LMFDB - Embedded newform 6022.2.a.b.1.9

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:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.71927 q^{3} +1.00000 q^{4} -3.84841 q^{5} -2.71927 q^{6} -3.35161 q^{7} +1.00000 q^{8} +4.39444 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.71927 q^{3} +1.00000 q^{4} -3.84841 q^{5} -2.71927 q^{6} -3.35161 q^{7} +1.00000 q^{8} +4.39444 q^{9} -3.84841 q^{10} +1.14785 q^{11} -2.71927 q^{12} -1.69109 q^{13} -3.35161 q^{14} +10.4649 q^{15} +1.00000 q^{16} -7.52299 q^{17} +4.39444 q^{18} +1.77272 q^{19} -3.84841 q^{20} +9.11394 q^{21} +1.14785 q^{22} +5.91449 q^{23} -2.71927 q^{24} +9.81029 q^{25} -1.69109 q^{26} -3.79187 q^{27} -3.35161 q^{28} +1.68035 q^{29} +10.4649 q^{30} +1.58215 q^{31} +1.00000 q^{32} -3.12131 q^{33} -7.52299 q^{34} +12.8984 q^{35} +4.39444 q^{36} +1.41901 q^{37} +1.77272 q^{38} +4.59853 q^{39} -3.84841 q^{40} +2.94565 q^{41} +9.11394 q^{42} -6.52170 q^{43} +1.14785 q^{44} -16.9116 q^{45} +5.91449 q^{46} +4.33137 q^{47} -2.71927 q^{48} +4.23328 q^{49} +9.81029 q^{50} +20.4571 q^{51} -1.69109 q^{52} +0.0164389 q^{53} -3.79187 q^{54} -4.41740 q^{55} -3.35161 q^{56} -4.82051 q^{57} +1.68035 q^{58} +2.32069 q^{59} +10.4649 q^{60} +10.0536 q^{61} +1.58215 q^{62} -14.7285 q^{63} +1.00000 q^{64} +6.50801 q^{65} -3.12131 q^{66} +10.9745 q^{67} -7.52299 q^{68} -16.0831 q^{69} +12.8984 q^{70} +2.77537 q^{71} +4.39444 q^{72} +0.329687 q^{73} +1.41901 q^{74} -26.6769 q^{75} +1.77272 q^{76} -3.84714 q^{77} +4.59853 q^{78} -1.57960 q^{79} -3.84841 q^{80} -2.87221 q^{81} +2.94565 q^{82} -4.58242 q^{83} +9.11394 q^{84} +28.9516 q^{85} -6.52170 q^{86} -4.56933 q^{87} +1.14785 q^{88} -4.01358 q^{89} -16.9116 q^{90} +5.66787 q^{91} +5.91449 q^{92} -4.30229 q^{93} +4.33137 q^{94} -6.82217 q^{95} -2.71927 q^{96} +2.11762 q^{97} +4.23328 q^{98} +5.04416 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) $ 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * 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
$3$	−2.71927	−1.56997	−0.784986	−	0.619513i	$-0.787330\pi$
$3$	−2.71927	−1.56997	−0.784986	+	0.619513i	$0.787330\pi$
$4$	1.00000	0.500000
$5$	−3.84841	−1.72106	−0.860532	−	0.509397i	$-0.829868\pi$
$5$	−3.84841	−1.72106	−0.860532	+	0.509397i	$0.829868\pi$
$6$	−2.71927	−1.11014
$7$	−3.35161	−1.26679	−0.633395	−	0.773829i	$-0.718339\pi$
$7$	−3.35161	−1.26679	−0.633395	+	0.773829i	$0.718339\pi$
$8$	1.00000	0.353553
$9$	4.39444	1.46481
$10$	−3.84841	−1.21698
$11$	1.14785	0.346090	0.173045	−	0.984914i	$-0.444639\pi$
$11$	1.14785	0.346090	0.173045	+	0.984914i	$0.444639\pi$
$12$	−2.71927	−0.784986
$13$	−1.69109	−0.469023	−0.234512	−	0.972113i	$-0.575349\pi$
$13$	−1.69109	−0.469023	−0.234512	+	0.972113i	$0.575349\pi$
$14$	−3.35161	−0.895755
$15$	10.4649	2.70202
$16$	1.00000	0.250000
$17$	−7.52299	−1.82459	−0.912297	−	0.409530i	$-0.865693\pi$
$17$	−7.52299	−1.82459	−0.912297	+	0.409530i	$0.865693\pi$
$18$	4.39444	1.03578
$19$	1.77272	0.406690	0.203345	−	0.979107i	$-0.434819\pi$
$19$	1.77272	0.406690	0.203345	+	0.979107i	$0.434819\pi$
$20$	−3.84841	−0.860532
$21$	9.11394	1.98882
$22$	1.14785	0.244722
$23$	5.91449	1.23326	0.616628	−	0.787255i	$-0.288498\pi$
$23$	5.91449	1.23326	0.616628	+	0.787255i	$0.288498\pi$
$24$	−2.71927	−0.555069
$25$	9.81029	1.96206
$26$	−1.69109	−0.331650
$27$	−3.79187	−0.729745
$28$	−3.35161	−0.633395
$29$	1.68035	0.312033	0.156016	−	0.987754i	$-0.450135\pi$
$29$	1.68035	0.312033	0.156016	+	0.987754i	$0.450135\pi$
$30$	10.4649	1.91062
$31$	1.58215	0.284162	0.142081	−	0.989855i	$-0.454621\pi$
$31$	1.58215	0.284162	0.142081	+	0.989855i	$0.454621\pi$
$32$	1.00000	0.176777
$33$	−3.12131	−0.543351
$34$	−7.52299	−1.29018
$35$	12.8984	2.18022
$36$	4.39444	0.732407
$37$	1.41901	0.233284	0.116642	−	0.993174i	$-0.462787\pi$
$37$	1.41901	0.233284	0.116642	+	0.993174i	$0.462787\pi$
$38$	1.77272	0.287573
$39$	4.59853	0.736354
$40$	−3.84841	−0.608488
$41$	2.94565	0.460034	0.230017	−	0.973187i	$-0.426122\pi$
$41$	2.94565	0.460034	0.230017	+	0.973187i	$0.426122\pi$
$42$	9.11394	1.40631
$43$	−6.52170	−0.994551	−0.497275	−	0.867593i	$-0.665666\pi$
$43$	−6.52170	−0.994551	−0.497275	+	0.867593i	$0.665666\pi$
$44$	1.14785	0.173045
$45$	−16.9116	−2.52104
$46$	5.91449	0.872044
$47$	4.33137	0.631795	0.315898	−	0.948793i	$-0.397694\pi$
$47$	4.33137	0.631795	0.315898	+	0.948793i	$0.397694\pi$
$48$	−2.71927	−0.392493
$49$	4.23328	0.604755
$50$	9.81029	1.38739
$51$	20.4571	2.86456
$52$	−1.69109	−0.234512
$53$	0.0164389	0.00225805	0.00112903	−	0.999999i	$-0.499641\pi$
$53$	0.0164389	0.00225805	0.00112903	+	0.999999i	$0.499641\pi$
$54$	−3.79187	−0.516008
$55$	−4.41740	−0.595642
$56$	−3.35161	−0.447878
$57$	−4.82051	−0.638492
$58$	1.68035	0.220641
$59$	2.32069	0.302127	0.151064	−	0.988524i	$-0.451730\pi$
$59$	2.32069	0.302127	0.151064	+	0.988524i	$0.451730\pi$
$60$	10.4649	1.35101
$61$	10.0536	1.28723	0.643613	−	0.765351i	$-0.277435\pi$
$61$	10.0536	1.28723	0.643613	+	0.765351i	$0.277435\pi$
$62$	1.58215	0.200933
$63$	−14.7285	−1.85561
$64$	1.00000	0.125000
$65$	6.50801	0.807219
$66$	−3.12131	−0.384207
$67$	10.9745	1.34075	0.670374	−	0.742023i	$-0.266134\pi$
$67$	10.9745	1.34075	0.670374	+	0.742023i	$0.266134\pi$
$68$	−7.52299	−0.912297
$69$	−16.0831	−1.93618
$70$	12.8984	1.54165
$71$	2.77537	0.329376	0.164688	−	0.986346i	$-0.447338\pi$
$71$	2.77537	0.329376	0.164688	+	0.986346i	$0.447338\pi$
$72$	4.39444	0.517890
$73$	0.329687	0.0385870	0.0192935	−	0.999814i	$-0.493858\pi$
$73$	0.329687	0.0385870	0.0192935	+	0.999814i	$0.493858\pi$
