LMFDB - Embedded newform 4018.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, 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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} +4.00000 q^{5} +1.00000 q^{8} -3.00000 q^{9} +4.00000 q^{10} -2.00000 q^{11} +6.00000 q^{13} +1.00000 q^{16} +6.00000 q^{17} -3.00000 q^{18} -4.00000 q^{19} +4.00000 q^{20} -2.00000 q^{22} +8.00000 q^{23} +11.0000 q^{25} +6.00000 q^{26} -8.00000 q^{29} +1.00000 q^{32} +6.00000 q^{34} -3.00000 q^{36} -2.00000 q^{37} -4.00000 q^{38} +4.00000 q^{40} +1.00000 q^{41} -8.00000 q^{43} -2.00000 q^{44} -12.0000 q^{45} +8.00000 q^{46} +11.0000 q^{50} +6.00000 q^{52} -8.00000 q^{55} -8.00000 q^{58} -2.00000 q^{59} +8.00000 q^{61} +1.00000 q^{64} +24.0000 q^{65} +10.0000 q^{67} +6.00000 q^{68} -12.0000 q^{71} -3.00000 q^{72} -10.0000 q^{73} -2.00000 q^{74} -4.00000 q^{76} +16.0000 q^{79} +4.00000 q^{80} +9.00000 q^{81} +1.00000 q^{82} +2.00000 q^{83} +24.0000 q^{85} -8.00000 q^{86} -2.00000 q^{88} +10.0000 q^{89} -12.0000 q^{90} +8.00000 q^{92} -16.0000 q^{95} +2.00000 q^{97} +6.00000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	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
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−3.00000	−1.00000
$10$	4.00000	1.26491
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	−3.00000	−0.707107
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	4.00000	0.894427
$21$	0	0
$22$	−2.00000	−0.426401
$23$	8.00000	1.66812	0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000	1.66812	0.834058	+	0.551677i	$0.186012\pi$
$24$	0	0
$25$	11.0000	2.20000
$26$	6.00000	1.17670
$27$	0	0
$28$	0	0
$29$	−8.00000	−1.48556	−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000	−1.48556	−0.742781	+	0.669534i	$0.766494\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	6.00000	1.02899
$35$	0	0
$36$	−3.00000	−0.500000
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−4.00000	−0.648886
$39$	0	0
$40$	4.00000	0.632456
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−2.00000	−0.301511
$45$	−12.0000	−1.78885
$46$	8.00000	1.17954
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	0	0
$50$	11.0000	1.55563
$51$	0	0
$52$	6.00000	0.832050
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	−8.00000	−1.07872
$56$	0	0
$57$	0	0
$58$	−8.00000	−1.05045
$59$	−2.00000	−0.260378	−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000	−0.260378	−0.130189	+	0.991489i	$0.541558\pi$
$60$	0	0
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	0.125000
$65$	24.0000	2.97683
$66$	0	0
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	−3.00000	−0.353553
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	−4.00000	−0.458831
$77$	0	0
$78$	0	0
$79$	16.0000	1.80014	0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000	1.80014	0.900070	+	0.435745i	$0.143515\pi$
$80$	4.00000	0.447214
$81$	9.00000	1.00000
$82$	1.00000	0.110432
$83$	2.00000	0.219529	0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000	0.219529	0.109764	+	0.993958i	$0.464990\pi$
$84$	0	0
$85$	24.0000	2.60317
$86$	−8.00000	−0.862662
$87$	0	0
$88$	−2.00000	−0.213201
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	−12.0000	−1.26491
$91$	0	0
$92$	8.00000	0.834058
$93$	0	0
$94$	0	0
$95$	−16.0000	−1.64157
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	0	0
$99$	6.00000	0.603023
$100$	11.0000	1.10000
$101$	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
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	6.00000	0.588348
$105$	0	0
$106$	0	0
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	−8.00000	−0.762770
$111$	0	0
$112$	0	0
$113$	−18.0000	−1.69330	−0.846649	−	0.532152i	$-0.821383\pi$
$113$	−18.0000	−1.69330	−0.846649	+	0.532152i	$0.821383\pi$
$114$	0	0
$115$	32.0000	2.98402
$116$	−8.00000	−0.742781
$117$	−18.0000	−1.66410
