LMFDB - Embedded newform 8470.2.a.ck.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, 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("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.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:	$67.6332905120$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.470683$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.77846 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.77846 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.71982 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.77846 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.77846 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.71982 q^{9} -1.00000 q^{10} -2.77846 q^{12} -2.77846 q^{13} +1.00000 q^{14} +2.77846 q^{15} +1.00000 q^{16} +6.71982 q^{17} +4.71982 q^{18} +7.49828 q^{19} -1.00000 q^{20} -2.77846 q^{21} -3.83709 q^{23} -2.77846 q^{24} +1.00000 q^{25} -2.77846 q^{26} -4.77846 q^{27} +1.00000 q^{28} -5.43965 q^{29} +2.77846 q^{30} +1.00000 q^{32} +6.71982 q^{34} -1.00000 q^{35} +4.71982 q^{36} -0.117266 q^{37} +7.49828 q^{38} +7.71982 q^{39} -1.00000 q^{40} +5.55691 q^{41} -2.77846 q^{42} +10.3940 q^{43} -4.71982 q^{45} -3.83709 q^{46} +2.11727 q^{47} -2.77846 q^{48} +1.00000 q^{49} +1.00000 q^{50} -18.6707 q^{51} -2.77846 q^{52} -2.71982 q^{53} -4.77846 q^{54} +1.00000 q^{56} -20.8337 q^{57} -5.43965 q^{58} -3.49828 q^{59} +2.77846 q^{60} -4.27674 q^{61} +4.71982 q^{63} +1.00000 q^{64} +2.77846 q^{65} -12.1595 q^{67} +6.71982 q^{68} +10.6612 q^{69} -1.00000 q^{70} +3.16291 q^{71} +4.71982 q^{72} +8.83709 q^{73} -0.117266 q^{74} -2.77846 q^{75} +7.49828 q^{76} +7.71982 q^{78} -8.55691 q^{79} -1.00000 q^{80} -0.882734 q^{81} +5.55691 q^{82} -0.778457 q^{83} -2.77846 q^{84} -6.71982 q^{85} +10.3940 q^{86} +15.1138 q^{87} +9.55691 q^{89} -4.71982 q^{90} -2.77846 q^{91} -3.83709 q^{92} +2.11727 q^{94} -7.49828 q^{95} -2.77846 q^{96} -4.83709 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 3 * q^8 + 5 * q^9	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 3 q^{8} + 5 q^{9} - 3 q^{10} + 3 q^{14} + 3 q^{16} + 11 q^{17} + 5 q^{18} + 5 q^{19} - 3 q^{20} - 4 q^{23} + 3 q^{25} - 6 q^{27} + 3 q^{28} + 2 q^{29} + 3 q^{32} + 11 q^{34} - 3 q^{35} + 5 q^{36} - 2 q^{37} + 5 q^{38} + 14 q^{39} - 3 q^{40} + 7 q^{43} - 5 q^{45} - 4 q^{46} + 8 q^{47} + 3 q^{49} + 3 q^{50} - 6 q^{51} + q^{53} - 6 q^{54} + 3 q^{56} - 20 q^{57} + 2 q^{58} + 7 q^{59} + 13 q^{61} + 5 q^{63} + 3 q^{64} - 9 q^{67} + 11 q^{68} + 22 q^{69} - 3 q^{70} + 17 q^{71} + 5 q^{72} + 19 q^{73} - 2 q^{74} + 5 q^{76} + 14 q^{78} - 9 q^{79} - 3 q^{80} - q^{81} + 6 q^{83} - 11 q^{85} + 7 q^{86} + 12 q^{87} + 12 q^{89} - 5 q^{90} - 4 q^{92} + 8 q^{94} - 5 q^{95} - 7 q^{97} + 3 q^{98}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 3 * q^8 + 5 * q^9 - 3 * q^10 + 3 * q^14 + 3 * q^16 + 11 * q^17 + 5 * q^18 + 5 * q^19 - 3 * q^20 - 4 * q^23 + 3 * q^25 - 6 * q^27 + 3 * q^28 + 2 * q^29 + 3 * q^32 + 11 * q^34 - 3 * q^35 + 5 * q^36 - 2 * q^37 + 5 * q^38 + 14 * q^39 - 3 * q^40 + 7 * q^43 - 5 * q^45 - 4 * q^46 + 8 * q^47 + 3 * q^49 + 3 * q^50 - 6 * q^51 + q^53 - 6 * q^54 + 3 * q^56 - 20 * q^57 + 2 * q^58 + 7 * q^59 + 13 * q^61 + 5 * q^63 + 3 * q^64 - 9 * q^67 + 11 * q^68 + 22 * q^69 - 3 * q^70 + 17 * q^71 + 5 * q^72 + 19 * q^73 - 2 * q^74 + 5 * q^76 + 14 * q^78 - 9 * q^79 - 3 * q^80 - q^81 + 6 * q^83 - 11 * q^85 + 7 * q^86 + 12 * q^87 + 12 * q^89 - 5 * q^90 - 4 * q^92 + 8 * q^94 - 5 * q^95 - 7 * q^97 + 3 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.77846	−1.60414	−0.802071	−	0.597228i	$-0.796269\pi$
$3$	−2.77846	−1.60414	−0.802071	+	0.597228i	$0.796269\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.77846	−1.13430
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	4.71982	1.57327
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	−2.77846	−0.802071
$13$	−2.77846	−0.770605	−0.385303	−	0.922790i	$-0.625903\pi$
$13$	−2.77846	−0.770605	−0.385303	+	0.922790i	$0.625903\pi$
$14$	1.00000	0.267261
$15$	2.77846	0.717395
$16$	1.00000	0.250000
$17$	6.71982	1.62980	0.814898	−	0.579604i	$-0.196793\pi$
$17$	6.71982	1.62980	0.814898	+	0.579604i	$0.196793\pi$
$18$	4.71982	1.11247
$19$	7.49828	1.72022	0.860112	−	0.510106i	$-0.170394\pi$
$19$	7.49828	1.72022	0.860112	+	0.510106i	$0.170394\pi$
$20$	−1.00000	−0.223607
$21$	−2.77846	−0.606309
$22$	0	0
$23$	−3.83709	−0.800089	−0.400044	−	0.916496i	$-0.631005\pi$
$23$	−3.83709	−0.800089	−0.400044	+	0.916496i	$0.631005\pi$
$24$	−2.77846	−0.567150
$25$	1.00000	0.200000
$26$	−2.77846	−0.544900
$27$	−4.77846	−0.919615
$28$	1.00000	0.188982
$29$	−5.43965	−1.01012	−0.505059	−	0.863085i	$-0.668529\pi$
$29$	−5.43965	−1.01012	−0.505059	+	0.863085i	$0.668529\pi$
$30$	2.77846	0.507275
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	6.71982	1.15244
$35$	−1.00000	−0.169031
$36$	4.71982	0.786637
$37$	−0.117266	−0.0192785	−0.00963923	−	0.999954i	$-0.503068\pi$
$37$	−0.117266	−0.0192785	−0.00963923	+	0.999954i	$0.503068\pi$
$38$	7.49828	1.21638
$39$	7.71982	1.23616
$40$	−1.00000	−0.158114
$41$	5.55691	0.867844	0.433922	−	0.900950i	$-0.357129\pi$
$41$	5.55691	0.867844	0.433922	+	0.900950i	$0.357129\pi$
$42$	−2.77846	−0.428725
$43$	10.3940	1.58507	0.792535	−	0.609826i	$-0.208761\pi$
$43$	10.3940	1.58507	0.792535	+	0.609826i	$0.208761\pi$
$44$	0	0
$45$	−4.71982	−0.703590
$46$	−3.83709	−0.565748
$47$	2.11727	0.308835	0.154418	−	0.988006i	$-0.450650\pi$
$47$	2.11727	0.308835	0.154418	+	0.988006i	$0.450650\pi$
$48$	−2.77846	−0.401036
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−18.6707	−2.61443
$52$	−2.77846	−0.385303
