LMFDB - Embedded newform 1681.2.a.m.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1681,2,Mod(1,1681)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1681, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1681.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1681 = 41^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1681.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:	$13.4228525798$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 41)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	1681.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.27053 q^{2} -0.854760 q^{3} -0.385748 q^{4} +3.44852 q^{5} +1.08600 q^{6} -1.72762 q^{7} +3.03117 q^{8} -2.26939 q^{9} +O(q^{10})$	\(q-1.27053 q^{2} -0.854760 q^{3} -0.385748 q^{4} +3.44852 q^{5} +1.08600 q^{6} -1.72762 q^{7} +3.03117 q^{8} -2.26939 q^{9} -4.38146 q^{10} +4.47992 q^{11} +0.329722 q^{12} +2.42995 q^{13} +2.19500 q^{14} -2.94766 q^{15} -3.07970 q^{16} +0.305568 q^{17} +2.88333 q^{18} -1.75466 q^{19} -1.33026 q^{20} +1.47670 q^{21} -5.69188 q^{22} +4.63585 q^{23} -2.59092 q^{24} +6.89230 q^{25} -3.08734 q^{26} +4.50406 q^{27} +0.666427 q^{28} -9.67581 q^{29} +3.74509 q^{30} +7.39343 q^{31} -2.14948 q^{32} -3.82926 q^{33} -0.388234 q^{34} -5.95774 q^{35} +0.875411 q^{36} +7.38315 q^{37} +2.22935 q^{38} -2.07703 q^{39} +10.4531 q^{40} -1.87620 q^{42} +2.60766 q^{43} -1.72812 q^{44} -7.82603 q^{45} -5.89000 q^{46} -6.33554 q^{47} +2.63241 q^{48} -4.01532 q^{49} -8.75689 q^{50} -0.261187 q^{51} -0.937350 q^{52} -1.22505 q^{53} -5.72255 q^{54} +15.4491 q^{55} -5.23671 q^{56} +1.49981 q^{57} +12.2934 q^{58} -3.29962 q^{59} +1.13705 q^{60} -1.11443 q^{61} -9.39359 q^{62} +3.92064 q^{63} +8.89039 q^{64} +8.37975 q^{65} +4.86519 q^{66} -10.2075 q^{67} -0.117872 q^{68} -3.96254 q^{69} +7.56950 q^{70} +0.534120 q^{71} -6.87889 q^{72} +8.56300 q^{73} -9.38052 q^{74} -5.89126 q^{75} +0.676856 q^{76} -7.73961 q^{77} +2.63893 q^{78} +8.62440 q^{79} -10.6204 q^{80} +2.95827 q^{81} +9.88122 q^{83} -0.569635 q^{84} +1.05376 q^{85} -3.31312 q^{86} +8.27049 q^{87} +13.5794 q^{88} +14.6290 q^{89} +9.94322 q^{90} -4.19804 q^{91} -1.78827 q^{92} -6.31960 q^{93} +8.04951 q^{94} -6.05098 q^{95} +1.83729 q^{96} -9.88253 q^{97} +5.10160 q^{98} -10.1667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 + 20 * q^4 + 12 * q^5 + 24 * q^8 + 24 * q^9	$ 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 20 q^{16} + 20 q^{18} + 40 q^{20} + 56 q^{21} + 48 q^{23} + 8 q^{25} + 32 q^{31} + 36 q^{32} + 24 q^{33} + 108 q^{36} + 60 q^{39} + 44 q^{40} - 40 q^{42} + 36 q^{43} - 36 q^{45} + 36 q^{46} + 32 q^{49} - 60 q^{50} + 36 q^{51} - 60 q^{57} + 116 q^{59} + 40 q^{61} + 48 q^{62} + 60 q^{64} + 16 q^{66} + 4 q^{72} + 16 q^{73} + 24 q^{74} - 16 q^{77} - 60 q^{78} + 84 q^{80} - 28 q^{81} + 80 q^{83} - 24 q^{84} - 24 q^{86} + 76 q^{87} + 56 q^{90} + 40 q^{91} - 40 q^{92} + 36 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 20 * q^4 + 12 * q^5 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 20 * q^16 + 20 * q^18 + 40 * q^20 + 56 * q^21 + 48 * q^23 + 8 * q^25 + 32 * q^31 + 36 * q^32 + 24 * q^33 + 108 * q^36 + 60 * q^39 + 44 * q^40 - 40 * q^42 + 36 * q^43 - 36 * q^45 + 36 * q^46 + 32 * q^49 - 60 * q^50 + 36 * q^51 - 60 * q^57 + 116 * q^59 + 40 * q^61 + 48 * q^62 + 60 * q^64 + 16 * q^66 + 4 * q^72 + 16 * q^73 + 24 * q^74 - 16 * q^77 - 60 * q^78 + 84 * q^80 - 28 * q^81 + 80 * q^83 - 24 * q^84 - 24 * q^86 + 76 * q^87 + 56 * q^90 + 40 * q^91 - 40 * q^92 + 36 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.27053	−0.898402	−0.449201	−	0.893431i	$-0.648291\pi$
$2$	−1.27053	−0.898402	−0.449201	+	0.893431i	$0.648291\pi$
$3$	−0.854760	−0.493496	−0.246748	−	0.969080i	$-0.579362\pi$
$3$	−0.854760	−0.493496	−0.246748	+	0.969080i	$0.579362\pi$
$4$	−0.385748	−0.192874
$5$	3.44852	1.54223	0.771113	−	0.636698i	$-0.219700\pi$
$5$	3.44852	1.54223	0.771113	+	0.636698i	$0.219700\pi$
$6$	1.08600	0.443357
$7$	−1.72762	−0.652980	−0.326490	−	0.945201i	$-0.605866\pi$
$7$	−1.72762	−0.652980	−0.326490	+	0.945201i	$0.605866\pi$
$8$	3.03117	1.07168
$9$	−2.26939	−0.756462
$10$	−4.38146	−1.38554
$11$	4.47992	1.35075	0.675373	−	0.737476i	$-0.263982\pi$
$11$	4.47992	1.35075	0.675373	+	0.737476i	$0.263982\pi$
$12$	0.329722	0.0951825
$13$	2.42995	0.673948	0.336974	−	0.941514i	$-0.390597\pi$
$13$	2.42995	0.673948	0.336974	+	0.941514i	$0.390597\pi$
$14$	2.19500	0.586638
$15$	−2.94766	−0.761082
$16$	−3.07970	−0.769926
$17$	0.305568	0.0741110	0.0370555	−	0.999313i	$-0.488202\pi$
$17$	0.305568	0.0741110	0.0370555	+	0.999313i	$0.488202\pi$
$18$	2.88333	0.679607
$19$	−1.75466	−0.402546	−0.201273	−	0.979535i	$-0.564508\pi$
$19$	−1.75466	−0.402546	−0.201273	+	0.979535i	$0.564508\pi$
$20$	−1.33026	−0.297455
$21$	1.47670	0.322243
$22$	−5.69188	−1.21351
$23$	4.63585	0.966641	0.483321	−	0.875443i	$-0.339431\pi$
$23$	4.63585	0.966641	0.483321	+	0.875443i	$0.339431\pi$
$24$	−2.59092	−0.528870
$25$	6.89230	1.37846
$26$	−3.08734	−0.605476
$27$	4.50406	0.866806
$28$	0.666427	0.125943
$29$	−9.67581	−1.79675	−0.898376	−	0.439226i	$-0.855253\pi$
$29$	−9.67581	−1.79675	−0.898376	+	0.439226i	$0.855253\pi$
$30$	3.74509	0.683757
$31$	7.39343	1.32790	0.663949	−	0.747777i	$-0.268879\pi$
$31$	7.39343	1.32790	0.663949	+	0.747777i	$0.268879\pi$
$32$	−2.14948	−0.379978
$33$	−3.82926	−0.666588
$34$	−0.388234	−0.0665815
$35$	−5.95774	−1.00704
$36$	0.875411	0.145902
$37$	7.38315	1.21378	0.606891	−	0.794785i	$-0.292417\pi$
$37$	7.38315	1.21378	0.606891	+	0.794785i	$0.292417\pi$
$38$	2.22935	0.361648
$39$	−2.07703	−0.332591
$40$	10.4531	1.65277
$41$	0	0
$41$	0	0
$42$	−1.87620	−0.289503
$43$	2.60766	0.397665	0.198832	−	0.980033i	$-0.436285\pi$
$43$	2.60766	0.397665	0.198832	+	0.980033i	$0.436285\pi$
$44$	−1.72812	−0.260524
$45$	−7.82603	−1.16664
$46$	−5.89000	−0.868432
$47$	−6.33554	−0.924134	−0.462067	−	0.886845i	$-0.652892\pi$
$47$	−6.33554	−0.924134	−0.462067	+	0.886845i	$0.652892\pi$
