LMFDB - Embedded newform 2008.1.bd.a.155.1

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			155.1
Root			$0.137790 - 0.990461i$ of defining polynomial
Character	$\chi$	$=$	2008.155
Dual form			2008.1.bd.a.1723.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.992115 - 0.125333i) q^{2} +(-0.507512 - 0.430706i) q^{3} +(0.968583 + 0.248690i) q^{4} +(0.449528 + 0.490918i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(-0.0905766 - 0.549510i) q^{9} +O(q^{10})$	\(q+(-0.992115 - 0.125333i) q^{2} +(-0.507512 - 0.430706i) q^{3} +(0.968583 + 0.248690i) q^{4} +(0.449528 + 0.490918i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(-0.0905766 - 0.549510i) q^{9} +(1.17735 - 1.57839i) q^{11} +(-0.384455 - 0.543387i) q^{12} +(0.876307 + 0.481754i) q^{16} +(0.0697491 - 0.614086i) q^{17} +(0.0209906 + 0.556529i) q^{18} +(-0.847259 - 0.0854639i) q^{19} +(-1.36589 + 1.41838i) q^{22} +(0.313319 + 0.587288i) q^{24} +(-0.425779 + 0.904827i) q^{25} +(-0.533139 + 0.888698i) q^{27} +(-0.809017 - 0.587785i) q^{32} +(-1.27734 + 0.293958i) q^{33} +(-0.146164 + 0.600501i) q^{34} +(0.0489265 - 0.554771i) q^{36} +(0.829867 + 0.190980i) q^{38} +(1.91897 + 0.341129i) q^{41} +(-1.44523 - 1.10656i) q^{43} +(1.53289 - 1.23601i) q^{44} +(-0.237242 - 0.621926i) q^{48} +(-0.984564 + 0.175023i) q^{49} +(0.535827 - 0.844328i) q^{50} +(-0.299889 + 0.281614i) q^{51} +(0.640319 - 0.814870i) q^{54} +(0.393184 + 0.408293i) q^{57} +(-0.213772 - 1.88210i) q^{59} +(0.728969 + 0.684547i) q^{64} +(1.30411 - 0.131547i) q^{66} +(-0.111033 - 0.798127i) q^{67} +(0.220275 - 0.577447i) q^{68} +(-0.118072 + 0.544265i) q^{72} +(0.373698 - 0.0282297i) q^{73} +(0.605802 - 0.275825i) q^{75} +(-0.799387 - 0.293484i) q^{76} +(0.125879 - 0.0426567i) q^{81} +(-1.86108 - 0.578950i) q^{82} +(0.636151 - 0.415018i) q^{83} +(1.29515 + 1.27897i) q^{86} +(-1.67572 + 1.03414i) q^{88} +(-1.09131 + 0.222427i) q^{89} +(0.157423 + 0.646756i) q^{96} +(0.800944 + 0.645819i) q^{97} +(0.998737 - 0.0502443i) q^{98} +(-0.973980 - 0.504001i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times$.

$n$	$257$	$503$	$1005$
$\chi(n)$	$e\left(\frac{33}{125}\right)$	$-1$	$-1$

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 $

$2$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$2$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$3$	−0.507512	−	0.430706i	−0.507512	−	0.430706i	0.356412	−	0.934329i	$-0.384000\pi$
$3$	−0.507512	−	0.430706i	−0.507512	−	0.430706i	−0.863923	+	0.503623i	$0.832000\pi$
$4$	0.968583	+	0.248690i	0.968583	+	0.248690i
$5$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$5$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$6$	0.449528	+	0.490918i	0.449528	+	0.490918i
$7$		0			0		−0.0878512	−	0.996134i	$-0.528000\pi$
$7$		0			0		0.0878512	+	0.996134i	$0.472000\pi$
$8$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$9$	−0.0905766	−	0.549510i	−0.0905766	−	0.549510i
$10$		0			0
$11$	1.17735	−	1.57839i	1.17735	−	1.57839i	0.448383	−	0.893841i	$-0.352000\pi$
$11$	1.17735	−	1.57839i	1.17735	−	1.57839i	0.728969	−	0.684547i	$-0.240000\pi$
$12$	−0.384455	−	0.543387i	−0.384455	−	0.543387i
$13$		0			0		−0.988652	−	0.150226i	$-0.952000\pi$
$13$		0			0		0.988652	+	0.150226i	$0.0480000\pi$
$14$		0			0
$15$		0			0
$16$	0.876307	+	0.481754i	0.876307	+	0.481754i
$17$	0.0697491	−	0.614086i	0.0697491	−	0.614086i	−0.910106	−	0.414376i	$-0.864000\pi$
$17$	0.0697491	−	0.614086i	0.0697491	−	0.614086i	0.979855	−	0.199710i	$-0.0640000\pi$
$18$	0.0209906	+	0.556529i	0.0209906	+	0.556529i
$19$	−0.847259	−	0.0854639i	−0.847259	−	0.0854639i	−0.332820	−	0.942991i	$-0.608000\pi$
$19$	−0.847259	−	0.0854639i	−0.847259	−	0.0854639i	−0.514440	+	0.857527i	$0.672000\pi$
$20$		0			0
$21$		0			0
$22$	−1.36589	+	1.41838i	−1.36589	+	1.41838i
$23$		0			0		−0.492727	−	0.870184i	$-0.664000\pi$
$23$		0			0		0.492727	+	0.870184i	$0.336000\pi$
$24$	0.313319	+	0.587288i	0.313319	+	0.587288i
$25$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$26$		0			0
$27$	−0.533139	+	0.888698i	−0.533139	+	0.888698i
$28$		0			0
$29$		0			0		0.962028	−	0.272952i	$-0.0880000\pi$
$29$		0			0		−0.962028	+	0.272952i	$0.912000\pi$
$30$		0			0
$31$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$31$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$32$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$33$	−1.27734	+	0.293958i	−1.27734	+	0.293958i
$34$	−0.146164	+	0.600501i	−0.146164	+	0.600501i
$35$		0			0
$36$	0.0489265	−	0.554771i	0.0489265	−	0.554771i
$37$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$37$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$38$	0.829867	+	0.190980i	0.829867	+	0.190980i
$39$		0			0
$40$		0			0
$41$	1.91897	+	0.341129i	1.91897	+	0.341129i	0.998737	−	0.0502443i	$-0.0160000\pi$
$41$	1.91897	+	0.341129i	1.91897	+	0.341129i	0.920232	+	0.391374i	$0.128000\pi$
$42$		0			0
$43$	−1.44523	−	1.10656i	−1.44523	−	1.10656i	−0.974527	−	0.224271i	$-0.928000\pi$
$43$	−1.44523	−	1.10656i	−1.44523	−	1.10656i	−0.470704	−	0.882291i	$-0.656000\pi$
$44$	1.53289	−	1.23601i	1.53289	−	1.23601i
$45$		0			0
$46$		0			0
$47$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$47$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$48$	−0.237242	−	0.621926i	−0.237242	−	0.621926i
$49$	−0.984564	+	0.175023i	−0.984564	+	0.175023i
$50$	0.535827	−	0.844328i	0.535827	−	0.844328i
$51$	−0.299889	+	0.281614i	−0.299889	+	0.281614i
$52$		0			0
$53$		0			0		−0.823533	−	0.567269i	$-0.808000\pi$
$53$		0			0		0.823533	+	0.567269i	$0.192000\pi$
$54$	0.640319	−	0.814870i	0.640319	−	0.814870i
$55$		0			0
$56$		0			0
$57$	0.393184	+	0.408293i	0.393184	+	0.408293i
$58$		0			0
$59$	−0.213772	−	1.88210i	−0.213772	−	1.88210i	−0.425779	−	0.904827i	$-0.640000\pi$
$59$	−0.213772	−	1.88210i	−0.213772	−	1.88210i	0.212007	−	0.977268i	$-0.432000\pi$
$60$		0			0
$61$		0			0		−0.332820	−	0.942991i	$-0.608000\pi$
$61$		0			0		0.332820	+	0.942991i	$0.392000\pi$
$62$		0			0
$63$		0			0