$74$	1.41901	0.164957
$75$	−26.6769	−3.08038
$76$	1.77272	0.203345
$77$	−3.84714	−0.438423
$78$	4.59853	0.520681
$79$	−1.57960	−0.177719	−0.0888596	−	0.996044i	$-0.528322\pi$
$79$	−1.57960	−0.177719	−0.0888596	+	0.996044i	$0.528322\pi$
$80$	−3.84841	−0.430266
$81$	−2.87221	−0.319134
$82$	2.94565	0.325293
$83$	−4.58242	−0.502986	−0.251493	−	0.967859i	$-0.580922\pi$
$83$	−4.58242	−0.502986	−0.251493	+	0.967859i	$0.580922\pi$
$84$	9.11394	0.994412
$85$	28.9516	3.14024
$86$	−6.52170	−0.703253
$87$	−4.56933	−0.489883
$88$	1.14785	0.122361
$89$	−4.01358	−0.425439	−0.212719	−	0.977113i	$-0.568232\pi$
$89$	−4.01358	−0.425439	−0.212719	+	0.977113i	$0.568232\pi$
$90$	−16.9116	−1.78264
$91$	5.66787	0.594154
$92$	5.91449	0.616628
$93$	−4.30229	−0.446127
$94$	4.33137	0.446747
$95$	−6.82217	−0.699939
$96$	−2.71927	−0.277535
$97$	2.11762	0.215012	0.107506	−	0.994204i	$-0.465713\pi$
$97$	2.11762	0.215012	0.107506	+	0.994204i	$0.465713\pi$
$98$	4.23328	0.427626
$99$	5.04416	0.506957
$100$	9.81029	0.981029
$101$	−2.86954	−0.285529	−0.142765	−	0.989757i	$-0.545599\pi$
$101$	−2.86954	−0.285529	−0.142765	+	0.989757i	$0.545599\pi$
$102$	20.4571	2.02555
$103$	−13.7450	−1.35433	−0.677165	−	0.735831i	$-0.736792\pi$
$103$	−13.7450	−1.35433	−0.677165	+	0.735831i	$0.736792\pi$
$104$	−1.69109	−0.165825
$105$	−35.0742	−3.42289
$106$	0.0164389	0.00159668
$107$	3.02810	0.292738	0.146369	−	0.989230i	$-0.453241\pi$
$107$	3.02810	0.292738	0.146369	+	0.989230i	$0.453241\pi$
$108$	−3.79187	−0.364873
$109$	2.21718	0.212367	0.106184	−	0.994347i	$-0.466137\pi$
$109$	2.21718	0.212367	0.106184	+	0.994347i	$0.466137\pi$
$110$	−4.41740	−0.421183
$111$	−3.85867	−0.366249
$112$	−3.35161	−0.316697
$113$	10.3451	0.973181	0.486591	−	0.873630i	$-0.338240\pi$
$113$	10.3451	0.973181	0.486591	+	0.873630i	$0.338240\pi$
$114$	−4.82051	−0.451482
$115$	−22.7614	−2.12251
$116$	1.68035	0.156016
$117$	−7.43139	−0.687032
$118$	2.32069	0.213636
$119$	25.2141	2.31137
$120$	10.4649	0.955309
$121$	−9.68244	−0.880222
$122$	10.0536	0.910206
$123$	−8.01003	−0.722240
$124$	1.58215	0.142081
$125$	−18.5120	−1.65576
$126$	−14.7285	−1.31211
$127$	−6.16256	−0.546839	−0.273419	−	0.961895i	$-0.588155\pi$
$127$	−6.16256	−0.546839	−0.273419	+	0.961895i	$0.588155\pi$
$128$	1.00000	0.0883883
$129$	17.7343	1.56142
$130$	6.50801	0.570790
$131$	1.29145	0.112834	0.0564171	−	0.998407i	$-0.482032\pi$
$131$	1.29145	0.112834	0.0564171	+	0.998407i	$0.482032\pi$
$132$	−3.12131	−0.271676
$133$	−5.94147	−0.515191
$134$	10.9745	0.948052
$135$	14.5927	1.25594
$136$	−7.52299	−0.645091
$137$	1.71596	0.146604	0.0733022	−	0.997310i	$-0.476646\pi$
$137$	1.71596	0.146604	0.0733022	+	0.997310i	$0.476646\pi$
$138$	−16.0831	−1.36908
$139$	−3.19480	−0.270980	−0.135490	−	0.990779i	$-0.543261\pi$
$139$	−3.19480	−0.270980	−0.135490	+	0.990779i	$0.543261\pi$
$140$	12.8984	1.09011
$141$	−11.7782	−0.991901
$142$	2.77537	0.232904
$143$	−1.94111	−0.162324
$144$	4.39444	0.366203
$145$	−6.46668	−0.537028
$146$	0.329687	0.0272851
$147$	−11.5115	−0.949448
$148$	1.41901	0.116642
$149$	−3.33460	−0.273181	−0.136590	−	0.990628i	$-0.543614\pi$
$149$	−3.33460	−0.273181	−0.136590	+	0.990628i	$0.543614\pi$
$150$	−26.6769	−2.17816
$151$	−9.11247	−0.741562	−0.370781	−	0.928720i	$-0.620910\pi$
$151$	−9.11247	−0.741562	−0.370781	+	0.928720i	$0.620910\pi$
$152$	1.77272	0.143787
$153$	−33.0593	−2.67269
$154$	−3.84714	−0.310012
$155$	−6.08876	−0.489061
$156$	4.59853	0.368177
$157$	9.89779	0.789929	0.394965	−	0.918696i	$-0.370757\pi$
$157$	9.89779	0.789929	0.394965	+	0.918696i	$0.370757\pi$
$158$	−1.57960	−0.125666
$159$	−0.0447017	−0.00354508
$160$	−3.84841	−0.304244
$161$	−19.8231	−1.56228
$162$	−2.87221	−0.225662
$163$	23.8502	1.86809	0.934045	−	0.357155i	$-0.116253\pi$
$163$	23.8502	1.86809	0.934045	+	0.357155i	$0.116253\pi$
$164$	2.94565	0.230017
$165$	12.0121	0.935142
$166$	−4.58242	−0.355665
$167$	1.61759	0.125173	0.0625866	−	0.998040i	$-0.480065\pi$
$167$	1.61759	0.125173	0.0625866	+	0.998040i	$0.480065\pi$
$168$	9.11394	0.703156
$169$	−10.1402	−0.780017
$170$	28.9516	2.22049
$171$	7.79012	0.595725
$172$	−6.52170	−0.497275
$173$	−11.9797	−0.910804	−0.455402	−	0.890286i	$-0.650504\pi$
$173$	−11.9797	−0.910804	−0.455402	+	0.890286i	$0.650504\pi$
$174$	−4.56933	−0.346400
$175$	−32.8803	−2.48551
$176$	1.14785	0.0865224
$177$	−6.31057	−0.474332
$178$	−4.01358	−0.300831
$179$	9.97909	0.745872	0.372936	−	0.927857i	$-0.378351\pi$
$179$	9.97909	0.745872	0.372936	+	0.927857i	$0.378351\pi$
$180$	−16.9116	−1.26052
$181$	14.2278	1.05754	0.528771	−	0.848765i	$-0.322653\pi$
$181$	14.2278	1.05754	0.528771	+	0.848765i	$0.322653\pi$
$182$	5.66787	0.420130
$183$	−27.3384	−2.02091
$184$	5.91449	0.436022
$185$	−5.46094	−0.401496
$186$	−4.30229	−0.315459
$187$	−8.63526	−0.631473
$188$	4.33137	0.315898
$189$	12.7089	0.924433
$190$	−6.82217	−0.494932
$191$	−12.2522	−0.886536	−0.443268	−	0.896389i	$-0.646181\pi$
$191$	−12.2522	−0.886536	−0.443268	+	0.896389i	$0.646181\pi$
$192$	−2.71927	−0.196247
$193$	12.5853	0.905907	0.452954	−	0.891534i	$-0.350370\pi$
$193$	12.5853	0.905907	0.452954	+	0.891534i	$0.350370\pi$
$194$	2.11762	0.152037
$195$	−17.6970	−1.26731
$196$	4.23328	0.302377
$197$	−19.3683	−1.37993	−0.689965	−	0.723842i	$-0.742374\pi$
$197$	−19.3683	−1.37993	−0.689965	+	0.723842i	$0.742374\pi$
$198$	5.04416	0.358473
$199$	23.9795	1.69986	0.849932	−	0.526892i	$-0.176643\pi$
$199$	23.9795	1.69986	0.849932	+	0.526892i	$0.176643\pi$
$200$	9.81029	0.693693
$201$	−29.8426	−2.10494
$202$	−2.86954	−0.201900
