LMFDB - Embedded newform 6026.2.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.87480 q^{3} +1.00000 q^{4} +0.417125 q^{5} -1.87480 q^{6} -3.88487 q^{7} +1.00000 q^{8} +0.514862 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.87480 q^{3} +1.00000 q^{4} +0.417125 q^{5} -1.87480 q^{6} -3.88487 q^{7} +1.00000 q^{8} +0.514862 q^{9} +0.417125 q^{10} +1.68591 q^{11} -1.87480 q^{12} +0.977747 q^{13} -3.88487 q^{14} -0.782024 q^{15} +1.00000 q^{16} +4.13211 q^{17} +0.514862 q^{18} +0.960672 q^{19} +0.417125 q^{20} +7.28334 q^{21} +1.68591 q^{22} -1.00000 q^{23} -1.87480 q^{24} -4.82601 q^{25} +0.977747 q^{26} +4.65913 q^{27} -3.88487 q^{28} +2.28577 q^{29} -0.782024 q^{30} -5.85147 q^{31} +1.00000 q^{32} -3.16074 q^{33} +4.13211 q^{34} -1.62048 q^{35} +0.514862 q^{36} -2.27934 q^{37} +0.960672 q^{38} -1.83308 q^{39} +0.417125 q^{40} -11.1745 q^{41} +7.28334 q^{42} +5.25637 q^{43} +1.68591 q^{44} +0.214762 q^{45} -1.00000 q^{46} +9.97639 q^{47} -1.87480 q^{48} +8.09223 q^{49} -4.82601 q^{50} -7.74687 q^{51} +0.977747 q^{52} -7.30545 q^{53} +4.65913 q^{54} +0.703236 q^{55} -3.88487 q^{56} -1.80107 q^{57} +2.28577 q^{58} +2.12265 q^{59} -0.782024 q^{60} +4.46010 q^{61} -5.85147 q^{62} -2.00017 q^{63} +1.00000 q^{64} +0.407843 q^{65} -3.16074 q^{66} -3.65432 q^{67} +4.13211 q^{68} +1.87480 q^{69} -1.62048 q^{70} +12.6910 q^{71} +0.514862 q^{72} +1.30227 q^{73} -2.27934 q^{74} +9.04778 q^{75} +0.960672 q^{76} -6.54955 q^{77} -1.83308 q^{78} +14.6175 q^{79} +0.417125 q^{80} -10.2795 q^{81} -11.1745 q^{82} +2.72150 q^{83} +7.28334 q^{84} +1.72361 q^{85} +5.25637 q^{86} -4.28536 q^{87} +1.68591 q^{88} +3.02090 q^{89} +0.214762 q^{90} -3.79842 q^{91} -1.00000 q^{92} +10.9703 q^{93} +9.97639 q^{94} +0.400720 q^{95} -1.87480 q^{96} -7.36745 q^{97} +8.09223 q^{98} +0.868013 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.87480	−1.08241	−0.541207	−	0.840889i	$-0.682033\pi$
$3$	−1.87480	−1.08241	−0.541207	+	0.840889i	$0.682033\pi$
$4$	1.00000	0.500000
$5$	0.417125	0.186544	0.0932719	−	0.995641i	$-0.470267\pi$
$5$	0.417125	0.186544	0.0932719	+	0.995641i	$0.470267\pi$
$6$	−1.87480	−0.765383
$7$	−3.88487	−1.46834	−0.734172	−	0.678964i	$-0.762429\pi$
$7$	−3.88487	−1.46834	−0.734172	+	0.678964i	$0.762429\pi$
$8$	1.00000	0.353553
$9$	0.514862	0.171621
$10$	0.417125	0.131906
$11$	1.68591	0.508322	0.254161	−	0.967162i	$-0.418201\pi$
$11$	1.68591	0.508322	0.254161	+	0.967162i	$0.418201\pi$
$12$	−1.87480	−0.541207
$13$	0.977747	0.271178	0.135589	−	0.990765i	$-0.456707\pi$
$13$	0.977747	0.271178	0.135589	+	0.990765i	$0.456707\pi$
$14$	−3.88487	−1.03828
$15$	−0.782024	−0.201918
$16$	1.00000	0.250000
$17$	4.13211	1.00219	0.501093	−	0.865394i	$-0.332932\pi$
$17$	4.13211	1.00219	0.501093	+	0.865394i	$0.332932\pi$
$18$	0.514862	0.121354
$19$	0.960672	0.220393	0.110197	−	0.993910i	$-0.464852\pi$
$19$	0.960672	0.220393	0.110197	+	0.993910i	$0.464852\pi$
$20$	0.417125	0.0932719
$21$	7.28334	1.58936
$22$	1.68591	0.359438
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.87480	−0.382691
$25$	−4.82601	−0.965201
$26$	0.977747	0.191752
$27$	4.65913	0.896650
$28$	−3.88487	−0.734172
$29$	2.28577	0.424457	0.212229	−	0.977220i	$-0.431928\pi$
$29$	2.28577	0.424457	0.212229	+	0.977220i	$0.431928\pi$
$30$	−0.782024	−0.142777
$31$	−5.85147	−1.05095	−0.525477	−	0.850808i	$-0.676113\pi$
$31$	−5.85147	−1.05095	−0.525477	+	0.850808i	$0.676113\pi$
$32$	1.00000	0.176777
$33$	−3.16074	−0.550215
$34$	4.13211	0.708652
$35$	−1.62048	−0.273910
$36$	0.514862	0.0858104
$37$	−2.27934	−0.374721	−0.187360	−	0.982291i	$-0.559993\pi$
$37$	−2.27934	−0.374721	−0.187360	+	0.982291i	$0.559993\pi$
$38$	0.960672	0.155842
$39$	−1.83308	−0.293527
$40$	0.417125	0.0659532
$41$	−11.1745	−1.74517	−0.872585	−	0.488462i	$-0.837558\pi$
$41$	−11.1745	−1.74517	−0.872585	+	0.488462i	$0.837558\pi$
$42$	7.28334	1.12384
$43$	5.25637	0.801589	0.400794	−	0.916168i	$-0.368734\pi$
$43$	5.25637	0.801589	0.400794	+	0.916168i	$0.368734\pi$
$44$	1.68591	0.254161
$45$	0.214762	0.0320148
$46$	−1.00000	−0.147442
$47$	9.97639	1.45521	0.727603	−	0.685998i	$-0.240634\pi$
$47$	9.97639	1.45521	0.727603	+	0.685998i	$0.240634\pi$
$48$	−1.87480	−0.270604
$49$	8.09223	1.15603
$50$	−4.82601	−0.682500
$51$	−7.74687	−1.08478
$52$	0.977747	0.135589
$53$	−7.30545	−1.00348	−0.501740	−	0.865018i	$-0.667307\pi$