$64$	0.728969	+	0.684547i	0.728969	+	0.684547i
$65$		0			0
$66$	1.30411	−	0.131547i	1.30411	−	0.131547i
$67$	−0.111033	−	0.798127i	−0.111033	−	0.798127i	−0.962028	−	0.272952i	$-0.912000\pi$
$67$	−0.111033	−	0.798127i	−0.111033	−	0.798127i	0.850994	−	0.525175i	$-0.176000\pi$
$68$	0.220275	−	0.577447i	0.220275	−	0.577447i
$69$		0			0
$70$		0			0
$71$		0			0		0.888136	−	0.459580i	$-0.152000\pi$
$71$		0			0		−0.888136	+	0.459580i	$0.848000\pi$
$72$	−0.118072	+	0.544265i	−0.118072	+	0.544265i
$73$	0.373698	−	0.0282297i	0.373698	−	0.0282297i	0.112856	−	0.993611i	$-0.464000\pi$
$73$	0.373698	−	0.0282297i	0.373698	−	0.0282297i	0.260842	+	0.965382i	$0.416000\pi$
$74$		0			0
$75$	0.605802	−	0.275825i	0.605802	−	0.275825i
$76$	−0.799387	−	0.293484i	−0.799387	−	0.293484i
$77$		0			0
$78$		0			0
$79$		0			0		−0.617860	−	0.786288i	$-0.712000\pi$
$79$		0			0		0.617860	+	0.786288i	$0.288000\pi$
$80$		0			0
$81$	0.125879	−	0.0426567i	0.125879	−	0.0426567i
$82$	−1.86108	−	0.578950i	−1.86108	−	0.578950i
$83$	0.636151	−	0.415018i	0.636151	−	0.415018i	−0.187381	−	0.982287i	$-0.560000\pi$
$83$	0.636151	−	0.415018i	0.636151	−	0.415018i	0.823533	+	0.567269i	$0.192000\pi$
$84$		0			0
$85$		0			0
$86$	1.29515	+	1.27897i	1.29515	+	1.27897i
$87$		0			0
$88$	−1.67572	+	1.03414i	−1.67572	+	1.03414i
$89$	−1.09131	+	0.222427i	−1.09131	+	0.222427i	−0.711536	−	0.702650i	$-0.752000\pi$
$89$	−1.09131	+	0.222427i	−1.09131	+	0.222427i	−0.379779	+	0.925077i	$0.624000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.157423	+	0.646756i	0.157423	+	0.646756i
$97$	0.800944	+	0.645819i	0.800944	+	0.645819i	0.938734	−	0.344643i	$-0.112000\pi$
$97$	0.800944	+	0.645819i	0.800944	+	0.645819i	−0.137790	+	0.990461i	$0.544000\pi$
$98$	0.998737	−	0.0502443i	0.998737	−	0.0502443i
$99$	−0.973980	−	0.504001i	−0.973980	−	0.504001i
$100$	−0.637424	+	0.770513i	−0.637424	+	0.770513i
$101$		0			0		0.954865	−	0.297042i	$-0.0960000\pi$
$101$		0			0		−0.954865	+	0.297042i	$0.904000\pi$
$102$	0.332820	−	0.241808i	0.332820	−	0.241808i
$103$		0			0		0.656586	−	0.754251i	$-0.272000\pi$
$103$		0			0		−0.656586	+	0.754251i	$0.728000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.189720	−	0.537541i	0.189720	−	0.537541i	−0.809017	−	0.587785i	$-0.800000\pi$
$107$	0.189720	−	0.537541i	0.189720	−	0.537541i	0.998737	+	0.0502443i	$0.0160000\pi$
$108$	−0.737400	+	0.728191i	−0.737400	+	0.728191i
$109$		0			0		0.938734	−	0.344643i	$-0.112000\pi$
$109$		0			0		−0.938734	+	0.344643i	$0.888000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.417379	+	1.28456i	−0.417379	+	1.28456i	0.492727	+	0.870184i	$0.336000\pi$
$113$	−0.417379	+	1.28456i	−0.417379	+	1.28456i	−0.910106	+	0.414376i	$0.864000\pi$
$114$	−0.338911	−	0.454353i	−0.338911	−	0.454353i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.0238026	+	1.89405i	−0.0238026	+	1.89405i
$119$		0			0
$120$		0			0
$121$	−0.820134	−	2.75812i	−0.820134	−	2.75812i
$122$		0			0
$123$	−0.826972	−	0.999638i	−0.826972	−	0.999638i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.837528	−	0.546394i	$-0.816000\pi$
$127$		0			0		0.837528	+	0.546394i	$0.184000\pi$
$128$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$129$	0.256869	+	1.18406i	0.256869	+	1.18406i
$130$		0			0
$131$	0.0618772	−	0.109279i	0.0618772	−	0.109279i	−0.837528	−	0.546394i	$-0.816000\pi$
$131$	0.0618772	−	0.109279i	0.0618772	−	0.109279i	0.899405	+	0.437116i	$0.144000\pi$
$132$	−1.31032	−	0.0329387i	−1.31032	−	0.0329387i
$133$		0			0
$134$	0.0101259	+	0.805749i	0.0101259	+	0.805749i
$135$		0			0
$136$	−0.290911	+	0.545286i	−0.290911	+	0.545286i
$137$	−0.984788	−	1.32023i	−0.984788	−	1.32023i	−0.947098	−	0.320944i	$-0.896000\pi$
$137$	−0.984788	−	1.32023i	−0.984788	−	1.32023i	−0.0376902	−	0.999289i	$-0.512000\pi$
$138$		0			0
$139$	0.614386	−	1.39564i	0.614386	−	1.39564i	−0.285019	−	0.958522i	$-0.592000\pi$
$139$	0.614386	−	1.39564i	0.614386	−	1.39564i	0.899405	−	0.437116i	$-0.144000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.185355	−	0.525175i	0.185355	−	0.525175i
$145$		0			0
$146$	−0.374289	−	0.0188297i	−0.374289	−	0.0188297i
$147$	0.575061	+	0.335231i	0.575061	+	0.335231i
$148$		0			0
$149$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$149$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$150$	−0.635595	+	0.197722i	−0.635595	+	0.197722i
$151$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$151$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$152$	0.756300	+	0.391359i	0.756300	+	0.391359i
$153$	−0.343764	+	0.0172940i	−0.343764	+	0.0172940i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$157$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.130233	+	0.0265435i	−0.130233	+	0.0265435i
$163$	−1.63736	+	1.01047i	−1.63736	+	1.01047i	−0.675333	+	0.737513i	$0.736000\pi$
$163$	−1.63736	+	1.01047i	−1.63736	+	1.01047i	−0.962028	+	0.272952i	$0.912000\pi$
$164$	1.77385	+	0.807640i	1.77385	+	0.807640i
$165$		0			0
$166$	−0.683151	+	0.332015i	−0.683151	+	0.332015i
$167$		0			0		0.762443	−	0.647056i	$-0.224000\pi$
$167$		0			0		−0.762443	+	0.647056i	$0.776000\pi$
$168$		0			0
$169$	0.954865	+	0.297042i	0.954865	+	0.297042i
$170$		0			0
$171$	0.0297787	+	0.473318i	0.0297787	+	0.473318i
$172$	−1.12464	−	1.43121i	−1.12464	−	1.43121i
$173$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$173$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$174$		0			0
$175$		0			0
$176$	1.79212	−	0.815959i	1.79212	−	0.815959i
$177$	−0.702137	+	1.04726i	−0.702137	+	1.04726i
$178$	1.11059	−	0.0838953i	1.11059	−	0.0838953i
$179$	0.190121	−	0.876381i	0.190121	−	0.876381i	−0.778462	−	0.627691i	$-0.784000\pi$
$179$	0.190121	−	0.876381i	0.190121	−	0.876381i	0.968583	−	0.248690i	$-0.0800000\pi$
$180$		0			0
$181$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$181$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.887146	−	0.833086i	−0.887146	−	0.833086i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.379779	−	0.925077i	$-0.376000\pi$
