LMFDB - Embedded newform 5586.2.a.bv.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, 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("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 798)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.86620$ of defining polynomial
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.866198 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.866198 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.866198 q^{10} -4.21509 q^{11} +1.00000 q^{12} -3.03461 q^{13} +0.866198 q^{15} +1.00000 q^{16} -2.13380 q^{17} +1.00000 q^{18} -1.00000 q^{19} +0.866198 q^{20} -4.21509 q^{22} -8.04668 q^{23} +1.00000 q^{24} -4.24970 q^{25} -3.03461 q^{26} +1.00000 q^{27} +5.24970 q^{29} +0.866198 q^{30} -8.73240 q^{31} +1.00000 q^{32} -4.21509 q^{33} -2.13380 q^{34} +1.00000 q^{36} -4.90081 q^{37} -1.00000 q^{38} -3.03461 q^{39} +0.866198 q^{40} -1.61650 q^{41} +7.52938 q^{43} -4.21509 q^{44} +0.866198 q^{45} -8.04668 q^{46} -1.66318 q^{47} +1.00000 q^{48} -4.24970 q^{50} -2.13380 q^{51} -3.03461 q^{52} -4.03461 q^{53} +1.00000 q^{54} -3.65111 q^{55} -1.00000 q^{57} +5.24970 q^{58} -5.38350 q^{59} +0.866198 q^{60} -1.73240 q^{61} -8.73240 q^{62} +1.00000 q^{64} -2.62857 q^{65} -4.21509 q^{66} -2.96539 q^{67} -2.13380 q^{68} -8.04668 q^{69} +3.52938 q^{71} +1.00000 q^{72} -4.18048 q^{73} -4.90081 q^{74} -4.24970 q^{75} -1.00000 q^{76} -3.03461 q^{78} +8.64528 q^{79} +0.866198 q^{80} +1.00000 q^{81} -1.61650 q^{82} +12.8950 q^{83} -1.84830 q^{85} +7.52938 q^{86} +5.24970 q^{87} -4.21509 q^{88} -1.61650 q^{89} +0.866198 q^{90} -8.04668 q^{92} -8.73240 q^{93} -1.66318 q^{94} -0.866198 q^{95} +1.00000 q^{96} -13.3835 q^{97} -4.21509 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} + 3 q^{8} + 3 q^{9} - 5 q^{10} + q^{11} + 3 q^{12} - 6 q^{13} - 5 q^{15} + 3 q^{16} - 14 q^{17} + 3 q^{18} - 3 q^{19} - 5 q^{20} + q^{22} - 6 q^{23} + 3 q^{24} + 4 q^{25} - 6 q^{26} + 3 q^{27} - q^{29} - 5 q^{30} - 11 q^{31} + 3 q^{32} + q^{33} - 14 q^{34} + 3 q^{36} - 4 q^{37} - 3 q^{38} - 6 q^{39} - 5 q^{40} - 14 q^{41} + 6 q^{43} + q^{44} - 5 q^{45} - 6 q^{46} + 4 q^{47} + 3 q^{48} + 4 q^{50} - 14 q^{51} - 6 q^{52} - 9 q^{53} + 3 q^{54} - 17 q^{55} - 3 q^{57} - q^{58} - 7 q^{59} - 5 q^{60} + 10 q^{61} - 11 q^{62} + 3 q^{64} - 2 q^{65} + q^{66} - 12 q^{67} - 14 q^{68} - 6 q^{69} - 6 q^{71} + 3 q^{72} - 2 q^{73} - 4 q^{74} + 4 q^{75} - 3 q^{76} - 6 q^{78} - 15 q^{79} - 5 q^{80} + 3 q^{81} - 14 q^{82} - 19 q^{83} + 34 q^{85} + 6 q^{86} - q^{87} + q^{88} - 14 q^{89} - 5 q^{90} - 6 q^{92} - 11 q^{93} + 4 q^{94} + 5 q^{95} + 3 q^{96} - 31 q^{97} + q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 + 3 * q^8 + 3 * q^9 - 5 * q^10 + q^11 + 3 * q^12 - 6 * q^13 - 5 * q^15 + 3 * q^16 - 14 * q^17 + 3 * q^18 - 3 * q^19 - 5 * q^20 + q^22 - 6 * q^23 + 3 * q^24 + 4 * q^25 - 6 * q^26 + 3 * q^27 - q^29 - 5 * q^30 - 11 * q^31 + 3 * q^32 + q^33 - 14 * q^34 + 3 * q^36 - 4 * q^37 - 3 * q^38 - 6 * q^39 - 5 * q^40 - 14 * q^41 + 6 * q^43 + q^44 - 5 * q^45 - 6 * q^46 + 4 * q^47 + 3 * q^48 + 4 * q^50 - 14 * q^51 - 6 * q^52 - 9 * q^53 + 3 * q^54 - 17 * q^55 - 3 * q^57 - q^58 - 7 * q^59 - 5 * q^60 + 10 * q^61 - 11 * q^62 + 3 * q^64 - 2 * q^65 + q^66 - 12 * q^67 - 14 * q^68 - 6 * q^69 - 6 * q^71 + 3 * q^72 - 2 * q^73 - 4 * q^74 + 4 * q^75 - 3 * q^76 - 6 * q^78 - 15 * q^79 - 5 * q^80 + 3 * q^81 - 14 * q^82 - 19 * q^83 + 34 * q^85 + 6 * q^86 - q^87 + q^88 - 14 * q^89 - 5 * q^90 - 6 * q^92 - 11 * q^93 + 4 * q^94 + 5 * q^95 + 3 * q^96 - 31 * q^97 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.866198	0.387376	0.193688	−	0.981063i	$-0.437955\pi$
$5$	0.866198	0.387376	0.193688	+	0.981063i	$0.437955\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.866198	0.273916
$11$	−4.21509	−1.27090	−0.635449	−	0.772143i	$-0.719185\pi$
$11$	−4.21509	−1.27090	−0.635449	+	0.772143i	$0.719185\pi$
$12$	1.00000	0.288675
$13$	−3.03461	−0.841649	−0.420824	−	0.907142i	$-0.638259\pi$
$13$	−3.03461	−0.841649	−0.420824	+	0.907142i	$0.638259\pi$
$14$	0	0
$15$	0.866198	0.223651
$16$	1.00000	0.250000
$17$	−2.13380	−0.517523	−0.258761	−	0.965941i	$-0.583314\pi$
$17$	−2.13380	−0.517523	−0.258761	+	0.965941i	$0.583314\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.866198	0.193688
$21$	0	0
$22$	−4.21509	−0.898661
$23$	−8.04668	−1.67785	−0.838925	−	0.544248i	$-0.816815\pi$
$23$	−8.04668	−1.67785	−0.838925	+	0.544248i	$0.816815\pi$
$24$	1.00000	0.204124
$25$	−4.24970	−0.849940
$26$	−3.03461	−0.595136
$27$	1.00000	0.192450
$28$	0	0
$29$	5.24970	0.974845	0.487422	−	0.873166i	$-0.337937\pi$
$29$	5.24970	0.974845	0.487422	+	0.873166i	$0.337937\pi$
$30$	0.866198	0.158145
$31$	−8.73240	−1.56838	−0.784192	−	0.620518i	$-0.786922\pi$
$31$	−8.73240	−1.56838	−0.784192	+	0.620518i	$0.786922\pi$
$32$	1.00000	0.176777
$33$	−4.21509	−0.733753
$34$	−2.13380	−0.365944
$35$	0	0
$36$	1.00000	0.166667
$37$	−4.90081	−0.805688	−0.402844	−	0.915269i	$-0.631978\pi$
$37$	−4.90081	−0.805688	−0.402844	+	0.915269i	$0.631978\pi$
$38$	−1.00000	−0.162221
$39$	−3.03461	−0.485926
$40$	0.866198	0.136958
$41$	−1.61650	−0.252455	−0.126227	−	0.992001i	$-0.540287\pi$
$41$	−1.61650	−0.252455	−0.126227	+	0.992001i	$0.540287\pi$
$42$	0	0
$43$	7.52938	1.14822	0.574110	−	0.818778i	$-0.305348\pi$
$43$	7.52938	1.14822	0.574110	+	0.818778i	$0.305348\pi$
$44$	−4.21509	−0.635449
$45$	0.866198	0.129125
$46$	−8.04668	−1.18642
$47$	−1.66318	−0.242600	−0.121300	−	0.992616i	$-0.538706\pi$
$47$	−1.66318	−0.242600	−0.121300	+	0.992616i	$0.538706\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−4.24970	−0.600998
$51$	−2.13380	−0.298792
$52$	−3.03461	−0.420824
$53$	−4.03461	−0.554196	−0.277098	−	0.960842i	$-0.589373\pi$
