LMFDB - Embedded newform 1944.1.bh.a.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1944,1,Mod(43,1944)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1944, base_ring=CyclotomicField(162))

chi = DirichletCharacter(H, H._module([81, 81, 130]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1944.43");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1944 = 2^{3} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1944.bh (of order $162$, degree $54$, 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:	$0.970182384559$
Analytic rank:	$0$
Dimension:	$54$
Coefficient field:	$\Q(\zeta_{162})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{54} - x^{27} + 1 $ x^54 - x^27 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{81}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{81} + \cdots)$

Embedding invariants

Embedding label			331.1
Root			$0.963371 + 0.268173i$ of defining polynomial
Character	$\chi$	$=$	1944.331
Dual form			1944.1.bh.a.787.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.740544 + 0.672008i) q^{2} +(0.0193913 - 0.999812i) q^{3} +(0.0968109 - 0.995303i) q^{4} +(0.657521 + 0.753436i) q^{6} +(0.597159 + 0.802123i) q^{8} +(-0.999248 - 0.0387754i) q^{9} +O(q^{10})$	\(q+(-0.740544 + 0.672008i) q^{2} +(0.0193913 - 0.999812i) q^{3} +(0.0968109 - 0.995303i) q^{4} +(0.657521 + 0.753436i) q^{6} +(0.597159 + 0.802123i) q^{8} +(-0.999248 - 0.0387754i) q^{9} +(-0.586047 + 1.51790i) q^{11} +(-0.993238 - 0.116093i) q^{12} +(-0.981255 - 0.192712i) q^{16} +(-1.27054 - 1.34669i) q^{17} +(0.766044 - 0.642788i) q^{18} +(-0.566717 - 1.89297i) q^{19} +(-0.586047 - 1.51790i) q^{22} +(0.813552 - 0.581492i) q^{24} +(-0.790393 - 0.612601i) q^{25} +(-0.0581448 + 0.998308i) q^{27} +(0.856167 - 0.516699i) q^{32} +(1.50625 + 0.615371i) q^{33} +(1.84588 + 0.143473i) q^{34} +(-0.135331 + 0.990800i) q^{36} +(1.69177 + 1.02099i) q^{38} +(0.370718 - 1.71143i) q^{41} +(-0.00821044 + 0.423328i) q^{43} +(1.45403 + 0.730243i) q^{44} +(-0.211704 + 0.977334i) q^{48} +(-0.875558 - 0.483113i) q^{49} +(0.996993 - 0.0774924i) q^{50} +(-1.37108 + 1.24419i) q^{51} +(-0.627812 - 0.778365i) q^{54} +(-1.90360 + 0.529904i) q^{57} +(-1.93894 - 0.303245i) q^{59} +(-0.286803 + 0.957990i) q^{64} +(-1.52898 + 0.556502i) q^{66} +(0.266006 - 0.422048i) q^{67} +(-1.46337 + 1.13420i) q^{68} +(-0.565607 - 0.824675i) q^{72} +(0.369181 - 0.855857i) q^{73} +(-0.627812 + 0.778365i) q^{75} +(-1.93894 + 0.380796i) q^{76} +(0.996993 + 0.0774924i) q^{81} +(0.875558 + 1.51651i) q^{82} +(0.353752 + 1.63310i) q^{83} +(-0.278400 - 0.319011i) q^{86} +(-1.56750 + 0.436345i) q^{88} +(0.569728 - 0.0665916i) q^{89} +(-0.500000 - 0.866025i) q^{96} +(-0.366212 - 1.07030i) q^{97} +(0.973045 - 0.230616i) q^{98} +(0.644463 - 1.49403i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q+O(q^{10}) $ 54 * q	$ 54 q - 27 q^{68} - 27 q^{96}+O(q^{100}) $ 54 * q - 27 * q^68 - 27 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1944\mathbb{Z}\right)^\times$.

$n$	$487$	$973$	$1217$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{62}{81}\right)$

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 $

$2$	−0.740544	+	0.672008i	−0.740544	+	0.672008i
$2$	−0.740544	+	0.672008i	−0.740544	+	0.672008i
$3$	0.0193913	−	0.999812i	0.0193913	−	0.999812i
$3$	0.0193913	−	0.999812i	0.0193913	−	0.999812i
$4$	0.0968109	−	0.995303i	0.0968109	−	0.995303i
$5$		0			0		0.323734	−	0.946148i	$-0.395062\pi$
$5$		0			0		−0.323734	+	0.946148i	$0.604938\pi$
$6$	0.657521	+	0.753436i	0.657521	+	0.753436i
$7$		0			0		0.249441	−	0.968390i	$-0.419753\pi$
$7$		0			0		−0.249441	+	0.968390i	$0.580247\pi$
$8$	0.597159	+	0.802123i	0.597159	+	0.802123i
$9$	−0.999248	−	0.0387754i	−0.999248	−	0.0387754i
$10$		0			0
$11$	−0.586047	+	1.51790i	−0.586047	+	1.51790i	0.249441	+	0.968390i	$0.419753\pi$
$11$	−0.586047	+	1.51790i	−0.586047	+	1.51790i	−0.835488	+	0.549509i	$0.814815\pi$
$12$	−0.993238	−	0.116093i	−0.993238	−	0.116093i
$13$		0			0		−0.925724	−	0.378200i	$-0.876543\pi$
$13$		0			0		0.925724	+	0.378200i	$0.123457\pi$
$14$		0			0
$15$		0			0
$16$	−0.981255	−	0.192712i	−0.981255	−	0.192712i
$17$	−1.27054	−	1.34669i	−1.27054	−	1.34669i	−0.910363	−	0.413811i	$-0.864198\pi$
$17$	−1.27054	−	1.34669i	−1.27054	−	1.34669i	−0.360178	−	0.932884i	$-0.617284\pi$
$18$	0.766044	−	0.642788i	0.766044	−	0.642788i
$19$	−0.566717	−	1.89297i	−0.566717	−	1.89297i	−0.431386	−	0.902167i	$-0.641975\pi$
$19$	−0.566717	−	1.89297i	−0.566717	−	1.89297i	−0.135331	−	0.990800i	$-0.543210\pi$
$20$		0			0
$21$		0			0
$22$	−0.586047	−	1.51790i	−0.586047	−	1.51790i
$23$		0			0		0.713930	−	0.700217i	$-0.246914\pi$
$23$		0			0		−0.713930	+	0.700217i	$0.753086\pi$
$24$	0.813552	−	0.581492i	0.813552	−	0.581492i
$25$	−0.790393	−	0.612601i	−0.790393	−	0.612601i
$26$		0			0
$27$	−0.0581448	+	0.998308i	−0.0581448	+	0.998308i
$28$		0			0
$29$		0			0		−0.533204	−	0.845986i	$-0.679012\pi$
$29$		0			0		0.533204	+	0.845986i	$0.320988\pi$
$30$		0			0
$31$		0			0		−0.565607	−	0.824675i	$-0.691358\pi$
$31$		0			0		0.565607	+	0.824675i	$0.308642\pi$
$32$	0.856167	−	0.516699i	0.856167	−	0.516699i
$33$	1.50625	+	0.615371i	1.50625	+	0.615371i
$34$	1.84588	+	0.143473i	1.84588	+	0.143473i
$35$		0			0
$36$	−0.135331	+	0.990800i	−0.135331	+	0.990800i
$37$		0			0		−0.0581448	−	0.998308i	$-0.518519\pi$
$37$		0			0		0.0581448	+	0.998308i	$0.481481\pi$
$38$	1.69177	+	1.02099i	1.69177	+	1.02099i
$39$		0			0
$40$		0			0
$41$	0.370718	−	1.71143i	0.370718	−	1.71143i	−0.286803	−	0.957990i	$-0.592593\pi$
$41$	0.370718	−	1.71143i	0.370718	−	1.71143i	0.657521	−	0.753436i	$-0.271605\pi$
$42$		0			0
$43$	−0.00821044	+	0.423328i	−0.00821044	+	0.423328i	0.973045	+	0.230616i	$0.0740741\pi$
$43$	−0.00821044	+	0.423328i	−0.00821044	+	0.423328i	−0.981255	+	0.192712i	$0.938272\pi$
$44$	1.45403	+	0.730243i	1.45403	+	0.730243i
$45$		0			0
$46$		0			0
$47$		0			0		0.565607	−	0.824675i	$-0.308642\pi$
$47$		0			0		−0.565607	+	0.824675i	$0.691358\pi$
$48$	−0.211704	+	0.977334i	−0.211704	+	0.977334i
$49$	−0.875558	−	0.483113i	−0.875558	−	0.483113i
