LMFDB - Embedded newform 4598.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{5} -1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{5} -1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} -4.00000 q^{10} -5.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} +3.00000 q^{18} -1.00000 q^{19} +4.00000 q^{20} +9.00000 q^{23} +11.0000 q^{25} +5.00000 q^{26} -1.00000 q^{28} +2.00000 q^{29} -10.0000 q^{31} -1.00000 q^{32} +3.00000 q^{34} -4.00000 q^{35} -3.00000 q^{36} -9.00000 q^{37} +1.00000 q^{38} -4.00000 q^{40} +2.00000 q^{41} +8.00000 q^{43} -12.0000 q^{45} -9.00000 q^{46} +9.00000 q^{47} -6.00000 q^{49} -11.0000 q^{50} -5.00000 q^{52} +6.00000 q^{53} +1.00000 q^{56} -2.00000 q^{58} +7.00000 q^{59} +12.0000 q^{61} +10.0000 q^{62} +3.00000 q^{63} +1.00000 q^{64} -20.0000 q^{65} -3.00000 q^{67} -3.00000 q^{68} +4.00000 q^{70} +12.0000 q^{71} +3.00000 q^{72} +15.0000 q^{73} +9.00000 q^{74} -1.00000 q^{76} +2.00000 q^{79} +4.00000 q^{80} +9.00000 q^{81} -2.00000 q^{82} +8.00000 q^{83} -12.0000 q^{85} -8.00000 q^{86} +14.0000 q^{89} +12.0000 q^{90} +5.00000 q^{91} +9.00000 q^{92} -9.00000 q^{94} -4.00000 q^{95} +2.00000 q^{97} +6.00000 q^{98} +O(q^{100})\)

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		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	4.00000	1.78885	0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000	1.78885	0.894427	+	0.447214i	$0.147584\pi$
$6$	0	0
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000	−0.353553
$9$	−3.00000	−1.00000
$10$	−4.00000	−1.26491
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	3.00000	0.707107
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	4.00000	0.894427
$21$	0	0
$22$	0	0
$23$	9.00000	1.87663	0.938315	−	0.345782i	$-0.112386\pi$
$23$	9.00000	1.87663	0.938315	+	0.345782i	$0.112386\pi$
$24$	0	0
$25$	11.0000	2.20000
$26$	5.00000	0.980581
$27$	0	0
$28$	−1.00000	−0.188982
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	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
$34$	3.00000	0.514496
$35$	−4.00000	−0.676123
$36$	−3.00000	−0.500000
$37$	−9.00000	−1.47959	−0.739795	−	0.672832i	$-0.765078\pi$
$37$	−9.00000	−1.47959	−0.739795	+	0.672832i	$0.765078\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	−4.00000	−0.632456
$41$	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
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	0	0
$45$	−12.0000	−1.78885
$46$	−9.00000	−1.32698
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	−11.0000	−1.55563
$51$	0	0
$52$	−5.00000	−0.693375
$53$	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
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	−2.00000	−0.262613
$59$	7.00000	0.911322	0.455661	−	0.890153i	$-0.349403\pi$
$59$	7.00000	0.911322	0.455661	+	0.890153i	$0.349403\pi$
$60$	0	0
$61$	12.0000	1.53644	0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000	1.53644	0.768221	+	0.640184i	$0.221142\pi$
$62$	10.0000	1.27000
$63$	3.00000	0.377964
$64$	1.00000	0.125000
$65$	−20.0000	−2.48069
$66$	0	0
$67$	−3.00000	−0.366508	−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000	−0.366508	−0.183254	+	0.983066i	$0.558663\pi$
$68$	−3.00000	−0.363803
$69$	0	0
$70$	4.00000	0.478091
$71$	12.0000	1.42414	0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000	1.42414	0.712069	+	0.702109i	$0.247758\pi$
$72$	3.00000	0.353553
$73$	15.0000	1.75562	0.877809	−	0.479012i	$-0.159005\pi$
$73$	15.0000	1.75562	0.877809	+	0.479012i	$0.159005\pi$
$74$	9.00000	1.04623
$75$	0	0
$76$	−1.00000	−0.114708
$77$	0	0
$78$	0	0
$79$	2.00000	0.225018	0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000	0.225018	0.112509	+	0.993651i	$0.464111\pi$
$80$	4.00000	0.447214
$81$	9.00000	1.00000
$82$	−2.00000	−0.220863
$83$	8.00000	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$84$	0	0
$85$	−12.0000	−1.30158
$86$	−8.00000	−0.862662
$87$	0	0
$88$	0	0
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	12.0000	1.26491
$91$	5.00000	0.524142
$92$	9.00000	0.938315
$93$	0	0
$94$	−9.00000	−0.928279
$95$	−4.00000	−0.410391
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	6.00000	0.606092
$99$	0	0
$100$	11.0000	1.10000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	0	0
