LMFDB - Embedded newform 8015.2.a.l.1.37

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.37
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.609593 q^{2} +2.28126 q^{3} -1.62840 q^{4} -1.00000 q^{5} +1.39064 q^{6} -1.00000 q^{7} -2.21184 q^{8} +2.20414 q^{9} +O(q^{10})$	\(q+0.609593 q^{2} +2.28126 q^{3} -1.62840 q^{4} -1.00000 q^{5} +1.39064 q^{6} -1.00000 q^{7} -2.21184 q^{8} +2.20414 q^{9} -0.609593 q^{10} +3.79775 q^{11} -3.71480 q^{12} +6.31536 q^{13} -0.609593 q^{14} -2.28126 q^{15} +1.90847 q^{16} +2.30733 q^{17} +1.34363 q^{18} -2.08034 q^{19} +1.62840 q^{20} -2.28126 q^{21} +2.31508 q^{22} +0.263969 q^{23} -5.04579 q^{24} +1.00000 q^{25} +3.84980 q^{26} -1.81556 q^{27} +1.62840 q^{28} +5.74574 q^{29} -1.39064 q^{30} -4.16265 q^{31} +5.58708 q^{32} +8.66366 q^{33} +1.40653 q^{34} +1.00000 q^{35} -3.58922 q^{36} +1.78740 q^{37} -1.26816 q^{38} +14.4070 q^{39} +2.21184 q^{40} -11.8375 q^{41} -1.39064 q^{42} +3.06067 q^{43} -6.18425 q^{44} -2.20414 q^{45} +0.160914 q^{46} +3.53800 q^{47} +4.35371 q^{48} +1.00000 q^{49} +0.609593 q^{50} +5.26362 q^{51} -10.2839 q^{52} -10.1754 q^{53} -1.10675 q^{54} -3.79775 q^{55} +2.21184 q^{56} -4.74579 q^{57} +3.50256 q^{58} +6.39001 q^{59} +3.71480 q^{60} +0.234512 q^{61} -2.53752 q^{62} -2.20414 q^{63} -0.411098 q^{64} -6.31536 q^{65} +5.28130 q^{66} -13.7050 q^{67} -3.75725 q^{68} +0.602182 q^{69} +0.609593 q^{70} -1.07440 q^{71} -4.87522 q^{72} +13.5549 q^{73} +1.08958 q^{74} +2.28126 q^{75} +3.38762 q^{76} -3.79775 q^{77} +8.78238 q^{78} -0.238780 q^{79} -1.90847 q^{80} -10.7542 q^{81} -7.21607 q^{82} +0.663084 q^{83} +3.71480 q^{84} -2.30733 q^{85} +1.86576 q^{86} +13.1075 q^{87} -8.40004 q^{88} +16.2882 q^{89} -1.34363 q^{90} -6.31536 q^{91} -0.429846 q^{92} -9.49609 q^{93} +2.15674 q^{94} +2.08034 q^{95} +12.7456 q^{96} +0.859629 q^{97} +0.609593 q^{98} +8.37079 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	0.609593	0.431047	0.215524	−	0.976499i	$-0.430854\pi$
$2$	0.609593	0.431047	0.215524	+	0.976499i	$0.430854\pi$
$3$	2.28126	1.31709	0.658543	−	0.752543i	$-0.271173\pi$
$3$	2.28126	1.31709	0.658543	+	0.752543i	$0.271173\pi$
$4$	−1.62840	−0.814198
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.39064	0.567726
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.21184	−0.782005
$9$	2.20414	0.734714
$10$	−0.609593	−0.192770
$11$	3.79775	1.14507	0.572533	−	0.819882i	$-0.305961\pi$
$11$	3.79775	1.14507	0.572533	+	0.819882i	$0.305961\pi$
$12$	−3.71480	−1.07237
$13$	6.31536	1.75157	0.875783	−	0.482706i	$-0.160346\pi$
$13$	6.31536	1.75157	0.875783	+	0.482706i	$0.160346\pi$
$14$	−0.609593	−0.162920
$15$	−2.28126	−0.589019
$16$	1.90847	0.477117
$17$	2.30733	0.559610	0.279805	−	0.960057i	$-0.409730\pi$
$17$	2.30733	0.559610	0.279805	+	0.960057i	$0.409730\pi$
$18$	1.34363	0.316697
$19$	−2.08034	−0.477262	−0.238631	−	0.971110i	$-0.576699\pi$
$19$	−2.08034	−0.477262	−0.238631	+	0.971110i	$0.576699\pi$
$20$	1.62840	0.364121
$21$	−2.28126	−0.497812
$22$	2.31508	0.493577
$23$	0.263969	0.0550414	0.0275207	−	0.999621i	$-0.491239\pi$
$23$	0.263969	0.0550414	0.0275207	+	0.999621i	$0.491239\pi$
$24$	−5.04579	−1.02997
$25$	1.00000	0.200000
$26$	3.84980	0.755007
$27$	−1.81556	−0.349404
$28$	1.62840	0.307738
$29$	5.74574	1.06696	0.533479	−	0.845813i	$-0.320884\pi$
$29$	5.74574	1.06696	0.533479	+	0.845813i	$0.320884\pi$
$30$	−1.39064	−0.253895
$31$	−4.16265	−0.747635	−0.373817	−	0.927502i	$-0.621951\pi$
$31$	−4.16265	−0.747635	−0.373817	+	0.927502i	$0.621951\pi$
$32$	5.58708	0.987665
$33$	8.66366	1.50815
$34$	1.40653	0.241218
$35$	1.00000	0.169031
$36$	−3.58922	−0.598203
$37$	1.78740	0.293846	0.146923	−	0.989148i	$-0.453063\pi$
$37$	1.78740	0.293846	0.146923	+	0.989148i	$0.453063\pi$
$38$	−1.26816	−0.205723
$39$	14.4070	2.30696
$40$	2.21184	0.349723
$41$	−11.8375	−1.84871	−0.924356	−	0.381531i	$-0.875397\pi$
$41$	−11.8375	−1.84871	−0.924356	+	0.381531i	$0.875397\pi$
$42$	−1.39064	−0.214580
$43$	3.06067	0.466748	0.233374	−	0.972387i	$-0.425023\pi$
$43$	3.06067	0.466748	0.233374	+	0.972387i	$0.425023\pi$
$44$	−6.18425	−0.932311
$45$	−2.20414	−0.328574
$46$	0.160914	0.0237254
$47$	3.53800	0.516071	0.258035	−	0.966135i	$-0.416925\pi$
$47$	3.53800	0.516071	0.258035	+	0.966135i	$0.416925\pi$
$48$	4.35371	0.628405
$49$	1.00000	0.142857
$50$	0.609593	0.0862094
$51$	5.26362	0.737054
$52$	−10.2839	−1.42612
$53$	−10.1754	−1.39769	−0.698847	−	0.715271i	$-0.746303\pi$
$53$	−10.1754	−1.39769	−0.698847	+	0.715271i	$0.746303\pi$
$54$	−1.10675	−0.150610
$55$	−3.79775	−0.512089
$56$	2.21184	0.295570
$57$	−4.74579	−0.628595
$58$	3.50256	0.459909
$59$	6.39001	0.831908	0.415954	−	0.909386i	$-0.363448\pi$
$59$	6.39001	0.831908	0.415954	+	0.909386i	$0.363448\pi$
$60$	3.71480	0.479578
$61$	0.234512	0.0300262	0.0150131	−	0.999887i	$-0.495221\pi$
$61$	0.234512	0.0300262	0.0150131	+	0.999887i	$0.495221\pi$
$62$	−2.53752	−0.322266
$63$	−2.20414	−0.277696
$64$	−0.411098	−0.0513873
$65$	−6.31536	−0.783324
$66$	5.28130	0.650084
$67$	−13.7050	−1.67433	−0.837164	−	0.546953i	$-0.815788\pi$
$67$	−13.7050	−1.67433	−0.837164	+	0.546953i	$0.815788\pi$
$68$	−3.75725	−0.455633
$69$	0.602182	0.0724942
$70$	0.609593	0.0728603
$71$	−1.07440	−0.127508	−0.0637541	−	0.997966i	$-0.520307\pi$
$71$	−1.07440	−0.127508	−0.0637541	+	0.997966i	$0.520307\pi$
$72$	−4.87522	−0.574550
$73$	13.5549	1.58648	0.793241	−	0.608907i	$-0.208392\pi$
$73$	13.5549	1.58648	0.793241	+	0.608907i	$0.208392\pi$
$74$	1.08958	0.126662
$75$	2.28126	0.263417
$76$	3.38762	0.388586
$77$	−3.79775	−0.432794
