LMFDB - Embedded newform 8470.2.a.dg.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, 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("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.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:	$67.6332905120$
Analytic rank:	$1$
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} - 16x^{6} + 69x^{4} - 10x^{3} - 70x^{2} + 10x + 5 $ x^8 - 16x^6 + 69x^4 - 10x^3 - 70x^2 + 10*x + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.90474$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.90474 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.90474 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.43751 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.90474 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.90474 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.43751 q^{9} +1.00000 q^{10} -2.90474 q^{12} +6.51020 q^{13} -1.00000 q^{14} +2.90474 q^{15} +1.00000 q^{16} -7.07831 q^{17} -5.43751 q^{18} -3.97479 q^{19} -1.00000 q^{20} -2.90474 q^{21} +9.39994 q^{23} +2.90474 q^{24} +1.00000 q^{25} -6.51020 q^{26} -7.08034 q^{27} +1.00000 q^{28} -1.17923 q^{29} -2.90474 q^{30} -1.28349 q^{31} -1.00000 q^{32} +7.07831 q^{34} -1.00000 q^{35} +5.43751 q^{36} -1.00807 q^{37} +3.97479 q^{38} -18.9104 q^{39} +1.00000 q^{40} +5.43144 q^{41} +2.90474 q^{42} +11.2003 q^{43} -5.43751 q^{45} -9.39994 q^{46} -11.3915 q^{47} -2.90474 q^{48} +1.00000 q^{49} -1.00000 q^{50} +20.5606 q^{51} +6.51020 q^{52} -7.75606 q^{53} +7.08034 q^{54} -1.00000 q^{56} +11.5457 q^{57} +1.17923 q^{58} -5.64597 q^{59} +2.90474 q^{60} -6.33662 q^{61} +1.28349 q^{62} +5.43751 q^{63} +1.00000 q^{64} -6.51020 q^{65} +3.88122 q^{67} -7.07831 q^{68} -27.3044 q^{69} +1.00000 q^{70} -0.259926 q^{71} -5.43751 q^{72} -4.82486 q^{73} +1.00807 q^{74} -2.90474 q^{75} -3.97479 q^{76} +18.9104 q^{78} -14.3428 q^{79} -1.00000 q^{80} +4.25401 q^{81} -5.43144 q^{82} -4.59502 q^{83} -2.90474 q^{84} +7.07831 q^{85} -11.2003 q^{86} +3.42535 q^{87} -1.43088 q^{89} +5.43751 q^{90} +6.51020 q^{91} +9.39994 q^{92} +3.72822 q^{93} +11.3915 q^{94} +3.97479 q^{95} +2.90474 q^{96} -8.60695 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{5} + 8 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^5 + 8 * q^7 - 8 * q^8 + 8 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} - 8 q^{5} + 8 q^{7} - 8 q^{8} + 8 q^{9} + 8 q^{10} + q^{13} - 8 q^{14} + 8 q^{16} - 6 q^{17} - 8 q^{18} - 5 q^{19} - 8 q^{20} + 10 q^{23} + 8 q^{25} - q^{26} + 8 q^{28} - 3 q^{29} - 8 q^{31} - 8 q^{32} + 6 q^{34} - 8 q^{35} + 8 q^{36} - 6 q^{37} + 5 q^{38} - 35 q^{39} + 8 q^{40} - 11 q^{41} + 5 q^{43} - 8 q^{45} - 10 q^{46} - 15 q^{47} + 8 q^{49} - 8 q^{50} + 6 q^{51} + q^{52} - 16 q^{53} - 8 q^{56} - 38 q^{57} + 3 q^{58} - 9 q^{59} - 32 q^{61} + 8 q^{62} + 8 q^{63} + 8 q^{64} - q^{65} + 33 q^{67} - 6 q^{68} - 22 q^{69} + 8 q^{70} + 11 q^{71} - 8 q^{72} + 34 q^{73} + 6 q^{74} - 5 q^{76} + 35 q^{78} - 31 q^{79} - 8 q^{80} + 20 q^{81} + 11 q^{82} - 50 q^{83} + 6 q^{85} - 5 q^{86} + 12 q^{87} + q^{89} + 8 q^{90} + q^{91} + 10 q^{92} + 26 q^{93} + 15 q^{94} + 5 q^{95} - 4 q^{97} - 8 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^5 + 8 * q^7 - 8 * q^8 + 8 * q^9 + 8 * q^10 + q^13 - 8 * q^14 + 8 * q^16 - 6 * q^17 - 8 * q^18 - 5 * q^19 - 8 * q^20 + 10 * q^23 + 8 * q^25 - q^26 + 8 * q^28 - 3 * q^29 - 8 * q^31 - 8 * q^32 + 6 * q^34 - 8 * q^35 + 8 * q^36 - 6 * q^37 + 5 * q^38 - 35 * q^39 + 8 * q^40 - 11 * q^41 + 5 * q^43 - 8 * q^45 - 10 * q^46 - 15 * q^47 + 8 * q^49 - 8 * q^50 + 6 * q^51 + q^52 - 16 * q^53 - 8 * q^56 - 38 * q^57 + 3 * q^58 - 9 * q^59 - 32 * q^61 + 8 * q^62 + 8 * q^63 + 8 * q^64 - q^65 + 33 * q^67 - 6 * q^68 - 22 * q^69 + 8 * q^70 + 11 * q^71 - 8 * q^72 + 34 * q^73 + 6 * q^74 - 5 * q^76 + 35 * q^78 - 31 * q^79 - 8 * q^80 + 20 * q^81 + 11 * q^82 - 50 * q^83 + 6 * q^85 - 5 * q^86 + 12 * q^87 + q^89 + 8 * q^90 + q^91 + 10 * q^92 + 26 * q^93 + 15 * q^94 + 5 * q^95 - 4 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.90474	−1.67705	−0.838526	−	0.544861i	$-0.816582\pi$
$3$	−2.90474	−1.67705	−0.838526	+	0.544861i	$0.816582\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.90474	1.18586
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	5.43751	1.81250
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−2.90474	−0.838526
$13$	6.51020	1.80560	0.902802	−	0.430056i	$-0.141506\pi$
$13$	6.51020	1.80560	0.902802	+	0.430056i	$0.141506\pi$
$14$	−1.00000	−0.267261
$15$	2.90474	0.750001
$16$	1.00000	0.250000
$17$	−7.07831	−1.71674	−0.858371	−	0.513030i	$-0.828523\pi$
$17$	−7.07831	−1.71674	−0.858371	+	0.513030i	$0.828523\pi$
$18$	−5.43751	−1.28163
$19$	−3.97479	−0.911879	−0.455940	−	0.890011i	$-0.650697\pi$
$19$	−3.97479	−0.911879	−0.455940	+	0.890011i	$0.650697\pi$
$20$	−1.00000	−0.223607
$21$	−2.90474	−0.633866
$22$	0	0
$23$	9.39994	1.96002	0.980011	−	0.198943i	$-0.0637509\pi$
$23$	9.39994	1.96002	0.980011	+	0.198943i	$0.0637509\pi$
$24$	2.90474	0.592928
$25$	1.00000	0.200000
$26$	−6.51020	−1.27676
$27$	−7.08034	−1.36261
$28$	1.00000	0.188982
$29$	−1.17923	−0.218977	−0.109489	−	0.993988i	$-0.534921\pi$
$29$	−1.17923	−0.218977	−0.109489	+	0.993988i	$0.534921\pi$
$30$	−2.90474	−0.530331
$31$	−1.28349	−0.230522	−0.115261	−	0.993335i	$-0.536770\pi$
$31$	−1.28349	−0.230522	−0.115261	+	0.993335i	$0.536770\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	7.07831	1.21392
$35$	−1.00000	−0.169031
$36$	5.43751	0.906252
$37$	−1.00807	−0.165726	−0.0828630	−	0.996561i	$-0.526406\pi$
$37$	−1.00807	−0.165726	−0.0828630	+	0.996561i	$0.526406\pi$
$38$	3.97479	0.644796
$39$	−18.9104	−3.02809
$40$	1.00000	0.158114
$41$	5.43144	0.848248	0.424124	−	0.905604i	$-0.360582\pi$
$41$	5.43144	0.848248	0.424124	+	0.905604i	$0.360582\pi$
$42$	2.90474	0.448211
$43$	11.2003	1.70803	0.854013	−	0.520251i	$-0.174162\pi$
