LMFDB - Embedded newform 5054.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} -1.00000 q^{10} -2.00000 q^{11} +5.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} +3.00000 q^{18} +1.00000 q^{20} +2.00000 q^{22} +1.00000 q^{23} -4.00000 q^{25} -5.00000 q^{26} +1.00000 q^{28} -6.00000 q^{29} -4.00000 q^{31} -1.00000 q^{32} +1.00000 q^{35} -3.00000 q^{36} +4.00000 q^{37} -1.00000 q^{40} +2.00000 q^{41} -8.00000 q^{43} -2.00000 q^{44} -3.00000 q^{45} -1.00000 q^{46} +1.00000 q^{49} +4.00000 q^{50} +5.00000 q^{52} +2.00000 q^{53} -2.00000 q^{55} -1.00000 q^{56} +6.00000 q^{58} +7.00000 q^{59} -7.00000 q^{61} +4.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +5.00000 q^{65} -12.0000 q^{67} -1.00000 q^{70} +15.0000 q^{71} +3.00000 q^{72} -14.0000 q^{73} -4.00000 q^{74} -2.00000 q^{77} +4.00000 q^{79} +1.00000 q^{80} +9.00000 q^{81} -2.00000 q^{82} -7.00000 q^{83} +8.00000 q^{86} +2.00000 q^{88} +3.00000 q^{90} +5.00000 q^{91} +1.00000 q^{92} -12.0000 q^{97} -1.00000 q^{98} +6.00000 q^{99} +O(q^{100})$

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
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−3.00000	−1.00000
$10$	−1.00000	−0.316228
$11$	−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
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	3.00000	0.707107
$19$	0	0
$19$	0	0
$20$	1.00000	0.223607
$21$	0	0
$22$	2.00000	0.426401
$23$	1.00000	0.208514	0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000	0.208514	0.104257	+	0.994550i	$0.466753\pi$
$24$	0	0
$25$	−4.00000	−0.800000
$26$	−5.00000	−0.980581
$27$	0	0
$28$	1.00000	0.188982
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	0	0
$35$	1.00000	0.169031
$36$	−3.00000	−0.500000
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	0	0
$39$	0	0
$40$	−1.00000	−0.158114
$41$	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	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−2.00000	−0.301511
$45$	−3.00000	−0.447214
$46$	−1.00000	−0.147442
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	4.00000	0.565685
$51$	0	0
$52$	5.00000	0.693375
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	0	0
$55$	−2.00000	−0.269680
$56$	−1.00000	−0.133631
$57$	0	0
$58$	6.00000	0.787839
$59$	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
$61$	−7.00000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	4.00000	0.508001
$63$	−3.00000	−0.377964
$64$	1.00000	0.125000
$65$	5.00000	0.620174
$66$	0	0
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	0	0
$69$	0	0
$70$	−1.00000	−0.119523
$71$	15.0000	1.78017	0.890086	−	0.455792i	$-0.150644\pi$
$71$	15.0000	1.78017	0.890086	+	0.455792i	$0.150644\pi$
$72$	3.00000	0.353553
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	0	0
$77$	−2.00000	−0.227921
$78$	0	0
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	1.00000	0.111803
$81$	9.00000	1.00000
$82$	−2.00000	−0.220863
$83$	−7.00000	−0.768350	−0.384175	−	0.923260i	$-0.625514\pi$
$83$	−7.00000	−0.768350	−0.384175	+	0.923260i	$0.625514\pi$
$84$	0	0
$85$	0	0
$86$	8.00000	0.862662
$87$	0	0
$88$	2.00000	0.213201
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	3.00000	0.316228
$91$	5.00000	0.524142
$92$	1.00000	0.104257
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	−1.00000	−0.101015
$99$	6.00000	0.603023
$100$	−4.00000	−0.400000
$101$	−18.0000	−1.79107	−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000	−1.79107	−0.895533	+	0.444994i	$0.853206\pi$
$102$	0	0
$103$	−6.00000	−0.591198	−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000	−0.591198	−0.295599	+	0.955312i	$0.595519\pi$
$104$	−5.00000	−0.490290
$105$	0	0
$106$	−2.00000	−0.194257
$107$	18.0000	1.74013	0.870063	−	0.492941i	$-0.164078\pi$
$107$	18.0000	1.74013	0.870063	+	0.492941i	$0.164078\pi$
$108$	0	0
$109$	10.0000	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$110$	2.00000	0.190693
$111$	0	0
$112$	1.00000	0.0944911
$113$	5.00000	0.470360	0.235180	−	0.971952i	$-0.424432\pi$
$113$	5.00000	0.470360	0.235180	+	0.971952i	$0.424432\pi$
$114$	0	0
$115$	1.00000	0.0932505
$116$	−6.00000	−0.557086
$117$	−15.0000	−1.38675