$78$	8.78238	0.994409
$79$	−0.238780	−0.0268648	−0.0134324	−	0.999910i	$-0.504276\pi$
$79$	−0.238780	−0.0268648	−0.0134324	+	0.999910i	$0.504276\pi$
$80$	−1.90847	−0.213373
$81$	−10.7542	−1.19491
$82$	−7.21607	−0.796882
$83$	0.663084	0.0727830	0.0363915	−	0.999338i	$-0.488414\pi$
$83$	0.663084	0.0727830	0.0363915	+	0.999338i	$0.488414\pi$
$84$	3.71480	0.405317
$85$	−2.30733	−0.250265
$86$	1.86576	0.201191
$87$	13.1075	1.40527
$88$	−8.40004	−0.895447
$89$	16.2882	1.72655	0.863276	−	0.504733i	$-0.168409\pi$
$89$	16.2882	1.72655	0.863276	+	0.504733i	$0.168409\pi$
$90$	−1.34363	−0.141631
$91$	−6.31536	−0.662029
$92$	−0.429846	−0.0448146
$93$	−9.49609	−0.984699
$94$	2.15674	0.222451
$95$	2.08034	0.213438
$96$	12.7456	1.30084
$97$	0.859629	0.0872821	0.0436411	−	0.999047i	$-0.486104\pi$
$97$	0.859629	0.0872821	0.0436411	+	0.999047i	$0.486104\pi$
$98$	0.609593	0.0615782
$99$	8.37079	0.841296
$100$	−1.62840	−0.162840
$101$	0.661812	0.0658528	0.0329264	−	0.999458i	$-0.489517\pi$
$101$	0.661812	0.0658528	0.0329264	+	0.999458i	$0.489517\pi$
$102$	3.20866	0.317705
$103$	−1.19785	−0.118027	−0.0590136	−	0.998257i	$-0.518796\pi$
$103$	−1.19785	−0.118027	−0.0590136	+	0.998257i	$0.518796\pi$
$104$	−13.9686	−1.36973
$105$	2.28126	0.222628
$106$	−6.20283	−0.602472
$107$	9.72768	0.940410	0.470205	−	0.882557i	$-0.344180\pi$
$107$	9.72768	0.940410	0.470205	+	0.882557i	$0.344180\pi$
$108$	2.95644	0.284484
$109$	17.7364	1.69884	0.849421	−	0.527716i	$-0.176951\pi$
$109$	17.7364	1.69884	0.849421	+	0.527716i	$0.176951\pi$
$110$	−2.31508	−0.220734
$111$	4.07751	0.387021
$112$	−1.90847	−0.180333
$113$	12.3006	1.15714	0.578571	−	0.815632i	$-0.303611\pi$
$113$	12.3006	1.15714	0.578571	+	0.815632i	$0.303611\pi$
$114$	−2.89300	−0.270954
$115$	−0.263969	−0.0246152
$116$	−9.35635	−0.868715
$117$	13.9200	1.28690
$118$	3.89530	0.358592
$119$	−2.30733	−0.211513
$120$	5.04579	0.460615
$121$	3.42293	0.311176
$122$	0.142957	0.0129427
$123$	−27.0045	−2.43491
$124$	6.77845	0.608723
$125$	−1.00000	−0.0894427
$126$	−1.34363	−0.119700
$127$	19.4000	1.72147	0.860737	−	0.509050i	$-0.170003\pi$
$127$	19.4000	1.72147	0.860737	+	0.509050i	$0.170003\pi$
$128$	−11.4248	−1.00982
$129$	6.98219	0.614747
$130$	−3.84980	−0.337649
$131$	19.4521	1.69954	0.849771	−	0.527152i	$-0.176740\pi$
$131$	19.4521	1.69954	0.849771	+	0.527152i	$0.176740\pi$
$132$	−14.1079	−1.22793
$133$	2.08034	0.180388
$134$	−8.35444	−0.721714
$135$	1.81556	0.156258
$136$	−5.10345	−0.437618
$137$	1.65064	0.141023	0.0705117	−	0.997511i	$-0.477537\pi$
$137$	1.65064	0.141023	0.0705117	+	0.997511i	$0.477537\pi$
$138$	0.367086	0.0312484
$139$	19.0852	1.61879	0.809393	−	0.587267i	$-0.199796\pi$
$139$	19.0852	1.61879	0.809393	+	0.587267i	$0.199796\pi$
$140$	−1.62840	−0.137625
$141$	8.07110	0.679709
$142$	−0.654948	−0.0549620
$143$	23.9842	2.00566
$144$	4.20654	0.350545
$145$	−5.74574	−0.477158
$146$	8.26298	0.683849
$147$	2.28126	0.188155
$148$	−2.91059	−0.239249
$149$	−2.28925	−0.187543	−0.0937713	−	0.995594i	$-0.529892\pi$
$149$	−2.28925	−0.187543	−0.0937713	+	0.995594i	$0.529892\pi$
$150$	1.39064	0.113545
$151$	−3.43002	−0.279131	−0.139566	−	0.990213i	$-0.544571\pi$
$151$	−3.43002	−0.279131	−0.139566	+	0.990213i	$0.544571\pi$
$152$	4.60138	0.373222
$153$	5.08569	0.411153
$154$	−2.31508	−0.186555
$155$	4.16265	0.334352
$156$	−23.4603	−1.87832
$157$	4.74723	0.378870	0.189435	−	0.981893i	$-0.439334\pi$
$157$	4.74723	0.378870	0.189435	+	0.981893i	$0.439334\pi$
$158$	−0.145558	−0.0115800
$159$	−23.2126	−1.84088
$160$	−5.58708	−0.441697
$161$	−0.263969	−0.0208037
$162$	−6.55567	−0.515062
$163$	−3.02512	−0.236946	−0.118473	−	0.992957i	$-0.537800\pi$
$163$	−3.02512	−0.236946	−0.118473	+	0.992957i	$0.537800\pi$
$164$	19.2762	1.50522
$165$	−8.66366	−0.674465
$166$	0.404211	0.0313729
$167$	8.65634	0.669848	0.334924	−	0.942245i	$-0.391289\pi$
$167$	8.65634	0.669848	0.334924	+	0.942245i	$0.391289\pi$
$168$	5.04579	0.389291
$169$	26.8837	2.06798
$170$	−1.40653	−0.107876
$171$	−4.58536	−0.350652
$172$	−4.98399	−0.380026
$173$	−13.1499	−0.999768	−0.499884	−	0.866092i	$-0.666624\pi$
$173$	−13.1499	−0.999768	−0.499884	+	0.866092i	$0.666624\pi$
$174$	7.99025	0.605740
$175$	−1.00000	−0.0755929
$176$	7.24790	0.546331
$177$	14.5773	1.09569
$178$	9.92920	0.744225
$179$	11.6213	0.868619	0.434310	−	0.900764i	$-0.356992\pi$
$179$	11.6213	0.868619	0.434310	+	0.900764i	$0.356992\pi$
$180$	3.58922	0.267525
$181$	7.67898	0.570774	0.285387	−	0.958412i	$-0.407878\pi$
$181$	7.67898	0.570774	0.285387	+	0.958412i	$0.407878\pi$
$182$	−3.84980	−0.285366
$183$	0.534983	0.0395471
$184$	−0.583859	−0.0430426
$185$	−1.78740	−0.131412
$186$	−5.78875	−0.424452
$187$	8.76267	0.640790
$188$	−5.76127	−0.420184
$189$	1.81556	0.132062
$190$	1.26816	0.0920019
$191$	−11.6654	−0.844075	−0.422038	−	0.906578i	$-0.638685\pi$
$191$	−11.6654	−0.844075	−0.422038	+	0.906578i	$0.638685\pi$
$192$	−0.937822	−0.0676815
$193$	−7.62481	−0.548846	−0.274423	−	0.961609i	$-0.588487\pi$
$193$	−7.62481	−0.548846	−0.274423	+	0.961609i	$0.588487\pi$
$194$	0.524024	0.0376227
$195$	−14.4070	−1.03170
$196$	−1.62840	−0.116314
$197$	1.98744	0.141600	0.0707998	−	0.997491i	$-0.477445\pi$
$197$	1.98744	0.141600	0.0707998	+	0.997491i	$0.477445\pi$
$198$	5.10277	0.362638
$199$	−20.2140	−1.43293	−0.716466	−	0.697622i	$-0.754241\pi$
$199$	−20.2140	−1.43293	−0.716466	+	0.697622i	$0.754241\pi$
$200$	−2.21184	−0.156401
$201$	−31.2646	−2.20523
$202$	0.403436	0.0283856
$203$	−5.74574	−0.403272
$204$	−8.57126	−0.600108
$205$	11.8375	0.826769