$53$	−4.03461	−0.554196	−0.277098	+	0.960842i	$0.589373\pi$
$54$	1.00000	0.136083
$55$	−3.65111	−0.492315
$56$	0	0
$57$	−1.00000	−0.132453
$58$	5.24970	0.689319
$59$	−5.38350	−0.700872	−0.350436	−	0.936587i	$-0.613967\pi$
$59$	−5.38350	−0.700872	−0.350436	+	0.936587i	$0.613967\pi$
$60$	0.866198	0.111826
$61$	−1.73240	−0.221811	−0.110905	−	0.993831i	$-0.535375\pi$
$61$	−1.73240	−0.221811	−0.110905	+	0.993831i	$0.535375\pi$
$62$	−8.73240	−1.10902
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.62857	−0.326034
$66$	−4.21509	−0.518842
$67$	−2.96539	−0.362280	−0.181140	−	0.983457i	$-0.557979\pi$
$67$	−2.96539	−0.362280	−0.181140	+	0.983457i	$0.557979\pi$
$68$	−2.13380	−0.258761
$69$	−8.04668	−0.968707
$70$	0	0
$71$	3.52938	0.418860	0.209430	−	0.977824i	$-0.432839\pi$
$71$	3.52938	0.418860	0.209430	+	0.977824i	$0.432839\pi$
$72$	1.00000	0.117851
$73$	−4.18048	−0.489289	−0.244644	−	0.969613i	$-0.578671\pi$
$73$	−4.18048	−0.489289	−0.244644	+	0.969613i	$0.578671\pi$
$74$	−4.90081	−0.569707
$75$	−4.24970	−0.490713
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−3.03461	−0.343602
$79$	8.64528	0.972670	0.486335	−	0.873773i	$-0.338334\pi$
$79$	8.64528	0.972670	0.486335	+	0.873773i	$0.338334\pi$
$80$	0.866198	0.0968439
$81$	1.00000	0.111111
$82$	−1.61650	−0.178512
$83$	12.8950	1.41541	0.707704	−	0.706509i	$-0.249731\pi$
$83$	12.8950	1.41541	0.707704	+	0.706509i	$0.249731\pi$
$84$	0	0
$85$	−1.84830	−0.200476
$86$	7.52938	0.811914
$87$	5.24970	0.562827
$88$	−4.21509	−0.449330
$89$	−1.61650	−0.171348	−0.0856742	−	0.996323i	$-0.527304\pi$
$89$	−1.61650	−0.171348	−0.0856742	+	0.996323i	$0.527304\pi$
$90$	0.866198	0.0913053
$91$	0	0
$92$	−8.04668	−0.838925
$93$	−8.73240	−0.905507
$94$	−1.66318	−0.171544
$95$	−0.866198	−0.0888701
$96$	1.00000	0.102062
$97$	−13.3835	−1.35889	−0.679444	−	0.733727i	$-0.737779\pi$
$97$	−13.3835	−1.35889	−0.679444	+	0.733727i	$0.737779\pi$
$98$	0	0
$99$	−4.21509	−0.423633
$100$	−4.24970	−0.424970
$101$	−12.6978	−1.26348	−0.631739	−	0.775182i	$-0.717658\pi$
$101$	−12.6978	−1.26348	−0.631739	+	0.775182i	$0.717658\pi$
$102$	−2.13380	−0.211278
$103$	9.55191	0.941178	0.470589	−	0.882353i	$-0.344041\pi$
$103$	9.55191	0.941178	0.470589	+	0.882353i	$0.344041\pi$
$104$	−3.03461	−0.297568
$105$	0	0
$106$	−4.03461	−0.391876
$107$	−4.23763	−0.409667	−0.204833	−	0.978797i	$-0.565665\pi$
$107$	−4.23763	−0.409667	−0.204833	+	0.978797i	$0.565665\pi$
$108$	1.00000	0.0962250
$109$	19.0634	1.82594	0.912971	−	0.408025i	$-0.133782\pi$
$109$	19.0634	1.82594	0.912971	+	0.408025i	$0.133782\pi$
$110$	−3.65111	−0.348119
$111$	−4.90081	−0.465164
$112$	0	0
$113$	−1.27968	−0.120382	−0.0601910	−	0.998187i	$-0.519171\pi$
$113$	−1.27968	−0.120382	−0.0601910	+	0.998187i	$0.519171\pi$
$114$	−1.00000	−0.0936586
$115$	−6.97002	−0.649958
$116$	5.24970	0.487422
$117$	−3.03461	−0.280550
$118$	−5.38350	−0.495592
$119$	0	0
$120$	0.866198	0.0790727
$121$	6.76700	0.615182
$122$	−1.73240	−0.156844
$123$	−1.61650	−0.145755
$124$	−8.73240	−0.784192
$125$	−8.01207	−0.716622
$126$	0	0
$127$	13.4994	1.19788	0.598939	−	0.800795i	$-0.295589\pi$
$127$	13.4994	1.19788	0.598939	+	0.800795i	$0.295589\pi$
$128$	1.00000	0.0883883
$129$	7.52938	0.662925
$130$	−2.62857	−0.230541
$131$	1.96539	0.171717	0.0858585	−	0.996307i	$-0.472637\pi$
$131$	1.96539	0.171717	0.0858585	+	0.996307i	$0.472637\pi$
$132$	−4.21509	−0.366877
$133$	0	0
$134$	−2.96539	−0.256171
$135$	0.866198	0.0745505
$136$	−2.13380	−0.182972
$137$	−1.80161	−0.153922	−0.0769611	−	0.997034i	$-0.524522\pi$
$137$	−1.80161	−0.153922	−0.0769611	+	0.997034i	$0.524522\pi$
$138$	−8.04668	−0.684979
$139$	1.26178	0.107022	0.0535112	−	0.998567i	$-0.482959\pi$
$139$	1.26178	0.107022	0.0535112	+	0.998567i	$0.482959\pi$
$140$	0	0
$141$	−1.66318	−0.140065
$142$	3.52938	0.296179
$143$	12.7912	1.06965
$144$	1.00000	0.0833333
$145$	4.54728	0.377631
$146$	−4.18048	−0.345979
$147$	0	0
$148$	−4.90081	−0.402844
$149$	11.6632	0.955485	0.477742	−	0.878500i	$-0.341455\pi$
$149$	11.6632	0.955485	0.477742	+	0.878500i	$0.341455\pi$
$150$	−4.24970	−0.346987
$151$	2.46479	0.200582	0.100291	−	0.994958i	$-0.468023\pi$
$151$	2.46479	0.200582	0.100291	+	0.994958i	$0.468023\pi$
$152$	−1.00000	−0.0811107
$153$	−2.13380	−0.172508
$154$	0	0
$155$	−7.56399	−0.607554
$156$	−3.03461	−0.242963
$157$	15.8016	1.26111	0.630553	−	0.776146i	$-0.282828\pi$
$157$	15.8016	1.26111	0.630553	+	0.776146i	$0.282828\pi$
$158$	8.64528	0.687781
$159$	−4.03461	−0.319965
$160$	0.866198	0.0684790
$161$	0	0
$162$	1.00000	0.0785674
$163$	6.83622	0.535454	0.267727	−	0.963495i	$-0.413727\pi$
$163$	6.83622	0.535454	0.267727	+	0.963495i	$0.413727\pi$
$164$	−1.61650	−0.126227
$165$	−3.65111	−0.284238
$166$	12.8950	1.00084
$167$	2.40141	0.185826	0.0929132	−	0.995674i	$-0.470382\pi$
$167$	2.40141	0.185826	0.0929132	+	0.995674i	$0.470382\pi$
$168$	0	0
$169$	−3.79115	−0.291627
$170$	−1.84830	−0.141758
$171$	−1.00000	−0.0764719
$172$	7.52938	0.574110
$173$	−14.2497	−1.08338	−0.541692	−	0.840577i	$-0.682216\pi$
$173$	−14.2497	−1.08338	−0.541692	+	0.840577i	$0.682216\pi$
$174$	5.24970	0.397979
$175$	0	0
$176$	−4.21509	−0.317725
$177$	−5.38350	−0.404649
$178$	−1.61650	−0.121162
$179$	−1.03461	−0.0773302	−0.0386651	−	0.999252i	$-0.512311\pi$
$179$	−1.03461	−0.0773302	−0.0386651	+	0.999252i	$0.512311\pi$
$180$	0.866198	0.0645626
$181$	−25.8258	−1.91961	−0.959807	−	0.280661i	$-0.909446\pi$
$181$	−25.8258	−1.91961	−0.959807	+	0.280661i	$0.909446\pi$
$182$	0	0
$183$	−1.73240	−0.128062
$184$	−8.04668	−0.593209
$185$	−4.24507	−0.312104
$186$	−8.73240	−0.640290
$187$	8.99417	0.657719
$188$	−1.66318	−0.121300
$189$	0	0
$190$	−0.866198	−0.0628406
