LMFDB - Embedded newform 1856.4.a.c.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:	$0$
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)

$f(q)$

$=$

$q-7.00000 q^{3} +15.0000 q^{5} +18.0000 q^{7} +22.0000 q^{9} +O(q^{10})$

$q-7.00000 q^{3} +15.0000 q^{5} +18.0000 q^{7} +22.0000 q^{9} +27.0000 q^{11} +57.0000 q^{13} -105.000 q^{15} -44.0000 q^{17} +152.000 q^{19} -126.000 q^{21} +152.000 q^{23} +100.000 q^{25} +35.0000 q^{27} +29.0000 q^{29} +173.000 q^{31} -189.000 q^{33} +270.000 q^{35} +120.000 q^{37} -399.000 q^{39} -314.000 q^{41} +339.000 q^{43} +330.000 q^{45} +357.000 q^{47} -19.0000 q^{49} +308.000 q^{51} +59.0000 q^{53} +405.000 q^{55} -1064.00 q^{57} -572.000 q^{59} +420.000 q^{61} +396.000 q^{63} +855.000 q^{65} +660.000 q^{67} -1064.00 q^{69} -726.000 q^{71} +1004.00 q^{73} -700.000 q^{75} +486.000 q^{77} -361.000 q^{79} -839.000 q^{81} -168.000 q^{83} -660.000 q^{85} -203.000 q^{87} +58.0000 q^{89} +1026.00 q^{91} -1211.00 q^{93} +2280.00 q^{95} -1206.00 q^{97} +594.000 q^{99} +O(q^{100})$

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
$5$	15.0000	1.34164	0.670820	−	0.741620i	$-0.265942\pi$
$5$	15.0000	1.34164	0.670820	+	0.741620i	$0.265942\pi$
$6$	0	0
$7$	18.0000	0.971909	0.485954	−	0.873984i	$-0.338472\pi$
$7$	18.0000	0.971909	0.485954	+	0.873984i	$0.338472\pi$
$8$	0	0
$9$	22.0000	0.814815
$10$	0	0
$11$	27.0000	0.740073	0.370037	−	0.929017i	$-0.379345\pi$
$11$	27.0000	0.740073	0.370037	+	0.929017i	$0.379345\pi$
$12$	0	0
$13$	57.0000	1.21607	0.608037	−	0.793909i	$-0.291957\pi$
$13$	57.0000	1.21607	0.608037	+	0.793909i	$0.291957\pi$
$14$	0	0
$15$	−105.000	−1.80739
$16$	0	0
$17$	−44.0000	−0.627739	−0.313870	−	0.949466i	$-0.601625\pi$
$17$	−44.0000	−0.627739	−0.313870	+	0.949466i	$0.601625\pi$
$18$	0	0
$19$	152.000	1.83533	0.917663	−	0.397360i	$-0.130073\pi$
$19$	152.000	1.83533	0.917663	+	0.397360i	$0.130073\pi$
$20$	0	0
$21$	−126.000	−1.30931
$22$	0	0
$23$	152.000	1.37801	0.689004	−	0.724757i	$-0.258048\pi$
$23$	152.000	1.37801	0.689004	+	0.724757i	$0.258048\pi$
$24$	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
$31$	173.000	1.00231	0.501157	−	0.865357i	$-0.332908\pi$
$31$	173.000	1.00231	0.501157	+	0.865357i	$0.332908\pi$
$32$	0	0
$33$	−189.000	−0.996990
$34$	0	0
$35$	270.000	1.30395
$36$	0	0
$37$	120.000	0.533186	0.266593	−	0.963809i	$-0.414102\pi$
$37$	120.000	0.533186	0.266593	+	0.963809i	$0.414102\pi$
$38$	0	0
$39$	−399.000	−1.63823
$40$	0	0
$41$	−314.000	−1.19606	−0.598031	−	0.801473i	$-0.704050\pi$
$41$	−314.000	−1.19606	−0.598031	+	0.801473i	$0.704050\pi$
$42$	0	0
$43$	339.000	1.20226	0.601128	−	0.799153i	$-0.294718\pi$
$43$	339.000	1.20226	0.601128	+	0.799153i	$0.294718\pi$
$44$	0	0
$45$	330.000	1.09319
$46$	0	0
$47$	357.000	1.10795	0.553977	−	0.832532i	$-0.313110\pi$
$47$	357.000	1.10795	0.553977	+	0.832532i	$0.313110\pi$
$48$	0	0
$49$	−19.0000	−0.0553936
$50$	0	0
$51$	308.000	0.845659
$52$	0	0
$53$	59.0000	0.152911	0.0764554	−	0.997073i	$-0.475640\pi$
$53$	59.0000	0.152911	0.0764554	+	0.997073i	$0.475640\pi$
$54$	0	0
$55$	405.000	0.992913
$56$	0	0
$57$	−1064.00	−2.47246
$58$	0	0
$59$	−572.000	−1.26217	−0.631085	−	0.775713i	$-0.717390\pi$
$59$	−572.000	−1.26217	−0.631085	+	0.775713i	$0.717390\pi$
$60$	0	0
$61$	420.000	0.881565	0.440783	−	0.897614i	$-0.354701\pi$
$61$	420.000	0.881565	0.440783	+	0.897614i	$0.354701\pi$
$62$	0	0
$63$	396.000	0.791926
$64$	0	0
$65$	855.000	1.63153
$66$	0	0
$67$	660.000	1.20346	0.601730	−	0.798699i	$-0.294478\pi$
$67$	660.000	1.20346	0.601730	+	0.798699i	$0.294478\pi$
$68$	0	0
$69$	−1064.00	−1.85638
$70$	0	0
$71$	−726.000	−1.21353	−0.606763	−	0.794883i	$-0.707532\pi$
$71$	−726.000	−1.21353	−0.606763	+	0.794883i	$0.707532\pi$
$72$	0	0
$73$	1004.00	1.60972	0.804858	−	0.593467i	$-0.202241\pi$
$73$	1004.00	1.60972	0.804858	+	0.593467i	$0.202241\pi$
$74$	0	0
$75$	−700.000	−1.07772
$76$	0	0
$77$	486.000	0.719284
$78$	0	0
$79$	−361.000	−0.514122	−0.257061	−	0.966395i	$-0.582754\pi$
$79$	−361.000	−0.514122	−0.257061	+	0.966395i	$0.582754\pi$
$80$	0	0
$81$	−839.000	−1.15089
$82$	0	0
$83$	−168.000	−0.222173	−0.111087	−	0.993811i	$-0.535433\pi$
$83$	−168.000	−0.222173	−0.111087	+	0.993811i	$0.535433\pi$
$84$	0	0
$85$	−660.000	−0.842201
$86$	0	0
$87$	−203.000	−0.250160
$88$	0	0
