LMFDB - Embedded newform 8043.2.a.t.1.15

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			1.15
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)

$f(q)$	$=$	$q-1.58348 q^{2} -1.00000 q^{3} +0.507395 q^{4} -2.03406 q^{5} +1.58348 q^{6} +1.00000 q^{7} +2.36350 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.58348 q^{2} -1.00000 q^{3} +0.507395 q^{4} -2.03406 q^{5} +1.58348 q^{6} +1.00000 q^{7} +2.36350 q^{8} +1.00000 q^{9} +3.22089 q^{10} +1.17498 q^{11} -0.507395 q^{12} +3.73140 q^{13} -1.58348 q^{14} +2.03406 q^{15} -4.75734 q^{16} -8.09560 q^{17} -1.58348 q^{18} -8.31210 q^{19} -1.03207 q^{20} -1.00000 q^{21} -1.86056 q^{22} +2.49738 q^{23} -2.36350 q^{24} -0.862589 q^{25} -5.90858 q^{26} -1.00000 q^{27} +0.507395 q^{28} -3.50435 q^{29} -3.22089 q^{30} +10.4075 q^{31} +2.80612 q^{32} -1.17498 q^{33} +12.8192 q^{34} -2.03406 q^{35} +0.507395 q^{36} -2.40440 q^{37} +13.1620 q^{38} -3.73140 q^{39} -4.80752 q^{40} -6.51764 q^{41} +1.58348 q^{42} +6.17846 q^{43} +0.596180 q^{44} -2.03406 q^{45} -3.95454 q^{46} -8.33923 q^{47} +4.75734 q^{48} +1.00000 q^{49} +1.36589 q^{50} +8.09560 q^{51} +1.89329 q^{52} +4.21927 q^{53} +1.58348 q^{54} -2.38999 q^{55} +2.36350 q^{56} +8.31210 q^{57} +5.54906 q^{58} +9.57535 q^{59} +1.03207 q^{60} -13.7336 q^{61} -16.4800 q^{62} +1.00000 q^{63} +5.07125 q^{64} -7.58990 q^{65} +1.86056 q^{66} +2.82956 q^{67} -4.10767 q^{68} -2.49738 q^{69} +3.22089 q^{70} +3.19338 q^{71} +2.36350 q^{72} -4.96110 q^{73} +3.80731 q^{74} +0.862589 q^{75} -4.21751 q^{76} +1.17498 q^{77} +5.90858 q^{78} +10.7268 q^{79} +9.67673 q^{80} +1.00000 q^{81} +10.3205 q^{82} -12.9827 q^{83} -0.507395 q^{84} +16.4670 q^{85} -9.78343 q^{86} +3.50435 q^{87} +2.77708 q^{88} -12.6293 q^{89} +3.22089 q^{90} +3.73140 q^{91} +1.26716 q^{92} -10.4075 q^{93} +13.2050 q^{94} +16.9073 q^{95} -2.80612 q^{96} -12.2662 q^{97} -1.58348 q^{98} +1.17498 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.58348	−1.11969	−0.559843	−	0.828599i	$-0.689139\pi$
$2$	−1.58348	−1.11969	−0.559843	+	0.828599i	$0.689139\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.507395	0.253697
$5$	−2.03406	−0.909660	−0.454830	−	0.890578i	$-0.650300\pi$
$5$	−2.03406	−0.909660	−0.454830	+	0.890578i	$0.650300\pi$
$6$	1.58348	0.646451
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.36350	0.835625
$9$	1.00000	0.333333
$10$	3.22089	1.01853
$11$	1.17498	0.354271	0.177135	−	0.984187i	$-0.443317\pi$
$11$	1.17498	0.354271	0.177135	+	0.984187i	$0.443317\pi$
$12$	−0.507395	−0.146472
$13$	3.73140	1.03490	0.517452	−	0.855712i	$-0.326881\pi$
$13$	3.73140	1.03490	0.517452	+	0.855712i	$0.326881\pi$
$14$	−1.58348	−0.423202
$15$	2.03406	0.525193
$16$	−4.75734	−1.18933
$17$	−8.09560	−1.96347	−0.981736	−	0.190248i	$-0.939071\pi$
$17$	−8.09560	−1.96347	−0.981736	+	0.190248i	$0.939071\pi$
$18$	−1.58348	−0.373229
$19$	−8.31210	−1.90693	−0.953463	−	0.301510i	$-0.902509\pi$
$19$	−8.31210	−1.90693	−0.953463	+	0.301510i	$0.902509\pi$
$20$	−1.03207	−0.230778
$21$	−1.00000	−0.218218
$22$	−1.86056	−0.396672
$23$	2.49738	0.520739	0.260370	−	0.965509i	$-0.416156\pi$
$23$	2.49738	0.520739	0.260370	+	0.965509i	$0.416156\pi$
$24$	−2.36350	−0.482448
$25$	−0.862589	−0.172518
$26$	−5.90858	−1.15877
$27$	−1.00000	−0.192450
$28$	0.507395	0.0958886
$29$	−3.50435	−0.650742	−0.325371	−	0.945586i	$-0.605489\pi$
$29$	−3.50435	−0.650742	−0.325371	+	0.945586i	$0.605489\pi$
$30$	−3.22089	−0.588051
$31$	10.4075	1.86924	0.934618	−	0.355654i	$-0.115742\pi$
$31$	10.4075	1.86924	0.934618	+	0.355654i	$0.115742\pi$
$32$	2.80612	0.496057
$33$	−1.17498	−0.204538
$34$	12.8192	2.19847
$35$	−2.03406	−0.343819
$36$	0.507395	0.0845658
$37$	−2.40440	−0.395282	−0.197641	−	0.980275i	$-0.563328\pi$
$37$	−2.40440	−0.395282	−0.197641	+	0.980275i	$0.563328\pi$
$38$	13.1620	2.13516
$39$	−3.73140	−0.597502
$40$	−4.80752	−0.760135
$41$	−6.51764	−1.01788	−0.508942	−	0.860801i	$-0.669963\pi$
$41$	−6.51764	−1.01788	−0.508942	+	0.860801i	$0.669963\pi$
$42$	1.58348	0.244336
$43$	6.17846	0.942206	0.471103	−	0.882078i	$-0.343856\pi$
$43$	6.17846	0.942206	0.471103	+	0.882078i	$0.343856\pi$
$44$	0.596180	0.0898775
$45$	−2.03406	−0.303220
$46$	−3.95454	−0.583065
$47$	−8.33923	−1.21640	−0.608201	−	0.793783i	$-0.708109\pi$
$47$	−8.33923	−1.21640	−0.608201	+	0.793783i	$0.708109\pi$
$48$	4.75734	0.686663
$49$	1.00000	0.142857
$50$	1.36589	0.193166
$51$	8.09560	1.13361
$52$	1.89329	0.262552
$53$	4.21927	0.579562	0.289781	−	0.957093i	$-0.406418\pi$
$53$	4.21927	0.579562	0.289781	+	0.957093i	$0.406418\pi$
$54$	1.58348	0.215484
$55$	−2.38999	−0.322266
$56$	2.36350	0.315837
$57$	8.31210	1.10096
$58$	5.54906	0.728627
$59$	9.57535	1.24660	0.623302	−	0.781981i	$-0.285791\pi$
$59$	9.57535	1.24660	0.623302	+	0.781981i	$0.285791\pi$
$60$	1.03207	0.133240
$61$	−13.7336	−1.75841	−0.879204	−	0.476446i	$-0.841925\pi$
$61$	−13.7336	−1.75841	−0.879204	+	0.476446i	$0.841925\pi$
$62$	−16.4800	−2.09296
$63$	1.00000	0.125988
$64$	5.07125	0.633907
$65$	−7.58990	−0.941411
$66$	1.86056	0.229019
$67$	2.82956	0.345686	0.172843	−	0.984949i	$-0.444705\pi$
$67$	2.82956	0.345686	0.172843	+	0.984949i	$0.444705\pi$
$68$	−4.10767	−0.498128
$69$	−2.49738	−0.300649
$70$	3.22089	0.384970
$71$	3.19338	0.378985	0.189492	−	0.981882i	$-0.439316\pi$
$71$	3.19338	0.378985	0.189492	+	0.981882i	$0.439316\pi$
$72$	2.36350	0.278542
$73$	−4.96110	−0.580653	−0.290326	−	0.956928i	$-0.593764\pi$
$73$	−4.96110	−0.580653	−0.290326	+	0.956928i	$0.593764\pi$
$74$	3.80731	0.442591