$50$	0.996993	−	0.0774924i	0.996993	−	0.0774924i
$51$	−1.37108	+	1.24419i	−1.37108	+	1.24419i
$52$		0			0
$53$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$53$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$54$	−0.627812	−	0.778365i	−0.627812	−	0.778365i
$55$		0			0
$56$		0			0
$57$	−1.90360	+	0.529904i	−1.90360	+	0.529904i
$58$		0			0
$59$	−1.93894	−	0.303245i	−1.93894	−	0.303245i	−0.939693	−	0.342020i	$-0.888889\pi$
$59$	−1.93894	−	0.303245i	−1.93894	−	0.303245i	−0.999248	+	0.0387754i	$0.987654\pi$
$60$		0			0
$61$		0			0		−0.0968109	−	0.995303i	$-0.530864\pi$
$61$		0			0		0.0968109	+	0.995303i	$0.469136\pi$
$62$		0			0
$63$		0			0
$64$	−0.286803	+	0.957990i	−0.286803	+	0.957990i
$65$		0			0
$66$	−1.52898	+	0.556502i	−1.52898	+	0.556502i
$67$	0.266006	−	0.422048i	0.266006	−	0.422048i	−0.686242	−	0.727374i	$-0.740741\pi$
$67$	0.266006	−	0.422048i	0.266006	−	0.422048i	0.952248	+	0.305326i	$0.0987654\pi$
$68$	−1.46337	+	1.13420i	−1.46337	+	1.13420i
$69$		0			0
$70$		0			0
$71$		0			0		−0.993238	−	0.116093i	$-0.962963\pi$
$71$		0			0		0.993238	+	0.116093i	$0.0370370\pi$
$72$	−0.565607	−	0.824675i	−0.565607	−	0.824675i
$73$	0.369181	−	0.855857i	0.369181	−	0.855857i	−0.627812	−	0.778365i	$-0.716049\pi$
$73$	0.369181	−	0.855857i	0.369181	−	0.855857i	0.996993	−	0.0774924i	$-0.0246914\pi$
$74$		0			0
$75$	−0.627812	+	0.778365i	−0.627812	+	0.778365i
$76$	−1.93894	+	0.380796i	−1.93894	+	0.380796i
$77$		0			0
$78$		0			0
$79$		0			0		−0.952248	−	0.305326i	$-0.901235\pi$
$79$		0			0		0.952248	+	0.305326i	$0.0987654\pi$
$80$		0			0
$81$	0.996993	+	0.0774924i	0.996993	+	0.0774924i
$82$	0.875558	+	1.51651i	0.875558	+	1.51651i
$83$	0.353752	+	1.63310i	0.353752	+	1.63310i	0.713930	+	0.700217i	$0.246914\pi$
$83$	0.353752	+	1.63310i	0.353752	+	1.63310i	−0.360178	+	0.932884i	$0.617284\pi$
$84$		0			0
$85$		0			0
$86$	−0.278400	−	0.319011i	−0.278400	−	0.319011i
$87$		0			0
$88$	−1.56750	+	0.436345i	−1.56750	+	0.436345i
$89$	0.569728	−	0.0665916i	0.569728	−	0.0665916i	0.173648	−	0.984808i	$-0.444444\pi$
$89$	0.569728	−	0.0665916i	0.569728	−	0.0665916i	0.396080	+	0.918216i	$0.370370\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$97$	−0.366212	−	1.07030i	−0.366212	−	1.07030i	−0.963371	−	0.268173i	$-0.913580\pi$
$97$	−0.366212	−	1.07030i	−0.366212	−	1.07030i	0.597159	−	0.802123i	$-0.296296\pi$
$98$	0.973045	−	0.230616i	0.973045	−	0.230616i
$99$	0.644463	−	1.49403i	0.644463	−	1.49403i
$100$	−0.686242	+	0.727374i	−0.686242	+	0.727374i
$101$		0			0		0.813552	−	0.581492i	$-0.197531\pi$
$101$		0			0		−0.813552	+	0.581492i	$0.802469\pi$
$102$	0.179240	−	1.84275i	0.179240	−	1.84275i
$103$		0			0		0.627812	−	0.778365i	$-0.283951\pi$
$103$		0			0		−0.627812	+	0.778365i	$0.716049\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.347035	+	1.96813i	−0.347035	+	1.96813i	−0.135331	+	0.990800i	$0.543210\pi$
$107$	−0.347035	+	1.96813i	−0.347035	+	1.96813i	−0.211704	+	0.977334i	$0.567901\pi$
$108$	0.987990	+	0.154519i	0.987990	+	0.154519i
$109$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$109$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.0231594	+	1.19409i	0.0231594	+	1.19409i	0.813552	+	0.581492i	$0.197531\pi$
$113$	0.0231594	+	1.19409i	0.0231594	+	1.19409i	−0.790393	+	0.612601i	$0.790123\pi$
$114$	1.05360	−	1.67165i	1.05360	−	1.67165i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.63965	−	1.07842i	1.63965	−	1.07842i
$119$		0			0
$120$		0			0
$121$	−1.22002	−	1.10711i	−1.22002	−	1.10711i
$122$		0			0
$123$	−1.70391	−	0.403835i	−1.70391	−	0.403835i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.893633	−	0.448799i	$-0.148148\pi$
$127$		0			0		−0.893633	+	0.448799i	$0.851852\pi$
$128$	−0.431386	−	0.902167i	−0.431386	−	0.902167i
$129$	0.423089	+	0.0164178i	0.423089	+	0.0164178i
$130$		0			0
$131$	0.856938	−	1.79213i	0.856938	−	1.79213i	0.323734	−	0.946148i	$-0.395062\pi$
$131$	0.856938	−	1.79213i	0.856938	−	1.79213i	0.533204	−	0.845986i	$-0.320988\pi$
$132$	0.758301	−	1.43960i	0.758301	−	1.43960i
$133$		0			0
$134$	0.0866300	+	0.491303i	0.0866300	+	0.491303i
$135$		0			0
$136$	0.321501	−	1.82332i	0.321501	−	1.82332i
$137$	0.116760	−	0.854835i	0.116760	−	0.854835i	−0.835488	−	0.549509i	$-0.814815\pi$
$137$	0.116760	−	0.854835i	0.116760	−	0.854835i	0.952248	−	0.305326i	$-0.0987654\pi$
$138$		0			0
$139$	0.497382	+	1.93096i	0.497382	+	1.93096i	0.323734	+	0.946148i	$0.395062\pi$
$139$	0.497382	+	1.93096i	0.497382	+	1.93096i	0.173648	+	0.984808i	$0.444444\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.973045	+	0.230616i	0.973045	+	0.230616i
$145$		0			0
$146$	0.301748	+	0.881892i	0.301748	+	0.881892i
$147$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$148$		0			0
$149$		0			0		−0.135331	−	0.990800i	$-0.543210\pi$
$149$		0			0		0.135331	+	0.990800i	$0.456790\pi$
$150$	−0.0581448	−	0.998308i	−0.0581448	−	0.998308i
$151$		0			0		−0.627812	−	0.778365i	$-0.716049\pi$
$151$		0			0		0.627812	+	0.778365i	$0.283951\pi$
$152$	1.17997	−	1.58498i	1.17997	−	1.58498i
$153$	1.21737	+	1.39495i	1.21737	+	1.39495i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.657521	−	0.753436i	$-0.728395\pi$
$157$		0			0		0.657521	+	0.753436i	$0.271605\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.790393	+	0.612601i	−0.790393	+	0.612601i
$163$	−0.396080	+	0.686030i	−0.396080	+	0.686030i	−0.993238	−	0.116093i	$-0.962963\pi$
$163$	−0.396080	+	0.686030i	−0.396080	+	0.686030i	0.597159	+	0.802123i	$0.296296\pi$
$164$	−1.66750	−	0.534661i	−1.66750	−	0.534661i
$165$		0			0
$166$	−1.35943	−	0.971659i	−1.35943	−	0.971659i
$167$		0			0		0.981255	−	0.192712i	$-0.0617284\pi$
$167$		0			0		−0.981255	+	0.192712i	$0.938272\pi$
$168$		0			0
$169$	0.713930	+	0.700217i	0.713930	+	0.700217i
$170$		0			0
$171$	0.492891	+	1.91352i	0.492891	+	1.91352i
$172$	0.420545	+	0.0491546i	0.420545	+	0.0491546i
$173$		0			0		0.987990	−	0.154519i	$-0.0493827\pi$
$173$		0			0		−0.987990	+	0.154519i	$0.950617\pi$
$174$		0			0
$175$		0			0
$176$	0.867579	−	1.37651i	0.867579	−	1.37651i
$177$	−0.340786	+	1.93270i	−0.340786	+	1.93270i
$178$	−0.377159	+	0.432176i	−0.377159	+	0.432176i