$89$	58.0000	0.0690785	0.0345393	−	0.999403i	$-0.489004\pi$
$89$	58.0000	0.0690785	0.0345393	+	0.999403i	$0.489004\pi$
$90$	0	0
$91$	1026.00	1.18191
$92$	0	0
$93$	−1211.00	−1.35027
$94$	0	0
$95$	2280.00	2.46235
$96$	0	0
$97$	−1206.00	−1.26238	−0.631189	−	0.775629i	$-0.717433\pi$
$97$	−1206.00	−1.26238	−0.631189	+	0.775629i	$0.717433\pi$
$98$	0	0
$99$	594.000	0.603023
$100$	0	0
$101$	−1440.00	−1.41867	−0.709333	−	0.704873i	$-0.751004\pi$
$101$	−1440.00	−1.41867	−0.709333	+	0.704873i	$0.751004\pi$
$102$	0	0
$103$	−1858.00	−1.77742	−0.888710	−	0.458471i	$-0.848397\pi$
$103$	−1858.00	−1.77742	−0.888710	+	0.458471i	$0.848397\pi$
$104$	0	0
$105$	−1890.00	−1.75662
$106$	0	0
$107$	−1914.00	−1.72928	−0.864642	−	0.502389i	$-0.832455\pi$
$107$	−1914.00	−1.72928	−0.864642	+	0.502389i	$0.832455\pi$
$108$	0	0
$109$	−989.000	−0.869074	−0.434537	−	0.900654i	$-0.643088\pi$
$109$	−989.000	−0.869074	−0.434537	+	0.900654i	$0.643088\pi$
$110$	0	0
$111$	−840.000	−0.718282
$112$	0	0
$113$	−278.000	−0.231434	−0.115717	−	0.993282i	$-0.536917\pi$
$113$	−278.000	−0.231434	−0.115717	+	0.993282i	$0.536917\pi$
$114$	0	0
$115$	2280.00	1.84879
$116$	0	0
$117$	1254.00	0.990875
$118$	0	0
$119$	−792.000	−0.610105
$120$	0	0
$121$	−602.000	−0.452292
$122$	0	0
$123$	2198.00	1.61128
$124$	0	0
$125$	−375.000	−0.268328
$126$	0	0
$127$	600.000	0.419224	0.209612	−	0.977785i	$-0.432780\pi$
$127$	600.000	0.419224	0.209612	+	0.977785i	$0.432780\pi$
$128$	0	0
$129$	−2373.00	−1.61962
$130$	0	0
$131$	−1652.00	−1.10180	−0.550900	−	0.834571i	$-0.685716\pi$
$131$	−1652.00	−1.10180	−0.550900	+	0.834571i	$0.685716\pi$
$132$	0	0
$133$	2736.00	1.78377
$134$	0	0
$135$	525.000	0.334702
$136$	0	0
$137$	−1212.00	−0.755826	−0.377913	−	0.925841i	$-0.623358\pi$
$137$	−1212.00	−0.755826	−0.377913	+	0.925841i	$0.623358\pi$
$138$	0	0
$139$	1328.00	0.810356	0.405178	−	0.914238i	$-0.367210\pi$
$139$	1328.00	0.810356	0.405178	+	0.914238i	$0.367210\pi$
$140$	0	0
$141$	−2499.00	−1.49258
$142$	0	0
$143$	1539.00	0.899984
$144$	0	0
$145$	435.000	0.249136
$146$	0	0
$147$	133.000	0.0746235
$148$	0	0
$149$	1777.00	0.977030	0.488515	−	0.872555i	$-0.337539\pi$
$149$	1777.00	0.977030	0.488515	+	0.872555i	$0.337539\pi$
$150$	0	0
$151$	1934.00	1.04230	0.521148	−	0.853466i	$-0.325504\pi$
$151$	1934.00	1.04230	0.521148	+	0.853466i	$0.325504\pi$
$152$	0	0
$153$	−968.000	−0.511491
$154$	0	0
$155$	2595.00	1.34474
$156$	0	0
$157$	−734.000	−0.373118	−0.186559	−	0.982444i	$-0.559734\pi$
$157$	−734.000	−0.373118	−0.186559	+	0.982444i	$0.559734\pi$
$158$	0	0
$159$	−413.000	−0.205994
$160$	0	0
$161$	2736.00	1.33930
$162$	0	0
$163$	−3337.00	−1.60352	−0.801761	−	0.597645i	$-0.796103\pi$
$163$	−3337.00	−1.60352	−0.801761	+	0.597645i	$0.796103\pi$
$164$	0	0
$165$	−2835.00	−1.33760
$166$	0	0
$167$	198.000	0.0917467	0.0458734	−	0.998947i	$-0.485393\pi$
$167$	198.000	0.0917467	0.0458734	+	0.998947i	$0.485393\pi$
$168$	0	0
$169$	1052.00	0.478835
$170$	0	0
$171$	3344.00	1.49545
$172$	0	0
$173$	2598.00	1.14175	0.570874	−	0.821038i	$-0.306605\pi$
$173$	2598.00	1.14175	0.570874	+	0.821038i	$0.306605\pi$
$174$	0	0
$175$	1800.00	0.777527
$176$	0	0
$177$	4004.00	1.70033
$178$	0	0
$179$	−1510.00	−0.630518	−0.315259	−	0.949006i	$-0.602091\pi$
$179$	−1510.00	−0.630518	−0.315259	+	0.949006i	$0.602091\pi$
$180$	0	0
$181$	2865.00	1.17654	0.588270	−	0.808665i	$-0.299809\pi$
$181$	2865.00	1.17654	0.588270	+	0.808665i	$0.299809\pi$
$182$	0	0
$183$	−2940.00	−1.18760
$184$	0	0
$185$	1800.00	0.715344
$186$	0	0
$187$	−1188.00	−0.464573
$188$	0	0
$189$	630.000	0.242464
$190$	0	0
$191$	1936.00	0.733424	0.366712	−	0.930334i	$-0.380483\pi$
$191$	1936.00	0.733424	0.366712	+	0.930334i	$0.380483\pi$
$192$	0	0
$193$	3850.00	1.43590	0.717951	−	0.696094i	$-0.245080\pi$
$193$	3850.00	1.43590	0.717951	+	0.696094i	$0.245080\pi$
$194$	0	0
$195$	−5985.00	−2.19792
$196$	0	0
$197$	−3034.00	−1.09728	−0.548638	−	0.836060i	$-0.684854\pi$
$197$	−3034.00	−1.09728	−0.548638	+	0.836060i	$0.684854\pi$
$198$	0	0
$199$	−246.000	−0.0876305	−0.0438153	−	0.999040i	$-0.513951\pi$
$199$	−246.000	−0.0876305	−0.0438153	+	0.999040i	$0.513951\pi$
$200$	0	0
$201$	−4620.00	−1.62124
$202$	0	0
$203$	522.000	0.180479
$204$	0	0
$205$	−4710.00	−1.60469
$206$	0	0
$207$	3344.00	1.12282
$208$	0	0
$209$	4104.00	1.35828
$210$	0	0
$211$	−1493.00	−0.487120	−0.243560	−	0.969886i	$-0.578315\pi$