$203$	−5.63187	−0.395280
$204$	20.4571	1.43228
$205$	−11.3361	−0.791747
$206$	−13.7450	−0.957657
$207$	25.9909	1.80649
$208$	−1.69109	−0.117256
$209$	2.03482	0.140751
$210$	−35.0742	−2.42035
$211$	−23.5091	−1.61844	−0.809218	−	0.587508i	$-0.800109\pi$
$211$	−23.5091	−1.61844	−0.809218	+	0.587508i	$0.800109\pi$
$212$	0.0164389	0.00112903
$213$	−7.54699	−0.517111
$214$	3.02810	0.206997
$215$	25.0982	1.71168
$216$	−3.79187	−0.258004
$217$	−5.30274	−0.359974
$218$	2.21718	0.150166
$219$	−0.896510	−0.0605805
$220$	−4.41740	−0.297821
$221$	12.7220	0.855777
$222$	−3.85867	−0.258977
$223$	−22.1439	−1.48287	−0.741434	−	0.671026i	$-0.765854\pi$
$223$	−22.1439	−1.48287	−0.741434	+	0.671026i	$0.765854\pi$
$224$	−3.35161	−0.223939
$225$	43.1108	2.87405
$226$	10.3451	0.688143
$227$	−27.4434	−1.82148	−0.910741	−	0.412978i	$-0.864489\pi$
$227$	−27.4434	−1.82148	−0.910741	+	0.412978i	$0.864489\pi$
$228$	−4.82051	−0.319246
$229$	5.18387	0.342560	0.171280	−	0.985222i	$-0.445210\pi$
$229$	5.18387	0.342560	0.171280	+	0.985222i	$0.445210\pi$
$230$	−22.7614	−1.50084
$231$	10.4614	0.688311
$232$	1.68035	0.110320
$233$	−16.5923	−1.08700	−0.543500	−	0.839409i	$-0.682901\pi$
$233$	−16.5923	−1.08700	−0.543500	+	0.839409i	$0.682901\pi$
$234$	−7.43139	−0.485805
$235$	−16.6689	−1.08736
$236$	2.32069	0.151064
$237$	4.29537	0.279014
$238$	25.2141	1.63439
$239$	1.11176	0.0719138	0.0359569	−	0.999353i	$-0.488552\pi$
$239$	1.11176	0.0719138	0.0359569	+	0.999353i	$0.488552\pi$
$240$	10.4649	0.675506
$241$	12.7550	0.821619	0.410809	−	0.911721i	$-0.365246\pi$
$241$	12.7550	0.821619	0.410809	+	0.911721i	$0.365246\pi$
$242$	−9.68244	−0.622411
$243$	19.1859	1.23078
$244$	10.0536	0.643613
$245$	−16.2914	−1.04082
$246$	−8.01003	−0.510701
$247$	−2.99783	−0.190747
$248$	1.58215	0.100467
$249$	12.4608	0.789674
$250$	−18.5120	−1.17080
$251$	6.58558	0.415678	0.207839	−	0.978163i	$-0.433357\pi$
$251$	6.58558	0.415678	0.207839	+	0.978163i	$0.433357\pi$
$252$	−14.7285	−0.927805
$253$	6.78894	0.426817
$254$	−6.16256	−0.386674
$255$	−78.7272	−4.93009
$256$	1.00000	0.0625000
$257$	−7.06924	−0.440967	−0.220483	−	0.975391i	$-0.570763\pi$
$257$	−7.06924	−0.440967	−0.220483	+	0.975391i	$0.570763\pi$
$258$	17.7343	1.10409
$259$	−4.75597	−0.295521
$260$	6.50801	0.403610
$261$	7.38419	0.457070
$262$	1.29145	0.0797858
$263$	4.28843	0.264436	0.132218	−	0.991221i	$-0.457790\pi$
$263$	4.28843	0.264436	0.132218	+	0.991221i	$0.457790\pi$
$264$	−3.12131	−0.192104
$265$	−0.0632635	−0.00388625
$266$	−5.94147	−0.364295
$267$	10.9140	0.667927
$268$	10.9745	0.670374
$269$	4.38466	0.267337	0.133669	−	0.991026i	$-0.457324\pi$
$269$	4.38466	0.267337	0.133669	+	0.991026i	$0.457324\pi$
$270$	14.5927	0.888082
$271$	−4.17119	−0.253382	−0.126691	−	0.991942i	$-0.540436\pi$
$271$	−4.17119	−0.253382	−0.126691	+	0.991942i	$0.540436\pi$
$272$	−7.52299	−0.456148
$273$	−15.4125	−0.932805
$274$	1.71596	0.103665
$275$	11.2607	0.679048
$276$	−16.0831	−0.968089
$277$	11.8677	0.713061	0.356531	−	0.934284i	$-0.383960\pi$
$277$	11.8677	0.713061	0.356531	+	0.934284i	$0.383960\pi$
$278$	−3.19480	−0.191612
$279$	6.95266	0.416245
$280$	12.8984	0.770826
$281$	6.47704	0.386388	0.193194	−	0.981161i	$-0.438115\pi$
$281$	6.47704	0.386388	0.193194	+	0.981161i	$0.438115\pi$
$282$	−11.7782	−0.701380
$283$	−25.8946	−1.53927	−0.769636	−	0.638483i	$-0.779562\pi$
$283$	−25.8946	−1.53927	−0.769636	+	0.638483i	$0.779562\pi$
$284$	2.77537	0.164688
$285$	18.5513	1.09889
$286$	−1.94111	−0.114780
$287$	−9.87268	−0.582766
$288$	4.39444	0.258945
$289$	39.5954	2.32914
$290$	−6.46668	−0.379736
$291$	−5.75840	−0.337563
$292$	0.329687	0.0192935
$293$	−0.464284	−0.0271238	−0.0135619	−	0.999908i	$-0.504317\pi$
$293$	−0.464284	−0.0271238	−0.0135619	+	0.999908i	$0.504317\pi$
$294$	−11.5115	−0.671361
$295$	−8.93096	−0.519980
$296$	1.41901	0.0824783
$297$	−4.35249	−0.252557
$298$	−3.33460	−0.193168
$299$	−10.0019	−0.578426
$300$	−26.6769	−1.54019
$301$	21.8582	1.25989
$302$	−9.11247	−0.524364
$303$	7.80305	0.448273
$304$	1.77272	0.101673
$305$	−38.6903	−2.21540
$306$	−33.0593	−1.88988
$307$	−16.8748	−0.963098	−0.481549	−	0.876419i	$-0.659926\pi$
$307$	−16.8748	−0.963098	−0.481549	+	0.876419i	$0.659926\pi$
$308$	−3.84714	−0.219211
$309$	37.3763	2.12626
$310$	−6.08876	−0.345818
$311$	−15.4209	−0.874440	−0.437220	−	0.899355i	$-0.644037\pi$
$311$	−15.4209	−0.874440	−0.437220	+	0.899355i	$0.644037\pi$
$312$	4.59853	0.260340
$313$	−12.1163	−0.684855	−0.342428	−	0.939544i	$-0.611249\pi$
$313$	−12.1163	−0.684855	−0.342428	+	0.939544i	$0.611249\pi$
$314$	9.89779	0.558564
$315$	56.6812	3.19362
$316$	−1.57960	−0.0888596
$317$	−1.12208	−0.0630220	−0.0315110	−	0.999503i	$-0.510032\pi$
$317$	−1.12208	−0.0630220	−0.0315110	+	0.999503i	$0.510032\pi$
$318$	−0.0447017	−0.00250675
$319$	1.92879	0.107991
$320$	−3.84841	−0.215133
$321$	−8.23423	−0.459590
$322$	−19.8231	−1.10470
$323$	−13.3362	−0.742044
$324$	−2.87221	−0.159567
$325$	−16.5901	−0.920252
$326$	23.8502	1.32094
$327$	−6.02911	−0.333411
$328$	2.94565	0.162646
$329$	−14.5171	−0.800351
$330$	12.0121	0.661245
$331$	17.4604	0.959709	0.479854	−	0.877348i	$-0.340689\pi$
$331$	17.4604	0.959709	0.479854	+	0.877348i	$0.340689\pi$
$332$	−4.58242	−0.251493
$333$	6.23575	0.341717
$334$	1.61759	0.0885108
$335$	−42.2344	−2.30751
$336$	9.11394	0.497206
$337$	−0.111481	−0.00607273	−0.00303637	−	0.999995i	$-0.500967\pi$
$337$	−0.111481	−0.00607273	−0.00303637	+	0.999995i	$0.500967\pi$
$338$	−10.1402	−0.551555
$339$	−28.1310	−1.52787
$340$	28.9516	1.57012
