LMFDB - Embedded newform 5586.2.a.ce.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 22x^{6} + 60x^{5} + 87x^{4} - 176x^{3} - 40x^{2} + 64x + 16 $ x^8 - 4x^7 - 22x^6 + 60x^5 + 87x^4 - 176x^3 - 40x^2 + 64*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.261561$ of defining polynomial
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.05470 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.05470 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.05470 q^{10} +2.36990 q^{11} -1.00000 q^{12} +4.98073 q^{13} +2.05470 q^{15} +1.00000 q^{16} +0.0143085 q^{17} +1.00000 q^{18} -1.00000 q^{19} -2.05470 q^{20} +2.36990 q^{22} +7.34471 q^{23} -1.00000 q^{24} -0.778190 q^{25} +4.98073 q^{26} -1.00000 q^{27} -8.46435 q^{29} +2.05470 q^{30} -1.54589 q^{31} +1.00000 q^{32} -2.36990 q^{33} +0.0143085 q^{34} +1.00000 q^{36} +9.88059 q^{37} -1.00000 q^{38} -4.98073 q^{39} -2.05470 q^{40} -10.1088 q^{41} +6.92491 q^{43} +2.36990 q^{44} -2.05470 q^{45} +7.34471 q^{46} +5.17125 q^{47} -1.00000 q^{48} -0.778190 q^{50} -0.0143085 q^{51} +4.98073 q^{52} -2.84922 q^{53} -1.00000 q^{54} -4.86945 q^{55} +1.00000 q^{57} -8.46435 q^{58} -8.99984 q^{59} +2.05470 q^{60} -5.36737 q^{61} -1.54589 q^{62} +1.00000 q^{64} -10.2339 q^{65} -2.36990 q^{66} -3.30719 q^{67} +0.0143085 q^{68} -7.34471 q^{69} +10.9665 q^{71} +1.00000 q^{72} -10.6736 q^{73} +9.88059 q^{74} +0.778190 q^{75} -1.00000 q^{76} -4.98073 q^{78} +10.1648 q^{79} -2.05470 q^{80} +1.00000 q^{81} -10.1088 q^{82} +14.7988 q^{83} -0.0293998 q^{85} +6.92491 q^{86} +8.46435 q^{87} +2.36990 q^{88} +8.10893 q^{89} -2.05470 q^{90} +7.34471 q^{92} +1.54589 q^{93} +5.17125 q^{94} +2.05470 q^{95} -1.00000 q^{96} +18.8131 q^{97} +2.36990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 8 q^{3} + 8 q^{4} - 4 q^{5} - 8 q^{6} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 - 4 * q^5 - 8 * q^6 + 8 * q^8 + 8 * q^9	$ 8 q + 8 q^{2} - 8 q^{3} + 8 q^{4} - 4 q^{5} - 8 q^{6} + 8 q^{8} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 8 q^{12} + 4 q^{13} + 4 q^{15} + 8 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 4 q^{20} + 8 q^{22} + 4 q^{23} - 8 q^{24} + 24 q^{25} + 4 q^{26} - 8 q^{27} + 16 q^{29} + 4 q^{30} - 4 q^{31} + 8 q^{32} - 8 q^{33} - 8 q^{34} + 8 q^{36} + 12 q^{37} - 8 q^{38} - 4 q^{39} - 4 q^{40} + 16 q^{43} + 8 q^{44} - 4 q^{45} + 4 q^{46} - 12 q^{47} - 8 q^{48} + 24 q^{50} + 8 q^{51} + 4 q^{52} + 24 q^{53} - 8 q^{54} + 8 q^{55} + 8 q^{57} + 16 q^{58} + 8 q^{59} + 4 q^{60} - 4 q^{62} + 8 q^{64} + 8 q^{65} - 8 q^{66} + 8 q^{67} - 8 q^{68} - 4 q^{69} + 24 q^{71} + 8 q^{72} + 16 q^{73} + 12 q^{74} - 24 q^{75} - 8 q^{76} - 4 q^{78} + 20 q^{79} - 4 q^{80} + 8 q^{81} - 16 q^{83} + 48 q^{85} + 16 q^{86} - 16 q^{87} + 8 q^{88} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 12 q^{94} + 4 q^{95} - 8 q^{96} + 8 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 - 4 * q^5 - 8 * q^6 + 8 * q^8 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 8 * q^12 + 4 * q^13 + 4 * q^15 + 8 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 4 * q^20 + 8 * q^22 + 4 * q^23 - 8 * q^24 + 24 * q^25 + 4 * q^26 - 8 * q^27 + 16 * q^29 + 4 * q^30 - 4 * q^31 + 8 * q^32 - 8 * q^33 - 8 * q^34 + 8 * q^36 + 12 * q^37 - 8 * q^38 - 4 * q^39 - 4 * q^40 + 16 * q^43 + 8 * q^44 - 4 * q^45 + 4 * q^46 - 12 * q^47 - 8 * q^48 + 24 * q^50 + 8 * q^51 + 4 * q^52 + 24 * q^53 - 8 * q^54 + 8 * q^55 + 8 * q^57 + 16 * q^58 + 8 * q^59 + 4 * q^60 - 4 * q^62 + 8 * q^64 + 8 * q^65 - 8 * q^66 + 8 * q^67 - 8 * q^68 - 4 * q^69 + 24 * q^71 + 8 * q^72 + 16 * q^73 + 12 * q^74 - 24 * q^75 - 8 * q^76 - 4 * q^78 + 20 * q^79 - 4 * q^80 + 8 * q^81 - 16 * q^83 + 48 * q^85 + 16 * q^86 - 16 * q^87 + 8 * q^88 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 12 * q^94 + 4 * q^95 - 8 * q^96 + 8 * q^97 + 8 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.05470	−0.918892	−0.459446	−	0.888206i	$-0.651952\pi$
$5$	−2.05470	−0.918892	−0.459446	+	0.888206i	$0.651952\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.05470	−0.649755
$11$	2.36990	0.714553	0.357276	−	0.933999i	$-0.383705\pi$
$11$	2.36990	0.714553	0.357276	+	0.933999i	$0.383705\pi$
$12$	−1.00000	−0.288675
$13$	4.98073	1.38141	0.690703	−	0.723139i	$-0.257301\pi$
$13$	4.98073	1.38141	0.690703	+	0.723139i	$0.257301\pi$
$14$	0	0
$15$	2.05470	0.530522
$16$	1.00000	0.250000
$17$	0.0143085	0.00347033	0.00173516	−	0.999998i	$-0.499448\pi$
$17$	0.0143085	0.00347033	0.00173516	+	0.999998i	$0.499448\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.05470	−0.459446
$21$	0	0
$22$	2.36990	0.505265
$23$	7.34471	1.53148	0.765739	−	0.643152i	$-0.222374\pi$
$23$	7.34471	1.53148	0.765739	+	0.643152i	$0.222374\pi$
$24$	−1.00000	−0.204124
$25$	−0.778190	−0.155638
$26$	4.98073	0.976802
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−8.46435	−1.57179	−0.785895	−	0.618360i	$-0.787797\pi$
$29$	−8.46435	−1.57179	−0.785895	+	0.618360i	$0.787797\pi$
$30$	2.05470	0.375136
$31$	−1.54589	−0.277650	−0.138825	−	0.990317i	$-0.544333\pi$
$31$	−1.54589	−0.277650	−0.138825	+	0.990317i	$0.544333\pi$
$32$	1.00000	0.176777
$33$	−2.36990	−0.412547
$34$	0.0143085	0.00245389
$35$	0	0
$36$	1.00000	0.166667
$37$	9.88059	1.62436	0.812180	−	0.583407i	$-0.198281\pi$
$37$	9.88059	1.62436	0.812180	+	0.583407i	$0.198281\pi$
$38$	−1.00000	−0.162221
$39$	−4.98073	−0.797555
$40$	−2.05470	−0.324877
$41$	−10.1088	−1.57872	−0.789361	−	0.613929i	$-0.789588\pi$
$41$	−10.1088	−1.57872	−0.789361	+	0.613929i	$0.789588\pi$
$42$	0	0
$43$	6.92491	1.05604	0.528019	−	0.849232i	$-0.322935\pi$
$43$	6.92491	1.05604	0.528019	+	0.849232i	$0.322935\pi$
$44$	2.36990	0.357276
$45$	−2.05470	−0.306297
$46$	7.34471	1.08292
$47$	5.17125	0.754305	0.377152	−	0.926151i	$-0.376903\pi$
