LMFDB - Embedded newform 1856.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1856,2,Mod(1,1856)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1856, 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("1856.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1856 = 2^{6} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1856.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:	$14.8202346151$
Analytic rank:	$2$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 116)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1856.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{3} -3.00000 q^{5} -4.00000 q^{7} -2.00000 q^{9} +O(q^{10})$

$q-1.00000 q^{3} -3.00000 q^{5} -4.00000 q^{7} -2.00000 q^{9} -3.00000 q^{11} -5.00000 q^{13} +3.00000 q^{15} -6.00000 q^{17} +4.00000 q^{19} +4.00000 q^{21} -6.00000 q^{23} +4.00000 q^{25} +5.00000 q^{27} +1.00000 q^{29} +5.00000 q^{31} +3.00000 q^{33} +12.0000 q^{35} -8.00000 q^{37} +5.00000 q^{39} +1.00000 q^{43} +6.00000 q^{45} -3.00000 q^{47} +9.00000 q^{49} +6.00000 q^{51} -3.00000 q^{53} +9.00000 q^{55} -4.00000 q^{57} -6.00000 q^{59} -2.00000 q^{61} +8.00000 q^{63} +15.0000 q^{65} -8.00000 q^{67} +6.00000 q^{69} +6.00000 q^{71} -16.0000 q^{73} -4.00000 q^{75} +12.0000 q^{77} +11.0000 q^{79} +1.00000 q^{81} -6.00000 q^{83} +18.0000 q^{85} -1.00000 q^{87} -12.0000 q^{89} +20.0000 q^{91} -5.00000 q^{93} -12.0000 q^{95} +8.00000 q^{97} +6.00000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	0	0
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	0	0
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	0	0
$9$	−2.00000	−0.666667
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	0	0
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	0	0
$15$	3.00000	0.774597
$16$	0	0
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	0	0
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	0	0
$21$	4.00000	0.872872
$22$	0	0
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	4.00000	0.800000
$26$	0	0
$27$	5.00000	0.962250
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	0	0
$33$	3.00000	0.522233
$34$	0	0
$35$	12.0000	2.02837
$36$	0	0
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	0	0
$39$	5.00000	0.800641
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	1.00000	0.152499	0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000	0.152499	0.0762493	+	0.997089i	$0.475706\pi$
$44$	0	0
$45$	6.00000	0.894427
$46$	0	0
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	0	0
$51$	6.00000	0.840168
$52$	0	0
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	0	0
$55$	9.00000	1.21356
$56$	0	0
$57$	−4.00000	−0.529813
$58$	0	0
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	0	0
$63$	8.00000	1.00791
$64$	0	0
$65$	15.0000	1.86052
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	0	0
$69$	6.00000	0.722315
$70$	0	0
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	0	0
$73$	−16.0000	−1.87266	−0.936329	−	0.351123i	$-0.885800\pi$
$73$	−16.0000	−1.87266	−0.936329	+	0.351123i	$0.885800\pi$
$74$	0	0
$75$	−4.00000	−0.461880
$76$	0	0
$77$	12.0000	1.36753
$78$	0	0
$79$	11.0000	1.23760	0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000	1.23760	0.618798	+	0.785550i	$0.287620\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	−6.00000	−0.658586	−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000	−0.658586	−0.329293	+	0.944228i	$0.606810\pi$
$84$	0	0
$85$	18.0000	1.95237
$86$	0	0
$87$	−1.00000	−0.107211
$88$	0	0
$89$	−12.0000	−1.27200	−0.635999	−	0.771690i	$-0.719412\pi$
$89$	−12.0000	−1.27200	−0.635999	+	0.771690i	$0.719412\pi$
$90$	0	0
$91$	20.0000	2.09657
$92$	0	0
$93$	−5.00000	−0.518476
$94$	0	0
$95$	−12.0000	−1.23117
$96$	0	0
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	0	0
$99$	6.00000	0.603023
$100$	0	0
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	0	0
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	0	0
$105$	−12.0000	−1.17108
