LMFDB - Embedded newform 1815.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,2,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, 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("1815.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1815.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:	$14.4928479669$
Analytic rank:	$1$
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	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+1.00000 q^{3} -2.00000 q^{4} -1.00000 q^{5} +1.00000 q^{7} +1.00000 q^{9} -2.00000 q^{12} -2.00000 q^{13} -1.00000 q^{15} +4.00000 q^{16} -6.00000 q^{17} +7.00000 q^{19} +2.00000 q^{20} +1.00000 q^{21} -6.00000 q^{23} +1.00000 q^{25} +1.00000 q^{27} -2.00000 q^{28} -1.00000 q^{31} -1.00000 q^{35} -2.00000 q^{36} -7.00000 q^{37} -2.00000 q^{39} +6.00000 q^{41} -8.00000 q^{43} -1.00000 q^{45} +4.00000 q^{48} -6.00000 q^{49} -6.00000 q^{51} +4.00000 q^{52} -6.00000 q^{53} +7.00000 q^{57} -12.0000 q^{59} +2.00000 q^{60} +1.00000 q^{61} +1.00000 q^{63} -8.00000 q^{64} +2.00000 q^{65} -7.00000 q^{67} +12.0000 q^{68} -6.00000 q^{69} +6.00000 q^{71} +13.0000 q^{73} +1.00000 q^{75} -14.0000 q^{76} -11.0000 q^{79} -4.00000 q^{80} +1.00000 q^{81} -2.00000 q^{84} +6.00000 q^{85} -18.0000 q^{89} -2.00000 q^{91} +12.0000 q^{92} -1.00000 q^{93} -7.00000 q^{95} -1.00000 q^{97} +O(q^{100})$

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	$0.5\pi$
$3$	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
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0
$11$	0	0
$12$	−2.00000	−0.577350
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	4.00000	1.00000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	0	0
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	2.00000	0.447214
$21$	1.00000	0.218218
$22$	0	0
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	1.00000	0.192450
$28$	−2.00000	−0.377964
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	−1.00000	−0.179605	−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000	−0.179605	−0.0898027	+	0.995960i	$0.528624\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	−1.00000	−0.169031
$36$	−2.00000	−0.333333
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	0	0
$39$	−2.00000	−0.320256
$40$	0	0
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	4.00000	0.577350
$49$	−6.00000	−0.857143
$50$	0	0
$51$	−6.00000	−0.840168
$52$	4.00000	0.554700
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	7.00000	0.927173
$58$	0	0
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	2.00000	0.258199
$61$	1.00000	0.128037	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000	0.128037	0.0640184	+	0.997949i	$0.479608\pi$
$62$	0	0
$63$	1.00000	0.125988
$64$	−8.00000	−1.00000
$65$	2.00000	0.248069
$66$	0	0
$67$	−7.00000	−0.855186	−0.427593	−	0.903971i	$-0.640638\pi$
$67$	−7.00000	−0.855186	−0.427593	+	0.903971i	$0.640638\pi$
$68$	12.0000	1.45521
$69$	−6.00000	−0.722315
$70$	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
$73$	13.0000	1.52153	0.760767	−	0.649025i	$-0.224823\pi$
$73$	13.0000	1.52153	0.760767	+	0.649025i	$0.224823\pi$
$74$	0	0
$75$	1.00000	0.115470
$76$	−14.0000	−1.60591
$77$	0	0
$78$	0	0
$79$	−11.0000	−1.23760	−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000	−1.23760	−0.618798	+	0.785550i	$0.712380\pi$
$80$	−4.00000	−0.447214
$81$	1.00000	0.111111
$82$	0	0
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	−2.00000	−0.218218
$85$	6.00000	0.650791
$86$	0	0
$87$	0	0
$88$	0	0
$89$	−18.0000	−1.90800	−0.953998	−	0.299813i	$-0.903076\pi$
$89$	−18.0000	−1.90800	−0.953998	+	0.299813i	$0.903076\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	12.0000	1.25109
$93$	−1.00000	−0.103695
$94$	0	0
$95$	−7.00000	−0.718185
$96$	0	0
