LMFDB - Embedded newform 2008.1.bd.a.395.1

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			395.1
Root			$-0.448383 + 0.893841i$ of defining polynomial
Character	$\chi$	$=$	2008.395
Dual form			2008.1.bd.a.1947.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535827 - 0.844328i) q^{2} +(-1.44523 - 1.10656i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-1.70869 + 0.627323i) q^{6} +(-0.992115 - 0.125333i) q^{8} +(0.603371 + 2.23309i) q^{9} +O(q^{10})$	\(q+(0.535827 - 0.844328i) q^{2} +(-1.44523 - 1.10656i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-1.70869 + 0.627323i) q^{6} +(-0.992115 - 0.125333i) q^{8} +(0.603371 + 2.23309i) q^{9} +(0.131055 + 0.297704i) q^{11} +(-0.385898 + 1.77884i) q^{12} +(-0.637424 + 0.770513i) q^{16} +(-0.999718 + 1.27224i) q^{17} +(2.20877 + 0.687108i) q^{18} +(-1.28989 + 1.33945i) q^{19} +(0.321583 + 0.0488645i) q^{22} +(1.29515 + 1.27897i) q^{24} +(-0.929776 + 0.368125i) q^{25} +(0.907767 - 2.21117i) q^{27} +(0.309017 + 0.951057i) q^{32} +(0.140024 - 0.575272i) q^{33} +(0.538513 + 1.52579i) q^{34} +(1.76366 - 1.49675i) q^{36} +(0.439782 + 1.80680i) q^{38} +(-0.0769271 + 0.466700i) q^{41} +(-0.948035 - 1.67428i) q^{43} +(0.213570 - 0.245339i) q^{44} +(1.77385 - 0.408220i) q^{48} +(0.162637 + 0.986686i) q^{49} +(-0.187381 + 0.982287i) q^{50} +(2.85264 - 0.732433i) q^{51} +(-1.38054 - 1.95126i) q^{54} +(3.34637 - 0.508481i) q^{57} +(-1.06757 - 1.35859i) q^{59} +(0.968583 + 0.248690i) q^{64} +(-0.410690 - 0.426472i) q^{66} +(-0.882924 - 1.76009i) q^{67} +(1.57682 + 0.362878i) q^{68} +(-0.318733 - 2.29111i) q^{72} +(0.103420 + 0.0712382i) q^{73} +(1.75109 + 0.496830i) q^{75} +(1.76118 + 0.596812i) q^{76} +(-1.76032 + 1.02618i) q^{81} +(0.352829 + 0.315022i) q^{82} +(0.175647 + 1.99164i) q^{83} +(-1.92163 - 0.0966728i) q^{86} +(-0.0927094 - 0.311783i) q^{88} +(-0.000947233 + 0.0251142i) q^{89} +(0.605802 - 1.71644i) q^{96} +(-0.498715 - 0.572898i) q^{97} +(0.920232 + 0.391374i) q^{98} +(-0.585727 + 0.472285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{111}{125}\right)$	$-1$	$-1$

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 $

$2$	0.535827	−	0.844328i	0.535827	−	0.844328i
$2$	0.535827	−	0.844328i	0.535827	−	0.844328i
$3$	−1.44523	−	1.10656i	−1.44523	−	1.10656i	−0.974527	−	0.224271i	$-0.928000\pi$
$3$	−1.44523	−	1.10656i	−1.44523	−	1.10656i	−0.470704	−	0.882291i	$-0.656000\pi$
$4$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$5$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$5$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$6$	−1.70869	+	0.627323i	−1.70869	+	0.627323i
$7$		0			0		−0.762443	−	0.647056i	$-0.776000\pi$
$7$		0			0		0.762443	+	0.647056i	$0.224000\pi$
$8$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$9$	0.603371	+	2.23309i	0.603371	+	2.23309i
$10$		0			0
$11$	0.131055	+	0.297704i	0.131055	+	0.297704i	0.968583	−	0.248690i	$-0.0800000\pi$
$11$	0.131055	+	0.297704i	0.131055	+	0.297704i	−0.837528	+	0.546394i	$0.816000\pi$
$12$	−0.385898	+	1.77884i	−0.385898	+	1.77884i
$13$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$13$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$14$		0			0
$15$		0			0
$16$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$17$	−0.999718	+	1.27224i	−0.999718	+	1.27224i	−0.0376902	+	0.999289i	$0.512000\pi$
$17$	−0.999718	+	1.27224i	−0.999718	+	1.27224i	−0.962028	+	0.272952i	$0.912000\pi$
$18$	2.20877	+	0.687108i	2.20877	+	0.687108i
$19$	−1.28989	+	1.33945i	−1.28989	+	1.33945i	−0.379779	+	0.925077i	$0.624000\pi$
$19$	−1.28989	+	1.33945i	−1.28989	+	1.33945i	−0.910106	+	0.414376i	$0.864000\pi$
$20$		0			0
$21$		0			0
$22$	0.321583	+	0.0488645i	0.321583	+	0.0488645i
$23$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$23$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$24$	1.29515	+	1.27897i	1.29515	+	1.27897i
$25$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$26$		0			0
$27$	0.907767	−	2.21117i	0.907767	−	2.21117i
$28$		0			0
$29$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$29$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$30$		0			0
$31$		0			0		−0.863923	−	0.503623i	$-0.832000\pi$
$31$		0			0		0.863923	+	0.503623i	$0.168000\pi$
$32$	0.309017	+	0.951057i	0.309017	+	0.951057i
$33$	0.140024	−	0.575272i	0.140024	−	0.575272i
$34$	0.538513	+	1.52579i	0.538513	+	1.52579i
$35$		0			0
$36$	1.76366	−	1.49675i	1.76366	−	1.49675i
$37$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$37$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$38$	0.439782	+	1.80680i	0.439782	+	1.80680i
$39$		0			0
$40$		0			0
$41$	−0.0769271	+	0.466700i	−0.0769271	+	0.466700i	0.920232	+	0.391374i	$0.128000\pi$
$41$	−0.0769271	+	0.466700i	−0.0769271	+	0.466700i	−0.997159	+	0.0753268i	$0.976000\pi$
$42$		0			0
$43$	−0.948035	−	1.67428i	−0.948035	−	1.67428i	−0.711536	−	0.702650i	$-0.752000\pi$
$43$	−0.948035	−	1.67428i	−0.948035	−	1.67428i	−0.236499	−	0.971632i	$-0.576000\pi$
$44$	0.213570	−	0.245339i	0.213570	−	0.245339i
$45$		0			0
$46$		0			0
$47$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$47$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$48$	1.77385	−	0.408220i	1.77385	−	0.408220i
$49$	0.162637	+	0.986686i	0.162637	+	0.986686i
$50$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$51$	2.85264	−	0.732433i	2.85264	−	0.732433i
$52$		0			0
$53$		0			0		−0.112856	−	0.993611i	$-0.536000\pi$
$53$		0			0		0.112856	+	0.993611i	$0.464000\pi$
$54$	−1.38054	−	1.95126i	−1.38054	−	1.95126i
$55$		0			0
$56$		0			0
$57$	3.34637	−	0.508481i	3.34637	−	0.508481i
$58$		0			0
$59$	−1.06757	−	1.35859i	−1.06757	−	1.35859i	−0.929776	−	0.368125i	$-0.880000\pi$
$59$	−1.06757	−	1.35859i	−1.06757	−	1.35859i	−0.137790	−	0.990461i	$-0.544000\pi$
$60$		0			0
$61$		0			0		0.910106	−	0.414376i	$-0.136000\pi$
$61$		0			0		−0.910106	+	0.414376i	$0.864000\pi$
$62$		0			0
$63$		0			0
$64$	0.968583	+	0.248690i	0.968583	+	0.248690i
