LMFDB - Embedded newform 435.2.a.b.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [435,2,Mod(1,435)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("435.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(435, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.a (trivial)

Newform invariants

comment:select newform

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

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	435.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{3} -2.00000 q^{4} -1.00000 q^{5} -2.00000 q^{7} +1.00000 q^{9} +1.00000 q^{11} +2.00000 q^{12} +6.00000 q^{13} +1.00000 q^{15} +4.00000 q^{16} +4.00000 q^{17} -2.00000 q^{19} +2.00000 q^{20} +2.00000 q^{21} +3.00000 q^{23} +1.00000 q^{25} -1.00000 q^{27} +4.00000 q^{28} +1.00000 q^{29} -4.00000 q^{31} -1.00000 q^{33} +2.00000 q^{35} -2.00000 q^{36} -3.00000 q^{37} -6.00000 q^{39} +7.00000 q^{41} +5.00000 q^{43} -2.00000 q^{44} -1.00000 q^{45} +6.00000 q^{47} -4.00000 q^{48} -3.00000 q^{49} -4.00000 q^{51} -12.0000 q^{52} +13.0000 q^{53} -1.00000 q^{55} +2.00000 q^{57} -2.00000 q^{60} -2.00000 q^{63} -8.00000 q^{64} -6.00000 q^{65} -10.0000 q^{67} -8.00000 q^{68} -3.00000 q^{69} +6.00000 q^{71} +3.00000 q^{73} -1.00000 q^{75} +4.00000 q^{76} -2.00000 q^{77} -4.00000 q^{80} +1.00000 q^{81} +9.00000 q^{83} -4.00000 q^{84} -4.00000 q^{85} -1.00000 q^{87} -10.0000 q^{89} -12.0000 q^{91} -6.00000 q^{92} +4.00000 q^{93} +2.00000 q^{95} +17.0000 q^{97} +1.00000 q^{99} +O(q^{100})$

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 $

$2$	0	0		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−2.00000	−1.00000
$5$	−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	$0.623376\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	2.00000	0.577350
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	4.00000	1.00000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	0	0
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	2.00000	0.447214
$21$	2.00000	0.436436
$22$	0	0
$23$	3.00000	0.625543	0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000	0.625543	0.312772	+	0.949828i	$0.398743\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	4.00000	0.755929
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	0	0
$33$	−1.00000	−0.174078
$34$	0	0
$35$	2.00000	0.338062
$36$	−2.00000	−0.333333
$37$	−3.00000	−0.493197	−0.246598	−	0.969118i	$-0.579313\pi$
$37$	−3.00000	−0.493197	−0.246598	+	0.969118i	$0.579313\pi$
$38$	0	0
$39$	−6.00000	−0.960769
$40$	0	0
$41$	7.00000	1.09322	0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000	1.09322	0.546608	+	0.837389i	$0.315919\pi$
$42$	0	0
$43$	5.00000	0.762493	0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000	0.762493	0.381246	+	0.924473i	$0.375495\pi$
$44$	−2.00000	−0.301511
$45$	−1.00000	−0.149071
$46$	0	0
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	−4.00000	−0.577350
$49$	−3.00000	−0.428571
$50$	0	0
$51$	−4.00000	−0.560112
$52$	−12.0000	−1.66410
$53$	13.0000	1.78569	0.892844	−	0.450367i	$-0.148707\pi$
$53$	13.0000	1.78569	0.892844	+	0.450367i	$0.148707\pi$
$54$	0	0
$55$	−1.00000	−0.134840
$56$	0	0
$57$	2.00000	0.264906
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−2.00000	−0.258199
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	−2.00000	−0.251976
$64$	−8.00000	−1.00000
$65$	−6.00000	−0.744208
$66$	0	0
$67$	−10.0000	−1.22169	−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000	−1.22169	−0.610847	+	0.791748i	$0.709171\pi$
$68$	−8.00000	−0.970143
$69$	−3.00000	−0.361158
$70$	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
$73$	3.00000	0.351123	0.175562	−	0.984468i	$-0.443826\pi$
$73$	3.00000	0.351123	0.175562	+	0.984468i	$0.443826\pi$
$74$	0	0
$75$	−1.00000	−0.115470
$76$	4.00000	0.458831
$77$	−2.00000	−0.227921
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−4.00000	−0.447214
$81$	1.00000	0.111111
$82$	0	0
$83$	9.00000	0.987878	0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000	0.987878	0.493939	+	0.869496i	$0.335557\pi$
$84$	−4.00000	−0.436436
$85$	−4.00000	−0.433861
$86$	0	0
$87$	−1.00000	−0.107211
$88$	0	0
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	0	0
$91$	−12.0000	−1.25794
$92$	−6.00000	−0.625543
