LMFDB - Embedded newform 2008.1.bd.a.115.1

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			115.1
Root			$-0.979855 + 0.199710i$ of defining polynomial
Character	$\chi$	$=$	2008.115
Dual form			2008.1.bd.a.227.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.728969 - 0.684547i) q^{2} +(-1.27992 + 0.622047i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-0.507200 + 1.32962i) q^{6} +(-0.637424 - 0.770513i) q^{8} +(0.633388 - 0.806049i) q^{9} +O(q^{10})$	\(q+(0.728969 - 0.684547i) q^{2} +(-1.27992 + 0.622047i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-0.507200 + 1.32962i) q^{6} +(-0.637424 - 0.770513i) q^{8} +(0.633388 - 0.806049i) q^{9} +(-0.225071 + 0.0170022i) q^{11} +(0.540453 + 1.31645i) q^{12} +(-0.992115 - 0.125333i) q^{16} +(0.161209 - 0.596639i) q^{17} +(-0.0900591 - 1.02117i) q^{18} +(-0.499529 - 1.67992i) q^{19} +(-0.152431 + 0.166466i) q^{22} +(1.29515 + 0.589686i) q^{24} +(0.876307 + 0.481754i) q^{25} +(-0.00758238 + 0.0349517i) q^{27} +(-0.809017 + 0.587785i) q^{32} +(0.277497 - 0.161766i) q^{33} +(-0.290911 - 0.545286i) q^{34} +(-0.764688 - 0.682750i) q^{36} +(-1.51412 - 0.882657i) q^{38} +(-0.194999 - 1.71681i) q^{41} +(-1.77403 - 0.917999i) q^{43} +(0.00283632 + 0.225695i) q^{44} +(1.34779 - 0.456726i) q^{48} +(0.112856 - 0.993611i) q^{49} +(0.968583 - 0.248690i) q^{50} +(0.164803 + 0.863928i) q^{51} +(0.0183988 + 0.0306692i) q^{54} +(1.68434 + 1.83943i) q^{57} +(-0.123378 - 0.456624i) q^{59} +(-0.187381 + 0.982287i) q^{64} +(0.0915497 - 0.307882i) q^{66} +(1.61389 + 0.328935i) q^{67} +(-0.585339 - 0.198354i) q^{68} +(-1.02481 + 0.0257617i) q^{72} +(0.838414 - 0.149042i) q^{73} +(-1.42127 - 0.0715012i) q^{75} +(-1.70797 + 0.393060i) q^{76} +(0.230406 + 0.946599i) q^{81} +(-1.31738 - 1.11801i) q^{82} +(-0.263142 + 0.0818589i) q^{83} +(-1.92163 + 0.545214i) q^{86} +(0.156566 + 0.162583i) q^{88} +(-1.09982 - 0.717509i) q^{89} +(0.669845 - 1.25556i) q^{96} +(0.00532818 - 0.423981i) q^{97} +(-0.597905 - 0.801567i) q^{98} +(-0.128853 + 0.192188i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{77}{125}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.728969	−	0.684547i	0.728969	−	0.684547i
$2$	0.728969	−	0.684547i	0.728969	−	0.684547i
$3$	−1.27992	+	0.622047i	−1.27992	+	0.622047i	−0.947098	−	0.320944i	$-0.896000\pi$
$3$	−1.27992	+	0.622047i	−1.27992	+	0.622047i	−0.332820	+	0.942991i	$0.608000\pi$
$4$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$5$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$5$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$6$	−0.507200	+	1.32962i	−0.507200	+	1.32962i
$7$		0			0		0.745941	−	0.666012i	$-0.232000\pi$
$7$		0			0		−0.745941	+	0.666012i	$0.768000\pi$
$8$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$9$	0.633388	−	0.806049i	0.633388	−	0.806049i
$10$		0			0
$11$	−0.225071	+	0.0170022i	−0.225071	+	0.0170022i	−0.187381	−	0.982287i	$-0.560000\pi$
$11$	−0.225071	+	0.0170022i	−0.225071	+	0.0170022i	−0.0376902	+	0.999289i	$0.512000\pi$
$12$	0.540453	+	1.31645i	0.540453	+	1.31645i
$13$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$13$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$14$		0			0
$15$		0			0
$16$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$17$	0.161209	−	0.596639i	0.161209	−	0.596639i	−0.837528	−	0.546394i	$-0.816000\pi$
$17$	0.161209	−	0.596639i	0.161209	−	0.596639i	0.998737	−	0.0502443i	$-0.0160000\pi$
$18$	−0.0900591	−	1.02117i	−0.0900591	−	1.02117i
$19$	−0.499529	−	1.67992i	−0.499529	−	1.67992i	−0.711536	−	0.702650i	$-0.752000\pi$
$19$	−0.499529	−	1.67992i	−0.499529	−	1.67992i	0.212007	−	0.977268i	$-0.432000\pi$
$20$		0			0
$21$		0			0
$22$	−0.152431	+	0.166466i	−0.152431	+	0.166466i
$23$		0			0		0.778462	−	0.627691i	$-0.216000\pi$
$23$		0			0		−0.778462	+	0.627691i	$0.784000\pi$
$24$	1.29515	+	0.589686i	1.29515	+	0.589686i
$25$	0.876307	+	0.481754i	0.876307	+	0.481754i
$26$		0			0
$27$	−0.00758238	+	0.0349517i	−0.00758238	+	0.0349517i
$28$		0			0
$29$		0			0		−0.920232	−	0.391374i	$-0.872000\pi$
$29$		0			0		0.920232	+	0.391374i	$0.128000\pi$
$30$		0			0
$31$		0			0		0.236499	−	0.971632i	$-0.424000\pi$
$31$		0			0		−0.236499	+	0.971632i	$0.576000\pi$
$32$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$33$	0.277497	−	0.161766i	0.277497	−	0.161766i
$34$	−0.290911	−	0.545286i	−0.290911	−	0.545286i
$35$		0			0
$36$	−0.764688	−	0.682750i	−0.764688	−	0.682750i
$37$		0			0		0.0376902	−	0.999289i	$-0.488000\pi$
$37$		0			0		−0.0376902	+	0.999289i	$0.512000\pi$
$38$	−1.51412	−	0.882657i	−1.51412	−	0.882657i
$39$		0			0
$40$		0			0
$41$	−0.194999	−	1.71681i	−0.194999	−	1.71681i	−0.597905	−	0.801567i	$-0.704000\pi$
$41$	−0.194999	−	1.71681i	−0.194999	−	1.71681i	0.402906	−	0.915241i	$-0.368000\pi$
$42$		0			0
$43$	−1.77403	−	0.917999i	−1.77403	−	0.917999i	−0.910106	−	0.414376i	$-0.864000\pi$
$43$	−1.77403	−	0.917999i	−1.77403	−	0.917999i	−0.863923	−	0.503623i	$-0.832000\pi$
$44$	0.00283632	+	0.225695i	0.00283632	+	0.225695i
$45$		0			0
$46$		0			0
$47$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$47$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$48$	1.34779	−	0.456726i	1.34779	−	0.456726i
$49$	0.112856	−	0.993611i	0.112856	−	0.993611i
$50$	0.968583	−	0.248690i	0.968583	−	0.248690i
$51$	0.164803	+	0.863928i	0.164803	+	0.863928i
$52$		0			0
$53$		0			0		−0.162637	−	0.986686i	$-0.552000\pi$
$53$		0			0		0.162637	+	0.986686i	$0.448000\pi$
$54$	0.0183988	+	0.0306692i	0.0183988	+	0.0306692i
$55$		0			0
$56$		0			0
$57$	1.68434	+	1.83943i	1.68434	+	1.83943i
$58$		0			0
$59$	−0.123378	−	0.456624i	−0.123378	−	0.456624i	0.876307	−	0.481754i	$-0.160000\pi$
$59$	−0.123378	−	0.456624i	−0.123378	−	0.456624i	−0.999684	+	0.0251301i	$0.992000\pi$
$60$		0			0
$61$		0			0		−0.711536	−	0.702650i	$-0.752000\pi$
$61$		0			0		0.711536	+	0.702650i	$0.248000\pi$
$62$		0			0
$63$		0			0
$64$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$65$		0			0
