LMFDB - Embedded newform 7098.2.a.bx.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:	$\Z[a_1, \ldots, a_{5}]$
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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.73205 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.73205 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.73205 q^{10} -1.73205 q^{11} +1.00000 q^{12} -1.00000 q^{14} -2.73205 q^{15} +1.00000 q^{16} +0.267949 q^{17} +1.00000 q^{18} +1.00000 q^{19} -2.73205 q^{20} -1.00000 q^{21} -1.73205 q^{22} +3.46410 q^{23} +1.00000 q^{24} +2.46410 q^{25} +1.00000 q^{27} -1.00000 q^{28} -0.464102 q^{29} -2.73205 q^{30} -8.19615 q^{31} +1.00000 q^{32} -1.73205 q^{33} +0.267949 q^{34} +2.73205 q^{35} +1.00000 q^{36} +3.26795 q^{37} +1.00000 q^{38} -2.73205 q^{40} -3.00000 q^{41} -1.00000 q^{42} +6.73205 q^{43} -1.73205 q^{44} -2.73205 q^{45} +3.46410 q^{46} +4.46410 q^{47} +1.00000 q^{48} +1.00000 q^{49} +2.46410 q^{50} +0.267949 q^{51} +7.00000 q^{53} +1.00000 q^{54} +4.73205 q^{55} -1.00000 q^{56} +1.00000 q^{57} -0.464102 q^{58} +12.9282 q^{59} -2.73205 q^{60} -5.19615 q^{61} -8.19615 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.73205 q^{66} +4.92820 q^{67} +0.267949 q^{68} +3.46410 q^{69} +2.73205 q^{70} +8.19615 q^{71} +1.00000 q^{72} -1.46410 q^{73} +3.26795 q^{74} +2.46410 q^{75} +1.00000 q^{76} +1.73205 q^{77} +15.9282 q^{79} -2.73205 q^{80} +1.00000 q^{81} -3.00000 q^{82} -10.1962 q^{83} -1.00000 q^{84} -0.732051 q^{85} +6.73205 q^{86} -0.464102 q^{87} -1.73205 q^{88} -3.53590 q^{89} -2.73205 q^{90} +3.46410 q^{92} -8.19615 q^{93} +4.46410 q^{94} -2.73205 q^{95} +1.00000 q^{96} -1.66025 q^{97} +1.00000 q^{98} -1.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 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^5 + 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^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{12} - 2 q^{14} - 2 q^{15} + 2 q^{16} + 4 q^{17} + 2 q^{18} + 2 q^{19} - 2 q^{20} - 2 q^{21} + 2 q^{24} - 2 q^{25} + 2 q^{27} - 2 q^{28} + 6 q^{29} - 2 q^{30} - 6 q^{31} + 2 q^{32} + 4 q^{34} + 2 q^{35} + 2 q^{36} + 10 q^{37} + 2 q^{38} - 2 q^{40} - 6 q^{41} - 2 q^{42} + 10 q^{43} - 2 q^{45} + 2 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} + 4 q^{51} + 14 q^{53} + 2 q^{54} + 6 q^{55} - 2 q^{56} + 2 q^{57} + 6 q^{58} + 12 q^{59} - 2 q^{60} - 6 q^{62} - 2 q^{63} + 2 q^{64} - 4 q^{67} + 4 q^{68} + 2 q^{70} + 6 q^{71} + 2 q^{72} + 4 q^{73} + 10 q^{74} - 2 q^{75} + 2 q^{76} + 18 q^{79} - 2 q^{80} + 2 q^{81} - 6 q^{82} - 10 q^{83} - 2 q^{84} + 2 q^{85} + 10 q^{86} + 6 q^{87} - 14 q^{89} - 2 q^{90} - 6 q^{93} + 2 q^{94} - 2 q^{95} + 2 q^{96} + 14 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^12 - 2 * q^14 - 2 * q^15 + 2 * q^16 + 4 * q^17 + 2 * q^18 + 2 * q^19 - 2 * q^20 - 2 * q^21 + 2 * q^24 - 2 * q^25 + 2 * q^27 - 2 * q^28 + 6 * q^29 - 2 * q^30 - 6 * q^31 + 2 * q^32 + 4 * q^34 + 2 * q^35 + 2 * q^36 + 10 * q^37 + 2 * q^38 - 2 * q^40 - 6 * q^41 - 2 * q^42 + 10 * q^43 - 2 * q^45 + 2 * q^47 + 2 * q^48 + 2 * q^49 - 2 * q^50 + 4 * q^51 + 14 * q^53 + 2 * q^54 + 6 * q^55 - 2 * q^56 + 2 * q^57 + 6 * q^58 + 12 * q^59 - 2 * q^60 - 6 * q^62 - 2 * q^63 + 2 * q^64 - 4 * q^67 + 4 * q^68 + 2 * q^70 + 6 * q^71 + 2 * q^72 + 4 * q^73 + 10 * q^74 - 2 * q^75 + 2 * q^76 + 18 * q^79 - 2 * q^80 + 2 * q^81 - 6 * q^82 - 10 * q^83 - 2 * q^84 + 2 * q^85 + 10 * q^86 + 6 * q^87 - 14 * q^89 - 2 * q^90 - 6 * q^93 + 2 * q^94 - 2 * q^95 + 2 * q^96 + 14 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−2.73205	−1.22181	−0.610905	−	0.791704i	$-0.709194\pi$
$5$	−2.73205	−1.22181	−0.610905	+	0.791704i	$0.709194\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.73205	−0.863950
$11$	−1.73205	−0.522233	−0.261116	−	0.965307i	$-0.584091\pi$
$11$	−1.73205	−0.522233	−0.261116	+	0.965307i	$0.584091\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	−2.73205	−0.705412
$16$	1.00000	0.250000
$17$	0.267949	0.0649872	0.0324936	−	0.999472i	$-0.489655\pi$
$17$	0.267949	0.0649872	0.0324936	+	0.999472i	$0.489655\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	−2.73205	−0.610905
$21$	−1.00000	−0.218218
$22$	−1.73205	−0.369274
$23$	3.46410	0.722315	0.361158	−	0.932505i	$-0.382382\pi$
$23$	3.46410	0.722315	0.361158	+	0.932505i	$0.382382\pi$
$24$	1.00000	0.204124
$25$	2.46410	0.492820
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−0.464102	−0.0861815	−0.0430908	−	0.999071i	$-0.513720\pi$
$29$	−0.464102	−0.0861815	−0.0430908	+	0.999071i	$0.513720\pi$
$30$	−2.73205	−0.498802
$31$	−8.19615	−1.47207	−0.736036	−	0.676942i	$-0.763305\pi$
$31$	−8.19615	−1.47207	−0.736036	+	0.676942i	$0.763305\pi$
$32$	1.00000	0.176777
$33$	−1.73205	−0.301511
$34$	0.267949	0.0459529
$35$	2.73205	0.461801
$36$	1.00000	0.166667
$37$	3.26795	0.537248	0.268624	−	0.963245i	$-0.413431\pi$
$37$	3.26795	0.537248	0.268624	+	0.963245i	$0.413431\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	−2.73205	−0.431975
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	−1.00000	−0.154303
$43$	6.73205	1.02663	0.513314	−	0.858201i	$-0.328418\pi$
$43$	6.73205	1.02663	0.513314	+	0.858201i	$0.328418\pi$
$44$	−1.73205	−0.261116
$45$	−2.73205	−0.407270
$46$	3.46410	0.510754
$47$	4.46410	0.651156	0.325578	−	0.945515i	$-0.394441\pi$
$47$	4.46410	0.651156	0.325578	+	0.945515i	$0.394441\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	2.46410	0.348477
$51$	0.267949	0.0375204
$52$	0	0
$53$	7.00000	0.961524	0.480762	−	0.876851i	$-0.340360\pi$
$53$	7.00000	0.961524	0.480762	+	0.876851i	$0.340360\pi$
$54$	1.00000	0.136083
$55$	4.73205	0.638070
$56$	−1.00000	−0.133631
$57$	1.00000	0.132453
$58$	−0.464102	−0.0609395
$59$	12.9282	1.68311	0.841554	−	0.540172i	$-0.181641\pi$
