LMFDB - Embedded newform 2366.2.a.t.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, 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("2366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.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:	$18.8926051182$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.73205 q^{3} +1.00000 q^{4} +0.267949 q^{5} -1.73205 q^{6} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} -1.73205 q^{3} +1.00000 q^{4} +0.267949 q^{5} -1.73205 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.267949 q^{10} -5.46410 q^{11} -1.73205 q^{12} -1.00000 q^{14} -0.464102 q^{15} +1.00000 q^{16} -3.46410 q^{17} +3.46410 q^{19} +0.267949 q^{20} +1.73205 q^{21} -5.46410 q^{22} +8.46410 q^{23} -1.73205 q^{24} -4.92820 q^{25} +5.19615 q^{27} -1.00000 q^{28} +8.92820 q^{29} -0.464102 q^{30} +0.535898 q^{31} +1.00000 q^{32} +9.46410 q^{33} -3.46410 q^{34} -0.267949 q^{35} -2.53590 q^{37} +3.46410 q^{38} +0.267949 q^{40} +9.46410 q^{41} +1.73205 q^{42} +4.00000 q^{43} -5.46410 q^{44} +8.46410 q^{46} +4.92820 q^{47} -1.73205 q^{48} +1.00000 q^{49} -4.92820 q^{50} +6.00000 q^{51} -6.92820 q^{53} +5.19615 q^{54} -1.46410 q^{55} -1.00000 q^{56} -6.00000 q^{57} +8.92820 q^{58} +2.80385 q^{59} -0.464102 q^{60} +3.19615 q^{61} +0.535898 q^{62} +1.00000 q^{64} +9.46410 q^{66} +4.92820 q^{67} -3.46410 q^{68} -14.6603 q^{69} -0.267949 q^{70} -2.46410 q^{71} -0.535898 q^{73} -2.53590 q^{74} +8.53590 q^{75} +3.46410 q^{76} +5.46410 q^{77} +1.07180 q^{79} +0.267949 q^{80} -9.00000 q^{81} +9.46410 q^{82} +10.3923 q^{83} +1.73205 q^{84} -0.928203 q^{85} +4.00000 q^{86} -15.4641 q^{87} -5.46410 q^{88} -8.53590 q^{89} +8.46410 q^{92} -0.928203 q^{93} +4.92820 q^{94} +0.928203 q^{95} -1.73205 q^{96} -3.07180 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + 4 q^{5} - 2 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + 4 * q^5 - 2 * q^7 + 2 * q^8	$ 2 q + 2 q^{2} + 2 q^{4} + 4 q^{5} - 2 q^{7} + 2 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{14} + 6 q^{15} + 2 q^{16} + 4 q^{20} - 4 q^{22} + 10 q^{23} + 4 q^{25} - 2 q^{28} + 4 q^{29} + 6 q^{30} + 8 q^{31} + 2 q^{32} + 12 q^{33} - 4 q^{35} - 12 q^{37} + 4 q^{40} + 12 q^{41} + 8 q^{43} - 4 q^{44} + 10 q^{46} - 4 q^{47} + 2 q^{49} + 4 q^{50} + 12 q^{51} + 4 q^{55} - 2 q^{56} - 12 q^{57} + 4 q^{58} + 16 q^{59} + 6 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{64} + 12 q^{66} - 4 q^{67} - 12 q^{69} - 4 q^{70} + 2 q^{71} - 8 q^{73} - 12 q^{74} + 24 q^{75} + 4 q^{77} + 16 q^{79} + 4 q^{80} - 18 q^{81} + 12 q^{82} + 12 q^{85} + 8 q^{86} - 24 q^{87} - 4 q^{88} - 24 q^{89} + 10 q^{92} + 12 q^{93} - 4 q^{94} - 12 q^{95} - 20 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + 4 * q^5 - 2 * q^7 + 2 * q^8 + 4 * q^10 - 4 * q^11 - 2 * q^14 + 6 * q^15 + 2 * q^16 + 4 * q^20 - 4 * q^22 + 10 * q^23 + 4 * q^25 - 2 * q^28 + 4 * q^29 + 6 * q^30 + 8 * q^31 + 2 * q^32 + 12 * q^33 - 4 * q^35 - 12 * q^37 + 4 * q^40 + 12 * q^41 + 8 * q^43 - 4 * q^44 + 10 * q^46 - 4 * q^47 + 2 * q^49 + 4 * q^50 + 12 * q^51 + 4 * q^55 - 2 * q^56 - 12 * q^57 + 4 * q^58 + 16 * q^59 + 6 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^64 + 12 * q^66 - 4 * q^67 - 12 * q^69 - 4 * q^70 + 2 * q^71 - 8 * q^73 - 12 * q^74 + 24 * q^75 + 4 * q^77 + 16 * q^79 + 4 * q^80 - 18 * q^81 + 12 * q^82 + 12 * q^85 + 8 * q^86 - 24 * q^87 - 4 * q^88 - 24 * q^89 + 10 * q^92 + 12 * q^93 - 4 * q^94 - 12 * q^95 - 20 * q^97 + 2 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.73205	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	−1.73205	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$4$	1.00000	0.500000
$5$	0.267949	0.119831	0.0599153	−	0.998203i	$-0.480917\pi$
$5$	0.267949	0.119831	0.0599153	+	0.998203i	$0.480917\pi$
$6$	−1.73205	−0.707107
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	0	0
$10$	0.267949	0.0847330
$11$	−5.46410	−1.64749	−0.823744	−	0.566961i	$-0.808119\pi$
$11$	−5.46410	−1.64749	−0.823744	+	0.566961i	$0.808119\pi$
$12$	−1.73205	−0.500000
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−0.464102	−0.119831
$16$	1.00000	0.250000
$17$	−3.46410	−0.840168	−0.420084	−	0.907485i	$-0.637999\pi$
$17$	−3.46410	−0.840168	−0.420084	+	0.907485i	$0.637999\pi$
$18$	0	0
$19$	3.46410	0.794719	0.397360	−	0.917663i	$-0.369927\pi$
$19$	3.46410	0.794719	0.397360	+	0.917663i	$0.369927\pi$
$20$	0.267949	0.0599153
$21$	1.73205	0.377964
$22$	−5.46410	−1.16495
$23$	8.46410	1.76489	0.882444	−	0.470418i	$-0.155897\pi$
$23$	8.46410	1.76489	0.882444	+	0.470418i	$0.155897\pi$
$24$	−1.73205	−0.353553
$25$	−4.92820	−0.985641
$26$	0	0
$27$	5.19615	1.00000
$28$	−1.00000	−0.188982
$29$	8.92820	1.65793	0.828963	−	0.559304i	$-0.188931\pi$
$29$	8.92820	1.65793	0.828963	+	0.559304i	$0.188931\pi$
$30$	−0.464102	−0.0847330
$31$	0.535898	0.0962502	0.0481251	−	0.998841i	$-0.484675\pi$
$31$	0.535898	0.0962502	0.0481251	+	0.998841i	$0.484675\pi$
$32$	1.00000	0.176777
$33$	9.46410	1.64749
$34$	−3.46410	−0.594089
$35$	−0.267949	−0.0452917
$36$	0	0
$37$	−2.53590	−0.416899	−0.208450	−	0.978033i	$-0.566842\pi$
$37$	−2.53590	−0.416899	−0.208450	+	0.978033i	$0.566842\pi$
$38$	3.46410	0.561951
$39$	0	0
$40$	0.267949	0.0423665
$41$	9.46410	1.47804	0.739022	−	0.673681i	$-0.235288\pi$
$41$	9.46410	1.47804	0.739022	+	0.673681i	$0.235288\pi$
$42$	1.73205	0.267261
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−5.46410	−0.823744
$45$	0	0
$46$	8.46410	1.24796
$47$	4.92820	0.718852	0.359426	−	0.933174i	$-0.382972\pi$
$47$	4.92820	0.718852	0.359426	+	0.933174i	$0.382972\pi$
$48$	−1.73205	−0.250000
$49$	1.00000	0.142857
$50$	−4.92820	−0.696953
$51$	6.00000	0.840168
$52$	0	0
$53$	−6.92820	−0.951662	−0.475831	−	0.879537i	$-0.657853\pi$
$53$	−6.92820	−0.951662	−0.475831	+	0.879537i	$0.657853\pi$
