LMFDB - Embedded newform 2888.1.bs.a.443.1

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			443.1
Root			$0.384804 + 0.922998i$ of defining polynomial
Character	$\chi$	$=$	2888.443
Dual form			2888.1.bs.a.339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.811171 + 0.584809i) q^{2} +(-0.589055 + 1.27853i) q^{3} +(0.315998 + 0.948760i) q^{4} +(-1.22552 + 0.692623i) q^{6} +(-0.298515 + 0.954405i) q^{8} +(-0.637859 - 0.746143i) q^{9} +O(q^{10})$	\(q+(0.811171 + 0.584809i) q^{2} +(-0.589055 + 1.27853i) q^{3} +(0.315998 + 0.948760i) q^{4} +(-1.22552 + 0.692623i) q^{6} +(-0.298515 + 0.954405i) q^{8} +(-0.637859 - 0.746143i) q^{9} +(1.25774 + 1.52719i) q^{11} +(-1.39916 - 0.154859i) q^{12} +(-0.800291 + 0.599612i) q^{16} +(1.95632 - 0.400826i) q^{17} +(-0.0810622 - 0.978276i) q^{18} +(-0.912045 - 0.410091i) q^{19} +(0.127129 + 1.97435i) q^{22} +(-1.04440 - 0.943858i) q^{24} +(0.690683 + 0.723158i) q^{25} +(-0.0248860 + 0.00703709i) q^{27} +(-0.999831 + 0.0183709i) q^{32} +(-2.69344 + 0.708461i) q^{33} +(1.82132 + 0.818936i) q^{34} +(0.506349 - 0.840955i) q^{36} +(-0.500000 - 0.866025i) q^{38} +(-1.02799 - 1.63842i) q^{41} +(-0.931487 - 1.68409i) q^{43} +(-1.05149 + 1.67588i) q^{44} +(-0.295207 - 1.37640i) q^{48} +(0.451533 - 0.892254i) q^{49} +(0.137354 + 0.990522i) q^{50} +(-0.639913 + 2.73733i) q^{51} +(-0.0243021 - 0.00884526i) q^{54} +(1.06156 - 0.924512i) q^{57} +(-1.12371 + 0.0413080i) q^{59} +(-0.821778 - 0.569808i) q^{64} +(-2.59915 - 1.00046i) q^{66} +(0.0306128 + 0.666045i) q^{67} +(0.998482 + 1.72942i) q^{68} +(0.902533 - 0.386041i) q^{72} +(-0.705430 - 0.795133i) q^{73} +(-1.33143 + 0.457080i) q^{75} +(0.100874 - 0.994899i) q^{76} +(0.158332 - 1.00565i) q^{81} +(0.124287 - 1.93021i) q^{82} +(1.45673 - 0.0803699i) q^{83} +(0.229277 - 1.91083i) q^{86} +(-1.83301 + 0.744504i) q^{88} +(0.599321 - 0.675532i) q^{89} +(0.565468 - 1.28914i) q^{96} +(-0.0159456 + 0.346930i) q^{97} +(0.888069 - 0.459710i) q^{98} +(0.337240 - 1.91259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times$.

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{34}{171}\right)$

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 $

$2$	0.811171	+	0.584809i	0.811171	+	0.584809i
$2$	0.811171	+	0.584809i	0.811171	+	0.584809i
$3$	−0.589055	+	1.27853i	−0.589055	+	1.27853i	0.350638	+	0.936511i	$0.385965\pi$
$3$	−0.589055	+	1.27853i	−0.589055	+	1.27853i	−0.939693	+	0.342020i	$0.888889\pi$
$4$	0.315998	+	0.948760i	0.315998	+	0.948760i
$5$		0			0		−0.919425	−	0.393266i	$-0.871345\pi$
$5$		0			0		0.919425	+	0.393266i	$0.128655\pi$
$6$	−1.22552	+	0.692623i	−1.22552	+	0.692623i
$7$		0			0		0.851919	−	0.523673i	$-0.175439\pi$
$7$		0			0		−0.851919	+	0.523673i	$0.824561\pi$
$8$	−0.298515	+	0.954405i	−0.298515	+	0.954405i
$9$	−0.637859	−	0.746143i	−0.637859	−	0.746143i
$10$		0			0
$11$	1.25774	+	1.52719i	1.25774	+	1.52719i	0.741914	+	0.670495i	$0.233918\pi$
$11$	1.25774	+	1.52719i	1.25774	+	1.52719i	0.515825	+	0.856694i	$0.327485\pi$
$12$	−1.39916	−	0.154859i	−1.39916	−	0.154859i
$13$		0			0		−0.263253	−	0.964727i	$-0.584795\pi$
$13$		0			0		0.263253	+	0.964727i	$0.415205\pi$
$14$		0			0
$15$		0			0
$16$	−0.800291	+	0.599612i	−0.800291	+	0.599612i
$17$	1.95632	−	0.400826i	1.95632	−	0.400826i	0.967104	−	0.254380i	$-0.0818713\pi$
$17$	1.95632	−	0.400826i	1.95632	−	0.400826i	0.989219	−	0.146447i	$-0.0467836\pi$
$18$	−0.0810622	−	0.978276i	−0.0810622	−	0.978276i
$19$	−0.912045	−	0.410091i	−0.912045	−	0.410091i
$19$	−0.912045	−	0.410091i	−0.912045	−	0.410091i
$20$		0			0
$21$		0			0
$22$	0.127129	+	1.97435i	0.127129	+	1.97435i
$23$		0			0		−0.995784	−	0.0917303i	$-0.970760\pi$
$23$		0			0		0.995784	+	0.0917303i	$0.0292398\pi$
$24$	−1.04440	−	0.943858i	−1.04440	−	0.943858i
$25$	0.690683	+	0.723158i	0.690683	+	0.723158i
$26$		0			0
$27$	−0.0248860	+	0.00703709i	−0.0248860	+	0.00703709i
$28$		0			0
$29$		0			0		−0.367783	−	0.929912i	$-0.619883\pi$
$29$		0			0		0.367783	+	0.929912i	$0.380117\pi$
$30$		0			0
$31$		0			0		−0.716783	−	0.697297i	$-0.754386\pi$
$31$		0			0		0.716783	+	0.697297i	$0.245614\pi$
$32$	−0.999831	+	0.0183709i	−0.999831	+	0.0183709i
$33$	−2.69344	+	0.708461i	−2.69344	+	0.708461i
$34$	1.82132	+	0.818936i	1.82132	+	0.818936i
$35$		0			0
$36$	0.506349	−	0.840955i	0.506349	−	0.840955i
$37$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$37$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$38$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$39$		0			0
$40$		0			0
$41$	−1.02799	−	1.63842i	−1.02799	−	1.63842i	−0.729471	−	0.684011i	$-0.760234\pi$
$41$	−1.02799	−	1.63842i	−1.02799	−	1.63842i	−0.298515	−	0.954405i	$-0.596491\pi$
$42$		0			0
$43$	−0.931487	−	1.68409i	−0.931487	−	1.68409i	−0.703852	−	0.710347i	$-0.748538\pi$
$43$	−0.931487	−	1.68409i	−0.931487	−	1.68409i	−0.227635	−	0.973746i	$-0.573099\pi$
$44$	−1.05149	+	1.67588i	−1.05149	+	1.67588i
$45$		0			0
$46$		0			0
$47$		0			0		−0.861396	−	0.507934i	$-0.830409\pi$
$47$		0			0		0.861396	+	0.507934i	$0.169591\pi$
$48$	−0.295207	−	1.37640i	−0.295207	−	1.37640i
$49$	0.451533	−	0.892254i	0.451533	−	0.892254i
$50$	0.137354	+	0.990522i	0.137354	+	0.990522i
$51$	−0.639913	+	2.73733i	−0.639913	+	2.73733i
$52$		0			0
$53$		0			0		0.00918581	−	0.999958i	$-0.497076\pi$
$53$		0			0		−0.00918581	+	0.999958i	$0.502924\pi$
$54$	−0.0243021	−	0.00884526i	−0.0243021	−	0.00884526i
$55$		0			0
$56$		0			0
$57$	1.06156	−	0.924512i	1.06156	−	0.924512i
$58$		0			0
$59$	−1.12371	+	0.0413080i	−1.12371	+	0.0413080i	−0.592235	−	0.805765i	$-0.701754\pi$
$59$	−1.12371	+	0.0413080i	−1.12371	+	0.0413080i	−0.531476	+	0.847073i	$0.678363\pi$
$60$		0			0
$61$		0			0		−0.606938	−	0.794749i	$-0.707602\pi$
$61$		0			0		0.606938	+	0.794749i	$0.292398\pi$
$62$		0			0
$63$		0			0
$64$	−0.821778	−	0.569808i	−0.821778	−	0.569808i
$65$		0			0
$66$	−2.59915	−	1.00046i	−2.59915	−	1.00046i
$67$	0.0306128	+	0.666045i	0.0306128	+	0.666045i	0.957107	+	0.289735i	$0.0935673\pi$
