LMFDB - Embedded newform 7098.2.a.bp.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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.732051 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.732051 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.732051 q^{10} -1.73205 q^{11} +1.00000 q^{12} -1.00000 q^{14} -0.732051 q^{15} +1.00000 q^{16} +3.73205 q^{17} -1.00000 q^{18} -1.00000 q^{19} -0.732051 q^{20} +1.00000 q^{21} +1.73205 q^{22} -3.46410 q^{23} -1.00000 q^{24} -4.46410 q^{25} +1.00000 q^{27} +1.00000 q^{28} +6.46410 q^{29} +0.732051 q^{30} -2.19615 q^{31} -1.00000 q^{32} -1.73205 q^{33} -3.73205 q^{34} -0.732051 q^{35} +1.00000 q^{36} -6.73205 q^{37} +1.00000 q^{38} +0.732051 q^{40} +3.00000 q^{41} -1.00000 q^{42} +3.26795 q^{43} -1.73205 q^{44} -0.732051 q^{45} +3.46410 q^{46} +2.46410 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.46410 q^{50} +3.73205 q^{51} +7.00000 q^{53} -1.00000 q^{54} +1.26795 q^{55} -1.00000 q^{56} -1.00000 q^{57} -6.46410 q^{58} +0.928203 q^{59} -0.732051 q^{60} +5.19615 q^{61} +2.19615 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.73205 q^{66} +8.92820 q^{67} +3.73205 q^{68} -3.46410 q^{69} +0.732051 q^{70} +2.19615 q^{71} -1.00000 q^{72} -5.46410 q^{73} +6.73205 q^{74} -4.46410 q^{75} -1.00000 q^{76} -1.73205 q^{77} +2.07180 q^{79} -0.732051 q^{80} +1.00000 q^{81} -3.00000 q^{82} -0.196152 q^{83} +1.00000 q^{84} -2.73205 q^{85} -3.26795 q^{86} +6.46410 q^{87} +1.73205 q^{88} +10.4641 q^{89} +0.732051 q^{90} -3.46410 q^{92} -2.19615 q^{93} -2.46410 q^{94} +0.732051 q^{95} -1.00000 q^{96} -15.6603 q^{97} -1.00000 q^{98} -1.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.732051	−0.327383	−0.163692	−	0.986512i	$-0.552340\pi$
$5$	−0.732051	−0.327383	−0.163692	+	0.986512i	$0.552340\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.732051	0.231495
$11$	−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
$15$	−0.732051	−0.189015
$16$	1.00000	0.250000
$17$	3.73205	0.905155	0.452578	−	0.891725i	$-0.350505\pi$
$17$	3.73205	0.905155	0.452578	+	0.891725i	$0.350505\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−0.732051	−0.163692
$21$	1.00000	0.218218
$22$	1.73205	0.369274
$23$	−3.46410	−0.722315	−0.361158	−	0.932505i	$-0.617618\pi$
$23$	−3.46410	−0.722315	−0.361158	+	0.932505i	$0.617618\pi$
$24$	−1.00000	−0.204124
$25$	−4.46410	−0.892820
$26$	0	0
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	6.46410	1.20035	0.600177	−	0.799867i	$-0.295097\pi$
$29$	6.46410	1.20035	0.600177	+	0.799867i	$0.295097\pi$
$30$	0.732051	0.133654
$31$	−2.19615	−0.394441	−0.197220	−	0.980359i	$-0.563191\pi$
$31$	−2.19615	−0.394441	−0.197220	+	0.980359i	$0.563191\pi$
$32$	−1.00000	−0.176777
$33$	−1.73205	−0.301511
$34$	−3.73205	−0.640041
$35$	−0.732051	−0.123739
$36$	1.00000	0.166667
$37$	−6.73205	−1.10674	−0.553371	−	0.832935i	$-0.686659\pi$
$37$	−6.73205	−1.10674	−0.553371	+	0.832935i	$0.686659\pi$
$38$	1.00000	0.162221
$39$	0	0
$40$	0.732051	0.115747
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	−1.00000	−0.154303
$43$	3.26795	0.498358	0.249179	−	0.968458i	$-0.419839\pi$
$43$	3.26795	0.498358	0.249179	+	0.968458i	$0.419839\pi$
$44$	−1.73205	−0.261116
$45$	−0.732051	−0.109128
$46$	3.46410	0.510754
$47$	2.46410	0.359426	0.179713	−	0.983719i	$-0.442483\pi$
$47$	2.46410	0.359426	0.179713	+	0.983719i	$0.442483\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	4.46410	0.631319
$51$	3.73205	0.522592
$52$	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
$55$	1.26795	0.170970
$56$	−1.00000	−0.133631
$57$	−1.00000	−0.132453
$58$	−6.46410	−0.848778
$59$	0.928203	0.120842	0.0604209	−	0.998173i	$-0.480756\pi$
$59$	0.928203	0.120842	0.0604209	+	0.998173i	$0.480756\pi$
$60$	−0.732051	−0.0945074
$61$	5.19615	0.665299	0.332650	−	0.943051i	$-0.392057\pi$
$61$	5.19615	0.665299	0.332650	+	0.943051i	$0.392057\pi$
$62$	2.19615	0.278912
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	1.73205	0.213201
$67$	8.92820	1.09075	0.545377	−	0.838191i	$-0.316387\pi$
$67$	8.92820	1.09075	0.545377	+	0.838191i	$0.316387\pi$
$68$	3.73205	0.452578
$69$	−3.46410	−0.417029
$70$	0.732051	0.0874968
$71$	2.19615	0.260635	0.130318	−	0.991472i	$-0.458400\pi$
$71$	2.19615	0.260635	0.130318	+	0.991472i	$0.458400\pi$
$72$	−1.00000	−0.117851
$73$	−5.46410	−0.639525	−0.319762	−	0.947498i	$-0.603603\pi$
$73$	−5.46410	−0.639525	−0.319762	+	0.947498i	$0.603603\pi$
$74$	6.73205	0.782585
$75$	−4.46410	−0.515470
$76$	−1.00000	−0.114708
$77$	−1.73205	−0.197386
$78$	0	0
$79$	2.07180	0.233095	0.116548	−	0.993185i	$-0.462817\pi$
$79$	2.07180	0.233095	0.116548	+	0.993185i	$0.462817\pi$
$80$	−0.732051	−0.0818458
$81$	1.00000	0.111111
$82$	−3.00000	−0.331295
$83$	−0.196152	−0.0215305	−0.0107653	−	0.999942i	$-0.503427\pi$
$83$	−0.196152	−0.0215305	−0.0107653	+	0.999942i	$0.503427\pi$
$84$	1.00000	0.109109
$85$	−2.73205	−0.296333
$86$	−3.26795	−0.352392
$87$	6.46410	0.693024
$88$	1.73205	0.184637
$89$	10.4641	1.10919	0.554596	−	0.832120i	$-0.312873\pi$
$89$	10.4641	1.10919	0.554596	+	0.832120i	$0.312873\pi$
$90$	0.732051	0.0771649
$91$	0	0
$92$	−3.46410	−0.361158
$93$	−2.19615	−0.227730
$94$	−2.46410	−0.254153
$95$	0.732051	0.0751068
$96$	−1.00000	−0.102062
$97$	−15.6603	−1.59006	−0.795029	−	0.606571i	$-0.792544\pi$