$54$	5.19615	0.707107
$55$	−1.46410	−0.197419
$56$	−1.00000	−0.133631
$57$	−6.00000	−0.794719
$58$	8.92820	1.17233
$59$	2.80385	0.365030	0.182515	−	0.983203i	$-0.441576\pi$
$59$	2.80385	0.365030	0.182515	+	0.983203i	$0.441576\pi$
$60$	−0.464102	−0.0599153
$61$	3.19615	0.409225	0.204613	−	0.978843i	$-0.434407\pi$
$61$	3.19615	0.409225	0.204613	+	0.978843i	$0.434407\pi$
$62$	0.535898	0.0680592
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	9.46410	1.16495
$67$	4.92820	0.602076	0.301038	−	0.953612i	$-0.402667\pi$
$67$	4.92820	0.602076	0.301038	+	0.953612i	$0.402667\pi$
$68$	−3.46410	−0.420084
$69$	−14.6603	−1.76489
$70$	−0.267949	−0.0320261
$71$	−2.46410	−0.292435	−0.146218	−	0.989252i	$-0.546710\pi$
$71$	−2.46410	−0.292435	−0.146218	+	0.989252i	$0.546710\pi$
$72$	0	0
$73$	−0.535898	−0.0627222	−0.0313611	−	0.999508i	$-0.509984\pi$
$73$	−0.535898	−0.0627222	−0.0313611	+	0.999508i	$0.509984\pi$
$74$	−2.53590	−0.294792
$75$	8.53590	0.985641
$76$	3.46410	0.397360
$77$	5.46410	0.622692
$78$	0	0
$79$	1.07180	0.120587	0.0602933	−	0.998181i	$-0.480796\pi$
$79$	1.07180	0.120587	0.0602933	+	0.998181i	$0.480796\pi$
$80$	0.267949	0.0299576
$81$	−9.00000	−1.00000
$82$	9.46410	1.04514
$83$	10.3923	1.14070	0.570352	−	0.821401i	$-0.306807\pi$
$83$	10.3923	1.14070	0.570352	+	0.821401i	$0.306807\pi$
$84$	1.73205	0.188982
$85$	−0.928203	−0.100678
$86$	4.00000	0.431331
$87$	−15.4641	−1.65793
$88$	−5.46410	−0.582475
$89$	−8.53590	−0.904803	−0.452402	−	0.891814i	$-0.649433\pi$
$89$	−8.53590	−0.904803	−0.452402	+	0.891814i	$0.649433\pi$
$90$	0	0
$91$	0	0
$92$	8.46410	0.882444
$93$	−0.928203	−0.0962502
$94$	4.92820	0.508305
$95$	0.928203	0.0952316
$96$	−1.73205	−0.176777
$97$	−3.07180	−0.311894	−0.155947	−	0.987765i	$-0.549843\pi$
$97$	−3.07180	−0.311894	−0.155947	+	0.987765i	$0.549843\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	−4.92820	−0.492820
$101$	16.0000	1.59206	0.796030	−	0.605257i	$-0.206930\pi$
$101$	16.0000	1.59206	0.796030	+	0.605257i	$0.206930\pi$
$102$	6.00000	0.594089
$103$	16.9282	1.66799	0.833993	−	0.551775i	$-0.186049\pi$
$103$	16.9282	1.66799	0.833993	+	0.551775i	$0.186049\pi$
$104$	0	0
$105$	0.464102	0.0452917
$106$	−6.92820	−0.672927
$107$	−14.3923	−1.39136	−0.695678	−	0.718353i	$-0.744896\pi$
$107$	−14.3923	−1.39136	−0.695678	+	0.718353i	$0.744896\pi$
$108$	5.19615	0.500000
$109$	−17.4641	−1.67276	−0.836379	−	0.548152i	$-0.815332\pi$
$109$	−17.4641	−1.67276	−0.836379	+	0.548152i	$0.815332\pi$
$110$	−1.46410	−0.139597
$111$	4.39230	0.416899
$112$	−1.00000	−0.0944911
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	−6.00000	−0.561951
$115$	2.26795	0.211487
$116$	8.92820	0.828963
$117$	0	0
$118$	2.80385	0.258115
$119$	3.46410	0.317554
$120$	−0.464102	−0.0423665
$121$	18.8564	1.71422
$122$	3.19615	0.289366
$123$	−16.3923	−1.47804
$124$	0.535898	0.0481251
$125$	−2.66025	−0.237940
$126$	0	0
$127$	11.3923	1.01090	0.505452	−	0.862855i	$-0.331326\pi$
$127$	11.3923	1.01090	0.505452	+	0.862855i	$0.331326\pi$
$128$	1.00000	0.0883883
$129$	−6.92820	−0.609994
$130$	0	0
$131$	−9.19615	−0.803472	−0.401736	−	0.915756i	$-0.631593\pi$
$131$	−9.19615	−0.803472	−0.401736	+	0.915756i	$0.631593\pi$
$132$	9.46410	0.823744
$133$	−3.46410	−0.300376
$134$	4.92820	0.425732
$135$	1.39230	0.119831
$136$	−3.46410	−0.297044
$137$	3.00000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	−14.6603	−1.24796
$139$	19.4641	1.65092	0.825462	−	0.564458i	$-0.190915\pi$
$139$	19.4641	1.65092	0.825462	+	0.564458i	$0.190915\pi$
$140$	−0.267949	−0.0226458
$141$	−8.53590	−0.718852
$142$	−2.46410	−0.206783
$143$	0	0
$144$	0	0
$145$	2.39230	0.198670
$146$	−0.535898	−0.0443513
$147$	−1.73205	−0.142857
$148$	−2.53590	−0.208450
$149$	−4.39230	−0.359832	−0.179916	−	0.983682i	$-0.557583\pi$
$149$	−4.39230	−0.359832	−0.179916	+	0.983682i	$0.557583\pi$
$150$	8.53590	0.696953
$151$	7.39230	0.601577	0.300789	−	0.953691i	$-0.402750\pi$
$151$	7.39230	0.601577	0.300789	+	0.953691i	$0.402750\pi$
$152$	3.46410	0.280976
$153$	0	0
$154$	5.46410	0.440310
$155$	0.143594	0.0115337
$156$	0	0
$157$	9.85641	0.786627	0.393313	−	0.919404i	$-0.371329\pi$
$157$	9.85641	0.786627	0.393313	+	0.919404i	$0.371329\pi$
$158$	1.07180	0.0852676
$159$	12.0000	0.951662
$160$	0.267949	0.0211832
$161$	−8.46410	−0.667065
$162$	−9.00000	−0.707107
$163$	0.392305	0.0307277	0.0153638	−	0.999882i	$-0.495109\pi$
$163$	0.392305	0.0307277	0.0153638	+	0.999882i	$0.495109\pi$
$164$	9.46410	0.739022
$165$	2.53590	0.197419
$166$	10.3923	0.806599
$167$	4.39230	0.339887	0.169943	−	0.985454i	$-0.445642\pi$
$167$	4.39230	0.339887	0.169943	+	0.985454i	$0.445642\pi$
$168$	1.73205	0.133631
$169$	0	0
$170$	−0.928203	−0.0711899
$171$	0	0
$172$	4.00000	0.304997
$173$	−15.1962	−1.15534	−0.577671	−	0.816270i	$-0.696038\pi$
$173$	−15.1962	−1.15534	−0.577671	+	0.816270i	$0.696038\pi$
$174$	−15.4641	−1.17233
$175$	4.92820	0.372537
$176$	−5.46410	−0.411872
$177$	−4.85641	−0.365030
$178$	−8.53590	−0.639793
$179$	−3.46410	−0.258919	−0.129460	−	0.991585i	$-0.541324\pi$
$179$	−3.46410	−0.258919	−0.129460	+	0.991585i	$0.541324\pi$
$180$	0	0
$181$	25.0526	1.86214	0.931071	−	0.364838i	$-0.118876\pi$
$181$	25.0526	1.86214	0.931071	+	0.364838i	$0.118876\pi$
$182$	0	0
$183$	−5.53590	−0.409225
$184$	8.46410	0.623982
$185$	−0.679492	−0.0499572
$186$	−0.928203	−0.0680592
$187$	18.9282	1.38417
$188$	4.92820	0.359426
$189$	−5.19615	−0.377964
$190$	0.928203	0.0673389
$191$	−8.00000	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$191$	−8.00000	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$192$	−1.73205	−0.125000
$193$	11.0000	0.791797	0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000	0.791797	0.395899	+	0.918294i	$0.370433\pi$
$194$	−3.07180	−0.220542
$195$	0	0
$196$	1.00000	0.0714286
