LMFDB - Embedded newform 8470.2.a.df.1.6

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:	$0$
Dimension:	$6$
Coefficient field:	6.6.10784448.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 11x^{4} - 4x^{3} + 31x^{2} + 22x - 2 $ x^6 - 11x^4 - 4x^3 + 31x^2 + 22x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.29207$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.81361 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.81361 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.91638 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.81361 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.81361 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.91638 q^{9} +1.00000 q^{10} +2.81361 q^{12} +0.500855 q^{13} +1.00000 q^{14} +2.81361 q^{15} +1.00000 q^{16} -2.39194 q^{17} +4.91638 q^{18} -3.43043 q^{19} +1.00000 q^{20} +2.81361 q^{21} +3.60363 q^{23} +2.81361 q^{24} +1.00000 q^{25} +0.500855 q^{26} +5.39194 q^{27} +1.00000 q^{28} +4.27139 q^{29} +2.81361 q^{30} +3.10278 q^{31} +1.00000 q^{32} -2.39194 q^{34} +1.00000 q^{35} +4.91638 q^{36} -2.27139 q^{37} -3.43043 q^{38} +1.40921 q^{39} +1.00000 q^{40} +0.0899376 q^{41} +2.81361 q^{42} -3.19923 q^{43} +4.91638 q^{45} +3.60363 q^{46} -1.29720 q^{47} +2.81361 q^{48} +1.00000 q^{49} +1.00000 q^{50} -6.72999 q^{51} +0.500855 q^{52} +8.60536 q^{53} +5.39194 q^{54} +1.00000 q^{56} -9.65187 q^{57} +4.27139 q^{58} +5.89109 q^{59} +2.81361 q^{60} +9.25687 q^{61} +3.10278 q^{62} +4.91638 q^{63} +1.00000 q^{64} +0.500855 q^{65} +3.90762 q^{67} -2.39194 q^{68} +10.1392 q^{69} +1.00000 q^{70} +15.5063 q^{71} +4.91638 q^{72} +7.66162 q^{73} -2.27139 q^{74} +2.81361 q^{75} -3.43043 q^{76} +1.40921 q^{78} -10.3606 q^{79} +1.00000 q^{80} +0.421663 q^{81} +0.0899376 q^{82} +4.19309 q^{83} +2.81361 q^{84} -2.39194 q^{85} -3.19923 q^{86} +12.0180 q^{87} -16.2856 q^{89} +4.91638 q^{90} +0.500855 q^{91} +3.60363 q^{92} +8.72999 q^{93} -1.29720 q^{94} -3.43043 q^{95} +2.81361 q^{96} +15.9907 q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 4 * q^3 + 6 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^7 + 6 * q^8 + 2 * q^9	$ 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{7} + 6 q^{8} + 2 q^{9} + 6 q^{10} + 4 q^{12} + 6 q^{14} + 4 q^{15} + 6 q^{16} + 2 q^{17} + 2 q^{18} + 6 q^{20} + 4 q^{21} + 4 q^{23} + 4 q^{24} + 6 q^{25} + 16 q^{27} + 6 q^{28} + 8 q^{29} + 4 q^{30} + 4 q^{31} + 6 q^{32} + 2 q^{34} + 6 q^{35} + 2 q^{36} + 4 q^{37} + 6 q^{40} + 12 q^{41} + 4 q^{42} - 6 q^{43} + 2 q^{45} + 4 q^{46} + 16 q^{47} + 4 q^{48} + 6 q^{49} + 6 q^{50} + 12 q^{53} + 16 q^{54} + 6 q^{56} + 8 q^{57} + 8 q^{58} + 22 q^{59} + 4 q^{60} - 4 q^{61} + 4 q^{62} + 2 q^{63} + 6 q^{64} + 20 q^{67} + 2 q^{68} + 12 q^{69} + 6 q^{70} + 14 q^{71} + 2 q^{72} + 18 q^{73} + 4 q^{74} + 4 q^{75} + 32 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} - 16 q^{83} + 4 q^{84} + 2 q^{85} - 6 q^{86} - 4 q^{87} + 4 q^{89} + 2 q^{90} + 4 q^{92} + 12 q^{93} + 16 q^{94} + 4 q^{96} + 4 q^{97} + 6 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 4 * q^3 + 6 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^7 + 6 * q^8 + 2 * q^9 + 6 * q^10 + 4 * q^12 + 6 * q^14 + 4 * q^15 + 6 * q^16 + 2 * q^17 + 2 * q^18 + 6 * q^20 + 4 * q^21 + 4 * q^23 + 4 * q^24 + 6 * q^25 + 16 * q^27 + 6 * q^28 + 8 * q^29 + 4 * q^30 + 4 * q^31 + 6 * q^32 + 2 * q^34 + 6 * q^35 + 2 * q^36 + 4 * q^37 + 6 * q^40 + 12 * q^41 + 4 * q^42 - 6 * q^43 + 2 * q^45 + 4 * q^46 + 16 * q^47 + 4 * q^48 + 6 * q^49 + 6 * q^50 + 12 * q^53 + 16 * q^54 + 6 * q^56 + 8 * q^57 + 8 * q^58 + 22 * q^59 + 4 * q^60 - 4 * q^61 + 4 * q^62 + 2 * q^63 + 6 * q^64 + 20 * q^67 + 2 * q^68 + 12 * q^69 + 6 * q^70 + 14 * q^71 + 2 * q^72 + 18 * q^73 + 4 * q^74 + 4 * q^75 + 32 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 - 16 * q^83 + 4 * q^84 + 2 * q^85 - 6 * q^86 - 4 * q^87 + 4 * q^89 + 2 * q^90 + 4 * q^92 + 12 * q^93 + 16 * q^94 + 4 * q^96 + 4 * q^97 + 6 * 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
$3$	2.81361	1.62444	0.812218	−	0.583354i	$-0.198260\pi$
$3$	2.81361	1.62444	0.812218	+	0.583354i	$0.198260\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.81361	1.14865
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	4.91638	1.63879
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	2.81361	0.812218
$13$	0.500855	0.138912	0.0694560	−	0.997585i	$-0.477874\pi$
$13$	0.500855	0.138912	0.0694560	+	0.997585i	$0.477874\pi$
$14$	1.00000	0.267261
$15$	2.81361	0.726470
$16$	1.00000	0.250000
$17$	−2.39194	−0.580132	−0.290066	−	0.957007i	$-0.593677\pi$
$17$	−2.39194	−0.580132	−0.290066	+	0.957007i	$0.593677\pi$
$18$	4.91638	1.15880
$19$	−3.43043	−0.786994	−0.393497	−	0.919326i	$-0.628735\pi$
$19$	−3.43043	−0.786994	−0.393497	+	0.919326i	$0.628735\pi$
$20$	1.00000	0.223607
$21$	2.81361	0.613979
$22$	0	0
$23$	3.60363	0.751409	0.375704	−	0.926740i	$-0.377401\pi$
$23$	3.60363	0.751409	0.375704	+	0.926740i	$0.377401\pi$
$24$	2.81361	0.574325
$25$	1.00000	0.200000
$26$	0.500855	0.0982257
$27$	5.39194	1.03768
$28$	1.00000	0.188982
$29$	4.27139	0.793177	0.396589	−	0.917996i	$-0.370194\pi$
$29$	4.27139	0.793177	0.396589	+	0.917996i	$0.370194\pi$
$30$	2.81361	0.513692
$31$	3.10278	0.557275	0.278637	−	0.960396i	$-0.410117\pi$
$31$	3.10278	0.557275	0.278637	+	0.960396i	$0.410117\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.39194	−0.410215
$35$	1.00000	0.169031
$36$	4.91638	0.819397
$37$	−2.27139	−0.373414	−0.186707	−	0.982416i	$-0.559782\pi$
$37$	−2.27139	−0.373414	−0.186707	+	0.982416i	$0.559782\pi$
$38$	−3.43043	−0.556489
$39$	1.40921	0.225654
$40$	1.00000	0.158114
$41$	0.0899376	0.0140459	0.00702295	−	0.999975i	$-0.497765\pi$
$41$	0.0899376	0.0140459	0.00702295	+	0.999975i	$0.497765\pi$
$42$	2.81361	0.434149
$43$	−3.19923	−0.487878	−0.243939	−	0.969791i	$-0.578440\pi$
