LMFDB - Embedded newform 7098.2.a.bz.1.1

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			1.1
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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.46410 q^{10} -4.00000 q^{11} +1.00000 q^{12} -1.00000 q^{14} -3.46410 q^{15} +1.00000 q^{16} -0.464102 q^{17} +1.00000 q^{18} -0.535898 q^{19} -3.46410 q^{20} -1.00000 q^{21} -4.00000 q^{22} +2.26795 q^{23} +1.00000 q^{24} +7.00000 q^{25} +1.00000 q^{27} -1.00000 q^{28} +8.00000 q^{29} -3.46410 q^{30} -0.464102 q^{31} +1.00000 q^{32} -4.00000 q^{33} -0.464102 q^{34} +3.46410 q^{35} +1.00000 q^{36} -8.92820 q^{37} -0.535898 q^{38} -3.46410 q^{40} +6.92820 q^{41} -1.00000 q^{42} -2.46410 q^{43} -4.00000 q^{44} -3.46410 q^{45} +2.26795 q^{46} +7.46410 q^{47} +1.00000 q^{48} +1.00000 q^{49} +7.00000 q^{50} -0.464102 q^{51} -11.7321 q^{53} +1.00000 q^{54} +13.8564 q^{55} -1.00000 q^{56} -0.535898 q^{57} +8.00000 q^{58} -9.73205 q^{59} -3.46410 q^{60} +5.19615 q^{61} -0.464102 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.00000 q^{66} -3.19615 q^{67} -0.464102 q^{68} +2.26795 q^{69} +3.46410 q^{70} +11.9282 q^{71} +1.00000 q^{72} -2.92820 q^{73} -8.92820 q^{74} +7.00000 q^{75} -0.535898 q^{76} +4.00000 q^{77} -2.53590 q^{79} -3.46410 q^{80} +1.00000 q^{81} +6.92820 q^{82} +1.73205 q^{83} -1.00000 q^{84} +1.60770 q^{85} -2.46410 q^{86} +8.00000 q^{87} -4.00000 q^{88} +8.26795 q^{89} -3.46410 q^{90} +2.26795 q^{92} -0.464102 q^{93} +7.46410 q^{94} +1.85641 q^{95} +1.00000 q^{96} +8.39230 q^{97} +1.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.782047\pi$
$5$	−3.46410	−1.54919	−0.774597	+	0.632456i	$0.782047\pi$
$6$	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
$17$	−0.464102	−0.112561	−0.0562806	−	0.998415i	$-0.517924\pi$
$17$	−0.464102	−0.112561	−0.0562806	+	0.998415i	$0.517924\pi$
$18$	1.00000	0.235702
$19$	−0.535898	−0.122944	−0.0614718	−	0.998109i	$-0.519579\pi$
$19$	−0.535898	−0.122944	−0.0614718	+	0.998109i	$0.519579\pi$
$20$	−3.46410	−0.774597
$21$	−1.00000	−0.218218
$22$	−4.00000	−0.852803
$23$	2.26795	0.472900	0.236450	−	0.971644i	$-0.424016\pi$
$23$	2.26795	0.472900	0.236450	+	0.971644i	$0.424016\pi$
$24$	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
$31$	−0.464102	−0.0833551	−0.0416776	−	0.999131i	$-0.513270\pi$
$31$	−0.464102	−0.0833551	−0.0416776	+	0.999131i	$0.513270\pi$
$32$	1.00000	0.176777
$33$	−4.00000	−0.696311
$34$	−0.464102	−0.0795928
$35$	3.46410	0.585540
$36$	1.00000	0.166667
$37$	−8.92820	−1.46779	−0.733894	−	0.679264i	$-0.762299\pi$
$37$	−8.92820	−1.46779	−0.733894	+	0.679264i	$0.762299\pi$
$38$	−0.535898	−0.0869342
$39$	0	0
$40$	−3.46410	−0.547723
$41$	6.92820	1.08200	0.541002	−	0.841021i	$-0.318045\pi$
$41$	6.92820	1.08200	0.541002	+	0.841021i	$0.318045\pi$
$42$	−1.00000	−0.154303
$43$	−2.46410	−0.375772	−0.187886	−	0.982191i	$-0.560164\pi$
$43$	−2.46410	−0.375772	−0.187886	+	0.982191i	$0.560164\pi$
$44$	−4.00000	−0.603023
$45$	−3.46410	−0.516398
$46$	2.26795	0.334391
$47$	7.46410	1.08875	0.544376	−	0.838842i	$-0.316767\pi$
$47$	7.46410	1.08875	0.544376	+	0.838842i	$0.316767\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	7.00000	0.989949
$51$	−0.464102	−0.0649872
$52$	0	0
$53$	−11.7321	−1.61152	−0.805761	−	0.592241i	$-0.798243\pi$
$53$	−11.7321	−1.61152	−0.805761	+	0.592241i	$0.798243\pi$
$54$	1.00000	0.136083
$55$	13.8564	1.86840
$56$	−1.00000	−0.133631
$57$	−0.535898	−0.0709815
$58$	8.00000	1.05045
$59$	−9.73205	−1.26701	−0.633503	−	0.773741i	$-0.718383\pi$
$59$	−9.73205	−1.26701	−0.633503	+	0.773741i	$0.718383\pi$
$60$	−3.46410	−0.447214
$61$	5.19615	0.665299	0.332650	−	0.943051i	$-0.392057\pi$
$61$	5.19615	0.665299	0.332650	+	0.943051i	$0.392057\pi$
$62$	−0.464102	−0.0589410
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−4.00000	−0.492366
$67$	−3.19615	−0.390472	−0.195236	−	0.980756i	$-0.562547\pi$
$67$	−3.19615	−0.390472	−0.195236	+	0.980756i	$0.562547\pi$
$68$	−0.464102	−0.0562806
$69$	2.26795	0.273029
$70$	3.46410	0.414039
$71$	11.9282	1.41562	0.707809	−	0.706404i	$-0.249684\pi$
$71$	11.9282	1.41562	0.707809	+	0.706404i	$0.249684\pi$
$72$	1.00000	0.117851
$73$	−2.92820	−0.342720	−0.171360	−	0.985208i	$-0.554816\pi$
$73$	−2.92820	−0.342720	−0.171360	+	0.985208i	$0.554816\pi$
$74$	−8.92820	−1.03788
$75$	7.00000	0.808290
$76$	−0.535898	−0.0614718
$77$	4.00000	0.455842
$78$	0	0
$79$	−2.53590	−0.285311	−0.142655	−	0.989772i	$-0.545564\pi$
$79$	−2.53590	−0.285311	−0.142655	+	0.989772i	$0.545564\pi$
$80$	−3.46410	−0.387298
$81$	1.00000	0.111111
$82$	6.92820	0.765092
$83$	1.73205	0.190117	0.0950586	−	0.995472i	$-0.469696\pi$
$83$	1.73205	0.190117	0.0950586	+	0.995472i	$0.469696\pi$
$84$	−1.00000	−0.109109
$85$	1.60770	0.174379
$86$	−2.46410	−0.265711
$87$	8.00000	0.857690
$88$	−4.00000	−0.426401
$89$	8.26795	0.876401	0.438200	−	0.898877i	$-0.355616\pi$
$89$	8.26795	0.876401	0.438200	+	0.898877i	$0.355616\pi$
$90$	−3.46410	−0.365148
$91$	0	0
$92$	2.26795	0.236450
$93$	−0.464102	−0.0481251
$94$	7.46410	0.769863
$95$	1.85641	0.190463
$96$	1.00000	0.102062
