LMFDB - Embedded newform 7098.2.a.bz.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7098,2,Mod(1,7098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, 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("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.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:	$56.6778153547$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.46410 q^{10} -4.00000 q^{11} +1.00000 q^{12} -1.00000 q^{14} +3.46410 q^{15} +1.00000 q^{16} +6.46410 q^{17} +1.00000 q^{18} -7.46410 q^{19} +3.46410 q^{20} -1.00000 q^{21} -4.00000 q^{22} +5.73205 q^{23} +1.00000 q^{24} +7.00000 q^{25} +1.00000 q^{27} -1.00000 q^{28} +8.00000 q^{29} +3.46410 q^{30} +6.46410 q^{31} +1.00000 q^{32} -4.00000 q^{33} +6.46410 q^{34} -3.46410 q^{35} +1.00000 q^{36} +4.92820 q^{37} -7.46410 q^{38} +3.46410 q^{40} -6.92820 q^{41} -1.00000 q^{42} +4.46410 q^{43} -4.00000 q^{44} +3.46410 q^{45} +5.73205 q^{46} +0.535898 q^{47} +1.00000 q^{48} +1.00000 q^{49} +7.00000 q^{50} +6.46410 q^{51} -8.26795 q^{53} +1.00000 q^{54} -13.8564 q^{55} -1.00000 q^{56} -7.46410 q^{57} +8.00000 q^{58} -6.26795 q^{59} +3.46410 q^{60} -5.19615 q^{61} +6.46410 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.00000 q^{66} +7.19615 q^{67} +6.46410 q^{68} +5.73205 q^{69} -3.46410 q^{70} -1.92820 q^{71} +1.00000 q^{72} +10.9282 q^{73} +4.92820 q^{74} +7.00000 q^{75} -7.46410 q^{76} +4.00000 q^{77} -9.46410 q^{79} +3.46410 q^{80} +1.00000 q^{81} -6.92820 q^{82} -1.73205 q^{83} -1.00000 q^{84} +22.3923 q^{85} +4.46410 q^{86} +8.00000 q^{87} -4.00000 q^{88} +11.7321 q^{89} +3.46410 q^{90} +5.73205 q^{92} +6.46410 q^{93} +0.535898 q^{94} -25.8564 q^{95} +1.00000 q^{96} -12.3923 q^{97} +1.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 8 q^{11} + 2 q^{12} - 2 q^{14} + 2 q^{16} + 6 q^{17} + 2 q^{18} - 8 q^{19} - 2 q^{21} - 8 q^{22} + 8 q^{23} + 2 q^{24} + 14 q^{25} + 2 q^{27} - 2 q^{28} + 16 q^{29} + 6 q^{31} + 2 q^{32} - 8 q^{33} + 6 q^{34} + 2 q^{36} - 4 q^{37} - 8 q^{38} - 2 q^{42} + 2 q^{43} - 8 q^{44} + 8 q^{46} + 8 q^{47} + 2 q^{48} + 2 q^{49} + 14 q^{50} + 6 q^{51} - 20 q^{53} + 2 q^{54} - 2 q^{56} - 8 q^{57} + 16 q^{58} - 16 q^{59} + 6 q^{62} - 2 q^{63} + 2 q^{64} - 8 q^{66} + 4 q^{67} + 6 q^{68} + 8 q^{69} + 10 q^{71} + 2 q^{72} + 8 q^{73} - 4 q^{74} + 14 q^{75} - 8 q^{76} + 8 q^{77} - 12 q^{79} + 2 q^{81} - 2 q^{84} + 24 q^{85} + 2 q^{86} + 16 q^{87} - 8 q^{88} + 20 q^{89} + 8 q^{92} + 6 q^{93} + 8 q^{94} - 24 q^{95} + 2 q^{96} - 4 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 8 * q^11 + 2 * q^12 - 2 * q^14 + 2 * q^16 + 6 * q^17 + 2 * q^18 - 8 * q^19 - 2 * q^21 - 8 * q^22 + 8 * q^23 + 2 * q^24 + 14 * q^25 + 2 * q^27 - 2 * q^28 + 16 * q^29 + 6 * q^31 + 2 * q^32 - 8 * q^33 + 6 * q^34 + 2 * q^36 - 4 * q^37 - 8 * q^38 - 2 * q^42 + 2 * q^43 - 8 * q^44 + 8 * q^46 + 8 * q^47 + 2 * q^48 + 2 * q^49 + 14 * q^50 + 6 * q^51 - 20 * q^53 + 2 * q^54 - 2 * q^56 - 8 * q^57 + 16 * q^58 - 16 * q^59 + 6 * q^62 - 2 * q^63 + 2 * q^64 - 8 * q^66 + 4 * q^67 + 6 * q^68 + 8 * q^69 + 10 * q^71 + 2 * q^72 + 8 * q^73 - 4 * q^74 + 14 * q^75 - 8 * q^76 + 8 * q^77 - 12 * q^79 + 2 * q^81 - 2 * q^84 + 24 * q^85 + 2 * q^86 + 16 * q^87 - 8 * q^88 + 20 * q^89 + 8 * q^92 + 6 * q^93 + 8 * q^94 - 24 * q^95 + 2 * q^96 - 4 * q^97 + 2 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.46410	1.54919	0.774597	−	0.632456i	$-0.217953\pi$
$5$	3.46410	1.54919	0.774597	+	0.632456i	$0.217953\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.46410	1.09545
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	3.46410	0.894427
$16$	1.00000	0.250000
$17$	6.46410	1.56777	0.783887	−	0.620903i	$-0.213234\pi$
$17$	6.46410	1.56777	0.783887	+	0.620903i	$0.213234\pi$
$18$	1.00000	0.235702
$19$	−7.46410	−1.71238	−0.856191	−	0.516659i	$-0.827175\pi$
$19$	−7.46410	−1.71238	−0.856191	+	0.516659i	$0.827175\pi$
$20$	3.46410	0.774597
$21$	−1.00000	−0.218218
$22$	−4.00000	−0.852803
$23$	5.73205	1.19522	0.597608	−	0.801789i	$-0.296118\pi$
$23$	5.73205	1.19522	0.597608	+	0.801789i	$0.296118\pi$
$24$	1.00000	0.204124
$25$	7.00000	1.40000
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	8.00000	1.48556	0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000	1.48556	0.742781	+	0.669534i	$0.233506\pi$
$30$	3.46410	0.632456
$31$	6.46410	1.16099	0.580493	−	0.814265i	$-0.302860\pi$
$31$	6.46410	1.16099	0.580493	+	0.814265i	$0.302860\pi$
$32$	1.00000	0.176777
$33$	−4.00000	−0.696311
$34$	6.46410	1.10858
$35$	−3.46410	−0.585540
$36$	1.00000	0.166667
$37$	4.92820	0.810192	0.405096	−	0.914274i	$-0.367238\pi$
$37$	4.92820	0.810192	0.405096	+	0.914274i	$0.367238\pi$
$38$	−7.46410	−1.21084
$39$	0	0
$40$	3.46410	0.547723
$41$	−6.92820	−1.08200	−0.541002	−	0.841021i	$-0.681955\pi$
$41$	−6.92820	−1.08200	−0.541002	+	0.841021i	$0.681955\pi$
$42$	−1.00000	−0.154303
$43$	4.46410	0.680769	0.340385	−	0.940286i	$-0.389443\pi$
$43$	4.46410	0.680769	0.340385	+	0.940286i	$0.389443\pi$
$44$	−4.00000	−0.603023
$45$	3.46410	0.516398
$46$	5.73205	0.845145
$47$	0.535898	0.0781688	0.0390844	−	0.999236i	$-0.487556\pi$
$47$	0.535898	0.0781688	0.0390844	+	0.999236i	$0.487556\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	7.00000	0.989949
$51$	6.46410	0.905155
$52$	0	0
$53$	−8.26795	−1.13569	−0.567845	−	0.823135i	$-0.692223\pi$
$53$	−8.26795	−1.13569	−0.567845	+	0.823135i	$0.692223\pi$
$54$	1.00000	0.136083
$55$	−13.8564	−1.86840
$56$	−1.00000	−0.133631
$57$	−7.46410	−0.988644
$58$	8.00000	1.05045
$59$	−6.26795	−0.816017	−0.408009	−	0.912978i	$-0.633777\pi$
$59$	−6.26795	−0.816017	−0.408009	+	0.912978i	$0.633777\pi$
$60$	3.46410	0.447214