$206$	−0.730198	−0.0508753
$207$	0.581826	0.0404397
$208$	12.0527	0.835702
$209$	−7.90061	−0.546497
$210$	1.39064	0.0959632
$211$	0.669141	0.0460656	0.0230328	−	0.999735i	$-0.492668\pi$
$211$	0.669141	0.0460656	0.0230328	+	0.999735i	$0.492668\pi$
$212$	16.5695	1.13800
$213$	−2.45099	−0.167939
$214$	5.92992	0.405361
$215$	−3.06067	−0.208736
$216$	4.01573	0.273236
$217$	4.16265	0.282579
$218$	10.8120	0.732281
$219$	30.9223	2.08953
$220$	6.18425	0.416942
$221$	14.5716	0.980193
$222$	2.48562	0.166824
$223$	8.37637	0.560923	0.280461	−	0.959865i	$-0.409513\pi$
$223$	8.37637	0.560923	0.280461	+	0.959865i	$0.409513\pi$
$224$	−5.58708	−0.373302
$225$	2.20414	0.146943
$226$	7.49834	0.498782
$227$	−3.34665	−0.222125	−0.111062	−	0.993813i	$-0.535425\pi$
$227$	−3.34665	−0.222125	−0.111062	+	0.993813i	$0.535425\pi$
$228$	7.72803	0.511801
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−0.160914	−0.0106103
$231$	−8.66366	−0.570027
$232$	−12.7087	−0.834366
$233$	−14.0456	−0.920158	−0.460079	−	0.887878i	$-0.652179\pi$
$233$	−14.0456	−0.920158	−0.460079	+	0.887878i	$0.652179\pi$
$234$	8.48550	0.554715
$235$	−3.53800	−0.230794
$236$	−10.4055	−0.677338
$237$	−0.544719	−0.0353833
$238$	−1.40653	−0.0911719
$239$	25.2062	1.63045	0.815225	−	0.579144i	$-0.196613\pi$
$239$	25.2062	1.63045	0.815225	+	0.579144i	$0.196613\pi$
$240$	−4.35371	−0.281031
$241$	6.11985	0.394214	0.197107	−	0.980382i	$-0.436845\pi$
$241$	6.11985	0.394214	0.197107	+	0.980382i	$0.436845\pi$
$242$	2.08659	0.134131
$243$	−19.0864	−1.22439
$244$	−0.381879	−0.0244473
$245$	−1.00000	−0.0638877
$246$	−16.4617	−1.04956
$247$	−13.1381	−0.835956
$248$	9.20714	0.584654
$249$	1.51267	0.0958614
$250$	−0.609593	−0.0385540
$251$	−20.6471	−1.30323	−0.651617	−	0.758548i	$-0.725909\pi$
$251$	−20.6471	−1.30323	−0.651617	+	0.758548i	$0.725909\pi$
$252$	3.58922	0.226100
$253$	1.00249	0.0630260
$254$	11.8261	0.742036
$255$	−5.26362	−0.329621
$256$	−6.14225	−0.383891
$257$	−1.24330	−0.0775547	−0.0387773	−	0.999248i	$-0.512346\pi$
$257$	−1.24330	−0.0775547	−0.0387773	+	0.999248i	$0.512346\pi$
$258$	4.25629	0.264985
$259$	−1.78740	−0.111063
$260$	10.2839	0.637781
$261$	12.6644	0.783909
$262$	11.8579	0.732583
$263$	17.0619	1.05208	0.526042	−	0.850459i	$-0.323676\pi$
$263$	17.0619	1.05208	0.526042	+	0.850459i	$0.323676\pi$
$264$	−19.1627	−1.17938
$265$	10.1754	0.625068
$266$	1.26816	0.0777558
$267$	37.1577	2.27402
$268$	22.3171	1.36323
$269$	14.6943	0.895927	0.447963	−	0.894052i	$-0.352150\pi$
$269$	14.6943	0.895927	0.447963	+	0.894052i	$0.352150\pi$
$270$	1.10675	0.0673546
$271$	−29.4092	−1.78648	−0.893242	−	0.449576i	$-0.851575\pi$
$271$	−29.4092	−1.78648	−0.893242	+	0.449576i	$0.851575\pi$
$272$	4.40347	0.267000
$273$	−14.4070	−0.871949
$274$	1.00622	0.0607877
$275$	3.79775	0.229013
$276$	−0.980591	−0.0590247
$277$	5.58984	0.335861	0.167930	−	0.985799i	$-0.446292\pi$
$277$	5.58984	0.335861	0.167930	+	0.985799i	$0.446292\pi$
$278$	11.6342	0.697773
$279$	−9.17508	−0.549298
$280$	−2.21184	−0.132183
$281$	11.8748	0.708389	0.354195	−	0.935172i	$-0.384755\pi$
$281$	11.8748	0.708389	0.354195	+	0.935172i	$0.384755\pi$
$282$	4.92008	0.292987
$283$	23.0995	1.37312	0.686561	−	0.727072i	$-0.259119\pi$
$283$	23.0995	1.37312	0.686561	+	0.727072i	$0.259119\pi$
$284$	1.74955	0.103817
$285$	4.74579	0.281116
$286$	14.6206	0.864533
$287$	11.8375	0.698748
$288$	12.3147	0.725652
$289$	−11.6762	−0.686837
$290$	−3.50256	−0.205678
$291$	1.96104	0.114958
$292$	−22.0728	−1.29171
$293$	−4.47880	−0.261654	−0.130827	−	0.991405i	$-0.541763\pi$
$293$	−4.47880	−0.261654	−0.130827	+	0.991405i	$0.541763\pi$
$294$	1.39064	0.0811037
$295$	−6.39001	−0.372041
$296$	−3.95344	−0.229789
$297$	−6.89503	−0.400090
$298$	−1.39551	−0.0808397
$299$	1.66706	0.0964085
$300$	−3.71480	−0.214474
$301$	−3.06067	−0.176414
$302$	−2.09091	−0.120319
$303$	1.50976	0.0867337
$304$	−3.97026	−0.227710
$305$	−0.234512	−0.0134281
$306$	3.10020	0.177226
$307$	−11.0768	−0.632187	−0.316094	−	0.948728i	$-0.602371\pi$
$307$	−11.0768	−0.632187	−0.316094	+	0.948728i	$0.602371\pi$
$308$	6.18425	0.352380
$309$	−2.73260	−0.155452
$310$	2.53752	0.144122
$311$	−13.7160	−0.777762	−0.388881	−	0.921288i	$-0.627138\pi$
$311$	−13.7160	−0.777762	−0.388881	+	0.921288i	$0.627138\pi$
$312$	−31.8660	−1.80406
$313$	19.9914	1.12998	0.564989	−	0.825098i	$-0.308880\pi$
$313$	19.9914	1.12998	0.564989	+	0.825098i	$0.308880\pi$
$314$	2.89388	0.163311
$315$	2.20414	0.124189
$316$	0.388828	0.0218733
$317$	21.3063	1.19668	0.598341	−	0.801242i	$-0.295827\pi$
$317$	21.3063	1.19668	0.598341	+	0.801242i	$0.295827\pi$
$318$	−14.1503	−0.793507
$319$	21.8209	1.22174
$320$	0.411098	0.0229811
$321$	22.1914	1.23860
$322$	−0.160914	−0.00896737
$323$	−4.80003	−0.267081
$324$	17.5121	0.972893
$325$	6.31536	0.350313
$326$	−1.84409	−0.102135
$327$	40.4614	2.23752
$328$	26.1828	1.44570
$329$	−3.53800	−0.195056
$330$	−5.28130	−0.290726
$331$	−0.788224	−0.0433247	−0.0216624	−	0.999765i	$-0.506896\pi$
$331$	−0.788224	−0.0433247	−0.0216624	+	0.999765i	$0.506896\pi$
$332$	−1.07976	−0.0592598
$333$	3.93968	0.215893
$334$	5.27684	0.288736
$335$	13.7050	0.748782
$336$	−4.35371	−0.237515
$337$	0.0861554	0.00469318	0.00234659	−	0.999997i	$-0.499253\pi$
$337$	0.0861554	0.00469318	0.00234659	+	0.999997i	$0.499253\pi$
$338$	16.3881	0.891397
$339$	28.0608	1.52405
$340$	3.75725	0.203765
$341$	−15.8087	−0.856091
$342$	−2.79520	−0.151147
$343$	−1.00000	−0.0539949
$344$	−6.76973	−0.364999
$345$	−0.602182	−0.0324204
$346$	−8.01608	−0.430947
$347$	−34.3437	−1.84367	−0.921834	−	0.387585i	$-0.873309\pi$
