LMFDB - Embedded newform 8015.2.a.l.1.13

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			1.13
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)

$f(q)$	$=$	$q-1.87703 q^{2} -2.63781 q^{3} +1.52324 q^{4} -1.00000 q^{5} +4.95125 q^{6} -1.00000 q^{7} +0.894900 q^{8} +3.95806 q^{9} +O(q^{10})$	\(q-1.87703 q^{2} -2.63781 q^{3} +1.52324 q^{4} -1.00000 q^{5} +4.95125 q^{6} -1.00000 q^{7} +0.894900 q^{8} +3.95806 q^{9} +1.87703 q^{10} -0.835767 q^{11} -4.01801 q^{12} -2.57449 q^{13} +1.87703 q^{14} +2.63781 q^{15} -4.72622 q^{16} +5.00673 q^{17} -7.42939 q^{18} +1.69114 q^{19} -1.52324 q^{20} +2.63781 q^{21} +1.56876 q^{22} +7.52045 q^{23} -2.36058 q^{24} +1.00000 q^{25} +4.83238 q^{26} -2.52718 q^{27} -1.52324 q^{28} -0.896200 q^{29} -4.95125 q^{30} +0.661756 q^{31} +7.08146 q^{32} +2.20460 q^{33} -9.39777 q^{34} +1.00000 q^{35} +6.02906 q^{36} -6.42100 q^{37} -3.17432 q^{38} +6.79101 q^{39} -0.894900 q^{40} +6.40349 q^{41} -4.95125 q^{42} +4.66509 q^{43} -1.27307 q^{44} -3.95806 q^{45} -14.1161 q^{46} +9.46667 q^{47} +12.4669 q^{48} +1.00000 q^{49} -1.87703 q^{50} -13.2068 q^{51} -3.92155 q^{52} +7.01772 q^{53} +4.74358 q^{54} +0.835767 q^{55} -0.894900 q^{56} -4.46092 q^{57} +1.68219 q^{58} -5.07702 q^{59} +4.01801 q^{60} +4.74747 q^{61} -1.24213 q^{62} -3.95806 q^{63} -3.83965 q^{64} +2.57449 q^{65} -4.13809 q^{66} +10.3551 q^{67} +7.62643 q^{68} -19.8376 q^{69} -1.87703 q^{70} -5.55683 q^{71} +3.54206 q^{72} +15.0713 q^{73} +12.0524 q^{74} -2.63781 q^{75} +2.57601 q^{76} +0.835767 q^{77} -12.7469 q^{78} +3.09837 q^{79} +4.72622 q^{80} -5.20795 q^{81} -12.0195 q^{82} +3.78224 q^{83} +4.01801 q^{84} -5.00673 q^{85} -8.75650 q^{86} +2.36401 q^{87} -0.747928 q^{88} +4.77527 q^{89} +7.42939 q^{90} +2.57449 q^{91} +11.4554 q^{92} -1.74559 q^{93} -17.7692 q^{94} -1.69114 q^{95} -18.6796 q^{96} +4.44039 q^{97} -1.87703 q^{98} -3.30801 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.87703	−1.32726	−0.663630	−	0.748061i	$-0.730985\pi$
$2$	−1.87703	−1.32726	−0.663630	+	0.748061i	$0.730985\pi$
$3$	−2.63781	−1.52294	−0.761471	−	0.648199i	$-0.775523\pi$
$3$	−2.63781	−1.52294	−0.761471	+	0.648199i	$0.775523\pi$
$4$	1.52324	0.761618
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	4.95125	2.02134
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.894900	0.316395
$9$	3.95806	1.31935
$10$	1.87703	0.593569
$11$	−0.835767	−0.251993	−0.125997	−	0.992031i	$-0.540213\pi$
$11$	−0.835767	−0.251993	−0.125997	+	0.992031i	$0.540213\pi$
$12$	−4.01801	−1.15990
$13$	−2.57449	−0.714034	−0.357017	−	0.934098i	$-0.616206\pi$
$13$	−2.57449	−0.714034	−0.357017	+	0.934098i	$0.616206\pi$
$14$	1.87703	0.501657
$15$	2.63781	0.681080
$16$	−4.72622	−1.18156
$17$	5.00673	1.21431	0.607155	−	0.794583i	$-0.292311\pi$
$17$	5.00673	1.21431	0.607155	+	0.794583i	$0.292311\pi$
$18$	−7.42939	−1.75112
$19$	1.69114	0.387975	0.193987	−	0.981004i	$-0.437858\pi$
$19$	1.69114	0.387975	0.193987	+	0.981004i	$0.437858\pi$
$20$	−1.52324	−0.340606
$21$	2.63781	0.575618
$22$	1.56876	0.334460
$23$	7.52045	1.56812	0.784061	−	0.620683i	$-0.213145\pi$
$23$	7.52045	1.56812	0.784061	+	0.620683i	$0.213145\pi$
$24$	−2.36058	−0.481851
$25$	1.00000	0.200000
$26$	4.83238	0.947708
$27$	−2.52718	−0.486355
$28$	−1.52324	−0.287865
$29$	−0.896200	−0.166420	−0.0832101	−	0.996532i	$-0.526517\pi$
$29$	−0.896200	−0.166420	−0.0832101	+	0.996532i	$0.526517\pi$
$30$	−4.95125	−0.903970
$31$	0.661756	0.118855	0.0594274	−	0.998233i	$-0.481073\pi$
$31$	0.661756	0.118855	0.0594274	+	0.998233i	$0.481073\pi$
$32$	7.08146	1.25184
$33$	2.20460	0.383771
$34$	−9.39777	−1.61170
$35$	1.00000	0.169031
$36$	6.02906	1.00484
$37$	−6.42100	−1.05561	−0.527803	−	0.849367i	$-0.676984\pi$
$37$	−6.42100	−1.05561	−0.527803	+	0.849367i	$0.676984\pi$
$38$	−3.17432	−0.514943
$39$	6.79101	1.08743
$40$	−0.894900	−0.141496
$41$	6.40349	1.00006	0.500029	−	0.866009i	$-0.333323\pi$
$41$	6.40349	1.00006	0.500029	+	0.866009i	$0.333323\pi$
$42$	−4.95125	−0.763994
$43$	4.66509	0.711419	0.355710	−	0.934597i	$-0.384239\pi$
$43$	4.66509	0.711419	0.355710	+	0.934597i	$0.384239\pi$
$44$	−1.27307	−0.191923
$45$	−3.95806	−0.590032
$46$	−14.1161	−2.08131
$47$	9.46667	1.38086	0.690428	−	0.723401i	$-0.257422\pi$
$47$	9.46667	1.38086	0.690428	+	0.723401i	$0.257422\pi$
$48$	12.4669	1.79944
$49$	1.00000	0.142857
$50$	−1.87703	−0.265452
$51$	−13.2068	−1.84932
$52$	−3.92155	−0.543821
$53$	7.01772	0.963958	0.481979	−	0.876183i	$-0.339918\pi$
$53$	7.01772	0.963958	0.481979	+	0.876183i	$0.339918\pi$
$54$	4.74358	0.645520
$55$	0.835767	0.112695
$56$	−0.894900	−0.119586
$57$	−4.46092	−0.590863
$58$	1.68219	0.220883
$59$	−5.07702	−0.660972	−0.330486	−	0.943811i	$-0.607213\pi$
$59$	−5.07702	−0.660972	−0.330486	+	0.943811i	$0.607213\pi$
$60$	4.01801	0.518723
$61$	4.74747	0.607851	0.303925	−	0.952696i	$-0.401703\pi$
$61$	4.74747	0.607851	0.303925	+	0.952696i	$0.401703\pi$
$62$	−1.24213	−0.157751
$63$	−3.95806	−0.498668
$64$	−3.83965	−0.479956
$65$	2.57449	0.319326
$66$	−4.13809	−0.509364
$67$	10.3551	1.26508	0.632539	−	0.774528i	$-0.282013\pi$
$67$	10.3551	1.26508	0.632539	+	0.774528i	$0.282013\pi$
$68$	7.62643	0.924840
$69$	−19.8376	−2.38816
$70$	−1.87703	−0.224348
$71$	−5.55683	−0.659474	−0.329737	−	0.944073i	$-0.606960\pi$
$71$	−5.55683	−0.659474	−0.329737	+	0.944073i	$0.606960\pi$
$72$	3.54206	0.417436
$73$	15.0713	1.76396	0.881980	−	0.471287i	$-0.156210\pi$
$73$	15.0713	1.76396	0.881980	+	0.471287i	$0.156210\pi$
$74$	12.0524	1.40106
$75$	−2.63781	−0.304588
