LMFDB - Embedded newform 2601.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2601,2,Mod(1,2601)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2601, 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("2601.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2601 = 3^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2601.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:	$20.7690895657$
Analytic rank:	$1$
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	$\chi$	$=$	2601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{7} +3.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} -1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{7} +3.00000 q^{8} -2.00000 q^{10} -6.00000 q^{11} +1.00000 q^{13} +1.00000 q^{14} -1.00000 q^{16} +5.00000 q^{19} -2.00000 q^{20} +6.00000 q^{22} +2.00000 q^{23} -1.00000 q^{25} -1.00000 q^{26} +1.00000 q^{28} +6.00000 q^{29} -7.00000 q^{31} -5.00000 q^{32} -2.00000 q^{35} -7.00000 q^{37} -5.00000 q^{38} +6.00000 q^{40} +6.00000 q^{41} +7.00000 q^{43} +6.00000 q^{44} -2.00000 q^{46} -12.0000 q^{47} -6.00000 q^{49} +1.00000 q^{50} -1.00000 q^{52} +12.0000 q^{53} -12.0000 q^{55} -3.00000 q^{56} -6.00000 q^{58} -6.00000 q^{59} -11.0000 q^{61} +7.00000 q^{62} +7.00000 q^{64} +2.00000 q^{65} -11.0000 q^{67} +2.00000 q^{70} -2.00000 q^{71} +6.00000 q^{73} +7.00000 q^{74} -5.00000 q^{76} +6.00000 q^{77} -2.00000 q^{80} -6.00000 q^{82} +2.00000 q^{83} -7.00000 q^{86} -18.0000 q^{88} +16.0000 q^{89} -1.00000 q^{91} -2.00000 q^{92} +12.0000 q^{94} +10.0000 q^{95} -17.0000 q^{97} +6.00000 q^{98} +O(q^{100})$

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	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	0	0
$3$	0	0
$4$	−1.00000	−0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	0	0
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	3.00000	1.06066
$9$	0	0
$10$	−2.00000	−0.632456
$11$	−6.00000	−1.80907	−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000	−1.80907	−0.904534	+	0.426401i	$0.859781\pi$
$12$	0	0
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	−1.00000	−0.250000
$17$	0	0
$17$	0	0
$18$	0	0
$19$	5.00000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	5.00000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	−2.00000	−0.447214
$21$	0	0
$22$	6.00000	1.27920
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	−1.00000	−0.196116
$27$	0	0
$28$	1.00000	0.188982
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−5.00000	−0.883883
$33$	0	0
$34$	0	0
$35$	−2.00000	−0.338062
$36$	0	0
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	−5.00000	−0.811107
$39$	0	0
$40$	6.00000	0.948683
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	0	0
$43$	7.00000	1.06749	0.533745	−	0.845645i	$-0.320784\pi$
$43$	7.00000	1.06749	0.533745	+	0.845645i	$0.320784\pi$
$44$	6.00000	0.904534
$45$	0	0
$46$	−2.00000	−0.294884
$47$	−12.0000	−1.75038	−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000	−1.75038	−0.875190	+	0.483779i	$0.839264\pi$
$48$	0	0
$49$	−6.00000	−0.857143
$50$	1.00000	0.141421
$51$	0	0
$52$	−1.00000	−0.138675
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	0	0
$55$	−12.0000	−1.61808
$56$	−3.00000	−0.400892
$57$	0	0
$58$	−6.00000	−0.787839
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	0	0
$61$	−11.0000	−1.40841	−0.704203	−	0.709999i	$-0.748695\pi$
$61$	−11.0000	−1.40841	−0.704203	+	0.709999i	$0.748695\pi$
$62$	7.00000	0.889001
$63$	0	0
$64$	7.00000	0.875000
$65$	2.00000	0.248069
$66$	0	0
$67$	−11.0000	−1.34386	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	−11.0000	−1.34386	−0.671932	+	0.740613i	$0.734535\pi$
$68$	0	0
$69$	0	0
$70$	2.00000	0.239046
$71$	−2.00000	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$72$	0	0
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	7.00000	0.813733
$75$	0	0
$76$	−5.00000	−0.573539
$77$	6.00000	0.683763
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	−2.00000	−0.223607
$81$	0	0
$82$	−6.00000	−0.662589
$83$	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
$85$	0	0
$86$	−7.00000	−0.754829
$87$	0	0
$88$	−18.0000	−1.91881
$89$	16.0000	1.69600	0.847998	−	0.529999i	$-0.177808\pi$
$89$	16.0000	1.69600	0.847998	+	0.529999i	$0.177808\pi$
