LMFDB - Embedded newform 8015.2.a.h.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.656564 q^{2} +2.76581 q^{3} -1.56892 q^{4} +1.00000 q^{5} -1.81593 q^{6} +1.00000 q^{7} +2.34323 q^{8} +4.64973 q^{9} +O(q^{10})$	\(q-0.656564 q^{2} +2.76581 q^{3} -1.56892 q^{4} +1.00000 q^{5} -1.81593 q^{6} +1.00000 q^{7} +2.34323 q^{8} +4.64973 q^{9} -0.656564 q^{10} -5.20200 q^{11} -4.33935 q^{12} -0.887601 q^{13} -0.656564 q^{14} +2.76581 q^{15} +1.59937 q^{16} -3.19882 q^{17} -3.05284 q^{18} -3.11669 q^{19} -1.56892 q^{20} +2.76581 q^{21} +3.41544 q^{22} -3.41030 q^{23} +6.48093 q^{24} +1.00000 q^{25} +0.582766 q^{26} +4.56283 q^{27} -1.56892 q^{28} -0.110161 q^{29} -1.81593 q^{30} +3.91453 q^{31} -5.73654 q^{32} -14.3878 q^{33} +2.10023 q^{34} +1.00000 q^{35} -7.29507 q^{36} +8.91873 q^{37} +2.04631 q^{38} -2.45494 q^{39} +2.34323 q^{40} +3.61363 q^{41} -1.81593 q^{42} -2.94495 q^{43} +8.16155 q^{44} +4.64973 q^{45} +2.23908 q^{46} -2.00854 q^{47} +4.42357 q^{48} +1.00000 q^{49} -0.656564 q^{50} -8.84734 q^{51} +1.39258 q^{52} +6.16881 q^{53} -2.99579 q^{54} -5.20200 q^{55} +2.34323 q^{56} -8.62019 q^{57} +0.0723279 q^{58} -4.92096 q^{59} -4.33935 q^{60} -10.9018 q^{61} -2.57014 q^{62} +4.64973 q^{63} +0.567659 q^{64} -0.887601 q^{65} +9.44648 q^{66} +0.0752980 q^{67} +5.01871 q^{68} -9.43224 q^{69} -0.656564 q^{70} +5.92419 q^{71} +10.8954 q^{72} +3.40709 q^{73} -5.85571 q^{74} +2.76581 q^{75} +4.88986 q^{76} -5.20200 q^{77} +1.61182 q^{78} -16.0663 q^{79} +1.59937 q^{80} -1.32923 q^{81} -2.37258 q^{82} +14.0150 q^{83} -4.33935 q^{84} -3.19882 q^{85} +1.93354 q^{86} -0.304686 q^{87} -12.1895 q^{88} -18.1765 q^{89} -3.05284 q^{90} -0.887601 q^{91} +5.35050 q^{92} +10.8269 q^{93} +1.31873 q^{94} -3.11669 q^{95} -15.8662 q^{96} -3.53977 q^{97} -0.656564 q^{98} -24.1879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) $ 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * 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 $

$2$	−0.656564	−0.464261	−0.232130	−	0.972685i	$-0.574570\pi$
$2$	−0.656564	−0.464261	−0.232130	+	0.972685i	$0.574570\pi$
$3$	2.76581	1.59684	0.798422	−	0.602099i	$-0.205669\pi$
$3$	2.76581	1.59684	0.798422	+	0.602099i	$0.205669\pi$
$4$	−1.56892	−0.784462
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.81593	−0.741351
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.34323	0.828455
$9$	4.64973	1.54991
$10$	−0.656564	−0.207624
$11$	−5.20200	−1.56846	−0.784231	−	0.620469i	$-0.786942\pi$
$11$	−5.20200	−1.56846	−0.784231	+	0.620469i	$0.786942\pi$
$12$	−4.33935	−1.25266
$13$	−0.887601	−0.246176	−0.123088	−	0.992396i	$-0.539280\pi$
$13$	−0.887601	−0.246176	−0.123088	+	0.992396i	$0.539280\pi$
$14$	−0.656564	−0.175474
$15$	2.76581	0.714130
$16$	1.59937	0.399843
$17$	−3.19882	−0.775828	−0.387914	−	0.921696i	$-0.626804\pi$
$17$	−3.19882	−0.775828	−0.387914	+	0.921696i	$0.626804\pi$
$18$	−3.05284	−0.719561
$19$	−3.11669	−0.715019	−0.357509	−	0.933910i	$-0.616374\pi$
$19$	−3.11669	−0.715019	−0.357509	+	0.933910i	$0.616374\pi$
$20$	−1.56892	−0.350822
$21$	2.76581	0.603550
$22$	3.41544	0.728175
$23$	−3.41030	−0.711096	−0.355548	−	0.934658i	$-0.615706\pi$
$23$	−3.41030	−0.711096	−0.355548	+	0.934658i	$0.615706\pi$
$24$	6.48093	1.32291
$25$	1.00000	0.200000
$26$	0.582766	0.114290
$27$	4.56283	0.878117
$28$	−1.56892	−0.296499
$29$	−0.110161	−0.0204565	−0.0102282	−	0.999948i	$-0.503256\pi$
$29$	−0.110161	−0.0204565	−0.0102282	+	0.999948i	$0.503256\pi$
$30$	−1.81593	−0.331542
$31$	3.91453	0.703071	0.351535	−	0.936175i	$-0.385660\pi$
$31$	3.91453	0.703071	0.351535	+	0.936175i	$0.385660\pi$
$32$	−5.73654	−1.01409
$33$	−14.3878	−2.50459
$34$	2.10023	0.360186
$35$	1.00000	0.169031
$36$	−7.29507	−1.21584
$37$	8.91873	1.46623	0.733115	−	0.680104i	$-0.238066\pi$
$37$	8.91873	1.46623	0.733115	+	0.680104i	$0.238066\pi$
$38$	2.04631	0.331955
$39$	−2.45494	−0.393105
$40$	2.34323	0.370496
$41$	3.61363	0.564355	0.282177	−	0.959362i	$-0.408943\pi$
$41$	3.61363	0.564355	0.282177	+	0.959362i	$0.408943\pi$
$42$	−1.81593	−0.280204
$43$	−2.94495	−0.449100	−0.224550	−	0.974463i	$-0.572091\pi$
$43$	−2.94495	−0.449100	−0.224550	+	0.974463i	$0.572091\pi$
$44$	8.16155	1.23040
$45$	4.64973	0.693140
$46$	2.23908	0.330134
$47$	−2.00854	−0.292975	−0.146488	−	0.989213i	$-0.546797\pi$
$47$	−2.00854	−0.292975	−0.146488	+	0.989213i	$0.546797\pi$
$48$	4.42357	0.638487
$49$	1.00000	0.142857
$50$	−0.656564	−0.0928521
$51$	−8.84734	−1.23888
$52$	1.39258	0.193116
$53$	6.16881	0.847351	0.423676	−	0.905814i	$-0.360740\pi$
$53$	6.16881	0.847351	0.423676	+	0.905814i	$0.360740\pi$
$54$	−2.99579	−0.407675
$55$	−5.20200	−0.701438
$56$	2.34323	0.313127
$57$	−8.62019	−1.14177
$58$	0.0723279	0.00949712
$59$	−4.92096	−0.640654	−0.320327	−	0.947307i	$-0.603793\pi$
$59$	−4.92096	−0.640654	−0.320327	+	0.947307i	$0.603793\pi$
$60$	−4.33935	−0.560208
$61$	−10.9018	−1.39583	−0.697916	−	0.716180i	$-0.745889\pi$
$61$	−10.9018	−1.39583	−0.697916	+	0.716180i	$0.745889\pi$
$62$	−2.57014	−0.326408
$63$	4.64973	0.585810
$64$	0.567659	0.0709574
$65$	−0.887601	−0.110093
$66$	9.44648	1.16278
$67$	0.0752980	0.00919911	0.00459956	−	0.999989i	$-0.498536\pi$
$67$	0.0752980	0.00919911	0.00459956	+	0.999989i	$0.498536\pi$
$68$	5.01871	0.608608
$69$	−9.43224	−1.13551
$70$	−0.656564	−0.0784744
$71$	5.92419	0.703072	0.351536	−	0.936174i	$-0.385660\pi$
$71$	5.92419	0.703072	0.351536	+	0.936174i	$0.385660\pi$
$72$	10.8954	1.28403
$73$	3.40709	0.398770	0.199385	−	0.979921i	$-0.436106\pi$
$73$	3.40709	0.398770	0.199385	+	0.979921i	$0.436106\pi$
$74$	−5.85571	−0.680713
$75$	2.76581	0.319369
$76$	4.88986	0.560905
$77$	−5.20200	−0.592823
$78$	1.61182	0.182503