$93$	4.00000	0.414781
$94$	0	0
$95$	2.00000	0.205196
$96$	0	0
$97$	17.0000	1.72609	0.863044	−	0.505128i	$-0.168555\pi$
$97$	17.0000	1.72609	0.863044	+	0.505128i	$0.168555\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−2.00000	−0.200000
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	0	0
$103$	−6.00000	−0.591198	−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000	−0.591198	−0.295599	+	0.955312i	$0.595519\pi$
$104$	0	0
$105$	−2.00000	−0.195180
$106$	0	0
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	2.00000	0.192450
$109$	11.0000	1.05361	0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000	1.05361	0.526804	+	0.849987i	$0.323390\pi$
$110$	0	0
$111$	3.00000	0.284747
$112$	−8.00000	−0.755929
$113$	−12.0000	−1.12887	−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000	−1.12887	−0.564433	+	0.825479i	$0.690905\pi$
$114$	0	0
$115$	−3.00000	−0.279751
$116$	−2.00000	−0.185695
$117$	6.00000	0.554700
$118$	0	0
$119$	−8.00000	−0.733359
$120$	0	0
$121$	−10.0000	−0.909091
$122$	0	0
$123$	−7.00000	−0.631169
$124$	8.00000	0.718421
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	7.00000	0.621150	0.310575	−	0.950549i	$-0.399478\pi$
$127$	7.00000	0.621150	0.310575	+	0.950549i	$0.399478\pi$
$128$	0	0
$129$	−5.00000	−0.440225
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	2.00000	0.174078
$133$	4.00000	0.346844
$134$	0	0
$135$	1.00000	0.0860663
$136$	0	0
$137$	16.0000	1.36697	0.683486	−	0.729964i	$-0.260463\pi$
$137$	16.0000	1.36697	0.683486	+	0.729964i	$0.260463\pi$
$138$	0	0
$139$	−19.0000	−1.61156	−0.805779	−	0.592216i	$-0.798253\pi$
$139$	−19.0000	−1.61156	−0.805779	+	0.592216i	$0.798253\pi$
$140$	−4.00000	−0.338062
$141$	−6.00000	−0.505291
$142$	0	0
$143$	6.00000	0.501745
$144$	4.00000	0.333333
$145$	−1.00000	−0.0830455
$146$	0	0
$147$	3.00000	0.247436
$148$	6.00000	0.493197
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	0	0
$151$	−11.0000	−0.895167	−0.447584	−	0.894242i	$-0.647715\pi$
$151$	−11.0000	−0.895167	−0.447584	+	0.894242i	$0.647715\pi$
$152$	0	0
$153$	4.00000	0.323381
$154$	0	0
$155$	4.00000	0.321288
$156$	12.0000	0.960769
$157$	−18.0000	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$158$	0	0
$159$	−13.0000	−1.03097
$160$	0	0
$161$	−6.00000	−0.472866
$162$	0	0
$163$	15.0000	1.17489	0.587445	−	0.809264i	$-0.300134\pi$
$163$	15.0000	1.17489	0.587445	+	0.809264i	$0.300134\pi$
$164$	−14.0000	−1.09322
$165$	1.00000	0.0778499
$166$	0	0
$167$	8.00000	0.619059	0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000	0.619059	0.309529	+	0.950890i	$0.399829\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	0	0
$171$	−2.00000	−0.152944
$172$	−10.0000	−0.762493
$173$	5.00000	0.380143	0.190071	−	0.981770i	$-0.439128\pi$
$173$	5.00000	0.380143	0.190071	+	0.981770i	$0.439128\pi$
$174$	0	0
$175$	−2.00000	−0.151186
$176$	4.00000	0.301511
$177$	0	0
$178$	0	0
$179$	−18.0000	−1.34538	−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000	−1.34538	−0.672692	+	0.739923i	$0.734862\pi$
$180$	2.00000	0.149071
$181$	25.0000	1.85824	0.929118	−	0.369784i	$-0.120568\pi$
$181$	25.0000	1.85824	0.929118	+	0.369784i	$0.120568\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	3.00000	0.220564
$186$	0	0
$187$	4.00000	0.292509
$188$	−12.0000	−0.875190
$189$	2.00000	0.145479
$190$	0	0
$191$	−27.0000	−1.95365	−0.976826	−	0.214036i	$-0.931339\pi$
$191$	−27.0000	−1.95365	−0.976826	+	0.214036i	$0.931339\pi$
$192$	8.00000	0.577350
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	0	0
$195$	6.00000	0.429669
$196$	6.00000	0.428571
$197$	13.0000	0.926212	0.463106	−	0.886303i	$-0.346735\pi$
$197$	13.0000	0.926212	0.463106	+	0.886303i	$0.346735\pi$
$198$	0	0
$199$	15.0000	1.06332	0.531661	−	0.846957i	$-0.321568\pi$
$199$	15.0000	1.06332	0.531661	+	0.846957i	$0.321568\pi$
$200$	0	0
$201$	10.0000	0.705346
$202$	0	0
$203$	−2.00000	−0.140372
$204$	8.00000	0.560112
$205$	−7.00000	−0.488901
$206$	0	0
$207$	3.00000	0.208514
$208$	24.0000	1.66410
$209$	−2.00000	−0.138343
$210$	0	0
$211$	−2.00000	−0.137686	−0.0688428	−	0.997628i	$-0.521931\pi$
$211$	−2.00000	−0.137686	−0.0688428	+	0.997628i	$0.521931\pi$
$212$	−26.0000	−1.78569
$213$	−6.00000	−0.411113
$214$	0	0
$215$	−5.00000	−0.340997
$216$	0	0
