LMFDB - Embedded newform 8470.2.a.cz.1.3

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			1.3
Root			$-1.84763$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.529317 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.529317 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.71982 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.529317 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.529317 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.71982 q^{9} -1.00000 q^{10} +0.529317 q^{12} -4.81243 q^{13} +1.00000 q^{14} +0.529317 q^{15} +1.00000 q^{16} -6.02760 q^{17} +2.71982 q^{18} -1.96321 q^{19} +1.00000 q^{20} -0.529317 q^{21} +2.56329 q^{23} -0.529317 q^{24} +1.00000 q^{25} +4.81243 q^{26} -3.02760 q^{27} -1.00000 q^{28} -8.14477 q^{29} -0.529317 q^{30} -2.24914 q^{31} -1.00000 q^{32} +6.02760 q^{34} -1.00000 q^{35} -2.71982 q^{36} -6.14477 q^{37} +1.96321 q^{38} -2.54730 q^{39} -1.00000 q^{40} +5.35973 q^{41} +0.529317 q^{42} +5.58127 q^{43} -2.71982 q^{45} -2.56329 q^{46} +6.23315 q^{47} +0.529317 q^{48} +1.00000 q^{49} -1.00000 q^{50} -3.19051 q^{51} -4.81243 q^{52} -0.648854 q^{53} +3.02760 q^{54} +1.00000 q^{56} -1.03916 q^{57} +8.14477 q^{58} -6.84003 q^{59} +0.529317 q^{60} -1.67669 q^{61} +2.24914 q^{62} +2.71982 q^{63} +1.00000 q^{64} -4.81243 q^{65} +7.80030 q^{67} -6.02760 q^{68} +1.35679 q^{69} +1.00000 q^{70} +8.56040 q^{71} +2.71982 q^{72} +5.50769 q^{73} +6.14477 q^{74} +0.529317 q^{75} -1.96321 q^{76} +2.54730 q^{78} -3.71916 q^{79} +1.00000 q^{80} +6.55691 q^{81} -5.35973 q^{82} +11.5079 q^{83} -0.529317 q^{84} -6.02760 q^{85} -5.58127 q^{86} -4.31116 q^{87} -14.2096 q^{89} +2.71982 q^{90} +4.81243 q^{91} +2.56329 q^{92} -1.19051 q^{93} -6.23315 q^{94} -1.96321 q^{95} -0.529317 q^{96} -3.26750 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.529317	0.305601	0.152801	−	0.988257i	$-0.451171\pi$
$3$	0.529317	0.305601	0.152801	+	0.988257i	$0.451171\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.529317	−0.216093
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.71982	−0.906608
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	0.529317	0.152801
$13$	−4.81243	−1.33473	−0.667364	−	0.744732i	$-0.732577\pi$
$13$	−4.81243	−1.33473	−0.667364	+	0.744732i	$0.732577\pi$
$14$	1.00000	0.267261
$15$	0.529317	0.136669
$16$	1.00000	0.250000
$17$	−6.02760	−1.46191	−0.730954	−	0.682427i	$-0.760924\pi$
$17$	−6.02760	−1.46191	−0.730954	+	0.682427i	$0.760924\pi$
$18$	2.71982	0.641069
$19$	−1.96321	−0.450391	−0.225196	−	0.974314i	$-0.572302\pi$
$19$	−1.96321	−0.450391	−0.225196	+	0.974314i	$0.572302\pi$
$20$	1.00000	0.223607
$21$	−0.529317	−0.115506
$22$	0	0
$23$	2.56329	0.534483	0.267241	−	0.963630i	$-0.413888\pi$
$23$	2.56329	0.534483	0.267241	+	0.963630i	$0.413888\pi$
$24$	−0.529317	−0.108046
$25$	1.00000	0.200000
$26$	4.81243	0.943795
$27$	−3.02760	−0.582661
$28$	−1.00000	−0.188982
$29$	−8.14477	−1.51245	−0.756223	−	0.654314i	$-0.772957\pi$
$29$	−8.14477	−1.51245	−0.756223	+	0.654314i	$0.772957\pi$
$30$	−0.529317	−0.0966395
$31$	−2.24914	−0.403958	−0.201979	−	0.979390i	$-0.564737\pi$
$31$	−2.24914	−0.403958	−0.201979	+	0.979390i	$0.564737\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	6.02760	1.03372
$35$	−1.00000	−0.169031
$36$	−2.71982	−0.453304
$37$	−6.14477	−1.01019	−0.505097	−	0.863063i	$-0.668543\pi$
$37$	−6.14477	−1.01019	−0.505097	+	0.863063i	$0.668543\pi$
$38$	1.96321	0.318475
$39$	−2.54730	−0.407894
$40$	−1.00000	−0.158114
$41$	5.35973	0.837049	0.418524	−	0.908206i	$-0.362547\pi$
$41$	5.35973	0.837049	0.418524	+	0.908206i	$0.362547\pi$
$42$	0.529317	0.0816753
$43$	5.58127	0.851136	0.425568	−	0.904927i	$-0.360074\pi$
$43$	5.58127	0.851136	0.425568	+	0.904927i	$0.360074\pi$
$44$	0	0
$45$	−2.71982	−0.405447
$46$	−2.56329	−0.377936
$47$	6.23315	0.909198	0.454599	−	0.890696i	$-0.349782\pi$
$47$	6.23315	0.909198	0.454599	+	0.890696i	$0.349782\pi$
$48$	0.529317	0.0764003
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−3.19051	−0.446760
$52$	−4.81243	−0.667364
$53$	−0.648854	−0.0891270	−0.0445635	−	0.999007i	$-0.514190\pi$
$53$	−0.648854	−0.0891270	−0.0445635	+	0.999007i	$0.514190\pi$
$54$	3.02760	0.412004
$55$	0	0
$56$	1.00000	0.133631
$57$	−1.03916	−0.137640
$58$	8.14477	1.06946
$59$	−6.84003	−0.890496	−0.445248	−	0.895407i	$-0.646884\pi$
$59$	−6.84003	−0.890496	−0.445248	+	0.895407i	$0.646884\pi$
$60$	0.529317	0.0683345
$61$	−1.67669	−0.214679	−0.107339	−	0.994222i	$-0.534233\pi$
$61$	−1.67669	−0.214679	−0.107339	+	0.994222i	$0.534233\pi$
$62$	2.24914	0.285641
$63$	2.71982	0.342666
$64$	1.00000	0.125000
$65$	−4.81243	−0.596908
$66$	0	0
$67$	7.80030	0.952958	0.476479	−	0.879186i	$-0.341913\pi$
$67$	7.80030	0.952958	0.476479	+	0.879186i	$0.341913\pi$
$68$	−6.02760	−0.730954
$69$	1.35679	0.163338
$70$	1.00000	0.119523
$71$	8.56040	1.01593	0.507966	−	0.861377i	$-0.330397\pi$
$71$	8.56040	1.01593	0.507966	+	0.861377i	$0.330397\pi$
$72$	2.71982	0.320534
$73$	5.50769	0.644626	0.322313	−	0.946633i	$-0.395540\pi$
$73$	5.50769	0.644626	0.322313	+	0.946633i	$0.395540\pi$
$74$	6.14477	0.714315
$75$	0.529317	0.0611202
$76$	−1.96321	−0.225196
$77$	0	0
$78$	2.54730	0.288425
$79$	−3.71916	−0.418438	−0.209219	−	0.977869i	$-0.567092\pi$
$79$	−3.71916	−0.418438	−0.209219	+	0.977869i	$0.567092\pi$
$80$	1.00000	0.111803
$81$	6.55691	0.728546
