LMFDB - Embedded newform 2008.1.bd.a.67.1

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			67.1
Root			$0.675333 - 0.737513i$ of defining polynomial
Character	$\chi$	$=$	2008.67
Dual form			2008.1.bd.a.1019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.728969 - 0.684547i) q^{2} +(-0.422111 + 0.791209i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(0.233914 + 0.865722i) q^{6} +(-0.637424 - 0.770513i) q^{8} +(0.109042 + 0.162639i) q^{9} +O(q^{10})$	\(q+(0.728969 - 0.684547i) q^{2} +(-0.422111 + 0.791209i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(0.233914 + 0.865722i) q^{6} +(-0.637424 - 0.770513i) q^{8} +(0.109042 + 0.162639i) q^{9} +(0.751353 - 0.637644i) q^{11} +(0.763143 + 0.470959i) q^{12} +(-0.992115 - 0.125333i) q^{16} +(-0.481116 + 0.387935i) q^{17} +(0.190822 + 0.0439145i) q^{18} +(1.44333 - 0.994203i) q^{19} +(0.111215 - 0.979159i) q^{22} +(0.878701 - 0.179093i) q^{24} +(0.876307 + 0.481754i) q^{25} +(-1.06695 + 0.107624i) q^{27} +(-0.809017 + 0.587785i) q^{32} +(0.187355 + 0.863634i) q^{33} +(-0.0851591 + 0.612139i) q^{34} +(0.169165 - 0.0986144i) q^{36} +(0.371566 - 1.71277i) q^{38} +(0.208923 - 0.368970i) q^{41} +(1.19186 - 1.17698i) q^{43} +(-0.589208 - 0.789908i) q^{44} +(0.517948 - 0.732066i) q^{48} +(0.492727 + 0.870184i) q^{49} +(0.968583 - 0.248690i) q^{50} +(-0.103853 - 0.544415i) q^{51} +(-0.704098 + 0.808831i) q^{54} +(0.177375 + 1.56164i) q^{57} +(0.591287 + 0.476768i) q^{59} +(-0.187381 + 0.982287i) q^{64} +(0.727774 + 0.501308i) q^{66} +(-1.07242 - 1.17116i) q^{67} +(0.356960 + 0.504525i) q^{68} +(0.0558096 - 0.187688i) q^{72} +(-0.765896 - 0.372230i) q^{73} +(-0.751067 + 0.489988i) q^{75} +(-0.901614 - 1.50291i) q^{76} +(0.290853 - 0.708469i) q^{81} +(-0.100279 - 0.411986i) q^{82} +(-1.31392 - 0.445247i) q^{83} +(0.0631332 - 1.67387i) q^{86} +(-0.970244 - 0.172477i) q^{88} +(0.655963 + 1.71960i) q^{89} +(-0.123566 - 0.888213i) q^{96} +(-1.18977 + 1.59504i) q^{97} +(0.954865 + 0.297042i) q^{98} +(0.185635 + 0.0526693i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{52}{125}\right)$	$-1$	$-1$

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 $

$2$	0.728969	−	0.684547i	0.728969	−	0.684547i
$2$	0.728969	−	0.684547i	0.728969	−	0.684547i
$3$	−0.422111	+	0.791209i	−0.422111	+	0.791209i	−0.999684	−	0.0251301i	$-0.992000\pi$
$3$	−0.422111	+	0.791209i	−0.422111	+	0.791209i	0.577573	+	0.816339i	$0.304000\pi$
$4$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$5$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$5$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$6$	0.233914	+	0.865722i	0.233914	+	0.865722i
$7$		0			0		−0.863923	−	0.503623i	$-0.832000\pi$
$7$		0			0		0.863923	+	0.503623i	$0.168000\pi$
$8$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$9$	0.109042	+	0.162639i	0.109042	+	0.162639i
$10$		0			0
$11$	0.751353	−	0.637644i	0.751353	−	0.637644i	−0.187381	−	0.982287i	$-0.560000\pi$
$11$	0.751353	−	0.637644i	0.751353	−	0.637644i	0.938734	+	0.344643i	$0.112000\pi$
$12$	0.763143	+	0.470959i	0.763143	+	0.470959i
$13$		0			0		0.617860	−	0.786288i	$-0.288000\pi$
$13$		0			0		−0.617860	+	0.786288i	$0.712000\pi$
$14$		0			0
$15$		0			0
$16$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$17$	−0.481116	+	0.387935i	−0.481116	+	0.387935i	−0.837528	−	0.546394i	$-0.816000\pi$
$17$	−0.481116	+	0.387935i	−0.481116	+	0.387935i	0.356412	+	0.934329i	$0.384000\pi$
$18$	0.190822	+	0.0439145i	0.190822	+	0.0439145i
$19$	1.44333	−	0.994203i	1.44333	−	0.994203i	0.448383	−	0.893841i	$-0.352000\pi$
$19$	1.44333	−	0.994203i	1.44333	−	0.994203i	0.994951	−	0.100362i	$-0.0320000\pi$
$20$		0			0
$21$		0			0
$22$	0.111215	−	0.979159i	0.111215	−	0.979159i
$23$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$23$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$24$	0.878701	−	0.179093i	0.878701	−	0.179093i
$25$	0.876307	+	0.481754i	0.876307	+	0.481754i
$26$		0			0
$27$	−1.06695	+	0.107624i	−1.06695	+	0.107624i
$28$		0			0
$29$		0			0		0.0878512	−	0.996134i	$-0.472000\pi$
$29$		0			0		−0.0878512	+	0.996134i	$0.528000\pi$
$30$		0			0
$31$		0			0		−0.379779	−	0.925077i	$-0.624000\pi$
$31$		0			0		0.379779	+	0.925077i	$0.376000\pi$
$32$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$33$	0.187355	+	0.863634i	0.187355	+	0.863634i
$34$	−0.0851591	+	0.612139i	−0.0851591	+	0.612139i
$35$		0			0
$36$	0.169165	−	0.0986144i	0.169165	−	0.0986144i
$37$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$37$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$38$	0.371566	−	1.71277i	0.371566	−	1.71277i
$39$		0			0
$40$		0			0
$41$	0.208923	−	0.368970i	0.208923	−	0.368970i	−0.745941	−	0.666012i	$-0.768000\pi$
$41$	0.208923	−	0.368970i	0.208923	−	0.368970i	0.954865	+	0.297042i	$0.0960000\pi$
$42$		0			0
$43$	1.19186	−	1.17698i	1.19186	−	1.17698i	0.212007	−	0.977268i	$-0.432000\pi$
$43$	1.19186	−	1.17698i	1.19186	−	1.17698i	0.979855	−	0.199710i	$-0.0640000\pi$
$44$	−0.589208	−	0.789908i	−0.589208	−	0.789908i
$45$		0			0
$46$		0			0
$47$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$47$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$48$	0.517948	−	0.732066i	0.517948	−	0.732066i
$49$	0.492727	+	0.870184i	0.492727	+	0.870184i
$50$	0.968583	−	0.248690i	0.968583	−	0.248690i
$51$	−0.103853	−	0.544415i	−0.103853	−	0.544415i
$52$		0			0
$53$		0			0		0.888136	−	0.459580i	$-0.152000\pi$
$53$		0			0		−0.888136	+	0.459580i	$0.848000\pi$
$54$	−0.704098	+	0.808831i	−0.704098	+	0.808831i
$55$		0			0
$56$		0			0
$57$	0.177375	+	1.56164i	0.177375	+	1.56164i
$58$		0			0
$59$	0.591287	+	0.476768i	0.591287	+	0.476768i	0.876307	−	0.481754i	$-0.160000\pi$
$59$	0.591287	+	0.476768i	0.591287	+	0.476768i	−0.285019	+	0.958522i	$0.592000\pi$
$60$		0			0
$61$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$61$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$62$		0			0
$63$		0			0
$64$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$65$		0			0
