LMFDB - Embedded newform 6017.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
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	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{3} -2.00000 q^{4} +4.00000 q^{5} +2.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

$q+2.00000 q^{3} -2.00000 q^{4} +4.00000 q^{5} +2.00000 q^{7} +1.00000 q^{9} +1.00000 q^{11} -4.00000 q^{12} +1.00000 q^{13} +8.00000 q^{15} +4.00000 q^{16} +8.00000 q^{17} -5.00000 q^{19} -8.00000 q^{20} +4.00000 q^{21} +6.00000 q^{23} +11.0000 q^{25} -4.00000 q^{27} -4.00000 q^{28} +5.00000 q^{29} +10.0000 q^{31} +2.00000 q^{33} +8.00000 q^{35} -2.00000 q^{36} +2.00000 q^{39} -10.0000 q^{43} -2.00000 q^{44} +4.00000 q^{45} -9.00000 q^{47} +8.00000 q^{48} -3.00000 q^{49} +16.0000 q^{51} -2.00000 q^{52} -10.0000 q^{53} +4.00000 q^{55} -10.0000 q^{57} -14.0000 q^{59} -16.0000 q^{60} -14.0000 q^{61} +2.00000 q^{63} -8.00000 q^{64} +4.00000 q^{65} -1.00000 q^{67} -16.0000 q^{68} +12.0000 q^{69} +12.0000 q^{71} -2.00000 q^{73} +22.0000 q^{75} +10.0000 q^{76} +2.00000 q^{77} +4.00000 q^{79} +16.0000 q^{80} -11.0000 q^{81} +6.00000 q^{83} -8.00000 q^{84} +32.0000 q^{85} +10.0000 q^{87} -6.00000 q^{89} +2.00000 q^{91} -12.0000 q^{92} +20.0000 q^{93} -20.0000 q^{95} -13.0000 q^{97} +1.00000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0	0		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	−2.00000	−1.00000
$5$	4.00000	1.78885	0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000	1.78885	0.894427	+	0.447214i	$0.147584\pi$
$6$	0	0
$7$	2.00000	0.755929	0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000	0.755929	0.377964	+	0.925820i	$0.376624\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.00000	−1.15470
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	0	0
$15$	8.00000	2.06559
$16$	4.00000	1.00000
$17$	8.00000	1.94029	0.970143	−	0.242536i	$-0.0779791\pi$
$17$	8.00000	1.94029	0.970143	+	0.242536i	$0.0779791\pi$
$18$	0	0
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	−8.00000	−1.78885
$21$	4.00000	0.872872
$22$	0	0
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	11.0000	2.20000
$26$	0	0
$27$	−4.00000	−0.769800
$28$	−4.00000	−0.755929
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	0	0
$31$	10.0000	1.79605	0.898027	−	0.439941i	$-0.145001\pi$
$31$	10.0000	1.79605	0.898027	+	0.439941i	$0.145001\pi$
$32$	0	0
$33$	2.00000	0.348155
$34$	0	0
$35$	8.00000	1.35225
$36$	−2.00000	−0.333333
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	2.00000	0.320256
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	−10.0000	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$44$	−2.00000	−0.301511
$45$	4.00000	0.596285
$46$	0	0
$47$	−9.00000	−1.31278	−0.656392	−	0.754420i	$-0.727918\pi$
$47$	−9.00000	−1.31278	−0.656392	+	0.754420i	$0.727918\pi$
$48$	8.00000	1.15470
$49$	−3.00000	−0.428571
$50$	0	0
$51$	16.0000	2.24045
$52$	−2.00000	−0.277350
$53$	−10.0000	−1.37361	−0.686803	−	0.726844i	$-0.740986\pi$
$53$	−10.0000	−1.37361	−0.686803	+	0.726844i	$0.740986\pi$
$54$	0	0
$55$	4.00000	0.539360
$56$	0	0
$57$	−10.0000	−1.32453
$58$	0	0
$59$	−14.0000	−1.82264	−0.911322	−	0.411693i	$-0.864937\pi$
$59$	−14.0000	−1.82264	−0.911322	+	0.411693i	$0.864937\pi$
$60$	−16.0000	−2.06559
$61$	−14.0000	−1.79252	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000	−1.79252	−0.896258	+	0.443533i	$0.853725\pi$
$62$	0	0
$63$	2.00000	0.251976
$64$	−8.00000	−1.00000
$65$	4.00000	0.496139
$66$	0	0
$67$	−1.00000	−0.122169	−0.0610847	−	0.998133i	$-0.519456\pi$
$67$	−1.00000	−0.122169	−0.0610847	+	0.998133i	$0.519456\pi$
$68$	−16.0000	−1.94029
$69$	12.0000	1.44463
$70$	0	0
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	0	0
$73$	−2.00000	−0.234082	−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000	−0.234082	−0.117041	+	0.993127i	$0.537341\pi$
$74$	0	0
$75$	22.0000	2.54034
$76$	10.0000	1.14708
$77$	2.00000	0.227921
$78$	0	0
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	16.0000	1.78885
$81$	−11.0000	−1.22222
$82$	0	0
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	−8.00000	−0.872872
$85$	32.0000	3.47089
