LMFDB - Embedded newform 8013.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$1$
Dimension:	$116$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58282 q^{2} -1.00000 q^{3} +4.67097 q^{4} -1.48132 q^{5} +2.58282 q^{6} +0.817005 q^{7} -6.89864 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.58282 q^{2} -1.00000 q^{3} +4.67097 q^{4} -1.48132 q^{5} +2.58282 q^{6} +0.817005 q^{7} -6.89864 q^{8} +1.00000 q^{9} +3.82598 q^{10} +0.666794 q^{11} -4.67097 q^{12} +6.87218 q^{13} -2.11018 q^{14} +1.48132 q^{15} +8.47602 q^{16} -5.60874 q^{17} -2.58282 q^{18} +7.20331 q^{19} -6.91920 q^{20} -0.817005 q^{21} -1.72221 q^{22} +5.84476 q^{23} +6.89864 q^{24} -2.80570 q^{25} -17.7496 q^{26} -1.00000 q^{27} +3.81621 q^{28} -4.66954 q^{29} -3.82598 q^{30} +4.78320 q^{31} -8.09478 q^{32} -0.666794 q^{33} +14.4864 q^{34} -1.21024 q^{35} +4.67097 q^{36} +7.30172 q^{37} -18.6049 q^{38} -6.87218 q^{39} +10.2191 q^{40} -2.05298 q^{41} +2.11018 q^{42} -9.77565 q^{43} +3.11457 q^{44} -1.48132 q^{45} -15.0960 q^{46} -7.43768 q^{47} -8.47602 q^{48} -6.33250 q^{49} +7.24661 q^{50} +5.60874 q^{51} +32.0998 q^{52} -6.29120 q^{53} +2.58282 q^{54} -0.987734 q^{55} -5.63622 q^{56} -7.20331 q^{57} +12.0606 q^{58} +9.19862 q^{59} +6.91920 q^{60} -6.46102 q^{61} -12.3542 q^{62} +0.817005 q^{63} +3.95533 q^{64} -10.1799 q^{65} +1.72221 q^{66} +0.505861 q^{67} -26.1982 q^{68} -5.84476 q^{69} +3.12585 q^{70} +6.01760 q^{71} -6.89864 q^{72} -14.2032 q^{73} -18.8590 q^{74} +2.80570 q^{75} +33.6464 q^{76} +0.544774 q^{77} +17.7496 q^{78} -3.47745 q^{79} -12.5557 q^{80} +1.00000 q^{81} +5.30249 q^{82} +16.4401 q^{83} -3.81621 q^{84} +8.30832 q^{85} +25.2488 q^{86} +4.66954 q^{87} -4.59997 q^{88} -18.1895 q^{89} +3.82598 q^{90} +5.61461 q^{91} +27.3007 q^{92} -4.78320 q^{93} +19.2102 q^{94} -10.6704 q^{95} +8.09478 q^{96} -8.44249 q^{97} +16.3557 q^{98} +0.666794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9}+O(q^{10}) $ 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9} + 3 q^{10} - 57 q^{11} - 116 q^{12} + 6 q^{13} - 9 q^{14} + 20 q^{15} + 112 q^{16} - 30 q^{17} - 16 q^{18} + 3 q^{19} - 54 q^{20} + 33 q^{21} - 22 q^{22} - 58 q^{23} + 45 q^{24} + 126 q^{25} - 21 q^{26} - 116 q^{27} - 77 q^{28} - 38 q^{29} - 3 q^{30} + 17 q^{31} - 106 q^{32} + 57 q^{33} + 35 q^{34} - 72 q^{35} + 116 q^{36} - 41 q^{37} - 45 q^{38} - 6 q^{39} + 5 q^{40} - 39 q^{41} + 9 q^{42} - 118 q^{43} - 103 q^{44} - 20 q^{45} - 8 q^{46} - 65 q^{47} - 112 q^{48} + 165 q^{49} - 72 q^{50} + 30 q^{51} - 10 q^{52} - 58 q^{53} + 16 q^{54} + 14 q^{55} - 23 q^{56} - 3 q^{57} - 27 q^{58} - 75 q^{59} + 54 q^{60} + 45 q^{61} - 73 q^{62} - 33 q^{63} + 111 q^{64} - 86 q^{65} + 22 q^{66} - 127 q^{67} - 94 q^{68} + 58 q^{69} - 7 q^{70} - 61 q^{71} - 45 q^{72} + 15 q^{73} - 51 q^{74} - 126 q^{75} + 96 q^{76} - 57 q^{77} + 21 q^{78} + 7 q^{79} - 144 q^{80} + 116 q^{81} - 37 q^{82} - 194 q^{83} + 77 q^{84} + 3 q^{85} - 57 q^{86} + 38 q^{87} - 42 q^{88} - 56 q^{89} + 3 q^{90} - 39 q^{91} - 138 q^{92} - 17 q^{93} + 51 q^{94} - 127 q^{95} + 106 q^{96} + 57 q^{97} - 105 q^{98} - 57 q^{99}+O(q^{100}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9 + 3 * q^10 - 57 * q^11 - 116 * q^12 + 6 * q^13 - 9 * q^14 + 20 * q^15 + 112 * q^16 - 30 * q^17 - 16 * q^18 + 3 * q^19 - 54 * q^20 + 33 * q^21 - 22 * q^22 - 58 * q^23 + 45 * q^24 + 126 * q^25 - 21 * q^26 - 116 * q^27 - 77 * q^28 - 38 * q^29 - 3 * q^30 + 17 * q^31 - 106 * q^32 + 57 * q^33 + 35 * q^34 - 72 * q^35 + 116 * q^36 - 41 * q^37 - 45 * q^38 - 6 * q^39 + 5 * q^40 - 39 * q^41 + 9 * q^42 - 118 * q^43 - 103 * q^44 - 20 * q^45 - 8 * q^46 - 65 * q^47 - 112 * q^48 + 165 * q^49 - 72 * q^50 + 30 * q^51 - 10 * q^52 - 58 * q^53 + 16 * q^54 + 14 * q^55 - 23 * q^56 - 3 * q^57 - 27 * q^58 - 75 * q^59 + 54 * q^60 + 45 * q^61 - 73 * q^62 - 33 * q^63 + 111 * q^64 - 86 * q^65 + 22 * q^66 - 127 * q^67 - 94 * q^68 + 58 * q^69 - 7 * q^70 - 61 * q^71 - 45 * q^72 + 15 * q^73 - 51 * q^74 - 126 * q^75 + 96 * q^76 - 57 * q^77 + 21 * q^78 + 7 * q^79 - 144 * q^80 + 116 * q^81 - 37 * q^82 - 194 * q^83 + 77 * q^84 + 3 * q^85 - 57 * q^86 + 38 * q^87 - 42 * q^88 - 56 * q^89 + 3 * q^90 - 39 * q^91 - 138 * q^92 - 17 * q^93 + 51 * q^94 - 127 * q^95 + 106 * q^96 + 57 * q^97 - 105 * q^98 - 57 * 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 $

$2$	−2.58282	−1.82633	−0.913166	−	0.407589i	$-0.866370\pi$
$2$	−2.58282	−1.82633	−0.913166	+	0.407589i	$0.866370\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.67097	2.33549
$5$	−1.48132	−0.662466	−0.331233	−	0.943549i	$-0.607465\pi$
$5$	−1.48132	−0.662466	−0.331233	+	0.943549i	$0.607465\pi$
$6$	2.58282	1.05443
$7$	0.817005	0.308799	0.154399	−	0.988009i	$-0.450656\pi$
$7$	0.817005	0.308799	0.154399	+	0.988009i	$0.450656\pi$
$8$	−6.89864	−2.43904
$9$	1.00000	0.333333
$10$	3.82598	1.20988
$11$	0.666794	0.201046	0.100523	−	0.994935i	$-0.467948\pi$
$11$	0.666794	0.201046	0.100523	+	0.994935i	$0.467948\pi$
$12$	−4.67097	−1.34839
$13$	6.87218	1.90600	0.953000	−	0.302970i	$-0.0979781\pi$
$13$	6.87218	1.90600	0.953000	+	0.302970i	$0.0979781\pi$
$14$	−2.11018	−0.563969
$15$	1.48132	0.382475
$16$	8.47602	2.11901
$17$	−5.60874	−1.36032	−0.680159	−	0.733065i	$-0.738089\pi$
$17$	−5.60874	−1.36032	−0.680159	+	0.733065i	$0.738089\pi$
$18$	−2.58282	−0.608777
$19$	7.20331	1.65255	0.826276	−	0.563265i	$-0.190455\pi$
$19$	7.20331	1.65255	0.826276	+	0.563265i	$0.190455\pi$
$20$	−6.91920	−1.54718
$21$	−0.817005	−0.178285
$22$	−1.72221	−0.367176
$23$	5.84476	1.21872	0.609358	−	0.792895i	$-0.291427\pi$
$23$	5.84476	1.21872	0.609358	+	0.792895i	$0.291427\pi$
$24$	6.89864	1.40818
$25$	−2.80570	−0.561139
$26$	−17.7496	−3.48099
$27$	−1.00000	−0.192450
$28$	3.81621	0.721195
$29$	−4.66954	−0.867111	−0.433556	−	0.901127i	$-0.642741\pi$
$29$	−4.66954	−0.867111	−0.433556	+	0.901127i	$0.642741\pi$
$30$	−3.82598	−0.698526
$31$	4.78320	0.859089	0.429544	−	0.903046i	$-0.358674\pi$
$31$	4.78320	0.859089	0.429544	+	0.903046i	$0.358674\pi$
$32$	−8.09478	−1.43097
$33$	−0.666794	−0.116074
$34$	14.4864	2.48439
$35$	−1.21024	−0.204569
$36$	4.67097	0.778495
