LMFDB - Embedded newform 6022.2.a.c.1.8

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			1.8
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.60317 q^{3} +1.00000 q^{4} +2.24226 q^{5} +2.60317 q^{6} -4.82749 q^{7} -1.00000 q^{8} +3.77649 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.60317 q^{3} +1.00000 q^{4} +2.24226 q^{5} +2.60317 q^{6} -4.82749 q^{7} -1.00000 q^{8} +3.77649 q^{9} -2.24226 q^{10} -2.77046 q^{11} -2.60317 q^{12} -1.26957 q^{13} +4.82749 q^{14} -5.83698 q^{15} +1.00000 q^{16} +3.37627 q^{17} -3.77649 q^{18} -6.99409 q^{19} +2.24226 q^{20} +12.5668 q^{21} +2.77046 q^{22} +0.550543 q^{23} +2.60317 q^{24} +0.0277336 q^{25} +1.26957 q^{26} -2.02132 q^{27} -4.82749 q^{28} -1.52440 q^{29} +5.83698 q^{30} -7.37488 q^{31} -1.00000 q^{32} +7.21196 q^{33} -3.37627 q^{34} -10.8245 q^{35} +3.77649 q^{36} +7.12574 q^{37} +6.99409 q^{38} +3.30490 q^{39} -2.24226 q^{40} -7.52454 q^{41} -12.5668 q^{42} -2.89878 q^{43} -2.77046 q^{44} +8.46787 q^{45} -0.550543 q^{46} -7.56402 q^{47} -2.60317 q^{48} +16.3047 q^{49} -0.0277336 q^{50} -8.78899 q^{51} -1.26957 q^{52} -11.7024 q^{53} +2.02132 q^{54} -6.21209 q^{55} +4.82749 q^{56} +18.2068 q^{57} +1.52440 q^{58} +12.6460 q^{59} -5.83698 q^{60} -14.5079 q^{61} +7.37488 q^{62} -18.2310 q^{63} +1.00000 q^{64} -2.84671 q^{65} -7.21196 q^{66} -8.82146 q^{67} +3.37627 q^{68} -1.43316 q^{69} +10.8245 q^{70} -12.5731 q^{71} -3.77649 q^{72} +4.90846 q^{73} -7.12574 q^{74} -0.0721951 q^{75} -6.99409 q^{76} +13.3744 q^{77} -3.30490 q^{78} +12.7335 q^{79} +2.24226 q^{80} -6.06761 q^{81} +7.52454 q^{82} -1.75608 q^{83} +12.5668 q^{84} +7.57047 q^{85} +2.89878 q^{86} +3.96827 q^{87} +2.77046 q^{88} -10.4716 q^{89} -8.46787 q^{90} +6.12884 q^{91} +0.550543 q^{92} +19.1981 q^{93} +7.56402 q^{94} -15.6826 q^{95} +2.60317 q^{96} +7.08408 q^{97} -16.3047 q^{98} -10.4626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.60317	−1.50294	−0.751470	−	0.659767i	$-0.770655\pi$
$3$	−2.60317	−1.50294	−0.751470	+	0.659767i	$0.770655\pi$
$4$	1.00000	0.500000
$5$	2.24226	1.00277	0.501385	−	0.865224i	$-0.332824\pi$
$5$	2.24226	1.00277	0.501385	+	0.865224i	$0.332824\pi$
$6$	2.60317	1.06274
$7$	−4.82749	−1.82462	−0.912310	−	0.409500i	$-0.865703\pi$
$7$	−4.82749	−1.82462	−0.912310	+	0.409500i	$0.865703\pi$
$8$	−1.00000	−0.353553
$9$	3.77649	1.25883
$10$	−2.24226	−0.709065
$11$	−2.77046	−0.835324	−0.417662	−	0.908602i	$-0.637150\pi$
$11$	−2.77046	−0.835324	−0.417662	+	0.908602i	$0.637150\pi$
$12$	−2.60317	−0.751470
$13$	−1.26957	−0.352115	−0.176058	−	0.984380i	$-0.556335\pi$
$13$	−1.26957	−0.352115	−0.176058	+	0.984380i	$0.556335\pi$
$14$	4.82749	1.29020
$15$	−5.83698	−1.50710
$16$	1.00000	0.250000
$17$	3.37627	0.818865	0.409432	−	0.912340i	$-0.365727\pi$
$17$	3.37627	0.818865	0.409432	+	0.912340i	$0.365727\pi$
$18$	−3.77649	−0.890126
$19$	−6.99409	−1.60455	−0.802277	−	0.596952i	$-0.796378\pi$
$19$	−6.99409	−1.60455	−0.802277	+	0.596952i	$0.796378\pi$
$20$	2.24226	0.501385
$21$	12.5668	2.74229
$22$	2.77046	0.590663
$23$	0.550543	0.114796	0.0573981	−	0.998351i	$-0.481720\pi$
$23$	0.550543	0.114796	0.0573981	+	0.998351i	$0.481720\pi$
$24$	2.60317	0.531370
$25$	0.0277336	0.00554671
$26$	1.26957	0.248983
$27$	−2.02132	−0.389004
$28$	−4.82749	−0.912310
$29$	−1.52440	−0.283074	−0.141537	−	0.989933i	$-0.545204\pi$
$29$	−1.52440	−0.283074	−0.141537	+	0.989933i	$0.545204\pi$
$30$	5.83698	1.06568
$31$	−7.37488	−1.32457	−0.662284	−	0.749253i	$-0.730413\pi$
$31$	−7.37488	−1.32457	−0.662284	+	0.749253i	$0.730413\pi$
$32$	−1.00000	−0.176777
$33$	7.21196	1.25544
$34$	−3.37627	−0.579025
$35$	−10.8245	−1.82967
$36$	3.77649	0.629414
$37$	7.12574	1.17146	0.585732	−	0.810505i	$-0.300807\pi$
$37$	7.12574	1.17146	0.585732	+	0.810505i	$0.300807\pi$
$38$	6.99409	1.13459
$39$	3.30490	0.529208
$40$	−2.24226	−0.354533
$41$	−7.52454	−1.17514	−0.587568	−	0.809175i	$-0.699914\pi$
$41$	−7.52454	−1.17514	−0.587568	+	0.809175i	$0.699914\pi$
$42$	−12.5668	−1.93909
$43$	−2.89878	−0.442059	−0.221030	−	0.975267i	$-0.570942\pi$
$43$	−2.89878	−0.442059	−0.221030	+	0.975267i	$0.570942\pi$
$44$	−2.77046	−0.417662
$45$	8.46787	1.26232
$46$	−0.550543	−0.0811732
$47$	−7.56402	−1.10333	−0.551663	−	0.834067i	$-0.686007\pi$
$47$	−7.56402	−1.10333	−0.551663	+	0.834067i	$0.686007\pi$
$48$	−2.60317	−0.375735
$49$	16.3047	2.32924
$50$	−0.0277336	−0.00392212
$51$	−8.78899	−1.23070
$52$	−1.26957	−0.176058
$53$	−11.7024	−1.60745	−0.803724	−	0.595003i	$-0.797151\pi$
$53$	−11.7024	−1.60745	−0.803724	+	0.595003i	$0.797151\pi$
$54$	2.02132	0.275067
$55$	−6.21209	−0.837637
$56$	4.82749	0.645101
$57$	18.2068	2.41155
$58$	1.52440	0.200164
$59$	12.6460	1.64637	0.823186	−	0.567772i	$-0.192194\pi$
$59$	12.6460	1.64637	0.823186	+	0.567772i	$0.192194\pi$
$60$	−5.83698	−0.753551
$61$	−14.5079	−1.85755	−0.928776	−	0.370642i	$-0.879138\pi$
$61$	−14.5079	−1.85755	−0.928776	+	0.370642i	$0.879138\pi$
$62$	7.37488	0.936611
$63$	−18.2310	−2.29688
$64$	1.00000	0.125000
$65$	−2.84671	−0.353091
$66$	−7.21196	−0.887731
$67$	−8.82146	−1.07771	−0.538857	−	0.842397i	$-0.681144\pi$
$67$	−8.82146	−1.07771	−0.538857	+	0.842397i	$0.681144\pi$
$68$	3.37627	0.409432
$69$	−1.43316	−0.172532
$70$	10.8245	1.29377
$71$	−12.5731	−1.49215	−0.746075	−	0.665862i	$-0.768064\pi$
$71$	−12.5731	−1.49215	−0.746075	+	0.665862i	$0.768064\pi$
$72$	−3.77649	−0.445063
$73$	4.90846	0.574492	0.287246	−	0.957857i	$-0.407260\pi$
$73$	4.90846	0.574492	0.287246	+	0.957857i	$0.407260\pi$
$74$	−7.12574	−0.828350
