LMFDB - Embedded newform 1856.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1856,4,Mod(1,1856)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1856, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1856.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1856 = 2^{6} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1856.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:	$109.507544971$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1856.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-7.00000 q^{3} -5.00000 q^{5} -2.00000 q^{7} +22.0000 q^{9} +O(q^{10})$

$q-7.00000 q^{3} -5.00000 q^{5} -2.00000 q^{7} +22.0000 q^{9} -37.0000 q^{11} -27.0000 q^{13} +35.0000 q^{15} +24.0000 q^{17} +88.0000 q^{19} +14.0000 q^{21} -28.0000 q^{23} -100.000 q^{25} +35.0000 q^{27} +29.0000 q^{29} -143.000 q^{31} +259.000 q^{33} +10.0000 q^{35} +360.000 q^{37} +189.000 q^{39} +386.000 q^{41} -381.000 q^{43} -110.000 q^{45} -103.000 q^{47} -339.000 q^{49} -168.000 q^{51} +431.000 q^{53} +185.000 q^{55} -616.000 q^{57} -288.000 q^{59} +840.000 q^{61} -44.0000 q^{63} +135.000 q^{65} +180.000 q^{67} +196.000 q^{69} +706.000 q^{71} +716.000 q^{73} +700.000 q^{75} +74.0000 q^{77} +931.000 q^{79} -839.000 q^{81} -1188.00 q^{83} -120.000 q^{85} -203.000 q^{87} -642.000 q^{89} +54.0000 q^{91} +1001.00 q^{93} -440.000 q^{95} +486.000 q^{97} -814.000 q^{99} +O(q^{100})$

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
$2$	0	0
$3$	−7.00000	−1.34715	−0.673575	−	0.739119i	$-0.735242\pi$
$3$	−7.00000	−1.34715	−0.673575	+	0.739119i	$0.735242\pi$
$4$	0	0
$5$	−5.00000	−0.447214	−0.223607	−	0.974679i	$-0.571783\pi$
$5$	−5.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	0	0
$7$	−2.00000	−0.107990	−0.0539949	−	0.998541i	$-0.517195\pi$
$7$	−2.00000	−0.107990	−0.0539949	+	0.998541i	$0.517195\pi$
$8$	0	0
$9$	22.0000	0.814815
$10$	0	0
$11$	−37.0000	−1.01417	−0.507087	−	0.861895i	$-0.669278\pi$
$11$	−37.0000	−1.01417	−0.507087	+	0.861895i	$0.669278\pi$
$12$	0	0
$13$	−27.0000	−0.576035	−0.288017	−	0.957625i	$-0.592996\pi$
$13$	−27.0000	−0.576035	−0.288017	+	0.957625i	$0.592996\pi$
$14$	0	0
$15$	35.0000	0.602464
$16$	0	0
$17$	24.0000	0.342403	0.171202	−	0.985236i	$-0.445235\pi$
$17$	24.0000	0.342403	0.171202	+	0.985236i	$0.445235\pi$
$18$	0	0
$19$	88.0000	1.06256	0.531279	−	0.847197i	$-0.321712\pi$
$19$	88.0000	1.06256	0.531279	+	0.847197i	$0.321712\pi$
$20$	0	0
$21$	14.0000	0.145479
$22$	0	0
$23$	−28.0000	−0.253844	−0.126922	−	0.991913i	$-0.540510\pi$
$23$	−28.0000	−0.253844	−0.126922	+	0.991913i	$0.540510\pi$
$24$	0	0
$25$	−100.000	−0.800000
$26$	0	0
$27$	35.0000	0.249472
$28$	0	0
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	0	0
$31$	−143.000	−0.828502	−0.414251	−	0.910163i	$-0.635956\pi$
$31$	−143.000	−0.828502	−0.414251	+	0.910163i	$0.635956\pi$
$32$	0	0
$33$	259.000	1.36625
$34$	0	0
$35$	10.0000	0.0482945
$36$	0	0
$37$	360.000	1.59956	0.799779	−	0.600295i	$-0.204950\pi$
$37$	360.000	1.59956	0.799779	+	0.600295i	$0.204950\pi$
$38$	0	0
$39$	189.000	0.776006
$40$	0	0
$41$	386.000	1.47032	0.735159	−	0.677894i	$-0.237107\pi$
$41$	386.000	1.47032	0.735159	+	0.677894i	$0.237107\pi$
$42$	0	0
$43$	−381.000	−1.35121	−0.675604	−	0.737265i	$-0.736117\pi$
$43$	−381.000	−1.35121	−0.675604	+	0.737265i	$0.736117\pi$
$44$	0	0
$45$	−110.000	−0.364396
$46$	0	0
$47$	−103.000	−0.319662	−0.159831	−	0.987144i	$-0.551095\pi$
$47$	−103.000	−0.319662	−0.159831	+	0.987144i	$0.551095\pi$
$48$	0	0
$49$	−339.000	−0.988338
$50$	0	0
$51$	−168.000	−0.461269
$52$	0	0
$53$	431.000	1.11703	0.558513	−	0.829496i	$-0.311372\pi$
$53$	431.000	1.11703	0.558513	+	0.829496i	$0.311372\pi$
$54$	0	0
$55$	185.000	0.453553
$56$	0	0
$57$	−616.000	−1.43142
$58$	0	0
$59$	−288.000	−0.635498	−0.317749	−	0.948175i	$-0.602927\pi$
$59$	−288.000	−0.635498	−0.317749	+	0.948175i	$0.602927\pi$
$60$	0	0
$61$	840.000	1.76313	0.881565	−	0.472062i	$-0.156490\pi$
$61$	840.000	1.76313	0.881565	+	0.472062i	$0.156490\pi$
$62$	0	0
$63$	−44.0000	−0.0879917
$64$	0	0
$65$	135.000	0.257611
$66$	0	0
$67$	180.000	0.328216	0.164108	−	0.986442i	$-0.447525\pi$
$67$	180.000	0.328216	0.164108	+	0.986442i	$0.447525\pi$
$68$	0	0
$69$	196.000	0.341966
$70$	0	0
$71$	706.000	1.18010	0.590048	−	0.807368i	$-0.299109\pi$
$71$	706.000	1.18010	0.590048	+	0.807368i	$0.299109\pi$
$72$	0	0
$73$	716.000	1.14797	0.573983	−	0.818867i	$-0.305398\pi$
