LMFDB - Embedded newform 8043.2.a.u.1.4

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:	$0$
Dimension:	$53$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.39422 q^{2} +1.00000 q^{3} +3.73230 q^{4} -2.33465 q^{5} -2.39422 q^{6} +1.00000 q^{7} -4.14751 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.39422 q^{2} +1.00000 q^{3} +3.73230 q^{4} -2.33465 q^{5} -2.39422 q^{6} +1.00000 q^{7} -4.14751 q^{8} +1.00000 q^{9} +5.58967 q^{10} +5.51776 q^{11} +3.73230 q^{12} -1.89346 q^{13} -2.39422 q^{14} -2.33465 q^{15} +2.46547 q^{16} -6.06024 q^{17} -2.39422 q^{18} -5.18852 q^{19} -8.71361 q^{20} +1.00000 q^{21} -13.2108 q^{22} +5.34991 q^{23} -4.14751 q^{24} +0.450590 q^{25} +4.53337 q^{26} +1.00000 q^{27} +3.73230 q^{28} +6.35136 q^{29} +5.58967 q^{30} -8.66817 q^{31} +2.39215 q^{32} +5.51776 q^{33} +14.5096 q^{34} -2.33465 q^{35} +3.73230 q^{36} +3.39569 q^{37} +12.4225 q^{38} -1.89346 q^{39} +9.68299 q^{40} -9.83139 q^{41} -2.39422 q^{42} -0.665504 q^{43} +20.5940 q^{44} -2.33465 q^{45} -12.8089 q^{46} +0.834162 q^{47} +2.46547 q^{48} +1.00000 q^{49} -1.07881 q^{50} -6.06024 q^{51} -7.06696 q^{52} -7.41882 q^{53} -2.39422 q^{54} -12.8820 q^{55} -4.14751 q^{56} -5.18852 q^{57} -15.2066 q^{58} +6.76528 q^{59} -8.71361 q^{60} +2.97737 q^{61} +20.7535 q^{62} +1.00000 q^{63} -10.6583 q^{64} +4.42057 q^{65} -13.2108 q^{66} +2.80028 q^{67} -22.6187 q^{68} +5.34991 q^{69} +5.58967 q^{70} +7.74372 q^{71} -4.14751 q^{72} -1.93956 q^{73} -8.13004 q^{74} +0.450590 q^{75} -19.3651 q^{76} +5.51776 q^{77} +4.53337 q^{78} -6.58361 q^{79} -5.75600 q^{80} +1.00000 q^{81} +23.5385 q^{82} -5.53355 q^{83} +3.73230 q^{84} +14.1485 q^{85} +1.59336 q^{86} +6.35136 q^{87} -22.8850 q^{88} +11.5150 q^{89} +5.58967 q^{90} -1.89346 q^{91} +19.9675 q^{92} -8.66817 q^{93} -1.99717 q^{94} +12.1134 q^{95} +2.39215 q^{96} +8.82417 q^{97} -2.39422 q^{98} +5.51776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9}+O(q^{10}) $ 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9	\( 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9} + 2 q^{10} + 46 q^{11} + 63 q^{12} + 32 q^{13} + 11 q^{14} + 24 q^{15} + 67 q^{16} + 46 q^{17} + 11 q^{18} + 14 q^{19} + 53 q^{20} + 53 q^{21} + 13 q^{22} + 68 q^{23} + 30 q^{24} + 71 q^{25} + 11 q^{26} + 53 q^{27} + 63 q^{28} + 55 q^{29} + 2 q^{30} - 2 q^{31} + 51 q^{32} + 46 q^{33} - 7 q^{34} + 24 q^{35} + 63 q^{36} + 53 q^{37} + 16 q^{38} + 32 q^{39} - 20 q^{40} + 38 q^{41} + 11 q^{42} + 36 q^{43} + 70 q^{44} + 24 q^{45} + 4 q^{46} + 51 q^{47} + 67 q^{48} + 53 q^{49} + 32 q^{50} + 46 q^{51} + 10 q^{52} + 104 q^{53} + 11 q^{54} + 11 q^{55} + 30 q^{56} + 14 q^{57} + 4 q^{58} + 36 q^{59} + 53 q^{60} + 3 q^{61} + 25 q^{62} + 53 q^{63} + 82 q^{64} + 46 q^{65} + 13 q^{66} + 54 q^{67} + 88 q^{68} + 68 q^{69} + 2 q^{70} + 101 q^{71} + 30 q^{72} + q^{73} + 32 q^{74} + 71 q^{75} - 35 q^{76} + 46 q^{77} + 11 q^{78} + 14 q^{79} + 39 q^{80} + 53 q^{81} - 29 q^{82} + 38 q^{83} + 63 q^{84} + 16 q^{85} + 23 q^{86} + 55 q^{87} - 8 q^{88} + 52 q^{89} + 2 q^{90} + 32 q^{91} + 76 q^{92} - 2 q^{93} - 53 q^{94} + 46 q^{95} + 51 q^{96} - 3 q^{97} + 11 q^{98} + 46 q^{99}+O(q^{100}) \) 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9 + 2 * q^10 + 46 * q^11 + 63 * q^12 + 32 * q^13 + 11 * q^14 + 24 * q^15 + 67 * q^16 + 46 * q^17 + 11 * q^18 + 14 * q^19 + 53 * q^20 + 53 * q^21 + 13 * q^22 + 68 * q^23 + 30 * q^24 + 71 * q^25 + 11 * q^26 + 53 * q^27 + 63 * q^28 + 55 * q^29 + 2 * q^30 - 2 * q^31 + 51 * q^32 + 46 * q^33 - 7 * q^34 + 24 * q^35 + 63 * q^36 + 53 * q^37 + 16 * q^38 + 32 * q^39 - 20 * q^40 + 38 * q^41 + 11 * q^42 + 36 * q^43 + 70 * q^44 + 24 * q^45 + 4 * q^46 + 51 * q^47 + 67 * q^48 + 53 * q^49 + 32 * q^50 + 46 * q^51 + 10 * q^52 + 104 * q^53 + 11 * q^54 + 11 * q^55 + 30 * q^56 + 14 * q^57 + 4 * q^58 + 36 * q^59 + 53 * q^60 + 3 * q^61 + 25 * q^62 + 53 * q^63 + 82 * q^64 + 46 * q^65 + 13 * q^66 + 54 * q^67 + 88 * q^68 + 68 * q^69 + 2 * q^70 + 101 * q^71 + 30 * q^72 + q^73 + 32 * q^74 + 71 * q^75 - 35 * q^76 + 46 * q^77 + 11 * q^78 + 14 * q^79 + 39 * q^80 + 53 * q^81 - 29 * q^82 + 38 * q^83 + 63 * q^84 + 16 * q^85 + 23 * q^86 + 55 * q^87 - 8 * q^88 + 52 * q^89 + 2 * q^90 + 32 * q^91 + 76 * q^92 - 2 * q^93 - 53 * q^94 + 46 * q^95 + 51 * q^96 - 3 * q^97 + 11 * q^98 + 46 * 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 $

$2$	−2.39422	−1.69297	−0.846485	−	0.532412i	$-0.821286\pi$
$2$	−2.39422	−1.69297	−0.846485	+	0.532412i	$0.821286\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.73230	1.86615
$5$	−2.33465	−1.04409	−0.522044	−	0.852919i	$-0.674830\pi$
$5$	−2.33465	−1.04409	−0.522044	+	0.852919i	$0.674830\pi$
$6$	−2.39422	−0.977437
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−4.14751	−1.46637
$9$	1.00000	0.333333
$10$	5.58967	1.76761
$11$	5.51776	1.66367	0.831834	−	0.555024i	$-0.187291\pi$
$11$	5.51776	1.66367	0.831834	+	0.555024i	$0.187291\pi$
$12$	3.73230	1.07742
$13$	−1.89346	−0.525152	−0.262576	−	0.964911i	$-0.584572\pi$
$13$	−1.89346	−0.525152	−0.262576	+	0.964911i	$0.584572\pi$
$14$	−2.39422	−0.639883
$15$	−2.33465	−0.602804
$16$	2.46547	0.616366
$17$	−6.06024	−1.46983	−0.734913	−	0.678162i	$-0.762777\pi$
$17$	−6.06024	−1.46983	−0.734913	+	0.678162i	$0.762777\pi$
$18$	−2.39422	−0.564324
$19$	−5.18852	−1.19033	−0.595164	−	0.803604i	$-0.702913\pi$
$19$	−5.18852	−1.19033	−0.595164	+	0.803604i	$0.702913\pi$
$20$	−8.71361	−1.94842
$21$	1.00000	0.218218
$22$	−13.2108	−2.81654
$23$	5.34991	1.11553	0.557767	−	0.829997i	$-0.311658\pi$
$23$	5.34991	1.11553	0.557767	+	0.829997i	$0.311658\pi$
$24$	−4.14751	−0.846607
$25$	0.450590	0.0901180
$26$	4.53337	0.889066
$27$	1.00000	0.192450
$28$	3.73230	0.705338
$29$	6.35136	1.17942	0.589709	−	0.807616i	$-0.299242\pi$
$29$	6.35136	1.17942	0.589709	+	0.807616i	$0.299242\pi$
$30$	5.58967	1.02053
$31$	−8.66817	−1.55685	−0.778425	−	0.627738i	$-0.783981\pi$
$31$	−8.66817	−1.55685	−0.778425	+	0.627738i	$0.783981\pi$
$32$	2.39215	0.422877
$33$	5.51776	0.960519
$34$	14.5096	2.48837
$35$	−2.33465	−0.394628
$36$	3.73230	0.622050