$118$	−7.00000	−0.644402
$119$	0	0
$120$	0	0
$121$	−7.00000	−0.636364
$122$	7.00000	0.633750
$123$	0	0
$124$	−4.00000	−0.359211
$125$	−9.00000	−0.804984
$126$	3.00000	0.267261
$127$	−13.0000	−1.15356	−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000	−1.15356	−0.576782	+	0.816898i	$0.695692\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	−5.00000	−0.438529
$131$	15.0000	1.31056	0.655278	−	0.755388i	$-0.272551\pi$
$131$	15.0000	1.31056	0.655278	+	0.755388i	$0.272551\pi$
$132$	0	0
$133$	0	0
$134$	12.0000	1.03664
$135$	0	0
$136$	0	0
$137$	−9.00000	−0.768922	−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000	−0.768922	−0.384461	+	0.923141i	$0.625613\pi$
$138$	0	0
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	1.00000	0.0845154
$141$	0	0
$142$	−15.0000	−1.25877
$143$	−10.0000	−0.836242
$144$	−3.00000	−0.250000
$145$	−6.00000	−0.498273
$146$	14.0000	1.15865
$147$	0	0
$148$	4.00000	0.328798
$149$	−4.00000	−0.327693	−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000	−0.327693	−0.163846	+	0.986486i	$0.552390\pi$
$150$	0	0
$151$	−19.0000	−1.54620	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	−19.0000	−1.54620	−0.773099	+	0.634285i	$0.781294\pi$
$152$	0	0
$153$	0	0
$154$	2.00000	0.161165
$155$	−4.00000	−0.321288
$156$	0	0
$157$	7.00000	0.558661	0.279330	−	0.960195i	$-0.409888\pi$
$157$	7.00000	0.558661	0.279330	+	0.960195i	$0.409888\pi$
$158$	−4.00000	−0.318223
$159$	0	0
$160$	−1.00000	−0.0790569
$161$	1.00000	0.0788110
$162$	−9.00000	−0.707107
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	7.00000	0.543305
$167$	−2.00000	−0.154765	−0.0773823	−	0.997001i	$-0.524656\pi$
$167$	−2.00000	−0.154765	−0.0773823	+	0.997001i	$0.524656\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	0	0
$172$	−8.00000	−0.609994
$173$	13.0000	0.988372	0.494186	−	0.869356i	$-0.335466\pi$
$173$	13.0000	0.988372	0.494186	+	0.869356i	$0.335466\pi$
$174$	0	0
$175$	−4.00000	−0.302372
$176$	−2.00000	−0.150756
$177$	0	0
$178$	0	0
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	−3.00000	−0.223607
$181$	−23.0000	−1.70958	−0.854788	−	0.518977i	$-0.826313\pi$
$181$	−23.0000	−1.70958	−0.854788	+	0.518977i	$0.826313\pi$
$182$	−5.00000	−0.370625
$183$	0	0
$184$	−1.00000	−0.0737210
$185$	4.00000	0.294086
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	17.0000	1.23008	0.615038	−	0.788497i	$-0.289140\pi$
$191$	17.0000	1.23008	0.615038	+	0.788497i	$0.289140\pi$
$192$	0	0
$193$	3.00000	0.215945	0.107972	−	0.994154i	$-0.465564\pi$
$193$	3.00000	0.215945	0.107972	+	0.994154i	$0.465564\pi$
$194$	12.0000	0.861550
$195$	0	0
$196$	1.00000	0.0714286
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	−6.00000	−0.426401
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	4.00000	0.282843
$201$	0	0
$202$	18.0000	1.26648
$203$	−6.00000	−0.421117
$204$	0	0
$205$	2.00000	0.139686
$206$	6.00000	0.418040
$207$	−3.00000	−0.208514
$208$	5.00000	0.346688
$209$	0	0
$210$	0	0
$211$	8.00000	0.550743	0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000	0.550743	0.275371	+	0.961338i	$0.411199\pi$
$212$	2.00000	0.137361
$213$	0	0
$214$	−18.0000	−1.23045
$215$	−8.00000	−0.545595
$216$	0	0
$217$	−4.00000	−0.271538
$218$	−10.0000	−0.677285
$219$	0	0
$220$	−2.00000	−0.134840
$221$	0	0
$222$	0	0
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	−1.00000	−0.0668153
$225$	12.0000	0.800000
$226$	−5.00000	−0.332595
$227$	3.00000	0.199117	0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000	0.199117	0.0995585	+	0.995032i	$0.468257\pi$
$228$	0	0
$229$	27.0000	1.78421	0.892105	−	0.451828i	$-0.149228\pi$
$229$	27.0000	1.78421	0.892105	+	0.451828i	$0.149228\pi$
$230$	−1.00000	−0.0659380
$231$	0	0
$232$	6.00000	0.393919
$233$	−11.0000	−0.720634	−0.360317	−	0.932830i	$-0.617331\pi$
$233$	−11.0000	−0.720634	−0.360317	+	0.932830i	$0.617331\pi$
$234$	15.0000	0.980581
$235$	0	0
$236$	7.00000	0.455661
$237$	0	0
$238$	0	0
$239$	−5.00000	−0.323423	−0.161712	−	0.986838i	$-0.551701\pi$
$239$	−5.00000	−0.323423	−0.161712	+	0.986838i	$0.551701\pi$
$240$	0	0
$241$	4.00000	0.257663	0.128831	−	0.991667i	$-0.458877\pi$
