LMFDB - Embedded newform 8015.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
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	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} -3.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} -3.00000 q^{8} -3.00000 q^{9} +1.00000 q^{10} -4.00000 q^{11} +2.00000 q^{13} +1.00000 q^{14} -1.00000 q^{16} -6.00000 q^{17} -3.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} -4.00000 q^{22} +1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{28} -10.0000 q^{29} +8.00000 q^{31} +5.00000 q^{32} -6.00000 q^{34} +1.00000 q^{35} +3.00000 q^{36} -2.00000 q^{37} -4.00000 q^{38} -3.00000 q^{40} -6.00000 q^{41} +8.00000 q^{43} +4.00000 q^{44} -3.00000 q^{45} +8.00000 q^{47} +1.00000 q^{49} +1.00000 q^{50} -2.00000 q^{52} +6.00000 q^{53} -4.00000 q^{55} -3.00000 q^{56} -10.0000 q^{58} +12.0000 q^{59} -2.00000 q^{61} +8.00000 q^{62} -3.00000 q^{63} +7.00000 q^{64} +2.00000 q^{65} -4.00000 q^{67} +6.00000 q^{68} +1.00000 q^{70} +9.00000 q^{72} +14.0000 q^{73} -2.00000 q^{74} +4.00000 q^{76} -4.00000 q^{77} -1.00000 q^{80} +9.00000 q^{81} -6.00000 q^{82} +16.0000 q^{83} -6.00000 q^{85} +8.00000 q^{86} +12.0000 q^{88} -6.00000 q^{89} -3.00000 q^{90} +2.00000 q^{91} +8.00000 q^{94} -4.00000 q^{95} +2.00000 q^{97} +1.00000 q^{98} +12.0000 q^{99} +O(q^{100})\)

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 $

$2$	1.00000	0.707107	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	−1.00000	−0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.00000	−1.06066
$9$	−3.00000	−1.00000
$10$	1.00000	0.316228
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	0	0
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	−1.00000	−0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−3.00000	−0.707107
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−4.00000	−0.852803
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	0	0
$28$	−1.00000	−0.188982
$29$	−10.0000	−1.85695	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−10.0000	−1.85695	−0.928477	+	0.371391i	$0.878881\pi$
$30$	0	0
$31$	8.00000	1.43684	0.718421	−	0.695608i	$-0.244865\pi$
$31$	8.00000	1.43684	0.718421	+	0.695608i	$0.244865\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	−6.00000	−1.02899
$35$	1.00000	0.169031
$36$	3.00000	0.500000
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−4.00000	−0.648886
$39$	0	0
$40$	−3.00000	−0.474342
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	4.00000	0.603023
$45$	−3.00000	−0.447214
$46$	0	0
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	0	0
$52$	−2.00000	−0.277350
$53$	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
$55$	−4.00000	−0.539360
$56$	−3.00000	−0.400892
$57$	0	0
$58$	−10.0000	−1.31306
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	8.00000	1.01600
$63$	−3.00000	−0.377964
$64$	7.00000	0.875000
$65$	2.00000	0.248069
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	1.00000	0.119523
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	9.00000	1.06066
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	4.00000	0.458831
$77$	−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
$81$	9.00000	1.00000
$82$	−6.00000	−0.662589
$83$	16.0000	1.75623	0.878114	−	0.478451i	$-0.158802\pi$
$83$	16.0000	1.75623	0.878114	+	0.478451i	$0.158802\pi$
$84$	0	0
$85$	−6.00000	−0.650791
$86$	8.00000	0.862662
$87$	0	0
$88$	12.0000	1.27920
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	−3.00000	−0.316228
$91$	2.00000	0.209657
$92$	0	0
$93$	0	0
$94$	8.00000	0.825137
$95$	−4.00000	−0.410391
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	1.00000	0.101015
$99$	12.0000	1.20605
$100$	−1.00000	−0.100000
$101$	−18.0000	−1.79107	−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000	−1.79107	−0.895533	+	0.444994i	$0.853206\pi$
$102$	0	0
