LMFDB - Embedded newform 6011.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6011,2,Mod(1,6011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6011.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:	$47.9980766550$
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	$\chi$	$=$	6011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -3.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} -3.00000 q^{8} -2.00000 q^{9} -3.00000 q^{10} +2.00000 q^{11} +1.00000 q^{12} +1.00000 q^{14} +3.00000 q^{15} -1.00000 q^{16} -2.00000 q^{18} +2.00000 q^{19} +3.00000 q^{20} -1.00000 q^{21} +2.00000 q^{22} +3.00000 q^{24} +4.00000 q^{25} +5.00000 q^{27} -1.00000 q^{28} +3.00000 q^{30} +4.00000 q^{31} +5.00000 q^{32} -2.00000 q^{33} -3.00000 q^{35} +2.00000 q^{36} +4.00000 q^{37} +2.00000 q^{38} +9.00000 q^{40} -9.00000 q^{41} -1.00000 q^{42} +5.00000 q^{43} -2.00000 q^{44} +6.00000 q^{45} +2.00000 q^{47} +1.00000 q^{48} -6.00000 q^{49} +4.00000 q^{50} +6.00000 q^{53} +5.00000 q^{54} -6.00000 q^{55} -3.00000 q^{56} -2.00000 q^{57} -3.00000 q^{60} +6.00000 q^{61} +4.00000 q^{62} -2.00000 q^{63} +7.00000 q^{64} -2.00000 q^{66} -8.00000 q^{67} -3.00000 q^{70} +5.00000 q^{71} +6.00000 q^{72} +5.00000 q^{73} +4.00000 q^{74} -4.00000 q^{75} -2.00000 q^{76} +2.00000 q^{77} -4.00000 q^{79} +3.00000 q^{80} +1.00000 q^{81} -9.00000 q^{82} +7.00000 q^{83} +1.00000 q^{84} +5.00000 q^{86} -6.00000 q^{88} +8.00000 q^{89} +6.00000 q^{90} -4.00000 q^{93} +2.00000 q^{94} -6.00000 q^{95} -5.00000 q^{96} -14.0000 q^{97} -6.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	−1.00000	−0.500000
$5$	−3.00000	−1.34164	−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000	−1.34164	−0.670820	+	0.741620i	$0.734058\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	−3.00000	−1.06066
$9$	−2.00000	−0.666667
$10$	−3.00000	−0.948683
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	1.00000	0.288675
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	1.00000	0.267261
$15$	3.00000	0.774597
$16$	−1.00000	−0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	−2.00000	−0.471405
$19$	2.00000	0.458831	0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000	0.458831	0.229416	+	0.973329i	$0.426318\pi$
$20$	3.00000	0.670820
$21$	−1.00000	−0.218218
$22$	2.00000	0.426401
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	3.00000	0.612372
$25$	4.00000	0.800000
$26$	0	0
$27$	5.00000	0.962250
$28$	−1.00000	−0.188982
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	3.00000	0.547723
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	5.00000	0.883883
$33$	−2.00000	−0.348155
$34$	0	0
$35$	−3.00000	−0.507093
$36$	2.00000	0.333333
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	2.00000	0.324443
$39$	0	0
$40$	9.00000	1.42302
$41$	−9.00000	−1.40556	−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000	−1.40556	−0.702782	+	0.711405i	$0.748059\pi$
$42$	−1.00000	−0.154303
$43$	5.00000	0.762493	0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000	0.762493	0.381246	+	0.924473i	$0.375495\pi$
$44$	−2.00000	−0.301511
$45$	6.00000	0.894427
$46$	0	0
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	1.00000	0.144338
$49$	−6.00000	−0.857143
$50$	4.00000	0.565685
$51$	0	0
$52$	0	0
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	5.00000	0.680414
$55$	−6.00000	−0.809040
$56$	−3.00000	−0.400892
$57$	−2.00000	−0.264906
$58$	0	0
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	−3.00000	−0.387298
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	4.00000	0.508001
$63$	−2.00000	−0.251976
$64$	7.00000	0.875000
$65$	0	0
$66$	−2.00000	−0.246183
$67$	−8.00000	−0.977356	−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000	−0.977356	−0.488678	+	0.872464i	$0.662521\pi$
$68$	0	0
$69$	0	0
$70$	−3.00000	−0.358569
$71$	5.00000	0.593391	0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000	0.593391	0.296695	+	0.954972i	$0.404115\pi$
$72$	6.00000	0.707107
$73$	5.00000	0.585206	0.292603	−	0.956234i	$-0.405479\pi$
$73$	5.00000	0.585206	0.292603	+	0.956234i	$0.405479\pi$
$74$	4.00000	0.464991
$75$	−4.00000	−0.461880
$76$	−2.00000	−0.229416
$77$	2.00000	0.227921
$78$	0	0
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	3.00000	0.335410
$81$	1.00000	0.111111
$82$	−9.00000	−0.993884
$83$	7.00000	0.768350	0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000	0.768350	0.384175	+	0.923260i	$0.374486\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	5.00000	0.539164
$87$	0	0
$88$	−6.00000	−0.639602
