LMFDB - Embedded newform 5239.2.a.s.1.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5239,2,Mod(1,5239)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5239.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5239, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.a (trivial)

Newform invariants

comment:select newform

sage:traces = [36,-2,-5,28,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$41.8336256189$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	5239.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.314789 q^{2} +1.77594 q^{3} -1.90091 q^{4} +0.987732 q^{5} +0.559047 q^{6} +0.624388 q^{7} -1.22796 q^{8} +0.153977 q^{9} +0.310927 q^{10} -4.02120 q^{11} -3.37591 q^{12} +0.196550 q^{14} +1.75416 q^{15} +3.41527 q^{16} +0.890404 q^{17} +0.0484701 q^{18} +4.17693 q^{19} -1.87759 q^{20} +1.10888 q^{21} -1.26583 q^{22} -0.895890 q^{23} -2.18079 q^{24} -4.02439 q^{25} -5.05438 q^{27} -1.18690 q^{28} +2.09204 q^{29} +0.552188 q^{30} +1.00000 q^{31} +3.53101 q^{32} -7.14143 q^{33} +0.280289 q^{34} +0.616728 q^{35} -0.292695 q^{36} -0.475907 q^{37} +1.31485 q^{38} -1.21290 q^{40} -3.26616 q^{41} +0.349062 q^{42} +3.14589 q^{43} +7.64394 q^{44} +0.152088 q^{45} -0.282016 q^{46} -8.35590 q^{47} +6.06532 q^{48} -6.61014 q^{49} -1.26683 q^{50} +1.58131 q^{51} -5.54163 q^{53} -1.59106 q^{54} -3.97187 q^{55} -0.766725 q^{56} +7.41800 q^{57} +0.658549 q^{58} +3.65296 q^{59} -3.33449 q^{60} +0.913094 q^{61} +0.314789 q^{62} +0.0961412 q^{63} -5.71901 q^{64} -2.24804 q^{66} +0.824213 q^{67} -1.69258 q^{68} -1.59105 q^{69} +0.194139 q^{70} -0.376435 q^{71} -0.189077 q^{72} -0.989383 q^{73} -0.149810 q^{74} -7.14708 q^{75} -7.93996 q^{76} -2.51079 q^{77} -7.84939 q^{79} +3.37337 q^{80} -9.43822 q^{81} -1.02815 q^{82} -8.58347 q^{83} -2.10788 q^{84} +0.879481 q^{85} +0.990289 q^{86} +3.71534 q^{87} +4.93788 q^{88} -9.19298 q^{89} +0.0478754 q^{90} +1.70300 q^{92} +1.77594 q^{93} -2.63034 q^{94} +4.12569 q^{95} +6.27088 q^{96} +12.5661 q^{97} -2.08080 q^{98} -0.619171 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{2} - 5 q^{3} + 28 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 15 q^{10} + q^{11} - 13 q^{12} - 19 q^{14} + 10 q^{15} + 4 q^{16} - 46 q^{17} + 9 q^{18} - 8 q^{19} + 5 q^{20} + 16 q^{21}+ \cdots + 47 q^{99}+O(q^{100}) $ 36 * q - 2 * q^2 - 5 * q^3 + 28 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 15 * q^10 + q^11 - 13 * q^12 - 19 * q^14 + 10 * q^15 + 4 * q^16 - 46 * q^17 + 9 * q^18 - 8 * q^19 + 5 * q^20 + 16 * q^21 - 21 * q^22 - 24 * q^23 - 57 * q^24 + 5 * q^25 - 11 * q^27 + 32 * q^28 - 73 * q^29 - 31 * q^30 + 36 * q^31 - 3 * q^32 + 8 * q^33 + 37 * q^34 - 31 * q^35 - 31 * q^36 - 6 * q^37 - 25 * q^38 - 22 * q^40 - 6 * q^41 - 37 * q^42 - 37 * q^43 + 16 * q^45 + 45 * q^46 - 13 * q^47 - 46 * q^48 - 5 * q^49 - 24 * q^50 - 46 * q^51 - 42 * q^53 + 26 * q^54 - 47 * q^55 - 95 * q^56 - 33 * q^57 - 9 * q^58 - 20 * q^59 + 40 * q^60 - 48 * q^61 - 2 * q^62 - 52 * q^63 + 21 * q^64 - 4 * q^66 + 50 * q^67 - 76 * q^68 - 33 * q^69 - 93 * q^70 - 16 * q^71 + 52 * q^72 + 43 * q^73 - 76 * q^74 - 40 * q^75 - 62 * q^76 - 47 * q^77 - 43 * q^79 + 46 * q^80 - 96 * q^81 + 7 * q^82 - 9 * q^83 + 77 * q^84 + 5 * q^85 - 64 * q^86 - 8 * q^87 - 54 * q^88 - 6 * q^89 + 27 * q^90 - 35 * q^92 - 5 * q^93 - 76 * q^94 - 63 * q^95 - 72 * q^96 + 4 * q^97 + 41 * q^98 + 47 * q^99

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 $

$2$	0.314789	0.222589	0.111295	−	0.993787i	$-0.464500\pi$
$2$	0.314789	0.222589	0.111295	+	0.993787i	$0.464500\pi$
$3$	1.77594	1.02534	0.512671	−	0.858585i	$-0.328656\pi$
$3$	1.77594	1.02534	0.512671	+	0.858585i	$0.328656\pi$
$4$	−1.90091	−0.950454
$5$	0.987732	0.441727	0.220864	−	0.975305i	$-0.429112\pi$
$5$	0.987732	0.441727	0.220864	+	0.975305i	$0.429112\pi$
$6$	0.559047	0.228230
$7$	0.624388	0.235997	0.117998	−	0.993014i	$-0.462352\pi$
$7$	0.624388	0.235997	0.117998	+	0.993014i	$0.462352\pi$
$8$	−1.22796	−0.434150
$9$	0.153977	0.0513255
$10$	0.310927	0.0983236
$11$	−4.02120	−1.21244	−0.606219	−	0.795298i	$-0.707315\pi$
$11$	−4.02120	−1.21244	−0.606219	+	0.795298i	$0.707315\pi$
$12$	−3.37591	−0.974540
$13$	0	0
$13$	0	0
$14$	0.196550	0.0525303
$15$	1.75416	0.452921
$16$	3.41527	0.853817
$17$	0.890404	0.215955	0.107977	−	0.994153i	$-0.465563\pi$
$17$	0.890404	0.215955	0.107977	+	0.994153i	$0.465563\pi$
$18$	0.0484701	0.0114245
$19$	4.17693	0.958254	0.479127	−	0.877746i	$-0.340953\pi$
$19$	4.17693	0.958254	0.479127	+	0.877746i	$0.340953\pi$
$20$	−1.87759	−0.419841
$21$	1.10888	0.241977
$22$	−1.26583	−0.269876
$23$	−0.895890	−0.186806	−0.0934030	−	0.995628i	$-0.529774\pi$
$23$	−0.895890	−0.186806	−0.0934030	+	0.995628i	$0.529774\pi$
$24$	−2.18079	−0.445152
$25$	−4.02439	−0.804877
$26$	0	0
$27$	−5.05438	−0.972715
$28$	−1.18690	−0.224304
$29$	2.09204	0.388481	0.194241	−	0.980954i	$-0.437776\pi$
$29$	2.09204	0.388481	0.194241	+	0.980954i	$0.437776\pi$
$30$	0.552188	0.100815
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	3.53101	0.624200
$33$	−7.14143	−1.24316
$34$	0.280289	0.0480692
$35$	0.616728	0.104246
$36$	−0.292695	−0.0487826
$37$	−0.475907	−0.0782386	−0.0391193	−	0.999235i	$-0.512455\pi$
$37$	−0.475907	−0.0782386	−0.0391193	+	0.999235i	$0.512455\pi$
$38$	1.31485	0.213297
$39$	0	0
$40$	−1.21290	−0.191776
$41$	−3.26616	−0.510088	−0.255044	−	0.966929i	$-0.582090\pi$
$41$	−3.26616	−0.510088	−0.255044	+	0.966929i	$0.582090\pi$
$42$	0.349062	0.0538615
$43$	3.14589	0.479743	0.239872	−	0.970805i	$-0.422895\pi$
$43$	3.14589	0.479743	0.239872	+	0.970805i	$0.422895\pi$
$44$	7.64394	1.15237
$45$	0.152088	0.0226719
$46$	−0.282016	−0.0415810
$47$	−8.35590	−1.21883	−0.609417	−	0.792850i	$-0.708596\pi$
$47$	−8.35590	−1.21883	−0.609417	+	0.792850i	$0.708596\pi$
$48$	6.06532	0.875454
