LMFDB - Embedded newform 1911.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1911,2,Mod(1,1911)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1911, 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("1911.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1911 = 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1911.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:	$15.2594118263$
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	$\chi$	$=$	1911.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+1.00000 q^{3} -2.00000 q^{4} +1.00000 q^{5} +1.00000 q^{9} -2.00000 q^{11} -2.00000 q^{12} -1.00000 q^{13} +1.00000 q^{15} +4.00000 q^{16} -2.00000 q^{17} -5.00000 q^{19} -2.00000 q^{20} +1.00000 q^{23} -4.00000 q^{25} +1.00000 q^{27} -3.00000 q^{29} -1.00000 q^{31} -2.00000 q^{33} -2.00000 q^{36} +4.00000 q^{37} -1.00000 q^{39} -6.00000 q^{41} -1.00000 q^{43} +4.00000 q^{44} +1.00000 q^{45} +3.00000 q^{47} +4.00000 q^{48} -2.00000 q^{51} +2.00000 q^{52} -11.0000 q^{53} -2.00000 q^{55} -5.00000 q^{57} +4.00000 q^{59} -2.00000 q^{60} +2.00000 q^{61} -8.00000 q^{64} -1.00000 q^{65} -8.00000 q^{67} +4.00000 q^{68} +1.00000 q^{69} -8.00000 q^{71} +1.00000 q^{73} -4.00000 q^{75} +10.0000 q^{76} -5.00000 q^{79} +4.00000 q^{80} +1.00000 q^{81} -13.0000 q^{83} -2.00000 q^{85} -3.00000 q^{87} +15.0000 q^{89} -2.00000 q^{92} -1.00000 q^{93} -5.00000 q^{95} +5.00000 q^{97} -2.00000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0	0		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−2.00000	−1.00000
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	−2.00000	−0.577350
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	1.00000	0.258199
$16$	4.00000	1.00000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	0	0
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	−2.00000	−0.447214
$21$	0	0
$22$	0	0
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	0	0
$25$	−4.00000	−0.800000
$26$	0	0
$27$	1.00000	0.192450
$28$	0	0
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	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
$33$	−2.00000	−0.348155
$34$	0	0
$35$	0	0
$36$	−2.00000	−0.333333
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	0	0
$39$	−1.00000	−0.160128
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	4.00000	0.603023
$45$	1.00000	0.149071
$46$	0	0
$47$	3.00000	0.437595	0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000	0.437595	0.218797	+	0.975770i	$0.429787\pi$
$48$	4.00000	0.577350
$49$	0	0
$50$	0	0
$51$	−2.00000	−0.280056
$52$	2.00000	0.277350
$53$	−11.0000	−1.51097	−0.755483	−	0.655168i	$-0.772598\pi$
$53$	−11.0000	−1.51097	−0.755483	+	0.655168i	$0.772598\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	0	0
$57$	−5.00000	−0.662266
$58$	0	0
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	−2.00000	−0.258199
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	0	0
$63$	0	0
$64$	−8.00000	−1.00000
$65$	−1.00000	−0.124035
$66$	0	0
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	4.00000	0.485071
$69$	1.00000	0.120386
$70$	0	0
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	0	0
$73$	1.00000	0.117041	0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000	0.117041	0.0585206	+	0.998286i	$0.481362\pi$
$74$	0	0
$75$	−4.00000	−0.461880
$76$	10.0000	1.14708
$77$	0	0
$78$	0	0
$79$	−5.00000	−0.562544	−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000	−0.562544	−0.281272	+	0.959628i	$0.590756\pi$
$80$	4.00000	0.447214
$81$	1.00000	0.111111
$82$	0	0
$83$	−13.0000	−1.42694	−0.713468	−	0.700688i	$-0.752876\pi$
$83$	−13.0000	−1.42694	−0.713468	+	0.700688i	$0.752876\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	0	0
$87$	−3.00000	−0.321634
$88$	0	0
$89$	15.0000	1.59000	0.794998	−	0.606612i	$-0.207472\pi$
$89$	15.0000	1.59000	0.794998	+	0.606612i	$0.207472\pi$
$90$	0	0
$91$	0	0
$92$	−2.00000	−0.208514
$93$	−1.00000	−0.103695
$94$	0	0
$95$	−5.00000	−0.512989
$96$	0	0
$97$	5.00000	0.507673	0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000	0.507673	0.253837	+	0.967247i	$0.418307\pi$
$98$	0	0
