LMFDB - Embedded newform 2008.1.bd.a.131.1

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			131.1
Root			$-0.998737 + 0.0502443i$ of defining polynomial
Character	$\chi$	$=$	2008.131
Dual form			2008.1.bd.a.1027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.187381 - 0.982287i) q^{2} +(-0.125694 - 1.10664i) q^{3} +(-0.929776 + 0.368125i) q^{4} +(-1.06348 + 0.330830i) q^{6} +(0.535827 + 0.844328i) q^{8} +(-0.234317 + 0.0539241i) q^{9} +O(q^{10})$	\(q+(-0.187381 - 0.982287i) q^{2} +(-0.125694 - 1.10664i) q^{3} +(-0.929776 + 0.368125i) q^{4} +(-1.06348 + 0.330830i) q^{6} +(0.535827 + 0.844328i) q^{8} +(-0.234317 + 0.0539241i) q^{9} +(0.494453 - 0.513453i) q^{11} +(0.524247 + 0.982653i) q^{12} +(0.728969 - 0.684547i) q^{16} +(-0.585339 + 0.198354i) q^{17} +(0.0968756 + 0.220062i) q^{18} +(-0.889695 - 1.77359i) q^{19} +(-0.597010 - 0.389483i) q^{22} +(0.867013 - 0.699092i) q^{24} +(-0.992115 - 0.125333i) q^{25} +(-0.281552 - 0.797731i) q^{27} +(-0.809017 - 0.587785i) q^{32} +(-0.630356 - 0.482641i) q^{33} +(0.304522 + 0.537803i) q^{34} +(0.198012 - 0.136395i) q^{36} +(-1.57546 + 1.20627i) q^{38} +(0.565975 - 1.48370i) q^{41} +(0.0155281 + 0.0197611i) q^{43} +(-0.270716 + 0.659417i) q^{44} +(-0.849171 - 0.720659i) q^{48} +(0.356412 + 0.934329i) q^{49} +(0.0627905 + 0.998027i) q^{50} +(0.293079 + 0.622825i) q^{51} +(-0.730844 + 0.426045i) q^{54} +(-1.85088 + 1.20750i) q^{57} +(-1.70365 - 0.577317i) q^{59} +(-0.425779 + 0.904827i) q^{64} +(-0.355975 + 0.709628i) q^{66} +(1.97481 + 0.0993483i) q^{67} +(0.471215 - 0.399903i) q^{68} +(-0.171083 - 0.168946i) q^{72} +(-1.18360 + 1.29258i) q^{73} +(-0.0139954 + 1.11366i) q^{75} +(1.48012 + 1.32152i) q^{76} +(-1.06366 + 0.516946i) q^{81} +(-1.56347 - 0.277933i) q^{82} +(1.81504 - 0.137111i) q^{83} +(0.0165014 - 0.0189559i) q^{86} +(0.698464 + 0.142358i) q^{88} +(-0.253520 - 0.339876i) q^{89} +(-0.548776 + 0.969168i) q^{96} +(0.252796 + 0.615768i) q^{97} +(0.850994 - 0.525175i) q^{98} +(-0.0881711 + 0.146974i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{113}{125}\right)$	$-1$	$-1$

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 $

$2$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$2$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$3$	−0.125694	−	1.10664i	−0.125694	−	1.10664i	−0.888136	−	0.459580i	$-0.848000\pi$
$3$	−0.125694	−	1.10664i	−0.125694	−	1.10664i	0.762443	−	0.647056i	$-0.224000\pi$
$4$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$5$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$5$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$6$	−1.06348	+	0.330830i	−1.06348	+	0.330830i
$7$		0			0		−0.823533	−	0.567269i	$-0.808000\pi$
$7$		0			0		0.823533	+	0.567269i	$0.192000\pi$
$8$	0.535827	+	0.844328i	0.535827	+	0.844328i
$9$	−0.234317	+	0.0539241i	−0.234317	+	0.0539241i
$10$		0			0
$11$	0.494453	−	0.513453i	0.494453	−	0.513453i	−0.425779	−	0.904827i	$-0.640000\pi$
$11$	0.494453	−	0.513453i	0.494453	−	0.513453i	0.920232	+	0.391374i	$0.128000\pi$
$12$	0.524247	+	0.982653i	0.524247	+	0.982653i
$13$		0			0		0.0878512	−	0.996134i	$-0.472000\pi$
$13$		0			0		−0.0878512	+	0.996134i	$0.528000\pi$
$14$		0			0
$15$		0			0
$16$	0.728969	−	0.684547i	0.728969	−	0.684547i
$17$	−0.585339	+	0.198354i	−0.585339	+	0.198354i	−0.597905	−	0.801567i	$-0.704000\pi$
$17$	−0.585339	+	0.198354i	−0.585339	+	0.198354i	0.0125660	+	0.999921i	$0.496000\pi$
$18$	0.0968756	+	0.220062i	0.0968756	+	0.220062i
$19$	−0.889695	−	1.77359i	−0.889695	−	1.77359i	−0.556876	−	0.830596i	$-0.688000\pi$
$19$	−0.889695	−	1.77359i	−0.889695	−	1.77359i	−0.332820	−	0.942991i	$-0.608000\pi$
$20$		0			0
$21$		0			0
$22$	−0.597010	−	0.389483i	−0.597010	−	0.389483i
$23$		0			0		0.577573	−	0.816339i	$-0.304000\pi$
$23$		0			0		−0.577573	+	0.816339i	$0.696000\pi$
$24$	0.867013	−	0.699092i	0.867013	−	0.699092i
$25$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$26$		0			0
$27$	−0.281552	−	0.797731i	−0.281552	−	0.797731i
$28$		0			0
$29$		0			0		−0.994951	−	0.100362i	$-0.968000\pi$
$29$		0			0		0.994951	+	0.100362i	$0.0320000\pi$
$30$		0			0
$31$		0			0		−0.899405	−	0.437116i	$-0.856000\pi$
$31$		0			0		0.899405	+	0.437116i	$0.144000\pi$
$32$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$33$	−0.630356	−	0.482641i	−0.630356	−	0.482641i
$34$	0.304522	+	0.537803i	0.304522	+	0.537803i
$35$		0			0
$36$	0.198012	−	0.136395i	0.198012	−	0.136395i
$37$		0			0		−0.920232	−	0.391374i	$-0.872000\pi$
$37$		0			0		0.920232	+	0.391374i	$0.128000\pi$
$38$	−1.57546	+	1.20627i	−1.57546	+	1.20627i
$39$		0			0
$40$		0			0
$41$	0.565975	−	1.48370i	0.565975	−	1.48370i	−0.285019	−	0.958522i	$-0.592000\pi$
$41$	0.565975	−	1.48370i	0.565975	−	1.48370i	0.850994	−	0.525175i	$-0.176000\pi$
$42$		0			0
$43$	0.0155281	+	0.0197611i	0.0155281	+	0.0197611i	0.793990	−	0.607930i	$-0.208000\pi$
$43$	0.0155281	+	0.0197611i	0.0155281	+	0.0197611i	−0.778462	+	0.627691i	$0.784000\pi$
$44$	−0.270716	+	0.659417i	−0.270716	+	0.659417i
$45$		0			0
$46$		0			0
$47$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$47$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$48$	−0.849171	−	0.720659i	−0.849171	−	0.720659i
$49$	0.356412	+	0.934329i	0.356412	+	0.934329i
$50$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$51$	0.293079	+	0.622825i	0.293079	+	0.622825i
$52$		0			0
$53$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$53$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$54$	−0.730844	+	0.426045i	−0.730844	+	0.426045i
$55$		0			0
$56$		0			0
$57$	−1.85088	+	1.20750i	−1.85088	+	1.20750i
$58$		0			0
$59$	−1.70365	−	0.577317i	−1.70365	−	0.577317i	−0.711536	−	0.702650i	$-0.752000\pi$
$59$	−1.70365	−	0.577317i	−1.70365	−	0.577317i	−0.992115	+	0.125333i	$0.960000\pi$
$60$		0			0
$61$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$61$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$62$		0			0
$63$		0			0
$64$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$65$		0			0