$67$	0.0306128	+	0.666045i	0.0306128	+	0.666045i	−0.926494	+	0.376309i	$0.877193\pi$
$68$	0.998482	+	1.72942i	0.998482	+	1.72942i
$69$		0			0
$70$		0			0
$71$		0			0		0.606938	−	0.794749i	$-0.292398\pi$
$71$		0			0		−0.606938	+	0.794749i	$0.707602\pi$
$72$	0.902533	−	0.386041i	0.902533	−	0.386041i
$73$	−0.705430	−	0.795133i	−0.705430	−	0.795133i	0.280931	−	0.959728i	$-0.409357\pi$
$73$	−0.705430	−	0.795133i	−0.705430	−	0.795133i	−0.986361	+	0.164595i	$0.947368\pi$
$74$		0			0
$75$	−1.33143	+	0.457080i	−1.33143	+	0.457080i
$76$	0.100874	−	0.994899i	0.100874	−	0.994899i
$77$		0			0
$78$		0			0
$79$		0			0		−0.999831	−	0.0183709i	$-0.994152\pi$
$79$		0			0		0.999831	+	0.0183709i	$0.00584795\pi$
$80$		0			0
$81$	0.158332	−	1.00565i	0.158332	−	1.00565i
$82$	0.124287	−	1.93021i	0.124287	−	1.93021i
$83$	1.45673	−	0.0803699i	1.45673	−	0.0803699i	0.690683	−	0.723158i	$-0.257310\pi$
$83$	1.45673	−	0.0803699i	1.45673	−	0.0803699i	0.766044	+	0.642788i	$0.222222\pi$
$84$		0			0
$85$		0			0
$86$	0.229277	−	1.91083i	0.229277	−	1.91083i
$87$		0			0
$88$	−1.83301	+	0.744504i	−1.83301	+	0.744504i
$89$	0.599321	−	0.675532i	0.599321	−	0.675532i	−0.367783	−	0.929912i	$-0.619883\pi$
$89$	0.599321	−	0.675532i	0.599321	−	0.675532i	0.967104	+	0.254380i	$0.0818713\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.565468	−	1.28914i	0.565468	−	1.28914i
$97$	−0.0159456	+	0.346930i	−0.0159456	+	0.346930i	0.975796	+	0.218681i	$0.0701754\pi$
$97$	−0.0159456	+	0.346930i	−0.0159456	+	0.346930i	−0.991742	+	0.128249i	$0.959064\pi$
$98$	0.888069	−	0.459710i	0.888069	−	0.459710i
$99$	0.337240	−	1.91259i	0.337240	−	1.91259i
$100$	−0.467849	+	0.883809i	−0.467849	+	0.883809i
$101$		0			0		0.983171	−	0.182687i	$-0.0584795\pi$
$101$		0			0		−0.983171	+	0.182687i	$0.941520\pi$
$102$	−2.11989	+	1.84622i	−2.11989	+	1.84622i
$103$		0			0		−0.851919	−	0.523673i	$-0.824561\pi$
$103$		0			0		0.851919	+	0.523673i	$0.175439\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.78307	+	0.504204i	1.78307	+	0.504204i	0.993931	−	0.110008i	$-0.0350877\pi$
$107$	1.78307	+	0.504204i	1.78307	+	0.504204i	0.789141	+	0.614213i	$0.210526\pi$
$108$	−0.0145404	−	0.0213871i	−0.0145404	−	0.0213871i
$109$		0			0		−0.00918581	−	0.999958i	$-0.502924\pi$
$109$		0			0		0.00918581	+	0.999958i	$0.497076\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.177431	+	0.0960210i	−0.177431	+	0.0960210i	−0.562235	−	0.826977i	$-0.690058\pi$
$113$	−0.177431	+	0.0960210i	−0.177431	+	0.0960210i	0.384804	+	0.922998i	$0.374269\pi$
$114$	1.40177	−	0.129129i	1.40177	−	0.129129i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.935680	−	0.623648i	−0.935680	−	0.623648i
$119$		0			0
$120$		0			0
$121$	−0.558686	+	2.86016i	−0.558686	+	2.86016i
$122$		0			0
$123$	2.70031	−	0.349195i	2.70031	−	0.349195i
$124$		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	$0.888889\pi$
$128$	−0.333374	−	0.942795i	−0.333374	−	0.942795i
$129$	2.70186	−	0.198912i	2.70186	−	0.198912i
$130$		0			0
$131$	0.103662	+	0.214536i	0.103662	+	0.214536i	0.945817	−	0.324699i	$-0.105263\pi$
$131$	0.103662	+	0.214536i	0.103662	+	0.214536i	−0.842155	+	0.539235i	$0.818713\pi$
$132$	−1.52328	−	2.33155i	−1.52328	−	2.33155i
$133$		0			0
$134$	−0.364676	+	0.558179i	−0.364676	+	0.558179i
$135$		0			0
$136$	−0.201441	+	1.98678i	−0.201441	+	1.98678i
$137$	−1.57188	+	1.00648i	−1.57188	+	1.00648i	−0.592235	+	0.805765i	$0.701754\pi$
$137$	−1.57188	+	1.00648i	−1.57188	+	1.00648i	−0.979649	+	0.200718i	$0.935673\pi$
$138$		0			0
$139$	1.51130	−	1.22153i	1.51130	−	1.22153i	0.606938	−	0.794749i	$-0.292398\pi$
$139$	1.51130	−	1.22153i	1.51130	−	1.22153i	0.904357	−	0.426776i	$-0.140351\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.957869	+	0.214664i	0.957869	+	0.214664i
$145$		0			0
$146$	−0.107224	−	1.05753i	−0.107224	−	1.05753i
$147$	0.874797	+	1.10289i	0.874797	+	1.10289i
$148$		0			0
$149$		0			0		0.951623	−	0.307269i	$-0.0994152\pi$
$149$		0			0		−0.951623	+	0.307269i	$0.900585\pi$
$150$	−1.34732	−	0.407861i	−1.34732	−	0.407861i
$151$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$151$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$152$	0.663651	−	0.748042i	0.663651	−	0.748042i
$153$	−1.54693	−	1.20403i	−1.54693	−	1.20403i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.995784	−	0.0917303i	$-0.0292398\pi$
$157$		0			0		−0.995784	+	0.0917303i	$0.970760\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.716545	−	0.723158i	0.716545	−	0.723158i
$163$	−1.28500	+	1.25006i	−1.28500	+	1.25006i	−0.333374	+	0.942795i	$0.608187\pi$
$163$	−1.28500	+	1.25006i	−1.28500	+	1.25006i	−0.951623	+	0.307269i	$0.900585\pi$
$164$	1.22962	−	1.49305i	1.22962	−	1.49305i
$165$		0			0
$166$	1.22866	+	0.786713i	1.22866	+	0.786713i
$167$		0			0		0.621436	−	0.783465i	$-0.286550\pi$
$167$		0			0		−0.621436	+	0.783465i	$0.713450\pi$
$168$		0			0
$169$	−0.861396	+	0.507934i	−0.861396	+	0.507934i
$170$		0			0
$171$	0.275770	+	0.942096i	0.275770	+	0.942096i
$172$	1.30345	−	1.41593i	1.30345	−	1.41593i
$173$		0			0		0.209708	−	0.977764i	$-0.432749\pi$
$173$		0			0		−0.209708	+	0.977764i	$0.567251\pi$
$174$		0			0
$175$		0			0
$176$	−1.92228	−	0.468040i	−1.92228	−	0.468040i
$177$	0.609114	−	1.46103i	0.609114	−	1.46103i
$178$	0.881209	−	0.197484i	0.881209	−	0.197484i
$179$	−0.382386	−	1.95761i	−0.382386	−	1.95761i	−0.263253	−	0.964727i	$-0.584795\pi$
$179$	−0.382386	−	1.95761i	−0.382386	−	1.95761i	−0.119134	−	0.992878i	$-0.538012\pi$
$180$		0			0
$181$		0			0		0.811171	−	0.584809i	$-0.198830\pi$
$181$		0			0		−0.811171	+	0.584809i	$0.801170\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.07268	+	2.48354i	3.07268	+	2.48354i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$191$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$192$	1.21259	−	0.715020i	1.21259	−	0.715020i
$193$	0.689473	+	0.128114i	0.689473	+	0.128114i	0.515825	−	0.856694i	$-0.327485\pi$
