LMFDB - Embedded newform 2008.1.bd.a.83.1

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			83.1
Root			$0.947098 - 0.320944i$ of defining polynomial
Character	$\chi$	$=$	2008.83
Dual form			2008.1.bd.a.1379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.425779 - 0.904827i) q^{2} +(-0.175480 - 0.00882805i) q^{3} +(-0.637424 + 0.770513i) q^{4} +(0.0667281 + 0.162538i) q^{6} +(0.968583 + 0.248690i) q^{8} +(-0.964236 - 0.0972634i) q^{9} +O(q^{10})$	\(q+(-0.425779 - 0.904827i) q^{2} +(-0.175480 - 0.00882805i) q^{3} +(-0.637424 + 0.770513i) q^{4} +(0.0667281 + 0.162538i) q^{6} +(0.968583 + 0.248690i) q^{8} +(-0.964236 - 0.0972634i) q^{9} +(0.0123833 + 0.0218695i) q^{11} +(0.118658 - 0.129583i) q^{12} +(-0.187381 - 0.982287i) q^{16} +(0.525944 - 0.324576i) q^{17} +(0.322545 + 0.913879i) q^{18} +(0.900801 + 1.14636i) q^{19} +(0.0145156 - 0.0205163i) q^{22} +(-0.167772 - 0.0521909i) q^{24} +(0.728969 - 0.684547i) q^{25} +(0.342054 + 0.0519751i) q^{27} +(-0.809017 + 0.587785i) q^{32} +(-0.00197996 - 0.00394700i) q^{33} +(-0.517621 - 0.337690i) q^{34} +(0.689570 - 0.680958i) q^{36} +(0.653715 - 1.30316i) q^{38} +(0.0112688 - 0.896696i) q^{41} +(1.40325 - 0.596800i) q^{43} +(-0.0247441 - 0.00439869i) q^{44} +(0.0242101 + 0.174026i) q^{48} +(0.0125660 + 0.999921i) q^{49} +(-0.929776 - 0.368125i) q^{50} +(-0.0951582 + 0.0523137i) q^{51} +(-0.0986111 - 0.331630i) q^{54} +(-0.147953 - 0.209116i) q^{57} +(1.66770 + 1.02919i) q^{59} +(0.876307 + 0.481754i) q^{64} +(-0.00272832 + 0.00347207i) q^{66} +(1.05483 + 0.357451i) q^{67} +(-0.0851591 + 0.612139i) q^{68} +(-0.909754 - 0.334003i) q^{72} +(1.54465 - 1.24548i) q^{73} +(-0.133963 + 0.113689i) q^{75} +(-1.45748 - 0.0366381i) q^{76} +(0.890041 + 0.181404i) q^{81} +(-0.816152 + 0.371598i) q^{82} +(-0.335529 - 0.628918i) q^{83} +(-1.13747 - 1.01559i) q^{86} +(0.00655549 + 0.0242620i) q^{88} +(-0.389529 - 1.60034i) q^{89} +(0.147156 - 0.0960028i) q^{96} +(-1.94678 + 0.346074i) q^{97} +(0.899405 - 0.437116i) q^{98} +(-0.00981328 - 0.0222918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{47}{125}\right)$	$-1$	$-1$

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 $

$2$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$2$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$3$	−0.175480	−	0.00882805i	−0.175480	−	0.00882805i	−0.0376902	−	0.999289i	$-0.512000\pi$
$3$	−0.175480	−	0.00882805i	−0.175480	−	0.00882805i	−0.137790	+	0.990461i	$0.544000\pi$
$4$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$5$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$5$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$6$	0.0667281	+	0.162538i	0.0667281	+	0.162538i
$7$		0			0		−0.711536	−	0.702650i	$-0.752000\pi$
$7$		0			0		0.711536	+	0.702650i	$0.248000\pi$
$8$	0.968583	+	0.248690i	0.968583	+	0.248690i
$9$	−0.964236	−	0.0972634i	−0.964236	−	0.0972634i
$10$		0			0
$11$	0.0123833	+	0.0218695i	0.0123833	+	0.0218695i	0.876307	−	0.481754i	$-0.160000\pi$
$11$	0.0123833	+	0.0218695i	0.0123833	+	0.0218695i	−0.863923	+	0.503623i	$0.832000\pi$
$12$	0.118658	−	0.129583i	0.118658	−	0.129583i
$13$		0			0		−0.212007	−	0.977268i	$-0.568000\pi$
$13$		0			0		0.212007	+	0.977268i	$0.432000\pi$
$14$		0			0
$15$		0			0
$16$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$17$	0.525944	−	0.324576i	0.525944	−	0.324576i	−0.236499	−	0.971632i	$-0.576000\pi$
$17$	0.525944	−	0.324576i	0.525944	−	0.324576i	0.762443	+	0.647056i	$0.224000\pi$
$18$	0.322545	+	0.913879i	0.322545	+	0.913879i
$19$	0.900801	+	1.14636i	0.900801	+	1.14636i	0.988652	+	0.150226i	$0.0480000\pi$
$19$	0.900801	+	1.14636i	0.900801	+	1.14636i	−0.0878512	+	0.996134i	$0.528000\pi$
$20$		0			0
$21$		0			0
$22$	0.0145156	−	0.0205163i	0.0145156	−	0.0205163i
$23$		0			0		−0.997159	−	0.0753268i	$-0.976000\pi$
$23$		0			0		0.997159	+	0.0753268i	$0.0240000\pi$
$24$	−0.167772	−	0.0521909i	−0.167772	−	0.0521909i
$25$	0.728969	−	0.684547i	0.728969	−	0.684547i
$26$		0			0
$27$	0.342054	+	0.0519751i	0.342054	+	0.0519751i
$28$		0			0
$29$		0			0		−0.793990	−	0.607930i	$-0.792000\pi$
$29$		0			0		0.793990	+	0.607930i	$0.208000\pi$
$30$		0			0
$31$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$31$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$32$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$33$	−0.00197996	−	0.00394700i	−0.00197996	−	0.00394700i
$34$	−0.517621	−	0.337690i	−0.517621	−	0.337690i
$35$		0			0
$36$	0.689570	−	0.680958i	0.689570	−	0.680958i
$37$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$37$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$38$	0.653715	−	1.30316i	0.653715	−	1.30316i
$39$		0			0
$40$		0			0
$41$	0.0112688	−	0.896696i	0.0112688	−	0.896696i	−0.888136	−	0.459580i	$-0.848000\pi$
$41$	0.0112688	−	0.896696i	0.0112688	−	0.896696i	0.899405	−	0.437116i	$-0.144000\pi$
$42$		0			0
$43$	1.40325	−	0.596800i	1.40325	−	0.596800i	0.448383	−	0.893841i	$-0.352000\pi$
$43$	1.40325	−	0.596800i	1.40325	−	0.596800i	0.954865	+	0.297042i	$0.0960000\pi$
$44$	−0.0247441	−	0.00439869i	−0.0247441	−	0.00439869i
$45$		0			0
$46$		0			0
$47$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$47$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$48$	0.0242101	+	0.174026i	0.0242101	+	0.174026i
$49$	0.0125660	+	0.999921i	0.0125660	+	0.999921i
$50$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$51$	−0.0951582	+	0.0523137i	−0.0951582	+	0.0523137i
$52$		0			0
$53$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$53$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$54$	−0.0986111	−	0.331630i	−0.0986111	−	0.331630i
$55$		0			0
$56$		0			0
$57$	−0.147953	−	0.209116i	−0.147953	−	0.209116i
$58$		0			0
$59$	1.66770	+	1.02919i	1.66770	+	1.02919i	0.938734	+	0.344643i	$0.112000\pi$
$59$	1.66770	+	1.02919i	1.66770	+	1.02919i	0.728969	+	0.684547i	$0.240000\pi$
$60$		0			0
$61$		0			0		0.0878512	−	0.996134i	$-0.472000\pi$
$61$		0			0		−0.0878512	+	0.996134i	$0.528000\pi$
$62$		0			0
$63$		0			0