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	0	0
$109$	−11.0000	−1.05361	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000	−1.05361	−0.526804	+	0.849987i	$0.676610\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	0	0
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	18.0000	1.67851
$116$	0	0
$117$	10.0000	0.924500
$118$	0	0
$119$	24.0000	2.20008
$120$	0	0
$121$	−2.00000	−0.181818
$122$	0	0
$123$	0	0
$124$	0	0
$125$	3.00000	0.268328
$126$	0	0
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	0	0
$129$	−1.00000	−0.0880451
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	−16.0000	−1.38738
$134$	0	0
$135$	−15.0000	−1.29099
$136$	0	0
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	0	0
$139$	−14.0000	−1.18746	−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000	−1.18746	−0.593732	+	0.804663i	$0.702346\pi$
$140$	0	0
$141$	3.00000	0.252646
$142$	0	0
$143$	15.0000	1.25436
$144$	0	0
$145$	−3.00000	−0.249136
$146$	0	0
$147$	−9.00000	−0.742307
$148$	0	0
$149$	15.0000	1.22885	0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000	1.22885	0.614424	+	0.788976i	$0.289388\pi$
$150$	0	0
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	0	0
$153$	12.0000	0.970143
$154$	0	0
$155$	−15.0000	−1.20483
$156$	0	0
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	0	0
$159$	3.00000	0.237915
$160$	0	0
$161$	24.0000	1.89146
$162$	0	0
$163$	13.0000	1.01824	0.509119	−	0.860696i	$-0.329971\pi$
$163$	13.0000	1.01824	0.509119	+	0.860696i	$0.329971\pi$
$164$	0	0
$165$	−9.00000	−0.700649
$166$	0	0
$167$	−6.00000	−0.464294	−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000	−0.464294	−0.232147	+	0.972681i	$0.574575\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	−8.00000	−0.611775
$172$	0	0
$173$	18.0000	1.36851	0.684257	−	0.729241i	$-0.260127\pi$
$173$	18.0000	1.36851	0.684257	+	0.729241i	$0.260127\pi$
$174$	0	0
$175$	−16.0000	−1.20949
$176$	0	0
$177$	6.00000	0.450988
$178$	0	0
$179$	−18.0000	−1.34538	−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000	−1.34538	−0.672692	+	0.739923i	$0.734862\pi$
$180$	0	0
$181$	−17.0000	−1.26360	−0.631800	−	0.775131i	$-0.717684\pi$
$181$	−17.0000	−1.26360	−0.631800	+	0.775131i	$0.717684\pi$
$182$	0	0
$183$	2.00000	0.147844
$184$	0	0
$185$	24.0000	1.76452
$186$	0	0
$187$	18.0000	1.31629
$188$	0	0
$189$	−20.0000	−1.45479
$190$	0	0
$191$	−24.0000	−1.73658	−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000	−1.73658	−0.868290	+	0.496058i	$0.834780\pi$
$192$	0	0
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	0	0
$195$	−15.0000	−1.07417
$196$	0	0
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	0	0
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	0	0
$201$	8.00000	0.564276
$202$	0	0
$203$	−4.00000	−0.280745
$204$	0	0
$205$	0	0
$206$	0	0
$207$	12.0000	0.834058
$208$	0	0
$209$	−12.0000	−0.830057
$210$	0	0
$211$	1.00000	0.0688428	0.0344214	−	0.999407i	$-0.489041\pi$
$211$	1.00000	0.0688428	0.0344214	+	0.999407i	$0.489041\pi$
$212$	0	0
$213$	−6.00000	−0.411113
$214$	0	0
$215$	−3.00000	−0.204598
$216$	0	0
$217$	−20.0000	−1.35769
$218$	0	0
$219$	16.0000	1.08118
$220$	0	0
$221$	30.0000	2.01802
$222$	0	0
$223$	−10.0000	−0.669650	−0.334825	−	0.942280i	$-0.608677\pi$
$223$	−10.0000	−0.669650	−0.334825	+	0.942280i	$0.608677\pi$
$224$	0	0
$225$	−8.00000	−0.533333
$226$	0	0
$227$	−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
$229$	4.00000	0.264327	0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000	0.264327	0.132164	+	0.991228i	$0.457808\pi$
$230$	0	0
$231$	−12.0000	−0.789542
$232$	0	0
$233$	−9.00000	−0.589610	−0.294805	−	0.955557i	$-0.595255\pi$
$233$	−9.00000	−0.589610	−0.294805	+	0.955557i	$0.595255\pi$
$234$	0	0
$235$	9.00000	0.587095
$236$	0	0
$237$	−11.0000	−0.714527
$238$	0	0
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	0	0
$241$	17.0000	1.09507	0.547533	−	0.836784i	$-0.315567\pi$
$241$	17.0000	1.09507	0.547533	+	0.836784i	$0.315567\pi$
$242$	0	0
