LMFDB - Embedded newform 8041.2.a.e.1.45

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:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.45
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)

$f(q)$	$=$	$q+1.36597 q^{2} -0.146919 q^{3} -0.134126 q^{4} +1.91833 q^{5} -0.200687 q^{6} -1.87783 q^{7} -2.91515 q^{8} -2.97841 q^{9} +O(q^{10})$	\(q+1.36597 q^{2} -0.146919 q^{3} -0.134126 q^{4} +1.91833 q^{5} -0.200687 q^{6} -1.87783 q^{7} -2.91515 q^{8} -2.97841 q^{9} +2.62039 q^{10} -1.00000 q^{11} +0.0197057 q^{12} -0.0301751 q^{13} -2.56506 q^{14} -0.281840 q^{15} -3.71376 q^{16} -1.00000 q^{17} -4.06843 q^{18} +1.35507 q^{19} -0.257299 q^{20} +0.275889 q^{21} -1.36597 q^{22} -5.38191 q^{23} +0.428291 q^{24} -1.31999 q^{25} -0.0412183 q^{26} +0.878343 q^{27} +0.251866 q^{28} +2.15048 q^{29} -0.384985 q^{30} +6.61162 q^{31} +0.757423 q^{32} +0.146919 q^{33} -1.36597 q^{34} -3.60231 q^{35} +0.399483 q^{36} +6.92881 q^{37} +1.85098 q^{38} +0.00443330 q^{39} -5.59224 q^{40} -0.880708 q^{41} +0.376857 q^{42} +1.00000 q^{43} +0.134126 q^{44} -5.71359 q^{45} -7.35153 q^{46} +4.75094 q^{47} +0.545622 q^{48} -3.47375 q^{49} -1.80307 q^{50} +0.146919 q^{51} +0.00404727 q^{52} -2.53605 q^{53} +1.19979 q^{54} -1.91833 q^{55} +5.47417 q^{56} -0.199085 q^{57} +2.93749 q^{58} +5.77373 q^{59} +0.0378021 q^{60} -8.38222 q^{61} +9.03127 q^{62} +5.59296 q^{63} +8.46213 q^{64} -0.0578860 q^{65} +0.200687 q^{66} +2.60131 q^{67} +0.134126 q^{68} +0.790705 q^{69} -4.92065 q^{70} +0.977318 q^{71} +8.68253 q^{72} +9.22135 q^{73} +9.46454 q^{74} +0.193932 q^{75} -0.181750 q^{76} +1.87783 q^{77} +0.00605576 q^{78} -0.903356 q^{79} -7.12423 q^{80} +8.80620 q^{81} -1.20302 q^{82} +3.64074 q^{83} -0.0370040 q^{84} -1.91833 q^{85} +1.36597 q^{86} -0.315946 q^{87} +2.91515 q^{88} +11.3521 q^{89} -7.80460 q^{90} +0.0566638 q^{91} +0.721855 q^{92} -0.971373 q^{93} +6.48964 q^{94} +2.59947 q^{95} -0.111280 q^{96} +11.3336 q^{97} -4.74503 q^{98} +2.97841 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * 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 $

$2$	1.36597	0.965887	0.482943	−	0.875652i	$-0.339568\pi$
$2$	1.36597	0.965887	0.482943	+	0.875652i	$0.339568\pi$
$3$	−0.146919	−0.0848238	−0.0424119	−	0.999100i	$-0.513504\pi$
$3$	−0.146919	−0.0848238	−0.0424119	+	0.999100i	$0.513504\pi$
$4$	−0.134126	−0.0670631
$5$	1.91833	0.857905	0.428953	−	0.903327i	$-0.358883\pi$
$5$	1.91833	0.857905	0.428953	+	0.903327i	$0.358883\pi$
$6$	−0.200687	−0.0819301
$7$	−1.87783	−0.709754	−0.354877	−	0.934913i	$-0.615477\pi$
$7$	−1.87783	−0.709754	−0.354877	+	0.934913i	$0.615477\pi$
$8$	−2.91515	−1.03066
$9$	−2.97841	−0.992805
$10$	2.62039	0.828639
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.0197057	0.00568854
$13$	−0.0301751	−0.00836907	−0.00418454	−	0.999991i	$-0.501332\pi$
$13$	−0.0301751	−0.00836907	−0.00418454	+	0.999991i	$0.501332\pi$
$14$	−2.56506	−0.685542
$15$	−0.281840	−0.0727708
$16$	−3.71376	−0.928439
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−4.06843	−0.958937
$19$	1.35507	0.310873	0.155437	−	0.987846i	$-0.450322\pi$
$19$	1.35507	0.310873	0.155437	+	0.987846i	$0.450322\pi$
$20$	−0.257299	−0.0575338
$21$	0.275889	0.0602040
$22$	−1.36597	−0.291226
$23$	−5.38191	−1.12221	−0.561103	−	0.827746i	$-0.689623\pi$
$23$	−5.38191	−1.12221	−0.561103	+	0.827746i	$0.689623\pi$
$24$	0.428291	0.0874246
$25$	−1.31999	−0.263999
$26$	−0.0412183	−0.00808358
$27$	0.878343	0.169037
$28$	0.251866	0.0475983
$29$	2.15048	0.399334	0.199667	−	0.979864i	$-0.436014\pi$
$29$	2.15048	0.399334	0.199667	+	0.979864i	$0.436014\pi$
$30$	−0.384985	−0.0702883
$31$	6.61162	1.18748	0.593741	−	0.804656i	$-0.297651\pi$
$31$	6.61162	1.18748	0.593741	+	0.804656i	$0.297651\pi$
$32$	0.757423	0.133895
$33$	0.146919	0.0255753
$34$	−1.36597	−0.234262
$35$	−3.60231	−0.608901
$36$	0.399483	0.0665806
$37$	6.92881	1.13909	0.569545	−	0.821960i	$-0.307120\pi$
$37$	6.92881	1.13909	0.569545	+	0.821960i	$0.307120\pi$
$38$	1.85098	0.300268
$39$	0.00443330	0.000709896 0
$40$	−5.59224	−0.884210
$41$	−0.880708	−0.137543	−0.0687717	−	0.997632i	$-0.521908\pi$
$41$	−0.880708	−0.137543	−0.0687717	+	0.997632i	$0.521908\pi$
$42$	0.376857	0.0581502
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	0.134126	0.0202203
$45$	−5.71359	−0.851732
$46$	−7.35153	−1.08392
$47$	4.75094	0.692996	0.346498	−	0.938051i	$-0.387371\pi$
$47$	4.75094	0.692996	0.346498	+	0.938051i	$0.387371\pi$
$48$	0.545622	0.0787537
$49$	−3.47375	−0.496250
$50$	−1.80307	−0.254993
$51$	0.146919	0.0205728
$52$	0.00404727	0.000561256 0
$53$	−2.53605	−0.348353	−0.174177	−	0.984714i	$-0.555726\pi$
$53$	−2.53605	−0.348353	−0.174177	+	0.984714i	$0.555726\pi$
$54$	1.19979	0.163271
$55$	−1.91833	−0.258668
$56$	5.47417	0.731516
$57$	−0.199085	−0.0263694
$58$	2.93749	0.385711
$59$	5.77373	0.751676	0.375838	−	0.926685i	$-0.377355\pi$
$59$	5.77373	0.751676	0.375838	+	0.926685i	$0.377355\pi$
$60$	0.0378021	0.00488023
$61$	−8.38222	−1.07323	−0.536617	−	0.843826i	$-0.680298\pi$
$61$	−8.38222	−1.07323	−0.536617	+	0.843826i	$0.680298\pi$
$62$	9.03127	1.14697
$63$	5.59296	0.704647
$64$	8.46213	1.05777
$65$	−0.0578860	−0.00717987
$66$	0.200687	0.0247029
$67$	2.60131	0.317800	0.158900	−	0.987295i	$-0.449205\pi$
$67$	2.60131	0.317800	0.158900	+	0.987295i	$0.449205\pi$
$68$	0.134126	0.0162652
$69$	0.790705	0.0951897
$70$	−4.92065	−0.588130
$71$	0.977318	0.115986	0.0579932	−	0.998317i	$-0.481530\pi$
$71$	0.977318	0.115986	0.0579932	+	0.998317i	$0.481530\pi$
$72$	8.68253	1.02325
$73$	9.22135	1.07928	0.539639	−	0.841897i	$-0.318561\pi$
$73$	9.22135	1.07928	0.539639	+	0.841897i	$0.318561\pi$
$74$	9.46454	1.10023