$66$	0.727774	+	0.501308i	0.727774	+	0.501308i
$67$	−1.07242	−	1.17116i	−1.07242	−	1.17116i	−0.984564	−	0.175023i	$-0.944000\pi$
$67$	−1.07242	−	1.17116i	−1.07242	−	1.17116i	−0.0878512	−	0.996134i	$-0.528000\pi$
$68$	0.356960	+	0.504525i	0.356960	+	0.504525i
$69$		0			0
$70$		0			0
$71$		0			0		0.962028	−	0.272952i	$-0.0880000\pi$
$71$		0			0		−0.962028	+	0.272952i	$0.912000\pi$
$72$	0.0558096	−	0.187688i	0.0558096	−	0.187688i
$73$	−0.765896	−	0.372230i	−0.765896	−	0.372230i	0.0125660	−	0.999921i	$-0.496000\pi$
$73$	−0.765896	−	0.372230i	−0.765896	−	0.372230i	−0.778462	+	0.627691i	$0.784000\pi$
$74$		0			0
$75$	−0.751067	+	0.489988i	−0.751067	+	0.489988i
$76$	−0.901614	−	1.50291i	−0.901614	−	1.50291i
$77$		0			0
$78$		0			0
$79$		0			0		−0.656586	−	0.754251i	$-0.728000\pi$
$79$		0			0		0.656586	+	0.754251i	$0.272000\pi$
$80$		0			0
$81$	0.290853	−	0.708469i	0.290853	−	0.708469i
$82$	−0.100279	−	0.411986i	−0.100279	−	0.411986i
$83$	−1.31392	−	0.445247i	−1.31392	−	0.445247i	−0.425779	−	0.904827i	$-0.640000\pi$
$83$	−1.31392	−	0.445247i	−1.31392	−	0.445247i	−0.888136	+	0.459580i	$0.848000\pi$
$84$		0			0
$85$		0			0
$86$	0.0631332	−	1.67387i	0.0631332	−	1.67387i
$87$		0			0
$88$	−0.970244	−	0.172477i	−0.970244	−	0.172477i
$89$	0.655963	+	1.71960i	0.655963	+	1.71960i	0.693653	+	0.720309i	$0.256000\pi$
$89$	0.655963	+	1.71960i	0.655963	+	1.71960i	−0.0376902	+	0.999289i	$0.512000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.123566	−	0.888213i	−0.123566	−	0.888213i
$97$	−1.18977	+	1.59504i	−1.18977	+	1.59504i	−0.514440	+	0.857527i	$0.672000\pi$
$97$	−1.18977	+	1.59504i	−1.18977	+	1.59504i	−0.675333	+	0.737513i	$0.736000\pi$
$98$	0.954865	+	0.297042i	0.954865	+	0.297042i
$99$	0.185635	+	0.0526693i	0.185635	+	0.0526693i
$100$	0.535827	−	0.844328i	0.535827	−	0.844328i
$101$		0			0		0.236499	−	0.971632i	$-0.424000\pi$
$101$		0			0		−0.236499	+	0.971632i	$0.576000\pi$
$102$	−0.448383	−	0.325769i	−0.448383	−	0.325769i
$103$		0			0		0.402906	−	0.915241i	$-0.368000\pi$
$103$		0			0		−0.402906	+	0.915241i	$0.632000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.145848	+	0.290744i	0.145848	+	0.290744i	0.954865	−	0.297042i	$-0.0960000\pi$
$107$	0.145848	+	0.290744i	0.145848	+	0.290744i	−0.809017	+	0.587785i	$0.800000\pi$
$108$	0.0404175	+	1.07160i	0.0404175	+	1.07160i
$109$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$109$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.161209	+	0.496150i	0.161209	+	0.496150i	0.998737	−	0.0502443i	$-0.0160000\pi$
$113$	0.161209	+	0.496150i	0.161209	+	0.496150i	−0.837528	+	0.546394i	$0.816000\pi$
$114$	1.19832	+	1.01697i	1.19832	+	1.01697i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.757400	−	0.0572151i	0.757400	−	0.0572151i
$119$		0			0
$120$		0			0
$121$	−0.00469681	+	0.0284946i	−0.00469681	+	0.0284946i
$122$		0			0
$123$	0.203744	+	0.321049i	0.203744	+	0.321049i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.947098	−	0.320944i	$-0.104000\pi$
$127$		0			0		−0.947098	+	0.320944i	$0.896000\pi$
$128$	0.535827	+	0.844328i	0.535827	+	0.844328i
$129$	0.428137	+	1.43983i	0.428137	+	1.43983i
$130$		0			0
$131$	−1.85720	−	0.0934320i	−1.85720	−	0.0934320i	−0.910106	−	0.414376i	$-0.864000\pi$
$131$	−1.85720	−	0.0934320i	−1.85720	−	0.0934320i	−0.947098	+	0.320944i	$0.896000\pi$
$132$	0.873694	−	0.132758i	0.873694	−	0.132758i
$133$		0			0
$134$	−1.58347	−	0.119618i	−1.58347	−	0.119618i
$135$		0			0
$136$	0.605584	+	0.123428i	0.605584	+	0.123428i
$137$	−1.35431	−	1.14935i	−1.35431	−	1.14935i	−0.974527	−	0.224271i	$-0.928000\pi$
$137$	−1.35431	−	1.14935i	−1.35431	−	1.14935i	−0.379779	−	0.925077i	$-0.624000\pi$
$138$		0			0
$139$	−0.747469	−	0.572310i	−0.747469	−	0.572310i	0.162637	−	0.986686i	$-0.448000\pi$
$139$	−0.747469	−	0.572310i	−0.747469	−	0.572310i	−0.910106	+	0.414376i	$0.864000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.0877979	−	0.175023i	−0.0877979	−	0.175023i
$145$		0			0
$146$	−0.813123	+	0.252948i	−0.813123	+	0.252948i
$147$	−0.896483	+	0.0225358i	−0.896483	+	0.0225358i
$148$		0			0
$149$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$149$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$150$	−0.212084	+	0.871327i	−0.212084	+	0.871327i
$151$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$151$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$152$	−1.68606	−	0.478379i	−1.68606	−	0.478379i
$153$	−0.115555	−	0.0359471i	−0.115555	−	0.0359471i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$157$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.272957	−	0.715554i	−0.272957	−	0.715554i
$163$	0.172990	+	0.0307520i	0.172990	+	0.0307520i	0.260842	−	0.965382i	$-0.416000\pi$
$163$	0.172990	+	0.0307520i	0.172990	+	0.0307520i	−0.0878512	+	0.996134i	$0.528000\pi$
$164$	−0.355124	−	0.231679i	−0.355124	−	0.231679i
$165$		0			0
$166$	−1.26260	+	0.574866i	−1.26260	+	0.574866i
$167$		0			0		−0.470704	−	0.882291i	$-0.656000\pi$
$167$		0			0		0.470704	+	0.882291i	$0.344000\pi$
$168$		0			0
$169$	−0.236499	−	0.971632i	−0.236499	−	0.971632i
$170$		0			0
$171$	0.319080	+	0.126333i	0.319080	+	0.126333i
$172$	−1.09982	−	1.26341i	−1.09982	−	1.26341i
$173$		0			0		−0.920232	−	0.391374i	$-0.872000\pi$
$173$		0			0		0.920232	+	0.391374i	$0.128000\pi$
$174$		0			0
$175$		0			0
$176$	−0.825346	+	0.538447i	−0.825346	+	0.538447i
$177$	−0.626813	+	0.266583i	−0.626813	+	0.266583i
$178$	1.65532	+	0.804496i	1.65532	+	0.804496i
$179$	−0.535114	+	1.79959i	−0.535114	+	1.79959i	0.0627905	+	0.998027i	$0.480000\pi$
$179$	−0.535114	+	1.79959i	−0.535114	+	1.79959i	−0.597905	+	0.801567i	$0.704000\pi$
$180$		0			0
$181$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$181$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.114124	+	0.598257i	−0.114124	+	0.598257i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.693653	−	0.720309i	$-0.744000\pi$
$191$		0			0		0.693653	+	0.720309i	$0.256000\pi$
$192$	−0.698099	−	0.562893i	−0.698099	−	0.562893i