$197$	−20.7846	−1.48084	−0.740421	−	0.672143i	$-0.765374\pi$
$197$	−20.7846	−1.48084	−0.740421	+	0.672143i	$0.765374\pi$
$198$	0	0
$199$	11.4641	0.812669	0.406334	−	0.913724i	$-0.366807\pi$
$199$	11.4641	0.812669	0.406334	+	0.913724i	$0.366807\pi$
$200$	−4.92820	−0.348477
$201$	−8.53590	−0.602076
$202$	16.0000	1.12576
$203$	−8.92820	−0.626637
$204$	6.00000	0.420084
$205$	2.53590	0.177115
$206$	16.9282	1.17944
$207$	0	0
$208$	0	0
$209$	−18.9282	−1.30929
$210$	0.464102	0.0320261
$211$	26.9282	1.85381	0.926907	−	0.375291i	$-0.122457\pi$
$211$	26.9282	1.85381	0.926907	+	0.375291i	$0.122457\pi$
$212$	−6.92820	−0.475831
$213$	4.26795	0.292435
$214$	−14.3923	−0.983838
$215$	1.07180	0.0730959
$216$	5.19615	0.353553
$217$	−0.535898	−0.0363792
$218$	−17.4641	−1.18282
$219$	0.928203	0.0627222
$220$	−1.46410	−0.0987097
$221$	0	0
$222$	4.39230	0.294792
$223$	−23.3205	−1.56166	−0.780828	−	0.624746i	$-0.785203\pi$
$223$	−23.3205	−1.56166	−0.780828	+	0.624746i	$0.785203\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	2.00000	0.133038
$227$	25.7321	1.70790	0.853948	−	0.520358i	$-0.174202\pi$
$227$	25.7321	1.70790	0.853948	+	0.520358i	$0.174202\pi$
$228$	−6.00000	−0.397360
$229$	−12.0000	−0.792982	−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000	−0.792982	−0.396491	+	0.918039i	$0.629772\pi$
$230$	2.26795	0.149544
$231$	−9.46410	−0.622692
$232$	8.92820	0.586165
$233$	26.8564	1.75942	0.879711	−	0.475509i	$-0.157736\pi$
$233$	26.8564	1.75942	0.879711	+	0.475509i	$0.157736\pi$
$234$	0	0
$235$	1.32051	0.0861404
$236$	2.80385	0.182515
$237$	−1.85641	−0.120587
$238$	3.46410	0.224544
$239$	−14.3205	−0.926317	−0.463158	−	0.886276i	$-0.653284\pi$
$239$	−14.3205	−0.926317	−0.463158	+	0.886276i	$0.653284\pi$
$240$	−0.464102	−0.0299576
$241$	−12.0000	−0.772988	−0.386494	−	0.922292i	$-0.626314\pi$
$241$	−12.0000	−0.772988	−0.386494	+	0.922292i	$0.626314\pi$
$242$	18.8564	1.21214
$243$	0	0
$244$	3.19615	0.204613
$245$	0.267949	0.0171186
$246$	−16.3923	−1.04514
$247$	0	0
$248$	0.535898	0.0340296
$249$	−18.0000	−1.14070
$250$	−2.66025	−0.168249
$251$	24.1244	1.52272	0.761358	−	0.648332i	$-0.224533\pi$
$251$	24.1244	1.52272	0.761358	+	0.648332i	$0.224533\pi$
$252$	0	0
$253$	−46.2487	−2.90763
$254$	11.3923	0.714817
$255$	1.60770	0.100678
$256$	1.00000	0.0625000
$257$	−7.85641	−0.490069	−0.245035	−	0.969514i	$-0.578799\pi$
$257$	−7.85641	−0.490069	−0.245035	+	0.969514i	$0.578799\pi$
$258$	−6.92820	−0.431331
$259$	2.53590	0.157573
$260$	0	0
$261$	0	0
$262$	−9.19615	−0.568140
$263$	5.53590	0.341358	0.170679	−	0.985327i	$-0.445404\pi$
$263$	5.53590	0.341358	0.170679	+	0.985327i	$0.445404\pi$
$264$	9.46410	0.582475
$265$	−1.85641	−0.114038
$266$	−3.46410	−0.212398
$267$	14.7846	0.904803
$268$	4.92820	0.301038
$269$	13.0526	0.795829	0.397914	−	0.917423i	$-0.369734\pi$
$269$	13.0526	0.795829	0.397914	+	0.917423i	$0.369734\pi$
$270$	1.39230	0.0847330
$271$	−22.7846	−1.38407	−0.692033	−	0.721866i	$-0.743285\pi$
$271$	−22.7846	−1.38407	−0.692033	+	0.721866i	$0.743285\pi$
$272$	−3.46410	−0.210042
$273$	0	0
$274$	3.00000	0.181237
$275$	26.9282	1.62383
$276$	−14.6603	−0.882444
$277$	−8.53590	−0.512872	−0.256436	−	0.966561i	$-0.582548\pi$
$277$	−8.53590	−0.512872	−0.256436	+	0.966561i	$0.582548\pi$
$278$	19.4641	1.16738
$279$	0	0
$280$	−0.267949	−0.0160130
$281$	−14.0000	−0.835170	−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000	−0.835170	−0.417585	+	0.908638i	$0.637123\pi$
$282$	−8.53590	−0.508305
$283$	12.6603	0.752574	0.376287	−	0.926503i	$-0.377201\pi$
$283$	12.6603	0.752574	0.376287	+	0.926503i	$0.377201\pi$
$284$	−2.46410	−0.146218
$285$	−1.60770	−0.0952316
$286$	0	0
$287$	−9.46410	−0.558648
$288$	0	0
$289$	−5.00000	−0.294118
$290$	2.39230	0.140481
$291$	5.32051	0.311894
$292$	−0.535898	−0.0313611
$293$	−21.8564	−1.27686	−0.638432	−	0.769678i	$-0.720417\pi$
$293$	−21.8564	−1.27686	−0.638432	+	0.769678i	$0.720417\pi$
$294$	−1.73205	−0.101015
$295$	0.751289	0.0437417
$296$	−2.53590	−0.147396
$297$	−28.3923	−1.64749
$298$	−4.39230	−0.254439
$299$	0	0
$300$	8.53590	0.492820
$301$	−4.00000	−0.230556
$302$	7.39230	0.425379
$303$	−27.7128	−1.59206
$304$	3.46410	0.198680
$305$	0.856406	0.0490377
$306$	0	0
$307$	2.80385	0.160024	0.0800120	−	0.996794i	$-0.474504\pi$
$307$	2.80385	0.160024	0.0800120	+	0.996794i	$0.474504\pi$
$308$	5.46410	0.311346
$309$	−29.3205	−1.66799
$310$	0.143594	0.00815557
$311$	−19.8564	−1.12595	−0.562977	−	0.826473i	$-0.690344\pi$
$311$	−19.8564	−1.12595	−0.562977	+	0.826473i	$0.690344\pi$
$312$	0	0
$313$	13.0718	0.738862	0.369431	−	0.929258i	$-0.379553\pi$
$313$	13.0718	0.738862	0.369431	+	0.929258i	$0.379553\pi$
$314$	9.85641	0.556229
$315$	0	0
$316$	1.07180	0.0602933
$317$	−5.07180	−0.284860	−0.142430	−	0.989805i	$-0.545492\pi$
$317$	−5.07180	−0.284860	−0.142430	+	0.989805i	$0.545492\pi$
$318$	12.0000	0.672927
$319$	−48.7846	−2.73141
$320$	0.267949	0.0149788
$321$	24.9282	1.39136
$322$	−8.46410	−0.471686
$323$	−12.0000	−0.667698
$324$	−9.00000	−0.500000
$325$	0	0
$326$	0.392305	0.0217278
$327$	30.2487	1.67276
$328$	9.46410	0.522568
$329$	−4.92820	−0.271701
$330$	2.53590	0.139597
$331$	15.8564	0.871547	0.435773	−	0.900056i	$-0.356475\pi$
$331$	15.8564	0.871547	0.435773	+	0.900056i	$0.356475\pi$
$332$	10.3923	0.570352
$333$	0	0
$334$	4.39230	0.240336
$335$	1.32051	0.0721471
$336$	1.73205	0.0944911
$337$	−11.8564	−0.645860	−0.322930	−	0.946423i	$-0.604668\pi$
$337$	−11.8564	−0.645860	−0.322930	+	0.946423i	$0.604668\pi$
$338$	0	0
$339$	−3.46410	−0.188144
$340$	−0.928203	−0.0503389
$341$	−2.92820	−0.158571
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	4.00000	0.215666
$345$	−3.92820	−0.211487
$346$	−15.1962	−0.816950
$347$	−18.2487	−0.979642	−0.489821	−	0.871823i	$-0.662938\pi$