$103$	6.00000	0.591198	0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000	0.591198	0.295599	+	0.955312i	$0.404481\pi$
$104$	5.00000	0.490290
$105$	0	0
$106$	−6.00000	−0.582772
$107$	−5.00000	−0.483368	−0.241684	−	0.970355i	$-0.577700\pi$
$107$	−5.00000	−0.483368	−0.241684	+	0.970355i	$0.577700\pi$
$108$	0	0
$109$	13.0000	1.24517	0.622587	−	0.782551i	$-0.286082\pi$
$109$	13.0000	1.24517	0.622587	+	0.782551i	$0.286082\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	8.00000	0.752577	0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000	0.752577	0.376288	+	0.926503i	$0.377200\pi$
$114$	0	0
$115$	36.0000	3.35702
$116$	2.00000	0.185695
$117$	15.0000	1.38675
$118$	−7.00000	−0.644402
$119$	3.00000	0.275010
$120$	0	0
$121$	0	0
$122$	−12.0000	−1.08643
$123$	0	0
$124$	−10.0000	−0.898027
$125$	24.0000	2.14663
$126$	−3.00000	−0.267261
$127$	−14.0000	−1.24230	−0.621150	−	0.783692i	$-0.713334\pi$
$127$	−14.0000	−1.24230	−0.621150	+	0.783692i	$0.713334\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	20.0000	1.75412
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	0	0
$133$	1.00000	0.0867110
$134$	3.00000	0.259161
$135$	0	0
$136$	3.00000	0.257248
$137$	−5.00000	−0.427179	−0.213589	−	0.976924i	$-0.568515\pi$
$137$	−5.00000	−0.427179	−0.213589	+	0.976924i	$0.568515\pi$
$138$	0	0
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	−4.00000	−0.338062
$141$	0	0
$142$	−12.0000	−1.00702
$143$	0	0
$144$	−3.00000	−0.250000
$145$	8.00000	0.664364
$146$	−15.0000	−1.24141
$147$	0	0
$148$	−9.00000	−0.739795
$149$	4.00000	0.327693	0.163846	−	0.986486i	$-0.447610\pi$
$149$	4.00000	0.327693	0.163846	+	0.986486i	$0.447610\pi$
$150$	0	0
$151$	−18.0000	−1.46482	−0.732410	−	0.680864i	$-0.761604\pi$
$151$	−18.0000	−1.46482	−0.732410	+	0.680864i	$0.761604\pi$
$152$	1.00000	0.0811107
$153$	9.00000	0.727607
$154$	0	0
$155$	−40.0000	−3.21288
$156$	0	0
$157$	−12.0000	−0.957704	−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000	−0.957704	−0.478852	+	0.877896i	$0.658947\pi$
$158$	−2.00000	−0.159111
$159$	0	0
$160$	−4.00000	−0.316228
$161$	−9.00000	−0.709299
$162$	−9.00000	−0.707107
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	−8.00000	−0.620920
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	12.0000	0.920358
$171$	3.00000	0.229416
$172$	8.00000	0.609994
$173$	11.0000	0.836315	0.418157	−	0.908375i	$-0.362676\pi$
$173$	11.0000	0.836315	0.418157	+	0.908375i	$0.362676\pi$
$174$	0	0
$175$	−11.0000	−0.831522
$176$	0	0
$177$	0	0
$178$	−14.0000	−1.04934
$179$	5.00000	0.373718	0.186859	−	0.982387i	$-0.440169\pi$
$179$	5.00000	0.373718	0.186859	+	0.982387i	$0.440169\pi$
$180$	−12.0000	−0.894427
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	−5.00000	−0.370625
$183$	0	0
$184$	−9.00000	−0.663489
$185$	−36.0000	−2.64677
$186$	0	0
$187$	0	0
$188$	9.00000	0.656392
$189$	0	0
$190$	4.00000	0.290191
$191$	−3.00000	−0.217072	−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000	−0.217072	−0.108536	+	0.994092i	$0.534616\pi$
$192$	0	0
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	−6.00000	−0.428571
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	0	0
$199$	−5.00000	−0.354441	−0.177220	−	0.984171i	$-0.556711\pi$
$199$	−5.00000	−0.354441	−0.177220	+	0.984171i	$0.556711\pi$
$200$	−11.0000	−0.777817
$201$	0	0
$202$	−14.0000	−0.985037
$203$	−2.00000	−0.140372
$204$	0	0
$205$	8.00000	0.558744
$206$	−6.00000	−0.418040
$207$	−27.0000	−1.87663
$208$	−5.00000	−0.346688
$209$	0	0
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	6.00000	0.412082
$213$	0	0
$214$	5.00000	0.341793
$215$	32.0000	2.18238
$216$	0	0
$217$	10.0000	0.678844
$218$	−13.0000	−0.880471
$219$	0	0
$220$	0	0
$221$	15.0000	1.00901
$222$	0	0
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	1.00000	0.0668153
$225$	−33.0000	−2.20000
$226$	−8.00000	−0.532152
$227$	−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
$229$	−10.0000	−0.660819	−0.330409	−	0.943838i	$-0.607187\pi$
$229$	−10.0000	−0.660819	−0.330409	+	0.943838i	$0.607187\pi$
$230$	−36.0000	−2.37377
$231$	0	0
$232$	−2.00000	−0.131306
$233$	21.0000	1.37576	0.687878	−	0.725826i	$-0.258542\pi$
$233$	21.0000	1.37576	0.687878	+	0.725826i	$0.258542\pi$