$53$	−2.71982	−0.373597	−0.186798	−	0.982398i	$-0.559811\pi$
$53$	−2.71982	−0.373597	−0.186798	+	0.982398i	$0.559811\pi$
$54$	−4.77846	−0.650266
$55$	0	0
$56$	1.00000	0.133631
$57$	−20.8337	−2.75948
$58$	−5.43965	−0.714261
$59$	−3.49828	−0.455437	−0.227719	−	0.973727i	$-0.573127\pi$
$59$	−3.49828	−0.455437	−0.227719	+	0.973727i	$0.573127\pi$
$60$	2.77846	0.358697
$61$	−4.27674	−0.547580	−0.273790	−	0.961789i	$-0.588277\pi$
$61$	−4.27674	−0.547580	−0.273790	+	0.961789i	$0.588277\pi$
$62$	0	0
$63$	4.71982	0.594642
$64$	1.00000	0.125000
$65$	2.77846	0.344625
$66$	0	0
$67$	−12.1595	−1.48552	−0.742758	−	0.669560i	$-0.766483\pi$
$67$	−12.1595	−1.48552	−0.742758	+	0.669560i	$0.766483\pi$
$68$	6.71982	0.814898
$69$	10.6612	1.28346
$70$	−1.00000	−0.119523
$71$	3.16291	0.375368	0.187684	−	0.982229i	$-0.439902\pi$
$71$	3.16291	0.375368	0.187684	+	0.982229i	$0.439902\pi$
$72$	4.71982	0.556237
$73$	8.83709	1.03430	0.517152	−	0.855894i	$-0.326992\pi$
$73$	8.83709	1.03430	0.517152	+	0.855894i	$0.326992\pi$
$74$	−0.117266	−0.0136319
$75$	−2.77846	−0.320829
$76$	7.49828	0.860112
$77$	0	0
$78$	7.71982	0.874098
$79$	−8.55691	−0.962728	−0.481364	−	0.876521i	$-0.659858\pi$
$79$	−8.55691	−0.962728	−0.481364	+	0.876521i	$0.659858\pi$
$80$	−1.00000	−0.111803
$81$	−0.882734	−0.0980815
$82$	5.55691	0.613659
$83$	−0.778457	−0.0854468	−0.0427234	−	0.999087i	$-0.513603\pi$
$83$	−0.778457	−0.0854468	−0.0427234	+	0.999087i	$0.513603\pi$
$84$	−2.77846	−0.303155
$85$	−6.71982	−0.728867
$86$	10.3940	1.12081
$87$	15.1138	1.62037
$88$	0	0
$89$	9.55691	1.01303	0.506515	−	0.862231i	$-0.330933\pi$
$89$	9.55691	1.01303	0.506515	+	0.862231i	$0.330933\pi$
$90$	−4.71982	−0.497513
$91$	−2.77846	−0.291261
$92$	−3.83709	−0.400044
$93$	0	0
$94$	2.11727	0.218379
$95$	−7.49828	−0.769307
$96$	−2.77846	−0.283575
$97$	−4.83709	−0.491132	−0.245566	−	0.969380i	$-0.578974\pi$
$97$	−4.83709	−0.491132	−0.245566	+	0.969380i	$0.578974\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−1.22154	−0.121548	−0.0607740	−	0.998152i	$-0.519357\pi$
$101$	−1.22154	−0.121548	−0.0607740	+	0.998152i	$0.519357\pi$
$102$	−18.6707	−1.84868
$103$	−8.27674	−0.815531	−0.407766	−	0.913087i	$-0.633692\pi$
$103$	−8.27674	−0.815531	−0.407766	+	0.913087i	$0.633692\pi$
$104$	−2.77846	−0.272450
$105$	2.77846	0.271150
$106$	−2.71982	−0.264173
$107$	−16.2767	−1.57353	−0.786766	−	0.617252i	$-0.788246\pi$
$107$	−16.2767	−1.57353	−0.786766	+	0.617252i	$0.788246\pi$
$108$	−4.77846	−0.459807
$109$	−1.88273	−0.180333	−0.0901666	−	0.995927i	$-0.528740\pi$
$109$	−1.88273	−0.180333	−0.0901666	+	0.995927i	$0.528740\pi$
$110$	0	0
$111$	0.325819	0.0309254
$112$	1.00000	0.0944911
$113$	15.1595	1.42608	0.713042	−	0.701122i	$-0.247317\pi$
$113$	15.1595	1.42608	0.713042	+	0.701122i	$0.247317\pi$
$114$	−20.8337	−1.95125
$115$	3.83709	0.357811
$116$	−5.43965	−0.505059
$117$	−13.1138	−1.21237
$118$	−3.49828	−0.322043
$119$	6.71982	0.616005
$120$	2.77846	0.253637
$121$	0	0
$122$	−4.27674	−0.387198
$123$	−15.4396	−1.39215
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	4.71982	0.420475
$127$	11.8371	1.05037	0.525186	−	0.850987i	$-0.323996\pi$
$127$	11.8371	1.05037	0.525186	+	0.850987i	$0.323996\pi$
$128$	1.00000	0.0883883
$129$	−28.8793	−2.54268
$130$	2.77846	0.243687
$131$	18.0096	1.57350	0.786751	−	0.617271i	$-0.211762\pi$
$131$	18.0096	1.57350	0.786751	+	0.617271i	$0.211762\pi$
$132$	0	0
$133$	7.49828	0.650183
$134$	−12.1595	−1.05042
$135$	4.77846	0.411264
$136$	6.71982	0.576220
$137$	−12.9509	−1.10647	−0.553236	−	0.833025i	$-0.686607\pi$
$137$	−12.9509	−1.10647	−0.553236	+	0.833025i	$0.686607\pi$
$138$	10.6612	0.907541
$139$	18.8207	1.59635	0.798174	−	0.602427i	$-0.205800\pi$
$139$	18.8207	1.59635	0.798174	+	0.602427i	$0.205800\pi$
$140$	−1.00000	−0.0845154
$141$	−5.88273	−0.495416
$142$	3.16291	0.265425
$143$	0	0
$144$	4.71982	0.393319
$145$	5.43965	0.451738
$146$	8.83709	0.731363
$147$	−2.77846	−0.229163
$148$	−0.117266	−0.00963923
$149$	16.6707	1.36572	0.682860	−	0.730549i	$-0.260736\pi$
$149$	16.6707	1.36572	0.682860	+	0.730549i	$0.260736\pi$
$150$	−2.77846	−0.226860
$151$	16.9509	1.37945	0.689723	−	0.724073i	$-0.257732\pi$
$151$	16.9509	1.37945	0.689723	+	0.724073i	$0.257732\pi$
$152$	7.49828	0.608191
$153$	31.7164	2.56412
$154$	0	0
$155$	0	0
$156$	7.71982	0.618081
$157$	−6.66119	−0.531621	−0.265810	−	0.964025i	$-0.585640\pi$
$157$	−6.66119	−0.531621	−0.265810	+	0.964025i	$0.585640\pi$
$158$	−8.55691	−0.680752
$159$	7.55691	0.599302
$160$	−1.00000	−0.0790569
$161$	−3.83709	−0.302405
$162$	−0.882734	−0.0693541
$163$	−16.5113	−1.29326	−0.646631	−	0.762803i	$-0.723823\pi$
$163$	−16.5113	−1.29326	−0.646631	+	0.762803i	$0.723823\pi$
$164$	5.55691	0.433922
$165$	0	0
$166$	−0.778457	−0.0604200
$167$	−4.51127	−0.349093	−0.174546	−	0.984649i	$-0.555846\pi$
$167$	−4.51127	−0.349093	−0.174546	+	0.984649i	$0.555846\pi$
$168$	−2.77846	−0.214363
$169$	−5.28018	−0.406167
$170$	−6.71982	−0.515387
$171$	35.3906	2.70638
$172$	10.3940	0.792535
$173$	10.5535	0.802366	0.401183	−	0.915998i	$-0.368599\pi$
$173$	10.5535	0.802366	0.401183	+	0.915998i	$0.368599\pi$
$174$	15.1138	1.14578
$175$	1.00000	0.0755929
$176$	0	0
$177$	9.71982	0.730587
$178$	9.55691	0.716321
$179$	8.32582	0.622301	0.311150	−	0.950361i	$-0.399286\pi$
$179$	8.32582	0.622301	0.311150	+	0.950361i	$0.399286\pi$
$180$	−4.71982	−0.351795
$181$	−21.9345	−1.63038	−0.815189	−	0.579195i	$-0.803367\pi$
$181$	−21.9345	−1.63038	−0.815189	+	0.579195i	$0.803367\pi$
$182$	−2.77846	−0.205953
$183$	11.8827	0.878397
$184$	−3.83709	−0.282874
$185$	0.117266	0.00862159
$186$	0	0
$187$	0	0
$188$	2.11727	0.154418
$189$	−4.77846	−0.347582
$190$	−7.49828	−0.543982
