LMFDB - Embedded newform 6019.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$123$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.19076 q^{2} +0.906147 q^{3} +2.79943 q^{4} -2.56920 q^{5} -1.98515 q^{6} -1.27799 q^{7} -1.75137 q^{8} -2.17890 q^{9} +O(q^{10})$	\(q-2.19076 q^{2} +0.906147 q^{3} +2.79943 q^{4} -2.56920 q^{5} -1.98515 q^{6} -1.27799 q^{7} -1.75137 q^{8} -2.17890 q^{9} +5.62849 q^{10} +1.29078 q^{11} +2.53670 q^{12} -1.00000 q^{13} +2.79978 q^{14} -2.32807 q^{15} -1.76204 q^{16} -4.22562 q^{17} +4.77344 q^{18} -6.17739 q^{19} -7.19229 q^{20} -1.15805 q^{21} -2.82779 q^{22} -3.55255 q^{23} -1.58700 q^{24} +1.60077 q^{25} +2.19076 q^{26} -4.69284 q^{27} -3.57766 q^{28} -7.68488 q^{29} +5.10025 q^{30} -3.41864 q^{31} +7.36294 q^{32} +1.16964 q^{33} +9.25732 q^{34} +3.28342 q^{35} -6.09968 q^{36} -9.07308 q^{37} +13.5332 q^{38} -0.906147 q^{39} +4.49960 q^{40} -0.101680 q^{41} +2.53701 q^{42} +2.85585 q^{43} +3.61345 q^{44} +5.59801 q^{45} +7.78278 q^{46} -12.1142 q^{47} -1.59667 q^{48} -5.36673 q^{49} -3.50691 q^{50} -3.82903 q^{51} -2.79943 q^{52} +3.48865 q^{53} +10.2809 q^{54} -3.31627 q^{55} +2.23823 q^{56} -5.59763 q^{57} +16.8357 q^{58} +10.3398 q^{59} -6.51728 q^{60} -2.98520 q^{61} +7.48942 q^{62} +2.78462 q^{63} -12.6064 q^{64} +2.56920 q^{65} -2.56240 q^{66} +2.60125 q^{67} -11.8293 q^{68} -3.21913 q^{69} -7.19318 q^{70} +12.2545 q^{71} +3.81605 q^{72} +4.30531 q^{73} +19.8770 q^{74} +1.45053 q^{75} -17.2932 q^{76} -1.64961 q^{77} +1.98515 q^{78} +9.30067 q^{79} +4.52703 q^{80} +2.28428 q^{81} +0.222756 q^{82} +1.50417 q^{83} -3.24188 q^{84} +10.8564 q^{85} -6.25647 q^{86} -6.96363 q^{87} -2.26063 q^{88} -10.0890 q^{89} -12.2639 q^{90} +1.27799 q^{91} -9.94511 q^{92} -3.09779 q^{93} +26.5394 q^{94} +15.8709 q^{95} +6.67191 q^{96} -6.42623 q^{97} +11.7572 q^{98} -2.81248 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) $ 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * 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 $

$2$	−2.19076	−1.54910	−0.774551	−	0.632512i	$-0.782024\pi$
$2$	−2.19076	−1.54910	−0.774551	+	0.632512i	$0.782024\pi$
$3$	0.906147	0.523164	0.261582	−	0.965181i	$-0.415756\pi$
$3$	0.906147	0.523164	0.261582	+	0.965181i	$0.415756\pi$
$4$	2.79943	1.39972
$5$	−2.56920	−1.14898	−0.574490	−	0.818512i	$-0.694800\pi$
$5$	−2.56920	−1.14898	−0.574490	+	0.818512i	$0.694800\pi$
$6$	−1.98515	−0.810435
$7$	−1.27799	−0.483036	−0.241518	−	0.970396i	$-0.577645\pi$
$7$	−1.27799	−0.483036	−0.241518	+	0.970396i	$0.577645\pi$
$8$	−1.75137	−0.619201
$9$	−2.17890	−0.726299
$10$	5.62849	1.77989
$11$	1.29078	0.389185	0.194593	−	0.980884i	$-0.437662\pi$
$11$	1.29078	0.389185	0.194593	+	0.980884i	$0.437662\pi$
$12$	2.53670	0.732282
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.79978	0.748272
$15$	−2.32807	−0.601105
$16$	−1.76204	−0.440510
$17$	−4.22562	−1.02486	−0.512432	−	0.858728i	$-0.671255\pi$
$17$	−4.22562	−1.02486	−0.512432	+	0.858728i	$0.671255\pi$
$18$	4.77344	1.12511
$19$	−6.17739	−1.41719	−0.708596	−	0.705615i	$-0.750671\pi$
$19$	−6.17739	−1.41719	−0.708596	+	0.705615i	$0.750671\pi$
$20$	−7.19229	−1.60825
$21$	−1.15805	−0.252707
$22$	−2.82779	−0.602887
$23$	−3.55255	−0.740757	−0.370379	−	0.928881i	$-0.620772\pi$
$23$	−3.55255	−0.740757	−0.370379	+	0.928881i	$0.620772\pi$
$24$	−1.58700	−0.323944
$25$	1.60077	0.320154
$26$	2.19076	0.429644
$27$	−4.69284	−0.903138
$28$	−3.57766	−0.676114
$29$	−7.68488	−1.42705	−0.713523	−	0.700632i	$-0.752902\pi$
$29$	−7.68488	−1.42705	−0.713523	+	0.700632i	$0.752902\pi$
$30$	5.10025	0.931173
$31$	−3.41864	−0.614006	−0.307003	−	0.951709i	$-0.599326\pi$
$31$	−3.41864	−0.614006	−0.307003	+	0.951709i	$0.599326\pi$
$32$	7.36294	1.30160
$33$	1.16964	0.203608
$34$	9.25732	1.58762
$35$	3.28342	0.554999
$36$	−6.09968	−1.01661
$37$	−9.07308	−1.49161	−0.745803	−	0.666167i	$-0.767934\pi$
$37$	−9.07308	−1.49161	−0.745803	+	0.666167i	$0.767934\pi$
$38$	13.5332	2.19537
$39$	−0.906147	−0.145100
$40$	4.49960	0.711450
$41$	−0.101680	−0.0158797	−0.00793985	−	0.999968i	$-0.502527\pi$
$41$	−0.101680	−0.0158797	−0.00793985	+	0.999968i	$0.502527\pi$
$42$	2.53701	0.391469
$43$	2.85585	0.435512	0.217756	−	0.976003i	$-0.430126\pi$
$43$	2.85585	0.435512	0.217756	+	0.976003i	$0.430126\pi$
$44$	3.61345	0.544749
$45$	5.59801	0.834503
$46$	7.78278	1.14751
$47$	−12.1142	−1.76704	−0.883521	−	0.468392i	$-0.844833\pi$
$47$	−12.1142	−1.76704	−0.883521	+	0.468392i	$0.844833\pi$
$48$	−1.59667	−0.230459
$49$	−5.36673	−0.766676
$50$	−3.50691	−0.495951
$51$	−3.82903	−0.536172
$52$	−2.79943	−0.388211
$53$	3.48865	0.479203	0.239601	−	0.970871i	$-0.422983\pi$
$53$	3.48865	0.479203	0.239601	+	0.970871i	$0.422983\pi$
$54$	10.2809	1.39905
$55$	−3.31627	−0.447166
$56$	2.23823	0.299097
$57$	−5.59763	−0.741424
$58$	16.8357	2.21064
$59$	10.3398	1.34612	0.673061	−	0.739587i	$-0.264979\pi$
$59$	10.3398	1.34612	0.673061	+	0.739587i	$0.264979\pi$
$60$	−6.51728	−0.841377
$61$	−2.98520	−0.382216	−0.191108	−	0.981569i	$-0.561208\pi$
$61$	−2.98520	−0.382216	−0.191108	+	0.981569i	$0.561208\pi$
$62$	7.48942	0.951157
$63$	2.78462	0.350829
$64$	−12.6064	−1.57580
$65$	2.56920	0.318670
$66$	−2.56240	−0.315409
$67$	2.60125	0.317793	0.158897	−	0.987295i	$-0.449206\pi$
$67$	2.60125	0.317793	0.158897	+	0.987295i	$0.449206\pi$
$68$	−11.8293	−1.43452
$69$	−3.21913	−0.387538
$70$	−7.19318	−0.859749
$71$	12.2545	1.45434	0.727168	−	0.686460i	$-0.240836\pi$
$71$	12.2545	1.45434	0.727168	+	0.686460i	$0.240836\pi$
$72$	3.81605	0.449725
