LMFDB - Embedded newform 6042.2.a.bf.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 27 x^{10} + 134 x^{9} + 294 x^{8} - 1313 x^{7} - 1685 x^{6} + 5910 x^{5} + \cdots + 4048 $ x^12 - 5x^11 - 27x^10 + 134x^9 + 294x^8 - 1313x^7 - 1685x^6 + 5910x^5 + 5237x^4 - 12206x^3 - 7876x^2 + 9264*x + 4048
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$2.22012$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.22012 q^{5} -1.00000 q^{6} -3.11298 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.22012 q^{5} -1.00000 q^{6} -3.11298 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.22012 q^{10} -4.98093 q^{11} +1.00000 q^{12} -0.252042 q^{13} +3.11298 q^{14} +1.22012 q^{15} +1.00000 q^{16} -2.60406 q^{17} -1.00000 q^{18} +1.00000 q^{19} +1.22012 q^{20} -3.11298 q^{21} +4.98093 q^{22} -7.35913 q^{23} -1.00000 q^{24} -3.51130 q^{25} +0.252042 q^{26} +1.00000 q^{27} -3.11298 q^{28} -2.54705 q^{29} -1.22012 q^{30} +5.18346 q^{31} -1.00000 q^{32} -4.98093 q^{33} +2.60406 q^{34} -3.79822 q^{35} +1.00000 q^{36} -4.63406 q^{37} -1.00000 q^{38} -0.252042 q^{39} -1.22012 q^{40} +3.50168 q^{41} +3.11298 q^{42} +9.35913 q^{43} -4.98093 q^{44} +1.22012 q^{45} +7.35913 q^{46} +13.3028 q^{47} +1.00000 q^{48} +2.69065 q^{49} +3.51130 q^{50} -2.60406 q^{51} -0.252042 q^{52} +1.00000 q^{53} -1.00000 q^{54} -6.07734 q^{55} +3.11298 q^{56} +1.00000 q^{57} +2.54705 q^{58} +6.44695 q^{59} +1.22012 q^{60} +2.50524 q^{61} -5.18346 q^{62} -3.11298 q^{63} +1.00000 q^{64} -0.307522 q^{65} +4.98093 q^{66} -2.00022 q^{67} -2.60406 q^{68} -7.35913 q^{69} +3.79822 q^{70} -3.26867 q^{71} -1.00000 q^{72} +13.8785 q^{73} +4.63406 q^{74} -3.51130 q^{75} +1.00000 q^{76} +15.5055 q^{77} +0.252042 q^{78} +3.79044 q^{79} +1.22012 q^{80} +1.00000 q^{81} -3.50168 q^{82} +9.49562 q^{83} -3.11298 q^{84} -3.17728 q^{85} -9.35913 q^{86} -2.54705 q^{87} +4.98093 q^{88} -4.41196 q^{89} -1.22012 q^{90} +0.784600 q^{91} -7.35913 q^{92} +5.18346 q^{93} -13.3028 q^{94} +1.22012 q^{95} -1.00000 q^{96} +5.66971 q^{97} -2.69065 q^{98} -4.98093 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9} + 7 q^{10} - 5 q^{11} + 12 q^{12} + 10 q^{13} - 5 q^{14} - 7 q^{15} + 12 q^{16} + 6 q^{17} - 12 q^{18} + 12 q^{19} - 7 q^{20} + 5 q^{21} + 5 q^{22} - 12 q^{24} + 21 q^{25} - 10 q^{26} + 12 q^{27} + 5 q^{28} + 7 q^{30} + 2 q^{31} - 12 q^{32} - 5 q^{33} - 6 q^{34} - 17 q^{35} + 12 q^{36} + 16 q^{37} - 12 q^{38} + 10 q^{39} + 7 q^{40} + 7 q^{41} - 5 q^{42} + 24 q^{43} - 5 q^{44} - 7 q^{45} + 4 q^{47} + 12 q^{48} + 29 q^{49} - 21 q^{50} + 6 q^{51} + 10 q^{52} + 12 q^{53} - 12 q^{54} - 2 q^{55} - 5 q^{56} + 12 q^{57} + 2 q^{59} - 7 q^{60} + 29 q^{61} - 2 q^{62} + 5 q^{63} + 12 q^{64} - 17 q^{65} + 5 q^{66} + 36 q^{67} + 6 q^{68} + 17 q^{70} - 3 q^{71} - 12 q^{72} + 7 q^{73} - 16 q^{74} + 21 q^{75} + 12 q^{76} - 35 q^{77} - 10 q^{78} + 40 q^{79} - 7 q^{80} + 12 q^{81} - 7 q^{82} + 24 q^{83} + 5 q^{84} - 22 q^{85} - 24 q^{86} + 5 q^{88} - 45 q^{89} + 7 q^{90} + 71 q^{91} + 2 q^{93} - 4 q^{94} - 7 q^{95} - 12 q^{96} + q^{97} - 29 q^{98} - 5 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9 + 7 * q^10 - 5 * q^11 + 12 * q^12 + 10 * q^13 - 5 * q^14 - 7 * q^15 + 12 * q^16 + 6 * q^17 - 12 * q^18 + 12 * q^19 - 7 * q^20 + 5 * q^21 + 5 * q^22 - 12 * q^24 + 21 * q^25 - 10 * q^26 + 12 * q^27 + 5 * q^28 + 7 * q^30 + 2 * q^31 - 12 * q^32 - 5 * q^33 - 6 * q^34 - 17 * q^35 + 12 * q^36 + 16 * q^37 - 12 * q^38 + 10 * q^39 + 7 * q^40 + 7 * q^41 - 5 * q^42 + 24 * q^43 - 5 * q^44 - 7 * q^45 + 4 * q^47 + 12 * q^48 + 29 * q^49 - 21 * q^50 + 6 * q^51 + 10 * q^52 + 12 * q^53 - 12 * q^54 - 2 * q^55 - 5 * q^56 + 12 * q^57 + 2 * q^59 - 7 * q^60 + 29 * q^61 - 2 * q^62 + 5 * q^63 + 12 * q^64 - 17 * q^65 + 5 * q^66 + 36 * q^67 + 6 * q^68 + 17 * q^70 - 3 * q^71 - 12 * q^72 + 7 * q^73 - 16 * q^74 + 21 * q^75 + 12 * q^76 - 35 * q^77 - 10 * q^78 + 40 * q^79 - 7 * q^80 + 12 * q^81 - 7 * q^82 + 24 * q^83 + 5 * q^84 - 22 * q^85 - 24 * q^86 + 5 * q^88 - 45 * q^89 + 7 * q^90 + 71 * q^91 + 2 * q^93 - 4 * q^94 - 7 * q^95 - 12 * q^96 + q^97 - 29 * q^98 - 5 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.22012	0.545656	0.272828	−	0.962063i	$-0.412041\pi$
$5$	1.22012	0.545656	0.272828	+	0.962063i	$0.412041\pi$
$6$	−1.00000	−0.408248
$7$	−3.11298	−1.17660	−0.588298	−	0.808644i	$-0.700202\pi$
$7$	−3.11298	−1.17660	−0.588298	+	0.808644i	$0.700202\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.22012	−0.385837
$11$	−4.98093	−1.50181	−0.750903	−	0.660413i	$-0.770381\pi$
$11$	−4.98093	−1.50181	−0.750903	+	0.660413i	$0.770381\pi$
$12$	1.00000	0.288675
$13$	−0.252042	−0.0699037	−0.0349519	−	0.999389i	$-0.511128\pi$
$13$	−0.252042	−0.0699037	−0.0349519	+	0.999389i	$0.511128\pi$
$14$	3.11298	0.831979
$15$	1.22012	0.315035
$16$	1.00000	0.250000
$17$	−2.60406	−0.631578	−0.315789	−	0.948829i	$-0.602269\pi$
$17$	−2.60406	−0.631578	−0.315789	+	0.948829i	$0.602269\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.22012	0.272828
$21$	−3.11298	−0.679308
$22$	4.98093	1.06194
$23$	−7.35913	−1.53448	−0.767242	−	0.641357i	$-0.778372\pi$
$23$	−7.35913	−1.53448	−0.767242	+	0.641357i	$0.778372\pi$
$24$	−1.00000	−0.204124
$25$	−3.51130	−0.702260
$26$	0.252042	0.0494294
$27$	1.00000	0.192450
$28$	−3.11298	−0.588298
$29$	−2.54705	−0.472976	−0.236488	−	0.971634i	$-0.575996\pi$
$29$	−2.54705	−0.472976	−0.236488	+	0.971634i	$0.575996\pi$
$30$	−1.22012	−0.222763
$31$	5.18346	0.930977	0.465489	−	0.885054i	$-0.345879\pi$
$31$	5.18346	0.930977	0.465489	+	0.885054i	$0.345879\pi$
$32$	−1.00000	−0.176777
$33$	−4.98093	−0.867068
$34$	2.60406	0.446593
$35$	−3.79822	−0.642017
$36$	1.00000	0.166667
$37$	−4.63406	−0.761835	−0.380917	−	0.924609i	$-0.624392\pi$
$37$	−4.63406	−0.761835	−0.380917	+	0.924609i	$0.624392\pi$
$38$	−1.00000	−0.162221
$39$	−0.252042	−0.0403589
$40$	−1.22012	−0.192918
$41$	3.50168	0.546870	0.273435	−	0.961890i	$-0.411840\pi$
$41$	3.50168	0.546870	0.273435	+	0.961890i	$0.411840\pi$
$42$	3.11298	0.480343
$43$	9.35913	1.42725	0.713627	−	0.700526i	$-0.247051\pi$