$73$	716.000	1.14797	0.573983	+	0.818867i	$0.305398\pi$
$74$	0	0
$75$	700.000	1.07772
$76$	0	0
$77$	74.0000	0.109521
$78$	0	0
$79$	931.000	1.32589	0.662947	−	0.748666i	$-0.269305\pi$
$79$	931.000	1.32589	0.662947	+	0.748666i	$0.269305\pi$
$80$	0	0
$81$	−839.000	−1.15089
$82$	0	0
$83$	−1188.00	−1.57108	−0.785542	−	0.618809i	$-0.787616\pi$
$83$	−1188.00	−1.57108	−0.785542	+	0.618809i	$0.787616\pi$
$84$	0	0
$85$	−120.000	−0.153127
$86$	0	0
$87$	−203.000	−0.250160
$88$	0	0
$89$	−642.000	−0.764628	−0.382314	−	0.924033i	$-0.624873\pi$
$89$	−642.000	−0.764628	−0.382314	+	0.924033i	$0.624873\pi$
$90$	0	0
$91$	54.0000	0.0622059
$92$	0	0
$93$	1001.00	1.11612
$94$	0	0
$95$	−440.000	−0.475190
$96$	0	0
$97$	486.000	0.508720	0.254360	−	0.967110i	$-0.418135\pi$
$97$	486.000	0.508720	0.254360	+	0.967110i	$0.418135\pi$
$98$	0	0
$99$	−814.000	−0.826364
$100$	0	0
$101$	−240.000	−0.236444	−0.118222	−	0.992987i	$-0.537720\pi$
$101$	−240.000	−0.236444	−0.118222	+	0.992987i	$0.537720\pi$
$102$	0	0
$103$	542.000	0.518494	0.259247	−	0.965811i	$-0.416526\pi$
$103$	542.000	0.518494	0.259247	+	0.965811i	$0.416526\pi$
$104$	0	0
$105$	−70.0000	−0.0650600
$106$	0	0
$107$	−374.000	−0.337906	−0.168953	−	0.985624i	$-0.554039\pi$
$107$	−374.000	−0.337906	−0.168953	+	0.985624i	$0.554039\pi$
$108$	0	0
$109$	−449.000	−0.394554	−0.197277	−	0.980348i	$-0.563210\pi$
$109$	−449.000	−0.394554	−0.197277	+	0.980348i	$0.563210\pi$
$110$	0	0
$111$	−2520.00	−2.15485
$112$	0	0
$113$	898.000	0.747582	0.373791	−	0.927513i	$-0.378058\pi$
$113$	898.000	0.747582	0.373791	+	0.927513i	$0.378058\pi$
$114$	0	0
$115$	140.000	0.113522
$116$	0	0
$117$	−594.000	−0.469362
$118$	0	0
$119$	−48.0000	−0.0369761
$120$	0	0
$121$	38.0000	0.0285500
$122$	0	0
$123$	−2702.00	−1.98074
$124$	0	0
$125$	1125.00	0.804984
$126$	0	0
$127$	1280.00	0.894344	0.447172	−	0.894448i	$-0.352431\pi$
$127$	1280.00	0.894344	0.447172	+	0.894448i	$0.352431\pi$
$128$	0	0
$129$	2667.00	1.82028
$130$	0	0
$131$	1292.00	0.861699	0.430849	−	0.902424i	$-0.358214\pi$
$131$	1292.00	0.861699	0.430849	+	0.902424i	$0.358214\pi$
$132$	0	0
$133$	−176.000	−0.114745
$134$	0	0
$135$	−175.000	−0.111567
$136$	0	0
$137$	1852.00	1.15494	0.577471	−	0.816411i	$-0.304040\pi$
$137$	1852.00	1.15494	0.577471	+	0.816411i	$0.304040\pi$
$138$	0	0
$139$	1532.00	0.934838	0.467419	−	0.884036i	$-0.345184\pi$
$139$	1532.00	0.934838	0.467419	+	0.884036i	$0.345184\pi$
$140$	0	0
$141$	721.000	0.430632
$142$	0	0
$143$	999.000	0.584200
$144$	0	0
$145$	−145.000	−0.0830455
$146$	0	0
$147$	2373.00	1.33144
$148$	0	0
$149$	1357.00	0.746106	0.373053	−	0.927810i	$-0.378311\pi$
$149$	1357.00	0.746106	0.373053	+	0.927810i	$0.378311\pi$
$150$	0	0
$151$	−2134.00	−1.15008	−0.575041	−	0.818124i	$-0.695014\pi$
$151$	−2134.00	−1.15008	−0.575041	+	0.818124i	$0.695014\pi$
$152$	0	0
$153$	528.000	0.278995
$154$	0	0
$155$	715.000	0.370517
$156$	0	0
$157$	−2386.00	−1.21289	−0.606444	−	0.795126i	$-0.707405\pi$
$157$	−2386.00	−1.21289	−0.606444	+	0.795126i	$0.707405\pi$
$158$	0	0
$159$	−3017.00	−1.50480
$160$	0	0
$161$	56.0000	0.0274125
$162$	0	0
$163$	−3937.00	−1.89184	−0.945919	−	0.324403i	$-0.894837\pi$
$163$	−3937.00	−1.89184	−0.945919	+	0.324403i	$0.894837\pi$
$164$	0	0
$165$	−1295.00	−0.611004
$166$	0	0
$167$	−2762.00	−1.27982	−0.639910	−	0.768450i	$-0.721028\pi$
$167$	−2762.00	−1.27982	−0.639910	+	0.768450i	$0.721028\pi$
$168$	0	0
$169$	−1468.00	−0.668184
$170$	0	0
$171$	1936.00	0.865787
$172$	0	0
$173$	3822.00	1.67966	0.839830	−	0.542849i	$-0.182654\pi$
$173$	3822.00	1.67966	0.839830	+	0.542849i	$0.182654\pi$
$174$	0	0
$175$	200.000	0.0863919
$176$	0	0
$177$	2016.00	0.856112
$178$	0	0
$179$	−1430.00	−0.597113	−0.298556	−	0.954392i	$-0.596505\pi$
$179$	−1430.00	−0.597113	−0.298556	+	0.954392i	$0.596505\pi$
$180$	0	0
$181$	525.000	0.215596	0.107798	−	0.994173i	$-0.465620\pi$
$181$	525.000	0.215596	0.107798	+	0.994173i	$0.465620\pi$
$182$	0	0
$183$	−5880.00	−2.37520
$184$	0	0
$185$	−1800.00	−0.715344
$186$	0	0
$187$	−888.000	−0.347257
$188$	0	0
$189$	−70.0000	−0.0269405
$190$	0	0
$191$	224.000	0.0848590	0.0424295	−	0.999099i	$-0.486490\pi$
$191$	224.000	0.0848590	0.0424295	+	0.999099i	$0.486490\pi$
$192$	0	0
$193$	−490.000	−0.182751	−0.0913756	−	0.995817i	$-0.529126\pi$
$193$	−490.000	−0.182751	−0.0913756	+	0.995817i	$0.529126\pi$
$194$	0	0
$195$	−945.000	−0.347040
$196$	0	0
$197$	−106.000	−0.0383360	−0.0191680	−	0.999816i	$-0.506102\pi$