$341$	1.81607	0.0983456
$342$	7.79012	0.421241
$343$	9.27295	0.500692
$344$	−6.52170	−0.351627
$345$	61.8945	3.33229
$346$	−11.9797	−0.644035
$347$	−35.7397	−1.91861	−0.959304	−	0.282376i	$-0.908877\pi$
$347$	−35.7397	−1.91861	−0.959304	+	0.282376i	$0.908877\pi$
$348$	−4.56933	−0.244942
$349$	−16.6717	−0.892415	−0.446207	−	0.894930i	$-0.647226\pi$
$349$	−16.6717	−0.892415	−0.446207	+	0.894930i	$0.647226\pi$
$350$	−32.8803	−1.75752
$351$	6.41238	0.342268
$352$	1.14785	0.0611806
$353$	2.57700	0.137160	0.0685799	−	0.997646i	$-0.478153\pi$
$353$	2.57700	0.137160	0.0685799	+	0.997646i	$0.478153\pi$
$354$	−6.31057	−0.335403
$355$	−10.6808	−0.566877
$356$	−4.01358	−0.212719
$357$	−68.5641	−3.62880
$358$	9.97909	0.527411
$359$	−29.6865	−1.56679	−0.783396	−	0.621522i	$-0.786514\pi$
$359$	−29.6865	−1.56679	−0.783396	+	0.621522i	$0.786514\pi$
$360$	−16.9116	−0.891321
$361$	−15.8575	−0.834603
$362$	14.2278	0.747795
$363$	26.3292	1.38192
$364$	5.66787	0.297077
$365$	−1.26877	−0.0664106
$366$	−27.3384	−1.42900
$367$	22.7250	1.18623	0.593117	−	0.805117i	$-0.297897\pi$
$367$	22.7250	1.18623	0.593117	+	0.805117i	$0.297897\pi$
$368$	5.91449	0.308314
$369$	12.9445	0.673864
$370$	−5.46094	−0.283901
$371$	−0.0550966	−0.00286047
$372$	−4.30229	−0.223063
$373$	−10.3889	−0.537919	−0.268959	−	0.963151i	$-0.586680\pi$
$373$	−10.3889	−0.537919	−0.268959	+	0.963151i	$0.586680\pi$
$374$	−8.63526	−0.446519
$375$	50.3392	2.59950
$376$	4.33137	0.223373
$377$	−2.84162	−0.146351
$378$	12.7089	0.653673
$379$	13.5017	0.693533	0.346767	−	0.937951i	$-0.387280\pi$
$379$	13.5017	0.693533	0.346767	+	0.937951i	$0.387280\pi$
$380$	−6.82217	−0.349970
$381$	16.7577	0.858522
$382$	−12.2522	−0.626876
$383$	−25.9893	−1.32799	−0.663995	−	0.747737i	$-0.731140\pi$
$383$	−25.9893	−1.32799	−0.663995	+	0.747737i	$0.731140\pi$
$384$	−2.71927	−0.138767
$385$	14.8054	0.754553
$386$	12.5853	0.640573
$387$	−28.6592	−1.45683
$388$	2.11762	0.107506
$389$	35.2433	1.78691	0.893453	−	0.449157i	$-0.148276\pi$
$389$	35.2433	1.78691	0.893453	+	0.449157i	$0.148276\pi$
$390$	−17.6970	−0.896125
$391$	−44.4946	−2.25019
$392$	4.23328	0.213813
$393$	−3.51179	−0.177147
$394$	−19.3683	−0.975758
$395$	6.07897	0.305866
$396$	5.04416	0.253478
$397$	34.9724	1.75522	0.877608	−	0.479378i	$-0.159138\pi$
$397$	34.9724	1.75522	0.877608	+	0.479378i	$0.159138\pi$
$398$	23.9795	1.20199
$399$	16.1565	0.808835
$400$	9.81029	0.490515
$401$	13.6917	0.683732	0.341866	−	0.939749i	$-0.388941\pi$
$401$	13.6917	0.683732	0.341866	+	0.939749i	$0.388941\pi$
$402$	−29.8426	−1.48842
$403$	−2.67555	−0.133279
$404$	−2.86954	−0.142765
$405$	11.0534	0.549250
$406$	−5.63187	−0.279505
$407$	1.62881	0.0807371
$408$	20.4571	1.01278
$409$	21.9386	1.08480	0.542398	−	0.840122i	$-0.317517\pi$
$409$	21.9386	1.08480	0.542398	+	0.840122i	$0.317517\pi$
$410$	−11.3361	−0.559850
$411$	−4.66616	−0.230165
$412$	−13.7450	−0.677165
$413$	−7.77803	−0.382732
$414$	25.9909	1.27738
$415$	17.6350	0.865670
$416$	−1.69109	−0.0829124
$417$	8.68754	0.425431
$418$	2.03482	0.0995261
$419$	11.7538	0.574209	0.287104	−	0.957899i	$-0.407307\pi$
$419$	11.7538	0.574209	0.287104	+	0.957899i	$0.407307\pi$
$420$	−35.0742	−1.71145
$421$	26.0427	1.26924	0.634622	−	0.772823i	$-0.281156\pi$
$421$	26.0427	1.26924	0.634622	+	0.772823i	$0.281156\pi$
$422$	−23.5091	−1.14441
$423$	19.0340	0.925462
$424$	0.0164389	0.000798342 0
$425$	−73.8028	−3.57996
$426$	−7.54699	−0.365653
$427$	−33.6956	−1.63064
$428$	3.02810	0.146369
$429$	5.27842	0.254844
$430$	25.0982	1.21034
$431$	24.9708	1.20280	0.601402	−	0.798947i	$-0.294609\pi$
$431$	24.9708	1.20280	0.601402	+	0.798947i	$0.294609\pi$
$432$	−3.79187	−0.182436
$433$	−5.70139	−0.273991	−0.136996	−	0.990572i	$-0.543745\pi$
$433$	−5.70139	−0.273991	−0.136996	+	0.990572i	$0.543745\pi$
$434$	−5.30274	−0.254540
$435$	17.5847	0.843120
$436$	2.21718	0.106184
$437$	10.4847	0.501553
$438$	−0.896510	−0.0428369
$439$	33.8396	1.61507	0.807537	−	0.589817i	$-0.200800\pi$
$439$	33.8396	1.61507	0.807537	+	0.589817i	$0.200800\pi$
$440$	−4.41740	−0.210591
$441$	18.6029	0.885853
$442$	12.7220	0.605126
$443$	−14.6503	−0.696058	−0.348029	−	0.937484i	$-0.613149\pi$
$443$	−14.6503	−0.696058	−0.348029	+	0.937484i	$0.613149\pi$
$444$	−3.85867	−0.183125
$445$	15.4459	0.732207
$446$	−22.1439	−1.04855
$447$	9.06768	0.428886
$448$	−3.35161	−0.158349
$449$	−28.4509	−1.34268	−0.671341	−	0.741149i	$-0.734281\pi$
$449$	−28.4509	−1.34268	−0.671341	+	0.741149i	$0.734281\pi$
$450$	43.1108	2.03226
$451$	3.38117	0.159213
$452$	10.3451	0.486591
$453$	24.7793	1.16423
$454$	−27.4434	−1.28798
$455$	−21.8123	−1.02258
$456$	−4.82051	−0.225741
$457$	−11.8890	−0.556145	−0.278073	−	0.960560i	$-0.589696\pi$
$457$	−11.8890	−0.556145	−0.278073	+	0.960560i	$0.589696\pi$
$458$	5.18387	0.242226
$459$	28.5262	1.33149
$460$	−22.7614	−1.06126
$461$	13.6367	0.635125	0.317563	−	0.948237i	$-0.397136\pi$
$461$	13.6367	0.635125	0.317563	+	0.948237i	$0.397136\pi$
$462$	10.4614	0.486710
$463$	−25.7242	−1.19550	−0.597752	−	0.801681i	$-0.703939\pi$
$463$	−25.7242	−1.19550	−0.597752	+	0.801681i	$0.703939\pi$
$464$	1.68035	0.0780082
$465$	16.5570	0.767813
$466$	−16.5923	−0.768624
$467$	13.6238	0.630434	0.315217	−	0.949020i	$-0.397923\pi$
$467$	13.6238	0.630434	0.315217	+	0.949020i	$0.397923\pi$
$468$	−7.43139	−0.343516
$469$	−36.7822	−1.69845
$470$	−16.6689	−0.768879
$471$	−26.9148	−1.24017
$472$	2.32069	0.106818
$473$	−7.48593	−0.344204
$474$	4.29537	0.197293
$475$	17.3909	0.797950
$476$	25.2141	1.15569
$477$	0.0722396	0.00330762
$478$	1.11176	0.0508507
