LMFDB - Embedded newform 1710.2.a.b.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1710,2,Mod(1,1710)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [1,-1,0,1,-1,0,-2,-1,0,1,-2,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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} +1.00000 q^{10} -2.00000 q^{11} +4.00000 q^{13} +2.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{19} -1.00000 q^{20} +2.00000 q^{22} -4.00000 q^{23} +1.00000 q^{25} -4.00000 q^{26} -2.00000 q^{28} -8.00000 q^{31} -1.00000 q^{32} -2.00000 q^{34} +2.00000 q^{35} +8.00000 q^{37} +1.00000 q^{38} +1.00000 q^{40} +8.00000 q^{41} -6.00000 q^{43} -2.00000 q^{44} +4.00000 q^{46} +12.0000 q^{47} -3.00000 q^{49} -1.00000 q^{50} +4.00000 q^{52} +6.00000 q^{53} +2.00000 q^{55} +2.00000 q^{56} +2.00000 q^{61} +8.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} +8.00000 q^{67} +2.00000 q^{68} -2.00000 q^{70} +8.00000 q^{71} +14.0000 q^{73} -8.00000 q^{74} -1.00000 q^{76} +4.00000 q^{77} -1.00000 q^{80} -8.00000 q^{82} -4.00000 q^{83} -2.00000 q^{85} +6.00000 q^{86} +2.00000 q^{88} -8.00000 q^{91} -4.00000 q^{92} -12.0000 q^{94} +1.00000 q^{95} -12.0000 q^{97} +3.00000 q^{98} +O(q^{100})

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	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	1.00000	0.316228
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	4.00000	1.10940	0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000	1.10940	0.554700	+	0.832050i	$0.312833\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	0	0
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.00000	−0.223607
$21$	0	0
$22$	2.00000	0.426401
$23$	−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
$26$	−4.00000	−0.784465
$27$	0	0
$28$	−2.00000	−0.377964
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	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
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	1.00000	0.158114
$41$	8.00000	1.24939	0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000	1.24939	0.624695	+	0.780869i	$0.285223\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	−2.00000	−0.301511
$45$	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
$52$	4.00000	0.554700
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	2.00000	0.269680
$56$	2.00000	0.267261
$57$	0	0
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	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
$65$	−4.00000	−0.496139
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	2.00000	0.242536
$69$	0	0
$70$	−2.00000	−0.239046
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	0	0
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	−1.00000	−0.114708
$77$	4.00000	0.455842
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−1.00000	−0.111803
$81$	0	0
$82$	−8.00000	−0.883452
$83$	−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
$88$	2.00000	0.213201
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	−8.00000	−0.838628
$92$	−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	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	3.00000	0.303046
$99$	0	0
$100$	1.00000	0.100000
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	0	0
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−4.00000	−0.392232
$105$	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
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	−2.00000	−0.190693
$111$	0	0
$112$	−2.00000	−0.188982
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	0	0
$115$	4.00000	0.373002
$116$	0	0
$117$	0	0
$118$	0	0
$119$	−4.00000	−0.366679
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−2.00000	−0.181071
$123$	0	0
$124$	−8.00000	−0.718421
