LMFDB - Embedded newform 8043.2.a.o.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-1.72607 q^{2} -1.00000 q^{3} +0.979322 q^{4} -3.72360 q^{5} +1.72607 q^{6} +1.00000 q^{7} +1.76176 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.72607 q^{2} -1.00000 q^{3} +0.979322 q^{4} -3.72360 q^{5} +1.72607 q^{6} +1.00000 q^{7} +1.76176 q^{8} +1.00000 q^{9} +6.42720 q^{10} +4.56245 q^{11} -0.979322 q^{12} -6.77605 q^{13} -1.72607 q^{14} +3.72360 q^{15} -4.99957 q^{16} -1.67942 q^{17} -1.72607 q^{18} +4.27331 q^{19} -3.64660 q^{20} -1.00000 q^{21} -7.87512 q^{22} +0.655845 q^{23} -1.76176 q^{24} +8.86518 q^{25} +11.6959 q^{26} -1.00000 q^{27} +0.979322 q^{28} -7.73977 q^{29} -6.42720 q^{30} +8.52971 q^{31} +5.10609 q^{32} -4.56245 q^{33} +2.89880 q^{34} -3.72360 q^{35} +0.979322 q^{36} -9.77981 q^{37} -7.37604 q^{38} +6.77605 q^{39} -6.56010 q^{40} +8.94848 q^{41} +1.72607 q^{42} +0.00274505 q^{43} +4.46811 q^{44} -3.72360 q^{45} -1.13204 q^{46} +4.10273 q^{47} +4.99957 q^{48} +1.00000 q^{49} -15.3019 q^{50} +1.67942 q^{51} -6.63593 q^{52} -12.6948 q^{53} +1.72607 q^{54} -16.9887 q^{55} +1.76176 q^{56} -4.27331 q^{57} +13.3594 q^{58} +9.06751 q^{59} +3.64660 q^{60} -9.81284 q^{61} -14.7229 q^{62} +1.00000 q^{63} +1.18566 q^{64} +25.2313 q^{65} +7.87512 q^{66} -8.07552 q^{67} -1.64469 q^{68} -0.655845 q^{69} +6.42720 q^{70} -8.57589 q^{71} +1.76176 q^{72} +1.26109 q^{73} +16.8806 q^{74} -8.86518 q^{75} +4.18495 q^{76} +4.56245 q^{77} -11.6959 q^{78} -2.84685 q^{79} +18.6164 q^{80} +1.00000 q^{81} -15.4457 q^{82} -5.57219 q^{83} -0.979322 q^{84} +6.25349 q^{85} -0.00473814 q^{86} +7.73977 q^{87} +8.03796 q^{88} +16.2365 q^{89} +6.42720 q^{90} -6.77605 q^{91} +0.642284 q^{92} -8.52971 q^{93} -7.08160 q^{94} -15.9121 q^{95} -5.10609 q^{96} +2.05421 q^{97} -1.72607 q^{98} +4.56245 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) $ 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9 - 18 * q^10 - 17 * q^11 - 34 * q^12 - 38 * q^13 - 4 * q^14 - 5 * q^15 + 16 * q^16 + 4 * q^17 - 4 * q^18 - 15 * q^19 + 23 * q^20 - 41 * q^21 - 31 * q^22 - 8 * q^23 + 15 * q^24 + 16 * q^25 + 15 * q^26 - 41 * q^27 + 34 * q^28 - 27 * q^29 + 18 * q^30 - 23 * q^31 - 24 * q^32 + 17 * q^33 - 9 * q^34 + 5 * q^35 + 34 * q^36 - 81 * q^37 + 38 * q^39 - 52 * q^40 + 29 * q^41 + 4 * q^42 - 47 * q^43 - 20 * q^44 + 5 * q^45 - 40 * q^46 + 26 * q^47 - 16 * q^48 + 41 * q^49 - 23 * q^50 - 4 * q^51 - 64 * q^52 - 66 * q^53 + 4 * q^54 - 14 * q^55 - 15 * q^56 + 15 * q^57 - 50 * q^58 + 41 * q^59 - 23 * q^60 - 47 * q^61 + 5 * q^62 + 41 * q^63 - 37 * q^64 - 24 * q^65 + 31 * q^66 - 73 * q^67 + 10 * q^68 + 8 * q^69 - 18 * q^70 + q^71 - 15 * q^72 - 14 * q^73 + 18 * q^74 - 16 * q^75 - 37 * q^76 - 17 * q^77 - 15 * q^78 - 80 * q^79 + 63 * q^80 + 41 * q^81 - 31 * q^82 + 20 * q^83 - 34 * q^84 - 82 * q^85 - 39 * q^86 + 27 * q^87 - 132 * q^88 + 17 * q^89 - 18 * q^90 - 38 * q^91 - 26 * q^92 + 23 * q^93 - 9 * q^94 - q^95 + 24 * q^96 - 73 * q^97 - 4 * q^98 - 17 * 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 $

$2$	−1.72607	−1.22052	−0.610258	−	0.792202i	$-0.708934\pi$
$2$	−1.72607	−1.22052	−0.610258	+	0.792202i	$0.708934\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.979322	0.489661
$5$	−3.72360	−1.66524	−0.832622	−	0.553842i	$-0.813161\pi$
$5$	−3.72360	−1.66524	−0.832622	+	0.553842i	$0.813161\pi$
$6$	1.72607	0.704666
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.76176	0.622877
$9$	1.00000	0.333333
$10$	6.42720	2.03246
$11$	4.56245	1.37563	0.687816	−	0.725885i	$-0.258570\pi$
$11$	4.56245	1.37563	0.687816	+	0.725885i	$0.258570\pi$
$12$	−0.979322	−0.282706
$13$	−6.77605	−1.87934	−0.939669	−	0.342086i	$-0.888867\pi$
$13$	−6.77605	−1.87934	−0.939669	+	0.342086i	$0.888867\pi$
$14$	−1.72607	−0.461312
$15$	3.72360	0.961429
$16$	−4.99957	−1.24989
$17$	−1.67942	−0.407319	−0.203660	−	0.979042i	$-0.565284\pi$
$17$	−1.67942	−0.407319	−0.203660	+	0.979042i	$0.565284\pi$
$18$	−1.72607	−0.406839
$19$	4.27331	0.980365	0.490183	−	0.871620i	$-0.336930\pi$
$19$	4.27331	0.980365	0.490183	+	0.871620i	$0.336930\pi$
$20$	−3.64660	−0.815405
$21$	−1.00000	−0.218218
$22$	−7.87512	−1.67898
$23$	0.655845	0.136753	0.0683766	−	0.997660i	$-0.478218\pi$
$23$	0.655845	0.136753	0.0683766	+	0.997660i	$0.478218\pi$
$24$	−1.76176	−0.359618
$25$	8.86518	1.77304
$26$	11.6959	2.29376
$27$	−1.00000	−0.192450
$28$	0.979322	0.185074
$29$	−7.73977	−1.43724	−0.718620	−	0.695403i	$-0.755226\pi$
$29$	−7.73977	−1.43724	−0.718620	+	0.695403i	$0.755226\pi$
$30$	−6.42720	−1.17344
$31$	8.52971	1.53198	0.765991	−	0.642851i	$-0.222249\pi$
$31$	8.52971	1.53198	0.765991	+	0.642851i	$0.222249\pi$
$32$	5.10609	0.902638
$33$	−4.56245	−0.794221
$34$	2.89880	0.497140
$35$	−3.72360	−0.629403
$36$	0.979322	0.163220
$37$	−9.77981	−1.60779	−0.803895	−	0.594771i	$-0.797243\pi$
$37$	−9.77981	−1.60779	−0.803895	+	0.594771i	$0.797243\pi$
$38$	−7.37604	−1.19655
$39$	6.77605	1.08504
$40$	−6.56010	−1.03724
$41$	8.94848	1.39752	0.698759	−	0.715357i	$-0.253736\pi$
$41$	8.94848	1.39752	0.698759	+	0.715357i	$0.253736\pi$
$42$	1.72607	0.266339
$43$	0.00274505	0.000418616 0	0.000209308	−	1.00000i	$-0.499933\pi$
$43$	0.00274505	0.000418616 0	0.000209308		1.00000i	$0.499933\pi$
$44$	4.46811	0.673593
$45$	−3.72360	−0.555081
$46$	−1.13204	−0.166910
$47$	4.10273	0.598444	0.299222	−	0.954184i	$-0.403273\pi$
$47$	4.10273	0.598444	0.299222	+	0.954184i	$0.403273\pi$
$48$	4.99957	0.721626
$49$	1.00000	0.142857
$50$	−15.3019	−2.16402
$51$	1.67942	0.235166
$52$	−6.63593	−0.920238
$53$	−12.6948	−1.74376	−0.871879	−	0.489721i	$-0.837099\pi$
$53$	−12.6948	−1.74376	−0.871879	+	0.489721i	$0.837099\pi$
$54$	1.72607	0.234889
$55$	−16.9887	−2.29076
$56$	1.76176	0.235425
$57$	−4.27331	−0.566014
$58$	13.3594	1.75417
$59$	9.06751	1.18049	0.590244	−	0.807225i	$-0.299031\pi$
