LMFDB - Embedded newform 1944.1.bh.a.211.1

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			211.1
Root			$-0.856167 - 0.516699i$ of defining polynomial
Character	$\chi$	$=$	1944.211
Dual form			1944.1.bh.a.691.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0968109 - 0.995303i) q^{2} +(-0.999248 - 0.0387754i) q^{3} +(-0.981255 - 0.192712i) q^{4} +(-0.135331 + 0.990800i) q^{6} +(-0.286803 + 0.957990i) q^{8} +(0.996993 + 0.0774924i) q^{9} +O(q^{10})$	\(q+(0.0968109 - 0.995303i) q^{2} +(-0.999248 - 0.0387754i) q^{3} +(-0.981255 - 0.192712i) q^{4} +(-0.135331 + 0.990800i) q^{6} +(-0.286803 + 0.957990i) q^{8} +(0.996993 + 0.0774924i) q^{9} +(-0.479478 - 0.435104i) q^{11} +(0.973045 + 0.230616i) q^{12} +(0.925724 + 0.378200i) q^{16} +(-0.0830226 + 1.42544i) q^{17} +(0.173648 - 0.984808i) q^{18} +(-1.59118 + 1.04654i) q^{19} +(-0.479478 + 0.435104i) q^{22} +(0.323734 - 0.946148i) q^{24} +(0.249441 + 0.968390i) q^{25} +(-0.993238 - 0.116093i) q^{27} +(0.466044 - 0.884762i) q^{32} +(0.462247 + 0.453368i) q^{33} +(1.41071 + 0.220631i) q^{34} +(-0.963371 - 0.268173i) q^{36} +(0.887578 + 1.68503i) q^{38} +(-0.970819 - 0.441291i) q^{41} +(1.81936 + 0.0705993i) q^{43} +(0.386641 + 0.519349i) q^{44} +(-0.910363 - 0.413811i) q^{48} +(0.533204 + 0.845986i) q^{49} +(0.987990 - 0.154519i) q^{50} +(0.138232 - 1.42115i) q^{51} +(-0.211704 + 0.977334i) q^{54} +(1.63057 - 0.984052i) q^{57} +(1.76304 + 0.565295i) q^{59} +(-0.835488 - 0.549509i) q^{64} +(0.495989 - 0.416184i) q^{66} +(0.755407 + 1.57980i) q^{67} +(0.356167 - 1.38272i) q^{68} +(-0.360178 + 0.932884i) q^{72} +(0.776286 + 0.822815i) q^{73} +(-0.211704 - 0.977334i) q^{75} +(1.76304 - 0.720280i) q^{76} +(0.987990 + 0.154519i) q^{81} +(-0.533204 + 0.923537i) q^{82} +(-0.721153 + 0.327804i) q^{83} +(0.246401 - 1.80398i) q^{86} +(0.554341 - 0.334546i) q^{88} +(-1.62593 + 0.385353i) q^{89} +(-0.500000 + 0.866025i) q^{96} +(0.569364 - 0.441290i) q^{97} +(0.893633 - 0.448799i) q^{98} +(-0.444319 - 0.470951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1944\mathbb{Z}\right)^\times$.

$n$	$487$	$973$	$1217$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{43}{81}\right)$

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 $

$2$	0.0968109	−	0.995303i	0.0968109	−	0.995303i
$2$	0.0968109	−	0.995303i	0.0968109	−	0.995303i
$3$	−0.999248	−	0.0387754i	−0.999248	−	0.0387754i
$3$	−0.999248	−	0.0387754i	−0.999248	−	0.0387754i
$4$	−0.981255	−	0.192712i	−0.981255	−	0.192712i
$5$		0			0		−0.790393	−	0.612601i	$-0.790123\pi$
$5$		0			0		0.790393	+	0.612601i	$0.209877\pi$
$6$	−0.135331	+	0.990800i	−0.135331	+	0.990800i
$7$		0			0		−0.875558	−	0.483113i	$-0.839506\pi$
$7$		0			0		0.875558	+	0.483113i	$0.160494\pi$
$8$	−0.286803	+	0.957990i	−0.286803	+	0.957990i
$9$	0.996993	+	0.0774924i	0.996993	+	0.0774924i
$10$		0			0
$11$	−0.479478	−	0.435104i	−0.479478	−	0.435104i	0.396080	−	0.918216i	$-0.370370\pi$
$11$	−0.479478	−	0.435104i	−0.479478	−	0.435104i	−0.875558	+	0.483113i	$0.839506\pi$
$12$	0.973045	+	0.230616i	0.973045	+	0.230616i
$13$		0			0		−0.713930	−	0.700217i	$-0.753086\pi$
$13$		0			0		0.713930	+	0.700217i	$0.246914\pi$
$14$		0			0
$15$		0			0
$16$	0.925724	+	0.378200i	0.925724	+	0.378200i
$17$	−0.0830226	+	1.42544i	−0.0830226	+	1.42544i	0.657521	+	0.753436i	$0.271605\pi$
$17$	−0.0830226	+	1.42544i	−0.0830226	+	1.42544i	−0.740544	+	0.672008i	$0.765432\pi$
$18$	0.173648	−	0.984808i	0.173648	−	0.984808i
$19$	−1.59118	+	1.04654i	−1.59118	+	1.04654i	−0.627812	+	0.778365i	$0.716049\pi$
$19$	−1.59118	+	1.04654i	−1.59118	+	1.04654i	−0.963371	+	0.268173i	$0.913580\pi$
$20$		0			0
$21$		0			0
$22$	−0.479478	+	0.435104i	−0.479478	+	0.435104i
$23$		0			0		0.0193913	−	0.999812i	$-0.493827\pi$
$23$		0			0		−0.0193913	+	0.999812i	$0.506173\pi$
$24$	0.323734	−	0.946148i	0.323734	−	0.946148i
$25$	0.249441	+	0.968390i	0.249441	+	0.968390i
$26$		0			0
$27$	−0.993238	−	0.116093i	−0.993238	−	0.116093i
$28$		0			0
$29$		0			0		0.431386	−	0.902167i	$-0.358025\pi$
$29$		0			0		−0.431386	+	0.902167i	$0.641975\pi$
$30$		0			0
$31$		0			0		0.360178	−	0.932884i	$-0.382716\pi$
$31$		0			0		−0.360178	+	0.932884i	$0.617284\pi$
$32$	0.466044	−	0.884762i	0.466044	−	0.884762i
$33$	0.462247	+	0.453368i	0.462247	+	0.453368i
$34$	1.41071	+	0.220631i	1.41071	+	0.220631i
$35$		0			0
$36$	−0.963371	−	0.268173i	−0.963371	−	0.268173i
$37$		0			0		0.993238	−	0.116093i	$-0.0370370\pi$
$37$		0			0		−0.993238	+	0.116093i	$0.962963\pi$
$38$	0.887578	+	1.68503i	0.887578	+	1.68503i
$39$		0			0
$40$		0			0
$41$	−0.970819	−	0.441291i	−0.970819	−	0.441291i	−0.135331	−	0.990800i	$-0.543210\pi$
$41$	−0.970819	−	0.441291i	−0.970819	−	0.441291i	−0.835488	+	0.549509i	$0.814815\pi$
$42$		0			0
$43$	1.81936	+	0.0705993i	1.81936	+	0.0705993i	0.925724	−	0.378200i	$-0.123457\pi$
$43$	1.81936	+	0.0705993i	1.81936	+	0.0705993i	0.893633	+	0.448799i	$0.148148\pi$
$44$	0.386641	+	0.519349i	0.386641	+	0.519349i
$45$		0			0
$46$		0			0
$47$		0			0		−0.360178	−	0.932884i	$-0.617284\pi$
$47$		0			0		0.360178	+	0.932884i	$0.382716\pi$
$48$	−0.910363	−	0.413811i	−0.910363	−	0.413811i
$49$	0.533204	+	0.845986i	0.533204	+	0.845986i
$50$	0.987990	−	0.154519i	0.987990	−	0.154519i
$51$	0.138232	−	1.42115i	0.138232	−	1.42115i
$52$		0			0
$53$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$53$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$54$	−0.211704	+	0.977334i	−0.211704	+	0.977334i
$55$		0			0
$56$		0			0
$57$	1.63057	−	0.984052i	1.63057	−	0.984052i
$58$		0			0
$59$	1.76304	+	0.565295i	1.76304	+	0.565295i	0.996993	−	0.0774924i	$-0.0246914\pi$
$59$	1.76304	+	0.565295i	1.76304	+	0.565295i	0.766044	+	0.642788i	$0.222222\pi$
$60$		0			0
$61$		0			0		0.981255	−	0.192712i	$-0.0617284\pi$
$61$		0			0		−0.981255	+	0.192712i	$0.938272\pi$
$62$		0			0
$63$		0			0
$64$	−0.835488	−	0.549509i	−0.835488	−	0.549509i
$65$		0			0
$66$	0.495989	−	0.416184i	0.495989	−	0.416184i