$75$	−0.0721951	−0.00833637
$76$	−6.99409	−0.802277
$77$	13.3744	1.52415
$78$	−3.30490	−0.374207
$79$	12.7335	1.43263	0.716314	−	0.697778i	$-0.245828\pi$
$79$	12.7335	1.43263	0.716314	+	0.697778i	$0.245828\pi$
$80$	2.24226	0.250692
$81$	−6.06761	−0.674179
$82$	7.52454	0.830946
$83$	−1.75608	−0.192754	−0.0963772	−	0.995345i	$-0.530726\pi$
$83$	−1.75608	−0.192754	−0.0963772	+	0.995345i	$0.530726\pi$
$84$	12.5668	1.37115
$85$	7.57047	0.821133
$86$	2.89878	0.312583
$87$	3.96827	0.425443
$88$	2.77046	0.295332
$89$	−10.4716	−1.10999	−0.554995	−	0.831854i	$-0.687280\pi$
$89$	−10.4716	−1.10999	−0.554995	+	0.831854i	$0.687280\pi$
$90$	−8.46787	−0.892592
$91$	6.12884	0.642477
$92$	0.550543	0.0573981
$93$	19.1981	1.99075
$94$	7.56402	0.780170
$95$	−15.6826	−1.60900
$96$	2.60317	0.265685
$97$	7.08408	0.719279	0.359640	−	0.933091i	$-0.382900\pi$
$97$	7.08408	0.719279	0.359640	+	0.933091i	$0.382900\pi$
$98$	−16.3047	−1.64702
$99$	−10.4626	−1.05153
$100$	0.0277336	0.00277336
$101$	−6.91549	−0.688117	−0.344058	−	0.938948i	$-0.611802\pi$
$101$	−6.91549	−0.688117	−0.344058	+	0.938948i	$0.611802\pi$
$102$	8.78899	0.870239
$103$	6.83897	0.673864	0.336932	−	0.941529i	$-0.390611\pi$
$103$	6.83897	0.673864	0.336932	+	0.941529i	$0.390611\pi$
$104$	1.26957	0.124492
$105$	28.1780	2.74989
$106$	11.7024	1.13664
$107$	−3.26191	−0.315340	−0.157670	−	0.987492i	$-0.550398\pi$
$107$	−3.26191	−0.315340	−0.157670	+	0.987492i	$0.550398\pi$
$108$	−2.02132	−0.194502
$109$	7.36017	0.704977	0.352488	−	0.935816i	$-0.385336\pi$
$109$	7.36017	0.704977	0.352488	+	0.935816i	$0.385336\pi$
$110$	6.21209	0.592299
$111$	−18.5495	−1.76064
$112$	−4.82749	−0.456155
$113$	−5.84609	−0.549954	−0.274977	−	0.961451i	$-0.588670\pi$
$113$	−5.84609	−0.549954	−0.274977	+	0.961451i	$0.588670\pi$
$114$	−18.2068	−1.70522
$115$	1.23446	0.115114
$116$	−1.52440	−0.141537
$117$	−4.79451	−0.443253
$118$	−12.6460	−1.16416
$119$	−16.2989	−1.49412
$120$	5.83698	0.532841
$121$	−3.32457	−0.302234
$122$	14.5079	1.31349
$123$	19.5876	1.76616
$124$	−7.37488	−0.662284
$125$	−11.1491	−0.997207
$126$	18.2310	1.62414
$127$	5.16827	0.458610	0.229305	−	0.973355i	$-0.426355\pi$
$127$	5.16827	0.458610	0.229305	+	0.973355i	$0.426355\pi$
$128$	−1.00000	−0.0883883
$129$	7.54600	0.664389
$130$	2.84671	0.249673
$131$	−5.59530	−0.488864	−0.244432	−	0.969666i	$-0.578601\pi$
$131$	−5.59530	−0.488864	−0.244432	+	0.969666i	$0.578601\pi$
$132$	7.21196	0.627721
$133$	33.7639	2.92770
$134$	8.82146	0.762058
$135$	−4.53234	−0.390081
$136$	−3.37627	−0.289512
$137$	−5.53177	−0.472611	−0.236306	−	0.971679i	$-0.575937\pi$
$137$	−5.53177	−0.472611	−0.236306	+	0.971679i	$0.575937\pi$
$138$	1.43316	0.121998
$139$	14.6843	1.24550	0.622751	−	0.782420i	$-0.286015\pi$
$139$	14.6843	1.24550	0.622751	+	0.782420i	$0.286015\pi$
$140$	−10.8245	−0.914837
$141$	19.6904	1.65823
$142$	12.5731	1.05511
$143$	3.51729	0.294130
$144$	3.77649	0.314707
$145$	−3.41810	−0.283858
$146$	−4.90846	−0.406227
$147$	−42.4438	−3.50071
$148$	7.12574	0.585732
$149$	6.05094	0.495712	0.247856	−	0.968797i	$-0.420274\pi$
$149$	6.05094	0.495712	0.247856	+	0.968797i	$0.420274\pi$
$150$	0.0721951	0.00589471
$151$	−16.6995	−1.35898	−0.679492	−	0.733683i	$-0.737800\pi$
$151$	−16.6995	−1.35898	−0.679492	+	0.733683i	$0.737800\pi$
$152$	6.99409	0.567295
$153$	12.7504	1.03081
$154$	−13.3744	−1.07774
$155$	−16.5364	−1.32824
$156$	3.30490	0.264604
$157$	−7.76850	−0.619994	−0.309997	−	0.950738i	$-0.600328\pi$
$157$	−7.76850	−0.619994	−0.309997	+	0.950738i	$0.600328\pi$
$158$	−12.7335	−1.01302
$159$	30.4633	2.41590
$160$	−2.24226	−0.177266
$161$	−2.65774	−0.209460
$162$	6.06761	0.476717
$163$	5.18357	0.406009	0.203004	−	0.979178i	$-0.434929\pi$
$163$	5.18357	0.406009	0.203004	+	0.979178i	$0.434929\pi$
$164$	−7.52454	−0.587568
$165$	16.1711	1.25892
$166$	1.75608	0.136298
$167$	19.7337	1.52704	0.763521	−	0.645782i	$-0.223469\pi$
$167$	19.7337	1.52704	0.763521	+	0.645782i	$0.223469\pi$
$168$	−12.5668	−0.969547
$169$	−11.3882	−0.876015
$170$	−7.57047	−0.580628
$171$	−26.4131	−2.01986
$172$	−2.89878	−0.221030
$173$	2.00464	0.152410	0.0762051	−	0.997092i	$-0.475720\pi$
$173$	2.00464	0.152410	0.0762051	+	0.997092i	$0.475720\pi$
$174$	−3.96827	−0.300834
$175$	−0.133883	−0.0101206
$176$	−2.77046	−0.208831
$177$	−32.9197	−2.47440
$178$	10.4716	0.784881
$179$	−11.1452	−0.833028	−0.416514	−	0.909129i	$-0.636748\pi$
$179$	−11.1452	−0.833028	−0.416514	+	0.909129i	$0.636748\pi$
$180$	8.46787	0.631158
$181$	2.25357	0.167507	0.0837533	−	0.996487i	$-0.473309\pi$
$181$	2.25357	0.167507	0.0837533	+	0.996487i	$0.473309\pi$
$182$	−6.12884	−0.454300
$183$	37.7666	2.79179
$184$	−0.550543	−0.0405866
$185$	15.9778	1.17471
$186$	−19.1981	−1.40767
$187$	−9.35380	−0.684017
$188$	−7.56402	−0.551663
$189$	9.75792	0.709785
$190$	15.6826	1.13773
$191$	−2.86384	−0.207220	−0.103610	−	0.994618i	$-0.533039\pi$
$191$	−2.86384	−0.207220	−0.103610	+	0.994618i	$0.533039\pi$
$192$	−2.60317	−0.187868
$193$	−5.03880	−0.362701	−0.181351	−	0.983419i	$-0.558047\pi$
$193$	−5.03880	−0.362701	−0.181351	+	0.983419i	$0.558047\pi$
$194$	−7.08408	−0.508607
$195$	7.41046	0.530674
$196$	16.3047	1.16462
$197$	9.49859	0.676747	0.338373	−	0.941012i	$-0.390123\pi$
$197$	9.49859	0.676747	0.338373	+	0.941012i	$0.390123\pi$
$198$	10.4626	0.743544
$199$	−15.0694	−1.06824	−0.534121	−	0.845408i	$-0.679357\pi$
$199$	−15.0694	−1.06824	−0.534121	+	0.845408i	$0.679357\pi$
$200$	−0.0277336	−0.00196106
$201$	22.9638	1.61974
$202$	6.91549	0.486572
$203$	7.35903	0.516503
