LMFDB - Embedded newform 2008.1.bd.a.3.1

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			3.1
Root			$0.470704 + 0.882291i$ of defining polynomial
Character	$\chi$	$=$	2008.3
Dual form			2008.1.bd.a.1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.992115 - 0.125333i) q^{2} +(-1.58347 - 0.119618i) q^{3} +(0.968583 + 0.248690i) q^{4} +(1.55599 + 0.317136i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(1.50441 + 0.228596i) q^{9} +O(q^{10})$	\(q+(-0.992115 - 0.125333i) q^{2} +(-1.58347 - 0.119618i) q^{3} +(0.968583 + 0.248690i) q^{4} +(1.55599 + 0.317136i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(1.50441 + 0.228596i) q^{9} +(0.0174330 - 1.38720i) q^{11} +(-1.50397 - 0.509652i) q^{12} +(0.876307 + 0.481754i) q^{16} +(-0.417379 + 0.455808i) q^{17} +(-1.46390 - 0.415346i) q^{18} +(-0.180536 - 0.832201i) q^{19} +(-0.191157 + 1.37407i) q^{22} +(1.42824 + 0.694131i) q^{24} +(-0.425779 + 0.904827i) q^{25} +(-0.807320 - 0.185791i) q^{27} +(-0.809017 - 0.587785i) q^{32} +(-0.193538 + 2.19450i) q^{33} +(0.471215 - 0.399903i) q^{34} +(1.40030 + 0.595547i) q^{36} +(0.0748104 + 0.848266i) q^{38} +(-0.121877 - 0.126560i) q^{41} +(0.811554 - 0.559018i) q^{43} +(0.361867 - 1.33928i) q^{44} +(-1.32998 - 0.867664i) q^{48} +(0.693653 - 0.720309i) q^{49} +(0.535827 - 0.844328i) q^{50} +(0.715429 - 0.671832i) q^{51} +(0.777668 + 0.285510i) q^{54} +(0.186328 + 1.33936i) q^{57} +(-1.28970 - 1.40845i) q^{59} +(0.728969 + 0.684547i) q^{64} +(0.467055 - 2.15294i) q^{66} +(-0.936655 + 1.75567i) q^{67} +(-0.517621 + 0.337690i) q^{68} +(-1.31462 - 0.766355i) q^{72} +(-0.318921 - 0.196816i) q^{73} +(0.782442 - 1.38184i) q^{75} +(0.0320954 - 0.850954i) q^{76} +(-0.196859 - 0.0612392i) q^{81} +(0.105053 + 0.140837i) q^{82} +(-0.472401 - 0.0237655i) q^{83} +(-0.875218 + 0.452895i) q^{86} +(-0.526870 + 1.28337i) q^{88} +(-1.12464 - 0.512052i) q^{89} +(1.21074 + 1.02751i) q^{96} +(-0.508394 - 1.88158i) q^{97} +(-0.778462 + 0.627691i) q^{98} +(0.343334 - 2.08293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{8}{125}\right)$	$-1$	$-1$

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 $

$2$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$2$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$3$	−1.58347	−	0.119618i	−1.58347	−	0.119618i	−0.745941	−	0.666012i	$-0.768000\pi$
$3$	−1.58347	−	0.119618i	−1.58347	−	0.119618i	−0.837528	+	0.546394i	$0.816000\pi$
$4$	0.968583	+	0.248690i	0.968583	+	0.248690i
$5$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$5$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$6$	1.55599	+	0.317136i	1.55599	+	0.317136i
$7$		0			0		0.920232	−	0.391374i	$-0.128000\pi$
$7$		0			0		−0.920232	+	0.391374i	$0.872000\pi$
$8$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$9$	1.50441	+	0.228596i	1.50441	+	0.228596i
$10$		0			0
$11$	0.0174330	−	1.38720i	0.0174330	−	1.38720i	−0.711536	−	0.702650i	$-0.752000\pi$
$11$	0.0174330	−	1.38720i	0.0174330	−	1.38720i	0.728969	−	0.684547i	$-0.240000\pi$
$12$	−1.50397	−	0.509652i	−1.50397	−	0.509652i
$13$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$13$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$14$		0			0
$15$		0			0
$16$	0.876307	+	0.481754i	0.876307	+	0.481754i
$17$	−0.417379	+	0.455808i	−0.417379	+	0.455808i	−0.910106	−	0.414376i	$-0.864000\pi$
$17$	−0.417379	+	0.455808i	−0.417379	+	0.455808i	0.492727	+	0.870184i	$0.336000\pi$
$18$	−1.46390	−	0.415346i	−1.46390	−	0.415346i
$19$	−0.180536	−	0.832201i	−0.180536	−	0.832201i	−0.974527	−	0.224271i	$-0.928000\pi$
$19$	−0.180536	−	0.832201i	−0.180536	−	0.832201i	0.793990	−	0.607930i	$-0.208000\pi$
$20$		0			0
$21$		0			0
$22$	−0.191157	+	1.37407i	−0.191157	+	1.37407i
$23$		0			0		0.112856	−	0.993611i	$-0.464000\pi$
$23$		0			0		−0.112856	+	0.993611i	$0.536000\pi$
$24$	1.42824	+	0.694131i	1.42824	+	0.694131i
$25$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$26$		0			0
$27$	−0.807320	−	0.185791i	−0.807320	−	0.185791i
$28$		0			0
$29$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$29$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$30$		0			0
$31$		0			0		0.954865	−	0.297042i	$-0.0960000\pi$
$31$		0			0		−0.954865	+	0.297042i	$0.904000\pi$
$32$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$33$	−0.193538	+	2.19450i	−0.193538	+	2.19450i
$34$	0.471215	−	0.399903i	0.471215	−	0.399903i
$35$		0			0
$36$	1.40030	+	0.595547i	1.40030	+	0.595547i
$37$		0			0		−0.711536	−	0.702650i	$-0.752000\pi$
$37$		0			0		0.711536	+	0.702650i	$0.248000\pi$
$38$	0.0748104	+	0.848266i	0.0748104	+	0.848266i
$39$		0			0
$40$		0			0
$41$	−0.121877	−	0.126560i	−0.121877	−	0.126560i	0.656586	−	0.754251i	$-0.272000\pi$
$41$	−0.121877	−	0.126560i	−0.121877	−	0.126560i	−0.778462	+	0.627691i	$0.784000\pi$
$42$		0			0
$43$	0.811554	−	0.559018i	0.811554	−	0.559018i	−0.0878512	−	0.996134i	$-0.528000\pi$
$43$	0.811554	−	0.559018i	0.811554	−	0.559018i	0.899405	+	0.437116i	$0.144000\pi$
$44$	0.361867	−	1.33928i	0.361867	−	1.33928i
$45$		0			0
$46$		0			0
$47$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$47$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$48$	−1.32998	−	0.867664i	−1.32998	−	0.867664i
$49$	0.693653	−	0.720309i	0.693653	−	0.720309i
$50$	0.535827	−	0.844328i	0.535827	−	0.844328i
$51$	0.715429	−	0.671832i	0.715429	−	0.671832i
$52$		0			0
$53$		0			0		0.285019	−	0.958522i	$-0.408000\pi$
$53$		0			0		−0.285019	+	0.958522i	$0.592000\pi$
$54$	0.777668	+	0.285510i	0.777668	+	0.285510i
$55$		0			0
$56$		0			0
$57$	0.186328	+	1.33936i	0.186328	+	1.33936i
$58$		0			0
$59$	−1.28970	−	1.40845i	−1.28970	−	1.40845i	−0.863923	−	0.503623i	$-0.832000\pi$
$59$	−1.28970	−	1.40845i	−1.28970	−	1.40845i	−0.425779	−	0.904827i	$-0.640000\pi$
$60$		0			0
$61$		0			0		0.793990	−	0.607930i	$-0.208000\pi$
$61$		0			0		−0.793990	+	0.607930i	$0.792000\pi$
$62$		0			0
$63$		0			0
$64$	0.728969	+	0.684547i	0.728969	+	0.684547i