$234$	−15.0000	−0.980581
$235$	36.0000	2.34838
$236$	7.00000	0.455661
$237$	0	0
$238$	−3.00000	−0.194461
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	0	0
$241$	−22.0000	−1.41714	−0.708572	−	0.705638i	$-0.750660\pi$
$241$	−22.0000	−1.41714	−0.708572	+	0.705638i	$0.750660\pi$
$242$	0	0
$243$	0	0
$244$	12.0000	0.768221
$245$	−24.0000	−1.53330
$246$	0	0
$247$	5.00000	0.318142
$248$	10.0000	0.635001
$249$	0	0
$250$	−24.0000	−1.51789
$251$	6.00000	0.378717	0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000	0.378717	0.189358	+	0.981908i	$0.439359\pi$
$252$	3.00000	0.188982
$253$	0	0
$254$	14.0000	0.878438
$255$	0	0
$256$	1.00000	0.0625000
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	0	0
$259$	9.00000	0.559233
$260$	−20.0000	−1.24035
$261$	−6.00000	−0.371391
$262$	4.00000	0.247121
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	0	0
$265$	24.0000	1.47431
$266$	−1.00000	−0.0613139
$267$	0	0
$268$	−3.00000	−0.183254
$269$	3.00000	0.182913	0.0914566	−	0.995809i	$-0.470848\pi$
$269$	3.00000	0.182913	0.0914566	+	0.995809i	$0.470848\pi$
$270$	0	0
$271$	9.00000	0.546711	0.273356	−	0.961913i	$-0.411866\pi$
$271$	9.00000	0.546711	0.273356	+	0.961913i	$0.411866\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	5.00000	0.302061
$275$	0	0
$276$	0	0
$277$	14.0000	0.841178	0.420589	−	0.907251i	$-0.361823\pi$
$277$	14.0000	0.841178	0.420589	+	0.907251i	$0.361823\pi$
$278$	10.0000	0.599760
$279$	30.0000	1.79605
$280$	4.00000	0.239046
$281$	4.00000	0.238620	0.119310	−	0.992857i	$-0.461932\pi$
$281$	4.00000	0.238620	0.119310	+	0.992857i	$0.461932\pi$
$282$	0	0
$283$	10.0000	0.594438	0.297219	−	0.954809i	$-0.403941\pi$
$283$	10.0000	0.594438	0.297219	+	0.954809i	$0.403941\pi$
$284$	12.0000	0.712069
$285$	0	0
$286$	0	0
$287$	−2.00000	−0.118056
$288$	3.00000	0.176777
$289$	−8.00000	−0.470588
$290$	−8.00000	−0.469776
$291$	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
$295$	28.0000	1.63022
$296$	9.00000	0.523114
$297$	0	0
$298$	−4.00000	−0.231714
$299$	−45.0000	−2.60242
$300$	0	0
$301$	−8.00000	−0.461112
$302$	18.0000	1.03578
$303$	0	0
$304$	−1.00000	−0.0573539
$305$	48.0000	2.74847
$306$	−9.00000	−0.514496
$307$	−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
$310$	40.0000	2.27185
$311$	−13.0000	−0.737162	−0.368581	−	0.929596i	$-0.620156\pi$
$311$	−13.0000	−0.737162	−0.368581	+	0.929596i	$0.620156\pi$
$312$	0	0
$313$	−15.0000	−0.847850	−0.423925	−	0.905697i	$-0.639348\pi$
$313$	−15.0000	−0.847850	−0.423925	+	0.905697i	$0.639348\pi$
$314$	12.0000	0.677199
$315$	12.0000	0.676123
$316$	2.00000	0.112509
$317$	7.00000	0.393159	0.196580	−	0.980488i	$-0.437017\pi$
$317$	7.00000	0.393159	0.196580	+	0.980488i	$0.437017\pi$
$318$	0	0
$319$	0	0
$320$	4.00000	0.223607
$321$	0	0
$322$	9.00000	0.501550
$323$	3.00000	0.166924
$324$	9.00000	0.500000
$325$	−55.0000	−3.05085
$326$	16.0000	0.886158
$327$	0	0
$328$	−2.00000	−0.110432
$329$	−9.00000	−0.496186
$330$	0	0
$331$	−31.0000	−1.70391	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	−31.0000	−1.70391	−0.851957	+	0.523612i	$0.824584\pi$
$332$	8.00000	0.439057
$333$	27.0000	1.47959
$334$	−12.0000	−0.656611
$335$	−12.0000	−0.655630
$336$	0	0
$337$	20.0000	1.08947	0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000	1.08947	0.544735	+	0.838608i	$0.316630\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	−12.0000	−0.650791
$341$	0	0
$342$	−3.00000	−0.162221
$343$	13.0000	0.701934
$344$	−8.00000	−0.431331
$345$	0	0
$346$	−11.0000	−0.591364
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	11.0000	0.587975
$351$	0	0
$352$	0	0
$353$	26.0000	1.38384	0.691920	−	0.721974i	$-0.256765\pi$
$353$	26.0000	1.38384	0.691920	+	0.721974i	$0.256765\pi$
$354$	0	0
$355$	48.0000	2.54758
$356$	14.0000	0.741999
$357$	0	0
$358$	−5.00000	−0.264258
$359$	−21.0000	−1.10834	−0.554169	−	0.832404i	$-0.686964\pi$
$359$	−21.0000	−1.10834	−0.554169	+	0.832404i	$0.686964\pi$
$360$	12.0000	0.632456
$361$	1.00000	0.0526316
$362$	−10.0000	−0.525588
$363$	0	0
$364$	5.00000	0.262071
$365$	60.0000	3.14054
$366$	0	0
$367$	−17.0000	−0.887393	−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000	−0.887393	−0.443696	+	0.896177i	$0.646333\pi$