$67$	0.755407	+	1.57980i	0.755407	+	1.57980i	0.813552	+	0.581492i	$0.197531\pi$
$67$	0.755407	+	1.57980i	0.755407	+	1.57980i	−0.0581448	+	0.998308i	$0.518519\pi$
$68$	0.356167	−	1.38272i	0.356167	−	1.38272i
$69$		0			0
$70$		0			0
$71$		0			0		−0.973045	−	0.230616i	$-0.925926\pi$
$71$		0			0		0.973045	+	0.230616i	$0.0740741\pi$
$72$	−0.360178	+	0.932884i	−0.360178	+	0.932884i
$73$	0.776286	+	0.822815i	0.776286	+	0.822815i	0.987990	−	0.154519i	$-0.0493827\pi$
$73$	0.776286	+	0.822815i	0.776286	+	0.822815i	−0.211704	+	0.977334i	$0.567901\pi$
$74$		0			0
$75$	−0.211704	−	0.977334i	−0.211704	−	0.977334i
$76$	1.76304	−	0.720280i	1.76304	−	0.720280i
$77$		0			0
$78$		0			0
$79$		0			0		−0.813552	−	0.581492i	$-0.802469\pi$
$79$		0			0		0.813552	+	0.581492i	$0.197531\pi$
$80$		0			0
$81$	0.987990	+	0.154519i	0.987990	+	0.154519i
$82$	−0.533204	+	0.923537i	−0.533204	+	0.923537i
$83$	−0.721153	+	0.327804i	−0.721153	+	0.327804i	−0.740544	−	0.672008i	$-0.765432\pi$
$83$	−0.721153	+	0.327804i	−0.721153	+	0.327804i	0.0193913	+	0.999812i	$0.493827\pi$
$84$		0			0
$85$		0			0
$86$	0.246401	−	1.80398i	0.246401	−	1.80398i
$87$		0			0
$88$	0.554341	−	0.334546i	0.554341	−	0.334546i
$89$	−1.62593	+	0.385353i	−1.62593	+	0.385353i	−0.939693	−	0.342020i	$-0.888889\pi$
$89$	−1.62593	+	0.385353i	−1.62593	+	0.385353i	−0.686242	+	0.727374i	$0.740741\pi$
$90$		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
$97$	0.569364	−	0.441290i	0.569364	−	0.441290i	−0.286803	−	0.957990i	$-0.592593\pi$
$97$	0.569364	−	0.441290i	0.569364	−	0.441290i	0.856167	+	0.516699i	$0.172840\pi$
$98$	0.893633	−	0.448799i	0.893633	−	0.448799i
$99$	−0.444319	−	0.470951i	−0.444319	−	0.470951i
$100$	−0.0581448	−	0.998308i	−0.0581448	−	0.998308i
$101$		0			0		0.323734	−	0.946148i	$-0.395062\pi$
$101$		0			0		−0.323734	+	0.946148i	$0.604938\pi$
$102$	−1.40109	−	0.275166i	−1.40109	−	0.275166i
$103$		0			0		−0.211704	−	0.977334i	$-0.567901\pi$
$103$		0			0		0.211704	+	0.977334i	$0.432099\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.87373	−	0.681983i	−1.87373	−	0.681983i	−0.963371	−	0.268173i	$-0.913580\pi$
$107$	−1.87373	−	0.681983i	−1.87373	−	0.681983i	−0.910363	−	0.413811i	$-0.864198\pi$
$108$	0.952248	+	0.305326i	0.952248	+	0.305326i
$109$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$109$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.573175	−	0.0222418i	0.573175	−	0.0222418i	0.249441	−	0.968390i	$-0.419753\pi$
$113$	0.573175	−	0.0222418i	0.573175	−	0.0222418i	0.323734	+	0.946148i	$0.395062\pi$
$114$	−0.821573	−	1.71817i	−0.821573	−	1.71817i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.733321	−	1.70003i	0.733321	−	1.70003i
$119$		0			0
$120$		0			0
$121$	−0.0562263	−	0.578057i	−0.0562263	−	0.578057i
$122$		0			0
$123$	0.952978	+	0.478603i	0.952978	+	0.478603i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.597159	−	0.802123i	$-0.296296\pi$
$127$		0			0		−0.597159	+	0.802123i	$0.703704\pi$
$128$	−0.627812	+	0.778365i	−0.627812	+	0.778365i
$129$	−1.81525	−	0.141092i	−1.81525	−	0.141092i
$130$		0			0
$131$	−1.22178	−	1.51477i	−1.22178	−	1.51477i	−0.790393	−	0.612601i	$-0.790123\pi$
$131$	−1.22178	−	1.51477i	−1.22178	−	1.51477i	−0.431386	−	0.902167i	$-0.641975\pi$
$132$	−0.366212	−	0.533951i	−0.366212	−	0.533951i
$133$		0			0
$134$	1.64551	−	0.598917i	1.64551	−	0.598917i
$135$		0			0
$136$	−1.34175	−	0.488357i	−1.34175	−	0.488357i
$137$	1.20963	+	0.336724i	1.20963	+	0.336724i	0.813552	−	0.581492i	$-0.197531\pi$
$137$	1.20963	+	0.336724i	1.20963	+	0.336724i	0.396080	+	0.918216i	$0.370370\pi$
$138$		0			0
$139$	−1.73009	+	0.954621i	−1.73009	+	0.954621i	−0.790393	+	0.612601i	$0.790123\pi$
$139$	−1.73009	+	0.954621i	−1.73009	+	0.954621i	−0.939693	+	0.342020i	$0.888889\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.893633	+	0.448799i	0.893633	+	0.448799i
$145$		0			0
$146$	0.894103	−	0.692982i	0.894103	−	0.692982i
$147$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$148$		0			0
$149$		0			0		0.963371	−	0.268173i	$-0.0864198\pi$
$149$		0			0		−0.963371	+	0.268173i	$0.913580\pi$
$150$	−0.993238	+	0.116093i	−0.993238	+	0.116093i
$151$		0			0		0.211704	−	0.977334i	$-0.432099\pi$
$151$		0			0		−0.211704	+	0.977334i	$0.567901\pi$
$152$	−0.546216	−	1.82449i	−0.546216	−	1.82449i
$153$	−0.193234	+	1.41472i	−0.193234	+	1.41472i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.135331	−	0.990800i	$-0.456790\pi$
$157$		0			0		−0.135331	+	0.990800i	$0.543210\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.249441	−	0.968390i	0.249441	−	0.968390i
$163$	0.686242	+	1.18861i	0.686242	+	1.18861i	0.973045	+	0.230616i	$0.0740741\pi$
$163$	0.686242	+	1.18861i	0.686242	+	1.18861i	−0.286803	+	0.957990i	$0.592593\pi$
$164$	0.867579	+	0.620108i	0.867579	+	0.620108i
$165$		0			0
$166$	0.256449	+	0.749500i	0.256449	+	0.749500i
$167$		0			0		0.925724	−	0.378200i	$-0.123457\pi$
$167$		0			0		−0.925724	+	0.378200i	$0.876543\pi$
$168$		0			0
$169$	0.0193913	+	0.999812i	0.0193913	+	0.999812i
$170$		0			0
$171$	−1.66750	+	0.920086i	−1.66750	+	0.920086i
$172$	−1.77165	−	0.419888i	−1.77165	−	0.419888i
$173$		0			0		0.952248	−	0.305326i	$-0.0987654\pi$
$173$		0			0		−0.952248	+	0.305326i	$0.901235\pi$
$174$		0			0
$175$		0			0
$176$	−0.279309	−	0.584124i	−0.279309	−	0.584124i
$177$	−1.73979	−	0.633232i	−1.73979	−	0.633232i
$178$	0.226135	+	1.65560i	0.226135	+	1.65560i
$179$	0.0971586	+	0.0639022i	0.0971586	+	0.0639022i	0.597159	−	0.802123i	$-0.296296\pi$
$179$	0.0971586	+	0.0639022i	0.0971586	+	0.0639022i	−0.500000	+	0.866025i	$0.666667\pi$
$180$		0			0
$181$		0			0		−0.893633	−	0.448799i	$-0.851852\pi$
$181$		0			0		0.893633	+	0.448799i	$0.148148\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.660023	−	0.647346i	0.660023	−	0.647346i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.565607	−	0.824675i	$-0.691358\pi$
$191$		0			0		0.565607	+	0.824675i	$0.308642\pi$
$192$	0.813552	+	0.581492i	0.813552	+	0.581492i