$217$	8.00000	0.543075
$218$	0	0
$219$	−3.00000	−0.202721
$220$	2.00000	0.134840
$221$	24.0000	1.61441
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	0	0
$227$	11.0000	0.730096	0.365048	−	0.930989i	$-0.381053\pi$
$227$	11.0000	0.730096	0.365048	+	0.930989i	$0.381053\pi$
$228$	−4.00000	−0.264906
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	0	0
$231$	2.00000	0.131590
$232$	0	0
$233$	−1.00000	−0.0655122	−0.0327561	−	0.999463i	$-0.510428\pi$
$233$	−1.00000	−0.0655122	−0.0327561	+	0.999463i	$0.510428\pi$
$234$	0	0
$235$	−6.00000	−0.391397
$236$	0	0
$237$	0	0
$238$	0	0
$239$	14.0000	0.905585	0.452792	−	0.891616i	$-0.350428\pi$
$239$	14.0000	0.905585	0.452792	+	0.891616i	$0.350428\pi$
$240$	4.00000	0.258199
$241$	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
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	3.00000	0.191663
$246$	0	0
$247$	−12.0000	−0.763542
$248$	0	0
$249$	−9.00000	−0.570352
$250$	0	0
$251$	−4.00000	−0.252478	−0.126239	−	0.992000i	$-0.540291\pi$
$251$	−4.00000	−0.252478	−0.126239	+	0.992000i	$0.540291\pi$
$252$	4.00000	0.251976
$253$	3.00000	0.188608
$254$	0	0
$255$	4.00000	0.250490
$256$	16.0000	1.00000
$257$	−21.0000	−1.30994	−0.654972	−	0.755653i	$-0.727320\pi$
$257$	−21.0000	−1.30994	−0.654972	+	0.755653i	$0.727320\pi$
$258$	0	0
$259$	6.00000	0.372822
$260$	12.0000	0.744208
$261$	1.00000	0.0618984
$262$	0	0
$263$	−20.0000	−1.23325	−0.616626	−	0.787256i	$-0.711501\pi$
$263$	−20.0000	−1.23325	−0.616626	+	0.787256i	$0.711501\pi$
$264$	0	0
$265$	−13.0000	−0.798584
$266$	0	0
$267$	10.0000	0.611990
$268$	20.0000	1.22169
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	0	0
$271$	26.0000	1.57939	0.789694	−	0.613501i	$-0.210239\pi$
$271$	26.0000	1.57939	0.789694	+	0.613501i	$0.210239\pi$
$272$	16.0000	0.970143
$273$	12.0000	0.726273
$274$	0	0
$275$	1.00000	0.0603023
$276$	6.00000	0.361158
$277$	4.00000	0.240337	0.120168	−	0.992754i	$-0.461657\pi$
$277$	4.00000	0.240337	0.120168	+	0.992754i	$0.461657\pi$
$278$	0	0
$279$	−4.00000	−0.239474
$280$	0	0
$281$	4.00000	0.238620	0.119310	−	0.992857i	$-0.461932\pi$
$281$	4.00000	0.238620	0.119310	+	0.992857i	$0.461932\pi$
$282$	0	0
$283$	−26.0000	−1.54554	−0.772770	−	0.634686i	$-0.781129\pi$
$283$	−26.0000	−1.54554	−0.772770	+	0.634686i	$0.781129\pi$
$284$	−12.0000	−0.712069
$285$	−2.00000	−0.118470
$286$	0	0
$287$	−14.0000	−0.826394
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	0	0
$291$	−17.0000	−0.996558
$292$	−6.00000	−0.351123
$293$	−8.00000	−0.467365	−0.233682	−	0.972313i	$-0.575078\pi$
$293$	−8.00000	−0.467365	−0.233682	+	0.972313i	$0.575078\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−1.00000	−0.0580259
$298$	0	0
$299$	18.0000	1.04097
$300$	2.00000	0.115470
$301$	−10.0000	−0.576390
$302$	0	0
$303$	3.00000	0.172345
$304$	−8.00000	−0.458831
$305$	0	0
$306$	0	0
$307$	−21.0000	−1.19853	−0.599267	−	0.800549i	$-0.704541\pi$
$307$	−21.0000	−1.19853	−0.599267	+	0.800549i	$0.704541\pi$
$308$	4.00000	0.227921
$309$	6.00000	0.341328
$310$	0	0
$311$	−23.0000	−1.30421	−0.652105	−	0.758129i	$-0.726114\pi$
$311$	−23.0000	−1.30421	−0.652105	+	0.758129i	$0.726114\pi$
$312$	0	0
$313$	−12.0000	−0.678280	−0.339140	−	0.940736i	$-0.610136\pi$
$313$	−12.0000	−0.678280	−0.339140	+	0.940736i	$0.610136\pi$
$314$	0	0
$315$	2.00000	0.112687
$316$	0	0
$317$	−8.00000	−0.449325	−0.224662	−	0.974437i	$-0.572128\pi$
$317$	−8.00000	−0.449325	−0.224662	+	0.974437i	$0.572128\pi$
$318$	0	0
$319$	1.00000	0.0559893
$320$	8.00000	0.447214
$321$	−12.0000	−0.669775
$322$	0	0
$323$	−8.00000	−0.445132
$324$	−2.00000	−0.111111
$325$	6.00000	0.332820
$326$	0	0
$327$	−11.0000	−0.608301
$328$	0	0
$329$	−12.0000	−0.661581
$330$	0	0
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	−18.0000	−0.987878
$333$	−3.00000	−0.164399
$334$	0	0
$335$	10.0000	0.546358
$336$	8.00000	0.436436
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	0	0
$339$	12.0000	0.651751
$340$	8.00000	0.433861
$341$	−4.00000	−0.216612
$342$	0	0
$343$	20.0000	1.07990
$344$	0	0
$345$	3.00000	0.161515
$346$	0	0
$347$	−5.00000	−0.268414	−0.134207	−	0.990953i	$-0.542849\pi$
$347$	−5.00000	−0.268414	−0.134207	+	0.990953i	$0.542849\pi$
$348$	2.00000	0.107211
