LMFDB - Embedded newform 1710.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(1,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, 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("1710.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 570)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1710.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +2.00000 q^{7} +1.00000 q^{8} +1.00000 q^{10} +6.00000 q^{11} +2.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{19} +1.00000 q^{20} +6.00000 q^{22} -4.00000 q^{23} +1.00000 q^{25} +2.00000 q^{28} +8.00000 q^{29} -8.00000 q^{31} +1.00000 q^{32} -2.00000 q^{34} +2.00000 q^{35} -4.00000 q^{37} -1.00000 q^{38} +1.00000 q^{40} +4.00000 q^{41} -6.00000 q^{43} +6.00000 q^{44} -4.00000 q^{46} +12.0000 q^{47} -3.00000 q^{49} +1.00000 q^{50} -6.00000 q^{53} +6.00000 q^{55} +2.00000 q^{56} +8.00000 q^{58} +4.00000 q^{59} +2.00000 q^{61} -8.00000 q^{62} +1.00000 q^{64} -8.00000 q^{67} -2.00000 q^{68} +2.00000 q^{70} +6.00000 q^{73} -4.00000 q^{74} -1.00000 q^{76} +12.0000 q^{77} +8.00000 q^{79} +1.00000 q^{80} +4.00000 q^{82} -4.00000 q^{83} -2.00000 q^{85} -6.00000 q^{86} +6.00000 q^{88} +4.00000 q^{89} -4.00000 q^{92} +12.0000 q^{94} -1.00000 q^{95} +12.0000 q^{97} -3.00000 q^{98} +O(q^{100})$

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	1.00000	0.353553
$9$	0	0
$10$	1.00000	0.316228
$11$	6.00000	1.80907	0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000	1.80907	0.904534	+	0.426401i	$0.140219\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	0	0
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.00000	0.223607
$21$	0	0
$22$	6.00000	1.27920
$23$	−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
$26$	0	0
$27$	0	0
$28$	2.00000	0.377964
$29$	8.00000	1.48556	0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000	1.48556	0.742781	+	0.669534i	$0.233506\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.00000	−0.342997
$35$	2.00000	0.338062
$36$	0	0
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	−1.00000	−0.162221
$39$	0	0
$40$	1.00000	0.158114
$41$	4.00000	0.624695	0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000	0.624695	0.312348	+	0.949968i	$0.398885\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	6.00000	0.904534
$45$	0	0
$46$	−4.00000	−0.589768
$47$	12.0000	1.75038	0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000	1.75038	0.875190	+	0.483779i	$0.160736\pi$
$48$	0	0
$49$	−3.00000	−0.428571
$50$	1.00000	0.141421
$51$	0	0
$52$	0	0
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	6.00000	0.809040
$56$	2.00000	0.267261
$57$	0	0
$58$	8.00000	1.05045
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−8.00000	−1.01600
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	2.00000	0.239046
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	−1.00000	−0.114708
$77$	12.0000	1.36753
$78$	0	0
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	1.00000	0.111803
$81$	0	0
$82$	4.00000	0.441726
$83$	−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
$85$	−2.00000	−0.216930
$86$	−6.00000	−0.646997
$87$	0	0
$88$	6.00000	0.639602
$89$	4.00000	0.423999	0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000	0.423999	0.212000	+	0.977270i	$0.432002\pi$
$90$	0	0
$91$	0	0
$92$	−4.00000	−0.417029
$93$	0	0
$94$	12.0000	1.23771
$95$	−1.00000	−0.102598
$96$	0	0
$97$	12.0000	1.21842	0.609208	−	0.793011i	$-0.291488\pi$
$97$	12.0000	1.21842	0.609208	+	0.793011i	$0.291488\pi$
$98$	−3.00000	−0.303046
$99$	0	0
$100$	1.00000	0.100000
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	0	0
$106$	−6.00000	−0.582772
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	−14.0000	−1.34096	−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000	−1.34096	−0.670478	+	0.741929i	$0.733911\pi$
$110$	6.00000	0.572078