$193$	−1.97449	+	0.308805i	−1.97449	+	0.308805i	−0.981255	+	0.192712i	$0.938272\pi$
$193$	−1.97449	+	0.308805i	−1.97449	+	0.308805i	−0.993238	+	0.116093i	$0.962963\pi$
$194$	−0.384097	−	0.609411i	−0.384097	−	0.609411i
$195$		0			0
$196$	−0.360178	−	0.932884i	−0.360178	−	0.932884i
$197$		0			0		−0.993238	−	0.116093i	$-0.962963\pi$
$197$		0			0		0.993238	+	0.116093i	$0.0370370\pi$
$198$	−0.511754	+	0.396639i	−0.511754	+	0.396639i
$199$		0			0		−0.597159	−	0.802123i	$-0.703704\pi$
$199$		0			0		0.597159	+	0.802123i	$0.296296\pi$
$200$	−0.999248	−	0.0387754i	−0.999248	−	0.0387754i
$201$	−0.693582	−	1.60790i	−0.693582	−	1.60790i
$202$		0			0
$203$		0			0
$204$	−0.409515	+	1.36787i	−0.409515	+	1.36787i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.21829	+	0.190537i	1.21829	+	0.190537i
$210$		0			0
$211$	−0.925785	+	1.75756i	−0.925785	+	1.75756i	−0.360178	+	0.932884i	$0.617284\pi$
$211$	−0.925785	+	1.75756i	−0.925785	+	1.75756i	−0.565607	+	0.824675i	$0.691358\pi$
$212$		0			0
$213$		0			0
$214$	−0.860178	+	1.79891i	−0.860178	+	1.79891i
$215$		0			0
$216$	0.396080	−	0.918216i	0.396080	−	0.918216i
$217$		0			0
$218$		0			0
$219$	−0.743797	−	0.852297i	−0.743797	−	0.852297i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.657521	−	0.753436i	$-0.728395\pi$
$223$		0			0		0.657521	+	0.753436i	$0.271605\pi$
$224$		0			0
$225$	0.173648	+	0.984808i	0.173648	+	0.984808i
$226$	0.0333522	−	0.572636i	0.0333522	−	0.572636i
$227$	1.50625	+	0.615371i	1.50625	+	0.615371i	0.973045	−	0.230616i	$-0.0740741\pi$
$227$	1.50625	+	0.615371i	1.50625	+	0.615371i	0.533204	+	0.845986i	$0.320988\pi$
$228$	−1.78964	+	0.651376i	−1.78964	+	0.651376i
$229$		0			0		0.565607	−	0.824675i	$-0.308642\pi$
$229$		0			0		−0.565607	+	0.824675i	$0.691358\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.185740	−	0.196873i	0.185740	−	0.196873i	−0.627812	−	0.778365i	$-0.716049\pi$
$233$	0.185740	−	0.196873i	0.185740	−	0.196873i	0.813552	+	0.581492i	$0.197531\pi$
$234$		0			0
$235$		0			0
$236$	−1.62105	−	0.894458i	−1.62105	−	0.894458i
$237$		0			0
$238$		0			0
$239$		0			0		−0.981255	−	0.192712i	$-0.938272\pi$
$239$		0			0		0.981255	+	0.192712i	$0.0617284\pi$
$240$		0			0
$241$	0.165773	−	1.70429i	0.165773	−	1.70429i	−0.431386	−	0.902167i	$-0.641975\pi$
$241$	0.165773	−	1.70429i	0.165773	−	1.70429i	0.597159	−	0.802123i	$-0.296296\pi$
$242$	−0.580785			−0.580785
$243$	−0.981255	−	0.192712i	−0.981255	−	0.192712i
$244$		0			0
$245$		0			0
$246$	0.568614	−	0.902167i	0.568614	−	0.902167i
$247$		0			0
$248$		0			0
$249$	0.733321	−	0.299595i	0.733321	−	0.299595i
$250$		0			0
$251$	−0.0555313	+	0.185488i	−0.0555313	+	0.185488i	−0.981255	−	0.192712i	$-0.938272\pi$
$251$	−0.0555313	+	0.185488i	−0.0555313	+	0.185488i	0.925724	+	0.378200i	$0.123457\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.713930	+	0.700217i	0.713930	+	0.700217i
$257$	−0.968508	+	1.41212i	−0.968508	+	1.41212i	−0.0581448	+	0.998308i	$0.518519\pi$
$257$	−0.968508	+	1.41212i	−0.968508	+	1.41212i	−0.910363	+	0.413811i	$0.864198\pi$
$258$	−0.316166	+	1.79306i	−0.316166	+	1.79306i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.62593	+	1.06939i	−1.62593	+	1.06939i
$263$		0			0		−0.657521	−	0.753436i	$-0.728395\pi$
$263$		0			0		0.657521	+	0.753436i	$0.271605\pi$
$264$	−0.566896	+	0.312800i	−0.566896	+	0.312800i
$265$		0			0
$266$		0			0
$267$	1.63965	−	0.322017i	1.63965	−	0.322017i
$268$	−0.436800	−	1.69576i	−0.436800	−	1.69576i
$269$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$269$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$270$		0			0
$271$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$271$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$272$	−0.615959	+	1.28817i	−0.615959	+	1.28817i
$273$		0			0
$274$	0.452248	−	1.17135i	0.452248	−	1.17135i
$275$	0.301748	−	0.572855i	0.301748	−	0.572855i
$276$		0			0
$277$		0			0		−0.987990	−	0.154519i	$-0.950617\pi$
$277$		0			0		0.987990	+	0.154519i	$0.0493827\pi$
$278$	0.782646	+	1.81438i	0.782646	+	1.81438i
$279$		0			0
$280$		0			0
$281$	−0.925785	−	1.75756i	−0.925785	−	1.75756i	−0.565607	−	0.824675i	$-0.691358\pi$
$281$	−0.925785	−	1.75756i	−0.925785	−	1.75756i	−0.360178	−	0.932884i	$-0.617284\pi$
$282$		0			0
$283$	0.971639	−	0.694486i	0.971639	−	0.694486i	0.0193913	−	0.999812i	$-0.493827\pi$
$283$	0.971639	−	0.694486i	0.971639	−	0.694486i	0.952248	+	0.305326i	$0.0987654\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.533204	−	0.845986i	0.533204	−	0.845986i
$289$	−1.03176	−	0.120595i	−1.03176	−	0.120595i
$290$		0			0
$291$	−0.586047	+	0.418881i	−0.586047	+	0.418881i
$292$	−0.603168	−	0.956991i	−0.603168	−	0.956991i
$293$		0			0		0.987990	−	0.154519i	$-0.0493827\pi$
$293$		0			0		−0.987990	+	0.154519i	$0.950617\pi$
$294$	−0.910363	+	0.413811i	−0.910363	+	0.413811i
$295$		0			0
$296$		0			0
$297$	0.425724	+	0.487826i	0.425724	+	0.487826i
$298$		0			0
$299$		0			0
$300$	0.0193913	+	0.999812i	0.0193913	+	0.999812i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−1.86880	+	0.367020i	−1.86880	+	0.367020i
$305$		0			0
$306$	1.38937	+	0.329287i	1.38937	+	0.329287i
$307$	0.226135	+	0.148732i	0.226135	+	0.148732i	0.657521	−	0.753436i	$-0.271605\pi$
$307$	0.226135	+	0.148732i	0.226135	+	0.148732i	−0.431386	+	0.902167i	$0.641975\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.249441	−	0.968390i	$-0.419753\pi$
$311$		0			0		−0.249441	+	0.968390i	$0.580247\pi$
$312$		0			0
$313$	0.887578	−	0.284590i	0.887578	−	0.284590i	0.173648	−	0.984808i	$-0.444444\pi$
$313$	0.887578	−	0.284590i	0.887578	−	0.284590i	0.713930	+	0.700217i	$0.246914\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.0193913	−	0.999812i	$-0.506173\pi$
$317$		0			0		0.0193913	+	0.999812i	$0.493827\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	1.84588	+	0.754125i	1.84588	+	0.754125i
$322$		0			0
$323$	−1.35968	−	2.35503i	−1.35968	−	2.35503i
$324$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$325$		0			0