$65$		0			0
$66$	−0.410690	−	0.426472i	−0.410690	−	0.426472i
$67$	−0.882924	−	1.76009i	−0.882924	−	1.76009i	−0.597905	−	0.801567i	$-0.704000\pi$
$67$	−0.882924	−	1.76009i	−0.882924	−	1.76009i	−0.285019	−	0.958522i	$-0.592000\pi$
$68$	1.57682	+	0.362878i	1.57682	+	0.362878i
$69$		0			0
$70$		0			0
$71$		0			0		−0.778462	−	0.627691i	$-0.784000\pi$
$71$		0			0		0.778462	+	0.627691i	$0.216000\pi$
$72$	−0.318733	−	2.29111i	−0.318733	−	2.29111i
$73$	0.103420	+	0.0712382i	0.103420	+	0.0712382i	0.617860	−	0.786288i	$-0.288000\pi$
$73$	0.103420	+	0.0712382i	0.103420	+	0.0712382i	−0.514440	+	0.857527i	$0.672000\pi$
$74$		0			0
$75$	1.75109	+	0.496830i	1.75109	+	0.496830i
$76$	1.76118	+	0.596812i	1.76118	+	0.596812i
$77$		0			0
$78$		0			0
$79$		0			0		0.577573	−	0.816339i	$-0.304000\pi$
$79$		0			0		−0.577573	+	0.816339i	$0.696000\pi$
$80$		0			0
$81$	−1.76032	+	1.02618i	−1.76032	+	1.02618i
$82$	0.352829	+	0.315022i	0.352829	+	0.315022i
$83$	0.175647	+	1.99164i	0.175647	+	1.99164i	0.112856	+	0.993611i	$0.464000\pi$
$83$	0.175647	+	1.99164i	0.175647	+	1.99164i	0.0627905	+	0.998027i	$0.480000\pi$
$84$		0			0
$85$		0			0
$86$	−1.92163	−	0.0966728i	−1.92163	−	0.0966728i
$87$		0			0
$88$	−0.0927094	−	0.311783i	−0.0927094	−	0.311783i
$89$	−0.000947233		0.0251142i	−0.000947233		0.0251142i	−0.999684	−	0.0251301i	$-0.992000\pi$
$89$	−0.000947233		0.0251142i	−0.000947233		0.0251142i	0.998737	+	0.0502443i	$0.0160000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.605802	−	1.71644i	0.605802	−	1.71644i
$97$	−0.498715	−	0.572898i	−0.498715	−	0.572898i	0.448383	−	0.893841i	$-0.352000\pi$
$97$	−0.498715	−	0.572898i	−0.498715	−	0.572898i	−0.947098	+	0.320944i	$0.896000\pi$
$98$	0.920232	+	0.391374i	0.920232	+	0.391374i
$99$	−0.585727	+	0.472285i	−0.585727	+	0.472285i
$100$	0.728969	+	0.684547i	0.728969	+	0.684547i
$101$		0			0		0.745941	−	0.666012i	$-0.232000\pi$
$101$		0			0		−0.745941	+	0.666012i	$0.768000\pi$
$102$	0.910106	−	2.80102i	0.910106	−	2.80102i
$103$		0			0		−0.850994	−	0.525175i	$-0.824000\pi$
$103$		0			0		0.850994	+	0.525175i	$0.176000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.22925	+	0.559683i	1.22925	+	0.559683i	0.920232	−	0.391374i	$-0.128000\pi$
$107$	1.22925	+	0.559683i	1.22925	+	0.559683i	0.309017	+	0.951057i	$0.400000\pi$
$108$	−2.38723	+	0.120097i	−2.38723	+	0.120097i
$109$		0			0		0.947098	−	0.320944i	$-0.104000\pi$
$109$		0			0		−0.947098	+	0.320944i	$0.896000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.51890	−	1.10355i	−1.51890	−	1.10355i	−0.962028	−	0.272952i	$-0.912000\pi$
$113$	−1.51890	−	1.10355i	−1.51890	−	1.10355i	−0.556876	−	0.830596i	$-0.688000\pi$
$114$	1.36375	−	3.09789i	1.36375	−	3.09789i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.71912	+	0.173410i	−1.71912	+	0.173410i
$119$		0			0
$120$		0			0
$121$	0.603880	−	0.659482i	0.603880	−	0.659482i
$122$		0			0
$123$	0.627610	−	0.589365i	0.627610	−	0.589365i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.0878512	−	0.996134i	$-0.472000\pi$
$127$		0			0		−0.0878512	+	0.996134i	$0.528000\pi$
$128$	0.728969	−	0.684547i	0.728969	−	0.684547i
$129$	−0.482568	+	3.46878i	−0.482568	+	3.46878i
$130$		0			0
$131$	−0.975988	+	1.45571i	−0.975988	+	1.45571i	−0.0878512	+	0.996134i	$0.528000\pi$
$131$	−0.975988	+	1.45571i	−0.975988	+	1.45571i	−0.888136	+	0.459580i	$0.848000\pi$
$132$	−0.580141	+	0.118242i	−0.580141	+	0.118242i
$133$		0			0
$134$	−1.95919	−	0.197625i	−1.95919	−	0.197625i
$135$		0			0
$136$	1.15129	−	1.13691i	1.15129	−	1.13691i
$137$	0.0909411	−	0.206582i	0.0909411	−	0.206582i	−0.863923	−	0.503623i	$-0.832000\pi$
$137$	0.0909411	−	0.206582i	0.0909411	−	0.206582i	0.954865	+	0.297042i	$0.0960000\pi$
$138$		0			0
$139$	−1.56347	+	0.277933i	−1.56347	+	0.277933i	−0.888136	−	0.459580i	$-0.848000\pi$
$139$	−1.56347	+	0.277933i	−1.56347	+	0.277933i	−0.675333	+	0.737513i	$0.736000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−2.10523	−	0.958522i	−2.10523	−	0.958522i
$145$		0			0
$146$	0.115564	−	0.0491491i	0.115564	−	0.0491491i
$147$	0.856781	−	1.60596i	0.856781	−	1.60596i
$148$		0			0
$149$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$149$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$150$	1.35777	−	1.21228i	1.35777	−	1.21228i
$151$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$151$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$152$	1.44759	−	1.16723i	1.44759	−	1.16723i
$153$	−3.44423	−	1.46483i	−3.44423	−	1.46483i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$157$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.0767972	+	2.03614i	−0.0767972	+	2.03614i
$163$	0.340829	+	1.14621i	0.340829	+	1.14621i	0.938734	+	0.344643i	$0.112000\pi$
$163$	0.340829	+	1.14621i	0.340829	+	1.14621i	−0.597905	+	0.801567i	$0.704000\pi$
$164$	0.455037	−	0.129106i	0.455037	−	0.129106i
$165$		0			0
$166$	1.77571	+	0.918869i	1.77571	+	0.918869i
$167$		0			0		0.793990	−	0.607930i	$-0.208000\pi$
$167$		0			0		−0.793990	+	0.607930i	$0.792000\pi$
$168$		0			0
$169$	−0.745941	−	0.666012i	−0.745941	−	0.666012i
$170$		0			0
$171$	−3.76940	−	2.07225i	−3.76940	−	2.07225i
$172$	−1.11128	+	1.57068i	−1.11128	+	1.57068i
$173$		0			0		0.0125660	−	0.999921i	$-0.496000\pi$
$173$		0			0		−0.0125660	+	0.999921i	$0.504000\pi$
$174$		0			0
$175$		0			0
$176$	−0.312923	−	0.0887843i	−0.312923	−	0.0887843i
$177$	0.0395208	+	3.14480i	0.0395208	+	3.14480i
$178$	0.0206971	+	0.0142566i	0.0206971	+	0.0142566i
$179$	0.230806	+	1.65908i	0.230806	+	1.65908i	0.656586	+	0.754251i	$0.272000\pi$
$179$	0.230806	+	1.65908i	0.230806	+	1.65908i	−0.425779	+	0.904827i	$0.640000\pi$
$180$		0			0
$181$		0			0		−0.470704	−	0.882291i	$-0.656000\pi$
$181$		0			0		0.470704	+	0.882291i	$0.344000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.509770	−	0.130887i	−0.509770	−	0.130887i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$191$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$192$	−1.12464	−	1.43121i	−1.12464	−	1.43121i
