LMFDB - Embedded newform 4598.2.a.e.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [4598,2,Mod(1,4598)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4598, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4598.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$4598 = 2 \cdot 11^{2} \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	4598.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-1,0,1,0,0,-3,-1,-3,0,0,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4598.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

f(q)

=

q-1.00000 q^{2} +1.00000 q^{4} -3.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} -1.00000 q^{13} +3.00000 q^{14} +1.00000 q^{16} -5.00000 q^{17} +3.00000 q^{18} -1.00000 q^{19} +5.00000 q^{23} -5.00000 q^{25} +1.00000 q^{26} -3.00000 q^{28} -6.00000 q^{29} +2.00000 q^{31} -1.00000 q^{32} +5.00000 q^{34} -3.00000 q^{36} -3.00000 q^{37} +1.00000 q^{38} +2.00000 q^{41} +4.00000 q^{43} -5.00000 q^{46} -3.00000 q^{47} +2.00000 q^{49} +5.00000 q^{50} -1.00000 q^{52} +2.00000 q^{53} +3.00000 q^{56} +6.00000 q^{58} +1.00000 q^{59} -2.00000 q^{62} +9.00000 q^{63} +1.00000 q^{64} +3.00000 q^{67} -5.00000 q^{68} -4.00000 q^{71} +3.00000 q^{72} -15.0000 q^{73} +3.00000 q^{74} -1.00000 q^{76} -10.0000 q^{79} +9.00000 q^{81} -2.00000 q^{82} -4.00000 q^{86} +6.00000 q^{89} +3.00000 q^{91} +5.00000 q^{92} +3.00000 q^{94} +2.00000 q^{97} -2.00000 q^{98} +O(q^{100})

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		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	0	0		−	1.00000i	$-0.5\pi$
$5$	0	0			1.00000i	$0.5\pi$
$6$	0	0
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	−1.00000	−0.353553
$9$	−3.00000	−1.00000
$10$	0	0
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−1.00000	−0.277350	−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000	−0.277350	−0.138675	+	0.990338i	$0.544284\pi$
$14$	3.00000	0.801784
$15$	0	0
$16$	1.00000	0.250000
$17$	−5.00000	−1.21268	−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000	−1.21268	−0.606339	+	0.795206i	$0.707363\pi$
$18$	3.00000	0.707107
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	0	0
$22$	0	0
$23$	5.00000	1.04257	0.521286	−	0.853382i	$-0.325452\pi$
$23$	5.00000	1.04257	0.521286	+	0.853382i	$0.325452\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	1.00000	0.196116
$27$	0	0
$28$	−3.00000	−0.566947
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	5.00000	0.857493
$35$	0	0
$36$	−3.00000	−0.500000
$37$	−3.00000	−0.493197	−0.246598	−	0.969118i	$-0.579313\pi$
$37$	−3.00000	−0.493197	−0.246598	+	0.969118i	$0.579313\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	0	0
$45$	0	0
$46$	−5.00000	−0.737210
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	0	0
$49$	2.00000	0.285714
$50$	5.00000	0.707107
$51$	0	0
$52$	−1.00000	−0.138675
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	0	0
$55$	0	0
$56$	3.00000	0.400892
$57$	0	0
$58$	6.00000	0.787839
$59$	1.00000	0.130189	0.0650945	−	0.997879i	$-0.479265\pi$
$59$	1.00000	0.130189	0.0650945	+	0.997879i	$0.479265\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	−2.00000	−0.254000
$63$	9.00000	1.13389
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	3.00000	0.366508	0.183254	−	0.983066i	$-0.441337\pi$
$67$	3.00000	0.366508	0.183254	+	0.983066i	$0.441337\pi$
$68$	−5.00000	−0.606339
$69$	0	0
$70$	0	0
$71$	−4.00000	−0.474713	−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000	−0.474713	−0.237356	+	0.971423i	$0.576281\pi$
$72$	3.00000	0.353553
$73$	−15.0000	−1.75562	−0.877809	−	0.479012i	$-0.840995\pi$
$73$	−15.0000	−1.75562	−0.877809	+	0.479012i	$0.840995\pi$
$74$	3.00000	0.348743
$75$	0	0
$76$	−1.00000	−0.114708
$77$	0	0
$78$	0	0
$79$	−10.0000	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	−2.00000	−0.220863
$83$	0	0		−	1.00000i	$-0.5\pi$
$83$	0	0			1.00000i	$0.5\pi$
$84$	0	0
$85$	0	0
$86$	−4.00000	−0.431331
$87$	0	0
$88$	0	0
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	3.00000	0.314485
