LMFDB - Embedded newform 2008.1.bd.a.147.1

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			147.1
Root			$0.999684 + 0.0251301i$ of defining polynomial
Character	$\chi$	$=$	2008.147
Dual form			2008.1.bd.a.683.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.637424 - 0.770513i) q^{2} +(0.702235 - 0.626989i) q^{3} +(-0.187381 + 0.982287i) q^{4} +(-0.930725 - 0.141424i) q^{6} +(0.876307 - 0.481754i) q^{8} +(-0.0128376 + 0.113025i) q^{9} +O(q^{10})$	\(q+(-0.637424 - 0.770513i) q^{2} +(0.702235 - 0.626989i) q^{3} +(-0.187381 + 0.982287i) q^{4} +(-0.930725 - 0.141424i) q^{6} +(0.876307 - 0.481754i) q^{8} +(-0.0128376 + 0.113025i) q^{9} +(1.51568 + 0.644618i) q^{11} +(0.484297 + 0.807282i) q^{12} +(-0.929776 - 0.368125i) q^{16} +(-0.263152 + 1.59649i) q^{17} +(0.0952698 - 0.0621530i) q^{18} +(0.106869 - 0.0659520i) q^{19} +(-0.469445 - 1.57875i) q^{22} +(0.313319 - 0.887739i) q^{24} +(0.0627905 + 0.998027i) q^{25} +(0.605582 + 0.855927i) q^{27} +(0.309017 + 0.951057i) q^{32} +(1.46853 - 0.497642i) q^{33} +(1.39786 - 0.814879i) q^{34} +(-0.108617 - 0.0337888i) q^{36} +(-0.118938 - 0.0403044i) q^{38} +(-1.55993 - 1.07452i) q^{41} +(-1.27992 + 0.622047i) q^{43} +(-0.917210 + 1.36805i) q^{44} +(-0.883731 + 0.324450i) q^{48} +(0.823533 - 0.567269i) q^{49} +(0.728969 - 0.684547i) q^{50} +(0.816187 + 1.28611i) q^{51} +(0.273491 - 1.01220i) q^{54} +(0.0336958 - 0.113319i) q^{57} +(-0.316989 - 1.92310i) q^{59} +(0.535827 - 0.844328i) q^{64} +(-1.31952 - 0.814315i) q^{66} +(1.99369 - 0.0501174i) q^{67} +(-1.51890 - 0.557644i) q^{68} +(0.0432003 + 0.105229i) q^{72} +(0.780497 - 1.77297i) q^{73} +(0.669845 + 0.661480i) q^{75} +(0.0447586 + 0.117334i) q^{76} +(0.851064 + 0.195858i) q^{81} +(0.166407 + 1.88687i) q^{82} +(-0.0159812 + 0.423713i) q^{83} +(1.29515 + 0.589686i) q^{86} +(1.63875 - 0.165302i) q^{88} +(-0.698099 - 1.39164i) q^{89} +(0.813304 + 0.474115i) q^{96} +(-0.643272 - 0.959459i) q^{97} +(-0.962028 - 0.272952i) q^{98} +(-0.0923153 + 0.163034i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{6}{125}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$2$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$3$	0.702235	−	0.626989i	0.702235	−	0.626989i	−0.236499	−	0.971632i	$-0.576000\pi$
$3$	0.702235	−	0.626989i	0.702235	−	0.626989i	0.938734	+	0.344643i	$0.112000\pi$
$4$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$5$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$5$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$6$	−0.930725	−	0.141424i	−0.930725	−	0.141424i
$7$		0			0		0.954865	−	0.297042i	$-0.0960000\pi$
$7$		0			0		−0.954865	+	0.297042i	$0.904000\pi$
$8$	0.876307	−	0.481754i	0.876307	−	0.481754i
$9$	−0.0128376	+	0.113025i	−0.0128376	+	0.113025i
$10$		0			0
$11$	1.51568	+	0.644618i	1.51568	+	0.644618i	0.979855	−	0.199710i	$-0.0640000\pi$
$11$	1.51568	+	0.644618i	1.51568	+	0.644618i	0.535827	+	0.844328i	$0.320000\pi$
$12$	0.484297	+	0.807282i	0.484297	+	0.807282i
$13$		0			0		0.675333	−	0.737513i	$-0.264000\pi$
$13$		0			0		−0.675333	+	0.737513i	$0.736000\pi$
$14$		0			0
$15$		0			0
$16$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$17$	−0.263152	+	1.59649i	−0.263152	+	1.59649i	0.448383	+	0.893841i	$0.352000\pi$
$17$	−0.263152	+	1.59649i	−0.263152	+	1.59649i	−0.711536	+	0.702650i	$0.752000\pi$
$18$	0.0952698	−	0.0621530i	0.0952698	−	0.0621530i
$19$	0.106869	−	0.0659520i	0.106869	−	0.0659520i	−0.470704	−	0.882291i	$-0.656000\pi$
$19$	0.106869	−	0.0659520i	0.106869	−	0.0659520i	0.577573	+	0.816339i	$0.304000\pi$
$20$		0			0
$21$		0			0
$22$	−0.469445	−	1.57875i	−0.469445	−	1.57875i
$23$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$23$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$24$	0.313319	−	0.887739i	0.313319	−	0.887739i
$25$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$26$		0			0
$27$	0.605582	+	0.855927i	0.605582	+	0.855927i
$28$		0			0
$29$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$29$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$30$		0			0
$31$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$31$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$32$	0.309017	+	0.951057i	0.309017	+	0.951057i
$33$	1.46853	−	0.497642i	1.46853	−	0.497642i
$34$	1.39786	−	0.814879i	1.39786	−	0.814879i
$35$		0			0
$36$	−0.108617	−	0.0337888i	−0.108617	−	0.0337888i
$37$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$37$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$38$	−0.118938	−	0.0403044i	−0.118938	−	0.0403044i
$39$		0			0
$40$		0			0
$41$	−1.55993	−	1.07452i	−1.55993	−	1.07452i	−0.962028	−	0.272952i	$-0.912000\pi$
$41$	−1.55993	−	1.07452i	−1.55993	−	1.07452i	−0.597905	−	0.801567i	$-0.704000\pi$
$42$		0			0
$43$	−1.27992	+	0.622047i	−1.27992	+	0.622047i	−0.947098	−	0.320944i	$-0.896000\pi$
$43$	−1.27992	+	0.622047i	−1.27992	+	0.622047i	−0.332820	+	0.942991i	$0.608000\pi$
$44$	−0.917210	+	1.36805i	−0.917210	+	1.36805i
$45$		0			0
$46$		0			0
$47$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$47$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$48$	−0.883731	+	0.324450i	−0.883731	+	0.324450i
$49$	0.823533	−	0.567269i	0.823533	−	0.567269i
$50$	0.728969	−	0.684547i	0.728969	−	0.684547i
$51$	0.816187	+	1.28611i	0.816187	+	1.28611i
$52$		0			0
$53$		0			0		0.984564	−	0.175023i	$-0.0560000\pi$
$53$		0			0		−0.984564	+	0.175023i	$0.944000\pi$
$54$	0.273491	−	1.01220i	0.273491	−	1.01220i
$55$		0			0
$56$		0			0
$57$	0.0336958	−	0.113319i	0.0336958	−	0.113319i
$58$		0			0
$59$	−0.316989	−	1.92310i	−0.316989	−	1.92310i	−0.379779	−	0.925077i	$-0.624000\pi$
$59$	−0.316989	−	1.92310i	−0.316989	−	1.92310i	0.0627905	−	0.998027i	$-0.480000\pi$
$60$		0			0
$61$		0			0		−0.470704	−	0.882291i	$-0.656000\pi$
$61$		0			0		0.470704	+	0.882291i	$0.344000\pi$
$62$		0			0
$63$		0			0
$64$	0.535827	−	0.844328i	0.535827	−	0.844328i
$65$		0			0
$66$	−1.31952	−	0.814315i	−1.31952	−	0.814315i