$99$	−2.00000	−0.201008
$100$	8.00000	0.800000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	0	0
$103$	−12.0000	−1.18240	−0.591198	−	0.806527i	$-0.701345\pi$
$103$	−12.0000	−1.18240	−0.591198	+	0.806527i	$0.701345\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	−2.00000	−0.192450
$109$	−4.00000	−0.383131	−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000	−0.383131	−0.191565	+	0.981480i	$0.561356\pi$
$110$	0	0
$111$	4.00000	0.379663
$112$	0	0
$113$	−13.0000	−1.22294	−0.611469	−	0.791269i	$-0.709421\pi$
$113$	−13.0000	−1.22294	−0.611469	+	0.791269i	$0.709421\pi$
$114$	0	0
$115$	1.00000	0.0932505
$116$	6.00000	0.557086
$117$	−1.00000	−0.0924500
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−7.00000	−0.636364
$122$	0	0
$123$	−6.00000	−0.541002
$124$	2.00000	0.179605
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	0	0
$129$	−1.00000	−0.0880451
$130$	0	0
$131$	14.0000	1.22319	0.611593	−	0.791173i	$-0.290529\pi$
$131$	14.0000	1.22319	0.611593	+	0.791173i	$0.290529\pi$
$132$	4.00000	0.348155
$133$	0	0
$134$	0	0
$135$	1.00000	0.0860663
$136$	0	0
$137$	−8.00000	−0.683486	−0.341743	−	0.939793i	$-0.611017\pi$
$137$	−8.00000	−0.683486	−0.341743	+	0.939793i	$0.611017\pi$
$138$	0	0
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	0	0
$141$	3.00000	0.252646
$142$	0	0
$143$	2.00000	0.167248
$144$	4.00000	0.333333
$145$	−3.00000	−0.249136
$146$	0	0
$147$	0	0
$148$	−8.00000	−0.657596
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	0	0
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	0	0
$153$	−2.00000	−0.161690
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	2.00000	0.160128
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	0	0
$159$	−11.0000	−0.872357
$160$	0	0
$161$	0	0
$162$	0	0
$163$	6.00000	0.469956	0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000	0.469956	0.234978	+	0.972001i	$0.424498\pi$
$164$	12.0000	0.937043
$165$	−2.00000	−0.155700
$166$	0	0
$167$	21.0000	1.62503	0.812514	−	0.582941i	$-0.198098\pi$
$167$	21.0000	1.62503	0.812514	+	0.582941i	$0.198098\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	−5.00000	−0.382360
$172$	2.00000	0.152499
$173$	16.0000	1.21646	0.608229	−	0.793762i	$-0.291880\pi$
$173$	16.0000	1.21646	0.608229	+	0.793762i	$0.291880\pi$
$174$	0	0
$175$	0	0
$176$	−8.00000	−0.603023
$177$	4.00000	0.300658
$178$	0	0
$179$	5.00000	0.373718	0.186859	−	0.982387i	$-0.440169\pi$
$179$	5.00000	0.373718	0.186859	+	0.982387i	$0.440169\pi$
$180$	−2.00000	−0.149071
$181$	−14.0000	−1.04061	−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000	−1.04061	−0.520306	+	0.853980i	$0.674182\pi$
$182$	0	0
$183$	2.00000	0.147844
$184$	0	0
$185$	4.00000	0.294086
$186$	0	0
$187$	4.00000	0.292509
$188$	−6.00000	−0.437595
$189$	0	0
$190$	0	0
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	−8.00000	−0.577350
$193$	−12.0000	−0.863779	−0.431889	−	0.901927i	$-0.642153\pi$
$193$	−12.0000	−0.863779	−0.431889	+	0.901927i	$0.642153\pi$
$194$	0	0
$195$	−1.00000	−0.0716115
$196$	0	0
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	0	0
$199$	−22.0000	−1.55954	−0.779769	−	0.626067i	$-0.784664\pi$
$199$	−22.0000	−1.55954	−0.779769	+	0.626067i	$0.784664\pi$
$200$	0	0
$201$	−8.00000	−0.564276
$202$	0	0
$203$	0	0
$204$	4.00000	0.280056
$205$	−6.00000	−0.419058
$206$	0	0
$207$	1.00000	0.0695048
$208$	−4.00000	−0.277350
$209$	10.0000	0.691714
$210$	0	0
$211$	15.0000	1.03264	0.516321	−	0.856395i	$-0.327301\pi$
$211$	15.0000	1.03264	0.516321	+	0.856395i	$0.327301\pi$
$212$	22.0000	1.51097
$213$	−8.00000	−0.548151
$214$	0	0
$215$	−1.00000	−0.0681994
$216$	0	0
$217$	0	0
$218$	0	0
$219$	1.00000	0.0675737
$220$	4.00000	0.269680
$221$	2.00000	0.134535
$222$	0	0
$223$	9.00000	0.602685	0.301342	−	0.953516i	$-0.402565\pi$
$223$	9.00000	0.602685	0.301342	+	0.953516i	$0.402565\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	0	0
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	10.0000	0.662266
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	1.00000	0.0655122	0.0327561	−	0.999463i	$-0.489572\pi$
