LMFDB - Embedded newform 2394.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2394,2,Mod(1,2394)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2394, 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("2394.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2394.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:	$19.1161862439$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 798)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2394.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{7} +1.00000 q^{8} +2.00000 q^{10} +2.00000 q^{11} +2.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +4.00000 q^{17} +1.00000 q^{19} +2.00000 q^{20} +2.00000 q^{22} -1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{28} +6.00000 q^{29} -10.0000 q^{31} +1.00000 q^{32} +4.00000 q^{34} -2.00000 q^{35} +1.00000 q^{38} +2.00000 q^{40} +6.00000 q^{41} -4.00000 q^{43} +2.00000 q^{44} -6.00000 q^{47} +1.00000 q^{49} -1.00000 q^{50} +2.00000 q^{52} +6.00000 q^{53} +4.00000 q^{55} -1.00000 q^{56} +6.00000 q^{58} +12.0000 q^{59} +10.0000 q^{61} -10.0000 q^{62} +1.00000 q^{64} +4.00000 q^{65} -2.00000 q^{67} +4.00000 q^{68} -2.00000 q^{70} -8.00000 q^{71} -6.00000 q^{73} +1.00000 q^{76} -2.00000 q^{77} +16.0000 q^{79} +2.00000 q^{80} +6.00000 q^{82} +12.0000 q^{83} +8.00000 q^{85} -4.00000 q^{86} +2.00000 q^{88} -10.0000 q^{89} -2.00000 q^{91} -6.00000 q^{94} +2.00000 q^{95} -12.0000 q^{97} +1.00000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	0	0
$10$	2.00000	0.632456
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	0	0
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.00000	0.447214
$21$	0	0
$22$	2.00000	0.426401
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	2.00000	0.392232
$27$	0	0
$28$	−1.00000	−0.188982
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	−10.0000	−1.79605	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000	−1.79605	−0.898027	+	0.439941i	$0.854999\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	4.00000	0.685994
$35$	−2.00000	−0.338062
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	2.00000	0.316228
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	0	0
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	0	0
$52$	2.00000	0.277350
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	4.00000	0.539360
$56$	−1.00000	−0.133631
$57$	0	0
$58$	6.00000	0.787839
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	−10.0000	−1.27000
$63$	0	0
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	0	0
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	4.00000	0.485071
$69$	0	0
$70$	−2.00000	−0.239046
$71$	−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
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	0	0
$75$	0	0
$76$	1.00000	0.114708
$77$	−2.00000	−0.227921
$78$	0	0
$79$	16.0000	1.80014	0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000	1.80014	0.900070	+	0.435745i	$0.143515\pi$
$80$	2.00000	0.223607
$81$	0	0
$82$	6.00000	0.662589
$83$	12.0000	1.31717	0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000	1.31717	0.658586	+	0.752506i	$0.271155\pi$
$84$	0	0
$85$	8.00000	0.867722
$86$	−4.00000	−0.431331
$87$	0	0
$88$	2.00000	0.213201
$89$	−10.0000	−1.06000	−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000	−1.06000	−0.529999	+	0.847998i	$0.677808\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	0	0
$93$	0	0
$94$	−6.00000	−0.618853
$95$	2.00000	0.205196
$96$	0	0
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	−1.00000	−0.100000
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	0	0
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	6.00000	0.582772
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	0	0
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	4.00000	0.381385
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	0	0
$115$	0	0
$116$	6.00000	0.557086