$347$	−18.2487	−0.979642	−0.489821	+	0.871823i	$0.662938\pi$
$348$	−15.4641	−0.828963
$349$	23.7321	1.27035	0.635174	−	0.772369i	$-0.280928\pi$
$349$	23.7321	1.27035	0.635174	+	0.772369i	$0.280928\pi$
$350$	4.92820	0.263424
$351$	0	0
$352$	−5.46410	−0.291238
$353$	0.535898	0.0285230	0.0142615	−	0.999898i	$-0.495460\pi$
$353$	0.535898	0.0285230	0.0142615	+	0.999898i	$0.495460\pi$
$354$	−4.85641	−0.258115
$355$	−0.660254	−0.0350426
$356$	−8.53590	−0.452402
$357$	−6.00000	−0.317554
$358$	−3.46410	−0.183083
$359$	−11.5359	−0.608841	−0.304421	−	0.952538i	$-0.598463\pi$
$359$	−11.5359	−0.608841	−0.304421	+	0.952538i	$0.598463\pi$
$360$	0	0
$361$	−7.00000	−0.368421
$362$	25.0526	1.31673
$363$	−32.6603	−1.71422
$364$	0	0
$365$	−0.143594	−0.00751603
$366$	−5.53590	−0.289366
$367$	−16.9282	−0.883645	−0.441823	−	0.897102i	$-0.645668\pi$
$367$	−16.9282	−0.883645	−0.441823	+	0.897102i	$0.645668\pi$
$368$	8.46410	0.441222
$369$	0	0
$370$	−0.679492	−0.0353251
$371$	6.92820	0.359694
$372$	−0.928203	−0.0481251
$373$	−10.9282	−0.565841	−0.282920	−	0.959143i	$-0.591303\pi$
$373$	−10.9282	−0.565841	−0.282920	+	0.959143i	$0.591303\pi$
$374$	18.9282	0.978754
$375$	4.60770	0.237940
$376$	4.92820	0.254153
$377$	0	0
$378$	−5.19615	−0.267261
$379$	−1.07180	−0.0550545	−0.0275273	−	0.999621i	$-0.508763\pi$
$379$	−1.07180	−0.0550545	−0.0275273	+	0.999621i	$0.508763\pi$
$380$	0.928203	0.0476158
$381$	−19.7321	−1.01090
$382$	−8.00000	−0.409316
$383$	29.3205	1.49821	0.749104	−	0.662452i	$-0.230484\pi$
$383$	29.3205	1.49821	0.749104	+	0.662452i	$0.230484\pi$
$384$	−1.73205	−0.0883883
$385$	1.46410	0.0746175
$386$	11.0000	0.559885
$387$	0	0
$388$	−3.07180	−0.155947
$389$	12.9282	0.655486	0.327743	−	0.944767i	$-0.393712\pi$
$389$	12.9282	0.655486	0.327743	+	0.944767i	$0.393712\pi$
$390$	0	0
$391$	−29.3205	−1.48280
$392$	1.00000	0.0505076
$393$	15.9282	0.803472
$394$	−20.7846	−1.04711
$395$	0.287187	0.0144500
$396$	0	0
$397$	26.1244	1.31114	0.655572	−	0.755133i	$-0.272428\pi$
$397$	26.1244	1.31114	0.655572	+	0.755133i	$0.272428\pi$
$398$	11.4641	0.574643
$399$	6.00000	0.300376
$400$	−4.92820	−0.246410
$401$	7.85641	0.392330	0.196165	−	0.980571i	$-0.437151\pi$
$401$	7.85641	0.392330	0.196165	+	0.980571i	$0.437151\pi$
$402$	−8.53590	−0.425732
$403$	0	0
$404$	16.0000	0.796030
$405$	−2.41154	−0.119831
$406$	−8.92820	−0.443099
$407$	13.8564	0.686837
$408$	6.00000	0.297044
$409$	15.0718	0.745252	0.372626	−	0.927982i	$-0.378457\pi$
$409$	15.0718	0.745252	0.372626	+	0.927982i	$0.378457\pi$
$410$	2.53590	0.125239
$411$	−5.19615	−0.256307
$412$	16.9282	0.833993
$413$	−2.80385	−0.137968
$414$	0	0
$415$	2.78461	0.136691
$416$	0	0
$417$	−33.7128	−1.65092
$418$	−18.9282	−0.925809
$419$	17.3205	0.846162	0.423081	−	0.906092i	$-0.360949\pi$
$419$	17.3205	0.846162	0.423081	+	0.906092i	$0.360949\pi$
$420$	0.464102	0.0226458
$421$	11.8564	0.577846	0.288923	−	0.957352i	$-0.406703\pi$
$421$	11.8564	0.577846	0.288923	+	0.957352i	$0.406703\pi$
$422$	26.9282	1.31084
$423$	0	0
$424$	−6.92820	−0.336463
$425$	17.0718	0.828104
$426$	4.26795	0.206783
$427$	−3.19615	−0.154673
$428$	−14.3923	−0.695678
$429$	0	0
$430$	1.07180	0.0516866
$431$	−6.46410	−0.311365	−0.155682	−	0.987807i	$-0.549758\pi$
$431$	−6.46410	−0.311365	−0.155682	+	0.987807i	$0.549758\pi$
$432$	5.19615	0.250000
$433$	−8.00000	−0.384455	−0.192228	−	0.981350i	$-0.561571\pi$
$433$	−8.00000	−0.384455	−0.192228	+	0.981350i	$0.561571\pi$
$434$	−0.535898	−0.0257239
$435$	−4.14359	−0.198670
$436$	−17.4641	−0.836379
$437$	29.3205	1.40259
$438$	0.928203	0.0443513
$439$	15.8564	0.756785	0.378392	−	0.925645i	$-0.376477\pi$
$439$	15.8564	0.756785	0.378392	+	0.925645i	$0.376477\pi$
$440$	−1.46410	−0.0697983
$441$	0	0
$442$	0	0
$443$	3.46410	0.164584	0.0822922	−	0.996608i	$-0.473776\pi$
$443$	3.46410	0.164584	0.0822922	+	0.996608i	$0.473776\pi$
$444$	4.39230	0.208450
$445$	−2.28719	−0.108423
$446$	−23.3205	−1.10426
$447$	7.60770	0.359832
$448$	−1.00000	−0.0472456
$449$	−17.9282	−0.846084	−0.423042	−	0.906110i	$-0.639038\pi$
$449$	−17.9282	−0.846084	−0.423042	+	0.906110i	$0.639038\pi$
$450$	0	0
$451$	−51.7128	−2.43506
$452$	2.00000	0.0940721
$453$	−12.8038	−0.601577
$454$	25.7321	1.20766
$455$	0	0
$456$	−6.00000	−0.280976
$457$	−29.0000	−1.35656	−0.678281	−	0.734802i	$-0.737275\pi$
$457$	−29.0000	−1.35656	−0.678281	+	0.734802i	$0.737275\pi$
$458$	−12.0000	−0.560723
$459$	−18.0000	−0.840168
$460$	2.26795	0.105744
$461$	16.2679	0.757674	0.378837	−	0.925463i	$-0.376324\pi$
$461$	16.2679	0.757674	0.378837	+	0.925463i	$0.376324\pi$
$462$	−9.46410	−0.440310
$463$	−0.607695	−0.0282420	−0.0141210	−	0.999900i	$-0.504495\pi$
$463$	−0.607695	−0.0282420	−0.0141210	+	0.999900i	$0.504495\pi$
$464$	8.92820	0.414481
$465$	−0.248711	−0.0115337
$466$	26.8564	1.24410
$467$	−35.0526	−1.62204	−0.811019	−	0.585019i	$-0.801087\pi$
$467$	−35.0526	−1.62204	−0.811019	+	0.585019i	$0.801087\pi$
$468$	0	0
$469$	−4.92820	−0.227563
$470$	1.32051	0.0609105
$471$	−17.0718	−0.786627
$472$	2.80385	0.129058
$473$	−21.8564	−1.00496
$474$	−1.85641	−0.0852676
$475$	−17.0718	−0.783308
$476$	3.46410	0.158777
$477$	0	0
$478$	−14.3205	−0.655005
$479$	−31.1769	−1.42451	−0.712255	−	0.701921i	$-0.752326\pi$
$479$	−31.1769	−1.42451	−0.712255	+	0.701921i	$0.752326\pi$
$480$	−0.464102	−0.0211832
$481$	0	0
$482$	−12.0000	−0.546585
$483$	14.6603	0.667065
$484$	18.8564	0.857109
$485$	−0.823085	−0.0373744
$486$	0	0
$487$	3.39230	0.153720	0.0768600	−	0.997042i	$-0.475511\pi$
$487$	3.39230	0.153720	0.0768600	+	0.997042i	$0.475511\pi$
$488$	3.19615	0.144683
$489$	−0.679492	−0.0307277
$490$	0.267949	0.0121047
$491$	−33.8564	−1.52792	−0.763959	−	0.645265i	$-0.776747\pi$
$491$	−33.8564	−1.52792	−0.763959	+	0.645265i	$0.776747\pi$
$492$	−16.3923	−0.739022
$493$	−30.9282	−1.39294