$64$	0.876307	+	0.481754i	0.876307	+	0.481754i
$65$		0			0
$66$	−0.00272832	+	0.00347207i	−0.00272832	+	0.00347207i
$67$	1.05483	+	0.357451i	1.05483	+	0.357451i	0.793990	−	0.607930i	$-0.208000\pi$
$67$	1.05483	+	0.357451i	1.05483	+	0.357451i	0.260842	+	0.965382i	$0.416000\pi$
$68$	−0.0851591	+	0.612139i	−0.0851591	+	0.612139i
$69$		0			0
$70$		0			0
$71$		0			0		0.402906	−	0.915241i	$-0.368000\pi$
$71$		0			0		−0.402906	+	0.915241i	$0.632000\pi$
$72$	−0.909754	−	0.334003i	−0.909754	−	0.334003i
$73$	1.54465	−	1.24548i	1.54465	−	1.24548i	0.693653	−	0.720309i	$-0.256000\pi$
$73$	1.54465	−	1.24548i	1.54465	−	1.24548i	0.850994	−	0.525175i	$-0.176000\pi$
$74$		0			0
$75$	−0.133963	+	0.113689i	−0.133963	+	0.113689i
$76$	−1.45748	−	0.0366381i	−1.45748	−	0.0366381i
$77$		0			0
$78$		0			0
$79$		0			0		0.285019	−	0.958522i	$-0.408000\pi$
$79$		0			0		−0.285019	+	0.958522i	$0.592000\pi$
$80$		0			0
$81$	0.890041	+	0.181404i	0.890041	+	0.181404i
$82$	−0.816152	+	0.371598i	−0.816152	+	0.371598i
$83$	−0.335529	−	0.628918i	−0.335529	−	0.628918i	0.656586	−	0.754251i	$-0.272000\pi$
$83$	−0.335529	−	0.628918i	−0.335529	−	0.628918i	−0.992115	+	0.125333i	$0.960000\pi$
$84$		0			0
$85$		0			0
$86$	−1.13747	−	1.01559i	−1.13747	−	1.01559i
$87$		0			0
$88$	0.00655549	+	0.0242620i	0.00655549	+	0.0242620i
$89$	−0.389529	−	1.60034i	−0.389529	−	1.60034i	−0.745941	−	0.666012i	$-0.768000\pi$
$89$	−0.389529	−	1.60034i	−0.389529	−	1.60034i	0.356412	−	0.934329i	$-0.384000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.147156	−	0.0960028i	0.147156	−	0.0960028i
$97$	−1.94678	+	0.346074i	−1.94678	+	0.346074i	−0.947098	+	0.320944i	$0.896000\pi$
$97$	−1.94678	+	0.346074i	−1.94678	+	0.346074i	−0.999684	+	0.0251301i	$0.992000\pi$
$98$	0.899405	−	0.437116i	0.899405	−	0.437116i
$99$	−0.00981328	−	0.0222918i	−0.00981328	−	0.0222918i
$100$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$101$		0			0		−0.910106	−	0.414376i	$-0.864000\pi$
$101$		0			0		0.910106	+	0.414376i	$0.136000\pi$
$102$	0.0878512	+	0.0638276i	0.0878512	+	0.0638276i
$103$		0			0		0.162637	−	0.986686i	$-0.448000\pi$
$103$		0			0		−0.162637	+	0.986686i	$0.552000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.0903883	+	1.02490i	0.0903883	+	1.02490i	0.899405	+	0.437116i	$0.144000\pi$
$107$	0.0903883	+	1.02490i	0.0903883	+	1.02490i	−0.809017	+	0.587785i	$0.800000\pi$
$108$	−0.258081	+	0.230427i	−0.258081	+	0.230427i
$109$		0			0		0.999684	−	0.0251301i	$-0.00800000\pi$
$109$		0			0		−0.999684	+	0.0251301i	$0.992000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.234716	−	0.722383i	−0.234716	−	0.722383i	−0.997159	−	0.0753268i	$-0.976000\pi$
$113$	−0.234716	−	0.722383i	−0.234716	−	0.722383i	0.762443	−	0.647056i	$-0.224000\pi$
$114$	−0.126219	+	0.222909i	−0.126219	+	0.222909i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.221166	−	1.94719i	0.221166	−	1.94719i
$119$		0			0
$120$		0			0
$121$	0.514115	−	0.856985i	0.514115	−	0.856985i
$122$		0			0
$123$	−0.00989353	+	0.157253i	−0.00989353	+	0.157253i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.470704	−	0.882291i	$-0.344000\pi$
$127$		0			0		−0.470704	+	0.882291i	$0.656000\pi$
$128$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$129$	−0.251511	+	0.0923388i	−0.251511	+	0.0923388i
$130$		0			0
$131$	−1.06861	+	0.0807242i	−1.06861	+	0.0807242i	−0.597905	−	0.801567i	$-0.704000\pi$
$131$	−1.06861	+	0.0807242i	−1.06861	+	0.0807242i	−0.470704	+	0.882291i	$0.656000\pi$
$132$	0.00430328		0.000990327i	0.00430328		0.000990327i
$133$		0			0
$134$	−0.125694	−	1.10664i	−0.125694	−	1.10664i
$135$		0			0
$136$	0.590139	−	0.183582i	0.590139	−	0.183582i
$137$	0.647036	−	1.14270i	0.647036	−	1.14270i	−0.332820	−	0.942991i	$-0.608000\pi$
$137$	0.647036	−	1.14270i	0.647036	−	1.14270i	0.979855	−	0.199710i	$-0.0640000\pi$
$138$		0			0
$139$	−1.11234	+	1.65909i	−1.11234	+	1.65909i	−0.514440	+	0.857527i	$0.672000\pi$
$139$	−1.11234	+	1.65909i	−1.11234	+	1.65909i	−0.597905	+	0.801567i	$0.704000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.0851391	+	0.965382i	0.0851391	+	0.965382i
$145$		0			0
$146$	−1.78463	−	0.867338i	−1.78463	−	0.867338i
$147$	0.00662226	−	0.175578i	0.00662226	−	0.175578i
$148$		0			0
$149$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$149$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$150$	0.159908	+	0.0728068i	0.159908	+	0.0728068i
$151$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$151$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$152$	0.587412	+	1.33436i	0.587412	+	1.33436i
$153$	−0.538703	+	0.261812i	−0.538703	+	0.261812i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$157$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.214821	−	0.882571i	−0.214821	−	0.882571i
$163$	0.414211	+	1.53301i	0.414211	+	1.53301i	0.793990	+	0.607930i	$0.208000\pi$
$163$	0.414211	+	1.53301i	0.414211	+	1.53301i	−0.379779	+	0.925077i	$0.624000\pi$
$164$	0.683733	+	0.580258i	0.683733	+	0.580258i
$165$		0			0
$166$	−0.426201	+	0.571376i	−0.426201	+	0.571376i
$167$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$167$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$168$		0			0
$169$	−0.910106	+	0.414376i	−0.910106	+	0.414376i
$170$		0			0
$171$	−0.757085	−	1.19298i	−0.757085	−	1.19298i
$172$	−0.434622	+	1.46164i	−0.434622	+	1.46164i
$173$		0			0		0.823533	−	0.567269i	$-0.192000\pi$
$173$		0			0		−0.823533	+	0.567269i	$0.808000\pi$
$174$		0			0
$175$		0			0
$176$	0.0191618	−	0.0162619i	0.0191618	−	0.0162619i
$177$	−0.283563	−	0.195325i	−0.283563	−	0.195325i
$178$	−1.28218	+	1.03385i	−1.28218	+	1.03385i
$179$	−1.62199	−	0.595490i	−1.62199	−	0.595490i	−0.637424	−	0.770513i	$-0.720000\pi$
$179$	−1.62199	−	0.595490i	−1.62199	−	0.595490i	−0.984564	+	0.175023i	$0.944000\pi$
$180$		0			0
$181$		0			0		−0.0376902	−	0.999289i	$-0.512000\pi$
$181$		0			0		0.0376902	+	0.999289i	$0.488000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.0136112	+	0.00748283i	0.0136112	+	0.00748283i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$191$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$192$	−0.149522	−	0.0922744i	−0.149522	−	0.0922744i