$66$	−0.355975	+	0.709628i	−0.355975	+	0.709628i
$67$	1.97481	+	0.0993483i	1.97481	+	0.0993483i	0.994951	−	0.100362i	$-0.0320000\pi$
$67$	1.97481	+	0.0993483i	1.97481	+	0.0993483i	0.979855	+	0.199710i	$0.0640000\pi$
$68$	0.471215	−	0.399903i	0.471215	−	0.399903i
$69$		0			0
$70$		0			0
$71$		0			0		−0.514440	−	0.857527i	$-0.672000\pi$
$71$		0			0		0.514440	+	0.857527i	$0.328000\pi$
$72$	−0.171083	−	0.168946i	−0.171083	−	0.168946i
$73$	−1.18360	+	1.29258i	−1.18360	+	1.29258i	−0.236499	+	0.971632i	$0.576000\pi$
$73$	−1.18360	+	1.29258i	−1.18360	+	1.29258i	−0.947098	+	0.320944i	$0.896000\pi$
$74$		0			0
$75$	−0.0139954	+	1.11366i	−0.0139954	+	1.11366i
$76$	1.48012	+	1.32152i	1.48012	+	1.32152i
$77$		0			0
$78$		0			0
$79$		0			0		−0.863923	−	0.503623i	$-0.832000\pi$
$79$		0			0		0.863923	+	0.503623i	$0.168000\pi$
$80$		0			0
$81$	−1.06366	+	0.516946i	−1.06366	+	0.516946i
$82$	−1.56347	−	0.277933i	−1.56347	−	0.277933i
$83$	1.81504	−	0.137111i	1.81504	−	0.137111i	0.876307	−	0.481754i	$-0.160000\pi$
$83$	1.81504	−	0.137111i	1.81504	−	0.137111i	0.938734	+	0.344643i	$0.112000\pi$
$84$		0			0
$85$		0			0
$86$	0.0165014	−	0.0189559i	0.0165014	−	0.0189559i
$87$		0			0
$88$	0.698464	+	0.142358i	0.698464	+	0.142358i
$89$	−0.253520	−	0.339876i	−0.253520	−	0.339876i	0.656586	−	0.754251i	$-0.272000\pi$
$89$	−0.253520	−	0.339876i	−0.253520	−	0.339876i	−0.910106	+	0.414376i	$0.864000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.548776	+	0.969168i	−0.548776	+	0.969168i
$97$	0.252796	+	0.615768i	0.252796	+	0.615768i	0.998737	−	0.0502443i	$-0.0160000\pi$
$97$	0.252796	+	0.615768i	0.252796	+	0.615768i	−0.745941	+	0.666012i	$0.768000\pi$
$98$	0.850994	−	0.525175i	0.850994	−	0.525175i
$99$	−0.0881711	+	0.146974i	−0.0881711	+	0.146974i
$100$	0.968583	−	0.248690i	0.968583	−	0.248690i
$101$		0			0		0.984564	−	0.175023i	$-0.0560000\pi$
$101$		0			0		−0.984564	+	0.175023i	$0.944000\pi$
$102$	0.556876	−	0.404594i	0.556876	−	0.404594i
$103$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$103$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.0419775	−	0.0626106i	0.0419775	−	0.0626106i	−0.809017	−	0.587785i	$-0.800000\pi$
$107$	0.0419775	−	0.0626106i	0.0419775	−	0.0626106i	0.850994	+	0.525175i	$0.176000\pi$
$108$	0.555445	+	0.638066i	0.555445	+	0.638066i
$109$		0			0		0.745941	−	0.666012i	$-0.232000\pi$
$109$		0			0		−0.745941	+	0.666012i	$0.768000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.590139	−	1.81626i	0.590139	−	1.81626i	0.0125660	−	0.999921i	$-0.496000\pi$
$113$	0.590139	−	1.81626i	0.590139	−	1.81626i	0.577573	−	0.816339i	$-0.304000\pi$
$114$	1.53293	+	1.59184i	1.53293	+	1.59184i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.247859	+	1.78165i	−0.247859	+	1.78165i
$119$		0			0
$120$		0			0
$121$	0.0185391	+	0.491533i	0.0185391	+	0.491533i
$122$		0			0
$123$	−1.71305	−	0.439837i	−1.71305	−	0.439837i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.997159	−	0.0753268i	$-0.976000\pi$
$127$		0			0		0.997159	+	0.0753268i	$0.0240000\pi$
$128$	0.968583	+	0.248690i	0.968583	+	0.248690i
$129$	0.0199165	−	0.0196678i	0.0199165	−	0.0196678i
$130$		0			0
$131$	−0.736317	−	1.04071i	−0.736317	−	1.04071i	−0.997159	−	0.0753268i	$-0.976000\pi$
$131$	−0.736317	−	1.04071i	−0.736317	−	1.04071i	0.260842	−	0.965382i	$-0.416000\pi$
$132$	0.763762	+	0.216699i	0.763762	+	0.216699i
$133$		0			0
$134$	−0.272453	−	1.95844i	−0.272453	−	1.95844i
$135$		0			0
$136$	−0.481116	−	0.387935i	−0.481116	−	0.387935i
$137$	1.30231	+	1.35236i	1.30231	+	1.35236i	0.899405	+	0.437116i	$0.144000\pi$
$137$	1.30231	+	1.35236i	1.30231	+	1.35236i	0.402906	+	0.915241i	$0.368000\pi$
$138$		0			0
$139$	0.223151	−	0.0339078i	0.223151	−	0.0339078i	−0.0376902	−	0.999289i	$-0.512000\pi$
$139$	0.223151	−	0.0339078i	0.223151	−	0.0339078i	0.260842	+	0.965382i	$0.416000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.133896	+	0.199710i	−0.133896	+	0.199710i
$145$		0			0
$146$	1.49146	+	0.920428i	1.49146	+	0.920428i
$147$	0.989163	−	0.511858i	0.989163	−	0.511858i
$148$		0			0
$149$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$149$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$150$	1.09656	−	0.194932i	1.09656	−	0.194932i
$151$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$151$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$152$	1.02077	−	1.70153i	1.02077	−	1.70153i
$153$	0.126459	−	0.0780416i	0.126459	−	0.0780416i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$157$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.707100	+	0.947957i	0.707100	+	0.947957i
$163$	1.94982	+	0.397403i	1.94982	+	0.397403i	0.994951	+	0.100362i	$0.0320000\pi$
$163$	1.94982	+	0.397403i	1.94982	+	0.397403i	0.954865	+	0.297042i	$0.0960000\pi$
$164$	0.0199546	+	1.58786i	0.0199546	+	1.58786i
$165$		0			0
$166$	−0.474787	−	1.75720i	−0.474787	−	1.75720i
$167$		0			0		0.112856	−	0.993611i	$-0.464000\pi$
$167$		0			0		−0.112856	+	0.993611i	$0.536000\pi$
$168$		0			0
$169$	−0.984564	−	0.175023i	−0.984564	−	0.175023i
$170$		0			0
$171$	0.304110	+	0.367605i	0.304110	+	0.367605i
$172$	−0.0217122	−	0.0126571i	−0.0217122	−	0.0126571i
$173$		0			0		−0.212007	−	0.977268i	$-0.568000\pi$
$173$		0			0		0.212007	+	0.977268i	$0.432000\pi$
$174$		0			0
$175$		0			0
$176$	0.00895737	−	0.712767i	0.00895737	−	0.712767i
$177$	−0.424741	+	1.95789i	−0.424741	+	1.95789i
$178$	−0.286351	+	0.312716i	−0.286351	+	0.312716i
$179$	−1.30956	−	1.29320i	−1.30956	−	1.29320i	−0.929776	−	0.368125i	$-0.880000\pi$
$179$	−1.30956	−	1.29320i	−1.30956	−	1.29320i	−0.379779	−	0.925077i	$-0.624000\pi$
$180$		0			0
$181$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$181$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.187577	+	0.398621i	−0.187577	+	0.398621i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.910106	−	0.414376i	$-0.136000\pi$
$191$		0			0		−0.910106	+	0.414376i	$0.864000\pi$
$192$	1.05483	+	0.357451i	1.05483	+	0.357451i