$479$	−29.6699	−1.35565	−0.677826	−	0.735222i	$-0.737078\pi$
$479$	−29.6699	−1.35565	−0.677826	+	0.735222i	$0.737078\pi$
$480$	10.4649	0.477655
$481$	−2.39967	−0.109416
$482$	12.7550	0.580972
$483$	53.9043	2.45273
$484$	−9.68244	−0.440111
$485$	−8.14950	−0.370050
$486$	19.1859	0.870291
$487$	−35.1869	−1.59447	−0.797235	−	0.603669i	$-0.793705\pi$
$487$	−35.1869	−1.59447	−0.797235	+	0.603669i	$0.793705\pi$
$488$	10.0536	0.455103
$489$	−64.8551	−2.93285
$490$	−16.2914	−0.735972
$491$	31.2110	1.40853	0.704266	−	0.709936i	$-0.251276\pi$
$491$	31.2110	1.40853	0.704266	+	0.709936i	$0.251276\pi$
$492$	−8.01003	−0.361120
$493$	−12.6412	−0.569333
$494$	−2.99783	−0.134879
$495$	−19.4120	−0.872505
$496$	1.58215	0.0710405
$497$	−9.30195	−0.417250
$498$	12.4608	0.558384
$499$	−24.0423	−1.07628	−0.538141	−	0.842855i	$-0.680873\pi$
$499$	−24.0423	−1.07628	−0.538141	+	0.842855i	$0.680873\pi$
$500$	−18.5120	−0.827882
$501$	−4.39868	−0.196518
$502$	6.58558	0.293929
$503$	−31.5270	−1.40572	−0.702859	−	0.711329i	$-0.748094\pi$
$503$	−31.5270	−1.40572	−0.702859	+	0.711329i	$0.748094\pi$
$504$	−14.7285	−0.656057
$505$	11.0432	0.491414
$506$	6.78894	0.301805
$507$	27.5740	1.22461
$508$	−6.16256	−0.273419
$509$	−10.0211	−0.444176	−0.222088	−	0.975027i	$-0.571287\pi$
$509$	−10.0211	−0.444176	−0.222088	+	0.975027i	$0.571287\pi$
$510$	−78.7272	−3.48610
$511$	−1.10498	−0.0488816
$512$	1.00000	0.0441942
$513$	−6.72192	−0.296780
$514$	−7.06924	−0.311811
$515$	52.8963	2.33089
$516$	17.7343	0.780709
$517$	4.97176	0.218658
$518$	−4.75597	−0.208965
$519$	32.5762	1.42994
$520$	6.50801	0.285395
$521$	28.6551	1.25540	0.627700	−	0.778455i	$-0.283996\pi$
$521$	28.6551	1.25540	0.627700	+	0.778455i	$0.283996\pi$
$522$	7.38419	0.323197
$523$	−39.1836	−1.71338	−0.856690	−	0.515831i	$-0.827483\pi$
$523$	−39.1836	−1.71338	−0.856690	+	0.515831i	$0.827483\pi$
$524$	1.29145	0.0564171
$525$	89.4104	3.90219
$526$	4.28843	0.186984
$527$	−11.9025	−0.518480
$528$	−3.12131	−0.135838
$529$	11.9812	0.520921
$530$	−0.0632635	−0.00274799
$531$	10.1981	0.442560
$532$	−5.94147	−0.257595
$533$	−4.98136	−0.215767
$534$	10.9140	0.472296
$535$	−11.6534	−0.503820
$536$	10.9745	0.474026
$537$	−27.1359	−1.17100
$538$	4.38466	0.189036
$539$	4.85917	0.209299
$540$	14.5927	0.627969
$541$	0.569261	0.0244744	0.0122372	−	0.999925i	$-0.496105\pi$
$541$	0.569261	0.0244744	0.0122372	+	0.999925i	$0.496105\pi$
$542$	−4.17119	−0.179168
$543$	−38.6892	−1.66031
$544$	−7.52299	−0.322546
$545$	−8.53262	−0.365497
$546$	−15.4125	−0.659593
$547$	28.4076	1.21462	0.607310	−	0.794465i	$-0.292249\pi$
$547$	28.4076	1.21462	0.607310	+	0.794465i	$0.292249\pi$
$548$	1.71596	0.0733022
$549$	44.1798	1.88555
$550$	11.2607	0.480160
$551$	2.97879	0.126901
$552$	−16.0831	−0.684542
$553$	5.29421	0.225133
$554$	11.8677	0.504210
$555$	14.8498	0.630338
$556$	−3.19480	−0.135490
$557$	4.50691	0.190964	0.0954820	−	0.995431i	$-0.469561\pi$
$557$	4.50691	0.190964	0.0954820	+	0.995431i	$0.469561\pi$
$558$	6.95266	0.294329
$559$	11.0288	0.466468
$560$	12.8984	0.545056
$561$	23.4816	0.991395
$562$	6.47704	0.273218
$563$	43.0162	1.81292	0.906458	−	0.422295i	$-0.138775\pi$
$563$	43.0162	1.81292	0.906458	+	0.422295i	$0.138775\pi$
$564$	−11.7782	−0.495951
$565$	−39.8121	−1.67491
$566$	−25.8946	−1.08843
$567$	9.62652	0.404276
$568$	2.77537	0.116452
$569$	9.32804	0.391052	0.195526	−	0.980699i	$-0.437359\pi$
$569$	9.32804	0.391052	0.195526	+	0.980699i	$0.437359\pi$
$570$	18.5513	0.777030
$571$	19.2871	0.807142	0.403571	−	0.914948i	$-0.367769\pi$
$571$	19.2871	0.807142	0.403571	+	0.914948i	$0.367769\pi$
$572$	−1.94111	−0.0811621
$573$	33.3170	1.39184
$574$	−9.87268	−0.412078
$575$	58.0229	2.41972
$576$	4.39444	0.183102
$577$	23.7507	0.988755	0.494378	−	0.869247i	$-0.335396\pi$
$577$	23.7507	0.988755	0.494378	+	0.869247i	$0.335396\pi$
$578$	39.5954	1.64695
$579$	−34.2228	−1.42225
$580$	−6.46668	−0.268514
$581$	15.3585	0.637177
$582$	−5.75840	−0.238693
$583$	0.0188693	0.000781488 0
$584$	0.329687	0.0136426
$585$	28.5991	1.18243
$586$	−0.464284	−0.0191794
$587$	−40.7815	−1.68323	−0.841617	−	0.540075i	$-0.818396\pi$
$587$	−40.7815	−1.68323	−0.841617	+	0.540075i	$0.818396\pi$
$588$	−11.5115	−0.474724
$589$	2.80471	0.115566
$590$	−8.93096	−0.367682
$591$	52.6675	2.16645
$592$	1.41901	0.0583209
$593$	−5.81239	−0.238686	−0.119343	−	0.992853i	$-0.538079\pi$
$593$	−5.81239	−0.238686	−0.119343	+	0.992853i	$0.538079\pi$
$594$	−4.35249	−0.178585
$595$	−97.0344	−3.97802
$596$	−3.33460	−0.136590
$597$	−65.2069	−2.66874
$598$	−10.0019	−0.409009
$599$	7.18429	0.293542	0.146771	−	0.989171i	$-0.453112\pi$
$599$	7.18429	0.293542	0.146771	+	0.989171i	$0.453112\pi$
$600$	−26.6769	−1.08908
$601$	−5.43039	−0.221510	−0.110755	−	0.993848i	$-0.535327\pi$
$601$	−5.43039	−0.221510	−0.110755	+	0.993848i	$0.535327\pi$
$602$	21.8582	0.890874
$603$	48.2268	1.96395
$604$	−9.11247	−0.370781
$605$	37.2621	1.51492
$606$	7.80305	0.316977
$607$	−15.7756	−0.640311	−0.320156	−	0.947365i	$-0.603735\pi$
$607$	−15.7756	−0.640311	−0.320156	+	0.947365i	$0.603735\pi$
$608$	1.77272	0.0718933
$609$	15.3146	0.620579
$610$	−38.6903	−1.56652
$611$	−7.32473	−0.296327
$612$	−33.0593	−1.33634
$613$	25.8318	1.04334	0.521668	−	0.853149i	$-0.325310\pi$
$613$	25.8318	1.04334	0.521668	+	0.853149i	$0.325310\pi$
$614$	−16.8748	−0.681013
$615$	30.8259	1.24302
$616$	−3.84714	−0.155006
$617$	28.8102	1.15986	0.579928	−	0.814668i	$-0.303081\pi$
$617$	28.8102	1.15986	0.579928	+	0.814668i	$0.303081\pi$
$618$	37.3763	1.50349
