LMFDB - Embedded newform 6022.2.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.42902 q^{3} +1.00000 q^{4} +1.04628 q^{5} +1.42902 q^{6} +2.47786 q^{7} -1.00000 q^{8} -0.957895 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.42902 q^{3} +1.00000 q^{4} +1.04628 q^{5} +1.42902 q^{6} +2.47786 q^{7} -1.00000 q^{8} -0.957895 q^{9} -1.04628 q^{10} -5.63258 q^{11} -1.42902 q^{12} -3.12451 q^{13} -2.47786 q^{14} -1.49515 q^{15} +1.00000 q^{16} +4.04230 q^{17} +0.957895 q^{18} -0.410080 q^{19} +1.04628 q^{20} -3.54092 q^{21} +5.63258 q^{22} -2.73069 q^{23} +1.42902 q^{24} -3.90530 q^{25} +3.12451 q^{26} +5.65592 q^{27} +2.47786 q^{28} +3.06876 q^{29} +1.49515 q^{30} -9.24305 q^{31} -1.00000 q^{32} +8.04908 q^{33} -4.04230 q^{34} +2.59253 q^{35} -0.957895 q^{36} -0.115265 q^{37} +0.410080 q^{38} +4.46500 q^{39} -1.04628 q^{40} +3.90405 q^{41} +3.54092 q^{42} -8.38888 q^{43} -5.63258 q^{44} -1.00222 q^{45} +2.73069 q^{46} -9.20502 q^{47} -1.42902 q^{48} -0.860199 q^{49} +3.90530 q^{50} -5.77654 q^{51} -3.12451 q^{52} -4.42422 q^{53} -5.65592 q^{54} -5.89324 q^{55} -2.47786 q^{56} +0.586014 q^{57} -3.06876 q^{58} +1.48209 q^{59} -1.49515 q^{60} +10.3819 q^{61} +9.24305 q^{62} -2.37353 q^{63} +1.00000 q^{64} -3.26911 q^{65} -8.04908 q^{66} +15.8623 q^{67} +4.04230 q^{68} +3.90222 q^{69} -2.59253 q^{70} +10.5527 q^{71} +0.957895 q^{72} +1.18129 q^{73} +0.115265 q^{74} +5.58077 q^{75} -0.410080 q^{76} -13.9568 q^{77} -4.46500 q^{78} +4.79709 q^{79} +1.04628 q^{80} -5.20875 q^{81} -3.90405 q^{82} -0.673126 q^{83} -3.54092 q^{84} +4.22937 q^{85} +8.38888 q^{86} -4.38532 q^{87} +5.63258 q^{88} -7.20463 q^{89} +1.00222 q^{90} -7.74211 q^{91} -2.73069 q^{92} +13.2085 q^{93} +9.20502 q^{94} -0.429058 q^{95} +1.42902 q^{96} +5.04523 q^{97} +0.860199 q^{98} +5.39542 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) $ 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.42902	−0.825046	−0.412523	−	0.910947i	$-0.635352\pi$
$3$	−1.42902	−0.825046	−0.412523	+	0.910947i	$0.635352\pi$
$4$	1.00000	0.500000
$5$	1.04628	0.467910	0.233955	−	0.972247i	$-0.424833\pi$
$5$	1.04628	0.467910	0.233955	+	0.972247i	$0.424833\pi$
$6$	1.42902	0.583396
$7$	2.47786	0.936544	0.468272	−	0.883584i	$-0.344877\pi$
$7$	2.47786	0.936544	0.468272	+	0.883584i	$0.344877\pi$
$8$	−1.00000	−0.353553
$9$	−0.957895	−0.319298
$10$	−1.04628	−0.330862
$11$	−5.63258	−1.69829	−0.849144	−	0.528162i	$-0.822881\pi$
$11$	−5.63258	−1.69829	−0.849144	+	0.528162i	$0.822881\pi$
$12$	−1.42902	−0.412523
$13$	−3.12451	−0.866583	−0.433292	−	0.901254i	$-0.642648\pi$
$13$	−3.12451	−0.866583	−0.433292	+	0.901254i	$0.642648\pi$
$14$	−2.47786	−0.662237
$15$	−1.49515	−0.386047
$16$	1.00000	0.250000
$17$	4.04230	0.980402	0.490201	−	0.871609i	$-0.336923\pi$
$17$	4.04230	0.980402	0.490201	+	0.871609i	$0.336923\pi$
$18$	0.957895	0.225778
$19$	−0.410080	−0.0940788	−0.0470394	−	0.998893i	$-0.514979\pi$
$19$	−0.410080	−0.0940788	−0.0470394	+	0.998893i	$0.514979\pi$
$20$	1.04628	0.233955
$21$	−3.54092	−0.772692
$22$	5.63258	1.20087
$23$	−2.73069	−0.569389	−0.284694	−	0.958618i	$-0.591892\pi$
$23$	−2.73069	−0.569389	−0.284694	+	0.958618i	$0.591892\pi$
$24$	1.42902	0.291698
$25$	−3.90530	−0.781061
$26$	3.12451	0.612767
$27$	5.65592	1.08848
$28$	2.47786	0.468272
$29$	3.06876	0.569854	0.284927	−	0.958549i	$-0.408031\pi$
$29$	3.06876	0.569854	0.284927	+	0.958549i	$0.408031\pi$
$30$	1.49515	0.272977
$31$	−9.24305	−1.66010	−0.830050	−	0.557688i	$-0.811688\pi$
$31$	−9.24305	−1.66010	−0.830050	+	0.557688i	$0.811688\pi$
$32$	−1.00000	−0.176777
$33$	8.04908	1.40117
$34$	−4.04230	−0.693249
$35$	2.59253	0.438218
$36$	−0.957895	−0.159649
$37$	−0.115265	−0.0189495	−0.00947473	−	0.999955i	$-0.503016\pi$
$37$	−0.115265	−0.0189495	−0.00947473	+	0.999955i	$0.503016\pi$
$38$	0.410080	0.0665238
$39$	4.46500	0.714972
$40$	−1.04628	−0.165431
$41$	3.90405	0.609710	0.304855	−	0.952399i	$-0.401392\pi$
$41$	3.90405	0.609710	0.304855	+	0.952399i	$0.401392\pi$
$42$	3.54092	0.546376
$43$	−8.38888	−1.27929	−0.639646	−	0.768669i	$-0.720919\pi$
$43$	−8.38888	−1.27929	−0.639646	+	0.768669i	$0.720919\pi$
$44$	−5.63258	−0.849144
$45$	−1.00222	−0.149403
$46$	2.73069	0.402619
$47$	−9.20502	−1.34269	−0.671345	−	0.741145i	$-0.734283\pi$
$47$	−9.20502	−1.34269	−0.671345	+	0.741145i	$0.734283\pi$
$48$	−1.42902	−0.206262
$49$	−0.860199	−0.122886
$50$	3.90530	0.552293
$51$	−5.77654	−0.808877
$52$	−3.12451	−0.433292
$53$	−4.42422	−0.607714	−0.303857	−	0.952718i	$-0.598274\pi$
$53$	−4.42422	−0.607714	−0.303857	+	0.952718i	$0.598274\pi$
$54$	−5.65592	−0.769673
$55$	−5.89324	−0.794645
$56$	−2.47786	−0.331118
$57$	0.586014	0.0776194
$58$	−3.06876	−0.402947
$59$	1.48209	0.192951	0.0964755	−	0.995335i	$-0.469243\pi$
$59$	1.48209	0.192951	0.0964755	+	0.995335i	$0.469243\pi$
$60$	−1.49515	−0.193024
$61$	10.3819	1.32926	0.664630	−	0.747172i	$-0.268589\pi$
$61$	10.3819	1.32926	0.664630	+	0.747172i	$0.268589\pi$
$62$	9.24305	1.17387
$63$	−2.37353	−0.299037
$64$	1.00000	0.125000
$65$	−3.26911	−0.405483
$66$	−8.04908	−0.990774
$67$	15.8623	1.93788	0.968942	−	0.247290i	$-0.0795400\pi$
$67$	15.8623	1.93788	0.968942	+	0.247290i	$0.0795400\pi$
$68$	4.04230	0.490201
$69$	3.90222	0.469772
$70$	−2.59253	−0.309867
$71$	10.5527	1.25237	0.626186	−	0.779673i	$-0.284615\pi$
$71$	10.5527	1.25237	0.626186	+	0.779673i	$0.284615\pi$
$72$	0.957895	0.112889
$73$	1.18129	0.138259	0.0691295	−	0.997608i	$-0.477978\pi$
$73$	1.18129	0.138259	0.0691295	+	0.997608i	$0.477978\pi$
$74$	0.115265	0.0133993
$75$	5.58077	0.644411