$43$	−3.19923	−0.487878	−0.243939	+	0.969791i	$0.578440\pi$
$44$	0	0
$45$	4.91638	0.732891
$46$	3.60363	0.531326
$47$	−1.29720	−0.189216	−0.0946078	−	0.995515i	$-0.530160\pi$
$47$	−1.29720	−0.189216	−0.0946078	+	0.995515i	$0.530160\pi$
$48$	2.81361	0.406109
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−6.72999	−0.942387
$52$	0.500855	0.0694560
$53$	8.60536	1.18204	0.591019	−	0.806658i	$-0.298726\pi$
$53$	8.60536	1.18204	0.591019	+	0.806658i	$0.298726\pi$
$54$	5.39194	0.733751
$55$	0	0
$56$	1.00000	0.133631
$57$	−9.65187	−1.27842
$58$	4.27139	0.560861
$59$	5.89109	0.766954	0.383477	−	0.923550i	$-0.374726\pi$
$59$	5.89109	0.766954	0.383477	+	0.923550i	$0.374726\pi$
$60$	2.81361	0.363235
$61$	9.25687	1.18522	0.592610	−	0.805489i	$-0.298097\pi$
$61$	9.25687	1.18522	0.592610	+	0.805489i	$0.298097\pi$
$62$	3.10278	0.394053
$63$	4.91638	0.619406
$64$	1.00000	0.125000
$65$	0.500855	0.0621234
$66$	0	0
$67$	3.90762	0.477391	0.238696	−	0.971094i	$-0.423280\pi$
$67$	3.90762	0.477391	0.238696	+	0.971094i	$0.423280\pi$
$68$	−2.39194	−0.290066
$69$	10.1392	1.22062
$70$	1.00000	0.119523
$71$	15.5063	1.84026	0.920131	−	0.391610i	$-0.128082\pi$
$71$	15.5063	1.84026	0.920131	+	0.391610i	$0.128082\pi$
$72$	4.91638	0.579401
$73$	7.66162	0.896725	0.448363	−	0.893852i	$-0.352007\pi$
$73$	7.66162	0.896725	0.448363	+	0.893852i	$0.352007\pi$
$74$	−2.27139	−0.264044
$75$	2.81361	0.324887
$76$	−3.43043	−0.393497
$77$	0	0
$78$	1.40921	0.159561
$79$	−10.3606	−1.16566	−0.582832	−	0.812593i	$-0.698055\pi$
$79$	−10.3606	−1.16566	−0.582832	+	0.812593i	$0.698055\pi$
$80$	1.00000	0.111803
$81$	0.421663	0.0468514
$82$	0.0899376	0.00993194
$83$	4.19309	0.460252	0.230126	−	0.973161i	$-0.426086\pi$
$83$	4.19309	0.460252	0.230126	+	0.973161i	$0.426086\pi$
$84$	2.81361	0.306990
$85$	−2.39194	−0.259443
$86$	−3.19923	−0.344982
$87$	12.0180	1.28847
$88$	0	0
$89$	−16.2856	−1.72627	−0.863135	−	0.504973i	$-0.831503\pi$
$89$	−16.2856	−1.72627	−0.863135	+	0.504973i	$0.831503\pi$
$90$	4.91638	0.518232
$91$	0.500855	0.0525038
$92$	3.60363	0.375704
$93$	8.72999	0.905258
$94$	−1.29720	−0.133796
$95$	−3.43043	−0.351954
$96$	2.81361	0.287163
$97$	15.9907	1.62360	0.811802	−	0.583932i	$-0.198487\pi$
$97$	15.9907	1.62360	0.811802	+	0.583932i	$0.198487\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−10.2349	−1.01841	−0.509207	−	0.860644i	$-0.670061\pi$
$101$	−10.2349	−1.01841	−0.509207	+	0.860644i	$0.670061\pi$
$102$	−6.72999	−0.666368
$103$	2.15822	0.212656	0.106328	−	0.994331i	$-0.466091\pi$
$103$	2.15822	0.212656	0.106328	+	0.994331i	$0.466091\pi$
$104$	0.500855	0.0491128
$105$	2.81361	0.274580
$106$	8.60536	0.835826
$107$	−4.14362	−0.400579	−0.200290	−	0.979737i	$-0.564188\pi$
$107$	−4.14362	−0.400579	−0.200290	+	0.979737i	$0.564188\pi$
$108$	5.39194	0.518840
$109$	−8.55011	−0.818952	−0.409476	−	0.912321i	$-0.634289\pi$
$109$	−8.55011	−0.818952	−0.409476	+	0.912321i	$0.634289\pi$
$110$	0	0
$111$	−6.39079	−0.606587
$112$	1.00000	0.0944911
$113$	−17.6102	−1.65663	−0.828313	−	0.560266i	$-0.810699\pi$
$113$	−17.6102	−1.65663	−0.828313	+	0.560266i	$0.810699\pi$
$114$	−9.65187	−0.903981
$115$	3.60363	0.336040
$116$	4.27139	0.396589
$117$	2.46239	0.227648
$118$	5.89109	0.542319
$119$	−2.39194	−0.219269
$120$	2.81361	0.256846
$121$	0	0
$122$	9.25687	0.838078
$123$	0.253049	0.0228167
$124$	3.10278	0.278637
$125$	1.00000	0.0894427
$126$	4.91638	0.437986
$127$	−12.6352	−1.12120	−0.560598	−	0.828088i	$-0.689429\pi$
$127$	−12.6352	−1.12120	−0.560598	+	0.828088i	$0.689429\pi$
$128$	1.00000	0.0883883
$129$	−9.00138	−0.792527
$130$	0.500855	0.0439279
$131$	−6.16025	−0.538224	−0.269112	−	0.963109i	$-0.586730\pi$
$131$	−6.16025	−0.538224	−0.269112	+	0.963109i	$0.586730\pi$
$132$	0	0
$133$	−3.43043	−0.297456
$134$	3.90762	0.337567
$135$	5.39194	0.464065
$136$	−2.39194	−0.205107
$137$	4.37378	0.373677	0.186839	−	0.982391i	$-0.440176\pi$
$137$	4.37378	0.373677	0.186839	+	0.982391i	$0.440176\pi$
$138$	10.1392	0.863106
$139$	12.2300	1.03734	0.518670	−	0.854975i	$-0.326428\pi$
$139$	12.2300	1.03734	0.518670	+	0.854975i	$0.326428\pi$
$140$	1.00000	0.0845154
$141$	−3.64980	−0.307369
$142$	15.5063	1.30126
$143$	0	0
$144$	4.91638	0.409698
$145$	4.27139	0.354720
$146$	7.66162	0.634080
$147$	2.81361	0.232062
$148$	−2.27139	−0.186707
$149$	7.45847	0.611021	0.305511	−	0.952189i	$-0.401173\pi$
$149$	7.45847	0.611021	0.305511	+	0.952189i	$0.401173\pi$
$150$	2.81361	0.229730
$151$	8.99272	0.731817	0.365908	−	0.930651i	$-0.380758\pi$
$151$	8.99272	0.731817	0.365908	+	0.930651i	$0.380758\pi$
$152$	−3.43043	−0.278244
$153$	−11.7597	−0.950716
$154$	0	0
$155$	3.10278	0.249221
$156$	1.40921	0.112827
$157$	−1.14513	−0.0913915	−0.0456958	−	0.998955i	$-0.514550\pi$
$157$	−1.14513	−0.0913915	−0.0456958	+	0.998955i	$0.514550\pi$
$158$	−10.3606	−0.824248
$159$	24.2121	1.92014
$160$	1.00000	0.0790569
$161$	3.60363	0.284006
$162$	0.421663	0.0331290
$163$	−5.36940	−0.420564	−0.210282	−	0.977641i	$-0.567438\pi$
$163$	−5.36940	−0.420564	−0.210282	+	0.977641i	$0.567438\pi$
$164$	0.0899376	0.00702295
$165$	0	0
$166$	4.19309	0.325447
$167$	−23.4652	−1.81579	−0.907897	−	0.419194i	$-0.862313\pi$
$167$	−23.4652	−1.81579	−0.907897	+	0.419194i	$0.862313\pi$
$168$	2.81361	0.217074
$169$	−12.7491	−0.980703
$170$	−2.39194	−0.183454
$171$	−16.8653	−1.28972
$172$	−3.19923	−0.243939
$173$	14.0465	1.06793	0.533966	−	0.845506i	$-0.320701\pi$
$173$	14.0465	1.06793	0.533966	+	0.845506i	$0.320701\pi$
$174$	12.0180	0.911083
$175$	1.00000	0.0755929
$176$	0	0
$177$	16.5752	1.24587
$178$	−16.2856	−1.22066
$179$	−6.46206	−0.482997	−0.241499	−	0.970401i	$-0.577639\pi$
$179$	−6.46206	−0.482997	−0.241499	+	0.970401i	$0.577639\pi$
$180$	4.91638	0.366445
$181$	13.1930	0.980629	0.490314	−	0.871546i	$-0.336882\pi$
$181$	13.1930	0.980629	0.490314	+	0.871546i	$0.336882\pi$