$43$	11.2003	1.70803	0.854013	+	0.520251i	$0.174162\pi$
$44$	0	0
$45$	−5.43751	−0.810577
$46$	−9.39994	−1.38594
$47$	−11.3915	−1.66161	−0.830807	−	0.556561i	$-0.812121\pi$
$47$	−11.3915	−1.66161	−0.830807	+	0.556561i	$0.812121\pi$
$48$	−2.90474	−0.419263
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	20.5606	2.87907
$52$	6.51020	0.902802
$53$	−7.75606	−1.06538	−0.532688	−	0.846311i	$-0.678818\pi$
$53$	−7.75606	−1.06538	−0.532688	+	0.846311i	$0.678818\pi$
$54$	7.08034	0.963513
$55$	0	0
$56$	−1.00000	−0.133631
$57$	11.5457	1.52927
$58$	1.17923	0.154840
$59$	−5.64597	−0.735042	−0.367521	−	0.930015i	$-0.619793\pi$
$59$	−5.64597	−0.735042	−0.367521	+	0.930015i	$0.619793\pi$
$60$	2.90474	0.375000
$61$	−6.33662	−0.811321	−0.405660	−	0.914024i	$-0.632958\pi$
$61$	−6.33662	−0.811321	−0.405660	+	0.914024i	$0.632958\pi$
$62$	1.28349	0.163004
$63$	5.43751	0.685062
$64$	1.00000	0.125000
$65$	−6.51020	−0.807491
$66$	0	0
$67$	3.88122	0.474166	0.237083	−	0.971489i	$-0.423809\pi$
$67$	3.88122	0.474166	0.237083	+	0.971489i	$0.423809\pi$
$68$	−7.07831	−0.858371
$69$	−27.3044	−3.28706
$70$	1.00000	0.119523
$71$	−0.259926	−0.0308475	−0.0154238	−	0.999881i	$-0.504910\pi$
$71$	−0.259926	−0.0308475	−0.0154238	+	0.999881i	$0.504910\pi$
$72$	−5.43751	−0.640817
$73$	−4.82486	−0.564707	−0.282354	−	0.959310i	$-0.591115\pi$
$73$	−4.82486	−0.564707	−0.282354	+	0.959310i	$0.591115\pi$
$74$	1.00807	0.117186
$75$	−2.90474	−0.335410
$76$	−3.97479	−0.455940
$77$	0	0
$78$	18.9104	2.14119
$79$	−14.3428	−1.61369	−0.806843	−	0.590765i	$-0.798826\pi$
$79$	−14.3428	−1.61369	−0.806843	+	0.590765i	$0.798826\pi$
$80$	−1.00000	−0.111803
$81$	4.25401	0.472668
$82$	−5.43144	−0.599802
$83$	−4.59502	−0.504368	−0.252184	−	0.967679i	$-0.581149\pi$
$83$	−4.59502	−0.504368	−0.252184	+	0.967679i	$0.581149\pi$
$84$	−2.90474	−0.316933
$85$	7.07831	0.767750
$86$	−11.2003	−1.20776
$87$	3.42535	0.367236
$88$	0	0
$89$	−1.43088	−0.151673	−0.0758366	−	0.997120i	$-0.524163\pi$
$89$	−1.43088	−0.151673	−0.0758366	+	0.997120i	$0.524163\pi$
$90$	5.43751	0.573164
$91$	6.51020	0.682454
$92$	9.39994	0.980011
$93$	3.72822	0.386598
$94$	11.3915	1.17494
$95$	3.97479	0.407805
$96$	2.90474	0.296464
$97$	−8.60695	−0.873903	−0.436952	−	0.899485i	$-0.643942\pi$
$97$	−8.60695	−0.873903	−0.436952	+	0.899485i	$0.643942\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	7.14255	0.710710	0.355355	−	0.934731i	$-0.384360\pi$
$101$	7.14255	0.710710	0.355355	+	0.934731i	$0.384360\pi$
$102$	−20.5606	−2.03581
$103$	3.12129	0.307550	0.153775	−	0.988106i	$-0.450857\pi$
$103$	3.12129	0.307550	0.153775	+	0.988106i	$0.450857\pi$
$104$	−6.51020	−0.638378
$105$	2.90474	0.283474
$106$	7.75606	0.753335
$107$	3.29188	0.318238	0.159119	−	0.987259i	$-0.449135\pi$
$107$	3.29188	0.318238	0.159119	+	0.987259i	$0.449135\pi$
$108$	−7.08034	−0.681306
$109$	−12.5855	−1.20547	−0.602736	−	0.797941i	$-0.705923\pi$
$109$	−12.5855	−1.20547	−0.602736	+	0.797941i	$0.705923\pi$
$110$	0	0
$111$	2.92819	0.277931
$112$	1.00000	0.0944911
$113$	1.20490	0.113347	0.0566737	−	0.998393i	$-0.481951\pi$
$113$	1.20490	0.113347	0.0566737	+	0.998393i	$0.481951\pi$
$114$	−11.5457	−1.08136
$115$	−9.39994	−0.876549
$116$	−1.17923	−0.109489
$117$	35.3993	3.27267
$118$	5.64597	0.519753
$119$	−7.07831	−0.648867
$120$	−2.90474	−0.265165
$121$	0	0
$122$	6.33662	0.573690
$123$	−15.7769	−1.42256
$124$	−1.28349	−0.115261
$125$	−1.00000	−0.0894427
$126$	−5.43751	−0.484412
$127$	16.0026	1.42000	0.710000	−	0.704202i	$-0.248695\pi$
$127$	16.0026	1.42000	0.710000	+	0.704202i	$0.248695\pi$
$128$	−1.00000	−0.0883883
$129$	−32.5339	−2.86445
$130$	6.51020	0.570982
$131$	−14.6019	−1.27577	−0.637887	−	0.770130i	$-0.720191\pi$
$131$	−14.6019	−1.27577	−0.637887	+	0.770130i	$0.720191\pi$
$132$	0	0
$133$	−3.97479	−0.344658
$134$	−3.88122	−0.335286
$135$	7.08034	0.609379
$136$	7.07831	0.606960
$137$	10.0996	0.862871	0.431435	−	0.902144i	$-0.358007\pi$
$137$	10.0996	0.862871	0.431435	+	0.902144i	$0.358007\pi$
$138$	27.3044	2.32430
$139$	18.5110	1.57009	0.785043	−	0.619442i	$-0.212641\pi$
$139$	18.5110	1.57009	0.785043	+	0.619442i	$0.212641\pi$
$140$	−1.00000	−0.0845154
$141$	33.0892	2.78661
$142$	0.259926	0.0218125
$143$	0	0
$144$	5.43751	0.453126
$145$	1.17923	0.0979296
$146$	4.82486	0.399308
$147$	−2.90474	−0.239579
$148$	−1.00807	−0.0828630
$149$	−11.5126	−0.943152	−0.471576	−	0.881826i	$-0.656315\pi$
$149$	−11.5126	−0.943152	−0.471576	+	0.881826i	$0.656315\pi$
$150$	2.90474	0.237171
$151$	−5.43407	−0.442218	−0.221109	−	0.975249i	$-0.570968\pi$
$151$	−5.43407	−0.442218	−0.221109	+	0.975249i	$0.570968\pi$
$152$	3.97479	0.322398
$153$	−38.4884	−3.11160
$154$	0	0
$155$	1.28349	0.103093
$156$	−18.9104	−1.51405
$157$	7.97651	0.636595	0.318297	−	0.947991i	$-0.396889\pi$
$157$	7.97651	0.636595	0.318297	+	0.947991i	$0.396889\pi$
$158$	14.3428	1.14105
$159$	22.5293	1.78669
$160$	1.00000	0.0790569
$161$	9.39994	0.740819
$162$	−4.25401	−0.334227
$163$	14.3432	1.12345	0.561723	−	0.827326i	$-0.310139\pi$
$163$	14.3432	1.12345	0.561723	+	0.827326i	$0.310139\pi$
$164$	5.43144	0.424124
$165$	0	0
$166$	4.59502	0.356642
$167$	1.91040	0.147831	0.0739155	−	0.997265i	$-0.476450\pi$
$167$	1.91040	0.147831	0.0739155	+	0.997265i	$0.476450\pi$
$168$	2.90474	0.224106
$169$	29.3827	2.26021
$170$	−7.07831	−0.542881
$171$	−21.6130	−1.65279
$172$	11.2003	0.854013
$173$	14.5926	1.10945	0.554726	−	0.832033i	$-0.312823\pi$
$173$	14.5926	1.10945	0.554726	+	0.832033i	$0.312823\pi$
$174$	−3.42535	−0.259675
$175$	1.00000	0.0755929
$176$	0	0
$177$	16.4001	1.23270
$178$	1.43088	0.107249
$179$	−3.15693	−0.235960	−0.117980	−	0.993016i	$-0.537642\pi$
$179$	−3.15693	−0.235960	−0.117980	+	0.993016i	$0.537642\pi$
$180$	−5.43751	−0.405288
$181$	−7.09045	−0.527029	−0.263514	−	0.964655i	$-0.584882\pi$
$181$	−7.09045	−0.527029	−0.263514	+	0.964655i	$0.584882\pi$