$193$	−0.292246	−	0.371913i	−0.292246	−	0.371913i	0.617860	−	0.786288i	$-0.288000\pi$
$193$	−0.292246	−	0.371913i	−0.292246	−	0.371913i	−0.910106	+	0.414376i	$0.864000\pi$
$194$	0.224573	+	1.97719i	0.224573	+	1.97719i
$195$		0			0
$196$	0.899405	−	0.437116i	0.899405	−	0.437116i
$197$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$197$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$198$	0.171376	−	0.0886814i	0.171376	−	0.0886814i
$199$		0			0		−0.745941	−	0.666012i	$-0.768000\pi$
$199$		0			0		0.745941	+	0.666012i	$0.232000\pi$
$200$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$201$	1.37931	−	0.354146i	1.37931	−	0.354146i
$202$		0			0
$203$		0			0
$204$	−0.549862	+	0.0694637i	−0.549862	+	0.0694637i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.450505	−	1.66733i	0.450505	−	1.66733i
$210$		0			0
$211$	0.829867	+	1.76356i	0.829867	+	1.76356i	0.617860	+	0.786288i	$0.288000\pi$
$211$	0.829867	+	1.76356i	0.829867	+	1.76356i	0.212007	+	0.977268i	$0.432000\pi$
$212$		0			0
$213$		0			0
$214$	0.305346	+	0.112103i	0.305346	+	0.112103i
$215$		0			0
$216$	0.763024	+	0.753495i	0.763024	+	0.753495i
$217$		0			0
$218$		0			0
$219$	0.617805	−	0.448862i	0.617805	−	0.448862i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.556876	−	0.830596i	$-0.312000\pi$
$223$		0			0		−0.556876	+	0.830596i	$0.688000\pi$
$224$		0			0
$225$	0.0172021	+	0.195053i	0.0172021	+	0.195053i
$226$	0.457154	+	0.251323i	0.457154	+	0.251323i
$227$	−1.24917	+	0.254600i	−1.24917	+	0.254600i	−0.778462	−	0.627691i	$-0.784000\pi$
$227$	−1.24917	+	0.254600i	−1.24917	+	0.254600i	−0.470704	+	0.882291i	$0.656000\pi$
$228$	1.56970	−	0.0789682i	1.56970	−	0.0789682i
$229$		0			0		0.112856	−	0.993611i	$-0.464000\pi$
$229$		0			0		−0.112856	+	0.993611i	$0.536000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.694666	−	0.159866i	−0.694666	−	0.159866i	−0.137790	−	0.990461i	$-0.544000\pi$
$233$	−0.694666	−	0.159866i	−0.694666	−	0.159866i	−0.556876	+	0.830596i	$0.688000\pi$
$234$		0			0
$235$		0			0
$236$	0.512955	−	0.560184i	0.512955	−	0.560184i
$237$		0			0
$238$		0			0
$239$		0			0		−0.850994	−	0.525175i	$-0.824000\pi$
$239$		0			0		0.850994	+	0.525175i	$0.176000\pi$
$240$		0			0
$241$	−1.68606	+	0.926921i	−1.68606	+	0.926921i	−0.711536	+	0.702650i	$0.752000\pi$
$241$	−1.68606	+	0.926921i	−1.68606	+	0.926921i	−0.974527	+	0.224271i	$0.928000\pi$
$242$	0.0160820	+	0.0239868i	0.0160820	+	0.0239868i
$243$	−0.245775	−	0.297091i	−0.245775	−	0.297091i
$244$		0			0
$245$		0			0
$246$	0.368296	+	0.0945623i	0.368296	+	0.0945623i
$247$		0			0
$248$		0			0
$249$	0.906903	−	0.851638i	0.906903	−	0.851638i
$250$		0			0
$251$	−0.863923	+	0.503623i	−0.863923	+	0.503623i
$251$	−0.863923	+	0.503623i	−0.863923	+	0.503623i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.968583	+	0.248690i	0.968583	+	0.248690i
$257$	0.397753	+	1.47210i	0.397753	+	1.47210i	0.823533	+	0.567269i	$0.192000\pi$
$257$	0.397753	+	1.47210i	0.397753	+	1.47210i	−0.425779	+	0.904827i	$0.640000\pi$
$258$	1.29773	+	0.756510i	1.29773	+	0.756510i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.41780	+	1.20323i	−1.41780	+	1.20323i
$263$		0			0		−0.850994	−	0.525175i	$-0.824000\pi$
$263$		0			0		0.850994	+	0.525175i	$0.176000\pi$
$264$	0.546017	−	0.694861i	0.546017	−	0.694861i
$265$		0			0
$266$		0			0
$267$	−1.63745	−	0.206858i	−1.63745	−	0.206858i
$268$	−1.23618	+	0.996762i	−1.23618	+	0.996762i
$269$		0			0		−0.974527	−	0.224271i	$-0.928000\pi$
$269$		0			0		0.974527	+	0.224271i	$0.0720000\pi$
$270$		0			0
$271$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$271$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$272$	0.525944	−	0.324576i	0.525944	−	0.324576i
$273$		0			0
$274$	−1.77403	+	0.0892476i	−1.77403	+	0.0892476i
$275$	0.965603	−	0.196805i	0.965603	−	0.196805i
$276$		0			0
$277$		0			0		−0.0878512	−	0.996134i	$-0.528000\pi$
$277$		0			0		0.0878512	+	0.996134i	$0.472000\pi$
$278$	−0.936655	+	0.0944813i	−0.936655	+	0.0944813i
$279$		0			0
$280$		0			0
$281$	−0.0187471	−	1.49176i	−0.0187471	−	1.49176i	−0.675333	−	0.737513i	$-0.736000\pi$
$281$	−0.0187471	−	1.49176i	−0.0187471	−	1.49176i	0.656586	−	0.754251i	$-0.272000\pi$
$282$		0			0
$283$	1.55659	−	1.13093i	1.55659	−	1.13093i	0.617860	−	0.786288i	$-0.288000\pi$
$283$	1.55659	−	1.13093i	1.55659	−	1.13093i	0.938734	−	0.344643i	$-0.112000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.183813	−	0.0674845i	−0.183813	−	0.0674845i
$289$	−0.131028	+	0.603985i	−0.131028	+	0.603985i
$290$		0			0
$291$	−0.759794	−	1.61464i	−0.759794	−	1.61464i
$292$	−0.419586	+	0.741012i	−0.419586	+	0.741012i
$293$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$293$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$294$	−0.638081	+	0.630113i	−0.638081	+	0.630113i
$295$		0			0
$296$		0			0
$297$	−0.733028	+	0.761197i	−0.733028	+	0.761197i
$298$		0			0
$299$		0			0
$300$	0.441861	+	0.780352i	0.441861	+	0.780352i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−1.55656	+	0.805466i	−1.55656	+	0.805466i
$305$		0			0
$306$	−0.108844	+	0.0528985i	−0.108844	+	0.0528985i
$307$	0.200974	+	1.21927i	0.200974	+	1.21927i	0.876307	+	0.481754i	$0.160000\pi$
$307$	0.200974	+	1.21927i	0.200974	+	1.21927i	−0.675333	+	0.737513i	$0.736000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.693653	−	0.720309i	$-0.744000\pi$
$311$		0			0		0.693653	+	0.720309i	$0.256000\pi$
$312$		0			0
$313$	1.77385	+	0.807640i	1.77385	+	0.807640i	0.979855	+	0.199710i	$0.0640000\pi$
$313$	1.77385	+	0.807640i	1.77385	+	0.807640i	0.793990	+	0.607930i	$0.208000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.823533	−	0.567269i	$-0.808000\pi$
$317$		0			0		0.823533	+	0.567269i	$0.192000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.291603	−	0.00733033i	−0.291603	−	0.00733033i
$322$		0			0
$323$	−0.308726	+	1.03825i	−0.308726	+	1.03825i
$324$	−0.688808	−	0.334764i	−0.688808	−	0.334764i
$325$		0			0
$326$	0.147156	−	0.0960028i	0.147156	−	0.0960028i
