LMFDB - Embedded newform 6027.2.a.bo.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.33013 q^{2} +1.00000 q^{3} -0.230742 q^{4} -3.44355 q^{5} +1.33013 q^{6} -2.96719 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.33013 q^{2} +1.00000 q^{3} -0.230742 q^{4} -3.44355 q^{5} +1.33013 q^{6} -2.96719 q^{8} +1.00000 q^{9} -4.58038 q^{10} +2.42981 q^{11} -0.230742 q^{12} -4.50765 q^{13} -3.44355 q^{15} -3.48527 q^{16} -4.56026 q^{17} +1.33013 q^{18} -1.29115 q^{19} +0.794570 q^{20} +3.23197 q^{22} -5.25675 q^{23} -2.96719 q^{24} +6.85802 q^{25} -5.99578 q^{26} +1.00000 q^{27} +6.83526 q^{29} -4.58038 q^{30} +2.39033 q^{31} +1.29849 q^{32} +2.42981 q^{33} -6.06576 q^{34} -0.230742 q^{36} -0.323629 q^{37} -1.71740 q^{38} -4.50765 q^{39} +10.2176 q^{40} -1.00000 q^{41} +3.93668 q^{43} -0.560658 q^{44} -3.44355 q^{45} -6.99219 q^{46} +12.2131 q^{47} -3.48527 q^{48} +9.12209 q^{50} -4.56026 q^{51} +1.04010 q^{52} +5.17996 q^{53} +1.33013 q^{54} -8.36716 q^{55} -1.29115 q^{57} +9.09182 q^{58} -1.20427 q^{59} +0.794570 q^{60} -4.84509 q^{61} +3.17946 q^{62} +8.69771 q^{64} +15.5223 q^{65} +3.23197 q^{66} +3.77777 q^{67} +1.05224 q^{68} -5.25675 q^{69} -5.00281 q^{71} -2.96719 q^{72} +8.20083 q^{73} -0.430471 q^{74} +6.85802 q^{75} +0.297922 q^{76} -5.99578 q^{78} -7.91250 q^{79} +12.0017 q^{80} +1.00000 q^{81} -1.33013 q^{82} +2.47939 q^{83} +15.7035 q^{85} +5.23631 q^{86} +6.83526 q^{87} -7.20969 q^{88} -2.30019 q^{89} -4.58038 q^{90} +1.21295 q^{92} +2.39033 q^{93} +16.2450 q^{94} +4.44614 q^{95} +1.29849 q^{96} -15.4518 q^{97} +2.42981 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9	$ 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 12 q^{11} + 32 q^{12} + 4 q^{15} + 44 q^{16} + 8 q^{17} + 8 q^{18} - 4 q^{19} + 28 q^{20} + 16 q^{22} + 20 q^{23} + 24 q^{24} + 48 q^{25} + 32 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 4 q^{31} + 36 q^{32} + 12 q^{33} + 16 q^{34} + 32 q^{36} + 64 q^{37} + 20 q^{38} - 48 q^{40} - 24 q^{41} + 20 q^{43} + 48 q^{44} + 4 q^{45} + 28 q^{46} + 32 q^{47} + 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} + 8 q^{54} - 24 q^{55} - 4 q^{57} + 28 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} - 4 q^{62} + 48 q^{64} + 28 q^{65} + 16 q^{66} + 44 q^{67} - 32 q^{68} + 20 q^{69} + 20 q^{71} + 24 q^{72} - 16 q^{73} + 44 q^{74} + 48 q^{75} - 16 q^{76} + 32 q^{78} + 4 q^{79} + 44 q^{80} + 24 q^{81} - 8 q^{82} + 8 q^{83} + 28 q^{85} + 56 q^{86} + 24 q^{87} + 60 q^{88} + 60 q^{89} - 4 q^{90} + 60 q^{92} - 4 q^{93} + 24 q^{94} + 28 q^{95} + 36 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 12 * q^11 + 32 * q^12 + 4 * q^15 + 44 * q^16 + 8 * q^17 + 8 * q^18 - 4 * q^19 + 28 * q^20 + 16 * q^22 + 20 * q^23 + 24 * q^24 + 48 * q^25 + 32 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 4 * q^31 + 36 * q^32 + 12 * q^33 + 16 * q^34 + 32 * q^36 + 64 * q^37 + 20 * q^38 - 48 * q^40 - 24 * q^41 + 20 * q^43 + 48 * q^44 + 4 * q^45 + 28 * q^46 + 32 * q^47 + 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 + 8 * q^54 - 24 * q^55 - 4 * q^57 + 28 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 - 4 * q^62 + 48 * q^64 + 28 * q^65 + 16 * q^66 + 44 * q^67 - 32 * q^68 + 20 * q^69 + 20 * q^71 + 24 * q^72 - 16 * q^73 + 44 * q^74 + 48 * q^75 - 16 * q^76 + 32 * q^78 + 4 * q^79 + 44 * q^80 + 24 * q^81 - 8 * q^82 + 8 * q^83 + 28 * q^85 + 56 * q^86 + 24 * q^87 + 60 * q^88 + 60 * q^89 - 4 * q^90 + 60 * q^92 - 4 * q^93 + 24 * q^94 + 28 * q^95 + 36 * q^96 - 48 * q^97 + 12 * q^99

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 $

$2$	1.33013	0.940547	0.470274	−	0.882521i	$-0.344155\pi$
$2$	1.33013	0.940547	0.470274	+	0.882521i	$0.344155\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.230742	−0.115371
$5$	−3.44355	−1.54000	−0.770001	−	0.638043i	$-0.779744\pi$
$5$	−3.44355	−1.54000	−0.770001	+	0.638043i	$0.779744\pi$
$6$	1.33013	0.543025
$7$	0	0
$7$	0	0
$8$	−2.96719	−1.04906
$9$	1.00000	0.333333
$10$	−4.58038	−1.44844
$11$	2.42981	0.732615	0.366307	−	0.930494i	$-0.380622\pi$
$11$	2.42981	0.732615	0.366307	+	0.930494i	$0.380622\pi$
$12$	−0.230742	−0.0666094
$13$	−4.50765	−1.25020	−0.625099	−	0.780546i	$-0.714941\pi$
$13$	−4.50765	−1.25020	−0.625099	+	0.780546i	$0.714941\pi$
$14$	0	0
$15$	−3.44355	−0.889120
$16$	−3.48527	−0.871319
$17$	−4.56026	−1.10602	−0.553012	−	0.833173i	$-0.686522\pi$
$17$	−4.56026	−1.10602	−0.553012	+	0.833173i	$0.686522\pi$
$18$	1.33013	0.313516
$19$	−1.29115	−0.296210	−0.148105	−	0.988972i	$-0.547317\pi$
$19$	−1.29115	−0.296210	−0.148105	+	0.988972i	$0.547317\pi$
$20$	0.794570	0.177671
$21$	0	0
$22$	3.23197	0.689059
$23$	−5.25675	−1.09611	−0.548054	−	0.836443i	$-0.684631\pi$
$23$	−5.25675	−1.09611	−0.548054	+	0.836443i	$0.684631\pi$
$24$	−2.96719	−0.605674
$25$	6.85802	1.37160
$26$	−5.99578	−1.17587
$27$	1.00000	0.192450
$28$	0	0
$29$	6.83526	1.26928	0.634638	−	0.772809i	$-0.281149\pi$
$29$	6.83526	1.26928	0.634638	+	0.772809i	$0.281149\pi$
$30$	−4.58038	−0.836260
$31$	2.39033	0.429316	0.214658	−	0.976689i	$-0.431136\pi$
$31$	2.39033	0.429316	0.214658	+	0.976689i	$0.431136\pi$
$32$	1.29849	0.229543
$33$	2.42981	0.422975
$34$	−6.06576	−1.04027
$35$	0	0
$36$	−0.230742	−0.0384569
$37$	−0.323629	−0.0532043	−0.0266022	−	0.999646i	$-0.508469\pi$
$37$	−0.323629	−0.0532043	−0.0266022	+	0.999646i	$0.508469\pi$
$38$	−1.71740	−0.278600
$39$	−4.50765	−0.721802
$40$	10.2176	1.61555
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	3.93668	0.600338	0.300169	−	0.953886i	$-0.402957\pi$
$43$	3.93668	0.600338	0.300169	+	0.953886i	$0.402957\pi$
$44$	−0.560658	−0.0845223
$45$	−3.44355	−0.513334
$46$	−6.99219	−1.03094
$47$	12.2131	1.78146	0.890730	−	0.454534i	$-0.150194\pi$