$89$	8.00000	0.847998	0.423999	−	0.905663i	$-0.360626\pi$
$89$	8.00000	0.847998	0.423999	+	0.905663i	$0.360626\pi$
$90$	6.00000	0.632456
$91$	0	0
$92$	0	0
$93$	−4.00000	−0.414781
$94$	2.00000	0.206284
$95$	−6.00000	−0.615587
$96$	−5.00000	−0.510310
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	−6.00000	−0.606092
$99$	−4.00000	−0.402015
$100$	−4.00000	−0.400000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	0	0
$103$	−9.00000	−0.886796	−0.443398	−	0.896325i	$-0.646227\pi$
$103$	−9.00000	−0.886796	−0.443398	+	0.896325i	$0.646227\pi$
$104$	0	0
$105$	3.00000	0.292770
$106$	6.00000	0.582772
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	−5.00000	−0.481125
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	−6.00000	−0.572078
$111$	−4.00000	−0.379663
$112$	−1.00000	−0.0944911
$113$	14.0000	1.31701	0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000	1.31701	0.658505	+	0.752577i	$0.271189\pi$
$114$	−2.00000	−0.187317
$115$	0	0
$116$	0	0
$117$	0	0
$118$	0	0
$119$	0	0
$120$	−9.00000	−0.821584
$121$	−7.00000	−0.636364
$122$	6.00000	0.543214
$123$	9.00000	0.811503
$124$	−4.00000	−0.359211
$125$	3.00000	0.268328
$126$	−2.00000	−0.178174
$127$	−22.0000	−1.95218	−0.976092	−	0.217357i	$-0.930256\pi$
$127$	−22.0000	−1.95218	−0.976092	+	0.217357i	$0.930256\pi$
$128$	−3.00000	−0.265165
$129$	−5.00000	−0.440225
$130$	0	0
$131$	3.00000	0.262111	0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000	0.262111	0.131056	+	0.991375i	$0.458163\pi$
$132$	2.00000	0.174078
$133$	2.00000	0.173422
$134$	−8.00000	−0.691095
$135$	−15.0000	−1.29099
$136$	0	0
$137$	−15.0000	−1.28154	−0.640768	−	0.767734i	$-0.721384\pi$
$137$	−15.0000	−1.28154	−0.640768	+	0.767734i	$0.721384\pi$
$138$	0	0
$139$	−12.0000	−1.01783	−0.508913	−	0.860818i	$-0.669953\pi$
$139$	−12.0000	−1.01783	−0.508913	+	0.860818i	$0.669953\pi$
$140$	3.00000	0.253546
$141$	−2.00000	−0.168430
$142$	5.00000	0.419591
$143$	0	0
$144$	2.00000	0.166667
$145$	0	0
$146$	5.00000	0.413803
$147$	6.00000	0.494872
$148$	−4.00000	−0.328798
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	−4.00000	−0.326599
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	−6.00000	−0.486664
$153$	0	0
$154$	2.00000	0.161165
$155$	−12.0000	−0.963863
$156$	0	0
$157$	−24.0000	−1.91541	−0.957704	−	0.287754i	$-0.907091\pi$
$157$	−24.0000	−1.91541	−0.957704	+	0.287754i	$0.907091\pi$
$158$	−4.00000	−0.318223
$159$	−6.00000	−0.475831
$160$	−15.0000	−1.18585
$161$	0	0
$162$	1.00000	0.0785674
$163$	2.00000	0.156652	0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000	0.156652	0.0783260	+	0.996928i	$0.475042\pi$
$164$	9.00000	0.702782
$165$	6.00000	0.467099
$166$	7.00000	0.543305
$167$	15.0000	1.16073	0.580367	−	0.814355i	$-0.302909\pi$
$167$	15.0000	1.16073	0.580367	+	0.814355i	$0.302909\pi$
$168$	3.00000	0.231455
$169$	−13.0000	−1.00000
$170$	0	0
$171$	−4.00000	−0.305888
$172$	−5.00000	−0.381246
$173$	8.00000	0.608229	0.304114	−	0.952636i	$-0.401639\pi$
$173$	8.00000	0.608229	0.304114	+	0.952636i	$0.401639\pi$
$174$	0	0
$175$	4.00000	0.302372
$176$	−2.00000	−0.150756
$177$	0	0
$178$	8.00000	0.599625
$179$	−15.0000	−1.12115	−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000	−1.12115	−0.560576	+	0.828103i	$0.689420\pi$
$180$	−6.00000	−0.447214
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	0	0
$183$	−6.00000	−0.443533
$184$	0	0
$185$	−12.0000	−0.882258
$186$	−4.00000	−0.293294
$187$	0	0
$188$	−2.00000	−0.145865
$189$	5.00000	0.363696
$190$	−6.00000	−0.435286
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	−7.00000	−0.505181
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−14.0000	−1.00514
$195$	0	0
$196$	6.00000	0.428571
$197$	−15.0000	−1.06871	−0.534353	−	0.845262i	$-0.679445\pi$
$197$	−15.0000	−1.06871	−0.534353	+	0.845262i	$0.679445\pi$
$198$	−4.00000	−0.284268
$199$	−25.0000	−1.77220	−0.886102	−	0.463491i	$-0.846597\pi$
$199$	−25.0000	−1.77220	−0.886102	+	0.463491i	$0.846597\pi$
$200$	−12.0000	−0.848528
$201$	8.00000	0.564276
$202$	−6.00000	−0.422159
$203$	0	0
$204$	0	0
$205$	27.0000	1.88576
$206$	−9.00000	−0.627060
$207$	0	0
$208$	0	0
$209$	4.00000	0.276686
$210$	3.00000	0.207020
$211$	2.00000	0.137686	0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000	0.137686	0.0688428	+	0.997628i	$0.478069\pi$
$212$	−6.00000	−0.412082
$213$	−5.00000	−0.342594
$214$	−12.0000	−0.820303
$215$	−15.0000	−1.02299
$216$	−15.0000	−1.02062
$217$	4.00000	0.271538
$218$	6.00000	0.406371
$219$	−5.00000	−0.337869
$220$	6.00000	0.404520
$221$	0	0
$222$	−4.00000	−0.268462