$49$	−6.61014	−0.944306
$50$	−1.26683	−0.179157
$51$	1.58131	0.221427
$52$	0	0
$53$	−5.54163	−0.761202	−0.380601	−	0.924739i	$-0.624283\pi$
$53$	−5.54163	−0.761202	−0.380601	+	0.924739i	$0.624283\pi$
$54$	−1.59106	−0.216516
$55$	−3.97187	−0.535567
$56$	−0.766725	−0.102458
$57$	7.41800	0.982537
$58$	0.658549	0.0864718
$59$	3.65296	0.475575	0.237788	−	0.971317i	$-0.423578\pi$
$59$	3.65296	0.475575	0.237788	+	0.971317i	$0.423578\pi$
$60$	−3.33449	−0.430481
$61$	0.913094	0.116910	0.0584549	−	0.998290i	$-0.481383\pi$
$61$	0.913094	0.116910	0.0584549	+	0.998290i	$0.481383\pi$
$62$	0.314789	0.0399782
$63$	0.0961412	0.0121127
$64$	−5.71901	−0.714877
$65$	0	0
$66$	−2.24804	−0.276715
$67$	0.824213	0.100694	0.0503468	−	0.998732i	$-0.483967\pi$
$67$	0.824213	0.100694	0.0503468	+	0.998732i	$0.483967\pi$
$68$	−1.69258	−0.205255
$69$	−1.59105	−0.191540
$70$	0.194139	0.0232040
$71$	−0.376435	−0.0446746	−0.0223373	−	0.999750i	$-0.507111\pi$
$71$	−0.376435	−0.0446746	−0.0223373	+	0.999750i	$0.507111\pi$
$72$	−0.189077	−0.0222830
$73$	−0.989383	−0.115799	−0.0578993	−	0.998322i	$-0.518440\pi$
$73$	−0.989383	−0.115799	−0.0578993	+	0.998322i	$0.518440\pi$
$74$	−0.149810	−0.0174151
$75$	−7.14708	−0.825274
$76$	−7.93996	−0.910776
$77$	−2.51079	−0.286131
$78$	0	0
$79$	−7.84939	−0.883125	−0.441562	−	0.897231i	$-0.645576\pi$
$79$	−7.84939	−0.883125	−0.441562	+	0.897231i	$0.645576\pi$
$80$	3.37337	0.377154
$81$	−9.43822	−1.04869
$82$	−1.02815	−0.113540
$83$	−8.58347	−0.942159	−0.471079	−	0.882091i	$-0.656135\pi$
$83$	−8.58347	−0.942159	−0.471079	+	0.882091i	$0.656135\pi$
$84$	−2.10788	−0.229988
$85$	0.879481	0.0953931
$86$	0.990289	0.106786
$87$	3.71534	0.398326
$88$	4.93788	0.526380
$89$	−9.19298	−0.974454	−0.487227	−	0.873275i	$-0.661991\pi$
$89$	−9.19298	−0.974454	−0.487227	+	0.873275i	$0.661991\pi$
$90$	0.0478754	0.00504651
$91$	0	0
$92$	1.70300	0.177550
$93$	1.77594	0.184157
$94$	−2.63034	−0.271299
$95$	4.12569	0.423287
$96$	6.27088	0.640019
$97$	12.5661	1.27589	0.637946	−	0.770081i	$-0.279784\pi$
$97$	12.5661	1.27589	0.637946	+	0.770081i	$0.279784\pi$
$98$	−2.08080	−0.210192
$99$	−0.619171	−0.0622291
$100$	7.64999	0.764999
$101$	6.06860	0.603848	0.301924	−	0.953332i	$-0.402371\pi$
$101$	6.06860	0.603848	0.301924	+	0.953332i	$0.402371\pi$
$102$	0.497778	0.0492873
$103$	−11.0910	−1.09283	−0.546416	−	0.837514i	$-0.684008\pi$
$103$	−11.0910	−1.09283	−0.546416	+	0.837514i	$0.684008\pi$
$104$	0	0
$105$	1.09527	0.106888
$106$	−1.74444	−0.169435
$107$	0.451699	0.0436674	0.0218337	−	0.999762i	$-0.493050\pi$
$107$	0.451699	0.0436674	0.0218337	+	0.999762i	$0.493050\pi$
$108$	9.60791	0.924521
$109$	−4.13545	−0.396105	−0.198052	−	0.980191i	$-0.563462\pi$
$109$	−4.13545	−0.396105	−0.198052	+	0.980191i	$0.563462\pi$
$110$	−1.25030	−0.119211
$111$	−0.845184	−0.0802213
$112$	2.13245	0.201498
$113$	−12.0896	−1.13729	−0.568647	−	0.822582i	$-0.692533\pi$
$113$	−12.0896	−1.13729	−0.568647	+	0.822582i	$0.692533\pi$
$114$	2.33510	0.218702
$115$	−0.884899	−0.0825172
$116$	−3.97677	−0.369234
$117$	0	0
$118$	1.14991	0.105858
$119$	0.555958	0.0509646
$120$	−2.15404	−0.196636
$121$	5.17008	0.470007
$122$	0.287432	0.0260228
$123$	−5.80051	−0.523014
$124$	−1.90091	−0.170707
$125$	−8.91367	−0.797263
$126$	0.0302642	0.00269615
$127$	−19.1249	−1.69706	−0.848529	−	0.529148i	$-0.822511\pi$
$127$	−19.1249	−1.69706	−0.848529	+	0.529148i	$0.822511\pi$
$128$	−8.86230	−0.783324
$129$	5.58692	0.491901
$130$	0	0
$131$	−16.0240	−1.40002	−0.700011	−	0.714132i	$-0.746822\pi$
$131$	−16.0240	−1.40002	−0.700011	+	0.714132i	$0.746822\pi$
$132$	13.5752	1.18157
$133$	2.60803	0.226145
$134$	0.259453	0.0224133
$135$	−4.99237	−0.429675
$136$	−1.09338	−0.0937567
$137$	−5.94011	−0.507498	−0.253749	−	0.967270i	$-0.581664\pi$
$137$	−5.94011	−0.507498	−0.253749	+	0.967270i	$0.581664\pi$
$138$	−0.500844	−0.0426347
$139$	12.4010	1.05184	0.525918	−	0.850535i	$-0.323722\pi$
$139$	12.4010	1.05184	0.525918	+	0.850535i	$0.323722\pi$
$140$	−1.17234	−0.0990811
$141$	−14.8396	−1.24972
$142$	−0.118497	−0.00994408
$143$	0	0
$144$	0.525871	0.0438226
$145$	2.06637	0.171603
$146$	−0.311446	−0.0257755
$147$	−11.7392	−0.968236
$148$	0.904655	0.0743622
$149$	6.77587	0.555101	0.277550	−	0.960711i	$-0.410477\pi$
$149$	6.77587	0.555101	0.277550	+	0.960711i	$0.410477\pi$
$150$	−2.24982	−0.183697
$151$	2.70461	0.220098	0.110049	−	0.993926i	$-0.464899\pi$
$151$	2.70461	0.220098	0.110049	+	0.993926i	$0.464899\pi$
$152$	−5.12911	−0.416026
$153$	0.137101	0.0110840
$154$	−0.790369	−0.0636897
$155$	0.987732	0.0793365
$156$	0	0
$157$	−12.4564	−0.994128	−0.497064	−	0.867714i	$-0.665589\pi$
$157$	−12.4564	−0.994128	−0.497064	+	0.867714i	$0.665589\pi$
$158$	−2.47090	−0.196574
$159$	−9.84163	−0.780492
$160$	3.48769	0.275726
$161$	−0.559383	−0.0440856
$162$	−2.97104	−0.233427
$163$	−1.14360	−0.0895738	−0.0447869	−	0.998997i	$-0.514261\pi$
$163$	−1.14360	−0.0895738	−0.0447869	+	0.998997i	$0.514261\pi$
$164$	6.20866	0.484815
$165$	−7.05382	−0.549139
$166$	−2.70198	−0.209714
$167$	0.837976	0.0648445	0.0324223	−	0.999474i	$-0.489678\pi$
$167$	0.837976	0.0648445	0.0324223	+	0.999474i	$0.489678\pi$
$168$	−1.36166	−0.105054
$169$	0	0
$170$	0.276850	0.0212335
$171$	0.643150	0.0491829
$172$	−5.98004	−0.455974
$173$	−6.80018	−0.517008	−0.258504	−	0.966010i	$-0.583230\pi$
$173$	−6.80018	−0.517008	−0.258504	+	0.966010i	$0.583230\pi$
$174$	1.16955	0.0886631
$175$	−2.51278	−0.189948
$176$	−13.7335	−1.03520
$177$	6.48746	0.487627
$178$	−2.89384	−0.216903
$179$	−23.8094	−1.77959	−0.889797	−	0.456356i	$-0.849154\pi$
$179$	−23.8094	−1.77959	−0.889797	+	0.456356i	$0.849154\pi$
$180$	−0.289105	−0.0215486
$181$	−14.5356	−1.08042	−0.540212	−	0.841529i	$-0.681656\pi$
$181$	−14.5356	−1.08042	−0.540212	+	0.841529i	$0.681656\pi$
$182$	0	0
$183$	1.62160	0.119872