$47$	5.17125	0.754305	0.377152	+	0.926151i	$0.376903\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−0.778190	−0.110053
$51$	−0.0143085	−0.00200359
$52$	4.98073	0.690703
$53$	−2.84922	−0.391370	−0.195685	−	0.980667i	$-0.562693\pi$
$53$	−2.84922	−0.391370	−0.195685	+	0.980667i	$0.562693\pi$
$54$	−1.00000	−0.136083
$55$	−4.86945	−0.656597
$56$	0	0
$57$	1.00000	0.132453
$58$	−8.46435	−1.11142
$59$	−8.99984	−1.17168	−0.585840	−	0.810427i	$-0.699235\pi$
$59$	−8.99984	−1.17168	−0.585840	+	0.810427i	$0.699235\pi$
$60$	2.05470	0.265261
$61$	−5.36737	−0.687221	−0.343610	−	0.939112i	$-0.611650\pi$
$61$	−5.36737	−0.687221	−0.343610	+	0.939112i	$0.611650\pi$
$62$	−1.54589	−0.196328
$63$	0	0
$64$	1.00000	0.125000
$65$	−10.2339	−1.26936
$66$	−2.36990	−0.291715
$67$	−3.30719	−0.404037	−0.202019	−	0.979382i	$-0.564750\pi$
$67$	−3.30719	−0.404037	−0.202019	+	0.979382i	$0.564750\pi$
$68$	0.0143085	0.00173516
$69$	−7.34471	−0.884199
$70$	0	0
$71$	10.9665	1.30148	0.650739	−	0.759301i	$-0.274459\pi$
$71$	10.9665	1.30148	0.650739	+	0.759301i	$0.274459\pi$
$72$	1.00000	0.117851
$73$	−10.6736	−1.24925	−0.624625	−	0.780925i	$-0.714748\pi$
$73$	−10.6736	−1.24925	−0.624625	+	0.780925i	$0.714748\pi$
$74$	9.88059	1.14860
$75$	0.778190	0.0898577
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−4.98073	−0.563957
$79$	10.1648	1.14362	0.571812	−	0.820385i	$-0.306241\pi$
$79$	10.1648	1.14362	0.571812	+	0.820385i	$0.306241\pi$
$80$	−2.05470	−0.229723
$81$	1.00000	0.111111
$82$	−10.1088	−1.11632
$83$	14.7988	1.62438	0.812191	−	0.583392i	$-0.198275\pi$
$83$	14.7988	1.62438	0.812191	+	0.583392i	$0.198275\pi$
$84$	0	0
$85$	−0.0293998	−0.00318885
$86$	6.92491	0.746732
$87$	8.46435	0.907473
$88$	2.36990	0.252633
$89$	8.10893	0.859545	0.429773	−	0.902937i	$-0.358594\pi$
$89$	8.10893	0.859545	0.429773	+	0.902937i	$0.358594\pi$
$90$	−2.05470	−0.216585
$91$	0	0
$92$	7.34471	0.765739
$93$	1.54589	0.160301
$94$	5.17125	0.533374
$95$	2.05470	0.210808
$96$	−1.00000	−0.102062
$97$	18.8131	1.91018	0.955092	−	0.296309i	$-0.0957559\pi$
$97$	18.8131	1.91018	0.955092	+	0.296309i	$0.0957559\pi$
$98$	0	0
$99$	2.36990	0.238184
$100$	−0.778190	−0.0778190
$101$	−3.57353	−0.355580	−0.177790	−	0.984068i	$-0.556895\pi$
$101$	−3.57353	−0.355580	−0.177790	+	0.984068i	$0.556895\pi$
$102$	−0.0143085	−0.00141675
$103$	−2.23342	−0.220065	−0.110033	−	0.993928i	$-0.535096\pi$
$103$	−2.23342	−0.220065	−0.110033	+	0.993928i	$0.535096\pi$
$104$	4.98073	0.488401
$105$	0	0
$106$	−2.84922	−0.276740
$107$	−15.4022	−1.48899	−0.744493	−	0.667631i	$-0.767309\pi$
$107$	−15.4022	−1.48899	−0.744493	+	0.667631i	$0.767309\pi$
$108$	−1.00000	−0.0962250
$109$	15.3686	1.47204	0.736022	−	0.676958i	$-0.236702\pi$
$109$	15.3686	1.47204	0.736022	+	0.676958i	$0.236702\pi$
$110$	−4.86945	−0.464284
$111$	−9.88059	−0.937824
$112$	0	0
$113$	10.3215	0.970970	0.485485	−	0.874245i	$-0.338643\pi$
$113$	10.3215	0.970970	0.485485	+	0.874245i	$0.338643\pi$
$114$	1.00000	0.0936586
$115$	−15.0912	−1.40726
$116$	−8.46435	−0.785895
$117$	4.98073	0.460469
$118$	−8.99984	−0.828503
$119$	0	0
$120$	2.05470	0.187568
$121$	−5.38356	−0.489414
$122$	−5.36737	−0.485939
$123$	10.1088	0.911476
$124$	−1.54589	−0.138825
$125$	11.8725	1.06191
$126$	0	0
$127$	9.13527	0.810624	0.405312	−	0.914178i	$-0.367163\pi$
$127$	9.13527	0.810624	0.405312	+	0.914178i	$0.367163\pi$
$128$	1.00000	0.0883883
$129$	−6.92491	−0.609704
$130$	−10.2339	−0.897575
$131$	2.58313	0.225689	0.112844	−	0.993613i	$-0.464004\pi$
$131$	2.58313	0.225689	0.112844	+	0.993613i	$0.464004\pi$
$132$	−2.36990	−0.206274
$133$	0	0
$134$	−3.30719	−0.285697
$135$	2.05470	0.176841
$136$	0.0143085	0.00122695
$137$	−16.1887	−1.38309	−0.691545	−	0.722333i	$-0.743070\pi$
$137$	−16.1887	−1.38309	−0.691545	+	0.722333i	$0.743070\pi$
$138$	−7.34471	−0.625223
$139$	−12.7514	−1.08156	−0.540781	−	0.841164i	$-0.681871\pi$
$139$	−12.7514	−1.08156	−0.540781	+	0.841164i	$0.681871\pi$
$140$	0	0
$141$	−5.17125	−0.435498
$142$	10.9665	0.920284
$143$	11.8039	0.987088
$144$	1.00000	0.0833333
$145$	17.3917	1.44430
$146$	−10.6736	−0.883353
$147$	0	0
$148$	9.88059	0.812180
$149$	8.99559	0.736948	0.368474	−	0.929638i	$-0.379880\pi$
$149$	8.99559	0.736948	0.368474	+	0.929638i	$0.379880\pi$
$150$	0.778190	0.0635390
$151$	−15.7534	−1.28199	−0.640997	−	0.767543i	$-0.721479\pi$
$151$	−15.7534	−1.28199	−0.640997	+	0.767543i	$0.721479\pi$
$152$	−1.00000	−0.0811107
$153$	0.0143085	0.00115678
$154$	0	0
$155$	3.17635	0.255130
$156$	−4.98073	−0.398778
$157$	20.5980	1.64390	0.821948	−	0.569563i	$-0.192887\pi$
$157$	20.5980	1.64390	0.821948	+	0.569563i	$0.192887\pi$
$158$	10.1648	0.808664
$159$	2.84922	0.225958
$160$	−2.05470	−0.162439
$161$	0	0
$162$	1.00000	0.0785674
$163$	5.97515	0.468010	0.234005	−	0.972235i	$-0.424817\pi$
$163$	5.97515	0.468010	0.234005	+	0.972235i	$0.424817\pi$
$164$	−10.1088	−0.789361
$165$	4.86945	0.379086
$166$	14.7988	1.14861
$167$	−2.96292	−0.229278	−0.114639	−	0.993407i	$-0.536571\pi$
$167$	−2.96292	−0.229278	−0.114639	+	0.993407i	$0.536571\pi$
$168$	0	0
$169$	11.8077	0.908283
$170$	−0.0293998	−0.00225486
$171$	−1.00000	−0.0764719
$172$	6.92491	0.528019
$173$	21.6640	1.64708	0.823542	−	0.567256i	$-0.191995\pi$
$173$	21.6640	1.64708	0.823542	+	0.567256i	$0.191995\pi$
$174$	8.46435	0.641681
$175$	0	0
$176$	2.36990	0.178638
$177$	8.99984	0.676470
$178$	8.10893	0.607790
$179$	20.7061	1.54765	0.773823	−	0.633401i	$-0.218342\pi$
$179$	20.7061	1.54765	0.773823	+	0.633401i	$0.218342\pi$
$180$	−2.05470	−0.153149
$181$	18.6947	1.38957	0.694784	−	0.719219i	$-0.255500\pi$
$181$	18.6947	1.38957	0.694784	+	0.719219i	$0.255500\pi$
$182$	0	0
$183$	5.36737	0.396767
$184$	7.34471	0.541459
$185$	−20.3017	−1.49261
$186$	1.54589	0.113350