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	5.00000	0.334077
$225$	−8.00000	−0.533333
$226$	14.0000	0.931266
$227$	18.0000	1.19470	0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000	1.19470	0.597351	+	0.801980i	$0.296220\pi$
$228$	2.00000	0.132453
$229$	−27.0000	−1.78421	−0.892105	−	0.451828i	$-0.850772\pi$
$229$	−27.0000	−1.78421	−0.892105	+	0.451828i	$0.850772\pi$
$230$	0	0
$231$	−2.00000	−0.131590
$232$	0	0
$233$	10.0000	0.655122	0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000	0.655122	0.327561	+	0.944830i	$0.393773\pi$
$234$	0	0
$235$	−6.00000	−0.391397
$236$	0	0
$237$	4.00000	0.259828
$238$	0	0
$239$	−14.0000	−0.905585	−0.452792	−	0.891616i	$-0.649572\pi$
$239$	−14.0000	−0.905585	−0.452792	+	0.891616i	$0.649572\pi$
$240$	−3.00000	−0.193649
$241$	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
$243$	−16.0000	−1.02640
$244$	−6.00000	−0.384111
$245$	18.0000	1.14998
$246$	9.00000	0.573819
$247$	0	0
$248$	−12.0000	−0.762001
$249$	−7.00000	−0.443607
$250$	3.00000	0.189737
$251$	−7.00000	−0.441836	−0.220918	−	0.975292i	$-0.570905\pi$
$251$	−7.00000	−0.441836	−0.220918	+	0.975292i	$0.570905\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	−22.0000	−1.38040
$255$	0	0
$256$	−17.0000	−1.06250
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	−5.00000	−0.311286
$259$	4.00000	0.248548
$260$	0	0
$261$	0	0
$262$	3.00000	0.185341
$263$	−26.0000	−1.60323	−0.801614	−	0.597841i	$-0.796025\pi$
$263$	−26.0000	−1.60323	−0.801614	+	0.597841i	$0.796025\pi$
$264$	6.00000	0.369274
$265$	−18.0000	−1.10573
$266$	2.00000	0.122628
$267$	−8.00000	−0.489592
$268$	8.00000	0.488678
$269$	25.0000	1.52428	0.762138	−	0.647414i	$-0.224150\pi$
$269$	25.0000	1.52428	0.762138	+	0.647414i	$0.224150\pi$
$270$	−15.0000	−0.912871
$271$	32.0000	1.94386	0.971931	−	0.235267i	$-0.0755965\pi$
$271$	32.0000	1.94386	0.971931	+	0.235267i	$0.0755965\pi$
$272$	0	0
$273$	0	0
$274$	−15.0000	−0.906183
$275$	8.00000	0.482418
$276$	0	0
$277$	−11.0000	−0.660926	−0.330463	−	0.943819i	$-0.607205\pi$
$277$	−11.0000	−0.660926	−0.330463	+	0.943819i	$0.607205\pi$
$278$	−12.0000	−0.719712
$279$	−8.00000	−0.478947
$280$	9.00000	0.537853
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	−2.00000	−0.119098
$283$	−13.0000	−0.772770	−0.386385	−	0.922338i	$-0.626276\pi$
$283$	−13.0000	−0.772770	−0.386385	+	0.922338i	$0.626276\pi$
$284$	−5.00000	−0.296695
$285$	6.00000	0.355409
$286$	0	0
$287$	−9.00000	−0.531253
$288$	−10.0000	−0.589256
$289$	−17.0000	−1.00000
$290$	0	0
$291$	14.0000	0.820695
$292$	−5.00000	−0.292603
$293$	−2.00000	−0.116841	−0.0584206	−	0.998292i	$-0.518606\pi$
$293$	−2.00000	−0.116841	−0.0584206	+	0.998292i	$0.518606\pi$
$294$	6.00000	0.349927
$295$	0	0
$296$	−12.0000	−0.697486
$297$	10.0000	0.580259
$298$	18.0000	1.04271
$299$	0	0
$300$	4.00000	0.230940
$301$	5.00000	0.288195
$302$	0	0
$303$	6.00000	0.344691
$304$	−2.00000	−0.114708
$305$	−18.0000	−1.03068
$306$	0	0
$307$	5.00000	0.285365	0.142683	−	0.989769i	$-0.454427\pi$
$307$	5.00000	0.285365	0.142683	+	0.989769i	$0.454427\pi$
$308$	−2.00000	−0.113961
$309$	9.00000	0.511992
$310$	−12.0000	−0.681554
$311$	25.0000	1.41762	0.708810	−	0.705399i	$-0.249232\pi$
$311$	25.0000	1.41762	0.708810	+	0.705399i	$0.249232\pi$
$312$	0	0
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	−24.0000	−1.35440
$315$	6.00000	0.338062
$316$	4.00000	0.225018
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	−6.00000	−0.336463
$319$	0	0
$320$	−21.0000	−1.17394
$321$	12.0000	0.669775
$322$	0	0
$323$	0	0
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	2.00000	0.110770
$327$	−6.00000	−0.331801
$328$	27.0000	1.49083
$329$	2.00000	0.110264
$330$	6.00000	0.330289
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	−7.00000	−0.384175
$333$	−8.00000	−0.438397
$334$	15.0000	0.820763
$335$	24.0000	1.31126
$336$	1.00000	0.0545545
$337$	3.00000	0.163420	0.0817102	−	0.996656i	$-0.473962\pi$
$337$	3.00000	0.163420	0.0817102	+	0.996656i	$0.473962\pi$
$338$	−13.0000	−0.707107
$339$	−14.0000	−0.760376
$340$	0	0
$341$	8.00000	0.433224
$342$	−4.00000	−0.216295
$343$	−13.0000	−0.701934
$344$	−15.0000	−0.808746
$345$	0	0
$346$	8.00000	0.430083
$347$	−27.0000	−1.44944	−0.724718	−	0.689046i	$-0.758030\pi$
$347$	−27.0000	−1.44944	−0.724718	+	0.689046i	$0.758030\pi$
$348$	0	0
$349$	7.00000	0.374701	0.187351	−	0.982293i	$-0.440010\pi$
$349$	7.00000	0.374701	0.187351	+	0.982293i	$0.440010\pi$
$350$	4.00000	0.213809
$351$	0	0
$352$	10.0000	0.533002
$353$	−20.0000	−1.06449	−0.532246	−	0.846590i	$-0.678652\pi$
