LMFDB - Embedded newform 5265.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5265,2,Mod(1,5265)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5265, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("5265.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5265 = 3^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5265.a (trivial)

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:	yes
Analytic conductor:	$42.0412366642$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5265.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +2.00000 q^{4} +1.00000 q^{5} +O(q^{10})$

$q+2.00000 q^{2} +2.00000 q^{4} +1.00000 q^{5} +2.00000 q^{10} -5.00000 q^{11} +1.00000 q^{13} -4.00000 q^{16} -4.00000 q^{17} +5.00000 q^{19} +2.00000 q^{20} -10.0000 q^{22} -4.00000 q^{23} +1.00000 q^{25} +2.00000 q^{26} -5.00000 q^{29} +1.00000 q^{31} -8.00000 q^{32} -8.00000 q^{34} +10.0000 q^{38} -3.00000 q^{41} +8.00000 q^{43} -10.0000 q^{44} -8.00000 q^{46} -8.00000 q^{47} -7.00000 q^{49} +2.00000 q^{50} +2.00000 q^{52} -12.0000 q^{53} -5.00000 q^{55} -10.0000 q^{58} +9.00000 q^{59} -2.00000 q^{61} +2.00000 q^{62} -8.00000 q^{64} +1.00000 q^{65} -4.00000 q^{67} -8.00000 q^{68} -9.00000 q^{71} +12.0000 q^{73} +10.0000 q^{76} -8.00000 q^{79} -4.00000 q^{80} -6.00000 q^{82} -4.00000 q^{83} -4.00000 q^{85} +16.0000 q^{86} +1.00000 q^{89} -8.00000 q^{92} -16.0000 q^{94} +5.00000 q^{95} -6.00000 q^{97} -14.0000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

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 $

$2$	2.00000	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$2$	2.00000	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$3$	0	0
$3$	0	0
$4$	2.00000	1.00000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	0	0
$9$	0	0
$10$	2.00000	0.632456
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	0	0
$16$	−4.00000	−1.00000
$17$	−4.00000	−0.970143	−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000	−0.970143	−0.485071	+	0.874475i	$0.661206\pi$
$18$	0	0
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	2.00000	0.447214
$21$	0	0
$22$	−10.0000	−2.13201
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	0	0
$28$	0	0
$29$	−5.00000	−0.928477	−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000	−0.928477	−0.464238	+	0.885710i	$0.653672\pi$
$30$	0	0
$31$	1.00000	0.179605	0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000	0.179605	0.0898027	+	0.995960i	$0.471376\pi$
$32$	−8.00000	−1.41421
$33$	0	0
$34$	−8.00000	−1.37199
$35$	0	0
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	10.0000	1.62221
$39$	0	0
$40$	0	0
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	−10.0000	−1.50756
$45$	0	0
$46$	−8.00000	−1.17954
$47$	−8.00000	−1.16692	−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000	−1.16692	−0.583460	+	0.812142i	$0.698301\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	2.00000	0.282843
$51$	0	0
$52$	2.00000	0.277350
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	0	0
$55$	−5.00000	−0.674200
$56$	0	0
$57$	0	0
$58$	−10.0000	−1.31306
$59$	9.00000	1.17170	0.585850	−	0.810419i	$-0.300761\pi$
$59$	9.00000	1.17170	0.585850	+	0.810419i	$0.300761\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	2.00000	0.254000
$63$	0	0
$64$	−8.00000	−1.00000
$65$	1.00000	0.124035
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−8.00000	−0.970143
$69$	0	0
$70$	0	0
$71$	−9.00000	−1.06810	−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000	−1.06810	−0.534052	+	0.845452i	$0.679331\pi$
$72$	0	0
$73$	12.0000	1.40449	0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000	1.40449	0.702247	+	0.711934i	$0.252180\pi$
$74$	0	0
$75$	0	0
$76$	10.0000	1.14708
$77$	0	0
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−4.00000	−0.447214
$81$	0	0
$82$	−6.00000	−0.662589
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	0	0
$85$	−4.00000	−0.433861
$86$	16.0000	1.72532
$87$	0	0
$88$	0	0
$89$	1.00000	0.106000	0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000	0.106000	0.0529999	+	0.998595i	$0.483122\pi$
$90$	0	0
$91$	0	0
$92$	−8.00000	−0.834058