$211$	−1493.00	−0.487120	−0.243560	+	0.969886i	$0.578315\pi$
$212$	0	0
$213$	5082.00	1.63480
$214$	0	0
$215$	5085.00	1.61300
$216$	0	0
$217$	3114.00	0.974157
$218$	0	0
$219$	−7028.00	−2.16853
$220$	0	0
$221$	−2508.00	−0.763377
$222$	0	0
$223$	−1402.00	−0.421008	−0.210504	−	0.977593i	$-0.567511\pi$
$223$	−1402.00	−0.421008	−0.210504	+	0.977593i	$0.567511\pi$
$224$	0	0
$225$	2200.00	0.651852
$226$	0	0
$227$	1166.00	0.340926	0.170463	−	0.985364i	$-0.445474\pi$
$227$	1166.00	0.340926	0.170463	+	0.985364i	$0.445474\pi$
$228$	0	0
$229$	1466.00	0.423039	0.211520	−	0.977374i	$-0.432159\pi$
$229$	1466.00	0.423039	0.211520	+	0.977374i	$0.432159\pi$
$230$	0	0
$231$	−3402.00	−0.968983
$232$	0	0
$233$	847.000	0.238149	0.119075	−	0.992885i	$-0.462007\pi$
$233$	847.000	0.238149	0.119075	+	0.992885i	$0.462007\pi$
$234$	0	0
$235$	5355.00	1.48648
$236$	0	0
$237$	2527.00	0.692600
$238$	0	0
$239$	444.000	0.120167	0.0600836	−	0.998193i	$-0.480863\pi$
$239$	444.000	0.120167	0.0600836	+	0.998193i	$0.480863\pi$
$240$	0	0
$241$	5297.00	1.41581	0.707904	−	0.706309i	$-0.249641\pi$
$241$	5297.00	1.41581	0.707904	+	0.706309i	$0.249641\pi$
$242$	0	0
$243$	4928.00	1.30095
$244$	0	0
$245$	−285.000	−0.0743183
$246$	0	0
$247$	8664.00	2.23189
$248$	0	0
$249$	1176.00	0.299301
$250$	0	0
$251$	4061.00	1.02123	0.510614	−	0.859810i	$-0.329418\pi$
$251$	4061.00	1.02123	0.510614	+	0.859810i	$0.329418\pi$
$252$	0	0
$253$	4104.00	1.01983
$254$	0	0
$255$	4620.00	1.13457
$256$	0	0
$257$	−6843.00	−1.66091	−0.830456	−	0.557084i	$-0.811920\pi$
$257$	−6843.00	−1.66091	−0.830456	+	0.557084i	$0.811920\pi$
$258$	0	0
$259$	2160.00	0.518208
$260$	0	0
$261$	638.000	0.151307
$262$	0	0
$263$	−3191.00	−0.748158	−0.374079	−	0.927397i	$-0.622041\pi$
$263$	−3191.00	−0.748158	−0.374079	+	0.927397i	$0.622041\pi$
$264$	0	0
$265$	885.000	0.205151
$266$	0	0
$267$	−406.000	−0.0930592
$268$	0	0
$269$	−7436.00	−1.68543	−0.842715	−	0.538359i	$-0.819044\pi$
$269$	−7436.00	−1.68543	−0.842715	+	0.538359i	$0.819044\pi$
$270$	0	0
$271$	2755.00	0.617544	0.308772	−	0.951136i	$-0.400082\pi$
$271$	2755.00	0.617544	0.308772	+	0.951136i	$0.400082\pi$
$272$	0	0
$273$	−7182.00	−1.59221
$274$	0	0
$275$	2700.00	0.592059
$276$	0	0
$277$	2410.00	0.522754	0.261377	−	0.965237i	$-0.415823\pi$
$277$	2410.00	0.522754	0.261377	+	0.965237i	$0.415823\pi$
$278$	0	0
$279$	3806.00	0.816700
$280$	0	0
$281$	2235.00	0.474480	0.237240	−	0.971451i	$-0.423757\pi$
$281$	2235.00	0.474480	0.237240	+	0.971451i	$0.423757\pi$
$282$	0	0
$283$	−1648.00	−0.346161	−0.173080	−	0.984908i	$-0.555372\pi$
$283$	−1648.00	−0.346161	−0.173080	+	0.984908i	$0.555372\pi$
$284$	0	0
$285$	−15960.0	−3.31715
$286$	0	0
$287$	−5652.00	−1.16246
$288$	0	0
$289$	−2977.00	−0.605943
$290$	0	0
$291$	8442.00	1.70061
$292$	0	0
$293$	−2878.00	−0.573838	−0.286919	−	0.957955i	$-0.592631\pi$
$293$	−2878.00	−0.573838	−0.286919	+	0.957955i	$0.592631\pi$
$294$	0	0
$295$	−8580.00	−1.69338
$296$	0	0
$297$	945.000	0.184628
$298$	0	0
$299$	8664.00	1.67576
$300$	0	0
$301$	6102.00	1.16848
$302$	0	0
$303$	10080.0	1.91116
$304$	0	0
$305$	6300.00	1.18274
$306$	0	0
$307$	4903.00	0.911495	0.455748	−	0.890109i	$-0.349372\pi$
$307$	4903.00	0.911495	0.455748	+	0.890109i	$0.349372\pi$
$308$	0	0
$309$	13006.0	2.39445
$310$	0	0
$311$	32.0000	0.00583458	0.00291729	−	0.999996i	$-0.499071\pi$
$311$	32.0000	0.00583458	0.00291729	+	0.999996i	$0.499071\pi$
$312$	0	0
$313$	−5455.00	−0.985095	−0.492548	−	0.870285i	$-0.663934\pi$
$313$	−5455.00	−0.985095	−0.492548	+	0.870285i	$0.663934\pi$
$314$	0	0
$315$	5940.00	1.06248
$316$	0	0
$317$	9552.00	1.69241	0.846205	−	0.532858i	$-0.178882\pi$
$317$	9552.00	1.69241	0.846205	+	0.532858i	$0.178882\pi$
$318$	0	0
$319$	783.000	0.137428
$320$	0	0
$321$	13398.0	2.32961
$322$	0	0
$323$	−6688.00	−1.15211
$324$	0	0
$325$	5700.00	0.972859
$326$	0	0
$327$	6923.00	1.17077
$328$	0	0
$329$	6426.00	1.07683
$330$	0	0
$331$	−2433.00	−0.404017	−0.202009	−	0.979384i	$-0.564747\pi$
$331$	−2433.00	−0.404017	−0.202009	+	0.979384i	$0.564747\pi$
$332$	0	0
$333$	2640.00	0.434448
$334$	0	0
$335$	9900.00	1.61461
$336$	0	0
$337$	−7460.00	−1.20585	−0.602926	−	0.797797i	$-0.705999\pi$
$337$	−7460.00	−1.20585	−0.602926	+	0.797797i	$0.705999\pi$
$338$	0	0
$339$	1946.00	0.311776
$340$	0	0
$341$	4671.00	0.741785