$326$	1.24946	−	0.567948i	1.24946	−	0.567948i
$327$		0			0
$328$	0.701187	−	0.803471i	0.701187	−	0.803471i
$329$		0			0
$330$		0			0
$331$	−0.0995634	+	0.0600868i	−0.0995634	+	0.0600868i	−0.565607	−	0.824675i	$-0.691358\pi$
$331$	−0.0995634	+	0.0600868i	−0.0995634	+	0.0600868i	0.466044	+	0.884762i	$0.345679\pi$
$332$	0.770807	−	0.182685i	0.770807	−	0.182685i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.186530	+	0.0519240i	−0.186530	+	0.0519240i	−0.360178	−	0.932884i	$-0.617284\pi$
$337$	−0.186530	+	0.0519240i	−0.186530	+	0.0519240i	0.173648	+	0.984808i	$0.444444\pi$
$338$	0.996993	+	0.0774924i	0.996993	+	0.0774924i
$339$	−0.573606			−0.573606
$340$		0			0
$341$		0			0
$342$	0.754332	+	1.74874i	0.754332	+	1.74874i
$343$		0			0
$344$	−0.589431	+	1.72268i	−0.589431	+	1.72268i
$345$		0			0
$346$		0			0
$347$	1.29678	−	0.715532i	1.29678	−	0.715532i	0.323734	−	0.946148i	$-0.395062\pi$
$347$	1.29678	−	0.715532i	1.29678	−	0.715532i	0.973045	+	0.230616i	$0.0740741\pi$
$348$		0			0
$349$		0			0		−0.963371	−	0.268173i	$-0.913580\pi$
$349$		0			0		0.963371	+	0.268173i	$0.0864198\pi$
$350$		0			0
$351$		0			0
$352$	−0.608421	+	0.221447i	−0.608421	+	0.221447i
$353$	−0.860178	+	0.0668583i	−0.860178	+	0.0668583i	−0.500000	−	0.866025i	$-0.666667\pi$
$353$	−0.860178	+	0.0668583i	−0.860178	+	0.0668583i	−0.360178	+	0.932884i	$0.617284\pi$
$354$	−0.798689	+	1.67032i	−0.798689	+	1.67032i
$355$		0			0
$356$	1.66972	−	0.0647927i	1.66972	−	0.0647927i
$357$		0			0
$358$	0.0730081	−	0.0905158i	0.0730081	−	0.0905158i
$359$		0			0		0.597159	−	0.802123i	$-0.296296\pi$
$359$		0			0		−0.597159	+	0.802123i	$0.703704\pi$
$360$		0			0
$361$	1.04054	−	2.41225i	1.04054	−	2.41225i
$362$		0			0
$363$	0.0337697	+	0.579803i	0.0337697	+	0.579803i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.533204	−	0.845986i	$-0.320988\pi$
$367$		0			0		−0.533204	+	0.845986i	$0.679012\pi$
$368$		0			0
$369$	−0.933703	−	0.515196i	−0.933703	−	0.515196i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.999248	−	0.0387754i	$-0.0123457\pi$
$373$		0			0		−0.999248	+	0.0387754i	$0.987654\pi$
$374$	−0.580408	−	0.719593i	−0.580408	−	0.719593i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.875875	−	0.318793i	−0.875875	−	0.318793i	−0.135331	−	0.990800i	$-0.543210\pi$
$379$	−0.875875	−	0.318793i	−0.875875	−	0.318793i	−0.740544	+	0.672008i	$0.765432\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.211704	−	0.977334i	$-0.567901\pi$
$383$		0			0		0.211704	+	0.977334i	$0.432099\pi$
$384$	0.657521	−	0.753436i	0.657521	−	0.753436i
$385$		0			0
$386$	0.116202	+	1.99511i	0.116202	+	1.99511i
$387$	1.80841	+	0.211373i	1.80841	+	0.211373i
$388$	−0.643733	+	0.323295i	−0.643733	+	0.323295i
$389$		0			0		0.790393	−	0.612601i	$-0.209877\pi$
$389$		0			0		−0.790393	+	0.612601i	$0.790123\pi$
$390$		0			0
$391$		0			0
$392$	−0.963371	+	0.268173i	−0.963371	+	0.268173i
$393$	1.16212	+	1.56100i	1.16212	+	1.56100i
$394$		0			0
$395$		0			0
$396$	0.345233	+	0.547749i	0.345233	+	0.547749i
$397$		0			0		0.973045	−	0.230616i	$-0.0740741\pi$
$397$		0			0		−0.973045	+	0.230616i	$0.925926\pi$
$398$		0			0
$399$		0			0
$400$	−0.135331	+	0.990800i	−0.135331	+	0.990800i
$401$	−0.278400	+	0.319011i	−0.278400	+	0.319011i	−0.875558	−	0.483113i	$-0.839506\pi$
$401$	−0.278400	+	0.319011i	−0.278400	+	0.319011i	0.597159	+	0.802123i	$0.296296\pi$
$402$	−1.66750	+	0.534661i	−1.66750	+	0.534661i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.32180	+	0.540016i	1.32180	+	0.540016i
$409$	−0.623752	−	1.82298i	−0.623752	−	1.82298i	−0.565607	−	0.824675i	$-0.691358\pi$
$409$	−0.623752	−	1.82298i	−0.623752	−	1.82298i	−0.0581448	−	0.998308i	$-0.518519\pi$
$410$		0			0
$411$	−1.19567	−	0.383375i	−1.19567	−	0.383375i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.76580	−	0.886818i	1.76580	−	0.886818i
$418$	0.307586	−	1.19412i	0.307586	−	1.19412i
$419$	0.592070	+	1.23821i	0.592070	+	1.23821i	0.952248	+	0.305326i	$0.0987654\pi$
$419$	0.592070	+	1.23821i	0.592070	+	1.23821i	−0.360178	+	0.932884i	$0.617284\pi$
$420$		0			0
$421$		0			0		−0.135331	−	0.990800i	$-0.543210\pi$
$421$		0			0		0.135331	+	0.990800i	$0.456790\pi$
$422$	1.65968	+	1.09159i	1.65968	+	1.09159i
$423$		0			0
$424$		0			0
$425$	−1.40109	+	0.275166i	−1.40109	+	0.275166i
$426$		0			0
$427$		0			0
$428$	1.70718	+	1.03029i	1.70718	+	1.03029i
$429$		0			0
$430$		0			0
$431$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$431$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$432$	−0.875558	−	0.483113i	−0.875558	−	0.483113i
$433$	0.0866300	−	0.491303i	0.0866300	−	0.491303i	−0.910363	−	0.413811i	$-0.864198\pi$
$433$	0.0866300	−	0.491303i	0.0866300	−	0.491303i	0.996993	−	0.0774924i	$-0.0246914\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.920301	+	0.657792i	−0.920301	+	0.657792i
$439$		0			0		−0.360178	−	0.932884i	$-0.617284\pi$
$439$		0			0		0.360178	+	0.932884i	$0.382716\pi$
$440$		0			0
$441$	0.466044	+	0.884762i	0.466044	+	0.884762i
$442$		0			0
$443$	1.99699	+	0.0774924i	1.99699	+	0.0774924i	1.00000			$0$
$443$	1.99699	+	0.0774924i	1.99699	+	0.0774924i	0.996993	+	0.0774924i	$0.0246914\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.96262	+	0.229397i	−1.96262	+	0.229397i	−0.999248	−	0.0387754i	$-0.987654\pi$
$449$	−1.96262	+	0.229397i	−1.96262	+	0.229397i	−0.963371	+	0.268173i	$0.913580\pi$
$450$	0.996993	−	0.0774924i	0.996993	−	0.0774924i
$451$	0.273479	+	0.633997i	0.273479	+	0.633997i
$452$	−0.566717	−	0.0886330i	−0.566717	−	0.0886330i
$453$		0			0
$454$	0.758301	−	1.43960i	0.758301	−	1.43960i
$455$		0			0
$456$	0.475060	+	1.84429i	0.475060	+	1.84429i
$457$	0.116760	−	0.244183i	0.116760	−	0.244183i	−0.835488	−	0.549509i	$-0.814815\pi$
$457$	0.116760	−	0.244183i	0.116760	−	0.244183i	0.952248	+	0.305326i	$0.0987654\pi$
$458$		0			0
$459$	0.247945	−	1.40617i	0.247945	−	1.40617i
$460$		0			0
$461$		0			0		−0.249441	−	0.968390i	$-0.580247\pi$
$461$		0			0		0.249441	+	0.968390i	$0.419753\pi$
$462$		0			0