$184$	1.10012	0.0811018
$185$	−0.470068	−0.0345601
$186$	0.559047	0.0409913
$187$	−3.58050	−0.261832
$188$	15.8838	1.15845
$189$	−3.15589	−0.229558
$190$	1.29872	0.0942190
$191$	1.18604	0.0858191	0.0429095	−	0.999079i	$-0.486337\pi$
$191$	1.18604	0.0858191	0.0429095	+	0.999079i	$0.486337\pi$
$192$	−10.1566	−0.732993
$193$	4.70333	0.338553	0.169277	−	0.985569i	$-0.445857\pi$
$193$	4.70333	0.338553	0.169277	+	0.985569i	$0.445857\pi$
$194$	3.95566	0.284000
$195$	0	0
$196$	12.5653	0.897519
$197$	13.8258	0.985046	0.492523	−	0.870299i	$-0.336075\pi$
$197$	13.8258	0.985046	0.492523	+	0.870299i	$0.336075\pi$
$198$	−0.194908	−0.0138515
$199$	3.81237	0.270252	0.135126	−	0.990828i	$-0.456856\pi$
$199$	3.81237	0.270252	0.135126	+	0.990828i	$0.456856\pi$
$200$	4.94179	0.349437
$201$	1.46376	0.103245
$202$	1.91032	0.134410
$203$	1.30624	0.0916803
$204$	−3.00592	−0.210457
$205$	−3.22609	−0.225320
$206$	−3.49133	−0.243253
$207$	−0.137946	−0.00958792
$208$	0	0
$209$	−16.7963	−1.16182
$210$	0.344780	0.0237921
$211$	2.31820	0.159592	0.0797959	−	0.996811i	$-0.474573\pi$
$211$	2.31820	0.159592	0.0797959	+	0.996811i	$0.474573\pi$
$212$	10.5341	0.723487
$213$	−0.668527	−0.0458067
$214$	0.142190	0.00971988
$215$	3.10729	0.211916
$216$	6.20658	0.422304
$217$	0.624388	0.0423862
$218$	−1.30179	−0.0881686
$219$	−1.75709	−0.118733
$220$	7.55016	0.509032
$221$	0	0
$222$	−0.266054	−0.0178564
$223$	27.0832	1.81362	0.906812	−	0.421535i	$-0.138509\pi$
$223$	27.0832	1.81362	0.906812	+	0.421535i	$0.138509\pi$
$224$	2.20472	0.147309
$225$	−0.619661	−0.0413108
$226$	−3.80567	−0.253149
$227$	9.18731	0.609783	0.304892	−	0.952387i	$-0.401380\pi$
$227$	9.18731	0.609783	0.304892	+	0.952387i	$0.401380\pi$
$228$	−14.1009	−0.933857
$229$	28.8260	1.90488	0.952438	−	0.304732i	$-0.0985670\pi$
$229$	28.8260	1.90488	0.952438	+	0.304732i	$0.0985670\pi$
$230$	−0.278556	−0.0183674
$231$	−4.45903	−0.293382
$232$	−2.56894	−0.168659
$233$	14.9628	0.980244	0.490122	−	0.871654i	$-0.336952\pi$
$233$	14.9628	0.980244	0.490122	+	0.871654i	$0.336952\pi$
$234$	0	0
$235$	−8.25339	−0.538392
$236$	−6.94395	−0.452012
$237$	−13.9401	−0.905505
$238$	0.175009	0.0113442
$239$	−22.4151	−1.44991	−0.724956	−	0.688796i	$-0.758140\pi$
$239$	−22.4151	−1.44991	−0.724956	+	0.688796i	$0.758140\pi$
$240$	5.99091	0.386712
$241$	12.3994	0.798719	0.399359	−	0.916794i	$-0.369233\pi$
$241$	12.3994	0.798719	0.399359	+	0.916794i	$0.369233\pi$
$242$	1.62748	0.104618
$243$	−1.59862	−0.102551
$244$	−1.73571	−0.111117
$245$	−6.52904	−0.417125
$246$	−1.82593	−0.116417
$247$	0	0
$248$	−1.22796	−0.0779756
$249$	−15.2438	−0.966034
$250$	−2.80592	−0.177462
$251$	−25.5893	−1.61518	−0.807591	−	0.589743i	$-0.799229\pi$
$251$	−25.5893	−1.61518	−0.807591	+	0.589743i	$0.799229\pi$
$252$	−0.182756	−0.0115125
$253$	3.60256	0.226491
$254$	−6.02029	−0.377747
$255$	1.56191	0.0978105
$256$	8.64828	0.540517
$257$	−0.978333	−0.0610267	−0.0305134	−	0.999534i	$-0.509714\pi$
$257$	−0.978333	−0.0610267	−0.0305134	+	0.999534i	$0.509714\pi$
$258$	1.75870	0.109492
$259$	−0.297151	−0.0184640
$260$	0	0
$261$	0.322125	0.0199390
$262$	−5.04417	−0.311630
$263$	19.7634	1.21866	0.609332	−	0.792915i	$-0.291438\pi$
$263$	19.7634	1.21866	0.609332	+	0.792915i	$0.291438\pi$
$264$	8.76940	0.539719
$265$	−5.47365	−0.336243
$266$	0.820977	0.0503373
$267$	−16.3262	−0.999148
$268$	−1.56675	−0.0957047
$269$	−4.99551	−0.304582	−0.152291	−	0.988336i	$-0.548665\pi$
$269$	−4.99551	−0.304582	−0.152291	+	0.988336i	$0.548665\pi$
$270$	−1.57154	−0.0956409
$271$	10.8601	0.659703	0.329852	−	0.944033i	$-0.393001\pi$
$271$	10.8601	0.659703	0.329852	+	0.944033i	$0.393001\pi$
$272$	3.04097	0.184386
$273$	0	0
$274$	−1.86988	−0.112964
$275$	16.1829	0.975864
$276$	3.02444	0.182050
$277$	−21.4190	−1.28694	−0.643470	−	0.765471i	$-0.722506\pi$
$277$	−21.4190	−1.28694	−0.643470	+	0.765471i	$0.722506\pi$
$278$	3.90368	0.234127
$279$	0.153977	0.00921834
$280$	−0.757318	−0.0452584
$281$	15.2491	0.909687	0.454844	−	0.890571i	$-0.349695\pi$
$281$	15.2491	0.909687	0.454844	+	0.890571i	$0.349695\pi$
$282$	−4.67134	−0.278174
$283$	−4.65745	−0.276857	−0.138428	−	0.990372i	$-0.544205\pi$
$283$	−4.65745	−0.276857	−0.138428	+	0.990372i	$0.544205\pi$
$284$	0.715568	0.0424611
$285$	7.32699	0.434013
$286$	0	0
$287$	−2.03935	−0.120379
$288$	0.543693	0.0320374
$289$	−16.2072	−0.953364
$290$	0.650470	0.0381969
$291$	22.3167	1.30823
$292$	1.88073	0.110061
$293$	−11.9600	−0.698711	−0.349356	−	0.936990i	$-0.613600\pi$
$293$	−11.9600	−0.698711	−0.349356	+	0.936990i	$0.613600\pi$
$294$	−3.69538	−0.215519
$295$	3.60815	0.210074
$296$	0.584395	0.0339673
$297$	20.3247	1.17936
$298$	2.13297	0.123559
$299$	0	0
$300$	13.5860	0.784385
$301$	1.96426	0.113218
$302$	0.851382	0.0489915
$303$	10.7775	0.619150
$304$	14.2653	0.818173
$305$	0.901892	0.0516422
$306$	0.0431580	0.00246718
$307$	34.6495	1.97755	0.988776	−	0.149403i	$-0.0477351\pi$
$307$	34.6495	1.97755	0.988776	+	0.149403i	$0.0477351\pi$
$308$	4.77279	0.271955
$309$	−19.6971	−1.12053
$310$	0.310927	0.0176594
$311$	22.2979	1.26440	0.632200	−	0.774805i	$-0.282152\pi$
$311$	22.2979	1.26440	0.632200	+	0.774805i	$0.282152\pi$
$312$	0	0
$313$	21.7431	1.22899	0.614495	−	0.788921i	$-0.289360\pi$
$313$	21.7431	1.22899	0.614495	+	0.788921i	$0.289360\pi$
$314$	−3.92113	−0.221282
$315$	0.0949617	0.00535049
$316$	14.9210	0.839370
$317$	−19.5584	−1.09851	−0.549256	−	0.835654i	$-0.685089\pi$
$317$	−19.5584	−1.09851	−0.549256	+	0.835654i	$0.685089\pi$
$318$	−3.09803	−0.173729
$319$	−8.41251	−0.471010
$320$	−5.64885	−0.315780
$321$	0.802192	0.0447740
$322$	−0.176087	−0.00981297
$323$	3.71916	0.206939
$324$	17.9412	0.996733
$325$	0	0
$326$	−0.359993	−0.0199382
$327$	−7.34433	−0.406143
$328$	4.01071	0.221455
$329$	−5.21733	−0.287641
$330$	−2.22046	−0.122232