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	6.00000	0.582772
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	0	0
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	−4.00000	−0.381385
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	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
$115$	0	0
$116$	10.0000	0.928477
$117$	−6.00000	−0.554700
$118$	12.0000	1.10469
$119$	−6.00000	−0.550019
$120$	0	0
$121$	5.00000	0.454545
$122$	−2.00000	−0.181071
$123$	0	0
$124$	−8.00000	−0.718421
$125$	1.00000	0.0894427
$126$	−3.00000	−0.267261
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−3.00000	−0.265165
$129$	0	0
$130$	2.00000	0.175412
$131$	20.0000	1.74741	0.873704	−	0.486458i	$-0.161711\pi$
$131$	20.0000	1.74741	0.873704	+	0.486458i	$0.161711\pi$
$132$	0	0
$133$	−4.00000	−0.346844
$134$	−4.00000	−0.345547
$135$	0	0
$136$	18.0000	1.54349
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	0	0
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	−1.00000	−0.0845154
$141$	0	0
$142$	0	0
$143$	−8.00000	−0.668994
$144$	3.00000	0.250000
$145$	−10.0000	−0.830455
$146$	14.0000	1.15865
$147$	0	0
$148$	2.00000	0.164399
$149$	−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
$151$	−24.0000	−1.95309	−0.976546	−	0.215308i	$-0.930924\pi$
$151$	−24.0000	−1.95309	−0.976546	+	0.215308i	$0.930924\pi$
$152$	12.0000	0.973329
$153$	18.0000	1.45521
$154$	−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
$160$	5.00000	0.395285
$161$	0	0
$162$	9.00000	0.707107
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	16.0000	1.24184
$167$	−4.00000	−0.309529	−0.154765	−	0.987951i	$-0.549462\pi$
$167$	−4.00000	−0.309529	−0.154765	+	0.987951i	$0.549462\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−6.00000	−0.460179
$171$	12.0000	0.917663
$172$	−8.00000	−0.609994
$173$	14.0000	1.06440	0.532200	−	0.846619i	$-0.321365\pi$
$173$	14.0000	1.06440	0.532200	+	0.846619i	$0.321365\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	4.00000	0.301511
$177$	0	0
$178$	−6.00000	−0.449719
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	3.00000	0.223607
$181$	6.00000	0.445976	0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000	0.445976	0.222988	+	0.974821i	$0.428419\pi$
$182$	2.00000	0.148250
$183$	0	0
$184$	0	0
$185$	−2.00000	−0.147043
$186$	0	0
$187$	24.0000	1.75505
$188$	−8.00000	−0.583460
$189$	0	0
$190$	−4.00000	−0.290191
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	−1.00000	−0.0714286
$197$	−22.0000	−1.56744	−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000	−1.56744	−0.783718	+	0.621117i	$0.786679\pi$
$198$	12.0000	0.852803
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	−3.00000	−0.212132
$201$	0	0
$202$	−18.0000	−1.26648
$203$	−10.0000	−0.701862
$204$	0	0
$205$	−6.00000	−0.419058
$206$	4.00000	0.278693
$207$	0	0
$208$	−2.00000	−0.138675
$209$	16.0000	1.10674
$210$	0	0
$211$	−28.0000	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$212$	−6.00000	−0.412082
$213$	0	0
$214$	−12.0000	−0.820303
$215$	8.00000	0.545595
$216$	0	0
$217$	8.00000	0.543075
$218$	−2.00000	−0.135457
$219$	0	0
$220$	4.00000	0.269680
$221$	−12.0000	−0.807207
$222$	0	0
$223$	24.0000	1.60716	0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000	1.60716	0.803579	+	0.595198i	$0.202926\pi$
$224$	5.00000	0.334077
$225$	−3.00000	−0.200000
$226$	6.00000	0.399114
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	0	0
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	0	0
$231$	0	0
$232$	30.0000	1.96960
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	−6.00000	−0.392232
$235$	8.00000	0.521862
$236$	−12.0000	−0.781133
$237$	0	0
$238$	−6.00000	−0.388922
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	2.00000	0.128037
$245$	1.00000	0.0638877
$246$	0	0
$247$	−8.00000	−0.509028
$248$	−24.0000	−1.52400