$193$	−0.531725	−	1.39391i	−0.531725	−	1.39391i	−0.888136	−	0.459580i	$-0.848000\pi$
$193$	−0.531725	−	1.39391i	−0.531725	−	1.39391i	0.356412	−	0.934329i	$-0.384000\pi$
$194$	−0.750939	+	0.114105i	−0.750939	+	0.114105i
$195$		0			0
$196$	0.823533	−	0.567269i	0.823533	−	0.567269i
$197$		0			0		−0.577573	−	0.816339i	$-0.696000\pi$
$197$		0			0		0.577573	+	0.816339i	$0.304000\pi$
$198$	0.0849149	+	0.747608i	0.0849149	+	0.747608i
$199$		0			0		0.997159	−	0.0753268i	$-0.0240000\pi$
$199$		0			0		−0.997159	+	0.0753268i	$0.976000\pi$
$200$	0.968583	−	0.248690i	0.968583	−	0.248690i
$201$	−0.671618	+	3.52074i	−0.671618	+	3.52074i
$202$		0			0
$203$		0			0
$204$	−1.87732	−	2.26929i	−1.87732	−	2.26929i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.567807	−	0.208462i	−0.567807	−	0.208462i
$210$		0			0
$211$	0.119913	+	1.90596i	0.119913	+	1.90596i	0.356412	+	0.934329i	$0.384000\pi$
$211$	0.119913	+	1.90596i	0.119913	+	1.90596i	−0.236499	+	0.971632i	$0.576000\pi$
$212$		0			0
$213$		0			0
$214$	1.13122	−	0.737996i	1.13122	−	0.737996i
$215$		0			0
$216$	−1.17774	+	2.07996i	−1.17774	+	2.07996i
$217$		0			0
$218$		0			0
$219$	−0.0706364	−	0.217396i	−0.0706364	−	0.217396i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$223$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$224$		0			0
$225$	−1.38306	−	1.85416i	−1.38306	−	1.85416i
$226$	−1.74563	+	0.691142i	−1.74563	+	0.691142i
$227$	1.41185	+	1.39422i	1.41185	+	1.39422i	0.793990	+	0.607930i	$0.208000\pi$
$227$	1.41185	+	1.39422i	1.41185	+	1.39422i	0.617860	+	0.786288i	$0.288000\pi$
$228$	−1.88490	−	2.81138i	−1.88490	−	2.81138i
$229$		0			0		−0.988652	−	0.150226i	$-0.952000\pi$
$229$		0			0		0.988652	+	0.150226i	$0.0480000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.0719780	−	0.0223911i	−0.0719780	−	0.0223911i	0.260842	−	0.965382i	$-0.416000\pi$
$233$	−0.0719780	−	0.0223911i	−0.0719780	−	0.0223911i	−0.332820	+	0.942991i	$0.608000\pi$
$234$		0			0
$235$		0			0
$236$	−0.774738	+	1.54442i	−0.774738	+	1.54442i
$237$		0			0
$238$		0			0
$239$		0			0		0.212007	−	0.977268i	$-0.432000\pi$
$239$		0			0		−0.212007	+	0.977268i	$0.568000\pi$
$240$		0			0
$241$	1.44759	+	0.573142i	1.44759	+	0.573142i	0.954865	−	0.297042i	$-0.0960000\pi$
$241$	1.44759	+	0.573142i	1.44759	+	0.573142i	0.492727	+	0.870184i	$0.336000\pi$
$242$	−0.233244	−	0.863241i	−0.233244	−	0.863241i
$243$	1.30820	+	0.165264i	1.30820	+	0.165264i
$244$		0			0
$245$		0			0
$246$	−0.161327	−	0.845707i	−0.161327	−	0.845707i
$247$		0			0
$248$		0			0
$249$	1.95002	−	3.07274i	1.95002	−	3.07274i
$250$		0			0
$251$	0.762443	−	0.647056i	0.762443	−	0.647056i
$251$	0.762443	−	0.647056i	0.762443	−	0.647056i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$257$	0.756444	−	0.277718i	0.756444	−	0.277718i	0.0627905	−	0.998027i	$-0.480000\pi$
$257$	0.756444	−	0.277718i	0.756444	−	0.277718i	0.693653	+	0.720309i	$0.256000\pi$
$258$	2.67022	+	2.26611i	2.67022	+	2.26611i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.706139	+	1.60406i	0.706139	+	1.60406i
$263$		0			0		0.212007	−	0.977268i	$-0.432000\pi$
$263$		0			0		−0.212007	+	0.977268i	$0.568000\pi$
$264$	−0.211020	+	0.553186i	−0.211020	+	0.553186i
$265$		0			0
$266$		0			0
$267$	0.0291594	−	0.0352477i	0.0291594	−	0.0352477i
$268$	−1.21665	+	1.54830i	−1.21665	+	1.54830i
$269$		0			0		−0.954865	−	0.297042i	$-0.904000\pi$
$269$		0			0		0.954865	+	0.297042i	$0.0960000\pi$
$270$		0			0
$271$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$271$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$272$	−0.343035	−	1.58125i	−0.343035	−	1.58125i
$273$		0			0
$274$	−0.125694	−	0.187476i	−0.125694	−	0.187476i
$275$	−0.231444	−	0.228554i	−0.231444	−	0.228554i
$276$		0			0
$277$		0			0		−0.597905	−	0.801567i	$-0.704000\pi$
$277$		0			0		0.597905	+	0.801567i	$0.296000\pi$
$278$	−0.603082	+	1.46900i	−0.603082	+	1.46900i
$279$		0			0
$280$		0			0
$281$	1.02596	+	1.71018i	1.02596	+	1.71018i	0.577573	+	0.816339i	$0.304000\pi$
$281$	1.02596	+	1.71018i	1.02596	+	1.71018i	0.448383	+	0.893841i	$0.352000\pi$
$282$		0			0
$283$	−0.481116	−	1.48072i	−0.481116	−	1.48072i	−0.837528	−	0.546394i	$-0.816000\pi$
$283$	−0.481116	−	1.48072i	−0.481116	−	1.48072i	0.356412	−	0.934329i	$-0.384000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.93735	+	1.26390i	−1.93735	+	1.26390i
$289$	−0.382663	−	1.57213i	−0.382663	−	1.57213i
$290$		0			0
$291$	0.0868115	+	1.37983i	0.0868115	+	1.37983i
$292$	0.0204241	−	0.123909i	0.0204241	−	0.123909i
$293$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$293$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$294$	−0.896868	−	1.58392i	−0.896868	−	1.58392i
$295$		0			0
$296$		0			0
$297$	0.777242	−	0.0195383i	0.777242	−	0.0195383i
$298$		0			0
$299$		0			0
$300$	−0.296034	−	1.79598i	−0.296034	−	1.79598i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.209862	−	1.84767i	−0.209862	−	1.84767i
$305$		0			0
$306$	−3.08231	+	2.12317i	−3.08231	+	2.12317i
$307$	−0.481393	−	0.525717i	−0.481393	−	0.525717i	0.448383	−	0.893841i	$-0.352000\pi$
$307$	−0.481393	−	0.525717i	−0.481393	−	0.525717i	−0.929776	+	0.368125i	$0.880000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$311$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$312$		0			0
$313$	−1.69610	+	0.877673i	−1.69610	+	0.877673i	−0.711536	+	0.702650i	$0.752000\pi$
$313$	−1.69610	+	0.877673i	−1.69610	+	0.877673i	−0.984564	+	0.175023i	$0.944000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.693653	−	0.720309i	$-0.744000\pi$
$317$		0			0		0.693653	+	0.720309i	$0.256000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.15722	−	2.16911i	−1.15722	−	2.16911i
$322$		0			0
$323$	−0.414586	−	2.98012i	−0.414586	−	2.98012i
$324$	1.67802	+	1.15586i	1.67802	+	1.15586i
$325$		0			0
$326$	1.15040	+	0.326399i	1.15040	+	0.326399i
$327$		0			0