$59$	9.06751	1.18049	0.590244	+	0.807225i	$0.299031\pi$
$60$	3.64660	0.470774
$61$	−9.81284	−1.25640	−0.628202	−	0.778050i	$-0.716209\pi$
$61$	−9.81284	−1.25640	−0.628202	+	0.778050i	$0.716209\pi$
$62$	−14.7229	−1.86981
$63$	1.00000	0.125988
$64$	1.18566	0.148208
$65$	25.2313	3.12955
$66$	7.87512	0.969360
$67$	−8.07552	−0.986581	−0.493291	−	0.869865i	$-0.664206\pi$
$67$	−8.07552	−0.986581	−0.493291	+	0.869865i	$0.664206\pi$
$68$	−1.64469	−0.199448
$69$	−0.655845	−0.0789545
$70$	6.42720	0.768197
$71$	−8.57589	−1.01777	−0.508885	−	0.860834i	$-0.669942\pi$
$71$	−8.57589	−1.01777	−0.508885	+	0.860834i	$0.669942\pi$
$72$	1.76176	0.207626
$73$	1.26109	0.147600	0.0737998	−	0.997273i	$-0.476487\pi$
$73$	1.26109	0.147600	0.0737998	+	0.997273i	$0.476487\pi$
$74$	16.8806	1.96233
$75$	−8.86518	−1.02366
$76$	4.18495	0.480047
$77$	4.56245	0.519940
$78$	−11.6959	−1.32430
$79$	−2.84685	−0.320296	−0.160148	−	0.987093i	$-0.551197\pi$
$79$	−2.84685	−0.320296	−0.160148	+	0.987093i	$0.551197\pi$
$80$	18.6164	2.08138
$81$	1.00000	0.111111
$82$	−15.4457	−1.70569
$83$	−5.57219	−0.611628	−0.305814	−	0.952091i	$-0.598929\pi$
$83$	−5.57219	−0.611628	−0.305814	+	0.952091i	$0.598929\pi$
$84$	−0.979322	−0.106853
$85$	6.25349	0.678286
$86$	−0.00473814	−0.000510927 0
$87$	7.73977	0.829790
$88$	8.03796	0.856849
$89$	16.2365	1.72107	0.860533	−	0.509395i	$-0.170131\pi$
$89$	16.2365	1.72107	0.860533	+	0.509395i	$0.170131\pi$
$90$	6.42720	0.677486
$91$	−6.77605	−0.710323
$92$	0.642284	0.0669627
$93$	−8.52971	−0.884490
$94$	−7.08160	−0.730411
$95$	−15.9121	−1.63255
$96$	−5.10609	−0.521138
$97$	2.05421	0.208573	0.104286	−	0.994547i	$-0.466744\pi$
$97$	2.05421	0.208573	0.104286	+	0.994547i	$0.466744\pi$
$98$	−1.72607	−0.174360
$99$	4.56245	0.458544
$100$	8.68187	0.868187
$101$	14.0415	1.39718	0.698592	−	0.715521i	$-0.253810\pi$
$101$	14.0415	1.39718	0.698592	+	0.715521i	$0.253810\pi$
$102$	−2.89880	−0.287024
$103$	5.90416	0.581754	0.290877	−	0.956760i	$-0.406053\pi$
$103$	5.90416	0.581754	0.290877	+	0.956760i	$0.406053\pi$
$104$	−11.9378	−1.17060
$105$	3.72360	0.363386
$106$	21.9120	2.12829
$107$	9.05006	0.874902	0.437451	−	0.899242i	$-0.355881\pi$
$107$	9.05006	0.874902	0.437451	+	0.899242i	$0.355881\pi$
$108$	−0.979322	−0.0942353
$109$	−19.8302	−1.89939	−0.949696	−	0.313172i	$-0.898608\pi$
$109$	−19.8302	−1.89939	−0.949696	+	0.313172i	$0.898608\pi$
$110$	29.3238	2.79591
$111$	9.77981	0.928258
$112$	−4.99957	−0.472415
$113$	4.83981	0.455291	0.227646	−	0.973744i	$-0.426897\pi$
$113$	4.83981	0.455291	0.227646	+	0.973744i	$0.426897\pi$
$114$	7.37604	0.690830
$115$	−2.44210	−0.227727
$116$	−7.57973	−0.703760
$117$	−6.77605	−0.626446
$118$	−15.6512	−1.44081
$119$	−1.67942	−0.153952
$120$	6.56010	0.598852
$121$	9.81597	0.892361
$122$	16.9377	1.53346
$123$	−8.94848	−0.806857
$124$	8.35334	0.750152
$125$	−14.3924	−1.28729
$126$	−1.72607	−0.153771
$127$	−15.8158	−1.40343	−0.701715	−	0.712458i	$-0.747582\pi$
$127$	−15.8158	−1.40343	−0.701715	+	0.712458i	$0.747582\pi$
$128$	−12.2587	−1.08353
$129$	−0.00274505	−0.000241688 0
$130$	−43.5510	−3.81967
$131$	−6.04619	−0.528258	−0.264129	−	0.964487i	$-0.585085\pi$
$131$	−6.04619	−0.528258	−0.264129	+	0.964487i	$0.585085\pi$
$132$	−4.46811	−0.388899
$133$	4.27331	0.370543
$134$	13.9389	1.20414
$135$	3.72360	0.320476
$136$	−2.95874	−0.253710
$137$	−9.35274	−0.799059	−0.399529	−	0.916720i	$-0.630826\pi$
$137$	−9.35274	−0.799059	−0.399529	+	0.916720i	$0.630826\pi$
$138$	1.13204	0.0963653
$139$	−1.37175	−0.116351	−0.0581753	−	0.998306i	$-0.518528\pi$
$139$	−1.37175	−0.116351	−0.0581753	+	0.998306i	$0.518528\pi$
$140$	−3.64660	−0.308194
$141$	−4.10273	−0.345512
$142$	14.8026	1.24221
$143$	−30.9154	−2.58528
$144$	−4.99957	−0.416631
$145$	28.8198	2.39335
$146$	−2.17673	−0.180148
$147$	−1.00000	−0.0824786
$148$	−9.57758	−0.787272
$149$	19.1450	1.56842	0.784210	−	0.620495i	$-0.213068\pi$
$149$	19.1450	1.56842	0.784210	+	0.620495i	$0.213068\pi$
$150$	15.3019	1.24940
$151$	11.3897	0.926884	0.463442	−	0.886127i	$-0.346614\pi$
$151$	11.3897	0.926884	0.463442	+	0.886127i	$0.346614\pi$
$152$	7.52857	0.610647
$153$	−1.67942	−0.135773
$154$	−7.87512	−0.634595
$155$	−31.7612	−2.55112
$156$	6.63593	0.531300
$157$	14.0945	1.12486	0.562432	−	0.826844i	$-0.309866\pi$
$157$	14.0945	1.12486	0.562432	+	0.826844i	$0.309866\pi$
$158$	4.91387	0.390927
$159$	12.6948	1.00676
$160$	−19.0130	−1.50311
$161$	0.655845	0.0516879
$162$	−1.72607	−0.135613
$163$	−10.3803	−0.813049	−0.406524	−	0.913640i	$-0.633259\pi$
$163$	−10.3803	−0.813049	−0.406524	+	0.913640i	$0.633259\pi$
$164$	8.76344	0.684310
$165$	16.9887	1.32257
$166$	9.61800	0.746502
$167$	3.17612	0.245775	0.122888	−	0.992421i	$-0.460784\pi$
$167$	3.17612	0.245775	0.122888	+	0.992421i	$0.460784\pi$
$168$	−1.76176	−0.135923
$169$	32.9148	2.53191
$170$	−10.7940	−0.827859
$171$	4.27331	0.326788
$172$	0.00268828	0.000204980 0
$173$	3.05980	0.232632	0.116316	−	0.993212i	$-0.462891\pi$
$173$	3.05980	0.232632	0.116316	+	0.993212i	$0.462891\pi$
$174$	−13.3594	−1.01277
$175$	8.86518	0.670145
$176$	−22.8103	−1.71939
$177$	−9.06751	−0.681556
$178$	−28.0254	−2.10059
$179$	2.37022	0.177159	0.0885794	−	0.996069i	$-0.471767\pi$
$179$	2.37022	0.177159	0.0885794	+	0.996069i	$0.471767\pi$
$180$	−3.64660	−0.271802
$181$	14.1226	1.04972	0.524862	−	0.851187i	$-0.324117\pi$
$181$	14.1226	1.04972	0.524862	+	0.851187i	$0.324117\pi$
$182$	11.6959	0.866961
$183$	9.81284	0.725386
$184$	1.15544	0.0851805
$185$	36.4161	2.67736
$186$	14.7229	1.07954
$187$	−7.66228	−0.560321
$188$	4.01789	0.293035
$189$	−1.00000	−0.0727393
$190$	27.4654	1.99255
$191$	24.6932	1.78674	0.893370	−	0.449321i	$-0.148334\pi$
$191$	24.6932	1.78674	0.893370	+	0.449321i	$0.148334\pi$
$192$	−1.18566	−0.0855680
$193$	23.6123	1.69965	0.849826	−	0.527063i	$-0.176707\pi$
