LMFDB - Embedded newform 8041.2.a.j.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.88314 q^{2} -1.39410 q^{3} +1.54622 q^{4} -3.71860 q^{5} +2.62529 q^{6} +0.268017 q^{7} +0.854526 q^{8} -1.05649 q^{9} +O(q^{10})$	\(q-1.88314 q^{2} -1.39410 q^{3} +1.54622 q^{4} -3.71860 q^{5} +2.62529 q^{6} +0.268017 q^{7} +0.854526 q^{8} -1.05649 q^{9} +7.00266 q^{10} +1.00000 q^{11} -2.15559 q^{12} +4.11678 q^{13} -0.504714 q^{14} +5.18410 q^{15} -4.70164 q^{16} +1.00000 q^{17} +1.98952 q^{18} -7.20890 q^{19} -5.74979 q^{20} -0.373642 q^{21} -1.88314 q^{22} +5.54871 q^{23} -1.19129 q^{24} +8.82800 q^{25} -7.75249 q^{26} +5.65515 q^{27} +0.414414 q^{28} +4.02113 q^{29} -9.76239 q^{30} +9.00678 q^{31} +7.14480 q^{32} -1.39410 q^{33} -1.88314 q^{34} -0.996648 q^{35} -1.63357 q^{36} +11.9900 q^{37} +13.5754 q^{38} -5.73920 q^{39} -3.17764 q^{40} -2.01260 q^{41} +0.703620 q^{42} +1.00000 q^{43} +1.54622 q^{44} +3.92866 q^{45} -10.4490 q^{46} -2.88297 q^{47} +6.55455 q^{48} -6.92817 q^{49} -16.6244 q^{50} -1.39410 q^{51} +6.36547 q^{52} +8.83666 q^{53} -10.6494 q^{54} -3.71860 q^{55} +0.229027 q^{56} +10.0499 q^{57} -7.57236 q^{58} +6.16726 q^{59} +8.01577 q^{60} +4.31404 q^{61} -16.9610 q^{62} -0.283157 q^{63} -4.05140 q^{64} -15.3087 q^{65} +2.62529 q^{66} -7.87681 q^{67} +1.54622 q^{68} -7.73545 q^{69} +1.87683 q^{70} +10.3270 q^{71} -0.902798 q^{72} +1.50125 q^{73} -22.5788 q^{74} -12.3071 q^{75} -11.1466 q^{76} +0.268017 q^{77} +10.8077 q^{78} -7.38185 q^{79} +17.4835 q^{80} -4.71436 q^{81} +3.79001 q^{82} +15.0476 q^{83} -0.577733 q^{84} -3.71860 q^{85} -1.88314 q^{86} -5.60585 q^{87} +0.854526 q^{88} -18.5244 q^{89} -7.39823 q^{90} +1.10337 q^{91} +8.57954 q^{92} -12.5563 q^{93} +5.42905 q^{94} +26.8070 q^{95} -9.96056 q^{96} +11.0659 q^{97} +13.0467 q^{98} -1.05649 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) $ 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * 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 $

$2$	−1.88314	−1.33158	−0.665791	−	0.746138i	$-0.731906\pi$
$2$	−1.88314	−1.33158	−0.665791	+	0.746138i	$0.731906\pi$
$3$	−1.39410	−0.804883	−0.402442	−	0.915446i	$-0.631838\pi$
$3$	−1.39410	−0.804883	−0.402442	+	0.915446i	$0.631838\pi$
$4$	1.54622	0.773112
$5$	−3.71860	−1.66301	−0.831505	−	0.555518i	$-0.812520\pi$
$5$	−3.71860	−1.66301	−0.831505	+	0.555518i	$0.812520\pi$
$6$	2.62529	1.07177
$7$	0.268017	0.101301	0.0506504	−	0.998716i	$-0.483871\pi$
$7$	0.268017	0.101301	0.0506504	+	0.998716i	$0.483871\pi$
$8$	0.854526	0.302121
$9$	−1.05649	−0.352163
$10$	7.00266	2.21443
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.15559	−0.622264
$13$	4.11678	1.14179	0.570895	−	0.821023i	$-0.306596\pi$
$13$	4.11678	1.14179	0.570895	+	0.821023i	$0.306596\pi$
$14$	−0.504714	−0.134890
$15$	5.18410	1.33853
$16$	−4.70164	−1.17541
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.98952	0.468934
$19$	−7.20890	−1.65384	−0.826918	−	0.562323i	$-0.809908\pi$
$19$	−7.20890	−1.65384	−0.826918	+	0.562323i	$0.809908\pi$
$20$	−5.74979	−1.28569
$21$	−0.373642	−0.0815353
$22$	−1.88314	−0.401487
$23$	5.54871	1.15699	0.578493	−	0.815687i	$-0.303641\pi$
$23$	5.54871	1.15699	0.578493	+	0.815687i	$0.303641\pi$
$24$	−1.19129	−0.243172
$25$	8.82800	1.76560
$26$	−7.75249	−1.52039
$27$	5.65515	1.08833
$28$	0.414414	0.0783168
$29$	4.02113	0.746705	0.373353	−	0.927689i	$-0.378208\pi$
$29$	4.02113	0.746705	0.373353	+	0.927689i	$0.378208\pi$
$30$	−9.76239	−1.78236
$31$	9.00678	1.61766	0.808832	−	0.588039i	$-0.200100\pi$
$31$	9.00678	1.61766	0.808832	+	0.588039i	$0.200100\pi$
$32$	7.14480	1.26303
$33$	−1.39410	−0.242681
$34$	−1.88314	−0.322956
$35$	−0.996648	−0.168464
$36$	−1.63357	−0.272261
$37$	11.9900	1.97114	0.985568	−	0.169279i	$-0.0541438\pi$
$37$	11.9900	1.97114	0.985568	+	0.169279i	$0.0541438\pi$
$38$	13.5754	2.20222
$39$	−5.73920	−0.919008
$40$	−3.17764	−0.502430
$41$	−2.01260	−0.314315	−0.157158	−	0.987574i	$-0.550233\pi$
$41$	−2.01260	−0.314315	−0.157158	+	0.987574i	$0.550233\pi$
$42$	0.703620	0.108571
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.54622	0.233102
$45$	3.92866	0.585650
$46$	−10.4490	−1.54062
$47$	−2.88297	−0.420525	−0.210263	−	0.977645i	$-0.567432\pi$
$47$	−2.88297	−0.420525	−0.210263	+	0.977645i	$0.567432\pi$
$48$	6.55455	0.946068
$49$	−6.92817	−0.989738
$50$	−16.6244	−2.35104
$51$	−1.39410	−0.195213
$52$	6.36547	0.882731
$53$	8.83666	1.21381	0.606904	−	0.794775i	$-0.292411\pi$
$53$	8.83666	1.21381	0.606904	+	0.794775i	$0.292411\pi$
$54$	−10.6494	−1.44921
$55$	−3.71860	−0.501416
$56$	0.229027	0.0306051
$57$	10.0499	1.33114
$58$	−7.57236	−0.994300
$59$	6.16726	0.802909	0.401454	−	0.915879i	$-0.368505\pi$
$59$	6.16726	0.802909	0.401454	+	0.915879i	$0.368505\pi$
$60$	8.01577	1.03483
$61$	4.31404	0.552357	0.276178	−	0.961106i	$-0.410932\pi$
$61$	4.31404	0.552357	0.276178	+	0.961106i	$0.410932\pi$
$62$	−16.9610	−2.15405
$63$	−0.283157	−0.0356744
$64$	−4.05140	−0.506425
$65$	−15.3087	−1.89881
$66$	2.62529	0.323150
$67$	−7.87681	−0.962305	−0.481153	−	0.876637i	$-0.659782\pi$
$67$	−7.87681	−0.962305	−0.481153	+	0.876637i	$0.659782\pi$
$68$	1.54622	0.187507
$69$	−7.73545	−0.931239
$70$	1.87683	0.224324
$71$	10.3270	1.22559	0.612794	−	0.790243i	$-0.290045\pi$
$71$	10.3270	1.22559	0.612794	+	0.790243i	$0.290045\pi$
$72$	−0.902798	−0.106396
$73$	1.50125	0.175708	0.0878541	−	0.996133i	$-0.471999\pi$
$73$	1.50125	0.175708	0.0878541	+	0.996133i	$0.471999\pi$
$74$	−22.5788	−2.62473
$75$	−12.3071	−1.42110
$76$	−11.1466	−1.27860
