LMFDB - Embedded newform 1617.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, 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("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} +2.00000 q^{6} +1.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} +2.00000 q^{6} +1.00000 q^{9} -1.00000 q^{11} -2.00000 q^{12} -5.00000 q^{13} -4.00000 q^{16} +6.00000 q^{17} -2.00000 q^{18} +7.00000 q^{19} +2.00000 q^{22} -4.00000 q^{23} -5.00000 q^{25} +10.0000 q^{26} -1.00000 q^{27} -2.00000 q^{29} -7.00000 q^{31} +8.00000 q^{32} +1.00000 q^{33} -12.0000 q^{34} +2.00000 q^{36} +7.00000 q^{37} -14.0000 q^{38} +5.00000 q^{39} +4.00000 q^{41} -9.00000 q^{43} -2.00000 q^{44} +8.00000 q^{46} +6.00000 q^{47} +4.00000 q^{48} +10.0000 q^{50} -6.00000 q^{51} -10.0000 q^{52} -2.00000 q^{53} +2.00000 q^{54} -7.00000 q^{57} +4.00000 q^{58} +12.0000 q^{59} -2.00000 q^{61} +14.0000 q^{62} -8.00000 q^{64} -2.00000 q^{66} +7.00000 q^{67} +12.0000 q^{68} +4.00000 q^{69} +8.00000 q^{71} -5.00000 q^{73} -14.0000 q^{74} +5.00000 q^{75} +14.0000 q^{76} -10.0000 q^{78} -11.0000 q^{79} +1.00000 q^{81} -8.00000 q^{82} -4.00000 q^{83} +18.0000 q^{86} +2.00000 q^{87} +6.00000 q^{89} -8.00000 q^{92} +7.00000 q^{93} -12.0000 q^{94} -8.00000 q^{96} +2.00000 q^{97} -1.00000 q^{99} +O(q^{100})\)

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 $

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.00000	1.00000
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	2.00000	0.816497
$7$	0	0
$7$	0	0
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.00000	−0.577350
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	0	0
$15$	0	0
$16$	−4.00000	−1.00000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	−2.00000	−0.471405
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	0	0
$21$	0	0
$22$	2.00000	0.426401
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	10.0000	1.96116
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	8.00000	1.41421
$33$	1.00000	0.174078
$34$	−12.0000	−2.05798
$35$	0	0
$36$	2.00000	0.333333
$37$	7.00000	1.15079	0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000	1.15079	0.575396	+	0.817875i	$0.304848\pi$
$38$	−14.0000	−2.27110
$39$	5.00000	0.800641
$40$	0	0
$41$	4.00000	0.624695	0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000	0.624695	0.312348	+	0.949968i	$0.398885\pi$
$42$	0	0
$43$	−9.00000	−1.37249	−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000	−1.37249	−0.686244	+	0.727372i	$0.740742\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	8.00000	1.17954
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	4.00000	0.577350
$49$	0	0
$50$	10.0000	1.41421
$51$	−6.00000	−0.840168
$52$	−10.0000	−1.38675
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	2.00000	0.272166
$55$	0	0
$56$	0	0
$57$	−7.00000	−0.927173
$58$	4.00000	0.525226
$59$	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	$0.540868\pi$
$62$	14.0000	1.77800
$63$	0	0
$64$	−8.00000	−1.00000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	7.00000	0.855186	0.427593	−	0.903971i	$-0.359362\pi$
$67$	7.00000	0.855186	0.427593	+	0.903971i	$0.359362\pi$
$68$	12.0000	1.45521
$69$	4.00000	0.481543
$70$	0	0
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	0	0
$73$	−5.00000	−0.585206	−0.292603	−	0.956234i	$-0.594521\pi$
$73$	−5.00000	−0.585206	−0.292603	+	0.956234i	$0.594521\pi$
$74$	−14.0000	−1.62747
$75$	5.00000	0.577350
$76$	14.0000	1.60591
$77$	0	0
$78$	−10.0000	−1.13228
$79$	−11.0000	−1.23760	−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000	−1.23760	−0.618798	+	0.785550i	$0.712380\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−8.00000	−0.883452
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	0	0
$85$	0	0
$86$	18.0000	1.94099
$87$	2.00000	0.214423
$88$	0	0
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	0	0
$92$	−8.00000	−0.834058
$93$	7.00000	0.725866
$94$	−12.0000	−1.23771
$95$	0	0
$96$	−8.00000	−0.816497
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	−10.0000	−1.00000
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	12.0000	1.18818
$103$	−19.0000	−1.87213	−0.936063	−	0.351833i	$-0.885559\pi$
$103$	−19.0000	−1.87213	−0.936063	+	0.351833i	$0.885559\pi$