$75$	0.193932	0.0223934
$76$	−0.181750	−0.0208481
$77$	1.87783	0.213999
$78$	0.00605576	0.000685679 0
$79$	−0.903356	−0.101635	−0.0508177	−	0.998708i	$-0.516183\pi$
$79$	−0.903356	−0.101635	−0.0508177	+	0.998708i	$0.516183\pi$
$80$	−7.12423	−0.796513
$81$	8.80620	0.978467
$82$	−1.20302	−0.132851
$83$	3.64074	0.399623	0.199812	−	0.979834i	$-0.435967\pi$
$83$	3.64074	0.399623	0.199812	+	0.979834i	$0.435967\pi$
$84$	−0.0370040	−0.00403747
$85$	−1.91833	−0.208073
$86$	1.36597	0.147296
$87$	−0.315946	−0.0338730
$88$	2.91515	0.310756
$89$	11.3521	1.20332	0.601662	−	0.798751i	$-0.294506\pi$
$89$	11.3521	1.20332	0.601662	+	0.798751i	$0.294506\pi$
$90$	−7.80460	−0.822677
$91$	0.0566638	0.00593998
$92$	0.721855	0.0752586
$93$	−0.971373	−0.100727
$94$	6.48964	0.669355
$95$	2.59947	0.266700
$96$	−0.111280	−0.0113575
$97$	11.3336	1.15075	0.575376	−	0.817889i	$-0.304856\pi$
$97$	11.3336	1.15075	0.575376	+	0.817889i	$0.304856\pi$
$98$	−4.74503	−0.479321
$99$	2.97841	0.299342
$100$	0.177046	0.0177046
$101$	−10.3343	−1.02830	−0.514150	−	0.857700i	$-0.671893\pi$
$101$	−10.3343	−1.02830	−0.514150	+	0.857700i	$0.671893\pi$
$102$	0.200687	0.0198710
$103$	−7.68401	−0.757128	−0.378564	−	0.925575i	$-0.623582\pi$
$103$	−7.68401	−0.757128	−0.378564	+	0.925575i	$0.623582\pi$
$104$	0.0879651	0.00862569
$105$	0.529248	0.0516493
$106$	−3.46417	−0.336470
$107$	−2.36470	−0.228604	−0.114302	−	0.993446i	$-0.536463\pi$
$107$	−2.36470	−0.228604	−0.114302	+	0.993446i	$0.536463\pi$
$108$	−0.117809	−0.0113362
$109$	11.8975	1.13957	0.569785	−	0.821794i	$-0.307026\pi$
$109$	11.8975	1.13957	0.569785	+	0.821794i	$0.307026\pi$
$110$	−2.62039	−0.249844
$111$	−1.01797	−0.0966218
$112$	6.97381	0.658963
$113$	−6.99068	−0.657628	−0.328814	−	0.944395i	$-0.606649\pi$
$113$	−6.99068	−0.657628	−0.328814	+	0.944395i	$0.606649\pi$
$114$	−0.271944	−0.0254699
$115$	−10.3243	−0.962746
$116$	−0.288435	−0.0267805
$117$	0.0898740	0.00830886
$118$	7.88675	0.726034
$119$	1.87783	0.172141
$120$	0.821606	0.0750020
$121$	1.00000	0.0909091
$122$	−11.4499	−1.03662
$123$	0.129393	0.0116670
$124$	−0.886791	−0.0796362
$125$	−12.1239	−1.08439
$126$	7.63982	0.680609
$127$	13.8124	1.22566	0.612828	−	0.790216i	$-0.290032\pi$
$127$	13.8124	1.22566	0.612828	+	0.790216i	$0.290032\pi$
$128$	10.0442	0.887788
$129$	−0.146919	−0.0129355
$130$	−0.0790705	−0.00693494
$131$	13.5173	1.18101	0.590506	−	0.807033i	$-0.298928\pi$
$131$	13.5173	1.18101	0.590506	+	0.807033i	$0.298928\pi$
$132$	−0.0197057	−0.00171516
$133$	−2.54458	−0.220643
$134$	3.55331	0.306959
$135$	1.68496	0.145018
$136$	2.91515	0.249972
$137$	12.9927	1.11004	0.555019	−	0.831838i	$-0.312711\pi$
$137$	12.9927	1.11004	0.555019	+	0.831838i	$0.312711\pi$
$138$	1.08008	0.0919425
$139$	−4.83962	−0.410491	−0.205246	−	0.978711i	$-0.565799\pi$
$139$	−4.83962	−0.410491	−0.205246	+	0.978711i	$0.565799\pi$
$140$	0.483164	0.0408348
$141$	−0.698004	−0.0587825
$142$	1.33499	0.112030
$143$	0.0301751	0.00252337
$144$	11.0611	0.921759
$145$	4.12533	0.342590
$146$	12.5961	1.04246
$147$	0.510360	0.0420938
$148$	−0.929335	−0.0763908
$149$	17.5310	1.43620	0.718099	−	0.695941i	$-0.245012\pi$
$149$	17.5310	1.43620	0.718099	+	0.695941i	$0.245012\pi$
$150$	0.264906	0.0216295
$151$	20.7249	1.68657	0.843286	−	0.537466i	$-0.180618\pi$
$151$	20.7249	1.68657	0.843286	+	0.537466i	$0.180618\pi$
$152$	−3.95022	−0.320405
$153$	2.97841	0.240791
$154$	2.56506	0.206699
$155$	12.6833	1.01875
$156$	−0.000594622 0	−4.76078e−5 0
$157$	13.0804	1.04393	0.521964	−	0.852967i	$-0.325200\pi$
$157$	13.0804	1.04393	0.521964	+	0.852967i	$0.325200\pi$
$158$	−1.23396	−0.0981684
$159$	0.372594	0.0295486
$160$	1.45299	0.114869
$161$	10.1063	0.796490
$162$	12.0290	0.945088
$163$	−14.6587	−1.14816	−0.574079	−	0.818800i	$-0.694640\pi$
$163$	−14.6587	−1.14816	−0.574079	+	0.818800i	$0.694640\pi$
$164$	0.118126	0.00922409
$165$	0.281840	0.0219412
$166$	4.97314	0.385991
$167$	8.23374	0.637146	0.318573	−	0.947898i	$-0.396796\pi$
$167$	8.23374	0.637146	0.318573	+	0.947898i	$0.396796\pi$
$168$	−0.804259	−0.0620500
$169$	−12.9991	−0.999930
$170$	−2.62039	−0.200974
$171$	−4.03595	−0.308636
$172$	−0.134126	−0.0102270
$173$	−1.62900	−0.123850	−0.0619252	−	0.998081i	$-0.519724\pi$
$173$	−1.62900	−0.123850	−0.0619252	+	0.998081i	$0.519724\pi$
$174$	−0.431573	−0.0327175
$175$	2.47873	0.187374
$176$	3.71376	0.279935
$177$	−0.848272	−0.0637600
$178$	15.5067	1.16227
$179$	−16.2233	−1.21258	−0.606292	−	0.795242i	$-0.707344\pi$
$179$	−16.2233	−1.21258	−0.606292	+	0.795242i	$0.707344\pi$
$180$	0.766343	0.0571198
$181$	5.35533	0.398059	0.199029	−	0.979994i	$-0.436221\pi$
$181$	5.35533	0.398059	0.199029	+	0.979994i	$0.436221\pi$
$182$	0.0774011	0.00573735
$183$	1.23151	0.0910357
$184$	15.6891	1.15661
$185$	13.2918	0.977230
$186$	−1.32687	−0.0972905
$187$	1.00000	0.0731272
$188$	−0.637225	−0.0464744
$189$	−1.64938	−0.119975
$190$	3.55079	0.257602
$191$	−15.4877	−1.12065	−0.560326	−	0.828272i	$-0.689324\pi$
$191$	−15.4877	−1.12065	−0.560326	+	0.828272i	$0.689324\pi$
$192$	−1.24325	−0.0897238
$193$	5.42287	0.390347	0.195173	−	0.980769i	$-0.437473\pi$
$193$	5.42287	0.390347	0.195173	+	0.980769i	$0.437473\pi$
$194$	15.4813	1.11150
$195$	0.00850455	0.000609024 0
$196$	0.465920	0.0332800
$197$	−1.35447	−0.0965022	−0.0482511	−	0.998835i	$-0.515365\pi$
$197$	−1.35447	−0.0965022	−0.0482511	+	0.998835i	$0.515365\pi$
$198$	4.06843	0.289130
$199$	12.3929	0.878513	0.439256	−	0.898362i	$-0.355242\pi$
$199$	12.3929	0.878513	0.439256	+	0.898362i	$0.355242\pi$
$200$	3.84798	0.272094
$201$	−0.382182	−0.0269570
$202$	−14.1163	−0.993222
$203$	−4.03824	−0.283429
$204$	−0.0197057	−0.00137967
$205$	−1.68949	−0.117999