$97$	8.39230	0.852109	0.426055	−	0.904697i	$-0.359903\pi$
$97$	8.39230	0.852109	0.426055	+	0.904697i	$0.359903\pi$
$98$	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	$0.5\pi$
$102$	−0.464102	−0.0459529
$103$	−6.66025	−0.656254	−0.328127	−	0.944634i	$-0.606417\pi$
$103$	−6.66025	−0.656254	−0.328127	+	0.944634i	$0.606417\pi$
$104$	0	0
$105$	3.46410	0.338062
$106$	−11.7321	−1.13952
$107$	15.4641	1.49497	0.747486	−	0.664278i	$-0.231261\pi$
$107$	15.4641	1.49497	0.747486	+	0.664278i	$0.231261\pi$
$108$	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
$111$	−8.92820	−0.847428
$112$	−1.00000	−0.0944911
$113$	16.3923	1.54206	0.771029	−	0.636800i	$-0.219742\pi$
$113$	16.3923	1.54206	0.771029	+	0.636800i	$0.219742\pi$
$114$	−0.535898	−0.0501915
$115$	−7.85641	−0.732614
$116$	8.00000	0.742781
$117$	0	0
$118$	−9.73205	−0.895908
$119$	0.464102	0.0425441
$120$	−3.46410	−0.316228
$121$	5.00000	0.454545
$122$	5.19615	0.470438
$123$	6.92820	0.624695
$124$	−0.464102	−0.0416776
$125$	−6.92820	−0.619677
$126$	−1.00000	−0.0890871
$127$	18.9282	1.67961	0.839803	−	0.542891i	$-0.182670\pi$
$127$	18.9282	1.67961	0.839803	+	0.542891i	$0.182670\pi$
$128$	1.00000	0.0883883
$129$	−2.46410	−0.216952
$130$	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
$133$	0.535898	0.0464683
$134$	−3.19615	−0.276106
$135$	−3.46410	−0.298142
$136$	−0.464102	−0.0397964
$137$	13.8564	1.18383	0.591916	−	0.805999i	$-0.298372\pi$
$137$	13.8564	1.18383	0.591916	+	0.805999i	$0.298372\pi$
$138$	2.26795	0.193061
$139$	−10.9282	−0.926918	−0.463459	−	0.886118i	$-0.653392\pi$
$139$	−10.9282	−0.926918	−0.463459	+	0.886118i	$0.653392\pi$
$140$	3.46410	0.292770
$141$	7.46410	0.628591
$142$	11.9282	1.00099
$143$	0	0
$144$	1.00000	0.0833333
$145$	−27.7128	−2.30142
$146$	−2.92820	−0.242340
$147$	1.00000	0.0824786
$148$	−8.92820	−0.733894
$149$	18.4641	1.51264	0.756319	−	0.654203i	$-0.226996\pi$
$149$	18.4641	1.51264	0.756319	+	0.654203i	$0.226996\pi$
$150$	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	$0.337627\pi$
$152$	−0.535898	−0.0434671
$153$	−0.464102	−0.0375204
$154$	4.00000	0.322329
$155$	1.60770	0.129133
$156$	0	0
$157$	10.9282	0.872166	0.436083	−	0.899907i	$-0.356365\pi$
$157$	10.9282	0.872166	0.436083	+	0.899907i	$0.356365\pi$
$158$	−2.53590	−0.201745
$159$	−11.7321	−0.930412
$160$	−3.46410	−0.273861
$161$	−2.26795	−0.178739
$162$	1.00000	0.0785674
$163$	18.6603	1.46158	0.730792	−	0.682600i	$-0.239151\pi$
$163$	18.6603	1.46158	0.730792	+	0.682600i	$0.239151\pi$
$164$	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
$170$	1.60770	0.123305
$171$	−0.535898	−0.0409812
$172$	−2.46410	−0.187886
$173$	14.9282	1.13497	0.567485	−	0.823384i	$-0.307916\pi$
$173$	14.9282	1.13497	0.567485	+	0.823384i	$0.307916\pi$
$174$	8.00000	0.606478
$175$	−7.00000	−0.529150
$176$	−4.00000	−0.301511
$177$	−9.73205	−0.731506
$178$	8.26795	0.619709
$179$	−3.07180	−0.229597	−0.114798	−	0.993389i	$-0.536622\pi$
$179$	−3.07180	−0.229597	−0.114798	+	0.993389i	$0.536622\pi$
$180$	−3.46410	−0.258199
$181$	−16.7846	−1.24759	−0.623795	−	0.781588i	$-0.714410\pi$
$181$	−16.7846	−1.24759	−0.623795	+	0.781588i	$0.714410\pi$
$182$	0	0
$183$	5.19615	0.384111
$184$	2.26795	0.167195
$185$	30.9282	2.27389
$186$	−0.464102	−0.0340296
$187$	1.85641	0.135754
$188$	7.46410	0.544376
$189$	−1.00000	−0.0727393
$190$	1.85641	0.134678
$191$	18.5167	1.33982	0.669909	−	0.742443i	$-0.266333\pi$
$191$	18.5167	1.33982	0.669909	+	0.742443i	$0.266333\pi$
$192$	1.00000	0.0721688
$193$	9.85641	0.709480	0.354740	−	0.934965i	$-0.384569\pi$
$193$	9.85641	0.709480	0.354740	+	0.934965i	$0.384569\pi$
$194$	8.39230	0.602532
$195$	0	0
$196$	1.00000	0.0714286
$197$	23.3923	1.66663	0.833316	−	0.552796i	$-0.186439\pi$
$197$	23.3923	1.66663	0.833316	+	0.552796i	$0.186439\pi$
$198$	−4.00000	−0.284268
$199$	2.12436	0.150592	0.0752958	−	0.997161i	$-0.476010\pi$
$199$	2.12436	0.150592	0.0752958	+	0.997161i	$0.476010\pi$
$200$	7.00000	0.494975
$201$	−3.19615	−0.225439
$202$	0	0
$203$	−8.00000	−0.561490
$204$	−0.464102	−0.0324936
$205$	−24.0000	−1.67623
$206$	−6.66025	−0.464042
$207$	2.26795	0.157633
$208$	0	0
$209$	2.14359	0.148275
$210$	3.46410	0.239046
$211$	−22.9282	−1.57844	−0.789221	−	0.614109i	$-0.789516\pi$
$211$	−22.9282	−1.57844	−0.789221	+	0.614109i	$0.789516\pi$
$212$	−11.7321	−0.805761
$213$	11.9282	0.817307
$214$	15.4641	1.05710
$215$	8.53590	0.582143
$216$	1.00000	0.0680414
$217$	0.464102	0.0315053
$218$	12.0000	0.812743
$219$	−2.92820	−0.197870
$220$	13.8564	0.934199
$221$	0	0
$222$	−8.92820	−0.599222
$223$	−14.4641	−0.968588	−0.484294	−	0.874905i	$-0.660923\pi$
$223$	−14.4641	−0.968588	−0.484294	+	0.874905i	$0.660923\pi$
$224$	−1.00000	−0.0668153
$225$	7.00000	0.466667
$226$	16.3923	1.09040
$227$	−21.3205	−1.41509	−0.707546	−	0.706667i	$-0.750198\pi$
$227$	−21.3205	−1.41509	−0.707546	+	0.706667i	$0.750198\pi$
$228$	−0.535898	−0.0354907
$229$	−6.07180	−0.401236	−0.200618	−	0.979670i	$-0.564295\pi$
$229$	−6.07180	−0.401236	−0.200618	+	0.979670i	$0.564295\pi$
$230$	−7.85641	−0.518036
$231$	4.00000	0.263181