$37$	3.39569	0.558248	0.279124	−	0.960255i	$-0.409956\pi$
$37$	3.39569	0.558248	0.279124	+	0.960255i	$0.409956\pi$
$38$	12.4225	2.01519
$39$	−1.89346	−0.303196
$40$	9.68299	1.53101
$41$	−9.83139	−1.53540	−0.767702	−	0.640807i	$-0.778600\pi$
$41$	−9.83139	−1.53540	−0.767702	+	0.640807i	$0.778600\pi$
$42$	−2.39422	−0.369437
$43$	−0.665504	−0.101488	−0.0507442	−	0.998712i	$-0.516159\pi$
$43$	−0.665504	−0.101488	−0.0507442	+	0.998712i	$0.516159\pi$
$44$	20.5940	3.10465
$45$	−2.33465	−0.348029
$46$	−12.8089	−1.88857
$47$	0.834162	0.121675	0.0608375	−	0.998148i	$-0.480623\pi$
$47$	0.834162	0.121675	0.0608375	+	0.998148i	$0.480623\pi$
$48$	2.46547	0.355859
$49$	1.00000	0.142857
$50$	−1.07881	−0.152567
$51$	−6.06024	−0.848604
$52$	−7.06696	−0.980012
$53$	−7.41882	−1.01905	−0.509527	−	0.860455i	$-0.670179\pi$
$53$	−7.41882	−1.01905	−0.509527	+	0.860455i	$0.670179\pi$
$54$	−2.39422	−0.325812
$55$	−12.8820	−1.73701
$56$	−4.14751	−0.554235
$57$	−5.18852	−0.687236
$58$	−15.2066	−1.99672
$59$	6.76528	0.880765	0.440382	−	0.897810i	$-0.354843\pi$
$59$	6.76528	0.880765	0.440382	+	0.897810i	$0.354843\pi$
$60$	−8.71361	−1.12492
$61$	2.97737	0.381213	0.190607	−	0.981666i	$-0.438954\pi$
$61$	2.97737	0.381213	0.190607	+	0.981666i	$0.438954\pi$
$62$	20.7535	2.63570
$63$	1.00000	0.125988
$64$	−10.6583	−1.33228
$65$	4.42057	0.548304
$66$	−13.2108	−1.62613
$67$	2.80028	0.342109	0.171055	−	0.985262i	$-0.445283\pi$
$67$	2.80028	0.342109	0.171055	+	0.985262i	$0.445283\pi$
$68$	−22.6187	−2.74291
$69$	5.34991	0.644054
$70$	5.58967	0.668093
$71$	7.74372	0.919010	0.459505	−	0.888175i	$-0.348027\pi$
$71$	7.74372	0.919010	0.459505	+	0.888175i	$0.348027\pi$
$72$	−4.14751	−0.488789
$73$	−1.93956	−0.227009	−0.113504	−	0.993537i	$-0.536208\pi$
$73$	−1.93956	−0.227009	−0.113504	+	0.993537i	$0.536208\pi$
$74$	−8.13004	−0.945098
$75$	0.450590	0.0520296
$76$	−19.3651	−2.22133
$77$	5.51776	0.628807
$78$	4.53337	0.513303
$79$	−6.58361	−0.740714	−0.370357	−	0.928889i	$-0.620765\pi$
$79$	−6.58361	−0.740714	−0.370357	+	0.928889i	$0.620765\pi$
$80$	−5.75600	−0.643540
$81$	1.00000	0.111111
$82$	23.5385	2.59940
$83$	−5.53355	−0.607386	−0.303693	−	0.952770i	$-0.598220\pi$
$83$	−5.53355	−0.607386	−0.303693	+	0.952770i	$0.598220\pi$
$84$	3.73230	0.407227
$85$	14.1485	1.53463
$86$	1.59336	0.171817
$87$	6.35136	0.680938
$88$	−22.8850	−2.43955
$89$	11.5150	1.22058	0.610292	−	0.792177i	$-0.291052\pi$
$89$	11.5150	1.22058	0.610292	+	0.792177i	$0.291052\pi$
$90$	5.58967	0.589203
$91$	−1.89346	−0.198489
$92$	19.9675	2.08175
$93$	−8.66817	−0.898847
$94$	−1.99717	−0.205992
$95$	12.1134	1.24281
$96$	2.39215	0.244148
$97$	8.82417	0.895959	0.447979	−	0.894044i	$-0.352144\pi$
$97$	8.82417	0.895959	0.447979	+	0.894044i	$0.352144\pi$
$98$	−2.39422	−0.241853
$99$	5.51776	0.554556
$100$	1.68174	0.168174
$101$	−5.80382	−0.577502	−0.288751	−	0.957404i	$-0.593240\pi$
$101$	−5.80382	−0.577502	−0.288751	+	0.957404i	$0.593240\pi$
$102$	14.5096	1.43666
$103$	17.2316	1.69788	0.848938	−	0.528493i	$-0.177243\pi$
$103$	17.2316	1.69788	0.848938	+	0.528493i	$0.177243\pi$
$104$	7.85315	0.770065
$105$	−2.33465	−0.227838
$106$	17.7623	1.72523
$107$	−1.01707	−0.0983241	−0.0491620	−	0.998791i	$-0.515655\pi$
$107$	−1.01707	−0.0983241	−0.0491620	+	0.998791i	$0.515655\pi$
$108$	3.73230	0.359141
$109$	−19.4758	−1.86544	−0.932720	−	0.360600i	$-0.882572\pi$
$109$	−19.4758	−1.86544	−0.932720	+	0.360600i	$0.882572\pi$
$110$	30.8425	2.94072
$111$	3.39569	0.322305
$112$	2.46547	0.232965
$113$	18.4736	1.73785	0.868926	−	0.494941i	$-0.164810\pi$
$113$	18.4736	1.73785	0.868926	+	0.494941i	$0.164810\pi$
$114$	12.4225	1.16347
$115$	−12.4902	−1.16471
$116$	23.7052	2.20097
$117$	−1.89346	−0.175051
$118$	−16.1976	−1.49111
$119$	−6.06024	−0.555542
$120$	9.68299	0.883932
$121$	19.4457	1.76779
$122$	−7.12849	−0.645383
$123$	−9.83139	−0.886466
$124$	−32.3522	−2.90531
$125$	10.6213	0.949996
$126$	−2.39422	−0.213294
$127$	−1.46097	−0.129640	−0.0648202	−	0.997897i	$-0.520647\pi$
$127$	−1.46097	−0.129640	−0.0648202	+	0.997897i	$0.520647\pi$
$128$	20.7340	1.83264
$129$	−0.665504	−0.0585944
$130$	−10.5838	−0.928263
$131$	14.4357	1.26125	0.630626	−	0.776087i	$-0.282798\pi$
$131$	14.4357	1.26125	0.630626	+	0.776087i	$0.282798\pi$
$132$	20.5940	1.79247
$133$	−5.18852	−0.449902
$134$	−6.70450	−0.579181
$135$	−2.33465	−0.200935
$136$	25.1349	2.15530
$137$	−0.289488	−0.0247326	−0.0123663	−	0.999924i	$-0.503936\pi$
$137$	−0.289488	−0.0247326	−0.0123663	+	0.999924i	$0.503936\pi$
$138$	−12.8089	−1.09036
$139$	10.4229	0.884062	0.442031	−	0.897000i	$-0.354258\pi$
$139$	10.4229	0.884062	0.442031	+	0.897000i	$0.354258\pi$
$140$	−8.71361	−0.736435
$141$	0.834162	0.0702491
$142$	−18.5402	−1.55586
$143$	−10.4477	−0.873678
$144$	2.46547	0.205455
$145$	−14.8282	−1.23142
$146$	4.64375	0.384319
$147$	1.00000	0.0824786
$148$	12.6737	1.04178
$149$	1.07601	0.0881502	0.0440751	−	0.999028i	$-0.485966\pi$
$149$	1.07601	0.0881502	0.0440751	+	0.999028i	$0.485966\pi$
$150$	−1.07881	−0.0880847
$151$	9.55337	0.777442	0.388721	−	0.921355i	$-0.372917\pi$
$151$	9.55337	0.777442	0.388721	+	0.921355i	$0.372917\pi$
$152$	21.5194	1.74546
$153$	−6.06024	−0.489942
$154$	−13.2108	−1.06455
$155$	20.2371	1.62549
$156$	−7.06696	−0.565810
$157$	2.60606	0.207987	0.103993	−	0.994578i	$-0.466838\pi$
$157$	2.60606	0.207987	0.103993	+	0.994578i	$0.466838\pi$
$158$	15.7626	1.25401
$159$	−7.41882	−0.588351
$160$	−5.58484	−0.441520
$161$	5.34991	0.421632
$162$	−2.39422	−0.188108
$163$	−5.98339	−0.468656	−0.234328	−	0.972158i	$-0.575289\pi$
$163$	−5.98339	−0.468656	−0.234328	+	0.972158i	$0.575289\pi$
$164$	−36.6937	−2.86530
$165$	−12.8820	−1.00287
$166$	13.2485	1.02829
$167$	10.3284	0.799237	0.399619	−	0.916681i	$-0.369143\pi$
$167$	10.3284	0.799237	0.399619	+	0.916681i	$0.369143\pi$
$168$	−4.14751	−0.319988
$169$	−9.41481	−0.724216
$170$	−33.8748	−2.59808
$171$	−5.18852	−0.396776
$172$	−2.48386	−0.189393
$173$	2.90031	0.220507	0.110253	−	0.993904i	$-0.464834\pi$
$173$	2.90031	0.220507	0.110253	+	0.993904i	$0.464834\pi$
$174$	−15.2066	−1.15281
$175$	0.450590	0.0340614
$176$	13.6039	1.02543