$48$	2.63241	0.379955
$49$	−4.01532	−0.573618
$50$	−8.75689	−1.23841
$51$	−0.261187	−0.0365735
$52$	−0.937350	−0.129987
$53$	−1.22505	−0.168274	−0.0841368	−	0.996454i	$-0.526813\pi$
$53$	−1.22505	−0.168274	−0.0841368	+	0.996454i	$0.526813\pi$
$54$	−5.72255	−0.778741
$55$	15.4491	2.08316
$56$	−5.23671	−0.699785
$57$	1.49981	0.198655
$58$	12.2934	1.61421
$59$	−3.29962	−0.429574	−0.214787	−	0.976661i	$-0.568906\pi$
$59$	−3.29962	−0.429574	−0.214787	+	0.976661i	$0.568906\pi$
$60$	1.13705	0.146793
$61$	−1.11443	−0.142688	−0.0713438	−	0.997452i	$-0.522729\pi$
$61$	−1.11443	−0.142688	−0.0713438	+	0.997452i	$0.522729\pi$
$62$	−9.39359	−1.19299
$63$	3.92064	0.493954
$64$	8.89039	1.11130
$65$	8.37975	1.03938
$66$	4.86519	0.598864
$67$	−10.2075	−1.24704	−0.623521	−	0.781807i	$-0.714298\pi$
$67$	−10.2075	−1.24704	−0.623521	+	0.781807i	$0.714298\pi$
$68$	−0.117872	−0.0142941
$69$	−3.96254	−0.477033
$70$	7.56950	0.904729
$71$	0.534120	0.0633884	0.0316942	−	0.999498i	$-0.489910\pi$
$71$	0.534120	0.0633884	0.0316942	+	0.999498i	$0.489910\pi$
$72$	−6.87889	−0.810685
$73$	8.56300	1.00222	0.501112	−	0.865383i	$-0.332925\pi$
$73$	8.56300	1.00222	0.501112	+	0.865383i	$0.332925\pi$
$74$	−9.38052	−1.09046
$75$	−5.89126	−0.680264
$76$	0.676856	0.0776407
$77$	−7.73961	−0.882010
$78$	2.63893	0.298800
$79$	8.62440	0.970321	0.485160	−	0.874425i	$-0.338761\pi$
$79$	8.62440	0.970321	0.485160	+	0.874425i	$0.338761\pi$
$80$	−10.6204	−1.18740
$81$	2.95827	0.328697
$82$	0	0
$83$	9.88122	1.08460	0.542302	−	0.840183i	$-0.317553\pi$
$83$	9.88122	1.08460	0.542302	+	0.840183i	$0.317553\pi$
$84$	−0.569635	−0.0621522
$85$	1.05376	0.114296
$86$	−3.31312	−0.357263
$87$	8.27049	0.886690
$88$	13.5794	1.44757
$89$	14.6290	1.55067	0.775337	−	0.631548i	$-0.217580\pi$
$89$	14.6290	1.55067	0.775337	+	0.631548i	$0.217580\pi$
$90$	9.94322	1.04811
$91$	−4.19804	−0.440074
$92$	−1.78827	−0.186440
$93$	−6.31960	−0.655312
$94$	8.04951	0.830244
$95$	−6.05098	−0.620817
$96$	1.83729	0.187517
$97$	−9.88253	−1.00342	−0.501709	−	0.865036i	$-0.667295\pi$
$97$	−9.88253	−1.00342	−0.501709	+	0.865036i	$0.667295\pi$
$98$	5.10160	0.515339
$99$	−10.1667	−1.02179
$100$	−2.65869	−0.265869
$101$	−1.73862	−0.173000	−0.0864998	−	0.996252i	$-0.527568\pi$
$101$	−1.73862	−0.173000	−0.0864998	+	0.996252i	$0.527568\pi$
$102$	0.331846	0.0328577
$103$	−8.45594	−0.833188	−0.416594	−	0.909093i	$-0.636776\pi$
$103$	−8.45594	−0.833188	−0.416594	+	0.909093i	$0.636776\pi$
$104$	7.36560	0.722257
$105$	5.09244	0.496971
$106$	1.55647	0.151177
$107$	−0.342555	−0.0331161	−0.0165580	−	0.999863i	$-0.505271\pi$
$107$	−0.342555	−0.0331161	−0.0165580	+	0.999863i	$0.505271\pi$
$108$	−1.73743	−0.167184
$109$	−0.0274405	−0.00262832	−0.00131416	−	0.999999i	$-0.500418\pi$
$109$	−0.0274405	−0.00262832	−0.00131416	+	0.999999i	$0.500418\pi$
$110$	−19.6286	−1.87151
$111$	−6.31082	−0.598996
$112$	5.32056	0.502746
$113$	4.64933	0.437372	0.218686	−	0.975795i	$-0.429823\pi$
$113$	4.64933	0.437372	0.218686	+	0.975795i	$0.429823\pi$
$114$	−1.90556	−0.178472
$115$	15.9868	1.49078
$116$	3.73242	0.346547
$117$	−5.51450	−0.509816
$118$	4.19228	0.385930
$119$	−0.527905	−0.0483930
$120$	−8.93485	−0.815636
$121$	9.06969	0.824517
$122$	1.41591	0.128191
$123$	0	0
$124$	−2.85200	−0.256117
$125$	6.52565	0.583672
$126$	−4.98130	−0.443769
$127$	20.9342	1.85761	0.928806	−	0.370565i	$-0.120836\pi$
$127$	20.9342	1.85761	0.928806	+	0.370565i	$0.120836\pi$
$128$	−6.99656	−0.618415
$129$	−2.22893	−0.196246
$130$	−10.6467	−0.933781
$131$	14.4402	1.26164	0.630822	−	0.775928i	$-0.282718\pi$
$131$	14.4402	1.26164	0.630822	+	0.775928i	$0.282718\pi$
$132$	1.47713	0.128567
$133$	3.03139	0.262855
$134$	12.9689	1.12034
$135$	15.5323	1.33681
$136$	0.926227	0.0794233
$137$	0.945778	0.0808032	0.0404016	−	0.999184i	$-0.487136\pi$
$137$	0.945778	0.0808032	0.0404016	+	0.999184i	$0.487136\pi$
$138$	5.03453	0.428568
$139$	7.57910	0.642851	0.321425	−	0.946935i	$-0.395838\pi$
$139$	7.57910	0.642851	0.321425	+	0.946935i	$0.395838\pi$
$140$	2.29819	0.194232
$141$	5.41537	0.456056
$142$	−0.678617	−0.0569483
$143$	10.8860	0.910333
$144$	6.98903	0.582419
$145$	−33.3672	−2.77100
$146$	−10.8796	−0.900399
$147$	3.43214	0.283078
$148$	−2.84803	−0.234107
$149$	9.62749	0.788715	0.394358	−	0.918957i	$-0.370967\pi$
$149$	9.62749	0.788715	0.394358	+	0.918957i	$0.370967\pi$
$150$	7.48504	0.611151
$151$	18.0001	1.46483	0.732414	−	0.680859i	$-0.238393\pi$
$151$	18.0001	1.46483	0.732414	+	0.680859i	$0.238393\pi$
$152$	−5.31867	−0.431401
$153$	−0.693451	−0.0560622
$154$	9.83342	0.792400
$155$	25.4964	2.04792
$156$	0.801209	0.0641481
$157$	11.1048	0.886261	0.443131	−	0.896457i	$-0.353868\pi$
$157$	11.1048	0.886261	0.443131	+	0.896457i	$0.353868\pi$
$158$	−10.9576	−0.871738
$159$	1.04712	0.0830423
$160$	−7.41252	−0.586011
$161$	−8.00899	−0.631197
$162$	−3.75858	−0.295302
$163$	−1.98697	−0.155631	−0.0778156	−	0.996968i	$-0.524795\pi$
$163$	−1.98697	−0.155631	−0.0778156	+	0.996968i	$0.524795\pi$
$164$	0	0
$165$	−13.2053	−1.02803
$166$	−12.5544	−0.974411
$167$	4.61596	0.357194	0.178597	−	0.983922i	$-0.442844\pi$
$167$	4.61596	0.357194	0.178597	+	0.983922i	$0.442844\pi$
$168$	4.47613	0.345341
$169$	−7.09532	−0.545794
$170$	−1.33883	−0.102684
$171$	3.98200	0.304511
$172$	−1.00590	−0.0766992
$173$	3.45816	0.262919	0.131460	−	0.991322i	$-0.458034\pi$
$173$	3.45816	0.262919	0.131460	+	0.991322i	$0.458034\pi$
$174$	−10.5079	−0.796604
$175$	−11.9073	−0.900107
$176$	−13.7968	−1.03997
$177$	2.82038	0.211993
$178$	−18.5867	−1.39313
$179$	15.9233	1.19016	0.595082	−	0.803665i	$-0.297119\pi$
$179$	15.9233	1.19016	0.595082	+	0.803665i	$0.297119\pi$
$180$	3.01887	0.225014
$181$	2.43240	0.180799	0.0903994	−	0.995906i	$-0.471186\pi$
$181$	2.43240	0.180799	0.0903994	+	0.995906i	$0.471186\pi$
$182$	5.33375	0.395364
$183$	0.952566	0.0704157
$184$	14.0520	1.03593
$185$	25.4609	1.87193
$186$	8.02926	0.588734
$187$	1.36892	0.100105