$92$	5.00000	0.521286
$93$	0	0
$94$	3.00000	0.309426
$95$	0	0
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−2.00000	−0.202031
$99$	0	0
$100$	−5.00000	−0.500000
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	0	0
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	−2.00000	−0.194257
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	0	0
$109$	17.0000	1.62830	0.814152	−	0.580651i	$-0.197202\pi$
$109$	17.0000	1.62830	0.814152	+	0.580651i	$0.197202\pi$
$110$	0	0
$111$	0	0
$112$	−3.00000	−0.283473
$113$	16.0000	1.50515	0.752577	−	0.658505i	$-0.228811\pi$
$113$	16.0000	1.50515	0.752577	+	0.658505i	$0.228811\pi$
$114$	0	0
$115$	0	0
$116$	−6.00000	−0.557086
$117$	3.00000	0.277350
$118$	−1.00000	−0.0920575
$119$	15.0000	1.37505
$120$	0	0
$121$	0	0
$122$	0	0
$123$	0	0
$124$	2.00000	0.179605
$125$	0	0
$126$	−9.00000	−0.801784
$127$	10.0000	0.887357	0.443678	−	0.896186i	$-0.353673\pi$
$127$	10.0000	0.887357	0.443678	+	0.896186i	$0.353673\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	3.00000	0.260133
$134$	−3.00000	−0.259161
$135$	0	0
$136$	5.00000	0.428746
$137$	3.00000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	0	0
$139$	14.0000	1.18746	0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000	1.18746	0.593732	+	0.804663i	$0.297654\pi$
$140$	0	0
$141$	0	0
$142$	4.00000	0.335673
$143$	0	0
$144$	−3.00000	−0.250000
$145$	0	0
$146$	15.0000	1.24141
$147$	0	0
$148$	−3.00000	−0.246598
$149$	−20.0000	−1.63846	−0.819232	−	0.573462i	$-0.805600\pi$
$149$	−20.0000	−1.63846	−0.819232	+	0.573462i	$0.805600\pi$
$150$	0	0
$151$	−6.00000	−0.488273	−0.244137	−	0.969741i	$-0.578505\pi$
$151$	−6.00000	−0.488273	−0.244137	+	0.969741i	$0.578505\pi$
$152$	1.00000	0.0811107
$153$	15.0000	1.21268
$154$	0	0
$155$	0	0
$156$	0	0
$157$	12.0000	0.957704	0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000	0.957704	0.478852	+	0.877896i	$0.341053\pi$
$158$	10.0000	0.795557
$159$	0	0
$160$	0	0
$161$	−15.0000	−1.18217
$162$	−9.00000	−0.707107
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	0	0
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	0	0
$171$	3.00000	0.229416
$172$	4.00000	0.304997
$173$	15.0000	1.14043	0.570214	−	0.821496i	$-0.306860\pi$
$173$	15.0000	1.14043	0.570214	+	0.821496i	$0.306860\pi$
$174$	0	0
$175$	15.0000	1.13389
$176$	0	0
$177$	0	0
$178$	−6.00000	−0.449719
$179$	−21.0000	−1.56961	−0.784807	−	0.619740i	$-0.787238\pi$
$179$	−21.0000	−1.56961	−0.784807	+	0.619740i	$0.787238\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	−3.00000	−0.222375
$183$	0	0
$184$	−5.00000	−0.368605
$185$	0	0
$186$	0	0
$187$	0	0
$188$	−3.00000	−0.218797
$189$	0	0
$190$	0	0
$191$	9.00000	0.651217	0.325609	−	0.945505i	$-0.394431\pi$
$191$	9.00000	0.651217	0.325609	+	0.945505i	$0.394431\pi$
$192$	0	0
$193$	20.0000	1.43963	0.719816	−	0.694165i	$-0.244226\pi$
$193$	20.0000	1.43963	0.719816	+	0.694165i	$0.244226\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	2.00000	0.142857
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	0	0
$199$	7.00000	0.496217	0.248108	−	0.968732i	$-0.420191\pi$
$199$	7.00000	0.496217	0.248108	+	0.968732i	$0.420191\pi$
$200$	5.00000	0.353553
$201$	0	0
$202$	10.0000	0.703598
$203$	18.0000	1.26335
$204$	0	0
$205$	0	0
$206$	−14.0000	−0.975426
$207$	−15.0000	−1.04257
$208$	−1.00000	−0.0693375
$209$	0	0
$210$	0	0
$211$	−28.0000	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$212$	2.00000	0.137361
$213$	0	0
$214$	−3.00000	−0.205076
$215$	0	0
$216$	0	0
$217$	−6.00000	−0.407307
$218$	−17.0000	−1.15139
$219$	0	0
$220$	0	0
$221$	5.00000	0.336336
$222$	0	0
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	3.00000	0.200446
$225$	15.0000	1.00000
$226$	−16.0000	−1.06430
$227$	−13.0000	−0.862840	−0.431420	−	0.902151i	$-0.641987\pi$
$227$	−13.0000	−0.862840	−0.431420	+	0.902151i	$0.641987\pi$
$228$	0	0
$229$	22.0000	1.45380	0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000	1.45380	0.726900	+	0.686743i	$0.240960\pi$
$230$	0	0
$231$	0	0
$232$	6.00000	0.393919