$342$	0	0
$343$	−6516.00	−1.02575
$344$	0	0
$345$	−15960.0	−2.49060
$346$	0	0
$347$	4002.00	0.619131	0.309566	−	0.950878i	$-0.399816\pi$
$347$	4002.00	0.619131	0.309566	+	0.950878i	$0.399816\pi$
$348$	0	0
$349$	2167.00	0.332369	0.166185	−	0.986095i	$-0.446855\pi$
$349$	2167.00	0.332369	0.166185	+	0.986095i	$0.446855\pi$
$350$	0	0
$351$	1995.00	0.303377
$352$	0	0
$353$	−2354.00	−0.354931	−0.177466	−	0.984127i	$-0.556790\pi$
$353$	−2354.00	−0.354931	−0.177466	+	0.984127i	$0.556790\pi$
$354$	0	0
$355$	−10890.0	−1.62812
$356$	0	0
$357$	5544.00	0.821904
$358$	0	0
$359$	3471.00	0.510285	0.255143	−	0.966903i	$-0.417878\pi$
$359$	3471.00	0.510285	0.255143	+	0.966903i	$0.417878\pi$
$360$	0	0
$361$	16245.0	2.36842
$362$	0	0
$363$	4214.00	0.609305
$364$	0	0
$365$	15060.0	2.15966
$366$	0	0
$367$	10880.0	1.54750	0.773748	−	0.633493i	$-0.218379\pi$
$367$	10880.0	1.54750	0.773748	+	0.633493i	$0.218379\pi$
$368$	0	0
$369$	−6908.00	−0.974569
$370$	0	0
$371$	1062.00	0.148615
$372$	0	0
$373$	−8827.00	−1.22532	−0.612661	−	0.790346i	$-0.709901\pi$
$373$	−8827.00	−1.22532	−0.612661	+	0.790346i	$0.709901\pi$
$374$	0	0
$375$	2625.00	0.361478
$376$	0	0
$377$	1653.00	0.225819
$378$	0	0
$379$	−876.000	−0.118726	−0.0593629	−	0.998236i	$-0.518907\pi$
$379$	−876.000	−0.118726	−0.0593629	+	0.998236i	$0.518907\pi$
$380$	0	0
$381$	−4200.00	−0.564757
$382$	0	0
$383$	−5446.00	−0.726573	−0.363287	−	0.931677i	$-0.618345\pi$
$383$	−5446.00	−0.726573	−0.363287	+	0.931677i	$0.618345\pi$
$384$	0	0
$385$	7290.00	0.965020
$386$	0	0
$387$	7458.00	0.979616
$388$	0	0
$389$	2216.00	0.288832	0.144416	−	0.989517i	$-0.453870\pi$
$389$	2216.00	0.288832	0.144416	+	0.989517i	$0.453870\pi$
$390$	0	0
$391$	−6688.00	−0.865030
$392$	0	0
$393$	11564.0	1.48429
$394$	0	0
$395$	−5415.00	−0.689768
$396$	0	0
$397$	−6823.00	−0.862561	−0.431280	−	0.902218i	$-0.641938\pi$
$397$	−6823.00	−0.862561	−0.431280	+	0.902218i	$0.641938\pi$
$398$	0	0
$399$	−19152.0	−2.40301
$400$	0	0
$401$	−5589.00	−0.696013	−0.348007	−	0.937492i	$-0.613141\pi$
$401$	−5589.00	−0.696013	−0.348007	+	0.937492i	$0.613141\pi$
$402$	0	0
$403$	9861.00	1.21889
$404$	0	0
$405$	−12585.0	−1.54408
$406$	0	0
$407$	3240.00	0.394597
$408$	0	0
$409$	−8258.00	−0.998366	−0.499183	−	0.866496i	$-0.666367\pi$
$409$	−8258.00	−0.998366	−0.499183	+	0.866496i	$0.666367\pi$
$410$	0	0
$411$	8484.00	1.01821
$412$	0	0
$413$	−10296.0	−1.22671
$414$	0	0
$415$	−2520.00	−0.298077
$416$	0	0
$417$	−9296.00	−1.09167
$418$	0	0
$419$	3946.00	0.460083	0.230041	−	0.973181i	$-0.426114\pi$
$419$	3946.00	0.460083	0.230041	+	0.973181i	$0.426114\pi$
$420$	0	0
$421$	−1380.00	−0.159756	−0.0798778	−	0.996805i	$-0.525453\pi$
$421$	−1380.00	−0.159756	−0.0798778	+	0.996805i	$0.525453\pi$
$422$	0	0
$423$	7854.00	0.902777
$424$	0	0
$425$	−4400.00	−0.502191
$426$	0	0
$427$	7560.00	0.856801
$428$	0	0
$429$	−10773.0	−1.21241
$430$	0	0
$431$	5820.00	0.650440	0.325220	−	0.945638i	$-0.394562\pi$
$431$	5820.00	0.650440	0.325220	+	0.945638i	$0.394562\pi$
$432$	0	0
$433$	−14504.0	−1.60974	−0.804870	−	0.593451i	$-0.797765\pi$
$433$	−14504.0	−1.60974	−0.804870	+	0.593451i	$0.797765\pi$
$434$	0	0
$435$	−3045.00	−0.335624
$436$	0	0
$437$	23104.0	2.52909
$438$	0	0
$439$	−14912.0	−1.62121	−0.810605	−	0.585594i	$-0.800861\pi$
$439$	−14912.0	−1.62121	−0.810605	+	0.585594i	$0.800861\pi$
$440$	0	0
$441$	−418.000	−0.0451355
$442$	0	0
$443$	7180.00	0.770050	0.385025	−	0.922906i	$-0.374193\pi$
$443$	7180.00	0.770050	0.385025	+	0.922906i	$0.374193\pi$
$444$	0	0
$445$	870.000	0.0926786
$446$	0	0
$447$	−12439.0	−1.31621
$448$	0	0
$449$	1398.00	0.146939	0.0734696	−	0.997297i	$-0.476593\pi$
$449$	1398.00	0.146939	0.0734696	+	0.997297i	$0.476593\pi$
$450$	0	0
$451$	−8478.00	−0.885174
$452$	0	0
$453$	−13538.0	−1.40413
$454$	0	0
$455$	15390.0	1.58570
$456$	0	0
$457$	−5658.00	−0.579147	−0.289573	−	0.957156i	$-0.593513\pi$
$457$	−5658.00	−0.579147	−0.289573	+	0.957156i	$0.593513\pi$
$458$	0	0
$459$	−1540.00	−0.156604
$460$	0	0
$461$	−11410.0	−1.15275	−0.576374	−	0.817186i	$-0.695533\pi$
$461$	−11410.0	−1.15275	−0.576374	+	0.817186i	$0.695533\pi$
$462$	0	0
$463$	2560.00	0.256962	0.128481	−	0.991712i	$-0.458990\pi$
$463$	2560.00	0.256962	0.128481	+	0.991712i	$0.458990\pi$
$464$	0	0
$465$	−18165.0	−1.81157
$466$	0	0
$467$	10395.0	1.03003	0.515014	−	0.857182i	$-0.327787\pi$