$61$	−5.19615	−0.665299	−0.332650	−	0.943051i	$-0.607943\pi$
$61$	−5.19615	−0.665299	−0.332650	+	0.943051i	$0.607943\pi$
$62$	6.46410	0.820942
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−4.00000	−0.492366
$67$	7.19615	0.879150	0.439575	−	0.898206i	$-0.355129\pi$
$67$	7.19615	0.879150	0.439575	+	0.898206i	$0.355129\pi$
$68$	6.46410	0.783887
$69$	5.73205	0.690058
$70$	−3.46410	−0.414039
$71$	−1.92820	−0.228836	−0.114418	−	0.993433i	$-0.536500\pi$
$71$	−1.92820	−0.228836	−0.114418	+	0.993433i	$0.536500\pi$
$72$	1.00000	0.117851
$73$	10.9282	1.27905	0.639525	−	0.768771i	$-0.279131\pi$
$73$	10.9282	1.27905	0.639525	+	0.768771i	$0.279131\pi$
$74$	4.92820	0.572892
$75$	7.00000	0.808290
$76$	−7.46410	−0.856191
$77$	4.00000	0.455842
$78$	0	0
$79$	−9.46410	−1.06479	−0.532397	−	0.846495i	$-0.678709\pi$
$79$	−9.46410	−1.06479	−0.532397	+	0.846495i	$0.678709\pi$
$80$	3.46410	0.387298
$81$	1.00000	0.111111
$82$	−6.92820	−0.765092
$83$	−1.73205	−0.190117	−0.0950586	−	0.995472i	$-0.530304\pi$
$83$	−1.73205	−0.190117	−0.0950586	+	0.995472i	$0.530304\pi$
$84$	−1.00000	−0.109109
$85$	22.3923	2.42879
$86$	4.46410	0.481376
$87$	8.00000	0.857690
$88$	−4.00000	−0.426401
$89$	11.7321	1.24359	0.621797	−	0.783178i	$-0.286403\pi$
$89$	11.7321	1.24359	0.621797	+	0.783178i	$0.286403\pi$
$90$	3.46410	0.365148
$91$	0	0
$92$	5.73205	0.597608
$93$	6.46410	0.670296
$94$	0.535898	0.0552737
$95$	−25.8564	−2.65281
$96$	1.00000	0.102062
$97$	−12.3923	−1.25825	−0.629124	−	0.777305i	$-0.716586\pi$
$97$	−12.3923	−1.25825	−0.629124	+	0.777305i	$0.716586\pi$
$98$	1.00000	0.101015
$99$	−4.00000	−0.402015
$100$	7.00000	0.700000
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	6.46410	0.640041
$103$	10.6603	1.05039	0.525193	−	0.850983i	$-0.323993\pi$
$103$	10.6603	1.05039	0.525193	+	0.850983i	$0.323993\pi$
$104$	0	0
$105$	−3.46410	−0.338062
$106$	−8.26795	−0.803054
$107$	8.53590	0.825196	0.412598	−	0.910913i	$-0.364621\pi$
$107$	8.53590	0.825196	0.412598	+	0.910913i	$0.364621\pi$
$108$	1.00000	0.0962250
$109$	12.0000	1.14939	0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000	1.14939	0.574696	+	0.818367i	$0.305120\pi$
$110$	−13.8564	−1.32116
$111$	4.92820	0.467764
$112$	−1.00000	−0.0944911
$113$	−4.39230	−0.413193	−0.206597	−	0.978426i	$-0.566239\pi$
$113$	−4.39230	−0.413193	−0.206597	+	0.978426i	$0.566239\pi$
$114$	−7.46410	−0.699077
$115$	19.8564	1.85162
$116$	8.00000	0.742781
$117$	0	0
$118$	−6.26795	−0.577011
$119$	−6.46410	−0.592563
$120$	3.46410	0.316228
$121$	5.00000	0.454545
$122$	−5.19615	−0.470438
$123$	−6.92820	−0.624695
$124$	6.46410	0.580493
$125$	6.92820	0.619677
$126$	−1.00000	−0.0890871
$127$	5.07180	0.450049	0.225025	−	0.974353i	$-0.427754\pi$
$127$	5.07180	0.450049	0.225025	+	0.974353i	$0.427754\pi$
$128$	1.00000	0.0883883
$129$	4.46410	0.393042
$130$	0	0
$131$	19.0000	1.66004	0.830019	−	0.557735i	$-0.188330\pi$
$131$	19.0000	1.66004	0.830019	+	0.557735i	$0.188330\pi$
$132$	−4.00000	−0.348155
$133$	7.46410	0.647220
$134$	7.19615	0.621653
$135$	3.46410	0.298142
$136$	6.46410	0.554292
$137$	−13.8564	−1.18383	−0.591916	−	0.805999i	$-0.701628\pi$
$137$	−13.8564	−1.18383	−0.591916	+	0.805999i	$0.701628\pi$
$138$	5.73205	0.487945
$139$	2.92820	0.248367	0.124183	−	0.992259i	$-0.460369\pi$
$139$	2.92820	0.248367	0.124183	+	0.992259i	$0.460369\pi$
$140$	−3.46410	−0.292770
$141$	0.535898	0.0451308
$142$	−1.92820	−0.161811
$143$	0	0
$144$	1.00000	0.0833333
$145$	27.7128	2.30142
$146$	10.9282	0.904425
$147$	1.00000	0.0824786
$148$	4.92820	0.405096
$149$	11.5359	0.945058	0.472529	−	0.881315i	$-0.343341\pi$
$149$	11.5359	0.945058	0.472529	+	0.881315i	$0.343341\pi$
$150$	7.00000	0.571548
$151$	12.0000	0.976546	0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000	0.976546	0.488273	+	0.872691i	$0.337627\pi$
$152$	−7.46410	−0.605419
$153$	6.46410	0.522592
$154$	4.00000	0.322329
$155$	22.3923	1.79859
$156$	0	0
$157$	−2.92820	−0.233696	−0.116848	−	0.993150i	$-0.537279\pi$
$157$	−2.92820	−0.233696	−0.116848	+	0.993150i	$0.537279\pi$
$158$	−9.46410	−0.752923
$159$	−8.26795	−0.655691
$160$	3.46410	0.273861
$161$	−5.73205	−0.451749
$162$	1.00000	0.0785674
$163$	1.33975	0.104937	0.0524685	−	0.998623i	$-0.483291\pi$
$163$	1.33975	0.104937	0.0524685	+	0.998623i	$0.483291\pi$
$164$	−6.92820	−0.541002
$165$	−13.8564	−1.07872
$166$	−1.73205	−0.134433
$167$	−20.0000	−1.54765	−0.773823	−	0.633402i	$-0.781658\pi$
$167$	−20.0000	−1.54765	−0.773823	+	0.633402i	$0.781658\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	22.3923	1.71741
$171$	−7.46410	−0.570794
$172$	4.46410	0.340385
$173$	1.07180	0.0814872	0.0407436	−	0.999170i	$-0.487027\pi$
$173$	1.07180	0.0814872	0.0407436	+	0.999170i	$0.487027\pi$
$174$	8.00000	0.606478
$175$	−7.00000	−0.529150
$176$	−4.00000	−0.301511
$177$	−6.26795	−0.471128
$178$	11.7321	0.879354
$179$	−16.9282	−1.26527	−0.632637	−	0.774449i	$-0.718027\pi$
$179$	−16.9282	−1.26527	−0.632637	+	0.774449i	$0.718027\pi$
$180$	3.46410	0.258199
$181$	24.7846	1.84223	0.921113	−	0.389296i	$-0.127282\pi$
$181$	24.7846	1.84223	0.921113	+	0.389296i	$0.127282\pi$
$182$	0	0
$183$	−5.19615	−0.384111
$184$	5.73205	0.422572
$185$	17.0718	1.25514
$186$	6.46410	0.473971
$187$	−25.8564	−1.89081
$188$	0.535898	0.0390844
$189$	−1.00000	−0.0727393
$190$	−25.8564	−1.87582
$191$	−26.5167	−1.91868	−0.959339	−	0.282256i	$-0.908917\pi$
$191$	−26.5167	−1.91868	−0.959339	+	0.282256i	$0.908917\pi$
$192$	1.00000	0.0721688
$193$	−17.8564	−1.28533	−0.642666	−	0.766146i	$-0.722172\pi$
$193$	−17.8564	−1.28533	−0.642666	+	0.766146i	$0.722172\pi$
$194$	−12.3923	−0.889716
$195$	0	0
$196$	1.00000	0.0714286
$197$	2.60770	0.185791	0.0928953	−	0.995676i	$-0.470388\pi$