$76$	−0.410080	−0.0470394
$77$	−13.9568	−1.59052
$78$	−4.46500	−0.505561
$79$	4.79709	0.539714	0.269857	−	0.962900i	$-0.413023\pi$
$79$	4.79709	0.539714	0.269857	+	0.962900i	$0.413023\pi$
$80$	1.04628	0.116977
$81$	−5.20875	−0.578750
$82$	−3.90405	−0.431130
$83$	−0.673126	−0.0738852	−0.0369426	−	0.999317i	$-0.511762\pi$
$83$	−0.673126	−0.0738852	−0.0369426	+	0.999317i	$0.511762\pi$
$84$	−3.54092	−0.386346
$85$	4.22937	0.458739
$86$	8.38888	0.904597
$87$	−4.38532	−0.470156
$88$	5.63258	0.600435
$89$	−7.20463	−0.763689	−0.381845	−	0.924227i	$-0.624711\pi$
$89$	−7.20463	−0.763689	−0.381845	+	0.924227i	$0.624711\pi$
$90$	1.00222	0.105644
$91$	−7.74211	−0.811593
$92$	−2.73069	−0.284694
$93$	13.2085	1.36966
$94$	9.20502	0.949425
$95$	−0.429058	−0.0440204
$96$	1.42902	0.145849
$97$	5.04523	0.512266	0.256133	−	0.966642i	$-0.417552\pi$
$97$	5.04523	0.512266	0.256133	+	0.966642i	$0.417552\pi$
$98$	0.860199	0.0868932
$99$	5.39542	0.542260
$100$	−3.90530	−0.390530
$101$	18.0585	1.79689	0.898445	−	0.439087i	$-0.144698\pi$
$101$	18.0585	1.79689	0.898445	+	0.439087i	$0.144698\pi$
$102$	5.77654	0.571962
$103$	8.31352	0.819155	0.409578	−	0.912275i	$-0.365676\pi$
$103$	8.31352	0.819155	0.409578	+	0.912275i	$0.365676\pi$
$104$	3.12451	0.306383
$105$	−3.70479	−0.361550
$106$	4.42422	0.429719
$107$	−4.02270	−0.388889	−0.194445	−	0.980914i	$-0.562290\pi$
$107$	−4.02270	−0.388889	−0.194445	+	0.980914i	$0.562290\pi$
$108$	5.65592	0.544241
$109$	6.82440	0.653659	0.326829	−	0.945083i	$-0.394020\pi$
$109$	6.82440	0.653659	0.326829	+	0.945083i	$0.394020\pi$
$110$	5.89324	0.561899
$111$	0.164716	0.0156342
$112$	2.47786	0.234136
$113$	10.1804	0.957691	0.478846	−	0.877899i	$-0.341055\pi$
$113$	10.1804	0.957691	0.478846	+	0.877899i	$0.341055\pi$
$114$	−0.586014	−0.0548852
$115$	−2.85706	−0.266422
$116$	3.06876	0.284927
$117$	2.99295	0.276699
$118$	−1.48209	−0.136437
$119$	10.0163	0.918189
$120$	1.49515	0.136488
$121$	20.7260	1.88418
$122$	−10.3819	−0.939929
$123$	−5.57897	−0.503039
$124$	−9.24305	−0.830050
$125$	−9.31742	−0.833375
$126$	2.37353	0.211451
$127$	−12.8792	−1.14285	−0.571424	−	0.820655i	$-0.693609\pi$
$127$	−12.8792	−1.14285	−0.571424	+	0.820655i	$0.693609\pi$
$128$	−1.00000	−0.0883883
$129$	11.9879	1.05548
$130$	3.26911	0.286720
$131$	5.58975	0.488379	0.244190	−	0.969728i	$-0.421478\pi$
$131$	5.58975	0.488379	0.244190	+	0.969728i	$0.421478\pi$
$132$	8.04908	0.700583
$133$	−1.01612	−0.0881089
$134$	−15.8623	−1.37029
$135$	5.91766	0.509311
$136$	−4.04230	−0.346624
$137$	−10.7929	−0.922097	−0.461049	−	0.887375i	$-0.652527\pi$
$137$	−10.7929	−0.922097	−0.461049	+	0.887375i	$0.652527\pi$
$138$	−3.90222	−0.332179
$139$	−10.5295	−0.893098	−0.446549	−	0.894759i	$-0.647347\pi$
$139$	−10.5295	−0.893098	−0.446549	+	0.894759i	$0.647347\pi$
$140$	2.59253	0.219109
$141$	13.1542	1.10778
$142$	−10.5527	−0.885561
$143$	17.5991	1.47171
$144$	−0.957895	−0.0798246
$145$	3.21077	0.266640
$146$	−1.18129	−0.0977638
$147$	1.22924	0.101386
$148$	−0.115265	−0.00947473
$149$	4.82279	0.395098	0.197549	−	0.980293i	$-0.436702\pi$
$149$	4.82279	0.395098	0.197549	+	0.980293i	$0.436702\pi$
$150$	−5.58077	−0.455668
$151$	−14.2112	−1.15649	−0.578244	−	0.815864i	$-0.696262\pi$
$151$	−14.2112	−1.15649	−0.578244	+	0.815864i	$0.696262\pi$
$152$	0.410080	0.0332619
$153$	−3.87210	−0.313041
$154$	13.9568	1.12467
$155$	−9.67080	−0.776777
$156$	4.46500	0.357486
$157$	−14.6982	−1.17304	−0.586521	−	0.809934i	$-0.699503\pi$
$157$	−14.6982	−1.17304	−0.586521	+	0.809934i	$0.699503\pi$
$158$	−4.79709	−0.381636
$159$	6.32231	0.501392
$160$	−1.04628	−0.0827155
$161$	−6.76628	−0.533257
$162$	5.20875	0.409238
$163$	8.78595	0.688169	0.344084	−	0.938939i	$-0.388189\pi$
$163$	8.78595	0.688169	0.344084	+	0.938939i	$0.388189\pi$
$164$	3.90405	0.304855
$165$	8.42158	0.655619
$166$	0.673126	0.0522447
$167$	21.1277	1.63491	0.817456	−	0.575990i	$-0.195383\pi$
$167$	21.1277	1.63491	0.817456	+	0.575990i	$0.195383\pi$
$168$	3.54092	0.273188
$169$	−3.23743	−0.249033
$170$	−4.22937	−0.324378
$171$	0.392814	0.0300392
$172$	−8.38888	−0.639646
$173$	10.0064	0.760770	0.380385	−	0.924828i	$-0.375792\pi$
$173$	10.0064	0.760770	0.380385	+	0.924828i	$0.375792\pi$
$174$	4.38532	0.332450
$175$	−9.67680	−0.731498
$176$	−5.63258	−0.424572
$177$	−2.11793	−0.159194
$178$	7.20463	0.540010
$179$	22.9939	1.71864	0.859322	−	0.511435i	$-0.170886\pi$
$179$	22.9939	1.71864	0.859322	+	0.511435i	$0.170886\pi$
$180$	−1.00222	−0.0747014
$181$	−2.91056	−0.216340	−0.108170	−	0.994132i	$-0.534499\pi$
$181$	−2.91056	−0.216340	−0.108170	+	0.994132i	$0.534499\pi$
$182$	7.74211	0.573883
$183$	−14.8359	−1.09670
$184$	2.73069	0.201309
$185$	−0.120599	−0.00886664
$186$	−13.2085	−0.968496
$187$	−22.7686	−1.66500
$188$	−9.20502	−0.671345
$189$	14.0146	1.01941
$190$	0.429058	0.0311271
$191$	−3.96415	−0.286836	−0.143418	−	0.989662i	$-0.545809\pi$
$191$	−3.96415	−0.286836	−0.143418	+	0.989662i	$0.545809\pi$
$192$	−1.42902	−0.103131
$193$	14.3862	1.03554	0.517772	−	0.855519i	$-0.326762\pi$
$193$	14.3862	1.03554	0.517772	+	0.855519i	$0.326762\pi$
$194$	−5.04523	−0.362227
$195$	4.67163	0.334542
$196$	−0.860199	−0.0614428
$197$	−24.3226	−1.73291	−0.866457	−	0.499252i	$-0.833608\pi$
$197$	−24.3226	−1.73291	−0.866457	+	0.499252i	$0.833608\pi$
$198$	−5.39542	−0.383436
$199$	−14.9722	−1.06135	−0.530674	−	0.847576i	$-0.678061\pi$
$199$	−14.9722	−1.06135	−0.530674	+	0.847576i	$0.678061\pi$
$200$	3.90530	0.276147
$201$	−22.6675	−1.59884
$202$	−18.0585	−1.27059
$203$	7.60395	0.533693
$204$	−5.77654	−0.404439