$368$	9.00000	0.469157
$369$	−6.00000	−0.312348
$370$	36.0000	1.87155
$371$	−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
$376$	−9.00000	−0.464140
$377$	−10.0000	−0.515026
$378$	0	0
$379$	−25.0000	−1.28416	−0.642082	−	0.766636i	$-0.721929\pi$
$379$	−25.0000	−1.28416	−0.642082	+	0.766636i	$0.721929\pi$
$380$	−4.00000	−0.205196
$381$	0	0
$382$	3.00000	0.153493
$383$	−10.0000	−0.510976	−0.255488	−	0.966812i	$-0.582236\pi$
$383$	−10.0000	−0.510976	−0.255488	+	0.966812i	$0.582236\pi$
$384$	0	0
$385$	0	0
$386$	16.0000	0.814379
$387$	−24.0000	−1.21999
$388$	2.00000	0.101535
$389$	−2.00000	−0.101404	−0.0507020	−	0.998714i	$-0.516146\pi$
$389$	−2.00000	−0.101404	−0.0507020	+	0.998714i	$0.516146\pi$
$390$	0	0
$391$	−27.0000	−1.36545
$392$	6.00000	0.303046
$393$	0	0
$394$	−10.0000	−0.503793
$395$	8.00000	0.402524
$396$	0	0
$397$	−12.0000	−0.602263	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	−12.0000	−0.602263	−0.301131	+	0.953583i	$0.597364\pi$
$398$	5.00000	0.250627
$399$	0	0
$400$	11.0000	0.550000
$401$	−20.0000	−0.998752	−0.499376	−	0.866385i	$-0.666437\pi$
$401$	−20.0000	−0.998752	−0.499376	+	0.866385i	$0.666437\pi$
$402$	0	0
$403$	50.0000	2.49068
$404$	14.0000	0.696526
$405$	36.0000	1.78885
$406$	2.00000	0.0992583
$407$	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	$0.743383\pi$
$410$	−8.00000	−0.395092
$411$	0	0
$412$	6.00000	0.295599
$413$	−7.00000	−0.344447
$414$	27.0000	1.32698
$415$	32.0000	1.57082
$416$	5.00000	0.245145
$417$	0	0
$418$	0	0
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	9.00000	0.438633	0.219317	−	0.975654i	$-0.429617\pi$
$421$	9.00000	0.438633	0.219317	+	0.975654i	$0.429617\pi$
$422$	−20.0000	−0.973585
$423$	−27.0000	−1.31278
$424$	−6.00000	−0.291386
$425$	−33.0000	−1.60074
$426$	0	0
$427$	−12.0000	−0.580721
$428$	−5.00000	−0.241684
$429$	0	0
$430$	−32.0000	−1.54318
$431$	−20.0000	−0.963366	−0.481683	−	0.876346i	$-0.659974\pi$
$431$	−20.0000	−0.963366	−0.481683	+	0.876346i	$0.659974\pi$
$432$	0	0
$433$	−6.00000	−0.288342	−0.144171	−	0.989553i	$-0.546051\pi$
$433$	−6.00000	−0.288342	−0.144171	+	0.989553i	$0.546051\pi$
$434$	−10.0000	−0.480015
$435$	0	0
$436$	13.0000	0.622587
$437$	−9.00000	−0.430528
$438$	0	0
$439$	−2.00000	−0.0954548	−0.0477274	−	0.998860i	$-0.515198\pi$
$439$	−2.00000	−0.0954548	−0.0477274	+	0.998860i	$0.515198\pi$
$440$	0	0
$441$	18.0000	0.857143
$442$	−15.0000	−0.713477
$443$	−26.0000	−1.23530	−0.617649	−	0.786454i	$-0.711915\pi$
$443$	−26.0000	−1.23530	−0.617649	+	0.786454i	$0.711915\pi$
$444$	0	0
$445$	56.0000	2.65465
$446$	−8.00000	−0.378811
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	10.0000	0.471929	0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000	0.471929	0.235965	+	0.971762i	$0.424175\pi$
$450$	33.0000	1.55563
$451$	0	0
$452$	8.00000	0.376288
$453$	0	0
$454$	13.0000	0.610120
$455$	20.0000	0.937614
$456$	0	0
$457$	19.0000	0.888783	0.444391	−	0.895833i	$-0.353420\pi$
$457$	19.0000	0.888783	0.444391	+	0.895833i	$0.353420\pi$
$458$	10.0000	0.467269
$459$	0	0
$460$	36.0000	1.67851
$461$	−20.0000	−0.931493	−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000	−0.931493	−0.465746	+	0.884918i	$0.654214\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	2.00000	0.0928477
$465$	0	0
$466$	−21.0000	−0.972806
$467$	6.00000	0.277647	0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000	0.277647	0.138823	+	0.990317i	$0.455668\pi$
$468$	15.0000	0.693375
$469$	3.00000	0.138527
$470$	−36.0000	−1.66056
$471$	0	0
$472$	−7.00000	−0.322201
$473$	0	0
$474$	0	0
$475$	−11.0000	−0.504715
$476$	3.00000	0.137505
$477$	−18.0000	−0.824163
$478$	16.0000	0.731823
$479$	17.0000	0.776750	0.388375	−	0.921501i	$-0.373037\pi$
$479$	17.0000	0.776750	0.388375	+	0.921501i	$0.373037\pi$
$480$	0	0
$481$	45.0000	2.05182
$482$	22.0000	1.00207
$483$	0	0
$484$	0	0
$485$	8.00000	0.363261
$486$	0	0
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	−12.0000	−0.543214
$489$	0	0
$490$	24.0000	1.08421
$491$	−18.0000	−0.812329	−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000	−0.812329	−0.406164	+	0.913800i	$0.633134\pi$
$492$	0	0
$493$	−6.00000	−0.270226
$494$	−5.00000	−0.224961
$495$	0	0
$496$	−10.0000	−0.449013
