LMFDB - Embedded newform 2008.1.bd.a.363.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2008,1,Mod(3,2008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2008, base_ring=CyclotomicField(250))

chi = DirichletCharacter(H, H._module([125, 125, 16]))

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

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

chi := DirichletCharacter("2008.3");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2008 = 2^{3} \cdot 251 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2008.bd (of order $250$, degree $100$, 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:	$1.00212254537$
Analytic rank:	$0$
Dimension:	$100$
Coefficient field:	$\Q(\zeta_{250})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{100} - x^{75} + x^{50} - x^{25} + 1 $ x^100 - x^75 + x^50 - x^25 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{125}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{125} - \cdots)$

Embedding invariants

Embedding label			363.1
Root			$-0.793990 + 0.607930i$ of defining polynomial
Character	$\chi$	$=$	2008.363
Dual form			2008.1.bd.a.1571.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.637424 + 0.770513i) q^{2} +(-1.95919 - 0.197625i) q^{3} +(-0.187381 - 0.982287i) q^{4} +(1.40111 - 1.38361i) q^{6} +(0.876307 + 0.481754i) q^{8} +(2.81950 + 0.574659i) q^{9} +O(q^{10})$	\(q+(-0.637424 + 0.770513i) q^{2} +(-1.95919 - 0.197625i) q^{3} +(-0.187381 - 0.982287i) q^{4} +(1.40111 - 1.38361i) q^{6} +(0.876307 + 0.481754i) q^{8} +(2.81950 + 0.574659i) q^{9} +(1.02855 - 1.71451i) q^{11} +(0.172990 + 1.96152i) q^{12} +(-0.929776 + 0.368125i) q^{16} +(-0.725499 + 1.44627i) q^{17} +(-2.24000 + 1.80616i) q^{18} +(-0.0296998 + 0.122019i) q^{19} +(0.665429 + 1.88539i) q^{22} +(-1.62164 - 1.11703i) q^{24} +(0.0627905 - 0.998027i) q^{25} +(-3.53011 - 1.09816i) q^{27} +(0.309017 - 0.951057i) q^{32} +(-2.35396 + 3.15578i) q^{33} +(-0.651916 - 1.48089i) q^{34} +(0.0361584 - 2.87724i) q^{36} +(-0.0750855 - 0.100662i) q^{38} +(1.19543 + 0.0300508i) q^{41} +(0.225628 - 0.234298i) q^{43} +(-1.87687 - 0.689068i) q^{44} +(1.89436 - 0.537477i) q^{48} +(-0.999684 + 0.0251301i) q^{49} +(0.728969 + 0.684547i) q^{50} +(1.70721 - 2.69013i) q^{51} +(3.09632 - 2.02001i) q^{54} +(0.0823014 - 0.233188i) q^{57} +(0.825233 + 1.64508i) q^{59} +(0.535827 + 0.844328i) q^{64} +(-0.931100 - 3.82533i) q^{66} +(-0.603082 - 0.461758i) q^{67} +(1.55659 + 0.441646i) q^{68} +(2.19390 + 1.86188i) q^{72} +(0.410693 - 1.89313i) q^{73} +(-0.320254 + 1.94291i) q^{75} +(0.125422 + 0.00630973i) q^{76} +(4.05119 + 1.72296i) q^{81} +(-0.785152 + 0.901941i) q^{82} +(0.830793 - 1.23915i) q^{83} +(0.0367093 + 0.323196i) q^{86} +(1.72730 - 1.00693i) q^{88} +(-0.633085 + 0.327599i) q^{89} +(-0.793375 + 1.80223i) q^{96} +(1.79273 - 0.658175i) q^{97} +(0.617860 - 0.786288i) q^{98} +(3.88527 - 4.24300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q+O(q^{10}) $ 100 * q	$ 100 q - 25 q^{22} - 25 q^{32}+O(q^{100}) $ 100 * q - 25 * q^22 - 25 * q^32

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{94}{125}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$2$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$3$	−1.95919	−	0.197625i	−1.95919	−	0.197625i	−0.962028	−	0.272952i	$-0.912000\pi$
$3$	−1.95919	−	0.197625i	−1.95919	−	0.197625i	−0.997159	+	0.0753268i	$0.976000\pi$
$4$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$5$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$5$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$6$	1.40111	−	1.38361i	1.40111	−	1.38361i
$7$		0			0		−0.0125660	−	0.999921i	$-0.504000\pi$
$7$		0			0		0.0125660	+	0.999921i	$0.496000\pi$
$8$	0.876307	+	0.481754i	0.876307	+	0.481754i
$9$	2.81950	+	0.574659i	2.81950	+	0.574659i
$10$		0			0
$11$	1.02855	−	1.71451i	1.02855	−	1.71451i	0.492727	−	0.870184i	$-0.336000\pi$
$11$	1.02855	−	1.71451i	1.02855	−	1.71451i	0.535827	−	0.844328i	$-0.320000\pi$
$12$	0.172990	+	1.96152i	0.172990	+	1.96152i
$13$		0			0		0.910106	−	0.414376i	$-0.136000\pi$
$13$		0			0		−0.910106	+	0.414376i	$0.864000\pi$
$14$		0			0
$15$		0			0
$16$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$17$	−0.725499	+	1.44627i	−0.725499	+	1.44627i	0.162637	+	0.986686i	$0.448000\pi$
$17$	−0.725499	+	1.44627i	−0.725499	+	1.44627i	−0.888136	+	0.459580i	$0.848000\pi$
$18$	−2.24000	+	1.80616i	−2.24000	+	1.80616i
$19$	−0.0296998	+	0.122019i	−0.0296998	+	0.122019i	−0.984564	−	0.175023i	$-0.944000\pi$
$19$	−0.0296998	+	0.122019i	−0.0296998	+	0.122019i	0.954865	+	0.297042i	$0.0960000\pi$
$20$		0			0
$21$		0			0
$22$	0.665429	+	1.88539i	0.665429	+	1.88539i
$23$		0			0		−0.988652	−	0.150226i	$-0.952000\pi$
$23$		0			0		0.988652	+	0.150226i	$0.0480000\pi$
$24$	−1.62164	−	1.11703i	−1.62164	−	1.11703i
$25$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$26$		0			0
$27$	−3.53011	−	1.09816i	−3.53011	−	1.09816i
$28$		0			0
$29$		0			0		−0.260842	−	0.965382i	$-0.584000\pi$
$29$		0			0		0.260842	+	0.965382i	$0.416000\pi$
$30$		0			0
$31$		0			0		0.920232	−	0.391374i	$-0.128000\pi$
$31$		0			0		−0.920232	+	0.391374i	$0.872000\pi$
$32$	0.309017	−	0.951057i	0.309017	−	0.951057i
$33$	−2.35396	+	3.15578i	−2.35396	+	3.15578i
$34$	−0.651916	−	1.48089i	−0.651916	−	1.48089i
$35$		0			0
$36$	0.0361584	−	2.87724i	0.0361584	−	2.87724i
$37$		0			0		0.492727	−	0.870184i	$-0.336000\pi$
$37$		0			0		−0.492727	+	0.870184i	$0.664000\pi$
$38$	−0.0750855	−	0.100662i	−0.0750855	−	0.100662i
$39$		0			0
$40$		0			0
$41$	1.19543	+	0.0300508i	1.19543	+	0.0300508i	0.617860	−	0.786288i	$-0.288000\pi$
$41$	1.19543	+	0.0300508i	1.19543	+	0.0300508i	0.577573	+	0.816339i	$0.304000\pi$
$42$		0			0
$43$	0.225628	−	0.234298i	0.225628	−	0.234298i	−0.597905	−	0.801567i	$-0.704000\pi$
$43$	0.225628	−	0.234298i	0.225628	−	0.234298i	0.823533	+	0.567269i	$0.192000\pi$
$44$	−1.87687	−	0.689068i	−1.87687	−	0.689068i
$45$		0			0
$46$		0			0
$47$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$47$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$48$	1.89436	−	0.537477i	1.89436	−	0.537477i