$328$	0.134814	−	0.453379i	0.134814	−	0.453379i
$329$		0			0
$330$		0			0
$331$	−1.30735	−	0.718720i	−1.30735	−	0.718720i	−0.332820	−	0.942991i	$-0.608000\pi$
$331$	−1.30735	−	0.718720i	−1.30735	−	0.718720i	−0.974527	+	0.224271i	$0.928000\pi$
$332$	1.72730	−	1.00693i	1.72730	−	1.00693i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.895634	+	0.0450574i	0.895634	+	0.0450574i	0.492727	−	0.870184i	$-0.336000\pi$
$337$	0.895634	+	0.0450574i	0.895634	+	0.0450574i	0.402906	+	0.915241i	$0.368000\pi$
$338$	−0.962028	+	0.272952i	−0.962028	+	0.272952i
$339$	0.974022	+	3.27564i	0.974022	+	3.27564i
$340$		0			0
$341$		0			0
$342$	−3.76940	+	2.07225i	−3.76940	+	2.07225i
$343$		0			0
$344$	0.730716	+	1.77990i	0.730716	+	1.77990i
$345$		0			0
$346$		0			0
$347$	−0.141120	+	0.399841i	−0.141120	+	0.399841i	−0.992115	−	0.125333i	$-0.960000\pi$
$347$	−0.141120	+	0.399841i	−0.141120	+	0.399841i	0.850994	+	0.525175i	$0.176000\pi$
$348$		0			0
$349$		0			0		−0.920232	−	0.391374i	$-0.872000\pi$
$349$		0			0		0.920232	+	0.391374i	$0.128000\pi$
$350$		0			0
$351$		0			0
$352$	−0.242636	+	0.216637i	−0.242636	+	0.216637i
$353$	−0.263146	+	0.809880i	−0.263146	+	0.809880i	0.728969	+	0.684547i	$0.240000\pi$
$353$	−0.263146	+	0.809880i	−0.263146	+	0.809880i	−0.992115	+	0.125333i	$0.960000\pi$
$354$	2.67642	+	1.65170i	2.67642	+	1.65170i
$355$		0			0
$356$	0.0231273	−	0.00983603i	0.0231273	−	0.00983603i
$357$		0			0
$358$	1.52448	+	0.694102i	1.52448	+	0.694102i
$359$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$359$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$360$		0			0
$361$	−0.0926401	−	2.45619i	−0.0926401	−	2.45619i
$362$		0			0
$363$	−1.60250	+	0.284872i	−1.60250	+	0.284872i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.979855	−	0.199710i	$-0.936000\pi$
$367$		0			0		0.979855	+	0.199710i	$0.0640000\pi$
$368$		0			0
$369$	−1.08860	+	0.109808i	−1.08860	+	0.109808i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.137790	−	0.990461i	$-0.456000\pi$
$373$		0			0		−0.137790	+	0.990461i	$0.544000\pi$
$374$	−0.383660	+	0.360281i	−0.383660	+	0.360281i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.686257	+	0.644438i	−0.686257	+	0.644438i	−0.947098	−	0.320944i	$-0.896000\pi$
$379$	−0.686257	+	0.644438i	−0.686257	+	0.644438i	0.260842	+	0.965382i	$0.416000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$383$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$384$	−1.81102	+	0.182680i	−1.81102	+	0.182680i
$385$		0			0
$386$	−1.46183	−	0.297944i	−1.46183	−	0.297944i
$387$	3.16681	−	3.12726i	3.16681	−	3.12726i
$388$	−0.306031	+	0.695179i	−0.306031	+	0.695179i
$389$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$389$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$390$		0			0
$391$		0			0
$392$	−0.0376902	−	0.999289i	−0.0376902	−	0.999289i
$393$	3.02136	−	1.02385i	3.02136	−	1.02385i
$394$		0			0
$395$		0			0
$396$	0.676726	+	0.328893i	0.676726	+	0.328893i
$397$		0			0		0.920232	−	0.391374i	$-0.128000\pi$
$397$		0			0		−0.920232	+	0.391374i	$0.872000\pi$
$398$		0			0
$399$		0			0
$400$	0.309017	−	0.951057i	0.309017	−	0.951057i
$401$	0.767483	−	0.685246i	0.767483	−	0.685246i	−0.187381	−	0.982287i	$-0.560000\pi$
$401$	0.767483	−	0.685246i	0.767483	−	0.685246i	0.954865	+	0.297042i	$0.0960000\pi$
$402$	2.61279	+	2.45358i	2.61279	+	2.45358i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−2.92194	+	0.369127i	−2.92194	+	0.369127i
$409$	−0.625521	−	1.52366i	−0.625521	−	1.52366i	−0.837528	−	0.546394i	$-0.816000\pi$
$409$	−0.625521	−	1.52366i	−0.625521	−	1.52366i	0.212007	−	0.977268i	$-0.432000\pi$
$410$		0			0
$411$	−0.360026	+	0.197926i	−0.360026	+	0.197926i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.56712	+	1.32840i	2.56712	+	1.32840i
$418$	−0.480257	+	0.367716i	−0.480257	+	0.367716i
$419$	−0.144697	−	1.64070i	−0.144697	−	1.64070i	−0.637424	−	0.770513i	$-0.720000\pi$
$419$	−0.144697	−	1.64070i	−0.144697	−	1.64070i	0.492727	−	0.870184i	$-0.336000\pi$
$420$		0			0
$421$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$421$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$422$	1.67351	+	0.920019i	1.67351	+	0.920019i
$423$		0			0
$424$		0			0
$425$	0.461171	−	1.55092i	0.461171	−	1.55092i
$426$		0			0
$427$		0			0
$428$	−0.0169725	−	1.35056i	−0.0169725	−	1.35056i
$429$		0			0
$430$		0			0
$431$		0			0		−0.778462	−	0.627691i	$-0.784000\pi$
$431$		0			0		0.778462	+	0.627691i	$0.216000\pi$
$432$	1.12510	+	2.10890i	1.12510	+	2.10890i
$433$	0.0915446	−	1.45506i	0.0915446	−	1.45506i	−0.637424	−	0.770513i	$-0.720000\pi$
$433$	0.0915446	−	1.45506i	0.0915446	−	1.45506i	0.728969	−	0.684547i	$-0.240000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.221403	−	0.0568466i	−0.221403	−	0.0568466i
$439$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$439$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$440$		0			0
$441$	−2.10523	+	0.958522i	−2.10523	+	0.958522i
$442$		0			0
$443$	0.381858	+	0.485953i	0.381858	+	0.485953i	0.938734	−	0.344643i	$-0.112000\pi$
$443$	0.381858	+	0.485953i	0.381858	+	0.485953i	−0.556876	+	0.830596i	$0.688000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.0751216	−	0.661387i	−0.0751216	−	0.661387i	−0.974527	−	0.224271i	$-0.928000\pi$
$449$	−0.0751216	−	0.661387i	−0.0751216	−	0.661387i	0.899405	−	0.437116i	$-0.144000\pi$
$450$	−2.30660	+	0.174244i	−2.30660	+	0.174244i
$451$	−0.149020	+	0.0382620i	−0.149020	+	0.0382620i
$452$	−0.351802	+	1.84421i	−0.351802	+	1.84421i
$453$		0			0
$454$	1.93368	−	0.445005i	1.93368	−	0.445005i
$455$		0			0
$456$	−3.38371	+	0.0850599i	−3.38371	+	0.0850599i
$457$	0.963851	−	0.468437i	0.963851	−	0.468437i	0.112856	−	0.993611i	$-0.464000\pi$
$457$	0.963851	−	0.468437i	0.963851	−	0.468437i	0.850994	+	0.525175i	$0.176000\pi$
$458$		0			0
$459$	1.90563	+	3.36544i	1.90563	+	3.36544i
$460$		0			0
$461$		0			0		0.162637	−	0.986686i	$-0.448000\pi$
$461$		0			0		−0.162637	+	0.986686i	$0.552000\pi$
