LMFDB - Embedded newform 3381.2.a.bh.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 100x^{5} + 26x^{4} + 100x^{3} - 17x^{2} - 28x - 2 $ x^10 - 4x^9 - 6x^8 + 36x^7 + x^6 - 100x^5 + 26x^4 + 100x^3 - 17x^2 - 28x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.54861$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.54861 q^{2} +1.00000 q^{3} +0.398191 q^{4} +1.02582 q^{5} +1.54861 q^{6} -2.48058 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.54861 q^{2} +1.00000 q^{3} +0.398191 q^{4} +1.02582 q^{5} +1.54861 q^{6} -2.48058 q^{8} +1.00000 q^{9} +1.58859 q^{10} -6.58109 q^{11} +0.398191 q^{12} +0.0967108 q^{13} +1.02582 q^{15} -4.63783 q^{16} +2.79145 q^{17} +1.54861 q^{18} -5.99168 q^{19} +0.408472 q^{20} -10.1915 q^{22} +1.00000 q^{23} -2.48058 q^{24} -3.94770 q^{25} +0.149767 q^{26} +1.00000 q^{27} +2.41057 q^{29} +1.58859 q^{30} -10.1033 q^{31} -2.22103 q^{32} -6.58109 q^{33} +4.32286 q^{34} +0.398191 q^{36} +0.972553 q^{37} -9.27877 q^{38} +0.0967108 q^{39} -2.54462 q^{40} -7.47823 q^{41} +6.72262 q^{43} -2.62053 q^{44} +1.02582 q^{45} +1.54861 q^{46} +5.72919 q^{47} -4.63783 q^{48} -6.11344 q^{50} +2.79145 q^{51} +0.0385094 q^{52} -4.91819 q^{53} +1.54861 q^{54} -6.75100 q^{55} -5.99168 q^{57} +3.73303 q^{58} -4.38060 q^{59} +0.408472 q^{60} -14.4067 q^{61} -15.6460 q^{62} +5.83615 q^{64} +0.0992076 q^{65} -10.1915 q^{66} -4.09150 q^{67} +1.11153 q^{68} +1.00000 q^{69} +1.63827 q^{71} -2.48058 q^{72} +7.70434 q^{73} +1.50610 q^{74} -3.94770 q^{75} -2.38583 q^{76} +0.149767 q^{78} +7.79626 q^{79} -4.75756 q^{80} +1.00000 q^{81} -11.5809 q^{82} +12.4798 q^{83} +2.86351 q^{85} +10.4107 q^{86} +2.41057 q^{87} +16.3249 q^{88} +2.59708 q^{89} +1.58859 q^{90} +0.398191 q^{92} -10.1033 q^{93} +8.87228 q^{94} -6.14637 q^{95} -2.22103 q^{96} +0.921222 q^{97} -6.58109 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} + 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 + 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 - 12 * q^8 + 10 * q^9	$ 10 q - 4 q^{2} + 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} - 12 q^{8} + 10 q^{9} - 8 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{15} + 4 q^{16} - 12 q^{17} - 4 q^{18} - 26 q^{19} - 8 q^{22} + 10 q^{23} - 12 q^{24} + 14 q^{25} + 12 q^{26} + 10 q^{27} - 16 q^{29} - 8 q^{30} - 20 q^{31} - 8 q^{32} - 2 q^{33} + 4 q^{34} + 8 q^{36} + 8 q^{37} + 8 q^{38} - 16 q^{39} + 12 q^{40} - 22 q^{41} - 4 q^{43} - 24 q^{44} - 4 q^{45} - 4 q^{46} - 6 q^{47} + 4 q^{48} - 48 q^{50} - 12 q^{51} - 24 q^{52} - 30 q^{53} - 4 q^{54} - 48 q^{55} - 26 q^{57} + 24 q^{58} - 42 q^{59} - 14 q^{61} - 40 q^{62} + 8 q^{64} - 44 q^{65} - 8 q^{66} - 8 q^{68} + 10 q^{69} + 8 q^{71} - 12 q^{72} - 24 q^{73} + 8 q^{74} + 14 q^{75} - 32 q^{76} + 12 q^{78} + 32 q^{79} - 28 q^{80} + 10 q^{81} + 64 q^{82} - 28 q^{83} - 4 q^{85} - 4 q^{86} - 16 q^{87} + 20 q^{88} - 8 q^{90} + 8 q^{92} - 20 q^{93} - 8 q^{94} - 16 q^{95} - 8 q^{96} + 12 q^{97} - 2 q^{99}+O(q^{100}) $ 10 * q - 4 * q^2 + 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 - 12 * q^8 + 10 * q^9 - 8 * q^10 - 2 * q^11 + 8 * q^12 - 16 * q^13 - 4 * q^15 + 4 * q^16 - 12 * q^17 - 4 * q^18 - 26 * q^19 - 8 * q^22 + 10 * q^23 - 12 * q^24 + 14 * q^25 + 12 * q^26 + 10 * q^27 - 16 * q^29 - 8 * q^30 - 20 * q^31 - 8 * q^32 - 2 * q^33 + 4 * q^34 + 8 * q^36 + 8 * q^37 + 8 * q^38 - 16 * q^39 + 12 * q^40 - 22 * q^41 - 4 * q^43 - 24 * q^44 - 4 * q^45 - 4 * q^46 - 6 * q^47 + 4 * q^48 - 48 * q^50 - 12 * q^51 - 24 * q^52 - 30 * q^53 - 4 * q^54 - 48 * q^55 - 26 * q^57 + 24 * q^58 - 42 * q^59 - 14 * q^61 - 40 * q^62 + 8 * q^64 - 44 * q^65 - 8 * q^66 - 8 * q^68 + 10 * q^69 + 8 * q^71 - 12 * q^72 - 24 * q^73 + 8 * q^74 + 14 * q^75 - 32 * q^76 + 12 * q^78 + 32 * q^79 - 28 * q^80 + 10 * q^81 + 64 * q^82 - 28 * q^83 - 4 * q^85 - 4 * q^86 - 16 * q^87 + 20 * q^88 - 8 * q^90 + 8 * q^92 - 20 * q^93 - 8 * q^94 - 16 * q^95 - 8 * q^96 + 12 * q^97 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.54861	1.09503	0.547516	−	0.836795i	$-0.315573\pi$
$2$	1.54861	1.09503	0.547516	+	0.836795i	$0.315573\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.398191	0.199096
$5$	1.02582	0.458760	0.229380	−	0.973337i	$-0.426330\pi$
$5$	1.02582	0.458760	0.229380	+	0.973337i	$0.426330\pi$
$6$	1.54861	0.632217
$7$	0	0
$7$	0	0
$8$	−2.48058	−0.877016
$9$	1.00000	0.333333
$10$	1.58859	0.502356
$11$	−6.58109	−1.98427	−0.992137	−	0.125157i	$-0.960057\pi$
$11$	−6.58109	−1.98427	−0.992137	+	0.125157i	$0.960057\pi$
$12$	0.398191	0.114948
$13$	0.0967108	0.0268228	0.0134114	−	0.999910i	$-0.495731\pi$
$13$	0.0967108	0.0268228	0.0134114	+	0.999910i	$0.495731\pi$
$14$	0	0
$15$	1.02582	0.264865
$16$	−4.63783	−1.15946
$17$	2.79145	0.677025	0.338513	−	0.940962i	$-0.390076\pi$
$17$	2.79145	0.677025	0.338513	+	0.940962i	$0.390076\pi$
$18$	1.54861	0.365011
$19$	−5.99168	−1.37459	−0.687293	−	0.726381i	$-0.741201\pi$
$19$	−5.99168	−1.37459	−0.687293	+	0.726381i	$0.741201\pi$
$20$	0.408472	0.0913370
$21$	0	0
$22$	−10.1915	−2.17284
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.48058	−0.506345
$25$	−3.94770	−0.789540
$26$	0.149767	0.0293718
$27$	1.00000	0.192450
$28$	0	0
$29$	2.41057	0.447632	0.223816	−	0.974631i	$-0.428149\pi$
$29$	2.41057	0.447632	0.223816	+	0.974631i	$0.428149\pi$
$30$	1.58859	0.290036
$31$	−10.1033	−1.81460	−0.907301	−	0.420481i	$-0.861861\pi$
$31$	−10.1033	−1.81460	−0.907301	+	0.420481i	$0.861861\pi$
$32$	−2.22103	−0.392626
$33$	−6.58109	−1.14562
$34$	4.32286	0.741364
$35$	0	0
$36$	0.398191	0.0663652
$37$	0.972553	0.159887	0.0799434	−	0.996799i	$-0.474526\pi$
$37$	0.972553	0.159887	0.0799434	+	0.996799i	$0.474526\pi$
$38$	−9.27877	−1.50522
$39$	0.0967108	0.0154861
$40$	−2.54462	−0.402339
$41$	−7.47823	−1.16790	−0.583952	−	0.811788i	$-0.698494\pi$