$191$	11.7198	0.848017	0.424008	−	0.905658i	$-0.360623\pi$
$191$	11.7198	0.848017	0.424008	+	0.905658i	$0.360623\pi$
$192$	−2.77846	−0.200518
$193$	−18.5991	−1.33879	−0.669397	−	0.742905i	$-0.733447\pi$
$193$	−18.5991	−1.33879	−0.669397	+	0.742905i	$0.733447\pi$
$194$	−4.83709	−0.347283
$195$	−7.71982	−0.552828
$196$	1.00000	0.0714286
$197$	−10.0682	−0.717328	−0.358664	−	0.933467i	$-0.616768\pi$
$197$	−10.0682	−0.717328	−0.358664	+	0.933467i	$0.616768\pi$
$198$	0	0
$199$	−16.5535	−1.17344	−0.586722	−	0.809788i	$-0.699582\pi$
$199$	−16.5535	−1.17344	−0.586722	+	0.809788i	$0.699582\pi$
$200$	1.00000	0.0707107
$201$	33.7846	2.38298
$202$	−1.22154	−0.0859475
$203$	−5.43965	−0.381788
$204$	−18.6707	−1.30721
$205$	−5.55691	−0.388112
$206$	−8.27674	−0.576668
$207$	−18.1104	−1.25876
$208$	−2.77846	−0.192651
$209$	0	0
$210$	2.77846	0.191732
$211$	−26.8793	−1.85045	−0.925224	−	0.379423i	$-0.876123\pi$
$211$	−26.8793	−1.85045	−0.925224	+	0.379423i	$0.876123\pi$
$212$	−2.71982	−0.186798
$213$	−8.78801	−0.602144
$214$	−16.2767	−1.11265
$215$	−10.3940	−0.708865
$216$	−4.77846	−0.325133
$217$	0	0
$218$	−1.88273	−0.127515
$219$	−24.5535	−1.65917
$220$	0	0
$221$	−18.6707	−1.25593
$222$	0.325819	0.0218676
$223$	−5.83365	−0.390650	−0.195325	−	0.980739i	$-0.562576\pi$
$223$	−5.83365	−0.390650	−0.195325	+	0.980739i	$0.562576\pi$
$224$	1.00000	0.0668153
$225$	4.71982	0.314655
$226$	15.1595	1.00839
$227$	−5.88273	−0.390451	−0.195225	−	0.980758i	$-0.562544\pi$
$227$	−5.88273	−0.390451	−0.195225	+	0.980758i	$0.562544\pi$
$228$	−20.8337	−1.37974
$229$	25.9509	1.71488	0.857442	−	0.514580i	$-0.172052\pi$
$229$	25.9509	1.71488	0.857442	+	0.514580i	$0.172052\pi$
$230$	3.83709	0.253010
$231$	0	0
$232$	−5.43965	−0.357130
$233$	17.2767	1.13184	0.565918	−	0.824461i	$-0.308522\pi$
$233$	17.2767	1.13184	0.565918	+	0.824461i	$0.308522\pi$
$234$	−13.1138	−0.857278
$235$	−2.11727	−0.138115
$236$	−3.49828	−0.227719
$237$	23.7750	1.54435
$238$	6.71982	0.435581
$239$	26.9440	1.74287	0.871433	−	0.490515i	$-0.163191\pi$
$239$	26.9440	1.74287	0.871433	+	0.490515i	$0.163191\pi$
$240$	2.77846	0.179349
$241$	24.9966	1.61017	0.805085	−	0.593159i	$-0.202120\pi$
$241$	24.9966	1.61017	0.805085	+	0.593159i	$0.202120\pi$
$242$	0	0
$243$	16.7880	1.07695
$244$	−4.27674	−0.273790
$245$	−1.00000	−0.0638877
$246$	−15.4396	−0.984396
$247$	−20.8337	−1.32561
$248$	0	0
$249$	2.16291	0.137069
$250$	−1.00000	−0.0632456
$251$	9.83365	0.620695	0.310347	−	0.950623i	$-0.399555\pi$
$251$	9.83365	0.620695	0.310347	+	0.950623i	$0.399555\pi$
$252$	4.71982	0.297321
$253$	0	0
$254$	11.8371	0.742725
$255$	18.6707	1.16921
$256$	1.00000	0.0625000
$257$	−8.15947	−0.508974	−0.254487	−	0.967076i	$-0.581907\pi$
$257$	−8.15947	−0.508974	−0.254487	+	0.967076i	$0.581907\pi$
$258$	−28.8793	−1.79795
$259$	−0.117266	−0.00728657
$260$	2.77846	0.172313
$261$	−25.6742	−1.58919
$262$	18.0096	1.11263
$263$	28.2733	1.74341	0.871703	−	0.490034i	$-0.163016\pi$
$263$	28.2733	1.74341	0.871703	+	0.490034i	$0.163016\pi$
$264$	0	0
$265$	2.71982	0.167077
$266$	7.49828	0.459749
$267$	−26.5535	−1.62505
$268$	−12.1595	−0.742758
$269$	3.06207	0.186698	0.0933489	−	0.995633i	$-0.470243\pi$
$269$	3.06207	0.186698	0.0933489	+	0.995633i	$0.470243\pi$
$270$	4.77846	0.290808
$271$	22.6707	1.37715	0.688575	−	0.725165i	$-0.258237\pi$
$271$	22.6707	1.37715	0.688575	+	0.725165i	$0.258237\pi$
$272$	6.71982	0.407449
$273$	7.71982	0.467225
$274$	−12.9509	−0.782394
$275$	0	0
$276$	10.6612	0.641728
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	18.8207	1.12879
$279$	0	0
$280$	−1.00000	−0.0597614
$281$	−24.6673	−1.47153	−0.735764	−	0.677238i	$-0.763177\pi$
$281$	−24.6673	−1.47153	−0.735764	+	0.677238i	$0.763177\pi$
$282$	−5.88273	−0.350312
$283$	21.2147	1.26108	0.630541	−	0.776156i	$-0.282833\pi$
$283$	21.2147	1.26108	0.630541	+	0.776156i	$0.282833\pi$
$284$	3.16291	0.187684
$285$	20.8337	1.23408
$286$	0	0
$287$	5.55691	0.328014
$288$	4.71982	0.278118
$289$	28.1560	1.65624
$290$	5.43965	0.319427
$291$	13.4396	0.787846
$292$	8.83709	0.517152
$293$	17.4492	1.01939	0.509697	−	0.860354i	$-0.329758\pi$
$293$	17.4492	1.01939	0.509697	+	0.860354i	$0.329758\pi$
$294$	−2.77846	−0.162043
$295$	3.49828	0.203678
$296$	−0.117266	−0.00681597
$297$	0	0
$298$	16.6707	0.965710
$299$	10.6612	0.616553
$300$	−2.77846	−0.160414
$301$	10.3940	0.599100
$302$	16.9509	0.975416
$303$	3.39400	0.194980
$304$	7.49828	0.430056
$305$	4.27674	0.244885
$306$	31.7164	1.81311
$307$	−2.43621	−0.139042	−0.0695209	−	0.997580i	$-0.522147\pi$
$307$	−2.43621	−0.139042	−0.0695209	+	0.997580i	$0.522147\pi$
$308$	0	0
$309$	22.9966	1.30823
$310$	0	0
$311$	23.7846	1.34870	0.674350	−	0.738412i	$-0.264424\pi$
$311$	23.7846	1.34870	0.674350	+	0.738412i	$0.264424\pi$
$312$	7.71982	0.437049
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	−6.66119	−0.375913
$315$	−4.71982	−0.265932
$316$	−8.55691	−0.481364
$317$	−20.7129	−1.16336	−0.581678	−	0.813419i	$-0.697603\pi$
$317$	−20.7129	−1.16336	−0.581678	+	0.813419i	$0.697603\pi$
$318$	7.55691	0.423771
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	45.2242	2.52417
$322$	−3.83709	−0.213833
$323$	50.3871	2.80361
$324$	−0.882734	−0.0490408
$325$	−2.77846	−0.154121
$326$	−16.5113	−0.914475
$327$	5.23109	0.289280
$328$	5.55691	0.306829
$329$	2.11727	0.116729
$330$	0	0
$331$	16.1173	0.885885	0.442943	−	0.896550i	$-0.353935\pi$
$331$	16.1173	0.885885	0.442943	+	0.896550i	$0.353935\pi$
$332$	−0.778457	−0.0427234
$333$	−0.553476	−0.0303303
$334$	−4.51127	−0.246846
$335$	12.1595	0.664343
$336$	−2.77846	−0.151577
$337$	−6.28018	−0.342103	−0.171051	−	0.985262i	$-0.554716\pi$
$337$	−6.28018	−0.342103	−0.171051	+	0.985262i	$0.554716\pi$