$188$	2.44392	0.178241
$189$	−7.78131	−0.566007
$190$	7.68796	0.557744
$191$	6.48054	0.468915	0.234458	−	0.972126i	$-0.424669\pi$
$191$	6.48054	0.468915	0.234458	+	0.972126i	$0.424669\pi$
$192$	−7.59914	−0.548421
$193$	1.26147	0.0908030	0.0454015	−	0.998969i	$-0.485543\pi$
$193$	1.26147	0.0908030	0.0454015	+	0.998969i	$0.485543\pi$
$194$	12.5561	0.901473
$195$	−7.16267	−0.512930
$196$	1.54890	0.110636
$197$	3.39105	0.241602	0.120801	−	0.992677i	$-0.461454\pi$
$197$	3.39105	0.241602	0.120801	+	0.992677i	$0.461454\pi$
$198$	12.9171	0.917977
$199$	7.74638	0.549126	0.274563	−	0.961569i	$-0.411467\pi$
$199$	7.74638	0.549126	0.274563	+	0.961569i	$0.411467\pi$
$200$	20.8917	1.47727
$201$	8.72494	0.615410
$202$	2.20898	0.155423
$203$	16.7161	1.17324
$204$	0.100752	0.00705408
$205$	0	0
$206$	10.7435	0.748538
$207$	−10.5205	−0.731227
$208$	−7.48354	−0.518890
$209$	−7.86073	−0.543738
$210$	−6.47011	−0.446480
$211$	15.2122	1.04725	0.523626	−	0.851948i	$-0.324579\pi$
$211$	15.2122	1.04725	0.523626	+	0.851948i	$0.324579\pi$
$212$	0.472561	0.0324556
$213$	−0.456545	−0.0312819
$214$	0.435228	0.0297515
$215$	8.99259	0.613289
$216$	13.6526	0.928939
$217$	−12.7730	−0.867091
$218$	0.0348640	0.00236129
$219$	−7.31931	−0.494593
$220$	−5.95946	−0.401787
$221$	0.742516	0.0499470
$222$	8.01809	0.538139
$223$	2.91654	0.195306	0.0976530	−	0.995221i	$-0.468866\pi$
$223$	2.91654	0.195306	0.0976530	+	0.995221i	$0.468866\pi$
$224$	3.71349	0.248118
$225$	−15.6413	−1.04275
$226$	−5.90712	−0.392936
$227$	16.6199	1.10310	0.551550	−	0.834142i	$-0.314037\pi$
$227$	16.6199	1.10310	0.551550	+	0.834142i	$0.314037\pi$
$228$	−0.578549	−0.0383154
$229$	12.4117	0.820188	0.410094	−	0.912043i	$-0.365496\pi$
$229$	12.4117	0.820188	0.410094	+	0.912043i	$0.365496\pi$
$230$	−20.3118	−1.33932
$231$	6.61551	0.435268
$232$	−29.3290	−1.92554
$233$	3.04723	0.199630	0.0998152	−	0.995006i	$-0.468175\pi$
$233$	3.04723	0.199630	0.0998152	+	0.995006i	$0.468175\pi$
$234$	7.00636	0.458020
$235$	−21.8483	−1.42522
$236$	1.27282	0.0828537
$237$	−7.37179	−0.478849
$238$	0.670721	0.0434764
$239$	−13.6988	−0.886103	−0.443051	−	0.896496i	$-0.646104\pi$
$239$	−13.6988	−0.886103	−0.443051	+	0.896496i	$0.646104\pi$
$240$	9.07791	0.585976
$241$	−13.2044	−0.850571	−0.425285	−	0.905059i	$-0.639826\pi$
$241$	−13.2044	−0.850571	−0.425285	+	0.905059i	$0.639826\pi$
$242$	−11.5233	−0.740748
$243$	−16.0408	−1.02902
$244$	0.429888	0.0275207
$245$	−13.8469	−0.884648
$246$	0	0
$247$	−4.26374	−0.271295
$248$	22.4107	1.42308
$249$	−8.44607	−0.535248
$250$	−8.29105	−0.524372
$251$	20.8475	1.31588	0.657941	−	0.753070i	$-0.271428\pi$
$251$	20.8475	1.31588	0.657941	+	0.753070i	$0.271428\pi$
$252$	−1.51238	−0.0952710
$253$	20.7682	1.30569
$254$	−26.5976	−1.66888
$255$	−0.900709	−0.0564046
$256$	−8.89141	−0.555713
$257$	−18.3038	−1.14176	−0.570879	−	0.821034i	$-0.693398\pi$
$257$	−18.3038	−1.14176	−0.570879	+	0.821034i	$0.693398\pi$
$258$	2.83192	0.176308
$259$	−12.7553	−0.792575
$260$	−3.23247	−0.200469
$261$	21.9581	1.35918
$262$	−18.3467	−1.13346
$263$	−21.5350	−1.32791	−0.663953	−	0.747774i	$-0.731122\pi$
$263$	−21.5350	−1.32791	−0.663953	+	0.747774i	$0.731122\pi$
$264$	−11.6071	−0.714369
$265$	−4.22461	−0.259516
$266$	−3.85147	−0.236149
$267$	−12.5043	−0.765251
$268$	3.93751	0.240522
$269$	2.94995	0.179862	0.0899309	−	0.995948i	$-0.471335\pi$
$269$	2.94995	0.179862	0.0899309	+	0.995948i	$0.471335\pi$
$270$	−19.7343	−1.20099
$271$	11.2312	0.682245	0.341123	−	0.940019i	$-0.389193\pi$
$271$	11.2312	0.682245	0.341123	+	0.940019i	$0.389193\pi$
$272$	−0.941057	−0.0570600
$273$	3.58832	0.217175
$274$	−1.20164	−0.0725938
$275$	30.8770	1.86195
$276$	1.52854	0.0920074
$277$	−29.6325	−1.78044	−0.890222	−	0.455527i	$-0.849451\pi$
$277$	−29.6325	−1.78044	−0.890222	+	0.455527i	$0.849451\pi$
$278$	−9.62949	−0.577538
$279$	−16.7785	−1.00451
$280$	−18.0589	−1.07923
$281$	2.46499	0.147049	0.0735246	−	0.997293i	$-0.476575\pi$
$281$	2.46499	0.147049	0.0735246	+	0.997293i	$0.476575\pi$
$282$	−6.88040	−0.409722
$283$	−16.0911	−0.956518	−0.478259	−	0.878219i	$-0.658732\pi$
$283$	−16.0911	−0.956518	−0.478259	+	0.878219i	$0.658732\pi$
$284$	−0.206036	−0.0122260
$285$	5.17213	0.306371
$286$	−13.8310	−0.817845
$287$	0	0
$288$	4.87800	0.287439
$289$	−16.9066	−0.994508
$290$	42.3942	2.48947
$291$	8.44719	0.495183
$292$	−3.30316	−0.193303
$293$	−26.4709	−1.54645	−0.773223	−	0.634135i	$-0.781356\pi$
$293$	−26.4709	−1.54645	−0.773223	+	0.634135i	$0.781356\pi$
$294$	−4.36064	−0.254318
$295$	−11.3788	−0.662500
$296$	22.3796	1.30079
$297$	20.1778	1.17084
$298$	−12.2320	−0.708583
$299$	11.2649	0.651466
$300$	2.27254	0.131205
$301$	−4.50506	−0.259667
$302$	−22.8697	−1.31600
$303$	1.48611	0.0853745
$304$	5.40383	0.309931
$305$	−3.84312	−0.220057
$306$	0.881052	0.0503664
$307$	11.4785	0.655111	0.327556	−	0.944832i	$-0.393775\pi$
$307$	11.4785	0.655111	0.327556	+	0.944832i	$0.393775\pi$
$308$	2.98554	0.170117
$309$	7.22779	0.411175
$310$	−32.3940	−1.83986
$311$	−18.4215	−1.04459	−0.522293	−	0.852766i	$-0.674923\pi$
$311$	−18.4215	−1.04459	−0.522293	+	0.852766i	$0.674923\pi$
$312$	−6.29582	−0.356431
$313$	−14.3779	−0.812688	−0.406344	−	0.913720i	$-0.633197\pi$
$313$	−14.3779	−0.812688	−0.406344	+	0.913720i	$0.633197\pi$
$314$	−14.1090	−0.796219
$315$	13.5204	0.761789
$316$	−3.32684	−0.187150
$317$	−23.9540	−1.34539	−0.672695	−	0.739920i	$-0.734863\pi$
$317$	−23.9540	−1.34539	−0.672695	+	0.739920i	$0.734863\pi$
$318$	−1.33040	−0.0746053
$319$	−43.3469	−2.42696
$320$	30.6587	1.71387
$321$	0.292803	0.0163426
$322$	10.1757	0.567069
$323$	−0.536167	−0.0298331
$324$	−1.14115	−0.0633971
$325$	16.7480	0.929011
$326$	2.52451	0.139819
$327$	0.0234550	0.00129707
$328$	0	0
$329$	10.9454	0.603441
$330$	16.7777	0.923583
$331$	−1.12788	−0.0619937	−0.0309969	−	0.999519i	$-0.509868\pi$
$331$	−1.12788	−0.0619937	−0.0309969	+	0.999519i	$0.509868\pi$
$332$	−3.81166	−0.209192
$333$	−16.7552	−0.918180