$197$	2.60770	0.185791	0.0928953	+	0.995676i	$0.470388\pi$
$198$	−4.00000	−0.284268
$199$	−22.1244	−1.56835	−0.784177	−	0.620537i	$-0.786915\pi$
$199$	−22.1244	−1.56835	−0.784177	+	0.620537i	$0.786915\pi$
$200$	7.00000	0.494975
$201$	7.19615	0.507577
$202$	0	0
$203$	−8.00000	−0.561490
$204$	6.46410	0.452578
$205$	−24.0000	−1.67623
$206$	10.6603	0.742735
$207$	5.73205	0.398405
$208$	0	0
$209$	29.8564	2.06521
$210$	−3.46410	−0.239046
$211$	−9.07180	−0.624528	−0.312264	−	0.949995i	$-0.601087\pi$
$211$	−9.07180	−0.624528	−0.312264	+	0.949995i	$0.601087\pi$
$212$	−8.26795	−0.567845
$213$	−1.92820	−0.132118
$214$	8.53590	0.583502
$215$	15.4641	1.05464
$216$	1.00000	0.0680414
$217$	−6.46410	−0.438812
$218$	12.0000	0.812743
$219$	10.9282	0.738460
$220$	−13.8564	−0.934199
$221$	0	0
$222$	4.92820	0.330759
$223$	−7.53590	−0.504641	−0.252321	−	0.967644i	$-0.581194\pi$
$223$	−7.53590	−0.504641	−0.252321	+	0.967644i	$0.581194\pi$
$224$	−1.00000	−0.0668153
$225$	7.00000	0.466667
$226$	−4.39230	−0.292172
$227$	13.3205	0.884113	0.442057	−	0.896987i	$-0.354249\pi$
$227$	13.3205	0.884113	0.442057	+	0.896987i	$0.354249\pi$
$228$	−7.46410	−0.494322
$229$	−19.9282	−1.31689	−0.658446	−	0.752628i	$-0.728786\pi$
$229$	−19.9282	−1.31689	−0.658446	+	0.752628i	$0.728786\pi$
$230$	19.8564	1.30929
$231$	4.00000	0.263181
$232$	8.00000	0.525226
$233$	13.4641	0.882063	0.441031	−	0.897492i	$-0.354613\pi$
$233$	13.4641	0.882063	0.441031	+	0.897492i	$0.354613\pi$
$234$	0	0
$235$	1.85641	0.121099
$236$	−6.26795	−0.408009
$237$	−9.46410	−0.614759
$238$	−6.46410	−0.419005
$239$	−12.8564	−0.831612	−0.415806	−	0.909453i	$-0.636500\pi$
$239$	−12.8564	−0.831612	−0.415806	+	0.909453i	$0.636500\pi$
$240$	3.46410	0.223607
$241$	15.8564	1.02140	0.510700	−	0.859759i	$-0.329386\pi$
$241$	15.8564	1.02140	0.510700	+	0.859759i	$0.329386\pi$
$242$	5.00000	0.321412
$243$	1.00000	0.0641500
$244$	−5.19615	−0.332650
$245$	3.46410	0.221313
$246$	−6.92820	−0.441726
$247$	0	0
$248$	6.46410	0.410471
$249$	−1.73205	−0.109764
$250$	6.92820	0.438178
$251$	−10.0718	−0.635726	−0.317863	−	0.948137i	$-0.602965\pi$
$251$	−10.0718	−0.635726	−0.317863	+	0.948137i	$0.602965\pi$
$252$	−1.00000	−0.0629941
$253$	−22.9282	−1.44148
$254$	5.07180	0.318233
$255$	22.3923	1.40226
$256$	1.00000	0.0625000
$257$	0.464102	0.0289499	0.0144749	−	0.999895i	$-0.495392\pi$
$257$	0.464102	0.0289499	0.0144749	+	0.999895i	$0.495392\pi$
$258$	4.46410	0.277923
$259$	−4.92820	−0.306224
$260$	0	0
$261$	8.00000	0.495188
$262$	19.0000	1.17382
$263$	−17.3205	−1.06803	−0.534014	−	0.845476i	$-0.679317\pi$
$263$	−17.3205	−1.06803	−0.534014	+	0.845476i	$0.679317\pi$
$264$	−4.00000	−0.246183
$265$	−28.6410	−1.75940
$266$	7.46410	0.457653
$267$	11.7321	0.717990
$268$	7.19615	0.439575
$269$	22.3923	1.36528	0.682641	−	0.730753i	$-0.260831\pi$
$269$	22.3923	1.36528	0.682641	+	0.730753i	$0.260831\pi$
$270$	3.46410	0.210819
$271$	−12.4641	−0.757140	−0.378570	−	0.925573i	$-0.623584\pi$
$271$	−12.4641	−0.757140	−0.378570	+	0.925573i	$0.623584\pi$
$272$	6.46410	0.391944
$273$	0	0
$274$	−13.8564	−0.837096
$275$	−28.0000	−1.68846
$276$	5.73205	0.345029
$277$	7.32051	0.439847	0.219923	−	0.975517i	$-0.429419\pi$
$277$	7.32051	0.439847	0.219923	+	0.975517i	$0.429419\pi$
$278$	2.92820	0.175622
$279$	6.46410	0.386996
$280$	−3.46410	−0.207020
$281$	2.39230	0.142713	0.0713565	−	0.997451i	$-0.477267\pi$
$281$	2.39230	0.142713	0.0713565	+	0.997451i	$0.477267\pi$
$282$	0.535898	0.0319123
$283$	−11.4641	−0.681470	−0.340735	−	0.940159i	$-0.610676\pi$
$283$	−11.4641	−0.681470	−0.340735	+	0.940159i	$0.610676\pi$
$284$	−1.92820	−0.114418
$285$	−25.8564	−1.53160
$286$	0	0
$287$	6.92820	0.408959
$288$	1.00000	0.0589256
$289$	24.7846	1.45792
$290$	27.7128	1.62735
$291$	−12.3923	−0.726450
$292$	10.9282	0.639525
$293$	−33.4641	−1.95499	−0.977497	−	0.210950i	$-0.932344\pi$
$293$	−33.4641	−1.95499	−0.977497	+	0.210950i	$0.932344\pi$
$294$	1.00000	0.0583212
$295$	−21.7128	−1.26417
$296$	4.92820	0.286446
$297$	−4.00000	−0.232104
$298$	11.5359	0.668257
$299$	0	0
$300$	7.00000	0.404145
$301$	−4.46410	−0.257307
$302$	12.0000	0.690522
$303$	0	0
$304$	−7.46410	−0.428096
$305$	−18.0000	−1.03068
$306$	6.46410	0.369528
$307$	22.0000	1.25561	0.627803	−	0.778372i	$-0.283954\pi$
$307$	22.0000	1.25561	0.627803	+	0.778372i	$0.283954\pi$
$308$	4.00000	0.227921
$309$	10.6603	0.606441
$310$	22.3923	1.27180
$311$	13.3205	0.755337	0.377668	−	0.925941i	$-0.376726\pi$
$311$	13.3205	0.755337	0.377668	+	0.925941i	$0.376726\pi$
$312$	0	0
$313$	0.679492	0.0384072	0.0192036	−	0.999816i	$-0.493887\pi$
$313$	0.679492	0.0384072	0.0192036	+	0.999816i	$0.493887\pi$
$314$	−2.92820	−0.165248
$315$	−3.46410	−0.195180
$316$	−9.46410	−0.532397
$317$	−16.4641	−0.924716	−0.462358	−	0.886693i	$-0.652997\pi$
$317$	−16.4641	−0.924716	−0.462358	+	0.886693i	$0.652997\pi$
$318$	−8.26795	−0.463644
$319$	−32.0000	−1.79166
$320$	3.46410	0.193649
$321$	8.53590	0.476427
$322$	−5.73205	−0.319435
$323$	−48.2487	−2.68463
$324$	1.00000	0.0555556
$325$	0	0
$326$	1.33975	0.0742017
$327$	12.0000	0.663602
$328$	−6.92820	−0.382546
$329$	−0.535898	−0.0295450
$330$	−13.8564	−0.762770
$331$	−21.3205	−1.17188	−0.585941	−	0.810354i	$-0.699275\pi$
$331$	−21.3205	−1.17188	−0.585941	+	0.810354i	$0.699275\pi$
$332$	−1.73205	−0.0950586
$333$	4.92820	0.270064
$334$	−20.0000	−1.09435
$335$	24.9282	1.36197
$336$	−1.00000	−0.0545545
$337$	6.00000	0.326841	0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000	0.326841	0.163420	+	0.986557i	$0.447747\pi$
$338$	0	0
$339$	−4.39230	−0.238557
$340$	22.3923	1.21439
$341$	−25.8564	−1.40020
$342$	−7.46410	−0.403612
$343$	−1.00000	−0.0539949