$82$	−5.35973	−0.591883
$83$	11.5079	1.26316	0.631578	−	0.775312i	$-0.282408\pi$
$83$	11.5079	1.26316	0.631578	+	0.775312i	$0.282408\pi$
$84$	−0.529317	−0.0577532
$85$	−6.02760	−0.653785
$86$	−5.58127	−0.601844
$87$	−4.31116	−0.462205
$88$	0	0
$89$	−14.2096	−1.50622	−0.753108	−	0.657897i	$-0.771446\pi$
$89$	−14.2096	−1.50622	−0.753108	+	0.657897i	$0.771446\pi$
$90$	2.71982	0.286695
$91$	4.81243	0.504480
$92$	2.56329	0.267241
$93$	−1.19051	−0.123450
$94$	−6.23315	−0.642900
$95$	−1.96321	−0.201421
$96$	−0.529317	−0.0540231
$97$	−3.26750	−0.331764	−0.165882	−	0.986146i	$-0.553047\pi$
$97$	−3.26750	−0.331764	−0.165882	+	0.986146i	$0.553047\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−0.584368	−0.0581468	−0.0290734	−	0.999577i	$-0.509256\pi$
$101$	−0.584368	−0.0581468	−0.0290734	+	0.999577i	$0.509256\pi$
$102$	3.19051	0.315907
$103$	12.8427	1.26543	0.632717	−	0.774383i	$-0.281940\pi$
$103$	12.8427	1.26543	0.632717	+	0.774383i	$0.281940\pi$
$104$	4.81243	0.471897
$105$	−0.529317	−0.0516560
$106$	0.648854	0.0630223
$107$	4.82110	0.466073	0.233037	−	0.972468i	$-0.425134\pi$
$107$	4.82110	0.466073	0.233037	+	0.972468i	$0.425134\pi$
$108$	−3.02760	−0.291331
$109$	9.52895	0.912708	0.456354	−	0.889798i	$-0.349155\pi$
$109$	9.52895	0.912708	0.456354	+	0.889798i	$0.349155\pi$
$110$	0	0
$111$	−3.25253	−0.308716
$112$	−1.00000	−0.0944911
$113$	−2.71812	−0.255699	−0.127850	−	0.991794i	$-0.540807\pi$
$113$	−2.71812	−0.255699	−0.127850	+	0.991794i	$0.540807\pi$
$114$	1.03916	0.0973262
$115$	2.56329	0.239028
$116$	−8.14477	−0.756223
$117$	13.0890	1.21007
$118$	6.84003	0.629675
$119$	6.02760	0.552549
$120$	−0.529317	−0.0483198
$121$	0	0
$122$	1.67669	0.151801
$123$	2.83699	0.255803
$124$	−2.24914	−0.201979
$125$	1.00000	0.0894427
$126$	−2.71982	−0.242301
$127$	3.60394	0.319798	0.159899	−	0.987133i	$-0.448883\pi$
$127$	3.60394	0.319798	0.159899	+	0.987133i	$0.448883\pi$
$128$	−1.00000	−0.0883883
$129$	2.95426	0.260108
$130$	4.81243	0.422078
$131$	5.17800	0.452404	0.226202	−	0.974080i	$-0.427369\pi$
$131$	5.17800	0.452404	0.226202	+	0.974080i	$0.427369\pi$
$132$	0	0
$133$	1.96321	0.170232
$134$	−7.80030	−0.673843
$135$	−3.02760	−0.260574
$136$	6.02760	0.516862
$137$	7.79465	0.665942	0.332971	−	0.942937i	$-0.391949\pi$
$137$	7.79465	0.665942	0.332971	+	0.942937i	$0.391949\pi$
$138$	−1.35679	−0.115498
$139$	−9.73564	−0.825767	−0.412883	−	0.910784i	$-0.635478\pi$
$139$	−9.73564	−0.825767	−0.412883	+	0.910784i	$0.635478\pi$
$140$	−1.00000	−0.0845154
$141$	3.29931	0.277852
$142$	−8.56040	−0.718373
$143$	0	0
$144$	−2.71982	−0.226652
$145$	−8.14477	−0.676386
$146$	−5.50769	−0.455820
$147$	0.529317	0.0436573
$148$	−6.14477	−0.505097
$149$	−5.26382	−0.431229	−0.215614	−	0.976479i	$-0.569175\pi$
$149$	−5.26382	−0.431229	−0.215614	+	0.976479i	$0.569175\pi$
$150$	−0.529317	−0.0432185
$151$	3.80904	0.309976	0.154988	−	0.987916i	$-0.450466\pi$
$151$	3.80904	0.309976	0.154988	+	0.987916i	$0.450466\pi$
$152$	1.96321	0.159237
$153$	16.3940	1.32538
$154$	0	0
$155$	−2.24914	−0.180655
$156$	−2.54730	−0.203947
$157$	15.8237	1.26287	0.631436	−	0.775428i	$-0.282466\pi$
$157$	15.8237	1.26287	0.631436	+	0.775428i	$0.282466\pi$
$158$	3.71916	0.295880
$159$	−0.343449	−0.0272373
$160$	−1.00000	−0.0790569
$161$	−2.56329	−0.202015
$162$	−6.55691	−0.515160
$163$	10.0410	0.786470	0.393235	−	0.919438i	$-0.371356\pi$
$163$	10.0410	0.786470	0.393235	+	0.919438i	$0.371356\pi$
$164$	5.35973	0.418524
$165$	0	0
$166$	−11.5079	−0.893186
$167$	−5.62687	−0.435420	−0.217710	−	0.976013i	$-0.569859\pi$
$167$	−5.62687	−0.435420	−0.217710	+	0.976013i	$0.569859\pi$
$168$	0.529317	0.0408377
$169$	10.1595	0.781498
$170$	6.02760	0.462296
$171$	5.33958	0.408328
$172$	5.58127	0.425568
$173$	−11.3235	−0.860909	−0.430455	−	0.902612i	$-0.641647\pi$
$173$	−11.3235	−0.860909	−0.430455	+	0.902612i	$0.641647\pi$
$174$	4.31116	0.326828
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−3.62054	−0.272136
$178$	14.2096	1.06506
$179$	23.7596	1.77587	0.887936	−	0.459966i	$-0.152139\pi$
$179$	23.7596	1.77587	0.887936	+	0.459966i	$0.152139\pi$
$180$	−2.71982	−0.202724
$181$	−1.06147	−0.0788986	−0.0394493	−	0.999222i	$-0.512560\pi$
$181$	−1.06147	−0.0788986	−0.0394493	+	0.999222i	$0.512560\pi$
$182$	−4.81243	−0.356721
$183$	−0.887502	−0.0656060
$184$	−2.56329	−0.188968
$185$	−6.14477	−0.451772
$186$	1.19051	0.0872922
$187$	0	0
$188$	6.23315	0.454599
$189$	3.02760	0.220225
$190$	1.96321	0.142426
$191$	16.9651	1.22755	0.613776	−	0.789480i	$-0.289650\pi$
$191$	16.9651	1.22755	0.613776	+	0.789480i	$0.289650\pi$
$192$	0.529317	0.0382001
$193$	−18.4425	−1.32752	−0.663761	−	0.747945i	$-0.731041\pi$
$193$	−18.4425	−1.32752	−0.663761	+	0.747945i	$0.731041\pi$
$194$	3.26750	0.234593
$195$	−2.54730	−0.182416
$196$	1.00000	0.0714286
$197$	20.3968	1.45321	0.726607	−	0.687053i	$-0.241096\pi$
$197$	20.3968	1.45321	0.726607	+	0.687053i	$0.241096\pi$
$198$	0	0
$199$	6.47192	0.458782	0.229391	−	0.973334i	$-0.426327\pi$
$199$	6.47192	0.458782	0.229391	+	0.973334i	$0.426327\pi$
$200$	−1.00000	−0.0707107
$201$	4.12883	0.291225
$202$	0.584368	0.0411160
$203$	8.14477	0.571651
$204$	−3.19051	−0.223380
$205$	5.35973	0.374340
$206$	−12.8427	−0.894797
$207$	−6.97169	−0.484566
$208$	−4.81243	−0.333682
$209$	0	0
$210$	0.529317	0.0365263
$211$	−17.7130	−1.21941	−0.609706	−	0.792628i	$-0.708712\pi$