$334$	−5.86473	−0.320904
$335$	−35.2007	−1.92322
$336$	−4.54780	−0.248103
$337$	9.36237	0.510001	0.255000	−	0.966941i	$-0.417924\pi$
$337$	9.36237	0.510001	0.255000	+	0.966941i	$0.417924\pi$
$338$	9.01483	0.490342
$339$	−3.97406	−0.215841
$340$	−0.406485	−0.0220447
$341$	33.1220	1.79366
$342$	−5.05926	−0.273573
$343$	19.0303	1.02754
$344$	7.90427	0.426170
$345$	−13.6649	−0.735693
$346$	−4.39370	−0.236207
$347$	6.83282	0.366805	0.183403	−	0.983038i	$-0.441289\pi$
$347$	6.83282	0.366805	0.183403	+	0.983038i	$0.441289\pi$
$348$	−3.19033	−0.171019
$349$	−3.69895	−0.198000	−0.0990001	−	0.995087i	$-0.531564\pi$
$349$	−3.69895	−0.198000	−0.0990001	+	0.995087i	$0.531564\pi$
$350$	15.1286	0.808658
$351$	10.9447	0.584183
$352$	−9.62949	−0.513254
$353$	−3.51770	−0.187228	−0.0936141	−	0.995609i	$-0.529842\pi$
$353$	−3.51770	−0.187228	−0.0936141	+	0.995609i	$0.529842\pi$
$354$	−3.58339	−0.190455
$355$	1.84193	0.0977593
$356$	−5.64312	−0.299085
$357$	0.451232	0.0238817
$358$	−20.2311	−1.06925
$359$	14.9207	0.787486	0.393743	−	0.919221i	$-0.371180\pi$
$359$	14.9207	0.787486	0.393743	+	0.919221i	$0.371180\pi$
$360$	−23.7220	−1.25026
$361$	−15.9212	−0.837956
$362$	−3.09044	−0.162430
$363$	−7.75241	−0.406896
$364$	1.61939	0.0848789
$365$	29.5297	1.54565
$366$	−1.21027	−0.0632616
$367$	−17.6242	−0.919976	−0.459988	−	0.887925i	$-0.652146\pi$
$367$	−17.6242	−0.919976	−0.459988	+	0.887925i	$0.652146\pi$
$368$	−14.2770	−0.744242
$369$	0	0
$370$	−32.3489	−1.68174
$371$	2.11642	0.109879
$372$	2.43777	0.126393
$373$	−2.99404	−0.155025	−0.0775127	−	0.996991i	$-0.524698\pi$
$373$	−2.99404	−0.155025	−0.0775127	+	0.996991i	$0.524698\pi$
$374$	−1.73926	−0.0899348
$375$	−5.57786	−0.288039
$376$	−19.2041	−0.990376
$377$	−23.5118	−1.21092
$378$	9.88640	0.508502
$379$	31.9445	1.64088	0.820440	−	0.571732i	$-0.193728\pi$
$379$	31.9445	1.64088	0.820440	+	0.571732i	$0.193728\pi$
$380$	2.33415	0.119740
$381$	−17.8937	−0.916724
$382$	−8.23373	−0.421274
$383$	2.51352	0.128435	0.0642175	−	0.997936i	$-0.479545\pi$
$383$	2.51352	0.128435	0.0642175	+	0.997936i	$0.479545\pi$
$384$	5.98038	0.305185
$385$	−26.6902	−1.36026
$386$	−1.60274	−0.0815775
$387$	−5.91780	−0.300818
$388$	3.81217	0.193533
$389$	−34.6738	−1.75803	−0.879015	−	0.476793i	$-0.841799\pi$
$389$	−34.6738	−1.75803	−0.879015	+	0.476793i	$0.841799\pi$
$390$	9.10041	0.460817
$391$	1.41657	0.0716388
$392$	−12.1711	−0.614735
$393$	−12.3429	−0.622616
$394$	−4.30844	−0.217056
$395$	29.7414	1.49645
$396$	3.92177	0.197077
$397$	34.3674	1.72485	0.862425	−	0.506186i	$-0.168945\pi$
$397$	34.3674	1.72485	0.862425	+	0.506186i	$0.168945\pi$
$398$	−9.84202	−0.493336
$399$	−2.59111	−0.129718
$400$	−21.2262	−1.06131
$401$	8.02435	0.400717	0.200359	−	0.979723i	$-0.435789\pi$
$401$	8.02435	0.400717	0.200359	+	0.979723i	$0.435789\pi$
$402$	−11.0853	−0.552885
$403$	17.9657	0.894935
$404$	0.670671	0.0333671
$405$	10.2017	0.506925
$406$	−21.2384	−1.05404
$407$	33.0759	1.63951
$408$	−0.791702	−0.0391951
$409$	−6.97227	−0.344757	−0.172378	−	0.985031i	$-0.555145\pi$
$409$	−6.97227	−0.344757	−0.172378	+	0.985031i	$0.555145\pi$
$410$	0	0
$411$	−0.808413	−0.0398760
$412$	3.26186	0.160700
$413$	5.70050	0.280503
$414$	13.3667	0.656936
$415$	34.0756	1.67271
$416$	−5.22313	−0.256085
$417$	−6.47831	−0.317244
$418$	9.98731	0.488495
$419$	15.4578	0.755163	0.377581	−	0.925976i	$-0.376756\pi$
$419$	15.4578	0.755163	0.377581	+	0.925976i	$0.376756\pi$
$420$	−1.96440	−0.0958528
$421$	21.3510	1.04058	0.520292	−	0.853988i	$-0.325823\pi$
$421$	21.3510	1.04058	0.520292	+	0.853988i	$0.325823\pi$
$422$	−19.3276	−0.940853
$423$	14.3778	0.699072
$424$	−3.71333	−0.180335
$425$	2.10606	0.102159
$426$	0.580055	0.0281037
$427$	1.92531	0.0931721
$428$	0.132140	0.00638723
$429$	−9.30492	−0.449246
$430$	−11.4254	−0.550980
$431$	10.1670	0.489727	0.244864	−	0.969558i	$-0.421257\pi$
$431$	10.1670	0.489727	0.244864	+	0.969558i	$0.421257\pi$
$432$	−13.8712	−0.667376
$433$	−20.5243	−0.986336	−0.493168	−	0.869934i	$-0.664161\pi$
$433$	−20.5243	−0.986336	−0.493168	+	0.869934i	$0.664161\pi$
$434$	16.2286	0.778996
$435$	28.5210	1.36748
$436$	0.0105851	0.000506935 0
$437$	−8.13433	−0.389118
$438$	9.29941	0.444343
$439$	4.10603	0.195970	0.0979852	−	0.995188i	$-0.468760\pi$
$439$	4.10603	0.195970	0.0979852	+	0.995188i	$0.468760\pi$
$440$	46.8289	2.23248
$441$	9.11232	0.433920
$442$	−0.943390	−0.0448725
$443$	−7.04618	−0.334774	−0.167387	−	0.985891i	$-0.553533\pi$
$443$	−7.04618	−0.334774	−0.167387	+	0.985891i	$0.553533\pi$
$444$	2.43438	0.115531
$445$	50.4485	2.39149
$446$	−3.70556	−0.175463
$447$	−8.22919	−0.389228
$448$	−15.3592	−0.725655
$449$	−13.7594	−0.649344	−0.324672	−	0.945827i	$-0.605254\pi$
$449$	−13.7594	−0.649344	−0.324672	+	0.945827i	$0.605254\pi$
$450$	19.8728	0.936811
$451$	0	0
$452$	−1.79347	−0.0843577
$453$	−15.3858	−0.722887
$454$	−21.1161	−0.991027
$455$	−14.4770	−0.678694
$456$	4.54618	0.212895
$457$	1.54449	0.0722482	0.0361241	−	0.999347i	$-0.488499\pi$
$457$	1.54449	0.0722482	0.0361241	+	0.999347i	$0.488499\pi$
$458$	−15.7695	−0.736859
$459$	1.37629	0.0642399
$460$	−6.16689	−0.287533
$461$	−31.1523	−1.45091	−0.725454	−	0.688271i	$-0.758370\pi$
$461$	−31.1523	−1.45091	−0.725454	+	0.688271i	$0.758370\pi$
$462$	−8.40521	−0.391046
$463$	−30.7875	−1.43082	−0.715408	−	0.698707i	$-0.753759\pi$
$463$	−30.7875	−1.43082	−0.715408	+	0.698707i	$0.753759\pi$
$464$	29.7986	1.38337
$465$	−21.7933	−1.01064
$466$	−3.87160	−0.179348
$467$	0.852724	0.0394594	0.0197297	−	0.999805i	$-0.493719\pi$
$467$	0.852724	0.0394594	0.0197297	+	0.999805i	$0.493719\pi$
$468$	2.12721	0.0983303
$469$	17.6347	0.814293
$470$	27.7589	1.28042
$471$	−9.49195	−0.437366
$472$	−10.0017	−0.460366
$473$	11.6821	0.537145
$474$	9.36609	0.430199
$475$	−12.0936	−0.554894
$476$	0.203638	0.00933375
$477$	2.78011	0.127293
$478$	17.4048	0.796076
$479$	−4.81350	−0.219934	−0.109967	−	0.993935i	$-0.535075\pi$
$479$	−4.81350	−0.219934	−0.109967	+	0.993935i	$0.535075\pi$