$79$	−16.0663	−1.80759	−0.903797	−	0.427961i	$-0.859232\pi$
$79$	−16.0663	−1.80759	−0.903797	+	0.427961i	$0.859232\pi$
$80$	1.59937	0.178815
$81$	−1.32923	−0.147692
$82$	−2.37258	−0.262008
$83$	14.0150	1.53834	0.769172	−	0.639041i	$-0.220669\pi$
$83$	14.0150	1.53834	0.769172	+	0.639041i	$0.220669\pi$
$84$	−4.33935	−0.473462
$85$	−3.19882	−0.346961
$86$	1.93354	0.208499
$87$	−0.304686	−0.0326657
$88$	−12.1895	−1.29940
$89$	−18.1765	−1.92671	−0.963354	−	0.268234i	$-0.913560\pi$
$89$	−18.1765	−1.92671	−0.963354	+	0.268234i	$0.913560\pi$
$90$	−3.05284	−0.321798
$91$	−0.887601	−0.0930458
$92$	5.35050	0.557828
$93$	10.8269	1.12269
$94$	1.31873	0.136017
$95$	−3.11669	−0.319766
$96$	−15.8662	−1.61934
$97$	−3.53977	−0.359409	−0.179705	−	0.983721i	$-0.557514\pi$
$97$	−3.53977	−0.359409	−0.179705	+	0.983721i	$0.557514\pi$
$98$	−0.656564	−0.0663229
$99$	−24.1879	−2.43097
$100$	−1.56892	−0.156892
$101$	−8.81576	−0.877201	−0.438601	−	0.898682i	$-0.644526\pi$
$101$	−8.81576	−0.877201	−0.438601	+	0.898682i	$0.644526\pi$
$102$	5.80884	0.575161
$103$	−13.7817	−1.35795	−0.678974	−	0.734162i	$-0.737575\pi$
$103$	−13.7817	−1.35795	−0.678974	+	0.734162i	$0.737575\pi$
$104$	−2.07985	−0.203946
$105$	2.76581	0.269916
$106$	−4.05021	−0.393392
$107$	−12.4554	−1.20411	−0.602054	−	0.798456i	$-0.705651\pi$
$107$	−12.4554	−1.20411	−0.602054	+	0.798456i	$0.705651\pi$
$108$	−7.15874	−0.688850
$109$	−13.5713	−1.29989	−0.649946	−	0.759980i	$-0.725209\pi$
$109$	−13.5713	−1.29989	−0.649946	+	0.759980i	$0.725209\pi$
$110$	3.41544	0.325650
$111$	24.6676	2.34134
$112$	1.59937	0.151126
$113$	10.7924	1.01527	0.507633	−	0.861574i	$-0.330521\pi$
$113$	10.7924	1.01527	0.507633	+	0.861574i	$0.330521\pi$
$114$	5.65971	0.530080
$115$	−3.41030	−0.318012
$116$	0.172835	0.0160473
$117$	−4.12710	−0.381551
$118$	3.23092	0.297430
$119$	−3.19882	−0.293235
$120$	6.48093	0.591625
$121$	16.0608	1.46007
$122$	7.15772	0.648030
$123$	9.99464	0.901186
$124$	−6.14160	−0.551532
$125$	1.00000	0.0894427
$126$	−3.05284	−0.271969
$127$	−17.9277	−1.59083	−0.795413	−	0.606068i	$-0.792746\pi$
$127$	−17.9277	−1.59083	−0.795413	+	0.606068i	$0.792746\pi$
$128$	11.1004	0.981144
$129$	−8.14517	−0.717143
$130$	0.582766	0.0511120
$131$	4.38223	0.382877	0.191438	−	0.981505i	$-0.438685\pi$
$131$	4.38223	0.382877	0.191438	+	0.981505i	$0.438685\pi$
$132$	22.5733	1.96476
$133$	−3.11669	−0.270252
$134$	−0.0494379	−0.00427079
$135$	4.56283	0.392706
$136$	−7.49556	−0.642739
$137$	−13.3524	−1.14077	−0.570386	−	0.821377i	$-0.693207\pi$
$137$	−13.3524	−1.14077	−0.570386	+	0.821377i	$0.693207\pi$
$138$	6.19287	0.527172
$139$	0.442523	0.0375343	0.0187672	−	0.999824i	$-0.494026\pi$
$139$	0.442523	0.0375343	0.0187672	+	0.999824i	$0.494026\pi$
$140$	−1.56892	−0.132598
$141$	−5.55524	−0.467835
$142$	−3.88961	−0.326408
$143$	4.61730	0.386118
$144$	7.43664	0.619720
$145$	−0.110161	−0.00914840
$146$	−2.23697	−0.185133
$147$	2.76581	0.228120
$148$	−13.9928	−1.15020
$149$	16.3749	1.34148	0.670741	−	0.741692i	$-0.265976\pi$
$149$	16.3749	1.34148	0.670741	+	0.741692i	$0.265976\pi$
$150$	−1.81593	−0.148270
$151$	17.9334	1.45940	0.729701	−	0.683767i	$-0.239659\pi$
$151$	17.9334	1.45940	0.729701	+	0.683767i	$0.239659\pi$
$152$	−7.30312	−0.592361
$153$	−14.8736	−1.20246
$154$	3.41544	0.275224
$155$	3.91453	0.314423
$156$	3.85161	0.308376
$157$	−19.2353	−1.53514	−0.767570	−	0.640965i	$-0.778534\pi$
$157$	−19.2353	−1.53514	−0.767570	+	0.640965i	$0.778534\pi$
$158$	10.5485	0.839195
$159$	17.0618	1.35309
$160$	−5.73654	−0.453513
$161$	−3.41030	−0.268769
$162$	0.872725	0.0685678
$163$	−19.9080	−1.55932	−0.779659	−	0.626205i	$-0.784607\pi$
$163$	−19.9080	−1.55932	−0.779659	+	0.626205i	$0.784607\pi$
$164$	−5.66952	−0.442715
$165$	−14.3878	−1.12009
$166$	−9.20173	−0.714193
$167$	−6.11632	−0.473295	−0.236647	−	0.971596i	$-0.576049\pi$
$167$	−6.11632	−0.473295	−0.236647	+	0.971596i	$0.576049\pi$
$168$	6.48093	0.500014
$169$	−12.2122	−0.939397
$170$	2.10023	0.161080
$171$	−14.4918	−1.10821
$172$	4.62040	0.352302
$173$	−10.8675	−0.826239	−0.413119	−	0.910677i	$-0.635561\pi$
$173$	−10.8675	−0.826239	−0.413119	+	0.910677i	$0.635561\pi$
$174$	0.200046	0.0151654
$175$	1.00000	0.0755929
$176$	−8.31994	−0.627139
$177$	−13.6104	−1.02302
$178$	11.9340	0.894494
$179$	9.12494	0.682030	0.341015	−	0.940058i	$-0.389229\pi$
$179$	9.12494	0.682030	0.341015	+	0.940058i	$0.389229\pi$
$180$	−7.29507	−0.543742
$181$	−12.9893	−0.965483	−0.482742	−	0.875763i	$-0.660359\pi$
$181$	−12.9893	−0.965483	−0.482742	+	0.875763i	$0.660359\pi$
$182$	0.582766	0.0431975
$183$	−30.1523	−2.22892
$184$	−7.99109	−0.589111
$185$	8.91873	0.655718
$186$	−7.10852	−0.521222
$187$	16.6403	1.21686
$188$	3.15124	0.229828
$189$	4.56283	0.331897
$190$	2.04631	0.148455
$191$	−23.2626	−1.68322	−0.841611	−	0.540084i	$-0.818393\pi$
$191$	−23.2626	−1.68322	−0.841611	+	0.540084i	$0.818393\pi$
$192$	1.57004	0.113308
$193$	−1.63878	−0.117962	−0.0589811	−	0.998259i	$-0.518785\pi$
$193$	−1.63878	−0.117962	−0.0589811	+	0.998259i	$0.518785\pi$
$194$	2.32408	0.166859
$195$	−2.45494	−0.175802
$196$	−1.56892	−0.112066
$197$	−17.0166	−1.21238	−0.606190	−	0.795320i	$-0.707303\pi$
$197$	−17.0166	−1.21238	−0.606190	+	0.795320i	$0.707303\pi$
$198$	15.8809	1.12860
$199$	12.5989	0.893111	0.446555	−	0.894756i	$-0.352651\pi$
$199$	12.5989	0.893111	0.446555	+	0.894756i	$0.352651\pi$
$200$	2.34323	0.165691
$201$	0.208260	0.0146895
$202$	5.78811	0.407250
$203$	−0.110161	−0.00773181
$204$	13.8808	0.971851
$205$	3.61363	0.252387
$206$	9.04854	0.630442
$207$	−15.8569	−1.10213
$208$	−1.41960	−0.0984318
$209$	16.2130	1.12148
$210$	−1.81593	−0.125311
$211$	−10.3932	−0.715496	−0.357748	−	0.933818i	$-0.616455\pi$