$65$		0			0
$66$	0.467055	−	2.15294i	0.467055	−	2.15294i
$67$	−0.936655	+	1.75567i	−0.936655	+	1.75567i	−0.379779	+	0.925077i	$0.624000\pi$
$67$	−0.936655	+	1.75567i	−0.936655	+	1.75567i	−0.556876	+	0.830596i	$0.688000\pi$
$68$	−0.517621	+	0.337690i	−0.517621	+	0.337690i
$69$		0			0
$70$		0			0
$71$		0			0		−0.162637	−	0.986686i	$-0.552000\pi$
$71$		0			0		0.162637	+	0.986686i	$0.448000\pi$
$72$	−1.31462	−	0.766355i	−1.31462	−	0.766355i
$73$	−0.318921	−	0.196816i	−0.318921	−	0.196816i	0.356412	−	0.934329i	$-0.384000\pi$
$73$	−0.318921	−	0.196816i	−0.318921	−	0.196816i	−0.675333	+	0.737513i	$0.736000\pi$
$74$		0			0
$75$	0.782442	−	1.38184i	0.782442	−	1.38184i
$76$	0.0320954	−	0.850954i	0.0320954	−	0.850954i
$77$		0			0
$78$		0			0
$79$		0			0		0.938734	−	0.344643i	$-0.112000\pi$
$79$		0			0		−0.938734	+	0.344643i	$0.888000\pi$
$80$		0			0
$81$	−0.196859	−	0.0612392i	−0.196859	−	0.0612392i
$82$	0.105053	+	0.140837i	0.105053	+	0.140837i
$83$	−0.472401	−	0.0237655i	−0.472401	−	0.0237655i	−0.187381	−	0.982287i	$-0.560000\pi$
$83$	−0.472401	−	0.0237655i	−0.472401	−	0.0237655i	−0.285019	+	0.958522i	$0.592000\pi$
$84$		0			0
$85$		0			0
$86$	−0.875218	+	0.452895i	−0.875218	+	0.452895i
$87$		0			0
$88$	−0.526870	+	1.28337i	−0.526870	+	1.28337i
$89$	−1.12464	−	0.512052i	−1.12464	−	0.512052i	−0.236499	−	0.971632i	$-0.576000\pi$
$89$	−1.12464	−	0.512052i	−1.12464	−	0.512052i	−0.888136	+	0.459580i	$0.848000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	1.21074	+	1.02751i	1.21074	+	1.02751i
$97$	−0.508394	−	1.88158i	−0.508394	−	1.88158i	−0.470704	−	0.882291i	$-0.656000\pi$
$97$	−0.508394	−	1.88158i	−0.508394	−	1.88158i	−0.0376902	−	0.999289i	$-0.512000\pi$
$98$	−0.778462	+	0.627691i	−0.778462	+	0.627691i
$99$	0.343334	−	2.08293i	0.343334	−	2.08293i
$100$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$101$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$101$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$102$	−0.793990	+	0.576868i	−0.793990	+	0.576868i
$103$		0			0		−0.514440	−	0.857527i	$-0.672000\pi$
$103$		0			0		0.514440	+	0.857527i	$0.328000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.58748	−	1.21548i	−1.58748	−	1.21548i	−0.809017	−	0.587785i	$-0.800000\pi$
$107$	−1.58748	−	1.21548i	−1.58748	−	1.21548i	−0.778462	−	0.627691i	$-0.784000\pi$
$108$	−0.735752	−	0.380726i	−0.735752	−	0.380726i
$109$		0			0		−0.0376902	−	0.999289i	$-0.512000\pi$
$109$		0			0		0.0376902	+	0.999289i	$0.488000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.605584	−	1.86380i	0.605584	−	1.86380i	0.112856	−	0.993611i	$-0.464000\pi$
$113$	0.605584	−	1.86380i	0.605584	−	1.86380i	0.492727	−	0.870184i	$-0.336000\pi$
$114$	−0.0169925	−	1.35215i	−0.0169925	−	1.35215i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.10301	+	1.55899i	1.10301	+	1.55899i
$119$		0			0
$120$		0			0
$121$	−0.924328	−	0.0232358i	−0.924328	−	0.0232358i
$122$		0			0
$123$	0.177849	+	0.214982i	0.177849	+	0.214982i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$127$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$128$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$129$	−1.35194	+	0.788111i	−1.35194	+	0.788111i
$130$		0			0
$131$	0.0141726	+	0.124779i	0.0141726	+	0.124779i	0.998737	−	0.0502443i	$-0.0160000\pi$
$131$	0.0141726	+	0.124779i	0.0141726	+	0.124779i	−0.984564	+	0.175023i	$0.944000\pi$
$132$	−0.733207	+	2.07742i	−0.733207	+	2.07742i
$133$		0			0
$134$	1.14931	−	1.62444i	1.14931	−	1.62444i
$135$		0			0
$136$	0.555863	−	0.270152i	0.555863	−	0.270152i
$137$	−0.00716313	−	0.569994i	−0.00716313	−	0.569994i	−0.962028	−	0.272952i	$-0.912000\pi$
$137$	−0.00716313	−	0.569994i	−0.00716313	−	0.569994i	0.954865	−	0.297042i	$-0.0960000\pi$
$138$		0			0
$139$	−1.98425	−	0.200153i	−1.98425	−	0.200153i	−0.999684	−	0.0251301i	$-0.992000\pi$
$139$	−1.98425	−	0.200153i	−1.98425	−	0.200153i	−0.984564	−	0.175023i	$-0.944000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	1.20820	+	0.925077i	1.20820	+	0.925077i
$145$		0			0
$146$	0.291739	+	0.235235i	0.291739	+	0.235235i
$147$	−1.18454	+	1.05761i	−1.18454	+	1.05761i
$148$		0			0
$149$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$149$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$150$	−0.949462	+	1.27287i	−0.949462	+	1.27287i
$151$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$151$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$152$	−0.138495	+	0.840221i	−0.138495	+	0.840221i
$153$	−0.732106	+	0.590313i	−0.732106	+	0.590313i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$157$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.187631	+	0.0854293i	0.187631	+	0.0854293i
$163$	0.422979	−	1.03031i	0.422979	−	1.03031i	−0.556876	−	0.830596i	$-0.688000\pi$
$163$	0.422979	−	1.03031i	0.422979	−	1.03031i	0.979855	−	0.199710i	$-0.0640000\pi$
$164$	−0.0865734	−	0.152893i	−0.0865734	−	0.152893i
$165$		0			0
$166$	0.465697	+	0.0827856i	0.465697	+	0.0827856i
$167$		0			0		0.997159	−	0.0753268i	$-0.0240000\pi$
$167$		0			0		−0.997159	+	0.0753268i	$0.976000\pi$
$168$		0			0
$169$	−0.597905	−	0.801567i	−0.597905	−	0.801567i
$170$		0			0
$171$	−0.0813641	−	1.29325i	−0.0813641	−	1.29325i
$172$	0.925080	−	0.339630i	0.925080	−	0.339630i
$173$		0			0		0.617860	−	0.786288i	$-0.288000\pi$
$173$		0			0		−0.617860	+	0.786288i	$0.712000\pi$
$174$		0			0
$175$		0			0
$176$	0.683564	−	1.20721i	0.683564	−	1.20721i
$177$	1.87373	+	2.38451i	1.87373	+	2.38451i
$178$	1.05159	+	0.648968i	1.05159	+	0.648968i
$179$	1.22942	+	0.716692i	1.22942	+	0.716692i	0.968583	−	0.248690i	$-0.0800000\pi$
$179$	1.22942	+	0.716692i	1.22942	+	0.716692i	0.260842	+	0.965382i	$0.416000\pi$
$180$		0			0
$181$		0			0		−0.745941	−	0.666012i	$-0.768000\pi$
$181$		0			0		0.745941	+	0.666012i	$0.232000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.625020	+	0.586932i	0.625020	+	0.586932i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.236499	−	0.971632i	$-0.576000\pi$
