LMFDB - Embedded newform 6015.2.a.i.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.87550 q^{2} +1.00000 q^{3} +1.51750 q^{4} +1.00000 q^{5} -1.87550 q^{6} +3.82548 q^{7} +0.904923 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.87550 q^{2} +1.00000 q^{3} +1.51750 q^{4} +1.00000 q^{5} -1.87550 q^{6} +3.82548 q^{7} +0.904923 q^{8} +1.00000 q^{9} -1.87550 q^{10} -2.14290 q^{11} +1.51750 q^{12} +4.52353 q^{13} -7.17469 q^{14} +1.00000 q^{15} -4.73219 q^{16} -1.16897 q^{17} -1.87550 q^{18} +3.17673 q^{19} +1.51750 q^{20} +3.82548 q^{21} +4.01902 q^{22} +0.00651434 q^{23} +0.904923 q^{24} +1.00000 q^{25} -8.48388 q^{26} +1.00000 q^{27} +5.80518 q^{28} -5.46712 q^{29} -1.87550 q^{30} -10.5654 q^{31} +7.06538 q^{32} -2.14290 q^{33} +2.19241 q^{34} +3.82548 q^{35} +1.51750 q^{36} +4.75719 q^{37} -5.95796 q^{38} +4.52353 q^{39} +0.904923 q^{40} -1.97464 q^{41} -7.17469 q^{42} +10.9491 q^{43} -3.25186 q^{44} +1.00000 q^{45} -0.0122176 q^{46} -2.99515 q^{47} -4.73219 q^{48} +7.63430 q^{49} -1.87550 q^{50} -1.16897 q^{51} +6.86447 q^{52} +6.01406 q^{53} -1.87550 q^{54} -2.14290 q^{55} +3.46177 q^{56} +3.17673 q^{57} +10.2536 q^{58} +7.75493 q^{59} +1.51750 q^{60} +2.82888 q^{61} +19.8155 q^{62} +3.82548 q^{63} -3.78675 q^{64} +4.52353 q^{65} +4.01902 q^{66} +5.61052 q^{67} -1.77392 q^{68} +0.00651434 q^{69} -7.17469 q^{70} -15.8178 q^{71} +0.904923 q^{72} +1.53092 q^{73} -8.92212 q^{74} +1.00000 q^{75} +4.82070 q^{76} -8.19763 q^{77} -8.48388 q^{78} -9.93869 q^{79} -4.73219 q^{80} +1.00000 q^{81} +3.70344 q^{82} +11.0282 q^{83} +5.80518 q^{84} -1.16897 q^{85} -20.5351 q^{86} -5.46712 q^{87} -1.93916 q^{88} +3.41512 q^{89} -1.87550 q^{90} +17.3047 q^{91} +0.00988553 q^{92} -10.5654 q^{93} +5.61741 q^{94} +3.17673 q^{95} +7.06538 q^{96} +11.6573 q^{97} -14.3181 q^{98} -2.14290 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) $ 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * 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 $

$2$	−1.87550	−1.32618	−0.663090	−	0.748540i	$-0.730755\pi$
$2$	−1.87550	−1.32618	−0.663090	+	0.748540i	$0.730755\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.51750	0.758752
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.87550	−0.765670
$7$	3.82548	1.44590	0.722948	−	0.690903i	$-0.242787\pi$
$7$	3.82548	1.44590	0.722948	+	0.690903i	$0.242787\pi$
$8$	0.904923	0.319939
$9$	1.00000	0.333333
$10$	−1.87550	−0.593085
$11$	−2.14290	−0.646109	−0.323055	−	0.946380i	$-0.604710\pi$
$11$	−2.14290	−0.646109	−0.323055	+	0.946380i	$0.604710\pi$
$12$	1.51750	0.438065
$13$	4.52353	1.25460	0.627300	−	0.778778i	$-0.284160\pi$
$13$	4.52353	1.25460	0.627300	+	0.778778i	$0.284160\pi$
$14$	−7.17469	−1.91752
$15$	1.00000	0.258199
$16$	−4.73219	−1.18305
$17$	−1.16897	−0.283517	−0.141759	−	0.989901i	$-0.545276\pi$
$17$	−1.16897	−0.283517	−0.141759	+	0.989901i	$0.545276\pi$
$18$	−1.87550	−0.442060
$19$	3.17673	0.728792	0.364396	−	0.931244i	$-0.381275\pi$
$19$	3.17673	0.728792	0.364396	+	0.931244i	$0.381275\pi$
$20$	1.51750	0.339324
$21$	3.82548	0.834788
$22$	4.01902	0.856857
$23$	0.00651434	0.00135833	0.000679167	−	1.00000i	$-0.499784\pi$
$23$	0.00651434	0.00135833	0.000679167		1.00000i	$0.499784\pi$
$24$	0.904923	0.184717
$25$	1.00000	0.200000
$26$	−8.48388	−1.66383
$27$	1.00000	0.192450
$28$	5.80518	1.09708
$29$	−5.46712	−1.01522	−0.507609	−	0.861587i	$-0.669471\pi$
$29$	−5.46712	−1.01522	−0.507609	+	0.861587i	$0.669471\pi$
$30$	−1.87550	−0.342418
$31$	−10.5654	−1.89761	−0.948803	−	0.315870i	$-0.897704\pi$
$31$	−10.5654	−1.89761	−0.948803	+	0.315870i	$0.897704\pi$
$32$	7.06538	1.24899
$33$	−2.14290	−0.373031
$34$	2.19241	0.375995
$35$	3.82548	0.646624
$36$	1.51750	0.252917
$37$	4.75719	0.782078	0.391039	−	0.920374i	$-0.372116\pi$
$37$	4.75719	0.782078	0.391039	+	0.920374i	$0.372116\pi$
$38$	−5.95796	−0.966509
$39$	4.52353	0.724344
$40$	0.904923	0.143081
$41$	−1.97464	−0.308387	−0.154194	−	0.988041i	$-0.549278\pi$
$41$	−1.97464	−0.308387	−0.154194	+	0.988041i	$0.549278\pi$
$42$	−7.17469	−1.10708
$43$	10.9491	1.66973	0.834863	−	0.550458i	$-0.185547\pi$
$43$	10.9491	1.66973	0.834863	+	0.550458i	$0.185547\pi$
$44$	−3.25186	−0.490237
$45$	1.00000	0.149071
$46$	−0.0122176	−0.00180139
$47$	−2.99515	−0.436888	−0.218444	−	0.975850i	$-0.570098\pi$
$47$	−2.99515	−0.436888	−0.218444	+	0.975850i	$0.570098\pi$
$48$	−4.73219	−0.683033
$49$	7.63430	1.09061
$50$	−1.87550	−0.265236
$51$	−1.16897	−0.163689
$52$	6.86447	0.951930
$53$	6.01406	0.826095	0.413047	−	0.910710i	$-0.364464\pi$
$53$	6.01406	0.826095	0.413047	+	0.910710i	$0.364464\pi$
$54$	−1.87550	−0.255223
$55$	−2.14290	−0.288949
$56$	3.46177	0.462598
$57$	3.17673	0.420768
$58$	10.2536	1.34636
$59$	7.75493	1.00961	0.504803	−	0.863234i	$-0.331565\pi$
$59$	7.75493	1.00961	0.504803	+	0.863234i	$0.331565\pi$
$60$	1.51750	0.195909
$61$	2.82888	0.362201	0.181101	−	0.983465i	$-0.442034\pi$
$61$	2.82888	0.362201	0.181101	+	0.983465i	$0.442034\pi$
$62$	19.8155	2.51656
$63$	3.82548	0.481965
$64$	−3.78675	−0.473343
$65$	4.52353	0.561074
$66$	4.01902	0.494707
$67$	5.61052	0.685434	0.342717	−	0.939439i	$-0.388653\pi$
$67$	5.61052	0.685434	0.342717	+	0.939439i	$0.388653\pi$
$68$	−1.77392	−0.215119
$69$	0.00651434	0.000784234 0
$70$	−7.17469	−0.857540
$71$	−15.8178	−1.87722	−0.938612	−	0.344975i	$-0.887888\pi$
$71$	−15.8178	−1.87722	−0.938612	+	0.344975i	$0.887888\pi$
$72$	0.904923	0.106646
$73$	1.53092	0.179180	0.0895900	−	0.995979i	$-0.471444\pi$
$73$	1.53092	0.179180	0.0895900	+	0.995979i	$0.471444\pi$
$74$	−8.92212	−1.03718