$249$	0	0
$250$	1.00000	0.0632456
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	3.00000	0.188982
$253$	0	0
$254$	8.00000	0.501965
$255$	0	0
$256$	−17.0000	−1.06250
$257$	14.0000	0.873296	0.436648	−	0.899632i	$-0.356166\pi$
$257$	14.0000	0.873296	0.436648	+	0.899632i	$0.356166\pi$
$258$	0	0
$259$	−2.00000	−0.124274
$260$	−2.00000	−0.124035
$261$	30.0000	1.85695
$262$	20.0000	1.23560
$263$	16.0000	0.986602	0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000	0.986602	0.493301	+	0.869859i	$0.335790\pi$
$264$	0	0
$265$	6.00000	0.368577
$266$	−4.00000	−0.245256
$267$	0	0
$268$	4.00000	0.244339
$269$	−10.0000	−0.609711	−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000	−0.609711	−0.304855	+	0.952399i	$0.598608\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	−2.00000	−0.120824
$275$	−4.00000	−0.241209
$276$	0	0
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	20.0000	1.19952
$279$	−24.0000	−1.43684
$280$	−3.00000	−0.179284
$281$	−30.0000	−1.78965	−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000	−1.78965	−0.894825	+	0.446417i	$0.852700\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	0	0
$285$	0	0
$286$	−8.00000	−0.473050
$287$	−6.00000	−0.354169
$288$	−15.0000	−0.883883
$289$	19.0000	1.11765
$290$	−10.0000	−0.587220
$291$	0	0
$292$	−14.0000	−0.819288
$293$	−18.0000	−1.05157	−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000	−1.05157	−0.525786	+	0.850617i	$0.676229\pi$
$294$	0	0
$295$	12.0000	0.698667
$296$	6.00000	0.348743
$297$	0	0
$298$	−10.0000	−0.579284
$299$	0	0
$300$	0	0
$301$	8.00000	0.461112
$302$	−24.0000	−1.38104
$303$	0	0
$304$	4.00000	0.229416
$305$	−2.00000	−0.114520
$306$	18.0000	1.02899
$307$	24.0000	1.36975	0.684876	−	0.728659i	$-0.259856\pi$
$307$	24.0000	1.36975	0.684876	+	0.728659i	$0.259856\pi$
$308$	4.00000	0.227921
$309$	0	0
$310$	8.00000	0.454369
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	18.0000	1.01580
$315$	−3.00000	−0.169031
$316$	0	0
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	0	0
$319$	40.0000	2.23957
$320$	7.00000	0.391312
$321$	0	0
$322$	0	0
$323$	24.0000	1.33540
$324$	−9.00000	−0.500000
$325$	2.00000	0.110940
$326$	4.00000	0.221540
$327$	0	0
$328$	18.0000	0.993884
$329$	8.00000	0.441054
$330$	0	0
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	−16.0000	−0.878114
$333$	6.00000	0.328798
$334$	−4.00000	−0.218870
$335$	−4.00000	−0.218543
$336$	0	0
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	6.00000	0.325396
$341$	−32.0000	−1.73290
$342$	12.0000	0.648886
$343$	1.00000	0.0539949
$344$	−24.0000	−1.29399
$345$	0	0
$346$	14.0000	0.752645
$347$	−8.00000	−0.429463	−0.214731	−	0.976673i	$-0.568888\pi$
$347$	−8.00000	−0.429463	−0.214731	+	0.976673i	$0.568888\pi$
$348$	0	0
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	−20.0000	−1.06600
$353$	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
$355$	0	0
$356$	6.00000	0.317999
$357$	0	0
$358$	12.0000	0.634220
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	9.00000	0.474342
$361$	−3.00000	−0.157895
$362$	6.00000	0.315353
$363$	0	0
$364$	−2.00000	−0.104828
$365$	14.0000	0.732793
$366$	0	0
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	0	0
$369$	18.0000	0.937043
$370$	−2.00000	−0.103975
$371$	6.00000	0.311504
$372$	0	0
$373$	−10.0000	−0.517780	−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000	−0.517780	−0.258890	+	0.965907i	$0.583357\pi$
$374$	24.0000	1.24101
$375$	0	0
$376$	−24.0000	−1.23771
$377$	−20.0000	−1.03005
$378$	0	0
$379$	28.0000	1.43826	0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000	1.43826	0.719132	+	0.694874i	$0.244540\pi$
$380$	4.00000	0.205196
$381$	0	0
$382$	0	0
$383$	20.0000	1.02195	0.510976	−	0.859595i	$-0.329284\pi$
$383$	20.0000	1.02195	0.510976	+	0.859595i	$0.329284\pi$
$384$	0	0
$385$	−4.00000	−0.203859