$179$	0.393633	−	1.31482i	0.393633	−	1.31482i	−0.500000	−	0.866025i	$-0.666667\pi$
$179$	0.393633	−	1.31482i	0.393633	−	1.31482i	0.893633	−	0.448799i	$-0.148148\pi$
$180$		0			0
$181$		0			0		−0.973045	−	0.230616i	$-0.925926\pi$
$181$		0			0		0.973045	+	0.230616i	$0.0740741\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.78874	−	1.13933i	2.78874	−	1.13933i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.466044	−	0.884762i	$-0.345679\pi$
$191$		0			0		−0.466044	+	0.884762i	$0.654321\pi$
$192$	0.952248	+	0.305326i	0.952248	+	0.305326i
$193$	0.0386660	−	0.00300536i	0.0386660	−	0.00300536i	−0.0581448	−	0.998308i	$-0.518519\pi$
$193$	0.0386660	−	0.00300536i	0.0386660	−	0.00300536i	0.0968109	+	0.995303i	$0.469136\pi$
$194$	0.990444	+	0.546504i	0.990444	+	0.546504i
$195$		0			0
$196$	−0.565607	+	0.824675i	−0.565607	+	0.824675i
$197$		0			0		0.0581448	−	0.998308i	$-0.481481\pi$
$197$		0			0		−0.0581448	+	0.998308i	$0.518519\pi$
$198$	0.526749	+	1.53948i	0.526749	+	1.53948i
$199$		0			0		−0.893633	−	0.448799i	$-0.851852\pi$
$199$		0			0		0.893633	+	0.448799i	$0.148148\pi$
$200$	0.0193913	−	0.999812i	0.0193913	−	0.999812i
$201$	−0.416810	−	0.274140i	−0.416810	−	0.274140i
$202$		0			0
$203$		0			0
$204$	1.10561	+	1.48509i	1.10561	+	1.48509i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.20546	+	0.249148i	3.20546	+	0.249148i
$210$		0			0
$211$	−0.0995634	+	0.0600868i	−0.0995634	+	0.0600868i	−0.565607	−	0.824675i	$-0.691358\pi$
$211$	−0.0995634	+	0.0600868i	−0.0995634	+	0.0600868i	0.466044	+	0.884762i	$0.345679\pi$
$212$		0			0
$213$		0			0
$214$	−1.06561	−	1.69070i	−1.06561	−	1.69070i
$215$		0			0
$216$	−0.835488	+	0.549509i	−0.835488	+	0.549509i
$217$		0			0
$218$		0			0
$219$	−0.848537	−	0.385708i	−0.848537	−	0.385708i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.910363	−	0.413811i	$-0.864198\pi$
$223$		0			0		0.910363	+	0.413811i	$0.135802\pi$
$224$		0			0
$225$	0.766044	+	0.642788i	0.766044	+	0.642788i
$226$	−0.819590	−	0.868715i	−0.819590	−	0.868715i
$227$	−1.86880	−	0.367020i	−1.86880	−	0.367020i	−0.875558	−	0.483113i	$-0.839506\pi$
$227$	−1.86880	−	0.367020i	−1.86880	−	0.367020i	−0.993238	+	0.116093i	$0.962963\pi$
$228$	0.343125	+	1.94596i	0.343125	+	1.94596i
$229$		0			0		−0.466044	−	0.884762i	$-0.654321\pi$
$229$		0			0		0.466044	+	0.884762i	$0.345679\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.520862	+	1.20749i	0.520862	+	1.20749i	0.952248	+	0.305326i	$0.0987654\pi$
$233$	0.520862	+	1.20749i	0.520862	+	1.20749i	−0.431386	+	0.902167i	$0.641975\pi$
$234$		0			0
$235$		0			0
$236$	−0.489531	+	1.90048i	−0.489531	+	1.90048i
$237$		0			0
$238$		0			0
$239$		0			0		0.0968109	−	0.995303i	$-0.469136\pi$
$239$		0			0		−0.0968109	+	0.995303i	$0.530864\pi$
$240$		0			0
$241$	1.42684	−	1.29479i	1.42684	−	1.29479i	0.533204	−	0.845986i	$-0.320988\pi$
$241$	1.42684	−	1.29479i	1.42684	−	1.29479i	0.893633	−	0.448799i	$-0.148148\pi$
$242$	1.64747			1.64747
$243$	0.0968109	−	0.995303i	0.0968109	−	0.995303i
$244$		0			0
$245$		0			0
$246$	1.53320	−	0.845986i	1.53320	−	0.845986i
$247$		0			0
$248$		0			0
$249$	1.63965	−	0.322017i	1.63965	−	0.322017i
$250$		0			0
$251$	−0.884444	−	1.18802i	−0.884444	−	1.18802i	−0.981255	−	0.192712i	$-0.938272\pi$
$251$	−0.884444	−	1.18802i	−0.884444	−	1.18802i	0.0968109	−	0.995303i	$-0.469136\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.925724	+	0.378200i	0.925724	+	0.378200i
$257$	−0.897946	−	1.70471i	−0.897946	−	1.70471i	−0.686242	−	0.727374i	$-0.740741\pi$
$257$	−0.897946	−	1.70471i	−0.897946	−	1.70471i	−0.211704	−	0.977334i	$-0.567901\pi$
$258$	−0.324349	+	0.272161i	−0.324349	+	0.272161i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.569728	+	1.90302i	0.569728	+	1.90302i
$263$		0			0		−0.910363	−	0.413811i	$-0.864198\pi$
$263$		0			0		0.910363	+	0.413811i	$0.135802\pi$
$264$	0.405867	+	1.57567i	0.405867	+	1.57567i
$265$		0			0
$266$		0			0
$267$	−0.0555313	−	0.570912i	−0.0555313	−	0.570912i
$268$	−0.394313	−	0.305616i	−0.394313	−	0.305616i
$269$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$269$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$270$		0			0
$271$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$271$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$272$	0.987200	+	1.56630i	0.987200	+	1.56630i
$273$		0			0
$274$	0.487990	+	0.711507i	0.487990	+	0.711507i
$275$	1.39307	−	0.840724i	1.39307	−	0.840724i
$276$		0			0
$277$		0			0		−0.996993	−	0.0774924i	$-0.975309\pi$
$277$		0			0		0.996993	+	0.0774924i	$0.0246914\pi$
$278$	−1.66595	−	1.09571i	−1.66595	−	1.09571i
$279$		0			0
$280$		0			0
$281$	−0.0995634	−	0.0600868i	−0.0995634	−	0.0600868i	0.466044	−	0.884762i	$-0.345679\pi$
$281$	−0.0995634	−	0.0600868i	−0.0995634	−	0.0600868i	−0.565607	+	0.824675i	$0.691358\pi$
$282$		0			0
$283$	1.70192	−	0.545699i	1.70192	−	0.545699i	0.713930	−	0.700217i	$-0.246914\pi$
$283$	1.70192	−	0.545699i	1.70192	−	0.545699i	0.987990	+	0.154519i	$0.0493827\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.875558	+	0.483113i	−0.875558	+	0.483113i
$289$	−0.141167	+	2.42375i	−0.141167	+	2.42375i
$290$		0			0
$291$	−1.07720	+	0.345389i	−1.07720	+	0.345389i
$292$	−0.816096	−	0.450303i	−0.816096	−	0.450303i
$293$		0			0		0.996993	−	0.0774924i	$-0.0246914\pi$
$293$		0			0		−0.996993	+	0.0774924i	$0.975309\pi$
$294$	−0.211704	−	0.977334i	−0.211704	−	0.977334i
$295$		0			0
$296$		0			0
$297$	−1.48126	−	0.673313i	−1.48126	−	0.673313i
$298$		0			0
$299$		0			0
$300$	0.713930	+	0.700217i	0.713930	+	0.700217i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.191296	+	1.96670i	0.191296	+	1.96670i
$305$		0			0
$306$	−1.83893	−	0.214940i	−1.83893	−	0.214940i
$307$	−0.377159	+	1.25980i	−0.377159	+	1.25980i	0.533204	+	0.845986i	$0.320988\pi$
$307$	−0.377159	+	1.25980i	−0.377159	+	1.25980i	−0.910363	+	0.413811i	$0.864198\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.790393	−	0.612601i	$-0.209877\pi$
$311$		0			0		−0.790393	+	0.612601i	$0.790123\pi$
$312$		0			0
$313$	1.69177	−	0.264588i	1.69177	−	0.264588i	0.766044	−	0.642788i	$-0.222222\pi$