$206$	−10.4961	−0.731300
$207$	16.0296	1.11413
$208$	0.112063	0.00777018
$209$	−1.35507	−0.0937318
$210$	0.722937	0.0498874
$211$	−24.7745	−1.70555	−0.852773	−	0.522282i	$-0.825081\pi$
$211$	−24.7745	−1.70555	−0.852773	+	0.522282i	$0.825081\pi$
$212$	0.340150	0.0233616
$213$	−0.143587	−0.00983840
$214$	−3.23011	−0.220806
$215$	1.91833	0.130829
$216$	−2.56050	−0.174220
$217$	−12.4155	−0.842819
$218$	16.2516	1.10070
$219$	−1.35479	−0.0915484
$220$	0.257299	0.0173471
$221$	0.0301751	0.00202980
$222$	−1.39052	−0.0933257
$223$	−0.0260489	−0.00174436	−0.000872181	−	1.00000i	$-0.500278\pi$
$223$	−0.0260489	−0.00174436	−0.000872181		1.00000i	$0.500278\pi$
$224$	−1.42231	−0.0950323
$225$	3.93149	0.262099
$226$	−9.54906	−0.635194
$227$	4.67635	0.310380	0.155190	−	0.987885i	$-0.450401\pi$
$227$	4.67635	0.310380	0.155190	+	0.987885i	$0.450401\pi$
$228$	0.0267025	0.00176842
$229$	−18.8871	−1.24810	−0.624049	−	0.781385i	$-0.714513\pi$
$229$	−18.8871	−1.24810	−0.624049	+	0.781385i	$0.714513\pi$
$230$	−14.1027	−0.929903
$231$	−0.275889	−0.0181522
$232$	−6.26897	−0.411578
$233$	20.7590	1.35997	0.679985	−	0.733226i	$-0.261986\pi$
$233$	20.7590	1.35997	0.679985	+	0.733226i	$0.261986\pi$
$234$	0.122765	0.00802541
$235$	9.11389	0.594525
$236$	−0.774409	−0.0504097
$237$	0.132720	0.00862111
$238$	2.56506	0.166268
$239$	−6.93408	−0.448528	−0.224264	−	0.974528i	$-0.571998\pi$
$239$	−6.93408	−0.448528	−0.224264	+	0.974528i	$0.571998\pi$
$240$	1.04669	0.0675632
$241$	−1.09250	−0.0703739	−0.0351870	−	0.999381i	$-0.511203\pi$
$241$	−1.09250	−0.0703739	−0.0351870	+	0.999381i	$0.511203\pi$
$242$	1.36597	0.0878079
$243$	−3.92883	−0.252034
$244$	1.12428	0.0719744
$245$	−6.66381	−0.425735
$246$	0.176747	0.0112690
$247$	−0.0408893	−0.00260172
$248$	−19.2739	−1.22389
$249$	−0.534894	−0.0338975
$250$	−16.5608	−1.04740
$251$	12.6098	0.795922	0.397961	−	0.917402i	$-0.369718\pi$
$251$	12.6098	0.795922	0.397961	+	0.917402i	$0.369718\pi$
$252$	−0.750163	−0.0472558
$253$	5.38191	0.338358
$254$	18.8674	1.18384
$255$	0.281840	0.0176495
$256$	−3.20423	−0.200264
$257$	11.0283	0.687926	0.343963	−	0.938983i	$-0.388231\pi$
$257$	11.0283	0.687926	0.343963	+	0.938983i	$0.388231\pi$
$258$	−0.200687	−0.0124942
$259$	−13.0111	−0.808473
$260$	0.00776402	0.000481504 0
$261$	−6.40501	−0.396460
$262$	18.4642	1.14072
$263$	−11.9487	−0.736786	−0.368393	−	0.929670i	$-0.620092\pi$
$263$	−11.9487	−0.736786	−0.368393	+	0.929670i	$0.620092\pi$
$264$	−0.428291	−0.0263595
$265$	−4.86499	−0.298854
$266$	−3.47583	−0.213117
$267$	−1.66784	−0.102070
$268$	−0.348904	−0.0213127
$269$	31.0075	1.89056	0.945279	−	0.326262i	$-0.105789\pi$
$269$	31.0075	1.89056	0.945279	+	0.326262i	$0.105789\pi$
$270$	2.30160	0.140071
$271$	2.41255	0.146552	0.0732761	−	0.997312i	$-0.476655\pi$
$271$	2.41255	0.146552	0.0732761	+	0.997312i	$0.476655\pi$
$272$	3.71376	0.225180
$273$	−0.00832500	−0.000503852 0
$274$	17.7476	1.07217
$275$	1.31999	0.0795986
$276$	−0.106054	−0.00638372
$277$	−26.9348	−1.61836	−0.809179	−	0.587562i	$-0.800088\pi$
$277$	−26.9348	−1.61836	−0.809179	+	0.587562i	$0.800088\pi$
$278$	−6.61077	−0.396488
$279$	−19.6921	−1.17894
$280$	10.5013	0.627572
$281$	14.7045	0.877195	0.438597	−	0.898684i	$-0.355475\pi$
$281$	14.7045	0.877195	0.438597	+	0.898684i	$0.355475\pi$
$282$	−0.953452	−0.0567772
$283$	−10.5844	−0.629176	−0.314588	−	0.949228i	$-0.601866\pi$
$283$	−10.5844	−0.629176	−0.314588	+	0.949228i	$0.601866\pi$
$284$	−0.131084	−0.00777840
$285$	−0.381911	−0.0226225
$286$	0.0412183	0.00243729
$287$	1.65382	0.0976220
$288$	−2.25592	−0.132931
$289$	1.00000	0.0588235
$290$	5.63508	0.330903
$291$	−1.66512	−0.0976111
$292$	−1.23682	−0.0723797
$293$	18.3366	1.07123	0.535617	−	0.844461i	$-0.320079\pi$
$293$	18.3366	1.07123	0.535617	+	0.844461i	$0.320079\pi$
$294$	0.697136	0.0406578
$295$	11.0760	0.644867
$296$	−20.1985	−1.17402
$297$	−0.878343	−0.0509666
$298$	23.9469	1.38721
$299$	0.162400	0.00939182
$300$	−0.0260114	−0.00150177
$301$	−1.87783	−0.108236
$302$	28.3096	1.62904
$303$	1.51830	0.0872243
$304$	−5.03238	−0.288627
$305$	−16.0799	−0.920733
$306$	4.06843	0.232576
$307$	−7.15817	−0.408538	−0.204269	−	0.978915i	$-0.565482\pi$
$307$	−7.15817	−0.408538	−0.204269	+	0.978915i	$0.565482\pi$
$308$	−0.251866	−0.0143514
$309$	1.12893	0.0642224
$310$	17.3250	0.983993
$311$	17.1623	0.973186	0.486593	−	0.873629i	$-0.338239\pi$
$311$	17.1623	0.973186	0.486593	+	0.873629i	$0.338239\pi$
$312$	−0.0129237	−0.000731663 0
$313$	−25.4269	−1.43721	−0.718606	−	0.695418i	$-0.755219\pi$
$313$	−25.4269	−1.43721	−0.718606	+	0.695418i	$0.755219\pi$
$314$	17.8674	1.00832
$315$	10.7292	0.604520
$316$	0.121164	0.00681599
$317$	−9.16900	−0.514983	−0.257491	−	0.966281i	$-0.582896\pi$
$317$	−9.16900	−0.514983	−0.257491	+	0.966281i	$0.582896\pi$
$318$	0.508952	0.0285406
$319$	−2.15048	−0.120404
$320$	16.2332	0.907463
$321$	0.347420	0.0193911
$322$	13.8049	0.769319
$323$	−1.35507	−0.0753978
$324$	−1.18114	−0.0656190
$325$	0.0398310	0.00220943
$326$	−20.0233	−1.10899
$327$	−1.74796	−0.0966626
$328$	2.56740	0.141761
$329$	−8.92147	−0.491856
$330$	0.384985	0.0211927
$331$	35.6180	1.95774	0.978872	−	0.204475i	$-0.0655489\pi$
$331$	35.6180	1.95774	0.978872	+	0.204475i	$0.0655489\pi$
$332$	−0.488319	−0.0268000
$333$	−20.6369	−1.13089
$334$	11.2470	0.615411
$335$	4.99018	0.272643
$336$	−1.02459	−0.0558958
$337$	−28.6969	−1.56322	−0.781609	−	0.623768i	$-0.785601\pi$
$337$	−28.6969	−1.56322	−0.781609	+	0.623768i	$0.785601\pi$
$338$	−17.7564	−0.965819
$339$	1.02706	0.0557825
$340$	0.257299	0.0139540
$341$	−6.61162	−0.358039
$342$	−5.51298	−0.298108
$343$	19.6679	1.06197
$344$	−2.91515	−0.157174