$353$	−20.0000	−1.06449	−0.532246	+	0.846590i	$0.678652\pi$
$354$	0	0
$355$	−15.0000	−0.796117
$356$	−8.00000	−0.423999
$357$	0	0
$358$	−15.0000	−0.792775
$359$	20.0000	1.05556	0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000	1.05556	0.527780	+	0.849381i	$0.323025\pi$
$360$	−18.0000	−0.948683
$361$	−15.0000	−0.789474
$362$	10.0000	0.525588
$363$	7.00000	0.367405
$364$	0	0
$365$	−15.0000	−0.785136
$366$	−6.00000	−0.313625
$367$	−25.0000	−1.30499	−0.652495	−	0.757793i	$-0.726278\pi$
$367$	−25.0000	−1.30499	−0.652495	+	0.757793i	$0.726278\pi$
$368$	0	0
$369$	18.0000	0.937043
$370$	−12.0000	−0.623850
$371$	6.00000	0.311504
$372$	4.00000	0.207390
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	0	0
$375$	−3.00000	−0.154919
$376$	−6.00000	−0.309426
$377$	0	0
$378$	5.00000	0.257172
$379$	2.00000	0.102733	0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000	0.102733	0.0513665	+	0.998680i	$0.483642\pi$
$380$	6.00000	0.307794
$381$	22.0000	1.12709
$382$	−6.00000	−0.306987
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	3.00000	0.153093
$385$	−6.00000	−0.305788
$386$	14.0000	0.712581
$387$	−10.0000	−0.508329
$388$	14.0000	0.710742
$389$	−34.0000	−1.72387	−0.861934	−	0.507020i	$-0.830747\pi$
$389$	−34.0000	−1.72387	−0.861934	+	0.507020i	$0.830747\pi$
$390$	0	0
$391$	0	0
$392$	18.0000	0.909137
$393$	−3.00000	−0.151330
$394$	−15.0000	−0.755689
$395$	12.0000	0.603786
$396$	4.00000	0.201008
$397$	−25.0000	−1.25471	−0.627357	−	0.778732i	$-0.715863\pi$
$397$	−25.0000	−1.25471	−0.627357	+	0.778732i	$0.715863\pi$
$398$	−25.0000	−1.25314
$399$	−2.00000	−0.100125
$400$	−4.00000	−0.200000
$401$	−25.0000	−1.24844	−0.624220	−	0.781248i	$-0.714583\pi$
$401$	−25.0000	−1.24844	−0.624220	+	0.781248i	$0.714583\pi$
$402$	8.00000	0.399004
$403$	0	0
$404$	6.00000	0.298511
$405$	−3.00000	−0.149071
$406$	0	0
$407$	8.00000	0.396545
$408$	0	0
$409$	38.0000	1.87898	0.939490	−	0.342578i	$-0.111300\pi$
$409$	38.0000	1.87898	0.939490	+	0.342578i	$0.111300\pi$
$410$	27.0000	1.33343
$411$	15.0000	0.739895
$412$	9.00000	0.443398
$413$	0	0
$414$	0	0
$415$	−21.0000	−1.03085
$416$	0	0
$417$	12.0000	0.587643
$418$	4.00000	0.195646
$419$	−30.0000	−1.46560	−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000	−1.46560	−0.732798	+	0.680446i	$0.761786\pi$
$420$	−3.00000	−0.146385
$421$	20.0000	0.974740	0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000	0.974740	0.487370	+	0.873195i	$0.337956\pi$
$422$	2.00000	0.0973585
$423$	−4.00000	−0.194487
$424$	−18.0000	−0.874157
$425$	0	0
$426$	−5.00000	−0.242251
$427$	6.00000	0.290360
$428$	12.0000	0.580042
$429$	0	0
$430$	−15.0000	−0.723364
$431$	33.0000	1.58955	0.794777	−	0.606902i	$-0.207588\pi$
$431$	33.0000	1.58955	0.794777	+	0.606902i	$0.207588\pi$
$432$	−5.00000	−0.240563
$433$	38.0000	1.82616	0.913082	−	0.407777i	$-0.133696\pi$
$433$	38.0000	1.82616	0.913082	+	0.407777i	$0.133696\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	−6.00000	−0.287348
$437$	0	0
$438$	−5.00000	−0.238909
$439$	−2.00000	−0.0954548	−0.0477274	−	0.998860i	$-0.515198\pi$
$439$	−2.00000	−0.0954548	−0.0477274	+	0.998860i	$0.515198\pi$
$440$	18.0000	0.858116
$441$	12.0000	0.571429
$442$	0	0
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	4.00000	0.189832
$445$	−24.0000	−1.13771
$446$	4.00000	0.189405
$447$	−18.0000	−0.851371
$448$	7.00000	0.330719
$449$	31.0000	1.46298	0.731490	−	0.681852i	$-0.238825\pi$
$449$	31.0000	1.46298	0.731490	+	0.681852i	$0.238825\pi$
$450$	−8.00000	−0.377124
$451$	−18.0000	−0.847587
$452$	−14.0000	−0.658505
$453$	0	0
$454$	18.0000	0.844782
$455$	0	0
$456$	6.00000	0.280976
$457$	−4.00000	−0.187112	−0.0935561	−	0.995614i	$-0.529823\pi$
$457$	−4.00000	−0.187112	−0.0935561	+	0.995614i	$0.529823\pi$
$458$	−27.0000	−1.26163
$459$	0	0
$460$	0	0
$461$	28.0000	1.30409	0.652045	−	0.758180i	$-0.273911\pi$
$461$	28.0000	1.30409	0.652045	+	0.758180i	$0.273911\pi$
$462$	−2.00000	−0.0930484
$463$	27.0000	1.25480	0.627398	−	0.778699i	$-0.284120\pi$
$463$	27.0000	1.25480	0.627398	+	0.778699i	$0.284120\pi$
$464$	0	0
$465$	12.0000	0.556487
$466$	10.0000	0.463241
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	−8.00000	−0.369406
$470$	−6.00000	−0.276759
$471$	24.0000	1.10586
$472$	0	0
$473$	10.0000	0.459800
$474$	4.00000	0.183726
$475$	8.00000	0.367065
$476$	0	0
$477$	−12.0000	−0.549442
$478$	−14.0000	−0.640345
$479$	−12.0000	−0.548294	−0.274147	−	0.961688i	$-0.588395\pi$
$479$	−12.0000	−0.548294	−0.274147	+	0.961688i	$0.588395\pi$
$480$	15.0000	0.684653