$338$	−5.28018	−0.287204
$339$	−42.1199	−2.28764
$340$	−6.71982	−0.364434
$341$	0	0
$342$	35.3906	1.91370
$343$	1.00000	0.0539949
$344$	10.3940	0.560407
$345$	−10.6612	−0.573979
$346$	10.5535	0.567358
$347$	28.7198	1.54176	0.770880	−	0.636980i	$-0.219817\pi$
$347$	28.7198	1.54176	0.770880	+	0.636980i	$0.219817\pi$
$348$	15.1138	0.810186
$349$	1.33193	0.0712968	0.0356484	−	0.999364i	$-0.488650\pi$
$349$	1.33193	0.0712968	0.0356484	+	0.999364i	$0.488650\pi$
$350$	1.00000	0.0534522
$351$	13.2767	0.708660
$352$	0	0
$353$	−14.5113	−0.772357	−0.386179	−	0.922424i	$-0.626205\pi$
$353$	−14.5113	−0.772357	−0.386179	+	0.922424i	$0.626205\pi$
$354$	9.71982	0.516603
$355$	−3.16291	−0.167870
$356$	9.55691	0.506515
$357$	−18.6707	−0.988160
$358$	8.32582	0.440033
$359$	14.8302	0.782709	0.391354	−	0.920240i	$-0.372007\pi$
$359$	14.8302	0.782709	0.391354	+	0.920240i	$0.372007\pi$
$360$	−4.71982	−0.248757
$361$	37.2242	1.95917
$362$	−21.9345	−1.15285
$363$	0	0
$364$	−2.77846	−0.145631
$365$	−8.83709	−0.462554
$366$	11.8827	0.621120
$367$	−18.9475	−0.989050	−0.494525	−	0.869163i	$-0.664658\pi$
$367$	−18.9475	−0.989050	−0.494525	+	0.869163i	$0.664658\pi$
$368$	−3.83709	−0.200022
$369$	26.2277	1.36536
$370$	0.117266	0.00609639
$371$	−2.71982	−0.141206
$372$	0	0
$373$	11.0716	0.573267	0.286633	−	0.958040i	$-0.407464\pi$
$373$	11.0716	0.573267	0.286633	+	0.958040i	$0.407464\pi$
$374$	0	0
$375$	2.77846	0.143479
$376$	2.11727	0.109190
$377$	15.1138	0.778402
$378$	−4.77846	−0.245777
$379$	30.0844	1.54533	0.772666	−	0.634813i	$-0.218923\pi$
$379$	30.0844	1.54533	0.772666	+	0.634813i	$0.218923\pi$
$380$	−7.49828	−0.384654
$381$	−32.8888	−1.68495
$382$	11.7198	0.599638
$383$	37.2733	1.90458	0.952288	−	0.305200i	$-0.0987232\pi$
$383$	37.2733	1.90458	0.952288	+	0.305200i	$0.0987232\pi$
$384$	−2.77846	−0.141788
$385$	0	0
$386$	−18.5991	−0.946670
$387$	49.0579	2.49375
$388$	−4.83709	−0.245566
$389$	24.3449	1.23434	0.617168	−	0.786831i	$-0.288280\pi$
$389$	24.3449	1.23434	0.617168	+	0.786831i	$0.288280\pi$
$390$	−7.71982	−0.390908
$391$	−25.7846	−1.30398
$392$	1.00000	0.0505076
$393$	−50.0388	−2.52412
$394$	−10.0682	−0.507228
$395$	8.55691	0.430545
$396$	0	0
$397$	14.3189	0.718647	0.359324	−	0.933213i	$-0.383007\pi$
$397$	14.3189	0.718647	0.359324	+	0.933213i	$0.383007\pi$
$398$	−16.5535	−0.829751
$399$	−20.8337	−1.04299
$400$	1.00000	0.0500000
$401$	17.7655	0.887165	0.443583	−	0.896234i	$-0.353707\pi$
$401$	17.7655	0.887165	0.443583	+	0.896234i	$0.353707\pi$
$402$	33.7846	1.68502
$403$	0	0
$404$	−1.22154	−0.0607740
$405$	0.882734	0.0438634
$406$	−5.43965	−0.269965
$407$	0	0
$408$	−18.6707	−0.924340
$409$	−9.88273	−0.488670	−0.244335	−	0.969691i	$-0.578570\pi$
$409$	−9.88273	−0.488670	−0.244335	+	0.969691i	$0.578570\pi$
$410$	−5.55691	−0.274436
$411$	35.9836	1.77494
$412$	−8.27674	−0.407766
$413$	−3.49828	−0.172139
$414$	−18.1104	−0.890077
$415$	0.778457	0.0382130
$416$	−2.77846	−0.136225
$417$	−52.2924	−2.56077
$418$	0	0
$419$	8.05863	0.393690	0.196845	−	0.980435i	$-0.436930\pi$
$419$	8.05863	0.393690	0.196845	+	0.980435i	$0.436930\pi$
$420$	2.77846	0.135575
$421$	−4.65164	−0.226707	−0.113354	−	0.993555i	$-0.536159\pi$
$421$	−4.65164	−0.226707	−0.113354	+	0.993555i	$0.536159\pi$
$422$	−26.8793	−1.30846
$423$	9.99312	0.485882
$424$	−2.71982	−0.132086
$425$	6.71982	0.325959
$426$	−8.78801	−0.425780
$427$	−4.27674	−0.206966
$428$	−16.2767	−0.786766
$429$	0	0
$430$	−10.3940	−0.501243
$431$	−37.8793	−1.82458	−0.912291	−	0.409543i	$-0.865688\pi$
$431$	−37.8793	−1.82458	−0.912291	+	0.409543i	$0.865688\pi$
$432$	−4.77846	−0.229904
$433$	15.4656	0.743231	0.371615	−	0.928387i	$-0.378804\pi$
$433$	15.4656	0.743231	0.371615	+	0.928387i	$0.378804\pi$
$434$	0	0
$435$	−15.1138	−0.724653
$436$	−1.88273	−0.0901666
$437$	−28.7716	−1.37633
$438$	−24.5535	−1.17321
$439$	33.6413	1.60561	0.802806	−	0.596240i	$-0.203339\pi$
$439$	33.6413	1.60561	0.802806	+	0.596240i	$0.203339\pi$
$440$	0	0
$441$	4.71982	0.224754
$442$	−18.6707	−0.888077
$443$	−11.8759	−0.564239	−0.282120	−	0.959379i	$-0.591037\pi$
$443$	−11.8759	−0.564239	−0.282120	+	0.959379i	$0.591037\pi$
$444$	0.325819	0.0154627
$445$	−9.55691	−0.453041
$446$	−5.83365	−0.276231
$447$	−46.3189	−2.19081
$448$	1.00000	0.0472456
$449$	−17.8793	−0.843776	−0.421888	−	0.906648i	$-0.638632\pi$
$449$	−17.8793	−0.843776	−0.421888	+	0.906648i	$0.638632\pi$
$450$	4.71982	0.222495
$451$	0	0
$452$	15.1595	0.713042
$453$	−47.0974	−2.21283
$454$	−5.88273	−0.276090
$455$	2.77846	0.130256
$456$	−20.8337	−0.975625
$457$	10.5078	0.491536	0.245768	−	0.969329i	$-0.420960\pi$
$457$	10.5078	0.491536	0.245768	+	0.969329i	$0.420960\pi$
$458$	25.9509	1.21261
$459$	−32.1104	−1.49878
$460$	3.83709	0.178905
$461$	−41.3837	−1.92743	−0.963715	−	0.266932i	$-0.913990\pi$
$461$	−41.3837	−1.92743	−0.963715	+	0.266932i	$0.913990\pi$
$462$	0	0
$463$	28.7424	1.33577	0.667886	−	0.744264i	$-0.267200\pi$
$463$	28.7424	1.33577	0.667886	+	0.744264i	$0.267200\pi$
$464$	−5.43965	−0.252529
$465$	0	0
$466$	17.2767	0.800329
$467$	16.3614	0.757113	0.378557	−	0.925578i	$-0.376421\pi$
$467$	16.3614	0.757113	0.378557	+	0.925578i	$0.376421\pi$
$468$	−13.1138	−0.606187
$469$	−12.1595	−0.561472
$470$	−2.11727	−0.0976622
$471$	18.5078	0.852796
$472$	−3.49828	−0.161021
$473$	0	0
$474$	23.7750	1.09202
$475$	7.49828	0.344045
$476$	6.71982	0.308003
$477$	−12.8371	−0.587770
$478$	26.9440	1.23239
$479$	41.9018	1.91454	0.957272	−	0.289189i	$-0.0933857\pi$
$479$	41.9018	1.91454	0.957272	+	0.289189i	$0.0933857\pi$
$480$	2.77846	0.126819
$481$	0.325819	0.0148561
$482$	24.9966	1.13856
$483$	10.6612	0.485101
$484$	0	0