$345$	1.51684	0.0816638
$346$	−2.22516	−0.119625
$347$	31.2987	1.68020	0.840100	−	0.542432i	$-0.182496\pi$
$347$	31.2987	1.68020	0.840100	+	0.542432i	$0.182496\pi$
$348$	0.0423767	0.00227163
$349$	−13.2211	−0.707711	−0.353856	−	0.935300i	$-0.615130\pi$
$349$	−13.2211	−0.707711	−0.353856	+	0.935300i	$0.615130\pi$
$350$	3.38587	0.180982
$351$	−0.0265041	−0.00141469
$352$	−0.757423	−0.0403708
$353$	12.7013	0.676023	0.338012	−	0.941142i	$-0.390246\pi$
$353$	12.7013	0.676023	0.338012	+	0.941142i	$0.390246\pi$
$354$	−1.15871	−0.0615849
$355$	1.87482	0.0995053
$356$	−1.52262	−0.0806986
$357$	−0.275889	−0.0146016
$358$	−22.1605	−1.17122
$359$	−7.09922	−0.374683	−0.187341	−	0.982295i	$-0.559987\pi$
$359$	−7.09922	−0.374683	−0.187341	+	0.982295i	$0.559987\pi$
$360$	16.6560	0.877848
$361$	−17.1638	−0.903358
$362$	7.31522	0.384480
$363$	−0.146919	−0.00771125
$364$	−0.00760010	−0.000398354 0
$365$	17.6896	0.925918
$366$	1.68220	0.0879302
$367$	7.21348	0.376540	0.188270	−	0.982117i	$-0.439712\pi$
$367$	7.21348	0.376540	0.188270	+	0.982117i	$0.439712\pi$
$368$	19.9871	1.04190
$369$	2.62311	0.136554
$370$	18.1562	0.943894
$371$	4.76227	0.247245
$372$	0.130286	0.00675504
$373$	27.7352	1.43607	0.718037	−	0.696005i	$-0.245041\pi$
$373$	27.7352	1.43607	0.718037	+	0.696005i	$0.245041\pi$
$374$	1.36597	0.0706326
$375$	1.78123	0.0919821
$376$	−13.8497	−0.714244
$377$	−0.0648909	−0.00334205
$378$	−2.25300	−0.115882
$379$	−6.26534	−0.321829	−0.160914	−	0.986968i	$-0.551444\pi$
$379$	−6.26534	−0.321829	−0.160914	+	0.986968i	$0.551444\pi$
$380$	−0.348657	−0.0178857
$381$	−2.02931	−0.103965
$382$	−21.1558	−1.08242
$383$	38.1472	1.94923	0.974616	−	0.223883i	$-0.0718732\pi$
$383$	38.1472	1.94923	0.974616	+	0.223883i	$0.0718732\pi$
$384$	−1.47568	−0.0753055
$385$	3.60231	0.183591
$386$	7.40747	0.377031
$387$	−2.97841	−0.151401
$388$	−1.52013	−0.0771730
$389$	−34.0151	−1.72464	−0.862318	−	0.506368i	$-0.830988\pi$
$389$	−34.0151	−1.72464	−0.862318	+	0.506368i	$0.830988\pi$
$390$	0.0116170	0.000588248 0
$391$	5.38191	0.272175
$392$	10.1265	0.511466
$393$	−1.98595	−0.100178
$394$	−1.85017	−0.0932102
$395$	−1.73294	−0.0871936
$396$	−0.399483	−0.0200748
$397$	23.6553	1.18723	0.593613	−	0.804751i	$-0.297701\pi$
$397$	23.6553	1.18723	0.593613	+	0.804751i	$0.297701\pi$
$398$	16.9284	0.848544
$399$	0.373848	0.0187158
$400$	4.90214	0.245107
$401$	−28.5029	−1.42337	−0.711683	−	0.702501i	$-0.752067\pi$
$401$	−28.5029	−1.42337	−0.711683	+	0.702501i	$0.752067\pi$
$402$	−0.522049	−0.0260374
$403$	−0.199506	−0.00993812
$404$	1.38610	0.0689610
$405$	16.8932	0.839431
$406$	−5.51611	−0.273760
$407$	−6.92881	−0.343448
$408$	−0.428291	−0.0212036
$409$	33.0729	1.63535	0.817674	−	0.575681i	$-0.195263\pi$
$409$	33.0729	1.63535	0.817674	+	0.575681i	$0.195263\pi$
$410$	−2.30779	−0.113974
$411$	−1.90887	−0.0941575
$412$	1.03063	0.0507753
$413$	−10.8421	−0.533505
$414$	21.8959	1.07612
$415$	6.98416	0.342839
$416$	−0.0228553	−0.00112057
$417$	0.711032	0.0348194
$418$	−1.85098	−0.0905343
$419$	18.2465	0.891399	0.445699	−	0.895183i	$-0.352955\pi$
$419$	18.2465	0.891399	0.445699	+	0.895183i	$0.352955\pi$
$420$	−0.0709860	−0.00346376
$421$	7.69057	0.374815	0.187408	−	0.982282i	$-0.439991\pi$
$421$	7.69057	0.374815	0.187408	+	0.982282i	$0.439991\pi$
$422$	−33.8412	−1.64736
$423$	−14.1503	−0.688010
$424$	7.39297	0.359034
$425$	1.31999	0.0640291
$426$	−0.196135	−0.00950278
$427$	15.7404	0.761732
$428$	0.317168	0.0153309
$429$	−0.00443330	−0.000214042 0
$430$	2.62039	0.126366
$431$	9.44080	0.454747	0.227374	−	0.973808i	$-0.426986\pi$
$431$	9.44080	0.454747	0.227374	+	0.973808i	$0.426986\pi$
$432$	−3.26195	−0.156941
$433$	−11.7589	−0.565095	−0.282547	−	0.959253i	$-0.591179\pi$
$433$	−11.7589	−0.565095	−0.282547	+	0.959253i	$0.591179\pi$
$434$	−16.9592	−0.814068
$435$	−0.606090	−0.0290598
$436$	−1.59576	−0.0764231
$437$	−7.29284	−0.348864
$438$	−1.85061	−0.0884254
$439$	18.3625	0.876396	0.438198	−	0.898878i	$-0.355617\pi$
$439$	18.3625	0.876396	0.438198	+	0.898878i	$0.355617\pi$
$440$	5.59224	0.266599
$441$	10.3463	0.492679
$442$	0.0412183	0.00196056
$443$	2.75338	0.130817	0.0654086	−	0.997859i	$-0.479165\pi$
$443$	2.75338	0.130817	0.0654086	+	0.997859i	$0.479165\pi$
$444$	0.136537	0.00647976
$445$	21.7772	1.03234
$446$	−0.0355820	−0.00168486
$447$	−2.57564	−0.121824
$448$	−15.8905	−0.750754
$449$	−12.0166	−0.567098	−0.283549	−	0.958958i	$-0.591512\pi$
$449$	−12.0166	−0.567098	−0.283549	+	0.958958i	$0.591512\pi$
$450$	5.37030	0.253158
$451$	0.880708	0.0414709
$452$	0.937633	0.0441026
$453$	−3.04489	−0.143061
$454$	6.38776	0.299792
$455$	0.108700	0.00509594
$456$	0.580363	0.0271780
$457$	−19.9085	−0.931279	−0.465639	−	0.884975i	$-0.654176\pi$
$457$	−19.9085	−0.931279	−0.465639	+	0.884975i	$0.654176\pi$
$458$	−25.7993	−1.20552
$459$	−0.878343	−0.0409976
$460$	1.38476	0.0645647
$461$	−6.56835	−0.305918	−0.152959	−	0.988233i	$-0.548880\pi$
$461$	−6.56835	−0.305918	−0.152959	+	0.988233i	$0.548880\pi$
$462$	−0.376857	−0.0175330
$463$	−5.47818	−0.254593	−0.127296	−	0.991865i	$-0.540630\pi$
$463$	−5.47818	−0.254593	−0.127296	+	0.991865i	$0.540630\pi$
$464$	−7.98635	−0.370757
$465$	−1.86342	−0.0864139
$466$	28.3562	1.31358
$467$	14.4495	0.668643	0.334321	−	0.942459i	$-0.391493\pi$
$467$	14.4495	0.668643	0.334321	+	0.942459i	$0.391493\pi$
$468$	−0.0120545	−0.000557218 0
$469$	−4.88482	−0.225560
$470$	12.4493	0.574243
$471$	−1.92176	−0.0885499
$472$	−16.8313	−0.774724
$473$	−1.00000	−0.0459800
$474$	0.181292	0.00832701
$475$	−1.78868	−0.0820702
$476$	−0.251866	−0.0115443
$477$	7.55340	0.345847
$478$	−9.47174	−0.433227
$479$	−10.8827	−0.497242	−0.248621	−	0.968601i	$-0.579977\pi$