$197$	−106.000	−0.0383360	−0.0191680	+	0.999816i	$0.506102\pi$
$198$	0	0
$199$	−2034.00	−0.724555	−0.362277	−	0.932070i	$-0.618001\pi$
$199$	−2034.00	−0.724555	−0.362277	+	0.932070i	$0.618001\pi$
$200$	0	0
$201$	−1260.00	−0.442157
$202$	0	0
$203$	−58.0000	−0.0200532
$204$	0	0
$205$	−1930.00	−0.657547
$206$	0	0
$207$	−616.000	−0.206836
$208$	0	0
$209$	−3256.00	−1.07762
$210$	0	0
$211$	−5717.00	−1.86528	−0.932641	−	0.360806i	$-0.882502\pi$
$211$	−5717.00	−1.86528	−0.932641	+	0.360806i	$0.882502\pi$
$212$	0	0
$213$	−4942.00	−1.58977
$214$	0	0
$215$	1905.00	0.604279
$216$	0	0
$217$	286.000	0.0894698
$218$	0	0
$219$	−5012.00	−1.54648
$220$	0	0
$221$	−648.000	−0.197236
$222$	0	0
$223$	3438.00	1.03240	0.516201	−	0.856468i	$-0.327346\pi$
$223$	3438.00	1.03240	0.516201	+	0.856468i	$0.327346\pi$
$224$	0	0
$225$	−2200.00	−0.651852
$226$	0	0
$227$	−5754.00	−1.68241	−0.841204	−	0.540719i	$-0.818152\pi$
$227$	−5754.00	−1.68241	−0.841204	+	0.540719i	$0.818152\pi$
$228$	0	0
$229$	−2074.00	−0.598488	−0.299244	−	0.954177i	$-0.596734\pi$
$229$	−2074.00	−0.598488	−0.299244	+	0.954177i	$0.596734\pi$
$230$	0	0
$231$	−518.000	−0.147541
$232$	0	0
$233$	5063.00	1.42355	0.711777	−	0.702405i	$-0.247891\pi$
$233$	5063.00	1.42355	0.711777	+	0.702405i	$0.247891\pi$
$234$	0	0
$235$	515.000	0.142957
$236$	0	0
$237$	−6517.00	−1.78618
$238$	0	0
$239$	−1624.00	−0.439531	−0.219765	−	0.975553i	$-0.570529\pi$
$239$	−1624.00	−0.439531	−0.219765	+	0.975553i	$0.570529\pi$
$240$	0	0
$241$	−4463.00	−1.19289	−0.596446	−	0.802653i	$-0.703421\pi$
$241$	−4463.00	−1.19289	−0.596446	+	0.802653i	$0.703421\pi$
$242$	0	0
$243$	4928.00	1.30095
$244$	0	0
$245$	1695.00	0.441998
$246$	0	0
$247$	−2376.00	−0.612070
$248$	0	0
$249$	8316.00	2.11649
$250$	0	0
$251$	2229.00	0.560531	0.280265	−	0.959923i	$-0.409578\pi$
$251$	2229.00	0.560531	0.280265	+	0.959923i	$0.409578\pi$
$252$	0	0
$253$	1036.00	0.257442
$254$	0	0
$255$	840.000	0.206286
$256$	0	0
$257$	−4187.00	−1.01626	−0.508128	−	0.861281i	$-0.669662\pi$
$257$	−4187.00	−1.01626	−0.508128	+	0.861281i	$0.669662\pi$
$258$	0	0
$259$	−720.000	−0.172736
$260$	0	0
$261$	638.000	0.151307
$262$	0	0
$263$	−7611.00	−1.78447	−0.892233	−	0.451576i	$-0.850862\pi$
$263$	−7611.00	−1.78447	−0.892233	+	0.451576i	$0.850862\pi$
$264$	0	0
$265$	−2155.00	−0.499549
$266$	0	0
$267$	4494.00	1.03007
$268$	0	0
$269$	−5136.00	−1.16412	−0.582058	−	0.813147i	$-0.697753\pi$
$269$	−5136.00	−1.16412	−0.582058	+	0.813147i	$0.697753\pi$
$270$	0	0
$271$	4015.00	0.899977	0.449989	−	0.893034i	$-0.351428\pi$
$271$	4015.00	0.899977	0.449989	+	0.893034i	$0.351428\pi$
$272$	0	0
$273$	−378.000	−0.0838007
$274$	0	0
$275$	3700.00	0.811340
$276$	0	0
$277$	−2150.00	−0.466357	−0.233179	−	0.972434i	$-0.574913\pi$
$277$	−2150.00	−0.466357	−0.233179	+	0.972434i	$0.574913\pi$
$278$	0	0
$279$	−3146.00	−0.675076
$280$	0	0
$281$	−1965.00	−0.417160	−0.208580	−	0.978005i	$-0.566884\pi$
$281$	−1965.00	−0.417160	−0.208580	+	0.978005i	$0.566884\pi$
$282$	0	0
$283$	2452.00	0.515040	0.257520	−	0.966273i	$-0.417095\pi$
$283$	2452.00	0.515040	0.257520	+	0.966273i	$0.417095\pi$
$284$	0	0
$285$	3080.00	0.640152
$286$	0	0
$287$	−772.000	−0.158780
$288$	0	0
$289$	−4337.00	−0.882760
$290$	0	0
$291$	−3402.00	−0.685322
$292$	0	0
$293$	−142.000	−0.0283131	−0.0141565	−	0.999900i	$-0.504506\pi$
$293$	−142.000	−0.0283131	−0.0141565	+	0.999900i	$0.504506\pi$
$294$	0	0
$295$	1440.00	0.284204
$296$	0	0
$297$	−1295.00	−0.253008
$298$	0	0
$299$	756.000	0.146223
$300$	0	0
$301$	762.000	0.145917
$302$	0	0
$303$	1680.00	0.318526
$304$	0	0
$305$	−4200.00	−0.788496
$306$	0	0
$307$	−9097.00	−1.69118	−0.845592	−	0.533830i	$-0.820752\pi$
$307$	−9097.00	−1.69118	−0.845592	+	0.533830i	$0.820752\pi$
$308$	0	0
$309$	−3794.00	−0.698489
$310$	0	0
$311$	−4592.00	−0.837262	−0.418631	−	0.908156i	$-0.637490\pi$
$311$	−4592.00	−0.837262	−0.418631	+	0.908156i	$0.637490\pi$
$312$	0	0
$313$	1225.00	0.221218	0.110609	−	0.993864i	$-0.464720\pi$
$313$	1225.00	0.221218	0.110609	+	0.993864i	$0.464720\pi$
$314$	0	0
$315$	220.000	0.0393511
$316$	0	0
$317$	−9852.00	−1.74556	−0.872781	−	0.488111i	$-0.837686\pi$
$317$	−9852.00	−1.74556	−0.872781	+	0.488111i	$0.837686\pi$
$318$	0	0
$319$	−1073.00	−0.188327
$320$	0	0
$321$	2618.00	0.455210
$322$	0	0
$323$	2112.00	0.363823
$324$	0	0
$325$	2700.00	0.460828
$326$	0	0
$327$	3143.00	0.531524
$328$	0	0
$329$	206.000	0.0345202
$330$	0	0