$53$	−7.30545	−1.00348	−0.501740	+	0.865018i	$0.667307\pi$
$54$	4.65913	0.634027
$55$	0.703236	0.0948243
$56$	−3.88487	−0.519138
$57$	−1.80107	−0.238557
$58$	2.28577	0.300137
$59$	2.12265	0.276346	0.138173	−	0.990408i	$-0.455877\pi$
$59$	2.12265	0.276346	0.138173	+	0.990408i	$0.455877\pi$
$60$	−0.782024	−0.100959
$61$	4.46010	0.571057	0.285529	−	0.958370i	$-0.407831\pi$
$61$	4.46010	0.571057	0.285529	+	0.958370i	$0.407831\pi$
$62$	−5.85147	−0.743137
$63$	−2.00017	−0.251998
$64$	1.00000	0.125000
$65$	0.407843	0.0505867
$66$	−3.16074	−0.389060
$67$	−3.65432	−0.446447	−0.223223	−	0.974767i	$-0.571658\pi$
$67$	−3.65432	−0.446447	−0.223223	+	0.974767i	$0.571658\pi$
$68$	4.13211	0.501093
$69$	1.87480	0.225699
$70$	−1.62048	−0.193684
$71$	12.6910	1.50614	0.753070	−	0.657940i	$-0.228572\pi$
$71$	12.6910	1.50614	0.753070	+	0.657940i	$0.228572\pi$
$72$	0.514862	0.0606771
$73$	1.30227	0.152419	0.0762093	−	0.997092i	$-0.475718\pi$
$73$	1.30227	0.152419	0.0762093	+	0.997092i	$0.475718\pi$
$74$	−2.27934	−0.264968
$75$	9.04778	1.04475
$76$	0.960672	0.110197
$77$	−6.54955	−0.746391
$78$	−1.83308	−0.207555
$79$	14.6175	1.64459	0.822297	−	0.569058i	$-0.192692\pi$
$79$	14.6175	1.64459	0.822297	+	0.569058i	$0.192692\pi$
$80$	0.417125	0.0466360
$81$	−10.2795	−1.14217
$82$	−11.1745	−1.23402
$83$	2.72150	0.298724	0.149362	−	0.988783i	$-0.452278\pi$
$83$	2.72150	0.298724	0.149362	+	0.988783i	$0.452278\pi$
$84$	7.28334	0.794678
$85$	1.72361	0.186951
$86$	5.25637	0.566809
$87$	−4.28536	−0.459439
$88$	1.68591	0.179719
$89$	3.02090	0.320215	0.160107	−	0.987100i	$-0.448816\pi$
$89$	3.02090	0.320215	0.160107	+	0.987100i	$0.448816\pi$
$90$	0.214762	0.0226379
$91$	−3.79842	−0.398183
$92$	−1.00000	−0.104257
$93$	10.9703	1.13757
$94$	9.97639	1.02899
$95$	0.400720	0.0411130
$96$	−1.87480	−0.191346
$97$	−7.36745	−0.748051	−0.374026	−	0.927418i	$-0.622023\pi$
$97$	−7.36745	−0.748051	−0.374026	+	0.927418i	$0.622023\pi$
$98$	8.09223	0.817438
$99$	0.868013	0.0872386
$100$	−4.82601	−0.482601
$101$	−17.8251	−1.77366	−0.886830	−	0.462097i	$-0.847097\pi$
$101$	−17.8251	−1.77366	−0.886830	+	0.462097i	$0.847097\pi$
$102$	−7.74687	−0.767055
$103$	−12.4613	−1.22785	−0.613925	−	0.789364i	$-0.710410\pi$
$103$	−12.4613	−1.22785	−0.613925	+	0.789364i	$0.710410\pi$
$104$	0.977747	0.0958760
$105$	3.03806	0.296485
$106$	−7.30545	−0.709568
$107$	−9.14975	−0.884540	−0.442270	−	0.896882i	$-0.645827\pi$
$107$	−9.14975	−0.884540	−0.442270	+	0.896882i	$0.645827\pi$
$108$	4.65913	0.448325
$109$	−0.730774	−0.0699955	−0.0349977	−	0.999387i	$-0.511142\pi$
$109$	−0.730774	−0.0699955	−0.0349977	+	0.999387i	$0.511142\pi$
$110$	0.703236	0.0670509
$111$	4.27330	0.405603
$112$	−3.88487	−0.367086
$113$	−7.99067	−0.751699	−0.375849	−	0.926681i	$-0.622649\pi$
$113$	−7.99067	−0.751699	−0.375849	+	0.926681i	$0.622649\pi$
$114$	−1.80107	−0.168685
$115$	−0.417125	−0.0388971
$116$	2.28577	0.212229
$117$	0.503405	0.0465398
$118$	2.12265	0.195406
$119$	−16.0527	−1.47155
$120$	−0.782024	−0.0713887
$121$	−8.15770	−0.741609
$122$	4.46010	0.403798
$123$	20.9500	1.88900
$124$	−5.85147	−0.525477
$125$	−4.09867	−0.366596
$126$	−2.00017	−0.178190
$127$	14.7090	1.30522	0.652608	−	0.757696i	$-0.273675\pi$
$127$	14.7090	1.30522	0.652608	+	0.757696i	$0.273675\pi$
$128$	1.00000	0.0883883
$129$	−9.85462	−0.867651
$130$	0.407843	0.0357702
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−3.16074	−0.275107
$133$	−3.73209	−0.323613
$134$	−3.65432	−0.315685
$135$	1.94344	0.167264
$136$	4.13211	0.354326
$137$	−8.68075	−0.741647	−0.370823	−	0.928703i	$-0.620925\pi$
$137$	−8.68075	−0.741647	−0.370823	+	0.928703i	$0.620925\pi$
$138$	1.87480	0.159593
$139$	−12.2880	−1.04226	−0.521129	−	0.853478i	$-0.674489\pi$
$139$	−12.2880	−1.04226	−0.521129	+	0.853478i	$0.674489\pi$
$140$	−1.62048	−0.136955
$141$	−18.7037	−1.57514
$142$	12.6910	1.06500
$143$	1.64840	0.137846
$144$	0.514862	0.0429052
$145$	0.953452	0.0791799
$146$	1.30227	0.107776
$147$	−15.1713	−1.25131
$148$	−2.27934	−0.187360
$149$	−12.9624	−1.06192	−0.530960	−	0.847397i	$-0.678169\pi$
$149$	−12.9624	−1.06192	−0.530960	+	0.847397i	$0.678169\pi$
$150$	9.04778	0.738748
$151$	−1.75525	−0.142840	−0.0714202	−	0.997446i	$-0.522753\pi$
$151$	−1.75525	−0.142840	−0.0714202	+	0.997446i	$0.522753\pi$
$152$	0.960672	0.0779208
$153$	2.12747	0.171996
$154$	−6.54955	−0.527778
$155$	−2.44079	−0.196049
$156$	−1.83308	−0.146764