$313$	1.69177	−	0.264588i	1.69177	−	0.264588i	0.925724	+	0.378200i	$0.123457\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.713930	−	0.700217i	$-0.753086\pi$
$317$		0			0		0.713930	+	0.700217i	$0.246914\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	1.96103	+	0.385135i	1.96103	+	0.385135i
$322$		0			0
$323$	−1.82921	+	3.16829i	−1.82921	+	3.16829i
$324$	0.173648	−	0.984808i	0.173648	−	0.984808i
$325$		0			0
$326$	−0.167703	−	0.774204i	−0.167703	−	0.774204i
$327$		0			0
$328$	1.59415	−	0.724631i	1.59415	−	0.724631i
$329$		0			0
$330$		0			0
$331$	1.32221	−	0.368062i	1.32221	−	0.368062i	0.466044	−	0.884762i	$-0.345679\pi$
$331$	1.32221	−	0.368062i	1.32221	−	0.368062i	0.856167	+	0.516699i	$0.172840\pi$
$332$	1.65968	−	0.193988i	1.65968	−	0.193988i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.200438	+	1.46746i	0.200438	+	1.46746i	0.766044	+	0.642788i	$0.222222\pi$
$337$	0.200438	+	1.46746i	0.200438	+	1.46746i	−0.565607	+	0.824675i	$0.691358\pi$
$338$	−0.999248	−	0.0387754i	−0.999248	−	0.0387754i
$339$	1.19432			1.19432
$340$		0			0
$341$		0			0
$342$	−1.65091	−	1.08582i	−1.65091	−	1.08582i
$343$		0			0
$344$	−0.344464	+	0.246208i	−0.344464	+	0.246208i
$345$		0			0
$346$		0			0
$347$	−0.179686	−	0.697585i	−0.179686	−	0.697585i	−0.993238	−	0.116093i	$-0.962963\pi$
$347$	−0.179686	−	0.697585i	−0.179686	−	0.697585i	0.813552	−	0.581492i	$-0.197531\pi$
$348$		0			0
$349$		0			0		0.135331	−	0.990800i	$-0.456790\pi$
$349$		0			0		−0.135331	+	0.990800i	$0.543210\pi$
$350$		0			0
$351$		0			0
$352$	0.282544	+	1.60238i	0.282544	+	1.60238i
$353$	−1.06561	+	0.0413504i	−1.06561	+	0.0413504i	−0.565607	−	0.824675i	$-0.691358\pi$
$353$	−1.06561	+	0.0413504i	−1.06561	+	0.0413504i	−0.500000	+	0.866025i	$0.666667\pi$
$354$	−1.04642	−	1.66026i	−1.04642	−	1.66026i
$355$		0			0
$356$	−0.0111230	−	0.573499i	−0.0111230	−	0.573499i
$357$		0			0
$358$	0.592070	+	1.23821i	0.592070	+	1.23821i
$359$		0			0		0.893633	−	0.448799i	$-0.148148\pi$
$359$		0			0		−0.893633	+	0.448799i	$0.851852\pi$
$360$		0			0
$361$	−2.42667	+	1.59605i	−2.42667	+	1.59605i
$362$		0			0
$363$	−1.13056	+	1.19832i	−1.13056	+	1.19832i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.875558	−	0.483113i	$-0.160494\pi$
$367$		0			0		−0.875558	+	0.483113i	$0.839506\pi$
$368$		0			0
$369$	−0.436800	+	1.69576i	−0.436800	+	1.69576i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.0193913	−	0.999812i	$-0.506173\pi$
$373$		0			0		0.0193913	+	0.999812i	$0.493827\pi$
$374$	−1.29955	+	2.71778i	−1.29955	+	2.71778i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.297344	−	1.68632i	0.297344	−	1.68632i	−0.360178	−	0.932884i	$-0.617284\pi$
$379$	0.297344	−	1.68632i	0.297344	−	1.68632i	0.657521	−	0.753436i	$-0.271605\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.627812	−	0.778365i	$-0.283951\pi$
$383$		0			0		−0.627812	+	0.778365i	$0.716049\pi$
$384$	−0.910363	+	0.413811i	−0.910363	+	0.413811i
$385$		0			0
$386$	−0.0266143	+	0.0282095i	−0.0266143	+	0.0282095i
$387$	0.0246190	−	0.422691i	0.0246190	−	0.422691i
$388$	−1.10072	+	0.260876i	−1.10072	+	0.260876i
$389$		0			0		−0.323734	−	0.946148i	$-0.604938\pi$
$389$		0			0		0.323734	+	0.946148i	$0.395062\pi$
$390$		0			0
$391$		0			0
$392$	−0.135331	−	0.990800i	−0.135331	−	0.990800i
$393$	−1.77518	−	0.891529i	−1.77518	−	0.891529i
$394$		0			0
$395$		0			0
$396$	−1.42462	−	0.786075i	−1.42462	−	0.786075i
$397$		0			0		0.993238	−	0.116093i	$-0.0370370\pi$
$397$		0			0		−0.993238	+	0.116093i	$0.962963\pi$
$398$		0			0
$399$		0			0
$400$	0.657521	+	0.753436i	0.657521	+	0.753436i
$401$	1.14307	−	0.519591i	1.14307	−	0.519591i	0.249441	−	0.968390i	$-0.419753\pi$
$401$	1.14307	−	0.519591i	1.14307	−	0.519591i	0.893633	+	0.448799i	$0.148148\pi$
$402$	0.492891	−	0.0770867i	0.492891	−	0.0770867i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.81674	−	0.356797i	−1.81674	−	0.356797i
$409$	−0.220198	−	0.157388i	−0.220198	−	0.157388i	0.466044	−	0.884762i	$-0.345679\pi$
$409$	−0.220198	−	0.157388i	−0.220198	−	0.157388i	−0.686242	+	0.727374i	$0.740741\pi$
$410$		0			0
$411$	−0.852410	−	0.133315i	−0.852410	−	0.133315i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.94024	−	0.459845i	1.94024	−	0.459845i
$418$	−2.54121	+	1.96959i	−2.54121	+	1.96959i
$419$	0.422383	−	0.670156i	0.422383	−	0.670156i	−0.565607	−	0.824675i	$-0.691358\pi$
$419$	0.422383	−	0.670156i	0.422383	−	0.670156i	0.987990	+	0.154519i	$0.0493827\pi$
$420$		0			0
$421$		0			0		0.657521	−	0.753436i	$-0.271605\pi$
$421$		0			0		−0.657521	+	0.753436i	$0.728395\pi$
$422$	0.0333522	−	0.111404i	0.0333522	−	0.111404i
$423$		0			0
$424$		0			0
$425$	0.179240	+	1.84275i	0.179240	+	1.84275i
$426$		0			0
$427$		0			0
$428$	1.92529	+	0.535942i	1.92529	+	0.535942i
$429$		0			0
$430$		0			0
$431$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$431$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$432$	0.249441	−	0.968390i	0.249441	−	0.968390i
$433$	−1.21095	+	1.01611i	−1.21095	+	1.01611i	−0.211704	+	0.977334i	$0.567901\pi$
$433$	−1.21095	+	1.01611i	−1.21095	+	1.01611i	−0.999248	+	0.0387754i	$0.987654\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.887578	−	0.284590i	0.887578	−	0.284590i
$439$		0			0		0.565607	−	0.824675i	$-0.308642\pi$
$439$		0			0		−0.565607	+	0.824675i	$0.691358\pi$
$440$		0			0
$441$	0.856167	+	0.516699i	0.856167	+	0.516699i
$442$		0			0
$443$	0.000752047	−	0.0387754i	0.000752047	−	0.0387754i	−0.999248	−	0.0387754i	$-0.987654\pi$
$443$	0.000752047	−	0.0387754i	0.000752047	−	0.0387754i	1.00000			$0$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.115940	−	1.99061i	−0.115940	−	1.99061i	−0.135331	−	0.990800i	$-0.543210\pi$
$449$	−0.115940	−	1.99061i	−0.115940	−	1.99061i	0.0193913	−	0.999812i	$-0.493827\pi$
$450$	−0.999248	+	0.0387754i	−0.999248	+	0.0387754i
$451$	2.38051	+	1.56569i	2.38051	+	1.56569i
$452$	1.19073	+	0.0925505i	1.19073	+	0.0925505i
$453$		0			0
$454$	1.63057	−	0.984052i	1.63057	−	0.984052i
$455$		0			0
$456$	−1.56180	−	1.21049i	−1.56180	−	1.21049i
$457$	0.701187	+	1.11251i	0.701187	+	1.11251i	0.987990	+	0.154519i	$0.0493827\pi$