$494$	0	0
$495$	0	0
$496$	0.535898	0.0240625
$497$	2.46410	0.110530
$498$	−18.0000	−0.806599
$499$	38.3923	1.71868	0.859338	−	0.511408i	$-0.170876\pi$
$499$	38.3923	1.71868	0.859338	+	0.511408i	$0.170876\pi$
$500$	−2.66025	−0.118970
$501$	−7.60770	−0.339887
$502$	24.1244	1.07672
$503$	−7.07180	−0.315316	−0.157658	−	0.987494i	$-0.550394\pi$
$503$	−7.07180	−0.315316	−0.157658	+	0.987494i	$0.550394\pi$
$504$	0	0
$505$	4.28719	0.190777
$506$	−46.2487	−2.05601
$507$	0	0
$508$	11.3923	0.505452
$509$	1.33975	0.0593832	0.0296916	−	0.999559i	$-0.490547\pi$
$509$	1.33975	0.0593832	0.0296916	+	0.999559i	$0.490547\pi$
$510$	1.60770	0.0711899
$511$	0.535898	0.0237067
$512$	1.00000	0.0441942
$513$	18.0000	0.794719
$514$	−7.85641	−0.346531
$515$	4.53590	0.199876
$516$	−6.92820	−0.304997
$517$	−26.9282	−1.18430
$518$	2.53590	0.111421
$519$	26.3205	1.15534
$520$	0	0
$521$	33.4641	1.46609	0.733044	−	0.680181i	$-0.238099\pi$
$521$	33.4641	1.46609	0.733044	+	0.680181i	$0.238099\pi$
$522$	0	0
$523$	6.80385	0.297511	0.148756	−	0.988874i	$-0.452473\pi$
$523$	6.80385	0.297511	0.148756	+	0.988874i	$0.452473\pi$
$524$	−9.19615	−0.401736
$525$	−8.53590	−0.372537
$526$	5.53590	0.241377
$527$	−1.85641	−0.0808663
$528$	9.46410	0.411872
$529$	48.6410	2.11483
$530$	−1.85641	−0.0806371
$531$	0	0
$532$	−3.46410	−0.150188
$533$	0	0
$534$	14.7846	0.639793
$535$	−3.85641	−0.166727
$536$	4.92820	0.212866
$537$	6.00000	0.258919
$538$	13.0526	0.562736
$539$	−5.46410	−0.235356
$540$	1.39230	0.0599153
$541$	9.60770	0.413067	0.206534	−	0.978440i	$-0.433782\pi$
$541$	9.60770	0.413067	0.206534	+	0.978440i	$0.433782\pi$
$542$	−22.7846	−0.978683
$543$	−43.3923	−1.86214
$544$	−3.46410	−0.148522
$545$	−4.67949	−0.200447
$546$	0	0
$547$	−3.60770	−0.154254	−0.0771270	−	0.997021i	$-0.524575\pi$
$547$	−3.60770	−0.154254	−0.0771270	+	0.997021i	$0.524575\pi$
$548$	3.00000	0.128154
$549$	0	0
$550$	26.9282	1.14822
$551$	30.9282	1.31759
$552$	−14.6603	−0.623982
$553$	−1.07180	−0.0455774
$554$	−8.53590	−0.362656
$555$	1.17691	0.0499572
$556$	19.4641	0.825462
$557$	−5.07180	−0.214899	−0.107449	−	0.994211i	$-0.534268\pi$
$557$	−5.07180	−0.214899	−0.107449	+	0.994211i	$0.534268\pi$
$558$	0	0
$559$	0	0
$560$	−0.267949	−0.0113229
$561$	−32.7846	−1.38417
$562$	−14.0000	−0.590554
$563$	−14.3923	−0.606563	−0.303282	−	0.952901i	$-0.598082\pi$
$563$	−14.3923	−0.606563	−0.303282	+	0.952901i	$0.598082\pi$
$564$	−8.53590	−0.359426
$565$	0.535898	0.0225454
$566$	12.6603	0.532150
$567$	9.00000	0.377964
$568$	−2.46410	−0.103391
$569$	26.8564	1.12588	0.562940	−	0.826498i	$-0.309670\pi$
$569$	26.8564	1.12588	0.562940	+	0.826498i	$0.309670\pi$
$570$	−1.60770	−0.0673389
$571$	0	0		−	1.00000i	$-0.5\pi$
$571$	0	0			1.00000i	$0.5\pi$
$572$	0	0
$573$	13.8564	0.578860
$574$	−9.46410	−0.395024
$575$	−41.7128	−1.73954
$576$	0	0
$577$	30.9282	1.28756	0.643779	−	0.765211i	$-0.277366\pi$
$577$	30.9282	1.28756	0.643779	+	0.765211i	$0.277366\pi$
$578$	−5.00000	−0.207973
$579$	−19.0526	−0.791797
$580$	2.39230	0.0993351
$581$	−10.3923	−0.431145
$582$	5.32051	0.220542
$583$	37.8564	1.56785
$584$	−0.535898	−0.0221756
$585$	0	0
$586$	−21.8564	−0.902880
$587$	−5.73205	−0.236587	−0.118294	−	0.992979i	$-0.537742\pi$
$587$	−5.73205	−0.236587	−0.118294	+	0.992979i	$0.537742\pi$
$588$	−1.73205	−0.0714286
$589$	1.85641	0.0764919
$590$	0.751289	0.0309301
$591$	36.0000	1.48084
$592$	−2.53590	−0.104225
$593$	−32.3923	−1.33019	−0.665096	−	0.746758i	$-0.731610\pi$
$593$	−32.3923	−1.33019	−0.665096	+	0.746758i	$0.731610\pi$
$594$	−28.3923	−1.16495
$595$	0.928203	0.0380526
$596$	−4.39230	−0.179916
$597$	−19.8564	−0.812669
$598$	0	0
$599$	5.39230	0.220324	0.110162	−	0.993914i	$-0.464863\pi$
$599$	5.39230	0.220324	0.110162	+	0.993914i	$0.464863\pi$
$600$	8.53590	0.348477
$601$	−46.7846	−1.90838	−0.954192	−	0.299195i	$-0.903282\pi$
$601$	−46.7846	−1.90838	−0.954192	+	0.299195i	$0.903282\pi$
$602$	−4.00000	−0.163028
$603$	0	0
$604$	7.39230	0.300789
$605$	5.05256	0.205416
$606$	−27.7128	−1.12576
$607$	10.3923	0.421811	0.210905	−	0.977506i	$-0.432359\pi$
$607$	10.3923	0.421811	0.210905	+	0.977506i	$0.432359\pi$
$608$	3.46410	0.140488
$609$	15.4641	0.626637
$610$	0.856406	0.0346749
$611$	0	0
$612$	0	0
$613$	−24.5359	−0.990996	−0.495498	−	0.868609i	$-0.665014\pi$
$613$	−24.5359	−0.990996	−0.495498	+	0.868609i	$0.665014\pi$
$614$	2.80385	0.113154
$615$	−4.39230	−0.177115
$616$	5.46410	0.220155
$617$	−23.9282	−0.963313	−0.481657	−	0.876360i	$-0.659965\pi$
$617$	−23.9282	−0.963313	−0.481657	+	0.876360i	$0.659965\pi$
$618$	−29.3205	−1.17944
$619$	19.5885	0.787327	0.393663	−	0.919255i	$-0.371208\pi$
$619$	19.5885	0.787327	0.393663	+	0.919255i	$0.371208\pi$
$620$	0.143594	0.00576686
$621$	43.9808	1.76489
$622$	−19.8564	−0.796169
$623$	8.53590	0.341984
$624$	0	0
$625$	23.9282	0.957128
$626$	13.0718	0.522454
$627$	32.7846	1.30929
$628$	9.85641	0.393313
$629$	8.78461	0.350265
$630$	0	0
$631$	−35.2487	−1.40323	−0.701615	−	0.712557i	$-0.747537\pi$
$631$	−35.2487	−1.40323	−0.701615	+	0.712557i	$0.747537\pi$
$632$	1.07180	0.0426338
$633$	−46.6410	−1.85381
$634$	−5.07180	−0.201427
$635$	3.05256	0.121137
$636$	12.0000	0.475831
$637$	0	0
$638$	−48.7846	−1.93140
$639$	0	0
$640$	0.267949	0.0105916
$641$	−7.78461	−0.307474	−0.153737	−	0.988112i	$-0.549131\pi$
$641$	−7.78461	−0.307474	−0.153737	+	0.988112i	$0.549131\pi$
$642$	24.9282	0.983838
$643$	−26.5167	−1.04572	−0.522858	−	0.852420i	$-0.675134\pi$
$643$	−26.5167	−1.04572	−0.522858	+	0.852420i	$0.675134\pi$
$644$	−8.46410	−0.333532
$645$	−1.85641	−0.0730959
$646$	−12.0000	−0.472134
$647$	10.9282	0.429632	0.214816	−	0.976655i	$-0.431085\pi$
$647$	10.9282	0.429632	0.214816	+	0.976655i	$0.431085\pi$
$648$	−9.00000	−0.353553
$649$	−15.3205	−0.601383
$650$	0	0
$651$	0.928203	0.0363792