$485$	4.83709	0.219641
$486$	16.7880	0.761520
$487$	−16.9509	−0.768119	−0.384060	−	0.923308i	$-0.625474\pi$
$487$	−16.9509	−0.768119	−0.384060	+	0.923308i	$0.625474\pi$
$488$	−4.27674	−0.193599
$489$	45.8759	2.07458
$490$	−1.00000	−0.0451754
$491$	−32.9966	−1.48911	−0.744557	−	0.667559i	$-0.767339\pi$
$491$	−32.9966	−1.48911	−0.744557	+	0.667559i	$0.767339\pi$
$492$	−15.4396	−0.696073
$493$	−36.5535	−1.64629
$494$	−20.8337	−0.937350
$495$	0	0
$496$	0	0
$497$	3.16291	0.141876
$498$	2.16291	0.0969223
$499$	7.67418	0.343544	0.171772	−	0.985137i	$-0.445051\pi$
$499$	7.67418	0.343544	0.171772	+	0.985137i	$0.445051\pi$
$500$	−1.00000	−0.0447214
$501$	12.5344	0.559994
$502$	9.83365	0.438897
$503$	29.0647	1.29593	0.647967	−	0.761669i	$-0.275620\pi$
$503$	29.0647	1.29593	0.647967	+	0.761669i	$0.275620\pi$
$504$	4.71982	0.210238
$505$	1.22154	0.0543579
$506$	0	0
$507$	14.6707	0.651551
$508$	11.8371	0.525186
$509$	−36.2603	−1.60721	−0.803605	−	0.595163i	$-0.797087\pi$
$509$	−36.2603	−1.60721	−0.803605	+	0.595163i	$0.797087\pi$
$510$	18.6707	0.826754
$511$	8.83709	0.390930
$512$	1.00000	0.0441942
$513$	−35.8302	−1.58194
$514$	−8.15947	−0.359899
$515$	8.27674	0.364717
$516$	−28.8793	−1.27134
$517$	0	0
$518$	−0.117266	−0.00515239
$519$	−29.3224	−1.28711
$520$	2.77846	0.121843
$521$	17.6742	0.774320	0.387160	−	0.922013i	$-0.373456\pi$
$521$	17.6742	0.774320	0.387160	+	0.922013i	$0.373456\pi$
$522$	−25.6742	−1.12373
$523$	−16.1268	−0.705177	−0.352588	−	0.935779i	$-0.614698\pi$
$523$	−16.1268	−0.705177	−0.352588	+	0.935779i	$0.614698\pi$
$524$	18.0096	0.786751
$525$	−2.77846	−0.121262
$526$	28.2733	1.23277
$527$	0	0
$528$	0	0
$529$	−8.27674	−0.359858
$530$	2.71982	0.118142
$531$	−16.5113	−0.716528
$532$	7.49828	0.325092
$533$	−15.4396	−0.668765
$534$	−26.5535	−1.14908
$535$	16.2767	0.703705
$536$	−12.1595	−0.525209
$537$	−23.1329	−0.998260
$538$	3.06207	0.132015
$539$	0	0
$540$	4.77846	0.205632
$541$	40.9897	1.76228	0.881142	−	0.472852i	$-0.156775\pi$
$541$	40.9897	1.76228	0.881142	+	0.472852i	$0.156775\pi$
$542$	22.6707	0.973792
$543$	60.9440	2.61536
$544$	6.71982	0.288110
$545$	1.88273	0.0806475
$546$	7.71982	0.330378
$547$	−19.6251	−0.839109	−0.419554	−	0.907730i	$-0.637814\pi$
$547$	−19.6251	−0.839109	−0.419554	+	0.907730i	$0.637814\pi$
$548$	−12.9509	−0.553236
$549$	−20.1855	−0.861494
$550$	0	0
$551$	−40.7880	−1.73763
$552$	10.6612	0.453770
$553$	−8.55691	−0.363877
$554$	−10.0000	−0.424859
$555$	−0.325819	−0.0138303
$556$	18.8207	0.798174
$557$	−21.4396	−0.908427	−0.454214	−	0.890893i	$-0.650080\pi$
$557$	−21.4396	−0.908427	−0.454214	+	0.890893i	$0.650080\pi$
$558$	0	0
$559$	−28.8793	−1.22146
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	−24.6673	−1.04053
$563$	5.89229	0.248330	0.124165	−	0.992262i	$-0.460375\pi$
$563$	5.89229	0.248330	0.124165	+	0.992262i	$0.460375\pi$
$564$	−5.88273	−0.247708
$565$	−15.1595	−0.637764
$566$	21.2147	0.891719
$567$	−0.882734	−0.0370713
$568$	3.16291	0.132713
$569$	−36.2311	−1.51889	−0.759443	−	0.650574i	$-0.774529\pi$
$569$	−36.2311	−1.51889	−0.759443	+	0.650574i	$0.774529\pi$
$570$	20.8337	0.872626
$571$	37.5500	1.57142	0.785710	−	0.618595i	$-0.212298\pi$
$571$	37.5500	1.57142	0.785710	+	0.618595i	$0.212298\pi$
$572$	0	0
$573$	−32.5630	−1.36034
$574$	5.55691	0.231941
$575$	−3.83709	−0.160018
$576$	4.71982	0.196659
$577$	42.7129	1.77816	0.889082	−	0.457749i	$-0.151344\pi$
$577$	42.7129	1.77816	0.889082	+	0.457749i	$0.151344\pi$
$578$	28.1560	1.17114
$579$	51.6769	2.14762
$580$	5.43965	0.225869
$581$	−0.778457	−0.0322958
$582$	13.4396	0.557091
$583$	0	0
$584$	8.83709	0.365681
$585$	13.1138	0.542190
$586$	17.4492	0.720820
$587$	5.54736	0.228964	0.114482	−	0.993425i	$-0.463479\pi$
$587$	5.54736	0.228964	0.114482	+	0.993425i	$0.463479\pi$
$588$	−2.77846	−0.114582
$589$	0	0
$590$	3.49828	0.144022
$591$	27.9740	1.15070
$592$	−0.117266	−0.00481962
$593$	−16.2699	−0.668123	−0.334062	−	0.942551i	$-0.608419\pi$
$593$	−16.2699	−0.668123	−0.334062	+	0.942551i	$0.608419\pi$
$594$	0	0
$595$	−6.71982	−0.275486
$596$	16.6707	0.682860
$597$	45.9931	1.88237
$598$	10.6612	0.435969
$599$	−17.4362	−0.712424	−0.356212	−	0.934405i	$-0.615932\pi$
$599$	−17.4362	−0.712424	−0.356212	+	0.934405i	$0.615932\pi$
$600$	−2.77846	−0.113430
$601$	−1.12070	−0.0457145	−0.0228572	−	0.999739i	$-0.507276\pi$
$601$	−1.12070	−0.0457145	−0.0228572	+	0.999739i	$0.507276\pi$
$602$	10.3940	0.423628
$603$	−57.3906	−2.33712
$604$	16.9509	0.689723
$605$	0	0
$606$	3.39400	0.137872
$607$	−24.5113	−0.994882	−0.497441	−	0.867498i	$-0.665727\pi$
$607$	−24.5113	−0.994882	−0.497441	+	0.867498i	$0.665727\pi$
$608$	7.49828	0.304095
$609$	15.1138	0.612443
$610$	4.27674	0.173160
$611$	−5.88273	−0.237990
$612$	31.7164	1.28206
$613$	4.71982	0.190632	0.0953159	−	0.995447i	$-0.469614\pi$
$613$	4.71982	0.190632	0.0953159	+	0.995447i	$0.469614\pi$
$614$	−2.43621	−0.0983174
$615$	15.4396	0.622587
$616$	0	0
$617$	20.4622	0.823777	0.411888	−	0.911234i	$-0.364869\pi$
$617$	20.4622	0.823777	0.411888	+	0.911234i	$0.364869\pi$
$618$	22.9966	0.925057
$619$	17.8854	0.718875	0.359438	−	0.933169i	$-0.382969\pi$
$619$	17.8854	0.718875	0.359438	+	0.933169i	$0.382969\pi$
$620$	0	0
$621$	18.3354	0.735773
$622$	23.7846	0.953674
$623$	9.55691	0.382890
$624$	7.71982	0.309040
$625$	1.00000	0.0400000
$626$	−10.0000	−0.399680
$627$	0	0
$628$	−6.66119	−0.265810
$629$	−0.788009	−0.0314200
$630$	−4.71982	−0.188042
$631$	39.6182	1.57718	0.788588	−	0.614922i	$-0.210812\pi$
$631$	39.6182	1.57718	0.788588	+	0.614922i	$0.210812\pi$
$632$	−8.55691	−0.340376
$633$	74.6830	2.96838
$634$	−20.7129	−0.822616
$635$	−11.8371	−0.469741
$636$	7.55691	0.299651