$76$	2.57601	0.295488
$77$	0.835767	0.0952445
$78$	−12.7469	−1.44330
$79$	3.09837	0.348594	0.174297	−	0.984693i	$-0.444235\pi$
$79$	3.09837	0.348594	0.174297	+	0.984693i	$0.444235\pi$
$80$	4.72622	0.528408
$81$	−5.20795	−0.578661
$82$	−12.0195	−1.32734
$83$	3.78224	0.415155	0.207577	−	0.978219i	$-0.433442\pi$
$83$	3.78224	0.415155	0.207577	+	0.978219i	$0.433442\pi$
$84$	4.01801	0.438401
$85$	−5.00673	−0.543056
$86$	−8.75650	−0.944238
$87$	2.36401	0.253448
$88$	−0.747928	−0.0797294
$89$	4.77527	0.506177	0.253089	−	0.967443i	$-0.418554\pi$
$89$	4.77527	0.506177	0.253089	+	0.967443i	$0.418554\pi$
$90$	7.42939	0.783126
$91$	2.57449	0.269879
$92$	11.4554	1.19431
$93$	−1.74559	−0.181009
$94$	−17.7692	−1.83275
$95$	−1.69114	−0.173508
$96$	−18.6796	−1.90647
$97$	4.44039	0.450853	0.225427	−	0.974260i	$-0.427622\pi$
$97$	4.44039	0.450853	0.225427	+	0.974260i	$0.427622\pi$
$98$	−1.87703	−0.189609
$99$	−3.30801	−0.332468
$100$	1.52324	0.152324
$101$	11.6798	1.16218	0.581091	−	0.813839i	$-0.302626\pi$
$101$	11.6798	1.16218	0.581091	+	0.813839i	$0.302626\pi$
$102$	24.7896	2.45453
$103$	−15.0595	−1.48386	−0.741929	−	0.670479i	$-0.766089\pi$
$103$	−15.0595	−1.48386	−0.741929	+	0.670479i	$0.766089\pi$
$104$	−2.30391	−0.225917
$105$	−2.63781	−0.257424
$106$	−13.1725	−1.27942
$107$	0.413285	0.0399538	0.0199769	−	0.999800i	$-0.493641\pi$
$107$	0.413285	0.0399538	0.0199769	+	0.999800i	$0.493641\pi$
$108$	−3.84949	−0.370417
$109$	−4.50672	−0.431666	−0.215833	−	0.976430i	$-0.569247\pi$
$109$	−4.50672	−0.431666	−0.215833	+	0.976430i	$0.569247\pi$
$110$	−1.56876	−0.149575
$111$	16.9374	1.60763
$112$	4.72622	0.446586
$113$	19.1810	1.80439	0.902197	−	0.431324i	$-0.141953\pi$
$113$	19.1810	1.80439	0.902197	+	0.431324i	$0.141953\pi$
$114$	8.37327	0.784229
$115$	−7.52045	−0.701286
$116$	−1.36512	−0.126749
$117$	−10.1900	−0.942062
$118$	9.52971	0.877281
$119$	−5.00673	−0.458966
$120$	2.36058	0.215490
$121$	−10.3015	−0.936499
$122$	−8.91113	−0.806776
$123$	−16.8912	−1.52303
$124$	1.00801	0.0905220
$125$	−1.00000	−0.0894427
$126$	7.42939	0.661862
$127$	17.4795	1.55105	0.775526	−	0.631316i	$-0.217485\pi$
$127$	17.4795	1.55105	0.775526	+	0.631316i	$0.217485\pi$
$128$	−6.95578	−0.614810
$129$	−12.3056	−1.08345
$130$	−4.83238	−0.423828
$131$	−17.1515	−1.49853	−0.749267	−	0.662268i	$-0.769594\pi$
$131$	−17.1515	−1.49853	−0.749267	+	0.662268i	$0.769594\pi$
$132$	3.35812	0.292287
$133$	−1.69114	−0.146641
$134$	−19.4369	−1.67909
$135$	2.52718	0.217505
$136$	4.48052	0.384201
$137$	14.2336	1.21606	0.608029	−	0.793915i	$-0.291960\pi$
$137$	14.2336	1.21606	0.608029	+	0.793915i	$0.291960\pi$
$138$	37.2356	3.16971
$139$	17.6851	1.50003	0.750014	−	0.661422i	$-0.230047\pi$
$139$	17.6851	1.50003	0.750014	+	0.661422i	$0.230047\pi$
$140$	1.52324	0.128737
$141$	−24.9713	−2.10296
$142$	10.4303	0.875293
$143$	2.15167	0.179932
$144$	−18.7067	−1.55889
$145$	0.896200	0.0744254
$146$	−28.2892	−2.34123
$147$	−2.63781	−0.217563
$148$	−9.78070	−0.803969
$149$	8.37621	0.686206	0.343103	−	0.939298i	$-0.388522\pi$
$149$	8.37621	0.686206	0.343103	+	0.939298i	$0.388522\pi$
$150$	4.95125	0.404268
$151$	23.9202	1.94660	0.973298	−	0.229546i	$-0.0737240\pi$
$151$	23.9202	1.94660	0.973298	+	0.229546i	$0.0737240\pi$
$152$	1.51340	0.122753
$153$	19.8169	1.60210
$154$	−1.56876	−0.126414
$155$	−0.661756	−0.0531535
$156$	10.3443	0.828208
$157$	−20.8928	−1.66743	−0.833715	−	0.552194i	$-0.813791\pi$
$157$	−20.8928	−1.66743	−0.833715	+	0.552194i	$0.813791\pi$
$158$	−5.81573	−0.462675
$159$	−18.5114	−1.46805
$160$	−7.08146	−0.559838
$161$	−7.52045	−0.592695
$162$	9.77548	0.768034
$163$	−15.8991	−1.24531	−0.622655	−	0.782496i	$-0.713946\pi$
$163$	−15.8991	−1.24531	−0.622655	+	0.782496i	$0.713946\pi$
$164$	9.75403	0.761662
$165$	−2.20460	−0.171628
$166$	−7.09937	−0.551018
$167$	9.50740	0.735704	0.367852	−	0.929884i	$-0.380093\pi$
$167$	9.50740	0.735704	0.367852	+	0.929884i	$0.380093\pi$
$168$	2.36058	0.182123
$169$	−6.37202	−0.490156
$170$	9.39777	0.720776
$171$	6.69364	0.511875
$172$	7.10603	0.541830
$173$	3.57021	0.271438	0.135719	−	0.990747i	$-0.456666\pi$
$173$	3.57021	0.271438	0.135719	+	0.990747i	$0.456666\pi$
$174$	−4.43731	−0.336392
$175$	−1.00000	−0.0755929
$176$	3.95002	0.297744
$177$	13.3922	1.00662
$178$	−8.96332	−0.671829
$179$	−25.4025	−1.89867	−0.949336	−	0.314262i	$-0.898243\pi$
$179$	−25.4025	−1.89867	−0.949336	+	0.314262i	$0.898243\pi$
$180$	−6.02906	−0.449379
$181$	4.20561	0.312601	0.156300	−	0.987710i	$-0.450043\pi$
$181$	4.20561	0.312601	0.156300	+	0.987710i	$0.450043\pi$
$182$	−4.83238	−0.358200
$183$	−12.5229	−0.925721
$184$	6.73005	0.496146
$185$	6.42100	0.472081
$186$	3.27652	0.240246
$187$	−4.18446	−0.305998
$188$	14.4200	1.05168
$189$	2.52718	0.183825
$190$	3.17432	0.230290
$191$	−17.8923	−1.29464	−0.647322	−	0.762217i	$-0.724111\pi$
$191$	−17.8923	−1.29464	−0.647322	+	0.762217i	$0.724111\pi$
$192$	10.1283	0.730945
$193$	−25.4087	−1.82896	−0.914481	−	0.404629i	$-0.867401\pi$
$193$	−25.4087	−1.82896	−0.914481	+	0.404629i	$0.867401\pi$
$194$	−8.33474	−0.598399
$195$	−6.79101	−0.486314
$196$	1.52324	0.108803
$197$	8.66587	0.617417	0.308709	−	0.951157i	$-0.400103\pi$
$197$	8.66587	0.617417	0.308709	+	0.951157i	$0.400103\pi$
$198$	6.20924	0.441271
$199$	13.2680	0.940541	0.470271	−	0.882522i	$-0.344156\pi$
$199$	13.2680	0.940541	0.470271	+	0.882522i	$0.344156\pi$
$200$	0.894900	0.0632790
$201$	−27.3149	−1.92664
$202$	−21.9233	−1.54252
$203$	0.896200	0.0629009
$204$	−20.1171	−1.40848