$75$	1.00000	0.115470
$76$	4.82070	0.552972
$77$	−8.19763	−0.934207
$78$	−8.48388	−0.960610
$79$	−9.93869	−1.11819	−0.559095	−	0.829103i	$-0.688851\pi$
$79$	−9.93869	−1.11819	−0.559095	+	0.829103i	$0.688851\pi$
$80$	−4.73219	−0.529075
$81$	1.00000	0.111111
$82$	3.70344	0.408977
$83$	11.0282	1.21051	0.605254	−	0.796033i	$-0.293072\pi$
$83$	11.0282	1.21051	0.605254	+	0.796033i	$0.293072\pi$
$84$	5.80518	0.633397
$85$	−1.16897	−0.126793
$86$	−20.5351	−2.21435
$87$	−5.46712	−0.586137
$88$	−1.93916	−0.206715
$89$	3.41512	0.362002	0.181001	−	0.983483i	$-0.442066\pi$
$89$	3.41512	0.362002	0.181001	+	0.983483i	$0.442066\pi$
$90$	−1.87550	−0.197695
$91$	17.3047	1.81402
$92$	0.00988553	0.00103064
$93$	−10.5654	−1.09558
$94$	5.61741	0.579391
$95$	3.17673	0.325926
$96$	7.06538	0.721107
$97$	11.6573	1.18362	0.591808	−	0.806079i	$-0.298415\pi$
$97$	11.6573	1.18362	0.591808	+	0.806079i	$0.298415\pi$
$98$	−14.3181	−1.44635
$99$	−2.14290	−0.215370
$100$	1.51750	0.151750
$101$	12.7785	1.27151	0.635753	−	0.771892i	$-0.280690\pi$
$101$	12.7785	1.27151	0.635753	+	0.771892i	$0.280690\pi$
$102$	2.19241	0.217081
$103$	6.84450	0.674409	0.337204	−	0.941431i	$-0.390519\pi$
$103$	6.84450	0.674409	0.337204	+	0.941431i	$0.390519\pi$
$104$	4.09344	0.401395
$105$	3.82548	0.373329
$106$	−11.2794	−1.09555
$107$	0.336700	0.0325500	0.0162750	−	0.999868i	$-0.494819\pi$
$107$	0.336700	0.0325500	0.0162750	+	0.999868i	$0.494819\pi$
$108$	1.51750	0.146022
$109$	14.1858	1.35876	0.679379	−	0.733788i	$-0.262249\pi$
$109$	14.1858	1.35876	0.679379	+	0.733788i	$0.262249\pi$
$110$	4.01902	0.383198
$111$	4.75719	0.451533
$112$	−18.1029	−1.71056
$113$	9.72770	0.915105	0.457553	−	0.889183i	$-0.348726\pi$
$113$	9.72770	0.915105	0.457553	+	0.889183i	$0.348726\pi$
$114$	−5.95796	−0.558014
$115$	0.00651434	0.000607465 0
$116$	−8.29637	−0.770299
$117$	4.52353	0.418200
$118$	−14.5444	−1.33892
$119$	−4.47188	−0.409937
$120$	0.904923	0.0826078
$121$	−6.40797	−0.582543
$122$	−5.30557	−0.480344
$123$	−1.97464	−0.178048
$124$	−16.0331	−1.43981
$125$	1.00000	0.0894427
$126$	−7.17469	−0.639172
$127$	−0.598877	−0.0531417	−0.0265709	−	0.999647i	$-0.508459\pi$
$127$	−0.598877	−0.0531417	−0.0265709	+	0.999647i	$0.508459\pi$
$128$	−7.02872	−0.621257
$129$	10.9491	0.964016
$130$	−8.48388	−0.744085
$131$	6.56405	0.573504	0.286752	−	0.958005i	$-0.407424\pi$
$131$	6.56405	0.573504	0.286752	+	0.958005i	$0.407424\pi$
$132$	−3.25186	−0.283038
$133$	12.1525	1.05376
$134$	−10.5225	−0.909008
$135$	1.00000	0.0860663
$136$	−1.05783	−0.0907082
$137$	13.1830	1.12630	0.563151	−	0.826354i	$-0.309589\pi$
$137$	13.1830	1.12630	0.563151	+	0.826354i	$0.309589\pi$
$138$	−0.0122176	−0.00104004
$139$	−2.21752	−0.188087	−0.0940437	−	0.995568i	$-0.529979\pi$
$139$	−2.21752	−0.188087	−0.0940437	+	0.995568i	$0.529979\pi$
$140$	5.80518	0.490627
$141$	−2.99515	−0.252237
$142$	29.6662	2.48954
$143$	−9.69348	−0.810609
$144$	−4.73219	−0.394349
$145$	−5.46712	−0.454019
$146$	−2.87123	−0.237625
$147$	7.63430	0.629666
$148$	7.21906	0.593403
$149$	−16.8286	−1.37865	−0.689325	−	0.724452i	$-0.742093\pi$
$149$	−16.8286	−1.37865	−0.689325	+	0.724452i	$0.742093\pi$
$150$	−1.87550	−0.153134
$151$	−1.83239	−0.149118	−0.0745588	−	0.997217i	$-0.523755\pi$
$151$	−1.83239	−0.149118	−0.0745588	+	0.997217i	$0.523755\pi$
$152$	2.87470	0.233169
$153$	−1.16897	−0.0945058
$154$	15.3747	1.23893
$155$	−10.5654	−0.848635
$156$	6.86447	0.549597
$157$	−10.6088	−0.846671	−0.423336	−	0.905973i	$-0.639141\pi$
$157$	−10.6088	−0.846671	−0.423336	+	0.905973i	$0.639141\pi$
$158$	18.6400	1.48292
$159$	6.01406	0.476946
$160$	7.06538	0.558567
$161$	0.0249205	0.00196401
$162$	−1.87550	−0.147353
$163$	18.7218	1.46640	0.733202	−	0.680011i	$-0.238025\pi$
$163$	18.7218	1.46640	0.733202	+	0.680011i	$0.238025\pi$
$164$	−2.99653	−0.233989
$165$	−2.14290	−0.166825
$166$	−20.6835	−1.60535
$167$	−10.1738	−0.787275	−0.393637	−	0.919266i	$-0.628783\pi$
$167$	−10.1738	−0.787275	−0.393637	+	0.919266i	$0.628783\pi$
$168$	3.46177	0.267081
$169$	7.46229	0.574022
$170$	2.19241	0.168150
$171$	3.17673	0.242931
$172$	16.6153	1.26691
$173$	−5.33300	−0.405460	−0.202730	−	0.979235i	$-0.564981\pi$
$173$	−5.33300	−0.405460	−0.202730	+	0.979235i	$0.564981\pi$
$174$	10.2536	0.777322
$175$	3.82548	0.289179
$176$	10.1406	0.764378
$177$	7.75493	0.582897
$178$	−6.40505	−0.480079
$179$	0.563738	0.0421358	0.0210679	−	0.999778i	$-0.493293\pi$
$179$	0.563738	0.0421358	0.0210679	+	0.999778i	$0.493293\pi$
$180$	1.51750	0.113108
$181$	1.44667	0.107530	0.0537650	−	0.998554i	$-0.482878\pi$
$181$	1.44667	0.107530	0.0537650	+	0.998554i	$0.482878\pi$
$182$	−32.4549	−2.40572
$183$	2.82888	0.209117
$184$	0.00589498	0.000434584 0
$185$	4.75719	0.349756
$186$	19.8155	1.45294
$187$	2.50499	0.183183
$188$	−4.54515	−0.331489
$189$	3.82548	0.278263
$190$	−5.95796	−0.432236
$191$	25.8790	1.87254	0.936270	−	0.351280i	$-0.114254\pi$
$191$	25.8790	1.87254	0.936270	+	0.351280i	$0.114254\pi$
$192$	−3.78675	−0.273285
$193$	17.2892	1.24451	0.622253	−	0.782816i	$-0.286217\pi$
$193$	17.2892	1.24451	0.622253	+	0.782816i	$0.286217\pi$
$194$	−21.8632	−1.56969
$195$	4.52353	0.323936
$196$	11.5851	0.827505
$197$	−6.02336	−0.429147	−0.214573	−	0.976708i	$-0.568836\pi$
$197$	−6.02336	−0.429147	−0.214573	+	0.976708i	$0.568836\pi$
$198$	4.01902	0.285619
$199$	6.46717	0.458446	0.229223	−	0.973374i	$-0.426382\pi$
$199$	6.46717	0.458446	0.229223	+	0.973374i	$0.426382\pi$
$200$	0.904923	0.0639877
$201$	5.61052	0.395735
$202$	−23.9660	−1.68625
$203$	−20.9144	−1.46790