$73$	4.30531	0.503898	0.251949	−	0.967741i	$-0.418928\pi$
$73$	4.30531	0.503898	0.251949	+	0.967741i	$0.418928\pi$
$74$	19.8770	2.31065
$75$	1.45053	0.167493
$76$	−17.2932	−1.98367
$77$	−1.64961	−0.187990
$78$	1.98515	0.224774
$79$	9.30067	1.04641	0.523203	−	0.852208i	$-0.324737\pi$
$79$	9.30067	1.04641	0.523203	+	0.852208i	$0.324737\pi$
$80$	4.52703	0.506137
$81$	2.28428	0.253809
$82$	0.222756	0.0245993
$83$	1.50417	0.165104	0.0825521	−	0.996587i	$-0.473693\pi$
$83$	1.50417	0.165104	0.0825521	+	0.996587i	$0.473693\pi$
$84$	−3.24188	−0.353719
$85$	10.8564	1.17755
$86$	−6.25647	−0.674653
$87$	−6.96363	−0.746580
$88$	−2.26063	−0.240984
$89$	−10.0890	−1.06944	−0.534719	−	0.845030i	$-0.679582\pi$
$89$	−10.0890	−1.06944	−0.534719	+	0.845030i	$0.679582\pi$
$90$	−12.2639	−1.29273
$91$	1.27799	0.133970
$92$	−9.94511	−1.03685
$93$	−3.09779	−0.321226
$94$	26.5394	2.73733
$95$	15.8709	1.62832
$96$	6.67191	0.680949
$97$	−6.42623	−0.652485	−0.326243	−	0.945286i	$-0.605783\pi$
$97$	−6.42623	−0.652485	−0.326243	+	0.945286i	$0.605783\pi$
$98$	11.7572	1.18766
$99$	−2.81248	−0.282665
$100$	4.48125	0.448125
$101$	−11.1212	−1.10660	−0.553302	−	0.832981i	$-0.686632\pi$
$101$	−11.1212	−1.10660	−0.553302	+	0.832981i	$0.686632\pi$
$102$	8.38850	0.830585
$103$	−7.15985	−0.705481	−0.352740	−	0.935721i	$-0.614750\pi$
$103$	−7.15985	−0.705481	−0.352740	+	0.935721i	$0.614750\pi$
$104$	1.75137	0.171736
$105$	2.97526	0.290356
$106$	−7.64279	−0.742334
$107$	−15.4697	−1.49551	−0.747756	−	0.663974i	$-0.768869\pi$
$107$	−15.4697	−1.49551	−0.747756	+	0.663974i	$0.768869\pi$
$108$	−13.1373	−1.26414
$109$	1.04938	0.100512	0.0502560	−	0.998736i	$-0.483996\pi$
$109$	1.04938	0.100512	0.0502560	+	0.998736i	$0.483996\pi$
$110$	7.26515	0.692705
$111$	−8.22155	−0.780355
$112$	2.25188	0.212782
$113$	−7.13940	−0.671618	−0.335809	−	0.941930i	$-0.609010\pi$
$113$	−7.13940	−0.671618	−0.335809	+	0.941930i	$0.609010\pi$
$114$	12.2631	1.14854
$115$	9.12719	0.851115
$116$	−21.5133	−1.99746
$117$	2.17890	0.201439
$118$	−22.6519	−2.08528
$119$	5.40031	0.495046
$120$	4.07730	0.372205
$121$	−9.33388	−0.848535
$122$	6.53986	0.592091
$123$	−0.0921368	−0.00830770
$124$	−9.57025	−0.859434
$125$	8.73329	0.781129
$126$	−6.10043	−0.543469
$127$	9.51610	0.844418	0.422209	−	0.906499i	$-0.361255\pi$
$127$	9.51610	0.844418	0.422209	+	0.906499i	$0.361255\pi$
$128$	12.8916	1.13947
$129$	2.58782	0.227845
$130$	−5.62849	−0.493652
$131$	−17.2766	−1.50947	−0.754733	−	0.656032i	$-0.772234\pi$
$131$	−17.2766	−1.50947	−0.754733	+	0.656032i	$0.772234\pi$
$132$	3.27432	0.284993
$133$	7.89467	0.684555
$134$	−5.69872	−0.492294
$135$	12.0568	1.03769
$136$	7.40061	0.634597
$137$	−1.25356	−0.107099	−0.0535496	−	0.998565i	$-0.517054\pi$
$137$	−1.25356	−0.107099	−0.0535496	+	0.998565i	$0.517054\pi$
$138$	7.05234	0.600335
$139$	−16.7149	−1.41774	−0.708869	−	0.705340i	$-0.750794\pi$
$139$	−16.7149	−1.41774	−0.708869	+	0.705340i	$0.750794\pi$
$140$	9.19170	0.776841
$141$	−10.9773	−0.924453
$142$	−26.8466	−2.25291
$143$	−1.29078	−0.107941
$144$	3.83931	0.319942
$145$	19.7440	1.63965
$146$	−9.43190	−0.780589
$147$	−4.86305	−0.401098
$148$	−25.3995	−2.08783
$149$	11.5828	0.948899	0.474450	−	0.880283i	$-0.342647\pi$
$149$	11.5828	0.948899	0.474450	+	0.880283i	$0.342647\pi$
$150$	−3.17777	−0.259464
$151$	−11.7529	−0.956439	−0.478220	−	0.878240i	$-0.658718\pi$
$151$	−11.7529	−0.956439	−0.478220	+	0.878240i	$0.658718\pi$
$152$	10.8189	0.877527
$153$	9.20719	0.744357
$154$	3.61390	0.291216
$155$	8.78316	0.705480
$156$	−2.53670	−0.203098
$157$	−11.7519	−0.937907	−0.468954	−	0.883223i	$-0.655369\pi$
$157$	−11.7519	−0.937907	−0.468954	+	0.883223i	$0.655369\pi$
$158$	−20.3755	−1.62099
$159$	3.16123	0.250702
$160$	−18.9168	−1.49551
$161$	4.54013	0.357812
$162$	−5.00432	−0.393176
$163$	−12.3337	−0.966051	−0.483025	−	0.875606i	$-0.660462\pi$
$163$	−12.3337	−0.966051	−0.483025	+	0.875606i	$0.660462\pi$
$164$	−0.284646	−0.0222271
$165$	−3.00503	−0.233941
$166$	−3.29528	−0.255763
$167$	16.2031	1.25384	0.626919	−	0.779085i	$-0.284316\pi$
$167$	16.2031	1.25384	0.626919	+	0.779085i	$0.284316\pi$
$168$	2.02817	0.156477
$169$	1.00000	0.0769231
$170$	−23.7839	−1.82414
$171$	13.4599	1.02930
$172$	7.99475	0.609594
$173$	−3.17007	−0.241016	−0.120508	−	0.992712i	$-0.538452\pi$
$173$	−3.17007	−0.241016	−0.120508	+	0.992712i	$0.538452\pi$
$174$	15.2557	1.15653
$175$	−2.04577	−0.154646
$176$	−2.27441	−0.171440
$177$	9.36934	0.704243
$178$	22.1027	1.65667
$179$	13.0697	0.976873	0.488436	−	0.872599i	$-0.337567\pi$
$179$	13.0697	0.976873	0.488436	+	0.872599i	$0.337567\pi$
$180$	15.6713	1.16807
$181$	−15.6007	−1.15959	−0.579794	−	0.814763i	$-0.696867\pi$
$181$	−15.6007	−1.15959	−0.579794	+	0.814763i	$0.696867\pi$
$182$	−2.79978	−0.207533
$183$	−2.70503	−0.199962
$184$	6.22181	0.458678
$185$	23.3105	1.71382
$186$	6.78652	0.497612
$187$	−5.45435	−0.398862
$188$	−33.9130	−2.47336
$189$	5.99742	0.436248
$190$	−34.7694	−2.52244
$191$	14.6219	1.05801	0.529003	−	0.848620i	$-0.322566\pi$
$191$	14.6219	1.05801	0.529003	+	0.848620i	$0.322566\pi$
$192$	−11.4232	−0.824400
$193$	−18.7458	−1.34935	−0.674677	−	0.738113i	$-0.735717\pi$
$193$	−18.7458	−1.34935	−0.674677	+	0.738113i	$0.735717\pi$
$194$	14.0783	1.01077
$195$	2.32807	0.166717
$196$	−15.0238	−1.07313
$197$	17.8803	1.27392	0.636961	−	0.770896i	$-0.280191\pi$
$197$	17.8803	1.27392	0.636961	+	0.770896i	$0.280191\pi$
$198$	6.16147	0.437876
$199$	−17.9110	−1.26968	−0.634838	−	0.772645i	$-0.718933\pi$
$199$	−17.9110	−1.26968	−0.634838	+	0.772645i	$0.718933\pi$