$205$	−6.40349	−0.447239
$206$	28.2671	1.96946
$207$	29.7664	2.06891
$208$	12.1676	0.843671
$209$	−1.41340	−0.0977670
$210$	4.95125	0.341669
$211$	20.9869	1.44480	0.722398	−	0.691478i	$-0.243040\pi$
$211$	20.9869	1.44480	0.722398	+	0.691478i	$0.243040\pi$
$212$	10.6896	0.734168
$213$	14.6579	1.00434
$214$	−0.775748	−0.0530291
$215$	−4.66509	−0.318156
$216$	−2.26157	−0.153880
$217$	−0.661756	−0.0449229
$218$	8.45924	0.572932
$219$	−39.7552	−2.68641
$220$	1.27307	0.0858304
$221$	−12.8897	−0.867058
$222$	−31.7920	−2.13374
$223$	−23.2213	−1.55501	−0.777505	−	0.628876i	$-0.783515\pi$
$223$	−23.2213	−1.55501	−0.777505	+	0.628876i	$0.783515\pi$
$224$	−7.08146	−0.473150
$225$	3.95806	0.263871
$226$	−36.0032	−2.39490
$227$	5.61757	0.372852	0.186426	−	0.982469i	$-0.440310\pi$
$227$	5.61757	0.372852	0.186426	+	0.982469i	$0.440310\pi$
$228$	−6.79503	−0.450012
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	14.1161	0.930788
$231$	−2.20460	−0.145052
$232$	−0.802010	−0.0526545
$233$	−3.64771	−0.238970	−0.119485	−	0.992836i	$-0.538124\pi$
$233$	−3.64771	−0.238970	−0.119485	+	0.992836i	$0.538124\pi$
$234$	19.1268	1.25036
$235$	−9.46667	−0.617538
$236$	−7.73350	−0.503408
$237$	−8.17292	−0.530888
$238$	9.39777	0.609167
$239$	−11.7715	−0.761435	−0.380717	−	0.924691i	$-0.624323\pi$
$239$	−11.7715	−0.761435	−0.380717	+	0.924691i	$0.624323\pi$
$240$	−12.4669	−0.804735
$241$	4.85143	0.312508	0.156254	−	0.987717i	$-0.450058\pi$
$241$	4.85143	0.312508	0.156254	+	0.987717i	$0.450058\pi$
$242$	19.3362	1.24298
$243$	21.3191	1.36762
$244$	7.23151	0.462950
$245$	−1.00000	−0.0638877
$246$	31.7053	2.02146
$247$	−4.35382	−0.277027
$248$	0.592205	0.0376051
$249$	−9.97684	−0.632256
$250$	1.87703	0.118714
$251$	−23.7678	−1.50021	−0.750107	−	0.661317i	$-0.769998\pi$
$251$	−23.7678	−1.50021	−0.750107	+	0.661317i	$0.769998\pi$
$252$	−6.02906	−0.379795
$253$	−6.28535	−0.395156
$254$	−32.8095	−2.05865
$255$	13.2068	0.827043
$256$	20.7355	1.29597
$257$	1.50627	0.0939583	0.0469791	−	0.998896i	$-0.485041\pi$
$257$	1.50627	0.0939583	0.0469791	+	0.998896i	$0.485041\pi$
$258$	23.0980	1.43802
$259$	6.42100	0.398982
$260$	3.92155	0.243204
$261$	−3.54721	−0.219567
$262$	32.1939	1.98894
$263$	−7.88263	−0.486064	−0.243032	−	0.970018i	$-0.578142\pi$
$263$	−7.88263	−0.486064	−0.243032	+	0.970018i	$0.578142\pi$
$264$	1.97289	0.121423
$265$	−7.01772	−0.431095
$266$	3.17432	0.194630
$267$	−12.5963	−0.770879
$268$	15.7733	0.963507
$269$	−1.23044	−0.0750215	−0.0375108	−	0.999296i	$-0.511943\pi$
$269$	−1.23044	−0.0750215	−0.0375108	+	0.999296i	$0.511943\pi$
$270$	−4.74358	−0.288685
$271$	−21.3318	−1.29581	−0.647906	−	0.761720i	$-0.724355\pi$
$271$	−21.3318	−1.29581	−0.647906	+	0.761720i	$0.724355\pi$
$272$	−23.6629	−1.43478
$273$	−6.79101	−0.411011
$274$	−26.7169	−1.61402
$275$	−0.835767	−0.0503986
$276$	−30.2173	−1.81887
$277$	−26.5974	−1.59808	−0.799042	−	0.601275i	$-0.794660\pi$
$277$	−26.5974	−1.59808	−0.799042	+	0.601275i	$0.794660\pi$
$278$	−33.1954	−1.99093
$279$	2.61927	0.156811
$280$	0.894900	0.0534805
$281$	−1.56037	−0.0930838	−0.0465419	−	0.998916i	$-0.514820\pi$
$281$	−1.56037	−0.0930838	−0.0465419	+	0.998916i	$0.514820\pi$
$282$	46.8719	2.79118
$283$	13.7741	0.818784	0.409392	−	0.912359i	$-0.365741\pi$
$283$	13.7741	0.818784	0.409392	+	0.912359i	$0.365741\pi$
$284$	−8.46436	−0.502267
$285$	4.46092	0.264242
$286$	−4.03875	−0.238816
$287$	−6.40349	−0.377986
$288$	28.0288	1.65161
$289$	8.06732	0.474548
$290$	−1.68219	−0.0987818
$291$	−11.7129	−0.686623
$292$	22.9571	1.34346
$293$	0.651516	0.0380619	0.0190310	−	0.999819i	$-0.493942\pi$
$293$	0.651516	0.0380619	0.0190310	+	0.999819i	$0.493942\pi$
$294$	4.95125	0.288763
$295$	5.07702	0.295596
$296$	−5.74615	−0.333988
$297$	2.11213	0.122558
$298$	−15.7224	−0.910774
$299$	−19.3613	−1.11969
$300$	−4.01801	−0.231980
$301$	−4.66509	−0.268891
$302$	−44.8988	−2.58364
$303$	−30.8091	−1.76994
$304$	−7.99272	−0.458414
$305$	−4.74747	−0.271839
$306$	−37.1969	−2.12641
$307$	12.8516	0.733480	0.366740	−	0.930324i	$-0.380474\pi$
$307$	12.8516	0.733480	0.366740	+	0.930324i	$0.380474\pi$
$308$	1.27307	0.0725399
$309$	39.7242	2.25983
$310$	1.24213	0.0705485
$311$	−4.36812	−0.247694	−0.123847	−	0.992301i	$-0.539523\pi$
$311$	−4.36812	−0.247694	−0.123847	+	0.992301i	$0.539523\pi$
$312$	6.07728	0.344058
$313$	29.3585	1.65944	0.829721	−	0.558178i	$-0.188499\pi$
$313$	29.3585	1.65944	0.829721	+	0.558178i	$0.188499\pi$
$314$	39.2165	2.21311
$315$	3.95806	0.223011
$316$	4.71955	0.265495
$317$	−9.39855	−0.527875	−0.263938	−	0.964540i	$-0.585021\pi$
$317$	−9.39855	−0.527875	−0.263938	+	0.964540i	$0.585021\pi$
$318$	34.7465	1.94849
$319$	0.749015	0.0419368
$320$	3.83965	0.214643
$321$	−1.09017	−0.0608473
$322$	14.1161	0.786660
$323$	8.46709	0.471121
$324$	−7.93294	−0.440719
$325$	−2.57449	−0.142807
$326$	29.8430	1.65285
$327$	11.8879	0.657402
$328$	5.73048	0.316413
$329$	−9.46667	−0.521915
$330$	4.13809	0.227794
$331$	−4.70679	−0.258709	−0.129354	−	0.991598i	$-0.541290\pi$
$331$	−4.70679	−0.258709	−0.129354	+	0.991598i	$0.541290\pi$
$332$	5.76124	0.316189
$333$	−25.4147	−1.39272
$334$	−17.8457	−0.976471
$335$	−10.3551	−0.565760
$336$	−12.4669	−0.680125
$337$	−10.8898	−0.593207	−0.296604	−	0.955001i	$-0.595854\pi$
$337$	−10.8898	−0.593207	−0.296604	+	0.955001i	$0.595854\pi$
$338$	11.9605	0.650564
$339$	−50.5958	−2.74799
$340$	−7.62643	−0.413601
$341$	−0.553074	−0.0299506
$342$	−12.5642	−0.679391
$343$	−1.00000	−0.0539949
$344$	4.17479	0.225089