$331$	−18.9346	−1.04074	−0.520371	−	0.853941i	$-0.674206\pi$
$331$	−18.9346	−1.04074	−0.520371	+	0.853941i	$0.674206\pi$
$332$	16.3164	0.895478
$333$	−0.0732785	−0.00401564
$334$	0.263785	0.0144337
$335$	0.814101	0.0444791
$336$	3.78712	0.206604
$337$	3.29812	0.179660	0.0898301	−	0.995957i	$-0.471368\pi$
$337$	3.29812	0.179660	0.0898301	+	0.995957i	$0.471368\pi$
$338$	0	0
$339$	−21.4705	−1.16612
$340$	−1.67181	−0.0906667
$341$	−4.02120	−0.217760
$342$	0.202456	0.0109476
$343$	−8.49801	−0.458850
$344$	−3.86303	−0.208281
$345$	−1.57153	−0.0846084
$346$	−2.14062	−0.115080
$347$	3.92888	0.210913	0.105457	−	0.994424i	$-0.466370\pi$
$347$	3.92888	0.210913	0.105457	+	0.994424i	$0.466370\pi$
$348$	−7.06252	−0.378591
$349$	10.2127	0.546676	0.273338	−	0.961918i	$-0.411872\pi$
$349$	10.2127	0.546676	0.273338	+	0.961918i	$0.411872\pi$
$350$	−0.790994	−0.0422804
$351$	0	0
$352$	−14.1989	−0.756804
$353$	11.9626	0.636705	0.318352	−	0.947972i	$-0.396871\pi$
$353$	11.9626	0.636705	0.318352	+	0.947972i	$0.396871\pi$
$354$	2.04218	0.108540
$355$	−0.371816	−0.0197340
$356$	17.4750	0.926173
$357$	0.987350	0.0522561
$358$	−7.49491	−0.396118
$359$	34.6340	1.82791	0.913955	−	0.405815i	$-0.133012\pi$
$359$	34.6340	1.82791	0.913955	+	0.405815i	$0.133012\pi$
$360$	−0.186758	−0.00984299
$361$	−1.55325	−0.0817498
$362$	−4.57565	−0.240491
$363$	9.18177	0.481918
$364$	0	0
$365$	−0.977245	−0.0511513
$366$	0.510462	0.0266823
$367$	−9.06182	−0.473023	−0.236512	−	0.971629i	$-0.576004\pi$
$367$	−9.06182	−0.473023	−0.236512	+	0.971629i	$0.576004\pi$
$368$	−3.05970	−0.159498
$369$	−0.502912	−0.0261805
$370$	−0.147972	−0.00769270
$371$	−3.46013	−0.179641
$372$	−3.37591	−0.175033
$373$	15.2874	0.791554	0.395777	−	0.918347i	$-0.370475\pi$
$373$	15.2874	0.791554	0.395777	+	0.918347i	$0.370475\pi$
$374$	−1.12710	−0.0582809
$375$	−15.8302	−0.817467
$376$	10.2607	0.529156
$377$	0	0
$378$	−0.993440	−0.0510970
$379$	−11.4272	−0.586977	−0.293489	−	0.955963i	$-0.594816\pi$
$379$	−11.4272	−0.586977	−0.293489	+	0.955963i	$0.594816\pi$
$380$	−7.84255	−0.402314
$381$	−33.9647	−1.74006
$382$	0.373353	0.0191024
$383$	−13.2369	−0.676372	−0.338186	−	0.941079i	$-0.609813\pi$
$383$	−13.2369	−0.676372	−0.338186	+	0.941079i	$0.609813\pi$
$384$	−15.7389	−0.803175
$385$	−2.47999	−0.126392
$386$	1.48056	0.0753583
$387$	0.484393	0.0246231
$388$	−23.8870	−1.21268
$389$	−15.6775	−0.794881	−0.397441	−	0.917628i	$-0.630102\pi$
$389$	−15.6775	−0.794881	−0.397441	+	0.917628i	$0.630102\pi$
$390$	0	0
$391$	−0.797704	−0.0403416
$392$	8.11700	0.409970
$393$	−28.4577	−1.43550
$394$	4.35220	0.219261
$395$	−7.75309	−0.390100
$396$	1.17699	0.0591459
$397$	−6.41466	−0.321943	−0.160971	−	0.986959i	$-0.551463\pi$
$397$	−6.41466	−0.321943	−0.160971	+	0.986959i	$0.551463\pi$
$398$	1.20009	0.0601551
$399$	4.63171	0.231876
$400$	−13.7444	−0.687218
$401$	4.80528	0.239964	0.119982	−	0.992776i	$-0.461716\pi$
$401$	4.80528	0.239964	0.119982	+	0.992776i	$0.461716\pi$
$402$	0.460774	0.0229813
$403$	0	0
$404$	−11.5358	−0.573930
$405$	−9.32243	−0.463235
$406$	0.411191	0.0204070
$407$	1.91372	0.0948595
$408$	−1.94179	−0.0961327
$409$	−20.6886	−1.02299	−0.511493	−	0.859287i	$-0.670907\pi$
$409$	−20.6886	−1.02299	−0.511493	+	0.859287i	$0.670907\pi$
$410$	−1.01553	−0.0501537
$411$	−10.5493	−0.520359
$412$	21.0831	1.03869
$413$	2.28087	0.112234
$414$	−0.0434239	−0.00213417
$415$	−8.47817	−0.416177
$416$	0	0
$417$	22.0234	1.07849
$418$	−5.28728	−0.258609
$419$	−0.943094	−0.0460731	−0.0230366	−	0.999735i	$-0.507333\pi$
$419$	−0.943094	−0.0460731	−0.0230366	+	0.999735i	$0.507333\pi$
$420$	−2.08202	−0.101592
$421$	−18.1427	−0.884223	−0.442112	−	0.896960i	$-0.645771\pi$
$421$	−18.1427	−0.884223	−0.442112	+	0.896960i	$0.645771\pi$
$422$	0.729744	0.0355234
$423$	−1.28661	−0.0625573
$424$	6.80491	0.330476
$425$	−3.58333	−0.173817
$426$	−0.210445	−0.0101961
$427$	0.570125	0.0275903
$428$	−0.858638	−0.0415038
$429$	0	0
$430$	0.978140	0.0471701
$431$	1.77685	0.0855878	0.0427939	−	0.999084i	$-0.486374\pi$
$431$	1.77685	0.0855878	0.0427939	+	0.999084i	$0.486374\pi$
$432$	−17.2621	−0.830521
$433$	7.96494	0.382771	0.191385	−	0.981515i	$-0.438702\pi$
$433$	7.96494	0.382771	0.191385	+	0.981515i	$0.438702\pi$
$434$	0.196550	0.00943472
$435$	3.66976	0.175951
$436$	7.86112	0.376479
$437$	−3.74207	−0.179007
$438$	−0.553111	−0.0264287
$439$	−20.9693	−1.00081	−0.500406	−	0.865791i	$-0.666816\pi$
$439$	−20.9693	−1.00081	−0.500406	+	0.865791i	$0.666816\pi$
$440$	4.87730	0.232516
$441$	−1.01781	−0.0484670
$442$	0	0
$443$	−23.7103	−1.12651	−0.563255	−	0.826283i	$-0.690451\pi$
$443$	−23.7103	−1.12651	−0.563255	+	0.826283i	$0.690451\pi$
$444$	1.60662	0.0762467
$445$	−9.08019	−0.430442
$446$	8.52548	0.403693
$447$	12.0336	0.569168
$448$	−3.57089	−0.168709
$449$	18.2107	0.859418	0.429709	−	0.902967i	$-0.358616\pi$
$449$	18.2107	0.859418	0.429709	+	0.902967i	$0.358616\pi$
$450$	−0.195062	−0.00919533
$451$	13.1339	0.618450
$452$	22.9812	1.08095
$453$	4.80324	0.225676
$454$	2.89206	0.135731
$455$	0	0
$456$	−9.10901	−0.426569
$457$	−19.7708	−0.924841	−0.462421	−	0.886661i	$-0.653019\pi$
$457$	−19.7708	−0.924841	−0.462421	+	0.886661i	$0.653019\pi$
$458$	9.07410	0.424005
$459$	−4.50044	−0.210063
$460$	1.68211	0.0784288
$461$	−26.5203	−1.23517	−0.617586	−	0.786503i	$-0.711889\pi$
$461$	−26.5203	−1.23517	−0.617586	+	0.786503i	$0.711889\pi$
$462$	−1.40365	−0.0653037
$463$	12.6951	0.589989	0.294995	−	0.955499i	$-0.404682\pi$
$463$	12.6951	0.589989	0.294995	+	0.955499i	$0.404682\pi$
$464$	7.14487	0.331692
$465$	1.75416	0.0813470
$466$	4.71011	0.218192
$467$	−9.42570	−0.436169	−0.218085	−	0.975930i	$-0.569981\pi$
$467$	−9.42570	−0.436169	−0.218085	+	0.975930i	$0.569981\pi$
$468$	0	0
$469$	0.514629	0.0237634
$470$	−2.59807	−0.119840
$471$	−22.1219	−1.01932