$75$	0.862589	0.0996032
$76$	−4.21751	−0.483782
$77$	1.17498	0.133902
$78$	5.90858	0.669015
$79$	10.7268	1.20686	0.603432	−	0.797414i	$-0.293799\pi$
$79$	10.7268	1.20686	0.603432	+	0.797414i	$0.293799\pi$
$80$	9.67673	1.08189
$81$	1.00000	0.111111
$82$	10.3205	1.13971
$83$	−12.9827	−1.42503	−0.712516	−	0.701655i	$-0.752445\pi$
$83$	−12.9827	−1.42503	−0.712516	+	0.701655i	$0.752445\pi$
$84$	−0.507395	−0.0553613
$85$	16.4670	1.78609
$86$	−9.78343	−1.05497
$87$	3.50435	0.375706
$88$	2.77708	0.296037
$89$	−12.6293	−1.33871	−0.669353	−	0.742945i	$-0.733429\pi$
$89$	−12.6293	−1.33871	−0.669353	+	0.742945i	$0.733429\pi$
$90$	3.22089	0.339511
$91$	3.73140	0.391157
$92$	1.26716	0.132110
$93$	−10.4075	−1.07920
$94$	13.2050	1.36199
$95$	16.9073	1.73466
$96$	−2.80612	−0.286399
$97$	−12.2662	−1.24544	−0.622720	−	0.782445i	$-0.713972\pi$
$97$	−12.2662	−1.24544	−0.622720	+	0.782445i	$0.713972\pi$
$98$	−1.58348	−0.159955
$99$	1.17498	0.118090
$100$	−0.437673	−0.0437673
$101$	10.4030	1.03514	0.517568	−	0.855642i	$-0.326837\pi$
$101$	10.4030	1.03514	0.517568	+	0.855642i	$0.326837\pi$
$102$	−12.8192	−1.26929
$103$	15.2288	1.50054	0.750269	−	0.661132i	$-0.229924\pi$
$103$	15.2288	1.50054	0.750269	+	0.661132i	$0.229924\pi$
$104$	8.81918	0.864791
$105$	2.03406	0.198504
$106$	−6.68111	−0.648927
$107$	1.38838	0.134219	0.0671097	−	0.997746i	$-0.478622\pi$
$107$	1.38838	0.134219	0.0671097	+	0.997746i	$0.478622\pi$
$108$	−0.507395	−0.0488241
$109$	2.93650	0.281266	0.140633	−	0.990062i	$-0.455086\pi$
$109$	2.93650	0.281266	0.140633	+	0.990062i	$0.455086\pi$
$110$	3.78449	0.360837
$111$	2.40440	0.228216
$112$	−4.75734	−0.449526
$113$	−4.96451	−0.467021	−0.233511	−	0.972354i	$-0.575021\pi$
$113$	−4.96451	−0.467021	−0.233511	+	0.972354i	$0.575021\pi$
$114$	−13.1620	−1.23273
$115$	−5.07982	−0.473696
$116$	−1.77809	−0.165091
$117$	3.73140	0.344968
$118$	−15.1623	−1.39581
$119$	−8.09560	−0.742123
$120$	4.80752	0.438864
$121$	−9.61941	−0.874492
$122$	21.7468	1.96887
$123$	6.51764	0.587676
$124$	5.28069	0.474220
$125$	11.9249	1.06659
$126$	−1.58348	−0.141067
$127$	4.90100	0.434893	0.217447	−	0.976072i	$-0.430227\pi$
$127$	4.90100	0.434893	0.217447	+	0.976072i	$0.430227\pi$
$128$	−13.6425	−1.20583
$129$	−6.17846	−0.543983
$130$	12.0184	1.05409
$131$	13.3143	1.16328	0.581639	−	0.813447i	$-0.302412\pi$
$131$	13.3143	1.16328	0.581639	+	0.813447i	$0.302412\pi$
$132$	−0.596180	−0.0518908
$133$	−8.31210	−0.720750
$134$	−4.48055	−0.387060
$135$	2.03406	0.175064
$136$	−19.1340	−1.64073
$137$	20.6490	1.76416	0.882082	−	0.471095i	$-0.156141\pi$
$137$	20.6490	1.76416	0.882082	+	0.471095i	$0.156141\pi$
$138$	3.95454	0.336632
$139$	−7.72470	−0.655201	−0.327600	−	0.944816i	$-0.606240\pi$
$139$	−7.72470	−0.655201	−0.327600	+	0.944816i	$0.606240\pi$
$140$	−1.03207	−0.0872260
$141$	8.33923	0.702290
$142$	−5.05664	−0.424344
$143$	4.38433	0.366636
$144$	−4.75734	−0.396445
$145$	7.12807	0.591954
$146$	7.85578	0.650149
$147$	−1.00000	−0.0824786
$148$	−1.21998	−0.100282
$149$	−13.2763	−1.08763	−0.543817	−	0.839204i	$-0.683021\pi$
$149$	−13.2763	−1.08763	−0.543817	+	0.839204i	$0.683021\pi$
$150$	−1.36589	−0.111524
$151$	1.33666	0.108776	0.0543879	−	0.998520i	$-0.482679\pi$
$151$	1.33666	0.108776	0.0543879	+	0.998520i	$0.482679\pi$
$152$	−19.6457	−1.59347
$153$	−8.09560	−0.654491
$154$	−1.86056	−0.149928
$155$	−21.1694	−1.70037
$156$	−1.89329	−0.151585
$157$	−5.99064	−0.478105	−0.239053	−	0.971007i	$-0.576837\pi$
$157$	−5.99064	−0.478105	−0.239053	+	0.971007i	$0.576837\pi$
$158$	−16.9857	−1.35131
$159$	−4.21927	−0.334610
$160$	−5.70783	−0.451244
$161$	2.49738	0.196821
$162$	−1.58348	−0.124410
$163$	10.6974	0.837886	0.418943	−	0.908012i	$-0.362401\pi$
$163$	10.6974	0.837886	0.418943	+	0.908012i	$0.362401\pi$
$164$	−3.30701	−0.258234
$165$	2.38999	0.186060
$166$	20.5577	1.59559
$167$	−12.7413	−0.985949	−0.492975	−	0.870044i	$-0.664090\pi$
$167$	−12.7413	−0.985949	−0.492975	+	0.870044i	$0.664090\pi$
$168$	−2.36350	−0.182348
$169$	0.923340	0.0710261
$170$	−26.0750	−1.99986
$171$	−8.31210	−0.635642
$172$	3.13492	0.239035
$173$	−17.7462	−1.34922	−0.674610	−	0.738174i	$-0.735688\pi$
$173$	−17.7462	−1.34922	−0.674610	+	0.738174i	$0.735688\pi$
$174$	−5.54906	−0.420673
$175$	−0.862589	−0.0652056
$176$	−5.58979	−0.421347
$177$	−9.57535	−0.719727
$178$	19.9982	1.49893
$179$	−6.76582	−0.505701	−0.252850	−	0.967505i	$-0.581368\pi$
$179$	−6.76582	−0.505701	−0.252850	+	0.967505i	$0.581368\pi$
$180$	−1.03207	−0.0769261
$181$	11.0685	0.822716	0.411358	−	0.911474i	$-0.365055\pi$
$181$	11.0685	0.822716	0.411358	+	0.911474i	$0.365055\pi$
$182$	−5.90858	−0.437973
$183$	13.7336	1.01522
$184$	5.90256	0.435143
$185$	4.89071	0.359572
$186$	16.4800	1.20837
$187$	−9.51220	−0.695601
$188$	−4.23128	−0.308598
$189$	−1.00000	−0.0727393
$190$	−26.7723	−1.94227
$191$	−19.4885	−1.41014	−0.705068	−	0.709140i	$-0.749084\pi$
$191$	−19.4885	−1.41014	−0.705068	+	0.709140i	$0.749084\pi$
$192$	−5.07125	−0.365986
$193$	3.02241	0.217558	0.108779	−	0.994066i	$-0.465306\pi$
$193$	3.02241	0.217558	0.108779	+	0.994066i	$0.465306\pi$
$194$	19.4232	1.39450
$195$	7.58990	0.543524
$196$	0.507395	0.0362425
$197$	−25.2988	−1.80247	−0.901233	−	0.433335i	$-0.857337\pi$
$197$	−25.2988	−1.80247	−0.901233	+	0.433335i	$0.857337\pi$
$198$	−1.86056	−0.132224
$199$	3.49513	0.247764	0.123882	−	0.992297i	$-0.460466\pi$
$199$	3.49513	0.247764	0.123882	+	0.992297i	$0.460466\pi$
$200$	−2.03873	−0.144160
$201$	−2.82956	−0.199582
$202$	−16.4729	−1.15903