$77$	0.268017	0.0305433
$78$	10.8077	1.22373
$79$	−7.38185	−0.830523	−0.415262	−	0.909702i	$-0.636310\pi$
$79$	−7.38185	−0.830523	−0.415262	+	0.909702i	$0.636310\pi$
$80$	17.4835	1.95472
$81$	−4.71436	−0.523818
$82$	3.79001	0.418536
$83$	15.0476	1.65169	0.825843	−	0.563899i	$-0.190699\pi$
$83$	15.0476	1.65169	0.825843	+	0.563899i	$0.190699\pi$
$84$	−0.577733	−0.0630359
$85$	−3.71860	−0.403339
$86$	−1.88314	−0.203064
$87$	−5.60585	−0.601011
$88$	0.854526	0.0910928
$89$	−18.5244	−1.96359	−0.981793	−	0.189956i	$-0.939165\pi$
$89$	−18.5244	−1.96359	−0.981793	+	0.189956i	$0.939165\pi$
$90$	−7.39823	−0.779842
$91$	1.10337	0.115664
$92$	8.57954	0.894479
$93$	−12.5563	−1.30203
$94$	5.42905	0.559964
$95$	26.8070	2.75034
$96$	−9.96056	−1.01660
$97$	11.0659	1.12357	0.561786	−	0.827282i	$-0.310114\pi$
$97$	11.0659	1.12357	0.561786	+	0.827282i	$0.310114\pi$
$98$	13.0467	1.31792
$99$	−1.05649	−0.106181
$100$	13.6501	1.36501
$101$	10.5670	1.05145	0.525727	−	0.850654i	$-0.323794\pi$
$101$	10.5670	1.05145	0.525727	+	0.850654i	$0.323794\pi$
$102$	2.62529	0.259942
$103$	11.5580	1.13885	0.569424	−	0.822044i	$-0.307166\pi$
$103$	11.5580	1.13885	0.569424	+	0.822044i	$0.307166\pi$
$104$	3.51790	0.344958
$105$	1.38942	0.135594
$106$	−16.6407	−1.61629
$107$	17.6236	1.70374	0.851870	−	0.523754i	$-0.175469\pi$
$107$	17.6236	1.70374	0.851870	+	0.523754i	$0.175469\pi$
$108$	8.74412	0.841403
$109$	−13.9390	−1.33511	−0.667555	−	0.744561i	$-0.732659\pi$
$109$	−13.9390	−1.33511	−0.667555	+	0.744561i	$0.732659\pi$
$110$	7.00266	0.667677
$111$	−16.7152	−1.58653
$112$	−1.26012	−0.119070
$113$	18.6373	1.75325	0.876625	−	0.481175i	$-0.159790\pi$
$113$	18.6373	1.75325	0.876625	+	0.481175i	$0.159790\pi$
$114$	−18.9254	−1.77253
$115$	−20.6334	−1.92408
$116$	6.21757	0.577286
$117$	−4.34934	−0.402096
$118$	−11.6138	−1.06914
$119$	0.268017	0.0245691
$120$	4.42995	0.404397
$121$	1.00000	0.0909091
$122$	−8.12396	−0.735508
$123$	2.80576	0.252987
$124$	13.9265	1.25064
$125$	−14.2348	−1.27320
$126$	0.533224	0.0475034
$127$	−16.8633	−1.49638	−0.748189	−	0.663485i	$-0.769076\pi$
$127$	−16.8633	−1.49638	−0.748189	+	0.663485i	$0.769076\pi$
$128$	−6.66025	−0.588689
$129$	−1.39410	−0.122744
$130$	28.8284	2.52842
$131$	3.99445	0.348997	0.174498	−	0.984657i	$-0.444170\pi$
$131$	3.99445	0.348997	0.174498	+	0.984657i	$0.444170\pi$
$132$	−2.15559	−0.187620
$133$	−1.93211	−0.167535
$134$	14.8331	1.28139
$135$	−21.0292	−1.80991
$136$	0.854526	0.0732750
$137$	22.0551	1.88429	0.942146	−	0.335203i	$-0.108805\pi$
$137$	22.0551	1.88429	0.942146	+	0.335203i	$0.108805\pi$
$138$	14.5669	1.24002
$139$	5.19228	0.440404	0.220202	−	0.975454i	$-0.429328\pi$
$139$	5.19228	0.440404	0.220202	+	0.975454i	$0.429328\pi$
$140$	−1.54104	−0.130242
$141$	4.01915	0.338474
$142$	−19.4472	−1.63197
$143$	4.11678	0.344263
$144$	4.96723	0.413936
$145$	−14.9530	−1.24178
$146$	−2.82707	−0.233970
$147$	9.65855	0.796624
$148$	18.5391	1.52391
$149$	−12.8961	−1.05649	−0.528245	−	0.849092i	$-0.677150\pi$
$149$	−12.8961	−1.05649	−0.528245	+	0.849092i	$0.677150\pi$
$150$	23.1760	1.89231
$151$	−3.84674	−0.313043	−0.156522	−	0.987675i	$-0.550028\pi$
$151$	−3.84674	−0.313043	−0.156522	+	0.987675i	$0.550028\pi$
$152$	−6.16020	−0.499658
$153$	−1.05649	−0.0854121
$154$	−0.504714	−0.0406710
$155$	−33.4926	−2.69019
$156$	−8.87409	−0.710496
$157$	−20.6773	−1.65023	−0.825115	−	0.564964i	$-0.808890\pi$
$157$	−20.6773	−1.65023	−0.825115	+	0.564964i	$0.808890\pi$
$158$	13.9011	1.10591
$159$	−12.3192	−0.976974
$160$	−26.5687	−2.10044
$161$	1.48715	0.117204
$162$	8.87781	0.697507
$163$	−2.62710	−0.205770	−0.102885	−	0.994693i	$-0.532807\pi$
$163$	−2.62710	−0.205770	−0.102885	+	0.994693i	$0.532807\pi$
$164$	−3.11193	−0.243001
$165$	5.18410	0.403581
$166$	−28.3367	−2.19936
$167$	0.863007	0.0667815	0.0333907	−	0.999442i	$-0.489369\pi$
$167$	0.863007	0.0667815	0.0333907	+	0.999442i	$0.489369\pi$
$168$	−0.319287	−0.0246335
$169$	3.94791	0.303685
$170$	7.00266	0.537079
$171$	7.61613	0.582420
$172$	1.54622	0.117898
$173$	−12.9176	−0.982109	−0.491055	−	0.871129i	$-0.663388\pi$
$173$	−12.9176	−0.982109	−0.491055	+	0.871129i	$0.663388\pi$
$174$	10.5566	0.800295
$175$	2.36605	0.178857
$176$	−4.70164	−0.354399
$177$	−8.59776	−0.646248
$178$	34.8841	2.61468
$179$	14.3762	1.07453	0.537264	−	0.843414i	$-0.319458\pi$
$179$	14.3762	1.07453	0.537264	+	0.843414i	$0.319458\pi$
$180$	6.07459	0.452773
$181$	5.21715	0.387788	0.193894	−	0.981022i	$-0.437888\pi$
$181$	5.21715	0.387788	0.193894	+	0.981022i	$0.437888\pi$
$182$	−2.07780	−0.154017
$183$	−6.01420	−0.444583
$184$	4.74152	0.349549
$185$	−44.5859	−3.27802
$186$	23.6454	1.73376
$187$	1.00000	0.0731272
$188$	−4.45772	−0.325113
$189$	1.51567	0.110249
$190$	−50.4814	−3.66231
$191$	−26.9109	−1.94720	−0.973601	−	0.228258i	$-0.926697\pi$
$191$	−26.9109	−1.94720	−0.973601	+	0.228258i	$0.926697\pi$
$192$	5.64805	0.407613
$193$	9.10495	0.655389	0.327694	−	0.944784i	$-0.393728\pi$
$193$	9.10495	0.655389	0.327694	+	0.944784i	$0.393728\pi$
$194$	−20.8387	−1.49613
$195$	21.3418	1.52832
$196$	−10.7125	−0.765178
$197$	−14.0809	−1.00322	−0.501612	−	0.865093i	$-0.667259\pi$
$197$	−14.0809	−1.00322	−0.501612	+	0.865093i	$0.667259\pi$
$198$	1.98952	0.141389
$199$	−20.9912	−1.48803	−0.744015	−	0.668163i	$-0.767081\pi$
$199$	−20.9912	−1.48803	−0.744015	+	0.668163i	$0.767081\pi$
$200$	7.54376	0.533424
$201$	10.9810	0.774543
$202$	−19.8991	−1.40010
$203$	1.07773	0.0756418
$204$	−2.15559	−0.150921
$205$	7.48405	0.522709
$206$	−21.7654	−1.51647
