LMFDB - Embedded newform 6534.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6534,2,Mod(1,6534)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6534, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6534.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6534 = 2 \cdot 3^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6534.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:	$52.1742526807$
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	$\chi$	$=$	6534.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} +3.00000 q^{5} -1.00000 q^{8} -3.00000 q^{10} +3.00000 q^{13} +1.00000 q^{16} -3.00000 q^{17} -6.00000 q^{19} +3.00000 q^{20} -3.00000 q^{23} +4.00000 q^{25} -3.00000 q^{26} -6.00000 q^{29} +4.00000 q^{31} -1.00000 q^{32} +3.00000 q^{34} -2.00000 q^{37} +6.00000 q^{38} -3.00000 q^{40} +3.00000 q^{41} -6.00000 q^{43} +3.00000 q^{46} -7.00000 q^{49} -4.00000 q^{50} +3.00000 q^{52} -9.00000 q^{53} +6.00000 q^{58} +12.0000 q^{59} -15.0000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +9.00000 q^{65} -5.00000 q^{67} -3.00000 q^{68} -12.0000 q^{71} -6.00000 q^{73} +2.00000 q^{74} -6.00000 q^{76} +15.0000 q^{79} +3.00000 q^{80} -3.00000 q^{82} -9.00000 q^{83} -9.00000 q^{85} +6.00000 q^{86} -6.00000 q^{89} -3.00000 q^{92} -18.0000 q^{95} +17.0000 q^{97} +7.00000 q^{98} +O(q^{100})$

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
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	3.00000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	−3.00000	−0.948683
$11$	0	0
$11$	0	0
$12$	0	0
$13$	3.00000	0.832050	0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000	0.832050	0.416025	+	0.909353i	$0.363423\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	0	0
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	3.00000	0.670820
$21$	0	0
$22$	0	0
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	0	0
$25$	4.00000	0.800000
$26$	−3.00000	−0.588348
$27$	0	0
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	3.00000	0.514496
$35$	0	0
$36$	0	0
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	6.00000	0.973329
$39$	0	0
$40$	−3.00000	−0.474342
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	0	0
$45$	0	0
$46$	3.00000	0.442326
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	−4.00000	−0.565685
$51$	0	0
$52$	3.00000	0.416025
$53$	−9.00000	−1.23625	−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000	−1.23625	−0.618123	+	0.786082i	$0.712106\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	6.00000	0.787839
$59$	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
$61$	−15.0000	−1.92055	−0.960277	−	0.279050i	$-0.909981\pi$
$61$	−15.0000	−1.92055	−0.960277	+	0.279050i	$0.909981\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	9.00000	1.11631
$66$	0	0
$67$	−5.00000	−0.610847	−0.305424	−	0.952217i	$-0.598798\pi$
$67$	−5.00000	−0.610847	−0.305424	+	0.952217i	$0.598798\pi$
$68$	−3.00000	−0.363803
$69$	0	0
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0	0
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	2.00000	0.232495
$75$	0	0
$76$	−6.00000	−0.688247
$77$	0	0
$78$	0	0
$79$	15.0000	1.68763	0.843816	−	0.536633i	$-0.180304\pi$
$79$	15.0000	1.68763	0.843816	+	0.536633i	$0.180304\pi$
$80$	3.00000	0.335410
$81$	0	0
$82$	−3.00000	−0.331295
$83$	−9.00000	−0.987878	−0.493939	−	0.869496i	$-0.664443\pi$
$83$	−9.00000	−0.987878	−0.493939	+	0.869496i	$0.664443\pi$
$84$	0	0
$85$	−9.00000	−0.976187
$86$	6.00000	0.646997
$87$	0	0
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	0	0
$91$	0	0
$92$	−3.00000	−0.312772
$93$	0	0
$94$	0	0
$95$	−18.0000	−1.84676
$96$	0	0
$97$	17.0000	1.72609	0.863044	−	0.505128i	$-0.168555\pi$
$97$	17.0000	1.72609	0.863044	+	0.505128i	$0.168555\pi$
$98$	7.00000	0.707107
$99$	0	0
$100$	4.00000	0.400000