$97$	−1.00000	−0.101535	−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000	−0.101535	−0.0507673	+	0.998711i	$0.516167\pi$
$98$	0	0
$99$	0	0
$100$	−2.00000	−0.200000
$101$	12.0000	1.19404	0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000	1.19404	0.597022	+	0.802225i	$0.296350\pi$
$102$	0	0
$103$	−1.00000	−0.0985329	−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000	−0.0985329	−0.0492665	+	0.998786i	$0.515688\pi$
$104$	0	0
$105$	−1.00000	−0.0975900
$106$	0	0
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	−2.00000	−0.192450
$109$	7.00000	0.670478	0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000	0.670478	0.335239	+	0.942133i	$0.391183\pi$
$110$	0	0
$111$	−7.00000	−0.664411
$112$	4.00000	0.377964
$113$	−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
$115$	6.00000	0.559503
$116$	0	0
$117$	−2.00000	−0.184900
$118$	0	0
$119$	−6.00000	−0.550019
$120$	0	0
$121$	0	0
$122$	0	0
$123$	6.00000	0.541002
$124$	2.00000	0.179605
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−17.0000	−1.50851	−0.754253	−	0.656584i	$-0.772001\pi$
$127$	−17.0000	−1.50851	−0.754253	+	0.656584i	$0.772001\pi$
$128$	0	0
$129$	−8.00000	−0.704361
$130$	0	0
$131$	−18.0000	−1.57267	−0.786334	−	0.617802i	$-0.788023\pi$
$131$	−18.0000	−1.57267	−0.786334	+	0.617802i	$0.788023\pi$
$132$	0	0
$133$	7.00000	0.606977
$134$	0	0
$135$	−1.00000	−0.0860663
$136$	0	0
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	0	0
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	2.00000	0.169031
$141$	0	0
$142$	0	0
$143$	0	0
$144$	4.00000	0.333333
$145$	0	0
$146$	0	0
$147$	−6.00000	−0.494872
$148$	14.0000	1.15079
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	16.0000	1.30206	0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000	1.30206	0.651031	+	0.759051i	$0.274337\pi$
$152$	0	0
$153$	−6.00000	−0.485071
$154$	0	0
$155$	1.00000	0.0803219
$156$	4.00000	0.320256
$157$	17.0000	1.35675	0.678374	−	0.734717i	$-0.262685\pi$
$157$	17.0000	1.35675	0.678374	+	0.734717i	$0.262685\pi$
$158$	0	0
$159$	−6.00000	−0.475831
$160$	0	0
$161$	−6.00000	−0.472866
$162$	0	0
$163$	−1.00000	−0.0783260	−0.0391630	−	0.999233i	$-0.512469\pi$
$163$	−1.00000	−0.0783260	−0.0391630	+	0.999233i	$0.512469\pi$
$164$	−12.0000	−0.937043
$165$	0	0
$166$	0	0
$167$	6.00000	0.464294	0.232147	−	0.972681i	$-0.425425\pi$
$167$	6.00000	0.464294	0.232147	+	0.972681i	$0.425425\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	7.00000	0.535303
$172$	16.0000	1.21999
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	0	0
$177$	−12.0000	−0.901975
$178$	0	0
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	2.00000	0.149071
$181$	17.0000	1.26360	0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000	1.26360	0.631800	+	0.775131i	$0.282316\pi$
$182$	0	0
$183$	1.00000	0.0739221
$184$	0	0
$185$	7.00000	0.514650
$186$	0	0
$187$	0	0
$188$	0	0
$189$	1.00000	0.0727393
$190$	0	0
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	−8.00000	−0.577350
$193$	−5.00000	−0.359908	−0.179954	−	0.983675i	$-0.557595\pi$
$193$	−5.00000	−0.359908	−0.179954	+	0.983675i	$0.557595\pi$
$194$	0	0
$195$	2.00000	0.143223
$196$	12.0000	0.857143
$197$	24.0000	1.70993	0.854965	−	0.518686i	$-0.173579\pi$
$197$	24.0000	1.70993	0.854965	+	0.518686i	$0.173579\pi$
$198$	0	0
$199$	11.0000	0.779769	0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000	0.779769	0.389885	+	0.920864i	$0.372515\pi$
$200$	0	0
$201$	−7.00000	−0.493742
$202$	0	0
$203$	0	0
$204$	12.0000	0.840168
$205$	−6.00000	−0.419058
$206$	0	0
$207$	−6.00000	−0.417029
$208$	−8.00000	−0.554700
$209$	0	0
$210$	0	0
$211$	−23.0000	−1.58339	−0.791693	−	0.610920i	$-0.790800\pi$
$211$	−23.0000	−1.58339	−0.791693	+	0.610920i	$0.790800\pi$
$212$	12.0000	0.824163
$213$	6.00000	0.411113
$214$	0	0
$215$	8.00000	0.545595
$216$	0	0
$217$	−1.00000	−0.0678844
$218$	0	0