$193$	−0.385898	+	1.77884i	−0.385898	+	1.77884i	0.212007	+	0.977268i	$0.432000\pi$
$193$	−0.385898	+	1.77884i	−0.385898	+	1.77884i	−0.597905	+	0.801567i	$0.704000\pi$
$194$	1.14204	+	1.61415i	1.14204	+	1.61415i
$195$		0			0
$196$	−0.778462	−	0.627691i	−0.778462	−	0.627691i
$197$		0			0		−0.285019	−	0.958522i	$-0.592000\pi$
$197$		0			0		0.285019	+	0.958522i	$0.408000\pi$
$198$	−0.0159919	+	0.0183707i	−0.0159919	+	0.0183707i
$199$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$199$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$200$	0.876307	−	0.481754i	0.876307	−	0.481754i
$201$	−0.181947	−	0.0720378i	−0.181947	−	0.0720378i
$202$		0			0
$203$		0			0
$204$	0.0203477	−	0.106667i	0.0203477	−	0.106667i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0139155	+	0.0338957i	−0.0139155	+	0.0338957i
$210$		0			0
$211$	0.660390	−	0.0834267i	0.660390	−	0.0834267i	0.212007	−	0.977268i	$-0.432000\pi$
$211$	0.660390	−	0.0834267i	0.660390	−	0.0834267i	0.448383	+	0.893841i	$0.352000\pi$
$212$		0			0
$213$		0			0
$214$	0.888873	−	0.518167i	0.888873	−	0.518167i
$215$		0			0
$216$	0.318382	+	0.135408i	0.318382	+	0.135408i
$217$		0			0
$218$		0			0
$219$	−0.282051	+	0.204922i	−0.282051	+	0.204922i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.994951	−	0.100362i	$-0.0320000\pi$
$223$		0			0		−0.994951	+	0.100362i	$0.968000\pi$
$224$		0			0
$225$	−0.769479	+	0.589163i	−0.769479	+	0.589163i
$226$	−0.553694	+	0.519953i	−0.553694	+	0.519953i
$227$	1.84973	+	0.575419i	1.84973	+	0.575419i	0.998737	+	0.0502443i	$0.0160000\pi$
$227$	1.84973	+	0.575419i	1.84973	+	0.575419i	0.850994	+	0.525175i	$0.176000\pi$
$228$	0.255435	+	0.0192959i	0.255435	+	0.0192959i
$229$		0			0		0.577573	−	0.816339i	$-0.304000\pi$
$229$		0			0		−0.577573	+	0.816339i	$0.696000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.157423	+	0.446033i	0.157423	+	0.446033i	0.994951	−	0.100362i	$-0.0320000\pi$
$233$	0.157423	+	0.446033i	0.157423	+	0.446033i	−0.837528	+	0.546394i	$0.816000\pi$
$234$		0			0
$235$		0			0
$236$	−1.85604	+	0.628956i	−1.85604	+	0.628956i
$237$		0			0
$238$		0			0
$239$		0			0		0.675333	−	0.737513i	$-0.264000\pi$
$239$		0			0		−0.675333	+	0.737513i	$0.736000\pi$
$240$		0			0
$241$	0.587412	+	0.551617i	0.587412	+	0.551617i	0.920232	−	0.391374i	$-0.128000\pi$
$241$	0.587412	+	0.551617i	0.587412	+	0.551617i	−0.332820	+	0.942991i	$0.608000\pi$
$242$	−0.994323	−	0.100298i	−0.994323	−	0.100298i
$243$	−0.489694	−	0.125732i	−0.489694	−	0.125732i
$244$		0			0
$245$		0			0
$246$	0.146499	−	0.0580032i	0.146499	−	0.0580032i
$247$		0			0
$248$		0			0
$249$	0.0533267	+	0.113325i	0.0533267	+	0.113325i
$250$		0			0
$251$	−0.711536	+	0.702650i	−0.711536	+	0.702650i
$251$	−0.711536	+	0.702650i	−0.711536	+	0.702650i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$257$	−0.374255	−	0.911622i	−0.374255	−	0.911622i	−0.992115	−	0.125333i	$-0.960000\pi$
$257$	−0.374255	−	0.911622i	−0.374255	−	0.911622i	0.617860	−	0.786288i	$-0.288000\pi$
$258$	0.190639	+	0.188258i	0.190639	+	0.188258i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.528033	+	0.932536i	0.528033	+	0.932536i
$263$		0			0		0.675333	−	0.737513i	$-0.264000\pi$
$263$		0			0		−0.675333	+	0.737513i	$0.736000\pi$
$264$	−0.000936174	−	0.00431539i	−0.000936174	−	0.00431539i
$265$		0			0
$266$		0			0
$267$	0.0542269	+	0.284267i	0.0542269	+	0.284267i
$268$	−0.947796	+	0.584914i	−0.947796	+	0.584914i
$269$		0			0		−0.332820	−	0.942991i	$-0.608000\pi$
$269$		0			0		0.332820	+	0.942991i	$0.392000\pi$
$270$		0			0
$271$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$271$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$272$	−0.417379	−	0.455808i	−0.417379	−	0.455808i
$273$		0			0
$274$	−1.30944	−	0.0989170i	−1.30944	−	0.0989170i
$275$	0.0239977	+	0.00746527i	0.0239977	+	0.00746527i
$276$		0			0
$277$		0			0		0.793990	−	0.607930i	$-0.208000\pi$
$277$		0			0		−0.793990	+	0.607930i	$0.792000\pi$
$278$	1.97481	+	0.300072i	1.97481	+	0.300072i
$279$		0			0
$280$		0			0
$281$	−1.23212	−	1.27947i	−1.23212	−	1.27947i	−0.947098	−	0.320944i	$-0.896000\pi$
$281$	−1.23212	−	1.27947i	−1.23212	−	1.27947i	−0.285019	−	0.958522i	$-0.592000\pi$
$282$		0			0
$283$	−0.651916	+	0.473645i	−0.651916	+	0.473645i	−0.863923	−	0.503623i	$-0.832000\pi$
$283$	−0.651916	+	0.473645i	−0.651916	+	0.473645i	0.212007	+	0.977268i	$0.432000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.837253	−	0.488076i	0.837253	−	0.488076i
$289$	−0.277116	+	0.552424i	−0.277116	+	0.552424i
$290$		0			0
$291$	0.344677	−	0.0435429i	0.344677	−	0.0435429i
$292$	−0.0249339	+	1.98407i	−0.0249339	+	1.98407i
$293$		0			0		0.379779	−	0.925077i	$-0.376000\pi$
$293$		0			0		−0.379779	+	0.925077i	$0.624000\pi$
$294$	−0.161687	+	0.0687653i	−0.161687	+	0.0687653i
$295$		0			0
$296$		0			0
$297$	0.00309908	+	0.00812419i	0.00309908	+	0.00812419i
$298$		0			0
$299$		0			0
$300$	−0.00220788	−	0.175689i	−0.00220788	−	0.175689i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.957261	−	1.09965i	0.957261	−	1.09965i
$305$		0			0
$306$	0.466263	+	0.375959i	0.466263	+	0.375959i
$307$	−0.218130	−	0.363603i	−0.218130	−	0.363603i	0.728969	−	0.684547i	$-0.240000\pi$
$307$	−0.218130	−	0.363603i	−0.218130	−	0.363603i	−0.947098	+	0.320944i	$0.896000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$311$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$312$		0			0
$313$	0.397989	+	0.533554i	0.397989	+	0.533554i	0.954865	−	0.297042i	$-0.0960000\pi$
$313$	0.397989	+	0.533554i	0.397989	+	0.533554i	−0.556876	+	0.830596i	$0.688000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.617860	−	0.786288i	$-0.288000\pi$
$317$		0			0		−0.617860	+	0.786288i	$0.712000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.00681350	−	0.180648i	−0.00681350	−	0.180648i
$322$		0			0
$323$	0.845851	+	0.310542i	0.845851	+	0.310542i
