LMFDB - Embedded newform 8043.2.a.t.1.10

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:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-1.90192 q^{2} -1.00000 q^{3} +1.61732 q^{4} +0.767188 q^{5} +1.90192 q^{6} +1.00000 q^{7} +0.727834 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.90192 q^{2} -1.00000 q^{3} +1.61732 q^{4} +0.767188 q^{5} +1.90192 q^{6} +1.00000 q^{7} +0.727834 q^{8} +1.00000 q^{9} -1.45913 q^{10} +0.295463 q^{11} -1.61732 q^{12} +3.77953 q^{13} -1.90192 q^{14} -0.767188 q^{15} -4.61892 q^{16} +5.24425 q^{17} -1.90192 q^{18} -3.76509 q^{19} +1.24079 q^{20} -1.00000 q^{21} -0.561948 q^{22} -1.71339 q^{23} -0.727834 q^{24} -4.41142 q^{25} -7.18839 q^{26} -1.00000 q^{27} +1.61732 q^{28} -7.83095 q^{29} +1.45913 q^{30} +0.600616 q^{31} +7.32917 q^{32} -0.295463 q^{33} -9.97417 q^{34} +0.767188 q^{35} +1.61732 q^{36} -3.78080 q^{37} +7.16091 q^{38} -3.77953 q^{39} +0.558386 q^{40} +8.68124 q^{41} +1.90192 q^{42} +2.68115 q^{43} +0.477857 q^{44} +0.767188 q^{45} +3.25875 q^{46} -10.2548 q^{47} +4.61892 q^{48} +1.00000 q^{49} +8.39019 q^{50} -5.24425 q^{51} +6.11270 q^{52} -7.17506 q^{53} +1.90192 q^{54} +0.226676 q^{55} +0.727834 q^{56} +3.76509 q^{57} +14.8939 q^{58} +9.38143 q^{59} -1.24079 q^{60} +10.0051 q^{61} -1.14233 q^{62} +1.00000 q^{63} -4.70168 q^{64} +2.89961 q^{65} +0.561948 q^{66} +0.510569 q^{67} +8.48161 q^{68} +1.71339 q^{69} -1.45913 q^{70} +7.64336 q^{71} +0.727834 q^{72} +6.16649 q^{73} +7.19080 q^{74} +4.41142 q^{75} -6.08934 q^{76} +0.295463 q^{77} +7.18839 q^{78} -1.92887 q^{79} -3.54358 q^{80} +1.00000 q^{81} -16.5111 q^{82} -4.65688 q^{83} -1.61732 q^{84} +4.02332 q^{85} -5.09934 q^{86} +7.83095 q^{87} +0.215048 q^{88} +5.88295 q^{89} -1.45913 q^{90} +3.77953 q^{91} -2.77110 q^{92} -0.600616 q^{93} +19.5039 q^{94} -2.88853 q^{95} -7.32917 q^{96} +18.0326 q^{97} -1.90192 q^{98} +0.295463 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) $ 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.90192	−1.34486	−0.672432	−	0.740159i	$-0.734750\pi$
$2$	−1.90192	−1.34486	−0.672432	+	0.740159i	$0.734750\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.61732	0.808658
$5$	0.767188	0.343097	0.171548	−	0.985176i	$-0.445123\pi$
$5$	0.767188	0.343097	0.171548	+	0.985176i	$0.445123\pi$
$6$	1.90192	0.776457
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.727834	0.257328
$9$	1.00000	0.333333
$10$	−1.45913	−0.461418
$11$	0.295463	0.0890855	0.0445427	−	0.999007i	$-0.485817\pi$
$11$	0.295463	0.0890855	0.0445427	+	0.999007i	$0.485817\pi$
$12$	−1.61732	−0.466879
$13$	3.77953	1.04825	0.524127	−	0.851640i	$-0.324392\pi$
$13$	3.77953	1.04825	0.524127	+	0.851640i	$0.324392\pi$
$14$	−1.90192	−0.508311
$15$	−0.767188	−0.198087
$16$	−4.61892	−1.15473
$17$	5.24425	1.27192	0.635959	−	0.771723i	$-0.280605\pi$
$17$	5.24425	1.27192	0.635959	+	0.771723i	$0.280605\pi$
$18$	−1.90192	−0.448288
$19$	−3.76509	−0.863771	−0.431885	−	0.901929i	$-0.642151\pi$
$19$	−3.76509	−0.863771	−0.431885	+	0.901929i	$0.642151\pi$
$20$	1.24079	0.277448
$21$	−1.00000	−0.218218
$22$	−0.561948	−0.119808
$23$	−1.71339	−0.357267	−0.178634	−	0.983916i	$-0.557168\pi$
$23$	−1.71339	−0.357267	−0.178634	+	0.983916i	$0.557168\pi$
$24$	−0.727834	−0.148569
$25$	−4.41142	−0.882285
$26$	−7.18839	−1.40976
$27$	−1.00000	−0.192450
$28$	1.61732	0.305644
$29$	−7.83095	−1.45417	−0.727086	−	0.686547i	$-0.759126\pi$
$29$	−7.83095	−1.45417	−0.727086	+	0.686547i	$0.759126\pi$
$30$	1.45913	0.266400
$31$	0.600616	0.107874	0.0539369	−	0.998544i	$-0.482823\pi$
$31$	0.600616	0.107874	0.0539369	+	0.998544i	$0.482823\pi$
$32$	7.32917	1.29563
$33$	−0.295463	−0.0514335
$34$	−9.97417	−1.71056
$35$	0.767188	0.129678
$36$	1.61732	0.269553
$37$	−3.78080	−0.621560	−0.310780	−	0.950482i	$-0.600590\pi$
$37$	−3.78080	−0.621560	−0.310780	+	0.950482i	$0.600590\pi$
$38$	7.16091	1.16165
$39$	−3.77953	−0.605210
$40$	0.558386	0.0882885
$41$	8.68124	1.35578	0.677891	−	0.735162i	$-0.262894\pi$
$41$	8.68124	1.35578	0.677891	+	0.735162i	$0.262894\pi$
$42$	1.90192	0.293473
$43$	2.68115	0.408871	0.204435	−	0.978880i	$-0.434464\pi$
$43$	2.68115	0.408871	0.204435	+	0.978880i	$0.434464\pi$
$44$	0.477857	0.0720397
$45$	0.767188	0.114366
$46$	3.25875	0.480476
$47$	−10.2548	−1.49582	−0.747910	−	0.663800i	$-0.768943\pi$
$47$	−10.2548	−1.49582	−0.747910	+	0.663800i	$0.768943\pi$
$48$	4.61892	0.666684
$49$	1.00000	0.142857
$50$	8.39019	1.18655
$51$	−5.24425	−0.734342
$52$	6.11270	0.847679
$53$	−7.17506	−0.985570	−0.492785	−	0.870151i	$-0.664021\pi$
$53$	−7.17506	−0.985570	−0.492785	+	0.870151i	$0.664021\pi$
$54$	1.90192	0.258819
$55$	0.226676	0.0305649
$56$	0.727834	0.0972610
$57$	3.76509	0.498698
$58$	14.8939	1.95566
$59$	9.38143	1.22136	0.610679	−	0.791878i	$-0.290897\pi$
$59$	9.38143	1.22136	0.610679	+	0.791878i	$0.290897\pi$
$60$	−1.24079	−0.160185
$61$	10.0051	1.28103	0.640514	−	0.767947i	$-0.278721\pi$
$61$	10.0051	1.28103	0.640514	+	0.767947i	$0.278721\pi$
$62$	−1.14233	−0.145075
$63$	1.00000	0.125988
$64$	−4.70168	−0.587711
$65$	2.89961	0.359653
$66$	0.561948	0.0691711
$67$	0.510569	0.0623759	0.0311880	−	0.999514i	$-0.490071\pi$
$67$	0.510569	0.0623759	0.0311880	+	0.999514i	$0.490071\pi$
$68$	8.48161	1.02855
$69$	1.71339	0.206268
$70$	−1.45913	−0.174400
$71$	7.64336	0.907100	0.453550	−	0.891231i	$-0.350157\pi$
$71$	7.64336	0.907100	0.453550	+	0.891231i	$0.350157\pi$
$72$	0.727834	0.0857761
$73$	6.16649	0.721734	0.360867	−	0.932617i	$-0.382481\pi$
$73$	6.16649	0.721734	0.360867	+	0.932617i	$0.382481\pi$