$205$	4.08472	0.285289
$206$	−8.31352	−0.579230
$207$	2.61572	0.181805
$208$	−3.12451	−0.216646
$209$	2.30981	0.159773
$210$	3.70479	0.255655
$211$	−16.5996	−1.14276	−0.571381	−	0.820685i	$-0.693592\pi$
$211$	−16.5996	−1.14276	−0.571381	+	0.820685i	$0.693592\pi$
$212$	−4.42422	−0.303857
$213$	−15.0800	−1.03327
$214$	4.02270	0.274986
$215$	−8.77710	−0.598593
$216$	−5.65592	−0.384837
$217$	−22.9030	−1.55476
$218$	−6.82440	−0.462206
$219$	−1.68808	−0.114070
$220$	−5.89324	−0.397322
$221$	−12.6302	−0.849600
$222$	−0.164716	−0.0110550
$223$	22.3447	1.49631	0.748157	−	0.663521i	$-0.230939\pi$
$223$	22.3447	1.49631	0.748157	+	0.663521i	$0.230939\pi$
$224$	−2.47786	−0.165559
$225$	3.74087	0.249391
$226$	−10.1804	−0.677190
$227$	−14.9562	−0.992680	−0.496340	−	0.868128i	$-0.665323\pi$
$227$	−14.9562	−0.992680	−0.496340	+	0.868128i	$0.665323\pi$
$228$	0.586014	0.0388097
$229$	25.6196	1.69299	0.846496	−	0.532396i	$-0.178708\pi$
$229$	25.6196	1.69299	0.846496	+	0.532396i	$0.178708\pi$
$230$	2.85706	0.188389
$231$	19.9445	1.31225
$232$	−3.06876	−0.201474
$233$	21.2986	1.39532	0.697658	−	0.716431i	$-0.254225\pi$
$233$	21.2986	1.39532	0.697658	+	0.716431i	$0.254225\pi$
$234$	−2.99295	−0.195655
$235$	−9.63101	−0.628258
$236$	1.48209	0.0964755
$237$	−6.85515	−0.445290
$238$	−10.0163	−0.649258
$239$	−15.4723	−1.00082	−0.500411	−	0.865788i	$-0.666818\pi$
$239$	−15.4723	−1.00082	−0.500411	+	0.865788i	$0.666818\pi$
$240$	−1.49515	−0.0965118
$241$	15.7866	1.01691	0.508453	−	0.861090i	$-0.330218\pi$
$241$	15.7866	1.01691	0.508453	+	0.861090i	$0.330218\pi$
$242$	−20.7260	−1.33232
$243$	−9.52434	−0.610987
$244$	10.3819	0.664630
$245$	−0.900007	−0.0574993
$246$	5.57897	0.355702
$247$	1.28130	0.0815271
$248$	9.24305	0.586934
$249$	0.961912	0.0609587
$250$	9.31742	0.589285
$251$	−18.5481	−1.17075	−0.585373	−	0.810764i	$-0.699052\pi$
$251$	−18.5481	−1.17075	−0.585373	+	0.810764i	$0.699052\pi$
$252$	−2.37353	−0.149518
$253$	15.3808	0.966985
$254$	12.8792	0.808116
$255$	−6.04386	−0.378481
$256$	1.00000	0.0625000
$257$	−11.7027	−0.729993	−0.364997	−	0.931009i	$-0.618930\pi$
$257$	−11.7027	−0.729993	−0.364997	+	0.931009i	$0.618930\pi$
$258$	−11.9879	−0.746334
$259$	−0.285611	−0.0177470
$260$	−3.26911	−0.202741
$261$	−2.93955	−0.181953
$262$	−5.58975	−0.345336
$263$	26.7386	1.64877	0.824387	−	0.566026i	$-0.191520\pi$
$263$	26.7386	1.64877	0.824387	+	0.566026i	$0.191520\pi$
$264$	−8.04908	−0.495387
$265$	−4.62897	−0.284355
$266$	1.01612	0.0623024
$267$	10.2956	0.630079
$268$	15.8623	0.968942
$269$	28.3117	1.72620	0.863098	−	0.505036i	$-0.168521\pi$
$269$	28.3117	1.72620	0.863098	+	0.505036i	$0.168521\pi$
$270$	−5.91766	−0.360138
$271$	−1.71897	−0.104420	−0.0522100	−	0.998636i	$-0.516627\pi$
$271$	−1.71897	−0.104420	−0.0522100	+	0.998636i	$0.516627\pi$
$272$	4.04230	0.245100
$273$	11.0636	0.669602
$274$	10.7929	0.652021
$275$	21.9969	1.32647
$276$	3.90222	0.234886
$277$	−4.96279	−0.298185	−0.149092	−	0.988823i	$-0.547635\pi$
$277$	−4.96279	−0.298185	−0.149092	+	0.988823i	$0.547635\pi$
$278$	10.5295	0.631516
$279$	8.85387	0.530067
$280$	−2.59253	−0.154933
$281$	16.1873	0.965651	0.482826	−	0.875716i	$-0.339610\pi$
$281$	16.1873	0.965651	0.482826	+	0.875716i	$0.339610\pi$
$282$	−13.1542	−0.783320
$283$	0.253011	0.0150399	0.00751996	−	0.999972i	$-0.497606\pi$
$283$	0.253011	0.0150399	0.00751996	+	0.999972i	$0.497606\pi$
$284$	10.5527	0.626186
$285$	0.613133	0.0363189
$286$	−17.5991	−1.04065
$287$	9.67369	0.571020
$288$	0.957895	0.0564445
$289$	−0.659810	−0.0388124
$290$	−3.21077	−0.188543
$291$	−7.20975	−0.422643
$292$	1.18129	0.0691295
$293$	−18.9781	−1.10872	−0.554358	−	0.832279i	$-0.687036\pi$
$293$	−18.9781	−1.10872	−0.554358	+	0.832279i	$0.687036\pi$
$294$	−1.22924	−0.0716909
$295$	1.55067	0.0902836
$296$	0.115265	0.00669965
$297$	−31.8574	−1.84856
$298$	−4.82279	−0.279377
$299$	8.53207	0.493423
$300$	5.58077	0.322206
$301$	−20.7865	−1.19811
$302$	14.2112	0.817761
$303$	−25.8060	−1.48252
$304$	−0.410080	−0.0235197
$305$	10.8623	0.621974
$306$	3.87210	0.221353
$307$	−2.03967	−0.116410	−0.0582050	−	0.998305i	$-0.518538\pi$
$307$	−2.03967	−0.116410	−0.0582050	+	0.998305i	$0.518538\pi$
$308$	−13.9568	−0.795260
$309$	−11.8802	−0.675841
$310$	9.67080	0.549264
$311$	22.6388	1.28373	0.641863	−	0.766819i	$-0.278162\pi$
$311$	22.6388	1.28373	0.641863	+	0.766819i	$0.278162\pi$
$312$	−4.46500	−0.252781
$313$	−29.8396	−1.68664	−0.843318	−	0.537415i	$-0.819401\pi$
$313$	−29.8396	−1.68664	−0.843318	+	0.537415i	$0.819401\pi$
$314$	14.6982	0.829466
$315$	−2.48337	−0.139922
$316$	4.79709	0.269857
$317$	32.2926	1.81373	0.906866	−	0.421418i	$-0.138468\pi$
$317$	32.2926	1.81373	0.906866	+	0.421418i	$0.138468\pi$
$318$	−6.32231	−0.354538
$319$	−17.2850	−0.967775
$320$	1.04628	0.0584887
$321$	5.74853	0.320852
$322$	6.76628	0.377070
$323$	−1.65767	−0.0922350
$324$	−5.20875	−0.289375
$325$	12.2022	0.676854
$326$	−8.78595	−0.486609
$327$	−9.75221	−0.539299
$328$	−3.90405	−0.215565
$329$	−22.8088	−1.25749
$330$	−8.42158	−0.463593
$331$	6.23774	0.342857	0.171429	−	0.985197i	$-0.445162\pi$
$331$	6.23774	0.342857	0.171429	+	0.985197i	$0.445162\pi$
$332$	−0.673126	−0.0369426
$333$	0.110412	0.00605053
$334$	−21.1277	−1.15606
$335$	16.5963	0.906754
$336$	−3.54092	−0.193173
$337$	−12.0017	−0.653774	−0.326887	−	0.945063i	$-0.606000\pi$
$337$	−12.0017	−0.653774	−0.326887	+	0.945063i	$0.606000\pi$
$338$	3.23743	0.176093
$339$	−14.5480	−0.790140
$340$	4.22937	0.229370
$341$	52.0622	2.81933
$342$	−0.392814	−0.0212409
$343$	−19.4765	−1.05163