$182$	0.500855	0.0371258
$183$	26.0452	1.92532
$184$	3.60363	0.265663
$185$	−2.27139	−0.166996
$186$	8.72999	0.640114
$187$	0	0
$188$	−1.29720	−0.0946078
$189$	5.39194	0.392206
$190$	−3.43043	−0.248869
$191$	−12.3673	−0.894867	−0.447434	−	0.894317i	$-0.647662\pi$
$191$	−12.3673	−0.894867	−0.447434	+	0.894317i	$0.647662\pi$
$192$	2.81361	0.203055
$193$	−12.2658	−0.882909	−0.441455	−	0.897284i	$-0.645537\pi$
$193$	−12.2658	−0.882909	−0.441455	+	0.897284i	$0.645537\pi$
$194$	15.9907	1.14806
$195$	1.40921	0.100915
$196$	1.00000	0.0714286
$197$	−8.65314	−0.616511	−0.308255	−	0.951304i	$-0.599745\pi$
$197$	−8.65314	−0.616511	−0.308255	+	0.951304i	$0.599745\pi$
$198$	0	0
$199$	12.4838	0.884954	0.442477	−	0.896780i	$-0.354100\pi$
$199$	12.4838	0.884954	0.442477	+	0.896780i	$0.354100\pi$
$200$	1.00000	0.0707107
$201$	10.9945	0.775492
$202$	−10.2349	−0.720128
$203$	4.27139	0.299793
$204$	−6.72999	−0.471193
$205$	0.0899376	0.00628151
$206$	2.15822	0.150370
$207$	17.7168	1.23140
$208$	0.500855	0.0347280
$209$	0	0
$210$	2.81361	0.194157
$211$	6.76072	0.465427	0.232714	−	0.972545i	$-0.425239\pi$
$211$	6.76072	0.465427	0.232714	+	0.972545i	$0.425239\pi$
$212$	8.60536	0.591019
$213$	43.6287	2.98939
$214$	−4.14362	−0.283252
$215$	−3.19923	−0.218186
$216$	5.39194	0.366875
$217$	3.10278	0.210630
$218$	−8.55011	−0.579087
$219$	21.5568	1.45667
$220$	0	0
$221$	−1.19802	−0.0805873
$222$	−6.39079	−0.428922
$223$	−6.14794	−0.411696	−0.205848	−	0.978584i	$-0.565995\pi$
$223$	−6.14794	−0.411696	−0.205848	+	0.978584i	$0.565995\pi$
$224$	1.00000	0.0668153
$225$	4.91638	0.327759
$226$	−17.6102	−1.17141
$227$	−11.2377	−0.745870	−0.372935	−	0.927858i	$-0.621649\pi$
$227$	−11.2377	−0.745870	−0.372935	+	0.927858i	$0.621649\pi$
$228$	−9.65187	−0.639211
$229$	−17.2115	−1.13737	−0.568685	−	0.822555i	$-0.692548\pi$
$229$	−17.2115	−1.13737	−0.568685	+	0.822555i	$0.692548\pi$
$230$	3.60363	0.237616
$231$	0	0
$232$	4.27139	0.280430
$233$	−7.59338	−0.497459	−0.248729	−	0.968573i	$-0.580013\pi$
$233$	−7.59338	−0.497459	−0.248729	+	0.968573i	$0.580013\pi$
$234$	2.46239	0.160972
$235$	−1.29720	−0.0846198
$236$	5.89109	0.383477
$237$	−29.1508	−1.89355
$238$	−2.39194	−0.155047
$239$	−28.8381	−1.86538	−0.932691	−	0.360676i	$-0.882546\pi$
$239$	−28.8381	−1.86538	−0.932691	+	0.360676i	$0.882546\pi$
$240$	2.81361	0.181618
$241$	−15.3781	−0.990589	−0.495295	−	0.868725i	$-0.664940\pi$
$241$	−15.3781	−0.990589	−0.495295	+	0.868725i	$0.664940\pi$
$242$	0	0
$243$	−14.9894	−0.961573
$244$	9.25687	0.592610
$245$	1.00000	0.0638877
$246$	0.253049	0.0161338
$247$	−1.71815	−0.109323
$248$	3.10278	0.197026
$249$	11.7977	0.747650
$250$	1.00000	0.0632456
$251$	9.22254	0.582122	0.291061	−	0.956705i	$-0.405992\pi$
$251$	9.22254	0.582122	0.291061	+	0.956705i	$0.405992\pi$
$252$	4.91638	0.309703
$253$	0	0
$254$	−12.6352	−0.792806
$255$	−6.72999	−0.421448
$256$	1.00000	0.0625000
$257$	0.000868886 0	5.41996e−5 0	2.70998e−5	−	1.00000i	$-0.499991\pi$
$257$	0.000868886 0	5.41996e−5 0	2.70998e−5		1.00000i	$0.499991\pi$
$258$	−9.00138	−0.560401
$259$	−2.27139	−0.141137
$260$	0.500855	0.0310617
$261$	20.9998	1.29985
$262$	−6.16025	−0.380582
$263$	−5.23650	−0.322896	−0.161448	−	0.986881i	$-0.551616\pi$
$263$	−5.23650	−0.322896	−0.161448	+	0.986881i	$0.551616\pi$
$264$	0	0
$265$	8.60536	0.528623
$266$	−3.43043	−0.210333
$267$	−45.8213	−2.80422
$268$	3.90762	0.238696
$269$	−27.8809	−1.69993	−0.849963	−	0.526842i	$-0.823376\pi$
$269$	−27.8809	−1.69993	−0.849963	+	0.526842i	$0.823376\pi$
$270$	5.39194	0.328143
$271$	7.08659	0.430479	0.215240	−	0.976561i	$-0.430947\pi$
$271$	7.08659	0.430479	0.215240	+	0.976561i	$0.430947\pi$
$272$	−2.39194	−0.145033
$273$	1.40921	0.0852891
$274$	4.37378	0.264230
$275$	0	0
$276$	10.1392	0.610308
$277$	−21.2777	−1.27846	−0.639228	−	0.769018i	$-0.720746\pi$
$277$	−21.2777	−1.27846	−0.639228	+	0.769018i	$0.720746\pi$
$278$	12.2300	0.733509
$279$	15.2544	0.913259
$280$	1.00000	0.0597614
$281$	−30.4417	−1.81600	−0.908001	−	0.418969i	$-0.862392\pi$
$281$	−30.4417	−1.81600	−0.908001	+	0.418969i	$0.862392\pi$
$282$	−3.64980	−0.217343
$283$	−14.8159	−0.880711	−0.440356	−	0.897823i	$-0.645148\pi$
$283$	−14.8159	−0.880711	−0.440356	+	0.897823i	$0.645148\pi$
$284$	15.5063	0.920131
$285$	−9.65187	−0.571728
$286$	0	0
$287$	0.0899376	0.00530885
$288$	4.91638	0.289701
$289$	−11.2786	−0.663447
$290$	4.27139	0.250825
$291$	44.9914	2.63744
$292$	7.66162	0.448363
$293$	31.4790	1.83902	0.919511	−	0.393065i	$-0.128585\pi$
$293$	31.4790	1.83902	0.919511	+	0.393065i	$0.128585\pi$
$294$	2.81361	0.164093
$295$	5.89109	0.342992
$296$	−2.27139	−0.132022
$297$	0	0
$298$	7.45847	0.432057
$299$	1.80489	0.104380
$300$	2.81361	0.162444
$301$	−3.19923	−0.184401
$302$	8.99272	0.517473
$303$	−28.7971	−1.65435
$304$	−3.43043	−0.196748
$305$	9.25687	0.530047
$306$	−11.7597	−0.672258
$307$	10.6499	0.607823	0.303911	−	0.952700i	$-0.401707\pi$
$307$	10.6499	0.607823	0.303911	+	0.952700i	$0.401707\pi$
$308$	0	0
$309$	6.07239	0.345446
$310$	3.10278	0.176226
$311$	0.450689	0.0255562	0.0127781	−	0.999918i	$-0.495932\pi$
$311$	0.450689	0.0255562	0.0127781	+	0.999918i	$0.495932\pi$
$312$	1.40921	0.0797807
$313$	−26.5206	−1.49903	−0.749517	−	0.661985i	$-0.769714\pi$
$313$	−26.5206	−1.49903	−0.749517	+	0.661985i	$0.769714\pi$
$314$	−1.14513	−0.0646236
$315$	4.91638	0.277007
$316$	−10.3606	−0.582832
$317$	29.2492	1.64280	0.821399	−	0.570354i	$-0.193194\pi$
$317$	29.2492	1.64280	0.821399	+	0.570354i	$0.193194\pi$
$318$	24.2121	1.35775
$319$	0	0
$320$	1.00000	0.0559017
$321$	−11.6585	−0.650715
$322$	3.60363	0.200822
$323$	8.20539	0.456560
$324$	0.421663	0.0234257
$325$	0.500855	0.0277824
$326$	−5.36940	−0.297383
$327$	−24.0567	−1.33034
$328$	0.0899376	0.00496597
$329$	−1.29720	−0.0715168
$330$	0	0
$331$	−16.5049	−0.907191	−0.453596	−	0.891208i	$-0.649859\pi$
