LMFDB - Embedded newform 8043.2.a.q.1.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.40
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.25363 q^{2} +1.00000 q^{3} +3.07885 q^{4} +1.02544 q^{5} +2.25363 q^{6} -1.00000 q^{7} +2.43132 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.25363 q^{2} +1.00000 q^{3} +3.07885 q^{4} +1.02544 q^{5} +2.25363 q^{6} -1.00000 q^{7} +2.43132 q^{8} +1.00000 q^{9} +2.31096 q^{10} -4.12314 q^{11} +3.07885 q^{12} -4.95929 q^{13} -2.25363 q^{14} +1.02544 q^{15} -0.678398 q^{16} +5.40608 q^{17} +2.25363 q^{18} -3.35122 q^{19} +3.15717 q^{20} -1.00000 q^{21} -9.29204 q^{22} -3.01769 q^{23} +2.43132 q^{24} -3.94847 q^{25} -11.1764 q^{26} +1.00000 q^{27} -3.07885 q^{28} -6.00218 q^{29} +2.31096 q^{30} -2.64958 q^{31} -6.39150 q^{32} -4.12314 q^{33} +12.1833 q^{34} -1.02544 q^{35} +3.07885 q^{36} -10.0215 q^{37} -7.55242 q^{38} -4.95929 q^{39} +2.49317 q^{40} -5.27471 q^{41} -2.25363 q^{42} -5.56920 q^{43} -12.6945 q^{44} +1.02544 q^{45} -6.80075 q^{46} +7.18129 q^{47} -0.678398 q^{48} +1.00000 q^{49} -8.89840 q^{50} +5.40608 q^{51} -15.2689 q^{52} -1.79109 q^{53} +2.25363 q^{54} -4.22804 q^{55} -2.43132 q^{56} -3.35122 q^{57} -13.5267 q^{58} +6.99289 q^{59} +3.15717 q^{60} +5.31623 q^{61} -5.97118 q^{62} -1.00000 q^{63} -13.0473 q^{64} -5.08546 q^{65} -9.29204 q^{66} +7.39752 q^{67} +16.6445 q^{68} -3.01769 q^{69} -2.31096 q^{70} +13.6013 q^{71} +2.43132 q^{72} -14.3959 q^{73} -22.5846 q^{74} -3.94847 q^{75} -10.3179 q^{76} +4.12314 q^{77} -11.1764 q^{78} +12.5843 q^{79} -0.695656 q^{80} +1.00000 q^{81} -11.8872 q^{82} +2.53548 q^{83} -3.07885 q^{84} +5.54361 q^{85} -12.5509 q^{86} -6.00218 q^{87} -10.0247 q^{88} +10.3606 q^{89} +2.31096 q^{90} +4.95929 q^{91} -9.29100 q^{92} -2.64958 q^{93} +16.1840 q^{94} -3.43648 q^{95} -6.39150 q^{96} +4.92101 q^{97} +2.25363 q^{98} -4.12314 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) $ 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * 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 $

$2$	2.25363	1.59356	0.796778	−	0.604272i	$-0.206536\pi$
$2$	2.25363	1.59356	0.796778	+	0.604272i	$0.206536\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.07885	1.53942
$5$	1.02544	0.458591	0.229295	−	0.973357i	$-0.426358\pi$
$5$	1.02544	0.458591	0.229295	+	0.973357i	$0.426358\pi$
$6$	2.25363	0.920040
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.43132	0.859601
$9$	1.00000	0.333333
$10$	2.31096	0.730790
$11$	−4.12314	−1.24317	−0.621587	−	0.783345i	$-0.713512\pi$
$11$	−4.12314	−1.24317	−0.621587	+	0.783345i	$0.713512\pi$
$12$	3.07885	0.888786
$13$	−4.95929	−1.37546	−0.687730	−	0.725966i	$-0.741393\pi$
$13$	−4.95929	−1.37546	−0.687730	+	0.725966i	$0.741393\pi$
$14$	−2.25363	−0.602308
$15$	1.02544	0.264767
$16$	−0.678398	−0.169600
$17$	5.40608	1.31117	0.655584	−	0.755122i	$-0.272422\pi$
$17$	5.40608	1.31117	0.655584	+	0.755122i	$0.272422\pi$
$18$	2.25363	0.531186
$19$	−3.35122	−0.768823	−0.384412	−	0.923162i	$-0.625596\pi$
$19$	−3.35122	−0.768823	−0.384412	+	0.923162i	$0.625596\pi$
$20$	3.15717	0.705965
$21$	−1.00000	−0.218218
$22$	−9.29204	−1.98107
$23$	−3.01769	−0.629231	−0.314616	−	0.949219i	$-0.601876\pi$
$23$	−3.01769	−0.629231	−0.314616	+	0.949219i	$0.601876\pi$
$24$	2.43132	0.496291
$25$	−3.94847	−0.789695
$26$	−11.1764	−2.19187
$27$	1.00000	0.192450
$28$	−3.07885	−0.581847
$29$	−6.00218	−1.11458	−0.557289	−	0.830319i	$-0.688158\pi$
$29$	−6.00218	−1.11458	−0.557289	+	0.830319i	$0.688158\pi$
$30$	2.31096	0.421922
$31$	−2.64958	−0.475879	−0.237940	−	0.971280i	$-0.576472\pi$
$31$	−2.64958	−0.475879	−0.237940	+	0.971280i	$0.576472\pi$
$32$	−6.39150	−1.12987
$33$	−4.12314	−0.717747
$34$	12.1833	2.08942
$35$	−1.02544	−0.173331
$36$	3.07885	0.513141
$37$	−10.0215	−1.64752	−0.823758	−	0.566941i	$-0.808127\pi$
$37$	−10.0215	−1.64752	−0.823758	+	0.566941i	$0.808127\pi$
$38$	−7.55242	−1.22516
$39$	−4.95929	−0.794122
$40$	2.49317	0.394205
$41$	−5.27471	−0.823771	−0.411885	−	0.911236i	$-0.635130\pi$
$41$	−5.27471	−0.823771	−0.411885	+	0.911236i	$0.635130\pi$
$42$	−2.25363	−0.347743
$43$	−5.56920	−0.849294	−0.424647	−	0.905359i	$-0.639602\pi$
$43$	−5.56920	−0.849294	−0.424647	+	0.905359i	$0.639602\pi$
$44$	−12.6945	−1.91377
$45$	1.02544	0.152864
$46$	−6.80075	−1.00272
$47$	7.18129	1.04750	0.523750	−	0.851872i	$-0.324533\pi$
$47$	7.18129	1.04750	0.523750	+	0.851872i	$0.324533\pi$
$48$	−0.678398	−0.0979183
$49$	1.00000	0.142857
$50$	−8.89840	−1.25842
$51$	5.40608	0.757003
$52$	−15.2689	−2.11742
$53$	−1.79109	−0.246025	−0.123013	−	0.992405i	$-0.539256\pi$
$53$	−1.79109	−0.246025	−0.123013	+	0.992405i	$0.539256\pi$
$54$	2.25363	0.306680
$55$	−4.22804	−0.570108
$56$	−2.43132	−0.324899
$57$	−3.35122	−0.443880
$58$	−13.5267	−1.77614
$59$	6.99289	0.910396	0.455198	−	0.890390i	$-0.349568\pi$
$59$	6.99289	0.910396	0.455198	+	0.890390i	$0.349568\pi$
$60$	3.15717	0.407589
$61$	5.31623	0.680673	0.340337	−	0.940304i	$-0.389459\pi$
$61$	5.31623	0.680673	0.340337	+	0.940304i	$0.389459\pi$
$62$	−5.97118	−0.758341
$63$	−1.00000	−0.125988
$64$	−13.0473	−1.63091
$65$	−5.08546	−0.630773
$66$	−9.29204	−1.14377
$67$	7.39752	0.903751	0.451875	−	0.892081i	$-0.350755\pi$
$67$	7.39752	0.903751	0.451875	+	0.892081i	$0.350755\pi$
$68$	16.6445	2.01844
$69$	−3.01769	−0.363287
$70$	−2.31096	−0.276213
$71$	13.6013	1.61418	0.807088	−	0.590431i	$-0.201042\pi$
$71$	13.6013	1.61418	0.807088	+	0.590431i	$0.201042\pi$
$72$	2.43132	0.286534
$73$	−14.3959	−1.68492	−0.842459	−	0.538761i	$-0.818893\pi$