$66$	0.0915497	−	0.307882i	0.0915497	−	0.307882i
$67$	1.61389	+	0.328935i	1.61389	+	0.328935i	0.920232	−	0.391374i	$-0.128000\pi$
$67$	1.61389	+	0.328935i	1.61389	+	0.328935i	0.693653	+	0.720309i	$0.256000\pi$
$68$	−0.585339	−	0.198354i	−0.585339	−	0.198354i
$69$		0			0
$70$		0			0
$71$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$71$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$72$	−1.02481	+	0.0257617i	−1.02481	+	0.0257617i
$73$	0.838414	−	0.149042i	0.838414	−	0.149042i	0.260842	−	0.965382i	$-0.416000\pi$
$73$	0.838414	−	0.149042i	0.838414	−	0.149042i	0.577573	+	0.816339i	$0.304000\pi$
$74$		0			0
$75$	−1.42127	−	0.0715012i	−1.42127	−	0.0715012i
$76$	−1.70797	+	0.393060i	−1.70797	+	0.393060i
$77$		0			0
$78$		0			0
$79$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$79$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$80$		0			0
$81$	0.230406	+	0.946599i	0.230406	+	0.946599i
$82$	−1.31738	−	1.11801i	−1.31738	−	1.11801i
$83$	−0.263142	+	0.0818589i	−0.263142	+	0.0818589i	−0.425779	−	0.904827i	$-0.640000\pi$
$83$	−0.263142	+	0.0818589i	−0.263142	+	0.0818589i	0.162637	+	0.986686i	$0.448000\pi$
$84$		0			0
$85$		0			0
$86$	−1.92163	+	0.545214i	−1.92163	+	0.545214i
$87$		0			0
$88$	0.156566	+	0.162583i	0.156566	+	0.162583i
$89$	−1.09982	−	0.717509i	−1.09982	−	0.717509i	−0.137790	−	0.990461i	$-0.544000\pi$
$89$	−1.09982	−	0.717509i	−1.09982	−	0.717509i	−0.962028	+	0.272952i	$0.912000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.669845	−	1.25556i	0.669845	−	1.25556i
$97$	0.00532818	−	0.423981i	0.00532818	−	0.423981i	−0.974527	−	0.224271i	$-0.928000\pi$
$97$	0.00532818	−	0.423981i	0.00532818	−	0.423981i	0.979855	−	0.199710i	$-0.0640000\pi$
$98$	−0.597905	−	0.801567i	−0.597905	−	0.801567i
$99$	−0.128853	+	0.192188i	−0.128853	+	0.192188i
$100$	0.535827	−	0.844328i	0.535827	−	0.844328i
$101$		0			0		0.762443	−	0.647056i	$-0.224000\pi$
$101$		0			0		−0.762443	+	0.647056i	$0.776000\pi$
$102$	0.711536	+	0.516961i	0.711536	+	0.516961i
$103$		0			0		−0.994951	−	0.100362i	$-0.968000\pi$
$103$		0			0		0.994951	+	0.100362i	$0.0320000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.40692	+	1.38935i	−1.40692	+	1.38935i	−0.597905	+	0.801567i	$0.704000\pi$
$107$	−1.40692	+	1.38935i	−1.40692	+	1.38935i	−0.809017	+	0.587785i	$0.800000\pi$
$108$	0.0344067	+	0.00976206i	0.0344067	+	0.00976206i
$109$		0			0		−0.974527	−	0.224271i	$-0.928000\pi$
$109$		0			0		0.974527	+	0.224271i	$0.0720000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.220275	+	0.677936i	0.220275	+	0.677936i	0.998737	+	0.0502443i	$0.0160000\pi$
$113$	0.220275	+	0.677936i	0.220275	+	0.677936i	−0.778462	+	0.627691i	$0.784000\pi$
$114$	2.48701	+	0.187872i	2.48701	+	0.187872i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.402519	−	0.248407i	−0.402519	−	0.248407i
$119$		0			0
$120$		0			0
$121$	−0.938284	+	0.142572i	−0.938284	+	0.142572i
$122$		0			0
$123$	1.31752	+	2.07608i	1.31752	+	2.07608i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.954865	−	0.297042i	$-0.904000\pi$
$127$		0			0		0.954865	+	0.297042i	$0.0960000\pi$
$128$	0.535827	+	0.844328i	0.535827	+	0.844328i
$129$	2.84165	+	0.0714335i	2.84165	+	0.0714335i
$130$		0			0
$131$	1.44759	+	1.16723i	1.44759	+	1.16723i	0.954865	+	0.297042i	$0.0960000\pi$
$131$	1.44759	+	1.16723i	1.44759	+	1.16723i	0.492727	+	0.870184i	$0.336000\pi$
$132$	−0.144023	−	0.287107i	−0.144023	−	0.287107i
$133$		0			0
$134$	1.40164	−	0.864997i	1.40164	−	0.864997i
$135$		0			0
$136$	−0.562476	+	0.256098i	−0.562476	+	0.256098i
$137$	−0.324350	−	0.0245019i	−0.324350	−	0.0245019i	−0.0878512	−	0.996134i	$-0.528000\pi$
$137$	−0.324350	−	0.0245019i	−0.324350	−	0.0245019i	−0.236499	+	0.971632i	$0.576000\pi$
$138$		0			0
$139$	1.48138	−	1.02041i	1.48138	−	1.02041i	0.492727	−	0.870184i	$-0.336000\pi$
$139$	1.48138	−	1.02041i	1.48138	−	1.02041i	0.988652	−	0.150226i	$-0.0480000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.729418	+	0.720309i	−0.729418	+	0.720309i
$145$		0			0
$146$	0.509151	−	0.682581i	0.509151	−	0.682581i
$147$	0.473626	+	1.34194i	0.473626	+	1.34194i
$148$		0			0
$149$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$149$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$150$	−1.08501	+	0.920807i	−1.08501	+	0.920807i
$151$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$151$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$152$	−0.975988	+	1.45571i	−0.975988	+	1.45571i
$153$	−0.378813	−	0.507846i	−0.378813	−	0.507846i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$157$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.815950	+	0.532317i	0.815950	+	0.532317i
$163$	1.27664	+	1.32570i	1.27664	+	1.32570i	0.920232	+	0.391374i	$0.128000\pi$
$163$	1.27664	+	1.32570i	1.27664	+	1.32570i	0.356412	+	0.934329i	$0.384000\pi$
$164$	−1.72566	+	0.0868145i	−1.72566	+	0.0868145i
$165$		0			0
$166$	−0.135786	+	0.239806i	−0.135786	+	0.239806i
$167$		0			0		−0.899405	−	0.437116i	$-0.856000\pi$
$167$		0			0		0.899405	+	0.437116i	$0.144000\pi$
$168$		0			0
$169$	0.762443	+	0.647056i	0.762443	+	0.647056i
$170$		0			0
$171$	−1.67049	−	0.661395i	−1.67049	−	0.661395i
$172$	−1.02758	+	1.71289i	−1.02758	+	1.71289i
$173$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$173$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$174$		0			0
$175$		0			0
$176$	0.225428	+	0.0113408i	0.225428	+	0.0113408i
$177$	0.441954	+	0.507694i	0.441954	+	0.507694i
$178$	−1.29290	+	0.229835i	−1.29290	+	0.229835i
$179$	0.0753566	−	0.00189432i	0.0753566	−	0.00189432i	0.0125660	−	0.999921i	$-0.496000\pi$
$179$	0.0753566	−	0.00189432i	0.0753566	−	0.00189432i	0.0627905	+	0.998027i	$0.480000\pi$
$180$		0			0
$181$		0			0		0.332820	−	0.942991i	$-0.392000\pi$
$181$		0			0		−0.332820	+	0.942991i	$0.608000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.0261393	+	0.137027i	−0.0261393	+	0.137027i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.137790	−	0.990461i	$-0.544000\pi$