$37$	7.30172	1.20039	0.600197	−	0.799852i	$-0.295089\pi$
$37$	7.30172	1.20039	0.600197	+	0.799852i	$0.295089\pi$
$38$	−18.6049	−3.01811
$39$	−6.87218	−1.10043
$40$	10.2191	1.61578
$41$	−2.05298	−0.320622	−0.160311	−	0.987067i	$-0.551250\pi$
$41$	−2.05298	−0.320622	−0.160311	+	0.987067i	$0.551250\pi$
$42$	2.11018	0.325608
$43$	−9.77565	−1.49077	−0.745386	−	0.666633i	$-0.767735\pi$
$43$	−9.77565	−1.49077	−0.745386	+	0.666633i	$0.767735\pi$
$44$	3.11457	0.469540
$45$	−1.48132	−0.220822
$46$	−15.0960	−2.22578
$47$	−7.43768	−1.08490	−0.542449	−	0.840089i	$-0.682503\pi$
$47$	−7.43768	−1.08490	−0.542449	+	0.840089i	$0.682503\pi$
$48$	−8.47602	−1.22341
$49$	−6.33250	−0.904643
$50$	7.24661	1.02483
$51$	5.60874	0.785380
$52$	32.0998	4.45144
$53$	−6.29120	−0.864162	−0.432081	−	0.901835i	$-0.642221\pi$
$53$	−6.29120	−0.864162	−0.432081	+	0.901835i	$0.642221\pi$
$54$	2.58282	0.351478
$55$	−0.987734	−0.133186
$56$	−5.63622	−0.753172
$57$	−7.20331	−0.954102
$58$	12.0606	1.58363
$59$	9.19862	1.19756	0.598779	−	0.800914i	$-0.295653\pi$
$59$	9.19862	1.19756	0.598779	+	0.800914i	$0.295653\pi$
$60$	6.91920	0.893264
$61$	−6.46102	−0.827249	−0.413624	−	0.910448i	$-0.635737\pi$
$61$	−6.46102	−0.827249	−0.413624	+	0.910448i	$0.635737\pi$
$62$	−12.3542	−1.56898
$63$	0.817005	0.102933
$64$	3.95533	0.494416
$65$	−10.1799	−1.26266
$66$	1.72221	0.211989
$67$	0.505861	0.0618008	0.0309004	−	0.999522i	$-0.490163\pi$
$67$	0.505861	0.0618008	0.0309004	+	0.999522i	$0.490163\pi$
$68$	−26.1982	−3.17700
$69$	−5.84476	−0.703627
$70$	3.12585	0.373610
$71$	6.01760	0.714157	0.357079	−	0.934074i	$-0.383773\pi$
$71$	6.01760	0.714157	0.357079	+	0.934074i	$0.383773\pi$
$72$	−6.89864	−0.813013
$73$	−14.2032	−1.66235	−0.831177	−	0.556008i	$-0.812332\pi$
$73$	−14.2032	−1.66235	−0.831177	+	0.556008i	$0.812332\pi$
$74$	−18.8590	−2.19232
$75$	2.80570	0.323974
$76$	33.6464	3.85951
$77$	0.544774	0.0620828
$78$	17.7496	2.00975
$79$	−3.47745	−0.391244	−0.195622	−	0.980679i	$-0.562673\pi$
$79$	−3.47745	−0.391244	−0.195622	+	0.980679i	$0.562673\pi$
$80$	−12.5557	−1.40377
$81$	1.00000	0.111111
$82$	5.30249	0.585562
$83$	16.4401	1.80453	0.902267	−	0.431178i	$-0.141902\pi$
$83$	16.4401	1.80453	0.902267	+	0.431178i	$0.141902\pi$
$84$	−3.81621	−0.416382
$85$	8.30832	0.901164
$86$	25.2488	2.72264
$87$	4.66954	0.500627
$88$	−4.59997	−0.490359
$89$	−18.1895	−1.92808	−0.964042	−	0.265750i	$-0.914381\pi$
$89$	−18.1895	−1.92808	−0.964042	+	0.265750i	$0.914381\pi$
$90$	3.82598	0.403294
$91$	5.61461	0.588571
$92$	27.3007	2.84630
$93$	−4.78320	−0.495995
$94$	19.2102	1.98138
$95$	−10.6704	−1.09476
$96$	8.09478	0.826170
$97$	−8.44249	−0.857205	−0.428603	−	0.903493i	$-0.640994\pi$
$97$	−8.44249	−0.857205	−0.428603	+	0.903493i	$0.640994\pi$
$98$	16.3557	1.65218
$99$	0.666794	0.0670153
$100$	−13.1053	−1.31053
$101$	5.93445	0.590500	0.295250	−	0.955420i	$-0.404597\pi$
$101$	5.93445	0.590500	0.295250	+	0.955420i	$0.404597\pi$
$102$	−14.4864	−1.43436
$103$	−12.9917	−1.28011	−0.640057	−	0.768327i	$-0.721089\pi$
$103$	−12.9917	−1.28011	−0.640057	+	0.768327i	$0.721089\pi$
$104$	−47.4087	−4.64881
$105$	1.21024	0.118108
$106$	16.2490	1.57825
$107$	−8.50089	−0.821812	−0.410906	−	0.911678i	$-0.634788\pi$
$107$	−8.50089	−0.821812	−0.410906	+	0.911678i	$0.634788\pi$
$108$	−4.67097	−0.449464
$109$	−9.11413	−0.872976	−0.436488	−	0.899710i	$-0.643778\pi$
$109$	−9.11413	−0.872976	−0.436488	+	0.899710i	$0.643778\pi$
$110$	2.55114	0.243242
$111$	−7.30172	−0.693048
$112$	6.92495	0.654347
$113$	0.340676	0.0320481	0.0160240	−	0.999872i	$-0.494899\pi$
$113$	0.340676	0.0320481	0.0160240	+	0.999872i	$0.494899\pi$
$114$	18.6049	1.74251
$115$	−8.65795	−0.807358
$116$	−21.8113	−2.02513
$117$	6.87218	0.635333
$118$	−23.7584	−2.18714
$119$	−4.58236	−0.420065
$120$	−10.2191	−0.932871
$121$	−10.5554	−0.959581
$122$	16.6877	1.51083
$123$	2.05298	0.185111
$124$	22.3422	2.00639
$125$	11.5627	1.03420
$126$	−2.11018	−0.187990
$127$	−10.3200	−0.915750	−0.457875	−	0.889017i	$-0.651389\pi$
$127$	−10.3200	−0.915750	−0.457875	+	0.889017i	$0.651389\pi$
$128$	5.97365	0.528001
$129$	9.77565	0.860698
$130$	26.2928	2.30604
$131$	21.6680	1.89314	0.946571	−	0.322495i	$-0.104522\pi$
$131$	21.6680	1.89314	0.946571	+	0.322495i	$0.104522\pi$
$132$	−3.11457	−0.271089
$133$	5.88514	0.510306
$134$	−1.30655	−0.112869
$135$	1.48132	0.127492
$136$	38.6927	3.31787
$137$	3.89800	0.333029	0.166514	−	0.986039i	$-0.446749\pi$
$137$	3.89800	0.333029	0.166514	+	0.986039i	$0.446749\pi$
$138$	15.0960	1.28506
$139$	−6.97822	−0.591885	−0.295942	−	0.955206i	$-0.595634\pi$
$139$	−6.97822	−0.591885	−0.295942	+	0.955206i	$0.595634\pi$
$140$	−5.65302	−0.477767
$141$	7.43768	0.626366
$142$	−15.5424	−1.30429
$143$	4.58233	0.383194
$144$	8.47602	0.706335
$145$	6.91707	0.574432
$146$	36.6842	3.03601
$147$	6.33250	0.522296
$148$	34.1061	2.80350
$149$	1.24369	0.101887	0.0509435	−	0.998702i	$-0.483777\pi$
$149$	1.24369	0.101887	0.0509435	+	0.998702i	$0.483777\pi$
$150$	−7.24661	−0.591683
$151$	−2.86569	−0.233206	−0.116603	−	0.993179i	$-0.537201\pi$
$151$	−2.86569	−0.233206	−0.116603	+	0.993179i	$0.537201\pi$
$152$	−49.6931	−4.03064
$153$	−5.60874	−0.453439
$154$	−1.40705	−0.113384
$155$	−7.08545	−0.569117
$156$	−32.0998	−2.57004
$157$	−3.76553	−0.300522	−0.150261	−	0.988646i	$-0.548011\pi$
$157$	−3.76553	−0.300522	−0.150261	+	0.988646i	$0.548011\pi$
$158$	8.98163	0.714540
$159$	6.29120	0.498924
$160$	11.9909	0.947967
$161$	4.77520	0.376338
$162$	−2.58282	−0.202926
$163$	6.30244	0.493646	0.246823	−	0.969061i	$-0.420613\pi$
$163$	6.30244	0.493646	0.246823	+	0.969061i	$0.420613\pi$
$164$	−9.58942	−0.748808
$165$	0.987734	0.0768950
$166$	−42.4618	−3.29568
$167$	−10.6818	−0.826582	−0.413291	−	0.910599i	$-0.635621\pi$
$167$	−10.6818	−0.826582	−0.413291	+	0.910599i	$0.635621\pi$
$168$	5.63622	0.434844
$169$	34.2269	2.63284
$170$	−21.4589	−1.64582
$171$	7.20331	0.550851
$172$	−45.6618	−3.48168
$173$	−19.2525	−1.46374	−0.731871	−	0.681443i	$-0.761353\pi$
$173$	−19.2525	−1.46374	−0.731871	+	0.681443i	$0.761353\pi$
$174$	−12.0606	−0.914310
$175$	−2.29227	−0.173279
$176$	5.65176	0.426018
$177$	−9.19862	−0.691410