$86$	0	0
$87$	10.0000	1.07211
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	−12.0000	−1.25109
$93$	20.0000	2.07390
$94$	0	0
$95$	−20.0000	−2.05196
$96$	0	0
$97$	−13.0000	−1.31995	−0.659975	−	0.751288i	$-0.729433\pi$
$97$	−13.0000	−1.31995	−0.659975	+	0.751288i	$0.729433\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−22.0000	−2.20000
$101$	8.00000	0.796030	0.398015	−	0.917379i	$-0.369699\pi$
$101$	8.00000	0.796030	0.398015	+	0.917379i	$0.369699\pi$
$102$	0	0
$103$	−10.0000	−0.985329	−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000	−0.985329	−0.492665	+	0.870219i	$0.663977\pi$
$104$	0	0
$105$	16.0000	1.56144
$106$	0	0
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	8.00000	0.769800
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	0	0
$111$	0	0
$112$	8.00000	0.755929
$113$	17.0000	1.59923	0.799613	−	0.600516i	$-0.205038\pi$
$113$	17.0000	1.59923	0.799613	+	0.600516i	$0.205038\pi$
$114$	0	0
$115$	24.0000	2.23801
$116$	−10.0000	−0.928477
$117$	1.00000	0.0924500
$118$	0	0
$119$	16.0000	1.46672
$120$	0	0
$121$	1.00000	0.0909091
$122$	0	0
$123$	0	0
$124$	−20.0000	−1.79605
$125$	24.0000	2.14663
$126$	0	0
$127$	13.0000	1.15356	0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000	1.15356	0.576782	+	0.816898i	$0.304308\pi$
$128$	0	0
$129$	−20.0000	−1.76090
$130$	0	0
$131$	3.00000	0.262111	0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000	0.262111	0.131056	+	0.991375i	$0.458163\pi$
$132$	−4.00000	−0.348155
$133$	−10.0000	−0.867110
$134$	0	0
$135$	−16.0000	−1.37706
$136$	0	0
$137$	3.00000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	0	0
$139$	−5.00000	−0.424094	−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000	−0.424094	−0.212047	+	0.977259i	$0.568013\pi$
$140$	−16.0000	−1.35225
$141$	−18.0000	−1.51587
$142$	0	0
$143$	1.00000	0.0836242
$144$	4.00000	0.333333
$145$	20.0000	1.66091
$146$	0	0
$147$	−6.00000	−0.494872
$148$	0	0
$149$	−21.0000	−1.72039	−0.860194	−	0.509968i	$-0.829657\pi$
$149$	−21.0000	−1.72039	−0.860194	+	0.509968i	$0.829657\pi$
$150$	0	0
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	0	0
$153$	8.00000	0.646762
$154$	0	0
$155$	40.0000	3.21288
$156$	−4.00000	−0.320256
$157$	−1.00000	−0.0798087	−0.0399043	−	0.999204i	$-0.512705\pi$
$157$	−1.00000	−0.0798087	−0.0399043	+	0.999204i	$0.512705\pi$
$158$	0	0
$159$	−20.0000	−1.58610
$160$	0	0
$161$	12.0000	0.945732
$162$	0	0
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	0	0
$165$	8.00000	0.622799
$166$	0	0
$167$	−3.00000	−0.232147	−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000	−0.232147	−0.116073	+	0.993241i	$0.537031\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−5.00000	−0.382360
$172$	20.0000	1.52499
$173$	4.00000	0.304114	0.152057	−	0.988372i	$-0.451410\pi$
$173$	4.00000	0.304114	0.152057	+	0.988372i	$0.451410\pi$
$174$	0	0
$175$	22.0000	1.66304
$176$	4.00000	0.301511
$177$	−28.0000	−2.10461
$178$	0	0
$179$	15.0000	1.12115	0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000	1.12115	0.560576	+	0.828103i	$0.310580\pi$
$180$	−8.00000	−0.596285
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	0	0
$183$	−28.0000	−2.06982
$184$	0	0
$185$	0	0
$186$	0	0
$187$	8.00000	0.585018
$188$	18.0000	1.31278
$189$	−8.00000	−0.581914
$190$	0	0
$191$	−13.0000	−0.940647	−0.470323	−	0.882494i	$-0.655863\pi$
$191$	−13.0000	−0.940647	−0.470323	+	0.882494i	$0.655863\pi$
$192$	−16.0000	−1.15470
$193$	13.0000	0.935760	0.467880	−	0.883792i	$-0.345018\pi$
$193$	13.0000	0.935760	0.467880	+	0.883792i	$0.345018\pi$
$194$	0	0
$195$	8.00000	0.572892
$196$	6.00000	0.428571
$197$	8.00000	0.569976	0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000	0.569976	0.284988	+	0.958531i	$0.408010\pi$
$198$	0	0
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	0	0
$201$	−2.00000	−0.141069
$202$	0	0
$203$	10.0000	0.701862
$204$	−32.0000	−2.24045
$205$	0	0
$206$	0	0
$207$	6.00000	0.417029
$208$	4.00000	0.277350
$209$	−5.00000	−0.345857
$210$	0	0
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	20.0000	1.37361
$213$	24.0000	1.64445
$214$	0	0
$215$	−40.0000	−2.72798
$216$	0	0