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	4.00000	0.350823
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	0	0
$133$	2.00000	0.173422
$134$	−8.00000	−0.691095
$135$	0	0
$136$	−2.00000	−0.171499
$137$	22.0000	1.87959	0.939793	−	0.341743i	$-0.111017\pi$
$137$	22.0000	1.87959	0.939793	+	0.341743i	$0.111017\pi$
$138$	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
$142$	−8.00000	−0.671345
$143$	−8.00000	−0.668994
$144$	0	0
$145$	0	0
$146$	−14.0000	−1.15865
$147$	0	0
$148$	8.00000	0.657596
$149$	−10.0000	−0.819232	−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000	−0.819232	−0.409616	+	0.912258i	$0.634337\pi$
$150$	0	0
$151$	−8.00000	−0.651031	−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	1.00000	0.0811107
$153$	0	0
$154$	−4.00000	−0.322329
$155$	8.00000	0.642575
$156$	0	0
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	0	0
$159$	0	0
$160$	1.00000	0.0790569
$161$	8.00000	0.630488
$162$	0	0
$163$	14.0000	1.09656	0.548282	−	0.836293i	$-0.315282\pi$
$163$	14.0000	1.09656	0.548282	+	0.836293i	$0.315282\pi$
$164$	8.00000	0.624695
$165$	0	0
$166$	4.00000	0.310460
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	2.00000	0.153393
$171$	0	0
$172$	−6.00000	−0.457496
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	0	0
$175$	−2.00000	−0.151186
$176$	−2.00000	−0.150756
$177$	0	0
$178$	0	0
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	8.00000	0.592999
$183$	0	0
$184$	4.00000	0.294884
$185$	−8.00000	−0.588172
$186$	0	0
$187$	−4.00000	−0.292509
$188$	12.0000	0.875190
$189$	0	0
$190$	−1.00000	−0.0725476
$191$	18.0000	1.30243	0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000	1.30243	0.651217	+	0.758891i	$0.274259\pi$
$192$	0	0
$193$	24.0000	1.72756	0.863779	−	0.503871i	$-0.168091\pi$
$193$	24.0000	1.72756	0.863779	+	0.503871i	$0.168091\pi$
$194$	12.0000	0.861550
$195$	0	0
$196$	−3.00000	−0.214286
$197$	−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
$199$	−20.0000	−1.41776	−0.708881	−	0.705328i	$-0.750800\pi$
$199$	−20.0000	−1.41776	−0.708881	+	0.705328i	$0.750800\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	2.00000	0.140720
$203$	0	0
$204$	0	0
$205$	−8.00000	−0.558744
$206$	−4.00000	−0.278693
$207$	0	0
$208$	4.00000	0.277350
$209$	2.00000	0.138343
$210$	0	0
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	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
$218$	−10.0000	−0.677285
$219$	0	0
$220$	2.00000	0.134840
$221$	8.00000	0.538138
$222$	0	0
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	2.00000	0.133631
$225$	0	0
$226$	−6.00000	−0.399114
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	0	0
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	0	0
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	−12.0000	−0.782794
$236$	0	0
$237$	0	0
$238$	4.00000	0.259281
$239$	−10.0000	−0.646846	−0.323423	−	0.946254i	$-0.604834\pi$
$239$	−10.0000	−0.646846	−0.323423	+	0.946254i	$0.604834\pi$
$240$	0	0
$241$	2.00000	0.128831	0.0644157	−	0.997923i	$-0.479482\pi$
$241$	2.00000	0.128831	0.0644157	+	0.997923i	$0.479482\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	2.00000	0.128037
$245$	3.00000	0.191663
$246$	0	0
$247$	−4.00000	−0.254514
$248$	8.00000	0.508001
$249$	0	0
$250$	1.00000	0.0632456
$251$	−2.00000	−0.126239	−0.0631194	−	0.998006i	$-0.520105\pi$
$251$	−2.00000	−0.126239	−0.0631194	+	0.998006i	$0.520105\pi$
$252$	0	0
$253$	8.00000	0.502956
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	0	0
$259$	−16.0000	−0.994192
$260$	−4.00000	−0.248069
$261$	0	0
$262$	−18.0000	−1.11204
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	0	0
$265$	−6.00000	−0.368577
$266$	−2.00000	−0.122628
$267$	0	0