$324$	−0.707108	+	0.570157i	−0.707108	+	0.570157i
$325$		0			0
$326$	1.21074	−	1.02751i	1.21074	−	1.02751i
$327$		0			0
$328$	0.233914	−	0.865722i	0.233914	−	0.865722i
$329$		0			0
$330$		0			0
$331$	−0.975318	−	1.53686i	−0.975318	−	1.53686i	−0.837528	−	0.546394i	$-0.816000\pi$
$331$	−0.975318	−	1.53686i	−0.975318	−	1.53686i	−0.137790	−	0.990461i	$-0.544000\pi$
$332$	0.698464	+	0.142358i	0.698464	+	0.142358i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.41296	+	1.26156i	1.41296	+	1.26156i	0.920232	+	0.391374i	$0.128000\pi$
$337$	1.41296	+	1.26156i	1.41296	+	1.26156i	0.492727	+	0.870184i	$0.336000\pi$
$338$	0.762443	+	0.647056i	0.762443	+	0.647056i
$339$	0.0348109	+	0.128836i	0.0348109	+	0.128836i
$340$		0			0
$341$		0			0
$342$	−0.757085	+	1.19298i	−0.757085	+	1.19298i
$343$		0			0
$344$	1.50758	−	0.229077i	1.50758	−	0.229077i
$345$		0			0
$346$		0			0
$347$	1.13122	−	0.737996i	1.13122	−	0.737996i	0.162637	−	0.986686i	$-0.448000\pi$
$347$	1.13122	−	0.737996i	1.13122	−	0.737996i	0.968583	+	0.248690i	$0.0800000\pi$
$348$		0			0
$349$		0			0		0.899405	−	0.437116i	$-0.144000\pi$
$349$		0			0		−0.899405	+	0.437116i	$0.856000\pi$
$350$		0			0
$351$		0			0
$352$	−0.0228729	−	0.0104141i	−0.0228729	−	0.0104141i
$353$	1.03137	+	0.749337i	1.03137	+	0.749337i	0.968583	−	0.248690i	$-0.0800000\pi$
$353$	1.03137	+	0.749337i	1.03137	+	0.749337i	0.0627905	+	0.998027i	$0.480000\pi$
$354$	−0.0560002	+	0.339741i	−0.0560002	+	0.339741i
$355$		0			0
$356$	1.48138	+	0.719958i	1.48138	+	0.719958i
$357$		0			0
$358$	0.151793	+	1.72117i	0.151793	+	1.72117i
$359$		0			0		0.745941	−	0.666012i	$-0.232000\pi$
$359$		0			0		−0.745941	+	0.666012i	$0.768000\pi$
$360$		0			0
$361$	−0.266199	+	1.09365i	−0.266199	+	1.09365i
$362$		0			0
$363$	−0.0977826	+	0.145846i	−0.0977826	+	0.145846i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$367$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$368$		0			0
$369$	−0.0980815	+	0.863530i	−0.0980815	+	0.863530i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.938734	−	0.344643i	$-0.112000\pi$
$373$		0			0		−0.938734	+	0.344643i	$0.888000\pi$
$374$	0.000975292	−	0.0155018i	0.000975292	−	0.0155018i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.00473317	+	0.0752316i	−0.00473317	+	0.0752316i	−0.999684	−	0.0251301i	$-0.992000\pi$
$379$	−0.00473317	+	0.0752316i	−0.00473317	+	0.0752316i	0.994951	+	0.100362i	$0.0320000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.974527	−	0.224271i	$-0.928000\pi$
$383$		0			0		0.974527	+	0.224271i	$0.0720000\pi$
$384$	−0.0198291	+	0.174580i	−0.0198291	+	0.174580i
$385$		0			0
$386$	1.77385	−	0.408220i	1.77385	−	0.408220i
$387$	−1.41111	+	0.438971i	−1.41111	+	0.438971i
$388$	0.974271	−	1.72062i	0.974271	−	1.72062i
$389$		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
$392$	−0.236499	+	0.971632i	−0.236499	+	0.971632i
$393$	0.188233	−	0.00473180i	0.188233	−	0.00473180i
$394$		0			0
$395$		0			0
$396$	0.0234314	+	0.00664808i	0.0234314	+	0.00664808i
$397$		0			0		−0.899405	−	0.437116i	$-0.856000\pi$
$397$		0			0		0.899405	+	0.437116i	$0.144000\pi$
$398$		0			0
$399$		0			0
$400$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$401$	−1.26260	−	0.574866i	−1.26260	−	0.574866i	−0.332820	−	0.942991i	$-0.608000\pi$
$401$	−1.26260	−	0.574866i	−1.26260	−	0.574866i	−0.929776	+	0.368125i	$0.880000\pi$
$402$	0.0122874	+	0.195303i	0.0122874	+	0.195303i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.105178	+	0.0270052i	−0.105178	+	0.0270052i
$409$	−1.53926	+	0.233890i	−1.53926	+	0.233890i	−0.863923	−	0.503623i	$-0.832000\pi$
$409$	−1.53926	+	0.233890i	−1.53926	+	0.233890i	−0.675333	+	0.737513i	$0.736000\pi$
$410$		0			0
$411$	−0.123630	+	0.194810i	−0.123630	+	0.194810i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.209841	−	0.281319i	0.209841	−	0.281319i
$418$	0.0365947	−	0.00184100i	0.0365947	−	0.00184100i
$419$	0.732851	+	1.37366i	0.732851	+	1.37366i	0.920232	+	0.391374i	$0.128000\pi$
$419$	0.732851	+	1.37366i	0.732851	+	1.37366i	−0.187381	+	0.982287i	$0.560000\pi$
$420$		0			0
$421$		0			0		−0.979855	−	0.199710i	$-0.936000\pi$
$421$		0			0		0.979855	+	0.199710i	$0.0640000\pi$
$422$	−0.356667	−	0.562018i	−0.356667	−	0.562018i
$423$		0			0
$424$		0			0
$425$	0.161209	−	0.596639i	0.161209	−	0.596639i
$426$		0			0
$427$		0			0
$428$	−0.847315	−	0.583651i	−0.847315	−	0.583651i
$429$		0			0
$430$		0			0
$431$		0			0		0.402906	−	0.915241i	$-0.368000\pi$
$431$		0			0		−0.402906	+	0.915241i	$0.632000\pi$
$432$	−0.0130401	−	0.345735i	−0.0130401	−	0.345735i
$433$	−0.124591	−	0.0157395i	−0.124591	−	0.0157395i	0.0627905	−	0.998027i	$-0.480000\pi$
$433$	−0.124591	−	0.0157395i	−0.124591	−	0.0157395i	−0.187381	+	0.982287i	$0.560000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.305510	+	0.167956i	0.305510	+	0.167956i
$439$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$439$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$440$		0			0
$441$	0.0851391	−	0.965382i	0.0851391	−	0.965382i
$442$		0			0
$443$	−1.37694	−	0.849750i	−1.37694	−	0.849750i	−0.379779	−	0.925077i	$-0.624000\pi$
$443$	−1.37694	−	0.849750i	−1.37694	−	0.849750i	−0.997159	+	0.0753268i	$0.976000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.09982	+	1.26341i	−1.09982	+	1.26341i	−0.137790	+	0.990461i	$0.544000\pi$
$449$	−1.09982	+	1.26341i	−1.09982	+	1.26341i	−0.962028	+	0.272952i	$0.912000\pi$
$450$	0.860718	+	0.445392i	0.860718	+	0.445392i
$451$	0.0197499	−	0.0108576i	0.0197499	−	0.0108576i
$452$	0.706219	+	0.279612i	0.706219	+	0.279612i
$453$		0			0
$454$	−0.266923	−	1.91869i	−0.266923	−	1.91869i
$455$		0			0
$456$	−0.0912996	−	0.239341i	−0.0912996	−	0.239341i
$457$	0.819223	−	0.232435i	0.819223	−	0.232435i	0.162637	−	0.986686i	$-0.448000\pi$
$457$	0.819223	−	0.232435i	0.819223	−	0.232435i	0.656586	+	0.754251i	$0.272000\pi$
$458$		0			0
$459$	0.196771	−	0.0836866i	0.196771	−	0.0836866i
$460$		0			0
$461$		0			0		0.0125660	−	0.999921i	$-0.496000\pi$