$191$	−21.1280	−1.52877	−0.764383	−	0.644762i	$-0.776956\pi$
$191$	−21.1280	−1.52877	−0.764383	+	0.644762i	$0.776956\pi$
$192$	1.00000	0.0721688
$193$	−0.0991936	−0.00714011	−0.00357006	−	0.999994i	$-0.501136\pi$
$193$	−0.0991936	−0.00714011	−0.00357006	+	0.999994i	$0.501136\pi$
$194$	−13.3835	−0.960879
$195$	−2.62857	−0.188236
$196$	0	0
$197$	16.8783	1.20253	0.601264	−	0.799051i	$-0.294664\pi$
$197$	16.8783	1.20253	0.601264	+	0.799051i	$0.294664\pi$
$198$	−4.21509	−0.299554
$199$	13.0346	0.923999	0.461999	−	0.886880i	$-0.347132\pi$
$199$	13.0346	0.923999	0.461999	+	0.886880i	$0.347132\pi$
$200$	−4.24970	−0.300499
$201$	−2.96539	−0.209163
$202$	−12.6978	−0.893413
$203$	0	0
$204$	−2.13380	−0.149396
$205$	−1.40021	−0.0977947
$206$	9.55191	0.665513
$207$	−8.04668	−0.559283
$208$	−3.03461	−0.210412
$209$	4.21509	0.291564
$210$	0	0
$211$	28.1400	1.93724	0.968620	−	0.248545i	$-0.0799523\pi$
$211$	28.1400	1.93724	0.968620	+	0.248545i	$0.0799523\pi$
$212$	−4.03461	−0.277098
$213$	3.52938	0.241829
$214$	−4.23763	−0.289678
$215$	6.52193	0.444792
$216$	1.00000	0.0680414
$217$	0	0
$218$	19.0634	1.29114
$219$	−4.18048	−0.282491
$220$	−3.65111	−0.246158
$221$	6.47525	0.435573
$222$	−4.90081	−0.328921
$223$	−17.9475	−1.20185	−0.600926	−	0.799304i	$-0.705202\pi$
$223$	−17.9475	−1.20185	−0.600926	+	0.799304i	$0.705202\pi$
$224$	0	0
$225$	−4.24970	−0.283313
$226$	−1.27968	−0.0851229
$227$	−0.866198	−0.0574916	−0.0287458	−	0.999587i	$-0.509151\pi$
$227$	−0.866198	−0.0574916	−0.0287458	+	0.999587i	$0.509151\pi$
$228$	−1.00000	−0.0662266
$229$	−25.6966	−1.69808	−0.849039	−	0.528330i	$-0.822818\pi$
$229$	−25.6966	−1.69808	−0.849039	+	0.528330i	$0.822818\pi$
$230$	−6.97002	−0.459590
$231$	0	0
$232$	5.24970	0.344660
$233$	22.8604	1.49763	0.748816	−	0.662778i	$-0.230623\pi$
$233$	22.8604	1.49763	0.748816	+	0.662778i	$0.230623\pi$
$234$	−3.03461	−0.198379
$235$	−1.44064	−0.0939772
$236$	−5.38350	−0.350436
$237$	8.64528	0.561571
$238$	0	0
$239$	8.49940	0.549781	0.274890	−	0.961476i	$-0.411358\pi$
$239$	8.49940	0.549781	0.274890	+	0.961476i	$0.411358\pi$
$240$	0.866198	0.0559129
$241$	−18.7791	−1.20967	−0.604833	−	0.796352i	$-0.706760\pi$
$241$	−18.7791	−1.20967	−0.604833	+	0.796352i	$0.706760\pi$
$242$	6.76700	0.435000
$243$	1.00000	0.0641500
$244$	−1.73240	−0.110905
$245$	0	0
$246$	−1.61650	−0.103064
$247$	3.03461	0.193087
$248$	−8.73240	−0.554508
$249$	12.8950	0.817186
$250$	−8.01207	−0.506728
$251$	−11.4123	−0.720337	−0.360168	−	0.932887i	$-0.617281\pi$
$251$	−11.4123	−0.720337	−0.360168	+	0.932887i	$0.617281\pi$
$252$	0	0
$253$	33.9175	2.13238
$254$	13.4994	0.847028
$255$	−1.84830	−0.115745
$256$	1.00000	0.0625000
$257$	−23.5340	−1.46801	−0.734006	−	0.679143i	$-0.762351\pi$
$257$	−23.5340	−1.46801	−0.734006	+	0.679143i	$0.762351\pi$
$258$	7.52938	0.468759
$259$	0	0
$260$	−2.62857	−0.163017
$261$	5.24970	0.324948
$262$	1.96539	0.121422
$263$	−10.5819	−0.652507	−0.326254	−	0.945282i	$-0.605786\pi$
$263$	−10.5819	−0.652507	−0.326254	+	0.945282i	$0.605786\pi$
$264$	−4.21509	−0.259421
$265$	−3.49477	−0.214682
$266$	0	0
$267$	−1.61650	−0.0989281
$268$	−2.96539	−0.181140
$269$	27.9117	1.70181	0.850903	−	0.525323i	$-0.176056\pi$
$269$	27.9117	1.70181	0.850903	+	0.525323i	$0.176056\pi$
$270$	0.866198	0.0527151
$271$	24.0634	1.46175	0.730873	−	0.682513i	$-0.239113\pi$
$271$	24.0634	1.46175	0.730873	+	0.682513i	$0.239113\pi$
$272$	−2.13380	−0.129381
$273$	0	0
$274$	−1.80161	−0.108839
$275$	17.9129	1.08019
$276$	−8.04668	−0.484353
$277$	−17.4423	−1.04800	−0.524002	−	0.851717i	$-0.675562\pi$
$277$	−17.4423	−1.04800	−0.524002	+	0.851717i	$0.675562\pi$
$278$	1.26178	0.0756762
$279$	−8.73240	−0.522795
$280$	0	0
$281$	2.36097	0.140844	0.0704218	−	0.997517i	$-0.477565\pi$
$281$	2.36097	0.140844	0.0704218	+	0.997517i	$0.477565\pi$
$282$	−1.66318	−0.0990409
$283$	16.7024	0.992856	0.496428	−	0.868078i	$-0.334645\pi$
$283$	16.7024	0.992856	0.496428	+	0.868078i	$0.334645\pi$
$284$	3.52938	0.209430
$285$	−0.866198	−0.0513092
$286$	12.7912	0.756357
$287$	0	0
$288$	1.00000	0.0589256
$289$	−12.4469	−0.732170
$290$	4.54728	0.267026
$291$	−13.3835	−0.784555
$292$	−4.18048	−0.244644
$293$	1.11127	0.0649210	0.0324605	−	0.999473i	$-0.489666\pi$
$293$	1.11127	0.0649210	0.0324605	+	0.999473i	$0.489666\pi$
$294$	0	0
$295$	−4.66318	−0.271501
$296$	−4.90081	−0.284854
$297$	−4.21509	−0.244584
$298$	11.6632	0.675630
$299$	24.4185	1.41216
$300$	−4.24970	−0.245357
$301$	0	0
$302$	2.46479	0.141833
$303$	−12.6978	−0.729469
$304$	−1.00000	−0.0573539
$305$	−1.50060	−0.0859240
$306$	−2.13380	−0.121981
$307$	−23.7099	−1.35319	−0.676597	−	0.736354i	$-0.736546\pi$
$307$	−23.7099	−1.35319	−0.676597	+	0.736354i	$0.736546\pi$
$308$	0	0
$309$	9.55191	0.543389
$310$	−7.56399	−0.429606
$311$	−32.8829	−1.86462	−0.932309	−	0.361662i	$-0.882209\pi$
$311$	−32.8829	−1.86462	−0.932309	+	0.361662i	$0.882209\pi$
$312$	−3.03461	−0.171801
$313$	10.0167	0.566178	0.283089	−	0.959094i	$-0.408641\pi$
$313$	10.0167	0.566178	0.283089	+	0.959094i	$0.408641\pi$
$314$	15.8016	0.891737
$315$	0	0
$316$	8.64528	0.486335
$317$	27.1626	1.52560	0.762801	−	0.646633i	$-0.223823\pi$
$317$	27.1626	1.52560	0.762801	+	0.646633i	$0.223823\pi$
$318$	−4.03461	−0.226250
$319$	−22.1280	−1.23893
$320$	0.866198	0.0484220
$321$	−4.23763	−0.236521
$322$	0	0
$323$	2.13380	0.118728
$324$	1.00000	0.0555556
$325$	12.8962	0.715351
$326$	6.83622	0.378623
$327$	19.0634	1.05421
$328$	−1.61650	−0.0892562
$329$	0	0
$330$	−3.65111	−0.200987
$331$	24.2093	1.33066	0.665331	−	0.746549i	$-0.268291\pi$
$331$	24.2093	1.33066	0.665331	+	0.746549i	$0.268291\pi$
$332$	12.8950	0.707704
$333$	−4.90081	−0.268563
$334$	2.40141	0.131399
$335$	−2.56862	−0.140339
