LMFDB - Embedded newform 4018.2.a.bu.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4018,2,Mod(1,4018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4018 = 2 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4018.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:	$32.0838915322$
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} - x^{9} - 23x^{8} + 19x^{7} + 181x^{6} - 109x^{5} - 579x^{4} + 231x^{3} + 608x^{2} - 204x - 12 $ x^10 - x^9 - 23x^8 + 19x^7 + 181x^6 - 109x^5 - 579x^4 + 231x^3 + 608x^2 - 204x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 574)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.97715$ of defining polynomial
Character	$\chi$	$=$	4018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.97715 q^{3} +1.00000 q^{4} +3.36998 q^{5} -1.97715 q^{6} +1.00000 q^{8} +0.909140 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.97715 q^{3} +1.00000 q^{4} +3.36998 q^{5} -1.97715 q^{6} +1.00000 q^{8} +0.909140 q^{9} +3.36998 q^{10} +3.91460 q^{11} -1.97715 q^{12} -2.75524 q^{13} -6.66296 q^{15} +1.00000 q^{16} +3.27912 q^{17} +0.909140 q^{18} -4.20412 q^{19} +3.36998 q^{20} +3.91460 q^{22} +0.885289 q^{23} -1.97715 q^{24} +6.35674 q^{25} -2.75524 q^{26} +4.13395 q^{27} +3.45506 q^{29} -6.66296 q^{30} +0.326157 q^{31} +1.00000 q^{32} -7.73977 q^{33} +3.27912 q^{34} +0.909140 q^{36} -0.414897 q^{37} -4.20412 q^{38} +5.44754 q^{39} +3.36998 q^{40} +1.00000 q^{41} +5.17113 q^{43} +3.91460 q^{44} +3.06378 q^{45} +0.885289 q^{46} -1.02881 q^{47} -1.97715 q^{48} +6.35674 q^{50} -6.48332 q^{51} -2.75524 q^{52} +11.0295 q^{53} +4.13395 q^{54} +13.1921 q^{55} +8.31219 q^{57} +3.45506 q^{58} -6.08564 q^{59} -6.66296 q^{60} +6.55489 q^{61} +0.326157 q^{62} +1.00000 q^{64} -9.28511 q^{65} -7.73977 q^{66} -1.34167 q^{67} +3.27912 q^{68} -1.75035 q^{69} +11.4065 q^{71} +0.909140 q^{72} -12.8565 q^{73} -0.414897 q^{74} -12.5682 q^{75} -4.20412 q^{76} +5.44754 q^{78} +6.28483 q^{79} +3.36998 q^{80} -10.9009 q^{81} +1.00000 q^{82} -14.2033 q^{83} +11.0505 q^{85} +5.17113 q^{86} -6.83118 q^{87} +3.91460 q^{88} -15.4870 q^{89} +3.06378 q^{90} +0.885289 q^{92} -0.644863 q^{93} -1.02881 q^{94} -14.1678 q^{95} -1.97715 q^{96} +17.7818 q^{97} +3.55892 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 2 q^{5} + q^{6} + 10 q^{8} + 17 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 2 * q^5 + q^6 + 10 * q^8 + 17 * q^9	$ 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 2 q^{5} + q^{6} + 10 q^{8} + 17 q^{9} - 2 q^{10} + 11 q^{11} + q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 5 q^{17} + 17 q^{18} - q^{19} - 2 q^{20} + 11 q^{22} + 9 q^{23} + q^{24} + 24 q^{25} + 4 q^{26} + 7 q^{27} + 23 q^{29} + 4 q^{30} - 5 q^{31} + 10 q^{32} - 5 q^{33} + 5 q^{34} + 17 q^{36} + 16 q^{37} - q^{38} - 7 q^{39} - 2 q^{40} + 10 q^{41} + 20 q^{43} + 11 q^{44} - 42 q^{45} + 9 q^{46} - 16 q^{47} + q^{48} + 24 q^{50} + 13 q^{51} + 4 q^{52} + 26 q^{53} + 7 q^{54} + 7 q^{55} + 37 q^{57} + 23 q^{58} - 10 q^{59} + 4 q^{60} - 5 q^{62} + 10 q^{64} + 18 q^{65} - 5 q^{66} + 7 q^{67} + 5 q^{68} + 39 q^{69} + 5 q^{71} + 17 q^{72} - 13 q^{73} + 16 q^{74} + 19 q^{75} - q^{76} - 7 q^{78} - q^{79} - 2 q^{80} + 18 q^{81} + 10 q^{82} + 21 q^{83} + 34 q^{85} + 20 q^{86} + 2 q^{87} + 11 q^{88} + 6 q^{89} - 42 q^{90} + 9 q^{92} - 5 q^{93} - 16 q^{94} + 24 q^{95} + q^{96} + 29 q^{97} + 48 q^{99}+O(q^{100}) $ 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 2 * q^5 + q^6 + 10 * q^8 + 17 * q^9 - 2 * q^10 + 11 * q^11 + q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 5 * q^17 + 17 * q^18 - q^19 - 2 * q^20 + 11 * q^22 + 9 * q^23 + q^24 + 24 * q^25 + 4 * q^26 + 7 * q^27 + 23 * q^29 + 4 * q^30 - 5 * q^31 + 10 * q^32 - 5 * q^33 + 5 * q^34 + 17 * q^36 + 16 * q^37 - q^38 - 7 * q^39 - 2 * q^40 + 10 * q^41 + 20 * q^43 + 11 * q^44 - 42 * q^45 + 9 * q^46 - 16 * q^47 + q^48 + 24 * q^50 + 13 * q^51 + 4 * q^52 + 26 * q^53 + 7 * q^54 + 7 * q^55 + 37 * q^57 + 23 * q^58 - 10 * q^59 + 4 * q^60 - 5 * q^62 + 10 * q^64 + 18 * q^65 - 5 * q^66 + 7 * q^67 + 5 * q^68 + 39 * q^69 + 5 * q^71 + 17 * q^72 - 13 * q^73 + 16 * q^74 + 19 * q^75 - q^76 - 7 * q^78 - q^79 - 2 * q^80 + 18 * q^81 + 10 * q^82 + 21 * q^83 + 34 * q^85 + 20 * q^86 + 2 * q^87 + 11 * q^88 + 6 * q^89 - 42 * q^90 + 9 * q^92 - 5 * q^93 - 16 * q^94 + 24 * q^95 + q^96 + 29 * q^97 + 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.97715	−1.14151	−0.570755	−	0.821120i	$-0.693350\pi$
$3$	−1.97715	−1.14151	−0.570755	+	0.821120i	$0.693350\pi$
$4$	1.00000	0.500000
$5$	3.36998	1.50710	0.753549	−	0.657391i	$-0.228340\pi$
$5$	3.36998	1.50710	0.753549	+	0.657391i	$0.228340\pi$
$6$	−1.97715	−0.807170
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	0.909140	0.303047
$10$	3.36998	1.06568
$11$	3.91460	1.18030	0.590148	−	0.807295i	$-0.299069\pi$
$11$	3.91460	1.18030	0.590148	+	0.807295i	$0.299069\pi$
$12$	−1.97715	−0.570755
$13$	−2.75524	−0.764167	−0.382084	−	0.924128i	$-0.624793\pi$
$13$	−2.75524	−0.764167	−0.382084	+	0.924128i	$0.624793\pi$
$14$	0	0
$15$	−6.66296	−1.72037
$16$	1.00000	0.250000
$17$	3.27912	0.795302	0.397651	−	0.917537i	$-0.369825\pi$
$17$	3.27912	0.795302	0.397651	+	0.917537i	$0.369825\pi$
$18$	0.909140	0.214286
$19$	−4.20412	−0.964490	−0.482245	−	0.876036i	$-0.660179\pi$
$19$	−4.20412	−0.964490	−0.482245	+	0.876036i	$0.660179\pi$
$20$	3.36998	0.753549
$21$	0	0
$22$	3.91460	0.834595
$23$	0.885289	0.184596	0.0922978	−	0.995731i	$-0.470579\pi$
$23$	0.885289	0.184596	0.0922978	+	0.995731i	$0.470579\pi$
$24$	−1.97715	−0.403585
$25$	6.35674	1.27135
$26$	−2.75524	−0.540348
$27$	4.13395	0.795580
$28$	0	0
$29$	3.45506	0.641588	0.320794	−	0.947149i	$-0.396050\pi$
$29$	3.45506	0.641588	0.320794	+	0.947149i	$0.396050\pi$
$30$	−6.66296	−1.21648
$31$	0.326157	0.0585796	0.0292898	−	0.999571i	$-0.490675\pi$