$344$	4.46410	0.240688
$345$	19.8564	1.06903
$346$	1.07180	0.0576202
$347$	25.7128	1.38034	0.690168	−	0.723649i	$-0.257537\pi$
$347$	25.7128	1.38034	0.690168	+	0.723649i	$0.257537\pi$
$348$	8.00000	0.428845
$349$	35.6410	1.90782	0.953910	−	0.300093i	$-0.0970177\pi$
$349$	35.6410	1.90782	0.953910	+	0.300093i	$0.0970177\pi$
$350$	−7.00000	−0.374166
$351$	0	0
$352$	−4.00000	−0.213201
$353$	9.33975	0.497105	0.248552	−	0.968618i	$-0.420045\pi$
$353$	9.33975	0.497105	0.248552	+	0.968618i	$0.420045\pi$
$354$	−6.26795	−0.333138
$355$	−6.67949	−0.354511
$356$	11.7321	0.621797
$357$	−6.46410	−0.342117
$358$	−16.9282	−0.894683
$359$	8.00000	0.422224	0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000	0.422224	0.211112	+	0.977462i	$0.432292\pi$
$360$	3.46410	0.182574
$361$	36.7128	1.93225
$362$	24.7846	1.30265
$363$	5.00000	0.262432
$364$	0	0
$365$	37.8564	1.98149
$366$	−5.19615	−0.271607
$367$	−33.0526	−1.72533	−0.862665	−	0.505776i	$-0.831206\pi$
$367$	−33.0526	−1.72533	−0.862665	+	0.505776i	$0.831206\pi$
$368$	5.73205	0.298804
$369$	−6.92820	−0.360668
$370$	17.0718	0.887520
$371$	8.26795	0.429251
$372$	6.46410	0.335148
$373$	−26.2487	−1.35911	−0.679553	−	0.733626i	$-0.737826\pi$
$373$	−26.2487	−1.35911	−0.679553	+	0.733626i	$0.737826\pi$
$374$	−25.8564	−1.33700
$375$	6.92820	0.357771
$376$	0.535898	0.0276368
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	−9.60770	−0.493514	−0.246757	−	0.969077i	$-0.579365\pi$
$379$	−9.60770	−0.493514	−0.246757	+	0.969077i	$0.579365\pi$
$380$	−25.8564	−1.32641
$381$	5.07180	0.259836
$382$	−26.5167	−1.35671
$383$	−7.32051	−0.374060	−0.187030	−	0.982354i	$-0.559886\pi$
$383$	−7.32051	−0.374060	−0.187030	+	0.982354i	$0.559886\pi$
$384$	1.00000	0.0510310
$385$	13.8564	0.706188
$386$	−17.8564	−0.908867
$387$	4.46410	0.226923
$388$	−12.3923	−0.629124
$389$	−14.6603	−0.743304	−0.371652	−	0.928372i	$-0.621209\pi$
$389$	−14.6603	−0.743304	−0.371652	+	0.928372i	$0.621209\pi$
$390$	0	0
$391$	37.0526	1.87383
$392$	1.00000	0.0505076
$393$	19.0000	0.958423
$394$	2.60770	0.131374
$395$	−32.7846	−1.64957
$396$	−4.00000	−0.201008
$397$	−29.7846	−1.49485	−0.747423	−	0.664348i	$-0.768709\pi$
$397$	−29.7846	−1.49485	−0.747423	+	0.664348i	$0.768709\pi$
$398$	−22.1244	−1.10899
$399$	7.46410	0.373672
$400$	7.00000	0.350000
$401$	16.3923	0.818593	0.409296	−	0.912402i	$-0.365774\pi$
$401$	16.3923	0.818593	0.409296	+	0.912402i	$0.365774\pi$
$402$	7.19615	0.358911
$403$	0	0
$404$	0	0
$405$	3.46410	0.172133
$406$	−8.00000	−0.397033
$407$	−19.7128	−0.977128
$408$	6.46410	0.320021
$409$	−6.39230	−0.316079	−0.158040	−	0.987433i	$-0.550517\pi$
$409$	−6.39230	−0.316079	−0.158040	+	0.987433i	$0.550517\pi$
$410$	−24.0000	−1.18528
$411$	−13.8564	−0.683486
$412$	10.6603	0.525193
$413$	6.26795	0.308426
$414$	5.73205	0.281715
$415$	−6.00000	−0.294528
$416$	0	0
$417$	2.92820	0.143395
$418$	29.8564	1.46032
$419$	−5.00000	−0.244266	−0.122133	−	0.992514i	$-0.538973\pi$
$419$	−5.00000	−0.244266	−0.122133	+	0.992514i	$0.538973\pi$
$420$	−3.46410	−0.169031
$421$	1.60770	0.0783543	0.0391771	−	0.999232i	$-0.487526\pi$
$421$	1.60770	0.0783543	0.0391771	+	0.999232i	$0.487526\pi$
$422$	−9.07180	−0.441608
$423$	0.535898	0.0260563
$424$	−8.26795	−0.401527
$425$	45.2487	2.19488
$426$	−1.92820	−0.0934218
$427$	5.19615	0.251459
$428$	8.53590	0.412598
$429$	0	0
$430$	15.4641	0.745745
$431$	4.85641	0.233925	0.116962	−	0.993136i	$-0.462684\pi$
$431$	4.85641	0.233925	0.116962	+	0.993136i	$0.462684\pi$
$432$	1.00000	0.0481125
$433$	9.85641	0.473669	0.236834	−	0.971550i	$-0.423890\pi$
$433$	9.85641	0.473669	0.236834	+	0.971550i	$0.423890\pi$
$434$	−6.46410	−0.310287
$435$	27.7128	1.32873
$436$	12.0000	0.574696
$437$	−42.7846	−2.04667
$438$	10.9282	0.522170
$439$	−13.6077	−0.649460	−0.324730	−	0.945807i	$-0.605273\pi$
$439$	−13.6077	−0.649460	−0.324730	+	0.945807i	$0.605273\pi$
$440$	−13.8564	−0.660578
$441$	1.00000	0.0476190
$442$	0	0
$443$	−22.3923	−1.06389	−0.531945	−	0.846779i	$-0.678539\pi$
$443$	−22.3923	−1.06389	−0.531945	+	0.846779i	$0.678539\pi$
$444$	4.92820	0.233882
$445$	40.6410	1.92657
$446$	−7.53590	−0.356835
$447$	11.5359	0.545629
$448$	−1.00000	−0.0472456
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	7.00000	0.329983
$451$	27.7128	1.30495
$452$	−4.39230	−0.206597
$453$	12.0000	0.563809
$454$	13.3205	0.625162
$455$	0	0
$456$	−7.46410	−0.349539
$457$	1.19615	0.0559537	0.0279768	−	0.999609i	$-0.491094\pi$
$457$	1.19615	0.0559537	0.0279768	+	0.999609i	$0.491094\pi$
$458$	−19.9282	−0.931184
$459$	6.46410	0.301718
$460$	19.8564	0.925810
$461$	5.07180	0.236217	0.118109	−	0.993001i	$-0.462317\pi$
$461$	5.07180	0.236217	0.118109	+	0.993001i	$0.462317\pi$
$462$	4.00000	0.186097
$463$	−8.24871	−0.383350	−0.191675	−	0.981458i	$-0.561392\pi$
$463$	−8.24871	−0.383350	−0.191675	+	0.981458i	$0.561392\pi$
$464$	8.00000	0.371391
$465$	22.3923	1.03842
$466$	13.4641	0.623712
$467$	−39.6410	−1.83437	−0.917184	−	0.398465i	$-0.869543\pi$
$467$	−39.6410	−1.83437	−0.917184	+	0.398465i	$0.869543\pi$
$468$	0	0
$469$	−7.19615	−0.332287
$470$	1.85641	0.0856296
$471$	−2.92820	−0.134924
$472$	−6.26795	−0.288506
$473$	−17.8564	−0.821038
$474$	−9.46410	−0.434701
$475$	−52.2487	−2.39734
$476$	−6.46410	−0.296282
$477$	−8.26795	−0.378563
$478$	−12.8564	−0.588038
$479$	4.39230	0.200690	0.100345	−	0.994953i	$-0.468005\pi$
$479$	4.39230	0.200690	0.100345	+	0.994953i	$0.468005\pi$
$480$	3.46410	0.158114
$481$	0	0
$482$	15.8564	0.722240
$483$	−5.73205	−0.260817
$484$	5.00000	0.227273
$485$	−42.9282	−1.94927
$486$	1.00000	0.0453609
$487$	−0.392305	−0.0177770	−0.00888851	−	0.999960i	$-0.502829\pi$
$487$	−0.392305	−0.0177770	−0.00888851	+	0.999960i	$0.502829\pi$