$41$	−7.47823	−1.16790	−0.583952	+	0.811788i	$0.698494\pi$
$42$	0	0
$43$	6.72262	1.02519	0.512595	−	0.858630i	$-0.328684\pi$
$43$	6.72262	1.02519	0.512595	+	0.858630i	$0.328684\pi$
$44$	−2.62053	−0.395060
$45$	1.02582	0.152920
$46$	1.54861	0.228330
$47$	5.72919	0.835689	0.417844	−	0.908519i	$-0.362786\pi$
$47$	5.72919	0.835689	0.417844	+	0.908519i	$0.362786\pi$
$48$	−4.63783	−0.669413
$49$	0	0
$50$	−6.11344	−0.864571
$51$	2.79145	0.390881
$52$	0.0385094	0.00534029
$53$	−4.91819	−0.675566	−0.337783	−	0.941224i	$-0.609677\pi$
$53$	−4.91819	−0.675566	−0.337783	+	0.941224i	$0.609677\pi$
$54$	1.54861	0.210739
$55$	−6.75100	−0.910305
$56$	0	0
$57$	−5.99168	−0.793617
$58$	3.73303	0.490171
$59$	−4.38060	−0.570305	−0.285153	−	0.958482i	$-0.592044\pi$
$59$	−4.38060	−0.570305	−0.285153	+	0.958482i	$0.592044\pi$
$60$	0.408472	0.0527335
$61$	−14.4067	−1.84459	−0.922294	−	0.386490i	$-0.873687\pi$
$61$	−14.4067	−1.84459	−0.922294	+	0.386490i	$0.873687\pi$
$62$	−15.6460	−1.98705
$63$	0	0
$64$	5.83615	0.729518
$65$	0.0992076	0.0123052
$66$	−10.1915	−1.25449
$67$	−4.09150	−0.499856	−0.249928	−	0.968264i	$-0.580407\pi$
$67$	−4.09150	−0.499856	−0.249928	+	0.968264i	$0.580407\pi$
$68$	1.11153	0.134793
$69$	1.00000	0.120386
$70$	0	0
$71$	1.63827	0.194427	0.0972134	−	0.995264i	$-0.469007\pi$
$71$	1.63827	0.194427	0.0972134	+	0.995264i	$0.469007\pi$
$72$	−2.48058	−0.292339
$73$	7.70434	0.901725	0.450862	−	0.892594i	$-0.351117\pi$
$73$	7.70434	0.901725	0.450862	+	0.892594i	$0.351117\pi$
$74$	1.50610	0.175081
$75$	−3.94770	−0.455841
$76$	−2.38583	−0.273674
$77$	0	0
$78$	0.149767	0.0169578
$79$	7.79626	0.877148	0.438574	−	0.898695i	$-0.355484\pi$
$79$	7.79626	0.877148	0.438574	+	0.898695i	$0.355484\pi$
$80$	−4.75756	−0.531912
$81$	1.00000	0.111111
$82$	−11.5809	−1.27889
$83$	12.4798	1.36983	0.684916	−	0.728622i	$-0.259839\pi$
$83$	12.4798	1.36983	0.684916	+	0.728622i	$0.259839\pi$
$84$	0	0
$85$	2.86351	0.310592
$86$	10.4107	1.12262
$87$	2.41057	0.258440
$88$	16.3249	1.74024
$89$	2.59708	0.275290	0.137645	−	0.990482i	$-0.456047\pi$
$89$	2.59708	0.275290	0.137645	+	0.990482i	$0.456047\pi$
$90$	1.58859	0.167452
$91$	0	0
$92$	0.398191	0.0415143
$93$	−10.1033	−1.04766
$94$	8.87228	0.915106
$95$	−6.14637	−0.630604
$96$	−2.22103	−0.226683
$97$	0.921222	0.0935359	0.0467679	−	0.998906i	$-0.485108\pi$
$97$	0.921222	0.0935359	0.0467679	+	0.998906i	$0.485108\pi$
$98$	0	0
$99$	−6.58109	−0.661425
$100$	−1.57194	−0.157194
$101$	−16.4828	−1.64010	−0.820052	−	0.572289i	$-0.806056\pi$
$101$	−16.4828	−1.64010	−0.820052	+	0.572289i	$0.806056\pi$
$102$	4.32286	0.428027
$103$	−2.02573	−0.199602	−0.0998008	−	0.995007i	$-0.531821\pi$
$103$	−2.02573	−0.199602	−0.0998008	+	0.995007i	$0.531821\pi$
$104$	−0.239899	−0.0235240
$105$	0	0
$106$	−7.61636	−0.739766
$107$	−16.9125	−1.63500	−0.817499	−	0.575930i	$-0.804640\pi$
$107$	−16.9125	−1.63500	−0.817499	+	0.575930i	$0.804640\pi$
$108$	0.398191	0.0383160
$109$	11.3564	1.08775	0.543875	−	0.839167i	$-0.316957\pi$
$109$	11.3564	1.08775	0.543875	+	0.839167i	$0.316957\pi$
$110$	−10.4547	−0.996813
$111$	0.972553	0.0923106
$112$	0	0
$113$	−13.0458	−1.22724	−0.613620	−	0.789601i	$-0.710288\pi$
$113$	−13.0458	−1.22724	−0.613620	+	0.789601i	$0.710288\pi$
$114$	−9.27877	−0.869036
$115$	1.02582	0.0956580
$116$	0.959869	0.0891216
$117$	0.0967108	0.00894092
$118$	−6.78384	−0.624503
$119$	0	0
$120$	−2.54462	−0.232291
$121$	32.3108	2.93734
$122$	−22.3103	−2.01988
$123$	−7.47823	−0.674290
$124$	−4.02304	−0.361280
$125$	−9.17871	−0.820968
$126$	0	0
$127$	−14.0382	−1.24569	−0.622846	−	0.782344i	$-0.714024\pi$
$127$	−14.0382	−1.24569	−0.622846	+	0.782344i	$0.714024\pi$
$128$	13.4800	1.19147
$129$	6.72262	0.591894
$130$	0.153634	0.0134746
$131$	−2.72724	−0.238280	−0.119140	−	0.992877i	$-0.538014\pi$
$131$	−2.72724	−0.238280	−0.119140	+	0.992877i	$0.538014\pi$
$132$	−2.62053	−0.228088
$133$	0	0
$134$	−6.33614	−0.547359
$135$	1.02582	0.0882883
$136$	−6.92439	−0.593762
$137$	14.5708	1.24487	0.622435	−	0.782672i	$-0.286144\pi$
$137$	14.5708	1.24487	0.622435	+	0.782672i	$0.286144\pi$
$138$	1.54861	0.131826
$139$	−3.91027	−0.331665	−0.165832	−	0.986154i	$-0.553031\pi$
$139$	−3.91027	−0.331665	−0.165832	+	0.986154i	$0.553031\pi$
$140$	0	0
$141$	5.72919	0.482485
$142$	2.53704	0.212904
$143$	−0.636463	−0.0532237
$144$	−4.63783	−0.386486
$145$	2.47281	0.205355
$146$	11.9310	0.987417
$147$	0	0
$148$	0.387262	0.0318327
$149$	20.7291	1.69819	0.849097	−	0.528237i	$-0.177147\pi$
$149$	20.7291	1.69819	0.849097	+	0.528237i	$0.177147\pi$
$150$	−6.11344	−0.499161
$151$	4.02391	0.327461	0.163730	−	0.986505i	$-0.447647\pi$
$151$	4.02391	0.327461	0.163730	+	0.986505i	$0.447647\pi$
$152$	14.8628	1.20553
$153$	2.79145	0.225675
$154$	0	0
$155$	−10.3641	−0.832466
$156$	0.0385094	0.00308322
$157$	−5.63781	−0.449947	−0.224973	−	0.974365i	$-0.572229\pi$
$157$	−5.63781	−0.449947	−0.224973	+	0.974365i	$0.572229\pi$
$158$	12.0734	0.960505
$159$	−4.91819	−0.390038
$160$	−2.27837	−0.180121
$161$	0	0
$162$	1.54861	0.121670
$163$	18.0803	1.41616	0.708079	−	0.706133i	$-0.249562\pi$
$163$	18.0803	1.41616	0.708079	+	0.706133i	$0.249562\pi$
$164$	−2.97777	−0.232525
$165$	−6.75100	−0.525565
$166$	19.3263	1.50001
$167$	−16.9232	−1.30955	−0.654776	−	0.755823i	$-0.727237\pi$
$167$	−16.9232	−1.30955	−0.654776	+	0.755823i	$0.727237\pi$
$168$	0	0
$169$	−12.9906	−0.999281
$170$	4.43447	0.340108
$171$	−5.99168	−0.458195
$172$	2.67689	0.204111
$173$	5.89586	0.448254	0.224127	−	0.974560i	$-0.428047\pi$
$173$	5.89586	0.448254	0.224127	+	0.974560i	$0.428047\pi$
$174$	3.73303	0.283001
$175$	0	0
$176$	30.5220	2.30068
$177$	−4.38060	−0.329266
$178$	4.02186	0.301451
$179$	−18.2272	−1.36237	−0.681183	−	0.732113i	$-0.738534\pi$
$179$	−18.2272	−1.36237	−0.681183	+	0.732113i	$0.738534\pi$