$637$	−2.77846	−0.110086
$638$	0	0
$639$	14.9284	0.590557
$640$	−1.00000	−0.0395285
$641$	−4.55691	−0.179987	−0.0899936	−	0.995942i	$-0.528685\pi$
$641$	−4.55691	−0.179987	−0.0899936	+	0.995942i	$0.528685\pi$
$642$	45.2242	1.78486
$643$	−33.8827	−1.33620	−0.668102	−	0.744069i	$-0.732893\pi$
$643$	−33.8827	−1.33620	−0.668102	+	0.744069i	$0.732893\pi$
$644$	−3.83709	−0.151203
$645$	28.8793	1.13712
$646$	50.3871	1.98246
$647$	10.8111	0.425029	0.212514	−	0.977158i	$-0.431835\pi$
$647$	10.8111	0.425029	0.212514	+	0.977158i	$0.431835\pi$
$648$	−0.882734	−0.0346771
$649$	0	0
$650$	−2.77846	−0.108980
$651$	0	0
$652$	−16.5113	−0.646631
$653$	11.3646	0.444731	0.222365	−	0.974963i	$-0.428622\pi$
$653$	11.3646	0.444731	0.222365	+	0.974963i	$0.428622\pi$
$654$	5.23109	0.204552
$655$	−18.0096	−0.703691
$656$	5.55691	0.216961
$657$	41.7095	1.62724
$658$	2.11727	0.0825396
$659$	18.2277	0.710049	0.355024	−	0.934857i	$-0.384473\pi$
$659$	18.2277	0.710049	0.355024	+	0.934857i	$0.384473\pi$
$660$	0	0
$661$	−11.8854	−0.462289	−0.231144	−	0.972919i	$-0.574247\pi$
$661$	−11.8854	−0.462289	−0.231144	+	0.972919i	$0.574247\pi$
$662$	16.1173	0.626415
$663$	51.8759	2.01469
$664$	−0.778457	−0.0302100
$665$	−7.49828	−0.290771
$666$	−0.553476	−0.0214468
$667$	20.8724	0.808183
$668$	−4.51127	−0.174546
$669$	16.2086	0.626659
$670$	12.1595	0.469761
$671$	0	0
$672$	−2.77846	−0.107181
$673$	−1.51127	−0.0582552	−0.0291276	−	0.999576i	$-0.509273\pi$
$673$	−1.51127	−0.0582552	−0.0291276	+	0.999576i	$0.509273\pi$
$674$	−6.28018	−0.241903
$675$	−4.77846	−0.183923
$676$	−5.28018	−0.203084
$677$	−9.10428	−0.349906	−0.174953	−	0.984577i	$-0.555977\pi$
$677$	−9.10428	−0.349906	−0.174953	+	0.984577i	$0.555977\pi$
$678$	−42.1199	−1.61761
$679$	−4.83709	−0.185630
$680$	−6.71982	−0.257693
$681$	16.3449	0.626339
$682$	0	0
$683$	16.7129	0.639503	0.319752	−	0.947501i	$-0.396401\pi$
$683$	16.7129	0.639503	0.319752	+	0.947501i	$0.396401\pi$
$684$	35.3906	1.35319
$685$	12.9509	0.494829
$686$	1.00000	0.0381802
$687$	−72.1035	−2.75092
$688$	10.3940	0.396268
$689$	7.55691	0.287896
$690$	−10.6612	−0.405865
$691$	29.1820	1.11014	0.555068	−	0.831805i	$-0.312692\pi$
$691$	29.1820	1.11014	0.555068	+	0.831805i	$0.312692\pi$
$692$	10.5535	0.401183
$693$	0	0
$694$	28.7198	1.09019
$695$	−18.8207	−0.713908
$696$	15.1138	0.572888
$697$	37.3415	1.41441
$698$	1.33193	0.0504144
$699$	−48.0027	−1.81563
$700$	1.00000	0.0377964
$701$	−4.99656	−0.188718	−0.0943588	−	0.995538i	$-0.530080\pi$
$701$	−4.99656	−0.188718	−0.0943588	+	0.995538i	$0.530080\pi$
$702$	13.2767	0.501098
$703$	−0.879296	−0.0331633
$704$	0	0
$705$	5.88273	0.221557
$706$	−14.5113	−0.546139
$707$	−1.22154	−0.0459408
$708$	9.71982	0.365293
$709$	17.3484	0.651531	0.325766	−	0.945451i	$-0.394378\pi$
$709$	17.3484	0.651531	0.325766	+	0.945451i	$0.394378\pi$
$710$	−3.16291	−0.118702
$711$	−40.3871	−1.51464
$712$	9.55691	0.358161
$713$	0	0
$714$	−18.6707	−0.698735
$715$	0	0
$716$	8.32582	0.311150
$717$	−74.8629	−2.79581
$718$	14.8302	0.553459
$719$	−5.20512	−0.194118	−0.0970590	−	0.995279i	$-0.530944\pi$
$719$	−5.20512	−0.194118	−0.0970590	+	0.995279i	$0.530944\pi$
$720$	−4.71982	−0.175897
$721$	−8.27674	−0.308242
$722$	37.2242	1.38534
$723$	−69.4519	−2.58294
$724$	−21.9345	−0.815189
$725$	−5.43965	−0.202023
$726$	0	0
$727$	20.9966	0.778719	0.389360	−	0.921086i	$-0.372696\pi$
$727$	20.9966	0.778719	0.389360	+	0.921086i	$0.372696\pi$
$728$	−2.77846	−0.102976
$729$	−43.9966	−1.62950
$730$	−8.83709	−0.327075
$731$	69.8459	2.58334
$732$	11.8827	0.439198
$733$	6.80444	0.251328	0.125664	−	0.992073i	$-0.459894\pi$
$733$	6.80444	0.251328	0.125664	+	0.992073i	$0.459894\pi$
$734$	−18.9475	−0.699364
$735$	2.77846	0.102485
$736$	−3.83709	−0.141437
$737$	0	0
$738$	26.2277	0.965453
$739$	−3.23797	−0.119111	−0.0595553	−	0.998225i	$-0.518968\pi$
$739$	−3.23797	−0.119111	−0.0595553	+	0.998225i	$0.518968\pi$
$740$	0.117266	0.00431080
$741$	57.8854	2.12647
$742$	−2.71982	−0.0998479
$743$	−16.5535	−0.607288	−0.303644	−	0.952786i	$-0.598203\pi$
$743$	−16.5535	−0.607288	−0.303644	+	0.952786i	$0.598203\pi$
$744$	0	0
$745$	−16.6707	−0.610769
$746$	11.0716	0.405361
$747$	−3.67418	−0.134431
$748$	0	0
$749$	−16.2767	−0.594739
$750$	2.77846	0.101455
$751$	−9.04221	−0.329955	−0.164977	−	0.986297i	$-0.552755\pi$
$751$	−9.04221	−0.329955	−0.164977	+	0.986297i	$0.552755\pi$
$752$	2.11727	0.0772088
$753$	−27.3224	−0.995683
$754$	15.1138	0.550413
$755$	−16.9509	−0.616907
$756$	−4.77846	−0.173791
$757$	−36.7198	−1.33460	−0.667302	−	0.744787i	$-0.732551\pi$
$757$	−36.7198	−1.33460	−0.667302	+	0.744787i	$0.732551\pi$
$758$	30.0844	1.09272
$759$	0	0
$760$	−7.49828	−0.271991
$761$	−1.23109	−0.0446272	−0.0223136	−	0.999751i	$-0.507103\pi$
$761$	−1.23109	−0.0446272	−0.0223136	+	0.999751i	$0.507103\pi$
$762$	−32.8888	−1.19144
$763$	−1.88273	−0.0681595
$764$	11.7198	0.424008
$765$	−31.7164	−1.14671
$766$	37.2733	1.34674
$767$	9.71982	0.350963
$768$	−2.77846	−0.100259
$769$	−6.34492	−0.228804	−0.114402	−	0.993435i	$-0.536495\pi$
$769$	−6.34492	−0.228804	−0.114402	+	0.993435i	$0.536495\pi$
$770$	0	0
$771$	22.6707	0.816467
$772$	−18.5991	−0.669397
$773$	36.2372	1.30336	0.651681	−	0.758493i	$-0.274064\pi$
$773$	36.2372	1.30336	0.651681	+	0.758493i	$0.274064\pi$
$774$	49.0579	1.76335
$775$	0	0
$776$	−4.83709	−0.173641
$777$	0.325819	0.0116887
$778$	24.3449	0.872808
$779$	41.6673	1.49289
$780$	−7.71982	−0.276414
$781$	0	0
$782$	−25.7846	−0.922054
$783$	25.9931	0.928918
$784$	1.00000	0.0357143
$785$	6.66119	0.237748
$786$	−50.0388	−1.78482
$787$	7.55691	0.269375	0.134687	−	0.990888i	$-0.456997\pi$
$787$	7.55691	0.269375	0.134687	+	0.990888i	$0.456997\pi$