$461$		0			0		−0.0125660	+	0.999921i	$0.504000\pi$
$462$		0			0
$463$		0			0		−0.162637	−	0.986686i	$-0.552000\pi$
$463$		0			0		0.162637	+	0.986686i	$0.448000\pi$
$464$		0			0
$465$		0			0
$466$	0.336555	−	0.332352i	0.336555	−	0.332352i
$467$	−0.866313	−	0.368442i	−0.866313	−	0.368442i	−0.0878512	−	0.996134i	$-0.528000\pi$
$467$	−0.866313	−	0.368442i	−0.866313	−	0.368442i	−0.778462	+	0.627691i	$0.784000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.35936	+	1.41160i	1.35936	+	1.41160i
$473$	0.0304285	+	0.0232980i	0.0304285	+	0.0232980i
$474$		0			0
$475$	1.44139	+	0.219019i	1.44139	+	0.219019i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.997159	−	0.0753268i	$-0.976000\pi$
$479$		0			0		0.997159	+	0.0753268i	$0.0240000\pi$
$480$		0			0
$481$		0			0
$482$	0.249010	−	0.766374i	0.249010	−	0.766374i
$483$		0			0
$484$	0.332609	+	0.942395i	0.332609	+	0.942395i
$485$		0			0
$486$	0.0947359	+	0.496623i	0.0947359	+	0.496623i
$487$		0			0		0.947098	−	0.320944i	$-0.104000\pi$
$487$		0			0		−0.947098	+	0.320944i	$0.896000\pi$
$488$		0			0
$489$	−0.0591525	−	0.272670i	−0.0591525	−	0.272670i
$490$		0			0
$491$	−0.701186	−	1.23833i	−0.701186	−	1.23833i	−0.962028	−	0.272952i	$-0.912000\pi$
$491$	−0.701186	−	1.23833i	−0.701186	−	1.23833i	0.260842	−	0.965382i	$-0.416000\pi$
$492$	−0.114859	−	0.107860i	−0.114859	−	0.107860i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.0798341	−	0.0965028i	0.0798341	−	0.0965028i
$499$	−1.92163	−	0.0966728i	−1.92163	−	0.0966728i	−0.947098	−	0.320944i	$-0.896000\pi$
$499$	−1.92163	−	0.0966728i	−1.92163	−	0.0966728i	−0.974527	+	0.224271i	$0.928000\pi$
$500$		0			0
$501$		0			0
$502$	0.938734	+	0.344643i	0.938734	+	0.344643i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.163364	−	0.0646804i	0.163364	−	0.0646804i
$508$		0			0
$509$		0			0		−0.711536	−	0.702650i	$-0.752000\pi$
$509$		0			0		0.711536	+	0.702650i	$0.248000\pi$
$510$		0			0
$511$		0			0
$512$	0.728969	+	0.684547i	0.728969	+	0.684547i
$513$	0.248541	+	0.438936i	0.248541	+	0.438936i
$514$	−0.665510	+	0.726786i	−0.665510	+	0.726786i
$515$		0			0
$516$	0.0891710	−	0.252652i	0.0891710	−	0.252652i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.06757	−	1.35859i	−1.06757	−	1.35859i	−0.929776	−	0.368125i	$-0.880000\pi$
$521$	−1.06757	−	1.35859i	−1.06757	−	1.35859i	−0.137790	−	0.990461i	$-0.544000\pi$
$522$		0			0
$523$	−1.21480	−	1.32665i	−1.21480	−	1.32665i	−0.929776	−	0.368125i	$-0.880000\pi$
$523$	−1.21480	−	1.32665i	−1.21480	−	1.32665i	−0.285019	−	0.958522i	$-0.592000\pi$
$524$	0.618958	−	0.874833i	0.618958	−	0.874833i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.00350608	+	0.00268448i	−0.00350608	+	0.00268448i
$529$	0.988652	+	0.150226i	0.988652	+	0.150226i
$530$		0			0
$531$	−1.50796	−	1.15459i	−1.50796	−	1.15459i
$532$		0			0
$533$		0			0
$534$	0.234124	−	0.170101i	0.234124	−	0.170101i
$535$		0			0
$536$	0.932798	+	0.608547i	0.932798	+	0.608547i
$537$	0.279370	+	0.118816i	0.279370	+	0.118816i
$538$		0			0
$539$	−0.0217122	+	0.0126571i	−0.0217122	+	0.0126571i
$540$		0			0
$541$		0			0		−0.162637	−	0.986686i	$-0.552000\pi$
$541$		0			0		0.162637	+	0.986686i	$0.448000\pi$
$542$		0			0
$543$		0			0
$544$	−0.234716	+	0.571729i	−0.234716	+	0.571729i
$545$		0			0
$546$		0			0
$547$	1.85099	−	0.525175i	1.85099	−	0.525175i	0.850994	−	0.525175i	$-0.176000\pi$
$547$	1.85099	−	0.525175i	1.85099	−	0.525175i	1.00000			$0$
$548$	0.468030	+	1.22693i	0.468030	+	1.22693i
$549$		0			0
$550$	−0.00346296	−	0.0248924i	−0.00346296	−	0.0248924i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.569319	−	1.91462i	−0.569319	−	1.91462i
$557$		0			0		−0.778462	−	0.627691i	$-0.784000\pi$
$557$		0			0		0.778462	+	0.627691i	$0.216000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.00232244	−	0.00143325i	−0.00232244	−	0.00143325i
$562$	−0.633085	+	1.65962i	−0.633085	+	1.65962i
$563$	−0.170182	+	1.92968i	−0.170182	+	1.92968i	0.162637	+	0.986686i	$0.448000\pi$
$563$	−0.170182	+	1.92968i	−0.170182	+	1.92968i	−0.332820	+	0.942991i	$0.608000\pi$
$564$		0			0
$565$		0			0
$566$	0.706139	+	0.388203i	0.706139	+	0.388203i
$567$		0			0
$568$		0			0
$569$	−0.933322	−	0.316275i	−0.933322	−	0.316275i	−0.187381	−	0.982287i	$-0.560000\pi$
$569$	−0.933322	−	0.316275i	−0.933322	−	0.316275i	−0.745941	+	0.666012i	$0.768000\pi$
$570$		0			0
$571$	−1.14604	−	0.144778i	−1.14604	−	0.144778i	−0.470704	−	0.882291i	$-0.656000\pi$
$571$	−1.14604	−	0.144778i	−1.14604	−	0.144778i	−0.675333	+	0.737513i	$0.736000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.798109	−	0.549757i	−0.798109	−	0.549757i
$577$	−0.0574732	+	0.0487753i	−0.0574732	+	0.0487753i	−0.675333	−	0.737513i	$-0.736000\pi$
$577$	−0.0574732	+	0.0487753i	−0.0574732	+	0.0487753i	0.617860	+	0.786288i	$0.288000\pi$
$578$	0.617839	+	0.0155313i	0.617839	+	0.0155313i
$579$	0.0834212	−	0.308744i	0.0834212	−	0.308744i
$580$		0			0
$581$		0			0
$582$	−0.186155	−	0.293334i	−0.186155	−	0.293334i
$583$		0			0
$584$	1.80586	−	0.822216i	1.80586	−	0.822216i
$585$		0			0
$586$		0			0
$587$	0.340829	−	0.456924i	0.340829	−	0.456924i	−0.597905	−	0.801567i	$-0.704000\pi$
$587$	0.340829	−	0.456924i	0.340829	−	0.456924i	0.938734	+	0.344643i	$0.112000\pi$
$588$	0.131064	+	0.117020i	0.131064	+	0.117020i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.551301	+	0.868711i	−0.551301	+	0.868711i	−0.999684	−	0.0251301i	$-0.992000\pi$
$593$	−0.551301	+	0.868711i	−0.551301	+	0.868711i	0.448383	+	0.893841i	$0.352000\pi$
$594$	0.00603146	−	0.00626324i	0.00603146	−	0.00626324i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.984564	−	0.175023i	$-0.0560000\pi$
$599$		0			0		−0.984564	+	0.175023i	$0.944000\pi$
$600$	−0.158028	+	0.0768023i	−0.158028	+	0.0768023i
$601$	0.706139	+	1.60406i	0.706139	+	1.60406i	0.793990	+	0.607930i	$0.208000\pi$
$601$	0.706139	+	1.60406i	0.706139	+	1.60406i	−0.0878512	+	0.996134i	$0.528000\pi$
$602$		0			0
$603$	−0.982339	−	0.447264i	−0.982339	−	0.447264i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.899405	−	0.437116i	$-0.856000\pi$