$49$	−0.999684	+	0.0251301i	−0.999684	+	0.0251301i
$50$	0.728969	+	0.684547i	0.728969	+	0.684547i
$51$	1.70721	−	2.69013i	1.70721	−	2.69013i
$52$		0			0
$53$		0			0		−0.137790	−	0.990461i	$-0.544000\pi$
$53$		0			0		0.137790	+	0.990461i	$0.456000\pi$
$54$	3.09632	−	2.02001i	3.09632	−	2.02001i
$55$		0			0
$56$		0			0
$57$	0.0823014	−	0.233188i	0.0823014	−	0.233188i
$58$		0			0
$59$	0.825233	+	1.64508i	0.825233	+	1.64508i	0.762443	+	0.647056i	$0.224000\pi$
$59$	0.825233	+	1.64508i	0.825233	+	1.64508i	0.0627905	+	0.998027i	$0.480000\pi$
$60$		0			0
$61$		0			0		−0.984564	−	0.175023i	$-0.944000\pi$
$61$		0			0		0.984564	+	0.175023i	$0.0560000\pi$
$62$		0			0
$63$		0			0
$64$	0.535827	+	0.844328i	0.535827	+	0.844328i
$65$		0			0
$66$	−0.931100	−	3.82533i	−0.931100	−	3.82533i
$67$	−0.603082	−	0.461758i	−0.603082	−	0.461758i	0.260842	−	0.965382i	$-0.416000\pi$
$67$	−0.603082	−	0.461758i	−0.603082	−	0.461758i	−0.863923	+	0.503623i	$0.832000\pi$
$68$	1.55659	+	0.441646i	1.55659	+	0.441646i
$69$		0			0
$70$		0			0
$71$		0			0		−0.675333	−	0.737513i	$-0.736000\pi$
$71$		0			0		0.675333	+	0.737513i	$0.264000\pi$
$72$	2.19390	+	1.86188i	2.19390	+	1.86188i
$73$	0.410693	−	1.89313i	0.410693	−	1.89313i	−0.0376902	−	0.999289i	$-0.512000\pi$
$73$	0.410693	−	1.89313i	0.410693	−	1.89313i	0.448383	−	0.893841i	$-0.352000\pi$
$74$		0			0
$75$	−0.320254	+	1.94291i	−0.320254	+	1.94291i
$76$	0.125422	+	0.00630973i	0.125422	+	0.00630973i
$77$		0			0
$78$		0			0
$79$		0			0		−0.837528	−	0.546394i	$-0.816000\pi$
$79$		0			0		0.837528	+	0.546394i	$0.184000\pi$
$80$		0			0
$81$	4.05119	+	1.72296i	4.05119	+	1.72296i
$82$	−0.785152	+	0.901941i	−0.785152	+	0.901941i
$83$	0.830793	−	1.23915i	0.830793	−	1.23915i	−0.137790	−	0.990461i	$-0.544000\pi$
$83$	0.830793	−	1.23915i	0.830793	−	1.23915i	0.968583	−	0.248690i	$-0.0800000\pi$
$84$		0			0
$85$		0			0
$86$	0.0367093	+	0.323196i	0.0367093	+	0.323196i
$87$		0			0
$88$	1.72730	−	1.00693i	1.72730	−	1.00693i
$89$	−0.633085	+	0.327599i	−0.633085	+	0.327599i	−0.745941	−	0.666012i	$-0.768000\pi$
$89$	−0.633085	+	0.327599i	−0.633085	+	0.327599i	0.112856	+	0.993611i	$0.464000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.793375	+	1.80223i	−0.793375	+	1.80223i
$97$	1.79273	−	0.658175i	1.79273	−	0.658175i	0.793990	−	0.607930i	$-0.208000\pi$
$97$	1.79273	−	0.658175i	1.79273	−	0.658175i	0.998737	−	0.0502443i	$-0.0160000\pi$
$98$	0.617860	−	0.786288i	0.617860	−	0.786288i
$99$	3.88527	−	4.24300i	3.88527	−	4.24300i
$100$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$101$		0			0		−0.656586	−	0.754251i	$-0.728000\pi$
$101$		0			0		0.656586	+	0.754251i	$0.272000\pi$
$102$	0.984564	+	3.03018i	0.984564	+	3.03018i
$103$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$103$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.926877	−	0.164768i	0.926877	−	0.164768i	0.309017	−	0.951057i	$-0.400000\pi$
$107$	0.926877	−	0.164768i	0.926877	−	0.164768i	0.617860	+	0.786288i	$0.288000\pi$
$108$	−0.417227	+	3.67336i	−0.417227	+	3.67336i
$109$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$109$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.15129	−	0.836460i	1.15129	−	0.836460i	0.162637	−	0.986686i	$-0.448000\pi$
$113$	1.15129	−	0.836460i	1.15129	−	0.836460i	0.988652	+	0.150226i	$0.0480000\pi$
$114$	0.127213	+	0.212054i	0.127213	+	0.212054i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.79358	−	0.412762i	−1.79358	−	0.412762i
$119$		0			0
$120$		0			0
$121$	−1.41092	−	2.64464i	−1.41092	−	2.64464i
$122$		0			0
$123$	−2.33614	−	0.295123i	−2.33614	−	0.295123i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$127$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$128$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$129$	−0.488350	+	0.414444i	−0.488350	+	0.414444i
$130$		0			0
$131$	−0.841895	+	0.127926i	−0.841895	+	0.127926i	−0.556876	−	0.830596i	$-0.688000\pi$
$131$	−0.841895	+	0.127926i	−0.841895	+	0.127926i	−0.285019	+	0.958522i	$0.592000\pi$
$132$	3.54097	+	1.72093i	3.54097	+	1.72093i
$133$		0			0
$134$	0.740210	−	0.170347i	0.740210	−	0.170347i
$135$		0			0
$136$	−1.33250	+	0.917860i	−1.33250	+	0.917860i
$137$	0.141770	+	0.236318i	0.141770	+	0.236318i	0.920232	−	0.391374i	$-0.128000\pi$
$137$	0.141770	+	0.236318i	0.141770	+	0.236318i	−0.778462	+	0.627691i	$0.784000\pi$
$138$		0			0
$139$	−0.755723	−	1.84081i	−0.755723	−	1.84081i	−0.470704	−	0.882291i	$-0.656000\pi$
$139$	−0.755723	−	1.84081i	−0.755723	−	1.84081i	−0.285019	−	0.958522i	$-0.592000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−2.83305	+	0.503623i	−2.83305	+	0.503623i
$145$		0			0
$146$	1.19690	+	1.52317i	1.19690	+	1.52317i
$147$	1.96353	+	0.148328i	1.96353	+	0.148328i
$148$		0			0
$149$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$149$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$150$	−1.29290	−	1.48522i	−1.29290	−	1.48522i
$151$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$151$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$152$	−0.0848090	+	0.0926177i	−0.0848090	+	0.0926177i
$153$	−2.87666	+	3.66083i	−2.87666	+	3.66083i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$157$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−3.90989	+	2.02323i	−3.90989	+	2.02323i
$163$	−0.450694	+	0.262732i	−0.450694	+	0.262732i	−0.711536	−	0.702650i	$-0.752000\pi$
$163$	−0.450694	+	0.262732i	−0.450694	+	0.262732i	0.260842	+	0.965382i	$0.416000\pi$
$164$	−0.194483	−	1.17989i	−0.194483	−	1.17989i
$165$		0			0
$166$	0.425215	+	1.43000i	0.425215	+	1.43000i
$167$		0			0		0.994951	−	0.100362i	$-0.0320000\pi$
$167$		0			0		−0.994951	+	0.100362i	$0.968000\pi$
$168$		0			0
$169$	0.656586	−	0.754251i	0.656586	−	0.754251i
$170$		0			0
$171$	−0.153858	+	0.326964i	−0.153858	+	0.326964i
$172$	−0.272426	−	0.177728i	−0.272426	−	0.177728i
$173$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$173$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$174$		0			0
$175$		0			0
$176$	−0.325172	+	1.97275i	−0.325172	+	1.97275i