$241$	4.00000	0.257663	0.128831	+	0.991667i	$0.458877\pi$
$242$	7.00000	0.449977
$243$	0	0
$244$	−7.00000	−0.448129
$245$	1.00000	0.0638877
$246$	0	0
$247$	0	0
$248$	4.00000	0.254000
$249$	0	0
$250$	9.00000	0.569210
$251$	9.00000	0.568075	0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000	0.568075	0.284037	+	0.958813i	$0.408326\pi$
$252$	−3.00000	−0.188982
$253$	−2.00000	−0.125739
$254$	13.0000	0.815693
$255$	0	0
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	0	0
$259$	4.00000	0.248548
$260$	5.00000	0.310087
$261$	18.0000	1.11417
$262$	−15.0000	−0.926703
$263$	−3.00000	−0.184988	−0.0924940	−	0.995713i	$-0.529484\pi$
$263$	−3.00000	−0.184988	−0.0924940	+	0.995713i	$0.529484\pi$
$264$	0	0
$265$	2.00000	0.122859
$266$	0	0
$267$	0	0
$268$	−12.0000	−0.733017
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	0	0
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	0	0
$273$	0	0
$274$	9.00000	0.543710
$275$	8.00000	0.482418
$276$	0	0
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	12.0000	0.719712
$279$	12.0000	0.718421
$280$	−1.00000	−0.0597614
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	0	0
$283$	−7.00000	−0.416107	−0.208053	−	0.978117i	$-0.566713\pi$
$283$	−7.00000	−0.416107	−0.208053	+	0.978117i	$0.566713\pi$
$284$	15.0000	0.890086
$285$	0	0
$286$	10.0000	0.591312
$287$	2.00000	0.118056
$288$	3.00000	0.176777
$289$	−17.0000	−1.00000
$290$	6.00000	0.352332
$291$	0	0
$292$	−14.0000	−0.819288
$293$	−21.0000	−1.22683	−0.613417	−	0.789760i	$-0.710205\pi$
$293$	−21.0000	−1.22683	−0.613417	+	0.789760i	$0.710205\pi$
$294$	0	0
$295$	7.00000	0.407556
$296$	−4.00000	−0.232495
$297$	0	0
$298$	4.00000	0.231714
$299$	5.00000	0.289157
$300$	0	0
$301$	−8.00000	−0.461112
$302$	19.0000	1.09333
$303$	0	0
$304$	0	0
$305$	−7.00000	−0.400819
$306$	0	0
$307$	−19.0000	−1.08439	−0.542194	−	0.840254i	$-0.682406\pi$
$307$	−19.0000	−1.08439	−0.542194	+	0.840254i	$0.682406\pi$
$308$	−2.00000	−0.113961
$309$	0	0
$310$	4.00000	0.227185
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	0	0
$313$	28.0000	1.58265	0.791327	−	0.611393i	$-0.209391\pi$
$313$	28.0000	1.58265	0.791327	+	0.611393i	$0.209391\pi$
$314$	−7.00000	−0.395033
$315$	−3.00000	−0.169031
$316$	4.00000	0.225018
$317$	−22.0000	−1.23564	−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−22.0000	−1.23564	−0.617822	+	0.786318i	$0.711985\pi$
$318$	0	0
$319$	12.0000	0.671871
$320$	1.00000	0.0559017
$321$	0	0
$322$	−1.00000	−0.0557278
$323$	0	0
$324$	9.00000	0.500000
$325$	−20.0000	−1.10940
$326$	4.00000	0.221540
$327$	0	0
$328$	−2.00000	−0.110432
$329$	0	0
$330$	0	0
$331$	18.0000	0.989369	0.494685	−	0.869072i	$-0.335284\pi$
$331$	18.0000	0.989369	0.494685	+	0.869072i	$0.335284\pi$
$332$	−7.00000	−0.384175
$333$	−12.0000	−0.657596
$334$	2.00000	0.109435
$335$	−12.0000	−0.655630
$336$	0	0
$337$	−13.0000	−0.708155	−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000	−0.708155	−0.354078	+	0.935216i	$0.615205\pi$
$338$	−12.0000	−0.652714
$339$	0	0
$340$	0	0
$341$	8.00000	0.433224
$342$	0	0
$343$	1.00000	0.0539949
$344$	8.00000	0.431331
$345$	0	0
$346$	−13.0000	−0.698884
$347$	18.0000	0.966291	0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000	0.966291	0.483145	+	0.875540i	$0.339494\pi$
$348$	0	0
$349$	−14.0000	−0.749403	−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000	−0.749403	−0.374701	+	0.927146i	$0.622255\pi$
$350$	4.00000	0.213809
$351$	0	0
$352$	2.00000	0.106600
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	0	0
$355$	15.0000	0.796117
$356$	0	0
$357$	0	0
$358$	12.0000	0.634220
$359$	−4.00000	−0.211112	−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000	−0.211112	−0.105556	+	0.994413i	$0.533662\pi$
$360$	3.00000	0.158114
$361$	0	0
$362$	23.0000	1.20885
$363$	0	0
$364$	5.00000	0.262071
$365$	−14.0000	−0.732793
$366$	0	0
$367$	−18.0000	−0.939592	−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000	−0.939592	−0.469796	+	0.882775i	$0.655673\pi$
$368$	1.00000	0.0521286
$369$	−6.00000	−0.312348
$370$	−4.00000	−0.207950
$371$	2.00000	0.103835
$372$	0	0
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	−30.0000	−1.54508