$481$	0	0
$482$	4.00000	0.182195
$483$	0	0
$484$	7.00000	0.318182
$485$	42.0000	1.90712
$486$	−16.0000	−0.725775
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	−18.0000	−0.814822
$489$	−2.00000	−0.0904431
$490$	18.0000	0.813157
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	−9.00000	−0.405751
$493$	0	0
$494$	0	0
$495$	12.0000	0.539360
$496$	−4.00000	−0.179605
$497$	5.00000	0.224281
$498$	−7.00000	−0.313678
$499$	−1.00000	−0.0447661	−0.0223831	−	0.999749i	$-0.507125\pi$
$499$	−1.00000	−0.0447661	−0.0223831	+	0.999749i	$0.507125\pi$
$500$	−3.00000	−0.134164
$501$	−15.0000	−0.670151
$502$	−7.00000	−0.312425
$503$	−19.0000	−0.847168	−0.423584	−	0.905857i	$-0.639228\pi$
$503$	−19.0000	−0.847168	−0.423584	+	0.905857i	$0.639228\pi$
$504$	6.00000	0.267261
$505$	18.0000	0.800989
$506$	0	0
$507$	13.0000	0.577350
$508$	22.0000	0.976092
$509$	−33.0000	−1.46270	−0.731350	−	0.682003i	$-0.761109\pi$
$509$	−33.0000	−1.46270	−0.731350	+	0.682003i	$0.761109\pi$
$510$	0	0
$511$	5.00000	0.221187
$512$	−11.0000	−0.486136
$513$	10.0000	0.441511
$514$	−6.00000	−0.264649
$515$	27.0000	1.18976
$516$	5.00000	0.220113
$517$	4.00000	0.175920
$518$	4.00000	0.175750
$519$	−8.00000	−0.351161
$520$	0	0
$521$	10.0000	0.438108	0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000	0.438108	0.219054	+	0.975713i	$0.429703\pi$
$522$	0	0
$523$	−38.0000	−1.66162	−0.830812	−	0.556553i	$-0.812124\pi$
$523$	−38.0000	−1.66162	−0.830812	+	0.556553i	$0.812124\pi$
$524$	−3.00000	−0.131056
$525$	−4.00000	−0.174574
$526$	−26.0000	−1.13365
$527$	0	0
$528$	2.00000	0.0870388
$529$	−23.0000	−1.00000
$530$	−18.0000	−0.781870
$531$	0	0
$532$	−2.00000	−0.0867110
$533$	0	0
$534$	−8.00000	−0.346194
$535$	36.0000	1.55642
$536$	24.0000	1.03664
$537$	15.0000	0.647298
$538$	25.0000	1.07783
$539$	−12.0000	−0.516877
$540$	15.0000	0.645497
$541$	−17.0000	−0.730887	−0.365444	−	0.930834i	$-0.619083\pi$
$541$	−17.0000	−0.730887	−0.365444	+	0.930834i	$0.619083\pi$
$542$	32.0000	1.37452
$543$	−10.0000	−0.429141
$544$	0	0
$545$	−18.0000	−0.771035
$546$	0	0
$547$	37.0000	1.58201	0.791003	−	0.611812i	$-0.209559\pi$
$547$	37.0000	1.58201	0.791003	+	0.611812i	$0.209559\pi$
$548$	15.0000	0.640768
$549$	−12.0000	−0.512148
$550$	8.00000	0.341121
$551$	0	0
$552$	0	0
$553$	−4.00000	−0.170097
$554$	−11.0000	−0.467345
$555$	12.0000	0.509372
$556$	12.0000	0.508913
$557$	31.0000	1.31351	0.656756	−	0.754103i	$-0.271928\pi$
$557$	31.0000	1.31351	0.656756	+	0.754103i	$0.271928\pi$
$558$	−8.00000	−0.338667
$559$	0	0
$560$	3.00000	0.126773
$561$	0	0
$562$	18.0000	0.759284
$563$	10.0000	0.421450	0.210725	−	0.977545i	$-0.432418\pi$
$563$	10.0000	0.421450	0.210725	+	0.977545i	$0.432418\pi$
$564$	2.00000	0.0842152
$565$	−42.0000	−1.76695
$566$	−13.0000	−0.546431
$567$	1.00000	0.0419961
$568$	−15.0000	−0.629386
$569$	24.0000	1.00613	0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000	1.00613	0.503066	+	0.864248i	$0.332205\pi$
$570$	6.00000	0.251312
$571$	−41.0000	−1.71580	−0.857898	−	0.513820i	$-0.828230\pi$
$571$	−41.0000	−1.71580	−0.857898	+	0.513820i	$0.828230\pi$
$572$	0	0
$573$	6.00000	0.250654
$574$	−9.00000	−0.375653
$575$	0	0
$576$	−14.0000	−0.583333
$577$	−24.0000	−0.999133	−0.499567	−	0.866276i	$-0.666507\pi$
$577$	−24.0000	−0.999133	−0.499567	+	0.866276i	$0.666507\pi$
$578$	−17.0000	−0.707107
$579$	−14.0000	−0.581820
$580$	0	0
$581$	7.00000	0.290409
$582$	14.0000	0.580319
$583$	12.0000	0.496989
$584$	−15.0000	−0.620704
$585$	0	0
$586$	−2.00000	−0.0826192
$587$	−40.0000	−1.65098	−0.825488	−	0.564419i	$-0.809100\pi$
$587$	−40.0000	−1.65098	−0.825488	+	0.564419i	$0.809100\pi$
$588$	−6.00000	−0.247436
$589$	8.00000	0.329634
$590$	0	0
$591$	15.0000	0.617018
$592$	−4.00000	−0.164399
$593$	−2.00000	−0.0821302	−0.0410651	−	0.999156i	$-0.513075\pi$
$593$	−2.00000	−0.0821302	−0.0410651	+	0.999156i	$0.513075\pi$
$594$	10.0000	0.410305
$595$	0	0
$596$	−18.0000	−0.737309
$597$	25.0000	1.02318
$598$	0	0
$599$	40.0000	1.63436	0.817178	−	0.576386i	$-0.195537\pi$
$599$	40.0000	1.63436	0.817178	+	0.576386i	$0.195537\pi$
$600$	12.0000	0.489898
$601$	−33.0000	−1.34610	−0.673049	−	0.739598i	$-0.735016\pi$
$601$	−33.0000	−1.34610	−0.673049	+	0.739598i	$0.735016\pi$
$602$	5.00000	0.203785
$603$	16.0000	0.651570
$604$	0	0
$605$	21.0000	0.853771
$606$	6.00000	0.243733
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	10.0000	0.405554
$609$	0	0
$610$	−18.0000	−0.728799
$611$	0	0
$612$	0	0
$613$	−5.00000	−0.201948	−0.100974	−	0.994889i	$-0.532196\pi$
$613$	−5.00000	−0.201948	−0.100974	+	0.994889i	$0.532196\pi$