$97$	−15.6603	−1.59006	−0.795029	+	0.606571i	$0.792544\pi$
$98$	−1.00000	−0.101015
$99$	−1.73205	−0.174078
$100$	−4.46410	−0.446410
$101$	3.07180	0.305655	0.152828	−	0.988253i	$-0.451162\pi$
$101$	3.07180	0.305655	0.152828	+	0.988253i	$0.451162\pi$
$102$	−3.73205	−0.369528
$103$	14.7321	1.45159	0.725796	−	0.687910i	$-0.241472\pi$
$103$	14.7321	1.45159	0.725796	+	0.687910i	$0.241472\pi$
$104$	0	0
$105$	−0.732051	−0.0714408
$106$	−7.00000	−0.679900
$107$	10.8564	1.04953	0.524764	−	0.851248i	$-0.324153\pi$
$107$	10.8564	1.04953	0.524764	+	0.851248i	$0.324153\pi$
$108$	1.00000	0.0962250
$109$	−4.73205	−0.453248	−0.226624	−	0.973982i	$-0.572769\pi$
$109$	−4.73205	−0.453248	−0.226624	+	0.973982i	$0.572769\pi$
$110$	−1.26795	−0.120894
$111$	−6.73205	−0.638978
$112$	1.00000	0.0944911
$113$	15.2679	1.43629	0.718144	−	0.695895i	$-0.244992\pi$
$113$	15.2679	1.43629	0.718144	+	0.695895i	$0.244992\pi$
$114$	1.00000	0.0936586
$115$	2.53590	0.236474
$116$	6.46410	0.600177
$117$	0	0
$118$	−0.928203	−0.0854480
$119$	3.73205	0.342117
$120$	0.732051	0.0668268
$121$	−8.00000	−0.727273
$122$	−5.19615	−0.470438
$123$	3.00000	0.270501
$124$	−2.19615	−0.197220
$125$	6.92820	0.619677
$126$	−1.00000	−0.0890871
$127$	−15.4641	−1.37222	−0.686109	−	0.727499i	$-0.740683\pi$
$127$	−15.4641	−1.37222	−0.686109	+	0.727499i	$0.740683\pi$
$128$	−1.00000	−0.0883883
$129$	3.26795	0.287727
$130$	0	0
$131$	−13.8564	−1.21064	−0.605320	−	0.795982i	$-0.706955\pi$
$131$	−13.8564	−1.21064	−0.605320	+	0.795982i	$0.706955\pi$
$132$	−1.73205	−0.150756
$133$	−1.00000	−0.0867110
$134$	−8.92820	−0.771279
$135$	−0.732051	−0.0630049
$136$	−3.73205	−0.320021
$137$	14.3923	1.22962	0.614809	−	0.788676i	$-0.289233\pi$
$137$	14.3923	1.22962	0.614809	+	0.788676i	$0.289233\pi$
$138$	3.46410	0.294884
$139$	11.5885	0.982920	0.491460	−	0.870900i	$-0.336463\pi$
$139$	11.5885	0.982920	0.491460	+	0.870900i	$0.336463\pi$
$140$	−0.732051	−0.0618696
$141$	2.46410	0.207515
$142$	−2.19615	−0.184297
$143$	0	0
$144$	1.00000	0.0833333
$145$	−4.73205	−0.392975
$146$	5.46410	0.452212
$147$	1.00000	0.0824786
$148$	−6.73205	−0.553371
$149$	−13.8564	−1.13516	−0.567581	−	0.823318i	$-0.692120\pi$
$149$	−13.8564	−1.13516	−0.567581	+	0.823318i	$0.692120\pi$
$150$	4.46410	0.364492
$151$	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
$153$	3.73205	0.301718
$154$	1.73205	0.139573
$155$	1.60770	0.129133
$156$	0	0
$157$	−0.535898	−0.0427693	−0.0213847	−	0.999771i	$-0.506807\pi$
$157$	−0.535898	−0.0427693	−0.0213847	+	0.999771i	$0.506807\pi$
$158$	−2.07180	−0.164823
$159$	7.00000	0.555136
$160$	0.732051	0.0578737
$161$	−3.46410	−0.273009
$162$	−1.00000	−0.0785674
$163$	2.73205	0.213991	0.106995	−	0.994260i	$-0.465877\pi$
$163$	2.73205	0.213991	0.106995	+	0.994260i	$0.465877\pi$
$164$	3.00000	0.234261
$165$	1.26795	0.0987097
$166$	0.196152	0.0152244
$167$	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
$170$	2.73205	0.209539
$171$	−1.00000	−0.0764719
$172$	3.26795	0.249179
$173$	−9.12436	−0.693712	−0.346856	−	0.937918i	$-0.612751\pi$
$173$	−9.12436	−0.693712	−0.346856	+	0.937918i	$0.612751\pi$
$174$	−6.46410	−0.490042
$175$	−4.46410	−0.337454
$176$	−1.73205	−0.130558
$177$	0.928203	0.0697680
$178$	−10.4641	−0.784318
$179$	11.4641	0.856867	0.428434	−	0.903573i	$-0.359066\pi$
$179$	11.4641	0.856867	0.428434	+	0.903573i	$0.359066\pi$
$180$	−0.732051	−0.0545638
$181$	−2.66025	−0.197735	−0.0988676	−	0.995101i	$-0.531522\pi$
$181$	−2.66025	−0.197735	−0.0988676	+	0.995101i	$0.531522\pi$
$182$	0	0
$183$	5.19615	0.384111
$184$	3.46410	0.255377
$185$	4.92820	0.362329
$186$	2.19615	0.161030
$187$	−6.46410	−0.472702
$188$	2.46410	0.179713
$189$	1.00000	0.0727393
$190$	−0.732051	−0.0531085
$191$	23.1244	1.67322	0.836610	−	0.547799i	$-0.184534\pi$
$191$	23.1244	1.67322	0.836610	+	0.547799i	$0.184534\pi$
$192$	1.00000	0.0721688
$193$	1.19615	0.0861009	0.0430505	−	0.999073i	$-0.486292\pi$
$193$	1.19615	0.0861009	0.0430505	+	0.999073i	$0.486292\pi$
$194$	15.6603	1.12434
$195$	0	0
$196$	1.00000	0.0714286
$197$	26.6603	1.89946	0.949732	−	0.313063i	$-0.101355\pi$
$197$	26.6603	1.89946	0.949732	+	0.313063i	$0.101355\pi$
$198$	1.73205	0.123091
$199$	−16.1962	−1.14811	−0.574057	−	0.818815i	$-0.694631\pi$
$199$	−16.1962	−1.14811	−0.574057	+	0.818815i	$0.694631\pi$
$200$	4.46410	0.315660
$201$	8.92820	0.629747
$202$	−3.07180	−0.216131
$203$	6.46410	0.453691
$204$	3.73205	0.261296
$205$	−2.19615	−0.153386
$206$	−14.7321	−1.02643
$207$	−3.46410	−0.240772
$208$	0	0
$209$	1.73205	0.119808
$210$	0.732051	0.0505163
$211$	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
$213$	2.19615	0.150478
$214$	−10.8564	−0.742129
$215$	−2.39230	−0.163154
$216$	−1.00000	−0.0680414
$217$	−2.19615	−0.149085
$218$	4.73205	0.320495
$219$	−5.46410	−0.369230
$220$	1.26795	0.0854851
$221$	0	0
$222$	6.73205	0.451826
$223$	24.3923	1.63343	0.816715	−	0.577042i	$-0.195793\pi$
$223$	24.3923	1.63343	0.816715	+	0.577042i	$0.195793\pi$
$224$	−1.00000	−0.0668153
$225$	−4.46410	−0.297607
$226$	−15.2679	−1.01561
$227$	−18.3923	−1.22074	−0.610370	−	0.792116i	$-0.708979\pi$
$227$	−18.3923	−1.22074	−0.610370	+	0.792116i	$0.708979\pi$
$228$	−1.00000	−0.0662266
$229$	−19.9282	−1.31689	−0.658446	−	0.752628i	$-0.728786\pi$