$378$	0	0
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	0	0
$381$	0	0
$382$	−17.0000	−0.869796
$383$	−36.0000	−1.83951	−0.919757	−	0.392488i	$-0.871614\pi$
$383$	−36.0000	−1.83951	−0.919757	+	0.392488i	$0.871614\pi$
$384$	0	0
$385$	−2.00000	−0.101929
$386$	−3.00000	−0.152696
$387$	24.0000	1.21999
$388$	−12.0000	−0.609208
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	0	0
$391$	0	0
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	−2.00000	−0.100759
$395$	4.00000	0.201262
$396$	6.00000	0.301511
$397$	−6.00000	−0.301131	−0.150566	−	0.988600i	$-0.548110\pi$
$397$	−6.00000	−0.301131	−0.150566	+	0.988600i	$0.548110\pi$
$398$	4.00000	0.200502
$399$	0	0
$400$	−4.00000	−0.200000
$401$	25.0000	1.24844	0.624220	−	0.781248i	$-0.285417\pi$
$401$	25.0000	1.24844	0.624220	+	0.781248i	$0.285417\pi$
$402$	0	0
$403$	−20.0000	−0.996271
$404$	−18.0000	−0.895533
$405$	9.00000	0.447214
$406$	6.00000	0.297775
$407$	−8.00000	−0.396545
$408$	0	0
$409$	4.00000	0.197787	0.0988936	−	0.995098i	$-0.468470\pi$
$409$	4.00000	0.197787	0.0988936	+	0.995098i	$0.468470\pi$
$410$	−2.00000	−0.0987730
$411$	0	0
$412$	−6.00000	−0.295599
$413$	7.00000	0.344447
$414$	3.00000	0.147442
$415$	−7.00000	−0.343616
$416$	−5.00000	−0.245145
$417$	0	0
$418$	0	0
$419$	−28.0000	−1.36789	−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000	−1.36789	−0.683945	+	0.729534i	$0.739737\pi$
$420$	0	0
$421$	−34.0000	−1.65706	−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000	−1.65706	−0.828529	+	0.559946i	$0.810822\pi$
$422$	−8.00000	−0.389434
$423$	0	0
$424$	−2.00000	−0.0971286
$425$	0	0
$426$	0	0
$427$	−7.00000	−0.338754
$428$	18.0000	0.870063
$429$	0	0
$430$	8.00000	0.385794
$431$	−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
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	10.0000	0.478913
$437$	0	0
$438$	0	0
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	2.00000	0.0953463
$441$	−3.00000	−0.142857
$442$	0	0
$443$	−34.0000	−1.61539	−0.807694	−	0.589601i	$-0.799285\pi$
$443$	−34.0000	−1.61539	−0.807694	+	0.589601i	$0.799285\pi$
$444$	0	0
$445$	0	0
$446$	−2.00000	−0.0947027
$447$	0	0
$448$	1.00000	0.0472456
$449$	−37.0000	−1.74614	−0.873069	−	0.487597i	$-0.837874\pi$
$449$	−37.0000	−1.74614	−0.873069	+	0.487597i	$0.837874\pi$
$450$	−12.0000	−0.565685
$451$	−4.00000	−0.188353
$452$	5.00000	0.235180
$453$	0	0
$454$	−3.00000	−0.140797
$455$	5.00000	0.234404
$456$	0	0
$457$	−39.0000	−1.82434	−0.912172	−	0.409809i	$-0.865595\pi$
$457$	−39.0000	−1.82434	−0.912172	+	0.409809i	$0.865595\pi$
$458$	−27.0000	−1.26163
$459$	0	0
$460$	1.00000	0.0466252
$461$	−37.0000	−1.72326	−0.861631	−	0.507535i	$-0.830557\pi$
$461$	−37.0000	−1.72326	−0.861631	+	0.507535i	$0.830557\pi$
$462$	0	0
$463$	−5.00000	−0.232370	−0.116185	−	0.993228i	$-0.537067\pi$
$463$	−5.00000	−0.232370	−0.116185	+	0.993228i	$0.537067\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	11.0000	0.509565
$467$	−36.0000	−1.66588	−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000	−1.66588	−0.832941	+	0.553362i	$0.813345\pi$
$468$	−15.0000	−0.693375
$469$	−12.0000	−0.554109
$470$	0	0
$471$	0	0
$472$	−7.00000	−0.322201
$473$	16.0000	0.735681
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−6.00000	−0.274721
$478$	5.00000	0.228695
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	20.0000	0.911922
$482$	−4.00000	−0.182195
$483$	0	0
$484$	−7.00000	−0.318182
$485$	−12.0000	−0.544892
$486$	0	0
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	7.00000	0.316875
$489$	0	0
$490$	−1.00000	−0.0451754
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	0	0
$493$	0	0
$494$	0	0
$495$	6.00000	0.269680
$496$	−4.00000	−0.179605
$497$	15.0000	0.672842
$498$	0	0
$499$	24.0000	1.07439	0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000	1.07439	0.537194	+	0.843459i	$0.319484\pi$
$500$	−9.00000	−0.402492
$501$	0	0
$502$	−9.00000	−0.401690
$503$	16.0000	0.713405	0.356702	−	0.934218i	$-0.383901\pi$
$503$	16.0000	0.713405	0.356702	+	0.934218i	$0.383901\pi$
$504$	3.00000	0.133631
$505$	−18.0000	−0.800989
$506$	2.00000	0.0889108