$193$	23.6123	1.69965	0.849826	+	0.527063i	$0.176707\pi$
$194$	−3.54571	−0.254567
$195$	−25.2313	−1.80685
$196$	0.979322	0.0699516
$197$	17.4904	1.24614	0.623070	−	0.782166i	$-0.285885\pi$
$197$	17.4904	1.24614	0.623070	+	0.782166i	$0.285885\pi$
$198$	−7.87512	−0.559660
$199$	12.9961	0.921266	0.460633	−	0.887591i	$-0.347622\pi$
$199$	12.9961	0.921266	0.460633	+	0.887591i	$0.347622\pi$
$200$	15.6183	1.10438
$201$	8.07552	0.569603
$202$	−24.2367	−1.70529
$203$	−7.73977	−0.543225
$204$	1.64469	0.115152
$205$	−33.3205	−2.32721
$206$	−10.1910	−0.710041
$207$	0.655845	0.0455844
$208$	33.8773	2.34897
$209$	19.4968	1.34862
$210$	−6.42720	−0.443519
$211$	−9.31539	−0.641298	−0.320649	−	0.947198i	$-0.603901\pi$
$211$	−9.31539	−0.641298	−0.320649	+	0.947198i	$0.603901\pi$
$212$	−12.4323	−0.853850
$213$	8.57589	0.587610
$214$	−15.6210	−1.06783
$215$	−0.0102214	−0.000697097 0
$216$	−1.76176	−0.119873
$217$	8.52971	0.579035
$218$	34.2284	2.31824
$219$	−1.26109	−0.0852167
$220$	−16.6374	−1.12170
$221$	11.3798	0.765491
$222$	−16.8806	−1.13295
$223$	−15.2640	−1.02215	−0.511076	−	0.859535i	$-0.670753\pi$
$223$	−15.2640	−1.02215	−0.511076	+	0.859535i	$0.670753\pi$
$224$	5.10609	0.341165
$225$	8.86518	0.591012
$226$	−8.35387	−0.555691
$227$	−8.94557	−0.593738	−0.296869	−	0.954918i	$-0.595943\pi$
$227$	−8.94557	−0.593738	−0.296869	+	0.954918i	$0.595943\pi$
$228$	−4.18495	−0.277155
$229$	−13.7825	−0.910776	−0.455388	−	0.890293i	$-0.650500\pi$
$229$	−13.7825	−0.910776	−0.455388	+	0.890293i	$0.650500\pi$
$230$	4.21525	0.277945
$231$	−4.56245	−0.300187
$232$	−13.6356	−0.895224
$233$	22.0140	1.44218	0.721092	−	0.692840i	$-0.243641\pi$
$233$	22.0140	1.44218	0.721092	+	0.692840i	$0.243641\pi$
$234$	11.6959	0.764588
$235$	−15.2769	−0.996555
$236$	8.88001	0.578039
$237$	2.84685	0.184923
$238$	2.89880	0.187901
$239$	11.4309	0.739405	0.369702	−	0.929150i	$-0.379460\pi$
$239$	11.4309	0.739405	0.369702	+	0.929150i	$0.379460\pi$
$240$	−18.6164	−1.20168
$241$	−17.2064	−1.10836	−0.554182	−	0.832395i	$-0.686969\pi$
$241$	−17.2064	−1.10836	−0.554182	+	0.832395i	$0.686969\pi$
$242$	−16.9431	−1.08914
$243$	−1.00000	−0.0641500
$244$	−9.60993	−0.615213
$245$	−3.72360	−0.237892
$246$	15.4457	0.984783
$247$	−28.9562	−1.84244
$248$	15.0273	0.954237
$249$	5.57219	0.353123
$250$	24.8423	1.57116
$251$	1.51825	0.0958313	0.0479156	−	0.998851i	$-0.484742\pi$
$251$	1.51825	0.0958313	0.0479156	+	0.998851i	$0.484742\pi$
$252$	0.979322	0.0616915
$253$	2.99226	0.188122
$254$	27.2993	1.71291
$255$	−6.25349	−0.391609
$256$	18.7881	1.17426
$257$	12.2250	0.762573	0.381286	−	0.924457i	$-0.375481\pi$
$257$	12.2250	0.762573	0.381286	+	0.924457i	$0.375481\pi$
$258$	0.00473814	0.000294984 0
$259$	−9.77981	−0.607688
$260$	24.7095	1.53242
$261$	−7.73977	−0.479080
$262$	10.4362	0.644748
$263$	14.2619	0.879424	0.439712	−	0.898139i	$-0.355080\pi$
$263$	14.2619	0.879424	0.439712	+	0.898139i	$0.355080\pi$
$264$	−8.03796	−0.494702
$265$	47.2702	2.90378
$266$	−7.37604	−0.452254
$267$	−16.2365	−0.993658
$268$	−7.90853	−0.483090
$269$	−5.94109	−0.362235	−0.181117	−	0.983461i	$-0.557971\pi$
$269$	−5.94109	−0.362235	−0.181117	+	0.983461i	$0.557971\pi$
$270$	−6.42720	−0.391147
$271$	15.7559	0.957105	0.478553	−	0.878059i	$-0.341162\pi$
$271$	15.7559	0.957105	0.478553	+	0.878059i	$0.341162\pi$
$272$	8.39639	0.509106
$273$	6.77605	0.410105
$274$	16.1435	0.975265
$275$	40.4470	2.43904
$276$	−0.642284	−0.0386609
$277$	−11.8101	−0.709603	−0.354801	−	0.934942i	$-0.615452\pi$
$277$	−11.8101	−0.709603	−0.354801	+	0.934942i	$0.615452\pi$
$278$	2.36774	0.142008
$279$	8.52971	0.510661
$280$	−6.56010	−0.392041
$281$	−4.72617	−0.281940	−0.140970	−	0.990014i	$-0.545022\pi$
$281$	−4.72617	−0.281940	−0.140970	+	0.990014i	$0.545022\pi$
$282$	7.08160	0.421703
$283$	14.0983	0.838058	0.419029	−	0.907973i	$-0.362371\pi$
$283$	14.0983	0.838058	0.419029	+	0.907973i	$0.362371\pi$
$284$	−8.39856	−0.498363
$285$	15.9121	0.942552
$286$	53.3622	3.15537
$287$	8.94848	0.528212
$288$	5.10609	0.300879
$289$	−14.1795	−0.834091
$290$	−49.7450	−2.92113
$291$	−2.05421	−0.120420
$292$	1.23501	0.0722738
$293$	−9.75902	−0.570128	−0.285064	−	0.958508i	$-0.592015\pi$
$293$	−9.75902	−0.570128	−0.285064	+	0.958508i	$0.592015\pi$
$294$	1.72607	0.100667
$295$	−33.7638	−1.96580
$296$	−17.2297	−1.00146
$297$	−4.56245	−0.264740
$298$	−33.0457	−1.91428
$299$	−4.44404	−0.257005
$300$	−8.68187	−0.501248
$301$	0.00274505	0.000158222 0
$302$	−19.6595	−1.13128
$303$	−14.0415	−0.806664
$304$	−21.3647	−1.22535
$305$	36.5391	2.09222
$306$	2.89880	0.165713
$307$	−7.32676	−0.418161	−0.209080	−	0.977898i	$-0.567047\pi$
$307$	−7.32676	−0.418161	−0.209080	+	0.977898i	$0.567047\pi$
$308$	4.46811	0.254594
$309$	−5.90416	−0.335876
$310$	54.8221	3.11369
$311$	31.0189	1.75892	0.879460	−	0.475974i	$-0.157904\pi$
$311$	31.0189	1.75892	0.879460	+	0.475974i	$0.157904\pi$
$312$	11.9378	0.675844
$313$	−6.77332	−0.382851	−0.191425	−	0.981507i	$-0.561311\pi$
$313$	−6.77332	−0.382851	−0.191425	+	0.981507i	$0.561311\pi$
$314$	−24.3281	−1.37292
$315$	−3.72360	−0.209801
$316$	−2.78799	−0.156836
$317$	13.4463	0.755222	0.377611	−	0.925964i	$-0.376746\pi$
$317$	13.4463	0.755222	0.377611	+	0.925964i	$0.376746\pi$
$318$	−21.9120	−1.22877
$319$	−35.3123	−1.97711
$320$	−4.41494	−0.246803
$321$	−9.05006	−0.505125
$322$	−1.13204	−0.0630859
$323$	−7.17669	−0.399322
$324$	0.979322	0.0544068
$325$	−60.0709	−3.33213
$326$	17.9172	0.992339
$327$	19.8302	1.09662
$328$	15.7651	0.870482
$329$	4.10273	0.226191
$330$	−29.3238	−1.61422
$331$	−3.43120	−0.188596	−0.0942980	−	0.995544i	$-0.530061\pi$
$331$	−3.43120	−0.188596	−0.0942980	+	0.995544i	$0.530061\pi$
$332$	−5.45697	−0.299490
$333$	−9.77981	−0.535930
$334$	−5.48221	−0.299973
$335$	30.0700	1.64290
$336$	4.99957	0.272749