$229$	−19.9282	−1.31689	−0.658446	+	0.752628i	$0.728786\pi$
$230$	−2.53590	−0.167212
$231$	−1.73205	−0.113961
$232$	−6.46410	−0.424389
$233$	−9.12436	−0.597756	−0.298878	−	0.954291i	$-0.596612\pi$
$233$	−9.12436	−0.597756	−0.298878	+	0.954291i	$0.596612\pi$
$234$	0	0
$235$	−1.80385	−0.117670
$236$	0.928203	0.0604209
$237$	2.07180	0.134578
$238$	−3.73205	−0.241913
$239$	−0.732051	−0.0473524	−0.0236762	−	0.999720i	$-0.507537\pi$
$239$	−0.732051	−0.0473524	−0.0236762	+	0.999720i	$0.507537\pi$
$240$	−0.732051	−0.0472537
$241$	−8.00000	−0.515325	−0.257663	−	0.966235i	$-0.582952\pi$
$241$	−8.00000	−0.515325	−0.257663	+	0.966235i	$0.582952\pi$
$242$	8.00000	0.514259
$243$	1.00000	0.0641500
$244$	5.19615	0.332650
$245$	−0.732051	−0.0467690
$246$	−3.00000	−0.191273
$247$	0	0
$248$	2.19615	0.139456
$249$	−0.196152	−0.0124307
$250$	−6.92820	−0.438178
$251$	13.1244	0.828402	0.414201	−	0.910185i	$-0.364061\pi$
$251$	13.1244	0.828402	0.414201	+	0.910185i	$0.364061\pi$
$252$	1.00000	0.0629941
$253$	6.00000	0.377217
$254$	15.4641	0.970304
$255$	−2.73205	−0.171088
$256$	1.00000	0.0625000
$257$	20.6603	1.28875	0.644376	−	0.764709i	$-0.277117\pi$
$257$	20.6603	1.28875	0.644376	+	0.764709i	$0.277117\pi$
$258$	−3.26795	−0.203454
$259$	−6.73205	−0.418309
$260$	0	0
$261$	6.46410	0.400118
$262$	13.8564	0.856052
$263$	−15.1244	−0.932608	−0.466304	−	0.884625i	$-0.654415\pi$
$263$	−15.1244	−0.932608	−0.466304	+	0.884625i	$0.654415\pi$
$264$	1.73205	0.106600
$265$	−5.12436	−0.314787
$266$	1.00000	0.0613139
$267$	10.4641	0.640393
$268$	8.92820	0.545377
$269$	−9.85641	−0.600956	−0.300478	−	0.953789i	$-0.597146\pi$
$269$	−9.85641	−0.600956	−0.300478	+	0.953789i	$0.597146\pi$
$270$	0.732051	0.0445512
$271$	28.0526	1.70407	0.852036	−	0.523484i	$-0.175368\pi$
$271$	28.0526	1.70407	0.852036	+	0.523484i	$0.175368\pi$
$272$	3.73205	0.226289
$273$	0	0
$274$	−14.3923	−0.869471
$275$	7.73205	0.466260
$276$	−3.46410	−0.208514
$277$	9.32051	0.560015	0.280008	−	0.959998i	$-0.409663\pi$
$277$	9.32051	0.560015	0.280008	+	0.959998i	$0.409663\pi$
$278$	−11.5885	−0.695029
$279$	−2.19615	−0.131480
$280$	0.732051	0.0437484
$281$	−0.339746	−0.0202675	−0.0101338	−	0.999949i	$-0.503226\pi$
$281$	−0.339746	−0.0202675	−0.0101338	+	0.999949i	$0.503226\pi$
$282$	−2.46410	−0.146735
$283$	−9.85641	−0.585903	−0.292951	−	0.956127i	$-0.594637\pi$
$283$	−9.85641	−0.585903	−0.292951	+	0.956127i	$0.594637\pi$
$284$	2.19615	0.130318
$285$	0.732051	0.0433629
$286$	0	0
$287$	3.00000	0.177084
$288$	−1.00000	−0.0589256
$289$	−3.07180	−0.180694
$290$	4.73205	0.277876
$291$	−15.6603	−0.918020
$292$	−5.46410	−0.319762
$293$	−17.0718	−0.997345	−0.498673	−	0.866790i	$-0.666179\pi$
$293$	−17.0718	−0.997345	−0.498673	+	0.866790i	$0.666179\pi$
$294$	−1.00000	−0.0583212
$295$	−0.679492	−0.0395615
$296$	6.73205	0.391293
$297$	−1.73205	−0.100504
$298$	13.8564	0.802680
$299$	0	0
$300$	−4.46410	−0.257735
$301$	3.26795	0.188361
$302$	−5.19615	−0.299005
$303$	3.07180	0.176470
$304$	−1.00000	−0.0573539
$305$	−3.80385	−0.217808
$306$	−3.73205	−0.213347
$307$	8.60770	0.491267	0.245634	−	0.969363i	$-0.421004\pi$
$307$	8.60770	0.491267	0.245634	+	0.969363i	$0.421004\pi$
$308$	−1.73205	−0.0986928
$309$	14.7321	0.838077
$310$	−1.60770	−0.0913109
$311$	4.26795	0.242013	0.121007	−	0.992652i	$-0.461388\pi$
$311$	4.26795	0.242013	0.121007	+	0.992652i	$0.461388\pi$
$312$	0	0
$313$	13.5167	0.764007	0.382003	−	0.924161i	$-0.375234\pi$
$313$	13.5167	0.764007	0.382003	+	0.924161i	$0.375234\pi$
$314$	0.535898	0.0302425
$315$	−0.732051	−0.0412464
$316$	2.07180	0.116548
$317$	−11.8564	−0.665922	−0.332961	−	0.942941i	$-0.608048\pi$
$317$	−11.8564	−0.665922	−0.332961	+	0.942941i	$0.608048\pi$
$318$	−7.00000	−0.392541
$319$	−11.1962	−0.626864
$320$	−0.732051	−0.0409229
$321$	10.8564	0.605946
$322$	3.46410	0.193047
$323$	−3.73205	−0.207657
$324$	1.00000	0.0555556
$325$	0	0
$326$	−2.73205	−0.151314
$327$	−4.73205	−0.261683
$328$	−3.00000	−0.165647
$329$	2.46410	0.135850
$330$	−1.26795	−0.0697983
$331$	−27.8564	−1.53113	−0.765563	−	0.643361i	$-0.777540\pi$
$331$	−27.8564	−1.53113	−0.765563	+	0.643361i	$0.777540\pi$
$332$	−0.196152	−0.0107653
$333$	−6.73205	−0.368914
$334$	−13.8564	−0.758189
$335$	−6.53590	−0.357094
$336$	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
$339$	15.2679	0.829241
$340$	−2.73205	−0.148166
$341$	3.80385	0.205990
$342$	1.00000	0.0540738
$343$	1.00000	0.0539949
$344$	−3.26795	−0.176196
$345$	2.53590	0.136528
$346$	9.12436	0.490528
$347$	5.39230	0.289474	0.144737	−	0.989470i	$-0.453766\pi$
$347$	5.39230	0.289474	0.144737	+	0.989470i	$0.453766\pi$
$348$	6.46410	0.346512
$349$	23.7128	1.26932	0.634659	−	0.772792i	$-0.281141\pi$
$349$	23.7128	1.26932	0.634659	+	0.772792i	$0.281141\pi$
$350$	4.46410	0.238616
$351$	0	0
$352$	1.73205	0.0923186
$353$	−9.46410	−0.503723	−0.251862	−	0.967763i	$-0.581043\pi$
$353$	−9.46410	−0.503723	−0.251862	+	0.967763i	$0.581043\pi$
$354$	−0.928203	−0.0493334
$355$	−1.60770	−0.0853276
$356$	10.4641	0.554596
$357$	3.73205	0.197521
$358$	−11.4641	−0.605897
$359$	−3.80385	−0.200759	−0.100380	−	0.994949i	$-0.532006\pi$
$359$	−3.80385	−0.200759	−0.100380	+	0.994949i	$0.532006\pi$
$360$	0.732051	0.0385825
$361$	−18.0000	−0.947368
$362$	2.66025	0.139820
$363$	−8.00000	−0.419891
$364$	0	0
$365$	4.00000	0.209370