$117$	0	0
$118$	12.0000	1.10469
$119$	−4.00000	−0.366679
$120$	0	0
$121$	−7.00000	−0.636364
$122$	10.0000	0.905357
$123$	0	0
$124$	−10.0000	−0.898027
$125$	−12.0000	−1.07331
$126$	0	0
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	4.00000	0.350823
$131$	−8.00000	−0.698963	−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000	−0.698963	−0.349482	+	0.936943i	$0.613642\pi$
$132$	0	0
$133$	−1.00000	−0.0867110
$134$	−2.00000	−0.172774
$135$	0	0
$136$	4.00000	0.342997
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	0	0
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	−2.00000	−0.169031
$141$	0	0
$142$	−8.00000	−0.671345
$143$	4.00000	0.334497
$144$	0	0
$145$	12.0000	0.996546
$146$	−6.00000	−0.496564
$147$	0	0
$148$	0	0
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	1.00000	0.0811107
$153$	0	0
$154$	−2.00000	−0.161165
$155$	−20.0000	−1.60644
$156$	0	0
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	16.0000	1.27289
$159$	0	0
$160$	2.00000	0.158114
$161$	0	0
$162$	0	0
$163$	−8.00000	−0.626608	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	−8.00000	−0.626608	−0.313304	+	0.949653i	$0.601436\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	12.0000	0.931381
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	8.00000	0.613572
$171$	0	0
$172$	−4.00000	−0.304997
$173$	−14.0000	−1.06440	−0.532200	−	0.846619i	$-0.678635\pi$
$173$	−14.0000	−1.06440	−0.532200	+	0.846619i	$0.678635\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	2.00000	0.150756
$177$	0	0
$178$	−10.0000	−0.749532
$179$	−24.0000	−1.79384	−0.896922	−	0.442189i	$-0.854202\pi$
$179$	−24.0000	−1.79384	−0.896922	+	0.442189i	$0.854202\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	−2.00000	−0.148250
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	8.00000	0.585018
$188$	−6.00000	−0.437595
$189$	0	0
$190$	2.00000	0.145095
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	−12.0000	−0.861550
$195$	0	0
$196$	1.00000	0.0714286
$197$	8.00000	0.569976	0.284988	−	0.958531i	$-0.408010\pi$
$197$	8.00000	0.569976	0.284988	+	0.958531i	$0.408010\pi$
$198$	0	0
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	10.0000	0.703598
$203$	−6.00000	−0.421117
$204$	0	0
$205$	12.0000	0.838116
$206$	−14.0000	−0.975426
$207$	0	0
$208$	2.00000	0.138675
$209$	2.00000	0.138343
$210$	0	0
$211$	26.0000	1.78991	0.894957	−	0.446153i	$-0.147206\pi$
$211$	26.0000	1.78991	0.894957	+	0.446153i	$0.147206\pi$
$212$	6.00000	0.412082
$213$	0	0
$214$	4.00000	0.273434
$215$	−8.00000	−0.545595
$216$	0	0
$217$	10.0000	0.678844
$218$	4.00000	0.270914
$219$	0	0
$220$	4.00000	0.269680
$221$	8.00000	0.538138
$222$	0	0
$223$	−6.00000	−0.401790	−0.200895	−	0.979613i	$-0.564385\pi$
$223$	−6.00000	−0.401790	−0.200895	+	0.979613i	$0.564385\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	−2.00000	−0.133038
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	0	0
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	0	0
$231$	0	0
$232$	6.00000	0.393919
$233$	2.00000	0.131024	0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000	0.131024	0.0655122	+	0.997852i	$0.479132\pi$
$234$	0	0
$235$	−12.0000	−0.782794
$236$	12.0000	0.781133
$237$	0	0
$238$	−4.00000	−0.259281
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	−24.0000	−1.54598	−0.772988	−	0.634421i	$-0.781239\pi$
$241$	−24.0000	−1.54598	−0.772988	+	0.634421i	$0.781239\pi$
$242$	−7.00000	−0.449977
$243$	0	0
$244$	10.0000	0.640184
$245$	2.00000	0.127775
$246$	0	0
$247$	2.00000	0.127257
$248$	−10.0000	−0.635001
$249$	0	0
$250$	−12.0000	−0.758947
$251$	−24.0000	−1.51487	−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000	−1.51487	−0.757433	+	0.652913i	$0.773547\pi$
$252$	0	0
$253$	0	0
$254$	8.00000	0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	0	0
$259$	0	0
$260$	4.00000	0.248069
$261$	0	0
$262$	−8.00000	−0.494242