$67$	1.99369	−	0.0501174i	1.99369	−	0.0501174i	0.994951	−	0.100362i	$-0.0320000\pi$
$67$	1.99369	−	0.0501174i	1.99369	−	0.0501174i	0.998737	+	0.0502443i	$0.0160000\pi$
$68$	−1.51890	−	0.557644i	−1.51890	−	0.557644i
$69$		0			0
$70$		0			0
$71$		0			0		−0.492727	−	0.870184i	$-0.664000\pi$
$71$		0			0		0.492727	+	0.870184i	$0.336000\pi$
$72$	0.0432003	+	0.105229i	0.0432003	+	0.105229i
$73$	0.780497	−	1.77297i	0.780497	−	1.77297i	0.162637	−	0.986686i	$-0.448000\pi$
$73$	0.780497	−	1.77297i	0.780497	−	1.77297i	0.617860	−	0.786288i	$-0.288000\pi$
$74$		0			0
$75$	0.669845	+	0.661480i	0.669845	+	0.661480i
$76$	0.0447586	+	0.117334i	0.0447586	+	0.117334i
$77$		0			0
$78$		0			0
$79$		0			0		−0.260842	−	0.965382i	$-0.584000\pi$
$79$		0			0		0.260842	+	0.965382i	$0.416000\pi$
$80$		0			0
$81$	0.851064	+	0.195858i	0.851064	+	0.195858i
$82$	0.166407	+	1.88687i	0.166407	+	1.88687i
$83$	−0.0159812	+	0.423713i	−0.0159812	+	0.423713i	0.968583	+	0.248690i	$0.0800000\pi$
$83$	−0.0159812	+	0.423713i	−0.0159812	+	0.423713i	−0.984564	+	0.175023i	$0.944000\pi$
$84$		0			0
$85$		0			0
$86$	1.29515	+	0.589686i	1.29515	+	0.589686i
$87$		0			0
$88$	1.63875	−	0.165302i	1.63875	−	0.165302i
$89$	−0.698099	−	1.39164i	−0.698099	−	1.39164i	−0.910106	−	0.414376i	$-0.864000\pi$
$89$	−0.698099	−	1.39164i	−0.698099	−	1.39164i	0.212007	−	0.977268i	$-0.432000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.813304	+	0.474115i	0.813304	+	0.474115i
$97$	−0.643272	−	0.959459i	−0.643272	−	0.959459i	−0.999684	−	0.0251301i	$-0.992000\pi$
$97$	−0.643272	−	0.959459i	−0.643272	−	0.959459i	0.356412	−	0.934329i	$-0.384000\pi$
$98$	−0.962028	−	0.272952i	−0.962028	−	0.272952i
$99$	−0.0923153	+	0.163034i	−0.0923153	+	0.163034i
$100$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$101$		0			0		0.0878512	−	0.996134i	$-0.472000\pi$
$101$		0			0		−0.0878512	+	0.996134i	$0.528000\pi$
$102$	0.470704	−	1.44868i	0.470704	−	1.44868i
$103$		0			0		−0.0125660	−	0.999921i	$-0.504000\pi$
$103$		0			0		0.0125660	+	0.999921i	$0.496000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.653011	+	1.22401i	−0.653011	+	1.22401i	0.309017	+	0.951057i	$0.400000\pi$
$107$	−0.653011	+	1.22401i	−0.653011	+	1.22401i	−0.962028	+	0.272952i	$0.912000\pi$
$108$	−0.954241	+	0.434470i	−0.954241	+	0.434470i
$109$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$109$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.59967	−	1.16223i	−1.59967	−	1.16223i	−0.888136	−	0.459580i	$-0.848000\pi$
$113$	−1.59967	−	1.16223i	−1.59967	−	1.16223i	−0.711536	−	0.702650i	$-0.752000\pi$
$114$	−0.108793	+	0.0462694i	−0.108793	+	0.0462694i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.27972	+	1.47008i	−1.27972	+	1.47008i
$119$		0			0
$120$		0			0
$121$	1.18811	+	1.23376i	1.18811	+	1.23376i
$122$		0			0
$123$	−1.76915	+	0.223496i	−1.76915	+	0.223496i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.0376902	−	0.999289i	$-0.512000\pi$
$127$		0			0		0.0376902	+	0.999289i	$0.488000\pi$
$128$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$129$	−0.508786	+	1.23932i	−0.508786	+	1.23932i
$130$		0			0
$131$	0.756300	−	0.391359i	0.756300	−	0.391359i	−0.0376902	−	0.999289i	$-0.512000\pi$
$131$	0.756300	−	0.391359i	0.756300	−	0.391359i	0.793990	+	0.607930i	$0.208000\pi$
$132$	0.213652	+	1.53577i	0.213652	+	1.53577i
$133$		0			0
$134$	−1.30944	−	1.50422i	−1.30944	−	1.50422i
$135$		0			0
$136$	0.538513	+	1.52579i	0.538513	+	1.52579i
$137$	−1.81205	+	0.770665i	−1.81205	+	0.770665i	−0.837528	+	0.546394i	$0.816000\pi$
$137$	−1.81205	+	0.770665i	−1.81205	+	0.770665i	−0.974527	+	0.224271i	$0.928000\pi$
$138$		0			0
$139$	1.48764	+	0.112379i	1.48764	+	0.112379i	0.793990	−	0.607930i	$-0.208000\pi$
$139$	1.48764	+	0.112379i	1.48764	+	0.112379i	0.693653	+	0.720309i	$0.256000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.0535432	−	0.100362i	0.0535432	−	0.100362i
$145$		0			0
$146$	−1.86361	+	0.528753i	−1.86361	+	0.528753i
$147$	0.222642	−	0.914702i	0.222642	−	0.914702i
$148$		0			0
$149$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$149$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$150$	0.0827038	−	0.937768i	0.0827038	−	0.937768i
$151$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$151$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$152$	0.0618772	−	0.109279i	0.0618772	−	0.109279i
$153$	−0.177064	−	0.0502377i	−0.177064	−	0.0502377i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$157$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.391577	−	0.780600i	−0.391577	−	0.780600i
$163$	1.98739	−	0.200470i	1.98739	−	0.200470i	0.988652	−	0.150226i	$-0.0480000\pi$
$163$	1.98739	−	0.200470i	1.98739	−	0.200470i	0.998737	−	0.0502443i	$-0.0160000\pi$
$164$	1.34779	−	1.33096i	1.34779	−	1.33096i
$165$		0			0
$166$	0.336663	−	0.257771i	0.336663	−	0.257771i
$167$		0			0		−0.745941	−	0.666012i	$-0.768000\pi$
$167$		0			0		0.745941	+	0.666012i	$0.232000\pi$
$168$		0			0
$169$	−0.0878512	−	0.996134i	−0.0878512	−	0.996134i
$170$		0			0
$171$	0.00608226	+	0.0129255i	0.00608226	+	0.0129255i
$172$	−0.371196	−	1.37381i	−0.371196	−	1.37381i
$173$		0			0		0.778462	−	0.627691i	$-0.216000\pi$
$173$		0			0		−0.778462	+	0.627691i	$0.784000\pi$
$174$		0			0
$175$		0			0
$176$	−1.17195	−	1.15731i	−1.17195	−	1.15731i
$177$	−1.42837	−	1.15172i	−1.42837	−	1.15172i
$178$	−0.627295	+	1.42496i	−0.627295	+	1.42496i
$179$	−0.744257	−	1.81288i	−0.744257	−	1.81288i	−0.556876	−	0.830596i	$-0.688000\pi$
$179$	−0.744257	−	1.81288i	−0.744257	−	1.81288i	−0.187381	−	0.982287i	$-0.560000\pi$
$180$		0			0
$181$		0			0		−0.236499	−	0.971632i	$-0.576000\pi$
$181$		0			0		0.236499	+	0.971632i	$0.424000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.42798	+	2.25014i	−1.42798	+	2.25014i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.212007	−	0.977268i	$-0.432000\pi$
$191$		0			0		−0.212007	+	0.977268i	$0.568000\pi$
$192$	−0.153108	−	0.928874i	−0.153108	−	0.928874i