$331$	−16.5049	−0.907191	−0.453596	+	0.891208i	$0.649859\pi$
$332$	4.19309	0.230126
$333$	−11.1670	−0.611949
$334$	−23.4652	−1.28396
$335$	3.90762	0.213496
$336$	2.81361	0.153495
$337$	26.9655	1.46890	0.734452	−	0.678660i	$-0.237439\pi$
$337$	26.9655	1.46890	0.734452	+	0.678660i	$0.237439\pi$
$338$	−12.7491	−0.693462
$339$	−49.5481	−2.69108
$340$	−2.39194	−0.129721
$341$	0	0
$342$	−16.8653	−0.911970
$343$	1.00000	0.0539949
$344$	−3.19923	−0.172491
$345$	10.1392	0.545876
$346$	14.0465	0.755142
$347$	−11.4888	−0.616751	−0.308375	−	0.951265i	$-0.599785\pi$
$347$	−11.4888	−0.616751	−0.308375	+	0.951265i	$0.599785\pi$
$348$	12.0180	0.644233
$349$	−12.0767	−0.646452	−0.323226	−	0.946322i	$-0.604767\pi$
$349$	−12.0767	−0.646452	−0.323226	+	0.946322i	$0.604767\pi$
$350$	1.00000	0.0534522
$351$	2.70058	0.144146
$352$	0	0
$353$	−1.27099	−0.0676477	−0.0338239	−	0.999428i	$-0.510769\pi$
$353$	−1.27099	−0.0676477	−0.0338239	+	0.999428i	$0.510769\pi$
$354$	16.5752	0.880962
$355$	15.5063	0.822990
$356$	−16.2856	−0.863135
$357$	−6.72999	−0.356189
$358$	−6.46206	−0.341530
$359$	−0.866556	−0.0457351	−0.0228675	−	0.999739i	$-0.507280\pi$
$359$	−0.866556	−0.0457351	−0.0228675	+	0.999739i	$0.507280\pi$
$360$	4.91638	0.259116
$361$	−7.23217	−0.380641
$362$	13.1930	0.693409
$363$	0	0
$364$	0.500855	0.0262519
$365$	7.66162	0.401028
$366$	26.0452	1.36140
$367$	18.3256	0.956588	0.478294	−	0.878200i	$-0.341255\pi$
$367$	18.3256	0.956588	0.478294	+	0.878200i	$0.341255\pi$
$368$	3.60363	0.187852
$369$	0.442167	0.0230183
$370$	−2.27139	−0.118084
$371$	8.60536	0.446768
$372$	8.72999	0.452629
$373$	−19.1453	−0.991308	−0.495654	−	0.868520i	$-0.665072\pi$
$373$	−19.1453	−0.991308	−0.495654	+	0.868520i	$0.665072\pi$
$374$	0	0
$375$	2.81361	0.145294
$376$	−1.29720	−0.0668978
$377$	2.13934	0.110182
$378$	5.39194	0.277332
$379$	−6.30548	−0.323891	−0.161945	−	0.986800i	$-0.551777\pi$
$379$	−6.30548	−0.323891	−0.161945	+	0.986800i	$0.551777\pi$
$380$	−3.43043	−0.175977
$381$	−35.5506	−1.82131
$382$	−12.3673	−0.632767
$383$	−8.05894	−0.411792	−0.205896	−	0.978574i	$-0.566011\pi$
$383$	−8.05894	−0.411792	−0.205896	+	0.978574i	$0.566011\pi$
$384$	2.81361	0.143581
$385$	0	0
$386$	−12.2658	−0.624311
$387$	−15.7286	−0.799532
$388$	15.9907	0.811802
$389$	33.7643	1.71192	0.855958	−	0.517046i	$-0.172968\pi$
$389$	33.7643	1.71192	0.855958	+	0.517046i	$0.172968\pi$
$390$	1.40921	0.0713580
$391$	−8.61968	−0.435916
$392$	1.00000	0.0505076
$393$	−17.3325	−0.874310
$394$	−8.65314	−0.435939
$395$	−10.3606	−0.521300
$396$	0	0
$397$	4.64243	0.232997	0.116498	−	0.993191i	$-0.462833\pi$
$397$	4.64243	0.232997	0.116498	+	0.993191i	$0.462833\pi$
$398$	12.4838	0.625757
$399$	−9.65187	−0.483198
$400$	1.00000	0.0500000
$401$	18.2561	0.911668	0.455834	−	0.890065i	$-0.349341\pi$
$401$	18.2561	0.911668	0.455834	+	0.890065i	$0.349341\pi$
$402$	10.9945	0.548356
$403$	1.55404	0.0774122
$404$	−10.2349	−0.509207
$405$	0.421663	0.0209526
$406$	4.27139	0.211985
$407$	0	0
$408$	−6.72999	−0.333184
$409$	−7.94680	−0.392944	−0.196472	−	0.980509i	$-0.562948\pi$
$409$	−7.94680	−0.392944	−0.196472	+	0.980509i	$0.562948\pi$
$410$	0.0899376	0.00444170
$411$	12.3061	0.607015
$412$	2.15822	0.106328
$413$	5.89109	0.289882
$414$	17.7168	0.870734
$415$	4.19309	0.205831
$416$	0.500855	0.0245564
$417$	34.4105	1.68509
$418$	0	0
$419$	−21.4201	−1.04644	−0.523221	−	0.852197i	$-0.675270\pi$
$419$	−21.4201	−1.04644	−0.523221	+	0.852197i	$0.675270\pi$
$420$	2.81361	0.137290
$421$	0.894942	0.0436168	0.0218084	−	0.999762i	$-0.493058\pi$
$421$	0.894942	0.0436168	0.0218084	+	0.999762i	$0.493058\pi$
$422$	6.76072	0.329107
$423$	−6.37751	−0.310085
$424$	8.60536	0.417913
$425$	−2.39194	−0.116026
$426$	43.6287	2.11382
$427$	9.25687	0.447971
$428$	−4.14362	−0.200290
$429$	0	0
$430$	−3.19923	−0.154281
$431$	37.2082	1.79226	0.896128	−	0.443796i	$-0.146369\pi$
$431$	37.2082	1.79226	0.896128	+	0.443796i	$0.146369\pi$
$432$	5.39194	0.259420
$433$	37.0912	1.78249	0.891245	−	0.453522i	$-0.149833\pi$
$433$	37.0912	1.78249	0.891245	+	0.453522i	$0.149833\pi$
$434$	3.10278	0.148938
$435$	12.0180	0.576219
$436$	−8.55011	−0.409476
$437$	−12.3620	−0.591354
$438$	21.5568	1.03002
$439$	16.6322	0.793813	0.396907	−	0.917859i	$-0.370084\pi$
$439$	16.6322	0.793813	0.396907	+	0.917859i	$0.370084\pi$
$440$	0	0
$441$	4.91638	0.234113
$442$	−1.19802	−0.0569838
$443$	18.9936	0.902411	0.451206	−	0.892420i	$-0.350994\pi$
$443$	18.9936	0.902411	0.451206	+	0.892420i	$0.350994\pi$
$444$	−6.39079	−0.303294
$445$	−16.2856	−0.772012
$446$	−6.14794	−0.291113
$447$	20.9852	0.992565
$448$	1.00000	0.0472456
$449$	−15.0632	−0.710877	−0.355439	−	0.934700i	$-0.615669\pi$
$449$	−15.0632	−0.710877	−0.355439	+	0.934700i	$0.615669\pi$
$450$	4.91638	0.231760
$451$	0	0
$452$	−17.6102	−0.828313
$453$	25.3020	1.18879
$454$	−11.2377	−0.527410
$455$	0.500855	0.0234804
$456$	−9.65187	−0.451990
$457$	13.0743	0.611590	0.305795	−	0.952097i	$-0.401078\pi$
$457$	13.0743	0.611590	0.305795	+	0.952097i	$0.401078\pi$
$458$	−17.2115	−0.804242
$459$	−12.8972	−0.601991
$460$	3.60363	0.168020
$461$	−40.0901	−1.86718	−0.933591	−	0.358342i	$-0.883342\pi$
$461$	−40.0901	−1.86718	−0.933591	+	0.358342i	$0.883342\pi$
$462$	0	0
$463$	4.38625	0.203846	0.101923	−	0.994792i	$-0.467500\pi$
$463$	4.38625	0.203846	0.101923	+	0.994792i	$0.467500\pi$
$464$	4.27139	0.198294
$465$	8.72999	0.404844
$466$	−7.59338	−0.351756
$467$	−2.76704	−0.128043	−0.0640217	−	0.997949i	$-0.520393\pi$
$467$	−2.76704	−0.128043	−0.0640217	+	0.997949i	$0.520393\pi$
$468$	2.46239	0.113824
$469$	3.90762	0.180437
$470$	−1.29720	−0.0598352
$471$	−3.22195	−0.148460
$472$	5.89109	0.271159
$473$	0	0
$474$	−29.1508	−1.33894
$475$	−3.43043	−0.157399
$476$	−2.39194	−0.109635
$477$	42.3072	1.93712
$478$	−28.8381	−1.31902