$232$	8.00000	0.525226
$233$	6.53590	0.428181	0.214090	−	0.976814i	$-0.431321\pi$
$233$	6.53590	0.428181	0.214090	+	0.976814i	$0.431321\pi$
$234$	0	0
$235$	−25.8564	−1.68669
$236$	−9.73205	−0.633503
$237$	−2.53590	−0.164724
$238$	0.464102	0.0300832
$239$	14.8564	0.960981	0.480491	−	0.877000i	$-0.340459\pi$
$239$	14.8564	0.960981	0.480491	+	0.877000i	$0.340459\pi$
$240$	−3.46410	−0.223607
$241$	−11.8564	−0.763738	−0.381869	−	0.924216i	$-0.624719\pi$
$241$	−11.8564	−0.763738	−0.381869	+	0.924216i	$0.624719\pi$
$242$	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
$248$	−0.464102	−0.0294705
$249$	1.73205	0.109764
$250$	−6.92820	−0.438178
$251$	−23.9282	−1.51033	−0.755167	−	0.655532i	$-0.772444\pi$
$251$	−23.9282	−1.51033	−0.755167	+	0.655532i	$0.772444\pi$
$252$	−1.00000	−0.0629941
$253$	−9.07180	−0.570339
$254$	18.9282	1.18766
$255$	1.60770	0.100678
$256$	1.00000	0.0625000
$257$	−6.46410	−0.403220	−0.201610	−	0.979466i	$-0.564617\pi$
$257$	−6.46410	−0.403220	−0.201610	+	0.979466i	$0.564617\pi$
$258$	−2.46410	−0.153408
$259$	8.92820	0.554772
$260$	0	0
$261$	8.00000	0.495188
$262$	19.0000	1.17382
$263$	17.3205	1.06803	0.534014	−	0.845476i	$-0.320683\pi$
$263$	17.3205	1.06803	0.534014	+	0.845476i	$0.320683\pi$
$264$	−4.00000	−0.246183
$265$	40.6410	2.49656
$266$	0.535898	0.0328580
$267$	8.26795	0.505990
$268$	−3.19615	−0.195236
$269$	1.60770	0.0980229	0.0490115	−	0.998798i	$-0.484393\pi$
$269$	1.60770	0.0980229	0.0490115	+	0.998798i	$0.484393\pi$
$270$	−3.46410	−0.210819
$271$	−5.53590	−0.336282	−0.168141	−	0.985763i	$-0.553776\pi$
$271$	−5.53590	−0.336282	−0.168141	+	0.985763i	$0.553776\pi$
$272$	−0.464102	−0.0281403
$273$	0	0
$274$	13.8564	0.837096
$275$	−28.0000	−1.68846
$276$	2.26795	0.136514
$277$	−27.3205	−1.64153	−0.820765	−	0.571266i	$-0.806453\pi$
$277$	−27.3205	−1.64153	−0.820765	+	0.571266i	$0.806453\pi$
$278$	−10.9282	−0.655430
$279$	−0.464102	−0.0277850
$280$	3.46410	0.207020
$281$	−18.3923	−1.09719	−0.548596	−	0.836087i	$-0.684838\pi$
$281$	−18.3923	−1.09719	−0.548596	+	0.836087i	$0.684838\pi$
$282$	7.46410	0.444481
$283$	−4.53590	−0.269631	−0.134816	−	0.990871i	$-0.543044\pi$
$283$	−4.53590	−0.269631	−0.134816	+	0.990871i	$0.543044\pi$
$284$	11.9282	0.707809
$285$	1.85641	0.109964
$286$	0	0
$287$	−6.92820	−0.408959
$288$	1.00000	0.0589256
$289$	−16.7846	−0.987330
$290$	−27.7128	−1.62735
$291$	8.39230	0.491966
$292$	−2.92820	−0.171360
$293$	−26.5359	−1.55024	−0.775122	−	0.631812i	$-0.782312\pi$
$293$	−26.5359	−1.55024	−0.775122	+	0.631812i	$0.782312\pi$
$294$	1.00000	0.0583212
$295$	33.7128	1.96284
$296$	−8.92820	−0.518941
$297$	−4.00000	−0.232104
$298$	18.4641	1.06960
$299$	0	0
$300$	7.00000	0.404145
$301$	2.46410	0.142028
$302$	12.0000	0.690522
$303$	0	0
$304$	−0.535898	−0.0307359
$305$	−18.0000	−1.03068
$306$	−0.464102	−0.0265309
$307$	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
$309$	−6.66025	−0.378889
$310$	1.60770	0.0913109
$311$	−21.3205	−1.20898	−0.604488	−	0.796615i	$-0.706622\pi$
$311$	−21.3205	−1.20898	−0.604488	+	0.796615i	$0.706622\pi$
$312$	0	0
$313$	35.3205	1.99643	0.998217	−	0.0596964i	$-0.0190133\pi$
$313$	35.3205	1.99643	0.998217	+	0.0596964i	$0.0190133\pi$
$314$	10.9282	0.616714
$315$	3.46410	0.195180
$316$	−2.53590	−0.142655
$317$	−9.53590	−0.535589	−0.267795	−	0.963476i	$-0.586295\pi$
$317$	−9.53590	−0.535589	−0.267795	+	0.963476i	$0.586295\pi$
$318$	−11.7321	−0.657901
$319$	−32.0000	−1.79166
$320$	−3.46410	−0.193649
$321$	15.4641	0.863122
$322$	−2.26795	−0.126388
$323$	0.248711	0.0138387
$324$	1.00000	0.0555556
$325$	0	0
$326$	18.6603	1.03350
$327$	12.0000	0.663602
$328$	6.92820	0.382546
$329$	−7.46410	−0.411509
$330$	13.8564	0.762770
$331$	13.3205	0.732161	0.366081	−	0.930583i	$-0.380699\pi$
$331$	13.3205	0.732161	0.366081	+	0.930583i	$0.380699\pi$
$332$	1.73205	0.0950586
$333$	−8.92820	−0.489263
$334$	−20.0000	−1.09435
$335$	11.0718	0.604917
$336$	−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
$339$	16.3923	0.890308
$340$	1.60770	0.0871895
$341$	1.85641	0.100530
$342$	−0.535898	−0.0289781
$343$	−1.00000	−0.0539949
$344$	−2.46410	−0.132855
$345$	−7.85641	−0.422975
$346$	14.9282	0.802545
$347$	−29.7128	−1.59507	−0.797534	−	0.603274i	$-0.793862\pi$
$347$	−29.7128	−1.59507	−0.797534	+	0.603274i	$0.793862\pi$
$348$	8.00000	0.428845
$349$	−33.6410	−1.80076	−0.900381	−	0.435102i	$-0.856712\pi$
$349$	−33.6410	−1.80076	−0.900381	+	0.435102i	$0.856712\pi$
$350$	−7.00000	−0.374166
$351$	0	0
$352$	−4.00000	−0.213201
$353$	26.6603	1.41898	0.709491	−	0.704714i	$-0.248925\pi$
$353$	26.6603	1.41898	0.709491	+	0.704714i	$0.248925\pi$
$354$	−9.73205	−0.517253
$355$	−41.3205	−2.19306
$356$	8.26795	0.438200
$357$	0.464102	0.0245629
$358$	−3.07180	−0.162350
$359$	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
$361$	−18.7128	−0.984885
$362$	−16.7846	−0.882179
$363$	5.00000	0.262432
$364$	0	0
$365$	10.1436	0.530940
$366$	5.19615	0.271607
$367$	5.05256	0.263741	0.131871	−	0.991267i	$-0.457902\pi$
$367$	5.05256	0.263741	0.131871	+	0.991267i	$0.457902\pi$
$368$	2.26795	0.118225