$193$	0.172990	+	1.96152i	0.172990	+	1.96152i	0.260842	+	0.965382i	$0.416000\pi$
$193$	0.172990	+	1.96152i	0.172990	+	1.96152i	−0.0878512	+	0.996134i	$0.528000\pi$
$194$	0.557491	−	0.363701i	0.557491	−	0.363701i
$195$		0			0
$196$	−0.675333	−	0.737513i	−0.675333	−	0.737513i
$197$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$197$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$198$	0.160892	+	0.0590693i	0.160892	+	0.0590693i
$199$		0			0		−0.285019	−	0.958522i	$-0.592000\pi$
$199$		0			0		0.285019	+	0.958522i	$0.408000\pi$
$200$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$201$	−0.138279	−	2.19788i	−0.138279	−	2.19788i
$202$		0			0
$203$		0			0
$204$	−0.501775	−	0.471198i	−0.501775	−	0.471198i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.35057	−	0.420137i	−1.35057	−	0.420137i
$210$		0			0
$211$	0.706139	−	0.388203i	0.706139	−	0.388203i	−0.0878512	−	0.996134i	$-0.528000\pi$
$211$	0.706139	−	0.388203i	0.706139	−	0.388203i	0.793990	+	0.607930i	$0.208000\pi$
$212$		0			0
$213$		0			0
$214$	−0.0693674	−	0.0295019i	−0.0693674	−	0.0295019i
$215$		0			0
$216$	0.522684	−	0.665168i	0.522684	−	0.665168i
$217$		0			0
$218$		0			0
$219$	1.57918	+	1.14734i	1.57918	+	1.14734i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.974527	−	0.224271i	$-0.928000\pi$
$223$		0			0		0.974527	+	0.224271i	$0.0720000\pi$
$224$		0			0
$225$	0.239228	−	0.0241312i	0.239228	−	0.0241312i
$226$	−1.89467	−	0.239353i	−1.89467	−	0.239353i
$227$	−0.834242	+	0.672668i	−0.834242	+	0.672668i	−0.947098	−	0.320944i	$-0.896000\pi$
$227$	−0.834242	+	0.672668i	−0.834242	+	0.672668i	0.112856	+	0.993611i	$0.464000\pi$
$228$	1.27640	−	1.80406i	1.27640	−	1.80406i
$229$		0			0		−0.837528	−	0.546394i	$-0.816000\pi$
$229$		0			0		0.837528	+	0.546394i	$0.184000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.481800	−	1.09445i	−0.481800	−	1.09445i	−0.974527	−	0.224271i	$-0.928000\pi$
$233$	−0.481800	−	1.09445i	−0.481800	−	1.09445i	0.492727	−	0.870184i	$-0.336000\pi$
$234$		0			0
$235$		0			0
$236$	1.79654	−	0.0903800i	1.79654	−	0.0903800i
$237$		0			0
$238$		0			0
$239$		0			0		−0.470704	−	0.882291i	$-0.656000\pi$
$239$		0			0		0.470704	+	0.882291i	$0.344000\pi$
$240$		0			0
$241$	1.02077	−	0.128953i	1.02077	−	0.128953i	0.402906	−	0.915241i	$-0.368000\pi$
$241$	1.02077	−	0.128953i	1.02077	−	0.128953i	0.617860	+	0.786288i	$0.288000\pi$
$242$	0.479353	−	0.110315i	0.479353	−	0.110315i
$243$	0.252480	+	0.397844i	0.252480	+	0.397844i
$244$		0			0
$245$		0			0
$246$	−0.111052	+	1.76513i	−0.111052	+	1.76513i
$247$		0			0
$248$		0			0
$249$	−0.379871	−	1.99135i	−0.379871	−	1.99135i
$250$		0			0
$251$	0.823533	−	0.567269i	0.823533	−	0.567269i
$251$	0.823533	−	0.567269i	0.823533	−	0.567269i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$257$	1.32469	−	0.412088i	1.32469	−	0.412088i	0.448383	−	0.893841i	$-0.352000\pi$
$257$	1.32469	−	0.412088i	1.32469	−	0.412088i	0.876307	+	0.481754i	$0.160000\pi$
$258$	−0.0230514	−	0.0158784i	−0.0230514	−	0.0158784i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.884303	+	0.918285i	−0.884303	+	0.918285i
$263$		0			0		−0.470704	−	0.882291i	$-0.656000\pi$
$263$		0			0		0.470704	+	0.882291i	$0.344000\pi$
$264$	0.0697458	−	0.790839i	0.0697458	−	0.790839i
$265$		0			0
$266$		0			0
$267$	−0.344253	+	0.323275i	−0.344253	+	0.323275i
$268$	−1.87270	+	0.634603i	−1.87270	+	0.634603i
$269$		0			0		−0.402906	−	0.915241i	$-0.632000\pi$
$269$		0			0		0.402906	+	0.915241i	$0.368000\pi$
$270$		0			0
$271$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$271$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$272$	−0.290911	+	0.545286i	−0.290911	+	0.545286i
$273$		0			0
$274$	1.08437	−	1.53265i	1.08437	−	1.53265i
$275$	−0.554906	+	0.447433i	−0.554906	+	0.447433i
$276$		0			0
$277$		0			0		0.994951	−	0.100362i	$-0.0320000\pi$
$277$		0			0		−0.994951	+	0.100362i	$0.968000\pi$
$278$	−0.0751216	−	0.212845i	−0.0751216	−	0.212845i
$279$		0			0
$280$		0			0
$281$	0.134814	+	0.553868i	0.134814	+	0.553868i	0.998737	+	0.0502443i	$0.0160000\pi$
$281$	0.134814	+	0.553868i	0.134814	+	0.553868i	−0.863923	+	0.503623i	$0.832000\pi$
$282$		0			0
$283$	0.832381	+	0.604760i	0.832381	+	0.604760i	0.920232	−	0.391374i	$-0.128000\pi$
$283$	0.832381	+	0.604760i	0.832381	+	0.604760i	−0.0878512	+	0.996134i	$0.528000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.221262	+	0.0941026i	0.221262	+	0.0941026i
$289$	−0.490713	+	0.375722i	−0.490713	+	0.375722i
$290$		0			0
$291$	0.649656	−	0.357151i	0.649656	−	0.357151i
$292$	0.624652	−	1.63752i	0.624652	−	1.63752i
$293$		0			0		−0.954865	−	0.297042i	$-0.904000\pi$
$293$		0			0		0.954865	+	0.297042i	$0.0960000\pi$
$294$	−0.688142	−	0.875730i	−0.688142	−	0.875730i
$295$		0			0
$296$		0			0
$297$	−0.548812	−	0.249877i	−0.548812	−	0.249877i
$298$		0			0
$299$		0			0
$300$	−0.396954	−	1.04061i	−0.396954	−	1.04061i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−1.86266	−	0.683851i	−1.86266	−	0.683851i
$305$		0			0
$306$	−0.100355	−	0.109595i	−0.100355	−	0.109595i
$307$	0.00662226	−	0.175578i	0.00662226	−	0.175578i	−0.992115	−	0.125333i	$-0.960000\pi$
$307$	0.00662226	−	0.175578i	0.00662226	−	0.175578i	0.998737	−	0.0502443i	$-0.0160000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.910106	−	0.414376i	$-0.136000\pi$
$311$		0			0		−0.910106	+	0.414376i	$0.864000\pi$
$312$		0			0
$313$	0.210189	−	0.777917i	0.210189	−	0.777917i	−0.778462	−	0.627691i	$-0.784000\pi$
$313$	0.210189	−	0.777917i	0.210189	−	0.777917i	0.988652	−	0.150226i	$-0.0480000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$317$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.0745635	−	0.0385840i	−0.0745635	−	0.0385840i
$322$		0			0
$323$	0.872571	+	0.861675i	0.872571	+	0.861675i
$324$	0.798669	−	0.872205i	0.798669	−	0.872205i
$325$		0			0
$326$	0.0250052	−	1.98974i	0.0250052	−	1.98974i
$327$		0			0
$328$	1.55599	−	0.317136i	1.55599	−	0.317136i
$329$		0			0
$330$		0			0