$43$	9.35913	1.42725	0.713627	+	0.700526i	$0.247051\pi$
$44$	−4.98093	−0.750903
$45$	1.22012	0.181885
$46$	7.35913	1.08504
$47$	13.3028	1.94041	0.970204	−	0.242290i	$-0.0778986\pi$
$47$	13.3028	1.94041	0.970204	+	0.242290i	$0.0778986\pi$
$48$	1.00000	0.144338
$49$	2.69065	0.384378
$50$	3.51130	0.496573
$51$	−2.60406	−0.364642
$52$	−0.252042	−0.0349519
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−1.00000	−0.136083
$55$	−6.07734	−0.819469
$56$	3.11298	0.415990
$57$	1.00000	0.132453
$58$	2.54705	0.334445
$59$	6.44695	0.839321	0.419661	−	0.907681i	$-0.362149\pi$
$59$	6.44695	0.839321	0.419661	+	0.907681i	$0.362149\pi$
$60$	1.22012	0.157517
$61$	2.50524	0.320763	0.160381	−	0.987055i	$-0.448728\pi$
$61$	2.50524	0.320763	0.160381	+	0.987055i	$0.448728\pi$
$62$	−5.18346	−0.658300
$63$	−3.11298	−0.392199
$64$	1.00000	0.125000
$65$	−0.307522	−0.0381434
$66$	4.98093	0.613110
$67$	−2.00022	−0.244366	−0.122183	−	0.992508i	$-0.538989\pi$
$67$	−2.00022	−0.244366	−0.122183	+	0.992508i	$0.538989\pi$
$68$	−2.60406	−0.315789
$69$	−7.35913	−0.885935
$70$	3.79822	0.453974
$71$	−3.26867	−0.387920	−0.193960	−	0.981009i	$-0.562133\pi$
$71$	−3.26867	−0.387920	−0.193960	+	0.981009i	$0.562133\pi$
$72$	−1.00000	−0.117851
$73$	13.8785	1.62436	0.812179	−	0.583409i	$-0.198281\pi$
$73$	13.8785	1.62436	0.812179	+	0.583409i	$0.198281\pi$
$74$	4.63406	0.538699
$75$	−3.51130	−0.405450
$76$	1.00000	0.114708
$77$	15.5055	1.76702
$78$	0.252042	0.0285381
$79$	3.79044	0.426458	0.213229	−	0.977002i	$-0.431602\pi$
$79$	3.79044	0.426458	0.213229	+	0.977002i	$0.431602\pi$
$80$	1.22012	0.136414
$81$	1.00000	0.111111
$82$	−3.50168	−0.386695
$83$	9.49562	1.04228	0.521140	−	0.853471i	$-0.325507\pi$
$83$	9.49562	1.04228	0.521140	+	0.853471i	$0.325507\pi$
$84$	−3.11298	−0.339654
$85$	−3.17728	−0.344624
$86$	−9.35913	−1.00922
$87$	−2.54705	−0.273073
$88$	4.98093	0.530968
$89$	−4.41196	−0.467667	−0.233834	−	0.972277i	$-0.575127\pi$
$89$	−4.41196	−0.467667	−0.233834	+	0.972277i	$0.575127\pi$
$90$	−1.22012	−0.128612
$91$	0.784600	0.0822485
$92$	−7.35913	−0.767242
$93$	5.18346	0.537500
$94$	−13.3028	−1.37208
$95$	1.22012	0.125182
$96$	−1.00000	−0.102062
$97$	5.66971	0.575672	0.287836	−	0.957680i	$-0.407064\pi$
$97$	5.66971	0.575672	0.287836	+	0.957680i	$0.407064\pi$
$98$	−2.69065	−0.271797
$99$	−4.98093	−0.500602
$100$	−3.51130	−0.351130
$101$	−4.33436	−0.431285	−0.215643	−	0.976472i	$-0.569185\pi$
$101$	−4.33436	−0.431285	−0.215643	+	0.976472i	$0.569185\pi$
$102$	2.60406	0.257841
$103$	9.44178	0.930326	0.465163	−	0.885225i	$-0.345996\pi$
$103$	9.44178	0.930326	0.465163	+	0.885225i	$0.345996\pi$
$104$	0.252042	0.0247147
$105$	−3.79822	−0.370668
$106$	−1.00000	−0.0971286
$107$	−4.94872	−0.478411	−0.239205	−	0.970969i	$-0.576887\pi$
$107$	−4.94872	−0.478411	−0.239205	+	0.970969i	$0.576887\pi$
$108$	1.00000	0.0962250
$109$	9.53029	0.912836	0.456418	−	0.889765i	$-0.349132\pi$
$109$	9.53029	0.912836	0.456418	+	0.889765i	$0.349132\pi$
$110$	6.07734	0.579452
$111$	−4.63406	−0.439846
$112$	−3.11298	−0.294149
$113$	2.77617	0.261160	0.130580	−	0.991438i	$-0.458316\pi$
$113$	2.77617	0.261160	0.130580	+	0.991438i	$0.458316\pi$
$114$	−1.00000	−0.0936586
$115$	−8.97905	−0.837301
$116$	−2.54705	−0.236488
$117$	−0.252042	−0.0233012
$118$	−6.44695	−0.593490
$119$	8.10640	0.743112
$120$	−1.22012	−0.111382
$121$	13.8096	1.25542
$122$	−2.50524	−0.226814
$123$	3.50168	0.315736
$124$	5.18346	0.465489
$125$	−10.3848	−0.928848
$126$	3.11298	0.277326
$127$	−4.20677	−0.373291	−0.186645	−	0.982427i	$-0.559762\pi$
$127$	−4.20677	−0.373291	−0.186645	+	0.982427i	$0.559762\pi$
$128$	−1.00000	−0.0883883
$129$	9.35913	0.824026
$130$	0.307522	0.0269714
$131$	14.7508	1.28878	0.644390	−	0.764697i	$-0.277111\pi$
$131$	14.7508	1.28878	0.644390	+	0.764697i	$0.277111\pi$
$132$	−4.98093	−0.433534
$133$	−3.11298	−0.269930
$134$	2.00022	0.172793
$135$	1.22012	0.105012
$136$	2.60406	0.223297
$137$	1.32414	0.113129	0.0565645	−	0.998399i	$-0.481985\pi$
$137$	1.32414	0.113129	0.0565645	+	0.998399i	$0.481985\pi$
$138$	7.35913	0.626451
$139$	−0.705140	−0.0598092	−0.0299046	−	0.999553i	$-0.509520\pi$
$139$	−0.705140	−0.0598092	−0.0299046	+	0.999553i	$0.509520\pi$
$140$	−3.79822	−0.321008
$141$	13.3028	1.12029
$142$	3.26867	0.274301
$143$	1.25540	0.104982
$144$	1.00000	0.0833333
$145$	−3.10772	−0.258082
$146$	−13.8785	−1.14859
$147$	2.69065	0.221921
$148$	−4.63406	−0.380917
$149$	13.2882	1.08861	0.544306	−	0.838887i	$-0.316793\pi$
$149$	13.2882	1.08861	0.544306	+	0.838887i	$0.316793\pi$
$150$	3.51130	0.286696
$151$	−6.91484	−0.562722	−0.281361	−	0.959602i	$-0.590786\pi$
$151$	−6.91484	−0.562722	−0.281361	+	0.959602i	$0.590786\pi$
$152$	−1.00000	−0.0811107
$153$	−2.60406	−0.210526
$154$	−15.5055	−1.24947
$155$	6.32447	0.507993
$156$	−0.252042	−0.0201795
$157$	13.0410	1.04079	0.520393	−	0.853927i	$-0.325786\pi$
$157$	13.0410	1.04079	0.520393	+	0.853927i	$0.325786\pi$
$158$	−3.79044	−0.301552
$159$	1.00000	0.0793052
$160$	−1.22012	−0.0964592
$161$	22.9088	1.80547
$162$	−1.00000	−0.0785674
$163$	9.99261	0.782682	0.391341	−	0.920246i	$-0.372011\pi$
$163$	9.99261	0.782682	0.391341	+	0.920246i	$0.372011\pi$
$164$	3.50168	0.273435
$165$	−6.07734	−0.473121
$166$	−9.49562	−0.737003
$167$	8.09686	0.626554	0.313277	−	0.949662i	$-0.398573\pi$
$167$	8.09686	0.626554	0.313277	+	0.949662i	$0.398573\pi$
$168$	3.11298	0.240172
$169$	−12.9365	−0.995113
$170$	3.17728	0.243686
$171$	1.00000	0.0764719
$172$	9.35913	0.713627
$173$	−10.0261	−0.762268	−0.381134	−	0.924520i	$-0.624466\pi$
$173$	−10.0261	−0.762268	−0.381134	+	0.924520i	$0.624466\pi$
$174$	2.54705	0.193092
$175$	10.9306	0.826276
$176$	−4.98093	−0.375451
$177$	6.44695	0.484582
$178$	4.41196	0.330691
$179$	7.16750	0.535724	0.267862	−	0.963457i	$-0.413683\pi$
$179$	7.16750	0.535724	0.267862	+	0.963457i	$0.413683\pi$
$180$	1.22012	0.0909426
$181$	−5.67509	−0.421826	−0.210913	−	0.977505i	$-0.567644\pi$
$181$	−5.67509	−0.421826	−0.210913	+	0.977505i	$0.567644\pi$
