LMFDB - Embedded newform 2008.1.bd.a.179.1

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			179.1
Root			$0.285019 + 0.958522i$ of defining polynomial
Character	$\chi$	$=$	2008.179
Dual form			2008.1.bd.a.875.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.637424 - 0.770513i) q^{2} +(0.238081 + 0.138789i) q^{3} +(-0.187381 + 0.982287i) q^{4} +(-0.0448196 - 0.271911i) q^{6} +(0.876307 - 0.481754i) q^{8} +(-0.455307 - 0.804098i) q^{9} +O(q^{10})$	\(q+(-0.637424 - 0.770513i) q^{2} +(0.238081 + 0.138789i) q^{3} +(-0.187381 + 0.982287i) q^{4} +(-0.0448196 - 0.271911i) q^{6} +(0.876307 - 0.481754i) q^{8} +(-0.455307 - 0.804098i) q^{9} +(-0.139506 + 1.58184i) q^{11} +(-0.180942 + 0.207857i) q^{12} +(-0.929776 - 0.368125i) q^{16} +(1.43703 + 0.743616i) q^{17} +(-0.329344 + 0.863372i) q^{18} +(-0.125224 - 0.00945962i) q^{19} +(1.30775 - 0.900812i) q^{22} +(0.275494 + 0.00692537i) q^{24} +(0.0627905 + 0.998027i) q^{25} +(0.00666292 - 0.530190i) q^{27} +(0.309017 + 0.951057i) q^{32} +(-0.252755 + 0.357244i) q^{33} +(-0.343035 - 1.58125i) q^{34} +(0.875171 - 0.296570i) q^{36} +(0.0725322 + 0.102517i) q^{38} +(0.917174 - 0.702248i) q^{41} +(-0.422111 + 0.791209i) q^{43} +(-1.52768 - 0.433442i) q^{44} +(-0.170270 - 0.216686i) q^{48} +(0.793990 + 0.607930i) q^{49} +(0.728969 - 0.684547i) q^{50} +(0.238924 + 0.376485i) q^{51} +(-0.412766 + 0.332822i) q^{54} +(-0.0285006 - 0.0196319i) q^{57} +(0.913785 - 0.472852i) q^{59} +(0.535827 - 0.844328i) q^{64} +(0.436373 - 0.0329643i) q^{66} +(-0.434622 + 1.46164i) q^{67} +(-0.999718 + 1.27224i) q^{68} +(-0.786366 - 0.485290i) q^{72} +(-1.44501 - 1.29018i) q^{73} +(-0.123566 + 0.246325i) q^{75} +(0.0327567 - 0.121234i) q^{76} +(-0.400200 + 0.667099i) q^{81} +(-1.12572 - 0.259065i) q^{82} +(1.86799 + 0.685806i) q^{83} +(0.878701 - 0.179093i) q^{86} +(0.639808 + 1.45339i) q^{88} +(1.97481 - 0.300072i) q^{89} +(-0.0584250 + 0.269316i) q^{96} +(-0.0241778 + 0.00685985i) q^{97} +(-0.0376902 - 0.999289i) q^{98} +(1.33547 - 0.608047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{56}{125}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$2$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$3$	0.238081	+	0.138789i	0.238081	+	0.138789i	0.617860	−	0.786288i	$-0.288000\pi$
$3$	0.238081	+	0.138789i	0.238081	+	0.138789i	−0.379779	+	0.925077i	$0.624000\pi$
$4$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$5$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$5$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$6$	−0.0448196	−	0.271911i	−0.0448196	−	0.271911i
$7$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$7$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$8$	0.876307	−	0.481754i	0.876307	−	0.481754i
$9$	−0.455307	−	0.804098i	−0.455307	−	0.804098i
$10$		0			0
$11$	−0.139506	+	1.58184i	−0.139506	+	1.58184i	0.535827	+	0.844328i	$0.320000\pi$
$11$	−0.139506	+	1.58184i	−0.139506	+	1.58184i	−0.675333	+	0.737513i	$0.736000\pi$
$12$	−0.180942	+	0.207857i	−0.180942	+	0.207857i
$13$		0			0		0.112856	−	0.993611i	$-0.464000\pi$
$13$		0			0		−0.112856	+	0.993611i	$0.536000\pi$
$14$		0			0
$15$		0			0
$16$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$17$	1.43703	+	0.743616i	1.43703	+	0.743616i	0.988652	−	0.150226i	$-0.0480000\pi$
$17$	1.43703	+	0.743616i	1.43703	+	0.743616i	0.448383	+	0.893841i	$0.352000\pi$
$18$	−0.329344	+	0.863372i	−0.329344	+	0.863372i
$19$	−0.125224	−	0.00945962i	−0.125224	−	0.00945962i	0.0125660	−	0.999921i	$-0.496000\pi$
$19$	−0.125224	−	0.00945962i	−0.125224	−	0.00945962i	−0.137790	+	0.990461i	$0.544000\pi$
$20$		0			0
$21$		0			0
$22$	1.30775	−	0.900812i	1.30775	−	0.900812i
$23$		0			0		0.711536	−	0.702650i	$-0.248000\pi$
$23$		0			0		−0.711536	+	0.702650i	$0.752000\pi$
$24$	0.275494	+	0.00692537i	0.275494	+	0.00692537i
$25$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$26$		0			0
$27$	0.00666292	−	0.530190i	0.00666292	−	0.530190i
$28$		0			0
$29$		0			0		−0.837528	−	0.546394i	$-0.816000\pi$
$29$		0			0		0.837528	+	0.546394i	$0.184000\pi$
$30$		0			0
$31$		0			0		−0.514440	−	0.857527i	$-0.672000\pi$
$31$		0			0		0.514440	+	0.857527i	$0.328000\pi$
$32$	0.309017	+	0.951057i	0.309017	+	0.951057i
$33$	−0.252755	+	0.357244i	−0.252755	+	0.357244i
$34$	−0.343035	−	1.58125i	−0.343035	−	1.58125i
$35$		0			0
$36$	0.875171	−	0.296570i	0.875171	−	0.296570i
$37$		0			0		0.675333	−	0.737513i	$-0.264000\pi$
$37$		0			0		−0.675333	+	0.737513i	$0.736000\pi$
$38$	0.0725322	+	0.102517i	0.0725322	+	0.102517i
$39$		0			0
$40$		0			0
$41$	0.917174	−	0.702248i	0.917174	−	0.702248i	−0.0376902	−	0.999289i	$-0.512000\pi$
$41$	0.917174	−	0.702248i	0.917174	−	0.702248i	0.954865	+	0.297042i	$0.0960000\pi$
$42$		0			0
$43$	−0.422111	+	0.791209i	−0.422111	+	0.791209i	−0.999684	−	0.0251301i	$-0.992000\pi$
$43$	−0.422111	+	0.791209i	−0.422111	+	0.791209i	0.577573	+	0.816339i	$0.304000\pi$
$44$	−1.52768	−	0.433442i	−1.52768	−	0.433442i
$45$		0			0
$46$		0			0
$47$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$47$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$48$	−0.170270	−	0.216686i	−0.170270	−	0.216686i
$49$	0.793990	+	0.607930i	0.793990	+	0.607930i
$50$	0.728969	−	0.684547i	0.728969	−	0.684547i
$51$	0.238924	+	0.376485i	0.238924	+	0.376485i
$52$		0			0
$53$		0			0		−0.899405	−	0.437116i	$-0.856000\pi$
$53$		0			0		0.899405	+	0.437116i	$0.144000\pi$
$54$	−0.412766	+	0.332822i	−0.412766	+	0.332822i
$55$		0			0
$56$		0			0
$57$	−0.0285006	−	0.0196319i	−0.0285006	−	0.0196319i
$58$		0			0
$59$	0.913785	−	0.472852i	0.913785	−	0.472852i	0.0627905	−	0.998027i	$-0.480000\pi$
$59$	0.913785	−	0.472852i	0.913785	−	0.472852i	0.850994	+	0.525175i	$0.176000\pi$
$60$		0			0
$61$		0			0		0.137790	−	0.990461i	$-0.456000\pi$
$61$		0			0		−0.137790	+	0.990461i	$0.544000\pi$
$62$		0			0
$63$		0			0
$64$	0.535827	−	0.844328i	0.535827	−	0.844328i
$65$		0			0
$66$	0.436373	−	0.0329643i	0.436373	−	0.0329643i
$67$	−0.434622	+	1.46164i	−0.434622	+	1.46164i	0.402906	+	0.915241i	$0.368000\pi$