$472$	−4.48570	−0.206471
$473$	−12.6503	−0.581659
$474$	−4.38817	−0.201556
$475$	−16.8096	−0.771277
$476$	−1.05683	−0.0484395
$477$	−0.853282	−0.0390691
$478$	−7.05601	−0.322734
$479$	−33.0219	−1.50881	−0.754404	−	0.656410i	$-0.772074\pi$
$479$	−33.0219	−1.50881	−0.754404	+	0.656410i	$0.772074\pi$
$480$	6.19394	0.282714
$481$	0	0
$482$	3.90320	0.177786
$483$	−0.993433	−0.0452028
$484$	−9.82784	−0.446720
$485$	12.4119	0.563596
$486$	−0.503227	−0.0228268
$487$	6.44478	0.292041	0.146021	−	0.989282i	$-0.453353\pi$
$487$	6.44478	0.292041	0.146021	+	0.989282i	$0.453353\pi$
$488$	−1.12124	−0.0507563
$489$	−2.03097	−0.0918438
$490$	−2.05527	−0.0928476
$491$	7.13297	0.321907	0.160953	−	0.986962i	$-0.448543\pi$
$491$	7.13297	0.321907	0.160953	+	0.986962i	$0.448543\pi$
$492$	11.0262	0.497101
$493$	1.86276	0.0838944
$494$	0	0
$495$	−0.611575	−0.0274883
$496$	3.41527	0.153350
$497$	−0.235041	−0.0105431
$498$	−4.79856	−0.215029
$499$	−3.77451	−0.168970	−0.0844851	−	0.996425i	$-0.526925\pi$
$499$	−3.77451	−0.168970	−0.0844851	+	0.996425i	$0.526925\pi$
$500$	16.9441	0.757762
$501$	1.48820	0.0664878
$502$	−8.05522	−0.359522
$503$	32.9944	1.47115	0.735573	−	0.677446i	$-0.236913\pi$
$503$	32.9944	1.47115	0.735573	+	0.677446i	$0.236913\pi$
$504$	−0.118058	−0.00525871
$505$	5.99414	0.266736
$506$	1.13404	0.0504144
$507$	0	0
$508$	36.3546	1.61298
$509$	13.6247	0.603903	0.301951	−	0.953323i	$-0.402362\pi$
$509$	13.6247	0.603903	0.301951	+	0.953323i	$0.402362\pi$
$510$	0.491671	0.0217716
$511$	−0.617759	−0.0273281
$512$	20.4470	0.903637
$513$	−21.1118	−0.932108
$514$	−0.307968	−0.0135839
$515$	−10.9550	−0.482734
$516$	−10.6202	−0.467529
$517$	33.6008	1.47776
$518$	−0.0935397	−0.00410990
$519$	−12.0767	−0.530110
$520$	0	0
$521$	−12.6423	−0.553870	−0.276935	−	0.960889i	$-0.589319\pi$
$521$	−12.6423	−0.553870	−0.276935	+	0.960889i	$0.589319\pi$
$522$	0.101401	0.00443821
$523$	23.7677	1.03929	0.519644	−	0.854383i	$-0.326065\pi$
$523$	23.7677	1.03929	0.519644	+	0.854383i	$0.326065\pi$
$524$	30.4601	1.33066
$525$	−4.46256	−0.194762
$526$	6.22130	0.271262
$527$	0.890404	0.0387866
$528$	−24.3899	−1.06143
$529$	−22.1974	−0.965104
$530$	−1.72304	−0.0748441
$531$	0.562471	0.0244092
$532$	−4.95762	−0.214940
$533$	0	0
$534$	−5.13930	−0.222399
$535$	0.446157	0.0192891
$536$	−1.01210	−0.0437161
$537$	−42.2841	−1.82469
$538$	−1.57253	−0.0677965
$539$	26.5807	1.14491
$540$	9.49003	0.408386
$541$	−13.8734	−0.596462	−0.298231	−	0.954494i	$-0.596397\pi$
$541$	−13.8734	−0.596462	−0.298231	+	0.954494i	$0.596397\pi$
$542$	3.41863	0.146843
$543$	−25.8144	−1.10780
$544$	3.14403	0.134799
$545$	−4.08472	−0.174970
$546$	0	0
$547$	15.3339	0.655631	0.327815	−	0.944742i	$-0.393688\pi$
$547$	15.3339	0.655631	0.327815	+	0.944742i	$0.393688\pi$
$548$	11.2916	0.482354
$549$	0.140595	0.00600045
$550$	5.09418	0.217217
$551$	8.73829	0.372264
$552$	1.95375	0.0831570
$553$	−4.90107	−0.208414
$554$	−6.74244	−0.286459
$555$	−0.834815	−0.0354359
$556$	−23.5731	−0.999722
$557$	−19.9009	−0.843228	−0.421614	−	0.906775i	$-0.638536\pi$
$557$	−19.9009	−0.843228	−0.421614	+	0.906775i	$0.638536\pi$
$558$	0.0484701	0.00205190
$559$	0	0
$560$	2.10629	0.0890071
$561$	−6.35876	−0.268467
$562$	4.80025	0.202487
$563$	−5.34683	−0.225342	−0.112671	−	0.993632i	$-0.535941\pi$
$563$	−5.34683	−0.225342	−0.112671	+	0.993632i	$0.535941\pi$
$564$	28.2087	1.18780
$565$	−11.9413	−0.502374
$566$	−1.46611	−0.0616253
$567$	−5.89312	−0.247488
$568$	0.462247	0.0193955
$569$	34.7169	1.45541	0.727705	−	0.685890i	$-0.240587\pi$
$569$	34.7169	1.45541	0.727705	+	0.685890i	$0.240587\pi$
$570$	2.30645	0.0966067
$571$	42.2991	1.77016	0.885081	−	0.465436i	$-0.154102\pi$
$571$	42.2991	1.77016	0.885081	+	0.465436i	$0.154102\pi$
$572$	0	0
$573$	2.10635	0.0879939
$574$	−0.641964	−0.0267951
$575$	3.60541	0.150356
$576$	−0.880595	−0.0366914
$577$	−11.8712	−0.494205	−0.247102	−	0.968989i	$-0.579478\pi$
$577$	−11.8712	−0.494205	−0.247102	+	0.968989i	$0.579478\pi$
$578$	−5.10184	−0.212208
$579$	8.35286	0.347133
$580$	−3.92798	−0.163101
$581$	−5.35942	−0.222346
$582$	7.02503	0.291197
$583$	22.2840	0.922910
$584$	1.21492	0.0502739
$585$	0	0
$586$	−3.76488	−0.155526
$587$	−28.4973	−1.17621	−0.588106	−	0.808784i	$-0.700126\pi$
$587$	−28.4973	−1.17621	−0.588106	+	0.808784i	$0.700126\pi$
$588$	22.3152	0.920264
$589$	4.17693	0.172107
$590$	1.13580	0.0467603
$591$	24.5538	1.01001
$592$	−1.62535	−0.0668015
$593$	−12.4171	−0.509909	−0.254955	−	0.966953i	$-0.582061\pi$
$593$	−12.4171	−0.509909	−0.254955	+	0.966953i	$0.582061\pi$
$594$	6.39798	0.262512
$595$	0.549137	0.0225124
$596$	−12.8803	−0.527598
$597$	6.77056	0.277100
$598$	0	0
$599$	−32.9899	−1.34793	−0.673965	−	0.738763i	$-0.735410\pi$
$599$	−32.9899	−1.34793	−0.673965	+	0.738763i	$0.735410\pi$
$600$	8.77634	0.358293
$601$	32.0104	1.30573	0.652866	−	0.757474i	$-0.273567\pi$
$601$	32.0104	1.30573	0.652866	+	0.757474i	$0.273567\pi$
$602$	0.618325	0.0252011
$603$	0.126910	0.00516816
$604$	−5.14122	−0.209193
$605$	5.10665	0.207615
$606$	3.39263	0.137816
$607$	−0.967410	−0.0392660	−0.0196330	−	0.999807i	$-0.506250\pi$
$607$	−0.967410	−0.0392660	−0.0196330	+	0.999807i	$0.506250\pi$
$608$	14.7488	0.598142
$609$	2.31982	0.0940037
$610$	0.283905	0.0114950
$611$	0	0
$612$	−0.260617	−0.0105348
$613$	−36.2294	−1.46329	−0.731646	−	0.681685i	$-0.761248\pi$
$613$	−36.2294	−1.46329	−0.731646	+	0.681685i	$0.761248\pi$
$614$	10.9073	0.440182
$615$	−5.72935	−0.231030
$616$	3.08316	0.124224
$617$	29.1855	1.17496	0.587482	−	0.809237i	$-0.300119\pi$
$617$	29.1855	1.17496	0.587482	+	0.809237i	$0.300119\pi$
$618$	−6.20041	−0.249417
$619$	18.0122	0.723970	0.361985	−	0.932184i	$-0.382099\pi$
$619$	18.0122	0.723970	0.361985	+	0.932184i	$0.382099\pi$
$620$	−1.87759	−0.0754057
$621$	4.52817	0.181709