$118$	−2.00000	−0.184115
$119$	0	0
$120$	0	0
$121$	−7.00000	−0.636364
$122$	8.00000	0.724286
$123$	0	0
$124$	0	0
$125$	24.0000	2.14663
$126$	0	0
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	24.0000	2.10494
$131$	−10.0000	−0.873704	−0.436852	−	0.899533i	$-0.643907\pi$
$131$	−10.0000	−0.873704	−0.436852	+	0.899533i	$0.643907\pi$
$132$	0	0
$133$	0	0
$134$	10.0000	0.863868
$135$	0	0
$136$	6.00000	0.514496
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	−14.0000	−1.18746	−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000	−1.18746	−0.593732	+	0.804663i	$0.702346\pi$
$140$	0	0
$141$	0	0
$142$	−12.0000	−1.00702
$143$	−12.0000	−1.00349
$144$	−3.00000	−0.250000
$145$	−32.0000	−2.65746
$146$	−10.0000	−0.827606
$147$	0	0
$148$	−2.00000	−0.164399
$149$	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	$-0.605538\pi$
$151$	−8.00000	−0.651031	−0.325515	+	0.945537i	$0.605538\pi$
$152$	−4.00000	−0.324443
$153$	−18.0000	−1.45521
$154$	0	0
$155$	0	0
$156$	0	0
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	16.0000	1.27289
$159$	0	0
$160$	4.00000	0.316228
$161$	0	0
$162$	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	$0.715557\pi$
$164$	1.00000	0.0780869
$165$	0	0
$166$	2.00000	0.155230
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	24.0000	1.84072
$171$	12.0000	0.917663
$172$	−8.00000	−0.609994
$173$	4.00000	0.304114	0.152057	−	0.988372i	$-0.451410\pi$
$173$	4.00000	0.304114	0.152057	+	0.988372i	$0.451410\pi$
$174$	0	0
$175$	0	0
$176$	−2.00000	−0.150756
$177$	0	0
$178$	10.0000	0.749532
$179$	−10.0000	−0.747435	−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000	−0.747435	−0.373718	+	0.927543i	$0.621917\pi$
$180$	−12.0000	−0.894427
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	0	0
$183$	0	0
$184$	8.00000	0.589768
$185$	−8.00000	−0.588172
$186$	0	0
$187$	−12.0000	−0.877527
$188$	0	0
$189$	0	0
$190$	−16.0000	−1.16076
$191$	−20.0000	−1.44715	−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000	−1.44715	−0.723575	+	0.690246i	$0.757502\pi$
$192$	0	0
$193$	6.00000	0.431889	0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000	0.431889	0.215945	+	0.976406i	$0.430717\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	0	0
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	6.00000	0.426401
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	11.0000	0.777817
$201$	0	0
$202$	10.0000	0.703598
$203$	0	0
$204$	0	0
$205$	4.00000	0.279372
$206$	−4.00000	−0.278693
$207$	−24.0000	−1.66812
$208$	6.00000	0.416025
$209$	8.00000	0.553372
$210$	0	0
$211$	−6.00000	−0.413057	−0.206529	−	0.978441i	$-0.566217\pi$
$211$	−6.00000	−0.413057	−0.206529	+	0.978441i	$0.566217\pi$
$212$	0	0
$213$	0	0
$214$	12.0000	0.820303
$215$	−32.0000	−2.18238
$216$	0	0
$217$	0	0
$218$	4.00000	0.270914
$219$	0	0
$220$	−8.00000	−0.539360
$221$	36.0000	2.42162
$222$	0	0
$223$	24.0000	1.60716	0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000	1.60716	0.803579	+	0.595198i	$0.202926\pi$
$224$	0	0
$225$	−33.0000	−2.20000
$226$	−18.0000	−1.19734
$227$	20.0000	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$228$	0	0
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	32.0000	2.11002
$231$	0	0
$232$	−8.00000	−0.525226
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	−18.0000	−1.17670
$235$	0	0
$236$	−2.00000	−0.130189
$237$	0	0
$238$	0	0
$239$	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	$0.395619\pi$
$242$	−7.00000	−0.449977
$243$	0	0
$244$	8.00000	0.512148
$245$	0	0
$246$	0	0
$247$	−24.0000	−1.52708
$248$	0	0
$249$	0	0
$250$	24.0000	1.51789
$251$	−6.00000	−0.378717	−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000	−0.378717	−0.189358	+	0.981908i	$0.560641\pi$
$252$	0	0
$253$	−16.0000	−1.00591
$254$	−16.0000	−1.00393
$255$	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
$260$	24.0000	1.48842
