LMFDB - Embedded newform 5586.2.a.ce.1.2

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			1.2
Root			$5.71612$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.15280 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.15280 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.15280 q^{10} -6.08382 q^{11} -1.00000 q^{12} -1.70748 q^{13} +3.15280 q^{15} +1.00000 q^{16} -6.58953 q^{17} +1.00000 q^{18} -1.00000 q^{19} -3.15280 q^{20} -6.08382 q^{22} -5.06183 q^{23} -1.00000 q^{24} +4.94013 q^{25} -1.70748 q^{26} -1.00000 q^{27} +7.52820 q^{29} +3.15280 q^{30} -7.99551 q^{31} +1.00000 q^{32} +6.08382 q^{33} -6.58953 q^{34} +1.00000 q^{36} +7.48072 q^{37} -1.00000 q^{38} +1.70748 q^{39} -3.15280 q^{40} +4.03392 q^{41} -11.2675 q^{43} -6.08382 q^{44} -3.15280 q^{45} -5.06183 q^{46} +5.60561 q^{47} -1.00000 q^{48} +4.94013 q^{50} +6.58953 q^{51} -1.70748 q^{52} +11.8620 q^{53} -1.00000 q^{54} +19.1811 q^{55} +1.00000 q^{57} +7.52820 q^{58} -6.81255 q^{59} +3.15280 q^{60} +6.58432 q^{61} -7.99551 q^{62} +1.00000 q^{64} +5.38334 q^{65} +6.08382 q^{66} -2.42167 q^{67} -6.58953 q^{68} +5.06183 q^{69} -0.0450445 q^{71} +1.00000 q^{72} +14.1432 q^{73} +7.48072 q^{74} -4.94013 q^{75} -1.00000 q^{76} +1.70748 q^{78} +1.62666 q^{79} -3.15280 q^{80} +1.00000 q^{81} +4.03392 q^{82} -7.81806 q^{83} +20.7755 q^{85} -11.2675 q^{86} -7.52820 q^{87} -6.08382 q^{88} -11.9334 q^{89} -3.15280 q^{90} -5.06183 q^{92} +7.99551 q^{93} +5.60561 q^{94} +3.15280 q^{95} -1.00000 q^{96} -10.4076 q^{97} -6.08382 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.15280	−1.40997	−0.704987	−	0.709220i	$-0.749047\pi$
$5$	−3.15280	−1.40997	−0.704987	+	0.709220i	$0.749047\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.15280	−0.997002
$11$	−6.08382	−1.83434	−0.917170	−	0.398495i	$-0.869533\pi$
$11$	−6.08382	−1.83434	−0.917170	+	0.398495i	$0.869533\pi$
$12$	−1.00000	−0.288675
$13$	−1.70748	−0.473570	−0.236785	−	0.971562i	$-0.576094\pi$
$13$	−1.70748	−0.473570	−0.236785	+	0.971562i	$0.576094\pi$
$14$	0	0
$15$	3.15280	0.814049
$16$	1.00000	0.250000
$17$	−6.58953	−1.59820	−0.799098	−	0.601200i	$-0.794689\pi$
$17$	−6.58953	−1.59820	−0.799098	+	0.601200i	$0.794689\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.15280	−0.704987
$21$	0	0
$22$	−6.08382	−1.29707
$23$	−5.06183	−1.05546	−0.527732	−	0.849411i	$-0.676957\pi$
$23$	−5.06183	−1.05546	−0.527732	+	0.849411i	$0.676957\pi$
$24$	−1.00000	−0.204124
$25$	4.94013	0.988026
$26$	−1.70748	−0.334865
$27$	−1.00000	−0.192450
$28$	0	0
$29$	7.52820	1.39795	0.698976	−	0.715145i	$-0.253639\pi$
$29$	7.52820	1.39795	0.698976	+	0.715145i	$0.253639\pi$
$30$	3.15280	0.575619
$31$	−7.99551	−1.43604	−0.718018	−	0.696024i	$-0.754951\pi$
$31$	−7.99551	−1.43604	−0.718018	+	0.696024i	$0.754951\pi$
$32$	1.00000	0.176777
$33$	6.08382	1.05906
$34$	−6.58953	−1.13010
$35$	0	0
$36$	1.00000	0.166667
$37$	7.48072	1.22982	0.614912	−	0.788596i	$-0.289192\pi$
$37$	7.48072	1.22982	0.614912	+	0.788596i	$0.289192\pi$
$38$	−1.00000	−0.162221
$39$	1.70748	0.273416
$40$	−3.15280	−0.498501
$41$	4.03392	0.629992	0.314996	−	0.949093i	$-0.397997\pi$
$41$	4.03392	0.629992	0.314996	+	0.949093i	$0.397997\pi$
$42$	0	0
$43$	−11.2675	−1.71828	−0.859139	−	0.511741i	$-0.829001\pi$
$43$	−11.2675	−1.71828	−0.859139	+	0.511741i	$0.829001\pi$
$44$	−6.08382	−0.917170
$45$	−3.15280	−0.469991
$46$	−5.06183	−0.746326
$47$	5.60561	0.817662	0.408831	−	0.912610i	$-0.365937\pi$
$47$	5.60561	0.817662	0.408831	+	0.912610i	$0.365937\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	4.94013	0.698640
$51$	6.58953	0.922719
$52$	−1.70748	−0.236785
$53$	11.8620	1.62938	0.814689	−	0.579899i	$-0.196908\pi$
$53$	11.8620	1.62938	0.814689	+	0.579899i	$0.196908\pi$
$54$	−1.00000	−0.136083
$55$	19.1811	2.58637
$56$	0	0
$57$	1.00000	0.132453
$58$	7.52820	0.988501
$59$	−6.81255	−0.886918	−0.443459	−	0.896295i	$-0.646249\pi$
$59$	−6.81255	−0.886918	−0.443459	+	0.896295i	$0.646249\pi$
$60$	3.15280	0.407024
$61$	6.58432	0.843036	0.421518	−	0.906820i	$-0.361497\pi$
$61$	6.58432	0.843036	0.421518	+	0.906820i	$0.361497\pi$
$62$	−7.99551	−1.01543
$63$	0	0
$64$	1.00000	0.125000
$65$	5.38334	0.667721
$66$	6.08382	0.748866
$67$	−2.42167	−0.295854	−0.147927	−	0.988998i	$-0.547260\pi$
$67$	−2.42167	−0.295854	−0.147927	+	0.988998i	$0.547260\pi$
$68$	−6.58953	−0.799098
$69$	5.06183	0.609372
$70$	0	0
$71$	−0.0450445	−0.00534580	−0.00267290	−	0.999996i	$-0.500851\pi$
$71$	−0.0450445	−0.00534580	−0.00267290	+	0.999996i	$0.500851\pi$
$72$	1.00000	0.117851
$73$	14.1432	1.65533	0.827665	−	0.561222i	$-0.189669\pi$
$73$	14.1432	1.65533	0.827665	+	0.561222i	$0.189669\pi$
$74$	7.48072	0.869616
$75$	−4.94013	−0.570437
$76$	−1.00000	−0.114708
$77$	0	0
$78$	1.70748	0.193334
$79$	1.62666	0.183014	0.0915068	−	0.995804i	$-0.470832\pi$
$79$	1.62666	0.183014	0.0915068	+	0.995804i	$0.470832\pi$
$80$	−3.15280	−0.352493
$81$	1.00000	0.111111
$82$	4.03392	0.445471
$83$	−7.81806	−0.858143	−0.429072	−	0.903270i	$-0.641159\pi$
$83$	−7.81806	−0.858143	−0.429072	+	0.903270i	$0.641159\pi$
$84$	0	0
$85$	20.7755	2.25342
$86$	−11.2675	−1.21501
$87$	−7.52820	−0.807108
$88$	−6.08382	−0.648537