$243$	−16.0000	−1.02640
$244$	0	0
$245$	−27.0000	−1.72497
$246$	0	0
$247$	−20.0000	−1.27257
$248$	0	0
$249$	6.00000	0.380235
$250$	0	0
$251$	−21.0000	−1.32551	−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000	−1.32551	−0.662754	+	0.748837i	$0.730613\pi$
$252$	0	0
$253$	18.0000	1.13165
$254$	0	0
$255$	−18.0000	−1.12720
$256$	0	0
$257$	−3.00000	−0.187135	−0.0935674	−	0.995613i	$-0.529827\pi$
$257$	−3.00000	−0.187135	−0.0935674	+	0.995613i	$0.529827\pi$
$258$	0	0
$259$	32.0000	1.98838
$260$	0	0
$261$	−2.00000	−0.123797
$262$	0	0
$263$	9.00000	0.554964	0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000	0.554964	0.277482	+	0.960731i	$0.410500\pi$
$264$	0	0
$265$	9.00000	0.552866
$266$	0	0
$267$	12.0000	0.734388
$268$	0	0
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	−1.00000	−0.0607457	−0.0303728	−	0.999539i	$-0.509669\pi$
$271$	−1.00000	−0.0607457	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	0	0
$273$	−20.0000	−1.21046
$274$	0	0
$275$	−12.0000	−0.723627
$276$	0	0
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	0	0
$279$	−10.0000	−0.598684
$280$	0	0
$281$	15.0000	0.894825	0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000	0.894825	0.447412	+	0.894328i	$0.352346\pi$
$282$	0	0
$283$	22.0000	1.30776	0.653882	−	0.756596i	$-0.273139\pi$
$283$	22.0000	1.30776	0.653882	+	0.756596i	$0.273139\pi$
$284$	0	0
$285$	12.0000	0.710819
$286$	0	0
$287$	0	0
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	−8.00000	−0.468968
$292$	0	0
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	0	0
$295$	18.0000	1.04800
$296$	0	0
$297$	−15.0000	−0.870388
$298$	0	0
$299$	30.0000	1.73494
$300$	0	0
$301$	−4.00000	−0.230556
$302$	0	0
$303$	12.0000	0.689382
$304$	0	0
$305$	6.00000	0.343559
$306$	0	0
$307$	−11.0000	−0.627803	−0.313902	−	0.949456i	$-0.601636\pi$
$307$	−11.0000	−0.627803	−0.313902	+	0.949456i	$0.601636\pi$
$308$	0	0
$309$	−14.0000	−0.796432
$310$	0	0
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	0	0
$313$	−7.00000	−0.395663	−0.197832	−	0.980236i	$-0.563390\pi$
$313$	−7.00000	−0.395663	−0.197832	+	0.980236i	$0.563390\pi$
$314$	0	0
$315$	−24.0000	−1.35225
$316$	0	0
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	0	0
$319$	−3.00000	−0.167968
$320$	0	0
$321$	0	0
$322$	0	0
$323$	−24.0000	−1.33540
$324$	0	0
$325$	−20.0000	−1.10940
$326$	0	0
$327$	11.0000	0.608301
$328$	0	0
$329$	12.0000	0.661581
$330$	0	0
$331$	1.00000	0.0549650	0.0274825	−	0.999622i	$-0.491251\pi$
$331$	1.00000	0.0549650	0.0274825	+	0.999622i	$0.491251\pi$
$332$	0	0
$333$	16.0000	0.876795
$334$	0	0
$335$	24.0000	1.31126
$336$	0	0
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	0	0
$339$	6.00000	0.325875
$340$	0	0
$341$	−15.0000	−0.812296
$342$	0	0
$343$	−8.00000	−0.431959
$344$	0	0
$345$	−18.0000	−0.969087
$346$	0	0
$347$	−18.0000	−0.966291	−0.483145	−	0.875540i	$-0.660506\pi$
$347$	−18.0000	−0.966291	−0.483145	+	0.875540i	$0.660506\pi$
$348$	0	0
$349$	−11.0000	−0.588817	−0.294408	−	0.955680i	$-0.595123\pi$
$349$	−11.0000	−0.588817	−0.294408	+	0.955680i	$0.595123\pi$
$350$	0	0
$351$	−25.0000	−1.33440
$352$	0	0
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	0	0
$355$	−18.0000	−0.955341
$356$	0	0
$357$	−24.0000	−1.27021
$358$	0	0
$359$	−33.0000	−1.74167	−0.870837	−	0.491572i	$-0.836422\pi$
$359$	−33.0000	−1.74167	−0.870837	+	0.491572i	$0.836422\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	0	0
$363$	2.00000	0.104973
$364$	0	0
$365$	48.0000	2.51243
$366$	0	0
$367$	−4.00000	−0.208798	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−4.00000	−0.208798	−0.104399	+	0.994535i	$0.533292\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	12.0000	0.623009
$372$	0	0
$373$	19.0000	0.983783	0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000	0.983783	0.491891	+	0.870657i	$0.336306\pi$
$374$	0	0
$375$	−3.00000	−0.154919
$376$	0	0
$377$	−5.00000	−0.257513
$378$	0	0
$379$	−8.00000	−0.410932	−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000	−0.410932	−0.205466	+	0.978664i	$0.565871\pi$