$200$	−2.80354	−0.198240
$201$	2.35712	0.166258
$202$	24.3639	1.71424
$203$	9.82123	0.689315
$204$	−10.7191	−0.750489
$205$	0.261235	0.0182455
$206$	15.6855	1.09286
$207$	7.74063	0.538011
$208$	1.76204	0.122176
$209$	−7.97366	−0.551550
$210$	−6.51808	−0.449790
$211$	8.91647	0.613835	0.306918	−	0.951736i	$-0.400702\pi$
$211$	8.91647	0.613835	0.306918	+	0.951736i	$0.400702\pi$
$212$	9.76624	0.670748
$213$	11.1043	0.760857
$214$	33.8904	2.31670
$215$	−7.33723	−0.500395
$216$	8.21889	0.559224
$217$	4.36900	0.296587
$218$	−2.29893	−0.155703
$219$	3.90124	0.263622
$220$	−9.28367	−0.625905
$221$	4.22562	0.284246
$222$	18.0115	1.20885
$223$	5.72445	0.383337	0.191669	−	0.981460i	$-0.438610\pi$
$223$	5.72445	0.383337	0.191669	+	0.981460i	$0.438610\pi$
$224$	−9.40979	−0.628718
$225$	−3.48791	−0.232528
$226$	15.6407	1.04040
$227$	10.1636	0.674581	0.337290	−	0.941401i	$-0.390490\pi$
$227$	10.1636	0.674581	0.337290	+	0.941401i	$0.390490\pi$
$228$	−15.6702	−1.03778
$229$	11.2669	0.744539	0.372270	−	0.928125i	$-0.378580\pi$
$229$	11.2669	0.744539	0.372270	+	0.928125i	$0.378580\pi$
$230$	−19.9955	−1.31846
$231$	−1.49479	−0.0983499
$232$	13.4590	0.883629
$233$	2.95803	0.193787	0.0968934	−	0.995295i	$-0.469109\pi$
$233$	2.95803	0.193787	0.0968934	+	0.995295i	$0.469109\pi$
$234$	−4.77344	−0.312050
$235$	31.1238	2.03029
$236$	28.9455	1.88419
$237$	8.42777	0.547443
$238$	−11.8308	−0.766877
$239$	−14.0665	−0.909888	−0.454944	−	0.890520i	$-0.650341\pi$
$239$	−14.0665	−0.909888	−0.454944	+	0.890520i	$0.650341\pi$
$240$	4.10216	0.264793
$241$	−10.4597	−0.673768	−0.336884	−	0.941546i	$-0.609373\pi$
$241$	−10.4597	−0.673768	−0.336884	+	0.941546i	$0.609373\pi$
$242$	20.4483	1.31447
$243$	16.1484	1.03592
$244$	−8.35687	−0.534994
$245$	13.7882	0.880895
$246$	0.201850	0.0128695
$247$	6.17739	0.393058
$248$	5.98729	0.380193
$249$	1.36300	0.0863766
$250$	−19.1325	−1.21005
$251$	−16.9887	−1.07232	−0.536159	−	0.844117i	$-0.680125\pi$
$251$	−16.9887	−1.07232	−0.536159	+	0.844117i	$0.680125\pi$
$252$	7.79534	0.491061
$253$	−4.58556	−0.288292
$254$	−20.8475	−1.30809
$255$	9.83754	0.616051
$256$	−3.02978	−0.189361
$257$	−12.2624	−0.764907	−0.382453	−	0.923975i	$-0.624921\pi$
$257$	−12.2624	−0.764907	−0.382453	+	0.923975i	$0.624921\pi$
$258$	−5.66929	−0.352954
$259$	11.5953	0.720499
$260$	7.19229	0.446047
$261$	16.7446	1.03646
$262$	37.8490	2.33832
$263$	21.7088	1.33862	0.669310	−	0.742983i	$-0.266590\pi$
$263$	21.7088	1.33862	0.669310	+	0.742983i	$0.266590\pi$
$264$	−2.04846	−0.126074
$265$	−8.96302	−0.550594
$266$	−17.2953	−1.06044
$267$	−9.14217	−0.559491
$268$	7.28203	0.444821
$269$	24.8563	1.51551	0.757757	−	0.652536i	$-0.226295\pi$
$269$	24.8563	1.51551	0.757757	+	0.652536i	$0.226295\pi$
$270$	−26.4136	−1.60748
$271$	16.9142	1.02747	0.513733	−	0.857950i	$-0.328262\pi$
$271$	16.9142	1.02747	0.513733	+	0.857950i	$0.328262\pi$
$272$	7.44572	0.451463
$273$	1.15805	0.0700884
$274$	2.74626	0.165907
$275$	2.06624	0.124599
$276$	−9.01174	−0.542443
$277$	−23.9205	−1.43724	−0.718622	−	0.695401i	$-0.755227\pi$
$277$	−23.9205	−1.43724	−0.718622	+	0.695401i	$0.755227\pi$
$278$	36.6183	2.19622
$279$	7.44886	0.445952
$280$	−5.75046	−0.343656
$281$	11.6377	0.694245	0.347122	−	0.937820i	$-0.387159\pi$
$281$	11.6377	0.694245	0.347122	+	0.937820i	$0.387159\pi$
$282$	24.0486	1.43207
$283$	−11.0376	−0.656116	−0.328058	−	0.944658i	$-0.606394\pi$
$283$	−11.0376	−0.656116	−0.328058	+	0.944658i	$0.606394\pi$
$284$	34.3055	2.03566
$285$	14.3814	0.851881
$286$	2.82779	0.167211
$287$	0.129946	0.00767047
$288$	−16.0431	−0.945348
$289$	0.855864	0.0503450
$290$	−43.2543	−2.53998
$291$	−5.82311	−0.341357
$292$	12.0524	0.705314
$293$	17.7828	1.03888	0.519440	−	0.854507i	$-0.326141\pi$
$293$	17.7828	1.03888	0.519440	+	0.854507i	$0.326141\pi$
$294$	10.6538	0.621341
$295$	−26.5649	−1.54667
$296$	15.8903	0.923604
$297$	−6.05743	−0.351488
$298$	−25.3751	−1.46994
$299$	3.55255	0.205449
$300$	4.06067	0.234443
$301$	−3.64975	−0.210368
$302$	25.7478	1.48162
$303$	−10.0775	−0.578936
$304$	10.8848	0.624288
$305$	7.66957	0.439158
$306$	−20.1708	−1.15309
$307$	−23.8798	−1.36289	−0.681445	−	0.731870i	$-0.738648\pi$
$307$	−23.8798	−1.36289	−0.681445	+	0.731870i	$0.738648\pi$
$308$	−4.61797	−0.263133
$309$	−6.48788	−0.369083
$310$	−19.2418	−1.09286
$311$	−12.9749	−0.735742	−0.367871	−	0.929877i	$-0.619913\pi$
$311$	−12.9749	−0.735742	−0.367871	+	0.929877i	$0.619913\pi$
$312$	1.58700	0.0898459
$313$	−5.53389	−0.312794	−0.156397	−	0.987694i	$-0.549988\pi$
$313$	−5.53389	−0.312794	−0.156397	+	0.987694i	$0.549988\pi$
$314$	25.7457	1.45291
$315$	−7.15423	−0.403095
$316$	26.0366	1.46467
$317$	−16.2846	−0.914635	−0.457318	−	0.889303i	$-0.651190\pi$
$317$	−16.2846	−0.914635	−0.457318	+	0.889303i	$0.651190\pi$
$318$	−6.92550	−0.388363
$319$	−9.91950	−0.555385
$320$	32.3882	1.81056
$321$	−14.0178	−0.782398
$322$	−9.94634	−0.554288
$323$	26.1033	1.45243
$324$	6.39470	0.355261
$325$	−1.60077	−0.0887948
$326$	27.0202	1.49651
$327$	0.950890	0.0525843
$328$	0.178078	0.00983274
$329$	15.4819	0.853545
$330$	6.58330	0.362399
$331$	−0.273430	−0.0150290	−0.00751452	−	0.999972i	$-0.502392\pi$
$331$	−0.273430	−0.0150290	−0.00751452	+	0.999972i	$0.502392\pi$
$332$	4.21082	0.231099
$333$	19.7693	1.08335
$334$	−35.4972	−1.94232
$335$	−6.68313	−0.365138
$336$	2.04053	0.111320
$337$	12.2203	0.665685	0.332842	−	0.942982i	$-0.391992\pi$
$337$	12.2203	0.665685	0.332842	+	0.942982i	$0.391992\pi$
$338$	−2.19076	−0.119162
$339$	−6.46935	−0.351367