$480$	6.33593	0.289194
$481$	17.9407	0.818026
$482$	16.7766	0.764154
$483$	6.84577	0.311493
$484$	−3.49862	−0.159028
$485$	−34.0801	−1.54750
$486$	20.3803	0.924471
$487$	−36.9966	−1.67648	−0.838239	−	0.545304i	$-0.816414\pi$
$487$	−36.9966	−1.67648	−0.838239	+	0.545304i	$0.816414\pi$
$488$	−3.37801	−0.152916
$489$	1.69838	0.0768034
$490$	17.5930	0.794769
$491$	−16.4508	−0.742413	−0.371206	−	0.928550i	$-0.621056\pi$
$491$	−16.4508	−0.742413	−0.371206	+	0.928550i	$0.621056\pi$
$492$	0	0
$493$	−2.95661	−0.133159
$494$	5.41722	0.243732
$495$	−35.0600	−1.57583
$496$	−22.7696	−1.02238
$497$	−0.922758	−0.0413914
$498$	10.7310	0.480868
$499$	2.48737	0.111350	0.0556751	−	0.998449i	$-0.482269\pi$
$499$	2.48737	0.111350	0.0556751	+	0.998449i	$0.482269\pi$
$500$	−2.51726	−0.112575
$501$	−3.94554	−0.176274
$502$	−26.4874	−1.18219
$503$	35.8690	1.59932	0.799660	−	0.600453i	$-0.205013\pi$
$503$	35.8690	1.59932	0.799660	+	0.600453i	$0.205013\pi$
$504$	11.8841	0.529361
$505$	−5.99568	−0.266804
$506$	−26.3867	−1.17303
$507$	6.06479	0.269347
$508$	−8.07534	−0.358285
$509$	5.65809	0.250791	0.125395	−	0.992107i	$-0.459980\pi$
$509$	5.65809	0.250791	0.125395	+	0.992107i	$0.459980\pi$
$510$	1.14438	0.0506740
$511$	−14.7936	−0.654431
$512$	25.2900	1.11767
$513$	−7.90309	−0.348930
$514$	23.2555	1.02576
$515$	−29.1605	−1.28496
$516$	0.859804	0.0378508
$517$	−28.3827	−1.24827
$518$	16.2060	0.712051
$519$	−2.95590	−0.129749
$520$	25.4004	1.11388
$521$	−34.3496	−1.50488	−0.752442	−	0.658659i	$-0.771124\pi$
$521$	−34.3496	−1.50488	−0.752442	+	0.658659i	$0.771124\pi$
$522$	−27.8985	−1.22109
$523$	−4.85901	−0.212469	−0.106235	−	0.994341i	$-0.533880\pi$
$523$	−4.85901	−0.212469	−0.106235	+	0.994341i	$0.533880\pi$
$524$	−5.57027	−0.243338
$525$	10.1779	0.444199
$526$	27.3609	1.19299
$527$	2.25919	0.0984120
$528$	11.7930	0.513223
$529$	−1.50890	−0.0656044
$530$	5.36751	0.233150
$531$	7.48811	0.324956
$532$	−1.16935	−0.0506978
$533$	0	0
$534$	15.8871	0.687503
$535$	−1.18131	−0.0510725
$536$	−30.9406	−1.33643
$537$	−13.6106	−0.587341
$538$	−3.74801	−0.161588
$539$	−17.9883	−0.774812
$540$	−5.99157	−0.257836
$541$	27.7668	1.19379	0.596894	−	0.802320i	$-0.296401\pi$
$541$	27.7668	1.19379	0.596894	+	0.802320i	$0.296401\pi$
$542$	−14.2696	−0.612931
$543$	−2.07912	−0.0892234
$544$	−0.656811	−0.0281605
$545$	−0.0946292	−0.00405347
$546$	−4.55907	−0.195110
$547$	39.9768	1.70929	0.854643	−	0.519216i	$-0.173776\pi$
$547$	39.9768	1.70929	0.854643	+	0.519216i	$0.173776\pi$
$548$	−0.364832	−0.0155848
$549$	2.52906	0.107938
$550$	−39.2302	−1.67278
$551$	16.9777	0.723276
$552$	−12.0111	−0.511227
$553$	−14.8997	−0.633600
$554$	37.6490	1.59955
$555$	−21.7630	−0.923787
$556$	−2.92362	−0.123989
$557$	12.7106	0.538567	0.269284	−	0.963061i	$-0.413213\pi$
$557$	12.7106	0.538567	0.269284	+	0.963061i	$0.413213\pi$
$558$	21.3177	0.902449
$559$	6.33650	0.268006
$560$	18.3481	0.775348
$561$	−1.17010	−0.0494015
$562$	−3.13185	−0.132109
$563$	8.02891	0.338378	0.169189	−	0.985584i	$-0.445885\pi$
$563$	8.02891	0.338378	0.169189	+	0.985584i	$0.445885\pi$
$564$	−2.08897	−0.0879614
$565$	16.0333	0.674526
$566$	20.4443	0.859337
$567$	−5.11077	−0.214632
$568$	1.61901	0.0679321
$569$	0.588468	0.0246699	0.0123349	−	0.999924i	$-0.496074\pi$
$569$	0.588468	0.0246699	0.0123349	+	0.999924i	$0.496074\pi$
$570$	−6.57136	−0.275244
$571$	−33.5679	−1.40477	−0.702386	−	0.711796i	$-0.747882\pi$
$571$	−33.5679	−1.40477	−0.702386	+	0.711796i	$0.747882\pi$
$572$	−4.19925	−0.175580
$573$	−5.53930	−0.231408
$574$	0	0
$575$	31.9517	1.33248
$576$	−20.1757	−0.840655
$577$	41.2719	1.71817	0.859086	−	0.511831i	$-0.171033\pi$
$577$	41.2719	1.71817	0.859086	+	0.511831i	$0.171033\pi$
$578$	21.4804	0.893467
$579$	−1.07826	−0.0448109
$580$	12.8713	0.534454
$581$	−17.0710	−0.708225
$582$	−10.7324	−0.444873
$583$	−5.48813	−0.227295
$584$	25.9559	1.07406
$585$	−19.0169	−0.786252
$586$	33.6321	1.38933
$587$	−24.3410	−1.00466	−0.502331	−	0.864676i	$-0.667524\pi$
$587$	−24.3410	−1.00466	−0.502331	+	0.864676i	$0.667524\pi$
$588$	−1.32394	−0.0545984
$589$	−12.9729	−0.534541
$590$	14.4572	0.595192
$591$	−2.89853	−0.119230
$592$	−22.7379	−0.934522
$593$	−42.0245	−1.72574	−0.862870	−	0.505425i	$-0.831336\pi$
$593$	−42.0245	−1.72574	−0.862870	+	0.505425i	$0.831336\pi$
$594$	−25.6366	−1.05188
$595$	−1.82049	−0.0746329
$596$	−3.71379	−0.152123
$597$	−6.62129	−0.270991
$598$	−14.3124	−0.585278
$599$	17.0548	0.696839	0.348420	−	0.937339i	$-0.386718\pi$
$599$	17.0548	0.696839	0.348420	+	0.937339i	$0.386718\pi$
$600$	−17.8574	−0.729026
$601$	25.2366	1.02942	0.514711	−	0.857364i	$-0.327899\pi$
$601$	25.2366	1.02942	0.514711	+	0.857364i	$0.327899\pi$
$602$	5.72382	0.233285
$603$	23.1647	0.943340
$604$	−6.94351	−0.282527
$605$	31.2770	1.27159
$606$	−1.88815	−0.0767006
$607$	0.0852346	0.00345957	0.00172978	−	0.999999i	$-0.499449\pi$
$607$	0.0852346	0.00345957	0.00172978	+	0.999999i	$0.499449\pi$
$608$	3.77160	0.152959
$609$	−14.2883	−0.578990
$610$	4.88281	0.197699
$611$	−15.3951	−0.622818
$612$	0.267497	0.0108129
$613$	−23.4355	−0.946551	−0.473276	−	0.880914i	$-0.656929\pi$
$613$	−23.4355	−0.946551	−0.473276	+	0.880914i	$0.656929\pi$
$614$	−14.5838	−0.588553
$615$	0	0
$616$	−23.4601	−0.945233
$617$	41.0309	1.65184	0.825920	−	0.563787i	$-0.190656\pi$
$617$	41.0309	1.65184	0.825920	+	0.563787i	$0.190656\pi$
$618$	−9.18314	−0.369400
$619$	26.5483	1.06707	0.533533	−	0.845779i	$-0.320864\pi$
$619$	26.5483	1.06707	0.533533	+	0.845779i	$0.320864\pi$
$620$	−9.83519	−0.394991
$621$	20.8801	0.837891
$622$	23.4051	0.938458
$623$	−25.2734	−1.01256
$624$	6.39663	0.256070
$625$	−11.9577	−0.478307
$626$	18.2676	0.730120
$627$	6.71904	0.268333
$628$	−4.28366	−0.170937
$629$	2.25605	0.0899546
$630$	−17.1781	−0.684393
$631$	−20.7313	−0.825301	−0.412651	−	0.910889i	$-0.635397\pi$
$631$	−20.7313	−0.825301	−0.412651	+	0.910889i	$0.635397\pi$
$632$	26.1420	1.03987