$90$	0	0
$91$	−1.00000	−0.104828
$92$	−2.00000	−0.208514
$93$	0	0
$94$	12.0000	1.23771
$95$	10.0000	1.02598
$96$	0	0
$97$	−17.0000	−1.72609	−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000	−1.72609	−0.863044	+	0.505128i	$0.831445\pi$
$98$	6.00000	0.606092
$99$	0	0
$100$	1.00000	0.100000
$101$	−4.00000	−0.398015	−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000	−0.398015	−0.199007	+	0.979998i	$0.563772\pi$
$102$	0	0
$103$	−7.00000	−0.689730	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000	−0.689730	−0.344865	+	0.938652i	$0.612075\pi$
$104$	3.00000	0.294174
$105$	0	0
$106$	−12.0000	−1.16554
$107$	16.0000	1.54678	0.773389	−	0.633932i	$-0.218560\pi$
$107$	16.0000	1.54678	0.773389	+	0.633932i	$0.218560\pi$
$108$	0	0
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	12.0000	1.14416
$111$	0	0
$112$	1.00000	0.0944911
$113$	−4.00000	−0.376288	−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000	−0.376288	−0.188144	+	0.982141i	$0.560247\pi$
$114$	0	0
$115$	4.00000	0.373002
$116$	−6.00000	−0.557086
$117$	0	0
$118$	6.00000	0.552345
$119$	0	0
$120$	0	0
$121$	25.0000	2.27273
$122$	11.0000	0.995893
$123$	0	0
$124$	7.00000	0.628619
$125$	−12.0000	−1.07331
$126$	0	0
$127$	5.00000	0.443678	0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000	0.443678	0.221839	+	0.975083i	$0.428794\pi$
$128$	3.00000	0.265165
$129$	0	0
$130$	−2.00000	−0.175412
$131$	−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
$133$	−5.00000	−0.433555
$134$	11.0000	0.950255
$135$	0	0
$136$	0	0
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	−13.0000	−1.10265	−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000	−1.10265	−0.551323	+	0.834292i	$0.685877\pi$
$140$	2.00000	0.169031
$141$	0	0
$142$	2.00000	0.167836
$143$	−6.00000	−0.501745
$144$	0	0
$145$	12.0000	0.996546
$146$	−6.00000	−0.496564
$147$	0	0
$148$	7.00000	0.575396
$149$	14.0000	1.14692	0.573462	−	0.819232i	$-0.305600\pi$
$149$	14.0000	1.14692	0.573462	+	0.819232i	$0.305600\pi$
$150$	0	0
$151$	5.00000	0.406894	0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000	0.406894	0.203447	+	0.979086i	$0.434786\pi$
$152$	15.0000	1.21666
$153$	0	0
$154$	−6.00000	−0.483494
$155$	−14.0000	−1.12451
$156$	0	0
$157$	−17.0000	−1.35675	−0.678374	−	0.734717i	$-0.737315\pi$
$157$	−17.0000	−1.35675	−0.678374	+	0.734717i	$0.737315\pi$
$158$	0	0
$159$	0	0
$160$	−10.0000	−0.790569
$161$	−2.00000	−0.157622
$162$	0	0
$163$	−12.0000	−0.939913	−0.469956	−	0.882690i	$-0.655730\pi$
$163$	−12.0000	−0.939913	−0.469956	+	0.882690i	$0.655730\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	−2.00000	−0.155230
$167$	−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
$171$	0	0
$172$	−7.00000	−0.533745
$173$	−16.0000	−1.21646	−0.608229	−	0.793762i	$-0.708120\pi$
$173$	−16.0000	−1.21646	−0.608229	+	0.793762i	$0.708120\pi$
$174$	0	0
$175$	1.00000	0.0755929
$176$	6.00000	0.452267
$177$	0	0
$178$	−16.0000	−1.19925
$179$	−18.0000	−1.34538	−0.672692	−	0.739923i	$-0.734862\pi$
$179$	−18.0000	−1.34538	−0.672692	+	0.739923i	$0.734862\pi$
$180$	0	0
$181$	−13.0000	−0.966282	−0.483141	−	0.875542i	$-0.660504\pi$
$181$	−13.0000	−0.966282	−0.483141	+	0.875542i	$0.660504\pi$
$182$	1.00000	0.0741249
$183$	0	0
$184$	6.00000	0.442326
$185$	−14.0000	−1.02930
$186$	0	0
$187$	0	0
$188$	12.0000	0.875190
$189$	0	0
$190$	−10.0000	−0.725476
$191$	−10.0000	−0.723575	−0.361787	−	0.932261i	$-0.617833\pi$
$191$	−10.0000	−0.723575	−0.361787	+	0.932261i	$0.617833\pi$
$192$	0	0
$193$	1.00000	0.0719816	0.0359908	−	0.999352i	$-0.488541\pi$
$193$	1.00000	0.0719816	0.0359908	+	0.999352i	$0.488541\pi$
$194$	17.0000	1.22053
$195$	0	0
$196$	6.00000	0.428571
$197$	−12.0000	−0.854965	−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000	−0.854965	−0.427482	+	0.904024i	$0.640599\pi$
$198$	0	0
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	−3.00000	−0.212132
$201$	0	0
$202$	4.00000	0.281439
$203$	−6.00000	−0.421117
$204$	0	0
$205$	12.0000	0.838116
$206$	7.00000	0.487713
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	−30.0000	−2.07514
$210$	0	0
$211$	1.00000	0.0688428	0.0344214	−	0.999407i	$-0.489041\pi$
$211$	1.00000	0.0688428	0.0344214	+	0.999407i	$0.489041\pi$