$207$	−5.86215	−0.407448
$208$	−19.3556	−1.34207
$209$	−7.20890	−0.498650
$210$	−2.61648	−0.180555
$211$	−13.3331	−0.917888	−0.458944	−	0.888465i	$-0.651772\pi$
$211$	−13.3331	−0.917888	−0.458944	+	0.888465i	$0.651772\pi$
$212$	13.6634	0.938409
$213$	−14.3968	−0.986455
$214$	−33.1878	−2.26867
$215$	−3.71860	−0.253607
$216$	4.83247	0.328808
$217$	2.41397	0.163871
$218$	26.2490	1.77781
$219$	−2.09289	−0.141425
$220$	−5.74979	−0.387651
$221$	4.11678	0.276925
$222$	31.4771	2.11260
$223$	27.0556	1.81178	0.905890	−	0.423514i	$-0.139203\pi$
$223$	27.0556	1.81178	0.905890	+	0.423514i	$0.139203\pi$
$224$	1.91493	0.127946
$225$	−9.32669	−0.621779
$226$	−35.0967	−2.33460
$227$	−22.8165	−1.51438	−0.757192	−	0.653192i	$-0.773429\pi$
$227$	−22.8165	−1.51438	−0.757192	+	0.653192i	$0.773429\pi$
$228$	15.5394	1.02912
$229$	−7.73835	−0.511365	−0.255682	−	0.966761i	$-0.582300\pi$
$229$	−7.73835	−0.511365	−0.255682	+	0.966761i	$0.582300\pi$
$230$	38.8557	2.56207
$231$	−0.373642	−0.0245838
$232$	3.43616	0.225595
$233$	−20.7681	−1.36056	−0.680281	−	0.732951i	$-0.738142\pi$
$233$	−20.7681	−1.36056	−0.680281	+	0.732951i	$0.738142\pi$
$234$	8.19042	0.535424
$235$	10.7206	0.699337
$236$	9.53596	0.620738
$237$	10.2910	0.668474
$238$	−0.504714	−0.0327157
$239$	6.03261	0.390217	0.195109	−	0.980782i	$-0.437494\pi$
$239$	6.03261	0.390217	0.195109	+	0.980782i	$0.437494\pi$
$240$	−24.3738	−1.57332
$241$	5.25130	0.338266	0.169133	−	0.985593i	$-0.445903\pi$
$241$	5.25130	0.338266	0.169133	+	0.985593i	$0.445903\pi$
$242$	−1.88314	−0.121053
$243$	−10.3932	−0.666721
$244$	6.67047	0.427033
$245$	25.7631	1.64594
$246$	−5.28364	−0.336873
$247$	−29.6775	−1.88833
$248$	7.69653	0.488730
$249$	−20.9778	−1.32942
$250$	26.8062	1.69537
$251$	29.7444	1.87745	0.938725	−	0.344668i	$-0.112009\pi$
$251$	29.7444	1.87745	0.938725	+	0.344668i	$0.112009\pi$
$252$	−0.437824	−0.0275803
$253$	5.54871	0.348844
$254$	31.7560	1.99255
$255$	5.18410	0.324641
$256$	20.6450	1.29031
$257$	1.51638	0.0945889	0.0472944	−	0.998881i	$-0.484940\pi$
$257$	1.51638	0.0945889	0.0472944	+	0.998881i	$0.484940\pi$
$258$	2.62529	0.163443
$259$	3.21351	0.199678
$260$	−23.6706	−1.46799
$261$	−4.24828	−0.262962
$262$	−7.52212	−0.464718
$263$	11.3156	0.697753	0.348876	−	0.937169i	$-0.386563\pi$
$263$	11.3156	0.697753	0.348876	+	0.937169i	$0.386563\pi$
$264$	−1.19129	−0.0733191
$265$	−32.8600	−2.01858
$266$	3.63843	0.223086
$267$	25.8249	1.58046
$268$	−12.1793	−0.743969
$269$	0.830705	0.0506490	0.0253245	−	0.999679i	$-0.491938\pi$
$269$	0.830705	0.0506490	0.0253245	+	0.999679i	$0.491938\pi$
$270$	39.6010	2.41004
$271$	4.87000	0.295831	0.147916	−	0.989000i	$-0.452744\pi$
$271$	4.87000	0.295831	0.147916	+	0.989000i	$0.452744\pi$
$272$	−4.70164	−0.285079
$273$	−1.53820	−0.0930962
$274$	−41.5328	−2.50909
$275$	8.82800	0.532349
$276$	−11.9607	−0.719951
$277$	31.0685	1.86673	0.933363	−	0.358935i	$-0.116860\pi$
$277$	31.0685	1.86673	0.933363	+	0.358935i	$0.116860\pi$
$278$	−9.77780	−0.586434
$279$	−9.51556	−0.569682
$280$	−0.851662	−0.0508965
$281$	0.817245	0.0487527	0.0243764	−	0.999703i	$-0.492240\pi$
$281$	0.817245	0.0487527	0.0243764	+	0.999703i	$0.492240\pi$
$282$	−7.56863	−0.450705
$283$	−27.1985	−1.61678	−0.808391	−	0.588646i	$-0.799661\pi$
$283$	−27.1985	−1.61678	−0.808391	+	0.588646i	$0.799661\pi$
$284$	15.9678	0.947516
$285$	−37.3716	−2.21371
$286$	−7.75249	−0.458414
$287$	−0.539410	−0.0318404
$288$	−7.54841	−0.444794
$289$	1.00000	0.0588235
$290$	28.1586	1.65353
$291$	−15.4270	−0.904345
$292$	2.32127	0.135842
$293$	5.76773	0.336954	0.168477	−	0.985706i	$-0.446115\pi$
$293$	5.76773	0.336954	0.168477	+	0.985706i	$0.446115\pi$
$294$	−18.1884	−1.06077
$295$	−22.9336	−1.33524
$296$	10.2457	0.595521
$297$	5.65515	0.328145
$298$	24.2852	1.40680
$299$	22.8428	1.32104
$300$	−19.0295	−1.09867
$301$	0.268017	0.0154482
$302$	7.24395	0.416843
$303$	−14.7314	−0.846297
$304$	33.8937	1.94393
$305$	−16.0422	−0.918574
$306$	1.98952	0.113733
$307$	−1.08423	−0.0618801	−0.0309401	−	0.999521i	$-0.509850\pi$
$307$	−1.08423	−0.0618801	−0.0309401	+	0.999521i	$0.509850\pi$
$308$	0.414414	0.0236134
$309$	−16.1131	−0.916640
$310$	63.0713	3.58221
$311$	−23.4481	−1.32962	−0.664811	−	0.747012i	$-0.731488\pi$
$311$	−23.4481	−1.32962	−0.664811	+	0.747012i	$0.731488\pi$
$312$	−4.90430	−0.277651
$313$	−21.2373	−1.20041	−0.600203	−	0.799848i	$-0.704914\pi$
$313$	−21.2373	−1.20041	−0.600203	+	0.799848i	$0.704914\pi$
$314$	38.9383	2.19742
$315$	1.05295	0.0593269
$316$	−11.4140	−0.642087
$317$	−1.68927	−0.0948790	−0.0474395	−	0.998874i	$-0.515106\pi$
$317$	−1.68927	−0.0948790	−0.0474395	+	0.998874i	$0.515106\pi$
$318$	23.1988	1.30092
$319$	4.02113	0.225140
$320$	15.0655	0.842189
$321$	−24.5691	−1.37131
$322$	−2.80051	−0.156066
$323$	−7.20890	−0.401114
$324$	−7.28946	−0.404970
$325$	36.3430	2.01595
$326$	4.94720	0.274000
$327$	19.4323	1.07461
$328$	−1.71982	−0.0949611
$329$	−0.772685	−0.0425995
$330$	−9.76239	−0.537402
$331$	−14.6981	−0.807882	−0.403941	−	0.914785i	$-0.632360\pi$
$331$	−14.6981	−0.807882	−0.403941	+	0.914785i	$0.632360\pi$
$332$	23.2669	1.27694
$333$	−12.6673	−0.694161
$334$	−1.62516	−0.0889250
$335$	29.2907	1.60032
$336$	1.75673	0.0958374
$337$	33.7847	1.84037	0.920186	−	0.391481i	$-0.128037\pi$
$337$	33.7847	1.84037	0.920186	+	0.391481i	$0.128037\pi$
$338$	−7.43447	−0.404382
$339$	−25.9822	−1.41116
$340$	−5.74979	−0.311826
$341$	9.00678	0.487744
$342$	−14.3422	−0.775540
$343$	−3.73298	−0.201562
$344$	0.854526	0.0460730
$345$	28.7651	1.54866