$31$	0.326157	0.0585796	0.0292898	+	0.999571i	$0.490675\pi$
$32$	1.00000	0.176777
$33$	−7.73977	−1.34732
$34$	3.27912	0.562364
$35$	0	0
$36$	0.909140	0.151523
$37$	−0.414897	−0.0682087	−0.0341043	−	0.999418i	$-0.510858\pi$
$37$	−0.414897	−0.0682087	−0.0341043	+	0.999418i	$0.510858\pi$
$38$	−4.20412	−0.681998
$39$	5.44754	0.872305
$40$	3.36998	0.532840
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	5.17113	0.788590	0.394295	−	0.918984i	$-0.370989\pi$
$43$	5.17113	0.788590	0.394295	+	0.918984i	$0.370989\pi$
$44$	3.91460	0.590148
$45$	3.06378	0.456721
$46$	0.885289	0.130529
$47$	−1.02881	−0.150067	−0.0750333	−	0.997181i	$-0.523906\pi$
$47$	−1.02881	−0.150067	−0.0750333	+	0.997181i	$0.523906\pi$
$48$	−1.97715	−0.285378
$49$	0	0
$50$	6.35674	0.898978
$51$	−6.48332	−0.907846
$52$	−2.75524	−0.382084
$53$	11.0295	1.51501	0.757507	−	0.652827i	$-0.226417\pi$
$53$	11.0295	1.51501	0.757507	+	0.652827i	$0.226417\pi$
$54$	4.13395	0.562560
$55$	13.1921	1.77882
$56$	0	0
$57$	8.31219	1.10098
$58$	3.45506	0.453671
$59$	−6.08564	−0.792283	−0.396142	−	0.918189i	$-0.629651\pi$
$59$	−6.08564	−0.792283	−0.396142	+	0.918189i	$0.629651\pi$
$60$	−6.66296	−0.860185
$61$	6.55489	0.839268	0.419634	−	0.907693i	$-0.362158\pi$
$61$	6.55489	0.839268	0.419634	+	0.907693i	$0.362158\pi$
$62$	0.326157	0.0414220
$63$	0	0
$64$	1.00000	0.125000
$65$	−9.28511	−1.15168
$66$	−7.73977	−0.952699
$67$	−1.34167	−0.163911	−0.0819557	−	0.996636i	$-0.526117\pi$
$67$	−1.34167	−0.163911	−0.0819557	+	0.996636i	$0.526117\pi$
$68$	3.27912	0.397651
$69$	−1.75035	−0.210718
$70$	0	0
$71$	11.4065	1.35370	0.676851	−	0.736120i	$-0.263344\pi$
$71$	11.4065	1.35370	0.676851	+	0.736120i	$0.263344\pi$
$72$	0.909140	0.107143
$73$	−12.8565	−1.50474	−0.752368	−	0.658743i	$-0.771088\pi$
$73$	−12.8565	−1.50474	−0.752368	+	0.658743i	$0.771088\pi$
$74$	−0.414897	−0.0482308
$75$	−12.5682	−1.45126
$76$	−4.20412	−0.482245
$77$	0	0
$78$	5.44754	0.616813
$79$	6.28483	0.707099	0.353549	−	0.935416i	$-0.384975\pi$
$79$	6.28483	0.707099	0.353549	+	0.935416i	$0.384975\pi$
$80$	3.36998	0.376775
$81$	−10.9009	−1.21121
$82$	1.00000	0.110432
$83$	−14.2033	−1.55901	−0.779505	−	0.626396i	$-0.784529\pi$
$83$	−14.2033	−1.55901	−0.779505	+	0.626396i	$0.784529\pi$
$84$	0	0
$85$	11.0505	1.19860
$86$	5.17113	0.557617
$87$	−6.83118	−0.732380
$88$	3.91460	0.417298
$89$	−15.4870	−1.64162	−0.820812	−	0.571199i	$-0.806479\pi$
$89$	−15.4870	−1.64162	−0.820812	+	0.571199i	$0.806479\pi$
$90$	3.06378	0.322951
$91$	0	0
$92$	0.885289	0.0922978
$93$	−0.644863	−0.0668692
$94$	−1.02881	−0.106113
$95$	−14.1678	−1.45358
$96$	−1.97715	−0.201792
$97$	17.7818	1.80546	0.902732	−	0.430203i	$-0.141558\pi$
$97$	17.7818	1.80546	0.902732	+	0.430203i	$0.141558\pi$
$98$	0	0
$99$	3.55892	0.357685
$100$	6.35674	0.635674
$101$	17.7743	1.76861	0.884307	−	0.466906i	$-0.154631\pi$
$101$	17.7743	1.76861	0.884307	+	0.466906i	$0.154631\pi$
$102$	−6.48332	−0.641944
$103$	10.0035	0.985674	0.492837	−	0.870122i	$-0.335960\pi$
$103$	10.0035	0.985674	0.492837	+	0.870122i	$0.335960\pi$
$104$	−2.75524	−0.270174
$105$	0	0
$106$	11.0295	1.07128
$107$	−9.65247	−0.933140	−0.466570	−	0.884484i	$-0.654510\pi$
$107$	−9.65247	−0.933140	−0.466570	+	0.884484i	$0.654510\pi$
$108$	4.13395	0.397790
$109$	−1.43399	−0.137351	−0.0686756	−	0.997639i	$-0.521877\pi$
$109$	−1.43399	−0.137351	−0.0686756	+	0.997639i	$0.521877\pi$
$110$	13.1921	1.25782
$111$	0.820316	0.0778609
$112$	0	0
$113$	17.3398	1.63119	0.815594	−	0.578625i	$-0.196410\pi$
$113$	17.3398	1.63119	0.815594	+	0.578625i	$0.196410\pi$
$114$	8.31219	0.778508
$115$	2.98340	0.278204
$116$	3.45506	0.320794
$117$	−2.50490	−0.231578
$118$	−6.08564	−0.560229
$119$	0	0
$120$	−6.66296	−0.608242
$121$	4.32408	0.393098
$122$	6.55489	0.593452
$123$	−1.97715	−0.178274
$124$	0.326157	0.0292898
$125$	4.57216	0.408947
$126$	0	0
$127$	−16.3745	−1.45300	−0.726502	−	0.687165i	$-0.758855\pi$
$127$	−16.3745	−1.45300	−0.726502	+	0.687165i	$0.758855\pi$
$128$	1.00000	0.0883883
$129$	−10.2241	−0.900184
$130$	−9.28511	−0.814358
$131$	−20.9035	−1.82634	−0.913172	−	0.407575i	$-0.866375\pi$
$131$	−20.9035	−1.82634	−0.913172	+	0.407575i	$0.866375\pi$
$132$	−7.73977	−0.673660
$133$	0	0
$134$	−1.34167	−0.115903
$135$	13.9313	1.19902
$136$	3.27912	0.281182
$137$	13.4293	1.14734	0.573670	−	0.819087i	$-0.305519\pi$
$137$	13.4293	1.14734	0.573670	+	0.819087i	$0.305519\pi$
$138$	−1.75035	−0.149000
$139$	4.15890	0.352754	0.176377	−	0.984323i	$-0.443562\pi$
$139$	4.15890	0.352754	0.176377	+	0.984323i	$0.443562\pi$
$140$	0	0
$141$	2.03411	0.171303
$142$	11.4065	0.957211
$143$	−10.7857	−0.901944
$144$	0.909140	0.0757617
$145$	11.6435	0.966937
$146$	−12.8565	−1.06401
$147$	0	0
$148$	−0.414897	−0.0341043
$149$	−9.52691	−0.780475	−0.390238	−	0.920714i	$-0.627607\pi$
$149$	−9.52691	−0.780475	−0.390238	+	0.920714i	$0.627607\pi$
$150$	−12.5682	−1.02619
$151$	15.8350	1.28863	0.644317	−	0.764759i	$-0.277142\pi$
$151$	15.8350	1.28863	0.644317	+	0.764759i	$0.277142\pi$
$152$	−4.20412	−0.340999
$153$	2.98118	0.241014
$154$	0	0
$155$	1.09914	0.0882852
$156$	5.44754	0.436153
$157$	15.9006	1.26900	0.634502	−	0.772921i	$-0.281205\pi$
$157$	15.9006	1.26900	0.634502	+	0.772921i	$0.281205\pi$
$158$	6.28483	0.499994
$159$	−21.8070	−1.72940
$160$	3.36998	0.266420
$161$	0	0
$162$	−10.9009	−0.856454
$163$	−8.55286	−0.669912	−0.334956	−	0.942234i	$-0.608721\pi$
$163$	−8.55286	−0.669912	−0.334956	+	0.942234i	$0.608721\pi$
$164$	1.00000	0.0780869
$165$	−26.0828	−2.03054
$166$	−14.2033	−1.10239
$167$	−13.6521	−1.05643	−0.528214	−	0.849111i	$-0.677138\pi$
$167$	−13.6521	−1.05643	−0.528214	+	0.849111i	$0.677138\pi$
$168$	0	0
$169$	−5.40863	−0.416048
$170$	11.0505	0.847538
$171$	−3.82213	−0.292286
$172$	5.17113	0.394295
$173$	20.7174	1.57512	0.787558	−	0.616241i	$-0.211345\pi$
