LMFDB - Embedded newform 8015.2.a.l.1.6

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:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.35302 q^{2} +1.42181 q^{3} +3.53669 q^{4} -1.00000 q^{5} -3.34553 q^{6} -1.00000 q^{7} -3.61585 q^{8} -0.978466 q^{9} +O(q^{10})$	\(q-2.35302 q^{2} +1.42181 q^{3} +3.53669 q^{4} -1.00000 q^{5} -3.34553 q^{6} -1.00000 q^{7} -3.61585 q^{8} -0.978466 q^{9} +2.35302 q^{10} -5.71770 q^{11} +5.02848 q^{12} -2.54493 q^{13} +2.35302 q^{14} -1.42181 q^{15} +1.43477 q^{16} -3.84787 q^{17} +2.30235 q^{18} +4.40419 q^{19} -3.53669 q^{20} -1.42181 q^{21} +13.4538 q^{22} -5.65179 q^{23} -5.14103 q^{24} +1.00000 q^{25} +5.98827 q^{26} -5.65661 q^{27} -3.53669 q^{28} -6.59897 q^{29} +3.34553 q^{30} -1.55208 q^{31} +3.85565 q^{32} -8.12947 q^{33} +9.05410 q^{34} +1.00000 q^{35} -3.46053 q^{36} -1.11540 q^{37} -10.3631 q^{38} -3.61840 q^{39} +3.61585 q^{40} -6.51642 q^{41} +3.34553 q^{42} +8.12476 q^{43} -20.2217 q^{44} +0.978466 q^{45} +13.2988 q^{46} -7.20728 q^{47} +2.03997 q^{48} +1.00000 q^{49} -2.35302 q^{50} -5.47093 q^{51} -9.00062 q^{52} +1.36357 q^{53} +13.3101 q^{54} +5.71770 q^{55} +3.61585 q^{56} +6.26191 q^{57} +15.5275 q^{58} -3.51950 q^{59} -5.02848 q^{60} +9.88504 q^{61} +3.65208 q^{62} +0.978466 q^{63} -11.9419 q^{64} +2.54493 q^{65} +19.1288 q^{66} +9.52626 q^{67} -13.6087 q^{68} -8.03576 q^{69} -2.35302 q^{70} -6.37994 q^{71} +3.53798 q^{72} -14.6405 q^{73} +2.62456 q^{74} +1.42181 q^{75} +15.5762 q^{76} +5.71770 q^{77} +8.51416 q^{78} -15.9245 q^{79} -1.43477 q^{80} -5.10721 q^{81} +15.3332 q^{82} -5.46210 q^{83} -5.02848 q^{84} +3.84787 q^{85} -19.1177 q^{86} -9.38247 q^{87} +20.6743 q^{88} -1.58947 q^{89} -2.30235 q^{90} +2.54493 q^{91} -19.9886 q^{92} -2.20676 q^{93} +16.9588 q^{94} -4.40419 q^{95} +5.48198 q^{96} +14.6538 q^{97} -2.35302 q^{98} +5.59458 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	−2.35302	−1.66383	−0.831917	−	0.554900i	$-0.812756\pi$
$2$	−2.35302	−1.66383	−0.831917	+	0.554900i	$0.812756\pi$
$3$	1.42181	0.820880	0.410440	−	0.911888i	$-0.365375\pi$
$3$	1.42181	0.820880	0.410440	+	0.911888i	$0.365375\pi$
$4$	3.53669	1.76834
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.34553	−1.36581
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.61585	−1.27839
$9$	−0.978466	−0.326155
$10$	2.35302	0.744089
$11$	−5.71770	−1.72395	−0.861976	−	0.506949i	$-0.830773\pi$
$11$	−5.71770	−1.72395	−0.861976	+	0.506949i	$0.830773\pi$
$12$	5.02848	1.45160
$13$	−2.54493	−0.705837	−0.352919	−	0.935654i	$-0.614811\pi$
$13$	−2.54493	−0.705837	−0.352919	+	0.935654i	$0.614811\pi$
$14$	2.35302	0.628870
$15$	−1.42181	−0.367109
$16$	1.43477	0.358693
$17$	−3.84787	−0.933246	−0.466623	−	0.884456i	$-0.654529\pi$
$17$	−3.84787	−0.933246	−0.466623	+	0.884456i	$0.654529\pi$
$18$	2.30235	0.542668
$19$	4.40419	1.01039	0.505195	−	0.863005i	$-0.331420\pi$
$19$	4.40419	1.01039	0.505195	+	0.863005i	$0.331420\pi$
$20$	−3.53669	−0.790827
$21$	−1.42181	−0.310264
$22$	13.4538	2.86837
$23$	−5.65179	−1.17848	−0.589240	−	0.807958i	$-0.700573\pi$
$23$	−5.65179	−1.17848	−0.589240	+	0.807958i	$0.700573\pi$
$24$	−5.14103	−1.04941
$25$	1.00000	0.200000
$26$	5.98827	1.17440
$27$	−5.65661	−1.08861
$28$	−3.53669	−0.668371
$29$	−6.59897	−1.22540	−0.612699	−	0.790316i	$-0.709916\pi$
$29$	−6.59897	−1.22540	−0.612699	+	0.790316i	$0.709916\pi$
$30$	3.34553	0.610808
$31$	−1.55208	−0.278762	−0.139381	−	0.990239i	$-0.544511\pi$
$31$	−1.55208	−0.278762	−0.139381	+	0.990239i	$0.544511\pi$
$32$	3.85565	0.681589
$33$	−8.12947	−1.41516
$34$	9.05410	1.55277
$35$	1.00000	0.169031
$36$	−3.46053	−0.576754
$37$	−1.11540	−0.183371	−0.0916854	−	0.995788i	$-0.529225\pi$
$37$	−1.11540	−0.183371	−0.0916854	+	0.995788i	$0.529225\pi$
$38$	−10.3631	−1.68112
$39$	−3.61840	−0.579408
$40$	3.61585	0.571715
$41$	−6.51642	−1.01769	−0.508847	−	0.860857i	$-0.669928\pi$
$41$	−6.51642	−1.01769	−0.508847	+	0.860857i	$0.669928\pi$
$42$	3.34553	0.516227
$43$	8.12476	1.23901	0.619507	−	0.784991i	$-0.287333\pi$
$43$	8.12476	1.23901	0.619507	+	0.784991i	$0.287333\pi$
$44$	−20.2217	−3.04854
$45$	0.978466	0.145861
$46$	13.2988	1.96080
$47$	−7.20728	−1.05129	−0.525645	−	0.850704i	$-0.676176\pi$
$47$	−7.20728	−1.05129	−0.525645	+	0.850704i	$0.676176\pi$
$48$	2.03997	0.294444
$49$	1.00000	0.142857
$50$	−2.35302	−0.332767
$51$	−5.47093	−0.766083
$52$	−9.00062	−1.24816
$53$	1.36357	0.187301	0.0936506	−	0.995605i	$-0.470146\pi$
$53$	1.36357	0.187301	0.0936506	+	0.995605i	$0.470146\pi$
$54$	13.3101	1.81127
$55$	5.71770	0.770975
$56$	3.61585	0.483188
$57$	6.26191	0.829410
$58$	15.5275	2.03886
$59$	−3.51950	−0.458200	−0.229100	−	0.973403i	$-0.573578\pi$
$59$	−3.51950	−0.458200	−0.229100	+	0.973403i	$0.573578\pi$
$60$	−5.02848	−0.649174
$61$	9.88504	1.26565	0.632825	−	0.774295i	$-0.281895\pi$
$61$	9.88504	1.26565	0.632825	+	0.774295i	$0.281895\pi$
$62$	3.65208	0.463814
$63$	0.978466	0.123275
$64$	−11.9419	−1.49274
$65$	2.54493	0.315660
$66$	19.1288	2.35459
$67$	9.52626	1.16382	0.581909	−	0.813254i	$-0.302306\pi$
$67$	9.52626	1.16382	0.581909	+	0.813254i	$0.302306\pi$
$68$	−13.6087	−1.65030
$69$	−8.03576	−0.967391
$70$	−2.35302	−0.281239
$71$	−6.37994	−0.757160	−0.378580	−	0.925569i	$-0.623587\pi$
$71$	−6.37994	−0.757160	−0.378580	+	0.925569i	$0.623587\pi$
$72$	3.53798	0.416955
$73$	−14.6405	−1.71354	−0.856771	−	0.515698i	$-0.827533\pi$
$73$	−14.6405	−1.71354	−0.856771	+	0.515698i	$0.827533\pi$
$74$	2.62456	0.305098
$75$	1.42181	0.164176