$157$	−10.1538	−0.810365	−0.405182	−	0.914236i	$-0.632792\pi$
$157$	−10.1538	−0.810365	−0.405182	+	0.914236i	$0.632792\pi$
$158$	14.6175	1.16290
$159$	13.6962	1.08618
$160$	0.417125	0.0329766
$161$	3.88487	0.306171
$162$	−10.2795	−0.807634
$163$	−0.964643	−0.0755567	−0.0377783	−	0.999286i	$-0.512028\pi$
$163$	−0.964643	−0.0755567	−0.0377783	+	0.999286i	$0.512028\pi$
$164$	−11.1745	−0.872585
$165$	−1.31842	−0.102639
$166$	2.72150	0.211230
$167$	−24.8436	−1.92245	−0.961226	−	0.275761i	$-0.911070\pi$
$167$	−24.8436	−1.92245	−0.961226	+	0.275761i	$0.911070\pi$
$168$	7.28334	0.561922
$169$	−12.0440	−0.926462
$170$	1.72361	0.132195
$171$	0.494614	0.0378241
$172$	5.25637	0.400794
$173$	16.0331	1.21897	0.609486	−	0.792797i	$-0.291376\pi$
$173$	16.0331	1.21897	0.609486	+	0.792797i	$0.291376\pi$
$174$	−4.28536	−0.324872
$175$	18.7484	1.41725
$176$	1.68591	0.127080
$177$	−3.97954	−0.299121
$178$	3.02090	0.226426
$179$	−23.3066	−1.74202	−0.871010	−	0.491265i	$-0.836535\pi$
$179$	−23.3066	−1.74202	−0.871010	+	0.491265i	$0.836535\pi$
$180$	0.214762	0.0160074
$181$	−19.0750	−1.41783	−0.708917	−	0.705292i	$-0.750816\pi$
$181$	−19.0750	−1.41783	−0.708917	+	0.705292i	$0.750816\pi$
$182$	−3.79842	−0.281558
$183$	−8.36178	−0.618120
$184$	−1.00000	−0.0737210
$185$	−0.950769	−0.0699019
$186$	10.9703	0.804382
$187$	6.96638	0.509432
$188$	9.97639	0.727603
$189$	−18.1001	−1.31659
$190$	0.400720	0.0290713
$191$	9.70689	0.702366	0.351183	−	0.936307i	$-0.385780\pi$
$191$	9.70689	0.702366	0.351183	+	0.936307i	$0.385780\pi$
$192$	−1.87480	−0.135302
$193$	−13.3085	−0.957963	−0.478982	−	0.877825i	$-0.658994\pi$
$193$	−13.3085	−0.957963	−0.478982	+	0.877825i	$0.658994\pi$
$194$	−7.36745	−0.528952
$195$	−0.764622	−0.0547557
$196$	8.09223	0.578016
$197$	−17.0979	−1.21818	−0.609089	−	0.793102i	$-0.708465\pi$
$197$	−17.0979	−1.21818	−0.609089	+	0.793102i	$0.708465\pi$
$198$	0.868013	0.0616870
$199$	13.2891	0.942042	0.471021	−	0.882122i	$-0.343886\pi$
$199$	13.2891	0.942042	0.471021	+	0.882122i	$0.343886\pi$
$200$	−4.82601	−0.341250
$201$	6.85111	0.483240
$202$	−17.8251	−1.25417
$203$	−8.87993	−0.623249
$204$	−7.74687	−0.542390
$205$	−4.66118	−0.325551
$206$	−12.4613	−0.868222
$207$	−0.514862	−0.0357854
$208$	0.977747	0.0677946
$209$	1.61961	0.112031
$210$	3.03806	0.209646
$211$	2.60305	0.179202	0.0896008	−	0.995978i	$-0.471441\pi$
$211$	2.60305	0.179202	0.0896008	+	0.995978i	$0.471441\pi$
$212$	−7.30545	−0.501740
$213$	−23.7930	−1.63027
$214$	−9.14975	−0.625464
$215$	2.19256	0.149531
$216$	4.65913	0.317013
$217$	22.7322	1.54316
$218$	−0.730774	−0.0494943
$219$	−2.44148	−0.164980
$220$	0.703236	0.0474121
$221$	4.04016	0.271771
$222$	4.27330	0.286805
$223$	3.63020	0.243096	0.121548	−	0.992586i	$-0.461214\pi$
$223$	3.63020	0.243096	0.121548	+	0.992586i	$0.461214\pi$
$224$	−3.88487	−0.259569
$225$	−2.48473	−0.165649
$226$	−7.99067	−0.531531
$227$	−21.1315	−1.40255	−0.701274	−	0.712892i	$-0.747385\pi$
$227$	−21.1315	−1.40255	−0.701274	+	0.712892i	$0.747385\pi$
$228$	−1.80107	−0.119278
$229$	−12.4428	−0.822241	−0.411120	−	0.911581i	$-0.634862\pi$
$229$	−12.4428	−0.822241	−0.411120	+	0.911581i	$0.634862\pi$
$230$	−0.417125	−0.0275044
$231$	12.2791	0.807904
$232$	2.28577	0.150068
$233$	3.95732	0.259253	0.129626	−	0.991563i	$-0.458622\pi$
$233$	3.95732	0.259253	0.129626	+	0.991563i	$0.458622\pi$
$234$	0.503405	0.0329086
$235$	4.16140	0.271460
$236$	2.12265	0.138173
$237$	−27.4048	−1.78013
$238$	−16.0527	−1.04054
$239$	4.03460	0.260977	0.130488	−	0.991450i	$-0.458345\pi$
$239$	4.03460	0.260977	0.130488	+	0.991450i	$0.458345\pi$
$240$	−0.782024	−0.0504794
$241$	10.6775	0.687797	0.343898	−	0.939007i	$-0.388252\pi$
$241$	10.6775	0.687797	0.343898	+	0.939007i	$0.388252\pi$
$242$	−8.15770	−0.524397
$243$	5.29460	0.339648
$244$	4.46010	0.285529
$245$	3.37547	0.215651
$246$	20.9500	1.33572
$247$	0.939295	0.0597659
$248$	−5.85147	−0.371569
$249$	−5.10227	−0.323343
$250$	−4.09867	−0.259223
$251$	−6.69192	−0.422391	−0.211195	−	0.977444i	$-0.567736\pi$
$251$	−6.69192	−0.422391	−0.211195	+	0.977444i	$0.567736\pi$
$252$	−2.00017	−0.125999
$253$	−1.68591	−0.105992
$254$	14.7090	0.922927
$255$	−3.23141	−0.202359
$256$	1.00000	0.0625000
$257$	5.68569	0.354663	0.177332	−	0.984151i	$-0.443253\pi$
$257$	5.68569	0.354663	0.177332	+	0.984151i	$0.443253\pi$
$258$	−9.85462	−0.613522
$259$	8.85494	0.550219