$347$	−34.3437	−1.84367	−0.921834	+	0.387585i	$0.873309\pi$
$348$	−21.3443	−1.14417
$349$	16.6826	0.893001	0.446501	−	0.894783i	$-0.352670\pi$
$349$	16.6826	0.893001	0.446501	+	0.894783i	$0.352670\pi$
$350$	−0.609593	−0.0325841
$351$	−11.4659	−0.612004
$352$	21.2183	1.13094
$353$	14.7560	0.785381	0.392690	−	0.919671i	$-0.371544\pi$
$353$	14.7560	0.785381	0.392690	+	0.919671i	$0.371544\pi$
$354$	8.88619	0.472296
$355$	1.07440	0.0570234
$356$	−26.5237	−1.40576
$357$	−5.26362	−0.278580
$358$	7.08428	0.374416
$359$	16.6736	0.879998	0.439999	−	0.897998i	$-0.354979\pi$
$359$	16.6736	0.879998	0.439999	+	0.897998i	$0.354979\pi$
$360$	4.87522	0.256947
$361$	−14.6722	−0.772221
$362$	4.68105	0.246031
$363$	7.80859	0.409845
$364$	10.2839	0.539023
$365$	−13.5549	−0.709497
$366$	0.326122	0.0170467
$367$	7.63042	0.398305	0.199152	−	0.979969i	$-0.436181\pi$
$367$	7.63042	0.398305	0.199152	+	0.979969i	$0.436181\pi$
$368$	0.503777	0.0262612
$369$	−26.0916	−1.35828
$370$	−1.08958	−0.0566448
$371$	10.1754	0.528279
$372$	15.4634	0.801740
$373$	27.0632	1.40128	0.700640	−	0.713515i	$-0.252898\pi$
$373$	27.0632	1.40128	0.700640	+	0.713515i	$0.252898\pi$
$374$	5.34166	0.276211
$375$	−2.28126	−0.117804
$376$	−7.82551	−0.403570
$377$	36.2864	1.86885
$378$	1.10675	0.0569250
$379$	9.09630	0.467245	0.233623	−	0.972327i	$-0.424942\pi$
$379$	9.09630	0.467245	0.233623	+	0.972327i	$0.424942\pi$
$380$	−3.38762	−0.173781
$381$	44.2565	2.26733
$382$	−7.11111	−0.363836
$383$	−8.50193	−0.434429	−0.217214	−	0.976124i	$-0.569697\pi$
$383$	−8.50193	−0.434429	−0.217214	+	0.976124i	$0.569697\pi$
$384$	−26.0628	−1.33001
$385$	3.79775	0.193551
$386$	−4.64803	−0.236578
$387$	6.74616	0.342927
$388$	−1.39982	−0.0710650
$389$	−34.3231	−1.74025	−0.870125	−	0.492831i	$-0.835962\pi$
$389$	−34.3231	−1.74025	−0.870125	+	0.492831i	$0.835962\pi$
$390$	−8.78238	−0.444713
$391$	0.609064	0.0308017
$392$	−2.21184	−0.111715
$393$	44.3754	2.23844
$394$	1.21153	0.0610361
$395$	0.238780	0.0120143
$396$	−13.6310	−0.684982
$397$	−32.9950	−1.65597	−0.827986	−	0.560748i	$-0.810514\pi$
$397$	−32.9950	−1.65597	−0.827986	+	0.560748i	$0.810514\pi$
$398$	−12.3223	−0.617661
$399$	4.74579	0.237587
$400$	1.90847	0.0954235
$401$	20.4563	1.02154	0.510769	−	0.859718i	$-0.329361\pi$
$401$	20.4563	1.02154	0.510769	+	0.859718i	$0.329361\pi$
$402$	−19.0586	−0.950559
$403$	−26.2886	−1.30953
$404$	−1.07769	−0.0536172
$405$	10.7542	0.534380
$406$	−3.50256	−0.173829
$407$	6.78809	0.336473
$408$	−11.6423	−0.576380
$409$	−6.65977	−0.329304	−0.164652	−	0.986352i	$-0.552650\pi$
$409$	−6.65977	−0.329304	−0.164652	+	0.986352i	$0.552650\pi$
$410$	7.21607	0.356376
$411$	3.76553	0.185740
$412$	1.95057	0.0960976
$413$	−6.39001	−0.314432
$414$	0.354677	0.0174314
$415$	−0.663084	−0.0325495
$416$	35.2844	1.72996
$417$	43.5383	2.13208
$418$	−4.81616	−0.235566
$419$	1.90366	0.0930001	0.0465000	−	0.998918i	$-0.485193\pi$
$419$	1.90366	0.0930001	0.0465000	+	0.998918i	$0.485193\pi$
$420$	−3.71480	−0.181263
$421$	−3.01582	−0.146982	−0.0734911	−	0.997296i	$-0.523414\pi$
$421$	−3.01582	−0.146982	−0.0734911	+	0.997296i	$0.523414\pi$
$422$	0.407904	0.0198564
$423$	7.79826	0.379165
$424$	22.5063	1.09300
$425$	2.30733	0.111922
$426$	−1.49411	−0.0723897
$427$	−0.234512	−0.0113488
$428$	−15.8405	−0.765681
$429$	54.7141	2.64162
$430$	−1.86576	−0.0899751
$431$	−4.68990	−0.225905	−0.112952	−	0.993600i	$-0.536031\pi$
$431$	−4.68990	−0.225905	−0.112952	+	0.993600i	$0.536031\pi$
$432$	−3.46493	−0.166707
$433$	22.3918	1.07608	0.538040	−	0.842919i	$-0.319165\pi$
$433$	22.3918	1.07608	0.538040	+	0.842919i	$0.319165\pi$
$434$	2.53752	0.121805
$435$	−13.1075	−0.628458
$436$	−28.8819	−1.38319
$437$	−0.549145	−0.0262692
$438$	18.8500	0.900687
$439$	−36.5093	−1.74249	−0.871247	−	0.490844i	$-0.836688\pi$
$439$	−36.5093	−1.74249	−0.871247	+	0.490844i	$0.836688\pi$
$440$	8.40004	0.400456
$441$	2.20414	0.104959
$442$	8.88275	0.422509
$443$	−32.1161	−1.52588	−0.762940	−	0.646470i	$-0.776245\pi$
$443$	−32.1161	−1.52588	−0.762940	+	0.646470i	$0.776245\pi$
$444$	−6.63981	−0.315111
$445$	−16.2882	−0.772137
$446$	5.10617	0.241784
$447$	−5.22237	−0.247010
$448$	0.411098	0.0194226
$449$	16.3807	0.773054	0.386527	−	0.922278i	$-0.373675\pi$
$449$	16.3807	0.773054	0.386527	+	0.922278i	$0.373675\pi$
$450$	1.34363	0.0633393
$451$	−44.9560	−2.11690
$452$	−20.0302	−0.942142
$453$	−7.82476	−0.367639
$454$	−2.04009	−0.0957463
$455$	6.31536	0.296069
$456$	10.4970	0.491565
$457$	−21.5899	−1.00993	−0.504967	−	0.863139i	$-0.668495\pi$
$457$	−21.5899	−1.00993	−0.504967	+	0.863139i	$0.668495\pi$
$458$	0.609593	0.0284844
$459$	−4.18909	−0.195530
$460$	0.429846	0.0200417
$461$	−4.31949	−0.201179	−0.100589	−	0.994928i	$-0.532073\pi$
$461$	−4.31949	−0.201179	−0.100589	+	0.994928i	$0.532073\pi$
$462$	−5.28130	−0.245708
$463$	8.35380	0.388234	0.194117	−	0.980978i	$-0.437816\pi$
$463$	8.35380	0.388234	0.194117	+	0.980978i	$0.437816\pi$
$464$	10.9656	0.509064
$465$	9.49609	0.440371
$466$	−8.56210	−0.396632
$467$	−22.4340	−1.03812	−0.519060	−	0.854738i	$-0.673718\pi$
$467$	−22.4340	−1.03812	−0.519060	+	0.854738i	$0.673718\pi$
$468$	−22.6672	−1.04779
$469$	13.7050	0.632836
$470$	−2.15674	−0.0994830
$471$	10.8297	0.499004
$472$	−14.1337	−0.650556
$473$	11.6237	0.534458
$474$	−0.332057	−0.0152519
$475$	−2.08034	−0.0954525
$476$	3.75725	0.172213
$477$	−22.4280	−1.02691
$478$	15.3655	0.702801
$479$	12.9007	0.589446	0.294723	−	0.955583i	$-0.404773\pi$
$479$	12.9007	0.589446	0.294723	+	0.955583i	$0.404773\pi$