$366$	−5.19615	−0.271607
$367$	25.3205	1.32172	0.660860	−	0.750509i	$-0.270192\pi$
$367$	25.3205	1.32172	0.660860	+	0.750509i	$0.270192\pi$
$368$	−3.46410	−0.180579
$369$	3.00000	0.156174
$370$	−4.92820	−0.256205
$371$	7.00000	0.363422
$372$	−2.19615	−0.113865
$373$	9.66025	0.500189	0.250094	−	0.968221i	$-0.419538\pi$
$373$	9.66025	0.500189	0.250094	+	0.968221i	$0.419538\pi$
$374$	6.46410	0.334251
$375$	6.92820	0.357771
$376$	−2.46410	−0.127076
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	28.4449	1.46111	0.730557	−	0.682851i	$-0.239260\pi$
$379$	28.4449	1.46111	0.730557	+	0.682851i	$0.239260\pi$
$380$	0.732051	0.0375534
$381$	−15.4641	−0.792250
$382$	−23.1244	−1.18314
$383$	5.53590	0.282871	0.141436	−	0.989947i	$-0.454828\pi$
$383$	5.53590	0.282871	0.141436	+	0.989947i	$0.454828\pi$
$384$	−1.00000	−0.0510310
$385$	1.26795	0.0646207
$386$	−1.19615	−0.0608826
$387$	3.26795	0.166119
$388$	−15.6603	−0.795029
$389$	8.39230	0.425507	0.212753	−	0.977106i	$-0.431757\pi$
$389$	8.39230	0.425507	0.212753	+	0.977106i	$0.431757\pi$
$390$	0	0
$391$	−12.9282	−0.653807
$392$	−1.00000	−0.0505076
$393$	−13.8564	−0.698963
$394$	−26.6603	−1.34312
$395$	−1.51666	−0.0763115
$396$	−1.73205	−0.0870388
$397$	8.07180	0.405112	0.202556	−	0.979271i	$-0.435075\pi$
$397$	8.07180	0.405112	0.202556	+	0.979271i	$0.435075\pi$
$398$	16.1962	0.811840
$399$	−1.00000	−0.0500626
$400$	−4.46410	−0.223205
$401$	38.7846	1.93681	0.968405	−	0.249381i	$-0.0802271\pi$
$401$	38.7846	1.93681	0.968405	+	0.249381i	$0.0802271\pi$
$402$	−8.92820	−0.445298
$403$	0	0
$404$	3.07180	0.152828
$405$	−0.732051	−0.0363759
$406$	−6.46410	−0.320808
$407$	11.6603	0.577977
$408$	−3.73205	−0.184764
$409$	38.7321	1.91518	0.957588	−	0.288140i	$-0.0930368\pi$
$409$	38.7321	1.91518	0.957588	+	0.288140i	$0.0930368\pi$
$410$	2.19615	0.108460
$411$	14.3923	0.709920
$412$	14.7321	0.725796
$413$	0.928203	0.0456739
$414$	3.46410	0.170251
$415$	0.143594	0.00704873
$416$	0	0
$417$	11.5885	0.567489
$418$	−1.73205	−0.0847174
$419$	0.732051	0.0357630	0.0178815	−	0.999840i	$-0.494308\pi$
$419$	0.732051	0.0357630	0.0178815	+	0.999840i	$0.494308\pi$
$420$	−0.732051	−0.0357204
$421$	−22.3923	−1.09133	−0.545667	−	0.838002i	$-0.683724\pi$
$421$	−22.3923	−1.09133	−0.545667	+	0.838002i	$0.683724\pi$
$422$	−26.0000	−1.26566
$423$	2.46410	0.119809
$424$	−7.00000	−0.339950
$425$	−16.6603	−0.808141
$426$	−2.19615	−0.106404
$427$	5.19615	0.251459
$428$	10.8564	0.524764
$429$	0	0
$430$	2.39230	0.115367
$431$	−14.1962	−0.683805	−0.341902	−	0.939736i	$-0.611071\pi$
$431$	−14.1962	−0.683805	−0.341902	+	0.939736i	$0.611071\pi$
$432$	1.00000	0.0481125
$433$	−27.0718	−1.30099	−0.650494	−	0.759512i	$-0.725438\pi$
$433$	−27.0718	−1.30099	−0.650494	+	0.759512i	$0.725438\pi$
$434$	2.19615	0.105419
$435$	−4.73205	−0.226884
$436$	−4.73205	−0.226624
$437$	3.46410	0.165710
$438$	5.46410	0.261085
$439$	−25.1769	−1.20163	−0.600814	−	0.799389i	$-0.705157\pi$
$439$	−25.1769	−1.20163	−0.600814	+	0.799389i	$0.705157\pi$
$440$	−1.26795	−0.0604471
$441$	1.00000	0.0476190
$442$	0	0
$443$	−33.6410	−1.59833	−0.799166	−	0.601110i	$-0.794725\pi$
$443$	−33.6410	−1.59833	−0.799166	+	0.601110i	$0.794725\pi$
$444$	−6.73205	−0.319489
$445$	−7.66025	−0.363131
$446$	−24.3923	−1.15501
$447$	−13.8564	−0.655386
$448$	1.00000	0.0472456
$449$	20.5885	0.971629	0.485815	−	0.874062i	$-0.338523\pi$
$449$	20.5885	0.971629	0.485815	+	0.874062i	$0.338523\pi$
$450$	4.46410	0.210440
$451$	−5.19615	−0.244677
$452$	15.2679	0.718144
$453$	5.19615	0.244137
$454$	18.3923	0.863194
$455$	0	0
$456$	1.00000	0.0468293
$457$	11.8564	0.554619	0.277310	−	0.960781i	$-0.410557\pi$
$457$	11.8564	0.554619	0.277310	+	0.960781i	$0.410557\pi$
$458$	19.9282	0.931184
$459$	3.73205	0.174197
$460$	2.53590	0.118237
$461$	26.9282	1.25417	0.627086	−	0.778950i	$-0.284248\pi$
$461$	26.9282	1.25417	0.627086	+	0.778950i	$0.284248\pi$
$462$	1.73205	0.0805823
$463$	−6.26795	−0.291296	−0.145648	−	0.989336i	$-0.546527\pi$
$463$	−6.26795	−0.291296	−0.145648	+	0.989336i	$0.546527\pi$
$464$	6.46410	0.300088
$465$	1.60770	0.0745551
$466$	9.12436	0.422678
$467$	−13.8564	−0.641198	−0.320599	−	0.947215i	$-0.603884\pi$
$467$	−13.8564	−0.641198	−0.320599	+	0.947215i	$0.603884\pi$
$468$	0	0
$469$	8.92820	0.412266
$470$	1.80385	0.0832053
$471$	−0.535898	−0.0246929
$472$	−0.928203	−0.0427240
$473$	−5.66025	−0.260259
$474$	−2.07180	−0.0951608
$475$	4.46410	0.204827
$476$	3.73205	0.171058
$477$	7.00000	0.320508
$478$	0.732051	0.0334832
$479$	32.4641	1.48332	0.741661	−	0.670775i	$-0.234038\pi$
$479$	32.4641	1.48332	0.741661	+	0.670775i	$0.234038\pi$
$480$	0.732051	0.0334134
$481$	0	0
$482$	8.00000	0.364390
$483$	−3.46410	−0.157622
$484$	−8.00000	−0.363636
$485$	11.4641	0.520558
$486$	−1.00000	−0.0453609
$487$	16.6603	0.754948	0.377474	−	0.926020i	$-0.376793\pi$
$487$	16.6603	0.754948	0.377474	+	0.926020i	$0.376793\pi$
$488$	−5.19615	−0.235219
$489$	2.73205	0.123548
$490$	0.732051	0.0330707
$491$	35.4641	1.60047	0.800236	−	0.599685i	$-0.204707\pi$
$491$	35.4641	1.60047	0.800236	+	0.599685i	$0.204707\pi$
$492$	3.00000	0.135250
$493$	24.1244	1.08651
$494$	0	0
$495$	1.26795	0.0569901
$496$	−2.19615	−0.0986102
$497$	2.19615	0.0985109
$498$	0.196152	0.00878980
$499$	11.5167	0.515557	0.257778	−	0.966204i	$-0.417010\pi$