$340$	30.3919	1.64823
$341$	−4.41271	−0.238962
$342$	−29.4874	−1.59450
$343$	15.8046	0.853368
$344$	−5.00163	−0.269670
$345$	8.27058	0.445273
$346$	6.94485	0.373358
$347$	29.4501	1.58097	0.790483	−	0.612484i	$-0.209830\pi$
$347$	29.4501	1.58097	0.790483	+	0.612484i	$0.209830\pi$
$348$	−19.4942	−1.04500
$349$	−23.3461	−1.24969	−0.624843	−	0.780750i	$-0.714837\pi$
$349$	−23.3461	−1.24969	−0.624843	+	0.780750i	$0.714837\pi$
$350$	4.48180	0.239562
$351$	4.69284	0.250485
$352$	9.50395	0.506562
$353$	−9.39312	−0.499945	−0.249973	−	0.968253i	$-0.580422\pi$
$353$	−9.39312	−0.499945	−0.249973	+	0.968253i	$0.580422\pi$
$354$	−20.5260	−1.09094
$355$	−31.4841	−1.67100
$356$	−28.2436	−1.49691
$357$	4.89348	0.258990
$358$	−28.6325	−1.51328
$359$	−33.4686	−1.76640	−0.883202	−	0.468992i	$-0.844617\pi$
$359$	−33.4686	−1.76640	−0.883202	+	0.468992i	$0.844617\pi$
$360$	−9.80417	−0.516725
$361$	19.1602	1.00843
$362$	34.1773	1.79632
$363$	−8.45788	−0.443923
$364$	3.57766	0.187520
$365$	−11.0612	−0.578969
$366$	5.92608	0.309761
$367$	−18.0139	−0.940318	−0.470159	−	0.882582i	$-0.655803\pi$
$367$	−18.0139	−0.940318	−0.470159	+	0.882582i	$0.655803\pi$
$368$	6.25973	0.326311
$369$	0.221550	0.0115334
$370$	−51.0678	−2.65489
$371$	−4.45847	−0.231472
$372$	−8.67206	−0.449625
$373$	0.0147641	0.000764455 0	0.000382227	−	1.00000i	$-0.499878\pi$
$373$	0.0147641	0.000764455 0	0.000382227		1.00000i	$0.499878\pi$
$374$	11.9492	0.617877
$375$	7.91365	0.408659
$376$	21.2164	1.09415
$377$	7.68488	0.395791
$378$	−13.1389	−0.675793
$379$	36.0955	1.85410	0.927050	−	0.374937i	$-0.122336\pi$
$379$	36.0955	1.85410	0.927050	+	0.374937i	$0.122336\pi$
$380$	44.4296	2.27919
$381$	8.62299	0.441769
$382$	−32.0332	−1.63896
$383$	−12.3209	−0.629571	−0.314786	−	0.949163i	$-0.601933\pi$
$383$	−12.3209	−0.629571	−0.314786	+	0.949163i	$0.601933\pi$
$384$	11.6817	0.596131
$385$	4.23817	0.215997
$386$	41.0676	2.09029
$387$	−6.22259	−0.316312
$388$	−17.9898	−0.913294
$389$	13.6644	0.692813	0.346406	−	0.938085i	$-0.387402\pi$
$389$	13.6644	0.692813	0.346406	+	0.938085i	$0.387402\pi$
$390$	−5.10025	−0.258261
$391$	15.0117	0.759175
$392$	9.39911	0.474727
$393$	−15.6552	−0.789699
$394$	−39.1716	−1.97343
$395$	−23.8952	−1.20230
$396$	−7.87334	−0.395650
$397$	−17.3825	−0.872403	−0.436201	−	0.899849i	$-0.643676\pi$
$397$	−17.3825	−0.872403	−0.436201	+	0.899849i	$0.643676\pi$
$398$	39.2387	1.96686
$399$	7.15373	0.358135
$400$	−2.82062	−0.141031
$401$	0.328038	0.0163814	0.00819071	−	0.999966i	$-0.497393\pi$
$401$	0.328038	0.0163814	0.00819071	+	0.999966i	$0.497393\pi$
$402$	−5.16388	−0.257551
$403$	3.41864	0.170295
$404$	−31.1331	−1.54893
$405$	−5.86877	−0.291622
$406$	−21.5160	−1.06782
$407$	−11.7114	−0.580511
$408$	6.70604	0.331999
$409$	−22.6065	−1.11782	−0.558910	−	0.829228i	$-0.688780\pi$
$409$	−22.6065	−1.11782	−0.558910	+	0.829228i	$0.688780\pi$
$410$	−0.572304	−0.0282641
$411$	−1.13591	−0.0560305
$412$	−20.0435	−0.987473
$413$	−13.2141	−0.650225
$414$	−16.9579	−0.833434
$415$	−3.86451	−0.189701
$416$	−7.36294	−0.360998
$417$	−15.1462	−0.741710
$418$	17.4684	0.854407
$419$	−9.91008	−0.484139	−0.242070	−	0.970259i	$-0.577826\pi$
$419$	−9.91008	−0.484139	−0.242070	+	0.970259i	$0.577826\pi$
$420$	8.32904	0.406415
$421$	−30.1026	−1.46711	−0.733556	−	0.679629i	$-0.762141\pi$
$421$	−30.1026	−1.46711	−0.733556	+	0.679629i	$0.762141\pi$
$422$	−19.5339	−0.950893
$423$	26.3956	1.28340
$424$	−6.10990	−0.296723
$425$	−6.76425	−0.328114
$426$	−24.3270	−1.17864
$427$	3.81507	0.184624
$428$	−43.3064	−2.09329
$429$	−1.16964	−0.0564706
$430$	16.0741	0.775162
$431$	7.35190	0.354129	0.177064	−	0.984199i	$-0.443340\pi$
$431$	7.35190	0.354129	0.177064	+	0.984199i	$0.443340\pi$
$432$	8.26899	0.397842
$433$	−4.18323	−0.201033	−0.100517	−	0.994935i	$-0.532050\pi$
$433$	−4.18323	−0.201033	−0.100517	+	0.994935i	$0.532050\pi$
$434$	−9.57143	−0.459443
$435$	17.8909	0.857805
$436$	2.93766	0.140688
$437$	21.9455	1.04979
$438$	−8.54669	−0.408377
$439$	34.9869	1.66984	0.834918	−	0.550375i	$-0.185515\pi$
$439$	34.9869	1.66984	0.834918	+	0.550375i	$0.185515\pi$
$440$	5.80800	0.276886
$441$	11.6936	0.556836
$442$	−9.25732	−0.440326
$443$	−4.59019	−0.218087	−0.109043	−	0.994037i	$-0.534779\pi$
$443$	−4.59019	−0.218087	−0.109043	+	0.994037i	$0.534779\pi$
$444$	−23.0157	−1.09228
$445$	25.9208	1.22876
$446$	−12.5409	−0.593828
$447$	10.4957	0.496430
$448$	16.1109	0.761166
$449$	15.8971	0.750230	0.375115	−	0.926978i	$-0.377603\pi$
$449$	15.8971	0.750230	0.375115	+	0.926978i	$0.377603\pi$
$450$	7.64119	0.360209
$451$	−0.131246	−0.00618014
$452$	−19.9863	−0.940075
$453$	−10.6499	−0.500375
$454$	−22.2660	−1.04499
$455$	−3.28342	−0.153929
$456$	9.80350	0.459091
$457$	21.1491	0.989311	0.494656	−	0.869089i	$-0.335294\pi$
$457$	21.1491	0.989311	0.494656	+	0.869089i	$0.335294\pi$
$458$	−24.6831	−1.15337
$459$	19.8302	0.925593
$460$	25.5510	1.19132
$461$	24.7211	1.15138	0.575689	−	0.817669i	$-0.304734\pi$
$461$	24.7211	1.15138	0.575689	+	0.817669i	$0.304734\pi$
$462$	3.27473	0.152354
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	13.5411	0.628629
$465$	7.95883	0.369082
$466$	−6.48033	−0.300195
$467$	−35.9169	−1.66204	−0.831018	−	0.556245i	$-0.812241\pi$
$467$	−35.9169	−1.66204	−0.831018	+	0.556245i	$0.812241\pi$
$468$	6.09968	0.281958
$469$	−3.32438	−0.153506
$470$	−68.1849	−3.14513
$471$	−10.6490	−0.490680
$472$	−18.1087	−0.833520
$473$	3.68627	0.169495
$474$	−18.4632	−0.848045
$475$	−9.88859	−0.453720
$476$	15.1178	0.692924
$477$	−7.60140	−0.348044