$47$	12.2131	1.78146	0.890730	+	0.454534i	$0.150194\pi$
$48$	−3.48527	−0.503056
$49$	0	0
$50$	9.12209	1.29006
$51$	−4.56026	−0.638564
$52$	1.04010	0.144236
$53$	5.17996	0.711522	0.355761	−	0.934577i	$-0.384222\pi$
$53$	5.17996	0.711522	0.355761	+	0.934577i	$0.384222\pi$
$54$	1.33013	0.181008
$55$	−8.36716	−1.12823
$56$	0	0
$57$	−1.29115	−0.171017
$58$	9.09182	1.19381
$59$	−1.20427	−0.156783	−0.0783914	−	0.996923i	$-0.524978\pi$
$59$	−1.20427	−0.156783	−0.0783914	+	0.996923i	$0.524978\pi$
$60$	0.794570	0.102579
$61$	−4.84509	−0.620350	−0.310175	−	0.950679i	$-0.600388\pi$
$61$	−4.84509	−0.620350	−0.310175	+	0.950679i	$0.600388\pi$
$62$	3.17946	0.403792
$63$	0	0
$64$	8.69771	1.08721
$65$	15.5223	1.92531
$66$	3.23197	0.397828
$67$	3.77777	0.461528	0.230764	−	0.973010i	$-0.425877\pi$
$67$	3.77777	0.461528	0.230764	+	0.973010i	$0.425877\pi$
$68$	1.05224	0.127603
$69$	−5.25675	−0.632839
$70$	0	0
$71$	−5.00281	−0.593725	−0.296862	−	0.954920i	$-0.595940\pi$
$71$	−5.00281	−0.593725	−0.296862	+	0.954920i	$0.595940\pi$
$72$	−2.96719	−0.349686
$73$	8.20083	0.959834	0.479917	−	0.877314i	$-0.340667\pi$
$73$	8.20083	0.959834	0.479917	+	0.877314i	$0.340667\pi$
$74$	−0.430471	−0.0500412
$75$	6.85802	0.791896
$76$	0.297922	0.0341740
$77$	0	0
$78$	−5.99578	−0.678889
$79$	−7.91250	−0.890226	−0.445113	−	0.895474i	$-0.646837\pi$
$79$	−7.91250	−0.890226	−0.445113	+	0.895474i	$0.646837\pi$
$80$	12.0017	1.34183
$81$	1.00000	0.111111
$82$	−1.33013	−0.146889
$83$	2.47939	0.272148	0.136074	−	0.990699i	$-0.456552\pi$
$83$	2.47939	0.272148	0.136074	+	0.990699i	$0.456552\pi$
$84$	0	0
$85$	15.7035	1.70328
$86$	5.23631	0.564646
$87$	6.83526	0.732817
$88$	−7.20969	−0.768556
$89$	−2.30019	−0.243819	−0.121910	−	0.992541i	$-0.538902\pi$
$89$	−2.30019	−0.243819	−0.121910	+	0.992541i	$0.538902\pi$
$90$	−4.58038	−0.482815
$91$	0	0
$92$	1.21295	0.126459
$93$	2.39033	0.247866
$94$	16.2450	1.67555
$95$	4.44614	0.456164
$96$	1.29849	0.132526
$97$	−15.4518	−1.56890	−0.784448	−	0.620195i	$-0.787054\pi$
$97$	−15.4518	−1.56890	−0.784448	+	0.620195i	$0.787054\pi$
$98$	0	0
$99$	2.42981	0.244205
$100$	−1.58243	−0.158243
$101$	2.10297	0.209253	0.104626	−	0.994512i	$-0.466635\pi$
$101$	2.10297	0.209253	0.104626	+	0.994512i	$0.466635\pi$
$102$	−6.06576	−0.600599
$103$	9.55463	0.941445	0.470723	−	0.882281i	$-0.343993\pi$
$103$	9.55463	0.941445	0.470723	+	0.882281i	$0.343993\pi$
$104$	13.3750	1.31153
$105$	0	0
$106$	6.89004	0.669220
$107$	−0.434379	−0.0419930	−0.0209965	−	0.999780i	$-0.506684\pi$
$107$	−0.434379	−0.0419930	−0.0209965	+	0.999780i	$0.506684\pi$
$108$	−0.230742	−0.0222031
$109$	11.2038	1.07313	0.536565	−	0.843859i	$-0.319722\pi$
$109$	11.2038	1.07313	0.536565	+	0.843859i	$0.319722\pi$
$110$	−11.1294	−1.06115
$111$	−0.323629	−0.0307175
$112$	0	0
$113$	3.07828	0.289580	0.144790	−	0.989462i	$-0.453749\pi$
$113$	3.07828	0.289580	0.144790	+	0.989462i	$0.453749\pi$
$114$	−1.71740	−0.160850
$115$	18.1019	1.68801
$116$	−1.57718	−0.146437
$117$	−4.50765	−0.416732
$118$	−1.60184	−0.147462
$119$	0	0
$120$	10.2176	0.932739
$121$	−5.09604	−0.463276
$122$	−6.44462	−0.583469
$123$	−1.00000	−0.0901670
$124$	−0.551549	−0.0495305
$125$	−6.39818	−0.572271
$126$	0	0
$127$	5.57946	0.495097	0.247549	−	0.968875i	$-0.420375\pi$
$127$	5.57946	0.495097	0.247549	+	0.968875i	$0.420375\pi$
$128$	8.97216	0.793034
$129$	3.93668	0.346605
$130$	20.6468	1.81084
$131$	5.67239	0.495599	0.247799	−	0.968811i	$-0.420293\pi$
$131$	5.67239	0.495599	0.247799	+	0.968811i	$0.420293\pi$
$132$	−0.560658	−0.0487990
$133$	0	0
$134$	5.02494	0.434089
$135$	−3.44355	−0.296373
$136$	13.5311	1.16029
$137$	20.9994	1.79410	0.897049	−	0.441931i	$-0.145707\pi$
$137$	20.9994	1.79410	0.897049	+	0.441931i	$0.145707\pi$
$138$	−6.99219	−0.595215
$139$	−1.80530	−0.153124	−0.0765618	−	0.997065i	$-0.524394\pi$
$139$	−1.80530	−0.153124	−0.0765618	+	0.997065i	$0.524394\pi$
$140$	0	0
$141$	12.2131	1.02853
$142$	−6.65442	−0.558426
$143$	−10.9527	−0.915913
$144$	−3.48527	−0.290440
$145$	−23.5376	−1.95469
$146$	10.9082	0.902769
$147$	0	0
$148$	0.0746748	0.00613823
$149$	6.51313	0.533576	0.266788	−	0.963755i	$-0.414038\pi$
$149$	6.51313	0.533576	0.266788	+	0.963755i	$0.414038\pi$
$150$	9.12209	0.744816
$151$	14.5560	1.18455	0.592275	−	0.805736i	$-0.298230\pi$
$151$	14.5560	1.18455	0.592275	+	0.805736i	$0.298230\pi$
$152$	3.83109	0.310742
$153$	−4.56026	−0.368675
$154$	0	0
$155$	−8.23122	−0.661147
$156$	1.04010	0.0832749
$157$	0.583942	0.0466036	0.0233018	−	0.999728i	$-0.492582\pi$
$157$	0.583942	0.0466036	0.0233018	+	0.999728i	$0.492582\pi$
$158$	−10.5247	−0.837300
$159$	5.17996	0.410798
$160$	−4.47141	−0.353496
$161$	0	0
$162$	1.33013	0.104505
$163$	13.7479	1.07682	0.538408	−	0.842684i	$-0.319026\pi$
$163$	13.7479	1.07682	0.538408	+	0.842684i	$0.319026\pi$
$164$	0.230742	0.0180179
$165$	−8.36716	−0.651382
$166$	3.29792	0.255968
$167$	−19.7472	−1.52809	−0.764043	−	0.645165i	$-0.776788\pi$
$167$	−19.7472	−1.52809	−0.764043	+	0.645165i	$0.776788\pi$
$168$	0	0
$169$	7.31891	0.562993
$170$	20.8877	1.60201
$171$	−1.29115	−0.0987368
$172$	−0.908356	−0.0692615
$173$	17.4423	1.32612	0.663059	−	0.748567i	$-0.269258\pi$
$173$	17.4423	1.32612	0.663059	+	0.748567i	$0.269258\pi$
$174$	9.09182	0.689249
$175$	0	0
$176$	−8.46855	−0.638341
$177$	−1.20427	−0.0905186
$178$	−3.05956	−0.229324
$179$	−5.51743	−0.412392	−0.206196	−	0.978511i	$-0.566108\pi$
$179$	−5.51743	−0.412392	−0.206196	+	0.978511i	$0.566108\pi$
$180$	0.794570	0.0592237
$181$	−6.26958	−0.466014	−0.233007	−	0.972475i	$-0.574857\pi$
$181$	−6.26958	−0.466014	−0.233007	+	0.972475i	$0.574857\pi$
$182$	0	0
$183$	−4.84509	−0.358159
$184$	15.5978	1.14988