$499$	11.5167	0.515557	0.257778	+	0.966204i	$0.417010\pi$
$500$	6.92820	0.309839
$501$	13.8564	0.619059
$502$	−13.1244	−0.585769
$503$	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
$505$	−2.24871	−0.100066
$506$	−6.00000	−0.266733
$507$	0	0
$508$	−15.4641	−0.686109
$509$	−22.3397	−0.990192	−0.495096	−	0.868838i	$-0.664867\pi$
$509$	−22.3397	−0.990192	−0.495096	+	0.868838i	$0.664867\pi$
$510$	2.73205	0.120977
$511$	−5.46410	−0.241718
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−20.6603	−0.911285
$515$	−10.7846	−0.475227
$516$	3.26795	0.143863
$517$	−4.26795	−0.187704
$518$	6.73205	0.295789
$519$	−9.12436	−0.400515
$520$	0	0
$521$	7.05256	0.308978	0.154489	−	0.987994i	$-0.450627\pi$
$521$	7.05256	0.308978	0.154489	+	0.987994i	$0.450627\pi$
$522$	−6.46410	−0.282926
$523$	−13.8756	−0.606740	−0.303370	−	0.952873i	$-0.598112\pi$
$523$	−13.8756	−0.606740	−0.303370	+	0.952873i	$0.598112\pi$
$524$	−13.8564	−0.605320
$525$	−4.46410	−0.194829
$526$	15.1244	0.659453
$527$	−8.19615	−0.357030
$528$	−1.73205	−0.0753778
$529$	−11.0000	−0.478261
$530$	5.12436	0.222588
$531$	0.928203	0.0402806
$532$	−1.00000	−0.0433555
$533$	0	0
$534$	−10.4641	−0.452826
$535$	−7.94744	−0.343598
$536$	−8.92820	−0.385640
$537$	11.4641	0.494713
$538$	9.85641	0.424940
$539$	−1.73205	−0.0746047
$540$	−0.732051	−0.0315025
$541$	−24.3397	−1.04645	−0.523224	−	0.852195i	$-0.675271\pi$
$541$	−24.3397	−1.04645	−0.523224	+	0.852195i	$0.675271\pi$
$542$	−28.0526	−1.20496
$543$	−2.66025	−0.114162
$544$	−3.73205	−0.160010
$545$	3.46410	0.148386
$546$	0	0
$547$	−1.26795	−0.0542136	−0.0271068	−	0.999633i	$-0.508629\pi$
$547$	−1.26795	−0.0542136	−0.0271068	+	0.999633i	$0.508629\pi$
$548$	14.3923	0.614809
$549$	5.19615	0.221766
$550$	−7.73205	−0.329696
$551$	−6.46410	−0.275380
$552$	3.46410	0.147442
$553$	2.07180	0.0881018
$554$	−9.32051	−0.395990
$555$	4.92820	0.209191
$556$	11.5885	0.491460
$557$	−13.0526	−0.553055	−0.276527	−	0.961006i	$-0.589184\pi$
$557$	−13.0526	−0.553055	−0.276527	+	0.961006i	$0.589184\pi$
$558$	2.19615	0.0929705
$559$	0	0
$560$	−0.732051	−0.0309348
$561$	−6.46410	−0.272915
$562$	0.339746	0.0143313
$563$	−36.1962	−1.52549	−0.762743	−	0.646702i	$-0.776148\pi$
$563$	−36.1962	−1.52549	−0.762743	+	0.646702i	$0.776148\pi$
$564$	2.46410	0.103757
$565$	−11.1769	−0.470216
$566$	9.85641	0.414296
$567$	1.00000	0.0419961
$568$	−2.19615	−0.0921485
$569$	−38.4449	−1.61169	−0.805846	−	0.592125i	$-0.798289\pi$
$569$	−38.4449	−1.61169	−0.805846	+	0.592125i	$0.798289\pi$
$570$	−0.732051	−0.0306622
$571$	16.9808	0.710623	0.355311	−	0.934748i	$-0.384375\pi$
$571$	16.9808	0.710623	0.355311	+	0.934748i	$0.384375\pi$
$572$	0	0
$573$	23.1244	0.966034
$574$	−3.00000	−0.125218
$575$	15.4641	0.644898
$576$	1.00000	0.0416667
$577$	10.3397	0.430449	0.215225	−	0.976565i	$-0.430952\pi$
$577$	10.3397	0.430449	0.215225	+	0.976565i	$0.430952\pi$
$578$	3.07180	0.127770
$579$	1.19615	0.0497104
$580$	−4.73205	−0.196488
$581$	−0.196152	−0.00813777
$582$	15.6603	0.649138
$583$	−12.1244	−0.502140
$584$	5.46410	0.226106
$585$	0	0
$586$	17.0718	0.705229
$587$	12.3397	0.509316	0.254658	−	0.967031i	$-0.418037\pi$
$587$	12.3397	0.509316	0.254658	+	0.967031i	$0.418037\pi$
$588$	1.00000	0.0412393
$589$	2.19615	0.0904909
$590$	0.679492	0.0279742
$591$	26.6603	1.09666
$592$	−6.73205	−0.276686
$593$	0.464102	0.0190584	0.00952918	−	0.999955i	$-0.496967\pi$
$593$	0.464102	0.0190584	0.00952918	+	0.999955i	$0.496967\pi$
$594$	1.73205	0.0710669
$595$	−2.73205	−0.112003
$596$	−13.8564	−0.567581
$597$	−16.1962	−0.662864
$598$	0	0
$599$	−28.6410	−1.17024	−0.585120	−	0.810947i	$-0.698953\pi$
$599$	−28.6410	−1.17024	−0.585120	+	0.810947i	$0.698953\pi$
$600$	4.46410	0.182246
$601$	−22.7321	−0.927260	−0.463630	−	0.886029i	$-0.653453\pi$
$601$	−22.7321	−0.927260	−0.463630	+	0.886029i	$0.653453\pi$
$602$	−3.26795	−0.133192
$603$	8.92820	0.363585
$604$	5.19615	0.211428
$605$	5.85641	0.238097
$606$	−3.07180	−0.124783
$607$	−31.5167	−1.27922	−0.639611	−	0.768699i	$-0.720905\pi$
$607$	−31.5167	−1.27922	−0.639611	+	0.768699i	$0.720905\pi$
$608$	1.00000	0.0405554
$609$	6.46410	0.261939
$610$	3.80385	0.154013
$611$	0	0
$612$	3.73205	0.150859
$613$	4.00000	0.161558	0.0807792	−	0.996732i	$-0.474259\pi$
$613$	4.00000	0.161558	0.0807792	+	0.996732i	$0.474259\pi$
$614$	−8.60770	−0.347378
$615$	−2.19615	−0.0885574
$616$	1.73205	0.0697863
$617$	−2.19615	−0.0884138	−0.0442069	−	0.999022i	$-0.514076\pi$
$617$	−2.19615	−0.0884138	−0.0442069	+	0.999022i	$0.514076\pi$
$618$	−14.7321	−0.592610
$619$	22.0718	0.887140	0.443570	−	0.896240i	$-0.353712\pi$
$619$	22.0718	0.887140	0.443570	+	0.896240i	$0.353712\pi$
$620$	1.60770	0.0645666
$621$	−3.46410	−0.139010
$622$	−4.26795	−0.171129
$623$	10.4641	0.419235
$624$	0	0
$625$	17.2487	0.689948
$626$	−13.5167	−0.540234
$627$	1.73205	0.0691714
$628$	−0.535898	−0.0213847
$629$	−25.1244	−1.00177
$630$	0.732051	0.0291656
$631$	16.8038	0.668951	0.334475	−	0.942405i	$-0.391441\pi$
$631$	16.8038	0.668951	0.334475	+	0.942405i	$0.391441\pi$
$632$	−2.07180	−0.0824117
$633$	26.0000	1.03341
$634$	11.8564	0.470878
$635$	11.3205	0.449241
$636$	7.00000	0.277568
$637$	0	0
$638$	11.1962	0.443260
$639$	2.19615	0.0868784
$640$	0.732051	0.0289368