$260$	0.407843	0.0252933
$261$	1.17686	0.0728457
$262$	1.00000	0.0617802
$263$	12.9950	0.801306	0.400653	−	0.916230i	$-0.368783\pi$
$263$	12.9950	0.801306	0.400653	+	0.916230i	$0.368783\pi$
$264$	−3.16074	−0.194530
$265$	−3.04728	−0.187193
$266$	−3.73209	−0.228829
$267$	−5.66358	−0.346605
$268$	−3.65432	−0.223223
$269$	−8.29937	−0.506021	−0.253011	−	0.967463i	$-0.581421\pi$
$269$	−8.29937	−0.506021	−0.253011	+	0.967463i	$0.581421\pi$
$270$	1.94344	0.118274
$271$	−2.25610	−0.137048	−0.0685241	−	0.997649i	$-0.521829\pi$
$271$	−2.25610	−0.137048	−0.0685241	+	0.997649i	$0.521829\pi$
$272$	4.13211	0.250546
$273$	7.12127	0.430999
$274$	−8.68075	−0.524424
$275$	−8.13622	−0.490633
$276$	1.87480	0.112849
$277$	29.1221	1.74978	0.874889	−	0.484324i	$-0.160935\pi$
$277$	29.1221	1.74978	0.874889	+	0.484324i	$0.160935\pi$
$278$	−12.2880	−0.736988
$279$	−3.01270	−0.180366
$280$	−1.62048	−0.0968420
$281$	−16.9777	−1.01281	−0.506403	−	0.862297i	$-0.669025\pi$
$281$	−16.9777	−1.01281	−0.506403	+	0.862297i	$0.669025\pi$
$282$	−18.7037	−1.11379
$283$	−2.13466	−0.126892	−0.0634462	−	0.997985i	$-0.520209\pi$
$283$	−2.13466	−0.126892	−0.0634462	+	0.997985i	$0.520209\pi$
$284$	12.6910	0.753070
$285$	−0.751269	−0.0445013
$286$	1.64840	0.0974717
$287$	43.4117	2.56251
$288$	0.514862	0.0303386
$289$	0.0743726	0.00437486
$290$	0.953452	0.0559886
$291$	13.8125	0.809702
$292$	1.30227	0.0762093
$293$	13.0875	0.764578	0.382289	−	0.924043i	$-0.375136\pi$
$293$	13.0875	0.764578	0.382289	+	0.924043i	$0.375136\pi$
$294$	−15.1713	−0.884807
$295$	0.885411	0.0515506
$296$	−2.27934	−0.132484
$297$	7.85488	0.455786
$298$	−12.9624	−0.750891
$299$	−0.977747	−0.0565446
$300$	9.04778	0.522374
$301$	−20.4203	−1.17701
$302$	−1.75525	−0.101003
$303$	33.4183	1.91983
$304$	0.960672	0.0550983
$305$	1.86042	0.106527
$306$	2.12747	0.121619
$307$	9.80204	0.559432	0.279716	−	0.960083i	$-0.409760\pi$
$307$	9.80204	0.559432	0.279716	+	0.960083i	$0.409760\pi$
$308$	−6.54955	−0.373195
$309$	23.3625	1.32904
$310$	−2.44079	−0.138628
$311$	−1.12763	−0.0639419	−0.0319710	−	0.999489i	$-0.510178\pi$
$311$	−1.12763	−0.0639419	−0.0319710	+	0.999489i	$0.510178\pi$
$312$	−1.83308	−0.103778
$313$	32.1468	1.81705	0.908523	−	0.417836i	$-0.137211\pi$
$313$	32.1468	1.81705	0.908523	+	0.417836i	$0.137211\pi$
$314$	−10.1538	−0.573015
$315$	−0.834322	−0.0470087
$316$	14.6175	0.822297
$317$	−32.7066	−1.83699	−0.918493	−	0.395437i	$-0.870593\pi$
$317$	−32.7066	−1.83699	−0.918493	+	0.395437i	$0.870593\pi$
$318$	13.6962	0.768046
$319$	3.85361	0.215761
$320$	0.417125	0.0233180
$321$	17.1539	0.957439
$322$	3.88487	0.216495
$323$	3.96961	0.220875
$324$	−10.2795	−0.571084
$325$	−4.71862	−0.261742
$326$	−0.964643	−0.0534267
$327$	1.37005	0.0757641
$328$	−11.1745	−0.617011
$329$	−38.7570	−2.13674
$330$	−1.31842	−0.0725768
$331$	−11.1917	−0.615150	−0.307575	−	0.951524i	$-0.599517\pi$
$331$	−11.1917	−0.615150	−0.307575	+	0.951524i	$0.599517\pi$
$332$	2.72150	0.149362
$333$	−1.17355	−0.0643099
$334$	−24.8436	−1.35938
$335$	−1.52431	−0.0832819
$336$	7.28334	0.397339
$337$	1.07863	0.0587565	0.0293782	−	0.999568i	$-0.490647\pi$
$337$	1.07863	0.0587565	0.0293782	+	0.999568i	$0.490647\pi$
$338$	−12.0440	−0.655108
$339$	14.9809	0.813649
$340$	1.72361	0.0934757
$341$	−9.86506	−0.534223
$342$	0.494614	0.0267457
$343$	−4.24316	−0.229109
$344$	5.25637	0.283404
$345$	0.782024	0.0421028
$346$	16.0331	0.861944
$347$	−3.30511	−0.177428	−0.0887138	−	0.996057i	$-0.528276\pi$
$347$	−3.30511	−0.177428	−0.0887138	+	0.996057i	$0.528276\pi$
$348$	−4.28536	−0.229719
$349$	−14.3520	−0.768242	−0.384121	−	0.923283i	$-0.625496\pi$
$349$	−14.3520	−0.768242	−0.384121	+	0.923283i	$0.625496\pi$
$350$	18.7484	1.00215
$351$	4.55545	0.243152
$352$	1.68591	0.0898594
$353$	−31.2147	−1.66139	−0.830696	−	0.556726i	$-0.812057\pi$
$353$	−31.2147	−1.66139	−0.830696	+	0.556726i	$0.812057\pi$
$354$	−3.97954	−0.211510
$355$	5.29372	0.280961
$356$	3.02090	0.160107
$357$	30.0956	1.59283
$358$	−23.3066	−1.23179
$359$	−22.0283	−1.16261	−0.581304	−	0.813686i	$-0.697457\pi$
$359$	−22.0283	−1.16261	−0.581304	+	0.813686i	$0.697457\pi$
$360$	0.214762	0.0113189
$361$	−18.0771	−0.951427
$362$	−19.0750	−1.00256
$363$	15.2940	0.802728
$364$	−3.79842	−0.199091
$365$	0.543207	0.0284328
$366$	−8.36178	−0.437077
$367$	−13.4731	−0.703292	−0.351646	−	0.936133i	$-0.614378\pi$