$73$	−14.3959	−1.68492	−0.842459	+	0.538761i	$0.818893\pi$
$74$	−22.5846	−2.62541
$75$	−3.94847	−0.455930
$76$	−10.3179	−1.18354
$77$	4.12314	0.469876
$78$	−11.1764	−1.26548
$79$	12.5843	1.41585	0.707924	−	0.706288i	$-0.249632\pi$
$79$	12.5843	1.41585	0.707924	+	0.706288i	$0.249632\pi$
$80$	−0.695656	−0.0777767
$81$	1.00000	0.111111
$82$	−11.8872	−1.31273
$83$	2.53548	0.278305	0.139152	−	0.990271i	$-0.455562\pi$
$83$	2.53548	0.278305	0.139152	+	0.990271i	$0.455562\pi$
$84$	−3.07885	−0.335930
$85$	5.54361	0.601289
$86$	−12.5509	−1.35340
$87$	−6.00218	−0.643502
$88$	−10.0247	−1.06863
$89$	10.3606	1.09822	0.549111	−	0.835749i	$-0.314966\pi$
$89$	10.3606	1.09822	0.549111	+	0.835749i	$0.314966\pi$
$90$	2.31096	0.243597
$91$	4.95929	0.519875
$92$	−9.29100	−0.968653
$93$	−2.64958	−0.274749
$94$	16.1840	1.66925
$95$	−3.43648	−0.352575
$96$	−6.39150	−0.652330
$97$	4.92101	0.499653	0.249826	−	0.968291i	$-0.419626\pi$
$97$	4.92101	0.499653	0.249826	+	0.968291i	$0.419626\pi$
$98$	2.25363	0.227651
$99$	−4.12314	−0.414392
$100$	−12.1567	−1.21567
$101$	7.59862	0.756091	0.378045	−	0.925787i	$-0.376596\pi$
$101$	7.59862	0.756091	0.378045	+	0.925787i	$0.376596\pi$
$102$	12.1833	1.20633
$103$	5.30516	0.522733	0.261367	−	0.965240i	$-0.415827\pi$
$103$	5.30516	0.522733	0.261367	+	0.965240i	$0.415827\pi$
$104$	−12.0576	−1.18235
$105$	−1.02544	−0.100073
$106$	−4.03646	−0.392056
$107$	−12.4204	−1.20072	−0.600361	−	0.799729i	$-0.704976\pi$
$107$	−12.4204	−1.20072	−0.600361	+	0.799729i	$0.704976\pi$
$108$	3.07885	0.296262
$109$	9.29371	0.890176	0.445088	−	0.895487i	$-0.353172\pi$
$109$	9.29371	0.890176	0.445088	+	0.895487i	$0.353172\pi$
$110$	−9.52843	−0.908500
$111$	−10.0215	−0.951194
$112$	0.678398	0.0641026
$113$	16.3088	1.53420	0.767100	−	0.641528i	$-0.221699\pi$
$113$	16.3088	1.53420	0.767100	+	0.641528i	$0.221699\pi$
$114$	−7.55242	−0.707349
$115$	−3.09446	−0.288560
$116$	−18.4798	−1.71581
$117$	−4.95929	−0.458487
$118$	15.7594	1.45077
$119$	−5.40608	−0.495575
$120$	2.49317	0.227594
$121$	6.00032	0.545483
$122$	11.9808	1.08469
$123$	−5.27471	−0.475604
$124$	−8.15766	−0.732580
$125$	−9.17612	−0.820737
$126$	−2.25363	−0.200769
$127$	0.529216	0.0469603	0.0234802	−	0.999724i	$-0.492525\pi$
$127$	0.529216	0.0469603	0.0234802	+	0.999724i	$0.492525\pi$
$128$	−16.6207	−1.46908
$129$	−5.56920	−0.490340
$130$	−11.4607	−1.00517
$131$	−15.0395	−1.31400	−0.657002	−	0.753889i	$-0.728176\pi$
$131$	−15.0395	−1.31400	−0.657002	+	0.753889i	$0.728176\pi$
$132$	−12.6945	−1.10492
$133$	3.35122	0.290588
$134$	16.6713	1.44018
$135$	1.02544	0.0882558
$136$	13.1439	1.12708
$137$	21.1027	1.80293	0.901465	−	0.432852i	$-0.142493\pi$
$137$	21.1027	1.80293	0.901465	+	0.432852i	$0.142493\pi$
$138$	−6.80075	−0.578918
$139$	−12.6361	−1.07178	−0.535888	−	0.844289i	$-0.680023\pi$
$139$	−12.6361	−1.07178	−0.535888	+	0.844289i	$0.680023\pi$
$140$	−3.15717	−0.266830
$141$	7.18129	0.604774
$142$	30.6523	2.57228
$143$	20.4479	1.70994
$144$	−0.678398	−0.0565332
$145$	−6.15488	−0.511135
$146$	−32.4431	−2.68501
$147$	1.00000	0.0824786
$148$	−30.8545	−2.53623
$149$	15.2811	1.25188	0.625939	−	0.779872i	$-0.284716\pi$
$149$	15.2811	1.25188	0.625939	+	0.779872i	$0.284716\pi$
$150$	−8.89840	−0.726551
$151$	−13.6016	−1.10688	−0.553440	−	0.832889i	$-0.686685\pi$
$151$	−13.6016	−1.10688	−0.553440	+	0.832889i	$0.686685\pi$
$152$	−8.14790	−0.660882
$153$	5.40608	0.437056
$154$	9.29204	0.748774
$155$	−2.71699	−0.218234
$156$	−15.2689	−1.22249
$157$	0.431538	0.0344404	0.0172202	−	0.999852i	$-0.494518\pi$
$157$	0.431538	0.0344404	0.0172202	+	0.999852i	$0.494518\pi$
$158$	28.3604	2.25624
$159$	−1.79109	−0.142043
$160$	−6.55410	−0.518147
$161$	3.01769	0.237827
$162$	2.25363	0.177062
$163$	−22.8315	−1.78830	−0.894149	−	0.447770i	$-0.852218\pi$
$163$	−22.8315	−1.78830	−0.894149	+	0.447770i	$0.852218\pi$
$164$	−16.2400	−1.26813
$165$	−4.22804	−0.329152
$166$	5.71403	0.443495
$167$	20.3401	1.57396	0.786981	−	0.616977i	$-0.211643\pi$
$167$	20.3401	1.57396	0.786981	+	0.616977i	$0.211643\pi$
$168$	−2.43132	−0.187580
$169$	11.5946	0.891891
$170$	12.4933	0.958189
$171$	−3.35122	−0.256274
$172$	−17.1467	−1.30742
$173$	5.53347	0.420702	0.210351	−	0.977626i	$-0.432539\pi$
$173$	5.53347	0.420702	0.210351	+	0.977626i	$0.432539\pi$
$174$	−13.5267	−1.02546
$175$	3.94847	0.298477
$176$	2.79713	0.210842
$177$	6.99289	0.525617
$178$	23.3490	1.75008
$179$	−9.88813	−0.739073	−0.369537	−	0.929216i	$-0.620484\pi$
$179$	−9.88813	−0.739073	−0.369537	+	0.929216i	$0.620484\pi$
$180$	3.15717	0.235322
$181$	−5.13471	−0.381660	−0.190830	−	0.981623i	$-0.561118\pi$
$181$	−5.13471	−0.381660	−0.190830	+	0.981623i	$0.561118\pi$
$182$	11.1764	0.828451
$183$	5.31623	0.392987
$184$	−7.33696	−0.540888
$185$	−10.2764	−0.755536
$186$	−5.97118	−0.437828
$187$	−22.2901	−1.63001
$188$	22.1101	1.61254
$189$	−1.00000	−0.0727393
$190$	−7.74455	−0.561849
$191$	−14.1692	−1.02525	−0.512624	−	0.858613i	$-0.671327\pi$
$191$	−14.1692	−1.02525	−0.512624	+	0.858613i	$0.671327\pi$
$192$	−13.0473	−0.941606
$193$	−15.3882	−1.10766	−0.553832	−	0.832628i	$-0.686835\pi$
$193$	−15.3882	−1.10766	−0.553832	+	0.832628i	$0.686835\pi$
$194$	11.0901	0.796225
$195$	−5.08546	−0.364177
$196$	3.07885	0.219918
$197$	−15.4404	−1.10008	−0.550040	−	0.835138i	$-0.685387\pi$
$197$	−15.4404	−1.10008	−0.550040	+	0.835138i	$0.685387\pi$
$198$	−9.29204	−0.660356
$199$	−9.67895	−0.686123	−0.343061	−	0.939313i	$-0.611464\pi$
$199$	−9.67895	−0.686123	−0.343061	+	0.939313i	$0.611464\pi$