$178$	46.9803	3.52132
$179$	−19.6522	−1.46888	−0.734439	−	0.678675i	$-0.762554\pi$
$179$	−19.6522	−1.46888	−0.734439	+	0.678675i	$0.762554\pi$
$180$	−6.91920	−0.515726
$181$	−14.5488	−1.08140	−0.540702	−	0.841214i	$-0.681841\pi$
$181$	−14.5488	−1.08140	−0.540702	+	0.841214i	$0.681841\pi$
$182$	−14.5015	−1.07493
$183$	6.46102	0.477612
$184$	−40.3209	−2.97250
$185$	−10.8162	−0.795220
$186$	12.3542	0.905851
$187$	−3.73987	−0.273486
$188$	−34.7412	−2.53376
$189$	−0.817005	−0.0594284
$190$	27.5597	1.99939
$191$	10.5493	0.763323	0.381661	−	0.924302i	$-0.375352\pi$
$191$	10.5493	0.763323	0.381661	+	0.924302i	$0.375352\pi$
$192$	−3.95533	−0.285451
$193$	7.18425	0.517134	0.258567	−	0.965993i	$-0.416750\pi$
$193$	7.18425	0.517134	0.258567	+	0.965993i	$0.416750\pi$
$194$	21.8055	1.56554
$195$	10.1799	0.728997
$196$	−29.5789	−2.11278
$197$	4.83861	0.344737	0.172368	−	0.985033i	$-0.444858\pi$
$197$	4.83861	0.344737	0.172368	+	0.985033i	$0.444858\pi$
$198$	−1.72221	−0.122392
$199$	−4.75078	−0.336774	−0.168387	−	0.985721i	$-0.553856\pi$
$199$	−4.75078	−0.336774	−0.168387	+	0.985721i	$0.553856\pi$
$200$	19.3555	1.36864
$201$	−0.505861	−0.0356807
$202$	−15.3276	−1.07845
$203$	−3.81503	−0.267763
$204$	26.1982	1.83424
$205$	3.04112	0.212401
$206$	33.5554	2.33791
$207$	5.84476	0.406239
$208$	58.2488	4.03883
$209$	4.80312	0.332239
$210$	−3.12585	−0.215704
$211$	20.3861	1.40344	0.701719	−	0.712454i	$-0.252416\pi$
$211$	20.3861	1.40344	0.701719	+	0.712454i	$0.252416\pi$
$212$	−29.3860	−2.01824
$213$	−6.01760	−0.412319
$214$	21.9563	1.50090
$215$	14.4808	0.987586
$216$	6.89864	0.469393
$217$	3.90790	0.265286
$218$	23.5402	1.59434
$219$	14.2032	0.959760
$220$	−4.61368	−0.311054
$221$	−38.5442	−2.59277
$222$	18.8590	1.26574
$223$	9.68342	0.648450	0.324225	−	0.945980i	$-0.394897\pi$
$223$	9.68342	0.648450	0.324225	+	0.945980i	$0.394897\pi$
$224$	−6.61347	−0.441881
$225$	−2.80570	−0.187046
$226$	−0.879905	−0.0585304
$227$	−8.84735	−0.587219	−0.293610	−	0.955925i	$-0.594857\pi$
$227$	−8.84735	−0.587219	−0.293610	+	0.955925i	$0.594857\pi$
$228$	−33.6464	−2.22829
$229$	25.2551	1.66890	0.834451	−	0.551081i	$-0.185785\pi$
$229$	25.2551	1.66890	0.834451	+	0.551081i	$0.185785\pi$
$230$	22.3620	1.47450
$231$	−0.544774	−0.0358435
$232$	32.2135	2.11492
$233$	−16.2806	−1.06658	−0.533290	−	0.845932i	$-0.679045\pi$
$233$	−16.2806	−1.06658	−0.533290	+	0.845932i	$0.679045\pi$
$234$	−17.7496	−1.16033
$235$	11.0176	0.718708
$236$	42.9665	2.79688
$237$	3.47745	0.225885
$238$	11.8354	0.767177
$239$	3.67434	0.237673	0.118837	−	0.992914i	$-0.462084\pi$
$239$	3.67434	0.237673	0.118837	+	0.992914i	$0.462084\pi$
$240$	12.5557	0.810466
$241$	−8.52259	−0.548988	−0.274494	−	0.961589i	$-0.588510\pi$
$241$	−8.52259	−0.548988	−0.274494	+	0.961589i	$0.588510\pi$
$242$	27.2627	1.75251
$243$	−1.00000	−0.0641500
$244$	−30.1792	−1.93203
$245$	9.38045	0.599295
$246$	−5.30249	−0.338074
$247$	49.5025	3.14977
$248$	−32.9976	−2.09535
$249$	−16.4401	−1.04185
$250$	−29.8645	−1.88879
$251$	−2.59851	−0.164017	−0.0820084	−	0.996632i	$-0.526133\pi$
$251$	−2.59851	−0.164017	−0.0820084	+	0.996632i	$0.526133\pi$
$252$	3.81621	0.240398
$253$	3.89725	0.245018
$254$	26.6547	1.67246
$255$	−8.30832	−0.520287
$256$	−23.3395	−1.45872
$257$	−7.81886	−0.487727	−0.243864	−	0.969810i	$-0.578415\pi$
$257$	−7.81886	−0.487727	−0.243864	+	0.969810i	$0.578415\pi$
$258$	−25.2488	−1.57192
$259$	5.96554	0.370680
$260$	−47.5500	−2.94892
$261$	−4.66954	−0.289037
$262$	−55.9646	−3.45750
$263$	−29.5962	−1.82498	−0.912490	−	0.409099i	$-0.865843\pi$
$263$	−29.5962	−1.82498	−0.912490	+	0.409099i	$0.865843\pi$
$264$	4.59997	0.283109
$265$	9.31927	0.572478
$266$	−15.2003	−0.931988
$267$	18.1895	1.11318
$268$	2.36286	0.144335
$269$	12.0242	0.733126	0.366563	−	0.930393i	$-0.380534\pi$
$269$	12.0242	0.733126	0.366563	+	0.930393i	$0.380534\pi$
$270$	−3.82598	−0.232842
$271$	−6.62201	−0.402258	−0.201129	−	0.979565i	$-0.564461\pi$
$271$	−6.62201	−0.402258	−0.201129	+	0.979565i	$0.564461\pi$
$272$	−47.5398	−2.88252
$273$	−5.61461	−0.339811
$274$	−10.0679	−0.608221
$275$	−1.87082	−0.112815
$276$	−27.3007	−1.64331
$277$	−19.4086	−1.16615	−0.583075	−	0.812418i	$-0.698151\pi$
$277$	−19.4086	−1.16615	−0.583075	+	0.812418i	$0.698151\pi$
$278$	18.0235	1.08098
$279$	4.78320	0.286363
$280$	8.34904	0.498951
$281$	−23.9888	−1.43105	−0.715526	−	0.698587i	$-0.753813\pi$
$281$	−23.9888	−1.43105	−0.715526	+	0.698587i	$0.753813\pi$
$282$	−19.2102	−1.14395
$283$	−10.6018	−0.630213	−0.315107	−	0.949056i	$-0.602040\pi$
$283$	−10.6018	−0.630213	−0.315107	+	0.949056i	$0.602040\pi$
$284$	28.1080	1.66790
$285$	10.6704	0.632060
$286$	−11.8353	−0.699838
$287$	−1.67730	−0.0990077
$288$	−8.09478	−0.476989
$289$	14.4579	0.850465
$290$	−17.8656	−1.04910
$291$	8.44249	0.494908
$292$	−66.3425	−3.88240
$293$	−9.71982	−0.567838	−0.283919	−	0.958848i	$-0.591635\pi$
$293$	−9.71982	−0.567838	−0.283919	+	0.958848i	$0.591635\pi$
$294$	−16.3557	−0.953885
$295$	−13.6261	−0.793341
$296$	−50.3719	−2.92781
$297$	−0.666794	−0.0386913
$298$	−3.21223	−0.186079
$299$	40.1663	2.32287
$300$	13.1053	0.756636
$301$	−7.98675	−0.460349
$302$	7.40156	0.425912
$303$	−5.93445	−0.340925
$304$	61.0554	3.50177
$305$	9.57083	0.548024
$306$	14.4864	0.828130
$307$	22.6122	1.29055	0.645273	−	0.763952i	$-0.276744\pi$
$307$	22.6122	1.29055	0.645273	+	0.763952i	$0.276744\pi$
$308$	2.54462	0.144993
$309$	12.9917	0.739075
$310$	18.3005	1.03940
$311$	18.2047	1.03230	0.516148	−	0.856499i	$-0.327365\pi$
$311$	18.2047	1.03230	0.516148	+	0.856499i	$0.327365\pi$
$312$	47.4087	2.68399
$313$	−21.1544	−1.19572	−0.597859	−	0.801601i	$-0.703982\pi$
$313$	−21.1544	−1.19572	−0.597859	+	0.801601i	$0.703982\pi$
$314$	9.72568	0.548852
$315$	−1.21024	−0.0681896
$316$	−16.2431	−0.913744
$317$	7.71933	0.433561	0.216781	−	0.976220i	$-0.430444\pi$
$317$	7.71933	0.433561	0.216781	+	0.976220i	$0.430444\pi$
$318$	−16.2490	−0.911201
$319$	−3.11362	−0.174329
$320$	−5.85910	−0.327534
$321$	8.50089	0.474474
$322$	−12.3335	−0.687319
$323$	−40.4015	−2.24800
$324$	4.67097	0.259498
$325$	−19.2812	−1.06953
$326$	−16.2781	−0.901560