$462$		0			0
$463$		0			0		0.850994	−	0.525175i	$-0.176000\pi$
$463$		0			0		−0.850994	+	0.525175i	$0.824000\pi$
$464$		0			0
$465$		0			0
$466$	−0.0574732	+	0.0487753i	−0.0574732	+	0.0487753i
$467$	−0.0865734	+	0.152893i	−0.0865734	+	0.152893i	−0.910106	−	0.414376i	$-0.864000\pi$
$467$	−0.0865734	+	0.152893i	−0.0865734	+	0.152893i	0.823533	+	0.567269i	$0.192000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.888873	+	1.48167i	0.888873	+	1.48167i
$473$	0.374196	−	0.501657i	0.374196	−	0.501657i
$474$		0			0
$475$	0.706219	−	1.72023i	0.706219	−	1.72023i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$479$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$480$		0			0
$481$		0			0
$482$	1.25958	−	0.915137i	1.25958	−	0.915137i
$483$		0			0
$484$	−0.853837	−	0.265614i	−0.853837	−	0.265614i
$485$		0			0
$486$	0.840505	−	1.01600i	0.840505	−	1.01600i
$487$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$487$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$488$		0			0
$489$	0.775776	−	2.03369i	0.775776	−	2.03369i
$490$		0			0
$491$	0.614386	+	1.39564i	0.614386	+	1.39564i	0.899405	+	0.437116i	$0.144000\pi$
$491$	0.614386	+	1.39564i	0.614386	+	1.39564i	−0.285019	+	0.958522i	$0.592000\pi$
$492$	−0.800497	−	0.316939i	−0.800497	−	0.316939i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.54953	−	3.29291i	−1.54953	−	3.29291i
$499$	1.42824	+	1.09355i	1.42824	+	1.09355i	0.979855	+	0.199710i	$0.0640000\pi$
$499$	1.42824	+	1.09355i	1.42824	+	1.09355i	0.448383	+	0.893841i	$0.352000\pi$
$500$		0			0
$501$		0			0
$502$	−0.137790	−	0.990461i	−0.137790	−	0.990461i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.341074	+	1.78797i	0.341074	+	1.78797i
$508$		0			0
$509$		0			0		−0.762443	−	0.647056i	$-0.776000\pi$
$509$		0			0		0.762443	+	0.647056i	$0.224000\pi$
$510$		0			0
$511$		0			0
$512$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$513$	1.79084	+	4.06806i	1.79084	+	4.06806i
$514$	0.170838	−	0.787495i	0.170838	−	0.787495i
$515$		0			0
$516$	3.34412	−	1.04030i	3.34412	−	1.04030i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.16191	+	1.20656i	−1.16191	+	1.20656i	−0.187381	+	0.982287i	$0.560000\pi$
$521$	−1.16191	+	1.20656i	−1.16191	+	1.20656i	−0.974527	+	0.224271i	$0.928000\pi$
$522$		0			0
$523$	0.390191	+	1.79863i	0.390191	+	1.79863i	0.577573	+	0.816339i	$0.304000\pi$
$523$	0.390191	+	1.79863i	0.390191	+	1.79863i	−0.187381	+	0.982287i	$0.560000\pi$
$524$	1.73272	+	0.263287i	1.73272	+	0.263287i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.354001	+	0.474582i	0.354001	+	0.474582i
$529$	−0.379779	+	0.925077i	−0.379779	+	0.925077i
$530$		0			0
$531$	2.38971	−	3.20371i	2.38971	−	3.20371i
$532$		0			0
$533$		0			0
$534$	−0.0141362	−	0.0435068i	−0.0141362	−	0.0435068i
$535$		0			0
$536$	0.655365	+	1.85687i	0.655365	+	1.85687i
$537$	1.50230	−	2.65315i	1.50230	−	2.65315i
$538$		0			0
$539$	−0.272426	+	0.177728i	−0.272426	+	0.177728i
$540$		0			0
$541$		0			0		0.850994	−	0.525175i	$-0.176000\pi$
$541$		0			0		−0.850994	+	0.525175i	$0.824000\pi$
$542$		0			0
$543$		0			0
$544$	−1.51890	−	0.557644i	−1.51890	−	0.557644i
$545$		0			0
$546$		0			0
$547$	1.61786	−	0.786288i	1.61786	−	0.786288i	0.617860	−	0.786288i	$-0.288000\pi$
$547$	1.61786	−	0.786288i	1.61786	−	0.786288i	1.00000			$0$
$548$	−0.225641	+	0.00567218i	−0.225641	+	0.00567218i
$549$		0			0
$550$	−0.316989	+	0.0729495i	−0.316989	+	0.0729495i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.917174	+	1.29633i	0.917174	+	1.29633i
$557$		0			0		0.823533	−	0.567269i	$-0.192000\pi$
$557$		0			0		−0.823533	+	0.567269i	$0.808000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.591901	+	0.753254i	0.591901	+	0.753254i
$562$	1.99369	+	0.0501174i	1.99369	+	0.0501174i
$563$	1.80586	−	0.822216i	1.80586	−	0.822216i	0.850994	−	0.525175i	$-0.176000\pi$
$563$	1.80586	−	0.822216i	1.80586	−	0.822216i	0.954865	−	0.297042i	$-0.0960000\pi$
$564$		0			0
$565$		0			0
$566$	−1.50801	−	0.387191i	−1.50801	−	0.387191i
$567$		0			0
$568$		0			0
$569$	0.361313	+	0.720269i	0.361313	+	0.720269i	0.998737	−	0.0502443i	$-0.0160000\pi$
$569$	0.361313	+	0.720269i	0.361313	+	0.720269i	−0.637424	+	0.770513i	$0.720000\pi$
$570$		0			0
$571$	0.124156	−	1.97340i	0.124156	−	1.97340i	−0.0878512	−	0.996134i	$-0.528000\pi$
$571$	0.124156	−	1.97340i	0.124156	−	1.97340i	0.212007	−	0.977268i	$-0.432000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.0290674	+	2.31299i	0.0290674	+	2.31299i
$577$	0.905660	+	0.256959i	0.905660	+	0.256959i	0.693653	−	0.720309i	$-0.256000\pi$
$577$	0.905660	+	0.256959i	0.905660	+	0.256959i	0.212007	+	0.977268i	$0.432000\pi$
$578$	−1.53244	−	0.519298i	−1.53244	−	0.519298i
$579$	−0.773982	+	2.60291i	−0.773982	+	2.60291i
$580$		0			0
$581$		0			0
$582$	1.21154	+	0.666052i	1.21154	+	0.666052i
$583$		0			0
$584$	−0.0936761	−	0.0836385i	−0.0936761	−	0.0836385i
$585$		0			0
$586$		0			0
$587$	−1.02593	−	0.530882i	−1.02593	−	0.530882i	−0.137790	−	0.990461i	$-0.544000\pi$
$587$	−1.02593	−	0.530882i	−1.02593	−	0.530882i	−0.888136	+	0.459580i	$0.848000\pi$
$588$	−1.81791	−	0.0914553i	−1.81791	−	0.0914553i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.18360	+	0.650688i	−1.18360	+	0.650688i	−0.947098	−	0.320944i	$-0.896000\pi$
$593$	−1.18360	+	0.650688i	−1.18360	+	0.650688i	−0.236499	+	0.971632i	$0.576000\pi$
$594$	0.399970	−	0.666716i	0.399970	−	0.666716i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.656586	−	0.754251i	$-0.728000\pi$
$599$		0			0		0.656586	+	0.754251i	$0.272000\pi$
$600$	−1.67502	−	0.712383i	−1.67502	−	0.712383i
$601$	−1.50801	+	1.21594i	−1.50801	+	1.21594i	−0.597905	+	0.801567i	$0.704000\pi$
$601$	−1.50801	+	1.21594i	−1.50801	+	1.21594i	−0.910106	+	0.414376i	$0.864000\pi$
$602$		0			0
$603$	3.39771	−	3.03364i	3.39771	−	3.03364i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.920232	−	0.391374i	$-0.128000\pi$