$89$	−11.9334	−1.26493	−0.632467	−	0.774587i	$-0.717958\pi$
$89$	−11.9334	−1.26493	−0.632467	+	0.774587i	$0.717958\pi$
$90$	−3.15280	−0.332334
$91$	0	0
$92$	−5.06183	−0.527732
$93$	7.99551	0.829096
$94$	5.60561	0.578174
$95$	3.15280	0.323470
$96$	−1.00000	−0.102062
$97$	−10.4076	−1.05673	−0.528365	−	0.849017i	$-0.677195\pi$
$97$	−10.4076	−1.05673	−0.528365	+	0.849017i	$0.677195\pi$
$98$	0	0
$99$	−6.08382	−0.611447
$100$	4.94013	0.494013
$101$	−15.6831	−1.56053	−0.780265	−	0.625450i	$-0.784916\pi$
$101$	−15.6831	−1.56053	−0.780265	+	0.625450i	$0.784916\pi$
$102$	6.58953	0.652461
$103$	−0.471586	−0.0464668	−0.0232334	−	0.999730i	$-0.507396\pi$
$103$	−0.471586	−0.0464668	−0.0232334	+	0.999730i	$0.507396\pi$
$104$	−1.70748	−0.167432
$105$	0	0
$106$	11.8620	1.15214
$107$	−1.60582	−0.155240	−0.0776202	−	0.996983i	$-0.524732\pi$
$107$	−1.60582	−0.155240	−0.0776202	+	0.996983i	$0.524732\pi$
$108$	−1.00000	−0.0962250
$109$	9.57478	0.917098	0.458549	−	0.888669i	$-0.348369\pi$
$109$	9.57478	0.917098	0.458549	+	0.888669i	$0.348369\pi$
$110$	19.1811	1.82884
$111$	−7.48072	−0.710039
$112$	0	0
$113$	−16.6914	−1.57019	−0.785097	−	0.619373i	$-0.787387\pi$
$113$	−16.6914	−1.57019	−0.785097	+	0.619373i	$0.787387\pi$
$114$	1.00000	0.0936586
$115$	15.9589	1.48818
$116$	7.52820	0.698976
$117$	−1.70748	−0.157857
$118$	−6.81255	−0.627146
$119$	0	0
$120$	3.15280	0.287810
$121$	26.0129	2.36481
$122$	6.58432	0.596117
$123$	−4.03392	−0.363726
$124$	−7.99551	−0.718018
$125$	0.188751	0.0168824
$126$	0	0
$127$	16.7710	1.48819	0.744094	−	0.668074i	$-0.232881\pi$
$127$	16.7710	1.48819	0.744094	+	0.668074i	$0.232881\pi$
$128$	1.00000	0.0883883
$129$	11.2675	0.992049
$130$	5.38334	0.472150
$131$	20.7429	1.81231	0.906157	−	0.422941i	$-0.139002\pi$
$131$	20.7429	1.81231	0.906157	+	0.422941i	$0.139002\pi$
$132$	6.08382	0.529529
$133$	0	0
$134$	−2.42167	−0.209200
$135$	3.15280	0.271350
$136$	−6.58953	−0.565048
$137$	−3.33617	−0.285028	−0.142514	−	0.989793i	$-0.545519\pi$
$137$	−3.33617	−0.285028	−0.142514	+	0.989793i	$0.545519\pi$
$138$	5.06183	0.430891
$139$	16.4451	1.39486	0.697429	−	0.716654i	$-0.254327\pi$
$139$	16.4451	1.39486	0.697429	+	0.716654i	$0.254327\pi$
$140$	0	0
$141$	−5.60561	−0.472077
$142$	−0.0450445	−0.00378005
$143$	10.3880	0.868689
$144$	1.00000	0.0833333
$145$	−23.7349	−1.97108
$146$	14.1432	1.17050
$147$	0	0
$148$	7.48072	0.614912
$149$	−9.66848	−0.792073	−0.396036	−	0.918235i	$-0.629615\pi$
$149$	−9.66848	−0.792073	−0.396036	+	0.918235i	$0.629615\pi$
$150$	−4.94013	−0.403360
$151$	5.80324	0.472261	0.236131	−	0.971721i	$-0.424121\pi$
$151$	5.80324	0.472261	0.236131	+	0.971721i	$0.424121\pi$
$152$	−1.00000	−0.0811107
$153$	−6.58953	−0.532732
$154$	0	0
$155$	25.2082	2.02477
$156$	1.70748	0.136708
$157$	2.93683	0.234385	0.117192	−	0.993109i	$-0.462611\pi$
$157$	2.93683	0.234385	0.117192	+	0.993109i	$0.462611\pi$
$158$	1.62666	0.129410
$159$	−11.8620	−0.940721
$160$	−3.15280	−0.249251
$161$	0	0
$162$	1.00000	0.0785674
$163$	−6.49895	−0.509037	−0.254519	−	0.967068i	$-0.581917\pi$
$163$	−6.49895	−0.509037	−0.254519	+	0.967068i	$0.581917\pi$
$164$	4.03392	0.314996
$165$	−19.1811	−1.49324
$166$	−7.81806	−0.606799
$167$	−15.4080	−1.19231	−0.596155	−	0.802869i	$-0.703306\pi$
$167$	−15.4080	−1.19231	−0.596155	+	0.802869i	$0.703306\pi$
$168$	0	0
$169$	−10.0845	−0.775731
$170$	20.7755	1.59341
$171$	−1.00000	−0.0764719
$172$	−11.2675	−0.859139
$173$	15.0434	1.14372	0.571862	−	0.820350i	$-0.306221\pi$
$173$	15.0434	1.14372	0.571862	+	0.820350i	$0.306221\pi$
$174$	−7.52820	−0.570712
$175$	0	0
$176$	−6.08382	−0.458585
$177$	6.81255	0.512062
$178$	−11.9334	−0.894444
$179$	−9.40014	−0.702599	−0.351300	−	0.936263i	$-0.614260\pi$
$179$	−9.40014	−0.702599	−0.351300	+	0.936263i	$0.614260\pi$
$180$	−3.15280	−0.234996
$181$	22.8987	1.70205	0.851023	−	0.525129i	$-0.175983\pi$
$181$	22.8987	1.70205	0.851023	+	0.525129i	$0.175983\pi$
$182$	0	0
$183$	−6.58432	−0.486727
$184$	−5.06183	−0.373163
$185$	−23.5852	−1.73402
$186$	7.99551	0.586259
$187$	40.0895	2.93164
$188$	5.60561	0.408831
$189$	0	0
$190$	3.15280	0.228728
$191$	−0.218710	−0.0158253	−0.00791264	−	0.999969i	$-0.502519\pi$
$191$	−0.218710	−0.0158253	−0.00791264	+	0.999969i	$0.502519\pi$
$192$	−1.00000	−0.0721688
$193$	−10.6905	−0.769517	−0.384758	−	0.923017i	$-0.625715\pi$
$193$	−10.6905	−0.769517	−0.384758	+	0.923017i	$0.625715\pi$
$194$	−10.4076	−0.747222
$195$	−5.38334	−0.385509
$196$	0	0
$197$	15.1489	1.07932	0.539658	−	0.841884i	$-0.318554\pi$
$197$	15.1489	1.07932	0.539658	+	0.841884i	$0.318554\pi$
$198$	−6.08382	−0.432358
$199$	−5.30035	−0.375732	−0.187866	−	0.982195i	$-0.560157\pi$
$199$	−5.30035	−0.375732	−0.187866	+	0.982195i	$0.560157\pi$
$200$	4.94013	0.349320
$201$	2.42167	0.170811
$202$	−15.6831	−1.10346
$203$	0	0
$204$	6.58953	0.461360
$205$	−12.7181	−0.888272
$206$	−0.471586	−0.0328570
$207$	−5.06183	−0.351821
$208$	−1.70748	−0.118392
$209$	6.08382	0.420827
$210$	0	0
$211$	9.41487	0.648147	0.324073	−	0.946032i	$-0.394948\pi$
$211$	9.41487	0.648147	0.324073	+	0.946032i	$0.394948\pi$
$212$	11.8620	0.814689
$213$	0.0450445	0.00308640
$214$	−1.60582	−0.109772
$215$	35.5242	2.42273
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	9.57478	0.648486