$614$	5.00000	0.201784
$615$	−27.0000	−1.08875
$616$	−6.00000	−0.241747
$617$	−27.0000	−1.08698	−0.543490	−	0.839416i	$-0.682897\pi$
$617$	−27.0000	−1.08698	−0.543490	+	0.839416i	$0.682897\pi$
$618$	9.00000	0.362033
$619$	22.0000	0.884255	0.442127	−	0.896952i	$-0.354224\pi$
$619$	22.0000	0.884255	0.442127	+	0.896952i	$0.354224\pi$
$620$	12.0000	0.481932
$621$	0	0
$622$	25.0000	1.00241
$623$	8.00000	0.320513
$624$	0	0
$625$	−29.0000	−1.16000
$626$	−6.00000	−0.239808
$627$	−4.00000	−0.159745
$628$	24.0000	0.957704
$629$	0	0
$630$	6.00000	0.239046
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	12.0000	0.477334
$633$	−2.00000	−0.0794929
$634$	12.0000	0.476581
$635$	66.0000	2.61913
$636$	6.00000	0.237915
$637$	0	0
$638$	0	0
$639$	−10.0000	−0.395594
$640$	9.00000	0.355756
$641$	−15.0000	−0.592464	−0.296232	−	0.955116i	$-0.595730\pi$
$641$	−15.0000	−0.592464	−0.296232	+	0.955116i	$0.595730\pi$
$642$	12.0000	0.473602
$643$	11.0000	0.433798	0.216899	−	0.976194i	$-0.430406\pi$
$643$	11.0000	0.433798	0.216899	+	0.976194i	$0.430406\pi$
$644$	0	0
$645$	15.0000	0.590624
$646$	0	0
$647$	−4.00000	−0.157256	−0.0786281	−	0.996904i	$-0.525054\pi$
$647$	−4.00000	−0.157256	−0.0786281	+	0.996904i	$0.525054\pi$
$648$	−3.00000	−0.117851
$649$	0	0
$650$	0	0
$651$	−4.00000	−0.156772
$652$	−2.00000	−0.0783260
$653$	−31.0000	−1.21312	−0.606562	−	0.795036i	$-0.707452\pi$
$653$	−31.0000	−1.21312	−0.606562	+	0.795036i	$0.707452\pi$
$654$	−6.00000	−0.234619
$655$	−9.00000	−0.351659
$656$	9.00000	0.351391
$657$	−10.0000	−0.390137
$658$	2.00000	0.0779681
$659$	−30.0000	−1.16863	−0.584317	−	0.811525i	$-0.698638\pi$
$659$	−30.0000	−1.16863	−0.584317	+	0.811525i	$0.698638\pi$
$660$	−6.00000	−0.233550
$661$	−20.0000	−0.777910	−0.388955	−	0.921257i	$-0.627164\pi$
$661$	−20.0000	−0.777910	−0.388955	+	0.921257i	$0.627164\pi$
$662$	4.00000	0.155464
$663$	0	0
$664$	−21.0000	−0.814958
$665$	−6.00000	−0.232670
$666$	−8.00000	−0.309994
$667$	0	0
$668$	−15.0000	−0.580367
$669$	−4.00000	−0.154649
$670$	24.0000	0.927201
$671$	12.0000	0.463255
$672$	−5.00000	−0.192879
$673$	26.0000	1.00223	0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000	1.00223	0.501113	+	0.865382i	$0.332924\pi$
$674$	3.00000	0.115556
$675$	20.0000	0.769800
$676$	13.0000	0.500000
$677$	20.0000	0.768662	0.384331	−	0.923195i	$-0.374432\pi$
$677$	20.0000	0.768662	0.384331	+	0.923195i	$0.374432\pi$
$678$	−14.0000	−0.537667
$679$	−14.0000	−0.537271
$680$	0	0
$681$	−18.0000	−0.689761
$682$	8.00000	0.306336
$683$	24.0000	0.918334	0.459167	−	0.888350i	$-0.348148\pi$
$683$	24.0000	0.918334	0.459167	+	0.888350i	$0.348148\pi$
$684$	4.00000	0.152944
$685$	45.0000	1.71936
$686$	−13.0000	−0.496342
$687$	27.0000	1.03011
$688$	−5.00000	−0.190623
$689$	0	0
$690$	0	0
$691$	8.00000	0.304334	0.152167	−	0.988355i	$-0.451375\pi$
$691$	8.00000	0.304334	0.152167	+	0.988355i	$0.451375\pi$
$692$	−8.00000	−0.304114
$693$	−4.00000	−0.151947
$694$	−27.0000	−1.02491
$695$	36.0000	1.36556
$696$	0	0
$697$	0	0
$698$	7.00000	0.264954
$699$	−10.0000	−0.378235
$700$	−4.00000	−0.151186
$701$	15.0000	0.566542	0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000	0.566542	0.283271	+	0.959040i	$0.408580\pi$
$702$	0	0
$703$	8.00000	0.301726
$704$	14.0000	0.527645
$705$	6.00000	0.225973
$706$	−20.0000	−0.752710
$707$	−6.00000	−0.225653
$708$	0	0
$709$	−42.0000	−1.57734	−0.788672	−	0.614815i	$-0.789231\pi$
$709$	−42.0000	−1.57734	−0.788672	+	0.614815i	$0.789231\pi$
$710$	−15.0000	−0.562940
$711$	8.00000	0.300023
$712$	−24.0000	−0.899438
$713$	0	0
$714$	0	0
$715$	0	0
$716$	15.0000	0.560576
$717$	14.0000	0.522840
$718$	20.0000	0.746393
$719$	−38.0000	−1.41716	−0.708580	−	0.705630i	$-0.750664\pi$
$719$	−38.0000	−1.41716	−0.708580	+	0.705630i	$0.750664\pi$
$720$	−6.00000	−0.223607
$721$	−9.00000	−0.335178
$722$	−15.0000	−0.558242
$723$	−4.00000	−0.148762
$724$	−10.0000	−0.371647
$725$	0	0
$726$	7.00000	0.259794
$727$	0	0		−	1.00000i	$-0.5\pi$
$727$	0	0			1.00000i	$0.5\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	−15.0000	−0.555175
$731$	0	0
$732$	6.00000	0.221766
$733$	3.00000	0.110808	0.0554038	−	0.998464i	$-0.482355\pi$
$733$	3.00000	0.110808	0.0554038	+	0.998464i	$0.482355\pi$
$734$	−25.0000	−0.922767
$735$	−18.0000	−0.663940
$736$	0	0
$737$	−16.0000	−0.589368
$738$	18.0000	0.662589
$739$	−24.0000	−0.882854	−0.441427	−	0.897297i	$-0.645528\pi$
$739$	−24.0000	−0.882854	−0.441427	+	0.897297i	$0.645528\pi$
$740$	12.0000	0.441129
$741$	0	0
$742$	6.00000	0.220267