$217$	20.0000	1.35769
$218$	0	0
$219$	−4.00000	−0.270295
$220$	−8.00000	−0.539360
$221$	8.00000	0.538138
$222$	0	0
$223$	12.0000	0.803579	0.401790	−	0.915732i	$-0.368388\pi$
$223$	12.0000	0.803579	0.401790	+	0.915732i	$0.368388\pi$
$224$	0	0
$225$	11.0000	0.733333
$226$	0	0
$227$	9.00000	0.597351	0.298675	−	0.954355i	$-0.403455\pi$
$227$	9.00000	0.597351	0.298675	+	0.954355i	$0.403455\pi$
$228$	20.0000	1.32453
$229$	−28.0000	−1.85029	−0.925146	−	0.379611i	$-0.876058\pi$
$229$	−28.0000	−1.85029	−0.925146	+	0.379611i	$0.876058\pi$
$230$	0	0
$231$	4.00000	0.263181
$232$	0	0
$233$	−5.00000	−0.327561	−0.163780	−	0.986497i	$-0.552369\pi$
$233$	−5.00000	−0.327561	−0.163780	+	0.986497i	$0.552369\pi$
$234$	0	0
$235$	−36.0000	−2.34838
$236$	28.0000	1.82264
$237$	8.00000	0.519656
$238$	0	0
$239$	8.00000	0.517477	0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000	0.517477	0.258738	+	0.965947i	$0.416693\pi$
$240$	32.0000	2.06559
$241$	−26.0000	−1.67481	−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000	−1.67481	−0.837404	+	0.546585i	$0.815928\pi$
$242$	0	0
$243$	−10.0000	−0.641500
$244$	28.0000	1.79252
$245$	−12.0000	−0.766652
$246$	0	0
$247$	−5.00000	−0.318142
$248$	0	0
$249$	12.0000	0.760469
$250$	0	0
$251$	24.0000	1.51487	0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000	1.51487	0.757433	+	0.652913i	$0.226453\pi$
$252$	−4.00000	−0.251976
$253$	6.00000	0.377217
$254$	0	0
$255$	64.0000	4.00784
$256$	16.0000	1.00000
$257$	−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
$259$	0	0
$260$	−8.00000	−0.496139
$261$	5.00000	0.309492
$262$	0	0
$263$	−1.00000	−0.0616626	−0.0308313	−	0.999525i	$-0.509815\pi$
$263$	−1.00000	−0.0616626	−0.0308313	+	0.999525i	$0.509815\pi$
$264$	0	0
$265$	−40.0000	−2.45718
$266$	0	0
$267$	−12.0000	−0.734388
$268$	2.00000	0.122169
$269$	−17.0000	−1.03651	−0.518254	−	0.855227i	$-0.673418\pi$
$269$	−17.0000	−1.03651	−0.518254	+	0.855227i	$0.673418\pi$
$270$	0	0
$271$	16.0000	0.971931	0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000	0.971931	0.485965	+	0.873978i	$0.338468\pi$
$272$	32.0000	1.94029
$273$	4.00000	0.242091
$274$	0	0
$275$	11.0000	0.663325
$276$	−24.0000	−1.44463
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	0	0
$279$	10.0000	0.598684
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−24.0000	−1.42414
$285$	−40.0000	−2.36940
$286$	0	0
$287$	0	0
$288$	0	0
$289$	47.0000	2.76471
$290$	0	0
$291$	−26.0000	−1.52415
$292$	4.00000	0.234082
$293$	31.0000	1.81104	0.905520	−	0.424304i	$-0.139481\pi$
$293$	31.0000	1.81104	0.905520	+	0.424304i	$0.139481\pi$
$294$	0	0
$295$	−56.0000	−3.26045
$296$	0	0
$297$	−4.00000	−0.232104
$298$	0	0
$299$	6.00000	0.346989
$300$	−44.0000	−2.54034
$301$	−20.0000	−1.15278
$302$	0	0
$303$	16.0000	0.919176
$304$	−20.0000	−1.14708
$305$	−56.0000	−3.20655
$306$	0	0
$307$	−4.00000	−0.228292	−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000	−0.228292	−0.114146	+	0.993464i	$0.536413\pi$
$308$	−4.00000	−0.227921
$309$	−20.0000	−1.13776
$310$	0	0
$311$	5.00000	0.283524	0.141762	−	0.989901i	$-0.454723\pi$
$311$	5.00000	0.283524	0.141762	+	0.989901i	$0.454723\pi$
$312$	0	0
$313$	7.00000	0.395663	0.197832	−	0.980236i	$-0.436610\pi$
$313$	7.00000	0.395663	0.197832	+	0.980236i	$0.436610\pi$
$314$	0	0
$315$	8.00000	0.450749
$316$	−8.00000	−0.450035
$317$	13.0000	0.730153	0.365076	−	0.930978i	$-0.381043\pi$
$317$	13.0000	0.730153	0.365076	+	0.930978i	$0.381043\pi$
$318$	0	0
$319$	5.00000	0.279946
$320$	−32.0000	−1.78885
$321$	36.0000	2.00932
$322$	0	0
$323$	−40.0000	−2.22566
$324$	22.0000	1.22222
$325$	11.0000	0.610170
$326$	0	0
$327$	20.0000	1.10600
$328$	0	0
$329$	−18.0000	−0.992372
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	−12.0000	−0.658586
$333$	0	0
$334$	0	0
$335$	−4.00000	−0.218543
$336$	16.0000	0.872872
$337$	−24.0000	−1.30736	−0.653682	−	0.756770i	$-0.726776\pi$
$337$	−24.0000	−1.30736	−0.653682	+	0.756770i	$0.726776\pi$
$338$	0	0
$339$	34.0000	1.84663
$340$	−64.0000	−3.47089
$341$	10.0000	0.541530
$342$	0	0
$343$	−20.0000	−1.07990
$344$	0	0
$345$	48.0000	2.58423
$346$	0	0
$347$	−9.00000	−0.483145	−0.241573	−	0.970383i	$-0.577663\pi$