$367$	−13.4731	−0.703292	−0.351646	+	0.936133i	$0.614378\pi$
$368$	−1.00000	−0.0521286
$369$	−5.75335	−0.299507
$370$	−0.950769	−0.0494281
$371$	28.3807	1.47345
$372$	10.9703	0.568784
$373$	18.4113	0.953300	0.476650	−	0.879093i	$-0.341851\pi$
$373$	18.4113	0.953300	0.476650	+	0.879093i	$0.341851\pi$
$374$	6.96638	0.360223
$375$	7.68417	0.396809
$376$	9.97639	0.514493
$377$	2.23491	0.115104
$378$	−18.1001	−0.930969
$379$	−19.0499	−0.978530	−0.489265	−	0.872135i	$-0.662735\pi$
$379$	−19.0499	−0.978530	−0.489265	+	0.872135i	$0.662735\pi$
$380$	0.400720	0.0205565
$381$	−27.5765	−1.41278
$382$	9.70689	0.496648
$383$	−35.7824	−1.82840	−0.914199	−	0.405266i	$-0.867179\pi$
$383$	−35.7824	−1.82840	−0.914199	+	0.405266i	$0.867179\pi$
$384$	−1.87480	−0.0956728
$385$	−2.73198	−0.139235
$386$	−13.3085	−0.677382
$387$	2.70631	0.137569
$388$	−7.36745	−0.374026
$389$	−18.6973	−0.947992	−0.473996	−	0.880527i	$-0.657189\pi$
$389$	−18.6973	−0.947992	−0.473996	+	0.880527i	$0.657189\pi$
$390$	−0.764622	−0.0387181
$391$	−4.13211	−0.208970
$392$	8.09223	0.408719
$393$	−1.87480	−0.0945710
$394$	−17.0979	−0.861382
$395$	6.09731	0.306789
$396$	0.868013	0.0436193
$397$	31.3086	1.57133	0.785667	−	0.618650i	$-0.212320\pi$
$397$	31.3086	1.57133	0.785667	+	0.618650i	$0.212320\pi$
$398$	13.2891	0.666124
$399$	6.99691	0.350283
$400$	−4.82601	−0.241300
$401$	9.39248	0.469038	0.234519	−	0.972112i	$-0.424648\pi$
$401$	9.39248	0.469038	0.234519	+	0.972112i	$0.424648\pi$
$402$	6.85111	0.341702
$403$	−5.72126	−0.284996
$404$	−17.8251	−0.886830
$405$	−4.28784	−0.213064
$406$	−8.87993	−0.440704
$407$	−3.84276	−0.190479
$408$	−7.74687	−0.383527
$409$	36.0745	1.78377	0.891886	−	0.452261i	$-0.149382\pi$
$409$	36.0745	1.78377	0.891886	+	0.452261i	$0.149382\pi$
$410$	−4.66118	−0.230199
$411$	16.2746	0.802769
$412$	−12.4613	−0.613925
$413$	−8.24623	−0.405771
$414$	−0.514862	−0.0253041
$415$	1.13521	0.0557251
$416$	0.977747	0.0479380
$417$	23.0376	1.12816
$418$	1.61961	0.0792177
$419$	26.0297	1.27163	0.635817	−	0.771840i	$-0.280663\pi$
$419$	26.0297	1.27163	0.635817	+	0.771840i	$0.280663\pi$
$420$	3.03806	0.148242
$421$	6.92411	0.337461	0.168730	−	0.985662i	$-0.446033\pi$
$421$	6.92411	0.337461	0.168730	+	0.985662i	$0.446033\pi$
$422$	2.60305	0.126715
$423$	5.13647	0.249744
$424$	−7.30545	−0.354784
$425$	−19.9416	−0.967310
$426$	−23.7930	−1.15277
$427$	−17.3269	−0.838508
$428$	−9.14975	−0.442270
$429$	−3.09041	−0.149206
$430$	2.19256	0.105735
$431$	24.4652	1.17845	0.589225	−	0.807969i	$-0.299433\pi$
$431$	24.4652	1.17845	0.589225	+	0.807969i	$0.299433\pi$
$432$	4.65913	0.224162
$433$	−33.9020	−1.62923	−0.814613	−	0.580005i	$-0.803051\pi$
$433$	−33.9020	−1.62923	−0.814613	+	0.580005i	$0.803051\pi$
$434$	22.7322	1.09118
$435$	−1.78753	−0.0857055
$436$	−0.730774	−0.0349977
$437$	−0.960672	−0.0459552
$438$	−2.44148	−0.116659
$439$	−29.6623	−1.41570	−0.707852	−	0.706361i	$-0.750335\pi$
$439$	−29.6623	−1.41570	−0.707852	+	0.706361i	$0.750335\pi$
$440$	0.703236	0.0335254
$441$	4.16638	0.198399
$442$	4.04016	0.192171
$443$	−9.71238	−0.461449	−0.230724	−	0.973019i	$-0.574110\pi$
$443$	−9.71238	−0.461449	−0.230724	+	0.973019i	$0.574110\pi$
$444$	4.27330	0.202802
$445$	1.26009	0.0597341
$446$	3.63020	0.171895
$447$	24.3018	1.14944
$448$	−3.88487	−0.183543
$449$	19.8899	0.938663	0.469331	−	0.883022i	$-0.344495\pi$
$449$	19.8899	0.938663	0.469331	+	0.883022i	$0.344495\pi$
$450$	−2.48473	−0.117131
$451$	−18.8393	−0.887108
$452$	−7.99067	−0.375849
$453$	3.29074	0.154612
$454$	−21.1315	−0.991751
$455$	−1.58442	−0.0742786
$456$	−1.80107	−0.0843426
$457$	−17.0791	−0.798929	−0.399464	−	0.916749i	$-0.630804\pi$
$457$	−17.0791	−0.798929	−0.399464	+	0.916749i	$0.630804\pi$
$458$	−12.4428	−0.581412
$459$	19.2521	0.898609
$460$	−0.417125	−0.0194485
$461$	−5.49174	−0.255776	−0.127888	−	0.991789i	$-0.540820\pi$
$461$	−5.49174	−0.255776	−0.127888	+	0.991789i	$0.540820\pi$
$462$	12.2791	0.571274
$463$	−33.2142	−1.54359	−0.771797	−	0.635869i	$-0.780642\pi$
$463$	−33.2142	−1.54359	−0.771797	+	0.635869i	$0.780642\pi$
$464$	2.28577	0.106114
$465$	4.57599	0.212206
$466$	3.95732	0.183319
$467$	22.6811	1.04956	0.524778	−	0.851239i	$-0.324149\pi$
$467$	22.6811	1.04956	0.524778	+	0.851239i	$0.324149\pi$
$468$	0.503405	0.0232699
$469$	14.1966	0.655537
$470$	4.16140	0.191951
$471$	19.0364	0.877151
$472$	2.12265	0.0977030
$473$	8.86177	0.407465