$488$	−5.19615	−0.235219
$489$	1.33975	0.0605854
$490$	3.46410	0.156492
$491$	−9.85641	−0.444813	−0.222407	−	0.974954i	$-0.571391\pi$
$491$	−9.85641	−0.444813	−0.222407	+	0.974954i	$0.571391\pi$
$492$	−6.92820	−0.312348
$493$	51.7128	2.32903
$494$	0	0
$495$	−13.8564	−0.622799
$496$	6.46410	0.290247
$497$	1.92820	0.0864917
$498$	−1.73205	−0.0776151
$499$	0.267949	0.0119951	0.00599753	−	0.999982i	$-0.498091\pi$
$499$	0.267949	0.0119951	0.00599753	+	0.999982i	$0.498091\pi$
$500$	6.92820	0.309839
$501$	−20.0000	−0.893534
$502$	−10.0718	−0.449526
$503$	−6.92820	−0.308913	−0.154457	−	0.988000i	$-0.549363\pi$
$503$	−6.92820	−0.308913	−0.154457	+	0.988000i	$0.549363\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	−22.9282	−1.01928
$507$	0	0
$508$	5.07180	0.225025
$509$	−34.2487	−1.51805	−0.759024	−	0.651063i	$-0.774323\pi$
$509$	−34.2487	−1.51805	−0.759024	+	0.651063i	$0.774323\pi$
$510$	22.3923	0.991548
$511$	−10.9282	−0.483435
$512$	1.00000	0.0441942
$513$	−7.46410	−0.329548
$514$	0.464102	0.0204706
$515$	36.9282	1.62725
$516$	4.46410	0.196521
$517$	−2.14359	−0.0942751
$518$	−4.92820	−0.216533
$519$	1.07180	0.0470467
$520$	0	0
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	8.00000	0.350150
$523$	14.9282	0.652765	0.326382	−	0.945238i	$-0.394170\pi$
$523$	14.9282	0.652765	0.326382	+	0.945238i	$0.394170\pi$
$524$	19.0000	0.830019
$525$	−7.00000	−0.305505
$526$	−17.3205	−0.755210
$527$	41.7846	1.82017
$528$	−4.00000	−0.174078
$529$	9.85641	0.428539
$530$	−28.6410	−1.24409
$531$	−6.26795	−0.272006
$532$	7.46410	0.323610
$533$	0	0
$534$	11.7321	0.507695
$535$	29.5692	1.27839
$536$	7.19615	0.310826
$537$	−16.9282	−0.730506
$538$	22.3923	0.965401
$539$	−4.00000	−0.172292
$540$	3.46410	0.149071
$541$	17.3205	0.744667	0.372333	−	0.928099i	$-0.378558\pi$
$541$	17.3205	0.744667	0.372333	+	0.928099i	$0.378558\pi$
$542$	−12.4641	−0.535379
$543$	24.7846	1.06361
$544$	6.46410	0.277146
$545$	41.5692	1.78063
$546$	0	0
$547$	−20.0000	−0.855138	−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000	−0.855138	−0.427569	+	0.903983i	$0.640630\pi$
$548$	−13.8564	−0.591916
$549$	−5.19615	−0.221766
$550$	−28.0000	−1.19392
$551$	−59.7128	−2.54385
$552$	5.73205	0.243972
$553$	9.46410	0.402455
$554$	7.32051	0.311019
$555$	17.0718	0.724657
$556$	2.92820	0.124183
$557$	−24.6077	−1.04266	−0.521331	−	0.853355i	$-0.674564\pi$
$557$	−24.6077	−1.04266	−0.521331	+	0.853355i	$0.674564\pi$
$558$	6.46410	0.273647
$559$	0	0
$560$	−3.46410	−0.146385
$561$	−25.8564	−1.09166
$562$	2.39230	0.100913
$563$	−13.8564	−0.583978	−0.291989	−	0.956422i	$-0.594317\pi$
$563$	−13.8564	−0.583978	−0.291989	+	0.956422i	$0.594317\pi$
$564$	0.535898	0.0225654
$565$	−15.2154	−0.640116
$566$	−11.4641	−0.481872
$567$	−1.00000	−0.0419961
$568$	−1.92820	−0.0809056
$569$	15.4641	0.648289	0.324144	−	0.946008i	$-0.394924\pi$
$569$	15.4641	0.648289	0.324144	+	0.946008i	$0.394924\pi$
$570$	−25.8564	−1.08301
$571$	−3.39230	−0.141964	−0.0709818	−	0.997478i	$-0.522613\pi$
$571$	−3.39230	−0.141964	−0.0709818	+	0.997478i	$0.522613\pi$
$572$	0	0
$573$	−26.5167	−1.10775
$574$	6.92820	0.289178
$575$	40.1244	1.67330
$576$	1.00000	0.0416667
$577$	−1.21539	−0.0505974	−0.0252987	−	0.999680i	$-0.508054\pi$
$577$	−1.21539	−0.0505974	−0.0252987	+	0.999680i	$0.508054\pi$
$578$	24.7846	1.03090
$579$	−17.8564	−0.742087
$580$	27.7128	1.15071
$581$	1.73205	0.0718576
$582$	−12.3923	−0.513678
$583$	33.0718	1.36969
$584$	10.9282	0.452212
$585$	0	0
$586$	−33.4641	−1.38239
$587$	8.12436	0.335328	0.167664	−	0.985844i	$-0.446378\pi$
$587$	8.12436	0.335328	0.167664	+	0.985844i	$0.446378\pi$
$588$	1.00000	0.0412393
$589$	−48.2487	−1.98805
$590$	−21.7128	−0.893902
$591$	2.60770	0.107266
$592$	4.92820	0.202548
$593$	−4.26795	−0.175264	−0.0876318	−	0.996153i	$-0.527930\pi$
$593$	−4.26795	−0.175264	−0.0876318	+	0.996153i	$0.527930\pi$
$594$	−4.00000	−0.164122
$595$	−22.3923	−0.917995
$596$	11.5359	0.472529
$597$	−22.1244	−0.905490
$598$	0	0
$599$	−19.0526	−0.778466	−0.389233	−	0.921139i	$-0.627260\pi$
$599$	−19.0526	−0.778466	−0.389233	+	0.921139i	$0.627260\pi$
$600$	7.00000	0.285774
$601$	−24.2487	−0.989126	−0.494563	−	0.869142i	$-0.664672\pi$
$601$	−24.2487	−0.989126	−0.494563	+	0.869142i	$0.664672\pi$
$602$	−4.46410	−0.181943
$603$	7.19615	0.293050
$604$	12.0000	0.488273
$605$	17.3205	0.704179
$606$	0	0
$607$	−15.1962	−0.616793	−0.308396	−	0.951258i	$-0.599792\pi$
$607$	−15.1962	−0.616793	−0.308396	+	0.951258i	$0.599792\pi$
$608$	−7.46410	−0.302709
$609$	−8.00000	−0.324176
$610$	−18.0000	−0.728799
$611$	0	0
$612$	6.46410	0.261296
$613$	34.3923	1.38909	0.694546	−	0.719448i	$-0.255605\pi$
$613$	34.3923	1.38909	0.694546	+	0.719448i	$0.255605\pi$
$614$	22.0000	0.887848
$615$	−24.0000	−0.967773
$616$	4.00000	0.161165
$617$	5.85641	0.235770	0.117885	−	0.993027i	$-0.462389\pi$
$617$	5.85641	0.235770	0.117885	+	0.993027i	$0.462389\pi$
$618$	10.6603	0.428818
$619$	−30.7846	−1.23734	−0.618669	−	0.785652i	$-0.712328\pi$
$619$	−30.7846	−1.23734	−0.618669	+	0.785652i	$0.712328\pi$
$620$	22.3923	0.899297
$621$	5.73205	0.230019
$622$	13.3205	0.534104
$623$	−11.7321	−0.470035
$624$	0	0
$625$	−11.0000	−0.440000
$626$	0.679492	0.0271580
$627$	29.8564	1.19235
$628$	−2.92820	−0.116848
$629$	31.8564	1.27020
$630$	−3.46410	−0.138013
$631$	34.9282	1.39047	0.695235	−	0.718783i	$-0.255300\pi$
$631$	34.9282	1.39047	0.695235	+	0.718783i	$0.255300\pi$
$632$	−9.46410	−0.376462
$633$	−9.07180	−0.360572
$634$	−16.4641	−0.653873
$635$	17.5692	0.697213
$636$	−8.26795	−0.327846
$637$	0	0
$638$	−32.0000	−1.26689
$639$	−1.92820	−0.0762785
$640$	3.46410	0.136931
$641$	−26.6410	−1.05226	−0.526128	−	0.850405i	$-0.676357\pi$