$67$	−0.434622	+	1.46164i	−0.434622	+	1.46164i	−0.837528	+	0.546394i	$0.816000\pi$
$68$	−0.999718	+	1.27224i	−0.999718	+	1.27224i
$69$		0			0
$70$		0			0
$71$		0			0		−0.910106	−	0.414376i	$-0.864000\pi$
$71$		0			0		0.910106	+	0.414376i	$0.136000\pi$
$72$	−0.786366	−	0.485290i	−0.786366	−	0.485290i
$73$	−1.44501	−	1.29018i	−1.44501	−	1.29018i	−0.888136	−	0.459580i	$-0.848000\pi$
$73$	−1.44501	−	1.29018i	−1.44501	−	1.29018i	−0.556876	−	0.830596i	$-0.688000\pi$
$74$		0			0
$75$	−0.123566	+	0.246325i	−0.123566	+	0.246325i
$76$	0.0327567	−	0.121234i	0.0327567	−	0.121234i
$77$		0			0
$78$		0			0
$79$		0			0		−0.778462	−	0.627691i	$-0.784000\pi$
$79$		0			0		0.778462	+	0.627691i	$0.216000\pi$
$80$		0			0
$81$	−0.400200	+	0.667099i	−0.400200	+	0.667099i
$82$	−1.12572	−	0.259065i	−1.12572	−	0.259065i
$83$	1.86799	+	0.685806i	1.86799	+	0.685806i	0.968583	+	0.248690i	$0.0800000\pi$
$83$	1.86799	+	0.685806i	1.86799	+	0.685806i	0.899405	+	0.437116i	$0.144000\pi$
$84$		0			0
$85$		0			0
$86$	0.878701	−	0.179093i	0.878701	−	0.179093i
$87$		0			0
$88$	0.639808	+	1.45339i	0.639808	+	1.45339i
$89$	1.97481	−	0.300072i	1.97481	−	0.300072i	0.979855	−	0.199710i	$-0.0640000\pi$
$89$	1.97481	−	0.300072i	1.97481	−	0.300072i	0.994951	−	0.100362i	$-0.0320000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.0584250	+	0.269316i	−0.0584250	+	0.269316i
$97$	−0.0241778	+	0.00685985i	−0.0241778	+	0.00685985i	−0.285019	−	0.958522i	$-0.592000\pi$
$97$	−0.0241778	+	0.00685985i	−0.0241778	+	0.00685985i	0.260842	+	0.965382i	$0.416000\pi$
$98$	−0.0376902	−	0.999289i	−0.0376902	−	0.999289i
$99$	1.33547	−	0.608047i	1.33547	−	0.608047i
$100$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$101$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$101$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$102$	0.137790	−	0.424075i	0.137790	−	0.424075i
$103$		0			0		−0.597905	−	0.801567i	$-0.704000\pi$
$103$		0			0		0.597905	+	0.801567i	$0.296000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.271327	+	1.95035i	0.271327	+	1.95035i	0.309017	+	0.951057i	$0.400000\pi$
$107$	0.271327	+	1.95035i	0.271327	+	1.95035i	−0.0376902	+	0.999289i	$0.512000\pi$
$108$	0.519551	+	0.105893i	0.519551	+	0.105893i
$109$		0			0		−0.260842	−	0.965382i	$-0.584000\pi$
$109$		0			0		0.260842	+	0.965382i	$0.416000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.263152	−	0.191191i	−0.263152	−	0.191191i	0.448383	−	0.893841i	$-0.352000\pi$
$113$	−0.263152	−	0.191191i	−0.263152	−	0.191191i	−0.711536	+	0.702650i	$0.752000\pi$
$114$	0.00304033	+	0.0344739i	0.00304033	+	0.0344739i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.946807	−	0.402676i	−0.946807	−	0.402676i
$119$		0			0
$120$		0			0
$121$	−1.49819	−	0.266330i	−1.49819	−	0.266330i
$122$		0			0
$123$	0.315825	−	0.0398980i	0.315825	−	0.0398980i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.938734	−	0.344643i	$-0.112000\pi$
$127$		0			0		−0.938734	+	0.344643i	$0.888000\pi$
$128$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$129$	−0.210307	+	0.129787i	−0.210307	+	0.129787i
$130$		0			0
$131$	0.605914	+	0.598348i	0.605914	+	0.598348i	0.938734	−	0.344643i	$-0.112000\pi$
$131$	0.605914	+	0.598348i	0.605914	+	0.598348i	−0.332820	+	0.942991i	$0.608000\pi$
$132$	−0.303554	−	0.315219i	−0.303554	−	0.315219i
$133$		0			0
$134$	1.40325	−	0.596800i	1.40325	−	0.596800i
$135$		0			0
$136$	1.61752	−	0.0406613i	1.61752	−	0.0406613i
$137$	−0.158028	−	1.79186i	−0.158028	−	1.79186i	−0.514440	−	0.857527i	$-0.672000\pi$
$137$	−0.158028	−	1.79186i	−0.158028	−	1.79186i	0.356412	−	0.934329i	$-0.384000\pi$
$138$		0			0
$139$	−1.31738	−	1.11801i	−1.31738	−	1.11801i	−0.984564	−	0.175023i	$-0.944000\pi$
$139$	−1.31738	−	1.11801i	−1.31738	−	1.11801i	−0.332820	−	0.942991i	$-0.608000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.127326	+	0.915241i	0.127326	+	0.915241i
$145$		0			0
$146$	−0.0730122	+	1.93579i	−0.0730122	+	1.93579i
$147$	0.104660	+	0.254933i	0.104660	+	0.254933i
$148$		0			0
$149$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$149$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$150$	0.268561	−	0.0618047i	0.268561	−	0.0618047i
$151$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$151$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$152$	−0.114292	+	0.0520377i	−0.114292	+	0.0520377i
$153$	−0.0563526	−	1.49409i	−0.0563526	−	1.49409i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$157$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.769105	−	0.116866i	0.769105	−	0.116866i
$163$	−0.674891	−	1.53308i	−0.674891	−	1.53308i	−0.837528	−	0.546394i	$-0.816000\pi$
$163$	−0.674891	−	1.53308i	−0.674891	−	1.53308i	0.162637	−	0.986686i	$-0.448000\pi$
$164$	0.517948	+	1.03252i	0.517948	+	1.03252i
$165$		0			0
$166$	−0.662278	−	1.87646i	−0.662278	−	1.87646i
$167$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$167$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$168$		0			0
$169$	−0.974527	−	0.224271i	−0.974527	−	0.224271i
$170$		0			0
$171$	0.0494091	+	0.105000i	0.0494091	+	0.105000i
$172$	−0.698099	−	0.562893i	−0.698099	−	0.562893i
$173$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$173$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$174$		0			0
$175$		0			0
$176$	0.712024	−	1.41940i	0.712024	−	1.41940i
$177$	0.283181	+	0.0142462i	0.283181	+	0.0142462i
$178$	−1.49000	−	1.33034i	−1.49000	−	1.33034i
$179$	−1.14941	−	0.709335i	−1.14941	−	0.709335i	−0.187381	−	0.982287i	$-0.560000\pi$
$179$	−1.14941	−	0.709335i	−1.14941	−	0.709335i	−0.962028	+	0.272952i	$0.912000\pi$
$180$		0			0
$181$		0			0		0.379779	−	0.925077i	$-0.376000\pi$
$181$		0			0		−0.379779	+	0.925077i	$0.624000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.37676	+	2.16942i	−1.37676	+	2.16942i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.994951	−	0.100362i	$-0.0320000\pi$
$191$		0			0		−0.994951	+	0.100362i	$0.968000\pi$