$331$	1.25517	+	1.51724i	1.25517	+	1.51724i	0.762443	+	0.647056i	$0.224000\pi$
$331$	1.25517	+	1.51724i	1.25517	+	1.51724i	0.492727	+	0.870184i	$0.336000\pi$
$332$	−1.63711	+	0.795643i	−1.63711	+	0.795643i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.31151	−	1.50660i	1.31151	−	1.50660i	0.617860	−	0.786288i	$-0.288000\pi$
$337$	1.31151	−	1.50660i	1.31151	−	1.50660i	0.693653	−	0.720309i	$-0.256000\pi$
$338$	0.0125660	+	0.999921i	0.0125660	+	0.999921i
$339$	−2.08412	−	0.424776i	−2.08412	−	0.424776i
$340$		0			0
$341$		0			0
$342$	0.304110	−	0.367605i	0.304110	−	0.367605i
$343$		0			0
$344$	−0.00836445	+	0.0236993i	−0.00836445	+	0.0236993i
$345$		0			0
$346$		0			0
$347$	−0.463857	+	0.819198i	−0.463857	+	0.819198i	−0.999684	−	0.0251301i	$-0.992000\pi$
$347$	−0.463857	+	0.819198i	−0.463857	+	0.819198i	0.535827	+	0.844328i	$0.320000\pi$
$348$		0			0
$349$		0			0		0.850994	−	0.525175i	$-0.176000\pi$
$349$		0			0		−0.850994	+	0.525175i	$0.824000\pi$
$350$		0			0
$351$		0			0
$352$	−0.701821	+	0.124761i	−0.701821	+	0.124761i
$353$	1.50441	−	1.09302i	1.50441	−	1.09302i	0.535827	−	0.844328i	$-0.320000\pi$
$353$	1.50441	−	1.09302i	1.50441	−	1.09302i	0.968583	−	0.248690i	$-0.0800000\pi$
$354$	2.00279	+	0.0503463i	2.00279	+	0.0503463i
$355$		0			0
$356$	0.360834	+	0.222682i	0.360834	+	0.222682i
$357$		0			0
$358$	−1.02491	+	1.52868i	−1.02491	+	1.52868i
$359$		0			0		−0.656586	−	0.754251i	$-0.728000\pi$
$359$		0			0		0.656586	+	0.754251i	$0.272000\pi$
$360$		0			0
$361$	−1.75615	+	2.35434i	−1.75615	+	2.35434i
$362$		0			0
$363$	0.541618	−	0.0822988i	0.541618	−	0.0822988i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.962028	−	0.272952i	$-0.0880000\pi$
$367$		0			0		−0.962028	+	0.272952i	$0.912000\pi$
$368$		0			0
$369$	−0.0526107	+	0.378175i	−0.0526107	+	0.378175i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.711536	−	0.702650i	$-0.248000\pi$
$373$		0			0		−0.711536	+	0.702650i	$0.752000\pi$
$374$	0.426709	+	0.109560i	0.426709	+	0.109560i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.72047	−	0.441741i	−1.72047	−	0.441741i	−0.745941	−	0.666012i	$-0.768000\pi$
$379$	−1.72047	−	0.441741i	−1.72047	−	0.441741i	−0.974527	+	0.224271i	$0.928000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.962028	−	0.272952i	$-0.912000\pi$
$383$		0			0		0.962028	+	0.272952i	$0.0880000\pi$
$384$	0.153464	−	1.10313i	0.153464	−	1.10313i
$385$		0			0
$386$	1.89436	−	0.537477i	1.89436	−	0.537477i
$387$	−0.00470409	−	0.00379302i	−0.00470409	−	0.00379302i
$388$	−0.461723	−	0.479466i	−0.461723	−	0.479466i
$389$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$389$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$390$		0			0
$391$		0			0
$392$	−0.597905	+	0.801567i	−0.597905	+	0.801567i
$393$	−1.05913	+	0.945646i	−1.05913	+	0.945646i
$394$		0			0
$395$		0			0
$396$	0.0278748	−	0.169111i	0.0278748	−	0.169111i
$397$		0			0		−0.850994	−	0.525175i	$-0.824000\pi$
$397$		0			0		0.850994	+	0.525175i	$0.176000\pi$
$398$		0			0
$399$		0			0
$400$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$401$	0.465697	−	0.0827856i	0.465697	−	0.0827856i	0.0627905	−	0.998027i	$-0.480000\pi$
$401$	0.465697	−	0.0827856i	0.465697	−	0.0827856i	0.402906	+	0.915241i	$0.368000\pi$
$402$	−2.13304	+	0.547671i	−2.13304	+	0.547671i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.368829	+	0.581181i	−0.368829	+	0.581181i
$409$	0.449528	−	1.27366i	0.449528	−	1.27366i	−0.470704	−	0.882291i	$-0.656000\pi$
$409$	0.449528	−	1.27366i	0.449528	−	1.27366i	0.920232	−	0.391374i	$-0.128000\pi$
$410$		0			0
$411$	1.33287	−	1.61117i	1.33287	−	1.61117i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.0655724	−	0.242685i	−0.0655724	−	0.242685i
$418$	−0.159625	+	1.40537i	−0.159625	+	1.40537i
$419$	1.34683	−	0.101741i	1.34683	−	0.101741i	0.617860	−	0.786288i	$-0.288000\pi$
$419$	1.34683	−	0.101741i	1.34683	−	0.101741i	0.728969	+	0.684547i	$0.240000\pi$
$420$		0			0
$421$		0			0		0.899405	−	0.437116i	$-0.144000\pi$
$421$		0			0		−0.899405	+	0.437116i	$0.856000\pi$
$422$	−0.513644	−	0.620889i	−0.513644	−	0.620889i
$423$		0			0
$424$		0			0
$425$	0.605584	−	0.123428i	0.605584	−	0.123428i
$426$		0			0
$427$		0			0
$428$	−0.0159812	+	0.0736668i	−0.0159812	+	0.0736668i
$429$		0			0
$430$		0			0
$431$		0			0		−0.514440	−	0.857527i	$-0.672000\pi$
$431$		0			0		0.514440	+	0.857527i	$0.328000\pi$
$432$	−0.751327	−	0.388786i	−0.751327	−	0.388786i
$433$	1.69755	+	0.933237i	1.69755	+	0.933237i	0.968583	+	0.248690i	$0.0800000\pi$
$433$	1.69755	+	0.933237i	1.69755	+	0.933237i	0.728969	+	0.684547i	$0.240000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.831111	−	1.76620i	0.831111	−	1.76620i
$439$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$439$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$440$		0			0
$441$	−0.133896	−	0.199710i	−0.133896	−	0.199710i
$442$		0			0
$443$	1.53244	+	0.519298i	1.53244	+	0.519298i	0.954865	−	0.297042i	$-0.0960000\pi$
$443$	1.53244	+	0.519298i	1.53244	+	0.519298i	0.577573	+	0.816339i	$0.304000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.925080	+	0.339630i	0.925080	+	0.339630i	0.762443	−	0.647056i	$-0.224000\pi$
$449$	0.925080	+	0.339630i	0.925080	+	0.339630i	0.162637	+	0.986686i	$0.448000\pi$
$450$	−0.0685305	−	0.230469i	−0.0685305	−	0.230469i
$451$	−0.481961	−	1.02422i	−0.481961	−	1.02422i
$452$	0.119913	+	1.90596i	0.119913	+	1.90596i
$453$		0			0
$454$	0.817074	+	0.693420i	0.817074	+	0.693420i
$455$		0			0
$456$	−2.01128	−	0.915744i	−2.01128	−	0.915744i
$457$	−0.0609503	−	0.369773i	−0.0609503	−	0.369773i	−0.999684	−	0.0251301i	$-0.992000\pi$
$457$	−0.0609503	−	0.369773i	−0.0609503	−	0.369773i	0.938734	−	0.344643i	$-0.112000\pi$
$458$		0			0
$459$	0.323036	+	0.411096i	0.323036	+	0.411096i
$460$		0			0
$461$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$461$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$462$		0			0
$463$		0			0		0.999684	−	0.0251301i	$-0.00800000\pi$