$191$		0			0		−0.379779	+	0.925077i	$0.624000\pi$
$192$	−0.0751216	−	0.661387i	−0.0751216	−	0.661387i
$193$	1.88806	−	0.286890i	1.88806	−	0.286890i	0.899405	−	0.437116i	$-0.144000\pi$
$193$	1.88806	−	0.286890i	1.88806	−	0.286890i	0.988652	+	0.150226i	$0.0480000\pi$
$194$	−0.713685	−	0.741111i	−0.713685	−	0.741111i
$195$		0			0
$196$	−0.997159	−	0.0753268i	−0.997159	−	0.0753268i
$197$		0			0		0.617860	−	0.786288i	$-0.288000\pi$
$197$		0			0		−0.617860	+	0.786288i	$0.712000\pi$
$198$	0.903132	+	0.622099i	0.903132	+	0.622099i
$199$		0			0		−0.920232	−	0.391374i	$-0.872000\pi$
$199$		0			0		0.920232	+	0.391374i	$0.128000\pi$
$200$	0.728969	−	0.684547i	0.728969	−	0.684547i
$201$	−0.287407	+	0.452881i	−0.287407	+	0.452881i
$202$		0			0
$203$		0			0
$204$	−0.360502	+	0.198187i	−0.360502	+	0.198187i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.13242	+	1.23668i	−1.13242	+	1.23668i
$210$		0			0
$211$	0.0141249	+	0.0740452i	0.0141249	+	0.0740452i	0.988652	−	0.150226i	$-0.0480000\pi$
$211$	0.0141249	+	0.0740452i	0.0141249	+	0.0740452i	−0.974527	+	0.224271i	$0.928000\pi$
$212$		0			0
$213$		0			0
$214$	−0.255596	+	0.509524i	−0.255596	+	0.509524i
$215$		0			0
$216$	0.822852	−	0.630028i	0.822852	−	0.630028i
$217$		0			0
$218$		0			0
$219$	−0.201815	−	0.146627i	−0.201815	−	0.146627i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.162637	−	0.986686i	$-0.448000\pi$
$223$		0			0		−0.162637	+	0.986686i	$0.552000\pi$
$224$		0			0
$225$	0.535777	+	0.152014i	0.535777	+	0.152014i
$226$	0.575085	−	1.22212i	0.575085	−	1.22212i
$227$	0.875299	+	1.64067i	0.875299	+	1.64067i	0.762443	+	0.647056i	$0.224000\pi$
$227$	0.875299	+	1.64067i	0.875299	+	1.64067i	0.112856	+	0.993611i	$0.464000\pi$
$228$	0.279293	+	0.493247i	0.279293	+	0.493247i
$229$		0			0		0.693653	−	0.720309i	$-0.256000\pi$
$229$		0			0		−0.693653	+	0.720309i	$0.744000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.0738618	−	1.95832i	−0.0738618	−	1.95832i	−0.236499	−	0.971632i	$-0.576000\pi$
$233$	−0.0738618	−	1.95832i	−0.0738618	−	1.95832i	0.162637	−	0.986686i	$-0.448000\pi$
$234$		0			0
$235$		0			0
$236$	0.261002	−	1.87613i	0.261002	−	1.87613i
$237$		0			0
$238$		0			0
$239$		0			0		−0.577573	−	0.816339i	$-0.696000\pi$
$239$		0			0		0.577573	+	0.816339i	$0.304000\pi$
$240$		0			0
$241$	0.756300	+	1.60722i	0.756300	+	1.60722i	0.793990	+	0.607930i	$0.208000\pi$
$241$	0.756300	+	1.60722i	0.756300	+	1.60722i	−0.0376902	+	0.999289i	$0.512000\pi$
$242$	0.467983	+	2.83916i	0.467983	+	2.83916i
$243$	0.881316	+	0.348938i	0.881316	+	0.348938i
$244$		0			0
$245$		0			0
$246$	0.695164	+	1.09540i	0.695164	+	1.09540i
$247$		0			0
$248$		0			0
$249$	−0.501605	−	0.0633674i	−0.501605	−	0.0633674i
$250$		0			0
$251$	−0.0878512	+	0.996134i	−0.0878512	+	0.996134i
$251$	−0.0878512	+	0.996134i	−0.0878512	+	0.996134i
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.535827	+	0.844328i	0.535827	+	0.844328i
$257$	0.807570	+	0.881926i	0.807570	+	0.881926i	0.994951	−	0.100362i	$-0.0320000\pi$
$257$	0.807570	+	0.881926i	0.807570	+	0.881926i	−0.187381	+	0.982287i	$0.560000\pi$
$258$	−0.106441	−	1.20692i	−0.106441	−	1.20692i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.0750855	+	0.100662i	−0.0750855	+	0.100662i
$263$		0			0		−0.577573	−	0.816339i	$-0.696000\pi$
$263$		0			0		0.577573	+	0.816339i	$0.304000\pi$
$264$	1.29585	+	0.196905i	1.29585	+	0.196905i
$265$		0			0
$266$		0			0
$267$	0.649656	+	0.357151i	0.649656	+	0.357151i
$268$	0.0909411	−	0.800665i	0.0909411	−	0.800665i
$269$		0			0		−0.0376902	−	0.999289i	$-0.512000\pi$
$269$		0			0		0.0376902	+	0.999289i	$0.488000\pi$
$270$		0			0
$271$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$271$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$272$	0.356960	−	0.504525i	0.356960	−	0.504525i
$273$		0			0
$274$	0.811554	+	1.43325i	0.811554	+	1.43325i
$275$	0.926877	+	1.73734i	0.926877	+	1.73734i
$276$		0			0
$277$		0			0		−0.962028	−	0.272952i	$-0.912000\pi$
$277$		0			0		0.962028	+	0.272952i	$0.0880000\pi$
$278$	−0.784461	+	1.30763i	−0.784461	+	1.30763i
$279$		0			0
$280$		0			0
$281$	0.480069	−	1.77675i	0.480069	−	1.77675i	−0.137790	−	0.990461i	$-0.544000\pi$
$281$	0.480069	−	1.77675i	0.480069	−	1.77675i	0.617860	−	0.786288i	$-0.288000\pi$
$282$		0			0
$283$	1.43703	+	1.04407i	1.43703	+	1.04407i	0.988652	+	0.150226i	$0.0480000\pi$
$283$	1.43703	+	1.04407i	1.43703	+	1.04407i	0.448383	+	0.893841i	$0.352000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.249716	+	0.497802i	−0.249716	+	0.497802i
$289$	0.602291	+	0.138607i	0.602291	+	0.138607i
$290$		0			0
$291$	−0.128330	−	0.672731i	−0.128330	−	0.672731i
$292$	0.368978	+	0.0655921i	0.368978	+	0.0655921i
$293$		0			0		0.675333	−	0.737513i	$-0.264000\pi$
$293$		0			0		−0.675333	+	0.737513i	$0.736000\pi$
$294$	−0.528511	−	0.404662i	−0.528511	−	0.404662i
$295$		0			0
$296$		0			0
$297$	0.775018	+	1.88781i	0.775018	+	1.88781i
$298$		0			0
$299$		0			0
$300$	0.655365	−	0.116502i	0.655365	−	0.116502i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.701286	−	0.483063i	−0.701286	−	0.483063i
$305$		0			0
$306$	0.343220	+	0.0259274i	0.343220	+	0.0259274i
$307$	−0.563570	+	1.89529i	−0.563570	+	1.89529i	−0.137790	+	0.990461i	$0.544000\pi$
$307$	−0.563570	+	1.89529i	−0.563570	+	1.89529i	−0.425779	+	0.904827i	$0.640000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.379779	−	0.925077i	$-0.376000\pi$
$311$		0			0		−0.379779	+	0.925077i	$0.624000\pi$
$312$		0			0
$313$	−0.0677975	−	0.0329499i	−0.0677975	−	0.0329499i	0.402906	−	0.915241i	$-0.368000\pi$
$313$	−0.0677975	−	0.0329499i	−0.0677975	−	0.0329499i	−0.470704	+	0.882291i	$0.656000\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.994951	−	0.100362i	$-0.0320000\pi$
$317$		0			0		−0.994951	+	0.100362i	$0.968000\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.327807	+	0.191095i	−0.327807	+	0.191095i
$322$		0			0
$323$	−0.111578	+	0.514329i	−0.111578	+	0.514329i