$173$	20.7174	1.57512	0.787558	+	0.616241i	$0.211345\pi$
$174$	−6.83118	−0.517871
$175$	0	0
$176$	3.91460	0.295074
$177$	12.0323	0.904400
$178$	−15.4870	−1.16080
$179$	−5.82513	−0.435391	−0.217695	−	0.976017i	$-0.569854\pi$
$179$	−5.82513	−0.435391	−0.217695	+	0.976017i	$0.569854\pi$
$180$	3.06378	0.228361
$181$	14.6879	1.09175	0.545873	−	0.837868i	$-0.316198\pi$
$181$	14.6879	1.09175	0.545873	+	0.837868i	$0.316198\pi$
$182$	0	0
$183$	−12.9600	−0.958033
$184$	0.885289	0.0652644
$185$	−1.39819	−0.102797
$186$	−0.644863	−0.0472837
$187$	12.8364	0.938692
$188$	−1.02881	−0.0750333
$189$	0	0
$190$	−14.1678	−1.02784
$191$	−0.962568	−0.0696490	−0.0348245	−	0.999393i	$-0.511087\pi$
$191$	−0.962568	−0.0696490	−0.0348245	+	0.999393i	$0.511087\pi$
$192$	−1.97715	−0.142689
$193$	4.76065	0.342679	0.171340	−	0.985212i	$-0.445190\pi$
$193$	4.76065	0.342679	0.171340	+	0.985212i	$0.445190\pi$
$194$	17.7818	1.27666
$195$	18.3581	1.31465
$196$	0	0
$197$	22.5876	1.60930	0.804650	−	0.593749i	$-0.202353\pi$
$197$	22.5876	1.60930	0.804650	+	0.593749i	$0.202353\pi$
$198$	3.55892	0.252921
$199$	−5.02467	−0.356190	−0.178095	−	0.984013i	$-0.556993\pi$
$199$	−5.02467	−0.356190	−0.178095	+	0.984013i	$0.556993\pi$
$200$	6.35674	0.449489
$201$	2.65269	0.187107
$202$	17.7743	1.25060
$203$	0	0
$204$	−6.48332	−0.453923
$205$	3.36998	0.235369
$206$	10.0035	0.696977
$207$	0.804852	0.0559411
$208$	−2.75524	−0.191042
$209$	−16.4574	−1.13838
$210$	0	0
$211$	13.7994	0.949991	0.474995	−	0.879988i	$-0.342450\pi$
$211$	13.7994	0.949991	0.474995	+	0.879988i	$0.342450\pi$
$212$	11.0295	0.757507
$213$	−22.5524	−1.54526
$214$	−9.65247	−0.659829
$215$	17.4266	1.18848
$216$	4.13395	0.281280
$217$	0	0
$218$	−1.43399	−0.0971219
$219$	25.4192	1.71767
$220$	13.1921	0.889411
$221$	−9.03477	−0.607744
$222$	0.820316	0.0550560
$223$	−5.09883	−0.341443	−0.170722	−	0.985319i	$-0.554610\pi$
$223$	−5.09883	−0.341443	−0.170722	+	0.985319i	$0.554610\pi$
$224$	0	0
$225$	5.77916	0.385278
$226$	17.3398	1.15342
$227$	−17.8860	−1.18714	−0.593569	−	0.804783i	$-0.702281\pi$
$227$	−17.8860	−1.18714	−0.593569	+	0.804783i	$0.702281\pi$
$228$	8.31219	0.550488
$229$	8.39224	0.554575	0.277287	−	0.960787i	$-0.410565\pi$
$229$	8.39224	0.554575	0.277287	+	0.960787i	$0.410565\pi$
$230$	2.98340	0.196720
$231$	0	0
$232$	3.45506	0.226836
$233$	−17.4921	−1.14595	−0.572974	−	0.819574i	$-0.694210\pi$
$233$	−17.4921	−1.14595	−0.572974	+	0.819574i	$0.694210\pi$
$234$	−2.50490	−0.163751
$235$	−3.46705	−0.226165
$236$	−6.08564	−0.396142
$237$	−12.4261	−0.807161
$238$	0	0
$239$	1.94044	0.125517	0.0627583	−	0.998029i	$-0.480010\pi$
$239$	1.94044	0.125517	0.0627583	+	0.998029i	$0.480010\pi$
$240$	−6.66296	−0.430092
$241$	10.5374	0.678773	0.339387	−	0.940647i	$-0.389780\pi$
$241$	10.5374	0.678773	0.339387	+	0.940647i	$0.389780\pi$
$242$	4.32408	0.277962
$243$	9.15088	0.587029
$244$	6.55489	0.419634
$245$	0	0
$246$	−1.97715	−0.126059
$247$	11.5834	0.737032
$248$	0.326157	0.0207110
$249$	28.0820	1.77963
$250$	4.57216	0.289169
$251$	−12.7615	−0.805497	−0.402749	−	0.915311i	$-0.631945\pi$
$251$	−12.7615	−0.805497	−0.402749	+	0.915311i	$0.631945\pi$
$252$	0	0
$253$	3.46555	0.217877
$254$	−16.3745	−1.02743
$255$	−21.8486	−1.36821
$256$	1.00000	0.0625000
$257$	17.3378	1.08150	0.540750	−	0.841183i	$-0.318140\pi$
$257$	17.3378	1.08150	0.540750	+	0.841183i	$0.318140\pi$
$258$	−10.2241	−0.636526
$259$	0	0
$260$	−9.28511	−0.575838
$261$	3.14113	0.194431
$262$	−20.9035	−1.29142
$263$	21.7341	1.34018	0.670092	−	0.742278i	$-0.266255\pi$
$263$	21.7341	1.34018	0.670092	+	0.742278i	$0.266255\pi$
$264$	−7.73977	−0.476350
$265$	37.1690	2.28328
$266$	0	0
$267$	30.6203	1.87393
$268$	−1.34167	−0.0819557
$269$	−2.24424	−0.136834	−0.0684169	−	0.997657i	$-0.521795\pi$
$269$	−2.24424	−0.136834	−0.0684169	+	0.997657i	$0.521795\pi$
$270$	13.9313	0.847833
$271$	16.1638	0.981879	0.490940	−	0.871194i	$-0.336654\pi$
$271$	16.1638	0.981879	0.490940	+	0.871194i	$0.336654\pi$
$272$	3.27912	0.198826
$273$	0	0
$274$	13.4293	0.811292
$275$	24.8841	1.50057
$276$	−1.75035	−0.105359
$277$	−4.05469	−0.243623	−0.121811	−	0.992553i	$-0.538870\pi$
$277$	−4.05469	−0.243623	−0.121811	+	0.992553i	$0.538870\pi$
$278$	4.15890	0.249434
$279$	0.296523	0.0177524
$280$	0	0
$281$	−7.58747	−0.452631	−0.226315	−	0.974054i	$-0.572668\pi$
$281$	−7.58747	−0.452631	−0.226315	+	0.974054i	$0.572668\pi$
$282$	2.03411	0.121129
$283$	1.00952	0.0600097	0.0300049	−	0.999550i	$-0.490448\pi$
$283$	1.00952	0.0600097	0.0300049	+	0.999550i	$0.490448\pi$
$284$	11.4065	0.676851
$285$	28.0119	1.65928
$286$	−10.7857	−0.637770
$287$	0	0
$288$	0.909140	0.0535716
$289$	−6.24740	−0.367494
$290$	11.6435	0.683728
$291$	−35.1573	−2.06096
$292$	−12.8565	−0.752368
$293$	28.3532	1.65641	0.828206	−	0.560423i	$-0.189361\pi$
$293$	28.3532	1.65641	0.828206	+	0.560423i	$0.189361\pi$
$294$	0	0
$295$	−20.5085	−1.19405
$296$	−0.414897	−0.0241154
$297$	16.1828	0.939019
$298$	−9.52691	−0.551879
$299$	−2.43919	−0.141062
$300$	−12.5682	−0.725628
$301$	0	0
$302$	15.8350	0.911202
$303$	−35.1426	−2.01889
$304$	−4.20412	−0.241123
$305$	22.0898	1.26486
$306$	2.98118	0.170422
$307$	22.5604	1.28759	0.643796	−	0.765197i	$-0.277359\pi$
$307$	22.5604	1.28759	0.643796	+	0.765197i	$0.277359\pi$
$308$	0	0
$309$	−19.7785	−1.12516
$310$	1.09914	0.0624271
$311$	16.3079	0.924738	0.462369	−	0.886688i	$-0.347000\pi$
$311$	16.3079	0.924738	0.462369	+	0.886688i	$0.347000\pi$
$312$	5.44754	0.308407
$313$	−8.89228	−0.502621	−0.251311	−	0.967906i	$-0.580862\pi$
$313$	−8.89228	−0.502621	−0.251311	+	0.967906i	$0.580862\pi$
$314$	15.9006	0.897321
$315$	0	0
$316$	6.28483	0.353549
$317$	−21.0188	−1.18054	−0.590268	−	0.807208i	$-0.700978\pi$
$317$	−21.0188	−1.18054	−0.590268	+	0.807208i	$0.700978\pi$
$318$	−21.8070	−1.22287
$319$	13.5252	0.757264
$320$	3.36998	0.188387