$263$	−8.00000	−0.493301	−0.246651	−	0.969104i	$-0.579330\pi$
$263$	−8.00000	−0.493301	−0.246651	+	0.969104i	$0.579330\pi$
$264$	0	0
$265$	12.0000	0.737154
$266$	−1.00000	−0.0613139
$267$	0	0
$268$	−2.00000	−0.122169
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	0	0
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	4.00000	0.242536
$273$	0	0
$274$	−2.00000	−0.120824
$275$	−2.00000	−0.120605
$276$	0	0
$277$	6.00000	0.360505	0.180253	−	0.983620i	$-0.442309\pi$
$277$	6.00000	0.360505	0.180253	+	0.983620i	$0.442309\pi$
$278$	4.00000	0.239904
$279$	0	0
$280$	−2.00000	−0.119523
$281$	30.0000	1.78965	0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000	1.78965	0.894825	+	0.446417i	$0.147300\pi$
$282$	0	0
$283$	−12.0000	−0.713326	−0.356663	−	0.934233i	$-0.616086\pi$
$283$	−12.0000	−0.713326	−0.356663	+	0.934233i	$0.616086\pi$
$284$	−8.00000	−0.474713
$285$	0	0
$286$	4.00000	0.236525
$287$	−6.00000	−0.354169
$288$	0	0
$289$	−1.00000	−0.0588235
$290$	12.0000	0.704664
$291$	0	0
$292$	−6.00000	−0.351123
$293$	30.0000	1.75262	0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000	1.75262	0.876309	+	0.481749i	$0.159998\pi$
$294$	0	0
$295$	24.0000	1.39733
$296$	0	0
$297$	0	0
$298$	0	0
$299$	0	0
$300$	0	0
$301$	4.00000	0.230556
$302$	8.00000	0.460348
$303$	0	0
$304$	1.00000	0.0573539
$305$	20.0000	1.14520
$306$	0	0
$307$	20.0000	1.14146	0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000	1.14146	0.570730	+	0.821138i	$0.306660\pi$
$308$	−2.00000	−0.113961
$309$	0	0
$310$	−20.0000	−1.13592
$311$	−10.0000	−0.567048	−0.283524	−	0.958965i	$-0.591504\pi$
$311$	−10.0000	−0.567048	−0.283524	+	0.958965i	$0.591504\pi$
$312$	0	0
$313$	−30.0000	−1.69570	−0.847850	−	0.530236i	$-0.822103\pi$
$313$	−30.0000	−1.69570	−0.847850	+	0.530236i	$0.822103\pi$
$314$	6.00000	0.338600
$315$	0	0
$316$	16.0000	0.900070
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	0	0
$319$	12.0000	0.671871
$320$	2.00000	0.111803
$321$	0	0
$322$	0	0
$323$	4.00000	0.222566
$324$	0	0
$325$	−2.00000	−0.110940
$326$	−8.00000	−0.443079
$327$	0	0
$328$	6.00000	0.331295
$329$	6.00000	0.330791
$330$	0	0
$331$	−6.00000	−0.329790	−0.164895	−	0.986311i	$-0.552728\pi$
$331$	−6.00000	−0.329790	−0.164895	+	0.986311i	$0.552728\pi$
$332$	12.0000	0.658586
$333$	0	0
$334$	0	0
$335$	−4.00000	−0.218543
$336$	0	0
$337$	−26.0000	−1.41631	−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000	−1.41631	−0.708155	+	0.706057i	$0.750472\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	8.00000	0.433861
$341$	−20.0000	−1.08306
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−4.00000	−0.215666
$345$	0	0
$346$	−14.0000	−0.752645
$347$	−10.0000	−0.536828	−0.268414	−	0.963304i	$-0.586500\pi$
$347$	−10.0000	−0.536828	−0.268414	+	0.963304i	$0.586500\pi$
$348$	0	0
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	2.00000	0.106600
$353$	24.0000	1.27739	0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000	1.27739	0.638696	+	0.769460i	$0.279474\pi$
$354$	0	0
$355$	−16.0000	−0.849192
$356$	−10.0000	−0.529999
$357$	0	0
$358$	−24.0000	−1.26844
$359$	−12.0000	−0.633336	−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000	−0.633336	−0.316668	+	0.948536i	$0.602564\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	2.00000	0.105118
$363$	0	0
$364$	−2.00000	−0.104828
$365$	−12.0000	−0.628109
$366$	0	0
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	−6.00000	−0.311504
$372$	0	0
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	8.00000	0.413670
$375$	0	0
$376$	−6.00000	−0.309426
$377$	12.0000	0.618031
$378$	0	0
$379$	2.00000	0.102733	0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000	0.102733	0.0513665	+	0.998680i	$0.483642\pi$
$380$	2.00000	0.102598
$381$	0	0
$382$	0	0
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	−4.00000	−0.203859
$386$	22.0000	1.11977
$387$	0	0
$388$	−12.0000	−0.609208
$389$	0	0		−	1.00000i	$-0.5\pi$