$219$	13.0000	0.878459
$220$	0	0
$221$	12.0000	0.807207
$222$	0	0
$223$	29.0000	1.94198	0.970992	−	0.239113i	$-0.0768565\pi$
$223$	29.0000	1.94198	0.970992	+	0.239113i	$0.0768565\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	0	0
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	−14.0000	−0.927173
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−24.0000	−1.57229	−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000	−1.57229	−0.786146	+	0.618041i	$0.787927\pi$
$234$	0	0
$235$	0	0
$236$	24.0000	1.56227
$237$	−11.0000	−0.714527
$238$	0	0
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	−4.00000	−0.258199
$241$	22.0000	1.41714	0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000	1.41714	0.708572	+	0.705638i	$0.249340\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	6.00000	0.383326
$246$	0	0
$247$	−14.0000	−0.890799
$248$	0	0
$249$	0	0
$250$	0	0
$251$	6.00000	0.378717	0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000	0.378717	0.189358	+	0.981908i	$0.439359\pi$
$252$	−2.00000	−0.125988
$253$	0	0
$254$	0	0
$255$	6.00000	0.375735
$256$	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
$259$	−7.00000	−0.434959
$260$	−4.00000	−0.248069
$261$	0	0
$262$	0	0
$263$	6.00000	0.369976	0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000	0.369976	0.184988	+	0.982741i	$0.440775\pi$
$264$	0	0
$265$	6.00000	0.368577
$266$	0	0
$267$	−18.0000	−1.10158
$268$	14.0000	0.855186
$269$	−24.0000	−1.46331	−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000	−1.46331	−0.731653	+	0.681677i	$0.761251\pi$
$270$	0	0
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	−24.0000	−1.45521
$273$	−2.00000	−0.121046
$274$	0	0
$275$	0	0
$276$	12.0000	0.722315
$277$	−11.0000	−0.660926	−0.330463	−	0.943819i	$-0.607205\pi$
$277$	−11.0000	−0.660926	−0.330463	+	0.943819i	$0.607205\pi$
$278$	0	0
$279$	−1.00000	−0.0598684
$280$	0	0
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	0	0
$283$	1.00000	0.0594438	0.0297219	−	0.999558i	$-0.490538\pi$
$283$	1.00000	0.0594438	0.0297219	+	0.999558i	$0.490538\pi$
$284$	−12.0000	−0.712069
$285$	−7.00000	−0.414644
$286$	0	0
$287$	6.00000	0.354169
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	−1.00000	−0.0586210
$292$	−26.0000	−1.52153
$293$	−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
$296$	0	0
$297$	0	0
$298$	0	0
$299$	12.0000	0.693978
$300$	−2.00000	−0.115470
$301$	−8.00000	−0.461112
$302$	0	0
$303$	12.0000	0.689382
$304$	28.0000	1.60591
$305$	−1.00000	−0.0572598
$306$	0	0
$307$	13.0000	0.741949	0.370975	−	0.928643i	$-0.379024\pi$
$307$	13.0000	0.741949	0.370975	+	0.928643i	$0.379024\pi$
$308$	0	0
$309$	−1.00000	−0.0568880
$310$	0	0
$311$	−30.0000	−1.70114	−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000	−1.70114	−0.850572	+	0.525859i	$0.823744\pi$
$312$	0	0
$313$	−22.0000	−1.24351	−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000	−1.24351	−0.621757	+	0.783210i	$0.713581\pi$
$314$	0	0
$315$	−1.00000	−0.0563436
$316$	22.0000	1.23760
$317$	−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
$319$	0	0
$320$	8.00000	0.447214
$321$	−12.0000	−0.669775
$322$	0	0
$323$	−42.0000	−2.33694
$324$	−2.00000	−0.111111
$325$	−2.00000	−0.110940
$326$	0	0
$327$	7.00000	0.387101
$328$	0	0
$329$	0	0
$330$	0	0
$331$	29.0000	1.59398	0.796992	−	0.603990i	$-0.206423\pi$
$331$	29.0000	1.59398	0.796992	+	0.603990i	$0.206423\pi$
$332$	0	0
$333$	−7.00000	−0.383598
$334$	0	0
$335$	7.00000	0.382451
$336$	4.00000	0.218218
$337$	13.0000	0.708155	0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000	0.708155	0.354078	+	0.935216i	$0.384795\pi$
$338$	0	0
$339$	−12.0000	−0.651751
$340$	−12.0000	−0.650791
$341$	0	0
$342$	0	0
$343$	−13.0000	−0.701934
$344$	0	0
$345$	6.00000	0.323029
$346$	0	0
$347$	30.0000	1.61048	0.805242	−	0.592946i	$-0.202035\pi$