$200$	−9.60000	−0.678823
$201$	7.39752	0.521781
$202$	17.1245	1.20487
$203$	6.00218	0.421271
$204$	16.6445	1.16535
$205$	−5.40889	−0.377774
$206$	11.9559	0.833005
$207$	−3.01769	−0.209744
$208$	3.36437	0.233277
$209$	13.8176	0.955782
$210$	−2.31096	−0.159472
$211$	25.0610	1.72527	0.862634	−	0.505829i	$-0.168813\pi$
$211$	25.0610	1.72527	0.862634	+	0.505829i	$0.168813\pi$
$212$	−5.51450	−0.378737
$213$	13.6013	0.931945
$214$	−27.9909	−1.91342
$215$	−5.71088	−0.389478
$216$	2.43132	0.165430
$217$	2.64958	0.179866
$218$	20.9446	1.41855
$219$	−14.3959	−0.972788
$220$	−13.0175	−0.877638
$221$	−26.8104	−1.80346
$222$	−22.5846	−1.51578
$223$	−14.7152	−0.985403	−0.492702	−	0.870198i	$-0.663991\pi$
$223$	−14.7152	−0.985403	−0.492702	+	0.870198i	$0.663991\pi$
$224$	6.39150	0.427050
$225$	−3.94847	−0.263232
$226$	36.7539	2.44483
$227$	9.33176	0.619370	0.309685	−	0.950839i	$-0.399776\pi$
$227$	9.33176	0.619370	0.309685	+	0.950839i	$0.399776\pi$
$228$	−10.3179	−0.683320
$229$	−17.5378	−1.15893	−0.579464	−	0.814998i	$-0.696738\pi$
$229$	−17.5378	−1.15893	−0.579464	+	0.814998i	$0.696738\pi$
$230$	−6.97376	−0.459836
$231$	4.12314	0.271283
$232$	−14.5932	−0.958093
$233$	−8.26910	−0.541727	−0.270863	−	0.962618i	$-0.587309\pi$
$233$	−8.26910	−0.541727	−0.270863	+	0.962618i	$0.587309\pi$
$234$	−11.1764	−0.730625
$235$	7.36398	0.480373
$236$	21.5300	1.40148
$237$	12.5843	0.817441
$238$	−12.1833	−0.789727
$239$	5.48339	0.354691	0.177346	−	0.984149i	$-0.443249\pi$
$239$	5.48339	0.354691	0.177346	+	0.984149i	$0.443249\pi$
$240$	−0.695656	−0.0449044
$241$	23.6507	1.52347	0.761736	−	0.647887i	$-0.224347\pi$
$241$	23.6507	1.52347	0.761736	+	0.647887i	$0.224347\pi$
$242$	13.5225	0.869258
$243$	1.00000	0.0641500
$244$	16.3678	1.04784
$245$	1.02544	0.0655130
$246$	−11.8872	−0.757902
$247$	16.6197	1.05749
$248$	−6.44199	−0.409067
$249$	2.53548	0.160679
$250$	−20.6796	−1.30789
$251$	−22.1460	−1.39785	−0.698923	−	0.715197i	$-0.746337\pi$
$251$	−22.1460	−1.39785	−0.698923	+	0.715197i	$0.746337\pi$
$252$	−3.07885	−0.193949
$253$	12.4424	0.782245
$254$	1.19266	0.0748339
$255$	5.54361	0.347155
$256$	−11.3624	−0.710151
$257$	−23.4564	−1.46317	−0.731585	−	0.681750i	$-0.761219\pi$
$257$	−23.4564	−1.46317	−0.731585	+	0.681750i	$0.761219\pi$
$258$	−12.5509	−0.781385
$259$	10.0215	0.622703
$260$	−15.6573	−0.971027
$261$	−6.00218	−0.371526
$262$	−33.8934	−2.09394
$263$	−16.7397	−1.03221	−0.516106	−	0.856525i	$-0.672619\pi$
$263$	−16.7397	−1.03221	−0.516106	+	0.856525i	$0.672619\pi$
$264$	−10.0247	−0.616977
$265$	−1.83666	−0.112825
$266$	7.55242	0.463068
$267$	10.3606	0.634059
$268$	22.7758	1.39125
$269$	−2.29070	−0.139667	−0.0698333	−	0.997559i	$-0.522247\pi$
$269$	−2.29070	−0.139667	−0.0698333	+	0.997559i	$0.522247\pi$
$270$	2.31096	0.140641
$271$	−28.6535	−1.74058	−0.870288	−	0.492544i	$-0.836067\pi$
$271$	−28.6535	−1.74058	−0.870288	+	0.492544i	$0.836067\pi$
$272$	−3.66748	−0.222373
$273$	4.95929	0.300150
$274$	47.5578	2.87307
$275$	16.2801	0.981728
$276$	−9.29100	−0.559252
$277$	−4.20565	−0.252693	−0.126347	−	0.991986i	$-0.540325\pi$
$277$	−4.20565	−0.252693	−0.126347	+	0.991986i	$0.540325\pi$
$278$	−28.4770	−1.70794
$279$	−2.64958	−0.158626
$280$	−2.49317	−0.148996
$281$	32.1879	1.92017	0.960085	−	0.279709i	$-0.0902379\pi$
$281$	32.1879	1.92017	0.960085	+	0.279709i	$0.0902379\pi$
$282$	16.1840	0.963741
$283$	−9.87199	−0.586829	−0.293415	−	0.955985i	$-0.594792\pi$
$283$	−9.87199	−0.586829	−0.293415	+	0.955985i	$0.594792\pi$
$284$	41.8763	2.48490
$285$	−3.43648	−0.203559
$286$	46.0819	2.72488
$287$	5.27471	0.311356
$288$	−6.39150	−0.376623
$289$	12.2258	0.719162
$290$	−13.8708	−0.814522
$291$	4.92101	0.288475
$292$	−44.3229	−2.59380
$293$	−22.1080	−1.29157	−0.645783	−	0.763521i	$-0.723469\pi$
$293$	−22.1080	−1.29157	−0.645783	+	0.763521i	$0.723469\pi$
$294$	2.25363	0.131434
$295$	7.17078	0.417499
$296$	−24.3654	−1.41621
$297$	−4.12314	−0.239249
$298$	34.4380	1.99494
$299$	14.9656	0.865483
$300$	−12.1567	−0.701870
$301$	5.56920	0.321003
$302$	−30.6529	−1.76388
$303$	7.59862	0.436529
$304$	2.27346	0.130392
$305$	5.45147	0.312150
$306$	12.1833	0.696474
$307$	−21.6718	−1.23687	−0.618437	−	0.785835i	$-0.712234\pi$
$307$	−21.6718	−1.23687	−0.618437	+	0.785835i	$0.712234\pi$
$308$	12.6945	0.723338
$309$	5.30516	0.301800
$310$	−6.12309	−0.347768
$311$	1.25864	0.0713708	0.0356854	−	0.999363i	$-0.488639\pi$
$311$	1.25864	0.0713708	0.0356854	+	0.999363i	$0.488639\pi$
$312$	−12.0576	−0.682629
$313$	−14.2041	−0.802863	−0.401431	−	0.915889i	$-0.631487\pi$
$313$	−14.2041	−0.802863	−0.401431	+	0.915889i	$0.631487\pi$
$314$	0.972526	0.0548828
$315$	−1.02544	−0.0577770
$316$	38.7452	2.17959
$317$	−33.1033	−1.85927	−0.929634	−	0.368484i	$-0.879877\pi$
$317$	−33.1033	−1.85927	−0.929634	+	0.368484i	$0.879877\pi$
$318$	−4.03646	−0.226353
$319$	24.7479	1.38561
$320$	−13.3792	−0.747920
$321$	−12.4204	−0.693237
$322$	6.80075	0.378991
$323$	−18.1170	−1.00806
$324$	3.07885	0.171047
$325$	19.5816	1.08619
$326$	−51.4536	−2.84975
$327$	9.29371	0.513943
$328$	−12.8245	−0.708114
$329$	−7.18129	−0.395917
$330$	−9.52843	−0.524523
$331$	−4.23854	−0.232971	−0.116486	−	0.993192i	$-0.537163\pi$
$331$	−4.23854	−0.232971	−0.116486	+	0.993192i	$0.537163\pi$
$332$	7.80635	0.428429
$333$	−10.0215	−0.549172
$334$	45.8390	2.50820
$335$	7.58571	0.414452
$336$	0.678398	0.0370096
$337$	−3.50580	−0.190973	−0.0954864	−	0.995431i	$-0.530441\pi$
$337$	−3.50580	−0.190973	−0.0954864	+	0.995431i	$0.530441\pi$
$338$	26.1299	1.42128