$389$	0	0			1.00000i	$0.5\pi$
$390$	0	0
$391$	0	0
$392$	1.00000	0.0505076
$393$	0	0
$394$	8.00000	0.403034
$395$	32.0000	1.61009
$396$	0	0
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	−4.00000	−0.200502
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	10.0000	0.499376	0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000	0.499376	0.249688	+	0.968326i	$0.419672\pi$
$402$	0	0
$403$	−20.0000	−0.996271
$404$	10.0000	0.497519
$405$	0	0
$406$	−6.00000	−0.297775
$407$	0	0
$408$	0	0
$409$	−28.0000	−1.38451	−0.692255	−	0.721653i	$-0.743383\pi$
$409$	−28.0000	−1.38451	−0.692255	+	0.721653i	$0.743383\pi$
$410$	12.0000	0.592638
$411$	0	0
$412$	−14.0000	−0.689730
$413$	−12.0000	−0.590481
$414$	0	0
$415$	24.0000	1.17811
$416$	2.00000	0.0980581
$417$	0	0
$418$	2.00000	0.0978232
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	0	0
$421$	36.0000	1.75453	0.877266	−	0.480004i	$-0.159365\pi$
$421$	36.0000	1.75453	0.877266	+	0.480004i	$0.159365\pi$
$422$	26.0000	1.26566
$423$	0	0
$424$	6.00000	0.291386
$425$	−4.00000	−0.194029
$426$	0	0
$427$	−10.0000	−0.483934
$428$	4.00000	0.193347
$429$	0	0
$430$	−8.00000	−0.385794
$431$	−40.0000	−1.92673	−0.963366	−	0.268190i	$-0.913575\pi$
$431$	−40.0000	−1.92673	−0.963366	+	0.268190i	$0.913575\pi$
$432$	0	0
$433$	−20.0000	−0.961139	−0.480569	−	0.876957i	$-0.659570\pi$
$433$	−20.0000	−0.961139	−0.480569	+	0.876957i	$0.659570\pi$
$434$	10.0000	0.480015
$435$	0	0
$436$	4.00000	0.191565
$437$	0	0
$438$	0	0
$439$	−34.0000	−1.62273	−0.811366	−	0.584539i	$-0.801275\pi$
$439$	−34.0000	−1.62273	−0.811366	+	0.584539i	$0.801275\pi$
$440$	4.00000	0.190693
$441$	0	0
$442$	8.00000	0.380521
$443$	10.0000	0.475114	0.237557	−	0.971374i	$-0.423653\pi$
$443$	10.0000	0.475114	0.237557	+	0.971374i	$0.423653\pi$
$444$	0	0
$445$	−20.0000	−0.948091
$446$	−6.00000	−0.284108
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	−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
$452$	−2.00000	−0.0940721
$453$	0	0
$454$	−12.0000	−0.563188
$455$	−4.00000	−0.187523
$456$	0	0
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	−10.0000	−0.467269
$459$	0	0
$460$	0	0
$461$	−10.0000	−0.465746	−0.232873	−	0.972507i	$-0.574813\pi$
$461$	−10.0000	−0.465746	−0.232873	+	0.972507i	$0.574813\pi$
$462$	0	0
$463$	−32.0000	−1.48717	−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000	−1.48717	−0.743583	+	0.668644i	$0.766875\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	2.00000	0.0926482
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	0	0
$469$	2.00000	0.0923514
$470$	−12.0000	−0.553519
$471$	0	0
$472$	12.0000	0.552345
$473$	−8.00000	−0.367840
$474$	0	0
$475$	−1.00000	−0.0458831
$476$	−4.00000	−0.183340
$477$	0	0
$478$	−12.0000	−0.548867
$479$	26.0000	1.18797	0.593985	−	0.804476i	$-0.297554\pi$
$479$	26.0000	1.18797	0.593985	+	0.804476i	$0.297554\pi$
$480$	0	0
$481$	0	0
$482$	−24.0000	−1.09317
$483$	0	0
$484$	−7.00000	−0.318182
$485$	−24.0000	−1.08978
$486$	0	0
$487$	4.00000	0.181257	0.0906287	−	0.995885i	$-0.471112\pi$
$487$	4.00000	0.181257	0.0906287	+	0.995885i	$0.471112\pi$
$488$	10.0000	0.452679
$489$	0	0
$490$	2.00000	0.0903508
$491$	−30.0000	−1.35388	−0.676941	−	0.736038i	$-0.736695\pi$
$491$	−30.0000	−1.35388	−0.676941	+	0.736038i	$0.736695\pi$
$492$	0	0
$493$	24.0000	1.08091
$494$	2.00000	0.0899843
$495$	0	0
$496$	−10.0000	−0.449013
$497$	8.00000	0.358849
$498$	0	0
$499$	12.0000	0.537194	0.268597	−	0.963253i	$-0.413440\pi$
$499$	12.0000	0.537194	0.268597	+	0.963253i	$0.413440\pi$
$500$	−12.0000	−0.536656
$501$	0	0
$502$	−24.0000	−1.07117
$503$	−26.0000	−1.15928	−0.579641	−	0.814872i	$-0.696807\pi$
$503$	−26.0000	−1.15928	−0.579641	+	0.814872i	$0.696807\pi$
$504$	0	0
$505$	20.0000	0.889988
$506$	0	0
$507$	0	0
$508$	8.00000	0.354943
$509$	30.0000	1.32973	0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000	1.32973	0.664863	+	0.746965i	$0.268490\pi$