$324$	0.132533	−	0.0100117i	0.132533	−	0.0100117i
$325$		0			0
$326$	1.75109	−	0.797282i	1.75109	−	0.797282i
$327$		0			0
$328$	−1.65863	−	1.02359i	−1.65863	−	1.02359i
$329$		0			0
$330$		0			0
$331$	0.119913	+	1.90596i	0.119913	+	1.90596i	0.356412	+	0.934329i	$0.384000\pi$
$331$	0.119913	+	1.90596i	0.119913	+	1.90596i	−0.236499	+	0.971632i	$0.576000\pi$
$332$	0.719376	−	0.243775i	0.719376	−	0.243775i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.196085	+	0.193637i	0.196085	+	0.193637i	0.793990	−	0.607930i	$-0.208000\pi$
$337$	0.196085	+	0.193637i	0.196085	+	0.193637i	−0.597905	+	0.801567i	$0.704000\pi$
$338$	−0.910106	−	0.414376i	−0.910106	−	0.414376i
$339$	0.765092	−	0.472161i	0.765092	−	0.472161i
$340$		0			0
$341$		0			0
$342$	0.0297787	−	0.473318i	0.0297787	−	0.473318i
$343$		0			0
$344$	0.936389	+	1.56088i	0.936389	+	1.56088i
$345$		0			0
$346$		0			0
$347$	−0.273191	−	1.12238i	−0.273191	−	1.12238i	−0.929776	−	0.368125i	$-0.880000\pi$
$347$	−0.273191	−	1.12238i	−0.273191	−	1.12238i	0.656586	−	0.754251i	$-0.272000\pi$
$348$		0			0
$349$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$349$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$350$		0			0
$351$		0			0
$352$	−1.88025	+	0.584913i	−1.88025	+	0.584913i
$353$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.637424	+	0.770513i	$0.720000\pi$
$353$	−1.56720	+	1.13864i	−1.56720	+	1.13864i	−0.929776	+	0.368125i	$0.880000\pi$
$354$	0.827857	−	0.950999i	0.827857	−	0.950999i
$355$		0			0
$356$	−1.11234	−	0.0559597i	−1.11234	−	0.0559597i
$357$		0			0
$358$	−0.298461	+	0.845642i	−0.298461	+	0.845642i
$359$		0			0		0.711536	−	0.702650i	$-0.248000\pi$
$359$		0			0		−0.711536	+	0.702650i	$0.752000\pi$
$360$		0			0
$361$	−0.269311	−	0.0548899i	−0.269311	−	0.0548899i
$362$		0			0
$363$	−0.771709	+	1.75301i	−0.771709	+	1.75301i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.999684	−	0.0251301i	$-0.00800000\pi$
$367$		0			0		−0.999684	+	0.0251301i	$0.992000\pi$
$368$		0			0
$369$	0.0136401	−	1.08539i	0.0136401	−	1.08539i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.212007	−	0.977268i	$-0.568000\pi$
$373$		0			0		0.212007	+	0.977268i	$0.432000\pi$
$374$	0.775738	+	0.937706i	0.775738	+	0.937706i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.10137	+	1.33133i	1.10137	+	1.33133i	0.938734	+	0.344643i	$0.112000\pi$
$379$	1.10137	+	1.33133i	1.10137	+	1.33133i	0.162637	+	0.986686i	$0.448000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$383$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$384$	−0.00836445	+	0.665587i	−0.00836445	+	0.665587i
$385$		0			0
$386$	−1.90913	+	0.0479917i	−1.90913	+	0.0479917i
$387$	−0.477162	+	0.894397i	−0.477162	+	0.894397i
$388$	0.615172	+	0.824715i	0.615172	+	0.824715i
$389$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$389$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$390$		0			0
$391$		0			0
$392$	0.979855	+	0.199710i	0.979855	+	0.199710i
$393$	−0.0784703	+	0.0288093i	−0.0784703	+	0.0288093i
$394$		0			0
$395$		0			0
$396$	−0.818041	−	0.730386i	−0.818041	−	0.730386i
$397$		0			0		−0.998737	−	0.0502443i	$-0.984000\pi$
$397$		0			0		0.998737	+	0.0502443i	$0.0160000\pi$
$398$		0			0
$399$		0			0
$400$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$401$	0.498137	−	0.154962i	0.498137	−	0.154962i	−0.0376902	−	0.999289i	$-0.512000\pi$
$401$	0.498137	−	0.154962i	0.498137	−	0.154962i	0.535827	+	0.844328i	$0.320000\pi$
$402$	0.341902	−	0.413288i	0.341902	−	0.413288i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.382498	−	0.151442i	0.382498	−	0.151442i
$409$	1.02596	+	1.71018i	1.02596	+	1.71018i	0.577573	+	0.816339i	$0.304000\pi$
$409$	1.02596	+	1.71018i	1.02596	+	1.71018i	0.448383	+	0.893841i	$0.352000\pi$
$410$		0			0
$411$	−0.0688404	+	1.09419i	−0.0688404	+	1.09419i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.912917	+	0.443683i	−0.912917	+	0.443683i
$418$	1.27849	−	1.08500i	1.27849	−	1.08500i
$419$	1.67030	−	1.08968i	1.67030	−	1.08968i	0.793990	−	0.607930i	$-0.208000\pi$
$419$	1.67030	−	1.08968i	1.67030	−	1.08968i	0.876307	−	0.481754i	$-0.160000\pi$
$420$		0			0
$421$		0			0		0.947098	−	0.320944i	$-0.104000\pi$
$421$		0			0		−0.947098	+	0.320944i	$0.896000\pi$
$422$	−0.00473317	−	0.0752316i	−0.00473317	−	0.0752316i
$423$		0			0
$424$		0			0
$425$	0.525944	+	0.324576i	0.525944	+	0.324576i
$426$		0			0
$427$		0			0
$428$	0.317441	−	0.473472i	0.317441	−	0.473472i
$429$		0			0
$430$		0			0
$431$		0			0		0.888136	−	0.459580i	$-0.152000\pi$
$431$		0			0		−0.888136	+	0.459580i	$0.848000\pi$
$432$	−0.895327	+	0.521930i	−0.895327	+	0.521930i
$433$	0.238883	−	1.25227i	0.238883	−	1.25227i	−0.637424	−	0.770513i	$-0.720000\pi$
$433$	0.238883	−	1.25227i	0.238883	−	1.25227i	0.876307	−	0.481754i	$-0.160000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.181846	+	0.170765i	0.181846	+	0.170765i
$439$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$439$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$440$		0			0
$441$	0.185355	+	0.525175i	0.185355	+	0.525175i
$442$		0			0
$443$	−0.182605	−	1.60770i	−0.182605	−	1.60770i	−0.675333	−	0.737513i	$-0.736000\pi$
$443$	−0.182605	−	1.60770i	−0.182605	−	1.60770i	0.492727	−	0.870184i	$-0.336000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.389529	−	0.268317i	−0.389529	−	0.268317i	0.356412	−	0.934329i	$-0.384000\pi$
$449$	−0.389529	−	0.268317i	−0.389529	−	0.268317i	−0.745941	+	0.666012i	$0.768000\pi$
$450$	−0.512500	−	0.217966i	−0.512500	−	0.217966i
$451$	2.79774	−	2.62725i	2.79774	−	2.62725i
$452$	−0.723723	+	1.14040i	−0.723723	+	1.14040i
$453$		0			0
$454$	−0.662767	−	1.73743i	−0.662767	−	1.73743i
$455$		0			0
$456$	−0.215270	−	0.524362i	−0.215270	−	0.524362i
$457$	1.48012	−	1.32152i	1.48012	−	1.32152i	0.656586	−	0.754251i	$-0.272000\pi$
$457$	1.48012	−	1.32152i	1.48012	−	1.32152i	0.823533	−	0.567269i	$-0.192000\pi$
$458$		0			0
$459$	0.508550	+	0.389379i	0.508550	+	0.389379i
$460$		0			0
$461$		0			0		−0.984564	−	0.175023i	$-0.944000\pi$