$191$		0			0		0.137790	+	0.990461i	$0.456000\pi$
$192$	−0.371196	−	1.37381i	−0.371196	−	1.37381i
$193$	1.43146	−	0.525541i	1.43146	−	0.525541i	0.492727	−	0.870184i	$-0.336000\pi$
$193$	1.43146	−	0.525541i	1.43146	−	0.525541i	0.938734	+	0.344643i	$0.112000\pi$
$194$	−0.286351	−	0.312716i	−0.286351	−	0.312716i
$195$		0			0
$196$	−0.984564	−	0.175023i	−0.984564	−	0.175023i
$197$		0			0		−0.514440	−	0.857527i	$-0.672000\pi$
$197$		0			0		0.514440	+	0.857527i	$0.328000\pi$
$198$	0.0376319	+	0.228305i	0.0376319	+	0.228305i
$199$		0			0		0.402906	−	0.915241i	$-0.368000\pi$
$199$		0			0		−0.402906	+	0.915241i	$0.632000\pi$
$200$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$201$	−2.27025	+	0.582902i	−2.27025	+	0.582902i
$202$		0			0
$203$		0			0
$204$	0.872571	−	0.110231i	0.872571	−	0.110231i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.140992	+	0.369609i	0.140992	+	0.369609i
$210$		0			0
$211$	0.0748104	+	0.158980i	0.0748104	+	0.158980i	0.938734	−	0.344643i	$-0.112000\pi$
$211$	0.0748104	+	0.158980i	0.0748104	+	0.158980i	−0.863923	+	0.503623i	$0.832000\pi$
$212$		0			0
$213$		0			0
$214$	−0.0745249	+	1.97590i	−0.0745249	+	1.97590i
$215$		0			0
$216$	0.0317640	−	0.0164368i	0.0317640	−	0.0164368i
$217$		0			0
$218$		0			0
$219$	−0.980390	+	0.712295i	−0.980390	+	0.712295i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.617860	−	0.786288i	$-0.712000\pi$
$223$		0			0		0.617860	+	0.786288i	$0.288000\pi$
$224$		0			0
$225$	0.943359	−	0.401210i	0.943359	−	0.401210i
$226$	0.624652	+	0.343405i	0.624652	+	0.343405i
$227$	1.16025	+	0.528266i	1.16025	+	0.528266i	0.899405	−	0.437116i	$-0.144000\pi$
$227$	1.16025	+	0.528266i	1.16025	+	0.528266i	0.260842	+	0.965382i	$0.416000\pi$
$228$	1.94156	−	1.56552i	1.94156	−	1.56552i
$229$		0			0		0.675333	−	0.737513i	$-0.264000\pi$
$229$		0			0		−0.675333	+	0.737513i	$0.736000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.147156	+	1.66858i	0.147156	+	1.66858i	0.617860	+	0.786288i	$0.288000\pi$
$233$	0.147156	+	1.66858i	0.147156	+	1.66858i	−0.470704	+	0.882291i	$0.656000\pi$
$234$		0			0
$235$		0			0
$236$	−0.463469	+	0.0944624i	−0.463469	+	0.0944624i
$237$		0			0
$238$		0			0
$239$		0			0		−0.379779	−	0.925077i	$-0.624000\pi$
$239$		0			0		0.379779	+	0.925077i	$0.376000\pi$
$240$		0			0
$241$	−0.975988	+	0.536554i	−0.975988	+	0.536554i	−0.888136	−	0.459580i	$-0.848000\pi$
$241$	−0.975988	+	0.536554i	−0.975988	+	0.536554i	−0.0878512	+	0.996134i	$0.528000\pi$
$242$	−0.586382	+	0.746230i	−0.586382	+	0.746230i
$243$	−0.906527	−	1.09580i	−0.906527	−	1.09580i
$244$		0			0
$245$		0			0
$246$	2.38160	+	0.611491i	2.38160	+	0.611491i
$247$		0			0
$248$		0			0
$249$	0.285880	−	0.268459i	0.285880	−	0.268459i
$250$		0			0
$251$	−0.745941	−	0.666012i	−0.745941	−	0.666012i
$251$	−0.745941	−	0.666012i	−0.745941	−	0.666012i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.968583	+	0.248690i	0.968583	+	0.248690i
$257$	−0.710799	+	1.86335i	−0.710799	+	1.86335i	−0.285019	+	0.958522i	$0.592000\pi$
$257$	−0.710799	+	1.86335i	−0.710799	+	1.86335i	−0.425779	+	0.904827i	$0.640000\pi$
$258$	2.12037	−	1.89317i	2.12037	−	1.89317i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.85427	−	0.140074i	1.85427	−	0.140074i
$263$		0			0		−0.379779	−	0.925077i	$-0.624000\pi$
$263$		0			0		0.379779	+	0.925077i	$0.376000\pi$
$264$	−0.301526	−	0.110701i	−0.301526	−	0.110701i
$265$		0			0
$266$		0			0
$267$	1.85400	+	0.234215i	1.85400	+	0.234215i
$268$	0.429623	−	1.59005i	0.429623	−	1.59005i
$269$		0			0		−0.0878512	−	0.996134i	$-0.528000\pi$
$269$		0			0		0.0878512	+	0.996134i	$0.472000\pi$
$270$		0			0
$271$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$271$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$272$	−0.234716	+	0.571729i	−0.234716	+	0.571729i
$273$		0			0
$274$	−0.253214	+	0.204172i	−0.253214	+	0.204172i
$275$	−0.205423	−	0.0935299i	−0.205423	−	0.0935299i
$276$		0			0
$277$		0			0		0.920232	−	0.391374i	$-0.128000\pi$
$277$		0			0		−0.920232	+	0.391374i	$0.872000\pi$
$278$	0.381361	−	1.75792i	0.381361	−	1.75792i
$279$		0			0
$280$		0			0
$281$	0.465416	−	0.657817i	0.465416	−	0.657817i	−0.514440	−	0.857527i	$-0.672000\pi$
$281$	0.465416	−	0.657817i	0.465416	−	0.657817i	0.979855	+	0.199710i	$0.0640000\pi$
$282$		0			0
$283$	0.901044	−	0.654647i	0.901044	−	0.654647i	−0.0376902	−	0.999289i	$-0.512000\pi$
$283$	0.901044	−	0.654647i	0.901044	−	0.654647i	0.938734	+	0.344643i	$0.112000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.0386374	+	1.02440i	−0.0386374	+	1.02440i
$289$	0.533934	+	0.311256i	0.533934	+	0.311256i
$290$		0			0
$291$	0.256916	+	0.545975i	0.256916	+	0.545975i
$292$	−0.0961038	−	0.846118i	−0.0961038	−	0.846118i
$293$		0			0		−0.356412	−	0.934329i	$-0.616000\pi$
$293$		0			0		0.356412	+	0.934329i	$0.384000\pi$
$294$	1.26388	+	0.654015i	1.26388	+	0.654015i
$295$		0			0
$296$		0			0
$297$	0.00111232	−	0.00799556i	0.00111232	−	0.00799556i
$298$		0			0
$299$		0			0
$300$	−0.160603	+	1.41398i	−0.160603	+	1.41398i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.285040	+	1.72928i	0.285040	+	1.72928i
$305$		0			0
$306$	−0.623787	−	0.110889i	−0.623787	−	0.110889i
$307$	1.85616	+	0.282044i	1.85616	+	0.282044i	0.979855	−	0.199710i	$-0.0640000\pi$
$307$	1.85616	+	0.282044i	1.85616	+	0.282044i	0.876307	+	0.481754i	$0.160000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.137790	−	0.990461i	$-0.544000\pi$
$311$		0			0		0.137790	+	0.990461i	$0.456000\pi$
$312$		0			0
$313$	−0.0865734	−	0.152893i	−0.0865734	−	0.152893i	0.823533	−	0.567269i	$-0.192000\pi$
$313$	−0.0865734	−	0.152893i	−0.0865734	−	0.152893i	−0.910106	+	0.414376i	$0.864000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.285019	−	0.958522i	$-0.408000\pi$
$317$		0			0		−0.285019	+	0.958522i	$0.592000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.936502	−	2.65343i	0.936502	−	2.65343i
$322$		0			0
$323$	−1.08283	+	0.0272203i	−1.08283	+	0.0272203i