$344$	8.38888	0.452298
$345$	4.08280	0.219811
$346$	−10.0064	−0.537946
$347$	24.4376	1.31188	0.655938	−	0.754815i	$-0.272273\pi$
$347$	24.4376	1.31188	0.655938	+	0.754815i	$0.272273\pi$
$348$	−4.38532	−0.235078
$349$	−25.3807	−1.35860	−0.679299	−	0.733861i	$-0.737716\pi$
$349$	−25.3807	−1.35860	−0.679299	+	0.733861i	$0.737716\pi$
$350$	9.67680	0.517247
$351$	−17.6720	−0.943261
$352$	5.63258	0.300218
$353$	13.6988	0.729115	0.364557	−	0.931181i	$-0.381220\pi$
$353$	13.6988	0.729115	0.364557	+	0.931181i	$0.381220\pi$
$354$	2.11793	0.112567
$355$	11.0410	0.585997
$356$	−7.20463	−0.381845
$357$	−14.3135	−0.757549
$358$	−22.9939	−1.21526
$359$	−14.8792	−0.785292	−0.392646	−	0.919690i	$-0.628440\pi$
$359$	−14.8792	−0.785292	−0.392646	+	0.919690i	$0.628440\pi$
$360$	1.00222	0.0528218
$361$	−18.8318	−0.991149
$362$	2.91056	0.152976
$363$	−29.6179	−1.55454
$364$	−7.74211	−0.405797
$365$	1.23595	0.0646927
$366$	14.8359	0.775485
$367$	29.7454	1.55270	0.776349	−	0.630303i	$-0.217069\pi$
$367$	29.7454	1.55270	0.776349	+	0.630303i	$0.217069\pi$
$368$	−2.73069	−0.142347
$369$	−3.73967	−0.194679
$370$	0.120599	0.00626966
$371$	−10.9626	−0.569151
$372$	13.2085	0.684830
$373$	−5.69766	−0.295014	−0.147507	−	0.989061i	$-0.547125\pi$
$373$	−5.69766	−0.295014	−0.147507	+	0.989061i	$0.547125\pi$
$374$	22.7686	1.17734
$375$	13.3148	0.687573
$376$	9.20502	0.474713
$377$	−9.58836	−0.493826
$378$	−14.0146	−0.720833
$379$	−0.337236	−0.0173227	−0.00866133	−	0.999962i	$-0.502757\pi$
$379$	−0.337236	−0.0173227	−0.00866133	+	0.999962i	$0.502757\pi$
$380$	−0.429058	−0.0220102
$381$	18.4047	0.942903
$382$	3.96415	0.202823
$383$	3.15866	0.161400	0.0807001	−	0.996738i	$-0.474284\pi$
$383$	3.15866	0.161400	0.0807001	+	0.996738i	$0.474284\pi$
$384$	1.42902	0.0729245
$385$	−14.6026	−0.744220
$386$	−14.3862	−0.732240
$387$	8.03567	0.408476
$388$	5.04523	0.256133
$389$	31.8653	1.61563	0.807817	−	0.589433i	$-0.200649\pi$
$389$	31.8653	1.61563	0.807817	+	0.589433i	$0.200649\pi$
$390$	−4.67163	−0.236557
$391$	−11.0383	−0.558230
$392$	0.860199	0.0434466
$393$	−7.98788	−0.402935
$394$	24.3226	1.22535
$395$	5.01908	0.252538
$396$	5.39542	0.271130
$397$	−21.2769	−1.06786	−0.533929	−	0.845529i	$-0.679285\pi$
$397$	−21.2769	−1.06786	−0.533929	+	0.845529i	$0.679285\pi$
$398$	14.9722	0.750487
$399$	1.45206	0.0726940
$400$	−3.90530	−0.195265
$401$	16.7041	0.834164	0.417082	−	0.908869i	$-0.363053\pi$
$401$	16.7041	0.834164	0.417082	+	0.908869i	$0.363053\pi$
$402$	22.6675	1.13055
$403$	28.8800	1.43862
$404$	18.0585	0.898445
$405$	−5.44980	−0.270803
$406$	−7.60395	−0.377378
$407$	0.649240	0.0321816
$408$	5.77654	0.285981
$409$	10.8784	0.537903	0.268952	−	0.963154i	$-0.413323\pi$
$409$	10.8784	0.537903	0.268952	+	0.963154i	$0.413323\pi$
$410$	−4.08472	−0.201730
$411$	15.4233	0.760773
$412$	8.31352	0.409578
$413$	3.67240	0.180707
$414$	−2.61572	−0.128555
$415$	−0.704277	−0.0345716
$416$	3.12451	0.153192
$417$	15.0469	0.736847
$418$	−2.30981	−0.112976
$419$	17.2442	0.842435	0.421217	−	0.906960i	$-0.361603\pi$
$419$	17.2442	0.842435	0.421217	+	0.906960i	$0.361603\pi$
$420$	−3.70479	−0.180775
$421$	−13.9307	−0.678940	−0.339470	−	0.940617i	$-0.610248\pi$
$421$	−13.9307	−0.678940	−0.339470	+	0.940617i	$0.610248\pi$
$422$	16.5996	0.808055
$423$	8.81744	0.428719
$424$	4.42422	0.214859
$425$	−15.7864	−0.765753
$426$	15.0800	0.730629
$427$	25.7248	1.24491
$428$	−4.02270	−0.194445
$429$	−25.1495	−1.21423
$430$	8.77710	0.423269
$431$	−26.4683	−1.27493	−0.637467	−	0.770477i	$-0.720018\pi$
$431$	−26.4683	−1.27493	−0.637467	+	0.770477i	$0.720018\pi$
$432$	5.65592	0.272121
$433$	19.0094	0.913534	0.456767	−	0.889586i	$-0.349007\pi$
$433$	19.0094	0.913534	0.456767	+	0.889586i	$0.349007\pi$
$434$	22.9030	1.09938
$435$	−4.58826	−0.219990
$436$	6.82440	0.326829
$437$	1.11980	0.0535674
$438$	1.68808	0.0806597
$439$	16.1501	0.770804	0.385402	−	0.922749i	$-0.374063\pi$
$439$	16.1501	0.770804	0.385402	+	0.922749i	$0.374063\pi$
$440$	5.89324	0.280949
$441$	0.823980	0.0392372
$442$	12.6302	0.600758
$443$	29.5066	1.40190	0.700951	−	0.713210i	$-0.252759\pi$
$443$	29.5066	1.40190	0.700951	+	0.713210i	$0.252759\pi$
$444$	0.164716	0.00781709
$445$	−7.53804	−0.357337
$446$	−22.3447	−1.05805
$447$	−6.89187	−0.325974
$448$	2.47786	0.117068
$449$	24.2727	1.14550	0.572749	−	0.819731i	$-0.305877\pi$
$449$	24.2727	1.14550	0.572749	+	0.819731i	$0.305877\pi$
$450$	−3.74087	−0.176346
$451$	−21.9899	−1.03546
$452$	10.1804	0.478846
$453$	20.3081	0.954157
$454$	14.9562	0.701930
$455$	−8.10039	−0.379752
$456$	−0.586014	−0.0274426
$457$	−1.77575	−0.0830660	−0.0415330	−	0.999137i	$-0.513224\pi$
$457$	−1.77575	−0.0830660	−0.0415330	+	0.999137i	$0.513224\pi$
$458$	−25.6196	−1.19713
$459$	22.8629	1.06715
$460$	−2.85706	−0.133211
$461$	39.9045	1.85854	0.929270	−	0.369401i	$-0.120437\pi$
$461$	39.9045	1.85854	0.929270	+	0.369401i	$0.120437\pi$
$462$	−19.9445	−0.927903
$463$	38.0280	1.76731	0.883654	−	0.468140i	$-0.155076\pi$
$463$	38.0280	1.76731	0.883654	+	0.468140i	$0.155076\pi$
$464$	3.06876	0.142463
$465$	13.8198	0.640877
$466$	−21.2986	−0.986638
$467$	−2.29115	−0.106022	−0.0530110	−	0.998594i	$-0.516882\pi$
$467$	−2.29115	−0.106022	−0.0530110	+	0.998594i	$0.516882\pi$
$468$	2.99295	0.138349
$469$	39.3045	1.81491
$470$	9.63101	0.444245
$471$	21.0040	0.967814
$472$	−1.48209	−0.0682185
$473$	47.2511	2.17261
$474$	6.85515	0.314867
$475$	1.60149	0.0734813
$476$	10.0163	0.459095
$477$	4.23794	0.194042
$478$	15.4723	0.707688
$479$	5.50756	0.251647	0.125823	−	0.992053i	$-0.459843\pi$