$193$	0.689473	+	0.128114i	0.689473	+	0.128114i	0.173648	+	0.984808i	$0.444444\pi$
$194$	−0.215822	+	0.272095i	−0.215822	+	0.272095i
$195$		0			0
$196$	0.989219	+	0.146447i	0.989219	+	0.146447i
$197$		0			0		0.635724	−	0.771917i	$-0.280702\pi$
$197$		0			0		−0.635724	+	0.771917i	$0.719298\pi$
$198$	1.39206	−	1.35421i	1.39206	−	1.35421i
$199$		0			0		0.703852	−	0.710347i	$-0.251462\pi$
$199$		0			0		−0.703852	+	0.710347i	$0.748538\pi$
$200$	−0.896364	+	0.443318i	−0.896364	+	0.443318i
$201$	−0.869592	−	0.353198i	−0.869592	−	0.353198i
$202$		0			0
$203$		0			0
$204$	−2.79928	+	0.257866i	−2.79928	+	0.257866i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.520829	−	1.90865i	−0.520829	−	1.90865i
$210$		0			0
$211$	−0.571421	−	0.172981i	−0.571421	−	0.172981i	−0.00918581	−	0.999958i	$-0.502924\pi$
$211$	−0.571421	−	0.172981i	−0.571421	−	0.172981i	−0.562235	+	0.826977i	$0.690058\pi$
$212$		0			0
$213$		0			0
$214$	1.15151	+	1.45175i	1.15151	+	1.45175i
$215$		0			0
$216$	0.000712605	−	0.0258520i	0.000712605	−	0.0258520i
$217$		0			0
$218$		0			0
$219$	1.43214	−	0.433537i	1.43214	−	0.433537i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.912045	−	0.410091i	$-0.134503\pi$
$223$		0			0		−0.912045	+	0.410091i	$0.865497\pi$
$224$		0			0
$225$	0.0990203	−	0.976621i	0.0990203	−	0.976621i
$226$	−0.200081	−	0.0258739i	−0.200081	−	0.0258739i
$227$	−0.921231	+	1.41005i	−0.921231	+	1.41005i	−0.00918581	+	0.999958i	$0.502924\pi$
$227$	−0.921231	+	1.41005i	−0.921231	+	1.41005i	−0.912045	+	0.410091i	$0.865497\pi$
$228$	1.21259	+	0.715020i	1.21259	+	0.715020i
$229$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$229$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.510758	−	1.44445i	−0.510758	−	1.44445i	−0.861396	−	0.507934i	$-0.830409\pi$
$233$	−0.510758	−	1.44445i	−0.510758	−	1.44445i	0.350638	−	0.936511i	$-0.385965\pi$
$234$		0			0
$235$		0			0
$236$	−0.394282	−	1.05308i	−0.394282	−	1.05308i
$237$		0			0
$238$		0			0
$239$		0			0		−0.0275543	−	0.999620i	$-0.508772\pi$
$239$		0			0		0.0275543	+	0.999620i	$0.491228\pi$
$240$		0			0
$241$	0.175505	+	0.380931i	0.175505	+	0.380931i	0.975796	−	0.218681i	$-0.0701754\pi$
$241$	0.175505	+	0.380931i	0.175505	+	0.380931i	−0.800291	+	0.599612i	$0.795322\pi$
$242$	−2.12584	+	1.99335i	−2.12584	+	1.99335i
$243$	1.17096	+	0.780470i	1.17096	+	0.780470i
$244$		0			0
$245$		0			0
$246$	2.39462	+	1.29591i	2.39462	+	1.29591i
$247$		0			0
$248$		0			0
$249$	−0.755337	+	1.90981i	−0.755337	+	1.90981i
$250$		0			0
$251$	0.245218	−	0.693488i	0.245218	−	0.693488i	−0.754107	−	0.656752i	$-0.771930\pi$
$251$	0.245218	−	0.693488i	0.245218	−	0.693488i	0.999325	−	0.0367355i	$-0.0116959\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.280931	−	0.959728i	0.280931	−	0.959728i
$257$	−1.29872	−	0.0477413i	−1.29872	−	0.0477413i	−0.621436	−	0.783465i	$-0.713450\pi$
$257$	−1.29872	−	0.0477413i	−1.29872	−	0.0477413i	−0.677282	+	0.735724i	$0.736842\pi$
$258$	2.30800	+	1.41872i	2.30800	+	1.41872i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.0413747	+	0.234647i	−0.0413747	+	0.234647i
$263$		0			0		0.888069	−	0.459710i	$-0.152047\pi$
$263$		0			0		−0.888069	+	0.459710i	$0.847953\pi$
$264$	0.127872	−	2.78212i	0.127872	−	2.78212i
$265$		0			0
$266$		0			0
$267$	0.510655	+	1.16418i	0.510655	+	1.16418i
$268$	−0.622243	+	0.239513i	−0.622243	+	0.239513i
$269$		0			0		−0.227635	−	0.973746i	$-0.573099\pi$
$269$		0			0		0.227635	+	0.973746i	$0.426901\pi$
$270$		0			0
$271$		0			0		0.315998	−	0.948760i	$-0.397661\pi$
$271$		0			0		−0.315998	+	0.948760i	$0.602339\pi$
$272$	−1.32529	+	1.49381i	−1.32529	+	1.49381i
$273$		0			0
$274$	−1.86367	−	0.102821i	−1.86367	−	0.102821i
$275$	−0.235698	+	1.96435i	−0.235698	+	1.96435i
$276$		0			0
$277$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$277$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$278$	1.94028	−	0.107048i	1.94028	−	0.107048i
$279$		0			0
$280$		0			0
$281$	1.92718	−	0.469234i	1.92718	−	0.469234i	0.933251	−	0.359225i	$-0.116959\pi$
$281$	1.92718	−	0.469234i	1.92718	−	0.469234i	0.993931	−	0.110008i	$-0.0350877\pi$
$282$		0			0
$283$	1.32281	+	1.33502i	1.32281	+	1.33502i	0.904357	+	0.426776i	$0.140351\pi$
$283$	1.32281	+	1.33502i	1.32281	+	1.33502i	0.418451	+	0.908239i	$0.362573\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.651459	+	0.734299i	0.651459	+	0.734299i
$289$	2.74711	−	1.17503i	2.74711	−	1.17503i
$290$		0			0
$291$	−0.434168	−	0.224748i	−0.434168	−	0.224748i
$292$	0.531476	−	0.920544i	0.531476	−	0.920544i
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	0.0646327	+	1.40622i	0.0646327	+	1.40622i
$295$		0			0
$296$		0			0
$297$	−0.0420470	−	0.0291548i	−0.0420470	−	0.0291548i
$298$		0			0
$299$		0			0
$300$	−0.854388	−	1.11877i	−0.854388	−	1.11877i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.975796	−	0.218681i	0.975796	−	0.218681i
$305$		0			0
$306$	−0.550703	−	1.88133i	−0.550703	−	1.88133i
$307$	−0.786431	−	0.286237i	−0.786431	−	0.286237i	−0.0825793	−	0.996584i	$-0.526316\pi$
$307$	−0.786431	−	0.286237i	−0.786431	−	0.286237i	−0.703852	+	0.710347i	$0.748538\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.137354	−	0.990522i	$-0.543860\pi$
$311$		0			0		0.137354	+	0.990522i	$0.456140\pi$
$312$		0			0
$313$	0.216346	+	1.00871i	0.216346	+	1.00871i	0.945817	+	0.324699i	$0.105263\pi$
$313$	0.216346	+	1.00871i	0.216346	+	1.00871i	−0.729471	+	0.684011i	$0.760234\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.531476	−	0.847073i	$-0.321637\pi$
$317$		0			0		−0.531476	+	0.847073i	$0.678363\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.69497	+	1.98271i	−1.69497	+	1.98271i
$322$		0			0
$323$	−1.94863	−	0.436698i	−1.94863	−	0.436698i
$324$	1.00415	−	0.167563i	1.00415	−	0.167563i
$325$		0			0
$326$	−1.77340	+	0.262539i	−1.77340	+	0.262539i
$327$		0			0
$328$	1.87058	−	0.492024i	1.87058	−	0.492024i
$329$		0			0