$212$	−12.0000	−0.824163
$213$	0	0
$214$	−16.0000	−1.09374
$215$	14.0000	0.954792
$216$	0	0
$217$	7.00000	0.475191
$218$	6.00000	0.406371
$219$	0	0
$220$	12.0000	0.809040
$221$	0	0
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	5.00000	0.334077
$225$	0	0
$226$	4.00000	0.266076
$227$	−18.0000	−1.19470	−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000	−1.19470	−0.597351	+	0.801980i	$0.703780\pi$
$228$	0	0
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	18.0000	1.18176
$233$	12.0000	0.786146	0.393073	−	0.919507i	$-0.371412\pi$
$233$	12.0000	0.786146	0.393073	+	0.919507i	$0.371412\pi$
$234$	0	0
$235$	−24.0000	−1.56559
$236$	6.00000	0.390567
$237$	0	0
$238$	0	0
$239$	20.0000	1.29369	0.646846	−	0.762620i	$-0.276088\pi$
$239$	20.0000	1.29369	0.646846	+	0.762620i	$0.276088\pi$
$240$	0	0
$241$	18.0000	1.15948	0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000	1.15948	0.579741	+	0.814801i	$0.303154\pi$
$242$	−25.0000	−1.60706
$243$	0	0
$244$	11.0000	0.704203
$245$	−12.0000	−0.766652
$246$	0	0
$247$	5.00000	0.318142
$248$	−21.0000	−1.33350
$249$	0	0
$250$	12.0000	0.758947
$251$	−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
$253$	−12.0000	−0.754434
$254$	−5.00000	−0.313728
$255$	0	0
$256$	−17.0000	−1.06250
$257$	−24.0000	−1.49708	−0.748539	−	0.663090i	$-0.769245\pi$
$257$	−24.0000	−1.49708	−0.748539	+	0.663090i	$0.769245\pi$
$258$	0	0
$259$	7.00000	0.434959
$260$	−2.00000	−0.124035
$261$	0	0
$262$	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
$265$	24.0000	1.47431
$266$	5.00000	0.306570
$267$	0	0
$268$	11.0000	0.671932
$269$	14.0000	0.853595	0.426798	−	0.904347i	$-0.359642\pi$
$269$	14.0000	0.853595	0.426798	+	0.904347i	$0.359642\pi$
$270$	0	0
$271$	−13.0000	−0.789694	−0.394847	−	0.918747i	$-0.629202\pi$
$271$	−13.0000	−0.789694	−0.394847	+	0.918747i	$0.629202\pi$
$272$	0	0
$273$	0	0
$274$	6.00000	0.362473
$275$	6.00000	0.361814
$276$	0	0
$277$	−5.00000	−0.300421	−0.150210	−	0.988654i	$-0.547995\pi$
$277$	−5.00000	−0.300421	−0.150210	+	0.988654i	$0.547995\pi$
$278$	13.0000	0.779688
$279$	0	0
$280$	−6.00000	−0.358569
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	0	0
$283$	−11.0000	−0.653882	−0.326941	−	0.945045i	$-0.606018\pi$
$283$	−11.0000	−0.653882	−0.326941	+	0.945045i	$0.606018\pi$
$284$	2.00000	0.118678
$285$	0	0
$286$	6.00000	0.354787
$287$	−6.00000	−0.354169
$288$	0	0
$289$	0	0
$290$	−12.0000	−0.704664
$291$	0	0
$292$	−6.00000	−0.351123
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	−12.0000	−0.698667
$296$	−21.0000	−1.22060
$297$	0	0
$298$	−14.0000	−0.810998
$299$	2.00000	0.115663
$300$	0	0
$301$	−7.00000	−0.403473
$302$	−5.00000	−0.287718
$303$	0	0
$304$	−5.00000	−0.286770
$305$	−22.0000	−1.25972
$306$	0	0
$307$	12.0000	0.684876	0.342438	−	0.939540i	$-0.388747\pi$
$307$	12.0000	0.684876	0.342438	+	0.939540i	$0.388747\pi$
$308$	−6.00000	−0.341882
$309$	0	0
$310$	14.0000	0.795147
$311$	−4.00000	−0.226819	−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000	−0.226819	−0.113410	+	0.993548i	$0.536177\pi$
$312$	0	0
$313$	1.00000	0.0565233	0.0282617	−	0.999601i	$-0.491003\pi$
$313$	1.00000	0.0565233	0.0282617	+	0.999601i	$0.491003\pi$
$314$	17.0000	0.959366
$315$	0	0
$316$	0	0
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	0	0
$319$	−36.0000	−2.01561
$320$	14.0000	0.782624
$321$	0	0
$322$	2.00000	0.111456
$323$	0	0
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	12.0000	0.664619
$327$	0	0
$328$	18.0000	0.993884
$329$	12.0000	0.661581
$330$	0	0
$331$	19.0000	1.04433	0.522167	−	0.852843i	$-0.325124\pi$
$331$	19.0000	1.04433	0.522167	+	0.852843i	$0.325124\pi$
$332$	−2.00000	−0.109764
$333$	0	0
$334$	8.00000	0.437741
$335$	−22.0000	−1.20199
$336$	0	0
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	12.0000	0.652714
$339$	0	0
$340$	0	0
$341$	42.0000	2.27443
$342$	0	0
$343$	13.0000	0.701934
$344$	21.0000	1.13224
$345$	0	0
$346$	16.0000	0.860165
$347$	−26.0000	−1.39575	−0.697877	−	0.716218i	$-0.745872\pi$
$347$	−26.0000	−1.39575	−0.697877	+	0.716218i	$0.745872\pi$
$348$	0	0
$349$	−30.0000	−1.60586	−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000	−1.60586	−0.802932	+	0.596071i	$0.796728\pi$
$350$	−1.00000	−0.0534522
$351$	0	0