$204$	−8.78899	−0.615352
$205$	−16.8720	−1.17839
$206$	−6.83897	−0.476494
$207$	2.07912	0.144509
$208$	−1.26957	−0.0880288
$209$	19.3768	1.34032
$210$	−28.1780	−1.94447
$211$	−10.3478	−0.712371	−0.356186	−	0.934415i	$-0.615923\pi$
$211$	−10.3478	−0.712371	−0.356186	+	0.934415i	$0.615923\pi$
$212$	−11.7024	−0.803724
$213$	32.7298	2.24261
$214$	3.26191	0.222979
$215$	−6.49981	−0.443284
$216$	2.02132	0.137534
$217$	35.6022	2.41683
$218$	−7.36017	−0.498494
$219$	−12.7776	−0.863427
$220$	−6.21209	−0.418819
$221$	−4.28641	−0.288335
$222$	18.5495	1.24496
$223$	−18.4775	−1.23734	−0.618671	−	0.785650i	$-0.712329\pi$
$223$	−18.4775	−1.23734	−0.618671	+	0.785650i	$0.712329\pi$
$224$	4.82749	0.322550
$225$	0.104735	0.00698236
$226$	5.84609	0.388876
$227$	−4.71981	−0.313265	−0.156632	−	0.987657i	$-0.550064\pi$
$227$	−4.71981	−0.313265	−0.156632	+	0.987657i	$0.550064\pi$
$228$	18.2068	1.20577
$229$	−9.27326	−0.612794	−0.306397	−	0.951904i	$-0.599124\pi$
$229$	−9.27326	−0.612794	−0.306397	+	0.951904i	$0.599124\pi$
$230$	−1.23446	−0.0813980
$231$	−34.8157	−2.29070
$232$	1.52440	0.100082
$233$	6.35030	0.416022	0.208011	−	0.978126i	$-0.433301\pi$
$233$	6.35030	0.416022	0.208011	+	0.978126i	$0.433301\pi$
$234$	4.79451	0.313427
$235$	−16.9605	−1.10638
$236$	12.6460	0.823186
$237$	−33.1474	−2.15315
$238$	16.2989	1.05650
$239$	21.2588	1.37512	0.687559	−	0.726128i	$-0.258682\pi$
$239$	21.2588	1.37512	0.687559	+	0.726128i	$0.258682\pi$
$240$	−5.83698	−0.376776
$241$	−19.2567	−1.24043	−0.620217	−	0.784430i	$-0.712956\pi$
$241$	−19.2567	−1.24043	−0.620217	+	0.784430i	$0.712956\pi$
$242$	3.32457	0.213712
$243$	21.8590	1.40225
$244$	−14.5079	−0.928776
$245$	36.5593	2.33569
$246$	−19.5876	−1.24886
$247$	8.87948	0.564988
$248$	7.37488	0.468305
$249$	4.57136	0.289698
$250$	11.1491	0.705132
$251$	−3.31747	−0.209397	−0.104698	−	0.994504i	$-0.533388\pi$
$251$	−3.31747	−0.209397	−0.104698	+	0.994504i	$0.533388\pi$
$252$	−18.2310	−1.14844
$253$	−1.52526	−0.0958921
$254$	−5.16827	−0.324286
$255$	−19.7072	−1.23411
$256$	1.00000	0.0625000
$257$	−22.3090	−1.39160	−0.695799	−	0.718236i	$-0.744950\pi$
$257$	−22.3090	−1.39160	−0.695799	+	0.718236i	$0.744950\pi$
$258$	−7.54600	−0.469794
$259$	−34.3994	−2.13748
$260$	−2.84671	−0.176545
$261$	−5.75688	−0.356342
$262$	5.59530	0.345679
$263$	−11.9585	−0.737395	−0.368698	−	0.929549i	$-0.620196\pi$
$263$	−11.9585	−0.737395	−0.368698	+	0.929549i	$0.620196\pi$
$264$	−7.21196	−0.443866
$265$	−26.2398	−1.61190
$266$	−33.7639	−2.07020
$267$	27.2594	1.66825
$268$	−8.82146	−0.538857
$269$	−16.9598	−1.03405	−0.517027	−	0.855969i	$-0.672961\pi$
$269$	−16.9598	−1.03405	−0.517027	+	0.855969i	$0.672961\pi$
$270$	4.53234	0.275829
$271$	24.0218	1.45922	0.729610	−	0.683863i	$-0.239702\pi$
$271$	24.0218	1.45922	0.729610	+	0.683863i	$0.239702\pi$
$272$	3.37627	0.204716
$273$	−15.9544	−0.965604
$274$	5.53177	0.334187
$275$	−0.0768346	−0.00463330
$276$	−1.43316	−0.0862659
$277$	−9.17090	−0.551026	−0.275513	−	0.961297i	$-0.588848\pi$
$277$	−9.17090	−0.551026	−0.275513	+	0.961297i	$0.588848\pi$
$278$	−14.6843	−0.880703
$279$	−27.8511	−1.66740
$280$	10.8245	0.646887
$281$	−17.2027	−1.02623	−0.513113	−	0.858321i	$-0.671508\pi$
$281$	−17.2027	−1.02623	−0.513113	+	0.858321i	$0.671508\pi$
$282$	−19.6904	−1.17255
$283$	2.42511	0.144158	0.0720789	−	0.997399i	$-0.477037\pi$
$283$	2.42511	0.144158	0.0720789	+	0.997399i	$0.477037\pi$
$284$	−12.5731	−0.746075
$285$	40.8244	2.41823
$286$	−3.51729	−0.207982
$287$	36.3246	2.14418
$288$	−3.77649	−0.222532
$289$	−5.60083	−0.329461
$290$	3.41810	0.200718
$291$	−18.4411	−1.08103
$292$	4.90846	0.287246
$293$	16.5326	0.965844	0.482922	−	0.875663i	$-0.339575\pi$
$293$	16.5326	0.965844	0.482922	+	0.875663i	$0.339575\pi$
$294$	42.4438	2.47537
$295$	28.3557	1.65093
$296$	−7.12574	−0.414175
$297$	5.59999	0.324944
$298$	−6.05094	−0.350522
$299$	−0.698953	−0.0404215
$300$	−0.0721951	−0.00416819
$301$	13.9938	0.806590
$302$	16.6995	0.960946
$303$	18.0022	1.03420
$304$	−6.99409	−0.401138
$305$	−32.5306	−1.86270
$306$	−12.7504	−0.728893
$307$	14.4649	0.825553	0.412776	−	0.910832i	$-0.364559\pi$
$307$	14.4649	0.825553	0.412776	+	0.910832i	$0.364559\pi$
$308$	13.3744	0.762074
$309$	−17.8030	−1.01278
$310$	16.5364	0.939205
$311$	34.6114	1.96263	0.981317	−	0.192398i	$-0.0616264\pi$
$311$	34.6114	1.96263	0.981317	+	0.192398i	$0.0616264\pi$
$312$	−3.30490	−0.187103
$313$	−12.8770	−0.727853	−0.363926	−	0.931428i	$-0.618564\pi$
$313$	−12.8770	−0.727853	−0.363926	+	0.931428i	$0.618564\pi$
$314$	7.76850	0.438402
$315$	−40.8785	−2.30325
$316$	12.7335	0.716314
$317$	4.83669	0.271656	0.135828	−	0.990732i	$-0.456631\pi$
$317$	4.83669	0.271656	0.135828	+	0.990732i	$0.456631\pi$
$318$	−30.4633	−1.70830
$319$	4.22329	0.236459
$320$	2.24226	0.125346
$321$	8.49129	0.473938
$322$	2.65774	0.148110
$323$	−23.6139	−1.31391
$324$	−6.06761	−0.337089
$325$	−0.0352097	−0.00195308
$326$	−5.18357	−0.287092
$327$	−19.1598	−1.05954
$328$	7.52454	0.415473
$329$	36.5153	2.01315
$330$	−16.1711	−0.890190
$331$	19.6495	1.08004	0.540018	−	0.841653i	$-0.318417\pi$
$331$	19.6495	1.08004	0.540018	+	0.841653i	$0.318417\pi$
$332$	−1.75608	−0.0963772
$333$	26.9103	1.47467
$334$	−19.7337	−1.07978
$335$	−19.7800	−1.08070
$336$	12.5668	0.685574
$337$	24.5619	1.33797	0.668985	−	0.743276i	$-0.266729\pi$
$337$	24.5619	1.33797	0.668985	+	0.743276i	$0.266729\pi$
$338$	11.3882	0.619436
$339$	15.2184	0.826547
$340$	7.57047	0.410566
$341$	20.4318	1.10644
$342$	26.4131	1.42826
$343$	−44.9182	−2.42535