$330$		0			0
$331$	1.76536	−	0.195390i	1.76536	−	0.195390i	0.832107	−	0.554615i	$-0.187135\pi$
$331$	1.76536	−	0.195390i	1.76536	−	0.195390i	0.933251	+	0.359225i	$0.116959\pi$
$332$	0.536574	+	1.35669i	0.536574	+	1.35669i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.416854	+	0.376726i	0.416854	+	0.376726i	0.851919	−	0.523673i	$-0.175439\pi$
$337$	0.416854	+	0.376726i	0.416854	+	0.376726i	−0.435066	+	0.900399i	$0.643275\pi$
$338$	−0.995784	−	0.0917303i	−0.995784	−	0.0917303i
$339$	−0.0182491	−	0.283413i	−0.0182491	−	0.283413i
$340$		0			0
$341$		0			0
$342$	−0.327249	+	0.925474i	−0.327249	+	0.925474i
$343$		0			0
$344$	1.88537	−	0.386289i	1.88537	−	0.386289i
$345$		0			0
$346$		0			0
$347$	−1.23952	−	0.0912534i	−1.23952	−	0.0912534i	−0.562235	−	0.826977i	$-0.690058\pi$
$347$	−1.23952	−	0.0912534i	−1.23952	−	0.0912534i	−0.677282	+	0.735724i	$0.736842\pi$
$348$		0			0
$349$		0			0		−0.993931	−	0.110008i	$-0.964912\pi$
$349$		0			0		0.993931	+	0.110008i	$0.0350877\pi$
$350$		0			0
$351$		0			0
$352$	−1.28558	−	1.50383i	−1.28558	−	1.50383i
$353$	−0.496793	+	1.58833i	−0.496793	+	1.58833i	0.280931	+	0.959728i	$0.409357\pi$
$353$	−0.496793	+	1.58833i	−0.496793	+	1.58833i	−0.777724	+	0.628606i	$0.783626\pi$
$354$	1.34852	−	0.828933i	1.34852	−	0.828933i
$355$		0			0
$356$	0.830302	+	0.355146i	0.830302	+	0.355146i
$357$		0			0
$358$	0.834644	−	1.81158i	0.834644	−	1.81158i
$359$		0			0		−0.811171	−	0.584809i	$-0.801170\pi$
$359$		0			0		0.811171	+	0.584809i	$0.198830\pi$
$360$		0			0
$361$	0.663651	+	0.748042i	0.663651	+	0.748042i
$362$		0			0
$363$	−3.32771	−	2.39909i	−3.32771	−	2.39909i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.870582	−	0.492024i	$-0.163743\pi$
$367$		0			0		−0.870582	+	0.492024i	$0.836257\pi$
$368$		0			0
$369$	−0.566782	+	1.81210i	−0.566782	+	1.81210i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.993931	−	0.110008i	$-0.964912\pi$
$373$		0			0		0.993931	+	0.110008i	$0.0350877\pi$
$374$	1.04008	+	3.81151i	1.04008	+	3.81151i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.162906	+	1.96598i	0.162906	+	1.96598i	0.245485	+	0.969400i	$0.421053\pi$
$379$	0.162906	+	1.96598i	0.162906	+	1.96598i	−0.0825793	+	0.996584i	$0.526316\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.0642573	−	0.997933i	$-0.520468\pi$
$383$		0			0		0.0642573	+	0.997933i	$0.479532\pi$
$384$	1.40177	+	0.129129i	1.40177	+	0.129129i
$385$		0			0
$386$	0.484359	+	0.507132i	0.484359	+	0.507132i
$387$	−0.662417	+	1.76924i	−0.662417	+	1.76924i
$388$	−0.334192	+	0.0945005i	−0.334192	+	0.0945005i
$389$		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
$392$	0.716783	+	0.697297i	0.716783	+	0.697297i
$393$	−0.335353	+	0.00616176i	−0.335353	+	0.00616176i
$394$		0			0
$395$		0			0
$396$	1.92115	−	0.284412i	1.92115	−	0.284412i
$397$		0			0		0.515825	−	0.856694i	$-0.327485\pi$
$397$		0			0		−0.515825	+	0.856694i	$0.672515\pi$
$398$		0			0
$399$		0			0
$400$	−0.986361	−	0.164595i	−0.986361	−	0.164595i
$401$	1.01073	−	1.18231i	1.01073	−	1.18231i	0.0275543	−	0.999620i	$-0.491228\pi$
$401$	1.01073	−	1.18231i	1.01073	−	1.18231i	0.983171	−	0.182687i	$-0.0584795\pi$
$402$	−0.498835	−	0.795048i	−0.498835	−	0.795048i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−2.42150	−	1.42787i	−2.42150	−	1.42787i
$409$	0.161393	+	0.752495i	0.161393	+	0.752495i	0.983171	+	0.182687i	$0.0584795\pi$
$409$	0.161393	+	0.752495i	0.161393	+	0.752495i	−0.821778	+	0.569808i	$0.807018\pi$
$410$		0			0
$411$	−0.360894	−	2.60258i	−0.360894	−	2.60258i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.671523	+	2.65178i	0.671523	+	2.65178i
$418$	0.693714	−	1.85283i	0.693714	−	1.85283i
$419$	0.418268	−	1.65170i	0.418268	−	1.65170i	−0.298515	−	0.954405i	$-0.596491\pi$
$419$	0.418268	−	1.65170i	0.418268	−	1.65170i	0.716783	−	0.697297i	$-0.245614\pi$
$420$		0			0
$421$		0			0		−0.870582	−	0.492024i	$-0.836257\pi$
$421$		0			0		0.870582	+	0.492024i	$0.163743\pi$
$422$	−0.362360	−	0.474489i	−0.362360	−	0.474489i
$423$		0			0
$424$		0			0
$425$	1.64106	+	1.13789i	1.64106	+	1.13789i
$426$		0			0
$427$		0			0
$428$	0.0850773	+	1.85103i	0.0850773	+	1.85103i
$429$		0			0
$430$		0			0
$431$		0			0		−0.888069	−	0.459710i	$-0.847953\pi$
$431$		0			0		0.888069	+	0.459710i	$0.152047\pi$
$432$	0.0156965	−	0.0205536i	0.0156965	−	0.0205536i
$433$	−0.151851	+	0.0649514i	−0.151851	+	0.0649514i	−0.467849	−	0.883809i	$-0.654971\pi$
$433$	−0.151851	+	0.0649514i	−0.151851	+	0.0649514i	0.315998	+	0.948760i	$0.397661\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.41525	+	0.485855i	1.41525	+	0.485855i
$439$		0			0		−0.703852	−	0.710347i	$-0.748538\pi$
$439$		0			0		0.703852	+	0.710347i	$0.251462\pi$
$440$		0			0
$441$	−0.953764	+	0.232224i	−0.953764	+	0.232224i
$442$		0			0
$443$	0.104247	−	1.61899i	0.104247	−	1.61899i	−0.531476	−	0.847073i	$-0.678363\pi$
$443$	0.104247	−	1.61899i	0.104247	−	1.61899i	0.635724	−	0.771917i	$-0.280702\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.06979	+	0.434511i	−1.06979	+	0.434511i	−0.842155	−	0.539235i	$-0.818713\pi$
$449$	−1.06979	+	0.434511i	−1.06979	+	0.434511i	−0.227635	+	0.973746i	$0.573099\pi$
$450$	0.651459	−	0.734299i	0.651459	−	0.734299i
$451$	1.20923	−	3.63063i	1.20923	−	3.63063i
$452$	−0.147169	−	0.137997i	−0.147169	−	0.137997i
$453$		0			0
$454$	−1.57188	+	0.605047i	−1.57188	+	0.605047i
$455$		0			0
$456$	0.565468	+	1.28914i	0.565468	+	1.28914i
$457$	−0.487608	+	1.11164i	−0.487608	+	1.11164i	0.484006	+	0.875065i	$0.339181\pi$
$457$	−0.487608	+	1.11164i	−0.487608	+	1.11164i	−0.971614	+	0.236570i	$0.923977\pi$
$458$		0			0
$459$	−0.0458644	+	0.0237418i	−0.0458644	+	0.0237418i
$460$		0			0
$461$		0			0		0.467849	−	0.883809i	$-0.345029\pi$
$461$		0			0		−0.467849	+	0.883809i	$0.654971\pi$
$462$		0			0
$463$		0			0		0.754107	−	0.656752i	$-0.228070\pi$
$463$		0			0		−0.754107	+	0.656752i	$0.771930\pi$
$464$		0			0
$465$		0			0