$641$	−26.6410	−1.05226	−0.526128	+	0.850405i	$0.676357\pi$
$642$	8.53590	0.336885
$643$	20.2487	0.798531	0.399266	−	0.916835i	$-0.369265\pi$
$643$	20.2487	0.798531	0.399266	+	0.916835i	$0.369265\pi$
$644$	−5.73205	−0.225874
$645$	15.4641	0.608898
$646$	−48.2487	−1.89832
$647$	37.3205	1.46722	0.733610	−	0.679570i	$-0.237834\pi$
$647$	37.3205	1.46722	0.733610	+	0.679570i	$0.237834\pi$
$648$	1.00000	0.0392837
$649$	25.0718	0.984154
$650$	0	0
$651$	−6.46410	−0.253348
$652$	1.33975	0.0524685
$653$	−37.5885	−1.47095	−0.735475	−	0.677552i	$-0.763041\pi$
$653$	−37.5885	−1.47095	−0.735475	+	0.677552i	$0.763041\pi$
$654$	12.0000	0.469237
$655$	65.8179	2.57172
$656$	−6.92820	−0.270501
$657$	10.9282	0.426350
$658$	−0.535898	−0.0208915
$659$	1.60770	0.0626269	0.0313135	−	0.999510i	$-0.490031\pi$
$659$	1.60770	0.0626269	0.0313135	+	0.999510i	$0.490031\pi$
$660$	−13.8564	−0.539360
$661$	−50.7128	−1.97250	−0.986250	−	0.165261i	$-0.947153\pi$
$661$	−50.7128	−1.97250	−0.986250	+	0.165261i	$0.947153\pi$
$662$	−21.3205	−0.828645
$663$	0	0
$664$	−1.73205	−0.0672166
$665$	25.8564	1.00267
$666$	4.92820	0.190964
$667$	45.8564	1.77557
$668$	−20.0000	−0.773823
$669$	−7.53590	−0.291355
$670$	24.9282	0.963061
$671$	20.7846	0.802381
$672$	−1.00000	−0.0385758
$673$	39.6410	1.52805	0.764024	−	0.645187i	$-0.223221\pi$
$673$	39.6410	1.52805	0.764024	+	0.645187i	$0.223221\pi$
$674$	6.00000	0.231111
$675$	7.00000	0.269430
$676$	0	0
$677$	1.07180	0.0411925	0.0205962	−	0.999788i	$-0.493444\pi$
$677$	1.07180	0.0411925	0.0205962	+	0.999788i	$0.493444\pi$
$678$	−4.39230	−0.168685
$679$	12.3923	0.475573
$680$	22.3923	0.858706
$681$	13.3205	0.510443
$682$	−25.8564	−0.990093
$683$	51.1769	1.95823	0.979115	−	0.203307i	$-0.0651688\pi$
$683$	51.1769	1.95823	0.979115	+	0.203307i	$0.0651688\pi$
$684$	−7.46410	−0.285397
$685$	−48.0000	−1.83399
$686$	−1.00000	−0.0381802
$687$	−19.9282	−0.760308
$688$	4.46410	0.170192
$689$	0	0
$690$	19.8564	0.755920
$691$	−41.1769	−1.56644	−0.783222	−	0.621742i	$-0.786425\pi$
$691$	−41.1769	−1.56644	−0.783222	+	0.621742i	$0.786425\pi$
$692$	1.07180	0.0407436
$693$	4.00000	0.151947
$694$	25.7128	0.976045
$695$	10.1436	0.384768
$696$	8.00000	0.303239
$697$	−44.7846	−1.69634
$698$	35.6410	1.34903
$699$	13.4641	0.509259
$700$	−7.00000	−0.264575
$701$	−2.12436	−0.0802358	−0.0401179	−	0.999195i	$-0.512773\pi$
$701$	−2.12436	−0.0802358	−0.0401179	+	0.999195i	$0.512773\pi$
$702$	0	0
$703$	−36.7846	−1.38736
$704$	−4.00000	−0.150756
$705$	1.85641	0.0699163
$706$	9.33975	0.351506
$707$	0	0
$708$	−6.26795	−0.235564
$709$	−7.71281	−0.289661	−0.144830	−	0.989456i	$-0.546264\pi$
$709$	−7.71281	−0.289661	−0.144830	+	0.989456i	$0.546264\pi$
$710$	−6.67949	−0.250677
$711$	−9.46410	−0.354932
$712$	11.7321	0.439677
$713$	37.0526	1.38763
$714$	−6.46410	−0.241913
$715$	0	0
$716$	−16.9282	−0.632637
$717$	−12.8564	−0.480131
$718$	8.00000	0.298557
$719$	34.5359	1.28797	0.643986	−	0.765037i	$-0.277280\pi$
$719$	34.5359	1.28797	0.643986	+	0.765037i	$0.277280\pi$
$720$	3.46410	0.129099
$721$	−10.6603	−0.397009
$722$	36.7128	1.36631
$723$	15.8564	0.589706
$724$	24.7846	0.921113
$725$	56.0000	2.07979
$726$	5.00000	0.185567
$727$	−22.9090	−0.849646	−0.424823	−	0.905276i	$-0.639664\pi$
$727$	−22.9090	−0.849646	−0.424823	+	0.905276i	$0.639664\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	37.8564	1.40113
$731$	28.8564	1.06729
$732$	−5.19615	−0.192055
$733$	−4.85641	−0.179375	−0.0896877	−	0.995970i	$-0.528587\pi$
$733$	−4.85641	−0.179375	−0.0896877	+	0.995970i	$0.528587\pi$
$734$	−33.0526	−1.21999
$735$	3.46410	0.127775
$736$	5.73205	0.211286
$737$	−28.7846	−1.06029
$738$	−6.92820	−0.255031
$739$	−7.73205	−0.284428	−0.142214	−	0.989836i	$-0.545422\pi$
$739$	−7.73205	−0.284428	−0.142214	+	0.989836i	$0.545422\pi$
$740$	17.0718	0.627572
$741$	0	0
$742$	8.26795	0.303526
$743$	1.78461	0.0654710	0.0327355	−	0.999464i	$-0.489578\pi$
$743$	1.78461	0.0654710	0.0327355	+	0.999464i	$0.489578\pi$
$744$	6.46410	0.236985
$745$	39.9615	1.46408
$746$	−26.2487	−0.961034
$747$	−1.73205	−0.0633724
$748$	−25.8564	−0.945404
$749$	−8.53590	−0.311895
$750$	6.92820	0.252982
$751$	29.3205	1.06992	0.534960	−	0.844877i	$-0.320327\pi$
$751$	29.3205	1.06992	0.534960	+	0.844877i	$0.320327\pi$
$752$	0.535898	0.0195422
$753$	−10.0718	−0.367037
$754$	0	0
$755$	41.5692	1.51286
$756$	−1.00000	−0.0363696
$757$	19.8564	0.721693	0.360847	−	0.932625i	$-0.382488\pi$
$757$	19.8564	0.721693	0.360847	+	0.932625i	$0.382488\pi$
$758$	−9.60770	−0.348967
$759$	−22.9282	−0.832241
$760$	−25.8564	−0.937910
$761$	6.92820	0.251147	0.125574	−	0.992084i	$-0.459923\pi$
$761$	6.92820	0.251147	0.125574	+	0.992084i	$0.459923\pi$
$762$	5.07180	0.183732
$763$	−12.0000	−0.434429
$764$	−26.5167	−0.959339
$765$	22.3923	0.809595
$766$	−7.32051	−0.264501
$767$	0	0
$768$	1.00000	0.0360844
$769$	42.6410	1.53767	0.768837	−	0.639445i	$-0.220836\pi$
$769$	42.6410	1.53767	0.768837	+	0.639445i	$0.220836\pi$
$770$	13.8564	0.499350
$771$	0.464102	0.0167142
$772$	−17.8564	−0.642666
$773$	−12.9282	−0.464995	−0.232498	−	0.972597i	$-0.574690\pi$
$773$	−12.9282	−0.464995	−0.232498	+	0.972597i	$0.574690\pi$
$774$	4.46410	0.160459
$775$	45.2487	1.62538
$776$	−12.3923	−0.444858
$777$	−4.92820	−0.176798
$778$	−14.6603	−0.525596
$779$	51.7128	1.85280
$780$	0	0
$781$	7.71281	0.275986
$782$	37.0526	1.32500
$783$	8.00000	0.285897
$784$	1.00000	0.0357143
$785$	−10.1436	−0.362040
$786$	19.0000	0.677708
$787$	−8.39230	−0.299153	−0.149577	−	0.988750i	$-0.547791\pi$
$787$	−8.39230	−0.299153	−0.149577	+	0.988750i	$0.547791\pi$
$788$	2.60770	0.0928953
$789$	−17.3205	−0.616626
$790$	−32.7846	−1.16642