$346$	24.3257	1.30776
$347$	−7.43894	−0.399343	−0.199672	−	0.979863i	$-0.563988\pi$
$347$	−7.43894	−0.399343	−0.199672	+	0.979863i	$0.563988\pi$
$348$	−8.66790	−0.464648
$349$	8.44151	0.451864	0.225932	−	0.974143i	$-0.427457\pi$
$349$	8.44151	0.451864	0.225932	+	0.974143i	$0.427457\pi$
$350$	−4.45561	−0.238162
$351$	23.2810	1.24265
$352$	7.14480	0.380819
$353$	−16.6812	−0.887851	−0.443926	−	0.896064i	$-0.646415\pi$
$353$	−16.6812	−0.887851	−0.443926	+	0.896064i	$0.646415\pi$
$354$	16.1908	0.860532
$355$	−38.4020	−2.03816
$356$	−28.6429	−1.51807
$357$	−0.373642	−0.0197752
$358$	−27.0724	−1.43082
$359$	33.6262	1.77472	0.887361	−	0.461075i	$-0.152536\pi$
$359$	33.6262	1.77472	0.887361	+	0.461075i	$0.152536\pi$
$360$	3.35715	0.176937
$361$	32.9682	1.73517
$362$	−9.82464	−0.516372
$363$	−1.39410	−0.0731712
$364$	1.70605	0.0894214
$365$	−5.58256	−0.292204
$366$	11.3256	0.591998
$367$	−23.9805	−1.25177	−0.625887	−	0.779914i	$-0.715263\pi$
$367$	−23.9805	−1.25177	−0.625887	+	0.779914i	$0.715263\pi$
$368$	−26.0880	−1.35993
$369$	2.12629	0.110690
$370$	83.9615	4.36495
$371$	2.36837	0.122960
$372$	−19.4149	−1.00662
$373$	−7.31294	−0.378650	−0.189325	−	0.981915i	$-0.560630\pi$
$373$	−7.31294	−0.378650	−0.189325	+	0.981915i	$0.560630\pi$
$374$	−1.88314	−0.0973749
$375$	19.8447	1.02478
$376$	−2.46358	−0.127049
$377$	16.5541	0.852581
$378$	−2.85423	−0.146806
$379$	27.0147	1.38765	0.693825	−	0.720144i	$-0.255924\pi$
$379$	27.0147	1.38765	0.693825	+	0.720144i	$0.255924\pi$
$380$	41.4497	2.12632
$381$	23.5091	1.20441
$382$	50.6770	2.59286
$383$	10.5477	0.538960	0.269480	−	0.963006i	$-0.413148\pi$
$383$	10.5477	0.538960	0.269480	+	0.963006i	$0.413148\pi$
$384$	9.28505	0.473826
$385$	−0.996648	−0.0507939
$386$	−17.1459	−0.872704
$387$	−1.05649	−0.0537044
$388$	17.1104	0.868647
$389$	−21.3522	−1.08260	−0.541299	−	0.840830i	$-0.682067\pi$
$389$	−21.3522	−1.08260	−0.541299	+	0.840830i	$0.682067\pi$
$390$	−40.1897	−2.03508
$391$	5.54871	0.280610
$392$	−5.92030	−0.299020
$393$	−5.56866	−0.280902
$394$	26.5164	1.33588
$395$	27.4502	1.38117
$396$	−1.63357	−0.0820899
$397$	−17.5852	−0.882578	−0.441289	−	0.897365i	$-0.645479\pi$
$397$	−17.5852	−0.882578	−0.441289	+	0.897365i	$0.645479\pi$
$398$	39.5295	1.98143
$399$	2.69355	0.134846
$400$	−41.5061	−2.07530
$401$	10.3884	0.518774	0.259387	−	0.965773i	$-0.416479\pi$
$401$	10.3884	0.518774	0.259387	+	0.965773i	$0.416479\pi$
$402$	−20.6789	−1.03137
$403$	37.0789	1.84703
$404$	16.3389	0.812891
$405$	17.5308	0.871115
$406$	−2.02952	−0.100723
$407$	11.9900	0.594320
$408$	−1.19129	−0.0589778
$409$	−7.00777	−0.346512	−0.173256	−	0.984877i	$-0.555429\pi$
$409$	−7.00777	−0.346512	−0.173256	+	0.984877i	$0.555429\pi$
$410$	−14.0935	−0.696030
$411$	−30.7469	−1.51663
$412$	17.8713	0.880457
$413$	1.65293	0.0813353
$414$	11.0393	0.542550
$415$	−55.9560	−2.74677
$416$	29.4136	1.44212
$417$	−7.23855	−0.354473
$418$	13.5754	0.663994
$419$	−23.8967	−1.16743	−0.583714	−	0.811959i	$-0.698401\pi$
$419$	−23.8967	−1.16743	−0.583714	+	0.811959i	$0.698401\pi$
$420$	2.14836	0.104829
$421$	−36.4372	−1.77584	−0.887921	−	0.459996i	$-0.847851\pi$
$421$	−36.4372	−1.77584	−0.887921	+	0.459996i	$0.847851\pi$
$422$	25.1081	1.22224
$423$	3.04583	0.148093
$424$	7.55116	0.366717
$425$	8.82800	0.428221
$426$	27.1113	1.31355
$427$	1.15624	0.0559542
$428$	27.2500	1.31718
$429$	−5.73920	−0.277091
$430$	7.00266	0.337698
$431$	22.9405	1.10501	0.552503	−	0.833511i	$-0.313673\pi$
$431$	22.9405	1.10501	0.552503	+	0.833511i	$0.313673\pi$
$432$	−26.5885	−1.27924
$433$	10.4123	0.500382	0.250191	−	0.968196i	$-0.419507\pi$
$433$	10.4123	0.500382	0.250191	+	0.968196i	$0.419507\pi$
$434$	−4.54584	−0.218207
$435$	20.8459	0.999486
$436$	−21.5527	−1.03219
$437$	−40.0001	−1.91346
$438$	3.94121	0.188319
$439$	33.9784	1.62170	0.810850	−	0.585254i	$-0.199005\pi$
$439$	33.9784	1.62170	0.810850	+	0.585254i	$0.199005\pi$
$440$	−3.17764	−0.151488
$441$	7.31953	0.348549
$442$	−7.75249	−0.368748
$443$	31.6269	1.50264	0.751320	−	0.659938i	$-0.229418\pi$
$443$	31.6269	1.50264	0.751320	+	0.659938i	$0.229418\pi$
$444$	−25.8454	−1.22657
$445$	68.8850	3.26546
$446$	−50.9496	−2.41253
$447$	17.9784	0.850351
$448$	−1.08584	−0.0513012
$449$	−4.48583	−0.211699	−0.105850	−	0.994382i	$-0.533756\pi$
$449$	−4.48583	−0.211699	−0.105850	+	0.994382i	$0.533756\pi$
$450$	17.5635	0.827950
$451$	−2.01260	−0.0947696
$452$	28.8174	1.35546
$453$	5.36273	0.251963
$454$	42.9667	2.01653
$455$	−4.10298	−0.192351
$456$	8.58792	0.402166
$457$	30.2004	1.41271	0.706357	−	0.707856i	$-0.250337\pi$
$457$	30.2004	1.41271	0.706357	+	0.707856i	$0.250337\pi$
$458$	14.5724	0.680924
$459$	5.65515	0.263960
$460$	−31.9039	−1.48753
$461$	1.89178	0.0881091	0.0440546	−	0.999029i	$-0.485972\pi$
$461$	1.89178	0.0881091	0.0440546	+	0.999029i	$0.485972\pi$
$462$	0.703620	0.0327354
$463$	19.4766	0.905153	0.452577	−	0.891725i	$-0.350505\pi$
$463$	19.4766	0.905153	0.452577	+	0.891725i	$0.350505\pi$
$464$	−18.9059	−0.877685
$465$	46.6920	2.16529
$466$	39.1092	1.81170
$467$	10.1469	0.469540	0.234770	−	0.972051i	$-0.424566\pi$
$467$	10.1469	0.469540	0.234770	+	0.972051i	$0.424566\pi$
$468$	−6.72505	−0.310865
$469$	−2.11112	−0.0974823
$470$	−20.1885	−0.931225
$471$	28.8262	1.32824
$472$	5.27008	0.242575
$473$	1.00000	0.0459800
$474$	−19.3795	−0.890128
$475$	−63.6402	−2.92001
$476$	0.414414	0.0189946
$477$	−9.33584	−0.427459
$478$	−11.3603	−0.519607
$479$	10.7061	0.489175	0.244588	−	0.969627i	$-0.421347\pi$