$101$	−12.0000	−1.19404	−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000	−1.19404	−0.597022	+	0.802225i	$0.703650\pi$
$102$	0	0
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	−3.00000	−0.294174
$105$	0	0
$106$	9.00000	0.874157
$107$	−15.0000	−1.45010	−0.725052	−	0.688694i	$-0.758184\pi$
$107$	−15.0000	−1.45010	−0.725052	+	0.688694i	$0.758184\pi$
$108$	0	0
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	−9.00000	−0.839254
$116$	−6.00000	−0.557086
$117$	0	0
$118$	−12.0000	−1.10469
$119$	0	0
$120$	0	0
$121$	0	0
$122$	15.0000	1.35804
$123$	0	0
$124$	4.00000	0.359211
$125$	−3.00000	−0.268328
$126$	0	0
$127$	15.0000	1.33103	0.665517	−	0.746382i	$-0.268211\pi$
$127$	15.0000	1.33103	0.665517	+	0.746382i	$0.268211\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−9.00000	−0.789352
$131$	3.00000	0.262111	0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000	0.262111	0.131056	+	0.991375i	$0.458163\pi$
$132$	0	0
$133$	0	0
$134$	5.00000	0.431934
$135$	0	0
$136$	3.00000	0.257248
$137$	−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
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	0	0
$142$	12.0000	1.00702
$143$	0	0
$144$	0	0
$145$	−18.0000	−1.49482
$146$	6.00000	0.496564
$147$	0	0
$148$	−2.00000	−0.164399
$149$	−24.0000	−1.96616	−0.983078	−	0.183186i	$-0.941359\pi$
$149$	−24.0000	−1.96616	−0.983078	+	0.183186i	$0.941359\pi$
$150$	0	0
$151$	21.0000	1.70896	0.854478	−	0.519488i	$-0.173877\pi$
$151$	21.0000	1.70896	0.854478	+	0.519488i	$0.173877\pi$
$152$	6.00000	0.486664
$153$	0	0
$154$	0	0
$155$	12.0000	0.963863
$156$	0	0
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	−15.0000	−1.19334
$159$	0	0
$160$	−3.00000	−0.237171
$161$	0	0
$162$	0	0
$163$	11.0000	0.861586	0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000	0.861586	0.430793	+	0.902451i	$0.358234\pi$
$164$	3.00000	0.234261
$165$	0	0
$166$	9.00000	0.698535
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	9.00000	0.690268
$171$	0	0
$172$	−6.00000	−0.457496
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	0	0
$178$	6.00000	0.449719
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	0	0
$181$	−16.0000	−1.18927	−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000	−1.18927	−0.594635	+	0.803996i	$0.702704\pi$
$182$	0	0
$183$	0	0
$184$	3.00000	0.221163
$185$	−6.00000	−0.441129
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	18.0000	1.30586
$191$	−3.00000	−0.217072	−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000	−0.217072	−0.108536	+	0.994092i	$0.534616\pi$
$192$	0	0
$193$	6.00000	0.431889	0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000	0.431889	0.215945	+	0.976406i	$0.430717\pi$
$194$	−17.0000	−1.22053
$195$	0	0
$196$	−7.00000	−0.500000
$197$	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
$199$	−2.00000	−0.141776	−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000	−0.141776	−0.0708881	+	0.997484i	$0.522583\pi$
$200$	−4.00000	−0.282843
$201$	0	0
$202$	12.0000	0.844317
$203$	0	0
$204$	0	0
$205$	9.00000	0.628587
$206$	−14.0000	−0.975426
$207$	0	0
$208$	3.00000	0.208013
$209$	0	0
$210$	0	0
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	−9.00000	−0.618123
$213$	0	0
$214$	15.0000	1.02538
$215$	−18.0000	−1.22759
$216$	0	0
$217$	0	0
$218$	6.00000	0.406371
$219$	0	0
$220$	0	0
$221$	−9.00000	−0.605406
$222$	0	0
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	0	0
$225$	0	0
$226$	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
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	9.00000	0.593442
$231$	0	0
$232$	6.00000	0.393919
$233$	21.0000	1.37576	0.687878	−	0.725826i	$-0.258542\pi$
$233$	21.0000	1.37576	0.687878	+	0.725826i	$0.258542\pi$
$234$	0	0
$235$	0	0
$236$	12.0000	0.781133
$237$	0	0
$238$	0	0
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	0	0
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	0	0
$243$	0	0
$244$	−15.0000	−0.960277