$204$	−1.77392	−0.124199
$205$	−1.97464	−0.137915
$206$	−12.8369	−0.894387
$207$	0.00651434	0.000452778 0
$208$	−21.4062	−1.48425
$209$	−6.80742	−0.470879
$210$	−7.17469	−0.495101
$211$	−1.40047	−0.0964122	−0.0482061	−	0.998837i	$-0.515350\pi$
$211$	−1.40047	−0.0964122	−0.0482061	+	0.998837i	$0.515350\pi$
$212$	9.12636	0.626801
$213$	−15.8178	−1.08382
$214$	−0.631480	−0.0431671
$215$	10.9491	0.746724
$216$	0.904923	0.0615722
$217$	−40.4178	−2.74374
$218$	−26.6056	−1.80196
$219$	1.53092	0.103450
$220$	−3.25186	−0.219240
$221$	−5.28788	−0.355701
$222$	−8.92212	−0.598813
$223$	−16.4482	−1.10146	−0.550728	−	0.834685i	$-0.685650\pi$
$223$	−16.4482	−1.10146	−0.550728	+	0.834685i	$0.685650\pi$
$224$	27.0285	1.80592
$225$	1.00000	0.0666667
$226$	−18.2443	−1.21359
$227$	22.3772	1.48523	0.742614	−	0.669719i	$-0.233586\pi$
$227$	22.3772	1.48523	0.742614	+	0.669719i	$0.233586\pi$
$228$	4.82070	0.319258
$229$	−16.7874	−1.10934	−0.554671	−	0.832069i	$-0.687156\pi$
$229$	−16.7874	−1.10934	−0.554671	+	0.832069i	$0.687156\pi$
$230$	−0.0122176	−0.000805608 0
$231$	−8.19763	−0.539365
$232$	−4.94732	−0.324808
$233$	−21.4201	−1.40328	−0.701640	−	0.712532i	$-0.747548\pi$
$233$	−21.4201	−1.40328	−0.701640	+	0.712532i	$0.747548\pi$
$234$	−8.48388	−0.554608
$235$	−2.99515	−0.195382
$236$	11.7681	0.766040
$237$	−9.93869	−0.645588
$238$	8.38701	0.543649
$239$	−20.6037	−1.33275	−0.666373	−	0.745619i	$-0.732154\pi$
$239$	−20.6037	−1.33275	−0.666373	+	0.745619i	$0.732154\pi$
$240$	−4.73219	−0.305462
$241$	−4.92229	−0.317072	−0.158536	−	0.987353i	$-0.550677\pi$
$241$	−4.92229	−0.317072	−0.158536	+	0.987353i	$0.550677\pi$
$242$	12.0181	0.772556
$243$	1.00000	0.0641500
$244$	4.29284	0.274821
$245$	7.63430	0.487737
$246$	3.70344	0.236123
$247$	14.3700	0.914343
$248$	−9.56089	−0.607117
$249$	11.0282	0.698887
$250$	−1.87550	−0.118617
$251$	−4.73669	−0.298977	−0.149489	−	0.988763i	$-0.547763\pi$
$251$	−4.73669	−0.298977	−0.149489	+	0.988763i	$0.547763\pi$
$252$	5.80518	0.365692
$253$	−0.0139596	−0.000877632 0
$254$	1.12319	0.0704755
$255$	−1.16897	−0.0732039
$256$	20.7559	1.29724
$257$	8.59769	0.536309	0.268154	−	0.963376i	$-0.413586\pi$
$257$	8.59769	0.536309	0.268154	+	0.963376i	$0.413586\pi$
$258$	−20.5351	−1.27846
$259$	18.1985	1.13080
$260$	6.86447	0.425716
$261$	−5.46712	−0.338406
$262$	−12.3109	−0.760569
$263$	−29.9733	−1.84823	−0.924115	−	0.382114i	$-0.875196\pi$
$263$	−29.9733	−1.84823	−0.924115	+	0.382114i	$0.875196\pi$
$264$	−1.93916	−0.119347
$265$	6.01406	0.369441
$266$	−22.7921	−1.39747
$267$	3.41512	0.209002
$268$	8.51398	0.520074
$269$	6.05294	0.369055	0.184527	−	0.982827i	$-0.440925\pi$
$269$	6.05294	0.369055	0.184527	+	0.982827i	$0.440925\pi$
$270$	−1.87550	−0.114139
$271$	−16.6696	−1.01261	−0.506305	−	0.862355i	$-0.668989\pi$
$271$	−16.6696	−1.01261	−0.506305	+	0.862355i	$0.668989\pi$
$272$	5.53180	0.335415
$273$	17.3047	1.04733
$274$	−24.7248	−1.49368
$275$	−2.14290	−0.129222
$276$	0.00988553	0.000595039 0
$277$	19.3318	1.16154	0.580768	−	0.814069i	$-0.302752\pi$
$277$	19.3318	1.16154	0.580768	+	0.814069i	$0.302752\pi$
$278$	4.15896	0.249438
$279$	−10.5654	−0.632535
$280$	3.46177	0.206880
$281$	6.13559	0.366018	0.183009	−	0.983111i	$-0.441416\pi$
$281$	6.13559	0.366018	0.183009	+	0.983111i	$0.441416\pi$
$282$	5.61741	0.334512
$283$	16.1906	0.962431	0.481215	−	0.876602i	$-0.340195\pi$
$283$	16.1906	0.962431	0.481215	+	0.876602i	$0.340195\pi$
$284$	−24.0035	−1.42435
$285$	3.17673	0.188173
$286$	18.1801	1.07501
$287$	−7.55396	−0.445896
$288$	7.06538	0.416332
$289$	−15.6335	−0.919618
$290$	10.2536	0.602111
$291$	11.6573	0.683360
$292$	2.32317	0.135953
$293$	−3.48448	−0.203566	−0.101783	−	0.994807i	$-0.532455\pi$
$293$	−3.48448	−0.203566	−0.101783	+	0.994807i	$0.532455\pi$
$294$	−14.3181	−0.835050
$295$	7.75493	0.451510
$296$	4.30490	0.250217
$297$	−2.14290	−0.124344
$298$	31.5620	1.82834
$299$	0.0294678	0.00170417
$300$	1.51750	0.0876131
$301$	41.8856	2.41425
$302$	3.43664	0.197757
$303$	12.7785	0.734105
$304$	−15.0329	−0.862195
$305$	2.82888	0.161981
$306$	2.19241	0.125332
$307$	−1.07377	−0.0612833	−0.0306416	−	0.999530i	$-0.509755\pi$
$307$	−1.07377	−0.0612833	−0.0306416	+	0.999530i	$0.509755\pi$
$308$	−12.4399	−0.708831
$309$	6.84450	0.389370
$310$	19.8155	1.12544
$311$	−12.7583	−0.723460	−0.361730	−	0.932283i	$-0.617814\pi$
$311$	−12.7583	−0.723460	−0.361730	+	0.932283i	$0.617814\pi$
$312$	4.09344	0.231746
$313$	18.7961	1.06242	0.531208	−	0.847241i	$-0.321738\pi$
$313$	18.7961	1.06242	0.531208	+	0.847241i	$0.321738\pi$
$314$	19.8967	1.12284
$315$	3.82548	0.215541
$316$	−15.0820	−0.848429
$317$	−4.85002	−0.272404	−0.136202	−	0.990681i	$-0.543490\pi$
$317$	−4.85002	−0.272404	−0.136202	+	0.990681i	$0.543490\pi$
$318$	−11.2794	−0.632516
$319$	11.7155	0.655942
$320$	−3.78675	−0.211685
$321$	0.336700	0.0187927
$322$	−0.0467384	−0.00260463
$323$	−3.71351	−0.206625
$324$	1.51750	0.0843057
$325$	4.52353	0.250920
$326$	−35.1128	−1.94472
$327$	14.1858	0.784479
$328$	−1.78690	−0.0986651
$329$	−11.4579	−0.631694
$330$	4.01902	0.221240
$331$	5.79767	0.318669	0.159334	−	0.987225i	$-0.449065\pi$
$331$	5.79767	0.318669	0.159334	+	0.987225i	$0.449065\pi$
$332$	16.7354	0.918474
$333$	4.75719	0.260693
$334$	19.0810	1.04407
$335$	5.61052	0.306535
$336$	−18.1029	−0.987594
$337$	17.7416	0.966446	0.483223	−	0.875497i	$-0.339466\pi$
$337$	17.7416	0.966446	0.483223	+	0.875497i	$0.339466\pi$
$338$	−13.9955	−0.761256
$339$	9.72770	0.528336
$340$	−1.77392	−0.0962043
$341$	22.6407	1.22606
$342$	−5.95796	−0.322170