$180$	0.408472	0.0304457
$181$	24.5989	1.82842	0.914210	−	0.405242i	$-0.132813\pi$
$181$	24.5989	1.82842	0.914210	+	0.405242i	$0.132813\pi$
$182$	0	0
$183$	−14.4067	−1.06497
$184$	−2.48058	−0.182870
$185$	0.997662	0.0733495
$186$	−15.6460	−1.14722
$187$	−18.3708	−1.34340
$188$	2.28132	0.166382
$189$	0	0
$190$	−9.51832	−0.690532
$191$	19.6107	1.41898	0.709490	−	0.704716i	$-0.248925\pi$
$191$	19.6107	1.41898	0.709490	+	0.704716i	$0.248925\pi$
$192$	5.83615	0.421188
$193$	−10.5101	−0.756533	−0.378267	−	0.925697i	$-0.623480\pi$
$193$	−10.5101	−0.756533	−0.378267	+	0.925697i	$0.623480\pi$
$194$	1.42661	0.102425
$195$	0.0992076	0.00710441
$196$	0	0
$197$	7.33222	0.522399	0.261199	−	0.965285i	$-0.415882\pi$
$197$	7.33222	0.522399	0.261199	+	0.965285i	$0.415882\pi$
$198$	−10.1915	−0.724281
$199$	−7.36088	−0.521799	−0.260899	−	0.965366i	$-0.584019\pi$
$199$	−7.36088	−0.521799	−0.260899	+	0.965366i	$0.584019\pi$
$200$	9.79257	0.692439
$201$	−4.09150	−0.288592
$202$	−25.5255	−1.79597
$203$	0	0
$204$	1.11153	0.0778226
$205$	−7.67130	−0.535787
$206$	−3.13707	−0.218570
$207$	1.00000	0.0695048
$208$	−0.448528	−0.0310998
$209$	39.4318	2.72755
$210$	0	0
$211$	−0.515133	−0.0354632	−0.0177316	−	0.999843i	$-0.505644\pi$
$211$	−0.515133	−0.0354632	−0.0177316	+	0.999843i	$0.505644\pi$
$212$	−1.95838	−0.134502
$213$	1.63827	0.112252
$214$	−26.1909	−1.79038
$215$	6.89619	0.470316
$216$	−2.48058	−0.168782
$217$	0	0
$218$	17.5867	1.19112
$219$	7.70434	0.520611
$220$	−2.68819	−0.181238
$221$	0.269963	0.0181597
$222$	1.50610	0.101083
$223$	−16.5692	−1.10956	−0.554778	−	0.831998i	$-0.687197\pi$
$223$	−16.5692	−1.10956	−0.554778	+	0.831998i	$0.687197\pi$
$224$	0	0
$225$	−3.94770	−0.263180
$226$	−20.2028	−1.34387
$227$	−2.13077	−0.141424	−0.0707120	−	0.997497i	$-0.522527\pi$
$227$	−2.13077	−0.141424	−0.0707120	+	0.997497i	$0.522527\pi$
$228$	−2.38583	−0.158006
$229$	14.4259	0.953290	0.476645	−	0.879096i	$-0.341853\pi$
$229$	14.4259	0.953290	0.476645	+	0.879096i	$0.341853\pi$
$230$	1.58859	0.104749
$231$	0	0
$232$	−5.97961	−0.392580
$233$	−2.22006	−0.145441	−0.0727206	−	0.997352i	$-0.523168\pi$
$233$	−2.22006	−0.145441	−0.0727206	+	0.997352i	$0.523168\pi$
$234$	0.149767	0.00979059
$235$	5.87711	0.383380
$236$	−1.74432	−0.113545
$237$	7.79626	0.506422
$238$	0	0
$239$	14.4611	0.935412	0.467706	−	0.883884i	$-0.345081\pi$
$239$	14.4611	0.935412	0.467706	+	0.883884i	$0.345081\pi$
$240$	−4.75756	−0.307099
$241$	17.8066	1.14703	0.573513	−	0.819196i	$-0.305580\pi$
$241$	17.8066	1.14703	0.573513	+	0.819196i	$0.305580\pi$
$242$	50.0368	3.21649
$243$	1.00000	0.0641500
$244$	−5.73662	−0.367249
$245$	0	0
$246$	−11.5809	−0.738369
$247$	−0.579460	−0.0368702
$248$	25.0620	1.59144
$249$	12.4798	0.790873
$250$	−14.2142	−0.898987
$251$	−27.5761	−1.74059	−0.870293	−	0.492535i	$-0.836070\pi$
$251$	−27.5761	−1.74059	−0.870293	+	0.492535i	$0.836070\pi$
$252$	0	0
$253$	−6.58109	−0.413750
$254$	−21.7397	−1.36407
$255$	2.86351	0.179320
$256$	9.20292	0.575182
$257$	17.0021	1.06056	0.530280	−	0.847822i	$-0.322087\pi$
$257$	17.0021	1.06056	0.530280	+	0.847822i	$0.322087\pi$
$258$	10.4107	0.648143
$259$	0	0
$260$	0.0395036	0.00244991
$261$	2.41057	0.149211
$262$	−4.22344	−0.260925
$263$	−20.0349	−1.23540	−0.617702	−	0.786412i	$-0.711936\pi$
$263$	−20.0349	−1.23540	−0.617702	+	0.786412i	$0.711936\pi$
$264$	16.3249	1.00473
$265$	−5.04517	−0.309922
$266$	0	0
$267$	2.59708	0.158939
$268$	−1.62920	−0.0995192
$269$	−18.1520	−1.10675	−0.553373	−	0.832934i	$-0.686660\pi$
$269$	−18.1520	−1.10675	−0.553373	+	0.832934i	$0.686660\pi$
$270$	1.58859	0.0966785
$271$	−7.58594	−0.460813	−0.230406	−	0.973094i	$-0.574006\pi$
$271$	−7.58594	−0.460813	−0.230406	+	0.973094i	$0.574006\pi$
$272$	−12.9462	−0.784981
$273$	0	0
$274$	22.5645	1.36317
$275$	25.9802	1.56666
$276$	0.398191	0.0239683
$277$	19.5130	1.17242	0.586212	−	0.810158i	$-0.300619\pi$
$277$	19.5130	1.17242	0.586212	+	0.810158i	$0.300619\pi$
$278$	−6.05548	−0.363184
$279$	−10.1033	−0.604868
$280$	0	0
$281$	1.47664	0.0880892	0.0440446	−	0.999030i	$-0.485976\pi$
$281$	1.47664	0.0880892	0.0440446	+	0.999030i	$0.485976\pi$
$282$	8.87228	0.528337
$283$	1.23515	0.0734218	0.0367109	−	0.999326i	$-0.488312\pi$
$283$	1.23515	0.0734218	0.0367109	+	0.999326i	$0.488312\pi$
$284$	0.652345	0.0387095
$285$	−6.14637	−0.364079
$286$	−0.985632	−0.0582817
$287$	0	0
$288$	−2.22103	−0.130875
$289$	−9.20783	−0.541637
$290$	3.82941	0.224871
$291$	0.921222	0.0540030
$292$	3.06780	0.179529
$293$	−9.74857	−0.569517	−0.284759	−	0.958599i	$-0.591913\pi$
$293$	−9.74857	−0.569517	−0.284759	+	0.958599i	$0.591913\pi$
$294$	0	0
$295$	−4.49369	−0.261633
$296$	−2.41249	−0.140223
$297$	−6.58109	−0.381874
$298$	32.1013	1.85958
$299$	0.0967108	0.00559293
$300$	−1.57194	−0.0907560
$301$	0	0
$302$	6.23146	0.358580
$303$	−16.4828	−0.946915
$304$	27.7884	1.59377
$305$	−14.7786	−0.846222
$306$	4.32286	0.247121
$307$	−27.7926	−1.58621	−0.793105	−	0.609085i	$-0.791537\pi$
$307$	−27.7926	−1.58621	−0.793105	+	0.609085i	$0.791537\pi$
$308$	0	0
$309$	−2.02573	−0.115240
$310$	−16.0500	−0.911577
$311$	3.96040	0.224574	0.112287	−	0.993676i	$-0.464182\pi$
$311$	3.96040	0.224574	0.112287	+	0.993676i	$0.464182\pi$
$312$	−0.239899	−0.0135816
$313$	4.81964	0.272422	0.136211	−	0.990680i	$-0.456508\pi$
$313$	4.81964	0.272422	0.136211	+	0.990680i	$0.456508\pi$
$314$	−8.73077	−0.492706
$315$	0	0
$316$	3.10440	0.174636
$317$	−16.8489	−0.946326	−0.473163	−	0.880975i	$-0.656888\pi$
$317$	−16.8489	−0.946326	−0.473163	+	0.880975i	$0.656888\pi$
$318$	−7.61636	−0.427104
$319$	−15.8642	−0.888225
$320$	5.98682	0.334673
$321$	−16.9125	−0.943966
$322$	0	0
$323$	−16.7254	−0.930629
$324$	0.398191	0.0221217
$325$	−0.381785	−0.0211776
$326$	27.9993	1.55074
$327$	11.3564	0.628012
$328$	18.5503	1.02427