$331$	4183.00	0.694618	0.347309	−	0.937751i	$-0.387096\pi$
$331$	4183.00	0.694618	0.347309	+	0.937751i	$0.387096\pi$
$332$	0	0
$333$	7920.00	1.30334
$334$	0	0
$335$	−900.000	−0.146783
$336$	0	0
$337$	−4480.00	−0.724158	−0.362079	−	0.932147i	$-0.617933\pi$
$337$	−4480.00	−0.724158	−0.362079	+	0.932147i	$0.617933\pi$
$338$	0	0
$339$	−6286.00	−1.00711
$340$	0	0
$341$	5291.00	0.840245
$342$	0	0
$343$	1364.00	0.214720
$344$	0	0
$345$	−980.000	−0.152932
$346$	0	0
$347$	5002.00	0.773837	0.386918	−	0.922114i	$-0.373539\pi$
$347$	5002.00	0.773837	0.386918	+	0.922114i	$0.373539\pi$
$348$	0	0
$349$	6427.00	0.985758	0.492879	−	0.870098i	$-0.335945\pi$
$349$	6427.00	0.985758	0.492879	+	0.870098i	$0.335945\pi$
$350$	0	0
$351$	−945.000	−0.143705
$352$	0	0
$353$	9734.00	1.46767	0.733836	−	0.679326i	$-0.237728\pi$
$353$	9734.00	1.46767	0.733836	+	0.679326i	$0.237728\pi$
$354$	0	0
$355$	−3530.00	−0.527755
$356$	0	0
$357$	336.000	0.0498123
$358$	0	0
$359$	5379.00	0.790788	0.395394	−	0.918512i	$-0.370608\pi$
$359$	5379.00	0.790788	0.395394	+	0.918512i	$0.370608\pi$
$360$	0	0
$361$	885.000	0.129028
$362$	0	0
$363$	−266.000	−0.0384611
$364$	0	0
$365$	−3580.00	−0.513386
$366$	0	0
$367$	−9640.00	−1.37113	−0.685564	−	0.728012i	$-0.740444\pi$
$367$	−9640.00	−1.37113	−0.685564	+	0.728012i	$0.740444\pi$
$368$	0	0
$369$	8492.00	1.19804
$370$	0	0
$371$	−862.000	−0.120628
$372$	0	0
$373$	−7543.00	−1.04708	−0.523541	−	0.852000i	$-0.675389\pi$
$373$	−7543.00	−1.04708	−0.523541	+	0.852000i	$0.675389\pi$
$374$	0	0
$375$	−7875.00	−1.08444
$376$	0	0
$377$	−783.000	−0.106967
$378$	0	0
$379$	−3804.00	−0.515563	−0.257781	−	0.966203i	$-0.582991\pi$
$379$	−3804.00	−0.515563	−0.257781	+	0.966203i	$0.582991\pi$
$380$	0	0
$381$	−8960.00	−1.20482
$382$	0	0
$383$	9174.00	1.22394	0.611971	−	0.790880i	$-0.290377\pi$
$383$	9174.00	1.22394	0.611971	+	0.790880i	$0.290377\pi$
$384$	0	0
$385$	−370.000	−0.0489791
$386$	0	0
$387$	−8382.00	−1.10098
$388$	0	0
$389$	4536.00	0.591219	0.295610	−	0.955309i	$-0.404477\pi$
$389$	4536.00	0.591219	0.295610	+	0.955309i	$0.404477\pi$
$390$	0	0
$391$	−672.000	−0.0869169
$392$	0	0
$393$	−9044.00	−1.16084
$394$	0	0
$395$	−4655.00	−0.592958
$396$	0	0
$397$	9853.00	1.24561	0.622806	−	0.782376i	$-0.285993\pi$
$397$	9853.00	1.24561	0.622806	+	0.782376i	$0.285993\pi$
$398$	0	0
$399$	1232.00	0.154579
$400$	0	0
$401$	−11429.0	−1.42328	−0.711642	−	0.702542i	$-0.752048\pi$
$401$	−11429.0	−1.42328	−0.711642	+	0.702542i	$0.752048\pi$
$402$	0	0
$403$	3861.00	0.477246
$404$	0	0
$405$	4195.00	0.514694
$406$	0	0
$407$	−13320.0	−1.62223
$408$	0	0
$409$	2662.00	0.321827	0.160914	−	0.986968i	$-0.448556\pi$
$409$	2662.00	0.321827	0.160914	+	0.986968i	$0.448556\pi$
$410$	0	0
$411$	−12964.0	−1.55588
$412$	0	0
$413$	576.000	0.0686274
$414$	0	0
$415$	5940.00	0.702610
$416$	0	0
$417$	−10724.0	−1.25937
$418$	0	0
$419$	−5126.00	−0.597665	−0.298832	−	0.954306i	$-0.596597\pi$
$419$	−5126.00	−0.597665	−0.298832	+	0.954306i	$0.596597\pi$
$420$	0	0
$421$	16200.0	1.87539	0.937696	−	0.347458i	$-0.112955\pi$
$421$	16200.0	1.87539	0.937696	+	0.347458i	$0.112955\pi$
$422$	0	0
$423$	−2266.00	−0.260465
$424$	0	0
$425$	−2400.00	−0.273923
$426$	0	0
$427$	−1680.00	−0.190400
$428$	0	0
$429$	−6993.00	−0.787005
$430$	0	0
$431$	12000.0	1.34111	0.670556	−	0.741859i	$-0.266055\pi$
$431$	12000.0	1.34111	0.670556	+	0.741859i	$0.266055\pi$
$432$	0	0
$433$	−3736.00	−0.414644	−0.207322	−	0.978273i	$-0.566475\pi$
$433$	−3736.00	−0.414644	−0.207322	+	0.978273i	$0.566475\pi$
$434$	0	0
$435$	1015.00	0.111875
$436$	0	0
$437$	−2464.00	−0.269723
$438$	0	0
$439$	3172.00	0.344855	0.172427	−	0.985022i	$-0.444839\pi$
$439$	3172.00	0.344855	0.172427	+	0.985022i	$0.444839\pi$
$440$	0	0
$441$	−7458.00	−0.805313
$442$	0	0
$443$	1540.00	0.165164	0.0825820	−	0.996584i	$-0.473683\pi$
$443$	1540.00	0.165164	0.0825820	+	0.996584i	$0.473683\pi$
$444$	0	0
$445$	3210.00	0.341952
$446$	0	0
$447$	−9499.00	−1.00512
$448$	0	0
$449$	8358.00	0.878482	0.439241	−	0.898369i	$-0.355247\pi$
$449$	8358.00	0.878482	0.439241	+	0.898369i	$0.355247\pi$
$450$	0	0
$451$	−14282.0	−1.49116
$452$	0	0
$453$	14938.0	1.54933
$454$	0	0
$455$	−270.000	−0.0278193
$456$	0	0
$457$	798.000	0.0816824	0.0408412	−	0.999166i	$-0.486996\pi$
$457$	798.000	0.0816824	0.0408412	+	0.999166i	$0.486996\pi$
$458$	0	0
$459$	840.000	0.0854201
$460$	0	0
$461$	−15330.0	−1.54878	−0.774392	−	0.632706i	$-0.781944\pi$