$457$	0.701187	+	1.11251i	0.701187	+	1.11251i	−0.286803	+	0.957990i	$0.592593\pi$
$458$		0			0
$459$	1.41829	−	1.19009i	1.41829	−	1.19009i
$460$		0			0
$461$		0			0		−0.790393	−	0.612601i	$-0.790123\pi$
$461$		0			0		0.790393	+	0.612601i	$0.209877\pi$
$462$		0			0
$463$		0			0		0.713930	−	0.700217i	$-0.246914\pi$
$463$		0			0		−0.713930	+	0.700217i	$0.753086\pi$
$464$		0			0
$465$		0			0
$466$	−1.19717	−	0.544179i	−1.19717	−	0.544179i
$467$	0.360117	+	1.20287i	0.360117	+	1.20287i	0.925724	+	0.378200i	$0.123457\pi$
$467$	0.360117	+	1.20287i	0.360117	+	1.20287i	−0.565607	+	0.824675i	$0.691358\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.914615	−	1.73635i	−0.914615	−	1.73635i
$473$	−0.637758	−	0.260553i	−0.637758	−	0.260553i
$474$		0			0
$475$	−0.711704	+	1.84336i	−0.711704	+	1.84336i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.249441	−	0.968390i	$-0.419753\pi$
$479$		0			0		−0.249441	+	0.968390i	$0.580247\pi$
$480$		0			0
$481$		0			0
$482$	−0.186530	+	1.91769i	−0.186530	+	1.91769i
$483$		0			0
$484$	−1.22002	+	1.10711i	−1.22002	+	1.10711i
$485$		0			0
$486$	0.597159	+	0.802123i	0.597159	+	0.802123i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$	0.678221	+	0.409308i	0.678221	+	0.409308i
$490$		0			0
$491$	0.345233	−	1.00898i	0.345233	−	1.00898i	−0.627812	−	0.778365i	$-0.716049\pi$
$491$	0.345233	−	1.00898i	0.345233	−	1.00898i	0.973045	−	0.230616i	$-0.0740741\pi$
$492$	−0.566896	+	1.65682i	−0.566896	+	1.65682i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.997837	+	1.34033i	−0.997837	+	1.34033i
$499$	−1.46337	−	0.597853i	−1.46337	−	0.597853i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	−1.46337	−	0.597853i	−1.46337	−	0.597853i	−0.963371	+	0.268173i	$0.913580\pi$
$500$		0			0
$501$		0			0
$502$	1.45333	+	0.285424i	1.45333	+	0.285424i
$503$		0			0		−0.686242	−	0.727374i	$-0.740741\pi$
$503$		0			0		0.686242	+	0.727374i	$0.259259\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.713930	−	0.700217i	0.713930	−	0.700217i
$508$		0			0
$509$		0			0		0.713930	−	0.700217i	$-0.246914\pi$
$509$		0			0		−0.713930	+	0.700217i	$0.753086\pi$
$510$		0			0
$511$		0			0
$512$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$513$	1.92272	−	0.455692i	1.92272	−	0.455692i
$514$	1.81055	+	0.658984i	1.81055	+	0.658984i
$515$		0			0
$516$	0.0573003	−	0.419513i	0.0573003	−	0.419513i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.59118	−	1.04654i	−1.59118	−	1.04654i	−0.963371	−	0.268173i	$-0.913580\pi$
$521$	−1.59118	−	1.04654i	−1.59118	−	1.04654i	−0.627812	−	0.778365i	$-0.716049\pi$
$522$		0			0
$523$	−0.0694434	−	1.19230i	−0.0694434	−	1.19230i	−0.835488	−	0.549509i	$-0.814815\pi$
$523$	−0.0694434	−	1.19230i	−0.0694434	−	1.19230i	0.766044	−	0.642788i	$-0.222222\pi$
$524$	−1.70076	−	1.02641i	−1.70076	−	1.02641i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.35943	−	0.894108i	−1.35943	−	0.894108i
$529$	0.0193913	−	0.999812i	0.0193913	−	0.999812i
$530$		0			0
$531$	1.92572	+	0.378200i	1.92572	+	0.378200i
$532$		0			0
$533$		0			0
$534$	0.424781	+	0.385468i	0.424781	+	0.385468i
$535$		0			0
$536$	0.497382	−	0.0386596i	0.497382	−	0.0386596i
$537$	−1.30694	−	0.419055i	−1.30694	−	0.419055i
$538$		0			0
$539$	1.24643	−	1.04588i	1.24643	−	1.04588i
$540$		0			0
$541$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$541$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$542$		0			0
$543$		0			0
$544$	−1.78363	−	0.496508i	−1.78363	−	0.496508i
$545$		0			0
$546$		0			0
$547$	−0.0262031	−	0.269391i	−0.0262031	−	0.269391i	−0.999248	−	0.0387754i	$-0.987654\pi$
$547$	−0.0262031	−	0.269391i	−0.0262031	−	0.269391i	0.973045	−	0.230616i	$-0.0740741\pi$
$548$	−0.839516	−	0.198969i	−0.839516	−	0.198969i
$549$		0			0
$550$	−0.466659	+	1.55875i	−0.466659	+	1.55875i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.97004	−	0.308108i	1.97004	−	0.308108i
$557$		0			0		−0.993238	−	0.116093i	$-0.962963\pi$
$557$		0			0		0.993238	+	0.116093i	$0.0370370\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−1.08503	−	2.81031i	−1.08503	−	2.81031i
$562$	0.114110	−	0.0224104i	0.114110	−	0.0224104i
$563$	1.62221	+	1.15949i	1.62221	+	1.15949i	0.856167	+	0.516699i	$0.172840\pi$
$563$	1.62221	+	1.15949i	1.62221	+	1.15949i	0.766044	+	0.642788i	$0.222222\pi$
$564$		0			0
$565$		0			0
$566$	−0.893633	+	1.54782i	−0.893633	+	1.54782i
$567$		0			0
$568$		0			0
$569$	−0.137071	−	0.632792i	−0.137071	−	0.632792i	−0.993238	−	0.116093i	$-0.962963\pi$
$569$	−0.137071	−	0.632792i	−0.137071	−	0.632792i	0.856167	−	0.516699i	$-0.172840\pi$
$570$		0			0
$571$	1.81936	−	0.826999i	1.81936	−	0.826999i	0.893633	−	0.448799i	$-0.148148\pi$
$571$	1.81936	−	0.826999i	1.81936	−	0.826999i	0.925724	−	0.378200i	$-0.123457\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.323734	−	0.946148i	0.323734	−	0.946148i
$577$	−0.515212	+	0.692050i	−0.515212	+	0.692050i	−0.981255	−	0.192712i	$-0.938272\pi$
$577$	−0.515212	+	0.692050i	−0.515212	+	0.692050i	0.466044	+	0.884762i	$0.345679\pi$
$578$	−1.52424	−	1.88976i	−1.52424	−	1.88976i
$579$	−0.00225501	−	0.0387170i	−0.00225501	−	0.0387170i
$580$		0			0
$581$		0			0
$582$	0.565607	−	0.979660i	0.565607	−	0.979660i
$583$		0			0
$584$	0.906963	−	0.214954i	0.906963	−	0.214954i
$585$		0			0
$586$		0			0
$587$	−1.56750	+	1.12039i	−1.56750	+	1.12039i	−0.627812	+	0.778365i	$0.716049\pi$
$587$	−1.56750	+	1.12039i	−1.56750	+	1.12039i	−0.939693	+	0.342020i	$0.888889\pi$
$588$	0.813552	+	0.581492i	0.813552	+	0.581492i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.337935	−	1.91652i	0.337935	−	1.91652i	−0.0581448	−	0.998308i	$-0.518519\pi$
$593$	0.337935	−	1.91652i	0.337935	−	1.91652i	0.396080	−	0.918216i	$-0.370370\pi$
$594$	1.54941	−	0.496797i	1.54941	−	0.496797i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.0193913	−	0.999812i	$-0.506173\pi$
$599$		0			0		0.0193913	+	0.999812i	$0.493827\pi$
$600$	−0.999248	−	0.0387754i	−0.999248	−	0.0387754i
$601$	−0.0835257	−	0.174679i	−0.0835257	−	0.174679i	0.856167	−	0.516699i	$-0.172840\pi$
$601$	−0.0835257	−	0.174679i	−0.0835257	−	0.174679i	−0.939693	+	0.342020i	$0.888889\pi$