$479$	−10.8827	−0.497242	−0.248621	+	0.968601i	$0.579977\pi$
$480$	−0.213472	−0.00974362
$481$	−0.209078	−0.00953312
$482$	−1.49232	−0.0679732
$483$	−1.48481	−0.0675613
$484$	−0.134126	−0.00609664
$485$	21.7416	0.987236
$486$	−5.36666	−0.243437
$487$	−31.6784	−1.43549	−0.717743	−	0.696308i	$-0.754825\pi$
$487$	−31.6784	−1.43549	−0.717743	+	0.696308i	$0.754825\pi$
$488$	24.4355	1.10614
$489$	2.15364	0.0973911
$490$	−9.10256	−0.411212
$491$	−29.7959	−1.34467	−0.672335	−	0.740247i	$-0.734709\pi$
$491$	−29.7959	−1.34467	−0.672335	+	0.740247i	$0.734709\pi$
$492$	−0.0173550	−0.000782422 0
$493$	−2.15048	−0.0968526
$494$	−0.0558535	−0.00251297
$495$	5.71359	0.256807
$496$	−24.5539	−1.10250
$497$	−1.83524	−0.0823218
$498$	−0.730649	−0.0327412
$499$	−17.1824	−0.769189	−0.384594	−	0.923086i	$-0.625659\pi$
$499$	−17.1824	−0.769189	−0.384594	+	0.923086i	$0.625659\pi$
$500$	1.62613	0.0727226
$501$	−1.20969	−0.0540451
$502$	17.2246	0.768770
$503$	3.07166	0.136959	0.0684793	−	0.997653i	$-0.478185\pi$
$503$	3.07166	0.136959	0.0684793	+	0.997653i	$0.478185\pi$
$504$	−16.3043	−0.726253
$505$	−19.8246	−0.882184
$506$	7.35153	0.326815
$507$	1.90981	0.0848178
$508$	−1.85261	−0.0821963
$509$	14.5548	0.645128	0.322564	−	0.946548i	$-0.395455\pi$
$509$	14.5548	0.645128	0.322564	+	0.946548i	$0.395455\pi$
$510$	0.384985	0.0170474
$511$	−17.3162	−0.766022
$512$	−24.4652	−1.08122
$513$	1.19021	0.0525492
$514$	15.0643	0.664458
$515$	−14.7405	−0.649544
$516$	0.0197057	0.000867495 0
$517$	−4.75094	−0.208946
$518$	−17.7728	−0.780893
$519$	0.239331	0.0105055
$520$	0.168746	0.00740002
$521$	−34.1918	−1.49797	−0.748984	−	0.662588i	$-0.769458\pi$
$521$	−34.1918	−1.49797	−0.748984	+	0.662588i	$0.769458\pi$
$522$	−8.74906	−0.382936
$523$	24.9643	1.09161	0.545806	−	0.837912i	$-0.316224\pi$
$523$	24.9643	1.09161	0.545806	+	0.837912i	$0.316224\pi$
$524$	−1.81302	−0.0792023
$525$	−0.364172	−0.0158938
$526$	−16.3215	−0.711652
$527$	−6.61162	−0.288007
$528$	−0.545622	−0.0237451
$529$	5.96495	0.259346
$530$	−6.64543	−0.288659
$531$	−17.1966	−0.746268
$532$	0.341295	0.0147970
$533$	0.0265755	0.00115111
$534$	−2.27822	−0.0985884
$535$	−4.53629	−0.196121
$536$	−7.58321	−0.327545
$537$	2.38351	0.102856
$538$	42.3553	1.82607
$539$	3.47375	0.149625
$540$	−0.225997	−0.00972535
$541$	−3.34371	−0.143757	−0.0718786	−	0.997413i	$-0.522899\pi$
$541$	−3.34371	−0.143757	−0.0718786	+	0.997413i	$0.522899\pi$
$542$	3.29548	0.141553
$543$	−0.786800	−0.0337648
$544$	−0.757423	−0.0324742
$545$	22.8233	0.977643
$546$	−0.0113717	−0.000486664 0
$547$	−16.4909	−0.705102	−0.352551	−	0.935793i	$-0.614686\pi$
$547$	−16.4909	−0.705102	−0.352551	+	0.935793i	$0.614686\pi$
$548$	−1.74265	−0.0744425
$549$	24.9657	1.06551
$550$	1.80307	0.0768832
$551$	2.91404	0.124142
$552$	−2.30503	−0.0981084
$553$	1.69635	0.0721362
$554$	−36.7922	−1.56315
$555$	−1.95281	−0.0828924
$556$	0.649119	0.0275288
$557$	−21.0351	−0.891285	−0.445642	−	0.895211i	$-0.647025\pi$
$557$	−21.0351	−0.891285	−0.445642	+	0.895211i	$0.647025\pi$
$558$	−26.8989	−1.13872
$559$	−0.0301751	−0.00127627
$560$	13.3781	0.565328
$561$	−0.146919	−0.00620293
$562$	20.0859	0.847271
$563$	4.71555	0.198737	0.0993684	−	0.995051i	$-0.468318\pi$
$563$	4.71555	0.198737	0.0993684	+	0.995051i	$0.468318\pi$
$564$	0.0936206	0.00394214
$565$	−13.4105	−0.564182
$566$	−14.4580	−0.607713
$567$	−16.5366	−0.694470
$568$	−2.84903	−0.119543
$569$	23.9326	1.00331	0.501654	−	0.865069i	$-0.332725\pi$
$569$	23.9326	1.00331	0.501654	+	0.865069i	$0.332725\pi$
$570$	−0.521679	−0.0218507
$571$	42.7017	1.78701	0.893506	−	0.449052i	$-0.148238\pi$
$571$	42.7017	1.78701	0.893506	+	0.449052i	$0.148238\pi$
$572$	−0.00404727	−0.000169225 0
$573$	2.27544	0.0950579
$574$	2.25907	0.0942917
$575$	7.10409	0.296261
$576$	−25.2037	−1.05016
$577$	6.43026	0.267695	0.133848	−	0.991002i	$-0.457267\pi$
$577$	6.43026	0.267695	0.133848	+	0.991002i	$0.457267\pi$
$578$	1.36597	0.0568169
$579$	−0.796723	−0.0331107
$580$	−0.553315	−0.0229752
$581$	−6.83670	−0.283634
$582$	−2.27451	−0.0942813
$583$	2.53605	0.105032
$584$	−26.8817	−1.11237
$585$	0.172408	0.00712821
$586$	25.0472	1.03469
$587$	4.55653	0.188068	0.0940340	−	0.995569i	$-0.470024\pi$
$587$	4.55653	0.188068	0.0940340	+	0.995569i	$0.470024\pi$
$588$	−0.0684526	−0.00282294
$589$	8.95917	0.369156
$590$	15.1294	0.622868
$591$	0.198998	0.00818568
$592$	−25.7319	−1.05758
$593$	3.15636	0.129616	0.0648080	−	0.997898i	$-0.479356\pi$
$593$	3.15636	0.129616	0.0648080	+	0.997898i	$0.479356\pi$
$594$	−1.19979	−0.0492280
$595$	3.60231	0.147680
$596$	−2.35137	−0.0963159
$597$	−1.82076	−0.0745188
$598$	0.221833	0.00907144
$599$	42.6216	1.74147	0.870736	−	0.491751i	$-0.163643\pi$
$599$	42.6216	1.74147	0.870736	+	0.491751i	$0.163643\pi$
$600$	−0.565342	−0.0230800
$601$	35.3504	1.44197	0.720986	−	0.692950i	$-0.243689\pi$
$601$	35.3504	1.44197	0.720986	+	0.692950i	$0.243689\pi$
$602$	−2.56506	−0.104544
$603$	−7.74778	−0.315514
$604$	−2.77976	−0.113107
$605$	1.91833	0.0779914
$606$	2.07396	0.0842488
$607$	2.60513	0.105739	0.0528695	−	0.998601i	$-0.483163\pi$
$607$	2.60513	0.105739	0.0528695	+	0.998601i	$0.483163\pi$
$608$	1.02636	0.0416243
$609$	0.593294	0.0240415
$610$	−21.9647	−0.889323
$611$	−0.143360	−0.00579973
$612$	−0.399483	−0.0161482
$613$	−3.18170	−0.128507	−0.0642537	−	0.997934i	$-0.520467\pi$
$613$	−3.18170	−0.128507	−0.0642537	+	0.997934i	$0.520467\pi$
$614$	−9.77784	−0.394602
$615$	0.248219	0.0100091
$616$	−5.47417	−0.220560
$617$	−27.2714	−1.09791	−0.548953	−	0.835853i	$-0.684973\pi$
$617$	−27.2714	−1.09791	−0.548953	+	0.835853i	$0.684973\pi$
$618$	1.54208	0.0620316
$619$	21.6571	0.870472	0.435236	−	0.900316i	$-0.356665\pi$