$111$	0	0
$112$	2.00000	0.188982
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	0	0
$115$	−4.00000	−0.373002
$116$	8.00000	0.742781
$117$	0	0
$118$	4.00000	0.368230
$119$	−4.00000	−0.366679
$120$	0	0
$121$	25.0000	2.27273
$122$	2.00000	0.181071
$123$	0	0
$124$	−8.00000	−0.718421
$125$	1.00000	0.0894427
$126$	0	0
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	−22.0000	−1.92215	−0.961074	−	0.276289i	$-0.910895\pi$
$131$	−22.0000	−1.92215	−0.961074	+	0.276289i	$0.910895\pi$
$132$	0	0
$133$	−2.00000	−0.173422
$134$	−8.00000	−0.691095
$135$	0	0
$136$	−2.00000	−0.171499
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	2.00000	0.169031
$141$	0	0
$142$	0	0
$143$	0	0
$144$	0	0
$145$	8.00000	0.664364
$146$	6.00000	0.496564
$147$	0	0
$148$	−4.00000	−0.328798
$149$	−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
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	−1.00000	−0.0811107
$153$	0	0
$154$	12.0000	0.966988
$155$	−8.00000	−0.642575
$156$	0	0
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	8.00000	0.636446
$159$	0	0
$160$	1.00000	0.0790569
$161$	−8.00000	−0.630488
$162$	0	0
$163$	6.00000	0.469956	0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000	0.469956	0.234978	+	0.972001i	$0.424498\pi$
$164$	4.00000	0.312348
$165$	0	0
$166$	−4.00000	−0.310460
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	−2.00000	−0.153393
$171$	0	0
$172$	−6.00000	−0.457496
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	0	0
$175$	2.00000	0.151186
$176$	6.00000	0.452267
$177$	0	0
$178$	4.00000	0.299813
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	0	0
$183$	0	0
$184$	−4.00000	−0.294884
$185$	−4.00000	−0.294086
$186$	0	0
$187$	−12.0000	−0.877527
$188$	12.0000	0.875190
$189$	0	0
$190$	−1.00000	−0.0725476
$191$	22.0000	1.59186	0.795932	−	0.605386i	$-0.206981\pi$
$191$	22.0000	1.59186	0.795932	+	0.605386i	$0.206981\pi$
$192$	0	0
$193$	−8.00000	−0.575853	−0.287926	−	0.957653i	$-0.592966\pi$
$193$	−8.00000	−0.575853	−0.287926	+	0.957653i	$0.592966\pi$
$194$	12.0000	0.861550
$195$	0	0
$196$	−3.00000	−0.214286
$197$	−14.0000	−0.997459	−0.498729	−	0.866758i	$-0.666200\pi$
$197$	−14.0000	−0.997459	−0.498729	+	0.866758i	$0.666200\pi$
$198$	0	0
$199$	20.0000	1.41776	0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000	1.41776	0.708881	+	0.705328i	$0.249200\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	10.0000	0.703598
$203$	16.0000	1.12298
$204$	0	0
$205$	4.00000	0.279372
$206$	0	0
$207$	0	0
$208$	0	0
$209$	−6.00000	−0.415029
$210$	0	0
$211$	−28.0000	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	12.0000	0.820303
$215$	−6.00000	−0.409197
$216$	0	0
$217$	−16.0000	−1.08615
$218$	−14.0000	−0.948200
$219$	0	0
$220$	6.00000	0.404520
$221$	0	0
$222$	0	0
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	2.00000	0.133631
$225$	0	0
$226$	−14.0000	−0.931266
$227$	28.0000	1.85843	0.929213	−	0.369546i	$-0.120487\pi$
$227$	28.0000	1.85843	0.929213	+	0.369546i	$0.120487\pi$
$228$	0	0
$229$	18.0000	1.18947	0.594737	−	0.803921i	$-0.297256\pi$
$229$	18.0000	1.18947	0.594737	+	0.803921i	$0.297256\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	8.00000	0.525226
$233$	−14.0000	−0.917170	−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000	−0.917170	−0.458585	+	0.888650i	$0.651644\pi$
$234$	0	0
$235$	12.0000	0.782794
$236$	4.00000	0.260378
$237$	0	0
$238$	−4.00000	−0.259281
$239$	18.0000	1.16432	0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000	1.16432	0.582162	+	0.813073i	$0.302207\pi$
$240$	0	0
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	25.0000	1.60706
$243$	0	0
$244$	2.00000	0.128037
$245$	−3.00000	−0.191663
$246$	0	0
$247$	0	0
$248$	−8.00000	−0.508001
$249$	0	0
$250$	1.00000	0.0632456
$251$	14.0000	0.883672	0.441836	−	0.897096i	$-0.354327\pi$