$386$	−14.0000	−0.712581
$387$	−24.0000	−1.21999
$388$	−2.00000	−0.101535
$389$	−26.0000	−1.31825	−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000	−1.31825	−0.659126	+	0.752032i	$0.729074\pi$
$390$	0	0
$391$	0	0
$392$	−3.00000	−0.151523
$393$	0	0
$394$	−22.0000	−1.10834
$395$	0	0
$396$	−12.0000	−0.603023
$397$	30.0000	1.50566	0.752828	−	0.658217i	$-0.228689\pi$
$397$	30.0000	1.50566	0.752828	+	0.658217i	$0.228689\pi$
$398$	−16.0000	−0.802008
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	−14.0000	−0.699127	−0.349563	−	0.936913i	$-0.613670\pi$
$401$	−14.0000	−0.699127	−0.349563	+	0.936913i	$0.613670\pi$
$402$	0	0
$403$	16.0000	0.797017
$404$	18.0000	0.895533
$405$	9.00000	0.447214
$406$	−10.0000	−0.496292
$407$	8.00000	0.396545
$408$	0	0
$409$	−22.0000	−1.08783	−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000	−1.08783	−0.543915	+	0.839140i	$0.683059\pi$
$410$	−6.00000	−0.296319
$411$	0	0
$412$	−4.00000	−0.197066
$413$	12.0000	0.590481
$414$	0	0
$415$	16.0000	0.785409
$416$	10.0000	0.490290
$417$	0	0
$418$	16.0000	0.782586
$419$	−28.0000	−1.36789	−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000	−1.36789	−0.683945	+	0.729534i	$0.739737\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	−28.0000	−1.36302
$423$	−24.0000	−1.16692
$424$	−18.0000	−0.874157
$425$	−6.00000	−0.291043
$426$	0	0
$427$	−2.00000	−0.0967868
$428$	12.0000	0.580042
$429$	0	0
$430$	8.00000	0.385794
$431$	−24.0000	−1.15604	−0.578020	−	0.816023i	$-0.696174\pi$
$431$	−24.0000	−1.15604	−0.578020	+	0.816023i	$0.696174\pi$
$432$	0	0
$433$	34.0000	1.63394	0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000	1.63394	0.816968	+	0.576683i	$0.195653\pi$
$434$	8.00000	0.384012
$435$	0	0
$436$	2.00000	0.0957826
$437$	0	0
$438$	0	0
$439$	−8.00000	−0.381819	−0.190910	−	0.981608i	$-0.561144\pi$
$439$	−8.00000	−0.381819	−0.190910	+	0.981608i	$0.561144\pi$
$440$	12.0000	0.572078
$441$	−3.00000	−0.142857
$442$	−12.0000	−0.570782
$443$	24.0000	1.14027	0.570137	−	0.821549i	$-0.306890\pi$
$443$	24.0000	1.14027	0.570137	+	0.821549i	$0.306890\pi$
$444$	0	0
$445$	−6.00000	−0.284427
$446$	24.0000	1.13643
$447$	0	0
$448$	7.00000	0.330719
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	−3.00000	−0.141421
$451$	24.0000	1.13012
$452$	−6.00000	−0.282216
$453$	0	0
$454$	−12.0000	−0.563188
$455$	2.00000	0.0937614
$456$	0	0
$457$	34.0000	1.59045	0.795226	−	0.606313i	$-0.207352\pi$
$457$	34.0000	1.59045	0.795226	+	0.606313i	$0.207352\pi$
$458$	1.00000	0.0467269
$459$	0	0
$460$	0	0
$461$	−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
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	10.0000	0.464238
$465$	0	0
$466$	10.0000	0.463241
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	6.00000	0.277350
$469$	−4.00000	−0.184703
$470$	8.00000	0.369012
$471$	0	0
$472$	−36.0000	−1.65703
$473$	−32.0000	−1.47136
$474$	0	0
$475$	−4.00000	−0.183533
$476$	6.00000	0.275010
$477$	−18.0000	−0.824163
$478$	24.0000	1.09773
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	18.0000	0.819878
$483$	0	0
$484$	−5.00000	−0.227273
$485$	2.00000	0.0908153
$486$	0	0
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	6.00000	0.271607
$489$	0	0
$490$	1.00000	0.0451754
$491$	−28.0000	−1.26362	−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000	−1.26362	−0.631811	+	0.775122i	$0.717688\pi$
$492$	0	0
$493$	60.0000	2.70226
$494$	−8.00000	−0.359937
$495$	12.0000	0.539360
$496$	−8.00000	−0.359211
$497$	0	0
$498$	0	0
$499$	−20.0000	−0.895323	−0.447661	−	0.894203i	$-0.647743\pi$
$499$	−20.0000	−0.895323	−0.447661	+	0.894203i	$0.647743\pi$
$500$	−1.00000	−0.0447214
$501$	0	0
$502$	−12.0000	−0.535586
$503$	36.0000	1.60516	0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000	1.60516	0.802580	+	0.596544i	$0.203460\pi$
$504$	9.00000	0.400892
$505$	−18.0000	−0.800989