$93$	0	0
$94$	−16.0000	−1.65027
$95$	5.00000	0.512989
$96$	0	0
$97$	−6.00000	−0.609208	−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000	−0.609208	−0.304604	+	0.952479i	$0.598524\pi$
$98$	−14.0000	−1.41421
$99$	0	0
$100$	2.00000	0.200000
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	0	0
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	0	0
$105$	0	0
$106$	−24.0000	−2.33109
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	0	0
$109$	−11.0000	−1.05361	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000	−1.05361	−0.526804	+	0.849987i	$0.676610\pi$
$110$	−10.0000	−0.953463
$111$	0	0
$112$	0	0
$113$	14.0000	1.31701	0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000	1.31701	0.658505	+	0.752577i	$0.271189\pi$
$114$	0	0
$115$	−4.00000	−0.373002
$116$	−10.0000	−0.928477
$117$	0	0
$118$	18.0000	1.65703
$119$	0	0
$120$	0	0
$121$	14.0000	1.27273
$122$	−4.00000	−0.362143
$123$	0	0
$124$	2.00000	0.179605
$125$	1.00000	0.0894427
$126$	0	0
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	0	0
$129$	0	0
$130$	2.00000	0.175412
$131$	15.0000	1.31056	0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000	1.31056	0.655278	+	0.755388i	$0.272551\pi$
$132$	0	0
$133$	0	0
$134$	−8.00000	−0.691095
$135$	0	0
$136$	0	0
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	0	0
$139$	1.00000	0.0848189	0.0424094	−	0.999100i	$-0.486497\pi$
$139$	1.00000	0.0848189	0.0424094	+	0.999100i	$0.486497\pi$
$140$	0	0
$141$	0	0
$142$	−18.0000	−1.51053
$143$	−5.00000	−0.418121
$144$	0	0
$145$	−5.00000	−0.415227
$146$	24.0000	1.98625
$147$	0	0
$148$	0	0
$149$	−22.0000	−1.80231	−0.901155	−	0.433497i	$-0.857280\pi$
$149$	−22.0000	−1.80231	−0.901155	+	0.433497i	$0.857280\pi$
$150$	0	0
$151$	−15.0000	−1.22068	−0.610341	−	0.792139i	$-0.708968\pi$
$151$	−15.0000	−1.22068	−0.610341	+	0.792139i	$0.708968\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	1.00000	0.0803219
$156$	0	0
$157$	22.0000	1.75579	0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000	1.75579	0.877896	+	0.478852i	$0.158947\pi$
$158$	−16.0000	−1.27289
$159$	0	0
$160$	−8.00000	−0.632456
$161$	0	0
$162$	0	0
$163$	−2.00000	−0.156652	−0.0783260	−	0.996928i	$-0.524958\pi$
$163$	−2.00000	−0.156652	−0.0783260	+	0.996928i	$0.524958\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	−8.00000	−0.620920
$167$	22.0000	1.70241	0.851206	−	0.524832i	$-0.175872\pi$
$167$	22.0000	1.70241	0.851206	+	0.524832i	$0.175872\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−8.00000	−0.613572
$171$	0	0
$172$	16.0000	1.21999
$173$	4.00000	0.304114	0.152057	−	0.988372i	$-0.451410\pi$
$173$	4.00000	0.304114	0.152057	+	0.988372i	$0.451410\pi$
$174$	0	0
$175$	0	0
$176$	20.0000	1.50756
$177$	0	0
$178$	2.00000	0.149906
$179$	3.00000	0.224231	0.112115	−	0.993695i	$-0.464237\pi$
$179$	3.00000	0.224231	0.112115	+	0.993695i	$0.464237\pi$
$180$	0	0
$181$	−5.00000	−0.371647	−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000	−0.371647	−0.185824	+	0.982583i	$0.559495\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	20.0000	1.46254
$188$	−16.0000	−1.16692
$189$	0	0
$190$	10.0000	0.725476
$191$	1.00000	0.0723575	0.0361787	−	0.999345i	$-0.488481\pi$
$191$	1.00000	0.0723575	0.0361787	+	0.999345i	$0.488481\pi$
$192$	0	0
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	−12.0000	−0.861550
$195$	0	0
$196$	−14.0000	−1.00000
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	0	0
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	0	0
$201$	0	0
$202$	−6.00000	−0.422159
$203$	0	0
$204$	0	0
$205$	−3.00000	−0.209529
$206$	−16.0000	−1.11477
$207$	0	0
$208$	−4.00000	−0.277350
$209$	−25.0000	−1.72929
$210$	0	0
$211$	11.0000	0.757271	0.378636	−	0.925546i	$-0.376393\pi$
$211$	11.0000	0.757271	0.378636	+	0.925546i	$0.376393\pi$
$212$	−24.0000	−1.64833
$213$	0	0
$214$	−12.0000	−0.820303
$215$	8.00000	0.545595
$216$	0	0
$217$	0	0
$218$	−22.0000	−1.49003
$219$	0	0
$220$	−10.0000	−0.674200
$221$	−4.00000	−0.269069
$222$	0	0
$223$	−12.0000	−0.803579	−0.401790	−	0.915732i	$-0.631612\pi$
$223$	−12.0000	−0.803579	−0.401790	+	0.915732i	$0.631612\pi$
$224$	0	0