$268$	8.00000	0.488678
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	12.0000	0.728948	0.364474	−	0.931214i	$-0.381249\pi$
$271$	12.0000	0.728948	0.364474	+	0.931214i	$0.381249\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	−22.0000	−1.32907
$275$	−2.00000	−0.120605
$276$	0	0
$277$	18.0000	1.08152	0.540758	−	0.841178i	$-0.318138\pi$
$277$	18.0000	1.08152	0.540758	+	0.841178i	$0.318138\pi$
$278$	0	0
$279$	0	0
$280$	−2.00000	−0.119523
$281$	−12.0000	−0.715860	−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000	−0.715860	−0.357930	+	0.933748i	$0.616517\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	8.00000	0.474713
$285$	0	0
$286$	8.00000	0.473050
$287$	−16.0000	−0.944450
$288$	0	0
$289$	−13.0000	−0.764706
$290$	0	0
$291$	0	0
$292$	14.0000	0.819288
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	0	0
$295$	0	0
$296$	−8.00000	−0.464991
$297$	0	0
$298$	10.0000	0.579284
$299$	−16.0000	−0.925304
$300$	0	0
$301$	12.0000	0.691669
$302$	8.00000	0.460348
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	−2.00000	−0.114520
$306$	0	0
$307$	−32.0000	−1.82634	−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000	−1.82634	−0.913168	+	0.407583i	$0.866372\pi$
$308$	4.00000	0.227921
$309$	0	0
$310$	−8.00000	−0.454369
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	0	0
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	−18.0000	−1.01580
$315$	0	0
$316$	0	0
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	0	0
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	0	0
$322$	−8.00000	−0.445823
$323$	−2.00000	−0.111283
$324$	0	0
$325$	4.00000	0.221880
$326$	−14.0000	−0.775388
$327$	0	0
$328$	−8.00000	−0.441726
$329$	−24.0000	−1.32316
$330$	0	0
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	−4.00000	−0.219529
$333$	0	0
$334$	8.00000	0.437741
$335$	−8.00000	−0.437087
$336$	0	0
$337$	28.0000	1.52526	0.762629	−	0.646837i	$-0.223908\pi$
$337$	28.0000	1.52526	0.762629	+	0.646837i	$0.223908\pi$
$338$	−3.00000	−0.163178
$339$	0	0
$340$	−2.00000	−0.108465
$341$	16.0000	0.866449
$342$	0	0
$343$	20.0000	1.07990
$344$	6.00000	0.323498
$345$	0	0
$346$	14.0000	0.752645
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	2.00000	0.106904
$351$	0	0
$352$	2.00000	0.106600
$353$	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
$355$	−8.00000	−0.424596
$356$	0	0
$357$	0	0
$358$	0	0
$359$	10.0000	0.527780	0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000	0.527780	0.263890	+	0.964553i	$0.414994\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−2.00000	−0.105118
$363$	0	0
$364$	−8.00000	−0.419314
$365$	−14.0000	−0.732793
$366$	0	0
$367$	18.0000	0.939592	0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000	0.939592	0.469796	+	0.882775i	$0.344327\pi$
$368$	−4.00000	−0.208514
$369$	0	0
$370$	8.00000	0.415900
$371$	−12.0000	−0.623009
$372$	0	0
$373$	−36.0000	−1.86401	−0.932005	−	0.362446i	$-0.881942\pi$
$373$	−36.0000	−1.86401	−0.932005	+	0.362446i	$0.881942\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	−12.0000	−0.618853
$377$	0	0
$378$	0	0
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	1.00000	0.0512989
$381$	0	0
$382$	−18.0000	−0.920960
$383$	−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
$385$	−4.00000	−0.203859
$386$	−24.0000	−1.22157
$387$	0	0
$388$	−12.0000	−0.609208
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	0	0
$391$	−8.00000	−0.404577
$392$	3.00000	0.151523
$393$	0	0
$394$	18.0000	0.906827
$395$	0	0
$396$	0	0
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	20.0000	1.00251
$399$	0	0
$400$	1.00000	0.0500000
$401$	−12.0000	−0.599251	−0.299626	−	0.954057i	$-0.596862\pi$
$401$	−12.0000	−0.599251	−0.299626	+	0.954057i	$0.596862\pi$