$104$	0	0
$105$	0	0
$106$	4.00000	0.388514
$107$	−20.0000	−1.93347	−0.966736	−	0.255774i	$-0.917670\pi$
$107$	−20.0000	−1.93347	−0.966736	+	0.255774i	$0.917670\pi$
$108$	−2.00000	−0.192450
$109$	−1.00000	−0.0957826	−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000	−0.0957826	−0.0478913	+	0.998853i	$0.515250\pi$
$110$	0	0
$111$	−7.00000	−0.664411
$112$	0	0
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	14.0000	1.31122
$115$	0	0
$116$	−4.00000	−0.371391
$117$	−5.00000	−0.462250
$118$	−24.0000	−2.20938
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	4.00000	0.362143
$123$	−4.00000	−0.360668
$124$	−14.0000	−1.25724
$125$	0	0
$126$	0	0
$127$	−13.0000	−1.15356	−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000	−1.15356	−0.576782	+	0.816898i	$0.695692\pi$
$128$	0	0
$129$	9.00000	0.792406
$130$	0	0
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	2.00000	0.174078
$133$	0	0
$134$	−14.0000	−1.20942
$135$	0	0
$136$	0	0
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	−8.00000	−0.681005
$139$	11.0000	0.933008	0.466504	−	0.884519i	$-0.345513\pi$
$139$	11.0000	0.933008	0.466504	+	0.884519i	$0.345513\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	−16.0000	−1.34269
$143$	5.00000	0.418121
$144$	−4.00000	−0.333333
$145$	0	0
$146$	10.0000	0.827606
$147$	0	0
$148$	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	$0.579041\pi$
$150$	−10.0000	−0.816497
$151$	−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
$153$	6.00000	0.485071
$154$	0	0
$155$	0	0
$156$	10.0000	0.800641
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	22.0000	1.75023
$159$	2.00000	0.158610
$160$	0	0
$161$	0	0
$162$	−2.00000	−0.157135
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	8.00000	0.624695
$165$	0	0
$166$	8.00000	0.620920
$167$	−6.00000	−0.464294	−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000	−0.464294	−0.232147	+	0.972681i	$0.574575\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	7.00000	0.535303
$172$	−18.0000	−1.37249
$173$	−10.0000	−0.760286	−0.380143	−	0.924928i	$-0.624125\pi$
$173$	−10.0000	−0.760286	−0.380143	+	0.924928i	$0.624125\pi$
$174$	−4.00000	−0.303239
$175$	0	0
$176$	4.00000	0.301511
$177$	−12.0000	−0.901975
$178$	−12.0000	−0.899438
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	0	0
$181$	5.00000	0.371647	0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000	0.371647	0.185824	+	0.982583i	$0.440505\pi$
$182$	0	0
$183$	2.00000	0.147844
$184$	0	0
$185$	0	0
$186$	−14.0000	−1.02653
$187$	−6.00000	−0.438763
$188$	12.0000	0.875190
$189$	0	0
$190$	0	0
$191$	22.0000	1.59186	0.795932	−	0.605386i	$-0.206981\pi$
$191$	22.0000	1.59186	0.795932	+	0.605386i	$0.206981\pi$
$192$	8.00000	0.577350
$193$	−7.00000	−0.503871	−0.251936	−	0.967744i	$-0.581067\pi$
$193$	−7.00000	−0.503871	−0.251936	+	0.967744i	$0.581067\pi$
$194$	−4.00000	−0.287183
$195$	0	0
$196$	0	0
$197$	−4.00000	−0.284988	−0.142494	−	0.989796i	$-0.545512\pi$
$197$	−4.00000	−0.284988	−0.142494	+	0.989796i	$0.545512\pi$
$198$	2.00000	0.142134
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	0	0
$201$	−7.00000	−0.493742
$202$	4.00000	0.281439
$203$	0	0
$204$	−12.0000	−0.840168
$205$	0	0
$206$	38.0000	2.64759
$207$	−4.00000	−0.278019
$208$	20.0000	1.38675
$209$	−7.00000	−0.484200
$210$	0	0
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	−4.00000	−0.274721
$213$	−8.00000	−0.548151
$214$	40.0000	2.73434
$215$	0	0
$216$	0	0
$217$	0	0
$218$	2.00000	0.135457
$219$	5.00000	0.337869
$220$	0	0
$221$	−30.0000	−2.01802
$222$	14.0000	0.939618
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	−5.00000	−0.333333
$226$	12.0000	0.798228
$227$	14.0000	0.929213	0.464606	−	0.885517i	$-0.346196\pi$
$227$	14.0000	0.929213	0.464606	+	0.885517i	$0.346196\pi$
$228$	−14.0000	−0.927173
$229$	5.00000	0.330409	0.165205	−	0.986259i	$-0.447172\pi$
$229$	5.00000	0.330409	0.165205	+	0.986259i	$0.447172\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	−20.0000	−1.31024	−0.655122	−	0.755523i	$-0.727383\pi$
$233$	−20.0000	−1.31024	−0.655122	+	0.755523i	$0.727383\pi$
$234$	10.0000	0.653720
$235$	0	0
$236$	24.0000	1.56227
$237$	11.0000	0.714527
$238$	0	0
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	−2.00000	−0.128565