$233$	19.0000	1.24473	0.622366	−	0.782727i	$-0.286172\pi$
$233$	19.0000	1.24473	0.622366	+	0.782727i	$0.286172\pi$
$234$	−3.00000	−0.196116
$235$	0	0
$236$	1.00000	0.0650945
$237$	0	0
$238$	−15.0000	−0.972306
$239$	24.0000	1.55243	0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000	1.55243	0.776215	+	0.630468i	$0.217137\pi$
$240$	0	0
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	0	0
$243$	0	0
$244$	0	0
$245$	0	0
$246$	0	0
$247$	1.00000	0.0636285
$248$	−2.00000	−0.127000
$249$	0	0
$250$	0	0
$251$	−18.0000	−1.13615	−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000	−1.13615	−0.568075	+	0.822977i	$0.692312\pi$
$252$	9.00000	0.566947
$253$	0	0
$254$	−10.0000	−0.627456
$255$	0	0
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	0	0
$259$	9.00000	0.559233
$260$	0	0
$261$	18.0000	1.11417
$262$	−12.0000	−0.741362
$263$	−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
$265$	0	0
$266$	−3.00000	−0.183942
$267$	0	0
$268$	3.00000	0.183254
$269$	9.00000	0.548740	0.274370	−	0.961624i	$-0.411531\pi$
$269$	9.00000	0.548740	0.274370	+	0.961624i	$0.411531\pi$
$270$	0	0
$271$	−29.0000	−1.76162	−0.880812	−	0.473466i	$-0.843003\pi$
$271$	−29.0000	−1.76162	−0.880812	+	0.473466i	$0.843003\pi$
$272$	−5.00000	−0.303170
$273$	0	0
$274$	−3.00000	−0.181237
$275$	0	0
$276$	0	0
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	−14.0000	−0.839664
$279$	−6.00000	−0.359211
$280$	0	0
$281$	24.0000	1.43172	0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000	1.43172	0.715860	+	0.698244i	$0.246035\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−4.00000	−0.237356
$285$	0	0
$286$	0	0
$287$	−6.00000	−0.354169
$288$	3.00000	0.176777
$289$	8.00000	0.470588
$290$	0	0
$291$	0	0
$292$	−15.0000	−0.877809
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	0	0
$295$	0	0
$296$	3.00000	0.174371
$297$	0	0
$298$	20.0000	1.15857
$299$	−5.00000	−0.289157
$300$	0	0
$301$	−12.0000	−0.691669
$302$	6.00000	0.345261
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	0	0
$306$	−15.0000	−0.857493
$307$	−7.00000	−0.399511	−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000	−0.399511	−0.199756	+	0.979846i	$0.564015\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−17.0000	−0.963982	−0.481991	−	0.876176i	$-0.660086\pi$
$311$	−17.0000	−0.963982	−0.481991	+	0.876176i	$0.660086\pi$
$312$	0	0
$313$	1.00000	0.0565233	0.0282617	−	0.999601i	$-0.491003\pi$
$313$	1.00000	0.0565233	0.0282617	+	0.999601i	$0.491003\pi$
$314$	−12.0000	−0.677199
$315$	0	0
$316$	−10.0000	−0.562544
$317$	−11.0000	−0.617822	−0.308911	−	0.951091i	$-0.599964\pi$
$317$	−11.0000	−0.617822	−0.308911	+	0.951091i	$0.599964\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	15.0000	0.835917
$323$	5.00000	0.278207
$324$	9.00000	0.500000
$325$	5.00000	0.277350
$326$	−4.00000	−0.221540
$327$	0	0
$328$	−2.00000	−0.110432
$329$	9.00000	0.496186
$330$	0	0
$331$	7.00000	0.384755	0.192377	−	0.981321i	$-0.438380\pi$
$331$	7.00000	0.384755	0.192377	+	0.981321i	$0.438380\pi$
$332$	0	0
$333$	9.00000	0.493197
$334$	8.00000	0.437741
$335$	0	0
$336$	0	0
$337$	4.00000	0.217894	0.108947	−	0.994048i	$-0.465252\pi$
$337$	4.00000	0.217894	0.108947	+	0.994048i	$0.465252\pi$
$338$	12.0000	0.652714
$339$	0	0
$340$	0	0
$341$	0	0
$342$	−3.00000	−0.162221
$343$	15.0000	0.809924
$344$	−4.00000	−0.215666
$345$	0	0
$346$	−15.0000	−0.806405
$347$	16.0000	0.858925	0.429463	−	0.903085i	$-0.358703\pi$
$347$	16.0000	0.858925	0.429463	+	0.903085i	$0.358703\pi$
$348$	0	0
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	−15.0000	−0.801784
$351$	0	0
$352$	0	0
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	0	0
$355$	0	0
$356$	6.00000	0.317999
$357$	0	0
$358$	21.0000	1.10988
$359$	1.00000	0.0527780	0.0263890	−	0.999652i	$-0.491599\pi$
$359$	1.00000	0.0527780	0.0263890	+	0.999652i	$0.491599\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	2.00000	0.105118
$363$	0	0
$364$	3.00000	0.157243
$365$	0	0
$366$	0	0
$367$	19.0000	0.991792	0.495896	−	0.868382i	$-0.334840\pi$