$211$	−10.3932	−0.715496	−0.357748	+	0.933818i	$0.616455\pi$
$212$	−9.67839	−0.664715
$213$	16.3852	1.12270
$214$	8.17775	0.559019
$215$	−2.94495	−0.200844
$216$	10.6917	0.727481
$217$	3.91453	0.265736
$218$	8.91040	0.603489
$219$	9.42339	0.636773
$220$	8.16155	0.550251
$221$	2.83928	0.190990
$222$	−16.1958	−1.08699
$223$	−13.6093	−0.911348	−0.455674	−	0.890147i	$-0.650602\pi$
$223$	−13.6093	−0.911348	−0.455674	+	0.890147i	$0.650602\pi$
$224$	−5.73654	−0.383289
$225$	4.64973	0.309982
$226$	−7.08591	−0.471348
$227$	27.0305	1.79408	0.897040	−	0.441950i	$-0.145713\pi$
$227$	27.0305	1.79408	0.897040	+	0.441950i	$0.145713\pi$
$228$	13.5244	0.895677
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	2.23908	0.147640
$231$	−14.3878	−0.946646
$232$	−0.258133	−0.0169473
$233$	−13.1626	−0.862309	−0.431155	−	0.902278i	$-0.641894\pi$
$233$	−13.1626	−0.862309	−0.431155	+	0.902278i	$0.641894\pi$
$234$	2.70970	0.177139
$235$	−2.00854	−0.131022
$236$	7.72061	0.502569
$237$	−44.4363	−2.88645
$238$	2.10023	0.136138
$239$	18.3726	1.18842	0.594211	−	0.804309i	$-0.297464\pi$
$239$	18.3726	1.18842	0.594211	+	0.804309i	$0.297464\pi$
$240$	4.42357	0.285540
$241$	5.15033	0.331762	0.165881	−	0.986146i	$-0.446953\pi$
$241$	5.15033	0.331762	0.165881	+	0.986146i	$0.446953\pi$
$242$	−10.5450	−0.677855
$243$	−17.3649	−1.11396
$244$	17.1041	1.09498
$245$	1.00000	0.0638877
$246$	−6.56212	−0.418385
$247$	2.76638	0.176021
$248$	9.17263	0.582463
$249$	38.7628	2.45650
$250$	−0.656564	−0.0415247
$251$	8.44229	0.532872	0.266436	−	0.963853i	$-0.414154\pi$
$251$	8.44229	0.532872	0.266436	+	0.963853i	$0.414154\pi$
$252$	−7.29507	−0.459546
$253$	17.7404	1.11533
$254$	11.7707	0.738557
$255$	−8.84734	−0.554042
$256$	−8.42342	−0.526464
$257$	18.8680	1.17695	0.588477	−	0.808514i	$-0.299728\pi$
$257$	18.8680	1.17695	0.588477	+	0.808514i	$0.299728\pi$
$258$	5.34782	0.332941
$259$	8.91873	0.554183
$260$	1.39258	0.0863641
$261$	−0.512220	−0.0317056
$262$	−2.87721	−0.177755
$263$	5.06769	0.312487	0.156244	−	0.987719i	$-0.450062\pi$
$263$	5.06769	0.312487	0.156244	+	0.987719i	$0.450062\pi$
$264$	−33.7138	−2.07494
$265$	6.16881	0.378947
$266$	2.04631	0.125467
$267$	−50.2729	−3.07665
$268$	−0.118137	−0.00721636
$269$	14.8429	0.904989	0.452494	−	0.891767i	$-0.350534\pi$
$269$	14.8429	0.904989	0.452494	+	0.891767i	$0.350534\pi$
$270$	−2.99579	−0.182318
$271$	18.6740	1.13437	0.567183	−	0.823592i	$-0.308033\pi$
$271$	18.6740	1.13437	0.567183	+	0.823592i	$0.308033\pi$
$272$	−5.11611	−0.310209
$273$	−2.45494	−0.148580
$274$	8.76670	0.529616
$275$	−5.20200	−0.313693
$276$	14.7985	0.890764
$277$	4.09828	0.246242	0.123121	−	0.992392i	$-0.460710\pi$
$277$	4.09828	0.246242	0.123121	+	0.992392i	$0.460710\pi$
$278$	−0.290545	−0.0174257
$279$	18.2015	1.08970
$280$	2.34323	0.140035
$281$	17.0316	1.01602	0.508011	−	0.861351i	$-0.330381\pi$
$281$	17.0316	1.01602	0.508011	+	0.861351i	$0.330381\pi$
$282$	3.64737	0.217197
$283$	24.8338	1.47621	0.738107	−	0.674683i	$-0.235720\pi$
$283$	24.8338	1.47621	0.738107	+	0.674683i	$0.235720\pi$
$284$	−9.29460	−0.551533
$285$	−8.62019	−0.510616
$286$	−3.03155	−0.179259
$287$	3.61363	0.213306
$288$	−26.6733	−1.57174
$289$	−6.76754	−0.398091
$290$	0.0723279	0.00424724
$291$	−9.79034	−0.573920
$292$	−5.34547	−0.312820
$293$	18.9389	1.10643	0.553213	−	0.833040i	$-0.313402\pi$
$293$	18.9389	1.10643	0.553213	+	0.833040i	$0.313402\pi$
$294$	−1.81593	−0.105907
$295$	−4.92096	−0.286509
$296$	20.8986	1.21471
$297$	−23.7359	−1.37729
$298$	−10.7511	−0.622797
$299$	3.02698	0.175055
$300$	−4.33935	−0.250533
$301$	−2.94495	−0.169744
$302$	−11.7744	−0.677542
$303$	−24.3828	−1.40075
$304$	−4.98475	−0.285895
$305$	−10.9018	−0.624235
$306$	9.76549	0.558256
$307$	7.86992	0.449160	0.224580	−	0.974456i	$-0.427899\pi$
$307$	7.86992	0.449160	0.224580	+	0.974456i	$0.427899\pi$
$308$	8.16155	0.465047
$309$	−38.1175	−2.16843
$310$	−2.57014	−0.145974
$311$	−21.7772	−1.23487	−0.617435	−	0.786622i	$-0.711828\pi$
$311$	−21.7772	−1.23487	−0.617435	+	0.786622i	$0.711828\pi$
$312$	−5.75247	−0.325670
$313$	−32.0499	−1.81156	−0.905782	−	0.423743i	$-0.860716\pi$
$313$	−32.0499	−1.81156	−0.905782	+	0.423743i	$0.860716\pi$
$314$	12.6292	0.712705
$315$	4.64973	0.261982
$316$	25.2067	1.41799
$317$	−20.3712	−1.14416	−0.572080	−	0.820197i	$-0.693864\pi$
$317$	−20.3712	−1.14416	−0.572080	+	0.820197i	$0.693864\pi$
$318$	−11.2021	−0.628185
$319$	0.573060	0.0320852
$320$	0.567659	0.0317331
$321$	−34.4493	−1.92277
$322$	2.23908	0.124779
$323$	9.96975	0.554732
$324$	2.08546	0.115859
$325$	−0.887601	−0.0492352
$326$	13.0709	0.723929
$327$	−37.5356	−2.07572
$328$	8.46756	0.467543
$329$	−2.00854	−0.110734
$330$	9.44648	0.520012
$331$	13.2503	0.728302	0.364151	−	0.931340i	$-0.381359\pi$
$331$	13.2503	0.728302	0.364151	+	0.931340i	$0.381359\pi$
$332$	−21.9885	−1.20677
$333$	41.4697	2.27252
$334$	4.01575	0.219732
$335$	0.0752980	0.00411397
$336$	4.42357	0.241325
$337$	−30.1721	−1.64358	−0.821789	−	0.569792i	$-0.807024\pi$
$337$	−30.1721	−1.64358	−0.821789	+	0.569792i	$0.807024\pi$
$338$	8.01806	0.436125
$339$	29.8498	1.62122
$340$	5.01871	0.272178
$341$	−20.3634	−1.10274
$342$	9.51477	0.514500
$343$	1.00000	0.0539949
$344$	−6.90068	−0.372059
$345$	−9.43224	−0.507815
$346$	7.13519	0.383590
$347$	13.6181	0.731060	0.365530	−	0.930800i	$-0.380888\pi$
$347$	13.6181	0.731060	0.365530	+	0.930800i	$0.380888\pi$
$348$	0.478029	0.0256250
$349$	4.48438	0.240043	0.120022	−	0.992771i	$-0.461704\pi$
$349$	4.48438	0.240043	0.120022	+	0.992771i	$0.461704\pi$
$350$	−0.656564	−0.0350948
$351$	−4.04997	−0.216172
$352$	29.8415	1.59056
$353$	−0.481761	−0.0256415	−0.0128208	−	0.999918i	$-0.504081\pi$