$329$	0	0
$330$	−10.4547	−0.575510
$331$	10.0553	0.552689	0.276344	−	0.961059i	$-0.410877\pi$
$331$	10.0553	0.552689	0.276344	+	0.961059i	$0.410877\pi$
$332$	4.96933	0.272728
$333$	0.972553	0.0532956
$334$	−26.2074	−1.43400
$335$	−4.19713	−0.229314
$336$	0	0
$337$	−28.6099	−1.55848	−0.779240	−	0.626725i	$-0.784395\pi$
$337$	−28.6099	−1.55848	−0.779240	+	0.626725i	$0.784395\pi$
$338$	−20.1174	−1.09424
$339$	−13.0458	−0.708548
$340$	1.14023	0.0618375
$341$	66.4906	3.60067
$342$	−9.27877	−0.501738
$343$	0	0
$344$	−16.6760	−0.899109
$345$	1.02582	0.0552282
$346$	9.13039	0.490853
$347$	19.4460	1.04392	0.521958	−	0.852971i	$-0.325202\pi$
$347$	19.4460	1.04392	0.521958	+	0.852971i	$0.325202\pi$
$348$	0.959869	0.0514544
$349$	11.4642	0.613663	0.306832	−	0.951764i	$-0.400731\pi$
$349$	11.4642	0.613663	0.306832	+	0.951764i	$0.400731\pi$
$350$	0	0
$351$	0.0967108	0.00516204
$352$	14.6168	0.779078
$353$	−31.1454	−1.65770	−0.828850	−	0.559471i	$-0.811004\pi$
$353$	−31.1454	−1.65770	−0.828850	+	0.559471i	$0.811004\pi$
$354$	−6.78384	−0.360557
$355$	1.68057	0.0891952
$356$	1.03413	0.0548090
$357$	0	0
$358$	−28.2268	−1.49183
$359$	−15.8708	−0.837628	−0.418814	−	0.908072i	$-0.637554\pi$
$359$	−15.8708	−0.837628	−0.418814	+	0.908072i	$0.637554\pi$
$360$	−2.54462	−0.134113
$361$	16.9002	0.889485
$362$	38.0940	2.00218
$363$	32.3108	1.69588
$364$	0	0
$365$	7.90324	0.413675
$366$	−22.3103	−1.16618
$367$	−0.586635	−0.0306221	−0.0153111	−	0.999883i	$-0.504874\pi$
$367$	−0.586635	−0.0306221	−0.0153111	+	0.999883i	$0.504874\pi$
$368$	−4.63783	−0.241763
$369$	−7.47823	−0.389301
$370$	1.54499	0.0803201
$371$	0	0
$372$	−4.02304	−0.208585
$373$	−10.9030	−0.564537	−0.282268	−	0.959335i	$-0.591087\pi$
$373$	−10.9030	−0.564537	−0.282268	+	0.959335i	$0.591087\pi$
$374$	−28.4491	−1.47107
$375$	−9.17871	−0.473986
$376$	−14.2117	−0.732913
$377$	0.233128	0.0120067
$378$	0	0
$379$	22.2093	1.14081	0.570407	−	0.821362i	$-0.306786\pi$
$379$	22.2093	1.14081	0.570407	+	0.821362i	$0.306786\pi$
$380$	−2.44743	−0.125551
$381$	−14.0382	−0.719201
$382$	30.3693	1.55383
$383$	−16.1733	−0.826417	−0.413209	−	0.910636i	$-0.635592\pi$
$383$	−16.1733	−0.826417	−0.413209	+	0.910636i	$0.635592\pi$
$384$	13.4800	0.687897
$385$	0	0
$386$	−16.2760	−0.828429
$387$	6.72262	0.341730
$388$	0.366822	0.0186226
$389$	−8.60710	−0.436397	−0.218199	−	0.975904i	$-0.570018\pi$
$389$	−8.60710	−0.436397	−0.218199	+	0.975904i	$0.570018\pi$
$390$	0.153634	0.00777955
$391$	2.79145	0.141170
$392$	0	0
$393$	−2.72724	−0.137571
$394$	11.3547	0.572044
$395$	7.99754	0.402400
$396$	−2.62053	−0.131687
$397$	−5.16626	−0.259287	−0.129644	−	0.991561i	$-0.541383\pi$
$397$	−5.16626	−0.259287	−0.129644	+	0.991561i	$0.541383\pi$
$398$	−11.3991	−0.571386
$399$	0	0
$400$	18.3087	0.915437
$401$	25.6945	1.28312	0.641561	−	0.767072i	$-0.278287\pi$
$401$	25.6945	1.28312	0.641561	+	0.767072i	$0.278287\pi$
$402$	−6.33614	−0.316018
$403$	−0.977096	−0.0486726
$404$	−6.56333	−0.326538
$405$	1.02582	0.0509733
$406$	0	0
$407$	−6.40046	−0.317259
$408$	−6.92439	−0.342809
$409$	14.7987	0.731749	0.365874	−	0.930664i	$-0.380770\pi$
$409$	14.7987	0.731749	0.365874	+	0.930664i	$0.380770\pi$
$410$	−11.8799	−0.586704
$411$	14.5708	0.718726
$412$	−0.806630	−0.0397398
$413$	0	0
$414$	1.54861	0.0761100
$415$	12.8020	0.628424
$416$	−0.214798	−0.0105313
$417$	−3.91027	−0.191487
$418$	61.0644	2.98676
$419$	6.43007	0.314130	0.157065	−	0.987588i	$-0.449797\pi$
$419$	6.43007	0.314130	0.157065	+	0.987588i	$0.449797\pi$
$420$	0	0
$421$	−18.1314	−0.883670	−0.441835	−	0.897096i	$-0.645672\pi$
$421$	−18.1314	−0.883670	−0.441835	+	0.897096i	$0.645672\pi$
$422$	−0.797740	−0.0388334
$423$	5.72919	0.278563
$424$	12.2000	0.592482
$425$	−11.0198	−0.534538
$426$	2.53704	0.122920
$427$	0	0
$428$	−6.73443	−0.325521
$429$	−0.636463	−0.0307287
$430$	10.6795	0.515011
$431$	−15.6712	−0.754856	−0.377428	−	0.926039i	$-0.623191\pi$
$431$	−15.6712	−0.754856	−0.377428	+	0.926039i	$0.623191\pi$
$432$	−4.63783	−0.223138
$433$	23.4459	1.12674	0.563368	−	0.826206i	$-0.309505\pi$
$433$	23.4459	1.12674	0.563368	+	0.826206i	$0.309505\pi$
$434$	0	0
$435$	2.47281	0.118562
$436$	4.52203	0.216566
$437$	−5.99168	−0.286621
$438$	11.9310	0.570086
$439$	−6.77828	−0.323510	−0.161755	−	0.986831i	$-0.551715\pi$
$439$	−6.77828	−0.323510	−0.161755	+	0.986831i	$0.551715\pi$
$440$	16.7464	0.798352
$441$	0	0
$442$	0.418067	0.0198854
$443$	−29.1655	−1.38569	−0.692847	−	0.721085i	$-0.743644\pi$
$443$	−29.1655	−1.38569	−0.692847	+	0.721085i	$0.743644\pi$
$444$	0.387262	0.0183786
$445$	2.66413	0.126292
$446$	−25.6592	−1.21500
$447$	20.7291	0.980453
$448$	0	0
$449$	36.9760	1.74501	0.872503	−	0.488609i	$-0.162496\pi$
$449$	36.9760	1.74501	0.872503	+	0.488609i	$0.162496\pi$
$450$	−6.11344	−0.288190
$451$	49.2150	2.31744
$452$	−5.19470	−0.244338
$453$	4.02391	0.189060
$454$	−3.29973	−0.154864
$455$	0	0
$456$	14.8628	0.696015
$457$	27.7671	1.29889	0.649445	−	0.760409i	$-0.275001\pi$
$457$	27.7671	1.29889	0.649445	+	0.760409i	$0.275001\pi$
$458$	22.3401	1.04388
$459$	2.79145	0.130294
$460$	0.408472	0.0190451
$461$	−26.9409	−1.25476	−0.627380	−	0.778713i	$-0.715873\pi$
$461$	−26.9409	−1.25476	−0.627380	+	0.778713i	$0.715873\pi$
$462$	0	0
$463$	26.8087	1.24591	0.622954	−	0.782258i	$-0.285932\pi$
$463$	26.8087	1.24591	0.622954	+	0.782258i	$0.285932\pi$
$464$	−11.1798	−0.519010
$465$	−10.3641	−0.480625
$466$	−3.43801	−0.159263
$467$	−16.0527	−0.742833	−0.371416	−	0.928466i	$-0.621128\pi$
$467$	−16.0527	−0.742833	−0.371416	+	0.928466i	$0.621128\pi$
$468$	0.0385094	0.00178010
$469$	0	0
$470$	9.10134	0.419814
$471$	−5.63781	−0.259777
$472$	10.8664	0.500167
$473$	−44.2422	−2.03426
$474$	12.0734	0.554548
$475$	23.6533	1.08529
$476$	0	0
$477$	−4.91819	−0.225189
$478$	22.3946	1.02431