$367$	19.0000	0.991792	0.495896	+	0.868382i	$0.334840\pi$
$368$	5.00000	0.260643
$369$	−6.00000	−0.312348
$370$	0	0
$371$	−6.00000	−0.311504
$372$	0	0
$373$	10.0000	0.517780	0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000	0.517780	0.258890	+	0.965907i	$0.416643\pi$
$374$	0	0
$375$	0	0
$376$	3.00000	0.154713
$377$	6.00000	0.309016
$378$	0	0
$379$	25.0000	1.28416	0.642082	−	0.766636i	$-0.278071\pi$
$379$	25.0000	1.28416	0.642082	+	0.766636i	$0.278071\pi$
$380$	0	0
$381$	0	0
$382$	−9.00000	−0.460480
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	0	0
$385$	0	0
$386$	−20.0000	−1.01797
$387$	−12.0000	−0.609994
$388$	2.00000	0.101535
$389$	10.0000	0.507020	0.253510	−	0.967333i	$-0.418415\pi$
$389$	10.0000	0.507020	0.253510	+	0.967333i	$0.418415\pi$
$390$	0	0
$391$	−25.0000	−1.26430
$392$	−2.00000	−0.101015
$393$	0	0
$394$	−2.00000	−0.100759
$395$	0	0
$396$	0	0
$397$	12.0000	0.602263	0.301131	−	0.953583i	$-0.402636\pi$
$397$	12.0000	0.602263	0.301131	+	0.953583i	$0.402636\pi$
$398$	−7.00000	−0.350878
$399$	0	0
$400$	−5.00000	−0.250000
$401$	12.0000	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	0	0
$403$	−2.00000	−0.0996271
$404$	−10.0000	−0.497519
$405$	0	0
$406$	−18.0000	−0.893325
$407$	0	0
$408$	0	0
$409$	28.0000	1.38451	0.692255	−	0.721653i	$-0.256617\pi$
$409$	28.0000	1.38451	0.692255	+	0.721653i	$0.256617\pi$
$410$	0	0
$411$	0	0
$412$	14.0000	0.689730
$413$	−3.00000	−0.147620
$414$	15.0000	0.737210
$415$	0	0
$416$	1.00000	0.0490290
$417$	0	0
$418$	0	0
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	0	0
$421$	35.0000	1.70580	0.852898	−	0.522078i	$-0.174843\pi$
$421$	35.0000	1.70580	0.852898	+	0.522078i	$0.174843\pi$
$422$	28.0000	1.36302
$423$	9.00000	0.437595
$424$	−2.00000	−0.0971286
$425$	25.0000	1.21268
$426$	0	0
$427$	0	0
$428$	3.00000	0.145010
$429$	0	0
$430$	0	0
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	6.00000	0.288009
$435$	0	0
$436$	17.0000	0.814152
$437$	−5.00000	−0.239182
$438$	0	0
$439$	−26.0000	−1.24091	−0.620456	−	0.784241i	$-0.713053\pi$
$439$	−26.0000	−1.24091	−0.620456	+	0.784241i	$0.713053\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	−5.00000	−0.237826
$443$	−38.0000	−1.80543	−0.902717	−	0.430234i	$-0.858431\pi$
$443$	−38.0000	−1.80543	−0.902717	+	0.430234i	$0.858431\pi$
$444$	0	0
$445$	0	0
$446$	8.00000	0.378811
$447$	0	0
$448$	−3.00000	−0.141737
$449$	14.0000	0.660701	0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000	0.660701	0.330350	+	0.943858i	$0.392833\pi$
$450$	−15.0000	−0.707107
$451$	0	0
$452$	16.0000	0.752577
$453$	0	0
$454$	13.0000	0.610120
$455$	0	0
$456$	0	0
$457$	13.0000	0.608114	0.304057	−	0.952654i	$-0.401659\pi$
$457$	13.0000	0.608114	0.304057	+	0.952654i	$0.401659\pi$
$458$	−22.0000	−1.02799
$459$	0	0
$460$	0	0
$461$	−12.0000	−0.558896	−0.279448	−	0.960161i	$-0.590151\pi$
$461$	−12.0000	−0.558896	−0.279448	+	0.960161i	$0.590151\pi$
$462$	0	0
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−19.0000	−0.880158
$467$	−14.0000	−0.647843	−0.323921	−	0.946084i	$-0.605001\pi$
$467$	−14.0000	−0.647843	−0.323921	+	0.946084i	$0.605001\pi$
$468$	3.00000	0.138675
$469$	−9.00000	−0.415581
$470$	0	0
$471$	0	0
$472$	−1.00000	−0.0460287
$473$	0	0
$474$	0	0
$475$	5.00000	0.229416
$476$	15.0000	0.687524
$477$	−6.00000	−0.274721
$478$	−24.0000	−1.09773
$479$	−5.00000	−0.228456	−0.114228	−	0.993455i	$-0.536439\pi$
$479$	−5.00000	−0.228456	−0.114228	+	0.993455i	$0.536439\pi$
$480$	0	0
$481$	3.00000	0.136788
$482$	−10.0000	−0.455488
$483$	0	0
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	2.00000	0.0902587	0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000	0.0902587	0.0451294	+	0.998981i	$0.485630\pi$
$492$	0	0
$493$	30.0000	1.35113
$494$	−1.00000	−0.0449921
$495$	0	0
$496$	2.00000	0.0898027
$497$	12.0000	0.538274
$498$	0	0
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	0	0
$501$	0	0
$502$	18.0000	0.803379
$503$	21.0000	0.936344	0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000	0.936344	0.468172	+	0.883637i	$0.344913\pi$