$233$	1.00000	0.0655122	0.0327561	+	0.999463i	$0.489572\pi$
$234$	0	0
$235$	3.00000	0.195698
$236$	−8.00000	−0.520756
$237$	−5.00000	−0.324785
$238$	0	0
$239$	30.0000	1.94054	0.970269	−	0.242028i	$-0.0778125\pi$
$239$	30.0000	1.94054	0.970269	+	0.242028i	$0.0778125\pi$
$240$	4.00000	0.258199
$241$	1.00000	0.0644157	0.0322078	−	0.999481i	$-0.489746\pi$
$241$	1.00000	0.0644157	0.0322078	+	0.999481i	$0.489746\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−4.00000	−0.256074
$245$	0	0
$246$	0	0
$247$	5.00000	0.318142
$248$	0	0
$249$	−13.0000	−0.823842
$250$	0	0
$251$	−6.00000	−0.378717	−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000	−0.378717	−0.189358	+	0.981908i	$0.560641\pi$
$252$	0	0
$253$	−2.00000	−0.125739
$254$	0	0
$255$	−2.00000	−0.125245
$256$	16.0000	1.00000
$257$	26.0000	1.62184	0.810918	−	0.585160i	$-0.198968\pi$
$257$	26.0000	1.62184	0.810918	+	0.585160i	$0.198968\pi$
$258$	0	0
$259$	0	0
$260$	2.00000	0.124035
$261$	−3.00000	−0.185695
$262$	0	0
$263$	−21.0000	−1.29492	−0.647458	−	0.762101i	$-0.724168\pi$
$263$	−21.0000	−1.29492	−0.647458	+	0.762101i	$0.724168\pi$
$264$	0	0
$265$	−11.0000	−0.675725
$266$	0	0
$267$	15.0000	0.917985
$268$	16.0000	0.977356
$269$	26.0000	1.58525	0.792624	−	0.609711i	$-0.208714\pi$
$269$	26.0000	1.58525	0.792624	+	0.609711i	$0.208714\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	−8.00000	−0.485071
$273$	0	0
$274$	0	0
$275$	8.00000	0.482418
$276$	−2.00000	−0.120386
$277$	21.0000	1.26177	0.630884	−	0.775877i	$-0.282692\pi$
$277$	21.0000	1.26177	0.630884	+	0.775877i	$0.282692\pi$
$278$	0	0
$279$	−1.00000	−0.0598684
$280$	0	0
$281$	16.0000	0.954480	0.477240	−	0.878773i	$-0.341637\pi$
$281$	16.0000	0.954480	0.477240	+	0.878773i	$0.341637\pi$
$282$	0	0
$283$	−8.00000	−0.475551	−0.237775	−	0.971320i	$-0.576418\pi$
$283$	−8.00000	−0.475551	−0.237775	+	0.971320i	$0.576418\pi$
$284$	16.0000	0.949425
$285$	−5.00000	−0.296174
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−13.0000	−0.764706
$290$	0	0
$291$	5.00000	0.293105
$292$	−2.00000	−0.117041
$293$	5.00000	0.292103	0.146052	−	0.989277i	$-0.453343\pi$
$293$	5.00000	0.292103	0.146052	+	0.989277i	$0.453343\pi$
$294$	0	0
$295$	4.00000	0.232889
$296$	0	0
$297$	−2.00000	−0.116052
$298$	0	0
$299$	−1.00000	−0.0578315
$300$	8.00000	0.461880
$301$	0	0
$302$	0	0
$303$	−6.00000	−0.344691
$304$	−20.0000	−1.14708
$305$	2.00000	0.114520
$306$	0	0
$307$	−23.0000	−1.31268	−0.656340	−	0.754466i	$-0.727896\pi$
$307$	−23.0000	−1.31268	−0.656340	+	0.754466i	$0.727896\pi$
$308$	0	0
$309$	−12.0000	−0.682656
$310$	0	0
$311$	16.0000	0.907277	0.453638	−	0.891186i	$-0.350126\pi$
$311$	16.0000	0.907277	0.453638	+	0.891186i	$0.350126\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	0	0
$315$	0	0
$316$	10.0000	0.562544
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	0	0
$319$	6.00000	0.335936
$320$	−8.00000	−0.447214
$321$	8.00000	0.446516
$322$	0	0
$323$	10.0000	0.556415
$324$	−2.00000	−0.111111
$325$	4.00000	0.221880
$326$	0	0
$327$	−4.00000	−0.221201
$328$	0	0
$329$	0	0
$330$	0	0
$331$	−22.0000	−1.20923	−0.604615	−	0.796518i	$-0.706673\pi$
$331$	−22.0000	−1.20923	−0.604615	+	0.796518i	$0.706673\pi$
$332$	26.0000	1.42694
$333$	4.00000	0.219199
$334$	0	0
$335$	−8.00000	−0.437087
$336$	0	0
$337$	5.00000	0.272367	0.136184	−	0.990684i	$-0.456516\pi$
$337$	5.00000	0.272367	0.136184	+	0.990684i	$0.456516\pi$
$338$	0	0
$339$	−13.0000	−0.706063
$340$	4.00000	0.216930
$341$	2.00000	0.108306
$342$	0	0
$343$	0	0
$344$	0	0
$345$	1.00000	0.0538382
$346$	0	0
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	6.00000	0.321634
$349$	25.0000	1.33822	0.669110	−	0.743164i	$-0.266676\pi$
$349$	25.0000	1.33822	0.669110	+	0.743164i	$0.266676\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	0	0
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	0	0
$355$	−8.00000	−0.424596
$356$	−30.0000	−1.59000
$357$	0	0
$358$	0	0
$359$	−10.0000	−0.527780	−0.263890	−	0.964553i	$-0.585006\pi$
$359$	−10.0000	−0.527780	−0.263890	+	0.964553i	$0.585006\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	0	0
$363$	−7.00000	−0.367405
$364$	0	0