$203$	−3.50435	−0.245957
$204$	4.10767	0.287594
$205$	13.2573	0.925929
$206$	−24.1144	−1.68013
$207$	2.49738	0.173580
$208$	−17.7515	−1.23085
$209$	−9.76657	−0.675568
$210$	−3.22089	−0.222262
$211$	6.26977	0.431629	0.215814	−	0.976434i	$-0.430759\pi$
$211$	6.26977	0.431629	0.215814	+	0.976434i	$0.430759\pi$
$212$	2.14084	0.147033
$213$	−3.19338	−0.218807
$214$	−2.19846	−0.150284
$215$	−12.5674	−0.857087
$216$	−2.36350	−0.160816
$217$	10.4075	0.706505
$218$	−4.64988	−0.314930
$219$	4.96110	0.335240
$220$	−1.21267	−0.0817580
$221$	−30.2079	−2.03200
$222$	−3.80731	−0.255530
$223$	−3.40829	−0.228236	−0.114118	−	0.993467i	$-0.536404\pi$
$223$	−3.40829	−0.228236	−0.114118	+	0.993467i	$0.536404\pi$
$224$	2.80612	0.187492
$225$	−0.862589	−0.0575060
$226$	7.86117	0.522917
$227$	−25.8890	−1.71831	−0.859156	−	0.511714i	$-0.829011\pi$
$227$	−25.8890	−1.71831	−0.859156	+	0.511714i	$0.829011\pi$
$228$	4.21751	0.279312
$229$	−6.00764	−0.396996	−0.198498	−	0.980101i	$-0.563606\pi$
$229$	−6.00764	−0.396996	−0.198498	+	0.980101i	$0.563606\pi$
$230$	8.04377	0.530391
$231$	−1.17498	−0.0773082
$232$	−8.28255	−0.543776
$233$	−10.3213	−0.676168	−0.338084	−	0.941116i	$-0.609779\pi$
$233$	−10.3213	−0.676168	−0.338084	+	0.941116i	$0.609779\pi$
$234$	−5.90858	−0.386256
$235$	16.9625	1.10651
$236$	4.85848	0.316260
$237$	−10.7268	−0.696783
$238$	12.8192	0.830945
$239$	−16.2362	−1.05023	−0.525117	−	0.851030i	$-0.675978\pi$
$239$	−16.2362	−1.05023	−0.525117	+	0.851030i	$0.675978\pi$
$240$	−9.67673	−0.624630
$241$	12.5949	0.811310	0.405655	−	0.914026i	$-0.367043\pi$
$241$	12.5949	0.811310	0.405655	+	0.914026i	$0.367043\pi$
$242$	15.2321	0.979157
$243$	−1.00000	−0.0641500
$244$	−6.96836	−0.446103
$245$	−2.03406	−0.129951
$246$	−10.3205	−0.658012
$247$	−31.0158	−1.97349
$248$	24.5981	1.56198
$249$	12.9827	0.822743
$250$	−18.8827	−1.19425
$251$	22.8035	1.43935	0.719673	−	0.694314i	$-0.244292\pi$
$251$	22.8035	1.43935	0.719673	+	0.694314i	$0.244292\pi$
$252$	0.507395	0.0319629
$253$	2.93438	0.184483
$254$	−7.76061	−0.486944
$255$	−16.4670	−1.03120
$256$	11.4600	0.716249
$257$	18.2621	1.13916	0.569580	−	0.821936i	$-0.307106\pi$
$257$	18.2621	1.13916	0.569580	+	0.821936i	$0.307106\pi$
$258$	9.78343	0.609090
$259$	−2.40440	−0.149402
$260$	−3.85107	−0.238833
$261$	−3.50435	−0.216914
$262$	−21.0829	−1.30251
$263$	26.3782	1.62655	0.813274	−	0.581881i	$-0.197683\pi$
$263$	26.3782	1.62655	0.813274	+	0.581881i	$0.197683\pi$
$264$	−2.77708	−0.170917
$265$	−8.58226	−0.527204
$266$	13.1620	0.807014
$267$	12.6293	0.772902
$268$	1.43571	0.0876997
$269$	−7.27730	−0.443705	−0.221852	−	0.975080i	$-0.571210\pi$
$269$	−7.27730	−0.443705	−0.221852	+	0.975080i	$0.571210\pi$
$270$	−3.22089	−0.196017
$271$	−10.6407	−0.646378	−0.323189	−	0.946334i	$-0.604755\pi$
$271$	−10.6407	−0.646378	−0.323189	+	0.946334i	$0.604755\pi$
$272$	38.5135	2.33523
$273$	−3.73140	−0.225835
$274$	−32.6972	−1.97531
$275$	−1.01353	−0.0611180
$276$	−1.26716	−0.0762738
$277$	−30.1397	−1.81092	−0.905459	−	0.424434i	$-0.860473\pi$
$277$	−30.1397	−1.81092	−0.905459	+	0.424434i	$0.860473\pi$
$278$	12.2319	0.733619
$279$	10.4075	0.623079
$280$	−4.80752	−0.287304
$281$	−21.8838	−1.30548	−0.652739	−	0.757583i	$-0.726380\pi$
$281$	−21.8838	−1.30548	−0.652739	+	0.757583i	$0.726380\pi$
$282$	−13.2050	−0.786345
$283$	15.4851	0.920495	0.460248	−	0.887791i	$-0.347761\pi$
$283$	15.4851	0.920495	0.460248	+	0.887791i	$0.347761\pi$
$284$	1.62031	0.0961474
$285$	−16.9073	−1.00150
$286$	−6.94248	−0.410517
$287$	−6.51764	−0.384724
$288$	2.80612	0.165352
$289$	48.5388	2.85522
$290$	−11.2871	−0.662803
$291$	12.2662	0.719055
$292$	−2.51724	−0.147310
$293$	9.98207	0.583158	0.291579	−	0.956547i	$-0.405819\pi$
$293$	9.98207	0.583158	0.291579	+	0.956547i	$0.405819\pi$
$294$	1.58348	0.0923502
$295$	−19.4769	−1.13399
$296$	−5.68282	−0.330307
$297$	−1.17498	−0.0681794
$298$	21.0226	1.21781
$299$	9.31871	0.538915
$300$	0.437673	0.0252691
$301$	6.17846	0.356120
$302$	−2.11657	−0.121795
$303$	−10.4030	−0.597636
$304$	39.5435	2.26797
$305$	27.9350	1.59955
$306$	12.8192	0.732824
$307$	4.79874	0.273879	0.136939	−	0.990579i	$-0.456273\pi$
$307$	4.79874	0.273879	0.136939	+	0.990579i	$0.456273\pi$
$308$	0.596180	0.0339705
$309$	−15.2288	−0.866336
$310$	33.5213	1.90388
$311$	−5.91843	−0.335603	−0.167802	−	0.985821i	$-0.553667\pi$
$311$	−5.91843	−0.335603	−0.167802	+	0.985821i	$0.553667\pi$
$312$	−8.81918	−0.499288
$313$	8.13144	0.459616	0.229808	−	0.973236i	$-0.426190\pi$
$313$	8.13144	0.459616	0.229808	+	0.973236i	$0.426190\pi$
$314$	9.48603	0.535328
$315$	−2.03406	−0.114606
$316$	5.44274	0.306178
$317$	4.12351	0.231600	0.115800	−	0.993273i	$-0.463057\pi$
$317$	4.12351	0.231600	0.115800	+	0.993273i	$0.463057\pi$
$318$	6.68111	0.374658
$319$	−4.11755	−0.230539
$320$	−10.3152	−0.576640
$321$	−1.38838	−0.0774916
$322$	−3.95454	−0.220378
$323$	67.2914	3.74420
$324$	0.507395	0.0281886
$325$	−3.21867	−0.178539
$326$	−16.9391	−0.938170
$327$	−2.93650	−0.162389
$328$	−15.4045	−0.850569
$329$	−8.33923	−0.459757
$330$	−3.78449	−0.208329
$331$	−7.88009	−0.433129	−0.216565	−	0.976268i	$-0.569485\pi$
$331$	−7.88009	−0.433129	−0.216565	+	0.976268i	$0.569485\pi$
$332$	−6.58734	−0.361527
$333$	−2.40440	−0.131761
$334$	20.1755	1.10395
$335$	−5.75551	−0.314457
$336$	4.75734	0.259534
$337$	5.71700	0.311425	0.155712	−	0.987802i	$-0.450233\pi$
$337$	5.71700	0.311425	0.155712	+	0.987802i	$0.450233\pi$
$338$	−1.46209	−0.0795270
$339$	4.96451	0.269635
$340$	8.35525	0.453127
$341$	12.2286	0.662215