$461$	−15330.0	−1.54878	−0.774392	+	0.632706i	$0.781944\pi$
$462$	0	0
$463$	−6020.00	−0.604262	−0.302131	−	0.953266i	$-0.597698\pi$
$463$	−6020.00	−0.604262	−0.302131	+	0.953266i	$0.597698\pi$
$464$	0	0
$465$	−5005.00	−0.499143
$466$	0	0
$467$	3275.00	0.324516	0.162258	−	0.986748i	$-0.448122\pi$
$467$	3275.00	0.324516	0.162258	+	0.986748i	$0.448122\pi$
$468$	0	0
$469$	−360.000	−0.0354440
$470$	0	0
$471$	16702.0	1.63394
$472$	0	0
$473$	14097.0	1.37036
$474$	0	0
$475$	−8800.00	−0.850046
$476$	0	0
$477$	9482.00	0.910170
$478$	0	0
$479$	13463.0	1.28422	0.642109	−	0.766614i	$-0.278060\pi$
$479$	13463.0	1.28422	0.642109	+	0.766614i	$0.278060\pi$
$480$	0	0
$481$	−9720.00	−0.921401
$482$	0	0
$483$	−392.000	−0.0369288
$484$	0	0
$485$	−2430.00	−0.227506
$486$	0	0
$487$	−12358.0	−1.14989	−0.574943	−	0.818194i	$-0.694976\pi$
$487$	−12358.0	−1.14989	−0.574943	+	0.818194i	$0.694976\pi$
$488$	0	0
$489$	27559.0	2.54859
$490$	0	0
$491$	−407.000	−0.0374087	−0.0187043	−	0.999825i	$-0.505954\pi$
$491$	−407.000	−0.0374087	−0.0187043	+	0.999825i	$0.505954\pi$
$492$	0	0
$493$	696.000	0.0635827
$494$	0	0
$495$	4070.00	0.369561
$496$	0	0
$497$	−1412.00	−0.127438
$498$	0	0
$499$	−14084.0	−1.26350	−0.631750	−	0.775172i	$-0.717663\pi$
$499$	−14084.0	−1.26350	−0.631750	+	0.775172i	$0.717663\pi$
$500$	0	0
$501$	19334.0	1.72411
$502$	0	0
$503$	13767.0	1.22036	0.610179	−	0.792263i	$-0.291097\pi$
$503$	13767.0	1.22036	0.610179	+	0.792263i	$0.291097\pi$
$504$	0	0
$505$	1200.00	0.105741
$506$	0	0
$507$	10276.0	0.900144
$508$	0	0
$509$	−21381.0	−1.86188	−0.930939	−	0.365174i	$-0.881009\pi$
$509$	−21381.0	−1.86188	−0.930939	+	0.365174i	$0.881009\pi$
$510$	0	0
$511$	−1432.00	−0.123969
$512$	0	0
$513$	3080.00	0.265079
$514$	0	0
$515$	−2710.00	−0.231877
$516$	0	0
$517$	3811.00	0.324193
$518$	0	0
$519$	−26754.0	−2.26276
$520$	0	0
$521$	10243.0	0.861332	0.430666	−	0.902511i	$-0.358279\pi$
$521$	10243.0	0.861332	0.430666	+	0.902511i	$0.358279\pi$
$522$	0	0
$523$	10568.0	0.883569	0.441784	−	0.897121i	$-0.354346\pi$
$523$	10568.0	0.883569	0.441784	+	0.897121i	$0.354346\pi$
$524$	0	0
$525$	−1400.00	−0.116383
$526$	0	0
$527$	−3432.00	−0.283682
$528$	0	0
$529$	−11383.0	−0.935563
$530$	0	0
$531$	−6336.00	−0.517814
$532$	0	0
$533$	−10422.0	−0.846955
$534$	0	0
$535$	1870.00	0.151116
$536$	0	0
$537$	10010.0	0.804401
$538$	0	0
$539$	12543.0	1.00235
$540$	0	0
$541$	15720.0	1.24927	0.624635	−	0.780916i	$-0.285248\pi$
$541$	15720.0	1.24927	0.624635	+	0.780916i	$0.285248\pi$
$542$	0	0
$543$	−3675.00	−0.290441
$544$	0	0
$545$	2245.00	0.176450
$546$	0	0
$547$	18106.0	1.41528	0.707639	−	0.706575i	$-0.249760\pi$
$547$	18106.0	1.41528	0.707639	+	0.706575i	$0.249760\pi$
$548$	0	0
$549$	18480.0	1.43663
$550$	0	0
$551$	2552.00	0.197312
$552$	0	0
$553$	−1862.00	−0.143183
$554$	0	0
$555$	12600.0	0.963676
$556$	0	0
$557$	2346.00	0.178462	0.0892309	−	0.996011i	$-0.471559\pi$
$557$	2346.00	0.178462	0.0892309	+	0.996011i	$0.471559\pi$
$558$	0	0
$559$	10287.0	0.778343
$560$	0	0
$561$	6216.00	0.467807
$562$	0	0
$563$	691.000	0.0517268	0.0258634	−	0.999665i	$-0.491767\pi$
$563$	691.000	0.0517268	0.0258634	+	0.999665i	$0.491767\pi$
$564$	0	0
$565$	−4490.00	−0.334329
$566$	0	0
$567$	1678.00	0.124285
$568$	0	0
$569$	−15542.0	−1.14509	−0.572544	−	0.819874i	$-0.694043\pi$
$569$	−15542.0	−1.14509	−0.572544	+	0.819874i	$0.694043\pi$
$570$	0	0
$571$	−12124.0	−0.888570	−0.444285	−	0.895885i	$-0.646542\pi$
$571$	−12124.0	−0.888570	−0.444285	+	0.895885i	$0.646542\pi$
$572$	0	0
$573$	−1568.00	−0.114318
$574$	0	0
$575$	2800.00	0.203075
$576$	0	0
$577$	15808.0	1.14055	0.570274	−	0.821455i	$-0.306837\pi$
$577$	15808.0	1.14055	0.570274	+	0.821455i	$0.306837\pi$
$578$	0	0
$579$	3430.00	0.246193
$580$	0	0
$581$	2376.00	0.169661
$582$	0	0
$583$	−15947.0	−1.13286
$584$	0	0
$585$	2970.00	0.209905
$586$	0	0
$587$	6516.00	0.458167	0.229084	−	0.973407i	$-0.426427\pi$
$587$	6516.00	0.458167	0.229084	+	0.973407i	$0.426427\pi$
$588$	0	0
$589$	−12584.0	−0.880331
$590$	0	0
$591$	742.000	0.0516443
$592$	0	0
$593$	14751.0	1.02150	0.510751	−	0.859729i	$-0.329367\pi$
$593$	14751.0	1.02150	0.510751	+	0.859729i	$0.329367\pi$
$594$	0	0
$595$	240.000	0.0165362
$596$	0	0
$597$	14238.0	0.976085
$598$	0	0
$599$	−18681.0	−1.27427	−0.637133	−	0.770754i	$-0.719880\pi$
$599$	−18681.0	−1.27427	−0.637133	+	0.770754i	$0.719880\pi$
$600$	0	0
$601$	−22526.0	−1.52888	−0.764438	−	0.644697i	$-0.776984\pi$