$463$		0			0		−0.999684	+	0.0251301i	$0.992000\pi$
$464$		0			0
$465$		0			0
$466$	−0.984788	+	0.678346i	−0.984788	+	0.678346i
$467$	−1.23221	+	1.56811i	−1.23221	+	1.56811i	−0.556876	+	0.830596i	$0.688000\pi$
$467$	−1.23221	+	1.56811i	−1.23221	+	1.56811i	−0.675333	+	0.737513i	$0.736000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.425417	−	1.74778i	−0.425417	−	1.74778i
$473$	0.0178243	+	0.00179795i	0.0178243	+	0.00179795i
$474$		0			0
$475$	0.660390	+	1.87111i	0.660390	+	1.87111i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.577573	−	0.816339i	$-0.304000\pi$
$479$		0			0		−0.577573	+	0.816339i	$0.696000\pi$
$480$		0			0
$481$		0			0
$482$	−0.317941	−	0.978522i	−0.317941	−	0.978522i
$483$		0			0
$484$	−0.198183	−	0.450191i	−0.198183	−	0.450191i
$485$		0			0
$486$	0.343487	−	0.322556i	0.343487	−	0.322556i
$487$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$487$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$488$		0			0
$489$	0.194701	−	2.20769i	0.194701	−	2.20769i
$490$		0			0
$491$	1.14249	−	1.18640i	1.14249	−	1.18640i	0.162637	−	0.986686i	$-0.448000\pi$
$491$	1.14249	−	1.18640i	1.14249	−	1.18640i	0.979855	−	0.199710i	$-0.0640000\pi$
$492$	1.75467	−	0.221666i	1.75467	−	0.221666i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.88490	+	0.746285i	−1.88490	+	0.746285i
$499$	0.0367093	+	0.323196i	0.0367093	+	0.323196i	0.998737	+	0.0502443i	$0.0160000\pi$
$499$	0.0367093	+	0.323196i	0.0367093	+	0.323196i	−0.962028	+	0.272952i	$0.912000\pi$
$500$		0			0
$501$		0			0
$502$	−0.711536	−	0.702650i	−0.711536	−	0.702650i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.0699330	+	1.11155i	−0.0699330	+	1.11155i
$508$		0			0
$509$		0			0		−0.823533	−	0.567269i	$-0.808000\pi$
$509$		0			0		0.823533	+	0.567269i	$0.192000\pi$
$510$		0			0
$511$		0			0
$512$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$513$	−1.16435	+	1.20909i	−1.16435	+	1.20909i
$514$	−0.653011	−	1.22401i	−0.653011	−	1.22401i
$515$		0			0
$516$	−0.0112777	+	0.0256184i	−0.0112777	+	0.0256184i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.825233	+	1.64508i	0.825233	+	1.64508i	0.762443	+	0.647056i	$0.224000\pi$
$521$	0.825233	+	1.64508i	0.825233	+	1.64508i	0.0627905	+	0.998027i	$0.480000\pi$
$522$		0			0
$523$	−0.801133	+	1.50165i	−0.801133	+	1.50165i	0.0627905	+	0.998027i	$0.480000\pi$
$523$	−0.801133	+	1.50165i	−0.801133	+	1.50165i	−0.863923	+	0.503623i	$0.832000\pi$
$524$	1.06772	+	0.696570i	1.06772	+	0.696570i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.789900	+	0.0796780i	−0.789900	+	0.0796780i
$529$	−0.332820	−	0.942991i	−0.332820	−	0.942991i
$530$		0			0
$531$	0.430326	+	0.0434074i	0.430326	+	0.0434074i
$532$		0			0
$533$		0			0
$534$	0.382055	+	0.277579i	0.382055	+	0.277579i
$535$		0			0
$536$	0.974271	+	1.72062i	0.974271	+	1.72062i
$537$	−1.26650	+	1.61175i	−1.26650	+	1.61175i
$538$		0			0
$539$	0.655963	+	0.278980i	0.655963	+	0.278980i
$540$		0			0
$541$		0			0		0.999684	−	0.0251301i	$-0.00800000\pi$
$541$		0			0		−0.999684	+	0.0251301i	$0.992000\pi$
$542$		0			0
$543$		0			0
$544$	0.590139	+	0.183582i	0.590139	+	0.183582i
$545$		0			0
$546$		0			0
$547$	0.0529017	+	0.320944i	0.0529017	+	0.320944i	1.00000			$0$
$547$	0.0529017	+	0.320944i	0.0529017	+	0.320944i	−0.947098	+	0.320944i	$0.896000\pi$
$548$	−1.70869	−	0.777977i	−1.70869	−	0.777977i
$549$		0			0
$550$	0.543487	+	0.461237i	0.543487	+	0.461237i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.194999	+	0.113674i	−0.194999	+	0.113674i
$557$		0			0		−0.675333	−	0.737513i	$-0.736000\pi$
$557$		0			0		0.675333	+	0.737513i	$0.264000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.464705	+	0.157475i	0.464705	+	0.157475i
$562$	0.518795	−	0.236210i	0.518795	−	0.236210i
$563$	−0.596778	−	0.890111i	−0.596778	−	0.890111i	0.402906	−	0.915241i	$-0.368000\pi$
$563$	−0.596778	−	0.890111i	−0.596778	−	0.890111i	−0.999684	+	0.0251301i	$0.992000\pi$
$564$		0			0
$565$		0			0
$566$	0.438075	−	0.930958i	0.438075	−	0.930958i
$567$		0			0
$568$		0			0
$569$	1.38555	+	0.0697043i	1.38555	+	0.0697043i	0.728969	−	0.684547i	$-0.240000\pi$
$569$	1.38555	+	0.0697043i	1.38555	+	0.0697043i	0.656586	+	0.754251i	$0.272000\pi$
$570$		0			0
$571$	−1.46786	−	0.806964i	−1.46786	−	0.806964i	−0.470704	−	0.882291i	$-0.656000\pi$
$571$	−1.46786	−	0.806964i	−1.46786	−	0.806964i	−0.997159	+	0.0753268i	$0.976000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.0509754	−	0.234976i	0.0509754	−	0.234976i
$577$	−0.0223207	+	1.77613i	−0.0223207	+	1.77613i	0.448383	+	0.893841i	$0.352000\pi$
$577$	−0.0223207	+	1.77613i	−0.0223207	+	1.77613i	−0.470704	+	0.882291i	$0.656000\pi$
$578$	0.461017	+	0.411618i	0.461017	+	0.411618i
$579$	2.14894	−	0.437988i	2.14894	−	0.437988i
$580$		0			0
$581$		0			0
$582$	−0.472558	−	0.571225i	−0.472558	−	0.571225i
$583$		0			0
$584$	−1.72556	−	0.306748i	−1.72556	−	0.306748i
$585$		0			0
$586$		0			0
$587$	−0.450694	−	1.66803i	−0.450694	−	1.66803i	−0.711536	−	0.702650i	$-0.752000\pi$
$587$	−0.450694	−	1.66803i	−0.450694	−	1.66803i	0.260842	−	0.965382i	$-0.416000\pi$
$588$	−0.731273	+	0.840048i	−0.731273	+	0.840048i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.0480493	−	0.0580816i	0.0480493	−	0.0580816i	−0.745941	−	0.666012i	$-0.768000\pi$
$593$	0.0480493	−	0.0580816i	0.0480493	−	0.0580816i	0.793990	+	0.607930i	$0.208000\pi$
$594$	−0.142614	+	0.585913i	−0.142614	+	0.585913i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.379779	−	0.925077i	$-0.624000\pi$
$599$		0			0		0.379779	+	0.925077i	$0.376000\pi$
$600$	−0.947796	+	0.584914i	−0.947796	+	0.584914i
$601$	0.438075	−	0.730234i	0.438075	−	0.730234i	−0.556876	−	0.830596i	$-0.688000\pi$
$601$	0.438075	−	0.730234i	0.438075	−	0.730234i	0.994951	+	0.100362i	$0.0320000\pi$
$602$		0			0
$603$	−0.468088	+	0.0832106i	−0.468088	+	0.0832106i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.850994	−	0.525175i	$-0.824000\pi$
$607$		0			0		0.850994	+	0.525175i	$0.176000\pi$