$345$	19.8376	1.06802
$346$	−6.70139	−0.360269
$347$	−8.97483	−0.481794	−0.240897	−	0.970551i	$-0.577442\pi$
$347$	−8.97483	−0.481794	−0.240897	+	0.970551i	$0.577442\pi$
$348$	3.60094	0.193031
$349$	20.8846	1.11793	0.558963	−	0.829192i	$-0.311199\pi$
$349$	20.8846	1.11793	0.558963	+	0.829192i	$0.311199\pi$
$350$	1.87703	0.100331
$351$	6.50618	0.347274
$352$	−5.91845	−0.315454
$353$	−21.6208	−1.15076	−0.575380	−	0.817886i	$-0.695146\pi$
$353$	−21.6208	−1.15076	−0.575380	+	0.817886i	$0.695146\pi$
$354$	−25.1376	−1.33605
$355$	5.55683	0.294926
$356$	7.27386	0.385514
$357$	13.2068	0.698979
$358$	47.6812	2.52003
$359$	−15.0577	−0.794714	−0.397357	−	0.917664i	$-0.630073\pi$
$359$	−15.0577	−0.794714	−0.397357	+	0.917664i	$0.630073\pi$
$360$	−3.54206	−0.186683
$361$	−16.1400	−0.849476
$362$	−7.89405	−0.414902
$363$	27.1734	1.42623
$364$	3.92155	0.205545
$365$	−15.0713	−0.788867
$366$	23.5059	1.22867
$367$	−14.0132	−0.731482	−0.365741	−	0.930717i	$-0.619184\pi$
$367$	−14.0132	−0.731482	−0.365741	+	0.930717i	$0.619184\pi$
$368$	−35.5433	−1.85283
$369$	25.3454	1.31943
$370$	−12.0524	−0.626575
$371$	−7.01772	−0.364342
$372$	−2.65894	−0.137860
$373$	19.3993	1.00446	0.502229	−	0.864735i	$-0.332514\pi$
$373$	19.3993	1.00446	0.502229	+	0.864735i	$0.332514\pi$
$374$	7.85435	0.406139
$375$	2.63781	0.136216
$376$	8.47172	0.436896
$377$	2.30726	0.118830
$378$	−4.74358	−0.243984
$379$	−0.956797	−0.0491474	−0.0245737	−	0.999698i	$-0.507823\pi$
$379$	−0.956797	−0.0491474	−0.0245737	+	0.999698i	$0.507823\pi$
$380$	−2.57601	−0.132146
$381$	−46.1076	−2.36216
$382$	33.5844	1.71833
$383$	−6.00556	−0.306870	−0.153435	−	0.988159i	$-0.549034\pi$
$383$	−6.00556	−0.306870	−0.153435	+	0.988159i	$0.549034\pi$
$384$	18.3481	0.936320
$385$	−0.835767	−0.0425946
$386$	47.6929	2.42751
$387$	18.4647	0.938613
$388$	6.76376	0.343378
$389$	0.329573	0.0167100	0.00835501	−	0.999965i	$-0.497340\pi$
$389$	0.329573	0.0167100	0.00835501	+	0.999965i	$0.497340\pi$
$390$	12.7469	0.645466
$391$	37.6529	1.90419
$392$	0.894900	0.0451993
$393$	45.2425	2.28218
$394$	−16.2661	−0.819473
$395$	−3.09837	−0.155896
$396$	−5.03889	−0.253214
$397$	−25.1035	−1.25991	−0.629954	−	0.776632i	$-0.716926\pi$
$397$	−25.1035	−1.25991	−0.629954	+	0.776632i	$0.716926\pi$
$398$	−24.9043	−1.24834
$399$	4.46092	0.223325
$400$	−4.72622	−0.236311
$401$	−28.0654	−1.40152	−0.700759	−	0.713398i	$-0.747155\pi$
$401$	−28.0654	−1.40152	−0.700759	+	0.713398i	$0.747155\pi$
$402$	51.2708	2.55715
$403$	−1.70368	−0.0848664
$404$	17.7911	0.885138
$405$	5.20795	0.258785
$406$	−1.68219	−0.0834859
$407$	5.36646	0.266006
$408$	−11.8188	−0.585116
$409$	8.41613	0.416151	0.208075	−	0.978113i	$-0.433280\pi$
$409$	8.41613	0.416151	0.208075	+	0.978113i	$0.433280\pi$
$410$	12.0195	0.593603
$411$	−37.5456	−1.85199
$412$	−22.9392	−1.13013
$413$	5.07702	0.249824
$414$	−55.8724	−2.74598
$415$	−3.78224	−0.185663
$416$	−18.2311	−0.893854
$417$	−46.6499	−2.28446
$418$	2.65299	0.129762
$419$	18.8440	0.920590	0.460295	−	0.887766i	$-0.347744\pi$
$419$	18.8440	0.920590	0.460295	+	0.887766i	$0.347744\pi$
$420$	−4.01801	−0.196059
$421$	2.72399	0.132759	0.0663796	−	0.997794i	$-0.478855\pi$
$421$	2.72399	0.132759	0.0663796	+	0.997794i	$0.478855\pi$
$422$	−39.3929	−1.91762
$423$	37.4696	1.82184
$424$	6.28016	0.304991
$425$	5.00673	0.242862
$426$	−27.5132	−1.33302
$427$	−4.74747	−0.229746
$428$	0.629531	0.0304295
$429$	−5.67570	−0.274026
$430$	8.75650	0.422276
$431$	−0.502546	−0.0242068	−0.0121034	−	0.999927i	$-0.503853\pi$
$431$	−0.502546	−0.0242068	−0.0121034	+	0.999927i	$0.503853\pi$
$432$	11.9440	0.574656
$433$	38.5521	1.85269	0.926347	−	0.376671i	$-0.122931\pi$
$433$	38.5521	1.85269	0.926347	+	0.376671i	$0.122931\pi$
$434$	1.24213	0.0596244
$435$	−2.36401	−0.113346
$436$	−6.86480	−0.328764
$437$	12.7182	0.608392
$438$	74.6217	3.56556
$439$	35.5405	1.69625	0.848127	−	0.529793i	$-0.177730\pi$
$439$	35.5405	1.69625	0.848127	+	0.529793i	$0.177730\pi$
$440$	0.747928	0.0356561
$441$	3.95806	0.188479
$442$	24.1944	1.15081
$443$	−9.88780	−0.469783	−0.234892	−	0.972022i	$-0.575474\pi$
$443$	−9.88780	−0.469783	−0.234892	+	0.972022i	$0.575474\pi$
$444$	25.7997	1.22440
$445$	−4.77527	−0.226369
$446$	43.5870	2.06390
$447$	−22.0949	−1.04505
$448$	3.83965	0.181406
$449$	40.5318	1.91281	0.956406	−	0.292040i	$-0.0943341\pi$
$449$	40.5318	1.91281	0.956406	+	0.292040i	$0.0943341\pi$
$450$	−7.42939	−0.350225
$451$	−5.35183	−0.252008
$452$	29.2172	1.37426
$453$	−63.0969	−2.96455
$454$	−10.5443	−0.494871
$455$	−2.57449	−0.120694
$456$	−3.99207	−0.186946
$457$	10.7056	0.500786	0.250393	−	0.968144i	$-0.419440\pi$
$457$	10.7056	0.500786	0.250393	+	0.968144i	$0.419440\pi$
$458$	−1.87703	−0.0877078
$459$	−12.6529	−0.590586
$460$	−11.4554	−0.534112
$461$	11.4693	0.534180	0.267090	−	0.963672i	$-0.413938\pi$
$461$	11.4693	0.534180	0.267090	+	0.963672i	$0.413938\pi$
$462$	4.13809	0.192521
$463$	23.9804	1.11447	0.557233	−	0.830356i	$-0.311863\pi$
$463$	23.9804	1.11447	0.557233	+	0.830356i	$0.311863\pi$
$464$	4.23564	0.196635
$465$	1.74559	0.0809497
$466$	6.84686	0.317175
$467$	−35.3534	−1.63596	−0.817981	−	0.575246i	$-0.804906\pi$
$467$	−35.3534	−1.63596	−0.817981	+	0.575246i	$0.804906\pi$
$468$	−15.5217	−0.717492
$469$	−10.3551	−0.478155
$470$	17.7692	0.819633
$471$	55.1114	2.53940
$472$	−4.54343	−0.209128
$473$	−3.89893	−0.179273
$474$	15.3408	0.704627
$475$	1.69114	0.0775949
$476$	−7.62643	−0.349557
$477$	27.7766	1.27180
$478$	22.0954	1.01062
$479$	1.30632	0.0596872	0.0298436	−	0.999555i	$-0.490499\pi$