$463$		0			0		0.0193913	−	0.999812i	$-0.493827\pi$
$463$		0			0		−0.0193913	+	0.999812i	$0.506173\pi$
$464$		0			0
$465$		0			0
$466$	−0.177966	−	0.203927i	−0.177966	−	0.203927i
$467$	0.353752	−	0.232666i	0.353752	−	0.232666i	−0.360178	−	0.932884i	$-0.617284\pi$
$467$	0.353752	−	0.232666i	0.353752	−	0.232666i	0.713930	+	0.700217i	$0.246914\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.04719	+	1.52684i	−1.04719	+	1.52684i
$473$	−0.841624	−	0.825459i	−0.841624	−	0.825459i
$474$		0			0
$475$	−1.41036	−	1.27984i	−1.41036	−	1.27984i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.875558	−	0.483113i	$-0.839506\pi$
$479$		0			0		0.875558	+	0.483113i	$0.160494\pi$
$480$		0			0
$481$		0			0
$482$	−1.68024	−	0.329988i	−1.68024	−	0.329988i
$483$		0			0
$484$	−0.0562263	+	0.578057i	−0.0562263	+	0.578057i
$485$		0			0
$486$	−0.286803	+	0.957990i	−0.286803	+	0.957990i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$	−0.639637	−	1.21432i	−0.639637	−	1.21432i
$490$		0			0
$491$	0.681929	+	0.528535i	0.681929	+	0.528535i	0.893633	−	0.448799i	$-0.148148\pi$
$491$	0.681929	+	0.528535i	0.681929	+	0.528535i	−0.211704	+	0.977334i	$0.567901\pi$
$492$	−0.842882	−	0.653283i	−0.842882	−	0.653283i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.227194	−	0.758881i	−0.227194	−	0.758881i
$499$	0.356167	+	0.349326i	0.356167	+	0.349326i	0.856167	−	0.516699i	$-0.172840\pi$
$499$	0.356167	+	0.349326i	0.356167	+	0.349326i	−0.500000	+	0.866025i	$0.666667\pi$
$500$		0			0
$501$		0			0
$502$	0.179240	+	0.0732277i	0.179240	+	0.0732277i
$503$		0			0		0.0581448	−	0.998308i	$-0.481481\pi$
$503$		0			0		−0.0581448	+	0.998308i	$0.518519\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.0193913	−	0.999812i	0.0193913	−	0.999812i
$508$		0			0
$509$		0			0		0.0193913	−	0.999812i	$-0.493827\pi$
$509$		0			0		−0.0193913	+	0.999812i	$0.506173\pi$
$510$		0			0
$511$		0			0
$512$	0.766044	−	0.642788i	0.766044	−	0.642788i
$513$	1.70192	−	0.854736i	1.70192	−	0.854736i
$514$	1.31172	+	1.10067i	1.31172	+	1.10067i
$515$		0			0
$516$	1.75403	+	0.488269i	1.75403	+	0.488269i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.644463	+	1.49403i	0.644463	+	1.49403i	0.856167	+	0.516699i	$0.172840\pi$
$521$	0.644463	+	1.49403i	0.644463	+	1.49403i	−0.211704	+	0.977334i	$0.567901\pi$
$522$		0			0
$523$	0.569728	−	0.0665916i	0.569728	−	0.0665916i	0.173648	−	0.984808i	$-0.444444\pi$
$523$	0.569728	−	0.0665916i	0.569728	−	0.0665916i	0.396080	+	0.918216i	$0.370370\pi$
$524$	0.906963	+	1.72183i	0.906963	+	1.72183i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.256449	+	0.594515i	0.256449	+	0.594515i
$529$	−0.999248	−	0.0387754i	−0.999248	−	0.0387754i
$530$		0			0
$531$	1.71393	+	0.700217i	1.71393	+	0.700217i
$532$		0			0
$533$		0			0
$534$	−0.161769	−	1.66313i	−0.161769	−	1.66313i
$535$		0			0
$536$	−1.73009	+	0.270580i	−1.73009	+	0.270580i
$537$	−0.0946077	−	0.0676215i	−0.0946077	−	0.0676215i
$538$		0			0
$539$	0.112432	−	0.637631i	0.112432	−	0.637631i
$540$		0			0
$541$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$541$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$542$		0			0
$543$		0			0
$544$	1.22249	+	0.737774i	1.22249	+	0.737774i
$545$		0			0
$546$		0			0
$547$	1.89063	−	0.371307i	1.89063	−	0.371307i	0.893633	−	0.448799i	$-0.148148\pi$
$547$	1.89063	−	0.371307i	1.89063	−	0.371307i	0.996993	+	0.0774924i	$0.0246914\pi$
$548$	−1.12207	−	0.563523i	−1.12207	−	0.563523i
$549$		0			0
$550$	−0.540952	−	0.355789i	−0.540952	−	0.355789i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.88162	−	0.603318i	1.88162	−	0.603318i
$557$		0			0		−0.973045	−	0.230616i	$-0.925926\pi$
$557$		0			0		0.973045	+	0.230616i	$0.0740741\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.684628	+	0.621267i	−0.684628	+	0.621267i
$562$	−1.83893	+	0.751285i	−1.83893	+	0.751285i
$563$	0.639692	+	1.86957i	0.639692	+	1.86957i	0.466044	+	0.884762i	$0.345679\pi$
$563$	0.639692	+	1.86957i	0.639692	+	1.86957i	0.173648	+	0.984808i	$0.444444\pi$
$564$		0			0
$565$		0			0
$566$	−0.597159	−	1.03431i	−0.597159	−	1.03431i
$567$		0			0
$568$		0			0
$569$	1.43909	−	0.654146i	1.43909	−	0.654146i	0.466044	−	0.884762i	$-0.345679\pi$
$569$	1.43909	−	0.654146i	1.43909	−	0.654146i	0.973045	+	0.230616i	$0.0740741\pi$
$570$		0			0
$571$	1.31109	−	1.50234i	1.31109	−	1.50234i	0.597159	−	0.802123i	$-0.296296\pi$
$571$	1.31109	−	1.50234i	1.31109	−	1.50234i	0.713930	−	0.700217i	$-0.246914\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.790393	−	0.612601i	−0.790393	−	0.612601i
$577$	0.360117	+	1.20287i	0.360117	+	1.20287i	0.925724	+	0.378200i	$0.123457\pi$
$577$	0.360117	+	1.20287i	0.360117	+	1.20287i	−0.565607	+	0.824675i	$0.691358\pi$
$578$	−0.219914	+	1.01524i	−0.219914	+	1.01524i
$579$	1.98498	−	0.232011i	1.98498	−	0.232011i
$580$		0			0
$581$		0			0
$582$	0.360178	+	0.623846i	0.360178	+	0.623846i
$583$		0			0
$584$	−1.01089	+	0.507688i	−1.01089	+	0.507688i
$585$		0			0
$586$		0			0
$587$	0.554341	−	1.62012i	0.554341	−	1.62012i	−0.211704	−	0.977334i	$-0.567901\pi$
$587$	0.554341	−	1.62012i	0.554341	−	1.62012i	0.766044	−	0.642788i	$-0.222222\pi$
$588$	0.323734	+	0.946148i	0.323734	+	0.946148i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.67948	−	0.611281i	−1.67948	−	0.611281i	−0.686242	−	0.727374i	$-0.740741\pi$
$593$	−1.67948	−	0.611281i	−1.67948	−	0.611281i	−0.993238	+	0.116093i	$0.962963\pi$
$594$	0.526749	−	0.376497i	0.526749	−	0.376497i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.999248	−	0.0387754i	$-0.0123457\pi$
$599$		0			0		−0.999248	+	0.0387754i	$0.987654\pi$
$600$	0.996993	+	0.0774924i	0.996993	+	0.0774924i
$601$	1.23209	−	1.52755i	1.23209	−	1.52755i	0.466044	−	0.884762i	$-0.345679\pi$
$601$	1.23209	−	1.52755i	1.23209	−	1.52755i	0.766044	−	0.642788i	$-0.222222\pi$
$602$		0			0
$603$	0.630713	+	1.63359i	0.630713	+	1.63359i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.0968109	−	0.995303i	$-0.530864\pi$