$633$	−13.0028	−0.516815
$634$	30.4343	1.20870
$635$	72.1922	2.86486
$636$	−0.403926	−0.0160167
$637$	−9.75705	−0.386588
$638$	55.0736	2.18038
$639$	−1.21213	−0.0479509
$640$	−24.1278	−0.953735
$641$	10.2657	0.405472	0.202736	−	0.979233i	$-0.435017\pi$
$641$	10.2657	0.405472	0.202736	+	0.979233i	$0.435017\pi$
$642$	−0.372015	−0.0146823
$643$	−42.0862	−1.65972	−0.829860	−	0.557972i	$-0.811580\pi$
$643$	−42.0862	−1.65972	−0.829860	+	0.557972i	$0.811580\pi$
$644$	3.08945	0.121742
$645$	−7.68650	−0.302656
$646$	0.681217	0.0268021
$647$	15.8237	0.622093	0.311046	−	0.950395i	$-0.399321\pi$
$647$	15.8237	0.622093	0.311046	+	0.950395i	$0.399321\pi$
$648$	8.96702	0.352258
$649$	−14.7820	−0.580246
$650$	−21.2789	−0.834625
$651$	10.9179	0.427906
$652$	0.766469	0.0300172
$653$	39.1932	1.53375	0.766874	−	0.641798i	$-0.221811\pi$
$653$	39.1932	1.53375	0.766874	+	0.641798i	$0.221811\pi$
$654$	−0.0298004	−0.00116529
$655$	49.7972	1.94574
$656$	0	0
$657$	−19.4328	−0.758144
$658$	−13.9065	−0.542132
$659$	35.9245	1.39942	0.699709	−	0.714428i	$-0.253313\pi$
$659$	35.9245	1.39942	0.699709	+	0.714428i	$0.253313\pi$
$660$	5.09391	0.198280
$661$	−24.5254	−0.953926	−0.476963	−	0.878923i	$-0.658262\pi$
$661$	−24.5254	−0.953926	−0.476963	+	0.878923i	$0.658262\pi$
$662$	1.43300	0.0556953
$663$	−0.634672	−0.0246486
$664$	29.9517	1.16235
$665$	10.4538	0.405381
$666$	21.2880	0.824894
$667$	−44.8556	−1.73682
$668$	−1.78060	−0.0688934
$669$	−2.49294	−0.0963827
$670$	44.7236	1.72782
$671$	−4.99254	−0.192735
$672$	−3.17414	−0.122445
$673$	−8.31259	−0.320427	−0.160213	−	0.987082i	$-0.551218\pi$
$673$	−8.31259	−0.320427	−0.160213	+	0.987082i	$0.551218\pi$
$674$	−11.8952	−0.458186
$675$	31.0433	1.19486
$676$	2.73701	0.105269
$677$	−40.7553	−1.56635	−0.783176	−	0.621800i	$-0.786402\pi$
$677$	−40.7553	−1.56635	−0.783176	+	0.621800i	$0.786402\pi$
$678$	5.04917	0.193912
$679$	17.0733	0.655212
$680$	3.19412	0.122489
$681$	−14.2060	−0.544375
$682$	−42.0825	−1.61142
$683$	−37.6949	−1.44236	−0.721178	−	0.692750i	$-0.756399\pi$
$683$	−37.6949	−1.44236	−0.721178	+	0.692750i	$0.756399\pi$
$684$	−1.53605	−0.0587323
$685$	3.26153	0.124617
$686$	−24.1786	−0.923144
$687$	−10.6090	−0.404759
$688$	−8.03083	−0.306172
$689$	−2.97682	−0.113408
$690$	17.3617	0.660948
$691$	−47.2456	−1.79731	−0.898654	−	0.438659i	$-0.855454\pi$
$691$	−47.2456	−1.79731	−0.898654	+	0.438659i	$0.855454\pi$
$692$	−1.33398	−0.0507103
$693$	17.5642	0.667207
$694$	−8.68132	−0.329538
$695$	26.1367	0.991421
$696$	25.0693	0.950248
$697$	0	0
$698$	4.69963	0.177884
$699$	−2.60465	−0.0985167
$700$	4.59322	0.173607
$701$	23.1846	0.875671	0.437836	−	0.899055i	$-0.355745\pi$
$701$	23.1846	0.875671	0.437836	+	0.899055i	$0.355745\pi$
$702$	−13.9055	−0.524831
$703$	−12.9549	−0.488603
$704$	39.8282	1.50108
$705$	18.6750	0.703342
$706$	4.46935	0.168206
$707$	3.00368	0.112965
$708$	−1.08796	−0.0408879
$709$	7.23432	0.271691	0.135845	−	0.990730i	$-0.456625\pi$
$709$	7.23432	0.271691	0.135845	+	0.990730i	$0.456625\pi$
$710$	−2.34023	−0.0878271
$711$	−19.5721	−0.734011
$712$	44.3431	1.66183
$713$	34.2748	1.28360
$714$	−0.573305	−0.0214554
$715$	37.5406	1.40394
$716$	−6.14239	−0.229552
$717$	11.7092	0.437288
$718$	−18.9573	−0.707479
$719$	21.4971	0.801707	0.400854	−	0.916142i	$-0.368714\pi$
$719$	21.4971	0.801707	0.400854	+	0.916142i	$0.368714\pi$
$720$	24.1018	0.898222
$721$	14.6087	0.544055
$722$	20.2284	0.752822
$723$	11.2866	0.419753
$724$	−0.938293	−0.0348714
$725$	−66.6886	−2.47675
$726$	9.84968	0.365556
$727$	37.3396	1.38485	0.692425	−	0.721490i	$-0.256542\pi$
$727$	37.3396	1.38485	0.692425	+	0.721490i	$0.256542\pi$
$728$	−12.7250	−0.471619
$729$	4.83620	0.179119
$730$	−37.5184	−1.38862
$731$	0.796818	0.0294714
$732$	−0.367451	−0.0135814
$733$	13.0376	0.481553	0.240777	−	0.970581i	$-0.422598\pi$
$733$	13.0376	0.481553	0.240777	+	0.970581i	$0.422598\pi$
$734$	22.3921	0.826508
$735$	11.8358	0.436570
$736$	−9.96466	−0.367302
$737$	−45.7287	−1.68444
$738$	0	0
$739$	−7.51921	−0.276599	−0.138299	−	0.990390i	$-0.544164\pi$
$739$	−7.51921	−0.276599	−0.138299	+	0.990390i	$0.544164\pi$
$740$	−9.82151	−0.361046
$741$	3.64447	0.133883
$742$	−2.68898	−0.0987157
$743$	25.2658	0.926911	0.463456	−	0.886120i	$-0.346609\pi$
$743$	25.2658	0.926911	0.463456	+	0.886120i	$0.346609\pi$
$744$	−19.1558	−0.702285
$745$	33.2006	1.21638
$746$	3.80402	0.139275
$747$	−22.4243	−0.820462
$748$	−0.528058	−0.0193077
$749$	0.591806	0.0216241
$750$	7.08685	0.258775
$751$	−25.4010	−0.926897	−0.463449	−	0.886124i	$-0.653388\pi$
$751$	−25.4010	−0.926897	−0.463449	+	0.886124i	$0.653388\pi$
$752$	19.5116	0.711514
$753$	−17.8196	−0.649382
$754$	29.8725	1.08789
$755$	62.0738	2.25910
$756$	3.00163	0.109168
$757$	−13.4505	−0.488865	−0.244433	−	0.969666i	$-0.578602\pi$
$757$	−13.4505	−0.488865	−0.244433	+	0.969666i	$0.578602\pi$
$758$	−40.5866	−1.47417
$759$	−17.7519	−0.644351
$760$	−18.3415	−0.665318
$761$	8.25630	0.299291	0.149645	−	0.988740i	$-0.452187\pi$
$761$	8.25630	0.299291	0.149645	+	0.988740i	$0.452187\pi$
$762$	22.7346	0.823587
$763$	0.0474068	0.00171624
$764$	−2.49986	−0.0904416
$765$	−2.39138	−0.0864606
$766$	−3.19351	−0.115386
$767$	−8.01793	−0.289511
$768$	7.60002	0.274242
$769$	−43.9279	−1.58408	−0.792040	−	0.610469i	$-0.790981\pi$
$769$	−43.9279	−1.58408	−0.792040	+	0.610469i	$0.790981\pi$
$770$	33.9108	1.22206
$771$	15.6453	0.563453
$772$	−0.486611	−0.0175135
$773$	−35.2149	−1.26659	−0.633296	−	0.773910i	$-0.718298\pi$
$773$	−35.2149	−1.26659	−0.633296	+	0.773910i	$0.718298\pi$
$774$	7.51875	0.270256
$775$	50.9577	1.83046
$776$	−29.9556	−1.07534
$777$	10.9027	0.391132
$778$	44.0542	1.57942
$779$	0	0
$780$	2.76299	0.0989308
$781$	2.39282	0.0856217
$782$	−1.79979	−0.0643604
$783$	−43.5804	−1.55744
$784$	12.3660	0.441643
$785$	38.2952	1.36682
$786$	15.6820	0.559359
$787$	−24.3296	−0.867257	−0.433628	−	0.901092i	$-0.642767\pi$
$787$	−24.3296	−0.867257	−0.433628	+	0.901092i	$0.642767\pi$