$191$		0			0		0.236499	+	0.971632i	$0.424000\pi$
$192$	−1.07242	−	1.17116i	−1.07242	−	1.17116i
$193$	−0.536181	−	1.06886i	−0.536181	−	1.06886i	−0.984564	−	0.175023i	$-0.944000\pi$
$193$	−0.536181	−	1.06886i	−0.536181	−	1.06886i	0.448383	−	0.893841i	$-0.352000\pi$
$194$	0.268561	+	1.93046i	0.268561	+	1.93046i
$195$		0			0
$196$	0.850994	−	0.525175i	0.850994	−	0.525175i
$197$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$197$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$198$	−0.601687	+	2.02348i	−0.601687	+	2.02348i
$199$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$199$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$200$	0.728969	−	0.684547i	0.728969	−	0.684547i
$201$	1.69317	−	2.66801i	1.69317	−	2.66801i
$202$		0			0
$203$		0			0
$204$	0.860030	−	0.472806i	0.860030	−	0.472806i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.15757	+	0.235932i	−1.15757	+	0.235932i
$210$		0			0
$211$	0.360532	+	1.88998i	0.360532	+	1.88998i	0.448383	+	0.893841i	$0.352000\pi$
$211$	0.360532	+	1.88998i	0.360532	+	1.88998i	−0.0878512	+	0.996134i	$0.528000\pi$
$212$		0			0
$213$		0			0
$214$	1.42262	+	1.40486i	1.42262	+	1.40486i
$215$		0			0
$216$	0.682233	+	0.469938i	0.682233	+	0.469938i
$217$		0			0
$218$		0			0
$219$	0.481459	+	0.349800i	0.481459	+	0.349800i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.988652	−	0.150226i	$-0.0480000\pi$
$223$		0			0		−0.988652	+	0.150226i	$0.952000\pi$
$224$		0			0
$225$	−0.847388	+	1.26390i	−0.847388	+	1.26390i
$226$	−0.834404	+	1.77320i	−0.834404	+	1.77320i
$227$	−1.67249	−	0.812840i	−1.67249	−	0.812840i	−0.997159	−	0.0753268i	$-0.976000\pi$
$227$	−1.67249	−	0.812840i	−1.67249	−	0.812840i	−0.675333	−	0.737513i	$-0.736000\pi$
$228$	−0.152611	+	1.34362i	−0.152611	+	1.34362i
$229$		0			0		0.137790	−	0.990461i	$-0.456000\pi$
$229$		0			0		−0.137790	+	0.990461i	$0.544000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.75109	+	0.496830i	1.75109	+	0.496830i	0.988652	−	0.150226i	$-0.0480000\pi$
$233$	1.75109	+	0.496830i	1.75109	+	0.496830i	0.762443	+	0.647056i	$0.224000\pi$
$234$		0			0
$235$		0			0
$236$	−0.898917	−	1.68494i	−0.898917	−	1.68494i
$237$		0			0
$238$		0			0
$239$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$239$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$240$		0			0
$241$	−0.138495	−	0.294317i	−0.138495	−	0.294317i	0.823533	−	0.567269i	$-0.192000\pi$
$241$	−0.138495	−	0.294317i	−0.138495	−	0.294317i	−0.962028	+	0.272952i	$0.912000\pi$
$242$	0.914127	+	0.138902i	0.914127	+	0.138902i
$243$	1.07464	+	0.425481i	1.07464	+	0.425481i
$244$		0			0
$245$		0			0
$246$	−0.149502	−	0.235578i	−0.149502	−	0.235578i
$247$		0			0
$248$		0			0
$249$	0.745189	+	0.0941393i	0.745189	+	0.0941393i
$250$		0			0
$251$	0.920232	+	0.391374i	0.920232	+	0.391374i
$251$	0.920232	+	0.391374i	0.920232	+	0.391374i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.535827	+	0.844328i	0.535827	+	0.844328i
$257$	0.0246258	+	0.00501913i	0.0246258	+	0.00501913i	0.212007	−	0.977268i	$-0.432000\pi$
$257$	0.0246258	+	0.00501913i	0.0246258	+	0.00501913i	−0.187381	+	0.982287i	$0.560000\pi$
$258$	1.44006	−	0.612454i	1.44006	−	0.612454i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.00157806	−	0.125571i	0.00157806	−	0.125571i
$263$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$263$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$264$	0.987796	−	1.96915i	0.987796	−	1.96915i
$265$		0			0
$266$		0			0
$267$	1.71958	+	0.945344i	1.71958	+	0.945344i
$268$	−1.34385	+	1.46758i	−1.34385	+	1.46758i
$269$		0			0		−0.962028	−	0.272952i	$-0.912000\pi$
$269$		0			0		0.962028	+	0.272952i	$0.0880000\pi$
$270$		0			0
$271$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$271$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$272$	−0.585339	+	0.198354i	−0.585339	+	0.198354i
$273$		0			0
$274$	−0.0643325	+	0.566397i	−0.0643325	+	0.566397i
$275$	1.24775	+	0.606414i	1.24775	+	0.606414i
$276$		0			0
$277$		0			0		0.556876	−	0.830596i	$-0.312000\pi$
$277$		0			0		−0.556876	+	0.830596i	$0.688000\pi$
$278$	1.94352	+	0.447267i	1.94352	+	0.447267i
$279$		0			0
$280$		0			0
$281$	0.468030	+	1.22693i	0.468030	+	1.22693i	0.938734	+	0.344643i	$0.112000\pi$
$281$	0.468030	+	1.22693i	0.468030	+	1.22693i	−0.470704	+	0.882291i	$0.656000\pi$
$282$		0			0
$283$	−0.263152	−	0.191191i	−0.263152	−	0.191191i	0.448383	−	0.893841i	$-0.352000\pi$
$283$	−0.263152	−	0.191191i	−0.263152	−	0.191191i	−0.711536	+	0.702650i	$0.752000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.08273	−	1.06921i	−1.08273	−	1.06921i
$289$	0.0542950	+	0.615644i	0.0542950	+	0.615644i
$290$		0			0
$291$	0.579956	+	3.04024i	0.579956	+	3.04024i
$292$	−0.259955	−	0.269945i	−0.259955	−	0.269945i
$293$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$293$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$294$	1.30775	−	0.900812i	1.30775	−	0.900812i
$295$		0			0
$296$		0			0
$297$	−0.271803	+	1.11667i	−0.271803	+	1.11667i
$298$		0			0
$299$		0			0
$300$	1.10151	−	1.14384i	1.10151	−	1.14384i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.242711	−	0.816237i	0.242711	−	0.816237i
$305$		0			0
$306$	0.800319	−	0.493901i	0.800319	−	0.493901i
$307$	−0.896483	+	0.0225358i	−0.896483	+	0.0225358i	−0.470704	−	0.882291i	$-0.656000\pi$
$307$	−0.896483	+	0.0225358i	−0.896483	+	0.0225358i	−0.425779	+	0.904827i	$0.640000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.236499	−	0.971632i	$-0.576000\pi$
$311$		0			0		0.236499	+	0.971632i	$0.424000\pi$
$312$		0			0
$313$	1.89436	−	0.336754i	1.89436	−	0.336754i	0.899405	−	0.437116i	$-0.144000\pi$
$313$	1.89436	−	0.336754i	1.89436	−	0.336754i	0.994951	+	0.100362i	$0.0320000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.212007	−	0.977268i	$-0.432000\pi$
$317$		0			0		−0.212007	+	0.977268i	$0.568000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	2.36833	+	2.11456i	2.36833	+	2.11456i
