LMFDB - Embedded newform 3381.2.a.bl.1.6

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:	$0$
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} + 108x^{3} - 33x^{2} - 36x + 14 $ x^10 - 4x^9 - 6x^8 + 36x^7 + x^6 - 100x^5 + 26x^4 + 108x^3 - 33x^2 - 36x + 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.533756$ 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)

$f(q)$	$=$	$q+0.533756 q^{2} +1.00000 q^{3} -1.71510 q^{4} -1.09368 q^{5} +0.533756 q^{6} -1.98296 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.533756 q^{2} +1.00000 q^{3} -1.71510 q^{4} -1.09368 q^{5} +0.533756 q^{6} -1.98296 q^{8} +1.00000 q^{9} -0.583758 q^{10} -3.05750 q^{11} -1.71510 q^{12} -4.92294 q^{13} -1.09368 q^{15} +2.37179 q^{16} +0.748606 q^{17} +0.533756 q^{18} +1.24069 q^{19} +1.87577 q^{20} -1.63196 q^{22} -1.00000 q^{23} -1.98296 q^{24} -3.80387 q^{25} -2.62765 q^{26} +1.00000 q^{27} +4.90399 q^{29} -0.583758 q^{30} +8.55439 q^{31} +5.23188 q^{32} -3.05750 q^{33} +0.399573 q^{34} -1.71510 q^{36} +5.89502 q^{37} +0.662226 q^{38} -4.92294 q^{39} +2.16872 q^{40} -3.90324 q^{41} -2.45996 q^{43} +5.24392 q^{44} -1.09368 q^{45} -0.533756 q^{46} +5.39151 q^{47} +2.37179 q^{48} -2.03034 q^{50} +0.748606 q^{51} +8.44336 q^{52} +11.0587 q^{53} +0.533756 q^{54} +3.34392 q^{55} +1.24069 q^{57} +2.61754 q^{58} +4.12244 q^{59} +1.87577 q^{60} -8.22736 q^{61} +4.56596 q^{62} -1.95104 q^{64} +5.38412 q^{65} -1.63196 q^{66} +3.21634 q^{67} -1.28394 q^{68} -1.00000 q^{69} -5.13467 q^{71} -1.98296 q^{72} +15.3666 q^{73} +3.14651 q^{74} -3.80387 q^{75} -2.12791 q^{76} -2.62765 q^{78} -8.94313 q^{79} -2.59398 q^{80} +1.00000 q^{81} -2.08338 q^{82} +2.24140 q^{83} -0.818734 q^{85} -1.31302 q^{86} +4.90399 q^{87} +6.06289 q^{88} +13.5577 q^{89} -0.583758 q^{90} +1.71510 q^{92} +8.55439 q^{93} +2.87775 q^{94} -1.35692 q^{95} +5.23188 q^{96} +6.67726 q^{97} -3.05750 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 4 q^{15} + 4 q^{16} + 12 q^{17} + 4 q^{18} + 26 q^{19} + 24 q^{20} - 8 q^{22} - 10 q^{23} + 12 q^{24} - 2 q^{25} + 4 q^{26} + 10 q^{27} + 16 q^{29} + 8 q^{30} + 12 q^{31} + 8 q^{32} + 2 q^{33} + 28 q^{34} + 8 q^{36} - 8 q^{37} + 32 q^{38} + 4 q^{40} + 10 q^{41} - 4 q^{43} - 16 q^{44} + 4 q^{45} - 4 q^{46} + 2 q^{47} + 4 q^{48} - 8 q^{50} + 12 q^{51} + 24 q^{52} + 14 q^{53} + 4 q^{54} + 16 q^{55} + 26 q^{57} - 8 q^{58} + 38 q^{59} + 24 q^{60} + 14 q^{61} - 8 q^{62} + 8 q^{64} + 12 q^{65} - 8 q^{66} + 8 q^{68} - 10 q^{69} + 24 q^{71} + 12 q^{72} + 8 q^{73} - 8 q^{74} - 2 q^{75} + 64 q^{76} + 4 q^{78} - 16 q^{79} + 28 q^{80} + 10 q^{81} - 40 q^{82} + 28 q^{83} - 4 q^{85} + 20 q^{86} + 16 q^{87} - 68 q^{88} + 32 q^{89} + 8 q^{90} - 8 q^{92} + 12 q^{93} + 56 q^{94} + 8 q^{95} + 8 q^{96} + 4 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 + 4 * q^15 + 4 * q^16 + 12 * q^17 + 4 * q^18 + 26 * q^19 + 24 * q^20 - 8 * q^22 - 10 * q^23 + 12 * q^24 - 2 * q^25 + 4 * q^26 + 10 * q^27 + 16 * q^29 + 8 * q^30 + 12 * q^31 + 8 * q^32 + 2 * q^33 + 28 * q^34 + 8 * q^36 - 8 * q^37 + 32 * q^38 + 4 * q^40 + 10 * q^41 - 4 * q^43 - 16 * q^44 + 4 * q^45 - 4 * q^46 + 2 * q^47 + 4 * q^48 - 8 * q^50 + 12 * q^51 + 24 * q^52 + 14 * q^53 + 4 * q^54 + 16 * q^55 + 26 * q^57 - 8 * q^58 + 38 * q^59 + 24 * q^60 + 14 * q^61 - 8 * q^62 + 8 * q^64 + 12 * q^65 - 8 * q^66 + 8 * q^68 - 10 * q^69 + 24 * q^71 + 12 * q^72 + 8 * q^73 - 8 * q^74 - 2 * q^75 + 64 * q^76 + 4 * q^78 - 16 * q^79 + 28 * q^80 + 10 * q^81 - 40 * q^82 + 28 * q^83 - 4 * q^85 + 20 * q^86 + 16 * q^87 - 68 * q^88 + 32 * q^89 + 8 * q^90 - 8 * q^92 + 12 * q^93 + 56 * q^94 + 8 * q^95 + 8 * q^96 + 4 * 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 $

$2$	0.533756	0.377423	0.188711	−	0.982033i	$-0.439569\pi$
$2$	0.533756	0.377423	0.188711	+	0.982033i	$0.439569\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.71510	−0.857552
$5$	−1.09368	−0.489108	−0.244554	−	0.969636i	$-0.578642\pi$
$5$	−1.09368	−0.489108	−0.244554	+	0.969636i	$0.578642\pi$
$6$	0.533756	0.217905
$7$	0	0
$7$	0	0
$8$	−1.98296	−0.701082
$9$	1.00000	0.333333
$10$	−0.583758	−0.184600
$11$	−3.05750	−0.921870	−0.460935	−	0.887434i	$-0.652486\pi$
$11$	−3.05750	−0.921870	−0.460935	+	0.887434i	$0.652486\pi$
$12$	−1.71510	−0.495108
$13$	−4.92294	−1.36538	−0.682689	−	0.730709i	$-0.739190\pi$
$13$	−4.92294	−1.36538	−0.682689	+	0.730709i	$0.739190\pi$
$14$	0	0
$15$	−1.09368	−0.282387
$16$	2.37179	0.592948
$17$	0.748606	0.181564	0.0907818	−	0.995871i	$-0.471063\pi$
$17$	0.748606	0.181564	0.0907818	+	0.995871i	$0.471063\pi$
$18$	0.533756	0.125808
$19$	1.24069	0.284634	0.142317	−	0.989821i	$-0.454545\pi$
$19$	1.24069	0.284634	0.142317	+	0.989821i	$0.454545\pi$
$20$	1.87577	0.419435
$21$	0	0
$22$	−1.63196	−0.347934
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.98296	−0.404770
$25$	−3.80387	−0.760774
$26$	−2.62765	−0.515325
$27$	1.00000	0.192450
$28$	0	0
$29$	4.90399	0.910649	0.455324	−	0.890326i	$-0.349523\pi$
$29$	4.90399	0.910649	0.455324	+	0.890326i	$0.349523\pi$
$30$	−0.583758	−0.106579
$31$	8.55439	1.53641	0.768207	−	0.640201i	$-0.221149\pi$
$31$	8.55439	1.53641	0.768207	+	0.640201i	$0.221149\pi$
$32$	5.23188	0.924874
$33$	−3.05750	−0.532242
$34$	0.399573	0.0685262
$35$	0	0
$36$	−1.71510	−0.285851
$37$	5.89502	0.969136	0.484568	−	0.874754i	$-0.338977\pi$
$37$	5.89502	0.969136	0.484568	+	0.874754i	$0.338977\pi$
$38$	0.662226	0.107427
$39$	−4.92294	−0.788302
$40$	2.16872	0.342905
$41$	−3.90324	−0.609584	−0.304792	−	0.952419i	$-0.598587\pi$
$41$	−3.90324	−0.609584	−0.304792	+	0.952419i	$0.598587\pi$
$42$	0	0
$43$	−2.45996	−0.375140	−0.187570	−	0.982251i	$-0.560061\pi$
$43$	−2.45996	−0.375140	−0.187570	+	0.982251i	$0.560061\pi$
$44$	5.24392	0.790551
$45$	−1.09368	−0.163036