$251$	14.0000	0.883672	0.441836	+	0.897096i	$0.354327\pi$
$252$	0	0
$253$	−24.0000	−1.50887
$254$	−12.0000	−0.752947
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	0	0
$259$	−8.00000	−0.497096
$260$	0	0
$261$	0	0
$262$	−22.0000	−1.35916
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	−6.00000	−0.368577
$266$	−2.00000	−0.122628
$267$	0	0
$268$	−8.00000	−0.488678
$269$	−8.00000	−0.487769	−0.243884	−	0.969804i	$-0.578422\pi$
$269$	−8.00000	−0.487769	−0.243884	+	0.969804i	$0.578422\pi$
$270$	0	0
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	−6.00000	−0.362473
$275$	6.00000	0.361814
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	0	0
$279$	0	0
$280$	2.00000	0.119523
$281$	−16.0000	−0.954480	−0.477240	−	0.878773i	$-0.658363\pi$
$281$	−16.0000	−0.954480	−0.477240	+	0.878773i	$0.658363\pi$
$282$	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
$285$	0	0
$286$	0	0
$287$	8.00000	0.472225
$288$	0	0
$289$	−13.0000	−0.764706
$290$	8.00000	0.469776
$291$	0	0
$292$	6.00000	0.351123
$293$	−10.0000	−0.584206	−0.292103	−	0.956387i	$-0.594355\pi$
$293$	−10.0000	−0.584206	−0.292103	+	0.956387i	$0.594355\pi$
$294$	0	0
$295$	4.00000	0.232889
$296$	−4.00000	−0.232495
$297$	0	0
$298$	−22.0000	−1.27443
$299$	0	0
$300$	0	0
$301$	−12.0000	−0.691669
$302$	0	0
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	2.00000	0.114520
$306$	0	0
$307$	−8.00000	−0.456584	−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000	−0.456584	−0.228292	+	0.973593i	$0.573314\pi$
$308$	12.0000	0.683763
$309$	0	0
$310$	−8.00000	−0.454369
$311$	6.00000	0.340229	0.170114	−	0.985424i	$-0.445586\pi$
$311$	6.00000	0.340229	0.170114	+	0.985424i	$0.445586\pi$
$312$	0	0
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	6.00000	0.338600
$315$	0	0
$316$	8.00000	0.450035
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	0	0
$319$	48.0000	2.68748
$320$	1.00000	0.0559017
$321$	0	0
$322$	−8.00000	−0.445823
$323$	2.00000	0.111283
$324$	0	0
$325$	0	0
$326$	6.00000	0.332309
$327$	0	0
$328$	4.00000	0.220863
$329$	24.0000	1.32316
$330$	0	0
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	−4.00000	−0.219529
$333$	0	0
$334$	16.0000	0.875481
$335$	−8.00000	−0.437087
$336$	0	0
$337$	−20.0000	−1.08947	−0.544735	−	0.838608i	$-0.683370\pi$
$337$	−20.0000	−1.08947	−0.544735	+	0.838608i	$0.683370\pi$
$338$	−13.0000	−0.707107
$339$	0	0
$340$	−2.00000	−0.108465
$341$	−48.0000	−2.59935
$342$	0	0
$343$	−20.0000	−1.07990
$344$	−6.00000	−0.323498
$345$	0	0
$346$	−18.0000	−0.967686
$347$	−36.0000	−1.93258	−0.966291	−	0.257454i	$-0.917117\pi$
$347$	−36.0000	−1.93258	−0.966291	+	0.257454i	$0.917117\pi$
$348$	0	0
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	2.00000	0.106904
$351$	0	0
$352$	6.00000	0.319801
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	0	0
$355$	0	0
$356$	4.00000	0.212000
$357$	0	0
$358$	−12.0000	−0.634220
$359$	6.00000	0.316668	0.158334	−	0.987386i	$-0.449388\pi$
$359$	6.00000	0.316668	0.158334	+	0.987386i	$0.449388\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	2.00000	0.105118
$363$	0	0
$364$	0	0
$365$	6.00000	0.314054
$366$	0	0
$367$	−10.0000	−0.521996	−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000	−0.521996	−0.260998	+	0.965339i	$0.584052\pi$
$368$	−4.00000	−0.208514
$369$	0	0
$370$	−4.00000	−0.207950
$371$	−12.0000	−0.623009
$372$	0	0
$373$	−24.0000	−1.24267	−0.621336	−	0.783544i	$-0.713410\pi$
$373$	−24.0000	−1.24267	−0.621336	+	0.783544i	$0.713410\pi$
$374$	−12.0000	−0.620505
$375$	0	0
$376$	12.0000	0.618853
$377$	0	0
$378$	0	0
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	−1.00000	−0.0512989
$381$	0	0
$382$	22.0000	1.12562
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	0	0
$385$	12.0000	0.611577
$386$	−8.00000	−0.407189
$387$	0	0
$388$	12.0000	0.609208