$479$	10.7061	0.489175	0.244588	+	0.969627i	$0.421347\pi$
$480$	37.0394	1.69061
$481$	49.3601	2.25062
$482$	−9.88895	−0.450429
$483$	−2.07323	−0.0943352
$484$	1.54622	0.0702829
$485$	−41.1497	−1.86851
$486$	19.5718	0.887794
$487$	8.86535	0.401728	0.200864	−	0.979619i	$-0.435625\pi$
$487$	8.86535	0.401728	0.200864	+	0.979619i	$0.435625\pi$
$488$	3.68646	0.166878
$489$	3.66243	0.165621
$490$	−48.5156	−2.19171
$491$	7.03978	0.317701	0.158850	−	0.987303i	$-0.449221\pi$
$491$	7.03978	0.317701	0.158850	+	0.987303i	$0.449221\pi$
$492$	4.33833	0.195587
$493$	4.02113	0.181103
$494$	55.8869	2.51447
$495$	3.92866	0.176580
$496$	−42.3466	−1.90142
$497$	2.76781	0.124153
$498$	39.5042	1.77023
$499$	−2.28533	−0.102305	−0.0511526	−	0.998691i	$-0.516290\pi$
$499$	−2.28533	−0.102305	−0.0511526	+	0.998691i	$0.516290\pi$
$500$	−22.0102	−0.984326
$501$	−1.20312	−0.0537513
$502$	−56.0129	−2.49998
$503$	−3.51163	−0.156576	−0.0782880	−	0.996931i	$-0.524945\pi$
$503$	−3.51163	−0.156576	−0.0782880	+	0.996931i	$0.524945\pi$
$504$	−0.241965	−0.0107780
$505$	−39.2944	−1.74858
$506$	−10.4490	−0.464515
$507$	−5.50377	−0.244431
$508$	−26.0745	−1.15687
$509$	18.9113	0.838229	0.419115	−	0.907933i	$-0.362341\pi$
$509$	18.9113	0.838229	0.419115	+	0.907933i	$0.362341\pi$
$510$	−9.76239	−0.432286
$511$	0.402361	0.0177994
$512$	−25.5569	−1.12947
$513$	−40.7674	−1.79992
$514$	−2.85555	−0.125953
$515$	−42.9798	−1.89392
$516$	−2.15559	−0.0948944
$517$	−2.88297	−0.126793
$518$	−6.05149	−0.265887
$519$	18.0084	0.790483
$520$	−13.0817	−0.573669
$521$	4.88973	0.214223	0.107111	−	0.994247i	$-0.465840\pi$
$521$	4.88973	0.214223	0.107111	+	0.994247i	$0.465840\pi$
$522$	8.00012	0.350156
$523$	−32.9050	−1.43884	−0.719418	−	0.694578i	$-0.755591\pi$
$523$	−32.9050	−1.43884	−0.719418	+	0.694578i	$0.755591\pi$
$524$	6.17631	0.269814
$525$	−3.29851	−0.143959
$526$	−21.3090	−0.929115
$527$	9.00678	0.392341
$528$	6.55455	0.285250
$529$	7.78819	0.338617
$530$	61.8801	2.68790
$531$	−6.51564	−0.282755
$532$	−2.98747	−0.129523
$533$	−8.28543	−0.358882
$534$	−48.6319	−2.10451
$535$	−65.5352	−2.83333
$536$	−6.73094	−0.290732
$537$	−20.0418	−0.864869
$538$	−1.56434	−0.0674433
$539$	−6.92817	−0.298417
$540$	−32.5159	−1.39926
$541$	−5.16862	−0.222216	−0.111108	−	0.993808i	$-0.535440\pi$
$541$	−5.16862	−0.222216	−0.111108	+	0.993808i	$0.535440\pi$
$542$	−9.17090	−0.393924
$543$	−7.27323	−0.312124
$544$	7.14480	0.306331
$545$	51.8334	2.22030
$546$	2.89665	0.123965
$547$	4.50332	0.192548	0.0962740	−	0.995355i	$-0.469307\pi$
$547$	4.50332	0.192548	0.0962740	+	0.995355i	$0.469307\pi$
$548$	34.1021	1.45677
$549$	−4.55774	−0.194520
$550$	−16.6244	−0.708866
$551$	−28.9879	−1.23493
$552$	−6.61015	−0.281346
$553$	−1.97846	−0.0841327
$554$	−58.5064	−2.48570
$555$	62.1571	2.63842
$556$	8.02843	0.340481
$557$	19.9158	0.843860	0.421930	−	0.906628i	$-0.361353\pi$
$557$	19.9158	0.843860	0.421930	+	0.906628i	$0.361353\pi$
$558$	17.9191	0.758578
$559$	4.11678	0.174121
$560$	4.68588	0.198015
$561$	−1.39410	−0.0588589
$562$	−1.53899	−0.0649183
$563$	8.60556	0.362681	0.181340	−	0.983420i	$-0.441956\pi$
$563$	8.60556	0.362681	0.181340	+	0.983420i	$0.441956\pi$
$564$	6.21450	0.261678
$565$	−69.3047	−2.91567
$566$	51.2186	2.15288
$567$	−1.26353	−0.0530632
$568$	8.82468	0.370276
$569$	20.3262	0.852117	0.426059	−	0.904696i	$-0.359902\pi$
$569$	20.3262	0.852117	0.426059	+	0.904696i	$0.359902\pi$
$570$	70.3761	2.94773
$571$	14.6511	0.613128	0.306564	−	0.951850i	$-0.400821\pi$
$571$	14.6511	0.613128	0.306564	+	0.951850i	$0.400821\pi$
$572$	6.36547	0.266154
$573$	37.5164	1.56727
$574$	1.01579	0.0423981
$575$	48.9840	2.04278
$576$	4.28026	0.178344
$577$	22.5456	0.938586	0.469293	−	0.883043i	$-0.344509\pi$
$577$	22.5456	0.938586	0.469293	+	0.883043i	$0.344509\pi$
$578$	−1.88314	−0.0783284
$579$	−12.6932	−0.527511
$580$	−23.1207	−0.960033
$581$	4.03300	0.167317
$582$	29.0512	1.20421
$583$	8.83666	0.365977
$584$	1.28286	0.0530851
$585$	16.1735	0.668690
$586$	−10.8615	−0.448683
$587$	−6.20168	−0.255971	−0.127985	−	0.991776i	$-0.540851\pi$
$587$	−6.20168	−0.255971	−0.127985	+	0.991776i	$0.540851\pi$
$588$	14.9343	0.615879
$589$	−64.9289	−2.67535
$590$	43.1872	1.77799
$591$	19.6302	0.807478
$592$	−56.3725	−2.31689
$593$	34.7628	1.42754	0.713768	−	0.700383i	$-0.246987\pi$
$593$	34.7628	1.42754	0.713768	+	0.700383i	$0.246987\pi$
$594$	−10.6494	−0.436952
$595$	−0.996648	−0.0408586
$596$	−19.9403	−0.816784
$597$	29.2639	1.19769
$598$	−43.0163	−1.75907
$599$	−18.6792	−0.763213	−0.381606	−	0.924325i	$-0.624629\pi$
$599$	−18.6792	−0.763213	−0.381606	+	0.924325i	$0.624629\pi$
$600$	−10.5167	−0.429344
$601$	−4.77135	−0.194627	−0.0973136	−	0.995254i	$-0.531025\pi$
$601$	−4.77135	−0.194627	−0.0973136	+	0.995254i	$0.531025\pi$
$602$	−0.504714	−0.0205706
$603$	8.32176	0.338888
$604$	−5.94792	−0.242017
$605$	−3.71860	−0.151183
$606$	27.7413	1.12691
$607$	−12.1515	−0.493214	−0.246607	−	0.969116i	$-0.579316\pi$
$607$	−12.1515	−0.493214	−0.246607	+	0.969116i	$0.579316\pi$
$608$	−51.5062	−2.08885
$609$	−1.50246	−0.0608829
$610$	30.2098	1.22316
$611$	−11.8686	−0.480151
$612$	−1.63357	−0.0660331
$613$	−30.3364	−1.22528	−0.612639	−	0.790363i	$-0.709892\pi$
$613$	−30.3364	−1.22528	−0.612639	+	0.790363i	$0.709892\pi$
$614$	2.04175	0.0823985
$615$	−10.4335	−0.420720
$616$	0.229027	0.00922777
$617$	31.0987	1.25199	0.625993	−	0.779828i	$-0.284694\pi$
$617$	31.0987	1.25199	0.625993	+	0.779828i	$0.284694\pi$
$618$	30.3432	1.22058
$619$	6.61058	0.265701	0.132851	−	0.991136i	$-0.457587\pi$