$479$	8.08384	0.369360	0.184680	−	0.982799i	$-0.440875\pi$
$479$	8.08384	0.369360	0.184680	+	0.982799i	$0.440875\pi$
$480$	−2.27837	−0.103993
$481$	0.0940564	0.00428860
$482$	27.5755	1.25603
$483$	0	0
$484$	12.8659	0.584812
$485$	0.945005	0.0429105
$486$	1.54861	0.0702464
$487$	−22.2419	−1.00787	−0.503937	−	0.863740i	$-0.668116\pi$
$487$	−22.2419	−1.00787	−0.503937	+	0.863740i	$0.668116\pi$
$488$	35.7369	1.61773
$489$	18.0803	0.817619
$490$	0	0
$491$	−25.0527	−1.13061	−0.565307	−	0.824881i	$-0.691242\pi$
$491$	−25.0527	−1.13061	−0.565307	+	0.824881i	$0.691242\pi$
$492$	−2.97777	−0.134248
$493$	6.72898	0.303058
$494$	−0.897357	−0.0403740
$495$	−6.75100	−0.303435
$496$	46.8573	2.10395
$497$	0	0
$498$	19.3263	0.866031
$499$	22.4671	1.00576	0.502882	−	0.864355i	$-0.332273\pi$
$499$	22.4671	1.00576	0.502882	+	0.864355i	$0.332273\pi$
$500$	−3.65488	−0.163451
$501$	−16.9232	−0.756071
$502$	−42.7045	−1.90600
$503$	−14.3313	−0.638999	−0.319500	−	0.947586i	$-0.603515\pi$
$503$	−14.3313	−0.638999	−0.319500	+	0.947586i	$0.603515\pi$
$504$	0	0
$505$	−16.9084	−0.752413
$506$	−10.1915	−0.453069
$507$	−12.9906	−0.576935
$508$	−5.58990	−0.248012
$509$	20.5708	0.911786	0.455893	−	0.890035i	$-0.349320\pi$
$509$	20.5708	0.911786	0.455893	+	0.890035i	$0.349320\pi$
$510$	4.43447	0.196361
$511$	0	0
$512$	−12.7082	−0.561629
$513$	−5.99168	−0.264539
$514$	26.3296	1.16135
$515$	−2.07803	−0.0915691
$516$	2.67689	0.117844
$517$	−37.7044	−1.65824
$518$	0	0
$519$	5.89586	0.258800
$520$	−0.246092	−0.0107919
$521$	30.8216	1.35032	0.675160	−	0.737672i	$-0.264075\pi$
$521$	30.8216	1.35032	0.675160	+	0.737672i	$0.264075\pi$
$522$	3.73303	0.163390
$523$	−3.49880	−0.152992	−0.0764958	−	0.997070i	$-0.524373\pi$
$523$	−3.49880	−0.152992	−0.0764958	+	0.997070i	$0.524373\pi$
$524$	−1.08597	−0.0474406
$525$	0	0
$526$	−31.0262	−1.35281
$527$	−28.2028	−1.22853
$528$	30.5220	1.32830
$529$	1.00000	0.0434783
$530$	−7.81299	−0.339375
$531$	−4.38060	−0.190102
$532$	0	0
$533$	−0.723226	−0.0313264
$534$	4.02186	0.174043
$535$	−17.3492	−0.750071
$536$	10.1493	0.438382
$537$	−18.2272	−0.786563
$538$	−28.1103	−1.21192
$539$	0	0
$540$	0.408472	0.0175778
$541$	−35.7811	−1.53835	−0.769175	−	0.639038i	$-0.779333\pi$
$541$	−35.7811	−1.53835	−0.769175	+	0.639038i	$0.779333\pi$
$542$	−11.7477	−0.504605
$543$	24.5989	1.05564
$544$	−6.19988	−0.265818
$545$	11.6496	0.499015
$546$	0	0
$547$	28.2676	1.20864	0.604318	−	0.796743i	$-0.293446\pi$
$547$	28.2676	1.20864	0.604318	+	0.796743i	$0.293446\pi$
$548$	5.80198	0.247848
$549$	−14.4067	−0.614862
$550$	40.2331	1.71555
$551$	−14.4434	−0.615308
$552$	−2.48058	−0.105580
$553$	0	0
$554$	30.2180	1.28384
$555$	0.997662	0.0423484
$556$	−1.55704	−0.0660330
$557$	13.3099	0.563960	0.281980	−	0.959420i	$-0.409009\pi$
$557$	13.3099	0.563960	0.281980	+	0.959420i	$0.409009\pi$
$558$	−15.6460	−0.662350
$559$	0.650151	0.0274984
$560$	0	0
$561$	−18.3708	−0.775614
$562$	2.28674	0.0964605
$563$	20.4179	0.860513	0.430257	−	0.902707i	$-0.358423\pi$
$563$	20.4179	0.860513	0.430257	+	0.902707i	$0.358423\pi$
$564$	2.28132	0.0960607
$565$	−13.3826	−0.563008
$566$	1.91276	0.0803992
$567$	0	0
$568$	−4.06385	−0.170515
$569$	−7.25109	−0.303982	−0.151991	−	0.988382i	$-0.548568\pi$
$569$	−7.25109	−0.303982	−0.151991	+	0.988382i	$0.548568\pi$
$570$	−9.51832	−0.398679
$571$	20.9061	0.874893	0.437446	−	0.899244i	$-0.355883\pi$
$571$	20.9061	0.874893	0.437446	+	0.899244i	$0.355883\pi$
$572$	−0.253434	−0.0105966
$573$	19.6107	0.819248
$574$	0	0
$575$	−3.94770	−0.164630
$576$	5.83615	0.243173
$577$	28.3400	1.17981	0.589905	−	0.807473i	$-0.299165\pi$
$577$	28.3400	1.17981	0.589905	+	0.807473i	$0.299165\pi$
$578$	−14.2593	−0.593110
$579$	−10.5101	−0.436785
$580$	0.984650	0.0408854
$581$	0	0
$582$	1.42661	0.0591350
$583$	32.3671	1.34051
$584$	−19.1112	−0.790827
$585$	0.0992076	0.00410173
$586$	−15.0967	−0.623640
$587$	−23.3149	−0.962310	−0.481155	−	0.876635i	$-0.659783\pi$
$587$	−23.3149	−0.962310	−0.481155	+	0.876635i	$0.659783\pi$
$588$	0	0
$589$	60.5356	2.49433
$590$	−6.95898	−0.286497
$591$	7.33222	0.301607
$592$	−4.51053	−0.185382
$593$	8.07712	0.331687	0.165844	−	0.986152i	$-0.446965\pi$
$593$	8.07712	0.331687	0.165844	+	0.986152i	$0.446965\pi$
$594$	−10.1915	−0.418164
$595$	0	0
$596$	8.25415	0.338103
$597$	−7.36088	−0.301261
$598$	0.149767	0.00612444
$599$	22.2393	0.908673	0.454337	−	0.890830i	$-0.349876\pi$
$599$	22.2393	0.908673	0.454337	+	0.890830i	$0.349876\pi$
$600$	9.79257	0.399780
$601$	34.9803	1.42688	0.713438	−	0.700719i	$-0.247137\pi$
$601$	34.9803	1.42688	0.713438	+	0.700719i	$0.247137\pi$
$602$	0	0
$603$	−4.09150	−0.166619
$604$	1.60228	0.0651960
$605$	33.1450	1.34753
$606$	−25.5255	−1.03690
$607$	14.3826	0.583771	0.291886	−	0.956453i	$-0.405717\pi$
$607$	14.3826	0.583771	0.291886	+	0.956453i	$0.405717\pi$
$608$	13.3077	0.539698
$609$	0	0
$610$	−22.8863	−0.926640
$611$	0.554075	0.0224155
$612$	1.11153	0.0449309
$613$	−30.0109	−1.21213	−0.606065	−	0.795415i	$-0.707253\pi$
$613$	−30.0109	−1.21213	−0.606065	+	0.795415i	$0.707253\pi$
$614$	−43.0400	−1.73695
$615$	−7.67130	−0.309337
$616$	0	0
$617$	−14.0763	−0.566690	−0.283345	−	0.959018i	$-0.591444\pi$
$617$	−14.0763	−0.566690	−0.283345	+	0.959018i	$0.591444\pi$
$618$	−3.13707	−0.126192
$619$	−27.4497	−1.10330	−0.551648	−	0.834077i	$-0.686001\pi$
$619$	−27.4497	−1.10330	−0.551648	+	0.834077i	$0.686001\pi$
$620$	−4.12690	−0.165740
$621$	1.00000	0.0401286
$622$	6.13311	0.245916
$623$	0	0
$624$	−0.448528	−0.0179555
$625$	10.3228	0.412913
$626$	7.46373	0.298311
$627$	39.4318	1.57475
$628$	−2.24493	−0.0895824
$629$	2.71483	0.108247
$630$	0	0
$631$	22.9335	0.912970	0.456485	−	0.889731i	$-0.349108\pi$
$631$	22.9335	0.912970	0.456485	+	0.889731i	$0.349108\pi$
$632$	−19.3392	−0.769273