$322$		0			0
$323$	0.454676	+	0.265053i	0.454676	+	0.265053i
$324$	−0.175444	−	0.108272i	−0.175444	−	0.108272i
$325$		0			0
$326$	−0.548776	+	0.969168i	−0.548776	+	0.969168i
$327$		0			0
$328$	0.0667281	+	0.162538i	0.0667281	+	0.162538i
$329$		0			0
$330$		0			0
$331$	−0.0750855	−	1.19345i	−0.0750855	−	1.19345i	−0.837528	−	0.546394i	$-0.816000\pi$
$331$	−0.0750855	−	1.19345i	−0.0750855	−	1.19345i	0.762443	−	0.647056i	$-0.224000\pi$
$332$	−0.451649	−	0.140500i	−0.451649	−	0.140500i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.836099	−	0.432652i	0.836099	−	0.432652i	0.0125660	−	0.999921i	$-0.496000\pi$
$337$	0.836099	−	0.432652i	0.836099	−	0.432652i	0.823533	+	0.567269i	$0.192000\pi$
$338$	0.492727	+	0.870184i	0.492727	+	0.870184i
$339$	−1.18187	+	2.87882i	−1.18187	+	2.87882i
$340$		0			0
$341$		0			0
$342$	−0.0813641	+	1.29325i	−0.0813641	+	1.29325i
$343$		0			0
$344$	−0.960352	+	0.221009i	−0.960352	+	0.221009i
$345$		0			0
$346$		0			0
$347$	−1.44422	−	1.22565i	−1.44422	−	1.22565i	−0.929776	−	0.368125i	$-0.880000\pi$
$347$	−1.44422	−	1.22565i	−1.44422	−	1.22565i	−0.514440	−	0.857527i	$-0.672000\pi$
$348$		0			0
$349$		0			0		0.778462	−	0.627691i	$-0.216000\pi$
$349$		0			0		−0.778462	+	0.627691i	$0.784000\pi$
$350$		0			0
$351$		0			0
$352$	−0.829478	+	1.11202i	−0.829478	+	1.11202i
$353$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.637424	+	0.770513i	$0.720000\pi$
$353$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.929776	+	0.368125i	$0.880000\pi$
$354$	−1.56010	−	2.60055i	−1.56010	−	2.60055i
$355$		0			0
$356$	−0.961961	−	0.775650i	−0.961961	−	0.775650i
$357$		0			0
$358$	−1.12990	−	0.865128i	−1.12990	−	0.865128i
$359$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$359$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$360$		0			0
$361$	0.250141	−	0.113890i	0.250141	−	0.113890i
$362$		0			0
$363$	1.46086	+	0.147359i	1.46086	+	0.147359i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.332820	−	0.942991i	$-0.608000\pi$
$367$		0			0		0.332820	+	0.942991i	$0.392000\pi$
$368$		0			0
$369$	−0.154422	−	0.218259i	−0.154422	−	0.218259i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$373$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$374$	−0.546529	−	0.660640i	−0.546529	−	0.660640i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.950962	+	1.14952i	0.950962	+	1.14952i	0.988652	+	0.150226i	$0.0480000\pi$
$379$	0.950962	+	1.14952i	0.950962	+	1.14952i	−0.0376902	+	0.999289i	$0.512000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.332820	−	0.942991i	$-0.392000\pi$
$383$		0			0		−0.332820	+	0.942991i	$0.608000\pi$
$384$	0.917174	+	1.29633i	0.917174	+	1.29633i
$385$		0			0
$386$	0.397989	+	1.12764i	0.397989	+	1.12764i
$387$	1.34870	−	0.655477i	1.34870	−	0.655477i
$388$	−0.0244919	−	1.94890i	−0.0244919	−	1.94890i
$389$		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
$392$	−0.910106	+	0.414376i	−0.910106	+	0.414376i
$393$	−0.00751619	−	0.199279i	−0.00751619	−	0.199279i
$394$		0			0
$395$		0			0
$396$	0.850552	−	1.93211i	0.850552	−	1.93211i
$397$		0			0		−0.778462	−	0.627691i	$-0.784000\pi$
$397$		0			0		0.778462	+	0.627691i	$0.216000\pi$
$398$		0			0
$399$		0			0
$400$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$401$	−0.426201	+	0.571376i	−0.426201	+	0.571376i	−0.962028	−	0.272952i	$-0.912000\pi$
$401$	−0.426201	+	0.571376i	−0.426201	+	0.571376i	0.535827	+	0.844328i	$0.320000\pi$
$402$	−2.01421	+	2.43476i	−2.01421	+	2.43476i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.912507	+	0.361287i	−0.912507	+	0.361287i
$409$	−1.65863	+	0.381706i	−1.65863	+	0.381706i	−0.947098	−	0.320944i	$-0.896000\pi$
$409$	−1.65863	+	0.381706i	−1.65863	+	0.381706i	−0.711536	+	0.702650i	$0.752000\pi$
$410$		0			0
$411$	−0.0568386	+	0.903424i	−0.0568386	+	0.903424i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	3.11805	+	0.554287i	3.11805	+	0.554287i
$418$	1.17802	−	0.0889890i	1.17802	−	0.0889890i
$419$	1.69984	+	0.0855153i	1.69984	+	0.0855153i	0.876307	−	0.481754i	$-0.160000\pi$
$419$	1.69984	+	0.0855153i	1.69984	+	0.0855153i	0.823533	+	0.567269i	$0.192000\pi$
$420$		0			0
$421$		0			0		−0.954865	−	0.297042i	$-0.904000\pi$
$421$		0			0		0.954865	+	0.297042i	$0.0960000\pi$
$422$	−0.120812	−	1.92026i	−0.120812	−	1.92026i
$423$		0			0
$424$		0			0
$425$	−0.234716	−	0.571729i	−0.234716	−	0.571729i
$426$		0			0
$427$		0			0
$428$	−1.23533	−	1.57208i	−1.23533	−	1.57208i
$429$		0			0
$430$		0			0
$431$		0			0		−0.162637	−	0.986686i	$-0.552000\pi$
$431$		0			0		0.162637	+	0.986686i	$0.448000\pi$
$432$	−0.617955	−	0.551739i	−0.617955	−	0.551739i
$433$	0.238883	−	1.25227i	0.238883	−	1.25227i	−0.637424	−	0.770513i	$-0.720000\pi$
$433$	0.238883	−	1.25227i	0.238883	−	1.25227i	0.876307	−	0.481754i	$-0.160000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.433821	−	0.407385i	−0.433821	−	0.407385i
$439$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$439$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$440$		0			0
$441$	1.20820	−	0.925077i	1.20820	−	0.925077i
$442$		0			0
$443$	1.09271	+	1.19332i	1.09271	+	1.19332i	0.979855	+	0.199710i	$0.0640000\pi$
$443$	1.09271	+	1.19332i	1.09271	+	1.19332i	0.112856	+	0.993611i	$0.464000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.434622	+	1.46164i	−0.434622	+	1.46164i	0.402906	+	0.915241i	$0.368000\pi$
$449$	−0.434622	+	1.46164i	−0.434622	+	1.46164i	−0.837528	+	0.546394i	$0.816000\pi$
$450$	0.999115	−	1.14773i	0.999115	−	1.14773i
$451$	−0.177688	+	0.166860i	−0.177688	+	0.166860i
$452$	1.05007	−	1.65464i	1.05007	−	1.65464i
$453$		0			0
$454$	1.55743	+	1.01605i	1.55743	+	1.01605i
$455$		0			0
$456$	0.319808	−	1.31390i	0.319808	−	1.31390i
$457$	−0.799459	−	1.81605i	−0.799459	−	1.81605i	−0.514440	−	0.857527i	$-0.672000\pi$
$457$	−0.799459	−	1.81605i	−0.799459	−	1.81605i	−0.285019	−	0.958522i	$-0.592000\pi$
$458$		0			0