$607$		0			0		0.0968109	+	0.995303i	$0.469136\pi$
$608$	0.184376	+	1.89555i	0.184376	+	1.89555i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.462247	−	1.35097i	0.462247	−	1.35097i
$613$		0			0		0.597159	−	0.802123i	$-0.296296\pi$
$613$		0			0		−0.597159	+	0.802123i	$0.703704\pi$
$614$	0.169925	−	0.210674i	0.169925	−	0.210674i
$615$		0			0
$616$		0			0
$617$	0.452248	+	0.560699i	0.452248	+	0.560699i	0.952248	−	0.305326i	$-0.0987654\pi$
$617$	0.452248	+	0.560699i	0.452248	+	0.560699i	−0.500000	+	0.866025i	$0.666667\pi$
$618$		0			0
$619$	−1.99249	+	0.154868i	−1.99249	+	0.154868i	−0.993238	+	0.116093i	$0.962963\pi$
$619$	−1.99249	+	0.154868i	−1.99249	+	0.154868i	−0.999248	+	0.0387754i	$0.987654\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.875558	+	0.483113i	−0.875558	+	0.483113i
$626$	−0.197326	−	0.910960i	−0.197326	−	0.910960i
$627$	−1.20999	−	0.237633i	−1.20999	−	0.237633i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.893633	−	0.448799i	$-0.148148\pi$
$631$		0			0		−0.893633	+	0.448799i	$0.851852\pi$
$632$		0			0
$633$	0.993238	−	1.72034i	0.993238	−	1.72034i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.26806	+	0.765277i	−1.26806	+	0.765277i	−0.981255	−	0.192712i	$-0.938272\pi$
$641$	−1.26806	+	0.765277i	−1.26806	+	0.765277i	−0.286803	+	0.957990i	$0.592593\pi$
$642$	0.929284	−	1.76420i	0.929284	−	1.76420i
$643$	−0.177966	+	1.30294i	−0.177966	+	1.30294i	0.657521	+	0.753436i	$0.271605\pi$
$643$	−0.177966	+	1.30294i	−0.177966	+	1.30294i	−0.835488	+	0.549509i	$0.814815\pi$
$644$		0			0
$645$		0			0
$646$	−2.47560	+	1.12530i	−2.47560	+	1.12530i
$647$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$647$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$648$	−0.431386	+	0.902167i	−0.431386	+	0.902167i
$649$	−0.599377	−	1.03815i	−0.599377	−	1.03815i
$650$		0			0
$651$		0			0
$652$	−0.444319	−	1.29857i	−0.444319	−	1.29857i
$653$		0			0		0.925724	−	0.378200i	$-0.123457\pi$
$653$		0			0		−0.925724	+	0.378200i	$0.876543\pi$
$654$		0			0
$655$		0			0
$656$	−0.731814	−	0.775678i	−0.731814	−	0.775678i
$657$	0.710190	+	0.880497i	0.710190	+	0.880497i
$658$		0			0
$659$	−1.89162	+	0.606523i	−1.89162	+	0.606523i	−0.910363	+	0.413811i	$0.864198\pi$
$659$	−1.89162	+	0.606523i	−1.89162	+	0.606523i	−0.981255	+	0.192712i	$0.938272\pi$
$660$		0			0
$661$		0			0		0.249441	−	0.968390i	$-0.419753\pi$
$661$		0			0		−0.249441	+	0.968390i	$0.580247\pi$
$662$	0.0501657	+	0.104913i	0.0501657	+	0.104913i
$663$		0			0
$664$	−0.107204	−	0.784872i	−0.107204	−	0.784872i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.852659	−	0.836282i	0.852659	−	0.836282i	−0.135331	−	0.990800i	$-0.543210\pi$
$673$	0.852659	−	0.836282i	0.852659	−	0.836282i	0.987990	+	0.154519i	$0.0493827\pi$
$674$	0.0336221	+	0.190680i	0.0336221	+	0.190680i
$675$	−0.135331	−	0.990800i	−0.135331	−	0.990800i
$676$	0.173648	−	0.984808i	0.173648	−	0.984808i
$677$		0			0		−0.565607	−	0.824675i	$-0.691358\pi$
$677$		0			0		0.565607	+	0.824675i	$0.308642\pi$
$678$	−0.0555313	+	0.570912i	−0.0555313	+	0.570912i
$679$		0			0
$680$		0			0
$681$	−1.48126	−	0.673313i	−1.48126	−	0.673313i
$682$		0			0
$683$	−0.0385204	−	0.00450239i	−0.0385204	−	0.00450239i	0.0968109	−	0.995303i	$-0.469136\pi$
$683$	−0.0385204	−	0.00450239i	−0.0385204	−	0.00450239i	−0.135331	+	0.990800i	$0.543210\pi$
$684$	1.81355	−	0.581492i	1.81355	−	0.581492i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	1.65752	+	0.753436i	1.65752	+	0.753436i
$689$		0			0
$690$		0			0
$691$	−0.778747	−	1.47842i	−0.778747	−	1.47842i	−0.875558	−	0.483113i	$-0.839506\pi$
$691$	−0.778747	−	1.47842i	−0.778747	−	1.47842i	0.0968109	−	0.995303i	$-0.469136\pi$
$692$		0			0
$693$		0			0
$694$	−0.586629	−	1.35996i	−0.586629	−	1.35996i
$695$		0			0
$696$		0			0
$697$	0.709636	−	1.34721i	0.709636	−	1.34721i
$698$		0			0
$699$	−0.193234	+	0.189523i	−0.193234	+	0.189523i
$700$		0			0
$701$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$701$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$702$		0			0
$703$		0			0
$704$	0.161505	+	0.627001i	0.161505	+	0.627001i
$705$		0			0
$706$	−0.0167303	+	0.862610i	−0.0167303	+	0.862610i
$707$		0			0
$708$	1.58515	+	0.956642i	1.58515	+	0.956642i
$709$		0			0		−0.657521	−	0.753436i	$-0.728395\pi$
$709$		0			0		0.657521	+	0.753436i	$0.271605\pi$
$710$		0			0
$711$		0			0
$712$	0.0971586	−	1.66815i	0.0971586	−	1.66815i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.0830226	−	0.0814280i	−0.0830226	−	0.0814280i
$717$		0			0
$718$		0			0
$719$		0			0		0.686242	−	0.727374i	$-0.259259\pi$
$719$		0			0		−0.686242	+	0.727374i	$0.740741\pi$
$720$		0			0
$721$		0			0
$722$	−2.30018	−	1.26919i	−2.30018	−	1.26919i
$723$	−0.231732	+	1.69658i	−0.231732	+	1.69658i
$724$		0			0
$725$		0			0
$726$	0.580349	+	0.0225202i	0.580349	+	0.0225202i
$727$		0			0		0.0968109	−	0.995303i	$-0.469136\pi$
$727$		0			0		−0.0968109	+	0.995303i	$0.530864\pi$
$728$		0			0
$729$	0.973045	+	0.230616i	0.973045	+	0.230616i
$730$		0			0
$731$	−0.251683	+	2.58753i	−0.251683	+	2.58753i
$732$		0			0
$733$		0			0		−0.981255	−	0.192712i	$-0.938272\pi$
$733$		0			0		0.981255	+	0.192712i	$0.0617284\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.325175	−	1.08616i	0.325175	−	1.08616i
$738$	−0.603168	+	0.879441i	−0.603168	+	0.879441i
$739$	1.34676	−	1.42748i	1.34676	−	1.42748i	0.533204	−	0.845986i	$-0.320988\pi$
$739$	1.34676	−	1.42748i	1.34676	−	1.42748i	0.813552	−	0.581492i	$-0.197531\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.565607	−	0.824675i	$-0.308642\pi$
$743$		0			0		−0.565607	+	0.824675i	$0.691358\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.744386	+	0.270935i	−0.744386	+	0.270935i
$748$	−0.772403	+	0.508017i	−0.772403	+	0.508017i
$749$		0			0
$750$		0			0
$751$		0			0		0.740544	−	0.672008i	$-0.234568\pi$
$751$		0			0		−0.740544	+	0.672008i	$0.765432\pi$
$752$		0			0