$74$	7.19080	0.835914
$75$	4.41142	0.509387
$76$	−6.08934	−0.698495
$77$	0.295463	0.0336711
$78$	7.18839	0.813925
$79$	−1.92887	−0.217015	−0.108507	−	0.994096i	$-0.534607\pi$
$79$	−1.92887	−0.217015	−0.108507	+	0.994096i	$0.534607\pi$
$80$	−3.54358	−0.396184
$81$	1.00000	0.111111
$82$	−16.5111	−1.82334
$83$	−4.65688	−0.511159	−0.255580	−	0.966788i	$-0.582266\pi$
$83$	−4.65688	−0.511159	−0.255580	+	0.966788i	$0.582266\pi$
$84$	−1.61732	−0.176464
$85$	4.02332	0.436391
$86$	−5.09934	−0.549876
$87$	7.83095	0.839566
$88$	0.215048	0.0229242
$89$	5.88295	0.623591	0.311796	−	0.950149i	$-0.399070\pi$
$89$	5.88295	0.623591	0.311796	+	0.950149i	$0.399070\pi$
$90$	−1.45913	−0.153806
$91$	3.77953	0.396203
$92$	−2.77110	−0.288907
$93$	−0.600616	−0.0622809
$94$	19.5039	2.01167
$95$	−2.88853	−0.296357
$96$	−7.32917	−0.748030
$97$	18.0326	1.83094	0.915468	−	0.402390i	$-0.131820\pi$
$97$	18.0326	1.83094	0.915468	+	0.402390i	$0.131820\pi$
$98$	−1.90192	−0.192123
$99$	0.295463	0.0296952
$100$	−7.13467	−0.713467
$101$	−14.1510	−1.40807	−0.704037	−	0.710163i	$-0.748621\pi$
$101$	−14.1510	−1.40807	−0.704037	+	0.710163i	$0.748621\pi$
$102$	9.97417	0.987590
$103$	−1.46581	−0.144430	−0.0722151	−	0.997389i	$-0.523007\pi$
$103$	−1.46581	−0.144430	−0.0722151	+	0.997389i	$0.523007\pi$
$104$	2.75087	0.269745
$105$	−0.767188	−0.0748699
$106$	13.6464	1.32546
$107$	−7.15713	−0.691906	−0.345953	−	0.938252i	$-0.612444\pi$
$107$	−7.15713	−0.691906	−0.345953	+	0.938252i	$0.612444\pi$
$108$	−1.61732	−0.155626
$109$	9.55398	0.915106	0.457553	−	0.889182i	$-0.348726\pi$
$109$	9.55398	0.915106	0.457553	+	0.889182i	$0.348726\pi$
$110$	−0.431120	−0.0411057
$111$	3.78080	0.358858
$112$	−4.61892	−0.436447
$113$	3.35560	0.315668	0.157834	−	0.987466i	$-0.449549\pi$
$113$	3.35560	0.315668	0.157834	+	0.987466i	$0.449549\pi$
$114$	−7.16091	−0.670681
$115$	−1.31449	−0.122577
$116$	−12.6651	−1.17593
$117$	3.77953	0.349418
$118$	−17.8428	−1.64256
$119$	5.24425	0.480740
$120$	−0.558386	−0.0509734
$121$	−10.9127	−0.992064
$122$	−19.0290	−1.72281
$123$	−8.68124	−0.782761
$124$	0.971386	0.0872330
$125$	−7.22033	−0.645806
$126$	−1.90192	−0.169437
$127$	−13.4223	−1.19104	−0.595518	−	0.803342i	$-0.703053\pi$
$127$	−13.4223	−1.19104	−0.595518	+	0.803342i	$0.703053\pi$
$128$	−5.71609	−0.505235
$129$	−2.68115	−0.236062
$130$	−5.51484	−0.483684
$131$	8.26951	0.722510	0.361255	−	0.932467i	$-0.382348\pi$
$131$	8.26951	0.722510	0.361255	+	0.932467i	$0.382348\pi$
$132$	−0.477857	−0.0415921
$133$	−3.76509	−0.326475
$134$	−0.971064	−0.0838871
$135$	−0.767188	−0.0660290
$136$	3.81695	0.327300
$137$	3.75976	0.321218	0.160609	−	0.987018i	$-0.448654\pi$
$137$	3.75976	0.321218	0.160609	+	0.987018i	$0.448654\pi$
$138$	−3.25875	−0.277403
$139$	19.7004	1.67096	0.835482	−	0.549518i	$-0.185189\pi$
$139$	19.7004	1.67096	0.835482	+	0.549518i	$0.185189\pi$
$140$	1.24079	0.104866
$141$	10.2548	0.863612
$142$	−14.5371	−1.21993
$143$	1.11671	0.0933842
$144$	−4.61892	−0.384910
$145$	−6.00781	−0.498922
$146$	−11.7282	−0.970633
$147$	−1.00000	−0.0824786
$148$	−6.11476	−0.502630
$149$	17.0164	1.39404	0.697019	−	0.717053i	$-0.254510\pi$
$149$	17.0164	1.39404	0.697019	+	0.717053i	$0.254510\pi$
$150$	−8.39019	−0.685056
$151$	22.3002	1.81476	0.907382	−	0.420307i	$-0.138078\pi$
$151$	22.3002	1.81476	0.907382	+	0.420307i	$0.138078\pi$
$152$	−2.74036	−0.222273
$153$	5.24425	0.423972
$154$	−0.561948	−0.0452831
$155$	0.460785	0.0370111
$156$	−6.11270	−0.489408
$157$	5.94616	0.474555	0.237277	−	0.971442i	$-0.423745\pi$
$157$	5.94616	0.474555	0.237277	+	0.971442i	$0.423745\pi$
$158$	3.66857	0.291855
$159$	7.17506	0.569019
$160$	5.62285	0.444525
$161$	−1.71339	−0.135034
$162$	−1.90192	−0.149429
$163$	8.03189	0.629106	0.314553	−	0.949240i	$-0.398145\pi$
$163$	8.03189	0.629106	0.314553	+	0.949240i	$0.398145\pi$
$164$	14.0403	1.09636
$165$	−0.226676	−0.0176467
$166$	8.85704	0.687440
$167$	−3.00437	−0.232486	−0.116243	−	0.993221i	$-0.537085\pi$
$167$	−3.00437	−0.232486	−0.116243	+	0.993221i	$0.537085\pi$
$168$	−0.727834	−0.0561536
$169$	1.28487	0.0988363
$170$	−7.65206	−0.586886
$171$	−3.76509	−0.287924
$172$	4.33626	0.330637
$173$	14.1731	1.07756	0.538779	−	0.842447i	$-0.318886\pi$
$173$	14.1731	1.07756	0.538779	+	0.842447i	$0.318886\pi$
$174$	−14.8939	−1.12910
$175$	−4.41142	−0.333472
$176$	−1.36472	−0.102870
$177$	−9.38143	−0.705152
$178$	−11.1889	−0.838645
$179$	−16.6373	−1.24353	−0.621764	−	0.783205i	$-0.713583\pi$
$179$	−16.6373	−1.24353	−0.621764	+	0.783205i	$0.713583\pi$
$180$	1.24079	0.0924827
$181$	3.39381	0.252260	0.126130	−	0.992014i	$-0.459744\pi$
$181$	3.39381	0.252260	0.126130	+	0.992014i	$0.459744\pi$
$182$	−7.18839	−0.532839
$183$	−10.0051	−0.739602
$184$	−1.24707	−0.0919350
$185$	−2.90059	−0.213255
$186$	1.14233	0.0837594
$187$	1.54948	0.113309
$188$	−16.5853	−1.20961
$189$	−1.00000	−0.0727393
$190$	5.49377	0.398560
$191$	−24.8240	−1.79620	−0.898101	−	0.439789i	$-0.855053\pi$
$191$	−24.8240	−1.79620	−0.898101	+	0.439789i	$0.855053\pi$
$192$	4.70168	0.339315
$193$	1.89762	0.136594	0.0682969	−	0.997665i	$-0.478243\pi$
$193$	1.89762	0.136594	0.0682969	+	0.997665i	$0.478243\pi$
$194$	−34.2967	−2.46236
$195$	−2.89961	−0.207645
$196$	1.61732	0.115523
$197$	−15.6176	−1.11271	−0.556353	−	0.830946i	$-0.687800\pi$
$197$	−15.6176	−1.11271	−0.556353	+	0.830946i	$0.687800\pi$
$198$	−0.561948	−0.0399359
$199$	6.07308	0.430509	0.215254	−	0.976558i	$-0.430942\pi$
$199$	6.07308	0.430509	0.215254	+	0.976558i	$0.430942\pi$
$200$	−3.21079	−0.227037
$201$	−0.510569	−0.0360128
