LMFDB - Embedded newform 3381.2.a.bg.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} + 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			1.6
Root			$-0.0765467$ 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)

$f(q)$	$=$	$q+0.0765467 q^{2} -1.00000 q^{3} -1.99414 q^{4} +2.75264 q^{5} -0.0765467 q^{6} -0.305738 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.0765467 q^{2} -1.00000 q^{3} -1.99414 q^{4} +2.75264 q^{5} -0.0765467 q^{6} -0.305738 q^{8} +1.00000 q^{9} +0.210706 q^{10} +4.59164 q^{11} +1.99414 q^{12} +4.62981 q^{13} -2.75264 q^{15} +3.96488 q^{16} -5.10173 q^{17} +0.0765467 q^{18} +5.16718 q^{19} -5.48916 q^{20} +0.351475 q^{22} +1.00000 q^{23} +0.305738 q^{24} +2.57704 q^{25} +0.354396 q^{26} -1.00000 q^{27} +0.812636 q^{29} -0.210706 q^{30} +4.06504 q^{31} +0.914974 q^{32} -4.59164 q^{33} -0.390520 q^{34} -1.99414 q^{36} +10.7691 q^{37} +0.395531 q^{38} -4.62981 q^{39} -0.841588 q^{40} -2.39737 q^{41} -11.9883 q^{43} -9.15638 q^{44} +2.75264 q^{45} +0.0765467 q^{46} -7.22492 q^{47} -3.96488 q^{48} +0.197264 q^{50} +5.10173 q^{51} -9.23249 q^{52} +3.67855 q^{53} -0.0765467 q^{54} +12.6392 q^{55} -5.16718 q^{57} +0.0622046 q^{58} +14.3789 q^{59} +5.48916 q^{60} -5.09158 q^{61} +0.311165 q^{62} -7.85972 q^{64} +12.7442 q^{65} -0.351475 q^{66} -13.4288 q^{67} +10.1736 q^{68} -1.00000 q^{69} -4.57449 q^{71} -0.305738 q^{72} -10.2007 q^{73} +0.824335 q^{74} -2.57704 q^{75} -10.3041 q^{76} -0.354396 q^{78} +5.11785 q^{79} +10.9139 q^{80} +1.00000 q^{81} -0.183511 q^{82} +16.3256 q^{83} -14.0432 q^{85} -0.917666 q^{86} -0.812636 q^{87} -1.40384 q^{88} +7.06970 q^{89} +0.210706 q^{90} -1.99414 q^{92} -4.06504 q^{93} -0.553044 q^{94} +14.2234 q^{95} -0.914974 q^{96} +0.960302 q^{97} +4.59164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.0765467	0.0541267	0.0270633	−	0.999634i	$-0.491384\pi$
$2$	0.0765467	0.0541267	0.0270633	+	0.999634i	$0.491384\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99414	−0.997070
$5$	2.75264	1.23102	0.615510	−	0.788129i	$-0.288950\pi$
$5$	2.75264	1.23102	0.615510	+	0.788129i	$0.288950\pi$
$6$	−0.0765467	−0.0312500
$7$	0	0
$7$	0	0
$8$	−0.305738	−0.108095
$9$	1.00000	0.333333
$10$	0.210706	0.0666310
$11$	4.59164	1.38443	0.692216	−	0.721690i	$-0.256634\pi$
$11$	4.59164	1.38443	0.692216	+	0.721690i	$0.256634\pi$
$12$	1.99414	0.575659
$13$	4.62981	1.28408	0.642039	−	0.766672i	$-0.278089\pi$
$13$	4.62981	1.28408	0.642039	+	0.766672i	$0.278089\pi$
$14$	0	0
$15$	−2.75264	−0.710729
$16$	3.96488	0.991219
$17$	−5.10173	−1.23735	−0.618676	−	0.785646i	$-0.712331\pi$
$17$	−5.10173	−1.23735	−0.618676	+	0.785646i	$0.712331\pi$
$18$	0.0765467	0.0180422
$19$	5.16718	1.18543	0.592717	−	0.805411i	$-0.298055\pi$
$19$	5.16718	1.18543	0.592717	+	0.805411i	$0.298055\pi$
$20$	−5.48916	−1.22741
$21$	0	0
$22$	0.351475	0.0749347
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.305738	0.0624085
$25$	2.57704	0.515409
$26$	0.354396	0.0695028
$27$	−1.00000	−0.192450
$28$	0	0
$29$	0.812636	0.150903	0.0754514	−	0.997149i	$-0.475960\pi$
$29$	0.812636	0.150903	0.0754514	+	0.997149i	$0.475960\pi$
$30$	−0.210706	−0.0384694
$31$	4.06504	0.730102	0.365051	−	0.930987i	$-0.381052\pi$
$31$	4.06504	0.730102	0.365051	+	0.930987i	$0.381052\pi$
$32$	0.914974	0.161746
$33$	−4.59164	−0.799302
$34$	−0.390520	−0.0669737
$35$	0	0
$36$	−1.99414	−0.332357
$37$	10.7691	1.77042	0.885211	−	0.465191i	$-0.154014\pi$
$37$	10.7691	1.77042	0.885211	+	0.465191i	$0.154014\pi$
$38$	0.395531	0.0641635
$39$	−4.62981	−0.741363
$40$	−0.841588	−0.133067
$41$	−2.39737	−0.374407	−0.187203	−	0.982321i	$-0.559942\pi$
$41$	−2.39737	−0.374407	−0.187203	+	0.982321i	$0.559942\pi$
$42$	0	0
$43$	−11.9883	−1.82820	−0.914101	−	0.405486i	$-0.867102\pi$
$43$	−11.9883	−1.82820	−0.914101	+	0.405486i	$0.867102\pi$
$44$	−9.15638	−1.38038
$45$	2.75264	0.410340
$46$	0.0765467	0.0112862
$47$	−7.22492	−1.05386	−0.526932	−	0.849908i	$-0.676658\pi$
$47$	−7.22492	−1.05386	−0.526932	+	0.849908i	$0.676658\pi$
$48$	−3.96488	−0.572281
$49$	0	0
$50$	0.197264	0.0278974
$51$	5.10173	0.714385
$52$	−9.23249	−1.28032
$53$	3.67855	0.505288	0.252644	−	0.967559i	$-0.418700\pi$
$53$	3.67855	0.505288	0.252644	+	0.967559i	$0.418700\pi$
$54$	−0.0765467	−0.0104167
$55$	12.6392	1.70426
$56$	0	0
$57$	−5.16718	−0.684410
$58$	0.0622046	0.00816786
$59$	14.3789	1.87198	0.935988	−	0.352033i	$-0.114510\pi$
$59$	14.3789	1.87198	0.935988	+	0.352033i	$0.114510\pi$
$60$	5.48916	0.708647
$61$	−5.09158	−0.651910	−0.325955	−	0.945385i	$-0.605686\pi$
$61$	−5.09158	−0.651910	−0.325955	+	0.945385i	$0.605686\pi$
$62$	0.311165	0.0395180
$63$	0	0
$64$	−7.85972	−0.982465
$65$	12.7442	1.58073
$66$	−0.351475	−0.0432636
$67$	−13.4288	−1.64059	−0.820294	−	0.571942i	$-0.806190\pi$
$67$	−13.4288	−1.64059	−0.820294	+	0.571942i	$0.806190\pi$
$68$	10.1736	1.23373
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−4.57449	−0.542892	−0.271446	−	0.962454i	$-0.587502\pi$
$71$	−4.57449	−0.542892	−0.271446	+	0.962454i	$0.587502\pi$
$72$	−0.305738	−0.0360316
$73$	−10.2007	−1.19390	−0.596952	−	0.802277i	$-0.703622\pi$
$73$	−10.2007	−1.19390	−0.596952	+	0.802277i	$0.703622\pi$
$74$	0.824335	0.0958270
$75$	−2.57704	−0.297571
$76$	−10.3041	−1.18196
$77$	0	0
$78$	−0.354396	−0.0401275