$479$	1.30632	0.0596872	0.0298436	+	0.999555i	$0.490499\pi$
$480$	18.6796	0.852601
$481$	16.5308	0.753739
$482$	−9.10627	−0.414779
$483$	19.8376	0.902640
$484$	−15.6916	−0.713255
$485$	−4.44039	−0.201628
$486$	−40.0166	−1.81519
$487$	23.2701	1.05447	0.527234	−	0.849720i	$-0.323229\pi$
$487$	23.2701	1.05447	0.527234	+	0.849720i	$0.323229\pi$
$488$	4.24851	0.192321
$489$	41.9387	1.89653
$490$	1.87703	0.0847955
$491$	−41.2192	−1.86020	−0.930099	−	0.367310i	$-0.880279\pi$
$491$	−41.2192	−1.86020	−0.930099	+	0.367310i	$0.880279\pi$
$492$	−25.7293	−1.15997
$493$	−4.48703	−0.202086
$494$	8.17225	0.367687
$495$	3.30801	0.148684
$496$	−3.12761	−0.140434
$497$	5.55683	0.249258
$498$	18.7268	0.839168
$499$	−21.3853	−0.957336	−0.478668	−	0.877996i	$-0.658880\pi$
$499$	−21.3853	−0.957336	−0.478668	+	0.877996i	$0.658880\pi$
$500$	−1.52324	−0.0681212
$501$	−25.0787	−1.12044
$502$	44.6129	1.99117
$503$	−3.84614	−0.171491	−0.0857455	−	0.996317i	$-0.527327\pi$
$503$	−3.84614	−0.171491	−0.0857455	+	0.996317i	$0.527327\pi$
$504$	−3.54206	−0.157776
$505$	−11.6798	−0.519743
$506$	11.7978	0.524475
$507$	16.8082	0.746479
$508$	26.6254	1.18131
$509$	−1.96040	−0.0868931	−0.0434466	−	0.999056i	$-0.513834\pi$
$509$	−1.96040	−0.0868931	−0.0434466	+	0.999056i	$0.513834\pi$
$510$	−24.7896	−1.09770
$511$	−15.0713	−0.666714
$512$	−25.0096	−1.10528
$513$	−4.27382	−0.188694
$514$	−2.82730	−0.124707
$515$	15.0595	0.663601
$516$	−18.7444	−0.825175
$517$	−7.91193	−0.347966
$518$	−12.0524	−0.529552
$519$	−9.41755	−0.413385
$520$	2.30391	0.101033
$521$	44.9547	1.96950	0.984751	−	0.173972i	$-0.0556604\pi$
$521$	44.9547	1.96950	0.984751	+	0.173972i	$0.0556604\pi$
$522$	6.65822	0.291422
$523$	40.1380	1.75511	0.877557	−	0.479473i	$-0.159172\pi$
$523$	40.1380	1.75511	0.877557	+	0.479473i	$0.159172\pi$
$524$	−26.1258	−1.14131
$525$	2.63781	0.115124
$526$	14.7959	0.645133
$527$	3.31323	0.144327
$528$	−10.4194	−0.453447
$529$	33.5572	1.45901
$530$	13.1725	0.572175
$531$	−20.0951	−0.872055
$532$	−2.57601	−0.111684
$533$	−16.4857	−0.714075
$534$	23.6436	1.02316
$535$	−0.413285	−0.0178679
$536$	9.26679	0.400264
$537$	67.0071	2.89157
$538$	2.30958	0.0995730
$539$	−0.835767	−0.0359990
$540$	3.84949	0.165656
$541$	−44.6724	−1.92062	−0.960309	−	0.278938i	$-0.910018\pi$
$541$	−44.6724	−1.92062	−0.960309	+	0.278938i	$0.910018\pi$
$542$	40.0403	1.71988
$543$	−11.0936	−0.476073
$544$	35.4549	1.52012
$545$	4.50672	0.193047
$546$	12.7469	0.545518
$547$	24.6582	1.05431	0.527153	−	0.849770i	$-0.323259\pi$
$547$	24.6582	1.05431	0.527153	+	0.849770i	$0.323259\pi$
$548$	21.6811	0.926171
$549$	18.7907	0.801969
$550$	1.56876	0.0668921
$551$	−1.51560	−0.0645668
$552$	−17.7526	−0.755602
$553$	−3.09837	−0.131756
$554$	49.9241	2.12107
$555$	−16.9374	−0.718953
$556$	26.9385	1.14245
$557$	38.6938	1.63951	0.819755	−	0.572714i	$-0.194110\pi$
$557$	38.6938	1.63951	0.819755	+	0.572714i	$0.194110\pi$
$558$	−4.91644	−0.208129
$559$	−12.0102	−0.507977
$560$	−4.72622	−0.199719
$561$	11.0378	0.466017
$562$	2.92886	0.123546
$563$	26.6125	1.12158	0.560792	−	0.827957i	$-0.310497\pi$
$563$	26.6125	1.12158	0.560792	+	0.827957i	$0.310497\pi$
$564$	−38.0372	−1.60165
$565$	−19.1810	−0.806950
$566$	−25.8543	−1.08674
$567$	5.20795	0.218713
$568$	−4.97280	−0.208654
$569$	20.5636	0.862072	0.431036	−	0.902335i	$-0.358148\pi$
$569$	20.5636	0.862072	0.431036	+	0.902335i	$0.358148\pi$
$570$	−8.37327	−0.350718
$571$	7.16049	0.299657	0.149829	−	0.988712i	$-0.452128\pi$
$571$	7.16049	0.299657	0.149829	+	0.988712i	$0.452128\pi$
$572$	3.27750	0.137039
$573$	47.1966	1.97167
$574$	12.0195	0.501686
$575$	7.52045	0.313625
$576$	−15.1976	−0.633231
$577$	43.7448	1.82112	0.910560	−	0.413377i	$-0.135651\pi$
$577$	43.7448	1.82112	0.910560	+	0.413377i	$0.135651\pi$
$578$	−15.1426	−0.629849
$579$	67.0235	2.78540
$580$	1.36512	0.0566837
$581$	−3.78224	−0.156914
$582$	21.9855	0.911327
$583$	−5.86518	−0.242911
$584$	13.4873	0.558108
$585$	10.1900	0.421303
$586$	−1.22291	−0.0505181
$587$	−43.7484	−1.80569	−0.902846	−	0.429965i	$-0.858526\pi$
$587$	−43.7484	−1.80569	−0.902846	+	0.429965i	$0.858526\pi$
$588$	−4.01801	−0.165700
$589$	1.11912	0.0461127
$590$	−9.52971	−0.392332
$591$	−22.8589	−0.940291
$592$	30.3471	1.24726
$593$	25.7238	1.05635	0.528175	−	0.849135i	$-0.322876\pi$
$593$	25.7238	1.05635	0.528175	+	0.849135i	$0.322876\pi$
$594$	−3.96453	−0.162667
$595$	5.00673	0.205256
$596$	12.7589	0.522627
$597$	−34.9984	−1.43239
$598$	36.3417	1.48612
$599$	−0.342812	−0.0140069	−0.00700345	−	0.999975i	$-0.502229\pi$
$599$	−0.342812	−0.0140069	−0.00700345	+	0.999975i	$0.502229\pi$
$600$	−2.36058	−0.0963702
$601$	3.49654	0.142627	0.0713134	−	0.997454i	$-0.477281\pi$
$601$	3.49654	0.142627	0.0713134	+	0.997454i	$0.477281\pi$
$602$	8.75650	0.356888
$603$	40.9862	1.66909
$604$	36.4361	1.48256
$605$	10.3015	0.418815
$606$	57.8295	2.34916
$607$	−2.89038	−0.117317	−0.0586586	−	0.998278i	$-0.518682\pi$
$607$	−2.89038	−0.117317	−0.0586586	+	0.998278i	$0.518682\pi$
$608$	11.9758	0.485681
$609$	−2.36401	−0.0957945
$610$	8.91113	0.360801
$611$	−24.3718	−0.985978
$612$	30.1858	1.22019
$613$	30.7954	1.24381	0.621907	−	0.783091i	$-0.286358\pi$
$613$	30.7954	1.24381	0.621907	+	0.783091i	$0.286358\pi$
$614$	−24.1228	−0.973518
$615$	16.8912	0.681120
$616$	0.747928	0.0301349
$617$	42.6220	1.71590	0.857949	−	0.513734i	$-0.171738\pi$
$617$	42.6220	1.71590	0.857949	+	0.513734i	$0.171738\pi$
$618$	−74.5634	−2.99938
$619$	−37.2296	−1.49638	−0.748191	−	0.663483i	$-0.769078\pi$