$743$	−9.00000	−0.330178	−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000	−0.330178	−0.165089	+	0.986279i	$0.552791\pi$
$744$	12.0000	0.439941
$745$	−54.0000	−1.97841
$746$	14.0000	0.512576
$747$	−14.0000	−0.512233
$748$	0	0
$749$	−12.0000	−0.438470
$750$	−3.00000	−0.109545
$751$	−11.0000	−0.401396	−0.200698	−	0.979653i	$-0.564321\pi$
$751$	−11.0000	−0.401396	−0.200698	+	0.979653i	$0.564321\pi$
$752$	−2.00000	−0.0729325
$753$	7.00000	0.255094
$754$	0	0
$755$	0	0
$756$	−5.00000	−0.181848
$757$	−46.0000	−1.67190	−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000	−1.67190	−0.835949	+	0.548807i	$0.815082\pi$
$758$	2.00000	0.0726433
$759$	0	0
$760$	18.0000	0.652929
$761$	22.0000	0.797499	0.398750	−	0.917060i	$-0.369444\pi$
$761$	22.0000	0.797499	0.398750	+	0.917060i	$0.369444\pi$
$762$	22.0000	0.796976
$763$	6.00000	0.217215
$764$	6.00000	0.217072
$765$	0	0
$766$	−6.00000	−0.216789
$767$	0	0
$768$	17.0000	0.613435
$769$	33.0000	1.19001	0.595005	−	0.803722i	$-0.297150\pi$
$769$	33.0000	1.19001	0.595005	+	0.803722i	$0.297150\pi$
$770$	−6.00000	−0.216225
$771$	6.00000	0.216085
$772$	−14.0000	−0.503871
$773$	43.0000	1.54660	0.773301	−	0.634039i	$-0.218604\pi$
$773$	43.0000	1.54660	0.773301	+	0.634039i	$0.218604\pi$
$774$	−10.0000	−0.359443
$775$	16.0000	0.574737
$776$	42.0000	1.50771
$777$	−4.00000	−0.143499
$778$	−34.0000	−1.21896
$779$	−18.0000	−0.644917
$780$	0	0
$781$	10.0000	0.357828
$782$	0	0
$783$	0	0
$784$	6.00000	0.214286
$785$	72.0000	2.56979
$786$	−3.00000	−0.107006
$787$	12.0000	0.427754	0.213877	−	0.976861i	$-0.431391\pi$
$787$	12.0000	0.427754	0.213877	+	0.976861i	$0.431391\pi$
$788$	15.0000	0.534353
$789$	26.0000	0.925625
$790$	12.0000	0.426941
$791$	14.0000	0.497783
$792$	12.0000	0.426401
$793$	0	0
$794$	−25.0000	−0.887217
$795$	18.0000	0.638394
$796$	25.0000	0.886102
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	−2.00000	−0.0707992
$799$	0	0
$800$	20.0000	0.707107
$801$	−16.0000	−0.565332
$802$	−25.0000	−0.882781
$803$	10.0000	0.352892
$804$	−8.00000	−0.282138
$805$	0	0
$806$	0	0
$807$	−25.0000	−0.880042
$808$	18.0000	0.633238
$809$	5.00000	0.175791	0.0878953	−	0.996130i	$-0.471986\pi$
$809$	5.00000	0.175791	0.0878953	+	0.996130i	$0.471986\pi$
$810$	−3.00000	−0.105409
$811$	−17.0000	−0.596951	−0.298475	−	0.954417i	$-0.596478\pi$
$811$	−17.0000	−0.596951	−0.298475	+	0.954417i	$0.596478\pi$
$812$	0	0
$813$	−32.0000	−1.12229
$814$	8.00000	0.280400
$815$	−6.00000	−0.210171
$816$	0	0
$817$	10.0000	0.349856
$818$	38.0000	1.32864
$819$	0	0
$820$	−27.0000	−0.942881
$821$	20.0000	0.698005	0.349002	−	0.937122i	$-0.386521\pi$
$821$	20.0000	0.698005	0.349002	+	0.937122i	$0.386521\pi$
$822$	15.0000	0.523185
$823$	16.0000	0.557725	0.278862	−	0.960331i	$-0.410043\pi$
$823$	16.0000	0.557725	0.278862	+	0.960331i	$0.410043\pi$
$824$	27.0000	0.940590
$825$	−8.00000	−0.278524
$826$	0	0
$827$	26.0000	0.904109	0.452054	−	0.891990i	$-0.350691\pi$
$827$	26.0000	0.904109	0.452054	+	0.891990i	$0.350691\pi$
$828$	0	0
$829$	−22.0000	−0.764092	−0.382046	−	0.924143i	$-0.624780\pi$
$829$	−22.0000	−0.764092	−0.382046	+	0.924143i	$0.624780\pi$
$830$	−21.0000	−0.728921
$831$	11.0000	0.381586
$832$	0	0
$833$	0	0
$834$	12.0000	0.415526
$835$	−45.0000	−1.55729
$836$	−4.00000	−0.138343
$837$	20.0000	0.691301
$838$	−30.0000	−1.03633
$839$	18.0000	0.621429	0.310715	−	0.950503i	$-0.399432\pi$
$839$	18.0000	0.621429	0.310715	+	0.950503i	$0.399432\pi$
$840$	−9.00000	−0.310530
$841$	−29.0000	−1.00000
$842$	20.0000	0.689246
$843$	−18.0000	−0.619953
$844$	−2.00000	−0.0688428
$845$	39.0000	1.34164
$846$	−4.00000	−0.137523
$847$	−7.00000	−0.240523
$848$	−6.00000	−0.206041
$849$	13.0000	0.446159
$850$	0	0
$851$	0	0
$852$	5.00000	0.171297
$853$	39.0000	1.33533	0.667667	−	0.744460i	$-0.267293\pi$
$853$	39.0000	1.33533	0.667667	+	0.744460i	$0.267293\pi$
$854$	6.00000	0.205316
$855$	12.0000	0.410391
$856$	36.0000	1.23045
$857$	48.0000	1.63965	0.819824	−	0.572615i	$-0.194071\pi$
$857$	48.0000	1.63965	0.819824	+	0.572615i	$0.194071\pi$
$858$	0	0
$859$	4.00000	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	15.0000	0.511496
$861$	9.00000	0.306719
$862$	33.0000	1.12398
$863$	6.00000	0.204242	0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000	0.204242	0.102121	+	0.994772i	$0.467437\pi$
$864$	25.0000	0.850517
$865$	−24.0000	−0.816024
$866$	38.0000	1.29129
$867$	17.0000	0.577350
$868$	−4.00000	−0.135769
$869$	−8.00000	−0.271381
$870$	0	0
$871$	0	0
$872$	−18.0000	−0.609557
$873$	28.0000	0.947656
$874$	0	0
$875$	3.00000	0.101419