$353$	−0.481761	−0.0256415	−0.0128208	+	0.999918i	$0.504081\pi$
$354$	8.93612	0.474950
$355$	5.92419	0.314423
$356$	28.5176	1.51143
$357$	−8.84734	−0.468251
$358$	−5.99110	−0.316640
$359$	9.38201	0.495163	0.247582	−	0.968867i	$-0.420364\pi$
$359$	9.38201	0.495163	0.247582	+	0.968867i	$0.420364\pi$
$360$	10.8954	0.574236
$361$	−9.28622	−0.488748
$362$	8.52827	0.448236
$363$	44.4212	2.33151
$364$	1.39258	0.0729909
$365$	3.40709	0.178335
$366$	19.7969	1.03480
$367$	17.7922	0.928746	0.464373	−	0.885640i	$-0.346280\pi$
$367$	17.7922	0.928746	0.464373	+	0.885640i	$0.346280\pi$
$368$	−5.45433	−0.284327
$369$	16.8024	0.874698
$370$	−5.85571	−0.304424
$371$	6.16881	0.320269
$372$	−16.9865	−0.880711
$373$	34.1101	1.76615	0.883076	−	0.469229i	$-0.155468\pi$
$373$	34.1101	1.76615	0.883076	+	0.469229i	$0.155468\pi$
$374$	−10.9254	−0.564939
$375$	2.76581	0.142826
$376$	−4.70645	−0.242717
$377$	0.0977793	0.00503589
$378$	−2.99579	−0.154087
$379$	−8.25378	−0.423968	−0.211984	−	0.977273i	$-0.567993\pi$
$379$	−8.25378	−0.423968	−0.211984	+	0.977273i	$0.567993\pi$
$380$	4.88986	0.250844
$381$	−49.5847	−2.54030
$382$	15.2734	0.781454
$383$	6.68965	0.341825	0.170913	−	0.985286i	$-0.445328\pi$
$383$	6.68965	0.341825	0.170913	+	0.985286i	$0.445328\pi$
$384$	30.7016	1.56673
$385$	−5.20200	−0.265119
$386$	1.07597	0.0547652
$387$	−13.6932	−0.696064
$388$	5.55363	0.281943
$389$	−32.1508	−1.63011	−0.815054	−	0.579385i	$-0.803293\pi$
$389$	−32.1508	−1.63011	−0.815054	+	0.579385i	$0.803293\pi$
$390$	1.61182	0.0816178
$391$	10.9089	0.551688
$392$	2.34323	0.118351
$393$	12.1204	0.611394
$394$	11.1724	0.562860
$395$	−16.0663	−0.808381
$396$	37.9490	1.90701
$397$	−29.6742	−1.48930	−0.744652	−	0.667453i	$-0.767384\pi$
$397$	−29.6742	−1.48930	−0.744652	+	0.667453i	$0.767384\pi$
$398$	−8.27196	−0.414636
$399$	−8.62019	−0.431550
$400$	1.59937	0.0799686
$401$	−27.6005	−1.37830	−0.689151	−	0.724618i	$-0.742016\pi$
$401$	−27.6005	−1.37830	−0.689151	+	0.724618i	$0.742016\pi$
$402$	−0.136736	−0.00681977
$403$	−3.47454	−0.173079
$404$	13.8313	0.688131
$405$	−1.32923	−0.0660501
$406$	0.0723279	0.00358958
$407$	−46.3953	−2.29973
$408$	−20.7313	−1.02635
$409$	−6.09192	−0.301226	−0.150613	−	0.988593i	$-0.548125\pi$
$409$	−6.09192	−0.301226	−0.150613	+	0.988593i	$0.548125\pi$
$410$	−2.37258	−0.117173
$411$	−36.9303	−1.82164
$412$	21.6224	1.06526
$413$	−4.92096	−0.242144
$414$	10.4111	0.511677
$415$	14.0150	0.687969
$416$	5.09176	0.249644
$417$	1.22394	0.0599365
$418$	−10.6449	−0.520659
$419$	−1.46387	−0.0715148	−0.0357574	−	0.999361i	$-0.511384\pi$
$419$	−1.46387	−0.0715148	−0.0357574	+	0.999361i	$0.511384\pi$
$420$	−4.33935	−0.211739
$421$	3.20922	0.156408	0.0782039	−	0.996937i	$-0.475081\pi$
$421$	3.20922	0.156408	0.0782039	+	0.996937i	$0.475081\pi$
$422$	6.82378	0.332176
$423$	−9.33914	−0.454084
$424$	14.4549	0.701993
$425$	−3.19882	−0.155166
$426$	−10.7579	−0.521223
$427$	−10.9018	−0.527575
$428$	19.5415	0.944576
$429$	12.7706	0.616570
$430$	1.93354	0.0932438
$431$	36.1985	1.74362	0.871809	−	0.489846i	$-0.162947\pi$
$431$	36.1985	1.74362	0.871809	+	0.489846i	$0.162947\pi$
$432$	7.29767	0.351109
$433$	−20.5999	−0.989969	−0.494985	−	0.868902i	$-0.664826\pi$
$433$	−20.5999	−0.989969	−0.494985	+	0.868902i	$0.664826\pi$
$434$	−2.57014	−0.123371
$435$	−0.304686	−0.0146086
$436$	21.2923	1.01972
$437$	10.6288	0.508447
$438$	−6.18705	−0.295629
$439$	31.8757	1.52135	0.760673	−	0.649136i	$-0.224869\pi$
$439$	31.8757	1.52135	0.760673	+	0.649136i	$0.224869\pi$
$440$	−12.1895	−0.581110
$441$	4.64973	0.221415
$442$	−1.86417	−0.0886693
$443$	27.2318	1.29382	0.646912	−	0.762565i	$-0.276060\pi$
$443$	27.2318	1.29382	0.646912	+	0.762565i	$0.276060\pi$
$444$	−38.7015	−1.83669
$445$	−18.1765	−0.861650
$446$	8.93539	0.423103
$447$	45.2899	2.14214
$448$	0.567659	0.0268194
$449$	27.6966	1.30709	0.653543	−	0.756890i	$-0.273282\pi$
$449$	27.6966	1.30709	0.653543	+	0.756890i	$0.273282\pi$
$450$	−3.05284	−0.143912
$451$	−18.7981	−0.885170
$452$	−16.9325	−0.796437
$453$	49.6005	2.33044
$454$	−17.7473	−0.832920
$455$	−0.887601	−0.0416114
$456$	−20.1991	−0.945908
$457$	25.7742	1.20567	0.602833	−	0.797868i	$-0.294039\pi$
$457$	25.7742	1.20567	0.602833	+	0.797868i	$0.294039\pi$
$458$	0.656564	0.0306792
$459$	−14.5957	−0.681268
$460$	5.35050	0.249468
$461$	9.21261	0.429074	0.214537	−	0.976716i	$-0.431176\pi$
$461$	9.21261	0.429074	0.214537	+	0.976716i	$0.431176\pi$
$462$	9.44648	0.439490
$463$	0.456020	0.0211930	0.0105965	−	0.999944i	$-0.496627\pi$
$463$	0.456020	0.0211930	0.0105965	+	0.999944i	$0.496627\pi$
$464$	−0.176189	−0.00817937
$465$	10.8269	0.502084
$466$	8.64207	0.400336
$467$	−35.6836	−1.65124	−0.825620	−	0.564226i	$-0.809175\pi$
$467$	−35.6836	−1.65124	−0.825620	+	0.564226i	$0.809175\pi$
$468$	6.47511	0.299312
$469$	0.0752980	0.00347694
$470$	1.31873	0.0608285
$471$	−53.2011	−2.45138
$472$	−11.5309	−0.530753
$473$	15.3196	0.704397
$474$	29.1752	1.34006
$475$	−3.11669	−0.143004
$476$	5.01871	0.230032
$477$	28.6833	1.31332
$478$	−12.0628	−0.551737
$479$	−10.3047	−0.470834	−0.235417	−	0.971894i	$-0.575646\pi$
$479$	−10.3047	−0.470834	−0.235417	+	0.971894i	$0.575646\pi$
$480$	−15.8662	−0.724190
$481$	−7.91627	−0.360951
$482$	−3.38152	−0.154024
$483$	−9.43224	−0.429182
$484$	−25.1982	−1.14537
$485$	−3.53977	−0.160733
$486$	11.4012	0.517167
$487$	−32.8271	−1.48754	−0.743770	−	0.668436i	$-0.766964\pi$
$487$	−32.8271	−1.48754	−0.743770	+	0.668436i	$0.766964\pi$
$488$	−25.5454	−1.15638
$489$	−55.0619	−2.48998
$490$	−0.656564	−0.0296605
$491$	−36.7287	−1.65754	−0.828772	−	0.559587i	$-0.810960\pi$
$491$	−36.7287	−1.65754	−0.828772	+	0.559587i	$0.810960\pi$
$492$	−15.6808	−0.706947
$493$	0.352387	0.0158707