$459$	0.421643	−	0.290438i	0.421643	−	0.290438i
$460$		0			0
$461$		0			0		−0.693653	−	0.720309i	$-0.744000\pi$
$461$		0			0		0.693653	+	0.720309i	$0.256000\pi$
$462$		0			0
$463$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$463$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$464$		0			0
$465$		0			0
$466$	−1.67502	−	0.712383i	−1.67502	−	0.712383i
$467$	1.64498	+	1.13310i	1.64498	+	1.13310i	0.850994	+	0.525175i	$0.176000\pi$
$467$	1.64498	+	1.13310i	1.64498	+	1.13310i	0.793990	+	0.607930i	$0.208000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.680650	+	1.78432i	0.680650	+	1.78432i
$473$	−0.761320	−	1.13553i	−0.761320	−	1.13553i
$474$		0			0
$475$	0.829867	+	0.190980i	0.829867	+	0.190980i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.112856	−	0.993611i	$-0.464000\pi$
$479$		0			0		−0.112856	+	0.993611i	$0.536000\pi$
$480$		0			0
$481$		0			0
$482$	0.100515	+	0.309354i	0.100515	+	0.309354i
$483$		0			0
$484$	−0.889510	−	0.252377i	−0.889510	−	0.252377i
$485$		0			0
$486$	−1.01284	−	0.556814i	−1.01284	−	0.556814i
$487$		0			0		−0.470704	−	0.882291i	$-0.656000\pi$
$487$		0			0		0.470704	+	0.882291i	$0.344000\pi$
$488$		0			0
$489$	−0.793018	+	1.58086i	−0.793018	+	1.58086i
$490$		0			0
$491$	0.0231273	−	1.84032i	0.0231273	−	1.84032i	−0.379779	−	0.925077i	$-0.624000\pi$
$491$	0.0231273	−	1.84032i	0.0231273	−	1.84032i	0.402906	−	0.915241i	$-0.368000\pi$
$492$	0.118798	+	0.252458i	0.118798	+	0.252458i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.727514	−	0.186794i	−0.727514	−	0.186794i
$499$	−0.803523	−	0.0606993i	−0.803523	−	0.0606993i	−0.332820	−	0.942991i	$-0.608000\pi$
$499$	−0.803523	−	0.0606993i	−0.803523	−	0.0606993i	−0.470704	+	0.882291i	$0.656000\pi$
$500$		0			0
$501$		0			0
$502$	−0.863923	−	0.503623i	−0.863923	−	0.503623i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.850883	+	1.34078i	0.850883	+	1.34078i
$508$		0			0
$509$		0			0		0.920232	−	0.391374i	$-0.128000\pi$
$509$		0			0		−0.920232	+	0.391374i	$0.872000\pi$
$510$		0			0
$511$		0			0
$512$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$513$	−0.00886472	+	0.705395i	−0.00886472	+	0.705395i
$514$	−0.0238026	−	0.00806598i	−0.0238026	−	0.00806598i
$515$		0			0
$516$	−1.50546	+	0.427138i	−1.50546	+	0.427138i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.301701	−	1.39072i	−0.301701	−	1.39072i	−0.837528	−	0.546394i	$-0.816000\pi$
$521$	−0.301701	−	1.39072i	−0.301701	−	1.39072i	0.535827	−	0.844328i	$-0.320000\pi$
$522$		0			0
$523$	1.47456	−	0.499685i	1.47456	−	0.499685i	0.535827	−	0.844328i	$-0.320000\pi$
$523$	1.47456	−	0.499685i	1.47456	−	0.499685i	0.938734	+	0.344643i	$0.112000\pi$
$524$	−0.0173038	+	0.124383i	−0.0173038	+	0.124383i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.22681	+	1.82982i	−1.22681	+	1.82982i
$529$	−0.974527	−	0.224271i	−0.974527	−	0.224271i
$530$		0			0
$531$	−1.61828	−	2.41371i	−1.61828	−	2.41371i
$532$		0			0
$533$		0			0
$534$	−1.58753	−	1.15341i	−1.58753	−	1.15341i
$535$		0			0
$536$	1.51719	−	1.28758i	1.51719	−	1.28758i
$537$	−1.86103	−	1.28192i	−1.86103	−	1.28192i
$538$		0			0
$539$	−0.987118	−	0.974791i	−0.987118	−	0.974791i
$540$		0			0
$541$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$541$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$542$		0			0
$543$		0			0
$544$	0.605584	−	0.123428i	0.605584	−	0.123428i
$545$		0			0
$546$		0			0
$547$	0.324667	+	0.737513i	0.324667	+	0.737513i	1.00000			$0$
$547$	0.324667	+	0.737513i	0.324667	+	0.737513i	−0.675333	+	0.737513i	$0.736000\pi$
$548$	0.134814	−	0.553868i	0.134814	−	0.553868i
$549$		0			0
$550$	−1.16191	−	0.758016i	−1.16191	−	0.758016i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.87213	−	0.687328i	−1.87213	−	0.687328i
$557$		0			0		0.850994	−	0.525175i	$-0.176000\pi$
$557$		0			0		−0.850994	+	0.525175i	$0.824000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.919492	−	1.00415i	−0.919492	−	1.00415i
$562$	−0.310564	−	1.27592i	−0.310564	−	1.27592i
$563$	−1.47647	+	1.13048i	−1.47647	+	1.13048i	−0.514440	+	0.857527i	$0.672000\pi$
$563$	−1.47647	+	1.13048i	−1.47647	+	1.13048i	−0.962028	+	0.272952i	$0.912000\pi$
$564$		0			0
$565$		0			0
$566$	0.237115	+	0.222666i	0.237115	+	0.222666i
$567$		0			0
$568$		0			0
$569$	−0.0118298	+	0.0221738i	−0.0118298	+	0.0221738i	−0.888136	−	0.459580i	$-0.848000\pi$
$569$	−0.0118298	+	0.0221738i	−0.0118298	+	0.0221738i	0.876307	+	0.481754i	$0.160000\pi$
$570$		0			0
$571$	0.0516387	−	0.270699i	0.0516387	−	0.270699i	−0.947098	−	0.320944i	$-0.896000\pi$
$571$	0.0516387	−	0.270699i	0.0516387	−	0.270699i	0.998737	+	0.0502443i	$0.0160000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.940186	+	1.19648i	0.940186	+	1.19648i
$577$	−0.735091	+	1.29821i	−0.735091	+	1.29821i	0.212007	+	0.977268i	$0.432000\pi$
$577$	−0.735091	+	1.29821i	−0.735091	+	1.29821i	−0.947098	+	0.320944i	$0.896000\pi$
$578$	0.0232938	−	0.617595i	0.0232938	−	0.617595i
$579$	0.721171	+	1.75665i	0.721171	+	1.75665i
$580$		0			0
$581$		0			0
$582$	−0.194340	−	3.08895i	−0.194340	−	3.08895i
$583$		0			0
$584$	0.224072	+	0.300397i	0.224072	+	0.300397i
$585$		0			0
$586$		0			0
$587$	−1.84849	−	0.328600i	−1.84849	−	0.328600i	−0.863923	−	0.503623i	$-0.832000\pi$
$587$	−1.84849	−	0.328600i	−1.84849	−	0.328600i	−0.984564	+	0.175023i	$0.944000\pi$
$588$	−1.41034	+	0.729804i	−1.41034	+	0.729804i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.125541	+	1.99542i	−0.125541	+	1.99542i	−0.0376902	+	0.999289i	$0.512000\pi$
$593$	−0.125541	+	1.99542i	−0.125541	+	1.99542i	−0.0878512	+	0.996134i	$0.528000\pi$
$594$	0.409616	−	1.07380i	0.409616	−	1.07380i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.260842	−	0.965382i	$-0.584000\pi$
$599$		0			0		0.260842	+	0.965382i	$0.416000\pi$
$600$	−1.23618	+	0.996762i	−1.23618	+	0.996762i
$601$	0.237115	−	1.43853i	0.237115	−	1.43853i	−0.556876	−	0.830596i	$-0.688000\pi$