$349$	31.0000	1.65939	0.829696	−	0.558216i	$-0.188514\pi$
$349$	31.0000	1.65939	0.829696	+	0.558216i	$0.188514\pi$
$350$	0	0
$351$	−6.00000	−0.320256
$352$	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
$355$	−6.00000	−0.318447
$356$	20.0000	1.06000
$357$	8.00000	0.423405
$358$	0	0
$359$	−15.0000	−0.791670	−0.395835	−	0.918322i	$-0.629545\pi$
$359$	−15.0000	−0.791670	−0.395835	+	0.918322i	$0.629545\pi$
$360$	0	0
$361$	−15.0000	−0.789474
$362$	0	0
$363$	10.0000	0.524864
$364$	24.0000	1.25794
$365$	−3.00000	−0.157027
$366$	0	0
$367$	−33.0000	−1.72259	−0.861293	−	0.508109i	$-0.830345\pi$
$367$	−33.0000	−1.72259	−0.861293	+	0.508109i	$0.830345\pi$
$368$	12.0000	0.625543
$369$	7.00000	0.364405
$370$	0	0
$371$	−26.0000	−1.34985
$372$	−8.00000	−0.414781
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	0	0
$377$	6.00000	0.309016
$378$	0	0
$379$	−4.00000	−0.205466	−0.102733	−	0.994709i	$-0.532759\pi$
$379$	−4.00000	−0.205466	−0.102733	+	0.994709i	$0.532759\pi$
$380$	−4.00000	−0.205196
$381$	−7.00000	−0.358621
$382$	0	0
$383$	27.0000	1.37964	0.689818	−	0.723983i	$-0.257691\pi$
$383$	27.0000	1.37964	0.689818	+	0.723983i	$0.257691\pi$
$384$	0	0
$385$	2.00000	0.101929
$386$	0	0
$387$	5.00000	0.254164
$388$	−34.0000	−1.72609
$389$	−21.0000	−1.06474	−0.532371	−	0.846511i	$-0.678699\pi$
$389$	−21.0000	−1.06474	−0.532371	+	0.846511i	$0.678699\pi$
$390$	0	0
$391$	12.0000	0.606866
$392$	0	0
$393$	−12.0000	−0.605320
$394$	0	0
$395$	0	0
$396$	−2.00000	−0.100504
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	0	0
$399$	−4.00000	−0.200250
$400$	4.00000	0.200000
$401$	−20.0000	−0.998752	−0.499376	−	0.866385i	$-0.666437\pi$
$401$	−20.0000	−0.998752	−0.499376	+	0.866385i	$0.666437\pi$
$402$	0	0
$403$	−24.0000	−1.19553
$404$	6.00000	0.298511
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−3.00000	−0.148704
$408$	0	0
$409$	−12.0000	−0.593362	−0.296681	−	0.954977i	$-0.595880\pi$
$409$	−12.0000	−0.593362	−0.296681	+	0.954977i	$0.595880\pi$
$410$	0	0
$411$	−16.0000	−0.789222
$412$	12.0000	0.591198
$413$	0	0
$414$	0	0
$415$	−9.00000	−0.441793
$416$	0	0
$417$	19.0000	0.930434
$418$	0	0
$419$	18.0000	0.879358	0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000	0.879358	0.439679	+	0.898155i	$0.355092\pi$
$420$	4.00000	0.195180
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	0	0
$423$	6.00000	0.291730
$424$	0	0
$425$	4.00000	0.194029
$426$	0	0
$427$	0	0
$428$	−24.0000	−1.16008
$429$	−6.00000	−0.289683
$430$	0	0
$431$	−22.0000	−1.05970	−0.529851	−	0.848091i	$-0.677752\pi$
$431$	−22.0000	−1.05970	−0.529851	+	0.848091i	$0.677752\pi$
$432$	−4.00000	−0.192450
$433$	−25.0000	−1.20142	−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000	−1.20142	−0.600712	+	0.799466i	$0.705116\pi$
$434$	0	0
$435$	1.00000	0.0479463
$436$	−22.0000	−1.05361
$437$	−6.00000	−0.287019
$438$	0	0
$439$	0	0		−	1.00000i	$-0.5\pi$
$439$	0	0			1.00000i	$0.5\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	0	0
$443$	−36.0000	−1.71041	−0.855206	−	0.518289i	$-0.826569\pi$
$443$	−36.0000	−1.71041	−0.855206	+	0.518289i	$0.826569\pi$
$444$	−6.00000	−0.284747
$445$	10.0000	0.474045
$446$	0	0
$447$	2.00000	0.0945968
$448$	16.0000	0.755929
$449$	−31.0000	−1.46298	−0.731490	−	0.681852i	$-0.761175\pi$
$449$	−31.0000	−1.46298	−0.731490	+	0.681852i	$0.761175\pi$
$450$	0	0
$451$	7.00000	0.329617
$452$	24.0000	1.12887
$453$	11.0000	0.516825
$454$	0	0
$455$	12.0000	0.562569
$456$	0	0
$457$	−28.0000	−1.30978	−0.654892	−	0.755722i	$-0.727286\pi$
$457$	−28.0000	−1.30978	−0.654892	+	0.755722i	$0.727286\pi$
$458$	0	0
$459$	−4.00000	−0.186704
$460$	6.00000	0.279751
$461$	−21.0000	−0.978068	−0.489034	−	0.872265i	$-0.662651\pi$
$461$	−21.0000	−0.978068	−0.489034	+	0.872265i	$0.662651\pi$
$462$	0	0
$463$	−18.0000	−0.836531	−0.418265	−	0.908325i	$-0.637362\pi$
$463$	−18.0000	−0.836531	−0.418265	+	0.908325i	$0.637362\pi$
$464$	4.00000	0.185695
$465$	−4.00000	−0.185496
$466$	0	0
$467$	34.0000	1.57333	0.786666	−	0.617379i	$-0.211805\pi$
$467$	34.0000	1.57333	0.786666	+	0.617379i	$0.211805\pi$
$468$	−12.0000	−0.554700
$469$	20.0000	0.923514
$470$	0	0
$471$	18.0000	0.829396
$472$	0	0
$473$	5.00000	0.229900
$474$	0	0
$475$	−2.00000	−0.0917663
$476$	16.0000	0.733359
$477$	13.0000	0.595229