$344$	2.89878	0.156292
$345$	−3.21351	−0.173010
$346$	−2.00464	−0.107770
$347$	13.2909	0.713491	0.356746	−	0.934202i	$-0.383886\pi$
$347$	13.2909	0.713491	0.356746	+	0.934202i	$0.383886\pi$
$348$	3.96827	0.212722
$349$	−14.5645	−0.779620	−0.389810	−	0.920895i	$-0.627459\pi$
$349$	−14.5645	−0.779620	−0.389810	+	0.920895i	$0.627459\pi$
$350$	0.133883	0.00715637
$351$	2.56621	0.136974
$352$	2.77046	0.147666
$353$	33.1279	1.76322	0.881609	−	0.471980i	$-0.156461\pi$
$353$	33.1279	1.76322	0.881609	+	0.471980i	$0.156461\pi$
$354$	32.9197	1.74966
$355$	−28.1921	−1.49628
$356$	−10.4716	−0.554995
$357$	42.4288	2.24557
$358$	11.1452	0.589040
$359$	−8.48389	−0.447763	−0.223881	−	0.974616i	$-0.571873\pi$
$359$	−8.48389	−0.447763	−0.223881	+	0.974616i	$0.571873\pi$
$360$	−8.46787	−0.446296
$361$	29.9173	1.57459
$362$	−2.25357	−0.118445
$363$	8.65442	0.454239
$364$	6.12884	0.321238
$365$	11.0061	0.576083
$366$	−37.7666	−1.97409
$367$	10.4225	0.544052	0.272026	−	0.962290i	$-0.412306\pi$
$367$	10.4225	0.544052	0.272026	+	0.962290i	$0.412306\pi$
$368$	0.550543	0.0286991
$369$	−28.4163	−1.47929
$370$	−15.9778	−0.830644
$371$	56.4932	2.93298
$372$	19.1981	0.995373
$373$	9.25977	0.479453	0.239726	−	0.970840i	$-0.422942\pi$
$373$	9.25977	0.479453	0.239726	+	0.970840i	$0.422942\pi$
$374$	9.35380	0.483673
$375$	29.0230	1.49874
$376$	7.56402	0.390085
$377$	1.93533	0.0996747
$378$	−9.75792	−0.501893
$379$	−24.6495	−1.26616	−0.633079	−	0.774087i	$-0.718209\pi$
$379$	−24.6495	−1.26616	−0.633079	+	0.774087i	$0.718209\pi$
$380$	−15.6826	−0.804499
$381$	−13.4539	−0.689264
$382$	2.86384	0.146527
$383$	9.82086	0.501823	0.250911	−	0.968010i	$-0.419270\pi$
$383$	9.82086	0.501823	0.250911	+	0.968010i	$0.419270\pi$
$384$	2.60317	0.132842
$385$	29.9888	1.52837
$386$	5.03880	0.256468
$387$	−10.9472	−0.556477
$388$	7.08408	0.359640
$389$	−6.09996	−0.309280	−0.154640	−	0.987971i	$-0.549422\pi$
$389$	−6.09996	−0.309280	−0.154640	+	0.987971i	$0.549422\pi$
$390$	−7.41046	−0.375243
$391$	1.85878	0.0940026
$392$	−16.3047	−0.823510
$393$	14.5655	0.734733
$394$	−9.49859	−0.478532
$395$	28.5518	1.43660
$396$	−10.4626	−0.525765
$397$	18.6756	0.937299	0.468650	−	0.883384i	$-0.344741\pi$
$397$	18.6756	0.937299	0.468650	+	0.883384i	$0.344741\pi$
$398$	15.0694	0.755361
$399$	−87.8931	−4.40016
$400$	0.0277336	0.00138668
$401$	−29.4752	−1.47192	−0.735961	−	0.677024i	$-0.763269\pi$
$401$	−29.4752	−1.47192	−0.735961	+	0.677024i	$0.763269\pi$
$402$	−22.9638	−1.14533
$403$	9.36293	0.466401
$404$	−6.91549	−0.344058
$405$	−13.6052	−0.676046
$406$	−7.35903	−0.365223
$407$	−19.7415	−0.978552
$408$	8.78899	0.435120
$409$	35.8915	1.77472	0.887360	−	0.461076i	$-0.152537\pi$
$409$	35.8915	1.77472	0.887360	+	0.461076i	$0.152537\pi$
$410$	16.8720	0.833248
$411$	14.4001	0.710307
$412$	6.83897	0.336932
$413$	−61.0486	−3.00400
$414$	−2.07912	−0.102183
$415$	−3.93758	−0.193288
$416$	1.26957	0.0622458
$417$	−38.2256	−1.87192
$418$	−19.3768	−0.947751
$419$	14.6680	0.716579	0.358289	−	0.933611i	$-0.383360\pi$
$419$	14.6680	0.716579	0.358289	+	0.933611i	$0.383360\pi$
$420$	28.1780	1.37494
$421$	21.2731	1.03679	0.518393	−	0.855142i	$-0.326530\pi$
$421$	21.2731	1.03679	0.518393	+	0.855142i	$0.326530\pi$
$422$	10.3478	0.503723
$423$	−28.5654	−1.38890
$424$	11.7024	0.568318
$425$	0.0936358	0.00454201
$426$	−32.7298	−1.58577
$427$	70.0370	3.38933
$428$	−3.26191	−0.157670
$429$	−9.15609	−0.442060
$430$	6.49981	0.313449
$431$	33.4334	1.61043	0.805215	−	0.592984i	$-0.202050\pi$
$431$	33.4334	1.61043	0.805215	+	0.592984i	$0.202050\pi$
$432$	−2.02132	−0.0972510
$433$	25.2484	1.21336	0.606681	−	0.794945i	$-0.292500\pi$
$433$	25.2484	1.21336	0.606681	+	0.794945i	$0.292500\pi$
$434$	−35.6022	−1.70896
$435$	8.89790	0.426622
$436$	7.36017	0.352488
$437$	−3.85055	−0.184197
$438$	12.7776	0.610535
$439$	9.30959	0.444323	0.222161	−	0.975010i	$-0.428689\pi$
$439$	9.30959	0.444323	0.222161	+	0.975010i	$0.428689\pi$
$440$	6.21209	0.296150
$441$	61.5744	2.93211
$442$	4.28641	0.203883
$443$	3.15860	0.150070	0.0750349	−	0.997181i	$-0.476093\pi$
$443$	3.15860	0.150070	0.0750349	+	0.997181i	$0.476093\pi$
$444$	−18.5495	−0.880320
$445$	−23.4801	−1.11306
$446$	18.4775	0.874933
$447$	−15.7516	−0.745026
$448$	−4.82749	−0.228078
$449$	14.0263	0.661940	0.330970	−	0.943641i	$-0.392624\pi$
$449$	14.0263	0.661940	0.330970	+	0.943641i	$0.392624\pi$
$450$	−0.104735	−0.00493727
$451$	20.8464	0.981619
$452$	−5.84609	−0.274977
$453$	43.4715	2.04247
$454$	4.71981	0.221512
$455$	13.7425	0.644256
$456$	−18.2068	−0.852611
$457$	−0.688761	−0.0322189	−0.0161094	−	0.999870i	$-0.505128\pi$
$457$	−0.688761	−0.0322189	−0.0161094	+	0.999870i	$0.505128\pi$
$458$	9.27326	0.433311
$459$	−6.82453	−0.318542
$460$	1.23446	0.0575571
$461$	−19.9237	−0.927937	−0.463969	−	0.885852i	$-0.653575\pi$
$461$	−19.9237	−0.927937	−0.463969	+	0.885852i	$0.653575\pi$
$462$	34.8157	1.61977
$463$	7.16100	0.332800	0.166400	−	0.986058i	$-0.446786\pi$
$463$	7.16100	0.332800	0.166400	+	0.986058i	$0.446786\pi$
$464$	−1.52440	−0.0707685
$465$	43.0470	1.99626
$466$	−6.35030	−0.294172
$467$	33.7194	1.56035	0.780173	−	0.625563i	$-0.215131\pi$
$467$	33.7194	1.56035	0.780173	+	0.625563i	$0.215131\pi$
$468$	−4.79451	−0.221626
$469$	42.5855	1.96642
$470$	16.9605	0.782330
$471$	20.2227	0.931814
$472$	−12.6460	−0.582080
$473$	8.03093	0.369263
$474$	33.1474	1.52251
$475$	−0.193971	−0.00890000
$476$	−16.2989	−0.747058
$477$	−44.1939	−2.02350
$478$	−21.2588	−0.972356
$479$	−27.6297	−1.26243	−0.631217	−	0.775607i	$-0.717444\pi$