$187$	0.0339098	0.00247973
$188$	5.17125	0.377152
$189$	0	0
$190$	2.05470	0.149064
$191$	−17.7902	−1.28725	−0.643627	−	0.765339i	$-0.722571\pi$
$191$	−17.7902	−1.28725	−0.643627	+	0.765339i	$0.722571\pi$
$192$	−1.00000	−0.0721688
$193$	4.02079	0.289423	0.144711	−	0.989474i	$-0.453775\pi$
$193$	4.02079	0.289423	0.144711	+	0.989474i	$0.453775\pi$
$194$	18.8131	1.35070
$195$	10.2339	0.732867
$196$	0	0
$197$	−2.79458	−0.199106	−0.0995528	−	0.995032i	$-0.531741\pi$
$197$	−2.79458	−0.199106	−0.0995528	+	0.995032i	$0.531741\pi$
$198$	2.36990	0.168422
$199$	−0.522218	−0.0370191	−0.0185095	−	0.999829i	$-0.505892\pi$
$199$	−0.522218	−0.0370191	−0.0185095	+	0.999829i	$0.505892\pi$
$200$	−0.778190	−0.0550264
$201$	3.30719	0.233271
$202$	−3.57353	−0.251433
$203$	0	0
$204$	−0.0143085	−0.00100180
$205$	20.7705	1.45067
$206$	−2.23342	−0.155610
$207$	7.34471	0.510492
$208$	4.98073	0.345351
$209$	−2.36990	−0.163930
$210$	0	0
$211$	10.7255	0.738377	0.369188	−	0.929355i	$-0.379636\pi$
$211$	10.7255	0.738377	0.369188	+	0.929355i	$0.379636\pi$
$212$	−2.84922	−0.195685
$213$	−10.9665	−0.751409
$214$	−15.4022	−1.05287
$215$	−14.2286	−0.970385
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	15.3686	1.04089
$219$	10.6736	0.721255
$220$	−4.86945	−0.328298
$221$	0.0712669	0.00479393
$222$	−9.88059	−0.663142
$223$	15.9043	1.06503	0.532514	−	0.846421i	$-0.321247\pi$
$223$	15.9043	1.06503	0.532514	+	0.846421i	$0.321247\pi$
$224$	0	0
$225$	−0.778190	−0.0518794
$226$	10.3215	0.686579
$227$	−5.41755	−0.359575	−0.179788	−	0.983705i	$-0.557541\pi$
$227$	−5.41755	−0.359575	−0.179788	+	0.983705i	$0.557541\pi$
$228$	1.00000	0.0662266
$229$	14.7315	0.973483	0.486741	−	0.873546i	$-0.338185\pi$
$229$	14.7315	0.973483	0.486741	+	0.873546i	$0.338185\pi$
$230$	−15.0912	−0.995084
$231$	0	0
$232$	−8.46435	−0.555712
$233$	14.1454	0.926693	0.463347	−	0.886177i	$-0.346649\pi$
$233$	14.1454	0.926693	0.463347	+	0.886177i	$0.346649\pi$
$234$	4.98073	0.325601
$235$	−10.6254	−0.693124
$236$	−8.99984	−0.585840
$237$	−10.1648	−0.660272
$238$	0	0
$239$	−0.570392	−0.0368956	−0.0184478	−	0.999830i	$-0.505872\pi$
$239$	−0.570392	−0.0368956	−0.0184478	+	0.999830i	$0.505872\pi$
$240$	2.05470	0.132631
$241$	13.6293	0.877940	0.438970	−	0.898502i	$-0.355343\pi$
$241$	13.6293	0.877940	0.438970	+	0.898502i	$0.355343\pi$
$242$	−5.38356	−0.346068
$243$	−1.00000	−0.0641500
$244$	−5.36737	−0.343610
$245$	0	0
$246$	10.1088	0.644511
$247$	−4.98073	−0.316916
$248$	−1.54589	−0.0981641
$249$	−14.7988	−0.937837
$250$	11.8725	0.750881
$251$	0.156077	0.00985147	0.00492573	−	0.999988i	$-0.498432\pi$
$251$	0.156077	0.00985147	0.00492573	+	0.999988i	$0.498432\pi$
$252$	0	0
$253$	17.4062	1.09432
$254$	9.13527	0.573198
$255$	0.0293998	0.00184109
$256$	1.00000	0.0625000
$257$	17.4274	1.08709	0.543544	−	0.839380i	$-0.317082\pi$
$257$	17.4274	1.08709	0.543544	+	0.839380i	$0.317082\pi$
$258$	−6.92491	−0.431126
$259$	0	0
$260$	−10.2339	−0.634681
$261$	−8.46435	−0.523930
$262$	2.58313	0.159586
$263$	2.73147	0.168430	0.0842149	−	0.996448i	$-0.473162\pi$
$263$	2.73147	0.168430	0.0842149	+	0.996448i	$0.473162\pi$
$264$	−2.36990	−0.145857
$265$	5.85430	0.359627
$266$	0	0
$267$	−8.10893	−0.496259
$268$	−3.30719	−0.202019
$269$	−9.84427	−0.600215	−0.300108	−	0.953905i	$-0.597023\pi$
$269$	−9.84427	−0.600215	−0.300108	+	0.953905i	$0.597023\pi$
$270$	2.05470	0.125045
$271$	7.38489	0.448600	0.224300	−	0.974520i	$-0.427990\pi$
$271$	7.38489	0.448600	0.224300	+	0.974520i	$0.427990\pi$
$272$	0.0143085	0.000867581 0
$273$	0	0
$274$	−16.1887	−0.977993
$275$	−1.84424	−0.111212
$276$	−7.34471	−0.442099
$277$	−17.0653	−1.02535	−0.512677	−	0.858582i	$-0.671346\pi$
$277$	−17.0653	−1.02535	−0.512677	+	0.858582i	$0.671346\pi$
$278$	−12.7514	−0.764779
$279$	−1.54589	−0.0925500
$280$	0	0
$281$	−9.78373	−0.583649	−0.291824	−	0.956472i	$-0.594262\pi$
$281$	−9.78373	−0.583649	−0.291824	+	0.956472i	$0.594262\pi$
$282$	−5.17125	−0.307944
$283$	9.75022	0.579591	0.289795	−	0.957089i	$-0.406413\pi$
$283$	9.75022	0.579591	0.289795	+	0.957089i	$0.406413\pi$
$284$	10.9665	0.650739
$285$	−2.05470	−0.121710
$286$	11.8039	0.697976
$287$	0	0
$288$	1.00000	0.0589256
$289$	−16.9998	−0.999988
$290$	17.3917	1.02128
$291$	−18.8131	−1.10285
$292$	−10.6736	−0.624625
$293$	−0.706340	−0.0412648	−0.0206324	−	0.999787i	$-0.506568\pi$
$293$	−0.706340	−0.0412648	−0.0206324	+	0.999787i	$0.506568\pi$
$294$	0	0
$295$	18.4920	1.07665
$296$	9.88059	0.574298
$297$	−2.36990	−0.137516
$298$	8.99559	0.521101
$299$	36.5820	2.11559
$300$	0.778190	0.0449288
$301$	0	0
$302$	−15.7534	−0.906507
$303$	3.57353	0.205294
$304$	−1.00000	−0.0573539
$305$	11.0284	0.631482
$306$	0.0143085	0.000817964 0
$307$	11.3564	0.648144	0.324072	−	0.946032i	$-0.394948\pi$
$307$	11.3564	0.648144	0.324072	+	0.946032i	$0.394948\pi$
$308$	0	0
$309$	2.23342	0.127055
$310$	3.17635	0.180404
$311$	9.68069	0.548942	0.274471	−	0.961595i	$-0.411497\pi$
$311$	9.68069	0.548942	0.274471	+	0.961595i	$0.411497\pi$
$312$	−4.98073	−0.281978
$313$	25.6999	1.45265	0.726323	−	0.687354i	$-0.241228\pi$
$313$	25.6999	1.45265	0.726323	+	0.687354i	$0.241228\pi$
$314$	20.5980	1.16241
$315$	0	0
$316$	10.1648	0.571812
$317$	−12.9971	−0.729990	−0.364995	−	0.931009i	$-0.618929\pi$
$317$	−12.9971	−0.729990	−0.364995	+	0.931009i	$0.618929\pi$
$318$	2.84922	0.159776
$319$	−20.0597	−1.12313
$320$	−2.05470	−0.114861
$321$	15.4022	0.859666
$322$	0	0
$323$	−0.0143085	−0.000796147 0
$324$	1.00000	0.0555556
$325$	−3.87596	−0.214999
$326$	5.97515	0.330933
$327$	−15.3686	−0.849885
$328$	−10.1088	−0.558162
$329$	0	0
$330$	4.86945	0.268054
$331$	−9.67441	−0.531754	−0.265877	−	0.964007i	$-0.585661\pi$
$331$	−9.67441	−0.531754	−0.265877	+	0.964007i	$0.585661\pi$
$332$	14.7988	0.812191