$321$	19.0844	1.06519
$322$	0	0
$323$	−13.7858	−0.767061
$324$	−10.9009	−0.605605
$325$	−17.5144	−0.971522
$326$	−8.55286	−0.473699
$327$	2.83522	0.156788
$328$	1.00000	0.0552158
$329$	0	0
$330$	−26.0828	−1.43581
$331$	0.876030	0.0481510	0.0240755	−	0.999710i	$-0.492336\pi$
$331$	0.876030	0.0481510	0.0240755	+	0.999710i	$0.492336\pi$
$332$	−14.2033	−0.779505
$333$	−0.377200	−0.0206704
$334$	−13.6521	−0.747007
$335$	−4.52140	−0.247031
$336$	0	0
$337$	9.88910	0.538694	0.269347	−	0.963043i	$-0.413192\pi$
$337$	9.88910	0.538694	0.269347	+	0.963043i	$0.413192\pi$
$338$	−5.40863	−0.294190
$339$	−34.2834	−1.86202
$340$	11.0505	0.599300
$341$	1.27677	0.0691412
$342$	−3.82213	−0.206677
$343$	0	0
$344$	5.17113	0.278809
$345$	−5.89865	−0.317573
$346$	20.7174	1.11377
$347$	−17.5975	−0.944681	−0.472341	−	0.881416i	$-0.656591\pi$
$347$	−17.5975	−0.944681	−0.472341	+	0.881416i	$0.656591\pi$
$348$	−6.83118	−0.366190
$349$	11.7608	0.629540	0.314770	−	0.949168i	$-0.398073\pi$
$349$	11.7608	0.629540	0.314770	+	0.949168i	$0.398073\pi$
$350$	0	0
$351$	−11.3901	−0.607956
$352$	3.91460	0.208649
$353$	23.3412	1.24232	0.621162	−	0.783682i	$-0.286661\pi$
$353$	23.3412	1.24232	0.621162	+	0.783682i	$0.286661\pi$
$354$	12.0323	0.639507
$355$	38.4396	2.04016
$356$	−15.4870	−0.820812
$357$	0	0
$358$	−5.82513	−0.307868
$359$	−5.46528	−0.288447	−0.144223	−	0.989545i	$-0.546068\pi$
$359$	−5.46528	−0.288447	−0.144223	+	0.989545i	$0.546068\pi$
$360$	3.06378	0.161475
$361$	−1.32541	−0.0697583
$362$	14.6879	0.771981
$363$	−8.54937	−0.448725
$364$	0	0
$365$	−43.3260	−2.26779
$366$	−12.9600	−0.677432
$367$	−18.7335	−0.977880	−0.488940	−	0.872317i	$-0.662616\pi$
$367$	−18.7335	−0.977880	−0.488940	+	0.872317i	$0.662616\pi$
$368$	0.885289	0.0461489
$369$	0.909140	0.0473279
$370$	−1.39819	−0.0726886
$371$	0	0
$372$	−0.644863	−0.0334346
$373$	16.5095	0.854830	0.427415	−	0.904056i	$-0.359424\pi$
$373$	16.5095	0.854830	0.427415	+	0.904056i	$0.359424\pi$
$374$	12.8364	0.663755
$375$	−9.03988	−0.466817
$376$	−1.02881	−0.0530566
$377$	−9.51953	−0.490281
$378$	0	0
$379$	6.96872	0.357959	0.178980	−	0.983853i	$-0.442720\pi$
$379$	6.96872	0.357959	0.178980	+	0.983853i	$0.442720\pi$
$380$	−14.1678	−0.726791
$381$	32.3749	1.65862
$382$	−0.962568	−0.0492493
$383$	−26.9890	−1.37907	−0.689537	−	0.724251i	$-0.742186\pi$
$383$	−26.9890	−1.37907	−0.689537	+	0.724251i	$0.742186\pi$
$384$	−1.97715	−0.100896
$385$	0	0
$386$	4.76065	0.242311
$387$	4.70128	0.238980
$388$	17.7818	0.902732
$389$	−33.3605	−1.69144	−0.845722	−	0.533624i	$-0.820830\pi$
$389$	−33.3605	−1.69144	−0.845722	+	0.533624i	$0.820830\pi$
$390$	18.3581	0.929598
$391$	2.90297	0.146809
$392$	0	0
$393$	41.3294	2.08479
$394$	22.5876	1.13795
$395$	21.1797	1.06567
$396$	3.55892	0.178842
$397$	−17.7874	−0.892722	−0.446361	−	0.894853i	$-0.647280\pi$
$397$	−17.7874	−0.892722	−0.446361	+	0.894853i	$0.647280\pi$
$398$	−5.02467	−0.251864
$399$	0	0
$400$	6.35674	0.317837
$401$	−22.4343	−1.12031	−0.560157	−	0.828386i	$-0.689259\pi$
$401$	−22.4343	−1.12031	−0.560157	+	0.828386i	$0.689259\pi$
$402$	2.65269	0.132304
$403$	−0.898643	−0.0447646
$404$	17.7743	0.884307
$405$	−36.7357	−1.82541
$406$	0	0
$407$	−1.62416	−0.0805064
$408$	−6.48332	−0.320972
$409$	−6.58938	−0.325824	−0.162912	−	0.986641i	$-0.552089\pi$
$409$	−6.58938	−0.325824	−0.162912	+	0.986641i	$0.552089\pi$
$410$	3.36998	0.166431
$411$	−26.5517	−1.30970
$412$	10.0035	0.492837
$413$	0	0
$414$	0.804852	0.0395563
$415$	−47.8646	−2.34958
$416$	−2.75524	−0.135087
$417$	−8.22279	−0.402672
$418$	−16.4574	−0.804959
$419$	17.2319	0.841835	0.420917	−	0.907099i	$-0.361708\pi$
$419$	17.2319	0.841835	0.420917	+	0.907099i	$0.361708\pi$
$420$	0	0
$421$	−36.5996	−1.78376	−0.891878	−	0.452275i	$-0.850612\pi$
$421$	−36.5996	−1.78376	−0.891878	+	0.452275i	$0.850612\pi$
$422$	13.7994	0.671745
$423$	−0.935328	−0.0454772
$424$	11.0295	0.535638
$425$	20.8445	1.01111
$426$	−22.5524	−1.09267
$427$	0	0
$428$	−9.65247	−0.466570
$429$	21.3249	1.02958
$430$	17.4266	0.840385
$431$	−21.5261	−1.03687	−0.518437	−	0.855116i	$-0.673486\pi$
$431$	−21.5261	−1.03687	−0.518437	+	0.855116i	$0.673486\pi$
$432$	4.13395	0.198895
$433$	−13.8999	−0.667988	−0.333994	−	0.942575i	$-0.608397\pi$
$433$	−13.8999	−0.667988	−0.333994	+	0.942575i	$0.608397\pi$
$434$	0	0
$435$	−23.0209	−1.10377
$436$	−1.43399	−0.0686756
$437$	−3.72186	−0.178041
$438$	25.4192	1.21458
$439$	3.31789	0.158354	0.0791772	−	0.996861i	$-0.474771\pi$
$439$	3.31789	0.158354	0.0791772	+	0.996861i	$0.474771\pi$
$440$	13.1921	0.628909
$441$	0	0
$442$	−9.03477	−0.429740
$443$	−10.3772	−0.493034	−0.246517	−	0.969138i	$-0.579286\pi$
$443$	−10.3772	−0.493034	−0.246517	+	0.969138i	$0.579286\pi$
$444$	0.820316	0.0389305
$445$	−52.1910	−2.47409
$446$	−5.09883	−0.241437
$447$	18.8362	0.890921
$448$	0	0
$449$	−37.6652	−1.77753	−0.888765	−	0.458363i	$-0.848436\pi$
$449$	−37.6652	−1.77753	−0.888765	+	0.458363i	$0.848436\pi$
$450$	5.77916	0.272432
$451$	3.91460	0.184331
$452$	17.3398	0.815594
$453$	−31.3082	−1.47099
$454$	−17.8860	−0.839433
$455$	0	0
$456$	8.31219	0.389254
$457$	25.6514	1.19992	0.599960	−	0.800030i	$-0.295183\pi$
$457$	25.6514	1.19992	0.599960	+	0.800030i	$0.295183\pi$
$458$	8.39224	0.392144
$459$	13.5557	0.632726
$460$	2.98340	0.139102
$461$	14.0242	0.653173	0.326587	−	0.945167i	$-0.394102\pi$
$461$	14.0242	0.653173	0.326587	+	0.945167i	$0.394102\pi$
$462$	0	0
$463$	−8.25708	−0.383739	−0.191870	−	0.981420i	$-0.561455\pi$
$463$	−8.25708	−0.383739	−0.191870	+	0.981420i	$0.561455\pi$
$464$	3.45506	0.160397
$465$	−2.17317	−0.100779
$466$	−17.4921	−0.810308
$467$	−22.2241	−1.02841	−0.514205	−	0.857667i	$-0.671913\pi$
$467$	−22.2241	−1.02841	−0.514205	+	0.857667i	$0.671913\pi$
$468$	−2.50490	−0.115789
$469$	0	0
$470$	−3.46705	−0.159923
$471$	−31.4379	−1.44858