$327$	9.11413	0.504013
$328$	14.1628	0.782009
$329$	−6.07663	−0.335015
$330$	−2.55114	−0.140436
$331$	−26.6036	−1.46226	−0.731132	−	0.682236i	$-0.761008\pi$
$331$	−26.6036	−1.46226	−0.731132	+	0.682236i	$0.761008\pi$
$332$	76.7912	4.21446
$333$	7.30172	0.400132
$334$	27.5892	1.50961
$335$	−0.749342	−0.0409409
$336$	−6.92495	−0.377787
$337$	16.1704	0.880856	0.440428	−	0.897788i	$-0.354827\pi$
$337$	16.1704	0.880856	0.440428	+	0.897788i	$0.354827\pi$
$338$	−88.4020	−4.80843
$339$	−0.340676	−0.0185030
$340$	38.8079	2.10466
$341$	3.18941	0.172716
$342$	−18.6049	−1.00604
$343$	−10.8927	−0.588152
$344$	67.4387	3.63605
$345$	8.65795	0.466129
$346$	49.7258	2.67328
$347$	23.0245	1.23602	0.618011	−	0.786170i	$-0.287939\pi$
$347$	23.0245	1.23602	0.618011	+	0.786170i	$0.287939\pi$
$348$	21.8113	1.16921
$349$	−10.6669	−0.570986	−0.285493	−	0.958381i	$-0.592157\pi$
$349$	−10.6669	−0.570986	−0.285493	+	0.958381i	$0.592157\pi$
$350$	5.92052	0.316465
$351$	−6.87218	−0.366810
$352$	−5.39755	−0.287690
$353$	11.9521	0.636145	0.318073	−	0.948066i	$-0.396964\pi$
$353$	11.9521	0.636145	0.318073	+	0.948066i	$0.396964\pi$
$354$	23.7584	1.26274
$355$	−8.91398	−0.473105
$356$	−84.9627	−4.50301
$357$	4.58236	0.242524
$358$	50.7582	2.68266
$359$	33.8711	1.78765	0.893825	−	0.448415i	$-0.148011\pi$
$359$	33.8711	1.78765	0.893825	+	0.448415i	$0.148011\pi$
$360$	10.2191	0.538593
$361$	32.8877	1.73093
$362$	37.5770	1.97500
$363$	10.5554	0.554014
$364$	26.2257	1.37460
$365$	21.0394	1.10125
$366$	−16.6877	−0.872278
$367$	−29.3370	−1.53138	−0.765690	−	0.643209i	$-0.777602\pi$
$367$	−29.3370	−1.53138	−0.765690	+	0.643209i	$0.777602\pi$
$368$	49.5403	2.58247
$369$	−2.05298	−0.106874
$370$	27.9362	1.45234
$371$	−5.13994	−0.266852
$372$	−22.3422	−1.15839
$373$	17.1548	0.888244	0.444122	−	0.895966i	$-0.353516\pi$
$373$	17.1548	0.888244	0.444122	+	0.895966i	$0.353516\pi$
$374$	9.65942	0.499477
$375$	−11.5627	−0.597096
$376$	51.3099	2.64611
$377$	−32.0899	−1.65271
$378$	2.11018	0.108536
$379$	14.4272	0.741078	0.370539	−	0.928817i	$-0.379173\pi$
$379$	14.4272	0.741078	0.370539	+	0.928817i	$0.379173\pi$
$380$	−49.8411	−2.55680
$381$	10.3200	0.528708
$382$	−27.2470	−1.39408
$383$	−16.7541	−0.856092	−0.428046	−	0.903757i	$-0.640798\pi$
$383$	−16.7541	−0.856092	−0.428046	+	0.903757i	$0.640798\pi$
$384$	−5.97365	−0.304842
$385$	−0.806984	−0.0411277
$386$	−18.5556	−0.944457
$387$	−9.77565	−0.496924
$388$	−39.4346	−2.00199
$389$	2.29595	0.116410	0.0582048	−	0.998305i	$-0.481462\pi$
$389$	2.29595	0.116410	0.0582048	+	0.998305i	$0.481462\pi$
$390$	−26.2928	−1.33139
$391$	−32.7817	−1.65784
$392$	43.6857	2.20646
$393$	−21.6680	−1.09301
$394$	−12.4973	−0.629603
$395$	5.15121	0.259186
$396$	3.11457	0.156513
$397$	35.6428	1.78886	0.894431	−	0.447207i	$-0.147581\pi$
$397$	35.6428	1.78886	0.894431	+	0.447207i	$0.147581\pi$
$398$	12.2704	0.615061
$399$	−5.88514	−0.294626
$400$	−23.7811	−1.18906
$401$	6.06166	0.302705	0.151352	−	0.988480i	$-0.451637\pi$
$401$	6.06166	0.302705	0.151352	+	0.988480i	$0.451637\pi$
$402$	1.30655	0.0651648
$403$	32.8710	1.63742
$404$	27.7197	1.37910
$405$	−1.48132	−0.0736073
$406$	9.85356	0.489024
$407$	4.86874	0.241334
$408$	−38.6927	−1.91557
$409$	30.9281	1.52930	0.764649	−	0.644447i	$-0.222912\pi$
$409$	30.9281	1.52930	0.764649	+	0.644447i	$0.222912\pi$
$410$	−7.85467	−0.387915
$411$	−3.89800	−0.192274
$412$	−60.6841	−2.98969
$413$	7.51531	0.369804
$414$	−15.0960	−0.741927
$415$	−24.3530	−1.19544
$416$	−55.6288	−2.72743
$417$	6.97822	0.341725
$418$	−12.4056	−0.606778
$419$	35.1825	1.71878	0.859388	−	0.511325i	$-0.170845\pi$
$419$	35.1825	1.71878	0.859388	+	0.511325i	$0.170845\pi$
$420$	5.65302	0.275839
$421$	−5.28708	−0.257676	−0.128838	−	0.991666i	$-0.541125\pi$
$421$	−5.28708	−0.257676	−0.128838	+	0.991666i	$0.541125\pi$
$422$	−52.6537	−2.56314
$423$	−7.43768	−0.361633
$424$	43.4007	2.10772
$425$	15.7364	0.763328
$426$	15.5424	0.753031
$427$	−5.27869	−0.255454
$428$	−39.7074	−1.91933
$429$	−4.58233	−0.221237
$430$	−37.4015	−1.80366
$431$	8.50896	0.409862	0.204931	−	0.978776i	$-0.434303\pi$
$431$	8.50896	0.409862	0.204931	+	0.978776i	$0.434303\pi$
$432$	−8.47602	−0.407803
$433$	−24.3682	−1.17106	−0.585531	−	0.810650i	$-0.699114\pi$
$433$	−24.3682	−1.17106	−0.585531	+	0.810650i	$0.699114\pi$
$434$	−10.0934	−0.484499
$435$	−6.91707	−0.331648
$436$	−42.5718	−2.03882
$437$	42.1016	2.01399
$438$	−36.6842	−1.75284
$439$	10.4500	0.498752	0.249376	−	0.968407i	$-0.419775\pi$
$439$	10.4500	0.498752	0.249376	+	0.968407i	$0.419775\pi$
$440$	6.81402	0.324846
$441$	−6.33250	−0.301548
$442$	99.5529	4.73525
$443$	4.80716	0.228395	0.114197	−	0.993458i	$-0.463570\pi$
$443$	4.80716	0.228395	0.114197	+	0.993458i	$0.463570\pi$
$444$	−34.1061	−1.61860
$445$	26.9445	1.27729
$446$	−25.0105	−1.18428
$447$	−1.24369	−0.0588244
$448$	3.23152	0.152675
$449$	24.4513	1.15393	0.576964	−	0.816769i	$-0.304237\pi$
$449$	24.4513	1.15393	0.576964	+	0.816769i	$0.304237\pi$
$450$	7.24661	0.341609
$451$	−1.36892	−0.0644597
$452$	1.59129	0.0748479
$453$	2.86569	0.134642
$454$	22.8511	1.07246
$455$	−8.31702	−0.389908
$456$	49.6931	2.32709
$457$	−3.67631	−0.171971	−0.0859853	−	0.996296i	$-0.527404\pi$
$457$	−3.67631	−0.171971	−0.0859853	+	0.996296i	$0.527404\pi$
$458$	−65.2294	−3.04797
$459$	5.60874	0.261793
$460$	−40.4410	−1.88557
$461$	4.03960	0.188143	0.0940715	−	0.995565i	$-0.470012\pi$
$461$	4.03960	0.188143	0.0940715	+	0.995565i	$0.470012\pi$
$462$	1.40705	0.0654621
$463$	−4.04251	−0.187871	−0.0939357	−	0.995578i	$-0.529945\pi$
$463$	−4.04251	−0.187871	−0.0939357	+	0.995578i	$0.529945\pi$
$464$	−39.5791	−1.83741
$465$	7.08545	0.328580
$466$	42.0500	1.94793
$467$	−28.2038	−1.30512	−0.652558	−	0.757739i	$-0.726304\pi$
$467$	−28.2038	−1.30512	−0.652558	+	0.757739i	$0.726304\pi$
$468$	32.0998	1.48381
$469$	0.413291	0.0190840
$470$	−28.4565	−1.31260
$471$	3.76553	0.173506
$472$	−63.4579	−2.92089
$473$	−6.51834	−0.299714
$474$	−8.98163	−0.412540
$475$	−20.2103	−0.927312
$476$	−21.4041	−0.981055
$477$	−6.29120	−0.288054
$478$	−9.49016	−0.434070
$479$	−18.7723	−0.857729	−0.428865	−	0.903369i	$-0.641086\pi$