$479$	5.50756	0.251647	0.125823	+	0.992053i	$0.459843\pi$
$480$	1.49515	0.0682441
$481$	0.360147	0.0164213
$482$	−15.7866	−0.719060
$483$	9.66916	0.439962
$484$	20.7260	0.942090
$485$	5.27871	0.239694
$486$	9.52434	0.432033
$487$	−2.53773	−0.114995	−0.0574977	−	0.998346i	$-0.518312\pi$
$487$	−2.53773	−0.114995	−0.0574977	+	0.998346i	$0.518312\pi$
$488$	−10.3819	−0.469965
$489$	−12.5553	−0.567771
$490$	0.900007	0.0406582
$491$	−3.36557	−0.151886	−0.0759431	−	0.997112i	$-0.524197\pi$
$491$	−3.36557	−0.151886	−0.0759431	+	0.997112i	$0.524197\pi$
$492$	−5.57897	−0.251519
$493$	12.4048	0.558686
$494$	−1.28130	−0.0576484
$495$	5.64511	0.253729
$496$	−9.24305	−0.415025
$497$	26.1481	1.17290
$498$	−0.961912	−0.0431043
$499$	16.3693	0.732791	0.366395	−	0.930459i	$-0.380592\pi$
$499$	16.3693	0.732791	0.366395	+	0.930459i	$0.380592\pi$
$500$	−9.31742	−0.416688
$501$	−30.1920	−1.34888
$502$	18.5481	0.827843
$503$	−8.35135	−0.372368	−0.186184	−	0.982515i	$-0.559612\pi$
$503$	−8.35135	−0.372368	−0.186184	+	0.982515i	$0.559612\pi$
$504$	2.37353	0.105726
$505$	18.8942	0.840782
$506$	−15.3808	−0.683762
$507$	4.62636	0.205464
$508$	−12.8792	−0.571424
$509$	35.8993	1.59121	0.795603	−	0.605818i	$-0.207154\pi$
$509$	35.8993	1.59121	0.795603	+	0.605818i	$0.207154\pi$
$510$	6.04386	0.267627
$511$	2.92706	0.129486
$512$	−1.00000	−0.0441942
$513$	−2.31938	−0.102403
$514$	11.7027	0.516183
$515$	8.69824	0.383290
$516$	11.9879	0.527738
$517$	51.8480	2.28027
$518$	0.285611	0.0125490
$519$	−14.2993	−0.627670
$520$	3.26911	0.143360
$521$	2.35360	0.103113	0.0515566	−	0.998670i	$-0.483582\pi$
$521$	2.35360	0.103113	0.0515566	+	0.998670i	$0.483582\pi$
$522$	2.93955	0.128660
$523$	−28.4811	−1.24539	−0.622695	−	0.782464i	$-0.713962\pi$
$523$	−28.4811	−1.24539	−0.622695	+	0.782464i	$0.713962\pi$
$524$	5.58975	0.244190
$525$	13.8284	0.603519
$526$	−26.7386	−1.16586
$527$	−37.3632	−1.62757
$528$	8.04908	0.350291
$529$	−15.5433	−0.675797
$530$	4.62897	0.201069
$531$	−1.41968	−0.0616089
$532$	−1.01612	−0.0440545
$533$	−12.1982	−0.528364
$534$	−10.2956	−0.445533
$535$	−4.20886	−0.181965
$536$	−15.8623	−0.685145
$537$	−32.8588	−1.41796
$538$	−28.3117	−1.22060
$539$	4.84514	0.208695
$540$	5.91766	0.254656
$541$	37.5815	1.61575	0.807877	−	0.589351i	$-0.200616\pi$
$541$	37.5815	1.61575	0.807877	+	0.589351i	$0.200616\pi$
$542$	1.71897	0.0738361
$543$	4.15926	0.178491
$544$	−4.04230	−0.173312
$545$	7.14021	0.305853
$546$	−11.0636	−0.473480
$547$	12.9095	0.551970	0.275985	−	0.961162i	$-0.410996\pi$
$547$	12.9095	0.551970	0.275985	+	0.961162i	$0.410996\pi$
$548$	−10.7929	−0.461049
$549$	−9.94473	−0.424431
$550$	−21.9969	−0.937953
$551$	−1.25844	−0.0536112
$552$	−3.90222	−0.166089
$553$	11.8865	0.505466
$554$	4.96279	0.210849
$555$	0.172339	0.00731539
$556$	−10.5295	−0.446549
$557$	18.0747	0.765849	0.382924	−	0.923780i	$-0.374917\pi$
$557$	18.0747	0.765849	0.382924	+	0.923780i	$0.374917\pi$
$558$	−8.85387	−0.374814
$559$	26.2112	1.10861
$560$	2.59253	0.109554
$561$	32.5368	1.37371
$562$	−16.1873	−0.682819
$563$	−23.6011	−0.994667	−0.497334	−	0.867559i	$-0.665688\pi$
$563$	−23.6011	−0.994667	−0.497334	+	0.867559i	$0.665688\pi$
$564$	13.1542	0.553891
$565$	10.6515	0.448113
$566$	−0.253011	−0.0106348
$567$	−12.9066	−0.542025
$568$	−10.5527	−0.442781
$569$	−1.51779	−0.0636292	−0.0318146	−	0.999494i	$-0.510129\pi$
$569$	−1.51779	−0.0636292	−0.0318146	+	0.999494i	$0.510129\pi$
$570$	−0.613133	−0.0256813
$571$	−3.99656	−0.167251	−0.0836255	−	0.996497i	$-0.526650\pi$
$571$	−3.99656	−0.167251	−0.0836255	+	0.996497i	$0.526650\pi$
$572$	17.5991	0.735854
$573$	5.66486	0.236653
$574$	−9.67369	−0.403772
$575$	10.6642	0.444727
$576$	−0.957895	−0.0399123
$577$	−43.4143	−1.80736	−0.903680	−	0.428209i	$-0.859145\pi$
$577$	−43.4143	−1.80736	−0.903680	+	0.428209i	$0.859145\pi$
$578$	0.659810	0.0274445
$579$	−20.5582	−0.854372
$580$	3.21077	0.133320
$581$	−1.66791	−0.0691967
$582$	7.20975	0.298854
$583$	24.9198	1.03207
$584$	−1.18129	−0.0488819
$585$	3.13146	0.129470
$586$	18.9781	0.783980
$587$	19.3179	0.797335	0.398667	−	0.917096i	$-0.369473\pi$
$587$	19.3179	0.797335	0.398667	+	0.917096i	$0.369473\pi$
$588$	1.22924	0.0506931
$589$	3.79039	0.156180
$590$	−1.55067	−0.0638402
$591$	34.7575	1.42973
$592$	−0.115265	−0.00473737
$593$	26.7465	1.09835	0.549173	−	0.835709i	$-0.314943\pi$
$593$	26.7465	1.09835	0.549173	+	0.835709i	$0.314943\pi$
$594$	31.8574	1.30713
$595$	10.4798	0.429630
$596$	4.82279	0.197549
$597$	21.3956	0.875662
$598$	−8.53207	−0.348902
$599$	−45.2308	−1.84808	−0.924041	−	0.382293i	$-0.875134\pi$
$599$	−45.2308	−1.84808	−0.924041	+	0.382293i	$0.875134\pi$
$600$	−5.58077	−0.227834
$601$	10.7469	0.438376	0.219188	−	0.975683i	$-0.429659\pi$
$601$	10.7469	0.438376	0.219188	+	0.975683i	$0.429659\pi$
$602$	20.7865	0.847194
$603$	−15.1944	−0.618763
$604$	−14.2112	−0.578244
$605$	21.6851	0.881625
$606$	25.8060	1.04830
$607$	−23.7022	−0.962043	−0.481022	−	0.876709i	$-0.659734\pi$
$607$	−23.7022	−0.962043	−0.481022	+	0.876709i	$0.659734\pi$
$608$	0.410080	0.0166309
$609$	−10.8662	−0.440321
$610$	−10.8623	−0.439802
$611$	28.7612	1.16355
$612$	−3.87210	−0.156520
$613$	38.4505	1.55300	0.776501	−	0.630116i	$-0.216993\pi$
$613$	38.4505	1.55300	0.776501	+	0.630116i	$0.216993\pi$
$614$	2.03967	0.0823143
$615$	−5.83715	−0.235377
$616$	13.9568	0.562334
$617$	−17.1102	−0.688831	−0.344415	−	0.938817i	$-0.611923\pi$
$617$	−17.1102	−0.688831	−0.344415	+	0.938817i	$0.611923\pi$
$618$	11.8802	0.477892
$619$	6.21331	0.249734	0.124867	−	0.992173i	$-0.460150\pi$