$192$	0.244753	−	0.126651i	0.244753	−	0.126651i
$193$	−0.219963	−	1.93660i	−0.219963	−	1.93660i	−0.332820	−	0.942991i	$-0.608000\pi$
$193$	−0.219963	−	1.93660i	−0.219963	−	1.93660i	0.112856	−	0.993611i	$-0.464000\pi$
$194$	0.0206971	+	0.0142566i	0.0206971	+	0.0142566i
$195$		0			0
$196$	−0.745941	+	0.666012i	−0.745941	+	0.666012i
$197$		0			0		0.778462	−	0.627691i	$-0.216000\pi$
$197$		0			0		−0.778462	+	0.627691i	$0.784000\pi$
$198$	−1.31977	−	0.641416i	−1.31977	−	0.641416i
$199$		0			0		−0.954865	−	0.297042i	$-0.904000\pi$
$199$		0			0		0.954865	+	0.297042i	$0.0960000\pi$
$200$	0.535827	+	0.844328i	0.535827	+	0.844328i
$201$	−0.306334	+	0.287666i	−0.306334	+	0.287666i
$202$		0			0
$203$		0			0
$204$	−0.414586	+	0.164146i	−0.414586	+	0.164146i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.0324331	−	0.196765i	0.0324331	−	0.196765i
$210$		0			0
$211$	0.690429	+	0.177272i	0.690429	+	0.177272i	0.577573	−	0.816339i	$-0.304000\pi$
$211$	0.690429	+	0.177272i	0.690429	+	0.177272i	0.112856	+	0.993611i	$0.464000\pi$
$212$		0			0
$213$		0			0
$214$	1.32982	−	1.45226i	1.32982	−	1.45226i
$215$		0			0
$216$	−0.249582	−	0.467819i	−0.249582	−	0.467819i
$217$		0			0
$218$		0			0
$219$	−0.164967	−	0.507717i	−0.164967	−	0.507717i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.492727	−	0.870184i	$-0.336000\pi$
$223$		0			0		−0.492727	+	0.870184i	$0.664000\pi$
$224$		0			0
$225$	0.773922	−	0.504899i	0.773922	−	0.504899i
$226$	0.0204241	+	0.324632i	0.0204241	+	0.324632i
$227$	−1.75206	−	0.0440433i	−1.75206	−	0.0440433i	−0.863923	−	0.503623i	$-0.832000\pi$
$227$	−1.75206	−	0.0440433i	−1.75206	−	0.0440433i	−0.888136	+	0.459580i	$0.848000\pi$
$228$	0.0246246	−	0.0243171i	0.0246246	−	0.0243171i
$229$		0			0		0.823533	−	0.567269i	$-0.192000\pi$
$229$		0			0		−0.823533	+	0.567269i	$0.808000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.704734	−	1.84745i	0.704734	−	1.84745i	0.212007	−	0.977268i	$-0.432000\pi$
$233$	0.704734	−	1.84745i	0.704734	−	1.84745i	0.492727	−	0.870184i	$-0.336000\pi$
$234$		0			0
$235$		0			0
$236$	0.293250	+	0.986203i	0.293250	+	0.986203i
$237$		0			0
$238$		0			0
$239$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$239$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$240$		0			0
$241$	−0.114292	+	1.81662i	−0.114292	+	1.81662i	0.356412	+	0.934329i	$0.384000\pi$
$241$	−0.114292	+	1.81662i	−0.114292	+	1.81662i	−0.470704	+	0.882291i	$0.656000\pi$
$242$	0.749775	+	1.32414i	0.749775	+	1.32414i
$243$	−0.652512	+	0.358721i	−0.652512	+	0.358721i
$244$		0			0
$245$		0			0
$246$	−0.232057	−	0.217916i	−0.232057	−	0.217916i
$247$		0			0
$248$		0			0
$249$	0.349550	+	0.422533i	0.349550	+	0.422533i
$250$		0			0
$251$	−0.947098	+	0.320944i	−0.947098	+	0.320944i
$251$	−0.947098	+	0.320944i	−0.947098	+	0.320944i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.728969	+	0.684547i	0.728969	+	0.684547i
$257$	−0.0285757	−	0.173363i	−0.0285757	−	0.173363i	0.968583	−	0.248690i	$-0.0800000\pi$
$257$	−0.0285757	−	0.173363i	−0.0285757	−	0.173363i	−0.997159	+	0.0753268i	$0.976000\pi$
$258$	0.234058	+	0.0793152i	0.234058	+	0.0793152i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.0748104	−	0.848266i	0.0748104	−	0.848266i
$263$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$263$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$264$	−0.0493878	+	0.434821i	−0.0493878	+	0.434821i
$265$		0			0
$266$		0			0
$267$	0.511809	+	0.202640i	0.511809	+	0.202640i
$268$	−1.35431	−	0.700806i	−1.35431	−	0.700806i
$269$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$269$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$270$		0			0
$271$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$271$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$272$	−1.06238	−	1.22040i	−1.06238	−	1.22040i
$273$		0			0
$274$	−1.27992	+	1.26393i	−1.27992	+	1.26393i
$275$	−1.58748	−	0.0399061i	−1.58748	−	0.0399061i
$276$		0			0
$277$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$277$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$278$	−0.0217122	+	1.72771i	−0.0217122	+	1.72771i
$279$		0			0
$280$		0			0
$281$	−1.06348	+	1.58621i	−1.06348	+	1.58621i	−0.285019	+	0.958522i	$0.592000\pi$
$281$	−1.06348	+	1.58621i	−1.06348	+	1.58621i	−0.778462	+	0.627691i	$0.784000\pi$
$282$		0			0
$283$	−0.562476	−	1.73112i	−0.562476	−	1.73112i	−0.675333	−	0.737513i	$-0.736000\pi$
$283$	−0.562476	−	1.73112i	−0.562476	−	1.73112i	0.112856	−	0.993611i	$-0.464000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.624045	−	0.681503i	0.624045	−	0.681503i
$289$	0.934532	+	1.32086i	0.934532	+	1.32086i
$290$		0			0
$291$	−0.00670832	−	0.00172240i	−0.00670832	−	0.00172240i
$292$	1.53809	−	1.17766i	1.53809	−	1.17766i
$293$		0			0		0.162637	−	0.986686i	$-0.448000\pi$
$293$		0			0		−0.162637	+	0.986686i	$0.552000\pi$
$294$	0.129717	−	0.243142i	0.129717	−	0.243142i
$295$		0			0
$296$		0			0
$297$	0.837747	+	0.0845044i	0.837747	+	0.0845044i
$298$		0			0
$299$		0			0
$300$	−0.218808	−	0.167534i	−0.218808	−	0.167534i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.112948	+	0.0548935i	0.112948	+	0.0548935i
$305$		0			0
$306$	−1.11530	+	0.995790i	−1.11530	+	0.995790i
$307$	−0.222229	+	0.0395049i	−0.222229	+	0.0395049i	−0.285019	−	0.958522i	$-0.592000\pi$
$307$	−0.222229	+	0.0395049i	−0.222229	+	0.0395049i	0.0627905	+	0.998027i	$0.480000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.994951	−	0.100362i	$-0.0320000\pi$
$311$		0			0		−0.994951	+	0.100362i	$0.968000\pi$
$312$		0			0
$313$	−0.237242	+	0.672186i	−0.237242	+	0.672186i	0.762443	+	0.647056i	$0.224000\pi$
$313$	−0.237242	+	0.672186i	−0.237242	+	0.672186i	−0.999684	+	0.0251301i	$0.992000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.997159	−	0.0753268i	$-0.0240000\pi$
$317$		0			0		−0.997159	+	0.0753268i	$0.976000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.206089	+	0.501996i	−0.206089	+	0.501996i
$322$		0			0
$323$	−0.172917	−	0.106713i	−0.172917	−	0.106713i