$788$	−10.0682	−0.358664
$789$	−78.5562	−2.79667
$790$	8.55691	0.304441
$791$	15.1595	0.539009
$792$	0	0
$793$	11.8827	0.421968
$794$	14.3189	0.508160
$795$	−7.55691	−0.268016
$796$	−16.5535	−0.586722
$797$	16.4267	0.581862	0.290931	−	0.956744i	$-0.406035\pi$
$797$	16.4267	0.581862	0.290931	+	0.956744i	$0.406035\pi$
$798$	−20.8337	−0.737503
$799$	14.2277	0.503338
$800$	1.00000	0.0353553
$801$	45.1070	1.59378
$802$	17.7655	0.627320
$803$	0	0
$804$	33.7846	1.19149
$805$	3.83709	0.135240
$806$	0	0
$807$	−8.50783	−0.299490
$808$	−1.22154	−0.0429737
$809$	29.4819	1.03653	0.518263	−	0.855221i	$-0.326579\pi$
$809$	29.4819	1.03653	0.518263	+	0.855221i	$0.326579\pi$
$810$	0.882734	0.0310161
$811$	−12.5275	−0.439900	−0.219950	−	0.975511i	$-0.570589\pi$
$811$	−12.5275	−0.439900	−0.219950	+	0.975511i	$0.570589\pi$
$812$	−5.43965	−0.190894
$813$	−62.9897	−2.20914
$814$	0	0
$815$	16.5113	0.578365
$816$	−18.6707	−0.653607
$817$	77.9372	2.72668
$818$	−9.88273	−0.345542
$819$	−13.1138	−0.458234
$820$	−5.55691	−0.194056
$821$	−4.44996	−0.155305	−0.0776524	−	0.996980i	$-0.524742\pi$
$821$	−4.44996	−0.155305	−0.0776524	+	0.996980i	$0.524742\pi$
$822$	35.9836	1.25507
$823$	−45.4396	−1.58393	−0.791963	−	0.610569i	$-0.790941\pi$
$823$	−45.4396	−1.58393	−0.791963	+	0.610569i	$0.790941\pi$
$824$	−8.27674	−0.288334
$825$	0	0
$826$	−3.49828	−0.121721
$827$	−35.8528	−1.24672	−0.623361	−	0.781934i	$-0.714233\pi$
$827$	−35.8528	−1.24672	−0.623361	+	0.781934i	$0.714233\pi$
$828$	−18.1104	−0.629380
$829$	−23.8854	−0.829575	−0.414787	−	0.909918i	$-0.636144\pi$
$829$	−23.8854	−0.829575	−0.414787	+	0.909918i	$0.636144\pi$
$830$	0.778457	0.0270206
$831$	27.7846	0.963836
$832$	−2.77846	−0.0963257
$833$	6.71982	0.232828
$834$	−52.2924	−1.81074
$835$	4.51127	0.156119
$836$	0	0
$837$	0	0
$838$	8.05863	0.278381
$839$	−9.22422	−0.318455	−0.159228	−	0.987242i	$-0.550900\pi$
$839$	−9.22422	−0.318455	−0.159228	+	0.987242i	$0.550900\pi$
$840$	2.77846	0.0958659
$841$	0.589769	0.0203369
$842$	−4.65164	−0.160306
$843$	68.5370	2.36054
$844$	−26.8793	−0.925224
$845$	5.28018	0.181644
$846$	9.99312	0.343571
$847$	0	0
$848$	−2.71982	−0.0933991
$849$	−58.9440	−2.02295
$850$	6.71982	0.230488
$851$	0.449961	0.0154245
$852$	−8.78801	−0.301072
$853$	−49.8923	−1.70828	−0.854140	−	0.520044i	$-0.825916\pi$
$853$	−49.8923	−1.70828	−0.854140	+	0.520044i	$0.825916\pi$
$854$	−4.27674	−0.146347
$855$	−35.3906	−1.21033
$856$	−16.2767	−0.556327
$857$	8.44309	0.288410	0.144205	−	0.989548i	$-0.453937\pi$
$857$	8.44309	0.288410	0.144205	+	0.989548i	$0.453937\pi$
$858$	0	0
$859$	30.3871	1.03680	0.518398	−	0.855140i	$-0.326529\pi$
$859$	30.3871	1.03680	0.518398	+	0.855140i	$0.326529\pi$
$860$	−10.3940	−0.354433
$861$	−15.4396	−0.526182
$862$	−37.8793	−1.29017
$863$	0.788009	0.0268241	0.0134121	−	0.999910i	$-0.495731\pi$
$863$	0.788009	0.0268241	0.0134121	+	0.999910i	$0.495731\pi$
$864$	−4.77846	−0.162566
$865$	−10.5535	−0.358829
$866$	15.4656	0.525543
$867$	−78.2303	−2.65684
$868$	0	0
$869$	0	0
$870$	−15.1138	−0.512407
$871$	33.7846	1.14475
$872$	−1.88273	−0.0637574
$873$	−22.8302	−0.772686
$874$	−28.7716	−0.973213
$875$	−1.00000	−0.0338062
$876$	−24.5535	−0.829585
$877$	27.6251	0.932833	0.466417	−	0.884565i	$-0.345545\pi$
$877$	27.6251	0.932833	0.466417	+	0.884565i	$0.345545\pi$
$878$	33.6413	1.13534
$879$	−48.4819	−1.63525
$880$	0	0
$881$	19.9087	0.670742	0.335371	−	0.942086i	$-0.391138\pi$
$881$	19.9087	0.670742	0.335371	+	0.942086i	$0.391138\pi$
$882$	4.71982	0.158925
$883$	1.60600	0.0540461	0.0270230	−	0.999635i	$-0.491397\pi$
$883$	1.60600	0.0540461	0.0270230	+	0.999635i	$0.491397\pi$
$884$	−18.6707	−0.627965
$885$	−9.71982	−0.326728
$886$	−11.8759	−0.398977
$887$	36.5466	1.22711	0.613557	−	0.789650i	$-0.289738\pi$
$887$	36.5466	1.22711	0.613557	+	0.789650i	$0.289738\pi$
$888$	0.325819	0.0109338
$889$	11.8371	0.397003
$890$	−9.55691	−0.320348
$891$	0	0
$892$	−5.83365	−0.195325
$893$	15.8759	0.531265
$894$	−46.3189	−1.54914
$895$	−8.32582	−0.278301
$896$	1.00000	0.0334077
$897$	−29.6217	−0.989038
$898$	−17.8793	−0.596640
$899$	0	0
$900$	4.71982	0.157327
$901$	−18.2767	−0.608886
$902$	0	0
$903$	−28.8793	−0.961043
$904$	15.1595	0.504197
$905$	21.9345	0.729127
$906$	−47.0974	−1.56471
$907$	29.9440	0.994276	0.497138	−	0.867672i	$-0.334384\pi$
$907$	29.9440	0.994276	0.497138	+	0.867672i	$0.334384\pi$
$908$	−5.88273	−0.195225
$909$	−5.76547	−0.191228
$910$	2.77846	0.0921050
$911$	0.993124	0.0329037	0.0164518	−	0.999865i	$-0.494763\pi$
$911$	0.993124	0.0329037	0.0164518	+	0.999865i	$0.494763\pi$
$912$	−20.8337	−0.689871
$913$	0	0
$914$	10.5078	0.347568
$915$	−11.8827	−0.392831
$916$	25.9509	0.857442
$917$	18.0096	0.594728
$918$	−32.1104	−1.05980
$919$	9.10695	0.300411	0.150205	−	0.988655i	$-0.452007\pi$
$919$	9.10695	0.300411	0.150205	+	0.988655i	$0.452007\pi$
$920$	3.83709	0.126505
$921$	6.76891	0.223043
$922$	−41.3837	−1.36290
$923$	−8.78801	−0.289261
$924$	0	0
$925$	−0.117266	−0.00385569
$926$	28.7424	0.944533
$927$	−39.0647	−1.28305
$928$	−5.43965	−0.178565
$929$	15.2964	0.501859	0.250929	−	0.968005i	$-0.419264\pi$
$929$	15.2964	0.501859	0.250929	+	0.968005i	$0.419264\pi$
$930$	0	0
$931$	7.49828	0.245746
$932$	17.2767	0.565918
$933$	−66.0844	−2.16351
$934$	16.3614	0.535360
$935$	0	0
$936$	−13.1138	−0.428639
$937$	−40.4293	−1.32077	−0.660384	−	0.750928i	$-0.729607\pi$
$937$	−40.4293	−1.32077	−0.660384	+	0.750928i	$0.729607\pi$
$938$	−12.1595	−0.397021
$939$	27.7846	0.906715
$940$	−2.11727	−0.0690576
$941$	−54.5888	−1.77954	−0.889772	−	0.456405i	$-0.849137\pi$
$941$	−54.5888	−1.77954	−0.889772	+	0.456405i	$0.849137\pi$
$942$	18.5078	0.603018