$343$	2.42650	0.131019
$344$	9.90811	0.534210
$345$	0.00651434	0.000350720 0
$346$	10.0020	0.537713
$347$	26.0666	1.39933	0.699663	−	0.714473i	$-0.253333\pi$
$347$	26.0666	1.39933	0.699663	+	0.714473i	$0.253333\pi$
$348$	−8.29637	−0.444732
$349$	−4.60914	−0.246722	−0.123361	−	0.992362i	$-0.539367\pi$
$349$	−4.60914	−0.246722	−0.123361	+	0.992362i	$0.539367\pi$
$350$	−7.17469	−0.383503
$351$	4.52353	0.241448
$352$	−15.1404	−0.806987
$353$	−17.4775	−0.930231	−0.465116	−	0.885250i	$-0.653987\pi$
$353$	−17.4775	−0.930231	−0.465116	+	0.885250i	$0.653987\pi$
$354$	−14.5444	−0.773025
$355$	−15.8178	−0.839520
$356$	5.18245	0.274669
$357$	−4.47188	−0.236677
$358$	−1.05729	−0.0558796
$359$	6.20230	0.327345	0.163673	−	0.986515i	$-0.447666\pi$
$359$	6.20230	0.327345	0.163673	+	0.986515i	$0.447666\pi$
$360$	0.904923	0.0476936
$361$	−8.90839	−0.468862
$362$	−2.71323	−0.142604
$363$	−6.40797	−0.336331
$364$	26.2599	1.37639
$365$	1.53092	0.0801318
$366$	−5.30557	−0.277327
$367$	15.8000	0.824753	0.412376	−	0.911014i	$-0.364699\pi$
$367$	15.8000	0.824753	0.412376	+	0.911014i	$0.364699\pi$
$368$	−0.0308271	−0.00160697
$369$	−1.97464	−0.102796
$370$	−8.92212	−0.463839
$371$	23.0067	1.19445
$372$	−16.0331	−0.831275
$373$	−12.7044	−0.657809	−0.328905	−	0.944363i	$-0.606679\pi$
$373$	−12.7044	−0.657809	−0.328905	+	0.944363i	$0.606679\pi$
$374$	−4.69812	−0.242934
$375$	1.00000	0.0516398
$376$	−2.71038	−0.139777
$377$	−24.7307	−1.27369
$378$	−7.17469	−0.369026
$379$	6.67915	0.343085	0.171543	−	0.985177i	$-0.445125\pi$
$379$	6.67915	0.343085	0.171543	+	0.985177i	$0.445125\pi$
$380$	4.82070	0.247297
$381$	−0.598877	−0.0306814
$382$	−48.5361	−2.48332
$383$	−33.7484	−1.72446	−0.862232	−	0.506514i	$-0.830934\pi$
$383$	−33.7484	−1.72446	−0.862232	+	0.506514i	$0.830934\pi$
$384$	−7.02872	−0.358683
$385$	−8.19763	−0.417790
$386$	−32.4260	−1.65044
$387$	10.9491	0.556575
$388$	17.6899	0.898070
$389$	18.1300	0.919226	0.459613	−	0.888119i	$-0.347988\pi$
$389$	18.1300	0.919226	0.459613	+	0.888119i	$0.347988\pi$
$390$	−8.48388	−0.429598
$391$	−0.00761508	−0.000385111 0
$392$	6.90845	0.348930
$393$	6.56405	0.331113
$394$	11.2968	0.569125
$395$	−9.93869	−0.500070
$396$	−3.25186	−0.163412
$397$	−18.6059	−0.933805	−0.466902	−	0.884309i	$-0.654630\pi$
$397$	−18.6059	−0.933805	−0.466902	+	0.884309i	$0.654630\pi$
$398$	−12.1292	−0.607981
$399$	12.1525	0.608387
$400$	−4.73219	−0.236610
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−10.5225	−0.524816
$403$	−47.7929	−2.38074
$404$	19.3914	0.964757
$405$	1.00000	0.0496904
$406$	39.2249	1.94670
$407$	−10.1942	−0.505308
$408$	−1.05783	−0.0523704
$409$	35.0453	1.73288	0.866440	−	0.499282i	$-0.166403\pi$
$409$	35.0453	1.73288	0.866440	+	0.499282i	$0.166403\pi$
$410$	3.70344	0.182900
$411$	13.1830	0.650271
$412$	10.3866	0.511709
$413$	29.6663	1.45979
$414$	−0.0122176	−0.000600465 0
$415$	11.0282	0.541355
$416$	31.9604	1.56699
$417$	−2.21752	−0.108592
$418$	12.7673	0.624470
$419$	−7.72512	−0.377397	−0.188698	−	0.982035i	$-0.560427\pi$
$419$	−7.72512	−0.377397	−0.188698	+	0.982035i	$0.560427\pi$
$420$	5.80518	0.283264
$421$	−0.397701	−0.0193828	−0.00969138	−	0.999953i	$-0.503085\pi$
$421$	−0.397701	−0.0193828	−0.00969138	+	0.999953i	$0.503085\pi$
$422$	2.62658	0.127860
$423$	−2.99515	−0.145629
$424$	5.44226	0.264300
$425$	−1.16897	−0.0567035
$426$	29.6662	1.43733
$427$	10.8218	0.523705
$428$	0.510943	0.0246973
$429$	−9.69348	−0.468005
$430$	−20.5351	−0.990290
$431$	−27.6777	−1.33319	−0.666594	−	0.745421i	$-0.732249\pi$
$431$	−27.6777	−1.33319	−0.666594	+	0.745421i	$0.732249\pi$
$432$	−4.73219	−0.227678
$433$	−40.9885	−1.96978	−0.984891	−	0.173173i	$-0.944598\pi$
$433$	−40.9885	−1.96978	−0.984891	+	0.173173i	$0.944598\pi$
$434$	75.8036	3.63869
$435$	−5.46712	−0.262128
$436$	21.5271	1.03096
$437$	0.0206943	0.000989943 0
$438$	−2.87123	−0.137193
$439$	0.937415	0.0447404	0.0223702	−	0.999750i	$-0.492879\pi$
$439$	0.937415	0.0447404	0.0223702	+	0.999750i	$0.492879\pi$
$440$	−1.93916	−0.0924459
$441$	7.63430	0.363538
$442$	9.91742	0.471723
$443$	14.3374	0.681191	0.340596	−	0.940210i	$-0.389371\pi$
$443$	14.3374	0.681191	0.340596	+	0.940210i	$0.389371\pi$
$444$	7.21906	0.342601
$445$	3.41512	0.161892
$446$	30.8487	1.46073
$447$	−16.8286	−0.795964
$448$	−14.4861	−0.684405
$449$	30.7165	1.44960	0.724801	−	0.688958i	$-0.241932\pi$
$449$	30.7165	1.44960	0.724801	+	0.688958i	$0.241932\pi$
$450$	−1.87550	−0.0884120
$451$	4.23147	0.199252
$452$	14.7618	0.694338
$453$	−1.83239	−0.0860930
$454$	−41.9685	−1.96968
$455$	17.3047	0.811255
$456$	2.87470	0.134620
$457$	20.1526	0.942700	0.471350	−	0.881946i	$-0.343767\pi$
$457$	20.1526	0.942700	0.471350	+	0.881946i	$0.343767\pi$
$458$	31.4848	1.47119
$459$	−1.16897	−0.0545629
$460$	0.00988553	0.000460915 0
$461$	18.2517	0.850066	0.425033	−	0.905178i	$-0.360262\pi$
$461$	18.2517	0.850066	0.425033	+	0.905178i	$0.360262\pi$
$462$	15.3747	0.715294
$463$	5.64890	0.262527	0.131263	−	0.991348i	$-0.458097\pi$
$463$	5.64890	0.262527	0.131263	+	0.991348i	$0.458097\pi$
$464$	25.8714	1.20105
$465$	−10.5654	−0.489960
$466$	40.1735	1.86100
$467$	12.7382	0.589453	0.294727	−	0.955582i	$-0.404771\pi$
$467$	12.7382	0.589453	0.294727	+	0.955582i	$0.404771\pi$
$468$	6.86447	0.317310
$469$	21.4629	0.991065
$470$	5.61741	0.259112
$471$	−10.6088	−0.488826
$472$	7.01762	0.323012
$473$	−23.4629	−1.07883
$474$	18.6400	0.856165
$475$	3.17673	0.145758
$476$	−6.78609	−0.311040
$477$	6.01406	0.275365
$478$	38.6423	1.76746
$479$	−40.7918	−1.86382	−0.931912	−	0.362685i	$-0.881860\pi$