$791$	4.39230	0.156172
$792$	−4.00000	−0.142134
$793$	0	0
$794$	−29.7846	−1.05702
$795$	−28.6410	−1.01579
$796$	−22.1244	−0.784177
$797$	42.2487	1.49653	0.748263	−	0.663402i	$-0.230888\pi$
$797$	42.2487	1.49653	0.748263	+	0.663402i	$0.230888\pi$
$798$	7.46410	0.264226
$799$	3.46410	0.122551
$800$	7.00000	0.247487
$801$	11.7321	0.414532
$802$	16.3923	0.578832
$803$	−43.7128	−1.54259
$804$	7.19615	0.253789
$805$	−19.8564	−0.699846
$806$	0	0
$807$	22.3923	0.788246
$808$	0	0
$809$	15.7128	0.552433	0.276217	−	0.961095i	$-0.410919\pi$
$809$	15.7128	0.552433	0.276217	+	0.961095i	$0.410919\pi$
$810$	3.46410	0.121716
$811$	−2.14359	−0.0752717	−0.0376359	−	0.999292i	$-0.511983\pi$
$811$	−2.14359	−0.0752717	−0.0376359	+	0.999292i	$0.511983\pi$
$812$	−8.00000	−0.280745
$813$	−12.4641	−0.437135
$814$	−19.7128	−0.690934
$815$	4.64102	0.162568
$816$	6.46410	0.226289
$817$	−33.3205	−1.16574
$818$	−6.39230	−0.223502
$819$	0	0
$820$	−24.0000	−0.838116
$821$	31.2487	1.09059	0.545294	−	0.838245i	$-0.316418\pi$
$821$	31.2487	1.09059	0.545294	+	0.838245i	$0.316418\pi$
$822$	−13.8564	−0.483298
$823$	23.6077	0.822913	0.411456	−	0.911430i	$-0.365020\pi$
$823$	23.6077	0.822913	0.411456	+	0.911430i	$0.365020\pi$
$824$	10.6603	0.371368
$825$	−28.0000	−0.974835
$826$	6.26795	0.218090
$827$	−36.3923	−1.26548	−0.632742	−	0.774363i	$-0.718071\pi$
$827$	−36.3923	−1.26548	−0.632742	+	0.774363i	$0.718071\pi$
$828$	5.73205	0.199203
$829$	7.21539	0.250601	0.125300	−	0.992119i	$-0.460011\pi$
$829$	7.21539	0.250601	0.125300	+	0.992119i	$0.460011\pi$
$830$	−6.00000	−0.208263
$831$	7.32051	0.253946
$832$	0	0
$833$	6.46410	0.223968
$834$	2.92820	0.101395
$835$	−69.2820	−2.39760
$836$	29.8564	1.03261
$837$	6.46410	0.223432
$838$	−5.00000	−0.172722
$839$	−1.60770	−0.0555038	−0.0277519	−	0.999615i	$-0.508835\pi$
$839$	−1.60770	−0.0555038	−0.0277519	+	0.999615i	$0.508835\pi$
$840$	−3.46410	−0.119523
$841$	35.0000	1.20690
$842$	1.60770	0.0554048
$843$	2.39230	0.0823954
$844$	−9.07180	−0.312264
$845$	0	0
$846$	0.535898	0.0184246
$847$	−5.00000	−0.171802
$848$	−8.26795	−0.283923
$849$	−11.4641	−0.393447
$850$	45.2487	1.55202
$851$	28.2487	0.968353
$852$	−1.92820	−0.0660592
$853$	−47.6410	−1.63120	−0.815599	−	0.578618i	$-0.803592\pi$
$853$	−47.6410	−1.63120	−0.815599	+	0.578618i	$0.803592\pi$
$854$	5.19615	0.177809
$855$	−25.8564	−0.884270
$856$	8.53590	0.291751
$857$	−33.7128	−1.15161	−0.575804	−	0.817588i	$-0.695311\pi$
$857$	−33.7128	−1.15161	−0.575804	+	0.817588i	$0.695311\pi$
$858$	0	0
$859$	−15.8564	−0.541014	−0.270507	−	0.962718i	$-0.587191\pi$
$859$	−15.8564	−0.541014	−0.270507	+	0.962718i	$0.587191\pi$
$860$	15.4641	0.527321
$861$	6.92820	0.236113
$862$	4.85641	0.165410
$863$	−42.9282	−1.46129	−0.730647	−	0.682756i	$-0.760781\pi$
$863$	−42.9282	−1.46129	−0.730647	+	0.682756i	$0.760781\pi$
$864$	1.00000	0.0340207
$865$	3.71281	0.126239
$866$	9.85641	0.334934
$867$	24.7846	0.841729
$868$	−6.46410	−0.219406
$869$	37.8564	1.28419
$870$	27.7128	0.939552
$871$	0	0
$872$	12.0000	0.406371
$873$	−12.3923	−0.419416
$874$	−42.7846	−1.44721
$875$	−6.92820	−0.234216
$876$	10.9282	0.369230
$877$	−25.7128	−0.868260	−0.434130	−	0.900850i	$-0.642944\pi$
$877$	−25.7128	−0.868260	−0.434130	+	0.900850i	$0.642944\pi$
$878$	−13.6077	−0.459237
$879$	−33.4641	−1.12872
$880$	−13.8564	−0.467099
$881$	32.0333	1.07923	0.539615	−	0.841912i	$-0.318570\pi$
$881$	32.0333	1.07923	0.539615	+	0.841912i	$0.318570\pi$
$882$	1.00000	0.0336718
$883$	−0.320508	−0.0107860	−0.00539298	−	0.999985i	$-0.501717\pi$
$883$	−0.320508	−0.0107860	−0.00539298	+	0.999985i	$0.501717\pi$
$884$	0	0
$885$	−21.7128	−0.729868
$886$	−22.3923	−0.752284
$887$	11.8564	0.398099	0.199050	−	0.979989i	$-0.436215\pi$
$887$	11.8564	0.398099	0.199050	+	0.979989i	$0.436215\pi$
$888$	4.92820	0.165380
$889$	−5.07180	−0.170103
$890$	40.6410	1.36229
$891$	−4.00000	−0.134005
$892$	−7.53590	−0.252321
$893$	−4.00000	−0.133855
$894$	11.5359	0.385818
$895$	−58.6410	−1.96015
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	18.0000	0.600668
$899$	51.7128	1.72472
$900$	7.00000	0.233333
$901$	−53.4449	−1.78051
$902$	27.7128	0.922736
$903$	−4.46410	−0.148556
$904$	−4.39230	−0.146086
$905$	85.8564	2.85396
$906$	12.0000	0.398673
$907$	−18.4641	−0.613090	−0.306545	−	0.951856i	$-0.599173\pi$
$907$	−18.4641	−0.613090	−0.306545	+	0.951856i	$0.599173\pi$
$908$	13.3205	0.442057
$909$	0	0
$910$	0	0
$911$	27.1769	0.900411	0.450206	−	0.892925i	$-0.351351\pi$
$911$	27.1769	0.900411	0.450206	+	0.892925i	$0.351351\pi$
$912$	−7.46410	−0.247161
$913$	6.92820	0.229290
$914$	1.19615	0.0395652
$915$	−18.0000	−0.595062
$916$	−19.9282	−0.658446
$917$	−19.0000	−0.627435
$918$	6.46410	0.213347
$919$	−26.0000	−0.857661	−0.428830	−	0.903385i	$-0.641074\pi$
$919$	−26.0000	−0.857661	−0.428830	+	0.903385i	$0.641074\pi$
$920$	19.8564	0.654646
$921$	22.0000	0.724925
$922$	5.07180	0.167031
$923$	0	0
$924$	4.00000	0.131590
$925$	34.4974	1.13427
$926$	−8.24871	−0.271069
$927$	10.6603	0.350129
$928$	8.00000	0.262613
$929$	−5.87564	−0.192774	−0.0963868	−	0.995344i	$-0.530729\pi$
$929$	−5.87564	−0.192774	−0.0963868	+	0.995344i	$0.530729\pi$
$930$	22.3923	0.734273
$931$	−7.46410	−0.244626
$932$	13.4641	0.441031
$933$	13.3205	0.436094
$934$	−39.6410	−1.29709
$935$	−89.5692	−2.92923
$936$	0	0
$937$	−44.9282	−1.46774	−0.733870	−	0.679290i	$-0.762288\pi$
$937$	−44.9282	−1.46774	−0.733870	+	0.679290i	$0.762288\pi$
$938$	−7.19615	−0.234963
$939$	0.679492	0.0221744
$940$	1.85641	0.0605493
$941$	19.6077	0.639193	0.319596	−	0.947554i	$-0.396453\pi$
$941$	19.6077	0.639193	0.319596	+	0.947554i	$0.396453\pi$
$942$	−2.92820	−0.0954060
$943$	−39.7128	−1.29323