$619$	32.0064	1.28645	0.643223	−	0.765679i	$-0.277597\pi$
$619$	32.0064	1.28645	0.643223	+	0.765679i	$0.277597\pi$
$620$	−6.08876	−0.244531
$621$	−22.4270	−0.899963
$622$	−15.4209	−0.618322
$623$	13.4520	0.538941
$624$	4.59853	0.184088
$625$	22.1904	0.887616
$626$	−12.1163	−0.484266
$627$	−5.53322	−0.220976
$628$	9.89779	0.394965
$629$	−10.6752	−0.425648
$630$	56.6812	2.25823
$631$	−2.47846	−0.0986660	−0.0493330	−	0.998782i	$-0.515710\pi$
$631$	−2.47846	−0.0986660	−0.0493330	+	0.998782i	$0.515710\pi$
$632$	−1.57960	−0.0628332
$633$	63.9278	2.54090
$634$	−1.12208	−0.0445633
$635$	23.7161	0.941144
$636$	−0.0447017	−0.00177254
$637$	−7.15886	−0.283644
$638$	1.92879	0.0763614
$639$	12.1962	0.482474
$640$	−3.84841	−0.152122
$641$	1.24927	0.0493434	0.0246717	−	0.999696i	$-0.492146\pi$
$641$	1.24927	0.0493434	0.0246717	+	0.999696i	$0.492146\pi$
$642$	−8.23423	−0.324979
$643$	22.2597	0.877838	0.438919	−	0.898527i	$-0.355361\pi$
$643$	22.2597	0.877838	0.438919	+	0.898527i	$0.355361\pi$
$644$	−19.8231	−0.781138
$645$	−68.2489	−2.68730
$646$	−13.3362	−0.524704
$647$	−21.6987	−0.853064	−0.426532	−	0.904473i	$-0.640265\pi$
$647$	−21.6987	−0.853064	−0.426532	+	0.904473i	$0.640265\pi$
$648$	−2.87221	−0.112831
$649$	2.66380	0.104563
$650$	−16.5901	−0.650716
$651$	14.4196	0.565149
$652$	23.8502	0.934045
$653$	43.6213	1.70703	0.853517	−	0.521065i	$-0.174465\pi$
$653$	43.6213	1.70703	0.853517	+	0.521065i	$0.174465\pi$
$654$	−6.02911	−0.235757
$655$	−4.97002	−0.194195
$656$	2.94565	0.115008
$657$	1.44879	0.0565228
$658$	−14.5171	−0.565934
$659$	16.8266	0.655471	0.327736	−	0.944769i	$-0.393714\pi$
$659$	16.8266	0.655471	0.327736	+	0.944769i	$0.393714\pi$
$660$	12.0121	0.467571
$661$	−45.8105	−1.78182	−0.890910	−	0.454179i	$-0.849933\pi$
$661$	−45.8105	−1.78182	−0.890910	+	0.454179i	$0.849933\pi$
$662$	17.4604	0.678617
$663$	−34.5947	−1.34355
$664$	−4.58242	−0.177832
$665$	22.8652	0.886676
$666$	6.23575	0.241631
$667$	9.93840	0.384817
$668$	1.61759	0.0625866
$669$	60.2154	2.32806
$670$	−42.2344	−1.63166
$671$	11.5400	0.445496
$672$	9.11394	0.351578
$673$	49.4526	1.90626	0.953129	−	0.302565i	$-0.0978430\pi$
$673$	49.4526	1.90626	0.953129	+	0.302565i	$0.0978430\pi$
$674$	−0.111481	−0.00429407
$675$	−37.1993	−1.43180
$676$	−10.1402	−0.390008
$677$	0.885177	0.0340201	0.0170101	−	0.999855i	$-0.494585\pi$
$677$	0.885177	0.0340201	0.0170101	+	0.999855i	$0.494585\pi$
$678$	−28.1310	−1.08037
$679$	−7.09745	−0.272375
$680$	28.9516	1.11024
$681$	74.6261	2.85968
$682$	1.81607	0.0695408
$683$	−16.1968	−0.619753	−0.309876	−	0.950777i	$-0.600288\pi$
$683$	−16.1968	−0.619753	−0.309876	+	0.950777i	$0.600288\pi$
$684$	7.79012	0.297863
$685$	−6.60373	−0.252315
$686$	9.27295	0.354043
$687$	−14.0963	−0.537809
$688$	−6.52170	−0.248638
$689$	−0.0277996	−0.00105908
$690$	61.8945	2.35628
$691$	4.95325	0.188430	0.0942152	−	0.995552i	$-0.469966\pi$
$691$	4.95325	0.188430	0.0942152	+	0.995552i	$0.469966\pi$
$692$	−11.9797	−0.455402
$693$	−16.9060	−0.642207
$694$	−35.7397	−1.35666
$695$	12.2949	0.466373
$696$	−4.56933	−0.173200
$697$	−22.1601	−0.839374
$698$	−16.6717	−0.631032
$699$	45.1190	1.70656
$700$	−32.8803	−1.24276
$701$	−5.10836	−0.192940	−0.0964700	−	0.995336i	$-0.530755\pi$
$701$	−5.10836	−0.192940	−0.0964700	+	0.995336i	$0.530755\pi$
$702$	6.41238	0.242020
$703$	2.51551	0.0948742
$704$	1.14785	0.0432612
$705$	45.3273	1.70712
$706$	2.57700	0.0969867
$707$	9.61756	0.361706
$708$	−6.31057	−0.237166
$709$	−24.2903	−0.912241	−0.456121	−	0.889918i	$-0.650761\pi$
$709$	−24.2903	−0.912241	−0.456121	+	0.889918i	$0.650761\pi$
$710$	−10.6808	−0.400842
$711$	−6.94147	−0.260326
$712$	−4.01358	−0.150415
$713$	9.35760	0.350445
$714$	−68.5641	−2.56595
$715$	7.47021	0.279370
$716$	9.97909	0.372936
$717$	−3.02318	−0.112903
$718$	−29.6865	−1.10789
$719$	20.6412	0.769787	0.384894	−	0.922961i	$-0.374238\pi$
$719$	20.6412	0.769787	0.384894	+	0.922961i	$0.374238\pi$
$720$	−16.9116	−0.630259
$721$	46.0677	1.71565
$722$	−15.8575	−0.590154
$723$	−34.6842	−1.28992
$724$	14.2278	0.528771
$725$	16.4847	0.612227
$726$	26.3292	0.977168
$727$	34.2075	1.26868	0.634342	−	0.773052i	$-0.281271\pi$
$727$	34.2075	1.26868	0.634342	+	0.773052i	$0.281271\pi$
$728$	5.66787	0.210065
$729$	−43.5551	−1.61315
$730$	−1.26877	−0.0469594
$731$	49.0627	1.81465
$732$	−27.3384	−1.01045
$733$	1.90024	0.0701870	0.0350935	−	0.999384i	$-0.488827\pi$
$733$	1.90024	0.0701870	0.0350935	+	0.999384i	$0.488827\pi$
$734$	22.7250	0.838794
$735$	44.3008	1.63406
$736$	5.91449	0.218011
$737$	12.5971	0.464019
$738$	12.9445	0.476494
$739$	−8.86325	−0.326040	−0.163020	−	0.986623i	$-0.552124\pi$
$739$	−8.86325	−0.326040	−0.163020	+	0.986623i	$0.552124\pi$
$740$	−5.46094	−0.200748
$741$	8.15191	0.299468
$742$	−0.0550966	−0.00202266
$743$	−4.71436	−0.172953	−0.0864765	−	0.996254i	$-0.527561\pi$
$743$	−4.71436	−0.172953	−0.0864765	+	0.996254i	$0.527561\pi$
$744$	−4.30229	−0.157730
$745$	12.8329	0.470161
$746$	−10.3889	−0.380366
$747$	−20.1372	−0.736781
$748$	−8.63526	−0.315736
$749$	−10.1490	−0.370837
$750$	50.3392	1.83813
$751$	5.93879	0.216710	0.108355	−	0.994112i	$-0.465442\pi$
$751$	5.93879	0.216710	0.108355	+	0.994112i	$0.465442\pi$
$752$	4.33137	0.157949
$753$	−17.9080	−0.652604
$754$	−2.84162	−0.103486
$755$	35.0686	1.27628
$756$	12.7089	0.462217
$757$	−2.09376	−0.0760989	−0.0380494	−	0.999276i	$-0.512114\pi$
$757$	−2.09376	−0.0760989	−0.0380494	+	0.999276i	$0.512114\pi$
$758$	13.5017	0.490402
$759$	−18.4610	−0.670091
$760$	−6.82217	−0.247466
$761$	−25.0273	−0.907237	−0.453619	−	0.891196i	$-0.649867\pi$