$193$	0.118658	+	0.129583i	0.118658	+	0.129583i	0.793990	−	0.607930i	$-0.208000\pi$
$193$	0.118658	+	0.129583i	0.118658	+	0.129583i	−0.675333	+	0.737513i	$0.736000\pi$
$194$	−0.329239	+	1.10723i	−0.329239	+	1.10723i
$195$		0			0
$196$	0.402906	+	0.915241i	0.402906	+	0.915241i
$197$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$197$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$198$	0.184464	−	0.0327916i	0.184464	−	0.0327916i
$199$		0			0		−0.597905	−	0.801567i	$-0.704000\pi$
$199$		0			0		0.597905	+	0.801567i	$0.296000\pi$
$200$	0.535827	+	0.844328i	0.535827	+	0.844328i
$201$	1.36861	−	1.28521i	1.36861	−	1.28521i
$202$		0			0
$203$		0			0
$204$	−1.41626	+	0.560738i	−1.41626	+	0.560738i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.204493	−	0.0310727i	0.204493	−	0.0310727i
$210$		0			0
$211$	−1.62243	−	0.416570i	−1.62243	−	0.416570i	−0.675333	−	0.737513i	$-0.736000\pi$
$211$	−1.62243	−	0.416570i	−1.62243	−	0.416570i	−0.947098	+	0.320944i	$0.896000\pi$
$212$		0			0
$213$		0			0
$214$	1.35936	−	0.277059i	1.35936	−	0.277059i
$215$		0			0
$216$	0.943021	+	0.458313i	0.943021	+	0.458313i
$217$		0			0
$218$		0			0
$219$	−0.563543	−	1.73441i	−0.563543	−	1.73441i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.112856	−	0.993611i	$-0.536000\pi$
$223$		0			0		0.112856	+	0.993611i	$0.464000\pi$
$224$		0			0
$225$	−0.113608	−	0.00571535i	−0.113608	−	0.00571535i
$226$	0.124156	+	1.97340i	0.124156	+	1.97340i
$227$	−0.583304	+	1.65270i	−0.583304	+	1.65270i	0.162637	+	0.986686i	$0.448000\pi$
$227$	−0.583304	+	1.65270i	−0.583304	+	1.65270i	−0.745941	+	0.666012i	$0.768000\pi$
$228$	0.104998	+	0.0543329i	0.104998	+	0.0543329i
$229$		0			0		−0.285019	−	0.958522i	$-0.592000\pi$
$229$		0			0		0.285019	+	0.958522i	$0.408000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.751067	+	0.489988i	−0.751067	+	0.489988i	−0.863923	−	0.503623i	$-0.832000\pi$
$233$	−0.751067	+	0.489988i	−0.751067	+	0.489988i	0.112856	+	0.993611i	$0.464000\pi$
$234$		0			0
$235$		0			0
$236$	1.94844	+	0.0489799i	1.94844	+	0.0489799i
$237$		0			0
$238$		0			0
$239$		0			0		−0.514440	−	0.857527i	$-0.672000\pi$
$239$		0			0		0.514440	+	0.857527i	$0.328000\pi$
$240$		0			0
$241$	0.0618772	−	0.983510i	0.0618772	−	0.983510i	−0.837528	−	0.546394i	$-0.816000\pi$
$241$	0.0618772	−	0.983510i	0.0618772	−	0.983510i	0.899405	−	0.437116i	$-0.144000\pi$
$242$	0.193303	−	1.70188i	0.193303	−	1.70188i
$243$	−0.198355	+	0.109047i	−0.198355	+	0.109047i
$244$		0			0
$245$		0			0
$246$	1.29991	+	1.22069i	1.29991	+	1.22069i
$247$		0			0
$248$		0			0
$249$	0.254441	+	0.307566i	0.254441	+	0.307566i
$250$		0			0
$251$	0.954865	+	0.297042i	0.954865	+	0.297042i
$251$	0.954865	+	0.297042i	0.954865	+	0.297042i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.728969	+	0.684547i	0.728969	+	0.684547i
$257$	1.81958	+	0.276485i	1.81958	+	0.276485i	0.968583	−	0.248690i	$-0.0800000\pi$
$257$	1.81958	+	0.276485i	1.81958	+	0.276485i	0.850994	+	0.525175i	$0.176000\pi$
$258$	1.27922	−	0.397944i	1.27922	−	0.397944i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.783631	−	0.333278i	−0.783631	−	0.333278i
$263$		0			0		−0.514440	−	0.857527i	$-0.672000\pi$
$263$		0			0		0.514440	+	0.857527i	$0.328000\pi$
$264$	1.04714	−	1.14356i	1.04714	−	1.14356i
$265$		0			0
$266$		0			0
$267$	−1.36277	−	0.539561i	−1.36277	−	0.539561i
$268$	−0.324350	+	1.96777i	−0.324350	+	1.96777i
$269$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$269$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$270$		0			0
$271$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$271$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$272$	0.832381	−	1.38751i	0.832381	−	1.38751i
$273$		0			0
$274$	1.74885	+	0.904972i	1.74885	+	0.904972i
$275$	−0.548175	+	1.55317i	−0.548175	+	1.55317i
$276$		0			0
$277$		0			0		−0.998737	−	0.0502443i	$-0.984000\pi$
$277$		0			0		0.998737	+	0.0502443i	$0.0160000\pi$
$278$	−0.861670	−	1.21788i	−0.861670	−	1.21788i
$279$		0			0
$280$		0			0
$281$	−0.738843	−	0.940252i	−0.738843	−	0.940252i	0.260842	−	0.965382i	$-0.416000\pi$
$281$	−0.738843	−	0.940252i	−0.738843	−	0.940252i	−0.999684	+	0.0251301i	$0.992000\pi$
$282$		0			0
$283$	0.304522	+	0.937223i	0.304522	+	0.937223i	0.979855	+	0.199710i	$0.0640000\pi$
$283$	0.304522	+	0.937223i	0.304522	+	0.937223i	−0.675333	+	0.737513i	$0.736000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.111460	+	0.0227173i	−0.111460	+	0.0227173i
$289$	−1.53244	−	0.519298i	−1.53244	−	0.519298i
$290$		0			0
$291$	−1.05330	−	0.270441i	−1.05330	−	0.270441i
$292$	1.59532	+	1.09889i	1.59532	+	1.09889i
$293$		0			0		0.988652	−	0.150226i	$-0.0480000\pi$
$293$		0			0		−0.988652	+	0.150226i	$0.952000\pi$
$294$	−0.846707	+	0.411504i	−0.846707	+	0.411504i
$295$		0			0
$296$		0			0
$297$	0.366123	+	1.68768i	0.366123	+	1.68768i
$298$		0			0
$299$		0			0
$300$	−0.775280	+	0.534031i	−0.775280	+	0.534031i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.123643	+	0.0219796i	−0.123643	+	0.0219796i
$305$		0			0
$306$	0.0741563	+	0.168453i	0.0741563	+	0.168453i
$307$	−0.936894	+	0.972897i	−0.936894	+	0.972897i	−0.999684	−	0.0251301i	$-0.992000\pi$
$307$	−0.936894	+	0.972897i	−0.936894	+	0.972897i	0.0627905	+	0.998027i	$0.480000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.212007	−	0.977268i	$-0.432000\pi$
$311$		0			0		−0.212007	+	0.977268i	$0.568000\pi$
$312$		0			0
$313$	−1.32998	−	1.01832i	−1.32998	−	1.01832i	−0.997159	−	0.0753268i	$-0.976000\pi$
$313$	−1.32998	−	1.01832i	−1.32998	−	1.01832i	−0.332820	−	0.942991i	$-0.608000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.850994	−	0.525175i	$-0.824000\pi$
$317$		0			0		0.850994	+	0.525175i	$0.176000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.308873	+	1.26897i	0.308873	+	1.26897i
$322$		0			0
$323$	0.0771690	+	0.187970i	0.0771690	+	0.187970i
$324$	−0.351862	+	0.799289i	−0.351862	+	0.799289i
$325$		0			0