$182$	−0.784600	−0.0581584
$183$	2.50524	0.185193
$184$	7.35913	0.542522
$185$	−5.65413	−0.415700
$186$	−5.18346	−0.380070
$187$	12.9706	0.948507
$188$	13.3028	0.970204
$189$	−3.11298	−0.226436
$190$	−1.22012	−0.0885171
$191$	4.29029	0.310435	0.155217	−	0.987880i	$-0.450392\pi$
$191$	4.29029	0.310435	0.155217	+	0.987880i	$0.450392\pi$
$192$	1.00000	0.0721688
$193$	−3.28440	−0.236416	−0.118208	−	0.992989i	$-0.537715\pi$
$193$	−3.28440	−0.236416	−0.118208	+	0.992989i	$0.537715\pi$
$194$	−5.66971	−0.407062
$195$	−0.307522	−0.0220221
$196$	2.69065	0.192189
$197$	4.82321	0.343639	0.171820	−	0.985128i	$-0.445035\pi$
$197$	4.82321	0.343639	0.171820	+	0.985128i	$0.445035\pi$
$198$	4.98093	0.353979
$199$	8.42464	0.597207	0.298603	−	0.954377i	$-0.403479\pi$
$199$	8.42464	0.597207	0.298603	+	0.954377i	$0.403479\pi$
$200$	3.51130	0.248286
$201$	−2.00022	−0.141085
$202$	4.33436	0.304965
$203$	7.92893	0.556502
$204$	−2.60406	−0.182321
$205$	4.27248	0.298403
$206$	−9.44178	−0.657840
$207$	−7.35913	−0.511495
$208$	−0.252042	−0.0174759
$209$	−4.98093	−0.344538
$210$	3.79822	0.262102
$211$	17.4970	1.20454	0.602272	−	0.798291i	$-0.294262\pi$
$211$	17.4970	1.20454	0.602272	+	0.798291i	$0.294262\pi$
$212$	1.00000	0.0686803
$213$	−3.26867	−0.223966
$214$	4.94872	0.338287
$215$	11.4193	0.778790
$216$	−1.00000	−0.0680414
$217$	−16.1360	−1.09538
$218$	−9.53029	−0.645473
$219$	13.8785	0.937823
$220$	−6.07734	−0.409735
$221$	0.656332	0.0441497
$222$	4.63406	0.311018
$223$	17.1635	1.14935	0.574675	−	0.818382i	$-0.305128\pi$
$223$	17.1635	1.14935	0.574675	+	0.818382i	$0.305128\pi$
$224$	3.11298	0.207995
$225$	−3.51130	−0.234087
$226$	−2.77617	−0.184668
$227$	28.1881	1.87091	0.935454	−	0.353449i	$-0.114991\pi$
$227$	28.1881	1.87091	0.935454	+	0.353449i	$0.114991\pi$
$228$	1.00000	0.0662266
$229$	−15.6200	−1.03220	−0.516101	−	0.856528i	$-0.672617\pi$
$229$	−15.6200	−1.03220	−0.516101	+	0.856528i	$0.672617\pi$
$230$	8.97905	0.592061
$231$	15.5055	1.02019
$232$	2.54705	0.167222
$233$	−12.9170	−0.846218	−0.423109	−	0.906079i	$-0.639061\pi$
$233$	−12.9170	−0.846218	−0.423109	+	0.906079i	$0.639061\pi$
$234$	0.252042	0.0164765
$235$	16.2310	1.05879
$236$	6.44695	0.419661
$237$	3.79044	0.246216
$238$	−8.10640	−0.525460
$239$	4.15507	0.268769	0.134384	−	0.990929i	$-0.457094\pi$
$239$	4.15507	0.268769	0.134384	+	0.990929i	$0.457094\pi$
$240$	1.22012	0.0787586
$241$	−18.3041	−1.17907	−0.589536	−	0.807742i	$-0.700690\pi$
$241$	−18.3041	−1.17907	−0.589536	+	0.807742i	$0.700690\pi$
$242$	−13.8096	−0.887716
$243$	1.00000	0.0641500
$244$	2.50524	0.160381
$245$	3.28292	0.209738
$246$	−3.50168	−0.223259
$247$	−0.252042	−0.0160370
$248$	−5.18346	−0.329150
$249$	9.49562	0.601761
$250$	10.3848	0.656795
$251$	−30.3335	−1.91463	−0.957317	−	0.289040i	$-0.906664\pi$
$251$	−30.3335	−1.91463	−0.957317	+	0.289040i	$0.906664\pi$
$252$	−3.11298	−0.196099
$253$	36.6553	2.30450
$254$	4.20677	0.263956
$255$	−3.17728	−0.198969
$256$	1.00000	0.0625000
$257$	−8.93082	−0.557089	−0.278545	−	0.960423i	$-0.589852\pi$
$257$	−8.93082	−0.557089	−0.278545	+	0.960423i	$0.589852\pi$
$258$	−9.35913	−0.582674
$259$	14.4257	0.896372
$260$	−0.307522	−0.0190717
$261$	−2.54705	−0.157659
$262$	−14.7508	−0.911305
$263$	−11.7430	−0.724106	−0.362053	−	0.932158i	$-0.617924\pi$
$263$	−11.7430	−0.724106	−0.362053	+	0.932158i	$0.617924\pi$
$264$	4.98093	0.306555
$265$	1.22012	0.0749516
$266$	3.11298	0.190869
$267$	−4.41196	−0.270008
$268$	−2.00022	−0.122183
$269$	−24.4616	−1.49145	−0.745726	−	0.666253i	$-0.767897\pi$
$269$	−24.4616	−1.49145	−0.745726	+	0.666253i	$0.767897\pi$
$270$	−1.22012	−0.0742544
$271$	−13.9902	−0.849842	−0.424921	−	0.905230i	$-0.639698\pi$
$271$	−13.9902	−0.849842	−0.424921	+	0.905230i	$0.639698\pi$
$272$	−2.60406	−0.157895
$273$	0.784600	0.0474862
$274$	−1.32414	−0.0799943
$275$	17.4895	1.05466
$276$	−7.35913	−0.442968
$277$	15.2580	0.916763	0.458382	−	0.888755i	$-0.348429\pi$
$277$	15.2580	0.916763	0.458382	+	0.888755i	$0.348429\pi$
$278$	0.705140	0.0422915
$279$	5.18346	0.310326
$280$	3.79822	0.226987
$281$	−10.7697	−0.642464	−0.321232	−	0.947001i	$-0.604097\pi$
$281$	−10.7697	−0.642464	−0.321232	+	0.947001i	$0.604097\pi$
$282$	−13.3028	−0.792168
$283$	−1.71019	−0.101660	−0.0508300	−	0.998707i	$-0.516187\pi$
$283$	−1.71019	−0.101660	−0.0508300	+	0.998707i	$0.516187\pi$
$284$	−3.26867	−0.193960
$285$	1.22012	0.0722739
$286$	−1.25540	−0.0742334
$287$	−10.9007	−0.643445
$288$	−1.00000	−0.0589256
$289$	−10.2189	−0.601109
$290$	3.10772	0.182492
$291$	5.66971	0.332364
$292$	13.8785	0.812179
$293$	−32.2680	−1.88512	−0.942558	−	0.334042i	$-0.891587\pi$
$293$	−32.2680	−1.88512	−0.942558	+	0.334042i	$0.891587\pi$
$294$	−2.69065	−0.156922
$295$	7.86607	0.457981
$296$	4.63406	0.269349
$297$	−4.98093	−0.289023
$298$	−13.2882	−0.769765
$299$	1.85481	0.107266
$300$	−3.51130	−0.202725
$301$	−29.1348	−1.67930
$302$	6.91484	0.397904
$303$	−4.33436	−0.249003
$304$	1.00000	0.0573539
$305$	3.05670	0.175026
$306$	2.60406	0.148864
$307$	−32.7904	−1.87145	−0.935724	−	0.352734i	$-0.885252\pi$
$307$	−32.7904	−1.87145	−0.935724	+	0.352734i	$0.885252\pi$
$308$	15.5055	0.883509
$309$	9.44178	0.537124
$310$	−6.32447	−0.359206
$311$	−6.13553	−0.347914	−0.173957	−	0.984753i	$-0.555655\pi$
$311$	−6.13553	−0.347914	−0.173957	+	0.984753i	$0.555655\pi$
$312$	0.252042	0.0142690
$313$	31.9586	1.80641	0.903203	−	0.429213i	$-0.141209\pi$
$313$	31.9586	1.80641	0.903203	+	0.429213i	$0.141209\pi$
$314$	−13.0410	−0.735946
$315$	−3.79822	−0.214006
$316$	3.79044	0.213229
$317$	−24.0995	−1.35356	−0.676781	−	0.736184i	$-0.736626\pi$
$317$	−24.0995	−1.35356	−0.676781	+	0.736184i	$0.736626\pi$
$318$	−1.00000	−0.0560772
$319$	12.6867	0.710318
$320$	1.22012	0.0682070
$321$	−4.94872	−0.276210
$322$	−22.9088	−1.27666
$323$	−2.60406	−0.144894
$324$	1.00000	0.0555556
$325$	0.884993	0.0490906
$326$	−9.99261	−0.553440
$327$	9.53029	0.527026
$328$	−3.50168	−0.193348
$329$	−41.4112	−2.28308
$330$	6.07734	0.334547
$331$	−11.2570	−0.618741	−0.309370	−	0.950942i	$-0.600118\pi$