$607$		0			0		−0.920232	+	0.391374i	$0.872000\pi$
$608$	−1.67249	−	0.812840i	−1.67249	−	0.812840i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.141066	+	3.74013i	0.141066	+	3.74013i
$613$		0			0		−0.997159	−	0.0753268i	$-0.976000\pi$
$613$		0			0		0.997159	+	0.0753268i	$0.0240000\pi$
$614$	−0.701821	+	0.124761i	−0.701821	+	0.124761i
$615$		0			0
$616$		0			0
$617$	−1.41589	+	1.39820i	−1.41589	+	1.39820i	−0.637424	+	0.770513i	$0.720000\pi$
$617$	−1.41589	+	1.39820i	−1.41589	+	1.39820i	−0.778462	+	0.627691i	$0.784000\pi$
$618$		0			0
$619$	−0.0749998	−	0.00756530i	−0.0749998	−	0.00756530i	0.0627905	−	0.998027i	$-0.480000\pi$
$619$	−0.0749998	−	0.00756530i	−0.0749998	−	0.00756530i	−0.137790	+	0.990461i	$0.544000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.728969	−	0.684547i	0.728969	−	0.684547i
$626$	−0.167772	+	1.90235i	−0.167772	+	1.90235i
$627$	0.589936	+	0.929590i	0.589936	+	0.929590i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.137790	−	0.990461i	$-0.456000\pi$
$631$		0			0		−0.137790	+	0.990461i	$0.544000\pi$
$632$		0			0
$633$	1.93576	−	2.88724i	1.93576	−	2.88724i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.368978	−	0.0655921i	0.368978	−	0.0655921i	0.0125660	−	0.999921i	$-0.496000\pi$
$641$	0.368978	−	0.0655921i	0.368978	−	0.0655921i	0.356412	+	0.934329i	$0.384000\pi$
$642$	−2.45151	−	0.185191i	−2.45151	−	0.185191i
$643$	0.0734602	+	1.94767i	0.0734602	+	1.94767i	0.260842	+	0.965382i	$0.416000\pi$
$643$	0.0734602	+	1.94767i	0.0734602	+	1.94767i	−0.187381	+	0.982287i	$0.560000\pi$
$644$		0			0
$645$		0			0
$646$	−2.73834	−	1.24678i	−2.73834	−	1.24678i
$647$		0			0		−0.899405	−	0.437116i	$-0.856000\pi$
$647$		0			0		0.899405	+	0.437116i	$0.144000\pi$
$648$	1.87506	−	0.797459i	1.87506	−	0.797459i
$649$	0.264547	−	0.495869i	0.264547	−	0.495869i
$650$		0			0
$651$		0			0
$652$	0.892004	−	0.796424i	0.892004	−	0.796424i
$653$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$653$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$654$		0			0
$655$		0			0
$656$	−0.310564	−	0.356759i	−0.310564	−	0.356759i
$657$	−0.0966809	+	0.273930i	−0.0966809	+	0.273930i
$658$		0			0
$659$	−1.73879	+	0.219661i	−1.73879	+	0.219661i	−0.929776	−	0.368125i	$-0.880000\pi$
$659$	−1.73879	+	0.219661i	−1.73879	+	0.219661i	−0.809017	+	0.587785i	$0.800000\pi$
$660$		0			0
$661$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$661$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$662$	−1.30735	+	0.718720i	−1.30735	+	0.718720i
$663$		0			0
$664$	0.0753566	−	1.99795i	0.0753566	−	1.99795i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.65990	−	0.912536i	−1.65990	−	0.912536i	−0.984564	−	0.175023i	$-0.944000\pi$
$673$	−1.65990	−	0.912536i	−1.65990	−	0.912536i	−0.675333	−	0.737513i	$-0.736000\pi$
$674$	0.517948	−	0.732066i	0.517948	−	0.732066i
$675$	−0.0300360	+	2.39006i	−0.0300360	+	2.39006i
$676$	−0.285019	+	0.958522i	−0.285019	+	0.958522i
$677$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$677$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$678$	3.28762	+	0.932783i	3.28762	+	0.932783i
$679$		0			0
$680$		0			0
$681$	−0.497660	−	3.57727i	−0.497660	−	3.57727i
$682$		0			0
$683$	0.836099	+	1.56719i	0.836099	+	1.56719i	0.823533	+	0.567269i	$0.192000\pi$
$683$	0.836099	+	1.56719i	0.836099	+	1.56719i	0.0125660	+	0.999921i	$0.496000\pi$
$684$	−0.270091	+	4.29298i	−0.270091	+	4.29298i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.89436	+	0.336754i	1.89436	+	0.336754i
$689$		0			0
$690$		0			0
$691$	−1.51160	+	0.782200i	−1.51160	+	0.782200i	−0.997159	−	0.0753268i	$-0.976000\pi$
$691$	−1.51160	+	0.782200i	−1.51160	+	0.782200i	−0.514440	+	0.857527i	$0.672000\pi$
$692$		0			0
$693$		0			0
$694$	0.261981	+	0.333397i	0.261981	+	0.333397i
$695$		0			0
$696$		0			0
$697$	−0.516850	−	0.564439i	−0.516850	−	0.564439i
$698$		0			0
$699$	0.0792477	+	0.112008i	0.0792477	+	0.112008i
$700$		0			0
$701$		0			0		0.997159	−	0.0753268i	$-0.0240000\pi$
$701$		0			0		−0.997159	+	0.0753268i	$0.976000\pi$
$702$		0			0
$703$		0			0
$704$	0.0529017	+	0.320944i	0.0529017	+	0.320944i
$705$		0			0
$706$	0.542804	+	0.656137i	0.542804	+	0.656137i
$707$		0			0
$708$	2.82867	−	1.37475i	2.82867	−	1.37475i
$709$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$709$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$710$		0			0
$711$		0			0
$712$	0.00408741	−	0.0247975i	0.00408741	−	0.0247975i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.40291	−	0.915241i	1.40291	−	0.915241i
$717$		0			0
$718$		0			0
$719$		0			0		−0.332820	−	0.942991i	$-0.608000\pi$
$719$		0			0		0.332820	+	0.942991i	$0.392000\pi$
$720$		0			0
$721$		0			0
$722$	−2.12347	−	1.23787i	−2.12347	−	1.23787i
$723$	−1.45789	−	2.43017i	−1.45789	−	2.43017i
$724$		0			0
$725$		0			0
$726$	−0.618139	+	1.50568i	−0.618139	+	1.50568i
$727$		0			0		−0.597905	−	0.801567i	$-0.704000\pi$
$727$		0			0		0.597905	+	0.801567i	$0.296000\pi$
$728$		0			0
$729$	−0.257956	−	0.254735i	−0.257956	−	0.254735i
$730$		0			0
$731$	3.07786	+	0.467680i	3.07786	+	0.467680i
$732$		0			0
$733$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$733$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.408275	−	0.493519i	0.408275	−	0.493519i
$738$	−0.490588	+	0.977975i	−0.490588	+	0.977975i
$739$	−1.69610	+	0.527627i	−1.69610	+	0.527627i	−0.984564	−	0.175023i	$-0.944000\pi$
$739$	−1.69610	+	0.527627i	−1.69610	+	0.527627i	−0.711536	+	0.702650i	$0.752000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$743$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.34153	+	1.59393i	−4.34153	+	1.59393i
$748$	0.0986197	+	0.516983i	0.0986197	+	0.516983i
$749$		0			0
$750$		0			0
$751$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$751$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$752$		0			0
$753$	−1.81791	+	0.0914553i	−1.81791	+	0.0914553i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$757$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$758$	0.176402	+	0.924733i	0.176402	+	0.924733i