$601$	−22526.0	−1.52888	−0.764438	+	0.644697i	$0.776984\pi$
$602$	0	0
$603$	3960.00	0.267436
$604$	0	0
$605$	−190.000	−0.0127679
$606$	0	0
$607$	−9329.00	−0.623810	−0.311905	−	0.950113i	$-0.600967\pi$
$607$	−9329.00	−0.623810	−0.311905	+	0.950113i	$0.600967\pi$
$608$	0	0
$609$	406.000	0.0270147
$610$	0	0
$611$	2781.00	0.184136
$612$	0	0
$613$	−19525.0	−1.28647	−0.643236	−	0.765668i	$-0.722409\pi$
$613$	−19525.0	−1.28647	−0.643236	+	0.765668i	$0.722409\pi$
$614$	0	0
$615$	13510.0	0.885814
$616$	0	0
$617$	−25332.0	−1.65288	−0.826441	−	0.563024i	$-0.809638\pi$
$617$	−25332.0	−1.65288	−0.826441	+	0.563024i	$0.809638\pi$
$618$	0	0
$619$	21091.0	1.36950	0.684749	−	0.728779i	$-0.259912\pi$
$619$	21091.0	1.36950	0.684749	+	0.728779i	$0.259912\pi$
$620$	0	0
$621$	−980.000	−0.0633270
$622$	0	0
$623$	1284.00	0.0825720
$624$	0	0
$625$	6875.00	0.440000
$626$	0	0
$627$	22792.0	1.45171
$628$	0	0
$629$	8640.00	0.547694
$630$	0	0
$631$	6242.00	0.393804	0.196902	−	0.980423i	$-0.436912\pi$
$631$	6242.00	0.393804	0.196902	+	0.980423i	$0.436912\pi$
$632$	0	0
$633$	40019.0	2.51282
$634$	0	0
$635$	−6400.00	−0.399963
$636$	0	0
$637$	9153.00	0.569317
$638$	0	0
$639$	15532.0	0.961559
$640$	0	0
$641$	15392.0	0.948436	0.474218	−	0.880407i	$-0.342731\pi$
$641$	15392.0	0.948436	0.474218	+	0.880407i	$0.342731\pi$
$642$	0	0
$643$	14870.0	0.911999	0.456000	−	0.889980i	$-0.349282\pi$
$643$	14870.0	0.911999	0.456000	+	0.889980i	$0.349282\pi$
$644$	0	0
$645$	−13335.0	−0.814054
$646$	0	0
$647$	17016.0	1.03395	0.516977	−	0.855999i	$-0.327057\pi$
$647$	17016.0	1.03395	0.516977	+	0.855999i	$0.327057\pi$
$648$	0	0
$649$	10656.0	0.644506
$650$	0	0
$651$	−2002.00	−0.120529
$652$	0	0
$653$	24122.0	1.44558	0.722792	−	0.691065i	$-0.242858\pi$
$653$	24122.0	1.44558	0.722792	+	0.691065i	$0.242858\pi$
$654$	0	0
$655$	−6460.00	−0.385363
$656$	0	0
$657$	15752.0	0.935379
$658$	0	0
$659$	20217.0	1.19506	0.597528	−	0.801848i	$-0.296149\pi$
$659$	20217.0	1.19506	0.597528	+	0.801848i	$0.296149\pi$
$660$	0	0
$661$	−3942.00	−0.231961	−0.115980	−	0.993252i	$-0.537001\pi$
$661$	−3942.00	−0.231961	−0.115980	+	0.993252i	$0.537001\pi$
$662$	0	0
$663$	4536.00	0.265707
$664$	0	0
$665$	880.000	0.0513157
$666$	0	0
$667$	−812.000	−0.0471376
$668$	0	0
$669$	−24066.0	−1.39080
$670$	0	0
$671$	−31080.0	−1.78812
$672$	0	0
$673$	−6551.00	−0.375219	−0.187610	−	0.982244i	$-0.560074\pi$
$673$	−6551.00	−0.375219	−0.187610	+	0.982244i	$0.560074\pi$
$674$	0	0
$675$	−3500.00	−0.199578
$676$	0	0
$677$	−14958.0	−0.849162	−0.424581	−	0.905390i	$-0.639579\pi$
$677$	−14958.0	−0.849162	−0.424581	+	0.905390i	$0.639579\pi$
$678$	0	0
$679$	−972.000	−0.0549366
$680$	0	0
$681$	40278.0	2.26646
$682$	0	0
$683$	27584.0	1.54535	0.772674	−	0.634803i	$-0.218919\pi$
$683$	27584.0	1.54535	0.772674	+	0.634803i	$0.218919\pi$
$684$	0	0
$685$	−9260.00	−0.516506
$686$	0	0
$687$	14518.0	0.806254
$688$	0	0
$689$	−11637.0	−0.643446
$690$	0	0
$691$	−24244.0	−1.33471	−0.667355	−	0.744739i	$-0.732574\pi$
$691$	−24244.0	−1.33471	−0.667355	+	0.744739i	$0.732574\pi$
$692$	0	0
$693$	1628.00	0.0892390
$694$	0	0
$695$	−7660.00	−0.418072
$696$	0	0
$697$	9264.00	0.503442
$698$	0	0
$699$	−35441.0	−1.91774
$700$	0	0
$701$	−7431.00	−0.400378	−0.200189	−	0.979757i	$-0.564156\pi$
$701$	−7431.00	−0.400378	−0.200189	+	0.979757i	$0.564156\pi$
$702$	0	0
$703$	31680.0	1.69962
$704$	0	0
$705$	−3605.00	−0.192585
$706$	0	0
$707$	480.000	0.0255336
$708$	0	0
$709$	28429.0	1.50589	0.752943	−	0.658085i	$-0.228633\pi$
$709$	28429.0	1.50589	0.752943	+	0.658085i	$0.228633\pi$
$710$	0	0
$711$	20482.0	1.08036
$712$	0	0
$713$	4004.00	0.210310
$714$	0	0
$715$	−4995.00	−0.261262
$716$	0	0
$717$	11368.0	0.592114
$718$	0	0
$719$	−29890.0	−1.55036	−0.775180	−	0.631740i	$-0.782341\pi$
$719$	−29890.0	−1.55036	−0.775180	+	0.631740i	$0.782341\pi$
$720$	0	0
$721$	−1084.00	−0.0559921
$722$	0	0
$723$	31241.0	1.60701
$724$	0	0
$725$	−2900.00	−0.148556
$726$	0	0
$727$	13072.0	0.666869	0.333434	−	0.942773i	$-0.391792\pi$
$727$	13072.0	0.666869	0.333434	+	0.942773i	$0.391792\pi$
$728$	0	0
$729$	−11843.0	−0.601687
$730$	0	0
$731$	−9144.00	−0.462658
$732$	0	0
$733$	−13456.0	−0.678047	−0.339024	−	0.940778i	$-0.610097\pi$
$733$	−13456.0	−0.678047	−0.339024	+	0.940778i	$0.610097\pi$
$734$	0	0
$735$	−11865.0	−0.595438
$736$	0	0
$737$	−6660.00	−0.332869
$738$	0	0
$739$	−16915.0	−0.841987	−0.420993	−	0.907064i	$-0.638318\pi$
$739$	−16915.0	−0.841987	−0.420993	+	0.907064i	$0.638318\pi$