$185$	1.11443	0.0819347
$186$	3.17946	0.233129
$187$	−11.0805	−0.810290
$188$	−2.81806	−0.205528
$189$	0	0
$190$	5.91396	0.429044
$191$	21.0906	1.52606	0.763030	−	0.646363i	$-0.223711\pi$
$191$	21.0906	1.52606	0.763030	+	0.646363i	$0.223711\pi$
$192$	8.69771	0.627703
$193$	−8.97043	−0.645706	−0.322853	−	0.946449i	$-0.604642\pi$
$193$	−8.97043	−0.645706	−0.322853	+	0.946449i	$0.604642\pi$
$194$	−20.5530	−1.47562
$195$	15.5223	1.11158
$196$	0	0
$197$	−21.6173	−1.54017	−0.770084	−	0.637943i	$-0.779786\pi$
$197$	−21.6173	−1.54017	−0.770084	+	0.637943i	$0.779786\pi$
$198$	3.23197	0.229686
$199$	6.63970	0.470676	0.235338	−	0.971914i	$-0.424380\pi$
$199$	6.63970	0.470676	0.235338	+	0.971914i	$0.424380\pi$
$200$	−20.3490	−1.43889
$201$	3.77777	0.266463
$202$	2.79723	0.196812
$203$	0	0
$204$	1.05224	0.0736716
$205$	3.44355	0.240508
$206$	12.7089	0.885474
$207$	−5.25675	−0.365370
$208$	15.7104	1.08932
$209$	−3.13725	−0.217008
$210$	0	0
$211$	−26.1364	−1.79931	−0.899653	−	0.436606i	$-0.856180\pi$
$211$	−26.1364	−1.79931	−0.899653	+	0.436606i	$0.856180\pi$
$212$	−1.19523	−0.0820889
$213$	−5.00281	−0.342787
$214$	−0.577783	−0.0394964
$215$	−13.5561	−0.924521
$216$	−2.96719	−0.201891
$217$	0	0
$218$	14.9026	1.00933
$219$	8.20083	0.554161
$220$	1.93065	0.130165
$221$	20.5560	1.38275
$222$	−0.430471	−0.0288913
$223$	7.82588	0.524059	0.262030	−	0.965060i	$-0.415608\pi$
$223$	7.82588	0.524059	0.262030	+	0.965060i	$0.415608\pi$
$224$	0	0
$225$	6.85802	0.457201
$226$	4.09453	0.272364
$227$	−15.8918	−1.05478	−0.527389	−	0.849624i	$-0.676829\pi$
$227$	−15.8918	−1.05478	−0.527389	+	0.849624i	$0.676829\pi$
$228$	0.297922	0.0197304
$229$	21.6629	1.43152	0.715761	−	0.698345i	$-0.246080\pi$
$229$	21.6629	1.43152	0.715761	+	0.698345i	$0.246080\pi$
$230$	24.0779	1.58765
$231$	0	0
$232$	−20.2815	−1.33155
$233$	10.1366	0.664073	0.332036	−	0.943267i	$-0.392264\pi$
$233$	10.1366	0.664073	0.332036	+	0.943267i	$0.392264\pi$
$234$	−5.99578	−0.391957
$235$	−42.0563	−2.74345
$236$	0.277876	0.0180882
$237$	−7.91250	−0.513972
$238$	0	0
$239$	28.9215	1.87078	0.935389	−	0.353620i	$-0.115049\pi$
$239$	28.9215	1.87078	0.935389	+	0.353620i	$0.115049\pi$
$240$	12.0017	0.774707
$241$	−1.59730	−0.102891	−0.0514454	−	0.998676i	$-0.516383\pi$
$241$	−1.59730	−0.102891	−0.0514454	+	0.998676i	$0.516383\pi$
$242$	−6.77841	−0.435733
$243$	1.00000	0.0641500
$244$	1.11796	0.0715703
$245$	0	0
$246$	−1.33013	−0.0848063
$247$	5.82006	0.370321
$248$	−7.09256	−0.450378
$249$	2.47939	0.157125
$250$	−8.51044	−0.538247
$251$	−15.4326	−0.974099	−0.487050	−	0.873374i	$-0.661927\pi$
$251$	−15.4326	−0.974099	−0.487050	+	0.873374i	$0.661927\pi$
$252$	0	0
$253$	−12.7729	−0.803025
$254$	7.42144	0.465663
$255$	15.7035	0.983389
$256$	−5.46125	−0.341328
$257$	8.02184	0.500389	0.250194	−	0.968196i	$-0.419505\pi$
$257$	8.02184	0.500389	0.250194	+	0.968196i	$0.419505\pi$
$258$	5.23631	0.325999
$259$	0	0
$260$	−3.58164	−0.222124
$261$	6.83526	0.423092
$262$	7.54504	0.466134
$263$	26.1307	1.61129	0.805645	−	0.592398i	$-0.201819\pi$
$263$	26.1307	1.61129	0.805645	+	0.592398i	$0.201819\pi$
$264$	−7.20969	−0.443726
$265$	−17.8374	−1.09575
$266$	0	0
$267$	−2.30019	−0.140769
$268$	−0.871689	−0.0532469
$269$	−14.6818	−0.895166	−0.447583	−	0.894243i	$-0.647715\pi$
$269$	−14.6818	−0.895166	−0.447583	+	0.894243i	$0.647715\pi$
$270$	−4.58038	−0.278753
$271$	2.98493	0.181322	0.0906609	−	0.995882i	$-0.471102\pi$
$271$	2.98493	0.181322	0.0906609	+	0.995882i	$0.471102\pi$
$272$	15.8937	0.963700
$273$	0	0
$274$	27.9320	1.68743
$275$	16.6637	1.00486
$276$	1.21295	0.0730111
$277$	5.30104	0.318509	0.159254	−	0.987238i	$-0.449091\pi$
$277$	5.30104	0.318509	0.159254	+	0.987238i	$0.449091\pi$
$278$	−2.40129	−0.144020
$279$	2.39033	0.143105
$280$	0	0
$281$	−24.6022	−1.46764	−0.733821	−	0.679343i	$-0.762265\pi$
$281$	−24.6022	−1.46764	−0.733821	+	0.679343i	$0.762265\pi$
$282$	16.2450	0.967377
$283$	−16.2722	−0.967282	−0.483641	−	0.875267i	$-0.660686\pi$
$283$	−16.2722	−0.967282	−0.483641	+	0.875267i	$0.660686\pi$
$284$	1.15436	0.0684985
$285$	4.44614	0.263367
$286$	−14.5686	−0.861459
$287$	0	0
$288$	1.29849	0.0765142
$289$	3.79594	0.223291
$290$	−31.3081	−1.83848
$291$	−15.4518	−0.905803
$292$	−1.89227	−0.110737
$293$	23.2890	1.36056	0.680279	−	0.732953i	$-0.261859\pi$
$293$	23.2890	1.36056	0.680279	+	0.732953i	$0.261859\pi$
$294$	0	0
$295$	4.14697	0.241446
$296$	0.960269	0.0558145
$297$	2.42981	0.140992
$298$	8.66334	0.501854
$299$	23.6956	1.37035
$300$	−1.58243	−0.0913617
$301$	0	0
$302$	19.3614	1.11413
$303$	2.10297	0.120812
$304$	4.50002	0.258094
$305$	16.6843	0.955340
$306$	−6.06576	−0.346756
$307$	−23.6521	−1.34990	−0.674948	−	0.737865i	$-0.735834\pi$
$307$	−23.6521	−1.34990	−0.674948	+	0.737865i	$0.735834\pi$
$308$	0	0
$309$	9.55463	0.543544
$310$	−10.9486	−0.621840
$311$	34.3154	1.94585	0.972925	−	0.231121i	$-0.0742395\pi$
$311$	34.3154	1.94585	0.972925	+	0.231121i	$0.0742395\pi$
$312$	13.3750	0.757213
$313$	−27.6991	−1.56565	−0.782824	−	0.622243i	$-0.786222\pi$
$313$	−27.6991	−1.56565	−0.782824	+	0.622243i	$0.786222\pi$
$314$	0.776721	0.0438329
$315$	0	0
$316$	1.82574	0.102706
$317$	−2.07093	−0.116315	−0.0581576	−	0.998307i	$-0.518523\pi$
$317$	−2.07093	−0.116315	−0.0581576	+	0.998307i	$0.518523\pi$
$318$	6.89004	0.386375
$319$	16.6084	0.929890
$320$	−29.9510	−1.67431
$321$	−0.434379	−0.0242447
$322$	0	0
$323$	5.88798	0.327616
$324$	−0.230742	−0.0128190
$325$	−30.9136	−1.71478
$326$	18.2865	1.01280
$327$	11.2038	0.619571
$328$	2.96719	0.163835
$329$	0	0
$330$	−11.1294	−0.612656
$331$	−7.68409	−0.422356	−0.211178	−	0.977448i	$-0.567730\pi$
$331$	−7.68409	−0.422356	−0.211178	+	0.977448i	$0.567730\pi$