$177$	6.76528	0.508510
$178$	−27.5694	−2.06641
$179$	0.579498	0.0433137	0.0216568	−	0.999765i	$-0.493106\pi$
$179$	0.579498	0.0433137	0.0216568	+	0.999765i	$0.493106\pi$
$180$	−8.71361	−0.649474
$181$	−13.9600	−1.03764	−0.518818	−	0.854884i	$-0.673628\pi$
$181$	−13.9600	−1.03764	−0.518818	+	0.854884i	$0.673628\pi$
$182$	4.53337	0.336035
$183$	2.97737	0.220094
$184$	−22.1888	−1.63578
$185$	−7.92775	−0.582860
$186$	20.7535	1.52172
$187$	−33.4390	−2.44530
$188$	3.11334	0.227064
$189$	1.00000	0.0727393
$190$	−29.0021	−2.10403
$191$	20.0081	1.44774	0.723868	−	0.689939i	$-0.242363\pi$
$191$	20.0081	1.44774	0.723868	+	0.689939i	$0.242363\pi$
$192$	−10.6583	−0.769195
$193$	−9.26677	−0.667037	−0.333518	−	0.942744i	$-0.608236\pi$
$193$	−9.26677	−0.667037	−0.333518	+	0.942744i	$0.608236\pi$
$194$	−21.1270	−1.51683
$195$	4.42057	0.316563
$196$	3.73230	0.266593
$197$	9.33036	0.664761	0.332380	−	0.943145i	$-0.392148\pi$
$197$	9.33036	0.664761	0.332380	+	0.943145i	$0.392148\pi$
$198$	−13.2108	−0.938847
$199$	−9.61088	−0.681297	−0.340649	−	0.940191i	$-0.610647\pi$
$199$	−9.61088	−0.681297	−0.340649	+	0.940191i	$0.610647\pi$
$200$	−1.86883	−0.132146
$201$	2.80028	0.197517
$202$	13.8956	0.977694
$203$	6.35136	0.445778
$204$	−22.6187	−1.58362
$205$	22.9528	1.60310
$206$	−41.2562	−2.87445
$207$	5.34991	0.371845
$208$	−4.66826	−0.323686
$209$	−28.6290	−1.98031
$210$	5.58967	0.385724
$211$	−6.11671	−0.421092	−0.210546	−	0.977584i	$-0.567524\pi$
$211$	−6.11671	−0.421092	−0.210546	+	0.977584i	$0.567524\pi$
$212$	−27.6893	−1.90171
$213$	7.74372	0.530591
$214$	2.43510	0.166460
$215$	1.55372	0.105963
$216$	−4.14751	−0.282202
$217$	−8.66817	−0.588434
$218$	46.6293	3.15814
$219$	−1.93956	−0.131064
$220$	−48.0797	−3.24153
$221$	11.4748	0.771881
$222$	−8.13004	−0.545653
$223$	4.83128	0.323526	0.161763	−	0.986830i	$-0.448282\pi$
$223$	4.83128	0.323526	0.161763	+	0.986830i	$0.448282\pi$
$224$	2.39215	0.159832
$225$	0.450590	0.0300393
$226$	−44.2300	−2.94213
$227$	−23.3448	−1.54945	−0.774726	−	0.632297i	$-0.782112\pi$
$227$	−23.3448	−1.54945	−0.774726	+	0.632297i	$0.782112\pi$
$228$	−19.3651	−1.28249
$229$	0.844195	0.0557860	0.0278930	−	0.999611i	$-0.491120\pi$
$229$	0.844195	0.0557860	0.0278930	+	0.999611i	$0.491120\pi$
$230$	29.9043	1.97183
$231$	5.51776	0.363042
$232$	−26.3424	−1.72946
$233$	3.30241	0.216348	0.108174	−	0.994132i	$-0.465500\pi$
$233$	3.30241	0.216348	0.108174	+	0.994132i	$0.465500\pi$
$234$	4.53337	0.296355
$235$	−1.94748	−0.127039
$236$	25.2501	1.64364
$237$	−6.58361	−0.427651
$238$	14.5096	0.940516
$239$	−9.03356	−0.584332	−0.292166	−	0.956368i	$-0.594376\pi$
$239$	−9.03356	−0.584332	−0.292166	+	0.956368i	$0.594376\pi$
$240$	−5.75600	−0.371548
$241$	20.6448	1.32985	0.664924	−	0.746911i	$-0.268464\pi$
$241$	20.6448	1.32985	0.664924	+	0.746911i	$0.268464\pi$
$242$	−46.5574	−2.99282
$243$	1.00000	0.0641500
$244$	11.1124	0.711401
$245$	−2.33465	−0.149155
$246$	23.5385	1.50076
$247$	9.82426	0.625103
$248$	35.9513	2.28291
$249$	−5.53355	−0.350674
$250$	−25.4297	−1.60832
$251$	18.7327	1.18240	0.591200	−	0.806525i	$-0.298655\pi$
$251$	18.7327	1.18240	0.591200	+	0.806525i	$0.298655\pi$
$252$	3.73230	0.235113
$253$	29.5196	1.85588
$254$	3.49789	0.219477
$255$	14.1485	0.886016
$256$	−28.3252	−1.77032
$257$	6.00632	0.374664	0.187332	−	0.982297i	$-0.440016\pi$
$257$	6.00632	0.374664	0.187332	+	0.982297i	$0.440016\pi$
$258$	1.59336	0.0991986
$259$	3.39569	0.210998
$260$	16.4989	1.02322
$261$	6.35136	0.393140
$262$	−34.5622	−2.13526
$263$	−0.626764	−0.0386479	−0.0193240	−	0.999813i	$-0.506151\pi$
$263$	−0.626764	−0.0386479	−0.0193240	+	0.999813i	$0.506151\pi$
$264$	−22.8850	−1.40847
$265$	17.3203	1.06398
$266$	12.4225	0.761670
$267$	11.5150	0.704704
$268$	10.4515	0.638427
$269$	−25.9496	−1.58217	−0.791087	−	0.611703i	$-0.790485\pi$
$269$	−25.9496	−1.58217	−0.791087	+	0.611703i	$0.790485\pi$
$270$	5.58967	0.340177
$271$	−28.5591	−1.73484	−0.867421	−	0.497576i	$-0.834224\pi$
$271$	−28.5591	−1.73484	−0.867421	+	0.497576i	$0.834224\pi$
$272$	−14.9413	−0.905951
$273$	−1.89346	−0.114597
$274$	0.693098	0.0418716
$275$	2.48625	0.149926
$276$	19.9675	1.20190
$277$	−8.22063	−0.493930	−0.246965	−	0.969024i	$-0.579433\pi$
$277$	−8.22063	−0.493930	−0.246965	+	0.969024i	$0.579433\pi$
$278$	−24.9548	−1.49669
$279$	−8.66817	−0.518950
$280$	9.68299	0.578669
$281$	4.74826	0.283258	0.141629	−	0.989920i	$-0.454766\pi$
$281$	4.74826	0.283258	0.141629	+	0.989920i	$0.454766\pi$
$282$	−1.99717	−0.118930
$283$	18.2660	1.08580	0.542901	−	0.839797i	$-0.317326\pi$
$283$	18.2660	1.08580	0.542901	+	0.839797i	$0.317326\pi$
$284$	28.9019	1.71501
$285$	12.1134	0.717535
$286$	25.0140	1.47911
$287$	−9.83139	−0.580328
$288$	2.39215	0.140959
$289$	19.7266	1.16039
$290$	35.5020	2.08475
$291$	8.82417	0.517282
$292$	−7.23903	−0.423632
$293$	−2.16647	−0.126567	−0.0632833	−	0.997996i	$-0.520157\pi$
$293$	−2.16647	−0.126567	−0.0632833	+	0.997996i	$0.520157\pi$
$294$	−2.39422	−0.139634
$295$	−15.7946	−0.919595
$296$	−14.0837	−0.818597
$297$	5.51776	0.320173
$298$	−2.57621	−0.149236
$299$	−10.1299	−0.585824
$300$	1.68174	0.0970951
$301$	−0.665504	−0.0383590
$302$	−22.8729	−1.31619
$303$	−5.80382	−0.333421
$304$	−12.7921	−0.733678
$305$	−6.95112	−0.398020
$306$	14.5096	0.829457
$307$	31.5971	1.80334	0.901672	−	0.432421i	$-0.142341\pi$
$307$	31.5971	1.80334	0.901672	+	0.432421i	$0.142341\pi$
$308$	20.5940	1.17345
$309$	17.2316	0.980269
$310$	−48.4522	−2.75190
$311$	−0.769141	−0.0436140	−0.0218070	−	0.999762i	$-0.506942\pi$
$311$	−0.769141	−0.0436140	−0.0218070	+	0.999762i	$0.506942\pi$
$312$	7.85315	0.444597
$313$	2.36586	0.133726	0.0668631	−	0.997762i	$-0.478701\pi$
$313$	2.36586	0.133726	0.0668631	+	0.997762i	$0.478701\pi$
$314$	−6.23950	−0.352115
$315$	−2.33465	−0.131543
$316$	−24.5720	−1.38228
$317$	19.8177	1.11307	0.556536	−	0.830823i	$-0.312130\pi$
$317$	19.8177	1.11307	0.556536	+	0.830823i	$0.312130\pi$
$318$	17.7623	0.996061
$319$	35.0453	1.96216
$320$	24.8833	1.39102
$321$	−1.01707	−0.0567674
$322$	−12.8089	−0.713811
$323$	31.4437	1.74957
$324$	3.73230	0.207350