$479$	−27.6297	−1.26243	−0.631217	+	0.775607i	$0.717444\pi$
$480$	5.83698	0.266421
$481$	−9.04662	−0.412491
$482$	19.2567	0.877120
$483$	6.91855	0.314805
$484$	−3.32457	−0.151117
$485$	15.8844	0.721272
$486$	−21.8590	−0.991544
$487$	−35.8788	−1.62582	−0.812911	−	0.582388i	$-0.802118\pi$
$487$	−35.8788	−1.62582	−0.812911	+	0.582388i	$0.802118\pi$
$488$	14.5079	0.656744
$489$	−13.4937	−0.610207
$490$	−36.5593	−1.65158
$491$	24.3141	1.09728	0.548641	−	0.836058i	$-0.315146\pi$
$491$	24.3141	1.09728	0.548641	+	0.836058i	$0.315146\pi$
$492$	19.5876	0.883079
$493$	−5.14678	−0.231799
$494$	−8.87948	−0.399507
$495$	−23.4599	−1.05444
$496$	−7.37488	−0.331142
$497$	60.6964	2.72261
$498$	−4.57136	−0.204848
$499$	−19.1158	−0.855741	−0.427871	−	0.903840i	$-0.640736\pi$
$499$	−19.1158	−0.855741	−0.427871	+	0.903840i	$0.640736\pi$
$500$	−11.1491	−0.498604
$501$	−51.3703	−2.29505
$502$	3.31747	0.148066
$503$	3.17885	0.141738	0.0708691	−	0.997486i	$-0.477423\pi$
$503$	3.17885	0.141738	0.0708691	+	0.997486i	$0.477423\pi$
$504$	18.2310	0.812071
$505$	−15.5063	−0.690023
$506$	1.52526	0.0678059
$507$	29.6454	1.31660
$508$	5.16827	0.229305
$509$	−23.8462	−1.05697	−0.528483	−	0.848944i	$-0.677239\pi$
$509$	−23.8462	−1.05697	−0.528483	+	0.848944i	$0.677239\pi$
$510$	19.7072	0.872650
$511$	−23.6956	−1.04823
$512$	−1.00000	−0.0441942
$513$	14.1373	0.624178
$514$	22.3090	0.984009
$515$	15.3348	0.675730
$516$	7.54600	0.332194
$517$	20.9558	0.921635
$518$	34.3994	1.51142
$519$	−5.21843	−0.229064
$520$	2.84671	0.124836
$521$	−4.73428	−0.207413	−0.103706	−	0.994608i	$-0.533070\pi$
$521$	−4.73428	−0.207413	−0.103706	+	0.994608i	$0.533070\pi$
$522$	5.75688	0.251972
$523$	−3.78708	−0.165597	−0.0827987	−	0.996566i	$-0.526386\pi$
$523$	−3.78708	−0.165597	−0.0827987	+	0.996566i	$0.526386\pi$
$524$	−5.59530	−0.244432
$525$	0.348521	0.0152107
$526$	11.9585	0.521417
$527$	−24.8996	−1.08464
$528$	7.21196	0.313860
$529$	−22.6969	−0.986822
$530$	26.2398	1.13978
$531$	47.7575	2.07250
$532$	33.7639	1.46385
$533$	9.55293	0.413783
$534$	−27.2594	−1.17963
$535$	−7.31404	−0.316214
$536$	8.82146	0.381029
$537$	29.0127	1.25199
$538$	16.9598	0.731187
$539$	−45.1714	−1.94567
$540$	−4.53234	−0.195041
$541$	42.4301	1.82421	0.912106	−	0.409955i	$-0.134456\pi$
$541$	42.4301	1.82421	0.912106	+	0.409955i	$0.134456\pi$
$542$	−24.0218	−1.03182
$543$	−5.86642	−0.251752
$544$	−3.37627	−0.144756
$545$	16.5034	0.706929
$546$	15.9544	0.682785
$547$	27.3574	1.16972	0.584858	−	0.811136i	$-0.301150\pi$
$547$	27.3574	1.16972	0.584858	+	0.811136i	$0.301150\pi$
$548$	−5.53177	−0.236306
$549$	−54.7891	−2.33834
$550$	0.0768346	0.00327624
$551$	10.6618	0.454208
$552$	1.43316	0.0609992
$553$	−61.4707	−2.61400
$554$	9.17090	0.389634
$555$	−41.5928	−1.76552
$556$	14.6843	0.622751
$557$	13.5532	0.574266	0.287133	−	0.957891i	$-0.407298\pi$
$557$	13.5532	0.574266	0.287133	+	0.957891i	$0.407298\pi$
$558$	27.8511	1.17903
$559$	3.68020	0.155656
$560$	−10.8245	−0.457418
$561$	24.3495	1.02804
$562$	17.2027	0.725651
$563$	26.7125	1.12580	0.562898	−	0.826527i	$-0.309686\pi$
$563$	26.7125	1.12580	0.562898	+	0.826527i	$0.309686\pi$
$564$	19.6904	0.829117
$565$	−13.1085	−0.551477
$566$	−2.42511	−0.101935
$567$	29.2913	1.23012
$568$	12.5731	0.527555
$569$	−14.9765	−0.627845	−0.313923	−	0.949449i	$-0.601643\pi$
$569$	−14.9765	−0.627845	−0.313923	+	0.949449i	$0.601643\pi$
$570$	−40.8244	−1.70994
$571$	30.0944	1.25941	0.629706	−	0.776833i	$-0.283175\pi$
$571$	30.0944	1.25941	0.629706	+	0.776833i	$0.283175\pi$
$572$	3.51729	0.147065
$573$	7.45505	0.311439
$574$	−36.3246	−1.51616
$575$	0.0152685	0.000636741 0
$576$	3.77649	0.157354
$577$	18.4215	0.766899	0.383450	−	0.923562i	$-0.374736\pi$
$577$	18.4215	0.766899	0.383450	+	0.923562i	$0.374736\pi$
$578$	5.60083	0.232964
$579$	13.1169	0.545118
$580$	−3.41810	−0.141929
$581$	8.47745	0.351704
$582$	18.4411	0.764406
$583$	32.4210	1.34274
$584$	−4.90846	−0.203114
$585$	−10.7505	−0.444480
$586$	−16.5326	−0.682955
$587$	−15.5076	−0.640068	−0.320034	−	0.947406i	$-0.603694\pi$
$587$	−15.5076	−0.640068	−0.320034	+	0.947406i	$0.603694\pi$
$588$	−42.4438	−1.75035
$589$	51.5806	2.12534
$590$	−28.3557	−1.16739
$591$	−24.7264	−1.01711
$592$	7.12574	0.292866
$593$	17.9052	0.735277	0.367638	−	0.929969i	$-0.380166\pi$
$593$	17.9052	0.735277	0.367638	+	0.929969i	$0.380166\pi$
$594$	−5.59999	−0.229770
$595$	−36.5464	−1.49825
$596$	6.05094	0.247856
$597$	39.2282	1.60550
$598$	0.698953	0.0285823
$599$	32.2294	1.31686	0.658429	−	0.752642i	$-0.271221\pi$
$599$	32.2294	1.31686	0.658429	+	0.752642i	$0.271221\pi$
$600$	0.0721951	0.00294735
$601$	−23.4540	−0.956710	−0.478355	−	0.878166i	$-0.658767\pi$
$601$	−23.4540	−0.956710	−0.478355	+	0.878166i	$0.658767\pi$
$602$	−13.9938	−0.570345
$603$	−33.3141	−1.35666
$604$	−16.6995	−0.679492
$605$	−7.45456	−0.303071
$606$	−18.0022	−0.731289
$607$	9.26008	0.375855	0.187928	−	0.982183i	$-0.439823\pi$
$607$	9.26008	0.375855	0.187928	+	0.982183i	$0.439823\pi$
$608$	6.99409	0.283648
$609$	−19.1568	−0.776273
$610$	32.5306	1.31713
$611$	9.60306	0.388498
$612$	12.7504	0.515405
$613$	28.6718	1.15804	0.579022	−	0.815312i	$-0.303435\pi$
$613$	28.6718	1.15804	0.579022	+	0.815312i	$0.303435\pi$
$614$	−14.4649	−0.583754
$615$	43.9206	1.77105
$616$	−13.3744	−0.538868
$617$	−23.7181	−0.954855	−0.477428	−	0.878671i	$-0.658431\pi$
$617$	−23.7181	−0.954855	−0.477428	+	0.878671i	$0.658431\pi$
$618$	17.8030	0.716141
$619$	−25.2165	−1.01354	−0.506768	−	0.862083i	$-0.669160\pi$