$225$	0	0
$226$	28.0000	1.86253
$227$	−6.00000	−0.398234	−0.199117	−	0.979976i	$-0.563807\pi$
$227$	−6.00000	−0.398234	−0.199117	+	0.979976i	$0.563807\pi$
$228$	0	0
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	−8.00000	−0.527504
$231$	0	0
$232$	0	0
$233$	−4.00000	−0.262049	−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000	−0.262049	−0.131024	+	0.991379i	$0.541827\pi$
$234$	0	0
$235$	−8.00000	−0.521862
$236$	18.0000	1.17170
$237$	0	0
$238$	0	0
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	19.0000	1.22390	0.611949	−	0.790897i	$-0.290386\pi$
$241$	19.0000	1.22390	0.611949	+	0.790897i	$0.290386\pi$
$242$	28.0000	1.79991
$243$	0	0
$244$	−4.00000	−0.256074
$245$	−7.00000	−0.447214
$246$	0	0
$247$	5.00000	0.318142
$248$	0	0
$249$	0	0
$250$	2.00000	0.126491
$251$	8.00000	0.504956	0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000	0.504956	0.252478	+	0.967603i	$0.418755\pi$
$252$	0	0
$253$	20.0000	1.25739
$254$	−8.00000	−0.501965
$255$	0	0
$256$	16.0000	1.00000
$257$	24.0000	1.49708	0.748539	−	0.663090i	$-0.230755\pi$
$257$	24.0000	1.49708	0.748539	+	0.663090i	$0.230755\pi$
$258$	0	0
$259$	0	0
$260$	2.00000	0.124035
$261$	0	0
$262$	30.0000	1.85341
$263$	−30.0000	−1.84988	−0.924940	−	0.380114i	$-0.875885\pi$
$263$	−30.0000	−1.84988	−0.924940	+	0.380114i	$0.875885\pi$
$264$	0	0
$265$	−12.0000	−0.737154
$266$	0	0
$267$	0	0
$268$	−8.00000	−0.488678
$269$	29.0000	1.76816	0.884081	−	0.467334i	$-0.154786\pi$
$269$	29.0000	1.76816	0.884081	+	0.467334i	$0.154786\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	16.0000	0.970143
$273$	0	0
$274$	24.0000	1.44989
$275$	−5.00000	−0.301511
$276$	0	0
$277$	−28.0000	−1.68236	−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−28.0000	−1.68236	−0.841178	+	0.540758i	$0.818138\pi$
$278$	2.00000	0.119952
$279$	0	0
$280$	0	0
$281$	26.0000	1.55103	0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000	1.55103	0.775515	+	0.631329i	$0.217490\pi$
$282$	0	0
$283$	16.0000	0.951101	0.475551	−	0.879688i	$-0.342249\pi$
$283$	16.0000	0.951101	0.475551	+	0.879688i	$0.342249\pi$
$284$	−18.0000	−1.06810
$285$	0	0
$286$	−10.0000	−0.591312
$287$	0	0
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	−10.0000	−0.587220
$291$	0	0
$292$	24.0000	1.40449
$293$	−12.0000	−0.701047	−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000	−0.701047	−0.350524	+	0.936554i	$0.613996\pi$
$294$	0	0
$295$	9.00000	0.524000
$296$	0	0
$297$	0	0
$298$	−44.0000	−2.54885
$299$	−4.00000	−0.231326
$300$	0	0
$301$	0	0
$302$	−30.0000	−1.72631
$303$	0	0
$304$	−20.0000	−1.14708
$305$	−2.00000	−0.114520
$306$	0	0
$307$	−10.0000	−0.570730	−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000	−0.570730	−0.285365	+	0.958419i	$0.592115\pi$
$308$	0	0
$309$	0	0
$310$	2.00000	0.113592
$311$	−9.00000	−0.510343	−0.255172	−	0.966896i	$-0.582132\pi$
$311$	−9.00000	−0.510343	−0.255172	+	0.966896i	$0.582132\pi$
$312$	0	0
$313$	26.0000	1.46961	0.734803	−	0.678280i	$-0.237274\pi$
$313$	26.0000	1.46961	0.734803	+	0.678280i	$0.237274\pi$
$314$	44.0000	2.48306
$315$	0	0
$316$	−16.0000	−0.900070
$317$	−12.0000	−0.673987	−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000	−0.673987	−0.336994	+	0.941507i	$0.609410\pi$
$318$	0	0
$319$	25.0000	1.39973
$320$	−8.00000	−0.447214
$321$	0	0
$322$	0	0
$323$	−20.0000	−1.11283
$324$	0	0
$325$	1.00000	0.0554700
$326$	−4.00000	−0.221540
$327$	0	0
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−31.0000	−1.70391	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	−31.0000	−1.70391	−0.851957	+	0.523612i	$0.824584\pi$
$332$	−8.00000	−0.439057
$333$	0	0
$334$	44.0000	2.40757
$335$	−4.00000	−0.218543
$336$	0	0
$337$	22.0000	1.19842	0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000	1.19842	0.599208	+	0.800593i	$0.295482\pi$
$338$	2.00000	0.108786
$339$	0	0
$340$	−8.00000	−0.433861
$341$	−5.00000	−0.270765
$342$	0	0
$343$	0	0
$344$	0	0
$345$	0	0
$346$	8.00000	0.430083
$347$	−10.0000	−0.536828	−0.268414	−	0.963304i	$-0.586500\pi$
$347$	−10.0000	−0.536828	−0.268414	+	0.963304i	$0.586500\pi$
$348$	0	0