$243$	−1.00000	−0.0641500
$244$	−4.00000	−0.256074
$245$	0	0
$246$	8.00000	0.510061
$247$	−35.0000	−2.22700
$248$	0	0
$249$	4.00000	0.253490
$250$	0	0
$251$	−18.0000	−1.13615	−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000	−1.13615	−0.568075	+	0.822977i	$0.692312\pi$
$252$	0	0
$253$	4.00000	0.251478
$254$	26.0000	1.63139
$255$	0	0
$256$	16.0000	1.00000
$257$	−8.00000	−0.499026	−0.249513	−	0.968371i	$-0.580271\pi$
$257$	−8.00000	−0.499026	−0.249513	+	0.968371i	$0.580271\pi$
$258$	−18.0000	−1.12063
$259$	0	0
$260$	0	0
$261$	−2.00000	−0.123797
$262$	8.00000	0.494242
$263$	−18.0000	−1.10993	−0.554964	−	0.831875i	$-0.687268\pi$
$263$	−18.0000	−1.10993	−0.554964	+	0.831875i	$0.687268\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−6.00000	−0.367194
$268$	14.0000	0.855186
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	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
$273$	0	0
$274$	20.0000	1.20824
$275$	5.00000	0.301511
$276$	8.00000	0.481543
$277$	−1.00000	−0.0600842	−0.0300421	−	0.999549i	$-0.509564\pi$
$277$	−1.00000	−0.0600842	−0.0300421	+	0.999549i	$0.509564\pi$
$278$	−22.0000	−1.31947
$279$	−7.00000	−0.419079
$280$	0	0
$281$	24.0000	1.43172	0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000	1.43172	0.715860	+	0.698244i	$0.246035\pi$
$282$	12.0000	0.714590
$283$	23.0000	1.36721	0.683604	−	0.729853i	$-0.260412\pi$
$283$	23.0000	1.36721	0.683604	+	0.729853i	$0.260412\pi$
$284$	16.0000	0.949425
$285$	0	0
$286$	−10.0000	−0.591312
$287$	0	0
$288$	8.00000	0.471405
$289$	19.0000	1.11765
$290$	0	0
$291$	−2.00000	−0.117242
$292$	−10.0000	−0.585206
$293$	12.0000	0.701047	0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000	0.701047	0.350524	+	0.936554i	$0.386004\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	1.00000	0.0580259
$298$	12.0000	0.695141
$299$	20.0000	1.15663
$300$	10.0000	0.577350
$301$	0	0
$302$	32.0000	1.84139
$303$	2.00000	0.114897
$304$	−28.0000	−1.60591
$305$	0	0
$306$	−12.0000	−0.685994
$307$	−3.00000	−0.171219	−0.0856095	−	0.996329i	$-0.527284\pi$
$307$	−3.00000	−0.171219	−0.0856095	+	0.996329i	$0.527284\pi$
$308$	0	0
$309$	19.0000	1.08087
$310$	0	0
$311$	−16.0000	−0.907277	−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000	−0.907277	−0.453638	+	0.891186i	$0.649874\pi$
$312$	0	0
$313$	3.00000	0.169570	0.0847850	−	0.996399i	$-0.472980\pi$
$313$	3.00000	0.169570	0.0847850	+	0.996399i	$0.472980\pi$
$314$	28.0000	1.58013
$315$	0	0
$316$	−22.0000	−1.23760
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	−4.00000	−0.224309
$319$	2.00000	0.111979
$320$	0	0
$321$	20.0000	1.11629
$322$	0	0
$323$	42.0000	2.33694
$324$	2.00000	0.111111
$325$	25.0000	1.38675
$326$	16.0000	0.886158
$327$	1.00000	0.0553001
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−33.0000	−1.81384	−0.906922	−	0.421299i	$-0.861574\pi$
$331$	−33.0000	−1.81384	−0.906922	+	0.421299i	$0.861574\pi$
$332$	−8.00000	−0.439057
$333$	7.00000	0.383598
$334$	12.0000	0.656611
$335$	0	0
$336$	0	0
$337$	−17.0000	−0.926049	−0.463025	−	0.886345i	$-0.653236\pi$
$337$	−17.0000	−0.926049	−0.463025	+	0.886345i	$0.653236\pi$
$338$	−24.0000	−1.30543
$339$	6.00000	0.325875
$340$	0	0
$341$	7.00000	0.379071
$342$	−14.0000	−0.757033
$343$	0	0
$344$	0	0
$345$	0	0
$346$	20.0000	1.07521
$347$	2.00000	0.107366	0.0536828	−	0.998558i	$-0.482904\pi$
$347$	2.00000	0.107366	0.0536828	+	0.998558i	$0.482904\pi$
$348$	4.00000	0.214423
$349$	6.00000	0.321173	0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000	0.321173	0.160586	+	0.987022i	$0.448662\pi$
$350$	0	0
$351$	5.00000	0.266880
$352$	−8.00000	−0.426401
$353$	30.0000	1.59674	0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000	1.59674	0.798369	+	0.602168i	$0.205696\pi$
$354$	24.0000	1.27559
$355$	0	0
$356$	12.0000	0.635999
$357$	0	0
$358$	32.0000	1.69125
$359$	36.0000	1.90001	0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000	1.90001	0.950004	+	0.312239i	$0.101079\pi$
$360$	0	0
$361$	30.0000	1.57895
$362$	−10.0000	−0.525588
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	0	0
$366$	−4.00000	−0.209083
$367$	−17.0000	−0.887393	−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000	−0.887393	−0.443696	+	0.896177i	$0.646333\pi$