$324$	0.959198	−	0.170514i	0.959198	−	0.170514i
$325$		0			0
$326$	1.83814	+	0.0924728i	1.83814	+	0.0924728i
$327$		0			0
$328$	−1.19853	+	1.24458i	−1.19853	+	1.24458i
$329$		0			0
$330$		0			0
$331$	−1.41780	−	0.561348i	−1.41780	−	0.561348i	−0.470704	−	0.882291i	$-0.656000\pi$
$331$	−1.41780	−	0.561348i	−1.41780	−	0.561348i	−0.947098	+	0.320944i	$0.896000\pi$
$332$	0.0651745	+	0.267763i	0.0651745	+	0.267763i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.88530	+	0.534907i	−1.88530	+	0.534907i	−0.888136	+	0.459580i	$0.848000\pi$
$337$	−1.88530	+	0.534907i	−1.88530	+	0.534907i	−0.997159	+	0.0753268i	$0.976000\pi$
$338$	0.998737	−	0.0502443i	0.998737	−	0.0502443i
$339$	−0.703641	−	0.730681i	−0.703641	−	0.730681i
$340$		0			0
$341$		0			0
$342$	−1.67049	+	0.661395i	−1.67049	+	0.661395i
$343$		0			0
$344$	0.423479	+	1.95207i	0.423479	+	1.95207i
$345$		0			0
$346$		0			0
$347$	0.357527	−	0.670152i	0.357527	−	0.670152i	−0.637424	−	0.770513i	$-0.720000\pi$
$347$	0.357527	−	0.670152i	0.357527	−	0.670152i	0.994951	+	0.100362i	$0.0320000\pi$
$348$		0			0
$349$		0			0		−0.597905	−	0.801567i	$-0.704000\pi$
$349$		0			0		0.597905	+	0.801567i	$0.296000\pi$
$350$		0			0
$351$		0			0
$352$	0.172093	−	0.146049i	0.172093	−	0.146049i
$353$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i	0.535827	−	0.844328i	$-0.320000\pi$
$353$	−0.101597	−	0.0738147i	−0.101597	−	0.0738147i	−0.637424	+	0.770513i	$0.720000\pi$
$354$	0.669711	+	0.0675545i	0.669711	+	0.0675545i
$355$		0			0
$356$	−0.785152	+	1.05259i	−0.785152	+	1.05259i
$357$		0			0
$358$	0.0536358	−	0.0529660i	0.0536358	−	0.0529660i
$359$		0			0		−0.962028	−	0.272952i	$-0.912000\pi$
$359$		0			0		0.962028	+	0.272952i	$0.0880000\pi$
$360$		0			0
$361$	−1.73507	+	1.13194i	−1.73507	+	1.13194i
$362$		0			0
$363$	1.11224	−	0.766137i	1.11224	−	0.766137i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$367$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$368$		0			0
$369$	−1.50734	−	0.930227i	−1.50734	−	0.930227i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$373$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$374$	0.0747469	+	0.117782i	0.0747469	+	0.117782i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.356667	−	0.562018i	−0.356667	−	0.562018i	0.617860	−	0.786288i	$-0.288000\pi$
$379$	−0.356667	−	0.562018i	−0.356667	−	0.562018i	−0.974527	+	0.224271i	$0.928000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.448383	−	0.893841i	$-0.648000\pi$
$383$		0			0		0.448383	+	0.893841i	$0.352000\pi$
$384$	−1.21103	−	0.747361i	−1.21103	−	0.747361i
$385$		0			0
$386$	0.683733	−	1.36301i	0.683733	−	1.36301i
$387$	−1.86360	+	0.848506i	−1.86360	+	0.848506i
$388$	−0.422810	−	0.0319396i	−0.422810	−	0.0319396i
$389$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$389$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$390$		0			0
$391$		0			0
$392$	−0.837528	+	0.546394i	−0.837528	+	0.546394i
$393$	−2.57887	−	0.593482i	−2.57887	−	0.593482i
$394$		0			0
$395$		0			0
$396$	0.183718	+	0.140666i	0.183718	+	0.140666i
$397$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$397$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$398$		0			0
$399$		0			0
$400$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$401$	0.880732	−	0.747444i	0.880732	−	0.747444i	−0.0878512	−	0.996134i	$-0.528000\pi$
$401$	0.880732	−	0.747444i	0.880732	−	0.747444i	0.968583	+	0.248690i	$0.0800000\pi$
$402$	−1.25592	+	1.97901i	−1.25592	+	1.97901i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.560619	−	0.677671i	0.560619	−	0.677671i
$409$	−0.417469	−	1.92437i	−0.417469	−	1.92437i	−0.379779	−	0.925077i	$-0.624000\pi$
$409$	−0.417469	−	1.92437i	−0.417469	−	1.92437i	−0.0376902	−	0.999289i	$-0.512000\pi$
$410$		0			0
$411$	0.430383	−	0.170401i	0.430383	−	0.170401i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.26130	+	2.22753i	−1.26130	+	2.22753i
$418$	0.355793	+	0.172917i	0.355793	+	0.172917i
$419$	−1.88025	+	0.584913i	−1.88025	+	0.584913i	−0.888136	+	0.459580i	$0.848000\pi$
$419$	−1.88025	+	0.584913i	−1.88025	+	0.584913i	−0.992115	+	0.125333i	$0.960000\pi$
$420$		0			0
$421$		0			0		−0.236499	−	0.971632i	$-0.576000\pi$
$421$		0			0		0.236499	+	0.971632i	$0.424000\pi$
$422$	0.163364	+	0.0646804i	0.163364	+	0.0646804i
$423$		0			0
$424$		0			0
$425$	0.428701	−	0.445175i	0.428701	−	0.445175i
$426$		0			0
$427$		0			0
$428$	1.29827	+	1.49138i	1.29827	+	1.49138i
$429$		0			0
$430$		0			0
$431$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$431$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$432$	0.0119032	−	0.0337258i	0.0119032	−	0.0337258i
$433$	−0.456288	+	0.969661i	−0.456288	+	0.969661i	0.535827	+	0.844328i	$0.320000\pi$
$433$	−0.456288	+	0.969661i	−0.456288	+	0.969661i	−0.992115	+	0.125333i	$0.960000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.227074	+	1.19036i	−0.227074	+	1.19036i
$439$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$439$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$440$		0			0
$441$	−0.729418	−	0.720309i	−0.729418	−	0.720309i
$442$		0			0
$443$	−0.422050	−	1.56202i	−0.422050	−	1.56202i	−0.778462	−	0.627691i	$-0.784000\pi$
$443$	−0.422050	−	1.56202i	−0.422050	−	1.56202i	0.356412	−	0.934329i	$-0.384000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.153108	−	0.928874i	−0.153108	−	0.928874i	−0.947098	−	0.320944i	$-0.896000\pi$
$449$	−0.153108	−	0.928874i	−0.153108	−	0.928874i	0.793990	−	0.607930i	$-0.208000\pi$
$450$	0.413032	−	0.938243i	0.413032	−	0.938243i
$451$	0.0730782	+	0.383089i	0.0730782	+	0.383089i
$452$	0.690429	−	0.177272i	0.690429	−	0.177272i
$453$		0			0
$454$	1.20741	−	0.409154i	1.20741	−	0.409154i
$455$		0			0
$456$	0.343662	−	2.47030i	0.343662	−	2.47030i
$457$	1.15759	−	0.886324i	1.15759	−	0.886324i	0.162637	−	0.986686i	$-0.448000\pi$
$457$	1.15759	−	0.886324i	1.15759	−	0.886324i	0.994951	+	0.100362i	$0.0320000\pi$
$458$		0			0