$211$	−17.7130	−1.21941	−0.609706	+	0.792628i	$0.708712\pi$
$212$	−0.648854	−0.0445635
$213$	4.53116	0.310470
$214$	−4.82110	−0.329564
$215$	5.58127	0.380639
$216$	3.02760	0.206002
$217$	2.24914	0.152682
$218$	−9.52895	−0.645382
$219$	2.91531	0.196998
$220$	0	0
$221$	29.0074	1.95125
$222$	3.25253	0.218295
$223$	21.6290	1.44839	0.724193	−	0.689598i	$-0.242213\pi$
$223$	21.6290	1.44839	0.724193	+	0.689598i	$0.242213\pi$
$224$	1.00000	0.0668153
$225$	−2.71982	−0.181322
$226$	2.71812	0.180807
$227$	15.3595	1.01944	0.509721	−	0.860339i	$-0.329748\pi$
$227$	15.3595	1.01944	0.509721	+	0.860339i	$0.329748\pi$
$228$	−1.03916	−0.0688200
$229$	21.2484	1.40414	0.702068	−	0.712110i	$-0.252260\pi$
$229$	21.2484	1.40414	0.702068	+	0.712110i	$0.252260\pi$
$230$	−2.56329	−0.169018
$231$	0	0
$232$	8.14477	0.534730
$233$	18.8912	1.23761	0.618803	−	0.785546i	$-0.287618\pi$
$233$	18.8912	1.23761	0.618803	+	0.785546i	$0.287618\pi$
$234$	−13.0890	−0.855652
$235$	6.23315	0.406606
$236$	−6.84003	−0.445248
$237$	−1.96861	−0.127875
$238$	−6.02760	−0.390711
$239$	−25.4078	−1.64349	−0.821747	−	0.569853i	$-0.807000\pi$
$239$	−25.4078	−1.64349	−0.821747	+	0.569853i	$0.807000\pi$
$240$	0.529317	0.0341672
$241$	−10.1147	−0.651544	−0.325772	−	0.945448i	$-0.605624\pi$
$241$	−10.1147	−0.651544	−0.325772	+	0.945448i	$0.605624\pi$
$242$	0	0
$243$	12.5535	0.805306
$244$	−1.67669	−0.107339
$245$	1.00000	0.0638877
$246$	−2.83699	−0.180880
$247$	9.44781	0.601150
$248$	2.24914	0.142821
$249$	6.09132	0.386022
$250$	−1.00000	−0.0632456
$251$	−15.5061	−0.978736	−0.489368	−	0.872078i	$-0.662772\pi$
$251$	−15.5061	−0.978736	−0.489368	+	0.872078i	$0.662772\pi$
$252$	2.71982	0.171333
$253$	0	0
$254$	−3.60394	−0.226131
$255$	−3.19051	−0.199797
$256$	1.00000	0.0625000
$257$	−18.6645	−1.16426	−0.582130	−	0.813095i	$-0.697781\pi$
$257$	−18.6645	−1.16426	−0.582130	+	0.813095i	$0.697781\pi$
$258$	−2.95426	−0.183924
$259$	6.14477	0.381817
$260$	−4.81243	−0.298454
$261$	22.1523	1.37119
$262$	−5.17800	−0.319898
$263$	2.35968	0.145504	0.0727521	−	0.997350i	$-0.476822\pi$
$263$	2.35968	0.145504	0.0727521	+	0.997350i	$0.476822\pi$
$264$	0	0
$265$	−0.648854	−0.0398588
$266$	−1.96321	−0.120372
$267$	−7.52138	−0.460301
$268$	7.80030	0.476479
$269$	−14.5570	−0.887556	−0.443778	−	0.896137i	$-0.646362\pi$
$269$	−14.5570	−0.887556	−0.443778	+	0.896137i	$0.646362\pi$
$270$	3.02760	0.184254
$271$	10.4172	0.632798	0.316399	−	0.948626i	$-0.397526\pi$
$271$	10.4172	0.632798	0.316399	+	0.948626i	$0.397526\pi$
$272$	−6.02760	−0.365477
$273$	2.54730	0.154170
$274$	−7.79465	−0.470892
$275$	0	0
$276$	1.35679	0.0816692
$277$	−14.9701	−0.899466	−0.449733	−	0.893163i	$-0.648481\pi$
$277$	−14.9701	−0.899466	−0.449733	+	0.893163i	$0.648481\pi$
$278$	9.73564	0.583905
$279$	6.11727	0.366231
$280$	1.00000	0.0597614
$281$	−8.00750	−0.477688	−0.238844	−	0.971058i	$-0.576768\pi$
$281$	−8.00750	−0.477688	−0.238844	+	0.971058i	$0.576768\pi$
$282$	−3.29931	−0.196471
$283$	−22.3793	−1.33031	−0.665154	−	0.746706i	$-0.731634\pi$
$283$	−22.3793	−1.33031	−0.665154	+	0.746706i	$0.731634\pi$
$284$	8.56040	0.507966
$285$	−1.03916	−0.0615545
$286$	0	0
$287$	−5.35973	−0.316375
$288$	2.71982	0.160267
$289$	19.3319	1.13717
$290$	8.14477	0.478277
$291$	−1.72954	−0.101388
$292$	5.50769	0.322313
$293$	−2.78343	−0.162610	−0.0813049	−	0.996689i	$-0.525909\pi$
$293$	−2.78343	−0.162610	−0.0813049	+	0.996689i	$0.525909\pi$
$294$	−0.529317	−0.0308704
$295$	−6.84003	−0.398242
$296$	6.14477	0.357157
$297$	0	0
$298$	5.26382	0.304925
$299$	−12.3356	−0.713389
$300$	0.529317	0.0305601
$301$	−5.58127	−0.321699
$302$	−3.80904	−0.219186
$303$	−0.309316	−0.0177697
$304$	−1.96321	−0.112598
$305$	−1.67669	−0.0960072
$306$	−16.3940	−0.937183
$307$	24.7810	1.41433	0.707164	−	0.707049i	$-0.249974\pi$
$307$	24.7810	1.41433	0.707164	+	0.707049i	$0.249974\pi$
$308$	0	0
$309$	6.79788	0.386718
$310$	2.24914	0.127743
$311$	18.8355	1.06807	0.534033	−	0.845464i	$-0.320676\pi$
$311$	18.8355	1.06807	0.534033	+	0.845464i	$0.320676\pi$
$312$	2.54730	0.144212
$313$	−12.1788	−0.688388	−0.344194	−	0.938899i	$-0.611848\pi$
$313$	−12.1788	−0.688388	−0.344194	+	0.938899i	$0.611848\pi$
$314$	−15.8237	−0.892985
$315$	2.71982	0.153245
$316$	−3.71916	−0.209219
$317$	−29.5674	−1.66067	−0.830334	−	0.557266i	$-0.811850\pi$
$317$	−29.5674	−1.66067	−0.830334	+	0.557266i	$0.811850\pi$
$318$	0.343449	0.0192597
$319$	0	0
$320$	1.00000	0.0559017
$321$	2.55189	0.142433
$322$	2.56329	0.142846
$323$	11.8334	0.658430
$324$	6.55691	0.364273
$325$	−4.81243	−0.266946
$326$	−10.0410	−0.556118
$327$	5.04383	0.278924
$328$	−5.35973	−0.295941
$329$	−6.23315	−0.343645
$330$	0	0
$331$	−25.7588	−1.41583	−0.707916	−	0.706297i	$-0.750364\pi$
$331$	−25.7588	−1.41583	−0.707916	+	0.706297i	$0.750364\pi$
$332$	11.5079	0.631578
$333$	16.7127	0.915849
$334$	5.62687	0.307888
$335$	7.80030	0.426176
$336$	−0.529317	−0.0288766
$337$	19.1851	1.04508	0.522539	−	0.852615i	$-0.324985\pi$
$337$	19.1851	1.04508	0.522539	+	0.852615i	$0.324985\pi$
$338$	−10.1595	−0.552602
$339$	−1.43875	−0.0781420
$340$	−6.02760	−0.326892
$341$	0	0
$342$	−5.33958	−0.288732
$343$	−1.00000	−0.0539949
$344$	−5.58127	−0.300922
$345$	1.35679	0.0730472
$346$	11.3235	0.608755
$347$	27.6006	1.48168	0.740840	−	0.671681i	$-0.234428\pi$
$347$	27.6006	1.48168	0.740840	+	0.671681i	$0.234428\pi$