$619$	21.6571	0.870472	0.435236	+	0.900316i	$0.356665\pi$
$620$	−1.70116	−0.0683203
$621$	−4.72716	−0.189695
$622$	23.4432	0.939987
$623$	−21.3174	−0.854063
$624$	−0.0164642	−0.000659096 0
$625$	−16.6576	−0.666306
$626$	−34.7323	−1.38818
$627$	0.199085	0.00795069
$628$	−1.75442	−0.0700090
$629$	−6.92881	−0.276270
$630$	14.6557	0.583898
$631$	−14.4632	−0.575770	−0.287885	−	0.957665i	$-0.592952\pi$
$631$	−14.4632	−0.575770	−0.287885	+	0.957665i	$0.592952\pi$
$632$	2.63342	0.104752
$633$	3.63984	0.144671
$634$	−12.5246	−0.497415
$635$	26.4969	1.05150
$636$	−0.0499746	−0.00198162
$637$	0.104821	0.00415315
$638$	−2.93749	−0.116296
$639$	−2.91086	−0.115152
$640$	19.2681	0.761638
$641$	4.31395	0.170391	0.0851954	−	0.996364i	$-0.472849\pi$
$641$	4.31395	0.170391	0.0851954	+	0.996364i	$0.472849\pi$
$642$	0.474565	0.0187296
$643$	31.5437	1.24396	0.621981	−	0.783032i	$-0.286328\pi$
$643$	31.5437	1.24396	0.621981	+	0.783032i	$0.286328\pi$
$644$	−1.35552	−0.0534151
$645$	−0.281840	−0.0110974
$646$	−1.85098	−0.0728258
$647$	−47.2717	−1.85844	−0.929221	−	0.369525i	$-0.879520\pi$
$647$	−47.2717	−1.85844	−0.929221	+	0.369525i	$0.879520\pi$
$648$	−25.6714	−1.00847
$649$	−5.77373	−0.226639
$650$	0.0544079	0.00213405
$651$	1.82407	0.0714911
$652$	1.96611	0.0769990
$653$	26.9660	1.05526	0.527630	−	0.849474i	$-0.323081\pi$
$653$	26.9660	1.05526	0.527630	+	0.849474i	$0.323081\pi$
$654$	−2.38767	−0.0933652
$655$	25.9307	1.01320
$656$	3.27073	0.127701
$657$	−27.4650	−1.07151
$658$	−12.1865	−0.475077
$659$	−0.949357	−0.0369817	−0.0184909	−	0.999829i	$-0.505886\pi$
$659$	−0.949357	−0.0369817	−0.0184909	+	0.999829i	$0.505886\pi$
$660$	−0.0378021	−0.00147145
$661$	2.33615	0.0908657	0.0454329	−	0.998967i	$-0.485533\pi$
$661$	2.33615	0.0908657	0.0454329	+	0.998967i	$0.485533\pi$
$662$	48.6531	1.89096
$663$	−0.00443330	−0.000172175 0
$664$	−10.6133	−0.411876
$665$	−4.88136	−0.189291
$666$	−28.1893	−1.09231
$667$	−11.5737	−0.448134
$668$	−1.10436	−0.0427290
$669$	0.00382708	0.000147963 0
$670$	6.81644	0.263342
$671$	8.38222	0.323592
$672$	0.208965	0.00806100
$673$	−29.9260	−1.15356	−0.576781	−	0.816899i	$-0.695691\pi$
$673$	−29.9260	−1.15356	−0.576781	+	0.816899i	$0.695691\pi$
$674$	−39.1991	−1.50989
$675$	−1.15941	−0.0446256
$676$	1.74352	0.0670584
$677$	3.93138	0.151095	0.0755476	−	0.997142i	$-0.475930\pi$
$677$	3.93138	0.151095	0.0755476	+	0.997142i	$0.475930\pi$
$678$	1.40294	0.0538795
$679$	−21.2826	−0.816751
$680$	5.59224	0.214452
$681$	−0.687045	−0.0263276
$682$	−9.03127	−0.345825
$683$	33.8863	1.29662	0.648311	−	0.761376i	$-0.275476\pi$
$683$	33.8863	1.29662	0.648311	+	0.761376i	$0.275476\pi$
$684$	0.541326	0.0206981
$685$	24.9242	0.952306
$686$	26.8658	1.02574
$687$	2.77488	0.105868
$688$	−3.71376	−0.141586
$689$	0.0765256	0.00291539
$690$	2.07195	0.0788779
$691$	17.0774	0.649655	0.324827	−	0.945773i	$-0.394694\pi$
$691$	17.0774	0.649655	0.324827	+	0.945773i	$0.394694\pi$
$692$	0.218491	0.00830579
$693$	−5.59296	−0.212459
$694$	42.7530	1.62288
$695$	−9.28400	−0.352162
$696$	0.921031	0.0349116
$697$	0.880708	0.0333592
$698$	−18.0597	−0.683569
$699$	−3.04990	−0.115358
$700$	−0.332462	−0.0125659
$701$	−47.3406	−1.78803	−0.894015	−	0.448036i	$-0.852124\pi$
$701$	−47.3406	−1.78803	−0.894015	+	0.448036i	$0.852124\pi$
$702$	−0.0362038	−0.00136643
$703$	9.38899	0.354112
$704$	−8.46213	−0.318929
$705$	−1.33900	−0.0504298
$706$	17.3496	0.652962
$707$	19.4061	0.729840
$708$	0.113775	0.00427594
$709$	9.60706	0.360801	0.180400	−	0.983593i	$-0.442261\pi$
$709$	9.60706	0.360801	0.180400	+	0.983593i	$0.442261\pi$
$710$	2.56095	0.0961108
$711$	2.69057	0.100904
$712$	−33.0932	−1.24022
$713$	−35.5831	−1.33260
$714$	−0.376857	−0.0141035
$715$	0.0578860	0.00216481
$716$	2.17597	0.0813197
$717$	1.01875	0.0380458
$718$	−9.69732	−0.361901
$719$	3.11234	0.116071	0.0580354	−	0.998315i	$-0.481516\pi$
$719$	3.11234	0.116071	0.0580354	+	0.998315i	$0.481516\pi$
$720$	21.2189	0.790782
$721$	14.4293	0.537374
$722$	−23.4452	−0.872541
$723$	0.160509	0.00596938
$724$	−0.718290	−0.0266950
$725$	−2.83862	−0.105424
$726$	−0.200687	−0.00744820
$727$	44.9670	1.66773	0.833867	−	0.551966i	$-0.186122\pi$
$727$	44.9670	1.66773	0.833867	+	0.551966i	$0.186122\pi$
$728$	−0.165184	−0.00612211
$729$	−25.8414	−0.957088
$730$	24.1635	0.894332
$731$	−1.00000	−0.0369863
$732$	−0.165178	−0.00610514
$733$	−2.62469	−0.0969453	−0.0484726	−	0.998825i	$-0.515435\pi$
$733$	−2.62469	−0.0969453	−0.0484726	+	0.998825i	$0.515435\pi$
$734$	9.85339	0.363695
$735$	0.979041	0.0361125
$736$	−4.07638	−0.150257
$737$	−2.60131	−0.0958205
$738$	3.58309	0.131895
$739$	39.4062	1.44958	0.724790	−	0.688970i	$-0.241937\pi$
$739$	39.4062	1.44958	0.724790	+	0.688970i	$0.241937\pi$
$740$	−1.78277	−0.0655361
$741$	0.00600741	0.000220688 0
$742$	6.50512	0.238811
$743$	−24.9244	−0.914389	−0.457195	−	0.889367i	$-0.651146\pi$
$743$	−24.9244	−0.914389	−0.457195	+	0.889367i	$0.651146\pi$
$744$	2.83170	0.103815
$745$	33.6304	1.23212
$746$	37.8854	1.38708
$747$	−10.8436	−0.396748
$748$	−0.134126	−0.00490414
$749$	4.44051	0.162253
$750$	2.43310	0.0888443
$751$	−18.1209	−0.661240	−0.330620	−	0.943764i	$-0.607258\pi$
$751$	−18.1209	−0.661240	−0.330620	+	0.943764i	$0.607258\pi$
$752$	−17.6438	−0.643405
$753$	−1.85262	−0.0675131
$754$	−0.0886390	−0.00322804
$755$	39.7574	1.44692
$756$	0.221225	0.00804588
$757$	0.218504	0.00794168	0.00397084	−	0.999992i	$-0.498736\pi$
$757$	0.218504	0.00794168	0.00397084	+	0.999992i	$0.498736\pi$
$758$	−8.55826	−0.310850
$759$	−0.790705	−0.0287008
$760$	−7.57784	−0.274877
$761$	−39.0424	−1.41529	−0.707644	−	0.706569i	$-0.750242\pi$