$79$	5.11785	0.575803	0.287901	−	0.957660i	$-0.407042\pi$
$79$	5.11785	0.575803	0.287901	+	0.957660i	$0.407042\pi$
$80$	10.9139	1.22021
$81$	1.00000	0.111111
$82$	−0.183511	−0.0202654
$83$	16.3256	1.79197	0.895984	−	0.444087i	$-0.146472\pi$
$83$	16.3256	1.79197	0.895984	+	0.444087i	$0.146472\pi$
$84$	0	0
$85$	−14.0432	−1.52320
$86$	−0.917666	−0.0989545
$87$	−0.812636	−0.0871237
$88$	−1.40384	−0.149650
$89$	7.06970	0.749387	0.374693	−	0.927149i	$-0.377748\pi$
$89$	7.06970	0.749387	0.374693	+	0.927149i	$0.377748\pi$
$90$	0.210706	0.0222103
$91$	0	0
$92$	−1.99414	−0.207904
$93$	−4.06504	−0.421525
$94$	−0.553044	−0.0570421
$95$	14.2234	1.45929
$96$	−0.914974	−0.0933842
$97$	0.960302	0.0975039	0.0487520	−	0.998811i	$-0.484476\pi$
$97$	0.960302	0.0975039	0.0487520	+	0.998811i	$0.484476\pi$
$98$	0	0
$99$	4.59164	0.461477
$100$	−5.13899	−0.513899
$101$	1.82419	0.181514	0.0907571	−	0.995873i	$-0.471071\pi$
$101$	1.82419	0.181514	0.0907571	+	0.995873i	$0.471071\pi$
$102$	0.390520	0.0386673
$103$	7.89875	0.778287	0.389143	−	0.921177i	$-0.372771\pi$
$103$	7.89875	0.778287	0.389143	+	0.921177i	$0.372771\pi$
$104$	−1.41551	−0.138802
$105$	0	0
$106$	0.281581	0.0273496
$107$	−14.3647	−1.38868	−0.694342	−	0.719645i	$-0.744304\pi$
$107$	−14.3647	−1.38868	−0.694342	+	0.719645i	$0.744304\pi$
$108$	1.99414	0.191886
$109$	−0.857844	−0.0821666	−0.0410833	−	0.999156i	$-0.513081\pi$
$109$	−0.857844	−0.0821666	−0.0410833	+	0.999156i	$0.513081\pi$
$110$	0.967485	0.0922461
$111$	−10.7691	−1.02215
$112$	0	0
$113$	−11.9826	−1.12723	−0.563613	−	0.826039i	$-0.690589\pi$
$113$	−11.9826	−1.12723	−0.563613	+	0.826039i	$0.690589\pi$
$114$	−0.395531	−0.0370448
$115$	2.75264	0.256685
$116$	−1.62051	−0.150461
$117$	4.62981	0.428026
$118$	1.10066	0.101324
$119$	0	0
$120$	0.841588	0.0768261
$121$	10.0832	0.916653
$122$	−0.389744	−0.0352857
$123$	2.39737	0.216164
$124$	−8.10626	−0.727963
$125$	−6.66953	−0.596541
$126$	0	0
$127$	15.4442	1.37045	0.685223	−	0.728333i	$-0.259705\pi$
$127$	15.4442	1.37045	0.685223	+	0.728333i	$0.259705\pi$
$128$	−2.43158	−0.214924
$129$	11.9883	1.05551
$130$	0.975527	0.0855594
$131$	9.28879	0.811566	0.405783	−	0.913970i	$-0.366999\pi$
$131$	9.28879	0.811566	0.405783	+	0.913970i	$0.366999\pi$
$132$	9.15638	0.796961
$133$	0	0
$134$	−1.02793	−0.0887995
$135$	−2.75264	−0.236910
$136$	1.55979	0.133751
$137$	−15.9151	−1.35972	−0.679858	−	0.733343i	$-0.737959\pi$
$137$	−15.9151	−1.35972	−0.679858	+	0.733343i	$0.737959\pi$
$138$	−0.0765467	−0.00651608
$139$	8.50898	0.721722	0.360861	−	0.932620i	$-0.382483\pi$
$139$	8.50898	0.721722	0.360861	+	0.932620i	$0.382483\pi$
$140$	0	0
$141$	7.22492	0.608448
$142$	−0.350162	−0.0293849
$143$	21.2584	1.77772
$144$	3.96488	0.330406
$145$	2.23690	0.185764
$146$	−0.780831	−0.0646220
$147$	0	0
$148$	−21.4750	−1.76523
$149$	−6.43199	−0.526929	−0.263464	−	0.964669i	$-0.584865\pi$
$149$	−6.43199	−0.526929	−0.263464	+	0.964669i	$0.584865\pi$
$150$	−0.197264	−0.0161065
$151$	17.6973	1.44018	0.720092	−	0.693879i	$-0.244100\pi$
$151$	17.6973	1.44018	0.720092	+	0.693879i	$0.244100\pi$
$152$	−1.57981	−0.128139
$153$	−5.10173	−0.412451
$154$	0	0
$155$	11.1896	0.898770
$156$	9.23249	0.739191
$157$	16.3993	1.30881	0.654404	−	0.756145i	$-0.272920\pi$
$157$	16.3993	1.30881	0.654404	+	0.756145i	$0.272920\pi$
$158$	0.391754	0.0311663
$159$	−3.67855	−0.291728
$160$	2.51860	0.199113
$161$	0	0
$162$	0.0765467	0.00601407
$163$	−8.09663	−0.634177	−0.317088	−	0.948396i	$-0.602705\pi$
$163$	−8.09663	−0.634177	−0.317088	+	0.948396i	$0.602705\pi$
$164$	4.78070	0.373310
$165$	−12.6392	−0.983957
$166$	1.24967	0.0969932
$167$	19.0197	1.47179	0.735896	−	0.677095i	$-0.236761\pi$
$167$	19.0197	1.47179	0.735896	+	0.677095i	$0.236761\pi$
$168$	0	0
$169$	8.43513	0.648856
$170$	−1.07496	−0.0824459
$171$	5.16718	0.395144
$172$	23.9064	1.82285
$173$	10.9605	0.833308	0.416654	−	0.909065i	$-0.363203\pi$
$173$	10.9605	0.833308	0.416654	+	0.909065i	$0.363203\pi$
$174$	−0.0622046	−0.00471572
$175$	0	0
$176$	18.2053	1.37228
$177$	−14.3789	−1.08079
$178$	0.541162	0.0405618
$179$	20.4155	1.52592	0.762962	−	0.646444i	$-0.223745\pi$
$179$	20.4155	1.52592	0.762962	+	0.646444i	$0.223745\pi$
$180$	−5.48916	−0.409138
$181$	9.87211	0.733788	0.366894	−	0.930263i	$-0.380421\pi$
$181$	9.87211	0.733788	0.366894	+	0.930263i	$0.380421\pi$
$182$	0	0
$183$	5.09158	0.376381
$184$	−0.305738	−0.0225393
$185$	29.6434	2.17942
$186$	−0.311165	−0.0228157
$187$	−23.4253	−1.71303
$188$	14.4075	1.05078
$189$	0	0
$190$	1.08875	0.0789866
$191$	−6.84993	−0.495644	−0.247822	−	0.968806i	$-0.579715\pi$
$191$	−6.84993	−0.495644	−0.247822	+	0.968806i	$0.579715\pi$
$192$	7.85972	0.567226
$193$	16.9779	1.22209	0.611046	−	0.791595i	$-0.290749\pi$
$193$	16.9779	1.22209	0.611046	+	0.791595i	$0.290749\pi$
$194$	0.0735079	0.00527756
$195$	−12.7442	−0.912632
$196$	0	0
$197$	−14.4937	−1.03263	−0.516317	−	0.856397i	$-0.672697\pi$
$197$	−14.4937	−1.03263	−0.516317	+	0.856397i	$0.672697\pi$
$198$	0.351475	0.0249782
$199$	5.84157	0.414098	0.207049	−	0.978331i	$-0.433614\pi$
$199$	5.84157	0.414098	0.207049	+	0.978331i	$0.433614\pi$
$200$	−0.787901	−0.0557130
$201$	13.4288	0.947194
$202$	0.139636	0.00982475
$203$	0	0
$204$	−10.1736	−0.712292
$205$	−6.59911	−0.460902
$206$	0.604623	0.0421260
$207$	1.00000	0.0695048