$325$	−0.853174	−0.0473256
$326$	14.3256	0.793420
$327$	−19.4758	−1.07701
$328$	40.7758	2.25147
$329$	0.834162	0.0459888
$330$	30.8425	1.69782
$331$	27.2667	1.49871	0.749356	−	0.662167i	$-0.230363\pi$
$331$	27.2667	1.49871	0.749356	+	0.662167i	$0.230363\pi$
$332$	−20.6529	−1.13347
$333$	3.39569	0.186083
$334$	−24.7285	−1.35309
$335$	−6.53768	−0.357192
$336$	2.46547	0.134502
$337$	−4.85494	−0.264466	−0.132233	−	0.991219i	$-0.542215\pi$
$337$	−4.85494	−0.264466	−0.132233	+	0.991219i	$0.542215\pi$
$338$	22.5411	1.22608
$339$	18.4736	1.00335
$340$	52.8066	2.86384
$341$	−47.8289	−2.59008
$342$	12.4225	0.671730
$343$	1.00000	0.0539949
$344$	2.76019	0.148819
$345$	−12.4902	−0.672448
$346$	−6.94399	−0.373311
$347$	19.2642	1.03416	0.517079	−	0.855937i	$-0.327019\pi$
$347$	19.2642	1.03416	0.517079	+	0.855937i	$0.327019\pi$
$348$	23.7052	1.27073
$349$	14.1910	0.759627	0.379814	−	0.925063i	$-0.375988\pi$
$349$	14.1910	0.759627	0.379814	+	0.925063i	$0.375988\pi$
$350$	−1.07881	−0.0576649
$351$	−1.89346	−0.101065
$352$	13.1993	0.703527
$353$	−5.20214	−0.276882	−0.138441	−	0.990371i	$-0.544209\pi$
$353$	−5.20214	−0.276882	−0.138441	+	0.990371i	$0.544209\pi$
$354$	−16.1976	−0.860892
$355$	−18.0789	−0.959527
$356$	42.9773	2.27779
$357$	−6.06024	−0.320742
$358$	−1.38745	−0.0733288
$359$	−2.65724	−0.140244	−0.0701219	−	0.997538i	$-0.522339\pi$
$359$	−2.65724	−0.140244	−0.0701219	+	0.997538i	$0.522339\pi$
$360$	9.68299	0.510338
$361$	7.92074	0.416881
$362$	33.4233	1.75669
$363$	19.4457	1.02064
$364$	−7.06696	−0.370410
$365$	4.52820	0.237017
$366$	−7.12849	−0.372612
$367$	−12.1443	−0.633926	−0.316963	−	0.948438i	$-0.602663\pi$
$367$	−12.1443	−0.633926	−0.316963	+	0.948438i	$0.602663\pi$
$368$	13.1900	0.687578
$369$	−9.83139	−0.511802
$370$	18.9808	0.986765
$371$	−7.41882	−0.385166
$372$	−32.3522	−1.67738
$373$	7.33303	0.379690	0.189845	−	0.981814i	$-0.439202\pi$
$373$	7.33303	0.379690	0.189845	+	0.981814i	$0.439202\pi$
$374$	80.0604	4.13982
$375$	10.6213	0.548481
$376$	−3.45970	−0.178420
$377$	−12.0261	−0.619373
$378$	−2.39422	−0.123146
$379$	−7.98163	−0.409989	−0.204994	−	0.978763i	$-0.565718\pi$
$379$	−7.98163	−0.409989	−0.204994	+	0.978763i	$0.565718\pi$
$380$	45.2108	2.31926
$381$	−1.46097	−0.0748479
$382$	−47.9038	−2.45097
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	20.7340	1.05808
$385$	−12.8820	−0.656530
$386$	22.1867	1.12927
$387$	−0.665504	−0.0338295
$388$	32.9345	1.67199
$389$	2.16537	0.109789	0.0548943	−	0.998492i	$-0.482518\pi$
$389$	2.16537	0.109789	0.0548943	+	0.998492i	$0.482518\pi$
$390$	−10.5838	−0.535933
$391$	−32.4218	−1.63964
$392$	−4.14751	−0.209481
$393$	14.4357	0.728184
$394$	−22.3390	−1.12542
$395$	15.3704	0.773370
$396$	20.5940	1.03488
$397$	21.3257	1.07031	0.535154	−	0.844755i	$-0.320254\pi$
$397$	21.3257	1.07031	0.535154	+	0.844755i	$0.320254\pi$
$398$	23.0106	1.15342
$399$	−5.18852	−0.259751
$400$	1.11091	0.0555457
$401$	−12.4364	−0.621042	−0.310521	−	0.950566i	$-0.600504\pi$
$401$	−12.4364	−0.621042	−0.310521	+	0.950566i	$0.600504\pi$
$402$	−6.70450	−0.334390
$403$	16.4128	0.817582
$404$	−21.6616	−1.07770
$405$	−2.33465	−0.116010
$406$	−15.2066	−0.754690
$407$	18.7366	0.928740
$408$	25.1349	1.24436
$409$	−29.4861	−1.45800	−0.728998	−	0.684516i	$-0.760014\pi$
$409$	−29.4861	−1.45800	−0.728998	+	0.684516i	$0.760014\pi$
$410$	−54.9542	−2.71400
$411$	−0.289488	−0.0142794
$412$	64.3133	3.16849
$413$	6.76528	0.332898
$414$	−12.8089	−0.629522
$415$	12.9189	0.634164
$416$	−4.52945	−0.222074
$417$	10.4229	0.510414
$418$	68.5442	3.35261
$419$	28.1424	1.37485	0.687423	−	0.726257i	$-0.258742\pi$
$419$	28.1424	1.37485	0.687423	+	0.726257i	$0.258742\pi$
$420$	−8.71361	−0.425181
$421$	24.5795	1.19793	0.598965	−	0.800775i	$-0.295579\pi$
$421$	24.5795	1.19793	0.598965	+	0.800775i	$0.295579\pi$
$422$	14.6448	0.712896
$423$	0.834162	0.0405583
$424$	30.7696	1.49431
$425$	−2.73068	−0.132458
$426$	−18.5402	−0.898275
$427$	2.97737	0.144085
$428$	−3.79602	−0.183488
$429$	−10.4477	−0.504418
$430$	−3.71995	−0.179392
$431$	24.4922	1.17975	0.589873	−	0.807496i	$-0.299178\pi$
$431$	24.4922	1.17975	0.589873	+	0.807496i	$0.299178\pi$
$432$	2.46547	0.118620
$433$	−12.8563	−0.617833	−0.308916	−	0.951089i	$-0.599966\pi$
$433$	−12.8563	−0.617833	−0.308916	+	0.951089i	$0.599966\pi$
$434$	20.7535	0.996201
$435$	−14.8282	−0.710958
$436$	−72.6894	−3.48119
$437$	−27.7581	−1.32785
$438$	4.64375	0.221887
$439$	−18.9692	−0.905351	−0.452676	−	0.891675i	$-0.649530\pi$
$439$	−18.9692	−0.905351	−0.452676	+	0.891675i	$0.649530\pi$
$440$	53.4284	2.54710
$441$	1.00000	0.0476190
$442$	−27.4733	−1.30677
$443$	−25.1553	−1.19516	−0.597582	−	0.801808i	$-0.703872\pi$
$443$	−25.1553	−1.19516	−0.597582	+	0.801808i	$0.703872\pi$
$444$	12.6737	0.601469
$445$	−26.8834	−1.27440
$446$	−11.5671	−0.547720
$447$	1.07601	0.0508935
$448$	−10.6583	−0.503556
$449$	−20.0105	−0.944353	−0.472177	−	0.881504i	$-0.656532\pi$
$449$	−20.0105	−0.944353	−0.472177	+	0.881504i	$0.656532\pi$
$450$	−1.07881	−0.0508557
$451$	−54.2473	−2.55440
$452$	68.9491	3.24309
$453$	9.55337	0.448856
$454$	55.8927	2.62318
$455$	4.42057	0.207239
$456$	21.5194	1.00774
$457$	−36.2186	−1.69423	−0.847117	−	0.531406i	$-0.821664\pi$
$457$	−36.2186	−1.69423	−0.847117	+	0.531406i	$0.821664\pi$
$458$	−2.02119	−0.0944441
$459$	−6.06024	−0.282868
$460$	−46.6171	−2.17353
$461$	−20.5965	−0.959277	−0.479638	−	0.877466i	$-0.659232\pi$
$461$	−20.5965	−0.959277	−0.479638	+	0.877466i	$0.659232\pi$
$462$	−13.2108	−0.614620
$463$	10.3392	0.480501	0.240251	−	0.970711i	$-0.422770\pi$
$463$	10.3392	0.480501	0.240251	+	0.970711i	$0.422770\pi$
$464$	15.6591	0.726954
$465$	20.2371	0.938475
$466$	−7.90670	−0.366271
$467$	14.9131	0.690095	0.345047	−	0.938585i	$-0.387863\pi$
$467$	14.9131	0.690095	0.345047	+	0.938585i	$0.387863\pi$
$468$	−7.06696	−0.326671
$469$	2.80028	0.129305
$470$	4.66269	0.215074
$471$	2.60606	0.120081
$472$	−28.0591	−1.29152
$473$	−3.67209	−0.168843
$474$	15.7626	0.724001
$475$	−2.33789	−0.107270
$476$	−22.6187	−1.03672
$477$	−7.41882	−0.339684
$478$	21.6283	0.989258
