LMFDB - Embedded newform 731.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 9x^{6} + 9x^{5} + 21x^{4} - 21x^{3} - 8x^{2} + 7x - 1 $ x^8 - x^7 - 9x^6 + 9x^5 + 21x^4 - 21x^3 - 8x^2 + 7x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.78724$ of defining polynomial
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.78724 q^{2} +1.17799 q^{3} +1.19423 q^{4} -1.95027 q^{5} -2.10535 q^{6} -1.57661 q^{7} +1.44011 q^{8} -1.61234 q^{9} +O(q^{10})$	\(q-1.78724 q^{2} +1.17799 q^{3} +1.19423 q^{4} -1.95027 q^{5} -2.10535 q^{6} -1.57661 q^{7} +1.44011 q^{8} -1.61234 q^{9} +3.48560 q^{10} +3.10281 q^{11} +1.40679 q^{12} +2.22735 q^{13} +2.81778 q^{14} -2.29740 q^{15} -4.96228 q^{16} +1.00000 q^{17} +2.88164 q^{18} +3.29121 q^{19} -2.32907 q^{20} -1.85723 q^{21} -5.54546 q^{22} -3.85303 q^{23} +1.69644 q^{24} -1.19644 q^{25} -3.98081 q^{26} -5.43329 q^{27} -1.88283 q^{28} -0.0511748 q^{29} +4.10601 q^{30} -9.84587 q^{31} +5.98856 q^{32} +3.65508 q^{33} -1.78724 q^{34} +3.07481 q^{35} -1.92550 q^{36} -11.4217 q^{37} -5.88218 q^{38} +2.62380 q^{39} -2.80861 q^{40} -2.81282 q^{41} +3.31931 q^{42} +1.00000 q^{43} +3.70546 q^{44} +3.14450 q^{45} +6.88629 q^{46} +0.384948 q^{47} -5.84551 q^{48} -4.51431 q^{49} +2.13832 q^{50} +1.17799 q^{51} +2.65996 q^{52} +6.87704 q^{53} +9.71059 q^{54} -6.05132 q^{55} -2.27049 q^{56} +3.87701 q^{57} +0.0914617 q^{58} +0.424073 q^{59} -2.74362 q^{60} +0.494887 q^{61} +17.5969 q^{62} +2.54203 q^{63} -0.778438 q^{64} -4.34394 q^{65} -6.53250 q^{66} -6.29881 q^{67} +1.19423 q^{68} -4.53883 q^{69} -5.49543 q^{70} -12.7711 q^{71} -2.32194 q^{72} -0.682273 q^{73} +20.4133 q^{74} -1.40939 q^{75} +3.93045 q^{76} -4.89191 q^{77} -4.68936 q^{78} -0.156573 q^{79} +9.67779 q^{80} -1.56335 q^{81} +5.02719 q^{82} +0.486412 q^{83} -2.21795 q^{84} -1.95027 q^{85} -1.78724 q^{86} -0.0602834 q^{87} +4.46838 q^{88} -7.53018 q^{89} -5.61997 q^{90} -3.51166 q^{91} -4.60139 q^{92} -11.5983 q^{93} -0.687995 q^{94} -6.41875 q^{95} +7.05446 q^{96} -1.92220 q^{97} +8.06815 q^{98} -5.00278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 12 q^{10} - 4 q^{11} - 13 q^{12} - 12 q^{13} + q^{14} - 9 q^{15} - 3 q^{16} + 8 q^{17} + 5 q^{18} - 5 q^{20} - 20 q^{21} - 14 q^{22} - 9 q^{23} - q^{24} - 7 q^{25} - 17 q^{26} - 12 q^{27} + q^{28} - 27 q^{29} + 10 q^{30} - 12 q^{31} + 5 q^{32} + 10 q^{33} + q^{34} + 15 q^{35} - 4 q^{36} - 24 q^{37} - q^{38} + 3 q^{39} - 9 q^{40} - 8 q^{41} - 9 q^{42} + 8 q^{43} - 16 q^{44} + 10 q^{45} - 14 q^{46} + 15 q^{47} + 10 q^{48} - 7 q^{49} + 21 q^{50} - 3 q^{51} + q^{52} - 23 q^{53} - 19 q^{54} - 14 q^{55} - 20 q^{56} - 13 q^{57} - 7 q^{58} + 16 q^{59} - 3 q^{60} - 34 q^{61} + 15 q^{62} + 9 q^{63} - 25 q^{64} + 10 q^{65} + 15 q^{66} + 3 q^{68} - 19 q^{69} + 11 q^{70} - 3 q^{71} - 19 q^{72} - 3 q^{73} - 4 q^{74} + 27 q^{75} + 13 q^{76} - 3 q^{77} + 4 q^{78} - 24 q^{79} + 20 q^{80} - 8 q^{81} + 33 q^{82} - 8 q^{83} + 17 q^{84} - 7 q^{85} + q^{86} + 48 q^{87} + 16 q^{88} + 23 q^{89} + 11 q^{90} - 16 q^{91} + 49 q^{92} + 17 q^{93} - 11 q^{94} + 3 q^{95} + 37 q^{96} - 10 q^{97} + 29 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 12 * q^10 - 4 * q^11 - 13 * q^12 - 12 * q^13 + q^14 - 9 * q^15 - 3 * q^16 + 8 * q^17 + 5 * q^18 - 5 * q^20 - 20 * q^21 - 14 * q^22 - 9 * q^23 - q^24 - 7 * q^25 - 17 * q^26 - 12 * q^27 + q^28 - 27 * q^29 + 10 * q^30 - 12 * q^31 + 5 * q^32 + 10 * q^33 + q^34 + 15 * q^35 - 4 * q^36 - 24 * q^37 - q^38 + 3 * q^39 - 9 * q^40 - 8 * q^41 - 9 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 14 * q^46 + 15 * q^47 + 10 * q^48 - 7 * q^49 + 21 * q^50 - 3 * q^51 + q^52 - 23 * q^53 - 19 * q^54 - 14 * q^55 - 20 * q^56 - 13 * q^57 - 7 * q^58 + 16 * q^59 - 3 * q^60 - 34 * q^61 + 15 * q^62 + 9 * q^63 - 25 * q^64 + 10 * q^65 + 15 * q^66 + 3 * q^68 - 19 * q^69 + 11 * q^70 - 3 * q^71 - 19 * q^72 - 3 * q^73 - 4 * q^74 + 27 * q^75 + 13 * q^76 - 3 * q^77 + 4 * q^78 - 24 * q^79 + 20 * q^80 - 8 * q^81 + 33 * q^82 - 8 * q^83 + 17 * q^84 - 7 * q^85 + q^86 + 48 * q^87 + 16 * q^88 + 23 * q^89 + 11 * q^90 - 16 * q^91 + 49 * q^92 + 17 * q^93 - 11 * q^94 + 3 * q^95 + 37 * q^96 - 10 * q^97 + 29 * q^98 - 15 * 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 $

$2$	−1.78724	−1.26377	−0.631885	−	0.775062i	$-0.717718\pi$
$2$	−1.78724	−1.26377	−0.631885	+	0.775062i	$0.717718\pi$
$3$	1.17799	0.680113	0.340057	−	0.940405i	$-0.389554\pi$
$3$	1.17799	0.680113	0.340057	+	0.940405i	$0.389554\pi$
$4$	1.19423	0.597113
$5$	−1.95027	−0.872188	−0.436094	−	0.899901i	$-0.643639\pi$
$5$	−1.95027	−0.872188	−0.436094	+	0.899901i	$0.643639\pi$
$6$	−2.10535	−0.859506
$7$	−1.57661	−0.595902	−0.297951	−	0.954581i	$-0.596303\pi$
$7$	−1.57661	−0.595902	−0.297951	+	0.954581i	$0.596303\pi$
$8$	1.44011	0.509156
$9$	−1.61234	−0.537446
$10$	3.48560	1.10225
$11$	3.10281	0.935532	0.467766	−	0.883852i	$-0.345059\pi$
$11$	3.10281	0.935532	0.467766	+	0.883852i	$0.345059\pi$
$12$	1.40679	0.406105
$13$	2.22735	0.617756	0.308878	−	0.951102i	$-0.400047\pi$
$13$	2.22735	0.617756	0.308878	+	0.951102i	$0.400047\pi$
$14$	2.81778	0.753083
$15$	−2.29740	−0.593187
$16$	−4.96228	−1.24057
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.88164	0.679208
$19$	3.29121	0.755055	0.377528	−	0.925998i	$-0.376774\pi$
$19$	3.29121	0.755055	0.377528	+	0.925998i	$0.376774\pi$
$20$	−2.32907	−0.520795
$21$	−1.85723	−0.405281
$22$	−5.54546	−1.18230
$23$	−3.85303	−0.803412	−0.401706	−	0.915769i	$-0.631583\pi$
$23$	−3.85303	−0.803412	−0.401706	+	0.915769i	$0.631583\pi$
$24$	1.69644	0.346284
$25$	−1.19644	−0.239287
$26$	−3.98081	−0.780701
$27$	−5.43329	−1.04564
$28$	−1.88283	−0.355821
$29$	−0.0511748	−0.00950292	−0.00475146	−	0.999989i	$-0.501512\pi$
$29$	−0.0511748	−0.00950292	−0.00475146	+	0.999989i	$0.501512\pi$
$30$	4.10601	0.749651
$31$	−9.84587	−1.76837	−0.884185	−	0.467137i	$-0.845285\pi$
$31$	−9.84587	−1.76837	−0.884185	+	0.467137i	$0.845285\pi$
$32$	5.98856	1.05864
$33$	3.65508	0.636267
$34$	−1.78724	−0.306509
$35$	3.07481	0.519739
$36$	−1.92550	−0.320916
$37$	−11.4217	−1.87771	−0.938856	−	0.344309i	$-0.888113\pi$
$37$	−11.4217	−1.87771	−0.938856	+	0.344309i	$0.888113\pi$