$479$	−2.13584	−0.0975889	−0.0487945	−	0.998809i	$-0.515538\pi$
$479$	−2.13584	−0.0975889	−0.0487945	+	0.998809i	$0.515538\pi$
$480$	2.81361	0.128423
$481$	−1.13764	−0.0518717
$482$	−15.3781	−0.700452
$483$	10.1392	0.461349
$484$	0	0
$485$	15.9907	0.726098
$486$	−14.9894	−0.679935
$487$	−30.0879	−1.36341	−0.681707	−	0.731625i	$-0.738762\pi$
$487$	−30.0879	−1.36341	−0.681707	+	0.731625i	$0.738762\pi$
$488$	9.25687	0.419039
$489$	−15.1074	−0.683179
$490$	1.00000	0.0451754
$491$	14.1922	0.640484	0.320242	−	0.947336i	$-0.396236\pi$
$491$	14.1922	0.640484	0.320242	+	0.947336i	$0.396236\pi$
$492$	0.253049	0.0114083
$493$	−10.2169	−0.460147
$494$	−1.71815	−0.0773030
$495$	0	0
$496$	3.10278	0.139319
$497$	15.5063	0.695554
$498$	11.7977	0.528668
$499$	17.9339	0.802831	0.401416	−	0.915896i	$-0.368518\pi$
$499$	17.9339	0.802831	0.401416	+	0.915896i	$0.368518\pi$
$500$	1.00000	0.0447214
$501$	−66.0219	−2.94964
$502$	9.22254	0.411622
$503$	4.82298	0.215046	0.107523	−	0.994203i	$-0.465708\pi$
$503$	4.82298	0.215046	0.107523	+	0.994203i	$0.465708\pi$
$504$	4.91638	0.218993
$505$	−10.2349	−0.455449
$506$	0	0
$507$	−35.8711	−1.59309
$508$	−12.6352	−0.560598
$509$	35.9415	1.59308	0.796540	−	0.604586i	$-0.206662\pi$
$509$	35.9415	1.59308	0.796540	+	0.604586i	$0.206662\pi$
$510$	−6.72999	−0.298009
$511$	7.66162	0.338930
$512$	1.00000	0.0441942
$513$	−18.4967	−0.816648
$514$	0.000868886 0	3.83249e−5 0
$515$	2.15822	0.0951026
$516$	−9.00138	−0.396264
$517$	0	0
$518$	−2.27139	−0.0997991
$519$	39.5212	1.73479
$520$	0.500855	0.0219639
$521$	14.6257	0.640766	0.320383	−	0.947288i	$-0.396188\pi$
$521$	14.6257	0.640766	0.320383	+	0.947288i	$0.396188\pi$
$522$	20.9998	0.919135
$523$	22.6277	0.989439	0.494720	−	0.869053i	$-0.335271\pi$
$523$	22.6277	0.989439	0.494720	+	0.869053i	$0.335271\pi$
$524$	−6.16025	−0.269112
$525$	2.81361	0.122796
$526$	−5.23650	−0.228322
$527$	−7.42166	−0.323293
$528$	0	0
$529$	−10.0139	−0.435385
$530$	8.60536	0.373793
$531$	28.9628	1.25688
$532$	−3.43043	−0.148728
$533$	0.0450457	0.00195114
$534$	−45.8213	−1.98288
$535$	−4.14362	−0.179144
$536$	3.90762	0.168783
$537$	−18.1817	−0.784598
$538$	−27.8809	−1.20203
$539$	0	0
$540$	5.39194	0.232032
$541$	−25.8522	−1.11147	−0.555737	−	0.831358i	$-0.687564\pi$
$541$	−25.8522	−1.11147	−0.555737	+	0.831358i	$0.687564\pi$
$542$	7.08659	0.304395
$543$	37.1199	1.59297
$544$	−2.39194	−0.102554
$545$	−8.55011	−0.366247
$546$	1.40921	0.0603085
$547$	−32.9722	−1.40979	−0.704896	−	0.709311i	$-0.749006\pi$
$547$	−32.9722	−1.40979	−0.704896	+	0.709311i	$0.749006\pi$
$548$	4.37378	0.186839
$549$	45.5103	1.94233
$550$	0	0
$551$	−14.6527	−0.624226
$552$	10.1392	0.431553
$553$	−10.3606	−0.440579
$554$	−21.2777	−0.904004
$555$	−6.39079	−0.271274
$556$	12.2300	0.518670
$557$	10.6402	0.450840	0.225420	−	0.974262i	$-0.427625\pi$
$557$	10.6402	0.450840	0.225420	+	0.974262i	$0.427625\pi$
$558$	15.2544	0.645771
$559$	−1.60235	−0.0677722
$560$	1.00000	0.0422577
$561$	0	0
$562$	−30.4417	−1.28411
$563$	27.8178	1.17238	0.586190	−	0.810174i	$-0.300627\pi$
$563$	27.8178	1.17238	0.586190	+	0.810174i	$0.300627\pi$
$564$	−3.64980	−0.153684
$565$	−17.6102	−0.740866
$566$	−14.8159	−0.622757
$567$	0.421663	0.0177082
$568$	15.5063	0.650631
$569$	23.2943	0.976547	0.488273	−	0.872691i	$-0.337627\pi$
$569$	23.2943	0.976547	0.488273	+	0.872691i	$0.337627\pi$
$570$	−9.65187	−0.404272
$571$	22.9549	0.960633	0.480317	−	0.877095i	$-0.340522\pi$
$571$	22.9549	0.960633	0.480317	+	0.877095i	$0.340522\pi$
$572$	0	0
$573$	−34.7968	−1.45366
$574$	0.0899376	0.00375392
$575$	3.60363	0.150282
$576$	4.91638	0.204849
$577$	−45.7343	−1.90394	−0.951972	−	0.306184i	$-0.900948\pi$
$577$	−45.7343	−1.90394	−0.951972	+	0.306184i	$0.900948\pi$
$578$	−11.2786	−0.469128
$579$	−34.5110	−1.43423
$580$	4.27139	0.177360
$581$	4.19309	0.173959
$582$	44.9914	1.86495
$583$	0	0
$584$	7.66162	0.317040
$585$	2.46239	0.101807
$586$	31.4790	1.30038
$587$	−29.5719	−1.22056	−0.610282	−	0.792184i	$-0.708944\pi$
$587$	−29.5719	−1.22056	−0.610282	+	0.792184i	$0.708944\pi$
$588$	2.81361	0.116031
$589$	−10.6438	−0.438572
$590$	5.89109	0.242532
$591$	−24.3465	−1.00148
$592$	−2.27139	−0.0933535
$593$	−30.8187	−1.26557	−0.632786	−	0.774327i	$-0.718089\pi$
$593$	−30.8187	−1.26557	−0.632786	+	0.774327i	$0.718089\pi$
$594$	0	0
$595$	−2.39194	−0.0980601
$596$	7.45847	0.305511
$597$	35.1246	1.43755
$598$	1.80489	0.0738076
$599$	0.426966	0.0174454	0.00872268	−	0.999962i	$-0.497223\pi$
$599$	0.426966	0.0174454	0.00872268	+	0.999962i	$0.497223\pi$
$600$	2.81361	0.114865
$601$	34.6294	1.41256	0.706282	−	0.707931i	$-0.250371\pi$
$601$	34.6294	1.41256	0.706282	+	0.707931i	$0.250371\pi$
$602$	−3.19923	−0.130391
$603$	19.2113	0.782346
$604$	8.99272	0.365908
$605$	0	0
$606$	−28.7971	−1.16980
$607$	8.77207	0.356047	0.178024	−	0.984026i	$-0.443030\pi$
$607$	8.77207	0.356047	0.178024	+	0.984026i	$0.443030\pi$
$608$	−3.43043	−0.139122
$609$	12.0180	0.486994
$610$	9.25687	0.374800
$611$	−0.649707	−0.0262843
$612$	−11.7597	−0.475358
$613$	−14.3859	−0.581043	−0.290521	−	0.956868i	$-0.593829\pi$
$613$	−14.3859	−0.581043	−0.290521	+	0.956868i	$0.593829\pi$
$614$	10.6499	0.429795
$615$	0.253049	0.0102039
$616$	0	0
$617$	−28.5656	−1.15001	−0.575005	−	0.818150i	$-0.695000\pi$
$617$	−28.5656	−1.15001	−0.575005	+	0.818150i	$0.695000\pi$
$618$	6.07239	0.244267
$619$	14.5070	0.583084	0.291542	−	0.956558i	$-0.405832\pi$
$619$	14.5070	0.583084	0.291542	+	0.956558i	$0.405832\pi$
$620$	3.10278	0.124610
$621$	19.4306	0.779722
$622$	0.450689	0.0180710
$623$	−16.2856	−0.652469
$624$	1.40921	0.0564135
$625$	1.00000	0.0400000
$626$	−26.5206	−1.05998
$627$	0	0
$628$	−1.14513	−0.0456958
$629$	5.43303	0.216629
$630$	4.91638	0.195873
$631$	−29.3973	−1.17029	−0.585143	−	0.810930i	$-0.698962\pi$
$631$	−29.3973	−1.17029	−0.585143	+	0.810930i	$0.698962\pi$