$342$	13.1620	0.711720
$343$	1.00000	0.0539949
$344$	14.6028	0.787330
$345$	5.07982	0.273488
$346$	28.1007	1.51070
$347$	−17.0545	−0.915536	−0.457768	−	0.889072i	$-0.651351\pi$
$347$	−17.0545	−0.915536	−0.457768	+	0.889072i	$0.651351\pi$
$348$	1.77809	0.0953156
$349$	7.88885	0.422280	0.211140	−	0.977456i	$-0.432282\pi$
$349$	7.88885	0.422280	0.211140	+	0.977456i	$0.432282\pi$
$350$	1.36589	0.0730099
$351$	−3.73140	−0.199167
$352$	3.29715	0.175739
$353$	−12.6774	−0.674752	−0.337376	−	0.941370i	$-0.609539\pi$
$353$	−12.6774	−0.674752	−0.337376	+	0.941370i	$0.609539\pi$
$354$	15.1623	0.805869
$355$	−6.49554	−0.344747
$356$	−6.40805	−0.339626
$357$	8.09560	0.428465
$358$	10.7135	0.566226
$359$	−34.5229	−1.82205	−0.911023	−	0.412355i	$-0.864706\pi$
$359$	−34.5229	−1.82205	−0.911023	+	0.412355i	$0.864706\pi$
$360$	−4.80752	−0.253378
$361$	50.0910	2.63637
$362$	−17.5267	−0.921183
$363$	9.61941	0.504888
$364$	1.89329	0.0992355
$365$	10.0912	0.528197
$366$	−21.7468	−1.13672
$367$	4.22048	0.220307	0.110154	−	0.993915i	$-0.464866\pi$
$367$	4.22048	0.220307	0.110154	+	0.993915i	$0.464866\pi$
$368$	−11.8809	−0.619333
$369$	−6.51764	−0.339295
$370$	−7.74432	−0.402608
$371$	4.21927	0.219054
$372$	−5.28069	−0.273791
$373$	33.9458	1.75765	0.878823	−	0.477148i	$-0.158329\pi$
$373$	33.9458	1.75765	0.878823	+	0.477148i	$0.158329\pi$
$374$	15.0623	0.778854
$375$	−11.9249	−0.615798
$376$	−19.7098	−1.01646
$377$	−13.0761	−0.673455
$378$	1.58348	0.0814452
$379$	32.6135	1.67524	0.837620	−	0.546253i	$-0.183946\pi$
$379$	32.6135	1.67524	0.837620	+	0.546253i	$0.183946\pi$
$380$	8.57869	0.440077
$381$	−4.90100	−0.251086
$382$	30.8595	1.57891
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	13.6425	0.696188
$385$	−2.38999	−0.121805
$386$	−4.78591	−0.243597
$387$	6.17846	0.314069
$388$	−6.22378	−0.315965
$389$	19.2296	0.974978	0.487489	−	0.873129i	$-0.337913\pi$
$389$	19.2296	0.974978	0.487489	+	0.873129i	$0.337913\pi$
$390$	−12.0184	−0.608576
$391$	−20.2178	−1.02246
$392$	2.36350	0.119375
$393$	−13.3143	−0.671619
$394$	40.0600	2.01820
$395$	−21.8191	−1.09784
$396$	0.596180	0.0299592
$397$	−7.72827	−0.387871	−0.193935	−	0.981014i	$-0.562125\pi$
$397$	−7.72827	−0.387871	−0.193935	+	0.981014i	$0.562125\pi$
$398$	−5.53446	−0.277417
$399$	8.31210	0.416125
$400$	4.10363	0.205182
$401$	33.9001	1.69289	0.846444	−	0.532477i	$-0.178739\pi$
$401$	33.9001	1.69289	0.846444	+	0.532477i	$0.178739\pi$
$402$	4.48055	0.223469
$403$	38.8344	1.93448
$404$	5.27842	0.262611
$405$	−2.03406	−0.101073
$406$	5.54906	0.275395
$407$	−2.82513	−0.140037
$408$	19.1340	0.947274
$409$	1.66653	0.0824048	0.0412024	−	0.999151i	$-0.486881\pi$
$409$	1.66653	0.0824048	0.0412024	+	0.999151i	$0.486881\pi$
$410$	−20.9926	−1.03675
$411$	−20.6490	−1.01854
$412$	7.72701	0.380683
$413$	9.57535	0.471172
$414$	−3.95454	−0.194355
$415$	26.4076	1.29630
$416$	10.4708	0.513372
$417$	7.72470	0.378280
$418$	15.4651	0.756424
$419$	27.9606	1.36597	0.682983	−	0.730434i	$-0.260682\pi$
$419$	27.9606	1.36597	0.682983	+	0.730434i	$0.260682\pi$
$420$	1.03207	0.0503600
$421$	−0.833488	−0.0406217	−0.0203109	−	0.999794i	$-0.506466\pi$
$421$	−0.833488	−0.0406217	−0.0203109	+	0.999794i	$0.506466\pi$
$422$	−9.92803	−0.483289
$423$	−8.33923	−0.405467
$424$	9.97227	0.484296
$425$	6.98318	0.338734
$426$	5.05664	0.244995
$427$	−13.7336	−0.664616
$428$	0.704455	0.0340511
$429$	−4.38433	−0.211677
$430$	19.9001	0.959669
$431$	−13.2665	−0.639025	−0.319513	−	0.947582i	$-0.603519\pi$
$431$	−13.2665	−0.639025	−0.319513	+	0.947582i	$0.603519\pi$
$432$	4.75734	0.228888
$433$	−26.6116	−1.27887	−0.639436	−	0.768845i	$-0.720832\pi$
$433$	−26.6116	−1.27887	−0.639436	+	0.768845i	$0.720832\pi$
$434$	−16.4800	−0.791064
$435$	−7.12807	−0.341765
$436$	1.48997	0.0713565
$437$	−20.7584	−0.993011
$438$	−7.85578	−0.375364
$439$	−3.42227	−0.163336	−0.0816680	−	0.996660i	$-0.526025\pi$
$439$	−3.42227	−0.163336	−0.0816680	+	0.996660i	$0.526025\pi$
$440$	−5.64875	−0.269294
$441$	1.00000	0.0476190
$442$	47.8335	2.27521
$443$	30.7219	1.45964	0.729821	−	0.683638i	$-0.239603\pi$
$443$	30.7219	1.45964	0.729821	+	0.683638i	$0.239603\pi$
$444$	1.21998	0.0578978
$445$	25.6888	1.21777
$446$	5.39694	0.255553
$447$	13.2763	0.627946
$448$	5.07125	0.239594
$449$	21.0431	0.993087	0.496544	−	0.868012i	$-0.334602\pi$
$449$	21.0431	0.993087	0.496544	+	0.868012i	$0.334602\pi$
$450$	1.36589	0.0643886
$451$	−7.65811	−0.360606
$452$	−2.51896	−0.118482
$453$	−1.33666	−0.0628017
$454$	40.9946	1.92397
$455$	−7.58990	−0.355820
$456$	19.6457	0.919993
$457$	25.9974	1.21611	0.608054	−	0.793896i	$-0.291950\pi$
$457$	25.9974	1.21611	0.608054	+	0.793896i	$0.291950\pi$
$458$	9.51296	0.444511
$459$	8.09560	0.377870
$460$	−2.57747	−0.120175
$461$	20.8371	0.970479	0.485239	−	0.874381i	$-0.338732\pi$
$461$	20.8371	0.970479	0.485239	+	0.874381i	$0.338732\pi$
$462$	1.86056	0.0865609
$463$	33.4805	1.55597	0.777986	−	0.628281i	$-0.216241\pi$
$463$	33.4805	1.55597	0.777986	+	0.628281i	$0.216241\pi$
$464$	16.6714	0.773950
$465$	21.1694	0.981709
$466$	16.3435	0.757096
$467$	−15.8486	−0.733386	−0.366693	−	0.930342i	$-0.619510\pi$
$467$	−15.8486	−0.733386	−0.366693	+	0.930342i	$0.619510\pi$
$468$	1.89329	0.0875175
$469$	2.82956	0.130657
$470$	−26.8597	−1.23895
$471$	5.99064	0.276034
$472$	22.6314	1.04169
$473$	7.25958	0.333796
$474$	16.9857	0.780179
$475$	7.16993	0.328979
$476$	−4.10767	−0.188275
$477$	4.21927	0.193187
$478$	25.7097	1.17593
$479$	34.1683	1.56119	0.780595	−	0.625037i	$-0.214916\pi$