$38$	−5.88218	−0.954216
$39$	2.62380	0.420144
$40$	−2.80861	−0.444080
$41$	−2.81282	−0.439289	−0.219645	−	0.975580i	$-0.570490\pi$
$41$	−2.81282	−0.439289	−0.219645	+	0.975580i	$0.570490\pi$
$42$	3.31931	0.512181
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	3.70546	0.558619
$45$	3.14450	0.468754
$46$	6.88629	1.01533
$47$	0.384948	0.0561505	0.0280753	−	0.999606i	$-0.491062\pi$
$47$	0.384948	0.0561505	0.0280753	+	0.999606i	$0.491062\pi$
$48$	−5.84551	−0.843727
$49$	−4.51431	−0.644901
$50$	2.13832	0.302404
$51$	1.17799	0.164952
$52$	2.65996	0.368870
$53$	6.87704	0.944633	0.472317	−	0.881429i	$-0.343418\pi$
$53$	6.87704	0.944633	0.472317	+	0.881429i	$0.343418\pi$
$54$	9.71059	1.32144
$55$	−6.05132	−0.815960
$56$	−2.27049	−0.303407
$57$	3.87701	0.513523
$58$	0.0914617	0.0120095
$59$	0.424073	0.0552096	0.0276048	−	0.999619i	$-0.491212\pi$
$59$	0.424073	0.0552096	0.0276048	+	0.999619i	$0.491212\pi$
$60$	−2.74362	−0.354200
$61$	0.494887	0.0633638	0.0316819	−	0.999498i	$-0.489914\pi$
$61$	0.494887	0.0633638	0.0316819	+	0.999498i	$0.489914\pi$
$62$	17.5969	2.23481
$63$	2.54203	0.320265
$64$	−0.778438	−0.0973048
$65$	−4.34394	−0.538799
$66$	−6.53250	−0.804095
$67$	−6.29881	−0.769522	−0.384761	−	0.923016i	$-0.625716\pi$
$67$	−6.29881	−0.769522	−0.384761	+	0.923016i	$0.625716\pi$
$68$	1.19423	0.144821
$69$	−4.53883	−0.546411
$70$	−5.49543	−0.656830
$71$	−12.7711	−1.51565	−0.757826	−	0.652456i	$-0.773739\pi$
$71$	−12.7711	−1.51565	−0.757826	+	0.652456i	$0.773739\pi$
$72$	−2.32194	−0.273644
$73$	−0.682273	−0.0798540	−0.0399270	−	0.999203i	$-0.512713\pi$
$73$	−0.682273	−0.0798540	−0.0399270	+	0.999203i	$0.512713\pi$
$74$	20.4133	2.37300
$75$	−1.40939	−0.162743
$76$	3.93045	0.450854
$77$	−4.89191	−0.557485
$78$	−4.68936	−0.530965
$79$	−0.156573	−0.0176158	−0.00880791	−	0.999961i	$-0.502804\pi$
$79$	−0.156573	−0.0176158	−0.00880791	+	0.999961i	$0.502804\pi$
$80$	9.67779	1.08201
$81$	−1.56335	−0.173705
$82$	5.02719	0.555161
$83$	0.486412	0.0533907	0.0266953	−	0.999644i	$-0.491502\pi$
$83$	0.486412	0.0533907	0.0266953	+	0.999644i	$0.491502\pi$
$84$	−2.21795	−0.241998
$85$	−1.95027	−0.211537
$86$	−1.78724	−0.192723
$87$	−0.0602834	−0.00646306
$88$	4.46838	0.476331
$89$	−7.53018	−0.798198	−0.399099	−	0.916908i	$-0.630677\pi$
$89$	−7.53018	−0.798198	−0.399099	+	0.916908i	$0.630677\pi$
$90$	−5.61997	−0.592397
$91$	−3.51166	−0.368122
$92$	−4.60139	−0.479728
$93$	−11.5983	−1.20269
$94$	−0.687995	−0.0709613
$95$	−6.41875	−0.658550
$96$	7.05446	0.719993
$97$	−1.92220	−0.195170	−0.0975850	−	0.995227i	$-0.531112\pi$
$97$	−1.92220	−0.195170	−0.0975850	+	0.995227i	$0.531112\pi$
$98$	8.06815	0.815006
$99$	−5.00278	−0.502798
$100$	−1.42882	−0.142882
$101$	7.54966	0.751219	0.375610	−	0.926778i	$-0.377433\pi$
$101$	7.54966	0.751219	0.375610	+	0.926778i	$0.377433\pi$
$102$	−2.10535	−0.208461
$103$	−16.8654	−1.66180	−0.830900	−	0.556422i	$-0.812174\pi$
$103$	−16.8654	−1.66180	−0.830900	+	0.556422i	$0.812174\pi$
$104$	3.20763	0.314534
$105$	3.62210	0.353481
$106$	−12.2909	−1.19380
$107$	1.91079	0.184723	0.0923616	−	0.995726i	$-0.470558\pi$
$107$	1.91079	0.184723	0.0923616	+	0.995726i	$0.470558\pi$
$108$	−6.48858	−0.624364
$109$	−4.55878	−0.436652	−0.218326	−	0.975876i	$-0.570060\pi$
$109$	−4.55878	−0.436652	−0.218326	+	0.975876i	$0.570060\pi$
$110$	10.8152	1.03119
$111$	−13.4546	−1.27706
$112$	7.82356	0.739257
$113$	0.405322	0.0381294	0.0190647	−	0.999818i	$-0.493931\pi$
$113$	0.405322	0.0381294	0.0190647	+	0.999818i	$0.493931\pi$
$114$	−6.92915	−0.648975
$115$	7.51445	0.700726
$116$	−0.0611143	−0.00567432
$117$	−3.59124	−0.332010
$118$	−0.757920	−0.0697722
$119$	−1.57661	−0.144527
$120$	−3.30851	−0.302024
$121$	−1.37259	−0.124780
$122$	−0.884482	−0.0800772
$123$	−3.31348	−0.298766
$124$	−11.7582	−1.05592
$125$	12.0847	1.08089
$126$	−4.54321	−0.404741
$127$	−10.6827	−0.947937	−0.473968	−	0.880542i	$-0.657179\pi$
$127$	−10.6827	−0.947937	−0.473968	+	0.880542i	$0.657179\pi$
$128$	−10.5859	−0.935667
$129$	1.17799	0.103716
$130$	7.76366	0.680918
$131$	−0.454686	−0.0397261	−0.0198631	−	0.999803i	$-0.506323\pi$
$131$	−0.454686	−0.0397261	−0.0198631	+	0.999803i	$0.506323\pi$
$132$	4.36499	0.379924
$133$	−5.18895	−0.449939
$134$	11.2575	0.972499
$135$	10.5964	0.911993
$136$	1.44011	0.123488
$137$	17.8859	1.52809	0.764047	−	0.645161i	$-0.223210\pi$
$137$	17.8859	1.52809	0.764047	+	0.645161i	$0.223210\pi$
$138$	8.11198	0.690537
$139$	3.99218	0.338613	0.169306	−	0.985563i	$-0.445847\pi$
$139$	3.99218	0.338613	0.169306	+	0.985563i	$0.445847\pi$
$140$	3.67203	0.310343
$141$	0.453466	0.0381887
$142$	22.8250	1.91544
$143$	6.91104	0.577930
$144$	8.00087	0.666739
$145$	0.0998048	0.00828834
$146$	1.21939	0.100917
$147$	−5.31781	−0.438606
$148$	−13.6401	−1.12121
$149$	14.2983	1.17136	0.585681	−	0.810541i	$-0.300827\pi$
$149$	14.2983	1.17136	0.585681	+	0.810541i	$0.300827\pi$
$150$	2.51892	0.205669
$151$	7.37873	0.600472	0.300236	−	0.953865i	$-0.402935\pi$
$151$	7.37873	0.600472	0.300236	+	0.953865i	$0.402935\pi$
$152$	4.73970	0.384441
$153$	−1.61234	−0.130350
$154$	8.74302	0.704533
$155$	19.2021	1.54235
$156$	3.13341	0.250873
$157$	−2.73373	−0.218175	−0.109088	−	0.994032i	$-0.534793\pi$
$157$	−2.73373	−0.218175	−0.109088	+	0.994032i	$0.534793\pi$
$158$	0.279833	0.0222623
$159$	8.10108	0.642458
$160$	−11.6793	−0.923331
$161$	6.07471	0.478755
$162$	2.79408	0.219524
$163$	23.6840	1.85507	0.927536	−	0.373733i	$-0.121922\pi$
$163$	23.6840	1.85507	0.927536	+	0.373733i	$0.121922\pi$
$164$	−3.35915	−0.262306
$165$	−7.12840	−0.554945
$166$	−0.869335	−0.0674735
$167$	−6.49210	−0.502374	−0.251187	−	0.967939i	$-0.580821\pi$
$167$	−6.49210	−0.502374	−0.251187	+	0.967939i	$0.580821\pi$
$168$	−2.67461	−0.206351
$169$	−8.03891	−0.618378
$170$	3.48560	0.267334
$171$	−5.30654	−0.405801
$172$	1.19423	0.0910589
$173$	−14.1440	−1.07535	−0.537674	−	0.843153i	$-0.680697\pi$
$173$	−14.1440	−1.07535	−0.537674	+	0.843153i	$0.680697\pi$
$174$	0.107741	0.00816782
$175$	1.88631	0.142592
$176$	−15.3970	−1.16059
$177$	0.499554	0.0375488
$178$	13.4582	1.00874
$179$	9.58932	0.716739	0.358370	−	0.933580i	$-0.383333\pi$