$619$	−25.2165	−1.01354	−0.506768	+	0.862083i	$0.669160\pi$
$620$	−16.5364	−0.664118
$621$	−1.11283	−0.0446562
$622$	−34.6114	−1.38779
$623$	50.5517	2.02531
$624$	3.30490	0.132302
$625$	−25.1379	−1.00552
$626$	12.8770	0.514670
$627$	−50.4411	−2.01442
$628$	−7.76850	−0.309997
$629$	24.0584	0.959271
$630$	40.8785	1.62864
$631$	−29.0192	−1.15524	−0.577619	−	0.816307i	$-0.696018\pi$
$631$	−29.0192	−1.15524	−0.577619	+	0.816307i	$0.696018\pi$
$632$	−12.7335	−0.506510
$633$	26.9370	1.07065
$634$	−4.83669	−0.192090
$635$	11.5886	0.459880
$636$	30.4633	1.20795
$637$	−20.6999	−0.820160
$638$	−4.22329	−0.167201
$639$	−47.4821	−1.87836
$640$	−2.24226	−0.0886331
$641$	−15.6257	−0.617179	−0.308590	−	0.951195i	$-0.599857\pi$
$641$	−15.6257	−0.617179	−0.308590	+	0.951195i	$0.599857\pi$
$642$	−8.49129	−0.335125
$643$	9.62988	0.379765	0.189883	−	0.981807i	$-0.439189\pi$
$643$	9.62988	0.379765	0.189883	+	0.981807i	$0.439189\pi$
$644$	−2.65774	−0.104730
$645$	16.9201	0.666229
$646$	23.6139	0.929076
$647$	−23.9148	−0.940189	−0.470095	−	0.882616i	$-0.655780\pi$
$647$	−23.9148	−0.940189	−0.470095	+	0.882616i	$0.655780\pi$
$648$	6.06761	0.238358
$649$	−35.0353	−1.37525
$650$	0.0352097	0.00138104
$651$	−92.6784	−3.63235
$652$	5.18357	0.203004
$653$	22.6207	0.885215	0.442607	−	0.896715i	$-0.354054\pi$
$653$	22.6207	0.885215	0.442607	+	0.896715i	$0.354054\pi$
$654$	19.1598	0.749206
$655$	−12.5461	−0.490218
$656$	−7.52454	−0.293784
$657$	18.5367	0.723187
$658$	−36.5153	−1.42351
$659$	13.4788	0.525058	0.262529	−	0.964924i	$-0.415443\pi$
$659$	13.4788	0.525058	0.262529	+	0.964924i	$0.415443\pi$
$660$	16.1711	0.629459
$661$	29.7934	1.15883	0.579414	−	0.815033i	$-0.303281\pi$
$661$	29.7934	1.15883	0.579414	+	0.815033i	$0.303281\pi$
$662$	−19.6495	−0.763701
$663$	11.1582	0.433350
$664$	1.75608	0.0681490
$665$	75.7075	2.93581
$666$	−26.9103	−1.04275
$667$	−0.839249	−0.0324958
$668$	19.7337	0.763521
$669$	48.0999	1.85965
$670$	19.7800	0.764169
$671$	40.1936	1.55166
$672$	−12.5668	−0.484774
$673$	5.86870	0.226222	0.113111	−	0.993582i	$-0.463918\pi$
$673$	5.86870	0.226222	0.113111	+	0.993582i	$0.463918\pi$
$674$	−24.5619	−0.946088
$675$	−0.0560585	−0.00215769
$676$	−11.3882	−0.438007
$677$	14.8171	0.569466	0.284733	−	0.958607i	$-0.408095\pi$
$677$	14.8171	0.569466	0.284733	+	0.958607i	$0.408095\pi$
$678$	−15.2184	−0.584457
$679$	−34.1983	−1.31241
$680$	−7.57047	−0.290314
$681$	12.2865	0.470818
$682$	−20.4318	−0.782373
$683$	−45.0563	−1.72403	−0.862016	−	0.506881i	$-0.830798\pi$
$683$	−45.0563	−1.72403	−0.862016	+	0.506881i	$0.830798\pi$
$684$	−26.4131	−1.00993
$685$	−12.4037	−0.473920
$686$	44.9182	1.71498
$687$	24.1399	0.920993
$688$	−2.89878	−0.110515
$689$	14.8570	0.566007
$690$	3.21351	0.122336
$691$	−23.5756	−0.896858	−0.448429	−	0.893818i	$-0.648016\pi$
$691$	−23.5756	−0.896858	−0.448429	+	0.893818i	$0.648016\pi$
$692$	2.00464	0.0762051
$693$	50.5081	1.91864
$694$	−13.2909	−0.504514
$695$	32.9259	1.24895
$696$	−3.96827	−0.150417
$697$	−25.4048	−0.962277
$698$	14.5645	0.551275
$699$	−16.5309	−0.625256
$700$	−0.133883	−0.00506032
$701$	−34.3701	−1.29814	−0.649070	−	0.760729i	$-0.724842\pi$
$701$	−34.3701	−1.29814	−0.649070	+	0.760729i	$0.724842\pi$
$702$	−2.56621	−0.0968554
$703$	−49.8380	−1.87968
$704$	−2.77046	−0.104416
$705$	44.1511	1.66283
$706$	−33.1279	−1.24678
$707$	33.3845	1.25555
$708$	−32.9197	−1.23720
$709$	4.90665	0.184273	0.0921365	−	0.995746i	$-0.470630\pi$
$709$	4.90665	0.184273	0.0921365	+	0.995746i	$0.470630\pi$
$710$	28.1921	1.05803
$711$	48.0878	1.80343
$712$	10.4716	0.392441
$713$	−4.06019	−0.152055
$714$	−42.4288	−1.58786
$715$	7.88668	0.294945
$716$	−11.1452	−0.416514
$717$	−55.3403	−2.06672
$718$	8.48389	0.316616
$719$	22.6085	0.843155	0.421577	−	0.906792i	$-0.361477\pi$
$719$	22.6085	0.843155	0.421577	+	0.906792i	$0.361477\pi$
$720$	8.46787	0.315579
$721$	−33.0151	−1.22955
$722$	−29.9173	−1.11341
$723$	50.1285	1.86430
$724$	2.25357	0.0837533
$725$	−0.0422771	−0.00157013
$726$	−8.65442	−0.321196
$727$	9.57842	0.355244	0.177622	−	0.984099i	$-0.443160\pi$
$727$	9.57842	0.355244	0.177622	+	0.984099i	$0.443160\pi$
$728$	−6.12884	−0.227150
$729$	−38.6998	−1.43333
$730$	−11.0061	−0.407352
$731$	−9.78704	−0.361987
$732$	37.7666	1.39589
$733$	27.5244	1.01664	0.508318	−	0.861169i	$-0.330267\pi$
$733$	27.5244	1.01664	0.508318	+	0.861169i	$0.330267\pi$
$734$	−10.4225	−0.384703
$735$	−95.1701	−3.51040
$736$	−0.550543	−0.0202933
$737$	24.4395	0.900240
$738$	28.4163	1.04602
$739$	9.87708	0.363334	0.181667	−	0.983360i	$-0.441851\pi$
$739$	9.87708	0.363334	0.181667	+	0.983360i	$0.441851\pi$
$740$	15.9778	0.587354
$741$	−23.1148	−0.849143
$742$	−56.4932	−2.07393
$743$	28.2425	1.03612	0.518058	−	0.855346i	$-0.326655\pi$
$743$	28.2425	1.03612	0.518058	+	0.855346i	$0.326655\pi$
$744$	−19.1981	−0.703835
$745$	13.5678	0.497085
$746$	−9.25977	−0.339024
$747$	−6.63180	−0.242645
$748$	−9.35380	−0.342009
$749$	15.7468	0.575376
$750$	−29.0230	−1.05977
$751$	38.4303	1.40234	0.701172	−	0.712993i	$-0.252661\pi$
$751$	38.4303	1.40234	0.701172	+	0.712993i	$0.252661\pi$
$752$	−7.56402	−0.275832
$753$	8.63593	0.314711
$754$	−1.93533	−0.0704807
$755$	−37.4446	−1.36275
$756$	9.75792	0.354892
$757$	19.3953	0.704934	0.352467	−	0.935824i	$-0.385343\pi$
$757$	19.3953	0.704934	0.352467	+	0.935824i	$0.385343\pi$
$758$	24.6495	0.895310
$759$	3.97050	0.144120
$760$	15.6826	0.568867
$761$	−26.7021	−0.967951	−0.483975	−	0.875082i	$-0.660808\pi$
$761$	−26.7021	−0.967951	−0.483975	+	0.875082i	$0.660808\pi$