$480$	−12.7456	−0.581753
$481$	11.2880	0.514691
$482$	3.73062	0.169925
$483$	−0.602182	−0.0274002
$484$	−5.57389	−0.253359
$485$	−0.859629	−0.0390338
$486$	−11.6349	−0.527771
$487$	−16.5679	−0.750762	−0.375381	−	0.926871i	$-0.622488\pi$
$487$	−16.5679	−0.750762	−0.375381	+	0.926871i	$0.622488\pi$
$488$	−0.518705	−0.0234807
$489$	−6.90108	−0.312078
$490$	−0.609593	−0.0275386
$491$	23.4466	1.05813	0.529065	−	0.848582i	$-0.322543\pi$
$491$	23.4466	1.05813	0.529065	+	0.848582i	$0.322543\pi$
$492$	43.9740	1.98250
$493$	13.2573	0.597080
$494$	−8.00888	−0.360336
$495$	−8.37079	−0.376239
$496$	−7.94430	−0.356709
$497$	1.07440	0.0481936
$498$	0.922111	0.0413208
$499$	−13.0359	−0.583566	−0.291783	−	0.956485i	$-0.594248\pi$
$499$	−13.0359	−0.583566	−0.291783	+	0.956485i	$0.594248\pi$
$500$	1.62840	0.0728241
$501$	19.7474	0.882247
$502$	−12.5863	−0.561755
$503$	−15.9848	−0.712727	−0.356364	−	0.934347i	$-0.615984\pi$
$503$	−15.9848	−0.712727	−0.356364	+	0.934347i	$0.615984\pi$
$504$	4.87522	0.217160
$505$	−0.661812	−0.0294503
$506$	0.611110	0.0271672
$507$	61.3288	2.72371
$508$	−31.5909	−1.40162
$509$	−31.3783	−1.39082	−0.695409	−	0.718614i	$-0.744777\pi$
$509$	−31.3783	−1.39082	−0.695409	+	0.718614i	$0.744777\pi$
$510$	−3.20866	−0.142082
$511$	−13.5549	−0.599634
$512$	19.1052	0.844340
$513$	3.77697	0.166757
$514$	−0.757904	−0.0334297
$515$	1.19785	0.0527834
$516$	−11.3698	−0.500526
$517$	13.4365	0.590935
$518$	−1.08958	−0.0478736
$519$	−29.9983	−1.31678
$520$	13.9686	0.612563
$521$	11.2520	0.492960	0.246480	−	0.969148i	$-0.420726\pi$
$521$	11.2520	0.492960	0.246480	+	0.969148i	$0.420726\pi$
$522$	7.72015	0.337902
$523$	−18.4116	−0.805083	−0.402541	−	0.915402i	$-0.631873\pi$
$523$	−18.4116	−0.805083	−0.402541	+	0.915402i	$0.631873\pi$
$524$	−31.6758	−1.38376
$525$	−2.28126	−0.0995623
$526$	10.4008	0.453498
$527$	−9.60461	−0.418384
$528$	16.5343	0.719564
$529$	−22.9303	−0.996970
$530$	6.20283	0.269434
$531$	14.0845	0.611215
$532$	−3.38762	−0.146872
$533$	−74.7583	−3.23814
$534$	22.6511	0.980208
$535$	−9.72768	−0.420564
$536$	30.3132	1.30933
$537$	26.5113	1.14405
$538$	8.95753	0.386187
$539$	3.79775	0.163581
$540$	−2.95644	−0.127225
$541$	14.4700	0.622114	0.311057	−	0.950391i	$-0.399317\pi$
$541$	14.4700	0.622114	0.311057	+	0.950391i	$0.399317\pi$
$542$	−17.9277	−0.770059
$543$	17.5177	0.751758
$544$	12.8912	0.552707
$545$	−17.7364	−0.759745
$546$	−8.78238	−0.375851
$547$	12.6106	0.539190	0.269595	−	0.962974i	$-0.413110\pi$
$547$	12.6106	0.539190	0.269595	+	0.962974i	$0.413110\pi$
$548$	−2.68789	−0.114821
$549$	0.516899	0.0220607
$550$	2.31508	0.0987155
$551$	−11.9531	−0.509219
$552$	−1.33193	−0.0566908
$553$	0.238780	0.0101540
$554$	3.40753	0.144772
$555$	−4.07751	−0.173081
$556$	−31.0783	−1.31801
$557$	−10.3207	−0.437303	−0.218651	−	0.975803i	$-0.570166\pi$
$557$	−10.3207	−0.437303	−0.218651	+	0.975803i	$0.570166\pi$
$558$	−5.59306	−0.236773
$559$	19.3292	0.817540
$560$	1.90847	0.0806476
$561$	19.9899	0.843975
$562$	7.23877	0.305349
$563$	−42.2694	−1.78144	−0.890720	−	0.454552i	$-0.849800\pi$
$563$	−42.2694	−1.78144	−0.890720	+	0.454552i	$0.849800\pi$
$564$	−13.1430	−0.553418
$565$	−12.3006	−0.517489
$566$	14.0813	0.591881
$567$	10.7542	0.451633
$568$	2.37641	0.0997120
$569$	9.06146	0.379876	0.189938	−	0.981796i	$-0.439171\pi$
$569$	9.06146	0.379876	0.189938	+	0.981796i	$0.439171\pi$
$570$	2.89300	0.121174
$571$	14.3577	0.600852	0.300426	−	0.953805i	$-0.402871\pi$
$571$	14.3577	0.600852	0.300426	+	0.953805i	$0.402871\pi$
$572$	−39.0557	−1.63300
$573$	−26.6117	−1.11172
$574$	7.21607	0.301193
$575$	0.263969	0.0110083
$576$	−0.906120	−0.0377550
$577$	−31.1895	−1.29844	−0.649219	−	0.760602i	$-0.724904\pi$
$577$	−31.1895	−1.29844	−0.649219	+	0.760602i	$0.724904\pi$
$578$	−7.11774	−0.296059
$579$	−17.3942	−0.722877
$580$	9.35635	0.388501
$581$	−0.663084	−0.0275094
$582$	1.19543	0.0495523
$583$	−38.6435	−1.60045
$584$	−29.9814	−1.24064
$585$	−13.9200	−0.575519
$586$	−2.73024	−0.112785
$587$	4.50524	0.185951	0.0929755	−	0.995668i	$-0.470362\pi$
$587$	4.50524	0.185951	0.0929755	+	0.995668i	$0.470362\pi$
$588$	−3.71480	−0.153196
$589$	8.65973	0.356818
$590$	−3.89530	−0.160367
$591$	4.53388	0.186499
$592$	3.41119	0.140199
$593$	39.1481	1.60762	0.803810	−	0.594886i	$-0.202803\pi$
$593$	39.1481	1.60762	0.803810	+	0.594886i	$0.202803\pi$
$594$	−4.20316	−0.172458
$595$	2.30733	0.0945913
$596$	3.72781	0.152697
$597$	−46.1133	−1.88729
$598$	1.01623	0.0415566
$599$	0.838810	0.0342729	0.0171364	−	0.999853i	$-0.494545\pi$
$599$	0.838810	0.0342729	0.0171364	+	0.999853i	$0.494545\pi$
$600$	−5.04579	−0.205993
$601$	26.1208	1.06549	0.532745	−	0.846276i	$-0.321161\pi$
$601$	26.1208	1.06549	0.532745	+	0.846276i	$0.321161\pi$
$602$	−1.86576	−0.0760429
$603$	−30.2077	−1.23015
$604$	5.58543	0.227268
$605$	−3.42293	−0.139162
$606$	0.920342	0.0373863
$607$	17.3205	0.703018	0.351509	−	0.936184i	$-0.385669\pi$
$607$	17.3205	0.703018	0.351509	+	0.936184i	$0.385669\pi$
$608$	−11.6230	−0.471375
$609$	−13.1075	−0.531144
$610$	−0.142957	−0.00578816
$611$	22.3437	0.903931
$612$	−8.28151	−0.334760
$613$	44.9456	1.81534	0.907668	−	0.419689i	$-0.137861\pi$
$613$	44.9456	1.81534	0.907668	+	0.419689i	$0.137861\pi$
$614$	−6.75234	−0.272502
$615$	27.0045	1.08893
$616$	8.40004	0.338447
$617$	−47.8359	−1.92580	−0.962901	−	0.269857i	$-0.913024\pi$
$617$	−47.8359	−1.92580	−0.962901	+	0.269857i	$0.913024\pi$
$618$	−1.66577	−0.0670071
$619$	−6.13786	−0.246701	−0.123351	−	0.992363i	$-0.539364\pi$
$619$	−6.13786	−0.246701	−0.123351	+	0.992363i	$0.539364\pi$
