i	0.150466	−	0.853338i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.690683	−	0.723158i	$-0.257310\pi$
$991$		0			0		−0.690683	+	0.723158i	$0.742690\pi$
$992$		0			0
$993$	−0.499136	+	0.468030i	−0.499136	+	0.468030i
$994$		0			0
$995$		0			0
$996$	−1.49564	+	2.03489i	−1.49564	+	2.03489i
$997$		0			0		0.896364	−	0.443318i	$-0.146199\pi$
$997$		0			0		−0.896364	+	0.443318i	$0.853801\pi$
$998$	−0.503922	+	0.152547i	−0.503922	+	0.152547i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.bs.a.291.1	✓	108
8.3	odd	2	CM	2888.1.bs.a.291.1	✓	108
361.263	even	171	inner	2888.1.bs.a.1707.1	yes	108
2888.1707	odd	342	inner	2888.1.bs.a.1707.1	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2888.1.bs.a.291.1	✓	108	1.1	even	1	trivial
2888.1.bs.a.291.1	✓	108	8.3	odd	2	CM
2888.1.bs.a.1707.1	yes	108	361.263	even	171	inner
2888.1.bs.a.1707.1	yes	108	2888.1707	odd	342	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.bs (of order \(342\), degree \(108\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.367783 + 0.929912i) q^{2} +(-1.13140 - 0.639431i) q^{3} +(-0.729471 - 0.684011i) q^{4} +(1.01073 - 0.816933i) q^{6} +(0.904357 - 0.426776i) q^{8} +(0.355376 + 0.590216i) q^{9} +O(q^{10})\)	\(q+(-0.367783 + 0.929912i) q^{2} +(-1.13140 - 0.639431i) q^{3} +(-0.729471 - 0.684011i) q^{4} +(1.01073 - 0.816933i) q^{6} +(0.904357 - 0.426776i) q^{8} +(0.355376 + 0.590216i) q^{9} +(1.20701 + 1.05119i) q^{11} +(0.387948 + 1.24034i) q^{12} +(0.0642573 + 0.997933i) q^{16} +(-1.13366 - 0.343183i) q^{17} +(-0.679549 + 0.113397i) q^{18} +(-0.621436 + 0.783465i) q^{19} +(-1.42143 + 0.735804i) q^{22} +(-1.29609 - 0.0954181i) q^{24} +(0.384804 - 0.922998i) q^{25} +(0.0111387 + 0.404091i) q^{27} +(-0.951623 - 0.307269i) q^{32} +(-0.693453 - 1.96111i) q^{33} +(0.736072 - 0.927991i) q^{34} +(0.144478 - 0.673626i) q^{36} +(-0.500000 - 0.866025i) q^{38} +(-0.0672572 + 0.663347i) q^{41} +(0.0408859 + 0.0369501i) q^{43} +(-0.161456 - 1.59242i) q^{44} +(0.565409 - 1.17015i) q^{48} +(0.993931 - 0.110008i) q^{49} +(0.716783 + 0.697297i) q^{50} +(1.06319 + 1.11318i) q^{51} +(-0.379865 - 0.138260i) q^{54} +(1.20407 - 0.489050i) q^{57} +(1.07667 + 0.776218i) q^{59} +(0.635724 - 0.771917i) q^{64} +(2.07870 + 0.0764138i) q^{66} +(-0.681337 + 0.687624i) q^{67} +(0.592235 + 1.02578i) q^{68} +(0.573277 + 0.382100i) q^{72} +(-0.0459248 - 0.196450i) q^{73} +(-1.02556 + 0.798227i) q^{75} +(0.989219 - 0.146447i) q^{76} +(0.568108 - 1.07321i) q^{81} +(-0.592118 - 0.306511i) q^{82} +(1.15085 + 1.56579i) q^{83} +(-0.0493975 + 0.0244307i) q^{86} +(1.54019 + 0.435524i) q^{88} +(-0.452508 + 1.93567i) q^{89} +(0.880191 + 0.956143i) q^{96} +(-0.244445 - 0.246701i) q^{97} +(-0.263253 + 0.964727i) q^{98} +(-0.191484 + 1.08596i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 108 * q + 3 * q^3 + 3 * q^6 + 3 * q^8 + 3 * q^9	\( 108 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9} - 6 q^{18} - 6 q^{22} + 3 q^{24} - 60 q^{27} + 3 q^{33} + 3 q^{36} - 54 q^{38} + 3 q^{41} - 6 q^{44} - 6 q^{48} + 3 q^{49} + 3 q^{50} - 3 q^{51} + 3 q^{54} + 3 q^{59} + 3 q^{64} + 3 q^{66} + 3 q^{67} - 3 q^{68} - 6 q^{72} - 6 q^{73} - 3 q^{81} + 3 q^{82} + 3 q^{97} - 3 q^{99}+O(q^{100}) \) 108 * q + 3 * q^3 + 3 * q^6 + 3 * q^8 + 3 * q^9 - 6 * q^18 - 6 * q^22 + 3 * q^24 - 60 * q^27 + 3 * q^33 + 3 * q^36 - 54 * q^38 + 3 * q^41 - 6 * q^44 - 6 * q^48 + 3 * q^49 + 3 * q^50 - 3 * q^51 + 3 * q^54 + 3 * q^59 + 3 * q^64 + 3 * q^66 + 3 * q^67 - 3 * q^68 - 6 * q^72 - 6 * q^73 - 3 * q^81 + 3 * q^82 + 3 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more