$349$	23.0000	1.23116	0.615581	−	0.788074i	$-0.288921\pi$
$349$	23.0000	1.23116	0.615581	+	0.788074i	$0.288921\pi$
$350$	0	0
$351$	0	0
$352$	40.0000	2.13201
$353$	−8.00000	−0.425797	−0.212899	−	0.977074i	$-0.568290\pi$
$353$	−8.00000	−0.425797	−0.212899	+	0.977074i	$0.568290\pi$
$354$	0	0
$355$	−9.00000	−0.477670
$356$	2.00000	0.106000
$357$	0	0
$358$	6.00000	0.317110
$359$	−17.0000	−0.897226	−0.448613	−	0.893726i	$-0.648082\pi$
$359$	−17.0000	−0.897226	−0.448613	+	0.893726i	$0.648082\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	−10.0000	−0.525588
$363$	0	0
$364$	0	0
$365$	12.0000	0.628109
$366$	0	0
$367$	−22.0000	−1.14839	−0.574195	−	0.818718i	$-0.694685\pi$
$367$	−22.0000	−1.14839	−0.574195	+	0.818718i	$0.694685\pi$
$368$	16.0000	0.834058
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	16.0000	0.828449	0.414224	−	0.910175i	$-0.364053\pi$
$373$	16.0000	0.828449	0.414224	+	0.910175i	$0.364053\pi$
$374$	40.0000	2.06835
$375$	0	0
$376$	0	0
$377$	−5.00000	−0.257513
$378$	0	0
$379$	−36.0000	−1.84920	−0.924598	−	0.380945i	$-0.875599\pi$
$379$	−36.0000	−1.84920	−0.924598	+	0.380945i	$0.875599\pi$
$380$	10.0000	0.512989
$381$	0	0
$382$	2.00000	0.102329
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	0	0
$385$	0	0
$386$	−28.0000	−1.42516
$387$	0	0
$388$	−12.0000	−0.609208
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	16.0000	0.809155
$392$	0	0
$393$	0	0
$394$	−36.0000	−1.81365
$395$	−8.00000	−0.402524
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	32.0000	1.60402
$399$	0	0
$400$	−4.00000	−0.200000
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	0	0
$403$	1.00000	0.0498135
$404$	−6.00000	−0.298511
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	34.0000	1.68119	0.840596	−	0.541663i	$-0.182205\pi$
$409$	34.0000	1.68119	0.840596	+	0.541663i	$0.182205\pi$
$410$	−6.00000	−0.296319
$411$	0	0
$412$	−16.0000	−0.788263
$413$	0	0
$414$	0	0
$415$	−4.00000	−0.196352
$416$	−8.00000	−0.392232
$417$	0	0
$418$	−50.0000	−2.44558
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	0	0
$421$	−37.0000	−1.80327	−0.901635	−	0.432498i	$-0.857632\pi$
$421$	−37.0000	−1.80327	−0.901635	+	0.432498i	$0.857632\pi$
$422$	22.0000	1.07094
$423$	0	0
$424$	0	0
$425$	−4.00000	−0.194029
$426$	0	0
$427$	0	0
$428$	−12.0000	−0.580042
$429$	0	0
$430$	16.0000	0.771589
$431$	−7.00000	−0.337178	−0.168589	−	0.985686i	$-0.553921\pi$
$431$	−7.00000	−0.337178	−0.168589	+	0.985686i	$0.553921\pi$
$432$	0	0
$433$	24.0000	1.15337	0.576683	−	0.816968i	$-0.304347\pi$
$433$	24.0000	1.15337	0.576683	+	0.816968i	$0.304347\pi$
$434$	0	0
$435$	0	0
$436$	−22.0000	−1.05361
$437$	−20.0000	−0.956730
$438$	0	0
$439$	−9.00000	−0.429547	−0.214773	−	0.976664i	$-0.568901\pi$
$439$	−9.00000	−0.429547	−0.214773	+	0.976664i	$0.568901\pi$
$440$	0	0
$441$	0	0
$442$	−8.00000	−0.380521
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	0	0
$445$	1.00000	0.0474045
$446$	−24.0000	−1.13643
$447$	0	0
$448$	0	0
$449$	27.0000	1.27421	0.637104	−	0.770778i	$-0.280132\pi$
$449$	27.0000	1.27421	0.637104	+	0.770778i	$0.280132\pi$
$450$	0	0
$451$	15.0000	0.706322
$452$	28.0000	1.31701
$453$	0	0
$454$	−12.0000	−0.563188
$455$	0	0
$456$	0	0
$457$	32.0000	1.49690	0.748448	−	0.663193i	$-0.230799\pi$
$457$	32.0000	1.49690	0.748448	+	0.663193i	$0.230799\pi$
$458$	−28.0000	−1.30835
$459$	0	0
$460$	−8.00000	−0.373002
$461$	15.0000	0.698620	0.349310	−	0.937007i	$-0.386416\pi$
$461$	15.0000	0.698620	0.349310	+	0.937007i	$0.386416\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	20.0000	0.928477
$465$	0	0
$466$	−8.00000	−0.370593
$467$	34.0000	1.57333	0.786666	−	0.617379i	$-0.211805\pi$
$467$	34.0000	1.57333	0.786666	+	0.617379i	$0.211805\pi$
$468$	0	0
$469$	0	0
$470$	−16.0000	−0.738025
$471$	0	0
$472$	0	0
$473$	−40.0000	−1.83920
$474$	0	0
$475$	5.00000	0.229416
$476$	0	0
$477$	0	0
$478$	48.0000	2.19547
$479$	−25.0000	−1.14228	−0.571140	−	0.820853i	$-0.693499\pi$
$479$	−25.0000	−1.14228	−0.571140	+	0.820853i	$0.693499\pi$
$480$	0	0
$481$	0	0
$482$	38.0000	1.73085
$483$	0	0
$484$	28.0000	1.27273
$485$	−6.00000	−0.272446
$486$	0	0