$759$		0			0
$760$		0			0
$761$	1.98360	+	0.250587i	1.98360	+	0.250587i	0.994951	+	0.100362i	$0.0320000\pi$
$761$	1.98360	+	0.250587i	1.98360	+	0.250587i	0.988652	+	0.150226i	$0.0480000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.816152	+	1.62698i	−0.816152	+	1.62698i
$769$	0.907100	−	1.09650i	0.907100	−	1.09650i	−0.0878512	−	0.996134i	$-0.528000\pi$
$769$	0.907100	−	1.09650i	0.907100	−	1.09650i	0.994951	−	0.100362i	$-0.0320000\pi$
$770$		0			0
$771$	−1.40055	−	0.435686i	−1.40055	−	0.435686i
$772$	−1.03485	+	1.07462i	−1.03485	+	1.07462i
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	−0.943574	−	4.34950i	−0.943574	−	4.34950i
$775$		0			0
$776$	0.422979	+	0.630886i	0.422979	+	0.630886i
$777$		0			0
$778$		0			0
$779$	−0.525896	−	0.705030i	−0.525896	−	0.705030i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.863923	−	0.503623i	−0.863923	−	0.503623i
$785$		0			0
$786$	0.754462	−	3.09963i	0.754462	−	3.09963i
$787$	−0.411272	−	1.16527i	−0.411272	−	1.16527i	−0.947098	−	0.320944i	$-0.896000\pi$
$787$	−0.411272	−	1.16527i	−0.411272	−	1.16527i	0.535827	−	0.844328i	$-0.320000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.640301	−	0.395149i	0.640301	−	0.395149i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$797$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$798$		0			0
$799$		0			0
$800$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$801$	−0.0566539	+	0.0130379i	−0.0566539	+	0.0130379i
$802$	−0.167334	−	1.01518i	−0.167334	−	1.01518i
$803$	−0.00765421	+	0.0401248i	−0.00765421	+	0.0401248i
$804$	3.47163	−	0.891362i	3.47163	−	0.891362i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.961047	+	1.04953i	0.961047	+	1.04953i	0.998737	+	0.0502443i	$0.0160000\pi$
$809$	0.961047	+	1.04953i	0.961047	+	1.04953i	−0.0376902	+	0.999289i	$0.512000\pi$
$810$		0			0
$811$	−0.426201	−	1.11728i	−0.426201	−	1.11728i	−0.962028	−	0.272952i	$-0.912000\pi$
$811$	−0.426201	−	1.11728i	−0.426201	−	1.11728i	0.535827	−	0.844328i	$-0.320000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.25399	+	2.66486i	−1.25399	+	2.66486i
$817$	3.46548	+	0.889783i	3.46548	+	0.889783i
$818$	−1.62164	−	0.288274i	−1.62164	−	0.288274i
$819$		0			0
$820$		0			0
$821$		0			0		−0.974527	−	0.224271i	$-0.928000\pi$
$821$		0			0		0.974527	+	0.224271i	$0.0720000\pi$
$822$	−0.0257972	+	0.410034i	−0.0257972	+	0.410034i
$823$		0			0		−0.470704	−	0.882291i	$-0.656000\pi$
$823$		0			0		0.470704	+	0.882291i	$0.344000\pi$
$824$		0			0
$825$	0.0815813	+	0.586421i	0.0815813	+	0.586421i
$826$		0			0
$827$	−0.00220788	−	0.175689i	−0.00220788	−	0.175689i	−0.997159	−	0.0753268i	$-0.976000\pi$
$827$	−0.00220788	−	0.175689i	−0.00220788	−	0.175689i	0.994951	−	0.100362i	$-0.0320000\pi$
$828$		0			0
$829$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$829$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.41789	−	0.779494i	−1.41789	−	0.779494i
$834$	2.49714	−	1.45570i	2.49714	−	1.45570i
$835$		0			0
$836$	0.0531381	+	0.602526i	0.0531381	+	0.602526i
$837$		0			0
$838$	−1.46282	−	0.756958i	−1.46282	−	0.756958i
$839$		0			0		−0.998737	−	0.0502443i	$-0.984000\pi$
$839$		0			0		0.998737	+	0.0502443i	$0.0160000\pi$
$840$		0			0
$841$	−0.285019	−	0.958522i	−0.285019	−	0.958522i
$842$		0			0
$843$	0.409678	−	3.60689i	0.409678	−	3.60689i
$844$	1.67351	−	0.920019i	1.67351	−	0.920019i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.943188	+	2.67237i	−0.943188	+	2.67237i
$850$	−1.06238	−	1.22040i	−1.06238	−	1.22040i
$851$		0			0
$852$		0			0
$853$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$853$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$854$		0			0
$855$		0			0
$856$	−1.14941	−	0.709335i	−1.14941	−	0.709335i
$857$	0.562872	−	1.05505i	0.562872	−	1.05505i	−0.425779	−	0.904827i	$-0.640000\pi$
$857$	0.562872	−	1.05505i	0.562872	−	1.05505i	0.988652	−	0.150226i	$-0.0480000\pi$
$858$		0			0
$859$	1.03894	+	0.504932i	1.03894	+	0.504932i	0.876307	−	0.481754i	$-0.160000\pi$
$859$	1.03894	+	0.504932i	1.03894	+	0.504932i	0.162637	+	0.986686i	$0.448000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.0376902	−	0.999289i	$-0.512000\pi$
$863$		0			0		0.0376902	+	0.999289i	$0.488000\pi$
$864$	2.38346	+	0.180050i	2.38346	+	0.180050i
$865$		0			0
$866$	−1.17950	−	0.856954i	−1.17950	−	0.856954i
$867$	−1.18663	+	2.69554i	−1.18663	+	2.69554i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.978424	−	1.45935i	0.978424	−	1.45935i
$874$		0			0
$875$		0			0
$876$	−0.166631	+	0.156477i	−0.166631	+	0.156477i
$877$		0			0		0.0878512	−	0.996134i	$-0.472000\pi$
$877$		0			0		−0.0878512	+	0.996134i	$0.528000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.29485	+	1.21594i	−1.29485	+	1.21594i	−0.332820	+	0.942991i	$0.608000\pi$
$881$	−1.29485	+	1.21594i	−1.29485	+	1.21594i	−0.962028	+	0.272952i	$0.912000\pi$
$882$	−0.318733	+	2.29111i	−0.318733	+	2.29111i
$883$	−0.0848090	+	0.0926177i	−0.0848090	+	0.0926177i	−0.778462	−	0.627691i	$-0.784000\pi$
$883$	−0.0848090	+	0.0926177i	−0.0848090	+	0.0926177i	0.693653	+	0.720309i	$0.256000\pi$
$884$		0			0
$885$		0			0
$886$	0.614914	−	0.0620270i	0.614914	−	0.0620270i
$887$		0			0		−0.994951	−	0.100362i	$-0.968000\pi$
$887$		0			0		0.994951	+	0.100362i	$0.0320000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.536197	−	0.389570i	−0.536197	−	0.389570i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.598679	−	0.290961i	−0.598679	−	0.290961i
$899$		0			0
$900$	−1.08882	+	2.04089i	−1.08882	+	2.04089i
$901$		0			0
$902$	−0.0475435	+	0.146324i	−0.0475435	+	0.146324i
$903$		0			0
$904$	1.36862	+	1.28522i	1.36862	+	1.28522i
$905$		0			0
$906$		0			0
$907$	−1.27972	−	1.47008i	−1.27972	−	1.47008i	−0.809017	−	0.587785i	$-0.800000\pi$
$907$	−1.27972	−	1.47008i	−1.27972	−	1.47008i	−0.470704	−	0.882291i	$-0.656000\pi$
$908$	0.660390	−	1.87111i	0.660390	−	1.87111i
