LMFDB - Embedded newform 6022.2.a.d.1.20

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:	$64$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.43853 q^{3} +1.00000 q^{4} -4.29281 q^{5} +1.43853 q^{6} +1.20415 q^{7} -1.00000 q^{8} -0.930640 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.43853 q^{3} +1.00000 q^{4} -4.29281 q^{5} +1.43853 q^{6} +1.20415 q^{7} -1.00000 q^{8} -0.930640 q^{9} +4.29281 q^{10} -4.33272 q^{11} -1.43853 q^{12} -4.48525 q^{13} -1.20415 q^{14} +6.17533 q^{15} +1.00000 q^{16} -1.25590 q^{17} +0.930640 q^{18} -6.01902 q^{19} -4.29281 q^{20} -1.73221 q^{21} +4.33272 q^{22} +2.96030 q^{23} +1.43853 q^{24} +13.4282 q^{25} +4.48525 q^{26} +5.65433 q^{27} +1.20415 q^{28} -4.13599 q^{29} -6.17533 q^{30} +9.36074 q^{31} -1.00000 q^{32} +6.23273 q^{33} +1.25590 q^{34} -5.16920 q^{35} -0.930640 q^{36} +10.0123 q^{37} +6.01902 q^{38} +6.45215 q^{39} +4.29281 q^{40} -3.08792 q^{41} +1.73221 q^{42} -5.42176 q^{43} -4.33272 q^{44} +3.99506 q^{45} -2.96030 q^{46} +10.2342 q^{47} -1.43853 q^{48} -5.55002 q^{49} -13.4282 q^{50} +1.80664 q^{51} -4.48525 q^{52} +6.88379 q^{53} -5.65433 q^{54} +18.5996 q^{55} -1.20415 q^{56} +8.65852 q^{57} +4.13599 q^{58} +0.0973902 q^{59} +6.17533 q^{60} +7.62365 q^{61} -9.36074 q^{62} -1.12063 q^{63} +1.00000 q^{64} +19.2543 q^{65} -6.23273 q^{66} +0.0361020 q^{67} -1.25590 q^{68} -4.25847 q^{69} +5.16920 q^{70} -10.5000 q^{71} +0.930640 q^{72} -4.36880 q^{73} -10.0123 q^{74} -19.3169 q^{75} -6.01902 q^{76} -5.21725 q^{77} -6.45215 q^{78} +1.59781 q^{79} -4.29281 q^{80} -5.34199 q^{81} +3.08792 q^{82} -7.56899 q^{83} -1.73221 q^{84} +5.39132 q^{85} +5.42176 q^{86} +5.94973 q^{87} +4.33272 q^{88} -8.82134 q^{89} -3.99506 q^{90} -5.40092 q^{91} +2.96030 q^{92} -13.4657 q^{93} -10.2342 q^{94} +25.8385 q^{95} +1.43853 q^{96} +12.6574 q^{97} +5.55002 q^{98} +4.03220 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) $ 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.43853	−0.830534	−0.415267	−	0.909700i	$-0.636312\pi$
$3$	−1.43853	−0.830534	−0.415267	+	0.909700i	$0.636312\pi$
$4$	1.00000	0.500000
$5$	−4.29281	−1.91980	−0.959902	−	0.280336i	$-0.909554\pi$
$5$	−4.29281	−1.91980	−0.959902	+	0.280336i	$0.909554\pi$
$6$	1.43853	0.587276
$7$	1.20415	0.455127	0.227563	−	0.973763i	$-0.426924\pi$
$7$	1.20415	0.455127	0.227563	+	0.973763i	$0.426924\pi$
$8$	−1.00000	−0.353553
$9$	−0.930640	−0.310213
$10$	4.29281	1.35751
$11$	−4.33272	−1.30636	−0.653182	−	0.757201i	$-0.726566\pi$
$11$	−4.33272	−1.30636	−0.653182	+	0.757201i	$0.726566\pi$
$12$	−1.43853	−0.415267
$13$	−4.48525	−1.24398	−0.621992	−	0.783024i	$-0.713676\pi$
$13$	−4.48525	−1.24398	−0.621992	+	0.783024i	$0.713676\pi$
$14$	−1.20415	−0.321823
$15$	6.17533	1.59446
$16$	1.00000	0.250000
$17$	−1.25590	−0.304599	−0.152300	−	0.988334i	$-0.548668\pi$
$17$	−1.25590	−0.304599	−0.152300	+	0.988334i	$0.548668\pi$
$18$	0.930640	0.219354
$19$	−6.01902	−1.38086	−0.690429	−	0.723400i	$-0.742578\pi$
$19$	−6.01902	−1.38086	−0.690429	+	0.723400i	$0.742578\pi$
$20$	−4.29281	−0.959902
$21$	−1.73221	−0.377998
$22$	4.33272	0.923739
$23$	2.96030	0.617265	0.308632	−	0.951181i	$-0.400129\pi$
$23$	2.96030	0.617265	0.308632	+	0.951181i	$0.400129\pi$
$24$	1.43853	0.293638
$25$	13.4282	2.68565
$26$	4.48525	0.879629
$27$	5.65433	1.08818
$28$	1.20415	0.227563
$29$	−4.13599	−0.768033	−0.384017	−	0.923326i	$-0.625459\pi$
$29$	−4.13599	−0.768033	−0.384017	+	0.923326i	$0.625459\pi$
$30$	−6.17533	−1.12746
$31$	9.36074	1.68124	0.840619	−	0.541626i	$-0.182191\pi$
$31$	9.36074	1.68124	0.840619	+	0.541626i	$0.182191\pi$
$32$	−1.00000	−0.176777
$33$	6.23273	1.08498
$34$	1.25590	0.215384
$35$	−5.16920	−0.873754
$36$	−0.930640	−0.155107
$37$	10.0123	1.64601	0.823007	−	0.568032i	$-0.192295\pi$
$37$	10.0123	1.64601	0.823007	+	0.568032i	$0.192295\pi$
$38$	6.01902	0.976414
$39$	6.45215	1.03317
$40$	4.29281	0.678753
$41$	−3.08792	−0.482252	−0.241126	−	0.970494i	$-0.577517\pi$
$41$	−3.08792	−0.482252	−0.241126	+	0.970494i	$0.577517\pi$
$42$	1.73221	0.267285
$43$	−5.42176	−0.826811	−0.413405	−	0.910547i	$-0.635661\pi$
$43$	−5.42176	−0.826811	−0.413405	+	0.910547i	$0.635661\pi$
$44$	−4.33272	−0.653182
$45$	3.99506	0.595549
$46$	−2.96030	−0.436472
$47$	10.2342	1.49281	0.746403	−	0.665495i	$-0.231779\pi$
$47$	10.2342	1.49281	0.746403	+	0.665495i	$0.231779\pi$
$48$	−1.43853	−0.207634
$49$	−5.55002	−0.792860
$50$	−13.4282	−1.89904
$51$	1.80664	0.252980
$52$	−4.48525	−0.621992
$53$	6.88379	0.945561	0.472780	−	0.881180i	$-0.343250\pi$
$53$	6.88379	0.945561	0.472780	+	0.881180i	$0.343250\pi$
$54$	−5.65433	−0.769457
$55$	18.5996	2.50796
$56$	−1.20415	−0.160912
$57$	8.65852	1.14685
$58$	4.13599	0.543081
$59$	0.0973902	0.0126791	0.00633956	−	0.999980i	$-0.497982\pi$
$59$	0.0973902	0.0126791	0.00633956	+	0.999980i	$0.497982\pi$
$60$	6.17533	0.797231
$61$	7.62365	0.976109	0.488054	−	0.872813i	$-0.337707\pi$
$61$	7.62365	0.976109	0.488054	+	0.872813i	$0.337707\pi$
$62$	−9.36074	−1.18882
$63$	−1.12063	−0.141186
$64$	1.00000	0.125000
$65$	19.2543	2.38820
$66$	−6.23273	−0.767197
$67$	0.0361020	0.00441056	0.00220528	−	0.999998i	$-0.499298\pi$
$67$	0.0361020	0.00441056	0.00220528	+	0.999998i	$0.499298\pi$
$68$	−1.25590	−0.152300
$69$	−4.25847	−0.512659
$70$	5.16920	0.617837
$71$	−10.5000	−1.24612	−0.623059	−	0.782175i	$-0.714110\pi$
$71$	−10.5000	−1.24612	−0.623059	+	0.782175i	$0.714110\pi$
$72$	0.930640	0.109677
$73$	−4.36880	−0.511329	−0.255664	−	0.966766i	$-0.582294\pi$
$73$	−4.36880	−0.511329	−0.255664	+	0.966766i	$0.582294\pi$