$622$	7.01914	0.281442
$623$	−5.73999	−0.229968
$624$	0	0
$625$	11.3176	0.452705
$626$	6.84447	0.273560
$627$	−29.8293	−1.19127
$628$	23.6785	0.944873
$629$	−0.423750	−0.0168960
$630$	0.0298929	0.00119096
$631$	−1.41290	−0.0562465	−0.0281232	−	0.999604i	$-0.508953\pi$
$631$	−1.41290	−0.0562465	−0.0281232	+	0.999604i	$0.508953\pi$
$632$	9.63874	0.383409
$633$	4.11700	0.163636
$634$	−6.15677	−0.244517
$635$	−18.8902	−0.749637
$636$	18.7080	0.741822
$637$	0	0
$638$	−2.64816	−0.104842
$639$	−0.0579622	−0.00229295
$640$	−8.75358	−0.346015
$641$	14.7425	0.582296	0.291148	−	0.956678i	$-0.405963\pi$
$641$	14.7425	0.582296	0.291148	+	0.956678i	$0.405963\pi$
$642$	0.252521	0.00996620
$643$	36.7900	1.45085	0.725427	−	0.688299i	$-0.241642\pi$
$643$	36.7900	1.45085	0.725427	+	0.688299i	$0.241642\pi$
$644$	1.06334	0.0419013
$645$	5.51838	0.217286
$646$	1.17075	0.0460625
$647$	15.7406	0.618827	0.309413	−	0.950928i	$-0.399867\pi$
$647$	15.7406	0.618827	0.309413	+	0.950928i	$0.399867\pi$
$648$	11.5898	0.455289
$649$	−14.6893	−0.576606
$650$	0	0
$651$	1.10888	0.0434604
$652$	2.17388	0.0851358
$653$	37.4073	1.46386	0.731930	−	0.681380i	$-0.238620\pi$
$653$	37.4073	1.46386	0.731930	+	0.681380i	$0.238620\pi$
$654$	−2.31191	−0.0904029
$655$	−15.8274	−0.618428
$656$	−11.1548	−0.435522
$657$	−0.152342	−0.00594342
$658$	−1.64236	−0.0640257
$659$	−26.3690	−1.02719	−0.513595	−	0.858033i	$-0.671686\pi$
$659$	−26.3690	−1.02719	−0.513595	+	0.858033i	$0.671686\pi$
$660$	13.4087	0.521931
$661$	−42.8478	−1.66659	−0.833294	−	0.552830i	$-0.813548\pi$
$661$	−42.8478	−1.66659	−0.833294	+	0.552830i	$0.813548\pi$
$662$	−5.96040	−0.231658
$663$	0	0
$664$	10.5402	0.409038
$665$	2.57603	0.0998942
$666$	−0.0230672	−0.000893838 0
$667$	−1.87423	−0.0725707
$668$	−1.59292	−0.0616317
$669$	48.0982	1.85958
$670$	0.256270	0.00990057
$671$	−3.67174	−0.141746
$672$	3.91546	0.151042
$673$	18.0875	0.697223	0.348612	−	0.937267i	$-0.386653\pi$
$673$	18.0875	0.697223	0.348612	+	0.937267i	$0.386653\pi$
$674$	1.03821	0.0399904
$675$	20.3408	0.782917
$676$	0	0
$677$	10.1149	0.388747	0.194374	−	0.980928i	$-0.437733\pi$
$677$	10.1149	0.388747	0.194374	+	0.980928i	$0.437733\pi$
$678$	−6.75865	−0.259565
$679$	7.84612	0.301106
$680$	−1.07997	−0.0414149
$681$	16.3161	0.625236
$682$	−1.26583	−0.0484711
$683$	33.8799	1.29638	0.648189	−	0.761480i	$-0.275527\pi$
$683$	33.8799	1.29638	0.648189	+	0.761480i	$0.275527\pi$
$684$	−1.22257	−0.0467461
$685$	−5.86724	−0.224176
$686$	−2.67508	−0.102135
$687$	51.1934	1.95315
$688$	10.7440	0.409613
$689$	0	0
$690$	−0.494700	−0.0188329
$691$	−26.5682	−1.01070	−0.505351	−	0.862914i	$-0.668637\pi$
$691$	−26.5682	−1.01070	−0.505351	+	0.862914i	$0.668637\pi$
$692$	12.9265	0.491393
$693$	−0.386603	−0.0146858
$694$	1.23677	0.0469470
$695$	12.2488	0.464625
$696$	−4.56229	−0.172933
$697$	−2.90820	−0.110156
$698$	3.21486	0.121684
$699$	26.5730	1.00508
$700$	4.77656	0.180537
$701$	7.55154	0.285218	0.142609	−	0.989779i	$-0.454451\pi$
$701$	7.55154	0.285218	0.142609	+	0.989779i	$0.454451\pi$
$702$	0	0
$703$	−1.98783	−0.0749724
$704$	22.9973	0.866744
$705$	−14.6576	−0.552035
$706$	3.76569	0.141724
$707$	3.78916	0.142506
$708$	−12.3321	−0.463467
$709$	−6.43577	−0.241700	−0.120850	−	0.992671i	$-0.538562\pi$
$709$	−6.43577	−0.241700	−0.120850	+	0.992671i	$0.538562\pi$
$710$	−0.117044	−0.00439257
$711$	−1.20862	−0.0453269
$712$	11.2886	0.423059
$713$	−0.895890	−0.0335513
$714$	0.310807	0.0116316
$715$	0	0
$716$	45.2594	1.69142
$717$	−39.8079	−1.48665
$718$	10.9024	0.406873
$719$	18.7209	0.698170	0.349085	−	0.937091i	$-0.386492\pi$
$719$	18.7209	0.698170	0.349085	+	0.937091i	$0.386492\pi$
$720$	0.519420	0.0193576
$721$	−6.92512	−0.257905
$722$	−0.488944	−0.0181966
$723$	22.0207	0.818960
$724$	27.6309	1.02689
$725$	−8.41916	−0.312680
$726$	2.89031	0.107270
$727$	−34.1439	−1.26633	−0.633163	−	0.774019i	$-0.718244\pi$
$727$	−34.1439	−1.26633	−0.633163	+	0.774019i	$0.718244\pi$
$728$	0	0
$729$	25.4756	0.943541
$730$	−0.307626	−0.0113857
$731$	2.80111	0.103603
$732$	−3.08252	−0.113933
$733$	24.3837	0.900634	0.450317	−	0.892869i	$-0.351311\pi$
$733$	24.3837	0.900634	0.450317	+	0.892869i	$0.351311\pi$
$734$	−2.85256	−0.105290
$735$	−11.5952	−0.427696
$736$	−3.16340	−0.116604
$737$	−3.31433	−0.122085
$738$	−0.158311	−0.00582750
$739$	−12.4385	−0.457558	−0.228779	−	0.973478i	$-0.573473\pi$
$739$	−12.4385	−0.457558	−0.228779	+	0.973478i	$0.573473\pi$
$740$	0.893557	0.0328478
$741$	0	0
$742$	−1.08921	−0.0399862
$743$	30.9826	1.13664	0.568321	−	0.822807i	$-0.307593\pi$
$743$	30.9826	1.13664	0.568321	+	0.822807i	$0.307593\pi$
$744$	−2.18079	−0.0799517
$745$	6.69274	0.245203
$746$	4.81231	0.176191
$747$	−1.32165	−0.0483568
$748$	6.80620	0.248859
$749$	0.282035	0.0103054
$750$	−4.98316	−0.181959
$751$	1.20834	0.0440930	0.0220465	−	0.999757i	$-0.492982\pi$
$751$	1.20834	0.0440930	0.0220465	+	0.999757i	$0.492982\pi$
$752$	−28.5376	−1.04066
$753$	−45.4451	−1.65611
$754$	0	0
$755$	2.67143	0.0972234
$756$	5.99907	0.218184
$757$	−21.9668	−0.798396	−0.399198	−	0.916865i	$-0.630711\pi$
$757$	−21.9668	−0.798396	−0.399198	+	0.916865i	$0.630711\pi$
$758$	−3.59716	−0.130655
$759$	6.39794	0.232230
$760$	−5.06618	−0.183770
$761$	40.7712	1.47795	0.738977	−	0.673731i	$-0.235309\pi$
$761$	40.7712	1.47795	0.738977	+	0.673731i	$0.235309\pi$
$762$	−10.6917	−0.387320
$763$	−2.58213	−0.0934793
$764$	−2.25456	−0.0815671
$765$	0.135419	0.00489610
$766$	−4.16681	−0.150553
$767$	0	0
$768$	15.3589	0.554215
$769$	18.6321	0.671892	0.335946	−	0.941881i	$-0.390944\pi$
$769$	18.6321	0.671892	0.335946	+	0.941881i	$0.390944\pi$
$770$	−0.780672	−0.0281335
$771$	−1.73746	−0.0625732
$772$	−8.94061	−0.321779
$773$	15.2041	0.546852	0.273426	−	0.961893i	$-0.411843\pi$
$773$	15.2041	0.546852	0.273426	+	0.961893i	$0.411843\pi$