$467$	10395.0	1.03003	0.515014	+	0.857182i	$0.327787\pi$
$468$	0	0
$469$	11880.0	1.16965
$470$	0	0
$471$	5138.00	0.502647
$472$	0	0
$473$	9153.00	0.889758
$474$	0	0
$475$	15200.0	1.46826
$476$	0	0
$477$	1298.00	0.124594
$478$	0	0
$479$	5627.00	0.536752	0.268376	−	0.963314i	$-0.413513\pi$
$479$	5627.00	0.536752	0.268376	+	0.963314i	$0.413513\pi$
$480$	0	0
$481$	6840.00	0.648393
$482$	0	0
$483$	−19152.0	−1.80424
$484$	0	0
$485$	−18090.0	−1.69366
$486$	0	0
$487$	−8738.00	−0.813053	−0.406526	−	0.913639i	$-0.633260\pi$
$487$	−8738.00	−0.813053	−0.406526	+	0.913639i	$0.633260\pi$
$488$	0	0
$489$	23359.0	2.16019
$490$	0	0
$491$	3177.00	0.292008	0.146004	−	0.989284i	$-0.453359\pi$
$491$	3177.00	0.292008	0.146004	+	0.989284i	$0.453359\pi$
$492$	0	0
$493$	−1276.00	−0.116568
$494$	0	0
$495$	8910.00	0.809040
$496$	0	0
$497$	−13068.0	−1.17944
$498$	0	0
$499$	−5816.00	−0.521763	−0.260882	−	0.965371i	$-0.584013\pi$
$499$	−5816.00	−0.521763	−0.260882	+	0.965371i	$0.584013\pi$
$500$	0	0
$501$	−1386.00	−0.123597
$502$	0	0
$503$	2267.00	0.200955	0.100478	−	0.994939i	$-0.467963\pi$
$503$	2267.00	0.200955	0.100478	+	0.994939i	$0.467963\pi$
$504$	0	0
$505$	−21600.0	−1.90334
$506$	0	0
$507$	−7364.00	−0.645063
$508$	0	0
$509$	−6481.00	−0.564372	−0.282186	−	0.959360i	$-0.591060\pi$
$509$	−6481.00	−0.564372	−0.282186	+	0.959360i	$0.591060\pi$
$510$	0	0
$511$	18072.0	1.56450
$512$	0	0
$513$	5320.00	0.457863
$514$	0	0
$515$	−27870.0	−2.38466
$516$	0	0
$517$	9639.00	0.819967
$518$	0	0
$519$	−18186.0	−1.53811
$520$	0	0
$521$	−21357.0	−1.79591	−0.897953	−	0.440091i	$-0.854946\pi$
$521$	−21357.0	−1.79591	−0.897953	+	0.440091i	$0.854946\pi$
$522$	0	0
$523$	−6192.00	−0.517700	−0.258850	−	0.965917i	$-0.583344\pi$
$523$	−6192.00	−0.517700	−0.258850	+	0.965917i	$0.583344\pi$
$524$	0	0
$525$	−12600.0	−1.04745
$526$	0	0
$527$	−7612.00	−0.629192
$528$	0	0
$529$	10937.0	0.898907
$530$	0	0
$531$	−12584.0	−1.02844
$532$	0	0
$533$	−17898.0	−1.45450
$534$	0	0
$535$	−28710.0	−2.32008
$536$	0	0
$537$	10570.0	0.849403
$538$	0	0
$539$	−513.000	−0.0409953
$540$	0	0
$541$	19800.0	1.57351	0.786755	−	0.617266i	$-0.211760\pi$
$541$	19800.0	1.57351	0.786755	+	0.617266i	$0.211760\pi$
$542$	0	0
$543$	−20055.0	−1.58498
$544$	0	0
$545$	−14835.0	−1.16598
$546$	0	0
$547$	10526.0	0.822777	0.411389	−	0.911460i	$-0.365044\pi$
$547$	10526.0	0.822777	0.411389	+	0.911460i	$0.365044\pi$
$548$	0	0
$549$	9240.00	0.718313
$550$	0	0
$551$	4408.00	0.340811
$552$	0	0
$553$	−6498.00	−0.499680
$554$	0	0
$555$	−12600.0	−0.963676
$556$	0	0
$557$	11834.0	0.900220	0.450110	−	0.892973i	$-0.351385\pi$
$557$	11834.0	0.900220	0.450110	+	0.892973i	$0.351385\pi$
$558$	0	0
$559$	19323.0	1.46203
$560$	0	0
$561$	8316.00	0.625850
$562$	0	0
$563$	21771.0	1.62973	0.814865	−	0.579650i	$-0.196811\pi$
$563$	21771.0	1.62973	0.814865	+	0.579650i	$0.196811\pi$
$564$	0	0
$565$	−4170.00	−0.310501
$566$	0	0
$567$	−15102.0	−1.11856
$568$	0	0
$569$	20778.0	1.53086	0.765430	−	0.643519i	$-0.222526\pi$
$569$	20778.0	1.53086	0.765430	+	0.643519i	$0.222526\pi$
$570$	0	0
$571$	−5596.00	−0.410132	−0.205066	−	0.978748i	$-0.565741\pi$
$571$	−5596.00	−0.410132	−0.205066	+	0.978748i	$0.565741\pi$
$572$	0	0
$573$	−13552.0	−0.988033
$574$	0	0
$575$	15200.0	1.10241
$576$	0	0
$577$	−14908.0	−1.07561	−0.537806	−	0.843069i	$-0.680747\pi$
$577$	−14908.0	−1.07561	−0.537806	+	0.843069i	$0.680747\pi$
$578$	0	0
$579$	−26950.0	−1.93438
$580$	0	0
$581$	−3024.00	−0.215932
$582$	0	0
$583$	1593.00	0.113165
$584$	0	0
$585$	18810.0	1.32940
$586$	0	0
$587$	8136.00	0.572076	0.286038	−	0.958218i	$-0.407662\pi$
$587$	8136.00	0.572076	0.286038	+	0.958218i	$0.407662\pi$
$588$	0	0
$589$	26296.0	1.83957
$590$	0	0
$591$	21238.0	1.47820
$592$	0	0
$593$	−3521.00	−0.243828	−0.121914	−	0.992541i	$-0.538903\pi$
$593$	−3521.00	−0.243828	−0.121914	+	0.992541i	$0.538903\pi$
$594$	0	0
$595$	−11880.0	−0.818542
$596$	0	0
$597$	1722.00	0.118052
$598$	0	0
$599$	−7749.00	−0.528574	−0.264287	−	0.964444i	$-0.585137\pi$
$599$	−7749.00	−0.528574	−0.264287	+	0.964444i	$0.585137\pi$
$600$	0	0
$601$	5054.00	0.343023	0.171512	−	0.985182i	$-0.445135\pi$
$601$	5054.00	0.343023	0.171512	+	0.985182i	$0.445135\pi$
$602$	0	0
$603$	14520.0	0.980597
$604$	0	0
$605$	−9030.00	−0.606813
$606$	0	0