$326$	−1.42127	−	1.40352i	−1.42127	−	1.40352i
$327$		0			0
$328$	−1.88463	−	0.190105i	−1.88463	−	0.190105i
$329$		0			0
$330$		0			0
$331$	0.0748104	+	0.158980i	0.0748104	+	0.158980i	0.938734	−	0.344643i	$-0.112000\pi$
$331$	0.0748104	+	0.158980i	0.0748104	+	0.158980i	−0.863923	+	0.503623i	$0.832000\pi$
$332$	−0.413213	−	0.0950940i	−0.413213	−	0.0950940i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.81964	+	0.828489i	1.81964	+	0.828489i	0.920232	+	0.391374i	$0.128000\pi$
$337$	1.81964	+	0.828489i	1.81964	+	0.828489i	0.899405	+	0.437116i	$0.144000\pi$
$338$	−0.711536	+	0.702650i	−0.711536	+	0.702650i
$339$	−1.85205	+	0.186818i	−1.85205	+	0.186818i
$340$		0			0
$341$		0			0
$342$	0.00608226	−	0.0129255i	0.00608226	−	0.0129255i
$343$		0			0
$344$	−0.821927	+	1.16171i	−0.821927	+	1.16171i
$345$		0			0
$346$		0			0
$347$	0.888873	+	0.518167i	0.888873	+	0.518167i	0.876307	−	0.481754i	$-0.160000\pi$
$347$	0.888873	+	0.518167i	0.888873	+	0.518167i	0.0125660	+	0.999921i	$0.496000\pi$
$348$		0			0
$349$		0			0		−0.962028	−	0.272952i	$-0.912000\pi$
$349$		0			0		0.962028	+	0.272952i	$0.0880000\pi$
$350$		0			0
$351$		0			0
$352$	−0.144697	+	1.64070i	−0.144697	+	1.64070i
$353$	−0.115808	+	0.356420i	−0.115808	+	0.356420i	−0.992115	−	0.125333i	$-0.960000\pi$
$353$	−0.115808	+	0.356420i	−0.115808	+	0.356420i	0.876307	+	0.481754i	$0.160000\pi$
$354$	0.0230569	+	1.83471i	0.0230569	+	1.83471i
$355$		0			0
$356$	1.49780	−	0.424966i	1.49780	−	0.424966i
$357$		0			0
$358$	−0.922443	+	1.72904i	−0.922443	+	1.72904i
$359$		0			0		0.910106	−	0.414376i	$-0.136000\pi$
$359$		0			0		−0.910106	+	0.414376i	$0.864000\pi$
$360$		0			0
$361$	−0.441312	+	0.879745i	−0.441312	+	0.879745i
$362$		0			0
$363$	1.60788	+	0.121462i	1.60788	+	0.121462i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.137790	−	0.990461i	$-0.456000\pi$
$367$		0			0		−0.137790	+	0.990461i	$0.544000\pi$
$368$		0			0
$369$	0.141473	−	0.162516i	0.141473	−	0.162516i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.379779	−	0.925077i	$-0.376000\pi$
$373$		0			0		−0.379779	+	0.925077i	$0.624000\pi$
$374$	2.64399	−	0.334014i	2.64399	−	0.334014i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.469268	−	0.0592824i	0.469268	−	0.0592824i	0.112856	−	0.993611i	$-0.464000\pi$
$379$	0.469268	−	0.0592824i	0.469268	−	0.0592824i	0.356412	+	0.934329i	$0.384000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.137790	−	0.990461i	$-0.544000\pi$
$383$		0			0		0.137790	+	0.990461i	$0.456000\pi$
$384$	−0.618115	+	0.710058i	−0.618115	+	0.710058i
$385$		0			0
$386$	0.0242101	−	0.174026i	0.0242101	−	0.174026i
$387$	−0.0538755	−	0.152648i	−0.0538755	−	0.152648i
$388$	1.06300	−	0.452093i	1.06300	−	0.452093i
$389$		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
$392$	0.448383	−	0.893841i	0.448383	−	0.893841i
$393$	0.285723	−	0.749018i	0.285723	−	0.749018i
$394$		0			0
$395$		0			0
$396$	−0.142848	−	0.121230i	−0.142848	−	0.121230i
$397$		0			0		0.962028	−	0.272952i	$-0.0880000\pi$
$397$		0			0		−0.962028	+	0.272952i	$0.912000\pi$
$398$		0			0
$399$		0			0
$400$	0.309017	−	0.951057i	0.309017	−	0.951057i
$401$	−0.108559	+	1.23094i	−0.108559	+	1.23094i	0.728969	+	0.684547i	$0.240000\pi$
$401$	−0.108559	+	1.23094i	−0.108559	+	1.23094i	−0.837528	+	0.546394i	$0.816000\pi$
$402$	−1.86266	−	0.235309i	−1.86266	−	0.235309i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.33482	+	0.733822i	1.33482	+	0.733822i
$409$	0.465416	−	0.657817i	0.465416	−	0.657817i	−0.514440	−	0.857527i	$-0.672000\pi$
$409$	0.465416	−	0.657817i	0.465416	−	0.657817i	0.979855	+	0.199710i	$0.0640000\pi$
$410$		0			0
$411$	−0.789290	+	1.67733i	−0.789290	+	1.67733i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.11514	−	0.853820i	1.11514	−	0.853820i
$418$	−0.154291	−	0.137758i	−0.154291	−	0.137758i
$419$	−0.0303712	+	0.805240i	−0.0303712	+	0.805240i	0.899405	+	0.437116i	$0.144000\pi$
$419$	−0.0303712	+	0.805240i	−0.0303712	+	0.805240i	−0.929776	+	0.368125i	$0.880000\pi$
$420$		0			0
$421$		0			0		−0.974527	−	0.224271i	$-0.928000\pi$
$421$		0			0		0.974527	+	0.224271i	$0.0720000\pi$
$422$	0.713204	+	1.51564i	0.713204	+	1.51564i
$423$		0			0
$424$		0			0
$425$	−1.60986	−	0.162389i	−1.60986	−	0.162389i
$426$		0			0
$427$		0			0
$428$	−1.07997	−	0.870800i	−1.07997	−	0.870800i
$429$		0			0
$430$		0			0
$431$		0			0		−0.492727	−	0.870184i	$-0.664000\pi$
$431$		0			0		0.492727	+	0.870184i	$0.336000\pi$
$432$	−0.247968	−	1.01875i	−0.247968	−	1.01875i
$433$	−1.92189	+	0.493458i	−1.92189	+	0.493458i	−0.929776	+	0.368125i	$0.880000\pi$
$433$	−1.92189	+	0.493458i	−1.92189	+	0.493458i	−0.992115	+	0.125333i	$0.960000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.977168	+	1.53977i	−0.977168	+	1.53977i
$439$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$439$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$440$		0			0
$441$	0.0535432	+	0.100362i	0.0535432	+	0.100362i
$442$		0			0
$443$	0.100515	+	0.609805i	0.100515	+	0.609805i	0.988652	+	0.150226i	$0.0480000\pi$
$443$	0.100515	+	0.609805i	0.100515	+	0.609805i	−0.888136	+	0.459580i	$0.848000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.70118	−	0.302413i	1.70118	−	0.302413i	0.762443	−	0.647056i	$-0.224000\pi$
$449$	1.70118	−	0.302413i	1.70118	−	0.302413i	0.938734	+	0.344643i	$0.112000\pi$
$450$	0.0680124	+	0.0911792i	0.0680124	+	0.0911792i
$451$	−1.67171	−	2.63419i	−1.67171	−	2.63419i
$452$	1.44139	−	1.35356i	1.44139	−	1.35356i
$453$		0			0
$454$	1.64524	−	0.604026i	1.64524	−	0.604026i
$455$		0			0
$456$	−0.0250641	−	0.115536i	−0.0250641	−	0.115536i
$457$	−0.971998	+	0.824898i	−0.971998	+	0.824898i	−0.984564	−	0.175023i	$-0.944000\pi$
$457$	−0.971998	+	0.824898i	−0.971998	+	0.824898i	0.0125660	+	0.999921i	$0.496000\pi$
$458$		0			0
$459$	−1.52584	+	0.741567i	−1.52584	+	0.741567i
$460$		0			0
$461$		0			0		−0.823533	−	0.567269i	$-0.808000\pi$
$461$		0			0		0.823533	+	0.567269i	$0.192000\pi$
$462$		0			0