$324$	−0.580293	−	0.518113i	−0.580293	−	0.518113i
$325$		0			0
$326$	−0.751067	+	1.49723i	−0.751067	+	1.49723i
$327$		0			0
$328$	0.465416	−	1.05724i	0.465416	−	1.05724i
$329$		0			0
$330$		0			0
$331$	0.829867	+	1.76356i	0.829867	+	1.76356i	0.617860	+	0.786288i	$0.288000\pi$
$331$	0.829867	+	1.76356i	0.829867	+	1.76356i	0.212007	+	0.977268i	$0.432000\pi$
$332$	−1.02368	+	1.70639i	−1.02368	+	1.70639i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.558555	+	0.113842i	−0.558555	+	0.113842i	−0.470704	−	0.882291i	$-0.656000\pi$
$337$	−0.558555	+	0.113842i	−0.558555	+	0.113842i	−0.0878512	+	0.996134i	$0.528000\pi$
$338$	0.448383	+	0.893841i	0.448383	+	0.893841i
$339$	−0.0361162	−	0.0820416i	−0.0361162	−	0.0820416i
$340$		0			0
$341$		0			0
$342$	0.0494091	−	0.105000i	0.0494091	−	0.105000i
$343$		0			0
$344$	0.0112688	+	0.896696i	0.0112688	+	0.896696i
$345$		0			0
$346$		0			0
$347$	0.278402	−	1.28332i	0.278402	−	1.28332i	−0.597905	−	0.801567i	$-0.704000\pi$
$347$	0.278402	−	1.28332i	0.278402	−	1.28332i	0.876307	−	0.481754i	$-0.160000\pi$
$348$		0			0
$349$		0			0		−0.0376902	−	0.999289i	$-0.512000\pi$
$349$		0			0		0.0376902	+	0.999289i	$0.488000\pi$
$350$		0			0
$351$		0			0
$352$	−1.54753	+	0.356138i	−1.54753	+	0.356138i
$353$	−0.115808	+	0.356420i	−0.115808	+	0.356420i	−0.992115	−	0.125333i	$-0.960000\pi$
$353$	−0.115808	+	0.356420i	−0.115808	+	0.356420i	0.876307	+	0.481754i	$0.160000\pi$
$354$	−0.169529	−	0.227276i	−0.169529	−	0.227276i
$355$		0			0
$356$	−0.0752852	+	1.99605i	−0.0752852	+	1.99605i
$357$		0			0
$358$	0.186109	+	1.33778i	0.186109	+	1.33778i
$359$		0			0		−0.979855	−	0.199710i	$-0.936000\pi$
$359$		0			0		0.979855	+	0.199710i	$0.0640000\pi$
$360$		0			0
$361$	−0.973060	−	0.147856i	−0.973060	−	0.147856i
$362$		0			0
$363$	−0.319727	−	0.271341i	−0.319727	−	0.271341i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.693653	−	0.720309i	$-0.256000\pi$
$367$		0			0		−0.693653	+	0.720309i	$0.744000\pi$
$368$		0			0
$369$	−0.982272	−	0.417759i	−0.982272	−	0.417759i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.850994	−	0.525175i	$-0.176000\pi$
$373$		0			0		−0.850994	+	0.525175i	$0.824000\pi$
$374$	2.54915	−	0.322032i	2.54915	−	0.322032i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.753569	−	0.0951979i	0.753569	−	0.0951979i	0.260842	−	0.965382i	$-0.416000\pi$
$379$	0.753569	−	0.0951979i	0.753569	−	0.0951979i	0.492727	+	0.870184i	$0.336000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.693653	−	0.720309i	$-0.744000\pi$
$383$		0			0		0.693653	+	0.720309i	$0.256000\pi$
$384$	−0.253598	−	0.107855i	−0.253598	−	0.107855i
$385$		0			0
$386$	−1.35197	+	1.40392i	−1.35197	+	1.40392i
$387$	0.828400	−	0.0208244i	0.828400	−	0.0208244i
$388$	−0.00220788	−	0.0250349i	−0.00220788	−	0.0250349i
$389$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$389$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$390$		0			0
$391$		0			0
$392$	0.988652	+	0.150226i	0.988652	+	0.150226i
$393$	0.0612125	+	0.226549i	0.0612125	+	0.226549i
$394$		0			0
$395$		0			0
$396$	0.347034	+	1.42576i	0.347034	+	1.42576i
$397$		0			0		0.0376902	−	0.999289i	$-0.488000\pi$
$397$		0			0		−0.0376902	+	0.999289i	$0.512000\pi$
$398$		0			0
$399$		0			0
$400$	0.309017	−	0.951057i	0.309017	−	0.951057i
$401$	1.08538	−	0.249782i	1.08538	−	0.249782i	0.356412	−	0.934329i	$-0.384000\pi$
$401$	1.08538	−	0.249782i	1.08538	−	0.249782i	0.728969	+	0.684547i	$0.240000\pi$
$402$	0.416915	+	0.0526686i	0.416915	+	0.0526686i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.390744	+	0.214813i	0.390744	+	0.214813i
$409$	−0.0187471	−	1.49176i	−0.0187471	−	1.49176i	−0.675333	−	0.737513i	$-0.736000\pi$
$409$	−0.0187471	−	1.49176i	−0.0187471	−	1.49176i	0.656586	−	0.754251i	$-0.272000\pi$
$410$		0			0
$411$	0.211066	−	0.448538i	0.211066	−	0.448538i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.158476	−	0.449015i	−0.158476	−	0.449015i
$418$	−0.172284	+	0.100433i	−0.172284	+	0.100433i
$419$	−1.40048	−	0.514167i	−1.40048	−	0.514167i	−0.470704	−	0.882291i	$-0.656000\pi$
$419$	−1.40048	−	0.514167i	−1.40048	−	0.514167i	−0.929776	+	0.368125i	$0.880000\pi$
$420$		0			0
$421$		0			0		0.514440	−	0.857527i	$-0.328000\pi$
$421$		0			0		−0.514440	+	0.857527i	$0.672000\pi$
$422$	−0.303506	−	0.644982i	−0.303506	−	0.644982i
$423$		0			0
$424$		0			0
$425$	−0.651916	+	1.48089i	−0.651916	+	1.48089i
$426$		0			0
$427$		0			0
$428$	−1.96664	−	0.0989375i	−1.96664	−	0.0989375i
$429$		0			0
$430$		0			0
$431$		0			0		−0.910106	−	0.414376i	$-0.864000\pi$
$431$		0			0		0.910106	+	0.414376i	$0.136000\pi$
$432$	−0.201371	+	0.490506i	−0.201371	+	0.490506i
$433$	−1.92189	+	0.493458i	−1.92189	+	0.493458i	−0.929776	+	0.368125i	$0.880000\pi$
$433$	−1.92189	+	0.493458i	−1.92189	+	0.493458i	−0.992115	+	0.125333i	$0.960000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.286049	+	0.450741i	−0.286049	+	0.450741i
$439$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$439$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$440$		0			0
$441$	0.127326	−	0.915241i	0.127326	−	0.915241i
$442$		0			0
$443$	−0.548899	+	0.284036i	−0.548899	+	0.284036i	−0.711536	−	0.702650i	$-0.752000\pi$
$443$	−0.548899	+	0.284036i	−0.548899	+	0.284036i	0.162637	+	0.986686i	$0.448000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.381361	+	0.185343i	0.381361	+	0.185343i	0.617860	−	0.786288i	$-0.288000\pi$
$449$	0.381361	+	0.185343i	0.381361	+	0.185343i	−0.236499	+	0.971632i	$0.576000\pi$
$450$	−0.882348	−	0.274483i	−0.882348	−	0.274483i
$451$	0.982893	+	1.54879i	0.982893	+	1.54879i
$452$	0.237115	−	0.222666i	0.237115	−	0.222666i
$453$		0			0
$454$	1.08287	+	1.37806i	1.08287	+	1.37806i
$455$		0			0
$456$	−0.0344330	−	0.00347329i	−0.0344330	−	0.00347329i
$457$	0.301500	−	1.23868i	0.301500	−	1.23868i	−0.597905	−	0.801567i	$-0.704000\pi$
$457$	0.301500	−	1.23868i	0.301500	−	1.23868i	0.899405	−	0.437116i	$-0.144000\pi$
$458$		0			0
$459$	0.403833	−	0.756948i	0.403833	−	0.756948i
$460$		0			0