$368$	16.0000	0.834058
$369$	4.00000	0.208232
$370$	0	0
$371$	0	0
$372$	14.0000	0.725866
$373$	21.0000	1.08734	0.543669	−	0.839299i	$-0.317035\pi$
$373$	21.0000	1.08734	0.543669	+	0.839299i	$0.317035\pi$
$374$	12.0000	0.620505
$375$	0	0
$376$	0	0
$377$	10.0000	0.515026
$378$	0	0
$379$	−5.00000	−0.256833	−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000	−0.256833	−0.128416	+	0.991720i	$0.540989\pi$
$380$	0	0
$381$	13.0000	0.666010
$382$	−44.0000	−2.25124
$383$	−38.0000	−1.94171	−0.970855	−	0.239669i	$-0.922961\pi$
$383$	−38.0000	−1.94171	−0.970855	+	0.239669i	$0.922961\pi$
$384$	0	0
$385$	0	0
$386$	14.0000	0.712581
$387$	−9.00000	−0.457496
$388$	4.00000	0.203069
$389$	22.0000	1.11544	0.557722	−	0.830028i	$-0.311675\pi$
$389$	22.0000	1.11544	0.557722	+	0.830028i	$0.311675\pi$
$390$	0	0
$391$	−24.0000	−1.21373
$392$	0	0
$393$	4.00000	0.201773
$394$	8.00000	0.403034
$395$	0	0
$396$	−2.00000	−0.100504
$397$	27.0000	1.35509	0.677546	−	0.735481i	$-0.263044\pi$
$397$	27.0000	1.35509	0.677546	+	0.735481i	$0.263044\pi$
$398$	−8.00000	−0.401004
$399$	0	0
$400$	20.0000	1.00000
$401$	36.0000	1.79775	0.898877	−	0.438201i	$-0.144384\pi$
$401$	36.0000	1.79775	0.898877	+	0.438201i	$0.144384\pi$
$402$	14.0000	0.698257
$403$	35.0000	1.74347
$404$	−4.00000	−0.199007
$405$	0	0
$406$	0	0
$407$	−7.00000	−0.346977
$408$	0	0
$409$	11.0000	0.543915	0.271957	−	0.962309i	$-0.412329\pi$
$409$	11.0000	0.543915	0.271957	+	0.962309i	$0.412329\pi$
$410$	0	0
$411$	10.0000	0.493264
$412$	−38.0000	−1.87213
$413$	0	0
$414$	8.00000	0.393179
$415$	0	0
$416$	−40.0000	−1.96116
$417$	−11.0000	−0.538672
$418$	14.0000	0.684762
$419$	−8.00000	−0.390826	−0.195413	−	0.980721i	$-0.562605\pi$
$419$	−8.00000	−0.390826	−0.195413	+	0.980721i	$0.562605\pi$
$420$	0	0
$421$	9.00000	0.438633	0.219317	−	0.975654i	$-0.429617\pi$
$421$	9.00000	0.438633	0.219317	+	0.975654i	$0.429617\pi$
$422$	8.00000	0.389434
$423$	6.00000	0.291730
$424$	0	0
$425$	−30.0000	−1.45521
$426$	16.0000	0.775203
$427$	0	0
$428$	−40.0000	−1.93347
$429$	−5.00000	−0.241402
$430$	0	0
$431$	10.0000	0.481683	0.240842	−	0.970564i	$-0.422577\pi$
$431$	10.0000	0.481683	0.240842	+	0.970564i	$0.422577\pi$
$432$	4.00000	0.192450
$433$	19.0000	0.913082	0.456541	−	0.889702i	$-0.349088\pi$
$433$	19.0000	0.913082	0.456541	+	0.889702i	$0.349088\pi$
$434$	0	0
$435$	0	0
$436$	−2.00000	−0.0957826
$437$	−28.0000	−1.33942
$438$	−10.0000	−0.477818
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	0	0
$441$	0	0
$442$	60.0000	2.85391
$443$	22.0000	1.04525	0.522626	−	0.852562i	$-0.324953\pi$
$443$	22.0000	1.04525	0.522626	+	0.852562i	$0.324953\pi$
$444$	−14.0000	−0.664411
$445$	0	0
$446$	0	0
$447$	6.00000	0.283790
$448$	0	0
$449$	0	0		−	1.00000i	$-0.5\pi$
$449$	0	0			1.00000i	$0.5\pi$
$450$	10.0000	0.471405
$451$	−4.00000	−0.188353
$452$	−12.0000	−0.564433
$453$	16.0000	0.751746
$454$	−28.0000	−1.31411
$455$	0	0
$456$	0	0
$457$	3.00000	0.140334	0.0701670	−	0.997535i	$-0.477647\pi$
$457$	3.00000	0.140334	0.0701670	+	0.997535i	$0.477647\pi$
$458$	−10.0000	−0.467269
$459$	−6.00000	−0.280056
$460$	0	0
$461$	−36.0000	−1.67669	−0.838344	−	0.545142i	$-0.816476\pi$
$461$	−36.0000	−1.67669	−0.838344	+	0.545142i	$0.816476\pi$
$462$	0	0
$463$	−29.0000	−1.34774	−0.673872	−	0.738848i	$-0.735370\pi$
$463$	−29.0000	−1.34774	−0.673872	+	0.738848i	$0.735370\pi$
$464$	8.00000	0.371391
$465$	0	0
$466$	40.0000	1.85296
$467$	8.00000	0.370196	0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000	0.370196	0.185098	+	0.982720i	$0.440740\pi$
$468$	−10.0000	−0.462250
$469$	0	0
$470$	0	0
$471$	14.0000	0.645086
$472$	0	0
$473$	9.00000	0.413820
$474$	−22.0000	−1.01049
$475$	−35.0000	−1.60591
$476$	0	0
$477$	−2.00000	−0.0915737
$478$	48.0000	2.19547
$479$	−38.0000	−1.73626	−0.868132	−	0.496333i	$-0.834679\pi$
$479$	−38.0000	−1.73626	−0.868132	+	0.496333i	$0.834679\pi$
$480$	0	0
$481$	−35.0000	−1.59586
$482$	20.0000	0.910975
$483$	0	0
$484$	2.00000	0.0909091
$485$	0	0
$486$	2.00000	0.0907218
$487$	−29.0000	−1.31412	−0.657058	−	0.753840i	$-0.728199\pi$
$487$	−29.0000	−1.31412	−0.657058	+	0.753840i	$0.728199\pi$
$488$	0	0
$489$	8.00000	0.361773
$490$	0	0