$327$		0			0
$328$	−0.417469	+	0.0742123i	−0.417469	+	0.0742123i
$329$		0			0
$330$		0			0
$331$	0.439782	+	0.174122i	0.439782	+	0.174122i	0.577573	−	0.816339i	$-0.304000\pi$
$331$	0.439782	+	0.174122i	0.439782	+	0.174122i	−0.137790	+	0.990461i	$0.544000\pi$
$332$	−0.526870	+	1.28337i	−0.526870	+	1.28337i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.0509068	−	1.34971i	0.0509068	−	1.34971i	−0.711536	−	0.702650i	$-0.752000\pi$
$337$	0.0509068	−	1.34971i	0.0509068	−	1.34971i	0.762443	−	0.647056i	$-0.224000\pi$
$338$	−0.837528	−	0.546394i	−0.837528	−	0.546394i
$339$	−0.460607	−	0.0818807i	−0.460607	−	0.0818807i
$340$		0			0
$341$		0			0
$342$	0.319080	−	0.126333i	0.319080	−	0.126333i
$343$		0			0
$344$	−1.66660	−	0.168112i	−1.66660	−	0.168112i
$345$		0			0
$346$		0			0
$347$	−0.234518	−	1.68575i	−0.234518	−	1.68575i	−0.637424	−	0.770513i	$-0.720000\pi$
$347$	−0.234518	−	1.68575i	−0.234518	−	1.68575i	0.402906	−	0.915241i	$-0.368000\pi$
$348$		0			0
$349$		0			0		−0.954865	−	0.297042i	$-0.904000\pi$
$349$		0			0		0.954865	+	0.297042i	$0.0960000\pi$
$350$		0			0
$351$		0			0
$352$	−0.233059	+	0.957499i	−0.233059	+	0.957499i
$353$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i	0.535827	−	0.844328i	$-0.320000\pi$
$353$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i	−0.637424	+	0.770513i	$0.720000\pi$
$354$	−0.274438	+	0.623413i	−0.274438	+	0.623413i
$355$		0			0
$356$	1.75739	−	0.546694i	1.75739	−	0.546694i
$357$		0			0
$358$	0.841825	+	1.67816i	0.841825	+	1.67816i
$359$		0			0		−0.0376902	−	0.999289i	$-0.512000\pi$
$359$		0			0		0.0376902	+	0.999289i	$0.488000\pi$
$360$		0			0
$361$	0.738362	−	1.93561i	0.738362	−	1.93561i
$362$		0			0
$363$	−0.0205626	−	0.0157440i	−0.0205626	−	0.0157440i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.988652	−	0.150226i	$-0.952000\pi$
$367$		0			0		0.988652	+	0.150226i	$0.0480000\pi$
$368$		0			0
$369$	0.0827903	−	0.00625410i	0.0827903	−	0.00625410i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.285019	−	0.958522i	$-0.592000\pi$
$373$		0			0		0.285019	+	0.958522i	$0.408000\pi$
$374$	0.326342	+	0.514233i	0.326342	+	0.514233i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.07132	−	1.68812i	−1.07132	−	1.68812i	−0.556876	−	0.830596i	$-0.688000\pi$
$379$	−1.07132	−	1.68812i	−1.07132	−	1.68812i	−0.514440	−	0.857527i	$-0.672000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.988652	−	0.150226i	$-0.0480000\pi$
$383$		0			0		−0.988652	+	0.150226i	$0.952000\pi$
$384$	−0.894219	+	0.0675506i	−0.894219	+	0.0675506i
$385$		0			0
$386$	−0.467630	−	0.0710564i	−0.467630	−	0.0710564i
$387$	0.321385	+	0.0655034i	0.321385	+	0.0655034i
$388$	1.51719	+	1.28758i	1.51719	+	1.28758i
$389$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$389$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$390$		0			0
$391$		0			0
$392$	0.356412	−	0.934329i	0.356412	−	0.934329i
$393$	0.857871	−	1.43000i	0.857871	−	1.43000i
$394$		0			0
$395$		0			0
$396$	0.0642215	−	0.181961i	0.0642215	−	0.181961i
$397$		0			0		0.954865	−	0.297042i	$-0.0960000\pi$
$397$		0			0		−0.954865	+	0.297042i	$0.904000\pi$
$398$		0			0
$399$		0			0
$400$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$401$	−0.00594371	+	0.0244191i	−0.00594371	+	0.0244191i	−0.974527	−	0.224271i	$-0.928000\pi$
$401$	−0.00594371	+	0.0244191i	−0.00594371	+	0.0244191i	0.968583	+	0.248690i	$0.0800000\pi$
$402$	0.763043	−	1.20236i	0.763043	−	1.20236i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.353281	+	0.427043i	−0.353281	+	0.427043i
$409$	1.78973	+	0.180532i	1.78973	+	0.180532i	0.938734	−	0.344643i	$-0.112000\pi$
$409$	1.78973	+	0.180532i	1.78973	+	0.180532i	0.850994	+	0.525175i	$0.176000\pi$
$410$		0			0
$411$	1.48104	−	0.586386i	1.48104	−	0.586386i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.768332	−	0.349825i	0.768332	−	0.349825i
$418$	−0.812963	−	1.52382i	−0.812963	−	1.52382i
$419$	−1.70365	−	0.577317i	−1.70365	−	0.577317i	−0.711536	−	0.702650i	$-0.752000\pi$
$419$	−1.70365	−	0.577317i	−1.70365	−	0.577317i	−0.992115	+	0.125333i	$0.960000\pi$
$420$		0			0
$421$		0			0		0.379779	−	0.925077i	$-0.376000\pi$
$421$		0			0		−0.379779	+	0.925077i	$0.624000\pi$
$422$	1.81218	+	0.717495i	1.81218	+	0.717495i
$423$		0			0
$424$		0			0
$425$	−0.608494	+	0.108170i	−0.608494	+	0.108170i
$426$		0			0
$427$		0			0
$428$	0.299328	−	0.127304i	0.299328	−	0.127304i
$429$		0			0
$430$		0			0
$431$		0			0		0.962028	−	0.272952i	$-0.0880000\pi$
$431$		0			0		−0.962028	+	0.272952i	$0.912000\pi$
$432$	1.07202	+	0.0269486i	1.07202	+	0.0269486i
$433$	−0.456288	+	0.969661i	−0.456288	+	0.969661i	0.535827	+	0.844328i	$0.320000\pi$
$433$	−0.456288	+	0.969661i	−0.456288	+	0.969661i	−0.992115	+	0.125333i	$0.960000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.143094	−	0.750123i	0.143094	−	0.750123i
$439$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$439$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$440$		0			0
$441$	−0.0877979	+	0.175023i	−0.0877979	+	0.175023i
$442$		0			0
$443$	1.25958	+	1.01563i	1.25958	+	1.01563i	0.998737	+	0.0502443i	$0.0160000\pi$
$443$	1.25958	+	1.01563i	1.25958	+	1.01563i	0.260842	+	0.965382i	$0.416000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.244753	−	0.126651i	0.244753	−	0.126651i	−0.332820	−	0.942991i	$-0.608000\pi$
$449$	0.244753	−	0.126651i	0.244753	−	0.126651i	0.577573	+	0.816339i	$0.304000\pi$
$450$	0.146063	+	0.130412i	0.146063	+	0.130412i
$451$	−0.0782967	−	0.410446i	−0.0782967	−	0.410446i
$452$	0.505293	−	0.129737i	0.505293	−	0.129737i
$453$		0			0
$454$	−0.736317	+	1.04071i	−0.736317	+	1.04071i
$455$		0			0
$456$	1.09020	−	1.13210i	1.09020	−	1.13210i
$457$	−0.485230	−	1.37482i	−0.485230	−	1.37482i	−0.888136	−	0.459580i	$-0.848000\pi$
$457$	−0.485230	−	1.37482i	−0.485230	−	1.37482i	0.402906	−	0.915241i	$-0.368000\pi$
$458$		0			0
$459$	0.471575	−	0.465686i	0.471575	−	0.465686i
$460$		0			0
$461$		0			0		0.492727	−	0.870184i	$-0.336000\pi$