$337$	−3.08039	−0.167800	−0.0838998	−	0.996474i	$-0.526738\pi$
$337$	−3.08039	−0.167800	−0.0838998	+	0.996474i	$0.526738\pi$
$338$	−56.8133	−3.09024
$339$	−4.83981	−0.262863
$340$	6.12418	0.332130
$341$	38.9164	2.10744
$342$	−7.37604	−0.398851
$343$	1.00000	0.0539949
$344$	0.00483612	0.000260746 0
$345$	2.44210	0.131478
$346$	−5.28143	−0.283931
$347$	1.31873	0.0707930	0.0353965	−	0.999373i	$-0.488731\pi$
$347$	1.31873	0.0707930	0.0353965	+	0.999373i	$0.488731\pi$
$348$	7.57973	0.406316
$349$	−14.6773	−0.785656	−0.392828	−	0.919612i	$-0.628503\pi$
$349$	−14.6773	−0.785656	−0.392828	+	0.919612i	$0.628503\pi$
$350$	−15.3019	−0.817923
$351$	6.77605	0.361679
$352$	23.2963	1.24170
$353$	−13.3363	−0.709818	−0.354909	−	0.934901i	$-0.615488\pi$
$353$	−13.3363	−0.709818	−0.354909	+	0.934901i	$0.615488\pi$
$354$	15.6512	0.831850
$355$	31.9332	1.69484
$356$	15.9008	0.842739
$357$	1.67942	0.0888844
$358$	−4.09117	−0.216225
$359$	−35.8910	−1.89425	−0.947127	−	0.320858i	$-0.896029\pi$
$359$	−35.8910	−1.89425	−0.947127	+	0.320858i	$0.896029\pi$
$360$	−6.56010	−0.345747
$361$	−0.738788	−0.0388836
$362$	−24.3766	−1.28121
$363$	−9.81597	−0.515205
$364$	−6.63593	−0.347817
$365$	−4.69580	−0.245789
$366$	−16.9377	−0.885345
$367$	−37.0331	−1.93311	−0.966556	−	0.256456i	$-0.917445\pi$
$367$	−37.0331	−1.93311	−0.966556	+	0.256456i	$0.917445\pi$
$368$	−3.27895	−0.170927
$369$	8.94848	0.465839
$370$	−62.8567	−3.26777
$371$	−12.6948	−0.659079
$372$	−8.35334	−0.433100
$373$	3.32277	0.172046	0.0860232	−	0.996293i	$-0.472584\pi$
$373$	3.32277	0.172046	0.0860232	+	0.996293i	$0.472584\pi$
$374$	13.2256	0.683881
$375$	14.3924	0.743220
$376$	7.22803	0.372757
$377$	52.4450	2.70106
$378$	1.72607	0.0887795
$379$	12.4351	0.638749	0.319374	−	0.947629i	$-0.396527\pi$
$379$	12.4351	0.638749	0.319374	+	0.947629i	$0.396527\pi$
$380$	−15.5831	−0.799395
$381$	15.8158	0.810270
$382$	−42.6223	−2.18075
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	12.2587	0.625576
$385$	−16.9887	−0.865826
$386$	−40.7566	−2.07445
$387$	0.00274505	0.000139539 0
$388$	2.01173	0.102130
$389$	−30.5241	−1.54763	−0.773816	−	0.633410i	$-0.781655\pi$
$389$	−30.5241	−1.54763	−0.773816	+	0.633410i	$0.781655\pi$
$390$	43.5510	2.20529
$391$	−1.10144	−0.0557022
$392$	1.76176	0.0889825
$393$	6.04619	0.304990
$394$	−30.1897	−1.52094
$395$	10.6005	0.533371
$396$	4.46811	0.224531
$397$	37.4852	1.88133	0.940663	−	0.339342i	$-0.110204\pi$
$397$	37.4852	1.88133	0.940663	+	0.339342i	$0.110204\pi$
$398$	−22.4321	−1.12442
$399$	−4.27331	−0.213933
$400$	−44.3221	−2.21611
$401$	−5.95893	−0.297575	−0.148787	−	0.988869i	$-0.547537\pi$
$401$	−5.95893	−0.297575	−0.148787	+	0.988869i	$0.547537\pi$
$402$	−13.9389	−0.695210
$403$	−57.7977	−2.87911
$404$	13.7512	0.684146
$405$	−3.72360	−0.185027
$406$	13.3594	0.663016
$407$	−44.6199	−2.21173
$408$	2.95874	0.146480
$409$	−21.8920	−1.08249	−0.541246	−	0.840864i	$-0.682047\pi$
$409$	−21.8920	−1.08249	−0.541246	+	0.840864i	$0.682047\pi$
$410$	57.5136	2.84039
$411$	9.35274	0.461337
$412$	5.78208	0.284862
$413$	9.06751	0.446183
$414$	−1.13204	−0.0556365
$415$	20.7486	1.01851
$416$	−34.5991	−1.69636
$417$	1.37175	0.0671750
$418$	−33.6529	−1.64601
$419$	−11.4233	−0.558065	−0.279032	−	0.960282i	$-0.590014\pi$
$419$	−11.4233	−0.558065	−0.279032	+	0.960282i	$0.590014\pi$
$420$	3.64660	0.177936
$421$	−2.45505	−0.119652	−0.0598258	−	0.998209i	$-0.519055\pi$
$421$	−2.45505	−0.119652	−0.0598258	+	0.998209i	$0.519055\pi$
$422$	16.0790	0.782715
$423$	4.10273	0.199481
$424$	−22.3651	−1.08615
$425$	−14.8884	−0.722192
$426$	−14.8026	−0.717188
$427$	−9.81284	−0.474876
$428$	8.86292	0.428405
$429$	30.9154	1.49261
$430$	0.0176429	0.000850818 0
$431$	20.9420	1.00874	0.504370	−	0.863488i	$-0.331725\pi$
$431$	20.9420	1.00874	0.504370	+	0.863488i	$0.331725\pi$
$432$	4.99957	0.240542
$433$	−6.16213	−0.296133	−0.148067	−	0.988977i	$-0.547305\pi$
$433$	−6.16213	−0.296133	−0.148067	+	0.988977i	$0.547305\pi$
$434$	−14.7229	−0.706722
$435$	−28.8198	−1.38180
$436$	−19.4202	−0.930059
$437$	2.80263	0.134068
$438$	2.17673	0.104008
$439$	−16.8617	−0.804765	−0.402382	−	0.915472i	$-0.631818\pi$
$439$	−16.8617	−0.804765	−0.402382	+	0.915472i	$0.631818\pi$
$440$	−29.9301	−1.42686
$441$	1.00000	0.0476190
$442$	−19.6424	−0.934294
$443$	18.2459	0.866890	0.433445	−	0.901180i	$-0.357298\pi$
$443$	18.2459	0.866890	0.433445	+	0.901180i	$0.357298\pi$
$444$	9.57758	0.454532
$445$	−60.4582	−2.86599
$446$	26.3467	1.24755
$447$	−19.1450	−0.905528
$448$	1.18566	0.0560174
$449$	−8.32385	−0.392827	−0.196413	−	0.980521i	$-0.562929\pi$
$449$	−8.32385	−0.392827	−0.196413	+	0.980521i	$0.562929\pi$
$450$	−15.3019	−0.721340
$451$	40.8270	1.92247
$452$	4.73974	0.222938
$453$	−11.3897	−0.535136
$454$	15.4407	0.724668
$455$	25.2313	1.18286
$456$	−7.52857	−0.352557
$457$	−11.8358	−0.553654	−0.276827	−	0.960920i	$-0.589283\pi$
$457$	−11.8358	−0.553654	−0.276827	+	0.960920i	$0.589283\pi$
$458$	23.7897	1.11162
$459$	1.67942	0.0783887
$460$	−2.39161	−0.111509
$461$	−11.2530	−0.524103	−0.262052	−	0.965054i	$-0.584399\pi$
$461$	−11.2530	−0.524103	−0.262052	+	0.965054i	$0.584399\pi$
$462$	7.87512	0.366384
$463$	−33.8452	−1.57292	−0.786460	−	0.617642i	$-0.788088\pi$
$463$	−33.8452	−1.57292	−0.786460	+	0.617642i	$0.788088\pi$
$464$	38.6955	1.79640
$465$	31.7612	1.47289
$466$	−37.9977	−1.76021
$467$	9.67449	0.447682	0.223841	−	0.974626i	$-0.428140\pi$
$467$	9.67449	0.447682	0.223841	+	0.974626i	$0.428140\pi$
$468$	−6.63593	−0.306746
$469$	−8.07552	−0.372893
$470$	26.3690	1.21631
$471$	−14.0945	−0.649441
$472$	15.9748	0.735300
$473$	0.0125241	0.000575861 0
$474$	−4.91387	−0.225702
$475$	37.8837	1.73822
$476$	−1.64469	−0.0753844
$477$	−12.6948	−0.581253
$478$	−19.7306	−0.902456
$479$	−42.2548	−1.93067	−0.965335	−	0.261015i	$-0.915943\pi$