$632$	−10.3606	−0.412124
$633$	19.0220	0.756057
$634$	29.2492	1.16163
$635$	−12.6352	−0.501414
$636$	24.2121	0.960072
$637$	0.500855	0.0198446
$638$	0	0
$639$	76.2350	3.01581
$640$	1.00000	0.0395285
$641$	−21.4821	−0.848491	−0.424245	−	0.905547i	$-0.639461\pi$
$641$	−21.4821	−0.848491	−0.424245	+	0.905547i	$0.639461\pi$
$642$	−11.6585	−0.460125
$643$	6.62789	0.261379	0.130689	−	0.991423i	$-0.458281\pi$
$643$	6.62789	0.261379	0.130689	+	0.991423i	$0.458281\pi$
$644$	3.60363	0.142003
$645$	−9.00138	−0.354429
$646$	8.20539	0.322837
$647$	−40.0796	−1.57569	−0.787847	−	0.615871i	$-0.788804\pi$
$647$	−40.0796	−1.57569	−0.787847	+	0.615871i	$0.788804\pi$
$648$	0.421663	0.0165645
$649$	0	0
$650$	0.500855	0.0196451
$651$	8.72999	0.342155
$652$	−5.36940	−0.210282
$653$	1.08840	0.0425923	0.0212962	−	0.999773i	$-0.493221\pi$
$653$	1.08840	0.0425923	0.0212962	+	0.999773i	$0.493221\pi$
$654$	−24.0567	−0.940690
$655$	−6.16025	−0.240701
$656$	0.0899376	0.00351147
$657$	37.6675	1.46955
$658$	−1.29720	−0.0505700
$659$	38.5368	1.50118	0.750591	−	0.660767i	$-0.229769\pi$
$659$	38.5368	1.50118	0.750591	+	0.660767i	$0.229769\pi$
$660$	0	0
$661$	23.8017	0.925777	0.462889	−	0.886416i	$-0.346813\pi$
$661$	23.8017	0.925777	0.462889	+	0.886416i	$0.346813\pi$
$662$	−16.5049	−0.641481
$663$	−3.37075	−0.130909
$664$	4.19309	0.162724
$665$	−3.43043	−0.133026
$666$	−11.1670	−0.432713
$667$	15.3925	0.596000
$668$	−23.4652	−0.907897
$669$	−17.2979	−0.668775
$670$	3.90762	0.150964
$671$	0	0
$672$	2.81361	0.108537
$673$	9.60964	0.370424	0.185212	−	0.982699i	$-0.440703\pi$
$673$	9.60964	0.370424	0.185212	+	0.982699i	$0.440703\pi$
$674$	26.9655	1.03867
$675$	5.39194	0.207536
$676$	−12.7491	−0.490352
$677$	4.45989	0.171407	0.0857037	−	0.996321i	$-0.472686\pi$
$677$	4.45989	0.171407	0.0857037	+	0.996321i	$0.472686\pi$
$678$	−49.5481	−1.90288
$679$	15.9907	0.613665
$680$	−2.39194	−0.0917268
$681$	−31.6184	−1.21162
$682$	0	0
$683$	−21.0977	−0.807281	−0.403641	−	0.914918i	$-0.632255\pi$
$683$	−21.0977	−0.807281	−0.403641	+	0.914918i	$0.632255\pi$
$684$	−16.8653	−0.644860
$685$	4.37378	0.167114
$686$	1.00000	0.0381802
$687$	−48.4265	−1.84759
$688$	−3.19923	−0.121970
$689$	4.31003	0.164199
$690$	10.1392	0.385993
$691$	−36.7936	−1.39969	−0.699847	−	0.714293i	$-0.746748\pi$
$691$	−36.7936	−1.39969	−0.699847	+	0.714293i	$0.746748\pi$
$692$	14.0465	0.533966
$693$	0	0
$694$	−11.4888	−0.436109
$695$	12.2300	0.463912
$696$	12.0180	0.455541
$697$	−0.215126	−0.00814846
$698$	−12.0767	−0.457110
$699$	−21.3648	−0.808090
$700$	1.00000	0.0377964
$701$	38.3577	1.44875	0.724374	−	0.689407i	$-0.242129\pi$
$701$	38.3577	1.44875	0.724374	+	0.689407i	$0.242129\pi$
$702$	2.70058	0.101927
$703$	7.79183	0.293875
$704$	0	0
$705$	−3.64980	−0.137459
$706$	−1.27099	−0.0478342
$707$	−10.2349	−0.384924
$708$	16.5752	0.622934
$709$	−37.3501	−1.40271	−0.701357	−	0.712811i	$-0.747422\pi$
$709$	−37.3501	−1.40271	−0.701357	+	0.712811i	$0.747422\pi$
$710$	15.5063	0.581942
$711$	−50.9369	−1.91028
$712$	−16.2856	−0.610329
$713$	11.1813	0.418741
$714$	−6.72999	−0.251863
$715$	0	0
$716$	−6.46206	−0.241499
$717$	−81.1391	−3.03020
$718$	−0.866556	−0.0323396
$719$	−33.1232	−1.23529	−0.617644	−	0.786458i	$-0.711913\pi$
$719$	−33.1232	−1.23529	−0.617644	+	0.786458i	$0.711913\pi$
$720$	4.91638	0.183223
$721$	2.15822	0.0803764
$722$	−7.23217	−0.269153
$723$	−43.2679	−1.60915
$724$	13.1930	0.490314
$725$	4.27139	0.158635
$726$	0	0
$727$	5.85088	0.216997	0.108498	−	0.994097i	$-0.465396\pi$
$727$	5.85088	0.216997	0.108498	+	0.994097i	$0.465396\pi$
$728$	0.500855	0.0185629
$729$	−43.4394	−1.60887
$730$	7.66162	0.283569
$731$	7.65238	0.283033
$732$	26.0452	0.962658
$733$	−5.37537	−0.198544	−0.0992719	−	0.995060i	$-0.531651\pi$
$733$	−5.37537	−0.198544	−0.0992719	+	0.995060i	$0.531651\pi$
$734$	18.3256	0.676410
$735$	2.81361	0.103781
$736$	3.60363	0.132832
$737$	0	0
$738$	0.442167	0.0162764
$739$	25.0957	0.923159	0.461580	−	0.887099i	$-0.347283\pi$
$739$	25.0957	0.923159	0.461580	+	0.887099i	$0.347283\pi$
$740$	−2.27139	−0.0834979
$741$	−4.83418	−0.177588
$742$	8.60536	0.315913
$743$	28.8312	1.05772	0.528858	−	0.848711i	$-0.322621\pi$
$743$	28.8312	1.05772	0.528858	+	0.848711i	$0.322621\pi$
$744$	8.72999	0.320057
$745$	7.45847	0.273257
$746$	−19.1453	−0.700960
$747$	20.6149	0.754258
$748$	0	0
$749$	−4.14362	−0.151405
$750$	2.81361	0.102738
$751$	29.2067	1.06577	0.532884	−	0.846188i	$-0.321108\pi$
$751$	29.2067	1.06577	0.532884	+	0.846188i	$0.321108\pi$
$752$	−1.29720	−0.0473039
$753$	25.9486	0.945620
$754$	2.13934	0.0779103
$755$	8.99272	0.327278
$756$	5.39194	0.196103
$757$	−9.52403	−0.346157	−0.173078	−	0.984908i	$-0.555371\pi$
$757$	−9.52403	−0.346157	−0.173078	+	0.984908i	$0.555371\pi$
$758$	−6.30548	−0.229025
$759$	0	0
$760$	−3.43043	−0.124435
$761$	29.0101	1.05162	0.525808	−	0.850604i	$-0.323763\pi$
$761$	29.0101	1.05162	0.525808	+	0.850604i	$0.323763\pi$
$762$	−35.5506	−1.28786
$763$	−8.55011	−0.309535
$764$	−12.3673	−0.447434
$765$	−11.7597	−0.425173
$766$	−8.05894	−0.291181
$767$	2.95058	0.106539
$768$	2.81361	0.101527
$769$	−6.81244	−0.245663	−0.122831	−	0.992428i	$-0.539197\pi$
$769$	−6.81244	−0.245663	−0.122831	+	0.992428i	$0.539197\pi$
$770$	0	0
$771$	0.00244470	8.80438e−5 0
$772$	−12.2658	−0.441455
$773$	40.1042	1.44245	0.721224	−	0.692702i	$-0.243580\pi$
$773$	40.1042	1.44245	0.721224	+	0.692702i	$0.243580\pi$
$774$	−15.7286	−0.565354
$775$	3.10278	0.111455
$776$	15.9907	0.574031
$777$	−6.39079	−0.229268
$778$	33.7643	1.21051
$779$	−0.308524	−0.0110540
$780$	1.40921	0.0504577
$781$	0	0
$782$	−8.61968	−0.308239
$783$	23.0311	0.823064
$784$	1.00000	0.0357143
$785$	−1.14513	−0.0408715
$786$	−17.3325	−0.618231
$787$	−24.0127	−0.855962	−0.427981	−	0.903788i	$-0.640775\pi$
$787$	−24.0127	−0.855962	−0.427981	+	0.903788i	$0.640775\pi$