$76$	15.5762	1.78672
$77$	5.71770	0.651593
$78$	8.51416	0.964038
$79$	−15.9245	−1.79165	−0.895825	−	0.444408i	$-0.853414\pi$
$79$	−15.9245	−1.79165	−0.895825	+	0.444408i	$0.853414\pi$
$80$	−1.43477	−0.160413
$81$	−5.10721	−0.567467
$82$	15.3332	1.69327
$83$	−5.46210	−0.599543	−0.299772	−	0.954011i	$-0.596910\pi$
$83$	−5.46210	−0.599543	−0.299772	+	0.954011i	$0.596910\pi$
$84$	−5.02848	−0.548652
$85$	3.84787	0.417360
$86$	−19.1177	−2.06151
$87$	−9.38247	−1.00591
$88$	20.6743	2.20389
$89$	−1.58947	−0.168484	−0.0842419	−	0.996445i	$-0.526847\pi$
$89$	−1.58947	−0.168484	−0.0842419	+	0.996445i	$0.526847\pi$
$90$	−2.30235	−0.242689
$91$	2.54493	0.266781
$92$	−19.9886	−2.08396
$93$	−2.20676	−0.228831
$94$	16.9588	1.74917
$95$	−4.40419	−0.451860
$96$	5.48198	0.559503
$97$	14.6538	1.48787	0.743935	−	0.668252i	$-0.232957\pi$
$97$	14.6538	1.48787	0.743935	+	0.668252i	$0.232957\pi$
$98$	−2.35302	−0.237691
$99$	5.59458	0.562276
$100$	3.53669	0.353669
$101$	−8.32577	−0.828446	−0.414223	−	0.910176i	$-0.635947\pi$
$101$	−8.32577	−0.828446	−0.414223	+	0.910176i	$0.635947\pi$
$102$	12.8732	1.27463
$103$	−6.89805	−0.679685	−0.339843	−	0.940482i	$-0.610374\pi$
$103$	−6.89805	−0.679685	−0.339843	+	0.940482i	$0.610374\pi$
$104$	9.20208	0.902338
$105$	1.42181	0.138754
$106$	−3.20851	−0.311638
$107$	−2.48737	−0.240463	−0.120232	−	0.992746i	$-0.538364\pi$
$107$	−2.48737	−0.240463	−0.120232	+	0.992746i	$0.538364\pi$
$108$	−20.0056	−1.92504
$109$	−16.3311	−1.56423	−0.782116	−	0.623132i	$-0.785860\pi$
$109$	−16.3311	−1.56423	−0.782116	+	0.623132i	$0.785860\pi$
$110$	−13.4538	−1.28277
$111$	−1.58588	−0.150525
$112$	−1.43477	−0.135573
$113$	−2.75707	−0.259363	−0.129681	−	0.991556i	$-0.541395\pi$
$113$	−2.75707	−0.259363	−0.129681	+	0.991556i	$0.541395\pi$
$114$	−14.7344	−1.38000
$115$	5.65179	0.527032
$116$	−23.3385	−2.16693
$117$	2.49013	0.230212
$118$	8.28145	0.762369
$119$	3.84787	0.352734
$120$	5.14103	0.469310
$121$	21.6921	1.97201
$122$	−23.2597	−2.10583
$123$	−9.26509	−0.835405
$124$	−5.48923	−0.492948
$125$	−1.00000	−0.0894427
$126$	−2.30235	−0.205109
$127$	−15.9007	−1.41096	−0.705478	−	0.708732i	$-0.749268\pi$
$127$	−15.9007	−1.41096	−0.705478	+	0.708732i	$0.749268\pi$
$128$	20.3883	1.80209
$129$	11.5518	1.01708
$130$	−5.98827	−0.525206
$131$	12.6377	1.10416	0.552081	−	0.833790i	$-0.313834\pi$
$131$	12.6377	1.10416	0.552081	+	0.833790i	$0.313834\pi$
$132$	−28.7514	−2.50249
$133$	−4.40419	−0.381892
$134$	−22.4154	−1.93640
$135$	5.65661	0.486843
$136$	13.9133	1.19306
$137$	8.89677	0.760102	0.380051	−	0.924965i	$-0.375906\pi$
$137$	8.89677	0.760102	0.380051	+	0.924965i	$0.375906\pi$
$138$	18.9083	1.60958
$139$	−4.34004	−0.368117	−0.184059	−	0.982915i	$-0.558924\pi$
$139$	−4.34004	−0.368117	−0.184059	+	0.982915i	$0.558924\pi$
$140$	3.53669	0.298904
$141$	−10.2474	−0.862983
$142$	15.0121	1.25979
$143$	14.5512	1.21683
$144$	−1.40388	−0.116990
$145$	6.59897	0.548015
$146$	34.4493	2.85105
$147$	1.42181	0.117269
$148$	−3.94482	−0.324262
$149$	15.8215	1.29615	0.648075	−	0.761576i	$-0.275574\pi$
$149$	15.8215	1.29615	0.648075	+	0.761576i	$0.275574\pi$
$150$	−3.34553	−0.273162
$151$	4.10427	0.334001	0.167000	−	0.985957i	$-0.446592\pi$
$151$	4.10427	0.334001	0.167000	+	0.985957i	$0.446592\pi$
$152$	−15.9249	−1.29168
$153$	3.76501	0.304383
$154$	−13.4538	−1.08414
$155$	1.55208	0.124666
$156$	−12.7971	−1.02459
$157$	−22.0419	−1.75913	−0.879567	−	0.475776i	$-0.842167\pi$
$157$	−22.0419	−1.75913	−0.879567	+	0.475776i	$0.842167\pi$
$158$	37.4707	2.98101
$159$	1.93874	0.153752
$160$	−3.85565	−0.304816
$161$	5.65179	0.445424
$162$	12.0173	0.944171
$163$	−9.71053	−0.760588	−0.380294	−	0.924866i	$-0.624177\pi$
$163$	−9.71053	−0.760588	−0.380294	+	0.924866i	$0.624177\pi$
$164$	−23.0465	−1.79963
$165$	8.12947	0.632878
$166$	12.8524	0.997540
$167$	20.9784	1.62335	0.811677	−	0.584107i	$-0.198555\pi$
$167$	20.9784	1.62335	0.811677	+	0.584107i	$0.198555\pi$
$168$	5.14103	0.396639
$169$	−6.52332	−0.501794
$170$	−9.05410	−0.694418
$171$	−4.30935	−0.329544
$172$	28.7347	2.19100
$173$	22.0835	1.67898	0.839488	−	0.543378i	$-0.182855\pi$
$173$	22.0835	1.67898	0.839488	+	0.543378i	$0.182855\pi$
$174$	22.0771	1.67366
$175$	−1.00000	−0.0755929
$176$	−8.20361	−0.618370
$177$	−5.00405	−0.376128
$178$	3.74005	0.280329
$179$	−6.35822	−0.475236	−0.237618	−	0.971359i	$-0.576367\pi$
$179$	−6.35822	−0.475236	−0.237618	+	0.971359i	$0.576367\pi$
$180$	3.46053	0.257932
$181$	−12.5770	−0.934843	−0.467422	−	0.884035i	$-0.654817\pi$
$181$	−12.5770	−0.934843	−0.467422	+	0.884035i	$0.654817\pi$
$182$	−5.98827	−0.443880
$183$	14.0546	1.03895
$184$	20.4360	1.50656
$185$	1.11540	0.0820059
$186$	5.19255	0.380736
$187$	22.0010	1.60887
$188$	−25.4899	−1.85904
$189$	5.65661	0.411458
$190$	10.3631	0.751821
$191$	20.8789	1.51075	0.755374	−	0.655294i	$-0.227455\pi$
$191$	20.8789	1.51075	0.755374	+	0.655294i	$0.227455\pi$
$192$	−16.9791	−1.22536
$193$	−21.2875	−1.53231	−0.766155	−	0.642656i	$-0.777832\pi$
$193$	−21.2875	−1.53231	−0.766155	+	0.642656i	$0.777832\pi$
$194$	−34.4807	−2.47557
$195$	3.61840	0.259119
$196$	3.53669	0.252620
$197$	−11.1750	−0.796186	−0.398093	−	0.917345i	$-0.630328\pi$
$197$	−11.1750	−0.796186	−0.398093	+	0.917345i	$0.630328\pi$
$198$	−13.1641	−0.935534
$199$	11.3928	0.807612	0.403806	−	0.914845i	$-0.367687\pi$
$199$	11.3928	0.807612	0.403806	+	0.914845i	$0.367687\pi$
$200$	−3.61585	−0.255679
$201$	13.5445	0.955355
$202$	19.5907	1.37840
$203$	6.59897	0.463157
$204$	−19.3489	−1.35470