$365$	1.00000	0.0523424
$366$	0	0
$367$	−20.0000	−1.04399	−0.521996	−	0.852948i	$-0.674812\pi$
$367$	−20.0000	−1.04399	−0.521996	+	0.852948i	$0.674812\pi$
$368$	4.00000	0.208514
$369$	−6.00000	−0.312348
$370$	0	0
$371$	0	0
$372$	2.00000	0.103695
$373$	−18.0000	−0.932005	−0.466002	−	0.884783i	$-0.654306\pi$
$373$	−18.0000	−0.932005	−0.466002	+	0.884783i	$0.654306\pi$
$374$	0	0
$375$	−9.00000	−0.464758
$376$	0	0
$377$	3.00000	0.154508
$378$	0	0
$379$	22.0000	1.13006	0.565032	−	0.825069i	$-0.308864\pi$
$379$	22.0000	1.13006	0.565032	+	0.825069i	$0.308864\pi$
$380$	10.0000	0.512989
$381$	−8.00000	−0.409852
$382$	0	0
$383$	−8.00000	−0.408781	−0.204390	−	0.978889i	$-0.565521\pi$
$383$	−8.00000	−0.408781	−0.204390	+	0.978889i	$0.565521\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−1.00000	−0.0508329
$388$	−10.0000	−0.507673
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	0	0
$391$	−2.00000	−0.101144
$392$	0	0
$393$	14.0000	0.706207
$394$	0	0
$395$	−5.00000	−0.251577
$396$	4.00000	0.201008
$397$	−19.0000	−0.953583	−0.476791	−	0.879017i	$-0.658200\pi$
$397$	−19.0000	−0.953583	−0.476791	+	0.879017i	$0.658200\pi$
$398$	0	0
$399$	0	0
$400$	−16.0000	−0.800000
$401$	−18.0000	−0.898877	−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000	−0.898877	−0.449439	+	0.893311i	$0.648376\pi$
$402$	0	0
$403$	1.00000	0.0498135
$404$	12.0000	0.597022
$405$	1.00000	0.0496904
$406$	0	0
$407$	−8.00000	−0.396545
$408$	0	0
$409$	33.0000	1.63174	0.815872	−	0.578232i	$-0.196257\pi$
$409$	33.0000	1.63174	0.815872	+	0.578232i	$0.196257\pi$
$410$	0	0
$411$	−8.00000	−0.394611
$412$	24.0000	1.18240
$413$	0	0
$414$	0	0
$415$	−13.0000	−0.638145
$416$	0	0
$417$	14.0000	0.685583
$418$	0	0
$419$	2.00000	0.0977064	0.0488532	−	0.998806i	$-0.484443\pi$
$419$	2.00000	0.0977064	0.0488532	+	0.998806i	$0.484443\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	0	0
$423$	3.00000	0.145865
$424$	0	0
$425$	8.00000	0.388057
$426$	0	0
$427$	0	0
$428$	−16.0000	−0.773389
$429$	2.00000	0.0965609
$430$	0	0
$431$	30.0000	1.44505	0.722525	−	0.691345i	$-0.242982\pi$
$431$	30.0000	1.44505	0.722525	+	0.691345i	$0.242982\pi$
$432$	4.00000	0.192450
$433$	−38.0000	−1.82616	−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000	−1.82616	−0.913082	+	0.407777i	$0.866304\pi$
$434$	0	0
$435$	−3.00000	−0.143839
$436$	8.00000	0.383131
$437$	−5.00000	−0.239182
$438$	0	0
$439$	14.0000	0.668184	0.334092	−	0.942541i	$-0.391570\pi$
$439$	14.0000	0.668184	0.334092	+	0.942541i	$0.391570\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−15.0000	−0.712672	−0.356336	−	0.934358i	$-0.615974\pi$
$443$	−15.0000	−0.712672	−0.356336	+	0.934358i	$0.615974\pi$
$444$	−8.00000	−0.379663
$445$	15.0000	0.711068
$446$	0	0
$447$	−18.0000	−0.851371
$448$	0	0
$449$	−14.0000	−0.660701	−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000	−0.660701	−0.330350	+	0.943858i	$0.607167\pi$
$450$	0	0
$451$	12.0000	0.565058
$452$	26.0000	1.22294
$453$	−4.00000	−0.187936
$454$	0	0
$455$	0	0
$456$	0	0
$457$	−2.00000	−0.0935561	−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$458$	0	0
$459$	−2.00000	−0.0933520
$460$	−2.00000	−0.0932505
$461$	14.0000	0.652045	0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000	0.652045	0.326023	+	0.945362i	$0.394291\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−12.0000	−0.557086
$465$	−1.00000	−0.0463739
$466$	0	0
$467$	8.00000	0.370196	0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000	0.370196	0.185098	+	0.982720i	$0.440740\pi$
$468$	2.00000	0.0924500
$469$	0	0
$470$	0	0
$471$	−10.0000	−0.460776
$472$	0	0
$473$	2.00000	0.0919601
$474$	0	0
$475$	20.0000	0.917663
$476$	0	0
$477$	−11.0000	−0.503655
$478$	0	0
$479$	21.0000	0.959514	0.479757	−	0.877401i	$-0.340725\pi$
$479$	21.0000	0.959514	0.479757	+	0.877401i	$0.340725\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	0	0
$483$	0	0
$484$	14.0000	0.636364
$485$	5.00000	0.227038
$486$	0	0
$487$	22.0000	0.996915	0.498458	−	0.866914i	$-0.333900\pi$
$487$	22.0000	0.996915	0.498458	+	0.866914i	$0.333900\pi$
$488$	0	0
$489$	6.00000	0.271329