$641$	31.1769	1.23141	0.615707	−	0.787975i	$-0.288870\pi$
$641$	31.1769	1.23141	0.615707	+	0.787975i	$0.288870\pi$
$642$	−10.8564	−0.428468
$643$	−32.8564	−1.29573	−0.647865	−	0.761755i	$-0.724338\pi$
$643$	−32.8564	−1.29573	−0.647865	+	0.761755i	$0.724338\pi$
$644$	−3.46410	−0.136505
$645$	−2.39230	−0.0941969
$646$	3.73205	0.146836
$647$	35.8372	1.40890	0.704452	−	0.709751i	$-0.251193\pi$
$647$	35.8372	1.40890	0.704452	+	0.709751i	$0.251193\pi$
$648$	−1.00000	−0.0392837
$649$	−1.60770	−0.0631076
$650$	0	0
$651$	−2.19615	−0.0860740
$652$	2.73205	0.106995
$653$	46.7128	1.82801	0.914007	−	0.405699i	$-0.132972\pi$
$653$	46.7128	1.82801	0.914007	+	0.405699i	$0.132972\pi$
$654$	4.73205	0.185038
$655$	10.1436	0.396343
$656$	3.00000	0.117130
$657$	−5.46410	−0.213175
$658$	−2.46410	−0.0960607
$659$	18.6077	0.724853	0.362426	−	0.932012i	$-0.381948\pi$
$659$	18.6077	0.724853	0.362426	+	0.932012i	$0.381948\pi$
$660$	1.26795	0.0493549
$661$	−12.3923	−0.482005	−0.241002	−	0.970525i	$-0.577476\pi$
$661$	−12.3923	−0.482005	−0.241002	+	0.970525i	$0.577476\pi$
$662$	27.8564	1.08267
$663$	0	0
$664$	0.196152	0.00761219
$665$	0.732051	0.0283877
$666$	6.73205	0.260862
$667$	−22.3923	−0.867034
$668$	13.8564	0.536120
$669$	24.3923	0.943061
$670$	6.53590	0.252504
$671$	−9.00000	−0.347441
$672$	−1.00000	−0.0385758
$673$	−32.7128	−1.26099	−0.630493	−	0.776195i	$-0.717147\pi$
$673$	−32.7128	−1.26099	−0.630493	+	0.776195i	$0.717147\pi$
$674$	−19.0000	−0.731853
$675$	−4.46410	−0.171823
$676$	0	0
$677$	36.7321	1.41173	0.705864	−	0.708348i	$-0.250559\pi$
$677$	36.7321	1.41173	0.705864	+	0.708348i	$0.250559\pi$
$678$	−15.2679	−0.586362
$679$	−15.6603	−0.600985
$680$	2.73205	0.104769
$681$	−18.3923	−0.704795
$682$	−3.80385	−0.145657
$683$	29.6077	1.13291	0.566453	−	0.824094i	$-0.308315\pi$
$683$	29.6077	1.13291	0.566453	+	0.824094i	$0.308315\pi$
$684$	−1.00000	−0.0382360
$685$	−10.5359	−0.402556
$686$	−1.00000	−0.0381802
$687$	−19.9282	−0.760308
$688$	3.26795	0.124589
$689$	0	0
$690$	−2.53590	−0.0965400
$691$	43.7128	1.66291	0.831457	−	0.555589i	$-0.187507\pi$
$691$	43.7128	1.66291	0.831457	+	0.555589i	$0.187507\pi$
$692$	−9.12436	−0.346856
$693$	−1.73205	−0.0657952
$694$	−5.39230	−0.204689
$695$	−8.48334	−0.321791
$696$	−6.46410	−0.245021
$697$	11.1962	0.424085
$698$	−23.7128	−0.897543
$699$	−9.12436	−0.345115
$700$	−4.46410	−0.168727
$701$	1.14359	0.0431929	0.0215965	−	0.999767i	$-0.493125\pi$
$701$	1.14359	0.0431929	0.0215965	+	0.999767i	$0.493125\pi$
$702$	0	0
$703$	6.73205	0.253904
$704$	−1.73205	−0.0652791
$705$	−1.80385	−0.0679368
$706$	9.46410	0.356186
$707$	3.07180	0.115527
$708$	0.928203	0.0348840
$709$	−32.0526	−1.20376	−0.601880	−	0.798587i	$-0.705581\pi$
$709$	−32.0526	−1.20376	−0.601880	+	0.798587i	$0.705581\pi$
$710$	1.60770	0.0603357
$711$	2.07180	0.0776984
$712$	−10.4641	−0.392159
$713$	7.60770	0.284910
$714$	−3.73205	−0.139668
$715$	0	0
$716$	11.4641	0.428434
$717$	−0.732051	−0.0273389
$718$	3.80385	0.141958
$719$	26.5167	0.988905	0.494452	−	0.869205i	$-0.335369\pi$
$719$	26.5167	0.988905	0.494452	+	0.869205i	$0.335369\pi$
$720$	−0.732051	−0.0272819
$721$	14.7321	0.548650
$722$	18.0000	0.669891
$723$	−8.00000	−0.297523
$724$	−2.66025	−0.0988676
$725$	−28.8564	−1.07170
$726$	8.00000	0.296908
$727$	−19.3205	−0.716558	−0.358279	−	0.933615i	$-0.616636\pi$
$727$	−19.3205	−0.716558	−0.358279	+	0.933615i	$0.616636\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−4.00000	−0.148047
$731$	12.1962	0.451091
$732$	5.19615	0.192055
$733$	48.1769	1.77945	0.889727	−	0.456492i	$-0.150894\pi$
$733$	48.1769	1.77945	0.889727	+	0.456492i	$0.150894\pi$
$734$	−25.3205	−0.934597
$735$	−0.732051	−0.0270021
$736$	3.46410	0.127688
$737$	−15.4641	−0.569628
$738$	−3.00000	−0.110432
$739$	−15.1769	−0.558292	−0.279146	−	0.960249i	$-0.590051\pi$
$739$	−15.1769	−0.558292	−0.279146	+	0.960249i	$0.590051\pi$
$740$	4.92820	0.181164
$741$	0	0
$742$	−7.00000	−0.256978
$743$	−14.0526	−0.515538	−0.257769	−	0.966207i	$-0.582987\pi$
$743$	−14.0526	−0.515538	−0.257769	+	0.966207i	$0.582987\pi$
$744$	2.19615	0.0805149
$745$	10.1436	0.371633
$746$	−9.66025	−0.353687
$747$	−0.196152	−0.00717684
$748$	−6.46410	−0.236351
$749$	10.8564	0.396684
$750$	−6.92820	−0.252982
$751$	−19.1436	−0.698560	−0.349280	−	0.937018i	$-0.613574\pi$
$751$	−19.1436	−0.698560	−0.349280	+	0.937018i	$0.613574\pi$
$752$	2.46410	0.0898565
$753$	13.1244	0.478278
$754$	0	0
$755$	−3.80385	−0.138436
$756$	1.00000	0.0363696
$757$	−0.588457	−0.0213878	−0.0106939	−	0.999943i	$-0.503404\pi$
$757$	−0.588457	−0.0213878	−0.0106939	+	0.999943i	$0.503404\pi$
$758$	−28.4449	−1.03316
$759$	6.00000	0.217786
$760$	−0.732051	−0.0265543
$761$	15.3205	0.555368	0.277684	−	0.960672i	$-0.410433\pi$
$761$	15.3205	0.555368	0.277684	+	0.960672i	$0.410433\pi$
$762$	15.4641	0.560205
$763$	−4.73205	−0.171312
$764$	23.1244	0.836610
$765$	−2.73205	−0.0987775
$766$	−5.53590	−0.200020
$767$	0	0
$768$	1.00000	0.0360844
$769$	42.3013	1.52542	0.762711	−	0.646739i	$-0.223868\pi$
$769$	42.3013	1.52542	0.762711	+	0.646739i	$0.223868\pi$
$770$	−1.26795	−0.0456937
$771$	20.6603	0.744061
$772$	1.19615	0.0430505
$773$	47.1769	1.69684	0.848418	−	0.529327i	$-0.177556\pi$
$773$	47.1769	1.69684	0.848418	+	0.529327i	$0.177556\pi$
$774$	−3.26795	−0.117464
$775$	9.80385	0.352165