$219$	−14.1432	−0.955706
$220$	19.1811	1.29319
$221$	11.2515	0.756858
$222$	−7.48072	−0.502073
$223$	18.0161	1.20645	0.603223	−	0.797573i	$-0.293883\pi$
$223$	18.0161	1.20645	0.603223	+	0.797573i	$0.293883\pi$
$224$	0	0
$225$	4.94013	0.329342
$226$	−16.6914	−1.11029
$227$	−18.7078	−1.24168	−0.620839	−	0.783938i	$-0.713208\pi$
$227$	−18.7078	−1.24168	−0.620839	+	0.783938i	$0.713208\pi$
$228$	1.00000	0.0662266
$229$	10.6854	0.706111	0.353056	−	0.935602i	$-0.385143\pi$
$229$	10.6854	0.706111	0.353056	+	0.935602i	$0.385143\pi$
$230$	15.9589	1.05230
$231$	0	0
$232$	7.52820	0.494251
$233$	−14.7049	−0.963349	−0.481675	−	0.876350i	$-0.659971\pi$
$233$	−14.7049	−0.963349	−0.481675	+	0.876350i	$0.659971\pi$
$234$	−1.70748	−0.111622
$235$	−17.6733	−1.15288
$236$	−6.81255	−0.443459
$237$	−1.62666	−0.105663
$238$	0	0
$239$	14.1590	0.915870	0.457935	−	0.888986i	$-0.348589\pi$
$239$	14.1590	0.915870	0.457935	+	0.888986i	$0.348589\pi$
$240$	3.15280	0.203512
$241$	−24.9596	−1.60779	−0.803896	−	0.594770i	$-0.797243\pi$
$241$	−24.9596	−1.60779	−0.803896	+	0.594770i	$0.797243\pi$
$242$	26.0129	1.67217
$243$	−1.00000	−0.0641500
$244$	6.58432	0.421518
$245$	0	0
$246$	−4.03392	−0.257193
$247$	1.70748	0.108644
$248$	−7.99551	−0.507716
$249$	7.81806	0.495449
$250$	0.188751	0.0119377
$251$	20.2036	1.27524	0.637619	−	0.770352i	$-0.279919\pi$
$251$	20.2036	1.27524	0.637619	+	0.770352i	$0.279919\pi$
$252$	0	0
$253$	30.7952	1.93608
$254$	16.7710	1.05231
$255$	−20.7755	−1.30101
$256$	1.00000	0.0625000
$257$	16.1803	1.00930	0.504648	−	0.863325i	$-0.331622\pi$
$257$	16.1803	1.00930	0.504648	+	0.863325i	$0.331622\pi$
$258$	11.2675	0.701484
$259$	0	0
$260$	5.38334	0.333861
$261$	7.52820	0.465984
$262$	20.7429	1.28150
$263$	−25.5609	−1.57615	−0.788075	−	0.615579i	$-0.788922\pi$
$263$	−25.5609	−1.57615	−0.788075	+	0.615579i	$0.788922\pi$
$264$	6.08382	0.374433
$265$	−37.3986	−2.29738
$266$	0	0
$267$	11.9334	0.730310
$268$	−2.42167	−0.147927
$269$	−1.76102	−0.107371	−0.0536856	−	0.998558i	$-0.517097\pi$
$269$	−1.76102	−0.107371	−0.0536856	+	0.998558i	$0.517097\pi$
$270$	3.15280	0.191873
$271$	0.579250	0.0351870	0.0175935	−	0.999845i	$-0.494400\pi$
$271$	0.579250	0.0351870	0.0175935	+	0.999845i	$0.494400\pi$
$272$	−6.58953	−0.399549
$273$	0	0
$274$	−3.33617	−0.201545
$275$	−30.0549	−1.81238
$276$	5.06183	0.304686
$277$	9.94397	0.597475	0.298738	−	0.954335i	$-0.403434\pi$
$277$	9.94397	0.597475	0.298738	+	0.954335i	$0.403434\pi$
$278$	16.4451	0.986313
$279$	−7.99551	−0.478679
$280$	0	0
$281$	0.910434	0.0543119	0.0271560	−	0.999631i	$-0.491355\pi$
$281$	0.910434	0.0543119	0.0271560	+	0.999631i	$0.491355\pi$
$282$	−5.60561	−0.333809
$283$	8.84942	0.526044	0.263022	−	0.964790i	$-0.415281\pi$
$283$	8.84942	0.526044	0.263022	+	0.964790i	$0.415281\pi$
$284$	−0.0450445	−0.00267290
$285$	−3.15280	−0.186756
$286$	10.3880	0.614256
$287$	0	0
$288$	1.00000	0.0589256
$289$	26.4219	1.55423
$290$	−23.7349	−1.39376
$291$	10.4076	0.610104
$292$	14.1432	0.827665
$293$	−2.58520	−0.151029	−0.0755144	−	0.997145i	$-0.524060\pi$
$293$	−2.58520	−0.151029	−0.0755144	+	0.997145i	$0.524060\pi$
$294$	0	0
$295$	21.4786	1.25053
$296$	7.48072	0.434808
$297$	6.08382	0.353019
$298$	−9.66848	−0.560080
$299$	8.64297	0.499836
$300$	−4.94013	−0.285219
$301$	0	0
$302$	5.80324	0.333939
$303$	15.6831	0.900972
$304$	−1.00000	−0.0573539
$305$	−20.7590	−1.18866
$306$	−6.58953	−0.376699
$307$	18.9892	1.08377	0.541886	−	0.840452i	$-0.317711\pi$
$307$	18.9892	1.08377	0.541886	+	0.840452i	$0.317711\pi$
$308$	0	0
$309$	0.471586	0.0268276
$310$	25.2082	1.43173
$311$	−2.74265	−0.155521	−0.0777607	−	0.996972i	$-0.524777\pi$
$311$	−2.74265	−0.155521	−0.0777607	+	0.996972i	$0.524777\pi$
$312$	1.70748	0.0966671
$313$	29.1231	1.64614	0.823069	−	0.567942i	$-0.192260\pi$
$313$	29.1231	1.64614	0.823069	+	0.567942i	$0.192260\pi$
$314$	2.93683	0.165735
$315$	0	0
$316$	1.62666	0.0915068
$317$	−1.14052	−0.0640578	−0.0320289	−	0.999487i	$-0.510197\pi$
$317$	−1.14052	−0.0640578	−0.0320289	+	0.999487i	$0.510197\pi$
$318$	−11.8620	−0.665190
$319$	−45.8002	−2.56432
$320$	−3.15280	−0.176247
$321$	1.60582	0.0896281
$322$	0	0
$323$	6.58953	0.366651
$324$	1.00000	0.0555556
$325$	−8.43518	−0.467900
$326$	−6.49895	−0.359944
$327$	−9.57478	−0.529487
$328$	4.03392	0.222736
$329$	0	0
$330$	−19.1811	−1.05588
$331$	−24.3035	−1.33584	−0.667922	−	0.744231i	$-0.732816\pi$
$331$	−24.3035	−1.33584	−0.667922	+	0.744231i	$0.732816\pi$
$332$	−7.81806	−0.429072
$333$	7.48072	0.409941
$334$	−15.4080	−0.843090
$335$	7.63502	0.417146
$336$	0	0
$337$	3.05203	0.166255	0.0831274	−	0.996539i	$-0.473509\pi$
$337$	3.05203	0.166255	0.0831274	+	0.996539i	$0.473509\pi$
$338$	−10.0845	−0.548525
$339$	16.6914	0.906552
$340$	20.7755	1.12671
$341$	48.6433	2.63418
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	−11.2675	−0.607503
$345$	−15.9589	−0.859199
$346$	15.0434	0.808736
$347$	31.7752	1.70578	0.852892	−	0.522087i	$-0.174846\pi$
$347$	31.7752	1.70578	0.852892	+	0.522087i	$0.174846\pi$
$348$	−7.52820	−0.403554
$349$	−9.76083	−0.522485	−0.261243	−	0.965273i	$-0.584132\pi$
$349$	−9.76083	−0.522485	−0.261243	+	0.965273i	$0.584132\pi$