$402$	0	0
$403$	−32.0000	−1.59403
$404$	−2.00000	−0.0995037
$405$	0	0
$406$	0	0
$407$	−16.0000	−0.793091
$408$	0	0
$409$	30.0000	1.48340	0.741702	−	0.670729i	$-0.234019\pi$
$409$	30.0000	1.48340	0.741702	+	0.670729i	$0.234019\pi$
$410$	8.00000	0.395092
$411$	0	0
$412$	4.00000	0.197066
$413$	0	0
$414$	0	0
$415$	4.00000	0.196352
$416$	−4.00000	−0.196116
$417$	0	0
$418$	−2.00000	−0.0978232
$419$	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	$0.319894\pi$
$422$	−12.0000	−0.584151
$423$	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
$431$	−12.0000	−0.578020	−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000	−0.578020	−0.289010	+	0.957326i	$0.593326\pi$
$432$	0	0
$433$	−16.0000	−0.768911	−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000	−0.768911	−0.384455	+	0.923144i	$0.625611\pi$
$434$	−16.0000	−0.768025
$435$	0	0
$436$	10.0000	0.478913
$437$	4.00000	0.191346
$438$	0	0
$439$	−40.0000	−1.90910	−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000	−1.90910	−0.954548	+	0.298057i	$0.903661\pi$
$440$	−2.00000	−0.0953463
$441$	0	0
$442$	−8.00000	−0.380521
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	0	0
$445$	0	0
$446$	−4.00000	−0.189405
$447$	0	0
$448$	−2.00000	−0.0944911
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	0	0
$451$	−16.0000	−0.753411
$452$	6.00000	0.282216
$453$	0	0
$454$	−12.0000	−0.563188
$455$	8.00000	0.375046
$456$	0	0
$457$	18.0000	0.842004	0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000	0.842004	0.421002	+	0.907060i	$0.361678\pi$
$458$	−10.0000	−0.467269
$459$	0	0
$460$	4.00000	0.186501
$461$	−2.00000	−0.0931493	−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000	−0.0931493	−0.0465746	+	0.998915i	$0.514831\pi$
$462$	0	0
$463$	−6.00000	−0.278844	−0.139422	−	0.990233i	$-0.544524\pi$
$463$	−6.00000	−0.278844	−0.139422	+	0.990233i	$0.544524\pi$
$464$	0	0
$465$	0	0
$466$	−6.00000	−0.277945
$467$	−8.00000	−0.370196	−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000	−0.370196	−0.185098	+	0.982720i	$0.559260\pi$
$468$	0	0
$469$	−16.0000	−0.738811
$470$	12.0000	0.553519
$471$	0	0
$472$	0	0
$473$	12.0000	0.551761
$474$	0	0
$475$	−1.00000	−0.0458831
$476$	−4.00000	−0.183340
$477$	0	0
$478$	10.0000	0.457389
$479$	10.0000	0.456912	0.228456	−	0.973554i	$-0.426632\pi$
$479$	10.0000	0.456912	0.228456	+	0.973554i	$0.426632\pi$
$480$	0	0
$481$	32.0000	1.45907
$482$	−2.00000	−0.0910975
$483$	0	0
$484$	−7.00000	−0.318182
$485$	12.0000	0.544892
$486$	0	0
$487$	28.0000	1.26880	0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000	1.26880	0.634401	+	0.773004i	$0.281247\pi$
$488$	−2.00000	−0.0905357
$489$	0	0
$490$	−3.00000	−0.135526
$491$	−22.0000	−0.992846	−0.496423	−	0.868081i	$-0.665354\pi$
$491$	−22.0000	−0.992846	−0.496423	+	0.868081i	$0.665354\pi$
$492$	0	0
$493$	0	0
$494$	4.00000	0.179969
$495$	0	0
$496$	−8.00000	−0.359211
$497$	−16.0000	−0.717698
$498$	0	0
$499$	−40.0000	−1.79065	−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000	−1.79065	−0.895323	+	0.445418i	$0.853055\pi$
$500$	−1.00000	−0.0447214
$501$	0	0
$502$	2.00000	0.0892644
$503$	16.0000	0.713405	0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000	0.713405	0.356702	+	0.934218i	$0.383901\pi$
$504$	0	0
$505$	2.00000	0.0889988
$506$	−8.00000	−0.355643
$507$	0	0
$508$	8.00000	0.354943
$509$	−20.0000	−0.886484	−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000	−0.886484	−0.443242	+	0.896402i	$0.646172\pi$
$510$	0	0
$511$	−28.0000	−1.23865
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	18.0000	0.793946
$515$	−4.00000	−0.176261
$516$	0	0
$517$	−24.0000	−1.05552
$518$	16.0000	0.703000
$519$	0	0
$520$	4.00000	0.175412