$601$	0.237115	−	1.43853i	0.237115	−	1.43853i	0.793990	−	0.607930i	$-0.208000\pi$
$602$		0			0
$603$	−1.81046	+	2.42714i	−1.81046	+	2.42714i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.778462	−	0.627691i	$-0.784000\pi$
$607$		0			0		0.778462	+	0.627691i	$0.216000\pi$
$608$	−0.343098	+	0.779381i	−0.343098	+	0.779381i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.855911	+	0.389700i	−0.855911	+	0.389700i
$613$		0			0		−0.656586	−	0.754251i	$-0.728000\pi$
$613$		0			0		0.656586	+	0.754251i	$0.272000\pi$
$614$	0.892239	+	0.0900010i	0.892239	+	0.0900010i
$615$		0			0
$616$		0			0
$617$	1.03894	−	0.504932i	1.03894	−	0.504932i	0.162637	−	0.986686i	$-0.448000\pi$
$617$	1.03894	−	0.504932i	1.03894	−	0.504932i	0.876307	+	0.481754i	$0.160000\pi$
$618$		0			0
$619$	−1.05130	+	1.48591i	−1.05130	+	1.48591i	−0.187381	+	0.982287i	$0.560000\pi$
$619$	−1.05130	+	1.48591i	−1.05130	+	1.48591i	−0.863923	+	0.503623i	$0.832000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$626$	−1.92163	+	0.0966728i	−1.92163	+	0.0966728i
$627$	1.86120	−	0.235125i	1.86120	−	0.235125i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$631$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$632$		0			0
$633$	−0.344817	−	3.03584i	−0.344817	−	3.03584i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.06624	+	0.107553i	1.06624	+	0.107553i	0.617860	−	0.786288i	$-0.288000\pi$
$641$	1.06624	+	0.107553i	1.06624	+	0.107553i	0.448383	+	0.893841i	$0.352000\pi$
$642$	−2.08463	−	2.39472i	−2.08463	−	2.39472i
$643$	1.52448	−	0.694102i	1.52448	−	0.694102i	0.535827	−	0.844328i	$-0.320000\pi$
$643$	1.52448	−	0.694102i	1.52448	−	0.694102i	0.988652	+	0.150226i	$0.0480000\pi$
$644$		0			0
$645$		0			0
$646$	−0.417871	−	0.319949i	−0.417871	−	0.319949i
$647$		0			0		0.402906	−	0.915241i	$-0.368000\pi$
$647$		0			0		−0.402906	+	0.915241i	$0.632000\pi$
$648$	0.160491	+	0.129407i	0.160491	+	0.129407i
$649$	−1.97628	+	1.76452i	−1.97628	+	1.76452i
$650$		0			0
$651$		0			0
$652$	0.665917	−	0.892746i	0.665917	−	0.892746i
$653$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$653$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$654$		0			0
$655$		0			0
$656$	−0.0458305	−	0.169620i	−0.0458305	−	0.169620i
$657$	−0.434798	−	0.368997i	−0.434798	−	0.368997i
$658$		0			0
$659$	−0.116762	+	0.0462295i	−0.116762	+	0.0462295i	−0.425779	−	0.904827i	$-0.640000\pi$
$659$	−0.116762	+	0.0462295i	−0.116762	+	0.0462295i	0.309017	+	0.951057i	$0.400000\pi$
$660$		0			0
$661$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$661$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$662$	−0.0750855	+	1.19345i	−0.0750855	+	1.19345i
$663$		0			0
$664$	0.430478	+	0.195999i	0.430478	+	0.195999i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.00473317	−	0.0752316i	−0.00473317	−	0.0752316i	0.994951	−	0.100362i	$-0.0320000\pi$
$673$	−0.00473317	−	0.0752316i	−0.00473317	−	0.0752316i	−0.999684	+	0.0251301i	$0.992000\pi$
$674$	−0.883731	+	0.324450i	−0.883731	+	0.324450i
$675$	0.511849	−	0.651379i	0.511849	−	0.651379i
$676$	−0.379779	−	0.925077i	−0.379779	−	0.925077i
$677$		0			0		0.0376902	−	0.999289i	$-0.488000\pi$
$677$		0			0		−0.0376902	+	0.999289i	$0.512000\pi$
$678$	1.53336	−	2.70800i	1.53336	−	2.70800i
$679$		0			0
$680$		0			0
$681$	2.55111	+	1.48717i	2.55111	+	1.48717i
$682$		0			0
$683$	1.46885	+	1.31146i	1.46885	+	1.31146i	0.850994	+	0.525175i	$0.176000\pi$
$683$	1.46885	+	1.31146i	1.46885	+	1.31146i	0.617860	+	0.786288i	$0.288000\pi$
$684$	0.242809	−	1.27285i	0.242809	−	1.27285i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.980479	−	0.0989019i	0.980479	−	0.0989019i
$689$		0			0
$690$		0			0
$691$	1.01300	−	0.180078i	1.01300	−	0.180078i	0.356412	−	0.934329i	$-0.384000\pi$
$691$	1.01300	−	0.180078i	1.01300	−	0.180078i	0.656586	+	0.754251i	$0.272000\pi$
$692$		0			0
$693$		0			0
$694$	1.27921	+	1.39699i	1.27921	+	1.39699i
$695$		0			0
$696$		0			0
$697$	0.108556	−	0.00272888i	0.108556	−	0.00272888i
$698$		0			0
$699$	−2.71337	−	0.996177i	−2.71337	−	0.996177i
$700$		0			0
$701$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$701$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$702$		0			0
$703$		0			0
$704$	0.962310	−	0.999289i	0.962310	−	0.999289i
$705$		0			0
$706$	1.69755	−	0.933237i	1.69755	−	0.933237i
$707$		0			0
$708$	1.22186	+	2.77557i	1.22186	+	2.77557i
$709$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$709$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$710$		0			0
$711$		0			0
$712$	0.857161	+	0.890100i	0.857161	+	0.890100i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.01257	+	0.999921i	1.01257	+	0.999921i
$717$		0			0
$718$		0			0
$719$		0			0		0.762443	−	0.647056i	$-0.224000\pi$
$719$		0			0		−0.762443	+	0.647056i	$0.776000\pi$
$720$		0			0
$721$		0			0
$722$	−0.262443	+	0.0816413i	−0.262443	+	0.0816413i
$723$	0.184097	+	0.482608i	0.184097	+	0.482608i
$724$		0			0
$725$		0			0
$726$	−1.43088	−	0.329292i	−1.43088	−	0.329292i
$727$		0			0		0.556876	−	0.830596i	$-0.312000\pi$
$727$		0			0		−0.556876	+	0.830596i	$0.688000\pi$
$728$		0			0
$729$	−1.46534	−	0.712164i	−1.46534	−	0.712164i
$730$		0			0
$731$	−0.0839204	+	0.603235i	−0.0839204	+	0.603235i
$732$		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
$737$	2.41914	+	1.32993i	2.41914	+	1.32993i
$738$	0.125849	+	0.235892i	0.125849	+	0.235892i
$739$	1.89436	−	0.537477i	1.89436	−	0.537477i	0.899405	−	0.437116i	$-0.144000\pi$
$739$	1.89436	−	0.537477i	1.89436	−	0.537477i	0.994951	−	0.100362i	$-0.0320000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$743$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.705254	−	0.143742i	−0.705254	−	0.143742i
$748$	0.459419	+	0.723929i	0.459419	+	0.723929i
$749$		0			0
$750$		0			0
$751$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$751$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$752$		0			0