$490$	0	0
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	12.0000	0.541002
$493$	6.00000	0.270226
$494$	0	0
$495$	−2.00000	−0.0898933
$496$	−4.00000	−0.179605
$497$	0	0
$498$	0	0
$499$	14.0000	0.626726	0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000	0.626726	0.313363	+	0.949633i	$0.398544\pi$
$500$	18.0000	0.804984
$501$	21.0000	0.938211
$502$	0	0
$503$	42.0000	1.87269	0.936344	−	0.351085i	$-0.114187\pi$
$503$	42.0000	1.87269	0.936344	+	0.351085i	$0.114187\pi$
$504$	0	0
$505$	−6.00000	−0.266996
$506$	0	0
$507$	1.00000	0.0444116
$508$	16.0000	0.709885
$509$	21.0000	0.930809	0.465404	−	0.885098i	$-0.345909\pi$
$509$	21.0000	0.930809	0.465404	+	0.885098i	$0.345909\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	−5.00000	−0.220755
$514$	0	0
$515$	−12.0000	−0.528783
$516$	2.00000	0.0880451
$517$	−6.00000	−0.263880
$518$	0	0
$519$	16.0000	0.702322
$520$	0	0
$521$	−28.0000	−1.22670	−0.613351	−	0.789810i	$-0.710179\pi$
$521$	−28.0000	−1.22670	−0.613351	+	0.789810i	$0.710179\pi$
$522$	0	0
$523$	2.00000	0.0874539	0.0437269	−	0.999044i	$-0.486077\pi$
$523$	2.00000	0.0874539	0.0437269	+	0.999044i	$0.486077\pi$
$524$	−28.0000	−1.22319
$525$	0	0
$526$	0	0
$527$	2.00000	0.0871214
$528$	−8.00000	−0.348155
$529$	−22.0000	−0.956522
$530$	0	0
$531$	4.00000	0.173585
$532$	0	0
$533$	6.00000	0.259889
$534$	0	0
$535$	8.00000	0.345870
$536$	0	0
$537$	5.00000	0.215766
$538$	0	0
$539$	0	0
$540$	−2.00000	−0.0860663
$541$	−20.0000	−0.859867	−0.429934	−	0.902861i	$-0.641463\pi$
$541$	−20.0000	−0.859867	−0.429934	+	0.902861i	$0.641463\pi$
$542$	0	0
$543$	−14.0000	−0.600798
$544$	0	0
$545$	−4.00000	−0.171341
$546$	0	0
$547$	5.00000	0.213785	0.106892	−	0.994271i	$-0.465910\pi$
$547$	5.00000	0.213785	0.106892	+	0.994271i	$0.465910\pi$
$548$	16.0000	0.683486
$549$	2.00000	0.0853579
$550$	0	0
$551$	15.0000	0.639021
$552$	0	0
$553$	0	0
$554$	0	0
$555$	4.00000	0.169791
$556$	−28.0000	−1.18746
$557$	28.0000	1.18640	0.593199	−	0.805056i	$-0.297865\pi$
$557$	28.0000	1.18640	0.593199	+	0.805056i	$0.297865\pi$
$558$	0	0
$559$	1.00000	0.0422955
$560$	0	0
$561$	4.00000	0.168880
$562$	0	0
$563$	−34.0000	−1.43293	−0.716465	−	0.697623i	$-0.754241\pi$
$563$	−34.0000	−1.43293	−0.716465	+	0.697623i	$0.754241\pi$
$564$	−6.00000	−0.252646
$565$	−13.0000	−0.546914
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−39.0000	−1.63497	−0.817483	−	0.575953i	$-0.804631\pi$
$569$	−39.0000	−1.63497	−0.817483	+	0.575953i	$0.804631\pi$
$570$	0	0
$571$	−5.00000	−0.209243	−0.104622	−	0.994512i	$-0.533363\pi$
$571$	−5.00000	−0.209243	−0.104622	+	0.994512i	$0.533363\pi$
$572$	−4.00000	−0.167248
$573$	0	0
$574$	0	0
$575$	−4.00000	−0.166812
$576$	−8.00000	−0.333333
$577$	−38.0000	−1.58196	−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000	−1.58196	−0.790980	+	0.611842i	$0.790429\pi$
$578$	0	0
$579$	−12.0000	−0.498703
$580$	6.00000	0.249136
$581$	0	0
$582$	0	0
$583$	22.0000	0.911147
$584$	0	0
$585$	−1.00000	−0.0413449
$586$	0	0
$587$	15.0000	0.619116	0.309558	−	0.950881i	$-0.399819\pi$
$587$	15.0000	0.619116	0.309558	+	0.950881i	$0.399819\pi$
$588$	0	0
$589$	5.00000	0.206021
$590$	0	0
$591$	10.0000	0.411345
$592$	16.0000	0.657596
$593$	5.00000	0.205325	0.102663	−	0.994716i	$-0.467264\pi$
$593$	5.00000	0.205325	0.102663	+	0.994716i	$0.467264\pi$
$594$	0	0
$595$	0	0
$596$	36.0000	1.47462
$597$	−22.0000	−0.900400
$598$	0	0
$599$	−47.0000	−1.92037	−0.960184	−	0.279368i	$-0.909875\pi$
$599$	−47.0000	−1.92037	−0.960184	+	0.279368i	$0.909875\pi$
$600$	0	0
$601$	28.0000	1.14214	0.571072	−	0.820900i	$-0.306528\pi$
$601$	28.0000	1.14214	0.571072	+	0.820900i	$0.306528\pi$
$602$	0	0
$603$	−8.00000	−0.325785
$604$	8.00000	0.325515
$605$	−7.00000	−0.284590
$606$	0	0
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	−3.00000	−0.121367
$612$	4.00000	0.161690
$613$	−38.0000	−1.53481	−0.767403	−	0.641165i	$-0.778451\pi$
$613$	−38.0000	−1.53481	−0.767403	+	0.641165i	$0.778451\pi$
$614$	0	0
$615$	−6.00000	−0.241943
$616$	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
$619$	24.0000	0.964641	0.482321	−	0.875995i	$-0.339794\pi$