$459$	0.0196312	+	0.0101585i	0.0196312	+	0.0101585i
$460$		0			0
$461$		0			0		−0.112856	−	0.993611i	$-0.536000\pi$
$461$		0			0		0.112856	+	0.993611i	$0.464000\pi$
$462$		0			0
$463$		0			0		0.994951	−	0.100362i	$-0.0320000\pi$
$463$		0			0		−0.994951	+	0.100362i	$0.968000\pi$
$464$		0			0
$465$		0			0
$466$	1.24949	+	1.11561i	1.24949	+	1.11561i
$467$	−1.69610	+	0.877673i	−1.69610	+	0.877673i	−0.711536	+	0.702650i	$0.752000\pi$
$467$	−1.69610	+	0.877673i	−1.69610	+	0.877673i	−0.984564	+	0.175023i	$0.944000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.273191	+	0.386127i	−0.273191	+	0.386127i
$473$	0.414891	+	0.176453i	0.414891	+	0.176453i
$474$		0			0
$475$	0.371566	−	1.71277i	0.371566	−	1.71277i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.778462	−	0.627691i	$-0.216000\pi$
$479$		0			0		−0.778462	+	0.627691i	$0.784000\pi$
$480$		0			0
$481$		0			0
$482$	−0.344168	+	1.05924i	−0.344168	+	1.05924i
$483$		0			0
$484$	0.0833755	+	0.945384i	0.0833755	+	0.945384i
$485$		0			0
$486$	−1.41096	−	0.178245i	−1.41096	−	0.178245i
$487$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$487$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$488$		0			0
$489$	−2.45865	−	0.902658i	−2.45865	−	0.902658i
$490$		0			0
$491$	1.48764	−	0.112379i	1.48764	−	0.112379i	0.693653	−	0.720309i	$-0.256000\pi$
$491$	1.48764	−	0.112379i	1.48764	−	0.112379i	0.793990	+	0.607930i	$0.208000\pi$
$492$	2.15471	−	1.18456i	2.15471	−	1.18456i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.0246246	−	0.391397i	0.0246246	−	0.391397i
$499$	1.42824	−	0.694131i	1.42824	−	0.694131i	0.448383	−	0.893841i	$-0.352000\pi$
$499$	1.42824	−	0.694131i	1.42824	−	0.694131i	0.979855	+	0.199710i	$0.0640000\pi$
$500$		0			0
$501$		0			0
$502$	−0.999684	+	0.0251301i	−0.999684	+	0.0251301i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.37836	−	0.353903i	−1.37836	−	0.353903i
$508$		0			0
$509$		0			0		0.745941	−	0.666012i	$-0.232000\pi$
$509$		0			0		−0.745941	+	0.666012i	$0.768000\pi$
$510$		0			0
$511$		0			0
$512$	0.876307	−	0.481754i	0.876307	−	0.481754i
$513$	0.0625037	−	0.00472162i	0.0625037	−	0.00472162i
$514$	0.757400	+	1.84490i	0.757400	+	1.84490i
$515$		0			0
$516$	0.249721	−	2.83156i	0.249721	−	2.83156i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.0214849	+	0.0722537i	0.0214849	+	0.0722537i	0.968583	−	0.248690i	$-0.0800000\pi$
$521$	0.0214849	+	0.0722537i	0.0214849	+	0.0722537i	−0.947098	+	0.320944i	$0.896000\pi$
$522$		0			0
$523$	0.454144	−	1.10622i	0.454144	−	1.10622i	−0.514440	−	0.857527i	$-0.672000\pi$
$523$	0.454144	−	1.10622i	0.454144	−	1.10622i	0.968583	−	0.248690i	$-0.0800000\pi$
$524$	1.25582	−	1.37144i	1.25582	−	1.37144i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.295583	+	0.125711i	−0.295583	+	0.125711i
$529$	0.212007	−	0.977268i	0.212007	−	0.977268i
$530$		0			0
$531$	−0.446207	−	0.189771i	−0.446207	−	0.189771i
$532$		0			0
$533$		0			0
$534$	1.51184	−	1.09842i	1.51184	−	1.09842i
$535$		0			0
$536$	−0.775280	−	1.45319i	−0.775280	−	1.45319i
$537$	−0.0952719	+	0.0492999i	−0.0952719	+	0.0492999i
$538$		0			0
$539$	−0.00850716	+	0.225552i	−0.00850716	+	0.225552i
$540$		0			0
$541$		0			0		0.994951	−	0.100362i	$-0.0320000\pi$
$541$		0			0		−0.994951	+	0.100362i	$0.968000\pi$
$542$		0			0
$543$		0			0
$544$	0.220275	+	0.577447i	0.220275	+	0.577447i
$545$		0			0
$546$		0			0
$547$	1.26084	−	0.965382i	1.26084	−	0.965382i	0.260842	−	0.965382i	$-0.416000\pi$
$547$	1.26084	−	0.965382i	1.26084	−	0.965382i	1.00000			$0$
$548$	−0.0448196	+	0.322172i	−0.0448196	+	0.322172i
$549$		0			0
$550$	−0.213772	+	0.0724411i	−0.213772	+	0.0724411i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.925379	−	1.54253i	−0.925379	−	1.54253i
$557$		0			0		−0.984564	−	0.175023i	$-0.944000\pi$
$557$		0			0		0.984564	+	0.175023i	$0.0560000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.0517812	−	0.191644i	−0.0517812	−	0.191644i
$562$	−0.111033	−	0.798127i	−0.111033	−	0.798127i
$563$	0.907100	+	0.895772i	0.907100	+	0.895772i	0.994951	−	0.100362i	$-0.0320000\pi$
$563$	0.907100	+	0.895772i	0.907100	+	0.895772i	−0.0878512	+	0.996134i	$0.528000\pi$
$564$		0			0
$565$		0			0
$566$	0.208696	−	1.09402i	0.208696	−	1.09402i
$567$		0			0
$568$		0			0
$569$	−1.95414	−	0.398285i	−1.95414	−	0.398285i	−0.992115	−	0.125333i	$-0.960000\pi$
$569$	−1.95414	−	0.398285i	−1.95414	−	0.398285i	−0.962028	−	0.272952i	$-0.912000\pi$
$570$		0			0
$571$	0.575085	−	1.22212i	0.575085	−	1.22212i	−0.379779	−	0.925077i	$-0.624000\pi$
$571$	0.575085	−	1.22212i	0.575085	−	1.22212i	0.954865	−	0.297042i	$-0.0960000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.673087	+	0.773207i	0.673087	+	0.773207i
$577$	−0.664798	−	0.0334446i	−0.664798	−	0.0334446i	−0.285019	−	0.958522i	$-0.592000\pi$
$577$	−0.664798	−	0.0334446i	−0.664798	−	0.0334446i	−0.379779	+	0.925077i	$0.624000\pi$
$578$	0.602291	−	0.138607i	0.602291	−	0.138607i
$579$	−1.50524	+	1.56309i	−1.50524	+	1.56309i
$580$		0			0
$581$		0			0
$582$	0.561029	+	0.222127i	0.561029	+	0.222127i
$583$		0			0
$584$	−0.649264	−	0.551006i	−0.649264	−	0.551006i
$585$		0			0
$586$		0			0
$587$	−0.506957	+	0.895314i	−0.506957	+	0.895314i	0.492727	+	0.870184i	$0.336000\pi$
$587$	−0.506957	+	0.895314i	−0.506957	+	0.895314i	−0.999684	+	0.0251301i	$0.992000\pi$
$588$	1.36903	−	0.388430i	1.36903	−	0.388430i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.83845	+	0.727894i	−1.83845	+	0.727894i	−0.863923	+	0.503623i	$0.832000\pi$
$593$	−1.83845	+	0.727894i	−1.83845	+	0.727894i	−0.974527	+	0.224271i	$0.928000\pi$
$594$	−0.00466249	−	0.00658995i	−0.00466249	−	0.00658995i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.0125660	−	0.999921i	$-0.496000\pi$
$599$		0			0		−0.0125660	+	0.999921i	$0.504000\pi$
$600$	0.850861	+	1.14069i	0.850861	+	1.14069i
$601$	0.208696	−	0.311276i	0.208696	−	0.311276i	−0.711536	−	0.702650i	$-0.752000\pi$
$601$	0.208696	−	0.311276i	0.208696	−	0.311276i	0.920232	+	0.391374i	$0.128000\pi$