$788$	−8.65314	−0.308255
$789$	−14.7334	−0.524525
$790$	−10.3606	−0.368615
$791$	−17.6102	−0.626146
$792$	0	0
$793$	4.63635	0.164641
$794$	4.64243	0.164754
$795$	24.2121	0.858715
$796$	12.4838	0.442477
$797$	−25.6941	−0.910133	−0.455066	−	0.890458i	$-0.650384\pi$
$797$	−25.6941	−0.910133	−0.455066	+	0.890458i	$0.650384\pi$
$798$	−9.65187	−0.341673
$799$	3.10282	0.109770
$800$	1.00000	0.0353553
$801$	−80.0662	−2.82900
$802$	18.2561	0.644647
$803$	0	0
$804$	10.9945	0.387746
$805$	3.60363	0.127011
$806$	1.55404	0.0547387
$807$	−78.4458	−2.76142
$808$	−10.2349	−0.360064
$809$	−15.0751	−0.530013	−0.265007	−	0.964247i	$-0.585374\pi$
$809$	−15.0751	−0.530013	−0.265007	+	0.964247i	$0.585374\pi$
$810$	0.421663	0.0148157
$811$	32.4904	1.14089	0.570447	−	0.821335i	$-0.306770\pi$
$811$	32.4904	1.14089	0.570447	+	0.821335i	$0.306770\pi$
$812$	4.27139	0.149896
$813$	19.9389	0.699287
$814$	0	0
$815$	−5.36940	−0.188082
$816$	−6.72999	−0.235597
$817$	10.9747	0.383957
$818$	−7.94680	−0.277853
$819$	2.46239	0.0860430
$820$	0.0899376	0.00314076
$821$	−39.6858	−1.38504	−0.692521	−	0.721398i	$-0.743500\pi$
$821$	−39.6858	−1.38504	−0.692521	+	0.721398i	$0.743500\pi$
$822$	12.3061	0.429225
$823$	47.5189	1.65641	0.828203	−	0.560429i	$-0.189364\pi$
$823$	47.5189	1.65641	0.828203	+	0.560429i	$0.189364\pi$
$824$	2.15822	0.0751852
$825$	0	0
$826$	5.89109	0.204977
$827$	10.6297	0.369630	0.184815	−	0.982773i	$-0.440831\pi$
$827$	10.6297	0.369630	0.184815	+	0.982773i	$0.440831\pi$
$828$	17.7168	0.615702
$829$	−4.00818	−0.139210	−0.0696050	−	0.997575i	$-0.522174\pi$
$829$	−4.00818	−0.139210	−0.0696050	+	0.997575i	$0.522174\pi$
$830$	4.19309	0.145544
$831$	−59.8672	−2.07677
$832$	0.500855	0.0173640
$833$	−2.39194	−0.0828759
$834$	34.4105	1.19154
$835$	−23.4652	−0.812048
$836$	0	0
$837$	16.7300	0.578273
$838$	−21.4201	−0.739946
$839$	24.5933	0.849055	0.424527	−	0.905415i	$-0.360440\pi$
$839$	24.5933	0.849055	0.424527	+	0.905415i	$0.360440\pi$
$840$	2.81361	0.0970786
$841$	−10.7552	−0.370870
$842$	0.894942	0.0308417
$843$	−85.6510	−2.94998
$844$	6.76072	0.232714
$845$	−12.7491	−0.438584
$846$	−6.37751	−0.219263
$847$	0	0
$848$	8.60536	0.295509
$849$	−41.6860	−1.43066
$850$	−2.39194	−0.0820430
$851$	−8.18524	−0.280587
$852$	43.6287	1.49469
$853$	9.44511	0.323395	0.161697	−	0.986840i	$-0.448303\pi$
$853$	9.44511	0.323395	0.161697	+	0.986840i	$0.448303\pi$
$854$	9.25687	0.316764
$855$	−16.8653	−0.576781
$856$	−4.14362	−0.141626
$857$	−5.17154	−0.176656	−0.0883282	−	0.996091i	$-0.528152\pi$
$857$	−5.17154	−0.176656	−0.0883282	+	0.996091i	$0.528152\pi$
$858$	0	0
$859$	−34.8136	−1.18782	−0.593912	−	0.804530i	$-0.702417\pi$
$859$	−34.8136	−1.18782	−0.593912	+	0.804530i	$0.702417\pi$
$860$	−3.19923	−0.109093
$861$	0.253049	0.00862389
$862$	37.2082	1.26732
$863$	−12.0780	−0.411140	−0.205570	−	0.978642i	$-0.565905\pi$
$863$	−12.0780	−0.411140	−0.205570	+	0.978642i	$0.565905\pi$
$864$	5.39194	0.183438
$865$	14.0465	0.477594
$866$	37.0912	1.26041
$867$	−31.7336	−1.07773
$868$	3.10278	0.105315
$869$	0	0
$870$	12.0180	0.407449
$871$	1.95715	0.0663154
$872$	−8.55011	−0.289543
$873$	78.6161	2.66075
$874$	−12.3620	−0.418151
$875$	1.00000	0.0338062
$876$	21.5568	0.728337
$877$	−22.5704	−0.762149	−0.381074	−	0.924544i	$-0.624446\pi$
$877$	−22.5704	−0.762149	−0.381074	+	0.924544i	$0.624446\pi$
$878$	16.6322	0.561311
$879$	88.5695	2.98737
$880$	0	0
$881$	26.5330	0.893920	0.446960	−	0.894554i	$-0.352507\pi$
$881$	26.5330	0.893920	0.446960	+	0.894554i	$0.352507\pi$
$882$	4.91638	0.165543
$883$	−19.5994	−0.659572	−0.329786	−	0.944056i	$-0.606977\pi$
$883$	−19.5994	−0.659572	−0.329786	+	0.944056i	$0.606977\pi$
$884$	−1.19802	−0.0402936
$885$	16.5752	0.557169
$886$	18.9936	0.638101
$887$	16.1610	0.542635	0.271317	−	0.962490i	$-0.412541\pi$
$887$	16.1610	0.542635	0.271317	+	0.962490i	$0.412541\pi$
$888$	−6.39079	−0.214461
$889$	−12.6352	−0.423772
$890$	−16.2856	−0.545895
$891$	0	0
$892$	−6.14794	−0.205848
$893$	4.44994	0.148912
$894$	20.9852	0.701850
$895$	−6.46206	−0.216003
$896$	1.00000	0.0334077
$897$	5.07826	0.169558
$898$	−15.0632	−0.502666
$899$	13.2532	0.442018
$900$	4.91638	0.163879
$901$	−20.5835	−0.685737
$902$	0	0
$903$	−9.00138	−0.299547
$904$	−17.6102	−0.585706
$905$	13.1930	0.438551
$906$	25.3020	0.840601
$907$	49.8041	1.65372	0.826859	−	0.562410i	$-0.190126\pi$
$907$	49.8041	1.65372	0.826859	+	0.562410i	$0.190126\pi$
$908$	−11.2377	−0.372935
$909$	−50.3189	−1.66897
$910$	0.500855	0.0166032
$911$	44.4515	1.47274	0.736372	−	0.676577i	$-0.236538\pi$
$911$	44.4515	1.47274	0.736372	+	0.676577i	$0.236538\pi$
$912$	−9.65187	−0.319605
$913$	0	0
$914$	13.0743	0.432459
$915$	26.0452	0.861028
$916$	−17.2115	−0.568685
$917$	−6.16025	−0.203429
$918$	−12.8972	−0.425672
$919$	−25.2876	−0.834162	−0.417081	−	0.908869i	$-0.636947\pi$
$919$	−25.2876	−0.834162	−0.417081	+	0.908869i	$0.636947\pi$
$920$	3.60363	0.118808
$921$	29.9647	0.987369
$922$	−40.0901	−1.32030
$923$	7.76642	0.255635
$924$	0	0
$925$	−2.27139	−0.0746828
$926$	4.38625	0.144141
$927$	10.6106	0.348499
$928$	4.27139	0.140215
$929$	58.4872	1.91890	0.959452	−	0.281873i	$-0.0909558\pi$
$929$	58.4872	1.91890	0.959452	+	0.281873i	$0.0909558\pi$
$930$	8.72999	0.286268
$931$	−3.43043	−0.112428
$932$	−7.59338	−0.248729
$933$	1.26806	0.0415144
$934$	−2.76704	−0.0905404
$935$	0	0
$936$	2.46239	0.0804858
$937$	4.14373	0.135370	0.0676849	−	0.997707i	$-0.478439\pi$
$937$	4.14373	0.135370	0.0676849	+	0.997707i	$0.478439\pi$
$938$	3.90762	0.127588
$939$	−74.6186	−2.43509
$940$	−1.29720	−0.0423099
$941$	−5.11048	−0.166597	−0.0832985	−	0.996525i	$-0.526545\pi$
$941$	−5.11048	−0.166597	−0.0832985	+	0.996525i	$0.526545\pi$
$942$	−3.22195	−0.104977
$943$	0.324102	0.0105542
$944$	5.89109	0.191739
$945$	5.39194	0.175400
$946$	0	0