$619$	24.0000	0.964641	0.482321	+	0.875995i	$0.339794\pi$
$620$	2.00000	0.0803219
$621$	1.00000	0.0401286
$622$	0	0
$623$	0	0
$624$	−4.00000	−0.160128
$625$	11.0000	0.440000
$626$	0	0
$627$	10.0000	0.399362
$628$	20.0000	0.798087
$629$	−8.00000	−0.318981
$630$	0	0
$631$	22.0000	0.875806	0.437903	−	0.899022i	$-0.355721\pi$
$631$	22.0000	0.875806	0.437903	+	0.899022i	$0.355721\pi$
$632$	0	0
$633$	15.0000	0.596196
$634$	0	0
$635$	−8.00000	−0.317470
$636$	22.0000	0.872357
$637$	0	0
$638$	0	0
$639$	−8.00000	−0.316475
$640$	0	0
$641$	3.00000	0.118493	0.0592464	−	0.998243i	$-0.481130\pi$
$641$	3.00000	0.118493	0.0592464	+	0.998243i	$0.481130\pi$
$642$	0	0
$643$	28.0000	1.10421	0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000	1.10421	0.552106	+	0.833774i	$0.313824\pi$
$644$	0	0
$645$	−1.00000	−0.0393750
$646$	0	0
$647$	−36.0000	−1.41531	−0.707653	−	0.706560i	$-0.750246\pi$
$647$	−36.0000	−1.41531	−0.707653	+	0.706560i	$0.750246\pi$
$648$	0	0
$649$	−8.00000	−0.314027
$650$	0	0
$651$	0	0
$652$	−12.0000	−0.469956
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	0	0
$655$	14.0000	0.547025
$656$	−24.0000	−0.937043
$657$	1.00000	0.0390137
$658$	0	0
$659$	23.0000	0.895953	0.447976	−	0.894045i	$-0.352145\pi$
$659$	23.0000	0.895953	0.447976	+	0.894045i	$0.352145\pi$
$660$	4.00000	0.155700
$661$	45.0000	1.75030	0.875149	−	0.483854i	$-0.160764\pi$
$661$	45.0000	1.75030	0.875149	+	0.483854i	$0.160764\pi$
$662$	0	0
$663$	2.00000	0.0776736
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−3.00000	−0.116160
$668$	−42.0000	−1.62503
$669$	9.00000	0.347960
$670$	0	0
$671$	−4.00000	−0.154418
$672$	0	0
$673$	1.00000	0.0385472	0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000	0.0385472	0.0192736	+	0.999814i	$0.493865\pi$
$674$	0	0
$675$	−4.00000	−0.153960
$676$	−2.00000	−0.0769231
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	24.0000	0.919682
$682$	0	0
$683$	−44.0000	−1.68361	−0.841807	−	0.539779i	$-0.818508\pi$
$683$	−44.0000	−1.68361	−0.841807	+	0.539779i	$0.818508\pi$
$684$	10.0000	0.382360
$685$	−8.00000	−0.305664
$686$	0	0
$687$	−22.0000	−0.839352
$688$	−4.00000	−0.152499
$689$	11.0000	0.419067
$690$	0	0
$691$	1.00000	0.0380418	0.0190209	−	0.999819i	$-0.493945\pi$
$691$	1.00000	0.0380418	0.0190209	+	0.999819i	$0.493945\pi$
$692$	−32.0000	−1.21646
$693$	0	0
$694$	0	0
$695$	14.0000	0.531050
$696$	0	0
$697$	12.0000	0.454532
$698$	0	0
$699$	1.00000	0.0378235
$700$	0	0
$701$	−17.0000	−0.642081	−0.321041	−	0.947065i	$-0.604033\pi$
$701$	−17.0000	−0.642081	−0.321041	+	0.947065i	$0.604033\pi$
$702$	0	0
$703$	−20.0000	−0.754314
$704$	16.0000	0.603023
$705$	3.00000	0.112987
$706$	0	0
$707$	0	0
$708$	−8.00000	−0.300658
$709$	−18.0000	−0.676004	−0.338002	−	0.941145i	$-0.609751\pi$
$709$	−18.0000	−0.676004	−0.338002	+	0.941145i	$0.609751\pi$
$710$	0	0
$711$	−5.00000	−0.187515
$712$	0	0
$713$	−1.00000	−0.0374503
$714$	0	0
$715$	2.00000	0.0747958
$716$	−10.0000	−0.373718
$717$	30.0000	1.12037
$718$	0	0
$719$	16.0000	0.596699	0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000	0.596699	0.298350	+	0.954457i	$0.403564\pi$
$720$	4.00000	0.149071
$721$	0	0
$722$	0	0
$723$	1.00000	0.0371904
$724$	28.0000	1.04061
$725$	12.0000	0.445669
$726$	0	0
$727$	4.00000	0.148352	0.0741759	−	0.997245i	$-0.476367\pi$
$727$	4.00000	0.148352	0.0741759	+	0.997245i	$0.476367\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	2.00000	0.0739727
$732$	−4.00000	−0.147844
$733$	41.0000	1.51437	0.757185	−	0.653201i	$-0.226574\pi$
$733$	41.0000	1.51437	0.757185	+	0.653201i	$0.226574\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	16.0000	0.589368
$738$	0	0
$739$	−30.0000	−1.10357	−0.551784	−	0.833987i	$-0.686053\pi$
$739$	−30.0000	−1.10357	−0.551784	+	0.833987i	$0.686053\pi$
$740$	−8.00000	−0.294086
$741$	5.00000	0.183680
$742$	0	0
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	0	0
$745$	−18.0000	−0.659469
$746$	0	0
$747$	−13.0000	−0.475645
$748$	−8.00000	−0.292509
$749$	0	0
$750$	0	0
$751$	23.0000	0.839282	0.419641	−	0.907690i	$-0.362156\pi$
$751$	23.0000	0.839282	0.419641	+	0.907690i	$0.362156\pi$