$182$	−6.51020	−0.482568
$183$	18.4062	1.36063
$184$	−9.39994	−0.692972
$185$	1.00807	0.0741149
$186$	−3.72822	−0.273366
$187$	0	0
$188$	−11.3915	−0.830807
$189$	−7.08034	−0.515019
$190$	−3.97479	−0.288362
$191$	7.61496	0.550999	0.275500	−	0.961301i	$-0.411157\pi$
$191$	7.61496	0.550999	0.275500	+	0.961301i	$0.411157\pi$
$192$	−2.90474	−0.209632
$193$	8.55503	0.615804	0.307902	−	0.951418i	$-0.400373\pi$
$193$	8.55503	0.615804	0.307902	+	0.951418i	$0.400373\pi$
$194$	8.60695	0.617943
$195$	18.9104	1.35420
$196$	1.00000	0.0714286
$197$	−5.30318	−0.377836	−0.188918	−	0.981993i	$-0.560498\pi$
$197$	−5.30318	−0.377836	−0.188918	+	0.981993i	$0.560498\pi$
$198$	0	0
$199$	27.8463	1.97397	0.986987	−	0.160798i	$-0.0514068\pi$
$199$	27.8463	1.97397	0.986987	+	0.160798i	$0.0514068\pi$
$200$	−1.00000	−0.0707107
$201$	−11.2739	−0.795201
$202$	−7.14255	−0.502548
$203$	−1.17923	−0.0827656
$204$	20.5606	1.43953
$205$	−5.43144	−0.379348
$206$	−3.12129	−0.217470
$207$	51.1123	3.55255
$208$	6.51020	0.451401
$209$	0	0
$210$	−2.90474	−0.200446
$211$	−9.26733	−0.637989	−0.318995	−	0.947757i	$-0.603345\pi$
$211$	−9.26733	−0.637989	−0.318995	+	0.947757i	$0.603345\pi$
$212$	−7.75606	−0.532688
$213$	0.755017	0.0517329
$214$	−3.29188	−0.225028
$215$	−11.2003	−0.763853
$216$	7.08034	0.481756
$217$	−1.28349	−0.0871293
$218$	12.5855	0.852397
$219$	14.0150	0.947044
$220$	0	0
$221$	−46.0812	−3.09976
$222$	−2.92819	−0.196527
$223$	26.0134	1.74198	0.870992	−	0.491297i	$-0.163477\pi$
$223$	26.0134	1.74198	0.870992	+	0.491297i	$0.163477\pi$
$224$	−1.00000	−0.0668153
$225$	5.43751	0.362501
$226$	−1.20490	−0.0801487
$227$	0.293119	0.0194550	0.00972750	−	0.999953i	$-0.496904\pi$
$227$	0.293119	0.0194550	0.00972750	+	0.999953i	$0.496904\pi$
$228$	11.5457	0.764635
$229$	−19.9552	−1.31867	−0.659337	−	0.751847i	$-0.729163\pi$
$229$	−19.9552	−1.31867	−0.659337	+	0.751847i	$0.729163\pi$
$230$	9.39994	0.619813
$231$	0	0
$232$	1.17923	0.0774202
$233$	−0.201558	−0.0132045	−0.00660225	−	0.999978i	$-0.502102\pi$
$233$	−0.201558	−0.0132045	−0.00660225	+	0.999978i	$0.502102\pi$
$234$	−35.3993	−2.31412
$235$	11.3915	0.743096
$236$	−5.64597	−0.367521
$237$	41.6620	2.70624
$238$	7.07831	0.458819
$239$	−23.9193	−1.54721	−0.773604	−	0.633669i	$-0.781548\pi$
$239$	−23.9193	−1.54721	−0.773604	+	0.633669i	$0.781548\pi$
$240$	2.90474	0.187500
$241$	18.5851	1.19717	0.598586	−	0.801059i	$-0.295730\pi$
$241$	18.5851	1.19717	0.598586	+	0.801059i	$0.295730\pi$
$242$	0	0
$243$	8.88423	0.569924
$244$	−6.33662	−0.405660
$245$	−1.00000	−0.0638877
$246$	15.7769	1.00590
$247$	−25.8767	−1.64649
$248$	1.28349	0.0815020
$249$	13.3473	0.845852
$250$	1.00000	0.0632456
$251$	−10.0947	−0.637174	−0.318587	−	0.947894i	$-0.603208\pi$
$251$	−10.0947	−0.637174	−0.318587	+	0.947894i	$0.603208\pi$
$252$	5.43751	0.342531
$253$	0	0
$254$	−16.0026	−1.00409
$255$	−20.5606	−1.28756
$256$	1.00000	0.0625000
$257$	−5.47320	−0.341409	−0.170704	−	0.985322i	$-0.554604\pi$
$257$	−5.47320	−0.341409	−0.170704	+	0.985322i	$0.554604\pi$
$258$	32.5339	2.02547
$259$	−1.00807	−0.0626385
$260$	−6.51020	−0.403745
$261$	−6.41207	−0.396897
$262$	14.6019	0.902109
$263$	12.8440	0.791998	0.395999	−	0.918251i	$-0.370398\pi$
$263$	12.8440	0.791998	0.395999	+	0.918251i	$0.370398\pi$
$264$	0	0
$265$	7.75606	0.476451
$266$	3.97479	0.243710
$267$	4.15634	0.254364
$268$	3.88122	0.237083
$269$	7.87541	0.480172	0.240086	−	0.970752i	$-0.422824\pi$
$269$	7.87541	0.480172	0.240086	+	0.970752i	$0.422824\pi$
$270$	−7.08034	−0.430896
$271$	−9.87947	−0.600135	−0.300068	−	0.953918i	$-0.597009\pi$
$271$	−9.87947	−0.600135	−0.300068	+	0.953918i	$0.597009\pi$
$272$	−7.07831	−0.429185
$273$	−18.9104	−1.14451
$274$	−10.0996	−0.610142
$275$	0	0
$276$	−27.3044	−1.64353
$277$	−27.0289	−1.62401	−0.812006	−	0.583649i	$-0.801624\pi$
$277$	−27.0289	−1.62401	−0.812006	+	0.583649i	$0.801624\pi$
$278$	−18.5110	−1.11022
$279$	−6.97902	−0.417823
$280$	1.00000	0.0597614
$281$	−13.6419	−0.813806	−0.406903	−	0.913471i	$-0.633391\pi$
$281$	−13.6419	−0.813806	−0.406903	+	0.913471i	$0.633391\pi$
$282$	−33.0892	−1.97043
$283$	−18.3850	−1.09287	−0.546437	−	0.837500i	$-0.684016\pi$
$283$	−18.3850	−1.09287	−0.546437	+	0.837500i	$0.684016\pi$
$284$	−0.259926	−0.0154238
$285$	−11.5457	−0.683910
$286$	0	0
$287$	5.43144	0.320608
$288$	−5.43751	−0.320409
$289$	33.1024	1.94720
$290$	−1.17923	−0.0692467
$291$	25.0009	1.46558
$292$	−4.82486	−0.282354
$293$	−9.87445	−0.576871	−0.288436	−	0.957499i	$-0.593135\pi$
$293$	−9.87445	−0.576871	−0.288436	+	0.957499i	$0.593135\pi$
$294$	2.90474	0.169408
$295$	5.64597	0.328721
$296$	1.00807	0.0585930
$297$	0	0
$298$	11.5126	0.666909
$299$	61.1955	3.53902
$300$	−2.90474	−0.167705
$301$	11.2003	0.645573
$302$	5.43407	0.312696
$303$	−20.7473	−1.19190
$304$	−3.97479	−0.227970
$305$	6.33662	0.362834
$306$	38.4884	2.20023
$307$	−6.50344	−0.371171	−0.185585	−	0.982628i	$-0.559418\pi$
$307$	−6.50344	−0.371171	−0.185585	+	0.982628i	$0.559418\pi$
$308$	0	0
$309$	−9.06653	−0.515777
$310$	−1.28349	−0.0728976
$311$	3.36996	0.191093	0.0955464	−	0.995425i	$-0.469540\pi$
$311$	3.36996	0.191093	0.0955464	+	0.995425i	$0.469540\pi$
$312$	18.9104	1.07059
$313$	−5.42220	−0.306481	−0.153240	−	0.988189i	$-0.548971\pi$
$313$	−5.42220	−0.306481	−0.153240	+	0.988189i	$0.548971\pi$
$314$	−7.97651	−0.450141
$315$	−5.43751	−0.306369
$316$	−14.3428	−0.806843
$317$	−7.15998	−0.402145	−0.201072	−	0.979576i	$-0.564443\pi$
$317$	−7.15998	−0.402145	−0.201072	+	0.979576i	$0.564443\pi$
$318$	−22.5293	−1.26338
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−9.56205	−0.533702
$322$	−9.39994	−0.523838
$323$	28.1348	1.56546
$324$	4.25401	0.236334
$325$	6.51020	0.361121
$326$	−14.3432	−0.794396
$327$	36.5576	2.02164
$328$	−5.43144	−0.299901
$329$	−11.3915	−0.628031
$330$	0	0
$331$	20.6983	1.13768	0.568842	−	0.822447i	$-0.307392\pi$