$74$	−10.0123	−1.16391
$75$	−19.3169	−2.23052
$76$	−6.01902	−0.690429
$77$	−5.21725	−0.594561
$78$	−6.45215	−0.730562
$79$	1.59781	0.179768	0.0898840	−	0.995952i	$-0.471350\pi$
$79$	1.59781	0.179768	0.0898840	+	0.995952i	$0.471350\pi$
$80$	−4.29281	−0.479951
$81$	−5.34199	−0.593554
$82$	3.08792	0.341004
$83$	−7.56899	−0.830805	−0.415403	−	0.909638i	$-0.636359\pi$
$83$	−7.56899	−0.830805	−0.415403	+	0.909638i	$0.636359\pi$
$84$	−1.73221	−0.188999
$85$	5.39132	0.584771
$86$	5.42176	0.584643
$87$	5.94973	0.637878
$88$	4.33272	0.461869
$89$	−8.82134	−0.935060	−0.467530	−	0.883977i	$-0.654856\pi$
$89$	−8.82134	−0.935060	−0.467530	+	0.883977i	$0.654856\pi$
$90$	−3.99506	−0.421117
$91$	−5.40092	−0.566170
$92$	2.96030	0.308632
$93$	−13.4657	−1.39633
$94$	−10.2342	−1.05557
$95$	25.8385	2.65098
$96$	1.43853	0.146819
$97$	12.6574	1.28517	0.642583	−	0.766216i	$-0.277863\pi$
$97$	12.6574	1.28517	0.642583	+	0.766216i	$0.277863\pi$
$98$	5.55002	0.560636
$99$	4.03220	0.405251
$100$	13.4282	1.34282
$101$	2.86372	0.284951	0.142475	−	0.989798i	$-0.454494\pi$
$101$	2.86372	0.284951	0.142475	+	0.989798i	$0.454494\pi$
$102$	−1.80664	−0.178884
$103$	1.61519	0.159149	0.0795747	−	0.996829i	$-0.474644\pi$
$103$	1.61519	0.159149	0.0795747	+	0.996829i	$0.474644\pi$
$104$	4.48525	0.439815
$105$	7.43603	0.725682
$106$	−6.88379	−0.668612
$107$	−8.14057	−0.786978	−0.393489	−	0.919329i	$-0.628732\pi$
$107$	−8.14057	−0.786978	−0.393489	+	0.919329i	$0.628732\pi$
$108$	5.65433	0.544088
$109$	6.39914	0.612927	0.306463	−	0.951882i	$-0.400854\pi$
$109$	6.39914	0.612927	0.306463	+	0.951882i	$0.400854\pi$
$110$	−18.5996	−1.77340
$111$	−14.4030	−1.36707
$112$	1.20415	0.113782
$113$	3.29358	0.309834	0.154917	−	0.987927i	$-0.450489\pi$
$113$	3.29358	0.309834	0.154917	+	0.987927i	$0.450489\pi$
$114$	−8.65852	−0.810945
$115$	−12.7080	−1.18503
$116$	−4.13599	−0.384017
$117$	4.17415	0.385900
$118$	−0.0973902	−0.00896550
$119$	−1.51229	−0.138631
$120$	−6.17533	−0.563728
$121$	7.77246	0.706587
$122$	−7.62365	−0.690213
$123$	4.44206	0.400527
$124$	9.36074	0.840619
$125$	−36.1809	−3.23611
$126$	1.12063	0.0998338
$127$	13.5441	1.20185	0.600924	−	0.799306i	$-0.294800\pi$
$127$	13.5441	1.20185	0.600924	+	0.799306i	$0.294800\pi$
$128$	−1.00000	−0.0883883
$129$	7.79935	0.686694
$130$	−19.2543	−1.68872
$131$	−5.67059	−0.495442	−0.247721	−	0.968831i	$-0.579682\pi$
$131$	−5.67059	−0.495442	−0.247721	+	0.968831i	$0.579682\pi$
$132$	6.23273	0.542490
$133$	−7.24781	−0.628465
$134$	−0.0361020	−0.00311873
$135$	−24.2730	−2.08909
$136$	1.25590	0.107692
$137$	8.11443	0.693263	0.346631	−	0.938001i	$-0.387326\pi$
$137$	8.11443	0.693263	0.346631	+	0.938001i	$0.387326\pi$
$138$	4.25847	0.362505
$139$	11.6772	0.990448	0.495224	−	0.868765i	$-0.335086\pi$
$139$	11.6772	0.990448	0.495224	+	0.868765i	$0.335086\pi$
$140$	−5.16920	−0.436877
$141$	−14.7221	−1.23983
$142$	10.5000	0.881138
$143$	19.4333	1.62510
$144$	−0.930640	−0.0775533
$145$	17.7550	1.47447
$146$	4.36880	0.361564
$147$	7.98385	0.658497
$148$	10.0123	0.823007
$149$	20.9904	1.71960	0.859802	−	0.510628i	$-0.170587\pi$
$149$	20.9904	1.71960	0.859802	+	0.510628i	$0.170587\pi$
$150$	19.3169	1.57722
$151$	−18.4014	−1.49748	−0.748742	−	0.662861i	$-0.769342\pi$
$151$	−18.4014	−1.49748	−0.748742	+	0.662861i	$0.769342\pi$
$152$	6.01902	0.488207
$153$	1.16879	0.0944908
$154$	5.21725	0.420418
$155$	−40.1839	−3.22765
$156$	6.45215	0.516585
$157$	−2.43257	−0.194140	−0.0970700	−	0.995278i	$-0.530947\pi$
$157$	−2.43257	−0.194140	−0.0970700	+	0.995278i	$0.530947\pi$
$158$	−1.59781	−0.127115
$159$	−9.90251	−0.785320
$160$	4.29281	0.339377
$161$	3.56465	0.280934
$162$	5.34199	0.419706
$163$	1.63545	0.128098	0.0640492	−	0.997947i	$-0.479599\pi$
$163$	1.63545	0.128098	0.0640492	+	0.997947i	$0.479599\pi$
$164$	−3.08792	−0.241126
$165$	−26.7560	−2.08295
$166$	7.56899	0.587468
$167$	−4.52248	−0.349960	−0.174980	−	0.984572i	$-0.555986\pi$
$167$	−4.52248	−0.349960	−0.174980	+	0.984572i	$0.555986\pi$
$168$	1.73221	0.133643
$169$	7.11744	0.547495
$170$	−5.39132	−0.413496
$171$	5.60154	0.428360
$172$	−5.42176	−0.413405
$173$	0.627959	0.0477428	0.0238714	−	0.999715i	$-0.492401\pi$
$173$	0.627959	0.0477428	0.0238714	+	0.999715i	$0.492401\pi$
$174$	−5.94973	−0.451048
$175$	16.1696	1.22231
$176$	−4.33272	−0.326591
$177$	−0.140098	−0.0105304
$178$	8.82134	0.661187
$179$	7.48418	0.559394	0.279697	−	0.960088i	$-0.409766\pi$
$179$	7.48418	0.559394	0.279697	+	0.960088i	$0.409766\pi$
$180$	3.99506	0.297774
$181$	−23.0613	−1.71413	−0.857067	−	0.515204i	$-0.827716\pi$
$181$	−23.0613	−1.71413	−0.857067	+	0.515204i	$0.827716\pi$
$182$	5.40092	0.400343
$183$	−10.9668	−0.810691
$184$	−2.96030	−0.218236
$185$	−42.9810	−3.16002
$186$	13.4657	0.987351
$187$	5.44144	0.397918
$188$	10.2342	0.746403
$189$	6.80868	0.495258
$190$	−25.8385	−1.87452
$191$	15.3452	1.11034	0.555170	−	0.831737i	$-0.312653\pi$
$191$	15.3452	1.11034	0.555170	+	0.831737i	$0.312653\pi$
$192$	−1.43853	−0.103817
$193$	5.95143	0.428393	0.214197	−	0.976791i	$-0.431287\pi$
$193$	5.95143	0.428393	0.214197	+	0.976791i	$0.431287\pi$
$194$	−12.6574	−0.908750
$195$	−27.6979	−1.98349
$196$	−5.55002	−0.396430
$197$	15.4777	1.10274	0.551370	−	0.834261i	$-0.314105\pi$
$197$	15.4777	1.10274	0.551370	+	0.834261i	$0.314105\pi$
$198$	−4.03220	−0.286556
$199$	9.29963	0.659234	0.329617	−	0.944115i	$-0.393080\pi$
$199$	9.29963	0.659234	0.329617	+	0.944115i	$0.393080\pi$
$200$	−13.4282	−0.949520
$201$	−0.0519336	−0.00366312
$202$	−2.86372	−0.201491