$208$	18.3566	1.27280
$209$	23.7259	1.64115
$210$	0	0
$211$	−18.6545	−1.28423	−0.642114	−	0.766609i	$-0.721942\pi$
$211$	−18.6545	−1.28423	−0.642114	+	0.766609i	$0.721942\pi$
$212$	−7.33555	−0.503808
$213$	4.57449	0.313439
$214$	−1.09957	−0.0751648
$215$	−32.9996	−2.25055
$216$	0.305738	0.0208028
$217$	0	0
$218$	−0.0656651	−0.00444740
$219$	10.2007	0.689301
$220$	−25.2042	−1.69927
$221$	−23.6200	−1.58886
$222$	−0.824335	−0.0553257
$223$	12.9607	0.867915	0.433958	−	0.900933i	$-0.357117\pi$
$223$	12.9607	0.867915	0.433958	+	0.900933i	$0.357117\pi$
$224$	0	0
$225$	2.57704	0.171803
$226$	−0.917227	−0.0610130
$227$	−18.9026	−1.25461	−0.627305	−	0.778773i	$-0.715842\pi$
$227$	−18.9026	−1.25461	−0.627305	+	0.778773i	$0.715842\pi$
$228$	10.3041	0.682405
$229$	10.6244	0.702078	0.351039	−	0.936361i	$-0.385828\pi$
$229$	10.6244	0.702078	0.351039	+	0.936361i	$0.385828\pi$
$230$	0.210706	0.0138935
$231$	0	0
$232$	−0.248454	−0.0163118
$233$	6.87511	0.450403	0.225202	−	0.974312i	$-0.427696\pi$
$233$	6.87511	0.450403	0.225202	+	0.974312i	$0.427696\pi$
$234$	0.354396	0.0231676
$235$	−19.8876	−1.29733
$236$	−28.6736	−1.86649
$237$	−5.11785	−0.332440
$238$	0	0
$239$	−7.09928	−0.459214	−0.229607	−	0.973283i	$-0.573744\pi$
$239$	−7.09928	−0.459214	−0.229607	+	0.973283i	$0.573744\pi$
$240$	−10.9139	−0.704489
$241$	−22.0037	−1.41738	−0.708692	−	0.705518i	$-0.750714\pi$
$241$	−22.0037	−1.41738	−0.708692	+	0.705518i	$0.750714\pi$
$242$	0.771834	0.0496153
$243$	−1.00000	−0.0641500
$244$	10.1533	0.650001
$245$	0	0
$246$	0.183511	0.0117002
$247$	23.9231	1.52219
$248$	−1.24284	−0.0789202
$249$	−16.3256	−1.03459
$250$	−0.510530	−0.0322888
$251$	10.8554	0.685186	0.342593	−	0.939484i	$-0.388695\pi$
$251$	10.8554	0.685186	0.342593	+	0.939484i	$0.388695\pi$
$252$	0	0
$253$	4.59164	0.288674
$254$	1.18220	0.0741777
$255$	14.0432	0.879422
$256$	15.5333	0.970832
$257$	2.82477	0.176205	0.0881023	−	0.996111i	$-0.471920\pi$
$257$	2.82477	0.176205	0.0881023	+	0.996111i	$0.471920\pi$
$258$	0.917666	0.0571314
$259$	0	0
$260$	−25.4138	−1.57609
$261$	0.812636	0.0503009
$262$	0.711026	0.0439273
$263$	1.01667	0.0626907	0.0313454	−	0.999509i	$-0.490021\pi$
$263$	1.01667	0.0626907	0.0313454	+	0.999509i	$0.490021\pi$
$264$	1.40384	0.0864004
$265$	10.1257	0.622019
$266$	0	0
$267$	−7.06970	−0.432659
$268$	26.7789	1.63578
$269$	6.43641	0.392435	0.196218	−	0.980560i	$-0.437134\pi$
$269$	6.43641	0.392435	0.196218	+	0.980560i	$0.437134\pi$
$270$	−0.210706	−0.0128231
$271$	22.0932	1.34206	0.671032	−	0.741428i	$-0.265851\pi$
$271$	22.0932	1.34206	0.671032	+	0.741428i	$0.265851\pi$
$272$	−20.2277	−1.22649
$273$	0	0
$274$	−1.21825	−0.0735969
$275$	11.8329	0.713549
$276$	1.99414	0.120033
$277$	−16.7331	−1.00540	−0.502699	−	0.864462i	$-0.667659\pi$
$277$	−16.7331	−1.00540	−0.502699	+	0.864462i	$0.667659\pi$
$278$	0.651334	0.0390644
$279$	4.06504	0.243367
$280$	0	0
$281$	16.7174	0.997278	0.498639	−	0.866810i	$-0.333833\pi$
$281$	16.7174	0.997278	0.498639	+	0.866810i	$0.333833\pi$
$282$	0.553044	0.0329333
$283$	−8.91974	−0.530223	−0.265112	−	0.964218i	$-0.585409\pi$
$283$	−8.91974	−0.530223	−0.265112	+	0.964218i	$0.585409\pi$
$284$	9.12218	0.541302
$285$	−14.2234	−0.842522
$286$	1.62726	0.0962220
$287$	0	0
$288$	0.914974	0.0539154
$289$	9.02766	0.531039
$290$	0.171227	0.0100548
$291$	−0.960302	−0.0562939
$292$	20.3417	1.19041
$293$	−25.2811	−1.47694	−0.738469	−	0.674288i	$-0.764451\pi$
$293$	−25.2811	−1.47694	−0.738469	+	0.674288i	$0.764451\pi$
$294$	0	0
$295$	39.5800	2.30444
$296$	−3.29251	−0.191373
$297$	−4.59164	−0.266434
$298$	−0.492347	−0.0285209
$299$	4.62981	0.267749
$300$	5.13899	0.296700
$301$	0	0
$302$	1.35467	0.0779523
$303$	−1.82419	−0.104797
$304$	20.4873	1.17502
$305$	−14.0153	−0.802514
$306$	−0.390520	−0.0223246
$307$	−2.11915	−0.120946	−0.0604732	−	0.998170i	$-0.519261\pi$
$307$	−2.11915	−0.120946	−0.0604732	+	0.998170i	$0.519261\pi$
$308$	0	0
$309$	−7.89875	−0.449344
$310$	0.856526	0.0486474
$311$	−10.6973	−0.606588	−0.303294	−	0.952897i	$-0.598086\pi$
$311$	−10.6973	−0.606588	−0.303294	+	0.952897i	$0.598086\pi$
$312$	1.41551	0.0801374
$313$	4.33319	0.244926	0.122463	−	0.992473i	$-0.460921\pi$
$313$	4.33319	0.244926	0.122463	+	0.992473i	$0.460921\pi$
$314$	1.25531	0.0708414
$315$	0	0
$316$	−10.2057	−0.574116
$317$	22.6310	1.27108	0.635541	−	0.772067i	$-0.280777\pi$
$317$	22.6310	1.27108	0.635541	+	0.772067i	$0.280777\pi$
$318$	−0.281581	−0.0157903
$319$	3.73133	0.208915
$320$	−21.6350	−1.20943
$321$	14.3647	0.801757
$322$	0	0
$323$	−26.3616	−1.46680
$324$	−1.99414	−0.110786
$325$	11.9312	0.661825
$326$	−0.619770	−0.0343259
$327$	0.857844	0.0474389
$328$	0.732968	0.0404714
$329$	0	0
$330$	−0.967485	−0.0532583
$331$	−25.3227	−1.39186	−0.695930	−	0.718110i	$-0.745008\pi$
$331$	−25.3227	−1.39186	−0.695930	+	0.718110i	$0.745008\pi$
$332$	−32.5555	−1.78672
$333$	10.7691	0.590140
$334$	1.45590	0.0796631
$335$	−36.9647	−2.01960
$336$	0	0
$337$	−1.19487	−0.0650889	−0.0325445	−	0.999470i	$-0.510361\pi$
$337$	−1.19487	−0.0650889	−0.0325445	+	0.999470i	$0.510361\pi$
$338$	0.645681	0.0351204
$339$	11.9826	0.650805
$340$	28.0042	1.51874
$341$	18.6652	1.01078
$342$	0.395531	0.0213878
$343$	0	0
$344$	3.66529	0.197619
$345$	−2.75264	−0.148197
$346$	0.838986	0.0451042