$205$	6.51642	0.455127
$206$	16.2312	1.13088
$207$	5.53009	0.384368
$208$	−3.65140	−0.253179
$209$	−25.1818	−1.74186
$210$	−3.34553	−0.230864
$211$	−7.59717	−0.523011	−0.261505	−	0.965202i	$-0.584219\pi$
$211$	−7.59717	−0.523011	−0.261505	+	0.965202i	$0.584219\pi$
$212$	4.82253	0.331213
$213$	−9.07104	−0.621538
$214$	5.85282	0.400091
$215$	−8.12476	−0.554104
$216$	20.4534	1.39168
$217$	1.55208	0.105362
$218$	38.4273	2.60262
$219$	−20.8160	−1.40661
$220$	20.2217	1.36335
$221$	9.79257	0.658719
$222$	3.73161	0.250449
$223$	12.1671	0.814768	0.407384	−	0.913257i	$-0.366441\pi$
$223$	12.1671	0.814768	0.407384	+	0.913257i	$0.366441\pi$
$224$	−3.85565	−0.257616
$225$	−0.978466	−0.0652311
$226$	6.48742	0.431537
$227$	3.05345	0.202664	0.101332	−	0.994853i	$-0.467689\pi$
$227$	3.05345	0.202664	0.101332	+	0.994853i	$0.467689\pi$
$228$	22.1464	1.46668
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−13.2988	−0.876894
$231$	8.12947	0.534880
$232$	23.8609	1.56654
$233$	14.9295	0.978063	0.489031	−	0.872266i	$-0.337350\pi$
$233$	14.9295	0.978063	0.489031	+	0.872266i	$0.337350\pi$
$234$	−5.85931	−0.383035
$235$	7.20728	0.470151
$236$	−12.4474	−0.810255
$237$	−22.6416	−1.47073
$238$	−9.05410	−0.586890
$239$	−25.6759	−1.66083	−0.830416	−	0.557143i	$-0.811897\pi$
$239$	−25.6759	−1.66083	−0.830416	+	0.557143i	$0.811897\pi$
$240$	−2.03997	−0.131680
$241$	22.0544	1.42065	0.710325	−	0.703874i	$-0.248548\pi$
$241$	22.0544	1.42065	0.710325	+	0.703874i	$0.248548\pi$
$242$	−51.0419	−3.28110
$243$	9.70837	0.622792
$244$	34.9603	2.23810
$245$	−1.00000	−0.0638877
$246$	21.8009	1.38998
$247$	−11.2084	−0.713171
$248$	5.61210	0.356368
$249$	−7.76605	−0.492153
$250$	2.35302	0.148818
$251$	−2.36970	−0.149574	−0.0747871	−	0.997200i	$-0.523828\pi$
$251$	−2.36970	−0.149574	−0.0747871	+	0.997200i	$0.523828\pi$
$252$	3.46053	0.217993
$253$	32.3153	2.03164
$254$	37.4145	2.34760
$255$	5.47093	0.342603
$256$	−24.0901	−1.50563
$257$	15.3174	0.955474	0.477737	−	0.878503i	$-0.341457\pi$
$257$	15.3174	0.955474	0.477737	+	0.878503i	$0.341457\pi$
$258$	−27.1817	−1.69226
$259$	1.11540	0.0693076
$260$	9.00062	0.558195
$261$	6.45687	0.399670
$262$	−29.7368	−1.83714
$263$	11.0808	0.683272	0.341636	−	0.939832i	$-0.389019\pi$
$263$	11.0808	0.683272	0.341636	+	0.939832i	$0.389019\pi$
$264$	29.3949	1.80913
$265$	−1.36357	−0.0837637
$266$	10.3631	0.635404
$267$	−2.25992	−0.138305
$268$	33.6914	2.05803
$269$	7.39826	0.451080	0.225540	−	0.974234i	$-0.427585\pi$
$269$	7.39826	0.451080	0.225540	+	0.974234i	$0.427585\pi$
$270$	−13.3101	−0.810026
$271$	12.4457	0.756021	0.378011	−	0.925801i	$-0.376608\pi$
$271$	12.4457	0.756021	0.378011	+	0.925801i	$0.376608\pi$
$272$	−5.52082	−0.334749
$273$	3.61840	0.218996
$274$	−20.9342	−1.26468
$275$	−5.71770	−0.344790
$276$	−28.4199	−1.71068
$277$	12.9875	0.780344	0.390172	−	0.920742i	$-0.372416\pi$
$277$	12.9875	0.780344	0.390172	+	0.920742i	$0.372416\pi$
$278$	10.2122	0.612486
$279$	1.51866	0.0909199
$280$	−3.61585	−0.216088
$281$	1.98709	0.118540	0.0592700	−	0.998242i	$-0.481123\pi$
$281$	1.98709	0.118540	0.0592700	+	0.998242i	$0.481123\pi$
$282$	24.1122	1.43586
$283$	8.87945	0.527829	0.263914	−	0.964546i	$-0.414986\pi$
$283$	8.87945	0.527829	0.263914	+	0.964546i	$0.414986\pi$
$284$	−22.5638	−1.33892
$285$	−6.26191	−0.370923
$286$	−34.2391	−2.02460
$287$	6.51642	0.384652
$288$	−3.77262	−0.222304
$289$	−2.19390	−0.129053
$290$	−15.5275	−0.911806
$291$	20.8349	1.22136
$292$	−51.7789	−3.03013
$293$	−23.7539	−1.38772	−0.693858	−	0.720112i	$-0.744091\pi$
$293$	−23.7539	−1.38772	−0.693858	+	0.720112i	$0.744091\pi$
$294$	−3.34553	−0.195116
$295$	3.51950	0.204913
$296$	4.03312	0.234420
$297$	32.3428	1.87672
$298$	−37.2283	−2.15658
$299$	14.3834	0.831815
$300$	5.02848	0.290320
$301$	−8.12476	−0.468303
$302$	−9.65742	−0.555722
$303$	−11.8376	−0.680055
$304$	6.31902	0.362420
$305$	−9.88504	−0.566016
$306$	−8.85913	−0.506443
$307$	19.5236	1.11427	0.557135	−	0.830422i	$-0.311901\pi$
$307$	19.5236	1.11427	0.557135	+	0.830422i	$0.311901\pi$
$308$	20.2217	1.15224
$309$	−9.80770	−0.557940
$310$	−3.65208	−0.207424
$311$	−17.4531	−0.989674	−0.494837	−	0.868986i	$-0.664772\pi$
$311$	−17.4531	−0.989674	−0.494837	+	0.868986i	$0.664772\pi$
$312$	13.0836	0.740712
$313$	−26.3918	−1.49175	−0.745875	−	0.666086i	$-0.767969\pi$
$313$	−26.3918	−1.49175	−0.745875	+	0.666086i	$0.767969\pi$
$314$	51.8649	2.92691
$315$	−0.978466	−0.0551303
$316$	−56.3201	−3.16825
$317$	24.7068	1.38767	0.693836	−	0.720133i	$-0.255919\pi$
$317$	24.7068	1.38767	0.693836	+	0.720133i	$0.255919\pi$
$318$	−4.56188	−0.255818
$319$	37.7310	2.11253
$320$	11.9419	0.667575
$321$	−3.53656	−0.197391
$322$	−13.2988	−0.741111
$323$	−16.9468	−0.942943
$324$	−18.0626	−1.00348
$325$	−2.54493	−0.141167
$326$	22.8490	1.26549
$327$	−23.2196	−1.28405
$328$	23.5624	1.30101
$329$	7.20728	0.397350
$330$	−19.1288	−1.05300
$331$	23.6227	1.29842	0.649211	−	0.760608i	$-0.275099\pi$
$331$	23.6227	1.29842	0.649211	+	0.760608i	$0.275099\pi$
$332$	−19.3177	−1.06020
$333$	1.09138	0.0598073
$334$	−49.3624	−2.70099
$335$	−9.52626	−0.520475
$336$	−2.03997	−0.111290
$337$	20.8674	1.13672	0.568361	−	0.822779i	$-0.307578\pi$
$337$	20.8674	1.13672	0.568361	+	0.822779i	$0.307578\pi$
$338$	15.3495	0.834902
$339$	−3.92001	−0.212906
$340$	13.6087	0.738036
$341$	8.87435	0.480573
$342$	10.1400	0.548307
$343$	−1.00000	−0.0539949
$344$	−29.3779	−1.58395
$345$	8.03576	0.432631
$346$	−51.9628	−2.79354