$369$	6.92820	0.360668
$370$	30.9282	1.60788
$371$	11.7321	0.609098
$372$	−0.464102	−0.0240625
$373$	22.2487	1.15199	0.575997	−	0.817452i	$-0.304614\pi$
$373$	22.2487	1.15199	0.575997	+	0.817452i	$0.304614\pi$
$374$	1.85641	0.0959925
$375$	−6.92820	−0.357771
$376$	7.46410	0.384932
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	−30.3923	−1.56115	−0.780574	−	0.625063i	$-0.785073\pi$
$379$	−30.3923	−1.56115	−0.780574	+	0.625063i	$0.785073\pi$
$380$	1.85641	0.0952316
$381$	18.9282	0.969721
$382$	18.5167	0.947395
$383$	27.3205	1.39601	0.698006	−	0.716092i	$-0.254071\pi$
$383$	27.3205	1.39601	0.698006	+	0.716092i	$0.254071\pi$
$384$	1.00000	0.0510310
$385$	−13.8564	−0.706188
$386$	9.85641	0.501678
$387$	−2.46410	−0.125257
$388$	8.39230	0.426055
$389$	2.66025	0.134880	0.0674401	−	0.997723i	$-0.478517\pi$
$389$	2.66025	0.134880	0.0674401	+	0.997723i	$0.478517\pi$
$390$	0	0
$391$	−1.05256	−0.0532302
$392$	1.00000	0.0505076
$393$	19.0000	0.958423
$394$	23.3923	1.17849
$395$	8.78461	0.442002
$396$	−4.00000	−0.201008
$397$	11.7846	0.591453	0.295726	−	0.955273i	$-0.404438\pi$
$397$	11.7846	0.591453	0.295726	+	0.955273i	$0.404438\pi$
$398$	2.12436	0.106484
$399$	0.535898	0.0268285
$400$	7.00000	0.350000
$401$	−4.39230	−0.219341	−0.109671	−	0.993968i	$-0.534980\pi$
$401$	−4.39230	−0.219341	−0.109671	+	0.993968i	$0.534980\pi$
$402$	−3.19615	−0.159410
$403$	0	0
$404$	0	0
$405$	−3.46410	−0.172133
$406$	−8.00000	−0.397033
$407$	35.7128	1.77022
$408$	−0.464102	−0.0229765
$409$	14.3923	0.711654	0.355827	−	0.934552i	$-0.384199\pi$
$409$	14.3923	0.711654	0.355827	+	0.934552i	$0.384199\pi$
$410$	−24.0000	−1.18528
$411$	13.8564	0.683486
$412$	−6.66025	−0.328127
$413$	9.73205	0.478883
$414$	2.26795	0.111464
$415$	−6.00000	−0.294528
$416$	0	0
$417$	−10.9282	−0.535156
$418$	2.14359	0.104847
$419$	−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
$421$	22.3923	1.09133	0.545667	−	0.838002i	$-0.316276\pi$
$421$	22.3923	1.09133	0.545667	+	0.838002i	$0.316276\pi$
$422$	−22.9282	−1.11613
$423$	7.46410	0.362917
$424$	−11.7321	−0.569759
$425$	−3.24871	−0.157586
$426$	11.9282	0.577923
$427$	−5.19615	−0.251459
$428$	15.4641	0.747486
$429$	0	0
$430$	8.53590	0.411638
$431$	−22.8564	−1.10095	−0.550477	−	0.834850i	$-0.685554\pi$
$431$	−22.8564	−1.10095	−0.550477	+	0.834850i	$0.685554\pi$
$432$	1.00000	0.0481125
$433$	−17.8564	−0.858124	−0.429062	−	0.903275i	$-0.641156\pi$
$433$	−17.8564	−0.858124	−0.429062	+	0.903275i	$0.641156\pi$
$434$	0.464102	0.0222776
$435$	−27.7128	−1.32873
$436$	12.0000	0.574696
$437$	−1.21539	−0.0581400
$438$	−2.92820	−0.139915
$439$	−34.3923	−1.64146	−0.820728	−	0.571320i	$-0.806432\pi$
$439$	−34.3923	−1.64146	−0.820728	+	0.571320i	$0.806432\pi$
$440$	13.8564	0.660578
$441$	1.00000	0.0476190
$442$	0	0
$443$	−1.60770	−0.0763839	−0.0381920	−	0.999270i	$-0.512160\pi$
$443$	−1.60770	−0.0763839	−0.0381920	+	0.999270i	$0.512160\pi$
$444$	−8.92820	−0.423714
$445$	−28.6410	−1.35771
$446$	−14.4641	−0.684895
$447$	18.4641	0.873322
$448$	−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
$452$	16.3923	0.771029
$453$	12.0000	0.563809
$454$	−21.3205	−1.00062
$455$	0	0
$456$	−0.535898	−0.0250957
$457$	−9.19615	−0.430178	−0.215089	−	0.976594i	$-0.569004\pi$
$457$	−9.19615	−0.430178	−0.215089	+	0.976594i	$0.569004\pi$
$458$	−6.07180	−0.283716
$459$	−0.464102	−0.0216624
$460$	−7.85641	−0.366307
$461$	18.9282	0.881574	0.440787	−	0.897612i	$-0.354699\pi$
$461$	18.9282	0.881574	0.440787	+	0.897612i	$0.354699\pi$
$462$	4.00000	0.186097
$463$	40.2487	1.87052	0.935258	−	0.353966i	$-0.115167\pi$
$463$	40.2487	1.87052	0.935258	+	0.353966i	$0.115167\pi$
$464$	8.00000	0.371391
$465$	1.60770	0.0745551
$466$	6.53590	0.302770
$467$	29.6410	1.37162	0.685811	−	0.727779i	$-0.259448\pi$
$467$	29.6410	1.37162	0.685811	+	0.727779i	$0.259448\pi$
$468$	0	0
$469$	3.19615	0.147585
$470$	−25.8564	−1.19267
$471$	10.9282	0.503545
$472$	−9.73205	−0.447954
$473$	9.85641	0.453198
$474$	−2.53590	−0.116478
$475$	−3.75129	−0.172121
$476$	0.464102	0.0212721
$477$	−11.7321	−0.537174
$478$	14.8564	0.679516
$479$	−16.3923	−0.748984	−0.374492	−	0.927230i	$-0.622183\pi$
$479$	−16.3923	−0.748984	−0.374492	+	0.927230i	$0.622183\pi$
$480$	−3.46410	−0.158114
$481$	0	0
$482$	−11.8564	−0.540045
$483$	−2.26795	−0.103195
$484$	5.00000	0.227273
$485$	−29.0718	−1.32008
$486$	1.00000	0.0453609
$487$	20.3923	0.924064	0.462032	−	0.886863i	$-0.347121\pi$
$487$	20.3923	0.924064	0.462032	+	0.886863i	$0.347121\pi$
$488$	5.19615	0.235219
$489$	18.6603	0.843846
$490$	−3.46410	−0.156492
$491$	17.8564	0.805848	0.402924	−	0.915233i	$-0.367994\pi$
$491$	17.8564	0.805848	0.402924	+	0.915233i	$0.367994\pi$
$492$	6.92820	0.312348
$493$	−3.71281	−0.167217
$494$	0	0
$495$	13.8564	0.622799
$496$	−0.464102	−0.0208388
$497$	−11.9282	−0.535053
$498$	1.73205	0.0776151
$499$	3.73205	0.167070	0.0835348	−	0.996505i	$-0.473379\pi$
$499$	3.73205	0.167070	0.0835348	+	0.996505i	$0.473379\pi$
$500$	−6.92820	−0.309839
$501$	−20.0000	−0.893534
$502$	−23.9282	−1.06797
$503$	6.92820	0.308913	0.154457	−	0.988000i	$-0.450637\pi$