$752$	12.0000	0.437595
$753$	−6.00000	−0.218652
$754$	0	0
$755$	−4.00000	−0.145575
$756$	0	0
$757$	1.00000	0.0363456	0.0181728	−	0.999835i	$-0.494215\pi$
$757$	1.00000	0.0363456	0.0181728	+	0.999835i	$0.494215\pi$
$758$	0	0
$759$	−2.00000	−0.0725954
$760$	0	0
$761$	−11.0000	−0.398750	−0.199375	−	0.979923i	$-0.563891\pi$
$761$	−11.0000	−0.398750	−0.199375	+	0.979923i	$0.563891\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−2.00000	−0.0723102
$766$	0	0
$767$	−4.00000	−0.144432
$768$	16.0000	0.577350
$769$	−5.00000	−0.180305	−0.0901523	−	0.995928i	$-0.528735\pi$
$769$	−5.00000	−0.180305	−0.0901523	+	0.995928i	$0.528735\pi$
$770$	0	0
$771$	26.0000	0.936367
$772$	24.0000	0.863779
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	0	0
$775$	4.00000	0.143684
$776$	0	0
$777$	0	0
$778$	0	0
$779$	30.0000	1.07486
$780$	2.00000	0.0716115
$781$	16.0000	0.572525
$782$	0	0
$783$	−3.00000	−0.107211
$784$	0	0
$785$	−10.0000	−0.356915
$786$	0	0
$787$	43.0000	1.53278	0.766392	−	0.642373i	$-0.222050\pi$
$787$	43.0000	1.53278	0.766392	+	0.642373i	$0.222050\pi$
$788$	−20.0000	−0.712470
$789$	−21.0000	−0.747620
$790$	0	0
$791$	0	0
$792$	0	0
$793$	−2.00000	−0.0710221
$794$	0	0
$795$	−11.0000	−0.390130
$796$	44.0000	1.55954
$797$	−12.0000	−0.425062	−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000	−0.425062	−0.212531	+	0.977154i	$0.568171\pi$
$798$	0	0
$799$	−6.00000	−0.212265
$800$	0	0
$801$	15.0000	0.529999
$802$	0	0
$803$	−2.00000	−0.0705785
$804$	16.0000	0.564276
$805$	0	0
$806$	0	0
$807$	26.0000	0.915243
$808$	0	0
$809$	−21.0000	−0.738321	−0.369160	−	0.929366i	$-0.620355\pi$
$809$	−21.0000	−0.738321	−0.369160	+	0.929366i	$0.620355\pi$
$810$	0	0
$811$	−52.0000	−1.82597	−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000	−1.82597	−0.912983	+	0.407997i	$0.866228\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	6.00000	0.210171
$816$	−8.00000	−0.280056
$817$	5.00000	0.174928
$818$	0	0
$819$	0	0
$820$	12.0000	0.419058
$821$	32.0000	1.11681	0.558404	−	0.829569i	$-0.311414\pi$
$821$	32.0000	1.11681	0.558404	+	0.829569i	$0.311414\pi$
$822$	0	0
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	0	0
$825$	8.00000	0.278524
$826$	0	0
$827$	6.00000	0.208640	0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000	0.208640	0.104320	+	0.994544i	$0.466733\pi$
$828$	−2.00000	−0.0695048
$829$	−28.0000	−0.972480	−0.486240	−	0.873825i	$-0.661632\pi$
$829$	−28.0000	−0.972480	−0.486240	+	0.873825i	$0.661632\pi$
$830$	0	0
$831$	21.0000	0.728482
$832$	8.00000	0.277350
$833$	0	0
$834$	0	0
$835$	21.0000	0.726735
$836$	−20.0000	−0.691714
$837$	−1.00000	−0.0345651
$838$	0	0
$839$	36.0000	1.24286	0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000	1.24286	0.621429	+	0.783470i	$0.286552\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	0	0
$843$	16.0000	0.551069
$844$	−30.0000	−1.03264
$845$	1.00000	0.0344010
$846$	0	0
$847$	0	0
$848$	−44.0000	−1.51097
$849$	−8.00000	−0.274559
$850$	0	0
$851$	4.00000	0.137118
$852$	16.0000	0.548151
$853$	−1.00000	−0.0342393	−0.0171197	−	0.999853i	$-0.505450\pi$
$853$	−1.00000	−0.0342393	−0.0171197	+	0.999853i	$0.505450\pi$
$854$	0	0
$855$	−5.00000	−0.170996
$856$	0	0
$857$	−22.0000	−0.751506	−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000	−0.751506	−0.375753	+	0.926720i	$0.622616\pi$
$858$	0	0
$859$	−48.0000	−1.63774	−0.818869	−	0.573980i	$-0.805399\pi$
$859$	−48.0000	−1.63774	−0.818869	+	0.573980i	$0.805399\pi$
$860$	2.00000	0.0681994
$861$	0	0
$862$	0	0
$863$	−52.0000	−1.77010	−0.885050	−	0.465495i	$-0.845876\pi$
$863$	−52.0000	−1.77010	−0.885050	+	0.465495i	$0.845876\pi$
$864$	0	0
$865$	16.0000	0.544016
$866$	0	0
$867$	−13.0000	−0.441503
$868$	0	0
$869$	10.0000	0.339227
$870$	0	0
$871$	8.00000	0.271070
$872$	0	0
$873$	5.00000	0.169224
$874$	0	0
$875$	0	0
$876$	−2.00000	−0.0675737
$877$	10.0000	0.337676	0.168838	−	0.985644i	$-0.445999\pi$
$877$	10.0000	0.337676	0.168838	+	0.985644i	$0.445999\pi$
$878$	0	0
$879$	5.00000	0.168646
$880$	−8.00000	−0.269680
$881$	−52.0000	−1.75192	−0.875962	−	0.482380i	$-0.839773\pi$