$506$	0	0
$507$	0	0
$508$	−8.00000	−0.354943
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	0	0
$511$	14.0000	0.619324
$512$	−11.0000	−0.486136
$513$	0	0
$514$	14.0000	0.617514
$515$	4.00000	0.176261
$516$	0	0
$517$	−32.0000	−1.40736
$518$	−2.00000	−0.0878750
$519$	0	0
$520$	−6.00000	−0.263117
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	30.0000	1.31306
$523$	−28.0000	−1.22435	−0.612177	−	0.790721i	$-0.709706\pi$
$523$	−28.0000	−1.22435	−0.612177	+	0.790721i	$0.709706\pi$
$524$	−20.0000	−0.873704
$525$	0	0
$526$	16.0000	0.697633
$527$	−48.0000	−2.09091
$528$	0	0
$529$	−23.0000	−1.00000
$530$	6.00000	0.260623
$531$	−36.0000	−1.56227
$532$	4.00000	0.173422
$533$	−12.0000	−0.519778
$534$	0	0
$535$	−12.0000	−0.518805
$536$	12.0000	0.518321
$537$	0	0
$538$	−10.0000	−0.431131
$539$	−4.00000	−0.172292
$540$	0	0
$541$	−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
$543$	0	0
$544$	−30.0000	−1.28624
$545$	−2.00000	−0.0856706
$546$	0	0
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	2.00000	0.0854358
$549$	6.00000	0.256074
$550$	−4.00000	−0.170561
$551$	40.0000	1.70406
$552$	0	0
$553$	0	0
$554$	22.0000	0.934690
$555$	0	0
$556$	−20.0000	−0.848189
$557$	22.0000	0.932170	0.466085	−	0.884740i	$-0.345664\pi$
$557$	22.0000	0.932170	0.466085	+	0.884740i	$0.345664\pi$
$558$	−24.0000	−1.01600
$559$	16.0000	0.676728
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−30.0000	−1.26547
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	0	0
$565$	6.00000	0.252422
$566$	−4.00000	−0.168133
$567$	9.00000	0.377964
$568$	0	0
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	0	0
$571$	−20.0000	−0.836974	−0.418487	−	0.908223i	$-0.637439\pi$
$571$	−20.0000	−0.836974	−0.418487	+	0.908223i	$0.637439\pi$
$572$	8.00000	0.334497
$573$	0	0
$574$	−6.00000	−0.250435
$575$	0	0
$576$	−21.0000	−0.875000
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	19.0000	0.790296
$579$	0	0
$580$	10.0000	0.415227
$581$	16.0000	0.663792
$582$	0	0
$583$	−24.0000	−0.993978
$584$	−42.0000	−1.73797
$585$	−6.00000	−0.248069
$586$	−18.0000	−0.743573
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	0	0
$589$	−32.0000	−1.31854
$590$	12.0000	0.494032
$591$	0	0
$592$	2.00000	0.0821995
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	0	0
$595$	−6.00000	−0.245976
$596$	10.0000	0.409616
$597$	0	0
$598$	0	0
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	0	0
$601$	26.0000	1.06056	0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000	1.06056	0.530281	+	0.847822i	$0.322086\pi$
$602$	8.00000	0.326056
$603$	12.0000	0.488678
$604$	24.0000	0.976546
$605$	5.00000	0.203279
$606$	0	0
$607$	−12.0000	−0.487065	−0.243532	−	0.969893i	$-0.578306\pi$
$607$	−12.0000	−0.487065	−0.243532	+	0.969893i	$0.578306\pi$
$608$	−20.0000	−0.811107
$609$	0	0
$610$	−2.00000	−0.0809776
$611$	16.0000	0.647291
$612$	−18.0000	−0.727607
$613$	−22.0000	−0.888572	−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000	−0.888572	−0.444286	+	0.895885i	$0.646543\pi$
$614$	24.0000	0.968561
$615$	0	0
$616$	12.0000	0.483494
$617$	18.0000	0.724653	0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000	0.724653	0.362326	+	0.932051i	$0.381983\pi$
$618$	0	0
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	−8.00000	−0.321288
$621$	0	0
$622$	−24.0000	−0.962312
$623$	−6.00000	−0.240385
$624$	0	0
$625$	1.00000	0.0400000
$626$	14.0000	0.559553
$627$	0	0
$628$	−18.0000	−0.718278
$629$	12.0000	0.478471
$630$	−3.00000	−0.119523
$631$	40.0000	1.59237	0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000	1.59237	0.796187	+	0.605050i	$0.206847\pi$
$632$	0	0
$633$	0	0
$634$	−6.00000	−0.238290
$635$	8.00000	0.317470
$636$	0	0
$637$	2.00000	0.0792429
$638$	40.0000	1.58362
$639$	0	0
$640$	−3.00000	−0.118585
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	0	0