$350$	0	0
$351$	1.70748	0.0911386
$352$	−6.08382	−0.324269
$353$	31.8204	1.69363	0.846815	−	0.531887i	$-0.178517\pi$
$353$	31.8204	1.69363	0.846815	+	0.531887i	$0.178517\pi$
$354$	6.81255	0.362083
$355$	0.142016	0.00753744
$356$	−11.9334	−0.632467
$357$	0	0
$358$	−9.40014	−0.496813
$359$	11.8217	0.623925	0.311963	−	0.950094i	$-0.399014\pi$
$359$	11.8217	0.623925	0.311963	+	0.950094i	$0.399014\pi$
$360$	−3.15280	−0.166167
$361$	1.00000	0.0526316
$362$	22.8987	1.20353
$363$	−26.0129	−1.36532
$364$	0	0
$365$	−44.5905	−2.33397
$366$	−6.58432	−0.344168
$367$	3.46070	0.180647	0.0903235	−	0.995912i	$-0.471210\pi$
$367$	3.46070	0.180647	0.0903235	+	0.995912i	$0.471210\pi$
$368$	−5.06183	−0.263866
$369$	4.03392	0.209997
$370$	−23.5852	−1.22614
$371$	0	0
$372$	7.99551	0.414548
$373$	−30.3768	−1.57285	−0.786425	−	0.617685i	$-0.788071\pi$
$373$	−30.3768	−1.57285	−0.786425	+	0.617685i	$0.788071\pi$
$374$	40.0895	2.07298
$375$	−0.188751	−0.00974706
$376$	5.60561	0.289087
$377$	−12.8543	−0.662028
$378$	0	0
$379$	4.99785	0.256722	0.128361	−	0.991728i	$-0.459028\pi$
$379$	4.99785	0.256722	0.128361	+	0.991728i	$0.459028\pi$
$380$	3.15280	0.161735
$381$	−16.7710	−0.859206
$382$	−0.218710	−0.0111902
$383$	−27.1295	−1.38625	−0.693126	−	0.720817i	$-0.743767\pi$
$383$	−27.1295	−1.38625	−0.693126	+	0.720817i	$0.743767\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−10.6905	−0.544131
$387$	−11.2675	−0.572760
$388$	−10.4076	−0.528365
$389$	0.147945	0.00750112	0.00375056	−	0.999993i	$-0.498806\pi$
$389$	0.147945	0.00750112	0.00375056	+	0.999993i	$0.498806\pi$
$390$	−5.38334	−0.272596
$391$	33.3551	1.68684
$392$	0	0
$393$	−20.7429	−1.04634
$394$	15.1489	0.763192
$395$	−5.12853	−0.258044
$396$	−6.08382	−0.305723
$397$	7.69901	0.386402	0.193201	−	0.981159i	$-0.438113\pi$
$397$	7.69901	0.386402	0.193201	+	0.981159i	$0.438113\pi$
$398$	−5.30035	−0.265683
$399$	0	0
$400$	4.94013	0.247007
$401$	−11.9453	−0.596518	−0.298259	−	0.954485i	$-0.596406\pi$
$401$	−11.9453	−0.596518	−0.298259	+	0.954485i	$0.596406\pi$
$402$	2.42167	0.120782
$403$	13.6522	0.680064
$404$	−15.6831	−0.780265
$405$	−3.15280	−0.156664
$406$	0	0
$407$	−45.5114	−2.25591
$408$	6.58953	0.326231
$409$	3.58359	0.177197	0.0885985	−	0.996067i	$-0.471761\pi$
$409$	3.58359	0.177197	0.0885985	+	0.996067i	$0.471761\pi$
$410$	−12.7181	−0.628103
$411$	3.33617	0.164561
$412$	−0.471586	−0.0232334
$413$	0	0
$414$	−5.06183	−0.248775
$415$	24.6488	1.20996
$416$	−1.70748	−0.0837161
$417$	−16.4451	−0.805321
$418$	6.08382	0.297569
$419$	−12.9062	−0.630508	−0.315254	−	0.949007i	$-0.602090\pi$
$419$	−12.9062	−0.630508	−0.315254	+	0.949007i	$0.602090\pi$
$420$	0	0
$421$	13.8465	0.674836	0.337418	−	0.941355i	$-0.390446\pi$
$421$	13.8465	0.674836	0.337418	+	0.941355i	$0.390446\pi$
$422$	9.41487	0.458309
$423$	5.60561	0.272554
$424$	11.8620	0.576072
$425$	−32.5532	−1.57906
$426$	0.0450445	0.00218242
$427$	0	0
$428$	−1.60582	−0.0776202
$429$	−10.3880	−0.501538
$430$	35.5242	1.71313
$431$	3.53073	0.170070	0.0850348	−	0.996378i	$-0.472900\pi$
$431$	3.53073	0.170070	0.0850348	+	0.996378i	$0.472900\pi$
$432$	−1.00000	−0.0481125
$433$	13.7760	0.662033	0.331016	−	0.943625i	$-0.392608\pi$
$433$	13.7760	0.662033	0.331016	+	0.943625i	$0.392608\pi$
$434$	0	0
$435$	23.7349	1.13800
$436$	9.57478	0.458549
$437$	5.06183	0.242140
$438$	−14.1432	−0.675786
$439$	−14.7088	−0.702013	−0.351007	−	0.936373i	$-0.614161\pi$
$439$	−14.7088	−0.702013	−0.351007	+	0.936373i	$0.614161\pi$
$440$	19.1811	0.914421
$441$	0	0
$442$	11.2515	0.535179
$443$	−30.4613	−1.44726	−0.723630	−	0.690188i	$-0.757528\pi$
$443$	−30.4613	−1.44726	−0.723630	+	0.690188i	$0.757528\pi$
$444$	−7.48072	−0.355019
$445$	37.6235	1.78352
$446$	18.0161	0.853086
$447$	9.66848	0.457303
$448$	0	0
$449$	−24.3814	−1.15063	−0.575315	−	0.817932i	$-0.695120\pi$
$449$	−24.3814	−1.15063	−0.575315	+	0.817932i	$0.695120\pi$
$450$	4.94013	0.232880
$451$	−24.5416	−1.15562
$452$	−16.6914	−0.785097
$453$	−5.80324	−0.272660
$454$	−18.7078	−0.877999
$455$	0	0
$456$	1.00000	0.0468293
$457$	−22.6911	−1.06145	−0.530723	−	0.847546i	$-0.678079\pi$
$457$	−22.6911	−1.06145	−0.530723	+	0.847546i	$0.678079\pi$
$458$	10.6854	0.499296
$459$	6.58953	0.307573
$460$	15.9589	0.744088
$461$	−26.5199	−1.23516	−0.617578	−	0.786509i	$-0.711886\pi$
$461$	−26.5199	−1.23516	−0.617578	+	0.786509i	$0.711886\pi$
$462$	0	0
$463$	13.3201	0.619040	0.309520	−	0.950893i	$-0.399832\pi$
$463$	13.3201	0.619040	0.309520	+	0.950893i	$0.399832\pi$
$464$	7.52820	0.349488
$465$	−25.2082	−1.16900
$466$	−14.7049	−0.681191
$467$	−6.02533	−0.278819	−0.139409	−	0.990235i	$-0.544520\pi$
$467$	−6.02533	−0.278819	−0.139409	+	0.990235i	$0.544520\pi$
$468$	−1.70748	−0.0789283
$469$	0	0
$470$	−17.6733	−0.815211
$471$	−2.93683	−0.135322
$472$	−6.81255	−0.313573
$473$	68.5495	3.15191
$474$	−1.62666	−0.0747150
$475$	−4.94013	−0.226669
$476$	0	0
$477$	11.8620	0.543126
$478$	14.1590	0.647618
$479$	2.61758	0.119600	0.0598002	−	0.998210i	$-0.480954\pi$
$479$	2.61758	0.119600	0.0598002	+	0.998210i	$0.480954\pi$
$480$	3.15280	0.143905
$481$	−12.7732	−0.582407
$482$	−24.9596	−1.13688
$483$	0	0
$484$	26.0129	1.18240
$485$	32.8130	1.48996