$479$	−40.7918	−1.86382	−0.931912	+	0.362685i	$0.881860\pi$
$480$	7.06538	0.322489
$481$	21.5193	0.981195
$482$	9.23175	0.420495
$483$	0.0249205	0.00113392
$484$	−9.72411	−0.442005
$485$	11.6573	0.529329
$486$	−1.87550	−0.0850744
$487$	11.4937	0.520830	0.260415	−	0.965497i	$-0.416141\pi$
$487$	11.4937	0.520830	0.260415	+	0.965497i	$0.416141\pi$
$488$	2.55992	0.115882
$489$	18.7218	0.846629
$490$	−14.3181	−0.646827
$491$	−25.1196	−1.13363	−0.566816	−	0.823845i	$-0.691825\pi$
$491$	−25.1196	−1.13363	−0.566816	+	0.823845i	$0.691825\pi$
$492$	−2.99653	−0.135094
$493$	6.39091	0.287832
$494$	−26.9510	−1.21258
$495$	−2.14290	−0.0963163
$496$	49.9976	2.24496
$497$	−60.5106	−2.71427
$498$	−20.6835	−0.926849
$499$	10.7283	0.480266	0.240133	−	0.970740i	$-0.422809\pi$
$499$	10.7283	0.480266	0.240133	+	0.970740i	$0.422809\pi$
$500$	1.51750	0.0678648
$501$	−10.1738	−0.454533
$502$	8.88367	0.396498
$503$	−33.3349	−1.48633	−0.743165	−	0.669108i	$-0.766676\pi$
$503$	−33.3349	−1.48633	−0.743165	+	0.669108i	$0.766676\pi$
$504$	3.46177	0.154199
$505$	12.7785	0.568635
$506$	0.0261812	0.00116390
$507$	7.46229	0.331412
$508$	−0.908797	−0.0403214
$509$	8.06571	0.357506	0.178753	−	0.983894i	$-0.442794\pi$
$509$	8.06571	0.357506	0.178753	+	0.983894i	$0.442794\pi$
$510$	2.19241	0.0970815
$511$	5.85649	0.259076
$512$	−24.8702	−1.09912
$513$	3.17673	0.140256
$514$	−16.1250	−0.711242
$515$	6.84450	0.301605
$516$	16.6153	0.731449
$517$	6.41832	0.282277
$518$	−34.1314	−1.49965
$519$	−5.33300	−0.234093
$520$	4.09344	0.179509
$521$	−5.15074	−0.225658	−0.112829	−	0.993614i	$-0.535991\pi$
$521$	−5.15074	−0.225658	−0.112829	+	0.993614i	$0.535991\pi$
$522$	10.2536	0.448787
$523$	−35.0757	−1.53375	−0.766876	−	0.641796i	$-0.778190\pi$
$523$	−35.0757	−1.53375	−0.766876	+	0.641796i	$0.778190\pi$
$524$	9.96097	0.435147
$525$	3.82548	0.166958
$526$	56.2149	2.45108
$527$	12.3507	0.538004
$528$	10.1406	0.441314
$529$	−23.0000	−0.999998
$530$	−11.2794	−0.489945
$531$	7.75493	0.336535
$532$	18.4415	0.799540
$533$	−8.93235	−0.386903
$534$	−6.40505	−0.277174
$535$	0.336700	0.0145568
$536$	5.07709	0.219297
$537$	0.563738	0.0243271
$538$	−11.3523	−0.489432
$539$	−16.3596	−0.704656
$540$	1.51750	0.0653029
$541$	−26.5645	−1.14210	−0.571048	−	0.820917i	$-0.693463\pi$
$541$	−26.5645	−1.14210	−0.571048	+	0.820917i	$0.693463\pi$
$542$	31.2639	1.34290
$543$	1.44667	0.0620825
$544$	−8.25923	−0.354112
$545$	14.1858	0.607655
$546$	−32.4549	−1.38894
$547$	−7.06810	−0.302210	−0.151105	−	0.988518i	$-0.548283\pi$
$547$	−7.06810	−0.302210	−0.151105	+	0.988518i	$0.548283\pi$
$548$	20.0053	0.854584
$549$	2.82888	0.120734
$550$	4.01902	0.171371
$551$	−17.3676	−0.739883
$552$	0.00589498	0.000250907 0
$553$	−38.0203	−1.61679
$554$	−36.2568	−1.54041
$555$	4.75719	0.201932
$556$	−3.36509	−0.142712
$557$	30.2914	1.28349	0.641745	−	0.766918i	$-0.278211\pi$
$557$	30.2914	1.28349	0.641745	+	0.766918i	$0.278211\pi$
$558$	19.8155	0.838855
$559$	49.5286	2.09484
$560$	−18.1029	−0.764987
$561$	2.50499	0.105761
$562$	−11.5073	−0.485406
$563$	16.2243	0.683774	0.341887	−	0.939741i	$-0.388934\pi$
$563$	16.2243	0.683774	0.341887	+	0.939741i	$0.388934\pi$
$564$	−4.54515	−0.191385
$565$	9.72770	0.409247
$566$	−30.3655	−1.27636
$567$	3.82548	0.160655
$568$	−14.3139	−0.600597
$569$	24.0966	1.01018	0.505091	−	0.863066i	$-0.331459\pi$
$569$	24.0966	1.01018	0.505091	+	0.863066i	$0.331459\pi$
$570$	−5.95796	−0.249551
$571$	−2.12781	−0.0890460	−0.0445230	−	0.999008i	$-0.514177\pi$
$571$	−2.12781	−0.0890460	−0.0445230	+	0.999008i	$0.514177\pi$
$572$	−14.7099	−0.615051
$573$	25.8790	1.08111
$574$	14.1675	0.591338
$575$	0.00651434	0.000271667 0
$576$	−3.78675	−0.157781
$577$	40.0690	1.66809	0.834046	−	0.551695i	$-0.186019\pi$
$577$	40.0690	1.66809	0.834046	+	0.551695i	$0.186019\pi$
$578$	29.3206	1.21958
$579$	17.2892	0.718516
$580$	−8.29637	−0.344488
$581$	42.1883	1.75027
$582$	−21.8632	−0.906258
$583$	−12.8875	−0.533748
$584$	1.38536	0.0573266
$585$	4.52353	0.187025
$586$	6.53515	0.269965
$587$	−18.5981	−0.767627	−0.383814	−	0.923411i	$-0.625390\pi$
$587$	−18.5981	−0.767627	−0.383814	+	0.923411i	$0.625390\pi$
$588$	11.5851	0.477760
$589$	−33.5635	−1.38296
$590$	−14.5444	−0.598783
$591$	−6.02336	−0.247768
$592$	−22.5119	−0.925235
$593$	−37.3380	−1.53329	−0.766644	−	0.642072i	$-0.778075\pi$
$593$	−37.3380	−1.53329	−0.766644	+	0.642072i	$0.778075\pi$
$594$	4.01902	0.164902
$595$	−4.47188	−0.183329
$596$	−25.5374	−1.04605
$597$	6.46717	0.264684
$598$	−0.0552669	−0.00226003
$599$	−1.02505	−0.0418825	−0.0209413	−	0.999781i	$-0.506666\pi$
$599$	−1.02505	−0.0418825	−0.0209413	+	0.999781i	$0.506666\pi$
$600$	0.904923	0.0369433
$601$	10.7853	0.439941	0.219971	−	0.975506i	$-0.429404\pi$
$601$	10.7853	0.439941	0.219971	+	0.975506i	$0.429404\pi$
$602$	−78.5566	−3.20173
$603$	5.61052	0.228478
$604$	−2.78065	−0.113143
$605$	−6.40797	−0.260521
$606$	−23.9660	−0.973554
$607$	−12.5642	−0.509965	−0.254983	−	0.966946i	$-0.582070\pi$
$607$	−12.5642	−0.509965	−0.254983	+	0.966946i	$0.582070\pi$
$608$	22.4448	0.910257
$609$	−20.9144	−0.847492
$610$	−5.30557	−0.214816
$611$	−13.5486	−0.548120
$612$	−1.77392	−0.0717064
$613$	32.8367	1.32626	0.663130	−	0.748504i	$-0.269227\pi$
$613$	32.8367	1.32626	0.663130	+	0.748504i	$0.269227\pi$
$614$	2.01386	0.0812726
$615$	−1.97464	−0.0796253
$616$	−7.41823	−0.298889
$617$	−42.3045	−1.70312	−0.851558	−	0.524260i	$-0.824342\pi$
$617$	−42.3045	−1.70312	−0.851558	+	0.524260i	$0.824342\pi$
$618$	−12.8369	−0.516375
$619$	23.1264	0.929528	0.464764	−	0.885435i	$-0.346139\pi$