$336$	0	0
$337$	−25.3718	−1.38209	−0.691046	−	0.722811i	$-0.742850\pi$
$337$	−25.3718	−1.38209	−0.691046	+	0.722811i	$0.742850\pi$
$338$	−3.79115	−0.206212
$339$	−1.27968	−0.0695026
$340$	−1.84830	−0.100238
$341$	36.8079	1.99326
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	7.52938	0.405957
$345$	−6.97002	−0.375253
$346$	−14.2497	−0.766069
$347$	−16.7849	−0.901061	−0.450531	−	0.892761i	$-0.648765\pi$
$347$	−16.7849	−0.901061	−0.450531	+	0.892761i	$0.648765\pi$
$348$	5.24970	0.281413
$349$	15.2439	0.815986	0.407993	−	0.912985i	$-0.366229\pi$
$349$	15.2439	0.815986	0.407993	+	0.912985i	$0.366229\pi$
$350$	0	0
$351$	−3.03461	−0.161975
$352$	−4.21509	−0.224665
$353$	−18.6332	−0.991745	−0.495873	−	0.868395i	$-0.665152\pi$
$353$	−18.6332	−0.991745	−0.495873	+	0.868395i	$0.665152\pi$
$354$	−5.38350	−0.286130
$355$	3.05714	0.162256
$356$	−1.61650	−0.0856742
$357$	0	0
$358$	−1.03461	−0.0546807
$359$	−26.8604	−1.41764	−0.708818	−	0.705391i	$-0.750771\pi$
$359$	−26.8604	−1.41764	−0.708818	+	0.705391i	$0.750771\pi$
$360$	0.866198	0.0456527
$361$	1.00000	0.0526316
$362$	−25.8258	−1.35737
$363$	6.76700	0.355176
$364$	0	0
$365$	−3.62113	−0.189539
$366$	−1.73240	−0.0905538
$367$	−12.0634	−0.629704	−0.314852	−	0.949141i	$-0.601955\pi$
$367$	−12.0634	−0.629704	−0.314852	+	0.949141i	$0.601955\pi$
$368$	−8.04668	−0.419462
$369$	−1.61650	−0.0841515
$370$	−4.24507	−0.220691
$371$	0	0
$372$	−8.73240	−0.452754
$373$	9.62737	0.498487	0.249243	−	0.968441i	$-0.419818\pi$
$373$	9.62737	0.498487	0.249243	+	0.968441i	$0.419818\pi$
$374$	8.99417	0.465078
$375$	−8.01207	−0.413742
$376$	−1.66318	−0.0857720
$377$	−15.9308	−0.820477
$378$	0	0
$379$	2.29175	0.117719	0.0588597	−	0.998266i	$-0.481254\pi$
$379$	2.29175	0.117719	0.0588597	+	0.998266i	$0.481254\pi$
$380$	−0.866198	−0.0444350
$381$	13.4994	0.691595
$382$	−21.1280	−1.08100
$383$	22.6978	1.15980	0.579901	−	0.814687i	$-0.303091\pi$
$383$	22.6978	1.15980	0.579901	+	0.814687i	$0.303091\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−0.0991936	−0.00504882
$387$	7.52938	0.382740
$388$	−13.3835	−0.679444
$389$	−30.2318	−1.53281	−0.766406	−	0.642356i	$-0.777957\pi$
$389$	−30.2318	−1.53281	−0.766406	+	0.642356i	$0.777957\pi$
$390$	−2.62857	−0.133103
$391$	17.1700	0.868326
$392$	0	0
$393$	1.96539	0.0991409
$394$	16.8783	0.850315
$395$	7.48852	0.376789
$396$	−4.21509	−0.211816
$397$	−1.19719	−0.0600852	−0.0300426	−	0.999549i	$-0.509564\pi$
$397$	−1.19719	−0.0600852	−0.0300426	+	0.999549i	$0.509564\pi$
$398$	13.0346	0.653366
$399$	0	0
$400$	−4.24970	−0.212485
$401$	29.6966	1.48298	0.741488	−	0.670966i	$-0.234120\pi$
$401$	29.6966	1.48298	0.741488	+	0.670966i	$0.234120\pi$
$402$	−2.96539	−0.147900
$403$	26.4994	1.32003
$404$	−12.6978	−0.631739
$405$	0.866198	0.0430417
$406$	0	0
$407$	20.6574	1.02395
$408$	−2.13380	−0.105639
$409$	2.97747	0.147226	0.0736131	−	0.997287i	$-0.476547\pi$
$409$	2.97747	0.147226	0.0736131	+	0.997287i	$0.476547\pi$
$410$	−1.40021	−0.0691513
$411$	−1.80161	−0.0888670
$412$	9.55191	0.470589
$413$	0	0
$414$	−8.04668	−0.395473
$415$	11.1696	0.548294
$416$	−3.03461	−0.148784
$417$	1.26178	0.0617894
$418$	4.21509	0.206167
$419$	11.4469	0.559217	0.279609	−	0.960114i	$-0.409795\pi$
$419$	11.4469	0.559217	0.279609	+	0.960114i	$0.409795\pi$
$420$	0	0
$421$	−8.16258	−0.397820	−0.198910	−	0.980018i	$-0.563740\pi$
$421$	−8.16258	−0.397820	−0.198910	+	0.980018i	$0.563740\pi$
$422$	28.1400	1.36984
$423$	−1.66318	−0.0808666
$424$	−4.03461	−0.195938
$425$	9.06802	0.439864
$426$	3.52938	0.170999
$427$	0	0
$428$	−4.23763	−0.204833
$429$	12.7912	0.617563
$430$	6.52193	0.314516
$431$	0.738225	0.0355590	0.0177795	−	0.999842i	$-0.494340\pi$
$431$	0.738225	0.0355590	0.0177795	+	0.999842i	$0.494340\pi$
$432$	1.00000	0.0481125
$433$	12.8783	0.618890	0.309445	−	0.950917i	$-0.399857\pi$
$433$	12.8783	0.618890	0.309445	+	0.950917i	$0.399857\pi$
$434$	0	0
$435$	4.54728	0.218025
$436$	19.0634	0.912971
$437$	8.04668	0.384925
$438$	−4.18048	−0.199751
$439$	−13.2497	−0.632374	−0.316187	−	0.948697i	$-0.602403\pi$
$439$	−13.2497	−0.632374	−0.316187	+	0.948697i	$0.602403\pi$
$440$	−3.65111	−0.174060
$441$	0	0
$442$	6.47525	0.307996
$443$	−20.5761	−0.977598	−0.488799	−	0.872396i	$-0.662565\pi$
$443$	−20.5761	−0.977598	−0.488799	+	0.872396i	$0.662565\pi$
$444$	−4.90081	−0.232582
$445$	−1.40021	−0.0663762
$446$	−17.9475	−0.849838
$447$	11.6632	0.551650
$448$	0	0
$449$	−31.8125	−1.50132	−0.750662	−	0.660686i	$-0.770265\pi$
$449$	−31.8125	−1.50132	−0.750662	+	0.660686i	$0.770265\pi$
$450$	−4.24970	−0.200333
$451$	6.81369	0.320844
$452$	−1.27968	−0.0601910
$453$	2.46479	0.115806
$454$	−0.866198	−0.0406527
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	−34.4710	−1.61249	−0.806244	−	0.591584i	$-0.798503\pi$
$457$	−34.4710	−1.61249	−0.806244	+	0.591584i	$0.798503\pi$
$458$	−25.6966	−1.20072
$459$	−2.13380	−0.0995973
$460$	−6.97002	−0.324979
$461$	−9.60323	−0.447267	−0.223633	−	0.974673i	$-0.571792\pi$
$461$	−9.60323	−0.447267	−0.223633	+	0.974673i	$0.571792\pi$
$462$	0	0
$463$	33.8950	1.57523	0.787617	−	0.616166i	$-0.211315\pi$
$463$	33.8950	1.57523	0.787617	+	0.616166i	$0.211315\pi$
$464$	5.24970	0.243711
$465$	−7.56399	−0.350771
$466$	22.8604	1.05899
$467$	−38.2380	−1.76945	−0.884723	−	0.466118i	$-0.845652\pi$
$467$	−38.2380	−1.76945	−0.884723	+	0.466118i	$0.845652\pi$
$468$	−3.03461	−0.140275
$469$	0	0
$470$	−1.44064	−0.0664519
$471$	15.8016	0.728100
$472$	−5.38350	−0.247796
$473$	−31.7370	−1.45927
$474$	8.64528	0.397091
$475$	4.24970	0.194990
$476$	0	0
$477$	−4.03461	−0.184732
$478$	8.49940	0.388754
$479$	−32.3252	−1.47697	−0.738487	−	0.674267i	$-0.764459\pi$
$479$	−32.3252	−1.47697	−0.738487	+	0.674267i	$0.764459\pi$