$339$	16.3088	0.885771
$340$	17.0679	0.925639
$341$	10.9246	0.591601
$342$	−7.55242	−0.408388
$343$	−1.00000	−0.0539949
$344$	−13.5405	−0.730055
$345$	−3.09446	−0.166600
$346$	12.4704	0.670413
$347$	17.8994	0.960888	0.480444	−	0.877025i	$-0.340476\pi$
$347$	17.8994	0.960888	0.480444	+	0.877025i	$0.340476\pi$
$348$	−18.4798	−0.990621
$349$	10.0004	0.535311	0.267656	−	0.963515i	$-0.413751\pi$
$349$	10.0004	0.535311	0.267656	+	0.963515i	$0.413751\pi$
$350$	8.89840	0.475639
$351$	−4.95929	−0.264707
$352$	26.3531	1.40462
$353$	−28.7055	−1.52784	−0.763920	−	0.645311i	$-0.776728\pi$
$353$	−28.7055	−1.52784	−0.763920	+	0.645311i	$0.776728\pi$
$354$	15.7594	0.837601
$355$	13.9473	0.740246
$356$	31.8987	1.69063
$357$	−5.40608	−0.286120
$358$	−22.2842	−1.17776
$359$	1.40057	0.0739193	0.0369596	−	0.999317i	$-0.488233\pi$
$359$	1.40057	0.0739193	0.0369596	+	0.999317i	$0.488233\pi$
$360$	2.49317	0.131402
$361$	−7.76930	−0.408911
$362$	−11.5717	−0.608197
$363$	6.00032	0.314935
$364$	15.2689	0.800308
$365$	−14.7622	−0.772687
$366$	11.9808	0.626247
$367$	−24.8942	−1.29947	−0.649734	−	0.760162i	$-0.725120\pi$
$367$	−24.8942	−1.29947	−0.649734	+	0.760162i	$0.725120\pi$
$368$	2.04719	0.106717
$369$	−5.27471	−0.274590
$370$	−23.1592	−1.20399
$371$	1.79109	0.0929889
$372$	−8.15766	−0.422955
$373$	20.1655	1.04413	0.522065	−	0.852906i	$-0.325162\pi$
$373$	20.1655	1.04413	0.522065	+	0.852906i	$0.325162\pi$
$374$	−50.2335	−2.59751
$375$	−9.17612	−0.473853
$376$	17.4600	0.900432
$377$	29.7666	1.53306
$378$	−2.25363	−0.115914
$379$	31.5472	1.62047	0.810235	−	0.586105i	$-0.199340\pi$
$379$	31.5472	1.62047	0.810235	+	0.586105i	$0.199340\pi$
$380$	−10.5804	−0.542762
$381$	0.529216	0.0271125
$382$	−31.9322	−1.63379
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−16.6207	−0.848173
$385$	4.22804	0.215481
$386$	−34.6792	−1.76513
$387$	−5.56920	−0.283098
$388$	15.1510	0.769177
$389$	−0.618216	−0.0313448	−0.0156724	−	0.999877i	$-0.504989\pi$
$389$	−0.618216	−0.0313448	−0.0156724	+	0.999877i	$0.504989\pi$
$390$	−11.4607	−0.580337
$391$	−16.3139	−0.825028
$392$	2.43132	0.122800
$393$	−15.0395	−0.758640
$394$	−34.7968	−1.75304
$395$	12.9045	0.649295
$396$	−12.6945	−0.637924
$397$	16.3887	0.822523	0.411262	−	0.911517i	$-0.365088\pi$
$397$	16.3887	0.822523	0.411262	+	0.911517i	$0.365088\pi$
$398$	−21.8128	−1.09338
$399$	3.35122	0.167771
$400$	2.67864	0.133932
$401$	13.9512	0.696692	0.348346	−	0.937366i	$-0.386743\pi$
$401$	13.9512	0.696692	0.348346	+	0.937366i	$0.386743\pi$
$402$	16.6713	0.831487
$403$	13.1401	0.654553
$404$	23.3950	1.16394
$405$	1.02544	0.0509545
$406$	13.5267	0.671319
$407$	41.3199	2.04815
$408$	13.1439	0.650721
$409$	−20.8716	−1.03203	−0.516017	−	0.856579i	$-0.672586\pi$
$409$	−20.8716	−1.03203	−0.516017	+	0.856579i	$0.672586\pi$
$410$	−12.1896	−0.602004
$411$	21.1027	1.04092
$412$	16.3338	0.804707
$413$	−6.99289	−0.344097
$414$	−6.80075	−0.334239
$415$	2.59998	0.127628
$416$	31.6973	1.55409
$417$	−12.6361	−0.618791
$418$	31.1397	1.52309
$419$	−36.7656	−1.79612	−0.898058	−	0.439876i	$-0.855022\pi$
$419$	−36.7656	−1.79612	−0.898058	+	0.439876i	$0.855022\pi$
$420$	−3.15717	−0.154054
$421$	−30.3293	−1.47816	−0.739080	−	0.673618i	$-0.764739\pi$
$421$	−30.3293	−1.47816	−0.739080	+	0.673618i	$0.764739\pi$
$422$	56.4781	2.74931
$423$	7.18129	0.349166
$424$	−4.35472	−0.211484
$425$	−21.3458	−1.03542
$426$	30.6523	1.48511
$427$	−5.31623	−0.257270
$428$	−38.2404	−1.84842
$429$	20.4479	0.987233
$430$	−12.8702	−0.620656
$431$	1.23755	0.0596106	0.0298053	−	0.999556i	$-0.490511\pi$
$431$	1.23755	0.0596106	0.0298053	+	0.999556i	$0.490511\pi$
$432$	−0.678398	−0.0326394
$433$	11.0624	0.531624	0.265812	−	0.964025i	$-0.414360\pi$
$433$	11.0624	0.531624	0.265812	+	0.964025i	$0.414360\pi$
$434$	5.97118	0.286626
$435$	−6.15488	−0.295104
$436$	28.6139	1.37036
$437$	10.1129	0.483768
$438$	−32.4431	−1.55019
$439$	39.0070	1.86170	0.930852	−	0.365396i	$-0.119066\pi$
$439$	39.0070	1.86170	0.930852	+	0.365396i	$0.119066\pi$
$440$	−10.2797	−0.490066
$441$	1.00000	0.0476190
$442$	−60.4206	−2.87392
$443$	7.36652	0.349994	0.174997	−	0.984569i	$-0.444008\pi$
$443$	7.36652	0.349994	0.174997	+	0.984569i	$0.444008\pi$
$444$	−30.8545	−1.46429
$445$	10.6242	0.503635
$446$	−33.1626	−1.57030
$447$	15.2811	0.722772
$448$	13.0473	0.616426
$449$	10.4627	0.493765	0.246882	−	0.969045i	$-0.420594\pi$
$449$	10.4627	0.493765	0.246882	+	0.969045i	$0.420594\pi$
$450$	−8.89840	−0.419474
$451$	21.7484	1.02409
$452$	50.2122	2.36178
$453$	−13.6016	−0.639058
$454$	21.0303	0.987002
$455$	5.08546	0.238410
$456$	−8.14790	−0.381560
$457$	−23.5767	−1.10287	−0.551436	−	0.834217i	$-0.685920\pi$
$457$	−23.5767	−1.10287	−0.551436	+	0.834217i	$0.685920\pi$
$458$	−39.5236	−1.84682
$459$	5.40608	0.252334
$460$	−9.52736	−0.444215
$461$	−7.14281	−0.332674	−0.166337	−	0.986069i	$-0.553194\pi$
$461$	−7.14281	−0.332674	−0.166337	+	0.986069i	$0.553194\pi$
$462$	9.29204	0.432305
$463$	−15.6457	−0.727119	−0.363560	−	0.931571i	$-0.618439\pi$
$463$	−15.6457	−0.727119	−0.363560	+	0.931571i	$0.618439\pi$
$464$	4.07187	0.189032
$465$	−2.71699	−0.125997
$466$	−18.6355	−0.863272
$467$	34.5827	1.60029	0.800147	−	0.599804i	$-0.204755\pi$
$467$	34.5827	1.60029	0.800147	+	0.599804i	$0.204755\pi$
$468$	−15.2689	−0.705805
$469$	−7.39752	−0.341586
$470$	16.5957	0.765502
$471$	0.431538	0.0198842
$472$	17.0019	0.782578
$473$	22.9626	1.05582
$474$	28.3604	1.30264
$475$	13.2322	0.607136
$476$	−16.6445	−0.762900
$477$	−1.79109	−0.0820085