$619$	6.21331	0.249734	0.124867	+	0.992173i	$0.460150\pi$
$620$	−9.67080	−0.388389
$621$	−15.4446	−0.619769
$622$	−22.6388	−0.907732
$623$	−17.8521	−0.715228
$624$	4.46500	0.178743
$625$	9.77791	0.391116
$626$	29.8396	1.19263
$627$	−3.30077	−0.131820
$628$	−14.6982	−0.586521
$629$	−0.465936	−0.0185781
$630$	2.48337	0.0989400
$631$	−4.92319	−0.195989	−0.0979946	−	0.995187i	$-0.531243\pi$
$631$	−4.92319	−0.195989	−0.0979946	+	0.995187i	$0.531243\pi$
$632$	−4.79709	−0.190818
$633$	23.7212	0.942832
$634$	−32.2926	−1.28250
$635$	−13.4753	−0.534750
$636$	6.32231	0.250696
$637$	2.68770	0.106491
$638$	17.2850	0.684320
$639$	−10.1084	−0.399880
$640$	−1.04628	−0.0413578
$641$	−7.81280	−0.308587	−0.154293	−	0.988025i	$-0.549310\pi$
$641$	−7.81280	−0.308587	−0.154293	+	0.988025i	$0.549310\pi$
$642$	−5.74853	−0.226876
$643$	−3.62353	−0.142898	−0.0714490	−	0.997444i	$-0.522762\pi$
$643$	−3.62353	−0.142898	−0.0714490	+	0.997444i	$0.522762\pi$
$644$	−6.76628	−0.266629
$645$	12.5427	0.493867
$646$	1.65767	0.0652200
$647$	−34.4500	−1.35437	−0.677185	−	0.735813i	$-0.736800\pi$
$647$	−34.4500	−1.35437	−0.677185	+	0.735813i	$0.736800\pi$
$648$	5.20875	0.204619
$649$	−8.34796	−0.327686
$650$	−12.2022	−0.478608
$651$	32.7289	1.28275
$652$	8.78595	0.344084
$653$	44.7349	1.75061	0.875306	−	0.483570i	$-0.160660\pi$
$653$	44.7349	1.75061	0.875306	+	0.483570i	$0.160660\pi$
$654$	9.75221	0.381342
$655$	5.84843	0.228517
$656$	3.90405	0.152427
$657$	−1.13155	−0.0441459
$658$	22.8088	0.889178
$659$	−30.7929	−1.19952	−0.599761	−	0.800180i	$-0.704738\pi$
$659$	−30.7929	−1.19952	−0.599761	+	0.800180i	$0.704738\pi$
$660$	8.42158	0.327809
$661$	−36.4934	−1.41943	−0.709714	−	0.704490i	$-0.751176\pi$
$661$	−36.4934	−1.41943	−0.709714	+	0.704490i	$0.751176\pi$
$662$	−6.23774	−0.242437
$663$	18.0489	0.700959
$664$	0.673126	0.0261224
$665$	−1.06315	−0.0412270
$666$	−0.110412	−0.00427837
$667$	−8.37983	−0.324468
$668$	21.1277	0.817456
$669$	−31.9311	−1.23453
$670$	−16.5963	−0.641172
$671$	−58.4766	−2.25747
$672$	3.54092	0.136594
$673$	4.86531	0.187544	0.0937720	−	0.995594i	$-0.470108\pi$
$673$	4.86531	0.187544	0.0937720	+	0.995594i	$0.470108\pi$
$674$	12.0017	0.462288
$675$	−22.0881	−0.850171
$676$	−3.23743	−0.124517
$677$	35.5396	1.36590	0.682949	−	0.730466i	$-0.260697\pi$
$677$	35.5396	1.36590	0.682949	+	0.730466i	$0.260697\pi$
$678$	14.5480	0.558713
$679$	12.5014	0.479759
$680$	−4.22937	−0.162189
$681$	21.3728	0.819007
$682$	−52.0622	−1.99357
$683$	35.8024	1.36994	0.684970	−	0.728572i	$-0.259815\pi$
$683$	35.8024	1.36994	0.684970	+	0.728572i	$0.259815\pi$
$684$	0.392814	0.0150196
$685$	−11.2923	−0.431458
$686$	19.4765	0.743616
$687$	−36.6110	−1.39680
$688$	−8.38888	−0.319823
$689$	13.8235	0.526635
$690$	−4.08280	−0.155430
$691$	−14.4030	−0.547917	−0.273958	−	0.961742i	$-0.588333\pi$
$691$	−14.4030	−0.547917	−0.273958	+	0.961742i	$0.588333\pi$
$692$	10.0064	0.380385
$693$	13.3691	0.507851
$694$	−24.4376	−0.927637
$695$	−11.0167	−0.417889
$696$	4.38532	0.166225
$697$	15.7813	0.597760
$698$	25.3807	0.960674
$699$	−30.4362	−1.15120
$700$	−9.67680	−0.365749
$701$	−19.1824	−0.724510	−0.362255	−	0.932079i	$-0.617993\pi$
$701$	−19.1824	−0.724510	−0.362255	+	0.932079i	$0.617993\pi$
$702$	17.6720	0.666986
$703$	0.0472679	0.00178274
$704$	−5.63258	−0.212286
$705$	13.7629	0.518342
$706$	−13.6988	−0.515562
$707$	44.7465	1.68287
$708$	−2.11793	−0.0795968
$709$	1.87858	0.0705516	0.0352758	−	0.999378i	$-0.488769\pi$
$709$	1.87858	0.0705516	0.0352758	+	0.999378i	$0.488769\pi$
$710$	−11.0410	−0.414363
$711$	−4.59511	−0.172330
$712$	7.20463	0.270005
$713$	25.2399	0.945242
$714$	14.3135	0.535668
$715$	18.4135	0.688626
$716$	22.9939	0.859322
$717$	22.1103	0.825725
$718$	14.8792	0.555285
$719$	−29.6953	−1.10745	−0.553724	−	0.832701i	$-0.686794\pi$
$719$	−29.6953	−1.10745	−0.553724	+	0.832701i	$0.686794\pi$
$720$	−1.00222	−0.0373507
$721$	20.5997	0.767175
$722$	18.8318	0.700848
$723$	−22.5594	−0.838994
$724$	−2.91056	−0.108170
$725$	−11.9844	−0.445090
$726$	29.6179	1.09922
$727$	−23.0133	−0.853516	−0.426758	−	0.904366i	$-0.640344\pi$
$727$	−23.0133	−0.853516	−0.426758	+	0.904366i	$0.640344\pi$
$728$	7.74211	0.286942
$729$	29.2367	1.08284
$730$	−1.23595	−0.0457446
$731$	−33.9104	−1.25422
$732$	−14.8359	−0.548351
$733$	−10.8451	−0.400574	−0.200287	−	0.979737i	$-0.564188\pi$
$733$	−10.8451	−0.400574	−0.200287	+	0.979737i	$0.564188\pi$
$734$	−29.7454	−1.09792
$735$	1.28613	0.0474396
$736$	2.73069	0.100655
$737$	−89.3454	−3.29108
$738$	3.73967	0.137659
$739$	26.5343	0.976078	0.488039	−	0.872822i	$-0.337712\pi$
$739$	26.5343	0.976078	0.488039	+	0.872822i	$0.337712\pi$
$740$	−0.120599	−0.00443332
$741$	−1.83101	−0.0672637
$742$	10.9626	0.402450
$743$	−47.3041	−1.73542	−0.867709	−	0.497072i	$-0.834408\pi$
$743$	−47.3041	−1.73542	−0.867709	+	0.497072i	$0.834408\pi$
$744$	−13.2085	−0.484248
$745$	5.04598	0.184870
$746$	5.69766	0.208606
$747$	0.644784	0.0235914
$748$	−22.7686	−0.832502
$749$	−9.96770	−0.364212
$750$	−13.3148	−0.486188
$751$	7.23798	0.264118	0.132059	−	0.991242i	$-0.457841\pi$
$751$	7.23798	0.264118	0.132059	+	0.991242i	$0.457841\pi$
$752$	−9.20502	−0.335673
$753$	26.5057	0.965920
$754$	9.58836	0.349187
$755$	−14.8688	−0.541132
$756$	14.0146	0.509706
$757$	24.0078	0.872579	0.436290	−	0.899806i	$-0.356292\pi$
$757$	24.0078	0.872579	0.436290	+	0.899806i	$0.356292\pi$
$758$	0.337236	0.0122490
$759$	−21.9796	−0.797808
$760$	0.429058	0.0155636
$761$	−1.86937	−0.0677647	−0.0338823	−	0.999426i	$-0.510787\pi$