$497$	−12.0000	−0.538274
$498$	0	0
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	24.0000	1.07331
$501$	0	0
$502$	−6.00000	−0.267793
$503$	−1.00000	−0.0445878	−0.0222939	−	0.999751i	$-0.507097\pi$
$503$	−1.00000	−0.0445878	−0.0222939	+	0.999751i	$0.507097\pi$
$504$	−3.00000	−0.133631
$505$	56.0000	2.49197
$506$	0	0
$507$	0	0
$508$	−14.0000	−0.621150
$509$	15.0000	0.664863	0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000	0.664863	0.332432	+	0.943127i	$0.392131\pi$
$510$	0	0
$511$	−15.0000	−0.663561
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−6.00000	−0.264649
$515$	24.0000	1.05757
$516$	0	0
$517$	0	0
$518$	−9.00000	−0.395437
$519$	0	0
$520$	20.0000	0.877058
$521$	8.00000	0.350486	0.175243	−	0.984525i	$-0.443929\pi$
$521$	8.00000	0.350486	0.175243	+	0.984525i	$0.443929\pi$
$522$	6.00000	0.262613
$523$	−29.0000	−1.26808	−0.634041	−	0.773300i	$-0.718605\pi$
$523$	−29.0000	−1.26808	−0.634041	+	0.773300i	$0.718605\pi$
$524$	−4.00000	−0.174741
$525$	0	0
$526$	24.0000	1.04645
$527$	30.0000	1.30682
$528$	0	0
$529$	58.0000	2.52174
$530$	−24.0000	−1.04249
$531$	−21.0000	−0.911322
$532$	1.00000	0.0433555
$533$	−10.0000	−0.433148
$534$	0	0
$535$	−20.0000	−0.864675
$536$	3.00000	0.129580
$537$	0	0
$538$	−3.00000	−0.129339
$539$	0	0
$540$	0	0
$541$	−38.0000	−1.63375	−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000	−1.63375	−0.816874	+	0.576816i	$0.804295\pi$
$542$	−9.00000	−0.386583
$543$	0	0
$544$	3.00000	0.128624
$545$	52.0000	2.22744
$546$	0	0
$547$	43.0000	1.83855	0.919274	−	0.393619i	$-0.128777\pi$
$547$	43.0000	1.83855	0.919274	+	0.393619i	$0.128777\pi$
$548$	−5.00000	−0.213589
$549$	−36.0000	−1.53644
$550$	0	0
$551$	−2.00000	−0.0852029
$552$	0	0
$553$	−2.00000	−0.0850487
$554$	−14.0000	−0.594803
$555$	0	0
$556$	−10.0000	−0.424094
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	−30.0000	−1.27000
$559$	−40.0000	−1.69182
$560$	−4.00000	−0.169031
$561$	0	0
$562$	−4.00000	−0.168730
$563$	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
$565$	32.0000	1.34625
$566$	−10.0000	−0.420331
$567$	−9.00000	−0.377964
$568$	−12.0000	−0.503509
$569$	44.0000	1.84458	0.922288	−	0.386503i	$-0.126317\pi$
$569$	44.0000	1.84458	0.922288	+	0.386503i	$0.126317\pi$
$570$	0	0
$571$	−2.00000	−0.0836974	−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000	−0.0836974	−0.0418487	+	0.999124i	$0.513325\pi$
$572$	0	0
$573$	0	0
$574$	2.00000	0.0834784
$575$	99.0000	4.12859
$576$	−3.00000	−0.125000
$577$	19.0000	0.790980	0.395490	−	0.918470i	$-0.370575\pi$
$577$	19.0000	0.790980	0.395490	+	0.918470i	$0.370575\pi$
$578$	8.00000	0.332756
$579$	0	0
$580$	8.00000	0.332182
$581$	−8.00000	−0.331896
$582$	0	0
$583$	0	0
$584$	−15.0000	−0.620704
$585$	60.0000	2.48069
$586$	6.00000	0.247858
$587$	26.0000	1.07313	0.536567	−	0.843857i	$-0.319721\pi$
$587$	26.0000	1.07313	0.536567	+	0.843857i	$0.319721\pi$
$588$	0	0
$589$	10.0000	0.412043
$590$	−28.0000	−1.15274
$591$	0	0
$592$	−9.00000	−0.369898
$593$	13.0000	0.533846	0.266923	−	0.963718i	$-0.413993\pi$
$593$	13.0000	0.533846	0.266923	+	0.963718i	$0.413993\pi$
$594$	0	0
$595$	12.0000	0.491952
$596$	4.00000	0.163846
$597$	0	0
$598$	45.0000	1.84019
$599$	26.0000	1.06233	0.531166	−	0.847268i	$-0.321754\pi$
$599$	26.0000	1.06233	0.531166	+	0.847268i	$0.321754\pi$
$600$	0	0
$601$	42.0000	1.71322	0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000	1.71322	0.856608	+	0.515968i	$0.172568\pi$
$602$	8.00000	0.326056
$603$	9.00000	0.366508
$604$	−18.0000	−0.732410
$605$	0	0
$606$	0	0
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	−48.0000	−1.94346
$611$	−45.0000	−1.82051
$612$	9.00000	0.363803
$613$	−4.00000	−0.161558	−0.0807792	−	0.996732i	$-0.525741\pi$
$613$	−4.00000	−0.161558	−0.0807792	+	0.996732i	$0.525741\pi$
$614$	7.00000	0.282497
$615$	0	0
$616$	0	0
$617$	−3.00000	−0.120775	−0.0603877	−	0.998175i	$-0.519234\pi$
$617$	−3.00000	−0.120775	−0.0603877	+	0.998175i	$0.519234\pi$
$618$	0	0
$619$	−8.00000	−0.321547	−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000	−0.321547	−0.160774	+	0.986991i	$0.551399\pi$
$620$	−40.0000	−1.60644
$621$	0	0
$622$	13.0000	0.521253
$623$	−14.0000	−0.560898
$624$	0	0
$625$	41.0000	1.64000