$478$	30.8164	1.40951
$479$	9.82554	0.448941	0.224470	−	0.974481i	$-0.427935\pi$
$479$	9.82554	0.448941	0.224470	+	0.974481i	$0.427935\pi$
$480$	−17.1415	−0.782397
$481$	9.07308	0.413697
$482$	22.9147	1.04374
$483$	4.11403	0.187195
$484$	−26.1296	−1.18771
$485$	16.5103	0.749692
$486$	−35.3773	−1.60475
$487$	39.2819	1.78003	0.890016	−	0.455929i	$-0.150693\pi$
$487$	39.2819	1.78003	0.890016	+	0.455929i	$0.150693\pi$
$488$	5.22818	0.236669
$489$	−11.1762	−0.505403
$490$	−30.2066	−1.36460
$491$	10.7208	0.483824	0.241912	−	0.970298i	$-0.422225\pi$
$491$	10.7208	0.483824	0.241912	+	0.970298i	$0.422225\pi$
$492$	−0.257931	−0.0116284
$493$	32.4734	1.46253
$494$	−13.5332	−0.608887
$495$	7.22581	0.324776
$496$	6.02378	0.270476
$497$	−15.6611	−0.702497
$498$	−2.98601	−0.133806
$499$	14.3408	0.641983	0.320991	−	0.947082i	$-0.395984\pi$
$499$	14.3408	0.641983	0.320991	+	0.947082i	$0.395984\pi$
$500$	24.4483	1.09336
$501$	14.6824	0.655963
$502$	37.2182	1.66113
$503$	7.68994	0.342878	0.171439	−	0.985195i	$-0.445158\pi$
$503$	7.68994	0.342878	0.171439	+	0.985195i	$0.445158\pi$
$504$	−4.87688	−0.217234
$505$	28.5726	1.27146
$506$	10.0459	0.446593
$507$	0.906147	0.0402434
$508$	26.6397	1.18195
$509$	25.1726	1.11575	0.557877	−	0.829923i	$-0.311616\pi$
$509$	25.1726	1.11575	0.557877	+	0.829923i	$0.311616\pi$
$510$	−21.5517	−0.954325
$511$	−5.50215	−0.243401
$512$	−19.1458	−0.846132
$513$	28.9895	1.27992
$514$	26.8640	1.18492
$515$	18.3951	0.810583
$516$	7.24442	0.318918
$517$	−15.6368	−0.687706
$518$	−25.4026	−1.11613
$519$	−2.87255	−0.126091
$520$	−4.49960	−0.197321
$521$	−22.6293	−0.991408	−0.495704	−	0.868492i	$-0.665090\pi$
$521$	−22.6293	−0.991408	−0.495704	+	0.868492i	$0.665090\pi$
$522$	−36.6833	−1.60559
$523$	13.4710	0.589044	0.294522	−	0.955645i	$-0.404840\pi$
$523$	13.4710	0.589044	0.294522	+	0.955645i	$0.404840\pi$
$524$	−48.3648	−2.11282
$525$	−1.85377	−0.0809053
$526$	−47.5587	−2.07366
$527$	14.4459	0.629272
$528$	−2.06095	−0.0896913
$529$	−10.3794	−0.451279
$530$	19.6358	0.852926
$531$	−22.5293	−0.977687
$532$	22.1006	0.958182
$533$	0.101680	0.00440424
$534$	20.0283	0.866709
$535$	39.7447	1.71831
$536$	−4.55574	−0.196778
$537$	11.8430	0.511065
$538$	−54.4542	−2.34769
$539$	−6.92728	−0.298379
$540$	33.7523	1.45247
$541$	−41.4824	−1.78347	−0.891734	−	0.452559i	$-0.850511\pi$
$541$	−41.4824	−1.78347	−0.891734	+	0.452559i	$0.850511\pi$
$542$	−37.0550	−1.59165
$543$	−14.1365	−0.606656
$544$	−31.1130	−1.33396
$545$	−2.69606	−0.115486
$546$	−2.53701	−0.108574
$547$	−28.7590	−1.22965	−0.614823	−	0.788665i	$-0.710773\pi$
$547$	−28.7590	−1.22965	−0.614823	+	0.788665i	$0.710773\pi$
$548$	−3.50927	−0.149908
$549$	6.50444	0.277603
$550$	−4.52665	−0.193017
$551$	47.4725	2.02240
$552$	5.63788	0.239964
$553$	−11.8862	−0.505452
$554$	52.4041	2.22644
$555$	21.1228	0.896612
$556$	−46.7922	−1.98443
$557$	−12.9901	−0.550408	−0.275204	−	0.961386i	$-0.588745\pi$
$557$	−12.9901	−0.550408	−0.275204	+	0.961386i	$0.588745\pi$
$558$	−16.3187	−0.690825
$559$	−2.85585	−0.120789
$560$	−5.78552	−0.244483
$561$	−4.94244	−0.208670
$562$	−25.4953	−1.07546
$563$	−24.2566	−1.02229	−0.511146	−	0.859494i	$-0.670779\pi$
$563$	−24.2566	−1.02229	−0.511146	+	0.859494i	$0.670779\pi$
$564$	−30.7301	−1.29397
$565$	18.3425	0.771675
$566$	24.1807	1.01639
$567$	−2.91930	−0.122599
$568$	−21.4620	−0.900527
$569$	−36.7037	−1.53870	−0.769350	−	0.638828i	$-0.779420\pi$
$569$	−36.7037	−1.53870	−0.769350	+	0.638828i	$0.779420\pi$
$570$	−31.5062	−1.31965
$571$	5.26350	0.220271	0.110135	−	0.993917i	$-0.464872\pi$
$571$	5.26350	0.220271	0.110135	+	0.993917i	$0.464872\pi$
$572$	−3.61345	−0.151086
$573$	13.2496	0.553511
$574$	−0.284681	−0.0118823
$575$	−5.68681	−0.237156
$576$	27.4680	1.14450
$577$	−1.67597	−0.0697714	−0.0348857	−	0.999391i	$-0.511107\pi$
$577$	−1.67597	−0.0697714	−0.0348857	+	0.999391i	$0.511107\pi$
$578$	−1.87499	−0.0779895
$579$	−16.9865	−0.705934
$580$	55.2719	2.29504
$581$	−1.92232	−0.0797513
$582$	12.7571	0.528797
$583$	4.50308	0.186499
$584$	−7.54017	−0.312014
$585$	−5.59801	−0.231449
$586$	−38.9578	−1.60933
$587$	40.4229	1.66843	0.834215	−	0.551439i	$-0.185921\pi$
$587$	40.4229	1.66843	0.834215	+	0.551439i	$0.185921\pi$
$588$	−13.6138	−0.561423
$589$	21.1183	0.870164
$590$	58.1973	2.39594
$591$	16.2022	0.666471
$592$	15.9871	0.657068
$593$	2.28931	0.0940107	0.0470053	−	0.998895i	$-0.485032\pi$
$593$	2.28931	0.0940107	0.0470053	+	0.998895i	$0.485032\pi$
$594$	13.2704	0.544491
$595$	−13.8745	−0.568798
$596$	32.4252	1.32819
$597$	−16.2300	−0.664249
$598$	−7.78278	−0.318261
$599$	41.8378	1.70945	0.854724	−	0.519083i	$-0.173727\pi$
$599$	41.8378	1.70945	0.854724	+	0.519083i	$0.173727\pi$
$600$	−2.54042	−0.103712
$601$	10.3090	0.420512	0.210256	−	0.977646i	$-0.432570\pi$
$601$	10.3090	0.420512	0.210256	+	0.977646i	$0.432570\pi$
$602$	7.99573	0.325882
$603$	−5.66786	−0.230813
$604$	−32.9015	−1.33874
$605$	23.9806	0.974949
$606$	22.0773	0.896830
$607$	−12.4473	−0.505219	−0.252610	−	0.967568i	$-0.581289\pi$
$607$	−12.4473	−0.505219	−0.252610	+	0.967568i	$0.581289\pi$
$608$	−45.4838	−1.84461
$609$	8.89948	0.360625
$610$	−16.8022	−0.680301
$611$	12.1142	0.490089
$612$	25.7749	1.04189
$613$	−0.823248	−0.0332507	−0.0166253	−	0.999862i	$-0.505292\pi$
$613$	−0.823248	−0.0332507	−0.0166253	+	0.999862i	$0.505292\pi$
$614$	52.3148	2.11125
$615$	0.236718	0.00954537
$616$	2.88907	0.116404
$617$	−28.4544	−1.14553	−0.572765	−	0.819719i	$-0.694129\pi$
$617$	−28.4544	−1.14553	−0.572765	+	0.819719i	$0.694129\pi$