$261$	24.0000	1.48556
$262$	−10.0000	−0.617802
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	10.0000	0.610847
$269$	16.0000	0.975537	0.487769	−	0.872973i	$-0.337811\pi$
$269$	16.0000	0.975537	0.487769	+	0.872973i	$0.337811\pi$
$270$	0	0
$271$	4.00000	0.242983	0.121491	−	0.992592i	$-0.461232\pi$
$271$	4.00000	0.242983	0.121491	+	0.992592i	$0.461232\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	6.00000	0.362473
$275$	−22.0000	−1.32665
$276$	0	0
$277$	2.00000	0.120168	0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000	0.120168	0.0600842	+	0.998193i	$0.480863\pi$
$278$	−14.0000	−0.839664
$279$	0	0
$280$	0	0
$281$	−22.0000	−1.31241	−0.656205	−	0.754583i	$-0.727839\pi$
$281$	−22.0000	−1.31241	−0.656205	+	0.754583i	$0.727839\pi$
$282$	0	0
$283$	6.00000	0.356663	0.178331	−	0.983970i	$-0.442930\pi$
$283$	6.00000	0.356663	0.178331	+	0.983970i	$0.442930\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	−12.0000	−0.709575
$287$	0	0
$288$	−3.00000	−0.176777
$289$	19.0000	1.11765
$290$	−32.0000	−1.87910
$291$	0	0
$292$	−10.0000	−0.585206
$293$	−26.0000	−1.51894	−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000	−1.51894	−0.759468	+	0.650545i	$0.774541\pi$
$294$	0	0
$295$	−8.00000	−0.465778
$296$	−2.00000	−0.116248
$297$	0	0
$298$	0	0
$299$	48.0000	2.77591
$300$	0	0
$301$	0	0
$302$	−8.00000	−0.460348
$303$	0	0
$304$	−4.00000	−0.229416
$305$	32.0000	1.83231
$306$	−18.0000	−1.02899
$307$	−26.0000	−1.48390	−0.741949	−	0.670456i	$-0.766098\pi$
$307$	−26.0000	−1.48390	−0.741949	+	0.670456i	$0.766098\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	0	0
$313$	−26.0000	−1.46961	−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000	−1.46961	−0.734803	+	0.678280i	$0.762726\pi$
$314$	14.0000	0.790066
$315$	0	0
$316$	16.0000	0.900070
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	16.0000	0.895828
$320$	4.00000	0.223607
$321$	0	0
$322$	0	0
$323$	−24.0000	−1.33540
$324$	9.00000	0.500000
$325$	66.0000	3.66102
$326$	−16.0000	−0.886158
$327$	0	0
$328$	1.00000	0.0552158
$329$	0	0
$330$	0	0
$331$	−14.0000	−0.769510	−0.384755	−	0.923019i	$-0.625714\pi$
$331$	−14.0000	−0.769510	−0.384755	+	0.923019i	$0.625714\pi$
$332$	2.00000	0.109764
$333$	6.00000	0.328798
$334$	0	0
$335$	40.0000	2.18543
$336$	0	0
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	23.0000	1.25104
$339$	0	0
$340$	24.0000	1.30158
$341$	0	0
$342$	12.0000	0.648886
$343$	0	0
$344$	−8.00000	−0.431331
$345$	0	0
$346$	4.00000	0.215041
$347$	6.00000	0.322097	0.161048	−	0.986947i	$-0.448512\pi$
$347$	6.00000	0.322097	0.161048	+	0.986947i	$0.448512\pi$
$348$	0	0
$349$	16.0000	0.856460	0.428230	−	0.903670i	$-0.359137\pi$
$349$	16.0000	0.856460	0.428230	+	0.903670i	$0.359137\pi$
$350$	0	0
$351$	0	0
$352$	−2.00000	−0.106600
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	0	0
$355$	−48.0000	−2.54758
$356$	10.0000	0.529999
$357$	0	0
$358$	−10.0000	−0.528516
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	−12.0000	−0.632456
$361$	−3.00000	−0.157895
$362$	2.00000	0.105118
$363$	0	0
$364$	0	0
$365$	−40.0000	−2.09370
$366$	0	0
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	8.00000	0.417029
$369$	−3.00000	−0.156174
$370$	−8.00000	−0.415900
$371$	0	0
$372$	0	0
$373$	−18.0000	−0.932005	−0.466002	−	0.884783i	$-0.654306\pi$
$373$	−18.0000	−0.932005	−0.466002	+	0.884783i	$0.654306\pi$
$374$	−12.0000	−0.620505
$375$	0	0
$376$	0	0
$377$	−48.0000	−2.47213
$378$	0	0
$379$	28.0000	1.43826	0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000	1.43826	0.719132	+	0.694874i	$0.244540\pi$
$380$	−16.0000	−0.820783
$381$	0	0
$382$	−20.0000	−1.02329
$383$	16.0000	0.817562	0.408781	−	0.912633i	$-0.365954\pi$
$383$	16.0000	0.817562	0.408781	+	0.912633i	$0.365954\pi$
$384$	0	0
$385$	0	0
$386$	6.00000	0.305392
$387$	24.0000	1.21999
$388$	2.00000	0.101535