$510$	0	0
$511$	6.00000	0.265424
$512$	1.00000	0.0441942
$513$	0	0
$514$	−6.00000	−0.264649
$515$	−28.0000	−1.23383
$516$	0	0
$517$	−12.0000	−0.527759
$518$	0	0
$519$	0	0
$520$	4.00000	0.175412
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	0	0
$523$	−28.0000	−1.22435	−0.612177	−	0.790721i	$-0.709706\pi$
$523$	−28.0000	−1.22435	−0.612177	+	0.790721i	$0.709706\pi$
$524$	−8.00000	−0.349482
$525$	0	0
$526$	−8.00000	−0.348817
$527$	−40.0000	−1.74243
$528$	0	0
$529$	−23.0000	−1.00000
$530$	12.0000	0.521247
$531$	0	0
$532$	−1.00000	−0.0433555
$533$	12.0000	0.519778
$534$	0	0
$535$	8.00000	0.345870
$536$	−2.00000	−0.0863868
$537$	0	0
$538$	−18.0000	−0.776035
$539$	2.00000	0.0861461
$540$	0	0
$541$	26.0000	1.11783	0.558914	−	0.829226i	$-0.311218\pi$
$541$	26.0000	1.11783	0.558914	+	0.829226i	$0.311218\pi$
$542$	−8.00000	−0.343629
$543$	0	0
$544$	4.00000	0.171499
$545$	8.00000	0.342682
$546$	0	0
$547$	30.0000	1.28271	0.641354	−	0.767245i	$-0.278373\pi$
$547$	30.0000	1.28271	0.641354	+	0.767245i	$0.278373\pi$
$548$	−2.00000	−0.0854358
$549$	0	0
$550$	−2.00000	−0.0852803
$551$	6.00000	0.255609
$552$	0	0
$553$	−16.0000	−0.680389
$554$	6.00000	0.254916
$555$	0	0
$556$	4.00000	0.169638
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	−8.00000	−0.338364
$560$	−2.00000	−0.0845154
$561$	0	0
$562$	30.0000	1.26547
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	0	0
$565$	−4.00000	−0.168281
$566$	−12.0000	−0.504398
$567$	0	0
$568$	−8.00000	−0.335673
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	0	0
$571$	−32.0000	−1.33916	−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000	−1.33916	−0.669579	+	0.742741i	$0.733526\pi$
$572$	4.00000	0.167248
$573$	0	0
$574$	−6.00000	−0.250435
$575$	0	0
$576$	0	0
$577$	−30.0000	−1.24892	−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000	−1.24892	−0.624458	+	0.781058i	$0.714680\pi$
$578$	−1.00000	−0.0415945
$579$	0	0
$580$	12.0000	0.498273
$581$	−12.0000	−0.497844
$582$	0	0
$583$	12.0000	0.496989
$584$	−6.00000	−0.248282
$585$	0	0
$586$	30.0000	1.23929
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	−10.0000	−0.412043
$590$	24.0000	0.988064
$591$	0	0
$592$	0	0
$593$	−4.00000	−0.164260	−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000	−0.164260	−0.0821302	+	0.996622i	$0.526172\pi$
$594$	0	0
$595$	−8.00000	−0.327968
$596$	0	0
$597$	0	0
$598$	0	0
$599$	16.0000	0.653742	0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000	0.653742	0.326871	+	0.945069i	$0.394006\pi$
$600$	0	0
$601$	16.0000	0.652654	0.326327	−	0.945257i	$-0.394189\pi$
$601$	16.0000	0.652654	0.326327	+	0.945257i	$0.394189\pi$
$602$	4.00000	0.163028
$603$	0	0
$604$	8.00000	0.325515
$605$	−14.0000	−0.569181
$606$	0	0
$607$	−26.0000	−1.05531	−0.527654	−	0.849460i	$-0.676928\pi$
$607$	−26.0000	−1.05531	−0.527654	+	0.849460i	$0.676928\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	20.0000	0.809776
$611$	−12.0000	−0.485468
$612$	0	0
$613$	−22.0000	−0.888572	−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000	−0.888572	−0.444286	+	0.895885i	$0.646543\pi$
$614$	20.0000	0.807134
$615$	0	0
$616$	−2.00000	−0.0805823
$617$	26.0000	1.04672	0.523360	−	0.852111i	$-0.324678\pi$
$617$	26.0000	1.04672	0.523360	+	0.852111i	$0.324678\pi$
$618$	0	0
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	−20.0000	−0.803219
$621$	0	0
$622$	−10.0000	−0.400963
$623$	10.0000	0.400642
$624$	0	0
$625$	−19.0000	−0.760000
$626$	−30.0000	−1.19904
$627$	0	0
$628$	6.00000	0.239426
$629$	0	0
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	16.0000	0.636446
$633$	0	0
$634$	18.0000	0.714871
$635$	16.0000	0.634941
$636$	0	0
$637$	2.00000	0.0792429
$638$	12.0000	0.475085
$639$	0	0
$640$	2.00000	0.0790569
$641$	26.0000	1.02694	0.513469	−	0.858108i	$-0.328360\pi$
$641$	26.0000	1.02694	0.513469	+	0.858108i	$0.328360\pi$
$642$	0	0