$245$	−21.0000	−1.34164
$246$	0	0
$247$	−18.0000	−1.14531
$248$	−4.00000	−0.254000
$249$	0	0
$250$	3.00000	0.189737
$251$	6.00000	0.378717	0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000	0.378717	0.189358	+	0.981908i	$0.439359\pi$
$252$	0	0
$253$	0	0
$254$	−15.0000	−0.941184
$255$	0	0
$256$	1.00000	0.0625000
$257$	0	0		−	1.00000i	$-0.5\pi$
$257$	0	0			1.00000i	$0.5\pi$
$258$	0	0
$259$	0	0
$260$	9.00000	0.558156
$261$	0	0
$262$	−3.00000	−0.185341
$263$	30.0000	1.84988	0.924940	−	0.380114i	$-0.124115\pi$
$263$	30.0000	1.84988	0.924940	+	0.380114i	$0.124115\pi$
$264$	0	0
$265$	−27.0000	−1.65860
$266$	0	0
$267$	0	0
$268$	−5.00000	−0.305424
$269$	27.0000	1.64622	0.823110	−	0.567883i	$-0.192237\pi$
$269$	27.0000	1.64622	0.823110	+	0.567883i	$0.192237\pi$
$270$	0	0
$271$	−3.00000	−0.182237	−0.0911185	−	0.995840i	$-0.529044\pi$
$271$	−3.00000	−0.182237	−0.0911185	+	0.995840i	$0.529044\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	12.0000	0.724947
$275$	0	0
$276$	0	0
$277$	−3.00000	−0.180253	−0.0901263	−	0.995930i	$-0.528727\pi$
$277$	−3.00000	−0.180253	−0.0901263	+	0.995930i	$0.528727\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	−15.0000	−0.894825	−0.447412	−	0.894328i	$-0.647654\pi$
$281$	−15.0000	−0.894825	−0.447412	+	0.894328i	$0.647654\pi$
$282$	0	0
$283$	12.0000	0.713326	0.356663	−	0.934233i	$-0.383914\pi$
$283$	12.0000	0.713326	0.356663	+	0.934233i	$0.383914\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−8.00000	−0.470588
$290$	18.0000	1.05700
$291$	0	0
$292$	−6.00000	−0.351123
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	0	0
$295$	36.0000	2.09600
$296$	2.00000	0.116248
$297$	0	0
$298$	24.0000	1.39028
$299$	−9.00000	−0.520483
$300$	0	0
$301$	0	0
$302$	−21.0000	−1.20841
$303$	0	0
$304$	−6.00000	−0.344124
$305$	−45.0000	−2.57669
$306$	0	0
$307$	18.0000	1.02731	0.513657	−	0.857996i	$-0.328290\pi$
$307$	18.0000	1.02731	0.513657	+	0.857996i	$0.328290\pi$
$308$	0	0
$309$	0	0
$310$	−12.0000	−0.681554
$311$	27.0000	1.53103	0.765515	−	0.643418i	$-0.222484\pi$
$311$	27.0000	1.53103	0.765515	+	0.643418i	$0.222484\pi$
$312$	0	0
$313$	1.00000	0.0565233	0.0282617	−	0.999601i	$-0.491003\pi$
$313$	1.00000	0.0565233	0.0282617	+	0.999601i	$0.491003\pi$
$314$	−4.00000	−0.225733
$315$	0	0
$316$	15.0000	0.843816
$317$	−30.0000	−1.68497	−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000	−1.68497	−0.842484	+	0.538721i	$0.818908\pi$
$318$	0	0
$319$	0	0
$320$	3.00000	0.167705
$321$	0	0
$322$	0	0
$323$	18.0000	1.00155
$324$	0	0
$325$	12.0000	0.665640
$326$	−11.0000	−0.609234
$327$	0	0
$328$	−3.00000	−0.165647
$329$	0	0
$330$	0	0
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	−9.00000	−0.493939
$333$	0	0
$334$	12.0000	0.656611
$335$	−15.0000	−0.819538
$336$	0	0
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	4.00000	0.217571
$339$	0	0
$340$	−9.00000	−0.488094
$341$	0	0
$342$	0	0
$343$	0	0
$344$	6.00000	0.323498
$345$	0	0
$346$	0	0
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	0	0
$349$	18.0000	0.963518	0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000	0.963518	0.481759	+	0.876304i	$0.339998\pi$
$350$	0	0
$351$	0	0
$352$	0	0
$353$	−12.0000	−0.638696	−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000	−0.638696	−0.319348	+	0.947638i	$0.603464\pi$
$354$	0	0
$355$	−36.0000	−1.91068
$356$	−6.00000	−0.317999
$357$	0	0
$358$	−6.00000	−0.317110
$359$	18.0000	0.950004	0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000	0.950004	0.475002	+	0.879985i	$0.342447\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	16.0000	0.840941
$363$	0	0
$364$	0	0
$365$	−18.0000	−0.942163
$366$	0	0
$367$	−10.0000	−0.521996	−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000	−0.521996	−0.260998	+	0.965339i	$0.584052\pi$
$368$	−3.00000	−0.156386
$369$	0	0
$370$	6.00000	0.311925
$371$	0	0