$466$	0.430412	−	1.47039i	0.430412	−	1.47039i
$467$	0.554153	−	0.753952i	0.554153	−	0.753952i	−0.435066	−	0.900399i	$-0.643275\pi$
$467$	0.554153	−	0.753952i	0.554153	−	0.753952i	0.989219	+	0.146447i	$0.0467836\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.296020	−	1.08481i	0.296020	−	1.08481i
$473$	1.40036	−	3.54071i	1.40036	−	3.54071i
$474$		0			0
$475$	−0.333374	−	0.942795i	−0.333374	−	0.942795i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.832107	−	0.554615i	$-0.812865\pi$
$479$		0			0		0.832107	+	0.554615i	$0.187135\pi$
$480$		0			0
$481$		0			0
$482$	−0.0804067	+	0.411637i	−0.0804067	+	0.411637i
$483$		0			0
$484$	−2.89015	+	0.373745i	−2.89015	+	0.373745i
$485$		0			0
$486$	0.493427	+	1.31788i	0.493427	+	1.31788i
$487$		0			0		−0.592235	−	0.805765i	$-0.701754\pi$
$487$		0			0		0.592235	+	0.805765i	$0.298246\pi$
$488$		0			0
$489$	−0.841312	−	2.37926i	−0.841312	−	2.37926i
$490$		0			0
$491$	−1.04170	+	1.09068i	−1.04170	+	1.09068i	−0.0459136	+	0.998945i	$0.514620\pi$
$491$	−1.04170	+	1.09068i	−1.04170	+	1.09068i	−0.995784	+	0.0917303i	$0.970760\pi$
$492$	1.18459	+	2.45160i	1.18459	+	2.45160i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.72958	+	1.10746i	−1.72958	+	1.10746i
$499$	−1.61992	+	0.728377i	−1.61992	+	0.728377i	−0.998482	−	0.0550878i	$-0.982456\pi$
$499$	−1.61992	+	0.728377i	−1.61992	+	0.728377i	−0.621436	+	0.783465i	$0.713450\pi$
$500$		0			0
$501$		0			0
$502$	0.604472	−	0.419131i	0.604472	−	0.419131i
$503$		0			0		0.957107	−	0.289735i	$-0.0935673\pi$
$503$		0			0		−0.957107	+	0.289735i	$0.906433\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.142000	−	1.40052i	−0.142000	−	1.40052i
$508$		0			0
$509$		0			0		−0.467849	−	0.883809i	$-0.654971\pi$
$509$		0			0		0.467849	+	0.883809i	$0.345029\pi$
$510$		0			0
$511$		0			0
$512$	0.789141	−	0.614213i	0.789141	−	0.614213i
$513$	0.0255830	+	0.00378737i	0.0255830	+	0.00378737i
$514$	−1.02556	−	0.798227i	−1.02556	−	0.798227i
$515$		0			0
$516$	1.04250	+	2.50056i	1.04250	+	2.50056i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.681497	+	0.276800i	0.681497	+	0.276800i	0.690683	−	0.723158i	$-0.257310\pi$
$521$	0.681497	+	0.276800i	0.681497	+	0.276800i	−0.00918581	+	0.999958i	$0.502924\pi$
$522$		0			0
$523$	−0.769941	+	0.777046i	−0.769941	+	0.777046i	−0.979649	−	0.200718i	$-0.935673\pi$
$523$	−0.769941	+	0.777046i	−0.769941	+	0.777046i	0.209708	+	0.977764i	$0.432749\pi$
$524$	−0.170786	+	0.166143i	−0.170786	+	0.166143i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.73073	−	2.18199i	1.73073	−	2.18199i
$529$	0.983171	+	0.182687i	0.983171	+	0.182687i
$530$		0			0
$531$	0.747592	+	0.812101i	0.747592	+	0.812101i
$532$		0			0
$533$		0			0
$534$	−0.266592	+	1.24298i	−0.266592	+	1.24298i
$535$		0			0
$536$	−0.644815	−	0.169607i	−0.644815	−	0.169607i
$537$	2.72811	+	0.664244i	2.72811	+	0.664244i
$538$		0			0
$539$	1.93055	−	0.432647i	1.93055	−	0.432647i
$540$		0			0
$541$		0			0		0.811171	−	0.584809i	$-0.198830\pi$
$541$		0			0		−0.811171	+	0.584809i	$0.801170\pi$
$542$		0			0
$543$		0			0
$544$	−1.94863	+	0.436698i	−1.94863	+	0.436698i
$545$		0			0
$546$		0			0
$547$	1.22962	+	0.323431i	1.22962	+	0.323431i	0.811171	−	0.584809i	$-0.198830\pi$
$547$	1.22962	+	0.323431i	1.22962	+	0.323431i	0.418451	+	0.908239i	$0.362573\pi$
$548$	−1.45162	−	1.17329i	−1.45162	−	1.17329i
$549$		0			0
$550$	−1.33996	+	1.45558i	−1.33996	+	1.45558i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.63650	+	1.04786i	1.63650	+	1.04786i
$557$		0			0		−0.989219	−	0.146447i	$-0.953216\pi$
$557$		0			0		0.989219	+	0.146447i	$0.0467836\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−4.98526	+	2.46558i	−4.98526	+	2.46558i
$562$	1.83769	+	0.746404i	1.83769	+	0.746404i
$563$	−1.72121	−	0.812260i	−1.72121	−	0.812260i	−0.991742	−	0.128249i	$-0.959064\pi$
$563$	−1.72121	−	0.812260i	−1.72121	−	0.812260i	−0.729471	−	0.684011i	$-0.760234\pi$
$564$		0			0
$565$		0			0
$566$	0.292295	+	1.85652i	0.292295	+	1.85652i
$567$		0			0
$568$		0			0
$569$	−1.19019	−	0.926364i	−1.19019	−	0.926364i	−0.191711	−	0.981451i	$-0.561404\pi$
$569$	−1.19019	−	0.926364i	−1.19019	−	0.926364i	−0.998482	+	0.0550878i	$0.982456\pi$
$570$		0			0
$571$	1.57722	−	1.22760i	1.57722	−	1.22760i	0.766044	−	0.642788i	$-0.222222\pi$
$571$	1.57722	−	1.22760i	1.57722	−	1.22760i	0.811171	−	0.584809i	$-0.198830\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.0990203	+	0.976621i	0.0990203	+	0.976621i
$577$	0.0230603	−	0.836585i	0.0230603	−	0.836585i	−0.896364	−	0.443318i	$-0.853801\pi$
$577$	0.0230603	−	0.836585i	0.0230603	−	0.836585i	0.919425	−	0.393266i	$-0.128655\pi$
$578$	2.91554	+	0.653389i	2.91554	+	0.653389i
$579$	−0.569935	+	0.806047i	−0.569935	+	0.806047i
$580$		0			0
$581$		0			0
$582$	−0.220750	−	0.436214i	−0.220750	−	0.436214i
$583$		0			0
$584$	0.969461	−	0.435907i	0.969461	−	0.435907i
$585$		0			0
$586$		0			0
$587$	−0.0546536	−	0.00706763i	−0.0546536	−	0.00706763i	0.100874	−	0.994899i	$-0.467836\pi$
$587$	−0.0546536	−	0.00706763i	−0.0546536	−	0.00706763i	−0.155527	+	0.987832i	$0.549708\pi$
$588$	−0.769941	+	1.17848i	−0.769941	+	1.17848i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.37764	−	0.101422i	1.37764	−	0.101422i	0.635724	−	0.771917i	$-0.280702\pi$
$593$	1.37764	−	0.101422i	1.37764	−	0.101422i	0.741914	+	0.670495i	$0.233918\pi$
$594$	−0.0170574	−	0.0482390i	−0.0170574	−	0.0482390i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.991742	−	0.128249i	$-0.0409357\pi$
$599$		0			0		−0.991742	+	0.128249i	$0.959064\pi$
$600$	−0.0387883	−	1.40717i	−0.0387883	−	1.40717i
$601$	0.360298	−	1.84453i	0.360298	−	1.84453i	−0.155527	−	0.987832i	$-0.549708\pi$
$601$	0.360298	−	1.84453i	0.360298	−	1.84453i	0.515825	−	0.856694i	$-0.327485\pi$
$602$		0			0
$603$	0.477438	−	0.447684i	0.477438	−	0.447684i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$607$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$608$	0.919425	+	0.393266i	0.919425	+	0.393266i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.653505	−	1.84814i	0.653505	−	1.84814i