$507$	0	0
$508$	−13.0000	−0.576782
$509$	−35.0000	−1.55135	−0.775674	−	0.631134i	$-0.782590\pi$
$509$	−35.0000	−1.55135	−0.775674	+	0.631134i	$0.782590\pi$
$510$	0	0
$511$	−14.0000	−0.619324
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	14.0000	0.617514
$515$	−6.00000	−0.264392
$516$	0	0
$517$	0	0
$518$	−4.00000	−0.175750
$519$	0	0
$520$	−5.00000	−0.219265
$521$	38.0000	1.66481	0.832405	−	0.554168i	$-0.186963\pi$
$521$	38.0000	1.66481	0.832405	+	0.554168i	$0.186963\pi$
$522$	−18.0000	−0.787839
$523$	28.0000	1.22435	0.612177	−	0.790721i	$-0.290294\pi$
$523$	28.0000	1.22435	0.612177	+	0.790721i	$0.290294\pi$
$524$	15.0000	0.655278
$525$	0	0
$526$	3.00000	0.130806
$527$	0	0
$528$	0	0
$529$	−22.0000	−0.956522
$530$	−2.00000	−0.0868744
$531$	−21.0000	−0.911322
$532$	0	0
$533$	10.0000	0.433148
$534$	0	0
$535$	18.0000	0.778208
$536$	12.0000	0.518321
$537$	0	0
$538$	14.0000	0.603583
$539$	−2.00000	−0.0861461
$540$	0	0
$541$	36.0000	1.54776	0.773880	−	0.633332i	$-0.218313\pi$
$541$	36.0000	1.54776	0.773880	+	0.633332i	$0.218313\pi$
$542$	20.0000	0.859074
$543$	0	0
$544$	0	0
$545$	10.0000	0.428353
$546$	0	0
$547$	−20.0000	−0.855138	−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000	−0.855138	−0.427569	+	0.903983i	$0.640630\pi$
$548$	−9.00000	−0.384461
$549$	21.0000	0.896258
$550$	−8.00000	−0.341121
$551$	0	0
$552$	0	0
$553$	4.00000	0.170097
$554$	2.00000	0.0849719
$555$	0	0
$556$	−12.0000	−0.508913
$557$	−2.00000	−0.0847427	−0.0423714	−	0.999102i	$-0.513491\pi$
$557$	−2.00000	−0.0847427	−0.0423714	+	0.999102i	$0.513491\pi$
$558$	−12.0000	−0.508001
$559$	−40.0000	−1.69182
$560$	1.00000	0.0422577
$561$	0	0
$562$	−22.0000	−0.928014
$563$	3.00000	0.126435	0.0632175	−	0.998000i	$-0.479864\pi$
$563$	3.00000	0.126435	0.0632175	+	0.998000i	$0.479864\pi$
$564$	0	0
$565$	5.00000	0.210352
$566$	7.00000	0.294232
$567$	9.00000	0.377964
$568$	−15.0000	−0.629386
$569$	−31.0000	−1.29959	−0.649794	−	0.760111i	$-0.725145\pi$
$569$	−31.0000	−1.29959	−0.649794	+	0.760111i	$0.725145\pi$
$570$	0	0
$571$	−30.0000	−1.25546	−0.627730	−	0.778431i	$-0.716016\pi$
$571$	−30.0000	−1.25546	−0.627730	+	0.778431i	$0.716016\pi$
$572$	−10.0000	−0.418121
$573$	0	0
$574$	−2.00000	−0.0834784
$575$	−4.00000	−0.166812
$576$	−3.00000	−0.125000
$577$	32.0000	1.33218	0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000	1.33218	0.666089	+	0.745873i	$0.267967\pi$
$578$	17.0000	0.707107
$579$	0	0
$580$	−6.00000	−0.249136
$581$	−7.00000	−0.290409
$582$	0	0
$583$	−4.00000	−0.165663
$584$	14.0000	0.579324
$585$	−15.0000	−0.620174
$586$	21.0000	0.867502
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	0	0
$589$	0	0
$590$	−7.00000	−0.288185
$591$	0	0
$592$	4.00000	0.164399
$593$	42.0000	1.72473	0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000	1.72473	0.862367	+	0.506284i	$0.168981\pi$
$594$	0	0
$595$	0	0
$596$	−4.00000	−0.163846
$597$	0	0
$598$	−5.00000	−0.204465
$599$	−5.00000	−0.204294	−0.102147	−	0.994769i	$-0.532571\pi$
$599$	−5.00000	−0.204294	−0.102147	+	0.994769i	$0.532571\pi$
$600$	0	0
$601$	0	0		−	1.00000i	$-0.5\pi$
$601$	0	0			1.00000i	$0.5\pi$
$602$	8.00000	0.326056
$603$	36.0000	1.46603
$604$	−19.0000	−0.773099
$605$	−7.00000	−0.284590
$606$	0	0
$607$	8.00000	0.324710	0.162355	−	0.986732i	$-0.448091\pi$
$607$	8.00000	0.324710	0.162355	+	0.986732i	$0.448091\pi$
$608$	0	0
$609$	0	0
$610$	7.00000	0.283422
$611$	0	0
$612$	0	0
$613$	−24.0000	−0.969351	−0.484675	−	0.874694i	$-0.661062\pi$
$613$	−24.0000	−0.969351	−0.484675	+	0.874694i	$0.661062\pi$
$614$	19.0000	0.766778
$615$	0	0
$616$	2.00000	0.0805823
$617$	13.0000	0.523360	0.261680	−	0.965155i	$-0.415723\pi$
$617$	13.0000	0.523360	0.261680	+	0.965155i	$0.415723\pi$
$618$	0	0
$619$	−17.0000	−0.683288	−0.341644	−	0.939829i	$-0.610984\pi$
$619$	−17.0000	−0.683288	−0.341644	+	0.939829i	$0.610984\pi$
$620$	−4.00000	−0.160644
$621$	0	0
$622$	−18.0000	−0.721734
$623$	0	0
$624$	0	0
$625$	11.0000	0.440000
$626$	−28.0000	−1.11911
$627$	0	0
$628$	7.00000	0.279330
$629$	0	0
$630$	3.00000	0.119523
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	−4.00000	−0.159111