$332$	−0.572098	−0.0313979
$333$	−0.323629	−0.0177348
$334$	−26.2665	−1.43724
$335$	−13.0089	−0.710753
$336$	0	0
$337$	29.8787	1.62760	0.813798	−	0.581147i	$-0.197396\pi$
$337$	29.8787	1.62760	0.813798	+	0.581147i	$0.197396\pi$
$338$	9.73514	0.529522
$339$	3.07828	0.167189
$340$	−3.62344	−0.196509
$341$	5.80804	0.314523
$342$	−1.71740	−0.0928666
$343$	0	0
$344$	−11.6809	−0.629790
$345$	18.1019	0.974572
$346$	23.2007	1.24728
$347$	12.4873	0.670355	0.335177	−	0.942155i	$-0.391204\pi$
$347$	12.4873	0.670355	0.335177	+	0.942155i	$0.391204\pi$
$348$	−1.57718	−0.0845457
$349$	30.7391	1.64543	0.822714	−	0.568455i	$-0.192459\pi$
$349$	30.7391	1.64543	0.822714	+	0.568455i	$0.192459\pi$
$350$	0	0
$351$	−4.50765	−0.240601
$352$	3.15508	0.168166
$353$	1.52558	0.0811985	0.0405993	−	0.999176i	$-0.487073\pi$
$353$	1.52558	0.0811985	0.0405993	+	0.999176i	$0.487073\pi$
$354$	−1.60184	−0.0851370
$355$	17.2274	0.914337
$356$	0.530749	0.0281296
$357$	0	0
$358$	−7.33893	−0.387874
$359$	29.4597	1.55482	0.777412	−	0.628992i	$-0.216532\pi$
$359$	29.4597	1.55482	0.777412	+	0.628992i	$0.216532\pi$
$360$	10.2176	0.538517
$361$	−17.3329	−0.912259
$362$	−8.33938	−0.438308
$363$	−5.09604	−0.267473
$364$	0	0
$365$	−28.2399	−1.47815
$366$	−6.44462	−0.336866
$367$	3.85518	0.201239	0.100619	−	0.994925i	$-0.467918\pi$
$367$	3.85518	0.201239	0.100619	+	0.994925i	$0.467918\pi$
$368$	18.3212	0.955060
$369$	−1.00000	−0.0520579
$370$	1.48235	0.0770635
$371$	0	0
$372$	−0.551549	−0.0285965
$373$	5.04932	0.261444	0.130722	−	0.991419i	$-0.458270\pi$
$373$	5.04932	0.261444	0.130722	+	0.991419i	$0.458270\pi$
$374$	−14.7386	−0.762116
$375$	−6.39818	−0.330401
$376$	−36.2385	−1.86886
$377$	−30.8110	−1.58685
$378$	0	0
$379$	−30.0604	−1.54410	−0.772048	−	0.635564i	$-0.780768\pi$
$379$	−30.0604	−1.54410	−0.772048	+	0.635564i	$0.780768\pi$
$380$	−1.02591	−0.0526281
$381$	5.57946	0.285845
$382$	28.0533	1.43533
$383$	23.9341	1.22298	0.611488	−	0.791254i	$-0.290571\pi$
$383$	23.9341	1.22298	0.611488	+	0.791254i	$0.290571\pi$
$384$	8.97216	0.457858
$385$	0	0
$386$	−11.9319	−0.607317
$387$	3.93668	0.200113
$388$	3.56538	0.181005
$389$	9.60257	0.486870	0.243435	−	0.969917i	$-0.421726\pi$
$389$	9.60257	0.486870	0.243435	+	0.969917i	$0.421726\pi$
$390$	20.6468	1.04549
$391$	23.9721	1.21232
$392$	0	0
$393$	5.67239	0.286134
$394$	−28.7539	−1.44860
$395$	27.2471	1.37095
$396$	−0.560658	−0.0281741
$397$	4.61217	0.231478	0.115739	−	0.993280i	$-0.463076\pi$
$397$	4.61217	0.231478	0.115739	+	0.993280i	$0.463076\pi$
$398$	8.83169	0.442693
$399$	0	0
$400$	−23.9021	−1.19510
$401$	−3.10914	−0.155263	−0.0776315	−	0.996982i	$-0.524736\pi$
$401$	−3.10914	−0.155263	−0.0776315	+	0.996982i	$0.524736\pi$
$402$	5.02494	0.250621
$403$	−10.7748	−0.536730
$404$	−0.485242	−0.0241417
$405$	−3.44355	−0.171111
$406$	0	0
$407$	−0.786357	−0.0389783
$408$	13.5311	0.669891
$409$	−12.4282	−0.614535	−0.307267	−	0.951623i	$-0.599415\pi$
$409$	−12.4282	−0.614535	−0.307267	+	0.951623i	$0.599415\pi$
$410$	4.58038	0.226209
$411$	20.9994	1.03582
$412$	−2.20465	−0.108615
$413$	0	0
$414$	−6.99219	−0.343647
$415$	−8.53788	−0.419108
$416$	−5.85313	−0.286973
$417$	−1.80530	−0.0884060
$418$	−4.17296	−0.204106
$419$	−4.45355	−0.217570	−0.108785	−	0.994065i	$-0.534696\pi$
$419$	−4.45355	−0.217570	−0.108785	+	0.994065i	$0.534696\pi$
$420$	0	0
$421$	4.19931	0.204662	0.102331	−	0.994750i	$-0.467370\pi$
$421$	4.19931	0.204662	0.102331	+	0.994750i	$0.467370\pi$
$422$	−34.7650	−1.69233
$423$	12.2131	0.593820
$424$	−15.3699	−0.746429
$425$	−31.2743	−1.51703
$426$	−6.65442	−0.322407
$427$	0	0
$428$	0.100229	0.00484477
$429$	−10.9527	−0.528802
$430$	−18.0315	−0.869556
$431$	21.7632	1.04830	0.524149	−	0.851626i	$-0.324383\pi$
$431$	21.7632	1.04830	0.524149	+	0.851626i	$0.324383\pi$
$432$	−3.48527	−0.167685
$433$	−7.84478	−0.376996	−0.188498	−	0.982074i	$-0.560362\pi$
$433$	−7.84478	−0.376996	−0.188498	+	0.982074i	$0.560362\pi$
$434$	0	0
$435$	−23.5376	−1.12854
$436$	−2.58518	−0.123808
$437$	6.78726	0.324679
$438$	10.9082	0.521214
$439$	12.3744	0.590600	0.295300	−	0.955405i	$-0.404580\pi$
$439$	12.3744	0.590600	0.295300	+	0.955405i	$0.404580\pi$
$440$	24.8269	1.18358
$441$	0	0
$442$	27.3423	1.30054
$443$	15.3963	0.731502	0.365751	−	0.930713i	$-0.380812\pi$
$443$	15.3963	0.731502	0.365751	+	0.930713i	$0.380812\pi$
$444$	0.0746748	0.00354391
$445$	7.92080	0.375482
$446$	10.4095	0.492903
$447$	6.51313	0.308060
$448$	0	0
$449$	−12.4629	−0.588159	−0.294079	−	0.955781i	$-0.595013\pi$
$449$	−12.4629	−0.588159	−0.294079	+	0.955781i	$0.595013\pi$
$450$	9.12209	0.430019
$451$	−2.42981	−0.114415
$452$	−0.710287	−0.0334091
$453$	14.5560	0.683901
$454$	−21.1383	−0.992069
$455$	0	0
$456$	3.83109	0.179407
$457$	−18.2640	−0.854354	−0.427177	−	0.904168i	$-0.640492\pi$
$457$	−18.2640	−0.854354	−0.427177	+	0.904168i	$0.640492\pi$
$458$	28.8145	1.34641
$459$	−4.56026	−0.212855
$460$	−4.17686	−0.194747
$461$	−36.6943	−1.70902	−0.854512	−	0.519432i	$-0.826144\pi$
$461$	−36.6943	−1.70902	−0.854512	+	0.519432i	$0.826144\pi$
$462$	0	0
$463$	6.66895	0.309932	0.154966	−	0.987920i	$-0.450473\pi$
$463$	6.66895	0.309932	0.154966	+	0.987920i	$0.450473\pi$
$464$	−23.8228	−1.10594
$465$	−8.23122	−0.381713
$466$	13.4831	0.624592
$467$	38.6299	1.78758	0.893789	−	0.448488i	$-0.148037\pi$
$467$	38.6299	1.78758	0.893789	+	0.448488i	$0.148037\pi$
$468$	1.04010	0.0480788
$469$	0	0
$470$	−55.9405	−2.58034
$471$	0.583942	0.0269066
$472$	3.57330	0.164474
$473$	9.56537	0.439816
$474$	−10.5247	−0.483415
$475$	−8.85474	−0.406283
$476$	0	0
$477$	5.17996	0.237174
$478$	38.4695	1.75956
$479$	−23.6927	−1.08255	−0.541274	−	0.840846i	$-0.682058\pi$