$347$	−8.85186	−0.475193	−0.237596	−	0.971364i	$-0.576360\pi$
$347$	−8.85186	−0.475193	−0.237596	+	0.971364i	$0.576360\pi$
$348$	−33.1828	−1.77879
$349$	2.85712	0.152938	0.0764691	−	0.997072i	$-0.475635\pi$
$349$	2.85712	0.152938	0.0764691	+	0.997072i	$0.475635\pi$
$350$	2.35302	0.125774
$351$	14.3957	0.768385
$352$	−22.0454	−1.17503
$353$	−16.7454	−0.891268	−0.445634	−	0.895215i	$-0.647022\pi$
$353$	−16.7454	−0.891268	−0.445634	+	0.895215i	$0.647022\pi$
$354$	11.7746	0.625814
$355$	6.37994	0.338612
$356$	−5.62146	−0.297937
$357$	5.47093	0.289552
$358$	14.9610	0.790713
$359$	8.93988	0.471829	0.235915	−	0.971774i	$-0.424191\pi$
$359$	8.93988	0.471829	0.235915	+	0.971774i	$0.424191\pi$
$360$	−3.53798	−0.186468
$361$	0.396895	0.0208892
$362$	29.5940	1.55542
$363$	30.8420	1.61878
$364$	9.00062	0.471761
$365$	14.6405	0.766319
$366$	−33.0708	−1.72864
$367$	−13.2877	−0.693611	−0.346806	−	0.937937i	$-0.612734\pi$
$367$	−13.2877	−0.693611	−0.346806	+	0.937937i	$0.612734\pi$
$368$	−8.10904	−0.422713
$369$	6.37610	0.331926
$370$	−2.62456	−0.136444
$371$	−1.36357	−0.0707932
$372$	−7.80463	−0.404651
$373$	12.0371	0.623260	0.311630	−	0.950204i	$-0.399125\pi$
$373$	12.0371	0.623260	0.311630	+	0.950204i	$0.399125\pi$
$374$	−51.7686	−2.67689
$375$	−1.42181	−0.0734218
$376$	26.0604	1.34396
$377$	16.7939	0.864932
$378$	−13.3101	−0.684597
$379$	35.3434	1.81547	0.907733	−	0.419548i	$-0.137811\pi$
$379$	35.3434	1.81547	0.907733	+	0.419548i	$0.137811\pi$
$380$	−15.5762	−0.799044
$381$	−22.6077	−1.15823
$382$	−49.1285	−2.51363
$383$	−17.6583	−0.902296	−0.451148	−	0.892449i	$-0.648985\pi$
$383$	−17.6583	−0.902296	−0.451148	+	0.892449i	$0.648985\pi$
$384$	28.9882	1.47930
$385$	−5.71770	−0.291401
$386$	50.0899	2.54951
$387$	−7.94980	−0.404111
$388$	51.8259	2.63106
$389$	−5.06377	−0.256743	−0.128372	−	0.991726i	$-0.540975\pi$
$389$	−5.06377	−0.256743	−0.128372	+	0.991726i	$0.540975\pi$
$390$	−8.51416	−0.431131
$391$	21.7474	1.09981
$392$	−3.61585	−0.182628
$393$	17.9684	0.906386
$394$	26.2950	1.32472
$395$	15.9245	0.801250
$396$	19.7863	0.994297
$397$	17.4344	0.875008	0.437504	−	0.899216i	$-0.355863\pi$
$397$	17.4344	0.875008	0.437504	+	0.899216i	$0.355863\pi$
$398$	−26.8074	−1.34373
$399$	−6.26191	−0.313487
$400$	1.43477	0.0717387
$401$	−18.5872	−0.928203	−0.464101	−	0.885782i	$-0.653623\pi$
$401$	−18.5872	−0.928203	−0.464101	+	0.885782i	$0.653623\pi$
$402$	−31.8704	−1.58955
$403$	3.94995	0.196761
$404$	−29.4456	−1.46498
$405$	5.10721	0.253779
$406$	−15.5275	−0.770617
$407$	6.37753	0.316122
$408$	19.7820	0.979356
$409$	−21.0220	−1.03947	−0.519737	−	0.854327i	$-0.673970\pi$
$409$	−21.0220	−1.03947	−0.519737	+	0.854327i	$0.673970\pi$
$410$	−15.3332	−0.757255
$411$	12.6495	0.623953
$412$	−24.3962	−1.20192
$413$	3.51950	0.173183
$414$	−13.0124	−0.639524
$415$	5.46210	0.268124
$416$	−9.81236	−0.481090
$417$	−6.17070	−0.302180
$418$	59.2533	2.89817
$419$	−4.74499	−0.231808	−0.115904	−	0.993260i	$-0.536977\pi$
$419$	−4.74499	−0.231808	−0.115904	+	0.993260i	$0.536977\pi$
$420$	5.02848	0.245365
$421$	−2.40152	−0.117043	−0.0585215	−	0.998286i	$-0.518639\pi$
$421$	−2.40152	−0.117043	−0.0585215	+	0.998286i	$0.518639\pi$
$422$	17.8763	0.870203
$423$	7.05208	0.342884
$424$	−4.93047	−0.239445
$425$	−3.84787	−0.186649
$426$	21.3443	1.03414
$427$	−9.88504	−0.478371
$428$	−8.79704	−0.425221
$429$	20.6889	0.998871
$430$	19.1177	0.921937
$431$	−12.6907	−0.611288	−0.305644	−	0.952146i	$-0.598872\pi$
$431$	−12.6907	−0.611288	−0.305644	+	0.952146i	$0.598872\pi$
$432$	−8.11595	−0.390479
$433$	34.7723	1.67105	0.835525	−	0.549453i	$-0.185164\pi$
$433$	34.7723	1.67105	0.835525	+	0.549453i	$0.185164\pi$
$434$	−3.65208	−0.175305
$435$	9.38247	0.449855
$436$	−57.7579	−2.76610
$437$	−24.8916	−1.19073
$438$	48.9803	2.34037
$439$	−21.5536	−1.02870	−0.514348	−	0.857581i	$-0.671966\pi$
$439$	−21.5536	−1.02870	−0.514348	+	0.857581i	$0.671966\pi$
$440$	−20.6743	−0.985610
$441$	−0.978466	−0.0465936
$442$	−23.0421	−1.09600
$443$	39.6840	1.88544	0.942721	−	0.333581i	$-0.108257\pi$
$443$	39.6840	1.88544	0.942721	+	0.333581i	$0.108257\pi$
$444$	−5.60877	−0.266181
$445$	1.58947	0.0753482
$446$	−28.6293	−1.35564
$447$	22.4952	1.06398
$448$	11.9419	0.564204
$449$	8.75751	0.413292	0.206646	−	0.978416i	$-0.433745\pi$
$449$	8.75751	0.413292	0.206646	+	0.978416i	$0.433745\pi$
$450$	2.30235	0.108534
$451$	37.2590	1.75446
$452$	−9.75087	−0.458643
$453$	5.83548	0.274175
$454$	−7.18481	−0.337200
$455$	−2.54493	−0.119308
$456$	−22.6421	−1.06031
$457$	−3.21350	−0.150321	−0.0751606	−	0.997171i	$-0.523947\pi$
$457$	−3.21350	−0.150321	−0.0751606	+	0.997171i	$0.523947\pi$
$458$	−2.35302	−0.109949
$459$	21.7659	1.01595
$460$	19.9886	0.931974
$461$	−26.7760	−1.24708	−0.623541	−	0.781791i	$-0.714307\pi$
$461$	−26.7760	−1.24708	−0.623541	+	0.781791i	$0.714307\pi$
$462$	−19.1288	−0.889951
$463$	40.1114	1.86414	0.932068	−	0.362285i	$-0.118003\pi$
$463$	40.1114	1.86414	0.932068	+	0.362285i	$0.118003\pi$
$464$	−9.46803	−0.439542
$465$	2.20676	0.102336
$466$	−35.1293	−1.62733
$467$	4.97707	0.230311	0.115156	−	0.993347i	$-0.463263\pi$
$467$	4.97707	0.230311	0.115156	+	0.993347i	$0.463263\pi$
$468$	8.80680	0.407095
$469$	−9.52626	−0.439882
$470$	−16.9588	−0.782253
$471$	−31.3393	−1.44404
$472$	12.7260	0.585761
$473$	−46.4549	−2.13600
$474$	53.2761	2.44705
$475$	4.40419	0.202078
$476$	13.6087	0.623754
$477$	−1.33421	−0.0610893
$478$	60.4157	2.76335
$479$	−20.2179	−0.923778	−0.461889	−	0.886938i	$-0.652828\pi$