$618$	14.2134	0.571746
$619$	30.0250	1.20681	0.603404	−	0.797436i	$-0.293811\pi$
$619$	30.0250	1.20681	0.603404	+	0.797436i	$0.293811\pi$
$620$	24.5879	0.987472
$621$	16.6715	0.669006
$622$	28.4250	1.13974
$623$	12.8937	0.516577
$624$	1.59667	0.0639179
$625$	−30.4414	−1.21766
$626$	12.1234	0.484549
$627$	−7.22531	−0.288551
$628$	−32.8988	−1.31280
$629$	38.3394	1.52869
$630$	15.6732	0.624435
$631$	32.0976	1.27778	0.638892	−	0.769296i	$-0.279393\pi$
$631$	32.0976	1.27778	0.638892	+	0.769296i	$0.279393\pi$
$632$	−16.2889	−0.647937
$633$	8.07964	0.321137
$634$	35.6757	1.41686
$635$	−24.4487	−0.970219
$636$	8.84965	0.350911
$637$	5.36673	0.212638
$638$	21.7312	0.860348
$639$	−26.7012	−1.05628
$640$	−33.1212	−1.30923
$641$	16.6339	0.656999	0.328500	−	0.944504i	$-0.393457\pi$
$641$	16.6339	0.656999	0.328500	+	0.944504i	$0.393457\pi$
$642$	30.7097	1.21201
$643$	5.39065	0.212586	0.106293	−	0.994335i	$-0.466102\pi$
$643$	5.39065	0.212586	0.106293	+	0.994335i	$0.466102\pi$
$644$	12.7098	0.500836
$645$	−6.64861	−0.261789
$646$	−57.1861	−2.24996
$647$	−21.4867	−0.844728	−0.422364	−	0.906426i	$-0.638800\pi$
$647$	−21.4867	−0.844728	−0.422364	+	0.906426i	$0.638800\pi$
$648$	−4.00061	−0.157159
$649$	13.3464	0.523890
$650$	3.50691	0.137552
$651$	3.95896	0.155164
$652$	−34.5274	−1.35220
$653$	−15.2095	−0.595194	−0.297597	−	0.954692i	$-0.596185\pi$
$653$	−15.2095	−0.595194	−0.297597	+	0.954692i	$0.596185\pi$
$654$	−2.08317	−0.0814585
$655$	44.3871	1.73435
$656$	0.179164	0.00699517
$657$	−9.38082	−0.365981
$658$	−33.9171	−1.32223
$659$	21.3062	0.829971	0.414986	−	0.909828i	$-0.363787\pi$
$659$	21.3062	0.829971	0.414986	+	0.909828i	$0.363787\pi$
$660$	−8.41238	−0.327451
$661$	−48.3356	−1.88004	−0.940018	−	0.341126i	$-0.889192\pi$
$661$	−48.3356	−1.88004	−0.940018	+	0.341126i	$0.889192\pi$
$662$	0.599019	0.0232815
$663$	3.82903	0.148707
$664$	−2.63435	−0.102233
$665$	−20.2830	−0.786539
$666$	−43.3098	−1.67822
$667$	27.3009	1.05709
$668$	45.3596	1.75502
$669$	5.18719	0.200548
$670$	14.6411	0.565636
$671$	−3.85324	−0.148753
$672$	−8.52666	−0.328923
$673$	−25.5190	−0.983687	−0.491843	−	0.870684i	$-0.663677\pi$
$673$	−25.5190	−0.983687	−0.491843	+	0.870684i	$0.663677\pi$
$674$	−26.7719	−1.03121
$675$	−7.51217	−0.289143
$676$	2.79943	0.107670
$677$	−45.6901	−1.75601	−0.878007	−	0.478647i	$-0.841127\pi$
$677$	−45.6901	−1.75601	−0.878007	+	0.478647i	$0.841127\pi$
$678$	14.1728	0.544303
$679$	8.21268	0.315174
$680$	−19.0136	−0.729139
$681$	9.20971	0.352917
$682$	9.66720	0.370176
$683$	3.77763	0.144547	0.0722735	−	0.997385i	$-0.476975\pi$
$683$	3.77763	0.144547	0.0722735	+	0.997385i	$0.476975\pi$
$684$	37.6801	1.44073
$685$	3.22065	0.123055
$686$	−34.6241	−1.32195
$687$	10.2095	0.389517
$688$	−5.03212	−0.191848
$689$	−3.48865	−0.132907
$690$	−18.1189	−0.689773
$691$	26.2778	0.999654	0.499827	−	0.866125i	$-0.333397\pi$
$691$	26.2778	0.999654	0.499827	+	0.866125i	$0.333397\pi$
$692$	−8.87439	−0.337353
$693$	3.59433	0.136537
$694$	−64.5182	−2.44908
$695$	42.9438	1.62895
$696$	12.1959	0.462283
$697$	0.429660	0.0162745
$698$	51.1457	1.93589
$699$	2.68041	0.101382
$700$	−5.72701	−0.216461
$701$	−5.41725	−0.204607	−0.102303	−	0.994753i	$-0.532621\pi$
$701$	−5.41725	−0.204607	−0.102303	+	0.994753i	$0.532621\pi$
$702$	−10.2809	−0.388028
$703$	56.0480	2.11389
$704$	−16.2721	−0.613276
$705$	28.2028	1.06218
$706$	20.5781	0.774466
$707$	14.2129	0.534529
$708$	26.2288	0.985740
$709$	30.0072	1.12694	0.563472	−	0.826135i	$-0.309465\pi$
$709$	30.0072	1.12694	0.563472	+	0.826135i	$0.309465\pi$
$710$	68.9741	2.58855
$711$	−20.2652	−0.760004
$712$	17.6696	0.662197
$713$	12.1449	0.454829
$714$	−10.7204	−0.401203
$715$	3.31627	0.124021
$716$	36.5877	1.36734
$717$	−12.7463	−0.476021
$718$	73.3217	2.73634
$719$	2.74024	0.102194	0.0510969	−	0.998694i	$-0.483728\pi$
$719$	2.74024	0.102194	0.0510969	+	0.998694i	$0.483728\pi$
$720$	−9.86393	−0.367607
$721$	9.15024	0.340773
$722$	−41.9754	−1.56216
$723$	−9.47802	−0.352491
$724$	−43.6730	−1.62310
$725$	−12.3017	−0.456875
$726$	18.5292	0.687682
$727$	−39.1451	−1.45181	−0.725906	−	0.687794i	$-0.758579\pi$
$727$	−39.1451	−1.45181	−0.725906	+	0.687794i	$0.758579\pi$
$728$	−2.23823	−0.0829545
$729$	7.78001	0.288148
$730$	24.2324	0.896881
$731$	−12.0677	−0.446341
$732$	−7.57256	−0.279890
$733$	18.6920	0.690403	0.345202	−	0.938529i	$-0.387811\pi$
$733$	18.6920	0.690403	0.345202	+	0.938529i	$0.387811\pi$
$734$	39.4642	1.45665
$735$	12.4941	0.460853
$736$	−26.1572	−0.964167
$737$	3.35765	0.123680
$738$	−0.485362	−0.0178664
$739$	−22.3003	−0.820329	−0.410165	−	0.912012i	$-0.634529\pi$
$739$	−22.3003	−0.820329	−0.410165	+	0.912012i	$0.634529\pi$
$740$	65.2563	2.39887
$741$	5.59763	0.205634
$742$	9.76744	0.358574
$743$	18.3135	0.671857	0.335928	−	0.941888i	$-0.390950\pi$
$743$	18.3135	0.671857	0.335928	+	0.941888i	$0.390950\pi$
$744$	5.42537	0.198904
$745$	−29.7585	−1.09027
$746$	−0.0323445	−0.00118422
$747$	−3.27743	−0.119915
$748$	−15.2691	−0.558293
$749$	19.7702	0.722386
$750$	−17.3369	−0.633054
$751$	25.2719	0.922186	0.461093	−	0.887352i	$-0.347457\pi$
$751$	25.2719	0.922186	0.461093	+	0.887352i	$0.347457\pi$
$752$	21.3458	0.778400
$753$	−15.3943	−0.560998
$754$	−16.8357	−0.613121
$755$	30.1956	1.09893
$756$	16.7894	0.610624
$757$	−21.9705	−0.798531	−0.399265	−	0.916835i	$-0.630735\pi$
$757$	−21.9705	−0.798531	−0.399265	+	0.916835i	$0.630735\pi$
$758$	−79.0766	−2.87219
$759$	−4.15519	−0.150824
$760$	−27.7958	−1.00826
$761$	21.0135	0.761737	0.380869	−	0.924629i	$-0.375625\pi$