$753$	0.0626819	−	0.183195i	0.0626819	−	0.183195i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$757$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$758$	−0.402089	+	0.840899i	−0.402089	+	0.840899i
$759$		0			0
$760$		0			0
$761$	0.714020	−	1.35553i	0.714020	−	1.35553i	−0.211704	−	0.977334i	$-0.567901\pi$
$761$	0.714020	−	1.35553i	0.714020	−	1.35553i	0.925724	−	0.378200i	$-0.123457\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.686242	−	0.727374i	−0.686242	−	0.727374i
$769$	−0.466659	+	0.333548i	−0.466659	+	0.333548i	−0.790393	−	0.612601i	$-0.790123\pi$
$769$	−0.466659	+	0.333548i	−0.466659	+	0.333548i	0.323734	+	0.946148i	$0.395062\pi$
$770$		0			0
$771$	1.02253	−	1.37350i	1.02253	−	1.37350i
$772$	1.99699	+	0.0774924i	1.99699	+	0.0774924i
$773$		0			0		−0.597159	−	0.802123i	$-0.703704\pi$
$773$		0			0		0.597159	+	0.802123i	$0.296296\pi$
$774$	0.385455	−	1.77946i	0.385455	−	1.77946i
$775$		0			0
$776$	0.259456	+	0.672008i	0.259456	+	0.672008i
$777$		0			0
$778$		0			0
$779$	2.00658	−	0.313823i	2.00658	−	0.313823i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.173648	+	0.984808i	0.173648	+	0.984808i
$785$		0			0
$786$	1.66618	−	1.00554i	1.66618	−	1.00554i
$787$	0.678221	+	0.409308i	0.678221	+	0.409308i	0.813552	−	0.581492i	$-0.197531\pi$
$787$	0.678221	+	0.409308i	0.678221	+	0.409308i	−0.135331	+	0.990800i	$0.543210\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.578598	−	0.290583i	0.578598	−	0.290583i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.249441	−	0.968390i	$-0.419753\pi$
$797$		0			0		−0.249441	+	0.968390i	$0.580247\pi$
$798$		0			0
$799$		0			0
$800$	0.973045	+	0.230616i	0.973045	+	0.230616i
$801$	−1.65091	+	0.258197i	−1.65091	+	0.258197i
$802$	0.290560	+	0.307976i	0.290560	+	0.307976i
$803$	−0.0142027	−	0.732287i	−0.0142027	−	0.732287i
$804$	0.370718	+	1.71143i	0.370718	+	1.71143i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.565607	+	0.979660i	0.565607	+	0.979660i	0.996993	+	0.0774924i	$0.0246914\pi$
$809$	0.565607	+	0.979660i	0.565607	+	0.979660i	−0.431386	+	0.902167i	$0.641975\pi$
$810$		0			0
$811$	−0.0193913	+	0.0335868i	−0.0193913	+	0.0335868i	−0.875558	−	0.483113i	$-0.839506\pi$
$811$	−0.0193913	+	0.0335868i	−0.0193913	+	0.0335868i	0.856167	+	0.516699i	$0.172840\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.665445	−	1.26332i	0.665445	−	1.26332i
$817$	−2.96881	+	1.79169i	−2.96881	+	1.79169i
$818$	−1.87481	+	0.444337i	−1.87481	+	0.444337i
$819$		0			0
$820$		0			0
$821$		0			0		0.211704	−	0.977334i	$-0.432099\pi$
$821$		0			0		−0.211704	+	0.977334i	$0.567901\pi$
$822$	−0.497327	+	1.15293i	−0.497327	+	1.15293i
$823$		0			0		0.963371	−	0.268173i	$-0.0864198\pi$
$823$		0			0		−0.963371	+	0.268173i	$0.913580\pi$
$824$		0			0
$825$	−0.323734	+	0.560724i	−0.323734	+	0.560724i
$826$		0			0
$827$	0.310355	−	0.155866i	0.310355	−	0.155866i	−0.286803	−	0.957990i	$-0.592593\pi$
$827$	0.310355	−	0.155866i	0.310355	−	0.155866i	0.597159	+	0.802123i	$0.296296\pi$
$828$		0			0
$829$		0			0		−0.0581448	−	0.998308i	$-0.518519\pi$
$829$		0			0		0.0581448	+	0.998308i	$0.481481\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.25017	+	0.689817i	−1.25017	+	0.689817i
$834$	−0.711704	−	1.84336i	−0.711704	−	1.84336i
$835$		0			0
$836$	−1.15873	−	0.421745i	−1.15873	−	0.421745i
$837$		0			0
$838$	1.28971	−	0.469417i	1.28971	−	0.469417i
$839$		0			0		0.996993	−	0.0774924i	$-0.0246914\pi$
$839$		0			0		−0.996993	+	0.0774924i	$0.975309\pi$
$840$		0			0
$841$	−0.627812	−	0.778365i	−0.627812	−	0.778365i
$842$		0			0
$843$	0.856938	+	1.79213i	0.856938	+	1.79213i
$844$	1.24713	−	1.54620i	1.24713	−	1.54620i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.997837	+	0.656288i	−0.997837	+	0.656288i
$850$	0.138232	+	1.42115i	0.138232	+	1.42115i
$851$		0			0
$852$		0			0
$853$		0			0		0.533204	−	0.845986i	$-0.320988\pi$
$853$		0			0		−0.533204	+	0.845986i	$0.679012\pi$
$854$		0			0
$855$		0			0
$856$	1.19073	−	1.59942i	1.19073	−	1.59942i
$857$	1.17990	−	1.46285i	1.17990	−	1.46285i	0.323734	−	0.946148i	$-0.395062\pi$
$857$	1.17990	−	1.46285i	1.17990	−	1.46285i	0.856167	−	0.516699i	$-0.172840\pi$
$858$		0			0
$859$	1.96103	−	0.0760971i	1.96103	−	0.0760971i	0.973045	−	0.230616i	$-0.0740741\pi$
$859$	1.96103	−	0.0760971i	1.96103	−	0.0760971i	0.987990	+	0.154519i	$0.0493827\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$863$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$864$	−0.565607	+	0.824675i	−0.565607	+	0.824675i
$865$		0			0
$866$	−0.480609	−	0.133787i	−0.480609	−	0.133787i
$867$	1.02631	+	0.160511i	1.02631	+	0.160511i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.601848	−	0.395842i	0.601848	−	0.395842i
$874$		0			0
$875$		0			0
$876$	0.565607	+	0.979660i	0.565607	+	0.979660i
$877$		0			0		−0.996993	−	0.0774924i	$-0.975309\pi$
$877$		0			0		0.996993	+	0.0774924i	$0.0246914\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.0333522	+	0.111404i	0.0333522	+	0.111404i	0.973045	−	0.230616i	$-0.0740741\pi$
$881$	0.0333522	+	0.111404i	0.0333522	+	0.111404i	−0.939693	+	0.342020i	$0.888889\pi$
$882$	0.925724	−	0.378200i	0.925724	−	0.378200i
$883$	−1.87481	+	0.444337i	−1.87481	+	0.444337i	−0.999248	−	0.0387754i	$-0.987654\pi$
$883$	−1.87481	+	0.444337i	−1.87481	+	0.444337i	−0.875558	+	0.483113i	$0.839506\pi$
$884$		0			0
$885$		0			0
$886$	0.270459	−	1.98011i	0.270459	−	1.98011i
$887$		0			0		0.657521	−	0.753436i	$-0.271605\pi$
$887$		0			0		−0.657521	+	0.753436i	$0.728395\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.406488	−	0.503966i	−0.406488	−	0.503966i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.0383169	+	1.97561i	0.0383169	+	1.97561i
$899$		0			0
$900$	0.0193913	−	0.999812i	0.0193913	−	0.999812i
$901$		0			0
$902$	0.657494	−	0.210817i	0.657494	−	0.210817i
$903$		0			0
$904$	−0.143081	+	0.555475i	−0.143081	+	0.555475i
$905$		0			0
$906$		0			0
$907$	−0.231732	−	1.69658i	−0.231732	−	1.69658i	−0.627812	−	0.778365i	$-0.716049\pi$
$907$	−0.231732	−	1.69658i	−0.231732	−	1.69658i	0.396080	−	0.918216i	$-0.370370\pi$