$608$	−0.322709	+	1.95781i	−0.322709	+	1.95781i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.0888494	+	0.119114i	−0.0888494	+	0.119114i
$613$		0			0		0.285019	−	0.958522i	$-0.408000\pi$
$613$		0			0		−0.285019	+	0.958522i	$0.592000\pi$
$614$	−0.173708	+	0.0263950i	−0.173708	+	0.0263950i
$615$		0			0
$616$		0			0
$617$	0.214529	+	0.172980i	0.214529	+	0.172980i	0.728969	−	0.684547i	$-0.240000\pi$
$617$	0.214529	+	0.172980i	0.214529	+	0.172980i	−0.514440	+	0.857527i	$0.672000\pi$
$618$		0			0
$619$	0.164771	+	1.18440i	0.164771	+	1.18440i	0.876307	+	0.481754i	$0.160000\pi$
$619$	0.164771	+	1.18440i	0.164771	+	1.18440i	−0.711536	+	0.702650i	$0.752000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.968583	+	0.248690i	0.968583	+	0.248690i
$626$	−0.803523	−	0.0606993i	−0.803523	−	0.0606993i
$627$	−0.295181	+	1.54739i	−0.295181	+	1.54739i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.711536	−	0.702650i	$-0.248000\pi$
$631$		0			0		−0.711536	+	0.702650i	$0.752000\pi$
$632$		0			0
$633$	−0.518357	−	0.732644i	−0.518357	−	0.732644i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.124156	−	0.0188655i	0.124156	−	0.0188655i	−0.0878512	−	0.996134i	$-0.528000\pi$
$641$	0.124156	−	0.0188655i	0.124156	−	0.0188655i	0.212007	+	0.977268i	$0.432000\pi$
$642$	−0.0239288	+	0.0804727i	−0.0239288	+	0.0804727i
$643$	−0.911736	+	1.22230i	−0.911736	+	1.22230i	0.0627905	+	0.998027i	$0.480000\pi$
$643$	−0.911736	+	1.22230i	−0.911736	+	1.22230i	−0.974527	+	0.224271i	$0.928000\pi$
$644$		0			0
$645$		0			0
$646$	0.682908	−	1.01858i	0.682908	−	1.01858i
$647$		0			0		0.162637	−	0.986686i	$-0.448000\pi$
$647$		0			0		−0.162637	+	0.986686i	$0.552000\pi$
$648$	−1.00641	−	0.621087i	−1.00641	−	0.621087i
$649$	−1.13880	+	0.589289i	−1.13880	+	0.589289i
$650$		0			0
$651$		0			0
$652$	−1.95919	+	0.348279i	−1.95919	+	0.348279i
$653$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$653$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$654$		0			0
$655$		0			0
$656$	−0.603082	−	1.46900i	−0.603082	−	1.46900i
$657$	0.207636	−	0.366697i	0.207636	−	0.366697i
$658$		0			0
$659$	−0.683098	+	1.07639i	−0.683098	+	1.07639i	0.309017	+	0.951057i	$0.400000\pi$
$659$	−0.683098	+	1.07639i	−0.683098	+	1.07639i	−0.992115	+	0.125333i	$0.960000\pi$
$660$		0			0
$661$		0			0		0.236499	−	0.971632i	$-0.424000\pi$
$661$		0			0		−0.236499	+	0.971632i	$0.576000\pi$
$662$	1.25517	−	1.51724i	1.25517	−	1.51724i
$663$		0			0
$664$	1.08831	+	1.45902i	1.08831	+	1.45902i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.950962	+	1.14952i	0.950962	+	1.14952i	0.988652	+	0.150226i	$0.0480000\pi$
$673$	0.950962	+	1.14952i	0.950962	+	1.14952i	−0.0376902	+	0.999289i	$0.512000\pi$
$674$	−1.72566	−	1.00597i	−1.72566	−	1.00597i
$675$	0.179349	+	0.826729i	0.179349	+	0.826729i
$676$	0.979855	−	0.199710i	0.979855	−	0.199710i
$677$		0			0		−0.745941	−	0.666012i	$-0.768000\pi$
$677$		0			0		0.745941	+	0.666012i	$0.232000\pi$
$678$	−0.0267275	+	2.12680i	−0.0267275	+	2.12680i
$679$		0			0
$680$		0			0
$681$	0.849257	+	0.838652i	0.849257	+	0.838652i
$682$		0			0
$683$	−0.463326	−	0.239755i	−0.463326	−	0.239755i	0.212007	−	0.977268i	$-0.432000\pi$
$683$	−0.463326	−	0.239755i	−0.463326	−	0.239755i	−0.675333	+	0.737513i	$0.736000\pi$
$684$	−0.418079	−	0.229841i	−0.418079	−	0.229841i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.0248469	+	0.00377548i	0.0248469	+	0.00377548i
$689$		0			0
$690$		0			0
$691$	−0.521518	+	1.93015i	−0.521518	+	1.93015i	−0.236499	+	0.971632i	$0.576000\pi$
$691$	−0.521518	+	1.93015i	−0.521518	+	1.93015i	−0.285019	+	0.958522i	$0.592000\pi$
$692$		0			0
$693$		0			0
$694$	0.891606	+	0.302139i	0.891606	+	0.302139i
$695$		0			0
$696$		0			0
$697$	−0.0369901	+	0.980729i	−0.0369901	+	0.980729i
$698$		0			0
$699$	−1.15060	+	0.670743i	−1.15060	+	0.670743i
$700$		0			0
$701$		0			0		−0.285019	−	0.958522i	$-0.592000\pi$
$701$		0			0		0.285019	+	0.958522i	$0.408000\pi$
$702$		0			0
$703$		0			0
$704$	0.254059	+	0.666012i	0.254059	+	0.666012i
$705$		0			0
$706$	−1.35556	−	1.27295i	−1.35556	−	1.27295i
$707$		0			0
$708$	−0.325832	−	1.97675i	−0.325832	−	1.97675i
$709$		0			0		0.379779	−	0.925077i	$-0.376000\pi$
$709$		0			0		−0.379779	+	0.925077i	$0.624000\pi$
$710$		0			0
$711$		0			0
$712$	0.151124	−	0.396169i	0.151124	−	0.396169i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.69365	+	0.720309i	1.69365	+	0.720309i
$717$		0			0
$718$		0			0
$719$		0			0		−0.492727	−	0.870184i	$-0.664000\pi$
$719$		0			0		0.492727	+	0.870184i	$0.336000\pi$
$720$		0			0
$721$		0			0
$722$	2.64170	+	1.28388i	2.64170	+	1.28388i
$723$	−0.271008	−	1.11341i	−0.271008	−	1.11341i
$724$		0			0
$725$		0			0
$726$	−0.182330	−	0.516603i	−0.182330	−	0.516603i
$727$		0			0		0.994951	−	0.100362i	$-0.0320000\pi$
$727$		0			0		−0.994951	+	0.100362i	$0.968000\pi$
$728$		0			0
$729$	−0.512099	+	0.412917i	−0.512099	+	0.412917i
$730$		0			0
$731$	−0.0130089	−	0.00848686i	−0.0130089	−	0.00848686i
$732$		0			0
$733$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$733$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.02746	−	0.964848i	1.02746	−	0.964848i
$738$	0.381335	−	0.0191841i	0.381335	−	0.0191841i
$739$	0.210189	−	0.477466i	0.210189	−	0.477466i	−0.778462	−	0.627691i	$-0.784000\pi$
$739$	0.210189	−	0.477466i	0.210189	−	0.477466i	0.988652	+	0.150226i	$0.0480000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$743$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.417901	+	0.130002i	−0.417901	+	0.130002i
$748$	0.0276623	−	0.439680i	0.0276623	−	0.439680i
$749$		0			0
$750$		0			0
$751$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$751$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$752$		0			0
$753$	−0.731273	−	0.840048i	−0.731273	−	0.840048i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$757$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$758$	−0.111533	+	1.77277i	−0.111533	+	1.77277i
$759$		0			0
$760$		0			0