$491$	−30.0000	−1.35388	−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000	−1.35388	−0.676941	+	0.736038i	$0.736695\pi$
$492$	−8.00000	−0.360668
$493$	−12.0000	−0.540453
$494$	70.0000	3.14945
$495$	0	0
$496$	28.0000	1.25724
$497$	0	0
$498$	−8.00000	−0.358489
$499$	13.0000	0.581960	0.290980	−	0.956729i	$-0.406019\pi$
$499$	13.0000	0.581960	0.290980	+	0.956729i	$0.406019\pi$
$500$	0	0
$501$	6.00000	0.268060
$502$	36.0000	1.60676
$503$	−44.0000	−1.96186	−0.980932	−	0.194354i	$-0.937739\pi$
$503$	−44.0000	−1.96186	−0.980932	+	0.194354i	$0.937739\pi$
$504$	0	0
$505$	0	0
$506$	−8.00000	−0.355643
$507$	−12.0000	−0.532939
$508$	−26.0000	−1.15356
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	0	0
$512$	−32.0000	−1.41421
$513$	−7.00000	−0.309058
$514$	16.0000	0.705730
$515$	0	0
$516$	18.0000	0.792406
$517$	−6.00000	−0.263880
$518$	0	0
$519$	10.0000	0.438951
$520$	0	0
$521$	22.0000	0.963837	0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000	0.963837	0.481919	+	0.876216i	$0.339940\pi$
$522$	4.00000	0.175075
$523$	−31.0000	−1.35554	−0.677768	−	0.735276i	$-0.737052\pi$
$523$	−31.0000	−1.35554	−0.677768	+	0.735276i	$0.737052\pi$
$524$	−8.00000	−0.349482
$525$	0	0
$526$	36.0000	1.56967
$527$	−42.0000	−1.82955
$528$	−4.00000	−0.174078
$529$	−7.00000	−0.304348
$530$	0	0
$531$	12.0000	0.520756
$532$	0	0
$533$	−20.0000	−0.866296
$534$	12.0000	0.519291
$535$	0	0
$536$	0	0
$537$	16.0000	0.690451
$538$	28.0000	1.20717
$539$	0	0
$540$	0	0
$541$	15.0000	0.644900	0.322450	−	0.946586i	$-0.395494\pi$
$541$	15.0000	0.644900	0.322450	+	0.946586i	$0.395494\pi$
$542$	40.0000	1.71815
$543$	−5.00000	−0.214571
$544$	48.0000	2.05798
$545$	0	0
$546$	0	0
$547$	32.0000	1.36822	0.684111	−	0.729378i	$-0.260191\pi$
$547$	32.0000	1.36822	0.684111	+	0.729378i	$0.260191\pi$
$548$	−20.0000	−0.854358
$549$	−2.00000	−0.0853579
$550$	−10.0000	−0.426401
$551$	−14.0000	−0.596420
$552$	0	0
$553$	0	0
$554$	2.00000	0.0849719
$555$	0	0
$556$	22.0000	0.933008
$557$	−36.0000	−1.52537	−0.762684	−	0.646771i	$-0.776119\pi$
$557$	−36.0000	−1.52537	−0.762684	+	0.646771i	$0.776119\pi$
$558$	14.0000	0.592667
$559$	45.0000	1.90330
$560$	0	0
$561$	6.00000	0.253320
$562$	−48.0000	−2.02476
$563$	18.0000	0.758610	0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000	0.758610	0.379305	+	0.925272i	$0.376163\pi$
$564$	−12.0000	−0.505291
$565$	0	0
$566$	−46.0000	−1.93352
$567$	0	0
$568$	0	0
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	0	0
$571$	35.0000	1.46470	0.732352	−	0.680926i	$-0.238422\pi$
$571$	35.0000	1.46470	0.732352	+	0.680926i	$0.238422\pi$
$572$	10.0000	0.418121
$573$	−22.0000	−0.919063
$574$	0	0
$575$	20.0000	0.834058
$576$	−8.00000	−0.333333
$577$	−17.0000	−0.707719	−0.353860	−	0.935299i	$-0.615131\pi$
$577$	−17.0000	−0.707719	−0.353860	+	0.935299i	$0.615131\pi$
$578$	−38.0000	−1.58059
$579$	7.00000	0.290910
$580$	0	0
$581$	0	0
$582$	4.00000	0.165805
$583$	2.00000	0.0828315
$584$	0	0
$585$	0	0
$586$	−24.0000	−0.991431
$587$	24.0000	0.990586	0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000	0.990586	0.495293	+	0.868726i	$0.335061\pi$
$588$	0	0
$589$	−49.0000	−2.01901
$590$	0	0
$591$	4.00000	0.164538
$592$	−28.0000	−1.15079
$593$	−26.0000	−1.06769	−0.533846	−	0.845582i	$-0.679254\pi$
$593$	−26.0000	−1.06769	−0.533846	+	0.845582i	$0.679254\pi$
$594$	−2.00000	−0.0820610
$595$	0	0
$596$	−12.0000	−0.491539
$597$	−4.00000	−0.163709
$598$	−40.0000	−1.63572
$599$	10.0000	0.408589	0.204294	−	0.978909i	$-0.434510\pi$
$599$	10.0000	0.408589	0.204294	+	0.978909i	$0.434510\pi$
$600$	0	0
$601$	−15.0000	−0.611863	−0.305931	−	0.952054i	$-0.598968\pi$
$601$	−15.0000	−0.611863	−0.305931	+	0.952054i	$0.598968\pi$
$602$	0	0
$603$	7.00000	0.285062
$604$	−32.0000	−1.30206
$605$	0	0
$606$	−4.00000	−0.162489
$607$	13.0000	0.527654	0.263827	−	0.964570i	$-0.415015\pi$
$607$	13.0000	0.527654	0.263827	+	0.964570i	$0.415015\pi$
$608$	56.0000	2.27110
$609$	0	0
$610$	0	0
$611$	−30.0000	−1.21367
$612$	12.0000	0.485071
$613$	−34.0000	−1.37325	−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000	−1.37325	−0.686624	+	0.727013i	$0.740908\pi$
$614$	6.00000	0.242140
$615$	0	0
$616$	0	0
$617$	−24.0000	−0.966204	−0.483102	−	0.875564i	$-0.660490\pi$
$617$	−24.0000	−0.966204	−0.483102	+	0.875564i	$0.660490\pi$