$478$	12.3575	0.565220
$479$	39.2543	1.79357	0.896786	−	0.442464i	$-0.145895\pi$
$479$	39.2543	1.79357	0.896786	+	0.442464i	$0.145895\pi$
$480$	−6.55410	−0.299152
$481$	49.6993	2.26609
$482$	53.2998	2.42774
$483$	3.01769	0.137310
$484$	18.4740	0.839729
$485$	5.04620	0.229136
$486$	2.25363	0.102227
$487$	8.48727	0.384595	0.192297	−	0.981337i	$-0.438406\pi$
$487$	8.48727	0.384595	0.192297	+	0.981337i	$0.438406\pi$
$488$	12.9255	0.585108
$489$	−22.8315	−1.03247
$490$	2.31096	0.104399
$491$	−24.1960	−1.09195	−0.545974	−	0.837802i	$-0.683840\pi$
$491$	−24.1960	−1.09195	−0.545974	+	0.837802i	$0.683840\pi$
$492$	−16.2400	−0.732156
$493$	−32.4483	−1.46140
$494$	37.4546	1.68516
$495$	−4.22804	−0.190036
$496$	1.79747	0.0807089
$497$	−13.6013	−0.610101
$498$	5.71403	0.256052
$499$	8.67806	0.388483	0.194242	−	0.980954i	$-0.437775\pi$
$499$	8.67806	0.388483	0.194242	+	0.980954i	$0.437775\pi$
$500$	−28.2519	−1.26346
$501$	20.3401	0.908728
$502$	−49.9090	−2.22755
$503$	41.3757	1.84485	0.922426	−	0.386174i	$-0.126204\pi$
$503$	41.3757	1.84485	0.922426	+	0.386174i	$0.126204\pi$
$504$	−2.43132	−0.108300
$505$	7.79193	0.346736
$506$	28.0405	1.24655
$507$	11.5946	0.514934
$508$	1.62937	0.0722918
$509$	1.27690	0.0565978	0.0282989	−	0.999600i	$-0.490991\pi$
$509$	1.27690	0.0565978	0.0282989	+	0.999600i	$0.490991\pi$
$510$	12.4933	0.553211
$511$	14.3959	0.636839
$512$	7.63478	0.337413
$513$	−3.35122	−0.147960
$514$	−52.8620	−2.33164
$515$	5.44012	0.239721
$516$	−17.1467	−0.754841
$517$	−29.6095	−1.30222
$518$	22.5846	0.992312
$519$	5.53347	0.242893
$520$	−12.3644	−0.542214
$521$	−8.55116	−0.374633	−0.187316	−	0.982300i	$-0.559979\pi$
$521$	−8.55116	−0.374633	−0.187316	+	0.982300i	$0.559979\pi$
$522$	−13.5267	−0.592048
$523$	39.8925	1.74438	0.872188	−	0.489171i	$-0.162700\pi$
$523$	39.8925	1.74438	0.872188	+	0.489171i	$0.162700\pi$
$524$	−46.3042	−2.02281
$525$	3.94847	0.172325
$526$	−37.7250	−1.64489
$527$	−14.3239	−0.623958
$528$	2.79713	0.121730
$529$	−13.8936	−0.604068
$530$	−4.13915	−0.179793
$531$	6.99289	0.303465
$532$	10.3179	0.447338
$533$	26.1588	1.13306
$534$	23.3490	1.01041
$535$	−12.7363	−0.550640
$536$	17.9857	0.776865
$537$	−9.88813	−0.426704
$538$	−5.16240	−0.222567
$539$	−4.12314	−0.177596
$540$	3.15717	0.135863
$541$	15.1112	0.649680	0.324840	−	0.945769i	$-0.394690\pi$
$541$	15.1112	0.649680	0.324840	+	0.945769i	$0.394690\pi$
$542$	−64.5744	−2.77371
$543$	−5.13471	−0.220352
$544$	−34.5530	−1.48145
$545$	9.53014	0.408226
$546$	11.1764	0.478306
$547$	16.5249	0.706553	0.353277	−	0.935519i	$-0.385067\pi$
$547$	16.5249	0.706553	0.353277	+	0.935519i	$0.385067\pi$
$548$	64.9721	2.77547
$549$	5.31623	0.226891
$550$	36.6894	1.56444
$551$	20.1147	0.856913
$552$	−7.33696	−0.312282
$553$	−12.5843	−0.535140
$554$	−9.47798	−0.402681
$555$	−10.2764	−0.436209
$556$	−38.9045	−1.64992
$557$	39.5929	1.67761	0.838803	−	0.544435i	$-0.183256\pi$
$557$	39.5929	1.67761	0.838803	+	0.544435i	$0.183256\pi$
$558$	−5.97118	−0.252780
$559$	27.6193	1.16817
$560$	0.695656	0.0293968
$561$	−22.2901	−0.941087
$562$	72.5396	3.05990
$563$	−23.9715	−1.01028	−0.505138	−	0.863038i	$-0.668559\pi$
$563$	−23.9715	−1.01028	−0.505138	+	0.863038i	$0.668559\pi$
$564$	22.1101	0.931003
$565$	16.7237	0.703570
$566$	−22.2478	−0.935146
$567$	−1.00000	−0.0419961
$568$	33.0691	1.38755
$569$	−45.3378	−1.90066	−0.950330	−	0.311243i	$-0.899255\pi$
$569$	−45.3378	−1.90066	−0.950330	+	0.311243i	$0.899255\pi$
$570$	−7.74455	−0.324383
$571$	−18.8733	−0.789821	−0.394911	−	0.918720i	$-0.629224\pi$
$571$	−18.8733	−0.789821	−0.394911	+	0.918720i	$0.629224\pi$
$572$	62.9559	2.63232
$573$	−14.1692	−0.591927
$574$	11.8872	0.496164
$575$	11.9153	0.496901
$576$	−13.0473	−0.543636
$577$	13.8486	0.576523	0.288262	−	0.957552i	$-0.406923\pi$
$577$	13.8486	0.576523	0.288262	+	0.957552i	$0.406923\pi$
$578$	27.5523	1.14603
$579$	−15.3882	−0.639510
$580$	−18.9499	−0.786853
$581$	−2.53548	−0.105189
$582$	11.0901	0.459701
$583$	7.38493	0.305853
$584$	−35.0011	−1.44836
$585$	−5.08546	−0.210258
$586$	−49.8233	−2.05818
$587$	10.8507	0.447856	0.223928	−	0.974606i	$-0.428112\pi$
$587$	10.8507	0.447856	0.223928	+	0.974606i	$0.428112\pi$
$588$	3.07885	0.126969
$589$	8.87935	0.365867
$590$	16.1603	0.665309
$591$	−15.4404	−0.635131
$592$	6.79853	0.279418
$593$	−40.0008	−1.64264	−0.821318	−	0.570471i	$-0.806761\pi$
$593$	−40.0008	−1.64264	−0.821318	+	0.570471i	$0.806761\pi$
$594$	−9.29204	−0.381257
$595$	−5.54361	−0.227266
$596$	47.0482	1.92717
$597$	−9.67895	−0.396133
$598$	33.7269	1.37920
$599$	4.40365	0.179928	0.0899640	−	0.995945i	$-0.471325\pi$
$599$	4.40365	0.179928	0.0899640	+	0.995945i	$0.471325\pi$
$600$	−9.60000	−0.391918
$601$	−10.1627	−0.414544	−0.207272	−	0.978283i	$-0.566459\pi$
$601$	−10.1627	−0.414544	−0.207272	+	0.978283i	$0.566459\pi$
$602$	12.5509	0.511537
$603$	7.39752	0.301250
$604$	−41.8772	−1.70396
$605$	6.15296	0.250153
$606$	17.1245	0.695634
$607$	30.8153	1.25075	0.625377	−	0.780323i	$-0.284945\pi$
$607$	30.8153	1.25075	0.625377	+	0.780323i	$0.284945\pi$
$608$	21.4193	0.868669
$609$	6.00218	0.243221
$610$	12.2856	0.497429
$611$	−35.6141	−1.44079
$612$	16.6445	0.672814
$613$	−44.4132	−1.79383	−0.896916	−	0.442200i	$-0.854198\pi$
$613$	−44.4132	−1.79383	−0.896916	+	0.442200i	$0.854198\pi$
$614$	−48.8401	−1.97103
$615$	−5.40889	−0.218108
$616$	10.0247	0.403906
$617$	−39.6861	−1.59770	−0.798851	−	0.601529i	$-0.794558\pi$
$617$	−39.6861	−1.59770	−0.798851	+	0.601529i	$0.794558\pi$
$618$	11.9559	0.480936