$607$	−27389.0	−1.83144	−0.915721	−	0.401815i	$-0.868380\pi$
$607$	−27389.0	−1.83144	−0.915721	+	0.401815i	$0.868380\pi$
$608$	0	0
$609$	−3654.00	−0.243132
$610$	0	0
$611$	20349.0	1.34735
$612$	0	0
$613$	2375.00	0.156485	0.0782425	−	0.996934i	$-0.475069\pi$
$613$	2375.00	0.156485	0.0782425	+	0.996934i	$0.475069\pi$
$614$	0	0
$615$	32970.0	2.16175
$616$	0	0
$617$	3412.00	0.222629	0.111314	−	0.993785i	$-0.464494\pi$
$617$	3412.00	0.222629	0.111314	+	0.993785i	$0.464494\pi$
$618$	0	0
$619$	17659.0	1.14665	0.573324	−	0.819329i	$-0.305654\pi$
$619$	17659.0	1.14665	0.573324	+	0.819329i	$0.305654\pi$
$620$	0	0
$621$	5320.00	0.343775
$622$	0	0
$623$	1044.00	0.0671380
$624$	0	0
$625$	−18125.0	−1.16000
$626$	0	0
$627$	−28728.0	−1.82980
$628$	0	0
$629$	−5280.00	−0.334702
$630$	0	0
$631$	−12742.0	−0.803884	−0.401942	−	0.915665i	$-0.631665\pi$
$631$	−12742.0	−0.803884	−0.401942	+	0.915665i	$0.631665\pi$
$632$	0	0
$633$	10451.0	0.656224
$634$	0	0
$635$	9000.00	0.562447
$636$	0	0
$637$	−1083.00	−0.0673627
$638$	0	0
$639$	−15972.0	−0.988799
$640$	0	0
$641$	−10988.0	−0.677067	−0.338533	−	0.940954i	$-0.609931\pi$
$641$	−10988.0	−0.677067	−0.338533	+	0.940954i	$0.609931\pi$
$642$	0	0
$643$	−13190.0	−0.808962	−0.404481	−	0.914546i	$-0.632548\pi$
$643$	−13190.0	−0.808962	−0.404481	+	0.914546i	$0.632548\pi$
$644$	0	0
$645$	−35595.0	−2.17295
$646$	0	0
$647$	−22924.0	−1.39295	−0.696473	−	0.717583i	$-0.745248\pi$
$647$	−22924.0	−1.39295	−0.696473	+	0.717583i	$0.745248\pi$
$648$	0	0
$649$	−15444.0	−0.934099
$650$	0	0
$651$	−21798.0	−1.31234
$652$	0	0
$653$	10278.0	0.615941	0.307970	−	0.951396i	$-0.400350\pi$
$653$	10278.0	0.615941	0.307970	+	0.951396i	$0.400350\pi$
$654$	0	0
$655$	−24780.0	−1.47822
$656$	0	0
$657$	22088.0	1.31162
$658$	0	0
$659$	−10607.0	−0.626996	−0.313498	−	0.949589i	$-0.601501\pi$
$659$	−10607.0	−0.626996	−0.313498	+	0.949589i	$0.601501\pi$
$660$	0	0
$661$	24698.0	1.45331	0.726657	−	0.687000i	$-0.241073\pi$
$661$	24698.0	1.45331	0.726657	+	0.687000i	$0.241073\pi$
$662$	0	0
$663$	17556.0	1.02838
$664$	0	0
$665$	41040.0	2.39318
$666$	0	0
$667$	4408.00	0.255890
$668$	0	0
$669$	9814.00	0.567162
$670$	0	0
$671$	11340.0	0.652423
$672$	0	0
$673$	16801.0	0.962305	0.481152	−	0.876637i	$-0.340218\pi$
$673$	16801.0	0.962305	0.481152	+	0.876637i	$0.340218\pi$
$674$	0	0
$675$	3500.00	0.199578
$676$	0	0
$677$	1258.00	0.0714163	0.0357082	−	0.999362i	$-0.488631\pi$
$677$	1258.00	0.0714163	0.0357082	+	0.999362i	$0.488631\pi$
$678$	0	0
$679$	−21708.0	−1.22692
$680$	0	0
$681$	−8162.00	−0.459278
$682$	0	0
$683$	−1256.00	−0.0703653	−0.0351827	−	0.999381i	$-0.511201\pi$
$683$	−1256.00	−0.0703653	−0.0351827	+	0.999381i	$0.511201\pi$
$684$	0	0
$685$	−18180.0	−1.01405
$686$	0	0
$687$	−10262.0	−0.569898
$688$	0	0
$689$	3363.00	0.185951
$690$	0	0
$691$	−15996.0	−0.880632	−0.440316	−	0.897843i	$-0.645134\pi$
$691$	−15996.0	−0.880632	−0.440316	+	0.897843i	$0.645134\pi$
$692$	0	0
$693$	10692.0	0.586083
$694$	0	0
$695$	19920.0	1.08721
$696$	0	0
$697$	13816.0	0.750815
$698$	0	0
$699$	−5929.00	−0.320823
$700$	0	0
$701$	189.000	0.0101832	0.00509161	−	0.999987i	$-0.498379\pi$
$701$	189.000	0.0101832	0.00509161	+	0.999987i	$0.498379\pi$
$702$	0	0
$703$	18240.0	0.978570
$704$	0	0
$705$	−37485.0	−2.00251
$706$	0	0
$707$	−25920.0	−1.37881
$708$	0	0
$709$	−2431.00	−0.128770	−0.0643851	−	0.997925i	$-0.520509\pi$
$709$	−2431.00	−0.128770	−0.0643851	+	0.997925i	$0.520509\pi$
$710$	0	0
$711$	−7942.00	−0.418915
$712$	0	0
$713$	26296.0	1.38120
$714$	0	0
$715$	23085.0	1.20745
$716$	0	0
$717$	−3108.00	−0.161883
$718$	0	0
$719$	3630.00	0.188284	0.0941420	−	0.995559i	$-0.469989\pi$
$719$	3630.00	0.188284	0.0941420	+	0.995559i	$0.469989\pi$
$720$	0	0
$721$	−33444.0	−1.72749
$722$	0	0
$723$	−37079.0	−1.90731
$724$	0	0
$725$	2900.00	0.148556
$726$	0	0
$727$	1712.00	0.0873378	0.0436689	−	0.999046i	$-0.486095\pi$
$727$	1712.00	0.0873378	0.0436689	+	0.999046i	$0.486095\pi$
$728$	0	0
$729$	−11843.0	−0.601687
$730$	0	0
$731$	−14916.0	−0.754703
$732$	0	0
$733$	−26584.0	−1.33957	−0.669783	−	0.742557i	$-0.733613\pi$
$733$	−26584.0	−1.33957	−0.669783	+	0.742557i	$0.733613\pi$
$734$	0	0
$735$	1995.00	0.100118
$736$	0	0
$737$	17820.0	0.890649
$738$	0	0
$739$	8125.00	0.404442	0.202221	−	0.979340i	$-0.435184\pi$
$739$	8125.00	0.404442	0.202221	+	0.979340i	$0.435184\pi$