$352$	30.0000	1.59901
$353$	24.0000	1.27739	0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000	1.27739	0.638696	+	0.769460i	$0.279474\pi$
$354$	0	0
$355$	−4.00000	−0.212298
$356$	−16.0000	−0.847998
$357$	0	0
$358$	18.0000	0.951330
$359$	−12.0000	−0.633336	−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000	−0.633336	−0.316668	+	0.948536i	$0.602564\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	13.0000	0.683265
$363$	0	0
$364$	1.00000	0.0524142
$365$	12.0000	0.628109
$366$	0	0
$367$	−7.00000	−0.365397	−0.182699	−	0.983169i	$-0.558483\pi$
$367$	−7.00000	−0.365397	−0.182699	+	0.983169i	$0.558483\pi$
$368$	−2.00000	−0.104257
$369$	0	0
$370$	14.0000	0.727825
$371$	−12.0000	−0.623009
$372$	0	0
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	0	0
$375$	0	0
$376$	−36.0000	−1.85656
$377$	6.00000	0.309016
$378$	0	0
$379$	−25.0000	−1.28416	−0.642082	−	0.766636i	$-0.721929\pi$
$379$	−25.0000	−1.28416	−0.642082	+	0.766636i	$0.721929\pi$
$380$	−10.0000	−0.512989
$381$	0	0
$382$	10.0000	0.511645
$383$	18.0000	0.919757	0.459879	−	0.887982i	$-0.347893\pi$
$383$	18.0000	0.919757	0.459879	+	0.887982i	$0.347893\pi$
$384$	0	0
$385$	12.0000	0.611577
$386$	−1.00000	−0.0508987
$387$	0	0
$388$	17.0000	0.863044
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	0	0
$391$	0	0
$392$	−18.0000	−0.909137
$393$	0	0
$394$	12.0000	0.604551
$395$	0	0
$396$	0	0
$397$	−30.0000	−1.50566	−0.752828	−	0.658217i	$-0.771311\pi$
$397$	−30.0000	−1.50566	−0.752828	+	0.658217i	$0.771311\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	1.00000	0.0500000
$401$	2.00000	0.0998752	0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000	0.0998752	0.0499376	+	0.998752i	$0.484098\pi$
$402$	0	0
$403$	−7.00000	−0.348695
$404$	4.00000	0.199007
$405$	0	0
$406$	6.00000	0.297775
$407$	42.0000	2.08186
$408$	0	0
$409$	5.00000	0.247234	0.123617	−	0.992330i	$-0.460551\pi$
$409$	5.00000	0.247234	0.123617	+	0.992330i	$0.460551\pi$
$410$	−12.0000	−0.592638
$411$	0	0
$412$	7.00000	0.344865
$413$	6.00000	0.295241
$414$	0	0
$415$	4.00000	0.196352
$416$	−5.00000	−0.245145
$417$	0	0
$418$	30.0000	1.46735
$419$	−2.00000	−0.0977064	−0.0488532	−	0.998806i	$-0.515557\pi$
$419$	−2.00000	−0.0977064	−0.0488532	+	0.998806i	$0.515557\pi$
$420$	0	0
$421$	13.0000	0.633581	0.316791	−	0.948495i	$-0.397395\pi$
$421$	13.0000	0.633581	0.316791	+	0.948495i	$0.397395\pi$
$422$	−1.00000	−0.0486792
$423$	0	0
$424$	36.0000	1.74831
$425$	0	0
$426$	0	0
$427$	11.0000	0.532327
$428$	−16.0000	−0.773389
$429$	0	0
$430$	−14.0000	−0.675140
$431$	−12.0000	−0.578020	−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000	−0.578020	−0.289010	+	0.957326i	$0.593326\pi$
$432$	0	0
$433$	−1.00000	−0.0480569	−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000	−0.0480569	−0.0240285	+	0.999711i	$0.507649\pi$
$434$	−7.00000	−0.336011
$435$	0	0
$436$	6.00000	0.287348
$437$	10.0000	0.478365
$438$	0	0
$439$	−1.00000	−0.0477274	−0.0238637	−	0.999715i	$-0.507597\pi$
$439$	−1.00000	−0.0477274	−0.0238637	+	0.999715i	$0.507597\pi$
$440$	−36.0000	−1.71623
$441$	0	0
$442$	0	0
$443$	−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
$445$	32.0000	1.51695
$446$	0	0
$447$	0	0
$448$	−7.00000	−0.330719
$449$	20.0000	0.943858	0.471929	−	0.881636i	$-0.343558\pi$
$449$	20.0000	0.943858	0.471929	+	0.881636i	$0.343558\pi$
$450$	0	0
$451$	−36.0000	−1.69517
$452$	4.00000	0.188144
$453$	0	0
$454$	18.0000	0.844782
$455$	−2.00000	−0.0937614
$456$	0	0
$457$	18.0000	0.842004	0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000	0.842004	0.421002	+	0.907060i	$0.361678\pi$
$458$	−6.00000	−0.280362
$459$	0	0
$460$	−4.00000	−0.186501
$461$	40.0000	1.86299	0.931493	−	0.363760i	$-0.118507\pi$
$461$	40.0000	1.86299	0.931493	+	0.363760i	$0.118507\pi$
$462$	0	0
$463$	41.0000	1.90543	0.952716	−	0.303863i	$-0.0982765\pi$
$463$	41.0000	1.90543	0.952716	+	0.303863i	$0.0982765\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−12.0000	−0.555889
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	0	0
$469$	11.0000	0.507933
$470$	24.0000	1.10704
$471$	0	0
$472$	−18.0000	−0.828517
$473$	−42.0000	−1.93116
$474$	0	0
$475$	−5.00000	−0.229416
$476$	0	0
$477$	0	0
$478$	−20.0000	−0.914779