$504$	−9.00000	−0.400892
$505$	0	0
$506$	0	0
$507$	0	0
$508$	10.0000	0.443678
$509$	−35.0000	−1.55135	−0.775674	−	0.631134i	$-0.782590\pi$
$509$	−35.0000	−1.55135	−0.775674	+	0.631134i	$0.782590\pi$
$510$	0	0
$511$	45.0000	1.99068
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−2.00000	−0.0882162
$515$	0	0
$516$	0	0
$517$	0	0
$518$	−9.00000	−0.395437
$519$	0	0
$520$	0	0
$521$	24.0000	1.05146	0.525730	−	0.850652i	$-0.323792\pi$
$521$	24.0000	1.05146	0.525730	+	0.850652i	$0.323792\pi$
$522$	−18.0000	−0.787839
$523$	27.0000	1.18063	0.590314	−	0.807174i	$-0.299004\pi$
$523$	27.0000	1.18063	0.590314	+	0.807174i	$0.299004\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	8.00000	0.348817
$527$	−10.0000	−0.435607
$528$	0	0
$529$	2.00000	0.0869565
$530$	0	0
$531$	−3.00000	−0.130189
$532$	3.00000	0.130066
$533$	−2.00000	−0.0866296
$534$	0	0
$535$	0	0
$536$	−3.00000	−0.129580
$537$	0	0
$538$	−9.00000	−0.388018
$539$	0	0
$540$	0	0
$541$	−2.00000	−0.0859867	−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000	−0.0859867	−0.0429934	+	0.999075i	$0.513689\pi$
$542$	29.0000	1.24566
$543$	0	0
$544$	5.00000	0.214373
$545$	0	0
$546$	0	0
$547$	11.0000	0.470326	0.235163	−	0.971956i	$-0.424438\pi$
$547$	11.0000	0.470326	0.235163	+	0.971956i	$0.424438\pi$
$548$	3.00000	0.128154
$549$	0	0
$550$	0	0
$551$	6.00000	0.255609
$552$	0	0
$553$	30.0000	1.27573
$554$	22.0000	0.934690
$555$	0	0
$556$	14.0000	0.593732
$557$	36.0000	1.52537	0.762684	−	0.646771i	$-0.223881\pi$
$557$	36.0000	1.52537	0.762684	+	0.646771i	$0.223881\pi$
$558$	6.00000	0.254000
$559$	−4.00000	−0.169182
$560$	0	0
$561$	0	0
$562$	−24.0000	−1.01238
$563$	41.0000	1.72794	0.863972	−	0.503540i	$-0.167969\pi$
$563$	41.0000	1.72794	0.863972	+	0.503540i	$0.167969\pi$
$564$	0	0
$565$	0	0
$566$	−14.0000	−0.588464
$567$	−27.0000	−1.13389
$568$	4.00000	0.167836
$569$	−8.00000	−0.335377	−0.167689	−	0.985840i	$-0.553630\pi$
$569$	−8.00000	−0.335377	−0.167689	+	0.985840i	$0.553630\pi$
$570$	0	0
$571$	34.0000	1.42286	0.711428	−	0.702759i	$-0.248049\pi$
$571$	34.0000	1.42286	0.711428	+	0.702759i	$0.248049\pi$
$572$	0	0
$573$	0	0
$574$	6.00000	0.250435
$575$	−25.0000	−1.04257
$576$	−3.00000	−0.125000
$577$	−13.0000	−0.541197	−0.270599	−	0.962692i	$-0.587222\pi$
$577$	−13.0000	−0.541197	−0.270599	+	0.962692i	$0.587222\pi$
$578$	−8.00000	−0.332756
$579$	0	0
$580$	0	0
$581$	0	0
$582$	0	0
$583$	0	0
$584$	15.0000	0.620704
$585$	0	0
$586$	6.00000	0.247858
$587$	−26.0000	−1.07313	−0.536567	−	0.843857i	$-0.680279\pi$
$587$	−26.0000	−1.07313	−0.536567	+	0.843857i	$0.680279\pi$
$588$	0	0
$589$	−2.00000	−0.0824086
$590$	0	0
$591$	0	0
$592$	−3.00000	−0.123299
$593$	35.0000	1.43728	0.718639	−	0.695383i	$-0.244765\pi$
$593$	35.0000	1.43728	0.718639	+	0.695383i	$0.244765\pi$
$594$	0	0
$595$	0	0
$596$	−20.0000	−0.819232
$597$	0	0
$598$	5.00000	0.204465
$599$	−30.0000	−1.22577	−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000	−1.22577	−0.612883	+	0.790173i	$0.709990\pi$
$600$	0	0
$601$	−18.0000	−0.734235	−0.367118	−	0.930175i	$-0.619655\pi$
$601$	−18.0000	−0.734235	−0.367118	+	0.930175i	$0.619655\pi$
$602$	12.0000	0.489083
$603$	−9.00000	−0.366508
$604$	−6.00000	−0.244137
$605$	0	0
$606$	0	0
$607$	34.0000	1.38002	0.690009	−	0.723801i	$-0.257607\pi$
$607$	34.0000	1.38002	0.690009	+	0.723801i	$0.257607\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	0	0
$611$	3.00000	0.121367
$612$	15.0000	0.606339
$613$	40.0000	1.61558	0.807792	−	0.589467i	$-0.200662\pi$
$613$	40.0000	1.61558	0.807792	+	0.589467i	$0.200662\pi$
$614$	7.00000	0.282497
$615$	0	0
$616$	0	0
$617$	−27.0000	−1.08698	−0.543490	−	0.839416i	$-0.682897\pi$
$617$	−27.0000	−1.08698	−0.543490	+	0.839416i	$0.682897\pi$
$618$	0	0
$619$	8.00000	0.321547	0.160774	−	0.986991i	$-0.448601\pi$
$619$	8.00000	0.321547	0.160774	+	0.986991i	$0.448601\pi$
$620$	0	0
$621$	0	0
$622$	17.0000	0.681638
$623$	−18.0000	−0.721155
$624$	0	0
$625$	25.0000	1.00000