$761$	−0.975318	−	1.53686i	−0.975318	−	1.53686i	−0.837528	−	0.546394i	$-0.816000\pi$
$761$	−0.975318	−	1.53686i	−0.975318	−	1.53686i	−0.137790	−	0.990461i	$-0.544000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.11234	+	0.0559597i	−1.11234	+	0.0559597i
$769$	−1.13495	+	1.06579i	−1.13495	+	1.06579i	−0.137790	+	0.990461i	$0.544000\pi$
$769$	−1.13495	+	1.06579i	−1.13495	+	1.06579i	−0.997159	+	0.0753268i	$0.976000\pi$
$770$		0			0
$771$	−0.622537	−	1.41415i	−0.622537	−	1.41415i
$772$	−0.882924	−	1.76009i	−0.882924	−	1.76009i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	−0.00284437	+	0.00533151i	−0.00284437	+	0.00533151i
$775$		0			0
$776$	−0.384455	+	0.543387i	−0.384455	+	0.543387i
$777$		0			0
$778$		0			0
$779$	−3.13501	+	0.316232i	−3.13501	+	0.316232i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.899405	+	0.437116i	0.899405	+	0.437116i
$785$		0			0
$786$	1.12736	+	0.863178i	1.12736	+	0.863178i
$787$	−0.933322	−	1.64830i	−0.933322	−	1.64830i	−0.745941	−	0.666012i	$-0.768000\pi$
$787$	−0.933322	−	1.64830i	−0.933322	−	1.64830i	−0.187381	−	0.982287i	$-0.560000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.171339	+	0.00430711i	−0.171339	+	0.00430711i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.379779	−	0.925077i	$-0.376000\pi$
$797$		0			0		−0.379779	+	0.925077i	$0.624000\pi$
$798$		0			0
$799$		0			0
$800$	0.728969	+	0.684547i	0.728969	+	0.684547i
$801$	0.0777316	+	0.0659678i	0.0777316	+	0.0659678i
$802$	−0.168582	−	0.441936i	−0.168582	−	0.441936i
$803$	0.0784445	+	1.24684i	0.0784445	+	1.24684i
$804$	0.937661	+	1.99263i	0.937661	+	1.99263i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.0586808	−	1.55582i	0.0586808	−	1.55582i	−0.597905	−	0.801567i	$-0.704000\pi$
$809$	0.0586808	−	1.55582i	0.0586808	−	1.55582i	0.656586	−	0.754251i	$-0.272000\pi$
$810$		0			0
$811$	−0.174815	−	1.98221i	−0.174815	−	1.98221i	−0.187381	−	0.982287i	$-0.560000\pi$
$811$	−0.174815	−	1.98221i	−0.174815	−	1.98221i	0.0125660	−	0.999921i	$-0.496000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.639999	+	0.253393i	0.639999	+	0.253393i
$817$	0.0212327	−	0.0451217i	0.0212327	−	0.0451217i
$818$	−1.33534	−	0.202905i	−1.33534	−	0.202905i
$819$		0			0
$820$		0			0
$821$		0			0		0.762443	−	0.647056i	$-0.224000\pi$
$821$		0			0		−0.762443	+	0.647056i	$0.776000\pi$
$822$	−1.83239	−	1.00736i	−1.83239	−	1.00736i
$823$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$823$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$824$		0			0
$825$	0.564894	+	0.557840i	0.564894	+	0.557840i
$826$		0			0
$827$	−0.422810	+	1.94898i	−0.422810	+	1.94898i	−0.137790	+	0.990461i	$0.544000\pi$
$827$	−0.422810	+	1.94898i	−0.422810	+	1.94898i	−0.285019	+	0.958522i	$0.592000\pi$
$828$		0			0
$829$		0			0		−0.745941	−	0.666012i	$-0.768000\pi$
$829$		0			0		0.745941	+	0.666012i	$0.232000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.393950	−	0.476203i	−0.393950	−	0.476203i
$834$	−0.226100	+	0.109886i	−0.226100	+	0.109886i
$835$		0			0
$836$	1.41039	−	0.106543i	1.41039	−	0.106543i
$837$		0			0
$838$	−0.352310	−	1.30391i	−0.352310	−	1.30391i
$839$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$839$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$840$		0			0
$841$	0.979855	+	0.199710i	0.979855	+	0.199710i
$842$		0			0
$843$	0.595984	−	0.218807i	0.595984	−	0.218807i
$844$	−0.513644	+	0.620889i	−0.513644	+	0.620889i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.564624	−	0.997157i	0.564624	−	0.997157i
$850$	−0.234716	−	0.571729i	−0.234716	−	0.571729i
$851$		0			0
$852$		0			0
$853$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$853$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$854$		0			0
$855$		0			0
$856$	0.0753566	+	0.00189432i	0.0753566	+	0.00189432i
$857$	−1.76730	+	0.914519i	−1.76730	+	0.914519i	−0.837528	+	0.546394i	$0.816000\pi$
$857$	−1.76730	+	0.914519i	−1.76730	+	0.914519i	−0.929776	+	0.368125i	$0.880000\pi$
$858$		0			0
$859$	−0.281012	+	1.70484i	−0.281012	+	1.70484i	0.356412	+	0.934329i	$0.384000\pi$
$859$	−0.281012	+	1.70484i	−0.281012	+	1.70484i	−0.637424	+	0.770513i	$0.720000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$863$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$864$	−0.241115	+	0.810870i	−0.241115	+	0.810870i
$865$		0			0
$866$	0.598617	−	1.84235i	0.598617	−	1.84235i
$867$	0.477467	+	0.495815i	0.477467	+	0.495815i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.0924390	−	0.130653i	−0.0924390	−	0.130653i
$874$		0			0
$875$		0			0
$876$	−1.89065	−	0.485437i	−1.89065	−	0.485437i
$877$		0			0		−0.997159	−	0.0753268i	$-0.976000\pi$
$877$		0			0		0.997159	+	0.0753268i	$0.0240000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.505293	+	0.129737i	0.505293	+	0.129737i	0.492727	−	0.870184i	$-0.336000\pi$
$881$	0.505293	+	0.129737i	0.505293	+	0.129737i	0.0125660	+	0.999921i	$0.496000\pi$
$882$	−0.171083	+	0.168946i	−0.171083	+	0.168946i
$883$	−0.0660563	−	1.75137i	−0.0660563	−	1.75137i	−0.514440	−	0.857527i	$-0.672000\pi$
$883$	−0.0660563	−	1.75137i	−0.0660563	−	1.75137i	0.448383	−	0.893841i	$-0.352000\pi$
$884$		0			0
$885$		0			0
$886$	0.222949	−	1.60260i	0.222949	−	1.60260i
$887$		0			0		−0.137790	−	0.990461i	$-0.544000\pi$
$887$		0			0		0.137790	+	0.990461i	$0.456000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.260503	+	0.801747i	−0.260503	+	0.801747i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.160272	−	0.972334i	0.160272	−	0.972334i
$899$		0			0
$900$	−0.213545	+	0.110502i	−0.213545	+	0.110502i
$901$		0			0
$902$	−0.915767	+	0.665344i	−0.915767	+	0.665344i
$903$		0			0
$904$	1.84973	−	0.474930i	1.84973	−	0.474930i
$905$		0			0
$906$		0			0
$907$	−0.579119	−	1.41064i	−0.579119	−	1.41064i	−0.888136	−	0.459580i	$-0.848000\pi$
$907$	−0.579119	−	1.41064i	−0.579119	−	1.41064i	0.309017	−	0.951057i	$-0.400000\pi$
$908$	0.528033	−	0.932536i	0.528033	−	0.932536i
$909$		0			0
$910$		0			0
$911$		0			0		0.332820	−	0.942991i	$-0.392000\pi$