$461$		0			0		0.793990	−	0.607930i	$-0.208000\pi$
$461$		0			0		−0.793990	+	0.607930i	$0.792000\pi$
$462$		0			0
$463$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$463$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$464$		0			0
$465$		0			0
$466$	−1.87270	+	0.634603i	−1.87270	+	0.634603i
$467$	−0.883731	−	1.65647i	−0.883731	−	1.65647i	−0.745941	−	0.666012i	$-0.768000\pi$
$467$	−0.883731	−	1.65647i	−0.883731	−	1.65647i	−0.137790	−	0.990461i	$-0.544000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.572958	−	0.854583i	0.572958	−	0.854583i
$473$	−1.19268	−	0.778092i	−1.19268	−	0.778092i
$474$		0			0
$475$	0.00157806	−	0.125571i	0.00157806	−	0.125571i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.711536	−	0.702650i	$-0.248000\pi$
$479$		0			0		−0.711536	+	0.702650i	$0.752000\pi$
$480$		0			0
$481$		0			0
$482$	1.47258	−	1.06989i	1.47258	−	1.06989i
$483$		0			0
$484$	0.542346	−	1.42175i	0.542346	−	1.42175i
$485$		0			0
$486$	0.692326	+	0.274111i	0.692326	+	0.274111i
$487$		0			0		−0.285019	−	0.958522i	$-0.592000\pi$
$487$		0			0		0.285019	+	0.958522i	$0.408000\pi$
$488$		0			0
$489$	0.0520960	−	0.458664i	0.0520960	−	0.458664i
$490$		0			0
$491$	0.166407	−	1.88687i	0.166407	−	1.88687i	−0.236499	−	0.971632i	$-0.576000\pi$
$491$	0.166407	−	1.88687i	0.166407	−	1.88687i	0.402906	−	0.915241i	$-0.368000\pi$
$492$	−0.0199885	+	0.317707i	−0.0199885	+	0.317707i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.102756	−	0.538665i	0.102756	−	0.538665i
$499$	0.408634	+	0.238213i	0.408634	+	0.238213i	0.693653	−	0.720309i	$-0.256000\pi$
$499$	0.408634	+	0.238213i	0.408634	+	0.238213i	−0.285019	+	0.958522i	$0.592000\pi$
$500$		0			0
$501$		0			0
$502$	0.850994	+	0.525175i	0.850994	+	0.525175i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.200890	−	0.188648i	−0.200890	−	0.188648i
$508$		0			0
$509$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$509$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$510$		0			0
$511$		0			0
$512$	0.0627905	−	0.998027i	0.0627905	−	0.998027i
$513$	−0.00584976	+	0.0663297i	−0.00584976	+	0.0663297i
$514$	−0.115364	+	0.132524i	−0.115364	+	0.132524i
$515$		0			0
$516$	−0.0880806	−	0.230902i	−0.0880806	−	0.230902i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.34683	+	0.101741i	1.34683	+	0.101741i	0.728969	−	0.684547i	$-0.240000\pi$
$521$	1.34683	+	0.101741i	1.34683	+	0.101741i	0.617860	+	0.786288i	$0.288000\pi$
$522$		0			0
$523$	−0.0494937	−	0.0568557i	−0.0494937	−	0.0568557i	0.728969	−	0.684547i	$-0.240000\pi$
$523$	−0.0494937	−	0.0568557i	−0.0494937	−	0.0568557i	−0.778462	+	0.627691i	$0.784000\pi$
$524$	−0.701286	+	0.483063i	−0.701286	+	0.483063i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.366516	−	0.239111i	0.366516	−	0.239111i
$529$	0.0125660	−	0.999921i	0.0125660	−	0.999921i
$530$		0			0
$531$	−0.796272	−	0.519480i	−0.796272	−	0.519480i
$532$		0			0
$533$		0			0
$534$	−0.170103	−	0.523523i	−0.170103	−	0.523523i
$535$		0			0
$536$	0.323286	+	1.49022i	0.323286	+	1.49022i
$537$	−0.175204	−	0.328404i	−0.175204	−	0.328404i
$538$		0			0
$539$	−1.07242	+	1.17116i	−1.07242	+	1.17116i
$540$		0			0
$541$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$541$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$542$		0			0
$543$		0			0
$544$	−0.263152	+	1.59649i	−0.263152	+	1.59649i
$545$		0			0
$546$		0			0
$547$	0.111864	−	0.459580i	0.111864	−	0.459580i	−0.888136	−	0.459580i	$-0.848000\pi$
$547$	0.111864	−	0.459580i	0.111864	−	0.459580i	1.00000			$0$
$548$	1.78973	+	0.180532i	1.78973	+	0.180532i
$549$		0			0
$550$	0.981149	+	1.24861i	0.981149	+	1.24861i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.34506	−	1.08455i	1.34506	−	1.08455i
$557$		0			0		0.745941	−	0.666012i	$-0.232000\pi$
$557$		0			0		−0.745941	+	0.666012i	$0.768000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.628870	+	0.325419i	−0.628870	+	0.325419i
$562$	1.90009	−	0.191664i	1.90009	−	0.191664i
$563$	−0.241493	+	1.73590i	−0.241493	+	1.73590i	0.356412	+	0.934329i	$0.384000\pi$
$563$	−0.241493	+	1.73590i	−0.241493	+	1.73590i	−0.597905	+	0.801567i	$0.704000\pi$
$564$		0			0
$565$		0			0
$566$	−0.975318	+	1.53686i	−0.975318	+	1.53686i
$567$		0			0
$568$		0			0
$569$	0.0500786	−	0.168415i	0.0500786	−	0.168415i	−0.929776	−	0.368125i	$-0.880000\pi$
$569$	0.0500786	−	0.168415i	0.0500786	−	0.168415i	0.979855	+	0.199710i	$0.0640000\pi$
$570$		0			0
$571$	1.59532	−	0.409608i	1.59532	−	0.409608i	0.656586	−	0.754251i	$-0.272000\pi$
$571$	1.59532	−	0.409608i	1.59532	−	0.409608i	0.938734	+	0.344643i	$0.112000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.922888	−	0.0464285i	−0.922888	−	0.0464285i
$577$	−0.340573	+	0.678925i	−0.340573	+	0.678925i	−0.997159	−	0.0753268i	$-0.976000\pi$
$577$	−0.340573	+	0.678925i	−0.340573	+	0.678925i	0.656586	+	0.754251i	$0.272000\pi$
$578$	0.422050	−	1.56202i	0.422050	−	1.56202i
$579$	0.216410	−	0.491596i	0.216410	−	0.491596i
$580$		0			0
$581$		0			0
$582$	0.00294891	+	0.00626675i	0.00294891	+	0.00626675i
$583$		0			0
$584$	−1.88782	−	0.434450i	−1.88782	−	0.434450i
$585$		0			0
$586$		0			0
$587$	0.518175	+	1.46817i	0.518175	+	1.46817i	0.850994	+	0.525175i	$0.176000\pi$
$587$	0.518175	+	1.46817i	0.518175	+	1.46817i	−0.332820	+	0.942991i	$0.608000\pi$
$588$	−0.270029	+	0.0550362i	−0.270029	+	0.0550362i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.838414	−	1.78172i	0.838414	−	1.78172i	0.260842	−	0.965382i	$-0.416000\pi$
$593$	0.838414	−	1.78172i	0.838414	−	1.78172i	0.577573	−	0.816339i	$-0.304000\pi$
$594$	−0.468889	−	0.699361i	−0.468889	−	0.699361i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.962028	−	0.272952i	$-0.0880000\pi$
$599$		0			0		−0.962028	+	0.272952i	$0.912000\pi$
$600$	0.0103867	+	0.275385i	0.0103867	+	0.275385i
$601$	−0.975318	+	0.444067i	−0.975318	+	0.444067i	−0.837528	−	0.546394i	$-0.816000\pi$
$601$	−0.975318	+	0.444067i	−0.975318	+	0.444067i	−0.137790	+	0.990461i	$0.544000\pi$
$602$		0			0