$618$	−38.0000	−1.52858
$619$	−21.0000	−0.844061	−0.422031	−	0.906582i	$-0.638683\pi$
$619$	−21.0000	−0.844061	−0.422031	+	0.906582i	$0.638683\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	32.0000	1.28308
$623$	0	0
$624$	−20.0000	−0.800641
$625$	25.0000	1.00000
$626$	−6.00000	−0.239808
$627$	7.00000	0.279553
$628$	−28.0000	−1.11732
$629$	42.0000	1.67465
$630$	0	0
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	0	0
$633$	4.00000	0.158986
$634$	−12.0000	−0.476581
$635$	0	0
$636$	4.00000	0.158610
$637$	0	0
$638$	−4.00000	−0.158362
$639$	8.00000	0.316475
$640$	0	0
$641$	24.0000	0.947943	0.473972	−	0.880540i	$-0.342820\pi$
$641$	24.0000	0.947943	0.473972	+	0.880540i	$0.342820\pi$
$642$	−40.0000	−1.57867
$643$	21.0000	0.828159	0.414080	−	0.910241i	$-0.364104\pi$
$643$	21.0000	0.828159	0.414080	+	0.910241i	$0.364104\pi$
$644$	0	0
$645$	0	0
$646$	−84.0000	−3.30494
$647$	6.00000	0.235884	0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000	0.235884	0.117942	+	0.993020i	$0.462370\pi$
$648$	0	0
$649$	−12.0000	−0.471041
$650$	−50.0000	−1.96116
$651$	0	0
$652$	−16.0000	−0.626608
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	−2.00000	−0.0782062
$655$	0	0
$656$	−16.0000	−0.624695
$657$	−5.00000	−0.195069
$658$	0	0
$659$	18.0000	0.701180	0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000	0.701180	0.350590	+	0.936529i	$0.385981\pi$
$660$	0	0
$661$	11.0000	0.427850	0.213925	−	0.976850i	$-0.431375\pi$
$661$	11.0000	0.427850	0.213925	+	0.976850i	$0.431375\pi$
$662$	66.0000	2.56516
$663$	30.0000	1.16510
$664$	0	0
$665$	0	0
$666$	−14.0000	−0.542489
$667$	8.00000	0.309761
$668$	−12.0000	−0.464294
$669$	0	0
$670$	0	0
$671$	2.00000	0.0772091
$672$	0	0
$673$	1.00000	0.0385472	0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000	0.0385472	0.0192736	+	0.999814i	$0.493865\pi$
$674$	34.0000	1.30963
$675$	5.00000	0.192450
$676$	24.0000	0.923077
$677$	12.0000	0.461197	0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000	0.461197	0.230599	+	0.973049i	$0.425932\pi$
$678$	−12.0000	−0.460857
$679$	0	0
$680$	0	0
$681$	−14.0000	−0.536481
$682$	−14.0000	−0.536088
$683$	−40.0000	−1.53056	−0.765279	−	0.643699i	$-0.777399\pi$
$683$	−40.0000	−1.53056	−0.765279	+	0.643699i	$0.777399\pi$
$684$	14.0000	0.535303
$685$	0	0
$686$	0	0
$687$	−5.00000	−0.190762
$688$	36.0000	1.37249
$689$	10.0000	0.380970
$690$	0	0
$691$	−5.00000	−0.190209	−0.0951045	−	0.995467i	$-0.530319\pi$
$691$	−5.00000	−0.190209	−0.0951045	+	0.995467i	$0.530319\pi$
$692$	−20.0000	−0.760286
$693$	0	0
$694$	−4.00000	−0.151838
$695$	0	0
$696$	0	0
$697$	24.0000	0.909065
$698$	−12.0000	−0.454207
$699$	20.0000	0.756469
$700$	0	0
$701$	22.0000	0.830929	0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000	0.830929	0.415464	+	0.909610i	$0.363619\pi$
$702$	−10.0000	−0.377426
$703$	49.0000	1.84807
$704$	8.00000	0.301511
$705$	0	0
$706$	−60.0000	−2.25813
$707$	0	0
$708$	−24.0000	−0.901975
$709$	30.0000	1.12667	0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000	1.12667	0.563337	+	0.826227i	$0.309517\pi$
$710$	0	0
$711$	−11.0000	−0.412532
$712$	0	0
$713$	28.0000	1.04861
$714$	0	0
$715$	0	0
$716$	−32.0000	−1.19590
$717$	24.0000	0.896296
$718$	−72.0000	−2.68702
$719$	−6.00000	−0.223762	−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000	−0.223762	−0.111881	+	0.993722i	$0.535688\pi$
$720$	0	0
$721$	0	0
$722$	−60.0000	−2.23297
$723$	10.0000	0.371904
$724$	10.0000	0.371647
$725$	10.0000	0.371391
$726$	2.00000	0.0742270
$727$	−5.00000	−0.185440	−0.0927199	−	0.995692i	$-0.529556\pi$
$727$	−5.00000	−0.185440	−0.0927199	+	0.995692i	$0.529556\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−54.0000	−1.99726
$732$	4.00000	0.147844
$733$	−13.0000	−0.480166	−0.240083	−	0.970752i	$-0.577175\pi$
$733$	−13.0000	−0.480166	−0.240083	+	0.970752i	$0.577175\pi$
$734$	34.0000	1.25496
$735$	0	0
$736$	−32.0000	−1.17954
$737$	−7.00000	−0.257848
$738$	−8.00000	−0.294484
$739$	−33.0000	−1.21392	−0.606962	−	0.794731i	$-0.707612\pi$
$739$	−33.0000	−1.21392	−0.606962	+	0.794731i	$0.707612\pi$
$740$	0	0
$741$	35.0000	1.28576
$742$	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
$745$	0	0
$746$	−42.0000	−1.53773
$747$	−4.00000	−0.146352