$203$	−4.98035	−0.349552
$204$	1.80664	0.126490
$205$	13.2559	0.925830
$206$	−1.61519	−0.112536
$207$	−2.75497	−0.191484
$208$	−4.48525	−0.310996
$209$	26.0787	1.80390
$210$	−7.43603	−0.513135
$211$	7.53189	0.518517	0.259258	−	0.965808i	$-0.416522\pi$
$211$	7.53189	0.518517	0.259258	+	0.965808i	$0.416522\pi$
$212$	6.88379	0.472780
$213$	15.1045	1.03494
$214$	8.14057	0.556478
$215$	23.2746	1.58731
$216$	−5.65433	−0.384729
$217$	11.2718	0.765177
$218$	−6.39914	−0.433405
$219$	6.28463	0.424676
$220$	18.5996	1.25398
$221$	5.63300	0.378917
$222$	14.4030	0.966664
$223$	10.8343	0.725520	0.362760	−	0.931883i	$-0.381835\pi$
$223$	10.8343	0.725520	0.362760	+	0.931883i	$0.381835\pi$
$224$	−1.20415	−0.0804558
$225$	−12.4969	−0.833124
$226$	−3.29358	−0.219086
$227$	−26.3499	−1.74891	−0.874453	−	0.485111i	$-0.838779\pi$
$227$	−26.3499	−1.74891	−0.874453	+	0.485111i	$0.838779\pi$
$228$	8.65852	0.573424
$229$	9.15160	0.604754	0.302377	−	0.953188i	$-0.402220\pi$
$229$	9.15160	0.604754	0.302377	+	0.953188i	$0.402220\pi$
$230$	12.7080	0.837941
$231$	7.50516	0.493803
$232$	4.13599	0.271541
$233$	−12.4475	−0.815463	−0.407731	−	0.913102i	$-0.633680\pi$
$233$	−12.4475	−0.815463	−0.407731	+	0.913102i	$0.633680\pi$
$234$	−4.17415	−0.272873
$235$	−43.9333	−2.86589
$236$	0.0973902	0.00633956
$237$	−2.29850	−0.149303
$238$	1.51229	0.0980272
$239$	−2.00637	−0.129781	−0.0648906	−	0.997892i	$-0.520670\pi$
$239$	−2.00637	−0.129781	−0.0648906	+	0.997892i	$0.520670\pi$
$240$	6.17533	0.398616
$241$	25.5178	1.64375	0.821873	−	0.569670i	$-0.192929\pi$
$241$	25.5178	1.64375	0.821873	+	0.569670i	$0.192929\pi$
$242$	−7.77246	−0.499632
$243$	−9.27840	−0.595210
$244$	7.62365	0.488054
$245$	23.8252	1.52214
$246$	−4.44206	−0.283215
$247$	26.9968	1.71776
$248$	−9.36074	−0.594408
$249$	10.8882	0.690012
$250$	36.1809	2.28828
$251$	8.38632	0.529340	0.264670	−	0.964339i	$-0.414737\pi$
$251$	8.38632	0.529340	0.264670	+	0.964339i	$0.414737\pi$
$252$	−1.12063	−0.0705932
$253$	−12.8261	−0.806372
$254$	−13.5441	−0.849835
$255$	−7.75557	−0.485672
$256$	1.00000	0.0625000
$257$	−7.31400	−0.456235	−0.228117	−	0.973634i	$-0.573257\pi$
$257$	−7.31400	−0.456235	−0.228117	+	0.973634i	$0.573257\pi$
$258$	−7.79935	−0.485566
$259$	12.0563	0.749144
$260$	19.2543	1.19410
$261$	3.84911	0.238254
$262$	5.67059	0.350330
$263$	−13.1398	−0.810237	−0.405119	−	0.914264i	$-0.632770\pi$
$263$	−13.1398	−0.810237	−0.405119	+	0.914264i	$0.632770\pi$
$264$	−6.23273	−0.383598
$265$	−29.5508	−1.81529
$266$	7.24781	0.444392
$267$	12.6897	0.776599
$268$	0.0361020	0.00220528
$269$	15.6422	0.953725	0.476862	−	0.878978i	$-0.341774\pi$
$269$	15.6422	0.953725	0.476862	+	0.878978i	$0.341774\pi$
$270$	24.2730	1.47721
$271$	13.3619	0.811676	0.405838	−	0.913945i	$-0.366980\pi$
$271$	13.3619	0.811676	0.405838	+	0.913945i	$0.366980\pi$
$272$	−1.25590	−0.0761499
$273$	7.76937	0.470224
$274$	−8.11443	−0.490211
$275$	−58.1808	−3.50843
$276$	−4.25847	−0.256330
$277$	−8.24822	−0.495587	−0.247794	−	0.968813i	$-0.579705\pi$
$277$	−8.24822	−0.495587	−0.247794	+	0.968813i	$0.579705\pi$
$278$	−11.6772	−0.700352
$279$	−8.71148	−0.521543
$280$	5.16920	0.308919
$281$	−0.434933	−0.0259459	−0.0129730	−	0.999916i	$-0.504130\pi$
$281$	−0.434933	−0.0259459	−0.0129730	+	0.999916i	$0.504130\pi$
$282$	14.7221	0.876689
$283$	−30.9920	−1.84228	−0.921141	−	0.389229i	$-0.872741\pi$
$283$	−30.9920	−1.84228	−0.921141	+	0.389229i	$0.872741\pi$
$284$	−10.5000	−0.623059
$285$	−37.1694	−2.20173
$286$	−19.4333	−1.14912
$287$	−3.71833	−0.219486
$288$	0.930640	0.0548385
$289$	−15.4227	−0.907219
$290$	−17.7550	−1.04261
$291$	−18.2080	−1.06737
$292$	−4.36880	−0.255664
$293$	0.600212	0.0350647	0.0175324	−	0.999846i	$-0.494419\pi$
$293$	0.600212	0.0350647	0.0175324	+	0.999846i	$0.494419\pi$
$294$	−7.98385	−0.465628
$295$	−0.418078	−0.0243414
$296$	−10.0123	−0.581953
$297$	−24.4986	−1.42155
$298$	−20.9904	−1.21594
$299$	−13.2777	−0.767867
$300$	−19.3169	−1.11526
$301$	−6.52862	−0.376304
$302$	18.4014	1.05888
$303$	−4.11954	−0.236661
$304$	−6.01902	−0.345214
$305$	−32.7269	−1.87394
$306$	−1.16879	−0.0668151
$307$	0.213931	0.0122097	0.00610483	−	0.999981i	$-0.498057\pi$
$307$	0.213931	0.0122097	0.00610483	+	0.999981i	$0.498057\pi$
$308$	−5.21725	−0.297281
$309$	−2.32349	−0.132179
$310$	40.1839	2.28229
$311$	−23.5846	−1.33736	−0.668681	−	0.743549i	$-0.733141\pi$
$311$	−23.5846	−1.33736	−0.668681	+	0.743549i	$0.733141\pi$
$312$	−6.45215	−0.365281
$313$	−27.0281	−1.52772	−0.763859	−	0.645383i	$-0.776698\pi$
$313$	−27.0281	−1.52772	−0.763859	+	0.645383i	$0.776698\pi$
$314$	2.43257	0.137278
$315$	4.81066	0.271050
$316$	1.59781	0.0898840
$317$	20.8363	1.17028	0.585140	−	0.810932i	$-0.301039\pi$
$317$	20.8363	1.17028	0.585140	+	0.810932i	$0.301039\pi$
$318$	9.90251	0.555305
$319$	17.9201	1.00333
$320$	−4.29281	−0.239976
$321$	11.7104	0.653612
$322$	−3.56465	−0.198650
$323$	7.55926	0.420608
$324$	−5.34199	−0.296777
$325$	−60.2290	−3.34090
$326$	−1.63545	−0.0905793
$327$	−9.20534	−0.509056
$328$	3.08792	0.170502
$329$	12.3235	0.679415
$330$	26.7560	1.47287
$331$	15.9152	0.874778	0.437389	−	0.899272i	$-0.355903\pi$
$331$	15.9152	0.874778	0.437389	+	0.899272i	$0.355903\pi$
$332$	−7.56899	−0.415403
$333$	−9.31785	−0.510615
$334$	4.52248	0.247459
$335$	−0.154979	−0.00846740
$336$	−1.73221	−0.0944995
$337$	−11.3588	−0.618755	−0.309378	−	0.950939i	$-0.600121\pi$
$337$	−11.3588	−0.618755	−0.309378	+	0.950939i	$0.600121\pi$
$338$	−7.11744	−0.387138
$339$	−4.73791	−0.257328
$340$	5.39132	0.292386
$341$	−40.5575	−2.19631