$479$	−20.2179	−0.923778	−0.461889	+	0.886938i	$0.652828\pi$
$480$	−5.48198	−0.250217
$481$	2.83862	0.129430
$482$	−51.8944	−2.36373
$483$	8.03576	0.365640
$484$	76.7182	3.48719
$485$	−14.6538	−0.665396
$486$	−22.8439	−1.03622
$487$	−29.0197	−1.31501	−0.657503	−	0.753452i	$-0.728387\pi$
$487$	−29.0197	−1.31501	−0.657503	+	0.753452i	$0.728387\pi$
$488$	−35.7428	−1.61800
$489$	−13.8065	−0.624352
$490$	2.35302	0.106298
$491$	−33.2928	−1.50249	−0.751243	−	0.660026i	$-0.770545\pi$
$491$	−33.2928	−1.50249	−0.751243	+	0.660026i	$0.770545\pi$
$492$	−32.7677	−1.47728
$493$	25.3920	1.14360
$494$	26.3735	1.18660
$495$	−5.59458	−0.251458
$496$	−2.22689	−0.0999902
$497$	6.37994	0.286179
$498$	18.2736	0.818861
$499$	−26.2479	−1.17502	−0.587509	−	0.809218i	$-0.699891\pi$
$499$	−26.2479	−1.17502	−0.587509	+	0.809218i	$0.699891\pi$
$500$	−3.53669	−0.158165
$501$	29.8272	1.33258
$502$	5.57595	0.248867
$503$	−31.1183	−1.38750	−0.693748	−	0.720218i	$-0.744042\pi$
$503$	−31.1183	−1.38750	−0.693748	+	0.720218i	$0.744042\pi$
$504$	−3.53798	−0.157594
$505$	8.32577	0.370492
$506$	−76.0384	−3.38032
$507$	−9.27490	−0.411913
$508$	−56.2357	−2.49505
$509$	−36.1055	−1.60035	−0.800174	−	0.599768i	$-0.795259\pi$
$509$	−36.1055	−1.60035	−0.800174	+	0.599768i	$0.795259\pi$
$510$	−12.8732	−0.570034
$511$	14.6405	0.647658
$512$	15.9078	0.703033
$513$	−24.9128	−1.09993
$514$	−36.0421	−1.58975
$515$	6.89805	0.303964
$516$	40.8552	1.79855
$517$	41.2091	1.81237
$518$	−2.62456	−0.115316
$519$	31.3984	1.37824
$520$	−9.20208	−0.403538
$521$	−44.8441	−1.96466	−0.982328	−	0.187168i	$-0.940069\pi$
$521$	−44.8441	−1.96466	−0.982328	+	0.187168i	$0.940069\pi$
$522$	−15.1931	−0.664985
$523$	38.2828	1.67399	0.836994	−	0.547212i	$-0.184311\pi$
$523$	38.2828	1.67399	0.836994	+	0.547212i	$0.184311\pi$
$524$	44.6956	1.95254
$525$	−1.42181	−0.0620527
$526$	−26.0733	−1.13685
$527$	5.97222	0.260154
$528$	−11.6639	−0.507608
$529$	8.94276	0.388816
$530$	3.20851	0.139369
$531$	3.44371	0.149444
$532$	−15.5762	−0.675316
$533$	16.5838	0.718326
$534$	5.31763	0.230116
$535$	2.48737	0.107538
$536$	−34.4455	−1.48782
$537$	−9.04016	−0.390112
$538$	−17.4082	−0.750522
$539$	−5.71770	−0.246279
$540$	20.0056	0.860906
$541$	−36.4667	−1.56782	−0.783912	−	0.620872i	$-0.786779\pi$
$541$	−36.4667	−1.56782	−0.783912	+	0.620872i	$0.786779\pi$
$542$	−29.2849	−1.25789
$543$	−17.8821	−0.767394
$544$	−14.8360	−0.636089
$545$	16.3311	0.699546
$546$	−8.51416	−0.364372
$547$	1.28065	0.0547568	0.0273784	−	0.999625i	$-0.491284\pi$
$547$	1.28065	0.0547568	0.0273784	+	0.999625i	$0.491284\pi$
$548$	31.4651	1.34412
$549$	−9.67218	−0.412799
$550$	13.4538	0.573674
$551$	−29.0631	−1.23813
$552$	29.0561	1.23671
$553$	15.9245	0.677180
$554$	−30.5598	−1.29836
$555$	1.58588	0.0673170
$556$	−15.3494	−0.650958
$557$	−0.632055	−0.0267810	−0.0133905	−	0.999910i	$-0.504262\pi$
$557$	−0.632055	−0.0267810	−0.0133905	+	0.999910i	$0.504262\pi$
$558$	−3.57343	−0.151276
$559$	−20.6770	−0.874542
$560$	1.43477	0.0606302
$561$	31.2811	1.32069
$562$	−4.67566	−0.197231
$563$	−4.02607	−0.169679	−0.0848394	−	0.996395i	$-0.527038\pi$
$563$	−4.02607	−0.169679	−0.0848394	+	0.996395i	$0.527038\pi$
$564$	−36.2417	−1.52605
$565$	2.75707	0.115991
$566$	−20.8935	−0.878219
$567$	5.10721	0.214483
$568$	23.0689	0.967949
$569$	3.42426	0.143552	0.0717761	−	0.997421i	$-0.477133\pi$
$569$	3.42426	0.143552	0.0717761	+	0.997421i	$0.477133\pi$
$570$	14.7344	0.617155
$571$	13.0457	0.545944	0.272972	−	0.962022i	$-0.411993\pi$
$571$	13.0457	0.545944	0.272972	+	0.962022i	$0.411993\pi$
$572$	51.4629	2.15177
$573$	29.6858	1.24014
$574$	−15.3332	−0.639997
$575$	−5.65179	−0.235696
$576$	11.6848	0.486866
$577$	−14.7833	−0.615437	−0.307718	−	0.951478i	$-0.599565\pi$
$577$	−14.7833	−0.615437	−0.307718	+	0.951478i	$0.599565\pi$
$578$	5.16228	0.214722
$579$	−30.2667	−1.25784
$580$	23.3385	0.969078
$581$	5.46210	0.226606
$582$	−49.0248	−2.03215
$583$	−7.79651	−0.322898
$584$	52.9378	2.19058
$585$	−2.49013	−0.102954
$586$	55.8933	2.30893
$587$	−3.05499	−0.126093	−0.0630464	−	0.998011i	$-0.520082\pi$
$587$	−3.05499	−0.126093	−0.0630464	+	0.998011i	$0.520082\pi$
$588$	5.02848	0.207371
$589$	−6.83567	−0.281659
$590$	−8.28145	−0.340942
$591$	−15.8887	−0.653574
$592$	−1.60035	−0.0657739
$593$	−2.85789	−0.117359	−0.0586797	−	0.998277i	$-0.518689\pi$
$593$	−2.85789	−0.117359	−0.0586797	+	0.998277i	$0.518689\pi$
$594$	−76.1031	−3.12255
$595$	−3.84787	−0.157747
$596$	55.9558	2.29204
$597$	16.1983	0.662953
$598$	−33.8444	−1.38400
$599$	−40.1098	−1.63884	−0.819421	−	0.573192i	$-0.805705\pi$
$599$	−40.1098	−1.63884	−0.819421	+	0.573192i	$0.805705\pi$
$600$	−5.14103	−0.209882
$601$	−44.6240	−1.82025	−0.910126	−	0.414332i	$-0.864015\pi$
$601$	−44.6240	−1.82025	−0.910126	+	0.414332i	$0.864015\pi$
$602$	19.1177	0.779179
$603$	−9.32112	−0.379585
$604$	14.5155	0.590628
$605$	−21.6921	−0.881910
$606$	27.8542	1.13150
$607$	9.34012	0.379104	0.189552	−	0.981871i	$-0.439296\pi$
$607$	9.34012	0.379104	0.189552	+	0.981871i	$0.439296\pi$
$608$	16.9810	0.688671
$609$	9.38247	0.380197
$610$	23.2597	0.941757
$611$	18.3420	0.742039
$612$	13.3157	0.538253
$613$	36.9880	1.49393	0.746966	−	0.664862i	$-0.231510\pi$
$613$	36.9880	1.49393	0.746966	+	0.664862i	$0.231510\pi$
$614$	−45.9393	−1.85396
$615$	9.26509	0.373605
$616$	−20.6743	−0.832992
$617$	32.7294	1.31764	0.658818	−	0.752302i	$-0.271057\pi$
$617$	32.7294	1.31764	0.658818	+	0.752302i	$0.271057\pi$
$618$	23.0777	0.928320
$619$	−17.5271	−0.704474	−0.352237	−	0.935911i	$-0.614579\pi$