$380$	0	0
$381$	16.0000	0.819705
$382$	0	0
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	0	0
$385$	−36.0000	−1.83473
$386$	0	0
$387$	−2.00000	−0.101666
$388$	0	0
$389$	−36.0000	−1.82527	−0.912636	−	0.408773i	$-0.865957\pi$
$389$	−36.0000	−1.82527	−0.912636	+	0.408773i	$0.865957\pi$
$390$	0	0
$391$	36.0000	1.82060
$392$	0	0
$393$	−12.0000	−0.605320
$394$	0	0
$395$	−33.0000	−1.66041
$396$	0	0
$397$	−29.0000	−1.45547	−0.727734	−	0.685859i	$-0.759427\pi$
$397$	−29.0000	−1.45547	−0.727734	+	0.685859i	$0.759427\pi$
$398$	0	0
$399$	16.0000	0.801002
$400$	0	0
$401$	−21.0000	−1.04869	−0.524345	−	0.851506i	$-0.675690\pi$
$401$	−21.0000	−1.04869	−0.524345	+	0.851506i	$0.675690\pi$
$402$	0	0
$403$	−25.0000	−1.24534
$404$	0	0
$405$	−3.00000	−0.149071
$406$	0	0
$407$	24.0000	1.18964
$408$	0	0
$409$	−10.0000	−0.494468	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000	−0.494468	−0.247234	+	0.968956i	$0.579522\pi$
$410$	0	0
$411$	12.0000	0.591916
$412$	0	0
$413$	24.0000	1.18096
$414$	0	0
$415$	18.0000	0.883585
$416$	0	0
$417$	14.0000	0.685583
$418$	0	0
$419$	30.0000	1.46560	0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000	1.46560	0.732798	+	0.680446i	$0.238214\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	0	0
$423$	6.00000	0.291730
$424$	0	0
$425$	−24.0000	−1.16417
$426$	0	0
$427$	8.00000	0.387147
$428$	0	0
$429$	−15.0000	−0.724207
$430$	0	0
$431$	−30.0000	−1.44505	−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000	−1.44505	−0.722525	+	0.691345i	$0.757018\pi$
$432$	0	0
$433$	20.0000	0.961139	0.480569	−	0.876957i	$-0.340430\pi$
$433$	20.0000	0.961139	0.480569	+	0.876957i	$0.340430\pi$
$434$	0	0
$435$	3.00000	0.143839
$436$	0	0
$437$	−24.0000	−1.14808
$438$	0	0
$439$	−10.0000	−0.477274	−0.238637	−	0.971109i	$-0.576701\pi$
$439$	−10.0000	−0.477274	−0.238637	+	0.971109i	$0.576701\pi$
$440$	0	0
$441$	−18.0000	−0.857143
$442$	0	0
$443$	−12.0000	−0.570137	−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000	−0.570137	−0.285069	+	0.958507i	$0.592016\pi$
$444$	0	0
$445$	36.0000	1.70656
$446$	0	0
$447$	−15.0000	−0.709476
$448$	0	0
$449$	−42.0000	−1.98210	−0.991051	−	0.133482i	$-0.957384\pi$
$449$	−42.0000	−1.98210	−0.991051	+	0.133482i	$0.957384\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	4.00000	0.187936
$454$	0	0
$455$	−60.0000	−2.81284
$456$	0	0
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	0	0
$459$	−30.0000	−1.40028
$460$	0	0
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	0	0
$463$	−10.0000	−0.464739	−0.232370	−	0.972628i	$-0.574648\pi$
$463$	−10.0000	−0.464739	−0.232370	+	0.972628i	$0.574648\pi$
$464$	0	0
$465$	15.0000	0.695608
$466$	0	0
$467$	9.00000	0.416470	0.208235	−	0.978079i	$-0.433228\pi$
$467$	9.00000	0.416470	0.208235	+	0.978079i	$0.433228\pi$
$468$	0	0
$469$	32.0000	1.47762
$470$	0	0
$471$	−4.00000	−0.184310
$472$	0	0
$473$	−3.00000	−0.137940
$474$	0	0
$475$	16.0000	0.734130
$476$	0	0
$477$	6.00000	0.274721
$478$	0	0
$479$	3.00000	0.137073	0.0685367	−	0.997649i	$-0.478167\pi$
$479$	3.00000	0.137073	0.0685367	+	0.997649i	$0.478167\pi$
$480$	0	0
$481$	40.0000	1.82384
$482$	0	0
$483$	−24.0000	−1.09204
$484$	0	0
$485$	−24.0000	−1.08978
$486$	0	0
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	0	0
$489$	−13.0000	−0.587880
$490$	0	0
$491$	3.00000	0.135388	0.0676941	−	0.997706i	$-0.478436\pi$
$491$	3.00000	0.135388	0.0676941	+	0.997706i	$0.478436\pi$
$492$	0	0
$493$	−6.00000	−0.270226
$494$	0	0
$495$	−18.0000	−0.809040
$496$	0	0
$497$	−24.0000	−1.07655
$498$	0	0
$499$	22.0000	0.984855	0.492428	−	0.870353i	$-0.336110\pi$
$499$	22.0000	0.984855	0.492428	+	0.870353i	$0.336110\pi$
$500$	0	0
$501$	6.00000	0.268060
$502$	0	0
$503$	−21.0000	−0.936344	−0.468172	−	0.883637i	$-0.655087\pi$
$503$	−21.0000	−0.936344	−0.468172	+	0.883637i	$0.655087\pi$
$504$	0	0
$505$	36.0000	1.60198
$506$	0	0
$507$	−12.0000	−0.532939
$508$	0	0