$478$	0	0
$479$	40.0000	1.82765	0.913823	−	0.406112i	$-0.133116\pi$
$479$	40.0000	1.82765	0.913823	+	0.406112i	$0.133116\pi$
$480$	0	0
$481$	−18.0000	−0.820729
$482$	0	0
$483$	6.00000	0.273009
$484$	20.0000	0.909091
$485$	−17.0000	−0.771930
$486$	0	0
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	0	0
$489$	−15.0000	−0.678323
$490$	0	0
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	14.0000	0.631169
$493$	4.00000	0.180151
$494$	0	0
$495$	−1.00000	−0.0449467
$496$	−16.0000	−0.718421
$497$	−12.0000	−0.538274
$498$	0	0
$499$	40.0000	1.79065	0.895323	−	0.445418i	$-0.146945\pi$
$499$	40.0000	1.79065	0.895323	+	0.445418i	$0.146945\pi$
$500$	2.00000	0.0894427
$501$	−8.00000	−0.357414
$502$	0	0
$503$	−30.0000	−1.33763	−0.668817	−	0.743427i	$-0.733199\pi$
$503$	−30.0000	−1.33763	−0.668817	+	0.743427i	$0.733199\pi$
$504$	0	0
$505$	3.00000	0.133498
$506$	0	0
$507$	−23.0000	−1.02147
$508$	−14.0000	−0.621150
$509$	34.0000	1.50702	0.753512	−	0.657434i	$-0.228358\pi$
$509$	34.0000	1.50702	0.753512	+	0.657434i	$0.228358\pi$
$510$	0	0
$511$	−6.00000	−0.265424
$512$	0	0
$513$	2.00000	0.0883022
$514$	0	0
$515$	6.00000	0.264392
$516$	10.0000	0.440225
$517$	6.00000	0.263880
$518$	0	0
$519$	−5.00000	−0.219476
$520$	0	0
$521$	22.0000	0.963837	0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000	0.963837	0.481919	+	0.876216i	$0.339940\pi$
$522$	0	0
$523$	−24.0000	−1.04945	−0.524723	−	0.851273i	$-0.675831\pi$
$523$	−24.0000	−1.04945	−0.524723	+	0.851273i	$0.675831\pi$
$524$	−24.0000	−1.04844
$525$	2.00000	0.0872872
$526$	0	0
$527$	−16.0000	−0.696971
$528$	−4.00000	−0.174078
$529$	−14.0000	−0.608696
$530$	0	0
$531$	0	0
$532$	−8.00000	−0.346844
$533$	42.0000	1.81922
$534$	0	0
$535$	−12.0000	−0.518805
$536$	0	0
$537$	18.0000	0.776757
$538$	0	0
$539$	−3.00000	−0.129219
$540$	−2.00000	−0.0860663
$541$	−2.00000	−0.0859867	−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000	−0.0859867	−0.0429934	+	0.999075i	$0.513689\pi$
$542$	0	0
$543$	−25.0000	−1.07285
$544$	0	0
$545$	−11.0000	−0.471188
$546$	0	0
$547$	40.0000	1.71028	0.855138	−	0.518400i	$-0.173472\pi$
$547$	40.0000	1.71028	0.855138	+	0.518400i	$0.173472\pi$
$548$	−32.0000	−1.36697
$549$	0	0
$550$	0	0
$551$	−2.00000	−0.0852029
$552$	0	0
$553$	0	0
$554$	0	0
$555$	−3.00000	−0.127343
$556$	38.0000	1.61156
$557$	37.0000	1.56774	0.783870	−	0.620925i	$-0.213243\pi$
$557$	37.0000	1.56774	0.783870	+	0.620925i	$0.213243\pi$
$558$	0	0
$559$	30.0000	1.26886
$560$	8.00000	0.338062
$561$	−4.00000	−0.168880
$562$	0	0
$563$	−6.00000	−0.252870	−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000	−0.252870	−0.126435	+	0.991975i	$0.540353\pi$
$564$	12.0000	0.505291
$565$	12.0000	0.504844
$566$	0	0
$567$	−2.00000	−0.0839921
$568$	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
$571$	5.00000	0.209243	0.104622	−	0.994512i	$-0.466637\pi$
$571$	5.00000	0.209243	0.104622	+	0.994512i	$0.466637\pi$
$572$	−12.0000	−0.501745
$573$	27.0000	1.12794
$574$	0	0
$575$	3.00000	0.125109
$576$	−8.00000	−0.333333
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	0	0
$579$	14.0000	0.581820
$580$	2.00000	0.0830455
$581$	−18.0000	−0.746766
$582$	0	0
$583$	13.0000	0.538405
$584$	0	0
$585$	−6.00000	−0.248069
$586$	0	0
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	−6.00000	−0.247436
$589$	8.00000	0.329634
$590$	0	0
$591$	−13.0000	−0.534749
$592$	−12.0000	−0.493197
$593$	10.0000	0.410651	0.205325	−	0.978694i	$-0.434175\pi$
$593$	10.0000	0.410651	0.205325	+	0.978694i	$0.434175\pi$
$594$	0	0
$595$	8.00000	0.327968
$596$	4.00000	0.163846
$597$	−15.0000	−0.613909
$598$	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
$601$	40.0000	1.63163	0.815817	−	0.578310i	$-0.196288\pi$
$601$	40.0000	1.63163	0.815817	+	0.578310i	$0.196288\pi$
$602$	0	0
$603$	−10.0000	−0.407231
$604$	22.0000	0.895167
$605$	10.0000	0.406558
$606$	0	0
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	0	0
$609$	2.00000	0.0810441
$610$	0	0
$611$	36.0000	1.45640
$612$	−8.00000	−0.323381
$613$	−6.00000	−0.242338	−0.121169	−	0.992632i	$-0.538664\pi$
$613$	−6.00000	−0.242338	−0.121169	+	0.992632i	$0.538664\pi$
$614$	0	0
$615$	7.00000	0.282267
$616$	0	0
$617$	30.0000	1.20775	0.603877	−	0.797077i	$-0.293622\pi$