$602$		0			0
$603$	1.28735	−	1.09253i	1.28735	−	1.09253i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$607$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$608$	1.39156	+	1.06547i	1.39156	+	1.06547i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.530630	+	0.346177i	−0.530630	+	0.346177i
$613$		0			0		−0.402906	−	0.915241i	$-0.632000\pi$
$613$		0			0		0.402906	+	0.915241i	$0.368000\pi$
$614$	1.54616	−	1.06503i	1.54616	−	1.06503i
$615$		0			0
$616$		0			0
$617$	−1.54899	+	0.705263i	−1.54899	+	0.705263i	−0.992115	−	0.125333i	$-0.960000\pi$
$617$	−1.54899	+	0.705263i	−1.54899	+	0.705263i	−0.556876	+	0.830596i	$0.688000\pi$
$618$		0			0
$619$	−1.42546	+	0.879697i	−1.42546	+	0.879697i	−0.999684	−	0.0251301i	$-0.992000\pi$
$619$	−1.42546	+	0.879697i	−1.42546	+	0.879697i	−0.425779	+	0.904827i	$0.640000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.535827	+	0.844328i	0.535827	+	0.844328i
$626$	−0.167772	−	0.0521909i	−0.167772	−	0.0521909i
$627$	−0.410372	−	0.385365i	−0.410372	−	0.385365i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$631$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$632$		0			0
$633$	−0.194644	−	0.156946i	−0.194644	−	0.156946i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.59532	−	1.09889i	1.59532	−	1.09889i	0.656586	−	0.754251i	$-0.272000\pi$
$641$	1.59532	−	1.09889i	1.59532	−	1.09889i	0.938734	−	0.344643i	$-0.112000\pi$
$642$	−1.13372	−	2.57535i	−1.13372	−	2.57535i
$643$	1.58644	−	1.03498i	1.58644	−	1.03498i	0.617860	−	0.786288i	$-0.288000\pi$
$643$	1.58644	−	1.03498i	1.58644	−	1.03498i	0.968583	−	0.248690i	$-0.0800000\pi$
$644$		0			0
$645$		0			0
$646$	−0.770717	+	0.761093i	−0.770717	+	0.761093i
$647$		0			0		−0.793990	−	0.607930i	$-0.792000\pi$
$647$		0			0		0.793990	+	0.607930i	$0.208000\pi$
$648$	0.582501	−	0.780916i	0.582501	−	0.780916i
$649$	0.0355324	+	0.100675i	0.0355324	+	0.100675i
$650$		0			0
$651$		0			0
$652$	1.40325	−	1.19088i	1.40325	−	1.19088i
$653$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$653$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$654$		0			0
$655$		0			0
$656$	−0.0217122	+	1.72771i	−0.0217122	+	1.72771i
$657$	0.410906	−	0.770205i	0.410906	−	0.770205i
$658$		0			0
$659$	1.18532	−	1.43281i	1.18532	−	1.43281i	0.309017	−	0.951057i	$-0.400000\pi$
$659$	1.18532	−	1.43281i	1.18532	−	1.43281i	0.876307	−	0.481754i	$-0.160000\pi$
$660$		0			0
$661$		0			0		−0.577573	−	0.816339i	$-0.696000\pi$
$661$		0			0		0.577573	+	0.816339i	$0.304000\pi$
$662$	−1.41780	+	0.561348i	−1.41780	+	0.561348i
$663$		0			0
$664$	0.230806	+	0.150576i	0.230806	+	0.150576i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.81218	+	0.717495i	1.81218	+	0.717495i	0.988652	+	0.150226i	$0.0480000\pi$
$673$	1.81218	+	0.717495i	1.81218	+	0.717495i	0.823533	+	0.567269i	$0.192000\pi$
$674$	−1.00815	+	1.68050i	−1.00815	+	1.68050i
$675$	−0.0234826	+	0.0269756i	−0.0234826	+	0.0269756i
$676$	0.693653	−	0.720309i	0.693653	−	0.720309i
$677$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$677$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$678$	−1.01312	−	0.0509678i	−1.01312	−	0.0509678i
$679$		0			0
$680$		0			0
$681$	−1.81363	+	0.0455910i	−1.81363	+	0.0455910i
$682$		0			0
$683$	−0.327979	+	0.929274i	−0.327979	+	0.929274i	0.656586	+	0.754251i	$0.272000\pi$
$683$	−0.327979	+	0.929274i	−0.327979	+	0.929274i	−0.984564	+	0.175023i	$0.944000\pi$
$684$	−0.764981	+	1.62567i	−0.764981	+	1.62567i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.64498	+	1.13310i	1.64498	+	1.13310i
$689$		0			0
$690$		0			0
$691$	0.980479	+	1.73158i	0.980479	+	1.73158i	0.577573	+	0.816339i	$0.304000\pi$
$691$	0.980479	+	1.73158i	0.980479	+	1.73158i	0.402906	+	0.915241i	$0.368000\pi$
$692$		0			0
$693$		0			0
$694$	−0.198124	−	0.733264i	−0.198124	−	0.733264i
$695$		0			0
$696$		0			0
$697$	−1.05575	−	0.160421i	−1.05575	−	0.160421i
$698$		0			0
$699$	−1.22628	−	2.04411i	−1.22628	−	2.04411i
$700$		0			0
$701$		0			0		0.402906	−	0.915241i	$-0.368000\pi$
$701$		0			0		−0.402906	+	0.915241i	$0.632000\pi$
$702$		0			0
$703$		0			0
$704$	0.0254731	−	0.224271i	0.0254731	−	0.224271i
$705$		0			0
$706$	−0.124591	+	0.0157395i	−0.124591	+	0.0157395i
$707$		0			0
$708$	0.534443	−	0.409204i	0.534443	−	0.409204i
$709$		0			0		−0.0125660	−	0.999921i	$-0.504000\pi$
$709$		0			0		0.0125660	+	0.999921i	$0.496000\pi$
$710$		0			0
$711$		0			0
$712$	0.148200	+	1.30478i	0.148200	+	1.30478i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.00284110	−	0.0753268i	0.00284110	−	0.0753268i
$717$		0			0
$718$		0			0
$719$		0			0		−0.470704	−	0.882291i	$-0.656000\pi$
$719$		0			0		0.470704	+	0.882291i	$0.344000\pi$
$720$		0			0
$721$		0			0
$722$	−0.489944	+	2.01288i	−0.489944	+	2.01288i
$723$	0.915422	−	1.29385i	0.915422	−	1.29385i
$724$		0			0
$725$		0			0
$726$	0.286331	−	1.31987i	0.286331	−	1.31987i
$727$		0			0		0.920232	−	0.391374i	$-0.128000\pi$
$727$		0			0		−0.920232	+	0.391374i	$0.872000\pi$
$728$		0			0
$729$	0.955262	+	0.434936i	0.955262	+	0.434936i
$730$		0			0
$731$	−0.833703	+	0.910465i	−0.833703	+	0.910465i
$732$		0			0
$733$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$733$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.368832	−	0.0465943i	−0.368832	−	0.0465943i
$738$	−1.73559	+	0.353741i	−1.73559	+	0.353741i
$739$	−0.0865734	+	0.981645i	−0.0865734	+	0.981645i	0.823533	+	0.567269i	$0.192000\pi$
$739$	−0.0865734	+	0.981645i	−0.0865734	+	0.981645i	−0.910106	+	0.414376i	$0.864000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$743$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.100689	+	0.263954i	−0.100689	+	0.263954i
$748$	0.135116	+	0.0346918i	0.135116	+	0.0346918i
$749$		0			0
$750$		0			0
$751$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$751$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$752$		0			0