$389$	−26.0000	−1.31825	−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000	−1.31825	−0.659126	+	0.752032i	$0.729074\pi$
$390$	0	0
$391$	48.0000	2.42746
$392$	0	0
$393$	0	0
$394$	−6.00000	−0.302276
$395$	64.0000	3.22019
$396$	6.00000	0.301511
$397$	34.0000	1.70641	0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000	1.70641	0.853206	+	0.521575i	$0.174655\pi$
$398$	0	0
$399$	0	0
$400$	11.0000	0.550000
$401$	−34.0000	−1.69788	−0.848939	−	0.528490i	$-0.822758\pi$
$401$	−34.0000	−1.69788	−0.848939	+	0.528490i	$0.822758\pi$
$402$	0	0
$403$	0	0
$404$	10.0000	0.497519
$405$	36.0000	1.78885
$406$	0	0
$407$	4.00000	0.198273
$408$	0	0
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	4.00000	0.197546
$411$	0	0
$412$	−4.00000	−0.197066
$413$	0	0
$414$	−24.0000	−1.17954
$415$	8.00000	0.392705
$416$	6.00000	0.294174
$417$	0	0
$418$	8.00000	0.391293
$419$	−34.0000	−1.66101	−0.830504	−	0.557012i	$-0.811948\pi$
$419$	−34.0000	−1.66101	−0.830504	+	0.557012i	$0.811948\pi$
$420$	0	0
$421$	−28.0000	−1.36464	−0.682318	−	0.731055i	$-0.739028\pi$
$421$	−28.0000	−1.36464	−0.682318	+	0.731055i	$0.739028\pi$
$422$	−6.00000	−0.292075
$423$	0	0
$424$	0	0
$425$	66.0000	3.20147
$426$	0	0
$427$	0	0
$428$	12.0000	0.580042
$429$	0	0
$430$	−32.0000	−1.54318
$431$	32.0000	1.54139	0.770693	−	0.637207i	$-0.219910\pi$
$431$	32.0000	1.54139	0.770693	+	0.637207i	$0.219910\pi$
$432$	0	0
$433$	−30.0000	−1.44171	−0.720854	−	0.693087i	$-0.756250\pi$
$433$	−30.0000	−1.44171	−0.720854	+	0.693087i	$0.756250\pi$
$434$	0	0
$435$	0	0
$436$	4.00000	0.191565
$437$	−32.0000	−1.53077
$438$	0	0
$439$	32.0000	1.52728	0.763638	−	0.645644i	$-0.223411\pi$
$439$	32.0000	1.52728	0.763638	+	0.645644i	$0.223411\pi$
$440$	−8.00000	−0.381385
$441$	0	0
$442$	36.0000	1.71235
$443$	32.0000	1.52037	0.760183	−	0.649709i	$-0.225109\pi$
$443$	32.0000	1.52037	0.760183	+	0.649709i	$0.225109\pi$
$444$	0	0
$445$	40.0000	1.89618
$446$	24.0000	1.13643
$447$	0	0
$448$	0	0
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	−33.0000	−1.55563
$451$	−2.00000	−0.0941763
$452$	−18.0000	−0.846649
$453$	0	0
$454$	20.0000	0.938647
$455$	0	0
$456$	0	0
$457$	6.00000	0.280668	0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000	0.280668	0.140334	+	0.990104i	$0.455182\pi$
$458$	10.0000	0.467269
$459$	0	0
$460$	32.0000	1.49201
$461$	36.0000	1.67669	0.838344	−	0.545142i	$-0.183524\pi$
$461$	36.0000	1.67669	0.838344	+	0.545142i	$0.183524\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−8.00000	−0.371391
$465$	0	0
$466$	10.0000	0.463241
$467$	−18.0000	−0.832941	−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000	−0.832941	−0.416470	+	0.909149i	$0.636733\pi$
$468$	−18.0000	−0.832050
$469$	0	0
$470$	0	0
$471$	0	0
$472$	−2.00000	−0.0920575
$473$	16.0000	0.735681
$474$	0	0
$475$	−44.0000	−2.01886
$476$	0	0
$477$	0	0
$478$	24.0000	1.09773
$479$	−32.0000	−1.46212	−0.731059	−	0.682315i	$-0.760973\pi$
$479$	−32.0000	−1.46212	−0.731059	+	0.682315i	$0.760973\pi$
$480$	0	0
$481$	−12.0000	−0.547153
$482$	10.0000	0.455488
$483$	0	0
$484$	−7.00000	−0.318182
$485$	8.00000	0.363261
$486$	0	0
$487$	0	0		−	1.00000i	$-0.5\pi$
$487$	0	0			1.00000i	$0.5\pi$
$488$	8.00000	0.362143
$489$	0	0
$490$	0	0
$491$	−8.00000	−0.361035	−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000	−0.361035	−0.180517	+	0.983572i	$0.557777\pi$
$492$	0	0
$493$	−48.0000	−2.16181
$494$	−24.0000	−1.07981
$495$	24.0000	1.07872
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−26.0000	−1.16392	−0.581960	−	0.813217i	$-0.697714\pi$
$499$	−26.0000	−1.16392	−0.581960	+	0.813217i	$0.697714\pi$
$500$	24.0000	1.07331
$501$	0	0
$502$	−6.00000	−0.267793
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	40.0000	1.77998
$506$	−16.0000	−0.711287
$507$	0	0
$508$	−16.0000	−0.709885