$643$	−16.0000	−0.630978	−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000	−0.630978	−0.315489	+	0.948929i	$0.602169\pi$
$644$	0	0
$645$	0	0
$646$	24.0000	0.944267
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	−27.0000	−1.06066
$649$	−48.0000	−1.88416
$650$	2.00000	0.0784465
$651$	0	0
$652$	−4.00000	−0.156652
$653$	26.0000	1.01746	0.508729	−	0.860927i	$-0.330115\pi$
$653$	26.0000	1.01746	0.508729	+	0.860927i	$0.330115\pi$
$654$	0	0
$655$	20.0000	0.781465
$656$	6.00000	0.234261
$657$	−42.0000	−1.63858
$658$	8.00000	0.311872
$659$	−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
$661$	22.0000	0.855701	0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000	0.855701	0.427850	+	0.903850i	$0.359271\pi$
$662$	4.00000	0.155464
$663$	0	0
$664$	−48.0000	−1.86276
$665$	−4.00000	−0.155113
$666$	6.00000	0.232495
$667$	0	0
$668$	4.00000	0.154765
$669$	0	0
$670$	−4.00000	−0.154533
$671$	8.00000	0.308837
$672$	0	0
$673$	34.0000	1.31060	0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000	1.31060	0.655302	+	0.755367i	$0.272541\pi$
$674$	26.0000	1.00148
$675$	0	0
$676$	9.00000	0.346154
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	0	0
$679$	2.00000	0.0767530
$680$	18.0000	0.690268
$681$	0	0
$682$	−32.0000	−1.22534
$683$	−16.0000	−0.612223	−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000	−0.612223	−0.306111	+	0.951996i	$0.599028\pi$
$684$	−12.0000	−0.458831
$685$	−2.00000	−0.0764161
$686$	1.00000	0.0381802
$687$	0	0
$688$	−8.00000	−0.304997
$689$	12.0000	0.457164
$690$	0	0
$691$	12.0000	0.456502	0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000	0.456502	0.228251	+	0.973602i	$0.426699\pi$
$692$	−14.0000	−0.532200
$693$	12.0000	0.455842
$694$	−8.00000	−0.303676
$695$	20.0000	0.758643
$696$	0	0
$697$	36.0000	1.36360
$698$	14.0000	0.529908
$699$	0	0
$700$	−1.00000	−0.0377964
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	0	0
$703$	8.00000	0.301726
$704$	−28.0000	−1.05529
$705$	0	0
$706$	6.00000	0.225813
$707$	−18.0000	−0.676960
$708$	0	0
$709$	−34.0000	−1.27690	−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000	−1.27690	−0.638448	+	0.769665i	$0.720423\pi$
$710$	0	0
$711$	0	0
$712$	18.0000	0.674579
$713$	0	0
$714$	0	0
$715$	−8.00000	−0.299183
$716$	−12.0000	−0.448461
$717$	0	0
$718$	24.0000	0.895672
$719$	8.00000	0.298350	0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000	0.298350	0.149175	+	0.988811i	$0.452338\pi$
$720$	3.00000	0.111803
$721$	4.00000	0.148968
$722$	−3.00000	−0.111648
$723$	0	0
$724$	−6.00000	−0.222988
$725$	−10.0000	−0.371391
$726$	0	0
$727$	−40.0000	−1.48352	−0.741759	−	0.670667i	$-0.766008\pi$
$727$	−40.0000	−1.48352	−0.741759	+	0.670667i	$0.766008\pi$
$728$	−6.00000	−0.222375
$729$	−27.0000	−1.00000
$730$	14.0000	0.518163
$731$	−48.0000	−1.77534
$732$	0	0
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	−28.0000	−1.03350
$735$	0	0
$736$	0	0
$737$	16.0000	0.589368
$738$	18.0000	0.662589
$739$	4.00000	0.147142	0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000	0.147142	0.0735712	+	0.997290i	$0.476560\pi$
$740$	2.00000	0.0735215
$741$	0	0
$742$	6.00000	0.220267
$743$	28.0000	1.02722	0.513610	−	0.858024i	$-0.328308\pi$
$743$	28.0000	1.02722	0.513610	+	0.858024i	$0.328308\pi$
$744$	0	0
$745$	−10.0000	−0.366372
$746$	−10.0000	−0.366126
$747$	−48.0000	−1.75623
$748$	−24.0000	−0.877527
$749$	−12.0000	−0.438470
$750$	0	0
$751$	−24.0000	−0.875772	−0.437886	−	0.899030i	$-0.644273\pi$
$751$	−24.0000	−0.875772	−0.437886	+	0.899030i	$0.644273\pi$
$752$	−8.00000	−0.291730
$753$	0	0
$754$	−20.0000	−0.728357
$755$	−24.0000	−0.873449
$756$	0	0
$757$	38.0000	1.38113	0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000	1.38113	0.690567	+	0.723269i	$0.257361\pi$
$758$	28.0000	1.01701
$759$	0	0
$760$	12.0000	0.435286
$761$	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