$761$	−25.0273	−0.907237	−0.453619	+	0.891196i	$0.649867\pi$
$762$	16.7577	0.607067
$763$	−7.43111	−0.269024
$764$	−12.2522	−0.443268
$765$	127.226	4.59987
$766$	−25.9893	−0.939030
$767$	−3.92448	−0.141705
$768$	−2.71927	−0.0981233
$769$	−31.2869	−1.12823	−0.564116	−	0.825695i	$-0.690783\pi$
$769$	−31.2869	−1.12823	−0.564116	+	0.825695i	$0.690783\pi$
$770$	14.8054	0.533549
$771$	19.2232	0.692306
$772$	12.5853	0.452954
$773$	41.8135	1.50393	0.751964	−	0.659204i	$-0.229107\pi$
$773$	41.8135	1.50393	0.751964	+	0.659204i	$0.229107\pi$
$774$	−28.6592	−1.03014
$775$	15.5213	0.557543
$776$	2.11762	0.0760183
$777$	12.9328	0.463960
$778$	35.2433	1.26353
$779$	5.22182	0.187091
$780$	−17.6970	−0.633656
$781$	3.18571	0.113994
$782$	−44.4946	−1.59113
$783$	−6.37166	−0.227704
$784$	4.23328	0.151189
$785$	−38.0908	−1.35952
$786$	−3.51179	−0.125262
$787$	−27.4954	−0.980105	−0.490052	−	0.871693i	$-0.663022\pi$
$787$	−27.4954	−0.980105	−0.490052	+	0.871693i	$0.663022\pi$
$788$	−19.3683	−0.689965
$789$	−11.6614	−0.415157
$790$	6.07897	0.216280
$791$	−34.6726	−1.23282
$792$	5.04416	0.179236
$793$	−17.0015	−0.603739
$794$	34.9724	1.24113
$795$	0.172031	0.00610130
$796$	23.9795	0.849932
$797$	17.5550	0.621828	0.310914	−	0.950438i	$-0.399365\pi$
$797$	17.5550	0.621828	0.310914	+	0.950438i	$0.399365\pi$
$798$	16.1565	0.571933
$799$	−32.5849	−1.15277
$800$	9.81029	0.346846
$801$	−17.6374	−0.623188
$802$	13.6917	0.483471
$803$	0.378431	0.0133546
$804$	−29.8426	−1.05247
$805$	76.2873	2.68878
$806$	−2.67555	−0.0942423
$807$	−11.9231	−0.419712
$808$	−2.86954	−0.100950
$809$	−26.9230	−0.946564	−0.473282	−	0.880911i	$-0.656931\pi$
$809$	−26.9230	−0.946564	−0.473282	+	0.880911i	$0.656931\pi$
$810$	11.0534	0.388378
$811$	−34.2080	−1.20120	−0.600602	−	0.799548i	$-0.705072\pi$
$811$	−34.2080	−1.20120	−0.600602	+	0.799548i	$0.705072\pi$
$812$	−5.63187	−0.197640
$813$	11.3426	0.397802
$814$	1.62881	0.0570897
$815$	−91.7854	−3.21510
$816$	20.4571	0.716140
$817$	−11.5612	−0.404474
$818$	21.9386	0.767067
$819$	24.9071	0.870325
$820$	−11.3361	−0.395874
$821$	−19.3978	−0.676989	−0.338494	−	0.940968i	$-0.609918\pi$
$821$	−19.3978	−0.676989	−0.338494	+	0.940968i	$0.609918\pi$
$822$	−4.66616	−0.162751
$823$	−27.6493	−0.963795	−0.481897	−	0.876228i	$-0.660052\pi$
$823$	−27.6493	−0.963795	−0.481897	+	0.876228i	$0.660052\pi$
$824$	−13.7450	−0.478828
$825$	−30.6210	−1.06609
$826$	−7.77803	−0.270632
$827$	−6.85420	−0.238344	−0.119172	−	0.992874i	$-0.538024\pi$
$827$	−6.85420	−0.238344	−0.119172	+	0.992874i	$0.538024\pi$
$828$	25.9909	0.903245
$829$	1.19973	0.0416682	0.0208341	−	0.999783i	$-0.493368\pi$
$829$	1.19973	0.0416682	0.0208341	+	0.999783i	$0.493368\pi$
$830$	17.6350	0.612121
$831$	−32.2715	−1.11949
$832$	−1.69109	−0.0586279
$833$	−31.8470	−1.10343
$834$	8.68754	0.300825
$835$	−6.22517	−0.215431
$836$	2.03482	0.0703756
$837$	−5.99929	−0.207366
$838$	11.7538	0.406027
$839$	−20.3037	−0.700960	−0.350480	−	0.936570i	$-0.613982\pi$
$839$	−20.3037	−0.700960	−0.350480	+	0.936570i	$0.613982\pi$
$840$	−35.0742	−1.21018
$841$	−26.1764	−0.902635
$842$	26.0427	0.897490
$843$	−17.6128	−0.606619
$844$	−23.5091	−0.809218
$845$	39.0238	1.34246
$846$	19.0340	0.654401
$847$	32.4518	1.11506
$848$	0.0164389	0.000564513 0
$849$	70.4144	2.41661
$850$	−73.8028	−2.53141
$851$	8.39272	0.287699
$852$	−7.54699	−0.258555
$853$	18.9527	0.648928	0.324464	−	0.945898i	$-0.394816\pi$
$853$	18.9527	0.648928	0.324464	+	0.945898i	$0.394816\pi$
$854$	−33.6956	−1.15304
$855$	−29.9796	−1.02528
$856$	3.02810	0.103498
$857$	−8.77328	−0.299689	−0.149845	−	0.988710i	$-0.547877\pi$
$857$	−8.77328	−0.299689	−0.149845	+	0.988710i	$0.547877\pi$
$858$	5.27842	0.180202
$859$	49.3037	1.68222	0.841110	−	0.540863i	$-0.181902\pi$
$859$	49.3037	1.68222	0.841110	+	0.540863i	$0.181902\pi$
$860$	25.0982	0.855842
$861$	26.8465	0.914926
$862$	24.9708	0.850510
$863$	−55.3092	−1.88275	−0.941373	−	0.337367i	$-0.890464\pi$
$863$	−55.3092	−1.88275	−0.941373	+	0.337367i	$0.890464\pi$
$864$	−3.79187	−0.129002
$865$	46.1030	1.56755
$866$	−5.70139	−0.193741
$867$	−107.671	−3.65669
$868$	−5.30274	−0.179987
$869$	−1.81315	−0.0615068
$870$	17.5847	0.596176
$871$	−18.5588	−0.628842
$872$	2.21718	0.0750831
$873$	9.30578	0.314953
$874$	10.4847	0.354652
$875$	62.0450	2.09750
$876$	−0.896510	−0.0302903
$877$	12.9516	0.437345	0.218672	−	0.975798i	$-0.429827\pi$
$877$	12.9516	0.437345	0.218672	+	0.975798i	$0.429827\pi$
$878$	33.8396	1.14203
$879$	1.26251	0.0425836
$880$	−4.41740	−0.148911
$881$	3.93105	0.132440	0.0662202	−	0.997805i	$-0.478906\pi$
$881$	3.93105	0.132440	0.0662202	+	0.997805i	$0.478906\pi$
$882$	18.6029	0.626393
$883$	1.22005	0.0410581	0.0205291	−	0.999789i	$-0.493465\pi$
$883$	1.22005	0.0410581	0.0205291	+	0.999789i	$0.493465\pi$
$884$	12.7220	0.427889
$885$	24.2857	0.816355
$886$	−14.6503	−0.492187
$887$	−24.0834	−0.808643	−0.404321	−	0.914617i	$-0.632492\pi$
$887$	−24.0834	−0.808643	−0.404321	+	0.914617i	$0.632492\pi$
$888$	−3.85867	−0.129489
$889$	20.6545	0.692730
$890$	15.4459	0.517748
$891$	−3.29686	−0.110449
$892$	−22.1439	−0.741434
$893$	7.67831	0.256945
$894$	9.06768	0.303268
$895$	−38.4037	−1.28369
$896$	−3.35161	−0.111969
$897$	27.1980	0.908113
$898$	−28.4509	−0.949420
$899$	2.65856	0.0886680
$900$	43.1108	1.43703
$901$	−0.123669	−0.00412002
$902$	3.38117	0.112581
$903$	−59.4384	−1.97799
$904$	10.3451	0.344071
$905$	−54.7544	−1.82010
$906$	24.7793	0.823237
$907$	41.3102	1.37168	0.685841	−	0.727751i	$-0.259435\pi$
$907$	41.3102	1.37168	0.685841	+	0.727751i	$0.259435\pi$