$202$	26.9141	1.89367
$203$	−7.83095	−0.549625
$204$	−8.48161	−0.593832
$205$	6.66014	0.465164
$206$	2.78785	0.194239
$207$	−1.71339	−0.119089
$208$	−17.4574	−1.21045
$209$	−1.11244	−0.0769494
$210$	1.45913	0.100690
$211$	−0.221019	−0.0152156	−0.00760779	−	0.999971i	$-0.502422\pi$
$211$	−0.221019	−0.0152156	−0.00760779	+	0.999971i	$0.502422\pi$
$212$	−11.6043	−0.796990
$213$	−7.64336	−0.523714
$214$	13.6123	0.930519
$215$	2.05694	0.140282
$216$	−0.727834	−0.0495229
$217$	0.600616	0.0407724
$218$	−18.1710	−1.23069
$219$	−6.16649	−0.416693
$220$	0.366606	0.0247166
$221$	19.8208	1.33329
$222$	−7.19080	−0.482615
$223$	2.40462	0.161025	0.0805125	−	0.996754i	$-0.474344\pi$
$223$	2.40462	0.161025	0.0805125	+	0.996754i	$0.474344\pi$
$224$	7.32917	0.489701
$225$	−4.41142	−0.294095
$226$	−6.38210	−0.424531
$227$	19.0248	1.26272	0.631361	−	0.775489i	$-0.282497\pi$
$227$	19.0248	1.26272	0.631361	+	0.775489i	$0.282497\pi$
$228$	6.08934	0.403277
$229$	23.2092	1.53371	0.766855	−	0.641821i	$-0.221821\pi$
$229$	23.2092	1.53371	0.766855	+	0.641821i	$0.221821\pi$
$230$	2.50007	0.164850
$231$	−0.295463	−0.0194400
$232$	−5.69964	−0.374200
$233$	5.31731	0.348349	0.174174	−	0.984715i	$-0.444274\pi$
$233$	5.31731	0.348349	0.174174	+	0.984715i	$0.444274\pi$
$234$	−7.18839	−0.469920
$235$	−7.86738	−0.513211
$236$	15.1727	0.987662
$237$	1.92887	0.125294
$238$	−9.97417	−0.646529
$239$	9.26093	0.599039	0.299520	−	0.954090i	$-0.403174\pi$
$239$	9.26093	0.599039	0.299520	+	0.954090i	$0.403174\pi$
$240$	3.54358	0.228737
$241$	−22.2302	−1.43198	−0.715988	−	0.698113i	$-0.754023\pi$
$241$	−22.2302	−1.43198	−0.715988	+	0.698113i	$0.754023\pi$
$242$	20.7551	1.33419
$243$	−1.00000	−0.0641500
$244$	16.1815	1.03591
$245$	0.767188	0.0490138
$246$	16.5111	1.05271
$247$	−14.2303	−0.905451
$248$	0.437149	0.0277590
$249$	4.65688	0.295118
$250$	13.7325	0.868521
$251$	−27.8959	−1.76078	−0.880388	−	0.474255i	$-0.842717\pi$
$251$	−27.8959	−1.76078	−0.880388	+	0.474255i	$0.842717\pi$
$252$	1.61732	0.101881
$253$	−0.506245	−0.0318273
$254$	25.5282	1.60178
$255$	−4.02332	−0.251950
$256$	20.2749	1.26718
$257$	−7.42797	−0.463344	−0.231672	−	0.972794i	$-0.574420\pi$
$257$	−7.42797	−0.463344	−0.231672	+	0.972794i	$0.574420\pi$
$258$	5.09934	0.317471
$259$	−3.78080	−0.234928
$260$	4.68959	0.290836
$261$	−7.83095	−0.484724
$262$	−15.7280	−0.971678
$263$	17.8180	1.09871	0.549354	−	0.835590i	$-0.314874\pi$
$263$	17.8180	1.09871	0.549354	+	0.835590i	$0.314874\pi$
$264$	−0.215048	−0.0132353
$265$	−5.50462	−0.338146
$266$	7.16091	0.439064
$267$	−5.88295	−0.360031
$268$	0.825752	0.0504408
$269$	12.2074	0.744298	0.372149	−	0.928173i	$-0.378621\pi$
$269$	12.2074	0.744298	0.372149	+	0.928173i	$0.378621\pi$
$270$	1.45913	0.0888000
$271$	6.36680	0.386755	0.193378	−	0.981124i	$-0.438056\pi$
$271$	6.36680	0.386755	0.193378	+	0.981124i	$0.438056\pi$
$272$	−24.2228	−1.46872
$273$	−3.77953	−0.228748
$274$	−7.15077	−0.431994
$275$	−1.30341	−0.0785987
$276$	2.77110	0.166801
$277$	23.3907	1.40541	0.702706	−	0.711481i	$-0.251975\pi$
$277$	23.3907	1.40541	0.702706	+	0.711481i	$0.251975\pi$
$278$	−37.4686	−2.24722
$279$	0.600616	0.0359579
$280$	0.558386	0.0333699
$281$	−13.8862	−0.828381	−0.414191	−	0.910190i	$-0.635935\pi$
$281$	−13.8862	−0.828381	−0.414191	+	0.910190i	$0.635935\pi$
$282$	−19.5039	−1.16144
$283$	15.0386	0.893954	0.446977	−	0.894546i	$-0.352501\pi$
$283$	15.0386	0.893954	0.446977	+	0.894546i	$0.352501\pi$
$284$	12.3617	0.733534
$285$	2.88853	0.171102
$286$	−2.12390	−0.125589
$287$	8.68124	0.512438
$288$	7.32917	0.431875
$289$	10.5022	0.617774
$290$	11.4264	0.670982
$291$	−18.0326	−1.05709
$292$	9.97317	0.583636
$293$	7.98940	0.466746	0.233373	−	0.972387i	$-0.425024\pi$
$293$	7.98940	0.466746	0.233373	+	0.972387i	$0.425024\pi$
$294$	1.90192	0.110922
$295$	7.19732	0.419044
$296$	−2.75180	−0.159945
$297$	−0.295463	−0.0171445
$298$	−32.3639	−1.87479
$299$	−6.47583	−0.374507
$300$	7.13467	0.411920
$301$	2.68115	0.154539
$302$	−42.4133	−2.44061
$303$	14.1510	0.812952
$304$	17.3906	0.997422
$305$	7.67582	0.439516
$306$	−9.97417	−0.570185
$307$	7.17730	0.409630	0.204815	−	0.978801i	$-0.434341\pi$
$307$	7.17730	0.409630	0.204815	+	0.978801i	$0.434341\pi$
$308$	0.477857	0.0272285
$309$	1.46581	0.0833869
$310$	−0.876378	−0.0497749
$311$	−9.33978	−0.529611	−0.264805	−	0.964302i	$-0.585308\pi$
$311$	−9.33978	−0.529611	−0.264805	+	0.964302i	$0.585308\pi$
$312$	−2.75087	−0.155738
$313$	8.57535	0.484707	0.242354	−	0.970188i	$-0.422081\pi$
$313$	8.57535	0.484707	0.242354	+	0.970188i	$0.422081\pi$
$314$	−11.3091	−0.638212
$315$	0.767188	0.0432261
$316$	−3.11959	−0.175491
$317$	−21.1175	−1.18608	−0.593039	−	0.805174i	$-0.702072\pi$
$317$	−21.1175	−1.18608	−0.593039	+	0.805174i	$0.702072\pi$
$318$	−13.6464	−0.765253
$319$	−2.31376	−0.129546
$320$	−3.60707	−0.201642
$321$	7.15713	0.399472
$322$	3.25875	0.181603
$323$	−19.7451	−1.09864
$324$	1.61732	0.0898509
$325$	−16.6731	−0.924858
$326$	−15.2761	−0.846062
$327$	−9.55398	−0.528337
$328$	6.31851	0.348881
$329$	−10.2548	−0.565367
$330$	0.431120	0.0237324
$331$	−11.9243	−0.655419	−0.327709	−	0.944779i	$-0.606277\pi$
$331$	−11.9243	−0.655419	−0.327709	+	0.944779i	$0.606277\pi$
$332$	−7.53166	−0.413353
$333$	−3.78080	−0.207187
$334$	5.71409	0.312661
$335$	0.391702	0.0214010
$336$	4.61892	0.251983
$337$	−20.7509	−1.13037	−0.565186	−	0.824964i	$-0.691195\pi$
$337$	−20.7509	−1.13037	−0.565186	+	0.824964i	$0.691195\pi$
$338$	−2.44373	−0.132921
$339$	−3.35560	−0.182251
$340$	6.50699	0.352891
$341$	0.177460	0.00960998