$613$		0			0		−0.00918581	−	0.999958i	$-0.502924\pi$
$613$		0			0		0.00918581	+	0.999958i	$0.497076\pi$
$614$	−0.470536	−	0.692099i	−0.470536	−	0.692099i
$615$		0			0
$616$		0			0
$617$	−0.127900	+	0.436936i	−0.127900	+	0.436936i	−0.998482	−	0.0550878i	$-0.982456\pi$
$617$	−0.127900	+	0.436936i	−0.127900	+	0.436936i	0.870582	+	0.492024i	$0.163743\pi$
$618$		0			0
$619$	−0.508621	−	0.312648i	−0.508621	−	0.312648i	0.245485	−	0.969400i	$-0.421053\pi$
$619$	−0.508621	−	0.312648i	−0.508621	−	0.312648i	−0.754107	+	0.656752i	$0.771930\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.0459136	+	0.998945i	−0.0459136	+	0.998945i
$626$	−0.414409	+	0.944758i	−0.414409	+	0.944758i
$627$	2.74707	+	0.458405i	2.74707	+	0.458405i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.729471	−	0.684011i	$-0.760234\pi$
$631$		0			0		0.729471	+	0.684011i	$0.239766\pi$
$632$		0			0
$633$	0.557760	−	0.628685i	0.557760	−	0.628685i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.283695	−	1.80189i	0.283695	−	1.80189i	−0.263253	−	0.964727i	$-0.584795\pi$
$641$	0.283695	−	1.80189i	0.283695	−	1.80189i	0.546948	−	0.837166i	$-0.315789\pi$
$642$	−2.53441	+	0.617084i	−2.53441	+	0.617084i
$643$	−0.419346	−	0.00770504i	−0.419346	−	0.00770504i	−0.191711	−	0.981451i	$-0.561404\pi$
$643$	−0.419346	−	0.00770504i	−0.419346	−	0.00770504i	−0.227635	+	0.973746i	$0.573099\pi$
$644$		0			0
$645$		0			0
$646$	−1.32529	−	1.49381i	−1.32529	−	1.49381i
$647$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$647$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$648$	0.912529	+	0.451313i	0.912529	+	0.451313i
$649$	−1.47642	−	1.66416i	−1.47642	−	1.66416i
$650$		0			0
$651$		0			0
$652$	−1.59207	−	0.824136i	−1.59207	−	0.824136i
$653$		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
$656$	1.80510	+	0.694817i	1.80510	+	0.694817i
$657$	−0.143318	+	1.03354i	−0.143318	+	1.03354i
$658$		0			0
$659$	−1.62141	−	0.523537i	−1.62141	−	0.523537i	−0.649797	−	0.760108i	$-0.725146\pi$
$659$	−1.62141	−	0.523537i	−1.62141	−	0.523537i	−0.971614	+	0.236570i	$0.923977\pi$
$660$		0			0
$661$		0			0		−0.606938	−	0.794749i	$-0.707602\pi$
$661$		0			0		0.606938	+	0.794749i	$0.292398\pi$
$662$	1.54627	+	0.873902i	1.54627	+	0.873902i
$663$		0			0
$664$	−0.358149	+	1.41430i	−0.358149	+	1.41430i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.742120	+	1.46647i	−0.742120	+	1.46647i	0.137354	+	0.990522i	$0.456140\pi$
$673$	−0.742120	+	1.46647i	−0.742120	+	1.46647i	−0.879474	+	0.475947i	$0.842105\pi$
$674$	0.117827	+	0.549369i	0.117827	+	0.549369i
$675$	−0.0222773	−	0.0131361i	−0.0222773	−	0.0131361i
$676$	−0.754107	−	0.656752i	−0.754107	−	0.656752i
$677$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$677$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$678$	0.150939	−	0.240569i	0.150939	−	0.240569i
$679$		0			0
$680$		0			0
$681$	−1.26014	−	2.00842i	−1.26014	−	2.00842i
$682$		0			0
$683$	−1.78405	−	0.297705i	−1.78405	−	0.297705i	−0.821778	−	0.569808i	$-0.807018\pi$
$683$	−1.78405	−	0.297705i	−1.78405	−	0.297705i	−0.962268	+	0.272103i	$0.912281\pi$
$684$	−0.806680	+	0.559340i	−0.806680	+	0.559340i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.75526	+	0.789234i	1.75526	+	0.789234i
$689$		0			0
$690$		0			0
$691$	0.502662	+	0.488997i	0.502662	+	0.488997i	0.904357	−	0.426776i	$-0.140351\pi$
$691$	0.502662	+	0.488997i	0.502662	+	0.488997i	−0.401695	+	0.915773i	$0.631579\pi$
$692$		0			0
$693$		0			0
$694$	−0.952095	−	0.798902i	−0.952095	−	0.798902i
$695$		0			0
$696$		0			0
$697$	−2.66779	−	2.79323i	−2.66779	−	2.79323i
$698$		0			0
$699$	2.14763	+	0.197837i	2.14763	+	0.197837i
$700$		0			0
$701$		0			0		−0.119134	−	0.992878i	$-0.538012\pi$
$701$		0			0		0.119134	+	0.992878i	$0.461988\pi$
$702$		0			0
$703$		0			0
$704$	−0.163378	−	1.97168i	−0.163378	−	1.97168i
$705$		0			0
$706$	−1.33186	+	0.997882i	−1.33186	+	0.997882i
$707$		0			0
$708$	1.57865	+	0.116220i	1.57865	+	0.116220i
$709$		0			0		−0.263253	−	0.964727i	$-0.584795\pi$
$709$		0			0		0.263253	+	0.964727i	$0.415205\pi$
$710$		0			0
$711$		0			0
$712$	0.465825	+	0.773652i	0.465825	+	0.773652i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.73646	−	0.981392i	1.73646	−	0.981392i
$717$		0			0
$718$		0			0
$719$		0			0		0.418451	−	0.908239i	$-0.362573\pi$
$719$		0			0		−0.418451	+	0.908239i	$0.637427\pi$
$720$		0			0
$721$		0			0
$722$	0.100874	+	0.994899i	0.100874	+	0.994899i
$723$	−0.590414			−0.590414
$724$		0			0
$725$		0			0
$726$	−1.29633	−	3.89214i	−1.29633	−	3.89214i
$727$		0			0		−0.919425	−	0.393266i	$-0.871345\pi$
$727$		0			0		0.919425	+	0.393266i	$0.128655\pi$
$728$		0			0
$729$	−0.820335	+	0.504258i	−0.820335	+	0.504258i
$730$		0			0
$731$	−2.49732	−	2.92127i	−2.49732	−	2.92127i
$732$		0			0
$733$		0			0		−0.635724	−	0.771917i	$-0.719298\pi$
$733$		0			0		0.635724	+	0.771917i	$0.280702\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.978673	+	0.884462i	−0.978673	+	0.884462i
$738$	−1.51949	+	1.13847i	−1.51949	+	1.13847i
$739$	−1.63035	+	0.334038i	−1.63035	+	0.334038i	−0.926494	−	0.376309i	$-0.877193\pi$
$739$	−1.63035	+	0.334038i	−1.63035	+	0.334038i	−0.703852	+	0.710347i	$0.748538\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.119134	−	0.992878i	$-0.538012\pi$
$743$		0			0		0.119134	+	0.992878i	$0.461988\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.989155	−	1.03566i	−0.989155	−	1.03566i
$748$	−1.38532	+	3.70003i	−1.38532	+	3.70003i
$749$		0			0
$750$		0			0
$751$		0			0		−0.367783	−	0.929912i	$-0.619883\pi$
$751$		0			0		0.367783	+	0.929912i	$0.380117\pi$
$752$		0			0
$753$	0.742198	+	0.722022i	0.742198	+	0.722022i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.989219	−	0.146447i	$-0.0467836\pi$
$757$		0			0		−0.989219	+	0.146447i	$0.953216\pi$