$480$	0.866198	0.0395364
$481$	14.8720	0.678106
$482$	−18.7791	−0.855364
$483$	0	0
$484$	6.76700	0.307591
$485$	−11.5928	−0.526400
$486$	1.00000	0.0453609
$487$	26.3956	1.19610	0.598049	−	0.801460i	$-0.295943\pi$
$487$	26.3956	1.19610	0.598049	+	0.801460i	$0.295943\pi$
$488$	−1.73240	−0.0784219
$489$	6.83622	0.309145
$490$	0	0
$491$	−34.4531	−1.55485	−0.777424	−	0.628977i	$-0.783474\pi$
$491$	−34.4531	−1.55485	−0.777424	+	0.628977i	$0.783474\pi$
$492$	−1.61650	−0.0728773
$493$	−11.2018	−0.504505
$494$	3.03461	0.136533
$495$	−3.65111	−0.164105
$496$	−8.73240	−0.392096
$497$	0	0
$498$	12.8950	0.577838
$499$	−17.8258	−0.797991	−0.398995	−	0.916953i	$-0.630641\pi$
$499$	−17.8258	−0.797991	−0.398995	+	0.916953i	$0.630641\pi$
$500$	−8.01207	−0.358311
$501$	2.40141	0.107287
$502$	−11.4123	−0.509355
$503$	21.8483	0.974167	0.487084	−	0.873355i	$-0.338061\pi$
$503$	21.8483	0.974167	0.487084	+	0.873355i	$0.338061\pi$
$504$	0	0
$505$	−10.9988	−0.489440
$506$	33.9175	1.50782
$507$	−3.79115	−0.168371
$508$	13.4994	0.598939
$509$	−43.9358	−1.94742	−0.973711	−	0.227788i	$-0.926851\pi$
$509$	−43.9358	−1.94742	−0.973711	+	0.227788i	$0.926851\pi$
$510$	−1.84830	−0.0818439
$511$	0	0
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	−23.5340	−1.03804
$515$	8.27385	0.364589
$516$	7.52938	0.331462
$517$	7.01046	0.308320
$518$	0	0
$519$	−14.2497	−0.625492
$520$	−2.62857	−0.115271
$521$	−0.222536	−0.00974950	−0.00487475	−	0.999988i	$-0.501552\pi$
$521$	−0.222536	−0.00974950	−0.00487475	+	0.999988i	$0.501552\pi$
$522$	5.24970	0.229773
$523$	−15.7791	−0.689971	−0.344985	−	0.938608i	$-0.612116\pi$
$523$	−15.7791	−0.689971	−0.344985	+	0.938608i	$0.612116\pi$
$524$	1.96539	0.0858585
$525$	0	0
$526$	−10.5819	−0.461392
$527$	18.6332	0.811675
$528$	−4.21509	−0.183438
$529$	41.7491	1.81518
$530$	−3.49477	−0.151803
$531$	−5.38350	−0.233624
$532$	0	0
$533$	4.90544	0.212478
$534$	−1.61650	−0.0699527
$535$	−3.67062	−0.158695
$536$	−2.96539	−0.128085
$537$	−1.03461	−0.0446466
$538$	27.9117	1.20336
$539$	0	0
$540$	0.866198	0.0372752
$541$	−35.9059	−1.54371	−0.771857	−	0.635797i	$-0.780672\pi$
$541$	−35.9059	−1.54371	−0.771857	+	0.635797i	$0.780672\pi$
$542$	24.0634	1.03361
$543$	−25.8258	−1.10829
$544$	−2.13380	−0.0914860
$545$	16.5127	0.707325
$546$	0	0
$547$	8.54608	0.365404	0.182702	−	0.983168i	$-0.441516\pi$
$547$	8.54608	0.365404	0.182702	+	0.983168i	$0.441516\pi$
$548$	−1.80161	−0.0769611
$549$	−1.73240	−0.0739369
$550$	17.9129	0.763808
$551$	−5.24970	−0.223645
$552$	−8.04668	−0.342490
$553$	0	0
$554$	−17.4423	−0.741051
$555$	−4.24507	−0.180193
$556$	1.26178	0.0535112
$557$	0.279678	0.0118503	0.00592517	−	0.999982i	$-0.498114\pi$
$557$	0.279678	0.0118503	0.00592517	+	0.999982i	$0.498114\pi$
$558$	−8.73240	−0.369672
$559$	−22.8487	−0.966398
$560$	0	0
$561$	8.99417	0.379734
$562$	2.36097	0.0995915
$563$	15.3835	0.648337	0.324169	−	0.945999i	$-0.394915\pi$
$563$	15.3835	0.648337	0.324169	+	0.945999i	$0.394915\pi$
$564$	−1.66318	−0.0700325
$565$	−1.10845	−0.0466330
$566$	16.7024	0.702055
$567$	0	0
$568$	3.52938	0.148089
$569$	37.8258	1.58574	0.792869	−	0.609392i	$-0.208586\pi$
$569$	37.8258	1.58574	0.792869	+	0.609392i	$0.208586\pi$
$570$	−0.866198	−0.0362811
$571$	−21.1326	−0.884372	−0.442186	−	0.896923i	$-0.645797\pi$
$571$	−21.1326	−0.884372	−0.442186	+	0.896923i	$0.645797\pi$
$572$	12.7912	0.534825
$573$	−21.1280	−0.882634
$574$	0	0
$575$	34.1960	1.42607
$576$	1.00000	0.0416667
$577$	−10.7082	−0.445790	−0.222895	−	0.974842i	$-0.571551\pi$
$577$	−10.7082	−0.445790	−0.222895	+	0.974842i	$0.571551\pi$
$578$	−12.4469	−0.517722
$579$	−0.0991936	−0.00412235
$580$	4.54728	0.188816
$581$	0	0
$582$	−13.3835	−0.554764
$583$	17.0062	0.704327
$584$	−4.18048	−0.172990
$585$	−2.62857	−0.108678
$586$	1.11127	0.0459061
$587$	36.6787	1.51389	0.756946	−	0.653478i	$-0.226691\pi$
$587$	36.6787	1.51389	0.756946	+	0.653478i	$0.226691\pi$
$588$	0	0
$589$	8.73240	0.359812
$590$	−4.66318	−0.191980
$591$	16.8783	0.694279
$592$	−4.90081	−0.201422
$593$	2.37263	0.0974321	0.0487160	−	0.998813i	$-0.484487\pi$
$593$	2.37263	0.0974321	0.0487160	+	0.998813i	$0.484487\pi$
$594$	−4.21509	−0.172947
$595$	0	0
$596$	11.6632	0.477742
$597$	13.0346	0.533471
$598$	24.4185	0.998548
$599$	−15.8062	−0.645826	−0.322913	−	0.946429i	$-0.604662\pi$
$599$	−15.8062	−0.645826	−0.322913	+	0.946429i	$0.604662\pi$
$600$	−4.24970	−0.173493
$601$	−31.9521	−1.30335	−0.651677	−	0.758497i	$-0.725934\pi$
$601$	−31.9521	−1.30335	−0.651677	+	0.758497i	$0.725934\pi$
$602$	0	0
$603$	−2.96539	−0.120760
$604$	2.46479	0.100291
$605$	5.86157	0.238307
$606$	−12.6978	−0.515812
$607$	27.5865	1.11970	0.559851	−	0.828593i	$-0.310858\pi$
$607$	27.5865	1.11970	0.559851	+	0.828593i	$0.310858\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	−1.50060	−0.0607575
$611$	5.04710	0.204184
$612$	−2.13380	−0.0862538
$613$	21.2797	0.859478	0.429739	−	0.902953i	$-0.358606\pi$
$613$	21.2797	0.859478	0.429739	+	0.902953i	$0.358606\pi$
$614$	−23.7099	−0.956852
$615$	−1.40021	−0.0564618
$616$	0	0
$617$	−30.6215	−1.23278	−0.616389	−	0.787442i	$-0.711405\pi$
$617$	−30.6215	−1.23278	−0.616389	+	0.787442i	$0.711405\pi$
$618$	9.55191	0.384234
$619$	29.1972	1.17353	0.586767	−	0.809756i	$-0.300400\pi$
$619$	29.1972	1.17353	0.586767	+	0.809756i	$0.300400\pi$
$620$	−7.56399	−0.303777
$621$	−8.04668	−0.322902
$622$	−32.8829	−1.31848
$623$	0	0
$624$	−3.03461	−0.121482
$625$	14.3085	0.572338
$626$	10.0167	0.400348
$627$	4.21509	0.168335
$628$	15.8016	0.630553
$629$	10.4573	0.416962
$630$	0	0
$631$	−13.0887	−0.521054	−0.260527	−	0.965467i	$-0.583896\pi$
$631$	−13.0887	−0.521054	−0.260527	+	0.965467i	$0.583896\pi$