$486$	−1.00000	−0.0453609
$487$	−20.7106	−0.938489	−0.469245	−	0.883068i	$-0.655474\pi$
$487$	−20.7106	−0.938489	−0.469245	+	0.883068i	$0.655474\pi$
$488$	6.58432	0.298058
$489$	6.49895	0.293893
$490$	0	0
$491$	32.4892	1.46622	0.733108	−	0.680112i	$-0.238069\pi$
$491$	32.4892	1.46622	0.733108	+	0.680112i	$0.238069\pi$
$492$	−4.03392	−0.181863
$493$	−49.6073	−2.23420
$494$	1.70748	0.0768232
$495$	19.1811	0.862124
$496$	−7.99551	−0.359009
$497$	0	0
$498$	7.81806	0.350336
$499$	−3.35867	−0.150355	−0.0751774	−	0.997170i	$-0.523952\pi$
$499$	−3.35867	−0.150355	−0.0751774	+	0.997170i	$0.523952\pi$
$500$	0.188751	0.00844121
$501$	15.4080	0.688380
$502$	20.2036	0.901730
$503$	−6.44710	−0.287462	−0.143731	−	0.989617i	$-0.545910\pi$
$503$	−6.44710	−0.287462	−0.143731	+	0.989617i	$0.545910\pi$
$504$	0	0
$505$	49.4457	2.20031
$506$	30.7952	1.36902
$507$	10.0845	0.447869
$508$	16.7710	0.744094
$509$	8.05014	0.356816	0.178408	−	0.983957i	$-0.442905\pi$
$509$	8.05014	0.356816	0.178408	+	0.983957i	$0.442905\pi$
$510$	−20.7755	−0.919953
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	16.1803	0.713680
$515$	1.48682	0.0655170
$516$	11.2675	0.496024
$517$	−34.1035	−1.49987
$518$	0	0
$519$	−15.0434	−0.660330
$520$	5.38334	0.236075
$521$	26.2404	1.14961	0.574807	−	0.818289i	$-0.305077\pi$
$521$	26.2404	1.14961	0.574807	+	0.818289i	$0.305077\pi$
$522$	7.52820	0.329500
$523$	−2.96545	−0.129670	−0.0648350	−	0.997896i	$-0.520652\pi$
$523$	−2.96545	−0.129670	−0.0648350	+	0.997896i	$0.520652\pi$
$524$	20.7429	0.906157
$525$	0	0
$526$	−25.5609	−1.11451
$527$	52.6867	2.29507
$528$	6.08382	0.264764
$529$	2.62209	0.114004
$530$	−37.3986	−1.62449
$531$	−6.81255	−0.295639
$532$	0	0
$533$	−6.88783	−0.298345
$534$	11.9334	0.516407
$535$	5.06283	0.218885
$536$	−2.42167	−0.104600
$537$	9.40014	0.405646
$538$	−1.76102	−0.0759229
$539$	0	0
$540$	3.15280	0.135675
$541$	22.0699	0.948861	0.474430	−	0.880293i	$-0.342654\pi$
$541$	22.0699	0.948861	0.474430	+	0.880293i	$0.342654\pi$
$542$	0.579250	0.0248809
$543$	−22.8987	−0.982677
$544$	−6.58953	−0.282524
$545$	−30.1873	−1.29308
$546$	0	0
$547$	16.1582	0.690874	0.345437	−	0.938442i	$-0.387731\pi$
$547$	16.1582	0.690874	0.345437	+	0.938442i	$0.387731\pi$
$548$	−3.33617	−0.142514
$549$	6.58432	0.281012
$550$	−30.0549	−1.28154
$551$	−7.52820	−0.320712
$552$	5.06183	0.215446
$553$	0	0
$554$	9.94397	0.422479
$555$	23.5852	1.00114
$556$	16.4451	0.697429
$557$	−26.6192	−1.12789	−0.563947	−	0.825811i	$-0.690718\pi$
$557$	−26.6192	−1.12789	−0.563947	+	0.825811i	$0.690718\pi$
$558$	−7.99551	−0.338477
$559$	19.2391	0.813725
$560$	0	0
$561$	−40.0895	−1.69258
$562$	0.910434	0.0384043
$563$	4.92337	0.207495	0.103748	−	0.994604i	$-0.466917\pi$
$563$	4.92337	0.207495	0.103748	+	0.994604i	$0.466917\pi$
$564$	−5.60561	−0.236039
$565$	52.6246	2.21393
$566$	8.84942	0.371969
$567$	0	0
$568$	−0.0450445	−0.00189003
$569$	−38.3564	−1.60799	−0.803993	−	0.594639i	$-0.797295\pi$
$569$	−38.3564	−1.60799	−0.803993	+	0.594639i	$0.797295\pi$
$570$	−3.15280	−0.132056
$571$	10.6756	0.446762	0.223381	−	0.974731i	$-0.428291\pi$
$571$	10.6756	0.446762	0.223381	+	0.974731i	$0.428291\pi$
$572$	10.3880	0.434344
$573$	0.218710	0.00913673
$574$	0	0
$575$	−25.0061	−1.04283
$576$	1.00000	0.0416667
$577$	−7.04990	−0.293491	−0.146746	−	0.989174i	$-0.546880\pi$
$577$	−7.04990	−0.293491	−0.146746	+	0.989174i	$0.546880\pi$
$578$	26.4219	1.09901
$579$	10.6905	0.444281
$580$	−23.7349	−0.985538
$581$	0	0
$582$	10.4076	0.431409
$583$	−72.1665	−2.98883
$584$	14.1432	0.585248
$585$	5.38334	0.222574
$586$	−2.58520	−0.106794
$587$	−5.40207	−0.222967	−0.111484	−	0.993766i	$-0.535560\pi$
$587$	−5.40207	−0.222967	−0.111484	+	0.993766i	$0.535560\pi$
$588$	0	0
$589$	7.99551	0.329449
$590$	21.4786	0.884259
$591$	−15.1489	−0.623143
$592$	7.48072	0.307456
$593$	1.30355	0.0535304	0.0267652	−	0.999642i	$-0.491479\pi$
$593$	1.30355	0.0535304	0.0267652	+	0.999642i	$0.491479\pi$
$594$	6.08382	0.249622
$595$	0	0
$596$	−9.66848	−0.396036
$597$	5.30035	0.216929
$598$	8.64297	0.353437
$599$	30.0129	1.22629	0.613147	−	0.789969i	$-0.289903\pi$
$599$	30.0129	1.22629	0.613147	+	0.789969i	$0.289903\pi$
$600$	−4.94013	−0.201680
$601$	7.16469	0.292254	0.146127	−	0.989266i	$-0.453319\pi$
$601$	7.16469	0.292254	0.146127	+	0.989266i	$0.453319\pi$
$602$	0	0
$603$	−2.42167	−0.0986179
$604$	5.80324	0.236131
$605$	−82.0133	−3.33431
$606$	15.6831	0.637083
$607$	−14.9050	−0.604974	−0.302487	−	0.953153i	$-0.597817\pi$
$607$	−14.9050	−0.604974	−0.302487	+	0.953153i	$0.597817\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	−20.7590	−0.840509
$611$	−9.57147	−0.387220
$612$	−6.58953	−0.266366
$613$	−16.7415	−0.676183	−0.338092	−	0.941113i	$-0.609781\pi$
$613$	−16.7415	−0.676183	−0.338092	+	0.941113i	$0.609781\pi$
$614$	18.9892	0.766342
$615$	12.7181	0.512844
$616$	0	0
$617$	23.8495	0.960144	0.480072	−	0.877229i	$-0.340611\pi$
$617$	23.8495	0.960144	0.480072	+	0.877229i	$0.340611\pi$
$618$	0.471586	0.0189700
$619$	2.39119	0.0961100	0.0480550	−	0.998845i	$-0.484698\pi$
$619$	2.39119	0.0961100	0.0480550	+	0.998845i	$0.484698\pi$
$620$	25.2082	1.01239
$621$	5.06183	0.203124
$622$	−2.74265	−0.109970