$619$	−37.2296	−1.49638	−0.748191	+	0.663483i	$0.769078\pi$
$620$	−1.00801	−0.0404827
$621$	−19.0055	−0.762665
$622$	8.19909	0.328754
$623$	−4.77527	−0.191317
$624$	−32.0958	−1.28486
$625$	1.00000	0.0400000
$626$	−55.1068	−2.20251
$627$	3.72829	0.148893
$628$	−31.8247	−1.26995
$629$	−32.1482	−1.28183
$630$	−7.42939	−0.295994
$631$	17.9955	0.716390	0.358195	−	0.933647i	$-0.383392\pi$
$631$	17.9955	0.716390	0.358195	+	0.933647i	$0.383392\pi$
$632$	2.77273	0.110293
$633$	−55.3594	−2.20034
$634$	17.6413	0.700627
$635$	−17.4795	−0.693652
$636$	−28.1973	−1.11810
$637$	−2.57449	−0.102005
$638$	−1.40592	−0.0556610
$639$	−21.9942	−0.870079
$640$	6.95578	0.274952
$641$	−10.7140	−0.423177	−0.211588	−	0.977359i	$-0.567864\pi$
$641$	−10.7140	−0.423177	−0.211588	+	0.977359i	$0.567864\pi$
$642$	2.04628	0.0807602
$643$	−32.5029	−1.28179	−0.640894	−	0.767629i	$-0.721436\pi$
$643$	−32.5029	−1.28179	−0.640894	+	0.767629i	$0.721436\pi$
$644$	−11.4554	−0.451407
$645$	12.3056	0.484534
$646$	−15.8930	−0.625300
$647$	31.2258	1.22761	0.613806	−	0.789457i	$-0.289638\pi$
$647$	31.2258	1.22761	0.613806	+	0.789457i	$0.289638\pi$
$648$	−4.66060	−0.183086
$649$	4.24321	0.166560
$650$	4.83238	0.189542
$651$	1.74559	0.0684150
$652$	−24.2180	−0.948450
$653$	−50.7514	−1.98606	−0.993028	−	0.117883i	$-0.962389\pi$
$653$	−50.7514	−1.98606	−0.993028	+	0.117883i	$0.962389\pi$
$654$	−22.3139	−0.872543
$655$	17.1515	0.670165
$656$	−30.2643	−1.18162
$657$	59.6530	2.32728
$658$	17.7692	0.692716
$659$	−10.9571	−0.426827	−0.213413	−	0.976962i	$-0.568458\pi$
$659$	−10.9571	−0.426827	−0.213413	+	0.976962i	$0.568458\pi$
$660$	−3.35812	−0.130715
$661$	−9.25264	−0.359886	−0.179943	−	0.983677i	$-0.557591\pi$
$661$	−9.25264	−0.359886	−0.179943	+	0.983677i	$0.557591\pi$
$662$	8.83478	0.343374
$663$	34.0007	1.32048
$664$	3.38472	0.131353
$665$	1.69114	0.0655797
$666$	47.7041	1.84850
$667$	−6.73983	−0.260967
$668$	14.4820	0.560326
$669$	61.2533	2.36819
$670$	19.4369	0.750911
$671$	−3.96778	−0.153174
$672$	18.6796	0.720580
$673$	19.5396	0.753197	0.376599	−	0.926377i	$-0.377094\pi$
$673$	19.5396	0.753197	0.376599	+	0.926377i	$0.377094\pi$
$674$	20.4405	0.787340
$675$	−2.52718	−0.0972711
$676$	−9.70609	−0.373311
$677$	23.7477	0.912700	0.456350	−	0.889800i	$-0.349156\pi$
$677$	23.7477	0.912700	0.456350	+	0.889800i	$0.349156\pi$
$678$	94.9698	3.64729
$679$	−4.44039	−0.170407
$680$	−4.48052	−0.171820
$681$	−14.8181	−0.567831
$682$	1.03813	0.0397522
$683$	4.43123	0.169556	0.0847782	−	0.996400i	$-0.472982\pi$
$683$	4.43123	0.169556	0.0847782	+	0.996400i	$0.472982\pi$
$684$	10.1960	0.389853
$685$	−14.2336	−0.543838
$686$	1.87703	0.0716653
$687$	−2.63781	−0.100639
$688$	−22.0483	−0.840582
$689$	−18.0670	−0.688299
$690$	−37.2356	−1.41754
$691$	23.8436	0.907053	0.453526	−	0.891243i	$-0.350166\pi$
$691$	23.8436	0.907053	0.453526	+	0.891243i	$0.350166\pi$
$692$	5.43827	0.206732
$693$	3.30801	0.125661
$694$	16.8460	0.639466
$695$	−17.6851	−0.670833
$696$	2.11555	0.0801898
$697$	32.0605	1.21438
$698$	−39.2010	−1.48378
$699$	9.62198	0.363937
$700$	−1.52324	−0.0575729
$701$	−32.1321	−1.21361	−0.606806	−	0.794850i	$-0.707549\pi$
$701$	−32.1321	−1.21361	−0.606806	+	0.794850i	$0.707549\pi$
$702$	−12.2123	−0.460923
$703$	−10.8588	−0.409549
$704$	3.20905	0.120946
$705$	24.9713	0.940474
$706$	40.5829	1.52736
$707$	−11.6798	−0.439263
$708$	20.3995	0.766661
$709$	18.0898	0.679378	0.339689	−	0.940538i	$-0.389678\pi$
$709$	18.0898	0.679378	0.339689	+	0.940538i	$0.389678\pi$
$710$	−10.4303	−0.391443
$711$	12.2635	0.459918
$712$	4.27339	0.160152
$713$	4.97670	0.186379
$714$	−24.7896	−0.927726
$715$	−2.15167	−0.0804679
$716$	−38.6940	−1.44606
$717$	31.0510	1.15962
$718$	28.2637	1.05479
$719$	6.27395	0.233979	0.116989	−	0.993133i	$-0.462676\pi$
$719$	6.27395	0.233979	0.116989	+	0.993133i	$0.462676\pi$
$720$	18.7067	0.697156
$721$	15.0595	0.560845
$722$	30.2953	1.12747
$723$	−12.7972	−0.475932
$724$	6.40614	0.238082
$725$	−0.896200	−0.0332840
$726$	−51.0053	−1.89298
$727$	−50.2441	−1.86345	−0.931725	−	0.363165i	$-0.881696\pi$
$727$	−50.2441	−1.86345	−0.931725	+	0.363165i	$0.881696\pi$
$728$	2.30391	0.0853885
$729$	−40.6120	−1.50415
$730$	28.2892	1.04703
$731$	23.3568	0.863883
$732$	−19.0754	−0.705046
$733$	43.4030	1.60313	0.801564	−	0.597909i	$-0.204002\pi$
$733$	43.4030	1.60313	0.801564	+	0.597909i	$0.204002\pi$
$734$	26.3031	0.970867
$735$	2.63781	0.0972972
$736$	53.2558	1.96303
$737$	−8.65447	−0.318791
$738$	−47.5740	−1.75122
$739$	39.2057	1.44221	0.721103	−	0.692828i	$-0.243635\pi$
$739$	39.2057	1.44221	0.721103	+	0.692828i	$0.243635\pi$
$740$	9.78070	0.359546
$741$	11.4846	0.421896
$742$	13.1725	0.483576
$743$	−44.6657	−1.63863	−0.819313	−	0.573347i	$-0.805645\pi$
$743$	−44.6657	−1.63863	−0.819313	+	0.573347i	$0.805645\pi$
$744$	−1.56213	−0.0572703
$745$	−8.37621	−0.306881
$746$	−36.4130	−1.33318
$747$	14.9703	0.547735
$748$	−6.37392	−0.233053
$749$	−0.413285	−0.0151011
$750$	−4.95125	−0.180794
$751$	−52.1124	−1.90161	−0.950804	−	0.309793i	$-0.899740\pi$
$751$	−52.1124	−1.90161	−0.950804	+	0.309793i	$0.899740\pi$
$752$	−44.7416	−1.63156
$753$	62.6951	2.28474
$754$	−4.33078	−0.157718
$755$	−23.9202	−0.870544
$756$	3.84949	0.140004
$757$	40.5574	1.47409	0.737043	−	0.675846i	$-0.236222\pi$
$757$	40.5574	1.47409	0.737043	+	0.675846i	$0.236222\pi$
$758$	1.79593	0.0652313
$759$	16.5796	0.601800
$760$	−1.51340	−0.0548969
$761$	−11.6861	−0.423621	−0.211811	−	0.977311i	$-0.567936\pi$