$46$	−0.533756	−0.0786981
$47$	5.39151	0.786433	0.393216	−	0.919446i	$-0.371362\pi$
$47$	5.39151	0.786433	0.393216	+	0.919446i	$0.371362\pi$
$48$	2.37179	0.342339
$49$	0	0
$50$	−2.03034	−0.287133
$51$	0.748606	0.104826
$52$	8.44336	1.17088
$53$	11.0587	1.51902	0.759512	−	0.650493i	$-0.225438\pi$
$53$	11.0587	1.51902	0.759512	+	0.650493i	$0.225438\pi$
$54$	0.533756	0.0726350
$55$	3.34392	0.450894
$56$	0	0
$57$	1.24069	0.164333
$58$	2.61754	0.343700
$59$	4.12244	0.536696	0.268348	−	0.963322i	$-0.413522\pi$
$59$	4.12244	0.536696	0.268348	+	0.963322i	$0.413522\pi$
$60$	1.87577	0.242161
$61$	−8.22736	−1.05341	−0.526703	−	0.850049i	$-0.676572\pi$
$61$	−8.22736	−1.05341	−0.526703	+	0.850049i	$0.676572\pi$
$62$	4.56596	0.579877
$63$	0	0
$64$	−1.95104	−0.243879
$65$	5.38412	0.667817
$66$	−1.63196	−0.200880
$67$	3.21634	0.392938	0.196469	−	0.980510i	$-0.437052\pi$
$67$	3.21634	0.392938	0.196469	+	0.980510i	$0.437052\pi$
$68$	−1.28394	−0.155700
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−5.13467	−0.609374	−0.304687	−	0.952453i	$-0.598552\pi$
$71$	−5.13467	−0.609374	−0.304687	+	0.952453i	$0.598552\pi$
$72$	−1.98296	−0.233694
$73$	15.3666	1.79852	0.899262	−	0.437409i	$-0.144104\pi$
$73$	15.3666	1.79852	0.899262	+	0.437409i	$0.144104\pi$
$74$	3.14651	0.365774
$75$	−3.80387	−0.439233
$76$	−2.12791	−0.244088
$77$	0	0
$78$	−2.62765	−0.297523
$79$	−8.94313	−1.00618	−0.503090	−	0.864234i	$-0.667804\pi$
$79$	−8.94313	−1.00618	−0.503090	+	0.864234i	$0.667804\pi$
$80$	−2.59398	−0.290015
$81$	1.00000	0.111111
$82$	−2.08338	−0.230071
$83$	2.24140	0.246026	0.123013	−	0.992405i	$-0.460744\pi$
$83$	2.24140	0.246026	0.123013	+	0.992405i	$0.460744\pi$
$84$	0	0
$85$	−0.818734	−0.0888041
$86$	−1.31302	−0.141586
$87$	4.90399	0.525763
$88$	6.06289	0.646306
$89$	13.5577	1.43711	0.718555	−	0.695470i	$-0.244804\pi$
$89$	13.5577	1.43711	0.718555	+	0.695470i	$0.244804\pi$
$90$	−0.583758	−0.0615335
$91$	0	0
$92$	1.71510	0.178812
$93$	8.55439	0.887049
$94$	2.87775	0.296818
$95$	−1.35692	−0.139217
$96$	5.23188	0.533976
$97$	6.67726	0.677973	0.338986	−	0.940791i	$-0.389916\pi$
$97$	6.67726	0.677973	0.338986	+	0.940791i	$0.389916\pi$
$98$	0	0
$99$	−3.05750	−0.307290
$100$	6.52403	0.652403
$101$	−6.39228	−0.636055	−0.318028	−	0.948081i	$-0.603020\pi$
$101$	−6.39228	−0.636055	−0.318028	+	0.948081i	$0.603020\pi$
$102$	0.399573	0.0395636
$103$	13.0815	1.28896	0.644481	−	0.764621i	$-0.277074\pi$
$103$	13.0815	1.28896	0.644481	+	0.764621i	$0.277074\pi$
$104$	9.76200	0.957243
$105$	0	0
$106$	5.90263	0.573314
$107$	14.5852	1.41000	0.705002	−	0.709205i	$-0.250946\pi$
$107$	14.5852	1.41000	0.705002	+	0.709205i	$0.250946\pi$
$108$	−1.71510	−0.165036
$109$	2.60203	0.249229	0.124615	−	0.992205i	$-0.460231\pi$
$109$	2.60203	0.249229	0.124615	+	0.992205i	$0.460231\pi$
$110$	1.78484	0.170177
$111$	5.89502	0.559531
$112$	0	0
$113$	−15.8691	−1.49284	−0.746418	−	0.665477i	$-0.768228\pi$
$113$	−15.8691	−1.49284	−0.746418	+	0.665477i	$0.768228\pi$
$114$	0.662226	0.0620231
$115$	1.09368	0.101986
$116$	−8.41086	−0.780929
$117$	−4.92294	−0.455126
$118$	2.20038	0.202561
$119$	0	0
$120$	2.16872	0.197976
$121$	−1.65172	−0.150156
$122$	−4.39141	−0.397579
$123$	−3.90324	−0.351944
$124$	−14.6717	−1.31756
$125$	9.62860	0.861208
$126$	0	0
$127$	−14.4699	−1.28399	−0.641997	−	0.766707i	$-0.721894\pi$
$127$	−14.4699	−1.28399	−0.641997	+	0.766707i	$0.721894\pi$
$128$	−11.5051	−1.01692
$129$	−2.45996	−0.216587
$130$	2.87380	0.252049
$131$	9.50326	0.830303	0.415152	−	0.909752i	$-0.363728\pi$
$131$	9.50326	0.830303	0.415152	+	0.909752i	$0.363728\pi$
$132$	5.24392	0.456425
$133$	0	0
$134$	1.71674	0.148304
$135$	−1.09368	−0.0941288
$136$	−1.48445	−0.127291
$137$	−9.48454	−0.810319	−0.405160	−	0.914246i	$-0.632784\pi$
$137$	−9.48454	−0.810319	−0.405160	+	0.914246i	$0.632784\pi$
$138$	−0.533756	−0.0454363
$139$	−6.85289	−0.581254	−0.290627	−	0.956836i	$-0.593864\pi$
$139$	−6.85289	−0.581254	−0.290627	+	0.956836i	$0.593864\pi$
$140$	0	0
$141$	5.39151	0.454047
$142$	−2.74066	−0.229991
$143$	15.0519	1.25870
$144$	2.37179	0.197649
$145$	−5.36339	−0.445406
$146$	8.20202	0.678804
$147$	0	0
$148$	−10.1106	−0.831085
$149$	8.82249	0.722766	0.361383	−	0.932417i	$-0.382305\pi$
$149$	8.82249	0.722766	0.361383	+	0.932417i	$0.382305\pi$
$150$	−2.03034	−0.165776
$151$	−3.11804	−0.253742	−0.126871	−	0.991919i	$-0.540493\pi$
$151$	−3.11804	−0.253742	−0.126871	+	0.991919i	$0.540493\pi$
$152$	−2.46024	−0.199552
$153$	0.748606	0.0605212
$154$	0	0
$155$	−9.35575	−0.751472
$156$	8.44336	0.676010
$157$	15.8909	1.26823	0.634115	−	0.773239i	$-0.281365\pi$
$157$	15.8909	1.26823	0.634115	+	0.773239i	$0.281365\pi$
$158$	−4.77345	−0.379755
$159$	11.0587	0.877009
$160$	−5.72199	−0.452363
$161$	0	0
$162$	0.533756	0.0419358
$163$	−12.2732	−0.961308	−0.480654	−	0.876910i	$-0.659601\pi$
$163$	−12.2732	−0.961308	−0.480654	+	0.876910i	$0.659601\pi$
$164$	6.69447	0.522750
$165$	3.34392	0.260324
$166$	1.19636	0.0928557
$167$	22.0861	1.70907	0.854536	−	0.519393i	$-0.173842\pi$
$167$	22.0861	1.70907	0.854536	+	0.519393i	$0.173842\pi$
$168$	0	0
$169$	11.2354	0.864258
$170$	−0.437004	−0.0335167
$171$	1.24069	0.0948779
$172$	4.21908	0.321702
$173$	5.38783	0.409629	0.204815	−	0.978801i	$-0.434341\pi$
$173$	5.38783	0.409629	0.204815	+	0.978801i	$0.434341\pi$
$174$	2.61754	0.198435
$175$	0	0
$176$	−7.25174	−0.546621
$177$	4.12244	0.309862
$178$	7.23649	0.542398
$179$	10.0945	0.754496	0.377248	−	0.926112i	$-0.376870\pi$
$179$	10.0945	0.754496	0.377248	+	0.926112i	$0.376870\pi$
$180$	1.87577	0.139812
$181$	−2.09721	−0.155884	−0.0779421	−	0.996958i	$-0.524835\pi$
$181$	−2.09721	−0.155884	−0.0779421	+	0.996958i	$0.524835\pi$
$182$	0	0
$183$	−8.22736	−0.608184