$762$	13.4539	0.487383
$763$	−35.5312	−1.28631
$764$	−2.86384	−0.103610
$765$	28.5898	1.03367
$766$	−9.82086	−0.354842
$767$	−16.0550	−0.579713
$768$	−2.60317	−0.0939338
$769$	43.3510	1.56328	0.781638	−	0.623733i	$-0.214385\pi$
$769$	43.3510	1.56328	0.781638	+	0.623733i	$0.214385\pi$
$770$	−29.9888	−1.08072
$771$	58.0741	2.09149
$772$	−5.03880	−0.181351
$773$	19.2188	0.691251	0.345626	−	0.938372i	$-0.387667\pi$
$773$	19.2188	0.691251	0.345626	+	0.938372i	$0.387667\pi$
$774$	10.9472	0.393489
$775$	−0.204532	−0.00734699
$776$	−7.08408	−0.254304
$777$	89.5475	3.21250
$778$	6.09996	0.218694
$779$	52.6273	1.88557
$780$	7.41046	0.265337
$781$	34.8332	1.24643
$782$	−1.85878	−0.0664699
$783$	3.08131	0.110117
$784$	16.3047	0.582310
$785$	−17.4190	−0.621711
$786$	−14.5655	−0.519535
$787$	−14.1094	−0.502946	−0.251473	−	0.967864i	$-0.580915\pi$
$787$	−14.1094	−0.502946	−0.251473	+	0.967864i	$0.580915\pi$
$788$	9.49859	0.338373
$789$	31.1301	1.10826
$790$	−28.5518	−1.01583
$791$	28.2219	1.00346
$792$	10.4626	0.371772
$793$	18.4188	0.654073
$794$	−18.6756	−0.662771
$795$	68.3067	2.42259
$796$	−15.0694	−0.534121
$797$	−41.6923	−1.47682	−0.738409	−	0.674353i	$-0.764423\pi$
$797$	−41.6923	−1.47682	−0.738409	+	0.674353i	$0.764423\pi$
$798$	87.8931	3.11138
$799$	−25.5382	−0.903475
$800$	−0.0277336	−0.000980529 0
$801$	−39.5459	−1.39729
$802$	29.4752	1.04081
$803$	−13.5987	−0.479887
$804$	22.9638	0.809869
$805$	−5.95935	−0.210040
$806$	−9.36293	−0.329795
$807$	44.1491	1.55412
$808$	6.91549	0.243286
$809$	34.0146	1.19589	0.597945	−	0.801537i	$-0.295984\pi$
$809$	34.0146	1.19589	0.597945	+	0.801537i	$0.295984\pi$
$810$	13.6052	0.478037
$811$	14.7262	0.517105	0.258553	−	0.965997i	$-0.416754\pi$
$811$	14.7262	0.517105	0.258553	+	0.965997i	$0.416754\pi$
$812$	7.35903	0.258251
$813$	−62.5328	−2.19312
$814$	19.7415	0.691941
$815$	11.6229	0.407133
$816$	−8.78899	−0.307676
$817$	20.2743	0.709308
$818$	−35.8915	−1.25492
$819$	23.1455	0.808768
$820$	−16.8720	−0.589195
$821$	24.4744	0.854162	0.427081	−	0.904213i	$-0.359542\pi$
$821$	24.4744	0.854162	0.427081	+	0.904213i	$0.359542\pi$
$822$	−14.4001	−0.502263
$823$	−31.4860	−1.09753	−0.548766	−	0.835976i	$-0.684902\pi$
$823$	−31.4860	−1.09753	−0.548766	+	0.835976i	$0.684902\pi$
$824$	−6.83897	−0.238247
$825$	0.200013	0.00696357
$826$	61.0486	2.12415
$827$	7.74409	0.269288	0.134644	−	0.990894i	$-0.457011\pi$
$827$	7.74409	0.269288	0.134644	+	0.990894i	$0.457011\pi$
$828$	2.07912	0.0722544
$829$	−40.3372	−1.40097	−0.700484	−	0.713668i	$-0.747032\pi$
$829$	−40.3372	−1.40097	−0.700484	+	0.713668i	$0.747032\pi$
$830$	3.93758	0.136675
$831$	23.8734	0.828159
$832$	−1.26957	−0.0440144
$833$	55.0489	1.90733
$834$	38.2256	1.32364
$835$	44.2482	1.53127
$836$	19.3768	0.670161
$837$	14.9070	0.515262
$838$	−14.6680	−0.506698
$839$	49.7214	1.71657	0.858287	−	0.513170i	$-0.171529\pi$
$839$	49.7214	1.71657	0.858287	+	0.513170i	$0.171529\pi$
$840$	−28.1780	−0.972233
$841$	−26.6762	−0.919869
$842$	−21.2731	−0.733119
$843$	44.7815	1.54236
$844$	−10.3478	−0.356186
$845$	−25.5353	−0.878441
$846$	28.5654	0.982100
$847$	16.0493	0.551462
$848$	−11.7024	−0.401862
$849$	−6.31297	−0.216660
$850$	−0.0936358	−0.00321168
$851$	3.92303	0.134480
$852$	32.7298	1.12131
$853$	−12.3634	−0.423316	−0.211658	−	0.977344i	$-0.567886\pi$
$853$	−12.3634	−0.423316	−0.211658	+	0.977344i	$0.567886\pi$
$854$	−70.0370	−2.39662
$855$	−59.2250	−2.02545
$856$	3.26191	0.111490
$857$	2.70601	0.0924355	0.0462177	−	0.998931i	$-0.485283\pi$
$857$	2.70601	0.0924355	0.0462177	+	0.998931i	$0.485283\pi$
$858$	9.15609	0.312584
$859$	−44.4336	−1.51606	−0.758028	−	0.652222i	$-0.773837\pi$
$859$	−44.4336	−1.51606	−0.758028	+	0.652222i	$0.773837\pi$
$860$	−6.49981	−0.221642
$861$	−94.5592	−3.22257
$862$	−33.4334	−1.13875
$863$	31.8202	1.08317	0.541587	−	0.840645i	$-0.317824\pi$
$863$	31.8202	1.08317	0.541587	+	0.840645i	$0.317824\pi$
$864$	2.02132	0.0687668
$865$	4.49494	0.152832
$866$	−25.2484	−0.857977
$867$	14.5799	0.495160
$868$	35.6022	1.20842
$869$	−35.2775	−1.19671
$870$	−8.89790	−0.301667
$871$	11.1995	0.379479
$872$	−7.36017	−0.249247
$873$	26.7529	0.905450
$874$	3.85055	0.130247
$875$	53.8223	1.81952
$876$	−12.7776	−0.431714
$877$	−18.1235	−0.611988	−0.305994	−	0.952034i	$-0.598989\pi$
$877$	−18.1235	−0.611988	−0.305994	+	0.952034i	$0.598989\pi$
$878$	−9.30959	−0.314184
$879$	−43.0371	−1.45161
$880$	−6.21209	−0.209409
$881$	24.4022	0.822130	0.411065	−	0.911606i	$-0.365157\pi$
$881$	24.4022	0.822130	0.411065	+	0.911606i	$0.365157\pi$
$882$	−61.5744	−2.07332
$883$	−9.90862	−0.333452	−0.166726	−	0.986003i	$-0.553319\pi$
$883$	−9.90862	−0.333452	−0.166726	+	0.986003i	$0.553319\pi$
$884$	−4.28641	−0.144167
$885$	−73.8146	−2.48125
$886$	−3.15860	−0.106115
$887$	−5.72059	−0.192079	−0.0960393	−	0.995378i	$-0.530617\pi$
$887$	−5.72059	−0.192079	−0.0960393	+	0.995378i	$0.530617\pi$
$888$	18.5495	0.622480
$889$	−24.9498	−0.836789
$890$	23.4801	0.787055
$891$	16.8101	0.563158
$892$	−18.4775	−0.618671
$893$	52.9034	1.77035
$894$	15.7516	0.526813
$895$	−24.9903	−0.835335
$896$	4.82749	0.161275
$897$	1.81949	0.0607511
$898$	−14.0263	−0.468062
$899$	11.2423	0.374951
$900$	0.104735	0.00349118
$901$	−39.5104	−1.31628
$902$	−20.8464	−0.694110
$903$	−36.4283	−1.21226
$904$	5.84609	0.194438
$905$	5.05309	0.167970
$906$	−43.4715	−1.44424
$907$	−44.9530	−1.49264	−0.746319	−	0.665588i	$-0.768181\pi$
$907$	−44.9530	−1.49264	−0.746319	+	0.665588i	$0.768181\pi$
$908$	−4.71981	−0.156632