$758$	−1.01758	+	1.69002i	−1.01758	+	1.69002i
$759$		0			0
$760$		0			0
$761$	−1.97139	−	0.328967i	−1.97139	−	0.328967i	−0.991742	−	0.128249i	$-0.959064\pi$
$761$	−1.97139	−	0.328967i	−1.97139	−	0.328967i	−0.979649	−	0.200718i	$-0.935673\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.06156	+	0.924512i	1.06156	+	0.924512i
$769$	−1.09522	−	0.645811i	−1.09522	−	0.645811i	−0.155527	−	0.987832i	$-0.549708\pi$
$769$	−1.09522	−	0.645811i	−1.09522	−	0.645811i	−0.939693	+	0.342020i	$0.888889\pi$
$770$		0			0
$771$	0.826055	−	1.63233i	0.826055	−	1.63233i
$772$	0.0963226	+	0.694628i	0.0963226	+	0.694628i
$773$		0			0		0.227635	−	0.973746i	$-0.426901\pi$
$773$		0			0		−0.227635	+	0.973746i	$0.573099\pi$
$774$	−1.57200	+	1.04777i	−1.57200	+	1.04777i
$775$		0			0
$776$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$777$		0			0
$778$		0			0
$779$	0.265670	+	1.91588i	0.265670	+	1.91588i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.173648	+	0.984808i	0.173648	+	0.984808i
$785$		0			0
$786$	−0.275632	−	0.191119i	−0.275632	−	0.191119i
$787$	0.270084	−	1.94771i	0.270084	−	1.94771i	−0.0459136	−	0.998945i	$-0.514620\pi$
$787$	0.270084	−	1.94771i	0.270084	−	1.94771i	0.315998	−	0.948760i	$-0.397661\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	1.72471	+	0.892799i	1.72471	+	0.892799i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$797$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$798$		0			0
$799$		0			0
$800$	−0.703852	−	0.710347i	−0.703852	−	0.710347i
$801$	−0.886326	−	0.0162853i	−0.886326	−	0.0162853i
$802$	1.51130	−	0.367973i	1.51130	−	0.367973i
$803$	0.327071	−	2.07740i	0.327071	−	2.07740i
$804$	0.0603108	−	0.936643i	0.0603108	−	0.936643i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.525706	+	0.0290040i	0.525706	+	0.0290040i	0.315998	−	0.948760i	$-0.397661\pi$
$809$	0.525706	+	0.0290040i	0.525706	+	0.0290040i	0.209708	+	0.977764i	$0.432749\pi$
$810$		0			0
$811$	1.04743	−	1.18062i	1.04743	−	1.18062i	0.0642573	−	0.997933i	$-0.479532\pi$
$811$	1.04743	−	1.18062i	1.04743	−	1.18062i	0.983171	−	0.182687i	$-0.0584795\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.12922	−	2.57436i	−1.12922	−	2.57436i
$817$	0.158927	+	1.91796i	0.158927	+	1.91796i
$818$	−0.309148	+	0.704787i	−0.309148	+	0.704787i
$819$		0			0
$820$		0			0
$821$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$821$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$822$	1.22926	−	2.32219i	1.22926	−	2.32219i
$823$		0			0		0.983171	−	0.182687i	$-0.0584795\pi$
$823$		0			0		−0.983171	+	0.182687i	$0.941520\pi$
$824$		0			0
$825$	−2.37264	−	1.45846i	−2.37264	−	1.45846i
$826$		0			0
$827$	−0.147912	+	0.505302i	−0.147912	+	0.505302i	−0.999831	−	0.0183709i	$-0.994152\pi$
$827$	−0.147912	+	0.505302i	−0.147912	+	0.505302i	0.851919	+	0.523673i	$0.175439\pi$
$828$		0			0
$829$		0			0		−0.962268	−	0.272103i	$-0.912281\pi$
$829$		0			0		0.962268	+	0.272103i	$0.0877193\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.525706	−	1.92652i	0.525706	−	1.92652i
$834$	−1.00607	+	2.54376i	−1.00607	+	2.54376i
$835$		0			0
$836$	1.64627	−	1.09727i	1.64627	−	1.09727i
$837$		0			0
$838$	1.30522	−	1.09521i	1.30522	−	1.09521i
$839$		0			0		0.562235	−	0.826977i	$-0.309942\pi$
$839$		0			0		−0.562235	+	0.826977i	$0.690058\pi$
$840$		0			0
$841$	−0.729471	+	0.684011i	−0.729471	+	0.684011i
$842$		0			0
$843$	−0.535286	+	2.74037i	−0.535286	+	2.74037i
$844$	−0.0164508	−	0.596803i	−0.0164508	−	0.596803i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2.48607	+	0.904854i	−2.48607	+	0.904854i
$850$	0.665735	+	1.88273i	0.665735	+	1.88273i
$851$		0			0
$852$		0			0
$853$		0			0		−0.435066	−	0.900399i	$-0.643275\pi$
$853$		0			0		0.435066	+	0.900399i	$0.356725\pi$
$854$		0			0
$855$		0			0
$856$	−1.01349	+	1.55126i	−1.01349	+	1.55126i
$857$	0.0910688	+	0.0117767i	0.0910688	+	0.0117767i	0.173648	−	0.984808i	$-0.444444\pi$
$857$	0.0910688	+	0.0117767i	0.0910688	+	0.0117767i	−0.0825793	+	0.996584i	$0.526316\pi$
$858$		0			0
$859$	0.383409	−	0.245498i	0.383409	−	0.245498i	−0.333374	−	0.942795i	$-0.608187\pi$
$859$	0.383409	−	0.245498i	0.383409	−	0.245498i	0.716783	+	0.697297i	$0.245614\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.821778	−	0.569808i	$-0.192982\pi$
$863$		0			0		−0.821778	+	0.569808i	$0.807018\pi$
$864$	0.0247525	−	0.00749307i	0.0247525	−	0.00749307i
$865$		0			0
$866$	−0.161161	−	0.0361171i	−0.161161	−	0.0361171i
$867$	−0.115894	+	4.20443i	−0.115894	+	4.20443i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.269031	−	0.209395i	0.269031	−	0.209395i
$874$		0			0
$875$		0			0
$876$	0.863876	+	1.22176i	0.863876	+	1.22176i
$877$		0			0		−0.384804	−	0.922998i	$-0.625731\pi$
$877$		0			0		0.384804	+	0.922998i	$0.374269\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.80383	+	0.851249i	1.80383	+	0.851249i	0.933251	+	0.359225i	$0.116959\pi$
$881$	1.80383	+	0.851249i	1.80383	+	0.851249i	0.870582	+	0.492024i	$0.163743\pi$
$882$	−0.909473	−	0.369396i	−0.909473	−	0.369396i
$883$	−1.64828	+	0.815195i	−1.64828	+	0.815195i	−0.649797	+	0.760108i	$0.725146\pi$
$883$	−1.64828	+	0.815195i	−1.64828	+	0.815195i	−0.998482	+	0.0550878i	$0.982456\pi$
$884$		0			0
$885$		0			0
$886$	1.03136	−	1.25231i	1.03136	−	1.25231i
$887$		0			0		−0.989219	−	0.146447i	$-0.953216\pi$
$887$		0			0		0.989219	+	0.146447i	$0.0467836\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.73495	−	1.02304i	1.73495	−	1.02304i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.12189	−	0.273160i	−1.12189	−	0.273160i
$899$		0			0
$900$	0.957869	−	0.214664i	0.957869	−	0.214664i
$901$		0			0
$902$	3.10412	−	2.23789i	3.10412	−	2.23789i
$903$		0			0
$904$	−0.0386771	−	0.198005i	−0.0386771	−	0.198005i
$905$		0			0
$906$		0			0
$907$	−0.124867	−	0.0304028i	−0.124867	−	0.0304028i	0.173648	−	0.984808i	$-0.444444\pi$
$907$	−0.124867	−	0.0304028i	−0.124867	−	0.0304028i	−0.298515	+	0.954405i	$0.596491\pi$