$461$		0			0		0.984564	+	0.175023i	$0.0560000\pi$
$462$		0			0
$463$		0			0		−0.656586	−	0.754251i	$-0.728000\pi$
$463$		0			0		0.656586	+	0.754251i	$0.272000\pi$
$464$		0			0
$465$		0			0
$466$	−0.172163	+	1.95213i	−0.172163	+	1.95213i
$467$	−1.32998	+	1.01832i	−1.32998	+	1.01832i	−0.332820	+	0.942991i	$0.608000\pi$
$467$	−1.32998	+	1.01832i	−1.32998	+	1.01832i	−0.997159	+	0.0753268i	$0.976000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.494085	+	1.82862i	−0.494085	+	1.82862i
$473$	−3.44813	+	0.978323i	−3.44813	+	0.978323i
$474$		0			0
$475$	0.438075	−	0.730234i	0.438075	−	0.730234i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.492727	−	0.870184i	$-0.664000\pi$
$479$		0			0		0.492727	+	0.870184i	$0.336000\pi$
$480$		0			0
$481$		0			0
$482$	−0.548899	−	1.68934i	−0.548899	−	1.68934i
$483$		0			0
$484$	−0.108452	−	2.87542i	−0.108452	−	2.87542i
$485$		0			0
$486$	−0.830633	−	0.456644i	−0.830633	−	0.456644i
$487$		0			0		0.137790	−	0.990461i	$-0.456000\pi$
$487$		0			0		−0.137790	+	0.990461i	$0.544000\pi$
$488$		0			0
$489$	1.26619	+	0.192398i	1.26619	+	0.192398i
$490$		0			0
$491$	0.105053	−	0.140837i	0.105053	−	0.140837i	−0.745941	−	0.666012i	$-0.768000\pi$
$491$	0.105053	−	0.140837i	0.105053	−	0.140837i	0.850994	+	0.525175i	$0.176000\pi$
$492$	−0.552392	−	1.17389i	−0.552392	−	1.17389i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.489708	+	0.125736i	0.489708	+	0.125736i
$499$	−1.13747	−	0.965331i	−1.13747	−	0.965331i	−0.137790	−	0.990461i	$-0.544000\pi$
$499$	−1.13747	−	0.965331i	−1.13747	−	0.965331i	−0.999684	+	0.0251301i	$0.992000\pi$
$500$		0			0
$501$		0			0
$502$	0.212007	−	0.977268i	0.212007	−	0.977268i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.356667	−	0.562018i	−0.356667	−	0.562018i
$508$		0			0
$509$		0			0		−0.0878512	−	0.996134i	$-0.528000\pi$
$509$		0			0		0.0878512	+	0.996134i	$0.472000\pi$
$510$		0			0
$511$		0			0
$512$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$513$	0.527659	−	0.707393i	0.527659	−	0.707393i
$514$	−0.690667	−	0.976187i	−0.690667	−	0.976187i
$515$		0			0
$516$	−0.0456656	+	1.21074i	−0.0456656	+	1.21074i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.892239	+	0.0900010i	0.892239	+	0.0900010i	0.535827	−	0.844328i	$-0.320000\pi$
$521$	0.892239	+	0.0900010i	0.892239	+	0.0900010i	0.356412	+	0.934329i	$0.384000\pi$
$522$		0			0
$523$	1.15369	−	1.63062i	1.15369	−	1.63062i	0.535827	−	0.844328i	$-0.320000\pi$
$523$	1.15369	−	1.63062i	1.15369	−	1.63062i	0.617860	−	0.786288i	$-0.288000\pi$
$524$	0.0871097	−	0.0904572i	0.0871097	−	0.0904572i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.26096	−	0.357766i	−1.26096	−	0.357766i
$529$	−0.514440	+	0.857527i	−0.514440	+	0.857527i
$530$		0			0
$531$	−1.01487	+	0.287944i	−1.01487	+	0.287944i
$532$		0			0
$533$		0			0
$534$	−0.599770	−	0.435758i	−0.599770	−	0.435758i
$535$		0			0
$536$	−0.190574	+	0.782953i	−0.190574	+	0.782953i
$537$	−0.473951	+	0.362887i	−0.473951	+	0.362887i
$538$		0			0
$539$	−0.882924	+	1.76009i	−0.882924	+	1.76009i
$540$		0			0
$541$		0			0		−0.656586	−	0.754251i	$-0.728000\pi$
$541$		0			0		0.656586	+	0.754251i	$0.272000\pi$
$542$		0			0
$543$		0			0
$544$	−0.417379	+	0.455808i	−0.417379	+	0.455808i
$545$		0			0
$546$		0			0
$547$	1.11286	−	0.993611i	1.11286	−	0.993611i	0.112856	−	0.993611i	$-0.464000\pi$
$547$	1.11286	−	0.993611i	1.11286	−	0.993611i	1.00000			$0$
$548$	−0.625521	−	1.52366i	−0.625521	−	1.52366i
$549$		0			0
$550$	−0.701821	−	1.83981i	−0.701821	−	1.83981i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.942165	−	1.19900i	0.942165	−	1.19900i
$557$		0			0		−0.997159	−	0.0753268i	$-0.976000\pi$
$557$		0			0		0.997159	+	0.0753268i	$0.0240000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.0914221	+	0.804900i	0.0914221	+	0.804900i
$562$	−0.698970	+	1.70257i	−0.698970	+	1.70257i
$563$	0.618896	+	1.75354i	0.618896	+	1.75354i	0.656586	+	0.754251i	$0.272000\pi$
$563$	0.618896	+	1.75354i	0.618896	+	1.75354i	−0.0376902	+	0.999289i	$0.512000\pi$
$564$		0			0
$565$		0			0
$566$	−1.29485	−	1.21594i	−1.29485	−	1.21594i
$567$		0			0
$568$		0			0
$569$	0.164771	+	1.18440i	0.164771	+	1.18440i	0.876307	+	0.481754i	$0.160000\pi$
$569$	0.164771	+	1.18440i	0.164771	+	1.18440i	−0.711536	+	0.702650i	$0.752000\pi$
$570$		0			0
$571$	−0.259955	+	1.36273i	−0.259955	+	1.36273i	0.577573	+	0.816339i	$0.304000\pi$
$571$	−0.259955	+	1.36273i	−0.259955	+	1.36273i	−0.837528	+	0.546394i	$0.816000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.310138	−	0.462579i	0.310138	−	0.462579i
$577$	1.57252	−	0.715978i	1.57252	−	0.715978i	0.577573	−	0.816339i	$-0.304000\pi$
$577$	1.57252	−	0.715978i	1.57252	−	0.715978i	0.994951	+	0.100362i	$0.0320000\pi$
$578$	−0.580169	−	0.213001i	−0.580169	−	0.213001i
$579$	−1.08178	−	0.667597i	−1.08178	−	0.667597i
$580$		0			0
$581$		0			0
$582$	0.0430028	+	0.683511i	0.0430028	+	0.683511i
$583$		0			0
$584$	−0.357848	−	0.111320i	−0.357848	−	0.111320i
$585$		0			0
$586$		0			0
$587$	1.11141	−	0.540152i	1.11141	−	0.540152i	0.212007	−	0.977268i	$-0.432000\pi$
$587$	1.11141	−	0.540152i	1.11141	−	0.540152i	0.899405	+	0.437116i	$0.144000\pi$
$588$	0.473626	+	0.467711i	0.473626	+	0.467711i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.0357930	+	0.568914i	−0.0357930	+	0.568914i	0.938734	+	0.344643i	$0.112000\pi$
$593$	−0.0357930	+	0.568914i	−0.0357930	+	0.568914i	−0.974527	+	0.224271i	$0.928000\pi$
$594$	−0.532301	−	1.97006i	−0.532301	−	1.97006i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.778462	−	0.627691i	$-0.784000\pi$
$599$		0			0		0.778462	+	0.627691i	$0.216000\pi$
$600$	−0.664798	+	0.0334446i	−0.664798	+	0.0334446i
$601$	−1.29485	−	0.670039i	−1.29485	−	0.670039i	−0.332820	−	0.942991i	$-0.608000\pi$
$601$	−1.29485	−	0.670039i	−1.29485	−	0.670039i	−0.962028	+	0.272952i	$0.912000\pi$
$602$		0			0
$603$	−0.428521	+	0.133305i	−0.428521	+	0.133305i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.998737	−	0.0502443i	$-0.984000\pi$