$342$	7.16091	0.387218
$343$	1.00000	0.0539949
$344$	1.95143	0.105214
$345$	1.31449	0.0707700
$346$	−26.9561	−1.44917
$347$	23.7950	1.27738	0.638691	−	0.769463i	$-0.279476\pi$
$347$	23.7950	1.27738	0.638691	+	0.769463i	$0.279476\pi$
$348$	12.6651	0.678922
$349$	27.5842	1.47655	0.738274	−	0.674501i	$-0.235641\pi$
$349$	27.5842	1.47655	0.738274	+	0.674501i	$0.235641\pi$
$350$	8.39019	0.448475
$351$	−3.77953	−0.201737
$352$	2.16550	0.115421
$353$	21.1141	1.12379	0.561895	−	0.827208i	$-0.310072\pi$
$353$	21.1141	1.12379	0.561895	+	0.827208i	$0.310072\pi$
$354$	17.8428	0.948333
$355$	5.86389	0.311223
$356$	9.51459	0.504272
$357$	−5.24425	−0.277555
$358$	31.6428	1.67237
$359$	−5.18095	−0.273440	−0.136720	−	0.990610i	$-0.543656\pi$
$359$	−5.18095	−0.273440	−0.136720	+	0.990610i	$0.543656\pi$
$360$	0.558386	0.0294295
$361$	−4.82411	−0.253900
$362$	−6.45476	−0.339255
$363$	10.9127	0.572768
$364$	6.11270	0.320393
$365$	4.73086	0.247624
$366$	19.0290	0.994663
$367$	−32.1695	−1.67923	−0.839616	−	0.543180i	$-0.817220\pi$
$367$	−32.1695	−1.67923	−0.839616	+	0.543180i	$0.817220\pi$
$368$	7.91403	0.412547
$369$	8.68124	0.451927
$370$	5.51670	0.286799
$371$	−7.17506	−0.372511
$372$	−0.971386	−0.0503640
$373$	−13.6941	−0.709055	−0.354527	−	0.935046i	$-0.615358\pi$
$373$	−13.6941	−0.709055	−0.354527	+	0.935046i	$0.615358\pi$
$374$	−2.94700	−0.152386
$375$	7.22033	0.372856
$376$	−7.46382	−0.384917
$377$	−29.5974	−1.52434
$378$	1.90192	0.0978244
$379$	13.6856	0.702981	0.351490	−	0.936191i	$-0.385675\pi$
$379$	13.6856	0.702981	0.351490	+	0.936191i	$0.385675\pi$
$380$	−4.67167	−0.239652
$381$	13.4223	0.687645
$382$	47.2134	2.41565
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	5.71609	0.291698
$385$	0.226676	0.0115525
$386$	−3.60913	−0.183700
$387$	2.68115	0.136290
$388$	29.1645	1.48060
$389$	7.83762	0.397383	0.198692	−	0.980062i	$-0.436331\pi$
$389$	7.83762	0.397383	0.198692	+	0.980062i	$0.436331\pi$
$390$	5.51484	0.279255
$391$	−8.98547	−0.454415
$392$	0.727834	0.0367612
$393$	−8.26951	−0.417142
$394$	29.7035	1.49644
$395$	−1.47981	−0.0744571
$396$	0.477857	0.0240132
$397$	25.5653	1.28309	0.641543	−	0.767087i	$-0.278294\pi$
$397$	25.5653	1.28309	0.641543	+	0.767087i	$0.278294\pi$
$398$	−11.5505	−0.578976
$399$	3.76509	0.188490
$400$	20.3760	1.01880
$401$	−5.32713	−0.266024	−0.133012	−	0.991114i	$-0.542465\pi$
$401$	−5.32713	−0.266024	−0.133012	+	0.991114i	$0.542465\pi$
$402$	0.971064	0.0484323
$403$	2.27005	0.113079
$404$	−22.8866	−1.13865
$405$	0.767188	0.0381219
$406$	14.8939	0.739171
$407$	−1.11709	−0.0553720
$408$	−3.81695	−0.188967
$409$	1.46525	0.0724517	0.0362259	−	0.999344i	$-0.488466\pi$
$409$	1.46525	0.0724517	0.0362259	+	0.999344i	$0.488466\pi$
$410$	−12.6671	−0.625583
$411$	−3.75976	−0.185455
$412$	−2.37067	−0.116795
$413$	9.38143	0.461630
$414$	3.25875	0.160159
$415$	−3.57270	−0.175377
$416$	27.7008	1.35815
$417$	−19.7004	−0.964731
$418$	2.11579	0.103486
$419$	−23.1847	−1.13265	−0.566325	−	0.824182i	$-0.691635\pi$
$419$	−23.1847	−1.13265	−0.566325	+	0.824182i	$0.691635\pi$
$420$	−1.24079	−0.0605441
$421$	33.2782	1.62188	0.810941	−	0.585128i	$-0.198956\pi$
$421$	33.2782	1.62188	0.810941	+	0.585128i	$0.198956\pi$
$422$	0.420361	0.0204629
$423$	−10.2548	−0.498607
$424$	−5.22226	−0.253615
$425$	−23.1346	−1.12219
$426$	14.5371	0.704324
$427$	10.0051	0.484183
$428$	−11.5753	−0.559516
$429$	−1.11671	−0.0539154
$430$	−3.91215	−0.188661
$431$	−3.59405	−0.173119	−0.0865596	−	0.996247i	$-0.527587\pi$
$431$	−3.59405	−0.173119	−0.0865596	+	0.996247i	$0.527587\pi$
$432$	4.61892	0.222228
$433$	−11.5775	−0.556379	−0.278190	−	0.960526i	$-0.589734\pi$
$433$	−11.5775	−0.556379	−0.278190	+	0.960526i	$0.589734\pi$
$434$	−1.14233	−0.0548334
$435$	6.00781	0.288053
$436$	15.4518	0.740008
$437$	6.45108	0.308597
$438$	11.7282	0.560395
$439$	−17.9531	−0.856853	−0.428426	−	0.903577i	$-0.640932\pi$
$439$	−17.9531	−0.856853	−0.428426	+	0.903577i	$0.640932\pi$
$440$	0.164982	0.00786522
$441$	1.00000	0.0476190
$442$	−37.6977	−1.79310
$443$	−16.7634	−0.796454	−0.398227	−	0.917287i	$-0.630374\pi$
$443$	−16.7634	−0.796454	−0.398227	+	0.917287i	$0.630374\pi$
$444$	6.11476	0.290194
$445$	4.51333	0.213952
$446$	−4.57340	−0.216557
$447$	−17.0164	−0.804848
$448$	−4.70168	−0.222134
$449$	−27.0944	−1.27866	−0.639332	−	0.768931i	$-0.720789\pi$
$449$	−27.0944	−1.27866	−0.639332	+	0.768931i	$0.720789\pi$
$450$	8.39019	0.395518
$451$	2.56499	0.120780
$452$	5.42707	0.255268
$453$	−22.3002	−1.04775
$454$	−36.1838	−1.69819
$455$	2.89961	0.135936
$456$	2.74036	0.128329
$457$	6.62146	0.309739	0.154869	−	0.987935i	$-0.450504\pi$
$457$	6.62146	0.309739	0.154869	+	0.987935i	$0.450504\pi$
$458$	−44.1422	−2.06263
$459$	−5.24425	−0.244781
$460$	−2.12595	−0.0991231
$461$	32.5390	1.51549	0.757747	−	0.652549i	$-0.226300\pi$
$461$	32.5390	1.51549	0.757747	+	0.652549i	$0.226300\pi$
$462$	0.561948	0.0261442
$463$	−19.9036	−0.924997	−0.462498	−	0.886620i	$-0.653047\pi$
$463$	−19.9036	−0.924997	−0.462498	+	0.886620i	$0.653047\pi$
$464$	36.1706	1.67918
$465$	−0.460785	−0.0213684
$466$	−10.1131	−0.468481
$467$	−19.0186	−0.880074	−0.440037	−	0.897980i	$-0.645035\pi$
$467$	−19.0186	−0.880074	−0.440037	+	0.897980i	$0.645035\pi$
$468$	6.11270	0.282560
$469$	0.510569	0.0235759
$470$	14.9632	0.690199
$471$	−5.94616	−0.273984
$472$	6.82813	0.314290
$473$	0.792179	0.0364245
$474$	−3.66857	−0.168503
$475$	16.6094	0.762092
$476$	8.48161	0.388754
$477$	−7.17506	−0.328523
$478$	−17.6136	−0.805626
$479$	31.6118	1.44438	0.722191	−	0.691694i	$-0.243135\pi$