$603$	1.37318	−	0.316015i	1.37318	−	0.316015i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.0376902	−	0.999289i	$-0.488000\pi$
$607$		0			0		−0.0376902	+	0.999289i	$0.512000\pi$
$608$	−0.0296998	−	0.122019i	−0.0296998	−	0.122019i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	1.47819	+	0.224610i	1.47819	+	0.224610i
$613$		0			0		0.954865	−	0.297042i	$-0.0960000\pi$
$613$		0			0		−0.954865	+	0.297042i	$0.904000\pi$
$614$	0.172093	+	0.146049i	0.172093	+	0.146049i
$615$		0			0
$616$		0			0
$617$	−1.83988	+	0.0462510i	−1.83988	+	0.0462510i	−0.929776	−	0.368125i	$-0.880000\pi$
$617$	−1.83988	+	0.0462510i	−1.83988	+	0.0462510i	−0.910106	+	0.414376i	$0.864000\pi$
$618$		0			0
$619$	1.81958	−	0.773865i	1.81958	−	0.773865i	0.850994	−	0.525175i	$-0.176000\pi$
$619$	1.81958	−	0.773865i	1.81958	−	0.773865i	0.968583	−	0.248690i	$-0.0800000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$626$	0.669152	−	0.245670i	0.669152	−	0.245670i
$627$	0.0350305	−	0.0423446i	0.0350305	−	0.0423446i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.850994	−	0.525175i	$-0.176000\pi$
$631$		0			0		−0.850994	+	0.525175i	$0.824000\pi$
$632$		0			0
$633$	0.139774	+	0.138029i	0.139774	+	0.138029i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.11159	+	0.943367i	1.11159	+	0.943367i	0.998737	−	0.0502443i	$-0.0160000\pi$
$641$	1.11159	+	0.943367i	1.11159	+	0.943367i	0.112856	+	0.993611i	$0.464000\pi$
$642$	0.518161	−	0.161191i	0.518161	−	0.161191i
$643$	1.22170	+	0.185637i	1.22170	+	0.185637i	0.728969	−	0.684547i	$-0.240000\pi$
$643$	1.22170	+	0.185637i	1.22170	+	0.185637i	0.492727	+	0.870184i	$0.336000\pi$
$644$		0			0
$645$		0			0
$646$	0.0279982	+	0.201256i	0.0279982	+	0.201256i
$647$		0			0		−0.236499	−	0.971632i	$-0.576000\pi$
$647$		0			0		0.236499	+	0.971632i	$0.424000\pi$
$648$	−0.0293205	+	0.777381i	−0.0293205	+	0.777381i
$649$	0.620498	+	1.51143i	0.620498	+	1.51143i
$650$		0			0
$651$		0			0
$652$	1.63239	−	0.375666i	1.63239	−	0.375666i
$653$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$653$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$654$		0			0
$655$		0			0
$656$	−1.11128	+	0.315299i	−1.11128	+	0.315299i
$657$	−0.379503	+	1.74936i	−0.379503	+	1.74936i
$658$		0			0
$659$	−0.746226	−	0.410241i	−0.746226	−	0.410241i	0.0627905	−	0.998027i	$-0.480000\pi$
$659$	−0.746226	−	0.410241i	−0.746226	−	0.410241i	−0.809017	+	0.587785i	$0.800000\pi$
$660$		0			0
$661$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$661$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$662$	0.829867	−	1.76356i	0.829867	−	1.76356i
$663$		0			0
$664$	1.96732	−	0.298934i	1.96732	−	0.298934i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.222122	−	0.472033i	−0.222122	−	0.472033i	0.762443	−	0.647056i	$-0.224000\pi$
$673$	−0.222122	−	0.472033i	−0.222122	−	0.472033i	−0.984564	+	0.175023i	$0.944000\pi$
$674$	0.443754	+	0.357808i	0.443754	+	0.357808i
$675$	0.529563	−	0.0266412i	0.529563	−	0.0266412i
$676$	0.402906	−	0.915241i	0.402906	−	0.915241i
$677$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$677$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$678$	−0.0401928	+	0.0801233i	−0.0401928	+	0.0801233i
$679$		0			0
$680$		0			0
$681$	−0.411019	−	0.253652i	−0.411019	−	0.253652i
$682$		0			0
$683$	0.252796	−	0.615768i	0.252796	−	0.615768i	−0.745941	−	0.666012i	$-0.768000\pi$
$683$	0.252796	−	0.615768i	0.252796	−	0.615768i	0.998737	+	0.0502443i	$0.0160000\pi$
$684$	−0.112398	+	0.0288589i	−0.112398	+	0.0288589i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.683733	−	0.580258i	0.683733	−	0.580258i
$689$		0			0
$690$		0			0
$691$	0.397989	−	1.12764i	0.397989	−	1.12764i	−0.556876	−	0.830596i	$-0.688000\pi$
$691$	0.397989	−	1.12764i	0.397989	−	1.12764i	0.954865	−	0.297042i	$-0.0960000\pi$
$692$		0			0
$693$		0			0
$694$	−1.16628	+	0.603507i	−1.16628	+	0.603507i
$695$		0			0
$696$		0			0
$697$	1.84021	−	0.327129i	1.84021	−	0.327129i
$698$		0			0
$699$	0.424189	−	0.342033i	0.424189	−	0.342033i
$700$		0			0
$701$		0			0		−0.954865	−	0.297042i	$-0.904000\pi$
$701$		0			0		0.954865	+	0.297042i	$0.0960000\pi$
$702$		0			0
$703$		0			0
$704$	1.26084	+	0.965382i	1.26084	+	0.965382i
$705$		0			0
$706$	0.348445	−	0.137959i	0.348445	−	0.137959i
$707$		0			0
$708$	−0.0670567	+	0.275496i	−0.0670567	+	0.275496i
$709$		0			0		−0.962028	−	0.272952i	$-0.912000\pi$
$709$		0			0		0.962028	+	0.272952i	$0.0880000\pi$
$710$		0			0
$711$		0			0
$712$	1.58598	−	1.21432i	1.58598	−	1.21432i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.912149	−	0.996134i	0.912149	−	0.996134i
$717$		0			0
$718$		0			0
$719$		0			0		−0.212007	−	0.977268i	$-0.568000\pi$
$719$		0			0		0.212007	+	0.977268i	$0.432000\pi$
$720$		0			0
$721$		0			0
$722$	0.506327	+	0.844003i	0.506327	+	0.844003i
$723$	−0.279337	+	0.416639i	−0.279337	+	0.416639i
$724$		0			0
$725$		0			0
$726$	−0.00526952	+	0.419313i	−0.00526952	+	0.419313i
$727$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$727$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$728$		0			0
$729$	0.572551	+	0.0143928i	0.572551	+	0.0143928i
$730$		0			0
$731$	−1.19494	+	0.823106i	−1.19494	+	0.823106i
$732$		0			0
$733$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$733$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.25144	−	0.891409i	−2.25144	−	0.891409i
$738$	0.304235	+	1.02314i	0.304235	+	1.02314i
$739$	−0.237242	−	0.621926i	−0.237242	−	0.621926i	0.762443	−	0.647056i	$-0.224000\pi$
$739$	−0.237242	−	0.621926i	−0.237242	−	0.621926i	−0.999684	+	0.0251301i	$0.992000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$743$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.299054	−	1.81430i	−0.299054	−	1.81430i
$748$	−1.87302	−	1.75888i	−1.87302	−	1.75888i
$749$		0			0
$750$		0			0
$751$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$751$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$752$		0			0