$372$	0	0
$373$	15.0000	0.776671	0.388335	−	0.921518i	$-0.373050\pi$
$373$	15.0000	0.776671	0.388335	+	0.921518i	$0.373050\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−18.0000	−0.927047
$378$	0	0
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	−18.0000	−0.923381
$381$	0	0
$382$	3.00000	0.153493
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	0	0
$385$	0	0
$386$	−6.00000	−0.305392
$387$	0	0
$388$	17.0000	0.863044
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	0	0
$391$	9.00000	0.455150
$392$	7.00000	0.353553
$393$	0	0
$394$	−24.0000	−1.20910
$395$	45.0000	2.26420
$396$	0	0
$397$	−34.0000	−1.70641	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000	−1.70641	−0.853206	+	0.521575i	$0.825345\pi$
$398$	2.00000	0.100251
$399$	0	0
$400$	4.00000	0.200000
$401$	36.0000	1.79775	0.898877	−	0.438201i	$-0.144384\pi$
$401$	36.0000	1.79775	0.898877	+	0.438201i	$0.144384\pi$
$402$	0	0
$403$	12.0000	0.597763
$404$	−12.0000	−0.597022
$405$	0	0
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	−9.00000	−0.444478
$411$	0	0
$412$	14.0000	0.689730
$413$	0	0
$414$	0	0
$415$	−27.0000	−1.32538
$416$	−3.00000	−0.147087
$417$	0	0
$418$	0	0
$419$	−18.0000	−0.879358	−0.439679	−	0.898155i	$-0.644908\pi$
$419$	−18.0000	−0.879358	−0.439679	+	0.898155i	$0.644908\pi$
$420$	0	0
$421$	10.0000	0.487370	0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000	0.487370	0.243685	+	0.969854i	$0.421644\pi$
$422$	12.0000	0.584151
$423$	0	0
$424$	9.00000	0.437079
$425$	−12.0000	−0.582086
$426$	0	0
$427$	0	0
$428$	−15.0000	−0.725052
$429$	0	0
$430$	18.0000	0.868037
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	0	0
$433$	−25.0000	−1.20142	−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000	−1.20142	−0.600712	+	0.799466i	$0.705116\pi$
$434$	0	0
$435$	0	0
$436$	−6.00000	−0.287348
$437$	18.0000	0.861057
$438$	0	0
$439$	9.00000	0.429547	0.214773	−	0.976664i	$-0.431099\pi$
$439$	9.00000	0.429547	0.214773	+	0.976664i	$0.431099\pi$
$440$	0	0
$441$	0	0
$442$	9.00000	0.428086
$443$	30.0000	1.42534	0.712672	−	0.701498i	$-0.247485\pi$
$443$	30.0000	1.42534	0.712672	+	0.701498i	$0.247485\pi$
$444$	0	0
$445$	−18.0000	−0.853282
$446$	−8.00000	−0.378811
$447$	0	0
$448$	0	0
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	0	0
$451$	0	0
$452$	−6.00000	−0.282216
$453$	0	0
$454$	12.0000	0.563188
$455$	0	0
$456$	0	0
$457$	6.00000	0.280668	0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000	0.280668	0.140334	+	0.990104i	$0.455182\pi$
$458$	14.0000	0.654177
$459$	0	0
$460$	−9.00000	−0.419627
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	−4.00000	−0.185896	−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000	−0.185896	−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−21.0000	−0.972806
$467$	−24.0000	−1.11059	−0.555294	−	0.831654i	$-0.687394\pi$
$467$	−24.0000	−1.11059	−0.555294	+	0.831654i	$0.687394\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	−12.0000	−0.552345
$473$	0	0
$474$	0	0
$475$	−24.0000	−1.10120
$476$	0	0
$477$	0	0
$478$	6.00000	0.274434
$479$	−6.00000	−0.274147	−0.137073	−	0.990561i	$-0.543770\pi$
$479$	−6.00000	−0.274147	−0.137073	+	0.990561i	$0.543770\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	−18.0000	−0.819878
$483$	0	0
$484$	0	0
$485$	51.0000	2.31579
$486$	0	0
$487$	−38.0000	−1.72194	−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000	−1.72194	−0.860972	+	0.508652i	$0.830144\pi$
$488$	15.0000	0.679018
$489$	0	0
$490$	21.0000	0.948683
$491$	−36.0000	−1.62466	−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000	−1.62466	−0.812329	+	0.583200i	$0.801800\pi$
$492$	0	0
$493$	18.0000	0.810679
$494$	18.0000	0.809858
$495$	0	0
$496$	4.00000	0.179605
$497$	0	0
$498$	0	0
$499$	13.0000	0.581960	0.290980	−	0.956729i	$-0.406019\pi$
$499$	13.0000	0.581960	0.290980	+	0.956729i	$0.406019\pi$