$521$	28.0000	1.22670	0.613351	−	0.789810i	$-0.289821\pi$
$521$	28.0000	1.22670	0.613351	+	0.789810i	$0.289821\pi$
$522$	0	0
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	18.0000	0.786334
$525$	0	0
$526$	24.0000	1.04645
$527$	−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
$533$	32.0000	1.38607
$534$	0	0
$535$	−12.0000	−0.518805
$536$	−8.00000	−0.345547
$537$	0	0
$538$	0	0
$539$	6.00000	0.258438
$540$	0	0
$541$	−18.0000	−0.773880	−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000	−0.773880	−0.386940	+	0.922105i	$0.626468\pi$
$542$	−12.0000	−0.515444
$543$	0	0
$544$	−2.00000	−0.0857493
$545$	−10.0000	−0.428353
$546$	0	0
$547$	−32.0000	−1.36822	−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000	−1.36822	−0.684111	+	0.729378i	$0.739809\pi$
$548$	22.0000	0.939793
$549$	0	0
$550$	2.00000	0.0852803
$551$	0	0
$552$	0	0
$553$	0	0
$554$	−18.0000	−0.764747
$555$	0	0
$556$	0	0
$557$	42.0000	1.77960	0.889799	−	0.456354i	$-0.150845\pi$
$557$	42.0000	1.77960	0.889799	+	0.456354i	$0.150845\pi$
$558$	0	0
$559$	−24.0000	−1.01509
$560$	2.00000	0.0845154
$561$	0	0
$562$	12.0000	0.506189
$563$	−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
$565$	−6.00000	−0.252422
$566$	−14.0000	−0.588464
$567$	0	0
$568$	−8.00000	−0.335673
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	32.0000	1.33916	0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000	1.33916	0.669579	+	0.742741i	$0.266474\pi$
$572$	−8.00000	−0.334497
$573$	0	0
$574$	16.0000	0.667827
$575$	−4.00000	−0.166812
$576$	0	0
$577$	−22.0000	−0.915872	−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000	−0.915872	−0.457936	+	0.888985i	$0.651411\pi$
$578$	13.0000	0.540729
$579$	0	0
$580$	0	0
$581$	8.00000	0.331896
$582$	0	0
$583$	−12.0000	−0.496989
$584$	−14.0000	−0.579324
$585$	0	0
$586$	14.0000	0.578335
$587$	−8.00000	−0.330195	−0.165098	−	0.986277i	$-0.552794\pi$
$587$	−8.00000	−0.330195	−0.165098	+	0.986277i	$0.552794\pi$
$588$	0	0
$589$	8.00000	0.329634
$590$	0	0
$591$	0	0
$592$	8.00000	0.328798
$593$	46.0000	1.88899	0.944497	−	0.328521i	$-0.106550\pi$
$593$	46.0000	1.88899	0.944497	+	0.328521i	$0.106550\pi$
$594$	0	0
$595$	4.00000	0.163984
$596$	−10.0000	−0.409616
$597$	0	0
$598$	16.0000	0.654289
$599$	−20.0000	−0.817178	−0.408589	−	0.912719i	$-0.633979\pi$
$599$	−20.0000	−0.817178	−0.408589	+	0.912719i	$0.633979\pi$
$600$	0	0
$601$	−18.0000	−0.734235	−0.367118	−	0.930175i	$-0.619655\pi$
$601$	−18.0000	−0.734235	−0.367118	+	0.930175i	$0.619655\pi$
$602$	−12.0000	−0.489083
$603$	0	0
$604$	−8.00000	−0.325515
$605$	7.00000	0.284590
$606$	0	0
$607$	−12.0000	−0.487065	−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000	−0.487065	−0.243532	+	0.969893i	$0.578306\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	2.00000	0.0809776
$611$	48.0000	1.94187
$612$	0	0
$613$	−6.00000	−0.242338	−0.121169	−	0.992632i	$-0.538664\pi$
$613$	−6.00000	−0.242338	−0.121169	+	0.992632i	$0.538664\pi$
$614$	32.0000	1.29141
$615$	0	0
$616$	−4.00000	−0.161165
$617$	42.0000	1.69086	0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000	1.69086	0.845428	+	0.534089i	$0.179345\pi$
$618$	0	0
$619$	−40.0000	−1.60774	−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000	−1.60774	−0.803868	+	0.594808i	$0.797228\pi$
$620$	8.00000	0.321288
$621$	0	0
$622$	−18.0000	−0.721734
$623$	0	0
$624$	0	0
$625$	1.00000	0.0400000
$626$	6.00000	0.239808
$627$	0	0
$628$	18.0000	0.718278
$629$	16.0000	0.637962
$630$	0	0
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	0	0
$633$	0	0
$634$	18.0000	0.714871
$635$	−8.00000	−0.317470
$636$	0	0
$637$	−12.0000	−0.475457
$638$	0	0
$639$	0	0
$640$	1.00000	0.0395285
$641$	−32.0000	−1.26392	−0.631962	−	0.774999i	$-0.717750\pi$