$347$	−9.00000	−0.483145	−0.241573	+	0.970383i	$0.577663\pi$
$348$	−20.0000	−1.07211
$349$	−25.0000	−1.33822	−0.669110	−	0.743164i	$-0.733324\pi$
$349$	−25.0000	−1.33822	−0.669110	+	0.743164i	$0.733324\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	0	0
$353$	−21.0000	−1.11772	−0.558859	−	0.829263i	$-0.688761\pi$
$353$	−21.0000	−1.11772	−0.558859	+	0.829263i	$0.688761\pi$
$354$	0	0
$355$	48.0000	2.54758
$356$	12.0000	0.635999
$357$	32.0000	1.69362
$358$	0	0
$359$	22.0000	1.16112	0.580558	−	0.814219i	$-0.302835\pi$
$359$	22.0000	1.16112	0.580558	+	0.814219i	$0.302835\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	0	0
$363$	2.00000	0.104973
$364$	−4.00000	−0.209657
$365$	−8.00000	−0.418739
$366$	0	0
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	24.0000	1.25109
$369$	0	0
$370$	0	0
$371$	−20.0000	−1.03835
$372$	−40.0000	−2.07390
$373$	−32.0000	−1.65690	−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000	−1.65690	−0.828449	+	0.560065i	$0.810776\pi$
$374$	0	0
$375$	48.0000	2.47871
$376$	0	0
$377$	5.00000	0.257513
$378$	0	0
$379$	5.00000	0.256833	0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000	0.256833	0.128416	+	0.991720i	$0.459011\pi$
$380$	40.0000	2.05196
$381$	26.0000	1.33202
$382$	0	0
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	0	0
$385$	8.00000	0.407718
$386$	0	0
$387$	−10.0000	−0.508329
$388$	26.0000	1.31995
$389$	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
$391$	48.0000	2.42746
$392$	0	0
$393$	6.00000	0.302660
$394$	0	0
$395$	16.0000	0.805047
$396$	−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
$399$	−20.0000	−1.00125
$400$	44.0000	2.20000
$401$	−5.00000	−0.249688	−0.124844	−	0.992176i	$-0.539843\pi$
$401$	−5.00000	−0.249688	−0.124844	+	0.992176i	$0.539843\pi$
$402$	0	0
$403$	10.0000	0.498135
$404$	−16.0000	−0.796030
$405$	−44.0000	−2.18638
$406$	0	0
$407$	0	0
$408$	0	0
$409$	5.00000	0.247234	0.123617	−	0.992330i	$-0.460551\pi$
$409$	5.00000	0.247234	0.123617	+	0.992330i	$0.460551\pi$
$410$	0	0
$411$	6.00000	0.295958
$412$	20.0000	0.985329
$413$	−28.0000	−1.37779
$414$	0	0
$415$	24.0000	1.17811
$416$	0	0
$417$	−10.0000	−0.489702
$418$	0	0
$419$	−1.00000	−0.0488532	−0.0244266	−	0.999702i	$-0.507776\pi$
$419$	−1.00000	−0.0488532	−0.0244266	+	0.999702i	$0.507776\pi$
$420$	−32.0000	−1.56144
$421$	28.0000	1.36464	0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000	1.36464	0.682318	+	0.731055i	$0.260972\pi$
$422$	0	0
$423$	−9.00000	−0.437595
$424$	0	0
$425$	88.0000	4.26863
$426$	0	0
$427$	−28.0000	−1.35501
$428$	−36.0000	−1.74013
$429$	2.00000	0.0965609
$430$	0	0
$431$	22.0000	1.05970	0.529851	−	0.848091i	$-0.322248\pi$
$431$	22.0000	1.05970	0.529851	+	0.848091i	$0.322248\pi$
$432$	−16.0000	−0.769800
$433$	−30.0000	−1.44171	−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000	−1.44171	−0.720854	+	0.693087i	$0.756250\pi$
$434$	0	0
$435$	40.0000	1.91785
$436$	−20.0000	−0.957826
$437$	−30.0000	−1.43509
$438$	0	0
$439$	−29.0000	−1.38409	−0.692047	−	0.721852i	$-0.743291\pi$
$439$	−29.0000	−1.38409	−0.692047	+	0.721852i	$0.743291\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	0	0
$443$	5.00000	0.237557	0.118779	−	0.992921i	$-0.462102\pi$
$443$	5.00000	0.237557	0.118779	+	0.992921i	$0.462102\pi$
$444$	0	0
$445$	−24.0000	−1.13771
$446$	0	0
$447$	−42.0000	−1.98653
$448$	−16.0000	−0.755929
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	0	0
$451$	0	0
$452$	−34.0000	−1.59923
$453$	−32.0000	−1.50349
$454$	0	0
$455$	8.00000	0.375046
$456$	0	0
$457$	22.0000	1.02912	0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000	1.02912	0.514558	+	0.857455i	$0.327956\pi$
$458$	0	0
$459$	−32.0000	−1.49363
$460$	−48.0000	−2.23801
$461$	−20.0000	−0.931493	−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000	−0.931493	−0.465746	+	0.884918i	$0.654214\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	20.0000	0.928477
$465$	80.0000	3.70991
$466$	0	0
$467$	−25.0000	−1.15686	−0.578431	−	0.815731i	$-0.696335\pi$
$467$	−25.0000	−1.15686	−0.578431	+	0.815731i	$0.696335\pi$
$468$	−2.00000	−0.0924500
$469$	−2.00000	−0.0923514