$348$	−4.31116	−0.231102
$349$	2.01175	0.107687	0.0538433	−	0.998549i	$-0.482853\pi$
$349$	2.01175	0.107687	0.0538433	+	0.998549i	$0.482853\pi$
$350$	1.00000	0.0534522
$351$	14.5701	0.777694
$352$	0	0
$353$	−26.8808	−1.43072	−0.715360	−	0.698756i	$-0.753737\pi$
$353$	−26.8808	−1.43072	−0.715360	+	0.698756i	$0.753737\pi$
$354$	3.62054	0.192430
$355$	8.56040	0.454339
$356$	−14.2096	−0.753108
$357$	3.19051	0.168860
$358$	−23.7596	−1.25573
$359$	11.7756	0.621491	0.310746	−	0.950493i	$-0.399421\pi$
$359$	11.7756	0.621491	0.310746	+	0.950493i	$0.399421\pi$
$360$	2.71982	0.143347
$361$	−15.1458	−0.797148
$362$	1.06147	0.0557897
$363$	0	0
$364$	4.81243	0.252240
$365$	5.50769	0.288286
$366$	0.887502	0.0463905
$367$	1.62917	0.0850419	0.0425210	−	0.999096i	$-0.486461\pi$
$367$	1.62917	0.0850419	0.0425210	+	0.999096i	$0.486461\pi$
$368$	2.56329	0.133621
$369$	−14.5775	−0.758875
$370$	6.14477	0.319451
$371$	0.648854	0.0336868
$372$	−1.19051	−0.0617249
$373$	28.4460	1.47288	0.736438	−	0.676505i	$-0.236506\pi$
$373$	28.4460	1.47288	0.736438	+	0.676505i	$0.236506\pi$
$374$	0	0
$375$	0.529317	0.0273338
$376$	−6.23315	−0.321450
$377$	39.1961	2.01870
$378$	−3.02760	−0.155723
$379$	−10.4292	−0.535711	−0.267855	−	0.963459i	$-0.586315\pi$
$379$	−10.4292	−0.535711	−0.267855	+	0.963459i	$0.586315\pi$
$380$	−1.96321	−0.100711
$381$	1.90763	0.0977306
$382$	−16.9651	−0.868011
$383$	6.50389	0.332333	0.166167	−	0.986098i	$-0.446861\pi$
$383$	6.50389	0.332333	0.166167	+	0.986098i	$0.446861\pi$
$384$	−0.529317	−0.0270116
$385$	0	0
$386$	18.4425	0.938700
$387$	−15.1801	−0.771646
$388$	−3.26750	−0.165882
$389$	33.4810	1.69755	0.848776	−	0.528753i	$-0.177340\pi$
$389$	33.4810	1.69755	0.848776	+	0.528753i	$0.177340\pi$
$390$	2.54730	0.128987
$391$	−15.4505	−0.781364
$392$	−1.00000	−0.0505076
$393$	2.74080	0.138255
$394$	−20.3968	−1.02758
$395$	−3.71916	−0.187131
$396$	0	0
$397$	−24.7013	−1.23972	−0.619860	−	0.784712i	$-0.712811\pi$
$397$	−24.7013	−1.23972	−0.619860	+	0.784712i	$0.712811\pi$
$398$	−6.47192	−0.324408
$399$	1.03916	0.0520230
$400$	1.00000	0.0500000
$401$	17.7421	0.885999	0.443000	−	0.896522i	$-0.353914\pi$
$401$	17.7421	0.885999	0.443000	+	0.896522i	$0.353914\pi$
$402$	−4.12883	−0.205927
$403$	10.8238	0.539173
$404$	−0.584368	−0.0290734
$405$	6.55691	0.325816
$406$	−8.14477	−0.404218
$407$	0	0
$408$	3.19051	0.157954
$409$	−32.8021	−1.62196	−0.810981	−	0.585073i	$-0.801066\pi$
$409$	−32.8021	−1.62196	−0.810981	+	0.585073i	$0.801066\pi$
$410$	−5.35973	−0.264698
$411$	4.12584	0.203513
$412$	12.8427	0.632717
$413$	6.84003	0.336576
$414$	6.97169	0.342640
$415$	11.5079	0.564900
$416$	4.81243	0.235949
$417$	−5.15324	−0.252355
$418$	0	0
$419$	−27.0785	−1.32287	−0.661437	−	0.750001i	$-0.730053\pi$
$419$	−27.0785	−1.32287	−0.661437	+	0.750001i	$0.730053\pi$
$420$	−0.529317	−0.0258280
$421$	−9.64201	−0.469923	−0.234961	−	0.972005i	$-0.575496\pi$
$421$	−9.64201	−0.469923	−0.234961	+	0.972005i	$0.575496\pi$
$422$	17.7130	0.862254
$423$	−16.9531	−0.824287
$424$	0.648854	0.0315111
$425$	−6.02760	−0.292381
$426$	−4.53116	−0.219535
$427$	1.67669	0.0811409
$428$	4.82110	0.233037
$429$	0	0
$430$	−5.58127	−0.269153
$431$	−9.17233	−0.441815	−0.220908	−	0.975295i	$-0.570902\pi$
$431$	−9.17233	−0.441815	−0.220908	+	0.975295i	$0.570902\pi$
$432$	−3.02760	−0.145665
$433$	−29.1569	−1.40119	−0.700595	−	0.713559i	$-0.747082\pi$
$433$	−29.1569	−1.40119	−0.700595	+	0.713559i	$0.747082\pi$
$434$	−2.24914	−0.107962
$435$	−4.31116	−0.206704
$436$	9.52895	0.456354
$437$	−5.03227	−0.240726
$438$	−2.91531	−0.139299
$439$	−3.57840	−0.170788	−0.0853938	−	0.996347i	$-0.527215\pi$
$439$	−3.57840	−0.170788	−0.0853938	+	0.996347i	$0.527215\pi$
$440$	0	0
$441$	−2.71982	−0.129515
$442$	−29.0074	−1.37974
$443$	4.36344	0.207313	0.103657	−	0.994613i	$-0.466946\pi$
$443$	4.36344	0.207313	0.103657	+	0.994613i	$0.466946\pi$
$444$	−3.25253	−0.154358
$445$	−14.2096	−0.673600
$446$	−21.6290	−1.02416
$447$	−2.78623	−0.131784
$448$	−1.00000	−0.0472456
$449$	0.918697	0.0433560	0.0216780	−	0.999765i	$-0.493099\pi$
$449$	0.918697	0.0433560	0.0216780	+	0.999765i	$0.493099\pi$
$450$	2.71982	0.128214
$451$	0	0
$452$	−2.71812	−0.127850
$453$	2.01619	0.0947288
$454$	−15.3595	−0.720855
$455$	4.81243	0.225610
$456$	1.03916	0.0486631
$457$	1.28030	0.0598901	0.0299450	−	0.999552i	$-0.490467\pi$
$457$	1.28030	0.0598901	0.0299450	+	0.999552i	$0.490467\pi$
$458$	−21.2484	−0.992874
$459$	18.2491	0.851797
$460$	2.56329	0.119514
$461$	3.42591	0.159561	0.0797803	−	0.996812i	$-0.474578\pi$
$461$	3.42591	0.159561	0.0797803	+	0.996812i	$0.474578\pi$
$462$	0	0
$463$	−35.9279	−1.66971	−0.834855	−	0.550469i	$-0.814449\pi$
$463$	−35.9279	−1.66971	−0.834855	+	0.550469i	$0.814449\pi$
$464$	−8.14477	−0.378111
$465$	−1.19051	−0.0552085
$466$	−18.8912	−0.875120
$467$	−0.633419	−0.0293111	−0.0146556	−	0.999893i	$-0.504665\pi$
$467$	−0.633419	−0.0293111	−0.0146556	+	0.999893i	$0.504665\pi$
$468$	13.0890	0.605037
$469$	−7.80030	−0.360184
$470$	−6.23315	−0.287514
$471$	8.37576	0.385935
$472$	6.84003	0.314838
$473$	0	0
$474$	1.96861	0.0904214
$475$	−1.96321	−0.0900782
$476$	6.02760	0.276274
$477$	1.76477	0.0808032
$478$	25.4078	1.16213
$479$	−32.8050	−1.49890	−0.749450	−	0.662061i	$-0.769682\pi$
$479$	−32.8050	−1.49890	−0.749450	+	0.662061i	$0.769682\pi$
$480$	−0.529317	−0.0241599