$487$	−2.00000	−0.0906287	−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000	−0.0906287	−0.0453143	+	0.998973i	$0.514429\pi$
$488$	0	0
$489$	0	0
$490$	−14.0000	−0.632456
$491$	−17.0000	−0.767199	−0.383600	−	0.923499i	$-0.625316\pi$
$491$	−17.0000	−0.767199	−0.383600	+	0.923499i	$0.625316\pi$
$492$	0	0
$493$	20.0000	0.900755
$494$	10.0000	0.449921
$495$	0	0
$496$	−4.00000	−0.179605
$497$	0	0
$498$	0	0
$499$	−23.0000	−1.02962	−0.514811	−	0.857304i	$-0.672138\pi$
$499$	−23.0000	−1.02962	−0.514811	+	0.857304i	$0.672138\pi$
$500$	2.00000	0.0894427
$501$	0	0
$502$	16.0000	0.714115
$503$	−30.0000	−1.33763	−0.668817	−	0.743427i	$-0.733199\pi$
$503$	−30.0000	−1.33763	−0.668817	+	0.743427i	$0.733199\pi$
$504$	0	0
$505$	−3.00000	−0.133498
$506$	40.0000	1.77822
$507$	0	0
$508$	−8.00000	−0.354943
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	0	0
$511$	0	0
$512$	32.0000	1.41421
$513$	0	0
$514$	48.0000	2.11719
$515$	−8.00000	−0.352522
$516$	0	0
$517$	40.0000	1.75920
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−10.0000	−0.438108	−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000	−0.438108	−0.219054	+	0.975713i	$0.570297\pi$
$522$	0	0
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	30.0000	1.31056
$525$	0	0
$526$	−60.0000	−2.61612
$527$	−4.00000	−0.174243
$528$	0	0
$529$	−7.00000	−0.304348
$530$	−24.0000	−1.04249
$531$	0	0
$532$	0	0
$533$	−3.00000	−0.129944
$534$	0	0
$535$	−6.00000	−0.259403
$536$	0	0
$537$	0	0
$538$	58.0000	2.50056
$539$	35.0000	1.50756
$540$	0	0
$541$	−7.00000	−0.300954	−0.150477	−	0.988614i	$-0.548081\pi$
$541$	−7.00000	−0.300954	−0.150477	+	0.988614i	$0.548081\pi$
$542$	−16.0000	−0.687259
$543$	0	0
$544$	32.0000	1.37199
$545$	−11.0000	−0.471188
$546$	0	0
$547$	18.0000	0.769624	0.384812	−	0.922995i	$-0.374266\pi$
$547$	18.0000	0.769624	0.384812	+	0.922995i	$0.374266\pi$
$548$	24.0000	1.02523
$549$	0	0
$550$	−10.0000	−0.426401
$551$	−25.0000	−1.06504
$552$	0	0
$553$	0	0
$554$	−56.0000	−2.37921
$555$	0	0
$556$	2.00000	0.0848189
$557$	36.0000	1.52537	0.762684	−	0.646771i	$-0.223881\pi$
$557$	36.0000	1.52537	0.762684	+	0.646771i	$0.223881\pi$
$558$	0	0
$559$	8.00000	0.338364
$560$	0	0
$561$	0	0
$562$	52.0000	2.19349
$563$	−38.0000	−1.60151	−0.800755	−	0.598993i	$-0.795568\pi$
$563$	−38.0000	−1.60151	−0.800755	+	0.598993i	$0.795568\pi$
$564$	0	0
$565$	14.0000	0.588984
$566$	32.0000	1.34506
$567$	0	0
$568$	0	0
$569$	−23.0000	−0.964210	−0.482105	−	0.876113i	$-0.660128\pi$
$569$	−23.0000	−0.964210	−0.482105	+	0.876113i	$0.660128\pi$
$570$	0	0
$571$	5.00000	0.209243	0.104622	−	0.994512i	$-0.466637\pi$
$571$	5.00000	0.209243	0.104622	+	0.994512i	$0.466637\pi$
$572$	−10.0000	−0.418121
$573$	0	0
$574$	0	0
$575$	−4.00000	−0.166812
$576$	0	0
$577$	−6.00000	−0.249783	−0.124892	−	0.992170i	$-0.539858\pi$
$577$	−6.00000	−0.249783	−0.124892	+	0.992170i	$0.539858\pi$
$578$	−2.00000	−0.0831890
$579$	0	0
$580$	−10.0000	−0.415227
$581$	0	0
$582$	0	0
$583$	60.0000	2.48495
$584$	0	0
$585$	0	0
$586$	−24.0000	−0.991431
$587$	18.0000	0.742940	0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000	0.742940	0.371470	+	0.928445i	$0.378854\pi$
$588$	0	0
$589$	5.00000	0.206021
$590$	18.0000	0.741048
$591$	0	0
$592$	0	0
$593$	−24.0000	−0.985562	−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000	−0.985562	−0.492781	+	0.870153i	$0.664020\pi$
$594$	0	0
$595$	0	0
$596$	−44.0000	−1.80231
$597$	0	0
$598$	−8.00000	−0.327144
$599$	−17.0000	−0.694601	−0.347301	−	0.937754i	$-0.612902\pi$
$599$	−17.0000	−0.694601	−0.347301	+	0.937754i	$0.612902\pi$
$600$	0	0
$601$	1.00000	0.0407909	0.0203954	−	0.999792i	$-0.493507\pi$
$601$	1.00000	0.0407909	0.0203954	+	0.999792i	$0.493507\pi$
$602$	0	0
$603$	0	0
$604$	−30.0000	−1.22068
$605$	14.0000	0.569181
$606$	0	0
$607$	14.0000	0.568242	0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000	0.568242	0.284121	+	0.958788i	$0.408298\pi$
$608$	−40.0000	−1.62221
$609$	0	0
$610$	−4.00000	−0.161955
$611$	−8.00000	−0.323645
$612$	0	0
$613$	24.0000	0.969351	0.484675	−	0.874694i	$-0.338938\pi$
$613$	24.0000	0.969351	0.484675	+	0.874694i	$0.338938\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	0	0