$470$	0	0
$471$	−2.00000	−0.0921551
$472$	0	0
$473$	−10.0000	−0.459800
$474$	0	0
$475$	−55.0000	−2.52357
$476$	−32.0000	−1.46672
$477$	−10.0000	−0.457869
$478$	0	0
$479$	21.0000	0.959514	0.479757	−	0.877401i	$-0.340725\pi$
$479$	21.0000	0.959514	0.479757	+	0.877401i	$0.340725\pi$
$480$	0	0
$481$	0	0
$482$	0	0
$483$	24.0000	1.09204
$484$	−2.00000	−0.0909091
$485$	−52.0000	−2.36120
$486$	0	0
$487$	−14.0000	−0.634401	−0.317200	−	0.948359i	$-0.602743\pi$
$487$	−14.0000	−0.634401	−0.317200	+	0.948359i	$0.602743\pi$
$488$	0	0
$489$	−8.00000	−0.361773
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	40.0000	1.80151
$494$	0	0
$495$	4.00000	0.179787
$496$	40.0000	1.79605
$497$	24.0000	1.07655
$498$	0	0
$499$	5.00000	0.223831	0.111915	−	0.993718i	$-0.464301\pi$
$499$	5.00000	0.223831	0.111915	+	0.993718i	$0.464301\pi$
$500$	−48.0000	−2.14663
$501$	−6.00000	−0.268060
$502$	0	0
$503$	34.0000	1.51599	0.757993	−	0.652263i	$-0.226180\pi$
$503$	34.0000	1.51599	0.757993	+	0.652263i	$0.226180\pi$
$504$	0	0
$505$	32.0000	1.42398
$506$	0	0
$507$	−24.0000	−1.06588
$508$	−26.0000	−1.15356
$509$	−2.00000	−0.0886484	−0.0443242	−	0.999017i	$-0.514113\pi$
$509$	−2.00000	−0.0886484	−0.0443242	+	0.999017i	$0.514113\pi$
$510$	0	0
$511$	−4.00000	−0.176950
$512$	0	0
$513$	20.0000	0.883022
$514$	0	0
$515$	−40.0000	−1.76261
$516$	40.0000	1.76090
$517$	−9.00000	−0.395820
$518$	0	0
$519$	8.00000	0.351161
$520$	0	0
$521$	6.00000	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$522$	0	0
$523$	20.0000	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$524$	−6.00000	−0.262111
$525$	44.0000	1.92032
$526$	0	0
$527$	80.0000	3.48485
$528$	8.00000	0.348155
$529$	13.0000	0.565217
$530$	0	0
$531$	−14.0000	−0.607548
$532$	20.0000	0.867110
$533$	0	0
$534$	0	0
$535$	72.0000	3.11283
$536$	0	0
$537$	30.0000	1.29460
$538$	0	0
$539$	−3.00000	−0.129219
$540$	32.0000	1.37706
$541$	−44.0000	−1.89171	−0.945854	−	0.324593i	$-0.894773\pi$
$541$	−44.0000	−1.89171	−0.945854	+	0.324593i	$0.894773\pi$
$542$	0	0
$543$	−20.0000	−0.858282
$544$	0	0
$545$	40.0000	1.71341
$546$	0	0
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−6.00000	−0.256307
$549$	−14.0000	−0.597505
$550$	0	0
$551$	−25.0000	−1.06504
$552$	0	0
$553$	8.00000	0.340195
$554$	0	0
$555$	0	0
$556$	10.0000	0.424094
$557$	−11.0000	−0.466085	−0.233042	−	0.972467i	$-0.574868\pi$
$557$	−11.0000	−0.466085	−0.233042	+	0.972467i	$0.574868\pi$
$558$	0	0
$559$	−10.0000	−0.422955
$560$	32.0000	1.35225
$561$	16.0000	0.675521
$562$	0	0
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	36.0000	1.51587
$565$	68.0000	2.86078
$566$	0	0
$567$	−22.0000	−0.923913
$568$	0	0
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	−13.0000	−0.544033	−0.272017	−	0.962293i	$-0.587691\pi$
$571$	−13.0000	−0.544033	−0.272017	+	0.962293i	$0.587691\pi$
$572$	−2.00000	−0.0836242
$573$	−26.0000	−1.08617
$574$	0	0
$575$	66.0000	2.75239
$576$	−8.00000	−0.333333
$577$	−20.0000	−0.832611	−0.416305	−	0.909225i	$-0.636675\pi$
$577$	−20.0000	−0.832611	−0.416305	+	0.909225i	$0.636675\pi$
$578$	0	0
$579$	26.0000	1.08052
$580$	−40.0000	−1.66091
$581$	12.0000	0.497844
$582$	0	0
$583$	−10.0000	−0.414158
$584$	0	0
$585$	4.00000	0.165380
$586$	0	0
$587$	45.0000	1.85735	0.928674	−	0.370896i	$-0.120949\pi$
$587$	45.0000	1.85735	0.928674	+	0.370896i	$0.120949\pi$
$588$	12.0000	0.494872
$589$	−50.0000	−2.06021
$590$	0	0
$591$	16.0000	0.658152
$592$	0	0
$593$	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
$595$	64.0000	2.62374
$596$	42.0000	1.72039
$597$	−16.0000	−0.654836
$598$	0	0
$599$	11.0000	0.449448	0.224724	−	0.974422i	$-0.427852\pi$
$599$	11.0000	0.449448	0.224724	+	0.974422i	$0.427852\pi$
$600$	0	0
$601$	19.0000	0.775026	0.387513	−	0.921864i	$-0.373334\pi$
$601$	19.0000	0.775026	0.387513	+	0.921864i	$0.373334\pi$
$602$	0	0
$603$	−1.00000	−0.0407231
$604$	32.0000	1.30206
$605$	4.00000	0.162623
$606$	0	0
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	0	0
$609$	20.0000	0.810441
$610$	0	0
$611$	−9.00000	−0.364101
$612$	−16.0000	−0.646762
$613$	−43.0000	−1.73675	−0.868377	−	0.495905i	$-0.834836\pi$