$479$	34.1683	1.56119	0.780595	+	0.625037i	$0.214916\pi$
$480$	5.70783	0.260526
$481$	−8.97179	−0.409078
$482$	−19.9437	−0.908413
$483$	−2.49738	−0.113635
$484$	−4.88084	−0.221856
$485$	24.9501	1.13293
$486$	1.58348	0.0718279
$487$	−37.5504	−1.70157	−0.850785	−	0.525513i	$-0.823873\pi$
$487$	−37.5504	−1.70157	−0.850785	+	0.525513i	$0.823873\pi$
$488$	−32.4594	−1.46937
$489$	−10.6974	−0.483754
$490$	3.22089	0.145505
$491$	−14.0685	−0.634904	−0.317452	−	0.948274i	$-0.602827\pi$
$491$	−14.0685	−0.634904	−0.317452	+	0.948274i	$0.602827\pi$
$492$	3.30701	0.149092
$493$	28.3698	1.27771
$494$	49.1127	2.20968
$495$	−2.38999	−0.107422
$496$	−49.5118	−2.22315
$497$	3.19338	0.143243
$498$	−20.5577	−0.921214
$499$	7.63867	0.341954	0.170977	−	0.985275i	$-0.445308\pi$
$499$	7.63867	0.341954	0.170977	+	0.985275i	$0.445308\pi$
$500$	6.05062	0.270592
$501$	12.7413	0.569238
$502$	−36.1088	−1.61161
$503$	−13.4944	−0.601686	−0.300843	−	0.953674i	$-0.597268\pi$
$503$	−13.4944	−0.601686	−0.300843	+	0.953674i	$0.597268\pi$
$504$	2.36350	0.105279
$505$	−21.1603	−0.941623
$506$	−4.64651	−0.206563
$507$	−0.923340	−0.0410070
$508$	2.48674	0.110331
$509$	−2.95066	−0.130786	−0.0653928	−	0.997860i	$-0.520830\pi$
$509$	−2.95066	−0.130786	−0.0653928	+	0.997860i	$0.520830\pi$
$510$	26.0750	1.15462
$511$	−4.96110	−0.219466
$512$	9.13830	0.403860
$513$	8.31210	0.366988
$514$	−28.9176	−1.27550
$515$	−30.9763	−1.36498
$516$	−3.13492	−0.138007
$517$	−9.79846	−0.430936
$518$	3.80731	0.167284
$519$	17.7462	0.778973
$520$	−17.9388	−0.786667
$521$	−16.1698	−0.708413	−0.354206	−	0.935167i	$-0.615249\pi$
$521$	−16.1698	−0.708413	−0.354206	+	0.935167i	$0.615249\pi$
$522$	5.54906	0.242876
$523$	23.4396	1.02494	0.512471	−	0.858704i	$-0.328730\pi$
$523$	23.4396	1.02494	0.512471	+	0.858704i	$0.328730\pi$
$524$	6.75562	0.295121
$525$	0.862589	0.0376465
$526$	−41.7692	−1.82122
$527$	−84.2547	−3.67019
$528$	5.58979	0.243265
$529$	−16.7631	−0.728831
$530$	13.5898	0.590303
$531$	9.57535	0.415535
$532$	−4.21751	−0.182852
$533$	−24.3199	−1.05341
$534$	−19.9982	−0.865408
$535$	−2.82404	−0.122094
$536$	6.68769	0.288864
$537$	6.76582	0.291967
$538$	11.5234	0.496810
$539$	1.17498	0.0506101
$540$	1.03207	0.0444133
$541$	−36.5762	−1.57253	−0.786267	−	0.617887i	$-0.787989\pi$
$541$	−36.5762	−1.57253	−0.786267	+	0.617887i	$0.787989\pi$
$542$	16.8493	0.723741
$543$	−11.0685	−0.474995
$544$	−22.7173	−0.973994
$545$	−5.97303	−0.255857
$546$	5.90858	0.252864
$547$	27.1642	1.16146	0.580728	−	0.814098i	$-0.302768\pi$
$547$	27.1642	1.16146	0.580728	+	0.814098i	$0.302768\pi$
$548$	10.4772	0.447564
$549$	−13.7336	−0.586136
$550$	1.60490	0.0684330
$551$	29.1285	1.24092
$552$	−5.90256	−0.251230
$553$	10.7268	0.456152
$554$	47.7255	2.02766
$555$	−4.89071	−0.207599
$556$	−3.91947	−0.166223
$557$	17.2971	0.732901	0.366451	−	0.930438i	$-0.380573\pi$
$557$	17.2971	0.732901	0.366451	+	0.930438i	$0.380573\pi$
$558$	−16.4800	−0.697652
$559$	23.0543	0.975092
$560$	9.67673	0.408916
$561$	9.51220	0.401605
$562$	34.6525	1.46173
$563$	−34.5133	−1.45456	−0.727280	−	0.686341i	$-0.759216\pi$
$563$	−34.5133	−1.45456	−0.727280	+	0.686341i	$0.759216\pi$
$564$	4.23128	0.178169
$565$	10.0981	0.424831
$566$	−24.5203	−1.03067
$567$	1.00000	0.0419961
$568$	7.54757	0.316689
$569$	8.65891	0.363000	0.181500	−	0.983391i	$-0.441905\pi$
$569$	8.65891	0.363000	0.181500	+	0.983391i	$0.441905\pi$
$570$	26.7723	1.12137
$571$	−4.29822	−0.179875	−0.0899375	−	0.995947i	$-0.528667\pi$
$571$	−4.29822	−0.179875	−0.0899375	+	0.995947i	$0.528667\pi$
$572$	2.22459	0.0930146
$573$	19.4885	0.814142
$574$	10.3205	0.430770
$575$	−2.15421	−0.0898368
$576$	5.07125	0.211302
$577$	36.4562	1.51769	0.758845	−	0.651271i	$-0.225764\pi$
$577$	36.4562	1.51769	0.758845	+	0.651271i	$0.225764\pi$
$578$	−76.8600	−3.19695
$579$	−3.02241	−0.125607
$580$	3.61675	0.150177
$581$	−12.9827	−0.538612
$582$	−19.4232	−0.805116
$583$	4.95757	0.205322
$584$	−11.7256	−0.485208
$585$	−7.58990	−0.313804
$586$	−15.8064	−0.652955
$587$	24.6640	1.01799	0.508996	−	0.860769i	$-0.330017\pi$
$587$	24.6640	1.01799	0.508996	+	0.860769i	$0.330017\pi$
$588$	−0.507395	−0.0209246
$589$	−86.5079	−3.56449
$590$	30.8411	1.26971
$591$	25.2988	1.04065
$592$	11.4386	0.470122
$593$	−3.78538	−0.155447	−0.0777234	−	0.996975i	$-0.524765\pi$
$593$	−3.78538	−0.155447	−0.0777234	+	0.996975i	$0.524765\pi$
$594$	1.86056	0.0763396
$595$	16.4670	0.675080
$596$	−6.73631	−0.275930
$597$	−3.49513	−0.143046
$598$	−14.7560	−0.603416
$599$	21.6900	0.886228	0.443114	−	0.896465i	$-0.353874\pi$
$599$	21.6900	0.886228	0.443114	+	0.896465i	$0.353874\pi$
$600$	2.03873	0.0832310
$601$	0.767439	0.0313045	0.0156522	−	0.999877i	$-0.495018\pi$
$601$	0.767439	0.0313045	0.0156522	+	0.999877i	$0.495018\pi$
$602$	−9.78343	−0.398743
$603$	2.82956	0.115229
$604$	0.678214	0.0275961
$605$	19.5665	0.795491
$606$	16.4729	0.669165
$607$	−10.5297	−0.427386	−0.213693	−	0.976901i	$-0.568549\pi$
$607$	−10.5297	−0.427386	−0.213693	+	0.976901i	$0.568549\pi$
$608$	−23.3248	−0.945944
$609$	3.50435	0.142004
$610$	−44.2344	−1.79100
$611$	−31.1170	−1.25886
$612$	−4.10767	−0.166043
$613$	14.3641	0.580161	0.290080	−	0.957002i	$-0.406318\pi$
$613$	14.3641	0.580161	0.290080	+	0.957002i	$0.406318\pi$
$614$	−7.59869	−0.306658
$615$	−13.2573	−0.534585
$616$	2.77708	0.111892
$617$	12.2239	0.492114	0.246057	−	0.969255i	$-0.420865\pi$
$617$	12.2239	0.492114	0.246057	+	0.969255i	$0.420865\pi$
$618$	24.1144	0.970025
$619$	−49.0827	−1.97280	−0.986400	−	0.164363i	$-0.947443\pi$