$472$	−6.08564	−0.280114
$473$	20.2429	0.930770
$474$	−12.4261	−0.570749
$475$	−26.7245	−1.22620
$476$	0	0
$477$	10.0273	0.459120
$478$	1.94044	0.0887537
$479$	40.9796	1.87240	0.936202	−	0.351463i	$-0.114316\pi$
$479$	40.9796	1.87240	0.936202	+	0.351463i	$0.114316\pi$
$480$	−6.66296	−0.304121
$481$	1.14314	0.0521229
$482$	10.5374	0.479965
$483$	0	0
$484$	4.32408	0.196549
$485$	59.9241	2.72101
$486$	9.15088	0.415092
$487$	−15.7625	−0.714268	−0.357134	−	0.934053i	$-0.616246\pi$
$487$	−15.7625	−0.714268	−0.357134	+	0.934053i	$0.616246\pi$
$488$	6.55489	0.296726
$489$	16.9103	0.764711
$490$	0	0
$491$	41.0462	1.85239	0.926195	−	0.377044i	$-0.123059\pi$
$491$	41.0462	1.85239	0.926195	+	0.377044i	$0.123059\pi$
$492$	−1.97715	−0.0891370
$493$	11.3295	0.510257
$494$	11.5834	0.521160
$495$	11.9935	0.539066
$496$	0.326157	0.0146449
$497$	0	0
$498$	28.0820	1.25839
$499$	−41.1894	−1.84389	−0.921945	−	0.387320i	$-0.873401\pi$
$499$	−41.1894	−1.84389	−0.921945	+	0.387320i	$0.873401\pi$
$500$	4.57216	0.204473
$501$	26.9922	1.20592
$502$	−12.7615	−0.569573
$503$	−15.4363	−0.688269	−0.344135	−	0.938920i	$-0.611828\pi$
$503$	−15.4363	−0.688269	−0.344135	+	0.938920i	$0.611828\pi$
$504$	0	0
$505$	59.8991	2.66548
$506$	3.46555	0.154063
$507$	10.6937	0.474923
$508$	−16.3745	−0.726502
$509$	−36.8106	−1.63160	−0.815802	−	0.578332i	$-0.803704\pi$
$509$	−36.8106	−1.63160	−0.815802	+	0.578332i	$0.803704\pi$
$510$	−21.8486	−0.967473
$511$	0	0
$512$	1.00000	0.0441942
$513$	−17.3796	−0.767329
$514$	17.3378	0.764736
$515$	33.7115	1.48551
$516$	−10.2241	−0.450092
$517$	−4.02736	−0.177123
$518$	0	0
$519$	−40.9615	−1.79801
$520$	−9.28511	−0.407179
$521$	−4.42094	−0.193685	−0.0968425	−	0.995300i	$-0.530874\pi$
$521$	−4.42094	−0.193685	−0.0968425	+	0.995300i	$0.530874\pi$
$522$	3.14113	0.137484
$523$	37.2017	1.62672	0.813358	−	0.581764i	$-0.197637\pi$
$523$	37.2017	1.62672	0.813358	+	0.581764i	$0.197637\pi$
$524$	−20.9035	−0.913172
$525$	0	0
$526$	21.7341	0.947653
$527$	1.06951	0.0465885
$528$	−7.73977	−0.336830
$529$	−22.2163	−0.965924
$530$	37.1690	1.61452
$531$	−5.53270	−0.240099
$532$	0	0
$533$	−2.75524	−0.119343
$534$	30.6203	1.32507
$535$	−32.5286	−1.40633
$536$	−1.34167	−0.0579514
$537$	11.5172	0.497003
$538$	−2.24424	−0.0967561
$539$	0	0
$540$	13.9313	0.599509
$541$	−15.1121	−0.649721	−0.324860	−	0.945762i	$-0.605317\pi$
$541$	−15.1121	−0.649721	−0.324860	+	0.945762i	$0.605317\pi$
$542$	16.1638	0.694294
$543$	−29.0403	−1.24624
$544$	3.27912	0.140591
$545$	−4.83250	−0.207002
$546$	0	0
$547$	41.9798	1.79493	0.897463	−	0.441091i	$-0.145408\pi$
$547$	41.9798	1.79493	0.897463	+	0.441091i	$0.145408\pi$
$548$	13.4293	0.573670
$549$	5.95932	0.254337
$550$	24.8841	1.06106
$551$	−14.5255	−0.618806
$552$	−1.75035	−0.0745000
$553$	0	0
$554$	−4.05469	−0.172267
$555$	2.76444	0.117344
$556$	4.15890	0.176377
$557$	−38.7624	−1.64242	−0.821208	−	0.570629i	$-0.806700\pi$
$557$	−38.7624	−1.64242	−0.821208	+	0.570629i	$0.806700\pi$
$558$	0.296523	0.0125528
$559$	−14.2477	−0.602615
$560$	0	0
$561$	−25.3796	−1.07153
$562$	−7.58747	−0.320058
$563$	−22.9986	−0.969274	−0.484637	−	0.874715i	$-0.661048\pi$
$563$	−22.9986	−0.969274	−0.484637	+	0.874715i	$0.661048\pi$
$564$	2.03411	0.0856514
$565$	58.4346	2.45836
$566$	1.00952	0.0424333
$567$	0	0
$568$	11.4065	0.478606
$569$	0.906587	0.0380061	0.0190031	−	0.999819i	$-0.493951\pi$
$569$	0.906587	0.0380061	0.0190031	+	0.999819i	$0.493951\pi$
$570$	28.0119	1.17329
$571$	−20.8663	−0.873228	−0.436614	−	0.899649i	$-0.643822\pi$
$571$	−20.8663	−0.873228	−0.436614	+	0.899649i	$0.643822\pi$
$572$	−10.7857	−0.450972
$573$	1.90315	0.0795051
$574$	0	0
$575$	5.62755	0.234685
$576$	0.909140	0.0378808
$577$	−21.5131	−0.895604	−0.447802	−	0.894133i	$-0.647793\pi$
$577$	−21.5131	−0.895604	−0.447802	+	0.894133i	$0.647793\pi$
$578$	−6.24740	−0.259858
$579$	−9.41254	−0.391172
$580$	11.6435	0.483468
$581$	0	0
$582$	−35.1573	−1.45732
$583$	43.1759	1.78816
$584$	−12.8565	−0.532004
$585$	−8.44146	−0.349012
$586$	28.3532	1.17126
$587$	−37.8635	−1.56279	−0.781396	−	0.624035i	$-0.785492\pi$
$587$	−37.8635	−1.56279	−0.781396	+	0.624035i	$0.785492\pi$
$588$	0	0
$589$	−1.37120	−0.0564994
$590$	−20.5085	−0.844320
$591$	−44.6592	−1.83703
$592$	−0.414897	−0.0170522
$593$	18.2134	0.747934	0.373967	−	0.927442i	$-0.377997\pi$
$593$	18.2134	0.747934	0.373967	+	0.927442i	$0.377997\pi$
$594$	16.1828	0.663987
$595$	0	0
$596$	−9.52691	−0.390238
$597$	9.93456	0.406594
$598$	−2.43919	−0.0997458
$599$	36.4910	1.49098	0.745490	−	0.666517i	$-0.232215\pi$
$599$	36.4910	1.49098	0.745490	+	0.666517i	$0.232215\pi$
$600$	−12.5682	−0.513097
$601$	−0.790029	−0.0322259	−0.0161130	−	0.999870i	$-0.505129\pi$
$601$	−0.790029	−0.0322259	−0.0161130	+	0.999870i	$0.505129\pi$
$602$	0	0
$603$	−1.21977	−0.0496728
$604$	15.8350	0.644317
$605$	14.5720	0.592437
$606$	−35.1426	−1.42757
$607$	−23.2572	−0.943979	−0.471989	−	0.881604i	$-0.656464\pi$
$607$	−23.2572	−0.943979	−0.471989	+	0.881604i	$0.656464\pi$
$608$	−4.20412	−0.170499
$609$	0	0
$610$	22.0898	0.894391
$611$	2.83461	0.114676
$612$	2.98118	0.120507
$613$	−18.6011	−0.751290	−0.375645	−	0.926764i	$-0.622579\pi$
$613$	−18.6011	−0.751290	−0.375645	+	0.926764i	$0.622579\pi$
$614$	22.5604	0.910465
$615$	−6.66296	−0.268677
$616$	0	0
$617$	14.7653	0.594428	0.297214	−	0.954811i	$-0.403942\pi$
$617$	14.7653	0.594428	0.297214	+	0.954811i	$0.403942\pi$
$618$	−19.7785	−0.795606
$619$	−12.7360	−0.511902	−0.255951	−	0.966690i	$-0.582389\pi$
$619$	−12.7360	−0.511902	−0.255951	+	0.966690i	$0.582389\pi$
$620$	1.09914	0.0441426
$621$	3.65974	0.146860
$622$	16.3079	0.653888
$623$	0	0
$624$	5.44754	0.218076
$625$	−16.3756	−0.655024
$626$	−8.89228	−0.355407
$627$	32.5389	1.29948
$628$	15.9006	0.634502
$629$	−1.36050	−0.0542465
$630$	0	0
$631$	−9.54061	−0.379806	−0.189903	−	0.981803i	$-0.560817\pi$