$494$	−1.81630	−0.0817194
$495$	−24.1879	−1.08716
$496$	6.26079	0.281118
$497$	5.92419	0.265736
$498$	−25.4503	−1.14045
$499$	1.41328	0.0632672	0.0316336	−	0.999500i	$-0.489929\pi$
$499$	1.41328	0.0632672	0.0316336	+	0.999500i	$0.489929\pi$
$500$	−1.56892	−0.0701644
$501$	−16.9166	−0.755778
$502$	−5.54290	−0.247392
$503$	−0.479765	−0.0213916	−0.0106958	−	0.999943i	$-0.503405\pi$
$503$	−0.479765	−0.0213916	−0.0106958	+	0.999943i	$0.503405\pi$
$504$	10.8954	0.485318
$505$	−8.81576	−0.392296
$506$	−11.6477	−0.517802
$507$	−33.7766	−1.50007
$508$	28.1272	1.24794
$509$	4.72019	0.209219	0.104609	−	0.994513i	$-0.466641\pi$
$509$	4.72019	0.209219	0.104609	+	0.994513i	$0.466641\pi$
$510$	5.80884	0.257220
$511$	3.40709	0.150721
$512$	−16.6702	−0.736728
$513$	−14.2210	−0.627870
$514$	−12.3880	−0.546413
$515$	−13.7817	−0.607293
$516$	12.7792	0.562571
$517$	10.4484	0.459520
$518$	−5.85571	−0.257285
$519$	−30.0574	−1.31937
$520$	−2.07985	−0.0912074
$521$	4.93991	0.216421	0.108211	−	0.994128i	$-0.465488\pi$
$521$	4.93991	0.216421	0.108211	+	0.994128i	$0.465488\pi$
$522$	0.336305	0.0147197
$523$	32.4228	1.41775	0.708876	−	0.705333i	$-0.249203\pi$
$523$	32.4228	1.41775	0.708876	+	0.705333i	$0.249203\pi$
$524$	−6.87538	−0.300352
$525$	2.76581	0.120710
$526$	−3.32726	−0.145075
$527$	−12.5219	−0.545462
$528$	−23.0114	−1.00144
$529$	−11.3699	−0.494343
$530$	−4.05021	−0.175930
$531$	−22.8811	−0.992955
$532$	4.88986	0.212002
$533$	−3.20746	−0.138931
$534$	33.0073	1.42837
$535$	−12.4554	−0.538493
$536$	0.176440	0.00762105
$537$	25.2379	1.08909
$538$	−9.74532	−0.420151
$539$	−5.20200	−0.224066
$540$	−7.15874	−0.308063
$541$	−22.4962	−0.967189	−0.483594	−	0.875292i	$-0.660669\pi$
$541$	−22.4962	−0.967189	−0.483594	+	0.875292i	$0.660669\pi$
$542$	−12.2607	−0.526641
$543$	−35.9258	−1.54173
$544$	18.3502	0.786757
$545$	−13.5713	−0.581330
$546$	1.61182	0.0689797
$547$	−33.5418	−1.43414	−0.717072	−	0.696999i	$-0.754518\pi$
$547$	−33.5418	−1.43414	−0.717072	+	0.696999i	$0.754518\pi$
$548$	20.9489	0.894893
$549$	−50.6903	−2.16341
$550$	3.41544	0.145635
$551$	0.343339	0.0146267
$552$	−22.1019	−0.940718
$553$	−16.0663	−0.683207
$554$	−2.69078	−0.114320
$555$	24.6676	1.04708
$556$	−0.694286	−0.0294443
$557$	−21.7696	−0.922409	−0.461204	−	0.887294i	$-0.652583\pi$
$557$	−21.7696	−0.922409	−0.461204	+	0.887294i	$0.652583\pi$
$558$	−11.9504	−0.505902
$559$	2.61394	0.110558
$560$	1.59937	0.0675858
$561$	46.0239	1.94313
$562$	−11.1823	−0.471699
$563$	2.00423	0.0844682	0.0422341	−	0.999108i	$-0.486552\pi$
$563$	2.00423	0.0844682	0.0422341	+	0.999108i	$0.486552\pi$
$564$	8.71574	0.366999
$565$	10.7924	0.454040
$566$	−16.3050	−0.685348
$567$	−1.32923	−0.0558225
$568$	13.8817	0.582464
$569$	44.8084	1.87847	0.939234	−	0.343278i	$-0.111537\pi$
$569$	44.8084	1.87847	0.939234	+	0.343278i	$0.111537\pi$
$570$	5.65971	0.237059
$571$	21.2338	0.888606	0.444303	−	0.895877i	$-0.353451\pi$
$571$	21.2338	0.888606	0.444303	+	0.895877i	$0.353451\pi$
$572$	−7.24420	−0.302895
$573$	−64.3400	−2.68784
$574$	−2.37258	−0.0990296
$575$	−3.41030	−0.142219
$576$	2.63946	0.109977
$577$	22.3466	0.930302	0.465151	−	0.885231i	$-0.346000\pi$
$577$	22.3466	0.930302	0.465151	+	0.885231i	$0.346000\pi$
$578$	4.44332	0.184818
$579$	−4.53257	−0.188367
$580$	0.172835	0.00717658
$581$	14.0150	0.581440
$582$	6.42798	0.266448
$583$	−32.0902	−1.32904
$584$	7.98359	0.330363
$585$	−4.12710	−0.170635
$586$	−12.4346	−0.513669
$587$	−9.92542	−0.409666	−0.204833	−	0.978797i	$-0.565665\pi$
$587$	−9.92542	−0.409666	−0.204833	+	0.978797i	$0.565665\pi$
$588$	−4.33935	−0.178952
$589$	−12.2004	−0.502709
$590$	3.23092	0.133015
$591$	−47.0646	−1.93598
$592$	14.2644	0.586262
$593$	−17.5625	−0.721207	−0.360604	−	0.932719i	$-0.617429\pi$
$593$	−17.5625	−0.721207	−0.360604	+	0.932719i	$0.617429\pi$
$594$	15.5841	0.639423
$595$	−3.19882	−0.131139
$596$	−25.6909	−1.05234
$597$	34.8462	1.42616
$598$	−1.98741	−0.0812711
$599$	43.2271	1.76621	0.883105	−	0.469175i	$-0.155449\pi$
$599$	43.2271	1.76621	0.883105	+	0.469175i	$0.155449\pi$
$600$	6.48093	0.264583
$601$	36.7249	1.49804	0.749021	−	0.662547i	$-0.230524\pi$
$601$	36.7249	1.49804	0.749021	+	0.662547i	$0.230524\pi$
$602$	1.93354	0.0788054
$603$	0.350115	0.0142578
$604$	−28.1362	−1.14485
$605$	16.0608	0.652965
$606$	16.0088	0.650314
$607$	−32.0338	−1.30021	−0.650106	−	0.759844i	$-0.725276\pi$
$607$	−32.0338	−1.30021	−0.650106	+	0.759844i	$0.725276\pi$
$608$	17.8790	0.725091
$609$	−0.304686	−0.0123465
$610$	7.15772	0.289808
$611$	1.78278	0.0721235
$612$	23.3356	0.943286
$613$	−12.3958	−0.500660	−0.250330	−	0.968161i	$-0.580539\pi$
$613$	−12.3958	−0.500660	−0.250330	+	0.968161i	$0.580539\pi$
$614$	−5.16710	−0.208527
$615$	9.99464	0.403023
$616$	−12.1895	−0.491127
$617$	24.9350	1.00385	0.501923	−	0.864912i	$-0.332626\pi$
$617$	24.9350	1.00385	0.501923	+	0.864912i	$0.332626\pi$
$618$	25.0266	1.00672
$619$	6.13638	0.246642	0.123321	−	0.992367i	$-0.460646\pi$
$619$	6.13638	0.246642	0.123321	+	0.992367i	$0.460646\pi$
$620$	−6.14160	−0.246653
$621$	−15.5606	−0.624426
$622$	14.2981	0.573302
$623$	−18.1765	−0.728227
$624$	−3.92636	−0.157180
$625$	1.00000	0.0400000
$626$	21.0428	0.841038
$627$	44.8423	1.79083
$628$	30.1787	1.20426
$629$	−28.5294	−1.13754
$630$	−3.05284	−0.121628
$631$	−14.9300	−0.594355	−0.297178	−	0.954822i	$-0.596045\pi$
$631$	−14.9300	−0.594355	−0.297178	+	0.954822i	$0.596045\pi$
$632$	−37.6469	−1.49751
$633$	−28.7456	−1.14253
$634$	13.3750	0.531189
$635$	−17.9277	−0.711439
$636$	−26.7686	−1.06145
$637$	−0.887601	−0.0351680
$638$	−0.376250	−0.0148959
$639$	27.5458	1.08970
$640$	11.1004	0.438781
$641$	−14.9124	−0.589004	−0.294502	−	0.955651i	$-0.595154\pi$