$509$	9.00000	0.398918	0.199459	−	0.979906i	$-0.436082\pi$
$509$	9.00000	0.398918	0.199459	+	0.979906i	$0.436082\pi$
$510$	0	0
$511$	64.0000	2.83119
$512$	0	0
$513$	20.0000	0.883022
$514$	0	0
$515$	−42.0000	−1.85074
$516$	0	0
$517$	9.00000	0.395820
$518$	0	0
$519$	−18.0000	−0.790112
$520$	0	0
$521$	15.0000	0.657162	0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000	0.657162	0.328581	+	0.944476i	$0.393430\pi$
$522$	0	0
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	0	0
$525$	16.0000	0.698297
$526$	0	0
$527$	−30.0000	−1.30682
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	12.0000	0.520756
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	18.0000	0.776757
$538$	0	0
$539$	−27.0000	−1.16297
$540$	0	0
$541$	−8.00000	−0.343947	−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000	−0.343947	−0.171973	+	0.985102i	$0.555014\pi$
$542$	0	0
$543$	17.0000	0.729540
$544$	0	0
$545$	33.0000	1.41356
$546$	0	0
$547$	−32.0000	−1.36822	−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000	−1.36822	−0.684111	+	0.729378i	$0.739809\pi$
$548$	0	0
$549$	4.00000	0.170716
$550$	0	0
$551$	4.00000	0.170406
$552$	0	0
$553$	−44.0000	−1.87107
$554$	0	0
$555$	−24.0000	−1.01874
$556$	0	0
$557$	−42.0000	−1.77960	−0.889799	−	0.456354i	$-0.849155\pi$
$557$	−42.0000	−1.77960	−0.889799	+	0.456354i	$0.849155\pi$
$558$	0	0
$559$	−5.00000	−0.211477
$560$	0	0
$561$	−18.0000	−0.759961
$562$	0	0
$563$	21.0000	0.885044	0.442522	−	0.896758i	$-0.354084\pi$
$563$	21.0000	0.885044	0.442522	+	0.896758i	$0.354084\pi$
$564$	0	0
$565$	18.0000	0.757266
$566$	0	0
$567$	−4.00000	−0.167984
$568$	0	0
$569$	−18.0000	−0.754599	−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000	−0.754599	−0.377300	+	0.926091i	$0.623147\pi$
$570$	0	0
$571$	−32.0000	−1.33916	−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000	−1.33916	−0.669579	+	0.742741i	$0.733526\pi$
$572$	0	0
$573$	24.0000	1.00261
$574$	0	0
$575$	−24.0000	−1.00087
$576$	0	0
$577$	26.0000	1.08239	0.541197	−	0.840896i	$-0.317971\pi$
$577$	26.0000	1.08239	0.541197	+	0.840896i	$0.317971\pi$
$578$	0	0
$579$	16.0000	0.664937
$580$	0	0
$581$	24.0000	0.995688
$582$	0	0
$583$	9.00000	0.372742
$584$	0	0
$585$	−30.0000	−1.24035
$586$	0	0
$587$	6.00000	0.247647	0.123823	−	0.992304i	$-0.460484\pi$
$587$	6.00000	0.247647	0.123823	+	0.992304i	$0.460484\pi$
$588$	0	0
$589$	20.0000	0.824086
$590$	0	0
$591$	−6.00000	−0.246807
$592$	0	0
$593$	27.0000	1.10876	0.554379	−	0.832265i	$-0.312956\pi$
$593$	27.0000	1.10876	0.554379	+	0.832265i	$0.312956\pi$
$594$	0	0
$595$	−72.0000	−2.95171
$596$	0	0
$597$	−20.0000	−0.818546
$598$	0	0
$599$	3.00000	0.122577	0.0612883	−	0.998120i	$-0.480479\pi$
$599$	3.00000	0.122577	0.0612883	+	0.998120i	$0.480479\pi$
$600$	0	0
$601$	44.0000	1.79480	0.897399	−	0.441221i	$-0.145454\pi$
$601$	44.0000	1.79480	0.897399	+	0.441221i	$0.145454\pi$
$602$	0	0
$603$	16.0000	0.651570
$604$	0	0
$605$	6.00000	0.243935
$606$	0	0
$607$	35.0000	1.42061	0.710303	−	0.703896i	$-0.248558\pi$
$607$	35.0000	1.42061	0.710303	+	0.703896i	$0.248558\pi$
$608$	0	0
$609$	4.00000	0.162088
$610$	0	0
$611$	15.0000	0.606835
$612$	0	0
$613$	−11.0000	−0.444286	−0.222143	−	0.975014i	$-0.571305\pi$
$613$	−11.0000	−0.444286	−0.222143	+	0.975014i	$0.571305\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	12.0000	0.483102	0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000	0.483102	0.241551	+	0.970388i	$0.422344\pi$
$618$	0	0
$619$	13.0000	0.522514	0.261257	−	0.965269i	$-0.415863\pi$
$619$	13.0000	0.522514	0.261257	+	0.965269i	$0.415863\pi$
$620$	0	0
$621$	−30.0000	−1.20386
$622$	0	0
$623$	48.0000	1.92308
$624$	0	0
$625$	−29.0000	−1.16000
$626$	0	0
$627$	12.0000	0.479234
$628$	0	0
$629$	48.0000	1.91389
$630$	0	0
$631$	−22.0000	−0.875806	−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000	−0.875806	−0.437903	+	0.899022i	$0.644279\pi$
$632$	0	0
$633$	−1.00000	−0.0397464
$634$	0	0
$635$	48.0000	1.90482
$636$	0	0
$637$	−45.0000	−1.78296