$631$	−9.54061	−0.379806	−0.189903	+	0.981803i	$0.560817\pi$
$632$	6.28483	0.249997
$633$	−27.2836	−1.08442
$634$	−21.0188	−0.834765
$635$	−55.1817	−2.18982
$636$	−21.8070	−0.864702
$637$	0	0
$638$	13.5252	0.535466
$639$	10.3701	0.410235
$640$	3.36998	0.133210
$641$	34.0104	1.34333	0.671665	−	0.740855i	$-0.265579\pi$
$641$	34.0104	1.34333	0.671665	+	0.740855i	$0.265579\pi$
$642$	19.0844	0.753202
$643$	1.74793	0.0689315	0.0344657	−	0.999406i	$-0.489027\pi$
$643$	1.74793	0.0689315	0.0344657	+	0.999406i	$0.489027\pi$
$644$	0	0
$645$	−34.4551	−1.35667
$646$	−13.7858	−0.542394
$647$	37.9828	1.49326	0.746629	−	0.665241i	$-0.231671\pi$
$647$	37.9828	1.49326	0.746629	+	0.665241i	$0.231671\pi$
$648$	−10.9009	−0.428227
$649$	−23.8228	−0.935128
$650$	−17.5144	−0.686970
$651$	0	0
$652$	−8.55286	−0.334956
$653$	8.31894	0.325545	0.162773	−	0.986664i	$-0.447956\pi$
$653$	8.31894	0.325545	0.162773	+	0.986664i	$0.447956\pi$
$654$	2.83522	0.110866
$655$	−70.4441	−2.75248
$656$	1.00000	0.0390434
$657$	−11.6883	−0.456005
$658$	0	0
$659$	9.94877	0.387549	0.193775	−	0.981046i	$-0.437927\pi$
$659$	9.94877	0.387549	0.193775	+	0.981046i	$0.437927\pi$
$660$	−26.0828	−1.01527
$661$	15.5871	0.606267	0.303133	−	0.952948i	$-0.401967\pi$
$661$	15.5871	0.606267	0.303133	+	0.952948i	$0.401967\pi$
$662$	0.876030	0.0340479
$663$	17.8631	0.693747
$664$	−14.2033	−0.551193
$665$	0	0
$666$	−0.377200	−0.0146162
$667$	3.05873	0.118434
$668$	−13.6521	−0.528214
$669$	10.0812	0.389761
$670$	−4.52140	−0.174677
$671$	25.6598	0.990584
$672$	0	0
$673$	−10.6085	−0.408927	−0.204464	−	0.978874i	$-0.565545\pi$
$673$	−10.6085	−0.408927	−0.204464	+	0.978874i	$0.565545\pi$
$674$	9.88910	0.380914
$675$	26.2784	1.01146
$676$	−5.40863	−0.208024
$677$	27.3372	1.05066	0.525328	−	0.850900i	$-0.323943\pi$
$677$	27.3372	1.05066	0.525328	+	0.850900i	$0.323943\pi$
$678$	−34.2834	−1.31665
$679$	0	0
$680$	11.0505	0.423769
$681$	35.3634	1.35513
$682$	1.27677	0.0488902
$683$	−21.1344	−0.808685	−0.404343	−	0.914608i	$-0.632500\pi$
$683$	−21.1344	−0.808685	−0.404343	+	0.914608i	$0.632500\pi$
$684$	−3.82213	−0.146143
$685$	45.2563	1.72915
$686$	0	0
$687$	−16.5928	−0.633053
$688$	5.17113	0.197148
$689$	−30.3889	−1.15772
$690$	−5.89865	−0.224558
$691$	−44.1245	−1.67857	−0.839287	−	0.543688i	$-0.817027\pi$
$691$	−44.1245	−1.67857	−0.839287	+	0.543688i	$0.817027\pi$
$692$	20.7174	0.787558
$693$	0	0
$694$	−17.5975	−0.667990
$695$	14.0154	0.531634
$696$	−6.83118	−0.258935
$697$	3.27912	0.124205
$698$	11.7608	0.445152
$699$	34.5847	1.30811
$700$	0	0
$701$	−41.0843	−1.55173	−0.775867	−	0.630896i	$-0.782687\pi$
$701$	−41.0843	−1.55173	−0.775867	+	0.630896i	$0.782687\pi$
$702$	−11.3901	−0.429890
$703$	1.74428	0.0657866
$704$	3.91460	0.147537
$705$	6.85489	0.258170
$706$	23.3412	0.878456
$707$	0	0
$708$	12.0323	0.452200
$709$	−32.2980	−1.21298	−0.606489	−	0.795092i	$-0.707422\pi$
$709$	−32.2980	−1.21298	−0.606489	+	0.795092i	$0.707422\pi$
$710$	38.4396	1.44261
$711$	5.71379	0.214284
$712$	−15.4870	−0.580402
$713$	0.288744	0.0108135
$714$	0	0
$715$	−36.3475	−1.35932
$716$	−5.82513	−0.217695
$717$	−3.83655	−0.143279
$718$	−5.46528	−0.203963
$719$	−44.5134	−1.66007	−0.830035	−	0.557712i	$-0.811679\pi$
$719$	−44.5134	−1.66007	−0.830035	+	0.557712i	$0.811679\pi$
$720$	3.06378	0.114180
$721$	0	0
$722$	−1.32541	−0.0493266
$723$	−20.8341	−0.774827
$724$	14.6879	0.545873
$725$	21.9629	0.815681
$726$	−8.54937	−0.317297
$727$	−6.53205	−0.242260	−0.121130	−	0.992637i	$-0.538652\pi$
$727$	−6.53205	−0.242260	−0.121130	+	0.992637i	$0.538652\pi$
$728$	0	0
$729$	14.6100	0.541110
$730$	−43.3260	−1.60357
$731$	16.9567	0.627168
$732$	−12.9600	−0.479017
$733$	−15.9016	−0.587338	−0.293669	−	0.955907i	$-0.594876\pi$
$733$	−15.9016	−0.587338	−0.293669	+	0.955907i	$0.594876\pi$
$734$	−18.7335	−0.691466
$735$	0	0
$736$	0.885289	0.0326322
$737$	−5.25211	−0.193464
$738$	0.909140	0.0334659
$739$	−12.1443	−0.446736	−0.223368	−	0.974734i	$-0.571705\pi$
$739$	−12.1443	−0.446736	−0.223368	+	0.974734i	$0.571705\pi$
$740$	−1.39819	−0.0513986
$741$	−22.9021	−0.841330
$742$	0	0
$743$	−14.0177	−0.514261	−0.257130	−	0.966377i	$-0.582777\pi$
$743$	−14.0177	−0.514261	−0.257130	+	0.966377i	$0.582777\pi$
$744$	−0.644863	−0.0236418
$745$	−32.1055	−1.17625
$746$	16.5095	0.604456
$747$	−12.9127	−0.472453
$748$	12.8364	0.469346
$749$	0	0
$750$	−9.03988	−0.330090
$751$	31.6722	1.15573	0.577867	−	0.816131i	$-0.303885\pi$
$751$	31.6722	1.15573	0.577867	+	0.816131i	$0.303885\pi$
$752$	−1.02881	−0.0375167
$753$	25.2314	0.919484
$754$	−9.51953	−0.346681
$755$	53.3636	1.94210
$756$	0	0
$757$	34.8012	1.26487	0.632436	−	0.774613i	$-0.282055\pi$
$757$	34.8012	1.26487	0.632436	+	0.774613i	$0.282055\pi$
$758$	6.96872	0.253115
$759$	−6.85193	−0.248709
$760$	−14.1678	−0.513919
$761$	7.03153	0.254893	0.127446	−	0.991845i	$-0.459322\pi$
$761$	7.03153	0.254893	0.127446	+	0.991845i	$0.459322\pi$
$762$	32.3749	1.17282
$763$	0	0
$764$	−0.962568	−0.0348245
$765$	10.0465	0.363232
$766$	−26.9890	−0.975152
$767$	16.7674	0.605437
$768$	−1.97715	−0.0713444
$769$	−36.4103	−1.31299	−0.656494	−	0.754332i	$-0.727961\pi$
$769$	−36.4103	−1.31299	−0.656494	+	0.754332i	$0.727961\pi$
$770$	0	0
$771$	−34.2795	−1.23454
$772$	4.76065	0.171340
$773$	−15.6730	−0.563717	−0.281859	−	0.959456i	$-0.590951\pi$
$773$	−15.6730	−0.563717	−0.281859	+	0.959456i	$0.590951\pi$
$774$	4.70128	0.168984
$775$	2.07330	0.0744750
$776$	17.7818	0.638328
$777$	0	0
$778$	−33.3605	−1.19603
$779$	−4.20412	−0.150628
$780$	18.3581	0.657325
$781$	44.6518	1.59777
$782$	2.90297	0.103810
$783$	14.2830	0.510435
$784$	0	0
$785$	53.5845	1.91251
$786$	41.3294	1.47417
$787$	17.6221	0.628160	0.314080	−	0.949397i	$-0.398304\pi$
$787$	17.6221	0.628160	0.314080	+	0.949397i	$0.398304\pi$
$788$	22.5876	0.804650