$753$	1.36903	+	0.388430i	1.36903	+	0.388430i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$757$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$758$	−0.644727	−	0.165538i	−0.644727	−	0.165538i
$759$		0			0
$760$		0			0
$761$	0.175662	+	0.212338i	0.175662	+	0.212338i	0.850994	−	0.525175i	$-0.176000\pi$
$761$	0.175662	+	0.212338i	0.175662	+	0.212338i	−0.675333	+	0.737513i	$0.736000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.39440	+	0.284202i	−1.39440	+	0.284202i
$769$	1.80586	+	0.228133i	1.80586	+	0.228133i	0.954865	−	0.297042i	$-0.0960000\pi$
$769$	1.80586	+	0.228133i	1.80586	+	0.228133i	0.850994	+	0.525175i	$0.176000\pi$
$770$		0			0
$771$	−0.249327	−	2.82708i	−0.249327	−	2.82708i
$772$	−0.434622	−	1.46164i	−0.434622	−	1.46164i
$773$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$773$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$774$	−0.777664	+	1.89426i	−0.777664	+	1.89426i
$775$		0			0
$776$	−0.330079	+	0.266150i	−0.330079	+	0.266150i
$777$		0			0
$778$		0			0
$779$	−2.78669	+	1.18518i	−2.78669	+	1.18518i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.236499	+	0.971632i	−0.236499	+	0.971632i
$785$		0			0
$786$	−2.28618	+	1.33273i	−2.28618	+	1.33273i
$787$	−0.245558	−	0.460276i	−0.245558	−	0.460276i	0.728969	−	0.684547i	$-0.240000\pi$
$787$	−0.245558	−	0.460276i	−0.245558	−	0.460276i	−0.974527	+	0.224271i	$0.928000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.230217	−	0.0232222i	0.230217	−	0.0232222i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.0125660	−	0.999921i	$-0.504000\pi$
$797$		0			0		0.0125660	+	0.999921i	$0.496000\pi$
$798$		0			0
$799$		0			0
$800$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$801$	−1.27496	+	0.432046i	−1.27496	+	0.432046i
$802$	0.130366	−	1.14777i	0.130366	−	1.14777i
$803$	−0.186169	+	0.0478001i	−0.186169	+	0.0478001i
$804$	0.439201	+	2.30237i	0.439201	+	2.30237i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.79956	−	0.273442i	−1.79956	−	0.273442i	−0.837528	−	0.546394i	$-0.816000\pi$
$809$	−1.79956	−	0.273442i	−1.79956	−	0.273442i	−0.962028	+	0.272952i	$0.912000\pi$
$810$		0			0
$811$	1.72771	−	0.634303i	1.72771	−	0.634303i	0.728969	−	0.684547i	$-0.240000\pi$
$811$	1.72771	−	0.634303i	1.72771	−	0.634303i	0.998737	+	0.0502443i	$0.0160000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.0552247	−	0.877771i	−0.0552247	−	0.877771i
$817$	−0.655984	+	3.43879i	−0.655984	+	3.43879i
$818$	−1.62164	−	1.11703i	−1.62164	−	1.11703i
$819$		0			0
$820$		0			0
$821$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$821$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$822$	0.197088	−	0.418834i	0.197088	−	0.418834i
$823$		0			0		0.332820	−	0.942991i	$-0.392000\pi$
$823$		0			0		−0.332820	+	0.942991i	$0.608000\pi$
$824$		0			0
$825$	0.321104	−	0.00807192i	0.321104	−	0.00807192i
$826$		0			0
$827$	1.25390	+	1.44042i	1.25390	+	1.44042i	0.850994	+	0.525175i	$0.176000\pi$
$827$	1.25390	+	1.44042i	1.25390	+	1.44042i	0.402906	+	0.915241i	$0.368000\pi$
$828$		0			0
$829$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$829$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.574633	−	0.227513i	−0.574633	−	0.227513i
$834$	0.605399	+	2.48722i	0.605399	+	2.48722i
$835$		0			0
$836$	0.377732	−	0.117506i	0.377732	−	0.117506i
$837$		0			0
$838$	−0.970244	+	1.71350i	−0.970244	+	1.71350i
$839$		0			0		0.962028	−	0.272952i	$-0.0880000\pi$
$839$		0			0		−0.962028	+	0.272952i	$0.912000\pi$
$840$		0			0
$841$	0.693653	+	0.720309i	0.693653	+	0.720309i
$842$		0			0
$843$	−0.186501	+	1.13146i	−0.186501	+	1.13146i
$844$	0.163364	−	0.0646804i	0.163364	−	0.0646804i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.746041	+	1.39839i	−0.746041	+	1.39839i
$850$	0.00776624	−	0.617985i	0.00776624	−	0.617985i
$851$		0			0
$852$		0			0
$853$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$853$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$854$		0			0
$855$		0			0
$856$	1.96732	+	0.198446i	1.96732	+	0.198446i
$857$	−0.612542	−	1.73554i	−0.612542	−	1.73554i	−0.675333	−	0.737513i	$-0.736000\pi$
$857$	−0.612542	−	1.73554i	−0.612542	−	1.73554i	0.0627905	−	0.998027i	$-0.480000\pi$
$858$		0			0
$859$	−0.816920	−	0.625487i	−0.816920	−	0.625487i	0.112856	−	0.993611i	$-0.464000\pi$
$859$	−0.816920	−	0.625487i	−0.816920	−	0.625487i	−0.929776	+	0.368125i	$0.880000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$863$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$864$	−0.0144098	−	0.0327334i	−0.0144098	−	0.0327334i
$865$		0			0
$866$	0.331159	+	1.01920i	0.331159	+	1.01920i
$867$	−0.877008	−	0.0662504i	−0.877008	−	0.0662504i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.338375	−	0.272839i	−0.338375	−	0.272839i
$874$		0			0
$875$		0			0
$876$	0.649330	+	1.02318i	0.649330	+	1.02318i
$877$		0			0		−0.954865	−	0.297042i	$-0.904000\pi$
$877$		0			0		0.954865	+	0.297042i	$0.0960000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.528033	+	0.832047i	0.528033	+	0.832047i	0.998737	−	0.0502443i	$-0.0160000\pi$
$881$	0.528033	+	0.832047i	0.528033	+	0.832047i	−0.470704	+	0.882291i	$0.656000\pi$
$882$	−1.02481	−	0.0257617i	−1.02481	−	0.0257617i
$883$	−0.841895	+	0.127926i	−0.841895	+	0.127926i	−0.556876	−	0.830596i	$-0.688000\pi$
$883$	−0.841895	+	0.127926i	−0.841895	+	0.127926i	−0.285019	+	0.958522i	$0.592000\pi$
$884$		0			0
$885$		0			0
$886$	−1.37694	−	0.849750i	−1.37694	−	0.849750i
$887$		0			0		0.850994	−	0.525175i	$-0.176000\pi$
$887$		0			0		−0.850994	+	0.525175i	$0.824000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.0679521	−	0.209135i	−0.0679521	−	0.209135i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.747469	−	0.572310i	−0.747469	−	0.572310i
$899$		0			0
$900$	−0.341184	−	0.966690i	−0.341184	−	0.966690i
$901$		0			0
$902$	0.315514	+	0.229235i	0.315514	+	0.229235i
$903$		0			0
$904$	0.381950	−	0.601857i	0.381950	−	0.601857i
$905$		0			0
$906$		0			0
$907$	−0.0238026	+	1.89405i	−0.0238026	+	1.89405i	0.309017	+	0.951057i	$0.400000\pi$