$481$	29.5713	1.34833
$482$	10.1147	0.460711
$483$	−1.35679	−0.0617361
$484$	0	0
$485$	−3.26750	−0.148370
$486$	−12.5535	−0.569437
$487$	−38.3866	−1.73946	−0.869732	−	0.493525i	$-0.835708\pi$
$487$	−38.3866	−1.73946	−0.869732	+	0.493525i	$0.835708\pi$
$488$	1.67669	0.0759004
$489$	5.31486	0.240346
$490$	−1.00000	−0.0451754
$491$	37.5492	1.69457	0.847285	−	0.531139i	$-0.178236\pi$
$491$	37.5492	1.69457	0.847285	+	0.531139i	$0.178236\pi$
$492$	2.83699	0.127902
$493$	49.0934	2.21105
$494$	−9.44781	−0.425077
$495$	0	0
$496$	−2.24914	−0.100989
$497$	−8.56040	−0.383986
$498$	−6.09132	−0.272959
$499$	26.5551	1.18877	0.594386	−	0.804180i	$-0.297395\pi$
$499$	26.5551	1.18877	0.594386	+	0.804180i	$0.297395\pi$
$500$	1.00000	0.0447214
$501$	−2.97839	−0.133065
$502$	15.5061	0.692071
$503$	−19.0642	−0.850030	−0.425015	−	0.905186i	$-0.639731\pi$
$503$	−19.0642	−0.850030	−0.425015	+	0.905186i	$0.639731\pi$
$504$	−2.71982	−0.121151
$505$	−0.584368	−0.0260040
$506$	0	0
$507$	5.37758	0.238827
$508$	3.60394	0.159899
$509$	15.8369	0.701960	0.350980	−	0.936383i	$-0.385849\pi$
$509$	15.8369	0.701960	0.350980	+	0.936383i	$0.385849\pi$
$510$	3.19051	0.141278
$511$	−5.50769	−0.243646
$512$	−1.00000	−0.0441942
$513$	5.94381	0.262426
$514$	18.6645	0.823257
$515$	12.8427	0.565919
$516$	2.95426	0.130054
$517$	0	0
$518$	−6.14477	−0.269986
$519$	−5.99371	−0.263095
$520$	4.81243	0.211039
$521$	−38.6470	−1.69316	−0.846579	−	0.532263i	$-0.821342\pi$
$521$	−38.6470	−1.69316	−0.846579	+	0.532263i	$0.821342\pi$
$522$	−22.1523	−0.969581
$523$	24.0284	1.05069	0.525344	−	0.850890i	$-0.323937\pi$
$523$	24.0284	1.05069	0.525344	+	0.850890i	$0.323937\pi$
$524$	5.17800	0.226202
$525$	−0.529317	−0.0231013
$526$	−2.35968	−0.102887
$527$	13.5569	0.590548
$528$	0	0
$529$	−16.4296	−0.714328
$530$	0.648854	0.0281844
$531$	18.6037	0.807330
$532$	1.96321	0.0851159
$533$	−25.7933	−1.11723
$534$	7.52138	0.325482
$535$	4.82110	0.208434
$536$	−7.80030	−0.336922
$537$	12.5763	0.542709
$538$	14.5570	0.627597
$539$	0	0
$540$	−3.02760	−0.130287
$541$	18.9007	0.812604	0.406302	−	0.913739i	$-0.366818\pi$
$541$	18.9007	0.812604	0.406302	+	0.913739i	$0.366818\pi$
$542$	−10.4172	−0.447456
$543$	−0.561855	−0.0241115
$544$	6.02760	0.258431
$545$	9.52895	0.408175
$546$	−2.54730	−0.109014
$547$	−0.760577	−0.0325199	−0.0162600	−	0.999868i	$-0.505176\pi$
$547$	−0.760577	−0.0325199	−0.0162600	+	0.999868i	$0.505176\pi$
$548$	7.79465	0.332971
$549$	4.56031	0.194629
$550$	0	0
$551$	15.9899	0.681192
$552$	−1.35679	−0.0577489
$553$	3.71916	0.158155
$554$	14.9701	0.636018
$555$	−3.25253	−0.138062
$556$	−9.73564	−0.412883
$557$	−6.85003	−0.290245	−0.145123	−	0.989414i	$-0.546358\pi$
$557$	−6.85003	−0.290245	−0.145123	+	0.989414i	$0.546358\pi$
$558$	−6.11727	−0.258965
$559$	−26.8595	−1.13603
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	8.00750	0.337776
$563$	37.3212	1.57290	0.786451	−	0.617652i	$-0.211916\pi$
$563$	37.3212	1.57290	0.786451	+	0.617652i	$0.211916\pi$
$564$	3.29931	0.138926
$565$	−2.71812	−0.114352
$566$	22.3793	0.940670
$567$	−6.55691	−0.275365
$568$	−8.56040	−0.359186
$569$	46.3025	1.94110	0.970551	−	0.240897i	$-0.0774415\pi$
$569$	46.3025	1.94110	0.970551	+	0.240897i	$0.0774415\pi$
$570$	1.03916	0.0435256
$571$	23.7033	0.991951	0.495975	−	0.868337i	$-0.334811\pi$
$571$	23.7033	0.991951	0.495975	+	0.868337i	$0.334811\pi$
$572$	0	0
$573$	8.97991	0.375141
$574$	5.35973	0.223711
$575$	2.56329	0.106897
$576$	−2.71982	−0.113326
$577$	30.3334	1.26280	0.631399	−	0.775458i	$-0.282481\pi$
$577$	30.3334	1.26280	0.631399	+	0.775458i	$0.282481\pi$
$578$	−19.3319	−0.804102
$579$	−9.76193	−0.405692
$580$	−8.14477	−0.338193
$581$	−11.5079	−0.477428
$582$	1.72954	0.0716918
$583$	0	0
$584$	−5.50769	−0.227910
$585$	13.0890	0.541162
$586$	2.78343	0.114983
$587$	28.8863	1.19227	0.596133	−	0.802886i	$-0.296703\pi$
$587$	28.8863	1.19227	0.596133	+	0.802886i	$0.296703\pi$
$588$	0.529317	0.0218286
$589$	4.41553	0.181939
$590$	6.84003	0.281599
$591$	10.7964	0.444104
$592$	−6.14477	−0.252548
$593$	−34.0215	−1.39710	−0.698548	−	0.715563i	$-0.746170\pi$
$593$	−34.0215	−1.39710	−0.698548	+	0.715563i	$0.746170\pi$
$594$	0	0
$595$	6.02760	0.247107
$596$	−5.26382	−0.215614
$597$	3.42569	0.140204
$598$	12.3356	0.504442
$599$	−12.8416	−0.524694	−0.262347	−	0.964974i	$-0.584496\pi$
$599$	−12.8416	−0.524694	−0.262347	+	0.964974i	$0.584496\pi$
$600$	−0.529317	−0.0216093
$601$	22.9731	0.937094	0.468547	−	0.883439i	$-0.344778\pi$
$601$	22.9731	0.937094	0.468547	+	0.883439i	$0.344778\pi$
$602$	5.58127	0.227476
$603$	−21.2154	−0.863960
$604$	3.80904	0.154988
$605$	0	0
$606$	0.309316	0.0125651
$607$	1.84682	0.0749600	0.0374800	−	0.999297i	$-0.488067\pi$
$607$	1.84682	0.0749600	0.0374800	+	0.999297i	$0.488067\pi$
$608$	1.96321	0.0796187
$609$	4.31116	0.174697
$610$	1.67669	0.0678873
$611$	−29.9966	−1.21353
$612$	16.3940	0.662688
$613$	−22.4753	−0.907769	−0.453884	−	0.891061i	$-0.649962\pi$
$613$	−22.4753	−0.907769	−0.453884	+	0.891061i	$0.649962\pi$
$614$	−24.7810	−1.00008
$615$	2.83699	0.114399
$616$	0	0
$617$	−12.3558	−0.497425	−0.248713	−	0.968577i	$-0.580007\pi$
$617$	−12.3558	−0.497425	−0.248713	+	0.968577i	$0.580007\pi$
$618$	−6.79788	−0.273451
$619$	−44.0581	−1.77085	−0.885423	−	0.464786i	$-0.846131\pi$
$619$	−44.0581	−1.77085	−0.885423	+	0.464786i	$0.846131\pi$