$347$	−0.323424	−0.0173623	−0.00868116	−	0.999962i	$-0.502763\pi$
$347$	−0.323424	−0.0173623	−0.00868116	+	0.999962i	$0.502763\pi$
$348$	1.62051	0.0868685
$349$	6.84940	0.366640	0.183320	−	0.983053i	$-0.441316\pi$
$349$	6.84940	0.366640	0.183320	+	0.983053i	$0.441316\pi$
$350$	0	0
$351$	−4.62981	−0.247121
$352$	4.20123	0.223927
$353$	−6.37022	−0.339052	−0.169526	−	0.985526i	$-0.554224\pi$
$353$	−6.37022	−0.339052	−0.169526	+	0.985526i	$0.554224\pi$
$354$	−1.10066	−0.0584993
$355$	−12.5919	−0.668311
$356$	−14.0980	−0.747191
$357$	0	0
$358$	1.56274	0.0825931
$359$	29.4094	1.55217	0.776085	−	0.630629i	$-0.217203\pi$
$359$	29.4094	1.55217	0.776085	+	0.630629i	$0.217203\pi$
$360$	−0.841588	−0.0443556
$361$	7.69980	0.405252
$362$	0.755677	0.0397175
$363$	−10.0832	−0.529230
$364$	0	0
$365$	−28.0789	−1.46972
$366$	0.389744	0.0203722
$367$	−20.6427	−1.07754	−0.538770	−	0.842453i	$-0.681111\pi$
$367$	−20.6427	−1.07754	−0.538770	+	0.842453i	$0.681111\pi$
$368$	3.96488	0.206684
$369$	−2.39737	−0.124802
$370$	2.26910	0.117965
$371$	0	0
$372$	8.10626	0.420290
$373$	32.5727	1.68655	0.843274	−	0.537483i	$-0.180625\pi$
$373$	32.5727	1.68655	0.843274	+	0.537483i	$0.180625\pi$
$374$	−1.79313	−0.0927206
$375$	6.66953	0.344413
$376$	2.20893	0.113917
$377$	3.76235	0.193771
$378$	0	0
$379$	30.4478	1.56400	0.782000	−	0.623279i	$-0.214200\pi$
$379$	30.4478	1.56400	0.782000	+	0.623279i	$0.214200\pi$
$380$	−28.3635	−1.45502
$381$	−15.4442	−0.791228
$382$	−0.524339	−0.0268275
$383$	4.83720	0.247169	0.123585	−	0.992334i	$-0.460561\pi$
$383$	4.83720	0.247169	0.123585	+	0.992334i	$0.460561\pi$
$384$	2.43158	0.124086
$385$	0	0
$386$	1.29960	0.0661478
$387$	−11.9883	−0.609401
$388$	−1.91498	−0.0972183
$389$	−13.1497	−0.666715	−0.333357	−	0.942801i	$-0.608182\pi$
$389$	−13.1497	−0.666715	−0.333357	+	0.942801i	$0.608182\pi$
$390$	−0.975527	−0.0493977
$391$	−5.10173	−0.258006
$392$	0	0
$393$	−9.28879	−0.468558
$394$	−1.10945	−0.0558931
$395$	14.0876	0.708824
$396$	−9.15638	−0.460125
$397$	−38.0053	−1.90743	−0.953714	−	0.300714i	$-0.902775\pi$
$397$	−38.0053	−1.90743	−0.953714	+	0.300714i	$0.902775\pi$
$398$	0.447153	0.0224138
$399$	0	0
$400$	10.2177	0.510883
$401$	−10.6956	−0.534112	−0.267056	−	0.963681i	$-0.586051\pi$
$401$	−10.6956	−0.534112	−0.267056	+	0.963681i	$0.586051\pi$
$402$	1.02793	0.0512684
$403$	18.8203	0.937508
$404$	−3.63770	−0.180982
$405$	2.75264	0.136780
$406$	0	0
$407$	49.4476	2.45103
$408$	−1.55979	−0.0772213
$409$	−18.2682	−0.903305	−0.451652	−	0.892194i	$-0.649165\pi$
$409$	−18.2682	−0.903305	−0.451652	+	0.892194i	$0.649165\pi$
$410$	−0.505140	−0.0249471
$411$	15.9151	0.785033
$412$	−15.7512	−0.776006
$413$	0	0
$414$	0.0765467	0.00376206
$415$	44.9386	2.20595
$416$	4.23616	0.207695
$417$	−8.50898	−0.416686
$418$	1.81614	0.0888301
$419$	−28.7904	−1.40650	−0.703251	−	0.710942i	$-0.748269\pi$
$419$	−28.7904	−1.40650	−0.703251	+	0.710942i	$0.748269\pi$
$420$	0	0
$421$	12.3740	0.603073	0.301536	−	0.953455i	$-0.402501\pi$
$421$	12.3740	0.603073	0.301536	+	0.953455i	$0.402501\pi$
$422$	−1.42794	−0.0695110
$423$	−7.22492	−0.351288
$424$	−1.12467	−0.0546190
$425$	−13.1474	−0.637742
$426$	0.350162	0.0169654
$427$	0	0
$428$	28.6452	1.38462
$429$	−21.2584	−1.02637
$430$	−2.52601	−0.121815
$431$	15.8877	0.765284	0.382642	−	0.923897i	$-0.375014\pi$
$431$	15.8877	0.765284	0.382642	+	0.923897i	$0.375014\pi$
$432$	−3.96488	−0.190760
$433$	21.3930	1.02808	0.514040	−	0.857766i	$-0.328148\pi$
$433$	21.3930	1.02808	0.514040	+	0.857766i	$0.328148\pi$
$434$	0	0
$435$	−2.23690	−0.107251
$436$	1.71066	0.0819259
$437$	5.16718	0.247180
$438$	0.780831	0.0373095
$439$	25.5402	1.21897	0.609485	−	0.792798i	$-0.291376\pi$
$439$	25.5402	1.21897	0.609485	+	0.792798i	$0.291376\pi$
$440$	−3.86427	−0.184222
$441$	0	0
$442$	−1.80804	−0.0859995
$443$	15.6353	0.742857	0.371429	−	0.928462i	$-0.378868\pi$
$443$	15.6353	0.742857	0.371429	+	0.928462i	$0.378868\pi$
$444$	21.4750	1.01916
$445$	19.4604	0.922510
$446$	0.992101	0.0469773
$447$	6.43199	0.304223
$448$	0	0
$449$	−27.8171	−1.31277	−0.656384	−	0.754427i	$-0.727915\pi$
$449$	−27.8171	−1.31277	−0.656384	+	0.754427i	$0.727915\pi$
$450$	0.197264	0.00929912
$451$	−11.0079	−0.518341
$452$	23.8950	1.12392
$453$	−17.6973	−0.831490
$454$	−1.44693	−0.0679079
$455$	0	0
$456$	1.57981	0.0739812
$457$	8.60210	0.402389	0.201195	−	0.979551i	$-0.435518\pi$
$457$	8.60210	0.402389	0.201195	+	0.979551i	$0.435518\pi$
$458$	0.813260	0.0380012
$459$	5.10173	0.238128
$460$	−5.48916	−0.255933
$461$	8.29643	0.386403	0.193202	−	0.981159i	$-0.438113\pi$
$461$	8.29643	0.386403	0.193202	+	0.981159i	$0.438113\pi$
$462$	0	0
$463$	−23.5103	−1.09262	−0.546308	−	0.837584i	$-0.683967\pi$
$463$	−23.5103	−1.09262	−0.546308	+	0.837584i	$0.683967\pi$
$464$	3.22200	0.149578
$465$	−11.1896	−0.518905
$466$	0.526266	0.0243788
$467$	14.0472	0.650026	0.325013	−	0.945710i	$-0.394631\pi$
$467$	14.0472	0.650026	0.325013	+	0.945710i	$0.394631\pi$
$468$	−9.23249	−0.426772
$469$	0	0
$470$	−1.52233	−0.0702199
$471$	−16.3993	−0.755641
$472$	−4.39618	−0.202351
$473$	−55.0461	−2.53102
$474$	−0.391754	−0.0179939
$475$	13.3161	0.610983
$476$	0	0
$477$	3.67855	0.168429
$478$	−0.543426	−0.0248557
$479$	13.8135	0.631155	0.315578	−	0.948900i	$-0.397802\pi$