$619$	−26.3664	−1.05975	−0.529877	−	0.848075i	$-0.677762\pi$
$619$	−26.3664	−1.05975	−0.529877	+	0.848075i	$0.677762\pi$
$620$	−8.36519	−0.335954
$621$	−3.01769	−0.121096
$622$	2.83650	0.113733
$623$	−10.3606	−0.415089
$624$	3.36437	0.134683
$625$	10.3328	0.413312
$626$	−32.0108	−1.27941
$627$	13.8176	0.551821
$628$	1.32864	0.0530184
$629$	−54.1768	−2.16017
$630$	−2.31096	−0.0920709
$631$	−28.9997	−1.15446	−0.577230	−	0.816581i	$-0.695866\pi$
$631$	−28.9997	−1.15446	−0.577230	+	0.816581i	$0.695866\pi$
$632$	30.5966	1.21707
$633$	25.0610	0.996084
$634$	−74.6026	−2.96285
$635$	0.542679	0.0215356
$636$	−5.51450	−0.218664
$637$	−4.95929	−0.196494
$638$	55.7725	2.20806
$639$	13.6013	0.538059
$640$	−17.0436	−0.673706
$641$	−11.6171	−0.458849	−0.229425	−	0.973326i	$-0.573684\pi$
$641$	−11.6171	−0.458849	−0.229425	+	0.973326i	$0.573684\pi$
$642$	−27.9909	−1.10471
$643$	−18.2236	−0.718667	−0.359334	−	0.933209i	$-0.616996\pi$
$643$	−18.2236	−0.718667	−0.359334	+	0.933209i	$0.616996\pi$
$644$	9.29100	0.366117
$645$	−5.71088	−0.224866
$646$	−40.8290	−1.60640
$647$	10.8544	0.426730	0.213365	−	0.976973i	$-0.431558\pi$
$647$	10.8544	0.426730	0.213365	+	0.976973i	$0.431558\pi$
$648$	2.43132	0.0955113
$649$	−28.8327	−1.13178
$650$	44.1298	1.73091
$651$	2.64958	0.103845
$652$	−70.2945	−2.75295
$653$	−23.9180	−0.935983	−0.467992	−	0.883733i	$-0.655022\pi$
$653$	−23.9180	−0.935983	−0.467992	+	0.883733i	$0.655022\pi$
$654$	20.9446	0.818998
$655$	−15.4221	−0.602590
$656$	3.57835	0.139711
$657$	−14.3959	−0.561639
$658$	−16.1840	−0.630917
$659$	19.3014	0.751876	0.375938	−	0.926645i	$-0.377321\pi$
$659$	19.3014	0.751876	0.375938	+	0.926645i	$0.377321\pi$
$660$	−13.0175	−0.506704
$661$	−35.2917	−1.37269	−0.686345	−	0.727276i	$-0.740786\pi$
$661$	−35.2917	−1.37269	−0.686345	+	0.727276i	$0.740786\pi$
$662$	−9.55209	−0.371253
$663$	−26.8104	−1.04123
$664$	6.16456	0.239231
$665$	3.43648	0.133261
$666$	−22.5846	−0.875137
$667$	18.1127	0.701327
$668$	62.6240	2.42299
$669$	−14.7152	−0.568923
$670$	17.0954	0.660452
$671$	−21.9196	−0.846196
$672$	6.39150	0.246557
$673$	13.0633	0.503555	0.251777	−	0.967785i	$-0.418985\pi$
$673$	13.0633	0.503555	0.251777	+	0.967785i	$0.418985\pi$
$674$	−7.90077	−0.304326
$675$	−3.94847	−0.151977
$676$	35.6979	1.37300
$677$	−29.0309	−1.11575	−0.557875	−	0.829925i	$-0.688383\pi$
$677$	−29.0309	−1.11575	−0.557875	+	0.829925i	$0.688383\pi$
$678$	36.7539	1.41153
$679$	−4.92101	−0.188851
$680$	13.4783	0.516869
$681$	9.33176	0.357594
$682$	24.6200	0.942750
$683$	17.4472	0.667598	0.333799	−	0.942644i	$-0.391669\pi$
$683$	17.4472	0.667598	0.333799	+	0.942644i	$0.391669\pi$
$684$	−10.3179	−0.394515
$685$	21.6396	0.826807
$686$	−2.25363	−0.0860440
$687$	−17.5378	−0.669107
$688$	3.77813	0.144040
$689$	8.88255	0.338398
$690$	−6.97376	−0.265487
$691$	12.3452	0.469635	0.234818	−	0.972039i	$-0.424551\pi$
$691$	12.3452	0.469635	0.234818	+	0.972039i	$0.424551\pi$
$692$	17.0367	0.647639
$693$	4.12314	0.156625
$694$	40.3385	1.53123
$695$	−12.9575	−0.491507
$696$	−14.5932	−0.553155
$697$	−28.5155	−1.08010
$698$	22.5373	0.853049
$699$	−8.26910	−0.312766
$700$	12.1567	0.459482
$701$	0.455790	0.0172150	0.00860748	−	0.999963i	$-0.497260\pi$
$701$	0.455790	0.0172150	0.00860748	+	0.999963i	$0.497260\pi$
$702$	−11.1764	−0.421826
$703$	33.5841	1.26665
$704$	53.7958	2.02750
$705$	7.36398	0.277344
$706$	−64.6916	−2.43470
$707$	−7.59862	−0.285775
$708$	21.5300	0.809148
$709$	46.5823	1.74943	0.874717	−	0.484634i	$-0.161047\pi$
$709$	46.5823	1.74943	0.874717	+	0.484634i	$0.161047\pi$
$710$	31.4321	1.17962
$711$	12.5843	0.471950
$712$	25.1900	0.944034
$713$	7.99562	0.299438
$714$	−12.1833	−0.455949
$715$	20.9681	0.784161
$716$	−30.4440	−1.13775
$717$	5.48339	0.204781
$718$	3.15637	0.117795
$719$	−15.6596	−0.584003	−0.292002	−	0.956418i	$-0.594321\pi$
$719$	−15.6596	−0.584003	−0.292002	+	0.956418i	$0.594321\pi$
$720$	−0.695656	−0.0259256
$721$	−5.30516	−0.197575
$722$	−17.5091	−0.651622
$723$	23.6507	0.879577
$724$	−15.8090	−0.587536
$725$	23.6995	0.880176
$726$	13.5225	0.501867
$727$	−42.8972	−1.59097	−0.795484	−	0.605975i	$-0.792783\pi$
$727$	−42.8972	−1.59097	−0.795484	+	0.605975i	$0.792783\pi$
$728$	12.0576	0.446885
$729$	1.00000	0.0370370
$730$	−33.2685	−1.23132
$731$	−30.1075	−1.11357
$732$	16.3678	0.604973
$733$	−22.6377	−0.836141	−0.418070	−	0.908415i	$-0.637293\pi$
$733$	−22.6377	−0.836141	−0.418070	+	0.908415i	$0.637293\pi$
$734$	−56.1024	−2.07078
$735$	1.02544	0.0378239
$736$	19.2875	0.710948
$737$	−30.5010	−1.12352
$738$	−11.8872	−0.437575
$739$	35.1883	1.29442	0.647211	−	0.762311i	$-0.275935\pi$
$739$	35.1883	1.29442	0.647211	+	0.762311i	$0.275935\pi$
$740$	−31.6395	−1.16309
$741$	16.6197	0.610540
$742$	4.03646	0.148183
$743$	−19.6411	−0.720562	−0.360281	−	0.932844i	$-0.617319\pi$
$743$	−19.6411	−0.720562	−0.360281	+	0.932844i	$0.617319\pi$
$744$	−6.44199	−0.236175
$745$	15.6699	0.574099
$746$	45.4455	1.66388
$747$	2.53548	0.0927683
$748$	−68.6277	−2.50928
$749$	12.4204	0.453830
$750$	−20.6796	−0.755111
$751$	−6.24803	−0.227994	−0.113997	−	0.993481i	$-0.536365\pi$
$751$	−6.24803	−0.227994	−0.113997	+	0.993481i	$0.536365\pi$
$752$	−4.87177	−0.177655
$753$	−22.1460	−0.807047
$754$	67.0829	2.44301
$755$	−13.9476	−0.507605
$756$	−3.07885	−0.111977
$757$	−5.18941	−0.188612	−0.0943062	−	0.995543i	$-0.530063\pi$
$757$	−5.18941	−0.188612	−0.0943062	+	0.995543i	$0.530063\pi$
$758$	71.0957	2.58231
$759$	12.4424	0.451629
$760$	−8.35518	−0.303074
$761$	30.5927	1.10898	0.554491	−	0.832189i	$-0.312913\pi$