$753$	−1.41034	−	0.729804i	−1.41034	−	0.729804i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$757$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$758$	−0.799391	−	1.25964i	−0.799391	−	1.25964i
$759$		0			0
$760$		0			0
$761$	0.439782	+	0.174122i	0.439782	+	0.174122i	0.577573	−	0.816339i	$-0.304000\pi$
$761$	0.439782	+	0.174122i	0.439782	+	0.174122i	−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
$768$	−0.747469	−	1.40106i	−0.747469	−	1.40106i
$769$	1.57631	+	0.866584i	1.57631	+	0.866584i	0.998737	+	0.0502443i	$0.0160000\pi$
$769$	1.57631	+	0.866584i	1.57631	+	0.866584i	0.577573	+	0.816339i	$0.304000\pi$
$770$		0			0
$771$	−0.0383938	−	0.0108933i	−0.0383938	−	0.0108933i
$772$	−0.253520	−	1.16863i	−0.253520	−	1.16863i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	−1.42022	+	0.481271i	−1.42022	+	0.481271i
$775$		0			0
$776$	−0.219963	+	1.93660i	−0.219963	+	1.93660i
$777$		0			0
$778$		0			0
$779$	−0.0833202	+	0.124274i	−0.0833202	+	0.124274i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.954865	−	0.297042i	0.954865	−	0.297042i
$785$		0			0
$786$	−0.0175193	+	0.198649i	−0.0175193	+	0.198649i
$787$	−1.02980	+	0.873956i	−1.02980	+	0.873956i	−0.992115	−	0.125333i	$-0.960000\pi$
$787$	−1.02980	+	0.873956i	−1.02980	+	0.873956i	−0.0376902	+	0.999289i	$0.512000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−1.08600	+	1.81027i	−1.08600	+	1.81027i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$797$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$798$		0			0
$799$		0			0
$800$	0.876307	−	0.481754i	0.876307	−	0.481754i
$801$	−1.57487	−	1.02743i	−1.57487	−	1.02743i
$802$	0.494453	−	0.513453i	0.494453	−	0.513453i
$803$	−0.278582	+	0.438975i	−0.278582	+	0.438975i
$804$	2.30349	−	2.16312i	2.30349	−	2.16312i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.79824	+	0.0452043i	−1.79824	+	0.0452043i	−0.910106	−	0.414376i	$-0.864000\pi$
$809$	−1.79824	+	0.0452043i	−1.79824	+	0.0452043i	−0.888136	+	0.459580i	$0.848000\pi$
$810$		0			0
$811$	−0.499387	−	0.995517i	−0.499387	−	0.995517i	−0.992115	−	0.125333i	$-0.960000\pi$
$811$	−0.499387	−	0.995517i	−0.499387	−	0.995517i	0.492727	−	0.870184i	$-0.336000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.950593	−	0.244071i	0.950593	−	0.244071i
$817$	−0.611730	−	0.574453i	−0.611730	−	0.574453i
$818$	1.69340	−	0.170815i	1.69340	−	0.170815i
$819$		0			0
$820$		0			0
$821$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$821$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$822$	0.169619	−	0.889176i	0.169619	−	0.889176i
$823$		0			0		−0.745941	−	0.666012i	$-0.768000\pi$
$823$		0			0		0.745941	+	0.666012i	$0.232000\pi$
$824$		0			0
$825$	−1.90324	−	1.10949i	−1.90324	−	1.10949i
$826$		0			0
$827$	1.23416	+	1.57059i	1.23416	+	1.57059i	0.656586	+	0.754251i	$0.272000\pi$
$827$	1.23416	+	1.57059i	1.23416	+	1.57059i	0.577573	+	0.816339i	$0.304000\pi$
$828$		0			0
$829$		0			0		0.0376902	−	0.999289i	$-0.488000\pi$
$829$		0			0		−0.0376902	+	0.999289i	$0.512000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.0388067	+	0.616814i	0.0388067	+	0.616814i
$834$	−3.02400	−	0.940712i	−3.02400	−	0.940712i
$835$		0			0
$836$	−1.17988	−	0.0593573i	−1.17988	−	0.0593573i
$837$		0			0
$838$	−1.67572	−	0.297887i	−1.67572	−	0.297887i
$839$		0			0		0.888136	−	0.459580i	$-0.152000\pi$
$839$		0			0		−0.888136	+	0.459580i	$0.848000\pi$
$840$		0			0
$841$	−0.379779	+	0.925077i	−0.379779	+	0.925077i
$842$		0			0
$843$	−0.594348	−	1.99880i	−0.594348	−	1.99880i
$844$	−0.120812	+	1.92026i	−0.120812	+	1.92026i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.393824	+	0.334223i	0.393824	+	0.334223i
$850$	0.161209	+	0.596639i	0.161209	+	0.596639i
$851$		0			0
$852$		0			0
$853$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$853$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$854$		0			0
$855$		0			0
$856$	1.02855	+	1.71451i	1.02855	+	1.71451i
$857$	0.830793	−	0.741772i	0.830793	−	0.741772i	−0.137790	−	0.990461i	$-0.544000\pi$
$857$	0.830793	−	0.741772i	0.830793	−	0.741772i	0.968583	+	0.248690i	$0.0800000\pi$
$858$		0			0
$859$	0.756444	−	1.71834i	0.756444	−	1.71834i	0.0627905	−	0.998027i	$-0.480000\pi$
$859$	0.756444	−	1.71834i	0.756444	−	1.71834i	0.693653	−	0.720309i	$-0.256000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.910106	−	0.414376i	$-0.136000\pi$
$863$		0			0		−0.910106	+	0.414376i	$0.864000\pi$
$864$	0.543930	+	0.624839i	0.543930	+	0.624839i
$865$		0			0
$866$	−0.393950	+	1.21245i	−0.393950	+	1.21245i
$867$	−0.0123326	−	0.981349i	−0.0123326	−	0.981349i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.334714	−	2.94689i	−0.334714	−	2.94689i
$874$		0			0
$875$		0			0
$876$	0.379341	+	0.458545i	0.379341	+	0.458545i
$877$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$877$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.25517	+	1.51724i	1.25517	+	1.51724i	0.762443	+	0.647056i	$0.224000\pi$
$881$	1.25517	+	1.51724i	1.25517	+	1.51724i	0.492727	+	0.870184i	$0.336000\pi$
$882$	−1.31462	+	0.766355i	−1.31462	+	0.766355i
$883$	0.374644	+	0.00941782i	0.374644	+	0.00941782i	0.212007	−	0.977268i	$-0.432000\pi$
$883$	0.374644	+	0.00941782i	0.374644	+	0.00941782i	0.162637	+	0.986686i	$0.448000\pi$
$884$		0			0
$885$		0			0
$886$	−0.934532	−	1.32086i	−0.934532	−	1.32086i
$887$		0			0		0.577573	−	0.816339i	$-0.304000\pi$
$887$		0			0		−0.577573	+	0.816339i	$0.696000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.0883827	+	0.272014i	−0.0883827	+	0.272014i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.614386	−	1.39564i	0.614386	−	1.39564i
$899$		0			0
$900$	−1.13509	+	1.01346i	−1.13509	+	1.01346i
$901$		0			0
$902$	0.197200	−	0.143274i	0.197200	−	0.143274i
$903$		0			0
$904$	−1.24917	+	1.50998i	−1.24917	+	1.50998i
$905$		0			0
$906$		0			0
$907$	−0.436924	−	1.61707i	−0.436924	−	1.61707i	−0.745941	−	0.666012i	$-0.768000\pi$
$907$	−0.436924	−	1.61707i	−0.436924	−	1.61707i	0.309017	−	0.951057i	$-0.400000\pi$