$479$	−18.7723	−0.857729	−0.428865	+	0.903369i	$0.641086\pi$
$480$	−11.9909	−0.547309
$481$	50.1787	2.28795
$482$	22.0123	1.00263
$483$	−4.77520	−0.217279
$484$	−49.3039	−2.24109
$485$	12.5060	0.567869
$486$	2.58282	0.117159
$487$	30.0189	1.36029	0.680143	−	0.733079i	$-0.261918\pi$
$487$	30.0189	1.36029	0.680143	+	0.733079i	$0.261918\pi$
$488$	44.5723	2.01769
$489$	−6.30244	−0.285006
$490$	−24.2280	−1.09451
$491$	−6.76231	−0.305179	−0.152589	−	0.988290i	$-0.548761\pi$
$491$	−6.76231	−0.305179	−0.152589	+	0.988290i	$0.548761\pi$
$492$	9.58942	0.432324
$493$	26.1902	1.17955
$494$	−127.856	−5.75252
$495$	−0.987734	−0.0443954
$496$	40.5425	1.82041
$497$	4.91641	0.220531
$498$	42.4618	1.90276
$499$	25.5349	1.14310	0.571551	−	0.820567i	$-0.306342\pi$
$499$	25.5349	1.14310	0.571551	+	0.820567i	$0.306342\pi$
$500$	54.0091	2.41536
$501$	10.6818	0.477228
$502$	6.71150	0.299549
$503$	12.2485	0.546133	0.273066	−	0.961995i	$-0.411962\pi$
$503$	12.2485	0.546133	0.273066	+	0.961995i	$0.411962\pi$
$504$	−5.63622	−0.251057
$505$	−8.79082	−0.391186
$506$	−10.0659	−0.447484
$507$	−34.2269	−1.52007
$508$	−48.2043	−2.13872
$509$	−33.9030	−1.50272	−0.751362	−	0.659890i	$-0.770603\pi$
$509$	−33.9030	−1.50272	−0.751362	+	0.659890i	$0.770603\pi$
$510$	21.4589	0.950217
$511$	−11.6041	−0.513333
$512$	48.3346	2.13611
$513$	−7.20331	−0.318034
$514$	20.1947	0.890751
$515$	19.2449	0.848032
$516$	45.6618	2.01015
$517$	−4.95940	−0.218114
$518$	−15.4079	−0.676985
$519$	19.2525	0.845092
$520$	70.2274	3.07968
$521$	−14.2661	−0.625010	−0.312505	−	0.949916i	$-0.601168\pi$
$521$	−14.2661	−0.625010	−0.312505	+	0.949916i	$0.601168\pi$
$522$	12.0606	0.527877
$523$	4.75412	0.207883	0.103941	−	0.994583i	$-0.466855\pi$
$523$	4.75412	0.207883	0.103941	+	0.994583i	$0.466855\pi$
$524$	101.211	4.42141
$525$	2.29227	0.100043
$526$	76.4417	3.33302
$527$	−26.8277	−1.16863
$528$	−5.65176	−0.245961
$529$	11.1612	0.485271
$530$	−24.0700	−1.04553
$531$	9.19862	0.399186
$532$	27.4893	1.19181
$533$	−14.1085	−0.611106
$534$	−46.9803	−2.03304
$535$	12.5925	0.544423
$536$	−3.48976	−0.150734
$537$	19.6522	0.848057
$538$	−31.0563	−1.33893
$539$	−4.22247	−0.181875
$540$	6.91920	0.297755
$541$	39.6133	1.70311	0.851554	−	0.524267i	$-0.175660\pi$
$541$	39.6133	1.70311	0.851554	+	0.524267i	$0.175660\pi$
$542$	17.1035	0.734657
$543$	14.5488	0.624349
$544$	45.4015	1.94657
$545$	13.5009	0.578316
$546$	14.5015	0.620608
$547$	−3.65356	−0.156215	−0.0781075	−	0.996945i	$-0.524888\pi$
$547$	−3.65356	−0.156215	−0.0781075	+	0.996945i	$0.524888\pi$
$548$	18.2075	0.777784
$549$	−6.46102	−0.275750
$550$	4.83200	0.206037
$551$	−33.6361	−1.43295
$552$	40.3209	1.71617
$553$	−2.84109	−0.120816
$554$	50.1290	2.12978
$555$	10.8162	0.459121
$556$	−32.5951	−1.38234
$557$	−41.9569	−1.77777	−0.888885	−	0.458131i	$-0.848519\pi$
$557$	−41.9569	−1.77777	−0.888885	+	0.458131i	$0.848519\pi$
$558$	−12.3542	−0.522993
$559$	−67.1800	−2.84141
$560$	−10.2581	−0.433482
$561$	3.73987	0.157897
$562$	61.9588	2.61357
$563$	15.5263	0.654357	0.327178	−	0.944963i	$-0.393902\pi$
$563$	15.5263	0.654357	0.327178	+	0.944963i	$0.393902\pi$
$564$	34.7412	1.46287
$565$	−0.504650	−0.0212308
$566$	27.3826	1.15098
$567$	0.817005	0.0343110
$568$	−41.5132	−1.74186
$569$	−7.26510	−0.304569	−0.152284	−	0.988337i	$-0.548663\pi$
$569$	−7.26510	−0.304569	−0.152284	+	0.988337i	$0.548663\pi$
$570$	−27.5597	−1.15435
$571$	−23.6172	−0.988350	−0.494175	−	0.869362i	$-0.664530\pi$
$571$	−23.6172	−0.988350	−0.494175	+	0.869362i	$0.664530\pi$
$572$	21.4039	0.894943
$573$	−10.5493	−0.440705
$574$	4.33216	0.180821
$575$	−16.3986	−0.683870
$576$	3.95533	0.164805
$577$	−9.24128	−0.384719	−0.192360	−	0.981324i	$-0.561614\pi$
$577$	−9.24128	−0.384719	−0.192360	+	0.981324i	$0.561614\pi$
$578$	−37.3422	−1.55323
$579$	−7.18425	−0.298567
$580$	32.3094	1.34158
$581$	13.4316	0.557238
$582$	−21.8055	−0.903865
$583$	−4.19493	−0.173736
$584$	97.9825	4.05454
$585$	−10.1799	−0.420887
$586$	25.1046	1.03706
$587$	12.4672	0.514577	0.257288	−	0.966335i	$-0.417171\pi$
$587$	12.4672	0.514577	0.257288	+	0.966335i	$0.417171\pi$
$588$	29.5789	1.21981
$589$	34.4549	1.41969
$590$	35.1937	1.44890
$591$	−4.83861	−0.199034
$592$	61.8895	2.54364
$593$	−20.4437	−0.839520	−0.419760	−	0.907635i	$-0.637886\pi$
$593$	−20.4437	−0.839520	−0.419760	+	0.907635i	$0.637886\pi$
$594$	1.72221	0.0706631
$595$	6.78794	0.278278
$596$	5.80923	0.237955
$597$	4.75078	0.194437
$598$	−103.742	−4.24234
$599$	−25.4240	−1.03880	−0.519399	−	0.854532i	$-0.673844\pi$
$599$	−25.4240	−1.03880	−0.519399	+	0.854532i	$0.673844\pi$
$600$	−19.3555	−0.790184
$601$	3.27930	0.133765	0.0668827	−	0.997761i	$-0.478695\pi$
$601$	3.27930	0.133765	0.0668827	+	0.997761i	$0.478695\pi$
$602$	20.6284	0.840749
$603$	0.505861	0.0206003
$604$	−13.3855	−0.544650
$605$	15.6359	0.635689
$606$	15.3276	0.622643
$607$	−6.63663	−0.269373	−0.134686	−	0.990888i	$-0.543003\pi$
$607$	−6.63663	−0.269373	−0.134686	+	0.990888i	$0.543003\pi$
$608$	−58.3092	−2.36475
$609$	3.81503	0.154593
$610$	−24.7198	−1.00087
$611$	−51.1131	−2.06782
$612$	−26.1982	−1.05900
$613$	5.28671	0.213528	0.106764	−	0.994284i	$-0.465951\pi$
$613$	5.28671	0.213528	0.106764	+	0.994284i	$0.465951\pi$
$614$	−58.4032	−2.35696
$615$	−3.04112	−0.122630
$616$	−3.75820	−0.151422
$617$	7.52806	0.303068	0.151534	−	0.988452i	$-0.451579\pi$
$617$	7.52806	0.303068	0.151534	+	0.988452i	$0.451579\pi$
$618$	−33.5554	−1.34979
$619$	35.1564	1.41306	0.706528	−	0.707685i	$-0.250260\pi$
$619$	35.1564	1.41306	0.706528	+	0.707685i	$0.250260\pi$
$620$	−33.0959	−1.32916
$621$	−5.84476	−0.234542
$622$	−47.0196	−1.88531
$623$	−14.8609	−0.595390
$624$	−58.2488	−2.33182
$625$	−3.09960	−0.123984
$626$	54.6381	2.18378
$627$	−4.80312	−0.191818
$628$	−17.5887	−0.701864
$629$	−40.9534	−1.63292
$630$	3.12585	0.124537
$631$	−40.7195	−1.62102	−0.810509	−	0.585726i	$-0.800810\pi$
$631$	−40.7195	−1.62102	−0.810509	+	0.585726i	$0.800810\pi$
$632$	23.9897	0.954258
$633$	−20.3861	−0.810276
$634$	−19.9377	−0.791826
$635$	15.2872	0.606653
$636$	29.3860	1.16523
$637$	−43.5181	−1.72425
$638$	8.04192	0.318383
$639$	6.01760	0.238052