$59$	12.9282	1.68311	0.841554	+	0.540172i	$0.181641\pi$
$60$	−2.73205	−0.352706
$61$	−5.19615	−0.665299	−0.332650	−	0.943051i	$-0.607943\pi$
$61$	−5.19615	−0.665299	−0.332650	+	0.943051i	$0.607943\pi$
$62$	−8.19615	−1.04091
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.73205	−0.213201
$67$	4.92820	0.602076	0.301038	−	0.953612i	$-0.402667\pi$
$67$	4.92820	0.602076	0.301038	+	0.953612i	$0.402667\pi$
$68$	0.267949	0.0324936
$69$	3.46410	0.417029
$70$	2.73205	0.326543
$71$	8.19615	0.972704	0.486352	−	0.873763i	$-0.338327\pi$
$71$	8.19615	0.972704	0.486352	+	0.873763i	$0.338327\pi$
$72$	1.00000	0.117851
$73$	−1.46410	−0.171360	−0.0856801	−	0.996323i	$-0.527306\pi$
$73$	−1.46410	−0.171360	−0.0856801	+	0.996323i	$0.527306\pi$
$74$	3.26795	0.379891
$75$	2.46410	0.284530
$76$	1.00000	0.114708
$77$	1.73205	0.197386
$78$	0	0
$79$	15.9282	1.79206	0.896031	−	0.443991i	$-0.146438\pi$
$79$	15.9282	1.79206	0.896031	+	0.443991i	$0.146438\pi$
$80$	−2.73205	−0.305453
$81$	1.00000	0.111111
$82$	−3.00000	−0.331295
$83$	−10.1962	−1.11917	−0.559587	−	0.828772i	$-0.689040\pi$
$83$	−10.1962	−1.11917	−0.559587	+	0.828772i	$0.689040\pi$
$84$	−1.00000	−0.109109
$85$	−0.732051	−0.0794021
$86$	6.73205	0.725936
$87$	−0.464102	−0.0497569
$88$	−1.73205	−0.184637
$89$	−3.53590	−0.374804	−0.187402	−	0.982283i	$-0.560007\pi$
$89$	−3.53590	−0.374804	−0.187402	+	0.982283i	$0.560007\pi$
$90$	−2.73205	−0.287983
$91$	0	0
$92$	3.46410	0.361158
$93$	−8.19615	−0.849901
$94$	4.46410	0.460437
$95$	−2.73205	−0.280302
$96$	1.00000	0.102062
$97$	−1.66025	−0.168573	−0.0842866	−	0.996442i	$-0.526861\pi$
$97$	−1.66025	−0.168573	−0.0842866	+	0.996442i	$0.526861\pi$
$98$	1.00000	0.101015
$99$	−1.73205	−0.174078
$100$	2.46410	0.246410
$101$	16.9282	1.68442	0.842210	−	0.539150i	$-0.181255\pi$
$101$	16.9282	1.68442	0.842210	+	0.539150i	$0.181255\pi$
$102$	0.267949	0.0265309
$103$	11.2679	1.11026	0.555132	−	0.831762i	$-0.312668\pi$
$103$	11.2679	1.11026	0.555132	+	0.831762i	$0.312668\pi$
$104$	0	0
$105$	2.73205	0.266621
$106$	7.00000	0.679900
$107$	−16.8564	−1.62957	−0.814785	−	0.579763i	$-0.803145\pi$
$107$	−16.8564	−1.62957	−0.814785	+	0.579763i	$0.803145\pi$
$108$	1.00000	0.0962250
$109$	1.26795	0.121448	0.0607238	−	0.998155i	$-0.480659\pi$
$109$	1.26795	0.121448	0.0607238	+	0.998155i	$0.480659\pi$
$110$	4.73205	0.451183
$111$	3.26795	0.310180
$112$	−1.00000	−0.0944911
$113$	18.7321	1.76216	0.881082	−	0.472964i	$-0.156816\pi$
$113$	18.7321	1.76216	0.881082	+	0.472964i	$0.156816\pi$
$114$	1.00000	0.0936586
$115$	−9.46410	−0.882532
$116$	−0.464102	−0.0430908
$117$	0	0
$118$	12.9282	1.19014
$119$	−0.267949	−0.0245629
$120$	−2.73205	−0.249401
$121$	−8.00000	−0.727273
$122$	−5.19615	−0.470438
$123$	−3.00000	−0.270501
$124$	−8.19615	−0.736036
$125$	6.92820	0.619677
$126$	−1.00000	−0.0890871
$127$	−8.53590	−0.757438	−0.378719	−	0.925512i	$-0.623635\pi$
$127$	−8.53590	−0.757438	−0.378719	+	0.925512i	$0.623635\pi$
$128$	1.00000	0.0883883
$129$	6.73205	0.592724
$130$	0	0
$131$	13.8564	1.21064	0.605320	−	0.795982i	$-0.293045\pi$
$131$	13.8564	1.21064	0.605320	+	0.795982i	$0.293045\pi$
$132$	−1.73205	−0.150756
$133$	−1.00000	−0.0867110
$134$	4.92820	0.425732
$135$	−2.73205	−0.235137
$136$	0.267949	0.0229765
$137$	6.39230	0.546131	0.273066	−	0.961995i	$-0.411962\pi$
$137$	6.39230	0.546131	0.273066	+	0.961995i	$0.411962\pi$
$138$	3.46410	0.294884
$139$	−19.5885	−1.66147	−0.830736	−	0.556667i	$-0.812080\pi$
$139$	−19.5885	−1.66147	−0.830736	+	0.556667i	$0.812080\pi$
$140$	2.73205	0.230900
$141$	4.46410	0.375945
$142$	8.19615	0.687806
$143$	0	0
$144$	1.00000	0.0833333
$145$	1.26795	0.105297
$146$	−1.46410	−0.121170
$147$	1.00000	0.0824786
$148$	3.26795	0.268624
$149$	−13.8564	−1.13516	−0.567581	−	0.823318i	$-0.692120\pi$
$149$	−13.8564	−1.13516	−0.567581	+	0.823318i	$0.692120\pi$
$150$	2.46410	0.201193
$151$	5.19615	0.422857	0.211428	−	0.977393i	$-0.432188\pi$
$151$	5.19615	0.422857	0.211428	+	0.977393i	$0.432188\pi$
$152$	1.00000	0.0811107
$153$	0.267949	0.0216624
$154$	1.73205	0.139573
$155$	22.3923	1.79859
$156$	0	0
$157$	−7.46410	−0.595700	−0.297850	−	0.954613i	$-0.596270\pi$
$157$	−7.46410	−0.595700	−0.297850	+	0.954613i	$0.596270\pi$
$158$	15.9282	1.26718
$159$	7.00000	0.555136
$160$	−2.73205	−0.215988
$161$	−3.46410	−0.273009
$162$	1.00000	0.0785674
$163$	0.732051	0.0573386	0.0286693	−	0.999589i	$-0.490873\pi$
$163$	0.732051	0.0573386	0.0286693	+	0.999589i	$0.490873\pi$
$164$	−3.00000	−0.234261
$165$	4.73205	0.368390
$166$	−10.1962	−0.791375
$167$	13.8564	1.07224	0.536120	−	0.844141i	$-0.319889\pi$
$167$	13.8564	1.07224	0.536120	+	0.844141i	$0.319889\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	−0.732051	−0.0561457
$171$	1.00000	0.0764719
$172$	6.73205	0.513314
$173$	15.1244	1.14988	0.574942	−	0.818194i	$-0.305025\pi$
$173$	15.1244	1.14988	0.574942	+	0.818194i	$0.305025\pi$
$174$	−0.464102	−0.0351835
$175$	−2.46410	−0.186269
$176$	−1.73205	−0.130558
$177$	12.9282	0.971743
$178$	−3.53590	−0.265027
$179$	4.53590	0.339029	0.169514	−	0.985528i	$-0.445780\pi$
$179$	4.53590	0.339029	0.169514	+	0.985528i	$0.445780\pi$
$180$	−2.73205	−0.203635
$181$	14.6603	1.08969	0.544844	−	0.838537i	$-0.316589\pi$
$181$	14.6603	1.08969	0.544844	+	0.838537i	$0.316589\pi$
$182$	0	0
$183$	−5.19615	−0.384111
$184$	3.46410	0.255377
$185$	−8.92820	−0.656415
$186$	−8.19615	−0.600971
$187$	−0.464102	−0.0339385
$188$	4.46410	0.325578
$189$	−1.00000	−0.0727393
$190$	−2.73205	−0.198204
$191$	−1.12436	−0.0813555	−0.0406778	−	0.999172i	$-0.512952\pi$
$191$	−1.12436	−0.0813555	−0.0406778	+	0.999172i	$0.512952\pi$
$192$	1.00000	0.0721688
$193$	9.19615	0.661954	0.330977	−	0.943639i	$-0.392622\pi$