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	0	0
$391$	8.00000	0.404577
$392$	−3.00000	−0.151523
$393$	0	0
$394$	−14.0000	−0.705310
$395$	8.00000	0.402524
$396$	0	0
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	20.0000	1.00251
$399$	0	0
$400$	1.00000	0.0500000
$401$	0	0		−	1.00000i	$-0.5\pi$
$401$	0	0			1.00000i	$0.5\pi$
$402$	0	0
$403$	0	0
$404$	10.0000	0.497519
$405$	0	0
$406$	16.0000	0.794067
$407$	−24.0000	−1.18964
$408$	0	0
$409$	14.0000	0.692255	0.346128	−	0.938187i	$-0.387496\pi$
$409$	14.0000	0.692255	0.346128	+	0.938187i	$0.387496\pi$
$410$	4.00000	0.197546
$411$	0	0
$412$	0	0
$413$	8.00000	0.393654
$414$	0	0
$415$	−4.00000	−0.196352
$416$	0	0
$417$	0	0
$418$	−6.00000	−0.293470
$419$	14.0000	0.683945	0.341972	−	0.939710i	$-0.388905\pi$
$419$	14.0000	0.683945	0.341972	+	0.939710i	$0.388905\pi$
$420$	0	0
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−28.0000	−1.36302
$423$	0	0
$424$	−6.00000	−0.291386
$425$	−2.00000	−0.0970143
$426$	0	0
$427$	4.00000	0.193574
$428$	12.0000	0.580042
$429$	0	0
$430$	−6.00000	−0.289346
$431$	−36.0000	−1.73406	−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000	−1.73406	−0.867029	+	0.498257i	$0.833974\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	−16.0000	−0.768025
$435$	0	0
$436$	−14.0000	−0.670478
$437$	4.00000	0.191346
$438$	0	0
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	6.00000	0.286039
$441$	0	0
$442$	0	0
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	0	0
$445$	4.00000	0.189618
$446$	−16.0000	−0.757622
$447$	0	0
$448$	2.00000	0.0944911
$449$	4.00000	0.188772	0.0943858	−	0.995536i	$-0.469911\pi$
$449$	4.00000	0.188772	0.0943858	+	0.995536i	$0.469911\pi$
$450$	0	0
$451$	24.0000	1.13012
$452$	−14.0000	−0.658505
$453$	0	0
$454$	28.0000	1.31411
$455$	0	0
$456$	0	0
$457$	−14.0000	−0.654892	−0.327446	−	0.944870i	$-0.606188\pi$
$457$	−14.0000	−0.654892	−0.327446	+	0.944870i	$0.606188\pi$
$458$	18.0000	0.841085
$459$	0	0
$460$	−4.00000	−0.186501
$461$	34.0000	1.58354	0.791769	−	0.610821i	$-0.209160\pi$
$461$	34.0000	1.58354	0.791769	+	0.610821i	$0.209160\pi$
$462$	0	0
$463$	−26.0000	−1.20832	−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000	−1.20832	−0.604161	+	0.796862i	$0.706492\pi$
$464$	8.00000	0.371391
$465$	0	0
$466$	−14.0000	−0.648537
$467$	8.00000	0.370196	0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000	0.370196	0.185098	+	0.982720i	$0.440740\pi$
$468$	0	0
$469$	−16.0000	−0.738811
$470$	12.0000	0.553519
$471$	0	0
$472$	4.00000	0.184115
$473$	−36.0000	−1.65528
$474$	0	0
$475$	−1.00000	−0.0458831
$476$	−4.00000	−0.183340
$477$	0	0
$478$	18.0000	0.823301
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	0	0
$481$	0	0
$482$	−22.0000	−1.00207
$483$	0	0
$484$	25.0000	1.13636
$485$	12.0000	0.544892
$486$	0	0
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	2.00000	0.0905357
$489$	0	0
$490$	−3.00000	−0.135526
$491$	34.0000	1.53440	0.767199	−	0.641409i	$-0.221650\pi$
$491$	34.0000	1.53440	0.767199	+	0.641409i	$0.221650\pi$
$492$	0	0
$493$	−16.0000	−0.720604
$494$	0	0
$495$	0	0
$496$	−8.00000	−0.359211
$497$	0	0
$498$	0	0
$499$	24.0000	1.07439	0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000	1.07439	0.537194	+	0.843459i	$0.319484\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	14.0000	0.624851
$503$	−40.0000	−1.78351	−0.891756	−	0.452517i	$-0.850526\pi$
$503$	−40.0000	−1.78351	−0.891756	+	0.452517i	$0.850526\pi$
$504$	0	0
$505$	10.0000	0.444994
$506$	−24.0000	−1.06693
$507$	0	0
$508$	−12.0000	−0.532414
$509$	−36.0000	−1.59567	−0.797836	−	0.602875i	$-0.794022\pi$
$509$	−36.0000	−1.59567	−0.797836	+	0.602875i	$0.794022\pi$
$510$	0	0
$511$	12.0000	0.530849
$512$	1.00000	0.0441942
$513$	0	0
$514$	−6.00000	−0.264649
$515$	0	0
$516$	0	0
$517$	72.0000	3.16656
$518$	−8.00000	−0.351500
$519$	0	0