$617$	16.0000	0.644136	0.322068	−	0.946717i	$-0.395622\pi$
$617$	16.0000	0.644136	0.322068	+	0.946717i	$0.395622\pi$
$618$	0	0
$619$	−8.00000	−0.321547	−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000	−0.321547	−0.160774	+	0.986991i	$0.551399\pi$
$620$	2.00000	0.0803219
$621$	0	0
$622$	−18.0000	−0.721734
$623$	0	0
$624$	0	0
$625$	1.00000	0.0400000
$626$	52.0000	2.07834
$627$	0	0
$628$	44.0000	1.75579
$629$	0	0
$630$	0	0
$631$	−27.0000	−1.07485	−0.537427	−	0.843311i	$-0.680603\pi$
$631$	−27.0000	−1.07485	−0.537427	+	0.843311i	$0.680603\pi$
$632$	0	0
$633$	0	0
$634$	−24.0000	−0.953162
$635$	−4.00000	−0.158735
$636$	0	0
$637$	−7.00000	−0.277350
$638$	50.0000	1.97952
$639$	0	0
$640$	0	0
$641$	3.00000	0.118493	0.0592464	−	0.998243i	$-0.481130\pi$
$641$	3.00000	0.118493	0.0592464	+	0.998243i	$0.481130\pi$
$642$	0	0
$643$	−14.0000	−0.552106	−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000	−0.552106	−0.276053	+	0.961142i	$0.589027\pi$
$644$	0	0
$645$	0	0
$646$	−40.0000	−1.57378
$647$	30.0000	1.17942	0.589711	−	0.807614i	$-0.299242\pi$
$647$	30.0000	1.17942	0.589711	+	0.807614i	$0.299242\pi$
$648$	0	0
$649$	−45.0000	−1.76640
$650$	2.00000	0.0784465
$651$	0	0
$652$	−4.00000	−0.156652
$653$	−18.0000	−0.704394	−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000	−0.704394	−0.352197	+	0.935926i	$0.614565\pi$
$654$	0	0
$655$	15.0000	0.586098
$656$	12.0000	0.468521
$657$	0	0
$658$	0	0
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	35.0000	1.36134	0.680671	−	0.732589i	$-0.261688\pi$
$661$	35.0000	1.36134	0.680671	+	0.732589i	$0.261688\pi$
$662$	−62.0000	−2.40970
$663$	0	0
$664$	0	0
$665$	0	0
$666$	0	0
$667$	20.0000	0.774403
$668$	44.0000	1.70241
$669$	0	0
$670$	−8.00000	−0.309067
$671$	10.0000	0.386046
$672$	0	0
$673$	−8.00000	−0.308377	−0.154189	−	0.988041i	$-0.549276\pi$
$673$	−8.00000	−0.308377	−0.154189	+	0.988041i	$0.549276\pi$
$674$	44.0000	1.69482
$675$	0	0
$676$	2.00000	0.0769231
$677$	−4.00000	−0.153732	−0.0768662	−	0.997041i	$-0.524491\pi$
$677$	−4.00000	−0.153732	−0.0768662	+	0.997041i	$0.524491\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	0	0
$682$	−10.0000	−0.382920
$683$	−32.0000	−1.22445	−0.612223	−	0.790685i	$-0.709725\pi$
$683$	−32.0000	−1.22445	−0.612223	+	0.790685i	$0.709725\pi$
$684$	0	0
$685$	12.0000	0.458496
$686$	0	0
$687$	0	0
$688$	−32.0000	−1.21999
$689$	−12.0000	−0.457164
$690$	0	0
$691$	24.0000	0.913003	0.456502	−	0.889723i	$-0.349102\pi$
$691$	24.0000	0.913003	0.456502	+	0.889723i	$0.349102\pi$
$692$	8.00000	0.304114
$693$	0	0
$694$	−20.0000	−0.759190
$695$	1.00000	0.0379322
$696$	0	0
$697$	12.0000	0.454532
$698$	46.0000	1.74113
$699$	0	0
$700$	0	0
$701$	−1.00000	−0.0377695	−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000	−0.0377695	−0.0188847	+	0.999822i	$0.506012\pi$
$702$	0	0
$703$	0	0
$704$	40.0000	1.50756
$705$	0	0
$706$	−16.0000	−0.602168
$707$	0	0
$708$	0	0
$709$	2.00000	0.0751116	0.0375558	−	0.999295i	$-0.488043\pi$
$709$	2.00000	0.0751116	0.0375558	+	0.999295i	$0.488043\pi$
$710$	−18.0000	−0.675528
$711$	0	0
$712$	0	0
$713$	−4.00000	−0.149801
$714$	0	0
$715$	−5.00000	−0.186989
$716$	6.00000	0.224231
$717$	0	0
$718$	−34.0000	−1.26887
$719$	−33.0000	−1.23069	−0.615346	−	0.788257i	$-0.710984\pi$
$719$	−33.0000	−1.23069	−0.615346	+	0.788257i	$0.710984\pi$
$720$	0	0
$721$	0	0
$722$	12.0000	0.446594
$723$	0	0
$724$	−10.0000	−0.371647
$725$	−5.00000	−0.185695
$726$	0	0
$727$	24.0000	0.890111	0.445055	−	0.895503i	$-0.353184\pi$
$727$	24.0000	0.890111	0.445055	+	0.895503i	$0.353184\pi$
$728$	0	0
$729$	0	0
$730$	24.0000	0.888280
$731$	−32.0000	−1.18356
$732$	0	0
$733$	24.0000	0.886460	0.443230	−	0.896408i	$-0.353832\pi$
$733$	24.0000	0.886460	0.443230	+	0.896408i	$0.353832\pi$
$734$	−44.0000	−1.62407
$735$	0	0
$736$	32.0000	1.17954
$737$	20.0000	0.736709
$738$	0	0
$739$	35.0000	1.28750	0.643748	−	0.765238i	$-0.277379\pi$
$739$	35.0000	1.28750	0.643748	+	0.765238i	$0.277379\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	0	0
$745$	−22.0000	−0.806018
$746$	32.0000	1.17160
$747$	0	0
$748$	40.0000	1.46254