$193$	9.19615	0.661954	0.330977	+	0.943639i	$0.392622\pi$
$194$	−1.66025	−0.119199
$195$	0	0
$196$	1.00000	0.0714286
$197$	−9.33975	−0.665429	−0.332715	−	0.943028i	$-0.607965\pi$
$197$	−9.33975	−0.665429	−0.332715	+	0.943028i	$0.607965\pi$
$198$	−1.73205	−0.123091
$199$	−5.80385	−0.411424	−0.205712	−	0.978613i	$-0.565951\pi$
$199$	−5.80385	−0.411424	−0.205712	+	0.978613i	$0.565951\pi$
$200$	2.46410	0.174238
$201$	4.92820	0.347609
$202$	16.9282	1.19106
$203$	0.464102	0.0325735
$204$	0.267949	0.0187602
$205$	8.19615	0.572444
$206$	11.2679	0.785075
$207$	3.46410	0.240772
$208$	0	0
$209$	−1.73205	−0.119808
$210$	2.73205	0.188529
$211$	26.0000	1.78991	0.894957	−	0.446153i	$-0.147206\pi$
$211$	26.0000	1.78991	0.894957	+	0.446153i	$0.147206\pi$
$212$	7.00000	0.480762
$213$	8.19615	0.561591
$214$	−16.8564	−1.15228
$215$	−18.3923	−1.25434
$216$	1.00000	0.0680414
$217$	8.19615	0.556391
$218$	1.26795	0.0858764
$219$	−1.46410	−0.0989348
$220$	4.73205	0.319035
$221$	0	0
$222$	3.26795	0.219330
$223$	−3.60770	−0.241589	−0.120795	−	0.992678i	$-0.538544\pi$
$223$	−3.60770	−0.241589	−0.120795	+	0.992678i	$0.538544\pi$
$224$	−1.00000	−0.0668153
$225$	2.46410	0.164273
$226$	18.7321	1.24604
$227$	−2.39230	−0.158783	−0.0793914	−	0.996844i	$-0.525298\pi$
$227$	−2.39230	−0.158783	−0.0793914	+	0.996844i	$0.525298\pi$
$228$	1.00000	0.0662266
$229$	6.07180	0.401236	0.200618	−	0.979670i	$-0.435705\pi$
$229$	6.07180	0.401236	0.200618	+	0.979670i	$0.435705\pi$
$230$	−9.46410	−0.624044
$231$	1.73205	0.113961
$232$	−0.464102	−0.0304698
$233$	15.1244	0.990829	0.495415	−	0.868657i	$-0.335016\pi$
$233$	15.1244	0.990829	0.495415	+	0.868657i	$0.335016\pi$
$234$	0	0
$235$	−12.1962	−0.795589
$236$	12.9282	0.841554
$237$	15.9282	1.03465
$238$	−0.267949	−0.0173686
$239$	−2.73205	−0.176722	−0.0883608	−	0.996089i	$-0.528163\pi$
$239$	−2.73205	−0.176722	−0.0883608	+	0.996089i	$0.528163\pi$
$240$	−2.73205	−0.176353
$241$	8.00000	0.515325	0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000	0.515325	0.257663	+	0.966235i	$0.417048\pi$
$242$	−8.00000	−0.514259
$243$	1.00000	0.0641500
$244$	−5.19615	−0.332650
$245$	−2.73205	−0.174544
$246$	−3.00000	−0.191273
$247$	0	0
$248$	−8.19615	−0.520456
$249$	−10.1962	−0.646155
$250$	6.92820	0.438178
$251$	−11.1244	−0.702163	−0.351082	−	0.936345i	$-0.614186\pi$
$251$	−11.1244	−0.702163	−0.351082	+	0.936345i	$0.614186\pi$
$252$	−1.00000	−0.0629941
$253$	−6.00000	−0.377217
$254$	−8.53590	−0.535590
$255$	−0.732051	−0.0458428
$256$	1.00000	0.0625000
$257$	3.33975	0.208328	0.104164	−	0.994560i	$-0.466783\pi$
$257$	3.33975	0.208328	0.104164	+	0.994560i	$0.466783\pi$
$258$	6.73205	0.419119
$259$	−3.26795	−0.203060
$260$	0	0
$261$	−0.464102	−0.0287272
$262$	13.8564	0.856052
$263$	9.12436	0.562632	0.281316	−	0.959615i	$-0.409229\pi$
$263$	9.12436	0.562632	0.281316	+	0.959615i	$0.409229\pi$
$264$	−1.73205	−0.106600
$265$	−19.1244	−1.17480
$266$	−1.00000	−0.0613139
$267$	−3.53590	−0.216393
$268$	4.92820	0.301038
$269$	17.8564	1.08872	0.544362	−	0.838850i	$-0.316772\pi$
$269$	17.8564	1.08872	0.544362	+	0.838850i	$0.316772\pi$
$270$	−2.73205	−0.166267
$271$	10.0526	0.610649	0.305325	−	0.952248i	$-0.401235\pi$
$271$	10.0526	0.610649	0.305325	+	0.952248i	$0.401235\pi$
$272$	0.267949	0.0162468
$273$	0	0
$274$	6.39230	0.386173
$275$	−4.26795	−0.257367
$276$	3.46410	0.208514
$277$	−25.3205	−1.52136	−0.760681	−	0.649126i	$-0.775135\pi$
$277$	−25.3205	−1.52136	−0.760681	+	0.649126i	$0.775135\pi$
$278$	−19.5885	−1.17484
$279$	−8.19615	−0.490691
$280$	2.73205	0.163271
$281$	17.6603	1.05352	0.526761	−	0.850013i	$-0.323406\pi$
$281$	17.6603	1.05352	0.526761	+	0.850013i	$0.323406\pi$
$282$	4.46410	0.265833
$283$	17.8564	1.06145	0.530727	−	0.847543i	$-0.321919\pi$
$283$	17.8564	1.06145	0.530727	+	0.847543i	$0.321919\pi$
$284$	8.19615	0.486352
$285$	−2.73205	−0.161833
$286$	0	0
$287$	3.00000	0.177084
$288$	1.00000	0.0589256
$289$	−16.9282	−0.995777
$290$	1.26795	0.0744565
$291$	−1.66025	−0.0973258
$292$	−1.46410	−0.0856801
$293$	30.9282	1.80684	0.903422	−	0.428752i	$-0.141046\pi$
$293$	30.9282	1.80684	0.903422	+	0.428752i	$0.141046\pi$
$294$	1.00000	0.0583212
$295$	−35.3205	−2.05644
$296$	3.26795	0.189946
$297$	−1.73205	−0.100504
$298$	−13.8564	−0.802680
$299$	0	0
$300$	2.46410	0.142265
$301$	−6.73205	−0.388029
$302$	5.19615	0.299005
$303$	16.9282	0.972500
$304$	1.00000	0.0573539
$305$	14.1962	0.812869
$306$	0.267949	0.0153176
$307$	−29.3923	−1.67751	−0.838754	−	0.544511i	$-0.816715\pi$
$307$	−29.3923	−1.67751	−0.838754	+	0.544511i	$0.816715\pi$
$308$	1.73205	0.0986928
$309$	11.2679	0.641011
$310$	22.3923	1.27180
$311$	7.73205	0.438444	0.219222	−	0.975675i	$-0.429648\pi$
$311$	7.73205	0.438444	0.219222	+	0.975675i	$0.429648\pi$
$312$	0	0
$313$	−31.5167	−1.78143	−0.890713	−	0.454565i	$-0.849795\pi$
$313$	−31.5167	−1.78143	−0.890713	+	0.454565i	$0.849795\pi$
$314$	−7.46410	−0.421224
$315$	2.73205	0.153934
$316$	15.9282	0.896031
$317$	−15.8564	−0.890585	−0.445292	−	0.895385i	$-0.646900\pi$
$317$	−15.8564	−0.890585	−0.445292	+	0.895385i	$0.646900\pi$
$318$	7.00000	0.392541
$319$	0.803848	0.0450068
$320$	−2.73205	−0.152726
$321$	−16.8564	−0.940833
$322$	−3.46410	−0.193047
$323$	0.267949	0.0149091
$324$	1.00000	0.0555556
$325$	0	0
$326$	0.732051	0.0405445
$327$	1.26795	0.0701178
$328$	−3.00000	−0.165647
$329$	−4.46410	−0.246114
$330$	4.73205	0.260491
$331$	0.143594	0.00789261	0.00394631	−	0.999992i	$-0.498744\pi$
$331$	0.143594	0.00789261	0.00394631	+	0.999992i	$0.498744\pi$
$332$	−10.1962	−0.559587
$333$	3.26795	0.179083
$334$	13.8564	0.758189
$335$	−13.4641	−0.735622
$336$	−1.00000	−0.0545545
$337$	19.0000	1.03500	0.517498	−	0.855684i	$-0.326864\pi$
$337$	19.0000	1.03500	0.517498	+	0.855684i	$0.326864\pi$