$947$	14.4259	0.468779	0.234389	−	0.972143i	$-0.424691\pi$
$947$	14.4259	0.468779	0.234389	+	0.972143i	$0.424691\pi$
$948$	−29.1508	−0.946773
$949$	3.83736	0.124566
$950$	−3.43043	−0.111298
$951$	82.2957	2.66862
$952$	−2.39194	−0.0775233
$953$	37.3047	1.20842	0.604208	−	0.796827i	$-0.293490\pi$
$953$	37.3047	1.20842	0.604208	+	0.796827i	$0.293490\pi$
$954$	42.3072	1.36975
$955$	−12.3673	−0.400197
$956$	−28.8381	−0.932691
$957$	0	0
$958$	−2.13584	−0.0690058
$959$	4.37378	0.141237
$960$	2.81361	0.0908088
$961$	−21.3728	−0.689445
$962$	−1.13764	−0.0366788
$963$	−20.3716	−0.656467
$964$	−15.3781	−0.495295
$965$	−12.2658	−0.394849
$966$	10.1392	0.326223
$967$	−55.7048	−1.79135	−0.895673	−	0.444712i	$-0.853306\pi$
$967$	−55.7048	−1.79135	−0.895673	+	0.444712i	$0.853306\pi$
$968$	0	0
$969$	23.0867	0.741653
$970$	15.9907	0.513429
$971$	0.975158	0.0312943	0.0156471	−	0.999878i	$-0.495019\pi$
$971$	0.975158	0.0312943	0.0156471	+	0.999878i	$0.495019\pi$
$972$	−14.9894	−0.480786
$973$	12.2300	0.392077
$974$	−30.0879	−0.964079
$975$	1.40921	0.0451308
$976$	9.25687	0.296305
$977$	14.8373	0.474688	0.237344	−	0.971426i	$-0.423723\pi$
$977$	14.8373	0.474688	0.237344	+	0.971426i	$0.423723\pi$
$978$	−15.1074	−0.483080
$979$	0	0
$980$	1.00000	0.0319438
$981$	−42.0356	−1.34209
$982$	14.1922	0.452891
$983$	−9.04686	−0.288550	−0.144275	−	0.989538i	$-0.546085\pi$
$983$	−9.04686	−0.288550	−0.144275	+	0.989538i	$0.546085\pi$
$984$	0.253049	0.00806691
$985$	−8.65314	−0.275712
$986$	−10.2169	−0.325373
$987$	−3.64980	−0.116174
$988$	−1.71815	−0.0546615
$989$	−11.5288	−0.366596
$990$	0	0
$991$	−34.7717	−1.10456	−0.552280	−	0.833659i	$-0.686242\pi$
$991$	−34.7717	−1.10456	−0.552280	+	0.833659i	$0.686242\pi$
$992$	3.10278	0.0985132
$993$	−46.4383	−1.47367
$994$	15.5063	0.491831
$995$	12.4838	0.395764
$996$	11.7977	0.373825
$997$	23.5849	0.746942	0.373471	−	0.927642i	$-0.378168\pi$
$997$	23.5849	0.746942	0.373471	+	0.927642i	$0.378168\pi$
$998$	17.9339	0.567688
$999$	−12.2472	−0.387484

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.df.1.6	yes	6
11.10	odd	2		8470.2.a.cz.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.cz.1.5	✓	6	11.10	odd	2
8470.2.a.df.1.6	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.81361 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.81361 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.91638 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.81361 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.81361 q^{6} +1.00000 q^{7} +1.00000 q^{8} +4.91638 q^{9} +1.00000 q^{10} +2.81361 q^{12} +0.500855 q^{13} +1.00000 q^{14} +2.81361 q^{15} +1.00000 q^{16} -2.39194 q^{17} +4.91638 q^{18} -3.43043 q^{19} +1.00000 q^{20} +2.81361 q^{21} +3.60363 q^{23} +2.81361 q^{24} +1.00000 q^{25} +0.500855 q^{26} +5.39194 q^{27} +1.00000 q^{28} +4.27139 q^{29} +2.81361 q^{30} +3.10278 q^{31} +1.00000 q^{32} -2.39194 q^{34} +1.00000 q^{35} +4.91638 q^{36} -2.27139 q^{37} -3.43043 q^{38} +1.40921 q^{39} +1.00000 q^{40} +0.0899376 q^{41} +2.81361 q^{42} -3.19923 q^{43} +4.91638 q^{45} +3.60363 q^{46} -1.29720 q^{47} +2.81361 q^{48} +1.00000 q^{49} +1.00000 q^{50} -6.72999 q^{51} +0.500855 q^{52} +8.60536 q^{53} +5.39194 q^{54} +1.00000 q^{56} -9.65187 q^{57} +4.27139 q^{58} +5.89109 q^{59} +2.81361 q^{60} +9.25687 q^{61} +3.10278 q^{62} +4.91638 q^{63} +1.00000 q^{64} +0.500855 q^{65} +3.90762 q^{67} -2.39194 q^{68} +10.1392 q^{69} +1.00000 q^{70} +15.5063 q^{71} +4.91638 q^{72} +7.66162 q^{73} -2.27139 q^{74} +2.81361 q^{75} -3.43043 q^{76} +1.40921 q^{78} -10.3606 q^{79} +1.00000 q^{80} +0.421663 q^{81} +0.0899376 q^{82} +4.19309 q^{83} +2.81361 q^{84} -2.39194 q^{85} -3.19923 q^{86} +12.0180 q^{87} -16.2856 q^{89} +4.91638 q^{90} +0.500855 q^{91} +3.60363 q^{92} +8.72999 q^{93} -1.29720 q^{94} -3.43043 q^{95} +2.81361 q^{96} +15.9907 q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 4 * q^3 + 6 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^7 + 6 * q^8 + 2 * q^9	\( 6 q + 6 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{7} + 6 q^{8} + 2 q^{9} + 6 q^{10} + 4 q^{12} + 6 q^{14} + 4 q^{15} + 6 q^{16} + 2 q^{17} + 2 q^{18} + 6 q^{20} + 4 q^{21} + 4 q^{23} + 4 q^{24} + 6 q^{25} + 16 q^{27} + 6 q^{28} + 8 q^{29} + 4 q^{30} + 4 q^{31} + 6 q^{32} + 2 q^{34} + 6 q^{35} + 2 q^{36} + 4 q^{37} + 6 q^{40} + 12 q^{41} + 4 q^{42} - 6 q^{43} + 2 q^{45} + 4 q^{46} + 16 q^{47} + 4 q^{48} + 6 q^{49} + 6 q^{50} + 12 q^{53} + 16 q^{54} + 6 q^{56} + 8 q^{57} + 8 q^{58} + 22 q^{59} + 4 q^{60} - 4 q^{61} + 4 q^{62} + 2 q^{63} + 6 q^{64} + 20 q^{67} + 2 q^{68} + 12 q^{69} + 6 q^{70} + 14 q^{71} + 2 q^{72} + 18 q^{73} + 4 q^{74} + 4 q^{75} + 32 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} - 16 q^{83} + 4 q^{84} + 2 q^{85} - 6 q^{86} - 4 q^{87} + 4 q^{89} + 2 q^{90} + 4 q^{92} + 12 q^{93} + 16 q^{94} + 4 q^{96} + 4 q^{97} + 6 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 4 * q^3 + 6 * q^4 + 6 * q^5 + 4 * q^6 + 6 * q^7 + 6 * q^8 + 2 * q^9 + 6 * q^10 + 4 * q^12 + 6 * q^14 + 4 * q^15 + 6 * q^16 + 2 * q^17 + 2 * q^18 + 6 * q^20 + 4 * q^21 + 4 * q^23 + 4 * q^24 + 6 * q^25 + 16 * q^27 + 6 * q^28 + 8 * q^29 + 4 * q^30 + 4 * q^31 + 6 * q^32 + 2 * q^34 + 6 * q^35 + 2 * q^36 + 4 * q^37 + 6 * q^40 + 12 * q^41 + 4 * q^42 - 6 * q^43 + 2 * q^45 + 4 * q^46 + 16 * q^47 + 4 * q^48 + 6 * q^49 + 6 * q^50 + 12 * q^53 + 16 * q^54 + 6 * q^56 + 8 * q^57 + 8 * q^58 + 22 * q^59 + 4 * q^60 - 4 * q^61 + 4 * q^62 + 2 * q^63 + 6 * q^64 + 20 * q^67 + 2 * q^68 + 12 * q^69 + 6 * q^70 + 14 * q^71 + 2 * q^72 + 18 * q^73 + 4 * q^74 + 4 * q^75 + 32 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 - 16 * q^83 + 4 * q^84 + 2 * q^85 - 6 * q^86 - 4 * q^87 + 4 * q^89 + 2 * q^90 + 4 * q^92 + 12 * q^93 + 16 * q^94 + 4 * q^96 + 4 * q^97 + 6 * q^98

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