$520$	0	0
$521$	−24.0000	−1.05146	−0.525730	−	0.850652i	$-0.676208\pi$
$521$	−24.0000	−1.05146	−0.525730	+	0.850652i	$0.676208\pi$
$522$	0	0
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	−22.0000	−0.961074
$525$	0	0
$526$	−16.0000	−0.697633
$527$	16.0000	0.696971
$528$	0	0
$529$	−7.00000	−0.304348
$530$	−6.00000	−0.260623
$531$	0	0
$532$	−2.00000	−0.0867110
$533$	0	0
$534$	0	0
$535$	12.0000	0.518805
$536$	−8.00000	−0.345547
$537$	0	0
$538$	−8.00000	−0.344904
$539$	−18.0000	−0.775315
$540$	0	0
$541$	−10.0000	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$542$	20.0000	0.859074
$543$	0	0
$544$	−2.00000	−0.0857493
$545$	−14.0000	−0.599694
$546$	0	0
$547$	40.0000	1.71028	0.855138	−	0.518400i	$-0.173472\pi$
$547$	40.0000	1.71028	0.855138	+	0.518400i	$0.173472\pi$
$548$	−6.00000	−0.256307
$549$	0	0
$550$	6.00000	0.255841
$551$	−8.00000	−0.340811
$552$	0	0
$553$	16.0000	0.680389
$554$	−2.00000	−0.0849719
$555$	0	0
$556$	0	0
$557$	22.0000	0.932170	0.466085	−	0.884740i	$-0.345664\pi$
$557$	22.0000	0.932170	0.466085	+	0.884740i	$0.345664\pi$
$558$	0	0
$559$	0	0
$560$	2.00000	0.0845154
$561$	0	0
$562$	−16.0000	−0.674919
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	0	0
$565$	−14.0000	−0.588984
$566$	22.0000	0.924729
$567$	0	0
$568$	0	0
$569$	20.0000	0.838444	0.419222	−	0.907884i	$-0.362303\pi$
$569$	20.0000	0.838444	0.419222	+	0.907884i	$0.362303\pi$
$570$	0	0
$571$	16.0000	0.669579	0.334790	−	0.942293i	$-0.391335\pi$
$571$	16.0000	0.669579	0.334790	+	0.942293i	$0.391335\pi$
$572$	0	0
$573$	0	0
$574$	8.00000	0.333914
$575$	−4.00000	−0.166812
$576$	0	0
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	−13.0000	−0.540729
$579$	0	0
$580$	8.00000	0.332182
$581$	−8.00000	−0.331896
$582$	0	0
$583$	−36.0000	−1.49097
$584$	6.00000	0.248282
$585$	0	0
$586$	−10.0000	−0.413096
$587$	−24.0000	−0.990586	−0.495293	−	0.868726i	$-0.664939\pi$
$587$	−24.0000	−0.990586	−0.495293	+	0.868726i	$0.664939\pi$
$588$	0	0
$589$	8.00000	0.329634
$590$	4.00000	0.164677
$591$	0	0
$592$	−4.00000	−0.164399
$593$	−14.0000	−0.574911	−0.287456	−	0.957794i	$-0.592809\pi$
$593$	−14.0000	−0.574911	−0.287456	+	0.957794i	$0.592809\pi$
$594$	0	0
$595$	−4.00000	−0.163984
$596$	−22.0000	−0.901155
$597$	0	0
$598$	0	0
$599$	36.0000	1.47092	0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000	1.47092	0.735460	+	0.677568i	$0.236966\pi$
$600$	0	0
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	−12.0000	−0.489083
$603$	0	0
$604$	0	0
$605$	25.0000	1.01639
$606$	0	0
$607$	40.0000	1.62355	0.811775	−	0.583970i	$-0.198502\pi$
$607$	40.0000	1.62355	0.811775	+	0.583970i	$0.198502\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	2.00000	0.0809776
$611$	0	0
$612$	0	0
$613$	−10.0000	−0.403896	−0.201948	−	0.979396i	$-0.564727\pi$
$613$	−10.0000	−0.403896	−0.201948	+	0.979396i	$0.564727\pi$
$614$	−8.00000	−0.322854
$615$	0	0
$616$	12.0000	0.483494
$617$	38.0000	1.52982	0.764911	−	0.644136i	$-0.222783\pi$
$617$	38.0000	1.52982	0.764911	+	0.644136i	$0.222783\pi$
$618$	0	0
$619$	−8.00000	−0.321547	−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000	−0.321547	−0.160774	+	0.986991i	$0.551399\pi$
$620$	−8.00000	−0.321288
$621$	0	0
$622$	6.00000	0.240578
$623$	8.00000	0.320513
$624$	0	0
$625$	1.00000	0.0400000
$626$	−14.0000	−0.559553
$627$	0	0
$628$	6.00000	0.239426
$629$	8.00000	0.318981
$630$	0	0
$631$	0	0		−	1.00000i	$-0.5\pi$
$631$	0	0			1.00000i	$0.5\pi$
$632$	8.00000	0.318223
$633$	0	0
$634$	−6.00000	−0.238290
$635$	−12.0000	−0.476205
$636$	0	0
$637$	0	0
$638$	48.0000	1.90034
$639$	0	0
$640$	1.00000	0.0395285
$641$	12.0000	0.473972	0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000	0.473972	0.236986	+	0.971513i	$0.423841\pi$
$642$	0	0
$643$	−26.0000	−1.02534	−0.512670	−	0.858586i	$-0.671344\pi$