$776$	15.6603	0.562170
$777$	−6.73205	−0.241511
$778$	−8.39230	−0.300879
$779$	−3.00000	−0.107486
$780$	0	0
$781$	−3.80385	−0.136112
$782$	12.9282	0.462312
$783$	6.46410	0.231008
$784$	1.00000	0.0357143
$785$	0.392305	0.0140020
$786$	13.8564	0.494242
$787$	3.67949	0.131160	0.0655799	−	0.997847i	$-0.479110\pi$
$787$	3.67949	0.131160	0.0655799	+	0.997847i	$0.479110\pi$
$788$	26.6603	0.949732
$789$	−15.1244	−0.538441
$790$	1.51666	0.0539604
$791$	15.2679	0.542866
$792$	1.73205	0.0615457
$793$	0	0
$794$	−8.07180	−0.286457
$795$	−5.12436	−0.181742
$796$	−16.1962	−0.574057
$797$	−2.87564	−0.101861	−0.0509303	−	0.998702i	$-0.516219\pi$
$797$	−2.87564	−0.101861	−0.0509303	+	0.998702i	$0.516219\pi$
$798$	1.00000	0.0353996
$799$	9.19615	0.325336
$800$	4.46410	0.157830
$801$	10.4641	0.369731
$802$	−38.7846	−1.36953
$803$	9.46410	0.333981
$804$	8.92820	0.314873
$805$	2.53590	0.0893787
$806$	0	0
$807$	−9.85641	−0.346962
$808$	−3.07180	−0.108065
$809$	−6.44486	−0.226589	−0.113295	−	0.993561i	$-0.536140\pi$
$809$	−6.44486	−0.226589	−0.113295	+	0.993561i	$0.536140\pi$
$810$	0.732051	0.0257216
$811$	24.5359	0.861572	0.430786	−	0.902454i	$-0.358236\pi$
$811$	24.5359	0.861572	0.430786	+	0.902454i	$0.358236\pi$
$812$	6.46410	0.226845
$813$	28.0526	0.983846
$814$	−11.6603	−0.408692
$815$	−2.00000	−0.0700569
$816$	3.73205	0.130648
$817$	−3.26795	−0.114331
$818$	−38.7321	−1.35423
$819$	0	0
$820$	−2.19615	−0.0766930
$821$	−51.8372	−1.80913	−0.904565	−	0.426336i	$-0.859804\pi$
$821$	−51.8372	−1.80913	−0.904565	+	0.426336i	$0.859804\pi$
$822$	−14.3923	−0.501989
$823$	−6.78461	−0.236497	−0.118248	−	0.992984i	$-0.537728\pi$
$823$	−6.78461	−0.236497	−0.118248	+	0.992984i	$0.537728\pi$
$824$	−14.7321	−0.513215
$825$	7.73205	0.269195
$826$	−0.928203	−0.0322963
$827$	−7.32051	−0.254559	−0.127280	−	0.991867i	$-0.540625\pi$
$827$	−7.32051	−0.254559	−0.127280	+	0.991867i	$0.540625\pi$
$828$	−3.46410	−0.120386
$829$	−17.3397	−0.602234	−0.301117	−	0.953587i	$-0.597360\pi$
$829$	−17.3397	−0.602234	−0.301117	+	0.953587i	$0.597360\pi$
$830$	−0.143594	−0.00498420
$831$	9.32051	0.323325
$832$	0	0
$833$	3.73205	0.129308
$834$	−11.5885	−0.401275
$835$	−10.1436	−0.351034
$836$	1.73205	0.0599042
$837$	−2.19615	−0.0759101
$838$	−0.732051	−0.0252883
$839$	−34.1051	−1.17744	−0.588720	−	0.808337i	$-0.700368\pi$
$839$	−34.1051	−1.17744	−0.588720	+	0.808337i	$0.700368\pi$
$840$	0.732051	0.0252582
$841$	12.7846	0.440849
$842$	22.3923	0.771690
$843$	−0.339746	−0.0117015
$844$	26.0000	0.894957
$845$	0	0
$846$	−2.46410	−0.0847176
$847$	−8.00000	−0.274883
$848$	7.00000	0.240381
$849$	−9.85641	−0.338271
$850$	16.6603	0.571442
$851$	23.3205	0.799417
$852$	2.19615	0.0752389
$853$	−7.92820	−0.271457	−0.135728	−	0.990746i	$-0.543337\pi$
$853$	−7.92820	−0.271457	−0.135728	+	0.990746i	$0.543337\pi$
$854$	−5.19615	−0.177809
$855$	0.732051	0.0250356
$856$	−10.8564	−0.371064
$857$	−32.5359	−1.11141	−0.555703	−	0.831381i	$-0.687551\pi$
$857$	−32.5359	−1.11141	−0.555703	+	0.831381i	$0.687551\pi$
$858$	0	0
$859$	42.7654	1.45914	0.729568	−	0.683908i	$-0.239721\pi$
$859$	42.7654	1.45914	0.729568	+	0.683908i	$0.239721\pi$
$860$	−2.39230	−0.0815769
$861$	3.00000	0.102240
$862$	14.1962	0.483523
$863$	−3.07180	−0.104565	−0.0522826	−	0.998632i	$-0.516650\pi$
$863$	−3.07180	−0.104565	−0.0522826	+	0.998632i	$0.516650\pi$
$864$	−1.00000	−0.0340207
$865$	6.67949	0.227110
$866$	27.0718	0.919937
$867$	−3.07180	−0.104324
$868$	−2.19615	−0.0745423
$869$	−3.58846	−0.121730
$870$	4.73205	0.160432
$871$	0	0
$872$	4.73205	0.160247
$873$	−15.6603	−0.530019
$874$	−3.46410	−0.117175
$875$	6.92820	0.234216
$876$	−5.46410	−0.184615
$877$	−23.2679	−0.785703	−0.392851	−	0.919602i	$-0.628511\pi$
$877$	−23.2679	−0.785703	−0.392851	+	0.919602i	$0.628511\pi$
$878$	25.1769	0.849680
$879$	−17.0718	−0.575817
$880$	1.26795	0.0427426
$881$	22.9282	0.772471	0.386235	−	0.922400i	$-0.373775\pi$
$881$	22.9282	0.772471	0.386235	+	0.922400i	$0.373775\pi$
$882$	−1.00000	−0.0336718
$883$	−8.05256	−0.270990	−0.135495	−	0.990778i	$-0.543262\pi$
$883$	−8.05256	−0.270990	−0.135495	+	0.990778i	$0.543262\pi$
$884$	0	0
$885$	−0.679492	−0.0228409
$886$	33.6410	1.13019
$887$	−15.4449	−0.518588	−0.259294	−	0.965798i	$-0.583490\pi$
$887$	−15.4449	−0.518588	−0.259294	+	0.965798i	$0.583490\pi$
$888$	6.73205	0.225913
$889$	−15.4641	−0.518649
$890$	7.66025	0.256772
$891$	−1.73205	−0.0580259
$892$	24.3923	0.816715
$893$	−2.46410	−0.0824580
$894$	13.8564	0.463428
$895$	−8.39230	−0.280524
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−20.5885	−0.687046
$899$	−14.1962	−0.473468
$900$	−4.46410	−0.148803
$901$	26.1244	0.870328
$902$	5.19615	0.173013
$903$	3.26795	0.108751
$904$	−15.2679	−0.507804
$905$	1.94744	0.0647351
$906$	−5.19615	−0.172631
$907$	−1.60770	−0.0533826	−0.0266913	−	0.999644i	$-0.508497\pi$
$907$	−1.60770	−0.0533826	−0.0266913	+	0.999644i	$0.508497\pi$
$908$	−18.3923	−0.610370
$909$	3.07180	0.101885
$910$	0	0
$911$	−50.8372	−1.68431	−0.842155	−	0.539235i	$-0.818713\pi$
$911$	−50.8372	−1.68431	−0.842155	+	0.539235i	$0.818713\pi$
$912$	−1.00000	−0.0331133
$913$	0.339746	0.0112440
$914$	−11.8564	−0.392175
$915$	−3.80385	−0.125751
$916$	−19.9282	−0.658446
$917$	−13.8564	−0.457579
$918$	−3.73205	−0.123176