$177$	−1.29168	−	3.38611i	−1.29168	−	3.38611i
$178$	0.151124	−	0.696620i	0.151124	−	0.696620i
$179$	0.751353	+	0.637644i	0.751353	+	0.637644i	0.938734	−	0.344643i	$-0.112000\pi$
$179$	0.751353	+	0.637644i	0.751353	+	0.637644i	−0.187381	+	0.982287i	$0.560000\pi$
$180$		0			0
$181$		0			0		0.997159	−	0.0753268i	$-0.0240000\pi$
$181$		0			0		−0.997159	+	0.0753268i	$0.976000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.73342	+	2.73144i	1.73342	+	2.73144i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.745941	−	0.666012i	$-0.768000\pi$
$191$		0			0		0.745941	+	0.666012i	$0.232000\pi$
$192$	−0.882924	−	1.76009i	−0.882924	−	1.76009i
$193$	−1.19513	−	0.544146i	−1.19513	−	0.544146i	−0.285019	−	0.958522i	$-0.592000\pi$
$193$	−1.19513	−	0.544146i	−1.19513	−	0.544146i	−0.910106	+	0.414376i	$0.864000\pi$
$194$	−0.635595	+	1.80086i	−0.635595	+	1.80086i
$195$		0			0
$196$	0.212007	+	0.977268i	0.212007	+	0.977268i
$197$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$197$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$198$	0.792724	+	5.69824i	0.792724	+	5.69824i
$199$		0			0		−0.577573	−	0.816339i	$-0.696000\pi$
$199$		0			0		0.577573	+	0.816339i	$0.304000\pi$
$200$	0.535827	−	0.844328i	0.535827	−	0.844328i
$201$	1.09029	+	1.02386i	1.09029	+	1.02386i
$202$		0			0
$203$		0			0
$204$	−2.96238	−	1.17289i	−2.96238	−	1.17289i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.178654	+	0.176423i	0.178654	+	0.176423i
$210$		0			0
$211$	−1.50801	+	0.387191i	−1.50801	+	0.387191i	−0.910106	−	0.414376i	$-0.864000\pi$
$211$	−1.50801	+	0.387191i	−1.50801	+	0.387191i	−0.597905	+	0.801567i	$0.704000\pi$
$212$		0			0
$213$		0			0
$214$	−0.463857	+	0.819198i	−0.463857	+	0.819198i
$215$		0			0
$216$	−2.56442	−	2.66296i	−2.56442	−	2.66296i
$217$		0			0
$218$		0			0
$219$	−1.17875	+	3.62783i	−1.17875	+	3.62783i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$223$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$224$		0			0
$225$	0.750563	−	2.77785i	0.750563	−	2.77785i
$226$	−0.0893554	+	1.42026i	−0.0893554	+	1.42026i
$227$	1.44333	+	0.994203i	1.44333	+	0.994203i	0.994951	+	0.100362i	$0.0320000\pi$
$227$	1.44333	+	0.994203i	1.44333	+	0.994203i	0.448383	+	0.893841i	$0.352000\pi$
$228$	−0.244479	−	0.0371486i	−0.244479	−	0.0371486i
$229$		0			0		−0.332820	−	0.942991i	$-0.608000\pi$
$229$		0			0		0.332820	+	0.942991i	$0.392000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.38276	−	1.11495i	1.38276	−	1.11495i	0.402906	−	0.915241i	$-0.368000\pi$
$233$	1.38276	−	1.11495i	1.38276	−	1.11495i	0.979855	−	0.199710i	$-0.0640000\pi$
$234$		0			0
$235$		0			0
$236$	1.46131	−	1.11887i	1.46131	−	1.11887i
$237$		0			0
$238$		0			0
$239$		0			0		−0.0878512	−	0.996134i	$-0.528000\pi$
$239$		0			0		0.0878512	+	0.996134i	$0.472000\pi$
$240$		0			0
$241$	−0.0848090	−	1.34800i	−0.0848090	−	1.34800i	−0.778462	−	0.627691i	$-0.784000\pi$
$241$	−0.0848090	−	1.34800i	−0.0848090	−	1.34800i	0.693653	−	0.720309i	$-0.256000\pi$
$242$	2.93709	+	0.598625i	2.93709	+	0.598625i
$243$	−4.35684	−	2.39519i	−4.35684	−	2.39519i
$244$		0			0
$245$		0			0
$246$	1.71651	−	1.61191i	1.71651	−	1.61191i
$247$		0			0
$248$		0			0
$249$	−1.87257	+	2.26354i	−1.87257	+	2.26354i
$250$		0			0
$251$	0.0125660	−	0.999921i	0.0125660	−	0.999921i
$251$	0.0125660	−	0.999921i	0.0125660	−	0.999921i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.728969	−	0.684547i	0.728969	−	0.684547i
$257$	0.732084	−	0.722942i	0.732084	−	0.722942i	−0.236499	−	0.971632i	$-0.576000\pi$
$257$	0.732084	−	0.722942i	0.732084	−	0.722942i	0.968583	+	0.248690i	$0.0800000\pi$
$258$	−0.00804864	−	0.640456i	−0.00804864	−	0.640456i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.438075	−	0.730234i	0.438075	−	0.730234i
$263$		0			0		−0.0878512	−	0.996134i	$-0.528000\pi$
$263$		0			0		0.0878512	+	0.996134i	$0.472000\pi$
$264$	−3.58310	+	1.63140i	−3.58310	+	1.63140i
$265$		0			0
$266$		0			0
$267$	1.30507	−	0.516715i	1.30507	−	0.516715i
$268$	−0.340573	+	0.678925i	−0.340573	+	0.678925i
$269$		0			0		0.778462	−	0.627691i	$-0.216000\pi$
$269$		0			0		−0.778462	+	0.627691i	$0.784000\pi$
$270$		0			0
$271$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$271$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$272$	0.142146	−	1.61178i	0.142146	−	1.61178i
$273$		0			0
$274$	−0.272453	−	0.0413993i	−0.272453	−	0.0413993i
$275$	−1.64655	−	1.13418i	−1.64655	−	1.13418i
$276$		0			0
$277$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$277$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$278$	1.90009	+	0.591084i	1.90009	+	0.591084i
$279$		0			0
$280$		0			0
$281$	−0.0435376	+	1.15432i	−0.0435376	+	1.15432i	0.793990	+	0.607930i	$0.208000\pi$
$281$	−0.0435376	+	1.15432i	−0.0435376	+	1.15432i	−0.837528	+	0.546394i	$0.816000\pi$
$282$		0			0
$283$	−0.417379	+	1.28456i	−0.417379	+	1.28456i	0.492727	+	0.870184i	$0.336000\pi$
$283$	−0.417379	+	1.28456i	−0.417379	+	1.28456i	−0.910106	+	0.414376i	$0.864000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.41781	−	2.50393i	1.41781	−	2.50393i
$289$	−0.967431	−	1.29696i	−0.967431	−	1.29696i
$290$		0			0
$291$	−3.64236	+	0.935199i	−3.64236	+	0.935199i
$292$	−1.93655	−	0.0486812i	−1.93655	−	0.0486812i
$293$		0			0		−0.711536	−	0.702650i	$-0.752000\pi$
$293$		0			0		0.711536	+	0.702650i	$0.248000\pi$
$294$	−1.36589	+	1.41838i	−1.36589	+	1.41838i
$295$		0			0
$296$		0			0
$297$	−5.51371	+	4.92290i	−5.51371	+	4.92290i
$298$		0			0
$299$		0			0
$300$	1.96851	−	0.0494844i	1.96851	−	0.0494844i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.0173038	−	0.124383i	−0.0173038	−	0.124383i
$305$		0			0
$306$	−0.987071	−	4.55000i	−0.987071	−	4.55000i
$307$	0.856781	−	1.60596i	0.856781	−	1.60596i	0.0627905	−	0.998027i	$-0.480000\pi$
$307$	0.856781	−	1.60596i	0.856781	−	1.60596i	0.793990	−	0.607930i	$-0.208000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.745941	−	0.666012i	$-0.768000\pi$
$311$		0			0		0.745941	+	0.666012i	$0.232000\pi$
$312$		0			0
$313$	0.443754	−	1.49235i	0.443754	−	1.49235i	−0.379779	−	0.925077i	$-0.624000\pi$