$479$	26.6343	1.21695	0.608475	−	0.793573i	$-0.291782\pi$
$479$	26.6343	1.21695	0.608475	+	0.793573i	$0.291782\pi$
$480$	−5.58484	−0.254912
$481$	−6.42961	−0.293165
$482$	−49.4282	−2.25139
$483$	5.34991	0.243430
$484$	72.5772	3.29897
$485$	−20.6014	−0.935459
$486$	−2.39422	−0.108604
$487$	38.0417	1.72384	0.861918	−	0.507048i	$-0.169263\pi$
$487$	38.0417	1.72384	0.861918	+	0.507048i	$0.169263\pi$
$488$	−12.3487	−0.558999
$489$	−5.98339	−0.270578
$490$	5.58967	0.252516
$491$	−11.2032	−0.505592	−0.252796	−	0.967520i	$-0.581350\pi$
$491$	−11.2032	−0.505592	−0.252796	+	0.967520i	$0.581350\pi$
$492$	−36.6937	−1.65428
$493$	−38.4908	−1.73354
$494$	−23.5215	−1.05828
$495$	−12.8820	−0.579005
$496$	−21.3711	−0.959589
$497$	7.74372	0.347353
$498$	13.2485	0.593681
$499$	−23.1082	−1.03447	−0.517233	−	0.855844i	$-0.673038\pi$
$499$	−23.1082	−1.03447	−0.517233	+	0.855844i	$0.673038\pi$
$500$	39.6418	1.77284
$501$	10.3284	0.461440
$502$	−44.8503	−2.00177
$503$	3.74287	0.166886	0.0834431	−	0.996513i	$-0.473408\pi$
$503$	3.74287	0.166886	0.0834431	+	0.996513i	$0.473408\pi$
$504$	−4.14751	−0.184745
$505$	13.5499	0.602962
$506$	−70.6764	−3.14195
$507$	−9.41481	−0.418126
$508$	−5.45279	−0.241928
$509$	−32.3940	−1.43584	−0.717918	−	0.696127i	$-0.754905\pi$
$509$	−32.3940	−1.43584	−0.717918	+	0.696127i	$0.754905\pi$
$510$	−33.8748	−1.50000
$511$	−1.93956	−0.0858012
$512$	26.3489	1.16447
$513$	−5.18852	−0.229079
$514$	−14.3805	−0.634295
$515$	−40.2296	−1.77273
$516$	−2.48386	−0.109346
$517$	4.60271	0.202427
$518$	−8.13004	−0.357214
$519$	2.90031	0.127310
$520$	−18.3344	−0.804015
$521$	−23.3771	−1.02417	−0.512086	−	0.858934i	$-0.671127\pi$
$521$	−23.3771	−1.02417	−0.512086	+	0.858934i	$0.671127\pi$
$522$	−15.2066	−0.665574
$523$	30.7539	1.34477	0.672386	−	0.740200i	$-0.265269\pi$
$523$	30.7539	1.34477	0.672386	+	0.740200i	$0.265269\pi$
$524$	53.8783	2.35369
$525$	0.450590	0.0196654
$526$	1.50061	0.0654298
$527$	52.5312	2.28830
$528$	13.6039	0.592032
$529$	5.62158	0.244417
$530$	−41.4688	−1.80129
$531$	6.76528	0.293588
$532$	−19.3651	−0.839584
$533$	18.6153	0.806320
$534$	−27.5694	−1.19304
$535$	2.37451	0.102659
$536$	−11.6142	−0.501658
$537$	0.579498	0.0250072
$538$	62.1291	2.67858
$539$	5.51776	0.237667
$540$	−8.71361	−0.374974
$541$	28.2394	1.21411	0.607054	−	0.794660i	$-0.292351\pi$
$541$	28.2394	1.21411	0.607054	+	0.794660i	$0.292351\pi$
$542$	68.3768	2.93704
$543$	−13.9600	−0.599080
$544$	−14.4970	−0.621555
$545$	45.4691	1.94768
$546$	4.53337	0.194010
$547$	7.45816	0.318888	0.159444	−	0.987207i	$-0.449030\pi$
$547$	7.45816	0.318888	0.159444	+	0.987207i	$0.449030\pi$
$548$	−1.08046	−0.0461548
$549$	2.97737	0.127071
$550$	−5.95263	−0.253821
$551$	−32.9542	−1.40389
$552$	−22.1888	−0.944419
$553$	−6.58361	−0.279964
$554$	19.6820	0.836208
$555$	−7.92775	−0.336514
$556$	38.9015	1.64979
$557$	−13.6985	−0.580422	−0.290211	−	0.956963i	$-0.593725\pi$
$557$	−13.6985	−0.580422	−0.290211	+	0.956963i	$0.593725\pi$
$558$	20.7535	0.878567
$559$	1.26011	0.0532968
$560$	−5.75600	−0.243235
$561$	−33.4390	−1.41180
$562$	−11.3684	−0.479547
$563$	12.5384	0.528429	0.264214	−	0.964464i	$-0.414887\pi$
$563$	12.5384	0.528429	0.264214	+	0.964464i	$0.414887\pi$
$564$	3.11334	0.131095
$565$	−43.1295	−1.81447
$566$	−43.7329	−1.83823
$567$	1.00000	0.0419961
$568$	−32.1172	−1.34761
$569$	−6.80204	−0.285156	−0.142578	−	0.989784i	$-0.545539\pi$
$569$	−6.80204	−0.285156	−0.142578	+	0.989784i	$0.545539\pi$
$570$	−29.0021	−1.21476
$571$	18.3127	0.766363	0.383181	−	0.923673i	$-0.374828\pi$
$571$	18.3127	0.766363	0.383181	+	0.923673i	$0.374828\pi$
$572$	−38.9938	−1.63041
$573$	20.0081	0.835850
$574$	23.5385	0.982479
$575$	2.41062	0.100530
$576$	−10.6583	−0.444095
$577$	31.6776	1.31876	0.659378	−	0.751812i	$-0.270820\pi$
$577$	31.6776	1.31876	0.659378	+	0.751812i	$0.270820\pi$
$578$	−47.2298	−1.96450
$579$	−9.26677	−0.385114
$580$	−55.3433	−2.29801
$581$	−5.53355	−0.229570
$582$	−21.1270	−0.875743
$583$	−40.9353	−1.69537
$584$	8.04436	0.332878
$585$	4.42057	0.182768
$586$	5.18702	0.214274
$587$	32.8707	1.35672	0.678359	−	0.734731i	$-0.262692\pi$
$587$	32.8707	1.35672	0.678359	+	0.734731i	$0.262692\pi$
$588$	3.73230	0.153917
$589$	44.9750	1.85316
$590$	37.8157	1.55685
$591$	9.33036	0.383800
$592$	8.37196	0.344086
$593$	−1.72709	−0.0709233	−0.0354616	−	0.999371i	$-0.511290\pi$
$593$	−1.72709	−0.0709233	−0.0354616	+	0.999371i	$0.511290\pi$
$594$	−13.2108	−0.542044
$595$	14.1485	0.580034
$596$	4.01599	0.164502
$597$	−9.61088	−0.393347
$598$	24.2531	0.991784
$599$	8.30268	0.339238	0.169619	−	0.985510i	$-0.445746\pi$
$599$	8.30268	0.339238	0.169619	+	0.985510i	$0.445746\pi$
$600$	−1.86883	−0.0762945
$601$	25.9049	1.05668	0.528342	−	0.849032i	$-0.322814\pi$
$601$	25.9049	1.05668	0.528342	+	0.849032i	$0.322814\pi$
$602$	1.59336	0.0649407
$603$	2.80028	0.114036
$604$	35.6560	1.45082
$605$	−45.3989	−1.84573
$606$	13.8956	0.564472
$607$	26.7079	1.08404	0.542020	−	0.840365i	$-0.317660\pi$
$607$	26.7079	1.08404	0.542020	+	0.840365i	$0.317660\pi$
$608$	−12.4117	−0.503362
$609$	6.35136	0.257370
$610$	16.6425	0.673836
$611$	−1.57945	−0.0638978
$612$	−22.6187	−0.914305
$613$	32.4423	1.31033	0.655166	−	0.755485i	$-0.272599\pi$
$613$	32.4423	1.31033	0.655166	+	0.755485i	$0.272599\pi$
$614$	−75.6506	−3.05301
$615$	22.9528	0.925548
$616$	−22.8850	−0.922063
$617$	−31.6155	−1.27279	−0.636397	−	0.771362i	$-0.719576\pi$
$617$	−31.6155	−1.27279	−0.636397	+	0.771362i	$0.719576\pi$
$618$	−41.2562	−1.65957
$619$	−31.7052	−1.27434	−0.637171	−	0.770723i	$-0.719895\pi$
$619$	−31.7052	−1.27434	−0.637171	+	0.770723i	$0.719895\pi$
$620$	75.5311	3.03340
$621$	5.34991	0.214685
$622$	1.84149	0.0738372
$623$	11.5150	0.461337
$624$	−4.66826	−0.186880
$625$	−27.0499	−1.08200
$626$	−5.66439	−0.226394
$627$	−28.6290	−1.14333
$628$	9.72661	0.388134
$629$	−20.5787	−0.820528
$630$	5.58967	0.222698
$631$	44.4679	1.77024	0.885120	−	0.465363i	$-0.154076\pi$
$631$	44.4679	1.77024	0.885120	+	0.465363i	$0.154076\pi$
$632$	27.3056	1.08616
$633$	−6.11671	−0.243117
$634$	−47.4480	−1.88440
$635$	3.41086	0.135356