$633$	−0.515133	−0.0204747
$634$	−26.0923	−1.03626
$635$	−14.4007	−0.571473
$636$	−1.95838	−0.0776549
$637$	0	0
$638$	−24.5674	−0.972635
$639$	1.63827	0.0648089
$640$	13.8280	0.546599
$641$	−4.93467	−0.194908	−0.0974539	−	0.995240i	$-0.531070\pi$
$641$	−4.93467	−0.194908	−0.0974539	+	0.995240i	$0.531070\pi$
$642$	−26.1909	−1.03367
$643$	−2.11089	−0.0832453	−0.0416226	−	0.999133i	$-0.513253\pi$
$643$	−2.11089	−0.0832453	−0.0416226	+	0.999133i	$0.513253\pi$
$644$	0	0
$645$	6.89619	0.271537
$646$	−25.9012	−1.01907
$647$	−29.9015	−1.17555	−0.587774	−	0.809025i	$-0.699996\pi$
$647$	−29.9015	−1.17555	−0.587774	+	0.809025i	$0.699996\pi$
$648$	−2.48058	−0.0974462
$649$	28.8291	1.13164
$650$	−0.591236	−0.0231902
$651$	0	0
$652$	7.19941	0.281951
$653$	−31.7412	−1.24213	−0.621065	−	0.783759i	$-0.713300\pi$
$653$	−31.7412	−1.24213	−0.621065	+	0.783759i	$0.713300\pi$
$654$	17.5867	0.687694
$655$	−2.79766	−0.109313
$656$	34.6828	1.35413
$657$	7.70434	0.300575
$658$	0	0
$659$	2.60404	0.101439	0.0507195	−	0.998713i	$-0.483849\pi$
$659$	2.60404	0.101439	0.0507195	+	0.998713i	$0.483849\pi$
$660$	−2.68819	−0.104638
$661$	−38.2421	−1.48744	−0.743722	−	0.668489i	$-0.766941\pi$
$661$	−38.2421	−1.48744	−0.743722	+	0.668489i	$0.766941\pi$
$662$	15.5717	0.605212
$663$	0.269963	0.0104845
$664$	−30.9570	−1.20136
$665$	0	0
$666$	1.50610	0.0583604
$667$	2.41057	0.0933377
$668$	−6.73865	−0.260726
$669$	−16.5692	−0.640603
$670$	−6.49972	−0.251106
$671$	94.8117	3.66017
$672$	0	0
$673$	31.2699	1.20536	0.602682	−	0.797981i	$-0.294099\pi$
$673$	31.2699	1.20536	0.602682	+	0.797981i	$0.294099\pi$
$674$	−44.3056	−1.70659
$675$	−3.94770	−0.151947
$676$	−5.17276	−0.198952
$677$	−10.1973	−0.391915	−0.195958	−	0.980612i	$-0.562781\pi$
$677$	−10.1973	−0.391915	−0.195958	+	0.980612i	$0.562781\pi$
$678$	−20.2028	−0.775883
$679$	0	0
$680$	−7.10317	−0.272394
$681$	−2.13077	−0.0816512
$682$	102.968	3.94285
$683$	−12.6603	−0.484432	−0.242216	−	0.970222i	$-0.577874\pi$
$683$	−12.6603	−0.484432	−0.242216	+	0.970222i	$0.577874\pi$
$684$	−2.38583	−0.0912246
$685$	14.9470	0.571096
$686$	0	0
$687$	14.4259	0.550382
$688$	−31.1784	−1.18866
$689$	−0.475642	−0.0181205
$690$	1.58859	0.0604766
$691$	6.74340	0.256531	0.128266	−	0.991740i	$-0.459059\pi$
$691$	6.74340	0.256531	0.128266	+	0.991740i	$0.459059\pi$
$692$	2.34768	0.0892454
$693$	0	0
$694$	30.1143	1.14312
$695$	−4.01122	−0.152154
$696$	−5.97961	−0.226656
$697$	−20.8751	−0.790700
$698$	17.7535	0.671981
$699$	−2.22006	−0.0839705
$700$	0	0
$701$	19.1107	0.721803	0.360901	−	0.932604i	$-0.382469\pi$
$701$	19.1107	0.721803	0.360901	+	0.932604i	$0.382469\pi$
$702$	0.149767	0.00565260
$703$	−5.82722	−0.219778
$704$	−38.4082	−1.44756
$705$	5.87711	0.221345
$706$	−48.2320	−1.81524
$707$	0	0
$708$	−1.74432	−0.0655554
$709$	10.9432	0.410980	0.205490	−	0.978659i	$-0.434121\pi$
$709$	10.9432	0.410980	0.205490	+	0.978659i	$0.434121\pi$
$710$	2.60254	0.0976716
$711$	7.79626	0.292383
$712$	−6.44225	−0.241434
$713$	−10.1033	−0.378371
$714$	0	0
$715$	−0.652895	−0.0244169
$716$	−7.25792	−0.271241
$717$	14.4611	0.540060
$718$	−24.5776	−0.917230
$719$	−45.3780	−1.69232	−0.846158	−	0.532932i	$-0.821090\pi$
$719$	−45.3780	−1.69232	−0.846158	+	0.532932i	$0.821090\pi$
$720$	−4.75756	−0.177304
$721$	0	0
$722$	26.1718	0.974014
$723$	17.8066	0.662236
$724$	9.79505	0.364030
$725$	−9.51621	−0.353423
$726$	50.0368	1.85704
$727$	−19.4657	−0.721942	−0.360971	−	0.932577i	$-0.617555\pi$
$727$	−19.4657	−0.721942	−0.360971	+	0.932577i	$0.617555\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	12.2390	0.452987
$731$	18.7658	0.694080
$732$	−5.73662	−0.212032
$733$	−10.3542	−0.382442	−0.191221	−	0.981547i	$-0.561245\pi$
$733$	−10.3542	−0.382442	−0.191221	+	0.981547i	$0.561245\pi$
$734$	−0.908469	−0.0335322
$735$	0	0
$736$	−2.22103	−0.0818682
$737$	26.9265	0.991852
$738$	−11.5809	−0.426298
$739$	−35.4220	−1.30302	−0.651510	−	0.758640i	$-0.725864\pi$
$739$	−35.4220	−1.30302	−0.651510	+	0.758640i	$0.725864\pi$
$740$	0.397260	0.0146036
$741$	−0.579460	−0.0212870
$742$	0	0
$743$	42.5211	1.55995	0.779974	−	0.625812i	$-0.215232\pi$
$743$	42.5211	1.55995	0.779974	+	0.625812i	$0.215232\pi$
$744$	25.0620	0.918816
$745$	21.2643	0.779063
$746$	−16.8845	−0.618186
$747$	12.4798	0.456611
$748$	−7.31508	−0.267466
$749$	0	0
$750$	−14.2142	−0.519030
$751$	−37.4114	−1.36516	−0.682581	−	0.730810i	$-0.739142\pi$
$751$	−37.4114	−1.36516	−0.682581	+	0.730810i	$0.739142\pi$
$752$	−26.5710	−0.968945
$753$	−27.5761	−1.00493
$754$	0.361025	0.0131477
$755$	4.12779	0.150226
$756$	0	0
$757$	53.8670	1.95783	0.978914	−	0.204271i	$-0.0654822\pi$
$757$	53.8670	1.95783	0.978914	+	0.204271i	$0.0654822\pi$
$758$	34.3935	1.24923
$759$	−6.58109	−0.238879
$760$	15.2465	0.553050
$761$	−19.9697	−0.723900	−0.361950	−	0.932197i	$-0.617889\pi$
$761$	−19.9697	−0.723900	−0.361950	+	0.932197i	$0.617889\pi$
$762$	−21.7397	−0.787548
$763$	0	0
$764$	7.80881	0.282513
$765$	2.86351	0.103531
$766$	−25.0461	−0.904953
$767$	−0.423651	−0.0152972
$768$	9.20292	0.332082
$769$	46.6660	1.68282	0.841409	−	0.540399i	$-0.181727\pi$
$769$	46.6660	1.68282	0.841409	+	0.540399i	$0.181727\pi$
$770$	0	0
$771$	17.0021	0.612315
$772$	−4.18503	−0.150623
$773$	−16.8883	−0.607429	−0.303714	−	0.952763i	$-0.598227\pi$
$773$	−16.8883	−0.607429	−0.303714	+	0.952763i	$0.598227\pi$
$774$	10.4107	0.374206
$775$	39.8847	1.43270
$776$	−2.28516	−0.0820325
$777$	0	0
$778$	−13.3290	−0.477869
$779$	44.8072	1.60538
$780$	0.0395036	0.00141446
$781$	−10.7816	−0.385796
$782$	4.32286	0.154585
$783$	2.41057	0.0861468
$784$	0	0
$785$	−5.78337	−0.206417
$786$	−4.22344	−0.150645
$787$	32.9203	1.17348	0.586741	−	0.809774i	$-0.300410\pi$
$787$	32.9203	1.17348	0.586741	+	0.809774i	$0.300410\pi$
$788$	2.91963	0.104007
$789$	−20.0349	−0.713261