$313$	0.443754	−	1.49235i	0.443754	−	1.49235i	0.823533	−	0.567269i	$-0.192000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.236499	−	0.971632i	$-0.576000\pi$
$317$		0			0		0.236499	+	0.971632i	$0.424000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.84849	+	0.139637i	−1.84849	+	0.139637i
$322$		0			0
$323$	−0.154924	−	0.131478i	−0.154924	−	0.131478i
$324$	0.933330	−	4.30228i	0.933330	−	4.30228i
$325$		0			0
$326$	0.0848450	−	0.514737i	0.0848450	−	0.514737i
$327$		0			0
$328$	1.03309	+	0.602238i	1.03309	+	0.602238i
$329$		0			0
$330$		0			0
$331$	−0.559121	+	1.18819i	−0.559121	+	1.18819i	0.402906	+	0.915241i	$0.368000\pi$
$331$	−0.559121	+	1.18819i	−0.559121	+	1.18819i	−0.962028	+	0.272952i	$0.912000\pi$
$332$	−1.37288	−	0.583883i	−1.37288	−	0.583883i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.179214	+	1.57784i	0.179214	+	1.57784i	0.693653	+	0.720309i	$0.256000\pi$
$337$	0.179214	+	1.57784i	0.179214	+	1.57784i	−0.514440	+	0.857527i	$0.672000\pi$
$338$	0.162637	+	0.986686i	0.162637	+	0.986686i
$339$	−2.42090	+	1.41126i	−2.42090	+	1.41126i
$340$		0			0
$341$		0			0
$342$	−0.153858	−	0.326964i	−0.153858	−	0.326964i
$343$		0			0
$344$	0.310593	−	0.0966200i	0.310593	−	0.0966200i
$345$		0			0
$346$		0			0
$347$	−0.0707916	+	0.160810i	−0.0707916	+	0.160810i	−0.947098	−	0.320944i	$-0.896000\pi$
$347$	−0.0707916	+	0.160810i	−0.0707916	+	0.160810i	0.876307	+	0.481754i	$0.160000\pi$
$348$		0			0
$349$		0			0		0.617860	−	0.786288i	$-0.288000\pi$
$349$		0			0		−0.617860	+	0.786288i	$0.712000\pi$
$350$		0			0
$351$		0			0
$352$	−1.31276	−	1.50803i	−1.31276	−	1.50803i
$353$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	0.876307	−	0.481754i	$-0.160000\pi$
$353$	−0.115808	−	0.356420i	−0.115808	−	0.356420i	−0.992115	+	0.125333i	$0.960000\pi$
$354$	3.43239	+	1.16313i	3.43239	+	1.16313i
$355$		0			0
$356$	0.440425	+	0.560485i	0.440425	+	0.560485i
$357$		0			0
$358$	−0.970244	+	0.172477i	−0.970244	+	0.172477i
$359$		0			0		0.112856	−	0.993611i	$-0.464000\pi$
$359$		0			0		−0.112856	+	0.993611i	$0.536000\pi$
$360$		0			0
$361$	0.874130	+	0.452332i	0.874130	+	0.452332i
$362$		0			0
$363$	2.24161	+	5.46019i	2.24161	+	5.46019i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.899405	−	0.437116i	$-0.144000\pi$
$367$		0			0		−0.899405	+	0.437116i	$0.856000\pi$
$368$		0			0
$369$	3.35325	+	0.771694i	3.35325	+	0.771694i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.762443	−	0.647056i	$-0.224000\pi$
$373$		0			0		−0.762443	+	0.647056i	$0.776000\pi$
$374$	−3.20954	−	0.405459i	−3.20954	−	0.405459i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.97859	+	0.249954i	1.97859	+	0.249954i	0.998737	+	0.0502443i	$0.0160000\pi$
$379$	1.97859	+	0.249954i	1.97859	+	0.249954i	0.979855	+	0.199710i	$0.0640000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.899405	−	0.437116i	$-0.856000\pi$
$383$		0			0		0.899405	+	0.437116i	$0.144000\pi$
$384$	1.91897	+	0.441618i	1.91897	+	0.441618i
$385$		0			0
$386$	1.18107	−	0.574008i	1.18107	−	0.574008i
$387$	0.770799	−	0.530945i	0.770799	−	0.530945i
$388$	−0.982440	−	1.63764i	−0.982440	−	1.63764i
$389$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$389$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$390$		0			0
$391$		0			0
$392$	−0.888136	−	0.459580i	−0.888136	−	0.459580i
$393$	1.67471	−	0.0842511i	1.67471	−	0.0842511i
$394$		0			0
$395$		0			0
$396$	−4.89587	−	3.02139i	−4.89587	−	3.02139i
$397$		0			0		−0.617860	−	0.786288i	$-0.712000\pi$
$397$		0			0		0.617860	+	0.786288i	$0.288000\pi$
$398$		0			0
$399$		0			0
$400$	0.309017	+	0.951057i	0.309017	+	0.951057i
$401$	−0.0494937	−	0.0568557i	−0.0494937	−	0.0568557i	0.728969	−	0.684547i	$-0.240000\pi$
$401$	−0.0494937	−	0.0568557i	−0.0494937	−	0.0568557i	−0.778462	+	0.627691i	$0.784000\pi$
$402$	−1.48387	+	0.187457i	−1.48387	+	0.187457i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	2.79202	−	1.53492i	2.79202	−	1.53492i
$409$	0.404876	−	0.125950i	0.404876	−	0.125950i	−0.0878512	−	0.996134i	$-0.528000\pi$
$409$	0.404876	−	0.125950i	0.404876	−	0.125950i	0.492727	+	0.870184i	$0.336000\pi$
$410$		0			0
$411$	−0.231051	−	0.491008i	−0.231051	−	0.491008i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.11681	+	3.75585i	1.11681	+	3.75585i
$418$	−0.249815	+	0.0251991i	−0.249815	+	0.0251991i
$419$	−0.236123	+	0.352184i	−0.236123	+	0.352184i	−0.929776	−	0.368125i	$-0.880000\pi$
$419$	−0.236123	+	0.352184i	−0.236123	+	0.352184i	0.693653	+	0.720309i	$0.256000\pi$
$420$		0			0
$421$		0			0		−0.920232	−	0.391374i	$-0.872000\pi$
$421$		0			0		0.920232	+	0.391374i	$0.128000\pi$
$422$	0.662906	−	1.40875i	0.662906	−	1.40875i
$423$		0			0
$424$		0			0
$425$	1.39786	+	0.814879i	1.39786	+	0.814879i
$426$		0			0
$427$		0			0
$428$	−0.335529	−	0.879585i	−0.335529	−	0.879585i
$429$		0			0
$430$		0			0
$431$		0			0		−0.675333	−	0.737513i	$-0.736000\pi$
$431$		0			0		0.675333	+	0.737513i	$0.264000\pi$
$432$	3.68647	−	0.278481i	3.68647	−	0.278481i
$433$	−1.92189	−	0.493458i	−1.92189	−	0.493458i	−0.992115	−	0.125333i	$-0.960000\pi$
$433$	−1.92189	−	0.493458i	−1.92189	−	0.493458i	−0.929776	−	0.368125i	$-0.880000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−2.04393	−	3.22071i	−2.04393	−	3.22071i
$439$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$439$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$440$		0			0
$441$	−2.83305	−	0.503623i	−2.83305	−	0.503623i
$442$		0			0
$443$	0.277116	+	0.552424i	0.277116	+	0.552424i	0.988652	−	0.150226i	$-0.0480000\pi$
$443$	0.277116	+	0.552424i	0.277116	+	0.552424i	−0.711536	+	0.702650i	$0.752000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.111033	−	0.798127i	−0.111033	−	0.798127i	−0.962028	−	0.272952i	$-0.912000\pi$
$449$	−0.111033	−	0.798127i	−0.111033	−	0.798127i	0.850994	−	0.525175i	$-0.176000\pi$
$450$	1.66195	+	2.34899i	1.66195	+	2.34899i
$451$	1.28109	−	2.01867i	1.28109	−	2.01867i
$452$	−1.03737	−	0.974159i	−1.03737	−	0.974159i
$453$		0			0
$454$	−1.68606	+	0.478379i	−1.68606	+	0.478379i
$455$		0			0