$342$	−5.60154	−0.302896
$343$	−15.1121	−0.815978
$344$	5.42176	0.292322
$345$	18.2808	0.984205
$346$	−0.627959	−0.0337593
$347$	−14.1813	−0.761293	−0.380646	−	0.924721i	$-0.624298\pi$
$347$	−14.1813	−0.761293	−0.380646	+	0.924721i	$0.624298\pi$
$348$	5.94973	0.318939
$349$	−32.2155	−1.72446	−0.862228	−	0.506520i	$-0.830932\pi$
$349$	−32.2155	−1.72446	−0.862228	+	0.506520i	$0.830932\pi$
$350$	−16.1696	−0.864304
$351$	−25.3611	−1.35367
$352$	4.33272	0.230935
$353$	−25.0755	−1.33464	−0.667318	−	0.744773i	$-0.732558\pi$
$353$	−25.0755	−1.33464	−0.667318	+	0.744773i	$0.732558\pi$
$354$	0.140098	0.00744615
$355$	45.0744	2.39230
$356$	−8.82134	−0.467530
$357$	2.17547	0.115138
$358$	−7.48418	−0.395551
$359$	13.2381	0.698680	0.349340	−	0.936996i	$-0.386406\pi$
$359$	13.2381	0.698680	0.349340	+	0.936996i	$0.386406\pi$
$360$	−3.99506	−0.210558
$361$	17.2286	0.906767
$362$	23.0613	1.21208
$363$	−11.1809	−0.586844
$364$	−5.40092	−0.283085
$365$	18.7544	0.981651
$366$	10.9668	0.573245
$367$	14.8000	0.772553	0.386277	−	0.922383i	$-0.373761\pi$
$367$	14.8000	0.772553	0.386277	+	0.922383i	$0.373761\pi$
$368$	2.96030	0.154316
$369$	2.87374	0.149601
$370$	42.9810	2.23447
$371$	8.28912	0.430350
$372$	−13.4657	−0.698163
$373$	8.55261	0.442837	0.221419	−	0.975179i	$-0.428931\pi$
$373$	8.55261	0.442837	0.221419	+	0.975179i	$0.428931\pi$
$374$	−5.44144	−0.281370
$375$	52.0471	2.68770
$376$	−10.2342	−0.527786
$377$	18.5509	0.955421
$378$	−6.80868	−0.350200
$379$	−14.4575	−0.742631	−0.371315	−	0.928507i	$-0.621093\pi$
$379$	−14.4575	−0.742631	−0.371315	+	0.928507i	$0.621093\pi$
$380$	25.8385	1.32549
$381$	−19.4836	−0.998175
$382$	−15.3452	−0.785129
$383$	28.2078	1.44135	0.720675	−	0.693273i	$-0.243832\pi$
$383$	28.2078	1.44135	0.720675	+	0.693273i	$0.243832\pi$
$384$	1.43853	0.0734095
$385$	22.3967	1.14144
$386$	−5.95143	−0.302920
$387$	5.04571	0.256488
$388$	12.6574	0.642583
$389$	36.4837	1.84980	0.924898	−	0.380216i	$-0.124150\pi$
$389$	36.4837	1.84980	0.924898	+	0.380216i	$0.124150\pi$
$390$	27.6979	1.40254
$391$	−3.71782	−0.188018
$392$	5.55002	0.280318
$393$	8.15730	0.411481
$394$	−15.4777	−0.779755
$395$	−6.85911	−0.345119
$396$	4.03220	0.202626
$397$	−24.2389	−1.21652	−0.608258	−	0.793739i	$-0.708131\pi$
$397$	−24.2389	−1.21652	−0.608258	+	0.793739i	$0.708131\pi$
$398$	−9.29963	−0.466149
$399$	10.4262	0.521962
$400$	13.4282	0.671412
$401$	−19.7815	−0.987839	−0.493919	−	0.869508i	$-0.664436\pi$
$401$	−19.7815	−0.987839	−0.493919	+	0.869508i	$0.664436\pi$
$402$	0.0519336	0.00259021
$403$	−41.9852	−2.09143
$404$	2.86372	0.142475
$405$	22.9322	1.13951
$406$	4.98035	0.247171
$407$	−43.3805	−2.15029
$408$	−1.80664	−0.0894420
$409$	−0.818260	−0.0404603	−0.0202302	−	0.999795i	$-0.506440\pi$
$409$	−0.818260	−0.0404603	−0.0202302	+	0.999795i	$0.506440\pi$
$410$	−13.2559	−0.654660
$411$	−11.6728	−0.575778
$412$	1.61519	0.0795747
$413$	0.117273	0.00577061
$414$	2.75497	0.135399
$415$	32.4923	1.59498
$416$	4.48525	0.219907
$417$	−16.7980	−0.822601
$418$	−26.0787	−1.27555
$419$	−14.8831	−0.727087	−0.363544	−	0.931577i	$-0.618433\pi$
$419$	−14.8831	−0.727087	−0.363544	+	0.931577i	$0.618433\pi$
$420$	7.43603	0.362841
$421$	20.5087	0.999532	0.499766	−	0.866160i	$-0.333419\pi$
$421$	20.5087	0.999532	0.499766	+	0.866160i	$0.333419\pi$
$422$	−7.53189	−0.366647
$423$	−9.52431	−0.463088
$424$	−6.88379	−0.334306
$425$	−16.8645	−0.818047
$426$	−15.1045	−0.731815
$427$	9.18004	0.444253
$428$	−8.14057	−0.393489
$429$	−27.9553	−1.34970
$430$	−23.2746	−1.12240
$431$	−22.9346	−1.10472	−0.552361	−	0.833605i	$-0.686273\pi$
$431$	−22.9346	−1.10472	−0.552361	+	0.833605i	$0.686273\pi$
$432$	5.65433	0.272044
$433$	21.4889	1.03269	0.516345	−	0.856381i	$-0.327292\pi$
$433$	21.4889	1.03269	0.516345	+	0.856381i	$0.327292\pi$
$434$	−11.2718	−0.541061
$435$	−25.5411	−1.22460
$436$	6.39914	0.306463
$437$	−17.8181	−0.852354
$438$	−6.28463	−0.300291
$439$	−36.5298	−1.74347	−0.871737	−	0.489974i	$-0.837006\pi$
$439$	−36.5298	−1.74347	−0.871737	+	0.489974i	$0.837006\pi$
$440$	−18.5996	−0.886699
$441$	5.16507	0.245956
$442$	−5.63300	−0.267935
$443$	−35.4936	−1.68635	−0.843176	−	0.537638i	$-0.819317\pi$
$443$	−35.4936	−1.68635	−0.843176	+	0.537638i	$0.819317\pi$
$444$	−14.4030	−0.683535
$445$	37.8684	1.79513
$446$	−10.8343	−0.513020
$447$	−30.1953	−1.42819
$448$	1.20415	0.0568908
$449$	22.4356	1.05880	0.529401	−	0.848372i	$-0.322417\pi$
$449$	22.4356	1.05880	0.529401	+	0.848372i	$0.322417\pi$
$450$	12.4969	0.589107
$451$	13.3791	0.629997
$452$	3.29358	0.154917
$453$	26.4709	1.24371
$454$	26.3499	1.23666
$455$	23.1851	1.08694
$456$	−8.65852	−0.405472
$457$	24.8660	1.16318	0.581592	−	0.813481i	$-0.302430\pi$
$457$	24.8660	1.16318	0.581592	+	0.813481i	$0.302430\pi$
$458$	−9.15160	−0.427626
$459$	−7.10125	−0.331458
$460$	−12.7080	−0.592513
$461$	5.44802	0.253740	0.126870	−	0.991919i	$-0.459507\pi$
$461$	5.44802	0.253740	0.126870	+	0.991919i	$0.459507\pi$
$462$	−7.50516	−0.349172
$463$	7.97014	0.370404	0.185202	−	0.982700i	$-0.440706\pi$
$463$	7.97014	0.370404	0.185202	+	0.982700i	$0.440706\pi$
$464$	−4.13599	−0.192008
$465$	57.8056	2.68067
$466$	12.4475	0.576619
$467$	−25.8532	−1.19634	−0.598172	−	0.801368i	$-0.704106\pi$
$467$	−25.8532	−1.19634	−0.598172	+	0.801368i	$0.704106\pi$
$468$	4.17415	0.192950
$469$	0.0434722	0.00200736
$470$	43.9333	2.02649
$471$	3.49931	0.161240
$472$	−0.0973902	−0.00448275
$473$	23.4910	1.08012
$474$	2.29850	0.105574
$475$	−80.8248	−3.70850
$476$	−1.51229	−0.0693157
$477$	−6.40632	−0.293325
$478$	2.00637	0.0917692