$331$	−11.2570	−0.618741	−0.309370	+	0.950942i	$0.600118\pi$
$332$	9.49562	0.521140
$333$	−4.63406	−0.253945
$334$	−8.09686	−0.443040
$335$	−2.44052	−0.133340
$336$	−3.11298	−0.169827
$337$	30.7533	1.67524	0.837618	−	0.546256i	$-0.183948\pi$
$337$	30.7533	1.67524	0.837618	+	0.546256i	$0.183948\pi$
$338$	12.9365	0.703651
$339$	2.77617	0.150781
$340$	−3.17728	−0.172312
$341$	−25.8184	−1.39815
$342$	−1.00000	−0.0540738
$343$	13.4149	0.724338
$344$	−9.35913	−0.504611
$345$	−8.97905	−0.483416
$346$	10.0261	0.539005
$347$	0.0516087	0.00277050	0.00138525	−	0.999999i	$-0.499559\pi$
$347$	0.0516087	0.00277050	0.00138525	+	0.999999i	$0.499559\pi$
$348$	−2.54705	−0.136536
$349$	25.4791	1.36387	0.681933	−	0.731415i	$-0.261140\pi$
$349$	25.4791	1.36387	0.681933	+	0.731415i	$0.261140\pi$
$350$	−10.9306	−0.584265
$351$	−0.252042	−0.0134530
$352$	4.98093	0.265484
$353$	13.2662	0.706091	0.353045	−	0.935606i	$-0.385146\pi$
$353$	13.2662	0.706091	0.353045	+	0.935606i	$0.385146\pi$
$354$	−6.44695	−0.342651
$355$	−3.98818	−0.211671
$356$	−4.41196	−0.233834
$357$	8.10640	0.429036
$358$	−7.16750	−0.378814
$359$	30.3571	1.60219	0.801094	−	0.598539i	$-0.204252\pi$
$359$	30.3571	1.60219	0.801094	+	0.598539i	$0.204252\pi$
$360$	−1.22012	−0.0643062
$361$	1.00000	0.0526316
$362$	5.67509	0.298276
$363$	13.8096	0.724817
$364$	0.784600	0.0411242
$365$	16.9335	0.886340
$366$	−2.50524	−0.130951
$367$	−21.9593	−1.14627	−0.573133	−	0.819463i	$-0.694272\pi$
$367$	−21.9593	−1.14627	−0.573133	+	0.819463i	$0.694272\pi$
$368$	−7.35913	−0.383621
$369$	3.50168	0.182290
$370$	5.65413	0.293944
$371$	−3.11298	−0.161618
$372$	5.18346	0.268750
$373$	2.53381	0.131196	0.0655979	−	0.997846i	$-0.479105\pi$
$373$	2.53381	0.131196	0.0655979	+	0.997846i	$0.479105\pi$
$374$	−12.9706	−0.670696
$375$	−10.3848	−0.536271
$376$	−13.3028	−0.686038
$377$	0.641963	0.0330628
$378$	3.11298	0.160114
$379$	6.84594	0.351652	0.175826	−	0.984421i	$-0.443740\pi$
$379$	6.84594	0.351652	0.175826	+	0.984421i	$0.443740\pi$
$380$	1.22012	0.0625910
$381$	−4.20677	−0.215519
$382$	−4.29029	−0.219510
$383$	12.2765	0.627298	0.313649	−	0.949539i	$-0.398449\pi$
$383$	12.2765	0.627298	0.313649	+	0.949539i	$0.398449\pi$
$384$	−1.00000	−0.0510310
$385$	18.9187	0.964184
$386$	3.28440	0.167171
$387$	9.35913	0.475751
$388$	5.66971	0.287836
$389$	−6.20145	−0.314426	−0.157213	−	0.987565i	$-0.550251\pi$
$389$	−6.20145	−0.314426	−0.157213	+	0.987565i	$0.550251\pi$
$390$	0.307522	0.0155720
$391$	19.1636	0.969147
$392$	−2.69065	−0.135898
$393$	14.7508	0.744077
$394$	−4.82321	−0.242990
$395$	4.62481	0.232700
$396$	−4.98093	−0.250301
$397$	5.91735	0.296983	0.148492	−	0.988914i	$-0.452558\pi$
$397$	5.91735	0.296983	0.148492	+	0.988914i	$0.452558\pi$
$398$	−8.42464	−0.422289
$399$	−3.11298	−0.155844
$400$	−3.51130	−0.175565
$401$	−21.6693	−1.08211	−0.541057	−	0.840986i	$-0.681976\pi$
$401$	−21.6693	−1.08211	−0.541057	+	0.840986i	$0.681976\pi$
$402$	2.00022	0.0997620
$403$	−1.30645	−0.0650788
$404$	−4.33436	−0.215643
$405$	1.22012	0.0606284
$406$	−7.92893	−0.393506
$407$	23.0819	1.14413
$408$	2.60406	0.128920
$409$	−24.9513	−1.23376	−0.616882	−	0.787056i	$-0.711604\pi$
$409$	−24.9513	−1.23376	−0.616882	+	0.787056i	$0.711604\pi$
$410$	−4.27248	−0.211003
$411$	1.32414	0.0653151
$412$	9.44178	0.465163
$413$	−20.0692	−0.987542
$414$	7.35913	0.361682
$415$	11.5858	0.568726
$416$	0.252042	0.0123574
$417$	−0.705140	−0.0345309
$418$	4.98093	0.243625
$419$	−3.92318	−0.191660	−0.0958300	−	0.995398i	$-0.530551\pi$
$419$	−3.92318	−0.191660	−0.0958300	+	0.995398i	$0.530551\pi$
$420$	−3.79822	−0.185334
$421$	32.8491	1.60097	0.800484	−	0.599355i	$-0.204576\pi$
$421$	32.8491	1.60097	0.800484	+	0.599355i	$0.204576\pi$
$422$	−17.4970	−0.851741
$423$	13.3028	0.646803
$424$	−1.00000	−0.0485643
$425$	9.14364	0.443532
$426$	3.26867	0.158368
$427$	−7.79876	−0.377408
$428$	−4.94872	−0.239205
$429$	1.25540	0.0606113
$430$	−11.4193	−0.550687
$431$	−34.8365	−1.67801	−0.839007	−	0.544120i	$-0.816864\pi$
$431$	−34.8365	−1.67801	−0.839007	+	0.544120i	$0.816864\pi$
$432$	1.00000	0.0481125
$433$	−15.1795	−0.729479	−0.364740	−	0.931110i	$-0.618842\pi$
$433$	−15.1795	−0.729479	−0.364740	+	0.931110i	$0.618842\pi$
$434$	16.1360	0.774554
$435$	−3.10772	−0.149004
$436$	9.53029	0.456418
$437$	−7.35913	−0.352035
$438$	−13.8785	−0.663141
$439$	39.7917	1.89915	0.949576	−	0.313536i	$-0.101514\pi$
$439$	39.7917	1.89915	0.949576	+	0.313536i	$0.101514\pi$
$440$	6.07734	0.289726
$441$	2.69065	0.128126
$442$	−0.656332	−0.0312185
$443$	−3.13508	−0.148952	−0.0744761	−	0.997223i	$-0.523728\pi$
$443$	−3.13508	−0.148952	−0.0744761	+	0.997223i	$0.523728\pi$
$444$	−4.63406	−0.219923
$445$	−5.38314	−0.255185
$446$	−17.1635	−0.812713
$447$	13.2882	0.628511
$448$	−3.11298	−0.147075
$449$	29.2320	1.37955	0.689773	−	0.724026i	$-0.257710\pi$
$449$	29.2320	1.37955	0.689773	+	0.724026i	$0.257710\pi$
$450$	3.51130	0.165524
$451$	−17.4416	−0.821292
$452$	2.77617	0.130580
$453$	−6.91484	−0.324888
$454$	−28.1881	−1.32293
$455$	0.957309	0.0448794
$456$	−1.00000	−0.0468293
$457$	−8.63971	−0.404148	−0.202074	−	0.979370i	$-0.564768\pi$
$457$	−8.63971	−0.404148	−0.202074	+	0.979370i	$0.564768\pi$
$458$	15.6200	0.729877
$459$	−2.60406	−0.121547
$460$	−8.97905	−0.418650
$461$	−30.6976	−1.42973	−0.714865	−	0.699262i	$-0.753512\pi$
$461$	−30.6976	−1.42973	−0.714865	+	0.699262i	$0.753512\pi$
$462$	−15.5055	−0.721382
$463$	24.4614	1.13682	0.568409	−	0.822746i	$-0.307559\pi$
$463$	24.4614	1.13682	0.568409	+	0.822746i	$0.307559\pi$
$464$	−2.54705	−0.118244
$465$	6.32447	0.293290
$466$	12.9170	0.598367
$467$	39.4032	1.82336	0.911682	−	0.410897i	$-0.134784\pi$
$467$	39.4032	1.82336	0.911682	+	0.410897i	$0.134784\pi$
$468$	−0.252042	−0.0116506
$469$	6.22665	0.287520
$470$	−16.2310	−0.748681
$471$	13.0410	0.600898
$472$	−6.44695	−0.296745
$473$	−46.6171	−2.14346
$474$	−3.79044	−0.174101
$475$	−3.51130	−0.161109
$476$	8.10640	0.371556
$477$	1.00000	0.0457869
$478$	−4.15507	−0.190048