$184$	1.98296	0.146186
$185$	−6.44726	−0.474012
$186$	4.56596	0.334792
$187$	−2.28886	−0.167378
$188$	−9.24700	−0.674407
$189$	0	0
$190$	−0.724262	−0.0525435
$191$	−14.5337	−1.05162	−0.525811	−	0.850601i	$-0.676238\pi$
$191$	−14.5337	−1.05162	−0.525811	+	0.850601i	$0.676238\pi$
$192$	−1.95104	−0.140804
$193$	15.2613	1.09854	0.549268	−	0.835646i	$-0.314907\pi$
$193$	15.2613	1.09854	0.549268	+	0.835646i	$0.314907\pi$
$194$	3.56403	0.255882
$195$	5.38412	0.385565
$196$	0	0
$197$	−15.7273	−1.12052	−0.560262	−	0.828315i	$-0.689300\pi$
$197$	−15.7273	−1.12052	−0.560262	+	0.828315i	$0.689300\pi$
$198$	−1.63196	−0.115978
$199$	−7.27105	−0.515431	−0.257716	−	0.966221i	$-0.582970\pi$
$199$	−7.27105	−0.515431	−0.257716	+	0.966221i	$0.582970\pi$
$200$	7.54292	0.533365
$201$	3.21634	0.226863
$202$	−3.41192	−0.240062
$203$	0	0
$204$	−1.28394	−0.0898935
$205$	4.26889	0.298153
$206$	6.98235	0.486483
$207$	−1.00000	−0.0695048
$208$	−11.6762	−0.809598
$209$	−3.79340	−0.262395
$210$	0	0
$211$	8.23718	0.567071	0.283535	−	0.958962i	$-0.408493\pi$
$211$	8.23718	0.567071	0.283535	+	0.958962i	$0.408493\pi$
$212$	−18.9668	−1.30264
$213$	−5.13467	−0.351822
$214$	7.78494	0.532168
$215$	2.69040	0.183484
$216$	−1.98296	−0.134923
$217$	0	0
$218$	1.38885	0.0940648
$219$	15.3666	1.03838
$220$	−5.73517	−0.386665
$221$	−3.68534	−0.247903
$222$	3.14651	0.211180
$223$	−19.6064	−1.31294	−0.656470	−	0.754352i	$-0.727951\pi$
$223$	−19.6064	−1.31294	−0.656470	+	0.754352i	$0.727951\pi$
$224$	0	0
$225$	−3.80387	−0.253591
$226$	−8.47021	−0.563430
$227$	−9.52636	−0.632287	−0.316143	−	0.948711i	$-0.602388\pi$
$227$	−9.52636	−0.632287	−0.316143	+	0.948711i	$0.602388\pi$
$228$	−2.12791	−0.140924
$229$	27.2245	1.79905	0.899524	−	0.436871i	$-0.143913\pi$
$229$	27.2245	1.79905	0.899524	+	0.436871i	$0.143913\pi$
$230$	0.583758	0.0384918
$231$	0	0
$232$	−9.72443	−0.638440
$233$	19.5070	1.27794	0.638971	−	0.769230i	$-0.279360\pi$
$233$	19.5070	1.27794	0.638971	+	0.769230i	$0.279360\pi$
$234$	−2.62765	−0.171775
$235$	−5.89658	−0.384650
$236$	−7.07042	−0.460245
$237$	−8.94313	−0.580919
$238$	0	0
$239$	11.3334	0.733096	0.366548	−	0.930399i	$-0.380540\pi$
$239$	11.3334	0.733096	0.366548	+	0.930399i	$0.380540\pi$
$240$	−2.59398	−0.167440
$241$	13.6233	0.877554	0.438777	−	0.898596i	$-0.355412\pi$
$241$	13.6233	0.877554	0.438777	+	0.898596i	$0.355412\pi$
$242$	−0.881615	−0.0566724
$243$	1.00000	0.0641500
$244$	14.1108	0.903350
$245$	0	0
$246$	−2.08338	−0.132832
$247$	−6.10784	−0.388633
$248$	−16.9630	−1.07715
$249$	2.24140	0.142043
$250$	5.13932	0.325039
$251$	−6.97247	−0.440098	−0.220049	−	0.975489i	$-0.570622\pi$
$251$	−6.97247	−0.440098	−0.220049	+	0.975489i	$0.570622\pi$
$252$	0	0
$253$	3.05750	0.192223
$254$	−7.72339	−0.484608
$255$	−0.818734	−0.0512711
$256$	−2.23887	−0.139929
$257$	21.1579	1.31979	0.659896	−	0.751357i	$-0.270600\pi$
$257$	21.1579	1.31979	0.659896	+	0.751357i	$0.270600\pi$
$258$	−1.31302	−0.0817449
$259$	0	0
$260$	−9.23432	−0.572688
$261$	4.90399	0.303550
$262$	5.07242	0.313375
$263$	6.53990	0.403268	0.201634	−	0.979461i	$-0.435375\pi$
$263$	6.53990	0.403268	0.201634	+	0.979461i	$0.435375\pi$
$264$	6.06289	0.373145
$265$	−12.0946	−0.742967
$266$	0	0
$267$	13.5577	0.829716
$268$	−5.51635	−0.336965
$269$	2.46163	0.150089	0.0750443	−	0.997180i	$-0.476090\pi$
$269$	2.46163	0.150089	0.0750443	+	0.997180i	$0.476090\pi$
$270$	−0.583758	−0.0355264
$271$	11.3061	0.686796	0.343398	−	0.939190i	$-0.388422\pi$
$271$	11.3061	0.686796	0.343398	+	0.939190i	$0.388422\pi$
$272$	1.77554	0.107658
$273$	0	0
$274$	−5.06243	−0.305833
$275$	11.6303	0.701334
$276$	1.71510	0.103237
$277$	5.66924	0.340632	0.170316	−	0.985390i	$-0.445521\pi$
$277$	5.66924	0.340632	0.170316	+	0.985390i	$0.445521\pi$
$278$	−3.65777	−0.219379
$279$	8.55439	0.512138
$280$	0	0
$281$	2.68879	0.160400	0.0802000	−	0.996779i	$-0.474444\pi$
$281$	2.68879	0.160400	0.0802000	+	0.996779i	$0.474444\pi$
$282$	2.87775	0.171368
$283$	20.2354	1.20287	0.601434	−	0.798923i	$-0.294596\pi$
$283$	20.2354	1.20287	0.601434	+	0.798923i	$0.294596\pi$
$284$	8.80650	0.522570
$285$	−1.35692	−0.0803767
$286$	8.03403	0.475062
$287$	0	0
$288$	5.23188	0.308291
$289$	−16.4396	−0.967035
$290$	−2.86274	−0.168106
$291$	6.67726	0.391428
$292$	−26.3553	−1.54233
$293$	0.701461	0.0409798	0.0204899	−	0.999790i	$-0.493477\pi$
$293$	0.701461	0.0409798	0.0204899	+	0.999790i	$0.493477\pi$
$294$	0	0
$295$	−4.50863	−0.262502
$296$	−11.6896	−0.679444
$297$	−3.05750	−0.177414
$298$	4.70906	0.272788
$299$	4.92294	0.284701
$300$	6.52403	0.376665
$301$	0	0
$302$	−1.66427	−0.0957680
$303$	−6.39228	−0.367227
$304$	2.94266	0.168773
$305$	8.99809	0.515229
$306$	0.399573	0.0228421
$307$	−9.58115	−0.546825	−0.273412	−	0.961897i	$-0.588152\pi$
$307$	−9.58115	−0.546825	−0.273412	+	0.961897i	$0.588152\pi$
$308$	0	0
$309$	13.0815	0.744182
$310$	−4.99369	−0.283623
$311$	7.67217	0.435049	0.217524	−	0.976055i	$-0.430202\pi$
$311$	7.67217	0.435049	0.217524	+	0.976055i	$0.430202\pi$
$312$	9.76200	0.552664
$313$	−18.6546	−1.05442	−0.527209	−	0.849736i	$-0.676762\pi$
$313$	−18.6546	−1.05442	−0.527209	+	0.849736i	$0.676762\pi$
$314$	8.48185	0.478659
$315$	0	0
$316$	15.3384	0.862852
$317$	−13.2674	−0.745173	−0.372587	−	0.927997i	$-0.621529\pi$
$317$	−13.2674	−0.745173	−0.372587	+	0.927997i	$0.621529\pi$
$318$	5.90263	0.331003
$319$	−14.9939	−0.839500
$320$	2.13381	0.119283
$321$	14.5852	0.814067
$322$	0	0
$323$	0.928787	0.0516791
$324$	−1.71510	−0.0952836
$325$	18.7262	1.03874
$326$	−6.55087	−0.362819
$327$	2.60203	0.143893
$328$	7.73998	0.427369
$329$	0	0
$330$	1.78484	0.0982520
$331$	17.5778	0.966162	0.483081	−	0.875576i	$-0.339518\pi$
$331$	17.5778	0.966162	0.483081	+	0.875576i	$0.339518\pi$
$332$	−3.84424	−0.210980