$749$	0	0
$750$	0	0
$751$	48.0000	1.75154	0.875772	−	0.482724i	$-0.160353\pi$
$751$	48.0000	1.75154	0.875772	+	0.482724i	$0.160353\pi$
$752$	32.0000	1.16692
$753$	0	0
$754$	−10.0000	−0.364179
$755$	−15.0000	−0.545906
$756$	0	0
$757$	−12.0000	−0.436147	−0.218074	−	0.975932i	$-0.569977\pi$
$757$	−12.0000	−0.436147	−0.218074	+	0.975932i	$0.569977\pi$
$758$	−72.0000	−2.61516
$759$	0	0
$760$	0	0
$761$	43.0000	1.55875	0.779374	−	0.626559i	$-0.215537\pi$
$761$	43.0000	1.55875	0.779374	+	0.626559i	$0.215537\pi$
$762$	0	0
$763$	0	0
$764$	2.00000	0.0723575
$765$	0	0
$766$	−12.0000	−0.433578
$767$	9.00000	0.324971
$768$	0	0
$769$	15.0000	0.540914	0.270457	−	0.962732i	$-0.412825\pi$
$769$	15.0000	0.540914	0.270457	+	0.962732i	$0.412825\pi$
$770$	0	0
$771$	0	0
$772$	−28.0000	−1.00774
$773$	−42.0000	−1.51064	−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000	−1.51064	−0.755318	+	0.655359i	$0.772517\pi$
$774$	0	0
$775$	1.00000	0.0359211
$776$	0	0
$777$	0	0
$778$	12.0000	0.430221
$779$	−15.0000	−0.537431
$780$	0	0
$781$	45.0000	1.61023
$782$	32.0000	1.14432
$783$	0	0
$784$	28.0000	1.00000
$785$	22.0000	0.785214
$786$	0	0
$787$	−16.0000	−0.570338	−0.285169	−	0.958477i	$-0.592050\pi$
$787$	−16.0000	−0.570338	−0.285169	+	0.958477i	$0.592050\pi$
$788$	−36.0000	−1.28245
$789$	0	0
$790$	−16.0000	−0.569254
$791$	0	0
$792$	0	0
$793$	−2.00000	−0.0710221
$794$	4.00000	0.141955
$795$	0	0
$796$	32.0000	1.13421
$797$	4.00000	0.141687	0.0708436	−	0.997487i	$-0.477431\pi$
$797$	4.00000	0.141687	0.0708436	+	0.997487i	$0.477431\pi$
$798$	0	0
$799$	32.0000	1.13208
$800$	−8.00000	−0.282843
$801$	0	0
$802$	60.0000	2.11867
$803$	−60.0000	−2.11735
$804$	0	0
$805$	0	0
$806$	2.00000	0.0704470
$807$	0	0
$808$	0	0
$809$	−33.0000	−1.16022	−0.580109	−	0.814539i	$-0.696990\pi$
$809$	−33.0000	−1.16022	−0.580109	+	0.814539i	$0.696990\pi$
$810$	0	0
$811$	−31.0000	−1.08856	−0.544279	−	0.838905i	$-0.683197\pi$
$811$	−31.0000	−1.08856	−0.544279	+	0.838905i	$0.683197\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	−2.00000	−0.0700569
$816$	0	0
$817$	40.0000	1.39942
$818$	68.0000	2.37756
$819$	0	0
$820$	−6.00000	−0.209529
$821$	13.0000	0.453703	0.226852	−	0.973929i	$-0.427157\pi$
$821$	13.0000	0.453703	0.226852	+	0.973929i	$0.427157\pi$
$822$	0	0
$823$	−6.00000	−0.209147	−0.104573	−	0.994517i	$-0.533348\pi$
$823$	−6.00000	−0.209147	−0.104573	+	0.994517i	$0.533348\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	54.0000	1.87776	0.938882	−	0.344239i	$-0.111863\pi$
$827$	54.0000	1.87776	0.938882	+	0.344239i	$0.111863\pi$
$828$	0	0
$829$	−13.0000	−0.451509	−0.225754	−	0.974184i	$-0.572485\pi$
$829$	−13.0000	−0.451509	−0.225754	+	0.974184i	$0.572485\pi$
$830$	−8.00000	−0.277684
$831$	0	0
$832$	−8.00000	−0.277350
$833$	28.0000	0.970143
$834$	0	0
$835$	22.0000	0.761341
$836$	−50.0000	−1.72929
$837$	0	0
$838$	−8.00000	−0.276355
$839$	43.0000	1.48452	0.742262	−	0.670109i	$-0.233753\pi$
$839$	43.0000	1.48452	0.742262	+	0.670109i	$0.233753\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	−74.0000	−2.55021
$843$	0	0
$844$	22.0000	0.757271
$845$	1.00000	0.0344010
$846$	0	0
$847$	0	0
$848$	48.0000	1.64833
$849$	0	0
$850$	−8.00000	−0.274398
$851$	0	0
$852$	0	0
$853$	−30.0000	−1.02718	−0.513590	−	0.858036i	$-0.671685\pi$
$853$	−30.0000	−1.02718	−0.513590	+	0.858036i	$0.671685\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−8.00000	−0.273275	−0.136637	−	0.990621i	$-0.543630\pi$
$857$	−8.00000	−0.273275	−0.136637	+	0.990621i	$0.543630\pi$
$858$	0	0
$859$	−25.0000	−0.852989	−0.426494	−	0.904490i	$-0.640252\pi$
$859$	−25.0000	−0.852989	−0.426494	+	0.904490i	$0.640252\pi$
$860$	16.0000	0.545595
$861$	0	0
$862$	−14.0000	−0.476842
$863$	56.0000	1.90626	0.953131	−	0.302558i	$-0.0978405\pi$
$863$	56.0000	1.90626	0.953131	+	0.302558i	$0.0978405\pi$
$864$	0	0
$865$	4.00000	0.136004
$866$	48.0000	1.63111
$867$	0	0
$868$	0	0
$869$	40.0000	1.35691
$870$	0	0
$871$	−4.00000	−0.135535
$872$	0	0
$873$	0	0
$874$	−40.0000	−1.35302
$875$	0	0
$876$	0	0
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	−18.0000	−0.607471
$879$	0	0