$638$	0	0
$639$	−12.0000	−0.474713
$640$	0	0
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	0	0
$643$	40.0000	1.57745	0.788723	−	0.614749i	$-0.210743\pi$
$643$	40.0000	1.57745	0.788723	+	0.614749i	$0.210743\pi$
$644$	0	0
$645$	3.00000	0.118125
$646$	0	0
$647$	−42.0000	−1.65119	−0.825595	−	0.564263i	$-0.809160\pi$
$647$	−42.0000	−1.65119	−0.825595	+	0.564263i	$0.809160\pi$
$648$	0	0
$649$	18.0000	0.706562
$650$	0	0
$651$	20.0000	0.783862
$652$	0	0
$653$	−12.0000	−0.469596	−0.234798	−	0.972044i	$-0.575443\pi$
$653$	−12.0000	−0.469596	−0.234798	+	0.972044i	$0.575443\pi$
$654$	0	0
$655$	−36.0000	−1.40664
$656$	0	0
$657$	32.0000	1.24844
$658$	0	0
$659$	−21.0000	−0.818044	−0.409022	−	0.912525i	$-0.634130\pi$
$659$	−21.0000	−0.818044	−0.409022	+	0.912525i	$0.634130\pi$
$660$	0	0
$661$	−26.0000	−1.01128	−0.505641	−	0.862744i	$-0.668744\pi$
$661$	−26.0000	−1.01128	−0.505641	+	0.862744i	$0.668744\pi$
$662$	0	0
$663$	−30.0000	−1.16510
$664$	0	0
$665$	48.0000	1.86136
$666$	0	0
$667$	−6.00000	−0.232321
$668$	0	0
$669$	10.0000	0.386622
$670$	0	0
$671$	6.00000	0.231627
$672$	0	0
$673$	−7.00000	−0.269830	−0.134915	−	0.990857i	$-0.543076\pi$
$673$	−7.00000	−0.269830	−0.134915	+	0.990857i	$0.543076\pi$
$674$	0	0
$675$	20.0000	0.769800
$676$	0	0
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	0	0
$679$	−32.0000	−1.22805
$680$	0	0
$681$	6.00000	0.229920
$682$	0	0
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	0	0
$685$	36.0000	1.37549
$686$	0	0
$687$	−4.00000	−0.152610
$688$	0	0
$689$	15.0000	0.571454
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	0	0
$693$	−24.0000	−0.911685
$694$	0	0
$695$	42.0000	1.59315
$696$	0	0
$697$	0	0
$698$	0	0
$699$	9.00000	0.340411
$700$	0	0
$701$	−21.0000	−0.793159	−0.396580	−	0.918000i	$-0.629803\pi$
$701$	−21.0000	−0.793159	−0.396580	+	0.918000i	$0.629803\pi$
$702$	0	0
$703$	−32.0000	−1.20690
$704$	0	0
$705$	−9.00000	−0.338960
$706$	0	0
$707$	48.0000	1.80523
$708$	0	0
$709$	43.0000	1.61490	0.807449	−	0.589937i	$-0.200847\pi$
$709$	43.0000	1.61490	0.807449	+	0.589937i	$0.200847\pi$
$710$	0	0
$711$	−22.0000	−0.825064
$712$	0	0
$713$	−30.0000	−1.12351
$714$	0	0
$715$	−45.0000	−1.68290
$716$	0	0
$717$	6.00000	0.224074
$718$	0	0
$719$	30.0000	1.11881	0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000	1.11881	0.559406	+	0.828894i	$0.311029\pi$
$720$	0	0
$721$	−56.0000	−2.08555
$722$	0	0
$723$	−17.0000	−0.632237
$724$	0	0
$725$	4.00000	0.148556
$726$	0	0
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−6.00000	−0.221918
$732$	0	0
$733$	−32.0000	−1.18195	−0.590973	−	0.806691i	$-0.701256\pi$
$733$	−32.0000	−1.18195	−0.590973	+	0.806691i	$0.701256\pi$
$734$	0	0
$735$	27.0000	0.995910
$736$	0	0
$737$	24.0000	0.884051
$738$	0	0
$739$	43.0000	1.58178	0.790890	−	0.611958i	$-0.209618\pi$
$739$	43.0000	1.58178	0.790890	+	0.611958i	$0.209618\pi$
$740$	0	0
$741$	20.0000	0.734718
$742$	0	0
$743$	48.0000	1.76095	0.880475	−	0.474093i	$-0.157224\pi$
$743$	48.0000	1.76095	0.880475	+	0.474093i	$0.157224\pi$
$744$	0	0
$745$	−45.0000	−1.64867
$746$	0	0
$747$	12.0000	0.439057
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−28.0000	−1.02173	−0.510867	−	0.859660i	$-0.670676\pi$
$751$	−28.0000	−1.02173	−0.510867	+	0.859660i	$0.670676\pi$
$752$	0	0
$753$	21.0000	0.765283
$754$	0	0
$755$	12.0000	0.436725
$756$	0	0
$757$	10.0000	0.363456	0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000	0.363456	0.181728	+	0.983349i	$0.441831\pi$
$758$	0	0
$759$	−18.0000	−0.653359
$760$	0	0
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	0	0
$763$	44.0000	1.59291
$764$	0	0
$765$	−36.0000	−1.30158
$766$	0	0
$767$	30.0000	1.08324
$768$	0	0
$769$	14.0000	0.504853	0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000	0.504853	0.252426	+	0.967616i	$0.418771\pi$
$770$	0	0
$771$	3.00000	0.108042
$772$	0	0
$773$	36.0000	1.29483	0.647415	−	0.762138i	$-0.275850\pi$
$773$	36.0000	1.29483	0.647415	+	0.762138i	$0.275850\pi$
$774$	0	0