$474$	−27.4048	−1.25874
$475$	−4.63621	−0.212724
$476$	−16.0527	−0.735776
$477$	−3.76130	−0.172218
$478$	4.03460	0.184538
$479$	31.5210	1.44023	0.720116	−	0.693854i	$-0.244089\pi$
$479$	31.5210	1.44023	0.720116	+	0.693854i	$0.244089\pi$
$480$	−0.782024	−0.0356944
$481$	−2.22862	−0.101616
$482$	10.6775	0.486346
$483$	−7.28334	−0.331404
$484$	−8.15770	−0.370805
$485$	−3.07315	−0.139544
$486$	5.29460	0.240168
$487$	−19.0074	−0.861310	−0.430655	−	0.902517i	$-0.641717\pi$
$487$	−19.0074	−0.861310	−0.430655	+	0.902517i	$0.641717\pi$
$488$	4.46010	0.201899
$489$	1.80851	0.0817837
$490$	3.37547	0.152488
$491$	7.30630	0.329729	0.164864	−	0.986316i	$-0.447281\pi$
$491$	7.30630	0.329729	0.164864	+	0.986316i	$0.447281\pi$
$492$	20.9500	0.944499
$493$	9.44507	0.425385
$494$	0.939295	0.0422609
$495$	0.362070	0.0162738
$496$	−5.85147	−0.262739
$497$	−49.3028	−2.21153
$498$	−5.10227	−0.228638
$499$	−17.9443	−0.803298	−0.401649	−	0.915794i	$-0.631563\pi$
$499$	−17.9443	−0.803298	−0.401649	+	0.915794i	$0.631563\pi$
$500$	−4.09867	−0.183298
$501$	46.5766	2.08089
$502$	−6.69192	−0.298675
$503$	−17.1381	−0.764152	−0.382076	−	0.924131i	$-0.624791\pi$
$503$	−17.1381	−0.764152	−0.382076	+	0.924131i	$0.624791\pi$
$504$	−2.00017	−0.0890948
$505$	−7.43527	−0.330865
$506$	−1.68591	−0.0749479
$507$	22.5801	1.00282
$508$	14.7090	0.652608
$509$	−10.0093	−0.443655	−0.221827	−	0.975086i	$-0.571202\pi$
$509$	−10.0093	−0.443655	−0.221827	+	0.975086i	$0.571202\pi$
$510$	−3.23141	−0.143089
$511$	−5.05913	−0.223803
$512$	1.00000	0.0441942
$513$	4.47589	0.197616
$514$	5.68569	0.250785
$515$	−5.19793	−0.229048
$516$	−9.85462	−0.433825
$517$	16.8193	0.739713
$518$	8.85494	0.389064
$519$	−30.0588	−1.31943
$520$	0.407843	0.0178851
$521$	34.9170	1.52974	0.764870	−	0.644184i	$-0.222803\pi$
$521$	34.9170	1.52974	0.764870	+	0.644184i	$0.222803\pi$
$522$	1.17686	0.0515097
$523$	27.2316	1.19076	0.595378	−	0.803446i	$-0.297002\pi$
$523$	27.2316	1.19076	0.595378	+	0.803446i	$0.297002\pi$
$524$	1.00000	0.0436852
$525$	−35.1495	−1.53405
$526$	12.9950	0.566609
$527$	−24.1789	−1.05325
$528$	−3.16074	−0.137554
$529$	1.00000	0.0434783
$530$	−3.04728	−0.132365
$531$	1.09287	0.0474267
$532$	−3.73209	−0.161807
$533$	−10.9259	−0.473252
$534$	−5.66358	−0.245087
$535$	−3.81659	−0.165005
$536$	−3.65432	−0.157843
$537$	43.6952	1.88559
$538$	−8.29937	−0.357811
$539$	13.6428	0.587636
$540$	1.94344	0.0836322
$541$	4.04815	0.174044	0.0870218	−	0.996206i	$-0.472265\pi$
$541$	4.04815	0.174044	0.0870218	+	0.996206i	$0.472265\pi$
$542$	−2.25610	−0.0969077
$543$	35.7617	1.53468
$544$	4.13211	0.177163
$545$	−0.304824	−0.0130572
$546$	7.12127	0.304762
$547$	33.2219	1.42047	0.710233	−	0.703966i	$-0.248589\pi$
$547$	33.2219	1.42047	0.710233	+	0.703966i	$0.248589\pi$
$548$	−8.68075	−0.370823
$549$	2.29634	0.0980053
$550$	−8.13622	−0.346930
$551$	2.19588	0.0935476
$552$	1.87480	0.0797966
$553$	−56.7870	−2.41483
$554$	29.1221	1.23728
$555$	1.78250	0.0756628
$556$	−12.2880	−0.521129
$557$	−14.5079	−0.614718	−0.307359	−	0.951594i	$-0.599445\pi$
$557$	−14.5079	−0.614718	−0.307359	+	0.951594i	$0.599445\pi$
$558$	−3.01270	−0.127538
$559$	5.13940	0.217373
$560$	−1.62048	−0.0684776
$561$	−13.0605	−0.551417
$562$	−16.9777	−0.716162
$563$	43.0791	1.81557	0.907784	−	0.419439i	$-0.137773\pi$
$563$	43.0791	1.81557	0.907784	+	0.419439i	$0.137773\pi$
$564$	−18.7037	−0.787568
$565$	−3.33310	−0.140225
$566$	−2.13466	−0.0897264
$567$	39.9346	1.67709
$568$	12.6910	0.532501
$569$	25.6347	1.07466	0.537331	−	0.843372i	$-0.319433\pi$
$569$	25.6347	1.07466	0.537331	+	0.843372i	$0.319433\pi$
$570$	−0.751269	−0.0314672
$571$	−34.9818	−1.46394	−0.731970	−	0.681336i	$-0.761399\pi$
$571$	−34.9818	−1.46394	−0.731970	+	0.681336i	$0.761399\pi$
$572$	1.64840	0.0689229
$573$	−18.1984	−0.760251
$574$	43.4117	1.81197
$575$	4.82601	0.201258
$576$	0.514862	0.0214526
$577$	26.6953	1.11134	0.555670	−	0.831403i	$-0.312462\pi$
$577$	26.6953	1.11134	0.555670	+	0.831403i	$0.312462\pi$
$578$	0.0743726	0.00309349
$579$	24.9506	1.03691
$580$	0.953452	0.0395900
$581$	−10.5727	−0.438629
$582$	13.8125	0.572545
$583$	−12.3163	−0.510091
$584$	1.30227	0.0538881
$585$	0.209983	0.00868172
$586$	13.0875	0.540638
$587$	−15.1474	−0.625201	−0.312600	−	0.949885i	$-0.601200\pi$
$587$	−15.1474	−0.625201	−0.312600	+	0.949885i	$0.601200\pi$
$588$	−15.1713	−0.625653