$613$	−43.0000	−1.73675	−0.868377	+	0.495905i	$0.834836\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	8.00000	0.322068	0.161034	−	0.986949i	$-0.448517\pi$
$617$	8.00000	0.322068	0.161034	+	0.986949i	$0.448517\pi$
$618$	0	0
$619$	−22.0000	−0.884255	−0.442127	−	0.896952i	$-0.645776\pi$
$619$	−22.0000	−0.884255	−0.442127	+	0.896952i	$0.645776\pi$
$620$	−80.0000	−3.21288
$621$	−24.0000	−0.963087
$622$	0	0
$623$	−12.0000	−0.480770
$624$	8.00000	0.320256
$625$	41.0000	1.64000
$626$	0	0
$627$	−10.0000	−0.399362
$628$	2.00000	0.0798087
$629$	0	0
$630$	0	0
$631$	−27.0000	−1.07485	−0.537427	−	0.843311i	$-0.680603\pi$
$631$	−27.0000	−1.07485	−0.537427	+	0.843311i	$0.680603\pi$
$632$	0	0
$633$	24.0000	0.953914
$634$	0	0
$635$	52.0000	2.06356
$636$	40.0000	1.58610
$637$	−3.00000	−0.118864
$638$	0	0
$639$	12.0000	0.474713
$640$	0	0
$641$	0	0		−	1.00000i	$-0.5\pi$
$641$	0	0			1.00000i	$0.5\pi$
$642$	0	0
$643$	−31.0000	−1.22252	−0.611260	−	0.791430i	$-0.709337\pi$
$643$	−31.0000	−1.22252	−0.611260	+	0.791430i	$0.709337\pi$
$644$	−24.0000	−0.945732
$645$	−80.0000	−3.15000
$646$	0	0
$647$	−12.0000	−0.471769	−0.235884	−	0.971781i	$-0.575799\pi$
$647$	−12.0000	−0.471769	−0.235884	+	0.971781i	$0.575799\pi$
$648$	0	0
$649$	−14.0000	−0.549548
$650$	0	0
$651$	40.0000	1.56772
$652$	8.00000	0.313304
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	0	0
$655$	12.0000	0.468879
$656$	0	0
$657$	−2.00000	−0.0780274
$658$	0	0
$659$	22.0000	0.856998	0.428499	−	0.903542i	$-0.359042\pi$
$659$	22.0000	0.856998	0.428499	+	0.903542i	$0.359042\pi$
$660$	−16.0000	−0.622799
$661$	−22.0000	−0.855701	−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000	−0.855701	−0.427850	+	0.903850i	$0.640729\pi$
$662$	0	0
$663$	16.0000	0.621389
$664$	0	0
$665$	−40.0000	−1.55113
$666$	0	0
$667$	30.0000	1.16160
$668$	6.00000	0.232147
$669$	24.0000	0.927894
$670$	0	0
$671$	−14.0000	−0.540464
$672$	0	0
$673$	−41.0000	−1.58043	−0.790217	−	0.612827i	$-0.790032\pi$
$673$	−41.0000	−1.58043	−0.790217	+	0.612827i	$0.790032\pi$
$674$	0	0
$675$	−44.0000	−1.69356
$676$	24.0000	0.923077
$677$	−3.00000	−0.115299	−0.0576497	−	0.998337i	$-0.518361\pi$
$677$	−3.00000	−0.115299	−0.0576497	+	0.998337i	$0.518361\pi$
$678$	0	0
$679$	−26.0000	−0.997788
$680$	0	0
$681$	18.0000	0.689761
$682$	0	0
$683$	−5.00000	−0.191320	−0.0956598	−	0.995414i	$-0.530496\pi$
$683$	−5.00000	−0.191320	−0.0956598	+	0.995414i	$0.530496\pi$
$684$	10.0000	0.382360
$685$	12.0000	0.458496
$686$	0	0
$687$	−56.0000	−2.13653
$688$	−40.0000	−1.52499
$689$	−10.0000	−0.380970
$690$	0	0
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	−8.00000	−0.304114
$693$	2.00000	0.0759737
$694$	0	0
$695$	−20.0000	−0.758643
$696$	0	0
$697$	0	0
$698$	0	0
$699$	−10.0000	−0.378235
$700$	−44.0000	−1.66304
$701$	19.0000	0.717620	0.358810	−	0.933411i	$-0.383183\pi$
$701$	19.0000	0.717620	0.358810	+	0.933411i	$0.383183\pi$
$702$	0	0
$703$	0	0
$704$	−8.00000	−0.301511
$705$	−72.0000	−2.71168
$706$	0	0
$707$	16.0000	0.601742
$708$	56.0000	2.10461
$709$	36.0000	1.35201	0.676004	−	0.736898i	$-0.263710\pi$
$709$	36.0000	1.35201	0.676004	+	0.736898i	$0.263710\pi$
$710$	0	0
$711$	4.00000	0.150012
$712$	0	0
$713$	60.0000	2.24702
$714$	0	0
$715$	4.00000	0.149592
$716$	−30.0000	−1.12115
$717$	16.0000	0.597531
$718$	0	0
$719$	26.0000	0.969636	0.484818	−	0.874615i	$-0.338886\pi$
$719$	26.0000	0.969636	0.484818	+	0.874615i	$0.338886\pi$
$720$	16.0000	0.596285
$721$	−20.0000	−0.744839
$722$	0	0
$723$	−52.0000	−1.93390
$724$	20.0000	0.743294
$725$	55.0000	2.04265
$726$	0	0
$727$	4.00000	0.148352	0.0741759	−	0.997245i	$-0.476367\pi$
$727$	4.00000	0.148352	0.0741759	+	0.997245i	$0.476367\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−80.0000	−2.95891
$732$	56.0000	2.06982
$733$	−24.0000	−0.886460	−0.443230	−	0.896408i	$-0.646168\pi$
$733$	−24.0000	−0.886460	−0.443230	+	0.896408i	$0.646168\pi$
$734$	0	0
$735$	−24.0000	−0.885253
$736$	0	0
$737$	−1.00000	−0.0368355
$738$	0	0
$739$	−34.0000	−1.25071	−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000	−1.25071	−0.625355	+	0.780340i	$0.715046\pi$
$740$	0	0
$741$	−10.0000	−0.367359
$742$	0	0