$636$	−27.6893	−1.09795
$637$	−1.89346	−0.0750216
$638$	−83.9063	−3.32188
$639$	7.74372	0.306337
$640$	−48.4066	−1.91344
$641$	−27.9390	−1.10352	−0.551762	−	0.834002i	$-0.686044\pi$
$641$	−27.9390	−1.10352	−0.551762	+	0.834002i	$0.686044\pi$
$642$	2.43510	0.0961056
$643$	−27.9839	−1.10358	−0.551788	−	0.833985i	$-0.686054\pi$
$643$	−27.9839	−1.10358	−0.551788	+	0.833985i	$0.686054\pi$
$644$	19.9675	0.786829
$645$	1.55372	0.0611776
$646$	−75.2832	−2.96198
$647$	33.4315	1.31433	0.657164	−	0.753748i	$-0.271756\pi$
$647$	33.4315	1.31433	0.657164	+	0.753748i	$0.271756\pi$
$648$	−4.14751	−0.162930
$649$	37.3292	1.46530
$650$	2.04269	0.0801208
$651$	−8.66817	−0.339732
$652$	−22.3318	−0.874582
$653$	27.4488	1.07415	0.537077	−	0.843533i	$-0.319528\pi$
$653$	27.4488	1.07415	0.537077	+	0.843533i	$0.319528\pi$
$654$	46.6293	1.82335
$655$	−33.7023	−1.31686
$656$	−24.2389	−0.946372
$657$	−1.93956	−0.0756696
$658$	−1.99717	−0.0778578
$659$	13.8303	0.538754	0.269377	−	0.963035i	$-0.413182\pi$
$659$	13.8303	0.538754	0.269377	+	0.963035i	$0.413182\pi$
$660$	−48.0797	−1.87150
$661$	−30.2672	−1.17726	−0.588628	−	0.808404i	$-0.700332\pi$
$661$	−30.2672	−1.17726	−0.588628	+	0.808404i	$0.700332\pi$
$662$	−65.2825	−2.53728
$663$	11.4748	0.445646
$664$	22.9505	0.890650
$665$	12.1134	0.469737
$666$	−8.13004	−0.315033
$667$	33.9792	1.31568
$668$	38.5488	1.49150
$669$	4.83128	0.186788
$670$	15.6527	0.604715
$671$	16.4284	0.634213
$672$	2.39215	0.0922793
$673$	28.4422	1.09637	0.548184	−	0.836358i	$-0.315319\pi$
$673$	28.4422	1.09637	0.548184	+	0.836358i	$0.315319\pi$
$674$	11.6238	0.447733
$675$	0.450590	0.0173432
$676$	−35.1389	−1.35150
$677$	17.7159	0.680878	0.340439	−	0.940267i	$-0.389424\pi$
$677$	17.7159	0.680878	0.340439	+	0.940267i	$0.389424\pi$
$678$	−44.2300	−1.69864
$679$	8.82417	0.338641
$680$	−58.6813	−2.25032
$681$	−23.3448	−0.894576
$682$	114.513	4.38493
$683$	13.3657	0.511424	0.255712	−	0.966753i	$-0.417690\pi$
$683$	13.3657	0.511424	0.255712	+	0.966753i	$0.417690\pi$
$684$	−19.3651	−0.740444
$685$	0.675853	0.0258230
$686$	−2.39422	−0.0914118
$687$	0.844195	0.0322081
$688$	−1.64078	−0.0625540
$689$	14.0472	0.535157
$690$	29.9043	1.13844
$691$	36.4018	1.38479	0.692395	−	0.721519i	$-0.256556\pi$
$691$	36.4018	1.38479	0.692395	+	0.721519i	$0.256556\pi$
$692$	10.8248	0.411499
$693$	5.51776	0.209602
$694$	−46.1229	−1.75080
$695$	−24.3339	−0.923038
$696$	−26.3424	−0.998504
$697$	59.5806	2.25678
$698$	−33.9764	−1.28603
$699$	3.30241	0.124908
$700$	1.68174	0.0635637
$701$	−52.2970	−1.97523	−0.987615	−	0.156894i	$-0.949852\pi$
$701$	−52.2970	−1.97523	−0.987615	+	0.156894i	$0.949852\pi$
$702$	4.53337	0.171101
$703$	−17.6186	−0.664499
$704$	−58.8098	−2.21648
$705$	−1.94748	−0.0733462
$706$	12.4551	0.468753
$707$	−5.80382	−0.218275
$708$	25.2501	0.948955
$709$	22.2964	0.837358	0.418679	−	0.908134i	$-0.362493\pi$
$709$	22.2964	0.837358	0.418679	+	0.908134i	$0.362493\pi$
$710$	43.2848	1.62445
$711$	−6.58361	−0.246905
$712$	−47.7584	−1.78982
$713$	−46.3740	−1.73672
$714$	14.5096	0.543007
$715$	24.3916	0.912196
$716$	2.16286	0.0808298
$717$	−9.03356	−0.337364
$718$	6.36203	0.237429
$719$	0.220639	0.00822844	0.00411422	−	0.999992i	$-0.498690\pi$
$719$	0.220639	0.00822844	0.00411422	+	0.999992i	$0.498690\pi$
$720$	−5.75600	−0.214513
$721$	17.2316	0.641736
$722$	−18.9640	−0.705767
$723$	20.6448	0.767788
$724$	−52.1028	−1.93639
$725$	2.86186	0.106287
$726$	−46.5574	−1.72791
$727$	22.7474	0.843655	0.421828	−	0.906676i	$-0.361389\pi$
$727$	22.7474	0.843655	0.421828	+	0.906676i	$0.361389\pi$
$728$	7.85315	0.291057
$729$	1.00000	0.0370370
$730$	−10.8415	−0.401263
$731$	4.03312	0.149170
$732$	11.1124	0.410728
$733$	7.35096	0.271514	0.135757	−	0.990742i	$-0.456653\pi$
$733$	7.35096	0.271514	0.135757	+	0.990742i	$0.456653\pi$
$734$	29.0761	1.07322
$735$	−2.33465	−0.0861149
$736$	12.7978	0.471734
$737$	15.4513	0.569156
$738$	23.5385	0.866465
$739$	−2.36564	−0.0870213	−0.0435106	−	0.999053i	$-0.513854\pi$
$739$	−2.36564	−0.0870213	−0.0435106	+	0.999053i	$0.513854\pi$
$740$	−29.5888	−1.08770
$741$	9.82426	0.360903
$742$	17.7623	0.652075
$743$	6.48543	0.237927	0.118964	−	0.992899i	$-0.462043\pi$
$743$	6.48543	0.237927	0.118964	+	0.992899i	$0.462043\pi$
$744$	35.9513	1.31804
$745$	−2.51211	−0.0920365
$746$	−17.5569	−0.642804
$747$	−5.53355	−0.202462
$748$	−124.804	−4.56330
$749$	−1.01707	−0.0371630
$750$	−25.4297	−0.928562
$751$	28.0431	1.02331	0.511654	−	0.859192i	$-0.329033\pi$
$751$	28.0431	1.02331	0.511654	+	0.859192i	$0.329033\pi$
$752$	2.05660	0.0749964
$753$	18.7327	0.682659
$754$	28.7931	1.04858
$755$	−22.3038	−0.811717
$756$	3.73230	0.135742
$757$	−27.6931	−1.00652	−0.503262	−	0.864134i	$-0.667867\pi$
$757$	−27.6931	−1.00652	−0.503262	+	0.864134i	$0.667867\pi$
$758$	19.1098	0.694099
$759$	29.5196	1.07149
$760$	−50.2404	−1.82241
$761$	16.9507	0.614462	0.307231	−	0.951635i	$-0.400598\pi$
$761$	16.9507	0.614462	0.307231	+	0.951635i	$0.400598\pi$
$762$	3.49789	0.126715
$763$	−19.4758	−0.705070
$764$	74.6762	2.70169
$765$	14.1485	0.511542
$766$	−2.39422	−0.0865068
$767$	−12.8098	−0.462535
$768$	−28.3252	−1.02210
$769$	39.0317	1.40752	0.703760	−	0.710438i	$-0.251503\pi$
$769$	39.0317	1.40752	0.703760	+	0.710438i	$0.251503\pi$
$770$	30.8425	1.11149
$771$	6.00632	0.216312
$772$	−34.5864	−1.24479
$773$	19.9010	0.715790	0.357895	−	0.933762i	$-0.383495\pi$
$773$	19.9010	0.715790	0.357895	+	0.933762i	$0.383495\pi$
$774$	1.59336	0.0572723
$775$	−3.90579	−0.140300
$776$	−36.5984	−1.31380
$777$	3.39569	0.121820
$778$	−5.18437	−0.185869
$779$	51.0103	1.82764
$780$	16.4989	0.590755
$781$	42.7280	1.52893
$782$	77.6250	2.77586
$783$	6.35136	0.226979
$784$	2.46547	0.0880523
$785$	−6.08425	−0.217156
$786$	−34.5622	−1.23279
$787$	−43.3530	−1.54537	−0.772683	−	0.634792i	$-0.781086\pi$
$787$	−43.3530	−1.54537	−0.772683	+	0.634792i	$0.781086\pi$
$788$	34.8237	1.24054
$789$	−0.626764	−0.0223134
$790$	−36.8002	−1.30929
$791$	18.4736	0.656847
$792$	−22.8850	−0.813183
$793$	−5.63754	−0.200195
$794$	−51.0585	−1.81200
$795$	17.3203	0.614289
$796$	−35.8707	−1.27140