$774$	0.152481	0.00548083
$775$	−4.02439	−0.144560
$776$	−15.4307	−0.553929
$777$	−0.527723	−0.0189320
$778$	−4.93510	−0.176932
$779$	−13.6425	−0.488794
$780$	0	0
$781$	1.51372	0.0541652
$782$	−0.251108	−0.00897961
$783$	−10.5739	−0.377882
$784$	−22.5754	−0.806264
$785$	−12.3036	−0.439133
$786$	−8.95816	−0.319527
$787$	−1.19009	−0.0424220	−0.0212110	−	0.999775i	$-0.506752\pi$
$787$	−1.19009	−0.0424220	−0.0212110	+	0.999775i	$0.506752\pi$
$788$	−26.2815	−0.936241
$789$	35.0987	1.24955
$790$	−2.44058	−0.0868321
$791$	−7.54861	−0.268398
$792$	0.760318	0.0270167
$793$	0	0
$794$	−2.01926	−0.0716609
$795$	−9.72089	−0.344764
$796$	−7.24697	−0.256862
$797$	−8.46050	−0.299686	−0.149843	−	0.988710i	$-0.547877\pi$
$797$	−8.46050	−0.299686	−0.149843	+	0.988710i	$0.547877\pi$
$798$	1.45801	0.0516130
$799$	−7.44013	−0.263213
$800$	−14.2101	−0.502405
$801$	−1.41550	−0.0500144
$802$	1.51265	0.0534135
$803$	3.97851	0.140399
$804$	−2.78247	−0.0981300
$805$	−0.552520	−0.0194738
$806$	0	0
$807$	−8.87174	−0.312300
$808$	−7.45200	−0.262161
$809$	46.9389	1.65029	0.825143	−	0.564924i	$-0.191095\pi$
$809$	46.9389	1.65029	0.825143	+	0.564924i	$0.191095\pi$
$810$	−2.93459	−0.103111
$811$	52.1661	1.83180	0.915900	−	0.401406i	$-0.131478\pi$
$811$	52.1661	1.83180	0.915900	+	0.401406i	$0.131478\pi$
$812$	−2.48305	−0.0871379
$813$	19.2869	0.676421
$814$	0.602417	0.0211147
$815$	−1.12957	−0.0395672
$816$	5.40059	0.189059
$817$	13.1402	0.459716
$818$	−6.51254	−0.227706
$819$	0	0
$820$	6.13249	0.214156
$821$	16.9288	0.590818	0.295409	−	0.955371i	$-0.404544\pi$
$821$	16.9288	0.590818	0.295409	+	0.955371i	$0.404544\pi$
$822$	−3.32080	−0.115826
$823$	−9.93810	−0.346420	−0.173210	−	0.984885i	$-0.555414\pi$
$823$	−9.93810	−0.346420	−0.173210	+	0.984885i	$0.555414\pi$
$824$	13.6194	0.474453
$825$	28.7399	1.00059
$826$	0.717991	0.0249821
$827$	17.9222	0.623215	0.311607	−	0.950211i	$-0.399133\pi$
$827$	17.9222	0.623215	0.311607	+	0.950211i	$0.399133\pi$
$828$	0.262223	0.00911287
$829$	40.1084	1.39302	0.696512	−	0.717545i	$-0.254734\pi$
$829$	40.1084	1.39302	0.696512	+	0.717545i	$0.254734\pi$
$830$	−2.66883	−0.0926365
$831$	−38.0389	−1.31955
$832$	0	0
$833$	−5.88570	−0.203927
$834$	6.93272	0.240061
$835$	0.827695	0.0286436
$836$	31.9282	1.10426
$837$	−5.05438	−0.174705
$838$	−0.296875	−0.0102554
$839$	36.0689	1.24524	0.622619	−	0.782525i	$-0.286069\pi$
$839$	36.0689	1.24524	0.622619	+	0.782525i	$0.286069\pi$
$840$	−1.34495	−0.0464054
$841$	−24.6234	−0.849082
$842$	−5.71113	−0.196819
$843$	27.0816	0.932740
$844$	−4.40669	−0.151685
$845$	0	0
$846$	−0.405011	−0.0139246
$847$	3.22814	0.110920
$848$	−18.9262	−0.649927
$849$	−8.27137	−0.283873
$850$	−1.12799	−0.0386898
$851$	0.426360	0.0146154
$852$	1.27081	0.0435372
$853$	−11.9012	−0.407490	−0.203745	−	0.979024i	$-0.565311\pi$
$853$	−11.9012	−0.407490	−0.203745	+	0.979024i	$0.565311\pi$
$854$	0.179469	0.00614130
$855$	0.635259	0.0217254
$856$	−0.554669	−0.0189582
$857$	−18.5578	−0.633921	−0.316960	−	0.948439i	$-0.602662\pi$
$857$	−18.5578	−0.633921	−0.316960	+	0.948439i	$0.602662\pi$
$858$	0	0
$859$	−54.4878	−1.85910	−0.929550	−	0.368697i	$-0.879804\pi$
$859$	−54.4878	−1.85910	−0.929550	+	0.368697i	$0.879804\pi$
$860$	−5.90668	−0.201416
$861$	−3.62177	−0.123430
$862$	0.559332	0.0190509
$863$	−39.5255	−1.34547	−0.672733	−	0.739886i	$-0.734880\pi$
$863$	−39.5255	−1.34547	−0.672733	+	0.739886i	$0.734880\pi$
$864$	−17.8471	−0.607169
$865$	−6.71676	−0.228377
$866$	2.50727	0.0852006
$867$	−28.7830	−0.977523
$868$	−1.18690	−0.0402862
$869$	31.5640	1.07073
$870$	1.15520	0.0391649
$871$	0	0
$872$	5.07818	0.171969
$873$	1.93488	0.0654859
$874$	−1.17796	−0.0398451
$875$	−5.56559	−0.188151
$876$	3.34006	0.112850
$877$	−44.7739	−1.51191	−0.755953	−	0.654626i	$-0.772826\pi$
$877$	−44.7739	−1.51191	−0.755953	+	0.654626i	$0.772826\pi$
$878$	−6.60091	−0.222770
$879$	−21.2403	−0.716418
$880$	−13.5650	−0.457276
$881$	−13.6944	−0.461377	−0.230688	−	0.973028i	$-0.574098\pi$
$881$	−13.6944	−0.461377	−0.230688	+	0.973028i	$0.574098\pi$
$882$	−0.320394	−0.0107882
$883$	−14.4381	−0.485881	−0.242941	−	0.970041i	$-0.578112\pi$
$883$	−14.4381	−0.485881	−0.242941	+	0.970041i	$0.578112\pi$
$884$	0	0
$885$	6.40787	0.215398
$886$	−7.46373	−0.250749
$887$	5.32747	0.178879	0.0894395	−	0.995992i	$-0.471492\pi$
$887$	5.32747	0.178879	0.0894395	+	0.995992i	$0.471492\pi$
$888$	1.03785	0.0348281
$889$	−11.9414	−0.400500
$890$	−2.85834	−0.0958118
$891$	37.9530	1.27147
$892$	−51.4826	−1.72377
$893$	−34.9020	−1.16795
$894$	3.78803	0.126691
$895$	−23.5173	−0.786095
$896$	−5.53352	−0.184862
$897$	0	0
$898$	5.73253	0.191297
$899$	2.09204	0.0697733
$900$	1.17792	0.0392640
$901$	−4.93429	−0.164385
$902$	4.13439	0.137660
$903$	3.48841	0.116087
$904$	14.8456	0.493756
$905$	−14.3573	−0.477252
$906$	1.51201	0.0502330
$907$	22.3881	0.743386	0.371693	−	0.928356i	$-0.378777\pi$
$907$	22.3881	0.743386	0.371693	+	0.928356i	$0.378777\pi$
$908$	−17.4642	−0.579571
$909$	0.934422	0.0309928
$910$	0	0
$911$	27.4932	0.910890	0.455445	−	0.890264i	$-0.349480\pi$
$911$	27.4932	0.910890	0.455445	+	0.890264i	$0.349480\pi$
$912$	25.3344	0.838907
$913$	34.5159	1.14231
$914$	−6.22364	−0.205860
$915$	1.60171	0.0529509
$916$	−54.7956	−1.81050
$917$	−10.0052	−0.330401
$918$	−1.41669	−0.0467576
$919$	26.7417	0.882127	0.441064	−	0.897476i	$-0.354601\pi$
$919$	26.7417	0.882127	0.441064	+	0.897476i	$0.354601\pi$
$920$	1.08662	0.0358249
$921$	61.5356	2.02767
$922$	−8.34828	−0.274936
$923$	0	0
$924$	8.47620	0.278847
$925$	1.91523	0.0629725
$926$	3.99626	0.131325
$927$	−1.70776	−0.0560902
$928$	7.38700	0.242490
$929$	−2.80505	−0.0920308	−0.0460154	−	0.998941i	$-0.514652\pi$
$929$	−2.80505	−0.0920308	−0.0460154	+	0.998941i	$0.514652\pi$
$930$	0.552188	0.0181070
$931$	−27.6101	−0.904884