$633$	0	0
$634$	22.0000	0.873732
$635$	−13.0000	−0.515889
$636$	0	0
$637$	5.00000	0.198107
$638$	−12.0000	−0.475085
$639$	−45.0000	−1.78017
$640$	−1.00000	−0.0395285
$641$	−39.0000	−1.54041	−0.770204	−	0.637798i	$-0.779845\pi$
$641$	−39.0000	−1.54041	−0.770204	+	0.637798i	$0.779845\pi$
$642$	0	0
$643$	−9.00000	−0.354925	−0.177463	−	0.984128i	$-0.556789\pi$
$643$	−9.00000	−0.354925	−0.177463	+	0.984128i	$0.556789\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	0	0
$647$	−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
$649$	−14.0000	−0.549548
$650$	20.0000	0.784465
$651$	0	0
$652$	−4.00000	−0.156652
$653$	24.0000	0.939193	0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000	0.939193	0.469596	+	0.882881i	$0.344399\pi$
$654$	0	0
$655$	15.0000	0.586098
$656$	2.00000	0.0780869
$657$	42.0000	1.63858
$658$	0	0
$659$	22.0000	0.856998	0.428499	−	0.903542i	$-0.359042\pi$
$659$	22.0000	0.856998	0.428499	+	0.903542i	$0.359042\pi$
$660$	0	0
$661$	−17.0000	−0.661223	−0.330612	−	0.943767i	$-0.607255\pi$
$661$	−17.0000	−0.661223	−0.330612	+	0.943767i	$0.607255\pi$
$662$	−18.0000	−0.699590
$663$	0	0
$664$	7.00000	0.271653
$665$	0	0
$666$	12.0000	0.464991
$667$	−6.00000	−0.232321
$668$	−2.00000	−0.0773823
$669$	0	0
$670$	12.0000	0.463600
$671$	14.0000	0.540464
$672$	0	0
$673$	−23.0000	−0.886585	−0.443292	−	0.896377i	$-0.646190\pi$
$673$	−23.0000	−0.886585	−0.443292	+	0.896377i	$0.646190\pi$
$674$	13.0000	0.500741
$675$	0	0
$676$	12.0000	0.461538
$677$	−34.0000	−1.30673	−0.653363	−	0.757045i	$-0.726642\pi$
$677$	−34.0000	−1.30673	−0.653363	+	0.757045i	$0.726642\pi$
$678$	0	0
$679$	−12.0000	−0.460518
$680$	0	0
$681$	0	0
$682$	−8.00000	−0.306336
$683$	30.0000	1.14792	0.573959	−	0.818884i	$-0.305407\pi$
$683$	30.0000	1.14792	0.573959	+	0.818884i	$0.305407\pi$
$684$	0	0
$685$	−9.00000	−0.343872
$686$	−1.00000	−0.0381802
$687$	0	0
$688$	−8.00000	−0.304997
$689$	10.0000	0.380970
$690$	0	0
$691$	−29.0000	−1.10321	−0.551606	−	0.834105i	$-0.685985\pi$
$691$	−29.0000	−1.10321	−0.551606	+	0.834105i	$0.685985\pi$
$692$	13.0000	0.494186
$693$	6.00000	0.227921
$694$	−18.0000	−0.683271
$695$	−12.0000	−0.455186
$696$	0	0
$697$	0	0
$698$	14.0000	0.529908
$699$	0	0
$700$	−4.00000	−0.151186
$701$	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
$703$	0	0
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	−18.0000	−0.677439
$707$	−18.0000	−0.676960
$708$	0	0
$709$	−34.0000	−1.27690	−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000	−1.27690	−0.638448	+	0.769665i	$0.720423\pi$
$710$	−15.0000	−0.562940
$711$	−12.0000	−0.450035
$712$	0	0
$713$	−4.00000	−0.149801
$714$	0	0
$715$	−10.0000	−0.373979
$716$	−12.0000	−0.448461
$717$	0	0
$718$	4.00000	0.149279
$719$	50.0000	1.86469	0.932343	−	0.361576i	$-0.117761\pi$
$719$	50.0000	1.86469	0.932343	+	0.361576i	$0.117761\pi$
$720$	−3.00000	−0.111803
$721$	−6.00000	−0.223452
$722$	0	0
$723$	0	0
$724$	−23.0000	−0.854788
$725$	24.0000	0.891338
$726$	0	0
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	−5.00000	−0.185312
$729$	−27.0000	−1.00000
$730$	14.0000	0.518163
$731$	0	0
$732$	0	0
$733$	13.0000	0.480166	0.240083	−	0.970752i	$-0.422825\pi$
$733$	13.0000	0.480166	0.240083	+	0.970752i	$0.422825\pi$
$734$	18.0000	0.664392
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	24.0000	0.884051
$738$	6.00000	0.220863
$739$	−38.0000	−1.39785	−0.698926	−	0.715194i	$-0.746338\pi$
$739$	−38.0000	−1.39785	−0.698926	+	0.715194i	$0.746338\pi$
$740$	4.00000	0.147043
$741$	0	0
$742$	−2.00000	−0.0734223
$743$	43.0000	1.57752	0.788759	−	0.614703i	$-0.210724\pi$
$743$	43.0000	1.57752	0.788759	+	0.614703i	$0.210724\pi$
$744$	0	0
$745$	−4.00000	−0.146549
$746$	−4.00000	−0.146450
$747$	21.0000	0.768350
$748$	0	0
$749$	18.0000	0.657706
$750$	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
$754$	30.0000	1.09254
$755$	−19.0000	−0.691481
$756$	0	0
$757$	34.0000	1.23575	0.617876	−	0.786276i	$-0.287994\pi$
$757$	34.0000	1.23575	0.617876	+	0.786276i	$0.287994\pi$
$758$	−12.0000	−0.435860
$759$	0	0
$760$	0	0
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	0	0