$626$	15.0000	0.599521
$627$	0	0
$628$	−12.0000	−0.478852
$629$	27.0000	1.07656
$630$	−12.0000	−0.478091
$631$	−13.0000	−0.517522	−0.258761	−	0.965941i	$-0.583314\pi$
$631$	−13.0000	−0.517522	−0.258761	+	0.965941i	$0.583314\pi$
$632$	−2.00000	−0.0795557
$633$	0	0
$634$	−7.00000	−0.278006
$635$	−56.0000	−2.22229
$636$	0	0
$637$	30.0000	1.18864
$638$	0	0
$639$	−36.0000	−1.42414
$640$	−4.00000	−0.158114
$641$	−6.00000	−0.236986	−0.118493	−	0.992955i	$-0.537806\pi$
$641$	−6.00000	−0.236986	−0.118493	+	0.992955i	$0.537806\pi$
$642$	0	0
$643$	−28.0000	−1.10421	−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000	−1.10421	−0.552106	+	0.833774i	$0.686176\pi$
$644$	−9.00000	−0.354650
$645$	0	0
$646$	−3.00000	−0.118033
$647$	−24.0000	−0.943537	−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000	−0.943537	−0.471769	+	0.881722i	$0.656384\pi$
$648$	−9.00000	−0.353553
$649$	0	0
$650$	55.0000	2.15728
$651$	0	0
$652$	−16.0000	−0.626608
$653$	−48.0000	−1.87839	−0.939193	−	0.343391i	$-0.888424\pi$
$653$	−48.0000	−1.87839	−0.939193	+	0.343391i	$0.888424\pi$
$654$	0	0
$655$	−16.0000	−0.625172
$656$	2.00000	0.0780869
$657$	−45.0000	−1.75562
$658$	9.00000	0.350857
$659$	−39.0000	−1.51922	−0.759612	−	0.650376i	$-0.774611\pi$
$659$	−39.0000	−1.51922	−0.759612	+	0.650376i	$0.774611\pi$
$660$	0	0
$661$	10.0000	0.388955	0.194477	−	0.980907i	$-0.437699\pi$
$661$	10.0000	0.388955	0.194477	+	0.980907i	$0.437699\pi$
$662$	31.0000	1.20485
$663$	0	0
$664$	−8.00000	−0.310460
$665$	4.00000	0.155113
$666$	−27.0000	−1.04623
$667$	18.0000	0.696963
$668$	12.0000	0.464294
$669$	0	0
$670$	12.0000	0.463600
$671$	0	0
$672$	0	0
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	−20.0000	−0.770371
$675$	0	0
$676$	12.0000	0.461538
$677$	21.0000	0.807096	0.403548	−	0.914959i	$-0.367777\pi$
$677$	21.0000	0.807096	0.403548	+	0.914959i	$0.367777\pi$
$678$	0	0
$679$	−2.00000	−0.0767530
$680$	12.0000	0.460179
$681$	0	0
$682$	0	0
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	3.00000	0.114708
$685$	−20.0000	−0.764161
$686$	−13.0000	−0.496342
$687$	0	0
$688$	8.00000	0.304997
$689$	−30.0000	−1.14291
$690$	0	0
$691$	−32.0000	−1.21734	−0.608669	−	0.793424i	$-0.708296\pi$
$691$	−32.0000	−1.21734	−0.608669	+	0.793424i	$0.708296\pi$
$692$	11.0000	0.418157
$693$	0	0
$694$	−12.0000	−0.455514
$695$	−40.0000	−1.51729
$696$	0	0
$697$	−6.00000	−0.227266
$698$	10.0000	0.378506
$699$	0	0
$700$	−11.0000	−0.415761
$701$	42.0000	1.58632	0.793159	−	0.609015i	$-0.208435\pi$
$701$	42.0000	1.58632	0.793159	+	0.609015i	$0.208435\pi$
$702$	0	0
$703$	9.00000	0.339441
$704$	0	0
$705$	0	0
$706$	−26.0000	−0.978523
$707$	−14.0000	−0.526524
$708$	0	0
$709$	−32.0000	−1.20179	−0.600893	−	0.799330i	$-0.705188\pi$
$709$	−32.0000	−1.20179	−0.600893	+	0.799330i	$0.705188\pi$
$710$	−48.0000	−1.80141
$711$	−6.00000	−0.225018
$712$	−14.0000	−0.524672
$713$	−90.0000	−3.37053
$714$	0	0
$715$	0	0
$716$	5.00000	0.186859
$717$	0	0
$718$	21.0000	0.783713
$719$	−25.0000	−0.932343	−0.466171	−	0.884694i	$-0.654367\pi$
$719$	−25.0000	−0.932343	−0.466171	+	0.884694i	$0.654367\pi$
$720$	−12.0000	−0.447214
$721$	−6.00000	−0.223452
$722$	−1.00000	−0.0372161
$723$	0	0
$724$	10.0000	0.371647
$725$	22.0000	0.817059
$726$	0	0
$727$	44.0000	1.63187	0.815935	−	0.578144i	$-0.196223\pi$
$727$	44.0000	1.63187	0.815935	+	0.578144i	$0.196223\pi$
$728$	−5.00000	−0.185312
$729$	−27.0000	−1.00000
$730$	−60.0000	−2.22070
$731$	−24.0000	−0.887672
$732$	0	0
$733$	0	0		−	1.00000i	$-0.5\pi$
$733$	0	0			1.00000i	$0.5\pi$
$734$	17.0000	0.627481
$735$	0	0
$736$	−9.00000	−0.331744
$737$	0	0
$738$	6.00000	0.220863
$739$	14.0000	0.514998	0.257499	−	0.966279i	$-0.417102\pi$
$739$	14.0000	0.514998	0.257499	+	0.966279i	$0.417102\pi$
$740$	−36.0000	−1.32339
$741$	0	0
$742$	6.00000	0.220267
$743$	46.0000	1.68758	0.843788	−	0.536676i	$-0.180320\pi$
$743$	46.0000	1.68758	0.843788	+	0.536676i	$0.180320\pi$
$744$	0	0
$745$	16.0000	0.586195
$746$	−10.0000	−0.366126
$747$	−24.0000	−0.878114
$748$	0	0
$749$	5.00000	0.182696
$750$	0	0
$751$	−34.0000	−1.24068	−0.620339	−	0.784334i	$-0.713005\pi$
$751$	−34.0000	−1.24068	−0.620339	+	0.784334i	$0.713005\pi$
$752$	9.00000	0.328196
$753$	0	0
$754$	10.0000	0.364179