$338$	0	0
$339$	18.7321	1.01739
$340$	−0.732051	−0.0397010
$341$	14.1962	0.768765
$342$	1.00000	0.0540738
$343$	−1.00000	−0.0539949
$344$	6.73205	0.362968
$345$	−9.46410	−0.509530
$346$	15.1244	0.813090
$347$	−15.3923	−0.826302	−0.413151	−	0.910662i	$-0.635572\pi$
$347$	−15.3923	−0.826302	−0.413151	+	0.910662i	$0.635572\pi$
$348$	−0.464102	−0.0248785
$349$	31.7128	1.69755	0.848774	−	0.528756i	$-0.177341\pi$
$349$	31.7128	1.69755	0.848774	+	0.528756i	$0.177341\pi$
$350$	−2.46410	−0.131712
$351$	0	0
$352$	−1.73205	−0.0923186
$353$	2.53590	0.134972	0.0674861	−	0.997720i	$-0.478502\pi$
$353$	2.53590	0.134972	0.0674861	+	0.997720i	$0.478502\pi$
$354$	12.9282	0.687126
$355$	−22.3923	−1.18846
$356$	−3.53590	−0.187402
$357$	−0.267949	−0.0141814
$358$	4.53590	0.239730
$359$	14.1962	0.749244	0.374622	−	0.927178i	$-0.377772\pi$
$359$	14.1962	0.749244	0.374622	+	0.927178i	$0.377772\pi$
$360$	−2.73205	−0.143992
$361$	−18.0000	−0.947368
$362$	14.6603	0.770526
$363$	−8.00000	−0.419891
$364$	0	0
$365$	4.00000	0.209370
$366$	−5.19615	−0.271607
$367$	−9.32051	−0.486527	−0.243263	−	0.969960i	$-0.578218\pi$
$367$	−9.32051	−0.486527	−0.243263	+	0.969960i	$0.578218\pi$
$368$	3.46410	0.180579
$369$	−3.00000	−0.156174
$370$	−8.92820	−0.464155
$371$	−7.00000	−0.363422
$372$	−8.19615	−0.424951
$373$	−7.66025	−0.396633	−0.198316	−	0.980138i	$-0.563547\pi$
$373$	−7.66025	−0.396633	−0.198316	+	0.980138i	$0.563547\pi$
$374$	−0.464102	−0.0239981
$375$	6.92820	0.357771
$376$	4.46410	0.230218
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	30.4449	1.56385	0.781924	−	0.623374i	$-0.214239\pi$
$379$	30.4449	1.56385	0.781924	+	0.623374i	$0.214239\pi$
$380$	−2.73205	−0.140151
$381$	−8.53590	−0.437307
$382$	−1.12436	−0.0575270
$383$	−12.4641	−0.636886	−0.318443	−	0.947942i	$-0.603160\pi$
$383$	−12.4641	−0.636886	−0.318443	+	0.947942i	$0.603160\pi$
$384$	1.00000	0.0510310
$385$	−4.73205	−0.241168
$386$	9.19615	0.468072
$387$	6.73205	0.342209
$388$	−1.66025	−0.0842866
$389$	−12.3923	−0.628315	−0.314157	−	0.949371i	$-0.601722\pi$
$389$	−12.3923	−0.628315	−0.314157	+	0.949371i	$0.601722\pi$
$390$	0	0
$391$	0.928203	0.0469413
$392$	1.00000	0.0505076
$393$	13.8564	0.698963
$394$	−9.33975	−0.470530
$395$	−43.5167	−2.18956
$396$	−1.73205	−0.0870388
$397$	−21.9282	−1.10054	−0.550272	−	0.834985i	$-0.685476\pi$
$397$	−21.9282	−1.10054	−0.550272	+	0.834985i	$0.685476\pi$
$398$	−5.80385	−0.290921
$399$	−1.00000	−0.0500626
$400$	2.46410	0.123205
$401$	2.78461	0.139057	0.0695284	−	0.997580i	$-0.477851\pi$
$401$	2.78461	0.139057	0.0695284	+	0.997580i	$0.477851\pi$
$402$	4.92820	0.245796
$403$	0	0
$404$	16.9282	0.842210
$405$	−2.73205	−0.135757
$406$	0.464102	0.0230330
$407$	−5.66025	−0.280568
$408$	0.267949	0.0132655
$409$	−35.2679	−1.74389	−0.871944	−	0.489606i	$-0.837141\pi$
$409$	−35.2679	−1.74389	−0.871944	+	0.489606i	$0.837141\pi$
$410$	8.19615	0.404779
$411$	6.39230	0.315309
$412$	11.2679	0.555132
$413$	−12.9282	−0.636155
$414$	3.46410	0.170251
$415$	27.8564	1.36742
$416$	0	0
$417$	−19.5885	−0.959251
$418$	−1.73205	−0.0847174
$419$	−2.73205	−0.133469	−0.0667347	−	0.997771i	$-0.521258\pi$
$419$	−2.73205	−0.133469	−0.0667347	+	0.997771i	$0.521258\pi$
$420$	2.73205	0.133310
$421$	1.60770	0.0783543	0.0391771	−	0.999232i	$-0.487526\pi$
$421$	1.60770	0.0783543	0.0391771	+	0.999232i	$0.487526\pi$
$422$	26.0000	1.26566
$423$	4.46410	0.217052
$424$	7.00000	0.339950
$425$	0.660254	0.0320270
$426$	8.19615	0.397105
$427$	5.19615	0.251459
$428$	−16.8564	−0.814785
$429$	0	0
$430$	−18.3923	−0.886956
$431$	3.80385	0.183225	0.0916124	−	0.995795i	$-0.470798\pi$
$431$	3.80385	0.183225	0.0916124	+	0.995795i	$0.470798\pi$
$432$	1.00000	0.0481125
$433$	−40.9282	−1.96688	−0.983442	−	0.181223i	$-0.941994\pi$
$433$	−40.9282	−1.96688	−0.983442	+	0.181223i	$0.941994\pi$
$434$	8.19615	0.393428
$435$	1.26795	0.0607935
$436$	1.26795	0.0607238
$437$	3.46410	0.165710
$438$	−1.46410	−0.0699575
$439$	37.1769	1.77436	0.887179	−	0.461426i	$-0.152662\pi$
$439$	37.1769	1.77436	0.887179	+	0.461426i	$0.152662\pi$
$440$	4.73205	0.225592
$441$	1.00000	0.0476190
$442$	0	0
$443$	35.6410	1.69336	0.846678	−	0.532106i	$-0.178599\pi$
$443$	35.6410	1.69336	0.846678	+	0.532106i	$0.178599\pi$
$444$	3.26795	0.155090
$445$	9.66025	0.457940
$446$	−3.60770	−0.170829
$447$	−13.8564	−0.655386
$448$	−1.00000	−0.0472456
$449$	10.5885	0.499700	0.249850	−	0.968285i	$-0.419619\pi$
$449$	10.5885	0.499700	0.249850	+	0.968285i	$0.419619\pi$
$450$	2.46410	0.116159
$451$	5.19615	0.244677
$452$	18.7321	0.881082
$453$	5.19615	0.244137
$454$	−2.39230	−0.112276
$455$	0	0
$456$	1.00000	0.0468293
$457$	15.8564	0.741731	0.370866	−	0.928687i	$-0.379061\pi$
$457$	15.8564	0.741731	0.370866	+	0.928687i	$0.379061\pi$
$458$	6.07180	0.283716
$459$	0.267949	0.0125068
$460$	−9.46410	−0.441266
$461$	−13.0718	−0.608814	−0.304407	−	0.952542i	$-0.598458\pi$
$461$	−13.0718	−0.608814	−0.304407	+	0.952542i	$0.598458\pi$
$462$	1.73205	0.0805823
$463$	9.73205	0.452287	0.226143	−	0.974094i	$-0.427388\pi$
$463$	9.73205	0.452287	0.226143	+	0.974094i	$0.427388\pi$
$464$	−0.464102	−0.0215454
$465$	22.3923	1.03842
$466$	15.1244	0.700622
$467$	13.8564	0.641198	0.320599	−	0.947215i	$-0.396116\pi$
$467$	13.8564	0.641198	0.320599	+	0.947215i	$0.396116\pi$
$468$	0	0
$469$	−4.92820	−0.227563
$470$	−12.1962	−0.562567
$471$	−7.46410	−0.343928
$472$	12.9282	0.595069
$473$	−11.6603	−0.536139
$474$	15.9282	0.731607
$475$	2.46410	0.113061
$476$	−0.267949	−0.0122814
$477$	7.00000	0.320508
$478$	−2.73205	−0.124961
$479$	−25.5359	−1.16676	−0.583382	−	0.812198i	$-0.698271\pi$
$479$	−25.5359	−1.16676	−0.583382	+	0.812198i	$0.698271\pi$
$480$	−2.73205	−0.124700
$481$	0	0
$482$	8.00000	0.364390