$503$	6.92820	0.308913	0.154457	+	0.988000i	$0.450637\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	−9.07180	−0.403291
$507$	0	0
$508$	18.9282	0.839803
$509$	14.2487	0.631563	0.315782	−	0.948832i	$-0.397733\pi$
$509$	14.2487	0.631563	0.315782	+	0.948832i	$0.397733\pi$
$510$	1.60770	0.0711899
$511$	2.92820	0.129536
$512$	1.00000	0.0441942
$513$	−0.535898	−0.0236605
$514$	−6.46410	−0.285119
$515$	23.0718	1.01666
$516$	−2.46410	−0.108476
$517$	−29.8564	−1.31308
$518$	8.92820	0.392283
$519$	14.9282	0.655275
$520$	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
$523$	1.07180	0.0468664	0.0234332	−	0.999725i	$-0.492540\pi$
$523$	1.07180	0.0468664	0.0234332	+	0.999725i	$0.492540\pi$
$524$	19.0000	0.830019
$525$	−7.00000	−0.305505
$526$	17.3205	0.755210
$527$	0.215390	0.00938255
$528$	−4.00000	−0.174078
$529$	−17.8564	−0.776365
$530$	40.6410	1.76533
$531$	−9.73205	−0.422335
$532$	0.535898	0.0232341
$533$	0	0
$534$	8.26795	0.357789
$535$	−53.5692	−2.31600
$536$	−3.19615	−0.138053
$537$	−3.07180	−0.132558
$538$	1.60770	0.0693127
$539$	−4.00000	−0.172292
$540$	−3.46410	−0.149071
$541$	−17.3205	−0.744667	−0.372333	−	0.928099i	$-0.621442\pi$
$541$	−17.3205	−0.744667	−0.372333	+	0.928099i	$0.621442\pi$
$542$	−5.53590	−0.237787
$543$	−16.7846	−0.720297
$544$	−0.464102	−0.0198982
$545$	−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
$551$	−4.28719	−0.182640
$552$	2.26795	0.0965303
$553$	2.53590	0.107837
$554$	−27.3205	−1.16074
$555$	30.9282	1.31283
$556$	−10.9282	−0.463459
$557$	−45.3923	−1.92333	−0.961667	−	0.274221i	$-0.911580\pi$
$557$	−45.3923	−1.92333	−0.961667	+	0.274221i	$0.911580\pi$
$558$	−0.464102	−0.0196470
$559$	0	0
$560$	3.46410	0.146385
$561$	1.85641	0.0783775
$562$	−18.3923	−0.775833
$563$	13.8564	0.583978	0.291989	−	0.956422i	$-0.405683\pi$
$563$	13.8564	0.583978	0.291989	+	0.956422i	$0.405683\pi$
$564$	7.46410	0.314295
$565$	−56.7846	−2.38895
$566$	−4.53590	−0.190658
$567$	−1.00000	−0.0419961
$568$	11.9282	0.500496
$569$	8.53590	0.357843	0.178922	−	0.983863i	$-0.442739\pi$
$569$	8.53590	0.357843	0.178922	+	0.983863i	$0.442739\pi$
$570$	1.85641	0.0777563
$571$	17.3923	0.727845	0.363923	−	0.931429i	$-0.381437\pi$
$571$	17.3923	0.727845	0.363923	+	0.931429i	$0.381437\pi$
$572$	0	0
$573$	18.5167	0.773545
$574$	−6.92820	−0.289178
$575$	15.8756	0.662060
$576$	1.00000	0.0416667
$577$	−42.7846	−1.78115	−0.890573	−	0.454840i	$-0.849697\pi$
$577$	−42.7846	−1.78115	−0.890573	+	0.454840i	$0.849697\pi$
$578$	−16.7846	−0.698148
$579$	9.85641	0.409618
$580$	−27.7128	−1.15071
$581$	−1.73205	−0.0718576
$582$	8.39230	0.347872
$583$	46.9282	1.94357
$584$	−2.92820	−0.121170
$585$	0	0
$586$	−26.5359	−1.09619
$587$	−16.1244	−0.665523	−0.332762	−	0.943011i	$-0.607980\pi$
$587$	−16.1244	−0.665523	−0.332762	+	0.943011i	$0.607980\pi$
$588$	1.00000	0.0412393
$589$	0.248711	0.0102480
$590$	33.7128	1.38793
$591$	23.3923	0.962231
$592$	−8.92820	−0.366947
$593$	−7.73205	−0.317517	−0.158759	−	0.987317i	$-0.550749\pi$
$593$	−7.73205	−0.317517	−0.158759	+	0.987317i	$0.550749\pi$
$594$	−4.00000	−0.164122
$595$	−1.60770	−0.0659091
$596$	18.4641	0.756319
$597$	2.12436	0.0869441
$598$	0	0
$599$	19.0526	0.778466	0.389233	−	0.921139i	$-0.372740\pi$
$599$	19.0526	0.778466	0.389233	+	0.921139i	$0.372740\pi$
$600$	7.00000	0.285774
$601$	24.2487	0.989126	0.494563	−	0.869142i	$-0.335328\pi$
$601$	24.2487	0.989126	0.494563	+	0.869142i	$0.335328\pi$
$602$	2.46410	0.100429
$603$	−3.19615	−0.130157
$604$	12.0000	0.488273
$605$	−17.3205	−0.704179
$606$	0	0
$607$	−4.80385	−0.194982	−0.0974911	−	0.995236i	$-0.531082\pi$
$607$	−4.80385	−0.194982	−0.0974911	+	0.995236i	$0.531082\pi$
$608$	−0.535898	−0.0217335
$609$	−8.00000	−0.324176
$610$	−18.0000	−0.728799
$611$	0	0
$612$	−0.464102	−0.0187602
$613$	13.6077	0.549610	0.274805	−	0.961500i	$-0.411387\pi$
$613$	13.6077	0.549610	0.274805	+	0.961500i	$0.411387\pi$
$614$	22.0000	0.887848
$615$	−24.0000	−0.967773
$616$	4.00000	0.161165
$617$	−21.8564	−0.879906	−0.439953	−	0.898021i	$-0.645005\pi$
$617$	−21.8564	−0.879906	−0.439953	+	0.898021i	$0.645005\pi$
$618$	−6.66025	−0.267915
$619$	10.7846	0.433470	0.216735	−	0.976230i	$-0.430459\pi$
$619$	10.7846	0.433470	0.216735	+	0.976230i	$0.430459\pi$
$620$	1.60770	0.0645666
$621$	2.26795	0.0910097
$622$	−21.3205	−0.854874
$623$	−8.26795	−0.331248
$624$	0	0
$625$	−11.0000	−0.440000
$626$	35.3205	1.41169
$627$	2.14359	0.0856069
$628$	10.9282	0.436083
$629$	4.14359	0.165216
$630$	3.46410	0.138013
$631$	21.0718	0.838855	0.419427	−	0.907789i	$-0.362231\pi$
$631$	21.0718	0.838855	0.419427	+	0.907789i	$0.362231\pi$
$632$	−2.53590	−0.100873
$633$	−22.9282	−0.911314
$634$	−9.53590	−0.378719
$635$	−65.5692	−2.60204
$636$	−11.7321	−0.465206
$637$	0	0
$638$	−32.0000	−1.26689
$639$	11.9282	0.471872
$640$	−3.46410	−0.136931
$641$	42.6410	1.68422	0.842109	−	0.539307i	$-0.181314\pi$
$641$	42.6410	1.68422	0.842109	+	0.539307i	$0.181314\pi$
$642$	15.4641	0.610319
$643$	−28.2487	−1.11402	−0.557010	−	0.830506i	$-0.688052\pi$
$643$	−28.2487	−1.11402	−0.557010	+	0.830506i	$0.688052\pi$