$740$	0	0
$741$	16632.0	0.824550
$742$	0	0
$743$	10164.0	0.501859	0.250929	−	0.968005i	$-0.419264\pi$
$743$	10164.0	0.501859	0.250929	+	0.968005i	$0.419264\pi$
$744$	0	0
$745$	−6785.00	−0.333669
$746$	0	0
$747$	−26136.0	−1.28014
$748$	0	0
$749$	748.000	0.0364904
$750$	0	0
$751$	5816.00	0.282595	0.141298	−	0.989967i	$-0.454873\pi$
$751$	5816.00	0.282595	0.141298	+	0.989967i	$0.454873\pi$
$752$	0	0
$753$	−15603.0	−0.755119
$754$	0	0
$755$	10670.0	0.514333
$756$	0	0
$757$	−30496.0	−1.46420	−0.732098	−	0.681200i	$-0.761459\pi$
$757$	−30496.0	−1.46420	−0.732098	+	0.681200i	$0.761459\pi$
$758$	0	0
$759$	−7252.00	−0.346813
$760$	0	0
$761$	−25654.0	−1.22202	−0.611010	−	0.791623i	$-0.709236\pi$
$761$	−25654.0	−1.22202	−0.611010	+	0.791623i	$0.709236\pi$
$762$	0	0
$763$	898.000	0.0426078
$764$	0	0
$765$	−2640.00	−0.124770
$766$	0	0
$767$	7776.00	0.366069
$768$	0	0
$769$	−15348.0	−0.719718	−0.359859	−	0.933007i	$-0.617175\pi$
$769$	−15348.0	−0.719718	−0.359859	+	0.933007i	$0.617175\pi$
$770$	0	0
$771$	29309.0	1.36905
$772$	0	0
$773$	−22062.0	−1.02654	−0.513270	−	0.858227i	$-0.671566\pi$
$773$	−22062.0	−1.02654	−0.513270	+	0.858227i	$0.671566\pi$
$774$	0	0
$775$	14300.0	0.662802
$776$	0	0
$777$	5040.00	0.232701
$778$	0	0
$779$	33968.0	1.56230
$780$	0	0
$781$	−26122.0	−1.19682
$782$	0	0
$783$	1015.00	0.0463259
$784$	0	0
$785$	11930.0	0.542420
$786$	0	0
$787$	14942.0	0.676779	0.338389	−	0.941006i	$-0.390118\pi$
$787$	14942.0	0.676779	0.338389	+	0.941006i	$0.390118\pi$
$788$	0	0
$789$	53277.0	2.40394
$790$	0	0
$791$	−1796.00	−0.0807312
$792$	0	0
$793$	−22680.0	−1.01562
$794$	0	0
$795$	15085.0	0.672968
$796$	0	0
$797$	−13744.0	−0.610837	−0.305419	−	0.952218i	$-0.598796\pi$
$797$	−13744.0	−0.610837	−0.305419	+	0.952218i	$0.598796\pi$
$798$	0	0
$799$	−2472.00	−0.109453
$800$	0	0
$801$	−14124.0	−0.623030
$802$	0	0
$803$	−26492.0	−1.16424
$804$	0	0
$805$	−280.000	−0.0122593
$806$	0	0
$807$	35952.0	1.56824
$808$	0	0
$809$	19376.0	0.842057	0.421028	−	0.907047i	$-0.361669\pi$
$809$	19376.0	0.842057	0.421028	+	0.907047i	$0.361669\pi$
$810$	0	0
$811$	−38174.0	−1.65286	−0.826431	−	0.563039i	$-0.809632\pi$
$811$	−38174.0	−1.65286	−0.826431	+	0.563039i	$0.809632\pi$
$812$	0	0
$813$	−28105.0	−1.21241
$814$	0	0
$815$	19685.0	0.846056
$816$	0	0
$817$	−33528.0	−1.43574
$818$	0	0
$819$	1188.00	0.0506863
$820$	0	0
$821$	15533.0	0.660299	0.330149	−	0.943929i	$-0.392901\pi$
$821$	15533.0	0.660299	0.330149	+	0.943929i	$0.392901\pi$
$822$	0	0
$823$	13624.0	0.577039	0.288519	−	0.957474i	$-0.406837\pi$
$823$	13624.0	0.577039	0.288519	+	0.957474i	$0.406837\pi$
$824$	0	0
$825$	−25900.0	−1.09300
$826$	0	0
$827$	37475.0	1.57574	0.787868	−	0.615844i	$-0.211185\pi$
$827$	37475.0	1.57574	0.787868	+	0.615844i	$0.211185\pi$
$828$	0	0
$829$	−11600.0	−0.485989	−0.242994	−	0.970028i	$-0.578130\pi$
$829$	−11600.0	−0.485989	−0.242994	+	0.970028i	$0.578130\pi$
$830$	0	0
$831$	15050.0	0.628254
$832$	0	0
$833$	−8136.00	−0.338410
$834$	0	0
$835$	13810.0	0.572353
$836$	0	0
$837$	−5005.00	−0.206688
$838$	0	0
$839$	−10783.0	−0.443707	−0.221854	−	0.975080i	$-0.571211\pi$
$839$	−10783.0	−0.443707	−0.221854	+	0.975080i	$0.571211\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	0	0
$843$	13755.0	0.561978
$844$	0	0
$845$	7340.00	0.298821
$846$	0	0
$847$	−76.0000	−0.00308311
$848$	0	0
$849$	−17164.0	−0.693836
$850$	0	0
$851$	−10080.0	−0.406038
$852$	0	0
$853$	20026.0	0.803842	0.401921	−	0.915674i	$-0.368343\pi$
$853$	20026.0	0.803842	0.401921	+	0.915674i	$0.368343\pi$
$854$	0	0
$855$	−9680.00	−0.387192
$856$	0	0
$857$	−37259.0	−1.48511	−0.742557	−	0.669783i	$-0.766387\pi$
$857$	−37259.0	−1.48511	−0.742557	+	0.669783i	$0.766387\pi$
$858$	0	0
$859$	19681.0	0.781731	0.390866	−	0.920448i	$-0.372176\pi$
$859$	19681.0	0.781731	0.390866	+	0.920448i	$0.372176\pi$
$860$	0	0
$861$	5404.00	0.213900
$862$	0	0
$863$	−12422.0	−0.489977	−0.244988	−	0.969526i	$-0.578784\pi$
$863$	−12422.0	−0.489977	−0.244988	+	0.969526i	$0.578784\pi$
$864$	0	0
$865$	−19110.0	−0.751167
$866$	0	0
$867$	30359.0	1.18921
$868$	0	0
$869$	−34447.0	−1.34469
$870$	0	0
$871$	−4860.00	−0.189064
$872$	0	0
$873$	10692.0	0.414512
$874$	0	0
$875$	−2250.00	−0.0869302
$876$	0	0
$877$	6111.00	0.235295	0.117648	−	0.993055i	$-0.462465\pi$
$877$	6111.00	0.235295	0.117648	+	0.993055i	$0.462465\pi$
$878$	0	0
$879$	994.000	0.0381420
$880$	0	0
$881$	−33998.0	−1.30014	−0.650069	−	0.759875i	$-0.725260\pi$