$652$	0.392305	0.0153638
$653$	−12.2487	−0.479329	−0.239665	−	0.970856i	$-0.577037\pi$
$653$	−12.2487	−0.479329	−0.239665	+	0.970856i	$0.577037\pi$
$654$	30.2487	1.18282
$655$	−2.46410	−0.0962804
$656$	9.46410	0.369511
$657$	0	0
$658$	−4.92820	−0.192121
$659$	21.7128	0.845811	0.422906	−	0.906174i	$-0.361010\pi$
$659$	21.7128	0.845811	0.422906	+	0.906174i	$0.361010\pi$
$660$	2.53590	0.0987097
$661$	31.4449	1.22306	0.611532	−	0.791220i	$-0.290554\pi$
$661$	31.4449	1.22306	0.611532	+	0.791220i	$0.290554\pi$
$662$	15.8564	0.616277
$663$	0	0
$664$	10.3923	0.403300
$665$	−0.928203	−0.0359942
$666$	0	0
$667$	75.5692	2.92605
$668$	4.39230	0.169943
$669$	40.3923	1.56166
$670$	1.32051	0.0510157
$671$	−17.4641	−0.674194
$672$	1.73205	0.0668153
$673$	44.6410	1.72078	0.860392	−	0.509632i	$-0.170219\pi$
$673$	44.6410	1.72078	0.860392	+	0.509632i	$0.170219\pi$
$674$	−11.8564	−0.456692
$675$	−25.6077	−0.985641
$676$	0	0
$677$	−2.66025	−0.102242	−0.0511209	−	0.998692i	$-0.516279\pi$
$677$	−2.66025	−0.102242	−0.0511209	+	0.998692i	$0.516279\pi$
$678$	−3.46410	−0.133038
$679$	3.07180	0.117885
$680$	−0.928203	−0.0355950
$681$	−44.5692	−1.70790
$682$	−2.92820	−0.112127
$683$	29.1769	1.11642	0.558212	−	0.829698i	$-0.311488\pi$
$683$	29.1769	1.11642	0.558212	+	0.829698i	$0.311488\pi$
$684$	0	0
$685$	0.803848	0.0307134
$686$	−1.00000	−0.0381802
$687$	20.7846	0.792982
$688$	4.00000	0.152499
$689$	0	0
$690$	−3.92820	−0.149544
$691$	−15.0526	−0.572626	−0.286313	−	0.958136i	$-0.592430\pi$
$691$	−15.0526	−0.572626	−0.286313	+	0.958136i	$0.592430\pi$
$692$	−15.1962	−0.577671
$693$	0	0
$694$	−18.2487	−0.692712
$695$	5.21539	0.197831
$696$	−15.4641	−0.586165
$697$	−32.7846	−1.24181
$698$	23.7321	0.898271
$699$	−46.5167	−1.75942
$700$	4.92820	0.186269
$701$	2.53590	0.0957796	0.0478898	−	0.998853i	$-0.484750\pi$
$701$	2.53590	0.0957796	0.0478898	+	0.998853i	$0.484750\pi$
$702$	0	0
$703$	−8.78461	−0.331318
$704$	−5.46410	−0.205936
$705$	−2.28719	−0.0861404
$706$	0.535898	0.0201688
$707$	−16.0000	−0.601742
$708$	−4.85641	−0.182515
$709$	40.5359	1.52236	0.761179	−	0.648542i	$-0.224621\pi$
$709$	40.5359	1.52236	0.761179	+	0.648542i	$0.224621\pi$
$710$	−0.660254	−0.0247789
$711$	0	0
$712$	−8.53590	−0.319896
$713$	4.53590	0.169871
$714$	−6.00000	−0.224544
$715$	0	0
$716$	−3.46410	−0.129460
$717$	24.8038	0.926317
$718$	−11.5359	−0.430516
$719$	5.46410	0.203777	0.101888	−	0.994796i	$-0.467512\pi$
$719$	5.46410	0.203777	0.101888	+	0.994796i	$0.467512\pi$
$720$	0	0
$721$	−16.9282	−0.630439
$722$	−7.00000	−0.260513
$723$	20.7846	0.772988
$724$	25.0526	0.931071
$725$	−44.0000	−1.63412
$726$	−32.6603	−1.21214
$727$	−19.3205	−0.716558	−0.358279	−	0.933615i	$-0.616636\pi$
$727$	−19.3205	−0.716558	−0.358279	+	0.933615i	$0.616636\pi$
$728$	0	0
$729$	27.0000	1.00000
$730$	−0.143594	−0.00531464
$731$	−13.8564	−0.512498
$732$	−5.53590	−0.204613
$733$	−25.8372	−0.954318	−0.477159	−	0.878817i	$-0.658333\pi$
$733$	−25.8372	−0.954318	−0.477159	+	0.878817i	$0.658333\pi$
$734$	−16.9282	−0.624831
$735$	−0.464102	−0.0171186
$736$	8.46410	0.311991
$737$	−26.9282	−0.991913
$738$	0	0
$739$	47.3205	1.74071	0.870357	−	0.492422i	$-0.163888\pi$
$739$	47.3205	1.74071	0.870357	+	0.492422i	$0.163888\pi$
$740$	−0.679492	−0.0249786
$741$	0	0
$742$	6.92820	0.254342
$743$	40.0000	1.46746	0.733729	−	0.679442i	$-0.237778\pi$
$743$	40.0000	1.46746	0.733729	+	0.679442i	$0.237778\pi$
$744$	−0.928203	−0.0340296
$745$	−1.17691	−0.0431188
$746$	−10.9282	−0.400110
$747$	0	0
$748$	18.9282	0.692084
$749$	14.3923	0.525883
$750$	4.60770	0.168249
$751$	35.5359	1.29672	0.648362	−	0.761332i	$-0.275454\pi$
$751$	35.5359	1.29672	0.648362	+	0.761332i	$0.275454\pi$
$752$	4.92820	0.179713
$753$	−41.7846	−1.52272
$754$	0	0
$755$	1.98076	0.0720873
$756$	−5.19615	−0.188982
$757$	26.5359	0.964464	0.482232	−	0.876044i	$-0.339826\pi$
$757$	26.5359	0.964464	0.482232	+	0.876044i	$0.339826\pi$
$758$	−1.07180	−0.0389294
$759$	80.1051	2.90763
$760$	0.928203	0.0336695
$761$	−37.8564	−1.37229	−0.686147	−	0.727463i	$-0.740699\pi$
$761$	−37.8564	−1.37229	−0.686147	+	0.727463i	$0.740699\pi$
$762$	−19.7321	−0.714817
$763$	17.4641	0.632243
$764$	−8.00000	−0.289430
$765$	0	0
$766$	29.3205	1.05939
$767$	0	0
$768$	−1.73205	−0.0625000
$769$	5.32051	0.191862	0.0959312	−	0.995388i	$-0.469417\pi$
$769$	5.32051	0.191862	0.0959312	+	0.995388i	$0.469417\pi$
$770$	1.46410	0.0527626
$771$	13.6077	0.490069
$772$	11.0000	0.395899
$773$	50.9282	1.83176	0.915880	−	0.401452i	$-0.131494\pi$
$773$	50.9282	1.83176	0.915880	+	0.401452i	$0.131494\pi$
$774$	0	0
$775$	−2.64102	−0.0948681
$776$	−3.07180	−0.110271
$777$	−4.39230	−0.157573
$778$	12.9282	0.463499
$779$	32.7846	1.17463
$780$	0	0
$781$	13.4641	0.481783
$782$	−29.3205	−1.04850
$783$	46.3923	1.65793
$784$	1.00000	0.0357143
$785$	2.64102	0.0942619
$786$	15.9282	0.568140
$787$	26.8038	0.955454	0.477727	−	0.878508i	$-0.341461\pi$
$787$	26.8038	0.955454	0.477727	+	0.878508i	$0.341461\pi$
$788$	−20.7846	−0.740421
$789$	−9.58846	−0.341358
$790$	0.287187	0.0102177
$791$	−2.00000	−0.0711118
$792$	0	0
$793$	0	0
$794$	26.1244	0.927119
$795$	3.21539	0.114038
$796$	11.4641	0.406334
$797$	−28.2679	−1.00130	−0.500651	−	0.865649i	$-0.666906\pi$
$797$	−28.2679	−1.00130	−0.500651	+	0.865649i	$0.666906\pi$
$798$	6.00000	0.212398
$799$	−17.0718	−0.603957
$800$	−4.92820	−0.174238
$801$	0	0
$802$	7.85641	0.277419
$803$	2.92820	0.103334
$804$	−8.53590	−0.301038
$805$	−2.26795	−0.0799347
$806$	0	0
$807$	−22.6077	−0.795829
$808$	16.0000	0.562878
$809$	−9.71281	−0.341484	−0.170742	−	0.985316i	$-0.554617\pi$
$809$	−9.71281	−0.341484	−0.170742	+	0.985316i	$0.554617\pi$
$810$	−2.41154	−0.0847330
$811$	26.8038	0.941210	0.470605	−	0.882344i	$-0.344036\pi$
$811$	26.8038	0.941210	0.470605	+	0.882344i	$0.344036\pi$