$461$		0			0		−0.492727	+	0.870184i	$0.664000\pi$
$462$		0			0
$463$		0			0		−0.402906	−	0.915241i	$-0.632000\pi$
$463$		0			0		0.402906	+	0.915241i	$0.368000\pi$
$464$		0			0
$465$		0			0
$466$	−0.615825	+	0.358995i	−0.615825	+	0.358995i
$467$	1.34779	+	1.33096i	1.34779	+	1.33096i	0.899405	+	0.437116i	$0.144000\pi$
$467$	1.34779	+	1.33096i	1.34779	+	1.33096i	0.448383	+	0.893841i	$0.352000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.00954464	−	0.759498i	−0.00954464	−	0.759498i
$473$	0.145015	−	1.64431i	0.145015	−	1.64431i
$474$		0			0
$475$	1.74376	−	0.175895i	1.74376	−	0.175895i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$479$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$480$		0			0
$481$		0			0
$482$	−0.594566	+	1.82989i	−0.594566	+	1.82989i
$483$		0			0
$484$	0.0281434	+	0.00647673i	0.0281434	+	0.00647673i
$485$		0			0
$486$	−0.382535	−	0.0483254i	−0.382535	−	0.0483254i
$487$		0			0		0.675333	−	0.737513i	$-0.264000\pi$
$487$		0			0		−0.675333	+	0.737513i	$0.736000\pi$
$488$		0			0
$489$	−0.0973524	+	0.123891i	−0.0973524	+	0.123891i
$490$		0			0
$491$	−1.31738	+	1.11801i	−1.31738	+	1.11801i	−0.332820	+	0.942991i	$0.608000\pi$
$491$	−1.31738	+	1.11801i	−1.31738	+	1.11801i	−0.984564	+	0.175023i	$0.944000\pi$
$492$	0.333208	−	0.183183i	0.333208	−	0.183183i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.0781171	−	1.24164i	0.0781171	−	1.24164i
$499$	0.313319	−	0.587288i	0.313319	−	0.587288i	−0.675333	−	0.737513i	$-0.736000\pi$
$499$	0.313319	−	0.587288i	0.313319	−	0.587288i	0.988652	+	0.150226i	$0.0480000\pi$
$500$		0			0
$501$		0			0
$502$	−0.285019	+	0.958522i	−0.285019	+	0.958522i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.868593	+	0.223017i	0.868593	+	0.223017i
$508$		0			0
$509$		0			0		−0.863923	−	0.503623i	$-0.832000\pi$
$509$		0			0		0.863923	+	0.503623i	$0.168000\pi$
$510$		0			0
$511$		0			0
$512$	0.876307	−	0.481754i	0.876307	−	0.481754i
$513$	−1.43296	+	1.21610i	−1.43296	+	1.21610i
$514$	1.29767	+	0.800831i	1.29767	+	0.800831i
$515$		0			0
$516$	1.46387	−	0.336885i	1.46387	−	0.336885i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.54616	−	1.06503i	1.54616	−	1.06503i	0.577573	−	0.816339i	$-0.304000\pi$
$521$	1.54616	−	1.06503i	1.54616	−	1.06503i	0.968583	−	0.248690i	$-0.0800000\pi$
$522$		0			0
$523$	1.62517	−	1.00294i	1.62517	−	1.00294i	0.656586	−	0.754251i	$-0.272000\pi$
$523$	1.62517	−	1.00294i	1.62517	−	1.00294i	0.968583	−	0.248690i	$-0.0800000\pi$
$524$	−0.209862	+	1.84767i	−0.209862	+	1.84767i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.0776361	−	0.880306i	−0.0776361	−	0.880306i
$529$	0.994951	−	0.100362i	0.994951	−	0.100362i
$530$		0			0
$531$	−0.0130660	+	0.148154i	−0.0130660	+	0.148154i
$532$		0			0
$533$		0			0
$534$	−1.33526	+	0.970120i	−1.33526	+	0.970120i
$535$		0			0
$536$	−0.218808	+	1.57283i	−0.218808	+	1.57283i
$537$	−1.19798	−	1.18302i	−1.19798	−	1.18302i
$538$		0			0
$539$	0.925080	+	0.339630i	0.925080	+	0.339630i
$540$		0			0
$541$		0			0		−0.402906	−	0.915241i	$-0.632000\pi$
$541$		0			0		0.402906	+	0.915241i	$0.368000\pi$
$542$		0			0
$543$		0			0
$544$	0.161209	−	0.596639i	0.161209	−	0.596639i
$545$		0			0
$546$		0			0
$547$	0.221538	+	0.627691i	0.221538	+	0.627691i	1.00000			$0$
$547$	0.221538	+	0.627691i	0.221538	+	0.627691i	−0.778462	+	0.627691i	$0.784000\pi$
$548$	−1.23212	+	1.27947i	−1.23212	+	1.27947i
$549$		0			0
$550$	0.569172	−	0.804465i	0.569172	−	0.804465i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.618115	+	0.710058i	−0.618115	+	0.710058i
$557$		0			0		0.899405	−	0.437116i	$-0.144000\pi$
$557$		0			0		−0.899405	+	0.437116i	$0.856000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.425173	−	0.342827i	−0.425173	−	0.342827i
$562$	−1.03485	−	1.07462i	−1.03485	−	1.07462i
$563$	−0.571620	+	1.13951i	−0.571620	+	1.13951i	0.402906	+	0.915241i	$0.368000\pi$
$563$	−0.571620	+	1.13951i	−0.571620	+	1.13951i	−0.974527	+	0.224271i	$0.928000\pi$
$564$		0			0
$565$		0			0
$566$	0.360532	−	1.88998i	0.360532	−	1.88998i
$567$		0			0
$568$		0			0
$569$	−1.02980	−	1.12462i	−1.02980	−	1.12462i	−0.992115	−	0.125333i	$-0.960000\pi$
$569$	−1.02980	−	1.12462i	−1.02980	−	1.12462i	−0.0376902	−	0.999289i	$-0.512000\pi$
$570$		0			0
$571$	−0.0961038	+	0.204231i	−0.0961038	+	0.204231i	−0.947098	−	0.320944i	$-0.896000\pi$
$571$	−0.0961038	+	0.204231i	−0.0961038	+	0.204231i	0.850994	+	0.525175i	$0.176000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.180191	+	0.0766349i	−0.180191	+	0.0766349i
$577$	1.67453	−	1.09244i	1.67453	−	1.09244i	0.823533	−	0.567269i	$-0.192000\pi$
$577$	1.67453	−	1.09244i	1.67453	−	1.09244i	0.850994	−	0.525175i	$-0.176000\pi$
$578$	0.317941	+	0.529981i	0.317941	+	0.529981i
$579$	0.417621	−	0.0742393i	0.417621	−	0.0742393i
$580$		0			0
$581$		0			0
$582$	−1.65917	−	0.656910i	−1.65917	−	0.656910i
$583$		0			0
$584$	0.201393	+	0.827401i	0.201393	+	0.827401i
$585$		0			0
$586$		0			0
$587$	−1.19513	+	0.544146i	−1.19513	+	0.544146i	−0.910106	−	0.414376i	$-0.864000\pi$
$587$	−1.19513	+	0.544146i	−1.19513	+	0.544146i	−0.285019	+	0.958522i	$0.592000\pi$
$588$	−0.0337993	+	0.896129i	−0.0337993	+	0.896129i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.302432	+	0.119741i	−0.302432	+	0.119741i	−0.514440	−	0.857527i	$-0.672000\pi$
$593$	−0.302432	+	0.119741i	−0.302432	+	0.119741i	0.212007	+	0.977268i	$0.432000\pi$
$594$	−0.0132793	+	1.05668i	−0.0132793	+	1.05668i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$599$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$600$	0.856290	+	0.266377i	0.856290	+	0.266377i
$601$	0.360532	+	0.102292i	0.360532	+	0.102292i	0.448383	−	0.893841i	$-0.352000\pi$
$601$	0.360532	+	0.102292i	0.360532	+	0.102292i	−0.0878512	+	0.996134i	$0.528000\pi$
$602$		0			0
$603$	0.0735376	−	0.302122i	0.0735376	−	0.302122i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.954865	−	0.297042i	$-0.0960000\pi$
$607$		0			0		−0.954865	+	0.297042i	$0.904000\pi$