$479$	6.00000	0.274147	0.137073	−	0.990561i	$-0.456230\pi$
$479$	6.00000	0.274147	0.137073	+	0.990561i	$0.456230\pi$
$480$	0	0
$481$	−7.00000	−0.319173
$482$	−18.0000	−0.819878
$483$	0	0
$484$	−25.0000	−1.13636
$485$	−34.0000	−1.54386
$486$	0	0
$487$	−5.00000	−0.226572	−0.113286	−	0.993562i	$-0.536138\pi$
$487$	−5.00000	−0.226572	−0.113286	+	0.993562i	$0.536138\pi$
$488$	−33.0000	−1.49384
$489$	0	0
$490$	12.0000	0.542105
$491$	−4.00000	−0.180517	−0.0902587	−	0.995918i	$-0.528769\pi$
$491$	−4.00000	−0.180517	−0.0902587	+	0.995918i	$0.528769\pi$
$492$	0	0
$493$	0	0
$494$	−5.00000	−0.224961
$495$	0	0
$496$	7.00000	0.314309
$497$	2.00000	0.0897123
$498$	0	0
$499$	13.0000	0.581960	0.290980	−	0.956729i	$-0.406019\pi$
$499$	13.0000	0.581960	0.290980	+	0.956729i	$0.406019\pi$
$500$	12.0000	0.536656
$501$	0	0
$502$	6.00000	0.267793
$503$	−6.00000	−0.267527	−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000	−0.267527	−0.133763	+	0.991013i	$0.542706\pi$
$504$	0	0
$505$	−8.00000	−0.355995
$506$	12.0000	0.533465
$507$	0	0
$508$	−5.00000	−0.221839
$509$	28.0000	1.24108	0.620539	−	0.784176i	$-0.286914\pi$
$509$	28.0000	1.24108	0.620539	+	0.784176i	$0.286914\pi$
$510$	0	0
$511$	−6.00000	−0.265424
$512$	11.0000	0.486136
$513$	0	0
$514$	24.0000	1.05859
$515$	−14.0000	−0.616914
$516$	0	0
$517$	72.0000	3.16656
$518$	−7.00000	−0.307562
$519$	0	0
$520$	6.00000	0.263117
$521$	−14.0000	−0.613351	−0.306676	−	0.951814i	$-0.599217\pi$
$521$	−14.0000	−0.613351	−0.306676	+	0.951814i	$0.599217\pi$
$522$	0	0
$523$	−36.0000	−1.57417	−0.787085	−	0.616844i	$-0.788411\pi$
$523$	−36.0000	−1.57417	−0.787085	+	0.616844i	$0.788411\pi$
$524$	10.0000	0.436852
$525$	0	0
$526$	16.0000	0.697633
$527$	0	0
$528$	0	0
$529$	−19.0000	−0.826087
$530$	−24.0000	−1.04249
$531$	0	0
$532$	5.00000	0.216777
$533$	6.00000	0.259889
$534$	0	0
$535$	32.0000	1.38348
$536$	−33.0000	−1.42538
$537$	0	0
$538$	−14.0000	−0.603583
$539$	36.0000	1.55063
$540$	0	0
$541$	30.0000	1.28980	0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$542$	13.0000	0.558398
$543$	0	0
$544$	0	0
$545$	−12.0000	−0.514024
$546$	0	0
$547$	41.0000	1.75303	0.876517	−	0.481371i	$-0.159861\pi$
$547$	41.0000	1.75303	0.876517	+	0.481371i	$0.159861\pi$
$548$	6.00000	0.256307
$549$	0	0
$550$	−6.00000	−0.255841
$551$	30.0000	1.27804
$552$	0	0
$553$	0	0
$554$	5.00000	0.212430
$555$	0	0
$556$	13.0000	0.551323
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	0	0
$559$	7.00000	0.296068
$560$	2.00000	0.0845154
$561$	0	0
$562$	−18.0000	−0.759284
$563$	32.0000	1.34864	0.674320	−	0.738440i	$-0.264437\pi$
$563$	32.0000	1.34864	0.674320	+	0.738440i	$0.264437\pi$
$564$	0	0
$565$	−8.00000	−0.336563
$566$	11.0000	0.462364
$567$	0	0
$568$	−6.00000	−0.251754
$569$	−20.0000	−0.838444	−0.419222	−	0.907884i	$-0.637697\pi$
$569$	−20.0000	−0.838444	−0.419222	+	0.907884i	$0.637697\pi$
$570$	0	0
$571$	23.0000	0.962520	0.481260	−	0.876578i	$-0.340179\pi$
$571$	23.0000	0.962520	0.481260	+	0.876578i	$0.340179\pi$
$572$	6.00000	0.250873
$573$	0	0
$574$	6.00000	0.250435
$575$	−2.00000	−0.0834058
$576$	0	0
$577$	−5.00000	−0.208153	−0.104076	−	0.994569i	$-0.533189\pi$
$577$	−5.00000	−0.208153	−0.104076	+	0.994569i	$0.533189\pi$
$578$	0	0
$579$	0	0
$580$	−12.0000	−0.498273
$581$	−2.00000	−0.0829740
$582$	0	0
$583$	−72.0000	−2.98194
$584$	18.0000	0.744845
$585$	0	0
$586$	0	0
$587$	34.0000	1.40333	0.701665	−	0.712507i	$-0.252440\pi$
$587$	34.0000	1.40333	0.701665	+	0.712507i	$0.252440\pi$
$588$	0	0
$589$	−35.0000	−1.44215
$590$	12.0000	0.494032
$591$	0	0
$592$	7.00000	0.287698
$593$	−6.00000	−0.246390	−0.123195	−	0.992382i	$-0.539314\pi$
$593$	−6.00000	−0.246390	−0.123195	+	0.992382i	$0.539314\pi$
$594$	0	0
$595$	0	0
$596$	−14.0000	−0.573462
$597$	0	0
$598$	−2.00000	−0.0817861
$599$	6.00000	0.245153	0.122577	−	0.992459i	$-0.460884\pi$
$599$	6.00000	0.245153	0.122577	+	0.992459i	$0.460884\pi$
$600$	0	0
$601$	−19.0000	−0.775026	−0.387513	−	0.921864i	$-0.626666\pi$
$601$	−19.0000	−0.775026	−0.387513	+	0.921864i	$0.626666\pi$
$602$	7.00000	0.285299
$603$	0	0
$604$	−5.00000	−0.203447
$605$	50.0000	2.03279
$606$	0	0
$607$	31.0000	1.25825	0.629126	−	0.777304i	$-0.283413\pi$
$607$	31.0000	1.25825	0.629126	+	0.777304i	$0.283413\pi$