$643$	−26.0000	−1.02534	−0.512670	+	0.858586i	$0.671344\pi$
$644$	−8.00000	−0.315244
$645$	0	0
$646$	2.00000	0.0786889
$647$	24.0000	0.943537	0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000	0.943537	0.471769	+	0.881722i	$0.343616\pi$
$648$	0	0
$649$	24.0000	0.942082
$650$	0	0
$651$	0	0
$652$	6.00000	0.234978
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	0	0
$655$	−22.0000	−0.859611
$656$	4.00000	0.156174
$657$	0	0
$658$	24.0000	0.935617
$659$	48.0000	1.86981	0.934907	−	0.354892i	$-0.115482\pi$
$659$	48.0000	1.86981	0.934907	+	0.354892i	$0.115482\pi$
$660$	0	0
$661$	26.0000	1.01128	0.505641	−	0.862744i	$-0.331256\pi$
$661$	26.0000	1.01128	0.505641	+	0.862744i	$0.331256\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	−4.00000	−0.155230
$665$	−2.00000	−0.0775567
$666$	0	0
$667$	−32.0000	−1.23904
$668$	16.0000	0.619059
$669$	0	0
$670$	−8.00000	−0.309067
$671$	12.0000	0.463255
$672$	0	0
$673$	−28.0000	−1.07932	−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000	−1.07932	−0.539660	+	0.841883i	$0.681447\pi$
$674$	−20.0000	−0.770371
$675$	0	0
$676$	−13.0000	−0.500000
$677$	−22.0000	−0.845529	−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000	−0.845529	−0.422764	+	0.906240i	$0.638940\pi$
$678$	0	0
$679$	24.0000	0.921035
$680$	−2.00000	−0.0766965
$681$	0	0
$682$	−48.0000	−1.83801
$683$	36.0000	1.37750	0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000	1.37750	0.688751	+	0.724998i	$0.258159\pi$
$684$	0	0
$685$	−6.00000	−0.229248
$686$	−20.0000	−0.763604
$687$	0	0
$688$	−6.00000	−0.228748
$689$	0	0
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	−18.0000	−0.684257
$693$	0	0
$694$	−36.0000	−1.36654
$695$	0	0
$696$	0	0
$697$	−8.00000	−0.303022
$698$	−2.00000	−0.0757011
$699$	0	0
$700$	2.00000	0.0755929
$701$	−6.00000	−0.226617	−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000	−0.226617	−0.113308	+	0.993560i	$0.536145\pi$
$702$	0	0
$703$	4.00000	0.150863
$704$	6.00000	0.226134
$705$	0	0
$706$	18.0000	0.677439
$707$	20.0000	0.752177
$708$	0	0
$709$	50.0000	1.87779	0.938895	−	0.344204i	$-0.111851\pi$
$709$	50.0000	1.87779	0.938895	+	0.344204i	$0.111851\pi$
$710$	0	0
$711$	0	0
$712$	4.00000	0.149906
$713$	32.0000	1.19841
$714$	0	0
$715$	0	0
$716$	−12.0000	−0.448461
$717$	0	0
$718$	6.00000	0.223918
$719$	−14.0000	−0.522112	−0.261056	−	0.965324i	$-0.584071\pi$
$719$	−14.0000	−0.522112	−0.261056	+	0.965324i	$0.584071\pi$
$720$	0	0
$721$	0	0
$722$	1.00000	0.0372161
$723$	0	0
$724$	2.00000	0.0743294
$725$	8.00000	0.297113
$726$	0	0
$727$	14.0000	0.519231	0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000	0.519231	0.259616	+	0.965712i	$0.416404\pi$
$728$	0	0
$729$	0	0
$730$	6.00000	0.222070
$731$	12.0000	0.443836
$732$	0	0
$733$	18.0000	0.664845	0.332423	−	0.943131i	$-0.392134\pi$
$733$	18.0000	0.664845	0.332423	+	0.943131i	$0.392134\pi$
$734$	−10.0000	−0.369107
$735$	0	0
$736$	−4.00000	−0.147442
$737$	−48.0000	−1.76810
$738$	0	0
$739$	−28.0000	−1.03000	−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000	−1.03000	−0.514998	+	0.857191i	$0.672207\pi$
$740$	−4.00000	−0.147043
$741$	0	0
$742$	−12.0000	−0.440534
$743$	8.00000	0.293492	0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000	0.293492	0.146746	+	0.989174i	$0.453120\pi$
$744$	0	0
$745$	−22.0000	−0.806018
$746$	−24.0000	−0.878702
$747$	0	0
$748$	−12.0000	−0.438763
$749$	24.0000	0.876941
$750$	0	0
$751$	40.0000	1.45962	0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000	1.45962	0.729810	+	0.683650i	$0.239608\pi$
$752$	12.0000	0.437595
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−38.0000	−1.38113	−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000	−1.38113	−0.690567	+	0.723269i	$0.742639\pi$
$758$	20.0000	0.726433
$759$	0	0
$760$	−1.00000	−0.0362738
$761$	18.0000	0.652499	0.326250	−	0.945284i	$-0.394215\pi$