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	0	0
$645$	0	0
$646$	4.00000	0.157378
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	0	0
$649$	24.0000	0.942082
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	−8.00000	−0.313304
$653$	12.0000	0.469596	0.234798	−	0.972044i	$-0.424557\pi$
$653$	12.0000	0.469596	0.234798	+	0.972044i	$0.424557\pi$
$654$	0	0
$655$	−16.0000	−0.625172
$656$	6.00000	0.234261
$657$	0	0
$658$	6.00000	0.233904
$659$	32.0000	1.24654	0.623272	−	0.782006i	$-0.285803\pi$
$659$	32.0000	1.24654	0.623272	+	0.782006i	$0.285803\pi$
$660$	0	0
$661$	22.0000	0.855701	0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000	0.855701	0.427850	+	0.903850i	$0.359271\pi$
$662$	−6.00000	−0.233197
$663$	0	0
$664$	12.0000	0.465690
$665$	−2.00000	−0.0775567
$666$	0	0
$667$	0	0
$668$	0	0
$669$	0	0
$670$	−4.00000	−0.154533
$671$	20.0000	0.772091
$672$	0	0
$673$	34.0000	1.31060	0.655302	−	0.755367i	$-0.272541\pi$
$673$	34.0000	1.31060	0.655302	+	0.755367i	$0.272541\pi$
$674$	−26.0000	−1.00148
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−30.0000	−1.15299	−0.576497	−	0.817099i	$-0.695581\pi$
$677$	−30.0000	−1.15299	−0.576497	+	0.817099i	$0.695581\pi$
$678$	0	0
$679$	12.0000	0.460518
$680$	8.00000	0.306786
$681$	0	0
$682$	−20.0000	−0.765840
$683$	−20.0000	−0.765279	−0.382639	−	0.923898i	$-0.624985\pi$
$683$	−20.0000	−0.765279	−0.382639	+	0.923898i	$0.624985\pi$
$684$	0	0
$685$	−4.00000	−0.152832
$686$	−1.00000	−0.0381802
$687$	0	0
$688$	−4.00000	−0.152499
$689$	12.0000	0.457164
$690$	0	0
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	−14.0000	−0.532200
$693$	0	0
$694$	−10.0000	−0.379595
$695$	8.00000	0.303457
$696$	0	0
$697$	24.0000	0.909065
$698$	−10.0000	−0.378506
$699$	0	0
$700$	1.00000	0.0377964
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	0	0
$703$	0	0
$704$	2.00000	0.0753778
$705$	0	0
$706$	24.0000	0.903252
$707$	−10.0000	−0.376089
$708$	0	0
$709$	46.0000	1.72757	0.863783	−	0.503864i	$-0.168089\pi$
$709$	46.0000	1.72757	0.863783	+	0.503864i	$0.168089\pi$
$710$	−16.0000	−0.600469
$711$	0	0
$712$	−10.0000	−0.374766
$713$	0	0
$714$	0	0
$715$	8.00000	0.299183
$716$	−24.0000	−0.896922
$717$	0	0
$718$	−12.0000	−0.447836
$719$	−42.0000	−1.56634	−0.783168	−	0.621810i	$-0.786397\pi$
$719$	−42.0000	−1.56634	−0.783168	+	0.621810i	$0.786397\pi$
$720$	0	0
$721$	14.0000	0.521387
$722$	1.00000	0.0372161
$723$	0	0
$724$	2.00000	0.0743294
$725$	−6.00000	−0.222834
$726$	0	0
$727$	28.0000	1.03846	0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000	1.03846	0.519231	+	0.854634i	$0.326218\pi$
$728$	−2.00000	−0.0741249
$729$	0	0
$730$	−12.0000	−0.444140
$731$	−16.0000	−0.591781
$732$	0	0
$733$	−34.0000	−1.25582	−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000	−1.25582	−0.627909	+	0.778287i	$0.716089\pi$
$734$	−16.0000	−0.590571
$735$	0	0
$736$	0	0
$737$	−4.00000	−0.147342
$738$	0	0
$739$	12.0000	0.441427	0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000	0.441427	0.220714	+	0.975339i	$0.429161\pi$
$740$	0	0
$741$	0	0
$742$	−6.00000	−0.220267
$743$	8.00000	0.293492	0.146746	−	0.989174i	$-0.453120\pi$
$743$	8.00000	0.293492	0.146746	+	0.989174i	$0.453120\pi$
$744$	0	0
$745$	0	0
$746$	4.00000	0.146450
$747$	0	0
$748$	8.00000	0.292509
$749$	−4.00000	−0.146157
$750$	0	0
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	−6.00000	−0.218797
$753$	0	0
$754$	12.0000	0.437014
$755$	16.0000	0.582300
$756$	0	0
$757$	−6.00000	−0.218074	−0.109037	−	0.994038i	$-0.534777\pi$
$757$	−6.00000	−0.218074	−0.109037	+	0.994038i	$0.534777\pi$
$758$	2.00000	0.0726433
$759$	0	0
$760$	2.00000	0.0725476
$761$	40.0000	1.45000	0.724999	−	0.688749i	$-0.241840\pi$
$761$	40.0000	1.45000	0.724999	+	0.688749i	$0.241840\pi$
$762$	0	0
$763$	−4.00000	−0.144810
$764$	0	0
$765$	0	0
$766$	−16.0000	−0.578103
$767$	24.0000	0.866590
$768$	0	0