$607$		0			0		0.899405	+	0.437116i	$0.144000\pi$
$608$	−1.40258	−	0.397947i	−1.40258	−	0.397947i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.141652	−	0.581963i	0.141652	−	0.581963i
$613$		0			0		0.888136	−	0.459580i	$-0.152000\pi$
$613$		0			0		−0.888136	+	0.459580i	$0.848000\pi$
$614$	−0.236123	+	0.352184i	−0.236123	+	0.352184i
$615$		0			0
$616$		0			0
$617$	0.215525	−	0.0670461i	0.215525	−	0.0670461i	−0.187381	−	0.982287i	$-0.560000\pi$
$617$	0.215525	−	0.0670461i	0.215525	−	0.0670461i	0.402906	+	0.915241i	$0.368000\pi$
$618$		0			0
$619$	−0.0533808	−	0.469976i	−0.0533808	−	0.469976i	−0.992115	−	0.125333i	$-0.960000\pi$
$619$	−0.0533808	−	0.469976i	−0.0533808	−	0.469976i	0.938734	−	0.344643i	$-0.112000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$626$	0.313319	−	0.587288i	0.313319	−	0.587288i
$627$	0.00274113	−	0.00582520i	0.00274113	−	0.00582520i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.938734	−	0.344643i	$-0.112000\pi$
$631$		0			0		−0.938734	+	0.344643i	$0.888000\pi$
$632$		0			0
$633$	−0.116622	+	0.00880980i	−0.116622	+	0.00880980i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.03554	−	1.54454i	1.03554	−	1.54454i	0.212007	−	0.977268i	$-0.432000\pi$
$641$	1.03554	−	1.54454i	1.03554	−	1.54454i	0.823533	−	0.567269i	$-0.192000\pi$
$642$	−0.160554	+	0.0830812i	−0.160554	+	0.0830812i
$643$	0.0651745	−	0.267763i	0.0651745	−	0.267763i	−0.929776	−	0.368125i	$-0.880000\pi$
$643$	0.0651745	−	0.267763i	0.0651745	−	0.267763i	0.994951	+	0.100362i	$0.0320000\pi$
$644$		0			0
$645$		0			0
$646$	−0.0791587	−	0.897571i	−0.0791587	−	0.897571i
$647$		0			0		−0.962028	−	0.272952i	$-0.912000\pi$
$647$		0			0		0.962028	+	0.272952i	$0.0880000\pi$
$648$	0.816965	+	0.397049i	0.816965	+	0.397049i
$649$	−0.00185630	+	0.0492166i	−0.00185630	+	0.0492166i
$650$		0			0
$651$		0			0
$652$	−1.44523	−	0.658020i	−1.44523	−	0.658020i
$653$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$653$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$654$		0			0
$655$		0			0
$656$	−0.882924	+	0.156955i	−0.882924	+	0.156955i
$657$	−1.61054	+	1.05070i	−1.61054	+	1.05070i
$658$		0			0
$659$	1.03799	−	0.266509i	1.03799	−	0.266509i	0.309017	−	0.951057i	$-0.400000\pi$
$659$	1.03799	−	0.266509i	1.03799	−	0.266509i	0.728969	+	0.684547i	$0.240000\pi$
$660$		0			0
$661$		0			0		0.693653	−	0.720309i	$-0.256000\pi$
$661$		0			0		−0.693653	+	0.720309i	$0.744000\pi$
$662$	−0.975318	+	1.53686i	−0.975318	+	1.53686i
$663$		0			0
$664$	−0.168582	−	0.692602i	−0.168582	−	0.692602i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.07132	−	1.68812i	−1.07132	−	1.68812i	−0.556876	−	0.830596i	$-0.688000\pi$
$673$	−1.07132	−	1.68812i	−1.07132	−	1.68812i	−0.514440	−	0.857527i	$-0.672000\pi$
$674$	0.539883	−	1.81563i	0.539883	−	1.81563i
$675$	0.284926	−	0.196264i	0.284926	−	0.196264i
$676$	0.260842	−	0.965382i	0.260842	−	0.965382i
$677$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$677$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$678$	0.101753	−	0.0863536i	0.101753	−	0.0863536i
$679$		0			0
$680$		0			0
$681$	−0.319512	−	0.117304i	−0.319512	−	0.117304i
$682$		0			0
$683$	0.0450703	+	1.19496i	0.0450703	+	1.19496i	0.823533	+	0.567269i	$0.192000\pi$
$683$	0.0450703	+	1.19496i	0.0450703	+	1.19496i	−0.778462	+	0.627691i	$0.784000\pi$
$684$	1.40179	+	0.177087i	1.40179	+	0.177087i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.849171	−	1.26656i	−0.849171	−	1.26656i
$689$		0			0
$690$		0			0
$691$	−0.194483	−	0.260729i	−0.194483	−	0.260729i	0.693653	−	0.720309i	$-0.256000\pi$
$691$	−0.194483	−	0.260729i	−0.194483	−	0.260729i	−0.888136	+	0.459580i	$0.848000\pi$
$692$		0			0
$693$		0			0
$694$	−1.14941	−	0.709335i	−1.14941	−	0.709335i
$695$		0			0
$696$		0			0
$697$	−0.285119	−	0.475269i	−0.285119	−	0.475269i
$698$		0			0
$699$	−0.0236871	−	0.0796598i	−0.0236871	−	0.0796598i
$700$		0			0
$701$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$701$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$702$		0			0
$703$		0			0
$704$	0.000315811		0.0251301i	0.000315811		0.0251301i
$705$		0			0
$706$	0.238883	−	1.25227i	0.238883	−	1.25227i
$707$		0			0
$708$	0.331251	−	0.0939844i	0.331251	−	0.0939844i
$709$		0			0		−0.984564	−	0.175023i	$-0.944000\pi$
$709$		0			0		0.984564	+	0.175023i	$0.0560000\pi$
$710$		0			0
$711$		0			0
$712$	0.0206971	−	1.64694i	0.0206971	−	1.64694i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.49273	−	0.870184i	1.49273	−	0.870184i
$717$		0			0
$718$		0			0
$719$		0			0		−0.837528	−	0.546394i	$-0.816000\pi$
$719$		0			0		0.837528	+	0.546394i	$0.184000\pi$
$720$		0			0
$721$		0			0
$722$	1.10291	−	0.224790i	1.10291	−	0.224790i
$723$	−0.0982097	−	0.101984i	−0.0982097	−	0.101984i
$724$		0			0
$725$		0			0
$726$	0.173599	+	0.0263783i	0.173599	+	0.0263783i
$727$		0			0		0.793990	−	0.607930i	$-0.208000\pi$
$727$		0			0		−0.793990	+	0.607930i	$0.792000\pi$
$728$		0			0
$729$	−0.782519	−	0.243428i	−0.782519	−	0.243428i
$730$		0			0
$731$	0.544322	−	0.769343i	0.544322	−	0.769343i
$732$		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
$737$	0.00524497	+	0.0274951i	0.00524497	+	0.0274951i
$738$	0.823106	−	0.278926i	0.823106	−	0.278926i
$739$	0.397989	−	1.12764i	0.397989	−	1.12764i	−0.556876	−	0.830596i	$-0.688000\pi$
$739$	0.397989	−	1.12764i	0.397989	−	1.12764i	0.954865	−	0.297042i	$-0.0960000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$743$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.262358	+	0.639060i	0.262358	+	0.639060i
$748$	−0.0144417	+	0.00571789i	−0.0144417	+	0.00571789i
$749$		0			0
$750$		0			0
$751$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$751$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$752$		0			0
$753$	0.131064	−	0.117020i	0.131064	−	0.117020i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$757$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$758$	0.0700869	−	0.0277494i	0.0700869	−	0.0277494i