$333$	9.88059	0.541453
$334$	−2.96292	−0.162124
$335$	6.79529	0.371266
$336$	0	0
$337$	25.7053	1.40025	0.700127	−	0.714018i	$-0.253127\pi$
$337$	25.7053	1.40025	0.700127	+	0.714018i	$0.253127\pi$
$338$	11.8077	0.642253
$339$	−10.3215	−0.560590
$340$	−0.0293998	−0.00159443
$341$	−3.66361	−0.198396
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	6.92491	0.373366
$345$	15.0912	0.812483
$346$	21.6640	1.16466
$347$	26.1636	1.40454	0.702269	−	0.711912i	$-0.252171\pi$
$347$	26.1636	1.40454	0.702269	+	0.711912i	$0.252171\pi$
$348$	8.46435	0.453737
$349$	−30.2714	−1.62039	−0.810196	−	0.586159i	$-0.800639\pi$
$349$	−30.2714	−1.62039	−0.810196	+	0.586159i	$0.800639\pi$
$350$	0	0
$351$	−4.98073	−0.265852
$352$	2.36990	0.126316
$353$	−36.0223	−1.91727	−0.958637	−	0.284632i	$-0.908129\pi$
$353$	−36.0223	−1.91727	−0.958637	+	0.284632i	$0.908129\pi$
$354$	8.99984	0.478336
$355$	−22.5328	−1.19592
$356$	8.10893	0.429773
$357$	0	0
$358$	20.7061	1.09435
$359$	−20.8862	−1.10233	−0.551166	−	0.834396i	$-0.685817\pi$
$359$	−20.8862	−1.10233	−0.551166	+	0.834396i	$0.685817\pi$
$360$	−2.05470	−0.108292
$361$	1.00000	0.0526316
$362$	18.6947	0.982572
$363$	5.38356	0.282563
$364$	0	0
$365$	21.9311	1.14793
$366$	5.36737	0.280557
$367$	1.57295	0.0821074	0.0410537	−	0.999157i	$-0.486929\pi$
$367$	1.57295	0.0821074	0.0410537	+	0.999157i	$0.486929\pi$
$368$	7.34471	0.382869
$369$	−10.1088	−0.526241
$370$	−20.3017	−1.05544
$371$	0	0
$372$	1.54589	0.0801507
$373$	−16.9187	−0.876016	−0.438008	−	0.898971i	$-0.644316\pi$
$373$	−16.9187	−0.876016	−0.438008	+	0.898971i	$0.644316\pi$
$374$	0.0339098	0.00175343
$375$	−11.8725	−0.613092
$376$	5.17125	0.266687
$377$	−42.1586	−2.17128
$378$	0	0
$379$	6.48462	0.333092	0.166546	−	0.986034i	$-0.446739\pi$
$379$	6.48462	0.333092	0.166546	+	0.986034i	$0.446739\pi$
$380$	2.05470	0.105404
$381$	−9.13527	−0.468014
$382$	−17.7902	−0.910226
$383$	7.37803	0.377000	0.188500	−	0.982073i	$-0.439637\pi$
$383$	7.37803	0.377000	0.188500	+	0.982073i	$0.439637\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	4.02079	0.204653
$387$	6.92491	0.352013
$388$	18.8131	0.955092
$389$	25.1647	1.27590	0.637950	−	0.770077i	$-0.279782\pi$
$389$	25.1647	1.27590	0.637950	+	0.770077i	$0.279782\pi$
$390$	10.2339	0.518215
$391$	0.105092	0.00531472
$392$	0	0
$393$	−2.58313	−0.130301
$394$	−2.79458	−0.140789
$395$	−20.8856	−1.05087
$396$	2.36990	0.119092
$397$	11.1922	0.561719	0.280860	−	0.959749i	$-0.409380\pi$
$397$	11.1922	0.561719	0.280860	+	0.959749i	$0.409380\pi$
$398$	−0.522218	−0.0261764
$399$	0	0
$400$	−0.778190	−0.0389095
$401$	−29.3336	−1.46485	−0.732425	−	0.680848i	$-0.761611\pi$
$401$	−29.3336	−1.46485	−0.732425	+	0.680848i	$0.761611\pi$
$402$	3.30719	0.164947
$403$	−7.69966	−0.383547
$404$	−3.57353	−0.177790
$405$	−2.05470	−0.102099
$406$	0	0
$407$	23.4161	1.16069
$408$	−0.0143085	−0.000708377 0
$409$	−28.4866	−1.40857	−0.704286	−	0.709916i	$-0.748733\pi$
$409$	−28.4866	−1.40857	−0.704286	+	0.709916i	$0.748733\pi$
$410$	20.7705	1.02578
$411$	16.1887	0.798528
$412$	−2.23342	−0.110033
$413$	0	0
$414$	7.34471	0.360973
$415$	−30.4072	−1.49263
$416$	4.98073	0.244200
$417$	12.7514	0.624440
$418$	−2.36990	−0.115916
$419$	−21.9244	−1.07108	−0.535539	−	0.844511i	$-0.679891\pi$
$419$	−21.9244	−1.07108	−0.535539	+	0.844511i	$0.679891\pi$
$420$	0	0
$421$	11.3998	0.555594	0.277797	−	0.960640i	$-0.410396\pi$
$421$	11.3998	0.555594	0.277797	+	0.960640i	$0.410396\pi$
$422$	10.7255	0.522111
$423$	5.17125	0.251435
$424$	−2.84922	−0.138370
$425$	−0.0111348	−0.000540115 0
$426$	−10.9665	−0.531326
$427$	0	0
$428$	−15.4022	−0.744493
$429$	−11.8039	−0.569895
$430$	−14.2286	−0.686166
$431$	−15.6139	−0.752094	−0.376047	−	0.926601i	$-0.622717\pi$
$431$	−15.6139	−0.752094	−0.376047	+	0.926601i	$0.622717\pi$
$432$	−1.00000	−0.0481125
$433$	8.94321	0.429783	0.214892	−	0.976638i	$-0.431060\pi$
$433$	8.94321	0.429783	0.214892	+	0.976638i	$0.431060\pi$
$434$	0	0
$435$	−17.3917	−0.833870
$436$	15.3686	0.736022
$437$	−7.34471	−0.351345
$438$	10.6736	0.510004
$439$	25.1391	1.19982	0.599912	−	0.800066i	$-0.295202\pi$
$439$	25.1391	1.19982	0.599912	+	0.800066i	$0.295202\pi$
$440$	−4.86945	−0.232142
$441$	0	0
$442$	0.0712669	0.00338982
$443$	5.48624	0.260659	0.130329	−	0.991471i	$-0.458396\pi$
$443$	5.48624	0.260659	0.130329	+	0.991471i	$0.458396\pi$
$444$	−9.88059	−0.468912
$445$	−16.6615	−0.789829
$446$	15.9043	0.753088
$447$	−8.99559	−0.425477
$448$	0	0
$449$	−40.0477	−1.88997	−0.944985	−	0.327114i	$-0.893924\pi$
$449$	−40.0477	−1.88997	−0.944985	+	0.327114i	$0.893924\pi$
$450$	−0.778190	−0.0366843
$451$	−23.9568	−1.12808
$452$	10.3215	0.485485
$453$	15.7534	0.740160
$454$	−5.41755	−0.254258
$455$	0	0
$456$	1.00000	0.0468293
$457$	39.3987	1.84299	0.921497	−	0.388386i	$-0.126967\pi$
$457$	39.3987	1.84299	0.921497	+	0.388386i	$0.126967\pi$
$458$	14.7315	0.688356
$459$	−0.0143085	−0.000667864 0
$460$	−15.0912	−0.703631
$461$	−20.4152	−0.950831	−0.475415	−	0.879761i	$-0.657702\pi$
$461$	−20.4152	−0.950831	−0.475415	+	0.879761i	$0.657702\pi$
$462$	0	0
$463$	19.0296	0.884379	0.442190	−	0.896922i	$-0.354202\pi$
$463$	19.0296	0.884379	0.442190	+	0.896922i	$0.354202\pi$
$464$	−8.46435	−0.392947
$465$	−3.17635	−0.147300
$466$	14.1454	0.655271
$467$	−18.4921	−0.855710	−0.427855	−	0.903847i	$-0.640731\pi$
$467$	−18.4921	−0.855710	−0.427855	+	0.903847i	$0.640731\pi$
$468$	4.98073	0.230234
$469$	0	0
$470$	−10.6254	−0.490113
$471$	−20.5980	−0.949104
$472$	−8.99984	−0.414251
$473$	16.4114	0.754596
$474$	−10.1648	−0.466883
$475$	0.778190	0.0357058
$476$	0	0
$477$	−2.84922	−0.130457
$478$	−0.570392	−0.0260891
$479$	13.5737	0.620200	0.310100	−	0.950704i	$-0.399637\pi$
$479$	13.5737	0.620200	0.310100	+	0.950704i	$0.399637\pi$