$909$		0			0
$910$		0			0
$911$		0			0		−0.379779	−	0.925077i	$-0.624000\pi$
$911$		0			0		0.379779	+	0.925077i	$0.376000\pi$
$912$	−1.74126	+	2.90254i	−1.74126	+	2.90254i
$913$	−0.569900	+	0.313305i	−0.569900	+	0.313305i
$914$	0.120943	−	1.06481i	0.120943	−	1.06481i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	3.86262	+	0.194320i	3.86262	+	0.194320i
$919$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$919$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$920$		0			0
$921$	0.113986	+	1.29247i	0.113986	+	1.29247i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.685756	−	0.194567i	−0.685756	−	0.194567i	−0.0878512	−	0.996134i	$-0.528000\pi$
$929$	−0.685756	−	0.194567i	−0.685756	−	0.194567i	−0.597905	+	0.801567i	$0.704000\pi$
$930$		0			0
$931$	−1.53140	−	1.05487i	−1.53140	−	1.05487i
$932$	0.0103867	+	0.0746613i	0.0103867	+	0.0746613i
$933$		0			0
$934$	0.0827038	+	0.155021i	0.0827038	+	0.155021i
$935$		0			0
$936$		0			0
$937$	−0.796451	−	1.58771i	−0.796451	−	1.58771i	−0.809017	−	0.587785i	$-0.800000\pi$
$937$	−0.796451	−	1.58771i	−0.796451	−	1.58771i	0.0125660	−	0.999921i	$-0.496000\pi$
$938$		0			0
$939$	3.42246	+	0.608400i	3.42246	+	0.608400i
$940$		0			0
$941$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$941$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$942$		0			0
$943$		0			0
$944$	1.72730	+	0.0434210i	1.72730	+	0.0434210i
$945$		0			0
$946$	−0.223059	−	0.584746i	−0.223059	−	0.584746i
$947$	−1.26038	+	0.191515i	−1.26038	+	0.191515i	−0.745941	−	0.666012i	$-0.768000\pi$
$947$	−1.26038	+	0.191515i	−1.26038	+	0.191515i	−0.514440	+	0.857527i	$0.672000\pi$
$948$		0			0
$949$		0			0
$950$	−1.07403	−	1.51803i	−1.07403	−	1.51803i
$951$		0			0
$952$		0			0
$953$	−0.0730122	+	0.0187463i	−0.0730122	+	0.0187463i	−0.285019	−	0.958522i	$-0.592000\pi$
$953$	−0.0730122	+	0.0187463i	−0.0730122	+	0.0187463i	0.212007	+	0.977268i	$0.432000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.492727	+	0.870184i	0.492727	+	0.870184i
$962$		0			0
$963$	−0.508131	+	3.08272i	−0.508131	+	3.08272i
$964$	−0.0977601	−	1.55385i	−0.0977601	−	1.55385i
$965$		0			0
$966$		0			0
$967$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$967$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$968$	−0.681774	+	0.578595i	−0.681774	+	0.578595i
$969$	−2.69851	+	4.76573i	−2.69851	+	4.76573i
$970$		0			0
$971$	−0.458138	+	1.88221i	−0.458138	+	1.88221i	0.0125660	+	0.999921i	$0.496000\pi$
$971$	−0.458138	+	1.88221i	−0.458138	+	1.88221i	−0.470704	+	0.882291i	$0.656000\pi$
$972$	−0.407469	−	1.25406i	−0.407469	−	1.25406i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.603082	+	1.46900i	−0.603082	+	1.46900i	0.260842	+	0.965382i	$0.416000\pi$
$977$	−0.603082	+	1.46900i	−0.603082	+	1.46900i	−0.863923	+	0.503623i	$0.832000\pi$
$978$	−1.30142	−	1.74471i	−1.30142	−	1.74471i
$979$	−0.00760076	+	0.00300935i	−0.00760076	+	0.00300935i
$980$		0			0
$981$		0			0
$982$	1.50758	+	0.229077i	1.50758	+	0.229077i
$983$		0			0		−0.212007	−	0.977268i	$-0.568000\pi$
$983$		0			0		0.212007	+	0.977268i	$0.432000\pi$
$984$	−0.696529	+	0.506058i	−0.696529	+	0.506058i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$991$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$992$		0			0
$993$	1.09411	+	2.48538i	1.09411	+	2.48538i
$994$		0			0
$995$		0			0
$996$	−3.61058	−	0.456122i	−3.61058	−	0.456122i
$997$		0			0		−0.762443	−	0.647056i	$-0.776000\pi$
$997$		0			0		0.762443	+	0.647056i	$0.224000\pi$
$998$	1.68860	−	0.619947i	1.68860	−	0.619947i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.395.1	✓	100
8.3	odd	2	CM	2008.1.bd.a.395.1	✓	100
251.190	even	125	inner	2008.1.bd.a.1947.1	yes	100
2008.1947	odd	250	inner	2008.1.bd.a.1947.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.395.1	✓	100	1.1	even	1	trivial
2008.1.bd.a.395.1	✓	100	8.3	odd	2	CM
2008.1.bd.a.1947.1	yes	100	251.190	even	125	inner
2008.1.bd.a.1947.1	yes	100	2008.1947	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)

\(f(q)\)	\(=\)	\(q+(0.535827 - 0.844328i) q^{2} +(-1.44523 - 1.10656i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-1.70869 + 0.627323i) q^{6} +(-0.992115 - 0.125333i) q^{8} +(0.603371 + 2.23309i) q^{9} +O(q^{10})\)	\(q+(0.535827 - 0.844328i) q^{2} +(-1.44523 - 1.10656i) q^{3} +(-0.425779 - 0.904827i) q^{4} +(-1.70869 + 0.627323i) q^{6} +(-0.992115 - 0.125333i) q^{8} +(0.603371 + 2.23309i) q^{9} +(0.131055 + 0.297704i) q^{11} +(-0.385898 + 1.77884i) q^{12} +(-0.637424 + 0.770513i) q^{16} +(-0.999718 + 1.27224i) q^{17} +(2.20877 + 0.687108i) q^{18} +(-1.28989 + 1.33945i) q^{19} +(0.321583 + 0.0488645i) q^{22} +(1.29515 + 1.27897i) q^{24} +(-0.929776 + 0.368125i) q^{25} +(0.907767 - 2.21117i) q^{27} +(0.309017 + 0.951057i) q^{32} +(0.140024 - 0.575272i) q^{33} +(0.538513 + 1.52579i) q^{34} +(1.76366 - 1.49675i) q^{36} +(0.439782 + 1.80680i) q^{38} +(-0.0769271 + 0.466700i) q^{41} +(-0.948035 - 1.67428i) q^{43} +(0.213570 - 0.245339i) q^{44} +(1.77385 - 0.408220i) q^{48} +(0.162637 + 0.986686i) q^{49} +(-0.187381 + 0.982287i) q^{50} +(2.85264 - 0.732433i) q^{51} +(-1.38054 - 1.95126i) q^{54} +(3.34637 - 0.508481i) q^{57} +(-1.06757 - 1.35859i) q^{59} +(0.968583 + 0.248690i) q^{64} +(-0.410690 - 0.426472i) q^{66} +(-0.882924 - 1.76009i) q^{67} +(1.57682 + 0.362878i) q^{68} +(-0.318733 - 2.29111i) q^{72} +(0.103420 + 0.0712382i) q^{73} +(1.75109 + 0.496830i) q^{75} +(1.76118 + 0.596812i) q^{76} +(-1.76032 + 1.02618i) q^{81} +(0.352829 + 0.315022i) q^{82} +(0.175647 + 1.99164i) q^{83} +(-1.92163 - 0.0966728i) q^{86} +(-0.0927094 - 0.311783i) q^{88} +(-0.000947233 + 0.0251142i) q^{89} +(0.605802 - 1.71644i) q^{96} +(-0.498715 - 0.572898i) q^{97} +(0.920232 + 0.391374i) q^{98} +(-0.585727 + 0.472285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 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

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