$908$	−1.41780	−	1.20323i	−1.41780	−	1.20323i
$909$		0			0
$910$		0			0
$911$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$911$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$912$	−0.481961	+	1.26345i	−0.481961	+	1.26345i
$913$	−0.0412027	+	0.654898i	−0.0412027	+	0.654898i
$914$	0.565544	+	1.90193i	0.565544	+	1.90193i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.454720	+	0.235302i	−0.454720	+	0.235302i
$919$		0			0		−0.984564	−	0.175023i	$-0.944000\pi$
$919$		0			0		0.984564	+	0.175023i	$0.0560000\pi$
$920$		0			0
$921$	1.42225	+	0.0715503i	1.42225	+	0.0715503i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.441861	−	0.780352i	0.441861	−	0.780352i	−0.556876	−	0.830596i	$-0.688000\pi$
$929$	0.441861	−	0.780352i	0.441861	−	0.780352i	0.998737	+	0.0502443i	$0.0160000\pi$
$930$		0			0
$931$	−0.724672	−	0.447217i	−0.724672	−	0.447217i
$932$	1.57252	+	0.916701i	1.57252	+	0.916701i
$933$		0			0
$934$	−1.49000	−	1.33034i	−1.49000	−	1.33034i
$935$		0			0
$936$		0			0
$937$	0.926877	−	1.73734i	0.926877	−	1.73734i	0.309017	−	0.951057i	$-0.400000\pi$
$937$	0.926877	−	1.73734i	0.926877	−	1.73734i	0.617860	−	0.786288i	$-0.288000\pi$
$938$		0			0
$939$	−3.03994	+	0.306641i	−3.03994	+	0.306641i
$940$		0			0
$941$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$941$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$942$		0			0
$943$		0			0
$944$	−0.451649	−	1.85555i	−0.451649	−	1.85555i
$945$		0			0
$946$	0.612997	+	1.22200i	0.612997	+	1.22200i
$947$	−0.241493	−	1.73590i	−0.241493	−	1.73590i	−0.597905	−	0.801567i	$-0.704000\pi$
$947$	−0.241493	−	1.73590i	−0.241493	−	1.73590i	0.356412	−	0.934329i	$-0.384000\pi$
$948$		0			0
$949$		0			0
$950$	−0.799387	−	0.293484i	−0.799387	−	0.293484i
$951$		0			0
$952$		0			0
$953$	−1.32688	+	1.24602i	−1.32688	+	1.24602i	−0.379779	+	0.925077i	$0.624000\pi$
$953$	−1.32688	+	1.24602i	−1.32688	+	1.24602i	−0.947098	+	0.320944i	$0.896000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.823533	−	0.567269i	0.823533	−	0.567269i
$962$		0			0
$963$	−2.11037	−	2.19147i	−2.11037	−	2.19147i
$964$	−0.0609503	−	0.319513i	−0.0609503	−	0.319513i
$965$		0			0
$966$		0			0
$967$		0			0		−0.711536	−	0.702650i	$-0.752000\pi$
$967$		0			0		0.711536	+	0.702650i	$0.248000\pi$
$968$	0.850864	+	0.361872i	0.850864	+	0.361872i
$969$	−0.688261	−	0.474090i	−0.688261	−	0.474090i
$970$		0			0
$971$	−0.128082	+	1.45230i	−0.128082	+	1.45230i	0.617860	+	0.786288i	$0.288000\pi$
$971$	−0.128082	+	1.45230i	−0.128082	+	1.45230i	−0.745941	+	0.666012i	$0.768000\pi$
$972$	0.935067	+	0.679366i	0.935067	+	0.679366i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.94352	+	0.447267i	1.94352	+	0.447267i	0.988652	+	0.150226i	$0.0480000\pi$
$977$	1.94352	+	0.447267i	1.94352	+	0.447267i	0.954865	+	0.297042i	$0.0960000\pi$
$978$	0.984899	−	1.46900i	0.984899	−	1.46900i
$979$	−0.729923	+	1.55116i	−0.729923	+	1.55116i
$980$		0			0
$981$		0			0
$982$	−0.253598	+	1.82291i	−0.253598	+	1.82291i
$983$		0			0		0.947098	−	0.320944i	$-0.104000\pi$
$983$		0			0		−0.947098	+	0.320944i	$0.896000\pi$
$984$	−0.0862195	−	0.265356i	−0.0862195	−	0.265356i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$991$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$992$		0			0
$993$	−0.0238619	+	1.89877i	−0.0238619	+	1.89877i
$994$		0			0
$995$		0			0
$996$	0.698366	+	0.276503i	0.698366	+	0.276503i
$997$		0			0		0.920232	−	0.391374i	$-0.128000\pi$
$997$		0			0		−0.920232	+	0.391374i	$0.872000\pi$
$998$	0.789580	+	0.160929i	0.789580	+	0.160929i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.3.1	✓	100
8.3	odd	2	CM	2008.1.bd.a.3.1	✓	100
251.84	even	125	inner	2008.1.bd.a.1339.1	yes	100
2008.1339	odd	250	inner	2008.1.bd.a.1339.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.3.1	✓	100	1.1	even	1	trivial
2008.1.bd.a.3.1	✓	100	8.3	odd	2	CM
2008.1.bd.a.1339.1	yes	100	251.84	even	125	inner
2008.1.bd.a.1339.1	yes	100	2008.1339	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)

\(f(q)\)	\(=\)	\(q+(-0.992115 - 0.125333i) q^{2} +(-1.58347 - 0.119618i) q^{3} +(0.968583 + 0.248690i) q^{4} +(1.55599 + 0.317136i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(1.50441 + 0.228596i) q^{9} +O(q^{10})\)	\(q+(-0.992115 - 0.125333i) q^{2} +(-1.58347 - 0.119618i) q^{3} +(0.968583 + 0.248690i) q^{4} +(1.55599 + 0.317136i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(1.50441 + 0.228596i) q^{9} +(0.0174330 - 1.38720i) q^{11} +(-1.50397 - 0.509652i) q^{12} +(0.876307 + 0.481754i) q^{16} +(-0.417379 + 0.455808i) q^{17} +(-1.46390 - 0.415346i) q^{18} +(-0.180536 - 0.832201i) q^{19} +(-0.191157 + 1.37407i) q^{22} +(1.42824 + 0.694131i) q^{24} +(-0.425779 + 0.904827i) q^{25} +(-0.807320 - 0.185791i) q^{27} +(-0.809017 - 0.587785i) q^{32} +(-0.193538 + 2.19450i) q^{33} +(0.471215 - 0.399903i) q^{34} +(1.40030 + 0.595547i) q^{36} +(0.0748104 + 0.848266i) q^{38} +(-0.121877 - 0.126560i) q^{41} +(0.811554 - 0.559018i) q^{43} +(0.361867 - 1.33928i) q^{44} +(-1.32998 - 0.867664i) q^{48} +(0.693653 - 0.720309i) q^{49} +(0.535827 - 0.844328i) q^{50} +(0.715429 - 0.671832i) q^{51} +(0.777668 + 0.285510i) q^{54} +(0.186328 + 1.33936i) q^{57} +(-1.28970 - 1.40845i) q^{59} +(0.728969 + 0.684547i) q^{64} +(0.467055 - 2.15294i) q^{66} +(-0.936655 + 1.75567i) q^{67} +(-0.517621 + 0.337690i) q^{68} +(-1.31462 - 0.766355i) q^{72} +(-0.318921 - 0.196816i) q^{73} +(0.782442 - 1.38184i) q^{75} +(0.0320954 - 0.850954i) q^{76} +(-0.196859 - 0.0612392i) q^{81} +(0.105053 + 0.140837i) q^{82} +(-0.472401 - 0.0237655i) q^{83} +(-0.875218 + 0.452895i) q^{86} +(-0.526870 + 1.28337i) q^{88} +(-1.12464 - 0.512052i) q^{89} +(1.21074 + 1.02751i) q^{96} +(-0.508394 - 1.88158i) q^{97} +(-0.778462 + 0.627691i) q^{98} +(0.343334 - 2.08293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 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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