$480$	2.05470	0.0937840
$481$	49.2126	2.24390
$482$	13.6293	0.620797
$483$	0	0
$484$	−5.38356	−0.244707
$485$	−38.6554	−1.75525
$486$	−1.00000	−0.0453609
$487$	−30.1511	−1.36628	−0.683138	−	0.730290i	$-0.739385\pi$
$487$	−30.1511	−1.36628	−0.683138	+	0.730290i	$0.739385\pi$
$488$	−5.36737	−0.242969
$489$	−5.97515	−0.270205
$490$	0	0
$491$	−17.6441	−0.796266	−0.398133	−	0.917328i	$-0.630342\pi$
$491$	−17.6441	−0.796266	−0.398133	+	0.917328i	$0.630342\pi$
$492$	10.1088	0.455738
$493$	−0.121112	−0.00545462
$494$	−4.98073	−0.224094
$495$	−4.86945	−0.218866
$496$	−1.54589	−0.0694125
$497$	0	0
$498$	−14.7988	−0.663151
$499$	−7.30595	−0.327059	−0.163530	−	0.986538i	$-0.552288\pi$
$499$	−7.30595	−0.327059	−0.163530	+	0.986538i	$0.552288\pi$
$500$	11.8725	0.530953
$501$	2.96292	0.132373
$502$	0.156077	0.00696604
$503$	−23.5582	−1.05041	−0.525205	−	0.850976i	$-0.676011\pi$
$503$	−23.5582	−1.05041	−0.525205	+	0.850976i	$0.676011\pi$
$504$	0	0
$505$	7.34255	0.326739
$506$	17.4062	0.773802
$507$	−11.8077	−0.524397
$508$	9.13527	0.405312
$509$	14.2456	0.631427	0.315714	−	0.948855i	$-0.397756\pi$
$509$	14.2456	0.631427	0.315714	+	0.948855i	$0.397756\pi$
$510$	0.0293998	0.00130184
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	17.4274	0.768688
$515$	4.58901	0.202216
$516$	−6.92491	−0.304852
$517$	12.2554	0.538991
$518$	0	0
$519$	−21.6640	−0.950944
$520$	−10.2339	−0.448787
$521$	1.79837	0.0787881	0.0393941	−	0.999224i	$-0.487457\pi$
$521$	1.79837	0.0787881	0.0393941	+	0.999224i	$0.487457\pi$
$522$	−8.46435	−0.370474
$523$	−15.8231	−0.691898	−0.345949	−	0.938253i	$-0.612443\pi$
$523$	−15.8231	−0.691898	−0.345949	+	0.938253i	$0.612443\pi$
$524$	2.58313	0.112844
$525$	0	0
$526$	2.73147	0.119098
$527$	−0.0221194	−0.000963536 0
$528$	−2.36990	−0.103137
$529$	30.9447	1.34542
$530$	5.85430	0.254294
$531$	−8.99984	−0.390560
$532$	0	0
$533$	−50.3490	−2.18086
$534$	−8.10893	−0.350908
$535$	31.6469	1.36822
$536$	−3.30719	−0.142849
$537$	−20.7061	−0.893534
$538$	−9.84427	−0.424416
$539$	0	0
$540$	2.05470	0.0884204
$541$	21.5624	0.927040	0.463520	−	0.886086i	$-0.346586\pi$
$541$	21.5624	0.927040	0.463520	+	0.886086i	$0.346586\pi$
$542$	7.38489	0.317208
$543$	−18.6947	−0.802267
$544$	0.0143085	0.000613473 0
$545$	−31.5779	−1.35265
$546$	0	0
$547$	−15.6750	−0.670214	−0.335107	−	0.942180i	$-0.608772\pi$
$547$	−15.6750	−0.670214	−0.335107	+	0.942180i	$0.608772\pi$
$548$	−16.1887	−0.691545
$549$	−5.36737	−0.229074
$550$	−1.84424	−0.0786385
$551$	8.46435	0.360593
$552$	−7.34471	−0.312611
$553$	0	0
$554$	−17.0653	−0.725035
$555$	20.3017	0.861759
$556$	−12.7514	−0.540781
$557$	19.4792	0.825362	0.412681	−	0.910876i	$-0.364592\pi$
$557$	19.4792	0.825362	0.412681	+	0.910876i	$0.364592\pi$
$558$	−1.54589	−0.0654427
$559$	34.4911	1.45882
$560$	0	0
$561$	−0.0339098	−0.00143167
$562$	−9.78373	−0.412702
$563$	30.3214	1.27790	0.638948	−	0.769250i	$-0.279370\pi$
$563$	30.3214	1.27790	0.638948	+	0.769250i	$0.279370\pi$
$564$	−5.17125	−0.217749
$565$	−21.2077	−0.892216
$566$	9.75022	0.409833
$567$	0	0
$568$	10.9665	0.460142
$569$	21.1402	0.886245	0.443122	−	0.896461i	$-0.353871\pi$
$569$	21.1402	0.886245	0.443122	+	0.896461i	$0.353871\pi$
$570$	−2.05470	−0.0860621
$571$	−20.7654	−0.869006	−0.434503	−	0.900670i	$-0.643076\pi$
$571$	−20.7654	−0.869006	−0.434503	+	0.900670i	$0.643076\pi$
$572$	11.8039	0.493544
$573$	17.7902	0.743197
$574$	0	0
$575$	−5.71558	−0.238356
$576$	1.00000	0.0416667
$577$	7.25399	0.301987	0.150994	−	0.988535i	$-0.451753\pi$
$577$	7.25399	0.301987	0.150994	+	0.988535i	$0.451753\pi$
$578$	−16.9998	−0.707098
$579$	−4.02079	−0.167098
$580$	17.3917	0.722152
$581$	0	0
$582$	−18.8131	−0.779829
$583$	−6.75237	−0.279654
$584$	−10.6736	−0.441677
$585$	−10.2339	−0.423121
$586$	−0.706340	−0.0291786
$587$	−15.3761	−0.634640	−0.317320	−	0.948318i	$-0.602783\pi$
$587$	−15.3761	−0.634640	−0.317320	+	0.948318i	$0.602783\pi$
$588$	0	0
$589$	1.54589	0.0636973
$590$	18.4920	0.761304
$591$	2.79458	0.114954
$592$	9.88059	0.406090
$593$	9.88815	0.406058	0.203029	−	0.979173i	$-0.434922\pi$
$593$	9.88815	0.406058	0.203029	+	0.979173i	$0.434922\pi$
$594$	−2.36990	−0.0972383
$595$	0	0
$596$	8.99559	0.368474
$597$	0.522218	0.0213730
$598$	36.5820	1.49595
$599$	−46.1973	−1.88757	−0.943786	−	0.330557i	$-0.892763\pi$
$599$	−46.1973	−1.88757	−0.943786	+	0.330557i	$0.892763\pi$
$600$	0.778190	0.0317695
$601$	−28.4365	−1.15995	−0.579975	−	0.814634i	$-0.696938\pi$
$601$	−28.4365	−1.15995	−0.579975	+	0.814634i	$0.696938\pi$
$602$	0	0
$603$	−3.30719	−0.134679
$604$	−15.7534	−0.640997
$605$	11.0616	0.449719
$606$	3.57353	0.145165
$607$	30.2455	1.22763	0.613813	−	0.789451i	$-0.289635\pi$
$607$	30.2455	1.22763	0.613813	+	0.789451i	$0.289635\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	11.0284	0.446525
$611$	25.7566	1.04200
$612$	0.0143085	0.000578388 0
$613$	11.7661	0.475229	0.237615	−	0.971360i	$-0.423635\pi$
$613$	11.7661	0.475229	0.237615	+	0.971360i	$0.423635\pi$
$614$	11.3564	0.458307
$615$	−20.7705	−0.837547
$616$	0	0
$617$	45.1911	1.81932	0.909662	−	0.415350i	$-0.136341\pi$
$617$	45.1911	1.81932	0.909662	+	0.415350i	$0.136341\pi$
$618$	2.23342	0.0898412
$619$	16.3562	0.657412	0.328706	−	0.944432i	$-0.393387\pi$
$619$	16.3562	0.657412	0.328706	+	0.944432i	$0.393387\pi$
$620$	3.17635	0.127565
$621$	−7.34471	−0.294733
$622$	9.68069	0.388160
$623$	0	0
$624$	−4.98073	−0.199389
$625$	−20.5035	−0.820139
$626$	25.6999	1.02718
$627$	2.36990	0.0946448
$628$	20.5980	0.821948
$629$	0.141377	0.00563706
$630$	0	0
$631$	−35.0343	−1.39470	−0.697348	−	0.716733i	$-0.745637\pi$
$631$	−35.0343	−1.39470	−0.697348	+	0.716733i	$0.745637\pi$
$632$	10.1648	0.404332
$633$	−10.7255	−0.426302
$634$	−12.9971	−0.516181