$479$	33.8980	1.54884	0.774419	−	0.632673i	$-0.218042\pi$
$479$	33.8980	1.54884	0.774419	+	0.632673i	$0.218042\pi$
$480$	−6.17533	−0.281864
$481$	−44.9077	−2.04761
$482$	−25.5178	−1.16230
$483$	−5.12784	−0.233325
$484$	7.77246	0.353293
$485$	−54.3360	−2.46727
$486$	9.27840	0.420877
$487$	−20.1830	−0.914580	−0.457290	−	0.889318i	$-0.651180\pi$
$487$	−20.1830	−0.914580	−0.457290	+	0.889318i	$0.651180\pi$
$488$	−7.62365	−0.345107
$489$	−2.35264	−0.106390
$490$	−23.8252	−1.07631
$491$	23.1063	1.04277	0.521387	−	0.853320i	$-0.325415\pi$
$491$	23.1063	1.04277	0.521387	+	0.853320i	$0.325415\pi$
$492$	4.44206	0.200263
$493$	5.19437	0.233942
$494$	−26.9968	−1.21464
$495$	−17.3095	−0.778003
$496$	9.36074	0.420310
$497$	−12.6436	−0.567141
$498$	−10.8882	−0.487912
$499$	38.5441	1.72547	0.862735	−	0.505657i	$-0.168750\pi$
$499$	38.5441	1.72547	0.862735	+	0.505657i	$0.168750\pi$
$500$	−36.1809	−1.61806
$501$	6.50571	0.290654
$502$	−8.38632	−0.374300
$503$	36.6451	1.63393	0.816963	−	0.576690i	$-0.195656\pi$
$503$	36.6451	1.63393	0.816963	+	0.576690i	$0.195656\pi$
$504$	1.12063	0.0499169
$505$	−12.2934	−0.547050
$506$	12.8261	0.570191
$507$	−10.2386	−0.454713
$508$	13.5441	0.600924
$509$	29.9901	1.32929	0.664644	−	0.747160i	$-0.268583\pi$
$509$	29.9901	1.32929	0.664644	+	0.747160i	$0.268583\pi$
$510$	7.75557	0.343422
$511$	−5.26070	−0.232719
$512$	−1.00000	−0.0441942
$513$	−34.0335	−1.50262
$514$	7.31400	0.322607
$515$	−6.93371	−0.305536
$516$	7.79935	0.343347
$517$	−44.3417	−1.95015
$518$	−12.0563	−0.529725
$519$	−0.903336	−0.0396520
$520$	−19.2543	−0.844358
$521$	−34.2605	−1.50098	−0.750490	−	0.660882i	$-0.770182\pi$
$521$	−34.2605	−1.50098	−0.750490	+	0.660882i	$0.770182\pi$
$522$	−3.84911	−0.168471
$523$	20.7333	0.906603	0.453301	−	0.891357i	$-0.350246\pi$
$523$	20.7333	0.906603	0.453301	+	0.891357i	$0.350246\pi$
$524$	−5.67059	−0.247721
$525$	−23.2605	−1.01517
$526$	13.1398	0.572924
$527$	−11.7561	−0.512104
$528$	6.23273	0.271245
$529$	−14.2366	−0.618985
$530$	29.5508	1.28360
$531$	−0.0906352	−0.00393323
$532$	−7.24781	−0.314233
$533$	13.8501	0.599914
$534$	−12.6897	−0.549138
$535$	34.9459	1.51084
$536$	−0.0361020	−0.00155937
$537$	−10.7662	−0.464596
$538$	−15.6422	−0.674385
$539$	24.0467	1.03576
$540$	−24.2730	−1.04454
$541$	−4.93707	−0.212261	−0.106131	−	0.994352i	$-0.533846\pi$
$541$	−4.93707	−0.212261	−0.106131	+	0.994352i	$0.533846\pi$
$542$	−13.3619	−0.573942
$543$	33.1743	1.42365
$544$	1.25590	0.0538461
$545$	−27.4703	−1.17670
$546$	−7.76937	−0.332498
$547$	24.2193	1.03554	0.517771	−	0.855519i	$-0.326762\pi$
$547$	24.2193	1.03554	0.517771	+	0.855519i	$0.326762\pi$
$548$	8.11443	0.346631
$549$	−7.09487	−0.302802
$550$	58.1808	2.48084
$551$	24.8946	1.06054
$552$	4.25847	0.181252
$553$	1.92401	0.0818172
$554$	8.24822	0.350433
$555$	61.8293	2.62451
$556$	11.6772	0.495224
$557$	15.5571	0.659175	0.329587	−	0.944125i	$-0.393090\pi$
$557$	15.5571	0.659175	0.329587	+	0.944125i	$0.393090\pi$
$558$	8.71148	0.368786
$559$	24.3179	1.02854
$560$	−5.16920	−0.218439
$561$	−7.82766	−0.330484
$562$	0.434933	0.0183465
$563$	1.08948	0.0459160	0.0229580	−	0.999736i	$-0.492692\pi$
$563$	1.08948	0.0459160	0.0229580	+	0.999736i	$0.492692\pi$
$564$	−14.7221	−0.619913
$565$	−14.1387	−0.594821
$566$	30.9920	1.30269
$567$	−6.43257	−0.270142
$568$	10.5000	0.440569
$569$	−27.0426	−1.13368	−0.566842	−	0.823827i	$-0.691835\pi$
$569$	−27.0426	−1.13368	−0.566842	+	0.823827i	$0.691835\pi$
$570$	37.1694	1.55685
$571$	43.6435	1.82642	0.913212	−	0.407486i	$-0.133594\pi$
$571$	43.6435	1.82642	0.913212	+	0.407486i	$0.133594\pi$
$572$	19.4333	0.812548
$573$	−22.0745	−0.922176
$574$	3.71833	0.155200
$575$	39.7516	1.65776
$576$	−0.930640	−0.0387767
$577$	29.4224	1.22487	0.612435	−	0.790521i	$-0.290190\pi$
$577$	29.4224	1.22487	0.612435	+	0.790521i	$0.290190\pi$
$578$	15.4227	0.641501
$579$	−8.56129	−0.355795
$580$	17.7550	0.737237
$581$	−9.11422	−0.378122
$582$	18.2080	0.754748
$583$	−29.8255	−1.23525
$584$	4.36880	0.180782
$585$	−17.9188	−0.740853
$586$	−0.600212	−0.0247945
$587$	14.0526	0.580011	0.290006	−	0.957025i	$-0.406343\pi$
$587$	14.0526	0.580011	0.290006	+	0.957025i	$0.406343\pi$
$588$	7.98385	0.329248
$589$	−56.3425	−2.32155
$590$	0.418078	0.0172120
$591$	−22.2651	−0.915863
$592$	10.0123	0.411503
$593$	−40.5613	−1.66565	−0.832827	−	0.553533i	$-0.813279\pi$
$593$	−40.5613	−1.66565	−0.832827	+	0.553533i	$0.813279\pi$
$594$	24.4986	1.00519
$595$	6.49197	0.266145
$596$	20.9904	0.859802
$597$	−13.3778	−0.547516
$598$	13.2777	0.542964
$599$	−45.9276	−1.87655	−0.938275	−	0.345891i	$-0.887577\pi$
$599$	−45.9276	−1.87655	−0.938275	+	0.345891i	$0.887577\pi$
$600$	19.3169	0.788609
$601$	21.7305	0.886407	0.443203	−	0.896421i	$-0.353842\pi$
$601$	21.7305	0.886407	0.443203	+	0.896421i	$0.353842\pi$
$602$	6.52862	0.266087
$603$	−0.0335979	−0.00136821
$604$	−18.4014	−0.748742
$605$	−33.3657	−1.35651
$606$	4.11954	0.167345
$607$	−10.9925	−0.446171	−0.223086	−	0.974799i	$-0.571613\pi$
$607$	−10.9925	−0.446171	−0.223086	+	0.974799i	$0.571613\pi$
$608$	6.01902	0.244103
$609$	7.16438	0.290315
$610$	32.7269	1.32507
$611$	−45.9027	−1.85703
$612$	1.16879	0.0472454
$613$	0.748236	0.0302209	0.0151105	−	0.999886i	$-0.495190\pi$
$613$	0.748236	0.0302209	0.0151105	+	0.999886i	$0.495190\pi$
$614$	−0.213931	−0.00863353
$615$	−19.0689	−0.768933
$616$	5.21725	0.210209
$617$	18.1347	0.730076	0.365038	−	0.930993i	$-0.381056\pi$
$617$	18.1347	0.730076	0.365038	+	0.930993i	$0.381056\pi$
$618$	2.32349	0.0934646