$479$	−23.6927	−1.08255	−0.541274	+	0.840846i	$0.682058\pi$
$480$	−4.47141	−0.204091
$481$	1.45881	0.0665159
$482$	−2.12462	−0.0967737
$483$	0	0
$484$	1.17587	0.0534485
$485$	53.2091	2.41610
$486$	1.33013	0.0603361
$487$	−3.45210	−0.156429	−0.0782147	−	0.996937i	$-0.524922\pi$
$487$	−3.45210	−0.156429	−0.0782147	+	0.996937i	$0.524922\pi$
$488$	14.3763	0.650784
$489$	13.7479	0.621700
$490$	0	0
$491$	41.9801	1.89453	0.947267	−	0.320447i	$-0.103833\pi$
$491$	41.9801	1.89453	0.947267	+	0.320447i	$0.103833\pi$
$492$	0.230742	0.0104026
$493$	−31.1706	−1.40385
$494$	7.74146	0.348305
$495$	−8.36716	−0.376076
$496$	−8.33096	−0.374071
$497$	0	0
$498$	3.29792	0.147783
$499$	−31.7195	−1.41996	−0.709981	−	0.704221i	$-0.751296\pi$
$499$	−31.7195	−1.41996	−0.709981	+	0.704221i	$0.751296\pi$
$500$	1.47633	0.0660233
$501$	−19.7472	−0.882241
$502$	−20.5275	−0.916186
$503$	−22.9497	−1.02328	−0.511639	−	0.859201i	$-0.670961\pi$
$503$	−22.9497	−1.02328	−0.511639	+	0.859201i	$0.670961\pi$
$504$	0	0
$505$	−7.24166	−0.322250
$506$	−16.9897	−0.755283
$507$	7.31891	0.325044
$508$	−1.28741	−0.0571198
$509$	−32.5353	−1.44210	−0.721051	−	0.692882i	$-0.756341\pi$
$509$	−32.5353	−1.44210	−0.721051	+	0.692882i	$0.756341\pi$
$510$	20.8877	0.924924
$511$	0	0
$512$	−25.2085	−1.11407
$513$	−1.29115	−0.0570057
$514$	10.6701	0.470639
$515$	−32.9018	−1.44983
$516$	−0.908356	−0.0399881
$517$	29.6754	1.30512
$518$	0	0
$519$	17.4423	0.765634
$520$	−46.0576	−2.01976
$521$	42.0823	1.84366	0.921829	−	0.387597i	$-0.126695\pi$
$521$	42.0823	1.84366	0.921829	+	0.387597i	$0.126695\pi$
$522$	9.09182	0.397938
$523$	13.2249	0.578283	0.289141	−	0.957286i	$-0.406630\pi$
$523$	13.2249	0.578283	0.289141	+	0.957286i	$0.406630\pi$
$524$	−1.30886	−0.0571776
$525$	0	0
$526$	34.7574	1.51549
$527$	−10.9005	−0.474834
$528$	−8.46855	−0.368546
$529$	4.63346	0.201455
$530$	−23.7262	−1.03060
$531$	−1.20427	−0.0522610
$532$	0	0
$533$	4.50765	0.195248
$534$	−3.05956	−0.132400
$535$	1.49581	0.0646693
$536$	−11.2093	−0.484170
$537$	−5.51743	−0.238095
$538$	−19.5288	−0.841945
$539$	0	0
$540$	0.794570	0.0341928
$541$	−23.1355	−0.994672	−0.497336	−	0.867558i	$-0.665688\pi$
$541$	−23.1355	−0.994672	−0.497336	+	0.867558i	$0.665688\pi$
$542$	3.97036	0.170542
$543$	−6.26958	−0.269053
$544$	−5.92144	−0.253880
$545$	−38.5808	−1.65262
$546$	0	0
$547$	−30.8794	−1.32031	−0.660154	−	0.751130i	$-0.729509\pi$
$547$	−30.8794	−1.32031	−0.660154	+	0.751130i	$0.729509\pi$
$548$	−4.84543	−0.206987
$549$	−4.84509	−0.206783
$550$	22.1649	0.945115
$551$	−8.82536	−0.375973
$552$	15.5978	0.663885
$553$	0	0
$554$	7.05110	0.299573
$555$	1.11443	0.0473050
$556$	0.416558	0.0176660
$557$	−44.7665	−1.89682	−0.948408	−	0.317051i	$-0.897307\pi$
$557$	−44.7665	−1.89682	−0.948408	+	0.317051i	$0.897307\pi$
$558$	3.17946	0.134597
$559$	−17.7452	−0.750541
$560$	0	0
$561$	−11.0805	−0.467821
$562$	−32.7242	−1.38039
$563$	26.7582	1.12772	0.563861	−	0.825869i	$-0.309315\pi$
$563$	26.7582	1.12772	0.563861	+	0.825869i	$0.309315\pi$
$564$	−2.81806	−0.118662
$565$	−10.6002	−0.445954
$566$	−21.6442	−0.909774
$567$	0	0
$568$	14.8443	0.622852
$569$	−42.2545	−1.77140	−0.885701	−	0.464257i	$-0.846322\pi$
$569$	−42.2545	−1.77140	−0.885701	+	0.464257i	$0.846322\pi$
$570$	5.91396	0.247709
$571$	25.9438	1.08571	0.542857	−	0.839825i	$-0.317343\pi$
$571$	25.9438	1.08571	0.542857	+	0.839825i	$0.317343\pi$
$572$	2.52725	0.105670
$573$	21.0906	0.881072
$574$	0	0
$575$	−36.0509	−1.50343
$576$	8.69771	0.362405
$577$	25.1709	1.04788	0.523940	−	0.851755i	$-0.324462\pi$
$577$	25.1709	1.04788	0.523940	+	0.851755i	$0.324462\pi$
$578$	5.04912	0.210016
$579$	−8.97043	−0.372798
$580$	5.43109	0.225514
$581$	0	0
$582$	−20.5530	−0.851950
$583$	12.5863	0.521272
$584$	−24.3334	−1.00692
$585$	15.5223	0.641769
$586$	30.9775	1.27967
$587$	37.6709	1.55484	0.777422	−	0.628979i	$-0.216527\pi$
$587$	37.6709	1.55484	0.777422	+	0.628979i	$0.216527\pi$
$588$	0	0
$589$	−3.08628	−0.127168
$590$	5.51603	0.227091
$591$	−21.6173	−0.889216
$592$	1.12794	0.0463579
$593$	−31.0474	−1.27496	−0.637482	−	0.770465i	$-0.720024\pi$
$593$	−31.0474	−1.27496	−0.637482	+	0.770465i	$0.720024\pi$
$594$	3.23197	0.132609
$595$	0	0
$596$	−1.50285	−0.0615591
$597$	6.63970	0.271745
$598$	31.5184	1.28888
$599$	8.37484	0.342187	0.171093	−	0.985255i	$-0.445270\pi$
$599$	8.37484	0.342187	0.171093	+	0.985255i	$0.445270\pi$
$600$	−20.3490	−0.830746
$601$	3.05224	0.124503	0.0622517	−	0.998060i	$-0.480172\pi$
$601$	3.05224	0.124503	0.0622517	+	0.998060i	$0.480172\pi$
$602$	0	0
$603$	3.77777	0.153843
$604$	−3.35868	−0.136663
$605$	17.5484	0.713446
$606$	2.79723	0.113630
$607$	−39.8725	−1.61838	−0.809188	−	0.587550i	$-0.800092\pi$
$607$	−39.8725	−1.61838	−0.809188	+	0.587550i	$0.800092\pi$
$608$	−1.67654	−0.0679929
$609$	0	0
$610$	22.1924	0.898543
$611$	−55.0522	−2.22718
$612$	1.05224	0.0425343
$613$	6.31640	0.255117	0.127559	−	0.991831i	$-0.459286\pi$
$613$	6.31640	0.255117	0.127559	+	0.991831i	$0.459286\pi$
$614$	−31.4605	−1.26964
$615$	3.44355	0.138857
$616$	0	0
$617$	−24.1061	−0.970477	−0.485238	−	0.874382i	$-0.661267\pi$
$617$	−24.1061	−0.970477	−0.485238	+	0.874382i	$0.661267\pi$
$618$	12.7089	0.511229
$619$	22.4446	0.902127	0.451063	−	0.892492i	$-0.351045\pi$
$619$	22.4446	0.902127	0.451063	+	0.892492i	$0.351045\pi$
$620$	1.89928	0.0762771
$621$	−5.25675	−0.210946
$622$	45.6442	1.83016
$623$	0	0
$624$	15.7104	0.628919
$625$	−12.2577	−0.490307
$626$	−36.8436	−1.47257
$627$	−3.13725	−0.125290
$628$	−0.134740	−0.00537670
$629$	1.47583	0.0588453
$630$	0	0
$631$	9.22009	0.367046	0.183523	−	0.983015i	$-0.441250\pi$
$631$	9.22009	0.367046	0.183523	+	0.983015i	$0.441250\pi$
$632$	23.4779	0.933900
$633$	−26.1364	−1.03883