$463$		0			0		0.0125660	−	0.999921i	$-0.496000\pi$
$463$		0			0		−0.0125660	+	0.999921i	$0.504000\pi$
$464$		0			0
$465$		0			0
$466$	0.856290	+	0.266377i	0.856290	+	0.266377i
$467$	−0.0677975	−	0.0329499i	−0.0677975	−	0.0329499i	0.402906	−	0.915241i	$-0.368000\pi$
$467$	−0.0677975	−	0.0329499i	−0.0677975	−	0.0329499i	−0.470704	+	0.882291i	$0.656000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.20424	−	1.53252i	−1.20424	−	1.53252i
$473$	−2.34093	+	0.117767i	−2.34093	+	0.117767i
$474$		0			0
$475$	0.0725322	+	0.102517i	0.0725322	+	0.102517i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$479$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$480$		0			0
$481$		0			0
$482$	−0.797250	+	0.579236i	−0.797250	+	0.579236i
$483$		0			0
$484$	−1.43454	+	0.935877i	−1.43454	+	0.935877i
$485$		0			0
$486$	0.210458	+	0.0833264i	0.210458	+	0.0833264i
$487$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$487$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$488$		0			0
$489$	1.26992	−	1.38685i	1.26992	−	1.38685i
$490$		0			0
$491$	1.75739	+	0.747418i	1.75739	+	0.747418i	0.994951	+	0.100362i	$0.0320000\pi$
$491$	1.75739	+	0.747418i	1.75739	+	0.747418i	0.762443	+	0.647056i	$0.224000\pi$
$492$	0.111969	−	1.77969i	0.111969	−	1.77969i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.0747971	−	0.392100i	0.0747971	−	0.392100i
$499$	−1.13747	+	1.01559i	−1.13747	+	1.01559i	−0.137790	+	0.990461i	$0.544000\pi$
$499$	−1.13747	+	1.01559i	−1.13747	+	1.01559i	−0.999684	+	0.0251301i	$0.992000\pi$
$500$		0			0
$501$		0			0
$502$	−0.379779	−	0.925077i	−0.379779	−	0.925077i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.686257	−	0.644438i	−0.686257	−	0.644438i
$508$		0			0
$509$		0			0		0.954865	−	0.297042i	$-0.0960000\pi$
$509$		0			0		−0.954865	+	0.297042i	$0.904000\pi$
$510$		0			0
$511$		0			0
$512$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$513$	0.121168	+	0.0515326i	0.121168	+	0.0515326i
$514$	−0.946807	−	1.57825i	−0.946807	−	1.57825i
$515$		0			0
$516$	−1.12203	−	0.731999i	−1.12203	−	0.731999i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.66770	−	1.02919i	1.66770	−	1.02919i	0.728969	−	0.684547i	$-0.240000\pi$
$521$	1.66770	−	1.02919i	1.66770	−	1.02919i	0.938734	−	0.344643i	$-0.112000\pi$
$522$		0			0
$523$	0.989810	−	1.64993i	0.989810	−	1.64993i	0.260842	−	0.965382i	$-0.416000\pi$
$523$	0.989810	−	1.64993i	0.989810	−	1.64993i	0.728969	−	0.684547i	$-0.240000\pi$
$524$	0.242711	+	0.816237i	0.242711	+	0.816237i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.54860	−	0.0779068i	−1.54860	−	0.0779068i
$529$	0.577573	+	0.816339i	0.577573	+	0.816339i
$530$		0			0
$531$	0.221427	−	0.0111395i	0.221427	−	0.0111395i
$532$		0			0
$533$		0			0
$534$	0.452927	+	1.39396i	0.452927	+	1.39396i
$535$		0			0
$536$	1.72294	−	1.00438i	1.72294	−	1.00438i
$537$	−1.65930	−	0.806429i	−1.65930	−	0.806429i
$538$		0			0
$539$	1.61389	−	0.328935i	1.61389	−	0.328935i
$540$		0			0
$541$		0			0		0.0125660	−	0.999921i	$-0.496000\pi$
$541$		0			0		−0.0125660	+	0.999921i	$0.504000\pi$
$542$		0			0
$543$		0			0
$544$	−1.59967	+	0.243070i	−1.59967	+	0.243070i
$545$		0			0
$546$		0			0
$547$	1.16264	−	0.986686i	1.16264	−	0.986686i	0.162637	−	0.986686i	$-0.448000\pi$
$547$	1.16264	−	0.986686i	1.16264	−	0.986686i	1.00000			$0$
$548$	−0.417469	−	1.92437i	−0.417469	−	1.92437i
$549$		0			0
$550$	1.54616	−	0.567649i	1.54616	−	0.567649i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.389145	+	1.44024i	−0.389145	+	1.44024i
$557$		0			0		−0.402906	−	0.915241i	$-0.632000\pi$
$557$		0			0		0.402906	+	0.915241i	$0.368000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.408034	+	2.47546i	0.408034	+	2.47546i
$562$	−0.253520	+	1.16863i	−0.253520	+	1.16863i
$563$	−0.824962	−	1.54632i	−0.824962	−	1.54632i	−0.837528	−	0.546394i	$-0.816000\pi$
$563$	−0.824962	−	1.54632i	−0.824962	−	1.54632i	0.0125660	−	0.999921i	$-0.496000\pi$
$564$		0			0
$565$		0			0
$566$	0.528033	−	0.832047i	0.528033	−	0.832047i
$567$		0			0
$568$		0			0
$569$	−1.83988	+	0.0462510i	−1.83988	+	0.0462510i	−0.929776	−	0.368125i	$-0.880000\pi$
$569$	−1.83988	+	0.0462510i	−1.83988	+	0.0462510i	−0.910106	+	0.414376i	$0.864000\pi$
$570$		0			0
$571$	−0.552130	+	0.141763i	−0.552130	+	0.141763i	−0.514440	−	0.857527i	$-0.672000\pi$
$571$	−0.552130	+	0.141763i	−0.552130	+	0.141763i	−0.0376902	+	0.999289i	$0.512000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.0885510	+	0.0714007i	0.0885510	+	0.0714007i
$577$	0.336555	+	0.332352i	0.336555	+	0.332352i	0.850994	−	0.525175i	$-0.176000\pi$
$577$	0.336555	+	0.332352i	0.336555	+	0.332352i	−0.514440	+	0.857527i	$0.672000\pi$
$578$	0.576687	+	1.51178i	0.576687	+	1.51178i
$579$	0.164572	+	0.0166006i	0.164572	+	0.0166006i
$580$		0			0
$581$		0			0
$582$	0.463019	+	0.983966i	0.463019	+	0.983966i
$583$		0			0
$584$	−0.170182	−	1.92968i	−0.170182	−	1.92968i
$585$		0			0
$586$		0			0
$587$	0.414211	−	0.317147i	0.414211	−	0.317147i	−0.379779	−	0.925077i	$-0.624000\pi$
$587$	0.414211	−	0.317147i	0.414211	−	0.317147i	0.793990	+	0.607930i	$0.208000\pi$
$588$	0.856781	+	0.390096i	0.856781	+	0.390096i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.590686	+	1.25527i	−0.590686	+	1.25527i	0.356412	+	0.934329i	$0.384000\pi$
$593$	−0.590686	+	1.25527i	−0.590686	+	1.25527i	−0.947098	+	0.320944i	$0.896000\pi$
$594$	1.06701	−	1.35787i	1.06701	−	1.35787i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$599$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$600$	0.905660	+	0.256959i	0.905660	+	0.256959i
$601$	0.528033	−	0.932536i	0.528033	−	0.932536i	−0.470704	−	0.882291i	$-0.656000\pi$
$601$	0.528033	−	0.932536i	0.528033	−	0.932536i	0.998737	−	0.0502443i	$-0.0160000\pi$
$602$		0			0
$603$	−0.0199296	+	0.225979i	−0.0199296	+	0.225979i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.962028	−	0.272952i	$-0.0880000\pi$
$607$		0			0		−0.962028	+	0.272952i	$0.912000\pi$