$761$	−1.86937	−0.0677647	−0.0338823	+	0.999426i	$0.510787\pi$
$762$	−18.4047	−0.666733
$763$	16.9099	0.612180
$764$	−3.96415	−0.143418
$765$	−4.05129	−0.146475
$766$	−3.15866	−0.114127
$767$	−4.63079	−0.167208
$768$	−1.42902	−0.0515654
$769$	−34.5170	−1.24471	−0.622357	−	0.782734i	$-0.713825\pi$
$769$	−34.5170	−1.24471	−0.622357	+	0.782734i	$0.713825\pi$
$770$	14.6026	0.526243
$771$	16.7234	0.602278
$772$	14.3862	0.517772
$773$	15.8467	0.569967	0.284984	−	0.958532i	$-0.408012\pi$
$773$	15.8467	0.569967	0.284984	+	0.958532i	$0.408012\pi$
$774$	−8.03567	−0.288836
$775$	36.0969	1.29664
$776$	−5.04523	−0.181113
$777$	0.408145	0.0146421
$778$	−31.8653	−1.14243
$779$	−1.60097	−0.0573607
$780$	4.67163	0.167271
$781$	−59.4388	−2.12689
$782$	11.0383	0.394728
$783$	17.3566	0.620276
$784$	−0.860199	−0.0307214
$785$	−15.3784	−0.548877
$786$	7.98788	0.284918
$787$	−4.08724	−0.145694	−0.0728472	−	0.997343i	$-0.523209\pi$
$787$	−4.08724	−0.145694	−0.0728472	+	0.997343i	$0.523209\pi$
$788$	−24.3226	−0.866457
$789$	−38.2101	−1.36032
$790$	−5.01908	−0.178571
$791$	25.2256	0.896920
$792$	−5.39542	−0.191718
$793$	−32.4382	−1.15191
$794$	21.2769	0.755090
$795$	6.61490	0.234606
$796$	−14.9722	−0.530674
$797$	9.43205	0.334100	0.167050	−	0.985948i	$-0.446576\pi$
$797$	9.43205	0.334100	0.167050	+	0.985948i	$0.446576\pi$
$798$	−1.45206	−0.0514024
$799$	−37.2095	−1.31638
$800$	3.90530	0.138073
$801$	6.90128	0.243845
$802$	−16.7041	−0.589843
$803$	−6.65368	−0.234803
$804$	−22.6675	−0.799422
$805$	−7.07940	−0.249516
$806$	−28.8800	−1.01725
$807$	−40.4581	−1.42419
$808$	−18.0585	−0.635296
$809$	2.92209	0.102735	0.0513676	−	0.998680i	$-0.483642\pi$
$809$	2.92209	0.102735	0.0513676	+	0.998680i	$0.483642\pi$
$810$	5.44980	0.191486
$811$	−26.2324	−0.921145	−0.460573	−	0.887622i	$-0.652356\pi$
$811$	−26.2324	−0.921145	−0.460573	+	0.887622i	$0.652356\pi$
$812$	7.60395	0.266846
$813$	2.45645	0.0861514
$814$	−0.649240	−0.0227559
$815$	9.19254	0.322001
$816$	−5.77654	−0.202219
$817$	3.44011	0.120354
$818$	−10.8784	−0.380355
$819$	7.41613	0.259140
$820$	4.08472	0.142644
$821$	45.4105	1.58484	0.792419	−	0.609978i	$-0.208822\pi$
$821$	45.4105	1.58484	0.792419	+	0.609978i	$0.208822\pi$
$822$	−15.4233	−0.537948
$823$	48.0007	1.67320	0.836600	−	0.547814i	$-0.184540\pi$
$823$	48.0007	1.67320	0.836600	+	0.547814i	$0.184540\pi$
$824$	−8.31352	−0.289615
$825$	−31.4341	−1.09440
$826$	−3.67240	−0.127779
$827$	−10.6007	−0.368622	−0.184311	−	0.982868i	$-0.559005\pi$
$827$	−10.6007	−0.368622	−0.184311	+	0.982868i	$0.559005\pi$
$828$	2.61572	0.0909024
$829$	17.9956	0.625012	0.312506	−	0.949916i	$-0.398831\pi$
$829$	17.9956	0.625012	0.312506	+	0.949916i	$0.398831\pi$
$830$	0.704277	0.0244458
$831$	7.09193	0.246016
$832$	−3.12451	−0.108323
$833$	−3.47718	−0.120477
$834$	−15.0469	−0.521030
$835$	22.1055	0.764991
$836$	2.30981	0.0798864
$837$	−52.2780	−1.80699
$838$	−17.2442	−0.595691
$839$	−5.35038	−0.184716	−0.0923578	−	0.995726i	$-0.529440\pi$
$839$	−5.35038	−0.184716	−0.0923578	+	0.995726i	$0.529440\pi$
$840$	3.70479	0.127827
$841$	−19.5827	−0.675267
$842$	13.9307	0.480083
$843$	−23.1320	−0.796707
$844$	−16.5996	−0.571381
$845$	−3.38725	−0.116525
$846$	−8.81744	−0.303150
$847$	51.3561	1.76462
$848$	−4.42422	−0.151928
$849$	−0.361558	−0.0124086
$850$	15.7864	0.541469
$851$	0.314753	0.0107896
$852$	−15.0800	−0.516633
$853$	54.8975	1.87965	0.939827	−	0.341650i	$-0.110986\pi$
$853$	54.8975	1.87965	0.939827	+	0.341650i	$0.110986\pi$
$854$	−25.7248	−0.880285
$855$	0.410992	0.0140556
$856$	4.02270	0.137493
$857$	−22.7267	−0.776331	−0.388165	−	0.921590i	$-0.626891\pi$
$857$	−22.7267	−0.776331	−0.388165	+	0.921590i	$0.626891\pi$
$858$	25.1495	0.858588
$859$	28.4351	0.970192	0.485096	−	0.874461i	$-0.338785\pi$
$859$	28.4351	0.970192	0.485096	+	0.874461i	$0.338785\pi$
$860$	−8.77710	−0.299297
$861$	−13.8239	−0.471118
$862$	26.4683	0.901515
$863$	−17.7880	−0.605509	−0.302755	−	0.953069i	$-0.597906\pi$
$863$	−17.7880	−0.605509	−0.302755	+	0.953069i	$0.597906\pi$
$864$	−5.65592	−0.192418
$865$	10.4694	0.355971
$866$	−19.0094	−0.645966
$867$	0.942883	0.0320220
$868$	−22.9030	−0.777379
$869$	−27.0200	−0.916590
$870$	4.58826	0.155557
$871$	−49.5618	−1.67934
$872$	−6.82440	−0.231103
$873$	−4.83280	−0.163566
$874$	−1.11980	−0.0378779
$875$	−23.0873	−0.780493
$876$	−1.68808	−0.0570350
$877$	−10.7059	−0.361512	−0.180756	−	0.983528i	$-0.557854\pi$
$877$	−10.7059	−0.361512	−0.180756	+	0.983528i	$0.557854\pi$
$878$	−16.1501	−0.545041
$879$	27.1202	0.914741
$880$	−5.89324	−0.198661
$881$	−2.46602	−0.0830824	−0.0415412	−	0.999137i	$-0.513227\pi$
$881$	−2.46602	−0.0830824	−0.0415412	+	0.999137i	$0.513227\pi$
$882$	−0.823980	−0.0277449
$883$	44.1025	1.48417	0.742084	−	0.670306i	$-0.233837\pi$
$883$	44.1025	1.48417	0.742084	+	0.670306i	$0.233837\pi$
$884$	−12.6302	−0.424800
$885$	−2.21595	−0.0744882
$886$	−29.5066	−0.991294
$887$	29.9480	1.00555	0.502777	−	0.864416i	$-0.332312\pi$
$887$	29.9480	1.00555	0.502777	+	0.864416i	$0.332312\pi$
$888$	−0.164716	−0.00552752
$889$	−31.9130	−1.07033
$890$	7.53804	0.252676
$891$	29.3387	0.982884
$892$	22.3447	0.748157
$893$	3.77479	0.126319
$894$	6.89187	0.230499
$895$	24.0580	0.804170
$896$	−2.47786	−0.0827796
$897$	−12.1925	−0.407097
$898$	−24.2727	−0.809989
$899$	−28.3647	−0.946015
$900$	3.74087	0.124696
$901$	−17.8840	−0.595804
$902$	21.9899	0.732182
$903$	29.7044	0.988500
$904$	−10.1804	−0.338595
$905$	−3.04525	−0.101228
$906$	−20.3081	−0.674691
$907$	28.8992	0.959582	0.479791	−	0.877383i	$-0.340712\pi$