$748$	−12.0000	−0.438763
$749$	0	0
$750$	0	0
$751$	−31.0000	−1.13121	−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000	−1.13121	−0.565603	+	0.824678i	$0.691357\pi$
$752$	−24.0000	−0.875190
$753$	18.0000	0.655956
$754$	−20.0000	−0.728357
$755$	0	0
$756$	0	0
$757$	30.0000	1.09037	0.545184	−	0.838316i	$-0.316460\pi$
$757$	30.0000	1.09037	0.545184	+	0.838316i	$0.316460\pi$
$758$	10.0000	0.363216
$759$	−4.00000	−0.145191
$760$	0	0
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	−26.0000	−0.941881
$763$	0	0
$764$	44.0000	1.59186
$765$	0	0
$766$	76.0000	2.74599
$767$	−60.0000	−2.16647
$768$	−16.0000	−0.577350
$769$	−3.00000	−0.108183	−0.0540914	−	0.998536i	$-0.517226\pi$
$769$	−3.00000	−0.108183	−0.0540914	+	0.998536i	$0.517226\pi$
$770$	0	0
$771$	8.00000	0.288113
$772$	−14.0000	−0.503871
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	18.0000	0.646997
$775$	35.0000	1.25724
$776$	0	0
$777$	0	0
$778$	−44.0000	−1.57748
$779$	28.0000	1.00320
$780$	0	0
$781$	−8.00000	−0.286263
$782$	48.0000	1.71648
$783$	2.00000	0.0714742
$784$	0	0
$785$	0	0
$786$	−8.00000	−0.285351
$787$	4.00000	0.142585	0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000	0.142585	0.0712923	+	0.997455i	$0.477288\pi$
$788$	−8.00000	−0.284988
$789$	18.0000	0.640817
$790$	0	0
$791$	0	0
$792$	0	0
$793$	10.0000	0.355110
$794$	−54.0000	−1.91639
$795$	0	0
$796$	8.00000	0.283552
$797$	−4.00000	−0.141687	−0.0708436	−	0.997487i	$-0.522569\pi$
$797$	−4.00000	−0.141687	−0.0708436	+	0.997487i	$0.522569\pi$
$798$	0	0
$799$	36.0000	1.27359
$800$	−40.0000	−1.41421
$801$	6.00000	0.212000
$802$	−72.0000	−2.54241
$803$	5.00000	0.176446
$804$	−14.0000	−0.493742
$805$	0	0
$806$	−70.0000	−2.46564
$807$	14.0000	0.492823
$808$	0	0
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	44.0000	1.54505	0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000	1.54505	0.772524	+	0.634985i	$0.218994\pi$
$812$	0	0
$813$	20.0000	0.701431
$814$	14.0000	0.490700
$815$	0	0
$816$	24.0000	0.840168
$817$	−63.0000	−2.20409
$818$	−22.0000	−0.769212
$819$	0	0
$820$	0	0
$821$	52.0000	1.81481	0.907406	−	0.420255i	$-0.138059\pi$
$821$	52.0000	1.81481	0.907406	+	0.420255i	$0.138059\pi$
$822$	−20.0000	−0.697580
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	0	0
$825$	−5.00000	−0.174078
$826$	0	0
$827$	22.0000	0.765015	0.382507	−	0.923952i	$-0.375061\pi$
$827$	22.0000	0.765015	0.382507	+	0.923952i	$0.375061\pi$
$828$	−8.00000	−0.278019
$829$	−31.0000	−1.07667	−0.538337	−	0.842729i	$-0.680947\pi$
$829$	−31.0000	−1.07667	−0.538337	+	0.842729i	$0.680947\pi$
$830$	0	0
$831$	1.00000	0.0346896
$832$	40.0000	1.38675
$833$	0	0
$834$	22.0000	0.761798
$835$	0	0
$836$	−14.0000	−0.484200
$837$	7.00000	0.241955
$838$	16.0000	0.552711
$839$	30.0000	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−18.0000	−0.620321
$843$	−24.0000	−0.826604
$844$	−8.00000	−0.275371
$845$	0	0
$846$	−12.0000	−0.412568
$847$	0	0
$848$	8.00000	0.274721
$849$	−23.0000	−0.789358
$850$	60.0000	2.05798
$851$	−28.0000	−0.959828
$852$	−16.0000	−0.548151
$853$	17.0000	0.582069	0.291034	−	0.956713i	$-0.406001\pi$
$853$	17.0000	0.582069	0.291034	+	0.956713i	$0.406001\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−32.0000	−1.09310	−0.546550	−	0.837427i	$-0.684059\pi$
$857$	−32.0000	−1.09310	−0.546550	+	0.837427i	$0.684059\pi$
$858$	10.0000	0.341394
$859$	0	0		−	1.00000i	$-0.5\pi$
$859$	0	0			1.00000i	$0.5\pi$
$860$	0	0
$861$	0	0
$862$	−20.0000	−0.681203
$863$	−44.0000	−1.49778	−0.748889	−	0.662696i	$-0.769412\pi$
$863$	−44.0000	−1.49778	−0.748889	+	0.662696i	$0.769412\pi$
$864$	−8.00000	−0.272166
$865$	0	0
$866$	−38.0000	−1.29129
$867$	−19.0000	−0.645274
$868$	0	0
$869$	11.0000	0.373149
$870$	0	0
$871$	−35.0000	−1.18593
$872$	0	0
$873$	2.00000	0.0676897
$874$	56.0000	1.89423
$875$	0	0
$876$	10.0000	0.337869
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	−32.0000	−1.07995
$879$	−12.0000	−0.404750
$880$	0	0
$881$	50.0000	1.68454	0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000	1.68454	0.842271	+	0.539054i	$0.181218\pi$
$882$	0	0
$883$	−9.00000	−0.302874	−0.151437	−	0.988467i	$-0.548390\pi$
$883$	−9.00000	−0.302874	−0.151437	+	0.988467i	$0.548390\pi$
$884$	−60.0000	−2.01802
$885$	0	0