$479$	−42.2548	−1.93067	−0.965335	+	0.261015i	$0.915943\pi$
$480$	19.0130	0.867822
$481$	66.2684	3.02158
$482$	29.6995	1.35278
$483$	−0.655845	−0.0298420
$484$	9.61300	0.436955
$485$	−7.64904	−0.347325
$486$	1.72607	0.0782962
$487$	−14.5336	−0.658581	−0.329291	−	0.944229i	$-0.606810\pi$
$487$	−14.5336	−0.658581	−0.329291	+	0.944229i	$0.606810\pi$
$488$	−17.2879	−0.782586
$489$	10.3803	0.469414
$490$	6.42720	0.290351
$491$	−0.625733	−0.0282389	−0.0141195	−	0.999900i	$-0.504495\pi$
$491$	−0.625733	−0.0282389	−0.0141195	+	0.999900i	$0.504495\pi$
$492$	−8.76344	−0.395086
$493$	12.9983	0.585415
$494$	49.9804	2.24873
$495$	−16.9887	−0.763587
$496$	−42.6449	−1.91481
$497$	−8.57589	−0.384681
$498$	−9.61800	−0.430993
$499$	−12.6018	−0.564135	−0.282067	−	0.959395i	$-0.591020\pi$
$499$	−12.6018	−0.564135	−0.282067	+	0.959395i	$0.591020\pi$
$500$	−14.0948	−0.630338
$501$	−3.17612	−0.141899
$502$	−2.62061	−0.116964
$503$	2.76332	0.123210	0.0616052	−	0.998101i	$-0.480378\pi$
$503$	2.76332	0.123210	0.0616052	+	0.998101i	$0.480378\pi$
$504$	1.76176	0.0784752
$505$	−52.2850	−2.32665
$506$	−5.16486	−0.229606
$507$	−32.9148	−1.46180
$508$	−15.4888	−0.687205
$509$	−37.1557	−1.64690	−0.823448	−	0.567392i	$-0.807952\pi$
$509$	−37.1557	−1.64690	−0.823448	+	0.567392i	$0.807952\pi$
$510$	10.7940	0.477965
$511$	1.26109	0.0557874
$512$	−7.91216	−0.349671
$513$	−4.27331	−0.188671
$514$	−21.1012	−0.930733
$515$	−21.9847	−0.968763
$516$	−0.00268828	−0.000118345 0
$517$	18.7185	0.823238
$518$	16.8806	0.741693
$519$	−3.05980	−0.134310
$520$	44.4515	1.94933
$521$	11.6975	0.512476	0.256238	−	0.966614i	$-0.417517\pi$
$521$	11.6975	0.512476	0.256238	+	0.966614i	$0.417517\pi$
$522$	13.3594	0.584725
$523$	34.7847	1.52103	0.760514	−	0.649322i	$-0.224947\pi$
$523$	34.7847	1.52103	0.760514	+	0.649322i	$0.224947\pi$
$524$	−5.92117	−0.258667
$525$	−8.86518	−0.386908
$526$	−24.6170	−1.07335
$527$	−14.3250	−0.624006
$528$	22.8103	0.992691
$529$	−22.5699	−0.981299
$530$	−81.5917	−3.54411
$531$	9.06751	0.393496
$532$	4.18495	0.181441
$533$	−60.6353	−2.62641
$534$	28.0254	1.21278
$535$	−33.6988	−1.45693
$536$	−14.2271	−0.614519
$537$	−2.37022	−0.102283
$538$	10.2547	0.442114
$539$	4.56245	0.196519
$540$	3.64660	0.156925
$541$	3.91542	0.168337	0.0841686	−	0.996452i	$-0.473177\pi$
$541$	3.91542	0.168337	0.0841686	+	0.996452i	$0.473177\pi$
$542$	−27.1959	−1.16816
$543$	−14.1226	−0.606058
$544$	−8.57528	−0.367662
$545$	73.8399	3.16295
$546$	−11.6959	−0.500540
$547$	−9.39545	−0.401720	−0.200860	−	0.979620i	$-0.564374\pi$
$547$	−9.39545	−0.401720	−0.200860	+	0.979620i	$0.564374\pi$
$548$	−9.15935	−0.391268
$549$	−9.81284	−0.418802
$550$	−69.8144	−2.97689
$551$	−33.0745	−1.40902
$552$	−1.15544	−0.0491790
$553$	−2.84685	−0.121060
$554$	20.3852	0.866082
$555$	−36.4161	−1.54578
$556$	−1.34339	−0.0569723
$557$	−42.9997	−1.82196	−0.910978	−	0.412455i	$-0.864672\pi$
$557$	−42.9997	−1.82196	−0.910978	+	0.412455i	$0.864672\pi$
$558$	−14.7229	−0.623270
$559$	−0.0186006	−0.000786720 0
$560$	18.6164	0.786686
$561$	7.66228	0.323502
$562$	8.15770	0.344112
$563$	−15.3712	−0.647819	−0.323910	−	0.946088i	$-0.604997\pi$
$563$	−15.3712	−0.647819	−0.323910	+	0.946088i	$0.604997\pi$
$564$	−4.01789	−0.169184
$565$	−18.0215	−0.758171
$566$	−24.3347	−1.02286
$567$	1.00000	0.0419961
$568$	−15.1087	−0.633946
$569$	−16.2184	−0.679909	−0.339954	−	0.940442i	$-0.610412\pi$
$569$	−16.2184	−0.679909	−0.339954	+	0.940442i	$0.610412\pi$
$570$	−27.4654	−1.15040
$571$	42.1214	1.76273	0.881363	−	0.472440i	$-0.156627\pi$
$571$	42.1214	1.76273	0.881363	+	0.472440i	$0.156627\pi$
$572$	−30.2761	−1.26591
$573$	−24.6932	−1.03158
$574$	−15.4457	−0.644691
$575$	5.81419	0.242468
$576$	1.18566	0.0494027
$577$	5.32969	0.221878	0.110939	−	0.993827i	$-0.464614\pi$
$577$	5.32969	0.221878	0.110939	+	0.993827i	$0.464614\pi$
$578$	24.4749	1.01802
$579$	−23.6123	−0.981295
$580$	28.2239	1.17193
$581$	−5.57219	−0.231174
$582$	3.54571	0.146974
$583$	−57.9192	−2.39877
$584$	2.22174	0.0919364
$585$	25.2313	1.04318
$586$	16.8448	0.695851
$587$	41.3411	1.70633	0.853165	−	0.521641i	$-0.174680\pi$
$587$	41.3411	1.70633	0.853165	+	0.521641i	$0.174680\pi$
$588$	−0.979322	−0.0403866
$589$	36.4501	1.50190
$590$	58.2786	2.39929
$591$	−17.4904	−0.719459
$592$	48.8948	2.00957
$593$	−29.4236	−1.20828	−0.604141	−	0.796878i	$-0.706484\pi$
$593$	−29.4236	−1.20828	−0.604141	+	0.796878i	$0.706484\pi$
$594$	7.87512	0.323120
$595$	6.25349	0.256368
$596$	18.7491	0.767994
$597$	−12.9961	−0.531893
$598$	7.67073	0.313679
$599$	−36.5811	−1.49466	−0.747332	−	0.664451i	$-0.768665\pi$
$599$	−36.5811	−1.49466	−0.747332	+	0.664451i	$0.768665\pi$
$600$	−15.6183	−0.637616
$601$	−13.5098	−0.551078	−0.275539	−	0.961290i	$-0.588856\pi$
$601$	−13.5098	−0.551078	−0.275539	+	0.961290i	$0.588856\pi$
$602$	−0.00473814	−0.000193112 0
$603$	−8.07552	−0.328860
$604$	11.1542	0.453859
$605$	−36.5507	−1.48600
$606$	24.2367	0.984547
$607$	17.3091	0.702554	0.351277	−	0.936272i	$-0.385748\pi$
$607$	17.3091	0.702554	0.351277	+	0.936272i	$0.385748\pi$
$608$	21.8199	0.884915
$609$	7.73977	0.313631
$610$	−63.0690	−2.55359
$611$	−27.8003	−1.12468
$612$	−1.64469	−0.0664828
$613$	4.88804	0.197426	0.0987130	−	0.995116i	$-0.468527\pi$
$613$	4.88804	0.197426	0.0987130	+	0.995116i	$0.468527\pi$
$614$	12.6465	0.510372
$615$	33.3205	1.34361
$616$	8.03796	0.323859
$617$	16.0006	0.644160	0.322080	−	0.946712i	$-0.395618\pi$
$617$	16.0006	0.644160	0.322080	+	0.946712i	$0.395618\pi$
$618$	10.1910	0.409942
$619$	30.8908	1.24161	0.620803	−	0.783967i	$-0.286807\pi$
$619$	30.8908	1.24161	0.620803	+	0.783967i	$0.286807\pi$
$620$	−31.1045	−1.24919
$621$	−0.655845	−0.0263182
$622$	−53.5408	−2.14679
$623$	16.2365	0.650502
$624$	−33.8773	−1.35618
$625$	9.26554	0.370622
$626$	11.6912	0.467276