$644$	−2.26795	−0.0893697
$645$	8.53590	0.336101
$646$	0.248711	0.00978542
$647$	2.67949	0.105342	0.0526708	−	0.998612i	$-0.483227\pi$
$647$	2.67949	0.105342	0.0526708	+	0.998612i	$0.483227\pi$
$648$	1.00000	0.0392837
$649$	38.9282	1.52807
$650$	0	0
$651$	0.464102	0.0181896
$652$	18.6603	0.730792
$653$	−6.41154	−0.250903	−0.125452	−	0.992100i	$-0.540038\pi$
$653$	−6.41154	−0.250903	−0.125452	+	0.992100i	$0.540038\pi$
$654$	12.0000	0.469237
$655$	−65.8179	−2.57172
$656$	6.92820	0.270501
$657$	−2.92820	−0.114240
$658$	−7.46410	−0.290981
$659$	22.3923	0.872280	0.436140	−	0.899879i	$-0.356345\pi$
$659$	22.3923	0.872280	0.436140	+	0.899879i	$0.356345\pi$
$660$	13.8564	0.539360
$661$	4.71281	0.183307	0.0916536	−	0.995791i	$-0.470785\pi$
$661$	4.71281	0.183307	0.0916536	+	0.995791i	$0.470785\pi$
$662$	13.3205	0.517716
$663$	0	0
$664$	1.73205	0.0672166
$665$	−1.85641	−0.0719884
$666$	−8.92820	−0.345961
$667$	18.1436	0.702523
$668$	−20.0000	−0.773823
$669$	−14.4641	−0.559214
$670$	11.0718	0.427741
$671$	−20.7846	−0.802381
$672$	−1.00000	−0.0385758
$673$	−29.6410	−1.14258	−0.571289	−	0.820749i	$-0.693556\pi$
$673$	−29.6410	−1.14258	−0.571289	+	0.820749i	$0.693556\pi$
$674$	6.00000	0.231111
$675$	7.00000	0.269430
$676$	0	0
$677$	14.9282	0.573737	0.286869	−	0.957970i	$-0.407386\pi$
$677$	14.9282	0.573737	0.286869	+	0.957970i	$0.407386\pi$
$678$	16.3923	0.629543
$679$	−8.39230	−0.322067
$680$	1.60770	0.0616523
$681$	−21.3205	−0.817004
$682$	1.85641	0.0710855
$683$	−11.1769	−0.427673	−0.213836	−	0.976869i	$-0.568596\pi$
$683$	−11.1769	−0.427673	−0.213836	+	0.976869i	$0.568596\pi$
$684$	−0.535898	−0.0204906
$685$	−48.0000	−1.83399
$686$	−1.00000	−0.0381802
$687$	−6.07180	−0.231653
$688$	−2.46410	−0.0939430
$689$	0	0
$690$	−7.85641	−0.299088
$691$	21.1769	0.805608	0.402804	−	0.915286i	$-0.368036\pi$
$691$	21.1769	0.805608	0.402804	+	0.915286i	$0.368036\pi$
$692$	14.9282	0.567485
$693$	4.00000	0.151947
$694$	−29.7128	−1.12788
$695$	37.8564	1.43598
$696$	8.00000	0.303239
$697$	−3.21539	−0.121792
$698$	−33.6410	−1.27333
$699$	6.53590	0.247210
$700$	−7.00000	−0.264575
$701$	22.1244	0.835625	0.417813	−	0.908533i	$-0.362797\pi$
$701$	22.1244	0.835625	0.417813	+	0.908533i	$0.362797\pi$
$702$	0	0
$703$	4.78461	0.180455
$704$	−4.00000	−0.150756
$705$	−25.8564	−0.973809
$706$	26.6603	1.00337
$707$	0	0
$708$	−9.73205	−0.365753
$709$	47.7128	1.79189	0.895946	−	0.444163i	$-0.146499\pi$
$709$	47.7128	1.79189	0.895946	+	0.444163i	$0.146499\pi$
$710$	−41.3205	−1.55073
$711$	−2.53590	−0.0951036
$712$	8.26795	0.309854
$713$	−1.05256	−0.0394186
$714$	0.464102	0.0173686
$715$	0	0
$716$	−3.07180	−0.114798
$717$	14.8564	0.554823
$718$	8.00000	0.298557
$719$	41.4641	1.54635	0.773175	−	0.634193i	$-0.218667\pi$
$719$	41.4641	1.54635	0.773175	+	0.634193i	$0.218667\pi$
$720$	−3.46410	−0.129099
$721$	6.66025	0.248041
$722$	−18.7128	−0.696419
$723$	−11.8564	−0.440945
$724$	−16.7846	−0.623795
$725$	56.0000	2.07979
$726$	5.00000	0.185567
$727$	42.9090	1.59141	0.795703	−	0.605687i	$-0.207102\pi$
$727$	42.9090	1.59141	0.795703	+	0.605687i	$0.207102\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	10.1436	0.375431
$731$	1.14359	0.0422973
$732$	5.19615	0.192055
$733$	22.8564	0.844221	0.422110	−	0.906544i	$-0.361289\pi$
$733$	22.8564	0.844221	0.422110	+	0.906544i	$0.361289\pi$
$734$	5.05256	0.186493
$735$	−3.46410	−0.127775
$736$	2.26795	0.0835977
$737$	12.7846	0.470927
$738$	6.92820	0.255031
$739$	−4.26795	−0.156999	−0.0784995	−	0.996914i	$-0.525013\pi$
$739$	−4.26795	−0.156999	−0.0784995	+	0.996914i	$0.525013\pi$
$740$	30.9282	1.13694
$741$	0	0
$742$	11.7321	0.430697
$743$	−39.7846	−1.45956	−0.729778	−	0.683684i	$-0.760377\pi$
$743$	−39.7846	−1.45956	−0.729778	+	0.683684i	$0.760377\pi$
$744$	−0.464102	−0.0170148
$745$	−63.9615	−2.34337
$746$	22.2487	0.814583
$747$	1.73205	0.0633724
$748$	1.85641	0.0678769
$749$	−15.4641	−0.565046
$750$	−6.92820	−0.252982
$751$	−5.32051	−0.194148	−0.0970740	−	0.995277i	$-0.530948\pi$
$751$	−5.32051	−0.194148	−0.0970740	+	0.995277i	$0.530948\pi$
$752$	7.46410	0.272188
$753$	−23.9282	−0.871992
$754$	0	0
$755$	−41.5692	−1.51286
$756$	−1.00000	−0.0363696
$757$	−7.85641	−0.285546	−0.142773	−	0.989755i	$-0.545602\pi$
$757$	−7.85641	−0.285546	−0.142773	+	0.989755i	$0.545602\pi$
$758$	−30.3923	−1.10390
$759$	−9.07180	−0.329285
$760$	1.85641	0.0673389
$761$	−6.92820	−0.251147	−0.125574	−	0.992084i	$-0.540077\pi$
$761$	−6.92820	−0.251147	−0.125574	+	0.992084i	$0.540077\pi$
$762$	18.9282	0.685696
$763$	−12.0000	−0.434429
$764$	18.5167	0.669909
$765$	1.60770	0.0581263
$766$	27.3205	0.987130
$767$	0	0
$768$	1.00000	0.0360844
$769$	−26.6410	−0.960700	−0.480350	−	0.877077i	$-0.659490\pi$
$769$	−26.6410	−0.960700	−0.480350	+	0.877077i	$0.659490\pi$
$770$	−13.8564	−0.499350
$771$	−6.46410	−0.232799
$772$	9.85641	0.354740
$773$	0.928203	0.0333851	0.0166926	−	0.999861i	$-0.494686\pi$
$773$	0.928203	0.0333851	0.0166926	+	0.999861i	$0.494686\pi$
$774$	−2.46410	−0.0885703
$775$	−3.24871	−0.116697
$776$	8.39230	0.301266
$777$	8.92820	0.320298