$640$	−8.84888	−0.349783
$641$	18.5404	0.732300	0.366150	−	0.930556i	$-0.380676\pi$
$641$	18.5404	0.732300	0.366150	+	0.930556i	$0.380676\pi$
$642$	−21.9563	−0.866546
$643$	3.54763	0.139905	0.0699524	−	0.997550i	$-0.477715\pi$
$643$	3.54763	0.139905	0.0699524	+	0.997550i	$0.477715\pi$
$644$	22.3048	0.878933
$645$	−14.4808	−0.570183
$646$	104.350	4.10559
$647$	−17.9844	−0.707041	−0.353520	−	0.935427i	$-0.615016\pi$
$647$	−17.9844	−0.707041	−0.353520	+	0.935427i	$0.615016\pi$
$648$	−6.89864	−0.271004
$649$	6.13358	0.240764
$650$	49.8000	1.95332
$651$	−3.90790	−0.153163
$652$	29.4385	1.15290
$653$	30.3127	1.18623	0.593113	−	0.805119i	$-0.297899\pi$
$653$	30.3127	1.18623	0.593113	+	0.805119i	$0.297899\pi$
$654$	−23.5402	−0.920494
$655$	−32.0972	−1.25414
$656$	−17.4011	−0.679400
$657$	−14.2032	−0.554118
$658$	15.6948	0.611849
$659$	−2.38178	−0.0927811	−0.0463905	−	0.998923i	$-0.514772\pi$
$659$	−2.38178	−0.0927811	−0.0463905	+	0.998923i	$0.514772\pi$
$660$	4.61368	0.179587
$661$	−0.817034	−0.0317789	−0.0158895	−	0.999874i	$-0.505058\pi$
$661$	−0.817034	−0.0317789	−0.0158895	+	0.999874i	$0.505058\pi$
$662$	68.7123	2.67058
$663$	38.5442	1.49693
$664$	−113.414	−4.40133
$665$	−8.71777	−0.338061
$666$	−18.8590	−0.730773
$667$	−27.2923	−1.05676
$668$	−49.8944	−1.93047
$669$	−9.68342	−0.374383
$670$	1.93542	0.0747717
$671$	−4.30817	−0.166315
$672$	6.61347	0.255120
$673$	−36.6693	−1.41350	−0.706749	−	0.707465i	$-0.749839\pi$
$673$	−36.6693	−1.41350	−0.706749	+	0.707465i	$0.749839\pi$
$674$	−41.7652	−1.60873
$675$	2.80570	0.107991
$676$	159.873	6.14895
$677$	18.5085	0.711338	0.355669	−	0.934612i	$-0.384253\pi$
$677$	18.5085	0.711338	0.355669	+	0.934612i	$0.384253\pi$
$678$	0.879905	0.0337926
$679$	−6.89756	−0.264704
$680$	−57.3161	−2.19797
$681$	8.84735	0.339031
$682$	−8.23768	−0.315437
$683$	−9.92057	−0.379600	−0.189800	−	0.981823i	$-0.560784\pi$
$683$	−9.92057	−0.379600	−0.189800	+	0.981823i	$0.560784\pi$
$684$	33.6464	1.28650
$685$	−5.77419	−0.220620
$686$	28.1340	1.07416
$687$	−25.2551	−0.963542
$688$	−82.8586	−3.15895
$689$	−43.2342	−1.64709
$690$	−22.3620	−0.851305
$691$	−25.7094	−0.978031	−0.489015	−	0.872275i	$-0.662644\pi$
$691$	−25.7094	−0.978031	−0.489015	+	0.872275i	$0.662644\pi$
$692$	−89.9279	−3.41855
$693$	0.544774	0.0206943
$694$	−59.4683	−2.25738
$695$	10.3370	0.392104
$696$	−32.2135	−1.22105
$697$	11.5146	0.436148
$698$	27.5507	1.04281
$699$	16.2806	0.615790
$700$	−10.7071	−0.404691
$701$	−44.6703	−1.68718	−0.843588	−	0.536991i	$-0.819561\pi$
$701$	−44.6703	−1.68718	−0.843588	+	0.536991i	$0.819561\pi$
$702$	17.7496	0.669916
$703$	52.5965	1.98372
$704$	2.63739	0.0994003
$705$	−11.0176	−0.414946
$706$	−30.8701	−1.16181
$707$	4.84848	0.182346
$708$	−42.9665	−1.61478
$709$	−44.1526	−1.65818	−0.829092	−	0.559112i	$-0.811142\pi$
$709$	−44.1526	−1.65818	−0.829092	+	0.559112i	$0.811142\pi$
$710$	23.0232	0.864046
$711$	−3.47745	−0.130415
$712$	125.483	4.70267
$713$	27.9567	1.04699
$714$	−11.8354	−0.442930
$715$	−6.78789	−0.253853
$716$	−91.7950	−3.43054
$717$	−3.67434	−0.137221
$718$	−87.4832	−3.26484
$719$	4.64981	0.173409	0.0867043	−	0.996234i	$-0.472366\pi$
$719$	4.64981	0.173409	0.0867043	+	0.996234i	$0.472366\pi$
$720$	−12.5557	−0.467923
$721$	−10.6143	−0.395298
$722$	−84.9430	−3.16125
$723$	8.52259	0.316959
$724$	−67.9570	−2.52560
$725$	13.1013	0.486570
$726$	−27.2627	−1.01181
$727$	−9.98988	−0.370504	−0.185252	−	0.982691i	$-0.559310\pi$
$727$	−9.98988	−0.370504	−0.185252	+	0.982691i	$0.559310\pi$
$728$	−38.7332	−1.43555
$729$	1.00000	0.0370370
$730$	−54.3410	−2.01125
$731$	54.8290	2.02792
$732$	30.1792	1.11546
$733$	−35.0942	−1.29624	−0.648118	−	0.761540i	$-0.724443\pi$
$733$	−35.0942	−1.29624	−0.648118	+	0.761540i	$0.724443\pi$
$734$	75.7723	2.79681
$735$	−9.38045	−0.346003
$736$	−47.3120	−1.74395
$737$	0.337305	0.0124248
$738$	5.30249	0.195187
$739$	5.83829	0.214765	0.107382	−	0.994218i	$-0.465753\pi$
$739$	5.83829	0.214765	0.107382	+	0.994218i	$0.465753\pi$
$740$	−50.5220	−1.85723
$741$	−49.5025	−1.81852
$742$	13.2755	0.487361
$743$	−41.1773	−1.51065	−0.755324	−	0.655352i	$-0.772520\pi$
$743$	−41.1773	−1.51065	−0.755324	+	0.655352i	$0.772520\pi$
$744$	32.9976	1.20975
$745$	−1.84230	−0.0674966
$746$	−44.3079	−1.62223
$747$	16.4401	0.601511
$748$	−17.4688	−0.638723
$749$	−6.94527	−0.253775
$750$	29.8645	1.09050
$751$	−29.4188	−1.07351	−0.536753	−	0.843739i	$-0.680349\pi$
$751$	−29.4188	−1.07351	−0.536753	+	0.843739i	$0.680349\pi$
$752$	−63.0420	−2.29890
$753$	2.59851	0.0946951
$754$	82.8825	3.01840
$755$	4.24500	0.154491
$756$	−3.81621	−0.138794
$757$	15.2292	0.553515	0.276758	−	0.960940i	$-0.410740\pi$
$757$	15.2292	0.553515	0.276758	+	0.960940i	$0.410740\pi$
$758$	−37.2630	−1.35345
$759$	−3.89725	−0.141461
$760$	73.6112	2.67016
$761$	−9.48383	−0.343789	−0.171894	−	0.985115i	$-0.554989\pi$
$761$	−9.48383	−0.343789	−0.171894	+	0.985115i	$0.554989\pi$
$762$	−26.6547	−0.965597
$763$	−7.44629	−0.269574
$764$	49.2756	1.78273
$765$	8.30832	0.300388
$766$	43.2727	1.56351
$767$	63.2146	2.28255
$768$	23.3395	0.842193
$769$	−0.521925	−0.0188211	−0.00941054	−	0.999956i	$-0.502996\pi$
$769$	−0.521925	−0.0188211	−0.00941054	+	0.999956i	$0.502996\pi$
$770$	2.08430	0.0751128
$771$	7.81886	0.281589
$772$	33.5574	1.20776
$773$	−8.70989	−0.313273	−0.156636	−	0.987656i	$-0.550065\pi$
$773$	−8.70989	−0.313273	−0.156636	+	0.987656i	$0.550065\pi$
$774$	25.2488	0.907548
$775$	−13.4202	−0.482068
$776$	58.2417	2.09076
$777$	−5.96554	−0.214012
$778$	−5.93004	−0.212602
$779$	−14.7883	−0.529845
$780$	47.5500	1.70256
$781$	4.01250	0.143578
$782$	84.6693	3.02777
$783$	4.66954	0.166876
$784$	−53.6744	−1.91694
$785$	5.57794	0.199085
$786$	55.9646	1.99619
$787$	−38.7180	−1.38015	−0.690073	−	0.723739i	$-0.742422\pi$
$787$	−38.7180	−1.38015	−0.690073	+	0.723739i	$0.742422\pi$
$788$	22.6010	0.805127
$789$	29.5962	1.05365
$790$	−13.3047	−0.473359
$791$	0.278334	0.00989642
$792$	−4.59997	−0.163453
$793$	−44.4013	−1.57674
$794$	−92.0590	−3.26705
$795$	−9.31927	−0.330520
$796$	−22.1908	−0.786531
$797$	−50.5659	−1.79113	−0.895567	−	0.444926i	$-0.853230\pi$