$743$	−36.0000	−1.32071	−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000	−1.32071	−0.660356	+	0.750953i	$0.729595\pi$
$744$	0	0
$745$	−84.0000	−3.07752
$746$	0	0
$747$	6.00000	0.219529
$748$	−16.0000	−0.585018
$749$	36.0000	1.31541
$750$	0	0
$751$	−41.0000	−1.49611	−0.748056	−	0.663636i	$-0.769012\pi$
$751$	−41.0000	−1.49611	−0.748056	+	0.663636i	$0.769012\pi$
$752$	−36.0000	−1.31278
$753$	48.0000	1.74922
$754$	0	0
$755$	−64.0000	−2.32920
$756$	16.0000	0.581914
$757$	−41.0000	−1.49017	−0.745085	−	0.666969i	$-0.767591\pi$
$757$	−41.0000	−1.49017	−0.745085	+	0.666969i	$0.767591\pi$
$758$	0	0
$759$	12.0000	0.435572
$760$	0	0
$761$	17.0000	0.616250	0.308125	−	0.951346i	$-0.400299\pi$
$761$	17.0000	0.616250	0.308125	+	0.951346i	$0.400299\pi$
$762$	0	0
$763$	20.0000	0.724049
$764$	26.0000	0.940647
$765$	32.0000	1.15696
$766$	0	0
$767$	−14.0000	−0.505511
$768$	32.0000	1.15470
$769$	0	0		−	1.00000i	$-0.5\pi$
$769$	0	0			1.00000i	$0.5\pi$
$770$	0	0
$771$	−12.0000	−0.432169
$772$	−26.0000	−0.935760
$773$	−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
$775$	110.000	3.95132
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	−16.0000	−0.572892
$781$	12.0000	0.429394
$782$	0	0
$783$	−20.0000	−0.714742
$784$	−12.0000	−0.428571
$785$	−4.00000	−0.142766
$786$	0	0
$787$	9.00000	0.320815	0.160408	−	0.987051i	$-0.448719\pi$
$787$	9.00000	0.320815	0.160408	+	0.987051i	$0.448719\pi$
$788$	−16.0000	−0.569976
$789$	−2.00000	−0.0712019
$790$	0	0
$791$	34.0000	1.20890
$792$	0	0
$793$	−14.0000	−0.497155
$794$	0	0
$795$	−80.0000	−2.83731
$796$	16.0000	0.567105
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	0	0
$799$	−72.0000	−2.54718
$800$	0	0
$801$	−6.00000	−0.212000
$802$	0	0
$803$	−2.00000	−0.0705785
$804$	4.00000	0.141069
$805$	48.0000	1.69178
$806$	0	0
$807$	−34.0000	−1.19686
$808$	0	0
$809$	−20.0000	−0.703163	−0.351581	−	0.936157i	$-0.614356\pi$
$809$	−20.0000	−0.703163	−0.351581	+	0.936157i	$0.614356\pi$
$810$	0	0
$811$	48.0000	1.68551	0.842754	−	0.538299i	$-0.180933\pi$
$811$	48.0000	1.68551	0.842754	+	0.538299i	$0.180933\pi$
$812$	−20.0000	−0.701862
$813$	32.0000	1.12229
$814$	0	0
$815$	−16.0000	−0.560456
$816$	64.0000	2.24045
$817$	50.0000	1.74928
$818$	0	0
$819$	2.00000	0.0698857
$820$	0	0
$821$	−32.0000	−1.11681	−0.558404	−	0.829569i	$-0.688586\pi$
$821$	−32.0000	−1.11681	−0.558404	+	0.829569i	$0.688586\pi$
$822$	0	0
$823$	−49.0000	−1.70803	−0.854016	−	0.520246i	$-0.825840\pi$
$823$	−49.0000	−1.70803	−0.854016	+	0.520246i	$0.825840\pi$
$824$	0	0
$825$	22.0000	0.765942
$826$	0	0
$827$	−16.0000	−0.556375	−0.278187	−	0.960527i	$-0.589734\pi$
$827$	−16.0000	−0.556375	−0.278187	+	0.960527i	$0.589734\pi$
$828$	−12.0000	−0.417029
$829$	23.0000	0.798823	0.399412	−	0.916772i	$-0.369214\pi$
$829$	23.0000	0.798823	0.399412	+	0.916772i	$0.369214\pi$
$830$	0	0
$831$	−20.0000	−0.693792
$832$	−8.00000	−0.277350
$833$	−24.0000	−0.831551
$834$	0	0
$835$	−12.0000	−0.415277
$836$	10.0000	0.345857
$837$	−40.0000	−1.38260
$838$	0	0
$839$	3.00000	0.103572	0.0517858	−	0.998658i	$-0.483509\pi$
$839$	3.00000	0.103572	0.0517858	+	0.998658i	$0.483509\pi$
$840$	0	0
$841$	−4.00000	−0.137931
$842$	0	0
$843$	−12.0000	−0.413302
$844$	−24.0000	−0.826114
$845$	−48.0000	−1.65125
$846$	0	0
$847$	2.00000	0.0687208
$848$	−40.0000	−1.37361
$849$	28.0000	0.960958
$850$	0	0
$851$	0	0
$852$	−48.0000	−1.64445
$853$	46.0000	1.57501	0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000	1.57501	0.787505	+	0.616308i	$0.211372\pi$
$854$	0	0
$855$	−20.0000	−0.683986
$856$	0	0
$857$	26.0000	0.888143	0.444072	−	0.895991i	$-0.353534\pi$
$857$	26.0000	0.888143	0.444072	+	0.895991i	$0.353534\pi$
$858$	0	0
$859$	−31.0000	−1.05771	−0.528853	−	0.848713i	$-0.677378\pi$
$859$	−31.0000	−1.05771	−0.528853	+	0.848713i	$0.677378\pi$
$860$	80.0000	2.72798
$861$	0	0
$862$	0	0
$863$	−42.0000	−1.42970	−0.714848	−	0.699280i	$-0.753504\pi$
$863$	−42.0000	−1.42970	−0.714848	+	0.699280i	$0.753504\pi$
$864$	0	0
$865$	16.0000	0.544016
$866$	0	0
$867$	94.0000	3.19241
$868$	−40.0000	−1.35769
$869$	4.00000	0.135691
$870$	0	0
$871$	−1.00000	−0.0338837
$872$	0	0