$347$	30.0000	1.61048	0.805242	+	0.592946i	$0.202035\pi$
$348$	0	0
$349$	−35.0000	−1.87351	−0.936754	−	0.349990i	$-0.886185\pi$
$349$	−35.0000	−1.87351	−0.936754	+	0.349990i	$0.886185\pi$
$350$	0	0
$351$	−2.00000	−0.106752
$352$	0	0
$353$	−6.00000	−0.319348	−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000	−0.319348	−0.159674	+	0.987170i	$0.551044\pi$
$354$	0	0
$355$	−6.00000	−0.318447
$356$	36.0000	1.90800
$357$	−6.00000	−0.317554
$358$	0	0
$359$	−6.00000	−0.316668	−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000	−0.316668	−0.158334	+	0.987386i	$0.550612\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	0	0
$363$	0	0
$364$	4.00000	0.209657
$365$	−13.0000	−0.680451
$366$	0	0
$367$	−4.00000	−0.208798	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−4.00000	−0.208798	−0.104399	+	0.994535i	$0.533292\pi$
$368$	−24.0000	−1.25109
$369$	6.00000	0.312348
$370$	0	0
$371$	−6.00000	−0.311504
$372$	2.00000	0.103695
$373$	31.0000	1.60512	0.802560	−	0.596572i	$-0.203471\pi$
$373$	31.0000	1.60512	0.802560	+	0.596572i	$0.203471\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	0	0
$377$	0	0
$378$	0	0
$379$	8.00000	0.410932	0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000	0.410932	0.205466	+	0.978664i	$0.434129\pi$
$380$	14.0000	0.718185
$381$	−17.0000	−0.870936
$382$	0	0
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−8.00000	−0.406663
$388$	2.00000	0.101535
$389$	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
$391$	36.0000	1.82060
$392$	0	0
$393$	−18.0000	−0.907980
$394$	0	0
$395$	11.0000	0.553470
$396$	0	0
$397$	−7.00000	−0.351320	−0.175660	−	0.984451i	$-0.556206\pi$
$397$	−7.00000	−0.351320	−0.175660	+	0.984451i	$0.556206\pi$
$398$	0	0
$399$	7.00000	0.350438
$400$	4.00000	0.200000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	0	0
$403$	2.00000	0.0996271
$404$	−24.0000	−1.19404
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	0	0
$408$	0	0
$409$	−5.00000	−0.247234	−0.123617	−	0.992330i	$-0.539449\pi$
$409$	−5.00000	−0.247234	−0.123617	+	0.992330i	$0.539449\pi$
$410$	0	0
$411$	−12.0000	−0.591916
$412$	2.00000	0.0985329
$413$	−12.0000	−0.590481
$414$	0	0
$415$	0	0
$416$	0	0
$417$	4.00000	0.195881
$418$	0	0
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	2.00000	0.0975900
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	0	0
$423$	0	0
$424$	0	0
$425$	−6.00000	−0.291043
$426$	0	0
$427$	1.00000	0.0483934
$428$	24.0000	1.16008
$429$	0	0
$430$	0	0
$431$	6.00000	0.289010	0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000	0.289010	0.144505	+	0.989504i	$0.453841\pi$
$432$	4.00000	0.192450
$433$	5.00000	0.240285	0.120142	−	0.992757i	$-0.461665\pi$
$433$	5.00000	0.240285	0.120142	+	0.992757i	$0.461665\pi$
$434$	0	0
$435$	0	0
$436$	−14.0000	−0.670478
$437$	−42.0000	−2.00913
$438$	0	0
$439$	19.0000	0.906821	0.453410	−	0.891302i	$-0.350207\pi$
$439$	19.0000	0.906821	0.453410	+	0.891302i	$0.350207\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	0	0
$443$	−18.0000	−0.855206	−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000	−0.855206	−0.427603	+	0.903967i	$0.640642\pi$
$444$	14.0000	0.664411
$445$	18.0000	0.853282
$446$	0	0
$447$	−6.00000	−0.283790
$448$	−8.00000	−0.377964
$449$	−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
$452$	24.0000	1.12887
$453$	16.0000	0.751746
$454$	0	0
$455$	2.00000	0.0937614
$456$	0	0
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	0	0
$459$	−6.00000	−0.280056
$460$	−12.0000	−0.559503
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	0	0
$463$	32.0000	1.48717	0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000	1.48717	0.743583	+	0.668644i	$0.233125\pi$
$464$	0	0
$465$	1.00000	0.0463739
$466$	0	0
$467$	−42.0000	−1.94353	−0.971764	−	0.235954i	$-0.924178\pi$
$467$	−42.0000	−1.94353	−0.971764	+	0.235954i	$0.924178\pi$