$331$	20.6983	1.13768	0.568842	+	0.822447i	$0.307392\pi$
$332$	−4.59502	−0.252184
$333$	−5.48140	−0.300379
$334$	−1.91040	−0.104532
$335$	−3.88122	−0.212053
$336$	−2.90474	−0.158467
$337$	7.81093	0.425488	0.212744	−	0.977108i	$-0.431760\pi$
$337$	7.81093	0.425488	0.212744	+	0.977108i	$0.431760\pi$
$338$	−29.3827	−1.59821
$339$	−3.49992	−0.190090
$340$	7.07831	0.383875
$341$	0	0
$342$	21.6130	1.16870
$343$	1.00000	0.0539949
$344$	−11.2003	−0.603879
$345$	27.3044	1.47002
$346$	−14.5926	−0.784502
$347$	27.9220	1.49893	0.749465	−	0.662044i	$-0.230311\pi$
$347$	27.9220	1.49893	0.749465	+	0.662044i	$0.230311\pi$
$348$	3.42535	0.183618
$349$	−20.5937	−1.10236	−0.551178	−	0.834387i	$-0.685822\pi$
$349$	−20.5937	−1.10236	−0.551178	+	0.834387i	$0.685822\pi$
$350$	−1.00000	−0.0534522
$351$	−46.0944	−2.46034
$352$	0	0
$353$	−5.61133	−0.298661	−0.149330	−	0.988787i	$-0.547712\pi$
$353$	−5.61133	−0.298661	−0.149330	+	0.988787i	$0.547712\pi$
$354$	−16.4001	−0.871653
$355$	0.259926	0.0137954
$356$	−1.43088	−0.0758366
$357$	20.5606	1.08818
$358$	3.15693	0.166849
$359$	−8.24264	−0.435030	−0.217515	−	0.976057i	$-0.569795\pi$
$359$	−8.24264	−0.435030	−0.217515	+	0.976057i	$0.569795\pi$
$360$	5.43751	0.286582
$361$	−3.20104	−0.168476
$362$	7.09045	0.372666
$363$	0	0
$364$	6.51020	0.341227
$365$	4.82486	0.252545
$366$	−18.4062	−0.962109
$367$	−4.10818	−0.214445	−0.107223	−	0.994235i	$-0.534196\pi$
$367$	−4.10818	−0.214445	−0.107223	+	0.994235i	$0.534196\pi$
$368$	9.39994	0.490006
$369$	29.5335	1.53745
$370$	−1.00807	−0.0524071
$371$	−7.75606	−0.402675
$372$	3.72822	0.193299
$373$	26.2182	1.35753	0.678764	−	0.734356i	$-0.262516\pi$
$373$	26.2182	1.35753	0.678764	+	0.734356i	$0.262516\pi$
$374$	0	0
$375$	2.90474	0.150000
$376$	11.3915	0.587469
$377$	−7.67702	−0.395386
$378$	7.08034	0.364174
$379$	19.7398	1.01397	0.506983	−	0.861956i	$-0.330761\pi$
$379$	19.7398	1.01397	0.506983	+	0.861956i	$0.330761\pi$
$380$	3.97479	0.203902
$381$	−46.4834	−2.38141
$382$	−7.61496	−0.389615
$383$	35.8040	1.82950	0.914749	−	0.404022i	$-0.132388\pi$
$383$	35.8040	1.82950	0.914749	+	0.404022i	$0.132388\pi$
$384$	2.90474	0.148232
$385$	0	0
$386$	−8.55503	−0.435439
$387$	60.9017	3.09581
$388$	−8.60695	−0.436952
$389$	−28.8835	−1.46445	−0.732226	−	0.681062i	$-0.761518\pi$
$389$	−28.8835	−1.46445	−0.732226	+	0.681062i	$0.761518\pi$
$390$	−18.9104	−0.957567
$391$	−66.5356	−3.36485
$392$	−1.00000	−0.0505076
$393$	42.4147	2.13954
$394$	5.30318	0.267171
$395$	14.3428	0.721663
$396$	0	0
$397$	−31.7117	−1.59156	−0.795782	−	0.605583i	$-0.792940\pi$
$397$	−31.7117	−1.59156	−0.795782	+	0.605583i	$0.792940\pi$
$398$	−27.8463	−1.39581
$399$	11.5457	0.578010
$400$	1.00000	0.0500000
$401$	−24.8442	−1.24066	−0.620331	−	0.784340i	$-0.713002\pi$
$401$	−24.8442	−1.24066	−0.620331	+	0.784340i	$0.713002\pi$
$402$	11.2739	0.562292
$403$	−8.35580	−0.416232
$404$	7.14255	0.355355
$405$	−4.25401	−0.211384
$406$	1.17923	0.0585242
$407$	0	0
$408$	−20.5606	−1.01790
$409$	−17.6373	−0.872107	−0.436054	−	0.899921i	$-0.643624\pi$
$409$	−17.6373	−0.872107	−0.436054	+	0.899921i	$0.643624\pi$
$410$	5.43144	0.268240
$411$	−29.3368	−1.44708
$412$	3.12129	0.153775
$413$	−5.64597	−0.277820
$414$	−51.1123	−2.51203
$415$	4.59502	0.225560
$416$	−6.51020	−0.319189
$417$	−53.7697	−2.63312
$418$	0	0
$419$	6.70771	0.327693	0.163847	−	0.986486i	$-0.447610\pi$
$419$	6.70771	0.327693	0.163847	+	0.986486i	$0.447610\pi$
$420$	2.90474	0.141737
$421$	16.0438	0.781925	0.390962	−	0.920407i	$-0.372142\pi$
$421$	16.0438	0.781925	0.390962	+	0.920407i	$0.372142\pi$
$422$	9.26733	0.451126
$423$	−61.9412	−3.01168
$424$	7.75606	0.376668
$425$	−7.07831	−0.343348
$426$	−0.755017	−0.0365807
$427$	−6.33662	−0.306650
$428$	3.29188	0.159119
$429$	0	0
$430$	11.2003	0.540125
$431$	−31.5480	−1.51961	−0.759807	−	0.650148i	$-0.774707\pi$
$431$	−31.5480	−1.51961	−0.759807	+	0.650148i	$0.774707\pi$
$432$	−7.08034	−0.340653
$433$	−8.26911	−0.397388	−0.198694	−	0.980062i	$-0.563670\pi$
$433$	−8.26911	−0.397388	−0.198694	+	0.980062i	$0.563670\pi$
$434$	1.28349	0.0616097
$435$	−3.42535	−0.164233
$436$	−12.5855	−0.602736
$437$	−37.3628	−1.78730
$438$	−14.0150	−0.669661
$439$	−11.1008	−0.529814	−0.264907	−	0.964274i	$-0.585341\pi$
$439$	−11.1008	−0.529814	−0.264907	+	0.964274i	$0.585341\pi$
$440$	0	0
$441$	5.43751	0.258929
$442$	46.0812	2.19186
$443$	4.53871	0.215641	0.107820	−	0.994170i	$-0.465613\pi$
$443$	4.53871	0.215641	0.107820	+	0.994170i	$0.465613\pi$
$444$	2.92819	0.138966
$445$	1.43088	0.0678303
$446$	−26.0134	−1.23177
$447$	33.4412	1.58171
$448$	1.00000	0.0472456
$449$	−9.71975	−0.458703	−0.229352	−	0.973344i	$-0.573661\pi$
$449$	−9.71975	−0.458703	−0.229352	+	0.973344i	$0.573661\pi$
$450$	−5.43751	−0.256327
$451$	0	0
$452$	1.20490	0.0566737
$453$	15.7846	0.741623
$454$	−0.293119	−0.0137568
$455$	−6.51020	−0.305203
$456$	−11.5457	−0.540678
$457$	−21.1478	−0.989251	−0.494626	−	0.869106i	$-0.664695\pi$
$457$	−21.1478	−0.989251	−0.494626	+	0.869106i	$0.664695\pi$
$458$	19.9552	0.932444
$459$	50.1168	2.33925
$460$	−9.39994	−0.438274
$461$	−20.5158	−0.955516	−0.477758	−	0.878492i	$-0.658550\pi$
$461$	−20.5158	−0.955516	−0.477758	+	0.878492i	$0.658550\pi$
$462$	0	0
$463$	−5.06175	−0.235239	−0.117620	−	0.993059i	$-0.537526\pi$
$463$	−5.06175	−0.235239	−0.117620	+	0.993059i	$0.537526\pi$
$464$	−1.17923	−0.0547443
$465$	−3.72822	−0.172892
$466$	0.201558	0.00933699
$467$	−7.48743	−0.346477	−0.173239	−	0.984880i	$-0.555423\pi$
$467$	−7.48743	−0.346477	−0.173239	+	0.984880i	$0.555423\pi$
$468$	35.3993	1.63633
$469$	3.88122	0.179218
$470$	−11.3915	−0.525448
$471$	−23.1697	−1.06760
$472$	5.64597	0.259877
$473$	0	0
$474$	−41.6620	−1.91360
$475$	−3.97479	−0.182376
$476$	−7.07831	−0.324434
$477$	−42.1737	−1.93100
$478$	23.9193	1.09404
$479$	0.414174	0.0189241	0.00946206	−	0.999955i	$-0.496988\pi$