$907$	28.8992	0.959582	0.479791	+	0.877383i	$0.340712\pi$
$908$	−14.9562	−0.496340
$909$	−17.2982	−0.573744
$910$	8.10039	0.268525
$911$	−25.4784	−0.844136	−0.422068	−	0.906564i	$-0.638696\pi$
$911$	−25.4784	−0.844136	−0.422068	+	0.906564i	$0.638696\pi$
$912$	0.586014	0.0194048
$913$	3.79144	0.125478
$914$	1.77575	0.0587365
$915$	−15.5225	−0.513157
$916$	25.6196	0.846496
$917$	13.8506	0.457388
$918$	−22.8629	−0.754589
$919$	−6.13019	−0.202216	−0.101108	−	0.994875i	$-0.532239\pi$
$919$	−6.13019	−0.202216	−0.101108	+	0.994875i	$0.532239\pi$
$920$	2.85706	0.0941945
$921$	2.91473	0.0960436
$922$	−39.9045	−1.31419
$923$	−32.9720	−1.08529
$924$	19.9445	0.656127
$925$	0.450145	0.0148007
$926$	−38.0280	−1.24968
$927$	−7.96347	−0.261555
$928$	−3.06876	−0.100737
$929$	39.8640	1.30790	0.653948	−	0.756540i	$-0.273112\pi$
$929$	39.8640	1.30790	0.653948	+	0.756540i	$0.273112\pi$
$930$	−13.8198	−0.453169
$931$	0.352750	0.0115609
$932$	21.2986	0.697658
$933$	−32.3513	−1.05913
$934$	2.29115	0.0749689
$935$	−23.8223	−0.779071
$936$	−2.99295	−0.0978277
$937$	12.5798	0.410965	0.205483	−	0.978661i	$-0.434124\pi$
$937$	12.5798	0.410965	0.205483	+	0.978661i	$0.434124\pi$
$938$	−39.3045	−1.28334
$939$	42.6415	1.39155
$940$	−9.63101	−0.314129
$941$	−40.1907	−1.31018	−0.655090	−	0.755551i	$-0.727369\pi$
$941$	−40.1907	−1.31018	−0.655090	+	0.755551i	$0.727369\pi$
$942$	−21.0040	−0.684348
$943$	−10.6607	−0.347162
$944$	1.48209	0.0482378
$945$	14.6632	0.476992
$946$	−47.2511	−1.53626
$947$	43.3284	1.40798	0.703992	−	0.710207i	$-0.251399\pi$
$947$	43.3284	1.40798	0.703992	+	0.710207i	$0.251399\pi$
$948$	−6.85515	−0.222645
$949$	−3.69094	−0.119813
$950$	−1.60149	−0.0519591
$951$	−46.1468	−1.49641
$952$	−10.0163	−0.324629
$953$	47.4064	1.53565	0.767823	−	0.640663i	$-0.221340\pi$
$953$	47.4064	1.53565	0.767823	+	0.640663i	$0.221340\pi$
$954$	−4.23794	−0.137208
$955$	−4.14760	−0.134213
$956$	−15.4723	−0.500411
$957$	24.7007	0.798459
$958$	−5.50756	−0.177941
$959$	−26.7433	−0.863585
$960$	−1.49515	−0.0482559
$961$	54.4340	1.75593
$962$	−0.360147	−0.0116116
$963$	3.85333	0.124172
$964$	15.7866	0.508453
$965$	15.0520	0.484541
$966$	−9.66916	−0.311100
$967$	11.2207	0.360835	0.180417	−	0.983590i	$-0.442255\pi$
$967$	11.2207	0.360835	0.180417	+	0.983590i	$0.442255\pi$
$968$	−20.7260	−0.666158
$969$	2.36884	0.0760982
$970$	−5.27871	−0.169489
$971$	31.3531	1.00617	0.503084	−	0.864237i	$-0.332199\pi$
$971$	31.3531	1.00617	0.503084	+	0.864237i	$0.332199\pi$
$972$	−9.52434	−0.305493
$973$	−26.0906	−0.836426
$974$	2.53773	0.0813140
$975$	−17.4372	−0.558436
$976$	10.3819	0.332315
$977$	33.4971	1.07167	0.535834	−	0.844324i	$-0.319997\pi$
$977$	33.4971	1.07167	0.535834	+	0.844324i	$0.319997\pi$
$978$	12.5553	0.401475
$979$	40.5807	1.29696
$980$	−0.900007	−0.0287497
$981$	−6.53705	−0.208712
$982$	3.36557	0.107400
$983$	23.3868	0.745924	0.372962	−	0.927847i	$-0.378342\pi$
$983$	23.3868	0.745924	0.372962	+	0.927847i	$0.378342\pi$
$984$	5.57897	0.177851
$985$	−25.4482	−0.810847
$986$	−12.4048	−0.395050
$987$	32.5942	1.03749
$988$	1.28130	0.0407636
$989$	22.9075	0.728415
$990$	−5.64511	−0.179413
$991$	34.1732	1.08555	0.542774	−	0.839879i	$-0.317374\pi$
$991$	34.1732	1.08555	0.542774	+	0.839879i	$0.317374\pi$
$992$	9.24305	0.293467
$993$	−8.91387	−0.282873
$994$	−26.1481	−0.829367
$995$	−15.6650	−0.496615
$996$	0.961912	0.0304794
$997$	5.47177	0.173293	0.0866464	−	0.996239i	$-0.472385\pi$
$997$	5.47177	0.173293	0.0866464	+	0.996239i	$0.472385\pi$
$998$	−16.3693	−0.518161
$999$	−0.651930	−0.0206262

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.c.1.16	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.c.1.16	✓	61	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.42902 q^{3} +1.00000 q^{4} +1.04628 q^{5} +1.42902 q^{6} +2.47786 q^{7} -1.00000 q^{8} -0.957895 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.42902 q^{3} +1.00000 q^{4} +1.04628 q^{5} +1.42902 q^{6} +2.47786 q^{7} -1.00000 q^{8} -0.957895 q^{9} -1.04628 q^{10} -5.63258 q^{11} -1.42902 q^{12} -3.12451 q^{13} -2.47786 q^{14} -1.49515 q^{15} +1.00000 q^{16} +4.04230 q^{17} +0.957895 q^{18} -0.410080 q^{19} +1.04628 q^{20} -3.54092 q^{21} +5.63258 q^{22} -2.73069 q^{23} +1.42902 q^{24} -3.90530 q^{25} +3.12451 q^{26} +5.65592 q^{27} +2.47786 q^{28} +3.06876 q^{29} +1.49515 q^{30} -9.24305 q^{31} -1.00000 q^{32} +8.04908 q^{33} -4.04230 q^{34} +2.59253 q^{35} -0.957895 q^{36} -0.115265 q^{37} +0.410080 q^{38} +4.46500 q^{39} -1.04628 q^{40} +3.90405 q^{41} +3.54092 q^{42} -8.38888 q^{43} -5.63258 q^{44} -1.00222 q^{45} +2.73069 q^{46} -9.20502 q^{47} -1.42902 q^{48} -0.860199 q^{49} +3.90530 q^{50} -5.77654 q^{51} -3.12451 q^{52} -4.42422 q^{53} -5.65592 q^{54} -5.89324 q^{55} -2.47786 q^{56} +0.586014 q^{57} -3.06876 q^{58} +1.48209 q^{59} -1.49515 q^{60} +10.3819 q^{61} +9.24305 q^{62} -2.37353 q^{63} +1.00000 q^{64} -3.26911 q^{65} -8.04908 q^{66} +15.8623 q^{67} +4.04230 q^{68} +3.90222 q^{69} -2.59253 q^{70} +10.5527 q^{71} +0.957895 q^{72} +1.18129 q^{73} +0.115265 q^{74} +5.58077 q^{75} -0.410080 q^{76} -13.9568 q^{77} -4.46500 q^{78} +4.79709 q^{79} +1.04628 q^{80} -5.20875 q^{81} -3.90405 q^{82} -0.673126 q^{83} -3.54092 q^{84} +4.22937 q^{85} +8.38888 q^{86} -4.38532 q^{87} +5.63258 q^{88} -7.20463 q^{89} +1.00222 q^{90} -7.74211 q^{91} -2.73069 q^{92} +13.2085 q^{93} +9.20502 q^{94} -0.429058 q^{95} +1.42902 q^{96} +5.04523 q^{97} +0.860199 q^{98} +5.39542 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

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