$608$	−25.0000	−1.01388
$609$	0	0
$610$	22.0000	0.890754
$611$	−12.0000	−0.485468
$612$	0	0
$613$	19.0000	0.767403	0.383701	−	0.923457i	$-0.374649\pi$
$613$	19.0000	0.767403	0.383701	+	0.923457i	$0.374649\pi$
$614$	−12.0000	−0.484281
$615$	0	0
$616$	18.0000	0.725241
$617$	24.0000	0.966204	0.483102	−	0.875564i	$-0.339510\pi$
$617$	24.0000	0.966204	0.483102	+	0.875564i	$0.339510\pi$
$618$	0	0
$619$	−24.0000	−0.964641	−0.482321	−	0.875995i	$-0.660206\pi$
$619$	−24.0000	−0.964641	−0.482321	+	0.875995i	$0.660206\pi$
$620$	14.0000	0.562254
$621$	0	0
$622$	4.00000	0.160385
$623$	−16.0000	−0.641026
$624$	0	0
$625$	−19.0000	−0.760000
$626$	−1.00000	−0.0399680
$627$	0	0
$628$	17.0000	0.678374
$629$	0	0
$630$	0	0
$631$	−17.0000	−0.676759	−0.338380	−	0.941010i	$-0.609879\pi$
$631$	−17.0000	−0.676759	−0.338380	+	0.941010i	$0.609879\pi$
$632$	0	0
$633$	0	0
$634$	2.00000	0.0794301
$635$	10.0000	0.396838
$636$	0	0
$637$	−6.00000	−0.237729
$638$	36.0000	1.42525
$639$	0	0
$640$	6.00000	0.237171
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	0	0
$643$	−17.0000	−0.670415	−0.335207	−	0.942144i	$-0.608806\pi$
$643$	−17.0000	−0.670415	−0.335207	+	0.942144i	$0.608806\pi$
$644$	2.00000	0.0788110
$645$	0	0
$646$	0	0
$647$	−4.00000	−0.157256	−0.0786281	−	0.996904i	$-0.525054\pi$
$647$	−4.00000	−0.157256	−0.0786281	+	0.996904i	$0.525054\pi$
$648$	0	0
$649$	36.0000	1.41312
$650$	1.00000	0.0392232
$651$	0	0
$652$	12.0000	0.469956
$653$	−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
$655$	−20.0000	−0.781465
$656$	−6.00000	−0.234261
$657$	0	0
$658$	−12.0000	−0.467809
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	0	0
$661$	−25.0000	−0.972387	−0.486194	−	0.873851i	$-0.661615\pi$
$661$	−25.0000	−0.972387	−0.486194	+	0.873851i	$0.661615\pi$
$662$	−19.0000	−0.738456
$663$	0	0
$664$	6.00000	0.232845
$665$	−10.0000	−0.387783
$666$	0	0
$667$	12.0000	0.464642
$668$	8.00000	0.309529
$669$	0	0
$670$	22.0000	0.849934
$671$	66.0000	2.54790
$672$	0	0
$673$	1.00000	0.0385472	0.0192736	−	0.999814i	$-0.493865\pi$
$673$	1.00000	0.0385472	0.0192736	+	0.999814i	$0.493865\pi$
$674$	−14.0000	−0.539260
$675$	0	0
$676$	12.0000	0.461538
$677$	42.0000	1.61419	0.807096	−	0.590421i	$-0.201038\pi$
$677$	42.0000	1.61419	0.807096	+	0.590421i	$0.201038\pi$
$678$	0	0
$679$	17.0000	0.652400
$680$	0	0
$681$	0	0
$682$	−42.0000	−1.60826
$683$	28.0000	1.07139	0.535695	−	0.844411i	$-0.320050\pi$
$683$	28.0000	1.07139	0.535695	+	0.844411i	$0.320050\pi$
$684$	0	0
$685$	−12.0000	−0.458496
$686$	−13.0000	−0.496342
$687$	0	0
$688$	−7.00000	−0.266872
$689$	12.0000	0.457164
$690$	0	0
$691$	35.0000	1.33146	0.665731	−	0.746191i	$-0.268120\pi$
$691$	35.0000	1.33146	0.665731	+	0.746191i	$0.268120\pi$
$692$	16.0000	0.608229
$693$	0	0
$694$	26.0000	0.986947
$695$	−26.0000	−0.986236
$696$	0	0
$697$	0	0
$698$	30.0000	1.13552
$699$	0	0
$700$	−1.00000	−0.0377964
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	0	0
$703$	−35.0000	−1.32005
$704$	−42.0000	−1.58293
$705$	0	0
$706$	−24.0000	−0.903252
$707$	4.00000	0.150435
$708$	0	0
$709$	−41.0000	−1.53979	−0.769894	−	0.638172i	$-0.779691\pi$
$709$	−41.0000	−1.53979	−0.769894	+	0.638172i	$0.779691\pi$
$710$	4.00000	0.150117
$711$	0	0
$712$	48.0000	1.79888
$713$	−14.0000	−0.524304
$714$	0	0
$715$	−12.0000	−0.448775
$716$	18.0000	0.672692
$717$	0	0
$718$	12.0000	0.447836
$719$	32.0000	1.19340	0.596699	−	0.802465i	$-0.296479\pi$
$719$	32.0000	1.19340	0.596699	+	0.802465i	$0.296479\pi$
$720$	0	0
$721$	7.00000	0.260694
$722$	−6.00000	−0.223297
$723$	0	0
$724$	13.0000	0.483141
$725$	−6.00000	−0.222834
$726$	0	0
$727$	13.0000	0.482143	0.241072	−	0.970507i	$-0.422501\pi$
$727$	13.0000	0.482143	0.241072	+	0.970507i	$0.422501\pi$
$728$	−3.00000	−0.111187
$729$	0	0
$730$	−12.0000	−0.444140
$731$	0	0
$732$	0	0
$733$	37.0000	1.36663	0.683313	−	0.730125i	$-0.260538\pi$
$733$	37.0000	1.36663	0.683313	+	0.730125i	$0.260538\pi$
$734$	7.00000	0.258375
$735$	0	0
$736$	−10.0000	−0.368605
$737$	66.0000	2.43114
$738$	0	0
$739$	19.0000	0.698926	0.349463	−	0.936950i	$-0.386364\pi$
$739$	19.0000	0.698926	0.349463	+	0.936950i	$0.386364\pi$
$740$	14.0000	0.514650
$741$	0	0
$742$	12.0000	0.440534