$479$	0.414174	0.0189241	0.00946206	+	0.999955i	$0.496988\pi$
$480$	−2.90474	−0.132583
$481$	−6.56275	−0.299235
$482$	−18.5851	−0.846528
$483$	−27.3044	−1.24239
$484$	0	0
$485$	8.60695	0.390821
$486$	−8.88423	−0.402997
$487$	−23.7328	−1.07544	−0.537718	−	0.843125i	$-0.680714\pi$
$487$	−23.7328	−1.07544	−0.537718	+	0.843125i	$0.680714\pi$
$488$	6.33662	0.286845
$489$	−41.6632	−1.88408
$490$	1.00000	0.0451754
$491$	−32.2162	−1.45390	−0.726949	−	0.686691i	$-0.759063\pi$
$491$	−32.2162	−1.45390	−0.726949	+	0.686691i	$0.759063\pi$
$492$	−15.7769	−0.711278
$493$	8.34695	0.375928
$494$	25.8767	1.16425
$495$	0	0
$496$	−1.28349	−0.0576306
$497$	−0.259926	−0.0116593
$498$	−13.3473	−0.598108
$499$	−4.48988	−0.200995	−0.100497	−	0.994937i	$-0.532043\pi$
$499$	−4.48988	−0.200995	−0.100497	+	0.994937i	$0.532043\pi$
$500$	−1.00000	−0.0447214
$501$	−5.54921	−0.247920
$502$	10.0947	0.450550
$503$	−30.8299	−1.37464	−0.687319	−	0.726355i	$-0.741213\pi$
$503$	−30.8299	−1.37464	−0.687319	+	0.726355i	$0.741213\pi$
$504$	−5.43751	−0.242206
$505$	−7.14255	−0.317839
$506$	0	0
$507$	−85.3491	−3.79049
$508$	16.0026	0.710000
$509$	−2.65682	−0.117762	−0.0588808	−	0.998265i	$-0.518753\pi$
$509$	−2.65682	−0.117762	−0.0588808	+	0.998265i	$0.518753\pi$
$510$	20.5606	0.910440
$511$	−4.82486	−0.213439
$512$	−1.00000	−0.0441942
$513$	28.1429	1.24254
$514$	5.47320	0.241412
$515$	−3.12129	−0.137540
$516$	−32.5339	−1.43222
$517$	0	0
$518$	1.00807	0.0442921
$519$	−42.3876	−1.86061
$520$	6.51020	0.285491
$521$	5.98594	0.262249	0.131124	−	0.991366i	$-0.458141\pi$
$521$	5.98594	0.262249	0.131124	+	0.991366i	$0.458141\pi$
$522$	6.41207	0.280649
$523$	−0.966746	−0.0422728	−0.0211364	−	0.999777i	$-0.506728\pi$
$523$	−0.966746	−0.0422728	−0.0211364	+	0.999777i	$0.506728\pi$
$524$	−14.6019	−0.637887
$525$	−2.90474	−0.126773
$526$	−12.8440	−0.560027
$527$	9.08497	0.395747
$528$	0	0
$529$	65.3588	2.84169
$530$	−7.75606	−0.336902
$531$	−30.7000	−1.33227
$532$	−3.97479	−0.172329
$533$	35.3597	1.53160
$534$	−4.15634	−0.179862
$535$	−3.29188	−0.142320
$536$	−3.88122	−0.167643
$537$	9.17005	0.395717
$538$	−7.87541	−0.339533
$539$	0	0
$540$	7.08034	0.304689
$541$	1.56401	0.0672420	0.0336210	−	0.999435i	$-0.489296\pi$
$541$	1.56401	0.0672420	0.0336210	+	0.999435i	$0.489296\pi$
$542$	9.87947	0.424360
$543$	20.5959	0.883855
$544$	7.07831	0.303480
$545$	12.5855	0.539103
$546$	18.9104	0.809292
$547$	14.5413	0.621741	0.310870	−	0.950452i	$-0.399380\pi$
$547$	14.5413	0.621741	0.310870	+	0.950452i	$0.399380\pi$
$548$	10.0996	0.431435
$549$	−34.4554	−1.47052
$550$	0	0
$551$	4.68719	0.199681
$552$	27.3044	1.16215
$553$	−14.3428	−0.609916
$554$	27.0289	1.14835
$555$	−2.92819	−0.124295
$556$	18.5110	0.785043
$557$	37.0040	1.56791	0.783956	−	0.620817i	$-0.213199\pi$
$557$	37.0040	1.56791	0.783956	+	0.620817i	$0.213199\pi$
$558$	6.97902	0.295445
$559$	72.9160	3.08402
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	13.6419	0.575448
$563$	−23.9389	−1.00890	−0.504452	−	0.863440i	$-0.668306\pi$
$563$	−23.9389	−1.00890	−0.504452	+	0.863440i	$0.668306\pi$
$564$	33.0892	1.39331
$565$	−1.20490	−0.0506905
$566$	18.3850	0.772779
$567$	4.25401	0.178652
$568$	0.259926	0.0109063
$569$	26.6076	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$569$	26.6076	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$570$	11.5457	0.483597
$571$	−17.4823	−0.731610	−0.365805	−	0.930692i	$-0.619206\pi$
$571$	−17.4823	−0.731610	−0.365805	+	0.930692i	$0.619206\pi$
$572$	0	0
$573$	−22.1195	−0.924055
$574$	−5.43144	−0.226704
$575$	9.39994	0.392004
$576$	5.43751	0.226563
$577$	31.3194	1.30385	0.651923	−	0.758285i	$-0.273963\pi$
$577$	31.3194	1.30385	0.651923	+	0.758285i	$0.273963\pi$
$578$	−33.1024	−1.37688
$579$	−24.8501	−1.03274
$580$	1.17923	0.0489648
$581$	−4.59502	−0.190633
$582$	−25.0009	−1.03632
$583$	0	0
$584$	4.82486	0.199654
$585$	−35.3993	−1.46358
$586$	9.87445	0.407910
$587$	4.04656	0.167019	0.0835097	−	0.996507i	$-0.473387\pi$
$587$	4.04656	0.167019	0.0835097	+	0.996507i	$0.473387\pi$
$588$	−2.90474	−0.119789
$589$	5.10162	0.210209
$590$	−5.64597	−0.232441
$591$	15.4044	0.633651
$592$	−1.00807	−0.0414315
$593$	−23.7125	−0.973756	−0.486878	−	0.873470i	$-0.661864\pi$
$593$	−23.7125	−0.973756	−0.486878	+	0.873470i	$0.661864\pi$
$594$	0	0
$595$	7.07831	0.290182
$596$	−11.5126	−0.471576
$597$	−80.8864	−3.31046
$598$	−61.1955	−2.50247
$599$	−10.4237	−0.425900	−0.212950	−	0.977063i	$-0.568307\pi$
$599$	−10.4237	−0.425900	−0.212950	+	0.977063i	$0.568307\pi$
$600$	2.90474	0.118586
$601$	15.5929	0.636049	0.318025	−	0.948082i	$-0.396981\pi$
$601$	15.5929	0.636049	0.318025	+	0.948082i	$0.396981\pi$
$602$	−11.2003	−0.456489
$603$	21.1042	0.859428
$604$	−5.43407	−0.221109
$605$	0	0
$606$	20.7473	0.842799
$607$	3.06966	0.124594	0.0622968	−	0.998058i	$-0.480157\pi$
$607$	3.06966	0.124594	0.0622968	+	0.998058i	$0.480157\pi$
$608$	3.97479	0.161199
$609$	3.42535	0.138802
$610$	−6.33662	−0.256562
$611$	−74.1606	−3.00022
$612$	−38.4884	−1.55580
$613$	−25.5273	−1.03104	−0.515520	−	0.856878i	$-0.672401\pi$
$613$	−25.5273	−1.03104	−0.515520	+	0.856878i	$0.672401\pi$
$614$	6.50344	0.262457
$615$	15.7769	0.636187
$616$	0	0
$617$	−14.4437	−0.581483	−0.290741	−	0.956802i	$-0.593902\pi$
$617$	−14.4437	−0.581483	−0.290741	+	0.956802i	$0.593902\pi$
$618$	9.06653	0.364709
$619$	1.76790	0.0710578	0.0355289	−	0.999369i	$-0.488688\pi$
$619$	1.76790	0.0710578	0.0355289	+	0.999369i	$0.488688\pi$
$620$	1.28349	0.0515464
$621$	−66.5548	−2.67075
$622$	−3.36996	−0.135123
$623$	−1.43088	−0.0573270
$624$	−18.9104	−0.757023
$625$	1.00000	0.0400000
$626$	5.42220	0.216715
$627$	0	0
$628$	7.97651	0.318297
$629$	7.13544	0.284509
$630$	5.43751	0.216636
$631$	21.3564	0.850185	0.425093	−	0.905150i	$-0.360242\pi$
$631$	21.3564	0.850185	0.425093	+	0.905150i	$0.360242\pi$
$632$	14.3428	0.570524
$633$	26.9192	1.06994