$759$		0			0
$760$		0			0
$761$	0.690429	+	0.177272i	0.690429	+	0.177272i	0.577573	−	0.816339i	$-0.304000\pi$
$761$	0.690429	+	0.177272i	0.690429	+	0.177272i	0.112856	+	0.993611i	$0.464000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.166407	−	0.0563906i	0.166407	−	0.0563906i
$769$	−0.357848	−	1.87590i	−0.357848	−	1.87590i	−0.470704	−	0.882291i	$-0.656000\pi$
$769$	−0.357848	−	1.87590i	−0.357848	−	1.87590i	0.112856	−	0.993611i	$-0.464000\pi$
$770$		0			0
$771$	0.0576266	+	0.163276i	0.0576266	+	0.163276i
$772$	−1.12464	−	1.43121i	−1.12464	−	1.43121i
$773$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$773$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$774$	0.998013	+	1.08990i	0.998013	+	1.08990i
$775$		0			0
$776$	−1.97169	−	0.148944i	−1.97169	−	0.148944i
$777$		0			0
$778$		0			0
$779$	1.03809	−	0.794826i	1.03809	−	0.794826i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.979855	−	0.199710i	0.979855	−	0.199710i
$785$		0			0
$786$	−0.0844270	−	0.168303i	−0.0844270	−	0.168303i
$787$	−1.42546	−	0.929957i	−1.42546	−	0.929957i	−0.999684	−	0.0251301i	$-0.992000\pi$
$787$	−1.42546	−	0.929957i	−1.42546	−	0.929957i	−0.425779	−	0.904827i	$-0.640000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.00396123	−	0.0240319i	−0.00396123	−	0.0240319i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.984564	−	0.175023i	$-0.944000\pi$
$797$		0			0		0.984564	+	0.175023i	$0.0560000\pi$
$798$		0			0
$799$		0			0
$800$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$801$	0.219943	+	1.58099i	0.219943	+	1.58099i
$802$	0.0174330	+	1.38720i	0.0174330	+	1.38720i
$803$	0.0463659	+	0.0183576i	0.0463659	+	0.0183576i
$804$	0.171483	−	0.0942738i	0.171483	−	0.0942738i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.982440	−	1.63764i	−0.982440	−	1.63764i	−0.745941	−	0.666012i	$-0.768000\pi$
$809$	−0.982440	−	1.63764i	−0.982440	−	1.63764i	−0.236499	−	0.971632i	$-0.576000\pi$
$810$		0			0
$811$	0.336663	−	1.55188i	0.336663	−	1.55188i	−0.425779	−	0.904827i	$-0.640000\pi$
$811$	0.336663	−	1.55188i	0.336663	−	1.55188i	0.762443	−	0.647056i	$-0.224000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.0692179	+	0.0836701i	0.0692179	+	0.0836701i
$817$	1.94819	+	1.07103i	1.94819	+	1.07103i
$818$	0.867013	+	1.29318i	0.867013	+	1.29318i
$819$		0			0
$820$		0			0
$821$		0			0		0.137790	−	0.990461i	$-0.456000\pi$
$821$		0			0		−0.137790	+	0.990461i	$0.544000\pi$
$822$	0.228908	+	0.0289178i	0.228908	+	0.0289178i
$823$		0			0		−0.0376902	−	0.999289i	$-0.512000\pi$
$823$		0			0		0.0376902	+	0.999289i	$0.488000\pi$
$824$		0			0
$825$	−0.00414523	−	0.00152186i	−0.00414523	−	0.00152186i
$826$		0			0
$827$	−0.775280	−	0.534031i	−0.775280	−	0.534031i	0.112856	−	0.993611i	$-0.464000\pi$
$827$	−0.775280	−	0.534031i	−0.775280	−	0.534031i	−0.888136	+	0.459580i	$0.848000\pi$
$828$		0			0
$829$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$829$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.331159	+	0.521823i	0.331159	+	0.521823i
$834$	−0.343891	−	0.0700904i	−0.343891	−	0.0700904i
$835$		0			0
$836$	−0.0172471	−	0.0323280i	−0.0172471	−	0.0323280i
$837$		0			0
$838$	0.930893	−	1.24798i	0.930893	−	1.24798i
$839$		0			0		−0.745941	−	0.666012i	$-0.768000\pi$
$839$		0			0		0.745941	+	0.666012i	$0.232000\pi$
$840$		0			0
$841$	0.260842	+	0.965382i	0.260842	+	0.965382i
$842$		0			0
$843$	0.204917	+	0.235398i	0.204917	+	0.235398i
$844$	−0.356667	+	0.562018i	−0.356667	+	0.562018i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.118580	−	0.0773603i	0.118580	−	0.0773603i
$850$	−0.608494	+	0.108170i	−0.608494	+	0.108170i
$851$		0			0
$852$		0			0
$853$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$853$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$854$		0			0
$855$		0			0
$856$	−0.167334	+	1.01518i	−0.167334	+	1.01518i
$857$	−0.0598513	+	1.58685i	−0.0598513	+	1.58685i	0.577573	+	0.816339i	$0.304000\pi$
$857$	−0.0598513	+	1.58685i	−0.0598513	+	1.58685i	−0.637424	+	0.770513i	$0.720000\pi$
$858$		0			0
$859$	0.548393	+	0.155593i	0.548393	+	0.155593i	0.535827	−	0.844328i	$-0.320000\pi$
$859$	0.548393	+	0.155593i	0.548393	+	0.155593i	0.0125660	+	0.999921i	$0.496000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.236499	−	0.971632i	$-0.424000\pi$
$863$		0			0		−0.236499	+	0.971632i	$0.576000\pi$
$864$	−0.307278	+	0.159006i	−0.307278	+	0.159006i
$865$		0			0
$866$	0.0388067	+	0.119435i	0.0388067	+	0.119435i
$867$	0.0535053	−	0.0944933i	0.0535053	−	0.0944933i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.91082	−	0.144346i	1.91082	−	0.144346i
$874$		0			0
$875$		0			0
$876$	0.0218909	−	0.347946i	0.0218909	−	0.347946i
$877$		0			0		0.470704	−	0.882291i	$-0.344000\pi$
$877$		0			0		−0.470704	+	0.882291i	$0.656000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.0750855	+	1.19345i	−0.0750855	+	1.19345i	0.762443	+	0.647056i	$0.224000\pi$
$881$	−0.0750855	+	1.19345i	−0.0750855	+	1.19345i	−0.837528	+	0.546394i	$0.816000\pi$
$882$	−0.909754	+	0.334003i	−0.909754	+	0.334003i
$883$	1.02077	−	1.70153i	1.02077	−	1.70153i	0.402906	−	0.915241i	$-0.368000\pi$
$883$	1.02077	−	1.70153i	1.02077	−	1.70153i	0.617860	−	0.786288i	$-0.288000\pi$
$884$		0			0
$885$		0			0
$886$	−0.182605	+	1.60770i	−0.182605	+	1.60770i
$887$		0			0		−0.112856	−	0.993611i	$-0.536000\pi$
$887$		0			0		0.112856	+	0.993611i	$0.464000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.00705438	+	0.0217111i	0.00705438	+	0.0217111i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.61145	+	0.457210i	1.61145	+	0.457210i
$899$		0			0
$900$	0.0365266	−	0.968440i	0.0365266	−	0.968440i
$901$		0			0
$902$	−0.0182333	−	0.0132473i	−0.0182333	−	0.0132473i
$903$		0			0
$904$	−0.0476931	−	0.758059i	−0.0476931	−	0.758059i
$905$		0			0
$906$		0			0
$907$	0.271327	−	0.0482330i	0.271327	−	0.0482330i	−0.0376902	−	0.999289i	$-0.512000\pi$
$907$	0.271327	−	0.0482330i	0.271327	−	0.0482330i	0.309017	+	0.951057i	$0.400000\pi$
$908$	−1.62243	+	1.05846i	−1.62243	+	1.05846i