$179$	9.58932	0.716739	0.358370	+	0.933580i	$0.383333\pi$
$180$	3.75525	0.279899
$181$	−14.9380	−1.11034	−0.555168	−	0.831738i	$-0.687346\pi$
$181$	−14.9380	−1.11034	−0.555168	+	0.831738i	$0.687346\pi$
$182$	6.27618	0.465221
$183$	0.582972	0.0430945
$184$	−5.54878	−0.409062
$185$	22.2754	1.63772
$186$	20.7290	1.51992
$187$	3.10281	0.226900
$188$	0.459716	0.0335282
$189$	8.56617	0.623097
$190$	11.4719	0.832256
$191$	11.4004	0.824903	0.412452	−	0.910980i	$-0.364673\pi$
$191$	11.4004	0.824903	0.412452	+	0.910980i	$0.364673\pi$
$192$	−0.916993	−0.0661783
$193$	18.2259	1.31193	0.655964	−	0.754792i	$-0.272262\pi$
$193$	18.2259	1.31193	0.655964	+	0.754792i	$0.272262\pi$
$194$	3.43544	0.246650
$195$	−5.11712	−0.366445
$196$	−5.39111	−0.385079
$197$	15.5065	1.10479	0.552396	−	0.833582i	$-0.313714\pi$
$197$	15.5065	1.10479	0.552396	+	0.833582i	$0.313714\pi$
$198$	8.94116	0.635421
$199$	−25.3277	−1.79543	−0.897716	−	0.440574i	$-0.854775\pi$
$199$	−25.3277	−1.79543	−0.897716	+	0.440574i	$0.854775\pi$
$200$	−1.72300	−0.121835
$201$	−7.41994	−0.523362
$202$	−13.4931	−0.949368
$203$	0.0806826	0.00566281
$204$	1.40679	0.0984948
$205$	5.48577	0.383143
$206$	30.1426	2.10013
$207$	6.21239	0.431791
$208$	−11.0527	−0.766369
$209$	10.2120	0.706378
$210$	−6.47357	−0.446719
$211$	−4.27413	−0.294243	−0.147122	−	0.989118i	$-0.547001\pi$
$211$	−4.27413	−0.294243	−0.147122	+	0.989118i	$0.547001\pi$
$212$	8.21274	0.564053
$213$	−15.0443	−1.03082
$214$	−3.41504	−0.233448
$215$	−1.95027	−0.133007
$216$	−7.82454	−0.532392
$217$	15.5231	1.05377
$218$	8.14763	0.551827
$219$	−0.803711	−0.0543098
$220$	−7.22665	−0.487221
$221$	2.22735	0.149828
$222$	24.0467	1.61391
$223$	18.3441	1.22841	0.614207	−	0.789145i	$-0.289476\pi$
$223$	18.3441	1.22841	0.614207	+	0.789145i	$0.289476\pi$
$224$	−9.44161	−0.630844
$225$	1.92906	0.128604
$226$	−0.724407	−0.0481868
$227$	22.8079	1.51382	0.756908	−	0.653521i	$-0.226709\pi$
$227$	22.8079	1.51382	0.756908	+	0.653521i	$0.226709\pi$
$228$	4.63003	0.306631
$229$	9.87905	0.652826	0.326413	−	0.945227i	$-0.394160\pi$
$229$	9.87905	0.652826	0.326413	+	0.945227i	$0.394160\pi$
$230$	−13.4301	−0.885557
$231$	−5.76262	−0.379153
$232$	−0.0736974	−0.00483847
$233$	−21.2376	−1.39132	−0.695662	−	0.718369i	$-0.744889\pi$
$233$	−21.2376	−1.39132	−0.695662	+	0.718369i	$0.744889\pi$
$234$	6.41841	0.419585
$235$	−0.750754	−0.0489738
$236$	0.506439	0.0329664
$237$	−0.184441	−0.0119807
$238$	2.81778	0.182649
$239$	−28.0997	−1.81762	−0.908808	−	0.417214i	$-0.863007\pi$
$239$	−28.0997	−1.81762	−0.908808	+	0.417214i	$0.863007\pi$
$240$	11.4003	0.735889
$241$	−14.8271	−0.955095	−0.477547	−	0.878606i	$-0.658474\pi$
$241$	−14.8271	−0.955095	−0.477547	+	0.878606i	$0.658474\pi$
$242$	2.45314	0.157694
$243$	14.4583	0.927498
$244$	0.591007	0.0378354
$245$	8.80413	0.562475
$246$	5.92198	0.377572
$247$	7.33067	0.466440
$248$	−14.1791	−0.900376
$249$	0.572989	0.0363117
$250$	−21.5983	−1.36600
$251$	−1.02914	−0.0649585	−0.0324792	−	0.999472i	$-0.510340\pi$
$251$	−1.02914	−0.0649585	−0.0324792	+	0.999472i	$0.510340\pi$
$252$	3.03576	0.191235
$253$	−11.9552	−0.751617
$254$	19.0926	1.19797
$255$	−2.29740	−0.143869
$256$	20.4763	1.27977
$257$	−11.9737	−0.746897	−0.373449	−	0.927651i	$-0.621825\pi$
$257$	−11.9737	−0.746897	−0.373449	+	0.927651i	$0.621825\pi$
$258$	−2.10535	−0.131073
$259$	18.0075	1.11893
$260$	−5.18765	−0.321724
$261$	0.0825111	0.00510731
$262$	0.812634	0.0502047
$263$	18.0777	1.11472	0.557358	−	0.830272i	$-0.311815\pi$
$263$	18.0777	1.11472	0.557358	+	0.830272i	$0.311815\pi$
$264$	5.26371	0.323959
$265$	−13.4121	−0.823898
$266$	9.27389	0.568619
$267$	−8.87048	−0.542865
$268$	−7.52221	−0.459492
$269$	11.3789	0.693784	0.346892	−	0.937905i	$-0.387237\pi$
$269$	11.3789	0.693784	0.346892	+	0.937905i	$0.387237\pi$
$270$	−18.9383	−1.15255
$271$	−0.0638761	−0.00388020	−0.00194010	−	0.999998i	$-0.500618\pi$
$271$	−0.0638761	−0.00388020	−0.00194010	+	0.999998i	$0.500618\pi$
$272$	−4.96228	−0.300882
$273$	−4.13670	−0.250364
$274$	−31.9664	−1.93116
$275$	−3.71232	−0.223861
$276$	−5.42039	−0.326269
$277$	11.6027	0.697137	0.348569	−	0.937283i	$-0.386668\pi$
$277$	11.6027	0.697137	0.348569	+	0.937283i	$0.386668\pi$
$278$	−7.13499	−0.427928
$279$	15.8749	0.950404
$280$	4.42807	0.264628
$281$	−29.9221	−1.78500	−0.892501	−	0.451045i	$-0.851051\pi$
$281$	−29.9221	−1.78500	−0.892501	+	0.451045i	$0.851051\pi$
$282$	−0.810452	−0.0482617
$283$	19.9276	1.18458	0.592288	−	0.805727i	$-0.298225\pi$
$283$	19.9276	1.18458	0.592288	+	0.805727i	$0.298225\pi$
$284$	−15.2516	−0.905016
$285$	−7.56123	−0.447889
$286$	−12.3517	−0.730370
$287$	4.43472	0.261773
$288$	−9.65558	−0.568961
$289$	1.00000	0.0588235
$290$	−0.178375	−0.0104746
$291$	−2.26434	−0.132738
$292$	−0.814789	−0.0476819
$293$	−22.3154	−1.30368	−0.651840	−	0.758357i	$-0.726003\pi$
$293$	−22.3154	−1.30368	−0.651840	+	0.758357i	$0.726003\pi$
$294$	9.50420	0.554296
$295$	−0.827057	−0.0481531
$296$	−16.4485	−0.956048
$297$	−16.8585	−0.978227
$298$	−25.5545	−1.48033
$299$	−8.58204	−0.496312
$300$	−1.68313	−0.0971758
$301$	−1.57661	−0.0908742
$302$	−13.1876	−0.758859
$303$	8.89343	0.510914
$304$	−16.3319	−0.936698
$305$	−0.965164	−0.0552652
$306$	2.88164	0.164732
$307$	32.5722	1.85899	0.929496	−	0.368832i	$-0.120242\pi$
$307$	32.5722	1.85899	0.929496	+	0.368832i	$0.120242\pi$
$308$	−5.84205	−0.332882
$309$	−19.8673	−1.13021
$310$	−34.3188	−1.94918
$311$	−30.9241	−1.75355	−0.876773	−	0.480904i	$-0.840309\pi$
$311$	−30.9241	−1.75355	−0.876773	+	0.480904i	$0.840309\pi$
$312$	3.77856	0.213919
$313$	−0.189837	−0.0107302	−0.00536510	−	0.999986i	$-0.501708\pi$
$313$	−0.189837	−0.0107302	−0.00536510	+	0.999986i	$0.501708\pi$
$314$	4.88583	0.275723
$315$	−4.95764	−0.279332
$316$	−0.186983	−0.0105186
$317$	6.30499	0.354123	0.177062	−	0.984200i	$-0.443341\pi$
$317$	6.30499	0.354123	0.177062	+	0.984200i	$0.443341\pi$
$318$	−14.4786	−0.811918
$319$	−0.158786	−0.00889029
$320$	1.51817	0.0848681
$321$	2.25089	0.125633
$322$	−10.8570	−0.605035
$323$	3.29121	0.183128
$324$	−1.86699	−0.103722
$325$	−2.66489	−0.147821
$326$	−42.3290	−2.34438