$479$	31.6118	1.44438	0.722191	+	0.691694i	$0.243135\pi$
$480$	−5.62285	−0.256647
$481$	−14.2897	−0.651553
$482$	42.2802	1.92581
$483$	1.71339	0.0779621
$484$	−17.6493	−0.802241
$485$	13.8344	0.628188
$486$	1.90192	0.0862730
$487$	12.0818	0.547479	0.273740	−	0.961804i	$-0.411739\pi$
$487$	12.0818	0.547479	0.273740	+	0.961804i	$0.411739\pi$
$488$	7.28209	0.329645
$489$	−8.03189	−0.363215
$490$	−1.45913	−0.0659169
$491$	−5.55174	−0.250547	−0.125273	−	0.992122i	$-0.539981\pi$
$491$	−5.55174	−0.250547	−0.125273	+	0.992122i	$0.539981\pi$
$492$	−14.0403	−0.632986
$493$	−41.0675	−1.84959
$494$	27.0649	1.21771
$495$	0.226676	0.0101883
$496$	−2.77420	−0.124565
$497$	7.64336	0.342851
$498$	−8.85704	−0.396893
$499$	−18.8268	−0.842804	−0.421402	−	0.906874i	$-0.638462\pi$
$499$	−18.8268	−0.842804	−0.421402	+	0.906874i	$0.638462\pi$
$500$	−11.6776	−0.522236
$501$	3.00437	0.134226
$502$	53.0559	2.36800
$503$	2.85168	0.127150	0.0635751	−	0.997977i	$-0.479750\pi$
$503$	2.85168	0.127150	0.0635751	+	0.997977i	$0.479750\pi$
$504$	0.727834	0.0324203
$505$	−10.8564	−0.483106
$506$	0.962839	0.0428034
$507$	−1.28487	−0.0570632
$508$	−21.7081	−0.963141
$509$	1.44698	0.0641361	0.0320681	−	0.999486i	$-0.489791\pi$
$509$	1.44698	0.0641361	0.0320681	+	0.999486i	$0.489791\pi$
$510$	7.65206	0.338839
$511$	6.16649	0.272790
$512$	−27.1292	−1.19895
$513$	3.76509	0.166233
$514$	14.1274	0.623135
$515$	−1.12455	−0.0495536
$516$	−4.33626	−0.190893
$517$	−3.02992	−0.133256
$518$	7.19080	0.315946
$519$	−14.1731	−0.622128
$520$	2.11044	0.0925488
$521$	−13.0860	−0.573309	−0.286654	−	0.958034i	$-0.592543\pi$
$521$	−13.0860	−0.573309	−0.286654	+	0.958034i	$0.592543\pi$
$522$	14.8939	0.651888
$523$	11.6582	0.509777	0.254888	−	0.966971i	$-0.417961\pi$
$523$	11.6582	0.509777	0.254888	+	0.966971i	$0.417961\pi$
$524$	13.3744	0.584264
$525$	4.41142	0.192530
$526$	−33.8886	−1.47761
$527$	3.14978	0.137206
$528$	1.36472	0.0593918
$529$	−20.0643	−0.872360
$530$	10.4694	0.454760
$531$	9.38143	0.407119
$532$	−6.08934	−0.264006
$533$	32.8110	1.42120
$534$	11.1889	0.484192
$535$	−5.49086	−0.237391
$536$	0.371610	0.0160511
$537$	16.6373	0.717951
$538$	−23.2175	−1.00098
$539$	0.295463	0.0127265
$540$	−1.24079	−0.0533949
$541$	10.5262	0.452556	0.226278	−	0.974063i	$-0.427344\pi$
$541$	10.5262	0.452556	0.226278	+	0.974063i	$0.427344\pi$
$542$	−12.1092	−0.520133
$543$	−3.39381	−0.145642
$544$	38.4360	1.64793
$545$	7.32970	0.313970
$546$	7.18839	0.307635
$547$	15.0590	0.643877	0.321938	−	0.946761i	$-0.395666\pi$
$547$	15.0590	0.643877	0.321938	+	0.946761i	$0.395666\pi$
$548$	6.08072	0.259755
$549$	10.0051	0.427009
$550$	2.47899	0.105705
$551$	29.4842	1.25607
$552$	1.24707	0.0530787
$553$	−1.92887	−0.0820239
$554$	−44.4874	−1.89009
$555$	2.90059	0.123123
$556$	31.8617	1.35124
$557$	12.1681	0.515579	0.257790	−	0.966201i	$-0.417006\pi$
$557$	12.1681	0.515579	0.257790	+	0.966201i	$0.417006\pi$
$558$	−1.14233	−0.0483585
$559$	10.1335	0.428600
$560$	−3.54358	−0.149744
$561$	−1.54948	−0.0654192
$562$	26.4105	1.11406
$563$	−9.57859	−0.403689	−0.201845	−	0.979418i	$-0.564694\pi$
$563$	−9.57859	−0.403689	−0.201845	+	0.979418i	$0.564694\pi$
$564$	16.5853	0.698367
$565$	2.57438	0.108305
$566$	−28.6023	−1.20225
$567$	1.00000	0.0419961
$568$	5.56310	0.233422
$569$	12.8056	0.536840	0.268420	−	0.963302i	$-0.413498\pi$
$569$	12.8056	0.536840	0.268420	+	0.963302i	$0.413498\pi$
$570$	−5.49377	−0.230109
$571$	14.6512	0.613134	0.306567	−	0.951849i	$-0.400820\pi$
$571$	14.6512	0.613134	0.306567	+	0.951849i	$0.400820\pi$
$572$	1.80608	0.0755159
$573$	24.8240	1.03704
$574$	−16.5111	−0.689159
$575$	7.55851	0.315211
$576$	−4.70168	−0.195904
$577$	38.7768	1.61430	0.807150	−	0.590346i	$-0.201009\pi$
$577$	38.7768	1.61430	0.807150	+	0.590346i	$0.201009\pi$
$578$	−19.9743	−0.830821
$579$	−1.89762	−0.0788625
$580$	−9.71654	−0.403457
$581$	−4.65688	−0.193200
$582$	34.2967	1.42164
$583$	−2.11997	−0.0878000
$584$	4.48819	0.185722
$585$	2.89961	0.119884
$586$	−15.1952	−0.627709
$587$	−14.9209	−0.615853	−0.307926	−	0.951410i	$-0.599635\pi$
$587$	−14.9209	−0.615853	−0.307926	+	0.951410i	$0.599635\pi$
$588$	−1.61732	−0.0666970
$589$	−2.26137	−0.0931782
$590$	−13.6888	−0.563557
$591$	15.6176	0.642421
$592$	17.4632	0.717734
$593$	9.73014	0.399569	0.199784	−	0.979840i	$-0.435976\pi$
$593$	9.73014	0.399569	0.199784	+	0.979840i	$0.435976\pi$
$594$	0.561948	0.0230570
$595$	4.02332	0.164940
$596$	27.5209	1.12730
$597$	−6.07308	−0.248554
$598$	12.3165	0.503661
$599$	25.5990	1.04595	0.522974	−	0.852349i	$-0.324823\pi$
$599$	25.5990	1.04595	0.522974	+	0.852349i	$0.324823\pi$
$600$	3.21079	0.131080
$601$	25.3901	1.03569	0.517843	−	0.855476i	$-0.326735\pi$
$601$	25.3901	1.03569	0.517843	+	0.855476i	$0.326735\pi$
$602$	−5.09934	−0.207833
$603$	0.510569	0.0207920
$604$	36.0665	1.46752
$605$	−8.37209	−0.340374
$606$	−26.9141	−1.09331
$607$	29.1121	1.18163	0.590813	−	0.806809i	$-0.298807\pi$
$607$	29.1121	1.18163	0.590813	+	0.806809i	$0.298807\pi$
$608$	−27.5950	−1.11912
$609$	7.83095	0.317326
$610$	−14.5988	−0.591090
$611$	−38.7585	−1.56800
$612$	8.48161	0.342849
$613$	40.4891	1.63534	0.817670	−	0.575688i	$-0.195266\pi$
$613$	40.4891	1.63534	0.817670	+	0.575688i	$0.195266\pi$
$614$	−13.6507	−0.550897
$615$	−6.66014	−0.268563
$616$	0.215048	0.00866454
$617$	4.43962	0.178732	0.0893661	−	0.995999i	$-0.471516\pi$
$617$	4.43962	0.178732	0.0893661	+	0.995999i	$0.471516\pi$
$618$	−2.78785	−0.112144
$619$	12.2384	0.491903	0.245951	−	0.969282i	$-0.420900\pi$