$619$	−17.5271	−0.704474	−0.352237	+	0.935911i	$0.614579\pi$
$620$	5.48923	0.220453
$621$	31.9700	1.28291
$622$	41.0674	1.64665
$623$	1.58947	0.0636809
$624$	−5.19158	−0.207830
$625$	1.00000	0.0400000
$626$	62.1002	2.48202
$627$	−35.8037	−1.42986
$628$	−77.9552	−3.11075
$629$	4.29192	0.171130
$630$	2.30235	0.0917277
$631$	−3.09103	−0.123052	−0.0615259	−	0.998105i	$-0.519597\pi$
$631$	−3.09103	−0.123052	−0.0615259	+	0.998105i	$0.519597\pi$
$632$	57.5806	2.29044
$633$	−10.8017	−0.429329
$634$	−58.1355	−2.30885
$635$	15.9007	0.630999
$636$	6.85671	0.271886
$637$	−2.54493	−0.100834
$638$	−88.7816	−3.51490
$639$	6.24256	0.246952
$640$	−20.3883	−0.805918
$641$	23.9906	0.947571	0.473786	−	0.880640i	$-0.342887\pi$
$641$	23.9906	0.947571	0.473786	+	0.880640i	$0.342887\pi$
$642$	8.32158	0.328427
$643$	−3.57180	−0.140858	−0.0704290	−	0.997517i	$-0.522437\pi$
$643$	−3.57180	−0.140858	−0.0704290	+	0.997517i	$0.522437\pi$
$644$	19.9886	0.787662
$645$	−11.5518	−0.454853
$646$	39.8760	1.56890
$647$	−19.8919	−0.782032	−0.391016	−	0.920384i	$-0.627876\pi$
$647$	−19.8919	−0.782032	−0.391016	+	0.920384i	$0.627876\pi$
$648$	18.4669	0.725447
$649$	20.1235	0.789915
$650$	5.98827	0.234879
$651$	2.20676	0.0864899
$652$	−34.3431	−1.34498
$653$	31.7591	1.24283	0.621415	−	0.783482i	$-0.286558\pi$
$653$	31.7591	1.24283	0.621415	+	0.783482i	$0.286558\pi$
$654$	54.6361	2.13644
$655$	−12.6377	−0.493797
$656$	−9.34959	−0.365040
$657$	14.3252	0.558881
$658$	−16.9588	−0.661124
$659$	14.0856	0.548699	0.274349	−	0.961630i	$-0.411537\pi$
$659$	14.0856	0.548699	0.274349	+	0.961630i	$0.411537\pi$
$660$	28.7514	1.11915
$661$	32.8115	1.27622	0.638110	−	0.769945i	$-0.279716\pi$
$661$	32.8115	1.27622	0.638110	+	0.769945i	$0.279716\pi$
$662$	−55.5846	−2.16036
$663$	13.9231	0.540730
$664$	19.7501	0.766453
$665$	4.40419	0.170787
$666$	−2.56804	−0.0995095
$667$	37.2960	1.44411
$668$	74.1939	2.87065
$669$	17.2992	0.668827
$670$	22.4154	0.865984
$671$	−56.5197	−2.18192
$672$	−5.48198	−0.211472
$673$	−12.4381	−0.479454	−0.239727	−	0.970840i	$-0.577058\pi$
$673$	−12.4381	−0.479454	−0.239727	+	0.970840i	$0.577058\pi$
$674$	−49.1014	−1.89132
$675$	−5.65661	−0.217723
$676$	−23.0709	−0.887344
$677$	19.9136	0.765342	0.382671	−	0.923885i	$-0.375004\pi$
$677$	19.9136	0.765342	0.382671	+	0.923885i	$0.375004\pi$
$678$	9.22386	0.354240
$679$	−14.6538	−0.562362
$680$	−13.9133	−0.533551
$681$	4.34141	0.166363
$682$	−20.8815	−0.799594
$683$	16.5389	0.632842	0.316421	−	0.948619i	$-0.397519\pi$
$683$	16.5389	0.632842	0.316421	+	0.948619i	$0.397519\pi$
$684$	−15.2408	−0.582747
$685$	−8.89677	−0.339928
$686$	2.35302	0.0898386
$687$	1.42181	0.0542453
$688$	11.6572	0.444426
$689$	−3.47020	−0.132204
$690$	−18.9083	−0.719825
$691$	−49.4078	−1.87956	−0.939781	−	0.341778i	$-0.888971\pi$
$691$	−49.4078	−1.87956	−0.939781	+	0.341778i	$0.888971\pi$
$692$	78.1023	2.96901
$693$	−5.59458	−0.212520
$694$	20.8286	0.790642
$695$	4.34004	0.164627
$696$	33.9256	1.28594
$697$	25.0743	0.949759
$698$	−6.72285	−0.254464
$699$	21.2268	0.802872
$700$	−3.53669	−0.133674
$701$	0.119440	0.00451118	0.00225559	−	0.999997i	$-0.499282\pi$
$701$	0.119440	0.00451118	0.00225559	+	0.999997i	$0.499282\pi$
$702$	−33.8733	−1.27846
$703$	−4.91244	−0.185276
$704$	68.2805	2.57342
$705$	10.2474	0.385938
$706$	39.4022	1.48292
$707$	8.32577	0.313123
$708$	−17.6978	−0.665123
$709$	23.9976	0.901247	0.450623	−	0.892714i	$-0.351202\pi$
$709$	23.9976	0.901247	0.450623	+	0.892714i	$0.351202\pi$
$710$	−15.0121	−0.563394
$711$	15.5816	0.584356
$712$	5.74729	0.215389
$713$	8.77206	0.328516
$714$	−12.8732	−0.481767
$715$	−14.5512	−0.544183
$716$	−22.4870	−0.840380
$717$	−36.5061	−1.36335
$718$	−21.0357	−0.785045
$719$	−27.6193	−1.03003	−0.515013	−	0.857182i	$-0.672213\pi$
$719$	−27.6193	−1.03003	−0.515013	+	0.857182i	$0.672213\pi$
$720$	1.40388	0.0523194
$721$	6.89805	0.256897
$722$	−0.933900	−0.0347562
$723$	31.3571	1.16618
$724$	−44.4810	−1.65312
$725$	−6.59897	−0.245080
$726$	−72.5717	−2.69339
$727$	−30.2129	−1.12053	−0.560266	−	0.828312i	$-0.689301\pi$
$727$	−30.2129	−1.12053	−0.560266	+	0.828312i	$0.689301\pi$
$728$	−9.20208	−0.341052
$729$	29.1250	1.07871
$730$	−34.4493	−1.27503
$731$	−31.2630	−1.15630
$732$	49.7068	1.83722
$733$	−7.84486	−0.289756	−0.144878	−	0.989449i	$-0.546279\pi$
$733$	−7.84486	−0.289756	−0.144878	+	0.989449i	$0.546279\pi$
$734$	31.2661	1.15405
$735$	−1.42181	−0.0524441
$736$	−21.7913	−0.803239
$737$	−54.4683	−2.00637
$738$	−15.0031	−0.552270
$739$	−25.5113	−0.938450	−0.469225	−	0.883079i	$-0.655467\pi$
$739$	−25.5113	−0.938450	−0.469225	+	0.883079i	$0.655467\pi$
$740$	3.94482	0.145014
$741$	−15.9361	−0.585428
$742$	3.20851	0.117788
$743$	32.8188	1.20401	0.602003	−	0.798494i	$-0.294369\pi$
$743$	32.8188	1.20401	0.602003	+	0.798494i	$0.294369\pi$
$744$	7.97931	0.292536
$745$	−15.8215	−0.579656
$746$	−28.3236	−1.03700
$747$	5.34448	0.195544
$748$	77.8105	2.84503
$749$	2.48737	0.0908865
$750$	3.34553	0.122162
$751$	−34.5115	−1.25934	−0.629671	−	0.776862i	$-0.716810\pi$
$751$	−34.5115	−1.25934	−0.629671	+	0.776862i	$0.716810\pi$
$752$	−10.3408	−0.377091
$753$	−3.36926	−0.122783
$754$	−39.5164	−1.43910
$755$	−4.10427	−0.149370
$756$	20.0056	0.727598
$757$	35.3452	1.28464	0.642321	−	0.766435i	$-0.277971\pi$
$757$	35.3452	1.28464	0.642321	+	0.766435i	$0.277971\pi$
$758$	−83.1635	−3.02063
$759$	45.9461	1.66774
$760$	15.9249	0.577656
$761$	16.9825	0.615613	0.307807	−	0.951449i	$-0.400405\pi$