$641$	−14.9124	−0.589004	−0.294502	+	0.955651i	$0.595154\pi$
$642$	22.6181	0.892666
$643$	15.1419	0.597139	0.298569	−	0.954388i	$-0.403491\pi$
$643$	15.1419	0.597139	0.298569	+	0.954388i	$0.403491\pi$
$644$	5.35050	0.210839
$645$	−8.14517	−0.320716
$646$	−6.54577	−0.257540
$647$	17.0657	0.670924	0.335462	−	0.942054i	$-0.391108\pi$
$647$	17.0657	0.670924	0.335462	+	0.942054i	$0.391108\pi$
$648$	−3.11469	−0.122357
$649$	25.5988	1.00484
$650$	0.582766	0.0228580
$651$	10.8269	0.424338
$652$	31.2342	1.22323
$653$	−42.0378	−1.64507	−0.822534	−	0.568716i	$-0.807440\pi$
$653$	−42.0378	−1.64507	−0.822534	+	0.568716i	$0.807440\pi$
$654$	24.6445	0.963677
$655$	4.38223	0.171228
$656$	5.77955	0.225653
$657$	15.8421	0.618057
$658$	1.31873	0.0514095
$659$	43.6497	1.70035	0.850175	−	0.526500i	$-0.176496\pi$
$659$	43.6497	1.70035	0.850175	+	0.526500i	$0.176496\pi$
$660$	22.5733	0.878665
$661$	−28.5777	−1.11155	−0.555773	−	0.831334i	$-0.687577\pi$
$661$	−28.5777	−1.11155	−0.555773	+	0.831334i	$0.687577\pi$
$662$	−8.69966	−0.338122
$663$	7.85291	0.304982
$664$	32.8403	1.27445
$665$	−3.11669	−0.120860
$666$	−27.2275	−1.05504
$667$	0.375683	0.0145465
$668$	9.59604	0.371282
$669$	−37.6409	−1.45528
$670$	−0.0494379	−0.00190995
$671$	56.7112	2.18931
$672$	−15.8662	−0.612052
$673$	37.2992	1.43778	0.718890	−	0.695124i	$-0.244650\pi$
$673$	37.2992	1.43778	0.718890	+	0.695124i	$0.244650\pi$
$674$	19.8099	0.763049
$675$	4.56283	0.175623
$676$	19.1600	0.736922
$677$	3.63652	0.139763	0.0698815	−	0.997555i	$-0.477738\pi$
$677$	3.63652	0.139763	0.0698815	+	0.997555i	$0.477738\pi$
$678$	−19.5983	−0.752668
$679$	−3.53977	−0.135844
$680$	−7.49556	−0.287442
$681$	74.7614	2.86486
$682$	13.3699	0.511959
$683$	−28.9980	−1.10958	−0.554789	−	0.831991i	$-0.687201\pi$
$683$	−28.9980	−1.10958	−0.554789	+	0.831991i	$0.687201\pi$
$684$	22.7365	0.869351
$685$	−13.3524	−0.510169
$686$	−0.656564	−0.0250677
$687$	−2.76581	−0.105522
$688$	−4.71007	−0.179570
$689$	−5.47544	−0.208598
$690$	6.19287	0.235758
$691$	37.3933	1.42251	0.711255	−	0.702934i	$-0.248127\pi$
$691$	37.3933	1.42251	0.711255	+	0.702934i	$0.248127\pi$
$692$	17.0502	0.648153
$693$	−24.1879	−0.918822
$694$	−8.94117	−0.339402
$695$	0.442523	0.0167859
$696$	−0.713948	−0.0270621
$697$	−11.5594	−0.437842
$698$	−2.94428	−0.111443
$699$	−36.4052	−1.37697
$700$	−1.56892	−0.0592998
$701$	12.4530	0.470344	0.235172	−	0.971954i	$-0.424435\pi$
$701$	12.4530	0.470344	0.235172	+	0.971954i	$0.424435\pi$
$702$	2.65906	0.100360
$703$	−27.7970	−1.04838
$704$	−2.95296	−0.111294
$705$	−5.55524	−0.209222
$706$	0.316306	0.0119043
$707$	−8.81576	−0.331551
$708$	21.3538	0.802523
$709$	−13.9276	−0.523060	−0.261530	−	0.965195i	$-0.584227\pi$
$709$	−13.9276	−0.523060	−0.261530	+	0.965195i	$0.584227\pi$
$710$	−3.88961	−0.145974
$711$	−74.7037	−2.80161
$712$	−42.5917	−1.59619
$713$	−13.3497	−0.499951
$714$	5.80884	0.217390
$715$	4.61730	0.172677
$716$	−14.3163	−0.535027
$717$	50.8151	1.89772
$718$	−6.15988	−0.229885
$719$	−17.8980	−0.667481	−0.333741	−	0.942665i	$-0.608311\pi$
$719$	−17.8980	−0.667481	−0.333741	+	0.942665i	$0.608311\pi$
$720$	7.43664	0.277147
$721$	−13.7817	−0.513256
$722$	6.09699	0.226907
$723$	14.2449	0.529772
$724$	20.3792	0.757385
$725$	−0.110161	−0.00409129
$726$	−29.1654	−1.08243
$727$	35.8212	1.32853	0.664267	−	0.747495i	$-0.268744\pi$
$727$	35.8212	1.32853	0.664267	+	0.747495i	$0.268744\pi$
$728$	−2.07985	−0.0770843
$729$	−44.0404	−1.63113
$730$	−2.23697	−0.0827941
$731$	9.42036	0.348425
$732$	47.3067	1.74851
$733$	−11.4542	−0.423069	−0.211534	−	0.977371i	$-0.567846\pi$
$733$	−11.4542	−0.423069	−0.211534	+	0.977371i	$0.567846\pi$
$734$	−11.6817	−0.431180
$735$	2.76581	0.102019
$736$	19.5633	0.721113
$737$	−0.391700	−0.0144285
$738$	−11.0318	−0.406088
$739$	13.8935	0.511082	0.255541	−	0.966798i	$-0.417746\pi$
$739$	13.8935	0.511082	0.255541	+	0.966798i	$0.417746\pi$
$740$	−13.9928	−0.514386
$741$	7.65129	0.281077
$742$	−4.05021	−0.148688
$743$	44.7858	1.64303	0.821515	−	0.570187i	$-0.193129\pi$
$743$	44.7858	1.64303	0.821515	+	0.570187i	$0.193129\pi$
$744$	25.3698	0.930102
$745$	16.3749	0.599929
$746$	−22.3954	−0.819955
$747$	65.1658	2.38429
$748$	−26.1073	−0.954579
$749$	−12.4554	−0.455110
$750$	−1.81593	−0.0663085
$751$	16.9707	0.619271	0.309636	−	0.950855i	$-0.399793\pi$
$751$	16.9707	0.619271	0.309636	+	0.950855i	$0.399793\pi$
$752$	−3.21240	−0.117144
$753$	23.3498	0.850914
$754$	−0.0641983	−0.00233797
$755$	17.9334	0.652664
$756$	−7.15874	−0.260361
$757$	10.0130	0.363927	0.181964	−	0.983305i	$-0.441755\pi$
$757$	10.0130	0.363927	0.181964	+	0.983305i	$0.441755\pi$
$758$	5.41913	0.196832
$759$	49.0666	1.78100
$760$	−7.30312	−0.264912
$761$	−21.2926	−0.771854	−0.385927	−	0.922529i	$-0.626118\pi$
$761$	−21.2926	−0.771854	−0.385927	+	0.922529i	$0.626118\pi$
$762$	32.5555	1.17936
$763$	−13.5713	−0.491313
$764$	36.4973	1.32042
$765$	−14.8736	−0.537758
$766$	−4.39218	−0.158696
$767$	4.36784	0.157714
$768$	−23.2976	−0.840680
$769$	26.4992	0.955586	0.477793	−	0.878473i	$-0.341437\pi$
$769$	26.4992	0.955586	0.477793	+	0.878473i	$0.341437\pi$
$770$	3.41544	0.123084
$771$	52.1854	1.87941
$772$	2.57113	0.0925369
$773$	−31.7382	−1.14154	−0.570772	−	0.821109i	$-0.693356\pi$
$773$	−31.7382	−1.14154	−0.570772	+	0.821109i	$0.693356\pi$
$774$	8.99045	0.323155
$775$	3.91453	0.140614
$776$	−8.29448	−0.297754
$777$	24.6676	0.884944
$778$	21.1090	0.756795
$779$	−11.2626	−0.403524
$780$	3.85161	0.137910
$781$	−30.8176	−1.10274
$782$	−7.16240	−0.256127
$783$	−0.502648	−0.0179632
$784$	1.59937	0.0571204
$785$	−19.2353	−0.686536
$786$	−7.95783	−0.283846
$787$	10.1853	0.363065	0.181533	−	0.983385i	$-0.441894\pi$