$743$	30.0000	1.10059	0.550297	−	0.834969i	$-0.314515\pi$
$743$	30.0000	1.10059	0.550297	+	0.834969i	$0.314515\pi$
$744$	0	0
$745$	28.0000	1.02584
$746$	6.00000	0.219676
$747$	0	0
$748$	0	0
$749$	−16.0000	−0.584627
$750$	0	0
$751$	−17.0000	−0.620339	−0.310169	−	0.950681i	$-0.600386\pi$
$751$	−17.0000	−0.620339	−0.310169	+	0.950681i	$0.600386\pi$
$752$	12.0000	0.437595
$753$	0	0
$754$	−6.00000	−0.218507
$755$	10.0000	0.363937
$756$	0	0
$757$	13.0000	0.472493	0.236247	−	0.971693i	$-0.424083\pi$
$757$	13.0000	0.472493	0.236247	+	0.971693i	$0.424083\pi$
$758$	25.0000	0.908041
$759$	0	0
$760$	30.0000	1.08821
$761$	−34.0000	−1.23250	−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000	−1.23250	−0.616250	+	0.787551i	$0.711349\pi$
$762$	0	0
$763$	6.00000	0.217215
$764$	10.0000	0.361787
$765$	0	0
$766$	−18.0000	−0.650366
$767$	−6.00000	−0.216647
$768$	0	0
$769$	22.0000	0.793340	0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000	0.793340	0.396670	+	0.917961i	$0.370166\pi$
$770$	−12.0000	−0.432450
$771$	0	0
$772$	−1.00000	−0.0359908
$773$	4.00000	0.143870	0.0719350	−	0.997409i	$-0.477083\pi$
$773$	4.00000	0.143870	0.0719350	+	0.997409i	$0.477083\pi$
$774$	0	0
$775$	7.00000	0.251447
$776$	−51.0000	−1.83079
$777$	0	0
$778$	−30.0000	−1.07555
$779$	30.0000	1.07486
$780$	0	0
$781$	12.0000	0.429394
$782$	0	0
$783$	0	0
$784$	6.00000	0.214286
$785$	−34.0000	−1.21351
$786$	0	0
$787$	35.0000	1.24762	0.623808	−	0.781578i	$-0.285585\pi$
$787$	35.0000	1.24762	0.623808	+	0.781578i	$0.285585\pi$
$788$	12.0000	0.427482
$789$	0	0
$790$	0	0
$791$	4.00000	0.142224
$792$	0	0
$793$	−11.0000	−0.390621
$794$	30.0000	1.06466
$795$	0	0
$796$	16.0000	0.567105
$797$	16.0000	0.566749	0.283375	−	0.959009i	$-0.408546\pi$
$797$	16.0000	0.566749	0.283375	+	0.959009i	$0.408546\pi$
$798$	0	0
$799$	0	0
$800$	5.00000	0.176777
$801$	0	0
$802$	−2.00000	−0.0706225
$803$	−36.0000	−1.27041
$804$	0	0
$805$	−4.00000	−0.140981
$806$	7.00000	0.246564
$807$	0	0
$808$	−12.0000	−0.422159
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	0	0
$811$	23.0000	0.807639	0.403820	−	0.914839i	$-0.367682\pi$
$811$	23.0000	0.807639	0.403820	+	0.914839i	$0.367682\pi$
$812$	6.00000	0.210559
$813$	0	0
$814$	−42.0000	−1.47210
$815$	−24.0000	−0.840683
$816$	0	0
$817$	35.0000	1.22449
$818$	−5.00000	−0.174821
$819$	0	0
$820$	−12.0000	−0.419058
$821$	−18.0000	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$822$	0	0
$823$	−11.0000	−0.383436	−0.191718	−	0.981450i	$-0.561406\pi$
$823$	−11.0000	−0.383436	−0.191718	+	0.981450i	$0.561406\pi$
$824$	−21.0000	−0.731570
$825$	0	0
$826$	−6.00000	−0.208767
$827$	18.0000	0.625921	0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000	0.625921	0.312961	+	0.949766i	$0.398679\pi$
$828$	0	0
$829$	17.0000	0.590434	0.295217	−	0.955430i	$-0.404608\pi$
$829$	17.0000	0.590434	0.295217	+	0.955430i	$0.404608\pi$
$830$	−4.00000	−0.138842
$831$	0	0
$832$	7.00000	0.242681
$833$	0	0
$834$	0	0
$835$	−16.0000	−0.553703
$836$	30.0000	1.03757
$837$	0	0
$838$	2.00000	0.0690889
$839$	−20.0000	−0.690477	−0.345238	−	0.938515i	$-0.612202\pi$
$839$	−20.0000	−0.690477	−0.345238	+	0.938515i	$0.612202\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−13.0000	−0.448010
$843$	0	0
$844$	−1.00000	−0.0344214
$845$	−24.0000	−0.825625
$846$	0	0
$847$	−25.0000	−0.859010
$848$	−12.0000	−0.412082
$849$	0	0
$850$	0	0
$851$	−14.0000	−0.479914
$852$	0	0
$853$	13.0000	0.445112	0.222556	−	0.974920i	$-0.428560\pi$
$853$	13.0000	0.445112	0.222556	+	0.974920i	$0.428560\pi$
$854$	−11.0000	−0.376412
$855$	0	0
$856$	48.0000	1.64061
$857$	32.0000	1.09310	0.546550	−	0.837427i	$-0.315941\pi$
$857$	32.0000	1.09310	0.546550	+	0.837427i	$0.315941\pi$
$858$	0	0
$859$	−11.0000	−0.375315	−0.187658	−	0.982235i	$-0.560090\pi$
$859$	−11.0000	−0.375315	−0.187658	+	0.982235i	$0.560090\pi$
$860$	−14.0000	−0.477396
$861$	0	0
$862$	12.0000	0.408722
$863$	4.00000	0.136162	0.0680808	−	0.997680i	$-0.478312\pi$
$863$	4.00000	0.136162	0.0680808	+	0.997680i	$0.478312\pi$
$864$	0	0
$865$	−32.0000	−1.08803
$866$	1.00000	0.0339814
$867$	0	0
$868$	−7.00000	−0.237595
$869$	0	0
$870$	0	0
$871$	−11.0000	−0.372721
$872$	−18.0000	−0.609557
$873$	0	0
$874$	−10.0000	−0.338255
$875$	12.0000	0.405674