$623$	0	0
$624$	1.70748	0.0683539
$625$	−25.2958	−1.01183
$626$	29.1231	1.16399
$627$	−6.08382	−0.242964
$628$	2.93683	0.117192
$629$	−49.2945	−1.96550
$630$	0	0
$631$	−30.9272	−1.23119	−0.615596	−	0.788062i	$-0.711085\pi$
$631$	−30.9272	−1.23119	−0.615596	+	0.788062i	$0.711085\pi$
$632$	1.62666	0.0647050
$633$	−9.41487	−0.374208
$634$	−1.14052	−0.0452957
$635$	−52.8757	−2.09831
$636$	−11.8620	−0.470361
$637$	0	0
$638$	−45.8002	−1.81325
$639$	−0.0450445	−0.00178193
$640$	−3.15280	−0.124625
$641$	41.2399	1.62888	0.814439	−	0.580249i	$-0.197045\pi$
$641$	41.2399	1.62888	0.814439	+	0.580249i	$0.197045\pi$
$642$	1.60582	0.0633767
$643$	−41.0637	−1.61940	−0.809698	−	0.586847i	$-0.800369\pi$
$643$	−41.0637	−1.61940	−0.809698	+	0.586847i	$0.800369\pi$
$644$	0	0
$645$	−35.5242	−1.39876
$646$	6.58953	0.259262
$647$	15.2089	0.597922	0.298961	−	0.954265i	$-0.403360\pi$
$647$	15.2089	0.597922	0.298961	+	0.954265i	$0.403360\pi$
$648$	1.00000	0.0392837
$649$	41.4463	1.62691
$650$	−8.43518	−0.330855
$651$	0	0
$652$	−6.49895	−0.254519
$653$	27.6795	1.08318	0.541592	−	0.840641i	$-0.317822\pi$
$653$	27.6795	1.08318	0.541592	+	0.840641i	$0.317822\pi$
$654$	−9.57478	−0.374404
$655$	−65.3981	−2.55532
$656$	4.03392	0.157498
$657$	14.1432	0.551777
$658$	0	0
$659$	−44.6472	−1.73921	−0.869605	−	0.493749i	$-0.835626\pi$
$659$	−44.6472	−1.73921	−0.869605	+	0.493749i	$0.835626\pi$
$660$	−19.1811	−0.746621
$661$	24.9619	0.970907	0.485454	−	0.874262i	$-0.338654\pi$
$661$	24.9619	0.970907	0.485454	+	0.874262i	$0.338654\pi$
$662$	−24.3035	−0.944584
$663$	−11.2515	−0.436972
$664$	−7.81806	−0.303400
$665$	0	0
$666$	7.48072	0.289872
$667$	−38.1065	−1.47549
$668$	−15.4080	−0.596155
$669$	−18.0161	−0.696542
$670$	7.63502	0.294967
$671$	−40.0578	−1.54642
$672$	0	0
$673$	−49.1601	−1.89498	−0.947492	−	0.319779i	$-0.896391\pi$
$673$	−49.1601	−1.89498	−0.947492	+	0.319779i	$0.896391\pi$
$674$	3.05203	0.117560
$675$	−4.94013	−0.190146
$676$	−10.0845	−0.387866
$677$	11.9740	0.460198	0.230099	−	0.973167i	$-0.426095\pi$
$677$	11.9740	0.460198	0.230099	+	0.973167i	$0.426095\pi$
$678$	16.6914	0.641029
$679$	0	0
$680$	20.7755	0.796703
$681$	18.7078	0.716883
$682$	48.6433	1.86265
$683$	29.0000	1.10965	0.554827	−	0.831966i	$-0.312785\pi$
$683$	29.0000	1.10965	0.554827	+	0.831966i	$0.312785\pi$
$684$	−1.00000	−0.0382360
$685$	10.5183	0.401882
$686$	0	0
$687$	−10.6854	−0.407673
$688$	−11.2675	−0.429570
$689$	−20.2542	−0.771624
$690$	−15.9589	−0.607545
$691$	−15.7727	−0.600021	−0.300011	−	0.953936i	$-0.596990\pi$
$691$	−15.7727	−0.600021	−0.300011	+	0.953936i	$0.596990\pi$
$692$	15.0434	0.571862
$693$	0	0
$694$	31.7752	1.20617
$695$	−51.8482	−1.96671
$696$	−7.52820	−0.285356
$697$	−26.5816	−1.00685
$698$	−9.76083	−0.369453
$699$	14.7049	0.556190
$700$	0	0
$701$	−29.1610	−1.10140	−0.550699	−	0.834704i	$-0.685639\pi$
$701$	−29.1610	−1.10140	−0.550699	+	0.834704i	$0.685639\pi$
$702$	1.70748	0.0644447
$703$	−7.48072	−0.282141
$704$	−6.08382	−0.229293
$705$	17.6733	0.665617
$706$	31.8204	1.19758
$707$	0	0
$708$	6.81255	0.256031
$709$	29.0789	1.09208	0.546040	−	0.837759i	$-0.316135\pi$
$709$	29.0789	1.09208	0.546040	+	0.837759i	$0.316135\pi$
$710$	0.142016	0.00532978
$711$	1.62666	0.0610045
$712$	−11.9334	−0.447222
$713$	40.4719	1.51568
$714$	0	0
$715$	−32.7513	−1.22483
$716$	−9.40014	−0.351300
$717$	−14.1590	−0.528778
$718$	11.8217	0.441182
$719$	−28.0291	−1.04531	−0.522655	−	0.852544i	$-0.675058\pi$
$719$	−28.0291	−1.04531	−0.522655	+	0.852544i	$0.675058\pi$
$720$	−3.15280	−0.117498
$721$	0	0
$722$	1.00000	0.0372161
$723$	24.9596	0.928259
$724$	22.8987	0.851023
$725$	37.1903	1.38121
$726$	−26.0129	−0.965428
$727$	−19.6035	−0.727052	−0.363526	−	0.931584i	$-0.618427\pi$
$727$	−19.6035	−0.727052	−0.363526	+	0.931584i	$0.618427\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−44.5905	−1.65037
$731$	74.2476	2.74615
$732$	−6.58432	−0.243364
$733$	−15.1043	−0.557890	−0.278945	−	0.960307i	$-0.589985\pi$
$733$	−15.1043	−0.557890	−0.278945	+	0.960307i	$0.589985\pi$
$734$	3.46070	0.127737
$735$	0	0
$736$	−5.06183	−0.186581
$737$	14.7330	0.542696
$738$	4.03392	0.148490
$739$	−25.9885	−0.956003	−0.478002	−	0.878359i	$-0.658639\pi$
$739$	−25.9885	−0.956003	−0.478002	+	0.878359i	$0.658639\pi$
$740$	−23.5852	−0.867009
$741$	−1.70748	−0.0627259
$742$	0	0
$743$	−13.5597	−0.497457	−0.248728	−	0.968573i	$-0.580013\pi$
$743$	−13.5597	−0.497457	−0.248728	+	0.968573i	$0.580013\pi$
$744$	7.99551	0.293130
$745$	30.4828	1.11680
$746$	−30.3768	−1.11217
$747$	−7.81806	−0.286048
$748$	40.0895	1.46582
$749$	0	0
$750$	−0.188751	−0.00689222
$751$	25.6828	0.937179	0.468590	−	0.883416i	$-0.344762\pi$
$751$	25.6828	0.937179	0.468590	+	0.883416i	$0.344762\pi$
$752$	5.60561	0.204416
$753$	−20.2036	−0.736260
$754$	−12.8543	−0.468125
$755$	−18.2965	−0.665876
$756$	0	0
$757$	28.9764	1.05316	0.526582	−	0.850124i	$-0.323473\pi$
$757$	28.9764	1.05316	0.526582	+	0.850124i	$0.323473\pi$
$758$	4.99785	0.181530
$759$	−30.7952	−1.11780
$760$	3.15280	0.114364
$761$	47.2682	1.71347	0.856736	−	0.515755i	$-0.172489\pi$
$761$	47.2682	1.71347	0.856736	+	0.515755i	$0.172489\pi$
$762$	−16.7710	−0.607551
$763$	0	0