$632$	8.64528	0.343891
$633$	28.1400	1.11847
$634$	27.1626	1.07876
$635$	11.6932	0.464029
$636$	−4.03461	−0.159983
$637$	0	0
$638$	−22.1280	−0.876055
$639$	3.52938	0.139620
$640$	0.866198	0.0342395
$641$	−34.4769	−1.36175	−0.680877	−	0.732398i	$-0.738401\pi$
$641$	−34.4769	−1.36175	−0.680877	+	0.732398i	$0.738401\pi$
$642$	−4.23763	−0.167246
$643$	−11.7728	−0.464275	−0.232138	−	0.972683i	$-0.574572\pi$
$643$	−11.7728	−0.464275	−0.232138	+	0.972683i	$0.574572\pi$
$644$	0	0
$645$	6.52193	0.256801
$646$	2.13380	0.0839533
$647$	23.4664	0.922560	0.461280	−	0.887255i	$-0.347390\pi$
$647$	23.4664	0.922560	0.461280	+	0.887255i	$0.347390\pi$
$648$	1.00000	0.0392837
$649$	22.6920	0.890737
$650$	12.8962	0.505830
$651$	0	0
$652$	6.83622	0.267727
$653$	−50.0696	−1.95938	−0.979688	−	0.200527i	$-0.935734\pi$
$653$	−50.0696	−1.95938	−0.979688	+	0.200527i	$0.935734\pi$
$654$	19.0634	0.745437
$655$	1.70242	0.0665190
$656$	−1.61650	−0.0631136
$657$	−4.18048	−0.163096
$658$	0	0
$659$	13.2151	0.514787	0.257393	−	0.966307i	$-0.417136\pi$
$659$	13.2151	0.514787	0.257393	+	0.966307i	$0.417136\pi$
$660$	−3.65111	−0.142119
$661$	10.7624	0.418608	0.209304	−	0.977851i	$-0.432880\pi$
$661$	10.7624	0.418608	0.209304	+	0.977851i	$0.432880\pi$
$662$	24.2093	0.940920
$663$	6.47525	0.251478
$664$	12.8950	0.500422
$665$	0	0
$666$	−4.90081	−0.189902
$667$	−42.2427	−1.63564
$668$	2.40141	0.0929132
$669$	−17.9475	−0.693890
$670$	−2.56862	−0.0992343
$671$	7.30221	0.281899
$672$	0	0
$673$	19.5974	0.755424	0.377712	−	0.925923i	$-0.376711\pi$
$673$	19.5974	0.755424	0.377712	+	0.925923i	$0.376711\pi$
$674$	−25.3718	−0.977287
$675$	−4.24970	−0.163571
$676$	−3.79115	−0.145814
$677$	−22.6274	−0.869641	−0.434820	−	0.900517i	$-0.643188\pi$
$677$	−22.6274	−0.869641	−0.434820	+	0.900517i	$0.643188\pi$
$678$	−1.27968	−0.0491457
$679$	0	0
$680$	−1.84830	−0.0708789
$681$	−0.866198	−0.0331928
$682$	36.8079	1.40945
$683$	41.3056	1.58052	0.790258	−	0.612774i	$-0.209946\pi$
$683$	41.3056	1.58052	0.790258	+	0.612774i	$0.209946\pi$
$684$	−1.00000	−0.0382360
$685$	−1.56055	−0.0596257
$686$	0	0
$687$	−25.6966	−0.980386
$688$	7.52938	0.287055
$689$	12.2435	0.466438
$690$	−6.97002	−0.265344
$691$	−7.29758	−0.277613	−0.138807	−	0.990320i	$-0.544327\pi$
$691$	−7.29758	−0.277613	−0.138807	+	0.990320i	$0.544327\pi$
$692$	−14.2497	−0.541692
$693$	0	0
$694$	−16.7849	−0.637146
$695$	1.09295	0.0414579
$696$	5.24970	0.198989
$697$	3.44929	0.130651
$698$	15.2439	0.576989
$699$	22.8604	0.864659
$700$	0	0
$701$	5.74447	0.216966	0.108483	−	0.994098i	$-0.465401\pi$
$701$	5.74447	0.216966	0.108483	+	0.994098i	$0.465401\pi$
$702$	−3.03461	−0.114534
$703$	4.90081	0.184837
$704$	−4.21509	−0.158862
$705$	−1.44064	−0.0542578
$706$	−18.6332	−0.701270
$707$	0	0
$708$	−5.38350	−0.202324
$709$	23.9867	0.900840	0.450420	−	0.892817i	$-0.351274\pi$
$709$	23.9867	0.900840	0.450420	+	0.892817i	$0.351274\pi$
$710$	3.05714	0.114732
$711$	8.64528	0.324223
$712$	−1.61650	−0.0605808
$713$	70.2668	2.63151
$714$	0	0
$715$	11.0797	0.414356
$716$	−1.03461	−0.0386651
$717$	8.49940	0.317416
$718$	−26.8604	−1.00242
$719$	−23.4048	−0.872853	−0.436427	−	0.899740i	$-0.643756\pi$
$719$	−23.4048	−0.872853	−0.436427	+	0.899740i	$0.643756\pi$
$720$	0.866198	0.0322813
$721$	0	0
$722$	1.00000	0.0372161
$723$	−18.7791	−0.698401
$724$	−25.8258	−0.959807
$725$	−22.3097	−0.828560
$726$	6.76700	0.251147
$727$	23.4706	0.870477	0.435239	−	0.900315i	$-0.356664\pi$
$727$	23.4706	0.870477	0.435239	+	0.900315i	$0.356664\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−3.62113	−0.134024
$731$	−16.0662	−0.594230
$732$	−1.73240	−0.0640312
$733$	27.7099	1.02349	0.511744	−	0.859138i	$-0.329000\pi$
$733$	27.7099	1.02349	0.511744	+	0.859138i	$0.329000\pi$
$734$	−12.0634	−0.445268
$735$	0	0
$736$	−8.04668	−0.296605
$737$	12.4994	0.460421
$738$	−1.61650	−0.0595041
$739$	13.2018	0.485637	0.242818	−	0.970072i	$-0.421928\pi$
$739$	13.2018	0.485637	0.242818	+	0.970072i	$0.421928\pi$
$740$	−4.24507	−0.156052
$741$	3.03461	0.111479
$742$	0	0
$743$	−39.9191	−1.46449	−0.732245	−	0.681041i	$-0.761528\pi$
$743$	−39.9191	−1.46449	−0.732245	+	0.681041i	$0.761528\pi$
$744$	−8.73240	−0.320145
$745$	10.1026	0.370132
$746$	9.62737	0.352483
$747$	12.8950	0.471803
$748$	8.99417	0.328859
$749$	0	0
$750$	−8.01207	−0.292560
$751$	−35.7491	−1.30450	−0.652252	−	0.758003i	$-0.726175\pi$
$751$	−35.7491	−1.30450	−0.652252	+	0.758003i	$0.726175\pi$
$752$	−1.66318	−0.0606499
$753$	−11.4123	−0.415887
$754$	−15.9308	−0.580165
$755$	2.13500	0.0777006
$756$	0	0
$757$	44.2093	1.60681	0.803407	−	0.595431i	$-0.203019\pi$
$757$	44.2093	1.60681	0.803407	+	0.595431i	$0.203019\pi$
$758$	2.29175	0.0832402
$759$	33.9175	1.23113
$760$	−0.866198	−0.0314203
$761$	32.3944	1.17430	0.587148	−	0.809480i	$-0.300251\pi$
$761$	32.3944	1.17430	0.587148	+	0.809480i	$0.300251\pi$
$762$	13.4994	0.489032
$763$	0	0
$764$	−21.1280	−0.764383
$765$	−1.84830	−0.0668253
$766$	22.6978	0.820104
$767$	16.3368	0.589888
$768$	1.00000	0.0360844
$769$	−19.2855	−0.695453	−0.347727	−	0.937596i	$-0.613046\pi$
$769$	−19.2855	−0.695453	−0.347727	+	0.937596i	$0.613046\pi$
$770$	0	0
$771$	−23.5340	−0.847557
$772$	−0.0991936	−0.00357006
$773$	23.9129	0.860087	0.430043	−	0.902808i	$-0.358498\pi$
$773$	23.9129	0.860087	0.430043	+	0.902808i	$0.358498\pi$
$774$	7.52938	0.270638
$775$	37.1101	1.33303
$776$	−13.3835	−0.480440
$777$	0	0
$778$	−30.2318	−1.08386
$779$	1.61650	0.0579170
$780$	−2.62857	−0.0941180
$781$	−14.8767	−0.532329
$782$	17.1700	0.613999
$783$	5.24970	0.187609
$784$	0	0
$785$	13.6873	0.488522
$786$	1.96539	0.0701032
$787$	24.6527	0.878775	0.439387	−	0.898298i	$-0.355196\pi$
$787$	24.6527	0.878775	0.439387	+	0.898298i	$0.355196\pi$