$619$	−37.8647	−1.52191	−0.760955	−	0.648805i	$-0.775269\pi$
$619$	−37.8647	−1.52191	−0.760955	+	0.648805i	$0.775269\pi$
$620$	−40.1839	−1.61382
$621$	16.7385	0.671693
$622$	23.5846	0.945658
$623$	−10.6222	−0.425571
$624$	6.45215	0.258293
$625$	88.1764	3.52706
$626$	27.0281	1.08026
$627$	−37.5149	−1.49820
$628$	−2.43257	−0.0970700
$629$	−12.5744	−0.501375
$630$	−4.81066	−0.191661
$631$	−24.8606	−0.989684	−0.494842	−	0.868983i	$-0.664774\pi$
$631$	−24.8606	−0.989684	−0.494842	+	0.868983i	$0.664774\pi$
$632$	−1.59781	−0.0635576
$633$	−10.8348	−0.430646
$634$	−20.8363	−0.827513
$635$	−58.1424	−2.30731
$636$	−9.90251	−0.392660
$637$	24.8932	0.986304
$638$	−17.9201	−0.709462
$639$	9.77169	0.386562
$640$	4.29281	0.169688
$641$	15.3610	0.606722	0.303361	−	0.952876i	$-0.401891\pi$
$641$	15.3610	0.606722	0.303361	+	0.952876i	$0.401891\pi$
$642$	−11.7104	−0.462174
$643$	36.6038	1.44351	0.721756	−	0.692148i	$-0.243335\pi$
$643$	36.6038	1.44351	0.721756	+	0.692148i	$0.243335\pi$
$644$	3.56465	0.140467
$645$	−33.4811	−1.31832
$646$	−7.55926	−0.297415
$647$	−1.78933	−0.0703459	−0.0351729	−	0.999381i	$-0.511198\pi$
$647$	−1.78933	−0.0703459	−0.0351729	+	0.999381i	$0.511198\pi$
$648$	5.34199	0.209853
$649$	−0.421964	−0.0165636
$650$	60.2290	2.36237
$651$	−16.2147	−0.635505
$652$	1.63545	0.0640492
$653$	−15.2858	−0.598179	−0.299089	−	0.954225i	$-0.596683\pi$
$653$	−15.2858	−0.598179	−0.299089	+	0.954225i	$0.596683\pi$
$654$	9.20534	0.359957
$655$	24.3428	0.951151
$656$	−3.08792	−0.120563
$657$	4.06578	0.158621
$658$	−12.3235	−0.480419
$659$	−27.5757	−1.07420	−0.537099	−	0.843519i	$-0.680480\pi$
$659$	−27.5757	−1.07420	−0.537099	+	0.843519i	$0.680480\pi$
$660$	−26.7560	−1.04147
$661$	42.2330	1.64267	0.821337	−	0.570443i	$-0.193229\pi$
$661$	42.2330	1.64267	0.821337	+	0.570443i	$0.193229\pi$
$662$	−15.9152	−0.618562
$663$	−8.10323	−0.314703
$664$	7.56899	0.293734
$665$	31.1135	1.20653
$666$	9.31785	0.361059
$667$	−12.2437	−0.474080
$668$	−4.52248	−0.174980
$669$	−15.5855	−0.602569
$670$	0.154979	0.00598736
$671$	−33.0311	−1.27515
$672$	1.73221	0.0668213
$673$	23.3159	0.898762	0.449381	−	0.893340i	$-0.351645\pi$
$673$	23.3159	0.898762	0.449381	+	0.893340i	$0.351645\pi$
$674$	11.3588	0.437526
$675$	75.9277	2.92246
$676$	7.11744	0.273748
$677$	20.8234	0.800307	0.400154	−	0.916448i	$-0.368957\pi$
$677$	20.8234	0.800307	0.400154	+	0.916448i	$0.368957\pi$
$678$	4.73791	0.181958
$679$	15.2415	0.584914
$680$	−5.39132	−0.206748
$681$	37.9051	1.45253
$682$	40.5575	1.55303
$683$	−23.7862	−0.910152	−0.455076	−	0.890452i	$-0.650388\pi$
$683$	−23.7862	−0.910152	−0.455076	+	0.890452i	$0.650388\pi$
$684$	5.60154	0.214180
$685$	−34.8337	−1.33093
$686$	15.1121	0.576984
$687$	−13.1648	−0.502269
$688$	−5.42176	−0.206703
$689$	−30.8755	−1.17626
$690$	−18.2808	−0.695938
$691$	−21.3876	−0.813622	−0.406811	−	0.913512i	$-0.633359\pi$
$691$	−21.3876	−0.813622	−0.406811	+	0.913512i	$0.633359\pi$
$692$	0.627959	0.0238714
$693$	4.85538	0.184441
$694$	14.1813	0.538315
$695$	−50.1281	−1.90147
$696$	−5.94973	−0.225524
$697$	3.87811	0.146894
$698$	32.2155	1.21938
$699$	17.9061	0.677270
$700$	16.1696	0.611155
$701$	−42.5646	−1.60764	−0.803822	−	0.594870i	$-0.797204\pi$
$701$	−42.5646	−1.60764	−0.803822	+	0.594870i	$0.797204\pi$
$702$	25.3611	0.957192
$703$	−60.2642	−2.27291
$704$	−4.33272	−0.163295
$705$	63.1993	2.38022
$706$	25.0755	0.943730
$707$	3.44836	0.129689
$708$	−0.140098	−0.00526522
$709$	15.5896	0.585478	0.292739	−	0.956192i	$-0.405433\pi$
$709$	15.5896	0.585478	0.292739	+	0.956192i	$0.405433\pi$
$710$	−45.0744	−1.69161
$711$	−1.48699	−0.0557664
$712$	8.82134	0.330594
$713$	27.7106	1.03777
$714$	−2.17547	−0.0814149
$715$	−83.4236	−3.11986
$716$	7.48418	0.279697
$717$	2.88622	0.107788
$718$	−13.2381	−0.494041
$719$	30.9428	1.15397	0.576985	−	0.816755i	$-0.304229\pi$
$719$	30.9428	1.15397	0.576985	+	0.816755i	$0.304229\pi$
$720$	3.99506	0.148887
$721$	1.94493	0.0724331
$722$	−17.2286	−0.641181
$723$	−36.7081	−1.36519
$724$	−23.0613	−0.857067
$725$	−55.5390	−2.06267
$726$	11.1809	0.414962
$727$	42.9550	1.59311	0.796556	−	0.604565i	$-0.206653\pi$
$727$	42.9550	1.59311	0.796556	+	0.604565i	$0.206653\pi$
$728$	5.40092	0.200171
$729$	29.3732	1.08790
$730$	−18.7544	−0.694132
$731$	6.80916	0.251846
$732$	−10.9668	−0.405346
$733$	−10.4605	−0.386367	−0.193183	−	0.981163i	$-0.561881\pi$
$733$	−10.4605	−0.386367	−0.193183	+	0.981163i	$0.561881\pi$
$734$	−14.8000	−0.546278
$735$	−34.2732	−1.26419
$736$	−2.96030	−0.109118
$737$	−0.156420	−0.00576179
$738$	−2.87374	−0.105784
$739$	15.7492	0.579343	0.289671	−	0.957126i	$-0.406454\pi$
$739$	15.7492	0.579343	0.289671	+	0.957126i	$0.406454\pi$
$740$	−42.9810	−1.58001
$741$	−38.8356	−1.42666
$742$	−8.28912	−0.304303
$743$	25.8441	0.948128	0.474064	−	0.880490i	$-0.342786\pi$
$743$	25.8441	0.948128	0.474064	+	0.880490i	$0.342786\pi$
$744$	13.4657	0.493676
$745$	−90.1080	−3.30130
$746$	−8.55261	−0.313133
$747$	7.04401	0.257727
$748$	5.44144	0.198959
$749$	−9.80248	−0.358175
$750$	−52.0471	−1.90049
$751$	−16.8286	−0.614084	−0.307042	−	0.951696i	$-0.599339\pi$
$751$	−16.8286	−0.614084	−0.307042	+	0.951696i	$0.599339\pi$
$752$	10.2342	0.373201
$753$	−12.0639	−0.439635
$754$	−18.5509	−0.675584
$755$	78.9938	2.87488
$756$	6.80868	0.247629
$757$	−29.8613	−1.08533	−0.542664	−	0.839950i	$-0.682584\pi$
$757$	−29.8613	−1.08533	−0.542664	+	0.839950i	$0.682584\pi$
$758$	14.4575	0.525119
$759$	18.4507	0.669719
$760$	−25.8385	−0.937261
$761$	44.5369	1.61446	0.807231	−	0.590235i	$-0.200965\pi$