$641$	−32.0000	−1.26392	−0.631962	+	0.774999i	$0.717750\pi$
$642$	0	0
$643$	14.0000	0.552106	0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000	0.552106	0.276053	+	0.961142i	$0.410973\pi$
$644$	8.00000	0.315244
$645$	0	0
$646$	2.00000	0.0786889
$647$	32.0000	1.25805	0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000	1.25805	0.629025	+	0.777385i	$0.283454\pi$
$648$	0	0
$649$	0	0
$650$	−4.00000	−0.156893
$651$	0	0
$652$	14.0000	0.548282
$653$	46.0000	1.80012	0.900060	−	0.435767i	$-0.143523\pi$
$653$	46.0000	1.80012	0.900060	+	0.435767i	$0.143523\pi$
$654$	0	0
$655$	−18.0000	−0.703318
$656$	8.00000	0.312348
$657$	0	0
$658$	24.0000	0.935617
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	0	0
$661$	42.0000	1.63361	0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000	1.63361	0.816805	+	0.576913i	$0.195743\pi$
$662$	−12.0000	−0.466393
$663$	0	0
$664$	4.00000	0.155230
$665$	−2.00000	−0.0775567
$666$	0	0
$667$	0	0
$668$	−8.00000	−0.309529
$669$	0	0
$670$	8.00000	0.309067
$671$	−4.00000	−0.154418
$672$	0	0
$673$	4.00000	0.154189	0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000	0.154189	0.0770943	+	0.997024i	$0.475436\pi$
$674$	−28.0000	−1.07852
$675$	0	0
$676$	3.00000	0.115385
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	0	0
$679$	24.0000	0.921035
$680$	2.00000	0.0766965
$681$	0	0
$682$	−16.0000	−0.612672
$683$	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
$685$	−22.0000	−0.840577
$686$	−20.0000	−0.763604
$687$	0	0
$688$	−6.00000	−0.228748
$689$	24.0000	0.914327
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	−14.0000	−0.532200
$693$	0	0
$694$	−12.0000	−0.455514
$695$	0	0
$696$	0	0
$697$	16.0000	0.606043
$698$	10.0000	0.378506
$699$	0	0
$700$	−2.00000	−0.0755929
$701$	−2.00000	−0.0755390	−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000	−0.0755390	−0.0377695	+	0.999286i	$0.512025\pi$
$702$	0	0
$703$	−8.00000	−0.301726
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	−6.00000	−0.225813
$707$	4.00000	0.150435
$708$	0	0
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	8.00000	0.300235
$711$	0	0
$712$	0	0
$713$	32.0000	1.19841
$714$	0	0
$715$	8.00000	0.299183
$716$	0	0
$717$	0	0
$718$	−10.0000	−0.373197
$719$	−50.0000	−1.86469	−0.932343	−	0.361576i	$-0.882239\pi$
$719$	−50.0000	−1.86469	−0.932343	+	0.361576i	$0.882239\pi$
$720$	0	0
$721$	−8.00000	−0.297936
$722$	−1.00000	−0.0372161
$723$	0	0
$724$	2.00000	0.0743294
$725$	0	0
$726$	0	0
$727$	18.0000	0.667583	0.333792	−	0.942647i	$-0.391672\pi$
$727$	18.0000	0.667583	0.333792	+	0.942647i	$0.391672\pi$
$728$	8.00000	0.296500
$729$	0	0
$730$	14.0000	0.518163
$731$	−12.0000	−0.443836
$732$	0	0
$733$	−26.0000	−0.960332	−0.480166	−	0.877178i	$-0.659424\pi$
$733$	−26.0000	−0.960332	−0.480166	+	0.877178i	$0.659424\pi$
$734$	−18.0000	−0.664392
$735$	0	0
$736$	4.00000	0.147442
$737$	−16.0000	−0.589368
$738$	0	0
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	−8.00000	−0.294086
$741$	0	0
$742$	12.0000	0.440534
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	0	0
$745$	10.0000	0.366372
$746$	36.0000	1.31805
$747$	0	0
$748$	−4.00000	−0.146254
$749$	−24.0000	−0.876941
$750$	0	0
$751$	−8.00000	−0.291924	−0.145962	−	0.989290i	$-0.546628\pi$
$751$	−8.00000	−0.291924	−0.145962	+	0.989290i	$0.546628\pi$
$752$	12.0000	0.437595
$753$	0	0
$754$	0	0
$755$	8.00000	0.291150
$756$	0	0
$757$	−2.00000	−0.0726912	−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000	−0.0726912	−0.0363456	+	0.999339i	$0.511572\pi$
$758$	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
$763$	−20.0000	−0.724049
$764$	18.0000	0.651217
$765$	0	0
$766$	24.0000	0.867155
$767$	0	0
$768$	0	0