$509$	18.0000	0.797836	0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000	0.797836	0.398918	+	0.916987i	$0.369386\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	−6.00000	−0.264649
$515$	−16.0000	−0.705044
$516$	0	0
$517$	0	0
$518$	0	0
$519$	0	0
$520$	24.0000	1.05247
$521$	14.0000	0.613351	0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000	0.613351	0.306676	+	0.951814i	$0.400783\pi$
$522$	24.0000	1.05045
$523$	−38.0000	−1.66162	−0.830812	−	0.556553i	$-0.812124\pi$
$523$	−38.0000	−1.66162	−0.830812	+	0.556553i	$0.812124\pi$
$524$	−10.0000	−0.436852
$525$	0	0
$526$	−16.0000	−0.697633
$527$	0	0
$528$	0	0
$529$	41.0000	1.78261
$530$	0	0
$531$	6.00000	0.260378
$532$	0	0
$533$	6.00000	0.259889
$534$	0	0
$535$	48.0000	2.07522
$536$	10.0000	0.431934
$537$	0	0
$538$	16.0000	0.689809
$539$	0	0
$540$	0	0
$541$	22.0000	0.945854	0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000	0.945854	0.472927	+	0.881102i	$0.343197\pi$
$542$	4.00000	0.171815
$543$	0	0
$544$	6.00000	0.257248
$545$	16.0000	0.685365
$546$	0	0
$547$	2.00000	0.0855138	0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000	0.0855138	0.0427569	+	0.999086i	$0.486386\pi$
$548$	6.00000	0.256307
$549$	−24.0000	−1.02430
$550$	−22.0000	−0.938083
$551$	32.0000	1.36325
$552$	0	0
$553$	0	0
$554$	2.00000	0.0849719
$555$	0	0
$556$	−14.0000	−0.593732
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	0	0
$559$	−48.0000	−2.03018
$560$	0	0
$561$	0	0
$562$	−22.0000	−0.928014
$563$	−28.0000	−1.18006	−0.590030	−	0.807382i	$-0.700884\pi$
$563$	−28.0000	−1.18006	−0.590030	+	0.807382i	$0.700884\pi$
$564$	0	0
$565$	−72.0000	−3.02906
$566$	6.00000	0.252199
$567$	0	0
$568$	−12.0000	−0.503509
$569$	−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
$571$	−14.0000	−0.585882	−0.292941	−	0.956131i	$-0.594634\pi$
$571$	−14.0000	−0.585882	−0.292941	+	0.956131i	$0.594634\pi$
$572$	−12.0000	−0.501745
$573$	0	0
$574$	0	0
$575$	88.0000	3.66985
$576$	−3.00000	−0.125000
$577$	14.0000	0.582828	0.291414	−	0.956597i	$-0.405874\pi$
$577$	14.0000	0.582828	0.291414	+	0.956597i	$0.405874\pi$
$578$	19.0000	0.790296
$579$	0	0
$580$	−32.0000	−1.32873
$581$	0	0
$582$	0	0
$583$	0	0
$584$	−10.0000	−0.413803
$585$	−72.0000	−2.97683
$586$	−26.0000	−1.07405
$587$	0	0		−	1.00000i	$-0.5\pi$
$587$	0	0			1.00000i	$0.5\pi$
$588$	0	0
$589$	0	0
$590$	−8.00000	−0.329355
$591$	0	0
$592$	−2.00000	−0.0821995
$593$	−38.0000	−1.56047	−0.780236	−	0.625485i	$-0.784901\pi$
$593$	−38.0000	−1.56047	−0.780236	+	0.625485i	$0.784901\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	48.0000	1.96287
$599$	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
$601$	6.00000	0.244745	0.122373	−	0.992484i	$-0.460950\pi$
$601$	6.00000	0.244745	0.122373	+	0.992484i	$0.460950\pi$
$602$	0	0
$603$	−30.0000	−1.22169
$604$	−8.00000	−0.325515
$605$	−28.0000	−1.13836
$606$	0	0
$607$	−44.0000	−1.78590	−0.892952	−	0.450151i	$-0.851370\pi$
$607$	−44.0000	−1.78590	−0.892952	+	0.450151i	$0.851370\pi$
$608$	−4.00000	−0.162221
$609$	0	0
$610$	32.0000	1.29564
$611$	0	0
$612$	−18.0000	−0.727607
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	−26.0000	−1.04927
$615$	0	0
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	0	0
$619$	−18.0000	−0.723481	−0.361741	−	0.932279i	$-0.617817\pi$
$619$	−18.0000	−0.723481	−0.361741	+	0.932279i	$0.617817\pi$
$620$	0	0
$621$	0	0
$622$	−24.0000	−0.962312
$623$	0	0
$624$	0	0
$625$	41.0000	1.64000
$626$	−26.0000	−1.03917
$627$	0	0
$628$	14.0000	0.558661
$629$	−12.0000	−0.478471
$630$	0	0
$631$	−24.0000	−0.955425	−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000	−0.955425	−0.477712	+	0.878516i	$0.658534\pi$
$632$	16.0000	0.636446
$633$	0	0
$634$	0	0
$635$	−64.0000	−2.53976
$636$	0	0
$637$	0	0
$638$	16.0000	0.633446
$639$	36.0000	1.42414
$640$	4.00000	0.158114
$641$	−42.0000	−1.65890	−0.829450	−	0.558581i	$-0.811346\pi$
$641$	−42.0000	−1.65890	−0.829450	+	0.558581i	$0.811346\pi$