$620$	−2.24914	−0.0903277
$621$	−7.76061	−0.311422
$622$	−18.8355	−0.755236
$623$	14.2096	0.569296
$624$	−2.54730	−0.101974
$625$	1.00000	0.0400000
$626$	12.1788	0.486763
$627$	0	0
$628$	15.8237	0.631436
$629$	37.0382	1.47681
$630$	−2.71982	−0.108360
$631$	−13.8538	−0.551510	−0.275755	−	0.961228i	$-0.588928\pi$
$631$	−13.8538	−0.551510	−0.275755	+	0.961228i	$0.588928\pi$
$632$	3.71916	0.147940
$633$	−9.37577	−0.372653
$634$	29.5674	1.17427
$635$	3.60394	0.143018
$636$	−0.343449	−0.0136186
$637$	−4.81243	−0.190675
$638$	0	0
$639$	−23.2828	−0.921052
$640$	−1.00000	−0.0395285
$641$	22.3155	0.881409	0.440704	−	0.897652i	$-0.354729\pi$
$641$	22.3155	0.881409	0.440704	+	0.897652i	$0.354729\pi$
$642$	−2.55189	−0.100715
$643$	43.6797	1.72256	0.861280	−	0.508130i	$-0.169663\pi$
$643$	43.6797	1.72256	0.861280	+	0.508130i	$0.169663\pi$
$644$	−2.56329	−0.101008
$645$	2.95426	0.116324
$646$	−11.8334	−0.465580
$647$	35.7267	1.40456	0.702280	−	0.711901i	$-0.252166\pi$
$647$	35.7267	1.40456	0.702280	+	0.711901i	$0.252166\pi$
$648$	−6.55691	−0.257580
$649$	0	0
$650$	4.81243	0.188759
$651$	1.19051	0.0466597
$652$	10.0410	0.393235
$653$	16.0177	0.626822	0.313411	−	0.949618i	$-0.398528\pi$
$653$	16.0177	0.626822	0.313411	+	0.949618i	$0.398528\pi$
$654$	−5.04383	−0.197229
$655$	5.17800	0.202321
$656$	5.35973	0.209262
$657$	−14.9799	−0.584423
$658$	6.23315	0.242994
$659$	−32.8329	−1.27899	−0.639494	−	0.768796i	$-0.720856\pi$
$659$	−32.8329	−1.27899	−0.639494	+	0.768796i	$0.720856\pi$
$660$	0	0
$661$	4.83580	0.188091	0.0940454	−	0.995568i	$-0.470020\pi$
$661$	4.83580	0.188091	0.0940454	+	0.995568i	$0.470020\pi$
$662$	25.7588	1.00114
$663$	15.3541	0.596303
$664$	−11.5079	−0.446593
$665$	1.96321	0.0761300
$666$	−16.7127	−0.647603
$667$	−20.8774	−0.808376
$668$	−5.62687	−0.217710
$669$	11.4486	0.442628
$670$	−7.80030	−0.301352
$671$	0	0
$672$	0.529317	0.0204188
$673$	47.4627	1.82955	0.914777	−	0.403959i	$-0.132366\pi$
$673$	47.4627	1.82955	0.914777	+	0.403959i	$0.132366\pi$
$674$	−19.1851	−0.738982
$675$	−3.02760	−0.116532
$676$	10.1595	0.390749
$677$	−7.70258	−0.296034	−0.148017	−	0.988985i	$-0.547289\pi$
$677$	−7.70258	−0.296034	−0.148017	+	0.988985i	$0.547289\pi$
$678$	1.43875	0.0552547
$679$	3.26750	0.125395
$680$	6.02760	0.231148
$681$	8.13001	0.311543
$682$	0	0
$683$	−10.0811	−0.385742	−0.192871	−	0.981224i	$-0.561780\pi$
$683$	−10.0811	−0.385742	−0.192871	+	0.981224i	$0.561780\pi$
$684$	5.33958	0.204164
$685$	7.79465	0.297818
$686$	1.00000	0.0381802
$687$	11.2471	0.429105
$688$	5.58127	0.212784
$689$	3.12256	0.118960
$690$	−1.35679	−0.0516522
$691$	1.47391	0.0560703	0.0280351	−	0.999607i	$-0.491075\pi$
$691$	1.47391	0.0560703	0.0280351	+	0.999607i	$0.491075\pi$
$692$	−11.3235	−0.430455
$693$	0	0
$694$	−27.6006	−1.04771
$695$	−9.73564	−0.369294
$696$	4.31116	0.163414
$697$	−32.3063	−1.22369
$698$	−2.01175	−0.0761459
$699$	9.99945	0.378214
$700$	−1.00000	−0.0377964
$701$	−22.3369	−0.843653	−0.421826	−	0.906677i	$-0.638611\pi$
$701$	−22.3369	−0.843653	−0.421826	+	0.906677i	$0.638611\pi$
$702$	−14.5701	−0.549913
$703$	12.0635	0.454982
$704$	0	0
$705$	3.29931	0.124259
$706$	26.8808	1.01167
$707$	0.584368	0.0219774
$708$	−3.62054	−0.136068
$709$	−1.82779	−0.0686440	−0.0343220	−	0.999411i	$-0.510927\pi$
$709$	−1.82779	−0.0686440	−0.0343220	+	0.999411i	$0.510927\pi$
$710$	−8.56040	−0.321266
$711$	10.1155	0.379359
$712$	14.2096	0.532528
$713$	−5.76520	−0.215908
$714$	−3.19051	−0.119402
$715$	0	0
$716$	23.7596	0.887936
$717$	−13.4488	−0.502253
$718$	−11.7756	−0.439461
$719$	6.70006	0.249870	0.124935	−	0.992165i	$-0.460128\pi$
$719$	6.70006	0.249870	0.124935	+	0.992165i	$0.460128\pi$
$720$	−2.71982	−0.101362
$721$	−12.8427	−0.478289
$722$	15.1458	0.563669
$723$	−5.35387	−0.199112
$724$	−1.06147	−0.0394493
$725$	−8.14477	−0.302489
$726$	0	0
$727$	−14.5561	−0.539855	−0.269928	−	0.962881i	$-0.587000\pi$
$727$	−14.5561	−0.539855	−0.269928	+	0.962881i	$0.587000\pi$
$728$	−4.81243	−0.178360
$729$	−13.0260	−0.482444
$730$	−5.50769	−0.203849
$731$	−33.6417	−1.24428
$732$	−0.887502	−0.0328030
$733$	39.6761	1.46547	0.732736	−	0.680513i	$-0.238243\pi$
$733$	39.6761	1.46547	0.732736	+	0.680513i	$0.238243\pi$
$734$	−1.62917	−0.0601337
$735$	0.529317	0.0195241
$736$	−2.56329	−0.0944841
$737$	0	0
$738$	14.5775	0.536606
$739$	−38.6096	−1.42028	−0.710139	−	0.704061i	$-0.751368\pi$
$739$	−38.6096	−1.42028	−0.710139	+	0.704061i	$0.751368\pi$
$740$	−6.14477	−0.225886
$741$	5.00088	0.183712
$742$	−0.648854	−0.0238202
$743$	18.3540	0.673342	0.336671	−	0.941622i	$-0.390699\pi$
$743$	18.3540	0.673342	0.336671	+	0.941622i	$0.390699\pi$
$744$	1.19051	0.0436461
$745$	−5.26382	−0.192851
$746$	−28.4460	−1.04148
$747$	−31.2995	−1.14519
$748$	0	0
$749$	−4.82110	−0.176159
$750$	−0.529317	−0.0193279
$751$	−37.3350	−1.36238	−0.681188	−	0.732109i	$-0.738536\pi$
$751$	−37.3350	−1.36238	−0.681188	+	0.732109i	$0.738536\pi$
$752$	6.23315	0.227300
$753$	−8.20763	−0.299103
$754$	−39.1961	−1.42744
$755$	3.80904	0.138625
$756$	3.02760	0.110113
$757$	11.2902	0.410350	0.205175	−	0.978725i	$-0.434224\pi$
$757$	11.2902	0.410350	0.205175	+	0.978725i	$0.434224\pi$
$758$	10.4292	0.378805
$759$	0	0
$760$	1.96321	0.0712131
$761$	52.6886	1.90996	0.954980	−	0.296669i	$-0.0958759\pi$
$761$	52.6886	1.90996	0.954980	+	0.296669i	$0.0958759\pi$
$762$	−1.90763	−0.0691060