$797$	43.7149	1.54846	0.774231	−	0.632904i	$-0.218137\pi$
$797$	43.7149	1.54846	0.774231	+	0.632904i	$0.218137\pi$
$798$	12.4225	0.439751
$799$	−5.05523	−0.178841
$800$	1.07788	0.0381088
$801$	11.5150	0.406861
$802$	29.7754	1.05141
$803$	−10.7021	−0.377667
$804$	10.4515	0.368596
$805$	−12.4902	−0.440221
$806$	−39.2960	−1.38414
$807$	−25.9496	−0.913469
$808$	24.0714	0.846829
$809$	40.6658	1.42973	0.714867	−	0.699260i	$-0.246487\pi$
$809$	40.6658	1.42973	0.714867	+	0.699260i	$0.246487\pi$
$810$	5.58967	0.196401
$811$	−31.7051	−1.11332	−0.556658	−	0.830742i	$-0.687916\pi$
$811$	−31.7051	−1.11332	−0.556658	+	0.830742i	$0.687916\pi$
$812$	23.7052	0.831889
$813$	−28.5591	−1.00161
$814$	−44.8597	−1.57233
$815$	13.9691	0.489317
$816$	−14.9413	−0.523051
$817$	3.45298	0.120805
$818$	70.5964	2.46834
$819$	−1.89346	−0.0661629
$820$	85.6669	2.99162
$821$	20.9435	0.730932	0.365466	−	0.930825i	$-0.380910\pi$
$821$	20.9435	0.730932	0.365466	+	0.930825i	$0.380910\pi$
$822$	0.693098	0.0241746
$823$	45.6060	1.58972	0.794862	−	0.606790i	$-0.207543\pi$
$823$	45.6060	1.58972	0.794862	+	0.606790i	$0.207543\pi$
$824$	−71.4681	−2.48971
$825$	2.48625	0.0865601
$826$	−16.1976	−0.563586
$827$	−49.6689	−1.72716	−0.863579	−	0.504213i	$-0.831783\pi$
$827$	−49.6689	−1.72716	−0.863579	+	0.504213i	$0.831783\pi$
$828$	19.9675	0.693918
$829$	−5.60082	−0.194525	−0.0972623	−	0.995259i	$-0.531009\pi$
$829$	−5.60082	−0.194525	−0.0972623	+	0.995259i	$0.531009\pi$
$830$	−30.9307	−1.07362
$831$	−8.22063	−0.285170
$832$	20.1810	0.699651
$833$	−6.06024	−0.209975
$834$	−24.9548	−0.864115
$835$	−24.1133	−0.834474
$836$	−106.852	−3.69556
$837$	−8.66817	−0.299616
$838$	−67.3791	−2.32757
$839$	34.6993	1.19795	0.598977	−	0.800766i	$-0.295574\pi$
$839$	34.6993	1.19795	0.598977	+	0.800766i	$0.295574\pi$
$840$	9.68299	0.334095
$841$	11.3398	0.391028
$842$	−58.8487	−2.02806
$843$	4.74826	0.163539
$844$	−22.8294	−0.785821
$845$	21.9803	0.756145
$846$	−1.99717	−0.0686641
$847$	19.4457	0.668163
$848$	−18.2908	−0.628110
$849$	18.2660	0.626888
$850$	6.53787	0.224247
$851$	18.1667	0.622745
$852$	28.9019	0.990162
$853$	−40.3313	−1.38092	−0.690459	−	0.723372i	$-0.742591\pi$
$853$	−40.3313	−1.38092	−0.690459	+	0.723372i	$0.742591\pi$
$854$	−7.12849	−0.243932
$855$	12.1134	0.414269
$856$	4.21832	0.144179
$857$	14.7224	0.502909	0.251454	−	0.967869i	$-0.419091\pi$
$857$	14.7224	0.502909	0.251454	+	0.967869i	$0.419091\pi$
$858$	25.0140	0.853965
$859$	33.4046	1.13975	0.569876	−	0.821731i	$-0.306991\pi$
$859$	33.4046	1.13975	0.569876	+	0.821731i	$0.306991\pi$
$860$	5.79895	0.197742
$861$	−9.83139	−0.335053
$862$	−58.6397	−1.99728
$863$	53.2509	1.81268	0.906341	−	0.422546i	$-0.138864\pi$
$863$	53.2509	1.81268	0.906341	+	0.422546i	$0.138864\pi$
$864$	2.39215	0.0813827
$865$	−6.77121	−0.230228
$866$	30.7808	1.04597
$867$	19.7266	0.669949
$868$	−32.3522	−1.09811
$869$	−36.3268	−1.23230
$870$	35.5020	1.20363
$871$	−5.30223	−0.179659
$872$	80.7760	2.73542
$873$	8.82417	0.298653
$874$	66.4591	2.24801
$875$	10.6213	0.359065
$876$	−7.23903	−0.244584
$877$	2.17512	0.0734485	0.0367243	−	0.999325i	$-0.488308\pi$
$877$	2.17512	0.0734485	0.0367243	+	0.999325i	$0.488308\pi$
$878$	45.4165	1.53273
$879$	−2.16647	−0.0730733
$880$	−31.7602	−1.07064
$881$	−18.2001	−0.613178	−0.306589	−	0.951842i	$-0.599188\pi$
$881$	−18.2001	−0.613178	−0.306589	+	0.951842i	$0.599188\pi$
$882$	−2.39422	−0.0806177
$883$	53.1311	1.78800	0.894002	−	0.448062i	$-0.147886\pi$
$883$	53.1311	1.78800	0.894002	+	0.448062i	$0.147886\pi$
$884$	42.8275	1.44045
$885$	−15.7946	−0.530928
$886$	60.2274	2.02338
$887$	25.6989	0.862885	0.431442	−	0.902141i	$-0.358005\pi$
$887$	25.6989	0.862885	0.431442	+	0.902141i	$0.358005\pi$
$888$	−14.0837	−0.472617
$889$	−1.46097	−0.0489995
$890$	64.3648	2.15751
$891$	5.51776	0.184852
$892$	18.0318	0.603748
$893$	−4.32807	−0.144833
$894$	−2.57621	−0.0861613
$895$	−1.35292	−0.0452233
$896$	20.7340	0.692673
$897$	−10.1299	−0.338226
$898$	47.9096	1.59876
$899$	−55.0547	−1.83618
$900$	1.68174	0.0560579
$901$	44.9599	1.49783
$902$	129.880	4.32453
$903$	−0.665504	−0.0221466
$904$	−76.6196	−2.54833
$905$	32.5917	1.08338
$906$	−22.8729	−0.759901
$907$	10.6747	0.354447	0.177224	−	0.984171i	$-0.443288\pi$
$907$	10.6747	0.354447	0.177224	+	0.984171i	$0.443288\pi$
$908$	−87.1300	−2.89151
$909$	−5.80382	−0.192501
$910$	−10.5838	−0.350850
$911$	41.2600	1.36700	0.683502	−	0.729949i	$-0.260456\pi$
$911$	41.2600	1.36700	0.683502	+	0.729949i	$0.260456\pi$
$912$	−12.7921	−0.423589
$913$	−30.5328	−1.01049
$914$	86.7153	2.86829
$915$	−6.95112	−0.229797
$916$	3.15079	0.104105
$917$	14.4357	0.476708
$918$	14.5096	0.478887
$919$	29.6706	0.978744	0.489372	−	0.872075i	$-0.337226\pi$
$919$	29.6706	0.978744	0.489372	+	0.872075i	$0.337226\pi$
$920$	51.8032	1.70790
$921$	31.5971	1.04116
$922$	49.3127	1.62403
$923$	−14.6624	−0.482620
$924$	20.5940	0.677491
$925$	1.53006	0.0503082
$926$	−24.7542	−0.813475
$927$	17.2316	0.565958
$928$	15.1934	0.498749
$929$	−57.1162	−1.87392	−0.936961	−	0.349434i	$-0.886374\pi$
$929$	−57.1162	−1.87392	−0.936961	+	0.349434i	$0.886374\pi$
$930$	−48.4522	−1.58881
$931$	−5.18852	−0.170047
$932$	12.3256	0.403738
$933$	−0.769141	−0.0251805
$934$	−35.7052	−1.16831
$935$	78.0683	2.55311
$936$	7.85315	0.256688
$937$	23.6340	0.772090	0.386045	−	0.922480i	$-0.373841\pi$
$937$	23.6340	0.772090	0.386045	+	0.922480i	$0.373841\pi$
$938$	−6.70450	−0.218910
$939$	2.36586	0.0772068
$940$	−7.26857	−0.237075
$941$	−26.2760	−0.856572	−0.428286	−	0.903643i	$-0.640882\pi$
$941$	−26.2760	−0.856572	−0.428286	+	0.903643i	$0.640882\pi$
$942$	−6.23950	−0.203294
$943$	−52.5971	−1.71280
$944$	16.6796	0.542874
$945$	−2.33465	−0.0759462
$946$	8.79181	0.285846
$947$	8.50845	0.276487	0.138244	−	0.990398i	$-0.455854\pi$
$947$	8.50845	0.276487	0.138244	+	0.990398i	$0.455854\pi$
$948$	−24.5720	−0.798062
$949$	3.67249	0.119214
$950$	5.59744	0.181605
$951$	19.8177	0.642633
$952$	25.1349	0.814628
$953$	7.85770	0.254536	0.127268	−	0.991868i	$-0.459379\pi$
$953$	7.85770	0.254536	0.127268	+	0.991868i	$0.459379\pi$
$954$	17.7623	0.575076