$607$		0			0		0.998737	+	0.0502443i	$0.0160000\pi$
$608$	0.635213	+	0.567148i	0.635213	+	0.567148i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.337264	−	0.0687398i	−0.337264	−	0.0687398i
$613$		0			0		0.920232	−	0.391374i	$-0.128000\pi$
$613$		0			0		−0.920232	+	0.391374i	$0.872000\pi$
$614$	0.796668	−	1.80971i	0.796668	−	1.80971i
$615$		0			0
$616$		0			0
$617$	−0.0118298	+	0.0221738i	−0.0118298	+	0.0221738i	−0.888136	−	0.459580i	$-0.848000\pi$
$617$	−0.0118298	+	0.0221738i	−0.0118298	+	0.0221738i	0.876307	+	0.481754i	$0.160000\pi$
$618$		0			0
$619$	0.0246258	+	1.95956i	0.0246258	+	1.95956i	0.212007	+	0.977268i	$0.432000\pi$
$619$	0.0246258	+	1.95956i	0.0246258	+	1.95956i	−0.187381	+	0.982287i	$0.560000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$626$	0.0631332	+	0.0411874i	0.0631332	+	0.0411874i
$627$	1.10736	−	0.139892i	1.10736	−	0.139892i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.212007	−	0.977268i	$-0.568000\pi$
$631$		0			0		0.212007	+	0.977268i	$0.432000\pi$
$632$		0			0
$633$	0.0247231	−	0.0436624i	0.0247231	−	0.0436624i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.431776	−	0.980821i	0.431776	−	0.980821i	−0.556876	−	0.830596i	$-0.688000\pi$
$641$	0.431776	−	0.980821i	0.431776	−	0.980821i	0.988652	−	0.150226i	$-0.0480000\pi$
$642$	0.349173	−	0.148503i	0.349173	−	0.148503i
$643$	0.698464	+	0.142358i	0.698464	+	0.142358i	0.535827	−	0.844328i	$-0.320000\pi$
$643$	0.698464	+	0.142358i	0.698464	+	0.142358i	0.162637	+	0.986686i	$0.448000\pi$
$644$		0			0
$645$		0			0
$646$	0.175160	−	0.496289i	0.175160	−	0.496289i
$647$		0			0		−0.745941	−	0.666012i	$-0.768000\pi$
$647$		0			0		0.745941	+	0.666012i	$0.232000\pi$
$648$	−0.132743	−	0.00667799i	−0.132743	−	0.00667799i
$649$	−3.22236	−	1.87847i	−3.22236	−	1.87847i
$650$		0			0
$651$		0			0
$652$	−1.83721	+	0.571524i	−1.83721	+	0.571524i
$653$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$653$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$654$		0			0
$655$		0			0
$656$	1.51726	+	1.22340i	1.51726	+	1.22340i
$657$	−0.0493608	−	0.202794i	−0.0493608	−	0.202794i
$658$		0			0
$659$	−0.116762	+	0.0462295i	−0.116762	+	0.0462295i	−0.425779	−	0.904827i	$-0.640000\pi$
$659$	−0.116762	+	0.0462295i	−0.116762	+	0.0462295i	0.309017	+	0.951057i	$0.400000\pi$
$660$		0			0
$661$		0			0		−0.260842	−	0.965382i	$-0.584000\pi$
$661$		0			0		0.260842	+	0.965382i	$0.416000\pi$
$662$	0.119913	−	1.90596i	0.119913	−	1.90596i
$663$		0			0
$664$	−0.744257	+	0.151691i	−0.744257	+	0.151691i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.117887	+	1.87376i	0.117887	+	1.87376i	0.402906	+	0.915241i	$0.368000\pi$
$673$	0.117887	+	1.87376i	0.117887	+	1.87376i	−0.285019	+	0.958522i	$0.592000\pi$
$674$	−0.170270	−	0.216686i	−0.170270	−	0.216686i
$675$	−0.577118	−	0.860788i	−0.577118	−	0.860788i
$676$	0.850994	+	0.525175i	0.850994	+	0.525175i
$677$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$677$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$678$	−0.818236	+	0.372547i	−0.818236	+	0.372547i
$679$		0			0
$680$		0			0
$681$	0.262421	−	1.20965i	0.262421	−	1.20965i
$682$		0			0
$683$	−1.55403	+	0.905923i	−1.55403	+	0.905923i	−0.556876	+	0.830596i	$0.688000\pi$
$683$	−1.55403	+	0.905923i	−1.55403	+	0.905923i	−0.997159	+	0.0753268i	$0.976000\pi$
$684$	−0.0888663	+	0.465854i	−0.0888663	+	0.465854i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.733375	−	1.66593i	−0.733375	−	1.66593i
$689$		0			0
$690$		0			0
$691$	1.18107	+	0.574008i	1.18107	+	0.574008i	0.920232	−	0.391374i	$-0.128000\pi$
$691$	1.18107	+	0.574008i	1.18107	+	0.574008i	0.260842	+	0.965382i	$0.416000\pi$
$692$		0			0
$693$		0			0
$694$	0.130366	+	1.14777i	0.130366	+	1.14777i
$695$		0			0
$696$		0			0
$697$	0.343329	−	1.15462i	0.343329	−	1.15462i
$698$		0			0
$699$	−0.805973	+	1.02568i	−0.805973	+	1.02568i
$700$		0			0
$701$		0			0		−0.920232	−	0.391374i	$-0.872000\pi$
$701$		0			0		0.920232	+	0.391374i	$0.128000\pi$
$702$		0			0
$703$		0			0
$704$	1.93873	−	0.344643i	1.93873	−	0.344643i
$705$		0			0
$706$	1.69755	−	0.933237i	1.69755	−	0.933237i
$707$		0			0
$708$	−0.940521	+	0.839742i	−0.940521	+	0.839742i
$709$		0			0		0.778462	−	0.627691i	$-0.216000\pi$
$709$		0			0		−0.778462	+	0.627691i	$0.784000\pi$
$710$		0			0
$711$		0			0
$712$	1.09656	+	0.194932i	1.09656	+	0.194932i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.402095	−	0.801567i	0.402095	−	0.801567i
$717$		0			0
$718$		0			0
$719$		0			0		0.236499	−	0.971632i	$-0.424000\pi$
$719$		0			0		−0.236499	+	0.971632i	$0.576000\pi$
$720$		0			0
$721$		0			0
$722$	0.260308	+	0.0882107i	0.260308	+	0.0882107i
$723$	0.308408	−	1.14143i	0.308408	−	1.14143i
$724$		0			0
$725$		0			0
$726$	0.985334	−	1.64247i	0.985334	−	1.64247i
$727$		0			0		−0.962028	−	0.272952i	$-0.912000\pi$
$727$		0			0		0.962028	+	0.272952i	$0.0880000\pi$
$728$		0			0
$729$	−0.359550	−	0.673943i	−0.359550	−	0.673943i
$730$		0			0
$731$	−0.780327	+	0.810314i	−0.780327	+	0.810314i
$732$		0			0
$733$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$733$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.39048	−	0.764422i	−1.39048	−	0.764422i
$738$	−0.149568	+	1.07512i	−0.149568	+	1.07512i
$739$	−0.0677975	+	1.79753i	−0.0677975	+	1.79753i	0.402906	+	0.915241i	$0.368000\pi$
$739$	−0.0677975	+	1.79753i	−0.0677975	+	1.79753i	−0.470704	+	0.882291i	$0.656000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$743$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.285677	−	0.311980i	−0.285677	−	0.311980i
$748$	−0.652095	−	1.02754i	−0.652095	−	1.02754i
$749$		0			0
$750$		0			0
$751$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$751$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$752$		0			0
$753$	0.473626	−	0.467711i	0.473626	−	0.467711i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$757$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$758$	−0.925827	−	1.45887i	−0.925827	−	1.45887i