$763$	10.0000	0.362024
$764$	17.0000	0.615038
$765$	0	0
$766$	36.0000	1.30073
$767$	35.0000	1.26378
$768$	0	0
$769$	−12.0000	−0.432731	−0.216366	−	0.976312i	$-0.569420\pi$
$769$	−12.0000	−0.432731	−0.216366	+	0.976312i	$0.569420\pi$
$770$	2.00000	0.0720750
$771$	0	0
$772$	3.00000	0.107972
$773$	−17.0000	−0.611448	−0.305724	−	0.952120i	$-0.598898\pi$
$773$	−17.0000	−0.611448	−0.305724	+	0.952120i	$0.598898\pi$
$774$	−24.0000	−0.862662
$775$	16.0000	0.574737
$776$	12.0000	0.430775
$777$	0	0
$778$	30.0000	1.07555
$779$	0	0
$780$	0	0
$781$	−30.0000	−1.07348
$782$	0	0
$783$	0	0
$784$	1.00000	0.0357143
$785$	7.00000	0.249841
$786$	0	0
$787$	−25.0000	−0.891154	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	−25.0000	−0.891154	−0.445577	+	0.895244i	$0.647001\pi$
$788$	2.00000	0.0712470
$789$	0	0
$790$	−4.00000	−0.142314
$791$	5.00000	0.177780
$792$	−6.00000	−0.213201
$793$	−35.0000	−1.24289
$794$	6.00000	0.212932
$795$	0	0
$796$	−4.00000	−0.141776
$797$	−7.00000	−0.247953	−0.123976	−	0.992285i	$-0.539565\pi$
$797$	−7.00000	−0.247953	−0.123976	+	0.992285i	$0.539565\pi$
$798$	0	0
$799$	0	0
$800$	4.00000	0.141421
$801$	0	0
$802$	−25.0000	−0.882781
$803$	28.0000	0.988099
$804$	0	0
$805$	1.00000	0.0352454
$806$	20.0000	0.704470
$807$	0	0
$808$	18.0000	0.633238
$809$	33.0000	1.16022	0.580109	−	0.814539i	$-0.303010\pi$
$809$	33.0000	1.16022	0.580109	+	0.814539i	$0.303010\pi$
$810$	−9.00000	−0.316228
$811$	12.0000	0.421377	0.210688	−	0.977553i	$-0.432429\pi$
$811$	12.0000	0.421377	0.210688	+	0.977553i	$0.432429\pi$
$812$	−6.00000	−0.210559
$813$	0	0
$814$	8.00000	0.280400
$815$	−4.00000	−0.140114
$816$	0	0
$817$	0	0
$818$	−4.00000	−0.139857
$819$	−15.0000	−0.524142
$820$	2.00000	0.0698430
$821$	−48.0000	−1.67521	−0.837606	−	0.546275i	$-0.816045\pi$
$821$	−48.0000	−1.67521	−0.837606	+	0.546275i	$0.816045\pi$
$822$	0	0
$823$	5.00000	0.174289	0.0871445	−	0.996196i	$-0.472226\pi$
$823$	5.00000	0.174289	0.0871445	+	0.996196i	$0.472226\pi$
$824$	6.00000	0.209020
$825$	0	0
$826$	−7.00000	−0.243561
$827$	−6.00000	−0.208640	−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000	−0.208640	−0.104320	+	0.994544i	$0.533267\pi$
$828$	−3.00000	−0.104257
$829$	31.0000	1.07667	0.538337	−	0.842729i	$-0.319053\pi$
$829$	31.0000	1.07667	0.538337	+	0.842729i	$0.319053\pi$
$830$	7.00000	0.242974
$831$	0	0
$832$	5.00000	0.173344
$833$	0	0
$834$	0	0
$835$	−2.00000	−0.0692129
$836$	0	0
$837$	0	0
$838$	28.0000	0.967244
$839$	−54.0000	−1.86429	−0.932144	−	0.362089i	$-0.882064\pi$
$839$	−54.0000	−1.86429	−0.932144	+	0.362089i	$0.882064\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	34.0000	1.17172
$843$	0	0
$844$	8.00000	0.275371
$845$	12.0000	0.412813
$846$	0	0
$847$	−7.00000	−0.240523
$848$	2.00000	0.0686803
$849$	0	0
$850$	0	0
$851$	4.00000	0.137118
$852$	0	0
$853$	26.0000	0.890223	0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000	0.890223	0.445112	+	0.895475i	$0.353164\pi$
$854$	7.00000	0.239535
$855$	0	0
$856$	−18.0000	−0.615227
$857$	−14.0000	−0.478231	−0.239115	−	0.970991i	$-0.576857\pi$
$857$	−14.0000	−0.478231	−0.239115	+	0.970991i	$0.576857\pi$
$858$	0	0
$859$	28.0000	0.955348	0.477674	−	0.878537i	$-0.341480\pi$
$859$	28.0000	0.955348	0.477674	+	0.878537i	$0.341480\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	12.0000	0.408722
$863$	32.0000	1.08929	0.544646	−	0.838666i	$-0.316664\pi$
$863$	32.0000	1.08929	0.544646	+	0.838666i	$0.316664\pi$
$864$	0	0
$865$	13.0000	0.442013
$866$	2.00000	0.0679628
$867$	0	0
$868$	−4.00000	−0.135769
$869$	−8.00000	−0.271381
$870$	0	0
$871$	−60.0000	−2.03302
$872$	−10.0000	−0.338643
$873$	36.0000	1.21842
$874$	0	0
$875$	−9.00000	−0.304256
$876$	0	0
$877$	46.0000	1.55331	0.776655	−	0.629926i	$-0.216915\pi$
$877$	46.0000	1.55331	0.776655	+	0.629926i	$0.216915\pi$
$878$	−20.0000	−0.674967
$879$	0	0
$880$	−2.00000	−0.0674200
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	3.00000	0.101015
$883$	34.0000	1.14419	0.572096	−	0.820187i	$-0.306131\pi$
$883$	34.0000	1.14419	0.572096	+	0.820187i	$0.306131\pi$
$884$	0	0
$885$	0	0
$886$	34.0000	1.14225