$626$	−1.00000	−0.0399680
$627$	0	0
$628$	12.0000	0.478852
$629$	15.0000	0.598089
$630$	0	0
$631$	−25.0000	−0.995234	−0.497617	−	0.867397i	$-0.665792\pi$
$631$	−25.0000	−0.995234	−0.497617	+	0.867397i	$0.665792\pi$
$632$	10.0000	0.397779
$633$	0	0
$634$	11.0000	0.436866
$635$	0	0
$636$	0	0
$637$	−2.00000	−0.0792429
$638$	0	0
$639$	12.0000	0.474713
$640$	0	0
$641$	−22.0000	−0.868948	−0.434474	−	0.900684i	$-0.643066\pi$
$641$	−22.0000	−0.868948	−0.434474	+	0.900684i	$0.643066\pi$
$642$	0	0
$643$	28.0000	1.10421	0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000	1.10421	0.552106	+	0.833774i	$0.313824\pi$
$644$	−15.0000	−0.591083
$645$	0	0
$646$	−5.00000	−0.196722
$647$	24.0000	0.943537	0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000	0.943537	0.471769	+	0.881722i	$0.343616\pi$
$648$	−9.00000	−0.353553
$649$	0	0
$650$	−5.00000	−0.196116
$651$	0	0
$652$	4.00000	0.156652
$653$	8.00000	0.313064	0.156532	−	0.987673i	$-0.449969\pi$
$653$	8.00000	0.313064	0.156532	+	0.987673i	$0.449969\pi$
$654$	0	0
$655$	0	0
$656$	2.00000	0.0780869
$657$	45.0000	1.75562
$658$	−9.00000	−0.350857
$659$	−31.0000	−1.20759	−0.603794	−	0.797140i	$-0.706345\pi$
$659$	−31.0000	−1.20759	−0.603794	+	0.797140i	$0.706345\pi$
$660$	0	0
$661$	−26.0000	−1.01128	−0.505641	−	0.862744i	$-0.668744\pi$
$661$	−26.0000	−1.01128	−0.505641	+	0.862744i	$0.668744\pi$
$662$	−7.00000	−0.272063
$663$	0	0
$664$	0	0
$665$	0	0
$666$	−9.00000	−0.348743
$667$	−30.0000	−1.16160
$668$	−8.00000	−0.309529
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	6.00000	0.231283	0.115642	−	0.993291i	$-0.463108\pi$
$673$	6.00000	0.231283	0.115642	+	0.993291i	$0.463108\pi$
$674$	−4.00000	−0.154074
$675$	0	0
$676$	−12.0000	−0.461538
$677$	−7.00000	−0.269032	−0.134516	−	0.990911i	$-0.542948\pi$
$677$	−7.00000	−0.269032	−0.134516	+	0.990911i	$0.542948\pi$
$678$	0	0
$679$	−6.00000	−0.230259
$680$	0	0
$681$	0	0
$682$	0	0
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	3.00000	0.114708
$685$	0	0
$686$	−15.0000	−0.572703
$687$	0	0
$688$	4.00000	0.152499
$689$	−2.00000	−0.0761939
$690$	0	0
$691$	−28.0000	−1.06517	−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000	−1.06517	−0.532585	+	0.846376i	$0.678779\pi$
$692$	15.0000	0.570214
$693$	0	0
$694$	−16.0000	−0.607352
$695$	0	0
$696$	0	0
$697$	−10.0000	−0.378777
$698$	−10.0000	−0.378506
$699$	0	0
$700$	15.0000	0.566947
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	0	0
$703$	3.00000	0.113147
$704$	0	0
$705$	0	0
$706$	30.0000	1.12906
$707$	30.0000	1.12827
$708$	0	0
$709$	−32.0000	−1.20179	−0.600893	−	0.799330i	$-0.705188\pi$
$709$	−32.0000	−1.20179	−0.600893	+	0.799330i	$0.705188\pi$
$710$	0	0
$711$	30.0000	1.12509
$712$	−6.00000	−0.224860
$713$	10.0000	0.374503
$714$	0	0
$715$	0	0
$716$	−21.0000	−0.784807
$717$	0	0
$718$	−1.00000	−0.0373197
$719$	−5.00000	−0.186469	−0.0932343	−	0.995644i	$-0.529721\pi$
$719$	−5.00000	−0.186469	−0.0932343	+	0.995644i	$0.529721\pi$
$720$	0	0
$721$	−42.0000	−1.56416
$722$	−1.00000	−0.0372161
$723$	0	0
$724$	−2.00000	−0.0743294
$725$	30.0000	1.11417
$726$	0	0
$727$	52.0000	1.92857	0.964287	−	0.264861i	$-0.0853260\pi$
$727$	52.0000	1.92857	0.964287	+	0.264861i	$0.0853260\pi$
$728$	−3.00000	−0.111187
$729$	−27.0000	−1.00000
$730$	0	0
$731$	−20.0000	−0.739727
$732$	0	0
$733$	24.0000	0.886460	0.443230	−	0.896408i	$-0.353832\pi$
$733$	24.0000	0.886460	0.443230	+	0.896408i	$0.353832\pi$
$734$	−19.0000	−0.701303
$735$	0	0
$736$	−5.00000	−0.184302
$737$	0	0
$738$	6.00000	0.220863
$739$	−2.00000	−0.0735712	−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000	−0.0735712	−0.0367856	+	0.999323i	$0.511712\pi$
$740$	0	0
$741$	0	0
$742$	6.00000	0.220267
$743$	22.0000	0.807102	0.403551	−	0.914957i	$-0.367776\pi$
$743$	22.0000	0.807102	0.403551	+	0.914957i	$0.367776\pi$
$744$	0	0
$745$	0	0
$746$	−10.0000	−0.366126
$747$	0	0
$748$	0	0
$749$	−9.00000	−0.328853
$750$	0	0
$751$	50.0000	1.82453	0.912263	−	0.409605i	$-0.134333\pi$
$751$	50.0000	1.82453	0.912263	+	0.409605i	$0.134333\pi$