$764$	−0.218710	−0.00791264
$765$	20.7755	0.751139
$766$	−27.1295	−0.980228
$767$	11.6323	0.420018
$768$	−1.00000	−0.0360844
$769$	0.766929	0.0276562	0.0138281	−	0.999904i	$-0.495598\pi$
$769$	0.766929	0.0276562	0.0138281	+	0.999904i	$0.495598\pi$
$770$	0	0
$771$	−16.1803	−0.582717
$772$	−10.6905	−0.384758
$773$	−47.3400	−1.70270	−0.851352	−	0.524596i	$-0.824217\pi$
$773$	−47.3400	−1.70270	−0.851352	+	0.524596i	$0.824217\pi$
$774$	−11.2675	−0.405002
$775$	−39.4989	−1.41884
$776$	−10.4076	−0.373611
$777$	0	0
$778$	0.147945	0.00530409
$779$	−4.03392	−0.144530
$780$	−5.38334	−0.192755
$781$	0.274043	0.00980603
$782$	33.3551	1.19278
$783$	−7.52820	−0.269036
$784$	0	0
$785$	−9.25924	−0.330476
$786$	−20.7429	−0.739874
$787$	23.3679	0.832974	0.416487	−	0.909142i	$-0.363261\pi$
$787$	23.3679	0.832974	0.416487	+	0.909142i	$0.363261\pi$
$788$	15.1489	0.539658
$789$	25.5609	0.909991
$790$	−5.12853	−0.182465
$791$	0	0
$792$	−6.08382	−0.216179
$793$	−11.2426	−0.399237
$794$	7.69901	0.273228
$795$	37.3986	1.32639
$796$	−5.30035	−0.187866
$797$	−3.34541	−0.118500	−0.0592502	−	0.998243i	$-0.518871\pi$
$797$	−3.34541	−0.118500	−0.0592502	+	0.998243i	$0.518871\pi$
$798$	0	0
$799$	−36.9383	−1.30678
$800$	4.94013	0.174660
$801$	−11.9334	−0.421645
$802$	−11.9453	−0.421802
$803$	−86.0444	−3.03644
$804$	2.42167	0.0854056
$805$	0	0
$806$	13.6522	0.480878
$807$	1.76102	0.0619908
$808$	−15.6831	−0.551730
$809$	1.55976	0.0548384	0.0274192	−	0.999624i	$-0.491271\pi$
$809$	1.55976	0.0548384	0.0274192	+	0.999624i	$0.491271\pi$
$810$	−3.15280	−0.110778
$811$	47.6564	1.67344	0.836721	−	0.547629i	$-0.184470\pi$
$811$	47.6564	1.67344	0.836721	+	0.547629i	$0.184470\pi$
$812$	0	0
$813$	−0.579250	−0.0203152
$814$	−45.5114	−1.59517
$815$	20.4899	0.717729
$816$	6.58953	0.230680
$817$	11.2675	0.394200
$818$	3.58359	0.125297
$819$	0	0
$820$	−12.7181	−0.444136
$821$	−39.5519	−1.38037	−0.690186	−	0.723632i	$-0.742471\pi$
$821$	−39.5519	−1.38037	−0.690186	+	0.723632i	$0.742471\pi$
$822$	3.33617	0.116362
$823$	−41.6956	−1.45342	−0.726709	−	0.686946i	$-0.758951\pi$
$823$	−41.6956	−1.45342	−0.726709	+	0.686946i	$0.758951\pi$
$824$	−0.471586	−0.0164285
$825$	30.0549	1.04638
$826$	0	0
$827$	38.9501	1.35443	0.677214	−	0.735786i	$-0.263187\pi$
$827$	38.9501	1.35443	0.677214	+	0.735786i	$0.263187\pi$
$828$	−5.06183	−0.175911
$829$	28.6706	0.995772	0.497886	−	0.867242i	$-0.334110\pi$
$829$	28.6706	0.995772	0.497886	+	0.867242i	$0.334110\pi$
$830$	24.6488	0.855571
$831$	−9.94397	−0.344952
$832$	−1.70748	−0.0591962
$833$	0	0
$834$	−16.4451	−0.569448
$835$	48.5784	1.68113
$836$	6.08382	0.210413
$837$	7.99551	0.276365
$838$	−12.9062	−0.445836
$839$	−12.6879	−0.438033	−0.219017	−	0.975721i	$-0.570285\pi$
$839$	−12.6879	−0.438033	−0.219017	+	0.975721i	$0.570285\pi$
$840$	0	0
$841$	27.6738	0.954270
$842$	13.8465	0.477181
$843$	−0.910434	−0.0313570
$844$	9.41487	0.324073
$845$	31.7944	1.09376
$846$	5.60561	0.192725
$847$	0	0
$848$	11.8620	0.407344
$849$	−8.84942	−0.303711
$850$	−32.5532	−1.11656
$851$	−37.8661	−1.29803
$852$	0.0450445	0.00154320
$853$	45.7689	1.56710	0.783549	−	0.621331i	$-0.213408\pi$
$853$	45.7689	1.56710	0.783549	+	0.621331i	$0.213408\pi$
$854$	0	0
$855$	3.15280	0.107823
$856$	−1.60582	−0.0548858
$857$	−1.45116	−0.0495706	−0.0247853	−	0.999693i	$-0.507890\pi$
$857$	−1.45116	−0.0495706	−0.0247853	+	0.999693i	$0.507890\pi$
$858$	−10.3880	−0.354641
$859$	−17.1126	−0.583873	−0.291937	−	0.956438i	$-0.594300\pi$
$859$	−17.1126	−0.583873	−0.291937	+	0.956438i	$0.594300\pi$
$860$	35.5242	1.21136
$861$	0	0
$862$	3.53073	0.120257
$863$	−0.562395	−0.0191441	−0.00957207	−	0.999954i	$-0.503047\pi$
$863$	−0.562395	−0.0191441	−0.00957207	+	0.999954i	$0.503047\pi$
$864$	−1.00000	−0.0340207
$865$	−47.4286	−1.61262
$866$	13.7760	0.468128
$867$	−26.4219	−0.897336
$868$	0	0
$869$	−9.89630	−0.335709
$870$	23.7349	0.804688
$871$	4.13495	0.140107
$872$	9.57478	0.324243
$873$	−10.4076	−0.352244
$874$	5.06183	0.171219
$875$	0	0
$876$	−14.1432	−0.477853
$877$	−21.4520	−0.724384	−0.362192	−	0.932104i	$-0.617971\pi$
$877$	−21.4520	−0.724384	−0.362192	+	0.932104i	$0.617971\pi$
$878$	−14.7088	−0.496398
$879$	2.58520	0.0871966
$880$	19.1811	0.646593
$881$	−20.4336	−0.688424	−0.344212	−	0.938892i	$-0.611854\pi$
$881$	−20.4336	−0.688424	−0.344212	+	0.938892i	$0.611854\pi$
$882$	0	0
$883$	−11.6808	−0.393091	−0.196545	−	0.980495i	$-0.562972\pi$
$883$	−11.6808	−0.393091	−0.196545	+	0.980495i	$0.562972\pi$
$884$	11.2515	0.378429
$885$	−21.4786	−0.721994
$886$	−30.4613	−1.02337
$887$	−53.4160	−1.79353	−0.896767	−	0.442503i	$-0.854091\pi$
$887$	−53.4160	−1.79353	−0.896767	+	0.442503i	$0.854091\pi$
$888$	−7.48072	−0.251037
$889$	0	0
$890$	37.6235	1.26114
$891$	−6.08382	−0.203816
$892$	18.0161	0.603223
$893$	−5.60561	−0.187585
$894$	9.66848	0.323362
$895$	29.6367	0.990647
$896$	0	0
$897$	−8.64297	−0.288580
$898$	−24.3814	−0.813618
$899$	−60.1918	−2.00751
$900$	4.94013	0.164671
$901$	−78.1653	−2.60406
$902$	−24.5416	−0.817146
$903$	0	0
$904$	−16.6914	−0.555147
$905$	−72.1949	−2.39984
$906$	−5.80324	−0.192800
$907$	−18.1312	−0.602037	−0.301018	−	0.953618i	$-0.597327\pi$
$907$	−18.1312	−0.602037	−0.301018	+	0.953618i	$0.597327\pi$