$619$	23.1264	0.929528	0.464764	+	0.885435i	$0.346139\pi$
$620$	−16.0331	−0.643903
$621$	0.00651434	0.000261411 0
$622$	23.9283	0.959437
$623$	13.0645	0.523417
$624$	−21.4062	−0.856933
$625$	1.00000	0.0400000
$626$	−35.2520	−1.40895
$627$	−6.80742	−0.271862
$628$	−16.0988	−0.642413
$629$	−5.56103	−0.221733
$630$	−7.17469	−0.285847
$631$	10.1171	0.402756	0.201378	−	0.979514i	$-0.435458\pi$
$631$	10.1171	0.402756	0.201378	+	0.979514i	$0.435458\pi$
$632$	−8.99376	−0.357752
$633$	−1.40047	−0.0556636
$634$	9.09622	0.361257
$635$	−0.598877	−0.0237657
$636$	9.12636	0.361884
$637$	34.5340	1.36828
$638$	−21.9724	−0.869897
$639$	−15.8178	−0.625741
$640$	−7.02872	−0.277834
$641$	−20.3165	−0.802455	−0.401227	−	0.915979i	$-0.631416\pi$
$641$	−20.3165	−0.802455	−0.401227	+	0.915979i	$0.631416\pi$
$642$	−0.631480	−0.0249225
$643$	41.5673	1.63926	0.819628	−	0.572896i	$-0.194180\pi$
$643$	41.5673	1.63926	0.819628	+	0.572896i	$0.194180\pi$
$644$	0.0378169	0.00149019
$645$	10.9491	0.431121
$646$	6.96469	0.274022
$647$	38.3692	1.50845	0.754224	−	0.656617i	$-0.228013\pi$
$647$	38.3692	1.50845	0.754224	+	0.656617i	$0.228013\pi$
$648$	0.904923	0.0355487
$649$	−16.6181	−0.652316
$650$	−8.48388	−0.332765
$651$	−40.4178	−1.58410
$652$	28.4104	1.11264
$653$	−18.8973	−0.739507	−0.369754	−	0.929130i	$-0.620558\pi$
$653$	−18.8973	−0.739507	−0.369754	+	0.929130i	$0.620558\pi$
$654$	−26.6056	−1.04036
$655$	6.56405	0.256479
$656$	9.34439	0.364837
$657$	1.53092	0.0597267
$658$	21.4893	0.837740
$659$	30.2047	1.17661	0.588305	−	0.808639i	$-0.299795\pi$
$659$	30.2047	1.17661	0.588305	+	0.808639i	$0.299795\pi$
$660$	−3.25186	−0.126579
$661$	46.1036	1.79322	0.896610	−	0.442820i	$-0.146022\pi$
$661$	46.1036	1.79322	0.896610	+	0.442820i	$0.146022\pi$
$662$	−10.8735	−0.422612
$663$	−5.28788	−0.205364
$664$	9.97972	0.387288
$665$	12.1525	0.471254
$666$	−8.92212	−0.345725
$667$	−0.0356147	−0.00137901
$668$	−15.4388	−0.597346
$669$	−16.4482	−0.635926
$670$	−10.5225	−0.406521
$671$	−6.06202	−0.234022
$672$	27.0285	1.04265
$673$	15.1730	0.584877	0.292439	−	0.956284i	$-0.405533\pi$
$673$	15.1730	0.584877	0.292439	+	0.956284i	$0.405533\pi$
$674$	−33.2744	−1.28168
$675$	1.00000	0.0384900
$676$	11.3240	0.435540
$677$	−11.3804	−0.437386	−0.218693	−	0.975794i	$-0.570179\pi$
$677$	−11.3804	−0.437386	−0.218693	+	0.975794i	$0.570179\pi$
$678$	−18.2443	−0.700669
$679$	44.5946	1.71138
$680$	−1.05783	−0.0405659
$681$	22.3772	0.857497
$682$	−42.4626	−1.62598
$683$	32.5328	1.24483	0.622416	−	0.782687i	$-0.286151\pi$
$683$	32.5328	1.24483	0.622416	+	0.782687i	$0.286151\pi$
$684$	4.82070	0.184324
$685$	13.1830	0.503698
$686$	−4.55090	−0.173754
$687$	−16.7874	−0.640479
$688$	−51.8133	−1.97536
$689$	27.2048	1.03642
$690$	−0.0122176	−0.000465118 0
$691$	9.47238	0.360346	0.180173	−	0.983635i	$-0.442334\pi$
$691$	9.47238	0.360346	0.180173	+	0.983635i	$0.442334\pi$
$692$	−8.09284	−0.307644
$693$	−8.19763	−0.311402
$694$	−48.8878	−1.85576
$695$	−2.21752	−0.0841152
$696$	−4.94732	−0.187528
$697$	2.30830	0.0874332
$698$	8.64445	0.327197
$699$	−21.4201	−0.810184
$700$	5.80518	0.219415
$701$	10.1037	0.381610	0.190805	−	0.981628i	$-0.438890\pi$
$701$	10.1037	0.381610	0.190805	+	0.981628i	$0.438890\pi$
$702$	−8.48388	−0.320203
$703$	15.1123	0.569972
$704$	8.11463	0.305831
$705$	−2.99515	−0.112804
$706$	32.7790	1.23365
$707$	48.8838	1.83847
$708$	11.7681	0.442274
$709$	−18.6850	−0.701730	−0.350865	−	0.936426i	$-0.614112\pi$
$709$	−18.6850	−0.701730	−0.350865	+	0.936426i	$0.614112\pi$
$710$	29.6662	1.11335
$711$	−9.93869	−0.372730
$712$	3.09042	0.115818
$713$	−0.0688267	−0.00257758
$714$	8.38701	0.313876
$715$	−9.69348	−0.362515
$716$	0.855475	0.0319706
$717$	−20.6037	−0.769461
$718$	−11.6324	−0.434118
$719$	32.1751	1.19993	0.599965	−	0.800026i	$-0.295181\pi$
$719$	32.1751	1.19993	0.599965	+	0.800026i	$0.295181\pi$
$720$	−4.73219	−0.176358
$721$	26.1835	0.975125
$722$	16.7077	0.621796
$723$	−4.92229	−0.183062
$724$	2.19532	0.0815886
$725$	−5.46712	−0.203044
$726$	12.0181	0.446035
$727$	8.33804	0.309241	0.154620	−	0.987974i	$-0.450585\pi$
$727$	8.33804	0.309241	0.154620	+	0.987974i	$0.450585\pi$
$728$	15.6594	0.580376
$729$	1.00000	0.0370370
$730$	−2.87123	−0.106269
$731$	−12.7992	−0.473396
$732$	4.29284	0.158668
$733$	−12.4997	−0.461686	−0.230843	−	0.972991i	$-0.574148\pi$
$733$	−12.4997	−0.461686	−0.230843	+	0.972991i	$0.574148\pi$
$734$	−29.6329	−1.09377
$735$	7.63430	0.281595
$736$	0.0460263	0.00169655
$737$	−12.0228	−0.442865
$738$	3.70344	0.136326
$739$	−6.89709	−0.253714	−0.126857	−	0.991921i	$-0.540489\pi$
$739$	−6.89709	−0.253714	−0.126857	+	0.991921i	$0.540489\pi$
$740$	7.21906	0.265378
$741$	14.3700	0.527896
$742$	−43.1490	−1.58405
$743$	−47.8127	−1.75408	−0.877039	−	0.480419i	$-0.840484\pi$
$743$	−47.8127	−1.75408	−0.877039	+	0.480419i	$0.840484\pi$
$744$	−9.56089	−0.350519
$745$	−16.8286	−0.616551
$746$	23.8271	0.872373
$747$	11.0282	0.403502
$748$	3.80134	0.138991
$749$	1.28804	0.0470639
$750$	−1.87550	−0.0684836
$751$	25.7653	0.940190	0.470095	−	0.882616i	$-0.344220\pi$
$751$	25.7653	0.940190	0.470095	+	0.882616i	$0.344220\pi$
$752$	14.1736	0.516859
$753$	−4.73669	−0.172615
$754$	46.3824	1.68915
$755$	−1.83239	−0.0666874
$756$	5.80518	0.211132
$757$	−45.1532	−1.64112	−0.820560	−	0.571560i	$-0.806338\pi$
$757$	−45.1532	−1.64112	−0.820560	+	0.571560i	$0.806338\pi$
$758$	−12.5268	−0.454992
$759$	−0.0139596	−0.000506701 0
$760$	2.87470	0.104276
$761$	22.7995	0.826481	0.413241	−	0.910622i	$-0.364397\pi$