$740$	0	0
$741$	−60648.0	−3.00669
$742$	0	0
$743$	31804.0	1.57036	0.785179	−	0.619269i	$-0.212571\pi$
$743$	31804.0	1.57036	0.785179	+	0.619269i	$0.212571\pi$
$744$	0	0
$745$	26655.0	1.31082
$746$	0	0
$747$	−3696.00	−0.181030
$748$	0	0
$749$	−34452.0	−1.68071
$750$	0	0
$751$	37504.0	1.82229	0.911145	−	0.412085i	$-0.135199\pi$
$751$	37504.0	1.82229	0.911145	+	0.412085i	$0.135199\pi$
$752$	0	0
$753$	−28427.0	−1.37575
$754$	0	0
$755$	29010.0	1.39839
$756$	0	0
$757$	76.0000	0.00364897	0.00182448	−	0.999998i	$-0.499419\pi$
$757$	76.0000	0.00364897	0.00182448	+	0.999998i	$0.499419\pi$
$758$	0	0
$759$	−28728.0	−1.37386
$760$	0	0
$761$	−23374.0	−1.11341	−0.556706	−	0.830709i	$-0.687935\pi$
$761$	−23374.0	−1.11341	−0.556706	+	0.830709i	$0.687935\pi$
$762$	0	0
$763$	−17802.0	−0.844660
$764$	0	0
$765$	−14520.0	−0.686238
$766$	0	0
$767$	−32604.0	−1.53489
$768$	0	0
$769$	−5448.00	−0.255475	−0.127737	−	0.991808i	$-0.540771\pi$
$769$	−5448.00	−0.255475	−0.127737	+	0.991808i	$0.540771\pi$
$770$	0	0
$771$	47901.0	2.23750
$772$	0	0
$773$	16062.0	0.747361	0.373680	−	0.927558i	$-0.378096\pi$
$773$	16062.0	0.747361	0.373680	+	0.927558i	$0.378096\pi$
$774$	0	0
$775$	17300.0	0.801851
$776$	0	0
$777$	−15120.0	−0.698104
$778$	0	0
$779$	−47728.0	−2.19516
$780$	0	0
$781$	−19602.0	−0.898098
$782$	0	0
$783$	1015.00	0.0463259
$784$	0	0
$785$	−11010.0	−0.500591
$786$	0	0
$787$	19182.0	0.868824	0.434412	−	0.900714i	$-0.356956\pi$
$787$	19182.0	0.868824	0.434412	+	0.900714i	$0.356956\pi$
$788$	0	0
$789$	22337.0	1.00788
$790$	0	0
$791$	−5004.00	−0.224933
$792$	0	0
$793$	23940.0	1.07205
$794$	0	0
$795$	−6195.00	−0.276370
$796$	0	0
$797$	−5556.00	−0.246931	−0.123465	−	0.992349i	$-0.539401\pi$
$797$	−5556.00	−0.246931	−0.123465	+	0.992349i	$0.539401\pi$
$798$	0	0
$799$	−15708.0	−0.695506
$800$	0	0
$801$	1276.00	0.0562862
$802$	0	0
$803$	27108.0	1.19131
$804$	0	0
$805$	41040.0	1.79686
$806$	0	0
$807$	52052.0	2.27053
$808$	0	0
$809$	2616.00	0.113688	0.0568440	−	0.998383i	$-0.481896\pi$
$809$	2616.00	0.113688	0.0568440	+	0.998383i	$0.481896\pi$
$810$	0	0
$811$	−9626.00	−0.416787	−0.208394	−	0.978045i	$-0.566824\pi$
$811$	−9626.00	−0.416787	−0.208394	+	0.978045i	$0.566824\pi$
$812$	0	0
$813$	−19285.0	−0.831924
$814$	0	0
$815$	−50055.0	−2.15135
$816$	0	0
$817$	51528.0	2.20653
$818$	0	0
$819$	22572.0	0.963040
$820$	0	0
$821$	−16007.0	−0.680448	−0.340224	−	0.940344i	$-0.610503\pi$
$821$	−16007.0	−0.680448	−0.340224	+	0.940344i	$0.610503\pi$
$822$	0	0
$823$	−23216.0	−0.983304	−0.491652	−	0.870792i	$-0.663607\pi$
$823$	−23216.0	−0.983304	−0.491652	+	0.870792i	$0.663607\pi$
$824$	0	0
$825$	−18900.0	−0.797592
$826$	0	0
$827$	−46765.0	−1.96636	−0.983179	−	0.182644i	$-0.941535\pi$
$827$	−46765.0	−1.96636	−0.983179	+	0.182644i	$0.941535\pi$
$828$	0	0
$829$	37820.0	1.58449	0.792245	−	0.610203i	$-0.208912\pi$
$829$	37820.0	1.58449	0.792245	+	0.610203i	$0.208912\pi$
$830$	0	0
$831$	−16870.0	−0.704228
$832$	0	0
$833$	836.000	0.0347727
$834$	0	0
$835$	2970.00	0.123091
$836$	0	0
$837$	6055.00	0.250049
$838$	0	0
$839$	−6747.00	−0.277631	−0.138815	−	0.990318i	$-0.544329\pi$
$839$	−6747.00	−0.277631	−0.138815	+	0.990318i	$0.544329\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	0	0
$843$	−15645.0	−0.639196
$844$	0	0
$845$	15780.0	0.642424
$846$	0	0
$847$	−10836.0	−0.439586
$848$	0	0
$849$	11536.0	0.466330
$850$	0	0
$851$	18240.0	0.734735
$852$	0	0
$853$	13274.0	0.532817	0.266409	−	0.963860i	$-0.414163\pi$
$853$	13274.0	0.532817	0.266409	+	0.963860i	$0.414163\pi$
$854$	0	0
$855$	50160.0	2.00636
$856$	0	0
$857$	39069.0	1.55726	0.778630	−	0.627483i	$-0.215915\pi$
$857$	39069.0	1.55726	0.778630	+	0.627483i	$0.215915\pi$
$858$	0	0
$859$	35329.0	1.40327	0.701636	−	0.712536i	$-0.252453\pi$
$859$	35329.0	1.40327	0.701636	+	0.712536i	$0.252453\pi$
$860$	0	0
$861$	39564.0	1.56601
$862$	0	0
$863$	36378.0	1.43490	0.717452	−	0.696608i	$-0.245308\pi$
$863$	36378.0	1.43490	0.717452	+	0.696608i	$0.245308\pi$
$864$	0	0
$865$	38970.0	1.53181
$866$	0	0
$867$	20839.0	0.816297
$868$	0	0
$869$	−9747.00	−0.380488
$870$	0	0
$871$	37620.0	1.46350
$872$	0	0
$873$	−26532.0	−1.02860
$874$	0	0
$875$	−6750.00	−0.260790
$876$	0	0
$877$	219.000	0.00843227	0.00421614	−	0.999991i	$-0.498658\pi$
$877$	219.000	0.00843227	0.00421614	+	0.999991i	$0.498658\pi$
$878$	0	0