$500$	−3.00000	−0.134164
$501$	0	0
$502$	−6.00000	−0.267793
$503$	−36.0000	−1.60516	−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000	−1.60516	−0.802580	+	0.596544i	$0.796540\pi$
$504$	0	0
$505$	−36.0000	−1.60198
$506$	0	0
$507$	0	0
$508$	15.0000	0.665517
$509$	15.0000	0.664863	0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000	0.664863	0.332432	+	0.943127i	$0.392131\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	0	0
$515$	42.0000	1.85074
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	−9.00000	−0.394676
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	0	0
$523$	−42.0000	−1.83653	−0.918266	−	0.395964i	$-0.870410\pi$
$523$	−42.0000	−1.83653	−0.918266	+	0.395964i	$0.870410\pi$
$524$	3.00000	0.131056
$525$	0	0
$526$	−30.0000	−1.30806
$527$	−12.0000	−0.522728
$528$	0	0
$529$	−14.0000	−0.608696
$530$	27.0000	1.17281
$531$	0	0
$532$	0	0
$533$	9.00000	0.389833
$534$	0	0
$535$	−45.0000	−1.94552
$536$	5.00000	0.215967
$537$	0	0
$538$	−27.0000	−1.16405
$539$	0	0
$540$	0	0
$541$	27.0000	1.16082	0.580410	−	0.814324i	$-0.302892\pi$
$541$	27.0000	1.16082	0.580410	+	0.814324i	$0.302892\pi$
$542$	3.00000	0.128861
$543$	0	0
$544$	3.00000	0.128624
$545$	−18.0000	−0.771035
$546$	0	0
$547$	−30.0000	−1.28271	−0.641354	−	0.767245i	$-0.721627\pi$
$547$	−30.0000	−1.28271	−0.641354	+	0.767245i	$0.721627\pi$
$548$	−12.0000	−0.512615
$549$	0	0
$550$	0	0
$551$	36.0000	1.53365
$552$	0	0
$553$	0	0
$554$	3.00000	0.127458
$555$	0	0
$556$	0	0
$557$	18.0000	0.762684	0.381342	−	0.924434i	$-0.375462\pi$
$557$	18.0000	0.762684	0.381342	+	0.924434i	$0.375462\pi$
$558$	0	0
$559$	−18.0000	−0.761319
$560$	0	0
$561$	0	0
$562$	15.0000	0.632737
$563$	−3.00000	−0.126435	−0.0632175	−	0.998000i	$-0.520136\pi$
$563$	−3.00000	−0.126435	−0.0632175	+	0.998000i	$0.520136\pi$
$564$	0	0
$565$	−18.0000	−0.757266
$566$	−12.0000	−0.504398
$567$	0	0
$568$	12.0000	0.503509
$569$	−15.0000	−0.628833	−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000	−0.628833	−0.314416	+	0.949285i	$0.601809\pi$
$570$	0	0
$571$	−18.0000	−0.753277	−0.376638	−	0.926360i	$-0.622920\pi$
$571$	−18.0000	−0.753277	−0.376638	+	0.926360i	$0.622920\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	−12.0000	−0.500435
$576$	0	0
$577$	34.0000	1.41544	0.707719	−	0.706494i	$-0.249724\pi$
$577$	34.0000	1.41544	0.707719	+	0.706494i	$0.249724\pi$
$578$	8.00000	0.332756
$579$	0	0
$580$	−18.0000	−0.747409
$581$	0	0
$582$	0	0
$583$	0	0
$584$	6.00000	0.248282
$585$	0	0
$586$	24.0000	0.991431
$587$	−36.0000	−1.48588	−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000	−1.48588	−0.742940	+	0.669359i	$0.766569\pi$
$588$	0	0
$589$	−24.0000	−0.988903
$590$	−36.0000	−1.48210
$591$	0	0
$592$	−2.00000	−0.0821995
$593$	30.0000	1.23195	0.615976	−	0.787765i	$-0.288762\pi$
$593$	30.0000	1.23195	0.615976	+	0.787765i	$0.288762\pi$
$594$	0	0
$595$	0	0
$596$	−24.0000	−0.983078
$597$	0	0
$598$	9.00000	0.368037
$599$	−9.00000	−0.367730	−0.183865	−	0.982952i	$-0.558861\pi$
$599$	−9.00000	−0.367730	−0.183865	+	0.982952i	$0.558861\pi$
$600$	0	0
$601$	−30.0000	−1.22373	−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000	−1.22373	−0.611863	+	0.790964i	$0.709580\pi$
$602$	0	0
$603$	0	0
$604$	21.0000	0.854478
$605$	0	0
$606$	0	0
$607$	27.0000	1.09590	0.547948	−	0.836512i	$-0.315409\pi$
$607$	27.0000	1.09590	0.547948	+	0.836512i	$0.315409\pi$
$608$	6.00000	0.243332
$609$	0	0
$610$	45.0000	1.82200
$611$	0	0
$612$	0	0
$613$	33.0000	1.33286	0.666429	−	0.745569i	$-0.267822\pi$
$613$	33.0000	1.33286	0.666429	+	0.745569i	$0.267822\pi$
$614$	−18.0000	−0.726421
$615$	0	0
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	0	0
$619$	−28.0000	−1.12542	−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000	−1.12542	−0.562708	+	0.826656i	$0.690240\pi$
$620$	12.0000	0.481932
$621$	0	0
$622$	−27.0000	−1.08260
$623$	0	0
$624$	0	0