$333$	5.89502	0.323045
$334$	11.7886	0.645042
$335$	−3.51764	−0.192189
$336$	0	0
$337$	−29.2930	−1.59569	−0.797846	−	0.602862i	$-0.794027\pi$
$337$	−29.2930	−1.59569	−0.797846	+	0.602862i	$0.794027\pi$
$338$	5.99694	0.326191
$339$	−15.8691	−0.861889
$340$	1.40421	0.0761542
$341$	−26.1550	−1.41637
$342$	0.662226	0.0358091
$343$	0	0
$344$	4.87799	0.263004
$345$	1.09368	0.0588817
$346$	2.87579	0.154603
$347$	19.4811	1.04580	0.522900	−	0.852394i	$-0.324850\pi$
$347$	19.4811	1.04580	0.522900	+	0.852394i	$0.324850\pi$
$348$	−8.41086	−0.450870
$349$	35.9545	1.92460	0.962299	−	0.271993i	$-0.0876829\pi$
$349$	35.9545	1.92460	0.962299	+	0.271993i	$0.0876829\pi$
$350$	0	0
$351$	−4.92294	−0.262767
$352$	−15.9964	−0.852613
$353$	−2.20411	−0.117313	−0.0586565	−	0.998278i	$-0.518682\pi$
$353$	−2.20411	−0.117313	−0.0586565	+	0.998278i	$0.518682\pi$
$354$	2.20038	0.116949
$355$	5.61568	0.298049
$356$	−23.2528	−1.23240
$357$	0	0
$358$	5.38799	0.284764
$359$	26.8308	1.41608	0.708038	−	0.706174i	$-0.249580\pi$
$359$	26.8308	1.41608	0.708038	+	0.706174i	$0.249580\pi$
$360$	2.16872	0.114302
$361$	−17.4607	−0.918984
$362$	−1.11940	−0.0588342
$363$	−1.65172	−0.0866927
$364$	0	0
$365$	−16.8061	−0.879673
$366$	−4.39141	−0.229542
$367$	3.35623	0.175194	0.0875969	−	0.996156i	$-0.472081\pi$
$367$	3.35623	0.175194	0.0875969	+	0.996156i	$0.472081\pi$
$368$	−2.37179	−0.123638
$369$	−3.90324	−0.203195
$370$	−3.44126	−0.178903
$371$	0	0
$372$	−14.6717	−0.760691
$373$	−4.54054	−0.235100	−0.117550	−	0.993067i	$-0.537504\pi$
$373$	−4.54054	−0.235100	−0.117550	+	0.993067i	$0.537504\pi$
$374$	−1.22169	−0.0631722
$375$	9.62860	0.497219
$376$	−10.6912	−0.551354
$377$	−24.1421	−1.24338
$378$	0	0
$379$	−29.3369	−1.50693	−0.753467	−	0.657486i	$-0.771620\pi$
$379$	−29.3369	−1.50693	−0.753467	+	0.657486i	$0.771620\pi$
$380$	2.32725	0.119385
$381$	−14.4699	−0.741314
$382$	−7.75746	−0.396906
$383$	−8.48309	−0.433466	−0.216733	−	0.976231i	$-0.569540\pi$
$383$	−8.48309	−0.433466	−0.216733	+	0.976231i	$0.569540\pi$
$384$	−11.5051	−0.587119
$385$	0	0
$386$	8.14584	0.414612
$387$	−2.45996	−0.125047
$388$	−11.4522	−0.581397
$389$	−34.1310	−1.73051	−0.865256	−	0.501330i	$-0.832844\pi$
$389$	−34.1310	−1.73051	−0.865256	+	0.501330i	$0.832844\pi$
$390$	2.87380	0.145521
$391$	−0.748606	−0.0378586
$392$	0	0
$393$	9.50326	0.479376
$394$	−8.39455	−0.422911
$395$	9.78091	0.492131
$396$	5.24392	0.263517
$397$	−19.7795	−0.992705	−0.496352	−	0.868121i	$-0.665328\pi$
$397$	−19.7795	−0.992705	−0.496352	+	0.868121i	$0.665328\pi$
$398$	−3.88097	−0.194535
$399$	0	0
$400$	−9.02198	−0.451099
$401$	22.1823	1.10773	0.553866	−	0.832606i	$-0.313152\pi$
$401$	22.1823	1.10773	0.553866	+	0.832606i	$0.313152\pi$
$402$	1.71674	0.0856232
$403$	−42.1128	−2.09779
$404$	10.9634	0.545451
$405$	−1.09368	−0.0543453
$406$	0	0
$407$	−18.0240	−0.893417
$408$	−1.48445	−0.0734915
$409$	−2.92732	−0.144747	−0.0723734	−	0.997378i	$-0.523057\pi$
$409$	−2.92732	−0.144747	−0.0723734	+	0.997378i	$0.523057\pi$
$410$	2.27855	0.112530
$411$	−9.48454	−0.467838
$412$	−22.4362	−1.10535
$413$	0	0
$414$	−0.533756	−0.0262327
$415$	−2.45137	−0.120333
$416$	−25.7562	−1.26280
$417$	−6.85289	−0.335587
$418$	−2.02475	−0.0990339
$419$	3.45118	0.168601	0.0843006	−	0.996440i	$-0.473134\pi$
$419$	3.45118	0.168601	0.0843006	+	0.996440i	$0.473134\pi$
$420$	0	0
$421$	−10.4259	−0.508125	−0.254063	−	0.967188i	$-0.581767\pi$
$421$	−10.4259	−0.508125	−0.254063	+	0.967188i	$0.581767\pi$
$422$	4.39665	0.214025
$423$	5.39151	0.262144
$424$	−21.9289	−1.06496
$425$	−2.84760	−0.138129
$426$	−2.74066	−0.132786
$427$	0	0
$428$	−25.0151	−1.20915
$429$	15.0519	0.726711
$430$	1.43602	0.0692509
$431$	19.8226	0.954822	0.477411	−	0.878680i	$-0.341575\pi$
$431$	19.8226	0.954822	0.477411	+	0.878680i	$0.341575\pi$
$432$	2.37179	0.114113
$433$	−10.6154	−0.510143	−0.255071	−	0.966922i	$-0.582099\pi$
$433$	−10.6154	−0.510143	−0.255071	+	0.966922i	$0.582099\pi$
$434$	0	0
$435$	−5.36339	−0.257155
$436$	−4.46276	−0.213727
$437$	−1.24069	−0.0593502
$438$	8.20202	0.391908
$439$	−14.4312	−0.688764	−0.344382	−	0.938830i	$-0.611911\pi$
$439$	−14.4312	−0.688764	−0.344382	+	0.938830i	$0.611911\pi$
$440$	−6.63085	−0.316114
$441$	0	0
$442$	−1.96707	−0.0935642
$443$	−15.8451	−0.752823	−0.376411	−	0.926453i	$-0.622842\pi$
$443$	−15.8451	−0.752823	−0.376411	+	0.926453i	$0.622842\pi$
$444$	−10.1106	−0.479827
$445$	−14.8277	−0.702902
$446$	−10.4650	−0.495533
$447$	8.82249	0.417289
$448$	0	0
$449$	14.1775	0.669078	0.334539	−	0.942382i	$-0.391419\pi$
$449$	14.1775	0.669078	0.334539	+	0.942382i	$0.391419\pi$
$450$	−2.03034	−0.0957110
$451$	11.9342	0.561957
$452$	27.2171	1.28018
$453$	−3.11804	−0.146498
$454$	−5.08475	−0.238639
$455$	0	0
$456$	−2.46024	−0.115211
$457$	−10.1315	−0.473933	−0.236967	−	0.971518i	$-0.576153\pi$
$457$	−10.1315	−0.473933	−0.236967	+	0.971518i	$0.576153\pi$
$458$	14.5313	0.679001
$459$	0.748606	0.0349419
$460$	−1.87577	−0.0874583
$461$	−33.5353	−1.56189	−0.780947	−	0.624597i	$-0.785263\pi$
$461$	−33.5353	−1.56189	−0.780947	+	0.624597i	$0.785263\pi$
$462$	0	0
$463$	27.5372	1.27976	0.639881	−	0.768474i	$-0.278983\pi$
$463$	27.5372	1.27976	0.639881	+	0.768474i	$0.278983\pi$
$464$	11.6313	0.539967
$465$	−9.35575	−0.433863
$466$	10.4120	0.482325
$467$	2.54072	0.117571	0.0587854	−	0.998271i	$-0.481277\pi$
$467$	2.54072	0.117571	0.0587854	+	0.998271i	$0.481277\pi$
$468$	8.44336	0.390294
$469$	0	0
$470$	−3.14734	−0.145176
$471$	15.8909	0.732213
$472$	−8.17464	−0.376268
$473$	7.52131	0.345830
$474$	−4.77345	−0.219252
$475$	−4.71942	−0.216542
$476$	0	0
$477$	11.0587	0.506341
$478$	6.04927	0.276687
$479$	−33.9135	−1.54955	−0.774774	−	0.632238i	$-0.782136\pi$
$479$	−33.9135	−1.54955	−0.774774	+	0.632238i	$0.782136\pi$