$761$	44.5369	1.61446	0.807231	+	0.590235i	$0.200965\pi$
$762$	19.4836	0.705817
$763$	7.70554	0.278959
$764$	15.3452	0.555170
$765$	−5.01738	−0.181404
$766$	−28.2078	−1.01919
$767$	−0.436819	−0.0157726
$768$	−1.43853	−0.0519084
$769$	−27.3137	−0.984956	−0.492478	−	0.870325i	$-0.663909\pi$
$769$	−27.3137	−0.984956	−0.492478	+	0.870325i	$0.663909\pi$
$770$	−22.3967	−0.807121
$771$	10.5214	0.378919
$772$	5.95143	0.214197
$773$	−53.7931	−1.93480	−0.967402	−	0.253245i	$-0.918502\pi$
$773$	−53.7931	−1.93480	−0.967402	+	0.253245i	$0.918502\pi$
$774$	−5.04571	−0.181364
$775$	125.698	4.51521
$776$	−12.6574	−0.454375
$777$	−17.3434	−0.622190
$778$	−36.4837	−1.30800
$779$	18.5862	0.665921
$780$	−27.6979	−0.991743
$781$	45.4934	1.62788
$782$	3.71782	0.132949
$783$	−23.3862	−0.835756
$784$	−5.55002	−0.198215
$785$	10.4426	0.372711
$786$	−8.15730	−0.290961
$787$	−37.2483	−1.32776	−0.663879	−	0.747840i	$-0.731091\pi$
$787$	−37.2483	−1.32776	−0.663879	+	0.747840i	$0.731091\pi$
$788$	15.4777	0.551370
$789$	18.9020	0.672929
$790$	6.85911	0.244036
$791$	3.96597	0.141014
$792$	−4.03220	−0.143278
$793$	−34.1940	−1.21426
$794$	24.2389	0.860207
$795$	42.5096	1.50766
$796$	9.29963	0.329617
$797$	−22.7963	−0.807487	−0.403743	−	0.914872i	$-0.632291\pi$
$797$	−22.7963	−0.807487	−0.403743	+	0.914872i	$0.632291\pi$
$798$	−10.4262	−0.369083
$799$	−12.8530	−0.454708
$800$	−13.4282	−0.474760
$801$	8.20949	0.290068
$802$	19.7815	0.698508
$803$	18.9288	0.667982
$804$	−0.0519336	−0.00183156
$805$	−15.3024	−0.539337
$806$	41.9852	1.47887
$807$	−22.5018	−0.792101
$808$	−2.86372	−0.100745
$809$	32.8334	1.15436	0.577181	−	0.816616i	$-0.304153\pi$
$809$	32.8334	1.15436	0.577181	+	0.816616i	$0.304153\pi$
$810$	−22.9322	−0.805754
$811$	43.8443	1.53958	0.769792	−	0.638295i	$-0.220360\pi$
$811$	43.8443	1.53958	0.769792	+	0.638295i	$0.220360\pi$
$812$	−4.98035	−0.174776
$813$	−19.2214	−0.674124
$814$	43.3805	1.52049
$815$	−7.02069	−0.245924
$816$	1.80664	0.0632450
$817$	32.6337	1.14171
$818$	0.818260	0.0286098
$819$	5.02631	0.175633
$820$	13.2559	0.462915
$821$	−46.1121	−1.60932	−0.804661	−	0.593734i	$-0.797653\pi$
$821$	−46.1121	−1.60932	−0.804661	+	0.593734i	$0.797653\pi$
$822$	11.6728	0.407137
$823$	19.4175	0.676853	0.338427	−	0.940993i	$-0.390105\pi$
$823$	19.4175	0.676853	0.338427	+	0.940993i	$0.390105\pi$
$824$	−1.61519	−0.0562678
$825$	83.6946	2.91387
$826$	−0.117273	−0.00408044
$827$	−19.0648	−0.662949	−0.331474	−	0.943464i	$-0.607546\pi$
$827$	−19.0648	−0.662949	−0.331474	+	0.943464i	$0.607546\pi$
$828$	−2.75497	−0.0957418
$829$	−26.6130	−0.924308	−0.462154	−	0.886800i	$-0.652923\pi$
$829$	−26.6130	−0.924308	−0.462154	+	0.886800i	$0.652923\pi$
$830$	−32.4923	−1.12782
$831$	11.8653	0.411602
$832$	−4.48525	−0.155498
$833$	6.97024	0.241505
$834$	16.7980	0.581666
$835$	19.4142	0.671855
$836$	26.0787	0.901951
$837$	52.9287	1.82948
$838$	14.8831	0.514128
$839$	−3.01585	−0.104119	−0.0520593	−	0.998644i	$-0.516578\pi$
$839$	−3.01585	−0.104119	−0.0520593	+	0.998644i	$0.516578\pi$
$840$	−7.43603	−0.256568
$841$	−11.8936	−0.410125
$842$	−20.5087	−0.706776
$843$	0.625663	0.0215490
$844$	7.53189	0.259258
$845$	−30.5538	−1.05108
$846$	9.52431	0.327453
$847$	9.35922	0.321587
$848$	6.88379	0.236390
$849$	44.5828	1.53008
$850$	16.8645	0.578447
$851$	29.6394	1.01603
$852$	15.1045	0.517471
$853$	15.9370	0.545672	0.272836	−	0.962061i	$-0.412038\pi$
$853$	15.9370	0.545672	0.272836	+	0.962061i	$0.412038\pi$
$854$	−9.18004	−0.314134
$855$	−24.0464	−0.822368
$856$	8.14057	0.278239
$857$	−1.67747	−0.0573013	−0.0286506	−	0.999589i	$-0.509121\pi$
$857$	−1.67747	−0.0573013	−0.0286506	+	0.999589i	$0.509121\pi$
$858$	27.9553	0.954380
$859$	−23.9504	−0.817177	−0.408589	−	0.912719i	$-0.633979\pi$
$859$	−23.9504	−0.817177	−0.408589	+	0.912719i	$0.633979\pi$
$860$	23.2746	0.793657
$861$	5.34891	0.182290
$862$	22.9346	0.781157
$863$	34.7699	1.18358	0.591791	−	0.806092i	$-0.298421\pi$
$863$	34.7699	1.18358	0.591791	+	0.806092i	$0.298421\pi$
$864$	−5.65433	−0.192364
$865$	−2.69571	−0.0916569
$866$	−21.4889	−0.730222
$867$	22.1860	0.753476
$868$	11.2718	0.382588
$869$	−6.92288	−0.234843
$870$	25.5411	0.865923
$871$	−0.161926	−0.00548666
$872$	−6.39914	−0.216702
$873$	−11.7795	−0.398676
$874$	17.8181	0.602705
$875$	−43.5672	−1.47284
$876$	6.28463	0.212338
$877$	−30.3017	−1.02322	−0.511608	−	0.859219i	$-0.670950\pi$
$877$	−30.3017	−1.02322	−0.511608	+	0.859219i	$0.670950\pi$
$878$	36.5298	1.23282
$879$	−0.863421	−0.0291225
$880$	18.5996	0.626991
$881$	21.2685	0.716553	0.358276	−	0.933616i	$-0.383365\pi$
$881$	21.2685	0.716553	0.358276	+	0.933616i	$0.383365\pi$
$882$	−5.16507	−0.173917
$883$	−1.49989	−0.0504753	−0.0252376	−	0.999681i	$-0.508034\pi$
$883$	−1.49989	−0.0504753	−0.0252376	+	0.999681i	$0.508034\pi$
$884$	5.63300	0.189458
$885$	0.601416	0.0202164
$886$	35.4936	1.19243
$887$	−4.58751	−0.154034	−0.0770168	−	0.997030i	$-0.524539\pi$
$887$	−4.58751	−0.154034	−0.0770168	+	0.997030i	$0.524539\pi$
$888$	14.4030	0.483332
$889$	16.3092	0.546993
$890$	−37.8684	−1.26935
$891$	23.1453	0.775398
$892$	10.8343	0.362760
$893$	−61.5996	−2.06135
$894$	30.1953	1.00988
$895$	−32.1282	−1.07393
$896$	−1.20415	−0.0402279
$897$	19.1003	0.637740
$898$	−22.4356	−0.748686
$899$	−38.7159	−1.29125
$900$	−12.4969	−0.416562
$901$	−8.64532	−0.288017
$902$	−13.3791	−0.445475
$903$	9.39160	0.312533
$904$	−3.29358	−0.109543
$905$	98.9979	3.29080
$906$	−26.4709	−0.879437
$907$	−12.8919	−0.428068	−0.214034	−	0.976826i	$-0.568660\pi$
$907$	−12.8919	−0.428068	−0.214034	+	0.976826i	$0.568660\pi$