$763$	−9.52895	−0.344971
$764$	16.9651	0.613776
$765$	16.3940	0.592726
$766$	−6.50389	−0.234995
$767$	32.9171	1.18857
$768$	0.529317	0.0191001
$769$	−2.47046	−0.0890870	−0.0445435	−	0.999007i	$-0.514183\pi$
$769$	−2.47046	−0.0890870	−0.0445435	+	0.999007i	$0.514183\pi$
$770$	0	0
$771$	−9.87944	−0.355799
$772$	−18.4425	−0.663761
$773$	34.3463	1.23535	0.617676	−	0.786433i	$-0.288074\pi$
$773$	34.3463	1.23535	0.617676	+	0.786433i	$0.288074\pi$
$774$	15.1801	0.545636
$775$	−2.24914	−0.0807915
$776$	3.26750	0.117296
$777$	3.25253	0.116684
$778$	−33.4810	−1.20035
$779$	−10.5223	−0.376999
$780$	−2.54730	−0.0912079
$781$	0	0
$782$	15.4505	0.552508
$783$	24.6591	0.881243
$784$	1.00000	0.0357143
$785$	15.8237	0.564773
$786$	−2.74080	−0.0977612
$787$	−41.2984	−1.47213	−0.736064	−	0.676912i	$-0.763318\pi$
$787$	−41.2984	−1.47213	−0.736064	+	0.676912i	$0.763318\pi$
$788$	20.3968	0.726607
$789$	1.24902	0.0444662
$790$	3.71916	0.132322
$791$	2.71812	0.0966452
$792$	0	0
$793$	8.06897	0.286538
$794$	24.7013	0.876615
$795$	−0.343449	−0.0121809
$796$	6.47192	0.229391
$797$	12.0500	0.426832	0.213416	−	0.976961i	$-0.431541\pi$
$797$	12.0500	0.426832	0.213416	+	0.976961i	$0.431541\pi$
$798$	−1.03916	−0.0367858
$799$	−37.5709	−1.32916
$800$	−1.00000	−0.0353553
$801$	38.6476	1.36555
$802$	−17.7421	−0.626496
$803$	0	0
$804$	4.12883	0.145613
$805$	−2.56329	−0.0903440
$806$	−10.8238	−0.381253
$807$	−7.70526	−0.271238
$808$	0.584368	0.0205580
$809$	2.86537	0.100741	0.0503705	−	0.998731i	$-0.483960\pi$
$809$	2.86537	0.100741	0.0503705	+	0.998731i	$0.483960\pi$
$810$	−6.55691	−0.230386
$811$	47.4986	1.66790	0.833952	−	0.551838i	$-0.186073\pi$
$811$	47.4986	1.66790	0.833952	+	0.551838i	$0.186073\pi$
$812$	8.14477	0.285825
$813$	5.51398	0.193384
$814$	0	0
$815$	10.0410	0.351720
$816$	−3.19051	−0.111690
$817$	−10.9572	−0.383344
$818$	32.8021	1.14690
$819$	−13.0890	−0.457365
$820$	5.35973	0.187170
$821$	−20.5458	−0.717052	−0.358526	−	0.933520i	$-0.616721\pi$
$821$	−20.5458	−0.717052	−0.358526	+	0.933520i	$0.616721\pi$
$822$	−4.12584	−0.143905
$823$	24.5540	0.855897	0.427949	−	0.903803i	$-0.359236\pi$
$823$	24.5540	0.855897	0.427949	+	0.903803i	$0.359236\pi$
$824$	−12.8427	−0.447398
$825$	0	0
$826$	−6.84003	−0.237995
$827$	−54.8582	−1.90761	−0.953803	−	0.300434i	$-0.902868\pi$
$827$	−54.8582	−1.90761	−0.953803	+	0.300434i	$0.902868\pi$
$828$	−6.97169	−0.242283
$829$	4.58811	0.159351	0.0796757	−	0.996821i	$-0.474612\pi$
$829$	4.58811	0.159351	0.0796757	+	0.996821i	$0.474612\pi$
$830$	−11.5079	−0.399445
$831$	−7.92392	−0.274878
$832$	−4.81243	−0.166841
$833$	−6.02760	−0.208844
$834$	5.15324	0.178442
$835$	−5.62687	−0.194726
$836$	0	0
$837$	6.80949	0.235370
$838$	27.0785	0.935413
$839$	4.66116	0.160921	0.0804605	−	0.996758i	$-0.474361\pi$
$839$	4.66116	0.160921	0.0804605	+	0.996758i	$0.474361\pi$
$840$	0.529317	0.0182632
$841$	37.3372	1.28749
$842$	9.64201	0.332285
$843$	−4.23851	−0.145982
$844$	−17.7130	−0.609706
$845$	10.1595	0.349496
$846$	16.9531	0.582859
$847$	0	0
$848$	−0.648854	−0.0222817
$849$	−11.8457	−0.406544
$850$	6.02760	0.206745
$851$	−15.7508	−0.539931
$852$	4.53116	0.155235
$853$	9.02516	0.309016	0.154508	−	0.987992i	$-0.450621\pi$
$853$	9.02516	0.309016	0.154508	+	0.987992i	$0.450621\pi$
$854$	−1.67669	−0.0573753
$855$	5.33958	0.182610
$856$	−4.82110	−0.164782
$857$	19.8659	0.678605	0.339303	−	0.940677i	$-0.389809\pi$
$857$	19.8659	0.678605	0.339303	+	0.940677i	$0.389809\pi$
$858$	0	0
$859$	−4.98915	−0.170228	−0.0851138	−	0.996371i	$-0.527125\pi$
$859$	−4.98915	−0.170228	−0.0851138	+	0.996371i	$0.527125\pi$
$860$	5.58127	0.190320
$861$	−2.83699	−0.0966844
$862$	9.17233	0.312411
$863$	35.2641	1.20040	0.600202	−	0.799849i	$-0.295087\pi$
$863$	35.2641	1.20040	0.600202	+	0.799849i	$0.295087\pi$
$864$	3.02760	0.103001
$865$	−11.3235	−0.385010
$866$	29.1569	0.990791
$867$	10.2327	0.347521
$868$	2.24914	0.0763408
$869$	0	0
$870$	4.31116	0.146162
$871$	−37.5384	−1.27194
$872$	−9.52895	−0.322691
$873$	8.88702	0.300780
$874$	5.03227	0.170219
$875$	−1.00000	−0.0338062
$876$	2.91531	0.0984992
$877$	−18.2415	−0.615971	−0.307985	−	0.951391i	$-0.599655\pi$
$877$	−18.2415	−0.615971	−0.307985	+	0.951391i	$0.599655\pi$
$878$	3.57840	0.120765
$879$	−1.47332	−0.0496938
$880$	0	0
$881$	26.1005	0.879349	0.439675	−	0.898157i	$-0.355094\pi$
$881$	26.1005	0.879349	0.439675	+	0.898157i	$0.355094\pi$
$882$	2.71982	0.0915812
$883$	11.8714	0.399506	0.199753	−	0.979846i	$-0.435986\pi$
$883$	11.8714	0.399506	0.199753	+	0.979846i	$0.435986\pi$
$884$	29.0074	0.975624
$885$	−3.62054	−0.121703
$886$	−4.36344	−0.146593
$887$	−41.1812	−1.38273	−0.691364	−	0.722506i	$-0.742990\pi$
$887$	−41.1812	−1.38273	−0.691364	+	0.722506i	$0.742990\pi$
$888$	3.25253	0.109148
$889$	−3.60394	−0.120872
$890$	14.2096	0.476307
$891$	0	0
$892$	21.6290	0.724193
$893$	−12.2370	−0.409495
$894$	2.78623	0.0931853
$895$	23.7596	0.794194
$896$	1.00000	0.0334077
$897$	−6.52946	−0.218012
$898$	−0.918697	−0.0306573
$899$	18.3187	0.610964
$900$	−2.71982	−0.0906608
$901$	3.91103	0.130295
$902$	0	0
$903$	−2.95426	−0.0983116
$904$	2.71812	0.0904033
$905$	−1.06147	−0.0352845
$906$	−2.01619	−0.0669834
$907$	−35.7007	−1.18542	−0.592711	−	0.805415i	$-0.701942\pi$
$907$	−35.7007	−1.18542	−0.592711	+	0.805415i	$0.701942\pi$
$908$	15.3595	0.509721
$909$	1.58938	0.0527164
$910$	−4.81243	−0.159530