$327$	−5.37019	−0.296972
$328$	−4.05078	−0.223667
$329$	−0.606913	−0.0334602
$330$	12.7402	0.701323
$331$	−25.0544	−1.37712	−0.688558	−	0.725182i	$-0.741756\pi$
$331$	−25.0544	−1.37712	−0.688558	+	0.725182i	$0.741756\pi$
$332$	0.580886	0.0318803
$333$	18.4156	1.00917
$334$	11.6029	0.634885
$335$	12.2844	0.671168
$336$	9.21608	0.502779
$337$	20.2731	1.10435	0.552174	−	0.833729i	$-0.313799\pi$
$337$	20.2731	1.10435	0.552174	+	0.833729i	$0.313799\pi$
$338$	14.3675	0.781487
$339$	0.477465	0.0259323
$340$	−2.32907	−0.126311
$341$	−30.5498	−1.65437
$342$	9.48407	0.512840
$343$	18.1535	0.980199
$344$	1.44011	0.0776455
$345$	8.85196	0.476573
$346$	25.2787	1.35899
$347$	−27.7756	−1.49107	−0.745536	−	0.666465i	$-0.767806\pi$
$347$	−27.7756	−1.49107	−0.745536	+	0.666465i	$0.767806\pi$
$348$	−0.0719921	−0.00385918
$349$	−2.19117	−0.117291	−0.0586454	−	0.998279i	$-0.518678\pi$
$349$	−2.19117	−0.117291	−0.0586454	+	0.998279i	$0.518678\pi$
$350$	−3.37129	−0.180203
$351$	−12.1018	−0.645948
$352$	18.5813	0.990389
$353$	19.3847	1.03175	0.515873	−	0.856665i	$-0.327468\pi$
$353$	19.3847	1.03175	0.515873	+	0.856665i	$0.327468\pi$
$354$	−0.892822	−0.0474530
$355$	24.9072	1.32193
$356$	−8.99274	−0.476614
$357$	−1.85723	−0.0982950
$358$	−17.1384	−0.905793
$359$	9.59548	0.506430	0.253215	−	0.967410i	$-0.418512\pi$
$359$	9.59548	0.506430	0.253215	+	0.967410i	$0.418512\pi$
$360$	4.52843	0.238669
$361$	−8.16794	−0.429892
$362$	26.6979	1.40321
$363$	−1.61689	−0.0848648
$364$	−4.19372	−0.219810
$365$	1.33062	0.0696477
$366$	−1.04191	−0.0544616
$367$	−16.5564	−0.864236	−0.432118	−	0.901817i	$-0.642234\pi$
$367$	−16.5564	−0.864236	−0.432118	+	0.901817i	$0.642234\pi$
$368$	19.1198	0.996688
$369$	4.53522	0.236094
$370$	−39.8115	−2.06970
$371$	−10.8424	−0.562909
$372$	−13.8510	−0.718143
$373$	−12.0772	−0.625336	−0.312668	−	0.949863i	$-0.601223\pi$
$373$	−12.0772	−0.625336	−0.312668	+	0.949863i	$0.601223\pi$
$374$	−5.54546	−0.286749
$375$	14.2357	0.735129
$376$	0.554368	0.0285894
$377$	−0.113984	−0.00587049
$378$	−15.3098	−0.787451
$379$	−8.16674	−0.419497	−0.209749	−	0.977755i	$-0.567265\pi$
$379$	−8.16674	−0.419497	−0.209749	+	0.977755i	$0.567265\pi$
$380$	−7.66545	−0.393229
$381$	−12.5841	−0.644704
$382$	−20.3752	−1.04249
$383$	3.71804	0.189983	0.0949915	−	0.995478i	$-0.469718\pi$
$383$	3.71804	0.189983	0.0949915	+	0.995478i	$0.469718\pi$
$384$	−12.4700	−0.636359
$385$	9.54056	0.486232
$386$	−32.5740	−1.65797
$387$	−1.61234	−0.0819598
$388$	−2.29554	−0.116539
$389$	14.9399	0.757483	0.378741	−	0.925503i	$-0.376357\pi$
$389$	14.9399	0.757483	0.378741	+	0.925503i	$0.376357\pi$
$390$	9.14552	0.463101
$391$	−3.85303	−0.194856
$392$	−6.50110	−0.328355
$393$	−0.535616	−0.0270183
$394$	−27.7138	−1.39620
$395$	0.305360	0.0153643
$396$	−5.97445	−0.300227
$397$	−33.5261	−1.68262	−0.841312	−	0.540550i	$-0.818216\pi$
$397$	−33.5261	−1.68262	−0.841312	+	0.540550i	$0.818216\pi$
$398$	45.2667	2.26901
$399$	−6.11253	−0.306009
$400$	5.93705	0.296853
$401$	10.1861	0.508671	0.254336	−	0.967116i	$-0.418143\pi$
$401$	10.1861	0.508671	0.254336	+	0.967116i	$0.418143\pi$
$402$	13.2612	0.661409
$403$	−21.9302	−1.09242
$404$	9.01601	0.448563
$405$	3.04896	0.151504
$406$	−0.144199	−0.00715649
$407$	−35.4393	−1.75666
$408$	1.69644	0.0839861
$409$	9.77814	0.483498	0.241749	−	0.970339i	$-0.422279\pi$
$409$	9.77814	0.483498	0.241749	+	0.970339i	$0.422279\pi$
$410$	−9.80439	−0.484205
$411$	21.0694	1.03928
$412$	−20.1411	−0.992283
$413$	−0.668597	−0.0328995
$414$	−11.1030	−0.545684
$415$	−0.948636	−0.0465667
$416$	13.3386	0.653979
$417$	4.70275	0.230295
$418$	−18.2513	−0.892699
$419$	37.5725	1.83554	0.917768	−	0.397117i	$-0.129989\pi$
$419$	37.5725	1.83554	0.917768	+	0.397117i	$0.129989\pi$
$420$	4.32561	0.211068
$421$	12.0576	0.587649	0.293825	−	0.955859i	$-0.405072\pi$
$421$	12.0576	0.587649	0.293825	+	0.955859i	$0.405072\pi$
$422$	7.63889	0.371856
$423$	−0.620667	−0.0301779
$424$	9.90369	0.480966
$425$	−1.19644	−0.0580357
$426$	26.8877	1.30271
$427$	−0.780243	−0.0377586
$428$	2.28192	0.110301
$429$	8.14114	0.393058
$430$	3.48560	0.168091
$431$	−5.82810	−0.280730	−0.140365	−	0.990100i	$-0.544828\pi$
$431$	−5.82810	−0.280730	−0.140365	+	0.990100i	$0.544828\pi$
$432$	26.9615	1.29719
$433$	−32.3682	−1.55552	−0.777759	−	0.628562i	$-0.783644\pi$
$433$	−32.3682	−1.55552	−0.777759	+	0.628562i	$0.783644\pi$
$434$	−27.7435	−1.33173
$435$	0.117569	0.00563701
$436$	−5.44421	−0.260731
$437$	−12.6811	−0.606620
$438$	1.43642	0.0686350
$439$	12.2009	0.582316	0.291158	−	0.956675i	$-0.405959\pi$
$439$	12.2009	0.582316	0.291158	+	0.956675i	$0.405959\pi$
$440$	−8.71457	−0.415451
$441$	7.27859	0.346600
$442$	−3.98081	−0.189348
$443$	−14.8480	−0.705451	−0.352726	−	0.935727i	$-0.614745\pi$
$443$	−14.8480	−0.705451	−0.352726	+	0.935727i	$0.614745\pi$
$444$	−16.0679	−0.762548
$445$	14.6859	0.696179
$446$	−32.7854	−1.55243
$447$	16.8433	0.796659
$448$	1.22729	0.0579841
$449$	−12.1948	−0.575510	−0.287755	−	0.957704i	$-0.592909\pi$
$449$	−12.1948	−0.575510	−0.287755	+	0.957704i	$0.592909\pi$
$450$	−3.44770	−0.162526
$451$	−8.72765	−0.410969
$452$	0.484046	0.0227676
$453$	8.69207	0.408389
$454$	−40.7633	−1.91311
$455$	6.84869	0.321072
$456$	5.58333	0.261463
$457$	8.71000	0.407437	0.203718	−	0.979030i	$-0.434697\pi$
$457$	8.71000	0.407437	0.203718	+	0.979030i	$0.434697\pi$
$458$	−17.6562	−0.825022
$459$	−5.43329	−0.253604
$460$	8.97396	0.418413
$461$	−9.61079	−0.447619	−0.223810	−	0.974633i	$-0.571849\pi$
$461$	−9.61079	−0.447619	−0.223810	+	0.974633i	$0.571849\pi$
$462$	10.2992	0.479162
$463$	27.2262	1.26531	0.632655	−	0.774433i	$-0.281965\pi$
$463$	27.2262	1.26531	0.632655	+	0.774433i	$0.281965\pi$
$464$	0.253944	0.0117890
$465$	22.6199	1.04897
$466$	37.9568	1.75831
$467$	25.6977	1.18915	0.594574	−	0.804041i	$-0.297321\pi$
$467$	25.6977	1.18915	0.594574	+	0.804041i	$0.297321\pi$
$468$	−4.28876	−0.198248
$469$	9.93076	0.458560
$470$	1.34178	0.0618916
$471$	−3.22031	−0.148384
$472$	0.610711	0.0281103
$473$	3.10281	0.142667
$474$	0.329641	0.0151409
$475$	−3.93773	−0.180675
$476$	−1.88283	−0.0862993
$477$	−11.0881	−0.507690