$812$	−8.92820	−0.313319
$813$	39.4641	1.38407
$814$	13.8564	0.485667
$815$	0.105118	0.00368211
$816$	6.00000	0.210042
$817$	13.8564	0.484774
$818$	15.0718	0.526973
$819$	0	0
$820$	2.53590	0.0885574
$821$	14.2487	0.497283	0.248642	−	0.968596i	$-0.420016\pi$
$821$	14.2487	0.497283	0.248642	+	0.968596i	$0.420016\pi$
$822$	−5.19615	−0.181237
$823$	9.67949	0.337406	0.168703	−	0.985667i	$-0.446042\pi$
$823$	9.67949	0.337406	0.168703	+	0.985667i	$0.446042\pi$
$824$	16.9282	0.589722
$825$	−46.6410	−1.62383
$826$	−2.80385	−0.0975583
$827$	47.3205	1.64550	0.822748	−	0.568407i	$-0.192440\pi$
$827$	47.3205	1.64550	0.822748	+	0.568407i	$0.192440\pi$
$828$	0	0
$829$	20.2679	0.703935	0.351967	−	0.936012i	$-0.385513\pi$
$829$	20.2679	0.703935	0.351967	+	0.936012i	$0.385513\pi$
$830$	2.78461	0.0966552
$831$	14.7846	0.512872
$832$	0	0
$833$	−3.46410	−0.120024
$834$	−33.7128	−1.16738
$835$	1.17691	0.0407288
$836$	−18.9282	−0.654646
$837$	2.78461	0.0962502
$838$	17.3205	0.598327
$839$	−40.9282	−1.41300	−0.706499	−	0.707714i	$-0.749727\pi$
$839$	−40.9282	−1.41300	−0.706499	+	0.707714i	$0.749727\pi$
$840$	0.464102	0.0160130
$841$	50.7128	1.74872
$842$	11.8564	0.408599
$843$	24.2487	0.835170
$844$	26.9282	0.926907
$845$	0	0
$846$	0	0
$847$	−18.8564	−0.647914
$848$	−6.92820	−0.237915
$849$	−21.9282	−0.752574
$850$	17.0718	0.585558
$851$	−21.4641	−0.735780
$852$	4.26795	0.146218
$853$	−45.0526	−1.54257	−0.771285	−	0.636490i	$-0.780386\pi$
$853$	−45.0526	−1.54257	−0.771285	+	0.636490i	$0.780386\pi$
$854$	−3.19615	−0.109370
$855$	0	0
$856$	−14.3923	−0.491919
$857$	37.7128	1.28825	0.644123	−	0.764922i	$-0.277223\pi$
$857$	37.7128	1.28825	0.644123	+	0.764922i	$0.277223\pi$
$858$	0	0
$859$	46.1051	1.57309	0.786543	−	0.617535i	$-0.211869\pi$
$859$	46.1051	1.57309	0.786543	+	0.617535i	$0.211869\pi$
$860$	1.07180	0.0365480
$861$	16.3923	0.558648
$862$	−6.46410	−0.220168
$863$	45.1051	1.53540	0.767698	−	0.640812i	$-0.221402\pi$
$863$	45.1051	1.53540	0.767698	+	0.640812i	$0.221402\pi$
$864$	5.19615	0.176777
$865$	−4.07180	−0.138445
$866$	−8.00000	−0.271851
$867$	8.66025	0.294118
$868$	−0.535898	−0.0181896
$869$	−5.85641	−0.198665
$870$	−4.14359	−0.140481
$871$	0	0
$872$	−17.4641	−0.591409
$873$	0	0
$874$	29.3205	0.991781
$875$	2.66025	0.0899330
$876$	0.928203	0.0313611
$877$	−31.8564	−1.07571	−0.537857	−	0.843036i	$-0.680766\pi$
$877$	−31.8564	−1.07571	−0.537857	+	0.843036i	$0.680766\pi$
$878$	15.8564	0.535128
$879$	37.8564	1.27686
$880$	−1.46410	−0.0493549
$881$	−20.5359	−0.691872	−0.345936	−	0.938258i	$-0.612439\pi$
$881$	−20.5359	−0.691872	−0.345936	+	0.938258i	$0.612439\pi$
$882$	0	0
$883$	43.0333	1.44819	0.724093	−	0.689702i	$-0.242258\pi$
$883$	43.0333	1.44819	0.724093	+	0.689702i	$0.242258\pi$
$884$	0	0
$885$	−1.30127	−0.0437417
$886$	3.46410	0.116379
$887$	13.4641	0.452080	0.226040	−	0.974118i	$-0.427422\pi$
$887$	13.4641	0.452080	0.226040	+	0.974118i	$0.427422\pi$
$888$	4.39230	0.147396
$889$	−11.3923	−0.382086
$890$	−2.28719	−0.0766667
$891$	49.1769	1.64749
$892$	−23.3205	−0.780828
$893$	17.0718	0.571286
$894$	7.60770	0.254439
$895$	−0.928203	−0.0310264
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−17.9282	−0.598272
$899$	4.78461	0.159576
$900$	0	0
$901$	24.0000	0.799556
$902$	−51.7128	−1.72185
$903$	6.92820	0.230556
$904$	2.00000	0.0665190
$905$	6.71281	0.223141
$906$	−12.8038	−0.425379
$907$	−16.1436	−0.536039	−0.268020	−	0.963413i	$-0.586369\pi$
$907$	−16.1436	−0.536039	−0.268020	+	0.963413i	$0.586369\pi$
$908$	25.7321	0.853948
$909$	0	0
$910$	0	0
$911$	−28.1769	−0.933543	−0.466771	−	0.884378i	$-0.654583\pi$
$911$	−28.1769	−0.933543	−0.466771	+	0.884378i	$0.654583\pi$
$912$	−6.00000	−0.198680
$913$	−56.7846	−1.87930
$914$	−29.0000	−0.959235
$915$	−1.48334	−0.0490377
$916$	−12.0000	−0.396491
$917$	9.19615	0.303684
$918$	−18.0000	−0.594089
$919$	2.32051	0.0765465	0.0382732	−	0.999267i	$-0.487814\pi$
$919$	2.32051	0.0765465	0.0382732	+	0.999267i	$0.487814\pi$
$920$	2.26795	0.0747721
$921$	−4.85641	−0.160024
$922$	16.2679	0.535756
$923$	0	0
$924$	−9.46410	−0.311346
$925$	12.4974	0.410913
$926$	−0.607695	−0.0199701
$927$	0	0
$928$	8.92820	0.293083
$929$	29.3205	0.961975	0.480987	−	0.876728i	$-0.340278\pi$
$929$	29.3205	0.961975	0.480987	+	0.876728i	$0.340278\pi$
$930$	−0.248711	−0.00815557
$931$	3.46410	0.113531
$932$	26.8564	0.879711
$933$	34.3923	1.12595
$934$	−35.0526	−1.14695
$935$	5.07180	0.165865
$936$	0	0
$937$	−18.9282	−0.618357	−0.309179	−	0.951004i	$-0.600054\pi$
$937$	−18.9282	−0.618357	−0.309179	+	0.951004i	$0.600054\pi$
$938$	−4.92820	−0.160912
$939$	−22.6410	−0.738862
$940$	1.32051	0.0430702
$941$	−18.9474	−0.617669	−0.308834	−	0.951116i	$-0.599939\pi$
$941$	−18.9474	−0.617669	−0.308834	+	0.951116i	$0.599939\pi$
$942$	−17.0718	−0.556229
$943$	80.1051	2.60858
$944$	2.80385	0.0912575
$945$	−1.39230	−0.0452917
$946$	−21.8564	−0.710613
$947$	−12.9282	−0.420110	−0.210055	−	0.977690i	$-0.567364\pi$
$947$	−12.9282	−0.420110	−0.210055	+	0.977690i	$0.567364\pi$
$948$	−1.85641	−0.0602933
$949$	0	0
$950$	−17.0718	−0.553882
$951$	8.78461	0.284860
$952$	3.46410	0.112272
$953$	−25.9282	−0.839897	−0.419948	−	0.907548i	$-0.637952\pi$
$953$	−25.9282	−0.839897	−0.419948	+	0.907548i	$0.637952\pi$
$954$	0	0
$955$	−2.14359	−0.0693651
$956$	−14.3205	−0.463158
$957$	84.4974	2.73141
$958$	−31.1769	−1.00728
$959$	−3.00000	−0.0968751
$960$	−0.464102	−0.0149788
$961$	−30.7128	−0.990736
$962$	0	0
$963$	0	0
$964$	−12.0000	−0.386494
$965$	2.94744	0.0948815
$966$	14.6603	0.471686
$967$	−48.7846	−1.56881	−0.784404	−	0.620251i	$-0.787031\pi$
$967$	−48.7846	−1.56881	−0.784404	+	0.620251i	$0.787031\pi$
$968$	18.8564	0.606068
$969$	20.7846	0.667698
$970$	−0.823085	−0.0264277
$971$	−37.9808	−1.21886	−0.609430	−	0.792840i	$-0.708602\pi$