$908$	−1.62890	−	0.428455i	−1.62890	−	0.428455i
$909$		0			0
$910$		0			0
$911$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$911$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$912$	−0.295207	+	1.37640i	−0.295207	+	1.37640i
$913$	1.95492	+	2.12361i	1.95492	+	2.12361i
$914$	−1.04563	+	0.616569i	−1.04563	+	0.616569i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.0510883	−	0.00756324i	−0.0510883	−	0.00756324i
$919$		0			0		0.635724	−	0.771917i	$-0.280702\pi$
$919$		0			0		−0.635724	+	0.771917i	$0.719298\pi$
$920$		0			0
$921$	0.829215	−	0.836867i	0.829215	−	0.836867i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.898011	−	1.27004i	−0.898011	−	1.27004i	−0.962268	−	0.272103i	$-0.912281\pi$
$929$	−0.898011	−	1.27004i	−0.898011	−	1.27004i	0.0642573	−	0.997933i	$-0.479532\pi$
$930$		0			0
$931$	−0.777724	+	0.628606i	−0.777724	+	0.628606i
$932$	1.20903	−	0.941028i	1.20903	−	0.941028i
$933$		0			0
$934$	0.890431	−	0.287511i	0.890431	−	0.287511i
$935$		0			0
$936$		0			0
$937$	0.163651	+	1.61407i	0.163651	+	1.61407i	0.663651	+	0.748042i	$0.269006\pi$
$937$	0.163651	+	1.61407i	0.163651	+	1.61407i	−0.500000	+	0.866025i	$0.666667\pi$
$938$		0			0
$939$	−1.41711	−	0.317581i	−1.41711	−	0.317581i
$940$		0			0
$941$		0			0		0.957107	−	0.289735i	$-0.0935673\pi$
$941$		0			0		−0.957107	+	0.289735i	$0.906433\pi$
$942$		0			0
$943$		0			0
$944$	0.874527	−	0.706849i	0.874527	−	0.706849i
$945$		0			0
$946$	3.20657	−	2.05318i	3.20657	−	2.05318i
$947$	0.0495260	−	0.488467i	0.0495260	−	0.488467i	−0.939693	−	0.342020i	$-0.888889\pi$
$947$	0.0495260	−	0.488467i	0.0495260	−	0.488467i	0.989219	−	0.146447i	$-0.0467836\pi$
$948$		0			0
$949$		0			0
$950$	0.280931	−	0.959728i	0.280931	−	0.959728i
$951$		0			0
$952$		0			0
$953$	0.0887629	−	0.0929363i	0.0887629	−	0.0929363i	−0.677282	−	0.735724i	$-0.736842\pi$
$953$	0.0887629	−	0.0929363i	0.0887629	−	0.0929363i	0.766044	+	0.642788i	$0.222222\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.0275543	+	0.999620i	0.0275543	+	0.999620i
$962$		0			0
$963$	−0.761140	−	1.65204i	−0.761140	−	1.65204i
$964$	−0.305953	+	0.286886i	−0.305953	+	0.286886i
$965$		0			0
$966$		0			0
$967$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$967$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$968$	−2.56297	−	1.38701i	−2.56297	−	1.38701i
$969$	1.70618	−	2.23414i	1.70618	−	2.23414i
$970$		0			0
$971$	−0.563476	+	1.42471i	−0.563476	+	1.42471i	0.315998	+	0.948760i	$0.397661\pi$
$971$	−0.563476	+	1.42471i	−0.563476	+	1.42471i	−0.879474	+	0.475947i	$0.842105\pi$
$972$	−0.370457	+	1.35759i	−0.370457	+	1.35759i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.10541	+	1.50396i	−1.10541	+	1.50396i	−0.263253	+	0.964727i	$0.584795\pi$
$977$	−1.10541	+	1.50396i	−1.10541	+	1.50396i	−0.842155	+	0.539235i	$0.818713\pi$
$978$	0.708966	−	2.42200i	0.708966	−	2.42200i
$979$	1.78545	+	0.0656339i	1.78545	+	0.0656339i
$980$		0			0
$981$		0			0
$982$	−1.48283	+	0.275531i	−1.48283	+	0.275531i
$983$		0			0		0.467849	−	0.883809i	$-0.345029\pi$
$983$		0			0		−0.467849	+	0.883809i	$0.654971\pi$
$984$	−0.472808	+	2.68143i	−0.472808	+	2.68143i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.227635	−	0.973746i	$-0.573099\pi$
$991$		0			0		0.227635	+	0.973746i	$0.426901\pi$
$992$		0			0
$993$	−0.790081	+	2.37216i	−0.790081	+	2.37216i
$994$		0			0
$995$		0			0
$996$	−2.05064	−	0.113137i	−2.05064	−	0.113137i
$997$		0			0		0.119134	−	0.992878i	$-0.461988\pi$
$997$		0			0		−0.119134	+	0.992878i	$0.538012\pi$
$998$	−1.73999	−	0.356503i	−1.73999	−	0.356503i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.bs.a.443.1	yes	108
8.3	odd	2	CM	2888.1.bs.a.443.1	yes	108
361.339	even	171	inner	2888.1.bs.a.339.1	✓	108
2888.339	odd	342	inner	2888.1.bs.a.339.1	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2888.1.bs.a.339.1	✓	108	361.339	even	171	inner
2888.1.bs.a.339.1	✓	108	2888.339	odd	342	inner
2888.1.bs.a.443.1	yes	108	1.1	even	1	trivial
2888.1.bs.a.443.1	yes	108	8.3	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(0.811171 + 0.584809i) q^{2} +(-0.589055 + 1.27853i) q^{3} +(0.315998 + 0.948760i) q^{4} +(-1.22552 + 0.692623i) q^{6} +(-0.298515 + 0.954405i) q^{8} +(-0.637859 - 0.746143i) q^{9} +O(q^{10})\)	\(q+(0.811171 + 0.584809i) q^{2} +(-0.589055 + 1.27853i) q^{3} +(0.315998 + 0.948760i) q^{4} +(-1.22552 + 0.692623i) q^{6} +(-0.298515 + 0.954405i) q^{8} +(-0.637859 - 0.746143i) q^{9} +(1.25774 + 1.52719i) q^{11} +(-1.39916 - 0.154859i) q^{12} +(-0.800291 + 0.599612i) q^{16} +(1.95632 - 0.400826i) q^{17} +(-0.0810622 - 0.978276i) q^{18} +(-0.912045 - 0.410091i) q^{19} +(0.127129 + 1.97435i) q^{22} +(-1.04440 - 0.943858i) q^{24} +(0.690683 + 0.723158i) q^{25} +(-0.0248860 + 0.00703709i) q^{27} +(-0.999831 + 0.0183709i) q^{32} +(-2.69344 + 0.708461i) q^{33} +(1.82132 + 0.818936i) q^{34} +(0.506349 - 0.840955i) q^{36} +(-0.500000 - 0.866025i) q^{38} +(-1.02799 - 1.63842i) q^{41} +(-0.931487 - 1.68409i) q^{43} +(-1.05149 + 1.67588i) q^{44} +(-0.295207 - 1.37640i) q^{48} +(0.451533 - 0.892254i) q^{49} +(0.137354 + 0.990522i) q^{50} +(-0.639913 + 2.73733i) q^{51} +(-0.0243021 - 0.00884526i) q^{54} +(1.06156 - 0.924512i) q^{57} +(-1.12371 + 0.0413080i) q^{59} +(-0.821778 - 0.569808i) q^{64} +(-2.59915 - 1.00046i) q^{66} +(0.0306128 + 0.666045i) q^{67} +(0.998482 + 1.72942i) q^{68} +(0.902533 - 0.386041i) q^{72} +(-0.705430 - 0.795133i) q^{73} +(-1.33143 + 0.457080i) q^{75} +(0.100874 - 0.994899i) q^{76} +(0.158332 - 1.00565i) q^{81} +(0.124287 - 1.93021i) q^{82} +(1.45673 - 0.0803699i) q^{83} +(0.229277 - 1.91083i) q^{86} +(-1.83301 + 0.744504i) q^{88} +(0.599321 - 0.675532i) q^{89} +(0.565468 - 1.28914i) q^{96} +(-0.0159456 + 0.346930i) q^{97} +(0.888069 - 0.459710i) q^{98} +(0.337240 - 1.91259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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

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