$627$	−19.4968	−0.778627
$628$	13.8031	0.550802
$629$	16.4244	0.654884
$630$	6.42720	0.256066
$631$	22.4756	0.894741	0.447371	−	0.894349i	$-0.352360\pi$
$631$	22.4756	0.894741	0.447371	+	0.894349i	$0.352360\pi$
$632$	−5.01548	−0.199505
$633$	9.31539	0.370254
$634$	−23.2093	−0.921760
$635$	58.8918	2.33705
$636$	12.4323	0.492971
$637$	−6.77605	−0.268477
$638$	60.9516	2.41310
$639$	−8.57589	−0.339257
$640$	45.6466	1.80434
$641$	−7.86031	−0.310464	−0.155232	−	0.987878i	$-0.549612\pi$
$641$	−7.86031	−0.310464	−0.155232	+	0.987878i	$0.549612\pi$
$642$	15.6210	0.616514
$643$	−28.3093	−1.11641	−0.558205	−	0.829703i	$-0.688510\pi$
$643$	−28.3093	−1.11641	−0.558205	+	0.829703i	$0.688510\pi$
$644$	0.642284	0.0253095
$645$	0.0102214	0.000402469 0
$646$	12.3875	0.487379
$647$	−13.8899	−0.546068	−0.273034	−	0.962004i	$-0.588027\pi$
$647$	−13.8899	−0.546068	−0.273034	+	0.962004i	$0.588027\pi$
$648$	1.76176	0.0692086
$649$	41.3701	1.62392
$650$	103.687	4.06692
$651$	−8.52971	−0.334306
$652$	−10.1657	−0.398118
$653$	39.1995	1.53399	0.766997	−	0.641651i	$-0.221750\pi$
$653$	39.1995	1.53399	0.766997	+	0.641651i	$0.221750\pi$
$654$	−34.2284	−1.33844
$655$	22.5136	0.879679
$656$	−44.7386	−1.74675
$657$	1.26109	0.0491999
$658$	−7.08160	−0.276069
$659$	29.3341	1.14270	0.571348	−	0.820708i	$-0.306421\pi$
$659$	29.3341	1.14270	0.571348	+	0.820708i	$0.306421\pi$
$660$	16.6374	0.647612
$661$	−33.2527	−1.29338	−0.646691	−	0.762752i	$-0.723848\pi$
$661$	−33.2527	−1.29338	−0.646691	+	0.762752i	$0.723848\pi$
$662$	5.92250	0.230185
$663$	−11.3798	−0.441956
$664$	−9.81688	−0.380969
$665$	−15.9121	−0.617045
$666$	16.8806	0.654112
$667$	−5.07609	−0.196547
$668$	3.11044	0.120347
$669$	15.2640	0.590140
$670$	−51.9029	−2.00518
$671$	−44.7706	−1.72835
$672$	−5.10609	−0.196972
$673$	37.2279	1.43503	0.717516	−	0.696542i	$-0.245279\pi$
$673$	37.2279	1.43503	0.717516	+	0.696542i	$0.245279\pi$
$674$	5.31697	0.204802
$675$	−8.86518	−0.341221
$676$	32.2342	1.23978
$677$	−27.7074	−1.06488	−0.532440	−	0.846468i	$-0.678725\pi$
$677$	−27.7074	−1.06488	−0.532440	+	0.846468i	$0.678725\pi$
$678$	8.35387	0.320828
$679$	2.05421	0.0788332
$680$	11.0172	0.422489
$681$	8.94557	0.342795
$682$	−67.1725	−2.57217
$683$	−35.8686	−1.37247	−0.686237	−	0.727378i	$-0.740739\pi$
$683$	−35.8686	−1.37247	−0.686237	+	0.727378i	$0.740739\pi$
$684$	4.18495	0.160016
$685$	34.8259	1.33063
$686$	−1.72607	−0.0659017
$687$	13.7825	0.525837
$688$	−0.0137241	−0.000523225 0
$689$	86.0202	3.27711
$690$	−4.21525	−0.160472
$691$	−37.1930	−1.41489	−0.707444	−	0.706769i	$-0.750152\pi$
$691$	−37.1930	−1.41489	−0.707444	+	0.706769i	$0.750152\pi$
$692$	2.99653	0.113911
$693$	4.56245	0.173313
$694$	−2.27622	−0.0864040
$695$	5.10786	0.193752
$696$	13.6356	0.516858
$697$	−15.0283	−0.569236
$698$	25.3340	0.958906
$699$	−22.0140	−0.832645
$700$	8.68187	0.328144
$701$	7.05282	0.266381	0.133191	−	0.991090i	$-0.457478\pi$
$701$	7.05282	0.266381	0.133191	+	0.991090i	$0.457478\pi$
$702$	−11.6959	−0.441435
$703$	−41.7922	−1.57622
$704$	5.40954	0.203880
$705$	15.2769	0.575361
$706$	23.0194	0.866345
$707$	14.0415	0.528086
$708$	−8.88001	−0.333731
$709$	6.94973	0.261003	0.130501	−	0.991448i	$-0.458341\pi$
$709$	6.94973	0.261003	0.130501	+	0.991448i	$0.458341\pi$
$710$	−55.1189	−2.06858
$711$	−2.84685	−0.106765
$712$	28.6049	1.07201
$713$	5.59417	0.209503
$714$	−2.89880	−0.108485
$715$	115.117	4.30511
$716$	2.32121	0.0867477
$717$	−11.4309	−0.426896
$718$	61.9504	2.31197
$719$	50.4409	1.88113	0.940564	−	0.339617i	$-0.110297\pi$
$719$	50.4409	1.88113	0.940564	+	0.339617i	$0.110297\pi$
$720$	18.6164	0.693792
$721$	5.90416	0.219883
$722$	1.27520	0.0474581
$723$	17.2064	0.639914
$724$	13.8306	0.514009
$725$	−68.6145	−2.54828
$726$	16.9431	0.628816
$727$	−24.4821	−0.907989	−0.453995	−	0.891004i	$-0.650001\pi$
$727$	−24.4821	−0.907989	−0.453995	+	0.891004i	$0.650001\pi$
$728$	−11.9378	−0.442444
$729$	1.00000	0.0370370
$730$	8.10528	0.299990
$731$	−0.00461009	−0.000170510 0
$732$	9.60993	0.355193
$733$	50.2901	1.85751	0.928753	−	0.370700i	$-0.120882\pi$
$733$	50.2901	1.85751	0.928753	+	0.370700i	$0.120882\pi$
$734$	63.9218	2.35940
$735$	3.72360	0.137347
$736$	3.34881	0.123439
$737$	−36.8442	−1.35717
$738$	−15.4457	−0.568564
$739$	−12.7680	−0.469680	−0.234840	−	0.972034i	$-0.575457\pi$
$739$	−12.7680	−0.469680	−0.234840	+	0.972034i	$0.575457\pi$
$740$	35.6631	1.31100
$741$	28.9562	1.06373
$742$	21.9120	0.804417
$743$	36.2237	1.32892	0.664459	−	0.747325i	$-0.268662\pi$
$743$	36.2237	1.32892	0.664459	+	0.747325i	$0.268662\pi$
$744$	−15.0273	−0.550929
$745$	−71.2883	−2.61180
$746$	−5.73533	−0.209985
$747$	−5.57219	−0.203876
$748$	−7.50384	−0.274367
$749$	9.05006	0.330682
$750$	−24.8423	−0.907112
$751$	−26.7227	−0.975126	−0.487563	−	0.873088i	$-0.662114\pi$
$751$	−26.7227	−0.975126	−0.487563	+	0.873088i	$0.662114\pi$
$752$	−20.5119	−0.747991
$753$	−1.51825	−0.0553282
$754$	−90.5239	−3.29669
$755$	−42.4108	−1.54349
$756$	−0.979322	−0.0356176
$757$	17.6159	0.640259	0.320130	−	0.947374i	$-0.396274\pi$
$757$	17.6159	0.640259	0.320130	+	0.947374i	$0.396274\pi$
$758$	−21.4639	−0.779604
$759$	−2.99226	−0.108612
$760$	−28.0334	−1.01688
$761$	19.0497	0.690552	0.345276	−	0.938501i	$-0.387785\pi$
$761$	19.0497	0.690552	0.345276	+	0.938501i	$0.387785\pi$
$762$	−27.2993	−0.988948
$763$	−19.8302	−0.717903
$764$	24.1826	0.874897
$765$	6.25349	0.226095
$766$	−1.72607	−0.0623655
$767$	−61.4419	−2.21854
$768$	−18.7881	−0.677957
$769$	−2.86747	−0.103403	−0.0517017	−	0.998663i	$-0.516465\pi$
$769$	−2.86747	−0.103403	−0.0517017	+	0.998663i	$0.516465\pi$
$770$	29.3238	1.05676
$771$	−12.2250	−0.440272
$772$	23.1241	0.832253
$773$	32.6055	1.17274	0.586368	−	0.810045i	$-0.300557\pi$
$773$	32.6055	1.17274	0.586368	+	0.810045i	$0.300557\pi$
$774$	−0.00473814	−0.000170309 0