$763$	−2.00000	−0.0724049
$764$	0	0
$765$	18.0000	0.650791
$766$	20.0000	0.722629
$767$	24.0000	0.866590
$768$	0	0
$769$	34.0000	1.22607	0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000	1.22607	0.613036	+	0.790055i	$0.289948\pi$
$770$	−4.00000	−0.144150
$771$	0	0
$772$	14.0000	0.503871
$773$	34.0000	1.22290	0.611448	−	0.791285i	$-0.290588\pi$
$773$	34.0000	1.22290	0.611448	+	0.791285i	$0.290588\pi$
$774$	−24.0000	−0.862662
$775$	8.00000	0.287368
$776$	−6.00000	−0.215387
$777$	0	0
$778$	−26.0000	−0.932145
$779$	24.0000	0.859889
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−1.00000	−0.0357143
$785$	18.0000	0.642448
$786$	0	0
$787$	−40.0000	−1.42585	−0.712923	−	0.701242i	$-0.752629\pi$
$787$	−40.0000	−1.42585	−0.712923	+	0.701242i	$0.752629\pi$
$788$	22.0000	0.783718
$789$	0	0
$790$	0	0
$791$	6.00000	0.213335
$792$	−36.0000	−1.27920
$793$	−4.00000	−0.142044
$794$	30.0000	1.06466
$795$	0	0
$796$	16.0000	0.567105
$797$	−6.00000	−0.212531	−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000	−0.212531	−0.106265	+	0.994338i	$0.533889\pi$
$798$	0	0
$799$	−48.0000	−1.69812
$800$	5.00000	0.176777
$801$	18.0000	0.635999
$802$	−14.0000	−0.494357
$803$	−56.0000	−1.97620
$804$	0	0
$805$	0	0
$806$	16.0000	0.563576
$807$	0	0
$808$	54.0000	1.89971
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	9.00000	0.316228
$811$	44.0000	1.54505	0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000	1.54505	0.772524	+	0.634985i	$0.218994\pi$
$812$	10.0000	0.350931
$813$	0	0
$814$	8.00000	0.280400
$815$	4.00000	0.140114
$816$	0	0
$817$	−32.0000	−1.11954
$818$	−22.0000	−0.769212
$819$	−6.00000	−0.209657
$820$	6.00000	0.209529
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	0	0
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	−12.0000	−0.418040
$825$	0	0
$826$	12.0000	0.417533
$827$	52.0000	1.80822	0.904109	−	0.427303i	$-0.140536\pi$
$827$	52.0000	1.80822	0.904109	+	0.427303i	$0.140536\pi$
$828$	0	0
$829$	38.0000	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$829$	38.0000	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$830$	16.0000	0.555368
$831$	0	0
$832$	14.0000	0.485363
$833$	−6.00000	−0.207888
$834$	0	0
$835$	−4.00000	−0.138426
$836$	−16.0000	−0.553372
$837$	0	0
$838$	−28.0000	−0.967244
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	0	0
$841$	71.0000	2.44828
$842$	22.0000	0.758170
$843$	0	0
$844$	28.0000	0.963800
$845$	−9.00000	−0.309609
$846$	−24.0000	−0.825137
$847$	5.00000	0.171802
$848$	−6.00000	−0.206041
$849$	0	0
$850$	−6.00000	−0.205798
$851$	0	0
$852$	0	0
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	−2.00000	−0.0684386
$855$	12.0000	0.410391
$856$	36.0000	1.23045
$857$	22.0000	0.751506	0.375753	−	0.926720i	$-0.377384\pi$
$857$	22.0000	0.751506	0.375753	+	0.926720i	$0.377384\pi$
$858$	0	0
$859$	−36.0000	−1.22830	−0.614152	−	0.789188i	$-0.710502\pi$
$859$	−36.0000	−1.22830	−0.614152	+	0.789188i	$0.710502\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	−24.0000	−0.817443
$863$	−52.0000	−1.77010	−0.885050	−	0.465495i	$-0.845876\pi$
$863$	−52.0000	−1.77010	−0.885050	+	0.465495i	$0.845876\pi$
$864$	0	0
$865$	14.0000	0.476014
$866$	34.0000	1.15537
$867$	0	0
$868$	−8.00000	−0.271538
$869$	0	0
$870$	0	0
$871$	−8.00000	−0.271070
$872$	6.00000	0.203186
$873$	−6.00000	−0.203069
$874$	0	0
$875$	1.00000	0.0338062
$876$	0	0
$877$	−46.0000	−1.55331	−0.776655	−	0.629926i	$-0.783085\pi$
$877$	−46.0000	−1.55331	−0.776655	+	0.629926i	$0.783085\pi$
$878$	−8.00000	−0.269987
$879$	0	0
$880$	4.00000	0.134840
$881$	2.00000	0.0673817	0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000	0.0673817	0.0336909	+	0.999432i	$0.489274\pi$
$882$	−3.00000	−0.101015
$883$	56.0000	1.88455	0.942275	−	0.334840i	$-0.108682\pi$