$478$	50.2209	2.29705
$479$	29.2332	1.33570	0.667848	−	0.744297i	$-0.267215\pi$
$479$	29.2332	1.33570	0.667848	+	0.744297i	$0.267215\pi$
$480$	−13.7581	−0.627970
$481$	−25.4401	−1.15997
$482$	26.4995	1.20702
$483$	7.15596	0.325607
$484$	−1.63918	−0.0745081
$485$	3.74882	0.170225
$486$	−25.8404	−1.17214
$487$	23.5995	1.06939	0.534697	−	0.845044i	$-0.320426\pi$
$487$	23.5995	1.06939	0.534697	+	0.845044i	$0.320426\pi$
$488$	0.712692	0.0322620
$489$	27.8995	1.26166
$490$	−15.7351	−0.710839
$491$	−27.5440	−1.24304	−0.621521	−	0.783398i	$-0.713485\pi$
$491$	−27.5440	−1.24304	−0.621521	+	0.783398i	$0.713485\pi$
$492$	−3.95705	−0.178397
$493$	−0.0511748	−0.00230480
$494$	−13.1017	−0.589472
$495$	9.75678	0.438534
$496$	48.8579	2.19378
$497$	20.1350	0.903180
$498$	−1.02407	−0.0458896
$499$	−26.4716	−1.18503	−0.592517	−	0.805558i	$-0.701866\pi$
$499$	−26.4716	−1.18503	−0.592517	+	0.805558i	$0.701866\pi$
$500$	14.4319	0.645415
$501$	−7.64763	−0.341671
$502$	1.83931	0.0820926
$503$	17.9143	0.798758	0.399379	−	0.916786i	$-0.369226\pi$
$503$	17.9143	0.798758	0.399379	+	0.916786i	$0.369226\pi$
$504$	3.66080	0.163065
$505$	−14.7239	−0.655205
$506$	21.3668	0.949871
$507$	−9.46976	−0.420567
$508$	−12.7576	−0.566026
$509$	10.5463	0.467458	0.233729	−	0.972302i	$-0.424907\pi$
$509$	10.5463	0.467458	0.233729	+	0.972302i	$0.424907\pi$
$510$	4.10601	0.181817
$511$	1.07568	0.0475852
$512$	−15.4244	−0.681670
$513$	−17.8821	−0.789514
$514$	21.3998	0.943906
$515$	32.8922	1.44940
$516$	1.40679	0.0619304
$517$	1.19442	0.0525306
$518$	−32.1837	−1.41407
$519$	−16.6615	−0.731359
$520$	−6.25575	−0.274333
$521$	−15.4106	−0.675153	−0.337576	−	0.941298i	$-0.609607\pi$
$521$	−15.4106	−0.675153	−0.337576	+	0.941298i	$0.609607\pi$
$522$	−0.147467	−0.00645446
$523$	20.1478	0.881003	0.440502	−	0.897752i	$-0.354801\pi$
$523$	20.1478	0.881003	0.440502	+	0.897752i	$0.354801\pi$
$524$	−0.542999	−0.0237210
$525$	2.22206	0.0969786
$526$	−32.3091	−1.40874
$527$	−9.84587	−0.428893
$528$	−18.1375	−0.789334
$529$	−8.15418	−0.354529
$530$	23.9706	1.04122
$531$	−0.683749	−0.0296722
$532$	−6.19678	−0.268664
$533$	−6.26514	−0.271374
$534$	15.8537	0.686056
$535$	−3.72656	−0.161113
$536$	−9.07098	−0.391807
$537$	11.2961	0.487464
$538$	−20.3368	−0.876783
$539$	−14.0070	−0.603325
$540$	12.6545	0.544563
$541$	−11.0283	−0.474142	−0.237071	−	0.971492i	$-0.576187\pi$
$541$	−11.0283	−0.474142	−0.237071	+	0.971492i	$0.576187\pi$
$542$	0.114162	0.00490368
$543$	−17.5969	−0.755154
$544$	5.98856	0.256757
$545$	8.89086	0.380842
$546$	7.39327	0.316403
$547$	32.6917	1.39780	0.698899	−	0.715221i	$-0.253674\pi$
$547$	32.6917	1.39780	0.698899	+	0.715221i	$0.253674\pi$
$548$	21.3598	0.912445
$549$	−0.797925	−0.0340546
$550$	6.63480	0.282909
$551$	−0.168427	−0.00717523
$552$	−6.53642	−0.278208
$553$	0.246854	0.0104973
$554$	−20.7368	−0.881021
$555$	26.2402	1.11383
$556$	4.76757	0.202190
$557$	10.9353	0.463344	0.231672	−	0.972794i	$-0.425580\pi$
$557$	10.9353	0.463344	0.231672	+	0.972794i	$0.425580\pi$
$558$	−28.3722	−1.20109
$559$	2.22735	0.0942069
$560$	−15.2581	−0.644772
$561$	3.65508	0.154318
$562$	53.4780	2.25583
$563$	−2.88643	−0.121649	−0.0608243	−	0.998148i	$-0.519373\pi$
$563$	−2.88643	−0.121649	−0.0608243	+	0.998148i	$0.519373\pi$
$564$	0.541541	0.0228030
$565$	−0.790488	−0.0332561
$566$	−35.6155	−1.49703
$567$	2.46479	0.103511
$568$	−18.3918	−0.771703
$569$	−38.6945	−1.62216	−0.811078	−	0.584938i	$-0.801119\pi$
$569$	−38.6945	−1.62216	−0.811078	+	0.584938i	$0.801119\pi$
$570$	13.5137	0.566028
$571$	25.2055	1.05482	0.527409	−	0.849612i	$-0.323164\pi$
$571$	25.2055	1.05482	0.527409	+	0.849612i	$0.323164\pi$
$572$	8.25335	0.345090
$573$	13.4295	0.561027
$574$	−7.92591	−0.330821
$575$	4.60991	0.192246
$576$	1.25511	0.0522961
$577$	−13.9422	−0.580423	−0.290212	−	0.956962i	$-0.593726\pi$
$577$	−13.9422	−0.580423	−0.290212	+	0.956962i	$0.593726\pi$
$578$	−1.78724	−0.0743394
$579$	21.4699	0.892259
$580$	0.119190	0.00494908
$581$	−0.766881	−0.0318156
$582$	4.04691	0.167750
$583$	21.3381	0.883734
$584$	−0.982548	−0.0406581
$585$	7.00390	0.289576
$586$	39.8830	1.64755
$587$	−8.47478	−0.349791	−0.174896	−	0.984587i	$-0.555959\pi$
$587$	−8.47478	−0.349791	−0.174896	+	0.984587i	$0.555959\pi$
$588$	−6.35067	−0.261897
$589$	−32.4048	−1.33522
$590$	1.47815	0.0608545
$591$	18.2665	0.751383
$592$	56.6775	2.32943
$593$	40.0847	1.64608	0.823041	−	0.567981i	$-0.192275\pi$
$593$	40.0847	1.64608	0.823041	+	0.567981i	$0.192275\pi$
$594$	30.1301	1.23625
$595$	3.07481	0.126055
$596$	17.0754	0.699436
$597$	−29.8358	−1.22110
$598$	15.3382	0.627224
$599$	−30.5906	−1.24990	−0.624949	−	0.780666i	$-0.714880\pi$
$599$	−30.5906	−1.24990	−0.624949	+	0.780666i	$0.714880\pi$
$600$	−2.02968	−0.0828613
$601$	−14.9378	−0.609325	−0.304663	−	0.952460i	$-0.598544\pi$
$601$	−14.9378	−0.609325	−0.304663	+	0.952460i	$0.598544\pi$
$602$	2.81778	0.114844
$603$	10.1558	0.413577
$604$	8.81187	0.358550
$605$	2.67692	0.108832
$606$	−15.8947	−0.645678
$607$	−14.5351	−0.589961	−0.294980	−	0.955503i	$-0.595313\pi$
$607$	−14.5351	−0.589961	−0.294980	+	0.955503i	$0.595313\pi$
$608$	19.7096	0.799330
$609$	0.0950433	0.00385135
$610$	1.72498	0.0698424
$611$	0.857415	0.0346873
$612$	−1.92550	−0.0778336
$613$	−19.0419	−0.769096	−0.384548	−	0.923105i	$-0.625643\pi$
$613$	−19.0419	−0.769096	−0.384548	+	0.923105i	$0.625643\pi$
$614$	−58.2143	−2.34934
$615$	6.46219	0.260581
$616$	−7.04489	−0.283847
$617$	−1.63860	−0.0659674	−0.0329837	−	0.999456i	$-0.510501\pi$
$617$	−1.63860	−0.0659674	−0.0329837	+	0.999456i	$0.510501\pi$
$618$	35.5076	1.42833
$619$	29.5608	1.18815	0.594074	−	0.804410i	$-0.297519\pi$
$619$	29.5608	1.18815	0.594074	+	0.804410i	$0.297519\pi$
$620$	22.9317	0.920959
$621$	20.9346	0.840077
$622$	55.2689	2.21608
$623$	11.8721	0.475647
$624$	−13.0200	−0.521217
$625$	−17.5863	−0.703454
$626$	0.339284	0.0135605
$627$	12.0296	0.480417
$628$	−3.26469	−0.130275
$629$	−11.4217	−0.455412
$630$	8.86050	0.353011
$631$	18.1334	0.721878	0.360939	−	0.932589i	$-0.382456\pi$
$631$	18.1334	0.721878	0.360939	+	0.932589i	$0.382456\pi$
$632$	−0.225482	−0.00896919
$633$	−5.03488	−0.200119