$787$	10.1853	0.363065	0.181533	+	0.983385i	$0.441894\pi$
$788$	26.6977	0.951066
$789$	14.0163	0.498993
$790$	10.5485	0.375299
$791$	10.7924	0.383734
$792$	−56.6777	−2.01395
$793$	9.67644	0.343620
$794$	19.4830	0.691425
$795$	17.0618	0.605119
$796$	−19.7667	−0.700612
$797$	−42.1653	−1.49357	−0.746786	−	0.665065i	$-0.768404\pi$
$797$	−42.1653	−1.49357	−0.746786	+	0.665065i	$0.768404\pi$
$798$	5.65971	0.200351
$799$	6.42495	0.227298
$800$	−5.73654	−0.202817
$801$	−84.5158	−2.98622
$802$	18.1215	0.639891
$803$	−17.7237	−0.625456
$804$	−0.326744	−0.0115234
$805$	−3.41030	−0.120197
$806$	2.28126	0.0803539
$807$	41.0527	1.44513
$808$	−20.6573	−0.726722
$809$	−37.2758	−1.31055	−0.655273	−	0.755392i	$-0.727446\pi$
$809$	−37.2758	−1.31055	−0.655273	+	0.755392i	$0.727446\pi$
$810$	0.872725	0.0306644
$811$	−21.4970	−0.754862	−0.377431	−	0.926038i	$-0.623193\pi$
$811$	−21.4970	−0.754862	−0.377431	+	0.926038i	$0.623193\pi$
$812$	0.172835	0.00606531
$813$	51.6488	1.81140
$814$	30.4614	1.06767
$815$	−19.9080	−0.697348
$816$	−14.1502	−0.495356
$817$	9.17850	0.321115
$818$	3.99973	0.139847
$819$	−4.12710	−0.144213
$820$	−5.66952	−0.197988
$821$	32.7946	1.14454	0.572270	−	0.820065i	$-0.306063\pi$
$821$	32.7946	1.14454	0.572270	+	0.820065i	$0.306063\pi$
$822$	24.2471	0.845713
$823$	40.1649	1.40006	0.700031	−	0.714112i	$-0.253169\pi$
$823$	40.1649	1.40006	0.700031	+	0.714112i	$0.253169\pi$
$824$	−32.2936	−1.12500
$825$	−14.3878	−0.500918
$826$	3.23092	0.112418
$827$	17.5717	0.611029	0.305514	−	0.952187i	$-0.401172\pi$
$827$	17.5717	0.611029	0.305514	+	0.952187i	$0.401172\pi$
$828$	24.8783	0.864582
$829$	10.6626	0.370327	0.185164	−	0.982708i	$-0.440718\pi$
$829$	10.6626	0.370327	0.185164	+	0.982708i	$0.440718\pi$
$830$	−9.20173	−0.319397
$831$	11.3351	0.393210
$832$	−0.503854	−0.0174680
$833$	−3.19882	−0.110833
$834$	−0.803593	−0.0278261
$835$	−6.11632	−0.211664
$836$	−25.4370	−0.879759
$837$	17.8614	0.617379
$838$	0.961124	0.0332015
$839$	−3.71758	−0.128345	−0.0641725	−	0.997939i	$-0.520441\pi$
$839$	−3.71758	−0.128345	−0.0641725	+	0.997939i	$0.520441\pi$
$840$	6.48093	0.223613
$841$	−28.9879	−0.999582
$842$	−2.10706	−0.0726140
$843$	47.1063	1.62243
$844$	16.3061	0.561279
$845$	−12.2122	−0.420111
$846$	6.13174	0.210813
$847$	16.0608	0.551856
$848$	9.86622	0.338807
$849$	68.6856	2.35728
$850$	2.10023	0.0720373
$851$	−30.4155	−1.04263
$852$	−25.7071	−0.880712
$853$	25.8125	0.883803	0.441901	−	0.897064i	$-0.354304\pi$
$853$	25.8125	0.883803	0.441901	+	0.897064i	$0.354304\pi$
$854$	7.15772	0.244932
$855$	−14.4918	−0.495608
$856$	−29.1858	−0.997549
$857$	−15.8872	−0.542698	−0.271349	−	0.962481i	$-0.587470\pi$
$857$	−15.8872	−0.542698	−0.271349	+	0.962481i	$0.587470\pi$
$858$	−8.38471	−0.286249
$859$	−16.6852	−0.569293	−0.284646	−	0.958633i	$-0.591876\pi$
$859$	−16.6852	−0.569293	−0.284646	+	0.958633i	$0.591876\pi$
$860$	4.62040	0.157554
$861$	9.99464	0.340616
$862$	−23.7666	−0.809493
$863$	−33.3492	−1.13522	−0.567609	−	0.823298i	$-0.692132\pi$
$863$	−33.3492	−1.13522	−0.567609	+	0.823298i	$0.692132\pi$
$864$	−26.1749	−0.890487
$865$	−10.8675	−0.369505
$866$	13.5252	0.459604
$867$	−18.7178	−0.635688
$868$	−6.14160	−0.208460
$869$	83.5767	2.83514
$870$	0.200046	0.00678218
$871$	−0.0668346	−0.00226460
$872$	−31.8006	−1.07690
$873$	−16.4590	−0.557051
$874$	−6.97852	−0.236052
$875$	1.00000	0.0338062
$876$	−14.7846	−0.499525
$877$	−0.434486	−0.0146715	−0.00733577	−	0.999973i	$-0.502335\pi$
$877$	−0.434486	−0.0146715	−0.00733577	+	0.999973i	$0.502335\pi$
$878$	−20.9284	−0.706300
$879$	52.3816	1.76679
$880$	−8.31994	−0.280465
$881$	36.7509	1.23817	0.619085	−	0.785324i	$-0.287504\pi$
$881$	36.7509	1.23817	0.619085	+	0.785324i	$0.287504\pi$
$882$	−3.05284	−0.102794
$883$	−2.87701	−0.0968191	−0.0484096	−	0.998828i	$-0.515415\pi$
$883$	−2.87701	−0.0968191	−0.0484096	+	0.998828i	$0.515415\pi$
$884$	−4.45461	−0.149825
$885$	−13.6104	−0.457510
$886$	−17.8794	−0.600671
$887$	−30.3075	−1.01763	−0.508813	−	0.860877i	$-0.669916\pi$
$887$	−30.3075	−1.01763	−0.508813	+	0.860877i	$0.669916\pi$
$888$	57.8016	1.93970
$889$	−17.9277	−0.601275
$890$	11.9340	0.400030
$891$	6.91467	0.231650
$892$	21.3520	0.714918
$893$	6.25999	0.209483
$894$	−29.7357	−0.994510
$895$	9.12494	0.305013
$896$	11.1004	0.370838
$897$	8.37207	0.279535
$898$	−18.1846	−0.606828
$899$	−0.431230	−0.0143823
$900$	−7.29507	−0.243169
$901$	−19.7329	−0.657399
$902$	12.3422	0.410949
$903$	−8.14517	−0.271054
$904$	25.2891	0.841102
$905$	−12.9893	−0.431777
$906$	−32.5659	−1.08193
$907$	17.6044	0.584544	0.292272	−	0.956335i	$-0.405589\pi$
$907$	17.6044	0.584544	0.292272	+	0.956335i	$0.405589\pi$
$908$	−42.4089	−1.40739
$909$	−40.9909	−1.35958
$910$	0.582766	0.0193185
$911$	55.0416	1.82361	0.911805	−	0.410624i	$-0.134689\pi$
$911$	55.0416	1.82361	0.911805	+	0.410624i	$0.134689\pi$
$912$	−13.7869	−0.456530
$913$	−72.9060	−2.41284
$914$	−16.9224	−0.559743
$915$	−30.1523	−0.996805
$916$	1.56892	0.0518387
$917$	4.38223	0.144714
$918$	9.58299	0.316286
$919$	17.6369	0.581787	0.290893	−	0.956755i	$-0.406047\pi$
$919$	17.6369	0.581787	0.290893	+	0.956755i	$0.406047\pi$
$920$	−7.99109	−0.263459
$921$	21.7667	0.717239
$922$	−6.04866	−0.199202
$923$	−5.25831	−0.173079
$924$	22.5733	0.742608
$925$	8.91873	0.293246
$926$	−0.299406	−0.00983909
$927$	−64.0810	−2.10470
$928$	0.631945	0.0207446
$929$	20.4885	0.672204	0.336102	−	0.941826i	$-0.390891\pi$
$929$	20.4885	0.672204	0.336102	+	0.941826i	$0.390891\pi$
$930$	−7.10852	−0.233098
$931$	−3.11669	−0.102146
$932$	20.6511	0.676449
$933$	−60.2316	−1.97189
$934$	23.4286	0.766606
$935$	16.6403	0.544195
$936$	−9.67073	−0.316098