$761$	−39.0424	−1.41529	−0.707644	+	0.706569i	$0.750242\pi$
$762$	−2.77198	−0.100418
$763$	−22.3414	−0.808814
$764$	2.07731	0.0751544
$765$	5.71359	0.206575
$766$	52.1080	1.88274
$767$	−0.174223	−0.00629083
$768$	0.470762	0.0169872
$769$	8.42423	0.303786	0.151893	−	0.988397i	$-0.451463\pi$
$769$	8.42423	0.303786	0.151893	+	0.988397i	$0.451463\pi$
$770$	4.92065	0.177328
$771$	−1.62027	−0.0583525
$772$	−0.727349	−0.0261778
$773$	−11.6946	−0.420624	−0.210312	−	0.977634i	$-0.567448\pi$
$773$	−11.6946	−0.420624	−0.210312	+	0.977634i	$0.567448\pi$
$774$	−4.06843	−0.146237
$775$	−8.72729	−0.313494
$776$	−33.0391	−1.18604
$777$	1.91158	0.0685777
$778$	−46.4636	−1.66580
$779$	−1.19342	−0.0427586
$780$	−0.00114068	−4.08430e−5 0
$781$	−0.977318	−0.0349712
$782$	7.35153	0.262890
$783$	1.88886	0.0675023
$784$	12.9007	0.460738
$785$	25.0925	0.895591
$786$	−2.71275	−0.0967605
$787$	−33.9481	−1.21012	−0.605060	−	0.796180i	$-0.706851\pi$
$787$	−33.9481	−1.21012	−0.605060	+	0.796180i	$0.706851\pi$
$788$	0.181670	0.00647174
$789$	1.75549	0.0624970
$790$	−2.36714	−0.0842191
$791$	13.1273	0.466754
$792$	−8.68253	−0.308520
$793$	0.252935	0.00898197
$794$	32.3124	1.14673
$795$	0.714760	0.0253499
$796$	−1.66222	−0.0589158
$797$	−25.3216	−0.896937	−0.448468	−	0.893799i	$-0.648030\pi$
$797$	−25.3216	−0.896937	−0.448468	+	0.893799i	$0.648030\pi$
$798$	0.510665	0.0180774
$799$	−4.75094	−0.168076
$800$	−0.999794	−0.0353480
$801$	−33.8113	−1.19467
$802$	−38.9341	−1.37481
$803$	−9.22135	−0.325415
$804$	0.0512606	0.00180782
$805$	19.3873	0.683313
$806$	−0.272520	−0.00959910
$807$	−4.55559	−0.160364
$808$	30.1260	1.05983
$809$	5.11787	0.179935	0.0899674	−	0.995945i	$-0.471324\pi$
$809$	5.11787	0.179935	0.0899674	+	0.995945i	$0.471324\pi$
$810$	23.0756	0.810796
$811$	4.70926	0.165365	0.0826823	−	0.996576i	$-0.473651\pi$
$811$	4.70926	0.165365	0.0826823	+	0.996576i	$0.473651\pi$
$812$	0.541633	0.0190076
$813$	−0.354450	−0.0124311
$814$	−9.46454	−0.331732
$815$	−28.1203	−0.985010
$816$	−0.545622	−0.0191006
$817$	1.35507	0.0474077
$818$	45.1765	1.57956
$819$	−0.168768	−0.00589724
$820$	0.226605	0.00791339
$821$	−18.5969	−0.649038	−0.324519	−	0.945879i	$-0.605202\pi$
$821$	−18.5969	−0.649038	−0.324519	+	0.945879i	$0.605202\pi$
$822$	−2.60746	−0.0909455
$823$	0.454979	0.0158596	0.00792979	−	0.999969i	$-0.497476\pi$
$823$	0.454979	0.0158596	0.00792979	+	0.999969i	$0.497476\pi$
$824$	22.4001	0.780343
$825$	−0.193932	−0.00675186
$826$	−14.8100	−0.515305
$827$	−10.5527	−0.366954	−0.183477	−	0.983024i	$-0.558735\pi$
$827$	−10.5527	−0.366954	−0.183477	+	0.983024i	$0.558735\pi$
$828$	−2.14998	−0.0747171
$829$	−0.843013	−0.0292791	−0.0146395	−	0.999893i	$-0.504660\pi$
$829$	−0.843013	−0.0292791	−0.0146395	+	0.999893i	$0.504660\pi$
$830$	9.54015	0.331143
$831$	3.95724	0.137275
$832$	−0.255346	−0.00885253
$833$	3.47375	0.120358
$834$	0.971249	0.0336316
$835$	15.7951	0.546611
$836$	0.181750	0.00628594
$837$	5.80727	0.200729
$838$	24.9241	0.860990
$839$	19.4424	0.671226	0.335613	−	0.942000i	$-0.391057\pi$
$839$	19.4424	0.671226	0.335613	+	0.942000i	$0.391057\pi$
$840$	−1.54284	−0.0532330
$841$	−24.3754	−0.840533
$842$	10.5051	0.362029
$843$	−2.16037	−0.0744070
$844$	3.32291	0.114379
$845$	−24.9366	−0.857845
$846$	−19.3288	−0.664539
$847$	−1.87783	−0.0645231
$848$	9.41827	0.323425
$849$	1.55505	0.0533691
$850$	1.80307	0.0618449
$851$	−37.2902	−1.27829
$852$	0.0192587	0.000659793 0
$853$	10.3073	0.352916	0.176458	−	0.984308i	$-0.443536\pi$
$853$	10.3073	0.352916	0.176458	+	0.984308i	$0.443536\pi$
$854$	21.5009	0.735746
$855$	−7.74229	−0.264781
$856$	6.89347	0.235614
$857$	−53.0582	−1.81244	−0.906218	−	0.422812i	$-0.861043\pi$
$857$	−53.0582	−1.81244	−0.906218	+	0.422812i	$0.861043\pi$
$858$	−0.00605576	−0.000206740 0
$859$	53.9068	1.83928	0.919638	−	0.392767i	$-0.128482\pi$
$859$	53.9068	1.83928	0.919638	+	0.392767i	$0.128482\pi$
$860$	−0.257299	−0.00877382
$861$	−0.242978	−0.00828066
$862$	12.8958	0.439234
$863$	−16.5605	−0.563725	−0.281862	−	0.959455i	$-0.590952\pi$
$863$	−16.5605	−0.563725	−0.281862	+	0.959455i	$0.590952\pi$
$864$	0.665277	0.0226332
$865$	−3.12496	−0.106252
$866$	−16.0622	−0.545817
$867$	−0.146919	−0.00498963
$868$	1.66524	0.0565221
$869$	0.903356	0.0306443
$870$	−0.827901	−0.0280685
$871$	−0.0784948	−0.00265970
$872$	−34.6829	−1.17451
$873$	−33.7561	−1.14247
$874$	−9.96180	−0.336963
$875$	22.7666	0.769651
$876$	0.181713	0.00613952
$877$	−47.6098	−1.60767	−0.803834	−	0.594854i	$-0.797210\pi$
$877$	−47.6098	−1.60767	−0.803834	+	0.594854i	$0.797210\pi$
$878$	25.0827	0.846499
$879$	−2.69399	−0.0908662
$880$	7.12423	0.240158
$881$	31.2678	1.05344	0.526719	−	0.850040i	$-0.323422\pi$
$881$	31.2678	1.05344	0.526719	+	0.850040i	$0.323422\pi$
$882$	14.1327	0.475872
$883$	48.6282	1.63647	0.818234	−	0.574885i	$-0.194953\pi$
$883$	48.6282	1.63647	0.818234	+	0.574885i	$0.194953\pi$
$884$	−0.00404727	−0.000136125 0
$885$	−1.62727	−0.0547000
$886$	3.76104	0.126355
$887$	31.5365	1.05889	0.529445	−	0.848344i	$-0.322400\pi$
$887$	31.5365	1.05889	0.529445	+	0.848344i	$0.322400\pi$
$888$	2.96755	0.0995845
$889$	−25.9375	−0.869914
$890$	29.7470	0.997120
$891$	−8.80620	−0.295019
$892$	0.00349384	0.000116982 0
$893$	6.43783	0.215434
$894$	−3.51825	−0.117668
$895$	−31.1217	−1.04028
$896$	−18.8613	−0.630111
$897$	−0.0238596	−0.000796650 0
$898$	−16.4143	−0.547753
$899$	14.2181	0.474201
$900$	−0.527316	−0.0175772
$901$	2.53605	0.0844880
$902$	1.20302	0.0400562
$903$	0.275889	0.00918102
$904$	20.3789	0.677792
$905$	10.2733	0.341497
$906$	−4.15923	−0.138181
$907$	−22.2693	−0.739440	−0.369720	−	0.929143i	$-0.620546\pi$
$907$	−22.2693	−0.739440	−0.369720	+	0.929143i	$0.620546\pi$