$883$	56.0000	1.88455	0.942275	+	0.334840i	$0.108682\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	24.0000	0.806296
$887$	−8.00000	−0.268614	−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000	−0.268614	−0.134307	+	0.990940i	$0.542881\pi$
$888$	0	0
$889$	8.00000	0.268311
$890$	−6.00000	−0.201120
$891$	−36.0000	−1.20605
$892$	−24.0000	−0.803579
$893$	−32.0000	−1.07084
$894$	0	0
$895$	12.0000	0.401116
$896$	−3.00000	−0.100223
$897$	0	0
$898$	18.0000	0.600668
$899$	−80.0000	−2.66815
$900$	3.00000	0.100000
$901$	−36.0000	−1.19933
$902$	24.0000	0.799113
$903$	0	0
$904$	−18.0000	−0.598671
$905$	6.00000	0.199447
$906$	0	0
$907$	24.0000	0.796907	0.398453	−	0.917189i	$-0.369547\pi$
$907$	24.0000	0.796907	0.398453	+	0.917189i	$0.369547\pi$
$908$	12.0000	0.398234
$909$	54.0000	1.79107
$910$	2.00000	0.0662994
$911$	40.0000	1.32526	0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000	1.32526	0.662630	+	0.748947i	$0.269440\pi$
$912$	0	0
$913$	−64.0000	−2.11809
$914$	34.0000	1.12462
$915$	0	0
$916$	−1.00000	−0.0330409
$917$	20.0000	0.660458
$918$	0	0
$919$	32.0000	1.05558	0.527791	−	0.849374i	$-0.323020\pi$
$919$	32.0000	1.05558	0.527791	+	0.849374i	$0.323020\pi$
$920$	0	0
$921$	0	0
$922$	−2.00000	−0.0658665
$923$	0	0
$924$	0	0
$925$	−2.00000	−0.0657596
$926$	4.00000	0.131448
$927$	−12.0000	−0.394132
$928$	−50.0000	−1.64133
$929$	10.0000	0.328089	0.164045	−	0.986453i	$-0.447546\pi$
$929$	10.0000	0.328089	0.164045	+	0.986453i	$0.447546\pi$
$930$	0	0
$931$	−4.00000	−0.131095
$932$	−10.0000	−0.327561
$933$	0	0
$934$	0	0
$935$	24.0000	0.784884
$936$	18.0000	0.588348
$937$	−58.0000	−1.89478	−0.947389	−	0.320085i	$-0.896288\pi$
$937$	−58.0000	−1.89478	−0.947389	+	0.320085i	$0.896288\pi$
$938$	−4.00000	−0.130605
$939$	0	0
$940$	−8.00000	−0.260931
$941$	30.0000	0.977972	0.488986	−	0.872292i	$-0.337367\pi$
$941$	30.0000	0.977972	0.488986	+	0.872292i	$0.337367\pi$
$942$	0	0
$943$	0	0
$944$	−12.0000	−0.390567
$945$	0	0
$946$	−32.0000	−1.04041
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	0	0
$949$	28.0000	0.908918
$950$	−4.00000	−0.129777
$951$	0	0
$952$	18.0000	0.583383
$953$	34.0000	1.10137	0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000	1.10137	0.550684	+	0.834714i	$0.314367\pi$
$954$	−18.0000	−0.582772
$955$	0	0
$956$	−24.0000	−0.776215
$957$	0	0
$958$	24.0000	0.775405
$959$	−2.00000	−0.0645834
$960$	0	0
$961$	33.0000	1.06452
$962$	−4.00000	−0.128965
$963$	36.0000	1.16008
$964$	−18.0000	−0.579741
$965$	−14.0000	−0.450676
$966$	0	0
$967$	4.00000	0.128631	0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000	0.128631	0.0643157	+	0.997930i	$0.479514\pi$
$968$	−15.0000	−0.482118
$969$	0	0
$970$	2.00000	0.0642161
$971$	−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
$973$	20.0000	0.641171
$974$	−8.00000	−0.256337
$975$	0	0
$976$	2.00000	0.0640184
$977$	34.0000	1.08776	0.543878	−	0.839164i	$-0.316955\pi$
$977$	34.0000	1.08776	0.543878	+	0.839164i	$0.316955\pi$
$978$	0	0
$979$	24.0000	0.767043
$980$	−1.00000	−0.0319438
$981$	6.00000	0.191565
$982$	−28.0000	−0.893516
$983$	32.0000	1.02064	0.510321	−	0.859984i	$-0.329527\pi$
$983$	32.0000	1.02064	0.510321	+	0.859984i	$0.329527\pi$
$984$	0	0
$985$	−22.0000	−0.700978
$986$	60.0000	1.91079
$987$	0	0
$988$	8.00000	0.254514
$989$	0	0
$990$	12.0000	0.381385
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	40.0000	1.27000
$993$	0	0
$994$	0	0
$995$	−16.0000	−0.507234
$996$	0	0
$997$	−2.00000	−0.0633406	−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000	−0.0633406	−0.0316703	+	0.999498i	$0.510083\pi$
$998$	−20.0000	−0.633089
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.d.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.d.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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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