$608$	−0.583304	+	1.65270i	−0.583304	+	1.65270i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.0431320	+	0.113070i	−0.0431320	+	0.113070i
$613$		0			0		0.745941	−	0.666012i	$-0.232000\pi$
$613$		0			0		−0.745941	+	0.666012i	$0.768000\pi$
$614$	0.981149	+	0.751231i	0.981149	+	0.751231i
$615$		0			0
$616$		0			0
$617$	−1.95414	−	0.398285i	−1.95414	−	0.398285i	−0.992115	−	0.125333i	$-0.960000\pi$
$617$	−1.95414	−	0.398285i	−1.95414	−	0.398285i	−0.962028	−	0.272952i	$-0.912000\pi$
$618$		0			0
$619$	−0.710799	−	0.0536947i	−0.710799	−	0.0536947i	−0.285019	−	0.958522i	$-0.592000\pi$
$619$	−0.710799	−	0.0536947i	−0.710799	−	0.0536947i	−0.425779	+	0.904827i	$0.640000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.535827	+	0.844328i	0.535827	+	0.844328i
$626$	1.84595	−	0.625536i	1.84595	−	0.625536i
$627$	1.12904	+	1.06024i	1.12904	+	1.06024i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.285019	−	0.958522i	$-0.592000\pi$
$631$		0			0		0.285019	+	0.958522i	$0.408000\pi$
$632$		0			0
$633$	−1.74564	−	0.0878193i	−1.74564	−	0.0878193i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.53809	+	1.17766i	1.53809	+	1.17766i	0.920232	+	0.391374i	$0.128000\pi$
$641$	1.53809	+	1.17766i	1.53809	+	1.17766i	0.617860	+	0.786288i	$0.288000\pi$
$642$	−0.217587	+	0.194272i	−0.217587	+	0.194272i
$643$	0.411708	−	1.07929i	0.411708	−	1.07929i	−0.556876	−	0.830596i	$-0.688000\pi$
$643$	0.411708	−	1.07929i	0.411708	−	1.07929i	0.968583	−	0.248690i	$-0.0800000\pi$
$644$		0			0
$645$		0			0
$646$	0.485677	+	0.968186i	0.485677	+	0.968186i
$647$		0			0		0.332820	−	0.942991i	$-0.392000\pi$
$647$		0			0		−0.332820	+	0.942991i	$0.608000\pi$
$648$	−0.731282	+	0.227489i	−0.731282	+	0.227489i
$649$	0.748274	−	0.0188101i	0.748274	−	0.0188101i
$650$		0			0
$651$		0			0
$652$	0.0415534	−	0.170718i	0.0415534	−	0.170718i
$653$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$653$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$654$		0			0
$655$		0			0
$656$	−0.253520	+	0.339876i	−0.253520	+	0.339876i
$657$	−0.0229757	−	0.165153i	−0.0229757	−	0.165153i
$658$		0			0
$659$	1.18532	−	1.43281i	1.18532	−	1.43281i	0.309017	−	0.951057i	$-0.400000\pi$
$659$	1.18532	−	1.43281i	1.18532	−	1.43281i	0.876307	−	0.481754i	$-0.160000\pi$
$660$		0			0
$661$		0			0		0.0125660	−	0.999921i	$-0.496000\pi$
$661$		0			0		−0.0125660	+	0.999921i	$0.504000\pi$
$662$	0.439782	−	0.174122i	0.439782	−	0.174122i
$663$		0			0
$664$	0.494453	+	1.29620i	0.494453	+	1.29620i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.956628	+	0.378756i	0.956628	+	0.378756i	0.793990	−	0.607930i	$-0.208000\pi$
$673$	0.956628	+	0.378756i	0.956628	+	0.378756i	0.162637	+	0.986686i	$0.448000\pi$
$674$	−0.886828	−	1.01874i	−0.886828	−	1.01874i
$675$	−0.986822	−	0.419694i	−0.986822	−	0.419694i
$676$	−0.984564	+	0.175023i	−0.984564	+	0.175023i
$677$		0			0		−0.514440	−	0.857527i	$-0.672000\pi$
$677$		0			0		0.514440	+	0.857527i	$0.328000\pi$
$678$	−0.391819	+	0.255618i	−0.391819	+	0.255618i
$679$		0			0
$680$		0			0
$681$	0.325846	−	1.09582i	0.325846	−	1.09582i
$682$		0			0
$683$	1.81964	+	0.0457421i	1.81964	+	0.0457421i	0.920232	−	0.391374i	$-0.128000\pi$
$683$	1.81964	+	0.0457421i	1.81964	+	0.0457421i	0.899405	+	0.437116i	$0.144000\pi$
$684$	0.146119	−	0.310518i	0.146119	−	0.310518i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−1.32998	+	1.01832i	−1.32998	+	1.01832i
$689$		0			0
$690$		0			0
$691$	−0.733375	−	0.333909i	−0.733375	−	0.333909i	0.0125660	−	0.999921i	$-0.496000\pi$
$691$	−0.733375	−	0.333909i	−0.733375	−	0.333909i	−0.745941	+	0.666012i	$0.768000\pi$
$692$		0			0
$693$		0			0
$694$	−1.32493	−	1.06832i	−1.32493	−	1.06832i
$695$		0			0
$696$		0			0
$697$	0.0426199	+	0.258566i	0.0426199	+	0.258566i
$698$		0			0
$699$	0.419714	−	0.482145i	0.419714	−	0.482145i
$700$		0			0
$701$		0			0		−0.745941	−	0.666012i	$-0.768000\pi$
$701$		0			0		0.745941	+	0.666012i	$0.232000\pi$
$702$		0			0
$703$		0			0
$704$	0.485560	+	0.857527i	0.485560	+	0.857527i
$705$		0			0
$706$	−0.124591	+	0.0157395i	−0.124591	+	0.0157395i
$707$		0			0
$708$	0.226699	+	0.642315i	0.226699	+	0.642315i
$709$		0			0		−0.597905	−	0.801567i	$-0.704000\pi$
$709$		0			0		0.597905	+	0.801567i	$0.296000\pi$
$710$		0			0
$711$		0			0
$712$	0.906847	−	1.60154i	0.906847	−	1.60154i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.76244	+	0.647056i	1.76244	+	0.647056i
$717$		0			0
$718$		0			0
$719$		0			0		0.137790	−	0.990461i	$-0.456000\pi$
$719$		0			0		−0.137790	+	0.990461i	$0.544000\pi$
$720$		0			0
$721$		0			0
$722$	−0.786771	−	1.91644i	−0.786771	−	1.91644i
$723$	−0.0216818	−	1.72529i	−0.0216818	−	1.72529i
$724$		0			0
$725$		0			0
$726$	−0.0257670	+	0.00259915i	−0.0257670	+	0.00259915i
$727$		0			0		−0.0878512	−	0.996134i	$-0.528000\pi$
$727$		0			0		0.0878512	+	0.996134i	$0.472000\pi$
$728$		0			0
$729$	1.08923	−	0.222001i	1.08923	−	0.222001i
$730$		0			0
$731$	−0.116834	+	1.02863i	−0.116834	+	1.02863i
$732$		0			0
$733$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$733$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.55254	−	0.196132i	−1.55254	−	0.196132i
$738$	0.0560703	−	0.0612329i	0.0560703	−	0.0612329i
$739$	1.77385	−	0.408220i	1.77385	−	0.408220i	0.793990	−	0.607930i	$-0.208000\pi$
$739$	1.77385	−	0.408220i	1.77385	−	0.408220i	0.979855	+	0.199710i	$0.0640000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$743$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.0708572	−	0.262244i	−0.0708572	−	0.262244i
$748$	0.589910	+	0.151463i	0.589910	+	0.151463i
$749$		0			0
$750$		0			0
$751$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$751$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$752$		0			0
$753$	−0.0337993	−	0.896129i	−0.0337993	−	0.896129i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$757$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$758$	−1.93655	−	0.497223i	−1.93655	−	0.497223i
$759$		0			0
$760$		0			0
$761$	−0.884303	−	1.06894i	−0.884303	−	1.06894i	−0.997159	−	0.0753268i	$-0.976000\pi$