$619$	6.61058	0.265701	0.132851	+	0.991136i	$0.457587\pi$
$620$	−51.7871	−2.07982
$621$	31.3788	1.25919
$622$	44.1561	1.77050
$623$	−4.96486	−0.198913
$624$	26.9837	1.08021
$625$	8.79361	0.351744
$626$	39.9929	1.59844
$627$	10.0499	0.401355
$628$	−31.9718	−1.27581
$629$	11.9900	0.478071
$630$	−1.98285	−0.0789986
$631$	−12.7104	−0.505992	−0.252996	−	0.967467i	$-0.581416\pi$
$631$	−12.7104	−0.505992	−0.252996	+	0.967467i	$0.581416\pi$
$632$	−6.30799	−0.250918
$633$	18.5877	0.738793
$634$	3.18114	0.126339
$635$	62.7080	2.48849
$636$	−19.0482	−0.755310
$637$	−28.5218	−1.13007
$638$	−7.57236	−0.299793
$639$	−10.9104	−0.431607
$640$	24.7668	0.978995
$641$	23.8135	0.940577	0.470289	−	0.882513i	$-0.344150\pi$
$641$	23.8135	0.940577	0.470289	+	0.882513i	$0.344150\pi$
$642$	46.2670	1.82601
$643$	12.3271	0.486133	0.243066	−	0.970010i	$-0.421847\pi$
$643$	12.3271	0.486133	0.243066	+	0.970010i	$0.421847\pi$
$644$	2.29946	0.0906115
$645$	5.18410	0.204124
$646$	13.5754	0.534116
$647$	17.4223	0.684942	0.342471	−	0.939528i	$-0.388736\pi$
$647$	17.4223	0.684942	0.342471	+	0.939528i	$0.388736\pi$
$648$	−4.02855	−0.158256
$649$	6.16726	0.242086
$650$	−68.4390	−2.68440
$651$	−3.36531	−0.131897
$652$	−4.06208	−0.159083
$653$	3.00249	0.117497	0.0587483	−	0.998273i	$-0.481289\pi$
$653$	3.00249	0.117497	0.0587483	+	0.998273i	$0.481289\pi$
$654$	−36.5937	−1.43093
$655$	−14.8538	−0.580385
$656$	9.46251	0.369449
$657$	−1.58606	−0.0618780
$658$	1.45508	0.0567248
$659$	−20.2166	−0.787528	−0.393764	−	0.919211i	$-0.628827\pi$
$659$	−20.2166	−0.787528	−0.393764	+	0.919211i	$0.628827\pi$
$660$	8.01577	0.312013
$661$	41.7230	1.62284	0.811419	−	0.584466i	$-0.198696\pi$
$661$	41.7230	1.62284	0.811419	+	0.584466i	$0.198696\pi$
$662$	27.6787	1.07576
$663$	−5.73920	−0.222892
$664$	12.8586	0.499009
$665$	7.18473	0.278612
$666$	23.8542	0.924333
$667$	22.3121	0.863928
$668$	1.33440	0.0516295
$669$	−37.7182	−1.45827
$670$	−55.1586	−2.13096
$671$	4.31404	0.166542
$672$	−2.66960	−0.102982
$673$	19.5486	0.753545	0.376772	−	0.926306i	$-0.377034\pi$
$673$	19.5486	0.753545	0.376772	+	0.926306i	$0.377034\pi$
$674$	−63.6215	−2.45061
$675$	49.9236	1.92156
$676$	6.10435	0.234783
$677$	−28.8002	−1.10688	−0.553440	−	0.832889i	$-0.686685\pi$
$677$	−28.8002	−1.10688	−0.553440	+	0.832889i	$0.686685\pi$
$678$	48.9282	1.87908
$679$	2.96585	0.113819
$680$	−3.17764	−0.121857
$681$	31.8084	1.21890
$682$	−16.9610	−0.649472
$683$	−5.70887	−0.218444	−0.109222	−	0.994017i	$-0.534836\pi$
$683$	−5.70887	−0.218444	−0.109222	+	0.994017i	$0.534836\pi$
$684$	11.7762	0.450275
$685$	−82.0140	−3.13360
$686$	7.02973	0.268396
$687$	10.7880	0.411589
$688$	−4.70164	−0.179248
$689$	36.3786	1.38591
$690$	−54.1687	−2.06217
$691$	14.1861	0.539664	0.269832	−	0.962907i	$-0.413032\pi$
$691$	14.1861	0.539664	0.269832	+	0.962907i	$0.413032\pi$
$692$	−19.9735	−0.759280
$693$	−0.283157	−0.0107562
$694$	14.0086	0.531758
$695$	−19.3080	−0.732395
$696$	−4.79035	−0.181578
$697$	−2.01260	−0.0762326
$698$	−15.8966	−0.601694
$699$	28.9528	1.09509
$700$	3.65844	0.138276
$701$	−2.46376	−0.0930549	−0.0465275	−	0.998917i	$-0.514815\pi$
$701$	−2.46376	−0.0930549	−0.0465275	+	0.998917i	$0.514815\pi$
$702$	−43.8414	−1.65469
$703$	−86.4344	−3.25993
$704$	−4.05140	−0.152693
$705$	−14.9456	−0.562885
$706$	31.4131	1.18225
$707$	2.83213	0.106513
$708$	−13.2941	−0.499621
$709$	−1.06179	−0.0398763	−0.0199382	−	0.999801i	$-0.506347\pi$
$709$	−1.06179	−0.0398763	−0.0199382	+	0.999801i	$0.506347\pi$
$710$	72.3164	2.71398
$711$	7.79885	0.292480
$712$	−15.8296	−0.593240
$713$	49.9760	1.87162
$714$	0.703620	0.0263323
$715$	−15.3087	−0.572512
$716$	22.2288	0.830729
$717$	−8.41006	−0.314079
$718$	−63.3229	−2.36319
$719$	−25.4788	−0.950199	−0.475099	−	0.879932i	$-0.657588\pi$
$719$	−25.4788	−0.950199	−0.475099	+	0.879932i	$0.657588\pi$
$720$	−18.4712	−0.688379
$721$	3.09775	0.115366
$722$	−62.0839	−2.31052
$723$	−7.32084	−0.272265
$724$	8.06688	0.299803
$725$	35.4986	1.31838
$726$	2.62529	0.0974335
$727$	13.6911	0.507775	0.253888	−	0.967234i	$-0.418291\pi$
$727$	13.6911	0.507775	0.253888	+	0.967234i	$0.418291\pi$
$728$	0.942856	0.0349446
$729$	28.6322	1.06045
$730$	10.5128	0.389094
$731$	1.00000	0.0369863
$732$	−9.29930	−0.343712
$733$	3.07724	0.113660	0.0568302	−	0.998384i	$-0.481901\pi$
$733$	3.07724	0.113660	0.0568302	+	0.998384i	$0.481901\pi$
$734$	45.1588	1.66684
$735$	−35.9163	−1.32479
$736$	39.6444	1.46131
$737$	−7.87681	−0.290146
$738$	−4.00410	−0.147393
$739$	−33.8930	−1.24677	−0.623387	−	0.781913i	$-0.714244\pi$
$739$	−33.8930	−1.24677	−0.623387	+	0.781913i	$0.714244\pi$
$740$	−68.9397	−2.53427
$741$	41.3733	1.51989
$742$	−4.45998	−0.163731
$743$	10.6012	0.388922	0.194461	−	0.980910i	$-0.437704\pi$
$743$	10.6012	0.388922	0.194461	+	0.980910i	$0.437704\pi$
$744$	−10.7297	−0.393370
$745$	47.9555	1.75695
$746$	13.7713	0.504203
$747$	−15.8976	−0.581663
$748$	1.54622	0.0565355
$749$	4.72342	0.172590
$750$	−37.3705	−1.36458
$751$	−22.6133	−0.825171	−0.412586	−	0.910919i	$-0.635374\pi$
$751$	−22.6133	−0.825171	−0.412586	+	0.910919i	$0.635374\pi$
$752$	13.5547	0.494289
$753$	−41.4666	−1.51113
$754$	−31.1738	−1.13528
$755$	14.3045	0.520594
$756$	2.34357	0.0852348
$757$	0.941456	0.0342178	0.0171089	−	0.999854i	$-0.494554\pi$
$757$	0.941456	0.0342178	0.0171089	+	0.999854i	$0.494554\pi$
$758$	−50.8725	−1.84777
$759$	−7.73545	−0.280779
$760$	22.9073	0.830936
$761$	25.7853	0.934715	0.467358	−	0.884068i	$-0.345206\pi$
$761$	25.7853	0.934715	0.467358	+	0.884068i	$0.345206\pi$