$642$	0	0
$643$	−20.0000	−0.788723	−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000	−0.788723	−0.394362	+	0.918955i	$0.629034\pi$
$644$	0	0
$645$	0	0
$646$	−24.0000	−0.944267
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	9.00000	0.353553
$649$	4.00000	0.157014
$650$	66.0000	2.58873
$651$	0	0
$652$	−16.0000	−0.626608
$653$	−24.0000	−0.939193	−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000	−0.939193	−0.469596	+	0.882881i	$0.655601\pi$
$654$	0	0
$655$	−40.0000	−1.56293
$656$	1.00000	0.0390434
$657$	30.0000	1.17041
$658$	0	0
$659$	26.0000	1.01282	0.506408	−	0.862294i	$-0.330973\pi$
$659$	26.0000	1.01282	0.506408	+	0.862294i	$0.330973\pi$
$660$	0	0
$661$	20.0000	0.777910	0.388955	−	0.921257i	$-0.372836\pi$
$661$	20.0000	0.777910	0.388955	+	0.921257i	$0.372836\pi$
$662$	−14.0000	−0.544125
$663$	0	0
$664$	2.00000	0.0776151
$665$	0	0
$666$	6.00000	0.232495
$667$	−64.0000	−2.47809
$668$	0	0
$669$	0	0
$670$	40.0000	1.54533
$671$	−16.0000	−0.617673
$672$	0	0
$673$	−18.0000	−0.693849	−0.346925	−	0.937893i	$-0.612774\pi$
$673$	−18.0000	−0.693849	−0.346925	+	0.937893i	$0.612774\pi$
$674$	2.00000	0.0770371
$675$	0	0
$676$	23.0000	0.884615
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	0	0
$680$	24.0000	0.920358
$681$	0	0
$682$	0	0
$683$	−26.0000	−0.994862	−0.497431	−	0.867503i	$-0.665723\pi$
$683$	−26.0000	−0.994862	−0.497431	+	0.867503i	$0.665723\pi$
$684$	12.0000	0.458831
$685$	24.0000	0.916993
$686$	0	0
$687$	0	0
$688$	−8.00000	−0.304997
$689$	0	0
$690$	0	0
$691$	32.0000	1.21734	0.608669	−	0.793424i	$-0.291704\pi$
$691$	32.0000	1.21734	0.608669	+	0.793424i	$0.291704\pi$
$692$	4.00000	0.152057
$693$	0	0
$694$	6.00000	0.227757
$695$	−56.0000	−2.12420
$696$	0	0
$697$	6.00000	0.227266
$698$	16.0000	0.605609
$699$	0	0
$700$	0	0
$701$	46.0000	1.73740	0.868698	−	0.495342i	$-0.164957\pi$
$701$	46.0000	1.73740	0.868698	+	0.495342i	$0.164957\pi$
$702$	0	0
$703$	8.00000	0.301726
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	−18.0000	−0.677439
$707$	0	0
$708$	0	0
$709$	48.0000	1.80268	0.901339	−	0.433114i	$-0.142585\pi$
$709$	48.0000	1.80268	0.901339	+	0.433114i	$0.142585\pi$
$710$	−48.0000	−1.80141
$711$	−48.0000	−1.80014
$712$	10.0000	0.374766
$713$	0	0
$714$	0	0
$715$	−48.0000	−1.79510
$716$	−10.0000	−0.373718
$717$	0	0
$718$	0	0
$719$	−16.0000	−0.596699	−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000	−0.596699	−0.298350	+	0.954457i	$0.596436\pi$
$720$	−12.0000	−0.447214
$721$	0	0
$722$	−3.00000	−0.111648
$723$	0	0
$724$	2.00000	0.0743294
$725$	−88.0000	−3.26824
$726$	0	0
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	−40.0000	−1.48047
$731$	−48.0000	−1.77534
$732$	0	0
$733$	−40.0000	−1.47743	−0.738717	−	0.674016i	$-0.764568\pi$
$733$	−40.0000	−1.47743	−0.738717	+	0.674016i	$0.764568\pi$
$734$	−28.0000	−1.03350
$735$	0	0
$736$	8.00000	0.294884
$737$	−20.0000	−0.736709
$738$	−3.00000	−0.110432
$739$	−8.00000	−0.294285	−0.147142	−	0.989115i	$-0.547008\pi$
$739$	−8.00000	−0.294285	−0.147142	+	0.989115i	$0.547008\pi$
$740$	−8.00000	−0.294086
$741$	0	0
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	0	0
$745$	0	0
$746$	−18.0000	−0.659027
$747$	−6.00000	−0.219529
$748$	−12.0000	−0.438763
$749$	0	0
$750$	0	0
$751$	48.0000	1.75154	0.875772	−	0.482724i	$-0.160353\pi$
$751$	48.0000	1.75154	0.875772	+	0.482724i	$0.160353\pi$
$752$	0	0
$753$	0	0
$754$	−48.0000	−1.74806
$755$	−32.0000	−1.16460
$756$	0	0
$757$	−32.0000	−1.16306	−0.581530	−	0.813525i	$-0.697546\pi$
$757$	−32.0000	−1.16306	−0.581530	+	0.813525i	$0.697546\pi$
$758$	28.0000	1.01701
$759$	0	0
$760$	−16.0000	−0.580381
$761$	−6.00000	−0.217500	−0.108750	−	0.994069i	$-0.534685\pi$
$761$	−6.00000	−0.217500	−0.108750	+	0.994069i	$0.534685\pi$
$762$	0	0
$763$	0	0
$764$	−20.0000	−0.723575
$765$	−72.0000	−2.60317
$766$	16.0000	0.578103