$908$	−27.4434	−0.910741
$909$	−12.6100	−0.418247
$910$	−21.8123	−0.723071
$911$	26.2434	0.869483	0.434741	−	0.900555i	$-0.356840\pi$
$911$	26.2434	0.869483	0.434741	+	0.900555i	$0.356840\pi$
$912$	−4.82051	−0.159623
$913$	−5.25993	−0.174078
$914$	−11.8890	−0.393254
$915$	105.209	3.47811
$916$	5.18387	0.171280
$917$	−4.32842	−0.142937
$918$	28.5262	0.941504
$919$	−44.4185	−1.46523	−0.732616	−	0.680642i	$-0.761701\pi$
$919$	−44.4185	−1.46523	−0.732616	+	0.680642i	$0.761701\pi$
$920$	−22.7614	−0.750421
$921$	45.8873	1.51204
$922$	13.6367	0.449101
$923$	−4.69339	−0.154485
$924$	10.4614	0.344156
$925$	13.9209	0.457716
$926$	−25.7242	−0.845349
$927$	−60.4014	−1.98384
$928$	1.68035	0.0551601
$929$	−17.9780	−0.589840	−0.294920	−	0.955522i	$-0.595293\pi$
$929$	−17.9780	−0.589840	−0.294920	+	0.955522i	$0.595293\pi$
$930$	16.5570	0.542925
$931$	7.50443	0.245948
$932$	−16.5923	−0.543500
$933$	41.9337	1.37285
$934$	13.6238	0.445784
$935$	33.2321	1.08680
$936$	−7.43139	−0.242903
$937$	34.8405	1.13819	0.569094	−	0.822272i	$-0.307294\pi$
$937$	34.8405	1.13819	0.569094	+	0.822272i	$0.307294\pi$
$938$	−36.7822	−1.20098
$939$	32.9476	1.07520
$940$	−16.6689	−0.543680
$941$	16.7344	0.545527	0.272763	−	0.962081i	$-0.412062\pi$
$941$	16.7344	0.545527	0.272763	+	0.962081i	$0.412062\pi$
$942$	−26.9148	−0.876931
$943$	17.4220	0.567339
$944$	2.32069	0.0755319
$945$	−48.9089	−1.59101
$946$	−7.48593	−0.243389
$947$	−46.2890	−1.50419	−0.752096	−	0.659054i	$-0.770957\pi$
$947$	−46.2890	−1.50419	−0.752096	+	0.659054i	$0.770957\pi$
$948$	4.29537	0.139507
$949$	−0.557530	−0.0180982
$950$	17.3909	0.564236
$951$	3.05123	0.0989428
$952$	25.2141	0.817194
$953$	−18.1484	−0.587884	−0.293942	−	0.955823i	$-0.594967\pi$
$953$	−18.1484	−0.587884	−0.293942	+	0.955823i	$0.594967\pi$
$954$	0.0722396	0.00233884
$955$	47.1515	1.52579
$956$	1.11176	0.0359569
$957$	−5.24490	−0.169543
$958$	−29.6699	−0.958591
$959$	−5.75123	−0.185717
$960$	10.4649	0.337753
$961$	−28.4968	−0.919252
$962$	−2.39967	−0.0773685
$963$	13.3068	0.428806
$964$	12.7550	0.410809
$965$	−48.4333	−1.55912
$966$	53.9043	1.73434
$967$	−30.2373	−0.972366	−0.486183	−	0.873857i	$-0.661611\pi$
$967$	−30.2373	−0.972366	−0.486183	+	0.873857i	$0.661611\pi$
$968$	−9.68244	−0.311205
$969$	36.2647	1.16499
$970$	−8.14950	−0.261665
$971$	−32.9524	−1.05749	−0.528747	−	0.848780i	$-0.677338\pi$
$971$	−32.9524	−1.05749	−0.528747	+	0.848780i	$0.677338\pi$
$972$	19.1859	0.615388
$973$	10.7077	0.343274
$974$	−35.1869	−1.12746
$975$	45.1129	1.44477
$976$	10.0536	0.321807
$977$	−41.5223	−1.32842	−0.664208	−	0.747548i	$-0.731231\pi$
$977$	−41.5223	−1.32842	−0.664208	+	0.747548i	$0.731231\pi$
$978$	−64.8551	−2.07384
$979$	−4.60699	−0.147240
$980$	−16.2914	−0.520411
$981$	9.74326	0.311078
$982$	31.2110	0.995983
$983$	−18.8503	−0.601231	−0.300615	−	0.953745i	$-0.597192\pi$
$983$	−18.8503	−0.601231	−0.300615	+	0.953745i	$0.597192\pi$
$984$	−8.01003	−0.255351
$985$	74.5371	2.37495
$986$	−12.6412	−0.402579
$987$	39.4758	1.25653
$988$	−2.99783	−0.0953736
$989$	−38.5725	−1.22654
$990$	−19.4120	−0.616954
$991$	−29.6050	−0.940433	−0.470217	−	0.882551i	$-0.655824\pi$
$991$	−29.6050	−0.940433	−0.470217	+	0.882551i	$0.655824\pi$
$992$	1.58215	0.0502333
$993$	−47.4795	−1.50672
$994$	−9.30195	−0.295040
$995$	−92.2832	−2.92557
$996$	12.4608	0.394837
$997$	4.67722	0.148129	0.0740645	−	0.997253i	$-0.476403\pi$
$997$	4.67722	0.148129	0.0740645	+	0.997253i	$0.476403\pi$
$998$	−24.0423	−0.761046
$999$	−5.38070	−0.170238

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.b.1.9	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.b.1.9	✓	54	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.71927 q^{3} +1.00000 q^{4} -3.84841 q^{5} -2.71927 q^{6} -3.35161 q^{7} +1.00000 q^{8} +4.39444 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.71927 q^{3} +1.00000 q^{4} -3.84841 q^{5} -2.71927 q^{6} -3.35161 q^{7} +1.00000 q^{8} +4.39444 q^{9} -3.84841 q^{10} +1.14785 q^{11} -2.71927 q^{12} -1.69109 q^{13} -3.35161 q^{14} +10.4649 q^{15} +1.00000 q^{16} -7.52299 q^{17} +4.39444 q^{18} +1.77272 q^{19} -3.84841 q^{20} +9.11394 q^{21} +1.14785 q^{22} +5.91449 q^{23} -2.71927 q^{24} +9.81029 q^{25} -1.69109 q^{26} -3.79187 q^{27} -3.35161 q^{28} +1.68035 q^{29} +10.4649 q^{30} +1.58215 q^{31} +1.00000 q^{32} -3.12131 q^{33} -7.52299 q^{34} +12.8984 q^{35} +4.39444 q^{36} +1.41901 q^{37} +1.77272 q^{38} +4.59853 q^{39} -3.84841 q^{40} +2.94565 q^{41} +9.11394 q^{42} -6.52170 q^{43} +1.14785 q^{44} -16.9116 q^{45} +5.91449 q^{46} +4.33137 q^{47} -2.71927 q^{48} +4.23328 q^{49} +9.81029 q^{50} +20.4571 q^{51} -1.69109 q^{52} +0.0164389 q^{53} -3.79187 q^{54} -4.41740 q^{55} -3.35161 q^{56} -4.82051 q^{57} +1.68035 q^{58} +2.32069 q^{59} +10.4649 q^{60} +10.0536 q^{61} +1.58215 q^{62} -14.7285 q^{63} +1.00000 q^{64} +6.50801 q^{65} -3.12131 q^{66} +10.9745 q^{67} -7.52299 q^{68} -16.0831 q^{69} +12.8984 q^{70} +2.77537 q^{71} +4.39444 q^{72} +0.329687 q^{73} +1.41901 q^{74} -26.6769 q^{75} +1.77272 q^{76} -3.84714 q^{77} +4.59853 q^{78} -1.57960 q^{79} -3.84841 q^{80} -2.87221 q^{81} +2.94565 q^{82} -4.58242 q^{83} +9.11394 q^{84} +28.9516 q^{85} -6.52170 q^{86} -4.56933 q^{87} +1.14785 q^{88} -4.01358 q^{89} -16.9116 q^{90} +5.66787 q^{91} +5.91449 q^{92} -4.30229 q^{93} +4.33137 q^{94} -6.82217 q^{95} -2.71927 q^{96} +2.11762 q^{97} +4.23328 q^{98} +5.04416 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * q^99

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