$456$	0.184460	−	0.164695i	0.184460	−	0.164695i
$457$	−1.08489	+	0.669518i	−1.08489	+	0.669518i	−0.947098	−	0.320944i	$-0.896000\pi$
$457$	−1.08489	+	0.669518i	−1.08489	+	0.669518i	−0.137790	+	0.990461i	$0.544000\pi$
$458$		0			0
$459$	4.14932	−	4.30877i	4.14932	−	4.30877i
$460$		0			0
$461$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$461$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$462$		0			0
$463$		0			0		0.947098	−	0.320944i	$-0.104000\pi$
$463$		0			0		−0.947098	+	0.320944i	$0.896000\pi$
$464$		0			0
$465$		0			0
$466$	−0.0223207	+	1.77613i	−0.0223207	+	1.77613i
$467$	−0.772557	−	0.802245i	−0.772557	−	0.802245i	0.212007	−	0.977268i	$-0.432000\pi$
$467$	−0.772557	−	0.802245i	−0.772557	−	0.802245i	−0.984564	+	0.175023i	$0.944000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.0693674	+	1.83916i	−0.0693674	+	1.83916i
$473$	−0.169637	−	0.627829i	−0.169637	−	0.627829i
$474$		0			0
$475$	0.119913	+	0.0373028i	0.119913	+	0.0373028i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.988652	−	0.150226i	$-0.952000\pi$
$479$		0			0		0.988652	+	0.150226i	$0.0480000\pi$
$480$		0			0
$481$		0			0
$482$	1.09271	+	0.793901i	1.09271	+	0.793901i
$483$		0			0
$484$	−2.33342	+	1.88149i	−2.33342	+	1.88149i
$485$		0			0
$486$	4.62268	−	1.83025i	4.62268	−	1.83025i
$487$		0			0		0.793990	−	0.607930i	$-0.208000\pi$
$487$		0			0		−0.793990	+	0.607930i	$0.792000\pi$
$488$		0			0
$489$	0.934916	−	0.425672i	0.934916	−	0.425672i
$490$		0			0
$491$	−0.0129289	+	0.0215514i	−0.0129289	+	0.0215514i	−0.863923	−	0.503623i	$-0.832000\pi$
$491$	−0.0129289	+	0.0215514i	−0.0129289	+	0.0215514i	0.850994	+	0.525175i	$0.176000\pi$
$492$	0.147853	+	2.35006i	0.147853	+	2.35006i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.550472	−	2.88567i	−0.550472	−	2.88567i
$499$	1.69340	+	0.170815i	1.69340	+	0.170815i	0.899405	−	0.437116i	$-0.144000\pi$
$499$	1.69340	+	0.170815i	1.69340	+	0.170815i	0.793990	+	0.607930i	$0.208000\pi$
$500$		0			0
$501$		0			0
$502$	0.762443	+	0.647056i	0.762443	+	0.647056i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.43543	+	1.34796i	−1.43543	+	1.34796i
$508$		0			0
$509$		0			0		−0.0125660	−	0.999921i	$-0.504000\pi$
$509$		0			0		0.0125660	+	0.999921i	$0.496000\pi$
$510$		0			0
$511$		0			0
$512$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$513$	0.238839	−	0.398124i	0.238839	−	0.398124i
$514$	0.0903883	+	1.02490i	0.0903883	+	1.02490i
$515$		0			0
$516$	0.498611	+	0.402041i	0.498611	+	0.402041i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.233059	+	0.957499i	−0.233059	+	0.957499i	0.728969	+	0.684547i	$0.240000\pi$
$521$	−0.233059	+	0.957499i	−0.233059	+	0.957499i	−0.962028	+	0.272952i	$0.912000\pi$
$522$		0			0
$523$	−0.108559	+	1.23094i	−0.108559	+	1.23094i	0.728969	+	0.684547i	$0.240000\pi$
$523$	−0.108559	+	1.23094i	−0.108559	+	1.23094i	−0.837528	+	0.546394i	$0.816000\pi$
$524$	0.283415	+	0.803012i	0.283415	+	0.803012i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.02694	−	3.80072i	1.02694	−	3.80072i
$529$	0.954865	+	0.297042i	0.954865	+	0.297042i
$530$		0			0
$531$	1.38138	+	5.11254i	1.38138	+	5.11254i
$532$		0			0
$533$		0			0
$534$	−0.433749	+	1.33494i	−0.433749	+	1.33494i
$535$		0			0
$536$	−0.306031	−	0.695179i	−0.306031	−	0.695179i
$537$	−1.34603	−	1.39775i	−1.34603	−	1.39775i
$538$		0			0
$539$	−0.985143	+	1.73982i	−0.985143	+	1.73982i
$540$		0			0
$541$		0			0		0.947098	−	0.320944i	$-0.104000\pi$
$541$		0			0		−0.947098	+	0.320944i	$0.896000\pi$
$542$		0			0
$543$		0			0
$544$	1.15129	+	1.13691i	1.15129	+	1.13691i
$545$		0			0
$546$		0			0
$547$	1.44838	−	0.893841i	1.44838	−	0.893841i	0.448383	−	0.893841i	$-0.352000\pi$
$547$	1.44838	−	0.893841i	1.44838	−	0.893841i	1.00000			$0$
$548$	0.205567	−	0.183540i	0.205567	−	0.183540i
$549$		0			0
$550$	1.92345	−	0.545731i	1.92345	−	0.545731i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.66660	+	1.08727i	−1.66660	+	1.08727i
$557$		0			0		−0.212007	−	0.977268i	$-0.568000\pi$
$557$		0			0		0.212007	+	0.977268i	$0.432000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−2.85630	−	5.69397i	−2.85630	−	5.69397i
$562$	−0.861670	−	0.769341i	−0.861670	−	0.769341i
$563$	−1.72556	−	0.306748i	−1.72556	−	0.306748i	−0.778462	−	0.627691i	$-0.784000\pi$
$563$	−1.72556	−	0.306748i	−1.72556	−	0.306748i	−0.947098	+	0.320944i	$0.896000\pi$
$564$		0			0
$565$		0			0
$566$	−0.723723	−	1.14040i	−0.723723	−	1.14040i
$567$		0			0
$568$		0			0
$569$	−0.816920	−	0.625487i	−0.816920	−	0.625487i	0.112856	−	0.993611i	$-0.464000\pi$
$569$	−0.816920	−	0.625487i	−0.816920	−	0.625487i	−0.929776	+	0.368125i	$0.880000\pi$
$570$		0			0
$571$	−0.644727	−	0.165538i	−0.644727	−	0.165538i	−0.0878512	−	0.996134i	$-0.528000\pi$
$571$	−0.644727	−	0.165538i	−0.644727	−	0.165538i	−0.556876	+	0.830596i	$0.688000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.02556	+	2.68850i	1.02556	+	2.68850i
$577$	−0.324350	+	1.96777i	−0.324350	+	1.96777i	−0.0878512	+	0.996134i	$0.528000\pi$
$577$	−0.324350	+	1.96777i	−0.324350	+	1.96777i	−0.236499	+	0.971632i	$0.576000\pi$
$578$	1.61599	+	0.0812970i	1.61599	+	0.0812970i
$579$	2.23394	+	1.30227i	2.23394	+	1.30227i
$580$		0			0
$581$		0			0
$582$	1.60114	−	3.40260i	1.60114	−	3.40260i
$583$		0			0
$584$	1.27192	−	1.46111i	1.27192	−	1.46111i
$585$		0			0
$586$		0			0
$587$	0.477423	+	1.60558i	0.477423	+	1.60558i	0.762443	+	0.647056i	$0.224000\pi$
$587$	0.477423	+	1.60558i	0.477423	+	1.60558i	−0.285019	+	0.958522i	$0.592000\pi$
$588$	−0.222229	−	1.95655i	−0.222229	−	1.95655i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.400832	+	0.851811i	0.400832	+	0.851811i	0.998737	+	0.0502443i	$0.0160000\pi$
$593$	0.400832	+	0.851811i	0.400832	+	0.851811i	−0.597905	+	0.801567i	$0.704000\pi$
$594$	−0.278591	−	7.38636i	−0.278591	−	7.38636i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.938734	−	0.344643i	$-0.112000\pi$
$599$		0			0		−0.938734	+	0.344643i	$0.888000\pi$
$600$	−1.21665	+	1.54830i	−1.21665	+	1.54830i
$601$	−0.723723	+	0.790359i	−0.723723	+	0.790359i	−0.984564	−	0.175023i	$-0.944000\pi$