$634$	7.15998	0.284359
$635$	−16.0026	−0.635043
$636$	22.5293	0.893346
$637$	6.51020	0.257943
$638$	0	0
$639$	−1.41335	−0.0559113
$640$	1.00000	0.0395285
$641$	46.1398	1.82241	0.911205	−	0.411952i	$-0.135153\pi$
$641$	46.1398	1.82241	0.911205	+	0.411952i	$0.135153\pi$
$642$	9.56205	0.377384
$643$	18.4699	0.728383	0.364191	−	0.931324i	$-0.381345\pi$
$643$	18.4699	0.728383	0.364191	+	0.931324i	$0.381345\pi$
$644$	9.39994	0.370409
$645$	32.5339	1.28102
$646$	−28.1348	−1.10695
$647$	36.3807	1.43027	0.715137	−	0.698984i	$-0.246364\pi$
$647$	36.3807	1.43027	0.715137	+	0.698984i	$0.246364\pi$
$648$	−4.25401	−0.167113
$649$	0	0
$650$	−6.51020	−0.255351
$651$	3.72822	0.146120
$652$	14.3432	0.561723
$653$	−2.89414	−0.113256	−0.0566281	−	0.998395i	$-0.518035\pi$
$653$	−2.89414	−0.113256	−0.0566281	+	0.998395i	$0.518035\pi$
$654$	−36.5576	−1.42951
$655$	14.6019	0.570544
$656$	5.43144	0.212062
$657$	−26.2352	−1.02353
$658$	11.3915	0.444085
$659$	−19.1764	−0.747008	−0.373504	−	0.927629i	$-0.621844\pi$
$659$	−19.1764	−0.747008	−0.373504	+	0.927629i	$0.621844\pi$
$660$	0	0
$661$	−24.9234	−0.969406	−0.484703	−	0.874679i	$-0.661072\pi$
$661$	−24.9234	−0.969406	−0.484703	+	0.874679i	$0.661072\pi$
$662$	−20.6983	−0.804463
$663$	133.854	5.19845
$664$	4.59502	0.178321
$665$	3.97479	0.154136
$666$	5.48140	0.212400
$667$	−11.0847	−0.429200
$668$	1.91040	0.0739155
$669$	−75.5621	−2.92140
$670$	3.88122	0.149944
$671$	0	0
$672$	2.90474	0.112053
$673$	−13.3066	−0.512932	−0.256466	−	0.966553i	$-0.582558\pi$
$673$	−13.3066	−0.512932	−0.256466	+	0.966553i	$0.582558\pi$
$674$	−7.81093	−0.300866
$675$	−7.08034	−0.272523
$676$	29.3827	1.13010
$677$	−28.2748	−1.08669	−0.543344	−	0.839510i	$-0.682842\pi$
$677$	−28.2748	−1.08669	−0.543344	+	0.839510i	$0.682842\pi$
$678$	3.49992	0.134414
$679$	−8.60695	−0.330304
$680$	−7.07831	−0.271441
$681$	−0.851435	−0.0326271
$682$	0	0
$683$	−20.1040	−0.769259	−0.384629	−	0.923071i	$-0.625671\pi$
$683$	−20.1040	−0.769259	−0.384629	+	0.923071i	$0.625671\pi$
$684$	−21.6130	−0.826393
$685$	−10.0996	−0.385887
$686$	−1.00000	−0.0381802
$687$	57.9646	2.21149
$688$	11.2003	0.427007
$689$	−50.4935	−1.92365
$690$	−27.3044	−1.03946
$691$	−1.68862	−0.0642382	−0.0321191	−	0.999484i	$-0.510226\pi$
$691$	−1.68862	−0.0642382	−0.0321191	+	0.999484i	$0.510226\pi$
$692$	14.5926	0.554726
$693$	0	0
$694$	−27.9220	−1.05990
$695$	−18.5110	−0.702164
$696$	−3.42535	−0.129838
$697$	−38.4454	−1.45622
$698$	20.5937	0.779484
$699$	0.585473	0.0221446
$700$	1.00000	0.0377964
$701$	−2.04142	−0.0771035	−0.0385517	−	0.999257i	$-0.512274\pi$
$701$	−2.04142	−0.0771035	−0.0385517	+	0.999257i	$0.512274\pi$
$702$	46.0944	1.73972
$703$	4.00687	0.151122
$704$	0	0
$705$	−33.0892	−1.24621
$706$	5.61133	0.211185
$707$	7.14255	0.268623
$708$	16.4001	0.616352
$709$	4.99388	0.187549	0.0937745	−	0.995593i	$-0.470107\pi$
$709$	4.99388	0.187549	0.0937745	+	0.995593i	$0.470107\pi$
$710$	−0.259926	−0.00975485
$711$	−77.9890	−2.92481
$712$	1.43088	0.0536245
$713$	−12.0648	−0.451829
$714$	−20.5606	−0.769463
$715$	0	0
$716$	−3.15693	−0.117980
$717$	69.4792	2.59475
$718$	8.24264	0.307613
$719$	34.3305	1.28031	0.640156	−	0.768245i	$-0.278870\pi$
$719$	34.3305	1.28031	0.640156	+	0.768245i	$0.278870\pi$
$720$	−5.43751	−0.202644
$721$	3.12129	0.116243
$722$	3.20104	0.119130
$723$	−53.9849	−2.00772
$724$	−7.09045	−0.263514
$725$	−1.17923	−0.0437955
$726$	0	0
$727$	26.6447	0.988196	0.494098	−	0.869406i	$-0.335498\pi$
$727$	26.6447	0.988196	0.494098	+	0.869406i	$0.335498\pi$
$728$	−6.51020	−0.241284
$729$	−38.5684	−1.42846
$730$	−4.82486	−0.178576
$731$	−79.2790	−2.93224
$732$	18.4062	0.680314
$733$	−14.1335	−0.522032	−0.261016	−	0.965334i	$-0.584058\pi$
$733$	−14.1335	−0.522032	−0.261016	+	0.965334i	$0.584058\pi$
$734$	4.10818	0.151636
$735$	2.90474	0.107143
$736$	−9.39994	−0.346486
$737$	0	0
$738$	−29.5335	−1.08714
$739$	−36.0918	−1.32766	−0.663829	−	0.747884i	$-0.731070\pi$
$739$	−36.0918	−1.32766	−0.663829	+	0.747884i	$0.731070\pi$
$740$	1.00807	0.0370574
$741$	75.1650	2.76126
$742$	7.75606	0.284734
$743$	29.3508	1.07678	0.538389	−	0.842697i	$-0.319033\pi$
$743$	29.3508	1.07678	0.538389	+	0.842697i	$0.319033\pi$
$744$	−3.72822	−0.136683
$745$	11.5126	0.421790
$746$	−26.2182	−0.959917
$747$	−24.9855	−0.914170
$748$	0	0
$749$	3.29188	0.120283
$750$	−2.90474	−0.106066
$751$	36.8418	1.34438	0.672189	−	0.740380i	$-0.265354\pi$
$751$	36.8418	1.34438	0.672189	+	0.740380i	$0.265354\pi$
$752$	−11.3915	−0.415404
$753$	29.3226	1.06857
$754$	7.67702	0.279580
$755$	5.43407	0.197766
$756$	−7.08034	−0.257510
$757$	−36.7671	−1.33632	−0.668161	−	0.744016i	$-0.732918\pi$
$757$	−36.7671	−1.33632	−0.668161	+	0.744016i	$0.732918\pi$
$758$	−19.7398	−0.716982
$759$	0	0
$760$	−3.97479	−0.144181
$761$	−35.6456	−1.29215	−0.646075	−	0.763274i	$-0.723591\pi$
$761$	−35.6456	−1.29215	−0.646075	+	0.763274i	$0.723591\pi$
$762$	46.4834	1.68391
$763$	−12.5855	−0.455625
$764$	7.61496	0.275500
$765$	38.4884	1.39155
$766$	−35.8040	−1.29365
$767$	−36.7564	−1.32720
$768$	−2.90474	−0.104816
$769$	−30.6264	−1.10442	−0.552209	−	0.833706i	$-0.686215\pi$
$769$	−30.6264	−1.10442	−0.552209	+	0.833706i	$0.686215\pi$
$770$	0	0
$771$	15.8982	0.572560
$772$	8.55503	0.307902
$773$	−10.7328	−0.386033	−0.193017	−	0.981195i	$-0.561827\pi$
$773$	−10.7328	−0.386033	−0.193017	+	0.981195i	$0.561827\pi$
$774$	−60.9017	−2.18907
$775$	−1.28349	−0.0461045
$776$	8.60695	0.308971
$777$	2.92819	0.105048
$778$	28.8835	1.03552
$779$	−21.5888	−0.773500
$780$	18.9104	0.677102
$781$	0	0
$782$	66.5356	2.37931
$783$	8.34934	0.298381
$784$	1.00000	0.0357143
$785$	−7.97651	−0.284694
$786$	−42.4147	−1.51288
$787$	18.2605	0.650917	0.325459	−	0.945556i	$-0.394481\pi$
$787$	18.2605	0.650917	0.325459	+	0.945556i	$0.394481\pi$
$788$	−5.30318	−0.188918
$789$	−37.3086	−1.32822
$790$	−14.3428	−0.510293
$791$	1.20490	0.0428413