$937$	−6.67908	−0.218196	−0.109098	−	0.994031i	$-0.534796\pi$
$937$	−6.67908	−0.218196	−0.109098	+	0.994031i	$0.534796\pi$
$938$	−0.0494379	−0.00161421
$939$	−88.6439	−2.89279
$940$	3.15124	0.102782
$941$	−18.1382	−0.591288	−0.295644	−	0.955298i	$-0.595534\pi$
$941$	−18.1382	−0.591288	−0.295644	+	0.955298i	$0.595534\pi$
$942$	34.9299	1.13808
$943$	−12.3236	−0.401310
$944$	−7.87044	−0.256161
$945$	4.56283	0.148429
$946$	−10.0583	−0.327024
$947$	−5.39221	−0.175223	−0.0876116	−	0.996155i	$-0.527923\pi$
$947$	−5.39221	−0.175223	−0.0876116	+	0.996155i	$0.527923\pi$
$948$	69.7171	2.26431
$949$	−3.02414	−0.0981677
$950$	2.04631	0.0663910
$951$	−56.3430	−1.82705
$952$	−7.49556	−0.242932
$953$	40.1644	1.30105	0.650527	−	0.759483i	$-0.274548\pi$
$953$	40.1644	1.30105	0.650527	+	0.759483i	$0.274548\pi$
$954$	−18.8324	−0.609721
$955$	−23.2626	−0.752760
$956$	−28.8252	−0.932272
$957$	1.58498	0.0512350
$958$	6.76569	0.218590
$959$	−13.3524	−0.431172
$960$	1.57004	0.0506728
$961$	−15.6764	−0.505692
$962$	5.19754	0.167575
$963$	−57.9141	−1.86626
$964$	−8.08048	−0.260255
$965$	−1.63878	−0.0527543
$966$	6.19287	0.199252
$967$	41.6561	1.33957	0.669784	−	0.742556i	$-0.266387\pi$
$967$	41.6561	1.33957	0.669784	+	0.742556i	$0.266387\pi$
$968$	37.6341	1.20961
$969$	27.5745	0.885819
$970$	2.32408	0.0746218
$971$	53.4594	1.71559	0.857797	−	0.513988i	$-0.171832\pi$
$971$	53.4594	1.71559	0.857797	+	0.513988i	$0.171832\pi$
$972$	27.2442	0.873859
$973$	0.442523	0.0141866
$974$	21.5531	0.690606
$975$	−2.45494	−0.0786210
$976$	−17.4360	−0.558114
$977$	48.0420	1.53700	0.768500	−	0.639850i	$-0.221003\pi$
$977$	48.0420	1.53700	0.768500	+	0.639850i	$0.221003\pi$
$978$	36.1516	1.15600
$979$	94.5543	3.02197
$980$	−1.56892	−0.0501174
$981$	−63.1027	−2.01471
$982$	24.1147	0.769532
$983$	19.1528	0.610881	0.305440	−	0.952211i	$-0.401196\pi$
$983$	19.1528	0.610881	0.305440	+	0.952211i	$0.401196\pi$
$984$	23.4197	0.746593
$985$	−17.0166	−0.542192
$986$	−0.231364	−0.00736814
$987$	−5.55524	−0.176825
$988$	−4.34024	−0.138081
$989$	10.0431	0.319353
$990$	15.8809	0.504727
$991$	−15.1215	−0.480350	−0.240175	−	0.970730i	$-0.577205\pi$
$991$	−15.1215	−0.480350	−0.240175	+	0.970730i	$0.577205\pi$
$992$	−22.4559	−0.712975
$993$	36.6478	1.16298
$994$	−3.88961	−0.123371
$995$	12.5989	0.399411
$996$	−60.8160	−1.92703
$997$	1.56799	0.0496588	0.0248294	−	0.999692i	$-0.492096\pi$
$997$	1.56799	0.0496588	0.0248294	+	0.999692i	$0.492096\pi$
$998$	−0.927910	−0.0293725
$999$	40.6947	1.28752

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.h.1.16	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.h.1.16	✓	38	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.656564 q^{2} +2.76581 q^{3} -1.56892 q^{4} +1.00000 q^{5} -1.81593 q^{6} +1.00000 q^{7} +2.34323 q^{8} +4.64973 q^{9} +O(q^{10})\)	\(q-0.656564 q^{2} +2.76581 q^{3} -1.56892 q^{4} +1.00000 q^{5} -1.81593 q^{6} +1.00000 q^{7} +2.34323 q^{8} +4.64973 q^{9} -0.656564 q^{10} -5.20200 q^{11} -4.33935 q^{12} -0.887601 q^{13} -0.656564 q^{14} +2.76581 q^{15} +1.59937 q^{16} -3.19882 q^{17} -3.05284 q^{18} -3.11669 q^{19} -1.56892 q^{20} +2.76581 q^{21} +3.41544 q^{22} -3.41030 q^{23} +6.48093 q^{24} +1.00000 q^{25} +0.582766 q^{26} +4.56283 q^{27} -1.56892 q^{28} -0.110161 q^{29} -1.81593 q^{30} +3.91453 q^{31} -5.73654 q^{32} -14.3878 q^{33} +2.10023 q^{34} +1.00000 q^{35} -7.29507 q^{36} +8.91873 q^{37} +2.04631 q^{38} -2.45494 q^{39} +2.34323 q^{40} +3.61363 q^{41} -1.81593 q^{42} -2.94495 q^{43} +8.16155 q^{44} +4.64973 q^{45} +2.23908 q^{46} -2.00854 q^{47} +4.42357 q^{48} +1.00000 q^{49} -0.656564 q^{50} -8.84734 q^{51} +1.39258 q^{52} +6.16881 q^{53} -2.99579 q^{54} -5.20200 q^{55} +2.34323 q^{56} -8.62019 q^{57} +0.0723279 q^{58} -4.92096 q^{59} -4.33935 q^{60} -10.9018 q^{61} -2.57014 q^{62} +4.64973 q^{63} +0.567659 q^{64} -0.887601 q^{65} +9.44648 q^{66} +0.0752980 q^{67} +5.01871 q^{68} -9.43224 q^{69} -0.656564 q^{70} +5.92419 q^{71} +10.8954 q^{72} +3.40709 q^{73} -5.85571 q^{74} +2.76581 q^{75} +4.88986 q^{76} -5.20200 q^{77} +1.61182 q^{78} -16.0663 q^{79} +1.59937 q^{80} -1.32923 q^{81} -2.37258 q^{82} +14.0150 q^{83} -4.33935 q^{84} -3.19882 q^{85} +1.93354 q^{86} -0.304686 q^{87} -12.1895 q^{88} -18.1765 q^{89} -3.05284 q^{90} -0.887601 q^{91} +5.35050 q^{92} +10.8269 q^{93} +1.31873 q^{94} -3.11669 q^{95} -15.8662 q^{96} -3.53977 q^{97} -0.656564 q^{98} -24.1879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9	\( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 38 * q - 6 * q^2 - 9 * q^3 + 24 * q^4 + 38 * q^5 - 10 * q^6 + 38 * q^7 - 21 * q^8 + 13 * q^9 - 6 * q^10 - 18 * q^11 - 20 * q^12 - 25 * q^13 - 6 * q^14 - 9 * q^15 - 21 * q^17 - 7 * q^18 - 14 * q^19 + 24 * q^20 - 9 * q^21 - 11 * q^22 - 16 * q^23 - 10 * q^24 + 38 * q^25 - 21 * q^26 - 15 * q^27 + 24 * q^28 - 52 * q^29 - 10 * q^30 - 30 * q^31 - 8 * q^32 - 13 * q^33 - 9 * q^34 + 38 * q^35 - 16 * q^36 - 47 * q^37 - 10 * q^38 - 50 * q^39 - 21 * q^40 - 35 * q^41 - 10 * q^42 - 18 * q^43 - 22 * q^44 + 13 * q^45 - 17 * q^46 - 23 * q^47 - 13 * q^48 + 38 * q^49 - 6 * q^50 - 5 * q^51 - 41 * q^52 - 12 * q^53 + 35 * q^54 - 18 * q^55 - 21 * q^56 - 3 * q^57 - 16 * q^58 - 16 * q^59 - 20 * q^60 - 47 * q^61 + 14 * q^62 + 13 * q^63 - 55 * q^64 - 25 * q^65 - 6 * q^66 - 54 * q^67 + 31 * q^68 - 95 * q^69 - 6 * q^70 - 41 * q^71 - 59 * q^73 - q^74 - 9 * q^75 - 23 * q^76 - 18 * q^77 + 19 * q^78 - 117 * q^79 - 38 * q^81 + 19 * q^82 - 21 * q^83 - 20 * q^84 - 21 * q^85 - 12 * q^86 - 14 * q^87 - 40 * q^88 - 96 * q^89 - 7 * q^90 - 25 * q^91 + 53 * q^92 - 53 * q^93 - 28 * q^94 - 14 * q^95 + 40 * q^96 - 70 * q^97 - 6 * q^98 - 52 * q^99

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