$955$	−46.7119	−1.51156
$956$	−33.7160	−1.09045
$957$	35.0453	1.13285
$958$	−63.7683	−2.06026
$959$	−0.289488	−0.00934805
$960$	24.8833	0.803106
$961$	44.1372	1.42378
$962$	15.3939	0.496320
$963$	−1.01707	−0.0327747
$964$	77.0525	2.48170
$965$	21.6347	0.696445
$966$	−12.8089	−0.412119
$967$	−43.1228	−1.38674	−0.693369	−	0.720583i	$-0.743874\pi$
$967$	−43.1228	−1.38674	−0.693369	+	0.720583i	$0.743874\pi$
$968$	−80.6513	−2.59223
$969$	31.4437	1.01012
$970$	49.3242	1.58371
$971$	−10.6543	−0.341913	−0.170956	−	0.985279i	$-0.554686\pi$
$971$	−10.6543	−0.341913	−0.170956	+	0.985279i	$0.554686\pi$
$972$	3.73230	0.119714
$973$	10.4229	0.334144
$974$	−91.0804	−2.91840
$975$	−0.853174	−0.0273234
$976$	7.34061	0.234967
$977$	−19.9126	−0.637061	−0.318530	−	0.947913i	$-0.603189\pi$
$977$	−19.9126	−0.637061	−0.318530	+	0.947913i	$0.603189\pi$
$978$	14.3256	0.458081
$979$	63.5368	2.03065
$980$	−8.71361	−0.278346
$981$	−19.4758	−0.621814
$982$	26.8229	0.855953
$983$	18.0022	0.574182	0.287091	−	0.957903i	$-0.407312\pi$
$983$	18.0022	0.574182	0.287091	+	0.957903i	$0.407312\pi$
$984$	40.7758	1.29988
$985$	−21.7831	−0.694068
$986$	92.1556	2.93483
$987$	0.834162	0.0265517
$988$	36.6671	1.16654
$989$	−3.56039	−0.113214
$990$	30.8425	0.980238
$991$	−1.16505	−0.0370089	−0.0185045	−	0.999829i	$-0.505890\pi$
$991$	−1.16505	−0.0370089	−0.0185045	+	0.999829i	$0.505890\pi$
$992$	−20.7356	−0.658355
$993$	27.2667	0.865282
$994$	−18.5402	−0.588059
$995$	22.4380	0.711333
$996$	−20.6529	−0.654411
$997$	−33.1651	−1.05035	−0.525174	−	0.850995i	$-0.676000\pi$
$997$	−33.1651	−1.05035	−0.525174	+	0.850995i	$0.676000\pi$
$998$	55.3263	1.75132
$999$	3.39569	0.107435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.u.1.4	✓	53

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.u.1.4	✓	53	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)

\(f(q)\)	\(=\)	\(q-2.39422 q^{2} +1.00000 q^{3} +3.73230 q^{4} -2.33465 q^{5} -2.39422 q^{6} +1.00000 q^{7} -4.14751 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.39422 q^{2} +1.00000 q^{3} +3.73230 q^{4} -2.33465 q^{5} -2.39422 q^{6} +1.00000 q^{7} -4.14751 q^{8} +1.00000 q^{9} +5.58967 q^{10} +5.51776 q^{11} +3.73230 q^{12} -1.89346 q^{13} -2.39422 q^{14} -2.33465 q^{15} +2.46547 q^{16} -6.06024 q^{17} -2.39422 q^{18} -5.18852 q^{19} -8.71361 q^{20} +1.00000 q^{21} -13.2108 q^{22} +5.34991 q^{23} -4.14751 q^{24} +0.450590 q^{25} +4.53337 q^{26} +1.00000 q^{27} +3.73230 q^{28} +6.35136 q^{29} +5.58967 q^{30} -8.66817 q^{31} +2.39215 q^{32} +5.51776 q^{33} +14.5096 q^{34} -2.33465 q^{35} +3.73230 q^{36} +3.39569 q^{37} +12.4225 q^{38} -1.89346 q^{39} +9.68299 q^{40} -9.83139 q^{41} -2.39422 q^{42} -0.665504 q^{43} +20.5940 q^{44} -2.33465 q^{45} -12.8089 q^{46} +0.834162 q^{47} +2.46547 q^{48} +1.00000 q^{49} -1.07881 q^{50} -6.06024 q^{51} -7.06696 q^{52} -7.41882 q^{53} -2.39422 q^{54} -12.8820 q^{55} -4.14751 q^{56} -5.18852 q^{57} -15.2066 q^{58} +6.76528 q^{59} -8.71361 q^{60} +2.97737 q^{61} +20.7535 q^{62} +1.00000 q^{63} -10.6583 q^{64} +4.42057 q^{65} -13.2108 q^{66} +2.80028 q^{67} -22.6187 q^{68} +5.34991 q^{69} +5.58967 q^{70} +7.74372 q^{71} -4.14751 q^{72} -1.93956 q^{73} -8.13004 q^{74} +0.450590 q^{75} -19.3651 q^{76} +5.51776 q^{77} +4.53337 q^{78} -6.58361 q^{79} -5.75600 q^{80} +1.00000 q^{81} +23.5385 q^{82} -5.53355 q^{83} +3.73230 q^{84} +14.1485 q^{85} +1.59336 q^{86} +6.35136 q^{87} -22.8850 q^{88} +11.5150 q^{89} +5.58967 q^{90} -1.89346 q^{91} +19.9675 q^{92} -8.66817 q^{93} -1.99717 q^{94} +12.1134 q^{95} +2.39215 q^{96} +8.82417 q^{97} -2.39422 q^{98} +5.51776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9}+O(q^{10}) \) 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9	\( 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9} + 2 q^{10} + 46 q^{11} + 63 q^{12} + 32 q^{13} + 11 q^{14} + 24 q^{15} + 67 q^{16} + 46 q^{17} + 11 q^{18} + 14 q^{19} + 53 q^{20} + 53 q^{21} + 13 q^{22} + 68 q^{23} + 30 q^{24} + 71 q^{25} + 11 q^{26} + 53 q^{27} + 63 q^{28} + 55 q^{29} + 2 q^{30} - 2 q^{31} + 51 q^{32} + 46 q^{33} - 7 q^{34} + 24 q^{35} + 63 q^{36} + 53 q^{37} + 16 q^{38} + 32 q^{39} - 20 q^{40} + 38 q^{41} + 11 q^{42} + 36 q^{43} + 70 q^{44} + 24 q^{45} + 4 q^{46} + 51 q^{47} + 67 q^{48} + 53 q^{49} + 32 q^{50} + 46 q^{51} + 10 q^{52} + 104 q^{53} + 11 q^{54} + 11 q^{55} + 30 q^{56} + 14 q^{57} + 4 q^{58} + 36 q^{59} + 53 q^{60} + 3 q^{61} + 25 q^{62} + 53 q^{63} + 82 q^{64} + 46 q^{65} + 13 q^{66} + 54 q^{67} + 88 q^{68} + 68 q^{69} + 2 q^{70} + 101 q^{71} + 30 q^{72} + q^{73} + 32 q^{74} + 71 q^{75} - 35 q^{76} + 46 q^{77} + 11 q^{78} + 14 q^{79} + 39 q^{80} + 53 q^{81} - 29 q^{82} + 38 q^{83} + 63 q^{84} + 16 q^{85} + 23 q^{86} + 55 q^{87} - 8 q^{88} + 52 q^{89} + 2 q^{90} + 32 q^{91} + 76 q^{92} - 2 q^{93} - 53 q^{94} + 46 q^{95} + 51 q^{96} - 3 q^{97} + 11 q^{98} + 46 q^{99}+O(q^{100}) \) 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9 + 2 * q^10 + 46 * q^11 + 63 * q^12 + 32 * q^13 + 11 * q^14 + 24 * q^15 + 67 * q^16 + 46 * q^17 + 11 * q^18 + 14 * q^19 + 53 * q^20 + 53 * q^21 + 13 * q^22 + 68 * q^23 + 30 * q^24 + 71 * q^25 + 11 * q^26 + 53 * q^27 + 63 * q^28 + 55 * q^29 + 2 * q^30 - 2 * q^31 + 51 * q^32 + 46 * q^33 - 7 * q^34 + 24 * q^35 + 63 * q^36 + 53 * q^37 + 16 * q^38 + 32 * q^39 - 20 * q^40 + 38 * q^41 + 11 * q^42 + 36 * q^43 + 70 * q^44 + 24 * q^45 + 4 * q^46 + 51 * q^47 + 67 * q^48 + 53 * q^49 + 32 * q^50 + 46 * q^51 + 10 * q^52 + 104 * q^53 + 11 * q^54 + 11 * q^55 + 30 * q^56 + 14 * q^57 + 4 * q^58 + 36 * q^59 + 53 * q^60 + 3 * q^61 + 25 * q^62 + 53 * q^63 + 82 * q^64 + 46 * q^65 + 13 * q^66 + 54 * q^67 + 88 * q^68 + 68 * q^69 + 2 * q^70 + 101 * q^71 + 30 * q^72 + q^73 + 32 * q^74 + 71 * q^75 - 35 * q^76 + 46 * q^77 + 11 * q^78 + 14 * q^79 + 39 * q^80 + 53 * q^81 - 29 * q^82 + 38 * q^83 + 63 * q^84 + 16 * q^85 + 23 * q^86 + 55 * q^87 - 8 * q^88 + 52 * q^89 + 2 * q^90 + 32 * q^91 + 76 * q^92 - 2 * q^93 - 53 * q^94 + 46 * q^95 + 51 * q^96 - 3 * q^97 + 11 * q^98 + 46 * q^99

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