$908$	−1.35943	−	0.894108i	−1.35943	−	0.894108i
$909$		0			0
$910$		0			0
$911$		0			0		0.981255	−	0.192712i	$-0.0617284\pi$
$911$		0			0		−0.981255	+	0.192712i	$0.938272\pi$
$912$	1.88162	−	0.294280i	1.88162	−	0.294280i
$913$	0.488406	+	0.156601i	0.488406	+	0.156601i
$914$	−0.231732	−	0.139851i	−0.231732	−	0.139851i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−1.37556	−	0.382913i	−1.37556	−	0.382913i
$919$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$919$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$920$		0			0
$921$	−0.220198	−	0.157388i	−0.220198	−	0.157388i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.87797	+	0.0728739i	1.87797	+	0.0728739i	0.952248	−	0.305326i	$-0.0987654\pi$
$929$	1.87797	+	0.0728739i	1.87797	+	0.0728739i	0.925724	+	0.378200i	$0.123457\pi$
$930$		0			0
$931$	−1.73378	−	0.788101i	−1.73378	−	0.788101i
$932$	−0.220198	+	0.157388i	−0.220198	+	0.157388i
$933$		0			0
$934$	−0.197326	−	0.374615i	−0.197326	−	0.374615i
$935$		0			0
$936$		0			0
$937$	0.707900	+	1.64110i	0.707900	+	1.64110i	0.766044	+	0.642788i	$0.222222\pi$
$937$	0.707900	+	1.64110i	0.707900	+	1.64110i	−0.0581448	+	0.998308i	$0.518519\pi$
$938$		0			0
$939$	−0.897946	+	0.249960i	−0.897946	+	0.249960i
$940$		0			0
$941$		0			0		0.360178	−	0.932884i	$-0.382716\pi$
$941$		0			0		−0.360178	+	0.932884i	$0.617284\pi$
$942$		0			0
$943$		0			0
$944$	1.41829	+	1.19009i	1.41829	+	1.19009i
$945$		0			0
$946$	−0.903060	+	0.757758i	−0.903060	+	0.757758i
$947$	−0.282171	−	1.09546i	−0.282171	−	1.09546i	−0.939693	−	0.342020i	$-0.888889\pi$
$947$	−0.282171	−	1.09546i	−0.282171	−	1.09546i	0.657521	−	0.753436i	$-0.271605\pi$
$948$		0			0
$949$		0			0
$950$	−1.41036	+	1.27984i	−1.41036	+	1.27984i
$951$		0			0
$952$		0			0
$953$	1.46304	−	0.962254i	1.46304	−	0.962254i	0.466044	−	0.884762i	$-0.345679\pi$
$953$	1.46304	−	0.962254i	1.46304	−	0.962254i	0.996993	−	0.0774924i	$-0.0246914\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.740544	−	0.672008i	−0.740544	−	0.672008i
$962$		0			0
$963$	−1.81525	−	0.825133i	−1.81525	−	0.825133i
$964$	−0.491103	+	1.64040i	−0.491103	+	1.64040i
$965$		0			0
$966$		0			0
$967$		0			0		−0.790393	−	0.612601i	$-0.790123\pi$
$967$		0			0		0.790393	+	0.612601i	$0.209877\pi$
$968$	0.569899	+	0.111924i	0.569899	+	0.111924i
$969$	1.26734	+	2.40598i	1.26734	+	2.40598i
$970$		0			0
$971$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$971$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$972$	0.925724	+	0.378200i	0.925724	+	0.378200i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.24944	+	0.968390i	1.24944	+	0.968390i	1.00000			$0$
$977$	1.24944	+	0.968390i	1.24944	+	0.968390i	0.249441	+	0.968390i	$0.419753\pi$
$978$	−1.27054	+	0.519073i	−1.27054	+	0.519073i
$979$	0.947269	+	0.522681i	0.947269	+	0.522681i
$980$		0			0
$981$		0			0
$982$	0.592070	−	0.627558i	0.592070	−	0.627558i
$983$		0			0		−0.740544	−	0.672008i	$-0.765432\pi$
$983$		0			0		0.740544	+	0.672008i	$0.234568\pi$
$984$	−0.731814	+	0.775678i	−0.731814	+	0.775678i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.835488	−	0.549509i	$-0.185185\pi$
$991$		0			0		−0.835488	+	0.549509i	$0.814815\pi$
$992$		0			0
$993$	0.101818	−	0.0561810i	0.101818	−	0.0561810i
$994$		0			0
$995$		0			0
$996$	−0.777311	+	0.152659i	−0.777311	+	0.152659i
$997$		0			0		−0.249441	−	0.968390i	$-0.580247\pi$
$997$		0			0		0.249441	+	0.968390i	$0.419753\pi$
$998$	0.382166	−	0.320675i	0.382166	−	0.320675i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1944.1.bh.a.211.1	✓	54
8.3	odd	2	CM	1944.1.bh.a.211.1	✓	54
243.205	even	81	inner	1944.1.bh.a.691.1	yes	54
1944.691	odd	162	inner	1944.1.bh.a.691.1	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1944.1.bh.a.211.1	✓	54	1.1	even	1	trivial
1944.1.bh.a.211.1	✓	54	8.3	odd	2	CM
1944.1.bh.a.691.1	yes	54	243.205	even	81	inner
1944.1.bh.a.691.1	yes	54	1944.691	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)

\(f(q)\)	\(=\)	\(q+(0.0968109 - 0.995303i) q^{2} +(-0.999248 - 0.0387754i) q^{3} +(-0.981255 - 0.192712i) q^{4} +(-0.135331 + 0.990800i) q^{6} +(-0.286803 + 0.957990i) q^{8} +(0.996993 + 0.0774924i) q^{9} +O(q^{10})\)	\(q+(0.0968109 - 0.995303i) q^{2} +(-0.999248 - 0.0387754i) q^{3} +(-0.981255 - 0.192712i) q^{4} +(-0.135331 + 0.990800i) q^{6} +(-0.286803 + 0.957990i) q^{8} +(0.996993 + 0.0774924i) q^{9} +(-0.479478 - 0.435104i) q^{11} +(0.973045 + 0.230616i) q^{12} +(0.925724 + 0.378200i) q^{16} +(-0.0830226 + 1.42544i) q^{17} +(0.173648 - 0.984808i) q^{18} +(-1.59118 + 1.04654i) q^{19} +(-0.479478 + 0.435104i) q^{22} +(0.323734 - 0.946148i) q^{24} +(0.249441 + 0.968390i) q^{25} +(-0.993238 - 0.116093i) q^{27} +(0.466044 - 0.884762i) q^{32} +(0.462247 + 0.453368i) q^{33} +(1.41071 + 0.220631i) q^{34} +(-0.963371 - 0.268173i) q^{36} +(0.887578 + 1.68503i) q^{38} +(-0.970819 - 0.441291i) q^{41} +(1.81936 + 0.0705993i) q^{43} +(0.386641 + 0.519349i) q^{44} +(-0.910363 - 0.413811i) q^{48} +(0.533204 + 0.845986i) q^{49} +(0.987990 - 0.154519i) q^{50} +(0.138232 - 1.42115i) q^{51} +(-0.211704 + 0.977334i) q^{54} +(1.63057 - 0.984052i) q^{57} +(1.76304 + 0.565295i) q^{59} +(-0.835488 - 0.549509i) q^{64} +(0.495989 - 0.416184i) q^{66} +(0.755407 + 1.57980i) q^{67} +(0.356167 - 1.38272i) q^{68} +(-0.360178 + 0.932884i) q^{72} +(0.776286 + 0.822815i) q^{73} +(-0.211704 - 0.977334i) q^{75} +(1.76304 - 0.720280i) q^{76} +(0.987990 + 0.154519i) q^{81} +(-0.533204 + 0.923537i) q^{82} +(-0.721153 + 0.327804i) q^{83} +(0.246401 - 1.80398i) q^{86} +(0.554341 - 0.334546i) q^{88} +(-1.62593 + 0.385353i) q^{89} +(-0.500000 + 0.866025i) q^{96} +(0.569364 - 0.441290i) q^{97} +(0.893633 - 0.448799i) q^{98} +(-0.444319 - 0.470951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q - 27 q^{68} - 27 q^{96}+O(q^{100}) \) 54 * q - 27 * q^68 - 27 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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