$479$	−42.6404	−1.94829	−0.974144	−	0.225929i	$-0.927458\pi$
$479$	−42.6404	−1.94829	−0.974144	+	0.225929i	$0.927458\pi$
$480$	−1.22012	−0.0556908
$481$	1.16798	0.0532551
$482$	18.3041	0.833730
$483$	22.9088	1.04239
$484$	13.8096	0.627710
$485$	6.91775	0.314119
$486$	−1.00000	−0.0453609
$487$	18.9222	0.857445	0.428723	−	0.903436i	$-0.358964\pi$
$487$	18.9222	0.857445	0.428723	+	0.903436i	$0.358964\pi$
$488$	−2.50524	−0.113407
$489$	9.99261	0.451882
$490$	−3.28292	−0.148307
$491$	−26.0064	−1.17365	−0.586826	−	0.809713i	$-0.699623\pi$
$491$	−26.0064	−1.17365	−0.586826	+	0.809713i	$0.699623\pi$
$492$	3.50168	0.157868
$493$	6.63269	0.298721
$494$	0.252042	0.0113399
$495$	−6.07734	−0.273156
$496$	5.18346	0.232744
$497$	10.1753	0.456425
$498$	−9.49562	−0.425509
$499$	8.64113	0.386830	0.193415	−	0.981117i	$-0.438044\pi$
$499$	8.64113	0.386830	0.193415	+	0.981117i	$0.438044\pi$
$500$	−10.3848	−0.464424
$501$	8.09686	0.361741
$502$	30.3335	1.35385
$503$	33.1276	1.47709	0.738543	−	0.674207i	$-0.235514\pi$
$503$	33.1276	1.47709	0.738543	+	0.674207i	$0.235514\pi$
$504$	3.11298	0.138663
$505$	−5.28846	−0.235333
$506$	−36.6553	−1.62953
$507$	−12.9365	−0.574529
$508$	−4.20677	−0.186645
$509$	−34.1643	−1.51431	−0.757153	−	0.653238i	$-0.773410\pi$
$509$	−34.1643	−1.51431	−0.757153	+	0.653238i	$0.773410\pi$
$510$	3.17728	0.140692
$511$	−43.2036	−1.91121
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	8.93082	0.393922
$515$	11.5201	0.507638
$516$	9.35913	0.412013
$517$	−66.2601	−2.91411
$518$	−14.4257	−0.633831
$519$	−10.0261	−0.440096
$520$	0.307522	0.0134857
$521$	−10.1037	−0.442650	−0.221325	−	0.975200i	$-0.571038\pi$
$521$	−10.1037	−0.442650	−0.221325	+	0.975200i	$0.571038\pi$
$522$	2.54705	0.111482
$523$	15.2716	0.667781	0.333891	−	0.942612i	$-0.391638\pi$
$523$	15.2716	0.667781	0.333891	+	0.942612i	$0.391638\pi$
$524$	14.7508	0.644390
$525$	10.9306	0.477051
$526$	11.7430	0.512020
$527$	−13.4981	−0.587985
$528$	−4.98093	−0.216767
$529$	31.1568	1.35464
$530$	−1.22012	−0.0529988
$531$	6.44695	0.279774
$532$	−3.11298	−0.134965
$533$	−0.882568	−0.0382283
$534$	4.41196	0.190924
$535$	−6.03805	−0.261048
$536$	2.00022	0.0863964
$537$	7.16750	0.309300
$538$	24.4616	1.05462
$539$	−13.4019	−0.577262
$540$	1.22012	0.0525058
$541$	25.2323	1.08482	0.542410	−	0.840114i	$-0.317512\pi$
$541$	25.2323	1.08482	0.542410	+	0.840114i	$0.317512\pi$
$542$	13.9902	0.600929
$543$	−5.67509	−0.243541
$544$	2.60406	0.111648
$545$	11.6281	0.498095
$546$	−0.784600	−0.0335778
$547$	13.6295	0.582755	0.291378	−	0.956608i	$-0.405886\pi$
$547$	13.6295	0.582755	0.291378	+	0.956608i	$0.405886\pi$
$548$	1.32414	0.0565645
$549$	2.50524	0.106921
$550$	−17.4895	−0.745755
$551$	−2.54705	−0.108508
$552$	7.35913	0.313225
$553$	−11.7996	−0.501769
$554$	−15.2580	−0.648250
$555$	−5.65413	−0.240004
$556$	−0.705140	−0.0299046
$557$	0.909995	0.0385577	0.0192789	−	0.999814i	$-0.493863\pi$
$557$	0.909995	0.0385577	0.0192789	+	0.999814i	$0.493863\pi$
$558$	−5.18346	−0.219433
$559$	−2.35889	−0.0997704
$560$	−3.79822	−0.160504
$561$	12.9706	0.547621
$562$	10.7697	0.454291
$563$	22.9835	0.968640	0.484320	−	0.874891i	$-0.339067\pi$
$563$	22.9835	0.968640	0.484320	+	0.874891i	$0.339067\pi$
$564$	13.3028	0.560147
$565$	3.38728	0.142504
$566$	1.71019	0.0718845
$567$	−3.11298	−0.130733
$568$	3.26867	0.137150
$569$	39.7713	1.66730	0.833649	−	0.552294i	$-0.186248\pi$
$569$	39.7713	1.66730	0.833649	+	0.552294i	$0.186248\pi$
$570$	−1.22012	−0.0511054
$571$	10.1939	0.426602	0.213301	−	0.976987i	$-0.431579\pi$
$571$	10.1939	0.426602	0.213301	+	0.976987i	$0.431579\pi$
$572$	1.25540	0.0524909
$573$	4.29029	0.179230
$574$	10.9007	0.454984
$575$	25.8401	1.07761
$576$	1.00000	0.0416667
$577$	−20.8045	−0.866102	−0.433051	−	0.901369i	$-0.642563\pi$
$577$	−20.8045	−0.866102	−0.433051	+	0.901369i	$0.642563\pi$
$578$	10.2189	0.425048
$579$	−3.28440	−0.136495
$580$	−3.10772	−0.129041
$581$	−29.5597	−1.22634
$582$	−5.66971	−0.235017
$583$	−4.98093	−0.206289
$584$	−13.8785	−0.574297
$585$	−0.307522	−0.0127145
$586$	32.2680	1.33298
$587$	3.37300	0.139218	0.0696092	−	0.997574i	$-0.477825\pi$
$587$	3.37300	0.139218	0.0696092	+	0.997574i	$0.477825\pi$
$588$	2.69065	0.110960
$589$	5.18346	0.213581
$590$	−7.86607	−0.323841
$591$	4.82321	0.198400
$592$	−4.63406	−0.190459
$593$	14.1957	0.582947	0.291473	−	0.956579i	$-0.405855\pi$
$593$	14.1957	0.582947	0.291473	+	0.956579i	$0.405855\pi$
$594$	4.98093	0.204370
$595$	9.89081	0.405484
$596$	13.2882	0.544306
$597$	8.42464	0.344798
$598$	−1.85481	−0.0758487
$599$	−20.7070	−0.846066	−0.423033	−	0.906114i	$-0.639035\pi$
$599$	−20.7070	−0.846066	−0.423033	+	0.906114i	$0.639035\pi$
$600$	3.51130	0.143348
$601$	24.3072	0.991512	0.495756	−	0.868462i	$-0.334891\pi$
$601$	24.3072	0.991512	0.495756	+	0.868462i	$0.334891\pi$
$602$	29.1348	1.18745
$603$	−2.00022	−0.0814553
$604$	−6.91484	−0.281361
$605$	16.8494	0.685027
$606$	4.33436	0.176071
$607$	38.5984	1.56666	0.783329	−	0.621607i	$-0.213520\pi$
$607$	38.5984	1.56666	0.783329	+	0.621607i	$0.213520\pi$
$608$	−1.00000	−0.0405554
$609$	7.92893	0.321296
$610$	−3.05670	−0.123762
$611$	−3.35285	−0.135642
$612$	−2.60406	−0.105263
$613$	−9.79057	−0.395437	−0.197719	−	0.980259i	$-0.563353\pi$
$613$	−9.79057	−0.395437	−0.197719	+	0.980259i	$0.563353\pi$
$614$	32.7904	1.32331
$615$	4.27248	0.172283
$616$	−15.5055	−0.624735
$617$	−17.6839	−0.711926	−0.355963	−	0.934500i	$-0.615847\pi$
$617$	−17.6839	−0.711926	−0.355963	+	0.934500i	$0.615847\pi$
$618$	−9.44178	−0.379804
$619$	19.2068	0.771988	0.385994	−	0.922501i	$-0.373859\pi$
$619$	19.2068	0.771988	0.385994	+	0.922501i	$0.373859\pi$
$620$	6.32447	0.253997
$621$	−7.35913	−0.295312
$622$	6.13553	0.246012
$623$	13.7344	0.550255
$624$	−0.252042	−0.0100897
$625$	4.88571	0.195428
$626$	−31.9586	−1.27732
$627$	−4.98093	−0.198919
$628$	13.0410	0.520393
$629$	12.0674	0.481158
$630$	3.79822	0.151325
$631$	4.99479	0.198839	0.0994197	−	0.995046i	$-0.468301\pi$
$631$	4.99479	0.198839	0.0994197	+	0.995046i	$0.468301\pi$