$617$	30.0000	1.20775	0.603877	+	0.797077i	$0.293622\pi$
$618$	0	0
$619$	2.00000	0.0803868	0.0401934	−	0.999192i	$-0.487203\pi$
$619$	2.00000	0.0803868	0.0401934	+	0.999192i	$0.487203\pi$
$620$	−8.00000	−0.321288
$621$	−3.00000	−0.120386
$622$	0	0
$623$	20.0000	0.801283
$624$	−24.0000	−0.960769
$625$	1.00000	0.0400000
$626$	0	0
$627$	2.00000	0.0798723
$628$	36.0000	1.43656
$629$	−12.0000	−0.478471
$630$	0	0
$631$	−48.0000	−1.91085	−0.955425	−	0.295234i	$-0.904602\pi$
$631$	−48.0000	−1.91085	−0.955425	+	0.295234i	$0.904602\pi$
$632$	0	0
$633$	2.00000	0.0794929
$634$	0	0
$635$	−7.00000	−0.277787
$636$	26.0000	1.03097
$637$	−18.0000	−0.713186
$638$	0	0
$639$	6.00000	0.237356
$640$	0	0
$641$	−47.0000	−1.85639	−0.928194	−	0.372096i	$-0.878639\pi$
$641$	−47.0000	−1.85639	−0.928194	+	0.372096i	$0.878639\pi$
$642$	0	0
$643$	16.0000	0.630978	0.315489	−	0.948929i	$-0.397831\pi$
$643$	16.0000	0.630978	0.315489	+	0.948929i	$0.397831\pi$
$644$	12.0000	0.472866
$645$	5.00000	0.196875
$646$	0	0
$647$	−3.00000	−0.117942	−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000	−0.117942	−0.0589711	+	0.998260i	$0.518782\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−8.00000	−0.313545
$652$	−30.0000	−1.17489
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	0	0
$655$	−12.0000	−0.468879
$656$	28.0000	1.09322
$657$	3.00000	0.117041
$658$	0	0
$659$	33.0000	1.28550	0.642749	−	0.766077i	$-0.277794\pi$
$659$	33.0000	1.28550	0.642749	+	0.766077i	$0.277794\pi$
$660$	−2.00000	−0.0778499
$661$	−1.00000	−0.0388955	−0.0194477	−	0.999811i	$-0.506191\pi$
$661$	−1.00000	−0.0388955	−0.0194477	+	0.999811i	$0.506191\pi$
$662$	0	0
$663$	−24.0000	−0.932083
$664$	0	0
$665$	−4.00000	−0.155113
$666$	0	0
$667$	3.00000	0.116160
$668$	−16.0000	−0.619059
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	6.00000	0.231283	0.115642	−	0.993291i	$-0.463108\pi$
$673$	6.00000	0.231283	0.115642	+	0.993291i	$0.463108\pi$
$674$	0	0
$675$	−1.00000	−0.0384900
$676$	−46.0000	−1.76923
$677$	12.0000	0.461197	0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000	0.461197	0.230599	+	0.973049i	$0.425932\pi$
$678$	0	0
$679$	−34.0000	−1.30480
$680$	0	0
$681$	−11.0000	−0.421521
$682$	0	0
$683$	7.00000	0.267848	0.133924	−	0.990992i	$-0.457242\pi$
$683$	7.00000	0.267848	0.133924	+	0.990992i	$0.457242\pi$
$684$	4.00000	0.152944
$685$	−16.0000	−0.611329
$686$	0	0
$687$	−10.0000	−0.381524
$688$	20.0000	0.762493
$689$	78.0000	2.97156
$690$	0	0
$691$	44.0000	1.67384	0.836919	−	0.547326i	$-0.184354\pi$
$691$	44.0000	1.67384	0.836919	+	0.547326i	$0.184354\pi$
$692$	−10.0000	−0.380143
$693$	−2.00000	−0.0759737
$694$	0	0
$695$	19.0000	0.720711
$696$	0	0
$697$	28.0000	1.06058
$698$	0	0
$699$	1.00000	0.0378235
$700$	4.00000	0.151186
$701$	34.0000	1.28416	0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000	1.28416	0.642081	+	0.766637i	$0.278071\pi$
$702$	0	0
$703$	6.00000	0.226294
$704$	−8.00000	−0.301511
$705$	6.00000	0.225973
$706$	0	0
$707$	6.00000	0.225653
$708$	0	0
$709$	−25.0000	−0.938895	−0.469447	−	0.882960i	$-0.655547\pi$
$709$	−25.0000	−0.938895	−0.469447	+	0.882960i	$0.655547\pi$
$710$	0	0
$711$	0	0
$712$	0	0
$713$	−12.0000	−0.449404
$714$	0	0
$715$	−6.00000	−0.224387
$716$	36.0000	1.34538
$717$	−14.0000	−0.522840
$718$	0	0
$719$	−4.00000	−0.149175	−0.0745874	−	0.997214i	$-0.523764\pi$
$719$	−4.00000	−0.149175	−0.0745874	+	0.997214i	$0.523764\pi$
$720$	−4.00000	−0.149071
$721$	12.0000	0.446903
$722$	0	0
$723$	−17.0000	−0.632237
$724$	−50.0000	−1.85824
$725$	1.00000	0.0371391
$726$	0	0
$727$	44.0000	1.63187	0.815935	−	0.578144i	$-0.196223\pi$
$727$	44.0000	1.63187	0.815935	+	0.578144i	$0.196223\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	20.0000	0.739727
$732$	0	0
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	0	0
$735$	−3.00000	−0.110657
$736$	0	0
$737$	−10.0000	−0.368355
$738$	0	0
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	−6.00000	−0.220564
$741$	12.0000	0.440831
$742$	0	0
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	0	0
$745$	2.00000	0.0732743
$746$	0	0
$747$	9.00000	0.329293
$748$	−8.00000	−0.292509
$749$	−24.0000	−0.876941
$750$	0	0
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	24.0000	0.875190
$753$	4.00000	0.145768