$881$	−33998.0	−1.30014	−0.650069	+	0.759875i	$0.725260\pi$
$882$	0	0
$883$	−5214.00	−0.198715	−0.0993573	−	0.995052i	$-0.531679\pi$
$883$	−5214.00	−0.198715	−0.0993573	+	0.995052i	$0.531679\pi$
$884$	0	0
$885$	−10080.0	−0.382865
$886$	0	0
$887$	−27507.0	−1.04126	−0.520628	−	0.853783i	$-0.674302\pi$
$887$	−27507.0	−1.04126	−0.520628	+	0.853783i	$0.674302\pi$
$888$	0	0
$889$	−2560.00	−0.0965800
$890$	0	0
$891$	31043.0	1.16720
$892$	0	0
$893$	−9064.00	−0.339659
$894$	0	0
$895$	7150.00	0.267037
$896$	0	0
$897$	−5292.00	−0.196984
$898$	0	0
$899$	−4147.00	−0.153849
$900$	0	0
$901$	10344.0	0.382473
$902$	0	0
$903$	−5334.00	−0.196572
$904$	0	0
$905$	−2625.00	−0.0964176
$906$	0	0
$907$	−49012.0	−1.79429	−0.897143	−	0.441741i	$-0.854361\pi$
$907$	−49012.0	−1.79429	−0.897143	+	0.441741i	$0.854361\pi$
$908$	0	0
$909$	−5280.00	−0.192658
$910$	0	0
$911$	38047.0	1.38370	0.691851	−	0.722040i	$-0.256795\pi$
$911$	38047.0	1.38370	0.691851	+	0.722040i	$0.256795\pi$
$912$	0	0
$913$	43956.0	1.59335
$914$	0	0
$915$	29400.0	1.06222
$916$	0	0
$917$	−2584.00	−0.0930547
$918$	0	0
$919$	23214.0	0.833253	0.416626	−	0.909078i	$-0.363212\pi$
$919$	23214.0	0.833253	0.416626	+	0.909078i	$0.363212\pi$
$920$	0	0
$921$	63679.0	2.27828
$922$	0	0
$923$	−19062.0	−0.679776
$924$	0	0
$925$	−36000.0	−1.27965
$926$	0	0
$927$	11924.0	0.422476
$928$	0	0
$929$	13890.0	0.490545	0.245272	−	0.969454i	$-0.421123\pi$
$929$	13890.0	0.490545	0.245272	+	0.969454i	$0.421123\pi$
$930$	0	0
$931$	−29832.0	−1.05017
$932$	0	0
$933$	32144.0	1.12792
$934$	0	0
$935$	4440.00	0.155298
$936$	0	0
$937$	20830.0	0.726240	0.363120	−	0.931742i	$-0.381712\pi$
$937$	20830.0	0.726240	0.363120	+	0.931742i	$0.381712\pi$
$938$	0	0
$939$	−8575.00	−0.298013
$940$	0	0
$941$	−32305.0	−1.11914	−0.559571	−	0.828782i	$-0.689034\pi$
$941$	−32305.0	−1.11914	−0.559571	+	0.828782i	$0.689034\pi$
$942$	0	0
$943$	−10808.0	−0.373231
$944$	0	0
$945$	350.000	0.0120481
$946$	0	0
$947$	35759.0	1.22704	0.613522	−	0.789677i	$-0.289752\pi$
$947$	35759.0	1.22704	0.613522	+	0.789677i	$0.289752\pi$
$948$	0	0
$949$	−19332.0	−0.661268
$950$	0	0
$951$	68964.0	2.35154
$952$	0	0
$953$	21847.0	0.742596	0.371298	−	0.928514i	$-0.378913\pi$
$953$	21847.0	0.742596	0.371298	+	0.928514i	$0.378913\pi$
$954$	0	0
$955$	−1120.00	−0.0379501
$956$	0	0
$957$	7511.00	0.253705
$958$	0	0
$959$	−3704.00	−0.124722
$960$	0	0
$961$	−9342.00	−0.313585
$962$	0	0
$963$	−8228.00	−0.275331
$964$	0	0
$965$	2450.00	0.0817288
$966$	0	0
$967$	−9151.00	−0.304319	−0.152159	−	0.988356i	$-0.548623\pi$
$967$	−9151.00	−0.304319	−0.152159	+	0.988356i	$0.548623\pi$
$968$	0	0
$969$	−14784.0	−0.490124
$970$	0	0
$971$	26980.0	0.891688	0.445844	−	0.895111i	$-0.352904\pi$
$971$	26980.0	0.891688	0.445844	+	0.895111i	$0.352904\pi$
$972$	0	0
$973$	−3064.00	−0.100953
$974$	0	0
$975$	−18900.0	−0.620805
$976$	0	0
$977$	−25659.0	−0.840229	−0.420115	−	0.907471i	$-0.638010\pi$
$977$	−25659.0	−0.840229	−0.420115	+	0.907471i	$0.638010\pi$
$978$	0	0
$979$	23754.0	0.775466
$980$	0	0
$981$	−9878.00	−0.321489
$982$	0	0
$983$	48693.0	1.57992	0.789962	−	0.613156i	$-0.210100\pi$
$983$	48693.0	1.57992	0.789962	+	0.613156i	$0.210100\pi$
$984$	0	0
$985$	530.000	0.0171444
$986$	0	0
$987$	−1442.00	−0.0465039
$988$	0	0
$989$	10668.0	0.342996
$990$	0	0
$991$	−10898.0	−0.349330	−0.174665	−	0.984628i	$-0.555884\pi$
$991$	−10898.0	−0.349330	−0.174665	+	0.984628i	$0.555884\pi$
$992$	0	0
$993$	−29281.0	−0.935755
$994$	0	0
$995$	10170.0	0.324031
$996$	0	0
$997$	41216.0	1.30925	0.654626	−	0.755953i	$-0.272826\pi$
$997$	41216.0	1.30925	0.654626	+	0.755953i	$0.272826\pi$
$998$	0	0
$999$	12600.0	0.399045

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1856.4.a.a.1.1		1
4.3	odd	2		1856.4.a.d.1.1		1
8.3	odd	2		464.4.a.a.1.1		1
8.5	even	2		58.4.a.a.1.1	✓	1
24.5	odd	2		522.4.a.e.1.1		1
40.29	even	2		1450.4.a.e.1.1		1
232.173	even	2		1682.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.4.a.a.1.1	✓	1	8.5	even	2
464.4.a.a.1.1		1	8.3	odd	2
522.4.a.e.1.1		1	24.5	odd	2
1450.4.a.e.1.1		1	40.29	even	2
1682.4.a.b.1.1		1	232.173	even	2
1856.4.a.a.1.1		1	1.1	even	1	trivial
1856.4.a.d.1.1		1	4.3	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:	\( N \)	\(=\)	\( 1856 = 2^{6} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1856.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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