$761$	−11.6861	−0.423621	−0.211811	+	0.977311i	$0.567936\pi$
$762$	86.5452	3.13520
$763$	4.50672	0.163154
$764$	−27.2542	−0.986024
$765$	−19.8169	−0.716482
$766$	11.2726	0.407296
$767$	13.0707	0.471956
$768$	−54.6964	−1.97369
$769$	−11.9369	−0.430456	−0.215228	−	0.976564i	$-0.569049\pi$
$769$	−11.9369	−0.430456	−0.215228	+	0.976564i	$0.569049\pi$
$770$	1.56876	0.0565341
$771$	−3.97325	−0.143093
$772$	−38.7035	−1.39297
$773$	−6.52893	−0.234829	−0.117415	−	0.993083i	$-0.537461\pi$
$773$	−6.52893	−0.234829	−0.117415	+	0.993083i	$0.537461\pi$
$774$	−34.6587	−1.24578
$775$	0.661756	0.0237710
$776$	3.97370	0.142648
$777$	−16.9374	−0.607626
$778$	−0.618618	−0.0221785
$779$	10.8292	0.387997
$780$	−10.3443	−0.370386
$781$	4.64421	0.166183
$782$	−70.6755	−2.52735
$783$	2.26486	0.0809394
$784$	−4.72622	−0.168794
$785$	20.8928	0.745698
$786$	−84.9214	−3.02905
$787$	−42.1405	−1.50215	−0.751073	−	0.660219i	$-0.770463\pi$
$787$	−42.1405	−1.50215	−0.751073	+	0.660219i	$0.770463\pi$
$788$	13.2002	0.470236
$789$	20.7929	0.740247
$790$	5.81573	0.206914
$791$	−19.1810	−0.681997
$792$	−2.96034	−0.105191
$793$	−12.2223	−0.434026
$794$	47.1200	1.67223
$795$	18.5114	0.656533
$796$	20.2102	0.716333
$797$	25.5112	0.903651	0.451826	−	0.892106i	$-0.350773\pi$
$797$	25.5112	0.903651	0.451826	+	0.892106i	$0.350773\pi$
$798$	−8.37327	−0.296411
$799$	47.3970	1.67679
$800$	7.08146	0.250367
$801$	18.9008	0.667827
$802$	52.6795	1.86018
$803$	−12.5961	−0.444506
$804$	−41.6070	−1.46737
$805$	7.52045	0.265061
$806$	3.19786	0.112640
$807$	3.24568	0.114253
$808$	10.4522	0.367708
$809$	−41.7146	−1.46661	−0.733304	−	0.679901i	$-0.762023\pi$
$809$	−41.7146	−1.46661	−0.733304	+	0.679901i	$0.762023\pi$
$810$	−9.77548	−0.343475
$811$	41.0939	1.44300	0.721501	−	0.692413i	$-0.243452\pi$
$811$	41.0939	1.44300	0.721501	+	0.692413i	$0.243452\pi$
$812$	1.36512	0.0479065
$813$	56.2692	1.97345
$814$	−10.0730	−0.353059
$815$	15.8991	0.556920
$816$	62.4184	2.18508
$817$	7.88933	0.276013
$818$	−15.7973	−0.552340
$819$	10.1900	0.356066
$820$	−9.75403	−0.340626
$821$	−44.2387	−1.54394	−0.771970	−	0.635658i	$-0.780729\pi$
$821$	−44.2387	−1.54394	−0.771970	+	0.635658i	$0.780729\pi$
$822$	70.4741	2.45807
$823$	−45.6664	−1.59183	−0.795915	−	0.605408i	$-0.793010\pi$
$823$	−45.6664	−1.59183	−0.795915	+	0.605408i	$0.793010\pi$
$824$	−13.4768	−0.469485
$825$	2.20460	0.0767542
$826$	−9.52971	−0.331581
$827$	−36.4509	−1.26752	−0.633760	−	0.773530i	$-0.718489\pi$
$827$	−36.4509	−1.26752	−0.633760	+	0.773530i	$0.718489\pi$
$828$	45.3412	1.57572
$829$	47.4883	1.64934	0.824668	−	0.565616i	$-0.191362\pi$
$829$	47.4883	1.64934	0.824668	+	0.565616i	$0.191362\pi$
$830$	7.09937	0.246423
$831$	70.1590	2.43379
$832$	9.88512	0.342705
$833$	5.00673	0.173473
$834$	87.5632	3.03206
$835$	−9.50740	−0.329017
$836$	−2.15294	−0.0744611
$837$	−1.67237	−0.0578057
$838$	−35.3707	−1.22186
$839$	22.3479	0.771536	0.385768	−	0.922596i	$-0.373936\pi$
$839$	22.3479	0.771536	0.385768	+	0.922596i	$0.373936\pi$
$840$	−2.36058	−0.0814477
$841$	−28.1968	−0.972304
$842$	−5.11301	−0.176206
$843$	4.11596	0.141761
$844$	31.9680	1.10038
$845$	6.37202	0.219204
$846$	−70.3316	−2.41805
$847$	10.3015	0.353964
$848$	−33.1673	−1.13897
$849$	−36.3335	−1.24696
$850$	−9.39777	−0.322341
$851$	−48.2889	−1.65532
$852$	22.3274	0.764924
$853$	8.02611	0.274809	0.137404	−	0.990515i	$-0.456124\pi$
$853$	8.02611	0.274809	0.137404	+	0.990515i	$0.456124\pi$
$854$	8.91113	0.304933
$855$	−6.69364	−0.228918
$856$	0.369849	0.0126412
$857$	14.3073	0.488728	0.244364	−	0.969684i	$-0.421421\pi$
$857$	14.3073	0.488728	0.244364	+	0.969684i	$0.421421\pi$
$858$	10.6535	0.363703
$859$	19.7835	0.675003	0.337501	−	0.941325i	$-0.390418\pi$
$859$	19.7835	0.675003	0.337501	+	0.941325i	$0.390418\pi$
$860$	−7.10603	−0.242314
$861$	16.8912	0.575651
$862$	0.943293	0.0321287
$863$	31.2974	1.06538	0.532688	−	0.846311i	$-0.321182\pi$
$863$	31.2974	1.06538	0.532688	+	0.846311i	$0.321182\pi$
$864$	−17.8961	−0.608837
$865$	−3.57021	−0.121391
$866$	−72.3633	−2.45901
$867$	−21.2801	−0.722710
$868$	−1.00801	−0.0342141
$869$	−2.58952	−0.0878433
$870$	4.43731	0.150439
$871$	−26.6591	−0.903309
$872$	−4.03306	−0.136577
$873$	17.5753	0.594834
$874$	−23.8723	−0.807494
$875$	1.00000	0.0338062
$876$	−60.5566	−2.04602
$877$	−20.3738	−0.687975	−0.343987	−	0.938974i	$-0.611778\pi$
$877$	−20.3738	−0.687975	−0.343987	+	0.938974i	$0.611778\pi$
$878$	−66.7105	−2.25137
$879$	−1.71858	−0.0579661
$880$	−3.95002	−0.133155
$881$	−3.08834	−0.104049	−0.0520243	−	0.998646i	$-0.516567\pi$
$881$	−3.08834	−0.104049	−0.0520243	+	0.998646i	$0.516567\pi$
$882$	−7.42939	−0.250160
$883$	−39.3746	−1.32506	−0.662530	−	0.749035i	$-0.730517\pi$
$883$	−39.3746	−1.32506	−0.662530	+	0.749035i	$0.730517\pi$
$884$	−19.6341	−0.660367
$885$	−13.3922	−0.450175
$886$	18.5597	0.623525
$887$	−16.1720	−0.543004	−0.271502	−	0.962438i	$-0.587520\pi$
$887$	−16.1720	−0.543004	−0.271502	+	0.962438i	$0.587520\pi$
$888$	15.1573	0.508645
$889$	−17.4795	−0.586243
$890$	8.96332	0.300451
$891$	4.35264	0.145819
$892$	−35.3715	−1.18432
$893$	16.0095	0.535737
$894$	41.4727	1.38706
$895$	25.4025	0.849112
$896$	6.95578	0.232376
$897$	51.0715	1.70523
$898$	−76.0793	−2.53880
$899$	−0.593066	−0.0197799
$900$	6.02906	0.200969
$901$	35.1358	1.17054
$902$	10.0455	0.334480
$903$	12.3056	0.409506
$904$	17.1651	0.570901
$905$	−4.20561	−0.139799
$906$	118.435	3.93473
$907$	−15.9244	−0.528762	−0.264381	−	0.964418i	$-0.585168\pi$
$907$	−15.9244	−0.528762	−0.264381	+	0.964418i	$0.585168\pi$