$608$	0.0957483	+	0.0812580i	0.0957483	+	0.0812580i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.0825264	−	0.164515i	0.0825264	−	0.164515i
$613$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$613$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$614$	1.34683	+	0.101741i	1.34683	+	0.101741i
$615$		0			0
$616$		0			0
$617$	−0.437049	−	1.23831i	−0.437049	−	1.23831i	−0.929776	−	0.368125i	$-0.880000\pi$
$617$	−0.437049	−	1.23831i	−0.437049	−	1.23831i	0.492727	−	0.870184i	$-0.336000\pi$
$618$		0			0
$619$	0.588804	+	0.676387i	0.588804	+	0.676387i	0.968583	−	0.248690i	$-0.0800000\pi$
$619$	0.588804	+	0.676387i	0.588804	+	0.676387i	−0.379779	+	0.925077i	$0.624000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$626$	0.0631332	+	1.67387i	0.0631332	+	1.67387i
$627$	0.124120	−	0.150035i	0.124120	−	0.150035i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.379779	−	0.925077i	$-0.376000\pi$
$631$		0			0		−0.379779	+	0.925077i	$0.624000\pi$
$632$		0			0
$633$	−1.40051	+	0.724717i	−1.40051	+	0.724717i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.45380	−	0.109822i	−1.45380	−	0.109822i	−0.675333	−	0.737513i	$-0.736000\pi$
$641$	−1.45380	−	0.109822i	−1.45380	−	0.109822i	−0.778462	+	0.627691i	$0.784000\pi$
$642$	0.780877	−	1.04686i	0.780877	−	1.04686i
$643$	0.841825	−	1.67816i	0.841825	−	1.67816i	0.112856	−	0.993611i	$-0.464000\pi$
$643$	0.841825	−	1.67816i	0.841825	−	1.67816i	0.728969	−	0.684547i	$-0.240000\pi$
$644$		0			0
$645$		0			0
$646$	0.0956444	−	0.179277i	0.0956444	−	0.179277i
$647$		0			0		−0.762443	−	0.647056i	$-0.776000\pi$
$647$		0			0		0.762443	+	0.647056i	$0.224000\pi$
$648$	0.840148	−	0.238371i	0.840148	−	0.238371i
$649$	0.759213	−	3.11915i	0.759213	−	3.11915i
$650$		0			0
$651$		0			0
$652$	−0.175480	+	1.98975i	−0.175480	+	1.98975i
$653$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$653$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$654$		0			0
$655$		0			0
$656$	1.05483	+	1.57331i	1.05483	+	1.57331i
$657$	0.190370	+	0.110976i	0.190370	+	0.110976i
$658$		0			0
$659$	−0.746226	−	0.410241i	−0.746226	−	0.410241i	0.0627905	−	0.998027i	$-0.480000\pi$
$659$	−0.746226	−	0.410241i	−0.746226	−	0.410241i	−0.809017	+	0.587785i	$0.800000\pi$
$660$		0			0
$661$		0			0		0.617860	−	0.786288i	$-0.288000\pi$
$661$		0			0		−0.617860	+	0.786288i	$0.712000\pi$
$662$	0.0748104	−	0.158980i	0.0748104	−	0.158980i
$663$		0			0
$664$	0.190121	+	0.379001i	0.190121	+	0.379001i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.303506	−	0.644982i	−0.303506	−	0.644982i	0.693653	−	0.720309i	$-0.256000\pi$
$673$	−0.303506	−	0.644982i	−0.303506	−	0.644982i	−0.997159	+	0.0753268i	$0.976000\pi$
$674$	−0.521518	−	1.93015i	−0.521518	−	1.93015i
$675$	−0.816213	+	0.658131i	−0.816213	+	0.658131i
$676$	0.994951	+	0.100362i	0.994951	+	0.100362i
$677$		0			0		−0.356412	−	0.934329i	$-0.616000\pi$
$677$		0			0		0.356412	+	0.934329i	$0.384000\pi$
$678$	1.32449	+	1.30795i	1.32449	+	1.30795i
$679$		0			0
$680$		0			0
$681$	0.626607	+	1.52631i	0.626607	+	1.52631i
$682$		0			0
$683$	−0.375556	−	1.54293i	−0.375556	−	1.54293i	−0.778462	−	0.627691i	$-0.784000\pi$
$683$	−0.375556	−	1.54293i	−0.375556	−	1.54293i	0.402906	−	0.915241i	$-0.368000\pi$
$684$	−0.0138362	+	0.00355253i	−0.0138362	+	0.00355253i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.41903	−	0.107195i	1.41903	−	0.107195i
$689$		0			0
$690$		0			0
$691$	0.0199546	+	0.0152786i	0.0199546	+	0.0152786i	0.617860	−	0.786288i	$-0.288000\pi$
$691$	0.0199546	+	0.0152786i	0.0199546	+	0.0152786i	−0.597905	+	0.801567i	$0.704000\pi$
$692$		0			0
$693$		0			0
$694$	−0.167334	−	1.01518i	−0.167334	−	1.01518i
$695$		0			0
$696$		0			0
$697$	2.12596	−	2.20766i	2.12596	−	2.20766i
$698$		0			0
$699$	−0.220208	+	0.814997i	−0.220208	+	0.814997i
$700$		0			0
$701$		0			0		−0.597905	−	0.801567i	$-0.704000\pi$
$701$		0			0		0.597905	+	0.801567i	$0.296000\pi$
$702$		0			0
$703$		0			0
$704$	1.35641	−	0.934329i	1.35641	−	0.934329i
$705$		0			0
$706$	0.348445	−	0.137959i	0.348445	−	0.137959i
$707$		0			0
$708$	1.39897	−	1.18725i	1.39897	−	1.18725i
$709$		0			0		0.556876	−	0.830596i	$-0.312000\pi$
$709$		0			0		−0.556876	+	0.830596i	$0.688000\pi$
$710$		0			0
$711$		0			0
$712$	−1.28218	−	0.883195i	−1.28218	−	0.883195i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.92023	−	0.391374i	1.92023	−	0.391374i
$717$		0			0
$718$		0			0
$719$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$719$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$720$		0			0
$721$		0			0
$722$	0.959158	−	0.220734i	0.959158	−	0.220734i
$723$	−0.573198	−	0.729451i	−0.573198	−	0.729451i
$724$		0			0
$725$		0			0
$726$	−0.931316	−	1.31632i	−0.931316	−	1.31632i
$727$		0			0		−0.998737	−	0.0502443i	$-0.984000\pi$
$727$		0			0		0.998737	+	0.0502443i	$0.0160000\pi$
$728$		0			0
$729$	−0.361575	+	1.02447i	−0.361575	+	1.02447i
$730$		0			0
$731$	−0.656279	−	2.20707i	−0.656279	−	2.20707i
$732$		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
$737$	3.05410	+	1.20921i	3.05410	+	1.20921i
$738$	−0.215399	−	0.00541471i	−0.215399	−	0.00541471i
$739$	−1.32998	−	0.867664i	−1.32998	−	0.867664i	−0.332820	−	0.942991i	$-0.608000\pi$
$739$	−1.32998	−	0.867664i	−1.32998	−	0.867664i	−0.997159	+	0.0753268i	$0.976000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$743$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.0476848	−	0.00724570i	−0.0476848	−	0.00724570i
$748$	−1.94271	−	1.82432i	−1.94271	−	1.82432i
$749$		0			0
$750$		0			0
$751$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$751$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$752$		0			0
$753$	0.856781	−	0.390096i	0.856781	−	0.390096i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$757$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$758$	−0.344801	−	0.323789i	−0.344801	−	0.323789i
$759$		0			0
$760$		0			0
$761$	0.371566	−	0.204270i	0.371566	−	0.204270i	−0.285019	−	0.958522i	$-0.592000\pi$