$468$	4.00000	0.184900
$469$	−7.00000	−0.323230
$470$	0	0
$471$	17.0000	0.783319
$472$	0	0
$473$	0	0
$474$	0	0
$475$	7.00000	0.321182
$476$	12.0000	0.550019
$477$	−6.00000	−0.274721
$478$	0	0
$479$	−24.0000	−1.09659	−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000	−1.09659	−0.548294	+	0.836286i	$0.684723\pi$
$480$	0	0
$481$	14.0000	0.638345
$482$	0	0
$483$	−6.00000	−0.273009
$484$	0	0
$485$	1.00000	0.0454077
$486$	0	0
$487$	8.00000	0.362515	0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000	0.362515	0.181257	+	0.983436i	$0.441983\pi$
$488$	0	0
$489$	−1.00000	−0.0452216
$490$	0	0
$491$	−42.0000	−1.89543	−0.947717	−	0.319113i	$-0.896615\pi$
$491$	−42.0000	−1.89543	−0.947717	+	0.319113i	$0.896615\pi$
$492$	−12.0000	−0.541002
$493$	0	0
$494$	0	0
$495$	0	0
$496$	−4.00000	−0.179605
$497$	6.00000	0.269137
$498$	0	0
$499$	23.0000	1.02962	0.514811	−	0.857304i	$-0.327862\pi$
$499$	23.0000	1.02962	0.514811	+	0.857304i	$0.327862\pi$
$500$	2.00000	0.0894427
$501$	6.00000	0.268060
$502$	0	0
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	0	0
$505$	−12.0000	−0.533993
$506$	0	0
$507$	−9.00000	−0.399704
$508$	34.0000	1.50851
$509$	24.0000	1.06378	0.531891	−	0.846813i	$-0.321482\pi$
$509$	24.0000	1.06378	0.531891	+	0.846813i	$0.321482\pi$
$510$	0	0
$511$	13.0000	0.575086
$512$	0	0
$513$	7.00000	0.309058
$514$	0	0
$515$	1.00000	0.0440653
$516$	16.0000	0.704361
$517$	0	0
$518$	0	0
$519$	6.00000	0.263371
$520$	0	0
$521$	0	0		−	1.00000i	$-0.5\pi$
$521$	0	0			1.00000i	$0.5\pi$
$522$	0	0
$523$	25.0000	1.09317	0.546587	−	0.837402i	$-0.315927\pi$
$523$	25.0000	1.09317	0.546587	+	0.837402i	$0.315927\pi$
$524$	36.0000	1.57267
$525$	1.00000	0.0436436
$526$	0	0
$527$	6.00000	0.261364
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	−12.0000	−0.520756
$532$	−14.0000	−0.606977
$533$	−12.0000	−0.519778
$534$	0	0
$535$	12.0000	0.518805
$536$	0	0
$537$	−12.0000	−0.517838
$538$	0	0
$539$	0	0
$540$	2.00000	0.0860663
$541$	−14.0000	−0.601907	−0.300954	−	0.953639i	$-0.597305\pi$
$541$	−14.0000	−0.601907	−0.300954	+	0.953639i	$0.597305\pi$
$542$	0	0
$543$	17.0000	0.729540
$544$	0	0
$545$	−7.00000	−0.299847
$546$	0	0
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	24.0000	1.02523
$549$	1.00000	0.0426790
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−11.0000	−0.467768
$554$	0	0
$555$	7.00000	0.297133
$556$	−8.00000	−0.339276
$557$	42.0000	1.77960	0.889799	−	0.456354i	$-0.150845\pi$
$557$	42.0000	1.77960	0.889799	+	0.456354i	$0.150845\pi$
$558$	0	0
$559$	16.0000	0.676728
$560$	−4.00000	−0.169031
$561$	0	0
$562$	0	0
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	0	0
$565$	12.0000	0.504844
$566$	0	0
$567$	1.00000	0.0419961
$568$	0	0
$569$	0	0		−	1.00000i	$-0.5\pi$
$569$	0	0			1.00000i	$0.5\pi$
$570$	0	0
$571$	−23.0000	−0.962520	−0.481260	−	0.876578i	$-0.659821\pi$
$571$	−23.0000	−0.962520	−0.481260	+	0.876578i	$0.659821\pi$
$572$	0	0
$573$	12.0000	0.501307
$574$	0	0
$575$	−6.00000	−0.250217
$576$	−8.00000	−0.333333
$577$	−43.0000	−1.79011	−0.895057	−	0.445952i	$-0.852865\pi$
$577$	−43.0000	−1.79011	−0.895057	+	0.445952i	$0.852865\pi$
$578$	0	0
$579$	−5.00000	−0.207793
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	0	0
$585$	2.00000	0.0826898
$586$	0	0
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	12.0000	0.494872
$589$	−7.00000	−0.288430
$590$	0	0
$591$	24.0000	0.987228
$592$	−28.0000	−1.15079
$593$	42.0000	1.72473	0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000	1.72473	0.862367	+	0.506284i	$0.168981\pi$
$594$	0	0
$595$	6.00000	0.245976
$596$	12.0000	0.491539
$597$	11.0000	0.450200
$598$	0	0
$599$	42.0000	1.71607	0.858037	−	0.513588i	$-0.171684\pi$
$599$	42.0000	1.71607	0.858037	+	0.513588i	$0.171684\pi$
$600$	0	0
$601$	−11.0000	−0.448699	−0.224350	−	0.974509i	$-0.572026\pi$