$788$	−1.30809	−0.0465988
$789$	18.4073	0.655316
$790$	−37.7874	−1.34442
$791$	−8.03228	−0.285595
$792$	−30.8169	−1.09503
$793$	−2.70800	−0.0961641
$794$	−43.6649	−1.54961
$795$	3.61103	0.128070
$796$	−2.98815	−0.105912
$797$	−39.4642	−1.39789	−0.698946	−	0.715174i	$-0.746347\pi$
$797$	−39.4642	−1.39789	−0.698946	+	0.715174i	$0.746347\pi$
$798$	3.29209	0.116539
$799$	−1.93594	−0.0684885
$800$	−14.8149	−0.523784
$801$	−33.1989	−1.17303
$802$	−10.1952	−0.360005
$803$	38.3616	1.35375
$804$	−3.36563	−0.118697
$805$	−27.6192	−0.973449
$806$	−22.8260	−0.804011
$807$	−2.52150	−0.0887610
$808$	−5.27006	−0.185400
$809$	6.46335	0.227239	0.113620	−	0.993524i	$-0.463755\pi$
$809$	6.46335	0.227239	0.113620	+	0.993524i	$0.463755\pi$
$810$	−12.9615	−0.455422
$811$	32.7119	1.14867	0.574336	−	0.818620i	$-0.305260\pi$
$811$	32.7119	1.14867	0.574336	+	0.818620i	$0.305260\pi$
$812$	−6.44822	−0.226288
$813$	−9.59996	−0.336685
$814$	−42.0240	−1.47294
$815$	−6.85210	−0.240019
$816$	0.804378	0.0281589
$817$	−4.57556	−0.160079
$818$	8.85849	0.309730
$819$	9.52698	0.332900
$820$	0	0
$821$	42.4481	1.48145	0.740725	−	0.671808i	$-0.234482\pi$
$821$	42.4481	1.48145	0.740725	+	0.671808i	$0.234482\pi$
$822$	1.02711	0.0358247
$823$	2.12880	0.0742051	0.0371026	−	0.999311i	$-0.488187\pi$
$823$	2.12880	0.0742051	0.0371026	+	0.999311i	$0.488187\pi$
$824$	−25.6314	−0.892911
$825$	−26.3924	−0.918865
$826$	−7.24267	−0.252005
$827$	52.0226	1.80900	0.904501	−	0.426471i	$-0.140243\pi$
$827$	52.0226	1.80900	0.904501	+	0.426471i	$0.140243\pi$
$828$	4.05827	0.141035
$829$	−25.8047	−0.896234	−0.448117	−	0.893975i	$-0.647905\pi$
$829$	−25.8047	−0.896234	−0.448117	+	0.893975i	$0.647905\pi$
$830$	−43.2942	−1.50276
$831$	25.3287	0.878641
$832$	21.6032	0.748957
$833$	−1.22695	−0.0425114
$834$	8.23090	0.285013
$835$	15.9182	0.550874
$836$	3.03226	0.104873
$837$	33.3004	1.15103
$838$	−19.6396	−0.678440
$839$	52.1493	1.80039	0.900197	−	0.435483i	$-0.143422\pi$
$839$	52.1493	1.80039	0.900197	+	0.435483i	$0.143422\pi$
$840$	15.4360	0.532594
$841$	64.6213	2.22832
$842$	−27.1271	−0.934863
$843$	−2.10698	−0.0725681
$844$	−5.86808	−0.201988
$845$	−24.4684	−0.841737
$846$	−18.2674	−0.628048
$847$	−15.6690	−0.538393
$848$	3.77279	0.129558
$849$	13.7540	0.472037
$850$	−2.67582	−0.0917800
$851$	34.2272	1.17329
$852$	0.176111	0.00603347
$853$	−1.13831	−0.0389749	−0.0194874	−	0.999810i	$-0.506203\pi$
$853$	−1.13831	−0.0389749	−0.0194874	+	0.999810i	$0.506203\pi$
$854$	−2.44616	−0.0837060
$855$	13.7320	0.469625
$856$	−1.03834	−0.0354899
$857$	−25.3666	−0.866505	−0.433253	−	0.901273i	$-0.642634\pi$
$857$	−25.3666	−0.866505	−0.433253	+	0.901273i	$0.642634\pi$
$858$	11.8222	0.403603
$859$	−32.9808	−1.12529	−0.562645	−	0.826699i	$-0.690216\pi$
$859$	−32.9808	−1.12529	−0.562645	+	0.826699i	$0.690216\pi$
$860$	−3.46887	−0.118288
$861$	0	0
$862$	−12.9175	−0.439972
$863$	−4.83494	−0.164583	−0.0822916	−	0.996608i	$-0.526224\pi$
$863$	−4.83494	−0.164583	−0.0822916	+	0.996608i	$0.526224\pi$
$864$	−9.68138	−0.329367
$865$	11.9255	0.405481
$866$	26.0768	0.886126
$867$	14.4511	0.490785
$868$	4.92718	0.167239
$869$	38.6366	1.31066
$870$	−36.2368	−1.22854
$871$	−24.8037	−0.840442
$872$	−0.0831768	−0.00281672
$873$	22.4273	0.759048
$874$	10.3349	0.349584
$875$	−11.2739	−0.381126
$876$	2.82341	0.0953941
$877$	−1.23304	−0.0416369	−0.0208184	−	0.999783i	$-0.506627\pi$
$877$	−1.23304	−0.0416369	−0.0208184	+	0.999783i	$0.506627\pi$
$878$	−5.21685	−0.176060
$879$	22.6262	0.763164
$880$	−47.5786	−1.60388
$881$	39.5709	1.33318	0.666589	−	0.745426i	$-0.267754\pi$
$881$	39.5709	1.33318	0.666589	+	0.745426i	$0.267754\pi$
$882$	−11.5775	−0.389834
$883$	−4.49606	−0.151305	−0.0756523	−	0.997134i	$-0.524104\pi$
$883$	−4.49606	−0.151305	−0.0756523	+	0.997134i	$0.524104\pi$
$884$	−0.286424	−0.00963348
$885$	9.72615	0.326941
$886$	8.95240	0.300762
$887$	−30.0568	−1.00921	−0.504605	−	0.863351i	$-0.668362\pi$
$887$	−30.0568	−1.00921	−0.504605	+	0.863351i	$0.668362\pi$
$888$	−19.1292	−0.641932
$889$	−36.1664	−1.21298
$890$	−64.0965	−2.14852
$891$	13.2528	0.443986
$892$	−1.12505	−0.0376694
$893$	11.1167	0.372007
$894$	10.4555	0.349683
$895$	54.9119	1.83550
$896$	12.0874	0.403812
$897$	−9.62878	−0.321496
$898$	17.4817	0.583372
$899$	−71.5374	−2.38591
$900$	6.03360	0.201120
$901$	−0.374336	−0.0124709
$902$	0	0
$903$	3.85074	0.128145
$904$	14.0929	0.468723
$905$	8.38818	0.278833
$906$	19.5481	0.649443
$907$	−47.2134	−1.56770	−0.783848	−	0.620953i	$-0.786746\pi$
$907$	−47.2134	−1.56770	−0.783848	+	0.620953i	$0.786746\pi$
$908$	−6.41109	−0.212759
$909$	3.94561	0.130868
$910$	18.3935	0.609740
$911$	−58.9483	−1.95305	−0.976523	−	0.215414i	$-0.930890\pi$
$911$	−58.9483	−1.95305	−0.976523	+	0.215414i	$0.930890\pi$
$912$	−4.61897	−0.152949
$913$	44.2671	1.46503
$914$	−1.96232	−0.0649079
$915$	3.28495	0.108597
$916$	−4.78779	−0.158193
$917$	−24.9472	−0.823828
$918$	−1.74863	−0.0577133
$919$	−12.3811	−0.408415	−0.204207	−	0.978928i	$-0.565462\pi$
$919$	−12.3811	−0.408415	−0.204207	+	0.978928i	$0.565462\pi$
$920$	48.4588	1.59764
$921$	−9.81134	−0.323295
$922$	39.5800	1.30350
$923$	1.29789	0.0427205
$924$	−2.55192	−0.0839520
$925$	50.8869	1.67315
$926$	39.1165	1.28545
$927$	19.1898	0.630275
$928$	20.7979	0.682726
$929$	59.0598	1.93769	0.968844	−	0.247672i	$-0.0796656\pi$
$929$	59.0598	1.93769	0.968844	+	0.247672i	$0.0796656\pi$
$930$	27.6891	0.907961
$931$	7.04552	0.230908
$932$	−1.17546	−0.0385035
$933$	15.7459	0.515499
$934$	−1.08341	−0.0354504
$935$	4.72075	0.154385
$936$	−16.7154	−0.546360
$937$	15.0791	0.492613	0.246307	−	0.969192i	$-0.420783\pi$
$937$	15.0791	0.492613	0.246307	+	0.969192i	$0.420783\pi$
$938$	−22.4054	−0.731562
$939$	12.2897	0.401058
$940$	8.42792	0.274889
$941$	19.2055	0.626082	0.313041	−	0.949740i	$-0.398652\pi$
$941$	19.2055	0.626082	0.313041	+	0.949740i	$0.398652\pi$
$942$	12.0598	0.392931
$943$	0	0
$944$	10.1619	0.330740
$945$	−26.8340	−0.872911