$775$	20.0000	0.718421
$776$	0	0
$777$	−32.0000	−1.14799
$778$	0	0
$779$	0	0
$780$	0	0
$781$	−18.0000	−0.644091
$782$	0	0
$783$	5.00000	0.178685
$784$	0	0
$785$	−12.0000	−0.428298
$786$	0	0
$787$	−26.0000	−0.926800	−0.463400	−	0.886149i	$-0.653371\pi$
$787$	−26.0000	−0.926800	−0.463400	+	0.886149i	$0.653371\pi$
$788$	0	0
$789$	−9.00000	−0.320408
$790$	0	0
$791$	24.0000	0.853342
$792$	0	0
$793$	10.0000	0.355110
$794$	0	0
$795$	−9.00000	−0.319197
$796$	0	0
$797$	6.00000	0.212531	0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000	0.212531	0.106265	+	0.994338i	$0.466111\pi$
$798$	0	0
$799$	18.0000	0.636794
$800$	0	0
$801$	24.0000	0.847998
$802$	0	0
$803$	48.0000	1.69388
$804$	0	0
$805$	−72.0000	−2.53767
$806$	0	0
$807$	6.00000	0.211210
$808$	0	0
$809$	−36.0000	−1.26569	−0.632846	−	0.774277i	$-0.718114\pi$
$809$	−36.0000	−1.26569	−0.632846	+	0.774277i	$0.718114\pi$
$810$	0	0
$811$	16.0000	0.561836	0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000	0.561836	0.280918	+	0.959732i	$0.409361\pi$
$812$	0	0
$813$	1.00000	0.0350715
$814$	0	0
$815$	−39.0000	−1.36611
$816$	0	0
$817$	4.00000	0.139942
$818$	0	0
$819$	−40.0000	−1.39771
$820$	0	0
$821$	−45.0000	−1.57051	−0.785255	−	0.619172i	$-0.787468\pi$
$821$	−45.0000	−1.57051	−0.785255	+	0.619172i	$0.787468\pi$
$822$	0	0
$823$	56.0000	1.95204	0.976019	−	0.217687i	$-0.0698512\pi$
$823$	56.0000	1.95204	0.976019	+	0.217687i	$0.0698512\pi$
$824$	0	0
$825$	12.0000	0.417786
$826$	0	0
$827$	−15.0000	−0.521601	−0.260801	−	0.965393i	$-0.583986\pi$
$827$	−15.0000	−0.521601	−0.260801	+	0.965393i	$0.583986\pi$
$828$	0	0
$829$	10.0000	0.347314	0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000	0.347314	0.173657	+	0.984806i	$0.444442\pi$
$830$	0	0
$831$	−10.0000	−0.346896
$832$	0	0
$833$	−54.0000	−1.87099
$834$	0	0
$835$	18.0000	0.622916
$836$	0	0
$837$	25.0000	0.864126
$838$	0	0
$839$	45.0000	1.55357	0.776786	−	0.629764i	$-0.216849\pi$
$839$	45.0000	1.55357	0.776786	+	0.629764i	$0.216849\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	−15.0000	−0.516627
$844$	0	0
$845$	−36.0000	−1.23844
$846$	0	0
$847$	8.00000	0.274883
$848$	0	0
$849$	−22.0000	−0.755038
$850$	0	0
$851$	48.0000	1.64542
$852$	0	0
$853$	10.0000	0.342393	0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000	0.342393	0.171197	+	0.985237i	$0.445237\pi$
$854$	0	0
$855$	24.0000	0.820783
$856$	0	0
$857$	9.00000	0.307434	0.153717	−	0.988115i	$-0.450876\pi$
$857$	9.00000	0.307434	0.153717	+	0.988115i	$0.450876\pi$
$858$	0	0
$859$	−5.00000	−0.170598	−0.0852989	−	0.996355i	$-0.527185\pi$
$859$	−5.00000	−0.170598	−0.0852989	+	0.996355i	$0.527185\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−18.0000	−0.612727	−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000	−0.612727	−0.306364	+	0.951915i	$0.599112\pi$
$864$	0	0
$865$	−54.0000	−1.83606
$866$	0	0
$867$	−19.0000	−0.645274
$868$	0	0
$869$	−33.0000	−1.11945
$870$	0	0
$871$	40.0000	1.35535
$872$	0	0
$873$	−16.0000	−0.541518
$874$	0	0
$875$	−12.0000	−0.405674
$876$	0	0
$877$	−11.0000	−0.371444	−0.185722	−	0.982602i	$-0.559462\pi$
$877$	−11.0000	−0.371444	−0.185722	+	0.982602i	$0.559462\pi$
$878$	0	0
$879$	18.0000	0.607125
$880$	0	0
$881$	−42.0000	−1.41502	−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000	−1.41502	−0.707508	+	0.706705i	$0.750181\pi$
$882$	0	0
$883$	16.0000	0.538443	0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000	0.538443	0.269221	+	0.963078i	$0.413234\pi$
$884$	0	0
$885$	−18.0000	−0.605063
$886$	0	0
$887$	21.0000	0.705111	0.352555	−	0.935791i	$-0.385313\pi$
$887$	21.0000	0.705111	0.352555	+	0.935791i	$0.385313\pi$
$888$	0	0
$889$	64.0000	2.14649
$890$	0	0
$891$	−3.00000	−0.100504
$892$	0	0
$893$	−12.0000	−0.401565
$894$	0	0
$895$	54.0000	1.80502
$896$	0	0
$897$	−30.0000	−1.00167
$898$	0	0
$899$	5.00000	0.166759
$900$	0	0
$901$	18.0000	0.599667
$902$	0	0
$903$	4.00000	0.133112
$904$	0	0
$905$	51.0000	1.69530
$906$	0	0
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	0	0