$479$	13.8135	0.631155	0.315578	+	0.948900i	$0.397802\pi$
$480$	−2.51860	−0.114958
$481$	49.8587	2.27336
$482$	−1.68431	−0.0767182
$483$	0	0
$484$	−20.1073	−0.913967
$485$	2.64337	0.120029
$486$	−0.0765467	−0.00347223
$487$	−14.7413	−0.667991	−0.333996	−	0.942575i	$-0.608397\pi$
$487$	−14.7413	−0.667991	−0.333996	+	0.942575i	$0.608397\pi$
$488$	1.55669	0.0704681
$489$	8.09663	0.366142
$490$	0	0
$491$	−17.2698	−0.779373	−0.389687	−	0.920947i	$-0.627417\pi$
$491$	−17.2698	−0.779373	−0.389687	+	0.920947i	$0.627417\pi$
$492$	−4.78070	−0.215531
$493$	−4.14585	−0.186720
$494$	1.83123	0.0823910
$495$	12.6392	0.568088
$496$	16.1174	0.723692
$497$	0	0
$498$	−1.24967	−0.0559991
$499$	−28.0773	−1.25691	−0.628457	−	0.777845i	$-0.716313\pi$
$499$	−28.0773	−1.25691	−0.628457	+	0.777845i	$0.716313\pi$
$500$	13.3000	0.594793
$501$	−19.0197	−0.849739
$502$	0.830944	0.0370868
$503$	18.0971	0.806910	0.403455	−	0.914999i	$-0.367809\pi$
$503$	18.0971	0.806910	0.403455	+	0.914999i	$0.367809\pi$
$504$	0	0
$505$	5.02136	0.223447
$506$	0.351475	0.0156250
$507$	−8.43513	−0.374617
$508$	−30.7978	−1.36643
$509$	−31.4071	−1.39209	−0.696047	−	0.717996i	$-0.745059\pi$
$509$	−31.4071	−1.39209	−0.696047	+	0.717996i	$0.745059\pi$
$510$	1.07496	0.0476002
$511$	0	0
$512$	6.05219	0.267472
$513$	−5.16718	−0.228137
$514$	0.216227	0.00953736
$515$	21.7424	0.958086
$516$	−23.9064	−1.05242
$517$	−33.1743	−1.45900
$518$	0	0
$519$	−10.9605	−0.481110
$520$	−3.89639	−0.170868
$521$	−20.5048	−0.898333	−0.449167	−	0.893448i	$-0.648279\pi$
$521$	−20.5048	−0.898333	−0.449167	+	0.893448i	$0.648279\pi$
$522$	0.0622046	0.00272262
$523$	34.1817	1.49466	0.747332	−	0.664451i	$-0.231335\pi$
$523$	34.1817	1.49466	0.747332	+	0.664451i	$0.231335\pi$
$524$	−18.5232	−0.809188
$525$	0	0
$526$	0.0778229	0.00339324
$527$	−20.7387	−0.903393
$528$	−18.2053	−0.792284
$529$	1.00000	0.0434783
$530$	0.775092	0.0336678
$531$	14.3789	0.623992
$532$	0	0
$533$	−11.0994	−0.480767
$534$	−0.541162	−0.0234184
$535$	−39.5408	−1.70950
$536$	4.10569	0.177339
$537$	−20.4155	−0.880992
$538$	0.492686	0.0212412
$539$	0	0
$540$	5.48916	0.236216
$541$	17.2220	0.740432	0.370216	−	0.928946i	$-0.379284\pi$
$541$	17.2220	0.740432	0.370216	+	0.928946i	$0.379284\pi$
$542$	1.69116	0.0726415
$543$	−9.87211	−0.423653
$544$	−4.66795	−0.200137
$545$	−2.36134	−0.101149
$546$	0	0
$547$	2.56784	0.109793	0.0548964	−	0.998492i	$-0.482517\pi$
$547$	2.56784	0.109793	0.0548964	+	0.998492i	$0.482517\pi$
$548$	31.7369	1.35573
$549$	−5.09158	−0.217303
$550$	0.905766	0.0386220
$551$	4.19904	0.178885
$552$	0.305738	0.0130131
$553$	0	0
$554$	−1.28087	−0.0544188
$555$	−29.6434	−1.25829
$556$	−16.9681	−0.719608
$557$	−39.7714	−1.68517	−0.842584	−	0.538565i	$-0.818967\pi$
$557$	−39.7714	−1.68517	−0.842584	+	0.538565i	$0.818967\pi$
$558$	0.311165	0.0131727
$559$	−55.5037	−2.34755
$560$	0	0
$561$	23.4253	0.989018
$562$	1.27966	0.0539793
$563$	16.2092	0.683136	0.341568	−	0.939857i	$-0.389042\pi$
$563$	16.2092	0.683136	0.341568	+	0.939857i	$0.389042\pi$
$564$	−14.4075	−0.606666
$565$	−32.9838	−1.38764
$566$	−0.682776	−0.0286992
$567$	0	0
$568$	1.39860	0.0586838
$569$	−25.3640	−1.06332	−0.531658	−	0.846959i	$-0.678431\pi$
$569$	−25.3640	−1.06332	−0.531658	+	0.846959i	$0.678431\pi$
$570$	−1.08875	−0.0456029
$571$	−21.8810	−0.915691	−0.457845	−	0.889032i	$-0.651379\pi$
$571$	−21.8810	−0.915691	−0.457845	+	0.889032i	$0.651379\pi$
$572$	−42.3923	−1.77251
$573$	6.84993	0.286160
$574$	0	0
$575$	2.57704	0.107470
$576$	−7.85972	−0.327488
$577$	−8.08214	−0.336464	−0.168232	−	0.985747i	$-0.553806\pi$
$577$	−8.08214	−0.336464	−0.168232	+	0.985747i	$0.553806\pi$
$578$	0.691037	0.0287434
$579$	−16.9779	−0.705576
$580$	−4.46069	−0.185220
$581$	0	0
$582$	−0.0735079	−0.00304700
$583$	16.8906	0.699537
$584$	3.11875	0.129055
$585$	12.7442	0.526908
$586$	−1.93518	−0.0799417
$587$	11.2517	0.464408	0.232204	−	0.972667i	$-0.425406\pi$
$587$	11.2517	0.464408	0.232204	+	0.972667i	$0.425406\pi$
$588$	0	0
$589$	21.0048	0.865488
$590$	3.02972	0.124732
$591$	14.4937	0.596192
$592$	42.6980	1.75488
$593$	4.64049	0.190562	0.0952811	−	0.995450i	$-0.469625\pi$
$593$	4.64049	0.190562	0.0952811	+	0.995450i	$0.469625\pi$
$594$	−0.351475	−0.0144212
$595$	0	0
$596$	12.8263	0.525385
$597$	−5.84157	−0.239080
$598$	0.354396	0.0144923
$599$	−12.8670	−0.525730	−0.262865	−	0.964833i	$-0.584667\pi$
$599$	−12.8670	−0.525730	−0.262865	+	0.964833i	$0.584667\pi$
$600$	0.787901	0.0321659
$601$	0.556914	0.0227170	0.0113585	−	0.999935i	$-0.496384\pi$
$601$	0.556914	0.0227170	0.0113585	+	0.999935i	$0.496384\pi$
$602$	0	0
$603$	−13.4288	−0.546863
$604$	−35.2908	−1.43596
$605$	27.7554	1.12842
$606$	−0.139636	−0.00567232
$607$	39.1231	1.58796	0.793979	−	0.607946i	$-0.208006\pi$
$607$	39.1231	1.58796	0.793979	+	0.607946i	$0.208006\pi$
$608$	4.72784	0.191739
$609$	0	0
$610$	−1.07283	−0.0434374
$611$	−33.4500	−1.35324
$612$	10.1736	0.411242
$613$	−23.3837	−0.944458	−0.472229	−	0.881476i	$-0.656550\pi$
$613$	−23.3837	−0.944458	−0.472229	+	0.881476i	$0.656550\pi$
$614$	−0.162214	−0.00654643
$615$	6.59911	0.266102
$616$	0	0
$617$	−14.2866	−0.575155	−0.287578	−	0.957757i	$-0.592850\pi$
$617$	−14.2866	−0.575155	−0.287578	+	0.957757i	$0.592850\pi$
$618$	−0.604623	−0.0243215
$619$	−20.9097	−0.840433	−0.420216	−	0.907424i	$-0.638046\pi$