$620$	−6.77845	−0.272229
$621$	−0.479251	−0.0192317
$622$	−8.36117	−0.335252
$623$	−16.2882	−0.652575
$624$	27.4953	1.10069
$625$	1.00000	0.0400000
$626$	12.1866	0.487074
$627$	−18.0233	−0.719783
$628$	−7.73037	−0.308475
$629$	4.12411	0.164439
$630$	1.34363	0.0535315
$631$	−7.33730	−0.292093	−0.146047	−	0.989278i	$-0.546655\pi$
$631$	−7.33730	−0.292093	−0.146047	+	0.989278i	$0.546655\pi$
$632$	0.528144	0.0210084
$633$	1.52648	0.0606723
$634$	12.9882	0.515826
$635$	−19.4000	−0.769866
$636$	37.7994	1.49884
$637$	6.31536	0.250224
$638$	13.3019	0.526626
$639$	−2.36814	−0.0936821
$640$	11.4248	0.451603
$641$	25.3709	1.00209	0.501046	−	0.865421i	$-0.332949\pi$
$641$	25.3709	1.00209	0.501046	+	0.865421i	$0.332949\pi$
$642$	13.5277	0.533895
$643$	−5.66988	−0.223598	−0.111799	−	0.993731i	$-0.535661\pi$
$643$	−5.66988	−0.223598	−0.111799	+	0.993731i	$0.535661\pi$
$644$	0.429846	0.0169383
$645$	−6.98219	−0.274923
$646$	−2.92606	−0.115124
$647$	9.55879	0.375795	0.187897	−	0.982189i	$-0.439833\pi$
$647$	9.55879	0.375795	0.187897	+	0.982189i	$0.439833\pi$
$648$	23.7866	0.934425
$649$	24.2677	0.952590
$650$	3.84980	0.151001
$651$	9.49609	0.372181
$652$	4.92609	0.192921
$653$	−32.2310	−1.26130	−0.630648	−	0.776069i	$-0.717211\pi$
$653$	−32.2310	−1.26130	−0.630648	+	0.776069i	$0.717211\pi$
$654$	24.6650	0.964477
$655$	−19.4521	−0.760058
$656$	−22.5916	−0.882053
$657$	29.8770	1.16561
$658$	−2.15674	−0.0840785
$659$	−6.43221	−0.250563	−0.125282	−	0.992121i	$-0.539983\pi$
$659$	−6.43221	−0.250563	−0.125282	+	0.992121i	$0.539983\pi$
$660$	14.1079	0.549148
$661$	20.2028	0.785799	0.392900	−	0.919581i	$-0.371472\pi$
$661$	20.2028	0.785799	0.392900	+	0.919581i	$0.371472\pi$
$662$	−0.480496	−0.0186750
$663$	33.2416	1.29100
$664$	−1.46664	−0.0569166
$665$	−2.08034	−0.0806721
$666$	2.40160	0.0930600
$667$	1.51670	0.0587268
$668$	−14.0960	−0.545389
$669$	19.1087	0.738784
$670$	8.35444	0.322760
$671$	0.890620	0.0343820
$672$	−12.7456	−0.491671
$673$	−40.2837	−1.55282	−0.776411	−	0.630227i	$-0.782962\pi$
$673$	−40.2837	−1.55282	−0.776411	+	0.630227i	$0.782962\pi$
$674$	0.0525197	0.00202298
$675$	−1.81556	−0.0698808
$676$	−43.7774	−1.68375
$677$	6.17098	0.237170	0.118585	−	0.992944i	$-0.462164\pi$
$677$	6.17098	0.237170	0.118585	+	0.992944i	$0.462164\pi$
$678$	17.1057	0.656939
$679$	−0.859629	−0.0329895
$680$	5.10345	0.195709
$681$	−7.63457	−0.292557
$682$	−9.63689	−0.369015
$683$	19.4027	0.742424	0.371212	−	0.928548i	$-0.378942\pi$
$683$	19.4027	0.742424	0.371212	+	0.928548i	$0.378942\pi$
$684$	7.46679	0.285500
$685$	−1.65064	−0.0630676
$686$	−0.609593	−0.0232744
$687$	2.28126	0.0870355
$688$	5.84120	0.222694
$689$	−64.2611	−2.44815
$690$	−0.367086	−0.0139747
$691$	23.2145	0.883123	0.441561	−	0.897231i	$-0.354425\pi$
$691$	23.2145	0.883123	0.441561	+	0.897231i	$0.354425\pi$
$692$	21.4133	0.814010
$693$	−8.37079	−0.317980
$694$	−20.9357	−0.794708
$695$	−19.0852	−0.723943
$696$	−28.9918	−1.09893
$697$	−27.3131	−1.03456
$698$	10.1696	0.384926
$699$	−32.0417	−1.21193
$700$	1.62840	0.0615476
$701$	−0.359130	−0.0135642	−0.00678208	−	0.999977i	$-0.502159\pi$
$701$	−0.359130	−0.0135642	−0.00678208	+	0.999977i	$0.502159\pi$
$702$	−6.98952	−0.263802
$703$	−3.71839	−0.140242
$704$	−1.56125	−0.0588418
$705$	−8.07110	−0.303975
$706$	8.99512	0.338536
$707$	−0.661812	−0.0248900
$708$	−23.7376	−0.892113
$709$	41.8277	1.57087	0.785435	−	0.618944i	$-0.212439\pi$
$709$	41.8277	1.57087	0.785435	+	0.618944i	$0.212439\pi$
$710$	0.654948	0.0245798
$711$	−0.526305	−0.0197380
$712$	−36.0271	−1.35017
$713$	−1.09881	−0.0411508
$714$	−3.20866	−0.120081
$715$	−23.9842	−0.896957
$716$	−18.9241	−0.707228
$717$	57.5018	2.14744
$718$	10.1641	0.379321
$719$	−11.5715	−0.431545	−0.215772	−	0.976444i	$-0.569227\pi$
$719$	−11.5715	−0.431545	−0.215772	+	0.976444i	$0.569227\pi$
$720$	−4.20654	−0.156769
$721$	1.19785	0.0446101
$722$	−8.94406	−0.332863
$723$	13.9610	0.519214
$724$	−12.5044	−0.464723
$725$	5.74574	0.213392
$726$	4.76006	0.176662
$727$	−41.5692	−1.54172	−0.770859	−	0.637006i	$-0.780173\pi$
$727$	−41.5692	−1.54172	−0.770859	+	0.637006i	$0.780173\pi$
$728$	13.9686	0.517710
$729$	−11.2785	−0.417722
$730$	−8.26298	−0.305826
$731$	7.06198	0.261197
$732$	−0.871165	−0.0321992
$733$	31.0415	1.14654	0.573271	−	0.819366i	$-0.305674\pi$
$733$	31.0415	1.14654	0.573271	+	0.819366i	$0.305674\pi$
$734$	4.65145	0.171688
$735$	−2.28126	−0.0841455
$736$	1.47482	0.0543624
$737$	−52.0481	−1.91721
$738$	−15.9053	−0.585481
$739$	−6.34693	−0.233476	−0.116738	−	0.993163i	$-0.537244\pi$
$739$	−6.34693	−0.233476	−0.116738	+	0.993163i	$0.537244\pi$
$740$	2.91059	0.106995
$741$	−29.9714	−1.10103
$742$	6.20283	0.227713
$743$	−3.10557	−0.113932	−0.0569662	−	0.998376i	$-0.518143\pi$
$743$	−3.10557	−0.113932	−0.0569662	+	0.998376i	$0.518143\pi$
$744$	21.0039	0.770039
$745$	2.28925	0.0838716
$746$	16.4975	0.604018
$747$	1.46153	0.0534747
$748$	−14.2691	−0.521730
$749$	−9.72768	−0.355442
$750$	−1.39064	−0.0507789
$751$	−26.9835	−0.984643	−0.492321	−	0.870413i	$-0.663852\pi$
$751$	−26.9835	−0.984643	−0.492321	+	0.870413i	$0.663852\pi$
$752$	6.75217	0.246226
$753$	−47.1014	−1.71647
$754$	22.1199	0.805561
$755$	3.43002	0.124831
$756$	−2.95644	−0.107525
$757$	−28.5549	−1.03784	−0.518922	−	0.854821i	$-0.673667\pi$
$757$	−28.5549	−1.03784	−0.518922	+	0.854821i	$0.673667\pi$
$758$	5.54504	0.201405
$759$	2.28694	0.0830106
$760$	−4.60138	−0.166910
$761$	32.6720	1.18436	0.592180	−	0.805806i	$-0.298267\pi$
$761$	32.6720	1.18436	0.592180	+	0.805806i	$0.298267\pi$