$634$	−11.2685	−0.447530
$635$	20.8342	0.826779
$636$	9.67453	0.383620
$637$	−10.0549	−0.398391
$638$	0.283788	0.0112353
$639$	20.5914	0.814582
$640$	20.6453	0.816078
$641$	−8.47684	−0.334815	−0.167407	−	0.985888i	$-0.553540\pi$
$641$	−8.47684	−0.334815	−0.167407	+	0.985888i	$0.553540\pi$
$642$	−4.02289	−0.158771
$643$	−3.35677	−0.132378	−0.0661891	−	0.997807i	$-0.521084\pi$
$643$	−3.35677	−0.132378	−0.0661891	+	0.997807i	$0.521084\pi$
$644$	7.25459	0.285871
$645$	−2.29740	−0.0904601
$646$	−5.88218	−0.231431
$647$	23.3618	0.918449	0.459224	−	0.888320i	$-0.348127\pi$
$647$	23.3618	0.918449	0.459224	+	0.888320i	$0.348127\pi$
$648$	−2.25140	−0.0884432
$649$	1.31582	0.0516503
$650$	4.76279	0.186812
$651$	18.2860	0.716686
$652$	28.2840	1.10769
$653$	−48.5559	−1.90014	−0.950069	−	0.312040i	$-0.898988\pi$
$653$	−48.5559	−1.90014	−0.950069	+	0.312040i	$0.898988\pi$
$654$	9.59783	0.375305
$655$	0.886762	0.0346487
$656$	13.9580	0.544969
$657$	1.10006	0.0429172
$658$	1.08470	0.0422860
$659$	1.14129	0.0444584	0.0222292	−	0.999753i	$-0.492924\pi$
$659$	1.14129	0.0444584	0.0222292	+	0.999753i	$0.492924\pi$
$660$	−8.51292	−0.331365
$661$	−16.8702	−0.656173	−0.328087	−	0.944648i	$-0.606404\pi$
$661$	−16.8702	−0.656173	−0.328087	+	0.944648i	$0.606404\pi$
$662$	44.7783	1.74036
$663$	2.62380	0.101900
$664$	0.700487	0.0271842
$665$	10.1199	0.392431
$666$	−32.9131	−1.27536
$667$	0.197178	0.00763476
$668$	−7.75304	−0.299974
$669$	21.6092	0.835461
$670$	−21.9552	−0.848202
$671$	1.53554	0.0592788
$672$	−11.1221	−0.429045
$673$	33.2670	1.28235	0.641174	−	0.767395i	$-0.278448\pi$
$673$	33.2670	1.28235	0.641174	+	0.767395i	$0.278448\pi$
$674$	−36.2329	−1.39564
$675$	6.50059	0.250208
$676$	−9.60028	−0.369242
$677$	−14.2105	−0.546154	−0.273077	−	0.961992i	$-0.588041\pi$
$677$	−14.2105	−0.546154	−0.273077	+	0.961992i	$0.588041\pi$
$678$	−0.853345	−0.0327725
$679$	3.03056	0.116302
$680$	−2.80861	−0.107705
$681$	26.8675	1.02957
$682$	54.5999	2.09074
$683$	−30.8773	−1.18149	−0.590744	−	0.806859i	$-0.701166\pi$
$683$	−30.8773	−1.18149	−0.590744	+	0.806859i	$0.701166\pi$
$684$	−6.33722	−0.242310
$685$	−34.8823	−1.33279
$686$	−32.4447	−1.23875
$687$	11.6374	0.443996
$688$	−4.96228	−0.189185
$689$	15.3176	0.583553
$690$	−15.8206	−0.602279
$691$	−7.19533	−0.273723	−0.136862	−	0.990590i	$-0.543702\pi$
$691$	−7.19533	−0.273723	−0.136862	+	0.990590i	$0.543702\pi$
$692$	−16.8911	−0.642105
$693$	7.88742	0.299618
$694$	49.6416	1.88437
$695$	−7.78584	−0.295334
$696$	−0.0868148	−0.00329071
$697$	−2.81282	−0.106543
$698$	3.91615	0.148229
$699$	−25.0177	−0.946258
$700$	2.25269	0.0851435
$701$	−7.78796	−0.294147	−0.147074	−	0.989126i	$-0.546985\pi$
$701$	−7.78796	−0.294147	−0.147074	+	0.989126i	$0.546985\pi$
$702$	21.6289	0.816330
$703$	−37.5911	−1.41778
$704$	−2.41534	−0.0910317
$705$	−0.884382	−0.0333077
$706$	−34.6452	−1.30389
$707$	−11.9029	−0.447653
$708$	0.596580	0.0224209
$709$	−22.9626	−0.862380	−0.431190	−	0.902261i	$-0.641906\pi$
$709$	−22.9626	−0.862380	−0.431190	+	0.902261i	$0.641906\pi$
$710$	−44.5151	−1.67062
$711$	0.252448	0.00946755
$712$	−10.8443	−0.406407
$713$	37.9364	1.42073
$714$	3.31931	0.124222
$715$	−13.4784	−0.504064
$716$	11.4518	0.427975
$717$	−33.1011	−1.23619
$718$	−17.1494	−0.640011
$719$	−30.5008	−1.13749	−0.568745	−	0.822514i	$-0.692571\pi$
$719$	−30.5008	−1.13749	−0.568745	+	0.822514i	$0.692571\pi$
$720$	−15.6039	−0.581522
$721$	26.5902	0.990269
$722$	14.5981	0.543284
$723$	−17.4661	−0.649572
$724$	−17.8394	−0.662996
$725$	0.0612275	0.00227393
$726$	2.88977	0.107250
$727$	−3.99449	−0.148148	−0.0740738	−	0.997253i	$-0.523600\pi$
$727$	−3.99449	−0.148148	−0.0740738	+	0.997253i	$0.523600\pi$
$728$	−5.05717	−0.187431
$729$	21.7217	0.804509
$730$	−2.37813	−0.0880187
$731$	1.00000	0.0369863
$732$	0.696201	0.0257323
$733$	−5.66126	−0.209103	−0.104552	−	0.994519i	$-0.533341\pi$
$733$	−5.66126	−0.209103	−0.104552	+	0.994519i	$0.533341\pi$
$734$	29.5902	1.09219
$735$	10.3712	0.382547
$736$	−23.0741	−0.850522
$737$	−19.5440	−0.719912
$738$	−8.10554	−0.298369
$739$	19.9783	0.734913	0.367456	−	0.930041i	$-0.380229\pi$
$739$	19.9783	0.734913	0.367456	+	0.930041i	$0.380229\pi$
$740$	26.6019	0.977904
$741$	8.63547	0.317232
$742$	19.3779	0.711387
$743$	7.98554	0.292961	0.146481	−	0.989214i	$-0.453205\pi$
$743$	7.98554	0.292961	0.146481	+	0.989214i	$0.453205\pi$
$744$	−16.7029	−0.612357
$745$	−27.8856	−1.02165
$746$	21.5849	0.790280
$747$	−0.784261	−0.0286946
$748$	3.70546	0.135485
$749$	−3.01257	−0.110077
$750$	−25.4426	−0.929033
$751$	23.2928	0.849967	0.424983	−	0.905201i	$-0.360280\pi$
$751$	23.2928	0.849967	0.424983	+	0.905201i	$0.360280\pi$
$752$	−1.91022	−0.0696586
$753$	−1.21231	−0.0441791
$754$	0.203717	0.00741894
$755$	−14.3905	−0.523725
$756$	10.2299	0.372060
$757$	−35.3351	−1.28428	−0.642139	−	0.766589i	$-0.721953\pi$
$757$	−35.3351	−1.28428	−0.642139	+	0.766589i	$0.721953\pi$
$758$	14.5959	0.530148
$759$	−14.0831	−0.511185
$760$	−9.24371	−0.335305
$761$	50.8360	1.84280	0.921402	−	0.388611i	$-0.127045\pi$
$761$	50.8360	1.84280	0.921402	+	0.388611i	$0.127045\pi$
$762$	22.4908	0.814757
$763$	7.18740	0.260201
$764$	13.6146	0.492561
$765$	3.14450	0.113690
$766$	−6.64503	−0.240095
$767$	0.944559	0.0341060
$768$	24.1209	0.870390
$769$	−32.9651	−1.18875	−0.594376	−	0.804187i	$-0.702601\pi$
$769$	−32.9651	−1.18875	−0.594376	+	0.804187i	$0.702601\pi$
$770$	−17.0513	−0.614485
$771$	−14.1049	−0.507975
$772$	21.7658	0.783369
$773$	0.00408493	0.000146925 0	7.34624e−5	−	1.00000i	$-0.499977\pi$
$773$	0.00408493	0.000146925 0	7.34624e−5		1.00000i	$0.499977\pi$
$774$	2.88164	0.103578
$775$	11.7800	0.423149
$776$	−2.76818	−0.0993719
$777$	21.2127	0.761001
$778$	−26.7012	−0.957283
$779$	−9.25759	−0.331688
$780$	−6.11100	−0.218809
$781$	−39.6263	−1.41794
$782$	6.88629	0.246253
$783$	0.278048	0.00993661
$784$	22.4012	0.800044
$785$	5.33152	0.190290
$786$	0.957275	0.0341449
$787$	29.7216	1.05946	0.529731	−	0.848166i	$-0.322293\pi$
$787$	29.7216	1.05946	0.529731	+	0.848166i	$0.322293\pi$
$788$	18.5183	0.659686
$789$	21.2953	0.758133
$790$	−0.545751	−0.0194169
$791$	−0.639033	−0.0227214