$759$		0			0
$760$		0			0
$761$	0.706219	+	0.279612i	0.706219	+	0.279612i	0.693653	−	0.720309i	$-0.256000\pi$
$761$	0.706219	+	0.279612i	0.706219	+	0.279612i	0.0125660	+	0.999921i	$0.496000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.0917186	−	0.659290i	0.0917186	−	0.659290i
$769$	−0.824962	−	0.453527i	−0.824962	−	0.453527i	0.0125660	−	0.999921i	$-0.496000\pi$
$769$	−0.824962	−	0.453527i	−0.824962	−	0.453527i	−0.837528	+	0.546394i	$0.816000\pi$
$770$		0			0
$771$	−0.0300006	−	0.795412i	−0.0300006	−	0.795412i
$772$	1.90009	+	0.191664i	1.90009	+	0.191664i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	0.585497	−	0.827540i	0.585497	−	0.827540i
$775$		0			0
$776$	−0.506957	−	0.895314i	−0.506957	−	0.895314i
$777$		0			0
$778$		0			0
$779$	−1.59671	−	0.453027i	−1.59671	−	0.453027i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.947098	−	0.320944i	−0.947098	−	0.320944i
$785$		0			0
$786$	0.0814623	−	0.0187472i	0.0814623	−	0.0187472i
$787$	−0.0533808	+	0.219310i	−0.0533808	+	0.219310i	−0.992115	−	0.125333i	$-0.960000\pi$
$787$	−0.0533808	+	0.219310i	−0.0533808	+	0.219310i	0.938734	+	0.344643i	$0.112000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.720049	+	0.827154i	0.720049	+	0.827154i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.778462	−	0.627691i	$-0.216000\pi$
$797$		0			0		−0.778462	+	0.627691i	$0.784000\pi$
$798$		0			0
$799$		0			0
$800$	0.876307	−	0.481754i	0.876307	−	0.481754i
$801$	0.221074	+	0.579541i	0.221074	+	0.579541i
$802$	−0.513630	+	0.0913066i	−0.513630	+	0.0913066i
$803$	0.395417	−	0.623077i	0.395417	−	0.623077i
$804$	−0.391005	+	0.367178i	−0.391005	+	0.367178i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.268319	−	0.902360i	0.268319	−	0.902360i	−0.711536	−	0.702650i	$-0.752000\pi$
$809$	0.268319	−	0.902360i	0.268319	−	0.902360i	0.979855	−	0.199710i	$-0.0640000\pi$
$810$		0			0
$811$	−1.90222	+	0.289042i	−1.90222	+	0.289042i	−0.992115	−	0.125333i	$-0.960000\pi$
$811$	−1.90222	+	0.289042i	−1.90222	+	0.289042i	−0.910106	+	0.414376i	$0.864000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.398463	+	0.102308i	−0.398463	+	0.102308i
$817$	1.12991	+	1.06106i	1.12991	+	1.06106i
$818$	−0.803523	−	1.82528i	−0.803523	−	1.82528i
$819$		0			0
$820$		0			0
$821$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$821$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$822$	0.205436	−	1.07693i	0.205436	−	1.07693i
$823$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$823$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$824$		0			0
$825$	0.277884	−	1.28093i	0.277884	−	1.28093i
$826$		0			0
$827$	0.932798	−	1.39129i	0.932798	−	1.39129i	0.0125660	−	0.999921i	$-0.496000\pi$
$827$	0.932798	−	1.39129i	0.932798	−	1.39129i	0.920232	−	0.391374i	$-0.128000\pi$
$828$		0			0
$829$		0			0		−0.938734	−	0.344643i	$-0.888000\pi$
$829$		0			0		0.938734	+	0.344643i	$0.112000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.0388067	+	0.616814i	0.0388067	+	0.616814i
$834$	0.961327	−	0.325765i	0.961327	−	0.325765i
$835$		0			0
$836$	−1.40439	+	0.916210i	−1.40439	+	0.916210i
$837$		0			0
$838$	−1.79370	+	0.871748i	−1.79370	+	0.871748i
$839$		0			0		−0.711536	−	0.702650i	$-0.752000\pi$
$839$		0			0		0.711536	+	0.702650i	$0.248000\pi$
$840$		0			0
$841$	0.850994	−	0.525175i	0.850994	−	0.525175i
$842$		0			0
$843$	−1.00890	+	0.694952i	−1.00890	+	0.694952i
$844$	−0.00473317	+	0.0752316i	−0.00473317	+	0.0752316i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.279626	−	1.14882i	−0.279626	−	1.14882i
$850$	−0.481116	−	0.387935i	−0.481116	−	0.387935i
$851$		0			0
$852$		0			0
$853$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$853$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$854$		0			0
$855$		0			0
$856$	−0.374279	+	0.429952i	−0.374279	+	0.429952i
$857$	1.66224	+	0.968999i	1.66224	+	0.968999i	0.968583	+	0.248690i	$0.0800000\pi$
$857$	1.66224	+	0.968999i	1.66224	+	0.968999i	0.693653	+	0.720309i	$0.256000\pi$
$858$		0			0
$859$	−0.921774	−	0.823004i	−0.921774	−	0.823004i	0.0627905	−	0.998027i	$-0.480000\pi$
$859$	−0.921774	−	0.823004i	−0.921774	−	0.823004i	−0.984564	+	0.175023i	$0.944000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.979855	−	0.199710i	$-0.936000\pi$
$863$		0			0		0.979855	+	0.199710i	$0.0640000\pi$
$864$	0.953682	−	0.405600i	0.953682	−	0.405600i
$865$		0			0
$866$	−0.393950	+	1.21245i	−0.393950	+	1.21245i
$867$	−0.245971	−	0.329755i	−0.245971	−	0.329755i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.282337	−	0.498622i	0.282337	−	0.498622i
$874$		0			0
$875$		0			0
$876$	−0.159010	−	0.192210i	−0.159010	−	0.192210i
$877$		0			0		−0.837528	−	0.546394i	$-0.816000\pi$
$877$		0			0		0.837528	+	0.546394i	$0.184000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.14660	−	1.38601i	−1.14660	−	1.38601i	−0.910106	−	0.414376i	$-0.864000\pi$
$881$	−1.14660	−	1.38601i	−1.14660	−	1.38601i	−0.236499	−	0.971632i	$-0.576000\pi$
$882$	−0.118072	−	0.544265i	−0.118072	−	0.544265i
$883$	0.106815	+	0.359218i	0.106815	+	0.359218i	0.994951	−	0.100362i	$-0.0320000\pi$
$883$	0.106815	+	0.359218i	0.106815	+	0.359218i	−0.888136	+	0.459580i	$0.848000\pi$
$884$		0			0
$885$		0			0
$886$	−0.0203323	+	1.61791i	−0.0203323	+	1.61791i
$887$		0			0		−0.0125660	−	0.999921i	$-0.504000\pi$
$887$		0			0		0.0125660	+	0.999921i	$0.496000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.0808752	−	0.248908i	0.0808752	−	0.248908i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.352829	+	0.315022i	0.352829	+	0.315022i
$899$		0			0
$900$	0.481140	+	0.280480i	0.481140	+	0.280480i
$901$		0			0
$902$	−3.10496	+	2.25588i	−3.10496	+	2.25588i
$903$		0			0
$904$	0.860947	−	1.04071i	0.860947	−	1.04071i
$905$		0			0
$906$		0			0
$907$	−0.554906	−	0.447433i	−0.554906	−	0.447433i	0.309017	−	0.951057i	$-0.400000\pi$
$907$	−0.554906	−	0.447433i	−0.554906	−	0.447433i	−0.863923	+	0.503623i	$0.832000\pi$
$908$	0.439782	+	1.80680i	0.439782	+	1.80680i
$909$		0			0