$625$	−29.0000	−1.16000
$626$	−1.00000	−0.0399680
$627$	0	0
$628$	4.00000	0.159617
$629$	6.00000	0.239236
$630$	0	0
$631$	−2.00000	−0.0796187	−0.0398094	−	0.999207i	$-0.512675\pi$
$631$	−2.00000	−0.0796187	−0.0398094	+	0.999207i	$0.512675\pi$
$632$	−15.0000	−0.596668
$633$	0	0
$634$	30.0000	1.19145
$635$	45.0000	1.78577
$636$	0	0
$637$	−21.0000	−0.832050
$638$	0	0
$639$	0	0
$640$	−3.00000	−0.118585
$641$	−42.0000	−1.65890	−0.829450	−	0.558581i	$-0.811346\pi$
$641$	−42.0000	−1.65890	−0.829450	+	0.558581i	$0.811346\pi$
$642$	0	0
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	0	0
$645$	0	0
$646$	−18.0000	−0.708201
$647$	−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
$650$	−12.0000	−0.470679
$651$	0	0
$652$	11.0000	0.430793
$653$	−3.00000	−0.117399	−0.0586995	−	0.998276i	$-0.518695\pi$
$653$	−3.00000	−0.117399	−0.0586995	+	0.998276i	$0.518695\pi$
$654$	0	0
$655$	9.00000	0.351659
$656$	3.00000	0.117130
$657$	0	0
$658$	0	0
$659$	−33.0000	−1.28550	−0.642749	−	0.766077i	$-0.722206\pi$
$659$	−33.0000	−1.28550	−0.642749	+	0.766077i	$0.722206\pi$
$660$	0	0
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	−8.00000	−0.310929
$663$	0	0
$664$	9.00000	0.349268
$665$	0	0
$666$	0	0
$667$	18.0000	0.696963
$668$	−12.0000	−0.464294
$669$	0	0
$670$	15.0000	0.579501
$671$	0	0
$672$	0	0
$673$	12.0000	0.462566	0.231283	−	0.972887i	$-0.425708\pi$
$673$	12.0000	0.462566	0.231283	+	0.972887i	$0.425708\pi$
$674$	−18.0000	−0.693334
$675$	0	0
$676$	−4.00000	−0.153846
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	0	0
$679$	0	0
$680$	9.00000	0.345134
$681$	0	0
$682$	0	0
$683$	−18.0000	−0.688751	−0.344375	−	0.938832i	$-0.611909\pi$
$683$	−18.0000	−0.688751	−0.344375	+	0.938832i	$0.611909\pi$
$684$	0	0
$685$	−36.0000	−1.37549
$686$	0	0
$687$	0	0
$688$	−6.00000	−0.228748
$689$	−27.0000	−1.02862
$690$	0	0
$691$	35.0000	1.33146	0.665731	−	0.746191i	$-0.268120\pi$
$691$	35.0000	1.33146	0.665731	+	0.746191i	$0.268120\pi$
$692$	0	0
$693$	0	0
$694$	12.0000	0.455514
$695$	0	0
$696$	0	0
$697$	−9.00000	−0.340899
$698$	−18.0000	−0.681310
$699$	0	0
$700$	0	0
$701$	−12.0000	−0.453234	−0.226617	−	0.973984i	$-0.572767\pi$
$701$	−12.0000	−0.453234	−0.226617	+	0.973984i	$0.572767\pi$
$702$	0	0
$703$	12.0000	0.452589
$704$	0	0
$705$	0	0
$706$	12.0000	0.451626
$707$	0	0
$708$	0	0
$709$	−26.0000	−0.976450	−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000	−0.976450	−0.488225	+	0.872718i	$0.662356\pi$
$710$	36.0000	1.35106
$711$	0	0
$712$	6.00000	0.224860
$713$	−12.0000	−0.449404
$714$	0	0
$715$	0	0
$716$	6.00000	0.224231
$717$	0	0
$718$	−18.0000	−0.671754
$719$	21.0000	0.783168	0.391584	−	0.920142i	$-0.371927\pi$
$719$	21.0000	0.783168	0.391584	+	0.920142i	$0.371927\pi$
$720$	0	0
$721$	0	0
$722$	−17.0000	−0.632674
$723$	0	0
$724$	−16.0000	−0.594635
$725$	−24.0000	−0.891338
$726$	0	0
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	0	0
$729$	0	0
$730$	18.0000	0.666210
$731$	18.0000	0.665754
$732$	0	0
$733$	3.00000	0.110808	0.0554038	−	0.998464i	$-0.482355\pi$
$733$	3.00000	0.110808	0.0554038	+	0.998464i	$0.482355\pi$
$734$	10.0000	0.369107
$735$	0	0
$736$	3.00000	0.110581
$737$	0	0
$738$	0	0
$739$	24.0000	0.882854	0.441427	−	0.897297i	$-0.354472\pi$
$739$	24.0000	0.882854	0.441427	+	0.897297i	$0.354472\pi$
$740$	−6.00000	−0.220564
$741$	0	0
$742$	0	0
$743$	−18.0000	−0.660356	−0.330178	−	0.943919i	$-0.607109\pi$
$743$	−18.0000	−0.660356	−0.330178	+	0.943919i	$0.607109\pi$
$744$	0	0
$745$	−72.0000	−2.63788
$746$	−15.0000	−0.549189
$747$	0	0
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−50.0000	−1.82453	−0.912263	−	0.409605i	$-0.865667\pi$
$751$	−50.0000	−1.82453	−0.912263	+	0.409605i	$0.865667\pi$
$752$	0	0
$753$	0	0
$754$	18.0000	0.655521
$755$	63.0000	2.29280
$756$	0	0
$757$	−20.0000	−0.726912	−0.363456	−	0.931611i	$-0.618403\pi$