$761$	0.371566	−	0.204270i	0.371566	−	0.204270i	0.656586	+	0.754251i	$0.272000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.941111	+	0.0236577i	0.941111	+	0.0236577i
$769$	0.618896	+	0.245038i	0.618896	+	0.245038i	0.656586	−	0.754251i	$-0.272000\pi$
$769$	0.618896	+	0.245038i	0.618896	+	0.245038i	−0.0376902	+	0.999289i	$0.512000\pi$
$770$		0			0
$771$	1.45112	−	0.946698i	1.45112	−	0.946698i
$772$	−0.149522	+	0.0922744i	−0.149522	+	0.0922744i
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	−0.0832755	+	0.138813i	−0.0832755	+	0.138813i
$775$		0			0
$776$	−1.02593	−	0.530882i	−1.02593	−	0.530882i
$777$		0			0
$778$		0			0
$779$	−0.237575	−	0.0119519i	−0.237575	−	0.0119519i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.974527	+	0.224271i	−0.974527	+	0.224271i
$785$		0			0
$786$	−0.759255	+	0.257289i	−0.759255	+	0.257289i
$787$	−0.281012	+	0.163816i	−0.281012	+	0.163816i	−0.637424	−	0.770513i	$-0.720000\pi$
$787$	−0.281012	+	0.163816i	−0.281012	+	0.163816i	0.356412	+	0.934329i	$0.384000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.00235432	+	0.187341i	−0.00235432	+	0.187341i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.556876	−	0.830596i	$-0.312000\pi$
$797$		0			0		−0.556876	+	0.830596i	$0.688000\pi$
$798$		0			0
$799$		0			0
$800$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$801$	0.166252	−	0.0610370i	0.166252	−	0.0610370i
$802$	1.01766	−	0.700985i	1.01766	−	0.700985i
$803$	2.32588	−	2.18414i	2.32588	−	2.18414i
$804$	1.00600	+	1.58520i	1.00600	+	1.58520i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.461723	+	0.479466i	−0.461723	+	0.479466i	−0.910106	−	0.414376i	$-0.864000\pi$
$809$	−0.461723	+	0.479466i	−0.461723	+	0.479466i	0.448383	+	0.893841i	$0.352000\pi$
$810$		0			0
$811$	−1.34896	−	1.47316i	−1.34896	−	1.47316i	−0.711536	−	0.702650i	$-0.752000\pi$
$811$	−1.34896	−	1.47316i	−1.34896	−	1.47316i	−0.637424	−	0.770513i	$-0.720000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.285425	−	1.49625i	−0.285425	−	1.49625i
$817$	−0.0957580	+	0.150891i	−0.0957580	+	0.150891i
$818$	−0.803523	+	0.0606993i	−0.803523	+	0.0606993i
$819$		0			0
$820$		0			0
$821$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$821$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$822$	1.79551	−	0.461010i	1.79551	−	0.461010i
$823$		0			0		−0.236499	−	0.971632i	$-0.576000\pi$
$823$		0			0		0.236499	+	0.971632i	$0.424000\pi$
$824$		0			0
$825$	0.588870	+	1.43439i	0.588870	+	1.43439i
$826$		0			0
$827$	0.0586808	+	0.0473156i	0.0586808	+	0.0473156i	0.656586	−	0.754251i	$-0.272000\pi$
$827$	0.0586808	+	0.0473156i	0.0586808	+	0.0473156i	−0.597905	+	0.801567i	$0.704000\pi$
$828$		0			0
$829$		0			0		−0.356412	−	0.934329i	$-0.616000\pi$
$829$		0			0		0.356412	+	0.934329i	$0.384000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.688925	+	1.46404i	0.688925	+	1.46404i
$834$	−1.36869	−	0.314981i	−1.36869	−	0.314981i
$835$		0			0
$836$	−0.00779584	+	0.206693i	−0.00779584	+	0.206693i
$837$		0			0
$838$	0.639808	−	0.489878i	0.639808	−	0.489878i
$839$		0			0		−0.910106	−	0.414376i	$-0.864000\pi$
$839$		0			0		0.910106	+	0.414376i	$0.136000\pi$
$840$		0			0
$841$	0.994951	−	0.100362i	0.994951	−	0.100362i
$842$		0			0
$843$	−1.10837	−	0.197031i	−1.10837	−	0.197031i
$844$	0.713204	−	1.51564i	0.713204	−	1.51564i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.801475	+	0.467219i	0.801475	+	0.467219i
$850$	0.901044	+	1.34393i	0.901044	+	1.34393i
$851$		0			0
$852$		0			0
$853$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$853$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$854$		0			0
$855$		0			0
$856$	0.0174330	+	1.38720i	0.0174330	+	1.38720i
$857$	−0.472401	+	1.94081i	−0.472401	+	1.94081i	−0.187381	+	0.982287i	$0.560000\pi$
$857$	−0.472401	+	1.94081i	−0.472401	+	1.94081i	−0.285019	+	0.958522i	$0.592000\pi$
$858$		0			0
$859$	0.397753	+	0.337558i	0.397753	+	0.337558i	0.823533	−	0.567269i	$-0.192000\pi$
$859$	0.397753	+	0.337558i	0.397753	+	0.337558i	−0.425779	+	0.904827i	$0.640000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$863$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$864$	−0.626900	+	0.840438i	−0.626900	+	0.840438i
$865$		0			0
$866$	1.60528	+	1.16630i	1.60528	+	1.16630i
$867$	−1.40172	+	0.596152i	−1.40172	+	0.596152i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.116700	−	0.0603884i	0.116700	−	0.0603884i
$874$		0			0
$875$		0			0
$876$	1.80928	−	0.228566i	1.80928	−	0.228566i
$877$		0			0		−0.0376902	−	0.999289i	$-0.512000\pi$
$877$		0			0		0.0376902	+	0.999289i	$0.488000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.57546	+	0.199027i	−1.57546	+	0.199027i	−0.863923	−	0.503623i	$-0.832000\pi$
$881$	−1.57546	+	0.199027i	−1.57546	+	0.199027i	−0.711536	+	0.702650i	$0.752000\pi$
$882$	0.0432003	−	0.105229i	0.0432003	−	0.105229i
$883$	1.34372	+	1.39536i	1.34372	+	1.39536i	0.850994	+	0.525175i	$0.176000\pi$
$883$	1.34372	+	1.39536i	1.34372	+	1.39536i	0.492727	+	0.870184i	$0.336000\pi$
$884$		0			0
$885$		0			0
$886$	0.405792	−	0.466153i	0.405792	−	0.466153i
$887$		0			0		−0.656586	−	0.754251i	$-0.728000\pi$
$887$		0			0		0.656586	+	0.754251i	$0.272000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.16369	+	0.845469i	1.16369	+	0.845469i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.31738	−	1.11801i	−1.31738	−	1.11801i
$899$		0			0
$900$	0.0269021	−	0.110524i	0.0269021	−	0.110524i
$901$		0			0
$902$	−0.964091	+	2.96717i	−0.964091	+	2.96717i
$903$		0			0
$904$	−1.96171	−	0.247822i	−1.96171	−	0.247822i
$905$		0			0
$906$		0			0
$907$	−1.04552	−	1.55942i	−1.04552	−	1.55942i	−0.809017	−	0.587785i	$-0.800000\pi$
$907$	−1.04552	−	1.55942i	−1.04552	−	1.55942i	−0.236499	−	0.971632i	$-0.576000\pi$
$908$	−1.51412	−	0.882657i	−1.51412	−	0.882657i
$909$		0			0
$910$		0			0
$911$		0			0		0.577573	−	0.816339i	$-0.304000\pi$
$911$		0			0		−0.577573	+	0.816339i	$0.696000\pi$
$912$	−0.0730452	+	0.0929574i	−0.0730452	+	0.0929574i