$909$		0			0
$910$		0			0
$911$		0			0		0.988652	−	0.150226i	$-0.0480000\pi$
$911$		0			0		−0.988652	+	0.150226i	$0.952000\pi$
$912$	−0.177688	+	0.184517i	−0.177688	+	0.184517i
$913$	0.00959920	−	0.0151259i	0.00959920	−	0.0151259i
$914$	−0.559121	−	0.642289i	−0.559121	−	0.642289i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.159503	−	0.142412i	−0.159503	−	0.142412i
$919$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$919$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$920$		0			0
$921$	0.0350676	+	0.0657310i	0.0350676	+	0.0657310i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.323286	−	0.274361i	0.323286	−	0.274361i	−0.470704	−	0.882291i	$-0.656000\pi$
$929$	0.323286	−	0.274361i	0.323286	−	0.274361i	0.793990	+	0.607930i	$0.208000\pi$
$930$		0			0
$931$	−1.13495	+	0.915135i	−1.13495	+	0.915135i
$932$	−0.444019	−	0.163015i	−0.444019	−	0.163015i
$933$		0			0
$934$	0.0354818	+	0.940739i	0.0354818	+	0.940739i
$935$		0			0
$936$		0			0
$937$	1.13255	+	0.383788i	1.13255	+	0.383788i	0.823533	−	0.567269i	$-0.192000\pi$
$937$	1.13255	+	0.383788i	1.13255	+	0.383788i	0.309017	+	0.951057i	$0.400000\pi$
$938$		0			0
$939$	−0.0651290	−	0.0971418i	−0.0651290	−	0.0971418i
$940$		0			0
$941$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$941$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$942$		0			0
$943$		0			0
$944$	0.698464	−	1.83101i	0.698464	−	1.83101i
$945$		0			0
$946$	0.00812486	−	0.0374524i	0.00812486	−	0.0374524i
$947$	−0.216453	−	0.305933i	−0.216453	−	0.305933i	0.693653	−	0.720309i	$-0.256000\pi$
$947$	−0.216453	−	0.305933i	−0.216453	−	0.305933i	−0.910106	+	0.414376i	$0.864000\pi$
$948$		0			0
$949$		0			0
$950$	−0.415540	−	1.39746i	−0.415540	−	1.39746i
$951$		0			0
$952$		0			0
$953$	−0.414491	+	0.227869i	−0.414491	+	0.227869i	−0.675333	−	0.737513i	$-0.736000\pi$
$953$	−0.414491	+	0.227869i	−0.414491	+	0.227869i	0.260842	+	0.965382i	$0.416000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.920232	−	0.391374i	0.920232	−	0.391374i
$962$		0			0
$963$	0.0125298	−	0.997037i	0.0125298	−	0.997037i
$964$	−0.799459	+	0.100995i	−0.799459	+	0.100995i
$965$		0			0
$966$		0			0
$967$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$967$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$968$	0.711086	−	0.702206i	0.711086	−	0.702206i
$969$	−0.145689	−	0.0619613i	−0.145689	−	0.0619613i
$970$		0			0
$971$	0.785842	+	1.56656i	0.785842	+	1.56656i	0.823533	+	0.567269i	$0.192000\pi$
$971$	0.785842	+	1.56656i	0.785842	+	1.56656i	−0.0376902	+	0.999289i	$0.512000\pi$
$972$	0.409021	−	0.297171i	0.409021	−	0.297171i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.97481	+	0.300072i	1.97481	+	0.300072i	0.994951	+	0.100362i	$0.0320000\pi$
$977$	1.97481	+	0.300072i	1.97481	+	0.300072i	0.979855	+	0.199710i	$0.0640000\pi$
$978$	−0.221533	+	0.169620i	−0.221533	+	0.169620i
$979$	0.0301751	−	0.0283363i	0.0301751	−	0.0283363i
$980$		0			0
$981$		0			0
$982$	−0.821927	+	1.16171i	−0.821927	+	1.16171i
$983$		0			0		−0.675333	−	0.737513i	$-0.736000\pi$
$983$		0			0		0.675333	+	0.737513i	$0.264000\pi$
$984$	−0.0486900	+	0.149852i	−0.0486900	+	0.149852i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.212007	−	0.977268i	$-0.568000\pi$
$991$		0			0		0.212007	+	0.977268i	$0.432000\pi$
$992$		0			0
$993$	0.157582	+	0.278298i	0.157582	+	0.278298i
$994$		0			0
$995$		0			0
$996$	−0.121310	−	0.0311471i	−0.121310	−	0.0311471i
$997$		0			0		−0.711536	−	0.702650i	$-0.752000\pi$
$997$		0			0		0.711536	+	0.702650i	$0.248000\pi$
$998$	0.730716	+	1.77990i	0.730716	+	1.77990i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.83.1	✓	100
8.3	odd	2	CM	2008.1.bd.a.83.1	✓	100
251.124	even	125	inner	2008.1.bd.a.1379.1	yes	100
2008.1379	odd	250	inner	2008.1.bd.a.1379.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.83.1	✓	100	1.1	even	1	trivial
2008.1.bd.a.83.1	✓	100	8.3	odd	2	CM
2008.1.bd.a.1379.1	yes	100	251.124	even	125	inner
2008.1.bd.a.1379.1	yes	100	2008.1379	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)

\(f(q)\)	\(=\)	\(q+(-0.425779 - 0.904827i) q^{2} +(-0.175480 - 0.00882805i) q^{3} +(-0.637424 + 0.770513i) q^{4} +(0.0667281 + 0.162538i) q^{6} +(0.968583 + 0.248690i) q^{8} +(-0.964236 - 0.0972634i) q^{9} +O(q^{10})\)	\(q+(-0.425779 - 0.904827i) q^{2} +(-0.175480 - 0.00882805i) q^{3} +(-0.637424 + 0.770513i) q^{4} +(0.0667281 + 0.162538i) q^{6} +(0.968583 + 0.248690i) q^{8} +(-0.964236 - 0.0972634i) q^{9} +(0.0123833 + 0.0218695i) q^{11} +(0.118658 - 0.129583i) q^{12} +(-0.187381 - 0.982287i) q^{16} +(0.525944 - 0.324576i) q^{17} +(0.322545 + 0.913879i) q^{18} +(0.900801 + 1.14636i) q^{19} +(0.0145156 - 0.0205163i) q^{22} +(-0.167772 - 0.0521909i) q^{24} +(0.728969 - 0.684547i) q^{25} +(0.342054 + 0.0519751i) q^{27} +(-0.809017 + 0.587785i) q^{32} +(-0.00197996 - 0.00394700i) q^{33} +(-0.517621 - 0.337690i) q^{34} +(0.689570 - 0.680958i) q^{36} +(0.653715 - 1.30316i) q^{38} +(0.0112688 - 0.896696i) q^{41} +(1.40325 - 0.596800i) q^{43} +(-0.0247441 - 0.00439869i) q^{44} +(0.0242101 + 0.174026i) q^{48} +(0.0125660 + 0.999921i) q^{49} +(-0.929776 - 0.368125i) q^{50} +(-0.0951582 + 0.0523137i) q^{51} +(-0.0986111 - 0.331630i) q^{54} +(-0.147953 - 0.209116i) q^{57} +(1.66770 + 1.02919i) q^{59} +(0.876307 + 0.481754i) q^{64} +(-0.00272832 + 0.00347207i) q^{66} +(1.05483 + 0.357451i) q^{67} +(-0.0851591 + 0.612139i) q^{68} +(-0.909754 - 0.334003i) q^{72} +(1.54465 - 1.24548i) q^{73} +(-0.133963 + 0.113689i) q^{75} +(-1.45748 - 0.0366381i) q^{76} +(0.890041 + 0.181404i) q^{81} +(-0.816152 + 0.371598i) q^{82} +(-0.335529 - 0.628918i) q^{83} +(-1.13747 - 1.01559i) q^{86} +(0.00655549 + 0.0242620i) q^{88} +(-0.389529 - 1.60034i) q^{89} +(0.147156 - 0.0960028i) q^{96} +(-1.94678 + 0.346074i) q^{97} +(0.899405 - 0.437116i) q^{98} +(-0.00981328 - 0.0222918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 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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