$619$	12.2384	0.491903	0.245951	+	0.969282i	$0.420900\pi$
$620$	0.745235	0.0299294
$621$	1.71339	0.0687561
$622$	17.7636	0.712254
$623$	5.88295	0.235695
$624$	17.4574	0.698854
$625$	16.5178	0.660711
$626$	−16.3097	−0.651865
$627$	1.11244	0.0444268
$628$	9.61682	0.383753
$629$	−19.8275	−0.790573
$630$	−1.45913	−0.0581333
$631$	37.9108	1.50921	0.754603	−	0.656182i	$-0.227830\pi$
$631$	37.9108	1.50921	0.754603	+	0.656182i	$0.227830\pi$
$632$	−1.40390	−0.0558441
$633$	0.221019	0.00878472
$634$	40.1639	1.59511
$635$	−10.2974	−0.408641
$636$	11.6043	0.460142
$637$	3.77953	0.149751
$638$	4.40059	0.174221
$639$	7.64336	0.302367
$640$	−4.38531	−0.173345
$641$	−4.08103	−0.161191	−0.0805955	−	0.996747i	$-0.525682\pi$
$641$	−4.08103	−0.161191	−0.0805955	+	0.996747i	$0.525682\pi$
$642$	−13.6123	−0.537236
$643$	23.8611	0.940991	0.470496	−	0.882402i	$-0.344075\pi$
$643$	23.8611	0.940991	0.470496	+	0.882402i	$0.344075\pi$
$644$	−2.77110	−0.109197
$645$	−2.05694	−0.0809920
$646$	37.5536	1.47753
$647$	−34.4655	−1.35498	−0.677489	−	0.735533i	$-0.736932\pi$
$647$	−34.4655	−1.35498	−0.677489	+	0.735533i	$0.736932\pi$
$648$	0.727834	0.0285920
$649$	2.77187	0.108805
$650$	31.7110	1.24381
$651$	−0.600616	−0.0235400
$652$	12.9901	0.508732
$653$	31.9447	1.25009	0.625046	−	0.780588i	$-0.285080\pi$
$653$	31.9447	1.25009	0.625046	+	0.780588i	$0.285080\pi$
$654$	18.1710	0.710541
$655$	6.34427	0.247891
$656$	−40.0980	−1.56556
$657$	6.16649	0.240578
$658$	19.5039	0.760341
$659$	−11.1976	−0.436196	−0.218098	−	0.975927i	$-0.569985\pi$
$659$	−11.1976	−0.436196	−0.218098	+	0.975927i	$0.569985\pi$
$660$	−0.366606	−0.0142701
$661$	−31.5028	−1.22532	−0.612658	−	0.790348i	$-0.709900\pi$
$661$	−31.5028	−1.22532	−0.612658	+	0.790348i	$0.709900\pi$
$662$	22.6791	0.881449
$663$	−19.8208	−0.769777
$664$	−3.38944	−0.131536
$665$	−2.88853	−0.112012
$666$	7.19080	0.278638
$667$	13.4175	0.519528
$668$	−4.85903	−0.188001
$669$	−2.40462	−0.0929679
$670$	−0.744988	−0.0287814
$671$	2.95615	0.114121
$672$	−7.32917	−0.282729
$673$	6.63070	0.255595	0.127797	−	0.991800i	$-0.459209\pi$
$673$	6.63070	0.255595	0.127797	+	0.991800i	$0.459209\pi$
$674$	39.4666	1.52020
$675$	4.41142	0.169796
$676$	2.07804	0.0799248
$677$	−6.09030	−0.234069	−0.117035	−	0.993128i	$-0.537339\pi$
$677$	−6.09030	−0.234069	−0.117035	+	0.993128i	$0.537339\pi$
$678$	6.38210	0.245103
$679$	18.0326	0.692029
$680$	2.92831	0.112296
$681$	−19.0248	−0.729033
$682$	−0.337515	−0.0129241
$683$	26.4849	1.01342	0.506709	−	0.862117i	$-0.330862\pi$
$683$	26.4849	1.01342	0.506709	+	0.862117i	$0.330862\pi$
$684$	−6.08934	−0.232832
$685$	2.88444	0.110209
$686$	−1.90192	−0.0726158
$687$	−23.2092	−0.885488
$688$	−12.3840	−0.472135
$689$	−27.1184	−1.03313
$690$	−2.50007	−0.0951760
$691$	−26.3606	−1.00281	−0.501403	−	0.865214i	$-0.667183\pi$
$691$	−26.3606	−1.00281	−0.501403	+	0.865214i	$0.667183\pi$
$692$	22.9223	0.871376
$693$	0.295463	0.0112237
$694$	−45.2563	−1.71790
$695$	15.1139	0.573302
$696$	5.69964	0.216044
$697$	45.5266	1.72444
$698$	−52.4631	−1.98576
$699$	−5.31731	−0.201119
$700$	−7.13467	−0.269665
$701$	0.142946	0.00539901	0.00269951	−	0.999996i	$-0.499141\pi$
$701$	0.142946	0.00539901	0.00269951	+	0.999996i	$0.499141\pi$
$702$	7.18839	0.271308
$703$	14.2351	0.536886
$704$	−1.38917	−0.0523565
$705$	7.86738	0.296303
$706$	−40.1575	−1.51135
$707$	−14.1510	−0.532202
$708$	−15.1727	−0.570227
$709$	12.7183	0.477644	0.238822	−	0.971063i	$-0.423239\pi$
$709$	12.7183	0.477644	0.238822	+	0.971063i	$0.423239\pi$
$710$	−11.1527	−0.418552
$711$	−1.92887	−0.0723383
$712$	4.28181	0.160468
$713$	−1.02909	−0.0385398
$714$	9.97417	0.373274
$715$	0.856728	0.0320398
$716$	−26.9077	−1.00559
$717$	−9.26093	−0.345856
$718$	9.85377	0.367739
$719$	1.48639	0.0554329	0.0277164	−	0.999616i	$-0.491176\pi$
$719$	1.48639	0.0554329	0.0277164	+	0.999616i	$0.491176\pi$
$720$	−3.54358	−0.132061
$721$	−1.46581	−0.0545895
$722$	9.17508	0.341461
$723$	22.2302	0.826751
$724$	5.48886	0.203992
$725$	34.5457	1.28299
$726$	−20.7551	−0.770295
$727$	35.5619	1.31892	0.659458	−	0.751741i	$-0.270786\pi$
$727$	35.5619	1.31892	0.659458	+	0.751741i	$0.270786\pi$
$728$	2.75087	0.101954
$729$	1.00000	0.0370370
$730$	−8.99774	−0.333021
$731$	14.0606	0.520050
$732$	−16.1815	−0.598085
$733$	24.3035	0.897671	0.448835	−	0.893615i	$-0.351839\pi$
$733$	24.3035	0.897671	0.448835	+	0.893615i	$0.351839\pi$
$734$	61.1839	2.25834
$735$	−0.767188	−0.0282981
$736$	−12.5578	−0.462885
$737$	0.150854	0.00555679
$738$	−16.5111	−0.607781
$739$	−5.99935	−0.220690	−0.110345	−	0.993893i	$-0.535196\pi$
$739$	−5.99935	−0.220690	−0.110345	+	0.993893i	$0.535196\pi$
$740$	−4.69117	−0.172451
$741$	14.2303	0.522762
$742$	13.6464	0.500976
$743$	−5.87179	−0.215415	−0.107708	−	0.994183i	$-0.534351\pi$
$743$	−5.87179	−0.215415	−0.107708	+	0.994183i	$0.534351\pi$
$744$	−0.437149	−0.0160266
$745$	13.0548	0.478290
$746$	26.0452	0.953582
$747$	−4.65688	−0.170386
$748$	2.50600	0.0916286
$749$	−7.15713	−0.261516
$750$	−13.7325	−0.501441
$751$	−29.3366	−1.07051	−0.535254	−	0.844691i	$-0.679784\pi$
$751$	−29.3366	−1.07051	−0.535254	+	0.844691i	$0.679784\pi$
$752$	47.3662	1.72727
$753$	27.8959	1.01658
$754$	56.2919	2.05003
$755$	17.1084	0.622640
$756$	−1.61732	−0.0588212
$757$	24.4811	0.889780	0.444890	−	0.895585i	$-0.353243\pi$
$757$	24.4811	0.889780	0.444890	+	0.895585i	$0.353243\pi$
$758$	−26.0289	−0.945414
$759$	0.506245	0.0183755
$760$	−2.10237	−0.0762610
$761$	50.0059	1.81271	0.906356	−	0.422515i	$-0.138853\pi$
$761$	50.0059	1.81271	0.906356	+	0.422515i	$0.138853\pi$