$792$	−7.20455	−0.256002
$793$	1.10229	0.0391433
$794$	59.9191	2.12645
$795$	−15.7993	−0.560344
$796$	−30.2470	−1.07208
$797$	1.48881	0.0527363	0.0263682	−	0.999652i	$-0.491606\pi$
$797$	1.48881	0.0527363	0.0263682	+	0.999652i	$0.491606\pi$
$798$	10.9246	0.386725
$799$	0.384948	0.0136185
$800$	−7.16494	−0.253319
$801$	12.1412	0.428988
$802$	−18.2051	−0.642843
$803$	−2.11696	−0.0747060
$804$	−8.86109	−0.312507
$805$	−11.8473	−0.417564
$806$	39.1945	1.38057
$807$	13.4042	0.471851
$808$	10.8723	0.382488
$809$	−45.9509	−1.61555	−0.807773	−	0.589493i	$-0.799327\pi$
$809$	−45.9509	−1.61555	−0.807773	+	0.589493i	$0.799327\pi$
$810$	−5.44922	−0.191466
$811$	−15.0480	−0.528407	−0.264203	−	0.964467i	$-0.585109\pi$
$811$	−15.0480	−0.528407	−0.264203	+	0.964467i	$0.585109\pi$
$812$	0.0963533	0.00338134
$813$	−0.0752455	−0.00263897
$814$	63.3385	2.22001
$815$	−46.1902	−1.61797
$816$	−5.84551	−0.204634
$817$	3.29121	0.115145
$818$	−17.4759	−0.611030
$819$	5.66198	0.197846
$820$	6.55126	0.228780
$821$	−14.8277	−0.517491	−0.258746	−	0.965945i	$-0.583309\pi$
$821$	−14.8277	−0.517491	−0.258746	+	0.965945i	$0.583309\pi$
$822$	−37.6561	−1.31341
$823$	−9.32496	−0.325048	−0.162524	−	0.986705i	$-0.551963\pi$
$823$	−9.32496	−0.325048	−0.162524	+	0.986705i	$0.551963\pi$
$824$	−24.2881	−0.846115
$825$	−4.37307	−0.152251
$826$	1.19494	0.0415774
$827$	36.4435	1.26726	0.633632	−	0.773635i	$-0.281563\pi$
$827$	36.4435	1.26726	0.633632	+	0.773635i	$0.281563\pi$
$828$	7.41900	0.257828
$829$	−16.9024	−0.587044	−0.293522	−	0.955952i	$-0.594827\pi$
$829$	−16.9024	−0.587044	−0.293522	+	0.955952i	$0.594827\pi$
$830$	1.69544	0.0588496
$831$	13.6678	0.474132
$832$	−1.73385	−0.0601106
$833$	−4.51431	−0.156411
$834$	−8.40495	−0.291040
$835$	12.6614	0.438165
$836$	12.1954	0.421788
$837$	53.4955	1.84907
$838$	−67.1510	−2.31969
$839$	−36.9165	−1.27450	−0.637250	−	0.770657i	$-0.719928\pi$
$839$	−36.9165	−1.27450	−0.637250	+	0.770657i	$0.719928\pi$
$840$	5.21623	0.179977
$841$	−28.9974	−0.999910
$842$	−21.5497	−0.742653
$843$	−35.2479	−1.21400
$844$	−5.10428	−0.175697
$845$	15.6781	0.539342
$846$	1.10928	0.0381379
$847$	2.16403	0.0743569
$848$	−34.1257	−1.17188
$849$	23.4746	0.805645
$850$	2.13832	0.0733438
$851$	44.0081	1.50858
$852$	−17.9662	−0.615514
$853$	−3.07522	−0.105294	−0.0526468	−	0.998613i	$-0.516766\pi$
$853$	−3.07522	−0.105294	−0.0526468	+	0.998613i	$0.516766\pi$
$854$	1.39448	0.0477182
$855$	10.3492	0.353935
$856$	2.75175	0.0940529
$857$	−48.9748	−1.67295	−0.836473	−	0.548008i	$-0.815386\pi$
$857$	−48.9748	−1.67295	−0.836473	+	0.548008i	$0.815386\pi$
$858$	−14.5502	−0.496735
$859$	27.0794	0.923938	0.461969	−	0.886896i	$-0.347143\pi$
$859$	27.0794	0.923938	0.461969	+	0.886896i	$0.347143\pi$
$860$	−2.32907	−0.0794205
$861$	5.22406	0.178035
$862$	10.4162	0.354778
$863$	42.9804	1.46307	0.731534	−	0.681805i	$-0.238805\pi$
$863$	42.9804	1.46307	0.731534	+	0.681805i	$0.238805\pi$
$864$	−32.5376	−1.10695
$865$	27.5847	0.937907
$866$	57.8498	1.96582
$867$	1.17799	0.0400067
$868$	18.5381	0.629223
$869$	−0.485815	−0.0164802
$870$	−0.210124	−0.00712388
$871$	−14.0297	−0.475377
$872$	−6.56514	−0.222324
$873$	3.09924	0.104893
$874$	22.6642	0.766628
$875$	−19.0529	−0.644106
$876$	−0.959813	−0.0324291
$877$	−37.8093	−1.27673	−0.638365	−	0.769734i	$-0.720389\pi$
$877$	−37.8093	−1.27673	−0.638365	+	0.769734i	$0.720389\pi$
$878$	−21.8059	−0.735914
$879$	−26.2873	−0.886650
$880$	30.0283	1.01225
$881$	49.9951	1.68438	0.842188	−	0.539183i	$-0.181267\pi$
$881$	49.9951	1.68438	0.842188	+	0.539183i	$0.181267\pi$
$882$	−13.0086	−0.438022
$883$	−5.07502	−0.170788	−0.0853940	−	0.996347i	$-0.527215\pi$
$883$	−5.07502	−0.170788	−0.0853940	+	0.996347i	$0.527215\pi$
$884$	2.65996	0.0894642
$885$	−0.974266	−0.0327496
$886$	26.5370	0.891528
$887$	3.24341	0.108903	0.0544515	−	0.998516i	$-0.482659\pi$
$887$	3.24341	0.108903	0.0544515	+	0.998516i	$0.482659\pi$
$888$	−19.3761	−0.650221
$889$	16.8424	0.564877
$890$	−26.2472	−0.879809
$891$	−4.85077	−0.162507
$892$	21.9071	0.733503
$893$	1.26695	0.0423967
$894$	−30.1030	−1.00679
$895$	−18.7018	−0.625132
$896$	16.6898	0.557565
$897$	−10.1096	−0.337549
$898$	21.7951	0.727312
$899$	0.503860	0.0168047
$900$	2.30374	0.0767913
$901$	6.87704	0.229107
$902$	15.5984	0.519370
$903$	−1.85723	−0.0618047
$904$	0.583708	0.0194138
$905$	29.1332	0.968422
$906$	−15.5348	−0.516110
$907$	4.60200	0.152807	0.0764034	−	0.997077i	$-0.475656\pi$
$907$	4.60200	0.152807	0.0764034	+	0.997077i	$0.475656\pi$
$908$	27.2378	0.903920
$909$	−12.1726	−0.403740
$910$	−12.2403	−0.405760
$911$	3.68868	0.122211	0.0611057	−	0.998131i	$-0.480537\pi$
$911$	3.68868	0.122211	0.0611057	+	0.998131i	$0.480537\pi$
$912$	−19.2388	−0.637061
$913$	1.50924	0.0499487
$914$	−15.5669	−0.514906
$915$	−1.13695	−0.0375866
$916$	11.7978	0.389811
$917$	0.716862	0.0236729
$918$	9.71059	0.320497
$919$	4.16218	0.137298	0.0686489	−	0.997641i	$-0.478131\pi$
$919$	4.16218	0.137298	0.0686489	+	0.997641i	$0.478131\pi$
$920$	10.8216	0.356779
$921$	38.3697	1.26433
$922$	17.1768	0.565687
$923$	−28.4457	−0.936303
$924$	−6.88188	−0.226397
$925$	13.6653	0.449313
$926$	−48.6598	−1.59906
$927$	27.1928	0.893128
$928$	−0.306463	−0.0100602
$929$	−26.2072	−0.859830	−0.429915	−	0.902869i	$-0.641457\pi$
$929$	−26.2072	−0.859830	−0.429915	+	0.902869i	$0.641457\pi$
$930$	−40.4272	−1.32566
$931$	−14.8575	−0.486936
$932$	−25.3626	−0.830778
$933$	−36.4283	−1.19261
$934$	−45.9280	−1.50281
$935$	−6.05132	−0.197899
$936$	−5.17178	−0.169045
$937$	30.0308	0.981063	0.490531	−	0.871424i	$-0.336803\pi$
$937$	30.0308	0.981063	0.490531	+	0.871424i	$0.336803\pi$
$938$	−17.7486	−0.579514
$939$	−0.223626	−0.00729775
$940$	−0.896571	−0.0292429
$941$	−15.1987	−0.495463	−0.247731	−	0.968829i	$-0.579685\pi$
$941$	−15.1987	−0.495463	−0.247731	+	0.968829i	$0.579685\pi$
$942$	5.75546	0.187523
$943$	10.8379	0.352930
$944$	−2.10437	−0.0684913
$945$	−16.7064	−0.543458
$946$	−5.54546	−0.180299
$947$	−5.43791	−0.176708	−0.0883542	−	0.996089i	$-0.528161\pi$
$947$	−5.43791	−0.176708	−0.0883542	+	0.996089i	$0.528161\pi$
$948$	−0.220265	−0.00715386
$949$	−1.51966	−0.0493303