$762$	−44.2710	−1.60377
$763$	−3.73587	−0.135248
$764$	−41.6102	−1.50540
$765$	3.92866	0.142041
$766$	−19.8627	−0.717670
$767$	25.3893	0.916753
$768$	−28.7812	−1.03855
$769$	−2.02442	−0.0730025	−0.0365013	−	0.999334i	$-0.511621\pi$
$769$	−2.02442	−0.0730025	−0.0365013	+	0.999334i	$0.511621\pi$
$770$	1.87683	0.0676362
$771$	−2.11398	−0.0761330
$772$	14.0783	0.506689
$773$	−7.69676	−0.276833	−0.138417	−	0.990374i	$-0.544201\pi$
$773$	−7.69676	−0.276833	−0.138417	+	0.990374i	$0.544201\pi$
$774$	1.98952	0.0715118
$775$	79.5118	2.85615
$776$	9.45611	0.339455
$777$	−4.47995	−0.160717
$778$	40.2092	1.44157
$779$	14.5086	0.519825
$780$	32.9992	1.18156
$781$	10.3270	0.369529
$782$	−10.4490	−0.373656
$783$	22.7401	0.812664
$784$	32.5737	1.16335
$785$	76.8908	2.74435
$786$	10.4866	0.374044
$787$	−3.51186	−0.125184	−0.0625922	−	0.998039i	$-0.519937\pi$
$787$	−3.51186	−0.125184	−0.0625922	+	0.998039i	$0.519937\pi$
$788$	−21.7722	−0.775604
$789$	−15.7751	−0.561609
$790$	−51.6926	−1.83914
$791$	4.99511	0.177606
$792$	−0.902798	−0.0320795
$793$	17.7600	0.630675
$794$	33.1155	1.17523
$795$	45.8101	1.62472
$796$	−32.4572	−1.15041
$797$	35.6789	1.26381	0.631906	−	0.775045i	$-0.282273\pi$
$797$	35.6789	1.26381	0.631906	+	0.775045i	$0.282273\pi$
$798$	−5.07233	−0.179559
$799$	−2.88297	−0.101992
$800$	63.0743	2.23001
$801$	19.5709	0.691502
$802$	−19.5629	−0.690791
$803$	1.50125	0.0529780
$804$	16.9791	0.598808
$805$	−5.53011	−0.194911
$806$	−69.8249	−2.45948
$807$	−1.15809	−0.0407665
$808$	9.02976	0.317666
$809$	−26.5986	−0.935158	−0.467579	−	0.883951i	$-0.654874\pi$
$809$	−26.5986	−0.935158	−0.467579	+	0.883951i	$0.654874\pi$
$810$	−33.0131	−1.15996
$811$	−34.7318	−1.21960	−0.609799	−	0.792556i	$-0.708750\pi$
$811$	−34.7318	−1.21960	−0.609799	+	0.792556i	$0.708750\pi$
$812$	1.66641	0.0584796
$813$	−6.78926	−0.238110
$814$	−22.5788	−0.791386
$815$	9.76913	0.342198
$816$	6.55455	0.229455
$817$	−7.20890	−0.252208
$818$	13.1966	0.461409
$819$	−1.16570	−0.0407327
$820$	11.5720	0.404112
$821$	41.3194	1.44206	0.721028	−	0.692906i	$-0.243670\pi$
$821$	41.3194	1.44206	0.721028	+	0.692906i	$0.243670\pi$
$822$	57.9009	2.01952
$823$	1.32929	0.0463361	0.0231681	−	0.999732i	$-0.492625\pi$
$823$	1.32929	0.0463361	0.0231681	+	0.999732i	$0.492625\pi$
$824$	9.87665	0.344070
$825$	−12.3071	−0.428478
$826$	−3.11270	−0.108305
$827$	15.7232	0.546748	0.273374	−	0.961908i	$-0.411860\pi$
$827$	15.7232	0.546748	0.273374	+	0.961908i	$0.411860\pi$
$828$	−9.06420	−0.315003
$829$	11.0233	0.382854	0.191427	−	0.981507i	$-0.438688\pi$
$829$	11.0233	0.382854	0.191427	+	0.981507i	$0.438688\pi$
$830$	105.373	3.65755
$831$	−43.3125	−1.50250
$832$	−16.6787	−0.578231
$833$	−6.92817	−0.240047
$834$	13.6312	0.472011
$835$	−3.20918	−0.111058
$836$	−11.1466	−0.385512
$837$	50.9346	1.76056
$838$	45.0008	1.55453
$839$	11.4887	0.396636	0.198318	−	0.980138i	$-0.436452\pi$
$839$	11.4887	0.396636	0.198318	+	0.980138i	$0.436452\pi$
$840$	1.18730	0.0409657
$841$	−12.8305	−0.442431
$842$	68.6165	2.36468
$843$	−1.13932	−0.0392402
$844$	−20.6159	−0.709630
$845$	−14.6807	−0.505031
$846$	−5.73573	−0.197199
$847$	0.268017	0.00920916
$848$	−41.5468	−1.42672
$849$	37.9174	1.30132
$850$	−16.6244	−0.570212
$851$	66.5288	2.28058
$852$	−22.2607	−0.762640
$853$	−4.38160	−0.150023	−0.0750115	−	0.997183i	$-0.523899\pi$
$853$	−4.38160	−0.150023	−0.0750115	+	0.997183i	$0.523899\pi$
$854$	−2.17736	−0.0745076
$855$	−28.3213	−0.968569
$856$	15.0598	0.514735
$857$	6.88626	0.235230	0.117615	−	0.993059i	$-0.462475\pi$
$857$	6.88626	0.235230	0.117615	+	0.993059i	$0.462475\pi$
$858$	10.8077	0.368970
$859$	28.1249	0.959609	0.479804	−	0.877376i	$-0.340708\pi$
$859$	28.1249	0.959609	0.479804	+	0.877376i	$0.340708\pi$
$860$	−5.74979	−0.196066
$861$	0.751991	0.0256278
$862$	−43.2003	−1.47141
$863$	18.9152	0.643880	0.321940	−	0.946760i	$-0.395665\pi$
$863$	18.9152	0.643880	0.321940	+	0.946760i	$0.395665\pi$
$864$	40.4049	1.37460
$865$	48.0355	1.63326
$866$	−19.6078	−0.666300
$867$	−1.39410	−0.0473461
$868$	3.73253	0.126690
$869$	−7.38185	−0.250412
$870$	−39.2559	−1.33090
$871$	−32.4271	−1.09875
$872$	−11.9112	−0.403364
$873$	−11.6910	−0.395681
$874$	75.3259	2.54794
$875$	−3.81517	−0.128976
$876$	−3.23608	−0.109337
$877$	−37.6775	−1.27228	−0.636139	−	0.771574i	$-0.719470\pi$
$877$	−37.6775	−1.27228	−0.636139	+	0.771574i	$0.719470\pi$
$878$	−63.9861	−2.15943
$879$	−8.04078	−0.271209
$880$	17.4835	0.589370
$881$	26.2568	0.884615	0.442308	−	0.896863i	$-0.354160\pi$
$881$	26.2568	0.884615	0.442308	+	0.896863i	$0.354160\pi$
$882$	−13.7837	−0.464122
$883$	−3.58650	−0.120695	−0.0603477	−	0.998177i	$-0.519221\pi$
$883$	−3.58650	−0.120695	−0.0603477	+	0.998177i	$0.519221\pi$
$884$	6.36547	0.214094
$885$	31.9717	1.07472
$886$	−59.5579	−2.00089
$887$	2.73119	0.0917043	0.0458522	−	0.998948i	$-0.485400\pi$
$887$	2.73119	0.0917043	0.0458522	+	0.998948i	$0.485400\pi$
$888$	−14.2836	−0.479325
$889$	−4.51965	−0.151584
$890$	−129.720	−4.34823
$891$	−4.71436	−0.157937
$892$	41.8341	1.40071
$893$	20.7831	0.695479
$894$	−33.8559	−1.13231
$895$	−53.4593	−1.78695
$896$	−1.78506	−0.0596346
$897$	−31.8452	−1.06328
$898$	8.44745	0.281895
$899$	36.2174	1.20792
$900$	−14.4211	−0.480705
$901$	8.83666	0.294392
$902$	3.79001	0.126193
$903$	−0.373642	−0.0124340
$904$	15.9261	0.529693
$905$	−19.4005	−0.644895
$906$	−10.0988	−0.335510
$907$	10.7295	0.356268	0.178134	−	0.984006i	$-0.442994\pi$
$907$	10.7295	0.356268	0.178134	+	0.984006i	$0.442994\pi$