$762$	−25.5282	−0.924789
$763$	9.55398	0.345877
$764$	−40.1483	−1.45251
$765$	4.02332	0.145464
$766$	1.90192	0.0687193
$767$	35.4574	1.28029
$768$	−20.2749	−0.731609
$769$	−35.6544	−1.28573	−0.642866	−	0.765979i	$-0.722255\pi$
$769$	−35.6544	−1.28573	−0.642866	+	0.765979i	$0.722255\pi$
$770$	−0.431120	−0.0155365
$771$	7.42797	0.267512
$772$	3.06906	0.110458
$773$	−14.7306	−0.529821	−0.264911	−	0.964273i	$-0.585342\pi$
$773$	−14.7306	−0.529821	−0.264911	+	0.964273i	$0.585342\pi$
$774$	−5.09934	−0.183292
$775$	−2.64957	−0.0951753
$776$	13.1248	0.471152
$777$	3.78080	0.135636
$778$	−14.9066	−0.534426
$779$	−32.6856	−1.17108
$780$	−4.68959	−0.167914
$781$	2.25833	0.0808094
$782$	17.0897	0.611126
$783$	7.83095	0.279855
$784$	−4.61892	−0.164961
$785$	4.56182	0.162818
$786$	15.7280	0.560998
$787$	−3.71374	−0.132381	−0.0661903	−	0.997807i	$-0.521084\pi$
$787$	−3.71374	−0.132381	−0.0661903	+	0.997807i	$0.521084\pi$
$788$	−25.2586	−0.899800
$789$	−17.8180	−0.634339
$790$	2.81448	0.100135
$791$	3.35560	0.119311
$792$	0.215048	0.00764141
$793$	37.8148	1.34284
$794$	−48.6233	−1.72558
$795$	5.50462	0.195229
$796$	9.82209	0.348135
$797$	21.3671	0.756860	0.378430	−	0.925630i	$-0.376464\pi$
$797$	21.3671	0.756860	0.378430	+	0.925630i	$0.376464\pi$
$798$	−7.16091	−0.253494
$799$	−53.7789	−1.90256
$800$	−32.3321	−1.14311
$801$	5.88295	0.207864
$802$	10.1318	0.357766
$803$	1.82197	0.0642960
$804$	−0.825752	−0.0291220
$805$	−1.31449	−0.0463299
$806$	−4.31746	−0.152076
$807$	−12.2074	−0.429721
$808$	−10.2996	−0.362337
$809$	−2.55237	−0.0897365	−0.0448683	−	0.998993i	$-0.514287\pi$
$809$	−2.55237	−0.0897365	−0.0448683	+	0.998993i	$0.514287\pi$
$810$	−1.45913	−0.0512687
$811$	7.37838	0.259090	0.129545	−	0.991574i	$-0.458648\pi$
$811$	7.37838	0.259090	0.129545	+	0.991574i	$0.458648\pi$
$812$	−12.6651	−0.444459
$813$	−6.36680	−0.223293
$814$	2.12462	0.0744678
$815$	6.16197	0.215844
$816$	24.2228	0.847967
$817$	−10.0948	−0.353171
$818$	−2.78679	−0.0974377
$819$	3.77953	0.132068
$820$	10.7716	0.376159
$821$	8.86130	0.309262	0.154631	−	0.987972i	$-0.450581\pi$
$821$	8.86130	0.309262	0.154631	+	0.987972i	$0.450581\pi$
$822$	7.15077	0.249412
$823$	26.1096	0.910122	0.455061	−	0.890460i	$-0.349617\pi$
$823$	26.1096	0.910122	0.455061	+	0.890460i	$0.349617\pi$
$824$	−1.06687	−0.0371660
$825$	1.30341	0.0453790
$826$	−17.8428	−0.620829
$827$	39.7746	1.38310	0.691549	−	0.722329i	$-0.256928\pi$
$827$	39.7746	1.38310	0.691549	+	0.722329i	$0.256928\pi$
$828$	−2.77110	−0.0963024
$829$	12.4044	0.430822	0.215411	−	0.976523i	$-0.430891\pi$
$829$	12.4044	0.430822	0.215411	+	0.976523i	$0.430891\pi$
$830$	6.79501	0.235858
$831$	−23.3907	−0.811415
$832$	−17.7702	−0.616070
$833$	5.24425	0.181702
$834$	37.4686	1.29743
$835$	−2.30492	−0.0797650
$836$	−1.79918	−0.0622258
$837$	−0.600616	−0.0207603
$838$	44.0956	1.52326
$839$	24.7912	0.855888	0.427944	−	0.903805i	$-0.359238\pi$
$839$	24.7912	0.855888	0.427944	+	0.903805i	$0.359238\pi$
$840$	−0.558386	−0.0192661
$841$	32.3238	1.11462
$842$	−63.2927	−2.18121
$843$	13.8862	0.478266
$844$	−0.357458	−0.0123042
$845$	0.985738	0.0339104
$846$	19.5039	0.670558
$847$	−10.9127	−0.374965
$848$	33.1410	1.13807
$849$	−15.0386	−0.516124
$850$	44.0003	1.50920
$851$	6.47801	0.222063
$852$	−12.3617	−0.423506
$853$	19.6021	0.671161	0.335581	−	0.942011i	$-0.391067\pi$
$853$	19.6021	0.671161	0.335581	+	0.942011i	$0.391067\pi$
$854$	−19.0290	−0.651160
$855$	−2.88853	−0.0987856
$856$	−5.20921	−0.178047
$857$	−53.8625	−1.83991	−0.919954	−	0.392027i	$-0.871774\pi$
$857$	−53.8625	−1.83991	−0.919954	+	0.392027i	$0.871774\pi$
$858$	2.12390	0.0725088
$859$	−30.7683	−1.04980	−0.524900	−	0.851164i	$-0.675897\pi$
$859$	−30.7683	−1.04980	−0.524900	+	0.851164i	$0.675897\pi$
$860$	3.32673	0.113440
$861$	−8.68124	−0.295856
$862$	6.83561	0.232822
$863$	−26.2585	−0.893851	−0.446926	−	0.894571i	$-0.647481\pi$
$863$	−26.2585	−0.893851	−0.446926	+	0.894571i	$0.647481\pi$
$864$	−7.32917	−0.249343
$865$	10.8734	0.369707
$866$	22.0195	0.748254
$867$	−10.5022	−0.356672
$868$	0.971386	0.0329710
$869$	−0.569910	−0.0193329
$870$	−11.4264	−0.387391
$871$	1.92971	0.0653858
$872$	6.95372	0.235483
$873$	18.0326	0.610312
$874$	−12.2695	−0.415021
$875$	−7.22033	−0.244092
$876$	−9.97317	−0.336962
$877$	−9.51226	−0.321206	−0.160603	−	0.987019i	$-0.551344\pi$
$877$	−9.51226	−0.321206	−0.160603	+	0.987019i	$0.551344\pi$
$878$	34.1454	1.15235
$879$	−7.98940	−0.269476
$880$	−1.04700	−0.0352942
$881$	25.2562	0.850901	0.425451	−	0.904982i	$-0.360116\pi$
$881$	25.2562	0.850901	0.425451	+	0.904982i	$0.360116\pi$
$882$	−1.90192	−0.0640411
$883$	5.80893	0.195486	0.0977431	−	0.995212i	$-0.468838\pi$
$883$	5.80893	0.195486	0.0977431	+	0.995212i	$0.468838\pi$
$884$	32.0565	1.07818
$885$	−7.19732	−0.241935
$886$	31.8827	1.07112
$887$	22.1020	0.742113	0.371057	−	0.928610i	$-0.378996\pi$
$887$	22.1020	0.742113	0.371057	+	0.928610i	$0.378996\pi$
$888$	2.75180	0.0923444
$889$	−13.4223	−0.450169
$890$	−8.58401	−0.287737
$891$	0.295463	0.00989839
$892$	3.88903	0.130214
$893$	38.6103	1.29205
$894$	32.3639	1.08241
$895$	−12.7639	−0.426650
$896$	−5.71609	−0.190961
$897$	6.47583	0.216222
$898$	51.5315	1.71963
$899$	−4.70339	−0.156867
$900$	−7.13467	−0.237822
$901$	−37.6278	−1.25356
$902$	−4.87841	−0.162433
$903$	−2.68115	−0.0892229
$904$	2.44232	0.0812305
$905$	2.60369	0.0865495
$906$	42.4133	1.40909
$907$	−11.3382	−0.376478	−0.188239	−	0.982123i	$-0.560278\pi$
$907$	−11.3382	−0.376478	−0.188239	+	0.982123i	$0.560278\pi$
$908$	30.7692	1.02111