$876$	0	0
$877$	54.0000	1.82345	0.911725	−	0.410801i	$-0.134751\pi$
$877$	54.0000	1.82345	0.911725	+	0.410801i	$0.134751\pi$
$878$	1.00000	0.0337484
$879$	0	0
$880$	12.0000	0.404520
$881$	−32.0000	−1.07811	−0.539054	−	0.842271i	$-0.681218\pi$
$881$	−32.0000	−1.07811	−0.539054	+	0.842271i	$0.681218\pi$
$882$	0	0
$883$	−36.0000	−1.21150	−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000	−1.21150	−0.605748	+	0.795656i	$0.707126\pi$
$884$	0	0
$885$	0	0
$886$	26.0000	0.873487
$887$	−48.0000	−1.61168	−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000	−1.61168	−0.805841	+	0.592132i	$0.798286\pi$
$888$	0	0
$889$	−5.00000	−0.167695
$890$	−32.0000	−1.07264
$891$	0	0
$892$	0	0
$893$	−60.0000	−2.00782
$894$	0	0
$895$	−36.0000	−1.20335
$896$	−3.00000	−0.100223
$897$	0	0
$898$	−20.0000	−0.667409
$899$	−42.0000	−1.40078
$900$	0	0
$901$	0	0
$902$	36.0000	1.19867
$903$	0	0
$904$	−12.0000	−0.399114
$905$	−26.0000	−0.864269
$906$	0	0
$907$	−11.0000	−0.365249	−0.182625	−	0.983183i	$-0.558459\pi$
$907$	−11.0000	−0.365249	−0.182625	+	0.983183i	$0.558459\pi$
$908$	18.0000	0.597351
$909$	0	0
$910$	2.00000	0.0662994
$911$	−50.0000	−1.65657	−0.828287	−	0.560304i	$-0.810684\pi$
$911$	−50.0000	−1.65657	−0.828287	+	0.560304i	$0.810684\pi$
$912$	0	0
$913$	−12.0000	−0.397142
$914$	−18.0000	−0.595387
$915$	0	0
$916$	−6.00000	−0.198246
$917$	10.0000	0.330229
$918$	0	0
$919$	0	0		−	1.00000i	$-0.5\pi$
$919$	0	0			1.00000i	$0.5\pi$
$920$	12.0000	0.395628
$921$	0	0
$922$	−40.0000	−1.31733
$923$	−2.00000	−0.0658308
$924$	0	0
$925$	7.00000	0.230159
$926$	−41.0000	−1.34734
$927$	0	0
$928$	−30.0000	−0.984798
$929$	12.0000	0.393707	0.196854	−	0.980433i	$-0.436928\pi$
$929$	12.0000	0.393707	0.196854	+	0.980433i	$0.436928\pi$
$930$	0	0
$931$	−30.0000	−0.983210
$932$	−12.0000	−0.393073
$933$	0	0
$934$	12.0000	0.392652
$935$	0	0
$936$	0	0
$937$	−17.0000	−0.555366	−0.277683	−	0.960673i	$-0.589566\pi$
$937$	−17.0000	−0.555366	−0.277683	+	0.960673i	$0.589566\pi$
$938$	−11.0000	−0.359163
$939$	0	0
$940$	24.0000	0.782794
$941$	−36.0000	−1.17357	−0.586783	−	0.809744i	$-0.699606\pi$
$941$	−36.0000	−1.17357	−0.586783	+	0.809744i	$0.699606\pi$
$942$	0	0
$943$	12.0000	0.390774
$944$	6.00000	0.195283
$945$	0	0
$946$	42.0000	1.36554
$947$	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
$949$	6.00000	0.194768
$950$	5.00000	0.162221
$951$	0	0
$952$	0	0
$953$	−34.0000	−1.10137	−0.550684	−	0.834714i	$-0.685633\pi$
$953$	−34.0000	−1.10137	−0.550684	+	0.834714i	$0.685633\pi$
$954$	0	0
$955$	−20.0000	−0.647185
$956$	−20.0000	−0.646846
$957$	0	0
$958$	−6.00000	−0.193851
$959$	6.00000	0.193750
$960$	0	0
$961$	18.0000	0.580645
$962$	7.00000	0.225689
$963$	0	0
$964$	−18.0000	−0.579741
$965$	2.00000	0.0643823
$966$	0	0
$967$	48.0000	1.54358	0.771788	−	0.635880i	$-0.219363\pi$
$967$	48.0000	1.54358	0.771788	+	0.635880i	$0.219363\pi$
$968$	75.0000	2.41059
$969$	0	0
$970$	34.0000	1.09167
$971$	0	0		−	1.00000i	$-0.5\pi$
$971$	0	0			1.00000i	$0.5\pi$
$972$	0	0
$973$	13.0000	0.416761
$974$	5.00000	0.160210
$975$	0	0
$976$	11.0000	0.352101
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	0	0
$979$	−96.0000	−3.06817
$980$	12.0000	0.383326
$981$	0	0
$982$	4.00000	0.127645
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	0	0
$985$	−24.0000	−0.764704
$986$	0	0
$987$	0	0
$988$	−5.00000	−0.159071
$989$	14.0000	0.445174
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	35.0000	1.11125
$993$	0	0
$994$	−2.00000	−0.0634361
$995$	−32.0000	−1.01447
$996$	0	0
$997$	29.0000	0.918439	0.459220	−	0.888323i	$-0.348129\pi$
$997$	29.0000	0.918439	0.459220	+	0.888323i	$0.348129\pi$
$998$	−13.0000	−0.411508
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.e.1.1	yes	1
3.2	odd	2		2601.2.a.h.1.1	yes	1
17.16	even	2		2601.2.a.d.1.1	✓	1
51.50	odd	2		2601.2.a.k.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2601.2.a.d.1.1	✓	1	17.16	even	2
2601.2.a.e.1.1	yes	1	1.1	even	1	trivial
2601.2.a.h.1.1	yes	1	3.2	odd	2
2601.2.a.k.1.1	yes	1	51.50	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:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2601.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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