$932$	−28.4429	−0.931677
$933$	39.5999	1.29644
$934$	−2.96710	−0.0970866
$935$	−3.53657	−0.115658
$936$	0	0
$937$	−51.2675	−1.67484	−0.837418	−	0.546562i	$-0.815936\pi$
$937$	−51.2675	−1.67484	−0.837418	+	0.546562i	$0.815936\pi$
$938$	0.161999	0.00528947
$939$	38.6144	1.26013
$940$	15.6889	0.511717
$941$	15.5783	0.507839	0.253920	−	0.967225i	$-0.418280\pi$
$941$	15.5783	0.507839	0.253920	+	0.967225i	$0.418280\pi$
$942$	−6.96371	−0.226890
$943$	2.92612	0.0952874
$944$	12.4758	0.406054
$945$	−3.11718	−0.101402
$946$	−3.98215	−0.129471
$947$	2.99652	0.0973739	0.0486870	−	0.998814i	$-0.484496\pi$
$947$	2.99652	0.0973739	0.0486870	+	0.998814i	$0.484496\pi$
$948$	26.4988	0.860641
$949$	0	0
$950$	−5.29147	−0.171678
$951$	−34.7347	−1.12635
$952$	−0.682695	−0.0221263
$953$	−25.6873	−0.832092	−0.416046	−	0.909344i	$-0.636584\pi$
$953$	−25.6873	−0.832092	−0.416046	+	0.909344i	$0.636584\pi$
$954$	−0.268603	−0.00869636
$955$	1.17149	0.0379086
$956$	42.6090	1.37807
$957$	−14.9401	−0.482946
$958$	−10.3949	−0.335844
$959$	−3.70894	−0.119768
$960$	−10.0320	−0.323783
$961$	1.00000	0.0322581
$962$	0	0
$963$	0.0695511	0.00224125
$964$	−23.5702	−0.759145
$965$	4.64563	0.149548
$966$	−0.312721	−0.0100616
$967$	24.6067	0.791299	0.395649	−	0.918402i	$-0.370520\pi$
$967$	24.6067	0.791299	0.395649	+	0.918402i	$0.370520\pi$
$968$	−6.34865	−0.204053
$969$	6.60502	0.212184
$970$	3.90713	0.125450
$971$	−9.51683	−0.305410	−0.152705	−	0.988272i	$-0.548798\pi$
$971$	−9.51683	−0.305410	−0.152705	+	0.988272i	$0.548798\pi$
$972$	3.03883	0.0974704
$973$	7.74302	0.248230
$974$	2.02874	0.0650052
$975$	0	0
$976$	3.11846	0.0998195
$977$	−0.830048	−0.0265556	−0.0132778	−	0.999912i	$-0.504227\pi$
$977$	−0.830048	−0.0265556	−0.0132778	+	0.999912i	$0.504227\pi$
$978$	−0.639327	−0.0204434
$979$	36.9668	1.18146
$980$	12.4111	0.396458
$981$	−0.636763	−0.0203303
$982$	2.24538	0.0716529
$983$	−60.7093	−1.93633	−0.968163	−	0.250322i	$-0.919463\pi$
$983$	−60.7093	−1.93633	−0.968163	+	0.250322i	$0.919463\pi$
$984$	7.12280	0.227067
$985$	13.6562	0.435122
$986$	0.586375	0.0186740
$987$	−9.26568	−0.294930
$988$	0	0
$989$	−2.81837	−0.0896189
$990$	−0.192517	−0.00611859
$991$	−36.9415	−1.17349	−0.586743	−	0.809773i	$-0.699590\pi$
$991$	−36.9415	−1.17349	−0.586743	+	0.809773i	$0.699590\pi$
$992$	3.53101	0.112110
$993$	−33.6268	−1.06712
$994$	−0.0739884	−0.00234677
$995$	3.76560	0.119378
$996$	28.9770	0.918171
$997$	−57.2717	−1.81381	−0.906906	−	0.421332i	$-0.861563\pi$
$997$	−57.2717	−1.81381	−0.906906	+	0.421332i	$0.861563\pi$
$998$	−1.18817	−0.0376109
$999$	2.40541	0.0761039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.s.1.20	✓	36
13.12	even	2		5239.2.a.t.1.17	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.s.1.20	✓	36	1.1	even	1	trivial
5239.2.a.t.1.17	yes	36	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q+0.314789 q^{2} +1.77594 q^{3} -1.90091 q^{4} +0.987732 q^{5} +0.559047 q^{6} +0.624388 q^{7} -1.22796 q^{8} +0.153977 q^{9} +0.310927 q^{10} -4.02120 q^{11} -3.37591 q^{12} +0.196550 q^{14} +1.75416 q^{15} +3.41527 q^{16} +0.890404 q^{17} +0.0484701 q^{18} +4.17693 q^{19} -1.87759 q^{20} +1.10888 q^{21} -1.26583 q^{22} -0.895890 q^{23} -2.18079 q^{24} -4.02439 q^{25} -5.05438 q^{27} -1.18690 q^{28} +2.09204 q^{29} +0.552188 q^{30} +1.00000 q^{31} +3.53101 q^{32} -7.14143 q^{33} +0.280289 q^{34} +0.616728 q^{35} -0.292695 q^{36} -0.475907 q^{37} +1.31485 q^{38} -1.21290 q^{40} -3.26616 q^{41} +0.349062 q^{42} +3.14589 q^{43} +7.64394 q^{44} +0.152088 q^{45} -0.282016 q^{46} -8.35590 q^{47} +6.06532 q^{48} -6.61014 q^{49} -1.26683 q^{50} +1.58131 q^{51} -5.54163 q^{53} -1.59106 q^{54} -3.97187 q^{55} -0.766725 q^{56} +7.41800 q^{57} +0.658549 q^{58} +3.65296 q^{59} -3.33449 q^{60} +0.913094 q^{61} +0.314789 q^{62} +0.0961412 q^{63} -5.71901 q^{64} -2.24804 q^{66} +0.824213 q^{67} -1.69258 q^{68} -1.59105 q^{69} +0.194139 q^{70} -0.376435 q^{71} -0.189077 q^{72} -0.989383 q^{73} -0.149810 q^{74} -7.14708 q^{75} -7.93996 q^{76} -2.51079 q^{77} -7.84939 q^{79} +3.37337 q^{80} -9.43822 q^{81} -1.02815 q^{82} -8.58347 q^{83} -2.10788 q^{84} +0.879481 q^{85} +0.990289 q^{86} +3.71534 q^{87} +4.93788 q^{88} -9.19298 q^{89} +0.0478754 q^{90} +1.70300 q^{92} +1.77594 q^{93} -2.63034 q^{94} +4.12569 q^{95} +6.27088 q^{96} +12.5661 q^{97} -2.08080 q^{98} -0.619171 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{2} - 5 q^{3} + 28 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 15 q^{10} + q^{11} - 13 q^{12} - 19 q^{14} + 10 q^{15} + 4 q^{16} - 46 q^{17} + 9 q^{18} - 8 q^{19} + 5 q^{20} + 16 q^{21}+ \cdots + 47 q^{99}+O(q^{100}) \) 36 * q - 2 * q^2 - 5 * q^3 + 28 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 15 * q^10 + q^11 - 13 * q^12 - 19 * q^14 + 10 * q^15 + 4 * q^16 - 46 * q^17 + 9 * q^18 - 8 * q^19 + 5 * q^20 + 16 * q^21 - 21 * q^22 - 24 * q^23 - 57 * q^24 + 5 * q^25 - 11 * q^27 + 32 * q^28 - 73 * q^29 - 31 * q^30 + 36 * q^31 - 3 * q^32 + 8 * q^33 + 37 * q^34 - 31 * q^35 - 31 * q^36 - 6 * q^37 - 25 * q^38 - 22 * q^40 - 6 * q^41 - 37 * q^42 - 37 * q^43 + 16 * q^45 + 45 * q^46 - 13 * q^47 - 46 * q^48 - 5 * q^49 - 24 * q^50 - 46 * q^51 - 42 * q^53 + 26 * q^54 - 47 * q^55 - 95 * q^56 - 33 * q^57 - 9 * q^58 - 20 * q^59 + 40 * q^60 - 48 * q^61 - 2 * q^62 - 52 * q^63 + 21 * q^64 - 4 * q^66 + 50 * q^67 - 76 * q^68 - 33 * q^69 - 93 * q^70 - 16 * q^71 + 52 * q^72 + 43 * q^73 - 76 * q^74 - 40 * q^75 - 62 * q^76 - 47 * q^77 - 43 * q^79 + 46 * q^80 - 96 * q^81 + 7 * q^82 - 9 * q^83 + 77 * q^84 + 5 * q^85 - 64 * q^86 - 8 * q^87 - 54 * q^88 - 6 * q^89 + 27 * q^90 - 35 * q^92 - 5 * q^93 - 76 * q^94 - 63 * q^95 - 72 * q^96 + 4 * q^97 + 41 * q^98 + 47 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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