$483$	−3.46410	−0.157622
$484$	−8.00000	−0.363636
$485$	4.53590	0.205965
$486$	1.00000	0.0453609
$487$	0.660254	0.0299190	0.0149595	−	0.999888i	$-0.495238\pi$
$487$	0.660254	0.0299190	0.0149595	+	0.999888i	$0.495238\pi$
$488$	−5.19615	−0.235219
$489$	0.732051	0.0331045
$490$	−2.73205	−0.123421
$491$	28.5359	1.28781	0.643904	−	0.765107i	$-0.277314\pi$
$491$	28.5359	1.28781	0.643904	+	0.765107i	$0.277314\pi$
$492$	−3.00000	−0.135250
$493$	−0.124356	−0.00560070
$494$	0	0
$495$	4.73205	0.212690
$496$	−8.19615	−0.368018
$497$	−8.19615	−0.367648
$498$	−10.1962	−0.456901
$499$	33.5167	1.50041	0.750206	−	0.661204i	$-0.229954\pi$
$499$	33.5167	1.50041	0.750206	+	0.661204i	$0.229954\pi$
$500$	6.92820	0.309839
$501$	13.8564	0.619059
$502$	−11.1244	−0.496504
$503$	−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
$505$	−46.2487	−2.05804
$506$	−6.00000	−0.266733
$507$	0	0
$508$	−8.53590	−0.378719
$509$	39.6603	1.75791	0.878955	−	0.476905i	$-0.158241\pi$
$509$	39.6603	1.75791	0.878955	+	0.476905i	$0.158241\pi$
$510$	−0.732051	−0.0324158
$511$	1.46410	0.0647680
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	3.33975	0.147310
$515$	−30.7846	−1.35653
$516$	6.73205	0.296362
$517$	−7.73205	−0.340055
$518$	−3.26795	−0.143585
$519$	15.1244	0.663886
$520$	0	0
$521$	−31.0526	−1.36044	−0.680219	−	0.733009i	$-0.738115\pi$
$521$	−31.0526	−1.36044	−0.680219	+	0.733009i	$0.738115\pi$
$522$	−0.464102	−0.0203132
$523$	−38.1244	−1.66706	−0.833531	−	0.552473i	$-0.813684\pi$
$523$	−38.1244	−1.66706	−0.833531	+	0.552473i	$0.813684\pi$
$524$	13.8564	0.605320
$525$	−2.46410	−0.107542
$526$	9.12436	0.397841
$527$	−2.19615	−0.0956659
$528$	−1.73205	−0.0753778
$529$	−11.0000	−0.478261
$530$	−19.1244	−0.830709
$531$	12.9282	0.561036
$532$	−1.00000	−0.0433555
$533$	0	0
$534$	−3.53590	−0.153013
$535$	46.0526	1.99103
$536$	4.92820	0.212866
$537$	4.53590	0.195738
$538$	17.8564	0.769844
$539$	−1.73205	−0.0746047
$540$	−2.73205	−0.117569
$541$	41.6603	1.79111	0.895557	−	0.444947i	$-0.146777\pi$
$541$	41.6603	1.79111	0.895557	+	0.444947i	$0.146777\pi$
$542$	10.0526	0.431794
$543$	14.6603	0.629132
$544$	0.267949	0.0114882
$545$	−3.46410	−0.148386
$546$	0	0
$547$	−4.73205	−0.202328	−0.101164	−	0.994870i	$-0.532257\pi$
$547$	−4.73205	−0.202328	−0.101164	+	0.994870i	$0.532257\pi$
$548$	6.39230	0.273066
$549$	−5.19615	−0.221766
$550$	−4.26795	−0.181986
$551$	−0.464102	−0.0197714
$552$	3.46410	0.147442
$553$	−15.9282	−0.677336
$554$	−25.3205	−1.07577
$555$	−8.92820	−0.378981
$556$	−19.5885	−0.830736
$557$	−25.0526	−1.06151	−0.530755	−	0.847525i	$-0.678092\pi$
$557$	−25.0526	−1.06151	−0.530755	+	0.847525i	$0.678092\pi$
$558$	−8.19615	−0.346971
$559$	0	0
$560$	2.73205	0.115450
$561$	−0.464102	−0.0195944
$562$	17.6603	0.744953
$563$	−25.8038	−1.08750	−0.543751	−	0.839246i	$-0.682997\pi$
$563$	−25.8038	−1.08750	−0.543751	+	0.839246i	$0.682997\pi$
$564$	4.46410	0.187973
$565$	−51.1769	−2.15303
$566$	17.8564	0.750561
$567$	−1.00000	−0.0419961
$568$	8.19615	0.343903
$569$	20.4449	0.857093	0.428547	−	0.903520i	$-0.359026\pi$
$569$	20.4449	0.857093	0.428547	+	0.903520i	$0.359026\pi$
$570$	−2.73205	−0.114433
$571$	−34.9808	−1.46390	−0.731950	−	0.681359i	$-0.761389\pi$
$571$	−34.9808	−1.46390	−0.731950	+	0.681359i	$0.761389\pi$
$572$	0	0
$573$	−1.12436	−0.0469706
$574$	3.00000	0.125218
$575$	8.53590	0.355972
$576$	1.00000	0.0416667
$577$	−27.6603	−1.15151	−0.575756	−	0.817622i	$-0.695292\pi$
$577$	−27.6603	−1.15151	−0.575756	+	0.817622i	$0.695292\pi$
$578$	−16.9282	−0.704120
$579$	9.19615	0.382179
$580$	1.26795	0.0526487
$581$	10.1962	0.423008
$582$	−1.66025	−0.0688197
$583$	−12.1244	−0.502140
$584$	−1.46410	−0.0605850
$585$	0	0
$586$	30.9282	1.27763
$587$	−29.6603	−1.22421	−0.612105	−	0.790777i	$-0.709677\pi$
$587$	−29.6603	−1.22421	−0.612105	+	0.790777i	$0.709677\pi$
$588$	1.00000	0.0412393
$589$	−8.19615	−0.337717
$590$	−35.3205	−1.45412
$591$	−9.33975	−0.384186
$592$	3.26795	0.134312
$593$	6.46410	0.265449	0.132724	−	0.991153i	$-0.457627\pi$
$593$	6.46410	0.265449	0.132724	+	0.991153i	$0.457627\pi$
$594$	−1.73205	−0.0710669
$595$	0.732051	0.0300112
$596$	−13.8564	−0.567581
$597$	−5.80385	−0.237536
$598$	0	0
$599$	40.6410	1.66055	0.830273	−	0.557356i	$-0.188184\pi$
$599$	40.6410	1.66055	0.830273	+	0.557356i	$0.188184\pi$
$600$	2.46410	0.100597
$601$	−19.2679	−0.785956	−0.392978	−	0.919548i	$-0.628555\pi$
$601$	−19.2679	−0.785956	−0.392978	+	0.919548i	$0.628555\pi$
$602$	−6.73205	−0.274378
$603$	4.92820	0.200692
$604$	5.19615	0.211428
$605$	21.8564	0.888589
$606$	16.9282	0.687661
$607$	13.5167	0.548624	0.274312	−	0.961641i	$-0.411550\pi$
$607$	13.5167	0.548624	0.274312	+	0.961641i	$0.411550\pi$
$608$	1.00000	0.0405554
$609$	0.464102	0.0188063
$610$	14.1962	0.574785
$611$	0	0
$612$	0.267949	0.0108312
$613$	−4.00000	−0.161558	−0.0807792	−	0.996732i	$-0.525741\pi$
$613$	−4.00000	−0.161558	−0.0807792	+	0.996732i	$0.525741\pi$
$614$	−29.3923	−1.18618
$615$	8.19615	0.330501
$616$	1.73205	0.0697863
$617$	−8.19615	−0.329965	−0.164982	−	0.986297i	$-0.552757\pi$
$617$	−8.19615	−0.329965	−0.164982	+	0.986297i	$0.552757\pi$
$618$	11.2679	0.453263
$619$	−35.9282	−1.44408	−0.722038	−	0.691853i	$-0.756795\pi$
$619$	−35.9282	−1.44408	−0.722038	+	0.691853i	$0.756795\pi$
$620$	22.3923	0.899297
$621$	3.46410	0.139010
$622$	7.73205	0.310027
$623$	3.53590	0.141663
$624$	0	0
$625$	−31.2487	−1.24995
$626$	−31.5167	−1.25966
$627$	−1.73205	−0.0691714
$628$	−7.46410	−0.297850
$629$	0.875644	0.0349142
$630$	2.73205	0.108848
$631$	−27.1962	−1.08266	−0.541331	−	0.840810i	$-0.682079\pi$
$631$	−27.1962	−1.08266	−0.541331	+	0.840810i	$0.682079\pi$
$632$	15.9282	0.633590
$633$	26.0000	1.03341
$634$	−15.8564	−0.629738