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	−4.00000	−0.144150
$771$	0	0
$772$	22.0000	0.791797
$773$	46.0000	1.65451	0.827253	−	0.561830i	$-0.189903\pi$
$773$	46.0000	1.65451	0.827253	+	0.561830i	$0.189903\pi$
$774$	0	0
$775$	10.0000	0.359211
$776$	−12.0000	−0.430775
$777$	0	0
$778$	0	0
$779$	6.00000	0.214972
$780$	0	0
$781$	−16.0000	−0.572525
$782$	0	0
$783$	0	0
$784$	1.00000	0.0357143
$785$	12.0000	0.428298
$786$	0	0
$787$	−24.0000	−0.855508	−0.427754	−	0.903895i	$-0.640695\pi$
$787$	−24.0000	−0.855508	−0.427754	+	0.903895i	$0.640695\pi$
$788$	8.00000	0.284988
$789$	0	0
$790$	32.0000	1.13851
$791$	2.00000	0.0711118
$792$	0	0
$793$	20.0000	0.710221
$794$	−14.0000	−0.496841
$795$	0	0
$796$	−4.00000	−0.141776
$797$	−14.0000	−0.495905	−0.247953	−	0.968772i	$-0.579758\pi$
$797$	−14.0000	−0.495905	−0.247953	+	0.968772i	$0.579758\pi$
$798$	0	0
$799$	−24.0000	−0.849059
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	10.0000	0.353112
$803$	−12.0000	−0.423471
$804$	0	0
$805$	0	0
$806$	−20.0000	−0.704470
$807$	0	0
$808$	10.0000	0.351799
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	0	0
$811$	44.0000	1.54505	0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000	1.54505	0.772524	+	0.634985i	$0.218994\pi$
$812$	−6.00000	−0.210559
$813$	0	0
$814$	0	0
$815$	−16.0000	−0.560456
$816$	0	0
$817$	−4.00000	−0.139942
$818$	−28.0000	−0.978997
$819$	0	0
$820$	12.0000	0.419058
$821$	12.0000	0.418803	0.209401	−	0.977830i	$-0.432848\pi$
$821$	12.0000	0.418803	0.209401	+	0.977830i	$0.432848\pi$
$822$	0	0
$823$	−24.0000	−0.836587	−0.418294	−	0.908312i	$-0.637372\pi$
$823$	−24.0000	−0.836587	−0.418294	+	0.908312i	$0.637372\pi$
$824$	−14.0000	−0.487713
$825$	0	0
$826$	−12.0000	−0.417533
$827$	−16.0000	−0.556375	−0.278187	−	0.960527i	$-0.589734\pi$
$827$	−16.0000	−0.556375	−0.278187	+	0.960527i	$0.589734\pi$
$828$	0	0
$829$	14.0000	0.486240	0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000	0.486240	0.243120	+	0.969996i	$0.421829\pi$
$830$	24.0000	0.833052
$831$	0	0
$832$	2.00000	0.0693375
$833$	4.00000	0.138592
$834$	0	0
$835$	0	0
$836$	2.00000	0.0691714
$837$	0	0
$838$	20.0000	0.690889
$839$	32.0000	1.10476	0.552381	−	0.833592i	$-0.313719\pi$
$839$	32.0000	1.10476	0.552381	+	0.833592i	$0.313719\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	36.0000	1.24064
$843$	0	0
$844$	26.0000	0.894957
$845$	−18.0000	−0.619219
$846$	0	0
$847$	7.00000	0.240523
$848$	6.00000	0.206041
$849$	0	0
$850$	−4.00000	−0.137199
$851$	0	0
$852$	0	0
$853$	−6.00000	−0.205436	−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000	−0.205436	−0.102718	+	0.994711i	$0.532754\pi$
$854$	−10.0000	−0.342193
$855$	0	0
$856$	4.00000	0.136717
$857$	−10.0000	−0.341593	−0.170797	−	0.985306i	$-0.554634\pi$
$857$	−10.0000	−0.341593	−0.170797	+	0.985306i	$0.554634\pi$
$858$	0	0
$859$	−52.0000	−1.77422	−0.887109	−	0.461561i	$-0.847290\pi$
$859$	−52.0000	−1.77422	−0.887109	+	0.461561i	$0.847290\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	−40.0000	−1.36241
$863$	56.0000	1.90626	0.953131	−	0.302558i	$-0.0978405\pi$
$863$	56.0000	1.90626	0.953131	+	0.302558i	$0.0978405\pi$
$864$	0	0
$865$	−28.0000	−0.952029
$866$	−20.0000	−0.679628
$867$	0	0
$868$	10.0000	0.339422
$869$	32.0000	1.08553
$870$	0	0
$871$	−4.00000	−0.135535
$872$	4.00000	0.135457
$873$	0	0
$874$	0	0
$875$	12.0000	0.405674
$876$	0	0
$877$	32.0000	1.08056	0.540282	−	0.841484i	$-0.318318\pi$
$877$	32.0000	1.08056	0.540282	+	0.841484i	$0.318318\pi$
$878$	−34.0000	−1.14744
$879$	0	0
$880$	4.00000	0.134840
$881$	24.0000	0.808581	0.404290	−	0.914631i	$-0.367519\pi$
$881$	24.0000	0.808581	0.404290	+	0.914631i	$0.367519\pi$
$882$	0	0
$883$	12.0000	0.403832	0.201916	−	0.979403i	$-0.435283\pi$
$883$	12.0000	0.403832	0.201916	+	0.979403i	$0.435283\pi$
$884$	8.00000	0.269069
$885$	0	0
$886$	10.0000	0.335957
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	0	0
$889$	−8.00000	−0.268311