$919$	32.8564	1.08383	0.541916	−	0.840432i	$-0.317699\pi$
$919$	32.8564	1.08383	0.541916	+	0.840432i	$0.317699\pi$
$920$	−2.53590	−0.0836061
$921$	8.60770	0.283633
$922$	−26.9282	−0.886833
$923$	0	0
$924$	−1.73205	−0.0569803
$925$	30.0526	0.988122
$926$	6.26795	0.205978
$927$	14.7321	0.483864
$928$	−6.46410	−0.212195
$929$	−2.32051	−0.0761334	−0.0380667	−	0.999275i	$-0.512120\pi$
$929$	−2.32051	−0.0761334	−0.0380667	+	0.999275i	$0.512120\pi$
$930$	−1.60770	−0.0527184
$931$	−1.00000	−0.0327737
$932$	−9.12436	−0.298878
$933$	4.26795	0.139726
$934$	13.8564	0.453395
$935$	4.73205	0.154755
$936$	0	0
$937$	1.07180	0.0350141	0.0175070	−	0.999847i	$-0.494427\pi$
$937$	1.07180	0.0350141	0.0175070	+	0.999847i	$0.494427\pi$
$938$	−8.92820	−0.291516
$939$	13.5167	0.441100
$940$	−1.80385	−0.0588350
$941$	11.6077	0.378400	0.189200	−	0.981939i	$-0.439411\pi$
$941$	11.6077	0.378400	0.189200	+	0.981939i	$0.439411\pi$
$942$	0.535898	0.0174605
$943$	−10.3923	−0.338420
$944$	0.928203	0.0302104
$945$	−0.732051	−0.0238136
$946$	5.66025	0.184031
$947$	32.5167	1.05665	0.528325	−	0.849042i	$-0.322820\pi$
$947$	32.5167	1.05665	0.528325	+	0.849042i	$0.322820\pi$
$948$	2.07180	0.0672888
$949$	0	0
$950$	−4.46410	−0.144835
$951$	−11.8564	−0.384470
$952$	−3.73205	−0.120956
$953$	34.1962	1.10772	0.553861	−	0.832609i	$-0.313154\pi$
$953$	34.1962	1.10772	0.553861	+	0.832609i	$0.313154\pi$
$954$	−7.00000	−0.226633
$955$	−16.9282	−0.547784
$956$	−0.732051	−0.0236762
$957$	−11.1962	−0.361920
$958$	−32.4641	−1.04887
$959$	14.3923	0.464752
$960$	−0.732051	−0.0236268
$961$	−26.1769	−0.844417
$962$	0	0
$963$	10.8564	0.349843
$964$	−8.00000	−0.257663
$965$	−0.875644	−0.0281880
$966$	3.46410	0.111456
$967$	−0.287187	−0.00923531	−0.00461766	−	0.999989i	$-0.501470\pi$
$967$	−0.287187	−0.00923531	−0.00461766	+	0.999989i	$0.501470\pi$
$968$	8.00000	0.257130
$969$	−3.73205	−0.119891
$970$	−11.4641	−0.368090
$971$	−54.1051	−1.73632	−0.868158	−	0.496288i	$-0.834696\pi$
$971$	−54.1051	−1.73632	−0.868158	+	0.496288i	$0.834696\pi$
$972$	1.00000	0.0320750
$973$	11.5885	0.371509
$974$	−16.6603	−0.533829
$975$	0	0
$976$	5.19615	0.166325
$977$	−16.3923	−0.524436	−0.262218	−	0.965009i	$-0.584454\pi$
$977$	−16.3923	−0.524436	−0.262218	+	0.965009i	$0.584454\pi$
$978$	−2.73205	−0.0873614
$979$	−18.1244	−0.579257
$980$	−0.732051	−0.0233845
$981$	−4.73205	−0.151083
$982$	−35.4641	−1.13170
$983$	−35.8564	−1.14364	−0.571821	−	0.820379i	$-0.693763\pi$
$983$	−35.8564	−1.14364	−0.571821	+	0.820379i	$0.693763\pi$
$984$	−3.00000	−0.0956365
$985$	−19.5167	−0.621853
$986$	−24.1244	−0.768276
$987$	2.46410	0.0784332
$988$	0	0
$989$	−11.3205	−0.359971
$990$	−1.26795	−0.0402981
$991$	−59.2487	−1.88210	−0.941049	−	0.338271i	$-0.890158\pi$
$991$	−59.2487	−1.88210	−0.941049	+	0.338271i	$0.890158\pi$
$992$	2.19615	0.0697279
$993$	−27.8564	−0.883996
$994$	−2.19615	−0.0696577
$995$	11.8564	0.375873
$996$	−0.196152	−0.00621533
$997$	−21.0526	−0.666741	−0.333371	−	0.942796i	$-0.608186\pi$
$997$	−21.0526	−0.666741	−0.333371	+	0.942796i	$0.608186\pi$
$998$	−11.5167	−0.364554
$999$	−6.73205	−0.212993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.bp.1.1		2
13.2	odd	12		546.2.s.a.43.1	✓	4
13.7	odd	12		546.2.s.a.127.1	yes	4
13.12	even	2		7098.2.a.bx.1.2		2
39.2	even	12		1638.2.bj.b.1135.2		4
39.20	even	12		1638.2.bj.b.127.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.a.43.1	✓	4	13.2	odd	12
546.2.s.a.127.1	yes	4	13.7	odd	12
1638.2.bj.b.127.2		4	39.20	even	12
1638.2.bj.b.1135.2		4	39.2	even	12
7098.2.a.bp.1.1		2	1.1	even	1	trivial
7098.2.a.bx.1.2		2	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.732051 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.732051 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.732051 q^{10} -1.73205 q^{11} +1.00000 q^{12} -1.00000 q^{14} -0.732051 q^{15} +1.00000 q^{16} +3.73205 q^{17} -1.00000 q^{18} -1.00000 q^{19} -0.732051 q^{20} +1.00000 q^{21} +1.73205 q^{22} -3.46410 q^{23} -1.00000 q^{24} -4.46410 q^{25} +1.00000 q^{27} +1.00000 q^{28} +6.46410 q^{29} +0.732051 q^{30} -2.19615 q^{31} -1.00000 q^{32} -1.73205 q^{33} -3.73205 q^{34} -0.732051 q^{35} +1.00000 q^{36} -6.73205 q^{37} +1.00000 q^{38} +0.732051 q^{40} +3.00000 q^{41} -1.00000 q^{42} +3.26795 q^{43} -1.73205 q^{44} -0.732051 q^{45} +3.46410 q^{46} +2.46410 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.46410 q^{50} +3.73205 q^{51} +7.00000 q^{53} -1.00000 q^{54} +1.26795 q^{55} -1.00000 q^{56} -1.00000 q^{57} -6.46410 q^{58} +0.928203 q^{59} -0.732051 q^{60} +5.19615 q^{61} +2.19615 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.73205 q^{66} +8.92820 q^{67} +3.73205 q^{68} -3.46410 q^{69} +0.732051 q^{70} +2.19615 q^{71} -1.00000 q^{72} -5.46410 q^{73} +6.73205 q^{74} -4.46410 q^{75} -1.00000 q^{76} -1.73205 q^{77} +2.07180 q^{79} -0.732051 q^{80} +1.00000 q^{81} -3.00000 q^{82} -0.196152 q^{83} +1.00000 q^{84} -2.73205 q^{85} -3.26795 q^{86} +6.46410 q^{87} +1.73205 q^{88} +10.4641 q^{89} +0.732051 q^{90} -3.46410 q^{92} -2.19615 q^{93} -2.46410 q^{94} +0.732051 q^{95} -1.00000 q^{96} -15.6603 q^{97} -1.00000 q^{98} -1.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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

Introduction

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