$761$	21.0135	0.761737	0.380869	+	0.924629i	$0.375625\pi$
$762$	−18.8909	−0.684346
$763$	−1.34110	−0.0485510
$764$	40.9331	1.48091
$765$	−23.6551	−0.855251
$766$	26.9923	0.975270
$767$	−10.3398	−0.373347
$768$	−2.74542	−0.0990670
$769$	−32.0159	−1.15452	−0.577262	−	0.816559i	$-0.695879\pi$
$769$	−32.0159	−1.15452	−0.577262	+	0.816559i	$0.695879\pi$
$770$	−9.28482	−0.334602
$771$	−11.1115	−0.400172
$772$	−52.4777	−1.88871
$773$	23.0834	0.830251	0.415126	−	0.909764i	$-0.363738\pi$
$773$	23.0834	0.830251	0.415126	+	0.909764i	$0.363738\pi$
$774$	13.6322	0.490000
$775$	−5.47246	−0.196576
$776$	11.2547	0.404020
$777$	10.5071	0.376940
$778$	−29.9354	−1.07324
$779$	0.628116	0.0225046
$780$	6.51728	0.233356
$781$	15.8178	0.566006
$782$	−32.8871	−1.17604
$783$	36.0639	1.28882
$784$	9.45641	0.337729
$785$	30.1931	1.07764
$786$	34.2967	1.22332
$787$	26.8607	0.957480	0.478740	−	0.877957i	$-0.341094\pi$
$787$	26.8607	0.957480	0.478740	+	0.877957i	$0.341094\pi$
$788$	50.0548	1.78313
$789$	19.6714	0.700319
$790$	52.3487	1.86248
$791$	9.12410	0.324416
$792$	4.92568	0.175026
$793$	2.98520	0.106008
$794$	38.0809	1.35144
$795$	−8.12182	−0.288051
$796$	−50.1406	−1.77719
$797$	40.8530	1.44709	0.723544	−	0.690279i	$-0.242512\pi$
$797$	40.8530	1.44709	0.723544	+	0.690279i	$0.242512\pi$
$798$	−15.6721	−0.554787
$799$	51.1901	1.81098
$800$	11.7864	0.416712
$801$	21.9830	0.776731
$802$	−0.718652	−0.0253765
$803$	5.55721	0.196110
$804$	6.59859	0.232714
$805$	−11.6645	−0.411119
$806$	−7.48942	−0.263804
$807$	22.5235	0.792863
$808$	19.4773	0.685210
$809$	−15.4003	−0.541444	−0.270722	−	0.962658i	$-0.587262\pi$
$809$	−15.4003	−0.541444	−0.270722	+	0.962658i	$0.587262\pi$
$810$	12.8571	0.451751
$811$	−1.10084	−0.0386557	−0.0193279	−	0.999813i	$-0.506153\pi$
$811$	−1.10084	−0.0386557	−0.0193279	+	0.999813i	$0.506153\pi$
$812$	27.4939	0.964845
$813$	15.3268	0.537533
$814$	25.6568	0.899270
$815$	31.6877	1.10997
$816$	6.74692	0.236189
$817$	−17.6417	−0.617204
$818$	49.5255	1.73162
$819$	−2.78462	−0.0973024
$820$	0.731310	0.0255385
$821$	−24.6508	−0.860319	−0.430159	−	0.902753i	$-0.641543\pi$
$821$	−24.6508	−0.860319	−0.430159	+	0.902753i	$0.641543\pi$
$822$	2.48851	0.0867969
$823$	−9.04869	−0.315418	−0.157709	−	0.987486i	$-0.550411\pi$
$823$	−9.04869	−0.315418	−0.157709	+	0.987486i	$0.550411\pi$
$824$	12.5395	0.436835
$825$	1.87232	0.0651859
$826$	28.9490	1.00727
$827$	−37.4075	−1.30079	−0.650393	−	0.759598i	$-0.725396\pi$
$827$	−37.4075	−1.30079	−0.650393	+	0.759598i	$0.725396\pi$
$828$	21.6694	0.753063
$829$	−1.33060	−0.0462136	−0.0231068	−	0.999733i	$-0.507356\pi$
$829$	−1.33060	−0.0462136	−0.0231068	+	0.999733i	$0.507356\pi$
$830$	8.46622	0.293867
$831$	−21.6755	−0.751915
$832$	12.6064	0.437047
$833$	22.6778	0.785738
$834$	33.1816	1.14898
$835$	−41.6291	−1.44063
$836$	−22.3217	−0.772013
$837$	16.0431	0.554532
$838$	21.7106	0.749981
$839$	−0.361756	−0.0124892	−0.00624461	−	0.999981i	$-0.501988\pi$
$839$	−0.361756	−0.0124892	−0.00624461	+	0.999981i	$0.501988\pi$
$840$	−5.21077	−0.179789
$841$	30.0574	1.03646
$842$	65.9477	2.27271
$843$	10.5454	0.363204
$844$	24.9611	0.859195
$845$	−2.56920	−0.0883830
$846$	−57.8265	−1.98812
$847$	11.9286	0.409873
$848$	−6.14714	−0.211094
$849$	−10.0017	−0.343257
$850$	14.8188	0.508282
$851$	32.2325	1.10492
$852$	31.0859	1.06498
$853$	−48.7107	−1.66782	−0.833912	−	0.551898i	$-0.813904\pi$
$853$	−48.7107	−1.66782	−0.833912	+	0.551898i	$0.813904\pi$
$854$	−8.35790	−0.286001
$855$	−34.5811	−1.18265
$856$	27.0931	0.926023
$857$	−1.72863	−0.0590487	−0.0295244	−	0.999564i	$-0.509399\pi$
$857$	−1.72863	−0.0590487	−0.0295244	+	0.999564i	$0.509399\pi$
$858$	2.56240	0.0874788
$859$	−32.0878	−1.09482	−0.547411	−	0.836864i	$-0.684387\pi$
$859$	−32.0878	−1.09482	−0.547411	+	0.836864i	$0.684387\pi$
$860$	−20.5401	−0.700411
$861$	0.117750	0.00401292
$862$	−16.1063	−0.548581
$863$	−31.6489	−1.07734	−0.538670	−	0.842517i	$-0.681073\pi$
$863$	−31.6489	−1.07734	−0.538670	+	0.842517i	$0.681073\pi$
$864$	−34.5531	−1.17552
$865$	8.14452	0.276922
$866$	9.16445	0.311421
$867$	0.775539	0.0263387
$868$	12.2307	0.415138
$869$	12.0051	0.407246
$870$	−39.1948	−1.32883
$871$	−2.60125	−0.0881400
$872$	−1.83784	−0.0622372
$873$	14.0021	0.473899
$874$	−48.0773	−1.62624
$875$	−11.1611	−0.377314
$876$	10.9213	0.368995
$877$	−38.1768	−1.28914	−0.644569	−	0.764546i	$-0.722963\pi$
$877$	−38.1768	−1.28914	−0.644569	+	0.764546i	$0.722963\pi$
$878$	−76.6480	−2.58674
$879$	16.1138	0.543505
$880$	5.84340	0.196981
$881$	49.1164	1.65477	0.827386	−	0.561633i	$-0.189827\pi$
$881$	49.1164	1.65477	0.827386	+	0.561633i	$0.189827\pi$
$882$	−25.6178	−0.862596
$883$	35.5485	1.19630	0.598151	−	0.801384i	$-0.295902\pi$
$883$	35.5485	1.19630	0.598151	+	0.801384i	$0.295902\pi$
$884$	11.8293	0.397864
$885$	−24.0717	−0.809161
$886$	10.0560	0.337838
$887$	30.7066	1.03103	0.515514	−	0.856881i	$-0.327601\pi$
$887$	30.7066	1.03103	0.515514	+	0.856881i	$0.327601\pi$
$888$	14.3989	0.483197
$889$	−12.1615	−0.407884
$890$	−56.7862	−1.90348
$891$	2.94851	0.0987787
$892$	16.0252	0.536563
$893$	74.8343	2.50424
$894$	−22.9936	−0.769021
$895$	−33.5785	−1.12241
$896$	−16.4754	−0.550406
$897$	3.21913	0.107484
$898$	−34.8267	−1.16218
$899$	26.2718	0.876215
$900$	−9.76418	−0.325473
$901$	−14.7417	−0.491117
$902$	0.287529	0.00957367
$903$	−3.30721	−0.110057
$904$	12.5037	0.415867
$905$	40.0812	1.33234
$906$	23.3313	0.775132
$907$	−24.5580	−0.815436	−0.407718	−	0.913108i	$-0.633675\pi$
$907$	−24.5580	−0.815436	−0.407718	+	0.913108i	$0.633675\pi$