$754$	0	0
$755$	11.0000	0.400331
$756$	−4.00000	−0.145479
$757$	−17.0000	−0.617876	−0.308938	−	0.951082i	$-0.599973\pi$
$757$	−17.0000	−0.617876	−0.308938	+	0.951082i	$0.599973\pi$
$758$	0	0
$759$	−3.00000	−0.108893
$760$	0	0
$761$	0	0		−	1.00000i	$-0.5\pi$
$761$	0	0			1.00000i	$0.5\pi$
$762$	0	0
$763$	−22.0000	−0.796453
$764$	54.0000	1.95365
$765$	−4.00000	−0.144620
$766$	0	0
$767$	0	0
$768$	−16.0000	−0.577350
$769$	−36.0000	−1.29819	−0.649097	−	0.760706i	$-0.724853\pi$
$769$	−36.0000	−1.29819	−0.649097	+	0.760706i	$0.724853\pi$
$770$	0	0
$771$	21.0000	0.756297
$772$	28.0000	1.00774
$773$	−10.0000	−0.359675	−0.179838	−	0.983696i	$-0.557557\pi$
$773$	−10.0000	−0.359675	−0.179838	+	0.983696i	$0.557557\pi$
$774$	0	0
$775$	−4.00000	−0.143684
$776$	0	0
$777$	−6.00000	−0.215249
$778$	0	0
$779$	−14.0000	−0.501602
$780$	−12.0000	−0.429669
$781$	6.00000	0.214697
$782$	0	0
$783$	−1.00000	−0.0357371
$784$	−12.0000	−0.428571
$785$	18.0000	0.642448
$786$	0	0
$787$	4.00000	0.142585	0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000	0.142585	0.0712923	+	0.997455i	$0.477288\pi$
$788$	−26.0000	−0.926212
$789$	20.0000	0.712019
$790$	0	0
$791$	24.0000	0.853342
$792$	0	0
$793$	0	0
$794$	0	0
$795$	13.0000	0.461062
$796$	−30.0000	−1.06332
$797$	−38.0000	−1.34603	−0.673015	−	0.739629i	$-0.735001\pi$
$797$	−38.0000	−1.34603	−0.673015	+	0.739629i	$0.735001\pi$
$798$	0	0
$799$	24.0000	0.849059
$800$	0	0
$801$	−10.0000	−0.353333
$802$	0	0
$803$	3.00000	0.105868
$804$	−20.0000	−0.705346
$805$	6.00000	0.211472
$806$	0	0
$807$	−18.0000	−0.633630
$808$	0	0
$809$	−9.00000	−0.316423	−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000	−0.316423	−0.158212	+	0.987405i	$0.550573\pi$
$810$	0	0
$811$	31.0000	1.08856	0.544279	−	0.838905i	$-0.316803\pi$
$811$	31.0000	1.08856	0.544279	+	0.838905i	$0.316803\pi$
$812$	4.00000	0.140372
$813$	−26.0000	−0.911860
$814$	0	0
$815$	−15.0000	−0.525427
$816$	−16.0000	−0.560112
$817$	−10.0000	−0.349856
$818$	0	0
$819$	−12.0000	−0.419314
$820$	14.0000	0.488901
$821$	48.0000	1.67521	0.837606	−	0.546275i	$-0.183955\pi$
$821$	48.0000	1.67521	0.837606	+	0.546275i	$0.183955\pi$
$822$	0	0
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	0	0
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	−22.0000	−0.765015	−0.382507	−	0.923952i	$-0.624939\pi$
$827$	−22.0000	−0.765015	−0.382507	+	0.923952i	$0.624939\pi$
$828$	−6.00000	−0.208514
$829$	−46.0000	−1.59765	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000	−1.59765	−0.798823	+	0.601566i	$0.794544\pi$
$830$	0	0
$831$	−4.00000	−0.138758
$832$	−48.0000	−1.66410
$833$	−12.0000	−0.415775
$834$	0	0
$835$	−8.00000	−0.276851
$836$	4.00000	0.138343
$837$	4.00000	0.138260
$838$	0	0
$839$	−32.0000	−1.10476	−0.552381	−	0.833592i	$-0.686281\pi$
$839$	−32.0000	−1.10476	−0.552381	+	0.833592i	$0.686281\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	−4.00000	−0.137767
$844$	4.00000	0.137686
$845$	−23.0000	−0.791224
$846$	0	0
$847$	20.0000	0.687208
$848$	52.0000	1.78569
$849$	26.0000	0.892318
$850$	0	0
$851$	−9.00000	−0.308516
$852$	12.0000	0.411113
$853$	−5.00000	−0.171197	−0.0855984	−	0.996330i	$-0.527280\pi$
$853$	−5.00000	−0.171197	−0.0855984	+	0.996330i	$0.527280\pi$
$854$	0	0
$855$	2.00000	0.0683986
$856$	0	0
$857$	−47.0000	−1.60549	−0.802745	−	0.596323i	$-0.796628\pi$
$857$	−47.0000	−1.60549	−0.802745	+	0.596323i	$0.796628\pi$
$858$	0	0
$859$	26.0000	0.887109	0.443554	−	0.896248i	$-0.353717\pi$
$859$	26.0000	0.887109	0.443554	+	0.896248i	$0.353717\pi$
$860$	10.0000	0.340997
$861$	14.0000	0.477119
$862$	0	0
$863$	−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
$865$	−5.00000	−0.170005
$866$	0	0
$867$	1.00000	0.0339618
$868$	−16.0000	−0.543075
$869$	0	0
$870$	0	0
$871$	−60.0000	−2.03302
$872$	0	0
$873$	17.0000	0.575363
$874$	0	0
$875$	2.00000	0.0676123
$876$	6.00000	0.202721
$877$	44.0000	1.48577	0.742887	−	0.669417i	$-0.233456\pi$
$877$	44.0000	1.48577	0.742887	+	0.669417i	$0.233456\pi$
$878$	0	0
$879$	8.00000	0.269833
$880$	−4.00000	−0.134840
$881$	−15.0000	−0.505363	−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000	−0.505363	−0.252681	+	0.967550i	$0.581312\pi$
$882$	0	0