$589$	−5.62134	−0.231623
$590$	0.885411	0.0364518
$591$	32.0552	1.31857
$592$	−2.27934	−0.0936802
$593$	−32.6917	−1.34249	−0.671243	−	0.741238i	$-0.734239\pi$
$593$	−32.6917	−1.34249	−0.671243	+	0.741238i	$0.734239\pi$
$594$	7.85488	0.322290
$595$	−6.69599	−0.274509
$596$	−12.9624	−0.530960
$597$	−24.9144	−1.01968
$598$	−0.977747	−0.0399831
$599$	2.45447	0.100287	0.0501435	−	0.998742i	$-0.484032\pi$
$599$	2.45447	0.100287	0.0501435	+	0.998742i	$0.484032\pi$
$600$	9.04778	0.369374
$601$	31.5861	1.28843	0.644213	−	0.764846i	$-0.277185\pi$
$601$	31.5861	1.28843	0.644213	+	0.764846i	$0.277185\pi$
$602$	−20.4203	−0.832270
$603$	−1.88147	−0.0766195
$604$	−1.75525	−0.0714202
$605$	−3.40278	−0.138343
$606$	33.4183	1.35753
$607$	5.25894	0.213454	0.106727	−	0.994288i	$-0.465963\pi$
$607$	5.25894	0.213454	0.106727	+	0.994288i	$0.465963\pi$
$608$	0.960672	0.0389604
$609$	16.6481	0.674614
$610$	1.86042	0.0753261
$611$	9.75439	0.394620
$612$	2.12747	0.0859979
$613$	23.8091	0.961639	0.480820	−	0.876820i	$-0.340339\pi$
$613$	23.8091	0.961639	0.480820	+	0.876820i	$0.340339\pi$
$614$	9.80204	0.395578
$615$	8.73876	0.352381
$616$	−6.54955	−0.263889
$617$	35.6586	1.43556	0.717781	−	0.696269i	$-0.245158\pi$
$617$	35.6586	1.43556	0.717781	+	0.696269i	$0.245158\pi$
$618$	23.3625	0.939776
$619$	−2.90105	−0.116603	−0.0583016	−	0.998299i	$-0.518569\pi$
$619$	−2.90105	−0.116603	−0.0583016	+	0.998299i	$0.518569\pi$
$620$	−2.44079	−0.0980246
$621$	−4.65913	−0.186964
$622$	−1.12763	−0.0452138
$623$	−11.7358	−0.470186
$624$	−1.83308	−0.0733818
$625$	22.4204	0.896815
$626$	32.1468	1.28484
$627$	−3.03644	−0.121264
$628$	−10.1538	−0.405182
$629$	−9.41849	−0.375540
$630$	−0.834322	−0.0332402
$631$	−19.2388	−0.765886	−0.382943	−	0.923772i	$-0.625089\pi$
$631$	−19.2388	−0.765886	−0.382943	+	0.923772i	$0.625089\pi$
$632$	14.6175	0.581452
$633$	−4.88020	−0.193970
$634$	−32.7066	−1.29895
$635$	6.13550	0.243480
$636$	13.6962	0.543091
$637$	7.91215	0.313491
$638$	3.85361	0.152566
$639$	6.53410	0.258485
$640$	0.417125	0.0164883
$641$	−18.2994	−0.722784	−0.361392	−	0.932414i	$-0.617698\pi$
$641$	−18.2994	−0.722784	−0.361392	+	0.932414i	$0.617698\pi$
$642$	17.1539	0.677011
$643$	−26.6054	−1.04922	−0.524608	−	0.851344i	$-0.675788\pi$
$643$	−26.6054	−1.04922	−0.524608	+	0.851344i	$0.675788\pi$
$644$	3.88487	0.153085
$645$	−4.11061	−0.161855
$646$	3.96961	0.156182
$647$	−11.7478	−0.461854	−0.230927	−	0.972971i	$-0.574176\pi$
$647$	−11.7478	−0.461854	−0.230927	+	0.972971i	$0.574176\pi$
$648$	−10.2795	−0.403817
$649$	3.57861	0.140473
$650$	−4.71862	−0.185079
$651$	−42.6182	−1.67034
$652$	−0.964643	−0.0377783
$653$	20.3330	0.795692	0.397846	−	0.917452i	$-0.369758\pi$
$653$	20.3330	0.795692	0.397846	+	0.917452i	$0.369758\pi$
$654$	1.37005	0.0535733
$655$	0.417125	0.0162984
$656$	−11.1745	−0.436293
$657$	0.670487	0.0261582
$658$	−38.7570	−1.51091
$659$	−47.3361	−1.84395	−0.921977	−	0.387244i	$-0.873427\pi$
$659$	−47.3361	−1.84395	−0.921977	+	0.387244i	$0.873427\pi$
$660$	−1.31842	−0.0513196
$661$	−33.8306	−1.31586	−0.657928	−	0.753081i	$-0.728567\pi$
$661$	−33.8306	−1.31586	−0.657928	+	0.753081i	$0.728567\pi$
$662$	−11.1917	−0.434976
$663$	−7.57449	−0.294169
$664$	2.72150	0.105615
$665$	−1.55675	−0.0603680
$666$	−1.17355	−0.0454740
$667$	−2.28577	−0.0885055
$668$	−24.8436	−0.961226
$669$	−6.80588	−0.263131
$670$	−1.52431	−0.0588892
$671$	7.51933	0.290281
$672$	7.28334	0.280961
$673$	47.3011	1.82332	0.911661	−	0.410943i	$-0.134800\pi$
$673$	47.3011	1.82332	0.911661	+	0.410943i	$0.134800\pi$
$674$	1.07863	0.0415471
$675$	−22.4850	−0.865447
$676$	−12.0440	−0.463231
$677$	8.03839	0.308940	0.154470	−	0.987997i	$-0.450633\pi$
$677$	8.03839	0.308940	0.154470	+	0.987997i	$0.450633\pi$
$678$	14.9809	0.575337
$679$	28.6216	1.09840
$680$	1.72361	0.0660973
$681$	39.6173	1.51814
$682$	−9.86506	−0.377753
$683$	32.4341	1.24106	0.620528	−	0.784185i	$-0.286918\pi$
$683$	32.4341	1.24106	0.620528	+	0.784185i	$0.286918\pi$
$684$	0.494614	0.0189120
$685$	−3.62096	−0.138350
$686$	−4.24316	−0.162005
$687$	23.3276	0.890005
$688$	5.25637	0.200397
$689$	−7.14288	−0.272122
$690$	0.782024	0.0297711
$691$	49.7318	1.89189	0.945943	−	0.324332i	$-0.105140\pi$
$691$	49.7318	1.89189	0.945943	+	0.324332i	$0.105140\pi$
$692$	16.0331	0.609486
$693$	−3.37212	−0.128096
$694$	−3.30511	−0.125460
$695$	−5.12565	−0.194427
$696$	−4.28536	−0.162436