$788$	16.8783	0.601264
$789$	−10.5819	−0.376725
$790$	7.48852	0.266430
$791$	0	0
$792$	−4.21509	−0.149777
$793$	5.25714	0.186687
$794$	−1.19719	−0.0424867
$795$	−3.49477	−0.123947
$796$	13.0346	0.461999
$797$	−11.6441	−0.412454	−0.206227	−	0.978504i	$-0.566119\pi$
$797$	−11.6441	−0.412454	−0.206227	+	0.978504i	$0.566119\pi$
$798$	0	0
$799$	3.54890	0.125551
$800$	−4.24970	−0.150250
$801$	−1.61650	−0.0571161
$802$	29.6966	1.04862
$803$	17.6211	0.621836
$804$	−2.96539	−0.104581
$805$	0	0
$806$	26.4994	0.933402
$807$	27.9117	0.982538
$808$	−12.6978	−0.446707
$809$	6.02878	0.211961	0.105980	−	0.994368i	$-0.466202\pi$
$809$	6.02878	0.211961	0.105980	+	0.994368i	$0.466202\pi$
$810$	0.866198	0.0304351
$811$	20.8137	0.730867	0.365434	−	0.930837i	$-0.380921\pi$
$811$	20.8137	0.730867	0.365434	+	0.930837i	$0.380921\pi$
$812$	0	0
$813$	24.0634	0.843940
$814$	20.6574	0.724040
$815$	5.92152	0.207422
$816$	−2.13380	−0.0746980
$817$	−7.52938	−0.263420
$818$	2.97747	0.104105
$819$	0	0
$820$	−1.40021	−0.0488974
$821$	20.8483	0.727611	0.363805	−	0.931475i	$-0.381477\pi$
$821$	20.8483	0.727611	0.363805	+	0.931475i	$0.381477\pi$
$822$	−1.80161	−0.0628385
$823$	13.9759	0.487168	0.243584	−	0.969880i	$-0.421677\pi$
$823$	13.9759	0.487168	0.243584	+	0.969880i	$0.421677\pi$
$824$	9.55191	0.332757
$825$	17.9129	0.623646
$826$	0	0
$827$	−46.8724	−1.62991	−0.814957	−	0.579521i	$-0.803240\pi$
$827$	−46.8724	−1.62991	−0.814957	+	0.579521i	$0.803240\pi$
$828$	−8.04668	−0.279642
$829$	24.7219	0.858628	0.429314	−	0.903155i	$-0.358755\pi$
$829$	24.7219	0.858628	0.429314	+	0.903155i	$0.358755\pi$
$830$	11.1696	0.387703
$831$	−17.4423	−0.605065
$832$	−3.03461	−0.105206
$833$	0	0
$834$	1.26178	0.0436917
$835$	2.08009	0.0719846
$836$	4.21509	0.145782
$837$	−8.73240	−0.301836
$838$	11.4469	0.395426
$839$	−12.2722	−0.423685	−0.211842	−	0.977304i	$-0.567946\pi$
$839$	−12.2722	−0.423685	−0.211842	+	0.977304i	$0.567946\pi$
$840$	0	0
$841$	−1.44064	−0.0496774
$842$	−8.16258	−0.281301
$843$	2.36097	0.0813161
$844$	28.1400	0.968620
$845$	−3.28389	−0.112969
$846$	−1.66318	−0.0571813
$847$	0	0
$848$	−4.03461	−0.138549
$849$	16.7024	0.573226
$850$	9.06802	0.311030
$851$	39.4352	1.35182
$852$	3.52938	0.120915
$853$	−37.3372	−1.27840	−0.639201	−	0.769039i	$-0.720735\pi$
$853$	−37.3372	−1.27840	−0.639201	+	0.769039i	$0.720735\pi$
$854$	0	0
$855$	−0.866198	−0.0296234
$856$	−4.23763	−0.144839
$857$	12.0000	0.409912	0.204956	−	0.978771i	$-0.434295\pi$
$857$	12.0000	0.409912	0.204956	+	0.978771i	$0.434295\pi$
$858$	12.7912	0.436683
$859$	24.0483	0.820517	0.410259	−	0.911969i	$-0.365438\pi$
$859$	24.0483	0.820517	0.410259	+	0.911969i	$0.365438\pi$
$860$	6.52193	0.222396
$861$	0	0
$862$	0.738225	0.0251440
$863$	−31.8662	−1.08474	−0.542369	−	0.840140i	$-0.682473\pi$
$863$	−31.8662	−1.08474	−0.542369	+	0.840140i	$0.682473\pi$
$864$	1.00000	0.0340207
$865$	−12.3431	−0.419677
$866$	12.8783	0.437622
$867$	−12.4469	−0.422719
$868$	0	0
$869$	−36.4406	−1.23616
$870$	4.54728	0.154167
$871$	8.99880	0.304913
$872$	19.0634	0.645568
$873$	−13.3835	−0.452963
$874$	8.04668	0.272183
$875$	0	0
$876$	−4.18048	−0.141245
$877$	−13.3551	−0.450971	−0.225486	−	0.974247i	$-0.572397\pi$
$877$	−13.3551	−0.450971	−0.225486	+	0.974247i	$0.572397\pi$
$878$	−13.2497	−0.447156
$879$	1.11127	0.0374821
$880$	−3.65111	−0.123079
$881$	−8.09337	−0.272672	−0.136336	−	0.990663i	$-0.543533\pi$
$881$	−8.09337	−0.272672	−0.136336	+	0.990663i	$0.543533\pi$
$882$	0	0
$883$	−31.5177	−1.06066	−0.530328	−	0.847793i	$-0.677931\pi$
$883$	−31.5177	−1.06066	−0.530328	+	0.847793i	$0.677931\pi$
$884$	6.47525	0.217786
$885$	−4.66318	−0.156751
$886$	−20.5761	−0.691266
$887$	−34.4924	−1.15814	−0.579070	−	0.815278i	$-0.696584\pi$
$887$	−34.4924	−1.15814	−0.579070	+	0.815278i	$0.696584\pi$
$888$	−4.90081	−0.164460
$889$	0	0
$890$	−1.40021	−0.0469351
$891$	−4.21509	−0.141211
$892$	−17.9475	−0.600926
$893$	1.66318	0.0556562
$894$	11.6632	0.390075
$895$	−0.896176	−0.0299559
$896$	0	0
$897$	24.4185	0.815311
$898$	−31.8125	−1.06160
$899$	−45.8425	−1.52893
$900$	−4.24970	−0.141657
$901$	8.60905	0.286809
$902$	6.81369	0.226871
$903$	0	0
$904$	−1.27968	−0.0425615
$905$	−22.3702	−0.743612
$906$	2.46479	0.0818873
$907$	51.3372	1.70462	0.852312	−	0.523033i	$-0.175200\pi$
$907$	51.3372	1.70462	0.852312	+	0.523033i	$0.175200\pi$
$908$	−0.866198	−0.0287458
$909$	−12.6978	−0.421159
$910$	0	0
$911$	−13.6966	−0.453788	−0.226894	−	0.973919i	$-0.572857\pi$
$911$	−13.6966	−0.453788	−0.226894	+	0.973919i	$0.572857\pi$
$912$	−1.00000	−0.0331133
$913$	−54.3535	−1.79884
$914$	−34.4710	−1.14020
$915$	−1.50060	−0.0496083
$916$	−25.6966	−0.849039
$917$	0	0
$918$	−2.13380	−0.0704260
$919$	1.38933	0.0458298	0.0229149	−	0.999737i	$-0.492705\pi$
$919$	1.38933	0.0458298	0.0229149	+	0.999737i	$0.492705\pi$
$920$	−6.97002	−0.229795
$921$	−23.7099	−0.781267
$922$	−9.60323	−0.316265
$923$	−10.7103	−0.352533
$924$	0	0
$925$	20.8270	0.684786
$926$	33.8950	1.11386
$927$	9.55191	0.313726
$928$	5.24970	0.172330
$929$	45.7254	1.50020	0.750100	−	0.661324i	$-0.230005\pi$
$929$	45.7254	1.50020	0.750100	+	0.661324i	$0.230005\pi$
$930$	−7.56399	−0.248033
$931$	0	0
$932$	22.8604	0.748816
$933$	−32.8829	−1.07654
$934$	−38.2380	−1.25119
$935$	7.79074	0.254784
$936$	−3.03461	−0.0991893
$937$	10.3264	0.337347	0.168674	−	0.985672i	$-0.446052\pi$
$937$	10.3264	0.337347	0.168674	+	0.985672i	$0.446052\pi$
$938$	0	0
$939$	10.0167	0.326883
$940$	−1.44064	−0.0469886
$941$	−40.4290	−1.31795	−0.658974	−	0.752166i	$-0.729009\pi$
$941$	−40.4290	−1.31795	−0.658974	+	0.752166i	$0.729009\pi$
$942$	15.8016	0.514844
$943$	13.0074	0.423581
$944$	−5.38350	−0.175218
$945$	0	0