$761$	18.0000	0.652499	0.326250	+	0.945284i	$0.394215\pi$
$762$	0	0
$763$	−28.0000	−1.01367
$764$	22.0000	0.795932
$765$	0	0
$766$	−24.0000	−0.867155
$767$	0	0
$768$	0	0
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	12.0000	0.432450
$771$	0	0
$772$	−8.00000	−0.287926
$773$	−6.00000	−0.215805	−0.107903	−	0.994161i	$-0.534413\pi$
$773$	−6.00000	−0.215805	−0.107903	+	0.994161i	$0.534413\pi$
$774$	0	0
$775$	−8.00000	−0.287368
$776$	12.0000	0.430775
$777$	0	0
$778$	30.0000	1.07555
$779$	−4.00000	−0.143315
$780$	0	0
$781$	0	0
$782$	8.00000	0.286079
$783$	0	0
$784$	−3.00000	−0.107143
$785$	6.00000	0.214149
$786$	0	0
$787$	44.0000	1.56843	0.784215	−	0.620489i	$-0.213066\pi$
$787$	44.0000	1.56843	0.784215	+	0.620489i	$0.213066\pi$
$788$	−14.0000	−0.498729
$789$	0	0
$790$	8.00000	0.284627
$791$	−28.0000	−0.995565
$792$	0	0
$793$	0	0
$794$	22.0000	0.780751
$795$	0	0
$796$	20.0000	0.708881
$797$	−2.00000	−0.0708436	−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000	−0.0708436	−0.0354218	+	0.999372i	$0.511277\pi$
$798$	0	0
$799$	−24.0000	−0.849059
$800$	1.00000	0.0353553
$801$	0	0
$802$	0	0
$803$	36.0000	1.27041
$804$	0	0
$805$	−8.00000	−0.281963
$806$	0	0
$807$	0	0
$808$	10.0000	0.351799
$809$	30.0000	1.05474	0.527372	−	0.849635i	$-0.323177\pi$
$809$	30.0000	1.05474	0.527372	+	0.849635i	$0.323177\pi$
$810$	0	0
$811$	−28.0000	−0.983213	−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000	−0.983213	−0.491606	+	0.870817i	$0.663590\pi$
$812$	16.0000	0.561490
$813$	0	0
$814$	−24.0000	−0.841200
$815$	6.00000	0.210171
$816$	0	0
$817$	6.00000	0.209913
$818$	14.0000	0.489499
$819$	0	0
$820$	4.00000	0.139686
$821$	50.0000	1.74501	0.872506	−	0.488603i	$-0.162493\pi$
$821$	50.0000	1.74501	0.872506	+	0.488603i	$0.162493\pi$
$822$	0	0
$823$	14.0000	0.488009	0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000	0.488009	0.244005	+	0.969774i	$0.421539\pi$
$824$	0	0
$825$	0	0
$826$	8.00000	0.278356
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	0	0
$829$	−30.0000	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$830$	−4.00000	−0.138842
$831$	0	0
$832$	0	0
$833$	6.00000	0.207888
$834$	0	0
$835$	16.0000	0.553703
$836$	−6.00000	−0.207514
$837$	0	0
$838$	14.0000	0.483622
$839$	−24.0000	−0.828572	−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000	−0.828572	−0.414286	+	0.910147i	$0.635969\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	−2.00000	−0.0689246
$843$	0	0
$844$	−28.0000	−0.963800
$845$	−13.0000	−0.447214
$846$	0	0
$847$	50.0000	1.71802
$848$	−6.00000	−0.206041
$849$	0	0
$850$	−2.00000	−0.0685994
$851$	16.0000	0.548473
$852$	0	0
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	4.00000	0.136877
$855$	0	0
$856$	12.0000	0.410152
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	0	0
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	−6.00000	−0.204598
$861$	0	0
$862$	−36.0000	−1.22616
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	0	0
$865$	−18.0000	−0.612018
$866$	0	0
$867$	0	0
$868$	−16.0000	−0.543075
$869$	48.0000	1.62829
$870$	0	0
$871$	0	0
$872$	−14.0000	−0.474100
$873$	0	0
$874$	4.00000	0.135302
$875$	2.00000	0.0676123
$876$	0	0
$877$	−32.0000	−1.08056	−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000	−1.08056	−0.540282	+	0.841484i	$0.681682\pi$
$878$	−8.00000	−0.269987
$879$	0	0
$880$	6.00000	0.202260
$881$	−14.0000	−0.471672	−0.235836	−	0.971793i	$-0.575783\pi$
$881$	−14.0000	−0.471672	−0.235836	+	0.971793i	$0.575783\pi$
$882$	0	0
$883$	14.0000	0.471138	0.235569	−	0.971858i	$-0.424305\pi$
$883$	14.0000	0.471138	0.235569	+	0.971858i	$0.424305\pi$
$884$	0	0
$885$	0	0
$886$	24.0000	0.806296
$887$	8.00000	0.268614	0.134307	−	0.990940i	$-0.457119\pi$
$887$	8.00000	0.268614	0.134307	+	0.990940i	$0.457119\pi$
$888$	0	0
$889$	−24.0000	−0.804934