$797$	−50.5659	−1.79113	−0.895567	+	0.444926i	$0.853230\pi$
$798$	15.2003	0.538084
$799$	41.7160	1.47581
$800$	22.7115	0.802972
$801$	−18.1895	−0.642695
$802$	−15.6562	−0.552839
$803$	−9.47058	−0.334209
$804$	−2.36286	−0.0833318
$805$	−7.07359	−0.249311
$806$	−84.9001	−2.99048
$807$	−12.0242	−0.423271
$808$	−40.9397	−1.44025
$809$	4.78015	0.168061	0.0840306	−	0.996463i	$-0.473221\pi$
$809$	4.78015	0.168061	0.0840306	+	0.996463i	$0.473221\pi$
$810$	3.82598	0.134431
$811$	−28.1439	−0.988266	−0.494133	−	0.869386i	$-0.664514\pi$
$811$	−28.1439	−0.988266	−0.494133	+	0.869386i	$0.664514\pi$
$812$	−17.8199	−0.625356
$813$	6.62201	0.232244
$814$	−12.5751	−0.440757
$815$	−9.33593	−0.327023
$816$	47.5398	1.66422
$817$	−70.4170	−2.46358
$818$	−79.8819	−2.79300
$819$	5.61461	0.196190
$820$	14.2050	0.496060
$821$	18.7723	0.655159	0.327580	−	0.944824i	$-0.393767\pi$
$821$	18.7723	0.655159	0.327580	+	0.944824i	$0.393767\pi$
$822$	10.0679	0.351157
$823$	−0.00268134	−9.34655e−5 0	−4.67328e−5	−	1.00000i	$-0.500015\pi$
$823$	−0.00268134	−9.34655e−5 0	−4.67328e−5		1.00000i	$0.500015\pi$
$824$	89.6254	3.12225
$825$	1.87082	0.0651336
$826$	−19.4107	−0.675385
$827$	−9.98245	−0.347124	−0.173562	−	0.984823i	$-0.555528\pi$
$827$	−9.98245	−0.347124	−0.173562	+	0.984823i	$0.555528\pi$
$828$	27.3007	0.948765
$829$	55.0104	1.91059	0.955295	−	0.295654i	$-0.0955376\pi$
$829$	55.0104	1.91059	0.955295	+	0.295654i	$0.0955376\pi$
$830$	62.8995	2.18327
$831$	19.4086	0.673277
$832$	27.1817	0.942357
$833$	35.5173	1.23060
$834$	−18.0235	−0.624103
$835$	15.8231	0.547583
$836$	22.4352	0.775939
$837$	−4.78320	−0.165332
$838$	−90.8700	−3.13905
$839$	−39.2886	−1.35639	−0.678196	−	0.734881i	$-0.737238\pi$
$839$	−39.2886	−1.35639	−0.678196	+	0.734881i	$0.737238\pi$
$840$	−8.34904	−0.288069
$841$	−7.19543	−0.248118
$842$	13.6556	0.470602
$843$	23.9888	0.826218
$844$	95.2230	3.27771
$845$	−50.7009	−1.74416
$846$	19.2102	0.660461
$847$	−8.62380	−0.296317
$848$	−53.3243	−1.83116
$849$	10.6018	0.363854
$850$	−40.6443	−1.39409
$851$	42.6768	1.46294
$852$	−28.1080	−0.962965
$853$	−22.2826	−0.762942	−0.381471	−	0.924381i	$-0.624582\pi$
$853$	−22.2826	−0.762942	−0.381471	+	0.924381i	$0.624582\pi$
$854$	13.6339	0.466543
$855$	−10.6704	−0.364920
$856$	58.6446	2.00443
$857$	−39.5575	−1.35126	−0.675629	−	0.737242i	$-0.736128\pi$
$857$	−39.5575	−1.35126	−0.675629	+	0.737242i	$0.736128\pi$
$858$	11.8353	0.404052
$859$	24.4168	0.833090	0.416545	−	0.909115i	$-0.363241\pi$
$859$	24.4168	0.833090	0.416545	+	0.909115i	$0.363241\pi$
$860$	67.6396	2.30649
$861$	1.67730	0.0571621
$862$	−21.9771	−0.748544
$863$	3.20867	0.109224	0.0546122	−	0.998508i	$-0.482608\pi$
$863$	3.20867	0.109224	0.0546122	+	0.998508i	$0.482608\pi$
$864$	8.09478	0.275390
$865$	28.5191	0.969679
$866$	62.9388	2.13875
$867$	−14.4579	−0.491016
$868$	18.2537	0.619571
$869$	−2.31874	−0.0786579
$870$	17.8656	0.605699
$871$	3.47637	0.117792
$872$	62.8751	2.12922
$873$	−8.44249	−0.285735
$874$	−108.741	−3.67822
$875$	9.44680	0.319360
$876$	66.3425	2.24151
$877$	−28.8151	−0.973016	−0.486508	−	0.873676i	$-0.661730\pi$
$877$	−28.8151	−0.973016	−0.486508	+	0.873676i	$0.661730\pi$
$878$	−26.9905	−0.910886
$879$	9.71982	0.327841
$880$	−8.37206	−0.282222
$881$	−12.5894	−0.424147	−0.212074	−	0.977254i	$-0.568022\pi$
$881$	−12.5894	−0.424147	−0.212074	+	0.977254i	$0.568022\pi$
$882$	16.3557	0.550726
$883$	−54.9845	−1.85037	−0.925187	−	0.379511i	$-0.876092\pi$
$883$	−54.9845	−1.85037	−0.925187	+	0.379511i	$0.876092\pi$
$884$	−180.039	−6.05537
$885$	13.6261	0.458036
$886$	−12.4160	−0.417125
$887$	11.9411	0.400944	0.200472	−	0.979699i	$-0.435752\pi$
$887$	11.9411	0.400944	0.200472	+	0.979699i	$0.435752\pi$
$888$	50.3719	1.69037
$889$	−8.43147	−0.282782
$890$	−69.5927	−2.33275
$891$	0.666794	0.0223384
$892$	45.2310	1.51444
$893$	−53.5760	−1.79285
$894$	3.21223	0.107433
$895$	29.1112	0.973081
$896$	4.88050	0.163046
$897$	−40.1663	−1.34111
$898$	−63.1534	−2.10746
$899$	−22.3353	−0.744925
$900$	−13.1053	−0.436844
$901$	35.2857	1.17554
$902$	3.53567	0.117725
$903$	7.98675	0.265782
$904$	−2.35020	−0.0781665
$905$	21.5514	0.716393
$906$	−7.40156	−0.245900
$907$	10.4501	0.346990	0.173495	−	0.984835i	$-0.444494\pi$
$907$	10.4501	0.346990	0.173495	+	0.984835i	$0.444494\pi$
$908$	−41.3257	−1.37144
$909$	5.93445	0.196833
$910$	21.4814	0.712101
$911$	−54.6876	−1.81188	−0.905941	−	0.423405i	$-0.860835\pi$
$911$	−54.6876	−1.81188	−0.905941	+	0.423405i	$0.860835\pi$
$912$	−61.0554	−2.02175
$913$	10.9621	0.362794
$914$	9.49526	0.314075
$915$	−9.57083	−0.316402
$916$	117.966	3.89770
$917$	17.7029	0.584600
$918$	−14.4864	−0.478121
$919$	36.1686	1.19309	0.596546	−	0.802579i	$-0.296539\pi$
$919$	36.1686	1.19309	0.596546	+	0.802579i	$0.296539\pi$
$920$	59.7281	1.96918
$921$	−22.6122	−0.745097
$922$	−10.4336	−0.343611
$923$	41.3540	1.36118
$924$	−2.54462	−0.0837120
$925$	−20.4864	−0.673588
$926$	10.4411	0.343116
$927$	−12.9917	−0.426705
$928$	37.7989	1.24081
$929$	40.9149	1.34237	0.671187	−	0.741288i	$-0.265785\pi$
$929$	40.9149	1.34237	0.671187	+	0.741288i	$0.265785\pi$
$930$	−18.3005	−0.600095
$931$	−45.6150	−1.49497
$932$	−76.0464	−2.49098
$933$	−18.2047	−0.595996
$934$	72.8454	2.38357
$935$	5.53994	0.181175
$936$	−47.4087	−1.54960
$937$	−34.8475	−1.13842	−0.569208	−	0.822193i	$-0.692750\pi$
$937$	−34.8475	−1.13842	−0.569208	+	0.822193i	$0.692750\pi$
$938$	−1.06746	−0.0348537
$939$	21.1544	0.690348
$940$	51.4628	1.67853
$941$	−4.01533	−0.130896	−0.0654481	−	0.997856i	$-0.520848\pi$
$941$	−4.01533	−0.130896	−0.0654481	+	0.997856i	$0.520848\pi$
$942$	−9.72568	−0.316880
$943$	−11.9992	−0.390747
$944$	77.9677	2.53763
$945$	1.21024	0.0393693
$946$	16.8357	0.547376
$947$	16.4361	0.534101	0.267050	−	0.963683i	$-0.413951\pi$
$947$	16.4361	0.534101	0.267050	+	0.963683i	$0.413951\pi$
$948$	16.2431	0.527550
$949$	−97.6067	−3.16845
$950$	52.1996	1.69358
$951$	−7.71933	−0.250317
$952$	31.6121	1.02455
$953$	49.8315	1.61420	0.807100	−	0.590415i	$-0.201036\pi$
$953$	49.8315	1.61420	0.807100	+	0.590415i	$0.201036\pi$
$954$	16.2490	0.526082
$955$	−15.6269	−0.505675
$956$	17.1627	0.555082