$908$	−0.627221	−0.0208151
$909$	30.7798	1.02090
$910$	0.148481	0.00492210
$911$	33.0034	1.09345	0.546725	−	0.837312i	$-0.315874\pi$
$911$	33.0034	1.09345	0.546725	+	0.837312i	$0.315874\pi$
$912$	0.739353	0.0244824
$913$	−3.64074	−0.120491
$914$	−27.1944	−0.899510
$915$	2.36244	0.0781000
$916$	2.53326	0.0837013
$917$	−25.3832	−0.838228
$918$	−1.19979	−0.0395990
$919$	16.7884	0.553798	0.276899	−	0.960899i	$-0.410693\pi$
$919$	16.7884	0.553798	0.276899	+	0.960899i	$0.410693\pi$
$920$	30.0969	0.992266
$921$	1.05167	0.0346538
$922$	−8.97216	−0.295483
$923$	−0.0294907	−0.000970698 0
$924$	0.0370040	0.00121734
$925$	−9.14599	−0.300718
$926$	−7.48303	−0.245908
$927$	22.8862	0.751680
$928$	1.62882	0.0534687
$929$	−12.6269	−0.414276	−0.207138	−	0.978312i	$-0.566415\pi$
$929$	−12.6269	−0.414276	−0.207138	+	0.978312i	$0.566415\pi$
$930$	−2.54537	−0.0834660
$931$	−4.70715	−0.154271
$932$	−2.78433	−0.0912038
$933$	−2.52147	−0.0825493
$934$	19.7376	0.645833
$935$	1.91833	0.0627362
$936$	−0.261997	−0.00856362
$937$	14.9118	0.487148	0.243574	−	0.969882i	$-0.421680\pi$
$937$	14.9118	0.487148	0.243574	+	0.969882i	$0.421680\pi$
$938$	−6.67252	−0.217865
$939$	3.73569	0.121910
$940$	−1.22241	−0.0398707
$941$	−19.0971	−0.622549	−0.311275	−	0.950320i	$-0.600756\pi$
$941$	−19.0971	−0.622549	−0.311275	+	0.950320i	$0.600756\pi$
$942$	−2.62506	−0.0855292
$943$	4.73989	0.154352
$944$	−21.4423	−0.697886
$945$	−3.16406	−0.102927
$946$	−1.36597	−0.0444115
$947$	9.41767	0.306033	0.153017	−	0.988224i	$-0.451101\pi$
$947$	9.41767	0.306033	0.153017	+	0.988224i	$0.451101\pi$
$948$	−0.0178013	−0.000578158 0
$949$	−0.278256	−0.00903256
$950$	−2.44328	−0.0792705
$951$	1.34710	0.0436828
$952$	−5.47417	−0.177419
$953$	37.2867	1.20784	0.603918	−	0.797046i	$-0.293605\pi$
$953$	37.2867	1.20784	0.603918	+	0.797046i	$0.293605\pi$
$954$	10.3177	0.334049
$955$	−29.7106	−0.961413
$956$	0.930041	0.0300797
$957$	0.315946	0.0102131
$958$	−14.8654	−0.480279
$959$	−24.3980	−0.787853
$960$	−2.38497	−0.0769745
$961$	12.7135	0.410112
$962$	−0.285594	−0.00920791
$963$	7.04306	0.226960
$964$	0.146532	0.00471949
$965$	10.4029	0.334880
$966$	−2.02821	−0.0652565
$967$	40.2861	1.29551	0.647757	−	0.761847i	$-0.275707\pi$
$967$	40.2861	1.29551	0.647757	+	0.761847i	$0.275707\pi$
$968$	−2.91515	−0.0936965
$969$	0.199085	0.00639553
$970$	29.6984	0.953558
$971$	0.988071	0.0317087	0.0158543	−	0.999874i	$-0.494953\pi$
$971$	0.988071	0.0317087	0.0158543	+	0.999874i	$0.494953\pi$
$972$	0.526959	0.0169022
$973$	9.08799	0.291348
$974$	−43.2718	−1.38652
$975$	−0.00585193	−0.000187412 0
$976$	31.1295	0.996432
$977$	52.7088	1.68630	0.843152	−	0.537676i	$-0.180698\pi$
$977$	52.7088	1.68630	0.843152	+	0.537676i	$0.180698\pi$
$978$	2.94181	0.0940687
$979$	−11.3521	−0.362816
$980$	0.893791	0.0285511
$981$	−35.4356	−1.13137
$982$	−40.7003	−1.29880
$983$	−31.3275	−0.999191	−0.499596	−	0.866259i	$-0.666518\pi$
$983$	−31.3275	−0.999191	−0.499596	+	0.866259i	$0.666518\pi$
$984$	−0.377200	−0.0120247
$985$	−2.59833	−0.0827898
$986$	−2.93749	−0.0935487
$987$	1.31073	0.0417211
$988$	0.00548432	0.000174479 0
$989$	−5.38191	−0.171135
$990$	7.80460	0.248046
$991$	−30.7422	−0.976557	−0.488279	−	0.872688i	$-0.662375\pi$
$991$	−30.7422	−0.976557	−0.488279	+	0.872688i	$0.662375\pi$
$992$	5.00779	0.158997
$993$	−5.23297	−0.166063
$994$	−2.50688	−0.0795135
$995$	23.7738	0.753681
$996$	0.0717433	0.00227327
$997$	50.9794	1.61453	0.807266	−	0.590187i	$-0.200946\pi$
$997$	50.9794	1.61453	0.807266	+	0.590187i	$0.200946\pi$
$998$	−23.4706	−0.742949
$999$	6.08587	0.192548

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.45	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.45	✓	66	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)

\(f(q)\)	\(=\)	\(q+1.36597 q^{2} -0.146919 q^{3} -0.134126 q^{4} +1.91833 q^{5} -0.200687 q^{6} -1.87783 q^{7} -2.91515 q^{8} -2.97841 q^{9} +O(q^{10})\)	\(q+1.36597 q^{2} -0.146919 q^{3} -0.134126 q^{4} +1.91833 q^{5} -0.200687 q^{6} -1.87783 q^{7} -2.91515 q^{8} -2.97841 q^{9} +2.62039 q^{10} -1.00000 q^{11} +0.0197057 q^{12} -0.0301751 q^{13} -2.56506 q^{14} -0.281840 q^{15} -3.71376 q^{16} -1.00000 q^{17} -4.06843 q^{18} +1.35507 q^{19} -0.257299 q^{20} +0.275889 q^{21} -1.36597 q^{22} -5.38191 q^{23} +0.428291 q^{24} -1.31999 q^{25} -0.0412183 q^{26} +0.878343 q^{27} +0.251866 q^{28} +2.15048 q^{29} -0.384985 q^{30} +6.61162 q^{31} +0.757423 q^{32} +0.146919 q^{33} -1.36597 q^{34} -3.60231 q^{35} +0.399483 q^{36} +6.92881 q^{37} +1.85098 q^{38} +0.00443330 q^{39} -5.59224 q^{40} -0.880708 q^{41} +0.376857 q^{42} +1.00000 q^{43} +0.134126 q^{44} -5.71359 q^{45} -7.35153 q^{46} +4.75094 q^{47} +0.545622 q^{48} -3.47375 q^{49} -1.80307 q^{50} +0.146919 q^{51} +0.00404727 q^{52} -2.53605 q^{53} +1.19979 q^{54} -1.91833 q^{55} +5.47417 q^{56} -0.199085 q^{57} +2.93749 q^{58} +5.77373 q^{59} +0.0378021 q^{60} -8.38222 q^{61} +9.03127 q^{62} +5.59296 q^{63} +8.46213 q^{64} -0.0578860 q^{65} +0.200687 q^{66} +2.60131 q^{67} +0.134126 q^{68} +0.790705 q^{69} -4.92065 q^{70} +0.977318 q^{71} +8.68253 q^{72} +9.22135 q^{73} +9.46454 q^{74} +0.193932 q^{75} -0.181750 q^{76} +1.87783 q^{77} +0.00605576 q^{78} -0.903356 q^{79} -7.12423 q^{80} +8.80620 q^{81} -1.20302 q^{82} +3.64074 q^{83} -0.0370040 q^{84} -1.91833 q^{85} +1.36597 q^{86} -0.315946 q^{87} +2.91515 q^{88} +11.3521 q^{89} -7.80460 q^{90} +0.0566638 q^{91} +0.721855 q^{92} -0.971373 q^{93} +6.48964 q^{94} +2.59947 q^{95} -0.111280 q^{96} +11.3336 q^{97} -4.74503 q^{98} +2.97841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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