$601$	−0.723723	+	0.790359i	−0.723723	+	0.790359i	0.260842	+	0.965382i	$0.416000\pi$
$602$		0			0
$603$	−1.43504	−	1.64849i	−1.43504	−	1.64849i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.617860	−	0.786288i	$-0.712000\pi$
$607$		0			0		0.617860	+	0.786288i	$0.288000\pi$
$608$	0.106869	+	0.0659520i	0.106869	+	0.0659520i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	4.13502	+	2.13973i	4.13502	+	2.13973i
$613$		0			0		0.577573	−	0.816339i	$-0.304000\pi$
$613$		0			0		−0.577573	+	0.816339i	$0.696000\pi$
$614$	0.691278	+	1.68384i	0.691278	+	1.68384i
$615$		0			0
$616$		0			0
$617$	−1.60511	+	1.10564i	−1.60511	+	1.10564i	−0.675333	+	0.737513i	$0.736000\pi$
$617$	−1.60511	+	1.10564i	−1.60511	+	1.10564i	−0.929776	+	0.368125i	$0.880000\pi$
$618$		0			0
$619$	1.73103	−	0.398366i	1.73103	−	0.398366i	0.762443	−	0.647056i	$-0.224000\pi$
$619$	1.73103	−	0.398366i	1.73103	−	0.398366i	0.968583	+	0.248690i	$0.0800000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$626$	0.867013	+	1.29318i	0.867013	+	1.29318i
$627$	−0.315152	−	0.380953i	−0.315152	−	0.380953i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.762443	−	0.647056i	$-0.224000\pi$
$631$		0			0		−0.762443	+	0.647056i	$0.776000\pi$
$632$		0			0
$633$	3.03099	−	0.460559i	3.03099	−	0.460559i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.553694	−	1.34870i	−0.553694	−	1.34870i	−0.910106	−	0.414376i	$-0.864000\pi$
$641$	−0.553694	−	1.34870i	−0.553694	−	1.34870i	0.356412	−	0.934329i	$-0.384000\pi$
$642$	1.07068	−	1.51329i	1.07068	−	1.51329i
$643$	1.70882	+	0.884257i	1.70882	+	0.884257i	0.979855	+	0.199710i	$0.0640000\pi$
$643$	1.70882	+	0.884257i	1.70882	+	0.884257i	0.728969	+	0.684547i	$0.240000\pi$
$644$		0			0
$645$		0			0
$646$	0.200058	−	0.0355637i	0.200058	−	0.0355637i
$647$		0			0		−0.850994	−	0.525175i	$-0.824000\pi$
$647$		0			0		0.850994	+	0.525175i	$0.176000\pi$
$648$	2.72004	+	3.46152i	2.72004	+	3.46152i
$649$	3.66931	+	0.277185i	3.66931	+	0.277185i
$650$		0			0
$651$		0			0
$652$	0.342530	+	0.393480i	0.342530	+	0.393480i
$653$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$653$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$654$		0			0
$655$		0			0
$656$	−1.12255	+	0.412127i	−1.12255	+	0.412127i
$657$	2.24585	−	5.10168i	2.24585	−	5.10168i
$658$		0			0
$659$	−0.746226	+	0.410241i	−0.746226	+	0.410241i	−0.809017	−	0.587785i	$-0.800000\pi$
$659$	−0.746226	+	0.410241i	−0.746226	+	0.410241i	0.0627905	+	0.998027i	$0.480000\pi$
$660$		0			0
$661$		0			0		−0.0376902	−	0.999289i	$-0.512000\pi$
$661$		0			0		0.0376902	+	0.999289i	$0.488000\pi$
$662$	−0.559121	−	1.18819i	−0.559121	−	1.18819i
$663$		0			0
$664$	1.32500	−	0.685639i	1.32500	−	0.685639i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.850483	+	1.80737i	−0.850483	+	1.80737i	−0.379779	+	0.925077i	$0.624000\pi$
$673$	−0.850483	+	1.80737i	−0.850483	+	1.80737i	−0.470704	+	0.882291i	$0.656000\pi$
$674$	−1.32998	−	0.867664i	−1.32998	−	0.867664i
$675$	−1.31765	+	3.45419i	−1.31765	+	3.45419i
$676$	−0.863923	−	0.503623i	−0.863923	−	0.503623i
$677$		0			0		−0.998737	−	0.0502443i	$-0.984000\pi$
$677$		0			0		0.998737	+	0.0502443i	$0.0160000\pi$
$678$	0.455744	−	2.76490i	0.455744	−	2.76490i
$679$		0			0
$680$		0			0
$681$	−2.63128	−	2.23307i	−2.63128	−	2.23307i
$682$		0			0
$683$	0.568419	−	0.0429392i	0.568419	−	0.0429392i	0.212007	−	0.977268i	$-0.432000\pi$
$683$	0.568419	−	0.0429392i	0.568419	−	0.0429392i	0.356412	+	0.934329i	$0.384000\pi$
$684$	0.350003	+	0.0898654i	0.350003	+	0.0898654i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.123532	+	0.300904i	−0.123532	+	0.300904i
$689$		0			0
$690$		0			0
$691$	0.539883	−	1.81563i	0.539883	−	1.81563i	−0.0376902	−	0.999289i	$-0.512000\pi$
$691$	0.539883	−	1.81563i	0.539883	−	1.81563i	0.577573	−	0.816339i	$-0.304000\pi$
$692$		0			0
$693$		0			0
$694$	−0.0787820	−	0.157050i	−0.0787820	−	0.157050i
$695$		0			0
$696$		0			0
$697$	−0.910747	+	1.70711i	−0.910747	+	1.70711i
$698$		0			0
$699$	−2.92943	+	1.91113i	−2.92943	+	1.91113i
$700$		0			0
$701$		0			0		−0.577573	−	0.816339i	$-0.696000\pi$
$701$		0			0		0.577573	+	0.816339i	$0.304000\pi$
$702$		0			0
$703$		0			0
$704$	1.99874	−	0.0502443i	1.99874	−	0.0502443i
$705$		0			0
$706$	0.348445	+	0.137959i	0.348445	+	0.137959i
$707$		0			0
$708$	−3.08410	+	1.90329i	−3.08410	+	1.90329i
$709$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$709$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$710$		0			0
$711$		0			0
$712$	−0.712599	−	0.0179133i	−0.712599	−	0.0179133i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.485560	−	0.857527i	0.485560	−	0.857527i
$717$		0			0
$718$		0			0
$719$		0			0		−0.402906	−	0.915241i	$-0.632000\pi$
$719$		0			0		0.402906	+	0.915241i	$0.368000\pi$
$720$		0			0
$721$		0			0
$722$	−0.905719	+	0.385201i	−0.905719	+	0.385201i
$723$	−0.100242	+	2.65774i	−0.100242	+	2.65774i
$724$		0			0
$725$		0			0
$726$	−5.63600	−	1.75326i	−5.63600	−	1.75326i
$727$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$727$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$728$		0			0
$729$	4.43704	+	3.05634i	4.43704	+	3.05634i
$730$		0			0
$731$	0.175165	+	0.496301i	0.175165	+	0.496301i
$732$		0			0
$733$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$733$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.41199	+	0.559047i	−1.41199	+	0.559047i
$738$	−2.73205	+	2.09183i	−2.73205	+	2.09183i
$739$	0.443754	+	0.357808i	0.443754	+	0.357808i	0.823533	−	0.567269i	$-0.192000\pi$
$739$	0.443754	+	0.357808i	0.443754	+	0.357808i	−0.379779	+	0.925077i	$0.624000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$743$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.05451	−	3.01637i	3.05451	−	3.01637i
$748$	2.35825	−	2.21454i	2.35825	−	2.21454i
$749$		0			0
$750$		0			0
$751$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$751$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$752$		0			0
$753$	−0.222229	+	1.95655i	−0.222229	+	1.95655i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$757$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$758$	−1.45380	+	1.36520i	−1.45380	+	1.36520i