$752$	−3.00000	−0.109399
$753$	0	0
$754$	−6.00000	−0.218507
$755$	0	0
$756$	0	0
$757$	−4.00000	−0.145382	−0.0726912	−	0.997354i	$-0.523159\pi$
$757$	−4.00000	−0.145382	−0.0726912	+	0.997354i	$0.523159\pi$
$758$	−25.0000	−0.908041
$759$	0	0
$760$	0	0
$761$	43.0000	1.55875	0.779374	−	0.626559i	$-0.215537\pi$
$761$	43.0000	1.55875	0.779374	+	0.626559i	$0.215537\pi$
$762$	0	0
$763$	−51.0000	−1.84632
$764$	9.00000	0.325609
$765$	0	0
$766$	−6.00000	−0.216789
$767$	−1.00000	−0.0361079
$768$	0	0
$769$	−22.0000	−0.793340	−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000	−0.793340	−0.396670	+	0.917961i	$0.629834\pi$
$770$	0	0
$771$	0	0
$772$	20.0000	0.719816
$773$	−51.0000	−1.83434	−0.917171	−	0.398493i	$-0.869533\pi$
$773$	−51.0000	−1.83434	−0.917171	+	0.398493i	$0.869533\pi$
$774$	12.0000	0.431331
$775$	−10.0000	−0.359211
$776$	−2.00000	−0.0717958
$777$	0	0
$778$	−10.0000	−0.358517
$779$	−2.00000	−0.0716574
$780$	0	0
$781$	0	0
$782$	25.0000	0.893998
$783$	0	0
$784$	2.00000	0.0714286
$785$	0	0
$786$	0	0
$787$	−8.00000	−0.285169	−0.142585	−	0.989783i	$-0.545541\pi$
$787$	−8.00000	−0.285169	−0.142585	+	0.989783i	$0.545541\pi$
$788$	2.00000	0.0712470
$789$	0	0
$790$	0	0
$791$	−48.0000	−1.70668
$792$	0	0
$793$	0	0
$794$	−12.0000	−0.425864
$795$	0	0
$796$	7.00000	0.248108
$797$	−53.0000	−1.87736	−0.938678	−	0.344795i	$-0.887949\pi$
$797$	−53.0000	−1.87736	−0.938678	+	0.344795i	$0.887949\pi$
$798$	0	0
$799$	15.0000	0.530662
$800$	5.00000	0.176777
$801$	−18.0000	−0.635999
$802$	−12.0000	−0.423735
$803$	0	0
$804$	0	0
$805$	0	0
$806$	2.00000	0.0704470
$807$	0	0
$808$	10.0000	0.351799
$809$	−42.0000	−1.47664	−0.738321	−	0.674450i	$-0.764381\pi$
$809$	−42.0000	−1.47664	−0.738321	+	0.674450i	$0.764381\pi$
$810$	0	0
$811$	−44.0000	−1.54505	−0.772524	−	0.634985i	$-0.781006\pi$
$811$	−44.0000	−1.54505	−0.772524	+	0.634985i	$0.781006\pi$
$812$	18.0000	0.631676
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−4.00000	−0.139942
$818$	−28.0000	−0.978997
$819$	−9.00000	−0.314485
$820$	0	0
$821$	36.0000	1.25641	0.628204	−	0.778048i	$-0.283790\pi$
$821$	36.0000	1.25641	0.628204	+	0.778048i	$0.283790\pi$
$822$	0	0
$823$	−28.0000	−0.976019	−0.488009	−	0.872838i	$-0.662277\pi$
$823$	−28.0000	−0.976019	−0.488009	+	0.872838i	$0.662277\pi$
$824$	−14.0000	−0.487713
$825$	0	0
$826$	3.00000	0.104383
$827$	3.00000	0.104320	0.0521601	−	0.998639i	$-0.483389\pi$
$827$	3.00000	0.104320	0.0521601	+	0.998639i	$0.483389\pi$
$828$	−15.0000	−0.521286
$829$	−23.0000	−0.798823	−0.399412	−	0.916772i	$-0.630786\pi$
$829$	−23.0000	−0.798823	−0.399412	+	0.916772i	$0.630786\pi$
$830$	0	0
$831$	0	0
$832$	−1.00000	−0.0346688
$833$	−10.0000	−0.346479
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	4.00000	0.138178
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−35.0000	−1.20618
$843$	0	0
$844$	−28.0000	−0.963800
$845$	0	0
$846$	−9.00000	−0.309426
$847$	0	0
$848$	2.00000	0.0686803
$849$	0	0
$850$	−25.0000	−0.857493
$851$	−15.0000	−0.514193
$852$	0	0
$853$	36.0000	1.23262	0.616308	−	0.787505i	$-0.288628\pi$
$853$	36.0000	1.23262	0.616308	+	0.787505i	$0.288628\pi$
$854$	0	0
$855$	0	0
$856$	−3.00000	−0.102538
$857$	−24.0000	−0.819824	−0.409912	−	0.912125i	$-0.634441\pi$
$857$	−24.0000	−0.819824	−0.409912	+	0.912125i	$0.634441\pi$
$858$	0	0
$859$	−18.0000	−0.614152	−0.307076	−	0.951685i	$-0.599351\pi$
$859$	−18.0000	−0.614152	−0.307076	+	0.951685i	$0.599351\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	−10.0000	−0.340404	−0.170202	−	0.985409i	$-0.554442\pi$
$863$	−10.0000	−0.340404	−0.170202	+	0.985409i	$0.554442\pi$
$864$	0	0
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	0	0
$868$	−6.00000	−0.203653
$869$	0	0
$870$	0	0
$871$	−3.00000	−0.101651
$872$	−17.0000	−0.575693
$873$	−6.00000	−0.203069
$874$	5.00000	0.169128
$875$	0	0
$876$	0	0
$877$	−27.0000	−0.911725	−0.455863	−	0.890050i	$-0.650669\pi$
$877$	−27.0000	−0.911725	−0.455863	+	0.890050i	$0.650669\pi$
$878$	26.0000	0.877457
$879$	0	0