$602$		0			0
$603$	−0.282171	+	0.411416i	−0.282171	+	0.411416i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.740544	−	0.672008i	$-0.765432\pi$
$607$		0			0		0.740544	+	0.672008i	$0.234568\pi$
$608$	−1.46330	−	1.32787i	−1.46330	−	1.32787i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	1.50625	−	1.07660i	1.50625	−	1.07660i
$613$		0			0		0.893633	−	0.448799i	$-0.148148\pi$
$613$		0			0		−0.893633	+	0.448799i	$0.851852\pi$
$614$	−0.567291	−	1.18639i	−0.567291	−	1.18639i
$615$		0			0
$616$		0			0
$617$	0.487990	−	1.02054i	0.487990	−	1.02054i	−0.500000	−	0.866025i	$-0.666667\pi$
$617$	0.487990	−	1.02054i	0.487990	−	1.02054i	0.987990	−	0.154519i	$-0.0493827\pi$
$618$		0			0
$619$	−0.0387535	+	0.00150381i	−0.0387535	+	0.00150381i	−0.0581448	−	0.998308i	$-0.518519\pi$
$619$	−0.0387535	+	0.00150381i	−0.0387535	+	0.00150381i	0.0193913	+	0.999812i	$0.493827\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.249441	+	0.968390i	0.249441	+	0.968390i
$626$	−1.07502	+	1.33282i	−1.07502	+	1.33282i
$627$	0.311259	−	3.20002i	0.311259	−	3.20002i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.973045	−	0.230616i	$-0.0740741\pi$
$631$		0			0		−0.973045	+	0.230616i	$0.925926\pi$
$632$		0			0
$633$	0.0581448	+	0.100710i	0.0581448	+	0.100710i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.693969	−	0.193180i	0.693969	−	0.193180i	0.0968109	−	0.995303i	$-0.469136\pi$
$641$	0.693969	−	0.193180i	0.693969	−	0.193180i	0.597159	+	0.802123i	$0.296296\pi$
$642$	−1.71105	+	1.03262i	−1.71105	+	1.03262i
$643$	−1.19717	−	1.37180i	−1.19717	−	1.37180i	−0.910363	−	0.413811i	$-0.864198\pi$
$643$	−1.19717	−	1.37180i	−1.19717	−	1.37180i	−0.286803	−	0.957990i	$-0.592593\pi$
$644$		0			0
$645$		0			0
$646$	−0.774502	−	3.57550i	−0.774502	−	3.57550i
$647$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$647$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$648$	0.533204	+	0.845986i	0.533204	+	0.845986i
$649$	1.59660	−	2.76540i	1.59660	−	2.76540i
$650$		0			0
$651$		0			0
$652$	0.644463	+	0.460634i	0.644463	+	0.460634i
$653$		0			0		0.981255	−	0.192712i	$-0.0617284\pi$
$653$		0			0		−0.981255	+	0.192712i	$0.938272\pi$
$654$		0			0
$655$		0			0
$656$	−0.693582	+	1.60790i	−0.693582	+	1.60790i
$657$	−0.402089	+	0.840899i	−0.402089	+	0.840899i
$658$		0			0
$659$	−0.114893	+	0.0179689i	−0.114893	+	0.0179689i	−0.211704	−	0.977334i	$-0.567901\pi$
$659$	−0.114893	+	0.0179689i	−0.114893	+	0.0179689i	0.0968109	+	0.995303i	$0.469136\pi$
$660$		0			0
$661$		0			0		0.790393	−	0.612601i	$-0.209877\pi$
$661$		0			0		−0.790393	+	0.612601i	$0.790123\pi$
$662$	−0.731814	+	1.16110i	−0.731814	+	1.16110i
$663$		0			0
$664$	−1.09870	+	1.25897i	−1.09870	+	1.25897i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.65451	−	0.675943i	1.65451	−	0.675943i	0.657521	−	0.753436i	$-0.271605\pi$
$673$	1.65451	−	0.675943i	1.65451	−	0.675943i	0.996993	+	0.0774924i	$0.0246914\pi$
$674$	−1.13458	−	0.952025i	−1.13458	−	0.952025i
$675$	0.657521	−	0.753436i	0.657521	−	0.753436i
$676$	0.766044	−	0.642788i	0.766044	−	0.642788i
$677$		0			0		0.466044	−	0.884762i	$-0.345679\pi$
$677$		0			0		−0.466044	+	0.884762i	$0.654321\pi$
$678$	−0.884444	+	0.802591i	−0.884444	+	0.802591i
$679$		0			0
$680$		0			0
$681$	−0.403189	+	1.86133i	−0.403189	+	1.86133i
$682$		0			0
$683$	−0.0830226	+	1.42544i	−0.0830226	+	1.42544i	0.657521	+	0.753436i	$0.271605\pi$
$683$	−0.0830226	+	1.42544i	−0.0830226	+	1.42544i	−0.740544	+	0.672008i	$0.765432\pi$
$684$	1.95225	−	0.305326i	1.95225	−	0.305326i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.0896371	−	0.413811i	0.0896371	−	0.413811i
$689$		0			0
$690$		0			0
$691$	−0.491103	−	0.296382i	−0.491103	−	0.296382i	0.249441	−	0.968390i	$-0.419753\pi$
$691$	−0.491103	−	0.296382i	−0.491103	−	0.296382i	−0.740544	+	0.672008i	$0.765432\pi$
$692$		0			0
$693$		0			0
$694$	0.601848	+	0.395842i	0.601848	+	0.395842i
$695$		0			0
$696$		0			0
$697$	−2.77578	+	1.67519i	−2.77578	+	1.67519i
$698$		0			0
$699$	1.21737	−	0.497349i	1.21737	−	0.497349i
$700$		0			0
$701$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$701$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$702$		0			0
$703$		0			0
$704$	−1.28605	−	0.996765i	−1.28605	−	0.996765i
$705$		0			0
$706$	0.761341	−	0.746718i	0.761341	−	0.746718i
$707$		0			0
$708$	1.89063	+	0.526292i	1.89063	+	0.526292i
$709$		0			0		−0.910363	−	0.413811i	$-0.864198\pi$
$709$		0			0		0.910363	+	0.413811i	$0.135802\pi$
$710$		0			0
$711$		0			0
$712$	0.393633	+	0.417226i	0.393633	+	0.417226i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.27054	−	0.519073i	−1.27054	−	0.519073i
$717$		0			0
$718$		0			0
$719$		0			0		−0.396080	−	0.918216i	$-0.629630\pi$
$719$		0			0		0.396080	+	0.918216i	$0.370370\pi$
$720$		0			0
$721$		0			0
$722$	0.724501	−	2.81268i	0.724501	−	2.81268i
$723$	−1.26687	−	1.45168i	−1.26687	−	1.45168i
$724$		0			0
$725$		0			0
$726$	0.0319466	−	1.64716i	0.0319466	−	1.64716i
$727$		0			0		0.740544	−	0.672008i	$-0.234568\pi$
$727$		0			0		−0.740544	+	0.672008i	$0.765432\pi$
$728$		0			0
$729$	−0.993238	−	0.116093i	−0.993238	−	0.116093i
$730$		0			0
$731$	0.580525	−	0.526799i	0.580525	−	0.526799i
$732$		0			0
$733$		0			0		0.0968109	−	0.995303i	$-0.469136\pi$
$733$		0			0		−0.0968109	+	0.995303i	$0.530864\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.484734	+	0.651110i	0.484734	+	0.651110i
$738$	−0.816096	−	1.54932i	−0.816096	−	1.54932i
$739$	0.0766897	+	0.177787i	0.0766897	+	0.177787i	0.952248	−	0.305326i	$-0.0987654\pi$
$739$	0.0766897	+	0.177787i	0.0766897	+	0.177787i	−0.875558	+	0.483113i	$0.839506\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.466044	−	0.884762i	$-0.654321\pi$
$743$		0			0		0.466044	+	0.884762i	$0.345679\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.290162	−	1.64559i	−0.290162	−	1.64559i
$748$	−0.863994	−	2.88594i	−0.863994	−	2.88594i
$749$		0			0
$750$		0			0
$751$		0			0		−0.360178	−	0.932884i	$-0.617284\pi$
$751$		0			0		0.360178	+	0.932884i	$0.382716\pi$
$752$		0			0