$881$	−52.0000	−1.75192	−0.875962	+	0.482380i	$0.839773\pi$
$882$	0	0
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	−4.00000	−0.134535
$885$	4.00000	0.134459
$886$	0	0
$887$	−26.0000	−0.872995	−0.436497	−	0.899706i	$-0.643781\pi$
$887$	−26.0000	−0.872995	−0.436497	+	0.899706i	$0.643781\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−2.00000	−0.0670025
$892$	−18.0000	−0.602685
$893$	−15.0000	−0.501956
$894$	0	0
$895$	5.00000	0.167132
$896$	0	0
$897$	−1.00000	−0.0333890
$898$	0	0
$899$	3.00000	0.100056
$900$	8.00000	0.266667
$901$	22.0000	0.732926
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−14.0000	−0.465376
$906$	0	0
$907$	−41.0000	−1.36138	−0.680691	−	0.732570i	$-0.738320\pi$
$907$	−41.0000	−1.36138	−0.680691	+	0.732570i	$0.738320\pi$
$908$	−48.0000	−1.59294
$909$	−6.00000	−0.199007
$910$	0	0
$911$	−21.0000	−0.695761	−0.347881	−	0.937539i	$-0.613099\pi$
$911$	−21.0000	−0.695761	−0.347881	+	0.937539i	$0.613099\pi$
$912$	−20.0000	−0.662266
$913$	26.0000	0.860474
$914$	0	0
$915$	2.00000	0.0661180
$916$	44.0000	1.45380
$917$	0	0
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	0	0
$921$	−23.0000	−0.757876
$922$	0	0
$923$	8.00000	0.263323
$924$	0	0
$925$	−16.0000	−0.526077
$926$	0	0
$927$	−12.0000	−0.394132
$928$	0	0
$929$	−7.00000	−0.229663	−0.114831	−	0.993385i	$-0.536633\pi$
$929$	−7.00000	−0.229663	−0.114831	+	0.993385i	$0.536633\pi$
$930$	0	0
$931$	0	0
$932$	−2.00000	−0.0655122
$933$	16.0000	0.523816
$934$	0	0
$935$	4.00000	0.130814
$936$	0	0
$937$	−44.0000	−1.43742	−0.718709	−	0.695311i	$-0.755266\pi$
$937$	−44.0000	−1.43742	−0.718709	+	0.695311i	$0.755266\pi$
$938$	0	0
$939$	14.0000	0.456873
$940$	−6.00000	−0.195698
$941$	−57.0000	−1.85815	−0.929073	−	0.369895i	$-0.879394\pi$
$941$	−57.0000	−1.85815	−0.929073	+	0.369895i	$0.879394\pi$
$942$	0	0
$943$	−6.00000	−0.195387
$944$	16.0000	0.520756
$945$	0	0
$946$	0	0
$947$	20.0000	0.649913	0.324956	−	0.945729i	$-0.394650\pi$
$947$	20.0000	0.649913	0.324956	+	0.945729i	$0.394650\pi$
$948$	10.0000	0.324785
$949$	−1.00000	−0.0324614
$950$	0	0
$951$	−18.0000	−0.583690
$952$	0	0
$953$	−57.0000	−1.84641	−0.923206	−	0.384307i	$-0.874441\pi$
$953$	−57.0000	−1.84641	−0.923206	+	0.384307i	$0.874441\pi$
$954$	0	0
$955$	0	0
$956$	−60.0000	−1.94054
$957$	6.00000	0.193952
$958$	0	0
$959$	0	0
$960$	−8.00000	−0.258199
$961$	−30.0000	−0.967742
$962$	0	0
$963$	8.00000	0.257796
$964$	−2.00000	−0.0644157
$965$	−12.0000	−0.386294
$966$	0	0
$967$	2.00000	0.0643157	0.0321578	−	0.999483i	$-0.489762\pi$
$967$	2.00000	0.0643157	0.0321578	+	0.999483i	$0.489762\pi$
$968$	0	0
$969$	10.0000	0.321246
$970$	0	0
$971$	−30.0000	−0.962746	−0.481373	−	0.876516i	$-0.659862\pi$
$971$	−30.0000	−0.962746	−0.481373	+	0.876516i	$0.659862\pi$
$972$	−2.00000	−0.0641500
$973$	0	0
$974$	0	0
$975$	4.00000	0.128103
$976$	8.00000	0.256074
$977$	42.0000	1.34370	0.671850	−	0.740688i	$-0.265500\pi$
$977$	42.0000	1.34370	0.671850	+	0.740688i	$0.265500\pi$
$978$	0	0
$979$	−30.0000	−0.958804
$980$	0	0
$981$	−4.00000	−0.127710
$982$	0	0
$983$	−19.0000	−0.606006	−0.303003	−	0.952990i	$-0.597989\pi$
$983$	−19.0000	−0.606006	−0.303003	+	0.952990i	$0.597989\pi$
$984$	0	0
$985$	10.0000	0.318626
$986$	0	0
$987$	0	0
$988$	−10.0000	−0.318142
$989$	−1.00000	−0.0317982
$990$	0	0
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	0	0
$993$	−22.0000	−0.698149
$994$	0	0
$995$	−22.0000	−0.697447
$996$	26.0000	0.823842
$997$	44.0000	1.39349	0.696747	−	0.717317i	$-0.254630\pi$
$997$	44.0000	1.39349	0.696747	+	0.717317i	$0.254630\pi$
$998$	0	0
$999$	4.00000	0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1911.2.a.e.1.1	yes	1
3.2	odd	2		5733.2.a.g.1.1		1
7.6	odd	2		1911.2.a.d.1.1	✓	1
21.20	even	2		5733.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1911.2.a.d.1.1	✓	1	7.6	odd	2
1911.2.a.e.1.1	yes	1	1.1	even	1	trivial
5733.2.a.g.1.1		1	3.2	odd	2
5733.2.a.h.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:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1911.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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