$753$	−0.270029	−	0.0550362i	−0.270029	−	0.0550362i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$757$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$758$	−0.553694	−	0.519953i	−0.553694	−	0.519953i
$759$		0			0
$760$		0			0
$761$	1.74376	−	0.958643i	1.74376	−	0.958643i	0.823533	−	0.567269i	$-0.192000\pi$
$761$	1.74376	−	0.958643i	1.74376	−	0.958643i	0.920232	−	0.391374i	$-0.128000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.0785458	+	0.264150i	0.0785458	+	0.264150i
$769$	1.85897	+	0.736017i	1.85897	+	0.736017i	0.938734	+	0.344643i	$0.112000\pi$
$769$	1.85897	+	0.736017i	1.85897	+	0.736017i	0.920232	+	0.391374i	$0.128000\pi$
$770$		0			0
$771$	0.0172575	−	0.0452404i	0.0172575	−	0.0452404i
$772$	1.94352	+	0.146816i	1.94352	+	0.146816i
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	−0.544088	−	0.625019i	−0.544088	−	0.625019i
$775$		0			0
$776$	−0.0178824	+	0.0176591i	−0.0178824	+	0.0176591i
$777$		0			0
$778$		0			0
$779$	−0.121495	+	0.0792623i	−0.121495	+	0.0792623i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.514440	−	0.857527i	−0.514440	−	0.857527i
$785$		0			0
$786$	0.135541	−	0.191573i	0.135541	−	0.191573i
$787$	−0.376582	−	1.73589i	−0.376582	−	1.73589i	−0.637424	−	0.770513i	$-0.720000\pi$
$787$	−0.376582	−	1.73589i	−0.376582	−	1.73589i	0.260842	−	0.965382i	$-0.416000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.877355	−	1.17621i	0.877355	−	1.17621i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.962028	−	0.272952i	$-0.912000\pi$
$797$		0			0		0.962028	+	0.272952i	$0.0880000\pi$
$798$		0			0
$799$		0			0
$800$	−0.929776	+	0.368125i	−0.929776	+	0.368125i
$801$	−1.14043	−	1.45131i	−1.14043	−	1.45131i
$802$	−0.884308	−	0.677083i	−0.884308	−	0.677083i
$803$	2.24244	−	2.10579i	2.24244	−	2.10579i
$804$	−0.225170	−	0.354811i	−0.225170	−	0.354811i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.96851	−	0.349936i	1.96851	−	0.349936i	0.979855	−	0.199710i	$-0.0640000\pi$
$809$	1.96851	−	0.349936i	1.96851	−	0.349936i	0.988652	−	0.150226i	$-0.0480000\pi$
$810$		0			0
$811$	−0.189041	−	1.66435i	−0.189041	−	1.66435i	−0.637424	−	0.770513i	$-0.720000\pi$
$811$	−0.189041	−	1.66435i	−0.189041	−	1.66435i	0.448383	−	0.893841i	$-0.352000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.0835531	−	0.438001i	−0.0835531	−	0.438001i
$817$	0.0603431	−	0.0950856i	0.0603431	−	0.0950856i
$818$	−1.13747	+	0.965331i	−1.13747	+	0.965331i
$819$		0			0
$820$		0			0
$821$		0			0		0.617860	−	0.786288i	$-0.288000\pi$
$821$		0			0		−0.617860	+	0.786288i	$0.712000\pi$
$822$	−0.480143	+	0.123280i	−0.480143	+	0.123280i
$823$		0			0		0.379779	−	0.925077i	$-0.376000\pi$
$823$		0			0		−0.379779	+	0.925077i	$0.624000\pi$
$824$		0			0
$825$	−0.372409	−	0.229825i	−0.372409	−	0.229825i
$826$		0			0
$827$	1.87510	+	0.0943321i	1.87510	+	0.0943321i	0.954865	−	0.297042i	$-0.0960000\pi$
$827$	1.87510	+	0.0943321i	1.87510	+	0.0943321i	0.920232	+	0.391374i	$0.128000\pi$
$828$		0			0
$829$		0			0		0.260842	−	0.965382i	$-0.416000\pi$
$829$		0			0		−0.260842	+	0.965382i	$0.584000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.688925	+	1.46404i	0.688925	+	1.46404i
$834$	−0.244956	+	0.408321i	−0.244956	+	0.408321i
$835$		0			0
$836$	0.187203	+	0.0687288i	0.187203	+	0.0687288i
$837$		0			0
$838$	0.496528	+	1.40683i	0.496528	+	1.40683i
$839$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$839$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$840$		0			0
$841$	0.402906	+	0.915241i	0.402906	+	0.915241i
$842$		0			0
$843$	−0.473343	+	0.230047i	−0.473343	+	0.230047i
$844$	−0.303506	+	0.644982i	−0.303506	+	0.644982i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.106346	−	0.490212i	0.106346	−	0.490212i
$850$	1.55659	−	0.441646i	1.55659	−	0.441646i
$851$		0			0
$852$		0			0
$853$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$853$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$854$		0			0
$855$		0			0
$856$	1.17735	+	1.57839i	1.17735	+	1.57839i
$857$	0.636151	+	1.54956i	0.636151	+	1.54956i	0.823533	+	0.567269i	$0.192000\pi$
$857$	0.636151	+	1.54956i	0.636151	+	1.54956i	−0.187381	+	0.982287i	$0.560000\pi$
$858$		0			0
$859$	0.368211	+	1.51276i	0.368211	+	1.51276i	0.793990	+	0.607930i	$0.208000\pi$
$859$	0.368211	+	1.51276i	0.368211	+	1.51276i	−0.425779	+	0.904827i	$0.640000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.988652	−	0.150226i	$-0.952000\pi$
$863$		0			0		0.988652	+	0.150226i	$0.0480000\pi$
$864$	0.506300	−	0.157501i	0.506300	−	0.157501i
$865$		0			0
$866$	1.60528	+	1.16630i	1.60528	+	1.16630i
$867$	0.0391727	+	0.444175i	0.0391727	+	0.444175i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.0165243	+	0.0163179i	0.0165243	+	0.0163179i
$874$		0			0
$875$		0			0
$876$	0.529636	−	0.0669086i	0.529636	−	0.0669086i
$877$		0			0		0.938734	−	0.344643i	$-0.112000\pi$
$877$		0			0		−0.938734	+	0.344643i	$0.888000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.660390	−	0.0834267i	0.660390	−	0.0834267i	0.212007	−	0.977268i	$-0.432000\pi$
$881$	0.660390	−	0.0834267i	0.660390	−	0.0834267i	0.448383	+	0.893841i	$0.352000\pi$
$882$	−0.786366	+	0.485290i	−0.786366	+	0.485290i
$883$	−1.90726	−	0.339049i	−1.90726	−	0.339049i	−0.910106	−	0.414376i	$-0.864000\pi$
$883$	−1.90726	−	0.339049i	−1.90726	−	0.339049i	−0.997159	+	0.0753268i	$0.976000\pi$
$884$		0			0
$885$		0			0
$886$	0.568735	+	0.241882i	0.568735	+	0.241882i
$887$		0			0		0.920232	−	0.391374i	$-0.128000\pi$
$887$		0			0		−0.920232	+	0.391374i	$0.872000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.999414	−	0.726117i	−0.999414	−	0.726117i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.100279	−	0.411986i	−0.100279	−	0.411986i
$899$		0			0
$900$	0.350937	+	0.854823i	0.350937	+	0.854823i
$901$		0			0
$902$	0.566845	−	1.74457i	0.566845	−	1.74457i
$903$		0			0
$904$	−0.322709	−	0.0407677i	−0.322709	−	0.0407677i
$905$		0			0
$906$		0			0
$907$	−1.18880	+	0.337292i	−1.18880	+	0.337292i	−0.809017	−	0.587785i	$-0.800000\pi$
$907$	−1.18880	+	0.337292i	−1.18880	+	0.337292i	−0.379779	+	0.925077i	$0.624000\pi$