$619$	−20.9097	−0.840433	−0.420216	+	0.907424i	$0.638046\pi$
$620$	−22.3136	−0.896137
$621$	−1.00000	−0.0401286
$622$	−0.818843	−0.0328326
$623$	0	0
$624$	−18.3566	−0.734853
$625$	−31.2441	−1.24976
$626$	0.331691	0.0132570
$627$	−23.7259	−0.947520
$628$	−32.7025	−1.30497
$629$	−54.9408	−2.19063
$630$	0	0
$631$	28.1881	1.12215	0.561075	−	0.827765i	$-0.310388\pi$
$631$	28.1881	1.12215	0.561075	+	0.827765i	$0.310388\pi$
$632$	−1.56472	−0.0622412
$633$	18.6545	0.741449
$634$	1.73232	0.0687994
$635$	42.5122	1.68705
$636$	7.33555	0.290874
$637$	0	0
$638$	0.285621	0.0113078
$639$	−4.57449	−0.180964
$640$	−6.69328	−0.264575
$641$	−30.5054	−1.20489	−0.602445	−	0.798160i	$-0.705807\pi$
$641$	−30.5054	−1.20489	−0.602445	+	0.798160i	$0.705807\pi$
$642$	1.09957	0.0433964
$643$	−26.1260	−1.03031	−0.515154	−	0.857098i	$-0.672265\pi$
$643$	−26.1260	−1.03031	−0.515154	+	0.857098i	$0.672265\pi$
$644$	0	0
$645$	32.9996	1.29936
$646$	−2.01789	−0.0793929
$647$	−33.0897	−1.30089	−0.650445	−	0.759554i	$-0.725417\pi$
$647$	−33.0897	−1.30089	−0.650445	+	0.759554i	$0.725417\pi$
$648$	−0.305738	−0.0120105
$649$	66.0228	2.59162
$650$	0.913295	0.0358224
$651$	0	0
$652$	16.1458	0.632319
$653$	12.3000	0.481335	0.240667	−	0.970608i	$-0.422634\pi$
$653$	12.3000	0.481335	0.240667	+	0.970608i	$0.422634\pi$
$654$	0.0656651	0.00256771
$655$	25.5687	0.999053
$656$	−9.50529	−0.371119
$657$	−10.2007	−0.397968
$658$	0	0
$659$	−5.38554	−0.209791	−0.104895	−	0.994483i	$-0.533451\pi$
$659$	−5.38554	−0.209791	−0.104895	+	0.994483i	$0.533451\pi$
$660$	25.2042	0.981074
$661$	2.08076	0.0809322	0.0404661	−	0.999181i	$-0.487116\pi$
$661$	2.08076	0.0809322	0.0404661	+	0.999181i	$0.487116\pi$
$662$	−1.93837	−0.0753367
$663$	23.6200	0.917326
$664$	−4.99136	−0.193702
$665$	0	0
$666$	0.824335	0.0319423
$667$	0.812636	0.0314654
$668$	−37.9280	−1.46748
$669$	−12.9607	−0.501091
$670$	−2.82952	−0.109314
$671$	−23.3787	−0.902526
$672$	0	0
$673$	−38.8428	−1.49728	−0.748641	−	0.662976i	$-0.769293\pi$
$673$	−38.8428	−1.49728	−0.748641	+	0.662976i	$0.769293\pi$
$674$	−0.0914636	−0.00352305
$675$	−2.57704	−0.0991905
$676$	−16.8208	−0.646955
$677$	0.265508	0.0102043	0.00510215	−	0.999987i	$-0.498376\pi$
$677$	0.265508	0.0102043	0.00510215	+	0.999987i	$0.498376\pi$
$678$	0.917227	0.0352259
$679$	0	0
$680$	4.29356	0.164650
$681$	18.9026	0.724350
$682$	1.42876	0.0547100
$683$	−32.9338	−1.26018	−0.630089	−	0.776523i	$-0.716982\pi$
$683$	−32.9338	−1.26018	−0.630089	+	0.776523i	$0.716982\pi$
$684$	−10.3041	−0.393987
$685$	−43.8085	−1.67384
$686$	0	0
$687$	−10.6244	−0.405345
$688$	−47.5322	−1.81215
$689$	17.0310	0.648829
$690$	−0.210706	−0.00802143
$691$	−6.03693	−0.229656	−0.114828	−	0.993385i	$-0.536632\pi$
$691$	−6.03693	−0.229656	−0.114828	+	0.993385i	$0.536632\pi$
$692$	−21.8567	−0.830866
$693$	0	0
$694$	−0.0247570	−0.000939764 0
$695$	23.4222	0.888454
$696$	0.248454	0.00941762
$697$	12.2308	0.463273
$698$	0.524299	0.0198450
$699$	−6.87511	−0.260040
$700$	0	0
$701$	−7.68618	−0.290303	−0.145152	−	0.989409i	$-0.546367\pi$
$701$	−7.68618	−0.290303	−0.145152	+	0.989409i	$0.546367\pi$
$702$	−0.354396	−0.0133758
$703$	55.6457	2.09872
$704$	−36.0890	−1.36016
$705$	19.8876	0.749012
$706$	−0.487619	−0.0183518
$707$	0	0
$708$	28.6736	1.07762
$709$	19.0298	0.714678	0.357339	−	0.933975i	$-0.383684\pi$
$709$	19.0298	0.714678	0.357339	+	0.933975i	$0.383684\pi$
$710$	−0.963871	−0.0361734
$711$	5.11785	0.191934
$712$	−2.16148	−0.0810048
$713$	4.06504	0.152237
$714$	0	0
$715$	58.5169	2.18841
$716$	−40.7113	−1.52145
$717$	7.09928	0.265127
$718$	2.25119	0.0840137
$719$	32.4773	1.21120	0.605600	−	0.795769i	$-0.292933\pi$
$719$	32.4773	1.21120	0.605600	+	0.795769i	$0.292933\pi$
$720$	10.9139	0.406737
$721$	0	0
$722$	0.589394	0.0219350
$723$	22.0037	0.818327
$724$	−19.6864	−0.731638
$725$	2.09420	0.0777766
$726$	−0.771834	−0.0286454
$727$	−27.7588	−1.02952	−0.514759	−	0.857335i	$-0.672119\pi$
$727$	−27.7588	−1.02952	−0.514759	+	0.857335i	$0.672119\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−2.14935	−0.0795509
$731$	61.1612	2.26213
$732$	−10.1533	−0.375278
$733$	−42.6834	−1.57655	−0.788274	−	0.615325i	$-0.789025\pi$
$733$	−42.6834	−1.57655	−0.788274	+	0.615325i	$0.789025\pi$
$734$	−1.58013	−0.0583237
$735$	0	0
$736$	0.914974	0.0337264
$737$	−61.6602	−2.27128
$738$	−0.183511	−0.00675513
$739$	21.3413	0.785054	0.392527	−	0.919741i	$-0.371601\pi$
$739$	21.3413	0.785054	0.392527	+	0.919741i	$0.371601\pi$
$740$	−59.1130	−2.17304
$741$	−23.9231	−0.878836
$742$	0	0
$743$	24.5447	0.900459	0.450230	−	0.892913i	$-0.351342\pi$
$743$	24.5447	0.900459	0.450230	+	0.892913i	$0.351342\pi$
$744$	1.24284	0.0455646
$745$	−17.7050	−0.648660
$746$	2.49333	0.0912872
$747$	16.3256	0.597323
$748$	46.7134	1.70801
$749$	0	0
$750$	0.510530	0.0186419
$751$	20.6346	0.752969	0.376484	−	0.926423i	$-0.377133\pi$
$751$	20.6346	0.752969	0.376484	+	0.926423i	$0.377133\pi$
$752$	−28.6459	−1.04461
$753$	−10.8554	−0.395593
$754$	0.287995	0.0104882
$755$	48.7143	1.77289
$756$	0	0
$757$	7.28222	0.264677	0.132338	−	0.991205i	$-0.457751\pi$
$757$	7.28222	0.264677	0.132338	+	0.991205i	$0.457751\pi$
$758$	2.33068	0.0846541
$759$	−4.59164	−0.166666
$760$	−4.34864	−0.157742
$761$	−16.9920	−0.615960	−0.307980	−	0.951393i	$-0.599653\pi$