$789$	−42.9717	−1.52983
$790$	21.1797	0.753541
$791$	0	0
$792$	3.55892	0.126461
$793$	−18.0603	−0.641341
$794$	−17.7874	−0.631250
$795$	−73.4889	−2.60638
$796$	−5.02467	−0.178095
$797$	−16.8741	−0.597712	−0.298856	−	0.954298i	$-0.596605\pi$
$797$	−16.8741	−0.597712	−0.298856	+	0.954298i	$0.596605\pi$
$798$	0	0
$799$	−3.37357	−0.119348
$800$	6.35674	0.224745
$801$	−14.0799	−0.497489
$802$	−22.4343	−0.792182
$803$	−50.3279	−1.77603
$804$	2.65269	0.0935533
$805$	0	0
$806$	−0.898643	−0.0316534
$807$	4.43721	0.156197
$808$	17.7743	0.625299
$809$	11.0814	0.389601	0.194801	−	0.980843i	$-0.437594\pi$
$809$	11.0814	0.389601	0.194801	+	0.980843i	$0.437594\pi$
$810$	−36.7357	−1.29076
$811$	−45.2832	−1.59011	−0.795054	−	0.606538i	$-0.792558\pi$
$811$	−45.2832	−1.59011	−0.795054	+	0.606538i	$0.792558\pi$
$812$	0	0
$813$	−31.9583	−1.12083
$814$	−1.62416	−0.0569266
$815$	−28.8229	−1.00962
$816$	−6.48332	−0.226962
$817$	−21.7400	−0.760588
$818$	−6.58938	−0.230392
$819$	0	0
$820$	3.36998	0.117685
$821$	−6.69616	−0.233698	−0.116849	−	0.993150i	$-0.537279\pi$
$821$	−6.69616	−0.233698	−0.116849	+	0.993150i	$0.537279\pi$
$822$	−26.5517	−0.926098
$823$	17.9581	0.625979	0.312990	−	0.949757i	$-0.398670\pi$
$823$	17.9581	0.625979	0.312990	+	0.949757i	$0.398670\pi$
$824$	10.0035	0.348488
$825$	−49.1996	−1.71291
$826$	0	0
$827$	−26.8965	−0.935284	−0.467642	−	0.883918i	$-0.654896\pi$
$827$	−26.8965	−0.935284	−0.467642	+	0.883918i	$0.654896\pi$
$828$	0.804852	0.0279705
$829$	33.8912	1.17709	0.588545	−	0.808465i	$-0.299701\pi$
$829$	33.8912	1.17709	0.588545	+	0.808465i	$0.299701\pi$
$830$	−47.8646	−1.66141
$831$	8.01675	0.278098
$832$	−2.75524	−0.0955209
$833$	0	0
$834$	−8.22279	−0.284732
$835$	−46.0071	−1.59214
$836$	−16.4574	−0.569192
$837$	1.34832	0.0466047
$838$	17.2319	0.595267
$839$	−48.7618	−1.68344	−0.841722	−	0.539911i	$-0.818458\pi$
$839$	−48.7618	−1.68344	−0.841722	+	0.539911i	$0.818458\pi$
$840$	0	0
$841$	−17.0626	−0.588365
$842$	−36.5996	−1.26131
$843$	15.0016	0.516683
$844$	13.7994	0.474995
$845$	−18.2269	−0.627026
$846$	−0.935328	−0.0321573
$847$	0	0
$848$	11.0295	0.378754
$849$	−1.99598	−0.0685018
$850$	20.8445	0.714959
$851$	−0.367304	−0.0125910
$852$	−22.5524	−0.772632
$853$	23.1155	0.791461	0.395730	−	0.918367i	$-0.370491\pi$
$853$	23.1155	0.791461	0.395730	+	0.918367i	$0.370491\pi$
$854$	0	0
$855$	−12.8805	−0.440503
$856$	−9.65247	−0.329915
$857$	−29.5350	−1.00890	−0.504448	−	0.863442i	$-0.668304\pi$
$857$	−29.5350	−1.00890	−0.504448	+	0.863442i	$0.668304\pi$
$858$	21.3249	0.728022
$859$	−30.3617	−1.03593	−0.517964	−	0.855402i	$-0.673310\pi$
$859$	−30.3617	−1.03593	−0.517964	+	0.855402i	$0.673310\pi$
$860$	17.4266	0.594242
$861$	0	0
$862$	−21.5261	−0.733181
$863$	−37.0177	−1.26010	−0.630048	−	0.776556i	$-0.716965\pi$
$863$	−37.0177	−1.26010	−0.630048	+	0.776556i	$0.716965\pi$
$864$	4.13395	0.140640
$865$	69.8172	2.37385
$866$	−13.8999	−0.472339
$867$	12.3521	0.419498
$868$	0	0
$869$	24.6026	0.834586
$870$	−23.0209	−0.780482
$871$	3.69664	0.125256
$872$	−1.43399	−0.0485610
$873$	16.1661	0.547140
$874$	−3.72186	−0.125894
$875$	0	0
$876$	25.4192	0.858836
$877$	34.8753	1.17766	0.588828	−	0.808259i	$-0.299590\pi$
$877$	34.8753	1.17766	0.588828	+	0.808259i	$0.299590\pi$
$878$	3.31789	0.111973
$879$	−56.0587	−1.89081
$880$	13.1921	0.444706
$881$	−40.1559	−1.35288	−0.676442	−	0.736495i	$-0.736479\pi$
$881$	−40.1559	−1.35288	−0.676442	+	0.736495i	$0.736479\pi$
$882$	0	0
$883$	5.01082	0.168627	0.0843137	−	0.996439i	$-0.473130\pi$
$883$	5.01082	0.168627	0.0843137	+	0.996439i	$0.473130\pi$
$884$	−9.03477	−0.303872
$885$	40.5484	1.36302
$886$	−10.3772	−0.348628
$887$	−38.3628	−1.28810	−0.644049	−	0.764985i	$-0.722747\pi$
$887$	−38.3628	−1.28810	−0.644049	+	0.764985i	$0.722747\pi$
$888$	0.820316	0.0275280
$889$	0	0
$890$	−52.1910	−1.74944
$891$	−42.6726	−1.42959
$892$	−5.09883	−0.170722
$893$	4.32522	0.144738
$894$	18.8362	0.629976
$895$	−19.6306	−0.656177
$896$	0	0
$897$	4.82265	0.161024
$898$	−37.6652	−1.25690
$899$	1.12689	0.0375840
$900$	5.77916	0.192639
$901$	36.1669	1.20489
$902$	3.91460	0.130342
$903$	0	0
$904$	17.3398	0.576712
$905$	49.4980	1.64537
$906$	−31.3082	−1.04015
$907$	−2.77360	−0.0920958	−0.0460479	−	0.998939i	$-0.514663\pi$
$907$	−2.77360	−0.0920958	−0.0460479	+	0.998939i	$0.514663\pi$
$908$	−17.8860	−0.593569
$909$	16.1594	0.535973
$910$	0	0
$911$	−22.0256	−0.729740	−0.364870	−	0.931058i	$-0.618887\pi$
$911$	−22.0256	−0.729740	−0.364870	+	0.931058i	$0.618887\pi$
$912$	8.31219	0.275244
$913$	−55.6000	−1.84009
$914$	25.6514	0.848471
$915$	−43.6750	−1.44385
$916$	8.39224	0.277287
$917$	0	0
$918$	13.5557	0.447405
$919$	−59.8987	−1.97588	−0.987938	−	0.154852i	$-0.950510\pi$
$919$	−59.8987	−1.97588	−0.987938	+	0.154852i	$0.950510\pi$
$920$	2.98340	0.0983599
$921$	−44.6055	−1.46980
$922$	14.0242	0.461863
$923$	−31.4277	−1.03445
$924$	0	0
$925$	−2.63739	−0.0867169
$926$	−8.25708	−0.271345
$927$	9.09458	0.298705
$928$	3.45506	0.113418
$929$	−13.9437	−0.457478	−0.228739	−	0.973488i	$-0.573460\pi$
$929$	−13.9437	−0.457478	−0.228739	+	0.973488i	$0.573460\pi$
$930$	−2.17317	−0.0712612
$931$	0	0
$932$	−17.4921	−0.572974
$933$	−32.2433	−1.05560
$934$	−22.2241	−0.727196
$935$	43.2584	1.41470
$936$	−2.50490	−0.0818753
$937$	29.6051	0.967158	0.483579	−	0.875301i	$-0.339337\pi$
$937$	29.6051	0.967158	0.483579	+	0.875301i	$0.339337\pi$
$938$	0	0
$939$	17.5814	0.573748
$940$	−3.46705	−0.113083
$941$	6.95956	0.226875	0.113438	−	0.993545i	$-0.463814\pi$
$941$	6.95956	0.226875	0.113438	+	0.993545i	$0.463814\pi$
$942$	−31.4379	−1.02430
$943$	0.885289	0.0288290
$944$	−6.08564	−0.198071
$945$	0	0
$946$	20.2429	0.658153
$947$	20.1411	0.654499	0.327250	−	0.944938i	$-0.393878\pi$
$947$	20.1411	0.654499	0.327250	+	0.944938i	$0.393878\pi$
$948$	−12.4261	−0.403580