$946$	−14.8425	−0.482572
$947$	35.3689	1.14933	0.574667	−	0.818387i	$-0.305131\pi$
$947$	35.3689	1.14933	0.574667	+	0.818387i	$0.305131\pi$
$948$	2.84365	0.0923575
$949$	20.8077	0.675447
$950$	15.3654	0.498518
$951$	20.4749	0.663944
$952$	−1.60017	−0.0518618
$953$	−3.91409	−0.126790	−0.0633949	−	0.997989i	$-0.520193\pi$
$953$	−3.91409	−0.126790	−0.0633949	+	0.997989i	$0.520193\pi$
$954$	−3.53222	−0.114360
$955$	22.3483	0.723173
$956$	5.28429	0.170906
$957$	37.0511	1.19769
$958$	6.11570	0.197589
$959$	−1.63395	−0.0527629
$960$	−26.2058	−0.845789
$961$	23.6628	0.763316
$962$	−22.7942	−0.734916
$963$	0.777390	0.0250511
$964$	5.09357	0.164053
$965$	4.35022	0.140039
$966$	−8.69777	−0.279846
$967$	−33.4900	−1.07697	−0.538483	−	0.842636i	$-0.681003\pi$
$967$	−33.4900	−1.07697	−0.538483	+	0.842636i	$0.681003\pi$
$968$	27.4918	0.883619
$969$	0.458294	0.0147225
$970$	43.2999	1.39028
$971$	20.4505	0.656289	0.328144	−	0.944628i	$-0.393577\pi$
$971$	20.4505	0.656289	0.328144	+	0.944628i	$0.393577\pi$
$972$	6.18770	0.198471
$973$	−13.0938	−0.419769
$974$	47.0054	1.50615
$975$	−14.3155	−0.458463
$976$	3.43210	0.109859
$977$	−6.15198	−0.196819	−0.0984096	−	0.995146i	$-0.531376\pi$
$977$	−6.15198	−0.196819	−0.0984096	+	0.995146i	$0.531376\pi$
$978$	−2.15785	−0.0690003
$979$	65.5369	2.09457
$980$	5.34143	0.170626
$981$	0.0622731	0.00198823
$982$	20.9012	0.666985
$983$	21.3411	0.680674	0.340337	−	0.940304i	$-0.389459\pi$
$983$	21.3411	0.680674	0.340337	+	0.940304i	$0.389459\pi$
$984$	0	0
$985$	11.6941	0.372605
$986$	3.75647	0.119631
$987$	−9.35571	−0.297795
$988$	1.64473	0.0523258
$989$	12.0887	0.384399
$990$	44.5448	1.41573
$991$	−40.3792	−1.28269	−0.641344	−	0.767254i	$-0.721623\pi$
$991$	−40.3792	−1.28269	−0.641344	+	0.767254i	$0.721623\pi$
$992$	−15.8920	−0.504572
$993$	0.964063	0.0305936
$994$	1.17239	0.0371861
$995$	26.7136	0.846877
$996$	3.25805	0.103235
$997$	−28.3734	−0.898594	−0.449297	−	0.893382i	$-0.648326\pi$
$997$	−28.3734	−0.898594	−0.449297	+	0.893382i	$0.648326\pi$
$998$	−3.16029	−0.100037
$999$	33.2541	1.05211

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1681.2.a.m.1.5		24
41.34	odd	40		41.2.g.a.8.3	✓	24
41.35	odd	40		41.2.g.a.36.3	yes	24
41.40	even	2	inner	1681.2.a.m.1.6		24
123.35	even	40		369.2.u.a.118.1		24
123.116	even	40		369.2.u.a.172.1		24
164.35	even	40		656.2.bs.d.241.3		24
164.75	even	40		656.2.bs.d.49.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.8.3	✓	24	41.34	odd	40
41.2.g.a.36.3	yes	24	41.35	odd	40
369.2.u.a.118.1		24	123.35	even	40
369.2.u.a.172.1		24	123.116	even	40
656.2.bs.d.49.3		24	164.75	even	40
656.2.bs.d.241.3		24	164.35	even	40
1681.2.a.m.1.5		24	1.1	even	1	trivial
1681.2.a.m.1.6		24	41.40	even	2	inner

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:	\( N \)	\(=\)	\( 1681 = 41^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1681.a (trivial)

\(f(q)\)	\(=\)	\(q-1.27053 q^{2} -0.854760 q^{3} -0.385748 q^{4} +3.44852 q^{5} +1.08600 q^{6} -1.72762 q^{7} +3.03117 q^{8} -2.26939 q^{9} +O(q^{10})\)	\(q-1.27053 q^{2} -0.854760 q^{3} -0.385748 q^{4} +3.44852 q^{5} +1.08600 q^{6} -1.72762 q^{7} +3.03117 q^{8} -2.26939 q^{9} -4.38146 q^{10} +4.47992 q^{11} +0.329722 q^{12} +2.42995 q^{13} +2.19500 q^{14} -2.94766 q^{15} -3.07970 q^{16} +0.305568 q^{17} +2.88333 q^{18} -1.75466 q^{19} -1.33026 q^{20} +1.47670 q^{21} -5.69188 q^{22} +4.63585 q^{23} -2.59092 q^{24} +6.89230 q^{25} -3.08734 q^{26} +4.50406 q^{27} +0.666427 q^{28} -9.67581 q^{29} +3.74509 q^{30} +7.39343 q^{31} -2.14948 q^{32} -3.82926 q^{33} -0.388234 q^{34} -5.95774 q^{35} +0.875411 q^{36} +7.38315 q^{37} +2.22935 q^{38} -2.07703 q^{39} +10.4531 q^{40} -1.87620 q^{42} +2.60766 q^{43} -1.72812 q^{44} -7.82603 q^{45} -5.89000 q^{46} -6.33554 q^{47} +2.63241 q^{48} -4.01532 q^{49} -8.75689 q^{50} -0.261187 q^{51} -0.937350 q^{52} -1.22505 q^{53} -5.72255 q^{54} +15.4491 q^{55} -5.23671 q^{56} +1.49981 q^{57} +12.2934 q^{58} -3.29962 q^{59} +1.13705 q^{60} -1.11443 q^{61} -9.39359 q^{62} +3.92064 q^{63} +8.89039 q^{64} +8.37975 q^{65} +4.86519 q^{66} -10.2075 q^{67} -0.117872 q^{68} -3.96254 q^{69} +7.56950 q^{70} +0.534120 q^{71} -6.87889 q^{72} +8.56300 q^{73} -9.38052 q^{74} -5.89126 q^{75} +0.676856 q^{76} -7.73961 q^{77} +2.63893 q^{78} +8.62440 q^{79} -10.6204 q^{80} +2.95827 q^{81} +9.88122 q^{83} -0.569635 q^{84} +1.05376 q^{85} -3.31312 q^{86} +8.27049 q^{87} +13.5794 q^{88} +14.6290 q^{89} +9.94322 q^{90} -4.19804 q^{91} -1.78827 q^{92} -6.31960 q^{93} +8.04951 q^{94} -6.05098 q^{95} +1.83729 q^{96} -9.88253 q^{97} +5.10160 q^{98} -10.1667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 + 20 * q^4 + 12 * q^5 + 24 * q^8 + 24 * q^9	\( 24 q + 8 q^{2} + 20 q^{4} + 12 q^{5} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 20 q^{16} + 20 q^{18} + 40 q^{20} + 56 q^{21} + 48 q^{23} + 8 q^{25} + 32 q^{31} + 36 q^{32} + 24 q^{33} + 108 q^{36} + 60 q^{39} + 44 q^{40} - 40 q^{42} + 36 q^{43} - 36 q^{45} + 36 q^{46} + 32 q^{49} - 60 q^{50} + 36 q^{51} - 60 q^{57} + 116 q^{59} + 40 q^{61} + 48 q^{62} + 60 q^{64} + 16 q^{66} + 4 q^{72} + 16 q^{73} + 24 q^{74} - 16 q^{77} - 60 q^{78} + 84 q^{80} - 28 q^{81} + 80 q^{83} - 24 q^{84} - 24 q^{86} + 76 q^{87} + 56 q^{90} + 40 q^{91} - 40 q^{92} + 36 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 20 * q^4 + 12 * q^5 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 20 * q^16 + 20 * q^18 + 40 * q^20 + 56 * q^21 + 48 * q^23 + 8 * q^25 + 32 * q^31 + 36 * q^32 + 24 * q^33 + 108 * q^36 + 60 * q^39 + 44 * q^40 - 40 * q^42 + 36 * q^43 - 36 * q^45 + 36 * q^46 + 32 * q^49 - 60 * q^50 + 36 * q^51 - 60 * q^57 + 116 * q^59 + 40 * q^61 + 48 * q^62 + 60 * q^64 + 16 * q^66 + 4 * q^72 + 16 * q^73 + 24 * q^74 - 16 * q^77 - 60 * q^78 + 84 * q^80 - 28 * q^81 + 80 * q^83 - 24 * q^84 - 24 * q^86 + 76 * q^87 + 56 * q^90 + 40 * q^91 - 40 * q^92 + 36 * q^98

Introduction

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