$619$	−49.0827	−1.97280	−0.986400	+	0.164363i	$0.947443\pi$
$620$	−10.7413	−0.431379
$621$	−2.49738	−0.100216
$622$	9.37168	0.375770
$623$	−12.6293	−0.505983
$624$	17.7515	0.710630
$625$	−19.9430	−0.797720
$626$	−12.8759	−0.514626
$627$	9.76657	0.390039
$628$	−3.03962	−0.121294
$629$	19.4651	0.776124
$630$	3.22089	0.128323
$631$	27.3662	1.08943	0.544716	−	0.838620i	$-0.316637\pi$
$631$	27.3662	1.08943	0.544716	+	0.838620i	$0.316637\pi$
$632$	25.3529	1.00849
$633$	−6.26977	−0.249201
$634$	−6.52948	−0.259319
$635$	−9.96894	−0.395605
$636$	−2.14084	−0.0848897
$637$	3.73140	0.147843
$638$	6.52005	0.258131
$639$	3.19338	0.126328
$640$	27.7496	1.09690
$641$	30.0221	1.18580	0.592900	−	0.805276i	$-0.297983\pi$
$641$	30.0221	1.18580	0.592900	+	0.805276i	$0.297983\pi$
$642$	2.19846	0.0867663
$643$	36.6432	1.44507	0.722534	−	0.691335i	$-0.242977\pi$
$643$	36.6432	1.44507	0.722534	+	0.691335i	$0.242977\pi$
$644$	1.26716	0.0499329
$645$	12.5674	0.494840
$646$	−106.554	−4.19233
$647$	17.2026	0.676306	0.338153	−	0.941091i	$-0.390198\pi$
$647$	17.2026	0.676306	0.338153	+	0.941091i	$0.390198\pi$
$648$	2.36350	0.0928472
$649$	11.2509	0.441635
$650$	5.09668	0.199908
$651$	−10.4075	−0.407901
$652$	5.42781	0.212570
$653$	14.1311	0.552993	0.276496	−	0.961015i	$-0.410827\pi$
$653$	14.1311	0.552993	0.276496	+	0.961015i	$0.410827\pi$
$654$	4.64988	0.181825
$655$	−27.0822	−1.05819
$656$	31.0066	1.21060
$657$	−4.96110	−0.193551
$658$	13.2050	0.514783
$659$	19.4818	0.758901	0.379451	−	0.925212i	$-0.376113\pi$
$659$	19.4818	0.758901	0.379451	+	0.925212i	$0.376113\pi$
$660$	1.21267	0.0472030
$661$	−22.5821	−0.878344	−0.439172	−	0.898403i	$-0.644728\pi$
$661$	−22.5821	−0.878344	−0.439172	+	0.898403i	$0.644728\pi$
$662$	12.4779	0.484969
$663$	30.2079	1.17318
$664$	−30.6846	−1.19079
$665$	16.9073	0.655638
$666$	3.80731	0.147530
$667$	−8.75169	−0.338867
$668$	−6.46485	−0.250133
$669$	3.40829	0.131772
$670$	9.11371	0.352093
$671$	−16.1368	−0.622952
$672$	−2.80612	−0.108249
$673$	−19.5706	−0.754390	−0.377195	−	0.926134i	$-0.623111\pi$
$673$	−19.5706	−0.754390	−0.377195	+	0.926134i	$0.623111\pi$
$674$	−9.05273	−0.348698
$675$	0.862589	0.0332011
$676$	0.468498	0.0180191
$677$	−29.1476	−1.12023	−0.560117	−	0.828413i	$-0.689244\pi$
$677$	−29.1476	−1.12023	−0.560117	+	0.828413i	$0.689244\pi$
$678$	−7.86117	−0.301907
$679$	−12.2662	−0.470732
$680$	38.9197	1.49250
$681$	25.8890	0.992068
$682$	−19.3637	−0.741474
$683$	−40.4250	−1.54682	−0.773410	−	0.633906i	$-0.781450\pi$
$683$	−40.4250	−1.54682	−0.773410	+	0.633906i	$0.781450\pi$
$684$	−4.21751	−0.161261
$685$	−42.0014	−1.60479
$686$	−1.58348	−0.0604574
$687$	6.00764	0.229206
$688$	−29.3930	−1.12060
$689$	15.7438	0.599791
$690$	−8.04377	−0.306221
$691$	47.9232	1.82308	0.911541	−	0.411208i	$-0.134893\pi$
$691$	47.9232	1.82308	0.911541	+	0.411208i	$0.134893\pi$
$692$	−9.00434	−0.342294
$693$	1.17498	0.0446339
$694$	27.0054	1.02511
$695$	15.7125	0.596010
$696$	8.28255	0.313949
$697$	52.7642	1.99859
$698$	−12.4918	−0.472822
$699$	10.3213	0.390386
$700$	−0.437673	−0.0165425
$701$	−44.1271	−1.66666	−0.833329	−	0.552778i	$-0.813568\pi$
$701$	−44.1271	−1.66666	−0.833329	+	0.552778i	$0.813568\pi$
$702$	5.90858	0.223005
$703$	19.9856	0.753773
$704$	5.95864	0.224575
$705$	−16.9625	−0.638846
$706$	20.0744	0.755510
$707$	10.4030	0.391245
$708$	−4.85848	−0.182593
$709$	−33.6912	−1.26530	−0.632650	−	0.774438i	$-0.718033\pi$
$709$	−33.6912	−1.26530	−0.632650	+	0.774438i	$0.718033\pi$
$710$	10.2855	0.386009
$711$	10.7268	0.402288
$712$	−29.8495	−1.11866
$713$	25.9914	0.973384
$714$	−12.8192	−0.479746
$715$	−8.91800	−0.333514
$716$	−3.43294	−0.128295
$717$	16.2362	0.606353
$718$	54.6661	2.04012
$719$	18.9323	0.706057	0.353029	−	0.935613i	$-0.385152\pi$
$719$	18.9323	0.706057	0.353029	+	0.935613i	$0.385152\pi$
$720$	9.67673	0.360630
$721$	15.2288	0.567150
$722$	−79.3178	−2.95190
$723$	−12.5949	−0.468410
$724$	5.61610	0.208721
$725$	3.02282	0.112265
$726$	−15.2321	−0.565317
$727$	6.78906	0.251792	0.125896	−	0.992043i	$-0.459819\pi$
$727$	6.78906	0.251792	0.125896	+	0.992043i	$0.459819\pi$
$728$	8.81918	0.326860
$729$	1.00000	0.0370370
$730$	−15.9792	−0.591415
$731$	−50.0183	−1.84999
$732$	6.96836	0.257558
$733$	21.4982	0.794054	0.397027	−	0.917807i	$-0.370042\pi$
$733$	21.4982	0.794054	0.397027	+	0.917807i	$0.370042\pi$
$734$	−6.68303	−0.246675
$735$	2.03406	0.0750275
$736$	7.00795	0.258316
$737$	3.32469	0.122467
$738$	10.3205	0.379904
$739$	4.08334	0.150208	0.0751041	−	0.997176i	$-0.476071\pi$
$739$	4.08334	0.150208	0.0751041	+	0.997176i	$0.476071\pi$
$740$	2.48152	0.0912225
$741$	31.0158	1.13939
$742$	−6.68111	−0.245271
$743$	−2.66701	−0.0978431	−0.0489216	−	0.998803i	$-0.515578\pi$
$743$	−2.66701	−0.0978431	−0.0489216	+	0.998803i	$0.515578\pi$
$744$	−24.5981	−0.901809
$745$	27.0048	0.989378
$746$	−53.7523	−1.96801
$747$	−12.9827	−0.475011
$748$	−4.82644	−0.176472
$749$	1.38838	0.0507302
$750$	18.8827	0.689500
$751$	51.9749	1.89659	0.948295	−	0.317391i	$-0.102807\pi$
$751$	51.9749	1.89659	0.948295	+	0.317391i	$0.102807\pi$
$752$	39.6726	1.44671
$753$	−22.8035	−0.831006
$754$	20.7057	0.754059
$755$	−2.71885	−0.0989491
$756$	−0.507395	−0.0184538
$757$	14.3161	0.520326	0.260163	−	0.965565i	$-0.416224\pi$
$757$	14.3161	0.520326	0.260163	+	0.965565i	$0.416224\pi$
$758$	−51.6426	−1.87574
$759$	−2.93438	−0.106511
$760$	39.9605	1.44952
$761$	−1.05740	−0.0383307	−0.0191653	−	0.999816i	$-0.506101\pi$
$761$	−1.05740	−0.0383307	−0.0191653	+	0.999816i	$0.506101\pi$