$911$		0			0		−0.332820	+	0.942991i	$0.608000\pi$
$912$	−0.522648	+	2.14725i	−0.522648	+	2.14725i
$913$	0.827051	−	0.999733i	0.827051	−	0.999733i
$914$	−0.351802	+	0.129159i	−0.351802	+	0.129159i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.343284	−	0.394346i	0.343284	−	0.394346i
$919$		0			0		−0.260842	−	0.965382i	$-0.584000\pi$
$919$		0			0		0.260842	+	0.965382i	$0.416000\pi$
$920$		0			0
$921$	−0.195133	+	0.0147406i	−0.195133	+	0.0147406i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.00220788	+	0.175689i	−0.00220788	+	0.175689i	0.994951	+	0.100362i	$0.0320000\pi$
$929$	−0.00220788	+	0.175689i	−0.00220788	+	0.175689i	−0.997159	+	0.0753268i	$0.976000\pi$
$930$		0			0
$931$	1.34002	−	1.46340i	1.34002	−	1.46340i
$932$	0.850861	+	0.840236i	0.850861	+	0.840236i
$933$		0			0
$934$	1.77123	+	0.916548i	1.77123	+	0.916548i
$935$		0			0
$936$		0			0
$937$	0.521024	+	0.0262116i	0.521024	+	0.0262116i	0.309017	−	0.951057i	$-0.400000\pi$
$937$	0.521024	+	0.0262116i	0.521024	+	0.0262116i	0.212007	+	0.977268i	$0.432000\pi$
$938$		0			0
$939$	−0.887290	−	0.134824i	−0.887290	−	0.134824i
$940$		0			0
$941$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$941$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$942$		0			0
$943$		0			0
$944$	−1.63711	+	0.745383i	−1.63711	+	0.745383i
$945$		0			0
$946$	−0.00157383	−	0.0178455i	−0.00157383	−	0.0178455i
$947$	−1.22106	+	0.796609i	−1.22106	+	0.796609i	−0.984564	−	0.175023i	$-0.944000\pi$
$947$	−1.22106	+	0.796609i	−1.22106	+	0.796609i	−0.236499	+	0.971632i	$0.576000\pi$
$948$		0			0
$949$		0			0
$950$	1.71422	−	0.999304i	1.71422	−	0.999304i
$951$		0			0
$952$		0			0
$953$	0.509151	+	1.08200i	0.509151	+	1.08200i	0.979855	+	0.199710i	$0.0640000\pi$
$953$	0.509151	+	1.08200i	0.509151	+	1.08200i	−0.470704	+	0.882291i	$0.656000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.617860	+	0.786288i	0.617860	+	0.786288i
$962$		0			0
$963$	−0.00645982	+	0.0169343i	−0.00645982	+	0.0169343i
$964$	−0.901614	+	0.495666i	−0.901614	+	0.495666i
$965$		0			0
$966$		0			0
$967$		0			0		−0.920232	−	0.391374i	$-0.872000\pi$
$967$		0			0		0.920232	+	0.391374i	$0.128000\pi$
$968$	−0.405081	+	0.279030i	−0.405081	+	0.279030i
$969$	0.843883	−	1.07393i	0.843883	−	1.07393i
$970$		0			0
$971$	−0.676129	−	0.517688i	−0.676129	−	0.517688i	0.212007	−	0.977268i	$-0.432000\pi$
$971$	−0.676129	−	0.517688i	−0.676129	−	0.517688i	−0.888136	+	0.459580i	$0.848000\pi$
$972$	−0.381206	−	0.276962i	−0.381206	−	0.276962i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.0751216	−	0.212845i	−0.0751216	−	0.212845i	0.899405	−	0.437116i	$-0.144000\pi$
$977$	−0.0751216	−	0.212845i	−0.0751216	−	0.212845i	−0.974527	+	0.224271i	$0.928000\pi$
$978$	−2.20507	+	0.222427i	−2.20507	+	0.222427i
$979$	−0.299864	−	0.0378816i	−0.299864	−	0.0378816i
$980$		0			0
$981$		0			0
$982$	−1.37946	−	0.899947i	−1.37946	−	0.899947i
$983$		0			0		0.470704	−	0.882291i	$-0.344000\pi$
$983$		0			0		−0.470704	+	0.882291i	$0.656000\pi$
$984$	−0.546532	−	1.68205i	−0.546532	−	1.68205i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.0878512	−	0.996134i	$-0.472000\pi$
$991$		0			0		−0.0878512	+	0.996134i	$0.528000\pi$
$992$		0			0
$993$	1.52126	−	1.57972i	1.52126	−	1.57972i
$994$		0			0
$995$		0			0
$996$	1.08626	+	1.71168i	1.08626	+	1.71168i
$997$		0			0		−0.823533	−	0.567269i	$-0.808000\pi$
$997$		0			0		0.823533	+	0.567269i	$0.192000\pi$
$998$	0.310593	−	0.0966200i	0.310593	−	0.0966200i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.131.1	✓	100
8.3	odd	2	CM	2008.1.bd.a.131.1	✓	100
251.23	even	125	inner	2008.1.bd.a.1027.1	yes	100
2008.1027	odd	250	inner	2008.1.bd.a.1027.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.131.1	✓	100	1.1	even	1	trivial
2008.1.bd.a.131.1	✓	100	8.3	odd	2	CM
2008.1.bd.a.1027.1	yes	100	251.23	even	125	inner
2008.1.bd.a.1027.1	yes	100	2008.1027	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)

\(f(q)\)	\(=\)	\(q+(-0.187381 - 0.982287i) q^{2} +(-0.125694 - 1.10664i) q^{3} +(-0.929776 + 0.368125i) q^{4} +(-1.06348 + 0.330830i) q^{6} +(0.535827 + 0.844328i) q^{8} +(-0.234317 + 0.0539241i) q^{9} +O(q^{10})\)	\(q+(-0.187381 - 0.982287i) q^{2} +(-0.125694 - 1.10664i) q^{3} +(-0.929776 + 0.368125i) q^{4} +(-1.06348 + 0.330830i) q^{6} +(0.535827 + 0.844328i) q^{8} +(-0.234317 + 0.0539241i) q^{9} +(0.494453 - 0.513453i) q^{11} +(0.524247 + 0.982653i) q^{12} +(0.728969 - 0.684547i) q^{16} +(-0.585339 + 0.198354i) q^{17} +(0.0968756 + 0.220062i) q^{18} +(-0.889695 - 1.77359i) q^{19} +(-0.597010 - 0.389483i) q^{22} +(0.867013 - 0.699092i) q^{24} +(-0.992115 - 0.125333i) q^{25} +(-0.281552 - 0.797731i) q^{27} +(-0.809017 - 0.587785i) q^{32} +(-0.630356 - 0.482641i) q^{33} +(0.304522 + 0.537803i) q^{34} +(0.198012 - 0.136395i) q^{36} +(-1.57546 + 1.20627i) q^{38} +(0.565975 - 1.48370i) q^{41} +(0.0155281 + 0.0197611i) q^{43} +(-0.270716 + 0.659417i) q^{44} +(-0.849171 - 0.720659i) q^{48} +(0.356412 + 0.934329i) q^{49} +(0.0627905 + 0.998027i) q^{50} +(0.293079 + 0.622825i) q^{51} +(-0.730844 + 0.426045i) q^{54} +(-1.85088 + 1.20750i) q^{57} +(-1.70365 - 0.577317i) q^{59} +(-0.425779 + 0.904827i) q^{64} +(-0.355975 + 0.709628i) q^{66} +(1.97481 + 0.0993483i) q^{67} +(0.471215 - 0.399903i) q^{68} +(-0.171083 - 0.168946i) q^{72} +(-1.18360 + 1.29258i) q^{73} +(-0.0139954 + 1.11366i) q^{75} +(1.48012 + 1.32152i) q^{76} +(-1.06366 + 0.516946i) q^{81} +(-1.56347 - 0.277933i) q^{82} +(1.81504 - 0.137111i) q^{83} +(0.0165014 - 0.0189559i) q^{86} +(0.698464 + 0.142358i) q^{88} +(-0.253520 - 0.339876i) q^{89} +(-0.548776 + 0.969168i) q^{96} +(0.252796 + 0.615768i) q^{97} +(0.850994 - 0.525175i) q^{98} +(-0.0881711 + 0.146974i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 100 * q	\( 100 q - 25 q^{22} - 25 q^{32}+O(q^{100}) \) 100 * q - 25 * q^22 - 25 * q^32

Introduction

L-functions

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Database

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