$880$	20.0000	0.674200
$881$	−5.00000	−0.168454	−0.0842271	−	0.996447i	$-0.526842\pi$
$881$	−5.00000	−0.168454	−0.0842271	+	0.996447i	$0.526842\pi$
$882$	0	0
$883$	−42.0000	−1.41341	−0.706706	−	0.707507i	$-0.749820\pi$
$883$	−42.0000	−1.41341	−0.706706	+	0.707507i	$0.749820\pi$
$884$	−8.00000	−0.269069
$885$	0	0
$886$	−8.00000	−0.268765
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	0	0
$889$	0	0
$890$	2.00000	0.0670402
$891$	0	0
$892$	−24.0000	−0.803579
$893$	−40.0000	−1.33855
$894$	0	0
$895$	3.00000	0.100279
$896$	0	0
$897$	0	0
$898$	54.0000	1.80200
$899$	−5.00000	−0.166759
$900$	0	0
$901$	48.0000	1.59911
$902$	30.0000	0.998891
$903$	0	0
$904$	0	0
$905$	−5.00000	−0.166206
$906$	0	0
$907$	32.0000	1.06254	0.531271	−	0.847202i	$-0.321714\pi$
$907$	32.0000	1.06254	0.531271	+	0.847202i	$0.321714\pi$
$908$	−12.0000	−0.398234
$909$	0	0
$910$	0	0
$911$	−49.0000	−1.62344	−0.811721	−	0.584045i	$-0.801469\pi$
$911$	−49.0000	−1.62344	−0.811721	+	0.584045i	$0.801469\pi$
$912$	0	0
$913$	20.0000	0.661903
$914$	64.0000	2.11693
$915$	0	0
$916$	−28.0000	−0.925146
$917$	0	0
$918$	0	0
$919$	29.0000	0.956622	0.478311	−	0.878191i	$-0.341249\pi$
$919$	29.0000	0.956622	0.478311	+	0.878191i	$0.341249\pi$
$920$	0	0
$921$	0	0
$922$	30.0000	0.987997
$923$	−9.00000	−0.296239
$924$	0	0
$925$	0	0
$926$	−32.0000	−1.05159
$927$	0	0
$928$	40.0000	1.31306
$929$	51.0000	1.67326	0.836628	−	0.547772i	$-0.184524\pi$
$929$	51.0000	1.67326	0.836628	+	0.547772i	$0.184524\pi$
$930$	0	0
$931$	−35.0000	−1.14708
$932$	−8.00000	−0.262049
$933$	0	0
$934$	68.0000	2.22503
$935$	20.0000	0.654070
$936$	0	0
$937$	−28.0000	−0.914720	−0.457360	−	0.889282i	$-0.651205\pi$
$937$	−28.0000	−0.914720	−0.457360	+	0.889282i	$0.651205\pi$
$938$	0	0
$939$	0	0
$940$	−16.0000	−0.521862
$941$	−14.0000	−0.456387	−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000	−0.456387	−0.228193	+	0.973616i	$0.573282\pi$
$942$	0	0
$943$	12.0000	0.390774
$944$	−36.0000	−1.17170
$945$	0	0
$946$	−80.0000	−2.60102
$947$	−42.0000	−1.36482	−0.682408	−	0.730971i	$-0.739067\pi$
$947$	−42.0000	−1.36482	−0.682408	+	0.730971i	$0.739067\pi$
$948$	0	0
$949$	12.0000	0.389536
$950$	10.0000	0.324443
$951$	0	0
$952$	0	0
$953$	4.00000	0.129573	0.0647864	−	0.997899i	$-0.479363\pi$
$953$	4.00000	0.129573	0.0647864	+	0.997899i	$0.479363\pi$
$954$	0	0
$955$	1.00000	0.0323592
$956$	48.0000	1.55243
$957$	0	0
$958$	−50.0000	−1.61543
$959$	0	0
$960$	0	0
$961$	−30.0000	−0.967742
$962$	0	0
$963$	0	0
$964$	38.0000	1.22390
$965$	−14.0000	−0.450676
$966$	0	0
$967$	−40.0000	−1.28631	−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000	−1.28631	−0.643157	+	0.765735i	$0.722376\pi$
$968$	0	0
$969$	0	0
$970$	−12.0000	−0.385297
$971$	−27.0000	−0.866471	−0.433236	−	0.901281i	$-0.642628\pi$
$971$	−27.0000	−0.866471	−0.433236	+	0.901281i	$0.642628\pi$
$972$	0	0
$973$	0	0
$974$	−4.00000	−0.128168
$975$	0	0
$976$	8.00000	0.256074
$977$	12.0000	0.383914	0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000	0.383914	0.191957	+	0.981403i	$0.438517\pi$
$978$	0	0
$979$	−5.00000	−0.159801
$980$	−14.0000	−0.447214
$981$	0	0
$982$	−34.0000	−1.08498
$983$	−12.0000	−0.382741	−0.191370	−	0.981518i	$-0.561293\pi$
$983$	−12.0000	−0.382741	−0.191370	+	0.981518i	$0.561293\pi$
$984$	0	0
$985$	−18.0000	−0.573528
$986$	40.0000	1.27386
$987$	0	0
$988$	10.0000	0.318142
$989$	−32.0000	−1.01754
$990$	0	0
$991$	−21.0000	−0.667087	−0.333543	−	0.942735i	$-0.608244\pi$
$991$	−21.0000	−0.667087	−0.333543	+	0.942735i	$0.608244\pi$
$992$	−8.00000	−0.254000
$993$	0	0
$994$	0	0
$995$	16.0000	0.507234
$996$	0	0
$997$	8.00000	0.253363	0.126681	−	0.991943i	$-0.459567\pi$
$997$	8.00000	0.253363	0.126681	+	0.991943i	$0.459567\pi$
$998$	−46.0000	−1.45610
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5265.2.a.o.1.1	yes	1
3.2	odd	2		5265.2.a.b.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5265.2.a.b.1.1	✓	1	3.2	odd	2
5265.2.a.o.1.1	yes	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5265 = 3^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5265.a (trivial)

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