$759$		0			0
$760$		0			0
$761$	−1.30735	−	0.718720i	−1.30735	−	0.718720i	−0.332820	−	0.942991i	$-0.608000\pi$
$761$	−1.30735	−	0.718720i	−1.30735	−	0.718720i	−0.974527	+	0.224271i	$0.928000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.56347	+	1.19709i	−1.56347	+	1.19709i
$769$	−1.53140	+	0.606325i	−1.53140	+	0.606325i	−0.974527	−	0.224271i	$-0.928000\pi$
$769$	−1.53140	+	0.606325i	−1.53140	+	0.606325i	−0.556876	+	0.830596i	$0.688000\pi$
$770$		0			0
$771$	−1.57716	+	1.27170i	−1.57716	+	1.27170i
$772$	−0.310564	+	1.27592i	−0.310564	+	1.27592i
$773$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$773$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$774$	−0.0822258	+	0.932348i	−0.0822258	+	0.932348i
$775$		0			0
$776$	1.88806	+	0.286890i	1.88806	+	0.286890i
$777$		0			0
$778$		0			0
$779$	−0.0391708	+	0.144972i	−0.0391708	+	0.144972i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.920232	−	0.391374i	0.920232	−	0.391374i
$785$		0			0
$786$	−1.00258	+	1.34409i	−1.00258	+	1.34409i
$787$	0.361313	+	0.820758i	0.361313	+	0.820758i	0.998737	+	0.0502443i	$0.0160000\pi$
$787$	0.361313	+	0.820758i	0.361313	+	0.820758i	−0.637424	+	0.770513i	$0.720000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	5.44877	−	1.84643i	5.44877	−	1.84643i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$797$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$798$		0			0
$799$		0			0
$800$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$801$	−1.97324	+	0.559859i	−1.97324	+	0.559859i
$802$	0.0753566	−	0.00189432i	0.0753566	−	0.00189432i
$803$	−2.82338	−	2.65133i	−2.82338	−	2.65133i
$804$	0.801419	−	1.26283i	0.801419	−	1.26283i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.775280	+	1.45319i	−0.775280	+	1.45319i	0.112856	+	0.993611i	$0.464000\pi$
$809$	−0.775280	+	1.45319i	−0.775280	+	1.45319i	−0.888136	+	0.459580i	$0.848000\pi$
$810$		0			0
$811$	−0.474787	−	0.216173i	−0.474787	−	0.216173i	0.162637	−	0.986686i	$-0.448000\pi$
$811$	−0.474787	−	0.216173i	−0.474787	−	0.216173i	−0.637424	+	0.770513i	$0.720000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.597019	+	3.12968i	−0.597019	+	3.12968i
$817$	0.0218876	+	0.0344894i	0.0218876	+	0.0344894i
$818$	−0.161032	+	0.392246i	−0.161032	+	0.392246i
$819$		0			0
$820$		0			0
$821$		0			0		−0.962028	−	0.272952i	$-0.912000\pi$
$821$		0			0		0.962028	+	0.272952i	$0.0880000\pi$
$822$	0.525605	+	0.134952i	0.525605	+	0.134952i
$823$		0			0		0.997159	−	0.0753268i	$-0.0240000\pi$
$823$		0			0		−0.997159	+	0.0753268i	$0.976000\pi$
$824$		0			0
$825$	3.00175	+	2.54747i	3.00175	+	2.54747i
$826$		0			0
$827$	−0.396954	−	1.04061i	−0.396954	−	1.04061i	−0.974527	−	0.224271i	$-0.928000\pi$
$827$	−0.396954	−	1.04061i	−0.396954	−	1.04061i	0.577573	−	0.816339i	$-0.304000\pi$
$828$		0			0
$829$		0			0		−0.998737	−	0.0502443i	$-0.984000\pi$
$829$		0			0		0.998737	+	0.0502443i	$0.0160000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.688925	−	1.46404i	0.688925	−	1.46404i
$834$	−3.60581	−	1.53355i	−3.60581	−	1.53355i
$835$		0			0
$836$	0.139822	−	0.208548i	0.139822	−	0.208548i
$837$		0			0
$838$	−0.120852	−	0.406427i	−0.120852	−	0.406427i
$839$		0			0		−0.112856	−	0.993611i	$-0.536000\pi$
$839$		0			0		0.112856	+	0.993611i	$0.464000\pi$
$840$		0			0
$841$	−0.863923	+	0.503623i	−0.863923	+	0.503623i
$842$		0			0
$843$	0.313422	−	2.25293i	0.313422	−	2.25293i
$844$	0.662906	+	1.40875i	0.662906	+	1.40875i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.07158	−	2.43421i	1.07158	−	2.43421i
$850$	−1.51890	+	0.557644i	−1.51890	+	0.557644i
$851$		0			0
$852$		0			0
$853$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$853$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$854$		0			0
$855$		0			0
$856$	0.891606	+	0.302139i	0.891606	+	0.302139i
$857$	−0.520201	−	0.0392967i	−0.520201	−	0.0392967i	−0.187381	−	0.982287i	$-0.560000\pi$
$857$	−0.520201	−	0.0392967i	−0.520201	−	0.0392967i	−0.332820	+	0.942991i	$0.608000\pi$
$858$		0			0
$859$	−1.42546	−	0.879697i	−1.42546	−	0.879697i	−0.425779	−	0.904827i	$-0.640000\pi$
$859$	−1.42546	−	0.879697i	−1.42546	−	0.879697i	−0.999684	+	0.0251301i	$0.992000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$863$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$864$	−2.13527	+	3.01799i	−2.13527	+	3.01799i
$865$		0			0
$866$	1.60528	−	1.16630i	1.60528	−	1.16630i
$867$	1.63906	+	2.73218i	1.63906	+	2.73218i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	5.43282	−	0.825517i	5.43282	−	0.825517i
$874$		0			0
$875$		0			0
$876$	3.78445	+	0.478087i	3.78445	+	0.478087i
$877$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$877$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.565544	+	0.0714448i	0.565544	+	0.0714448i	0.402906	−	0.915241i	$-0.368000\pi$
$881$	0.565544	+	0.0714448i	0.565544	+	0.0714448i	0.162637	+	0.986686i	$0.448000\pi$
$882$	2.19390	−	1.86188i	2.19390	−	1.86188i
$883$	−0.911832	−	1.70914i	−0.911832	−	1.70914i	−0.675333	−	0.737513i	$-0.736000\pi$
$883$	−0.911832	−	1.70914i	−0.911832	−	1.70914i	−0.236499	−	0.971632i	$-0.576000\pi$
$884$		0			0
$885$		0			0
$886$	−0.602291	−	0.138607i	−0.602291	−	0.138607i
$887$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$887$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	7.12091	−	5.17364i	7.12091	−	5.17364i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.685742	+	0.423192i	0.685742	+	0.423192i
$899$		0			0
$900$	−2.86929	−	0.216750i	−2.86929	−	0.216750i
$901$		0			0
$902$	0.738818	+	2.27385i	0.738818	+	2.27385i
$903$		0			0
$904$	1.41185	−	0.178358i	1.41185	−	0.178358i
$905$		0			0
$906$		0			0
$907$	−1.80618	+	0.663112i	−1.80618	+	0.663112i	−0.809017	+	0.587785i	$0.800000\pi$
$907$	−1.80618	+	0.663112i	−1.80618	+	0.663112i	−0.997159	+	0.0753268i	$0.976000\pi$
$908$	0.706139	−	1.60406i	0.706139	−	1.60406i
$909$		0			0
$910$		0			0
$911$		0			0		0.954865	−	0.297042i	$-0.0960000\pi$
$911$		0			0		−0.954865	+	0.297042i	$0.904000\pi$