$767$	−12.0000	−0.433295
$768$	0	0
$769$	26.0000	0.937584	0.468792	−	0.883309i	$-0.344689\pi$
$769$	26.0000	0.937584	0.468792	+	0.883309i	$0.344689\pi$
$770$	0	0
$771$	0	0
$772$	6.00000	0.215945
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	24.0000	0.862662
$775$	0	0
$776$	2.00000	0.0717958
$777$	0	0
$778$	−26.0000	−0.932145
$779$	−4.00000	−0.143315
$780$	0	0
$781$	24.0000	0.858788
$782$	48.0000	1.71648
$783$	0	0
$784$	0	0
$785$	56.0000	1.99873
$786$	0	0
$787$	−26.0000	−0.926800	−0.463400	−	0.886149i	$-0.653371\pi$
$787$	−26.0000	−0.926800	−0.463400	+	0.886149i	$0.653371\pi$
$788$	−6.00000	−0.213741
$789$	0	0
$790$	64.0000	2.27702
$791$	0	0
$792$	6.00000	0.213201
$793$	48.0000	1.70453
$794$	34.0000	1.20661
$795$	0	0
$796$	0	0
$797$	−48.0000	−1.70025	−0.850124	−	0.526583i	$-0.823473\pi$
$797$	−48.0000	−1.70025	−0.850124	+	0.526583i	$0.823473\pi$
$798$	0	0
$799$	0	0
$800$	11.0000	0.388909
$801$	−30.0000	−1.06000
$802$	−34.0000	−1.20058
$803$	20.0000	0.705785
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	10.0000	0.351799
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	36.0000	1.26491
$811$	30.0000	1.05344	0.526721	−	0.850038i	$-0.323421\pi$
$811$	30.0000	1.05344	0.526721	+	0.850038i	$0.323421\pi$
$812$	0	0
$813$	0	0
$814$	4.00000	0.140200
$815$	−64.0000	−2.24182
$816$	0	0
$817$	32.0000	1.11954
$818$	−14.0000	−0.489499
$819$	0	0
$820$	4.00000	0.139686
$821$	−22.0000	−0.767805	−0.383903	−	0.923374i	$-0.625420\pi$
$821$	−22.0000	−0.767805	−0.383903	+	0.923374i	$0.625420\pi$
$822$	0	0
$823$	36.0000	1.25488	0.627441	−	0.778664i	$-0.284103\pi$
$823$	36.0000	1.25488	0.627441	+	0.778664i	$0.284103\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	0	0
$827$	30.0000	1.04320	0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000	1.04320	0.521601	+	0.853189i	$0.325335\pi$
$828$	−24.0000	−0.834058
$829$	28.0000	0.972480	0.486240	−	0.873825i	$-0.338368\pi$
$829$	28.0000	0.972480	0.486240	+	0.873825i	$0.338368\pi$
$830$	8.00000	0.277684
$831$	0	0
$832$	6.00000	0.208013
$833$	0	0
$834$	0	0
$835$	0	0
$836$	8.00000	0.276686
$837$	0	0
$838$	−34.0000	−1.17451
$839$	−8.00000	−0.276191	−0.138095	−	0.990419i	$-0.544098\pi$
$839$	−8.00000	−0.276191	−0.138095	+	0.990419i	$0.544098\pi$
$840$	0	0
$841$	35.0000	1.20690
$842$	−28.0000	−0.964944
$843$	0	0
$844$	−6.00000	−0.206529
$845$	92.0000	3.16490
$846$	0	0
$847$	0	0
$848$	0	0
$849$	0	0
$850$	66.0000	2.26378
$851$	−16.0000	−0.548473
$852$	0	0
$853$	−12.0000	−0.410872	−0.205436	−	0.978671i	$-0.565861\pi$
$853$	−12.0000	−0.410872	−0.205436	+	0.978671i	$0.565861\pi$
$854$	0	0
$855$	48.0000	1.64157
$856$	12.0000	0.410152
$857$	26.0000	0.888143	0.444072	−	0.895991i	$-0.353534\pi$
$857$	26.0000	0.888143	0.444072	+	0.895991i	$0.353534\pi$
$858$	0	0
$859$	26.0000	0.887109	0.443554	−	0.896248i	$-0.353717\pi$
$859$	26.0000	0.887109	0.443554	+	0.896248i	$0.353717\pi$
$860$	−32.0000	−1.09119
$861$	0	0
$862$	32.0000	1.08992
$863$	16.0000	0.544646	0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000	0.544646	0.272323	+	0.962206i	$0.412208\pi$
$864$	0	0
$865$	16.0000	0.544016
$866$	−30.0000	−1.01944
$867$	0	0
$868$	0	0
$869$	−32.0000	−1.08553
$870$	0	0
$871$	60.0000	2.03302
$872$	4.00000	0.135457
$873$	−6.00000	−0.203069
$874$	−32.0000	−1.08242
$875$	0	0
$876$	0	0
$877$	34.0000	1.14810	0.574049	−	0.818821i	$-0.305372\pi$
$877$	34.0000	1.14810	0.574049	+	0.818821i	$0.305372\pi$
$878$	32.0000	1.07995
$879$	0	0
$880$	−8.00000	−0.269680
$881$	−42.0000	−1.41502	−0.707508	−	0.706705i	$-0.750181\pi$
$881$	−42.0000	−1.41502	−0.707508	+	0.706705i	$0.750181\pi$
$882$	0	0
$883$	−2.00000	−0.0673054	−0.0336527	−	0.999434i	$-0.510714\pi$
$883$	−2.00000	−0.0673054	−0.0336527	+	0.999434i	$0.510714\pi$
$884$	36.0000	1.21081
$885$	0	0
$886$	32.0000	1.07506
$887$	40.0000	1.34307	0.671534	−	0.740973i	$-0.265636\pi$