$908$	8.55689	0.283970
$909$	46.2292	1.53333
$910$	4.83238	0.160192
$911$	44.8109	1.48465	0.742326	−	0.670038i	$-0.233722\pi$
$911$	44.8109	1.48465	0.742326	+	0.670038i	$0.233722\pi$
$912$	21.0833	0.698138
$913$	−3.16107	−0.104616
$914$	−20.0947	−0.664673
$915$	12.5229	0.413995
$916$	1.52324	0.0503291
$917$	17.1515	0.566393
$918$	23.7498	0.783861
$919$	−4.48235	−0.147859	−0.0739296	−	0.997263i	$-0.523554\pi$
$919$	−4.48235	−0.147859	−0.0739296	+	0.997263i	$0.523554\pi$
$920$	−6.73005	−0.221883
$921$	−33.9001	−1.11705
$922$	−21.5283	−0.708996
$923$	14.3060	0.470887
$924$	−3.35812	−0.110474
$925$	−6.42100	−0.211121
$926$	−45.0120	−1.47918
$927$	−59.6064	−1.95773
$928$	−6.34641	−0.208331
$929$	33.5100	1.09943	0.549714	−	0.835353i	$-0.314737\pi$
$929$	33.5100	1.09943	0.549714	+	0.835353i	$0.314737\pi$
$930$	−3.27652	−0.107441
$931$	1.69114	0.0554250
$932$	−5.55632	−0.182003
$933$	11.5223	0.377223
$934$	66.3594	2.17135
$935$	4.18446	0.136846
$936$	−9.11900	−0.298064
$937$	−8.38107	−0.273798	−0.136899	−	0.990585i	$-0.543714\pi$
$937$	−8.38107	−0.273798	−0.136899	+	0.990585i	$0.543714\pi$
$938$	19.4369	0.634636
$939$	−77.4423	−2.52723
$940$	−14.4200	−0.470328
$941$	13.8655	0.452003	0.226002	−	0.974127i	$-0.427435\pi$
$941$	13.8655	0.452003	0.226002	+	0.974127i	$0.427435\pi$
$942$	−103.446	−3.37044
$943$	48.1572	1.56821
$944$	23.9951	0.780975
$945$	−2.52718	−0.0822091
$946$	7.31840	0.237942
$947$	30.2186	0.981973	0.490986	−	0.871167i	$-0.336636\pi$
$947$	30.2186	0.981973	0.490986	+	0.871167i	$0.336636\pi$
$948$	−12.4493	−0.404334
$949$	−38.8008	−1.25953
$950$	−3.17432	−0.102989
$951$	24.7916	0.803923
$952$	−4.48052	−0.145214
$953$	28.2354	0.914633	0.457316	−	0.889304i	$-0.348811\pi$
$953$	28.2354	0.914633	0.457316	+	0.889304i	$0.348811\pi$
$954$	−52.1374	−1.68801
$955$	17.8923	0.578982
$956$	−17.9308	−0.579922
$957$	−1.97576	−0.0638673
$958$	−2.45200	−0.0792205
$959$	−14.2336	−0.459627
$960$	−10.1283	−0.326889
$961$	−30.5621	−0.985874
$962$	−31.0287	−1.00041
$963$	1.63581	0.0527131
$964$	7.38987	0.238012
$965$	25.4087	0.817937
$966$	−37.2356	−1.19804
$967$	11.5248	0.370612	0.185306	−	0.982681i	$-0.440672\pi$
$967$	11.5248	0.370612	0.185306	+	0.982681i	$0.440672\pi$
$968$	−9.21880	−0.296304
$969$	−22.3346	−0.717491
$970$	8.33474	0.267612
$971$	22.7562	0.730282	0.365141	−	0.930952i	$-0.381021\pi$
$971$	22.7562	0.730282	0.365141	+	0.930952i	$0.381021\pi$
$972$	32.4741	1.04161
$973$	−17.6851	−0.566957
$974$	−43.6786	−1.39955
$975$	6.79101	0.217486
$976$	−22.4376	−0.718210
$977$	−53.5666	−1.71375	−0.856874	−	0.515525i	$-0.827597\pi$
$977$	−53.5666	−1.71375	−0.856874	+	0.515525i	$0.827597\pi$
$978$	−78.7202	−2.51719
$979$	−3.99101	−0.127553
$980$	−1.52324	−0.0486580
$981$	−17.8379	−0.569519
$982$	77.3696	2.46896
$983$	25.2092	0.804050	0.402025	−	0.915629i	$-0.368306\pi$
$983$	25.2092	0.804050	0.402025	+	0.915629i	$0.368306\pi$
$984$	−15.1159	−0.481879
$985$	−8.66587	−0.276117
$986$	8.42229	0.268220
$987$	24.9713	0.794846
$988$	−6.63190	−0.210989
$989$	35.0836	1.11559
$990$	−6.20924	−0.197342
$991$	10.9941	0.349241	0.174620	−	0.984636i	$-0.444130\pi$
$991$	10.9941	0.349241	0.174620	+	0.984636i	$0.444130\pi$
$992$	4.68620	0.148787
$993$	12.4156	0.393998
$994$	−10.4303	−0.330830
$995$	−13.2680	−0.420623
$996$	−15.1971	−0.481538
$997$	−12.2800	−0.388912	−0.194456	−	0.980911i	$-0.562294\pi$
$997$	−12.2800	−0.388912	−0.194456	+	0.980911i	$0.562294\pi$
$998$	40.1408	1.27063
$999$	16.2270	0.513400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.13	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-1.87703 q^{2} -2.63781 q^{3} +1.52324 q^{4} -1.00000 q^{5} +4.95125 q^{6} -1.00000 q^{7} +0.894900 q^{8} +3.95806 q^{9} +O(q^{10})\)	\(q-1.87703 q^{2} -2.63781 q^{3} +1.52324 q^{4} -1.00000 q^{5} +4.95125 q^{6} -1.00000 q^{7} +0.894900 q^{8} +3.95806 q^{9} +1.87703 q^{10} -0.835767 q^{11} -4.01801 q^{12} -2.57449 q^{13} +1.87703 q^{14} +2.63781 q^{15} -4.72622 q^{16} +5.00673 q^{17} -7.42939 q^{18} +1.69114 q^{19} -1.52324 q^{20} +2.63781 q^{21} +1.56876 q^{22} +7.52045 q^{23} -2.36058 q^{24} +1.00000 q^{25} +4.83238 q^{26} -2.52718 q^{27} -1.52324 q^{28} -0.896200 q^{29} -4.95125 q^{30} +0.661756 q^{31} +7.08146 q^{32} +2.20460 q^{33} -9.39777 q^{34} +1.00000 q^{35} +6.02906 q^{36} -6.42100 q^{37} -3.17432 q^{38} +6.79101 q^{39} -0.894900 q^{40} +6.40349 q^{41} -4.95125 q^{42} +4.66509 q^{43} -1.27307 q^{44} -3.95806 q^{45} -14.1161 q^{46} +9.46667 q^{47} +12.4669 q^{48} +1.00000 q^{49} -1.87703 q^{50} -13.2068 q^{51} -3.92155 q^{52} +7.01772 q^{53} +4.74358 q^{54} +0.835767 q^{55} -0.894900 q^{56} -4.46092 q^{57} +1.68219 q^{58} -5.07702 q^{59} +4.01801 q^{60} +4.74747 q^{61} -1.24213 q^{62} -3.95806 q^{63} -3.83965 q^{64} +2.57449 q^{65} -4.13809 q^{66} +10.3551 q^{67} +7.62643 q^{68} -19.8376 q^{69} -1.87703 q^{70} -5.55683 q^{71} +3.54206 q^{72} +15.0713 q^{73} +12.0524 q^{74} -2.63781 q^{75} +2.57601 q^{76} +0.835767 q^{77} -12.7469 q^{78} +3.09837 q^{79} +4.72622 q^{80} -5.20795 q^{81} -12.0195 q^{82} +3.78224 q^{83} +4.01801 q^{84} -5.00673 q^{85} -8.75650 q^{86} +2.36401 q^{87} -0.747928 q^{88} +4.77527 q^{89} +7.42939 q^{90} +2.57449 q^{91} +11.4554 q^{92} -1.74559 q^{93} -17.7692 q^{94} -1.69114 q^{95} -18.6796 q^{96} +4.44039 q^{97} -1.87703 q^{98} -3.30801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 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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