$634$	−2.75462	−0.109400
$635$	−19.2132	−0.762451
$636$	−1.19523	−0.0473941
$637$	0	0
$638$	22.0914	0.874606
$639$	−5.00281	−0.197908
$640$	−30.8960	−1.22127
$641$	−39.9640	−1.57848	−0.789241	−	0.614084i	$-0.789526\pi$
$641$	−39.9640	−1.57848	−0.789241	+	0.614084i	$0.789526\pi$
$642$	−0.577783	−0.0228033
$643$	26.3406	1.03877	0.519385	−	0.854540i	$-0.326161\pi$
$643$	26.3406	1.03877	0.519385	+	0.854540i	$0.326161\pi$
$644$	0	0
$645$	−13.5561	−0.533772
$646$	7.83181	0.308138
$647$	40.3248	1.58533	0.792667	−	0.609655i	$-0.208692\pi$
$647$	40.3248	1.58533	0.792667	+	0.609655i	$0.208692\pi$
$648$	−2.96719	−0.116562
$649$	−2.92615	−0.114861
$650$	−41.1192	−1.61283
$651$	0	0
$652$	−3.17221	−0.124233
$653$	34.7576	1.36017	0.680084	−	0.733134i	$-0.261943\pi$
$653$	34.7576	1.36017	0.680084	+	0.733134i	$0.261943\pi$
$654$	14.9026	0.582736
$655$	−19.5331	−0.763223
$656$	3.48527	0.136077
$657$	8.20083	0.319945
$658$	0	0
$659$	3.55366	0.138431	0.0692154	−	0.997602i	$-0.477950\pi$
$659$	3.55366	0.138431	0.0692154	+	0.997602i	$0.477950\pi$
$660$	1.93065	0.0751505
$661$	26.4437	1.02854	0.514270	−	0.857628i	$-0.328063\pi$
$661$	26.4437	1.02854	0.514270	+	0.857628i	$0.328063\pi$
$662$	−10.2209	−0.397246
$663$	20.5560	0.798331
$664$	−7.35680	−0.285499
$665$	0	0
$666$	−0.430471	−0.0166804
$667$	−35.9313	−1.39127
$668$	4.55651	0.176297
$669$	7.82588	0.302566
$670$	−17.3036	−0.668497
$671$	−11.7726	−0.454478
$672$	0	0
$673$	31.8563	1.22797	0.613985	−	0.789318i	$-0.289566\pi$
$673$	31.8563	1.22797	0.613985	+	0.789318i	$0.289566\pi$
$674$	39.7427	1.53083
$675$	6.85802	0.263965
$676$	−1.68878	−0.0649530
$677$	11.1442	0.428306	0.214153	−	0.976800i	$-0.431301\pi$
$677$	11.1442	0.428306	0.214153	+	0.976800i	$0.431301\pi$
$678$	4.09453	0.157249
$679$	0	0
$680$	−46.5951	−1.78684
$681$	−15.8918	−0.608976
$682$	7.72548	0.295824
$683$	−47.9051	−1.83304	−0.916519	−	0.399992i	$-0.869013\pi$
$683$	−47.9051	−1.83304	−0.916519	+	0.399992i	$0.869013\pi$
$684$	0.297922	0.0113913
$685$	−72.3123	−2.76291
$686$	0	0
$687$	21.6629	0.826489
$688$	−13.7204	−0.523086
$689$	−23.3495	−0.889543
$690$	24.0779	0.916631
$691$	−6.92965	−0.263616	−0.131808	−	0.991275i	$-0.542078\pi$
$691$	−6.92965	−0.263616	−0.131808	+	0.991275i	$0.542078\pi$
$692$	−4.02468	−0.152995
$693$	0	0
$694$	16.6098	0.630500
$695$	6.21664	0.235811
$696$	−20.2815	−0.768768
$697$	4.56026	0.172732
$698$	40.8872	1.54760
$699$	10.1366	0.383403
$700$	0	0
$701$	−20.9178	−0.790053	−0.395026	−	0.918670i	$-0.629265\pi$
$701$	−20.9178	−0.790053	−0.395026	+	0.918670i	$0.629265\pi$
$702$	−5.99578	−0.226296
$703$	0.417854	0.0157597
$704$	21.1338	0.796509
$705$	−42.0563	−1.58393
$706$	2.02923	0.0763710
$707$	0	0
$708$	0.277876	0.0104432
$709$	−17.1067	−0.642455	−0.321228	−	0.947002i	$-0.604095\pi$
$709$	−17.1067	−0.642455	−0.321228	+	0.947002i	$0.604095\pi$
$710$	22.9148	0.859977
$711$	−7.91250	−0.296742
$712$	6.82509	0.255781
$713$	−12.5654	−0.470577
$714$	0	0
$715$	37.7162	1.41051
$716$	1.27310	0.0475780
$717$	28.9215	1.08009
$718$	39.1854	1.46239
$719$	−0.652683	−0.0243410	−0.0121705	−	0.999926i	$-0.503874\pi$
$719$	−0.652683	−0.0243410	−0.0121705	+	0.999926i	$0.503874\pi$
$720$	12.0017	0.447277
$721$	0	0
$722$	−23.0551	−0.858023
$723$	−1.59730	−0.0594041
$724$	1.44665	0.0537644
$725$	46.8764	1.74094
$726$	−6.77841	−0.251571
$727$	−53.3784	−1.97969	−0.989847	−	0.142134i	$-0.954604\pi$
$727$	−53.3784	−1.97969	−0.989847	+	0.142134i	$0.954604\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−37.5629	−1.39027
$731$	−17.9523	−0.663988
$732$	1.11796	0.0413212
$733$	−21.9700	−0.811479	−0.405740	−	0.913989i	$-0.632986\pi$
$733$	−21.9700	−0.811479	−0.405740	+	0.913989i	$0.632986\pi$
$734$	5.12790	0.189274
$735$	0	0
$736$	−6.82583	−0.251604
$737$	9.17925	0.338122
$738$	−1.33013	−0.0489629
$739$	36.2447	1.33328	0.666642	−	0.745378i	$-0.267731\pi$
$739$	36.2447	1.33328	0.666642	+	0.745378i	$0.267731\pi$
$740$	−0.257146	−0.00945288
$741$	5.82006	0.213805
$742$	0	0
$743$	37.3789	1.37130	0.685650	−	0.727931i	$-0.259518\pi$
$743$	37.3789	1.37130	0.685650	+	0.727931i	$0.259518\pi$
$744$	−7.09256	−0.260026
$745$	−22.4283	−0.821708
$746$	6.71628	0.245901
$747$	2.47939	0.0907160
$748$	2.55674	0.0934838
$749$	0	0
$750$	−8.51044	−0.310757
$751$	3.40592	0.124284	0.0621420	−	0.998067i	$-0.480207\pi$
$751$	3.40592	0.124284	0.0621420	+	0.998067i	$0.480207\pi$
$752$	−42.5659	−1.55222
$753$	−15.4326	−0.562396
$754$	−40.9828	−1.49250
$755$	−50.1243	−1.82421
$756$	0	0
$757$	24.9914	0.908327	0.454163	−	0.890918i	$-0.349938\pi$
$757$	24.9914	0.908327	0.454163	+	0.890918i	$0.349938\pi$
$758$	−39.9843	−1.45230
$759$	−12.7729	−0.463627
$760$	−13.1925	−0.478543
$761$	−47.9442	−1.73798	−0.868988	−	0.494834i	$-0.835229\pi$
$761$	−47.9442	−1.73798	−0.868988	+	0.494834i	$0.835229\pi$
$762$	7.42144	0.268850
$763$	0	0
$764$	−4.86648	−0.176063
$765$	15.7035	0.567760
$766$	31.8356	1.15027
$767$	5.42844	0.196010
$768$	−5.46125	−0.197066
$769$	50.4114	1.81788	0.908940	−	0.416926i	$-0.136893\pi$
$769$	50.4114	1.81788	0.908940	+	0.416926i	$0.136893\pi$
$770$	0	0
$771$	8.02184	0.288900
$772$	2.06985	0.0744956
$773$	1.16820	0.0420172	0.0210086	−	0.999779i	$-0.493312\pi$
$773$	1.16820	0.0420172	0.0210086	+	0.999779i	$0.493312\pi$
$774$	5.23631	0.188215
$775$	16.3929	0.588851
$776$	45.8485	1.64586
$777$	0	0
$778$	12.7727	0.457924
$779$	1.29115	0.0462603
$780$	−3.58164	−0.128243
$781$	−12.1559	−0.434971
$782$	31.8862	1.14025
$783$	6.83526	0.244272
$784$	0	0
$785$	−2.01083	−0.0717696
$786$	7.54504	0.269123
$787$	39.1683	1.39620	0.698100	−	0.716001i	$-0.254029\pi$
$787$	39.1683	1.39620	0.698100	+	0.716001i	$0.254029\pi$
$788$	4.98801	0.177690