$971$	−37.9808	−1.21886	−0.609430	+	0.792840i	$0.708602\pi$
$972$	0	0
$973$	−19.4641	−0.623990
$974$	3.39230	0.108696
$975$	0	0
$976$	3.19615	0.102306
$977$	23.7846	0.760937	0.380469	−	0.924794i	$-0.375763\pi$
$977$	23.7846	0.760937	0.380469	+	0.924794i	$0.375763\pi$
$978$	−0.679492	−0.0217278
$979$	46.6410	1.49065
$980$	0.267949	0.00855932
$981$	0	0
$982$	−33.8564	−1.08040
$983$	−39.5692	−1.26206	−0.631031	−	0.775758i	$-0.717368\pi$
$983$	−39.5692	−1.26206	−0.631031	+	0.775758i	$0.717368\pi$
$984$	−16.3923	−0.522568
$985$	−5.56922	−0.177450
$986$	−30.9282	−0.984955
$987$	8.53590	0.271701
$988$	0	0
$989$	33.8564	1.07657
$990$	0	0
$991$	−10.1769	−0.323280	−0.161640	−	0.986850i	$-0.551678\pi$
$991$	−10.1769	−0.323280	−0.161640	+	0.986850i	$0.551678\pi$
$992$	0.535898	0.0170148
$993$	−27.4641	−0.871547
$994$	2.46410	0.0781566
$995$	3.07180	0.0973825
$996$	−18.0000	−0.570352
$997$	33.0526	1.04679	0.523393	−	0.852092i	$-0.324666\pi$
$997$	33.0526	1.04679	0.523393	+	0.852092i	$0.324666\pi$
$998$	38.3923	1.21529
$999$	−13.1769	−0.416899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.t.1.1		2
13.3	even	3		182.2.g.e.113.2	yes	4
13.5	odd	4		2366.2.d.l.337.1		4
13.8	odd	4		2366.2.d.l.337.3		4
13.9	even	3		182.2.g.e.29.2	✓	4
13.12	even	2		2366.2.a.r.1.1		2
39.29	odd	6		1638.2.r.v.1387.2		4
39.35	odd	6		1638.2.r.v.757.2		4
52.3	odd	6		1456.2.s.l.113.1		4
52.35	odd	6		1456.2.s.l.1121.1		4
91.3	odd	6		1274.2.h.p.373.2		4
91.9	even	3		1274.2.h.o.263.1		4
91.16	even	3		1274.2.e.o.165.2		4
91.48	odd	6		1274.2.g.l.393.1		4
91.55	odd	6		1274.2.g.l.295.1		4
91.61	odd	6		1274.2.h.p.263.2		4
91.68	odd	6		1274.2.e.p.165.1		4
91.74	even	3		1274.2.e.o.471.2		4
91.81	even	3		1274.2.h.o.373.1		4
91.87	odd	6		1274.2.e.p.471.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.g.e.29.2	✓	4	13.9	even	3
182.2.g.e.113.2	yes	4	13.3	even	3
1274.2.e.o.165.2		4	91.16	even	3
1274.2.e.o.471.2		4	91.74	even	3
1274.2.e.p.165.1		4	91.68	odd	6
1274.2.e.p.471.1		4	91.87	odd	6
1274.2.g.l.295.1		4	91.55	odd	6
1274.2.g.l.393.1		4	91.48	odd	6
1274.2.h.o.263.1		4	91.9	even	3
1274.2.h.o.373.1		4	91.81	even	3
1274.2.h.p.263.2		4	91.61	odd	6
1274.2.h.p.373.2		4	91.3	odd	6
1456.2.s.l.113.1		4	52.3	odd	6
1456.2.s.l.1121.1		4	52.35	odd	6
1638.2.r.v.757.2		4	39.35	odd	6
1638.2.r.v.1387.2		4	39.29	odd	6
2366.2.a.r.1.1		2	13.12	even	2
2366.2.a.t.1.1		2	1.1	even	1	trivial
2366.2.d.l.337.1		4	13.5	odd	4
2366.2.d.l.337.3		4	13.8	odd	4

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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.73205 q^{3} +1.00000 q^{4} +0.267949 q^{5} -1.73205 q^{6} -1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} -1.73205 q^{3} +1.00000 q^{4} +0.267949 q^{5} -1.73205 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.267949 q^{10} -5.46410 q^{11} -1.73205 q^{12} -1.00000 q^{14} -0.464102 q^{15} +1.00000 q^{16} -3.46410 q^{17} +3.46410 q^{19} +0.267949 q^{20} +1.73205 q^{21} -5.46410 q^{22} +8.46410 q^{23} -1.73205 q^{24} -4.92820 q^{25} +5.19615 q^{27} -1.00000 q^{28} +8.92820 q^{29} -0.464102 q^{30} +0.535898 q^{31} +1.00000 q^{32} +9.46410 q^{33} -3.46410 q^{34} -0.267949 q^{35} -2.53590 q^{37} +3.46410 q^{38} +0.267949 q^{40} +9.46410 q^{41} +1.73205 q^{42} +4.00000 q^{43} -5.46410 q^{44} +8.46410 q^{46} +4.92820 q^{47} -1.73205 q^{48} +1.00000 q^{49} -4.92820 q^{50} +6.00000 q^{51} -6.92820 q^{53} +5.19615 q^{54} -1.46410 q^{55} -1.00000 q^{56} -6.00000 q^{57} +8.92820 q^{58} +2.80385 q^{59} -0.464102 q^{60} +3.19615 q^{61} +0.535898 q^{62} +1.00000 q^{64} +9.46410 q^{66} +4.92820 q^{67} -3.46410 q^{68} -14.6603 q^{69} -0.267949 q^{70} -2.46410 q^{71} -0.535898 q^{73} -2.53590 q^{74} +8.53590 q^{75} +3.46410 q^{76} +5.46410 q^{77} +1.07180 q^{79} +0.267949 q^{80} -9.00000 q^{81} +9.46410 q^{82} +10.3923 q^{83} +1.73205 q^{84} -0.928203 q^{85} +4.00000 q^{86} -15.4641 q^{87} -5.46410 q^{88} -8.53590 q^{89} +8.46410 q^{92} -0.928203 q^{93} +4.92820 q^{94} +0.928203 q^{95} -1.73205 q^{96} -3.07180 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + 4 q^{5} - 2 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + 4 * q^5 - 2 * q^7 + 2 * q^8	\( 2 q + 2 q^{2} + 2 q^{4} + 4 q^{5} - 2 q^{7} + 2 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{14} + 6 q^{15} + 2 q^{16} + 4 q^{20} - 4 q^{22} + 10 q^{23} + 4 q^{25} - 2 q^{28} + 4 q^{29} + 6 q^{30} + 8 q^{31} + 2 q^{32} + 12 q^{33} - 4 q^{35} - 12 q^{37} + 4 q^{40} + 12 q^{41} + 8 q^{43} - 4 q^{44} + 10 q^{46} - 4 q^{47} + 2 q^{49} + 4 q^{50} + 12 q^{51} + 4 q^{55} - 2 q^{56} - 12 q^{57} + 4 q^{58} + 16 q^{59} + 6 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{64} + 12 q^{66} - 4 q^{67} - 12 q^{69} - 4 q^{70} + 2 q^{71} - 8 q^{73} - 12 q^{74} + 24 q^{75} + 4 q^{77} + 16 q^{79} + 4 q^{80} - 18 q^{81} + 12 q^{82} + 12 q^{85} + 8 q^{86} - 24 q^{87} - 4 q^{88} - 24 q^{89} + 10 q^{92} + 12 q^{93} - 4 q^{94} - 12 q^{95} - 20 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + 4 * q^5 - 2 * q^7 + 2 * q^8 + 4 * q^10 - 4 * q^11 - 2 * q^14 + 6 * q^15 + 2 * q^16 + 4 * q^20 - 4 * q^22 + 10 * q^23 + 4 * q^25 - 2 * q^28 + 4 * q^29 + 6 * q^30 + 8 * q^31 + 2 * q^32 + 12 * q^33 - 4 * q^35 - 12 * q^37 + 4 * q^40 + 12 * q^41 + 8 * q^43 - 4 * q^44 + 10 * q^46 - 4 * q^47 + 2 * q^49 + 4 * q^50 + 12 * q^51 + 4 * q^55 - 2 * q^56 - 12 * q^57 + 4 * q^58 + 16 * q^59 + 6 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^64 + 12 * q^66 - 4 * q^67 - 12 * q^69 - 4 * q^70 + 2 * q^71 - 8 * q^73 - 12 * q^74 + 24 * q^75 + 4 * q^77 + 16 * q^79 + 4 * q^80 - 18 * q^81 + 12 * q^82 + 12 * q^85 + 8 * q^86 - 24 * q^87 - 4 * q^88 - 24 * q^89 + 10 * q^92 + 12 * q^93 - 4 * q^94 - 12 * q^95 - 20 * q^97 + 2 * q^98

Introduction

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