$635$	23.3205	0.925446
$636$	7.00000	0.277568
$637$	0	0
$638$	0.803848	0.0318246
$639$	8.19615	0.324235
$640$	−2.73205	−0.107994
$641$	−31.1769	−1.23141	−0.615707	−	0.787975i	$-0.711130\pi$
$641$	−31.1769	−1.23141	−0.615707	+	0.787975i	$0.711130\pi$
$642$	−16.8564	−0.665269
$643$	5.14359	0.202844	0.101422	−	0.994844i	$-0.467661\pi$
$643$	5.14359	0.202844	0.101422	+	0.994844i	$0.467661\pi$
$644$	−3.46410	−0.136505
$645$	−18.3923	−0.724196
$646$	0.267949	0.0105423
$647$	−43.8372	−1.72342	−0.861708	−	0.507404i	$-0.830605\pi$
$647$	−43.8372	−1.72342	−0.861708	+	0.507404i	$0.830605\pi$
$648$	1.00000	0.0392837
$649$	−22.3923	−0.878975
$650$	0	0
$651$	8.19615	0.321233
$652$	0.732051	0.0286693
$653$	−8.71281	−0.340959	−0.170479	−	0.985361i	$-0.554532\pi$
$653$	−8.71281	−0.340959	−0.170479	+	0.985361i	$0.554532\pi$
$654$	1.26795	0.0495807
$655$	−37.8564	−1.47917
$656$	−3.00000	−0.117130
$657$	−1.46410	−0.0571200
$658$	−4.46410	−0.174029
$659$	39.3923	1.53451	0.767253	−	0.641344i	$-0.221623\pi$
$659$	39.3923	1.53451	0.767253	+	0.641344i	$0.221623\pi$
$660$	4.73205	0.184195
$661$	−8.39230	−0.326423	−0.163211	−	0.986591i	$-0.552185\pi$
$661$	−8.39230	−0.326423	−0.163211	+	0.986591i	$0.552185\pi$
$662$	0.143594	0.00558092
$663$	0	0
$664$	−10.1962	−0.395687
$665$	2.73205	0.105944
$666$	3.26795	0.126630
$667$	−1.60770	−0.0622502
$668$	13.8564	0.536120
$669$	−3.60770	−0.139482
$670$	−13.4641	−0.520164
$671$	9.00000	0.347441
$672$	−1.00000	−0.0385758
$673$	22.7128	0.875515	0.437757	−	0.899093i	$-0.355773\pi$
$673$	22.7128	0.875515	0.437757	+	0.899093i	$0.355773\pi$
$674$	19.0000	0.731853
$675$	2.46410	0.0948433
$676$	0	0
$677$	33.2679	1.27859	0.639296	−	0.768961i	$-0.279226\pi$
$677$	33.2679	1.27859	0.639296	+	0.768961i	$0.279226\pi$
$678$	18.7321	0.719400
$679$	1.66025	0.0637147
$680$	−0.732051	−0.0280729
$681$	−2.39230	−0.0916733
$682$	14.1962	0.543599
$683$	−50.3923	−1.92821	−0.964104	−	0.265525i	$-0.914455\pi$
$683$	−50.3923	−1.92821	−0.964104	+	0.265525i	$0.914455\pi$
$684$	1.00000	0.0382360
$685$	−17.4641	−0.667269
$686$	−1.00000	−0.0381802
$687$	6.07180	0.231653
$688$	6.73205	0.256657
$689$	0	0
$690$	−9.46410	−0.360292
$691$	11.7128	0.445576	0.222788	−	0.974867i	$-0.428484\pi$
$691$	11.7128	0.445576	0.222788	+	0.974867i	$0.428484\pi$
$692$	15.1244	0.574942
$693$	1.73205	0.0657952
$694$	−15.3923	−0.584284
$695$	53.5167	2.03000
$696$	−0.464102	−0.0175917
$697$	−0.803848	−0.0304479
$698$	31.7128	1.20035
$699$	15.1244	0.572056
$700$	−2.46410	−0.0931343
$701$	28.8564	1.08989	0.544946	−	0.838471i	$-0.316550\pi$
$701$	28.8564	1.08989	0.544946	+	0.838471i	$0.316550\pi$
$702$	0	0
$703$	3.26795	0.123253
$704$	−1.73205	−0.0652791
$705$	−12.1962	−0.459334
$706$	2.53590	0.0954398
$707$	−16.9282	−0.636651
$708$	12.9282	0.485872
$709$	−6.05256	−0.227309	−0.113654	−	0.993520i	$-0.536256\pi$
$709$	−6.05256	−0.227309	−0.113654	+	0.993520i	$0.536256\pi$
$710$	−22.3923	−0.840368
$711$	15.9282	0.597354
$712$	−3.53590	−0.132513
$713$	−28.3923	−1.06330
$714$	−0.267949	−0.0100277
$715$	0	0
$716$	4.53590	0.169514
$717$	−2.73205	−0.102030
$718$	14.1962	0.529796
$719$	−18.5167	−0.690555	−0.345277	−	0.938501i	$-0.612215\pi$
$719$	−18.5167	−0.690555	−0.345277	+	0.938501i	$0.612215\pi$
$720$	−2.73205	−0.101818
$721$	−11.2679	−0.419640
$722$	−18.0000	−0.669891
$723$	8.00000	0.297523
$724$	14.6603	0.544844
$725$	−1.14359	−0.0424720
$726$	−8.00000	−0.296908
$727$	15.3205	0.568206	0.284103	−	0.958794i	$-0.408304\pi$
$727$	15.3205	0.568206	0.284103	+	0.958794i	$0.408304\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	4.00000	0.148047
$731$	1.80385	0.0667177
$732$	−5.19615	−0.192055
$733$	14.1769	0.523636	0.261818	−	0.965117i	$-0.415678\pi$
$733$	14.1769	0.523636	0.261818	+	0.965117i	$0.415678\pi$
$734$	−9.32051	−0.344026
$735$	−2.73205	−0.100773
$736$	3.46410	0.127688
$737$	−8.53590	−0.314424
$738$	−3.00000	−0.110432
$739$	−47.1769	−1.73543	−0.867715	−	0.497061i	$-0.834412\pi$
$739$	−47.1769	−1.73543	−0.867715	+	0.497061i	$0.834412\pi$
$740$	−8.92820	−0.328207
$741$	0	0
$742$	−7.00000	−0.256978
$743$	−24.0526	−0.882403	−0.441201	−	0.897408i	$-0.645448\pi$
$743$	−24.0526	−0.882403	−0.441201	+	0.897408i	$0.645448\pi$
$744$	−8.19615	−0.300486
$745$	37.8564	1.38695
$746$	−7.66025	−0.280462
$747$	−10.1962	−0.373058
$748$	−0.464102	−0.0169692
$749$	16.8564	0.615920
$750$	6.92820	0.252982
$751$	−46.8564	−1.70981	−0.854907	−	0.518781i	$-0.826386\pi$
$751$	−46.8564	−1.70981	−0.854907	+	0.518781i	$0.826386\pi$
$752$	4.46410	0.162789
$753$	−11.1244	−0.405394
$754$	0	0
$755$	−14.1962	−0.516651
$756$	−1.00000	−0.0363696
$757$	30.5885	1.11176	0.555878	−	0.831264i	$-0.312382\pi$
$757$	30.5885	1.11176	0.555878	+	0.831264i	$0.312382\pi$
$758$	30.4449	1.10581
$759$	−6.00000	−0.217786
$760$	−2.73205	−0.0991019
$761$	19.3205	0.700368	0.350184	−	0.936681i	$-0.386119\pi$
$761$	19.3205	0.700368	0.350184	+	0.936681i	$0.386119\pi$
$762$	−8.53590	−0.309223
$763$	−1.26795	−0.0459028
$764$	−1.12436	−0.0406778
$765$	−0.732051	−0.0264674
$766$	−12.4641	−0.450346
$767$	0	0
$768$	1.00000	0.0360844
$769$	44.3013	1.59754	0.798772	−	0.601633i	$-0.205483\pi$
$769$	44.3013	1.59754	0.798772	+	0.601633i	$0.205483\pi$
$770$	−4.73205	−0.170531
$771$	3.33975	0.120278
$772$	9.19615	0.330977
$773$	15.1769	0.545876	0.272938	−	0.962032i	$-0.412005\pi$
$773$	15.1769	0.545876	0.272938	+	0.962032i	$0.412005\pi$
$774$	6.73205	0.241979
$775$	−20.1962	−0.725467
$776$	−1.66025	−0.0595996
$777$	−3.26795	−0.117237
$778$	−12.3923	−0.444286
$779$	−3.00000	−0.107486
$780$	0	0
$781$	−14.1962	−0.507978
$782$	0.928203	0.0331925
$783$	−0.464102	−0.0165856
$784$	1.00000	0.0357143
$785$	20.3923	0.727833
$786$	13.8564	0.494242