$910$		0			0
$911$		0			0		−0.514440	−	0.857527i	$-0.672000\pi$
$911$		0			0		0.514440	+	0.857527i	$0.328000\pi$
$912$	0.147853	+	0.547208i	0.147853	+	0.547208i
$913$	0.0939138	−	1.49272i	0.0939138	−	1.49272i
$914$	−1.63408	+	1.12559i	−1.63408	+	1.12559i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.455738	−	0.450047i	−0.455738	−	0.450047i
$919$		0			0		0.899405	−	0.437116i	$-0.144000\pi$
$919$		0			0		−0.899405	+	0.437116i	$0.856000\pi$
$920$		0			0
$921$	1.10233	−	0.719148i	1.10233	−	0.719148i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.79956	+	0.819346i	−1.79956	+	0.819346i	−0.837528	+	0.546394i	$0.816000\pi$
$929$	−1.79956	+	0.819346i	−1.79956	+	0.819346i	−0.962028	+	0.272952i	$0.912000\pi$
$930$		0			0
$931$	0.849139	−	0.0641452i	0.849139	−	0.0641452i
$932$	0.415472	−	1.91516i	0.415472	−	1.91516i
$933$		0			0
$934$	1.44712	−	0.843597i	1.44712	−	0.843597i
$935$		0			0
$936$		0			0
$937$	−0.247859	−	1.78165i	−0.247859	−	1.78165i	−0.556876	−	0.830596i	$-0.688000\pi$
$937$	−0.247859	−	1.78165i	−0.247859	−	1.78165i	0.309017	−	0.951057i	$-0.400000\pi$
$938$		0			0
$939$	0.0202163	+	0.0459232i	0.0202163	+	0.0459232i
$940$		0			0
$941$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$941$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$942$		0			0
$943$		0			0
$944$	0.719376	−	1.75228i	0.719376	−	1.75228i
$945$		0			0
$946$	3.54356	−	0.538443i	3.54356	−	0.538443i
$947$	1.21571	+	1.26242i	1.21571	+	1.26242i	0.954865	+	0.297042i	$0.0960000\pi$
$947$	1.21571	+	1.26242i	1.21571	+	1.26242i	0.260842	+	0.965382i	$0.416000\pi$
$948$		0			0
$949$		0			0
$950$	−0.526144	+	0.669571i	−0.526144	+	0.669571i
$951$		0			0
$952$		0			0
$953$	1.42857	−	1.34151i	1.42857	−	1.34151i	0.577573	−	0.816339i	$-0.304000\pi$
$953$	1.42857	−	1.34151i	1.42857	−	1.34151i	0.850994	−	0.525175i	$-0.176000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.793990	+	0.607930i	0.793990	+	0.607930i
$962$		0			0
$963$	−0.312568	−	0.0555643i	−0.312568	−	0.0555643i
$964$	0.332840	+	1.74481i	0.332840	+	1.74481i
$965$		0			0
$966$		0			0
$967$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$967$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$968$	−0.252789	+	2.86634i	−0.252789	+	2.86634i
$969$	0.278151	−	0.212971i	0.278151	−	0.212971i
$970$		0			0
$971$	−1.42080	+	0.326973i	−1.42080	+	0.326973i	−0.863923	−	0.503623i	$-0.832000\pi$
$971$	−1.42080	+	0.326973i	−1.42080	+	0.326973i	−0.556876	+	0.830596i	$0.688000\pi$
$972$	0.766851	+	0.557150i	0.766851	+	0.557150i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.784461	+	1.30763i	−0.784461	+	1.30763i	0.162637	+	0.986686i	$0.448000\pi$
$977$	−0.784461	+	1.30763i	−0.784461	+	1.30763i	−0.947098	+	0.320944i	$0.896000\pi$
$978$	−1.23209	−	0.349577i	−1.23209	−	0.349577i
$979$	−0.933785	+	1.98439i	−0.933785	+	1.98439i
$980$		0			0
$981$		0			0
$982$	−0.121877	+	0.126560i	−0.121877	+	0.126560i
$983$		0			0		0.577573	−	0.816339i	$-0.304000\pi$
$983$		0			0		−0.577573	+	0.816339i	$0.696000\pi$
$984$	0.400908	+	1.23387i	0.400908	+	1.23387i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.988652	−	0.150226i	$-0.952000\pi$
$991$		0			0		0.988652	+	0.150226i	$0.0480000\pi$
$992$		0			0
$993$	0.760051	−	1.01894i	0.760051	−	1.01894i
$994$		0			0
$995$		0			0
$996$	−0.470087	−	0.186121i	−0.470087	−	0.186121i
$997$		0			0		−0.0878512	−	0.996134i	$-0.528000\pi$
$997$		0			0		0.0878512	+	0.996134i	$0.472000\pi$
$998$	1.00752	+	1.10028i	1.00752	+	1.10028i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2008.1.bd.a.155.1	✓	100
8.3	odd	2	CM	2008.1.bd.a.155.1	✓	100
251.217	even	125	inner	2008.1.bd.a.1723.1	yes	100
2008.1723	odd	250	inner	2008.1.bd.a.1723.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2008.1.bd.a.155.1	✓	100	1.1	even	1	trivial
2008.1.bd.a.155.1	✓	100	8.3	odd	2	CM
2008.1.bd.a.1723.1	yes	100	251.217	even	125	inner
2008.1.bd.a.1723.1	yes	100	2008.1723	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)

\(f(q)\)	\(=\)	\(q+(-0.992115 - 0.125333i) q^{2} +(-0.507512 - 0.430706i) q^{3} +(0.968583 + 0.248690i) q^{4} +(0.449528 + 0.490918i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(-0.0905766 - 0.549510i) q^{9} +O(q^{10})\)	\(q+(-0.992115 - 0.125333i) q^{2} +(-0.507512 - 0.430706i) q^{3} +(0.968583 + 0.248690i) q^{4} +(0.449528 + 0.490918i) q^{6} +(-0.929776 - 0.368125i) q^{8} +(-0.0905766 - 0.549510i) q^{9} +(1.17735 - 1.57839i) q^{11} +(-0.384455 - 0.543387i) q^{12} +(0.876307 + 0.481754i) q^{16} +(0.0697491 - 0.614086i) q^{17} +(0.0209906 + 0.556529i) q^{18} +(-0.847259 - 0.0854639i) q^{19} +(-1.36589 + 1.41838i) q^{22} +(0.313319 + 0.587288i) q^{24} +(-0.425779 + 0.904827i) q^{25} +(-0.533139 + 0.888698i) q^{27} +(-0.809017 - 0.587785i) q^{32} +(-1.27734 + 0.293958i) q^{33} +(-0.146164 + 0.600501i) q^{34} +(0.0489265 - 0.554771i) q^{36} +(0.829867 + 0.190980i) q^{38} +(1.91897 + 0.341129i) q^{41} +(-1.44523 - 1.10656i) q^{43} +(1.53289 - 1.23601i) q^{44} +(-0.237242 - 0.621926i) q^{48} +(-0.984564 + 0.175023i) q^{49} +(0.535827 - 0.844328i) q^{50} +(-0.299889 + 0.281614i) q^{51} +(0.640319 - 0.814870i) q^{54} +(0.393184 + 0.408293i) q^{57} +(-0.213772 - 1.88210i) q^{59} +(0.728969 + 0.684547i) q^{64} +(1.30411 - 0.131547i) q^{66} +(-0.111033 - 0.798127i) q^{67} +(0.220275 - 0.577447i) q^{68} +(-0.118072 + 0.544265i) q^{72} +(0.373698 - 0.0282297i) q^{73} +(0.605802 - 0.275825i) q^{75} +(-0.799387 - 0.293484i) q^{76} +(0.125879 - 0.0426567i) q^{81} +(-1.86108 - 0.578950i) q^{82} +(0.636151 - 0.415018i) q^{83} +(1.29515 + 1.27897i) q^{86} +(-1.67572 + 1.03414i) q^{88} +(-1.09131 + 0.222427i) q^{89} +(0.157423 + 0.646756i) q^{96} +(0.800944 + 0.645819i) q^{97} +(0.998737 - 0.0502443i) q^{98} +(-0.973980 - 0.504001i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 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

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Database

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