$762$	26.9784	0.977325
$763$	−17.7364	−0.642102
$764$	18.9958	0.687245
$765$	−5.08569	−0.183873
$766$	−5.18272	−0.187259
$767$	40.3552	1.45714
$768$	−14.0121	−0.505617
$769$	36.5131	1.31670	0.658348	−	0.752714i	$-0.271256\pi$
$769$	36.5131	1.31670	0.658348	+	0.752714i	$0.271256\pi$
$770$	2.31508	0.0834298
$771$	−2.83628	−0.102146
$772$	12.4162	0.446869
$773$	−20.2383	−0.727919	−0.363960	−	0.931415i	$-0.618575\pi$
$773$	−20.2383	−0.727919	−0.363960	+	0.931415i	$0.618575\pi$
$774$	4.11241	0.147818
$775$	−4.16265	−0.149527
$776$	−1.90137	−0.0682551
$777$	−4.07751	−0.146280
$778$	−20.9231	−0.750130
$779$	24.6261	0.882321
$780$	23.4603	0.840012
$781$	−4.08032	−0.146005
$782$	0.371281	0.0132770
$783$	−10.4317	−0.372799
$784$	1.90847	0.0681596
$785$	−4.74723	−0.169436
$786$	27.0509	0.964874
$787$	−0.668350	−0.0238241	−0.0119121	−	0.999929i	$-0.503792\pi$
$787$	−0.668350	−0.0238241	−0.0119121	+	0.999929i	$0.503792\pi$
$788$	−3.23635	−0.115290
$789$	38.9227	1.38568
$790$	0.145558	0.00517874
$791$	−12.3006	−0.437358
$792$	−18.5149	−0.657898
$793$	1.48103	0.0525929
$794$	−20.1135	−0.713802
$795$	23.2126	0.823267
$796$	32.9164	1.16669
$797$	−43.8557	−1.55345	−0.776724	−	0.629841i	$-0.783120\pi$
$797$	−43.8557	−1.55345	−0.776724	+	0.629841i	$0.783120\pi$
$798$	2.89300	0.102411
$799$	8.16334	0.288798
$800$	5.58708	0.197533
$801$	35.9016	1.26852
$802$	12.4700	0.440331
$803$	51.4782	1.81663
$804$	50.9111	1.79550
$805$	0.263969	0.00930369
$806$	−16.0254	−0.564469
$807$	33.5215	1.18001
$808$	−1.46383	−0.0514972
$809$	41.8880	1.47270	0.736352	−	0.676599i	$-0.236547\pi$
$809$	41.8880	1.47270	0.736352	+	0.676599i	$0.236547\pi$
$810$	6.55567	0.230343
$811$	−20.0408	−0.703729	−0.351864	−	0.936051i	$-0.614452\pi$
$811$	−20.0408	−0.703729	−0.351864	+	0.936051i	$0.614452\pi$
$812$	9.35635	0.328344
$813$	−67.0901	−2.35295
$814$	4.13797	0.145036
$815$	3.02512	0.105965
$816$	10.0455	0.351661
$817$	−6.36724	−0.222761
$818$	−4.05974	−0.141946
$819$	−13.9200	−0.486403
$820$	−19.2762	−0.673154
$821$	−3.57754	−0.124857	−0.0624285	−	0.998049i	$-0.519885\pi$
$821$	−3.57754	−0.124857	−0.0624285	+	0.998049i	$0.519885\pi$
$822$	2.29544	0.0800626
$823$	27.1110	0.945029	0.472515	−	0.881323i	$-0.343346\pi$
$823$	27.1110	0.945029	0.472515	+	0.881323i	$0.343346\pi$
$824$	2.64945	0.0922978
$825$	8.66366	0.301630
$826$	−3.89530	−0.135535
$827$	−13.2119	−0.459424	−0.229712	−	0.973259i	$-0.573778\pi$
$827$	−13.2119	−0.459424	−0.229712	+	0.973259i	$0.573778\pi$
$828$	−0.947443	−0.0329259
$829$	−7.55284	−0.262321	−0.131161	−	0.991361i	$-0.541870\pi$
$829$	−7.55284	−0.262321	−0.131161	+	0.991361i	$0.541870\pi$
$830$	−0.404211	−0.0140304
$831$	12.7519	0.442358
$832$	−2.59623	−0.0900082
$833$	2.30733	0.0799443
$834$	26.5406	0.919027
$835$	−8.65634	−0.299565
$836$	12.8653	0.444957
$837$	7.55753	0.261226
$838$	1.16046	0.0400874
$839$	−21.4644	−0.741032	−0.370516	−	0.928826i	$-0.620819\pi$
$839$	−21.4644	−0.741032	−0.370516	+	0.928826i	$0.620819\pi$
$840$	−5.04579	−0.174096
$841$	4.01358	0.138399
$842$	−1.83842	−0.0633562
$843$	27.0894	0.933009
$844$	−1.08963	−0.0375065
$845$	−26.8837	−0.924829
$846$	4.75376	0.163438
$847$	−3.42293	−0.117613
$848$	−19.4194	−0.666864
$849$	52.6959	1.80852
$850$	1.40653	0.0482436
$851$	0.471817	0.0161737
$852$	3.99119	0.136736
$853$	52.3177	1.79133	0.895663	−	0.444734i	$-0.146702\pi$
$853$	52.3177	1.79133	0.895663	+	0.444734i	$0.146702\pi$
$854$	−0.142957	−0.00489189
$855$	4.58536	0.156816
$856$	−21.5161	−0.735405
$857$	5.25720	0.179583	0.0897913	−	0.995961i	$-0.471380\pi$
$857$	5.25720	0.179583	0.0897913	+	0.995961i	$0.471380\pi$
$858$	33.3533	1.13866
$859$	−29.6058	−1.01014	−0.505068	−	0.863079i	$-0.668533\pi$
$859$	−29.6058	−1.01014	−0.505068	+	0.863079i	$0.668533\pi$
$860$	4.98399	0.169953
$861$	27.0045	0.920310
$862$	−2.85893	−0.0973755
$863$	−14.3280	−0.487731	−0.243866	−	0.969809i	$-0.578416\pi$
$863$	−14.3280	−0.487731	−0.243866	+	0.969809i	$0.578416\pi$
$864$	−10.1436	−0.345094
$865$	13.1499	0.447110
$866$	13.6499	0.463841
$867$	−26.6365	−0.904623
$868$	−6.77845	−0.230076
$869$	−0.906827	−0.0307620
$870$	−7.99025	−0.270895
$871$	−86.5517	−2.93269
$872$	−39.2302	−1.32850
$873$	1.89475	0.0641274
$874$	−0.334755	−0.0113233
$875$	1.00000	0.0338062
$876$	−50.3537	−1.70129
$877$	13.9713	0.471776	0.235888	−	0.971780i	$-0.424200\pi$
$877$	13.9713	0.471776	0.235888	+	0.971780i	$0.424200\pi$
$878$	−22.2558	−0.751097
$879$	−10.2173	−0.344621
$880$	−7.24790	−0.244327
$881$	−7.31628	−0.246492	−0.123246	−	0.992376i	$-0.539330\pi$
$881$	−7.31628	−0.246492	−0.123246	+	0.992376i	$0.539330\pi$
$882$	1.34363	0.0452424
$883$	−7.48992	−0.252056	−0.126028	−	0.992027i	$-0.540223\pi$
$883$	−7.48992	−0.252056	−0.126028	+	0.992027i	$0.540223\pi$
$884$	−23.7284	−0.798072
$885$	−14.5773	−0.490009
$886$	−19.5777	−0.657726
$887$	7.56087	0.253869	0.126935	−	0.991911i	$-0.459486\pi$
$887$	7.56087	0.253869	0.126935	+	0.991911i	$0.459486\pi$
$888$	−9.01882	−0.302652
$889$	−19.4000	−0.650656
$890$	−9.92920	−0.332827
$891$	−40.8417	−1.36825
$892$	−13.6400	−0.456703
$893$	−7.36024	−0.246301
$894$	−3.18352	−0.106473
$895$	−11.6213	−0.388458
$896$	11.4248	0.381674
$897$	3.80299	0.126978
$898$	9.98557	0.333223
$899$	−23.9175	−0.797695
$900$	−3.58922	−0.119641
$901$	−23.4779	−0.782163
$902$	−27.4049	−0.912482
$903$	−6.98219	−0.232353
$904$	−27.2070	−0.904890
$905$	−7.67898	−0.255258
$906$	−4.76992	−0.158470
$907$	19.0567	0.632769	0.316384	−	0.948631i	$-0.397531\pi$
$907$	19.0567	0.632769	0.316384	+	0.948631i	$0.397531\pi$