$480$	−5.72199	−0.261172
$481$	−29.0209	−1.32324
$482$	7.27153	0.331209
$483$	0	0
$484$	2.83287	0.128767
$485$	−7.30277	−0.331602
$486$	0.533756	0.0242117
$487$	−39.7864	−1.80290	−0.901448	−	0.432888i	$-0.857495\pi$
$487$	−39.7864	−1.80290	−0.901448	+	0.432888i	$0.857495\pi$
$488$	16.3145	0.738524
$489$	−12.2732	−0.555011
$490$	0	0
$491$	29.6611	1.33858	0.669292	−	0.742999i	$-0.266597\pi$
$491$	29.6611	1.33858	0.669292	+	0.742999i	$0.266597\pi$
$492$	6.69447	0.301810
$493$	3.67116	0.165341
$494$	−3.26010	−0.146679
$495$	3.34392	0.150298
$496$	20.2892	0.911013
$497$	0	0
$498$	1.19636	0.0536103
$499$	−9.61678	−0.430506	−0.215253	−	0.976558i	$-0.569058\pi$
$499$	−9.61678	−0.430506	−0.215253	+	0.976558i	$0.569058\pi$
$500$	−16.5141	−0.738531
$501$	22.0861	0.986733
$502$	−3.72160	−0.166103
$503$	23.0762	1.02892	0.514459	−	0.857515i	$-0.327993\pi$
$503$	23.0762	1.02892	0.514459	+	0.857515i	$0.327993\pi$
$504$	0	0
$505$	6.99109	0.311100
$506$	1.63196	0.0725494
$507$	11.2354	0.498980
$508$	24.8173	1.10109
$509$	−15.4716	−0.685765	−0.342882	−	0.939378i	$-0.611403\pi$
$509$	−15.4716	−0.685765	−0.342882	+	0.939378i	$0.611403\pi$
$510$	−0.437004	−0.0193509
$511$	0	0
$512$	21.8153	0.964107
$513$	1.24069	0.0547778
$514$	11.2931	0.498119
$515$	−14.3070	−0.630441
$516$	4.21908	0.185735
$517$	−16.4845	−0.724989
$518$	0	0
$519$	5.38783	0.236499
$520$	−10.6765	−0.468195
$521$	13.1591	0.576511	0.288256	−	0.957554i	$-0.406925\pi$
$521$	13.1591	0.576511	0.288256	+	0.957554i	$0.406925\pi$
$522$	2.61754	0.114567
$523$	4.00635	0.175186	0.0875928	−	0.996156i	$-0.472083\pi$
$523$	4.00635	0.175186	0.0875928	+	0.996156i	$0.472083\pi$
$524$	−16.2991	−0.712029
$525$	0	0
$526$	3.49071	0.152202
$527$	6.40387	0.278957
$528$	−7.25174	−0.315592
$529$	1.00000	0.0434783
$530$	−6.45558	−0.280412
$531$	4.12244	0.178899
$532$	0	0
$533$	19.2154	0.832313
$534$	7.23649	0.313153
$535$	−15.9515	−0.689644
$536$	−6.37787	−0.275482
$537$	10.0945	0.435609
$538$	1.31391	0.0566468
$539$	0	0
$540$	1.87577	0.0807204
$541$	3.14254	0.135108	0.0675541	−	0.997716i	$-0.478480\pi$
$541$	3.14254	0.135108	0.0675541	+	0.997716i	$0.478480\pi$
$542$	6.03470	0.259212
$543$	−2.09721	−0.0899998
$544$	3.91661	0.167923
$545$	−2.84579	−0.121900
$546$	0	0
$547$	14.8798	0.636213	0.318107	−	0.948055i	$-0.396953\pi$
$547$	14.8798	0.636213	0.318107	+	0.948055i	$0.396953\pi$
$548$	16.2670	0.694891
$549$	−8.22736	−0.351135
$550$	6.20775	0.264699
$551$	6.08434	0.259201
$552$	1.98296	0.0844004
$553$	0	0
$554$	3.02599	0.128562
$555$	−6.44726	−0.273671
$556$	11.7534	0.498456
$557$	32.9194	1.39484	0.697421	−	0.716662i	$-0.254331\pi$
$557$	32.9194	1.39484	0.697421	+	0.716662i	$0.254331\pi$
$558$	4.56596	0.193292
$559$	12.1102	0.512208
$560$	0	0
$561$	−2.28886	−0.0966357
$562$	1.43516	0.0605386
$563$	16.4750	0.694340	0.347170	−	0.937802i	$-0.387143\pi$
$563$	16.4750	0.694340	0.347170	+	0.937802i	$0.387143\pi$
$564$	−9.24700	−0.389369
$565$	17.3557	0.730158
$566$	10.8008	0.453989
$567$	0	0
$568$	10.1819	0.427221
$569$	41.1919	1.72685	0.863426	−	0.504475i	$-0.168314\pi$
$569$	41.1919	1.72685	0.863426	+	0.504475i	$0.168314\pi$
$570$	−0.724262	−0.0303360
$571$	7.72134	0.323128	0.161564	−	0.986862i	$-0.448346\pi$
$571$	7.72134	0.323128	0.161564	+	0.986862i	$0.448346\pi$
$572$	−25.8155	−1.07940
$573$	−14.5337	−0.607155
$574$	0	0
$575$	3.80387	0.158632
$576$	−1.95104	−0.0812931
$577$	−25.7851	−1.07345	−0.536723	−	0.843758i	$-0.680338\pi$
$577$	−25.7851	−1.07345	−0.536723	+	0.843758i	$0.680338\pi$
$578$	−8.77473	−0.364981
$579$	15.2613	0.634240
$580$	9.19878	0.381958
$581$	0	0
$582$	3.56403	0.147734
$583$	−33.8118	−1.40034
$584$	−30.4714	−1.26091
$585$	5.38412	0.222606
$586$	0.374409	0.0154667
$587$	−28.5352	−1.17778	−0.588888	−	0.808215i	$-0.700434\pi$
$587$	−28.5352	−1.17778	−0.588888	+	0.808215i	$0.700434\pi$
$588$	0	0
$589$	10.6133	0.437315
$590$	−2.40651	−0.0990743
$591$	−15.7273	−0.646935
$592$	13.9818	0.574647
$593$	29.5523	1.21357	0.606783	−	0.794868i	$-0.292460\pi$
$593$	29.5523	1.21357	0.606783	+	0.794868i	$0.292460\pi$
$594$	−1.63196	−0.0669600
$595$	0	0
$596$	−15.1315	−0.619810
$597$	−7.27105	−0.297584
$598$	2.62765	0.107453
$599$	−41.0354	−1.67666	−0.838330	−	0.545162i	$-0.816468\pi$
$599$	−41.0354	−1.67666	−0.838330	+	0.545162i	$0.816468\pi$
$600$	7.54292	0.307938
$601$	−14.0087	−0.571427	−0.285713	−	0.958315i	$-0.592231\pi$
$601$	−14.0087	−0.571427	−0.285713	+	0.958315i	$0.592231\pi$
$602$	0	0
$603$	3.21634	0.130979
$604$	5.34776	0.217597
$605$	1.80645	0.0734426
$606$	−3.41192	−0.138600
$607$	−29.7614	−1.20798	−0.603989	−	0.796993i	$-0.706423\pi$
$607$	−29.7614	−1.20798	−0.603989	+	0.796993i	$0.706423\pi$
$608$	6.49114	0.263250
$609$	0	0
$610$	4.80279	0.194459
$611$	−26.5421	−1.07378
$612$	−1.28394	−0.0519001
$613$	−34.5043	−1.39361	−0.696807	−	0.717259i	$-0.745397\pi$
$613$	−34.5043	−1.39361	−0.696807	+	0.717259i	$0.745397\pi$
$614$	−5.11400	−0.206384
$615$	4.26889	0.172138
$616$	0	0
$617$	38.8231	1.56296	0.781480	−	0.623931i	$-0.214465\pi$
$617$	38.8231	1.56296	0.781480	+	0.623931i	$0.214465\pi$
$618$	6.98235	0.280871
$619$	18.8536	0.757791	0.378896	−	0.925439i	$-0.376304\pi$
$619$	18.8536	0.757791	0.378896	+	0.925439i	$0.376304\pi$
$620$	16.0461	0.644427
$621$	−1.00000	−0.0401286
$622$	4.09507	0.164197
$623$	0	0
$624$	−11.6762	−0.467422
$625$	8.48875	0.339550
$626$	−9.95699	−0.397961
$627$	−3.79340	−0.151494
$628$	−27.2545	−1.08757
$629$	4.41305	0.175960
$630$	0	0
$631$	40.6909	1.61988	0.809940	−	0.586513i	$-0.199500\pi$
$631$	40.6909	1.61988	0.809940	+	0.586513i	$0.199500\pi$
$632$	17.7339	0.705415
$633$	8.23718	0.327399
$634$	−7.08157	−0.281245
$635$	15.8254	0.628011
$636$	−18.9668	−0.752081