$909$	−14.1510	−0.469358
$910$	−5.51484	−0.182815
$911$	0.809435	0.0268178	0.0134089	−	0.999910i	$-0.495732\pi$
$911$	0.809435	0.0268178	0.0134089	+	0.999910i	$0.495732\pi$
$912$	−17.3906	−0.575862
$913$	−1.37594	−0.0455369
$914$	−12.5935	−0.416557
$915$	−7.67582	−0.253755
$916$	37.5367	1.24025
$917$	8.26951	0.273083
$918$	9.97417	0.329197
$919$	−12.4541	−0.410821	−0.205411	−	0.978676i	$-0.565853\pi$
$919$	−12.4541	−0.410821	−0.205411	+	0.978676i	$0.565853\pi$
$920$	−0.956735	−0.0315426
$921$	−7.17730	−0.236500
$922$	−61.8868	−2.03813
$923$	28.8883	0.950871
$924$	−0.477857	−0.0157204
$925$	16.6787	0.548393
$926$	37.8551	1.24399
$927$	−1.46581	−0.0481434
$928$	−57.3944	−1.88406
$929$	−42.2794	−1.38714	−0.693571	−	0.720389i	$-0.743963\pi$
$929$	−42.2794	−1.38714	−0.693571	+	0.720389i	$0.743963\pi$
$930$	0.876378	0.0287376
$931$	−3.76509	−0.123396
$932$	8.59978	0.281695
$933$	9.33978	0.305771
$934$	36.1719	1.18358
$935$	1.18874	0.0388761
$936$	2.75087	0.0899151
$937$	−16.6054	−0.542474	−0.271237	−	0.962513i	$-0.587433\pi$
$937$	−16.6054	−0.542474	−0.271237	+	0.962513i	$0.587433\pi$
$938$	−0.971064	−0.0317064
$939$	−8.57535	−0.279846
$940$	−12.7240	−0.415012
$941$	19.4063	0.632626	0.316313	−	0.948655i	$-0.397555\pi$
$941$	19.4063	0.632626	0.316313	+	0.948655i	$0.397555\pi$
$942$	11.3091	0.368472
$943$	−14.8744	−0.484377
$944$	−43.3321	−1.41034
$945$	−0.767188	−0.0249566
$946$	−1.50667	−0.0489859
$947$	−46.2388	−1.50256	−0.751280	−	0.659984i	$-0.770563\pi$
$947$	−46.2388	−1.50256	−0.751280	+	0.659984i	$0.770563\pi$
$948$	3.11959	0.101320
$949$	23.3065	0.756560
$950$	−31.5898	−1.02491
$951$	21.1175	0.684783
$952$	3.81695	0.123708
$953$	38.1796	1.23676	0.618379	−	0.785880i	$-0.287790\pi$
$953$	38.1796	1.23676	0.618379	+	0.785880i	$0.287790\pi$
$954$	13.6464	0.441819
$955$	−19.0447	−0.616271
$956$	14.9779	0.484418
$957$	2.31376	0.0747932
$958$	−60.1233	−1.94250
$959$	3.75976	0.121409
$960$	3.60707	0.116418
$961$	−30.6393	−0.988363
$962$	27.1779	0.876250
$963$	−7.15713	−0.230635
$964$	−35.9533	−1.15798
$965$	1.45583	0.0468649
$966$	−3.25875	−0.104848
$967$	−49.8459	−1.60293	−0.801467	−	0.598038i	$-0.795947\pi$
$967$	−49.8459	−1.60293	−0.801467	+	0.598038i	$0.795947\pi$
$968$	−7.94264	−0.255286
$969$	19.7451	0.634303
$970$	−26.3120	−0.844828
$971$	−35.2170	−1.13017	−0.565084	−	0.825033i	$-0.691156\pi$
$971$	−35.2170	−1.13017	−0.565084	+	0.825033i	$0.691156\pi$
$972$	−1.61732	−0.0518755
$973$	19.7004	0.631565
$974$	−22.9787	−0.736285
$975$	16.6731	0.533967
$976$	−46.2130	−1.47924
$977$	−14.0709	−0.450166	−0.225083	−	0.974340i	$-0.572265\pi$
$977$	−14.0709	−0.450166	−0.225083	+	0.974340i	$0.572265\pi$
$978$	15.2761	0.488474
$979$	1.73819	0.0555529
$980$	1.24079	0.0396354
$981$	9.55398	0.305035
$982$	10.5590	0.336951
$983$	−23.1123	−0.737168	−0.368584	−	0.929595i	$-0.620157\pi$
$983$	−23.1123	−0.737168	−0.368584	+	0.929595i	$0.620157\pi$
$984$	−6.31851	−0.201427
$985$	−11.9816	−0.381766
$986$	78.1072	2.48744
$987$	10.2548	0.326415
$988$	−23.0149	−0.732201
$989$	−4.59386	−0.146076
$990$	−0.431120	−0.0137019
$991$	−40.0720	−1.27293	−0.636465	−	0.771306i	$-0.719604\pi$
$991$	−40.0720	−1.27293	−0.636465	+	0.771306i	$0.719604\pi$
$992$	4.40201	0.139764
$993$	11.9243	0.378406
$994$	−14.5371	−0.461088
$995$	4.65919	0.147706
$996$	7.53166	0.238650
$997$	7.16819	0.227019	0.113509	−	0.993537i	$-0.463791\pi$
$997$	7.16819	0.227019	0.113509	+	0.993537i	$0.463791\pi$
$998$	35.8072	1.13346
$999$	3.78080	0.119619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.10	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.10	✓	52	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)

\(f(q)\)	\(=\)	\(q-1.90192 q^{2} -1.00000 q^{3} +1.61732 q^{4} +0.767188 q^{5} +1.90192 q^{6} +1.00000 q^{7} +0.727834 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.90192 q^{2} -1.00000 q^{3} +1.61732 q^{4} +0.767188 q^{5} +1.90192 q^{6} +1.00000 q^{7} +0.727834 q^{8} +1.00000 q^{9} -1.45913 q^{10} +0.295463 q^{11} -1.61732 q^{12} +3.77953 q^{13} -1.90192 q^{14} -0.767188 q^{15} -4.61892 q^{16} +5.24425 q^{17} -1.90192 q^{18} -3.76509 q^{19} +1.24079 q^{20} -1.00000 q^{21} -0.561948 q^{22} -1.71339 q^{23} -0.727834 q^{24} -4.41142 q^{25} -7.18839 q^{26} -1.00000 q^{27} +1.61732 q^{28} -7.83095 q^{29} +1.45913 q^{30} +0.600616 q^{31} +7.32917 q^{32} -0.295463 q^{33} -9.97417 q^{34} +0.767188 q^{35} +1.61732 q^{36} -3.78080 q^{37} +7.16091 q^{38} -3.77953 q^{39} +0.558386 q^{40} +8.68124 q^{41} +1.90192 q^{42} +2.68115 q^{43} +0.477857 q^{44} +0.767188 q^{45} +3.25875 q^{46} -10.2548 q^{47} +4.61892 q^{48} +1.00000 q^{49} +8.39019 q^{50} -5.24425 q^{51} +6.11270 q^{52} -7.17506 q^{53} +1.90192 q^{54} +0.226676 q^{55} +0.727834 q^{56} +3.76509 q^{57} +14.8939 q^{58} +9.38143 q^{59} -1.24079 q^{60} +10.0051 q^{61} -1.14233 q^{62} +1.00000 q^{63} -4.70168 q^{64} +2.89961 q^{65} +0.561948 q^{66} +0.510569 q^{67} +8.48161 q^{68} +1.71339 q^{69} -1.45913 q^{70} +7.64336 q^{71} +0.727834 q^{72} +6.16649 q^{73} +7.19080 q^{74} +4.41142 q^{75} -6.08934 q^{76} +0.295463 q^{77} +7.18839 q^{78} -1.92887 q^{79} -3.54358 q^{80} +1.00000 q^{81} -16.5111 q^{82} -4.65688 q^{83} -1.61732 q^{84} +4.02332 q^{85} -5.09934 q^{86} +7.83095 q^{87} +0.215048 q^{88} +5.88295 q^{89} -1.45913 q^{90} +3.77953 q^{91} -2.77110 q^{92} -0.600616 q^{93} +19.5039 q^{94} -2.88853 q^{95} -7.32917 q^{96} +18.0326 q^{97} -1.90192 q^{98} +0.295463 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

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