$790$	12.3851	0.440641
$791$	0	0
$792$	16.3249	0.580080
$793$	−1.39328	−0.0494769
$794$	−8.00052	−0.283928
$795$	−5.04517	−0.178934
$796$	−2.93104	−0.103888
$797$	21.6726	0.767684	0.383842	−	0.923399i	$-0.374601\pi$
$797$	21.6726	0.767684	0.383842	+	0.923399i	$0.374601\pi$
$798$	0	0
$799$	15.9927	0.565782
$800$	8.76796	0.309994
$801$	2.59708	0.0917632
$802$	39.7908	1.40506
$803$	−50.7030	−1.78927
$804$	−1.62920	−0.0574575
$805$	0	0
$806$	−1.51314	−0.0532981
$807$	−18.1520	−0.638980
$808$	40.8869	1.43840
$809$	−53.1040	−1.86704	−0.933519	−	0.358529i	$-0.883278\pi$
$809$	−53.1040	−1.86704	−0.933519	+	0.358529i	$0.883278\pi$
$810$	1.58859	0.0558174
$811$	−29.7443	−1.04446	−0.522232	−	0.852804i	$-0.674900\pi$
$811$	−29.7443	−1.04446	−0.522232	+	0.852804i	$0.674900\pi$
$812$	0	0
$813$	−7.58594	−0.266050
$814$	−9.91181	−0.347409
$815$	18.5471	0.649676
$816$	−12.9462	−0.453209
$817$	−40.2798	−1.40921
$818$	22.9174	0.801288
$819$	0	0
$820$	−3.05465	−0.106673
$821$	26.3798	0.920663	0.460331	−	0.887747i	$-0.347731\pi$
$821$	26.3798	0.920663	0.460331	+	0.887747i	$0.347731\pi$
$822$	22.5645	0.787028
$823$	−5.25436	−0.183155	−0.0915777	−	0.995798i	$-0.529191\pi$
$823$	−5.25436	−0.183155	−0.0915777	+	0.995798i	$0.529191\pi$
$824$	5.02499	0.175054
$825$	25.9802	0.904513
$826$	0	0
$827$	1.44455	0.0502318	0.0251159	−	0.999685i	$-0.492005\pi$
$827$	1.44455	0.0502318	0.0251159	+	0.999685i	$0.492005\pi$
$828$	0.398191	0.0138381
$829$	−30.9757	−1.07583	−0.537915	−	0.842999i	$-0.680788\pi$
$829$	−30.9757	−1.07583	−0.537915	+	0.842999i	$0.680788\pi$
$830$	19.8252	0.688144
$831$	19.5130	0.676899
$832$	0.564418	0.0195677
$833$	0	0
$834$	−6.05548	−0.209684
$835$	−17.3601	−0.600770
$836$	15.7014	0.543044
$837$	−10.1033	−0.349220
$838$	9.95767	0.343982
$839$	−27.1001	−0.935598	−0.467799	−	0.883835i	$-0.654953\pi$
$839$	−27.1001	−0.935598	−0.467799	+	0.883835i	$0.654953\pi$
$840$	0	0
$841$	−23.1891	−0.799626
$842$	−28.0784	−0.967647
$843$	1.47664	0.0508583
$844$	−0.205121	−0.00706057
$845$	−13.3260	−0.458429
$846$	8.87228	0.305035
$847$	0	0
$848$	22.8097	0.783289
$849$	1.23515	0.0423901
$850$	−17.0653	−0.585337
$851$	0.972553	0.0333387
$852$	0.652345	0.0223490
$853$	−44.5874	−1.52664	−0.763322	−	0.646019i	$-0.776433\pi$
$853$	−44.5874	−1.52664	−0.763322	+	0.646019i	$0.776433\pi$
$854$	0	0
$855$	−6.14637	−0.210201
$856$	41.9529	1.43392
$857$	−10.7743	−0.368045	−0.184022	−	0.982922i	$-0.558912\pi$
$857$	−10.7743	−0.368045	−0.184022	+	0.982922i	$0.558912\pi$
$858$	−0.985632	−0.0336489
$859$	−22.9846	−0.784224	−0.392112	−	0.919917i	$-0.628255\pi$
$859$	−22.9846	−0.784224	−0.392112	+	0.919917i	$0.628255\pi$
$860$	2.74600	0.0936379
$861$	0	0
$862$	−24.2686	−0.826591
$863$	−23.9034	−0.813682	−0.406841	−	0.913499i	$-0.633370\pi$
$863$	−23.9034	−0.813682	−0.406841	+	0.913499i	$0.633370\pi$
$864$	−2.22103	−0.0755610
$865$	6.04808	0.205641
$866$	36.3085	1.23381
$867$	−9.20783	−0.312714
$868$	0	0
$869$	−51.3079	−1.74050
$870$	3.82941	0.129829
$871$	−0.395692	−0.0134075
$872$	−28.1705	−0.953973
$873$	0.921222	0.0311786
$874$	−9.27877	−0.313859
$875$	0	0
$876$	3.06780	0.103651
$877$	20.0265	0.676247	0.338123	−	0.941102i	$-0.390208\pi$
$877$	20.0265	0.676247	0.338123	+	0.941102i	$0.390208\pi$
$878$	−10.4969	−0.354253
$879$	−9.74857	−0.328811
$880$	31.3100	1.05546
$881$	8.33251	0.280730	0.140365	−	0.990100i	$-0.455172\pi$
$881$	8.33251	0.280730	0.140365	+	0.990100i	$0.455172\pi$
$882$	0	0
$883$	49.0846	1.65183	0.825915	−	0.563795i	$-0.190659\pi$
$883$	49.0846	1.65183	0.825915	+	0.563795i	$0.190659\pi$
$884$	0.107497	0.00361551
$885$	−4.49369	−0.151054
$886$	−45.1659	−1.51738
$887$	−3.74487	−0.125740	−0.0628701	−	0.998022i	$-0.520025\pi$
$887$	−3.74487	−0.125740	−0.0628701	+	0.998022i	$0.520025\pi$
$888$	−2.41249	−0.0809579
$889$	0	0
$890$	4.12569	0.138294
$891$	−6.58109	−0.220475
$892$	−6.59772	−0.220908
$893$	−34.3275	−1.14873
$894$	32.1013	1.07363
$895$	−18.6978	−0.624998
$896$	0	0
$897$	0.0967108	0.00322908
$898$	57.2614	1.91084
$899$	−24.3547	−0.812274
$900$	−1.57194	−0.0523980
$901$	−13.7289	−0.457375
$902$	76.2147	2.53767
$903$	0	0
$904$	32.3610	1.07631
$905$	25.2339	0.838805
$906$	6.23146	0.207026
$907$	10.0339	0.333170	0.166585	−	0.986027i	$-0.446726\pi$
$907$	10.0339	0.333170	0.166585	+	0.986027i	$0.446726\pi$
$908$	−0.848453	−0.0281569
$909$	−16.4828	−0.546701
$910$	0	0
$911$	−6.63188	−0.219724	−0.109862	−	0.993947i	$-0.535041\pi$
$911$	−6.63188	−0.219724	−0.109862	+	0.993947i	$0.535041\pi$
$912$	27.7884	0.920165
$913$	−82.1305	−2.71812
$914$	43.0004	1.42233
$915$	−14.7786	−0.488567
$916$	5.74427	0.189796
$917$	0	0
$918$	4.32286	0.142676
$919$	6.24684	0.206064	0.103032	−	0.994678i	$-0.467146\pi$
$919$	6.24684	0.206064	0.103032	+	0.994678i	$0.467146\pi$
$920$	−2.54462	−0.0838936
$921$	−27.7926	−0.915799
$922$	−41.7209	−1.37400
$923$	0.158438	0.00521506
$924$	0	0
$925$	−3.83935	−0.126237
$926$	41.5163	1.36431
$927$	−2.02573	−0.0665339
$928$	−5.35395	−0.175752
$929$	−1.74181	−0.0571471	−0.0285735	−	0.999592i	$-0.509096\pi$
$929$	−1.74181	−0.0571471	−0.0285735	+	0.999592i	$0.509096\pi$
$930$	−16.0500	−0.526299
$931$	0	0
$932$	−0.884010	−0.0289567
$933$	3.96040	0.129658
$934$	−24.8594	−0.813426
$935$	−18.8451	−0.616299
$936$	−0.239899	−0.00784133
$937$	−1.99662	−0.0652267	−0.0326134	−	0.999468i	$-0.510383\pi$
$937$	−1.99662	−0.0652267	−0.0326134	+	0.999468i	$0.510383\pi$
$938$	0	0
$939$	4.81964	0.157283
$940$	2.34021	0.0763293
$941$	33.7616	1.10060	0.550298	−	0.834968i	$-0.314514\pi$
$941$	33.7616	1.10060	0.550298	+	0.834968i	$0.314514\pi$
$942$	−8.73077	−0.284464
$943$	−7.47823	−0.243525
$944$	20.3165	0.661244
$945$	0	0
$946$	−68.5139	−2.22758
$947$	−4.41249	−0.143387	−0.0716933	−	0.997427i	$-0.522840\pi$
$947$	−4.41249	−0.143387	−0.0716933	+	0.997427i	$0.522840\pi$