$761$	22.7995	0.826481	0.413241	+	0.910622i	$0.364397\pi$
$762$	1.12319	0.0406890
$763$	54.2677	1.96462
$764$	39.2715	1.42079
$765$	−1.16897	−0.0422643
$766$	63.2952	2.28695
$767$	35.0796	1.26665
$768$	20.7559	0.748962
$769$	−8.56742	−0.308949	−0.154475	−	0.987997i	$-0.549368\pi$
$769$	−8.56742	−0.308949	−0.154475	+	0.987997i	$0.549368\pi$
$770$	15.3747	0.554064
$771$	8.59769	0.309638
$772$	26.2365	0.944272
$773$	0.981625	0.0353066	0.0176533	−	0.999844i	$-0.494380\pi$
$773$	0.981625	0.0353066	0.0176533	+	0.999844i	$0.494380\pi$
$774$	−20.5351	−0.738118
$775$	−10.5654	−0.379521
$776$	10.5489	0.378684
$777$	18.1985	0.652869
$778$	−34.0028	−1.21906
$779$	−6.27291	−0.224750
$780$	6.86447	0.245787
$781$	33.8959	1.21289
$782$	0.0142821	0.000510727 0
$783$	−5.46712	−0.195379
$784$	−36.1270	−1.29025
$785$	−10.6088	−0.378643
$786$	−12.3109	−0.439115
$787$	24.1420	0.860569	0.430284	−	0.902693i	$-0.358413\pi$
$787$	24.1420	0.860569	0.430284	+	0.902693i	$0.358413\pi$
$788$	−9.14047	−0.325616
$789$	−29.9733	−1.06708
$790$	18.6400	0.663182
$791$	37.2131	1.32315
$792$	−1.93916	−0.0689051
$793$	12.7965	0.454418
$794$	34.8954	1.23839
$795$	6.01406	0.213297
$796$	9.81395	0.347846
$797$	48.7718	1.72759	0.863793	−	0.503846i	$-0.168082\pi$
$797$	48.7718	1.72759	0.863793	+	0.503846i	$0.168082\pi$
$798$	−22.7921	−0.806830
$799$	3.50125	0.123865
$800$	7.06538	0.249799
$801$	3.41512	0.120667
$802$	−1.87550	−0.0662262
$803$	−3.28060	−0.115770
$804$	8.51398	0.300265
$805$	0.0249205	0.000878331 0
$806$	89.6357	3.15728
$807$	6.05294	0.213074
$808$	11.5635	0.406804
$809$	−13.8418	−0.486652	−0.243326	−	0.969945i	$-0.578238\pi$
$809$	−13.8418	−0.486652	−0.243326	+	0.969945i	$0.578238\pi$
$810$	−1.87550	−0.0658984
$811$	23.3252	0.819059	0.409530	−	0.912297i	$-0.365693\pi$
$811$	23.3252	0.819059	0.409530	+	0.912297i	$0.365693\pi$
$812$	−31.7376	−1.11377
$813$	−16.6696	−0.584630
$814$	19.1192	0.670129
$815$	18.7218	0.655796
$816$	5.53180	0.193652
$817$	34.7824	1.21688
$818$	−65.7275	−2.29811
$819$	17.3047	0.604674
$820$	−2.99653	−0.104643
$821$	27.4898	0.959399	0.479700	−	0.877433i	$-0.340746\pi$
$821$	27.4898	0.959399	0.479700	+	0.877433i	$0.340746\pi$
$822$	−24.7248	−0.862376
$823$	−5.93125	−0.206750	−0.103375	−	0.994642i	$-0.532964\pi$
$823$	−5.93125	−0.206750	−0.103375	+	0.994642i	$0.532964\pi$
$824$	6.19375	0.215769
$825$	−2.14290	−0.0746063
$826$	−55.6393	−1.93594
$827$	−29.8977	−1.03965	−0.519823	−	0.854274i	$-0.674002\pi$
$827$	−29.8977	−1.03965	−0.519823	+	0.854274i	$0.674002\pi$
$828$	0.00988553	0.000343546 0
$829$	−39.6718	−1.37786	−0.688930	−	0.724828i	$-0.741919\pi$
$829$	−39.6718	−1.37786	−0.688930	+	0.724828i	$0.741919\pi$
$830$	−20.6835	−0.717934
$831$	19.3318	0.670613
$832$	−17.1294	−0.593857
$833$	−8.92428	−0.309208
$834$	4.15896	0.144013
$835$	−10.1738	−0.352080
$836$	−10.3303	−0.357280
$837$	−10.5654	−0.365194
$838$	14.4885	0.500496
$839$	4.07728	0.140763	0.0703817	−	0.997520i	$-0.477578\pi$
$839$	4.07728	0.140763	0.0703817	+	0.997520i	$0.477578\pi$
$840$	3.46177	0.119442
$841$	0.889386	0.0306685
$842$	0.745888	0.0257050
$843$	6.13559	0.211321
$844$	−2.12522	−0.0731529
$845$	7.46229	0.256711
$846$	5.61741	0.193130
$847$	−24.5136	−0.842296
$848$	−28.4597	−0.977309
$849$	16.1906	0.555660
$850$	2.19241	0.0751990
$851$	0.0309900	0.00106232
$852$	−24.0035	−0.822347
$853$	25.4758	0.872276	0.436138	−	0.899880i	$-0.356346\pi$
$853$	25.4758	0.872276	0.436138	+	0.899880i	$0.356346\pi$
$854$	−20.2964	−0.694527
$855$	3.17673	0.108642
$856$	0.304687	0.0104140
$857$	−30.8822	−1.05492	−0.527458	−	0.849581i	$-0.676855\pi$
$857$	−30.8822	−1.05492	−0.527458	+	0.849581i	$0.676855\pi$
$858$	18.1801	0.620659
$859$	−42.9823	−1.46654	−0.733269	−	0.679939i	$-0.762006\pi$
$859$	−42.9823	−1.46654	−0.733269	+	0.679939i	$0.762006\pi$
$860$	16.6153	0.566578
$861$	−7.55396	−0.257438
$862$	51.9096	1.76805
$863$	16.5394	0.563008	0.281504	−	0.959560i	$-0.409167\pi$
$863$	16.5394	0.563008	0.281504	+	0.959560i	$0.409167\pi$
$864$	7.06538	0.240369
$865$	−5.33300	−0.181327
$866$	76.8740	2.61229
$867$	−15.6335	−0.530942
$868$	−61.3341	−2.08182
$869$	21.2977	0.722473
$870$	10.2536	0.347629
$871$	25.3793	0.859945
$872$	12.8371	0.434719
$873$	11.6573	0.394538
$874$	−0.0388122	−0.00131284
$875$	3.82548	0.129325
$876$	2.32317	0.0784926
$877$	22.0997	0.746254	0.373127	−	0.927780i	$-0.378285\pi$
$877$	22.0997	0.746254	0.373127	+	0.927780i	$0.378285\pi$
$878$	−1.75812	−0.0593337
$879$	−3.48448	−0.117529
$880$	10.1406	0.341840
$881$	41.1309	1.38574	0.692868	−	0.721065i	$-0.256347\pi$
$881$	41.1309	1.38574	0.692868	+	0.721065i	$0.256347\pi$
$882$	−14.3181	−0.482117
$883$	−35.8922	−1.20787	−0.603934	−	0.797034i	$-0.706401\pi$
$883$	−35.8922	−1.20787	−0.603934	+	0.797034i	$0.706401\pi$
$884$	−8.02437	−0.269889
$885$	7.75493	0.260679
$886$	−26.8898	−0.903382
$887$	24.1807	0.811907	0.405954	−	0.913894i	$-0.366939\pi$
$887$	24.1807	0.811907	0.405954	+	0.913894i	$0.366939\pi$
$888$	4.30490	0.144463
$889$	−2.29099	−0.0768374
$890$	−6.40505	−0.214698
$891$	−2.14290	−0.0717899
$892$	−24.9603	−0.835731
$893$	−9.51479	−0.318400
$894$	31.5620	1.05559
$895$	0.563738	0.0188437
$896$	−26.8882	−0.898272
$897$	0.0294678	0.000983901 0
$898$	−57.6089	−1.92243
$899$	57.7624	1.92648
$900$	1.51750	0.0505834
$901$	−7.03027	−0.234212
$902$	−7.93612	−0.264244
$903$	41.8856	1.39387
$904$	8.80282	0.292778
$905$	1.44667	0.0480889
$906$	3.43664	0.114175
$907$	19.4020	0.644232	0.322116	−	0.946700i	$-0.395606\pi$
$907$	19.4020	0.644232	0.322116	+	0.946700i	$0.395606\pi$