$887$	42.0000	1.41022	0.705111	−	0.709097i	$-0.250897\pi$
$887$	42.0000	1.41022	0.705111	+	0.709097i	$0.250897\pi$
$888$	0	0
$889$	−13.0000	−0.436006
$890$	0	0
$891$	−18.0000	−0.603023
$892$	2.00000	0.0669650
$893$	0	0
$894$	0	0
$895$	−12.0000	−0.401116
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	37.0000	1.23471
$899$	24.0000	0.800445
$900$	12.0000	0.400000
$901$	0	0
$902$	4.00000	0.133185
$903$	0	0
$904$	−5.00000	−0.166298
$905$	−23.0000	−0.764546
$906$	0	0
$907$	10.0000	0.332045	0.166022	−	0.986122i	$-0.446908\pi$
$907$	10.0000	0.332045	0.166022	+	0.986122i	$0.446908\pi$
$908$	3.00000	0.0995585
$909$	54.0000	1.79107
$910$	−5.00000	−0.165748
$911$	−9.00000	−0.298183	−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000	−0.298183	−0.149092	+	0.988823i	$0.547635\pi$
$912$	0	0
$913$	14.0000	0.463332
$914$	39.0000	1.29001
$915$	0	0
$916$	27.0000	0.892105
$917$	15.0000	0.495344
$918$	0	0
$919$	3.00000	0.0989609	0.0494804	−	0.998775i	$-0.484243\pi$
$919$	3.00000	0.0989609	0.0494804	+	0.998775i	$0.484243\pi$
$920$	−1.00000	−0.0329690
$921$	0	0
$922$	37.0000	1.21853
$923$	75.0000	2.46866
$924$	0	0
$925$	−16.0000	−0.526077
$926$	5.00000	0.164310
$927$	18.0000	0.591198
$928$	6.00000	0.196960
$929$	36.0000	1.18112	0.590561	−	0.806993i	$-0.298907\pi$
$929$	36.0000	1.18112	0.590561	+	0.806993i	$0.298907\pi$
$930$	0	0
$931$	0	0
$932$	−11.0000	−0.360317
$933$	0	0
$934$	36.0000	1.17796
$935$	0	0
$936$	15.0000	0.490290
$937$	58.0000	1.89478	0.947389	−	0.320085i	$-0.103712\pi$
$937$	58.0000	1.89478	0.947389	+	0.320085i	$0.103712\pi$
$938$	12.0000	0.391814
$939$	0	0
$940$	0	0
$941$	−17.0000	−0.554184	−0.277092	−	0.960843i	$-0.589371\pi$
$941$	−17.0000	−0.554184	−0.277092	+	0.960843i	$0.589371\pi$
$942$	0	0
$943$	2.00000	0.0651290
$944$	7.00000	0.227831
$945$	0	0
$946$	−16.0000	−0.520205
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	0	0
$949$	−70.0000	−2.27230
$950$	0	0
$951$	0	0
$952$	0	0
$953$	22.0000	0.712650	0.356325	−	0.934362i	$-0.384030\pi$
$953$	22.0000	0.712650	0.356325	+	0.934362i	$0.384030\pi$
$954$	6.00000	0.194257
$955$	17.0000	0.550107
$956$	−5.00000	−0.161712
$957$	0	0
$958$	−24.0000	−0.775405
$959$	−9.00000	−0.290625
$960$	0	0
$961$	−15.0000	−0.483871
$962$	−20.0000	−0.644826
$963$	−54.0000	−1.74013
$964$	4.00000	0.128831
$965$	3.00000	0.0965734
$966$	0	0
$967$	−57.0000	−1.83300	−0.916498	−	0.400039i	$-0.868997\pi$
$967$	−57.0000	−1.83300	−0.916498	+	0.400039i	$0.868997\pi$
$968$	7.00000	0.224989
$969$	0	0
$970$	12.0000	0.385297
$971$	41.0000	1.31575	0.657876	−	0.753126i	$-0.271455\pi$
$971$	41.0000	1.31575	0.657876	+	0.753126i	$0.271455\pi$
$972$	0	0
$973$	−12.0000	−0.384702
$974$	−16.0000	−0.512673
$975$	0	0
$976$	−7.00000	−0.224065
$977$	37.0000	1.18373	0.591867	−	0.806035i	$-0.298391\pi$
$977$	37.0000	1.18373	0.591867	+	0.806035i	$0.298391\pi$
$978$	0	0
$979$	0	0
$980$	1.00000	0.0319438
$981$	−30.0000	−0.957826
$982$	−20.0000	−0.638226
$983$	−42.0000	−1.33959	−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000	−1.33959	−0.669796	+	0.742545i	$0.733618\pi$
$984$	0	0
$985$	2.00000	0.0637253
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−8.00000	−0.254385
$990$	−6.00000	−0.190693
$991$	31.0000	0.984747	0.492374	−	0.870384i	$-0.336129\pi$
$991$	31.0000	0.984747	0.492374	+	0.870384i	$0.336129\pi$
$992$	4.00000	0.127000
$993$	0	0
$994$	−15.0000	−0.475771
$995$	−4.00000	−0.126809
$996$	0	0
$997$	17.0000	0.538395	0.269198	−	0.963085i	$-0.413241\pi$
$997$	17.0000	0.538395	0.269198	+	0.963085i	$0.413241\pi$
$998$	−24.0000	−0.759707
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.a.1.1		1
19.8	odd	6		266.2.f.a.197.1	✓	2
19.12	odd	6		266.2.f.a.239.1	yes	2
19.18	odd	2		5054.2.a.b.1.1		1
57.8	even	6		2394.2.o.i.1261.1		2
57.50	even	6		2394.2.o.i.505.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.f.a.197.1	✓	2	19.8	odd	6
266.2.f.a.239.1	yes	2	19.12	odd	6
2394.2.o.i.505.1		2	57.50	even	6
2394.2.o.i.1261.1		2	57.8	even	6
5054.2.a.a.1.1		1	1.1	even	1	trivial
5054.2.a.b.1.1		1	19.18	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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