$753$	−1.20494	+	0.861241i	−1.20494	+	0.861241i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$757$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$758$	0.913024	+	1.44861i	0.913024	+	1.44861i
$759$		0			0
$760$		0			0
$761$	−1.60907	+	0.971077i	−1.60907	+	0.971077i	−0.627812	+	0.778365i	$0.716049\pi$
$761$	−1.60907	+	0.971077i	−1.60907	+	0.971077i	−0.981255	+	0.192712i	$0.938272\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.396080	−	0.918216i	0.396080	−	0.918216i
$769$	1.13729	−	0.364656i	1.13729	−	0.364656i	0.323734	−	0.946148i	$-0.395062\pi$
$769$	1.13729	−	0.364656i	1.13729	−	0.364656i	0.813552	+	0.581492i	$0.197531\pi$
$770$		0			0
$771$	−1.72180	+	0.864720i	−1.72180	+	0.864720i
$772$	0.000752047	−	0.0387754i	0.000752047	−	0.0387754i
$773$		0			0		−0.893633	−	0.448799i	$-0.851852\pi$
$773$		0			0		0.893633	+	0.448799i	$0.148148\pi$
$774$	0.265821	+	0.329566i	0.265821	+	0.329566i
$775$		0			0
$776$	0.639822	−	0.932884i	0.639822	−	0.932884i
$777$		0			0
$778$		0			0
$779$	−3.44977	+	0.268137i	−3.44977	+	0.268137i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.766044	+	0.642788i	0.766044	+	0.642788i
$785$		0			0
$786$	1.91371	−	0.532719i	1.91371	−	0.532719i
$787$	1.60977	+	0.448110i	1.60977	+	0.448110i	0.952248	−	0.305326i	$-0.0987654\pi$
$787$	1.60977	+	0.448110i	1.60977	+	0.448110i	0.657521	+	0.753436i	$0.271605\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	1.58325	−	0.375236i	1.58325	−	0.375236i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.790393	−	0.612601i	$-0.209877\pi$
$797$		0			0		−0.790393	+	0.612601i	$0.790123\pi$
$798$		0			0
$799$		0			0
$800$	−0.993238	−	0.116093i	−0.993238	−	0.116093i
$801$	−0.571882	+	0.0444502i	−0.571882	+	0.0444502i
$802$	−0.497327	+	1.15293i	−0.497327	+	1.15293i
$803$	1.08275	+	1.06195i	1.08275	+	1.06195i
$804$	−0.313204	+	0.388312i	−0.313204	+	0.388312i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.466044	+	0.807211i	−0.466044	+	0.807211i	−0.999248	−	0.0387754i	$-0.987654\pi$
$809$	−0.466044	+	0.807211i	−0.466044	+	0.807211i	0.533204	+	0.845986i	$0.320988\pi$
$810$		0			0
$811$	−0.713930	−	1.23656i	−0.713930	−	1.23656i	−0.963371	−	0.268173i	$-0.913580\pi$
$811$	−0.713930	−	1.23656i	−0.713930	−	1.23656i	0.249441	−	0.968390i	$-0.419753\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	1.58515	−	0.956642i	1.58515	−	0.956642i
$817$	0.806000	−	0.224365i	0.806000	−	0.224365i
$818$	0.268832	−	0.0314220i	0.268832	−	0.0314220i
$819$		0			0
$820$		0			0
$821$		0			0		−0.627812	−	0.778365i	$-0.716049\pi$
$821$		0			0		0.627812	+	0.778365i	$0.283951\pi$
$822$	0.720836	−	0.474101i	0.720836	−	0.474101i
$823$		0			0		−0.135331	−	0.990800i	$-0.543210\pi$
$823$		0			0		0.135331	+	0.990800i	$0.456790\pi$
$824$		0			0
$825$	−0.813552	−	1.40911i	−0.813552	−	1.40911i
$826$		0			0
$827$	1.49079	−	0.353324i	1.49079	−	0.353324i	0.597159	−	0.802123i	$-0.296296\pi$
$827$	1.49079	−	0.353324i	1.49079	−	0.353324i	0.893633	+	0.448799i	$0.148148\pi$
$828$		0			0
$829$		0			0		0.686242	−	0.727374i	$-0.259259\pi$
$829$		0			0		−0.686242	+	0.727374i	$0.740741\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.461827	+	1.79292i	0.461827	+	1.79292i
$834$	−1.12781	+	1.64439i	−1.12781	+	1.64439i
$835$		0			0
$836$	0.558301	−	3.16628i	0.558301	−	3.16628i
$837$		0			0
$838$	0.137557	+	0.780125i	0.137557	+	0.780125i
$839$		0			0		0.999248	−	0.0387754i	$-0.0123457\pi$
$839$		0			0		−0.999248	+	0.0387754i	$0.987654\pi$
$840$		0			0
$841$	−0.431386	+	0.902167i	−0.431386	+	0.902167i
$842$		0			0
$843$	−0.0620062	+	0.0983795i	−0.0620062	+	0.0983795i
$844$	0.0501657	+	0.104913i	0.0501657	+	0.104913i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.512593	−	1.71218i	−0.512593	−	1.71218i
$850$	−1.37108	−	1.24419i	−1.37108	−	1.24419i
$851$		0			0
$852$		0			0
$853$		0			0		0.875558	−	0.483113i	$-0.160494\pi$
$853$		0			0		−0.875558	+	0.483113i	$0.839506\pi$
$854$		0			0
$855$		0			0
$856$	−1.78592	+	0.896923i	−1.78592	+	0.896923i
$857$	−0.149819	−	0.313319i	−0.149819	−	0.313319i	0.813552	−	0.581492i	$-0.197531\pi$
$857$	−0.149819	−	0.313319i	−0.149819	−	0.313319i	−0.963371	+	0.268173i	$0.913580\pi$
$858$		0			0
$859$	0.00375458	+	0.193585i	0.00375458	+	0.193585i	0.996993	+	0.0774924i	$0.0246914\pi$
$859$	0.00375458	+	0.193585i	0.00375458	+	0.193585i	−0.993238	+	0.116093i	$0.962963\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$863$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$864$	0.466044	+	0.884762i	0.466044	+	0.884762i
$865$		0			0
$866$	0.213930	−	1.56624i	0.213930	−	1.56624i
$867$	2.42056	+	0.188141i	2.42056	+	0.188141i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.324436	+	1.08369i	0.324436	+	1.08369i
$874$		0			0
$875$		0			0
$876$	−0.466044	+	0.807211i	−0.466044	+	0.807211i
$877$		0			0		−0.999248	−	0.0387754i	$-0.987654\pi$
$877$		0			0		0.999248	+	0.0387754i	$0.0123457\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.819590	+	1.10090i	−0.819590	+	1.10090i	0.173648	+	0.984808i	$0.444444\pi$
$881$	−0.819590	+	1.10090i	−0.819590	+	1.10090i	−0.993238	+	0.116093i	$0.962963\pi$
$882$	−0.981255	+	0.192712i	−0.981255	+	0.192712i
$883$	0.268832	−	0.0314220i	0.268832	−	0.0314220i	0.0193913	−	0.999812i	$-0.493827\pi$
$883$	0.268832	−	0.0314220i	0.268832	−	0.0314220i	0.249441	+	0.968390i	$0.419753\pi$
$884$		0			0
$885$		0			0
$886$	0.0255004	+	0.0292203i	0.0255004	+	0.0292203i
$887$		0			0		0.910363	−	0.413811i	$-0.135802\pi$
$887$		0			0		−0.910363	+	0.413811i	$0.864198\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.701910	+	1.46792i	−0.701910	+	1.46792i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.42357	+	1.39622i	1.42357	+	1.39622i
$899$		0			0
$900$	0.713930	−	0.700217i	0.713930	−	0.700217i
$901$		0			0
$902$	−2.81503	+	0.440262i	−2.81503	+	0.440262i
$903$		0			0
$904$	−0.943980	+	0.731639i	−0.943980	+	0.731639i
$905$		0			0
$906$		0			0
$907$	−1.26687	+	1.45168i	−1.26687	+	1.45168i	−0.431386	+	0.902167i	$0.641975\pi$
$907$	−1.26687	+	1.45168i	−1.26687	+	1.45168i	−0.835488	+	0.549509i	$0.814815\pi$
$908$	−0.546216	+	1.82449i	−0.546216	+	1.82449i
$909$		0			0
$910$		0			0