$873$	−13.0000	−0.439983
$874$	0	0
$875$	48.0000	1.62270
$876$	8.00000	0.270295
$877$	−34.0000	−1.14810	−0.574049	−	0.818821i	$-0.694628\pi$
$877$	−34.0000	−1.14810	−0.574049	+	0.818821i	$0.694628\pi$
$878$	0	0
$879$	62.0000	2.09121
$880$	16.0000	0.539360
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	0	0
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−16.0000	−0.538138
$885$	−112.000	−3.76484
$886$	0	0
$887$	4.00000	0.134307	0.0671534	−	0.997743i	$-0.478608\pi$
$887$	4.00000	0.134307	0.0671534	+	0.997743i	$0.478608\pi$
$888$	0	0
$889$	26.0000	0.872012
$890$	0	0
$891$	−11.0000	−0.368514
$892$	−24.0000	−0.803579
$893$	45.0000	1.50587
$894$	0	0
$895$	60.0000	2.00558
$896$	0	0
$897$	12.0000	0.400668
$898$	0	0
$899$	50.0000	1.66759
$900$	−22.0000	−0.733333
$901$	−80.0000	−2.66519
$902$	0	0
$903$	−40.0000	−1.33112
$904$	0	0
$905$	−40.0000	−1.32964
$906$	0	0
$907$	−28.0000	−0.929725	−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000	−0.929725	−0.464862	+	0.885383i	$0.653896\pi$
$908$	−18.0000	−0.597351
$909$	8.00000	0.265343
$910$	0	0
$911$	−30.0000	−0.993944	−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000	−0.993944	−0.496972	+	0.867766i	$0.665555\pi$
$912$	−40.0000	−1.32453
$913$	6.00000	0.198571
$914$	0	0
$915$	−112.000	−3.70261
$916$	56.0000	1.85029
$917$	6.00000	0.198137
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	−8.00000	−0.263609
$922$	0	0
$923$	12.0000	0.394985
$924$	−8.00000	−0.263181
$925$	0	0
$926$	0	0
$927$	−10.0000	−0.328443
$928$	0	0
$929$	−4.00000	−0.131236	−0.0656179	−	0.997845i	$-0.520902\pi$
$929$	−4.00000	−0.131236	−0.0656179	+	0.997845i	$0.520902\pi$
$930$	0	0
$931$	15.0000	0.491605
$932$	10.0000	0.327561
$933$	10.0000	0.327385
$934$	0	0
$935$	32.0000	1.04651
$936$	0	0
$937$	44.0000	1.43742	0.718709	−	0.695311i	$-0.244734\pi$
$937$	44.0000	1.43742	0.718709	+	0.695311i	$0.244734\pi$
$938$	0	0
$939$	14.0000	0.456873
$940$	72.0000	2.34838
$941$	53.0000	1.72775	0.863875	−	0.503706i	$-0.168030\pi$
$941$	53.0000	1.72775	0.863875	+	0.503706i	$0.168030\pi$
$942$	0	0
$943$	0	0
$944$	−56.0000	−1.82264
$945$	−32.0000	−1.04096
$946$	0	0
$947$	36.0000	1.16984	0.584921	−	0.811090i	$-0.301125\pi$
$947$	36.0000	1.16984	0.584921	+	0.811090i	$0.301125\pi$
$948$	−16.0000	−0.519656
$949$	−2.00000	−0.0649227
$950$	0	0
$951$	26.0000	0.843108
$952$	0	0
$953$	17.0000	0.550684	0.275342	−	0.961346i	$-0.411209\pi$
$953$	17.0000	0.550684	0.275342	+	0.961346i	$0.411209\pi$
$954$	0	0
$955$	−52.0000	−1.68268
$956$	−16.0000	−0.517477
$957$	10.0000	0.323254
$958$	0	0
$959$	6.00000	0.193750
$960$	−64.0000	−2.06559
$961$	69.0000	2.22581
$962$	0	0
$963$	18.0000	0.580042
$964$	52.0000	1.67481
$965$	52.0000	1.67394
$966$	0	0
$967$	36.0000	1.15768	0.578841	−	0.815440i	$-0.303505\pi$
$967$	36.0000	1.15768	0.578841	+	0.815440i	$0.303505\pi$
$968$	0	0
$969$	−80.0000	−2.56997
$970$	0	0
$971$	18.0000	0.577647	0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000	0.577647	0.288824	+	0.957382i	$0.406736\pi$
$972$	20.0000	0.641500
$973$	−10.0000	−0.320585
$974$	0	0
$975$	22.0000	0.704564
$976$	−56.0000	−1.79252
$977$	−22.0000	−0.703842	−0.351921	−	0.936030i	$-0.614471\pi$
$977$	−22.0000	−0.703842	−0.351921	+	0.936030i	$0.614471\pi$
$978$	0	0
$979$	−6.00000	−0.191761
$980$	24.0000	0.766652
$981$	10.0000	0.319275
$982$	0	0
$983$	−52.0000	−1.65854	−0.829271	−	0.558846i	$-0.811244\pi$
$983$	−52.0000	−1.65854	−0.829271	+	0.558846i	$0.811244\pi$
$984$	0	0
$985$	32.0000	1.01960
$986$	0	0
$987$	−36.0000	−1.14589
$988$	10.0000	0.318142
$989$	−60.0000	−1.90789
$990$	0	0
$991$	−45.0000	−1.42947	−0.714736	−	0.699394i	$-0.753453\pi$
$991$	−45.0000	−1.42947	−0.714736	+	0.699394i	$0.753453\pi$
$992$	0	0
$993$	40.0000	1.26936
$994$	0	0
$995$	−32.0000	−1.01447
$996$	−24.0000	−0.760469
$997$	46.0000	1.45683	0.728417	−	0.685134i	$-0.240256\pi$
$997$	46.0000	1.45683	0.728417	+	0.685134i	$0.240256\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.b.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.b.1.1	✓	1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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