$944$	−6.26795	−0.204004
$945$	−3.46410	−0.112687
$946$	−17.8564	−0.580562
$947$	−30.2487	−0.982951	−0.491476	−	0.870891i	$-0.663542\pi$
$947$	−30.2487	−0.982951	−0.491476	+	0.870891i	$0.663542\pi$
$948$	−9.46410	−0.307380
$949$	0	0
$950$	−52.2487	−1.69517
$951$	−16.4641	−0.533885
$952$	−6.46410	−0.209503
$953$	30.0000	0.971795	0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000	0.971795	0.485898	+	0.874016i	$0.338493\pi$
$954$	−8.26795	−0.267685
$955$	−91.8564	−2.97240
$956$	−12.8564	−0.415806
$957$	−32.0000	−1.03441
$958$	4.39230	0.141909
$959$	13.8564	0.447447
$960$	3.46410	0.111803
$961$	10.7846	0.347891
$962$	0	0
$963$	8.53590	0.275065
$964$	15.8564	0.510700
$965$	−61.8564	−1.99123
$966$	−5.73205	−0.184426
$967$	−16.5359	−0.531759	−0.265879	−	0.964006i	$-0.585662\pi$
$967$	−16.5359	−0.531759	−0.265879	+	0.964006i	$0.585662\pi$
$968$	5.00000	0.160706
$969$	−48.2487	−1.54997
$970$	−42.9282	−1.37834
$971$	23.9282	0.767893	0.383946	−	0.923355i	$-0.374565\pi$
$971$	23.9282	0.767893	0.383946	+	0.923355i	$0.374565\pi$
$972$	1.00000	0.0320750
$973$	−2.92820	−0.0938739
$974$	−0.392305	−0.0125703
$975$	0	0
$976$	−5.19615	−0.166325
$977$	−25.8564	−0.827220	−0.413610	−	0.910454i	$-0.635732\pi$
$977$	−25.8564	−0.827220	−0.413610	+	0.910454i	$0.635732\pi$
$978$	1.33975	0.0428404
$979$	−46.9282	−1.49983
$980$	3.46410	0.110657
$981$	12.0000	0.383131
$982$	−9.85641	−0.314531
$983$	−19.0718	−0.608296	−0.304148	−	0.952625i	$-0.598372\pi$
$983$	−19.0718	−0.608296	−0.304148	+	0.952625i	$0.598372\pi$
$984$	−6.92820	−0.220863
$985$	9.03332	0.287826
$986$	51.7128	1.64687
$987$	−0.535898	−0.0170578
$988$	0	0
$989$	25.5885	0.813666
$990$	−13.8564	−0.440386
$991$	0.143594	0.00456140	0.00228070	−	0.999997i	$-0.499274\pi$
$991$	0.143594	0.00456140	0.00228070	+	0.999997i	$0.499274\pi$
$992$	6.46410	0.205235
$993$	−21.3205	−0.676586
$994$	1.92820	0.0611589
$995$	−76.6410	−2.42968
$996$	−1.73205	−0.0548821
$997$	33.9808	1.07618	0.538091	−	0.842887i	$-0.319146\pi$
$997$	33.9808	1.07618	0.538091	+	0.842887i	$0.319146\pi$
$998$	0.267949	0.00848178
$999$	4.92820	0.155921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.bz.1.2		2
13.2	odd	12		546.2.s.c.43.2	✓	4
13.7	odd	12		546.2.s.c.127.2	yes	4
13.12	even	2		7098.2.a.bn.1.1		2
39.2	even	12		1638.2.bj.e.1135.1		4
39.20	even	12		1638.2.bj.e.127.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.c.43.2	✓	4	13.2	odd	12
546.2.s.c.127.2	yes	4	13.7	odd	12
1638.2.bj.e.127.1		4	39.20	even	12
1638.2.bj.e.1135.1		4	39.2	even	12
7098.2.a.bn.1.1		2	13.12	even	2
7098.2.a.bz.1.2		2	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:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.46410 q^{10} -4.00000 q^{11} +1.00000 q^{12} -1.00000 q^{14} +3.46410 q^{15} +1.00000 q^{16} +6.46410 q^{17} +1.00000 q^{18} -7.46410 q^{19} +3.46410 q^{20} -1.00000 q^{21} -4.00000 q^{22} +5.73205 q^{23} +1.00000 q^{24} +7.00000 q^{25} +1.00000 q^{27} -1.00000 q^{28} +8.00000 q^{29} +3.46410 q^{30} +6.46410 q^{31} +1.00000 q^{32} -4.00000 q^{33} +6.46410 q^{34} -3.46410 q^{35} +1.00000 q^{36} +4.92820 q^{37} -7.46410 q^{38} +3.46410 q^{40} -6.92820 q^{41} -1.00000 q^{42} +4.46410 q^{43} -4.00000 q^{44} +3.46410 q^{45} +5.73205 q^{46} +0.535898 q^{47} +1.00000 q^{48} +1.00000 q^{49} +7.00000 q^{50} +6.46410 q^{51} -8.26795 q^{53} +1.00000 q^{54} -13.8564 q^{55} -1.00000 q^{56} -7.46410 q^{57} +8.00000 q^{58} -6.26795 q^{59} +3.46410 q^{60} -5.19615 q^{61} +6.46410 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.00000 q^{66} +7.19615 q^{67} +6.46410 q^{68} +5.73205 q^{69} -3.46410 q^{70} -1.92820 q^{71} +1.00000 q^{72} +10.9282 q^{73} +4.92820 q^{74} +7.00000 q^{75} -7.46410 q^{76} +4.00000 q^{77} -9.46410 q^{79} +3.46410 q^{80} +1.00000 q^{81} -6.92820 q^{82} -1.73205 q^{83} -1.00000 q^{84} +22.3923 q^{85} +4.46410 q^{86} +8.00000 q^{87} -4.00000 q^{88} +11.7321 q^{89} +3.46410 q^{90} +5.73205 q^{92} +6.46410 q^{93} +0.535898 q^{94} -25.8564 q^{95} +1.00000 q^{96} -12.3923 q^{97} +1.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 8 q^{11} + 2 q^{12} - 2 q^{14} + 2 q^{16} + 6 q^{17} + 2 q^{18} - 8 q^{19} - 2 q^{21} - 8 q^{22} + 8 q^{23} + 2 q^{24} + 14 q^{25} + 2 q^{27} - 2 q^{28} + 16 q^{29} + 6 q^{31} + 2 q^{32} - 8 q^{33} + 6 q^{34} + 2 q^{36} - 4 q^{37} - 8 q^{38} - 2 q^{42} + 2 q^{43} - 8 q^{44} + 8 q^{46} + 8 q^{47} + 2 q^{48} + 2 q^{49} + 14 q^{50} + 6 q^{51} - 20 q^{53} + 2 q^{54} - 2 q^{56} - 8 q^{57} + 16 q^{58} - 16 q^{59} + 6 q^{62} - 2 q^{63} + 2 q^{64} - 8 q^{66} + 4 q^{67} + 6 q^{68} + 8 q^{69} + 10 q^{71} + 2 q^{72} + 8 q^{73} - 4 q^{74} + 14 q^{75} - 8 q^{76} + 8 q^{77} - 12 q^{79} + 2 q^{81} - 2 q^{84} + 24 q^{85} + 2 q^{86} + 16 q^{87} - 8 q^{88} + 20 q^{89} + 8 q^{92} + 6 q^{93} + 8 q^{94} - 24 q^{95} + 2 q^{96} - 4 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 8 * q^11 + 2 * q^12 - 2 * q^14 + 2 * q^16 + 6 * q^17 + 2 * q^18 - 8 * q^19 - 2 * q^21 - 8 * q^22 + 8 * q^23 + 2 * q^24 + 14 * q^25 + 2 * q^27 - 2 * q^28 + 16 * q^29 + 6 * q^31 + 2 * q^32 - 8 * q^33 + 6 * q^34 + 2 * q^36 - 4 * q^37 - 8 * q^38 - 2 * q^42 + 2 * q^43 - 8 * q^44 + 8 * q^46 + 8 * q^47 + 2 * q^48 + 2 * q^49 + 14 * q^50 + 6 * q^51 - 20 * q^53 + 2 * q^54 - 2 * q^56 - 8 * q^57 + 16 * q^58 - 16 * q^59 + 6 * q^62 - 2 * q^63 + 2 * q^64 - 8 * q^66 + 4 * q^67 + 6 * q^68 + 8 * q^69 + 10 * q^71 + 2 * q^72 + 8 * q^73 - 4 * q^74 + 14 * q^75 - 8 * q^76 + 8 * q^77 - 12 * q^79 + 2 * q^81 - 2 * q^84 + 24 * q^85 + 2 * q^86 + 16 * q^87 - 8 * q^88 + 20 * q^89 + 8 * q^92 + 6 * q^93 + 8 * q^94 - 24 * q^95 + 2 * q^96 - 4 * q^97 + 2 * q^98 - 8 * q^99

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