$787$	−38.3205	−1.36598	−0.682989	−	0.730428i	$-0.739320\pi$
$787$	−38.3205	−1.36598	−0.682989	+	0.730428i	$0.739320\pi$
$788$	−9.33975	−0.332715
$789$	9.12436	0.324836
$790$	−43.5167	−1.54825
$791$	−18.7321	−0.666035
$792$	−1.73205	−0.0615457
$793$	0	0
$794$	−21.9282	−0.778203
$795$	−19.1244	−0.678271
$796$	−5.80385	−0.205712
$797$	−27.1244	−0.960794	−0.480397	−	0.877051i	$-0.659507\pi$
$797$	−27.1244	−0.960794	−0.480397	+	0.877051i	$0.659507\pi$
$798$	−1.00000	−0.0353996
$799$	1.19615	0.0423168
$800$	2.46410	0.0871191
$801$	−3.53590	−0.124935
$802$	2.78461	0.0983280
$803$	2.53590	0.0894899
$804$	4.92820	0.173804
$805$	9.46410	0.333566
$806$	0	0
$807$	17.8564	0.628575
$808$	16.9282	0.595532
$809$	52.4449	1.84386	0.921932	−	0.387353i	$-0.126610\pi$
$809$	52.4449	1.84386	0.921932	+	0.387353i	$0.126610\pi$
$810$	−2.73205	−0.0959945
$811$	−31.4641	−1.10485	−0.552427	−	0.833561i	$-0.686298\pi$
$811$	−31.4641	−1.10485	−0.552427	+	0.833561i	$0.686298\pi$
$812$	0.464102	0.0162868
$813$	10.0526	0.352559
$814$	−5.66025	−0.198392
$815$	−2.00000	−0.0700569
$816$	0.267949	0.00938010
$817$	6.73205	0.235525
$818$	−35.2679	−1.23311
$819$	0	0
$820$	8.19615	0.286222
$821$	−27.8372	−0.971524	−0.485762	−	0.874091i	$-0.661458\pi$
$821$	−27.8372	−0.971524	−0.485762	+	0.874091i	$0.661458\pi$
$822$	6.39230	0.222957
$823$	34.7846	1.21252	0.606258	−	0.795268i	$-0.292670\pi$
$823$	34.7846	1.21252	0.606258	+	0.795268i	$0.292670\pi$
$824$	11.2679	0.392538
$825$	−4.26795	−0.148591
$826$	−12.9282	−0.449830
$827$	−27.3205	−0.950027	−0.475014	−	0.879978i	$-0.657557\pi$
$827$	−27.3205	−0.950027	−0.475014	+	0.879978i	$0.657557\pi$
$828$	3.46410	0.120386
$829$	−34.6603	−1.20380	−0.601900	−	0.798571i	$-0.705590\pi$
$829$	−34.6603	−1.20380	−0.601900	+	0.798571i	$0.705590\pi$
$830$	27.8564	0.966910
$831$	−25.3205	−0.878359
$832$	0	0
$833$	0.267949	0.00928389
$834$	−19.5885	−0.678293
$835$	−37.8564	−1.31007
$836$	−1.73205	−0.0599042
$837$	−8.19615	−0.283300
$838$	−2.73205	−0.0943771
$839$	−42.1051	−1.45363	−0.726815	−	0.686833i	$-0.759000\pi$
$839$	−42.1051	−1.45363	−0.726815	+	0.686833i	$0.759000\pi$
$840$	2.73205	0.0942647
$841$	−28.7846	−0.992573
$842$	1.60770	0.0554048
$843$	17.6603	0.608251
$844$	26.0000	0.894957
$845$	0	0
$846$	4.46410	0.153479
$847$	8.00000	0.274883
$848$	7.00000	0.240381
$849$	17.8564	0.612830
$850$	0.660254	0.0226465
$851$	11.3205	0.388062
$852$	8.19615	0.280796
$853$	−5.92820	−0.202978	−0.101489	−	0.994837i	$-0.532361\pi$
$853$	−5.92820	−0.202978	−0.101489	+	0.994837i	$0.532361\pi$
$854$	5.19615	0.177809
$855$	−2.73205	−0.0934342
$856$	−16.8564	−0.576140
$857$	−39.4641	−1.34807	−0.674034	−	0.738700i	$-0.735440\pi$
$857$	−39.4641	−1.34807	−0.674034	+	0.738700i	$0.735440\pi$
$858$	0	0
$859$	−50.7654	−1.73209	−0.866046	−	0.499964i	$-0.833346\pi$
$859$	−50.7654	−1.73209	−0.866046	+	0.499964i	$0.833346\pi$
$860$	−18.3923	−0.627172
$861$	3.00000	0.102240
$862$	3.80385	0.129560
$863$	16.9282	0.576243	0.288121	−	0.957594i	$-0.406969\pi$
$863$	16.9282	0.576243	0.288121	+	0.957594i	$0.406969\pi$
$864$	1.00000	0.0340207
$865$	−41.3205	−1.40494
$866$	−40.9282	−1.39080
$867$	−16.9282	−0.574912
$868$	8.19615	0.278196
$869$	−27.5885	−0.935874
$870$	1.26795	0.0429875
$871$	0	0
$872$	1.26795	0.0429382
$873$	−1.66025	−0.0561911
$874$	3.46410	0.117175
$875$	−6.92820	−0.234216
$876$	−1.46410	−0.0494674
$877$	26.7321	0.902677	0.451339	−	0.892353i	$-0.350947\pi$
$877$	26.7321	0.902677	0.451339	+	0.892353i	$0.350947\pi$
$878$	37.1769	1.25466
$879$	30.9282	1.04318
$880$	4.73205	0.159517
$881$	9.07180	0.305637	0.152818	−	0.988254i	$-0.451165\pi$
$881$	9.07180	0.305637	0.152818	+	0.988254i	$0.451165\pi$
$882$	1.00000	0.0336718
$883$	30.0526	1.01135	0.505675	−	0.862724i	$-0.331244\pi$
$883$	30.0526	1.01135	0.505675	+	0.862724i	$0.331244\pi$
$884$	0	0
$885$	−35.3205	−1.18729
$886$	35.6410	1.19738
$887$	43.4449	1.45874	0.729368	−	0.684122i	$-0.239814\pi$
$887$	43.4449	1.45874	0.729368	+	0.684122i	$0.239814\pi$
$888$	3.26795	0.109665
$889$	8.53590	0.286285
$890$	9.66025	0.323812
$891$	−1.73205	−0.0580259
$892$	−3.60770	−0.120795
$893$	4.46410	0.149385
$894$	−13.8564	−0.463428
$895$	−12.3923	−0.414229
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	10.5885	0.353341
$899$	3.80385	0.126865
$900$	2.46410	0.0821367
$901$	1.87564	0.0624868
$902$	5.19615	0.173013
$903$	−6.73205	−0.224029
$904$	18.7321	0.623019
$905$	−40.0526	−1.33139
$906$	5.19615	0.172631
$907$	−22.3923	−0.743524	−0.371762	−	0.928328i	$-0.621246\pi$
$907$	−22.3923	−0.743524	−0.371762	+	0.928328i	$0.621246\pi$
$908$	−2.39230	−0.0793914
$909$	16.9282	0.561473
$910$	0	0
$911$	28.8372	0.955418	0.477709	−	0.878518i	$-0.341467\pi$
$911$	28.8372	0.955418	0.477709	+	0.878518i	$0.341467\pi$
$912$	1.00000	0.0331133
$913$	17.6603	0.584469
$914$	15.8564	0.524483
$915$	14.1962	0.469310
$916$	6.07180	0.200618
$917$	−13.8564	−0.457579
$918$	0.267949	0.00884364
$919$	5.14359	0.169671	0.0848357	−	0.996395i	$-0.472963\pi$
$919$	5.14359	0.169671	0.0848357	+	0.996395i	$0.472963\pi$
$920$	−9.46410	−0.312022
$921$	−29.3923	−0.968509
$922$	−13.0718	−0.430497
$923$	0	0
$924$	1.73205	0.0569803
$925$	8.05256	0.264767
$926$	9.73205	0.319815
$927$	11.2679	0.370088
$928$	−0.464102	−0.0152349
$929$	−32.3205	−1.06040	−0.530201	−	0.847872i	$-0.677883\pi$
$929$	−32.3205	−1.06040	−0.530201	+	0.847872i	$0.677883\pi$
$930$	22.3923	0.734273
$931$	1.00000	0.0327737
$932$	15.1244	0.495415
$933$	7.73205	0.253136
$934$	13.8564	0.453395
$935$	1.26795	0.0414664
$936$	0	0
$937$	14.9282	0.487683	0.243842	−	0.969815i	$-0.421592\pi$
$937$	14.9282	0.487683	0.243842	+	0.969815i	$0.421592\pi$
$938$	−4.92820	−0.160912
$939$	−31.5167	−1.02851
$940$	−12.1962	−0.397795