$908$	28.4523	0.944222
$909$	24.2320	0.803725
$910$	7.19318	0.238452
$911$	15.2207	0.504285	0.252143	−	0.967690i	$-0.418865\pi$
$911$	15.2207	0.504285	0.252143	+	0.967690i	$0.418865\pi$
$912$	9.86326	0.326605
$913$	1.94155	0.0642561
$914$	−46.3325	−1.53254
$915$	6.94976	0.229752
$916$	31.5410	1.04214
$917$	22.0794	0.729127
$918$	−43.4432	−1.43384
$919$	43.8269	1.44572	0.722858	−	0.690997i	$-0.242828\pi$
$919$	43.8269	1.44572	0.722858	+	0.690997i	$0.242828\pi$
$920$	−15.9851	−0.527011
$921$	−21.6386	−0.713015
$922$	−54.1581	−1.78360
$923$	−12.2545	−0.403360
$924$	−4.18456	−0.137662
$925$	−14.5239	−0.477544
$926$	−2.19076	−0.0719929
$927$	15.6006	0.512390
$928$	−56.5833	−1.85744
$929$	−36.1646	−1.18652	−0.593261	−	0.805010i	$-0.702160\pi$
$929$	−36.1646	−1.18652	−0.593261	+	0.805010i	$0.702160\pi$
$930$	−17.4359	−0.571746
$931$	33.1524	1.08653
$932$	8.28080	0.271247
$933$	−11.7572	−0.384914
$934$	78.6854	2.57466
$935$	14.0133	0.458284
$936$	−3.81605	−0.124731
$937$	32.5647	1.06384	0.531921	−	0.846794i	$-0.321470\pi$
$937$	32.5647	1.06384	0.531921	+	0.846794i	$0.321470\pi$
$938$	7.28293	0.237796
$939$	−5.01452	−0.163643
$940$	87.1291	2.84184
$941$	8.31442	0.271042	0.135521	−	0.990774i	$-0.456729\pi$
$941$	8.31442	0.271042	0.135521	+	0.990774i	$0.456729\pi$
$942$	23.3294	0.760113
$943$	0.361222	0.0117630
$944$	−18.2191	−0.592981
$945$	−15.4086	−0.501240
$946$	−8.07574	−0.262565
$947$	−56.5394	−1.83728	−0.918642	−	0.395091i	$-0.870713\pi$
$947$	−56.5394	−1.83728	−0.918642	+	0.395091i	$0.870713\pi$
$948$	23.5930	0.766265
$949$	−4.30531	−0.139756
$950$	21.6635	0.702858
$951$	−14.7563	−0.478505
$952$	−9.45793	−0.306533
$953$	−15.0950	−0.488975	−0.244487	−	0.969652i	$-0.578620\pi$
$953$	−15.0950	−0.488975	−0.244487	+	0.969652i	$0.578620\pi$
$954$	16.6529	0.539156
$955$	−37.5666	−1.21563
$956$	−39.3783	−1.27358
$957$	−8.98853	−0.290558
$958$	−21.5254	−0.695455
$959$	1.60205	0.0517327
$960$	29.3485	0.947219
$961$	−19.3129	−0.622997
$962$	−19.8770	−0.640859
$963$	33.7069	1.08619
$964$	−29.2812	−0.943084
$965$	48.1617	1.55038
$966$	−9.01285	−0.289984
$967$	−26.2728	−0.844876	−0.422438	−	0.906392i	$-0.638826\pi$
$967$	−26.2728	−0.844876	−0.422438	+	0.906392i	$0.638826\pi$
$968$	16.3471	0.525414
$969$	23.6535	0.759859
$970$	−36.1700	−1.16135
$971$	−45.9733	−1.47535	−0.737676	−	0.675155i	$-0.764077\pi$
$971$	−45.9733	−1.47535	−0.737676	+	0.675155i	$0.764077\pi$
$972$	45.2064	1.45000
$973$	21.3615	0.684819
$974$	−86.0572	−2.75745
$975$	−1.45053	−0.0464543
$976$	5.26005	0.168370
$977$	1.69184	0.0541268	0.0270634	−	0.999634i	$-0.491384\pi$
$977$	1.69184	0.0541268	0.0270634	+	0.999634i	$0.491384\pi$
$978$	24.4843	0.782921
$979$	−13.0228	−0.416209
$980$	38.5991	1.23300
$981$	−2.28648	−0.0730018
$982$	−23.4868	−0.749493
$983$	−0.176270	−0.00562214	−0.00281107	−	0.999996i	$-0.500895\pi$
$983$	−0.176270	−0.00562214	−0.00281107	+	0.999996i	$0.500895\pi$
$984$	0.161365	0.00514414
$985$	−45.9381	−1.46371
$986$	−71.1414	−2.26560
$987$	14.0289	0.446544
$988$	17.2932	0.550170
$989$	−10.1455	−0.322609
$990$	−15.8300	−0.503111
$991$	24.4492	0.776655	0.388327	−	0.921522i	$-0.373053\pi$
$991$	24.4492	0.776655	0.388327	+	0.921522i	$0.373053\pi$
$992$	−25.1712	−0.799188
$993$	−0.247768	−0.00786266
$994$	34.3097	1.08824
$995$	46.0168	1.45883
$996$	3.81563	0.120903
$997$	44.2260	1.40065	0.700325	−	0.713824i	$-0.253038\pi$
$997$	44.2260	1.40065	0.700325	+	0.713824i	$0.253038\pi$
$998$	−31.4173	−0.994497
$999$	42.5786	1.34713

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.16	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.16	✓	123	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.19076 q^{2} +0.906147 q^{3} +2.79943 q^{4} -2.56920 q^{5} -1.98515 q^{6} -1.27799 q^{7} -1.75137 q^{8} -2.17890 q^{9} +O(q^{10})\)	\(q-2.19076 q^{2} +0.906147 q^{3} +2.79943 q^{4} -2.56920 q^{5} -1.98515 q^{6} -1.27799 q^{7} -1.75137 q^{8} -2.17890 q^{9} +5.62849 q^{10} +1.29078 q^{11} +2.53670 q^{12} -1.00000 q^{13} +2.79978 q^{14} -2.32807 q^{15} -1.76204 q^{16} -4.22562 q^{17} +4.77344 q^{18} -6.17739 q^{19} -7.19229 q^{20} -1.15805 q^{21} -2.82779 q^{22} -3.55255 q^{23} -1.58700 q^{24} +1.60077 q^{25} +2.19076 q^{26} -4.69284 q^{27} -3.57766 q^{28} -7.68488 q^{29} +5.10025 q^{30} -3.41864 q^{31} +7.36294 q^{32} +1.16964 q^{33} +9.25732 q^{34} +3.28342 q^{35} -6.09968 q^{36} -9.07308 q^{37} +13.5332 q^{38} -0.906147 q^{39} +4.49960 q^{40} -0.101680 q^{41} +2.53701 q^{42} +2.85585 q^{43} +3.61345 q^{44} +5.59801 q^{45} +7.78278 q^{46} -12.1142 q^{47} -1.59667 q^{48} -5.36673 q^{49} -3.50691 q^{50} -3.82903 q^{51} -2.79943 q^{52} +3.48865 q^{53} +10.2809 q^{54} -3.31627 q^{55} +2.23823 q^{56} -5.59763 q^{57} +16.8357 q^{58} +10.3398 q^{59} -6.51728 q^{60} -2.98520 q^{61} +7.48942 q^{62} +2.78462 q^{63} -12.6064 q^{64} +2.56920 q^{65} -2.56240 q^{66} +2.60125 q^{67} -11.8293 q^{68} -3.21913 q^{69} -7.19318 q^{70} +12.2545 q^{71} +3.81605 q^{72} +4.30531 q^{73} +19.8770 q^{74} +1.45053 q^{75} -17.2932 q^{76} -1.64961 q^{77} +1.98515 q^{78} +9.30067 q^{79} +4.52703 q^{80} +2.28428 q^{81} +0.222756 q^{82} +1.50417 q^{83} -3.24188 q^{84} +10.8564 q^{85} -6.25647 q^{86} -6.96363 q^{87} -2.26063 q^{88} -10.0890 q^{89} -12.2639 q^{90} +1.27799 q^{91} -9.94511 q^{92} -3.09779 q^{93} +26.5394 q^{94} +15.8709 q^{95} +6.67191 q^{96} -6.42623 q^{97} +11.7572 q^{98} -2.81248 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * q^99

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