$755$	−72.0000	−2.62035
$756$	0	0
$757$	52.0000	1.88997	0.944986	−	0.327111i	$-0.106075\pi$
$757$	52.0000	1.88997	0.944986	+	0.327111i	$0.106075\pi$
$758$	25.0000	0.908041
$759$	0	0
$760$	4.00000	0.145095
$761$	−3.00000	−0.108750	−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000	−0.108750	−0.0543750	+	0.998521i	$0.517317\pi$
$762$	0	0
$763$	−13.0000	−0.470632
$764$	−3.00000	−0.108536
$765$	36.0000	1.30158
$766$	10.0000	0.361315
$767$	−35.0000	−1.26378
$768$	0	0
$769$	46.0000	1.65880	0.829401	−	0.558653i	$-0.188682\pi$
$769$	46.0000	1.65880	0.829401	+	0.558653i	$0.188682\pi$
$770$	0	0
$771$	0	0
$772$	−16.0000	−0.575853
$773$	−1.00000	−0.0359675	−0.0179838	−	0.999838i	$-0.505725\pi$
$773$	−1.00000	−0.0359675	−0.0179838	+	0.999838i	$0.505725\pi$
$774$	24.0000	0.862662
$775$	−110.000	−3.95132
$776$	−2.00000	−0.0717958
$777$	0	0
$778$	2.00000	0.0717035
$779$	−2.00000	−0.0716574
$780$	0	0
$781$	0	0
$782$	27.0000	0.965518
$783$	0	0
$784$	−6.00000	−0.214286
$785$	−48.0000	−1.71319
$786$	0	0
$787$	40.0000	1.42585	0.712923	−	0.701242i	$-0.247371\pi$
$787$	40.0000	1.42585	0.712923	+	0.701242i	$0.247371\pi$
$788$	10.0000	0.356235
$789$	0	0
$790$	−8.00000	−0.284627
$791$	−8.00000	−0.284447
$792$	0	0
$793$	−60.0000	−2.13066
$794$	12.0000	0.425864
$795$	0	0
$796$	−5.00000	−0.177220
$797$	33.0000	1.16892	0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000	1.16892	0.584460	+	0.811423i	$0.301306\pi$
$798$	0	0
$799$	−27.0000	−0.955191
$800$	−11.0000	−0.388909
$801$	−42.0000	−1.48400
$802$	20.0000	0.706225
$803$	0	0
$804$	0	0
$805$	−36.0000	−1.26883
$806$	−50.0000	−1.76117
$807$	0	0
$808$	−14.0000	−0.492518
$809$	26.0000	0.914111	0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000	0.914111	0.457056	+	0.889438i	$0.348904\pi$
$810$	−36.0000	−1.26491
$811$	4.00000	0.140459	0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000	0.140459	0.0702295	+	0.997531i	$0.477627\pi$
$812$	−2.00000	−0.0701862
$813$	0	0
$814$	0	0
$815$	−64.0000	−2.24182
$816$	0	0
$817$	−8.00000	−0.279885
$818$	28.0000	0.978997
$819$	−15.0000	−0.524142
$820$	8.00000	0.279372
$821$	20.0000	0.698005	0.349002	−	0.937122i	$-0.386521\pi$
$821$	20.0000	0.698005	0.349002	+	0.937122i	$0.386521\pi$
$822$	0	0
$823$	44.0000	1.53374	0.766872	−	0.641800i	$-0.221812\pi$
$823$	44.0000	1.53374	0.766872	+	0.641800i	$0.221812\pi$
$824$	−6.00000	−0.209020
$825$	0	0
$826$	7.00000	0.243561
$827$	11.0000	0.382507	0.191254	−	0.981541i	$-0.438745\pi$
$827$	11.0000	0.382507	0.191254	+	0.981541i	$0.438745\pi$
$828$	−27.0000	−0.938315
$829$	11.0000	0.382046	0.191023	−	0.981586i	$-0.438820\pi$
$829$	11.0000	0.382046	0.191023	+	0.981586i	$0.438820\pi$
$830$	−32.0000	−1.11074
$831$	0	0
$832$	−5.00000	−0.173344
$833$	18.0000	0.623663
$834$	0	0
$835$	48.0000	1.66111
$836$	0	0
$837$	0	0
$838$	−12.0000	−0.414533
$839$	−16.0000	−0.552381	−0.276191	−	0.961103i	$-0.589072\pi$
$839$	−16.0000	−0.552381	−0.276191	+	0.961103i	$0.589072\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−9.00000	−0.310160
$843$	0	0
$844$	20.0000	0.688428
$845$	48.0000	1.65125
$846$	27.0000	0.928279
$847$	0	0
$848$	6.00000	0.206041
$849$	0	0
$850$	33.0000	1.13189
$851$	−81.0000	−2.77664
$852$	0	0
$853$	12.0000	0.410872	0.205436	−	0.978671i	$-0.434139\pi$
$853$	12.0000	0.410872	0.205436	+	0.978671i	$0.434139\pi$
$854$	12.0000	0.410632
$855$	12.0000	0.410391
$856$	5.00000	0.170896
$857$	0	0		−	1.00000i	$-0.5\pi$
$857$	0	0			1.00000i	$0.5\pi$
$858$	0	0
$859$	58.0000	1.97893	0.989467	−	0.144757i	$-0.0462401\pi$
$859$	58.0000	1.97893	0.989467	+	0.144757i	$0.0462401\pi$
$860$	32.0000	1.09119
$861$	0	0
$862$	20.0000	0.681203
$863$	58.0000	1.97434	0.987171	−	0.159664i	$-0.0510410\pi$
$863$	58.0000	1.97434	0.987171	+	0.159664i	$0.0510410\pi$
$864$	0	0
$865$	44.0000	1.49604
$866$	6.00000	0.203888
$867$	0	0
$868$	10.0000	0.339422
$869$	0	0
$870$	0	0
$871$	15.0000	0.508256
$872$	−13.0000	−0.440236
$873$	−6.00000	−0.203069
$874$	9.00000	0.304430
$875$	−24.0000	−0.811348
$876$	0	0
$877$	−15.0000	−0.506514	−0.253257	−	0.967399i	$-0.581502\pi$
$877$	−15.0000	−0.506514	−0.253257	+	0.967399i	$0.581502\pi$
$878$	2.00000	0.0674967
$879$	0	0
$880$	0	0