$886$	−44.0000	−1.47821
$887$	22.0000	0.738688	0.369344	−	0.929293i	$-0.379582\pi$
$887$	22.0000	0.738688	0.369344	+	0.929293i	$0.379582\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−1.00000	−0.0335013
$892$	0	0
$893$	42.0000	1.40548
$894$	−12.0000	−0.401340
$895$	0	0
$896$	0	0
$897$	−20.0000	−0.667781
$898$	0	0
$899$	14.0000	0.466926
$900$	−10.0000	−0.333333
$901$	−12.0000	−0.399778
$902$	8.00000	0.266371
$903$	0	0
$904$	0	0
$905$	0	0
$906$	−32.0000	−1.06313
$907$	39.0000	1.29497	0.647487	−	0.762077i	$-0.275820\pi$
$907$	39.0000	1.29497	0.647487	+	0.762077i	$0.275820\pi$
$908$	28.0000	0.929213
$909$	−2.00000	−0.0663358
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	28.0000	0.927173
$913$	4.00000	0.132381
$914$	−6.00000	−0.198462
$915$	0	0
$916$	10.0000	0.330409
$917$	0	0
$918$	12.0000	0.396059
$919$	−31.0000	−1.02260	−0.511298	−	0.859404i	$-0.670835\pi$
$919$	−31.0000	−1.02260	−0.511298	+	0.859404i	$0.670835\pi$
$920$	0	0
$921$	3.00000	0.0988534
$922$	72.0000	2.37119
$923$	−40.0000	−1.31662
$924$	0	0
$925$	−35.0000	−1.15079
$926$	58.0000	1.90600
$927$	−19.0000	−0.624042
$928$	−16.0000	−0.525226
$929$	0	0		−	1.00000i	$-0.5\pi$
$929$	0	0			1.00000i	$0.5\pi$
$930$	0	0
$931$	0	0
$932$	−40.0000	−1.31024
$933$	16.0000	0.523816
$934$	−16.0000	−0.523536
$935$	0	0
$936$	0	0
$937$	−47.0000	−1.53542	−0.767712	−	0.640796i	$-0.778605\pi$
$937$	−47.0000	−1.53542	−0.767712	+	0.640796i	$0.778605\pi$
$938$	0	0
$939$	−3.00000	−0.0979013
$940$	0	0
$941$	8.00000	0.260793	0.130396	−	0.991462i	$-0.458375\pi$
$941$	8.00000	0.260793	0.130396	+	0.991462i	$0.458375\pi$
$942$	−28.0000	−0.912289
$943$	−16.0000	−0.521032
$944$	−48.0000	−1.56227
$945$	0	0
$946$	−18.0000	−0.585230
$947$	−54.0000	−1.75476	−0.877382	−	0.479792i	$-0.840712\pi$
$947$	−54.0000	−1.75476	−0.877382	+	0.479792i	$0.840712\pi$
$948$	22.0000	0.714527
$949$	25.0000	0.811534
$950$	70.0000	2.27110
$951$	−6.00000	−0.194563
$952$	0	0
$953$	14.0000	0.453504	0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000	0.453504	0.226752	+	0.973952i	$0.427189\pi$
$954$	4.00000	0.129505
$955$	0	0
$956$	−48.0000	−1.55243
$957$	−2.00000	−0.0646508
$958$	76.0000	2.45545
$959$	0	0
$960$	0	0
$961$	18.0000	0.580645
$962$	70.0000	2.25689
$963$	−20.0000	−0.644491
$964$	−20.0000	−0.644157
$965$	0	0
$966$	0	0
$967$	17.0000	0.546683	0.273342	−	0.961917i	$-0.411871\pi$
$967$	17.0000	0.546683	0.273342	+	0.961917i	$0.411871\pi$
$968$	0	0
$969$	−42.0000	−1.34923
$970$	0	0
$971$	−8.00000	−0.256732	−0.128366	−	0.991727i	$-0.540973\pi$
$971$	−8.00000	−0.256732	−0.128366	+	0.991727i	$0.540973\pi$
$972$	−2.00000	−0.0641500
$973$	0	0
$974$	58.0000	1.85844
$975$	−25.0000	−0.800641
$976$	8.00000	0.256074
$977$	52.0000	1.66363	0.831814	−	0.555055i	$-0.187303\pi$
$977$	52.0000	1.66363	0.831814	+	0.555055i	$0.187303\pi$
$978$	−16.0000	−0.511624
$979$	−6.00000	−0.191761
$980$	0	0
$981$	−1.00000	−0.0319275
$982$	60.0000	1.91468
$983$	34.0000	1.08443	0.542216	−	0.840239i	$-0.317586\pi$
$983$	34.0000	1.08443	0.542216	+	0.840239i	$0.317586\pi$
$984$	0	0
$985$	0	0
$986$	24.0000	0.764316
$987$	0	0
$988$	−70.0000	−2.22700
$989$	36.0000	1.14473
$990$	0	0
$991$	29.0000	0.921215	0.460608	−	0.887604i	$-0.347632\pi$
$991$	29.0000	0.921215	0.460608	+	0.887604i	$0.347632\pi$
$992$	−56.0000	−1.77800
$993$	33.0000	1.04722
$994$	0	0
$995$	0	0
$996$	8.00000	0.253490
$997$	−11.0000	−0.348373	−0.174187	−	0.984713i	$-0.555730\pi$
$997$	−11.0000	−0.348373	−0.174187	+	0.984713i	$0.555730\pi$
$998$	−26.0000	−0.823016
$999$	−7.00000	−0.221470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.a.1.1		1
3.2	odd	2		4851.2.a.r.1.1		1
7.2	even	3		231.2.i.c.67.1	✓	2
7.4	even	3		231.2.i.c.100.1	yes	2
7.6	odd	2		1617.2.a.b.1.1		1
21.2	odd	6		693.2.i.a.298.1		2
21.11	odd	6		693.2.i.a.100.1		2
21.20	even	2		4851.2.a.s.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.c.67.1	✓	2	7.2	even	3
231.2.i.c.100.1	yes	2	7.4	even	3
693.2.i.a.100.1		2	21.11	odd	6
693.2.i.a.298.1		2	21.2	odd	6
1617.2.a.a.1.1		1	1.1	even	1	trivial
1617.2.a.b.1.1		1	7.6	odd	2
4851.2.a.r.1.1		1	3.2	odd	2
4851.2.a.s.1.1		1	21.20	even	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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