$890$	4.00000	0.134080
$891$	0	0
$892$	−16.0000	−0.535720
$893$	−12.0000	−0.401565
$894$	0	0
$895$	−12.0000	−0.401116
$896$	2.00000	0.0668153
$897$	0	0
$898$	4.00000	0.133482
$899$	−64.0000	−2.13452
$900$	0	0
$901$	12.0000	0.399778
$902$	24.0000	0.799113
$903$	0	0
$904$	−14.0000	−0.465633
$905$	2.00000	0.0664822
$906$	0	0
$907$	−28.0000	−0.929725	−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000	−0.929725	−0.464862	+	0.885383i	$0.653896\pi$
$908$	28.0000	0.929213
$909$	0	0
$910$	0	0
$911$	−16.0000	−0.530104	−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000	−0.530104	−0.265052	+	0.964234i	$0.585389\pi$
$912$	0	0
$913$	−24.0000	−0.794284
$914$	−14.0000	−0.463079
$915$	0	0
$916$	18.0000	0.594737
$917$	−44.0000	−1.45301
$918$	0	0
$919$	32.0000	1.05558	0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000	1.05558	0.527791	+	0.849374i	$0.323020\pi$
$920$	−4.00000	−0.131876
$921$	0	0
$922$	34.0000	1.11973
$923$	0	0
$924$	0	0
$925$	−4.00000	−0.131519
$926$	−26.0000	−0.854413
$927$	0	0
$928$	8.00000	0.262613
$929$	6.00000	0.196854	0.0984268	−	0.995144i	$-0.468619\pi$
$929$	6.00000	0.196854	0.0984268	+	0.995144i	$0.468619\pi$
$930$	0	0
$931$	3.00000	0.0983210
$932$	−14.0000	−0.458585
$933$	0	0
$934$	8.00000	0.261768
$935$	−12.0000	−0.392442
$936$	0	0
$937$	−34.0000	−1.11073	−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000	−1.11073	−0.555366	+	0.831606i	$0.687422\pi$
$938$	−16.0000	−0.522419
$939$	0	0
$940$	12.0000	0.391397
$941$	40.0000	1.30396	0.651981	−	0.758235i	$-0.273938\pi$
$941$	40.0000	1.30396	0.651981	+	0.758235i	$0.273938\pi$
$942$	0	0
$943$	−16.0000	−0.521032
$944$	4.00000	0.130189
$945$	0	0
$946$	−36.0000	−1.17046
$947$	−44.0000	−1.42981	−0.714904	−	0.699223i	$-0.753530\pi$
$947$	−44.0000	−1.42981	−0.714904	+	0.699223i	$0.753530\pi$
$948$	0	0
$949$	0	0
$950$	−1.00000	−0.0324443
$951$	0	0
$952$	−4.00000	−0.129641
$953$	34.0000	1.10137	0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000	1.10137	0.550684	+	0.834714i	$0.314367\pi$
$954$	0	0
$955$	22.0000	0.711903
$956$	18.0000	0.582162
$957$	0	0
$958$	−18.0000	−0.581554
$959$	−12.0000	−0.387500
$960$	0	0
$961$	33.0000	1.06452
$962$	0	0
$963$	0	0
$964$	−22.0000	−0.708572
$965$	−8.00000	−0.257529
$966$	0	0
$967$	−18.0000	−0.578841	−0.289420	−	0.957202i	$-0.593463\pi$
$967$	−18.0000	−0.578841	−0.289420	+	0.957202i	$0.593463\pi$
$968$	25.0000	0.803530
$969$	0	0
$970$	12.0000	0.385297
$971$	24.0000	0.770197	0.385098	−	0.922876i	$-0.374168\pi$
$971$	24.0000	0.770197	0.385098	+	0.922876i	$0.374168\pi$
$972$	0	0
$973$	0	0
$974$	16.0000	0.512673
$975$	0	0
$976$	2.00000	0.0640184
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	0	0
$979$	24.0000	0.767043
$980$	−3.00000	−0.0958315
$981$	0	0
$982$	34.0000	1.08498
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	0	0
$985$	−14.0000	−0.446077
$986$	−16.0000	−0.509544
$987$	0	0
$988$	0	0
$989$	24.0000	0.763156
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	−8.00000	−0.254000
$993$	0	0
$994$	0	0
$995$	20.0000	0.634043
$996$	0	0
$997$	−58.0000	−1.83688	−0.918439	−	0.395562i	$-0.870550\pi$
$997$	−58.0000	−1.83688	−0.918439	+	0.395562i	$0.870550\pi$
$998$	24.0000	0.759707
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.a.s.1.1		1
3.2	odd	2		570.2.a.b.1.1	✓	1
5.4	even	2		8550.2.a.g.1.1		1
12.11	even	2		4560.2.a.r.1.1		1
15.2	even	4		2850.2.d.j.799.1		2
15.8	even	4		2850.2.d.j.799.2		2
15.14	odd	2		2850.2.a.y.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.a.b.1.1	✓	1	3.2	odd	2
1710.2.a.s.1.1		1	1.1	even	1	trivial
2850.2.a.y.1.1		1	15.14	odd	2
2850.2.d.j.799.1		2	15.2	even	4
2850.2.d.j.799.2		2	15.8	even	4
4560.2.a.r.1.1		1	12.11	even	2
8550.2.a.g.1.1		1	5.4	even	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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