$908$	−26.3499	−0.874453
$909$	−2.66509	−0.0883955
$910$	−23.1851	−0.768580
$911$	4.04391	0.133981	0.0669903	−	0.997754i	$-0.478660\pi$
$911$	4.04391	0.133981	0.0669903	+	0.997754i	$0.478660\pi$
$912$	8.65852	0.286712
$913$	32.7943	1.08533
$914$	−24.8660	−0.822495
$915$	47.0786	1.55637
$916$	9.15160	0.302377
$917$	−6.82825	−0.225489
$918$	7.10125	0.234376
$919$	−4.84136	−0.159702	−0.0798509	−	0.996807i	$-0.525444\pi$
$919$	−4.84136	−0.159702	−0.0798509	+	0.996807i	$0.525444\pi$
$920$	12.7080	0.418970
$921$	−0.307745	−0.0101405
$922$	−5.44802	−0.179421
$923$	47.0950	1.55015
$924$	7.50516	0.246902
$925$	134.448	4.42061
$926$	−7.97014	−0.261915
$927$	−1.50316	−0.0493702
$928$	4.13599	0.135770
$929$	−4.75844	−0.156119	−0.0780597	−	0.996949i	$-0.524872\pi$
$929$	−4.75844	−0.156119	−0.0780597	+	0.996949i	$0.524872\pi$
$930$	−57.8056	−1.89552
$931$	33.4057	1.09483
$932$	−12.4475	−0.407731
$933$	33.9271	1.11072
$934$	25.8532	0.845943
$935$	−23.3591	−0.763924
$936$	−4.17415	−0.136436
$937$	−45.8228	−1.49697	−0.748483	−	0.663154i	$-0.769217\pi$
$937$	−45.8228	−1.49697	−0.748483	+	0.663154i	$0.769217\pi$
$938$	−0.0434722	−0.00141942
$939$	38.8806	1.26882
$940$	−43.9333	−1.43295
$941$	−28.1218	−0.916745	−0.458373	−	0.888760i	$-0.651567\pi$
$941$	−28.1218	−0.916745	−0.458373	+	0.888760i	$0.651567\pi$
$942$	−3.49931	−0.114014
$943$	−9.14116	−0.297677
$944$	0.0973902	0.00316978
$945$	−29.2284	−0.950799
$946$	−23.4910	−0.763757
$947$	50.3609	1.63651	0.818255	−	0.574856i	$-0.194942\pi$
$947$	50.3609	1.63651	0.818255	+	0.574856i	$0.194942\pi$
$948$	−2.29850	−0.0746517
$949$	19.5951	0.636085
$950$	80.8248	2.62230
$951$	−29.9735	−0.971958
$952$	1.51229	0.0490136
$953$	−52.9206	−1.71427	−0.857133	−	0.515095i	$-0.827757\pi$
$953$	−52.9206	−1.71427	−0.857133	+	0.515095i	$0.827757\pi$
$954$	6.40632	0.207412
$955$	−65.8741	−2.13164
$956$	−2.00637	−0.0648906
$957$	−25.7785	−0.833300
$958$	−33.8980	−1.09519
$959$	9.77101	0.315522
$960$	6.17533	0.199308
$961$	56.6235	1.82656
$962$	44.9077	1.44788
$963$	7.57594	0.244131
$964$	25.5178	0.821873
$965$	−25.5484	−0.822431
$966$	5.12784	0.164986
$967$	56.5262	1.81776	0.908880	−	0.417057i	$-0.136939\pi$
$967$	56.5262	1.81776	0.908880	+	0.417057i	$0.136939\pi$
$968$	−7.77246	−0.249816
$969$	−10.8742	−0.349330
$970$	54.3360	1.74462
$971$	39.2296	1.25894	0.629469	−	0.777025i	$-0.283272\pi$
$971$	39.2296	1.25894	0.629469	+	0.777025i	$0.283272\pi$
$972$	−9.27840	−0.297605
$973$	14.0611	0.450779
$974$	20.1830	0.646706
$975$	86.6410	2.77473
$976$	7.62365	0.244027
$977$	23.0418	0.737171	0.368586	−	0.929594i	$-0.379842\pi$
$977$	23.0418	0.737171	0.368586	+	0.929594i	$0.379842\pi$
$978$	2.35264	0.0752292
$979$	38.2204	1.22153
$980$	23.8252	0.761068
$981$	−5.95530	−0.190138
$982$	−23.1063	−0.737353
$983$	−25.9602	−0.828000	−0.414000	−	0.910277i	$-0.635869\pi$
$983$	−25.9602	−0.828000	−0.414000	+	0.910277i	$0.635869\pi$
$984$	−4.44206	−0.141608
$985$	−66.4429	−2.11705
$986$	−5.19437	−0.165422
$987$	−17.7277	−0.564278
$988$	26.9968	0.858882
$989$	−16.0500	−0.510361
$990$	17.3095	0.550131
$991$	−15.8292	−0.502830	−0.251415	−	0.967879i	$-0.580896\pi$
$991$	−15.8292	−0.502830	−0.251415	+	0.967879i	$0.580896\pi$
$992$	−9.36074	−0.297204
$993$	−22.8944	−0.726533
$994$	12.6436	0.401029
$995$	−39.9216	−1.26560
$996$	10.8882	0.345006
$997$	−39.6511	−1.25576	−0.627882	−	0.778309i	$-0.716078\pi$
$997$	−39.6511	−1.25576	−0.627882	+	0.778309i	$0.716078\pi$
$998$	−38.5441	−1.22009
$999$	56.6129	1.79115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.d.1.20	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.d.1.20	✓	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.43853 q^{3} +1.00000 q^{4} -4.29281 q^{5} +1.43853 q^{6} +1.20415 q^{7} -1.00000 q^{8} -0.930640 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.43853 q^{3} +1.00000 q^{4} -4.29281 q^{5} +1.43853 q^{6} +1.20415 q^{7} -1.00000 q^{8} -0.930640 q^{9} +4.29281 q^{10} -4.33272 q^{11} -1.43853 q^{12} -4.48525 q^{13} -1.20415 q^{14} +6.17533 q^{15} +1.00000 q^{16} -1.25590 q^{17} +0.930640 q^{18} -6.01902 q^{19} -4.29281 q^{20} -1.73221 q^{21} +4.33272 q^{22} +2.96030 q^{23} +1.43853 q^{24} +13.4282 q^{25} +4.48525 q^{26} +5.65433 q^{27} +1.20415 q^{28} -4.13599 q^{29} -6.17533 q^{30} +9.36074 q^{31} -1.00000 q^{32} +6.23273 q^{33} +1.25590 q^{34} -5.16920 q^{35} -0.930640 q^{36} +10.0123 q^{37} +6.01902 q^{38} +6.45215 q^{39} +4.29281 q^{40} -3.08792 q^{41} +1.73221 q^{42} -5.42176 q^{43} -4.33272 q^{44} +3.99506 q^{45} -2.96030 q^{46} +10.2342 q^{47} -1.43853 q^{48} -5.55002 q^{49} -13.4282 q^{50} +1.80664 q^{51} -4.48525 q^{52} +6.88379 q^{53} -5.65433 q^{54} +18.5996 q^{55} -1.20415 q^{56} +8.65852 q^{57} +4.13599 q^{58} +0.0973902 q^{59} +6.17533 q^{60} +7.62365 q^{61} -9.36074 q^{62} -1.12063 q^{63} +1.00000 q^{64} +19.2543 q^{65} -6.23273 q^{66} +0.0361020 q^{67} -1.25590 q^{68} -4.25847 q^{69} +5.16920 q^{70} -10.5000 q^{71} +0.930640 q^{72} -4.36880 q^{73} -10.0123 q^{74} -19.3169 q^{75} -6.01902 q^{76} -5.21725 q^{77} -6.45215 q^{78} +1.59781 q^{79} -4.29281 q^{80} -5.34199 q^{81} +3.08792 q^{82} -7.56899 q^{83} -1.73221 q^{84} +5.39132 q^{85} +5.42176 q^{86} +5.94973 q^{87} +4.33272 q^{88} -8.82134 q^{89} -3.99506 q^{90} -5.40092 q^{91} +2.96030 q^{92} -13.4657 q^{93} -10.2342 q^{94} +25.8385 q^{95} +1.43853 q^{96} +12.6574 q^{97} +5.55002 q^{98} +4.03220 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * q^99

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