$941$	−32.3923	−1.05596	−0.527979	−	0.849257i	$-0.677050\pi$
$941$	−32.3923	−1.05596	−0.527979	+	0.849257i	$0.677050\pi$
$942$	−7.46410	−0.243194
$943$	−10.3923	−0.338420
$944$	12.9282	0.420777
$945$	2.73205	0.0888736
$946$	−11.6603	−0.379108
$947$	12.5167	0.406737	0.203368	−	0.979102i	$-0.434811\pi$
$947$	12.5167	0.406737	0.203368	+	0.979102i	$0.434811\pi$
$948$	15.9282	0.517324
$949$	0	0
$950$	2.46410	0.0799460
$951$	−15.8564	−0.514179
$952$	−0.267949	−0.00868428
$953$	23.8038	0.771082	0.385541	−	0.922691i	$-0.374015\pi$
$953$	23.8038	0.771082	0.385541	+	0.922691i	$0.374015\pi$
$954$	7.00000	0.226633
$955$	3.07180	0.0994010
$956$	−2.73205	−0.0883608
$957$	0.803848	0.0259847
$958$	−25.5359	−0.825027
$959$	−6.39230	−0.206418
$960$	−2.73205	−0.0881766
$961$	36.1769	1.16700
$962$	0	0
$963$	−16.8564	−0.543190
$964$	8.00000	0.257663
$965$	−25.1244	−0.808782
$966$	−3.46410	−0.111456
$967$	55.7128	1.79160	0.895802	−	0.444454i	$-0.146602\pi$
$967$	55.7128	1.79160	0.895802	+	0.444454i	$0.146602\pi$
$968$	−8.00000	−0.257130
$969$	0.267949	0.00860777
$970$	4.53590	0.145639
$971$	22.1051	0.709387	0.354693	−	0.934983i	$-0.384585\pi$
$971$	22.1051	0.709387	0.354693	+	0.934983i	$0.384585\pi$
$972$	1.00000	0.0320750
$973$	19.5885	0.627977
$974$	0.660254	0.0211559
$975$	0	0
$976$	−5.19615	−0.166325
$977$	−4.39230	−0.140522	−0.0702611	−	0.997529i	$-0.522383\pi$
$977$	−4.39230	−0.140522	−0.0702611	+	0.997529i	$0.522383\pi$
$978$	0.732051	0.0234084
$979$	6.12436	0.195735
$980$	−2.73205	−0.0872722
$981$	1.26795	0.0404825
$982$	28.5359	0.910617
$983$	8.14359	0.259740	0.129870	−	0.991531i	$-0.458544\pi$
$983$	8.14359	0.259740	0.129870	+	0.991531i	$0.458544\pi$
$984$	−3.00000	−0.0956365
$985$	25.5167	0.813028
$986$	−0.124356	−0.00396029
$987$	−4.46410	−0.142094
$988$	0	0
$989$	23.3205	0.741549
$990$	4.73205	0.150394
$991$	−10.7513	−0.341526	−0.170763	−	0.985312i	$-0.554623\pi$
$991$	−10.7513	−0.341526	−0.170763	+	0.985312i	$0.554623\pi$
$992$	−8.19615	−0.260228
$993$	0.143594	0.00455680
$994$	−8.19615	−0.259966
$995$	15.8564	0.502682
$996$	−10.1962	−0.323077
$997$	17.0526	0.540060	0.270030	−	0.962852i	$-0.412966\pi$
$997$	17.0526	0.540060	0.270030	+	0.962852i	$0.412966\pi$
$998$	33.5167	1.06095
$999$	3.26795	0.103393

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.a.43.2	✓	4	13.2	odd	12
546.2.s.a.127.2	yes	4	13.7	odd	12
1638.2.bj.b.127.1		4	39.20	even	12
1638.2.bj.b.1135.1		4	39.2	even	12
7098.2.a.bp.1.2		2	13.12	even	2
7098.2.a.bx.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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.73205 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.73205 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.73205 q^{10} -1.73205 q^{11} +1.00000 q^{12} -1.00000 q^{14} -2.73205 q^{15} +1.00000 q^{16} +0.267949 q^{17} +1.00000 q^{18} +1.00000 q^{19} -2.73205 q^{20} -1.00000 q^{21} -1.73205 q^{22} +3.46410 q^{23} +1.00000 q^{24} +2.46410 q^{25} +1.00000 q^{27} -1.00000 q^{28} -0.464102 q^{29} -2.73205 q^{30} -8.19615 q^{31} +1.00000 q^{32} -1.73205 q^{33} +0.267949 q^{34} +2.73205 q^{35} +1.00000 q^{36} +3.26795 q^{37} +1.00000 q^{38} -2.73205 q^{40} -3.00000 q^{41} -1.00000 q^{42} +6.73205 q^{43} -1.73205 q^{44} -2.73205 q^{45} +3.46410 q^{46} +4.46410 q^{47} +1.00000 q^{48} +1.00000 q^{49} +2.46410 q^{50} +0.267949 q^{51} +7.00000 q^{53} +1.00000 q^{54} +4.73205 q^{55} -1.00000 q^{56} +1.00000 q^{57} -0.464102 q^{58} +12.9282 q^{59} -2.73205 q^{60} -5.19615 q^{61} -8.19615 q^{62} -1.00000 q^{63} +1.00000 q^{64} -1.73205 q^{66} +4.92820 q^{67} +0.267949 q^{68} +3.46410 q^{69} +2.73205 q^{70} +8.19615 q^{71} +1.00000 q^{72} -1.46410 q^{73} +3.26795 q^{74} +2.46410 q^{75} +1.00000 q^{76} +1.73205 q^{77} +15.9282 q^{79} -2.73205 q^{80} +1.00000 q^{81} -3.00000 q^{82} -10.1962 q^{83} -1.00000 q^{84} -0.732051 q^{85} +6.73205 q^{86} -0.464102 q^{87} -1.73205 q^{88} -3.53590 q^{89} -2.73205 q^{90} +3.46410 q^{92} -8.19615 q^{93} +4.46410 q^{94} -2.73205 q^{95} +1.00000 q^{96} -1.66025 q^{97} +1.00000 q^{98} -1.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{12} - 2 q^{14} - 2 q^{15} + 2 q^{16} + 4 q^{17} + 2 q^{18} + 2 q^{19} - 2 q^{20} - 2 q^{21} + 2 q^{24} - 2 q^{25} + 2 q^{27} - 2 q^{28} + 6 q^{29} - 2 q^{30} - 6 q^{31} + 2 q^{32} + 4 q^{34} + 2 q^{35} + 2 q^{36} + 10 q^{37} + 2 q^{38} - 2 q^{40} - 6 q^{41} - 2 q^{42} + 10 q^{43} - 2 q^{45} + 2 q^{47} + 2 q^{48} + 2 q^{49} - 2 q^{50} + 4 q^{51} + 14 q^{53} + 2 q^{54} + 6 q^{55} - 2 q^{56} + 2 q^{57} + 6 q^{58} + 12 q^{59} - 2 q^{60} - 6 q^{62} - 2 q^{63} + 2 q^{64} - 4 q^{67} + 4 q^{68} + 2 q^{70} + 6 q^{71} + 2 q^{72} + 4 q^{73} + 10 q^{74} - 2 q^{75} + 2 q^{76} + 18 q^{79} - 2 q^{80} + 2 q^{81} - 6 q^{82} - 10 q^{83} - 2 q^{84} + 2 q^{85} + 10 q^{86} + 6 q^{87} - 14 q^{89} - 2 q^{90} - 6 q^{93} + 2 q^{94} - 2 q^{95} + 2 q^{96} + 14 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^12 - 2 * q^14 - 2 * q^15 + 2 * q^16 + 4 * q^17 + 2 * q^18 + 2 * q^19 - 2 * q^20 - 2 * q^21 + 2 * q^24 - 2 * q^25 + 2 * q^27 - 2 * q^28 + 6 * q^29 - 2 * q^30 - 6 * q^31 + 2 * q^32 + 4 * q^34 + 2 * q^35 + 2 * q^36 + 10 * q^37 + 2 * q^38 - 2 * q^40 - 6 * q^41 - 2 * q^42 + 10 * q^43 - 2 * q^45 + 2 * q^47 + 2 * q^48 + 2 * q^49 - 2 * q^50 + 4 * q^51 + 14 * q^53 + 2 * q^54 + 6 * q^55 - 2 * q^56 + 2 * q^57 + 6 * q^58 + 12 * q^59 - 2 * q^60 - 6 * q^62 - 2 * q^63 + 2 * q^64 - 4 * q^67 + 4 * q^68 + 2 * q^70 + 6 * q^71 + 2 * q^72 + 4 * q^73 + 10 * q^74 - 2 * q^75 + 2 * q^76 + 18 * q^79 - 2 * q^80 + 2 * q^81 - 6 * q^82 - 10 * q^83 - 2 * q^84 + 2 * q^85 + 10 * q^86 + 6 * q^87 - 14 * q^89 - 2 * q^90 - 6 * q^93 + 2 * q^94 - 2 * q^95 + 2 * q^96 + 14 * q^97 + 2 * q^98

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