$880$	0	0
$881$	−19.0000	−0.640126	−0.320063	−	0.947396i	$-0.603704\pi$
$881$	−19.0000	−0.640126	−0.320063	+	0.947396i	$0.603704\pi$
$882$	6.00000	0.202031
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	5.00000	0.168168
$885$	0	0
$886$	38.0000	1.27663
$887$	−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
$889$	−30.0000	−1.00617
$890$	0	0
$891$	0	0
$892$	−8.00000	−0.267860
$893$	3.00000	0.100391
$894$	0	0
$895$	0	0
$896$	3.00000	0.100223
$897$	0	0
$898$	−14.0000	−0.467186
$899$	−12.0000	−0.400222
$900$	15.0000	0.500000
$901$	−10.0000	−0.333148
$902$	0	0
$903$	0	0
$904$	−16.0000	−0.532152
$905$	0	0
$906$	0	0
$907$	43.0000	1.42779	0.713896	−	0.700252i	$-0.246929\pi$
$907$	43.0000	1.42779	0.713896	+	0.700252i	$0.246929\pi$
$908$	−13.0000	−0.431420
$909$	30.0000	0.995037
$910$	0	0
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	0	0
$913$	0	0
$914$	−13.0000	−0.430002
$915$	0	0
$916$	22.0000	0.726900
$917$	−36.0000	−1.18882
$918$	0	0
$919$	9.00000	0.296883	0.148441	−	0.988921i	$-0.452574\pi$
$919$	9.00000	0.296883	0.148441	+	0.988921i	$0.452574\pi$
$920$	0	0
$921$	0	0
$922$	12.0000	0.395199
$923$	4.00000	0.131662
$924$	0	0
$925$	15.0000	0.493197
$926$	−8.00000	−0.262896
$927$	−42.0000	−1.37946
$928$	6.00000	0.196960
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	0	0
$931$	−2.00000	−0.0655474
$932$	19.0000	0.622366
$933$	0	0
$934$	14.0000	0.458094
$935$	0	0
$936$	−3.00000	−0.0980581
$937$	26.0000	0.849383	0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000	0.849383	0.424691	+	0.905338i	$0.360383\pi$
$938$	9.00000	0.293860
$939$	0	0
$940$	0	0
$941$	15.0000	0.488986	0.244493	−	0.969651i	$-0.421378\pi$
$941$	15.0000	0.488986	0.244493	+	0.969651i	$0.421378\pi$
$942$	0	0
$943$	10.0000	0.325645
$944$	1.00000	0.0325472
$945$	0	0
$946$	0	0
$947$	40.0000	1.29983	0.649913	−	0.760009i	$-0.274805\pi$
$947$	40.0000	1.29983	0.649913	+	0.760009i	$0.274805\pi$
$948$	0	0
$949$	15.0000	0.486921
$950$	−5.00000	−0.162221
$951$	0	0
$952$	−15.0000	−0.486153
$953$	−26.0000	−0.842223	−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000	−0.842223	−0.421111	+	0.907009i	$0.638360\pi$
$954$	6.00000	0.194257
$955$	0	0
$956$	24.0000	0.776215
$957$	0	0
$958$	5.00000	0.161543
$959$	−9.00000	−0.290625
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−3.00000	−0.0967239
$963$	−9.00000	−0.290021
$964$	10.0000	0.322078
$965$	0	0
$966$	0	0
$967$	−37.0000	−1.18984	−0.594920	−	0.803785i	$-0.702816\pi$
$967$	−37.0000	−1.18984	−0.594920	+	0.803785i	$0.702816\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−45.0000	−1.44412	−0.722059	−	0.691831i	$-0.756804\pi$
$971$	−45.0000	−1.44412	−0.722059	+	0.691831i	$0.756804\pi$
$972$	0	0
$973$	−42.0000	−1.34646
$974$	12.0000	0.384505
$975$	0	0
$976$	0	0
$977$	24.0000	0.767828	0.383914	−	0.923369i	$-0.374576\pi$
$977$	24.0000	0.767828	0.383914	+	0.923369i	$0.374576\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	−51.0000	−1.62830
$982$	−2.00000	−0.0638226
$983$	−42.0000	−1.33959	−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000	−1.33959	−0.669796	+	0.742545i	$0.733618\pi$
$984$	0	0
$985$	0	0
$986$	−30.0000	−0.955395
$987$	0	0
$988$	1.00000	0.0318142
$989$	20.0000	0.635963
$990$	0	0
$991$	−10.0000	−0.317660	−0.158830	−	0.987306i	$-0.550772\pi$
$991$	−10.0000	−0.317660	−0.158830	+	0.987306i	$0.550772\pi$
$992$	−2.00000	−0.0635001
$993$	0	0
$994$	−12.0000	−0.380617
$995$	0	0
$996$	0	0
$997$	−8.00000	−0.253363	−0.126681	−	0.991943i	$-0.540433\pi$
$997$	−8.00000	−0.253363	−0.126681	+	0.991943i	$0.540433\pi$
$998$	4.00000	0.126618
$999$	0	0

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.e.1.1	✓	1
11.10	odd	2		4598.2.a.n.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.e.1.1	✓	1	1.1	even	1	trivial
4598.2.a.n.1.1	yes	1	11.10	odd	2

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	4598.2.a.e.1.1

Level	$4598$
Weight	$2$
Character	4598.1
Self dual	yes
Analytic conductor	$36.715$
Analytic rank	$0$
Dimension	$1$
CM	no
Inner twists	$1$