$637$	0	0
$638$	−8.00311	−0.316846
$639$	−5.13467	−0.203125
$640$	12.5829	0.497383
$641$	6.56825	0.259430	0.129715	−	0.991551i	$-0.458594\pi$
$641$	6.56825	0.259430	0.129715	+	0.991551i	$0.458594\pi$
$642$	7.78494	0.307247
$643$	0.579549	0.0228552	0.0114276	−	0.999935i	$-0.496362\pi$
$643$	0.579549	0.0228552	0.0114276	+	0.999935i	$0.496362\pi$
$644$	0	0
$645$	2.69040	0.105934
$646$	0.495746	0.0195049
$647$	5.09276	0.200217	0.100108	−	0.994977i	$-0.468081\pi$
$647$	5.09276	0.200217	0.100108	+	0.994977i	$0.468081\pi$
$648$	−1.98296	−0.0778980
$649$	−12.6043	−0.494764
$650$	9.99524	0.392045
$651$	0	0
$652$	21.0497	0.824372
$653$	14.6218	0.572197	0.286099	−	0.958200i	$-0.407642\pi$
$653$	14.6218	0.572197	0.286099	+	0.958200i	$0.407642\pi$
$654$	1.38885	0.0543084
$655$	−10.3935	−0.406108
$656$	−9.25768	−0.361452
$657$	15.3666	0.599508
$658$	0	0
$659$	20.6016	0.802524	0.401262	−	0.915963i	$-0.368572\pi$
$659$	20.6016	0.802524	0.401262	+	0.915963i	$0.368572\pi$
$660$	−5.73517	−0.223241
$661$	−24.6790	−0.959903	−0.479952	−	0.877295i	$-0.659346\pi$
$661$	−24.6790	−0.959903	−0.479952	+	0.877295i	$0.659346\pi$
$662$	9.38224	0.364651
$663$	−3.68534	−0.143127
$664$	−4.44461	−0.172484
$665$	0	0
$666$	3.14651	0.121925
$667$	−4.90399	−0.189883
$668$	−37.8799	−1.46562
$669$	−19.6064	−0.758027
$670$	−1.87756	−0.0725365
$671$	25.1551	0.971103
$672$	0	0
$673$	−19.8655	−0.765759	−0.382880	−	0.923798i	$-0.625068\pi$
$673$	−19.8655	−0.765759	−0.382880	+	0.923798i	$0.625068\pi$
$674$	−15.6353	−0.602250
$675$	−3.80387	−0.146411
$676$	−19.2698	−0.741147
$677$	48.9512	1.88135	0.940673	−	0.339315i	$-0.110195\pi$
$677$	48.9512	1.88135	0.940673	+	0.339315i	$0.110195\pi$
$678$	−8.47021	−0.325296
$679$	0	0
$680$	1.62352	0.0622590
$681$	−9.52636	−0.365051
$682$	−13.9604	−0.534571
$683$	−3.09472	−0.118416	−0.0592080	−	0.998246i	$-0.518858\pi$
$683$	−3.09472	−0.118416	−0.0592080	+	0.998246i	$0.518858\pi$
$684$	−2.12791	−0.0813628
$685$	10.3730	0.396333
$686$	0	0
$687$	27.2245	1.03868
$688$	−5.83450	−0.222438
$689$	−54.4412	−2.07404
$690$	0.583758	0.0222233
$691$	1.79492	0.0682819	0.0341409	−	0.999417i	$-0.489130\pi$
$691$	1.79492	0.0682819	0.0341409	+	0.999417i	$0.489130\pi$
$692$	−9.24069	−0.351278
$693$	0	0
$694$	10.3981	0.394708
$695$	7.49486	0.284296
$696$	−9.72443	−0.368603
$697$	−2.92199	−0.110678
$698$	19.1909	0.726387
$699$	19.5070	0.737821
$700$	0	0
$701$	51.9959	1.96386	0.981929	−	0.189250i	$-0.0606057\pi$
$701$	51.9959	1.96386	0.981929	+	0.189250i	$0.0606057\pi$
$702$	−2.62765	−0.0991743
$703$	7.31389	0.275849
$704$	5.96528	0.224825
$705$	−5.89658	−0.222078
$706$	−1.17646	−0.0442766
$707$	0	0
$708$	−7.07042	−0.265723
$709$	−24.7596	−0.929867	−0.464934	−	0.885346i	$-0.653922\pi$
$709$	−24.7596	−0.929867	−0.464934	+	0.885346i	$0.653922\pi$
$710$	2.99741	0.112491
$711$	−8.94313	−0.335394
$712$	−26.8843	−1.00753
$713$	−8.55439	−0.320364
$714$	0	0
$715$	−16.4619	−0.615641
$716$	−17.3131	−0.647020
$717$	11.3334	0.423253
$718$	14.3211	0.534459
$719$	1.83138	0.0682989	0.0341495	−	0.999417i	$-0.489128\pi$
$719$	1.83138	0.0682989	0.0341495	+	0.999417i	$0.489128\pi$
$720$	−2.59398	−0.0966718
$721$	0	0
$722$	−9.31975	−0.346845
$723$	13.6233	0.506656
$724$	3.59693	0.133679
$725$	−18.6541	−0.692798
$726$	−0.881615	−0.0327198
$727$	−31.2628	−1.15947	−0.579737	−	0.814803i	$-0.696845\pi$
$727$	−31.2628	−1.15947	−0.579737	+	0.814803i	$0.696845\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−8.97037	−0.332008
$731$	−1.84154	−0.0681117
$732$	14.1108	0.521550
$733$	41.1582	1.52021	0.760106	−	0.649799i	$-0.225147\pi$
$733$	41.1582	1.52021	0.760106	+	0.649799i	$0.225147\pi$
$734$	1.79141	0.0661221
$735$	0	0
$736$	−5.23188	−0.192850
$737$	−9.83394	−0.362238
$738$	−2.08338	−0.0766903
$739$	−26.6268	−0.979481	−0.489741	−	0.871868i	$-0.662908\pi$
$739$	−26.6268	−0.979481	−0.489741	+	0.871868i	$0.662908\pi$
$740$	11.0577	0.406490
$741$	−6.10784	−0.224377
$742$	0	0
$743$	33.6229	1.23350	0.616752	−	0.787157i	$-0.288448\pi$
$743$	33.6229	1.23350	0.616752	+	0.787157i	$0.288448\pi$
$744$	−16.9630	−0.621894
$745$	−9.64896	−0.353511
$746$	−2.42354	−0.0887322
$747$	2.24140	0.0820086
$748$	3.92563	0.143535
$749$	0	0
$750$	5.13932	0.187662
$751$	−27.8567	−1.01651	−0.508253	−	0.861208i	$-0.669708\pi$
$751$	−27.8567	−1.01651	−0.508253	+	0.861208i	$0.669708\pi$
$752$	12.7875	0.466314
$753$	−6.97247	−0.254091
$754$	−12.8860	−0.469280
$755$	3.41013	0.124107
$756$	0	0
$757$	−13.8093	−0.501908	−0.250954	−	0.967999i	$-0.580744\pi$
$757$	−13.8093	−0.501908	−0.250954	+	0.967999i	$0.580744\pi$
$758$	−15.6587	−0.568751
$759$	3.05750	0.110980
$760$	2.69071	0.0976023
$761$	−0.109748	−0.00397835	−0.00198917	−	0.999998i	$-0.500633\pi$
$761$	−0.109748	−0.00397835	−0.00198917	+	0.999998i	$0.500633\pi$
$762$	−7.72339	−0.279789
$763$	0	0
$764$	24.9268	0.901821
$765$	−0.818734	−0.0296014
$766$	−4.52790	−0.163600
$767$	−20.2945	−0.732793
$768$	−2.23887	−0.0807881
$769$	7.32316	0.264080	0.132040	−	0.991244i	$-0.457847\pi$
$769$	7.32316	0.264080	0.132040	+	0.991244i	$0.457847\pi$
$770$	0	0
$771$	21.1579	0.761982
$772$	−26.1748	−0.942052
$773$	2.17635	0.0782780	0.0391390	−	0.999234i	$-0.487538\pi$
$773$	2.17635	0.0782780	0.0391390	+	0.999234i	$0.487538\pi$
$774$	−1.31302	−0.0471954
$775$	−32.5398	−1.16886
$776$	−13.2407	−0.475315
$777$	0	0
$778$	−18.2177	−0.653135
$779$	−4.84272	−0.173508
$780$	−9.23432	−0.330642
$781$	15.6992	0.561763
$782$	−0.399573	−0.0142887
$783$	4.90399	0.175254
$784$	0	0
$785$	−17.3795	−0.620301
$786$	5.07242	0.180927
$787$	−24.9811	−0.890482	−0.445241	−	0.895411i	$-0.646882\pi$
$787$	−24.9811	−0.890482	−0.445241	+	0.895411i	$0.646882\pi$
$788$	26.9740	0.960908
$789$	6.53990	0.232827
$790$	5.22062	0.185741