$943$	−21.3224	−0.694352
$944$	−3.49828	−0.113859
$945$	4.77846	0.155443
$946$	0	0
$947$	47.4588	1.54220	0.771101	−	0.636713i	$-0.219706\pi$
$947$	47.4588	1.54220	0.771101	+	0.636713i	$0.219706\pi$
$948$	23.7750	0.772177
$949$	−24.5535	−0.797040
$950$	7.49828	0.243276
$951$	57.5500	1.86619
$952$	6.71982	0.217791
$953$	35.1855	1.13977	0.569884	−	0.821725i	$-0.306988\pi$
$953$	35.1855	1.13977	0.569884	+	0.821725i	$0.306988\pi$
$954$	−12.8371	−0.415616
$955$	−11.7198	−0.379245
$956$	26.9440	0.871433
$957$	0	0
$958$	41.9018	1.35379
$959$	−12.9509	−0.418207
$960$	2.77846	0.0896743
$961$	−31.0000	−1.00000
$962$	0.325819	0.0105048
$963$	−76.8233	−2.47560
$964$	24.9966	0.805085
$965$	18.5991	0.598727
$966$	10.6612	0.343018
$967$	−25.2051	−0.810542	−0.405271	−	0.914197i	$-0.632823\pi$
$967$	−25.2051	−0.810542	−0.405271	+	0.914197i	$0.632823\pi$
$968$	0	0
$969$	−139.998	−4.49740
$970$	4.83709	0.155310
$971$	13.1465	0.421891	0.210945	−	0.977498i	$-0.432346\pi$
$971$	13.1465	0.421891	0.210945	+	0.977498i	$0.432346\pi$
$972$	16.7880	0.538476
$973$	18.8207	0.603363
$974$	−16.9509	−0.543142
$975$	7.71982	0.247232
$976$	−4.27674	−0.136895
$977$	58.7164	1.87850	0.939252	−	0.343229i	$-0.111521\pi$
$977$	58.7164	1.87850	0.939252	+	0.343229i	$0.111521\pi$
$978$	45.8759	1.46695
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	−8.88617	−0.283714
$982$	−32.9966	−1.05296
$983$	−4.43621	−0.141493	−0.0707466	−	0.997494i	$-0.522538\pi$
$983$	−4.43621	−0.141493	−0.0707466	+	0.997494i	$0.522538\pi$
$984$	−15.4396	−0.492198
$985$	10.0682	0.320799
$986$	−36.5535	−1.16410
$987$	−5.88273	−0.187249
$988$	−20.8337	−0.662807
$989$	−39.8827	−1.26820
$990$	0	0
$991$	14.8827	0.472766	0.236383	−	0.971660i	$-0.424038\pi$
$991$	14.8827	0.472766	0.236383	+	0.971660i	$0.424038\pi$
$992$	0	0
$993$	−44.7811	−1.42109
$994$	3.16291	0.100321
$995$	16.5535	0.524780
$996$	2.16291	0.0685344
$997$	−15.0061	−0.475248	−0.237624	−	0.971357i	$-0.576369\pi$
$997$	−15.0061	−0.475248	−0.237624	+	0.971357i	$0.576369\pi$
$998$	7.67418	0.242922
$999$	0.560352	0.0177288

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.ck.1.1	yes	3
11.10	odd	2		8470.2.a.cg.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.cg.1.1	✓	3	11.10	odd	2
8470.2.a.ck.1.1	yes	3	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:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.77846 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.77846 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.71982 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.77846 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.77846 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.71982 q^{9} -1.00000 q^{10} -2.77846 q^{12} -2.77846 q^{13} +1.00000 q^{14} +2.77846 q^{15} +1.00000 q^{16} +6.71982 q^{17} +4.71982 q^{18} +7.49828 q^{19} -1.00000 q^{20} -2.77846 q^{21} -3.83709 q^{23} -2.77846 q^{24} +1.00000 q^{25} -2.77846 q^{26} -4.77846 q^{27} +1.00000 q^{28} -5.43965 q^{29} +2.77846 q^{30} +1.00000 q^{32} +6.71982 q^{34} -1.00000 q^{35} +4.71982 q^{36} -0.117266 q^{37} +7.49828 q^{38} +7.71982 q^{39} -1.00000 q^{40} +5.55691 q^{41} -2.77846 q^{42} +10.3940 q^{43} -4.71982 q^{45} -3.83709 q^{46} +2.11727 q^{47} -2.77846 q^{48} +1.00000 q^{49} +1.00000 q^{50} -18.6707 q^{51} -2.77846 q^{52} -2.71982 q^{53} -4.77846 q^{54} +1.00000 q^{56} -20.8337 q^{57} -5.43965 q^{58} -3.49828 q^{59} +2.77846 q^{60} -4.27674 q^{61} +4.71982 q^{63} +1.00000 q^{64} +2.77846 q^{65} -12.1595 q^{67} +6.71982 q^{68} +10.6612 q^{69} -1.00000 q^{70} +3.16291 q^{71} +4.71982 q^{72} +8.83709 q^{73} -0.117266 q^{74} -2.77846 q^{75} +7.49828 q^{76} +7.71982 q^{78} -8.55691 q^{79} -1.00000 q^{80} -0.882734 q^{81} +5.55691 q^{82} -0.778457 q^{83} -2.77846 q^{84} -6.71982 q^{85} +10.3940 q^{86} +15.1138 q^{87} +9.55691 q^{89} -4.71982 q^{90} -2.77846 q^{91} -3.83709 q^{92} +2.11727 q^{94} -7.49828 q^{95} -2.77846 q^{96} -4.83709 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 3 * q^8 + 5 * q^9	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 3 q^{8} + 5 q^{9} - 3 q^{10} + 3 q^{14} + 3 q^{16} + 11 q^{17} + 5 q^{18} + 5 q^{19} - 3 q^{20} - 4 q^{23} + 3 q^{25} - 6 q^{27} + 3 q^{28} + 2 q^{29} + 3 q^{32} + 11 q^{34} - 3 q^{35} + 5 q^{36} - 2 q^{37} + 5 q^{38} + 14 q^{39} - 3 q^{40} + 7 q^{43} - 5 q^{45} - 4 q^{46} + 8 q^{47} + 3 q^{49} + 3 q^{50} - 6 q^{51} + q^{53} - 6 q^{54} + 3 q^{56} - 20 q^{57} + 2 q^{58} + 7 q^{59} + 13 q^{61} + 5 q^{63} + 3 q^{64} - 9 q^{67} + 11 q^{68} + 22 q^{69} - 3 q^{70} + 17 q^{71} + 5 q^{72} + 19 q^{73} - 2 q^{74} + 5 q^{76} + 14 q^{78} - 9 q^{79} - 3 q^{80} - q^{81} + 6 q^{83} - 11 q^{85} + 7 q^{86} + 12 q^{87} + 12 q^{89} - 5 q^{90} - 4 q^{92} + 8 q^{94} - 5 q^{95} - 7 q^{97} + 3 q^{98}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 3 * q^8 + 5 * q^9 - 3 * q^10 + 3 * q^14 + 3 * q^16 + 11 * q^17 + 5 * q^18 + 5 * q^19 - 3 * q^20 - 4 * q^23 + 3 * q^25 - 6 * q^27 + 3 * q^28 + 2 * q^29 + 3 * q^32 + 11 * q^34 - 3 * q^35 + 5 * q^36 - 2 * q^37 + 5 * q^38 + 14 * q^39 - 3 * q^40 + 7 * q^43 - 5 * q^45 - 4 * q^46 + 8 * q^47 + 3 * q^49 + 3 * q^50 - 6 * q^51 + q^53 - 6 * q^54 + 3 * q^56 - 20 * q^57 + 2 * q^58 + 7 * q^59 + 13 * q^61 + 5 * q^63 + 3 * q^64 - 9 * q^67 + 11 * q^68 + 22 * q^69 - 3 * q^70 + 17 * q^71 + 5 * q^72 + 19 * q^73 - 2 * q^74 + 5 * q^76 + 14 * q^78 - 9 * q^79 - 3 * q^80 - q^81 + 6 * q^83 - 11 * q^85 + 7 * q^86 + 12 * q^87 + 12 * q^89 - 5 * q^90 - 4 * q^92 + 8 * q^94 - 5 * q^95 - 7 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

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Database

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