$762$	7.76061	0.281137
$763$	2.93650	0.106309
$764$	−9.88834	−0.357748
$765$	16.4670	0.595364
$766$	1.58348	0.0572133
$767$	35.7294	1.29012
$768$	−11.4600	−0.413526
$769$	37.7716	1.36208	0.681040	−	0.732246i	$-0.261528\pi$
$769$	37.7716	1.36208	0.681040	+	0.732246i	$0.261528\pi$
$770$	3.78449	0.136384
$771$	−18.2621	−0.657695
$772$	1.53356	0.0551939
$773$	36.3383	1.30700	0.653498	−	0.756928i	$-0.273301\pi$
$773$	36.3383	1.30700	0.653498	+	0.756928i	$0.273301\pi$
$774$	−9.78343	−0.351658
$775$	−8.97737	−0.322477
$776$	−28.9911	−1.04072
$777$	2.40440	0.0862575
$778$	−30.4495	−1.09167
$779$	54.1752	1.94103
$780$	3.85107	0.137891
$781$	3.75217	0.134263
$782$	32.0144	1.14483
$783$	3.50435	0.125235
$784$	−4.75734	−0.169905
$785$	12.1853	0.434913
$786$	21.0829	0.752003
$787$	−3.97456	−0.141678	−0.0708388	−	0.997488i	$-0.522568\pi$
$787$	−3.97456	−0.141678	−0.0708388	+	0.997488i	$0.522568\pi$
$788$	−12.8365	−0.457281
$789$	−26.3782	−0.939088
$790$	34.5500	1.22923
$791$	−4.96451	−0.176518
$792$	2.77708	0.0986791
$793$	−51.2456	−1.81978
$794$	12.2375	0.434293
$795$	8.58226	0.304382
$796$	1.77341	0.0628569
$797$	41.3980	1.46639	0.733196	−	0.680018i	$-0.238028\pi$
$797$	41.3980	1.46639	0.733196	+	0.680018i	$0.238028\pi$
$798$	−13.1620	−0.465930
$799$	67.5111	2.38837
$800$	−2.42053	−0.0855787
$801$	−12.6293	−0.446235
$802$	−53.6799	−1.89550
$803$	−5.82921	−0.205708
$804$	−1.43571	−0.0506334
$805$	−5.07982	−0.179040
$806$	−61.4933	−2.16601
$807$	7.27730	0.256173
$808$	24.5875	0.864986
$809$	−47.1729	−1.65851	−0.829256	−	0.558869i	$-0.811236\pi$
$809$	−47.1729	−1.65851	−0.829256	+	0.558869i	$0.811236\pi$
$810$	3.22089	0.113170
$811$	45.1440	1.58522	0.792610	−	0.609728i	$-0.208721\pi$
$811$	45.1440	1.58522	0.792610	+	0.609728i	$0.208721\pi$
$812$	−1.77809	−0.0623987
$813$	10.6407	0.373187
$814$	4.47353	0.156797
$815$	−21.7592	−0.762192
$816$	−38.5135	−1.34824
$817$	−51.3559	−1.79672
$818$	−2.63891	−0.0922675
$819$	3.73140	0.130386
$820$	6.72667	0.234906
$821$	15.9729	0.557459	0.278730	−	0.960370i	$-0.410087\pi$
$821$	15.9729	0.557459	0.278730	+	0.960370i	$0.410087\pi$
$822$	32.6972	1.14045
$823$	23.6259	0.823547	0.411773	−	0.911286i	$-0.364910\pi$
$823$	23.6259	0.823547	0.411773	+	0.911286i	$0.364910\pi$
$824$	35.9933	1.25389
$825$	1.01353	0.0352865
$826$	−15.1623	−0.527565
$827$	26.3407	0.915955	0.457978	−	0.888964i	$-0.348574\pi$
$827$	26.3407	0.915955	0.457978	+	0.888964i	$0.348574\pi$
$828$	1.26716	0.0440367
$829$	−18.4133	−0.639519	−0.319760	−	0.947499i	$-0.603602\pi$
$829$	−18.4133	−0.639519	−0.319760	+	0.947499i	$0.603602\pi$
$830$	−41.8157	−1.45144
$831$	30.1397	1.04553
$832$	18.9229	0.656032
$833$	−8.09560	−0.280496
$834$	−12.2319	−0.423555
$835$	25.9165	0.896879
$836$	−4.95551	−0.171390
$837$	−10.4075	−0.359735
$838$	−44.2750	−1.52945
$839$	−35.0262	−1.20924	−0.604620	−	0.796514i	$-0.706675\pi$
$839$	−35.0262	−1.20924	−0.604620	+	0.796514i	$0.706675\pi$
$840$	4.80752	0.165875
$841$	−16.7195	−0.576535
$842$	1.31981	0.0454836
$843$	21.8838	0.753718
$844$	3.18125	0.109503
$845$	−1.87813	−0.0646097
$846$	13.2050	0.453996
$847$	−9.61941	−0.330527
$848$	−20.0725	−0.689293
$849$	−15.4851	−0.531448
$850$	−11.0577	−0.379276
$851$	−6.00470	−0.205839
$852$	−1.62031	−0.0555107
$853$	7.20790	0.246794	0.123397	−	0.992357i	$-0.460621\pi$
$853$	7.20790	0.246794	0.123397	+	0.992357i	$0.460621\pi$
$854$	21.7468	0.744161
$855$	16.9073	0.578218
$856$	3.28143	0.112157
$857$	7.31936	0.250025	0.125012	−	0.992155i	$-0.460103\pi$
$857$	7.31936	0.250025	0.125012	+	0.992155i	$0.460103\pi$
$858$	6.94248	0.237012
$859$	−49.4834	−1.68835	−0.844176	−	0.536065i	$-0.819910\pi$
$859$	−49.4834	−1.68835	−0.844176	+	0.536065i	$0.819910\pi$
$860$	−6.37661	−0.217441
$861$	6.51764	0.222120
$862$	21.0072	0.715508
$863$	−46.5393	−1.58422	−0.792108	−	0.610381i	$-0.791016\pi$
$863$	−46.5393	−1.58422	−0.792108	+	0.610381i	$0.791016\pi$
$864$	−2.80612	−0.0954663
$865$	36.0969	1.22733
$866$	42.1388	1.43193
$867$	−48.5388	−1.64846
$868$	5.28069	0.179238
$869$	12.6039	0.427557
$870$	11.2871	0.382669
$871$	10.5582	0.357752
$872$	6.94044	0.235033
$873$	−12.2662	−0.415146
$874$	32.8705	1.11186
$875$	11.9249	0.403134
$876$	2.51724	0.0850495
$877$	12.5085	0.422382	0.211191	−	0.977445i	$-0.432266\pi$
$877$	12.5085	0.422382	0.211191	+	0.977445i	$0.432266\pi$
$878$	5.41908	0.182885
$879$	−9.98207	−0.336687
$880$	11.3700	0.383282
$881$	40.5582	1.36644	0.683221	−	0.730212i	$-0.260579\pi$
$881$	40.5582	1.36644	0.683221	+	0.730212i	$0.260579\pi$
$882$	−1.58348	−0.0533184
$883$	16.9527	0.570503	0.285251	−	0.958453i	$-0.407923\pi$
$883$	16.9527	0.570503	0.285251	+	0.958453i	$0.407923\pi$
$884$	−15.3273	−0.515514
$885$	19.4769	0.654707
$886$	−48.6474	−1.63434
$887$	3.93843	0.132240	0.0661198	−	0.997812i	$-0.478938\pi$
$887$	3.93843	0.132240	0.0661198	+	0.997812i	$0.478938\pi$
$888$	5.68282	0.190703
$889$	4.90100	0.164374
$890$	−40.6776	−1.36352
$891$	1.17498	0.0393634
$892$	−1.72935	−0.0579029
$893$	69.3165	2.31959
$894$	−21.0226	−0.703102
$895$	13.7621	0.460016
$896$	−13.6425	−0.455762
$897$	−9.31871	−0.311143
$898$	−33.3213	−1.11195
$899$	−36.4714	−1.21639
$900$	−0.437673	−0.0145891
$901$	−34.1576	−1.13795
$902$	12.1264	0.403766
$903$	−6.17846	−0.205606
$904$	−11.7336	−0.390255
$905$	−22.5140	−0.748392
$906$	2.11657	0.0703183
$907$	22.2551	0.738968	0.369484	−	0.929237i	$-0.379534\pi$
$907$	22.2551	0.738968	0.369484	+	0.929237i	$0.379534\pi$
$908$	−13.1359	−0.435931