$761$	30.5927	1.10898	0.554491	+	0.832189i	$0.312913\pi$
$762$	1.19266	0.0432054
$763$	−9.29371	−0.336455
$764$	−43.6248	−1.57829
$765$	5.54361	0.200430
$766$	2.25363	0.0814269
$767$	−34.6798	−1.25221
$768$	−11.3624	−0.410006
$769$	25.6558	0.925174	0.462587	−	0.886574i	$-0.346921\pi$
$769$	25.6558	0.925174	0.462587	+	0.886574i	$0.346921\pi$
$770$	9.52843	0.343381
$771$	−23.4564	−0.844761
$772$	−47.3778	−1.70516
$773$	−9.39951	−0.338077	−0.169038	−	0.985609i	$-0.554066\pi$
$773$	−9.39951	−0.338077	−0.169038	+	0.985609i	$0.554066\pi$
$774$	−12.5509	−0.451133
$775$	10.4618	0.375799
$776$	11.9645	0.429502
$777$	10.0215	0.359518
$778$	−1.39323	−0.0499497
$779$	17.6767	0.633334
$780$	−15.6573	−0.560623
$781$	−56.0801	−2.00670
$782$	−36.7654	−1.31473
$783$	−6.00218	−0.214501
$784$	−0.678398	−0.0242285
$785$	0.442516	0.0157941
$786$	−33.8934	−1.20894
$787$	−14.1297	−0.503670	−0.251835	−	0.967770i	$-0.581034\pi$
$787$	−14.1297	−0.503670	−0.251835	+	0.967770i	$0.581034\pi$
$788$	−47.5385	−1.69349
$789$	−16.7397	−0.595947
$790$	29.0819	1.03469
$791$	−16.3088	−0.579873
$792$	−10.0247	−0.356212
$793$	−26.3647	−0.936239
$794$	36.9340	1.31074
$795$	−1.83666	−0.0651395
$796$	−29.8000	−1.05623
$797$	19.2957	0.683488	0.341744	−	0.939793i	$-0.388983\pi$
$797$	19.2957	0.683488	0.341744	+	0.939793i	$0.388983\pi$
$798$	7.55242	0.267353
$799$	38.8227	1.37345
$800$	25.2367	0.892251
$801$	10.3606	0.366074
$802$	31.4409	1.11022
$803$	59.3565	2.09465
$804$	22.7758	0.803241
$805$	3.09446	0.109065
$806$	29.6128	1.04307
$807$	−2.29070	−0.0806366
$808$	18.4747	0.649937
$809$	55.8916	1.96504	0.982521	−	0.186149i	$-0.0596009\pi$
$809$	55.8916	1.96504	0.982521	+	0.186149i	$0.0596009\pi$
$810$	2.31096	0.0811989
$811$	10.4866	0.368235	0.184117	−	0.982904i	$-0.441057\pi$
$811$	10.4866	0.368235	0.184117	+	0.982904i	$0.441057\pi$
$812$	18.4798	0.648514
$813$	−28.6535	−1.00492
$814$	93.1197	3.26385
$815$	−23.4123	−0.820097
$816$	−3.66748	−0.128387
$817$	18.6636	0.652957
$818$	−47.0368	−1.64460
$819$	4.95929	0.173292
$820$	−16.6532	−0.581553
$821$	−50.0254	−1.74590	−0.872949	−	0.487811i	$-0.837795\pi$
$821$	−50.0254	−1.74590	−0.872949	+	0.487811i	$0.837795\pi$
$822$	47.5578	1.65877
$823$	−34.3080	−1.19590	−0.597951	−	0.801533i	$-0.704018\pi$
$823$	−34.3080	−1.19590	−0.597951	+	0.801533i	$0.704018\pi$
$824$	12.8985	0.449342
$825$	16.2801	0.566801
$826$	−15.7594	−0.548339
$827$	5.90617	0.205378	0.102689	−	0.994714i	$-0.467255\pi$
$827$	5.90617	0.205378	0.102689	+	0.994714i	$0.467255\pi$
$828$	−9.29100	−0.322884
$829$	33.9009	1.17743	0.588713	−	0.808342i	$-0.299635\pi$
$829$	33.9009	1.17743	0.588713	+	0.808342i	$0.299635\pi$
$830$	5.85939	0.203383
$831$	−4.20565	−0.145892
$832$	64.7052	2.24325
$833$	5.40608	0.187310
$834$	−28.4770	−0.986078
$835$	20.8575	0.721805
$836$	42.5422	1.47135
$837$	−2.64958	−0.0915830
$838$	−82.8560	−2.86221
$839$	1.32886	0.0458773	0.0229386	−	0.999737i	$-0.492698\pi$
$839$	1.32886	0.0458773	0.0229386	+	0.999737i	$0.492698\pi$
$840$	−2.49317	−0.0860226
$841$	7.02622	0.242283
$842$	−68.3510	−2.35553
$843$	32.1879	1.10861
$844$	77.1589	2.65592
$845$	11.8896	0.409013
$846$	16.1840	0.556416
$847$	−6.00032	−0.206173
$848$	1.21507	0.0417258
$849$	−9.87199	−0.338806
$850$	−48.1055	−1.65000
$851$	30.2416	1.03667
$852$	41.8763	1.43466
$853$	−44.6220	−1.52783	−0.763915	−	0.645317i	$-0.776725\pi$
$853$	−44.6220	−1.52783	−0.763915	+	0.645317i	$0.776725\pi$
$854$	−11.9808	−0.409975
$855$	−3.43648	−0.117525
$856$	−30.1979	−1.03214
$857$	31.0171	1.05952	0.529762	−	0.848146i	$-0.322281\pi$
$857$	31.0171	1.05952	0.529762	+	0.848146i	$0.322281\pi$
$858$	46.0819	1.57321
$859$	−55.0910	−1.87968	−0.939840	−	0.341614i	$-0.889026\pi$
$859$	−55.0910	−1.87968	−0.939840	+	0.341614i	$0.889026\pi$
$860$	−17.5829	−0.599572
$861$	5.27471	0.179762
$862$	2.78898	0.0949929
$863$	−44.2305	−1.50562	−0.752812	−	0.658235i	$-0.771303\pi$
$863$	−44.2305	−1.50562	−0.752812	+	0.658235i	$0.771303\pi$
$864$	−6.39150	−0.217443
$865$	5.67424	0.192930
$866$	24.9305	0.847173
$867$	12.2258	0.415208
$868$	8.15766	0.276889
$869$	−51.8870	−1.76015
$870$	−13.8708	−0.470265
$871$	−36.6865	−1.24307
$872$	22.5960	0.765196
$873$	4.92101	0.166551
$874$	22.7908	0.770911
$875$	9.17612	0.310210
$876$	−44.3229	−1.49753
$877$	−9.02560	−0.304773	−0.152386	−	0.988321i	$-0.548696\pi$
$877$	−9.02560	−0.304773	−0.152386	+	0.988321i	$0.548696\pi$
$878$	87.9074	2.96673
$879$	−22.1080	−0.745686
$880$	2.86829	0.0966901
$881$	11.1164	0.374520	0.187260	−	0.982310i	$-0.440039\pi$
$881$	11.1164	0.374520	0.187260	+	0.982310i	$0.440039\pi$
$882$	2.25363	0.0758837
$883$	−1.81599	−0.0611130	−0.0305565	−	0.999533i	$-0.509728\pi$
$883$	−1.81599	−0.0611130	−0.0305565	+	0.999533i	$0.509728\pi$
$884$	−82.5450	−2.77629
$885$	7.17078	0.241043
$886$	16.6014	0.557736
$887$	26.5790	0.892435	0.446218	−	0.894924i	$-0.352771\pi$
$887$	26.5790	0.892435	0.446218	+	0.894924i	$0.352771\pi$
$888$	−24.3654	−0.817648
$889$	−0.529216	−0.0177493
$890$	23.9430	0.802570
$891$	−4.12314	−0.138131
$892$	−45.3059	−1.51695
$893$	−24.0661	−0.805342
$894$	34.4380	1.15178
$895$	−10.1397	−0.338932
$896$	16.6207	0.555259
$897$	14.9656	0.499687
$898$	23.5790	0.786842
$899$	15.9033	0.530405
$900$	−12.1567	−0.405225
$901$	−9.68280	−0.322581
$902$	49.0128	1.63195
$903$	5.56920	0.185331
$904$	39.6518	1.31880
$905$	−5.26534	−0.175026
$906$	−30.6529	−1.01838
$907$	47.9344	1.59164	0.795818	−	0.605536i	$-0.207041\pi$
$907$	47.9344	1.59164	0.795818	+	0.605536i	$0.207041\pi$