$907$	−0.0238026	+	1.89405i	−0.0238026	+	1.89405i	−0.332820	+	0.942991i	$0.608000\pi$
$908$	0.600076	−	1.12479i	0.600076	−	1.12479i
$909$		0			0
$910$		0			0
$911$		0			0		−0.212007	−	0.977268i	$-0.568000\pi$
$911$		0			0		0.212007	+	0.977268i	$0.432000\pi$
$912$	−1.44052	−	2.03603i	−1.44052	−	2.03603i
$913$	0.0578340	−	0.0228981i	0.0578340	−	0.0228981i
$914$	0.237115	−	1.43853i	0.237115	−	1.43853i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.0212645	−	0.00603328i	0.0212645	−	0.00603328i
$919$		0			0		0.492727	−	0.870184i	$-0.336000\pi$
$919$		0			0		−0.492727	+	0.870184i	$0.664000\pi$
$920$		0			0
$921$	−2.55118	+	0.793627i	−2.55118	+	0.793627i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.87510	+	0.0943321i	1.87510	+	0.0943321i	0.954865	−	0.297042i	$-0.0960000\pi$
$929$	1.87510	+	0.0943321i	1.87510	+	0.0943321i	0.920232	+	0.391374i	$0.128000\pi$
$930$		0			0
$931$	−1.72556	+	0.306748i	−1.72556	+	0.306748i
$932$	1.67453	−	0.0420943i	1.67453	−	0.0420943i
$933$		0			0
$934$	−0.635595	+	1.80086i	−0.635595	+	1.80086i
$935$		0			0
$936$		0			0
$937$	0.965603	+	0.196805i	0.965603	+	0.196805i	0.656586	−	0.754251i	$-0.272000\pi$
$937$	0.965603	+	0.196805i	0.965603	+	0.196805i	0.309017	+	0.951057i	$0.400000\pi$
$938$		0			0
$939$	0.205914	+	0.141838i	0.205914	+	0.141838i
$940$		0			0
$941$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$941$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$942$		0			0
$943$		0			0
$944$	0.0651745	+	0.468486i	0.0651745	+	0.468486i
$945$		0			0
$946$	0.423233	−	0.155384i	0.423233	−	0.155384i
$947$	1.34002	+	1.46340i	1.34002	+	1.46340i	0.762443	+	0.647056i	$0.224000\pi$
$947$	1.34002	+	1.46340i	1.34002	+	1.46340i	0.577573	+	0.816339i	$0.304000\pi$
$948$		0			0
$949$		0			0
$950$	−0.901614	−	1.50291i	−0.901614	−	1.50291i
$951$		0			0
$952$		0			0
$953$	0.313874	+	1.64539i	0.313874	+	1.64539i	0.693653	+	0.720309i	$0.256000\pi$
$953$	0.313874	+	1.64539i	0.313874	+	1.64539i	−0.379779	+	0.925077i	$0.624000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.888136	−	0.459580i	−0.888136	−	0.459580i
$962$		0			0
$963$	0.228760	+	2.01405i	0.228760	+	2.01405i
$964$	0.474212	+	1.00775i	0.474212	+	1.00775i
$965$		0			0
$966$		0			0
$967$		0			0		0.0376902	−	0.999289i	$-0.488000\pi$
$967$		0			0		−0.0376902	+	0.999289i	$0.512000\pi$
$968$	0.707938	+	0.632081i	0.707938	+	0.632081i
$969$	1.36900	−	0.708412i	1.36900	−	0.708412i
$970$		0			0
$971$	0.323766	−	0.188739i	0.323766	−	0.188739i	−0.332820	−	0.942991i	$-0.608000\pi$
$971$	0.323766	−	0.188739i	0.323766	−	0.188739i	0.656586	+	0.754251i	$0.272000\pi$
$972$	−1.15056	+	0.835932i	−1.15056	+	0.835932i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.381361	−	1.75792i	0.381361	−	1.75792i	−0.236499	−	0.971632i	$-0.576000\pi$
$977$	0.381361	−	1.75792i	0.381361	−	1.75792i	0.617860	−	0.786288i	$-0.288000\pi$
$978$	−2.41019	+	1.02505i	−2.41019	+	1.02505i
$979$	0.259737	+	0.142792i	0.259737	+	0.142792i
$980$		0			0
$981$		0			0
$982$	1.00752	−	1.10028i	1.00752	−	1.10028i
$983$		0			0		0.379779	−	0.925077i	$-0.376000\pi$
$983$		0			0		−0.379779	+	0.925077i	$0.624000\pi$
$984$	0.759826	−	2.33850i	0.759826	−	2.33850i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$991$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$992$		0			0
$993$	2.16385	−	0.163461i	2.16385	−	0.163461i
$994$		0			0
$995$		0			0
$996$	−0.249979	−	0.302173i	−0.249979	−	0.302173i
$997$		0			0		0.745941	−	0.666012i	$-0.232000\pi$
$997$		0			0		−0.745941	+	0.666012i	$0.768000\pi$
$998$	0.565975	−	1.48370i	0.565975	−	1.48370i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.115.1	✓	100
8.3	odd	2	CM	2008.1.bd.a.115.1	✓	100
251.227	even	125	inner	2008.1.bd.a.227.1	yes	100
2008.227	odd	250	inner	2008.1.bd.a.227.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.115.1	✓	100	1.1	even	1	trivial
2008.1.bd.a.115.1	✓	100	8.3	odd	2	CM
2008.1.bd.a.227.1	yes	100	251.227	even	125	inner
2008.1.bd.a.227.1	yes	100	2008.227	odd	250	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.728969 - 0.684547i) q^{2} +(-1.27992 + 0.622047i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-0.507200 + 1.32962i) q^{6} +(-0.637424 - 0.770513i) q^{8} +(0.633388 - 0.806049i) q^{9} +O(q^{10})\)	\(q+(0.728969 - 0.684547i) q^{2} +(-1.27992 + 0.622047i) q^{3} +(0.0627905 - 0.998027i) q^{4} +(-0.507200 + 1.32962i) q^{6} +(-0.637424 - 0.770513i) q^{8} +(0.633388 - 0.806049i) q^{9} +(-0.225071 + 0.0170022i) q^{11} +(0.540453 + 1.31645i) q^{12} +(-0.992115 - 0.125333i) q^{16} +(0.161209 - 0.596639i) q^{17} +(-0.0900591 - 1.02117i) q^{18} +(-0.499529 - 1.67992i) q^{19} +(-0.152431 + 0.166466i) q^{22} +(1.29515 + 0.589686i) q^{24} +(0.876307 + 0.481754i) q^{25} +(-0.00758238 + 0.0349517i) q^{27} +(-0.809017 + 0.587785i) q^{32} +(0.277497 - 0.161766i) q^{33} +(-0.290911 - 0.545286i) q^{34} +(-0.764688 - 0.682750i) q^{36} +(-1.51412 - 0.882657i) q^{38} +(-0.194999 - 1.71681i) q^{41} +(-1.77403 - 0.917999i) q^{43} +(0.00283632 + 0.225695i) q^{44} +(1.34779 - 0.456726i) q^{48} +(0.112856 - 0.993611i) q^{49} +(0.968583 - 0.248690i) q^{50} +(0.164803 + 0.863928i) q^{51} +(0.0183988 + 0.0306692i) q^{54} +(1.68434 + 1.83943i) q^{57} +(-0.123378 - 0.456624i) q^{59} +(-0.187381 + 0.982287i) q^{64} +(0.0915497 - 0.307882i) q^{66} +(1.61389 + 0.328935i) q^{67} +(-0.585339 - 0.198354i) q^{68} +(-1.02481 + 0.0257617i) q^{72} +(0.838414 - 0.149042i) q^{73} +(-1.42127 - 0.0715012i) q^{75} +(-1.70797 + 0.393060i) q^{76} +(0.230406 + 0.946599i) q^{81} +(-1.31738 - 1.11801i) q^{82} +(-0.263142 + 0.0818589i) q^{83} +(-1.92163 + 0.545214i) q^{86} +(0.156566 + 0.162583i) q^{88} +(-1.09982 - 0.717509i) q^{89} +(0.669845 - 1.25556i) q^{96} +(0.00532818 - 0.423981i) q^{97} +(-0.597905 - 0.801567i) q^{98} +(-0.128853 + 0.192188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 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

Related objects

Downloads

Learn more