$769$	50.0000	1.80305	0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000	1.80305	0.901523	+	0.432731i	$0.142450\pi$
$770$	4.00000	0.144150
$771$	0	0
$772$	24.0000	0.863779
$773$	−34.0000	−1.22290	−0.611448	−	0.791285i	$-0.709412\pi$
$773$	−34.0000	−1.22290	−0.611448	+	0.791285i	$0.709412\pi$
$774$	0	0
$775$	−8.00000	−0.287368
$776$	12.0000	0.430775
$777$	0	0
$778$	30.0000	1.07555
$779$	−8.00000	−0.286630
$780$	0	0
$781$	−16.0000	−0.572525
$782$	8.00000	0.286079
$783$	0	0
$784$	−3.00000	−0.107143
$785$	−18.0000	−0.642448
$786$	0	0
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	−18.0000	−0.641223
$789$	0	0
$790$	0	0
$791$	−12.0000	−0.426671
$792$	0	0
$793$	8.00000	0.284088
$794$	22.0000	0.780751
$795$	0	0
$796$	−20.0000	−0.708881
$797$	2.00000	0.0708436	0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000	0.0708436	0.0354218	+	0.999372i	$0.488723\pi$
$798$	0	0
$799$	24.0000	0.849059
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	12.0000	0.423735
$803$	−28.0000	−0.988099
$804$	0	0
$805$	−8.00000	−0.281963
$806$	32.0000	1.12715
$807$	0	0
$808$	2.00000	0.0703598
$809$	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
$811$	12.0000	0.421377	0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000	0.421377	0.210688	+	0.977553i	$0.432429\pi$
$812$	0	0
$813$	0	0
$814$	16.0000	0.560800
$815$	−14.0000	−0.490399
$816$	0	0
$817$	6.00000	0.209913
$818$	−30.0000	−1.04893
$819$	0	0
$820$	−8.00000	−0.279372
$821$	38.0000	1.32621	0.663105	−	0.748527i	$-0.269238\pi$
$821$	38.0000	1.32621	0.663105	+	0.748527i	$0.269238\pi$
$822$	0	0
$823$	34.0000	1.18517	0.592583	−	0.805510i	$-0.298108\pi$
$823$	34.0000	1.18517	0.592583	+	0.805510i	$0.298108\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	0	0
$827$	−28.0000	−0.973655	−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000	−0.973655	−0.486828	+	0.873498i	$0.661846\pi$
$828$	0	0
$829$	10.0000	0.347314	0.173657	−	0.984806i	$-0.444442\pi$
$829$	10.0000	0.347314	0.173657	+	0.984806i	$0.444442\pi$
$830$	−4.00000	−0.138842
$831$	0	0
$832$	4.00000	0.138675
$833$	−6.00000	−0.207888
$834$	0	0
$835$	8.00000	0.276851
$836$	2.00000	0.0691714
$837$	0	0
$838$	−30.0000	−1.03633
$839$	40.0000	1.38095	0.690477	−	0.723355i	$-0.257401\pi$
$839$	40.0000	1.38095	0.690477	+	0.723355i	$0.257401\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	−22.0000	−0.758170
$843$	0	0
$844$	12.0000	0.413057
$845$	−3.00000	−0.103203
$846$	0	0
$847$	14.0000	0.481046
$848$	6.00000	0.206041
$849$	0	0
$850$	−2.00000	−0.0685994
$851$	−32.0000	−1.09695
$852$	0	0
$853$	14.0000	0.479351	0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000	0.479351	0.239675	+	0.970853i	$0.422959\pi$
$854$	4.00000	0.136877
$855$	0	0
$856$	−12.0000	−0.410152
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	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
$862$	12.0000	0.408722
$863$	16.0000	0.544646	0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000	0.544646	0.272323	+	0.962206i	$0.412208\pi$
$864$	0	0
$865$	14.0000	0.476014
$866$	16.0000	0.543702
$867$	0	0
$868$	16.0000	0.543075
$869$	0	0
$870$	0	0
$871$	32.0000	1.08428
$872$	−10.0000	−0.338643
$873$	0	0
$874$	−4.00000	−0.135302
$875$	2.00000	0.0676123
$876$	0	0
$877$	−12.0000	−0.405211	−0.202606	−	0.979260i	$-0.564941\pi$
$877$	−12.0000	−0.405211	−0.202606	+	0.979260i	$0.564941\pi$
$878$	40.0000	1.34993
$879$	0	0
$880$	2.00000	0.0674200
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	0	0
$883$	−26.0000	−0.874970	−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000	−0.874970	−0.437485	+	0.899226i	$0.644131\pi$
$884$	8.00000	0.269069
$885$	0	0
$886$	24.0000	0.806296