$909$	24.0000	0.796030
$910$	0	0
$911$	−9.00000	−0.298183	−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000	−0.298183	−0.149092	+	0.988823i	$0.547635\pi$
$912$	0	0
$913$	18.0000	0.595713
$914$	0	0
$915$	−6.00000	−0.198354
$916$	0	0
$917$	−48.0000	−1.58510
$918$	0	0
$919$	38.0000	1.25350	0.626752	−	0.779219i	$-0.284384\pi$
$919$	38.0000	1.25350	0.626752	+	0.779219i	$0.284384\pi$
$920$	0	0
$921$	11.0000	0.362462
$922$	0	0
$923$	−30.0000	−0.987462
$924$	0	0
$925$	−32.0000	−1.05215
$926$	0	0
$927$	−28.0000	−0.919641
$928$	0	0
$929$	42.0000	1.37798	0.688988	−	0.724773i	$-0.258055\pi$
$929$	42.0000	1.37798	0.688988	+	0.724773i	$0.258055\pi$
$930$	0	0
$931$	36.0000	1.17985
$932$	0	0
$933$	24.0000	0.785725
$934$	0	0
$935$	−54.0000	−1.76599
$936$	0	0
$937$	−22.0000	−0.718709	−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000	−0.718709	−0.359354	+	0.933201i	$0.617003\pi$
$938$	0	0
$939$	7.00000	0.228436
$940$	0	0
$941$	21.0000	0.684580	0.342290	−	0.939594i	$-0.388797\pi$
$941$	21.0000	0.684580	0.342290	+	0.939594i	$0.388797\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	60.0000	1.95180
$946$	0	0
$947$	−15.0000	−0.487435	−0.243717	−	0.969846i	$-0.578367\pi$
$947$	−15.0000	−0.487435	−0.243717	+	0.969846i	$0.578367\pi$
$948$	0	0
$949$	80.0000	2.59691
$950$	0	0
$951$	−6.00000	−0.194563
$952$	0	0
$953$	3.00000	0.0971795	0.0485898	−	0.998819i	$-0.484527\pi$
$953$	3.00000	0.0971795	0.0485898	+	0.998819i	$0.484527\pi$
$954$	0	0
$955$	72.0000	2.32987
$956$	0	0
$957$	3.00000	0.0969762
$958$	0	0
$959$	48.0000	1.55000
$960$	0	0
$961$	−6.00000	−0.193548
$962$	0	0
$963$	0	0
$964$	0	0
$965$	48.0000	1.54517
$966$	0	0
$967$	−43.0000	−1.38279	−0.691393	−	0.722478i	$-0.743003\pi$
$967$	−43.0000	−1.38279	−0.691393	+	0.722478i	$0.743003\pi$
$968$	0	0
$969$	24.0000	0.770991
$970$	0	0
$971$	60.0000	1.92549	0.962746	−	0.270408i	$-0.0871586\pi$
$971$	60.0000	1.92549	0.962746	+	0.270408i	$0.0871586\pi$
$972$	0	0
$973$	56.0000	1.79528
$974$	0	0
$975$	20.0000	0.640513
$976$	0	0
$977$	33.0000	1.05576	0.527882	−	0.849318i	$-0.322986\pi$
$977$	33.0000	1.05576	0.527882	+	0.849318i	$0.322986\pi$
$978$	0	0
$979$	36.0000	1.15056
$980$	0	0
$981$	22.0000	0.702406
$982$	0	0
$983$	−15.0000	−0.478426	−0.239213	−	0.970967i	$-0.576889\pi$
$983$	−15.0000	−0.478426	−0.239213	+	0.970967i	$0.576889\pi$
$984$	0	0
$985$	−18.0000	−0.573528
$986$	0	0
$987$	−12.0000	−0.381964
$988$	0	0
$989$	−6.00000	−0.190789
$990$	0	0
$991$	−10.0000	−0.317660	−0.158830	−	0.987306i	$-0.550772\pi$
$991$	−10.0000	−0.317660	−0.158830	+	0.987306i	$0.550772\pi$
$992$	0	0
$993$	−1.00000	−0.0317340
$994$	0	0
$995$	−60.0000	−1.90213
$996$	0	0
$997$	−8.00000	−0.253363	−0.126681	−	0.991943i	$-0.540433\pi$
$997$	−8.00000	−0.253363	−0.126681	+	0.991943i	$0.540433\pi$
$998$	0	0
$999$	−40.0000	−1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1856.2.a.d.1.1		1
4.3	odd	2		1856.2.a.i.1.1		1
8.3	odd	2		464.2.a.c.1.1		1
8.5	even	2		116.2.a.b.1.1	✓	1
24.5	odd	2		1044.2.a.b.1.1		1
24.11	even	2		4176.2.a.f.1.1		1
40.13	odd	4		2900.2.c.c.349.2		2
40.29	even	2		2900.2.a.b.1.1		1
40.37	odd	4		2900.2.c.c.349.1		2
56.13	odd	2		5684.2.a.d.1.1		1
232.133	odd	4		3364.2.c.a.1681.1		2
232.157	odd	4		3364.2.c.a.1681.2		2
232.173	even	2		3364.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.2.a.b.1.1	✓	1	8.5	even	2
464.2.a.c.1.1		1	8.3	odd	2
1044.2.a.b.1.1		1	24.5	odd	2
1856.2.a.d.1.1		1	1.1	even	1	trivial
1856.2.a.i.1.1		1	4.3	odd	2
2900.2.a.b.1.1		1	40.29	even	2
2900.2.c.c.349.1		2	40.37	odd	4
2900.2.c.c.349.2		2	40.13	odd	4
3364.2.a.b.1.1		1	232.173	even	2
3364.2.c.a.1681.1		2	232.133	odd	4
3364.2.c.a.1681.2		2	232.157	odd	4
4176.2.a.f.1.1		1	24.11	even	2
5684.2.a.d.1.1		1	56.13	odd	2

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:	\( N \)	\(=\)	\( 1856 = 2^{6} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1856.a (trivial)

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