$946$	−31.7370	−1.03186
$947$	19.7145	0.640635	0.320317	−	0.947310i	$-0.396210\pi$
$947$	19.7145	0.640635	0.320317	+	0.947310i	$0.396210\pi$
$948$	8.64528	0.280786
$949$	12.6861	0.411809
$950$	4.24970	0.137878
$951$	27.1626	0.880807
$952$	0	0
$953$	−36.2676	−1.17482	−0.587411	−	0.809288i	$-0.699853\pi$
$953$	−36.2676	−1.17482	−0.587411	+	0.809288i	$0.699853\pi$
$954$	−4.03461	−0.130625
$955$	−18.3010	−0.592207
$956$	8.49940	0.274890
$957$	−22.1280	−0.715296
$958$	−32.3252	−1.04438
$959$	0	0
$960$	0.866198	0.0279564
$961$	45.2547	1.45983
$962$	14.8720	0.479493
$963$	−4.23763	−0.136556
$964$	−18.7791	−0.604833
$965$	−0.0859214	−0.00276591
$966$	0	0
$967$	2.48733	0.0799870	0.0399935	−	0.999200i	$-0.487266\pi$
$967$	2.48733	0.0799870	0.0399935	+	0.999200i	$0.487266\pi$
$968$	6.76700	0.217500
$969$	2.13380	0.0685476
$970$	−11.5928	−0.372221
$971$	−13.8712	−0.445149	−0.222575	−	0.974916i	$-0.571446\pi$
$971$	−13.8712	−0.445149	−0.222575	+	0.974916i	$0.571446\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	26.3956	0.845769
$975$	12.8962	0.413008
$976$	−1.73240	−0.0554527
$977$	−47.6849	−1.52558	−0.762788	−	0.646649i	$-0.776170\pi$
$977$	−47.6849	−1.52558	−0.762788	+	0.646649i	$0.776170\pi$
$978$	6.83622	0.218598
$979$	6.81369	0.217766
$980$	0	0
$981$	19.0634	0.608647
$982$	−34.4531	−1.09944
$983$	22.9654	0.732482	0.366241	−	0.930520i	$-0.380645\pi$
$983$	22.9654	0.732482	0.366241	+	0.930520i	$0.380645\pi$
$984$	−1.61650	−0.0515321
$985$	14.6199	0.465830
$986$	−11.2018	−0.356739
$987$	0	0
$988$	3.03461	0.0965437
$989$	−60.5865	−1.92654
$990$	−3.65111	−0.116040
$991$	−44.6515	−1.41840	−0.709201	−	0.705006i	$-0.750944\pi$
$991$	−44.6515	−1.41840	−0.709201	+	0.705006i	$0.750944\pi$
$992$	−8.73240	−0.277254
$993$	24.2093	0.768258
$994$	0	0
$995$	11.2906	0.357935
$996$	12.8950	0.408593
$997$	−30.5236	−0.966691	−0.483345	−	0.875430i	$-0.660578\pi$
$997$	−30.5236	−0.966691	−0.483345	+	0.875430i	$0.660578\pi$
$998$	−17.8258	−0.564265
$999$	−4.90081	−0.155055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.bv.1.3		3
7.2	even	3		798.2.j.i.571.1	yes	6
7.4	even	3		798.2.j.i.457.1	✓	6
7.6	odd	2		5586.2.a.bu.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.i.457.1	✓	6	7.4	even	3
798.2.j.i.571.1	yes	6	7.2	even	3
5586.2.a.bu.1.1		3	7.6	odd	2
5586.2.a.bv.1.3		3	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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.866198 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.866198 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.866198 q^{10} -4.21509 q^{11} +1.00000 q^{12} -3.03461 q^{13} +0.866198 q^{15} +1.00000 q^{16} -2.13380 q^{17} +1.00000 q^{18} -1.00000 q^{19} +0.866198 q^{20} -4.21509 q^{22} -8.04668 q^{23} +1.00000 q^{24} -4.24970 q^{25} -3.03461 q^{26} +1.00000 q^{27} +5.24970 q^{29} +0.866198 q^{30} -8.73240 q^{31} +1.00000 q^{32} -4.21509 q^{33} -2.13380 q^{34} +1.00000 q^{36} -4.90081 q^{37} -1.00000 q^{38} -3.03461 q^{39} +0.866198 q^{40} -1.61650 q^{41} +7.52938 q^{43} -4.21509 q^{44} +0.866198 q^{45} -8.04668 q^{46} -1.66318 q^{47} +1.00000 q^{48} -4.24970 q^{50} -2.13380 q^{51} -3.03461 q^{52} -4.03461 q^{53} +1.00000 q^{54} -3.65111 q^{55} -1.00000 q^{57} +5.24970 q^{58} -5.38350 q^{59} +0.866198 q^{60} -1.73240 q^{61} -8.73240 q^{62} +1.00000 q^{64} -2.62857 q^{65} -4.21509 q^{66} -2.96539 q^{67} -2.13380 q^{68} -8.04668 q^{69} +3.52938 q^{71} +1.00000 q^{72} -4.18048 q^{73} -4.90081 q^{74} -4.24970 q^{75} -1.00000 q^{76} -3.03461 q^{78} +8.64528 q^{79} +0.866198 q^{80} +1.00000 q^{81} -1.61650 q^{82} +12.8950 q^{83} -1.84830 q^{85} +7.52938 q^{86} +5.24970 q^{87} -4.21509 q^{88} -1.61650 q^{89} +0.866198 q^{90} -8.04668 q^{92} -8.73240 q^{93} -1.66318 q^{94} -0.866198 q^{95} +1.00000 q^{96} -13.3835 q^{97} -4.21509 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} + 3 q^{8} + 3 q^{9} - 5 q^{10} + q^{11} + 3 q^{12} - 6 q^{13} - 5 q^{15} + 3 q^{16} - 14 q^{17} + 3 q^{18} - 3 q^{19} - 5 q^{20} + q^{22} - 6 q^{23} + 3 q^{24} + 4 q^{25} - 6 q^{26} + 3 q^{27} - q^{29} - 5 q^{30} - 11 q^{31} + 3 q^{32} + q^{33} - 14 q^{34} + 3 q^{36} - 4 q^{37} - 3 q^{38} - 6 q^{39} - 5 q^{40} - 14 q^{41} + 6 q^{43} + q^{44} - 5 q^{45} - 6 q^{46} + 4 q^{47} + 3 q^{48} + 4 q^{50} - 14 q^{51} - 6 q^{52} - 9 q^{53} + 3 q^{54} - 17 q^{55} - 3 q^{57} - q^{58} - 7 q^{59} - 5 q^{60} + 10 q^{61} - 11 q^{62} + 3 q^{64} - 2 q^{65} + q^{66} - 12 q^{67} - 14 q^{68} - 6 q^{69} - 6 q^{71} + 3 q^{72} - 2 q^{73} - 4 q^{74} + 4 q^{75} - 3 q^{76} - 6 q^{78} - 15 q^{79} - 5 q^{80} + 3 q^{81} - 14 q^{82} - 19 q^{83} + 34 q^{85} + 6 q^{86} - q^{87} + q^{88} - 14 q^{89} - 5 q^{90} - 6 q^{92} - 11 q^{93} + 4 q^{94} + 5 q^{95} + 3 q^{96} - 31 q^{97} + q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 + 3 * q^8 + 3 * q^9 - 5 * q^10 + q^11 + 3 * q^12 - 6 * q^13 - 5 * q^15 + 3 * q^16 - 14 * q^17 + 3 * q^18 - 3 * q^19 - 5 * q^20 + q^22 - 6 * q^23 + 3 * q^24 + 4 * q^25 - 6 * q^26 + 3 * q^27 - q^29 - 5 * q^30 - 11 * q^31 + 3 * q^32 + q^33 - 14 * q^34 + 3 * q^36 - 4 * q^37 - 3 * q^38 - 6 * q^39 - 5 * q^40 - 14 * q^41 + 6 * q^43 + q^44 - 5 * q^45 - 6 * q^46 + 4 * q^47 + 3 * q^48 + 4 * q^50 - 14 * q^51 - 6 * q^52 - 9 * q^53 + 3 * q^54 - 17 * q^55 - 3 * q^57 - q^58 - 7 * q^59 - 5 * q^60 + 10 * q^61 - 11 * q^62 + 3 * q^64 - 2 * q^65 + q^66 - 12 * q^67 - 14 * q^68 - 6 * q^69 - 6 * q^71 + 3 * q^72 - 2 * q^73 - 4 * q^74 + 4 * q^75 - 3 * q^76 - 6 * q^78 - 15 * q^79 - 5 * q^80 + 3 * q^81 - 14 * q^82 - 19 * q^83 + 34 * q^85 + 6 * q^86 - q^87 + q^88 - 14 * q^89 - 5 * q^90 - 6 * q^92 - 11 * q^93 + 4 * q^94 + 5 * q^95 + 3 * q^96 - 31 * q^97 + q^99

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