$635$	−18.7703	−0.744876
$636$	2.84922	0.112979
$637$	0	0
$638$	−20.0597	−0.794171
$639$	10.9665	0.433826
$640$	−2.05470	−0.0812193
$641$	19.4503	0.768242	0.384121	−	0.923283i	$-0.374505\pi$
$641$	19.4503	0.768242	0.384121	+	0.923283i	$0.374505\pi$
$642$	15.4022	0.607876
$643$	0.585298	0.0230819	0.0115409	−	0.999933i	$-0.496326\pi$
$643$	0.585298	0.0230819	0.0115409	+	0.999933i	$0.496326\pi$
$644$	0	0
$645$	14.2286	0.560252
$646$	−0.0143085	−0.000562961 0
$647$	−21.1148	−0.830109	−0.415055	−	0.909797i	$-0.636238\pi$
$647$	−21.1148	−0.830109	−0.415055	+	0.909797i	$0.636238\pi$
$648$	1.00000	0.0392837
$649$	−21.3288	−0.837227
$650$	−3.87596	−0.152028
$651$	0	0
$652$	5.97515	0.234005
$653$	1.90298	0.0744693	0.0372346	−	0.999307i	$-0.488145\pi$
$653$	1.90298	0.0744693	0.0372346	+	0.999307i	$0.488145\pi$
$654$	−15.3686	−0.600959
$655$	−5.30756	−0.207383
$656$	−10.1088	−0.394680
$657$	−10.6736	−0.416417
$658$	0	0
$659$	−29.3044	−1.14154	−0.570768	−	0.821111i	$-0.693354\pi$
$659$	−29.3044	−1.14154	−0.570768	+	0.821111i	$0.693354\pi$
$660$	4.86945	0.189543
$661$	13.0211	0.506462	0.253231	−	0.967406i	$-0.418507\pi$
$661$	13.0211	0.506462	0.253231	+	0.967406i	$0.418507\pi$
$662$	−9.67441	−0.376007
$663$	−0.0712669	−0.00276778
$664$	14.7988	0.574306
$665$	0	0
$666$	9.88059	0.382865
$667$	−62.1682	−2.40716
$668$	−2.96292	−0.114639
$669$	−15.9043	−0.614894
$670$	6.79529	0.262525
$671$	−12.7201	−0.491056
$672$	0	0
$673$	−15.7816	−0.608336	−0.304168	−	0.952618i	$-0.598378\pi$
$673$	−15.7816	−0.608336	−0.304168	+	0.952618i	$0.598378\pi$
$674$	25.7053	0.990129
$675$	0.778190	0.0299526
$676$	11.8077	0.454141
$677$	−2.07508	−0.0797520	−0.0398760	−	0.999205i	$-0.512696\pi$
$677$	−2.07508	−0.0797520	−0.0398760	+	0.999205i	$0.512696\pi$
$678$	−10.3215	−0.396397
$679$	0	0
$680$	−0.0293998	−0.00112743
$681$	5.41755	0.207601
$682$	−3.66361	−0.140287
$683$	−20.8222	−0.796739	−0.398370	−	0.917225i	$-0.630424\pi$
$683$	−20.8222	−0.796739	−0.398370	+	0.917225i	$0.630424\pi$
$684$	−1.00000	−0.0382360
$685$	33.2629	1.27091
$686$	0	0
$687$	−14.7315	−0.562041
$688$	6.92491	0.264010
$689$	−14.1912	−0.540641
$690$	15.0912	0.574512
$691$	−18.3478	−0.697985	−0.348992	−	0.937126i	$-0.613476\pi$
$691$	−18.3478	−0.697985	−0.348992	+	0.937126i	$0.613476\pi$
$692$	21.6640	0.823542
$693$	0	0
$694$	26.1636	0.993158
$695$	26.2004	0.993838
$696$	8.46435	0.320840
$697$	−0.144641	−0.00547868
$698$	−30.2714	−1.14579
$699$	−14.1454	−0.535027
$700$	0	0
$701$	−1.20714	−0.0455932	−0.0227966	−	0.999740i	$-0.507257\pi$
$701$	−1.20714	−0.0455932	−0.0227966	+	0.999740i	$0.507257\pi$
$702$	−4.98073	−0.187986
$703$	−9.88059	−0.372654
$704$	2.36990	0.0893191
$705$	10.6254	0.400176
$706$	−36.0223	−1.35572
$707$	0	0
$708$	8.99984	0.338235
$709$	10.3305	0.387970	0.193985	−	0.981005i	$-0.437859\pi$
$709$	10.3305	0.387970	0.193985	+	0.981005i	$0.437859\pi$
$710$	−22.5328	−0.845642
$711$	10.1648	0.381208
$712$	8.10893	0.303895
$713$	−11.3541	−0.425215
$714$	0	0
$715$	−24.2534	−0.907027
$716$	20.7061	0.773823
$717$	0.570392	0.0213017
$718$	−20.8862	−0.779466
$719$	−1.43044	−0.0533466	−0.0266733	−	0.999644i	$-0.508491\pi$
$719$	−1.43044	−0.0533466	−0.0266733	+	0.999644i	$0.508491\pi$
$720$	−2.05470	−0.0765743
$721$	0	0
$722$	1.00000	0.0372161
$723$	−13.6293	−0.506879
$724$	18.6947	0.694784
$725$	6.58688	0.244630
$726$	5.38356	0.199803
$727$	29.6628	1.10013	0.550067	−	0.835121i	$-0.314602\pi$
$727$	29.6628	1.10013	0.550067	+	0.835121i	$0.314602\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	21.9311	0.811706
$731$	0.0990852	0.00366480
$732$	5.36737	0.198384
$733$	−45.2322	−1.67069	−0.835344	−	0.549728i	$-0.814731\pi$
$733$	−45.2322	−1.67069	−0.835344	+	0.549728i	$0.814731\pi$
$734$	1.57295	0.0580587
$735$	0	0
$736$	7.34471	0.270729
$737$	−7.83771	−0.288706
$738$	−10.1088	−0.372108
$739$	48.8370	1.79650	0.898249	−	0.439487i	$-0.144840\pi$
$739$	48.8370	1.79650	0.898249	+	0.439487i	$0.144840\pi$
$740$	−20.3017	−0.746305
$741$	4.98073	0.182972
$742$	0	0
$743$	22.1252	0.811694	0.405847	−	0.913941i	$-0.366977\pi$
$743$	22.1252	0.811694	0.405847	+	0.913941i	$0.366977\pi$
$744$	1.54589	0.0566751
$745$	−18.4833	−0.677175
$746$	−16.9187	−0.619437
$747$	14.7988	0.541461
$748$	0.0339098	0.00123987
$749$	0	0
$750$	−11.8725	−0.433521
$751$	−7.25989	−0.264917	−0.132459	−	0.991189i	$-0.542287\pi$
$751$	−7.25989	−0.264917	−0.132459	+	0.991189i	$0.542287\pi$
$752$	5.17125	0.188576
$753$	−0.156077	−0.00568775
$754$	−42.1586	−1.53533
$755$	32.3686	1.17801
$756$	0	0
$757$	−23.5334	−0.855334	−0.427667	−	0.903936i	$-0.640664\pi$
$757$	−23.5334	−0.855334	−0.427667	+	0.903936i	$0.640664\pi$
$758$	6.48462	0.235532
$759$	−17.4062	−0.631807
$760$	2.05470	0.0745320
$761$	28.3879	1.02906	0.514531	−	0.857472i	$-0.327966\pi$
$761$	28.3879	1.02906	0.514531	+	0.857472i	$0.327966\pi$
$762$	−9.13527	−0.330936
$763$	0	0
$764$	−17.7902	−0.643627
$765$	−0.0293998	−0.00106295
$766$	7.37803	0.266579
$767$	−44.8258	−1.61857
$768$	−1.00000	−0.0360844
$769$	−2.03203	−0.0732770	−0.0366385	−	0.999329i	$-0.511665\pi$
$769$	−2.03203	−0.0732770	−0.0366385	+	0.999329i	$0.511665\pi$
$770$	0	0
$771$	−17.4274	−0.627631
$772$	4.02079	0.144711
$773$	−2.09739	−0.0754380	−0.0377190	−	0.999288i	$-0.512009\pi$
$773$	−2.09739	−0.0754380	−0.0377190	+	0.999288i	$0.512009\pi$
$774$	6.92491	0.248911
$775$	1.20300	0.0432129
$776$	18.8131	0.675352
$777$	0	0
$778$	25.1647	0.902198
$779$	10.1088	0.362184
$780$	10.2339	0.366433
$781$	25.9894	0.929975
$782$	0.105092	0.00375808
$783$	8.46435	0.302491
$784$	0	0
$785$	−42.3227	−1.51056
$786$	−2.58313	−0.0921370
$787$	4.48492	0.159870	0.0799351	−	0.996800i	$-0.474529\pi$
$787$	4.48492	0.159870	0.0799351	+	0.996800i	$0.474529\pi$
$788$	−2.79458	−0.0995528