$890$	−20.0000	−0.670402
$891$	0	0
$892$	−6.00000	−0.200895
$893$	−6.00000	−0.200782
$894$	0	0
$895$	−48.0000	−1.60446
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−14.0000	−0.467186
$899$	−60.0000	−2.00111
$900$	0	0
$901$	24.0000	0.799556
$902$	12.0000	0.399556
$903$	0	0
$904$	−2.00000	−0.0665190
$905$	4.00000	0.132964
$906$	0	0
$907$	−22.0000	−0.730498	−0.365249	−	0.930910i	$-0.619016\pi$
$907$	−22.0000	−0.730498	−0.365249	+	0.930910i	$0.619016\pi$
$908$	−12.0000	−0.398234
$909$	0	0
$910$	−4.00000	−0.132599
$911$	56.0000	1.85536	0.927681	−	0.373373i	$-0.121799\pi$
$911$	56.0000	1.85536	0.927681	+	0.373373i	$0.121799\pi$
$912$	0	0
$913$	24.0000	0.794284
$914$	−10.0000	−0.330771
$915$	0	0
$916$	−10.0000	−0.330409
$917$	8.00000	0.264183
$918$	0	0
$919$	24.0000	0.791687	0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000	0.791687	0.395843	+	0.918318i	$0.370452\pi$
$920$	0	0
$921$	0	0
$922$	−10.0000	−0.329332
$923$	−16.0000	−0.526646
$924$	0	0
$925$	0	0
$926$	−32.0000	−1.05159
$927$	0	0
$928$	6.00000	0.196960
$929$	28.0000	0.918650	0.459325	−	0.888268i	$-0.348091\pi$
$929$	28.0000	0.918650	0.459325	+	0.888268i	$0.348091\pi$
$930$	0	0
$931$	1.00000	0.0327737
$932$	2.00000	0.0655122
$933$	0	0
$934$	12.0000	0.392652
$935$	16.0000	0.523256
$936$	0	0
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	2.00000	0.0653023
$939$	0	0
$940$	−12.0000	−0.391397
$941$	−10.0000	−0.325991	−0.162995	−	0.986627i	$-0.552116\pi$
$941$	−10.0000	−0.325991	−0.162995	+	0.986627i	$0.552116\pi$
$942$	0	0
$943$	0	0
$944$	12.0000	0.390567
$945$	0	0
$946$	−8.00000	−0.260102
$947$	42.0000	1.36482	0.682408	−	0.730971i	$-0.260933\pi$
$947$	42.0000	1.36482	0.682408	+	0.730971i	$0.260933\pi$
$948$	0	0
$949$	−12.0000	−0.389536
$950$	−1.00000	−0.0324443
$951$	0	0
$952$	−4.00000	−0.129641
$953$	14.0000	0.453504	0.226752	−	0.973952i	$-0.427189\pi$
$953$	14.0000	0.453504	0.226752	+	0.973952i	$0.427189\pi$
$954$	0	0
$955$	0	0
$956$	−12.0000	−0.388108
$957$	0	0
$958$	26.0000	0.840022
$959$	2.00000	0.0645834
$960$	0	0
$961$	69.0000	2.22581
$962$	0	0
$963$	0	0
$964$	−24.0000	−0.772988
$965$	44.0000	1.41641
$966$	0	0
$967$	−16.0000	−0.514525	−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000	−0.514525	−0.257263	+	0.966342i	$0.582821\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	−24.0000	−0.770594
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	0	0
$973$	−4.00000	−0.128234
$974$	4.00000	0.128168
$975$	0	0
$976$	10.0000	0.320092
$977$	−38.0000	−1.21573	−0.607864	−	0.794041i	$-0.707973\pi$
$977$	−38.0000	−1.21573	−0.607864	+	0.794041i	$0.707973\pi$
$978$	0	0
$979$	−20.0000	−0.639203
$980$	2.00000	0.0638877
$981$	0	0
$982$	−30.0000	−0.957338
$983$	−44.0000	−1.40338	−0.701691	−	0.712481i	$-0.747571\pi$
$983$	−44.0000	−1.40338	−0.701691	+	0.712481i	$0.747571\pi$
$984$	0	0
$985$	16.0000	0.509802
$986$	24.0000	0.764316
$987$	0	0
$988$	2.00000	0.0636285
$989$	0	0
$990$	0	0
$991$	20.0000	0.635321	0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000	0.635321	0.317660	+	0.948205i	$0.397103\pi$
$992$	−10.0000	−0.317500
$993$	0	0
$994$	8.00000	0.253745
$995$	−8.00000	−0.253617
$996$	0	0
$997$	22.0000	0.696747	0.348373	−	0.937356i	$-0.386734\pi$
$997$	22.0000	0.696747	0.348373	+	0.937356i	$0.386734\pi$
$998$	12.0000	0.379853
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2394.2.a.m.1.1		1
3.2	odd	2		798.2.a.b.1.1	✓	1
12.11	even	2		6384.2.a.g.1.1		1
21.20	even	2		5586.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.a.b.1.1	✓	1	3.2	odd	2
2394.2.a.m.1.1		1	1.1	even	1	trivial
5586.2.a.j.1.1		1	21.20	even	2
6384.2.a.g.1.1		1	12.11	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:	\( N \)	\(=\)	\( 2394 = 2 \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2394.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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