$761$	−16.9920	−0.615960	−0.307980	+	0.951393i	$0.599653\pi$
$762$	−1.18220	−0.0428265
$763$	0	0
$764$	13.6597	0.494191
$765$	−14.0432	−0.507735
$766$	0.370271	0.0133785
$767$	66.5716	2.40376
$768$	−15.5333	−0.560510
$769$	38.0773	1.37310	0.686551	−	0.727082i	$-0.259124\pi$
$769$	38.0773	1.37310	0.686551	+	0.727082i	$0.259124\pi$
$770$	0	0
$771$	−2.82477	−0.101732
$772$	−33.8562	−1.21851
$773$	−15.1595	−0.545251	−0.272625	−	0.962120i	$-0.587892\pi$
$773$	−15.1595	−0.545251	−0.272625	+	0.962120i	$0.587892\pi$
$774$	−0.917666	−0.0329848
$775$	10.4758	0.376301
$776$	−0.293601	−0.0105397
$777$	0	0
$778$	−1.00656	−0.0360870
$779$	−12.3877	−0.443834
$780$	25.4138	0.909958
$781$	−21.0044	−0.751598
$782$	−0.390520	−0.0139650
$783$	−0.812636	−0.0290412
$784$	0	0
$785$	45.1415	1.61117
$786$	−0.711026	−0.0253615
$787$	−4.34729	−0.154964	−0.0774821	−	0.996994i	$-0.524688\pi$
$787$	−4.34729	−0.154964	−0.0774821	+	0.996994i	$0.524688\pi$
$788$	28.9025	1.02961
$789$	−1.01667	−0.0361945
$790$	1.07836	0.0383663
$791$	0	0
$792$	−1.40384	−0.0498833
$793$	−23.5731	−0.837104
$794$	−2.90917	−0.103243
$795$	−10.1257	−0.359123
$796$	−11.6489	−0.412885
$797$	9.74274	0.345106	0.172553	−	0.985000i	$-0.444798\pi$
$797$	9.74274	0.345106	0.172553	+	0.985000i	$0.444798\pi$
$798$	0	0
$799$	36.8596	1.30400
$800$	2.35793	0.0833654
$801$	7.06970	0.249796
$802$	−0.818711	−0.0289097
$803$	−46.8380	−1.65288
$804$	−26.7789	−0.944419
$805$	0	0
$806$	1.44063	0.0507442
$807$	−6.43641	−0.226573
$808$	−0.557726	−0.0196207
$809$	0.947898	0.0333263	0.0166632	−	0.999861i	$-0.494696\pi$
$809$	0.947898	0.0333263	0.0166632	+	0.999861i	$0.494696\pi$
$810$	0.210706	0.00740344
$811$	−1.90262	−0.0668101	−0.0334050	−	0.999442i	$-0.510635\pi$
$811$	−1.90262	−0.0668101	−0.0334050	+	0.999442i	$0.510635\pi$
$812$	0	0
$813$	−22.0932	−0.774841
$814$	3.78505	0.132666
$815$	−22.2871	−0.780684
$816$	20.2277	0.708113
$817$	−61.9459	−2.16721
$818$	−1.39837	−0.0488929
$819$	0	0
$820$	13.1596	0.459552
$821$	−38.1545	−1.33160	−0.665801	−	0.746129i	$-0.731910\pi$
$821$	−38.1545	−1.33160	−0.665801	+	0.746129i	$0.731910\pi$
$822$	1.21825	0.0424912
$823$	35.9174	1.25200	0.626002	−	0.779822i	$-0.284690\pi$
$823$	35.9174	1.25200	0.626002	+	0.779822i	$0.284690\pi$
$824$	−2.41495	−0.0841287
$825$	−11.8329	−0.411968
$826$	0	0
$827$	−3.09853	−0.107746	−0.0538731	−	0.998548i	$-0.517157\pi$
$827$	−3.09853	−0.107746	−0.0538731	+	0.998548i	$0.517157\pi$
$828$	−1.99414	−0.0693012
$829$	−13.5117	−0.469282	−0.234641	−	0.972082i	$-0.575391\pi$
$829$	−13.5117	−0.469282	−0.234641	+	0.972082i	$0.575391\pi$
$830$	3.43990	0.119401
$831$	16.7331	0.580466
$832$	−36.3890	−1.26156
$833$	0	0
$834$	−0.651334	−0.0225538
$835$	52.3545	1.81180
$836$	−47.3127	−1.63634
$837$	−4.06504	−0.140508
$838$	−2.20381	−0.0761292
$839$	30.6510	1.05819	0.529095	−	0.848562i	$-0.322531\pi$
$839$	30.6510	1.05819	0.529095	+	0.848562i	$0.322531\pi$
$840$	0	0
$841$	−28.3396	−0.977228
$842$	0.947189	0.0326423
$843$	−16.7174	−0.575779
$844$	37.1997	1.28047
$845$	23.2189	0.798755
$846$	−0.553044	−0.0190140
$847$	0	0
$848$	14.5850	0.500851
$849$	8.91974	0.306125
$850$	−1.00639	−0.0345188
$851$	10.7691	0.369158
$852$	−9.12218	−0.312521
$853$	49.4046	1.69158	0.845791	−	0.533514i	$-0.179129\pi$
$853$	49.4046	1.69158	0.845791	+	0.533514i	$0.179129\pi$
$854$	0	0
$855$	14.2234	0.486431
$856$	4.39182	0.150109
$857$	−28.4626	−0.972263	−0.486131	−	0.873886i	$-0.661592\pi$
$857$	−28.4626	−0.972263	−0.486131	+	0.873886i	$0.661592\pi$
$858$	−1.62726	−0.0555538
$859$	44.5024	1.51840	0.759201	−	0.650856i	$-0.225590\pi$
$859$	44.5024	1.51840	0.759201	+	0.650856i	$0.225590\pi$
$860$	65.8058	2.24396
$861$	0	0
$862$	1.21615	0.0414223
$863$	−51.6358	−1.75770	−0.878851	−	0.477096i	$-0.841690\pi$
$863$	−51.6358	−1.75770	−0.878851	+	0.477096i	$0.841690\pi$
$864$	−0.914974	−0.0311281
$865$	30.1702	1.02582
$866$	1.63756	0.0556465
$867$	−9.02766	−0.306595
$868$	0	0
$869$	23.4993	0.797160
$870$	−0.171227	−0.00580514
$871$	−62.1727	−2.10664
$872$	0.262276	0.00888178
$873$	0.960302	0.0325013
$874$	0.395531	0.0133790
$875$	0	0
$876$	−20.3417	−0.687281
$877$	1.85065	0.0624921	0.0312461	−	0.999512i	$-0.490052\pi$
$877$	1.85065	0.0624921	0.0312461	+	0.999512i	$0.490052\pi$
$878$	1.95502	0.0659787
$879$	25.2811	0.852710
$880$	50.1127	1.68930
$881$	−56.2234	−1.89422	−0.947108	−	0.320916i	$-0.896009\pi$
$881$	−56.2234	−1.89422	−0.947108	+	0.320916i	$0.896009\pi$
$882$	0	0
$883$	9.48572	0.319220	0.159610	−	0.987180i	$-0.448976\pi$
$883$	9.48572	0.319220	0.159610	+	0.987180i	$0.448976\pi$
$884$	47.1017	1.58420
$885$	−39.5800	−1.33047
$886$	1.19683	0.0402084
$887$	38.1889	1.28226	0.641129	−	0.767433i	$-0.278466\pi$
$887$	38.1889	1.28226	0.641129	+	0.767433i	$0.278466\pi$
$888$	3.29251	0.110489
$889$	0	0
$890$	1.48963	0.0499324
$891$	4.59164	0.153826
$892$	−25.8455	−0.865372
$893$	−37.3325	−1.24929
$894$	0.492347	0.0164665
$895$	56.1965	1.87844
$896$	0	0
$897$	−4.62981	−0.154585
$898$	−2.12930	−0.0710558
$899$	3.30340	0.110174
$900$	−5.13899	−0.171300
$901$	−18.7670	−0.625219
$902$	−0.842616	−0.0280561
$903$	0	0
$904$	3.66353	0.121847
$905$	27.1744	0.903307
$906$	−1.35467	−0.0450058
$907$	9.34855	0.310413	0.155207	−	0.987882i	$-0.450396\pi$
$907$	9.34855	0.310413	0.155207	+	0.987882i	$0.450396\pi$