$789$	−2.73147	−0.0972430
$790$	−20.8856	−0.743075
$791$	0	0
$792$	2.36990	0.0842109
$793$	−26.7334	−0.949331
$794$	11.1922	0.397195
$795$	−5.85430	−0.207630
$796$	−0.522218	−0.0185095
$797$	−35.5891	−1.26063	−0.630315	−	0.776340i	$-0.717074\pi$
$797$	−35.5891	−1.26063	−0.630315	+	0.776340i	$0.717074\pi$
$798$	0	0
$799$	0.0739930	0.00261768
$800$	−0.778190	−0.0275132
$801$	8.10893	0.286515
$802$	−29.3336	−1.03580
$803$	−25.2954	−0.892655
$804$	3.30719	0.116635
$805$	0	0
$806$	−7.69966	−0.271209
$807$	9.84427	0.346535
$808$	−3.57353	−0.125716
$809$	−9.45173	−0.332305	−0.166153	−	0.986100i	$-0.553134\pi$
$809$	−9.45173	−0.332305	−0.166153	+	0.986100i	$0.553134\pi$
$810$	−2.05470	−0.0721949
$811$	34.3300	1.20549	0.602744	−	0.797934i	$-0.294074\pi$
$811$	34.3300	1.20549	0.602744	+	0.797934i	$0.294074\pi$
$812$	0	0
$813$	−7.38489	−0.258999
$814$	23.4161	0.820732
$815$	−12.2772	−0.430050
$816$	−0.0143085	−0.000500898 0
$817$	−6.92491	−0.242272
$818$	−28.4866	−0.996011
$819$	0	0
$820$	20.7705	0.725337
$821$	52.2910	1.82497	0.912485	−	0.409110i	$-0.134161\pi$
$821$	52.2910	1.82497	0.912485	+	0.409110i	$0.134161\pi$
$822$	16.1887	0.564644
$823$	5.21027	0.181619	0.0908094	−	0.995868i	$-0.471055\pi$
$823$	5.21027	0.181619	0.0908094	+	0.995868i	$0.471055\pi$
$824$	−2.23342	−0.0778048
$825$	1.84424	0.0642081
$826$	0	0
$827$	8.82611	0.306914	0.153457	−	0.988155i	$-0.450959\pi$
$827$	8.82611	0.306914	0.153457	+	0.988155i	$0.450959\pi$
$828$	7.34471	0.255246
$829$	31.7784	1.10371	0.551855	−	0.833940i	$-0.313920\pi$
$829$	31.7784	1.10371	0.551855	+	0.833940i	$0.313920\pi$
$830$	−30.4072	−1.05545
$831$	17.0653	0.591988
$832$	4.98073	0.172676
$833$	0	0
$834$	12.7514	0.441546
$835$	6.08792	0.210681
$836$	−2.36990	−0.0819648
$837$	1.54589	0.0534338
$838$	−21.9244	−0.757366
$839$	43.1790	1.49071	0.745353	−	0.666671i	$-0.232281\pi$
$839$	43.1790	1.49071	0.745353	+	0.666671i	$0.232281\pi$
$840$	0	0
$841$	42.6452	1.47052
$842$	11.3998	0.392865
$843$	9.78373	0.336970
$844$	10.7255	0.369188
$845$	−24.2613	−0.834613
$846$	5.17125	0.177791
$847$	0	0
$848$	−2.84922	−0.0978425
$849$	−9.75022	−0.334627
$850$	−0.0111348	−0.000381919 0
$851$	72.5701	2.48767
$852$	−10.9665	−0.375704
$853$	−18.9801	−0.649867	−0.324933	−	0.945737i	$-0.605342\pi$
$853$	−18.9801	−0.649867	−0.324933	+	0.945737i	$0.605342\pi$
$854$	0	0
$855$	2.05470	0.0702694
$856$	−15.4022	−0.526436
$857$	12.3868	0.423123	0.211562	−	0.977365i	$-0.432145\pi$
$857$	12.3868	0.423123	0.211562	+	0.977365i	$0.432145\pi$
$858$	−11.8039	−0.402977
$859$	8.63397	0.294587	0.147294	−	0.989093i	$-0.452944\pi$
$859$	8.63397	0.294587	0.147294	+	0.989093i	$0.452944\pi$
$860$	−14.2286	−0.485193
$861$	0	0
$862$	−15.6139	−0.531811
$863$	−30.0763	−1.02381	−0.511904	−	0.859043i	$-0.671060\pi$
$863$	−30.0763	−1.02381	−0.511904	+	0.859043i	$0.671060\pi$
$864$	−1.00000	−0.0340207
$865$	−44.5131	−1.51349
$866$	8.94321	0.303903
$867$	16.9998	0.577343
$868$	0	0
$869$	24.0895	0.817180
$870$	−17.3917	−0.589635
$871$	−16.4722	−0.558139
$872$	15.3686	0.520446
$873$	18.8131	0.636728
$874$	−7.34471	−0.248438
$875$	0	0
$876$	10.6736	0.360627
$877$	−34.4309	−1.16265	−0.581324	−	0.813672i	$-0.697465\pi$
$877$	−34.4309	−1.16265	−0.581324	+	0.813672i	$0.697465\pi$
$878$	25.1391	0.848403
$879$	0.706340	0.0238243
$880$	−4.86945	−0.164149
$881$	−19.3808	−0.652957	−0.326478	−	0.945205i	$-0.605862\pi$
$881$	−19.3808	−0.652957	−0.326478	+	0.945205i	$0.605862\pi$
$882$	0	0
$883$	12.0307	0.404867	0.202433	−	0.979296i	$-0.435115\pi$
$883$	12.0307	0.404867	0.202433	+	0.979296i	$0.435115\pi$
$884$	0.0712669	0.00239696
$885$	−18.4920	−0.621602
$886$	5.48624	0.184314
$887$	−43.6732	−1.46640	−0.733202	−	0.680011i	$-0.761975\pi$
$887$	−43.6732	−1.46640	−0.733202	+	0.680011i	$0.761975\pi$
$888$	−9.88059	−0.331571
$889$	0	0
$890$	−16.6615	−0.558493
$891$	2.36990	0.0793948
$892$	15.9043	0.532514
$893$	−5.17125	−0.173049
$894$	−8.99559	−0.300858
$895$	−42.5449	−1.42212
$896$	0	0
$897$	−36.5820	−1.22144
$898$	−40.0477	−1.33641
$899$	13.0849	0.436408
$900$	−0.778190	−0.0259397
$901$	−0.0407681	−0.00135818
$902$	−23.9568	−0.797673
$903$	0	0
$904$	10.3215	0.343290
$905$	−38.4121	−1.27686
$906$	15.7534	0.523372
$907$	−53.0525	−1.76158	−0.880789	−	0.473509i	$-0.842987\pi$
$907$	−53.0525	−1.76158	−0.880789	+	0.473509i	$0.842987\pi$
$908$	−5.41755	−0.179788
$909$	−3.57353	−0.118527
$910$	0	0
$911$	−50.4737	−1.67227	−0.836135	−	0.548524i	$-0.815190\pi$
$911$	−50.4737	−1.67227	−0.836135	+	0.548524i	$0.815190\pi$
$912$	1.00000	0.0331133
$913$	35.0718	1.16071
$914$	39.3987	1.30319
$915$	−11.0284	−0.364586
$916$	14.7315	0.486741
$917$	0	0
$918$	−0.0143085	−0.000472251 0
$919$	55.5326	1.83185	0.915926	−	0.401347i	$-0.131458\pi$
$919$	55.5326	1.83185	0.915926	+	0.401347i	$0.131458\pi$
$920$	−15.0912	−0.497542
$921$	−11.3564	−0.374206
$922$	−20.4152	−0.672339
$923$	54.6209	1.79787
$924$	0	0
$925$	−7.68898	−0.252812
$926$	19.0296	0.625351
$927$	−2.23342	−0.0733550
$928$	−8.46435	−0.277856
$929$	−28.0201	−0.919311	−0.459656	−	0.888097i	$-0.652027\pi$
$929$	−28.0201	−0.919311	−0.459656	+	0.888097i	$0.652027\pi$
$930$	−3.17635	−0.104157
$931$	0	0
$932$	14.1454	0.463347
$933$	−9.68069	−0.316932
$934$	−18.4921	−0.605079
$935$	−0.0696746	−0.00227860
$936$	4.98073	0.162800
$937$	−13.9451	−0.455565	−0.227783	−	0.973712i	$-0.573148\pi$
$937$	−13.9451	−0.455565	−0.227783	+	0.973712i	$0.573148\pi$
$938$	0	0
$939$	−25.6999	−0.838686
$940$	−10.6254	−0.346562
$941$	21.9681	0.716140	0.358070	−	0.933695i	$-0.383435\pi$
$941$	21.9681	0.716140	0.358070	+	0.933695i	$0.383435\pi$
$942$	−20.5980	−0.671118
$943$	−74.2458	−2.41778
$944$	−8.99984	−0.292920
$945$	0	0
$946$	16.4114	0.533580
$947$	7.96418	0.258801	0.129401	−	0.991592i	$-0.458695\pi$