$913$	−0.297355	+	0.631912i	−0.297355	+	0.631912i
$914$	1.25517	+	0.223128i	1.25517	+	0.223128i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	1.54399	+	0.702988i	1.54399	+	0.702988i
$919$		0			0		0.793990	−	0.607930i	$-0.208000\pi$
$919$		0			0		−0.793990	+	0.607930i	$0.792000\pi$
$920$		0			0
$921$	−0.0479241	+	1.27062i	−0.0479241	+	1.27062i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.961047	+	0.949045i	0.961047	+	0.949045i	0.998737	−	0.0502443i	$-0.0160000\pi$
$929$	0.961047	+	0.949045i	0.961047	+	0.949045i	−0.0376902	+	0.999289i	$0.512000\pi$
$930$		0			0
$931$	0.0505974	−	0.114937i	0.0505974	−	0.114937i
$932$	−0.340573	−	0.829578i	−0.340573	−	0.829578i
$933$		0			0
$934$	0.0178274	+	0.0732420i	0.0178274	+	0.0732420i
$935$		0			0
$936$		0			0
$937$	−1.58748	+	0.0399061i	−1.58748	+	0.0399061i	−0.809017	−	0.587785i	$-0.800000\pi$
$937$	−1.58748	+	0.0399061i	−1.58748	+	0.0399061i	−0.778462	+	0.627691i	$0.784000\pi$
$938$		0			0
$939$	−1.57243	+	0.118784i	−1.57243	+	0.118784i
$940$		0			0
$941$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$941$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$942$		0			0
$943$		0			0
$944$	−0.413213	+	1.90475i	−0.413213	+	1.90475i
$945$		0			0
$946$	1.58291	+	1.72865i	1.58291	+	1.72865i
$947$	0.530008	−	1.78242i	0.530008	−	1.78242i	−0.0878512	−	0.996134i	$-0.528000\pi$
$947$	0.530008	−	1.78242i	0.530008	−	1.78242i	0.617860	−	0.786288i	$-0.288000\pi$
$948$		0			0
$949$		0			0
$950$	0.0327567	−	0.121234i	0.0327567	−	0.121234i
$951$		0			0
$952$		0			0
$953$	0.480511	+	0.757165i	0.480511	+	0.757165i	0.994951	−	0.100362i	$-0.0320000\pi$
$953$	0.480511	+	0.757165i	0.480511	+	0.757165i	−0.514440	+	0.857527i	$0.672000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.899405	−	0.437116i	0.899405	−	0.437116i
$962$		0			0
$963$	−0.129960	−	0.0895195i	−0.129960	−	0.0895195i
$964$	0.954495	+	0.245073i	0.954495	+	0.245073i
$965$		0			0
$966$		0			0
$967$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$967$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$968$	1.63551	+	0.508780i	1.63551	+	0.508780i
$969$	0.172046	+	0.0836153i	0.172046	+	0.0836153i
$970$		0			0
$971$	−1.01496	+	0.343940i	−1.01496	+	0.343940i	−0.778462	−	0.627691i	$-0.784000\pi$
$971$	−1.01496	+	0.343940i	−1.01496	+	0.343940i	−0.236499	+	0.971632i	$0.576000\pi$
$972$	−0.0699472	−	0.215275i	−0.0699472	−	0.215275i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.861670	−	1.21788i	−0.861670	−	1.21788i	−0.974527	−	0.224271i	$-0.928000\pi$
$977$	−0.861670	−	1.21788i	−0.861670	−	1.21788i	0.112856	−	0.993611i	$-0.464000\pi$
$978$	−1.87806	−	0.0944813i	−1.87806	−	0.0944813i
$979$	−0.161017	−	2.55930i	−0.161017	−	2.55930i
$980$		0			0
$981$		0			0
$982$	−0.544310	−	1.83052i	−0.544310	−	1.83052i
$983$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$983$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$984$	−1.44265	+	1.04815i	−1.44265	+	1.04815i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.675333	−	0.737513i	$-0.264000\pi$
$991$		0			0		−0.675333	+	0.737513i	$0.736000\pi$
$992$		0			0
$993$	0.152213	+	0.0647362i	0.152213	+	0.0647362i
$994$		0			0
$995$		0			0
$996$	−0.349796	+	0.192302i	−0.349796	+	0.192302i
$997$		0			0		0.954865	−	0.297042i	$-0.0960000\pi$
$997$		0			0		−0.954865	+	0.297042i	$0.904000\pi$
$998$	1.50758	+	0.229077i	1.50758	+	0.229077i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.147.1	✓	100
8.3	odd	2	CM	2008.1.bd.a.147.1	✓	100
251.181	even	125	inner	2008.1.bd.a.683.1	yes	100
2008.683	odd	250	inner	2008.1.bd.a.683.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.147.1	✓	100	1.1	even	1	trivial
2008.1.bd.a.147.1	✓	100	8.3	odd	2	CM
2008.1.bd.a.683.1	yes	100	251.181	even	125	inner
2008.1.bd.a.683.1	yes	100	2008.683	odd	250	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2008 = 2^{3} \cdot 251 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2008.bd (of order \(250\), degree \(100\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.637424 - 0.770513i) q^{2} +(0.702235 - 0.626989i) q^{3} +(-0.187381 + 0.982287i) q^{4} +(-0.930725 - 0.141424i) q^{6} +(0.876307 - 0.481754i) q^{8} +(-0.0128376 + 0.113025i) q^{9} +O(q^{10})\)	\(q+(-0.637424 - 0.770513i) q^{2} +(0.702235 - 0.626989i) q^{3} +(-0.187381 + 0.982287i) q^{4} +(-0.930725 - 0.141424i) q^{6} +(0.876307 - 0.481754i) q^{8} +(-0.0128376 + 0.113025i) q^{9} +(1.51568 + 0.644618i) q^{11} +(0.484297 + 0.807282i) q^{12} +(-0.929776 - 0.368125i) q^{16} +(-0.263152 + 1.59649i) q^{17} +(0.0952698 - 0.0621530i) q^{18} +(0.106869 - 0.0659520i) q^{19} +(-0.469445 - 1.57875i) q^{22} +(0.313319 - 0.887739i) q^{24} +(0.0627905 + 0.998027i) q^{25} +(0.605582 + 0.855927i) q^{27} +(0.309017 + 0.951057i) q^{32} +(1.46853 - 0.497642i) q^{33} +(1.39786 - 0.814879i) q^{34} +(-0.108617 - 0.0337888i) q^{36} +(-0.118938 - 0.0403044i) q^{38} +(-1.55993 - 1.07452i) q^{41} +(-1.27992 + 0.622047i) q^{43} +(-0.917210 + 1.36805i) q^{44} +(-0.883731 + 0.324450i) q^{48} +(0.823533 - 0.567269i) q^{49} +(0.728969 - 0.684547i) q^{50} +(0.816187 + 1.28611i) q^{51} +(0.273491 - 1.01220i) q^{54} +(0.0336958 - 0.113319i) q^{57} +(-0.316989 - 1.92310i) q^{59} +(0.535827 - 0.844328i) q^{64} +(-1.31952 - 0.814315i) q^{66} +(1.99369 - 0.0501174i) q^{67} +(-1.51890 - 0.557644i) q^{68} +(0.0432003 + 0.105229i) q^{72} +(0.780497 - 1.77297i) q^{73} +(0.669845 + 0.661480i) q^{75} +(0.0447586 + 0.117334i) q^{76} +(0.851064 + 0.195858i) q^{81} +(0.166407 + 1.88687i) q^{82} +(-0.0159812 + 0.423713i) q^{83} +(1.29515 + 0.589686i) q^{86} +(1.63875 - 0.165302i) q^{88} +(-0.698099 - 1.39164i) q^{89} +(0.813304 + 0.474115i) q^{96} +(-0.643272 - 0.959459i) q^{97} +(-0.962028 - 0.272952i) q^{98} +(-0.0923153 + 0.163034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 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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