$792$	0	0
$793$	−41.2526	−1.46492
$794$	31.7117	1.12541
$795$	−22.5293	−0.799033
$796$	27.8463	0.986987
$797$	−29.4786	−1.04418	−0.522092	−	0.852889i	$-0.674848\pi$
$797$	−29.4786	−1.04418	−0.522092	+	0.852889i	$0.674848\pi$
$798$	−11.5457	−0.408714
$799$	80.6322	2.85256
$800$	−1.00000	−0.0353553
$801$	−7.78044	−0.274908
$802$	24.8442	0.877281
$803$	0	0
$804$	−11.2739	−0.397601
$805$	−9.39994	−0.331304
$806$	8.35580	0.294321
$807$	−22.8760	−0.805274
$808$	−7.14255	−0.251274
$809$	22.3819	0.786904	0.393452	−	0.919345i	$-0.371281\pi$
$809$	22.3819	0.786904	0.393452	+	0.919345i	$0.371281\pi$
$810$	4.25401	0.149471
$811$	27.0318	0.949214	0.474607	−	0.880198i	$-0.342590\pi$
$811$	27.0318	0.949214	0.474607	+	0.880198i	$0.342590\pi$
$812$	−1.17923	−0.0413828
$813$	28.6973	1.00646
$814$	0	0
$815$	−14.3432	−0.502420
$816$	20.5606	0.719766
$817$	−44.5188	−1.55751
$818$	17.6373	0.616673
$819$	35.3993	1.23695
$820$	−5.43144	−0.189674
$821$	14.4241	0.503404	0.251702	−	0.967805i	$-0.419010\pi$
$821$	14.4241	0.503404	0.251702	+	0.967805i	$0.419010\pi$
$822$	29.3368	1.02324
$823$	−15.3358	−0.534572	−0.267286	−	0.963617i	$-0.586127\pi$
$823$	−15.3358	−0.534572	−0.267286	+	0.963617i	$0.586127\pi$
$824$	−3.12129	−0.108735
$825$	0	0
$826$	5.64597	0.196448
$827$	−44.2084	−1.53728	−0.768638	−	0.639685i	$-0.779065\pi$
$827$	−44.2084	−1.53728	−0.768638	+	0.639685i	$0.779065\pi$
$828$	51.1123	1.77627
$829$	−27.9599	−0.971087	−0.485544	−	0.874212i	$-0.661378\pi$
$829$	−27.9599	−0.971087	−0.485544	+	0.874212i	$0.661378\pi$
$830$	−4.59502	−0.159495
$831$	78.5120	2.72355
$832$	6.51020	0.225701
$833$	−7.07831	−0.245249
$834$	53.7697	1.86189
$835$	−1.91040	−0.0661120
$836$	0	0
$837$	9.08758	0.314113
$838$	−6.70771	−0.231714
$839$	−4.45002	−0.153632	−0.0768159	−	0.997045i	$-0.524475\pi$
$839$	−4.45002	−0.153632	−0.0768159	+	0.997045i	$0.524475\pi$
$840$	−2.90474	−0.100223
$841$	−27.6094	−0.952049
$842$	−16.0438	−0.552904
$843$	39.6261	1.36480
$844$	−9.26733	−0.318995
$845$	−29.3827	−1.01080
$846$	61.9412	2.12958
$847$	0	0
$848$	−7.75606	−0.266344
$849$	53.4036	1.83281
$850$	7.07831	0.242784
$851$	−9.47581	−0.324826
$852$	0.755017	0.0258665
$853$	−2.31141	−0.0791411	−0.0395705	−	0.999217i	$-0.512599\pi$
$853$	−2.31141	−0.0791411	−0.0395705	+	0.999217i	$0.512599\pi$
$854$	6.33662	0.216835
$855$	21.6130	0.739148
$856$	−3.29188	−0.112514
$857$	−2.10357	−0.0718566	−0.0359283	−	0.999354i	$-0.511439\pi$
$857$	−2.10357	−0.0718566	−0.0359283	+	0.999354i	$0.511439\pi$
$858$	0	0
$859$	−6.91941	−0.236087	−0.118044	−	0.993008i	$-0.537662\pi$
$859$	−6.91941	−0.236087	−0.118044	+	0.993008i	$0.537662\pi$
$860$	−11.2003	−0.381926
$861$	−15.7769	−0.537676
$862$	31.5480	1.07453
$863$	−37.5821	−1.27931	−0.639655	−	0.768662i	$-0.720923\pi$
$863$	−37.5821	−1.27931	−0.639655	+	0.768662i	$0.720923\pi$
$864$	7.08034	0.240878
$865$	−14.5926	−0.496162
$866$	8.26911	0.280996
$867$	−96.1540	−3.26556
$868$	−1.28349	−0.0435646
$869$	0	0
$870$	3.42535	0.116130
$871$	25.2675	0.856156
$872$	12.5855	0.426199
$873$	−46.8004	−1.58395
$874$	37.3628	1.26381
$875$	−1.00000	−0.0338062
$876$	14.0150	0.473522
$877$	−34.1431	−1.15293	−0.576465	−	0.817122i	$-0.695568\pi$
$877$	−34.1431	−1.15293	−0.576465	+	0.817122i	$0.695568\pi$
$878$	11.1008	0.374635
$879$	28.6827	0.967443
$880$	0	0
$881$	38.7897	1.30686	0.653429	−	0.756987i	$-0.273330\pi$
$881$	38.7897	1.30686	0.653429	+	0.756987i	$0.273330\pi$
$882$	−5.43751	−0.183091
$883$	1.29604	0.0436152	0.0218076	−	0.999762i	$-0.493058\pi$
$883$	1.29604	0.0436152	0.0218076	+	0.999762i	$0.493058\pi$
$884$	−46.0812	−1.54988
$885$	−16.4001	−0.551282
$886$	−4.53871	−0.152481
$887$	−6.44111	−0.216271	−0.108136	−	0.994136i	$-0.534488\pi$
$887$	−6.44111	−0.216271	−0.108136	+	0.994136i	$0.534488\pi$
$888$	−2.92819	−0.0982635
$889$	16.0026	0.536710
$890$	−1.43088	−0.0479633
$891$	0	0
$892$	26.0134	0.870992
$893$	45.2786	1.51519
$894$	−33.4412	−1.11844
$895$	3.15693	0.105524
$896$	−1.00000	−0.0334077
$897$	−177.757	−5.93513
$898$	9.71975	0.324352
$899$	1.51353	0.0504792
$900$	5.43751	0.181250
$901$	54.8998	1.82898
$902$	0	0
$903$	−32.5339	−1.08266
$904$	−1.20490	−0.0400744
$905$	7.09045	0.235694
$906$	−15.7846	−0.524407
$907$	35.2975	1.17203	0.586017	−	0.810299i	$-0.300695\pi$
$907$	35.2975	1.17203	0.586017	+	0.810299i	$0.300695\pi$
$908$	0.293119	0.00972750
$909$	38.8377	1.28817
$910$	6.51020	0.215811
$911$	−36.9287	−1.22350	−0.611752	−	0.791050i	$-0.709535\pi$
$911$	−36.9287	−1.22350	−0.611752	+	0.791050i	$0.709535\pi$
$912$	11.5457	0.382317
$913$	0	0
$914$	21.1478	0.699506
$915$	−18.4062	−0.608491
$916$	−19.9552	−0.659337
$917$	−14.6019	−0.482197
$918$	−50.1168	−1.65410
$919$	35.4760	1.17025	0.585123	−	0.810945i	$-0.301046\pi$
$919$	35.4760	1.17025	0.585123	+	0.810945i	$0.301046\pi$
$920$	9.39994	0.309907
$921$	18.8908	0.622473
$922$	20.5158	0.675652
$923$	−1.69217	−0.0556984
$924$	0	0
$925$	−1.00807	−0.0331452
$926$	5.06175	0.166339
$927$	16.9720	0.557435
$928$	1.17923	0.0387101
$929$	−17.7706	−0.583034	−0.291517	−	0.956566i	$-0.594160\pi$
$929$	−17.7706	−0.583034	−0.291517	+	0.956566i	$0.594160\pi$
$930$	3.72822	0.122253
$931$	−3.97479	−0.130268
$932$	−0.201558	−0.00660225
$933$	−9.78885	−0.320473
$934$	7.48743	0.244996
$935$	0	0
$936$	−35.3993	−1.15706
$937$	−6.01550	−0.196518	−0.0982589	−	0.995161i	$-0.531327\pi$
$937$	−6.01550	−0.196518	−0.0982589	+	0.995161i	$0.531327\pi$
$938$	−3.88122	−0.126726
$939$	15.7501	0.513985
$940$	11.3915	0.371548
$941$	−30.6883	−1.00041	−0.500205	−	0.865907i	$-0.666742\pi$
$941$	−30.6883	−1.00041	−0.500205	+	0.865907i	$0.666742\pi$
$942$	23.1697	0.754909
$943$	51.0552	1.66258
$944$	−5.64597	−0.183761
$945$	7.08034	0.230324
$946$	0	0
$947$	32.3767	1.05210	0.526051	−	0.850453i	$-0.323672\pi$
$947$	32.3767	1.05210	0.526051	+	0.850453i	$0.323672\pi$
$948$	41.6620	1.35312
$949$	−31.4108	−1.01964