$947$	7.96418	0.258801	0.129401	+	0.991592i	$0.458695\pi$
$948$	−10.1648	−0.330136
$949$	−53.1623	−1.72572
$950$	0.778190	0.0252478
$951$	12.9971	0.421460
$952$	0	0
$953$	−7.60921	−0.246487	−0.123243	−	0.992376i	$-0.539330\pi$
$953$	−7.60921	−0.246487	−0.123243	+	0.992376i	$0.539330\pi$
$954$	−2.84922	−0.0922468
$955$	36.5536	1.18285
$956$	−0.570392	−0.0184478
$957$	20.0597	0.648438
$958$	13.5737	0.438548
$959$	0	0
$960$	2.05470	0.0663153
$961$	−28.6102	−0.922910
$962$	49.2126	1.58668
$963$	−15.4022	−0.496328
$964$	13.6293	0.438970
$965$	−8.26153	−0.265948
$966$	0	0
$967$	−12.0649	−0.387981	−0.193990	−	0.981003i	$-0.562143\pi$
$967$	−12.0649	−0.387981	−0.193990	+	0.981003i	$0.562143\pi$
$968$	−5.38356	−0.173034
$969$	0.0143085	0.000459656 0
$970$	−38.6554	−1.24115
$971$	−41.3659	−1.32749	−0.663747	−	0.747957i	$-0.731035\pi$
$971$	−41.3659	−1.32749	−0.663747	+	0.747957i	$0.731035\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−30.1511	−0.966102
$975$	3.87596	0.124130
$976$	−5.36737	−0.171805
$977$	37.0829	1.18639	0.593194	−	0.805060i	$-0.297867\pi$
$977$	37.0829	1.18639	0.593194	+	0.805060i	$0.297867\pi$
$978$	−5.97515	−0.191064
$979$	19.2174	0.614190
$980$	0	0
$981$	15.3686	0.490681
$982$	−17.6441	−0.563045
$983$	−36.5785	−1.16667	−0.583337	−	0.812230i	$-0.698253\pi$
$983$	−36.5785	−1.16667	−0.583337	+	0.812230i	$0.698253\pi$
$984$	10.1088	0.322255
$985$	5.74204	0.182957
$986$	−0.121112	−0.00385700
$987$	0	0
$988$	−4.98073	−0.158458
$989$	50.8614	1.61730
$990$	−4.86945	−0.154761
$991$	−22.9785	−0.729936	−0.364968	−	0.931020i	$-0.618920\pi$
$991$	−22.9785	−0.729936	−0.364968	+	0.931020i	$0.618920\pi$
$992$	−1.54589	−0.0490821
$993$	9.67441	0.307008
$994$	0	0
$995$	1.07300	0.0340165
$996$	−14.7988	−0.468919
$997$	−16.7231	−0.529625	−0.264813	−	0.964300i	$-0.585310\pi$
$997$	−16.7231	−0.529625	−0.264813	+	0.964300i	$0.585310\pi$
$998$	−7.30595	−0.231266
$999$	−9.88059	−0.312608

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.ce.1.4	✓	8
7.6	odd	2		5586.2.a.cf.1.5	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5586.2.a.ce.1.4	✓	8	1.1	even	1	trivial
5586.2.a.cf.1.5	yes	8	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.05470 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.05470 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.05470 q^{10} +2.36990 q^{11} -1.00000 q^{12} +4.98073 q^{13} +2.05470 q^{15} +1.00000 q^{16} +0.0143085 q^{17} +1.00000 q^{18} -1.00000 q^{19} -2.05470 q^{20} +2.36990 q^{22} +7.34471 q^{23} -1.00000 q^{24} -0.778190 q^{25} +4.98073 q^{26} -1.00000 q^{27} -8.46435 q^{29} +2.05470 q^{30} -1.54589 q^{31} +1.00000 q^{32} -2.36990 q^{33} +0.0143085 q^{34} +1.00000 q^{36} +9.88059 q^{37} -1.00000 q^{38} -4.98073 q^{39} -2.05470 q^{40} -10.1088 q^{41} +6.92491 q^{43} +2.36990 q^{44} -2.05470 q^{45} +7.34471 q^{46} +5.17125 q^{47} -1.00000 q^{48} -0.778190 q^{50} -0.0143085 q^{51} +4.98073 q^{52} -2.84922 q^{53} -1.00000 q^{54} -4.86945 q^{55} +1.00000 q^{57} -8.46435 q^{58} -8.99984 q^{59} +2.05470 q^{60} -5.36737 q^{61} -1.54589 q^{62} +1.00000 q^{64} -10.2339 q^{65} -2.36990 q^{66} -3.30719 q^{67} +0.0143085 q^{68} -7.34471 q^{69} +10.9665 q^{71} +1.00000 q^{72} -10.6736 q^{73} +9.88059 q^{74} +0.778190 q^{75} -1.00000 q^{76} -4.98073 q^{78} +10.1648 q^{79} -2.05470 q^{80} +1.00000 q^{81} -10.1088 q^{82} +14.7988 q^{83} -0.0293998 q^{85} +6.92491 q^{86} +8.46435 q^{87} +2.36990 q^{88} +8.10893 q^{89} -2.05470 q^{90} +7.34471 q^{92} +1.54589 q^{93} +5.17125 q^{94} +2.05470 q^{95} -1.00000 q^{96} +18.8131 q^{97} +2.36990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 8 q^{3} + 8 q^{4} - 4 q^{5} - 8 q^{6} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 - 4 * q^5 - 8 * q^6 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} - 8 q^{3} + 8 q^{4} - 4 q^{5} - 8 q^{6} + 8 q^{8} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 8 q^{12} + 4 q^{13} + 4 q^{15} + 8 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 4 q^{20} + 8 q^{22} + 4 q^{23} - 8 q^{24} + 24 q^{25} + 4 q^{26} - 8 q^{27} + 16 q^{29} + 4 q^{30} - 4 q^{31} + 8 q^{32} - 8 q^{33} - 8 q^{34} + 8 q^{36} + 12 q^{37} - 8 q^{38} - 4 q^{39} - 4 q^{40} + 16 q^{43} + 8 q^{44} - 4 q^{45} + 4 q^{46} - 12 q^{47} - 8 q^{48} + 24 q^{50} + 8 q^{51} + 4 q^{52} + 24 q^{53} - 8 q^{54} + 8 q^{55} + 8 q^{57} + 16 q^{58} + 8 q^{59} + 4 q^{60} - 4 q^{62} + 8 q^{64} + 8 q^{65} - 8 q^{66} + 8 q^{67} - 8 q^{68} - 4 q^{69} + 24 q^{71} + 8 q^{72} + 16 q^{73} + 12 q^{74} - 24 q^{75} - 8 q^{76} - 4 q^{78} + 20 q^{79} - 4 q^{80} + 8 q^{81} - 16 q^{83} + 48 q^{85} + 16 q^{86} - 16 q^{87} + 8 q^{88} - 4 q^{90} + 4 q^{92} + 4 q^{93} - 12 q^{94} + 4 q^{95} - 8 q^{96} + 8 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 - 4 * q^5 - 8 * q^6 + 8 * q^8 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 8 * q^12 + 4 * q^13 + 4 * q^15 + 8 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 4 * q^20 + 8 * q^22 + 4 * q^23 - 8 * q^24 + 24 * q^25 + 4 * q^26 - 8 * q^27 + 16 * q^29 + 4 * q^30 - 4 * q^31 + 8 * q^32 - 8 * q^33 - 8 * q^34 + 8 * q^36 + 12 * q^37 - 8 * q^38 - 4 * q^39 - 4 * q^40 + 16 * q^43 + 8 * q^44 - 4 * q^45 + 4 * q^46 - 12 * q^47 - 8 * q^48 + 24 * q^50 + 8 * q^51 + 4 * q^52 + 24 * q^53 - 8 * q^54 + 8 * q^55 + 8 * q^57 + 16 * q^58 + 8 * q^59 + 4 * q^60 - 4 * q^62 + 8 * q^64 + 8 * q^65 - 8 * q^66 + 8 * q^67 - 8 * q^68 - 4 * q^69 + 24 * q^71 + 8 * q^72 + 16 * q^73 + 12 * q^74 - 24 * q^75 - 8 * q^76 - 4 * q^78 + 20 * q^79 - 4 * q^80 + 8 * q^81 - 16 * q^83 + 48 * q^85 + 16 * q^86 - 16 * q^87 + 8 * q^88 - 4 * q^90 + 4 * q^92 + 4 * q^93 - 12 * q^94 + 4 * q^95 - 8 * q^96 + 8 * q^97 + 8 * q^99

Introduction

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