$775$	75.6175	2.71626
$776$	3.61902	0.129915
$777$	9.77981	0.350849
$778$	52.6867	1.88891
$779$	38.2397	1.37008
$780$	−24.7095	−0.884744
$781$	−39.1271	−1.40008
$782$	1.90116	0.0679855
$783$	7.73977	0.276597
$784$	−4.99957	−0.178556
$785$	−52.4823	−1.87317
$786$	−10.4362	−0.372245
$787$	4.18729	0.149261	0.0746303	−	0.997211i	$-0.476222\pi$
$787$	4.18729	0.149261	0.0746303	+	0.997211i	$0.476222\pi$
$788$	17.1287	0.610186
$789$	−14.2619	−0.507736
$790$	−18.2973	−0.650988
$791$	4.83981	0.172084
$792$	8.03796	0.285616
$793$	66.4922	2.36121
$794$	−64.7021	−2.29619
$795$	−47.2702	−1.67650
$796$	12.7273	0.451108
$797$	−36.3655	−1.28813	−0.644066	−	0.764970i	$-0.722754\pi$
$797$	−36.3655	−1.28813	−0.644066	+	0.764970i	$0.722754\pi$
$798$	7.37604	0.261109
$799$	−6.89020	−0.243758
$800$	45.2664	1.60041
$801$	16.2365	0.573688
$802$	10.2855	0.363195
$803$	5.75367	0.203043
$804$	7.90853	0.278912
$805$	−2.44210	−0.0860729
$806$	99.7630	3.51400
$807$	5.94109	0.209136
$808$	24.7378	0.870274
$809$	−50.2179	−1.76557	−0.882783	−	0.469780i	$-0.844333\pi$
$809$	−50.2179	−1.76557	−0.882783	+	0.469780i	$0.844333\pi$
$810$	6.42720	0.225829
$811$	27.0530	0.949958	0.474979	−	0.879997i	$-0.342456\pi$
$811$	27.0530	0.949958	0.474979	+	0.879997i	$0.342456\pi$
$812$	−7.57973	−0.265996
$813$	−15.7559	−0.552585
$814$	77.0171	2.69945
$815$	38.6521	1.35392
$816$	−8.39639	−0.293932
$817$	0.0117304	0.000410396 0
$818$	37.7872	1.32120
$819$	−6.77605	−0.236774
$820$	−32.6315	−1.13954
$821$	29.1631	1.01780	0.508899	−	0.860826i	$-0.330053\pi$
$821$	29.1631	1.01780	0.508899	+	0.860826i	$0.330053\pi$
$822$	−16.1435	−0.563069
$823$	−44.4328	−1.54883	−0.774415	−	0.632678i	$-0.781956\pi$
$823$	−44.4328	−1.54883	−0.774415	+	0.632678i	$0.781956\pi$
$824$	10.4017	0.362362
$825$	−40.4470	−1.40818
$826$	−15.6512	−0.544574
$827$	−2.83820	−0.0986938	−0.0493469	−	0.998782i	$-0.515714\pi$
$827$	−2.83820	−0.0986938	−0.0493469	+	0.998782i	$0.515714\pi$
$828$	0.642284	0.0223209
$829$	31.7440	1.10251	0.551257	−	0.834335i	$-0.314148\pi$
$829$	31.7440	1.10251	0.551257	+	0.834335i	$0.314148\pi$
$830$	−35.8136	−1.24311
$831$	11.8101	0.409689
$832$	−8.03412	−0.278533
$833$	−1.67942	−0.0581885
$834$	−2.36774	−0.0819883
$835$	−11.8266	−0.409276
$836$	19.0936	0.660367
$837$	−8.52971	−0.294830
$838$	19.7174	0.681128
$839$	−15.6379	−0.539879	−0.269940	−	0.962877i	$-0.587004\pi$
$839$	−15.6379	−0.539879	−0.269940	+	0.962877i	$0.587004\pi$
$840$	6.56010	0.226345
$841$	30.9040	1.06566
$842$	4.23759	0.146037
$843$	4.72617	0.162778
$844$	−9.12277	−0.314019
$845$	−122.562	−4.21625
$846$	−7.08160	−0.243470
$847$	9.81597	0.337281
$848$	63.4683	2.17951
$849$	−14.0983	−0.483853
$850$	25.6984	0.881447
$851$	−6.41404	−0.219870
$852$	8.39856	0.287730
$853$	−22.2216	−0.760854	−0.380427	−	0.924811i	$-0.624223\pi$
$853$	−22.2216	−0.760854	−0.380427	+	0.924811i	$0.624223\pi$
$854$	16.9377	0.579595
$855$	−15.9121	−0.544182
$856$	15.9441	0.544957
$857$	23.2881	0.795506	0.397753	−	0.917492i	$-0.369790\pi$
$857$	23.2881	0.795506	0.397753	+	0.917492i	$0.369790\pi$
$858$	−53.3622	−1.82175
$859$	3.15020	0.107484	0.0537418	−	0.998555i	$-0.482885\pi$
$859$	3.15020	0.107484	0.0537418	+	0.998555i	$0.482885\pi$
$860$	−0.0100101	−0.000341341 0
$861$	−8.94848	−0.304963
$862$	−36.1474	−1.23118
$863$	−8.92408	−0.303779	−0.151890	−	0.988397i	$-0.548536\pi$
$863$	−8.92408	−0.303779	−0.151890	+	0.988397i	$0.548536\pi$
$864$	−5.10609	−0.173713
$865$	−11.3935	−0.387389
$866$	10.6363	0.361435
$867$	14.1795	0.481563
$868$	8.35334	0.283531
$869$	−12.9886	−0.440609
$870$	49.7450	1.68651
$871$	54.7201	1.85412
$872$	−34.9362	−1.18309
$873$	2.05421	0.0695243
$874$	−4.83754	−0.163632
$875$	−14.3924	−0.486551
$876$	−1.23501	−0.0417273
$877$	9.65217	0.325931	0.162965	−	0.986632i	$-0.447894\pi$
$877$	9.65217	0.325931	0.162965	+	0.986632i	$0.447894\pi$
$878$	29.1045	0.982229
$879$	9.75902	0.329164
$880$	84.9364	2.86321
$881$	−56.0114	−1.88707	−0.943536	−	0.331270i	$-0.892523\pi$
$881$	−56.0114	−1.88707	−0.943536	+	0.331270i	$0.892523\pi$
$882$	−1.72607	−0.0581198
$883$	−53.3361	−1.79490	−0.897451	−	0.441114i	$-0.854584\pi$
$883$	−53.3361	−1.79490	−0.897451	+	0.441114i	$0.854584\pi$
$884$	11.1445	0.374831
$885$	33.7638	1.13496
$886$	−31.4938	−1.05805
$887$	41.1266	1.38090	0.690448	−	0.723382i	$-0.257413\pi$
$887$	41.1266	1.38090	0.690448	+	0.723382i	$0.257413\pi$
$888$	17.2297	0.578191
$889$	−15.8158	−0.530446
$890$	104.355	3.49799
$891$	4.56245	0.152848
$892$	−14.9484	−0.500508
$893$	17.5322	0.586694
$894$	33.0457	1.10521
$895$	−8.82576	−0.295012
$896$	−12.2587	−0.409535
$897$	4.44404	0.148382
$898$	14.3676	0.479451
$899$	−66.0180	−2.20182
$900$	8.68187	0.289396
$901$	21.3198	0.710267
$902$	−70.4703	−2.34641
$903$	−0.00274505	−9.13494e−5 0
$904$	8.52661	0.283591
$905$	−52.5869	−1.74805
$906$	19.6595	0.653143
$907$	9.68423	0.321560	0.160780	−	0.986990i	$-0.448599\pi$
$907$	9.68423	0.321560	0.160780	+	0.986990i	$0.448599\pi$
$908$	−8.76060	−0.290731
$909$	14.0415	0.465728
$910$	−43.5510	−1.44370
$911$	−8.15454	−0.270172	−0.135086	−	0.990834i	$-0.543131\pi$
$911$	−8.15454	−0.270172	−0.135086	+	0.990834i	$0.543131\pi$
$912$	21.3647	0.707457
$913$	−25.4229	−0.841374
$914$	20.4294	0.675744
$915$	−36.5391	−1.20794
$916$	−13.4976	−0.445972
$917$	−6.04619	−0.199663
$918$	−2.89880	−0.0956747
$919$	12.1639	0.401249	0.200625	−	0.979668i	$-0.435703\pi$
$919$	12.1639	0.401249	0.200625	+	0.979668i	$0.435703\pi$
$920$	−4.30241	−0.141846
$921$	7.32676	0.241425
$922$	19.4234	0.639677
$923$	58.1106	1.91273
$924$	−4.46811	−0.146990
$925$	−86.6998	−2.85067
$926$	58.4192	1.91977
$927$	5.90416	0.193918
$928$	−39.5200	−1.29731
$929$	0.515211	0.0169035	0.00845177	−	0.999964i	$-0.497310\pi$
$929$	0.515211	0.0169035	0.00845177	+	0.999964i	$0.497310\pi$