$912$	0.00932023	+	0.247110i	0.00932023	+	0.247110i
$913$	−1.27002	−	2.69894i	−1.27002	−	2.69894i
$914$	0.175662	−	1.26269i	0.175662	−	1.26269i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.675088	+	5.94362i	0.675088	+	5.94362i
$919$		0			0		−0.285019	−	0.958522i	$-0.592000\pi$
$919$		0			0		0.285019	+	0.958522i	$0.408000\pi$
$920$		0			0
$921$	−1.99597	+	2.97705i	−1.99597	+	2.97705i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.296034	+	1.79598i	−0.296034	+	1.79598i	0.260842	+	0.965382i	$0.416000\pi$
$929$	−0.296034	+	1.79598i	−0.296034	+	1.79598i	−0.556876	+	0.830596i	$0.688000\pi$
$930$		0			0
$931$	0.0266241	−	0.122726i	0.0266241	−	0.122726i
$932$	−1.35431	−	1.14935i	−1.35431	−	1.14935i
$933$		0			0
$934$	1.11059	−	0.0838953i	1.11059	−	0.0838953i
$935$		0			0
$936$		0			0
$937$	−0.452605	−	0.346544i	−0.452605	−	0.346544i	0.356412	−	0.934329i	$-0.384000\pi$
$937$	−0.452605	−	0.346544i	−0.452605	−	0.346544i	−0.809017	+	0.587785i	$0.800000\pi$
$938$		0			0
$939$	−1.16432	+	2.83609i	−1.16432	+	2.83609i
$940$		0			0
$941$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$941$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$942$		0			0
$943$		0			0
$944$	−1.37288	−	1.22577i	−1.37288	−	1.22577i
$945$		0			0
$946$	0.591881	+	0.269486i	0.591881	+	0.269486i
$947$	0.618896	−	1.75354i	0.618896	−	1.75354i	−0.0376902	−	0.999289i	$-0.512000\pi$
$947$	0.618896	−	1.75354i	0.618896	−	1.75354i	0.656586	−	0.754251i	$-0.272000\pi$
$948$		0			0
$949$		0			0
$950$	−0.105178	+	0.0686168i	−0.105178	+	0.0686168i
$951$		0			0
$952$		0			0
$953$	−0.951775	+	1.49976i	−0.951775	+	1.49976i	−0.0878512	+	0.996134i	$0.528000\pi$
$953$	−0.951775	+	1.49976i	−0.951775	+	1.49976i	−0.863923	+	0.503623i	$0.832000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.693653	−	0.720309i	0.693653	−	0.720309i
$962$		0			0
$963$	2.70802	+	0.0680742i	2.70802	+	0.0680742i
$964$	−1.30823	+	0.335897i	−1.30823	+	0.335897i
$965$		0			0
$966$		0			0
$967$		0			0		0.492727	−	0.870184i	$-0.336000\pi$
$967$		0			0		−0.492727	+	0.870184i	$0.664000\pi$
$968$	0.0376664	−	2.99724i	0.0376664	−	2.99724i
$969$	0.277542	+	0.288207i	0.277542	+	0.288207i
$970$		0			0
$971$	−0.640747	+	0.859002i	−0.640747	+	0.859002i	−0.997159	−	0.0753268i	$-0.976000\pi$
$971$	−0.640747	+	0.859002i	−0.640747	+	0.859002i	0.356412	+	0.934329i	$0.384000\pi$
$972$	−1.53638	+	4.72849i	−1.53638	+	4.72849i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.90009	+	0.591084i	1.90009	+	0.591084i	0.979855	+	0.199710i	$0.0640000\pi$
$977$	1.90009	+	0.591084i	1.90009	+	0.591084i	0.920232	+	0.391374i	$0.128000\pi$
$978$	−0.267952	+	0.991699i	−0.267952	+	0.991699i
$979$	−0.0894889	+	1.42238i	−0.0894889	+	1.42238i
$980$		0			0
$981$		0			0
$982$	−0.00836445	−	0.0236993i	−0.00836445	−	0.0236993i
$983$		0			0		0.0878512	−	0.996134i	$-0.472000\pi$
$983$		0			0		−0.0878512	+	0.996134i	$0.528000\pi$
$984$	−1.90500	−	1.38406i	−1.90500	−	1.38406i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.910106	−	0.414376i	$-0.136000\pi$
$991$		0			0		−0.910106	+	0.414376i	$0.864000\pi$
$992$		0			0
$993$	1.33024	−	2.21740i	1.33024	−	2.21740i
$994$		0			0
$995$		0			0
$996$	2.57433	+	1.41525i	2.57433	+	1.41525i
$997$		0			0		−0.0125660	−	0.999921i	$-0.504000\pi$
$997$		0			0		0.0125660	+	0.999921i	$0.496000\pi$
$998$	−1.21103	+	1.19590i	−1.21103	+	1.19590i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.363.1	✓	100
8.3	odd	2	CM	2008.1.bd.a.363.1	✓	100
251.65	even	125	inner	2008.1.bd.a.1571.1	yes	100
2008.1571	odd	250	inner	2008.1.bd.a.1571.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.363.1	✓	100	1.1	even	1	trivial
2008.1.bd.a.363.1	✓	100	8.3	odd	2	CM
2008.1.bd.a.1571.1	yes	100	251.65	even	125	inner
2008.1.bd.a.1571.1	yes	100	2008.1571	odd	250	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:	\( N \)	\(=\)	\( 2008 = 2^{3} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2008.bd (of order \(250\), degree \(100\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.637424 + 0.770513i) q^{2} +(-1.95919 - 0.197625i) q^{3} +(-0.187381 - 0.982287i) q^{4} +(1.40111 - 1.38361i) q^{6} +(0.876307 + 0.481754i) q^{8} +(2.81950 + 0.574659i) q^{9} +O(q^{10})\)	\(q+(-0.637424 + 0.770513i) q^{2} +(-1.95919 - 0.197625i) q^{3} +(-0.187381 - 0.982287i) q^{4} +(1.40111 - 1.38361i) q^{6} +(0.876307 + 0.481754i) q^{8} +(2.81950 + 0.574659i) q^{9} +(1.02855 - 1.71451i) q^{11} +(0.172990 + 1.96152i) q^{12} +(-0.929776 + 0.368125i) q^{16} +(-0.725499 + 1.44627i) q^{17} +(-2.24000 + 1.80616i) q^{18} +(-0.0296998 + 0.122019i) q^{19} +(0.665429 + 1.88539i) q^{22} +(-1.62164 - 1.11703i) q^{24} +(0.0627905 - 0.998027i) q^{25} +(-3.53011 - 1.09816i) q^{27} +(0.309017 - 0.951057i) q^{32} +(-2.35396 + 3.15578i) q^{33} +(-0.651916 - 1.48089i) q^{34} +(0.0361584 - 2.87724i) q^{36} +(-0.0750855 - 0.100662i) q^{38} +(1.19543 + 0.0300508i) q^{41} +(0.225628 - 0.234298i) q^{43} +(-1.87687 - 0.689068i) q^{44} +(1.89436 - 0.537477i) q^{48} +(-0.999684 + 0.0251301i) q^{49} +(0.728969 + 0.684547i) q^{50} +(1.70721 - 2.69013i) q^{51} +(3.09632 - 2.02001i) q^{54} +(0.0823014 - 0.233188i) q^{57} +(0.825233 + 1.64508i) q^{59} +(0.535827 + 0.844328i) q^{64} +(-0.931100 - 3.82533i) q^{66} +(-0.603082 - 0.461758i) q^{67} +(1.55659 + 0.441646i) q^{68} +(2.19390 + 1.86188i) q^{72} +(0.410693 - 1.89313i) q^{73} +(-0.320254 + 1.94291i) q^{75} +(0.125422 + 0.00630973i) q^{76} +(4.05119 + 1.72296i) q^{81} +(-0.785152 + 0.901941i) q^{82} +(0.830793 - 1.23915i) q^{83} +(0.0367093 + 0.323196i) q^{86} +(1.72730 - 1.00693i) q^{88} +(-0.633085 + 0.327599i) q^{89} +(-0.793375 + 1.80223i) q^{96} +(1.79273 - 0.658175i) q^{97} +(0.617860 - 0.786288i) q^{98} +(3.88527 - 4.24300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 100 * q	\( 100 q - 25 q^{22} - 25 q^{32}+O(q^{100}) \) 100 * q - 25 * q^22 - 25 * q^32

Introduction

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Modular forms

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Database

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