$949$	35.4227	1.14987
$950$	−26.7245	−0.867056
$951$	41.5575	1.34759
$952$	0	0
$953$	−24.4387	−0.791649	−0.395824	−	0.918326i	$-0.629541\pi$
$953$	−24.4387	−0.791649	−0.395824	+	0.918326i	$0.629541\pi$
$954$	10.0273	0.324647
$955$	−3.24383	−0.104968
$956$	1.94044	0.0627583
$957$	−26.7413	−0.864425
$958$	40.9796	1.32399
$959$	0	0
$960$	−6.66296	−0.215046
$961$	−30.8936	−0.996568
$962$	1.14314	0.0368564
$963$	−8.77545	−0.282785
$964$	10.5374	0.339387
$965$	16.0433	0.516451
$966$	0	0
$967$	−0.356775	−0.0114731	−0.00573656	−	0.999984i	$-0.501826\pi$
$967$	−0.356775	−0.0114731	−0.00573656	+	0.999984i	$0.501826\pi$
$968$	4.32408	0.138981
$969$	27.2566	0.875609
$970$	59.9241	1.92405
$971$	−28.7739	−0.923399	−0.461700	−	0.887036i	$-0.652760\pi$
$971$	−28.7739	−0.923399	−0.461700	+	0.887036i	$0.652760\pi$
$972$	9.15088	0.293514
$973$	0	0
$974$	−15.7625	−0.505064
$975$	34.6286	1.10900
$976$	6.55489	0.209817
$977$	9.55610	0.305727	0.152863	−	0.988247i	$-0.451151\pi$
$977$	9.55610	0.305727	0.152863	+	0.988247i	$0.451151\pi$
$978$	16.9103	0.540733
$979$	−60.6256	−1.93760
$980$	0	0
$981$	−1.30370	−0.0416238
$982$	41.0462	1.30984
$983$	−8.15704	−0.260169	−0.130085	−	0.991503i	$-0.541525\pi$
$983$	−8.15704	−0.260169	−0.130085	+	0.991503i	$0.541525\pi$
$984$	−1.97715	−0.0630294
$985$	76.1197	2.42538
$986$	11.3295	0.360806
$987$	0	0
$988$	11.5834	0.368516
$989$	4.57795	0.145570
$990$	11.9935	0.381177
$991$	−27.0141	−0.858130	−0.429065	−	0.903274i	$-0.641157\pi$
$991$	−27.0141	−0.858130	−0.429065	+	0.903274i	$0.641157\pi$
$992$	0.326157	0.0103555
$993$	−1.73205	−0.0549648
$994$	0	0
$995$	−16.9330	−0.536813
$996$	28.0820	0.889813
$997$	−37.8256	−1.19795	−0.598975	−	0.800768i	$-0.704425\pi$
$997$	−37.8256	−1.19795	−0.598975	+	0.800768i	$0.704425\pi$
$998$	−41.1894	−1.30383
$999$	−1.71517	−0.0542654

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4018.2.a.bu.1.3		10
7.3	odd	6		574.2.e.h.247.3	yes	20
7.5	odd	6		574.2.e.h.165.3	✓	20
7.6	odd	2		4018.2.a.bt.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.e.h.165.3	✓	20	7.5	odd	6
574.2.e.h.247.3	yes	20	7.3	odd	6
4018.2.a.bt.1.8		10	7.6	odd	2
4018.2.a.bu.1.3		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.97715 q^{3} +1.00000 q^{4} +3.36998 q^{5} -1.97715 q^{6} +1.00000 q^{8} +0.909140 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.97715 q^{3} +1.00000 q^{4} +3.36998 q^{5} -1.97715 q^{6} +1.00000 q^{8} +0.909140 q^{9} +3.36998 q^{10} +3.91460 q^{11} -1.97715 q^{12} -2.75524 q^{13} -6.66296 q^{15} +1.00000 q^{16} +3.27912 q^{17} +0.909140 q^{18} -4.20412 q^{19} +3.36998 q^{20} +3.91460 q^{22} +0.885289 q^{23} -1.97715 q^{24} +6.35674 q^{25} -2.75524 q^{26} +4.13395 q^{27} +3.45506 q^{29} -6.66296 q^{30} +0.326157 q^{31} +1.00000 q^{32} -7.73977 q^{33} +3.27912 q^{34} +0.909140 q^{36} -0.414897 q^{37} -4.20412 q^{38} +5.44754 q^{39} +3.36998 q^{40} +1.00000 q^{41} +5.17113 q^{43} +3.91460 q^{44} +3.06378 q^{45} +0.885289 q^{46} -1.02881 q^{47} -1.97715 q^{48} +6.35674 q^{50} -6.48332 q^{51} -2.75524 q^{52} +11.0295 q^{53} +4.13395 q^{54} +13.1921 q^{55} +8.31219 q^{57} +3.45506 q^{58} -6.08564 q^{59} -6.66296 q^{60} +6.55489 q^{61} +0.326157 q^{62} +1.00000 q^{64} -9.28511 q^{65} -7.73977 q^{66} -1.34167 q^{67} +3.27912 q^{68} -1.75035 q^{69} +11.4065 q^{71} +0.909140 q^{72} -12.8565 q^{73} -0.414897 q^{74} -12.5682 q^{75} -4.20412 q^{76} +5.44754 q^{78} +6.28483 q^{79} +3.36998 q^{80} -10.9009 q^{81} +1.00000 q^{82} -14.2033 q^{83} +11.0505 q^{85} +5.17113 q^{86} -6.83118 q^{87} +3.91460 q^{88} -15.4870 q^{89} +3.06378 q^{90} +0.885289 q^{92} -0.644863 q^{93} -1.02881 q^{94} -14.1678 q^{95} -1.97715 q^{96} +17.7818 q^{97} +3.55892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 2 q^{5} + q^{6} + 10 q^{8} + 17 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 2 * q^5 + q^6 + 10 * q^8 + 17 * q^9	\( 10 q + 10 q^{2} + q^{3} + 10 q^{4} - 2 q^{5} + q^{6} + 10 q^{8} + 17 q^{9} - 2 q^{10} + 11 q^{11} + q^{12} + 4 q^{13} + 4 q^{15} + 10 q^{16} + 5 q^{17} + 17 q^{18} - q^{19} - 2 q^{20} + 11 q^{22} + 9 q^{23} + q^{24} + 24 q^{25} + 4 q^{26} + 7 q^{27} + 23 q^{29} + 4 q^{30} - 5 q^{31} + 10 q^{32} - 5 q^{33} + 5 q^{34} + 17 q^{36} + 16 q^{37} - q^{38} - 7 q^{39} - 2 q^{40} + 10 q^{41} + 20 q^{43} + 11 q^{44} - 42 q^{45} + 9 q^{46} - 16 q^{47} + q^{48} + 24 q^{50} + 13 q^{51} + 4 q^{52} + 26 q^{53} + 7 q^{54} + 7 q^{55} + 37 q^{57} + 23 q^{58} - 10 q^{59} + 4 q^{60} - 5 q^{62} + 10 q^{64} + 18 q^{65} - 5 q^{66} + 7 q^{67} + 5 q^{68} + 39 q^{69} + 5 q^{71} + 17 q^{72} - 13 q^{73} + 16 q^{74} + 19 q^{75} - q^{76} - 7 q^{78} - q^{79} - 2 q^{80} + 18 q^{81} + 10 q^{82} + 21 q^{83} + 34 q^{85} + 20 q^{86} + 2 q^{87} + 11 q^{88} + 6 q^{89} - 42 q^{90} + 9 q^{92} - 5 q^{93} - 16 q^{94} + 24 q^{95} + q^{96} + 29 q^{97} + 48 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + q^3 + 10 * q^4 - 2 * q^5 + q^6 + 10 * q^8 + 17 * q^9 - 2 * q^10 + 11 * q^11 + q^12 + 4 * q^13 + 4 * q^15 + 10 * q^16 + 5 * q^17 + 17 * q^18 - q^19 - 2 * q^20 + 11 * q^22 + 9 * q^23 + q^24 + 24 * q^25 + 4 * q^26 + 7 * q^27 + 23 * q^29 + 4 * q^30 - 5 * q^31 + 10 * q^32 - 5 * q^33 + 5 * q^34 + 17 * q^36 + 16 * q^37 - q^38 - 7 * q^39 - 2 * q^40 + 10 * q^41 + 20 * q^43 + 11 * q^44 - 42 * q^45 + 9 * q^46 - 16 * q^47 + q^48 + 24 * q^50 + 13 * q^51 + 4 * q^52 + 26 * q^53 + 7 * q^54 + 7 * q^55 + 37 * q^57 + 23 * q^58 - 10 * q^59 + 4 * q^60 - 5 * q^62 + 10 * q^64 + 18 * q^65 - 5 * q^66 + 7 * q^67 + 5 * q^68 + 39 * q^69 + 5 * q^71 + 17 * q^72 - 13 * q^73 + 16 * q^74 + 19 * q^75 - q^76 - 7 * q^78 - q^79 - 2 * q^80 + 18 * q^81 + 10 * q^82 + 21 * q^83 + 34 * q^85 + 20 * q^86 + 2 * q^87 + 11 * q^88 + 6 * q^89 - 42 * q^90 + 9 * q^92 - 5 * q^93 - 16 * q^94 + 24 * q^95 + q^96 + 29 * q^97 + 48 * q^99

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