$879$	20146.0	0.773046
$880$	0	0
$881$	−5598.00	−0.214077	−0.107038	−	0.994255i	$-0.534137\pi$
$881$	−5598.00	−0.214077	−0.107038	+	0.994255i	$0.534137\pi$
$882$	0	0
$883$	5886.00	0.224326	0.112163	−	0.993690i	$-0.464222\pi$
$883$	5886.00	0.224326	0.112163	+	0.993690i	$0.464222\pi$
$884$	0	0
$885$	60060.0	2.28124
$886$	0	0
$887$	29673.0	1.12325	0.561624	−	0.827392i	$-0.310177\pi$
$887$	29673.0	1.12325	0.561624	+	0.827392i	$0.310177\pi$
$888$	0	0
$889$	10800.0	0.407447
$890$	0	0
$891$	−22653.0	−0.851744
$892$	0	0
$893$	54264.0	2.03346
$894$	0	0
$895$	−22650.0	−0.845928
$896$	0	0
$897$	−60648.0	−2.25750
$898$	0	0
$899$	5017.00	0.186125
$900$	0	0
$901$	−2596.00	−0.0959881
$902$	0	0
$903$	−42714.0	−1.57412
$904$	0	0
$905$	42975.0	1.57849
$906$	0	0
$907$	13668.0	0.500373	0.250187	−	0.968198i	$-0.419508\pi$
$907$	13668.0	0.500373	0.250187	+	0.968198i	$0.419508\pi$
$908$	0	0
$909$	−31680.0	−1.15595
$910$	0	0
$911$	4963.00	0.180496	0.0902478	−	0.995919i	$-0.471234\pi$
$911$	4963.00	0.180496	0.0902478	+	0.995919i	$0.471234\pi$
$912$	0	0
$913$	−4536.00	−0.164425
$914$	0	0
$915$	−44100.0	−1.59333
$916$	0	0
$917$	−29736.0	−1.07085
$918$	0	0
$919$	−9954.00	−0.357293	−0.178646	−	0.983913i	$-0.557172\pi$
$919$	−9954.00	−0.357293	−0.178646	+	0.983913i	$0.557172\pi$
$920$	0	0
$921$	−34321.0	−1.22792
$922$	0	0
$923$	−41382.0	−1.47574
$924$	0	0
$925$	12000.0	0.426549
$926$	0	0
$927$	−40876.0	−1.44827
$928$	0	0
$929$	30930.0	1.09234	0.546168	−	0.837676i	$-0.316086\pi$
$929$	30930.0	1.09234	0.546168	+	0.837676i	$0.316086\pi$
$930$	0	0
$931$	−2888.00	−0.101665
$932$	0	0
$933$	−224.000	−0.00786005
$934$	0	0
$935$	−17820.0	−0.623290
$936$	0	0
$937$	−38770.0	−1.35172	−0.675859	−	0.737030i	$-0.736227\pi$
$937$	−38770.0	−1.35172	−0.675859	+	0.737030i	$0.736227\pi$
$938$	0	0
$939$	38185.0	1.32707
$940$	0	0
$941$	30115.0	1.04327	0.521637	−	0.853167i	$-0.325322\pi$
$941$	30115.0	1.04327	0.521637	+	0.853167i	$0.325322\pi$
$942$	0	0
$943$	−47728.0	−1.64818
$944$	0	0
$945$	9450.00	0.325300
$946$	0	0
$947$	31319.0	1.07469	0.537345	−	0.843363i	$-0.319427\pi$
$947$	31319.0	1.07469	0.537345	+	0.843363i	$0.319427\pi$
$948$	0	0
$949$	57228.0	1.95753
$950$	0	0
$951$	−66864.0	−2.27993
$952$	0	0
$953$	7623.00	0.259111	0.129556	−	0.991572i	$-0.458645\pi$
$953$	7623.00	0.259111	0.129556	+	0.991572i	$0.458645\pi$
$954$	0	0
$955$	29040.0	0.983992
$956$	0	0
$957$	−5481.00	−0.185136
$958$	0	0
$959$	−21816.0	−0.734594
$960$	0	0
$961$	138.000	0.00463227
$962$	0	0
$963$	−42108.0	−1.40905
$964$	0	0
$965$	57750.0	1.92646
$966$	0	0
$967$	6269.00	0.208477	0.104239	−	0.994552i	$-0.466759\pi$
$967$	6269.00	0.208477	0.104239	+	0.994552i	$0.466759\pi$
$968$	0	0
$969$	46816.0	1.55206
$970$	0	0
$971$	−34020.0	−1.12436	−0.562180	−	0.827015i	$-0.690037\pi$
$971$	−34020.0	−1.12436	−0.562180	+	0.827015i	$0.690037\pi$
$972$	0	0
$973$	23904.0	0.787592
$974$	0	0
$975$	−39900.0	−1.31059
$976$	0	0
$977$	−51291.0	−1.67957	−0.839787	−	0.542915i	$-0.817320\pi$
$977$	−51291.0	−1.67957	−0.839787	+	0.542915i	$0.817320\pi$
$978$	0	0
$979$	1566.00	0.0511232
$980$	0	0
$981$	−21758.0	−0.708134
$982$	0	0
$983$	−38687.0	−1.25526	−0.627632	−	0.778511i	$-0.715976\pi$
$983$	−38687.0	−1.25526	−0.627632	+	0.778511i	$0.715976\pi$
$984$	0	0
$985$	−45510.0	−1.47215
$986$	0	0
$987$	−44982.0	−1.45065
$988$	0	0
$989$	51528.0	1.65672
$990$	0	0
$991$	3158.00	0.101228	0.0506141	−	0.998718i	$-0.483882\pi$
$991$	3158.00	0.101228	0.0506141	+	0.998718i	$0.483882\pi$
$992$	0	0
$993$	17031.0	0.544272
$994$	0	0
$995$	−3690.00	−0.117569
$996$	0	0
$997$	21944.0	0.697065	0.348532	−	0.937297i	$-0.386680\pi$
$997$	21944.0	0.697065	0.348532	+	0.937297i	$0.386680\pi$
$998$	0	0
$999$	4200.00	0.133015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1856.4.a.c.1.1		1
4.3	odd	2		1856.4.a.f.1.1		1
8.3	odd	2		58.4.a.b.1.1	✓	1
8.5	even	2		464.4.a.b.1.1		1
24.11	even	2		522.4.a.b.1.1		1
40.19	odd	2		1450.4.a.d.1.1		1
232.115	odd	2		1682.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.4.a.b.1.1	✓	1	8.3	odd	2
464.4.a.b.1.1		1	8.5	even	2
522.4.a.b.1.1		1	24.11	even	2
1450.4.a.d.1.1		1	40.19	odd	2
1682.4.a.a.1.1		1	232.115	odd	2
1856.4.a.c.1.1		1	1.1	even	1	trivial
1856.4.a.f.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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