$881$	−35.0000	−1.17918	−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000	−1.17918	−0.589590	+	0.807703i	$0.700711\pi$
$882$	−18.0000	−0.606092
$883$	−4.00000	−0.134611	−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000	−0.134611	−0.0673054	+	0.997732i	$0.521440\pi$
$884$	15.0000	0.504505
$885$	0	0
$886$	26.0000	0.873487
$887$	−4.00000	−0.134307	−0.0671534	−	0.997743i	$-0.521392\pi$
$887$	−4.00000	−0.134307	−0.0671534	+	0.997743i	$0.521392\pi$
$888$	0	0
$889$	14.0000	0.469545
$890$	−56.0000	−1.87712
$891$	0	0
$892$	8.00000	0.267860
$893$	−9.00000	−0.301174
$894$	0	0
$895$	20.0000	0.668526
$896$	1.00000	0.0334077
$897$	0	0
$898$	−10.0000	−0.333704
$899$	−20.0000	−0.667037
$900$	−33.0000	−1.10000
$901$	−18.0000	−0.599667
$902$	0	0
$903$	0	0
$904$	−8.00000	−0.266076
$905$	40.0000	1.32964
$906$	0	0
$907$	13.0000	0.431658	0.215829	−	0.976431i	$-0.430755\pi$
$907$	13.0000	0.431658	0.215829	+	0.976431i	$0.430755\pi$
$908$	−13.0000	−0.431420
$909$	−42.0000	−1.39305
$910$	−20.0000	−0.662994
$911$	24.0000	0.795155	0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000	0.795155	0.397578	+	0.917568i	$0.369851\pi$
$912$	0	0
$913$	0	0
$914$	−19.0000	−0.628464
$915$	0	0
$916$	−10.0000	−0.330409
$917$	4.00000	0.132092
$918$	0	0
$919$	3.00000	0.0989609	0.0494804	−	0.998775i	$-0.484243\pi$
$919$	3.00000	0.0989609	0.0494804	+	0.998775i	$0.484243\pi$
$920$	−36.0000	−1.18688
$921$	0	0
$922$	20.0000	0.658665
$923$	−60.0000	−1.97492
$924$	0	0
$925$	−99.0000	−3.25510
$926$	−16.0000	−0.525793
$927$	−18.0000	−0.591198
$928$	−2.00000	−0.0656532
$929$	30.0000	0.984268	0.492134	−	0.870519i	$-0.336217\pi$
$929$	30.0000	0.984268	0.492134	+	0.870519i	$0.336217\pi$
$930$	0	0
$931$	6.00000	0.196642
$932$	21.0000	0.687878
$933$	0	0
$934$	−6.00000	−0.196326
$935$	0	0
$936$	−15.0000	−0.490290
$937$	14.0000	0.457360	0.228680	−	0.973502i	$-0.426559\pi$
$937$	14.0000	0.457360	0.228680	+	0.973502i	$0.426559\pi$
$938$	−3.00000	−0.0979535
$939$	0	0
$940$	36.0000	1.17419
$941$	−45.0000	−1.46696	−0.733479	−	0.679712i	$-0.762105\pi$
$941$	−45.0000	−1.46696	−0.733479	+	0.679712i	$0.762105\pi$
$942$	0	0
$943$	18.0000	0.586161
$944$	7.00000	0.227831
$945$	0	0
$946$	0	0
$947$	28.0000	0.909878	0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000	0.909878	0.454939	+	0.890523i	$0.349661\pi$
$948$	0	0
$949$	−75.0000	−2.43460
$950$	11.0000	0.356887
$951$	0	0
$952$	−3.00000	−0.0972306
$953$	−34.0000	−1.10137	−0.550684	−	0.834714i	$-0.685633\pi$
$953$	−34.0000	−1.10137	−0.550684	+	0.834714i	$0.685633\pi$
$954$	18.0000	0.582772
$955$	−12.0000	−0.388311
$956$	−16.0000	−0.517477
$957$	0	0
$958$	−17.0000	−0.549245
$959$	5.00000	0.161458
$960$	0	0
$961$	69.0000	2.22581
$962$	−45.0000	−1.45086
$963$	15.0000	0.483368
$964$	−22.0000	−0.708572
$965$	−64.0000	−2.06023
$966$	0	0
$967$	1.00000	0.0321578	0.0160789	−	0.999871i	$-0.494882\pi$
$967$	1.00000	0.0321578	0.0160789	+	0.999871i	$0.494882\pi$
$968$	0	0
$969$	0	0
$970$	−8.00000	−0.256865
$971$	13.0000	0.417190	0.208595	−	0.978002i	$-0.433111\pi$
$971$	13.0000	0.417190	0.208595	+	0.978002i	$0.433111\pi$
$972$	0	0
$973$	10.0000	0.320585
$974$	−16.0000	−0.512673
$975$	0	0
$976$	12.0000	0.384111
$977$	−12.0000	−0.383914	−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000	−0.383914	−0.191957	+	0.981403i	$0.561483\pi$
$978$	0	0
$979$	0	0
$980$	−24.0000	−0.766652
$981$	−39.0000	−1.24517
$982$	18.0000	0.574403
$983$	−22.0000	−0.701691	−0.350846	−	0.936433i	$-0.614106\pi$
$983$	−22.0000	−0.701691	−0.350846	+	0.936433i	$0.614106\pi$
$984$	0	0
$985$	40.0000	1.27451
$986$	6.00000	0.191079
$987$	0	0
$988$	5.00000	0.159071
$989$	72.0000	2.28947
$990$	0	0
$991$	−26.0000	−0.825917	−0.412959	−	0.910750i	$-0.635505\pi$
$991$	−26.0000	−0.825917	−0.412959	+	0.910750i	$0.635505\pi$
$992$	10.0000	0.317500
$993$	0	0
$994$	12.0000	0.380617
$995$	−20.0000	−0.634043
$996$	0	0
$997$	−52.0000	−1.64686	−0.823428	−	0.567420i	$-0.807941\pi$
$997$	−52.0000	−1.64686	−0.823428	+	0.567420i	$0.807941\pi$
$998$	−4.00000	−0.126618
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4598.2.a.g.1.1	✓	1	1.1	even	1	trivial
4598.2.a.o.1.1	yes	1	11.10	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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