$908$	0.371566	−	1.71277i	0.371566	−	1.71277i
$909$		0			0
$910$		0			0
$911$		0			0		−0.0125660	−	0.999921i	$-0.504000\pi$
$911$		0			0		0.0125660	+	0.999921i	$0.496000\pi$
$912$	0.0192722	+	0.0287450i	0.0192722	+	0.0287450i
$913$	−1.34543	+	2.85919i	−1.34543	+	2.85919i
$914$	−1.14660	+	0.557256i	−1.14660	+	0.557256i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.840651	+	0.171338i	−0.840651	+	0.171338i
$919$		0			0		−0.332820	−	0.942991i	$-0.608000\pi$
$919$		0			0		0.332820	+	0.942991i	$0.392000\pi$
$920$		0			0
$921$	−0.0583912	−	0.0214375i	−0.0583912	−	0.0214375i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.101206	−	0.201751i	0.101206	−	0.201751i	−0.837528	−	0.546394i	$-0.816000\pi$
$929$	0.101206	−	0.201751i	0.101206	−	0.201751i	0.938734	+	0.344643i	$0.112000\pi$
$930$		0			0
$931$	−0.0936761	−	0.0836385i	−0.0936761	−	0.0836385i
$932$	1.68267	+	1.03843i	1.68267	+	1.03843i
$933$		0			0
$934$	−0.713023	+	1.73680i	−0.713023	+	1.73680i
$935$		0			0
$936$		0			0
$937$	0.189720	−	0.638030i	0.189720	−	0.638030i	−0.809017	−	0.587785i	$-0.800000\pi$
$937$	0.189720	−	0.638030i	0.189720	−	0.638030i	0.998737	−	0.0502443i	$-0.0160000\pi$
$938$		0			0
$939$	−0.149775	+	0.127108i	−0.149775	+	0.127108i
$940$		0			0
$941$		0			0		−0.187381	−	0.982287i	$-0.560000\pi$
$941$		0			0		0.187381	+	0.982287i	$0.440000\pi$
$942$		0			0
$943$		0			0
$944$	−1.02368	+	0.103260i	−1.02368	+	0.103260i
$945$		0			0
$946$	0.160713	+	1.41495i	0.160713	+	1.41495i
$947$	−1.53140	−	1.05487i	−1.53140	−	1.05487i	−0.974527	−	0.224271i	$-0.928000\pi$
$947$	−1.53140	−	1.05487i	−1.53140	−	1.05487i	−0.556876	−	0.830596i	$-0.688000\pi$
$948$		0			0
$949$		0			0
$950$	−0.0977601	+	0.0788261i	−0.0977601	+	0.0788261i
$951$		0			0
$952$		0			0
$953$	1.05949	+	1.66949i	1.05949	+	1.66949i	0.656586	+	0.754251i	$0.272000\pi$
$953$	1.05949	+	1.66949i	1.05949	+	1.66949i	0.402906	+	0.915241i	$0.368000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.470704	+	0.882291i	−0.470704	+	0.882291i
$962$		0			0
$963$	1.44473	−	1.10618i	1.44473	−	1.10618i
$964$	−1.76303	−	0.452668i	−1.76303	−	0.452668i
$965$		0			0
$966$		0			0
$967$		0			0		0.675333	−	0.737513i	$-0.264000\pi$
$967$		0			0		−0.675333	+	0.737513i	$0.736000\pi$
$968$	−1.44118	+	0.488374i	−1.44118	+	0.488374i
$969$	−0.0263577	−	0.0494052i	−0.0263577	−	0.0494052i
$970$		0			0
$971$	0.618958	−	0.874833i	0.618958	−	0.874833i	−0.379779	−	0.925077i	$-0.624000\pi$
$971$	0.618958	−	0.874833i	0.618958	−	0.874833i	0.998737	+	0.0502443i	$0.0160000\pi$
$972$	−0.230099	−	0.708172i	−0.230099	−	0.708172i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.0217122	+	1.72771i	−0.0217122	+	1.72771i	0.492727	+	0.870184i	$0.336000\pi$
$977$	−0.0217122	+	1.72771i	−0.0217122	+	1.72771i	−0.514440	+	0.857527i	$0.672000\pi$
$978$	−0.386614	+	0.252223i	−0.386614	+	0.252223i
$979$	0.199168	+	3.16569i	0.199168	+	3.16569i
$980$		0			0
$981$		0			0
$982$	−1.55993	+	1.07452i	−1.55993	+	1.07452i
$983$		0			0		−0.656586	−	0.754251i	$-0.728000\pi$
$983$		0			0		0.656586	+	0.754251i	$0.272000\pi$
$984$	0.257539	−	0.187113i	0.257539	−	0.187113i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.112856	−	0.993611i	$-0.464000\pi$
$991$		0			0		−0.112856	+	0.993611i	$0.536000\pi$
$992$		0			0
$993$	−0.0471868	+	0.535045i	−0.0471868	+	0.535045i
$994$		0			0
$995$		0			0
$996$	−0.480548	+	0.264183i	−0.480548	+	0.264183i
$997$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$997$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$998$	−0.0769271	−	0.466700i	−0.0769271	−	0.466700i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.179.1	✓	100
8.3	odd	2	CM	2008.1.bd.a.179.1	✓	100
251.122	even	125	inner	2008.1.bd.a.875.1	yes	100
2008.875	odd	250	inner	2008.1.bd.a.875.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.179.1	✓	100	1.1	even	1	trivial
2008.1.bd.a.179.1	✓	100	8.3	odd	2	CM
2008.1.bd.a.875.1	yes	100	251.122	even	125	inner
2008.1.bd.a.875.1	yes	100	2008.875	odd	250	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.637424 - 0.770513i) q^{2} +(0.238081 + 0.138789i) q^{3} +(-0.187381 + 0.982287i) q^{4} +(-0.0448196 - 0.271911i) q^{6} +(0.876307 - 0.481754i) q^{8} +(-0.455307 - 0.804098i) q^{9} +O(q^{10})\)	\(q+(-0.637424 - 0.770513i) q^{2} +(0.238081 + 0.138789i) q^{3} +(-0.187381 + 0.982287i) q^{4} +(-0.0448196 - 0.271911i) q^{6} +(0.876307 - 0.481754i) q^{8} +(-0.455307 - 0.804098i) q^{9} +(-0.139506 + 1.58184i) q^{11} +(-0.180942 + 0.207857i) q^{12} +(-0.929776 - 0.368125i) q^{16} +(1.43703 + 0.743616i) q^{17} +(-0.329344 + 0.863372i) q^{18} +(-0.125224 - 0.00945962i) q^{19} +(1.30775 - 0.900812i) q^{22} +(0.275494 + 0.00692537i) q^{24} +(0.0627905 + 0.998027i) q^{25} +(0.00666292 - 0.530190i) q^{27} +(0.309017 + 0.951057i) q^{32} +(-0.252755 + 0.357244i) q^{33} +(-0.343035 - 1.58125i) q^{34} +(0.875171 - 0.296570i) q^{36} +(0.0725322 + 0.102517i) q^{38} +(0.917174 - 0.702248i) q^{41} +(-0.422111 + 0.791209i) q^{43} +(-1.52768 - 0.433442i) q^{44} +(-0.170270 - 0.216686i) q^{48} +(0.793990 + 0.607930i) q^{49} +(0.728969 - 0.684547i) q^{50} +(0.238924 + 0.376485i) q^{51} +(-0.412766 + 0.332822i) q^{54} +(-0.0285006 - 0.0196319i) q^{57} +(0.913785 - 0.472852i) q^{59} +(0.535827 - 0.844328i) q^{64} +(0.436373 - 0.0329643i) q^{66} +(-0.434622 + 1.46164i) q^{67} +(-0.999718 + 1.27224i) q^{68} +(-0.786366 - 0.485290i) q^{72} +(-1.44501 - 1.29018i) q^{73} +(-0.123566 + 0.246325i) q^{75} +(0.0327567 - 0.121234i) q^{76} +(-0.400200 + 0.667099i) q^{81} +(-1.12572 - 0.259065i) q^{82} +(1.86799 + 0.685806i) q^{83} +(0.878701 - 0.179093i) q^{86} +(0.639808 + 1.45339i) q^{88} +(1.97481 - 0.300072i) q^{89} +(-0.0584250 + 0.269316i) q^{96} +(-0.0241778 + 0.00685985i) q^{97} +(-0.0376902 - 0.999289i) q^{98} +(1.33547 - 0.608047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 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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