$911$	−30.1957	−1.00043	−0.500214	−	0.865902i	$-0.666745\pi$
$911$	−30.1957	−1.00043	−0.500214	+	0.865902i	$0.666745\pi$
$912$	−1.03916	−0.0344100
$913$	0	0
$914$	−1.28030	−0.0423487
$915$	−0.887502	−0.0293399
$916$	21.2484	0.702068
$917$	−5.17800	−0.170993
$918$	−18.2491	−0.602311
$919$	46.5051	1.53406	0.767030	−	0.641611i	$-0.221734\pi$
$919$	46.5051	1.53406	0.767030	+	0.641611i	$0.221734\pi$
$920$	−2.56329	−0.0845091
$921$	13.1170	0.432220
$922$	−3.42591	−0.112826
$923$	−41.1963	−1.35599
$924$	0	0
$925$	−6.14477	−0.202039
$926$	35.9279	1.18066
$927$	−34.9300	−1.14725
$928$	8.14477	0.267365
$929$	52.8390	1.73359	0.866796	−	0.498664i	$-0.166176\pi$
$929$	52.8390	1.73359	0.866796	+	0.498664i	$0.166176\pi$
$930$	1.19051	0.0390383
$931$	−1.96321	−0.0643416
$932$	18.8912	0.618803
$933$	9.96996	0.326402
$934$	0.633419	0.0207261
$935$	0	0
$936$	−13.0890	−0.427826
$937$	10.7968	0.352717	0.176358	−	0.984326i	$-0.443568\pi$
$937$	10.7968	0.352717	0.176358	+	0.984326i	$0.443568\pi$
$938$	7.80030	0.254689
$939$	−6.44645	−0.210372
$940$	6.23315	0.203303
$941$	15.5858	0.508082	0.254041	−	0.967194i	$-0.418240\pi$
$941$	15.5858	0.508082	0.254041	+	0.967194i	$0.418240\pi$
$942$	−8.37576	−0.272897
$943$	13.7385	0.447388
$944$	−6.84003	−0.222624
$945$	3.02760	0.0984878
$946$	0	0
$947$	4.99210	0.162221	0.0811107	−	0.996705i	$-0.474153\pi$
$947$	4.99210	0.162221	0.0811107	+	0.996705i	$0.474153\pi$
$948$	−1.96861	−0.0639376
$949$	−26.5054	−0.860400
$950$	1.96321	0.0636949
$951$	−15.6505	−0.507502
$952$	−6.02760	−0.195356
$953$	−19.6682	−0.637117	−0.318558	−	0.947903i	$-0.603199\pi$
$953$	−19.6682	−0.637117	−0.318558	+	0.947903i	$0.603199\pi$
$954$	−1.76477	−0.0571365
$955$	16.9651	0.548978
$956$	−25.4078	−0.821747
$957$	0	0
$958$	32.8050	1.05988
$959$	−7.79465	−0.251703
$960$	0.529317	0.0170836
$961$	−25.9414	−0.836818
$962$	−29.5713	−0.953415
$963$	−13.1125	−0.422546
$964$	−10.1147	−0.325772
$965$	−18.4425	−0.593686
$966$	1.35679	0.0436540
$967$	44.8169	1.44122	0.720608	−	0.693343i	$-0.243863\pi$
$967$	44.8169	1.44122	0.720608	+	0.693343i	$0.243863\pi$
$968$	0	0
$969$	6.26363	0.201217
$970$	3.26750	0.104913
$971$	38.2665	1.22803	0.614015	−	0.789294i	$-0.289553\pi$
$971$	38.2665	1.22803	0.614015	+	0.789294i	$0.289553\pi$
$972$	12.5535	0.402653
$973$	9.73564	0.312110
$974$	38.3866	1.22999
$975$	−2.54730	−0.0815788
$976$	−1.67669	−0.0536697
$977$	45.4470	1.45398	0.726989	−	0.686649i	$-0.240919\pi$
$977$	45.4470	1.45398	0.726989	+	0.686649i	$0.240919\pi$
$978$	−5.31486	−0.169950
$979$	0	0
$980$	1.00000	0.0319438
$981$	−25.9171	−0.827468
$982$	−37.5492	−1.19824
$983$	3.97367	0.126740	0.0633702	−	0.997990i	$-0.479815\pi$
$983$	3.97367	0.126740	0.0633702	+	0.997990i	$0.479815\pi$
$984$	−2.83699	−0.0904400
$985$	20.3968	0.649897
$986$	−49.0934	−1.56345
$987$	−3.29931	−0.105018
$988$	9.44781	0.300575
$989$	14.3064	0.454917
$990$	0	0
$991$	−28.4012	−0.902193	−0.451097	−	0.892475i	$-0.648967\pi$
$991$	−28.4012	−0.902193	−0.451097	+	0.892475i	$0.648967\pi$
$992$	2.24914	0.0714103
$993$	−13.6346	−0.432680
$994$	8.56040	0.271519
$995$	6.47192	0.205174
$996$	6.09132	0.193011
$997$	34.4767	1.09189	0.545944	−	0.837821i	$-0.316171\pi$
$997$	34.4767	1.09189	0.545944	+	0.837821i	$0.316171\pi$
$998$	−26.5551	−0.840588
$999$	18.6039	0.588601

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cz.1.3	✓	6
11.10	odd	2		8470.2.a.df.1.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.cz.1.3	✓	6	1.1	even	1	trivial
8470.2.a.df.1.4	yes	6	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.529317 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.529317 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.71982 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.529317 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.529317 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.71982 q^{9} -1.00000 q^{10} +0.529317 q^{12} -4.81243 q^{13} +1.00000 q^{14} +0.529317 q^{15} +1.00000 q^{16} -6.02760 q^{17} +2.71982 q^{18} -1.96321 q^{19} +1.00000 q^{20} -0.529317 q^{21} +2.56329 q^{23} -0.529317 q^{24} +1.00000 q^{25} +4.81243 q^{26} -3.02760 q^{27} -1.00000 q^{28} -8.14477 q^{29} -0.529317 q^{30} -2.24914 q^{31} -1.00000 q^{32} +6.02760 q^{34} -1.00000 q^{35} -2.71982 q^{36} -6.14477 q^{37} +1.96321 q^{38} -2.54730 q^{39} -1.00000 q^{40} +5.35973 q^{41} +0.529317 q^{42} +5.58127 q^{43} -2.71982 q^{45} -2.56329 q^{46} +6.23315 q^{47} +0.529317 q^{48} +1.00000 q^{49} -1.00000 q^{50} -3.19051 q^{51} -4.81243 q^{52} -0.648854 q^{53} +3.02760 q^{54} +1.00000 q^{56} -1.03916 q^{57} +8.14477 q^{58} -6.84003 q^{59} +0.529317 q^{60} -1.67669 q^{61} +2.24914 q^{62} +2.71982 q^{63} +1.00000 q^{64} -4.81243 q^{65} +7.80030 q^{67} -6.02760 q^{68} +1.35679 q^{69} +1.00000 q^{70} +8.56040 q^{71} +2.71982 q^{72} +5.50769 q^{73} +6.14477 q^{74} +0.529317 q^{75} -1.96321 q^{76} +2.54730 q^{78} -3.71916 q^{79} +1.00000 q^{80} +6.55691 q^{81} -5.35973 q^{82} +11.5079 q^{83} -0.529317 q^{84} -6.02760 q^{85} -5.58127 q^{86} -4.31116 q^{87} -14.2096 q^{89} +2.71982 q^{90} +4.81243 q^{91} +2.56329 q^{92} -1.19051 q^{93} -6.23315 q^{94} -1.96321 q^{95} -0.529317 q^{96} -3.26750 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 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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