$876$	5.00000	0.168934
$877$	−28.0000	−0.945493	−0.472746	−	0.881199i	$-0.656737\pi$
$877$	−28.0000	−0.945493	−0.472746	+	0.881199i	$0.656737\pi$
$878$	−2.00000	−0.0674967
$879$	2.00000	0.0674583
$880$	6.00000	0.202260
$881$	−26.0000	−0.875962	−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000	−0.875962	−0.437981	+	0.898984i	$0.644306\pi$
$882$	12.0000	0.404061
$883$	−37.0000	−1.24515	−0.622575	−	0.782560i	$-0.713913\pi$
$883$	−37.0000	−1.24515	−0.622575	+	0.782560i	$0.713913\pi$
$884$	0	0
$885$	0	0
$886$	4.00000	0.134383
$887$	−13.0000	−0.436497	−0.218249	−	0.975893i	$-0.570034\pi$
$887$	−13.0000	−0.436497	−0.218249	+	0.975893i	$0.570034\pi$
$888$	12.0000	0.402694
$889$	−22.0000	−0.737856
$890$	−24.0000	−0.804482
$891$	2.00000	0.0670025
$892$	−4.00000	−0.133930
$893$	4.00000	0.133855
$894$	−18.0000	−0.602010
$895$	45.0000	1.50418
$896$	−3.00000	−0.100223
$897$	0	0
$898$	31.0000	1.03448
$899$	0	0
$900$	8.00000	0.266667
$901$	0	0
$902$	−18.0000	−0.599334
$903$	−5.00000	−0.166390
$904$	−42.0000	−1.39690
$905$	−30.0000	−0.997234
$906$	0	0
$907$	22.0000	0.730498	0.365249	−	0.930910i	$-0.380984\pi$
$907$	22.0000	0.730498	0.365249	+	0.930910i	$0.380984\pi$
$908$	−18.0000	−0.597351
$909$	12.0000	0.398015
$910$	0	0
$911$	55.0000	1.82223	0.911116	−	0.412151i	$-0.135222\pi$
$911$	55.0000	1.82223	0.911116	+	0.412151i	$0.135222\pi$
$912$	2.00000	0.0662266
$913$	14.0000	0.463332
$914$	−4.00000	−0.132308
$915$	18.0000	0.595062
$916$	27.0000	0.892105
$917$	3.00000	0.0990687
$918$	0	0
$919$	−41.0000	−1.35247	−0.676233	−	0.736688i	$-0.736389\pi$
$919$	−41.0000	−1.35247	−0.676233	+	0.736688i	$0.736389\pi$
$920$	0	0
$921$	−5.00000	−0.164756
$922$	28.0000	0.922131
$923$	0	0
$924$	2.00000	0.0657952
$925$	16.0000	0.526077
$926$	27.0000	0.887275
$927$	18.0000	0.591198
$928$	0	0
$929$	−45.0000	−1.47640	−0.738201	−	0.674581i	$-0.764324\pi$
$929$	−45.0000	−1.47640	−0.738201	+	0.674581i	$0.764324\pi$
$930$	12.0000	0.393496
$931$	−12.0000	−0.393284
$932$	−10.0000	−0.327561
$933$	−25.0000	−0.818463
$934$	0	0
$935$	0	0
$936$	0	0
$937$	33.0000	1.07806	0.539032	−	0.842286i	$-0.318790\pi$
$937$	33.0000	1.07806	0.539032	+	0.842286i	$0.318790\pi$
$938$	−8.00000	−0.261209
$939$	6.00000	0.195803
$940$	6.00000	0.195698
$941$	−45.0000	−1.46696	−0.733479	−	0.679712i	$-0.762105\pi$
$941$	−45.0000	−1.46696	−0.733479	+	0.679712i	$0.762105\pi$
$942$	24.0000	0.781962
$943$	0	0
$944$	0	0
$945$	−15.0000	−0.487950
$946$	10.0000	0.325128
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	−4.00000	−0.129914
$949$	0	0
$950$	8.00000	0.259554
$951$	−12.0000	−0.389127
$952$	0	0
$953$	−44.0000	−1.42530	−0.712650	−	0.701520i	$-0.752505\pi$
$953$	−44.0000	−1.42530	−0.712650	+	0.701520i	$0.752505\pi$
$954$	−12.0000	−0.388514
$955$	18.0000	0.582466
$956$	14.0000	0.452792
$957$	0	0
$958$	−12.0000	−0.387702
$959$	−15.0000	−0.484375
$960$	21.0000	0.677772
$961$	−15.0000	−0.483871
$962$	0	0
$963$	24.0000	0.773389
$964$	−4.00000	−0.128831
$965$	−42.0000	−1.35203
$966$	0	0
$967$	−11.0000	−0.353736	−0.176868	−	0.984235i	$-0.556597\pi$
$967$	−11.0000	−0.353736	−0.176868	+	0.984235i	$0.556597\pi$
$968$	21.0000	0.674966
$969$	0	0
$970$	42.0000	1.34854
$971$	−48.0000	−1.54039	−0.770197	−	0.637806i	$-0.779842\pi$
$971$	−48.0000	−1.54039	−0.770197	+	0.637806i	$0.779842\pi$
$972$	16.0000	0.513200
$973$	−12.0000	−0.384702
$974$	−12.0000	−0.384505
$975$	0	0
$976$	−6.00000	−0.192055
$977$	40.0000	1.27971	0.639857	−	0.768494i	$-0.278994\pi$
$977$	40.0000	1.27971	0.639857	+	0.768494i	$0.278994\pi$
$978$	−2.00000	−0.0639529
$979$	16.0000	0.511362
$980$	−18.0000	−0.574989
$981$	−12.0000	−0.383131
$982$	−20.0000	−0.638226
$983$	−25.0000	−0.797376	−0.398688	−	0.917087i	$-0.630534\pi$
$983$	−25.0000	−0.797376	−0.398688	+	0.917087i	$0.630534\pi$
$984$	−27.0000	−0.860729
$985$	45.0000	1.43382
$986$	0	0
$987$	−2.00000	−0.0636607
$988$	0	0
$989$	0	0
$990$	12.0000	0.381385
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	20.0000	0.635001
$993$	−4.00000	−0.126936
$994$	5.00000	0.158590
$995$	75.0000	2.37766
$996$	7.00000	0.221803
$997$	46.0000	1.45683	0.728417	−	0.685134i	$-0.240256\pi$
$997$	46.0000	1.45683	0.728417	+	0.685134i	$0.240256\pi$
$998$	−1.00000	−0.0316544
$999$	20.0000	0.632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6011.2.a.c.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6011.2.a.c.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6011.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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