$632$	−3.79044	−0.150776
$633$	17.4970	0.695444
$634$	24.0995	0.957114
$635$	−5.13278	−0.203688
$636$	1.00000	0.0396526
$637$	−0.678155	−0.0268695
$638$	−12.6867	−0.502271
$639$	−3.26867	−0.129307
$640$	−1.22012	−0.0482296
$641$	33.0951	1.30718	0.653589	−	0.756849i	$-0.273262\pi$
$641$	33.0951	1.30718	0.653589	+	0.756849i	$0.273262\pi$
$642$	4.94872	0.195310
$643$	−35.2013	−1.38820	−0.694101	−	0.719877i	$-0.744198\pi$
$643$	−35.2013	−1.38820	−0.694101	+	0.719877i	$0.744198\pi$
$644$	22.9088	0.902734
$645$	11.4193	0.449634
$646$	2.60406	0.102455
$647$	−12.1462	−0.477517	−0.238758	−	0.971079i	$-0.576740\pi$
$647$	−12.1462	−0.477517	−0.238758	+	0.971079i	$0.576740\pi$
$648$	−1.00000	−0.0392837
$649$	−32.1118	−1.26050
$650$	−0.884993	−0.0347123
$651$	−16.1360	−0.632420
$652$	9.99261	0.391341
$653$	−2.78013	−0.108795	−0.0543974	−	0.998519i	$-0.517324\pi$
$653$	−2.78013	−0.108795	−0.0543974	+	0.998519i	$0.517324\pi$
$654$	−9.53029	−0.372664
$655$	17.9977	0.703230
$656$	3.50168	0.136717
$657$	13.8785	0.541452
$658$	41.4112	1.61438
$659$	14.0048	0.545550	0.272775	−	0.962078i	$-0.412059\pi$
$659$	14.0048	0.545550	0.272775	+	0.962078i	$0.412059\pi$
$660$	−6.07734	−0.236560
$661$	−15.6395	−0.608304	−0.304152	−	0.952623i	$-0.598373\pi$
$661$	−15.6395	−0.608304	−0.304152	+	0.952623i	$0.598373\pi$
$662$	11.2570	0.437516
$663$	0.656332	0.0254898
$664$	−9.49562	−0.368502
$665$	−3.79822	−0.147289
$666$	4.63406	0.179566
$667$	18.7441	0.725775
$668$	8.09686	0.313277
$669$	17.1635	0.663577
$670$	2.44052	0.0942854
$671$	−12.4784	−0.481724
$672$	3.11298	0.120086
$673$	9.95477	0.383728	0.191864	−	0.981422i	$-0.438547\pi$
$673$	9.95477	0.383728	0.191864	+	0.981422i	$0.438547\pi$
$674$	−30.7533	−1.18457
$675$	−3.51130	−0.135150
$676$	−12.9365	−0.497557
$677$	31.2542	1.20120	0.600599	−	0.799551i	$-0.294929\pi$
$677$	31.2542	1.20120	0.600599	+	0.799551i	$0.294929\pi$
$678$	−2.77617	−0.106618
$679$	−17.6497	−0.677333
$680$	3.17728	0.121843
$681$	28.1881	1.08017
$682$	25.8184	0.988639
$683$	−46.0439	−1.76182	−0.880910	−	0.473284i	$-0.843068\pi$
$683$	−46.0439	−1.76182	−0.880910	+	0.473284i	$0.843068\pi$
$684$	1.00000	0.0382360
$685$	1.61562	0.0617295
$686$	−13.4149	−0.512184
$687$	−15.6200	−0.595942
$688$	9.35913	0.356814
$689$	−0.252042	−0.00960202
$690$	8.97905	0.341827
$691$	21.6792	0.824714	0.412357	−	0.911022i	$-0.364706\pi$
$691$	21.6792	0.824714	0.412357	+	0.911022i	$0.364706\pi$
$692$	−10.0261	−0.381134
$693$	15.5055	0.589006
$694$	−0.0516087	−0.00195904
$695$	−0.860359	−0.0326353
$696$	2.54705	0.0965458
$697$	−9.11859	−0.345391
$698$	−25.4791	−0.964399
$699$	−12.9170	−0.488564
$700$	10.9306	0.413138
$701$	9.03401	0.341210	0.170605	−	0.985340i	$-0.445428\pi$
$701$	9.03401	0.341210	0.170605	+	0.985340i	$0.445428\pi$
$702$	0.252042	0.00951269
$703$	−4.63406	−0.174777
$704$	−4.98093	−0.187726
$705$	16.2310	0.611295
$706$	−13.2662	−0.499282
$707$	13.4928	0.507448
$708$	6.44695	0.242291
$709$	17.8443	0.670155	0.335078	−	0.942191i	$-0.391237\pi$
$709$	17.8443	0.670155	0.335078	+	0.942191i	$0.391237\pi$
$710$	3.98818	0.149674
$711$	3.79044	0.142153
$712$	4.41196	0.165345
$713$	−38.1458	−1.42857
$714$	−8.10640	−0.303374
$715$	1.53174	0.0572839
$716$	7.16750	0.267862
$717$	4.15507	0.155174
$718$	−30.3571	−1.13292
$719$	−51.0002	−1.90199	−0.950993	−	0.309213i	$-0.899935\pi$
$719$	−51.0002	−1.90199	−0.950993	+	0.309213i	$0.899935\pi$
$720$	1.22012	0.0454713
$721$	−29.3921	−1.09462
$722$	−1.00000	−0.0372161
$723$	−18.3041	−0.680738
$724$	−5.67509	−0.210913
$725$	8.94347	0.332152
$726$	−13.8096	−0.512523
$727$	48.9024	1.81369	0.906845	−	0.421465i	$-0.138484\pi$
$727$	48.9024	1.81369	0.906845	+	0.421465i	$0.138484\pi$
$728$	−0.784600	−0.0290792
$729$	1.00000	0.0370370
$730$	−16.9335	−0.626737
$731$	−24.3718	−0.901422
$732$	2.50524	0.0925963
$733$	−9.08978	−0.335739	−0.167869	−	0.985809i	$-0.553689\pi$
$733$	−9.08978	−0.335739	−0.167869	+	0.985809i	$0.553689\pi$
$734$	21.9593	0.810532
$735$	3.28292	0.121092
$736$	7.35913	0.271261
$737$	9.96296	0.366990
$738$	−3.50168	−0.128898
$739$	38.9240	1.43184	0.715921	−	0.698181i	$-0.246007\pi$
$739$	38.9240	1.43184	0.715921	+	0.698181i	$0.246007\pi$
$740$	−5.65413	−0.207850
$741$	−0.252042	−0.00925898
$742$	3.11298	0.114281
$743$	−2.64457	−0.0970200	−0.0485100	−	0.998823i	$-0.515447\pi$
$743$	−2.64457	−0.0970200	−0.0485100	+	0.998823i	$0.515447\pi$
$744$	−5.18346	−0.190035
$745$	16.2133	0.594008
$746$	−2.53381	−0.0927694
$747$	9.49562	0.347427
$748$	12.9706	0.474254
$749$	15.4053	0.562896
$750$	10.3848	0.379201
$751$	26.3846	0.962786	0.481393	−	0.876505i	$-0.340131\pi$
$751$	26.3846	0.962786	0.481393	+	0.876505i	$0.340131\pi$
$752$	13.3028	0.485102
$753$	−30.3335	−1.10541
$754$	−0.641963	−0.0233789
$755$	−8.43696	−0.307052
$756$	−3.11298	−0.113218
$757$	43.6344	1.58592	0.792960	−	0.609274i	$-0.208539\pi$
$757$	43.6344	1.58592	0.792960	+	0.609274i	$0.208539\pi$
$758$	−6.84594	−0.248656
$759$	36.6553	1.33050
$760$	−1.22012	−0.0442585
$761$	−17.9495	−0.650668	−0.325334	−	0.945599i	$-0.605477\pi$
$761$	−17.9495	−0.650668	−0.325334	+	0.945599i	$0.605477\pi$
$762$	4.20677	0.152395
$763$	−29.6676	−1.07404
$764$	4.29029	0.155217
$765$	−3.17728	−0.114875
$766$	−12.2765	−0.443567
$767$	−1.62490	−0.0586717
$768$	1.00000	0.0360844
$769$	−9.18984	−0.331394	−0.165697	−	0.986177i	$-0.552987\pi$
$769$	−9.18984	−0.331394	−0.165697	+	0.986177i	$0.552987\pi$
$770$	−18.9187	−0.681781
$771$	−8.93082	−0.321636
$772$	−3.28440	−0.118208
$773$	−3.75529	−0.135068	−0.0675341	−	0.997717i	$-0.521513\pi$
$773$	−3.75529	−0.135068	−0.0675341	+	0.997717i	$0.521513\pi$
$774$	−9.35913	−0.336407
$775$	−18.2007	−0.653788
$776$	−5.66971	−0.203531
$777$	14.4257	0.517521
$778$	6.20145	0.222333
$779$	3.50168	0.125461
$780$	−0.307522	−0.0110110
$781$	16.2810	0.582580
$782$	−19.1636	−0.685290
$783$	−2.54705	−0.0910243
$784$	2.69065	0.0960946
$785$	15.9116	0.567911
$786$	−14.7508	−0.526142
$787$	13.9603	0.497632	0.248816	−	0.968551i	$-0.419959\pi$