$908$	28.7310	0.953473
$909$	7.59862	0.252030
$910$	11.4607	0.379920
$911$	37.7067	1.24928	0.624639	−	0.780914i	$-0.285246\pi$
$911$	37.7067	1.24928	0.624639	+	0.780914i	$0.285246\pi$
$912$	2.27346	0.0752819
$913$	−10.4541	−0.345982
$914$	−53.1332	−1.75749
$915$	5.45147	0.180220
$916$	−53.9961	−1.78408
$917$	15.0395	0.496647
$918$	12.1833	0.402109
$919$	8.60834	0.283963	0.141981	−	0.989869i	$-0.454653\pi$
$919$	8.60834	0.283963	0.141981	+	0.989869i	$0.454653\pi$
$920$	−7.52362	−0.248046
$921$	−21.6718	−0.714109
$922$	−16.0972	−0.530134
$923$	−67.4528	−2.22024
$924$	12.6945	0.417619
$925$	39.5694	1.30104
$926$	−35.2597	−1.15871
$927$	5.30516	0.174244
$928$	38.3629	1.25933
$929$	−56.6365	−1.85818	−0.929091	−	0.369851i	$-0.879409\pi$
$929$	−56.6365	−1.85818	−0.929091	+	0.369851i	$0.879409\pi$
$930$	−6.12309	−0.200784
$931$	−3.35122	−0.109832
$932$	−25.4593	−0.833947
$933$	1.25864	0.0412059
$934$	77.9365	2.55016
$935$	−22.8571	−0.747508
$936$	−12.0576	−0.394116
$937$	54.0486	1.76569	0.882846	−	0.469663i	$-0.155625\pi$
$937$	54.0486	1.76569	0.882846	+	0.469663i	$0.155625\pi$
$938$	−16.6713	−0.544336
$939$	−14.2041	−0.463533
$940$	22.6726	0.739498
$941$	25.1147	0.818716	0.409358	−	0.912374i	$-0.365753\pi$
$941$	25.1147	0.818716	0.409358	+	0.912374i	$0.365753\pi$
$942$	0.972526	0.0316866
$943$	15.9174	0.518342
$944$	−4.74396	−0.154403
$945$	−1.02544	−0.0333576
$946$	51.7492	1.68251
$947$	18.3499	0.596293	0.298146	−	0.954520i	$-0.403632\pi$
$947$	18.3499	0.596293	0.298146	+	0.954520i	$0.403632\pi$
$948$	38.7452	1.25839
$949$	71.3937	2.31754
$950$	29.8205	0.967505
$951$	−33.1033	−1.07345
$952$	−13.1439	−0.425997
$953$	57.0345	1.84753	0.923765	−	0.382960i	$-0.125095\pi$
$953$	57.0345	1.84753	0.923765	+	0.382960i	$0.125095\pi$
$954$	−4.03646	−0.130685
$955$	−14.5297	−0.470169
$956$	16.8825	0.546020
$957$	24.7479	0.799985
$958$	88.4646	2.85816
$959$	−21.1027	−0.681443
$960$	−13.3792	−0.431812
$961$	−23.9797	−0.773539
$962$	112.004	3.61115
$963$	−12.4204	−0.400241
$964$	72.8167	2.34527
$965$	−15.7796	−0.507965
$966$	6.80075	0.218811
$967$	−2.98524	−0.0959987	−0.0479993	−	0.998847i	$-0.515285\pi$
$967$	−2.98524	−0.0959987	−0.0479993	+	0.998847i	$0.515285\pi$
$968$	14.5887	0.468898
$969$	−18.1170	−0.582002
$970$	11.3723	0.365141
$971$	41.5299	1.33276	0.666380	−	0.745613i	$-0.267843\pi$
$971$	41.5299	1.33276	0.666380	+	0.745613i	$0.267843\pi$
$972$	3.07885	0.0987540
$973$	12.6361	0.405093
$974$	19.1272	0.612874
$975$	19.5816	0.627114
$976$	−3.60652	−0.115442
$977$	−12.4175	−0.397272	−0.198636	−	0.980073i	$-0.563651\pi$
$977$	−12.4175	−0.397272	−0.198636	+	0.980073i	$0.563651\pi$
$978$	−51.4536	−1.64531
$979$	−42.7183	−1.36528
$980$	3.15717	0.100852
$981$	9.29371	0.296725
$982$	−54.5288	−1.74008
$983$	−4.35895	−0.139029	−0.0695145	−	0.997581i	$-0.522145\pi$
$983$	−4.35895	−0.139029	−0.0695145	+	0.997581i	$0.522145\pi$
$984$	−12.8245	−0.408830
$985$	−15.8332	−0.504486
$986$	−73.1265	−2.32882
$987$	−7.18129	−0.228583
$988$	51.1695	1.62792
$989$	16.8061	0.534403
$990$	−9.52843	−0.302833
$991$	−4.34237	−0.137940	−0.0689700	−	0.997619i	$-0.521971\pi$
$991$	−4.34237	−0.137940	−0.0689700	+	0.997619i	$0.521971\pi$
$992$	16.9348	0.537681
$993$	−4.23854	−0.134506
$994$	−30.6523	−0.972231
$995$	−9.92519	−0.314650
$996$	7.80635	0.247354
$997$	−57.5895	−1.82388	−0.911940	−	0.410324i	$-0.865415\pi$
$997$	−57.5895	−1.82388	−0.911940	+	0.410324i	$0.865415\pi$
$998$	19.5571	0.619070
$999$	−10.0215	−0.317065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.q.1.40	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.q.1.40	✓	44	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q+2.25363 q^{2} +1.00000 q^{3} +3.07885 q^{4} +1.02544 q^{5} +2.25363 q^{6} -1.00000 q^{7} +2.43132 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.25363 q^{2} +1.00000 q^{3} +3.07885 q^{4} +1.02544 q^{5} +2.25363 q^{6} -1.00000 q^{7} +2.43132 q^{8} +1.00000 q^{9} +2.31096 q^{10} -4.12314 q^{11} +3.07885 q^{12} -4.95929 q^{13} -2.25363 q^{14} +1.02544 q^{15} -0.678398 q^{16} +5.40608 q^{17} +2.25363 q^{18} -3.35122 q^{19} +3.15717 q^{20} -1.00000 q^{21} -9.29204 q^{22} -3.01769 q^{23} +2.43132 q^{24} -3.94847 q^{25} -11.1764 q^{26} +1.00000 q^{27} -3.07885 q^{28} -6.00218 q^{29} +2.31096 q^{30} -2.64958 q^{31} -6.39150 q^{32} -4.12314 q^{33} +12.1833 q^{34} -1.02544 q^{35} +3.07885 q^{36} -10.0215 q^{37} -7.55242 q^{38} -4.95929 q^{39} +2.49317 q^{40} -5.27471 q^{41} -2.25363 q^{42} -5.56920 q^{43} -12.6945 q^{44} +1.02544 q^{45} -6.80075 q^{46} +7.18129 q^{47} -0.678398 q^{48} +1.00000 q^{49} -8.89840 q^{50} +5.40608 q^{51} -15.2689 q^{52} -1.79109 q^{53} +2.25363 q^{54} -4.22804 q^{55} -2.43132 q^{56} -3.35122 q^{57} -13.5267 q^{58} +6.99289 q^{59} +3.15717 q^{60} +5.31623 q^{61} -5.97118 q^{62} -1.00000 q^{63} -13.0473 q^{64} -5.08546 q^{65} -9.29204 q^{66} +7.39752 q^{67} +16.6445 q^{68} -3.01769 q^{69} -2.31096 q^{70} +13.6013 q^{71} +2.43132 q^{72} -14.3959 q^{73} -22.5846 q^{74} -3.94847 q^{75} -10.3179 q^{76} +4.12314 q^{77} -11.1764 q^{78} +12.5843 q^{79} -0.695656 q^{80} +1.00000 q^{81} -11.8872 q^{82} +2.53548 q^{83} -3.07885 q^{84} +5.54361 q^{85} -12.5509 q^{86} -6.00218 q^{87} -10.0247 q^{88} +10.3606 q^{89} +2.31096 q^{90} +4.95929 q^{91} -9.29100 q^{92} -2.64958 q^{93} +16.1840 q^{94} -3.43648 q^{95} -6.39150 q^{96} +4.92101 q^{97} +2.25363 q^{98} -4.12314 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

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