$601$	−11.0000	−0.448699	−0.224350	+	0.974509i	$0.572026\pi$
$602$	0	0
$603$	−7.00000	−0.285062
$604$	−32.0000	−1.30206
$605$	0	0
$606$	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
$609$	0	0
$610$	0	0
$611$	0	0
$612$	12.0000	0.485071
$613$	−5.00000	−0.201948	−0.100974	−	0.994889i	$-0.532196\pi$
$613$	−5.00000	−0.201948	−0.100974	+	0.994889i	$0.532196\pi$
$614$	0	0
$615$	−6.00000	−0.241943
$616$	0	0
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	0	0
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	−2.00000	−0.0803219
$621$	−6.00000	−0.240772
$622$	0	0
$623$	−18.0000	−0.721155
$624$	−8.00000	−0.320256
$625$	1.00000	0.0400000
$626$	0	0
$627$	0	0
$628$	−34.0000	−1.35675
$629$	42.0000	1.67465
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	0	0
$633$	−23.0000	−0.914168
$634$	0	0
$635$	17.0000	0.674624
$636$	12.0000	0.475831
$637$	12.0000	0.475457
$638$	0	0
$639$	6.00000	0.237356
$640$	0	0
$641$	30.0000	1.18493	0.592464	−	0.805597i	$-0.298155\pi$
$641$	30.0000	1.18493	0.592464	+	0.805597i	$0.298155\pi$
$642$	0	0
$643$	29.0000	1.14365	0.571824	−	0.820376i	$-0.306236\pi$
$643$	29.0000	1.14365	0.571824	+	0.820376i	$0.306236\pi$
$644$	12.0000	0.472866
$645$	8.00000	0.315000
$646$	0	0
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−1.00000	−0.0391931
$652$	2.00000	0.0783260
$653$	−42.0000	−1.64359	−0.821794	−	0.569785i	$-0.807026\pi$
$653$	−42.0000	−1.64359	−0.821794	+	0.569785i	$0.807026\pi$
$654$	0	0
$655$	18.0000	0.703318
$656$	24.0000	0.937043
$657$	13.0000	0.507178
$658$	0	0
$659$	−6.00000	−0.233727	−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000	−0.233727	−0.116863	+	0.993148i	$0.537284\pi$
$660$	0	0
$661$	−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
$663$	12.0000	0.466041
$664$	0	0
$665$	−7.00000	−0.271448
$666$	0	0
$667$	0	0
$668$	−12.0000	−0.464294
$669$	29.0000	1.12120
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−29.0000	−1.11787	−0.558934	−	0.829212i	$-0.688789\pi$
$673$	−29.0000	−1.11787	−0.558934	+	0.829212i	$0.688789\pi$
$674$	0	0
$675$	1.00000	0.0384900
$676$	18.0000	0.692308
$677$	−48.0000	−1.84479	−0.922395	−	0.386248i	$-0.873771\pi$
$677$	−48.0000	−1.84479	−0.922395	+	0.386248i	$0.873771\pi$
$678$	0	0
$679$	−1.00000	−0.0383765
$680$	0	0
$681$	12.0000	0.459841
$682$	0	0
$683$	−30.0000	−1.14792	−0.573959	−	0.818884i	$-0.694593\pi$
$683$	−30.0000	−1.14792	−0.573959	+	0.818884i	$0.694593\pi$
$684$	−14.0000	−0.535303
$685$	12.0000	0.458496
$686$	0	0
$687$	14.0000	0.534133
$688$	−32.0000	−1.21999
$689$	12.0000	0.457164
$690$	0	0
$691$	−13.0000	−0.494543	−0.247272	−	0.968946i	$-0.579534\pi$
$691$	−13.0000	−0.494543	−0.247272	+	0.968946i	$0.579534\pi$
$692$	−12.0000	−0.456172
$693$	0	0
$694$	0	0
$695$	−4.00000	−0.151729
$696$	0	0
$697$	−36.0000	−1.36360
$698$	0	0
$699$	−24.0000	−0.907763
$700$	−2.00000	−0.0755929
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	0	0
$703$	−49.0000	−1.84807
$704$	0	0
$705$	0	0
$706$	0	0
$707$	12.0000	0.451306
$708$	24.0000	0.901975
$709$	−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
$711$	−11.0000	−0.412532
$712$	0	0
$713$	6.00000	0.224702
$714$	0	0
$715$	0	0
$716$	24.0000	0.896922
$717$	12.0000	0.448148
$718$	0	0
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	−4.00000	−0.149071
$721$	−1.00000	−0.0372419
$722$	0	0
$723$	22.0000	0.818189
$724$	−34.0000	−1.26360
$725$	0	0
$726$	0	0
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	48.0000	1.77534
$732$	−2.00000	−0.0739221
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	0	0
$735$	6.00000	0.221313
$736$	0	0
$737$	0	0
$738$	0	0
$739$	19.0000	0.698926	0.349463	−	0.936950i	$-0.386364\pi$
$739$	19.0000	0.698926	0.349463	+	0.936950i	$0.386364\pi$
$740$	−14.0000	−0.514650
$741$	−14.0000	−0.514303
$742$	0	0