$757$	−20.0000	−0.726912	−0.363456	+	0.931611i	$0.618403\pi$
$758$	−20.0000	−0.726433
$759$	0	0
$760$	18.0000	0.652929
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	0	0
$763$	0	0
$764$	−3.00000	−0.108536
$765$	0	0
$766$	−24.0000	−0.867155
$767$	36.0000	1.29988
$768$	0	0
$769$	−42.0000	−1.51456	−0.757279	−	0.653091i	$-0.773472\pi$
$769$	−42.0000	−1.51456	−0.757279	+	0.653091i	$0.773472\pi$
$770$	0	0
$771$	0	0
$772$	6.00000	0.215945
$773$	18.0000	0.647415	0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000	0.647415	0.323708	+	0.946157i	$0.395071\pi$
$774$	0	0
$775$	16.0000	0.574737
$776$	−17.0000	−0.610264
$777$	0	0
$778$	6.00000	0.215110
$779$	−18.0000	−0.644917
$780$	0	0
$781$	0	0
$782$	−9.00000	−0.321839
$783$	0	0
$784$	−7.00000	−0.250000
$785$	12.0000	0.428298
$786$	0	0
$787$	−42.0000	−1.49714	−0.748569	−	0.663057i	$-0.769259\pi$
$787$	−42.0000	−1.49714	−0.748569	+	0.663057i	$0.769259\pi$
$788$	24.0000	0.854965
$789$	0	0
$790$	−45.0000	−1.60103
$791$	0	0
$792$	0	0
$793$	−45.0000	−1.59800
$794$	34.0000	1.20661
$795$	0	0
$796$	−2.00000	−0.0708881
$797$	15.0000	0.531327	0.265664	−	0.964066i	$-0.414409\pi$
$797$	15.0000	0.531327	0.265664	+	0.964066i	$0.414409\pi$
$798$	0	0
$799$	0	0
$800$	−4.00000	−0.141421
$801$	0	0
$802$	−36.0000	−1.27120
$803$	0	0
$804$	0	0
$805$	0	0
$806$	−12.0000	−0.422682
$807$	0	0
$808$	12.0000	0.422159
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	0	0
$811$	24.0000	0.842754	0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000	0.842754	0.421377	+	0.906886i	$0.361547\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	33.0000	1.15594
$816$	0	0
$817$	36.0000	1.25948
$818$	0	0
$819$	0	0
$820$	9.00000	0.314294
$821$	−6.00000	−0.209401	−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000	−0.209401	−0.104701	+	0.994504i	$0.533388\pi$
$822$	0	0
$823$	14.0000	0.488009	0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000	0.488009	0.244005	+	0.969774i	$0.421539\pi$
$824$	−14.0000	−0.487713
$825$	0	0
$826$	0	0
$827$	3.00000	0.104320	0.0521601	−	0.998639i	$-0.483389\pi$
$827$	3.00000	0.104320	0.0521601	+	0.998639i	$0.483389\pi$
$828$	0	0
$829$	−52.0000	−1.80603	−0.903017	−	0.429604i	$-0.858653\pi$
$829$	−52.0000	−1.80603	−0.903017	+	0.429604i	$0.858653\pi$
$830$	27.0000	0.937184
$831$	0	0
$832$	3.00000	0.104006
$833$	21.0000	0.727607
$834$	0	0
$835$	−36.0000	−1.24583
$836$	0	0
$837$	0	0
$838$	18.0000	0.621800
$839$	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
$841$	7.00000	0.241379
$842$	−10.0000	−0.344623
$843$	0	0
$844$	−12.0000	−0.413057
$845$	−12.0000	−0.412813
$846$	0	0
$847$	0	0
$848$	−9.00000	−0.309061
$849$	0	0
$850$	12.0000	0.411597
$851$	6.00000	0.205677
$852$	0	0
$853$	42.0000	1.43805	0.719026	−	0.694983i	$-0.244588\pi$
$853$	42.0000	1.43805	0.719026	+	0.694983i	$0.244588\pi$
$854$	0	0
$855$	0	0
$856$	15.0000	0.512689
$857$	−27.0000	−0.922302	−0.461151	−	0.887322i	$-0.652563\pi$
$857$	−27.0000	−0.922302	−0.461151	+	0.887322i	$0.652563\pi$
$858$	0	0
$859$	−49.0000	−1.67186	−0.835929	−	0.548837i	$-0.815071\pi$
$859$	−49.0000	−1.67186	−0.835929	+	0.548837i	$0.815071\pi$
$860$	−18.0000	−0.613795
$861$	0	0
$862$	−12.0000	−0.408722
$863$	9.00000	0.306364	0.153182	−	0.988198i	$-0.451048\pi$
$863$	9.00000	0.306364	0.153182	+	0.988198i	$0.451048\pi$
$864$	0	0
$865$	0	0
$866$	25.0000	0.849535
$867$	0	0
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−15.0000	−0.508256
$872$	6.00000	0.203186
$873$	0	0
$874$	−18.0000	−0.608859
$875$	0	0
$876$	0	0
$877$	27.0000	0.911725	0.455863	−	0.890050i	$-0.349331\pi$
$877$	27.0000	0.911725	0.455863	+	0.890050i	$0.349331\pi$
$878$	−9.00000	−0.303735
$879$	0	0
$880$	0	0
$881$	−48.0000	−1.61716	−0.808581	−	0.588386i	$-0.799764\pi$
$881$	−48.0000	−1.61716	−0.808581	+	0.588386i	$0.799764\pi$
$882$	0	0
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	−9.00000	−0.302703