$908$	33.9575	1.12692
$909$	12.7785	0.423835
$910$	−32.4549	−1.07587
$911$	−41.4204	−1.37232	−0.686160	−	0.727451i	$-0.740705\pi$
$911$	−41.4204	−1.37232	−0.686160	+	0.727451i	$0.740705\pi$
$912$	−15.0329	−0.497789
$913$	−23.6325	−0.782120
$914$	−37.7963	−1.25019
$915$	2.82888	0.0935200
$916$	−25.4749	−0.841716
$917$	25.1106	0.829226
$918$	2.19241	0.0723603
$919$	−16.1733	−0.533507	−0.266754	−	0.963765i	$-0.585951\pi$
$919$	−16.1733	−0.533507	−0.266754	+	0.963765i	$0.585951\pi$
$920$	0.00589498	0.000194352 0
$921$	−1.07377	−0.0353819
$922$	−34.2311	−1.12734
$923$	−71.5521	−2.35517
$924$	−12.4399	−0.409244
$925$	4.75719	0.156416
$926$	−10.5945	−0.348157
$927$	6.84450	0.224803
$928$	−38.6273	−1.26800
$929$	19.6381	0.644305	0.322152	−	0.946688i	$-0.395594\pi$
$929$	19.6381	0.644305	0.322152	+	0.946688i	$0.395594\pi$
$930$	19.8155	0.649774
$931$	24.2521	0.794831
$932$	−32.5051	−1.06474
$933$	−12.7583	−0.417690
$934$	−23.8905	−0.781721
$935$	2.50499	0.0819220
$936$	4.09344	0.133798
$937$	20.6352	0.674122	0.337061	−	0.941483i	$-0.390567\pi$
$937$	20.6352	0.674122	0.337061	+	0.941483i	$0.390567\pi$
$938$	−40.2537	−1.31433
$939$	18.7961	0.613386
$940$	−4.54515	−0.148247
$941$	−15.8685	−0.517297	−0.258649	−	0.965971i	$-0.583277\pi$
$941$	−15.8685	−0.517297	−0.258649	+	0.965971i	$0.583277\pi$
$942$	19.8967	0.648271
$943$	−0.0128635	−0.000418893 0
$944$	−36.6978	−1.19441
$945$	3.82548	0.124443
$946$	44.0047	1.43072
$947$	16.1875	0.526024	0.263012	−	0.964793i	$-0.415284\pi$
$947$	16.1875	0.526024	0.263012	+	0.964793i	$0.415284\pi$
$948$	−15.0820	−0.489841
$949$	6.92514	0.224799
$950$	−5.95796	−0.193302
$951$	−4.85002	−0.157273
$952$	−4.04671	−0.131155
$953$	10.9362	0.354257	0.177129	−	0.984188i	$-0.443319\pi$
$953$	10.9362	0.354257	0.177129	+	0.984188i	$0.443319\pi$
$954$	−11.2794	−0.365183
$955$	25.8790	0.837426
$956$	−31.2662	−1.01122
$957$	11.7155	0.378708
$958$	76.5050	2.47176
$959$	50.4314	1.62852
$960$	−3.78675	−0.122217
$961$	80.6281	2.60091
$962$	−40.3594	−1.30124
$963$	0.336700	0.0108500
$964$	−7.46959	−0.240579
$965$	17.2892	0.556560
$966$	−0.0467384	−0.00150378
$967$	−21.7489	−0.699399	−0.349699	−	0.936862i	$-0.613716\pi$
$967$	−21.7489	−0.699399	−0.349699	+	0.936862i	$0.613716\pi$
$968$	−5.79872	−0.186378
$969$	−3.71351	−0.119295
$970$	−21.8632	−0.701985
$971$	10.8931	0.349575	0.174788	−	0.984606i	$-0.444076\pi$
$971$	10.8931	0.349575	0.174788	+	0.984606i	$0.444076\pi$
$972$	1.51750	0.0486739
$973$	−8.48307	−0.271955
$974$	−21.5565	−0.690713
$975$	4.52353	0.144869
$976$	−13.3868	−0.428501
$977$	−19.7887	−0.633096	−0.316548	−	0.948577i	$-0.602524\pi$
$977$	−19.7887	−0.633096	−0.316548	+	0.948577i	$0.602524\pi$
$978$	−35.1128	−1.12278
$979$	−7.31826	−0.233893
$980$	11.5851	0.370072
$981$	14.1858	0.452919
$982$	47.1118	1.50340
$983$	14.3829	0.458743	0.229371	−	0.973339i	$-0.426333\pi$
$983$	14.3829	0.458743	0.229371	+	0.973339i	$0.426333\pi$
$984$	−1.78690	−0.0569643
$985$	−6.02336	−0.191920
$986$	−11.9862	−0.381717
$987$	−11.4579	−0.364709
$988$	21.8066	0.693759
$989$	0.0713263	0.00226804
$990$	4.01902	0.127733
$991$	−29.7273	−0.944319	−0.472159	−	0.881513i	$-0.656525\pi$
$991$	−29.7273	−0.944319	−0.472159	+	0.881513i	$0.656525\pi$
$992$	−74.6487	−2.37010
$993$	5.79767	0.183983
$994$	113.488	3.59961
$995$	6.46717	0.205023
$996$	16.7354	0.530281
$997$	11.7415	0.371857	0.185929	−	0.982563i	$-0.440471\pi$
$997$	11.7415	0.371857	0.185929	+	0.982563i	$0.440471\pi$
$998$	−20.1210	−0.636919
$999$	4.75719	0.150511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.i.1.9	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.i.1.9	✓	43	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.87550 q^{2} +1.00000 q^{3} +1.51750 q^{4} +1.00000 q^{5} -1.87550 q^{6} +3.82548 q^{7} +0.904923 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.87550 q^{2} +1.00000 q^{3} +1.51750 q^{4} +1.00000 q^{5} -1.87550 q^{6} +3.82548 q^{7} +0.904923 q^{8} +1.00000 q^{9} -1.87550 q^{10} -2.14290 q^{11} +1.51750 q^{12} +4.52353 q^{13} -7.17469 q^{14} +1.00000 q^{15} -4.73219 q^{16} -1.16897 q^{17} -1.87550 q^{18} +3.17673 q^{19} +1.51750 q^{20} +3.82548 q^{21} +4.01902 q^{22} +0.00651434 q^{23} +0.904923 q^{24} +1.00000 q^{25} -8.48388 q^{26} +1.00000 q^{27} +5.80518 q^{28} -5.46712 q^{29} -1.87550 q^{30} -10.5654 q^{31} +7.06538 q^{32} -2.14290 q^{33} +2.19241 q^{34} +3.82548 q^{35} +1.51750 q^{36} +4.75719 q^{37} -5.95796 q^{38} +4.52353 q^{39} +0.904923 q^{40} -1.97464 q^{41} -7.17469 q^{42} +10.9491 q^{43} -3.25186 q^{44} +1.00000 q^{45} -0.0122176 q^{46} -2.99515 q^{47} -4.73219 q^{48} +7.63430 q^{49} -1.87550 q^{50} -1.16897 q^{51} +6.86447 q^{52} +6.01406 q^{53} -1.87550 q^{54} -2.14290 q^{55} +3.46177 q^{56} +3.17673 q^{57} +10.2536 q^{58} +7.75493 q^{59} +1.51750 q^{60} +2.82888 q^{61} +19.8155 q^{62} +3.82548 q^{63} -3.78675 q^{64} +4.52353 q^{65} +4.01902 q^{66} +5.61052 q^{67} -1.77392 q^{68} +0.00651434 q^{69} -7.17469 q^{70} -15.8178 q^{71} +0.904923 q^{72} +1.53092 q^{73} -8.92212 q^{74} +1.00000 q^{75} +4.82070 q^{76} -8.19763 q^{77} -8.48388 q^{78} -9.93869 q^{79} -4.73219 q^{80} +1.00000 q^{81} +3.70344 q^{82} +11.0282 q^{83} +5.80518 q^{84} -1.16897 q^{85} -20.5351 q^{86} -5.46712 q^{87} -1.93916 q^{88} +3.41512 q^{89} -1.87550 q^{90} +17.3047 q^{91} +0.00988553 q^{92} -10.5654 q^{93} +5.61741 q^{94} +3.17673 q^{95} +7.06538 q^{96} +11.6573 q^{97} -14.3181 q^{98} -2.14290 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * q^99

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