$887$	40.0000	1.34307	0.671534	+	0.740973i	$0.265636\pi$
$888$	0	0
$889$	0	0
$890$	40.0000	1.34080
$891$	−18.0000	−0.603023
$892$	24.0000	0.803579
$893$	0	0
$894$	0	0
$895$	−40.0000	−1.33705
$896$	0	0
$897$	0	0
$898$	−6.00000	−0.200223
$899$	0	0
$900$	−33.0000	−1.10000
$901$	0	0
$902$	−2.00000	−0.0665927
$903$	0	0
$904$	−18.0000	−0.598671
$905$	8.00000	0.265929
$906$	0	0
$907$	−8.00000	−0.265636	−0.132818	−	0.991140i	$-0.542403\pi$
$907$	−8.00000	−0.265636	−0.132818	+	0.991140i	$0.542403\pi$
$908$	20.0000	0.663723
$909$	−30.0000	−0.995037
$910$	0	0
$911$	−40.0000	−1.32526	−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000	−1.32526	−0.662630	+	0.748947i	$0.730560\pi$
$912$	0	0
$913$	−4.00000	−0.132381
$914$	6.00000	0.198462
$915$	0	0
$916$	10.0000	0.330409
$917$	0	0
$918$	0	0
$919$	−36.0000	−1.18753	−0.593765	−	0.804638i	$-0.702359\pi$
$919$	−36.0000	−1.18753	−0.593765	+	0.804638i	$0.702359\pi$
$920$	32.0000	1.05501
$921$	0	0
$922$	36.0000	1.18560
$923$	−72.0000	−2.36991
$924$	0	0
$925$	−22.0000	−0.723356
$926$	16.0000	0.525793
$927$	12.0000	0.394132
$928$	−8.00000	−0.262613
$929$	2.00000	0.0656179	0.0328089	−	0.999462i	$-0.489555\pi$
$929$	2.00000	0.0656179	0.0328089	+	0.999462i	$0.489555\pi$
$930$	0	0
$931$	0	0
$932$	10.0000	0.327561
$933$	0	0
$934$	−18.0000	−0.588978
$935$	−48.0000	−1.56977
$936$	−18.0000	−0.588348
$937$	−22.0000	−0.718709	−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000	−0.718709	−0.359354	+	0.933201i	$0.617003\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	24.0000	0.782378	0.391189	−	0.920310i	$-0.372064\pi$
$941$	24.0000	0.782378	0.391189	+	0.920310i	$0.372064\pi$
$942$	0	0
$943$	8.00000	0.260516
$944$	−2.00000	−0.0650945
$945$	0	0
$946$	16.0000	0.520205
$947$	−52.0000	−1.68977	−0.844886	−	0.534946i	$-0.820332\pi$
$947$	−52.0000	−1.68977	−0.844886	+	0.534946i	$0.820332\pi$
$948$	0	0
$949$	−60.0000	−1.94768
$950$	−44.0000	−1.42755
$951$	0	0
$952$	0	0
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	0	0
$955$	−80.0000	−2.58874
$956$	24.0000	0.776215
$957$	0	0
$958$	−32.0000	−1.03387
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	−12.0000	−0.386896
$963$	−36.0000	−1.16008
$964$	10.0000	0.322078
$965$	24.0000	0.772587
$966$	0	0
$967$	−44.0000	−1.41494	−0.707472	−	0.706741i	$-0.750165\pi$
$967$	−44.0000	−1.41494	−0.707472	+	0.706741i	$0.750165\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	8.00000	0.256865
$971$	20.0000	0.641831	0.320915	−	0.947108i	$-0.396010\pi$
$971$	20.0000	0.641831	0.320915	+	0.947108i	$0.396010\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	0	0
$976$	8.00000	0.256074
$977$	−42.0000	−1.34370	−0.671850	−	0.740688i	$-0.734500\pi$
$977$	−42.0000	−1.34370	−0.671850	+	0.740688i	$0.734500\pi$
$978$	0	0
$979$	−20.0000	−0.639203
$980$	0	0
$981$	−12.0000	−0.383131
$982$	−8.00000	−0.255290
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	0	0
$985$	−24.0000	−0.764704
$986$	−48.0000	−1.52863
$987$	0	0
$988$	−24.0000	−0.763542
$989$	−64.0000	−2.03508
$990$	24.0000	0.762770
$991$	4.00000	0.127064	0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000	0.127064	0.0635321	+	0.997980i	$0.479763\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−22.0000	−0.696747	−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000	−0.696747	−0.348373	+	0.937356i	$0.613266\pi$
$998$	−26.0000	−0.823016
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.n.1.1		1
7.6	odd	2		574.2.a.j.1.1	✓	1
21.20	even	2		5166.2.a.t.1.1		1
28.27	even	2		4592.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.a.j.1.1	✓	1	7.6	odd	2
4018.2.a.n.1.1		1	1.1	even	1	trivial
4592.2.a.f.1.1		1	28.27	even	2
5166.2.a.t.1.1		1	21.20	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:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

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