$950$	7.03766	0.228332
$951$	7.42722	0.240844
$952$	−2.27049	−0.0735870
$953$	12.0027	0.388806	0.194403	−	0.980922i	$-0.437723\pi$
$953$	12.0027	0.388806	0.194403	+	0.980922i	$0.437723\pi$
$954$	19.8171	0.641603
$955$	−22.2339	−0.719471
$956$	−33.5574	−1.08532
$957$	−0.187048	−0.00604640
$958$	−52.2467	−1.68801
$959$	−28.1990	−0.910594
$960$	1.78839	0.0577199
$961$	65.9411	2.12713
$962$	45.4675	1.46593
$963$	−3.08084	−0.0992788
$964$	−17.7069	−0.570300
$965$	−35.5454	−1.14425
$966$	−12.7894	−0.411493
$967$	4.06705	0.130787	0.0653937	−	0.997860i	$-0.479170\pi$
$967$	4.06705	0.130787	0.0653937	+	0.997860i	$0.479170\pi$
$968$	−1.97667	−0.0635327
$969$	3.87701	0.124548
$970$	−6.70004	−0.215125
$971$	−48.7974	−1.56598	−0.782991	−	0.622032i	$-0.786307\pi$
$971$	−48.7974	−1.56598	−0.782991	+	0.622032i	$0.786307\pi$
$972$	17.2664	0.553821
$973$	−6.29411	−0.201780
$974$	−42.1779	−1.35147
$975$	−3.13921	−0.100535
$976$	−2.45577	−0.0786071
$977$	49.2909	1.57696	0.788478	−	0.615063i	$-0.210870\pi$
$977$	49.2909	1.57696	0.788478	+	0.615063i	$0.210870\pi$
$978$	−49.8631	−1.59445
$979$	−23.3647	−0.746739
$980$	10.5141	0.335861
$981$	7.35029	0.234677
$982$	49.2277	1.57092
$983$	41.5113	1.32401	0.662003	−	0.749501i	$-0.269707\pi$
$983$	41.5113	1.32401	0.662003	+	0.749501i	$0.269707\pi$
$984$	−4.77178	−0.152119
$985$	−30.2419	−0.963586
$986$	0.0914617	0.00291273
$987$	−0.714938	−0.0227567
$988$	8.75449	0.278517
$989$	−3.85303	−0.122519
$990$	−17.4377	−0.554206
$991$	1.27715	0.0405700	0.0202850	−	0.999794i	$-0.493543\pi$
$991$	1.27715	0.0405700	0.0202850	+	0.999794i	$0.493543\pi$
$992$	−58.9625	−1.87206
$993$	−29.5139	−0.936594
$994$	−35.9861	−1.14141
$995$	49.3959	1.56596
$996$	0.684279	0.0216822
$997$	21.5086	0.681185	0.340592	−	0.940211i	$-0.389372\pi$
$997$	21.5086	0.681185	0.340592	+	0.940211i	$0.389372\pi$
$998$	47.3112	1.49761
$999$	62.0573	1.96341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.d.1.2	✓	8
3.2	odd	2		6579.2.a.k.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.d.1.2	✓	8	1.1	even	1	trivial
6579.2.a.k.1.7		8	3.2	odd	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q-1.78724 q^{2} +1.17799 q^{3} +1.19423 q^{4} -1.95027 q^{5} -2.10535 q^{6} -1.57661 q^{7} +1.44011 q^{8} -1.61234 q^{9} +O(q^{10})\)	\(q-1.78724 q^{2} +1.17799 q^{3} +1.19423 q^{4} -1.95027 q^{5} -2.10535 q^{6} -1.57661 q^{7} +1.44011 q^{8} -1.61234 q^{9} +3.48560 q^{10} +3.10281 q^{11} +1.40679 q^{12} +2.22735 q^{13} +2.81778 q^{14} -2.29740 q^{15} -4.96228 q^{16} +1.00000 q^{17} +2.88164 q^{18} +3.29121 q^{19} -2.32907 q^{20} -1.85723 q^{21} -5.54546 q^{22} -3.85303 q^{23} +1.69644 q^{24} -1.19644 q^{25} -3.98081 q^{26} -5.43329 q^{27} -1.88283 q^{28} -0.0511748 q^{29} +4.10601 q^{30} -9.84587 q^{31} +5.98856 q^{32} +3.65508 q^{33} -1.78724 q^{34} +3.07481 q^{35} -1.92550 q^{36} -11.4217 q^{37} -5.88218 q^{38} +2.62380 q^{39} -2.80861 q^{40} -2.81282 q^{41} +3.31931 q^{42} +1.00000 q^{43} +3.70546 q^{44} +3.14450 q^{45} +6.88629 q^{46} +0.384948 q^{47} -5.84551 q^{48} -4.51431 q^{49} +2.13832 q^{50} +1.17799 q^{51} +2.65996 q^{52} +6.87704 q^{53} +9.71059 q^{54} -6.05132 q^{55} -2.27049 q^{56} +3.87701 q^{57} +0.0914617 q^{58} +0.424073 q^{59} -2.74362 q^{60} +0.494887 q^{61} +17.5969 q^{62} +2.54203 q^{63} -0.778438 q^{64} -4.34394 q^{65} -6.53250 q^{66} -6.29881 q^{67} +1.19423 q^{68} -4.53883 q^{69} -5.49543 q^{70} -12.7711 q^{71} -2.32194 q^{72} -0.682273 q^{73} +20.4133 q^{74} -1.40939 q^{75} +3.93045 q^{76} -4.89191 q^{77} -4.68936 q^{78} -0.156573 q^{79} +9.67779 q^{80} -1.56335 q^{81} +5.02719 q^{82} +0.486412 q^{83} -2.21795 q^{84} -1.95027 q^{85} -1.78724 q^{86} -0.0602834 q^{87} +4.46838 q^{88} -7.53018 q^{89} -5.61997 q^{90} -3.51166 q^{91} -4.60139 q^{92} -11.5983 q^{93} -0.687995 q^{94} -6.41875 q^{95} +7.05446 q^{96} -1.92220 q^{97} +8.06815 q^{98} -5.00278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9	\( 8 q + q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 5 q^{9} - 12 q^{10} - 4 q^{11} - 13 q^{12} - 12 q^{13} + q^{14} - 9 q^{15} - 3 q^{16} + 8 q^{17} + 5 q^{18} - 5 q^{20} - 20 q^{21} - 14 q^{22} - 9 q^{23} - q^{24} - 7 q^{25} - 17 q^{26} - 12 q^{27} + q^{28} - 27 q^{29} + 10 q^{30} - 12 q^{31} + 5 q^{32} + 10 q^{33} + q^{34} + 15 q^{35} - 4 q^{36} - 24 q^{37} - q^{38} + 3 q^{39} - 9 q^{40} - 8 q^{41} - 9 q^{42} + 8 q^{43} - 16 q^{44} + 10 q^{45} - 14 q^{46} + 15 q^{47} + 10 q^{48} - 7 q^{49} + 21 q^{50} - 3 q^{51} + q^{52} - 23 q^{53} - 19 q^{54} - 14 q^{55} - 20 q^{56} - 13 q^{57} - 7 q^{58} + 16 q^{59} - 3 q^{60} - 34 q^{61} + 15 q^{62} + 9 q^{63} - 25 q^{64} + 10 q^{65} + 15 q^{66} + 3 q^{68} - 19 q^{69} + 11 q^{70} - 3 q^{71} - 19 q^{72} - 3 q^{73} - 4 q^{74} + 27 q^{75} + 13 q^{76} - 3 q^{77} + 4 q^{78} - 24 q^{79} + 20 q^{80} - 8 q^{81} + 33 q^{82} - 8 q^{83} + 17 q^{84} - 7 q^{85} + q^{86} + 48 q^{87} + 16 q^{88} + 23 q^{89} + 11 q^{90} - 16 q^{91} + 49 q^{92} + 17 q^{93} - 11 q^{94} + 3 q^{95} + 37 q^{96} - 10 q^{97} + 29 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 5 * q^9 - 12 * q^10 - 4 * q^11 - 13 * q^12 - 12 * q^13 + q^14 - 9 * q^15 - 3 * q^16 + 8 * q^17 + 5 * q^18 - 5 * q^20 - 20 * q^21 - 14 * q^22 - 9 * q^23 - q^24 - 7 * q^25 - 17 * q^26 - 12 * q^27 + q^28 - 27 * q^29 + 10 * q^30 - 12 * q^31 + 5 * q^32 + 10 * q^33 + q^34 + 15 * q^35 - 4 * q^36 - 24 * q^37 - q^38 + 3 * q^39 - 9 * q^40 - 8 * q^41 - 9 * q^42 + 8 * q^43 - 16 * q^44 + 10 * q^45 - 14 * q^46 + 15 * q^47 + 10 * q^48 - 7 * q^49 + 21 * q^50 - 3 * q^51 + q^52 - 23 * q^53 - 19 * q^54 - 14 * q^55 - 20 * q^56 - 13 * q^57 - 7 * q^58 + 16 * q^59 - 3 * q^60 - 34 * q^61 + 15 * q^62 + 9 * q^63 - 25 * q^64 + 10 * q^65 + 15 * q^66 + 3 * q^68 - 19 * q^69 + 11 * q^70 - 3 * q^71 - 19 * q^72 - 3 * q^73 - 4 * q^74 + 27 * q^75 + 13 * q^76 - 3 * q^77 + 4 * q^78 - 24 * q^79 + 20 * q^80 - 8 * q^81 + 33 * q^82 - 8 * q^83 + 17 * q^84 - 7 * q^85 + q^86 + 48 * q^87 + 16 * q^88 + 23 * q^89 + 11 * q^90 - 16 * q^91 + 49 * q^92 + 17 * q^93 - 11 * q^94 + 3 * q^95 + 37 * q^96 - 10 * q^97 + 29 * q^98 - 15 * q^99

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