$930$	−54.8221	−1.79769
$931$	4.27331	0.140052
$932$	21.5588	0.706181
$933$	−31.0189	−1.01551
$934$	−16.6989	−0.546403
$935$	28.5312	0.933071
$936$	−11.9378	−0.390199
$937$	2.85423	0.0932436	0.0466218	−	0.998913i	$-0.485154\pi$
$937$	2.85423	0.0932436	0.0466218	+	0.998913i	$0.485154\pi$
$938$	13.9389	0.455122
$939$	6.77332	0.221039
$940$	−14.9610	−0.487974
$941$	−42.3812	−1.38159	−0.690794	−	0.723052i	$-0.742739\pi$
$941$	−42.3812	−1.38159	−0.690794	+	0.723052i	$0.742739\pi$
$942$	24.3281	0.792653
$943$	5.86882	0.191115
$944$	−45.3337	−1.47548
$945$	3.72360	0.121129
$946$	−0.0216176	−0.000702847 0
$947$	−29.8303	−0.969355	−0.484678	−	0.874693i	$-0.661063\pi$
$947$	−29.8303	−0.969355	−0.484678	+	0.874693i	$0.661063\pi$
$948$	2.78799	0.0905496
$949$	−8.54522	−0.277389
$950$	−65.3900	−2.12153
$951$	−13.4463	−0.436027
$952$	−2.95874	−0.0958934
$953$	−37.4996	−1.21473	−0.607365	−	0.794423i	$-0.707773\pi$
$953$	−37.4996	−1.21473	−0.607365	+	0.794423i	$0.707773\pi$
$954$	21.9120	0.709429
$955$	−91.9477	−2.97536
$956$	11.1946	0.362058
$957$	35.3123	1.14149
$958$	72.9347	2.35641
$959$	−9.35274	−0.302016
$960$	4.41494	0.142492
$961$	41.7560	1.34697
$962$	−114.384	−3.68789
$963$	9.05006	0.291634
$964$	−16.8506	−0.542723
$965$	−87.9228	−2.83033
$966$	1.13204	0.0364227
$967$	−26.9715	−0.867344	−0.433672	−	0.901071i	$-0.642782\pi$
$967$	−26.9715	−0.867344	−0.433672	+	0.901071i	$0.642782\pi$
$968$	17.2934	0.555832
$969$	7.17669	0.230549
$970$	13.2028	0.423916
$971$	−10.6471	−0.341683	−0.170842	−	0.985299i	$-0.554649\pi$
$971$	−10.6471	−0.341683	−0.170842	+	0.985299i	$0.554649\pi$
$972$	−0.979322	−0.0314118
$973$	−1.37175	−0.0439764
$974$	25.0861	0.803809
$975$	60.0709	1.92381
$976$	49.0600	1.57037
$977$	−23.8777	−0.763915	−0.381957	−	0.924180i	$-0.624750\pi$
$977$	−23.8777	−0.763915	−0.381957	+	0.924180i	$0.624750\pi$
$978$	−17.9172	−0.572927
$979$	74.0783	2.36755
$980$	−3.64660	−0.116486
$981$	−19.8302	−0.633131
$982$	1.08006	0.0344661
$983$	33.8645	1.08011	0.540054	−	0.841630i	$-0.318404\pi$
$983$	33.8645	1.08011	0.540054	+	0.841630i	$0.318404\pi$
$984$	−15.7651	−0.502573
$985$	−65.1273	−2.07513
$986$	−22.4360	−0.714509
$987$	−4.10273	−0.130591
$988$	−28.3574	−0.902170
$989$	0.00180033	5.72470e−5 0
$990$	29.3238	0.931971
$991$	−5.62431	−0.178662	−0.0893311	−	0.996002i	$-0.528473\pi$
$991$	−5.62431	−0.178662	−0.0893311	+	0.996002i	$0.528473\pi$
$992$	43.5535	1.38283
$993$	3.43120	0.108886
$994$	14.8026	0.469510
$995$	−48.3921	−1.53413
$996$	5.45697	0.172911
$997$	59.3610	1.87998	0.939990	−	0.341201i	$-0.110834\pi$
$997$	59.3610	1.87998	0.939990	+	0.341201i	$0.110834\pi$
$998$	21.7516	0.688536
$999$	9.77981	0.309419

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.o.1.11	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.o.1.11	✓	41	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)

\(f(q)\)	\(=\)	\(q-1.72607 q^{2} -1.00000 q^{3} +0.979322 q^{4} -3.72360 q^{5} +1.72607 q^{6} +1.00000 q^{7} +1.76176 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.72607 q^{2} -1.00000 q^{3} +0.979322 q^{4} -3.72360 q^{5} +1.72607 q^{6} +1.00000 q^{7} +1.76176 q^{8} +1.00000 q^{9} +6.42720 q^{10} +4.56245 q^{11} -0.979322 q^{12} -6.77605 q^{13} -1.72607 q^{14} +3.72360 q^{15} -4.99957 q^{16} -1.67942 q^{17} -1.72607 q^{18} +4.27331 q^{19} -3.64660 q^{20} -1.00000 q^{21} -7.87512 q^{22} +0.655845 q^{23} -1.76176 q^{24} +8.86518 q^{25} +11.6959 q^{26} -1.00000 q^{27} +0.979322 q^{28} -7.73977 q^{29} -6.42720 q^{30} +8.52971 q^{31} +5.10609 q^{32} -4.56245 q^{33} +2.89880 q^{34} -3.72360 q^{35} +0.979322 q^{36} -9.77981 q^{37} -7.37604 q^{38} +6.77605 q^{39} -6.56010 q^{40} +8.94848 q^{41} +1.72607 q^{42} +0.00274505 q^{43} +4.46811 q^{44} -3.72360 q^{45} -1.13204 q^{46} +4.10273 q^{47} +4.99957 q^{48} +1.00000 q^{49} -15.3019 q^{50} +1.67942 q^{51} -6.63593 q^{52} -12.6948 q^{53} +1.72607 q^{54} -16.9887 q^{55} +1.76176 q^{56} -4.27331 q^{57} +13.3594 q^{58} +9.06751 q^{59} +3.64660 q^{60} -9.81284 q^{61} -14.7229 q^{62} +1.00000 q^{63} +1.18566 q^{64} +25.2313 q^{65} +7.87512 q^{66} -8.07552 q^{67} -1.64469 q^{68} -0.655845 q^{69} +6.42720 q^{70} -8.57589 q^{71} +1.76176 q^{72} +1.26109 q^{73} +16.8806 q^{74} -8.86518 q^{75} +4.18495 q^{76} +4.56245 q^{77} -11.6959 q^{78} -2.84685 q^{79} +18.6164 q^{80} +1.00000 q^{81} -15.4457 q^{82} -5.57219 q^{83} -0.979322 q^{84} +6.25349 q^{85} -0.00473814 q^{86} +7.73977 q^{87} +8.03796 q^{88} +16.2365 q^{89} +6.42720 q^{90} -6.77605 q^{91} +0.642284 q^{92} -8.52971 q^{93} -7.08160 q^{94} -15.9121 q^{95} -5.10609 q^{96} +2.05421 q^{97} -1.72607 q^{98} +4.56245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9 - 18 * q^10 - 17 * q^11 - 34 * q^12 - 38 * q^13 - 4 * q^14 - 5 * q^15 + 16 * q^16 + 4 * q^17 - 4 * q^18 - 15 * q^19 + 23 * q^20 - 41 * q^21 - 31 * q^22 - 8 * q^23 + 15 * q^24 + 16 * q^25 + 15 * q^26 - 41 * q^27 + 34 * q^28 - 27 * q^29 + 18 * q^30 - 23 * q^31 - 24 * q^32 + 17 * q^33 - 9 * q^34 + 5 * q^35 + 34 * q^36 - 81 * q^37 + 38 * q^39 - 52 * q^40 + 29 * q^41 + 4 * q^42 - 47 * q^43 - 20 * q^44 + 5 * q^45 - 40 * q^46 + 26 * q^47 - 16 * q^48 + 41 * q^49 - 23 * q^50 - 4 * q^51 - 64 * q^52 - 66 * q^53 + 4 * q^54 - 14 * q^55 - 15 * q^56 + 15 * q^57 - 50 * q^58 + 41 * q^59 - 23 * q^60 - 47 * q^61 + 5 * q^62 + 41 * q^63 - 37 * q^64 - 24 * q^65 + 31 * q^66 - 73 * q^67 + 10 * q^68 + 8 * q^69 - 18 * q^70 + q^71 - 15 * q^72 - 14 * q^73 + 18 * q^74 - 16 * q^75 - 37 * q^76 - 17 * q^77 - 15 * q^78 - 80 * q^79 + 63 * q^80 + 41 * q^81 - 31 * q^82 + 20 * q^83 - 34 * q^84 - 82 * q^85 - 39 * q^86 + 27 * q^87 - 132 * q^88 + 17 * q^89 - 18 * q^90 - 38 * q^91 - 26 * q^92 + 23 * q^93 - 9 * q^94 - q^95 + 24 * q^96 - 73 * q^97 - 4 * q^98 - 17 * q^99

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