$909$	−26.1162	−0.866221
$910$	−13.7425	−0.455558
$911$	−39.4903	−1.30837	−0.654186	−	0.756333i	$-0.726989\pi$
$911$	−39.4903	−1.30837	−0.654186	+	0.756333i	$0.726989\pi$
$912$	18.2068	0.602887
$913$	4.86513	0.161012
$914$	0.688761	0.0227822
$915$	84.6826	2.79952
$916$	−9.27326	−0.306397
$917$	27.0113	0.891990
$918$	6.82453	0.225243
$919$	16.3880	0.540589	0.270294	−	0.962778i	$-0.412879\pi$
$919$	16.3880	0.540589	0.270294	+	0.962778i	$0.412879\pi$
$920$	−1.23446	−0.0406990
$921$	−37.6545	−1.24076
$922$	19.9237	0.656151
$923$	15.9624	0.525409
$924$	−34.8157	−1.14535
$925$	0.197622	0.00649777
$926$	−7.16100	−0.235325
$927$	25.8273	0.848279
$928$	1.52440	0.0500409
$929$	50.6417	1.66150	0.830750	−	0.556645i	$-0.187912\pi$
$929$	50.6417	1.66150	0.830750	+	0.556645i	$0.187912\pi$
$930$	−43.0470	−1.41157
$931$	−114.036	−3.73739
$932$	6.35030	0.208011
$933$	−90.0994	−2.94972
$934$	−33.7194	−1.10333
$935$	−20.9737	−0.685912
$936$	4.79451	0.156714
$937$	−53.6163	−1.75157	−0.875783	−	0.482705i	$-0.839655\pi$
$937$	−53.6163	−1.75157	−0.875783	+	0.482705i	$0.839655\pi$
$938$	−42.5855	−1.39047
$939$	33.5211	1.09392
$940$	−16.9605	−0.553191
$941$	−8.18776	−0.266913	−0.133457	−	0.991055i	$-0.542608\pi$
$941$	−8.18776	−0.266913	−0.133457	+	0.991055i	$0.542608\pi$
$942$	−20.2227	−0.658892
$943$	−4.14259	−0.134901
$944$	12.6460	0.411593
$945$	21.8798	0.711750
$946$	−8.03093	−0.261108
$947$	−40.1715	−1.30540	−0.652699	−	0.757618i	$-0.726363\pi$
$947$	−40.1715	−1.30540	−0.652699	+	0.757618i	$0.726363\pi$
$948$	−33.1474	−1.07658
$949$	−6.23164	−0.202288
$950$	0.193971	0.00629325
$951$	−12.5907	−0.408282
$952$	16.2989	0.528250
$953$	20.3930	0.660593	0.330297	−	0.943877i	$-0.392851\pi$
$953$	20.3930	0.660593	0.330297	+	0.943877i	$0.392851\pi$
$954$	44.1939	1.43083
$955$	−6.42147	−0.207794
$956$	21.2588	0.687559
$957$	−10.9939	−0.355383
$958$	27.6297	0.892675
$959$	26.7046	0.862336
$960$	−5.83698	−0.188388
$961$	23.3889	0.754479
$962$	9.04662	0.291675
$963$	−12.3185	−0.396960
$964$	−19.2567	−0.620217
$965$	−11.2983	−0.363706
$966$	−6.91855	−0.222601
$967$	−32.1426	−1.03364	−0.516818	−	0.856095i	$-0.672884\pi$
$967$	−32.1426	−1.03364	−0.516818	+	0.856095i	$0.672884\pi$
$968$	3.32457	0.106856
$969$	61.4710	1.97473
$970$	−15.8844	−0.510016
$971$	23.0030	0.738200	0.369100	−	0.929390i	$-0.379666\pi$
$971$	23.0030	0.738200	0.369100	+	0.929390i	$0.379666\pi$
$972$	21.8590	0.701127
$973$	−70.8881	−2.27257
$974$	35.8788	1.14963
$975$	0.0916567	0.00293536
$976$	−14.5079	−0.464388
$977$	−30.7315	−0.983189	−0.491595	−	0.870824i	$-0.663586\pi$
$977$	−30.7315	−0.983189	−0.491595	+	0.870824i	$0.663586\pi$
$978$	13.4937	0.431481
$979$	29.0112	0.927201
$980$	36.5593	1.16784
$981$	27.7956	0.887445
$982$	−24.3141	−0.775895
$983$	−47.8264	−1.52543	−0.762713	−	0.646737i	$-0.776133\pi$
$983$	−47.8264	−1.52543	−0.762713	+	0.646737i	$0.776133\pi$
$984$	−19.5876	−0.624431
$985$	21.2983	0.678621
$986$	5.14678	0.163907
$987$	−95.0554	−3.02565
$988$	8.87948	0.282494
$989$	−1.59590	−0.0507467
$990$	23.4599	0.745603
$991$	−33.4169	−1.06152	−0.530762	−	0.847521i	$-0.678094\pi$
$991$	−33.4169	−1.06152	−0.530762	+	0.847521i	$0.678094\pi$
$992$	7.37488	0.234153
$993$	−51.1511	−1.62323
$994$	−60.6964	−1.92517
$995$	−33.7895	−1.07120
$996$	4.57136	0.144849
$997$	−41.0556	−1.30024	−0.650122	−	0.759830i	$-0.725282\pi$
$997$	−41.0556	−1.30024	−0.650122	+	0.759830i	$0.725282\pi$
$998$	19.1158	0.605100
$999$	−14.4034	−0.455704

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.c.1.8	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.c.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.60317 q^{3} +1.00000 q^{4} +2.24226 q^{5} +2.60317 q^{6} -4.82749 q^{7} -1.00000 q^{8} +3.77649 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.60317 q^{3} +1.00000 q^{4} +2.24226 q^{5} +2.60317 q^{6} -4.82749 q^{7} -1.00000 q^{8} +3.77649 q^{9} -2.24226 q^{10} -2.77046 q^{11} -2.60317 q^{12} -1.26957 q^{13} +4.82749 q^{14} -5.83698 q^{15} +1.00000 q^{16} +3.37627 q^{17} -3.77649 q^{18} -6.99409 q^{19} +2.24226 q^{20} +12.5668 q^{21} +2.77046 q^{22} +0.550543 q^{23} +2.60317 q^{24} +0.0277336 q^{25} +1.26957 q^{26} -2.02132 q^{27} -4.82749 q^{28} -1.52440 q^{29} +5.83698 q^{30} -7.37488 q^{31} -1.00000 q^{32} +7.21196 q^{33} -3.37627 q^{34} -10.8245 q^{35} +3.77649 q^{36} +7.12574 q^{37} +6.99409 q^{38} +3.30490 q^{39} -2.24226 q^{40} -7.52454 q^{41} -12.5668 q^{42} -2.89878 q^{43} -2.77046 q^{44} +8.46787 q^{45} -0.550543 q^{46} -7.56402 q^{47} -2.60317 q^{48} +16.3047 q^{49} -0.0277336 q^{50} -8.78899 q^{51} -1.26957 q^{52} -11.7024 q^{53} +2.02132 q^{54} -6.21209 q^{55} +4.82749 q^{56} +18.2068 q^{57} +1.52440 q^{58} +12.6460 q^{59} -5.83698 q^{60} -14.5079 q^{61} +7.37488 q^{62} -18.2310 q^{63} +1.00000 q^{64} -2.84671 q^{65} -7.21196 q^{66} -8.82146 q^{67} +3.37627 q^{68} -1.43316 q^{69} +10.8245 q^{70} -12.5731 q^{71} -3.77649 q^{72} +4.90846 q^{73} -7.12574 q^{74} -0.0721951 q^{75} -6.99409 q^{76} +13.3744 q^{77} -3.30490 q^{78} +12.7335 q^{79} +2.24226 q^{80} -6.06761 q^{81} +7.52454 q^{82} -1.75608 q^{83} +12.5668 q^{84} +7.57047 q^{85} +2.89878 q^{86} +3.96827 q^{87} +2.77046 q^{88} -10.4716 q^{89} -8.46787 q^{90} +6.12884 q^{91} +0.550543 q^{92} +19.1981 q^{93} +7.56402 q^{94} -15.6826 q^{95} +2.60317 q^{96} +7.08408 q^{97} -16.3047 q^{98} -10.4626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) \) 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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