$883$	−16.0000	−0.538443	−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000	−0.538443	−0.269221	+	0.963078i	$0.586766\pi$
$884$	−48.0000	−1.61441
$885$	0	0
$886$	0	0
$887$	30.0000	1.00730	0.503651	−	0.863907i	$-0.331990\pi$
$887$	30.0000	1.00730	0.503651	+	0.863907i	$0.331990\pi$
$888$	0	0
$889$	−14.0000	−0.469545
$890$	0	0
$891$	1.00000	0.0335013
$892$	0	0
$893$	−12.0000	−0.401565
$894$	0	0
$895$	18.0000	0.601674
$896$	0	0
$897$	−18.0000	−0.601003
$898$	0	0
$899$	−4.00000	−0.133407
$900$	−2.00000	−0.0666667
$901$	52.0000	1.73237
$902$	0	0
$903$	10.0000	0.332779
$904$	0	0
$905$	−25.0000	−0.831028
$906$	0	0
$907$	−17.0000	−0.564476	−0.282238	−	0.959344i	$-0.591077\pi$
$907$	−17.0000	−0.564476	−0.282238	+	0.959344i	$0.591077\pi$
$908$	−22.0000	−0.730096
$909$	−3.00000	−0.0995037
$910$	0	0
$911$	51.0000	1.68971	0.844853	−	0.534999i	$-0.179688\pi$
$911$	51.0000	1.68971	0.844853	+	0.534999i	$0.179688\pi$
$912$	8.00000	0.264906
$913$	9.00000	0.297857
$914$	0	0
$915$	0	0
$916$	−20.0000	−0.660819
$917$	−24.0000	−0.792550
$918$	0	0
$919$	−4.00000	−0.131948	−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000	−0.131948	−0.0659739	+	0.997821i	$0.521015\pi$
$920$	0	0
$921$	21.0000	0.691974
$922$	0	0
$923$	36.0000	1.18495
$924$	−4.00000	−0.131590
$925$	−3.00000	−0.0986394
$926$	0	0
$927$	−6.00000	−0.197066
$928$	0	0
$929$	−56.0000	−1.83730	−0.918650	−	0.395072i	$-0.870720\pi$
$929$	−56.0000	−1.83730	−0.918650	+	0.395072i	$0.870720\pi$
$930$	0	0
$931$	6.00000	0.196642
$932$	2.00000	0.0655122
$933$	23.0000	0.752986
$934$	0	0
$935$	−4.00000	−0.130814
$936$	0	0
$937$	56.0000	1.82944	0.914720	−	0.404088i	$-0.132411\pi$
$937$	56.0000	1.82944	0.914720	+	0.404088i	$0.132411\pi$
$938$	0	0
$939$	12.0000	0.391605
$940$	12.0000	0.391397
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	0	0
$943$	21.0000	0.683854
$944$	0	0
$945$	−2.00000	−0.0650600
$946$	0	0
$947$	−42.0000	−1.36482	−0.682408	−	0.730971i	$-0.739067\pi$
$947$	−42.0000	−1.36482	−0.682408	+	0.730971i	$0.739067\pi$
$948$	0	0
$949$	18.0000	0.584305
$950$	0	0
$951$	8.00000	0.259418
$952$	0	0
$953$	−42.0000	−1.36051	−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000	−1.36051	−0.680257	+	0.732974i	$0.738132\pi$
$954$	0	0
$955$	27.0000	0.873699
$956$	−28.0000	−0.905585
$957$	−1.00000	−0.0323254
$958$	0	0
$959$	−32.0000	−1.03333
$960$	−8.00000	−0.258199
$961$	−15.0000	−0.483871
$962$	0	0
$963$	12.0000	0.386695
$964$	−34.0000	−1.09507
$965$	14.0000	0.450676
$966$	0	0
$967$	−13.0000	−0.418052	−0.209026	−	0.977910i	$-0.567029\pi$
$967$	−13.0000	−0.418052	−0.209026	+	0.977910i	$0.567029\pi$
$968$	0	0
$969$	8.00000	0.256997
$970$	0	0
$971$	13.0000	0.417190	0.208595	−	0.978002i	$-0.433111\pi$
$971$	13.0000	0.417190	0.208595	+	0.978002i	$0.433111\pi$
$972$	2.00000	0.0641500
$973$	38.0000	1.21822
$974$	0	0
$975$	−6.00000	−0.192154
$976$	0	0
$977$	−39.0000	−1.24772	−0.623860	−	0.781536i	$-0.714437\pi$
$977$	−39.0000	−1.24772	−0.623860	+	0.781536i	$0.714437\pi$
$978$	0	0
$979$	−10.0000	−0.319601
$980$	−6.00000	−0.191663
$981$	11.0000	0.351203
$982$	0	0
$983$	54.0000	1.72233	0.861166	−	0.508323i	$-0.169735\pi$
$983$	54.0000	1.72233	0.861166	+	0.508323i	$0.169735\pi$
$984$	0	0
$985$	−13.0000	−0.414214
$986$	0	0
$987$	12.0000	0.381964
$988$	24.0000	0.763542
$989$	15.0000	0.476972
$990$	0	0
$991$	−25.0000	−0.794151	−0.397076	−	0.917786i	$-0.629975\pi$
$991$	−25.0000	−0.794151	−0.397076	+	0.917786i	$0.629975\pi$
$992$	0	0
$993$	20.0000	0.634681
$994$	0	0
$995$	−15.0000	−0.475532
$996$	18.0000	0.570352
$997$	25.0000	0.791758	0.395879	−	0.918303i	$-0.370440\pi$
$997$	25.0000	0.791758	0.395879	+	0.918303i	$0.370440\pi$
$998$	0	0
$999$	3.00000	0.0949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.a.b.1.1	✓	1
3.2	odd	2		1305.2.a.c.1.1		1
4.3	odd	2		6960.2.a.bc.1.1		1
5.2	odd	4		2175.2.c.d.349.2		2
5.3	odd	4		2175.2.c.d.349.1		2
5.4	even	2		2175.2.a.g.1.1		1
15.14	odd	2		6525.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.a.b.1.1	✓	1	1.1	even	1	trivial
1305.2.a.c.1.1		1	3.2	odd	2
2175.2.a.g.1.1		1	5.4	even	2
2175.2.c.d.349.1		2	5.3	odd	4
2175.2.c.d.349.2		2	5.2	odd	4
6525.2.a.i.1.1		1	15.14	odd	2
6960.2.a.bc.1.1		1	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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