$948$	3.10440	0.100826
$949$	0.745093	0.0241867
$950$	36.6298	1.18843
$951$	−16.8489	−0.546361
$952$	0	0
$953$	26.9581	0.873258	0.436629	−	0.899642i	$-0.356172\pi$
$953$	26.9581	0.873258	0.436629	+	0.899642i	$0.356172\pi$
$954$	−7.61636	−0.246589
$955$	20.1170	0.650970
$956$	5.75829	0.186236
$957$	−15.8642	−0.512817
$958$	12.5187	0.404461
$959$	0	0
$960$	5.98682	0.193224
$961$	71.0763	2.29278
$962$	0.145657	0.00469616
$963$	−16.9125	−0.544999
$964$	7.09045	0.228368
$965$	−10.7814	−0.347067
$966$	0	0
$967$	−25.8724	−0.832001	−0.416000	−	0.909364i	$-0.636568\pi$
$967$	−25.8724	−0.832001	−0.416000	+	0.909364i	$0.636568\pi$
$968$	−80.1493	−2.57610
$969$	−16.7254	−0.537299
$970$	1.46344	0.0469884
$971$	−16.1998	−0.519877	−0.259938	−	0.965625i	$-0.583702\pi$
$971$	−16.1998	−0.519877	−0.259938	+	0.965625i	$0.583702\pi$
$972$	0.398191	0.0127720
$973$	0	0
$974$	−34.4439	−1.10366
$975$	−0.381785	−0.0122269
$976$	66.8157	2.13872
$977$	−19.2228	−0.614992	−0.307496	−	0.951549i	$-0.599491\pi$
$977$	−19.2228	−0.614992	−0.307496	+	0.951549i	$0.599491\pi$
$978$	27.9993	0.895319
$979$	−17.0916	−0.546250
$980$	0	0
$981$	11.3564	0.362583
$982$	−38.7969	−1.23806
$983$	53.9905	1.72203	0.861014	−	0.508581i	$-0.169830\pi$
$983$	53.9905	1.72203	0.861014	+	0.508581i	$0.169830\pi$
$984$	18.5503	0.591363
$985$	7.52152	0.239655
$986$	10.4206	0.331858
$987$	0	0
$988$	−0.230736	−0.00734069
$989$	6.72262	0.213767
$990$	−10.4547	−0.332271
$991$	19.5181	0.620011	0.310006	−	0.950735i	$-0.399669\pi$
$991$	19.5181	0.620011	0.310006	+	0.950735i	$0.399669\pi$
$992$	22.4397	0.712461
$993$	10.0553	0.319095
$994$	0	0
$995$	−7.55092	−0.239380
$996$	4.96933	0.157459
$997$	−47.2150	−1.49531	−0.747657	−	0.664085i	$-0.768821\pi$
$997$	−47.2150	−1.49531	−0.747657	+	0.664085i	$0.768821\pi$
$998$	34.7927	1.10134
$999$	0.972553	0.0307702

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bh.1.9	yes	10
7.6	odd	2		3381.2.a.bg.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.bg.1.9	✓	10	7.6	odd	2
3381.2.a.bh.1.9	yes	10	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+1.54861 q^{2} +1.00000 q^{3} +0.398191 q^{4} +1.02582 q^{5} +1.54861 q^{6} -2.48058 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.54861 q^{2} +1.00000 q^{3} +0.398191 q^{4} +1.02582 q^{5} +1.54861 q^{6} -2.48058 q^{8} +1.00000 q^{9} +1.58859 q^{10} -6.58109 q^{11} +0.398191 q^{12} +0.0967108 q^{13} +1.02582 q^{15} -4.63783 q^{16} +2.79145 q^{17} +1.54861 q^{18} -5.99168 q^{19} +0.408472 q^{20} -10.1915 q^{22} +1.00000 q^{23} -2.48058 q^{24} -3.94770 q^{25} +0.149767 q^{26} +1.00000 q^{27} +2.41057 q^{29} +1.58859 q^{30} -10.1033 q^{31} -2.22103 q^{32} -6.58109 q^{33} +4.32286 q^{34} +0.398191 q^{36} +0.972553 q^{37} -9.27877 q^{38} +0.0967108 q^{39} -2.54462 q^{40} -7.47823 q^{41} +6.72262 q^{43} -2.62053 q^{44} +1.02582 q^{45} +1.54861 q^{46} +5.72919 q^{47} -4.63783 q^{48} -6.11344 q^{50} +2.79145 q^{51} +0.0385094 q^{52} -4.91819 q^{53} +1.54861 q^{54} -6.75100 q^{55} -5.99168 q^{57} +3.73303 q^{58} -4.38060 q^{59} +0.408472 q^{60} -14.4067 q^{61} -15.6460 q^{62} +5.83615 q^{64} +0.0992076 q^{65} -10.1915 q^{66} -4.09150 q^{67} +1.11153 q^{68} +1.00000 q^{69} +1.63827 q^{71} -2.48058 q^{72} +7.70434 q^{73} +1.50610 q^{74} -3.94770 q^{75} -2.38583 q^{76} +0.149767 q^{78} +7.79626 q^{79} -4.75756 q^{80} +1.00000 q^{81} -11.5809 q^{82} +12.4798 q^{83} +2.86351 q^{85} +10.4107 q^{86} +2.41057 q^{87} +16.3249 q^{88} +2.59708 q^{89} +1.58859 q^{90} +0.398191 q^{92} -10.1033 q^{93} +8.87228 q^{94} -6.14637 q^{95} -2.22103 q^{96} +0.921222 q^{97} -6.58109 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} + 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 + 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 - 12 * q^8 + 10 * q^9	\( 10 q - 4 q^{2} + 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} - 12 q^{8} + 10 q^{9} - 8 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{15} + 4 q^{16} - 12 q^{17} - 4 q^{18} - 26 q^{19} - 8 q^{22} + 10 q^{23} - 12 q^{24} + 14 q^{25} + 12 q^{26} + 10 q^{27} - 16 q^{29} - 8 q^{30} - 20 q^{31} - 8 q^{32} - 2 q^{33} + 4 q^{34} + 8 q^{36} + 8 q^{37} + 8 q^{38} - 16 q^{39} + 12 q^{40} - 22 q^{41} - 4 q^{43} - 24 q^{44} - 4 q^{45} - 4 q^{46} - 6 q^{47} + 4 q^{48} - 48 q^{50} - 12 q^{51} - 24 q^{52} - 30 q^{53} - 4 q^{54} - 48 q^{55} - 26 q^{57} + 24 q^{58} - 42 q^{59} - 14 q^{61} - 40 q^{62} + 8 q^{64} - 44 q^{65} - 8 q^{66} - 8 q^{68} + 10 q^{69} + 8 q^{71} - 12 q^{72} - 24 q^{73} + 8 q^{74} + 14 q^{75} - 32 q^{76} + 12 q^{78} + 32 q^{79} - 28 q^{80} + 10 q^{81} + 64 q^{82} - 28 q^{83} - 4 q^{85} - 4 q^{86} - 16 q^{87} + 20 q^{88} - 8 q^{90} + 8 q^{92} - 20 q^{93} - 8 q^{94} - 16 q^{95} - 8 q^{96} + 12 q^{97} - 2 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 + 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 - 12 * q^8 + 10 * q^9 - 8 * q^10 - 2 * q^11 + 8 * q^12 - 16 * q^13 - 4 * q^15 + 4 * q^16 - 12 * q^17 - 4 * q^18 - 26 * q^19 - 8 * q^22 + 10 * q^23 - 12 * q^24 + 14 * q^25 + 12 * q^26 + 10 * q^27 - 16 * q^29 - 8 * q^30 - 20 * q^31 - 8 * q^32 - 2 * q^33 + 4 * q^34 + 8 * q^36 + 8 * q^37 + 8 * q^38 - 16 * q^39 + 12 * q^40 - 22 * q^41 - 4 * q^43 - 24 * q^44 - 4 * q^45 - 4 * q^46 - 6 * q^47 + 4 * q^48 - 48 * q^50 - 12 * q^51 - 24 * q^52 - 30 * q^53 - 4 * q^54 - 48 * q^55 - 26 * q^57 + 24 * q^58 - 42 * q^59 - 14 * q^61 - 40 * q^62 + 8 * q^64 - 44 * q^65 - 8 * q^66 - 8 * q^68 + 10 * q^69 + 8 * q^71 - 12 * q^72 - 24 * q^73 + 8 * q^74 + 14 * q^75 - 32 * q^76 + 12 * q^78 + 32 * q^79 - 28 * q^80 + 10 * q^81 + 64 * q^82 - 28 * q^83 - 4 * q^85 - 4 * q^86 - 16 * q^87 + 20 * q^88 - 8 * q^90 + 8 * q^92 - 20 * q^93 - 8 * q^94 - 16 * q^95 - 8 * q^96 + 12 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more