$791$	0	0
$792$	6.06289	0.215435
$793$	40.5028	1.43830
$794$	−10.5574	−0.374669
$795$	−12.0946	−0.428952
$796$	12.4706	0.442009
$797$	31.1298	1.10267	0.551336	−	0.834283i	$-0.314118\pi$
$797$	31.1298	1.10267	0.551336	+	0.834283i	$0.314118\pi$
$798$	0	0
$799$	4.03612	0.142788
$800$	−19.9014	−0.703620
$801$	13.5577	0.479037
$802$	11.8399	0.418083
$803$	−46.9833	−1.65801
$804$	−5.51635	−0.194547
$805$	0	0
$806$	−22.4780	−0.791752
$807$	2.46163	0.0866536
$808$	12.6756	0.445927
$809$	−8.53464	−0.300062	−0.150031	−	0.988681i	$-0.547937\pi$
$809$	−8.53464	−0.300062	−0.150031	+	0.988681i	$0.547937\pi$
$810$	−0.583758	−0.0205112
$811$	7.94816	0.279098	0.139549	−	0.990215i	$-0.455435\pi$
$811$	7.94816	0.279098	0.139549	+	0.990215i	$0.455435\pi$
$812$	0	0
$813$	11.3061	0.396522
$814$	−9.62043	−0.337196
$815$	13.4229	0.470183
$816$	1.77554	0.0621562
$817$	−3.05204	−0.106777
$818$	−1.56248	−0.0546307
$819$	0	0
$820$	−7.32160	−0.255681
$821$	10.8048	0.377091	0.188546	−	0.982064i	$-0.439623\pi$
$821$	10.8048	0.377091	0.188546	+	0.982064i	$0.439623\pi$
$822$	−5.06243	−0.176573
$823$	5.14061	0.179190	0.0895952	−	0.995978i	$-0.471443\pi$
$823$	5.14061	0.179190	0.0895952	+	0.995978i	$0.471443\pi$
$824$	−25.9401	−0.903668
$825$	11.6303	0.404915
$826$	0	0
$827$	36.7234	1.27700	0.638499	−	0.769622i	$-0.279555\pi$
$827$	36.7234	1.27700	0.638499	+	0.769622i	$0.279555\pi$
$828$	1.71510	0.0596040
$829$	12.7475	0.442741	0.221370	−	0.975190i	$-0.428947\pi$
$829$	12.7475	0.442741	0.221370	+	0.975190i	$0.428947\pi$
$830$	−1.30843	−0.0454164
$831$	5.66924	0.196664
$832$	9.60483	0.332988
$833$	0	0
$834$	−3.65777	−0.126658
$835$	−24.1551	−0.835920
$836$	6.50608	0.225018
$837$	8.55439	0.295683
$838$	1.84209	0.0636339
$839$	41.8255	1.44398	0.721989	−	0.691905i	$-0.243228\pi$
$839$	41.8255	1.44398	0.721989	+	0.691905i	$0.243228\pi$
$840$	0	0
$841$	−4.95083	−0.170718
$842$	−5.56487	−0.191778
$843$	2.68879	0.0926070
$844$	−14.1276	−0.486293
$845$	−12.2879	−0.422716
$846$	2.87775	0.0989392
$847$	0	0
$848$	26.2288	0.900702
$849$	20.2354	0.694476
$850$	−1.51992	−0.0521329
$851$	−5.89502	−0.202079
$852$	8.80650	0.301706
$853$	23.3022	0.797851	0.398925	−	0.916983i	$-0.369383\pi$
$853$	23.3022	0.797851	0.398925	+	0.916983i	$0.369383\pi$
$854$	0	0
$855$	−1.35692	−0.0464055
$856$	−28.9219	−0.988529
$857$	−31.1273	−1.06329	−0.531645	−	0.846968i	$-0.678426\pi$
$857$	−31.1273	−1.06329	−0.531645	+	0.846968i	$0.678426\pi$
$858$	8.03403	0.274277
$859$	50.0579	1.70795	0.853977	−	0.520311i	$-0.174184\pi$
$859$	50.0579	1.70795	0.853977	+	0.520311i	$0.174184\pi$
$860$	−4.61432	−0.157347
$861$	0	0
$862$	10.5805	0.360372
$863$	41.5649	1.41488	0.707442	−	0.706771i	$-0.249849\pi$
$863$	41.5649	1.41488	0.707442	+	0.706771i	$0.249849\pi$
$864$	5.23188	0.177992
$865$	−5.89255	−0.200353
$866$	−5.66603	−0.192539
$867$	−16.4396	−0.558318
$868$	0	0
$869$	27.3436	0.927567
$870$	−2.86274	−0.0970561
$871$	−15.8338	−0.536509
$872$	−5.15972	−0.174730
$873$	6.67726	0.225991
$874$	−0.662226	−0.0224001
$875$	0	0
$876$	−26.3553	−0.890464
$877$	−3.24788	−0.109673	−0.0548366	−	0.998495i	$-0.517464\pi$
$877$	−3.24788	−0.109673	−0.0548366	+	0.998495i	$0.517464\pi$
$878$	−7.70274	−0.259955
$879$	0.701461	0.0236597
$880$	7.93107	0.267356
$881$	−20.9783	−0.706778	−0.353389	−	0.935477i	$-0.614971\pi$
$881$	−20.9783	−0.706778	−0.353389	+	0.935477i	$0.614971\pi$
$882$	0	0
$883$	−15.3341	−0.516035	−0.258017	−	0.966140i	$-0.583069\pi$
$883$	−15.3341	−0.516035	−0.258017	+	0.966140i	$0.583069\pi$
$884$	6.32075	0.212590
$885$	−4.50863	−0.151556
$886$	−8.45741	−0.284132
$887$	−12.9118	−0.433534	−0.216767	−	0.976223i	$-0.569551\pi$
$887$	−12.9118	−0.433534	−0.216767	+	0.976223i	$0.569551\pi$
$888$	−11.6896	−0.392277
$889$	0	0
$890$	−7.91439	−0.265291
$891$	−3.05750	−0.102430
$892$	33.6270	1.12591
$893$	6.68919	0.223845
$894$	4.70906	0.157494
$895$	−11.0401	−0.369030
$896$	0	0
$897$	4.92294	0.164372
$898$	7.56733	0.252525
$899$	41.9507	1.39913
$900$	6.52403	0.217468
$901$	8.27858	0.275799
$902$	6.36993	0.212095
$903$	0	0
$904$	31.4677	1.04660
$905$	2.29367	0.0762442
$906$	−1.66427	−0.0552917
$907$	38.4657	1.27723	0.638617	−	0.769525i	$-0.279507\pi$
$907$	38.4657	1.27723	0.638617	+	0.769525i	$0.279507\pi$
$908$	16.3387	0.542219
$909$	−6.39228	−0.212018
$910$	0	0
$911$	−44.7984	−1.48424	−0.742119	−	0.670268i	$-0.766179\pi$
$911$	−44.7984	−1.48424	−0.742119	+	0.670268i	$0.766179\pi$
$912$	2.94266	0.0974411
$913$	−6.85307	−0.226804
$914$	−5.40777	−0.178873
$915$	8.99809	0.297468
$916$	−46.6929	−1.54278
$917$	0	0
$918$	0.399573	0.0131879
$919$	−45.1488	−1.48932	−0.744661	−	0.667442i	$-0.767389\pi$
$919$	−45.1488	−1.48932	−0.744661	+	0.667442i	$0.767389\pi$
$920$	−2.16872	−0.0715006
$921$	−9.58115	−0.315710
$922$	−17.8997	−0.589494
$923$	25.2777	0.832026
$924$	0	0
$925$	−22.4239	−0.737293
$926$	14.6982	0.483011
$927$	13.0815	0.429654
$928$	25.6571	0.842236
$929$	25.1196	0.824148	0.412074	−	0.911150i	$-0.364804\pi$
$929$	25.1196	0.824148	0.412074	+	0.911150i	$0.364804\pi$
$930$	−4.99369	−0.163750
$931$	0	0
$932$	−33.4565	−1.09590
$933$	7.67217	0.251176
$934$	1.35613	0.0443739
$935$	2.50328	0.0818659
$936$	9.76200	0.319081
$937$	−51.1806	−1.67200	−0.835999	−	0.548731i	$-0.815111\pi$
$937$	−51.1806	−1.67200	−0.835999	+	0.548731i	$0.815111\pi$
$938$	0	0
$939$	−18.6546	−0.608769
$940$	10.1132	0.329858
$941$	−19.6858	−0.641739	−0.320869	−	0.947123i	$-0.603975\pi$
$941$	−19.6858	−0.641739	−0.320869	+	0.947123i	$0.603975\pi$
$942$	8.48185	0.276354
$943$	3.90324	0.127107
$944$	9.77757	0.318233
$945$	0	0
$946$	4.01454	0.130524
$947$	−49.9931	−1.62456	−0.812279	−	0.583268i	$-0.801774\pi$
$947$	−49.9931	−1.62456	−0.812279	+	0.583268i	$0.801774\pi$
$948$	15.3384	0.498168