$778$	2.66025	0.0953747
$779$	−3.71281	−0.133025
$780$	0	0
$781$	−47.7128	−1.70730
$782$	−1.05256	−0.0376394
$783$	8.00000	0.285897
$784$	1.00000	0.0357143
$785$	−37.8564	−1.35115
$786$	19.0000	0.677708
$787$	12.3923	0.441738	0.220869	−	0.975303i	$-0.429111\pi$
$787$	12.3923	0.441738	0.220869	+	0.975303i	$0.429111\pi$
$788$	23.3923	0.833316
$789$	17.3205	0.616626
$790$	8.78461	0.312542
$791$	−16.3923	−0.582843
$792$	−4.00000	−0.142134
$793$	0	0
$794$	11.7846	0.418220
$795$	40.6410	1.44139
$796$	2.12436	0.0752958
$797$	−6.24871	−0.221341	−0.110670	−	0.993857i	$-0.535300\pi$
$797$	−6.24871	−0.221341	−0.110670	+	0.993857i	$0.535300\pi$
$798$	0.535898	0.0189706
$799$	−3.46410	−0.122551
$800$	7.00000	0.247487
$801$	8.26795	0.292134
$802$	−4.39230	−0.155098
$803$	11.7128	0.413336
$804$	−3.19615	−0.112720
$805$	7.85641	0.276902
$806$	0	0
$807$	1.60770	0.0565935
$808$	0	0
$809$	−39.7128	−1.39623	−0.698114	−	0.715987i	$-0.745977\pi$
$809$	−39.7128	−1.39623	−0.698114	+	0.715987i	$0.745977\pi$
$810$	−3.46410	−0.121716
$811$	−29.8564	−1.04840	−0.524200	−	0.851595i	$-0.675636\pi$
$811$	−29.8564	−1.04840	−0.524200	+	0.851595i	$0.675636\pi$
$812$	−8.00000	−0.280745
$813$	−5.53590	−0.194152
$814$	35.7128	1.25173
$815$	−64.6410	−2.26428
$816$	−0.464102	−0.0162468
$817$	1.32051	0.0461987
$818$	14.3923	0.503215
$819$	0	0
$820$	−24.0000	−0.838116
$821$	−17.2487	−0.601984	−0.300992	−	0.953627i	$-0.597318\pi$
$821$	−17.2487	−0.601984	−0.300992	+	0.953627i	$0.597318\pi$
$822$	13.8564	0.483298
$823$	44.3923	1.54742	0.773709	−	0.633541i	$-0.218399\pi$
$823$	44.3923	1.54742	0.773709	+	0.633541i	$0.218399\pi$
$824$	−6.66025	−0.232021
$825$	−28.0000	−0.974835
$826$	9.73205	0.338621
$827$	−15.6077	−0.542733	−0.271366	−	0.962476i	$-0.587475\pi$
$827$	−15.6077	−0.542733	−0.271366	+	0.962476i	$0.587475\pi$
$828$	2.26795	0.0788167
$829$	48.7846	1.69436	0.847180	−	0.531306i	$-0.178299\pi$
$829$	48.7846	1.69436	0.847180	+	0.531306i	$0.178299\pi$
$830$	−6.00000	−0.208263
$831$	−27.3205	−0.947738
$832$	0	0
$833$	−0.464102	−0.0160802
$834$	−10.9282	−0.378413
$835$	69.2820	2.39760
$836$	2.14359	0.0741377
$837$	−0.464102	−0.0160417
$838$	−5.00000	−0.172722
$839$	−22.3923	−0.773068	−0.386534	−	0.922275i	$-0.626328\pi$
$839$	−22.3923	−0.773068	−0.386534	+	0.922275i	$0.626328\pi$
$840$	3.46410	0.119523
$841$	35.0000	1.20690
$842$	22.3923	0.771690
$843$	−18.3923	−0.633465
$844$	−22.9282	−0.789221
$845$	0	0
$846$	7.46410	0.256621
$847$	−5.00000	−0.171802
$848$	−11.7321	−0.402880
$849$	−4.53590	−0.155672
$850$	−3.24871	−0.111430
$851$	−20.2487	−0.694117
$852$	11.9282	0.408654
$853$	21.6410	0.740974	0.370487	−	0.928838i	$-0.379191\pi$
$853$	21.6410	0.740974	0.370487	+	0.928838i	$0.379191\pi$
$854$	−5.19615	−0.177809
$855$	1.85641	0.0634878
$856$	15.4641	0.528552
$857$	21.7128	0.741696	0.370848	−	0.928694i	$-0.379067\pi$
$857$	21.7128	0.741696	0.370848	+	0.928694i	$0.379067\pi$
$858$	0	0
$859$	11.8564	0.404535	0.202268	−	0.979330i	$-0.435169\pi$
$859$	11.8564	0.404535	0.202268	+	0.979330i	$0.435169\pi$
$860$	8.53590	0.291072
$861$	−6.92820	−0.236113
$862$	−22.8564	−0.778492
$863$	−29.0718	−0.989615	−0.494808	−	0.869002i	$-0.664762\pi$
$863$	−29.0718	−0.989615	−0.494808	+	0.869002i	$0.664762\pi$
$864$	1.00000	0.0340207
$865$	−51.7128	−1.75829
$866$	−17.8564	−0.606785
$867$	−16.7846	−0.570035
$868$	0.464102	0.0157526
$869$	10.1436	0.344098
$870$	−27.7128	−0.939552
$871$	0	0
$872$	12.0000	0.406371
$873$	8.39230	0.284036
$874$	−1.21539	−0.0411112
$875$	6.92820	0.234216
$876$	−2.92820	−0.0989348
$877$	29.7128	1.00333	0.501665	−	0.865062i	$-0.332721\pi$
$877$	29.7128	1.00333	0.501665	+	0.865062i	$0.332721\pi$
$878$	−34.3923	−1.16068
$879$	−26.5359	−0.895034
$880$	13.8564	0.467099
$881$	−58.0333	−1.95519	−0.977596	−	0.210489i	$-0.932494\pi$
$881$	−58.0333	−1.95519	−0.977596	+	0.210489i	$0.932494\pi$
$882$	1.00000	0.0336718
$883$	34.3205	1.15498	0.577489	−	0.816399i	$-0.304033\pi$
$883$	34.3205	1.15498	0.577489	+	0.816399i	$0.304033\pi$
$884$	0	0
$885$	33.7128	1.13324
$886$	−1.60770	−0.0540116
$887$	−15.8564	−0.532406	−0.266203	−	0.963917i	$-0.585769\pi$
$887$	−15.8564	−0.532406	−0.266203	+	0.963917i	$0.585769\pi$
$888$	−8.92820	−0.299611
$889$	−18.9282	−0.634832
$890$	−28.6410	−0.960049
$891$	−4.00000	−0.134005
$892$	−14.4641	−0.484294
$893$	−4.00000	−0.133855
$894$	18.4641	0.617532
$895$	10.6410	0.355690
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	18.0000	0.600668
$899$	−3.71281	−0.123829
$900$	7.00000	0.233333
$901$	5.44486	0.181395
$902$	−27.7128	−0.922736
$903$	2.46410	0.0820002
$904$	16.3923	0.545200
$905$	58.1436	1.93276
$906$	12.0000	0.398673
$907$	−11.5359	−0.383043	−0.191522	−	0.981488i	$-0.561342\pi$
$907$	−11.5359	−0.383043	−0.191522	+	0.981488i	$0.561342\pi$
$908$	−21.3205	−0.707546
$909$	0	0
$910$	0	0
$911$	−35.1769	−1.16546	−0.582732	−	0.812665i	$-0.698016\pi$
$911$	−35.1769	−1.16546	−0.582732	+	0.812665i	$0.698016\pi$
$912$	−0.535898	−0.0177454
$913$	−6.92820	−0.229290
$914$	−9.19615	−0.304182
$915$	−18.0000	−0.595062
$916$	−6.07180	−0.200618