$761$	16.9825	0.615613	0.307807	+	0.951449i	$0.400405\pi$
$762$	53.1962	1.92710
$763$	16.3311	0.591224
$764$	73.8423	2.67152
$765$	−3.76501	−0.136124
$766$	41.5502	1.50127
$767$	8.95689	0.323415
$768$	−34.2515	−1.23594
$769$	−22.0900	−0.796585	−0.398292	−	0.917258i	$-0.630397\pi$
$769$	−22.0900	−0.796585	−0.398292	+	0.917258i	$0.630397\pi$
$770$	13.4538	0.484843
$771$	21.7784	0.784330
$772$	−75.2873	−2.70965
$773$	5.33896	0.192029	0.0960146	−	0.995380i	$-0.469390\pi$
$773$	5.33896	0.192029	0.0960146	+	0.995380i	$0.469390\pi$
$774$	18.7060	0.672373
$775$	−1.55208	−0.0557525
$776$	−52.9859	−1.90208
$777$	1.58588	0.0568933
$778$	11.9151	0.427178
$779$	−28.6996	−1.02827
$780$	12.7971	0.458211
$781$	36.4786	1.30531
$782$	−51.1719	−1.82990
$783$	37.3278	1.33399
$784$	1.43477	0.0512419
$785$	22.0419	0.786708
$786$	−42.2799	−1.50808
$787$	13.3199	0.474804	0.237402	−	0.971411i	$-0.423704\pi$
$787$	13.3199	0.474804	0.237402	+	0.971411i	$0.423704\pi$
$788$	−39.5225	−1.40793
$789$	15.7548	0.560885
$790$	−37.4707	−1.33315
$791$	2.75707	0.0980300
$792$	−20.2291	−0.718811
$793$	−25.1568	−0.893343
$794$	−41.0235	−1.45587
$795$	−1.93874	−0.0687599
$796$	40.2926	1.42813
$797$	−16.0532	−0.568635	−0.284318	−	0.958730i	$-0.591767\pi$
$797$	−16.0532	−0.568635	−0.284318	+	0.958730i	$0.591767\pi$
$798$	14.7344	0.521591
$799$	27.7327	0.981111
$800$	3.85565	0.136318
$801$	1.55524	0.0549519
$802$	43.7361	1.54438
$803$	83.7100	2.95406
$804$	47.9026	1.68940
$805$	−5.65179	−0.199200
$806$	−9.29429	−0.327377
$807$	10.5189	0.370282
$808$	30.1047	1.05908
$809$	−11.1320	−0.391380	−0.195690	−	0.980666i	$-0.562695\pi$
$809$	−11.1320	−0.391380	−0.195690	+	0.980666i	$0.562695\pi$
$810$	−12.0173	−0.422246
$811$	45.0957	1.58352	0.791761	−	0.610831i	$-0.209164\pi$
$811$	45.0957	1.58352	0.791761	+	0.610831i	$0.209164\pi$
$812$	23.3385	0.819021
$813$	17.6953	0.620603
$814$	−15.0064	−0.525975
$815$	9.71053	0.340145
$816$	−7.84954	−0.274789
$817$	35.7830	1.25189
$818$	49.4652	1.72951
$819$	−2.49013	−0.0870121
$820$	23.0465	0.804820
$821$	−24.7895	−0.865158	−0.432579	−	0.901596i	$-0.642396\pi$
$821$	−24.7895	−0.865158	−0.432579	+	0.901596i	$0.642396\pi$
$822$	−29.7644	−1.03815
$823$	37.6751	1.31327	0.656636	−	0.754207i	$-0.271979\pi$
$823$	37.6751	1.31327	0.656636	+	0.754207i	$0.271979\pi$
$824$	24.9423	0.868906
$825$	−8.12947	−0.283032
$826$	−8.28145	−0.288148
$827$	47.5809	1.65455	0.827275	−	0.561798i	$-0.189890\pi$
$827$	47.5809	1.65455	0.827275	+	0.561798i	$0.189890\pi$
$828$	19.5582	0.679694
$829$	−54.5024	−1.89295	−0.946473	−	0.322784i	$-0.895381\pi$
$829$	−54.5024	−1.89295	−0.946473	+	0.322784i	$0.895381\pi$
$830$	−12.8524	−0.446114
$831$	18.4657	0.640569
$832$	30.3914	1.05363
$833$	−3.84787	−0.133321
$834$	14.5198	0.502778
$835$	−20.9784	−0.725986
$836$	−89.0603	−3.08021
$837$	8.77953	0.303465
$838$	11.1650	0.385690
$839$	45.9443	1.58617	0.793086	−	0.609110i	$-0.208473\pi$
$839$	45.9443	1.58617	0.793086	+	0.609110i	$0.208473\pi$
$840$	−5.14103	−0.177383
$841$	14.5465	0.501602
$842$	5.65082	0.194740
$843$	2.82526	0.0973072
$844$	−26.8688	−0.924863
$845$	6.52332	0.224409
$846$	−16.5936	−0.570501
$847$	−21.6921	−0.745350
$848$	1.95642	0.0671837
$849$	12.6249	0.433284
$850$	9.05410	0.310553
$851$	6.30401	0.216099
$852$	−32.0814	−1.09909
$853$	18.1091	0.620044	0.310022	−	0.950729i	$-0.399664\pi$
$853$	18.1091	0.620044	0.310022	+	0.950729i	$0.399664\pi$
$854$	23.2597	0.795930
$855$	4.30935	0.147377
$856$	8.99394	0.307407
$857$	34.1013	1.16488	0.582440	−	0.812874i	$-0.302098\pi$
$857$	34.1013	1.16488	0.582440	+	0.812874i	$0.302098\pi$
$858$	−48.6814	−1.66196
$859$	21.6599	0.739027	0.369513	−	0.929225i	$-0.379524\pi$
$859$	21.6599	0.739027	0.369513	+	0.929225i	$0.379524\pi$
$860$	−28.7347	−0.979846
$861$	9.26509	0.315754
$862$	29.8614	1.01708
$863$	6.72174	0.228811	0.114405	−	0.993434i	$-0.463504\pi$
$863$	6.72174	0.228811	0.114405	+	0.993434i	$0.463504\pi$
$864$	−21.8099	−0.741987
$865$	−22.0835	−0.750861
$866$	−81.8198	−2.78035
$867$	−3.11930	−0.105937
$868$	5.48923	0.186317
$869$	91.0517	3.08872
$870$	−22.0771	−0.748484
$871$	−24.2437	−0.821466
$872$	59.0506	1.99971
$873$	−14.3383	−0.485277
$874$	58.5703	1.98117
$875$	1.00000	0.0338062
$876$	−73.6195	−2.48737
$877$	13.2343	0.446892	0.223446	−	0.974716i	$-0.428269\pi$
$877$	13.2343	0.446892	0.223446	+	0.974716i	$0.428269\pi$
$878$	50.7159	1.71158
$879$	−33.7734	−1.13915
$880$	8.20361	0.276544
$881$	−7.01602	−0.236376	−0.118188	−	0.992991i	$-0.537708\pi$
$881$	−7.01602	−0.236376	−0.118188	+	0.992991i	$0.537708\pi$
$882$	2.30235	0.0775240
$883$	−0.518990	−0.0174654	−0.00873269	−	0.999962i	$-0.502780\pi$
$883$	−0.518990	−0.0174654	−0.00873269	+	0.999962i	$0.502780\pi$
$884$	34.6332	1.16484
$885$	5.00405	0.168209
$886$	−93.3770	−3.13706
$887$	−34.7981	−1.16841	−0.584203	−	0.811608i	$-0.698593\pi$
$887$	−34.7981	−1.16841	−0.584203	+	0.811608i	$0.698593\pi$
$888$	5.73431	0.192431
$889$	15.9007	0.533291
$890$	−3.74005	−0.125367
$891$	29.2015	0.978287
$892$	43.0311	1.44079
$893$	−31.7422	−1.06221
$894$	−52.9315	−1.77029
$895$	6.35822	0.212532
$896$	−20.3883	−0.681125
$897$	20.4505	0.682821
$898$	−20.6066	−0.687650
$899$	10.2422	0.341595
$900$	−3.46053	−0.115351
$901$	−5.24685	−0.174798
$902$	−87.6709	−2.91912
$903$	−11.5518	−0.384421
$904$	9.96912	0.331568
$905$	12.5770	0.418075
$906$	−13.7310	−0.456181
$907$	−59.1313	−1.96342	−0.981712	−	0.190373i	$-0.939030\pi$
$907$	−59.1313	−1.96342	−0.981712	+	0.190373i	$0.939030\pi$