$908$	−18.7078	−0.620839
$909$	−15.6831	−0.520176
$910$	0	0
$911$	59.5588	1.97327	0.986635	−	0.162947i	$-0.0521000\pi$
$911$	59.5588	1.97327	0.986635	+	0.162947i	$0.0521000\pi$
$912$	1.00000	0.0331133
$913$	47.5637	1.57413
$914$	−22.6911	−0.750555
$915$	20.7590	0.686273
$916$	10.6854	0.353056
$917$	0	0
$918$	6.58953	0.217487
$919$	−42.9861	−1.41798	−0.708990	−	0.705219i	$-0.750849\pi$
$919$	−42.9861	−1.41798	−0.708990	+	0.705219i	$0.750849\pi$
$920$	15.9589	0.526150
$921$	−18.9892	−0.625716
$922$	−26.5199	−0.873388
$923$	0.0769127	0.00253161
$924$	0	0
$925$	36.9558	1.21510
$926$	13.3201	0.437727
$927$	−0.471586	−0.0154889
$928$	7.52820	0.247125
$929$	43.0489	1.41239	0.706194	−	0.708019i	$-0.250411\pi$
$929$	43.0489	1.41239	0.706194	+	0.708019i	$0.250411\pi$
$930$	−25.2082	−0.826610
$931$	0	0
$932$	−14.7049	−0.481675
$933$	2.74265	0.0897904
$934$	−6.02533	−0.197155
$935$	−126.394	−4.13353
$936$	−1.70748	−0.0558108
$937$	−12.0552	−0.393825	−0.196912	−	0.980421i	$-0.563091\pi$
$937$	−12.0552	−0.393825	−0.196912	+	0.980421i	$0.563091\pi$
$938$	0	0
$939$	−29.1231	−0.950398
$940$	−17.6733	−0.576441
$941$	18.0386	0.588042	0.294021	−	0.955799i	$-0.405006\pi$
$941$	18.0386	0.588042	0.294021	+	0.955799i	$0.405006\pi$
$942$	−2.93683	−0.0956872
$943$	−20.4190	−0.664934
$944$	−6.81255	−0.221729
$945$	0	0
$946$	68.5495	2.22874
$947$	22.4052	0.728072	0.364036	−	0.931385i	$-0.381399\pi$
$947$	22.4052	0.728072	0.364036	+	0.931385i	$0.381399\pi$
$948$	−1.62666	−0.0528315
$949$	−24.1492	−0.783915
$950$	−4.94013	−0.160279
$951$	1.14052	0.0369838
$952$	0	0
$953$	39.1197	1.26721	0.633605	−	0.773657i	$-0.281574\pi$
$953$	39.1197	1.26721	0.633605	+	0.773657i	$0.281574\pi$
$954$	11.8620	0.384048
$955$	0.689548	0.0223132
$956$	14.1590	0.457935
$957$	45.8002	1.48051
$958$	2.61758	0.0845703
$959$	0	0
$960$	3.15280	0.101756
$961$	32.9282	1.06220
$962$	−12.7732	−0.411824
$963$	−1.60582	−0.0517468
$964$	−24.9596	−0.803896
$965$	33.7049	1.08500
$966$	0	0
$967$	42.7383	1.37437	0.687186	−	0.726481i	$-0.258846\pi$
$967$	42.7383	1.37437	0.687186	+	0.726481i	$0.258846\pi$
$968$	26.0129	0.836085
$969$	−6.58953	−0.211686
$970$	32.8130	1.05356
$971$	41.9412	1.34596	0.672979	−	0.739661i	$-0.265014\pi$
$971$	41.9412	1.34596	0.672979	+	0.739661i	$0.265014\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−20.7106	−0.663612
$975$	8.43518	0.270142
$976$	6.58432	0.210759
$977$	−28.1269	−0.899858	−0.449929	−	0.893064i	$-0.648551\pi$
$977$	−28.1269	−0.899858	−0.449929	+	0.893064i	$0.648551\pi$
$978$	6.49895	0.207813
$979$	72.6005	2.32032
$980$	0	0
$981$	9.57478	0.305699
$982$	32.4892	1.03677
$983$	−14.7287	−0.469773	−0.234887	−	0.972023i	$-0.575472\pi$
$983$	−14.7287	−0.469773	−0.234887	+	0.972023i	$0.575472\pi$
$984$	−4.03392	−0.128597
$985$	−47.7615	−1.52181
$986$	−49.6073	−1.57982
$987$	0	0
$988$	1.70748	0.0543222
$989$	57.0342	1.81358
$990$	19.1811	0.609614
$991$	14.7650	0.469027	0.234513	−	0.972113i	$-0.424650\pi$
$991$	14.7650	0.469027	0.234513	+	0.972113i	$0.424650\pi$
$992$	−7.99551	−0.253858
$993$	24.3035	0.771250
$994$	0	0
$995$	16.7109	0.529772
$996$	7.81806	0.247725
$997$	20.4490	0.647628	0.323814	−	0.946121i	$-0.395035\pi$
$997$	20.4490	0.647628	0.323814	+	0.946121i	$0.395035\pi$
$998$	−3.35867	−0.106317
$999$	−7.48072	−0.236680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.ce.1.2	✓	8
7.6	odd	2		5586.2.a.cf.1.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5586.2.a.ce.1.2	✓	8	1.1	even	1	trivial
5586.2.a.cf.1.7	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.15280 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.15280 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.15280 q^{10} -6.08382 q^{11} -1.00000 q^{12} -1.70748 q^{13} +3.15280 q^{15} +1.00000 q^{16} -6.58953 q^{17} +1.00000 q^{18} -1.00000 q^{19} -3.15280 q^{20} -6.08382 q^{22} -5.06183 q^{23} -1.00000 q^{24} +4.94013 q^{25} -1.70748 q^{26} -1.00000 q^{27} +7.52820 q^{29} +3.15280 q^{30} -7.99551 q^{31} +1.00000 q^{32} +6.08382 q^{33} -6.58953 q^{34} +1.00000 q^{36} +7.48072 q^{37} -1.00000 q^{38} +1.70748 q^{39} -3.15280 q^{40} +4.03392 q^{41} -11.2675 q^{43} -6.08382 q^{44} -3.15280 q^{45} -5.06183 q^{46} +5.60561 q^{47} -1.00000 q^{48} +4.94013 q^{50} +6.58953 q^{51} -1.70748 q^{52} +11.8620 q^{53} -1.00000 q^{54} +19.1811 q^{55} +1.00000 q^{57} +7.52820 q^{58} -6.81255 q^{59} +3.15280 q^{60} +6.58432 q^{61} -7.99551 q^{62} +1.00000 q^{64} +5.38334 q^{65} +6.08382 q^{66} -2.42167 q^{67} -6.58953 q^{68} +5.06183 q^{69} -0.0450445 q^{71} +1.00000 q^{72} +14.1432 q^{73} +7.48072 q^{74} -4.94013 q^{75} -1.00000 q^{76} +1.70748 q^{78} +1.62666 q^{79} -3.15280 q^{80} +1.00000 q^{81} +4.03392 q^{82} -7.81806 q^{83} +20.7755 q^{85} -11.2675 q^{86} -7.52820 q^{87} -6.08382 q^{88} -11.9334 q^{89} -3.15280 q^{90} -5.06183 q^{92} +7.99551 q^{93} +5.60561 q^{94} +3.15280 q^{95} -1.00000 q^{96} -10.4076 q^{97} -6.08382 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 8 q^{3} + 8 q^{4} - 4 q^{5} - 8 q^{6} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 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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