$787$	13.9603	0.497632	0.248816	+	0.968551i	$0.419959\pi$
$788$	4.82321	0.171820
$789$	−11.7430	−0.418063
$790$	−4.62481	−0.164543
$791$	−8.64218	−0.307280
$792$	4.98093	0.176989
$793$	−0.631424	−0.0224225
$794$	−5.91735	−0.209999
$795$	1.22012	0.0432733
$796$	8.42464	0.298603
$797$	48.0878	1.70336	0.851679	−	0.524065i	$-0.175585\pi$
$797$	48.0878	1.70336	0.851679	+	0.524065i	$0.175585\pi$
$798$	3.11298	0.110198
$799$	−34.6412	−1.22552
$800$	3.51130	0.124143
$801$	−4.41196	−0.155889
$802$	21.6693	0.765170
$803$	−69.1279	−2.43947
$804$	−2.00022	−0.0705424
$805$	27.9516	0.985165
$806$	1.30645	0.0460177
$807$	−24.4616	−0.861090
$808$	4.33436	0.152482
$809$	−11.6728	−0.410394	−0.205197	−	0.978721i	$-0.565784\pi$
$809$	−11.6728	−0.410394	−0.205197	+	0.978721i	$0.565784\pi$
$810$	−1.22012	−0.0428708
$811$	18.9914	0.666878	0.333439	−	0.942772i	$-0.391791\pi$
$811$	18.9914	0.666878	0.333439	+	0.942772i	$0.391791\pi$
$812$	7.92893	0.278251
$813$	−13.9902	−0.490657
$814$	−23.0819	−0.809021
$815$	12.1922	0.427075
$816$	−2.60406	−0.0911604
$817$	9.35913	0.327435
$818$	24.9513	0.872403
$819$	0.784600	0.0274162
$820$	4.27248	0.149201
$821$	3.59082	0.125321	0.0626603	−	0.998035i	$-0.480042\pi$
$821$	3.59082	0.125321	0.0626603	+	0.998035i	$0.480042\pi$
$822$	−1.32414	−0.0461847
$823$	4.19067	0.146078	0.0730388	−	0.997329i	$-0.476730\pi$
$823$	4.19067	0.146078	0.0730388	+	0.997329i	$0.476730\pi$
$824$	−9.44178	−0.328920
$825$	17.4895	0.608907
$826$	20.0692	0.698298
$827$	22.5567	0.784373	0.392186	−	0.919886i	$-0.371719\pi$
$827$	22.5567	0.784373	0.392186	+	0.919886i	$0.371719\pi$
$828$	−7.35913	−0.255747
$829$	−12.8962	−0.447903	−0.223952	−	0.974600i	$-0.571896\pi$
$829$	−12.8962	−0.447903	−0.223952	+	0.974600i	$0.571896\pi$
$830$	−11.5858	−0.402150
$831$	15.2580	0.529294
$832$	−0.252042	−0.00873797
$833$	−7.00662	−0.242765
$834$	0.705140	0.0244170
$835$	9.87917	0.341883
$836$	−4.98093	−0.172269
$837$	5.18346	0.179167
$838$	3.92318	0.135524
$839$	55.5712	1.91853	0.959265	−	0.282509i	$-0.0911666\pi$
$839$	55.5712	1.91853	0.959265	+	0.282509i	$0.0911666\pi$
$840$	3.79822	0.131051
$841$	−22.5125	−0.776294
$842$	−32.8491	−1.13205
$843$	−10.7697	−0.370927
$844$	17.4970	0.602272
$845$	−15.7841	−0.542990
$846$	−13.3028	−0.457358
$847$	−42.9891	−1.47712
$848$	1.00000	0.0343401
$849$	−1.71019	−0.0586935
$850$	−9.14364	−0.313624
$851$	34.1027	1.16902
$852$	−3.26867	−0.111983
$853$	−43.8975	−1.50302	−0.751511	−	0.659721i	$-0.770674\pi$
$853$	−43.8975	−1.50302	−0.751511	+	0.659721i	$0.770674\pi$
$854$	7.79876	0.266868
$855$	1.22012	0.0417273
$856$	4.94872	0.169144
$857$	43.9964	1.50289	0.751444	−	0.659797i	$-0.229358\pi$
$857$	43.9964	1.50289	0.751444	+	0.659797i	$0.229358\pi$
$858$	−1.25540	−0.0428586
$859$	−5.10671	−0.174239	−0.0871194	−	0.996198i	$-0.527766\pi$
$859$	−5.10671	−0.174239	−0.0871194	+	0.996198i	$0.527766\pi$
$860$	11.4193	0.389395
$861$	−10.9007	−0.371493
$862$	34.8365	1.18654
$863$	16.6032	0.565180	0.282590	−	0.959241i	$-0.408806\pi$
$863$	16.6032	0.565180	0.282590	+	0.959241i	$0.408806\pi$
$864$	−1.00000	−0.0340207
$865$	−12.2330	−0.415936
$866$	15.1795	0.515820
$867$	−10.2189	−0.347051
$868$	−16.1360	−0.547692
$869$	−18.8799	−0.640458
$870$	3.10772	0.105362
$871$	0.504139	0.0170821
$872$	−9.53029	−0.322736
$873$	5.66971	0.191891
$874$	7.35913	0.248926
$875$	32.3278	1.09288
$876$	13.8785	0.468912
$877$	−10.1396	−0.342389	−0.171194	−	0.985237i	$-0.554763\pi$
$877$	−10.1396	−0.342389	−0.171194	+	0.985237i	$0.554763\pi$
$878$	−39.7917	−1.34290
$879$	−32.2680	−1.08837
$880$	−6.07734	−0.204867
$881$	0.109358	0.00368436	0.00184218	−	0.999998i	$-0.499414\pi$
$881$	0.109358	0.00368436	0.00184218	+	0.999998i	$0.499414\pi$
$882$	−2.69065	−0.0905988
$883$	16.1314	0.542865	0.271433	−	0.962457i	$-0.412503\pi$
$883$	16.1314	0.542865	0.271433	+	0.962457i	$0.412503\pi$
$884$	0.656332	0.0220748
$885$	7.86607	0.264415
$886$	3.13508	0.105325
$887$	−34.2466	−1.14989	−0.574943	−	0.818193i	$-0.694976\pi$
$887$	−34.2466	−1.14989	−0.574943	+	0.818193i	$0.694976\pi$
$888$	4.63406	0.155509
$889$	13.0956	0.439212
$890$	5.38314	0.180443
$891$	−4.98093	−0.166867
$892$	17.1635	0.574675
$893$	13.3028	0.445160
$894$	−13.2882	−0.444424
$895$	8.74523	0.292321
$896$	3.11298	0.103997
$897$	1.85481	0.0619302
$898$	−29.2320	−0.975486
$899$	−13.2026	−0.440330
$900$	−3.51130	−0.117043
$901$	−2.60406	−0.0867539
$902$	17.4416	0.580741
$903$	−29.1348	−0.969545
$904$	−2.77617	−0.0923342
$905$	−6.92431	−0.230172
$906$	6.91484	0.229730
$907$	−12.5292	−0.416025	−0.208013	−	0.978126i	$-0.566700\pi$
$907$	−12.5292	−0.416025	−0.208013	+	0.978126i	$0.566700\pi$
$908$	28.1881	0.935454
$909$	−4.33436	−0.143762
$910$	−0.957309	−0.0317345
$911$	−59.5401	−1.97265	−0.986325	−	0.164810i	$-0.947299\pi$
$911$	−59.5401	−1.97265	−0.986325	+	0.164810i	$0.947299\pi$
$912$	1.00000	0.0331133
$913$	−47.2970	−1.56530
$914$	8.63971	0.285776
$915$	3.05670	0.101051
$916$	−15.6200	−0.516101
$917$	−45.9188	−1.51637
$918$	2.60406	0.0859469
$919$	52.8767	1.74424	0.872121	−	0.489291i	$-0.162744\pi$
$919$	52.8767	1.74424	0.872121	+	0.489291i	$0.162744\pi$
$920$	8.97905	0.296030
$921$	−32.7904	−1.08048
$922$	30.6976	1.01097
$923$	0.823840	0.0271170
$924$	15.5055	0.510094
$925$	16.2716	0.535006
$926$	−24.4614	−0.803852
$927$	9.44178	0.310109
$928$	2.54705	0.0836112
$929$	−29.5421	−0.969244	−0.484622	−	0.874724i	$-0.661043\pi$
$929$	−29.5421	−0.969244	−0.484622	+	0.874724i	$0.661043\pi$
$930$	−6.32447	−0.207387
$931$	2.69065	0.0881824
$932$	−12.9170	−0.423109
$933$	−6.13553	−0.200868
$934$	−39.4032	−1.28931
$935$	15.8258	0.517559
$936$	0.252042	0.00823823
$937$	9.34004	0.305126	0.152563	−	0.988294i	$-0.451247\pi$
$937$	9.34004	0.305126	0.152563	+	0.988294i	$0.451247\pi$
$938$	−6.22665	−0.203307
$939$	31.9586	1.04293
$940$	16.2310	0.529397
$941$	28.3070	0.922782	0.461391	−	0.887197i	$-0.347351\pi$
$941$	28.3070	0.922782	0.461391	+	0.887197i	$0.347351\pi$
$942$	−13.0410	−0.424899
$943$	−25.7693	−0.839164
$944$	6.44695	0.209830
$945$	−3.79822	−0.123556