$887$	−48.0000	−1.61168	−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000	−1.61168	−0.805841	+	0.592132i	$0.798286\pi$
$888$	0	0
$889$	−16.0000	−0.536623
$890$	0	0
$891$	0	0
$892$	4.00000	0.133930
$893$	−12.0000	−0.401565
$894$	0	0
$895$	0	0
$896$	2.00000	0.0668153
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	12.0000	0.399778
$902$	16.0000	0.532742
$903$	0	0
$904$	−6.00000	−0.199557
$905$	−2.00000	−0.0664822
$906$	0	0
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	12.0000	0.398234
$909$	0	0
$910$	−8.00000	−0.265197
$911$	−32.0000	−1.06021	−0.530104	−	0.847933i	$-0.677847\pi$
$911$	−32.0000	−1.06021	−0.530104	+	0.847933i	$0.677847\pi$
$912$	0	0
$913$	8.00000	0.264761
$914$	−18.0000	−0.595387
$915$	0	0
$916$	10.0000	0.330409
$917$	−36.0000	−1.18882
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	−4.00000	−0.131876
$921$	0	0
$922$	2.00000	0.0658665
$923$	32.0000	1.05329
$924$	0	0
$925$	8.00000	0.263038
$926$	6.00000	0.197172
$927$	0	0
$928$	0	0
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	0	0
$931$	3.00000	0.0983210
$932$	6.00000	0.196537
$933$	0	0
$934$	8.00000	0.261768
$935$	4.00000	0.130814
$936$	0	0
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	16.0000	0.522419
$939$	0	0
$940$	−12.0000	−0.391397
$941$	8.00000	0.260793	0.130396	−	0.991462i	$-0.458375\pi$
$941$	8.00000	0.260793	0.130396	+	0.991462i	$0.458375\pi$
$942$	0	0
$943$	−32.0000	−1.04206
$944$	0	0
$945$	0	0
$946$	−12.0000	−0.390154
$947$	52.0000	1.68977	0.844886	−	0.534946i	$-0.179668\pi$
$947$	52.0000	1.68977	0.844886	+	0.534946i	$0.179668\pi$
$948$	0	0
$949$	56.0000	1.81784
$950$	1.00000	0.0324443
$951$	0	0
$952$	4.00000	0.129641
$953$	−34.0000	−1.10137	−0.550684	−	0.834714i	$-0.685633\pi$
$953$	−34.0000	−1.10137	−0.550684	+	0.834714i	$0.685633\pi$
$954$	0	0
$955$	−18.0000	−0.582466
$956$	−10.0000	−0.323423
$957$	0	0
$958$	−10.0000	−0.323085
$959$	−44.0000	−1.42083
$960$	0	0
$961$	33.0000	1.06452
$962$	−32.0000	−1.03172
$963$	0	0
$964$	2.00000	0.0644157
$965$	−24.0000	−0.772587
$966$	0	0
$967$	58.0000	1.86515	0.932577	−	0.360971i	$-0.117555\pi$
$967$	58.0000	1.86515	0.932577	+	0.360971i	$0.117555\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	−12.0000	−0.385297
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	0	0
$973$	0	0
$974$	−28.0000	−0.897178
$975$	0	0
$976$	2.00000	0.0640184
$977$	−38.0000	−1.21573	−0.607864	−	0.794041i	$-0.707973\pi$
$977$	−38.0000	−1.21573	−0.607864	+	0.794041i	$0.707973\pi$
$978$	0	0
$979$	0	0
$980$	3.00000	0.0958315
$981$	0	0
$982$	22.0000	0.702048
$983$	−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
$985$	18.0000	0.573528
$986$	0	0
$987$	0	0
$988$	−4.00000	−0.127257
$989$	24.0000	0.763156
$990$	0	0
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	8.00000	0.254000
$993$	0	0
$994$	16.0000	0.507489
$995$	20.0000	0.634043
$996$	0	0
$997$	−62.0000	−1.96356	−0.981780	−	0.190022i	$-0.939144\pi$
$997$	−62.0000	−1.96356	−0.981780	+	0.190022i	$0.939144\pi$
$998$	40.0000	1.26618
$999$	0	0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.a.b.1.1		1
3.2	odd	2		570.2.a.l.1.1	✓	1
5.4	even	2		8550.2.a.bf.1.1		1
12.11	even	2		4560.2.a.o.1.1		1
15.2	even	4		2850.2.d.q.799.2		2
15.8	even	4		2850.2.d.q.799.1		2
15.14	odd	2		2850.2.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.a.l.1.1	✓	1	3.2	odd	2
1710.2.a.b.1.1		1	1.1	even	1	trivial
2850.2.a.e.1.1		1	15.14	odd	2
2850.2.d.q.799.1		2	15.8	even	4
2850.2.d.q.799.2		2	15.2	even	4
4560.2.a.o.1.1		1	12.11	even	2
8550.2.a.bf.1.1		1	5.4	even	2

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1710.2.a.b.1.1

Level	$1710$
Weight	$2$
Character	1710.1
Self dual	yes
Analytic conductor	$13.654$
Analytic rank	$0$
Dimension	$1$
CM	no
Inner twists	$1$