$743$	36.0000	1.32071	0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000	1.32071	0.660356	+	0.750953i	$0.270405\pi$
$744$	0	0
$745$	6.00000	0.219823
$746$	0	0
$747$	0	0
$748$	0	0
$749$	−12.0000	−0.438470
$750$	0	0
$751$	−37.0000	−1.35015	−0.675075	−	0.737749i	$-0.735889\pi$
$751$	−37.0000	−1.35015	−0.675075	+	0.737749i	$0.735889\pi$
$752$	0	0
$753$	6.00000	0.218652
$754$	0	0
$755$	−16.0000	−0.582300
$756$	−2.00000	−0.0727393
$757$	−25.0000	−0.908640	−0.454320	−	0.890838i	$-0.650118\pi$
$757$	−25.0000	−0.908640	−0.454320	+	0.890838i	$0.650118\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	0	0
$763$	7.00000	0.253417
$764$	−24.0000	−0.868290
$765$	6.00000	0.216930
$766$	0	0
$767$	24.0000	0.866590
$768$	16.0000	0.577350
$769$	25.0000	0.901523	0.450762	−	0.892644i	$-0.351152\pi$
$769$	25.0000	0.901523	0.450762	+	0.892644i	$0.351152\pi$
$770$	0	0
$771$	−6.00000	−0.216085
$772$	10.0000	0.359908
$773$	12.0000	0.431610	0.215805	−	0.976436i	$-0.430762\pi$
$773$	12.0000	0.431610	0.215805	+	0.976436i	$0.430762\pi$
$774$	0	0
$775$	−1.00000	−0.0359211
$776$	0	0
$777$	−7.00000	−0.251124
$778$	0	0
$779$	42.0000	1.50481
$780$	−4.00000	−0.143223
$781$	0	0
$782$	0	0
$783$	0	0
$784$	−24.0000	−0.857143
$785$	−17.0000	−0.606756
$786$	0	0
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	−48.0000	−1.70993
$789$	6.00000	0.213606
$790$	0	0
$791$	−12.0000	−0.426671
$792$	0	0
$793$	−2.00000	−0.0710221
$794$	0	0
$795$	6.00000	0.212798
$796$	−22.0000	−0.779769
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−18.0000	−0.635999
$802$	0	0
$803$	0	0
$804$	14.0000	0.493742
$805$	6.00000	0.211472
$806$	0	0
$807$	−24.0000	−0.844840
$808$	0	0
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	0	0
$811$	−11.0000	−0.386262	−0.193131	−	0.981173i	$-0.561864\pi$
$811$	−11.0000	−0.386262	−0.193131	+	0.981173i	$0.561864\pi$
$812$	0	0
$813$	−20.0000	−0.701431
$814$	0	0
$815$	1.00000	0.0350285
$816$	−24.0000	−0.840168
$817$	−56.0000	−1.95919
$818$	0	0
$819$	−2.00000	−0.0698857
$820$	12.0000	0.419058
$821$	42.0000	1.46581	0.732905	−	0.680331i	$-0.238164\pi$
$821$	42.0000	1.46581	0.732905	+	0.680331i	$0.238164\pi$
$822$	0	0
$823$	−13.0000	−0.453152	−0.226576	−	0.973994i	$-0.572753\pi$
$823$	−13.0000	−0.453152	−0.226576	+	0.973994i	$0.572753\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	12.0000	0.417029
$829$	−7.00000	−0.243120	−0.121560	−	0.992584i	$-0.538790\pi$
$829$	−7.00000	−0.243120	−0.121560	+	0.992584i	$0.538790\pi$
$830$	0	0
$831$	−11.0000	−0.381586
$832$	16.0000	0.554700
$833$	36.0000	1.24733
$834$	0	0
$835$	−6.00000	−0.207639
$836$	0	0
$837$	−1.00000	−0.0345651
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	0	0
$843$	30.0000	1.03325
$844$	46.0000	1.58339
$845$	9.00000	0.309609
$846$	0	0
$847$	0	0
$848$	−24.0000	−0.824163
$849$	1.00000	0.0343199
$850$	0	0
$851$	42.0000	1.43974
$852$	−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
$855$	−7.00000	−0.239395
$856$	0	0
$857$	−54.0000	−1.84460	−0.922302	−	0.386469i	$-0.873695\pi$
$857$	−54.0000	−1.84460	−0.922302	+	0.386469i	$0.873695\pi$
$858$	0	0
$859$	−49.0000	−1.67186	−0.835929	−	0.548837i	$-0.815071\pi$
$859$	−49.0000	−1.67186	−0.835929	+	0.548837i	$0.815071\pi$
$860$	−16.0000	−0.545595
$861$	6.00000	0.204479
$862$	0	0
$863$	−36.0000	−1.22545	−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000	−1.22545	−0.612727	+	0.790295i	$0.709928\pi$
$864$	0	0
$865$	−6.00000	−0.204006
$866$	0	0
$867$	19.0000	0.645274
$868$	2.00000	0.0678844
$869$	0	0
$870$	0	0
$871$	14.0000	0.474372
$872$	0	0
$873$	−1.00000	−0.0338449
$874$	0	0
$875$	−1.00000	−0.0338062
$876$	−26.0000	−0.878459
$877$	−5.00000	−0.168838	−0.0844190	−	0.996430i	$-0.526903\pi$
$877$	−5.00000	−0.168838	−0.0844190	+	0.996430i	$0.526903\pi$
$878$	0	0
$879$	−18.0000	−0.607125
$880$	0	0