$946$	46.6171	1.51565
$947$	43.5326	1.41462	0.707310	−	0.706904i	$-0.249909\pi$
$947$	43.5326	1.41462	0.707310	+	0.706904i	$0.249909\pi$
$948$	3.79044	0.123108
$949$	−3.49796	−0.113549
$950$	3.51130	0.113922
$951$	−24.0995	−0.781480
$952$	−8.10640	−0.262730
$953$	16.8633	0.546254	0.273127	−	0.961978i	$-0.411942\pi$
$953$	16.8633	0.546254	0.273127	+	0.961978i	$0.411942\pi$
$954$	−1.00000	−0.0323762
$955$	5.23469	0.169390
$956$	4.15507	0.134384
$957$	12.6867	0.410102
$958$	42.6404	1.37765
$959$	−4.12203	−0.133107
$960$	1.22012	0.0393793
$961$	−4.13171	−0.133281
$962$	−1.16798	−0.0376570
$963$	−4.94872	−0.159470
$964$	−18.3041	−0.589536
$965$	−4.00737	−0.129002
$966$	−22.9088	−0.737080
$967$	−15.1499	−0.487188	−0.243594	−	0.969877i	$-0.578326\pi$
$967$	−15.1499	−0.487188	−0.243594	+	0.969877i	$0.578326\pi$
$968$	−13.8096	−0.443858
$969$	−2.60406	−0.0836546
$970$	−6.91775	−0.222116
$971$	−14.9722	−0.480481	−0.240241	−	0.970713i	$-0.577226\pi$
$971$	−14.9722	−0.480481	−0.240241	+	0.970713i	$0.577226\pi$
$972$	1.00000	0.0320750
$973$	2.19509	0.0703713
$974$	−18.9222	−0.606305
$975$	0.884993	0.0283425
$976$	2.50524	0.0801907
$977$	−0.755198	−0.0241609	−0.0120805	−	0.999927i	$-0.503845\pi$
$977$	−0.755198	−0.0241609	−0.0120805	+	0.999927i	$0.503845\pi$
$978$	−9.99261	−0.319528
$979$	21.9757	0.702345
$980$	3.28292	0.104869
$981$	9.53029	0.304279
$982$	26.0064	0.829897
$983$	6.24894	0.199310	0.0996552	−	0.995022i	$-0.468226\pi$
$983$	6.24894	0.199310	0.0996552	+	0.995022i	$0.468226\pi$
$984$	−3.50168	−0.111629
$985$	5.88491	0.187509
$986$	−6.63269	−0.211228
$987$	−41.4112	−1.31813
$988$	−0.252042	−0.00801851
$989$	−68.8751	−2.19010
$990$	6.07734	0.193151
$991$	40.6932	1.29266	0.646331	−	0.763057i	$-0.276302\pi$
$991$	40.6932	1.29266	0.646331	+	0.763057i	$0.276302\pi$
$992$	−5.18346	−0.164575
$993$	−11.2570	−0.357230
$994$	−10.1753	−0.322741
$995$	10.2791	0.325870
$996$	9.49562	0.300880
$997$	−13.2666	−0.420158	−0.210079	−	0.977684i	$-0.567372\pi$
$997$	−13.2666	−0.420158	−0.210079	+	0.977684i	$0.567372\pi$
$998$	−8.64113	−0.273530
$999$	−4.63406	−0.146615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bf.1.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bf.1.9	✓	12	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.22012 q^{5} -1.00000 q^{6} -3.11298 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.22012 q^{5} -1.00000 q^{6} -3.11298 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.22012 q^{10} -4.98093 q^{11} +1.00000 q^{12} -0.252042 q^{13} +3.11298 q^{14} +1.22012 q^{15} +1.00000 q^{16} -2.60406 q^{17} -1.00000 q^{18} +1.00000 q^{19} +1.22012 q^{20} -3.11298 q^{21} +4.98093 q^{22} -7.35913 q^{23} -1.00000 q^{24} -3.51130 q^{25} +0.252042 q^{26} +1.00000 q^{27} -3.11298 q^{28} -2.54705 q^{29} -1.22012 q^{30} +5.18346 q^{31} -1.00000 q^{32} -4.98093 q^{33} +2.60406 q^{34} -3.79822 q^{35} +1.00000 q^{36} -4.63406 q^{37} -1.00000 q^{38} -0.252042 q^{39} -1.22012 q^{40} +3.50168 q^{41} +3.11298 q^{42} +9.35913 q^{43} -4.98093 q^{44} +1.22012 q^{45} +7.35913 q^{46} +13.3028 q^{47} +1.00000 q^{48} +2.69065 q^{49} +3.51130 q^{50} -2.60406 q^{51} -0.252042 q^{52} +1.00000 q^{53} -1.00000 q^{54} -6.07734 q^{55} +3.11298 q^{56} +1.00000 q^{57} +2.54705 q^{58} +6.44695 q^{59} +1.22012 q^{60} +2.50524 q^{61} -5.18346 q^{62} -3.11298 q^{63} +1.00000 q^{64} -0.307522 q^{65} +4.98093 q^{66} -2.00022 q^{67} -2.60406 q^{68} -7.35913 q^{69} +3.79822 q^{70} -3.26867 q^{71} -1.00000 q^{72} +13.8785 q^{73} +4.63406 q^{74} -3.51130 q^{75} +1.00000 q^{76} +15.5055 q^{77} +0.252042 q^{78} +3.79044 q^{79} +1.22012 q^{80} +1.00000 q^{81} -3.50168 q^{82} +9.49562 q^{83} -3.11298 q^{84} -3.17728 q^{85} -9.35913 q^{86} -2.54705 q^{87} +4.98093 q^{88} -4.41196 q^{89} -1.22012 q^{90} +0.784600 q^{91} -7.35913 q^{92} +5.18346 q^{93} -13.3028 q^{94} +1.22012 q^{95} -1.00000 q^{96} +5.66971 q^{97} -2.69065 q^{98} -4.98093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9} + 7 q^{10} - 5 q^{11} + 12 q^{12} + 10 q^{13} - 5 q^{14} - 7 q^{15} + 12 q^{16} + 6 q^{17} - 12 q^{18} + 12 q^{19} - 7 q^{20} + 5 q^{21} + 5 q^{22} - 12 q^{24} + 21 q^{25} - 10 q^{26} + 12 q^{27} + 5 q^{28} + 7 q^{30} + 2 q^{31} - 12 q^{32} - 5 q^{33} - 6 q^{34} - 17 q^{35} + 12 q^{36} + 16 q^{37} - 12 q^{38} + 10 q^{39} + 7 q^{40} + 7 q^{41} - 5 q^{42} + 24 q^{43} - 5 q^{44} - 7 q^{45} + 4 q^{47} + 12 q^{48} + 29 q^{49} - 21 q^{50} + 6 q^{51} + 10 q^{52} + 12 q^{53} - 12 q^{54} - 2 q^{55} - 5 q^{56} + 12 q^{57} + 2 q^{59} - 7 q^{60} + 29 q^{61} - 2 q^{62} + 5 q^{63} + 12 q^{64} - 17 q^{65} + 5 q^{66} + 36 q^{67} + 6 q^{68} + 17 q^{70} - 3 q^{71} - 12 q^{72} + 7 q^{73} - 16 q^{74} + 21 q^{75} + 12 q^{76} - 35 q^{77} - 10 q^{78} + 40 q^{79} - 7 q^{80} + 12 q^{81} - 7 q^{82} + 24 q^{83} + 5 q^{84} - 22 q^{85} - 24 q^{86} + 5 q^{88} - 45 q^{89} + 7 q^{90} + 71 q^{91} + 2 q^{93} - 4 q^{94} - 7 q^{95} - 12 q^{96} + q^{97} - 29 q^{98} - 5 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9 + 7 * q^10 - 5 * q^11 + 12 * q^12 + 10 * q^13 - 5 * q^14 - 7 * q^15 + 12 * q^16 + 6 * q^17 - 12 * q^18 + 12 * q^19 - 7 * q^20 + 5 * q^21 + 5 * q^22 - 12 * q^24 + 21 * q^25 - 10 * q^26 + 12 * q^27 + 5 * q^28 + 7 * q^30 + 2 * q^31 - 12 * q^32 - 5 * q^33 - 6 * q^34 - 17 * q^35 + 12 * q^36 + 16 * q^37 - 12 * q^38 + 10 * q^39 + 7 * q^40 + 7 * q^41 - 5 * q^42 + 24 * q^43 - 5 * q^44 - 7 * q^45 + 4 * q^47 + 12 * q^48 + 29 * q^49 - 21 * q^50 + 6 * q^51 + 10 * q^52 + 12 * q^53 - 12 * q^54 - 2 * q^55 - 5 * q^56 + 12 * q^57 + 2 * q^59 - 7 * q^60 + 29 * q^61 - 2 * q^62 + 5 * q^63 + 12 * q^64 - 17 * q^65 + 5 * q^66 + 36 * q^67 + 6 * q^68 + 17 * q^70 - 3 * q^71 - 12 * q^72 + 7 * q^73 - 16 * q^74 + 21 * q^75 + 12 * q^76 - 35 * q^77 - 10 * q^78 + 40 * q^79 - 7 * q^80 + 12 * q^81 - 7 * q^82 + 24 * q^83 + 5 * q^84 - 22 * q^85 - 24 * q^86 + 5 * q^88 - 45 * q^89 + 7 * q^90 + 71 * q^91 + 2 * q^93 - 4 * q^94 - 7 * q^95 - 12 * q^96 + q^97 - 29 * q^98 - 5 * q^99

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