$949$	−75.6489	−2.45567
$950$	−2.51902	−0.0817278
$951$	−13.2674	−0.430226
$952$	0	0
$953$	−12.1714	−0.394271	−0.197136	−	0.980376i	$-0.563164\pi$
$953$	−12.1714	−0.394271	−0.197136	+	0.980376i	$0.563164\pi$
$954$	5.90263	0.191105
$955$	15.8952	0.514357
$956$	−19.4379	−0.628668
$957$	−14.9939	−0.484685
$958$	−18.1016	−0.584835
$959$	0	0
$960$	2.13381	0.0688683
$961$	42.1776	1.36057
$962$	−15.4901	−0.499420
$963$	14.5852	0.470002
$964$	−23.3654	−0.752549
$965$	−16.6910	−0.537302
$966$	0	0
$967$	23.6632	0.760956	0.380478	−	0.924790i	$-0.375759\pi$
$967$	23.6632	0.760956	0.380478	+	0.924790i	$0.375759\pi$
$968$	3.27529	0.105272
$969$	0.928787	0.0298369
$970$	−3.89790	−0.125154
$971$	1.52202	0.0488441	0.0244220	−	0.999702i	$-0.492225\pi$
$971$	1.52202	0.0488441	0.0244220	+	0.999702i	$0.492225\pi$
$972$	−1.71510	−0.0550120
$973$	0	0
$974$	−21.2363	−0.680454
$975$	18.7262	0.599719
$976$	−19.5136	−0.624615
$977$	−53.4110	−1.70877	−0.854384	−	0.519642i	$-0.826065\pi$
$977$	−53.4110	−1.70877	−0.854384	+	0.519642i	$0.826065\pi$
$978$	−6.55087	−0.209474
$979$	−41.4525	−1.32483
$980$	0	0
$981$	2.60203	0.0830765
$982$	15.8318	0.505212
$983$	35.2296	1.12365	0.561824	−	0.827257i	$-0.310100\pi$
$983$	35.2296	1.12365	0.561824	+	0.827257i	$0.310100\pi$
$984$	7.73998	0.246741
$985$	17.2006	0.548057
$986$	1.95950	0.0624033
$987$	0	0
$988$	10.4756	0.333273
$989$	2.45996	0.0782221
$990$	1.78484	0.0567258
$991$	−0.612876	−0.0194687	−0.00973433	−	0.999953i	$-0.503099\pi$
$991$	−0.612876	−0.0194687	−0.00973433	+	0.999953i	$0.503099\pi$
$992$	44.7555	1.42099
$993$	17.5778	0.557814
$994$	0	0
$995$	7.95219	0.252101
$996$	−3.84424	−0.121809
$997$	−29.1981	−0.924713	−0.462357	−	0.886694i	$-0.652996\pi$
$997$	−29.1981	−0.924713	−0.462357	+	0.886694i	$0.652996\pi$
$998$	−5.13301	−0.162483
$999$	5.89502	0.186510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bl.1.6	yes	10
7.6	odd	2		3381.2.a.bk.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.bk.1.6	✓	10	7.6	odd	2
3381.2.a.bl.1.6	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)

\(f(q)\)	\(=\)	\(q+0.533756 q^{2} +1.00000 q^{3} -1.71510 q^{4} -1.09368 q^{5} +0.533756 q^{6} -1.98296 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.533756 q^{2} +1.00000 q^{3} -1.71510 q^{4} -1.09368 q^{5} +0.533756 q^{6} -1.98296 q^{8} +1.00000 q^{9} -0.583758 q^{10} -3.05750 q^{11} -1.71510 q^{12} -4.92294 q^{13} -1.09368 q^{15} +2.37179 q^{16} +0.748606 q^{17} +0.533756 q^{18} +1.24069 q^{19} +1.87577 q^{20} -1.63196 q^{22} -1.00000 q^{23} -1.98296 q^{24} -3.80387 q^{25} -2.62765 q^{26} +1.00000 q^{27} +4.90399 q^{29} -0.583758 q^{30} +8.55439 q^{31} +5.23188 q^{32} -3.05750 q^{33} +0.399573 q^{34} -1.71510 q^{36} +5.89502 q^{37} +0.662226 q^{38} -4.92294 q^{39} +2.16872 q^{40} -3.90324 q^{41} -2.45996 q^{43} +5.24392 q^{44} -1.09368 q^{45} -0.533756 q^{46} +5.39151 q^{47} +2.37179 q^{48} -2.03034 q^{50} +0.748606 q^{51} +8.44336 q^{52} +11.0587 q^{53} +0.533756 q^{54} +3.34392 q^{55} +1.24069 q^{57} +2.61754 q^{58} +4.12244 q^{59} +1.87577 q^{60} -8.22736 q^{61} +4.56596 q^{62} -1.95104 q^{64} +5.38412 q^{65} -1.63196 q^{66} +3.21634 q^{67} -1.28394 q^{68} -1.00000 q^{69} -5.13467 q^{71} -1.98296 q^{72} +15.3666 q^{73} +3.14651 q^{74} -3.80387 q^{75} -2.12791 q^{76} -2.62765 q^{78} -8.94313 q^{79} -2.59398 q^{80} +1.00000 q^{81} -2.08338 q^{82} +2.24140 q^{83} -0.818734 q^{85} -1.31302 q^{86} +4.90399 q^{87} +6.06289 q^{88} +13.5577 q^{89} -0.583758 q^{90} +1.71510 q^{92} +8.55439 q^{93} +2.87775 q^{94} -1.35692 q^{95} +5.23188 q^{96} +6.67726 q^{97} -3.05750 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 10 q^{3} + 8 q^{4} + 4 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 + 10 * q^3 + 8 * q^4 + 4 * q^5 + 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} + 10 q^{3} + 8 q^{4} + 4 q^{5} + 4 q^{6} + 12 q^{8} + 10 q^{9} + 8 q^{10} + 2 q^{11} + 8 q^{12} + 4 q^{15} + 4 q^{16} + 12 q^{17} + 4 q^{18} + 26 q^{19} + 24 q^{20} - 8 q^{22} - 10 q^{23} + 12 q^{24} - 2 q^{25} + 4 q^{26} + 10 q^{27} + 16 q^{29} + 8 q^{30} + 12 q^{31} + 8 q^{32} + 2 q^{33} + 28 q^{34} + 8 q^{36} - 8 q^{37} + 32 q^{38} + 4 q^{40} + 10 q^{41} - 4 q^{43} - 16 q^{44} + 4 q^{45} - 4 q^{46} + 2 q^{47} + 4 q^{48} - 8 q^{50} + 12 q^{51} + 24 q^{52} + 14 q^{53} + 4 q^{54} + 16 q^{55} + 26 q^{57} - 8 q^{58} + 38 q^{59} + 24 q^{60} + 14 q^{61} - 8 q^{62} + 8 q^{64} + 12 q^{65} - 8 q^{66} + 8 q^{68} - 10 q^{69} + 24 q^{71} + 12 q^{72} + 8 q^{73} - 8 q^{74} - 2 q^{75} + 64 q^{76} + 4 q^{78} - 16 q^{79} + 28 q^{80} + 10 q^{81} - 40 q^{82} + 28 q^{83} - 4 q^{85} + 20 q^{86} + 16 q^{87} - 68 q^{88} + 32 q^{89} + 8 q^{90} - 8 q^{92} + 12 q^{93} + 56 q^{94} + 8 q^{95} + 8 q^{96} + 4 q^{97} + 2 q^{99}+O(q^{100}) \) 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 + 4 * q^15 + 4 * q^16 + 12 * q^17 + 4 * q^18 + 26 * q^19 + 24 * q^20 - 8 * q^22 - 10 * q^23 + 12 * q^24 - 2 * q^25 + 4 * q^26 + 10 * q^27 + 16 * q^29 + 8 * q^30 + 12 * q^31 + 8 * q^32 + 2 * q^33 + 28 * q^34 + 8 * q^36 - 8 * q^37 + 32 * q^38 + 4 * q^40 + 10 * q^41 - 4 * q^43 - 16 * q^44 + 4 * q^45 - 4 * q^46 + 2 * q^47 + 4 * q^48 - 8 * q^50 + 12 * q^51 + 24 * q^52 + 14 * q^53 + 4 * q^54 + 16 * q^55 + 26 * q^57 - 8 * q^58 + 38 * q^59 + 24 * q^60 + 14 * q^61 - 8 * q^62 + 8 * q^64 + 12 * q^65 - 8 * q^66 + 8 * q^68 - 10 * q^69 + 24 * q^71 + 12 * q^72 + 8 * q^73 - 8 * q^74 - 2 * q^75 + 64 * q^76 + 4 * q^78 - 16 * q^79 + 28 * q^80 + 10 * q^81 - 40 * q^82 + 28 * q^83 - 4 * q^85 + 20 * q^86 + 16 * q^87 - 68 * q^88 + 32 * q^89 + 8 * q^90 - 8 * q^92 + 12 * q^93 + 56 * q^94 + 8 * q^95 + 8 * q^96 + 4 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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