$957$	3.11362	0.100649
$958$	48.4856	1.56650
$959$	3.18469	0.102839
$960$	5.85910	0.189102
$961$	−8.12097	−0.261967
$962$	−129.603	−4.17856
$963$	−8.50089	−0.273937
$964$	−39.8088	−1.28215
$965$	−10.6422	−0.342583
$966$	12.3335	0.396824
$967$	43.1014	1.38605	0.693023	−	0.720915i	$-0.256278\pi$
$967$	43.1014	1.38605	0.693023	+	0.720915i	$0.256278\pi$
$968$	72.8178	2.34045
$969$	40.4015	1.29788
$970$	−32.3008	−1.03712
$971$	40.3713	1.29558	0.647789	−	0.761820i	$-0.275694\pi$
$971$	40.3713	1.29558	0.647789	+	0.761820i	$0.275694\pi$
$972$	−4.67097	−0.149821
$973$	−5.70124	−0.182773
$974$	−77.5335	−2.48433
$975$	19.2812	0.617494
$976$	−54.7638	−1.75295
$977$	−17.7237	−0.567033	−0.283516	−	0.958967i	$-0.591501\pi$
$977$	−17.7237	−0.567033	−0.283516	+	0.958967i	$0.591501\pi$
$978$	16.2781	0.520516
$979$	−12.1287	−0.387633
$980$	43.8158	1.39965
$981$	−9.11413	−0.290992
$982$	17.4658	0.557357
$983$	−12.1167	−0.386464	−0.193232	−	0.981153i	$-0.561897\pi$
$983$	−12.1167	−0.386464	−0.193232	+	0.981153i	$0.561897\pi$
$984$	−14.1628	−0.451493
$985$	−7.16752	−0.228376
$986$	−67.6446	−2.15424
$987$	6.07663	0.193421
$988$	231.225	7.35623
$989$	−57.1363	−1.81683
$990$	2.55114	0.0810806
$991$	−59.2940	−1.88354	−0.941768	−	0.336263i	$-0.890837\pi$
$991$	−59.2940	−1.88354	−0.941768	+	0.336263i	$0.890837\pi$
$992$	−38.7190	−1.22933
$993$	26.6036	0.844239
$994$	−12.6982	−0.402762
$995$	7.03742	0.223101
$996$	−76.7912	−2.43322
$997$	6.89965	0.218514	0.109257	−	0.994014i	$-0.465153\pi$
$997$	6.89965	0.218514	0.109257	+	0.994014i	$0.465153\pi$
$998$	−65.9522	−2.08768
$999$	−7.30172	−0.231016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.c.1.9	✓	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.c.1.9	✓	116	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58282 q^{2} -1.00000 q^{3} +4.67097 q^{4} -1.48132 q^{5} +2.58282 q^{6} +0.817005 q^{7} -6.89864 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.58282 q^{2} -1.00000 q^{3} +4.67097 q^{4} -1.48132 q^{5} +2.58282 q^{6} +0.817005 q^{7} -6.89864 q^{8} +1.00000 q^{9} +3.82598 q^{10} +0.666794 q^{11} -4.67097 q^{12} +6.87218 q^{13} -2.11018 q^{14} +1.48132 q^{15} +8.47602 q^{16} -5.60874 q^{17} -2.58282 q^{18} +7.20331 q^{19} -6.91920 q^{20} -0.817005 q^{21} -1.72221 q^{22} +5.84476 q^{23} +6.89864 q^{24} -2.80570 q^{25} -17.7496 q^{26} -1.00000 q^{27} +3.81621 q^{28} -4.66954 q^{29} -3.82598 q^{30} +4.78320 q^{31} -8.09478 q^{32} -0.666794 q^{33} +14.4864 q^{34} -1.21024 q^{35} +4.67097 q^{36} +7.30172 q^{37} -18.6049 q^{38} -6.87218 q^{39} +10.2191 q^{40} -2.05298 q^{41} +2.11018 q^{42} -9.77565 q^{43} +3.11457 q^{44} -1.48132 q^{45} -15.0960 q^{46} -7.43768 q^{47} -8.47602 q^{48} -6.33250 q^{49} +7.24661 q^{50} +5.60874 q^{51} +32.0998 q^{52} -6.29120 q^{53} +2.58282 q^{54} -0.987734 q^{55} -5.63622 q^{56} -7.20331 q^{57} +12.0606 q^{58} +9.19862 q^{59} +6.91920 q^{60} -6.46102 q^{61} -12.3542 q^{62} +0.817005 q^{63} +3.95533 q^{64} -10.1799 q^{65} +1.72221 q^{66} +0.505861 q^{67} -26.1982 q^{68} -5.84476 q^{69} +3.12585 q^{70} +6.01760 q^{71} -6.89864 q^{72} -14.2032 q^{73} -18.8590 q^{74} +2.80570 q^{75} +33.6464 q^{76} +0.544774 q^{77} +17.7496 q^{78} -3.47745 q^{79} -12.5557 q^{80} +1.00000 q^{81} +5.30249 q^{82} +16.4401 q^{83} -3.81621 q^{84} +8.30832 q^{85} +25.2488 q^{86} +4.66954 q^{87} -4.59997 q^{88} -18.1895 q^{89} +3.82598 q^{90} +5.61461 q^{91} +27.3007 q^{92} -4.78320 q^{93} +19.2102 q^{94} -10.6704 q^{95} +8.09478 q^{96} -8.44249 q^{97} +16.3557 q^{98} +0.666794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9}+O(q^{10}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9	\( 116 q - 16 q^{2} - 116 q^{3} + 116 q^{4} - 20 q^{5} + 16 q^{6} - 33 q^{7} - 45 q^{8} + 116 q^{9} + 3 q^{10} - 57 q^{11} - 116 q^{12} + 6 q^{13} - 9 q^{14} + 20 q^{15} + 112 q^{16} - 30 q^{17} - 16 q^{18} + 3 q^{19} - 54 q^{20} + 33 q^{21} - 22 q^{22} - 58 q^{23} + 45 q^{24} + 126 q^{25} - 21 q^{26} - 116 q^{27} - 77 q^{28} - 38 q^{29} - 3 q^{30} + 17 q^{31} - 106 q^{32} + 57 q^{33} + 35 q^{34} - 72 q^{35} + 116 q^{36} - 41 q^{37} - 45 q^{38} - 6 q^{39} + 5 q^{40} - 39 q^{41} + 9 q^{42} - 118 q^{43} - 103 q^{44} - 20 q^{45} - 8 q^{46} - 65 q^{47} - 112 q^{48} + 165 q^{49} - 72 q^{50} + 30 q^{51} - 10 q^{52} - 58 q^{53} + 16 q^{54} + 14 q^{55} - 23 q^{56} - 3 q^{57} - 27 q^{58} - 75 q^{59} + 54 q^{60} + 45 q^{61} - 73 q^{62} - 33 q^{63} + 111 q^{64} - 86 q^{65} + 22 q^{66} - 127 q^{67} - 94 q^{68} + 58 q^{69} - 7 q^{70} - 61 q^{71} - 45 q^{72} + 15 q^{73} - 51 q^{74} - 126 q^{75} + 96 q^{76} - 57 q^{77} + 21 q^{78} + 7 q^{79} - 144 q^{80} + 116 q^{81} - 37 q^{82} - 194 q^{83} + 77 q^{84} + 3 q^{85} - 57 q^{86} + 38 q^{87} - 42 q^{88} - 56 q^{89} + 3 q^{90} - 39 q^{91} - 138 q^{92} - 17 q^{93} + 51 q^{94} - 127 q^{95} + 106 q^{96} + 57 q^{97} - 105 q^{98} - 57 q^{99}+O(q^{100}) \) 116 * q - 16 * q^2 - 116 * q^3 + 116 * q^4 - 20 * q^5 + 16 * q^6 - 33 * q^7 - 45 * q^8 + 116 * q^9 + 3 * q^10 - 57 * q^11 - 116 * q^12 + 6 * q^13 - 9 * q^14 + 20 * q^15 + 112 * q^16 - 30 * q^17 - 16 * q^18 + 3 * q^19 - 54 * q^20 + 33 * q^21 - 22 * q^22 - 58 * q^23 + 45 * q^24 + 126 * q^25 - 21 * q^26 - 116 * q^27 - 77 * q^28 - 38 * q^29 - 3 * q^30 + 17 * q^31 - 106 * q^32 + 57 * q^33 + 35 * q^34 - 72 * q^35 + 116 * q^36 - 41 * q^37 - 45 * q^38 - 6 * q^39 + 5 * q^40 - 39 * q^41 + 9 * q^42 - 118 * q^43 - 103 * q^44 - 20 * q^45 - 8 * q^46 - 65 * q^47 - 112 * q^48 + 165 * q^49 - 72 * q^50 + 30 * q^51 - 10 * q^52 - 58 * q^53 + 16 * q^54 + 14 * q^55 - 23 * q^56 - 3 * q^57 - 27 * q^58 - 75 * q^59 + 54 * q^60 + 45 * q^61 - 73 * q^62 - 33 * q^63 + 111 * q^64 - 86 * q^65 + 22 * q^66 - 127 * q^67 - 94 * q^68 + 58 * q^69 - 7 * q^70 - 61 * q^71 - 45 * q^72 + 15 * q^73 - 51 * q^74 - 126 * q^75 + 96 * q^76 - 57 * q^77 + 21 * q^78 + 7 * q^79 - 144 * q^80 + 116 * q^81 - 37 * q^82 - 194 * q^83 + 77 * q^84 + 3 * q^85 - 57 * q^86 + 38 * q^87 - 42 * q^88 - 56 * q^89 + 3 * q^90 - 39 * q^91 - 138 * q^92 - 17 * q^93 + 51 * q^94 - 127 * q^95 + 106 * q^96 + 57 * q^97 - 105 * q^98 - 57 * q^99

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