$909$	10.4030	0.345046
$910$	12.0184	0.398407
$911$	−27.1176	−0.898447	−0.449224	−	0.893419i	$-0.648299\pi$
$911$	−27.1176	−0.898447	−0.449224	+	0.893419i	$0.648299\pi$
$912$	−39.5435	−1.30942
$913$	−15.2544	−0.504847
$914$	−41.1663	−1.36166
$915$	−27.9350	−0.923503
$916$	−3.04825	−0.100717
$917$	13.3143	0.439678
$918$	−12.8192	−0.423096
$919$	−0.0136658	−0.000450794 0	−0.000225397	−	1.00000i	$-0.500072\pi$
$919$	−0.0136658	−0.000450794 0	−0.000225397		1.00000i	$0.500072\pi$
$920$	−12.0062	−0.395832
$921$	−4.79874	−0.158124
$922$	−32.9950	−1.08663
$923$	11.9158	0.392213
$924$	−0.596180	−0.0196129
$925$	2.07401	0.0681931
$926$	−53.0156	−1.74220
$927$	15.2288	0.500180
$928$	−9.83364	−0.322805
$929$	35.1265	1.15246	0.576232	−	0.817286i	$-0.304522\pi$
$929$	35.1265	1.15246	0.576232	+	0.817286i	$0.304522\pi$
$930$	−33.5213	−1.09921
$931$	−8.31210	−0.272418
$932$	−5.23695	−0.171542
$933$	5.91843	0.193761
$934$	25.0959	0.821162
$935$	19.3484	0.632760
$936$	8.81918	0.288264
$937$	9.27557	0.303020	0.151510	−	0.988456i	$-0.451586\pi$
$937$	9.27557	0.303020	0.151510	+	0.988456i	$0.451586\pi$
$938$	−4.48055	−0.146295
$939$	−8.13144	−0.265359
$940$	8.60669	0.280719
$941$	−47.5286	−1.54939	−0.774693	−	0.632337i	$-0.782096\pi$
$941$	−47.5286	−1.54939	−0.774693	+	0.632337i	$0.782096\pi$
$942$	−9.48603	−0.309072
$943$	−16.2770	−0.530052
$944$	−45.5532	−1.48263
$945$	2.03406	0.0661681
$946$	−11.4954	−0.373747
$947$	40.3978	1.31275	0.656376	−	0.754434i	$-0.272089\pi$
$947$	40.3978	1.31275	0.656376	+	0.754434i	$0.272089\pi$
$948$	−5.44274	−0.176772
$949$	−18.5118	−0.600920
$950$	−11.3534	−0.368353
$951$	−4.12351	−0.133714
$952$	−19.1340	−0.620136
$953$	−2.58733	−0.0838117	−0.0419059	−	0.999122i	$-0.513343\pi$
$953$	−2.58733	−0.0838117	−0.0419059	+	0.999122i	$0.513343\pi$
$954$	−6.68111	−0.216309
$955$	39.6408	1.28275
$956$	−8.23817	−0.266442
$957$	4.11755	0.133102
$958$	−54.1047	−1.74804
$959$	20.6490	0.666792
$960$	10.3152	0.332923
$961$	77.3153	2.49404
$962$	14.2066	0.458039
$963$	1.38838	0.0447398
$964$	6.39060	0.205827
$965$	−6.14777	−0.197904
$966$	3.95454	0.127235
$967$	−28.0460	−0.901899	−0.450949	−	0.892550i	$-0.648914\pi$
$967$	−28.0460	−0.901899	−0.450949	+	0.892550i	$0.648914\pi$
$968$	−22.7355	−0.730747
$969$	−67.2914	−2.16171
$970$	−39.5079	−1.26852
$971$	−25.9142	−0.831625	−0.415813	−	0.909450i	$-0.636503\pi$
$971$	−25.9142	−0.831625	−0.415813	+	0.909450i	$0.636503\pi$
$972$	−0.507395	−0.0162747
$973$	−7.72470	−0.247643
$974$	59.4601	1.90523
$975$	3.21867	0.103080
$976$	65.3354	2.09134
$977$	−6.52762	−0.208837	−0.104419	−	0.994533i	$-0.533298\pi$
$977$	−6.52762	−0.208837	−0.104419	+	0.994533i	$0.533298\pi$
$978$	16.9391	0.541653
$979$	−14.8392	−0.474264
$980$	−1.03207	−0.0329683
$981$	2.93650	0.0937554
$982$	22.2772	0.710894
$983$	60.1942	1.91990	0.959949	−	0.280175i	$-0.0903926\pi$
$983$	60.1942	1.91990	0.959949	+	0.280175i	$0.0903926\pi$
$984$	15.4045	0.491076
$985$	51.4594	1.63963
$986$	−44.9229	−1.43064
$987$	8.33923	0.265441
$988$	−15.7372	−0.500668
$989$	15.4299	0.490643
$990$	3.78449	0.120279
$991$	−53.8861	−1.71175	−0.855874	−	0.517184i	$-0.826980\pi$
$991$	−53.8861	−1.71175	−0.855874	+	0.517184i	$0.826980\pi$
$992$	29.2046	0.927248
$993$	7.88009	0.250067
$994$	−5.05664	−0.160387
$995$	−7.10932	−0.225381
$996$	6.58734	0.208728
$997$	−26.1583	−0.828442	−0.414221	−	0.910176i	$-0.635946\pi$
$997$	−26.1583	−0.828442	−0.414221	+	0.910176i	$0.635946\pi$
$998$	−12.0956	−0.382881
$999$	2.40440	0.0760720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.15	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-1.58348 q^{2} -1.00000 q^{3} +0.507395 q^{4} -2.03406 q^{5} +1.58348 q^{6} +1.00000 q^{7} +2.36350 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.58348 q^{2} -1.00000 q^{3} +0.507395 q^{4} -2.03406 q^{5} +1.58348 q^{6} +1.00000 q^{7} +2.36350 q^{8} +1.00000 q^{9} +3.22089 q^{10} +1.17498 q^{11} -0.507395 q^{12} +3.73140 q^{13} -1.58348 q^{14} +2.03406 q^{15} -4.75734 q^{16} -8.09560 q^{17} -1.58348 q^{18} -8.31210 q^{19} -1.03207 q^{20} -1.00000 q^{21} -1.86056 q^{22} +2.49738 q^{23} -2.36350 q^{24} -0.862589 q^{25} -5.90858 q^{26} -1.00000 q^{27} +0.507395 q^{28} -3.50435 q^{29} -3.22089 q^{30} +10.4075 q^{31} +2.80612 q^{32} -1.17498 q^{33} +12.8192 q^{34} -2.03406 q^{35} +0.507395 q^{36} -2.40440 q^{37} +13.1620 q^{38} -3.73140 q^{39} -4.80752 q^{40} -6.51764 q^{41} +1.58348 q^{42} +6.17846 q^{43} +0.596180 q^{44} -2.03406 q^{45} -3.95454 q^{46} -8.33923 q^{47} +4.75734 q^{48} +1.00000 q^{49} +1.36589 q^{50} +8.09560 q^{51} +1.89329 q^{52} +4.21927 q^{53} +1.58348 q^{54} -2.38999 q^{55} +2.36350 q^{56} +8.31210 q^{57} +5.54906 q^{58} +9.57535 q^{59} +1.03207 q^{60} -13.7336 q^{61} -16.4800 q^{62} +1.00000 q^{63} +5.07125 q^{64} -7.58990 q^{65} +1.86056 q^{66} +2.82956 q^{67} -4.10767 q^{68} -2.49738 q^{69} +3.22089 q^{70} +3.19338 q^{71} +2.36350 q^{72} -4.96110 q^{73} +3.80731 q^{74} +0.862589 q^{75} -4.21751 q^{76} +1.17498 q^{77} +5.90858 q^{78} +10.7268 q^{79} +9.67673 q^{80} +1.00000 q^{81} +10.3205 q^{82} -12.9827 q^{83} -0.507395 q^{84} +16.4670 q^{85} -9.78343 q^{86} +3.50435 q^{87} +2.77708 q^{88} -12.6293 q^{89} +3.22089 q^{90} +3.73140 q^{91} +1.26716 q^{92} -10.4075 q^{93} +13.2050 q^{94} +16.9073 q^{95} -2.80612 q^{96} -12.2662 q^{97} -1.58348 q^{98} +1.17498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 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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