$761$	−0.884303	−	1.06894i	−0.884303	−	1.06894i	0.112856	−	0.993611i	$-0.464000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.605616	+	0.661377i	−0.605616	+	0.661377i
$769$	−1.94426	−	0.245617i	−1.94426	−	0.245617i	−0.947098	−	0.320944i	$-0.896000\pi$
$769$	−1.94426	−	0.245617i	−1.94426	−	0.245617i	−0.997159	+	0.0753268i	$0.976000\pi$
$770$		0			0
$771$	−1.33263	−	0.306683i	−1.33263	−	0.306683i
$772$	−0.389529	+	0.268317i	−0.389529	+	0.268317i
$773$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$773$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$774$	0.279120	−	0.172253i	0.279120	−	0.172253i
$775$		0			0
$776$	1.98739	−	0.0999813i	1.98739	−	0.0999813i
$777$		0			0
$778$		0			0
$779$	−0.0652851	−	0.740260i	−0.0652851	−	0.740260i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.379779	−	0.925077i	−0.379779	−	0.925077i
$785$		0			0
$786$	−0.353540	−	1.62968i	−0.353540	−	1.62968i
$787$	0.214529	−	1.54207i	0.214529	−	1.54207i	−0.514440	−	0.857527i	$-0.672000\pi$
$787$	0.214529	−	1.54207i	0.214529	−	1.54207i	0.728969	−	0.684547i	$-0.240000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.0777456	−	0.176607i	−0.0777456	−	0.176607i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.597905	−	0.801567i	$-0.704000\pi$
$797$		0			0		0.597905	+	0.801567i	$0.296000\pi$
$798$		0			0
$799$		0			0
$800$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$801$	−0.208146	+	0.294193i	−0.208146	+	0.294193i
$802$	0.0123833	+	0.0218695i	0.0123833	+	0.0218695i
$803$	−0.812808	+	0.208694i	−0.812808	+	0.208694i
$804$	−0.266840	−	1.39882i	−0.266840	−	1.39882i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.318722	+	1.93362i	0.318722	+	1.93362i	0.356412	+	0.934329i	$0.384000\pi$
$809$	0.318722	+	1.93362i	0.318722	+	1.93362i	−0.0376902	+	0.999289i	$0.512000\pi$
$810$		0			0
$811$	−0.108559	−	0.138153i	−0.108559	−	0.138153i	0.728969	−	0.684547i	$-0.240000\pi$
$811$	−0.108559	−	0.138153i	−0.108559	−	0.138153i	−0.837528	+	0.546394i	$0.816000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.0348005	+	0.553138i	0.0348005	+	0.553138i
$817$	0.550100	−	2.88373i	0.550100	−	2.88373i
$818$	1.42824	−	1.09355i	1.42824	−	1.09355i
$819$		0			0
$820$		0			0
$821$		0			0		−0.577573	−	0.816339i	$-0.696000\pi$
$821$		0			0		0.577573	+	0.816339i	$0.304000\pi$
$822$	0.678225	−	1.44130i	0.678225	−	1.44130i
$823$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$823$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$824$		0			0
$825$	−0.251878	+	0.847067i	−0.251878	+	0.847067i
$826$		0			0
$827$	−1.74310	+	0.741339i	−1.74310	+	0.741339i	−0.745941	+	0.666012i	$0.768000\pi$
$827$	−1.74310	+	0.741339i	−1.74310	+	0.741339i	−0.997159	+	0.0753268i	$0.976000\pi$
$828$		0			0
$829$		0			0		−0.514440	−	0.857527i	$-0.672000\pi$
$829$		0			0		0.514440	+	0.857527i	$0.328000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.574633	−	0.227513i	−0.574633	−	0.227513i
$834$	0.320618	−	0.780971i	0.320618	−	0.780971i
$835$		0			0
$836$	−1.63575	−	0.554308i	−1.63575	−	0.554308i
$837$		0			0
$838$	−1.63711	+	0.745383i	−1.63711	+	0.745383i
$839$		0			0		0.0376902	−	0.999289i	$-0.488000\pi$
$839$		0			0		−0.0376902	+	0.999289i	$0.512000\pi$
$840$		0			0
$841$	−0.984564	−	0.175023i	−0.984564	−	0.175023i
$842$		0			0
$843$	1.18821	+	0.614858i	1.18821	+	0.614858i
$844$	1.81218	−	0.717495i	1.81218	−	0.717495i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.237747	+	1.70897i	0.237747	+	1.70897i
$850$	−0.369526	+	0.495396i	−0.369526	+	0.495396i
$851$		0			0
$852$		0			0
$853$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$853$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$854$		0			0
$855$		0			0
$856$	0.131055	−	0.297704i	0.131055	−	0.297704i
$857$	0.175647	−	0.00441542i	0.175647	−	0.00441542i	0.0627905	−	0.998027i	$-0.480000\pi$
$857$	0.175647	−	0.00441542i	0.175647	−	0.00441542i	0.112856	+	0.993611i	$0.464000\pi$
$858$		0			0
$859$	−0.437049	+	1.23831i	−0.437049	+	1.23831i	0.492727	+	0.870184i	$0.336000\pi$
$859$	−0.437049	+	1.23831i	−0.437049	+	1.23831i	−0.929776	+	0.368125i	$0.880000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$863$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$864$	0.799919	−	0.714206i	0.799919	−	0.714206i
$865$		0			0
$866$	0.331159	+	1.01920i	0.331159	+	1.01920i
$867$	−0.422570	−	0.358619i	−0.422570	−	0.358619i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.389151	−	0.0195773i	−0.389151	−	0.0195773i
$874$		0			0
$875$		0			0
$876$	−0.409184	−	0.644770i	−0.409184	−	0.644770i
$877$		0			0		0.947098	−	0.320944i	$-0.104000\pi$
$877$		0			0		−0.947098	+	0.320944i	$0.896000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.975318	−	1.53686i	−0.975318	−	1.53686i	−0.837528	−	0.546394i	$-0.816000\pi$
$881$	−0.975318	−	1.53686i	−0.975318	−	1.53686i	−0.137790	−	0.990461i	$-0.544000\pi$
$882$	0.0558096	+	0.187688i	0.0558096	+	0.187688i
$883$	−0.138495	+	0.840221i	−0.138495	+	0.840221i	0.823533	+	0.567269i	$0.192000\pi$
$883$	−0.138495	+	0.840221i	−0.138495	+	0.840221i	−0.962028	+	0.272952i	$0.912000\pi$
$884$		0			0
$885$		0			0
$886$	1.61344	−	0.121881i	1.61344	−	0.121881i
$887$		0			0		−0.997159	−	0.0753268i	$-0.976000\pi$
$887$		0			0		0.997159	+	0.0753268i	$0.0240000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.233218	−	0.717771i	−0.233218	−	0.717771i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.0917186	−	0.259870i	0.0917186	−	0.259870i
$899$		0			0
$900$	0.195748	−	0.00492072i	0.195748	−	0.00492072i
$901$		0			0
$902$	−0.338045	−	0.245604i	−0.338045	−	0.245604i
$903$		0			0
$904$	0.279532	−	0.440472i	0.279532	−	0.440472i
$905$		0			0
$906$		0			0
$907$	−0.690667	+	0.925926i	−0.690667	+	0.925926i	−0.999684	−	0.0251301i	$-0.992000\pi$
$907$	−0.690667	+	0.925926i	−0.690667	+	0.925926i	0.309017	+	0.951057i	$0.400000\pi$
$908$	0.175662	+	1.26269i	0.175662	+	1.26269i
$909$		0			0
$910$		0			0
$911$		0			0		−0.994951	−	0.100362i	$-0.968000\pi$