$911$		0			0		−0.0968109	−	0.995303i	$-0.530864\pi$
$911$		0			0		0.0968109	+	0.995303i	$0.469136\pi$
$912$	1.97004	−	0.153123i	1.97004	−	0.153123i
$913$	−2.68620	−	0.420114i	−2.68620	−	0.420114i
$914$	−1.26687	−	0.352658i	−1.26687	−	0.352658i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.250559	+	1.83442i	−0.250559	+	1.83442i
$919$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$919$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$920$		0			0
$921$	1.25225	+	0.401517i	1.25225	+	0.401517i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.00673454	−	0.347231i	0.00673454	−	0.347231i	−0.981255	−	0.192712i	$-0.938272\pi$
$929$	0.00673454	−	0.347231i	0.00673454	−	0.347231i	0.987990	−	0.154519i	$-0.0493827\pi$
$930$		0			0
$931$	−0.418323	+	1.93119i	−0.418323	+	1.93119i
$932$	1.25225	−	0.401517i	1.25225	−	0.401517i
$933$		0			0
$934$	−1.07502	−	0.648780i	−1.07502	−	0.648780i
$935$		0			0
$936$		0			0
$937$	−1.62593	−	1.06939i	−1.62593	−	1.06939i	−0.939693	−	0.342020i	$-0.888889\pi$
$937$	−1.62593	−	1.06939i	−1.62593	−	1.06939i	−0.686242	−	0.727374i	$-0.740741\pi$
$938$		0			0
$939$	−0.231732	−	1.69658i	−0.231732	−	1.69658i
$940$		0			0
$941$		0			0		−0.565607	−	0.824675i	$-0.691358\pi$
$941$		0			0		0.565607	+	0.824675i	$0.308642\pi$
$942$		0			0
$943$		0			0
$944$	1.84416	+	0.671218i	1.84416	+	0.671218i
$945$		0			0
$946$	0.647381	−	0.235627i	0.647381	−	0.235627i
$947$	−0.736715	−	0.570997i	−0.736715	−	0.570997i	0.173648	−	0.984808i	$-0.444444\pi$
$947$	−0.736715	−	0.570997i	−0.736715	−	0.570997i	−0.910363	+	0.413811i	$0.864198\pi$
$948$		0			0
$949$		0			0
$950$	−0.711704	−	1.84336i	−0.711704	−	1.84336i
$951$		0			0
$952$		0			0
$953$	−0.143081	−	0.477924i	−0.143081	−	0.477924i	0.856167	−	0.516699i	$-0.172840\pi$
$953$	−0.143081	−	0.477924i	−0.143081	−	0.477924i	−0.999248	+	0.0387754i	$0.987654\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.360178	+	0.932884i	−0.360178	+	0.932884i
$962$		0			0
$963$	0.423089	−	1.95320i	0.423089	−	1.95320i
$964$	−1.15057	−	1.54548i	−1.15057	−	1.54548i
$965$		0			0
$966$		0			0
$967$		0			0		0.323734	−	0.946148i	$-0.395062\pi$
$967$		0			0		−0.323734	+	0.946148i	$0.604938\pi$
$968$	0.159493	−	1.63973i	0.159493	−	1.63973i
$969$	3.13222	+	1.89031i	3.13222	+	1.89031i
$970$		0			0
$971$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$971$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$972$	−0.981255	−	0.192712i	−0.981255	−	0.192712i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.209607	−	0.612601i	0.209607	−	0.612601i	−0.790393	−	0.612601i	$-0.790123\pi$
$977$	0.209607	−	0.612601i	0.209607	−	0.612601i	1.00000			$0$
$978$	−0.777311	+	0.152659i	−0.777311	+	0.152659i
$979$	−0.232808	+	0.903815i	−0.232808	+	0.903815i
$980$		0			0
$981$		0			0
$982$	0.422383	+	0.979194i	0.422383	+	0.979194i
$983$		0			0		0.360178	−	0.932884i	$-0.382716\pi$
$983$		0			0		−0.360178	+	0.932884i	$0.617284\pi$
$984$	−0.693582	−	1.60790i	−0.693582	−	1.60790i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.286803	−	0.957990i	$-0.592593\pi$
$991$		0			0		0.286803	+	0.957990i	$0.407407\pi$
$992$		0			0
$993$	−0.342354	−	1.32910i	−0.342354	−	1.32910i
$994$		0			0
$995$		0			0
$996$	−0.161769	−	1.66313i	−0.161769	−	1.66313i
$997$		0			0		−0.790393	−	0.612601i	$-0.790123\pi$
$997$		0			0		0.790393	+	0.612601i	$0.209877\pi$
$998$	1.48545	−	0.540660i	1.48545	−	0.540660i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1944.1.bh.a.331.1	✓	54
8.3	odd	2	CM	1944.1.bh.a.331.1	✓	54
243.58	even	81	inner	1944.1.bh.a.787.1	yes	54
1944.787	odd	162	inner	1944.1.bh.a.787.1	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1944.1.bh.a.331.1	✓	54	1.1	even	1	trivial
1944.1.bh.a.331.1	✓	54	8.3	odd	2	CM
1944.1.bh.a.787.1	yes	54	243.58	even	81	inner
1944.1.bh.a.787.1	yes	54	1944.787	odd	162	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:	\( N \)	\(=\)	\( 1944 = 2^{3} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1944.bh (of order \(162\), degree \(54\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.740544 + 0.672008i) q^{2} +(0.0193913 - 0.999812i) q^{3} +(0.0968109 - 0.995303i) q^{4} +(0.657521 + 0.753436i) q^{6} +(0.597159 + 0.802123i) q^{8} +(-0.999248 - 0.0387754i) q^{9} +O(q^{10})\)	\(q+(-0.740544 + 0.672008i) q^{2} +(0.0193913 - 0.999812i) q^{3} +(0.0968109 - 0.995303i) q^{4} +(0.657521 + 0.753436i) q^{6} +(0.597159 + 0.802123i) q^{8} +(-0.999248 - 0.0387754i) q^{9} +(-0.586047 + 1.51790i) q^{11} +(-0.993238 - 0.116093i) q^{12} +(-0.981255 - 0.192712i) q^{16} +(-1.27054 - 1.34669i) q^{17} +(0.766044 - 0.642788i) q^{18} +(-0.566717 - 1.89297i) q^{19} +(-0.586047 - 1.51790i) q^{22} +(0.813552 - 0.581492i) q^{24} +(-0.790393 - 0.612601i) q^{25} +(-0.0581448 + 0.998308i) q^{27} +(0.856167 - 0.516699i) q^{32} +(1.50625 + 0.615371i) q^{33} +(1.84588 + 0.143473i) q^{34} +(-0.135331 + 0.990800i) q^{36} +(1.69177 + 1.02099i) q^{38} +(0.370718 - 1.71143i) q^{41} +(-0.00821044 + 0.423328i) q^{43} +(1.45403 + 0.730243i) q^{44} +(-0.211704 + 0.977334i) q^{48} +(-0.875558 - 0.483113i) q^{49} +(0.996993 - 0.0774924i) q^{50} +(-1.37108 + 1.24419i) q^{51} +(-0.627812 - 0.778365i) q^{54} +(-1.90360 + 0.529904i) q^{57} +(-1.93894 - 0.303245i) q^{59} +(-0.286803 + 0.957990i) q^{64} +(-1.52898 + 0.556502i) q^{66} +(0.266006 - 0.422048i) q^{67} +(-1.46337 + 1.13420i) q^{68} +(-0.565607 - 0.824675i) q^{72} +(0.369181 - 0.855857i) q^{73} +(-0.627812 + 0.778365i) q^{75} +(-1.93894 + 0.380796i) q^{76} +(0.996993 + 0.0774924i) q^{81} +(0.875558 + 1.51651i) q^{82} +(0.353752 + 1.63310i) q^{83} +(-0.278400 - 0.319011i) q^{86} +(-1.56750 + 0.436345i) q^{88} +(0.569728 - 0.0665916i) q^{89} +(-0.500000 - 0.866025i) q^{96} +(-0.366212 - 1.07030i) q^{97} +(0.973045 - 0.230616i) q^{98} +(0.644463 - 1.49403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q - 27 q^{68} - 27 q^{96}+O(q^{100}) \) 54 * q - 27 * q^68 - 27 * q^96

Introduction

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Modular forms

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Database

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