$917$	−19.0000	−0.627435
$918$	−0.464102	−0.0153176
$919$	−26.0000	−0.857661	−0.428830	−	0.903385i	$-0.641074\pi$
$919$	−26.0000	−0.857661	−0.428830	+	0.903385i	$0.641074\pi$
$920$	−7.85641	−0.259018
$921$	22.0000	0.724925
$922$	18.9282	0.623367
$923$	0	0
$924$	4.00000	0.131590
$925$	−62.4974	−2.05490
$926$	40.2487	1.32265
$927$	−6.66025	−0.218751
$928$	8.00000	0.262613
$929$	−30.1244	−0.988348	−0.494174	−	0.869363i	$-0.664529\pi$
$929$	−30.1244	−0.988348	−0.494174	+	0.869363i	$0.664529\pi$
$930$	1.60770	0.0527184
$931$	−0.535898	−0.0175634
$932$	6.53590	0.214090
$933$	−21.3205	−0.698002
$934$	29.6410	0.969884
$935$	−6.43078	−0.210309
$936$	0	0
$937$	−31.0718	−1.01507	−0.507536	−	0.861631i	$-0.669443\pi$
$937$	−31.0718	−1.01507	−0.507536	+	0.861631i	$0.669443\pi$
$938$	3.19615	0.104358
$939$	35.3205	1.15264
$940$	−25.8564	−0.843343
$941$	40.3923	1.31675	0.658376	−	0.752689i	$-0.271244\pi$
$941$	40.3923	1.31675	0.658376	+	0.752689i	$0.271244\pi$
$942$	10.9282	0.356060
$943$	15.7128	0.511680
$944$	−9.73205	−0.316751
$945$	3.46410	0.112687
$946$	9.85641	0.320459
$947$	18.2487	0.593003	0.296502	−	0.955032i	$-0.404180\pi$
$947$	18.2487	0.593003	0.296502	+	0.955032i	$0.404180\pi$
$948$	−2.53590	−0.0823622
$949$	0	0
$950$	−3.75129	−0.121708
$951$	−9.53590	−0.309223
$952$	0.464102	0.0150416
$953$	30.0000	0.971795	0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000	0.971795	0.485898	+	0.874016i	$0.338493\pi$
$954$	−11.7321	−0.379839
$955$	−64.1436	−2.07564
$956$	14.8564	0.480491
$957$	−32.0000	−1.03441
$958$	−16.3923	−0.529611
$959$	−13.8564	−0.447447
$960$	−3.46410	−0.111803
$961$	−30.7846	−0.993052
$962$	0	0
$963$	15.4641	0.498324
$964$	−11.8564	−0.381869
$965$	−34.1436	−1.09912
$966$	−2.26795	−0.0729701
$967$	−23.4641	−0.754555	−0.377277	−	0.926100i	$-0.623140\pi$
$967$	−23.4641	−0.754555	−0.377277	+	0.926100i	$0.623140\pi$
$968$	5.00000	0.160706
$969$	0.248711	0.00798976
$970$	−29.0718	−0.933439
$971$	10.0718	0.323219	0.161610	−	0.986855i	$-0.448331\pi$
$971$	10.0718	0.323219	0.161610	+	0.986855i	$0.448331\pi$
$972$	1.00000	0.0320750
$973$	10.9282	0.350342
$974$	20.3923	0.653412
$975$	0	0
$976$	5.19615	0.166325
$977$	1.85641	0.0593917	0.0296959	−	0.999559i	$-0.490546\pi$
$977$	1.85641	0.0593917	0.0296959	+	0.999559i	$0.490546\pi$
$978$	18.6603	0.596689
$979$	−33.0718	−1.05698
$980$	−3.46410	−0.110657
$981$	12.0000	0.383131
$982$	17.8564	0.569821
$983$	−32.9282	−1.05025	−0.525123	−	0.851026i	$-0.675981\pi$
$983$	−32.9282	−1.05025	−0.525123	+	0.851026i	$0.675981\pi$
$984$	6.92820	0.220863
$985$	−81.0333	−2.58194
$986$	−3.71281	−0.118240
$987$	−7.46410	−0.237585
$988$	0	0
$989$	−5.58846	−0.177703
$990$	13.8564	0.440386
$991$	27.8564	0.884888	0.442444	−	0.896796i	$-0.354112\pi$
$991$	27.8564	0.884888	0.442444	+	0.896796i	$0.354112\pi$
$992$	−0.464102	−0.0147352
$993$	13.3205	0.422714
$994$	−11.9282	−0.378340
$995$	−7.35898	−0.233295
$996$	1.73205	0.0548821
$997$	−17.9808	−0.569456	−0.284728	−	0.958608i	$-0.591903\pi$
$997$	−17.9808	−0.569456	−0.284728	+	0.958608i	$0.591903\pi$
$998$	3.73205	0.118136
$999$	−8.92820	−0.282476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.bz.1.1		2
13.6	odd	12		546.2.s.c.127.1	yes	4
13.11	odd	12		546.2.s.c.43.1	✓	4
13.12	even	2		7098.2.a.bn.1.2		2
39.11	even	12		1638.2.bj.e.1135.2		4
39.32	even	12		1638.2.bj.e.127.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.c.43.1	✓	4	13.11	odd	12
546.2.s.c.127.1	yes	4	13.6	odd	12
1638.2.bj.e.127.2		4	39.32	even	12
1638.2.bj.e.1135.2		4	39.11	even	12
7098.2.a.bn.1.2		2	13.12	even	2
7098.2.a.bz.1.1		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.46410 q^{10} -4.00000 q^{11} +1.00000 q^{12} -1.00000 q^{14} -3.46410 q^{15} +1.00000 q^{16} -0.464102 q^{17} +1.00000 q^{18} -0.535898 q^{19} -3.46410 q^{20} -1.00000 q^{21} -4.00000 q^{22} +2.26795 q^{23} +1.00000 q^{24} +7.00000 q^{25} +1.00000 q^{27} -1.00000 q^{28} +8.00000 q^{29} -3.46410 q^{30} -0.464102 q^{31} +1.00000 q^{32} -4.00000 q^{33} -0.464102 q^{34} +3.46410 q^{35} +1.00000 q^{36} -8.92820 q^{37} -0.535898 q^{38} -3.46410 q^{40} +6.92820 q^{41} -1.00000 q^{42} -2.46410 q^{43} -4.00000 q^{44} -3.46410 q^{45} +2.26795 q^{46} +7.46410 q^{47} +1.00000 q^{48} +1.00000 q^{49} +7.00000 q^{50} -0.464102 q^{51} -11.7321 q^{53} +1.00000 q^{54} +13.8564 q^{55} -1.00000 q^{56} -0.535898 q^{57} +8.00000 q^{58} -9.73205 q^{59} -3.46410 q^{60} +5.19615 q^{61} -0.464102 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.00000 q^{66} -3.19615 q^{67} -0.464102 q^{68} +2.26795 q^{69} +3.46410 q^{70} +11.9282 q^{71} +1.00000 q^{72} -2.92820 q^{73} -8.92820 q^{74} +7.00000 q^{75} -0.535898 q^{76} +4.00000 q^{77} -2.53590 q^{79} -3.46410 q^{80} +1.00000 q^{81} +6.92820 q^{82} +1.73205 q^{83} -1.00000 q^{84} +1.60770 q^{85} -2.46410 q^{86} +8.00000 q^{87} -4.00000 q^{88} +8.26795 q^{89} -3.46410 q^{90} +2.26795 q^{92} -0.464102 q^{93} +7.46410 q^{94} +1.85641 q^{95} +1.00000 q^{96} +8.39230 q^{97} +1.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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