$908$	5.44967	0.180854
$909$	1.45873	0.0483830
$910$	3.84980	0.127619
$911$	−28.3228	−0.938376	−0.469188	−	0.883098i	$-0.655453\pi$
$911$	−28.3228	−0.938376	−0.469188	+	0.883098i	$0.655453\pi$
$912$	−9.05720	−0.299914
$913$	2.51823	0.0833413
$914$	−13.1611	−0.435329
$915$	−0.534983	−0.0176860
$916$	−1.62840	−0.0538037
$917$	−19.4521	−0.642366
$918$	−2.55364	−0.0842825
$919$	−46.8679	−1.54603	−0.773014	−	0.634389i	$-0.781252\pi$
$919$	−46.8679	−1.54603	−0.773014	+	0.634389i	$0.781252\pi$
$920$	0.583859	0.0192492
$921$	−25.2691	−0.832644
$922$	−2.63313	−0.0867175
$923$	−6.78524	−0.223339
$924$	14.1079	0.464115
$925$	1.78740	0.0587692
$926$	5.09241	0.167347
$927$	−2.64022	−0.0867163
$928$	32.1019	1.05380
$929$	−0.543077	−0.0178178	−0.00890889	−	0.999960i	$-0.502836\pi$
$929$	−0.543077	−0.0178178	−0.00890889	+	0.999960i	$0.502836\pi$
$930$	5.78875	0.189820
$931$	−2.08034	−0.0681803
$932$	22.8718	0.749192
$933$	−31.2897	−1.02438
$934$	−13.6756	−0.447479
$935$	−8.76267	−0.286570
$936$	−30.7888	−1.00636
$937$	−40.3388	−1.31781	−0.658906	−	0.752225i	$-0.728981\pi$
$937$	−40.3388	−1.31781	−0.658906	+	0.752225i	$0.728981\pi$
$938$	8.35444	0.272782
$939$	45.6055	1.48828
$940$	5.76127	0.187912
$941$	−25.9572	−0.846179	−0.423089	−	0.906088i	$-0.639054\pi$
$941$	−25.9572	−0.846179	−0.423089	+	0.906088i	$0.639054\pi$
$942$	6.60168	0.215094
$943$	−3.12474	−0.101756
$944$	12.1951	0.396918
$945$	−1.81556	−0.0590600
$946$	7.08571	0.230376
$947$	−21.6527	−0.703618	−0.351809	−	0.936072i	$-0.614433\pi$
$947$	−21.6527	−0.703618	−0.351809	+	0.936072i	$0.614433\pi$
$948$	0.887019	0.0288090
$949$	85.6041	2.77883
$950$	−1.26816	−0.0411445
$951$	48.6052	1.57613
$952$	5.10345	0.165404
$953$	−45.8460	−1.48510	−0.742549	−	0.669792i	$-0.766383\pi$
$953$	−45.8460	−1.48510	−0.742549	+	0.669792i	$0.766383\pi$
$954$	−13.6719	−0.442645
$955$	11.6654	0.377482
$956$	−41.0456	−1.32751
$957$	49.7792	1.60913
$958$	7.86415	0.254079
$959$	−1.65064	−0.0533018
$960$	0.937822	0.0302681
$961$	−13.6723	−0.441043
$962$	6.88111	0.221856
$963$	21.4412	0.690933
$964$	−9.96555	−0.320969
$965$	7.62481	0.245451
$966$	−0.367086	−0.0118108
$967$	46.0290	1.48019	0.740097	−	0.672500i	$-0.234780\pi$
$967$	46.0290	1.48019	0.740097	+	0.672500i	$0.234780\pi$
$968$	−7.57099	−0.243341
$969$	−10.9501	−0.351768
$970$	−0.524024	−0.0168254
$971$	16.3045	0.523237	0.261619	−	0.965171i	$-0.415744\pi$
$971$	16.3045	0.523237	0.261619	+	0.965171i	$0.415744\pi$
$972$	31.0802	0.996899
$973$	−19.0852	−0.611844
$974$	−10.0997	−0.323614
$975$	14.4070	0.461392
$976$	0.447560	0.0143260
$977$	−19.3729	−0.619796	−0.309898	−	0.950770i	$-0.600295\pi$
$977$	−19.3729	−0.619796	−0.309898	+	0.950770i	$0.600295\pi$
$978$	−4.20685	−0.134520
$979$	61.8588	1.97701
$980$	1.62840	0.0520172
$981$	39.0936	1.24816
$982$	14.2929	0.456103
$983$	30.7155	0.979672	0.489836	−	0.871815i	$-0.337057\pi$
$983$	30.7155	0.979672	0.489836	+	0.871815i	$0.337057\pi$
$984$	59.7297	1.90411
$985$	−1.98744	−0.0633253
$986$	8.08157	0.257370
$987$	−8.07110	−0.256906
$988$	21.3940	0.680634
$989$	0.807923	0.0256905
$990$	−5.10277	−0.162177
$991$	−15.5511	−0.493997	−0.246998	−	0.969016i	$-0.579444\pi$
$991$	−15.5511	−0.493997	−0.246998	+	0.969016i	$0.579444\pi$
$992$	−23.2571	−0.738413
$993$	−1.79814	−0.0570623
$994$	0.654948	0.0207737
$995$	20.2140	0.640826
$996$	−2.46322	−0.0780502
$997$	28.5147	0.903071	0.451535	−	0.892253i	$-0.350876\pi$
$997$	28.5147	0.903071	0.451535	+	0.892253i	$0.350876\pi$
$998$	−7.94657	−0.251544
$999$	−3.24512	−0.102671

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.37	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.37	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.609593 q^{2} +2.28126 q^{3} -1.62840 q^{4} -1.00000 q^{5} +1.39064 q^{6} -1.00000 q^{7} -2.21184 q^{8} +2.20414 q^{9} +O(q^{10})\)	\(q+0.609593 q^{2} +2.28126 q^{3} -1.62840 q^{4} -1.00000 q^{5} +1.39064 q^{6} -1.00000 q^{7} -2.21184 q^{8} +2.20414 q^{9} -0.609593 q^{10} +3.79775 q^{11} -3.71480 q^{12} +6.31536 q^{13} -0.609593 q^{14} -2.28126 q^{15} +1.90847 q^{16} +2.30733 q^{17} +1.34363 q^{18} -2.08034 q^{19} +1.62840 q^{20} -2.28126 q^{21} +2.31508 q^{22} +0.263969 q^{23} -5.04579 q^{24} +1.00000 q^{25} +3.84980 q^{26} -1.81556 q^{27} +1.62840 q^{28} +5.74574 q^{29} -1.39064 q^{30} -4.16265 q^{31} +5.58708 q^{32} +8.66366 q^{33} +1.40653 q^{34} +1.00000 q^{35} -3.58922 q^{36} +1.78740 q^{37} -1.26816 q^{38} +14.4070 q^{39} +2.21184 q^{40} -11.8375 q^{41} -1.39064 q^{42} +3.06067 q^{43} -6.18425 q^{44} -2.20414 q^{45} +0.160914 q^{46} +3.53800 q^{47} +4.35371 q^{48} +1.00000 q^{49} +0.609593 q^{50} +5.26362 q^{51} -10.2839 q^{52} -10.1754 q^{53} -1.10675 q^{54} -3.79775 q^{55} +2.21184 q^{56} -4.74579 q^{57} +3.50256 q^{58} +6.39001 q^{59} +3.71480 q^{60} +0.234512 q^{61} -2.53752 q^{62} -2.20414 q^{63} -0.411098 q^{64} -6.31536 q^{65} +5.28130 q^{66} -13.7050 q^{67} -3.75725 q^{68} +0.602182 q^{69} +0.609593 q^{70} -1.07440 q^{71} -4.87522 q^{72} +13.5549 q^{73} +1.08958 q^{74} +2.28126 q^{75} +3.38762 q^{76} -3.79775 q^{77} +8.78238 q^{78} -0.238780 q^{79} -1.90847 q^{80} -10.7542 q^{81} -7.21607 q^{82} +0.663084 q^{83} +3.71480 q^{84} -2.30733 q^{85} +1.86576 q^{86} +13.1075 q^{87} -8.40004 q^{88} +16.2882 q^{89} -1.34363 q^{90} -6.31536 q^{91} -0.429846 q^{92} -9.49609 q^{93} +2.15674 q^{94} +2.08034 q^{95} +12.7456 q^{96} +0.859629 q^{97} +0.609593 q^{98} +8.37079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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