$908$	10.7991	0.358380
$909$	8.14649	0.270202
$910$	5.98827	0.198509
$911$	14.3450	0.475272	0.237636	−	0.971354i	$-0.423627\pi$
$911$	14.3450	0.475272	0.237636	+	0.971354i	$0.423627\pi$
$912$	8.98442	0.297504
$913$	31.2306	1.03358
$914$	7.56142	0.250109
$915$	−14.0546	−0.464631
$916$	3.53669	0.116855
$917$	−12.6377	−0.417334
$918$	−51.2155	−1.69036
$919$	23.2289	0.766250	0.383125	−	0.923697i	$-0.374848\pi$
$919$	23.2289	0.766250	0.383125	+	0.923697i	$0.374848\pi$
$920$	−20.4360	−0.673755
$921$	27.7588	0.914683
$922$	63.0043	2.07494
$923$	16.2365	0.534431
$924$	28.7514	0.945851
$925$	−1.11540	−0.0366741
$926$	−94.3828	−3.10161
$927$	6.74951	0.221683
$928$	−25.4433	−0.835218
$929$	20.0055	0.656358	0.328179	−	0.944615i	$-0.393565\pi$
$929$	20.0055	0.656358	0.328179	+	0.944615i	$0.393565\pi$
$930$	−5.19255	−0.170270
$931$	4.40419	0.144342
$932$	52.8009	1.72955
$933$	−24.8149	−0.812404
$934$	−11.7111	−0.383200
$935$	−22.0010	−0.719509
$936$	−9.00392	−0.294302
$937$	−23.2834	−0.760634	−0.380317	−	0.924856i	$-0.624185\pi$
$937$	−23.2834	−0.760634	−0.380317	+	0.924856i	$0.624185\pi$
$938$	22.4154	0.731890
$939$	−37.5240	−1.22455
$940$	25.4899	0.831388
$941$	−28.6143	−0.932798	−0.466399	−	0.884574i	$-0.654449\pi$
$941$	−28.6143	−0.932798	−0.466399	+	0.884574i	$0.654449\pi$
$942$	73.7419	2.40264
$943$	36.8295	1.19933
$944$	−5.04969	−0.164353
$945$	−5.65661	−0.184010
$946$	109.309	3.55395
$947$	−4.43218	−0.144027	−0.0720133	−	0.997404i	$-0.522942\pi$
$947$	−4.43218	−0.144027	−0.0720133	+	0.997404i	$0.522942\pi$
$948$	−80.0762	−2.60075
$949$	37.2591	1.20948
$950$	−10.3631	−0.336224
$951$	35.1283	1.13911
$952$	−13.9133	−0.450933
$953$	−8.07985	−0.261732	−0.130866	−	0.991400i	$-0.541776\pi$
$953$	−8.07985	−0.261732	−0.130866	+	0.991400i	$0.541776\pi$
$954$	3.13942	0.101642
$955$	−20.8789	−0.675627
$956$	−90.8074	−2.93692
$957$	53.6461	1.73413
$958$	47.5730	1.53701
$959$	−8.89677	−0.287292
$960$	16.9791	0.547999
$961$	−28.5910	−0.922291
$962$	−6.67931	−0.215350
$963$	2.43381	0.0784283
$964$	77.9995	2.51220
$965$	21.2875	0.685270
$966$	−18.9083	−0.608363
$967$	−53.3012	−1.71405	−0.857025	−	0.515274i	$-0.827690\pi$
$967$	−53.3012	−1.71405	−0.857025	+	0.515274i	$0.827690\pi$
$968$	−78.4354	−2.52101
$969$	−24.0950	−0.774043
$970$	34.4807	1.10711
$971$	15.3663	0.493127	0.246564	−	0.969127i	$-0.420699\pi$
$971$	15.3663	0.493127	0.246564	+	0.969127i	$0.420699\pi$
$972$	34.3354	1.10131
$973$	4.34004	0.139135
$974$	68.2837	2.18795
$975$	−3.61840	−0.115882
$976$	14.1828	0.453980
$977$	−8.81407	−0.281987	−0.140993	−	0.990011i	$-0.545030\pi$
$977$	−8.81407	−0.281987	−0.140993	+	0.990011i	$0.545030\pi$
$978$	32.4869	1.03882
$979$	9.08813	0.290458
$980$	−3.53669	−0.112975
$981$	15.9794	0.510183
$982$	78.3386	2.49989
$983$	46.0365	1.46834	0.734168	−	0.678968i	$-0.237572\pi$
$983$	46.0365	1.46834	0.734168	+	0.678968i	$0.237572\pi$
$984$	33.5011	1.06798
$985$	11.1750	0.356065
$986$	−59.7478	−1.90276
$987$	10.2474	0.326177
$988$	−39.6405	−1.26113
$989$	−45.9194	−1.46015
$990$	13.1641	0.418384
$991$	−15.8978	−0.505011	−0.252506	−	0.967595i	$-0.581255\pi$
$991$	−15.8978	−0.505011	−0.252506	+	0.967595i	$0.581255\pi$
$992$	−5.98429	−0.190001
$993$	33.5869	1.06585
$994$	−15.0121	−0.476155
$995$	−11.3928	−0.361175
$996$	−27.4661	−0.870296
$997$	−31.4617	−0.996403	−0.498202	−	0.867061i	$-0.666006\pi$
$997$	−31.4617	−0.996403	−0.498202	+	0.867061i	$0.666006\pi$
$998$	61.7618	1.95503
$999$	6.30938	0.199620

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.6	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.6	✓	62	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)

\(f(q)\)	\(=\)	\(q-2.35302 q^{2} +1.42181 q^{3} +3.53669 q^{4} -1.00000 q^{5} -3.34553 q^{6} -1.00000 q^{7} -3.61585 q^{8} -0.978466 q^{9} +O(q^{10})\)	\(q-2.35302 q^{2} +1.42181 q^{3} +3.53669 q^{4} -1.00000 q^{5} -3.34553 q^{6} -1.00000 q^{7} -3.61585 q^{8} -0.978466 q^{9} +2.35302 q^{10} -5.71770 q^{11} +5.02848 q^{12} -2.54493 q^{13} +2.35302 q^{14} -1.42181 q^{15} +1.43477 q^{16} -3.84787 q^{17} +2.30235 q^{18} +4.40419 q^{19} -3.53669 q^{20} -1.42181 q^{21} +13.4538 q^{22} -5.65179 q^{23} -5.14103 q^{24} +1.00000 q^{25} +5.98827 q^{26} -5.65661 q^{27} -3.53669 q^{28} -6.59897 q^{29} +3.34553 q^{30} -1.55208 q^{31} +3.85565 q^{32} -8.12947 q^{33} +9.05410 q^{34} +1.00000 q^{35} -3.46053 q^{36} -1.11540 q^{37} -10.3631 q^{38} -3.61840 q^{39} +3.61585 q^{40} -6.51642 q^{41} +3.34553 q^{42} +8.12476 q^{43} -20.2217 q^{44} +0.978466 q^{45} +13.2988 q^{46} -7.20728 q^{47} +2.03997 q^{48} +1.00000 q^{49} -2.35302 q^{50} -5.47093 q^{51} -9.00062 q^{52} +1.36357 q^{53} +13.3101 q^{54} +5.71770 q^{55} +3.61585 q^{56} +6.26191 q^{57} +15.5275 q^{58} -3.51950 q^{59} -5.02848 q^{60} +9.88504 q^{61} +3.65208 q^{62} +0.978466 q^{63} -11.9419 q^{64} +2.54493 q^{65} +19.1288 q^{66} +9.52626 q^{67} -13.6087 q^{68} -8.03576 q^{69} -2.35302 q^{70} -6.37994 q^{71} +3.53798 q^{72} -14.6405 q^{73} +2.62456 q^{74} +1.42181 q^{75} +15.5762 q^{76} +5.71770 q^{77} +8.51416 q^{78} -15.9245 q^{79} -1.43477 q^{80} -5.10721 q^{81} +15.3332 q^{82} -5.46210 q^{83} -5.02848 q^{84} +3.84787 q^{85} -19.1177 q^{86} -9.38247 q^{87} +20.6743 q^{88} -1.58947 q^{89} -2.30235 q^{90} +2.54493 q^{91} -19.9886 q^{92} -2.20676 q^{93} +16.9588 q^{94} -4.40419 q^{95} +5.48198 q^{96} +14.6538 q^{97} -2.35302 q^{98} +5.59458 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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