$789$	26.1307	0.930279
$790$	36.2423	1.28944
$791$	0	0
$792$	−7.20969	−0.256185
$793$	21.8400	0.775560
$794$	6.13481	0.217716
$795$	−17.8374	−0.632629
$796$	−1.53205	−0.0543022
$797$	33.5386	1.18800	0.593999	−	0.804465i	$-0.297548\pi$
$797$	33.5386	1.18800	0.593999	+	0.804465i	$0.297548\pi$
$798$	0	0
$799$	−55.6947	−1.97034
$800$	8.90506	0.314841
$801$	−2.30019	−0.0812731
$802$	−4.13557	−0.146032
$803$	19.9264	0.703189
$804$	−0.871689	−0.0307421
$805$	0	0
$806$	−14.3319	−0.504820
$807$	−14.6818	−0.516824
$808$	−6.23989	−0.219519
$809$	−44.6359	−1.56932	−0.784658	−	0.619929i	$-0.787161\pi$
$809$	−44.6359	−1.56932	−0.784658	+	0.619929i	$0.787161\pi$
$810$	−4.58038	−0.160938
$811$	−36.6559	−1.28716	−0.643582	−	0.765377i	$-0.722552\pi$
$811$	−36.6559	−1.28716	−0.643582	+	0.765377i	$0.722552\pi$
$812$	0	0
$813$	2.98493	0.104686
$814$	−1.04596	−0.0366609
$815$	−47.3415	−1.65830
$816$	15.8937	0.556393
$817$	−5.08285	−0.177826
$818$	−16.5312	−0.577999
$819$	0	0
$820$	−0.794570	−0.0277476
$821$	−33.6318	−1.17376	−0.586878	−	0.809675i	$-0.699643\pi$
$821$	−33.6318	−1.17376	−0.586878	+	0.809675i	$0.699643\pi$
$822$	27.9320	0.974240
$823$	−7.53917	−0.262799	−0.131399	−	0.991330i	$-0.541947\pi$
$823$	−7.53917	−0.262799	−0.131399	+	0.991330i	$0.541947\pi$
$824$	−28.3504	−0.987632
$825$	16.6637	0.580154
$826$	0	0
$827$	−16.7185	−0.581360	−0.290680	−	0.956820i	$-0.593882\pi$
$827$	−16.7185	−0.581360	−0.290680	+	0.956820i	$0.593882\pi$
$828$	1.21295	0.0421530
$829$	−54.9115	−1.90716	−0.953578	−	0.301146i	$-0.902631\pi$
$829$	−54.9115	−1.90716	−0.953578	+	0.301146i	$0.902631\pi$
$830$	−11.3565	−0.394191
$831$	5.30104	0.183891
$832$	−39.2063	−1.35923
$833$	0	0
$834$	−2.40129	−0.0831500
$835$	68.0005	2.35325
$836$	0.723894	0.0250364
$837$	2.39033	0.0826219
$838$	−5.92383	−0.204635
$839$	8.62503	0.297769	0.148885	−	0.988855i	$-0.452432\pi$
$839$	8.62503	0.297769	0.148885	+	0.988855i	$0.452432\pi$
$840$	0	0
$841$	17.7208	0.611063
$842$	5.58565	0.192494
$843$	−24.6022	−0.847343
$844$	6.03076	0.207587
$845$	−25.2030	−0.867011
$846$	16.2450	0.558515
$847$	0	0
$848$	−18.0536	−0.619963
$849$	−16.2722	−0.558460
$850$	−41.5991	−1.42684
$851$	1.70124	0.0583177
$852$	1.15436	0.0395476
$853$	9.03717	0.309427	0.154713	−	0.987959i	$-0.450555\pi$
$853$	9.03717	0.309427	0.154713	+	0.987959i	$0.450555\pi$
$854$	0	0
$855$	4.44614	0.152055
$856$	1.28888	0.0440532
$857$	35.6635	1.21824	0.609121	−	0.793077i	$-0.291522\pi$
$857$	35.6635	1.21824	0.609121	+	0.793077i	$0.291522\pi$
$858$	−14.5686	−0.497364
$859$	20.3978	0.695965	0.347982	−	0.937501i	$-0.386867\pi$
$859$	20.3978	0.695965	0.347982	+	0.937501i	$0.386867\pi$
$860$	3.12797	0.106663
$861$	0	0
$862$	28.9481	0.985975
$863$	9.46480	0.322185	0.161093	−	0.986939i	$-0.448498\pi$
$863$	9.46480	0.322185	0.161093	+	0.986939i	$0.448498\pi$
$864$	1.29849	0.0441755
$865$	−60.0636	−2.04222
$866$	−10.4346	−0.354582
$867$	3.79594	0.128917
$868$	0	0
$869$	−19.2259	−0.652193
$870$	−31.3081	−1.06144
$871$	−17.0289	−0.577001
$872$	−33.2438	−1.12578
$873$	−15.4518	−0.522965
$874$	9.02797	0.305376
$875$	0	0
$876$	−1.89227	−0.0639340
$877$	13.8614	0.468066	0.234033	−	0.972229i	$-0.424808\pi$
$877$	13.8614	0.468066	0.234033	+	0.972229i	$0.424808\pi$
$878$	16.4597	0.555487
$879$	23.2890	0.785519
$880$	29.1618	0.983046
$881$	48.5099	1.63434	0.817170	−	0.576396i	$-0.195542\pi$
$881$	48.5099	1.63434	0.817170	+	0.576396i	$0.195542\pi$
$882$	0	0
$883$	16.6693	0.560966	0.280483	−	0.959859i	$-0.409505\pi$
$883$	16.6693	0.560966	0.280483	+	0.959859i	$0.409505\pi$
$884$	−4.74314	−0.159529
$885$	4.14697	0.139399
$886$	20.4792	0.688012
$887$	12.2497	0.411303	0.205652	−	0.978625i	$-0.434069\pi$
$887$	12.2497	0.411303	0.205652	+	0.978625i	$0.434069\pi$
$888$	0.960269	0.0322245
$889$	0	0
$890$	10.5357	0.353159
$891$	2.42981	0.0814016
$892$	−1.80576	−0.0604612
$893$	−15.7689	−0.527687
$894$	8.66334	0.289745
$895$	18.9995	0.635084
$896$	0	0
$897$	23.6956	0.791173
$898$	−16.5773	−0.553191
$899$	16.3385	0.544921
$900$	−1.58243	−0.0527477
$901$	−23.6219	−0.786961
$902$	−3.23197	−0.107613
$903$	0	0
$904$	−9.13383	−0.303787
$905$	21.5896	0.717662
$906$	19.3614	0.643241
$907$	26.9564	0.895071	0.447536	−	0.894266i	$-0.352302\pi$
$907$	26.9564	0.895071	0.447536	+	0.894266i	$0.352302\pi$
$908$	3.66691	0.121691
$909$	2.10297	0.0697510
$910$	0	0
$911$	−24.3767	−0.807636	−0.403818	−	0.914839i	$-0.632317\pi$
$911$	−24.3767	−0.807636	−0.403818	+	0.914839i	$0.632317\pi$
$912$	4.50002	0.149010
$913$	6.02443	0.199380
$914$	−24.2936	−0.803561
$915$	16.6843	0.551566
$916$	−4.99852	−0.165156
$917$	0	0
$918$	−6.06576	−0.200200
$919$	−7.40854	−0.244385	−0.122193	−	0.992506i	$-0.538993\pi$
$919$	−7.40854	−0.244385	−0.122193	+	0.992506i	$0.538993\pi$
$920$	−53.7117	−1.77082
$921$	−23.6521	−0.779363
$922$	−48.8084	−1.60742
$923$	22.5509	0.742273
$924$	0	0
$925$	−2.21946	−0.0729753
$926$	8.87060	0.291506
$927$	9.55463	0.313815
$928$	8.87551	0.291353
$929$	6.32793	0.207613	0.103806	−	0.994598i	$-0.466898\pi$
$929$	6.32793	0.207613	0.103806	+	0.994598i	$0.466898\pi$
$930$	−10.9486	−0.359020
$931$	0	0
$932$	−2.33894	−0.0766146
$933$	34.3154	1.12344
$934$	51.3830	1.68130
$935$	38.1564	1.24785
$936$	13.3750	0.437177
$937$	−55.1940	−1.80311	−0.901555	−	0.432665i	$-0.857573\pi$
$937$	−55.1940	−1.80311	−0.901555	+	0.432665i	$0.857573\pi$
$938$	0	0
$939$	−27.6991	−0.903927
$940$	9.70414	0.316514
$941$	−8.57076	−0.279399	−0.139699	−	0.990194i	$-0.544614\pi$
$941$	−8.57076	−0.279399	−0.139699	+	0.990194i	$0.544614\pi$
$942$	0.776721	0.0253069
$943$	5.25675	0.171183
$944$	4.19722	0.136608
$945$	0	0
$946$	12.7232	0.413668
$947$	−19.0572	−0.619275	−0.309638	−	0.950855i	$-0.600208\pi$