$908$	37.6945	1.25094
$909$	1.82419	0.0605047
$910$	0	0
$911$	−11.6146	−0.384809	−0.192404	−	0.981316i	$-0.561628\pi$
$911$	−11.6146	−0.384809	−0.192404	+	0.981316i	$0.561628\pi$
$912$	−20.4873	−0.678401
$913$	74.9613	2.48086
$914$	0.658462	0.0217800
$915$	14.0153	0.463332
$916$	−21.1865	−0.700021
$917$	0	0
$918$	0.390520	0.0128891
$919$	53.8146	1.77518	0.887589	−	0.460636i	$-0.152379\pi$
$919$	53.8146	1.77518	0.887589	+	0.460636i	$0.152379\pi$
$920$	−0.841588	−0.0277463
$921$	2.11915	0.0698285
$922$	0.635064	0.0209147
$923$	−21.1790	−0.697116
$924$	0	0
$925$	27.7523	0.912491
$926$	−1.79964	−0.0591397
$927$	7.89875	0.259429
$928$	0.743541	0.0244079
$929$	44.6042	1.46342	0.731709	−	0.681618i	$-0.238723\pi$
$929$	44.6042	1.46342	0.731709	+	0.681618i	$0.238723\pi$
$930$	−0.856526	−0.0280866
$931$	0	0
$932$	−13.7099	−0.449084
$933$	10.6973	0.350214
$934$	1.07526	0.0351837
$935$	−64.4816	−2.10877
$936$	−1.41551	−0.0462674
$937$	−6.38454	−0.208574	−0.104287	−	0.994547i	$-0.533256\pi$
$937$	−6.38454	−0.208574	−0.104287	+	0.994547i	$0.533256\pi$
$938$	0	0
$939$	−4.33319	−0.141408
$940$	39.6587	1.29353
$941$	15.4932	0.505064	0.252532	−	0.967589i	$-0.418737\pi$
$941$	15.4932	0.505064	0.252532	+	0.967589i	$0.418737\pi$
$942$	−1.25531	−0.0409003
$943$	−2.39737	−0.0780692
$944$	57.0106	1.85554
$945$	0	0
$946$	−4.21359	−0.136996
$947$	−23.3962	−0.760273	−0.380137	−	0.924930i	$-0.624123\pi$
$947$	−23.3962	−0.760273	−0.380137	+	0.924930i	$0.624123\pi$
$948$	10.2057	0.331466
$949$	−47.2274	−1.53307
$950$	1.01930	0.0330705
$951$	−22.6310	−0.733859
$952$	0	0
$953$	−12.6904	−0.411083	−0.205541	−	0.978648i	$-0.565895\pi$
$953$	−12.6904	−0.411083	−0.205541	+	0.978648i	$0.565895\pi$
$954$	0.281581	0.00911652
$955$	−18.8554	−0.610147
$956$	14.1570	0.457869
$957$	−3.73133	−0.120617
$958$	1.05738	0.0341623
$959$	0	0
$960$	21.6350	0.698267
$961$	−14.4755	−0.466951
$962$	3.81651	0.123049
$963$	−14.3647	−0.462895
$964$	43.8785	1.41323
$965$	46.7340	1.50442
$966$	0	0
$967$	45.6229	1.46713	0.733566	−	0.679618i	$-0.237855\pi$
$967$	45.6229	1.46713	0.733566	+	0.679618i	$0.237855\pi$
$968$	−3.08281	−0.0990853
$969$	26.3616	0.846856
$970$	0.202341	0.00649678
$971$	−27.6553	−0.887502	−0.443751	−	0.896150i	$-0.646352\pi$
$971$	−27.6553	−0.887502	−0.443751	+	0.896150i	$0.646352\pi$
$972$	1.99414	0.0639621
$973$	0	0
$974$	−1.12840	−0.0361561
$975$	−11.9312	−0.382105
$976$	−20.1875	−0.646186
$977$	42.3765	1.35574	0.677872	−	0.735180i	$-0.262902\pi$
$977$	42.3765	1.35574	0.677872	+	0.735180i	$0.262902\pi$
$978$	0.619770	0.0198181
$979$	32.4615	1.03748
$980$	0	0
$981$	−0.857844	−0.0273889
$982$	−1.32194	−0.0421849
$983$	−5.45680	−0.174045	−0.0870225	−	0.996206i	$-0.527735\pi$
$983$	−5.45680	−0.174045	−0.0870225	+	0.996206i	$0.527735\pi$
$984$	−0.732968	−0.0233662
$985$	−39.8960	−1.27119
$986$	−0.317351	−0.0101065
$987$	0	0
$988$	−47.7060	−1.51773
$989$	−11.9883	−0.381207
$990$	0.967485	0.0307487
$991$	−55.3832	−1.75931	−0.879653	−	0.475615i	$-0.842225\pi$
$991$	−55.3832	−1.75931	−0.879653	+	0.475615i	$0.842225\pi$
$992$	3.71940	0.118091
$993$	25.3227	0.803591
$994$	0	0
$995$	16.0798	0.509763
$996$	32.5555	1.03156
$997$	9.07597	0.287439	0.143719	−	0.989618i	$-0.454094\pi$
$997$	9.07597	0.287439	0.143719	+	0.989618i	$0.454094\pi$
$998$	−2.14922	−0.0680325
$999$	−10.7691	−0.340718

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.bg.1.6	✓	10	1.1	even	1	trivial
3381.2.a.bh.1.6	yes	10	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0765467 q^{2} -1.00000 q^{3} -1.99414 q^{4} +2.75264 q^{5} -0.0765467 q^{6} -0.305738 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.0765467 q^{2} -1.00000 q^{3} -1.99414 q^{4} +2.75264 q^{5} -0.0765467 q^{6} -0.305738 q^{8} +1.00000 q^{9} +0.210706 q^{10} +4.59164 q^{11} +1.99414 q^{12} +4.62981 q^{13} -2.75264 q^{15} +3.96488 q^{16} -5.10173 q^{17} +0.0765467 q^{18} +5.16718 q^{19} -5.48916 q^{20} +0.351475 q^{22} +1.00000 q^{23} +0.305738 q^{24} +2.57704 q^{25} +0.354396 q^{26} -1.00000 q^{27} +0.812636 q^{29} -0.210706 q^{30} +4.06504 q^{31} +0.914974 q^{32} -4.59164 q^{33} -0.390520 q^{34} -1.99414 q^{36} +10.7691 q^{37} +0.395531 q^{38} -4.62981 q^{39} -0.841588 q^{40} -2.39737 q^{41} -11.9883 q^{43} -9.15638 q^{44} +2.75264 q^{45} +0.0765467 q^{46} -7.22492 q^{47} -3.96488 q^{48} +0.197264 q^{50} +5.10173 q^{51} -9.23249 q^{52} +3.67855 q^{53} -0.0765467 q^{54} +12.6392 q^{55} -5.16718 q^{57} +0.0622046 q^{58} +14.3789 q^{59} +5.48916 q^{60} -5.09158 q^{61} +0.311165 q^{62} -7.85972 q^{64} +12.7442 q^{65} -0.351475 q^{66} -13.4288 q^{67} +10.1736 q^{68} -1.00000 q^{69} -4.57449 q^{71} -0.305738 q^{72} -10.2007 q^{73} +0.824335 q^{74} -2.57704 q^{75} -10.3041 q^{76} -0.354396 q^{78} +5.11785 q^{79} +10.9139 q^{80} +1.00000 q^{81} -0.183511 q^{82} +16.3256 q^{83} -14.0432 q^{85} -0.917666 q^{86} -0.812636 q^{87} -1.40384 q^{88} +7.06970 q^{89} +0.210706 q^{90} -1.99414 q^{92} -4.06504 q^{93} -0.553044 q^{94} +14.2234 q^{95} -0.914974 q^{96} +0.960302 q^{97} +4.59164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 10 q^{3} + 8 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 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

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