$908$	−35.2794	−1.17079
$909$	−11.1639	−0.370283
$910$	7.72650	0.256131
$911$	−48.0816	−1.59301	−0.796507	−	0.604629i	$-0.793321\pi$
$911$	−48.0816	−1.59301	−0.796507	+	0.604629i	$0.793321\pi$
$912$	−47.2511	−1.56464
$913$	15.0476	0.498002
$914$	−56.8716	−1.88114
$915$	22.3644	0.739345
$916$	−11.9652	−0.395342
$917$	1.07058	0.0353537
$918$	−10.6494	−0.351484
$919$	−17.5073	−0.577512	−0.288756	−	0.957403i	$-0.593242\pi$
$919$	−17.5073	−0.577512	−0.288756	+	0.957403i	$0.593242\pi$
$920$	−17.6318	−0.581304
$921$	1.51152	0.0498063
$922$	−3.56250	−0.117325
$923$	42.5140	1.39936
$924$	−0.577733	−0.0190060
$925$	105.847	3.48024
$926$	−36.6772	−1.20529
$927$	−12.2110	−0.401060
$928$	28.7302	0.943115
$929$	30.2025	0.990911	0.495455	−	0.868633i	$-0.335001\pi$
$929$	30.2025	0.990911	0.495455	+	0.868633i	$0.335001\pi$
$930$	−87.9277	−2.88326
$931$	49.9445	1.63686
$932$	−32.1121	−1.05187
$933$	32.6890	1.07019
$934$	−19.1080	−0.625232
$935$	−3.71860	−0.121611
$936$	−3.71662	−0.121482
$937$	−39.6641	−1.29577	−0.647886	−	0.761738i	$-0.724346\pi$
$937$	−39.6641	−1.29577	−0.647886	+	0.761738i	$0.724346\pi$
$938$	3.97553	0.129806
$939$	29.6070	0.966187
$940$	16.5765	0.540666
$941$	−16.2573	−0.529973	−0.264986	−	0.964252i	$-0.585367\pi$
$941$	−16.2573	−0.529973	−0.264986	+	0.964252i	$0.585367\pi$
$942$	−54.2839	−1.76866
$943$	−11.1673	−0.363658
$944$	−28.9962	−0.943747
$945$	−5.63619	−0.183345
$946$	−1.88314	−0.0612262
$947$	−6.11803	−0.198809	−0.0994047	−	0.995047i	$-0.531694\pi$
$947$	−6.11803	−0.198809	−0.0994047	+	0.995047i	$0.531694\pi$
$948$	15.9122	0.516805
$949$	6.18033	0.200622
$950$	119.843	3.88824
$951$	2.35501	0.0763665
$952$	0.229027	0.00742282
$953$	6.05132	0.196022	0.0980108	−	0.995185i	$-0.468752\pi$
$953$	6.05132	0.196022	0.0980108	+	0.995185i	$0.468752\pi$
$954$	17.5807	0.569196
$955$	100.071	3.23821
$956$	9.32777	0.301682
$957$	−5.60585	−0.181212
$958$	−20.1611	−0.651377
$959$	5.91113	0.190880
$960$	−21.0028	−0.677864
$961$	50.1220	1.61684
$962$	−92.9520	−2.99689
$963$	−18.6192	−0.599994
$964$	8.11969	0.261518
$965$	−33.8577	−1.08992
$966$	3.90419	0.125615
$967$	−5.35053	−0.172062	−0.0860308	−	0.996292i	$-0.527418\pi$
$967$	−5.35053	−0.172062	−0.0860308	+	0.996292i	$0.527418\pi$
$968$	0.854526	0.0274655
$969$	10.0499	0.322850
$970$	77.4907	2.48808
$971$	10.6797	0.342729	0.171365	−	0.985208i	$-0.445182\pi$
$971$	10.6797	0.342729	0.171365	+	0.985208i	$0.445182\pi$
$972$	−16.0701	−0.515450
$973$	1.39162	0.0446132
$974$	−16.6947	−0.534933
$975$	−50.6657	−1.62260
$976$	−20.2831	−0.649246
$977$	21.9043	0.700781	0.350390	−	0.936604i	$-0.386049\pi$
$977$	21.9043	0.700781	0.350390	+	0.936604i	$0.386049\pi$
$978$	−6.89688	−0.220538
$979$	−18.5244	−0.592043
$980$	39.8355	1.27250
$981$	14.7264	0.470176
$982$	−13.2569	−0.423045
$983$	−5.85558	−0.186764	−0.0933820	−	0.995630i	$-0.529768\pi$
$983$	−5.85558	−0.186764	−0.0933820	+	0.995630i	$0.529768\pi$
$984$	2.39760	0.0764326
$985$	52.3613	1.66837
$986$	−7.57236	−0.241153
$987$	1.07720	0.0342876
$988$	−45.8880	−1.45989
$989$	5.54871	0.176439
$990$	−7.39823	−0.235131
$991$	43.2988	1.37543	0.687716	−	0.725980i	$-0.258613\pi$
$991$	43.2988	1.37543	0.687716	+	0.725980i	$0.258613\pi$
$992$	64.3516	2.04317
$993$	20.4906	0.650251
$994$	−5.21217	−0.165320
$995$	78.0581	2.47461
$996$	−32.4364	−1.02779
$997$	62.0036	1.96368	0.981838	−	0.189723i	$-0.0607591\pi$
$997$	62.0036	1.96368	0.981838	+	0.189723i	$0.0607591\pi$
$998$	4.30359	0.136228
$999$	67.8049	2.14525

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.16	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.16	✓	82	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.88314 q^{2} -1.39410 q^{3} +1.54622 q^{4} -3.71860 q^{5} +2.62529 q^{6} +0.268017 q^{7} +0.854526 q^{8} -1.05649 q^{9} +O(q^{10})\)	\(q-1.88314 q^{2} -1.39410 q^{3} +1.54622 q^{4} -3.71860 q^{5} +2.62529 q^{6} +0.268017 q^{7} +0.854526 q^{8} -1.05649 q^{9} +7.00266 q^{10} +1.00000 q^{11} -2.15559 q^{12} +4.11678 q^{13} -0.504714 q^{14} +5.18410 q^{15} -4.70164 q^{16} +1.00000 q^{17} +1.98952 q^{18} -7.20890 q^{19} -5.74979 q^{20} -0.373642 q^{21} -1.88314 q^{22} +5.54871 q^{23} -1.19129 q^{24} +8.82800 q^{25} -7.75249 q^{26} +5.65515 q^{27} +0.414414 q^{28} +4.02113 q^{29} -9.76239 q^{30} +9.00678 q^{31} +7.14480 q^{32} -1.39410 q^{33} -1.88314 q^{34} -0.996648 q^{35} -1.63357 q^{36} +11.9900 q^{37} +13.5754 q^{38} -5.73920 q^{39} -3.17764 q^{40} -2.01260 q^{41} +0.703620 q^{42} +1.00000 q^{43} +1.54622 q^{44} +3.92866 q^{45} -10.4490 q^{46} -2.88297 q^{47} +6.55455 q^{48} -6.92817 q^{49} -16.6244 q^{50} -1.39410 q^{51} +6.36547 q^{52} +8.83666 q^{53} -10.6494 q^{54} -3.71860 q^{55} +0.229027 q^{56} +10.0499 q^{57} -7.57236 q^{58} +6.16726 q^{59} +8.01577 q^{60} +4.31404 q^{61} -16.9610 q^{62} -0.283157 q^{63} -4.05140 q^{64} -15.3087 q^{65} +2.62529 q^{66} -7.87681 q^{67} +1.54622 q^{68} -7.73545 q^{69} +1.87683 q^{70} +10.3270 q^{71} -0.902798 q^{72} +1.50125 q^{73} -22.5788 q^{74} -12.3071 q^{75} -11.1466 q^{76} +0.268017 q^{77} +10.8077 q^{78} -7.38185 q^{79} +17.4835 q^{80} -4.71436 q^{81} +3.79001 q^{82} +15.0476 q^{83} -0.577733 q^{84} -3.71860 q^{85} -1.88314 q^{86} -5.60585 q^{87} +0.854526 q^{88} -18.5244 q^{89} -7.39823 q^{90} +1.10337 q^{91} +8.57954 q^{92} -12.5563 q^{93} +5.42905 q^{94} +26.8070 q^{95} -9.96056 q^{96} +11.0659 q^{97} +13.0467 q^{98} -1.05649 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

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