$947$	−19.0572	−0.619275	−0.309638	+	0.950855i	$0.600208\pi$
$948$	1.82574	0.0592974
$949$	−36.9665	−1.19998
$950$	−11.7780	−0.382129
$951$	−2.07093	−0.0671546
$952$	0	0
$953$	48.0117	1.55525	0.777626	−	0.628727i	$-0.216424\pi$
$953$	48.0117	1.55525	0.777626	+	0.628727i	$0.216424\pi$
$954$	6.89004	0.223073
$955$	−72.6264	−2.35014
$956$	−6.67340	−0.215833
$957$	16.6084	0.536873
$958$	−31.5145	−1.01819
$959$	0	0
$960$	−29.9510	−0.966664
$961$	−25.2863	−0.815688
$962$	1.94041	0.0625614
$963$	−0.434379	−0.0139977
$964$	0.368563	0.0118706
$965$	30.8901	0.994388
$966$	0	0
$967$	−29.7309	−0.956081	−0.478040	−	0.878338i	$-0.658653\pi$
$967$	−29.7309	−0.956081	−0.478040	+	0.878338i	$0.658653\pi$
$968$	15.1209	0.486004
$969$	5.88798	0.189149
$970$	70.7753	2.27246
$971$	39.3323	1.26223	0.631117	−	0.775688i	$-0.282597\pi$
$971$	39.3323	1.26223	0.631117	+	0.775688i	$0.282597\pi$
$972$	−0.230742	−0.00740104
$973$	0	0
$974$	−4.59175	−0.147129
$975$	−30.9136	−0.990026
$976$	16.8865	0.540523
$977$	−43.9645	−1.40655	−0.703275	−	0.710918i	$-0.748280\pi$
$977$	−43.9645	−1.40655	−0.703275	+	0.710918i	$0.748280\pi$
$978$	18.2865	0.584739
$979$	−5.58901	−0.178626
$980$	0	0
$981$	11.2038	0.357710
$982$	55.8391	1.78190
$983$	16.4200	0.523716	0.261858	−	0.965106i	$-0.415665\pi$
$983$	16.4200	0.523716	0.261858	+	0.965106i	$0.415665\pi$
$984$	2.96719	0.0945905
$985$	74.4401	2.37186
$986$	−41.4610	−1.32039
$987$	0	0
$988$	−1.34293	−0.0427243
$989$	−20.6941	−0.658036
$990$	−11.1294	−0.353717
$991$	46.0055	1.46141	0.730707	−	0.682691i	$-0.239191\pi$
$991$	46.0055	1.46141	0.730707	+	0.682691i	$0.239191\pi$
$992$	3.10382	0.0985463
$993$	−7.68409	−0.243847
$994$	0	0
$995$	−22.8641	−0.724841
$996$	−0.572098	−0.0181276
$997$	49.3335	1.56241	0.781205	−	0.624275i	$-0.214606\pi$
$997$	49.3335	1.56241	0.781205	+	0.624275i	$0.214606\pi$
$998$	−42.1913	−1.33554
$999$	−0.323629	−0.0102392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bo.1.15	yes	24
7.6	odd	2		6027.2.a.bn.1.15	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.15	✓	24	7.6	odd	2
6027.2.a.bo.1.15	yes	24	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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+1.33013 q^{2} +1.00000 q^{3} -0.230742 q^{4} -3.44355 q^{5} +1.33013 q^{6} -2.96719 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.33013 q^{2} +1.00000 q^{3} -0.230742 q^{4} -3.44355 q^{5} +1.33013 q^{6} -2.96719 q^{8} +1.00000 q^{9} -4.58038 q^{10} +2.42981 q^{11} -0.230742 q^{12} -4.50765 q^{13} -3.44355 q^{15} -3.48527 q^{16} -4.56026 q^{17} +1.33013 q^{18} -1.29115 q^{19} +0.794570 q^{20} +3.23197 q^{22} -5.25675 q^{23} -2.96719 q^{24} +6.85802 q^{25} -5.99578 q^{26} +1.00000 q^{27} +6.83526 q^{29} -4.58038 q^{30} +2.39033 q^{31} +1.29849 q^{32} +2.42981 q^{33} -6.06576 q^{34} -0.230742 q^{36} -0.323629 q^{37} -1.71740 q^{38} -4.50765 q^{39} +10.2176 q^{40} -1.00000 q^{41} +3.93668 q^{43} -0.560658 q^{44} -3.44355 q^{45} -6.99219 q^{46} +12.2131 q^{47} -3.48527 q^{48} +9.12209 q^{50} -4.56026 q^{51} +1.04010 q^{52} +5.17996 q^{53} +1.33013 q^{54} -8.36716 q^{55} -1.29115 q^{57} +9.09182 q^{58} -1.20427 q^{59} +0.794570 q^{60} -4.84509 q^{61} +3.17946 q^{62} +8.69771 q^{64} +15.5223 q^{65} +3.23197 q^{66} +3.77777 q^{67} +1.05224 q^{68} -5.25675 q^{69} -5.00281 q^{71} -2.96719 q^{72} +8.20083 q^{73} -0.430471 q^{74} +6.85802 q^{75} +0.297922 q^{76} -5.99578 q^{78} -7.91250 q^{79} +12.0017 q^{80} +1.00000 q^{81} -1.33013 q^{82} +2.47939 q^{83} +15.7035 q^{85} +5.23631 q^{86} +6.83526 q^{87} -7.20969 q^{88} -2.30019 q^{89} -4.58038 q^{90} +1.21295 q^{92} +2.39033 q^{93} +16.2450 q^{94} +4.44614 q^{95} +1.29849 q^{96} -15.4518 q^{97} +2.42981 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 12 q^{11} + 32 q^{12} + 4 q^{15} + 44 q^{16} + 8 q^{17} + 8 q^{18} - 4 q^{19} + 28 q^{20} + 16 q^{22} + 20 q^{23} + 24 q^{24} + 48 q^{25} + 32 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 4 q^{31} + 36 q^{32} + 12 q^{33} + 16 q^{34} + 32 q^{36} + 64 q^{37} + 20 q^{38} - 48 q^{40} - 24 q^{41} + 20 q^{43} + 48 q^{44} + 4 q^{45} + 28 q^{46} + 32 q^{47} + 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} + 8 q^{54} - 24 q^{55} - 4 q^{57} + 28 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} - 4 q^{62} + 48 q^{64} + 28 q^{65} + 16 q^{66} + 44 q^{67} - 32 q^{68} + 20 q^{69} + 20 q^{71} + 24 q^{72} - 16 q^{73} + 44 q^{74} + 48 q^{75} - 16 q^{76} + 32 q^{78} + 4 q^{79} + 44 q^{80} + 24 q^{81} - 8 q^{82} + 8 q^{83} + 28 q^{85} + 56 q^{86} + 24 q^{87} + 60 q^{88} + 60 q^{89} - 4 q^{90} + 60 q^{92} - 4 q^{93} + 24 q^{94} + 28 q^{95} + 36 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 12 * q^11 + 32 * q^12 + 4 * q^15 + 44 * q^16 + 8 * q^17 + 8 * q^18 - 4 * q^19 + 28 * q^20 + 16 * q^22 + 20 * q^23 + 24 * q^24 + 48 * q^25 + 32 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 4 * q^31 + 36 * q^32 + 12 * q^33 + 16 * q^34 + 32 * q^36 + 64 * q^37 + 20 * q^38 - 48 * q^40 - 24 * q^41 + 20 * q^43 + 48 * q^44 + 4 * q^45 + 28 * q^46 + 32 * q^47 + 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 + 8 * q^54 - 24 * q^55 - 4 * q^57 + 28 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 - 4 * q^62 + 48 * q^64 + 28 * q^65 + 16 * q^66 + 44 * q^67 - 32 * q^68 + 20 * q^69 + 20 * q^71 + 24 * q^72 - 16 * q^73 + 44 * q^74 + 48 * q^75 - 16 * q^76 + 32 * q^78 + 4 * q^79 + 44 * q^80 + 24 * q^81 - 8 * q^82 + 8 * q^83 + 28 * q^85 + 56 * q^86 + 24 * q^87 + 60 * q^88 + 60 * q^89 - 4 * q^90 + 60 * q^92 - 4 * q^93 + 24 * q^94 + 28 * q^95 + 36 * q^96 - 48 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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