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	0	0
$883$	−25.0000	−0.841317	−0.420658	−	0.907219i	$-0.638201\pi$
$883$	−25.0000	−0.841317	−0.420658	+	0.907219i	$0.638201\pi$
$884$	−24.0000	−0.807207
$885$	12.0000	0.403376
$886$	0	0
$887$	6.00000	0.201460	0.100730	−	0.994914i	$-0.467882\pi$
$887$	6.00000	0.201460	0.100730	+	0.994914i	$0.467882\pi$
$888$	0	0
$889$	−17.0000	−0.570162
$890$	0	0
$891$	0	0
$892$	−58.0000	−1.94198
$893$	0	0
$894$	0	0
$895$	12.0000	0.401116
$896$	0	0
$897$	12.0000	0.400668
$898$	0	0
$899$	0	0
$900$	−2.00000	−0.0666667
$901$	36.0000	1.19933
$902$	0	0
$903$	−8.00000	−0.266223
$904$	0	0
$905$	−17.0000	−0.565099
$906$	0	0
$907$	35.0000	1.16216	0.581078	−	0.813848i	$-0.302631\pi$
$907$	35.0000	1.16216	0.581078	+	0.813848i	$0.302631\pi$
$908$	−24.0000	−0.796468
$909$	12.0000	0.398015
$910$	0	0
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	28.0000	0.927173
$913$	0	0
$914$	0	0
$915$	−1.00000	−0.0330590
$916$	−28.0000	−0.925146
$917$	−18.0000	−0.594412
$918$	0	0
$919$	−11.0000	−0.362857	−0.181428	−	0.983404i	$-0.558072\pi$
$919$	−11.0000	−0.362857	−0.181428	+	0.983404i	$0.558072\pi$
$920$	0	0
$921$	13.0000	0.428365
$922$	0	0
$923$	−12.0000	−0.394985
$924$	0	0
$925$	−7.00000	−0.230159
$926$	0	0
$927$	−1.00000	−0.0328443
$928$	0	0
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	0	0
$931$	−42.0000	−1.37649
$932$	48.0000	1.57229
$933$	−30.0000	−0.982156
$934$	0	0
$935$	0	0
$936$	0	0
$937$	43.0000	1.40475	0.702374	−	0.711808i	$-0.252123\pi$
$937$	43.0000	1.40475	0.702374	+	0.711808i	$0.252123\pi$
$938$	0	0
$939$	−22.0000	−0.717943
$940$	0	0
$941$	−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
$943$	−36.0000	−1.17232
$944$	−48.0000	−1.56227
$945$	−1.00000	−0.0325300
$946$	0	0
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	22.0000	0.714527
$949$	−26.0000	−0.843996
$950$	0	0
$951$	−6.00000	−0.194563
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	0	0
$955$	−12.0000	−0.388311
$956$	−24.0000	−0.776215
$957$	0	0
$958$	0	0
$959$	−12.0000	−0.387500
$960$	8.00000	0.258199
$961$	−30.0000	−0.967742
$962$	0	0
$963$	−12.0000	−0.386695
$964$	−44.0000	−1.41714
$965$	5.00000	0.160956
$966$	0	0
$967$	−23.0000	−0.739630	−0.369815	−	0.929105i	$-0.620579\pi$
$967$	−23.0000	−0.739630	−0.369815	+	0.929105i	$0.620579\pi$
$968$	0	0
$969$	−42.0000	−1.34923
$970$	0	0
$971$	18.0000	0.577647	0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000	0.577647	0.288824	+	0.957382i	$0.406736\pi$
$972$	−2.00000	−0.0641500
$973$	4.00000	0.128234
$974$	0	0
$975$	−2.00000	−0.0640513
$976$	4.00000	0.128037
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	0	0
$979$	0	0
$980$	−12.0000	−0.383326
$981$	7.00000	0.223493
$982$	0	0
$983$	−30.0000	−0.956851	−0.478426	−	0.878128i	$-0.658792\pi$
$983$	−30.0000	−0.956851	−0.478426	+	0.878128i	$0.658792\pi$
$984$	0	0
$985$	−24.0000	−0.764704
$986$	0	0
$987$	0	0
$988$	28.0000	0.890799
$989$	48.0000	1.52631
$990$	0	0
$991$	−40.0000	−1.27064	−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000	−1.27064	−0.635321	+	0.772248i	$0.719132\pi$
$992$	0	0
$993$	29.0000	0.920287
$994$	0	0
$995$	−11.0000	−0.348723
$996$	0	0
$997$	−41.0000	−1.29848	−0.649242	−	0.760582i	$-0.724914\pi$
$997$	−41.0000	−1.29848	−0.649242	+	0.760582i	$0.724914\pi$
$998$	0	0
$999$	−7.00000	−0.221470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.2.a.c.1.1	yes	1
3.2	odd	2		5445.2.a.g.1.1		1
5.4	even	2		9075.2.a.j.1.1		1
11.10	odd	2		1815.2.a.b.1.1	✓	1
33.32	even	2		5445.2.a.f.1.1		1
55.54	odd	2		9075.2.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.a.b.1.1	✓	1	11.10	odd	2
1815.2.a.c.1.1	yes	1	1.1	even	1	trivial
5445.2.a.f.1.1		1	33.32	even	2
5445.2.a.g.1.1		1	3.2	odd	2
9075.2.a.j.1.1		1	5.4	even	2
9075.2.a.k.1.1		1	55.54	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more