$950$	3.97479	0.128959
$951$	20.7979	0.674417
$952$	7.07831	0.229409
$953$	−11.8836	−0.384948	−0.192474	−	0.981302i	$-0.561651\pi$
$953$	−11.8836	−0.384948	−0.192474	+	0.981302i	$0.561651\pi$
$954$	42.1737	1.36542
$955$	−7.61496	−0.246414
$956$	−23.9193	−0.773604
$957$	0	0
$958$	−0.414174	−0.0133814
$959$	10.0996	0.326134
$960$	2.90474	0.0937501
$961$	−29.3526	−0.946859
$962$	6.56275	0.211591
$963$	17.8996	0.576808
$964$	18.5851	0.598586
$965$	−8.55503	−0.275396
$966$	27.3044	0.878504
$967$	−24.0988	−0.774965	−0.387483	−	0.921877i	$-0.626655\pi$
$967$	−24.0988	−0.774965	−0.387483	+	0.921877i	$0.626655\pi$
$968$	0	0
$969$	−81.7242	−2.62536
$970$	−8.60695	−0.276352
$971$	−2.52446	−0.0810139	−0.0405069	−	0.999179i	$-0.512897\pi$
$971$	−2.52446	−0.0810139	−0.0405069	+	0.999179i	$0.512897\pi$
$972$	8.88423	0.284962
$973$	18.5110	0.593437
$974$	23.7328	0.760448
$975$	−18.9104	−0.605619
$976$	−6.33662	−0.202830
$977$	−25.8513	−0.827056	−0.413528	−	0.910491i	$-0.635704\pi$
$977$	−25.8513	−0.827056	−0.413528	+	0.910491i	$0.635704\pi$
$978$	41.6632	1.33224
$979$	0	0
$980$	−1.00000	−0.0319438
$981$	−68.4338	−2.18492
$982$	32.2162	1.02806
$983$	−0.975472	−0.0311127	−0.0155564	−	0.999879i	$-0.504952\pi$
$983$	−0.975472	−0.0311127	−0.0155564	+	0.999879i	$0.504952\pi$
$984$	15.7769	0.502950
$985$	5.30318	0.168973
$986$	−8.34695	−0.265821
$987$	33.0892	1.05324
$988$	−25.8767	−0.823247
$989$	105.282	3.34777
$990$	0	0
$991$	3.48309	0.110644	0.0553220	−	0.998469i	$-0.482381\pi$
$991$	3.48309	0.110644	0.0553220	+	0.998469i	$0.482381\pi$
$992$	1.28349	0.0407510
$993$	−60.1233	−1.90795
$994$	0.259926	0.00824435
$995$	−27.8463	−0.882788
$996$	13.3473	0.422926
$997$	−43.0019	−1.36188	−0.680942	−	0.732337i	$-0.738430\pi$
$997$	−43.0019	−1.36188	−0.680942	+	0.732337i	$0.738430\pi$
$998$	4.48988	0.142125
$999$	7.13749	0.225820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.dg.1.1		8
11.2	odd	10		770.2.n.k.631.1	yes	16
11.6	odd	10		770.2.n.k.421.1	✓	16
11.10	odd	2		8470.2.a.dh.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.k.421.1	✓	16	11.6	odd	10
770.2.n.k.631.1	yes	16	11.2	odd	10
8470.2.a.dg.1.1		8	1.1	even	1	trivial
8470.2.a.dh.1.1		8	11.10	odd	2

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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:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.90474 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.90474 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.43751 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.90474 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.90474 q^{6} +1.00000 q^{7} -1.00000 q^{8} +5.43751 q^{9} +1.00000 q^{10} -2.90474 q^{12} +6.51020 q^{13} -1.00000 q^{14} +2.90474 q^{15} +1.00000 q^{16} -7.07831 q^{17} -5.43751 q^{18} -3.97479 q^{19} -1.00000 q^{20} -2.90474 q^{21} +9.39994 q^{23} +2.90474 q^{24} +1.00000 q^{25} -6.51020 q^{26} -7.08034 q^{27} +1.00000 q^{28} -1.17923 q^{29} -2.90474 q^{30} -1.28349 q^{31} -1.00000 q^{32} +7.07831 q^{34} -1.00000 q^{35} +5.43751 q^{36} -1.00807 q^{37} +3.97479 q^{38} -18.9104 q^{39} +1.00000 q^{40} +5.43144 q^{41} +2.90474 q^{42} +11.2003 q^{43} -5.43751 q^{45} -9.39994 q^{46} -11.3915 q^{47} -2.90474 q^{48} +1.00000 q^{49} -1.00000 q^{50} +20.5606 q^{51} +6.51020 q^{52} -7.75606 q^{53} +7.08034 q^{54} -1.00000 q^{56} +11.5457 q^{57} +1.17923 q^{58} -5.64597 q^{59} +2.90474 q^{60} -6.33662 q^{61} +1.28349 q^{62} +5.43751 q^{63} +1.00000 q^{64} -6.51020 q^{65} +3.88122 q^{67} -7.07831 q^{68} -27.3044 q^{69} +1.00000 q^{70} -0.259926 q^{71} -5.43751 q^{72} -4.82486 q^{73} +1.00807 q^{74} -2.90474 q^{75} -3.97479 q^{76} +18.9104 q^{78} -14.3428 q^{79} -1.00000 q^{80} +4.25401 q^{81} -5.43144 q^{82} -4.59502 q^{83} -2.90474 q^{84} +7.07831 q^{85} -11.2003 q^{86} +3.42535 q^{87} -1.43088 q^{89} +5.43751 q^{90} +6.51020 q^{91} +9.39994 q^{92} +3.72822 q^{93} +11.3915 q^{94} +3.97479 q^{95} +2.90474 q^{96} -8.60695 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{5} + 8 q^{7} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^5 + 8 * q^7 - 8 * q^8 + 8 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{5} + 8 q^{7} - 8 q^{8} + 8 q^{9} + 8 q^{10} + q^{13} - 8 q^{14} + 8 q^{16} - 6 q^{17} - 8 q^{18} - 5 q^{19} - 8 q^{20} + 10 q^{23} + 8 q^{25} - q^{26} + 8 q^{28} - 3 q^{29} - 8 q^{31} - 8 q^{32} + 6 q^{34} - 8 q^{35} + 8 q^{36} - 6 q^{37} + 5 q^{38} - 35 q^{39} + 8 q^{40} - 11 q^{41} + 5 q^{43} - 8 q^{45} - 10 q^{46} - 15 q^{47} + 8 q^{49} - 8 q^{50} + 6 q^{51} + q^{52} - 16 q^{53} - 8 q^{56} - 38 q^{57} + 3 q^{58} - 9 q^{59} - 32 q^{61} + 8 q^{62} + 8 q^{63} + 8 q^{64} - q^{65} + 33 q^{67} - 6 q^{68} - 22 q^{69} + 8 q^{70} + 11 q^{71} - 8 q^{72} + 34 q^{73} + 6 q^{74} - 5 q^{76} + 35 q^{78} - 31 q^{79} - 8 q^{80} + 20 q^{81} + 11 q^{82} - 50 q^{83} + 6 q^{85} - 5 q^{86} + 12 q^{87} + q^{89} + 8 q^{90} + q^{91} + 10 q^{92} + 26 q^{93} + 15 q^{94} + 5 q^{95} - 4 q^{97} - 8 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 8 * q^5 + 8 * q^7 - 8 * q^8 + 8 * q^9 + 8 * q^10 + q^13 - 8 * q^14 + 8 * q^16 - 6 * q^17 - 8 * q^18 - 5 * q^19 - 8 * q^20 + 10 * q^23 + 8 * q^25 - q^26 + 8 * q^28 - 3 * q^29 - 8 * q^31 - 8 * q^32 + 6 * q^34 - 8 * q^35 + 8 * q^36 - 6 * q^37 + 5 * q^38 - 35 * q^39 + 8 * q^40 - 11 * q^41 + 5 * q^43 - 8 * q^45 - 10 * q^46 - 15 * q^47 + 8 * q^49 - 8 * q^50 + 6 * q^51 + q^52 - 16 * q^53 - 8 * q^56 - 38 * q^57 + 3 * q^58 - 9 * q^59 - 32 * q^61 + 8 * q^62 + 8 * q^63 + 8 * q^64 - q^65 + 33 * q^67 - 6 * q^68 - 22 * q^69 + 8 * q^70 + 11 * q^71 - 8 * q^72 + 34 * q^73 + 6 * q^74 - 5 * q^76 + 35 * q^78 - 31 * q^79 - 8 * q^80 + 20 * q^81 + 11 * q^82 - 50 * q^83 + 6 * q^85 - 5 * q^86 + 12 * q^87 + q^89 + 8 * q^90 + q^91 + 10 * q^92 + 26 * q^93 + 15 * q^94 + 5 * q^95 - 4 * q^97 - 8 * q^98

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