$911$		0			0		0.994951	+	0.100362i	$0.0320000\pi$
$912$	0.0197499	−	1.57156i	0.0197499	−	1.57156i
$913$	−1.27112	+	0.503273i	−1.27112	+	0.503273i
$914$	−1.29485	−	0.670039i	−1.29485	−	0.670039i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.0249794	−	0.662285i	0.0249794	−	0.662285i
$919$		0			0		0.910106	−	0.414376i	$-0.136000\pi$
$919$		0			0		−0.910106	+	0.414376i	$0.864000\pi$
$920$		0			0
$921$	−1.04953	−	0.355654i	−1.04953	−	0.355654i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.03495	+	0.675190i	−1.03495	+	0.675190i	−0.947098	−	0.320944i	$-0.896000\pi$
$929$	−1.03495	+	0.675190i	−1.03495	+	0.675190i	−0.0878512	+	0.996134i	$0.528000\pi$
$930$		0			0
$931$	1.57631	+	0.766095i	1.57631	+	0.766095i
$932$	−0.203169	+	0.683257i	−0.203169	+	0.683257i
$933$		0			0
$934$	1.89360	+	0.0476013i	1.89360	+	0.0476013i
$935$		0			0
$936$		0			0
$937$	1.22925	+	1.34243i	1.22925	+	1.34243i	0.920232	+	0.391374i	$0.128000\pi$
$937$	1.22925	+	1.34243i	1.22925	+	1.34243i	0.309017	+	0.951057i	$0.400000\pi$
$938$		0			0
$939$	−1.38777	+	1.06257i	−1.38777	+	1.06257i
$940$		0			0
$941$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$941$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$942$		0			0
$943$		0			0
$944$	−0.526870	−	0.547117i	−0.526870	−	0.547117i
$945$		0			0
$946$	−1.01990	−	1.29792i	−1.01990	−	1.29792i
$947$	−0.223933	−	1.97155i	−0.223933	−	1.97155i	−0.236499	−	0.971632i	$-0.576000\pi$
$947$	−0.223933	−	1.97155i	−0.223933	−	1.97155i	0.0125660	−	0.999921i	$-0.496000\pi$
$948$		0			0
$949$		0			0
$950$	1.15074	−	1.32191i	1.15074	−	1.32191i
$951$		0			0
$952$		0			0
$953$	−0.133570	−	0.700198i	−0.133570	−	0.700198i	−0.984564	−	0.175023i	$-0.944000\pi$
$953$	−0.133570	−	0.700198i	−0.133570	−	0.700198i	0.850994	−	0.525175i	$-0.176000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.711536	+	0.702650i	−0.711536	+	0.702650i
$962$		0			0
$963$	−0.0313828	+	0.0554237i	−0.0313828	+	0.0554237i
$964$	0.819223	+	1.74094i	0.819223	+	1.74094i
$965$		0			0
$966$		0			0
$967$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$967$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$968$	0.0249493	−	0.0145442i	0.0249493	−	0.0145442i
$969$	−0.691153	−	0.682522i	−0.691153	−	0.682522i
$970$		0			0
$971$	−0.0794523	−	0.366244i	−0.0794523	−	0.366244i	0.920232	−	0.391374i	$-0.128000\pi$
$971$	−0.0794523	−	0.366244i	−0.0794523	−	0.366244i	−0.999684	+	0.0251301i	$0.992000\pi$
$972$	−0.311937	+	0.226635i	−0.311937	+	0.226635i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.936655	+	0.0944813i	−0.936655	+	0.0944813i	−0.556876	−	0.830596i	$-0.688000\pi$
$977$	−0.936655	+	0.0944813i	−0.936655	+	0.0944813i	−0.379779	+	0.925077i	$0.624000\pi$
$978$	0.0138422	+	0.156955i	0.0138422	+	0.156955i
$979$	1.58935	+	0.873754i	1.58935	+	0.873754i
$980$		0			0
$981$		0			0
$982$	−0.194999	+	1.71681i	−0.194999	+	1.71681i
$983$		0			0		0.850994	−	0.525175i	$-0.176000\pi$
$983$		0			0		−0.850994	+	0.525175i	$0.824000\pi$
$984$	0.117501	−	0.361631i	0.117501	−	0.361631i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.617860	−	0.786288i	$-0.288000\pi$
$991$		0			0		−0.617860	+	0.786288i	$0.712000\pi$
$992$		0			0
$993$	−0.323404	+	0.274461i	−0.323404	+	0.274461i
$994$		0			0
$995$		0			0
$996$	−0.793013	−	0.958588i	−0.793013	−	0.958588i
$997$		0			0		−0.863923	−	0.503623i	$-0.832000\pi$
$997$		0			0		0.863923	+	0.503623i	$0.168000\pi$
$998$	−0.173626	−	0.642596i	−0.173626	−	0.642596i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.67.1	✓	100
8.3	odd	2	CM	2008.1.bd.a.67.1	✓	100
251.15	even	125	inner	2008.1.bd.a.1019.1	yes	100
2008.1019	odd	250	inner	2008.1.bd.a.1019.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.67.1	✓	100	1.1	even	1	trivial
2008.1.bd.a.67.1	✓	100	8.3	odd	2	CM
2008.1.bd.a.1019.1	yes	100	251.15	even	125	inner
2008.1.bd.a.1019.1	yes	100	2008.1019	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)

\(f(q)\)	\(=\)	\(q+(0.728969 - 0.684547i) q^{2} +(-0.422111 + 0.791209i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(0.233914 + 0.865722i) q^{6} +(-0.637424 - 0.770513i) q^{8} +(0.109042 + 0.162639i) q^{9} +O(q^{10})\)	\(q+(0.728969 - 0.684547i) q^{2} +(-0.422111 + 0.791209i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(0.233914 + 0.865722i) q^{6} +(-0.637424 - 0.770513i) q^{8} +(0.109042 + 0.162639i) q^{9} +(0.751353 - 0.637644i) q^{11} +(0.763143 + 0.470959i) q^{12} +(-0.992115 - 0.125333i) q^{16} +(-0.481116 + 0.387935i) q^{17} +(0.190822 + 0.0439145i) q^{18} +(1.44333 - 0.994203i) q^{19} +(0.111215 - 0.979159i) q^{22} +(0.878701 - 0.179093i) q^{24} +(0.876307 + 0.481754i) q^{25} +(-1.06695 + 0.107624i) q^{27} +(-0.809017 + 0.587785i) q^{32} +(0.187355 + 0.863634i) q^{33} +(-0.0851591 + 0.612139i) q^{34} +(0.169165 - 0.0986144i) q^{36} +(0.371566 - 1.71277i) q^{38} +(0.208923 - 0.368970i) q^{41} +(1.19186 - 1.17698i) q^{43} +(-0.589208 - 0.789908i) q^{44} +(0.517948 - 0.732066i) q^{48} +(0.492727 + 0.870184i) q^{49} +(0.968583 - 0.248690i) q^{50} +(-0.103853 - 0.544415i) q^{51} +(-0.704098 + 0.808831i) q^{54} +(0.177375 + 1.56164i) q^{57} +(0.591287 + 0.476768i) q^{59} +(-0.187381 + 0.982287i) q^{64} +(0.727774 + 0.501308i) q^{66} +(-1.07242 - 1.17116i) q^{67} +(0.356960 + 0.504525i) q^{68} +(0.0558096 - 0.187688i) q^{72} +(-0.765896 - 0.372230i) q^{73} +(-0.751067 + 0.489988i) q^{75} +(-0.901614 - 1.50291i) q^{76} +(0.290853 - 0.708469i) q^{81} +(-0.100279 - 0.411986i) q^{82} +(-1.31392 - 0.445247i) q^{83} +(0.0631332 - 1.67387i) q^{86} +(-0.970244 - 0.172477i) q^{88} +(0.655963 + 1.71960i) q^{89} +(-0.123566 - 0.888213i) q^{96} +(-1.18977 + 1.59504i) q^{97} +(0.954865 + 0.297042i) q^{98} +(0.185635 + 0.0526693i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 100 * q	\( 100 q - 25 q^{22} - 25 q^{32}+O(q^{100}) \) 100 * q - 25 * q^22 - 25 * q^32

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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