$885$	0	0
$886$	−30.0000	−1.00787
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	0	0
$889$	0	0
$890$	18.0000	0.603361
$891$	0	0
$892$	8.00000	0.267860
$893$	0	0
$894$	0	0
$895$	18.0000	0.601674
$896$	0	0
$897$	0	0
$898$	−30.0000	−1.00111
$899$	−24.0000	−0.800445
$900$	0	0
$901$	27.0000	0.899500
$902$	0	0
$903$	0	0
$904$	6.00000	0.199557
$905$	−48.0000	−1.59557
$906$	0	0
$907$	−1.00000	−0.0332045	−0.0166022	−	0.999862i	$-0.505285\pi$
$907$	−1.00000	−0.0332045	−0.0166022	+	0.999862i	$0.505285\pi$
$908$	−12.0000	−0.398234
$909$	0	0
$910$	0	0
$911$	45.0000	1.49092	0.745458	−	0.666552i	$-0.232231\pi$
$911$	45.0000	1.49092	0.745458	+	0.666552i	$0.232231\pi$
$912$	0	0
$913$	0	0
$914$	−6.00000	−0.198462
$915$	0	0
$916$	−14.0000	−0.462573
$917$	0	0
$918$	0	0
$919$	−27.0000	−0.890648	−0.445324	−	0.895370i	$-0.646911\pi$
$919$	−27.0000	−0.890648	−0.445324	+	0.895370i	$0.646911\pi$
$920$	9.00000	0.296721
$921$	0	0
$922$	0	0
$923$	−36.0000	−1.18495
$924$	0	0
$925$	−8.00000	−0.263038
$926$	4.00000	0.131448
$927$	0	0
$928$	6.00000	0.196960
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	0	0
$931$	42.0000	1.37649
$932$	21.0000	0.687878
$933$	0	0
$934$	24.0000	0.785304
$935$	0	0
$936$	0	0
$937$	18.0000	0.588034	0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000	0.588034	0.294017	+	0.955800i	$0.405008\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	48.0000	1.56476	0.782378	−	0.622804i	$-0.214007\pi$
$941$	48.0000	1.56476	0.782378	+	0.622804i	$0.214007\pi$
$942$	0	0
$943$	−9.00000	−0.293080
$944$	12.0000	0.390567
$945$	0	0
$946$	0	0
$947$	6.00000	0.194974	0.0974869	−	0.995237i	$-0.468920\pi$
$947$	6.00000	0.194974	0.0974869	+	0.995237i	$0.468920\pi$
$948$	0	0
$949$	−18.0000	−0.584305
$950$	24.0000	0.778663
$951$	0	0
$952$	0	0
$953$	45.0000	1.45769	0.728846	−	0.684677i	$-0.240057\pi$
$953$	45.0000	1.45769	0.728846	+	0.684677i	$0.240057\pi$
$954$	0	0
$955$	−9.00000	−0.291233
$956$	−6.00000	−0.194054
$957$	0	0
$958$	6.00000	0.193851
$959$	0	0
$960$	0	0
$961$	−15.0000	−0.483871
$962$	6.00000	0.193448
$963$	0	0
$964$	18.0000	0.579741
$965$	18.0000	0.579441
$966$	0	0
$967$	21.0000	0.675314	0.337657	−	0.941269i	$-0.390366\pi$
$967$	21.0000	0.675314	0.337657	+	0.941269i	$0.390366\pi$
$968$	0	0
$969$	0	0
$970$	−51.0000	−1.63751
$971$	42.0000	1.34784	0.673922	−	0.738802i	$-0.264608\pi$
$971$	42.0000	1.34784	0.673922	+	0.738802i	$0.264608\pi$
$972$	0	0
$973$	0	0
$974$	38.0000	1.21760
$975$	0	0
$976$	−15.0000	−0.480138
$977$	24.0000	0.767828	0.383914	−	0.923369i	$-0.374576\pi$
$977$	24.0000	0.767828	0.383914	+	0.923369i	$0.374576\pi$
$978$	0	0
$979$	0	0
$980$	−21.0000	−0.670820
$981$	0	0
$982$	36.0000	1.14881
$983$	−3.00000	−0.0956851	−0.0478426	−	0.998855i	$-0.515235\pi$
$983$	−3.00000	−0.0956851	−0.0478426	+	0.998855i	$0.515235\pi$
$984$	0	0
$985$	72.0000	2.29411
$986$	−18.0000	−0.573237
$987$	0	0
$988$	−18.0000	−0.572656
$989$	18.0000	0.572367
$990$	0	0
$991$	34.0000	1.08005	0.540023	−	0.841650i	$-0.318416\pi$
$991$	34.0000	1.08005	0.540023	+	0.841650i	$0.318416\pi$
$992$	−4.00000	−0.127000
$993$	0	0
$994$	0	0
$995$	−6.00000	−0.190213
$996$	0	0
$997$	−9.00000	−0.285033	−0.142516	−	0.989792i	$-0.545519\pi$
$997$	−9.00000	−0.285033	−0.142516	+	0.989792i	$0.545519\pi$
$998$	−13.0000	−0.411508
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6534.2.a.n.1.1	yes	1
3.2	odd	2		6534.2.a.q.1.1	yes	1
11.10	odd	2		6534.2.a.bb.1.1	yes	1
33.32	even	2		6534.2.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6534.2.a.a.1.1	✓	1	33.32	even	2
6534.2.a.n.1.1	yes	1	1.1	even	1	trivial
6534.2.a.q.1.1	yes	1	3.2	odd	2
6534.2.a.bb.1.1	yes	1	11.10	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:	\( N \)	\(=\)	\( 6534 = 2 \cdot 3^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6534.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more