$697$	−46.1745	−1.74898
$698$	−14.3520	−0.543229
$699$	−7.41917	−0.280619
$700$	18.7484	0.708624
$701$	−38.4135	−1.45086	−0.725429	−	0.688297i	$-0.758358\pi$
$701$	−38.4135	−1.45086	−0.725429	+	0.688297i	$0.758358\pi$
$702$	4.55545	0.171934
$703$	−2.18970	−0.0825860
$704$	1.68591	0.0635402
$705$	−7.80178	−0.293832
$706$	−31.2147	−1.17478
$707$	69.2480	2.60434
$708$	−3.97954	−0.149560
$709$	1.63620	0.0614487	0.0307244	−	0.999528i	$-0.490219\pi$
$709$	1.63620	0.0614487	0.0307244	+	0.999528i	$0.490219\pi$
$710$	5.29372	0.198670
$711$	7.52599	0.282247
$712$	3.02090	0.113213
$713$	5.85147	0.219139
$714$	30.0956	1.12630
$715$	0.687587	0.0257143
$716$	−23.3066	−0.871010
$717$	−7.56406	−0.282485
$718$	−22.0283	−0.822088
$719$	23.9734	0.894058	0.447029	−	0.894519i	$-0.352482\pi$
$719$	23.9734	0.894058	0.447029	+	0.894519i	$0.352482\pi$
$720$	0.214762	0.00800370
$721$	48.4106	1.80291
$722$	−18.0771	−0.672760
$723$	−20.0181	−0.744481
$724$	−19.0750	−0.708917
$725$	−11.0312	−0.409687
$726$	15.2940	0.567615
$727$	−1.21584	−0.0450931	−0.0225466	−	0.999746i	$-0.507177\pi$
$727$	−1.21584	−0.0450931	−0.0225466	+	0.999746i	$0.507177\pi$
$728$	−3.79842	−0.140779
$729$	20.9122	0.774527
$730$	0.543207	0.0201050
$731$	21.7199	0.803340
$732$	−8.36178	−0.309060
$733$	10.2224	0.377573	0.188787	−	0.982018i	$-0.439545\pi$
$733$	10.2224	0.377573	0.188787	+	0.982018i	$0.439545\pi$
$734$	−13.4731	−0.497303
$735$	−6.32832	−0.233423
$736$	−1.00000	−0.0368605
$737$	−6.16087	−0.226938
$738$	−5.75335	−0.211784
$739$	−22.1471	−0.814694	−0.407347	−	0.913274i	$-0.633546\pi$
$739$	−22.1471	−0.814694	−0.407347	+	0.913274i	$0.633546\pi$
$740$	−0.950769	−0.0349510
$741$	−1.76099	−0.0646915
$742$	28.3807	1.04189
$743$	19.2872	0.707579	0.353789	−	0.935325i	$-0.384893\pi$
$743$	19.2872	0.707579	0.353789	+	0.935325i	$0.384893\pi$
$744$	10.9703	0.402191
$745$	−5.40693	−0.198095
$746$	18.4113	0.674085
$747$	1.40120	0.0512672
$748$	6.96638	0.254716
$749$	35.5456	1.29881
$750$	7.68417	0.280586
$751$	−13.3178	−0.485974	−0.242987	−	0.970030i	$-0.578127\pi$
$751$	−13.3178	−0.485974	−0.242987	+	0.970030i	$0.578127\pi$
$752$	9.97639	0.363802
$753$	12.5460	0.457202
$754$	2.23491	0.0813906
$755$	−0.732159	−0.0266460
$756$	−18.1001	−0.658295
$757$	−1.31555	−0.0478144	−0.0239072	−	0.999714i	$-0.507611\pi$
$757$	−1.31555	−0.0478144	−0.0239072	+	0.999714i	$0.507611\pi$
$758$	−19.0499	−0.691925
$759$	3.16074	0.114728
$760$	0.400720	0.0145356
$761$	−2.03186	−0.0736549	−0.0368274	−	0.999322i	$-0.511725\pi$
$761$	−2.03186	−0.0736549	−0.0368274	+	0.999322i	$0.511725\pi$
$762$	−27.5765	−0.998990
$763$	2.83896	0.102777
$764$	9.70689	0.351183
$765$	0.887421	0.0320848
$766$	−35.7824	−1.29287
$767$	2.07542	0.0749390
$768$	−1.87480	−0.0676509
$769$	−8.86428	−0.319654	−0.159827	−	0.987145i	$-0.551094\pi$
$769$	−8.86428	−0.319654	−0.159827	+	0.987145i	$0.551094\pi$
$770$	−2.73198	−0.0984537
$771$	−10.6595	−0.383893
$772$	−13.3085	−0.478982
$773$	−6.74544	−0.242617	−0.121308	−	0.992615i	$-0.538709\pi$
$773$	−6.74544	−0.242617	−0.121308	+	0.992615i	$0.538709\pi$
$774$	2.70631	0.0972762
$775$	28.2392	1.01438
$776$	−7.36745	−0.264476
$777$	−16.6012	−0.595565
$778$	−18.6973	−0.670331
$779$	−10.7351	−0.384624
$780$	−0.764622	−0.0273779
$781$	21.3959	0.765604
$782$	−4.13211	−0.147764
$783$	10.6497	0.380589
$784$	8.09223	0.289008
$785$	−4.23542	−0.151169
$786$	−1.87480	−0.0668718
$787$	44.2476	1.57726	0.788628	−	0.614870i	$-0.210792\pi$
$787$	44.2476	1.57726	0.788628	+	0.614870i	$0.210792\pi$
$788$	−17.0979	−0.609089
$789$	−24.3630	−0.867345
$790$	6.09731	0.216933
$791$	31.0427	1.10375
$792$	0.868013	0.0308435
$793$	4.36085	0.154858
$794$	31.3086	1.11110
$795$	5.71303	0.202620
$796$	13.2891	0.471021
$797$	29.9607	1.06126	0.530632	−	0.847602i	$-0.321955\pi$
$797$	29.9607	1.06126	0.530632	+	0.847602i	$0.321955\pi$
$798$	6.99691	0.247688
$799$	41.2236	1.45839
$800$	−4.82601	−0.170625
$801$	1.55535	0.0549555
$802$	9.39248	0.331660
$803$	2.19550	0.0774777
$804$	6.85111	0.241620
$805$	1.62048	0.0571143
$806$	−5.72126	−0.201523
$807$	15.5596	0.547725
$808$	−17.8251	−0.627083
$809$	7.10327	0.249738	0.124869	−	0.992173i	$-0.460149\pi$
$809$	7.10327	0.249738	0.124869	+	0.992173i	$0.460149\pi$
$810$	−4.28784	−0.150659
$811$	−6.21259	−0.218153	−0.109077	−	0.994033i	$-0.534789\pi$
$811$	−6.21259	−0.218153	−0.109077	+	0.994033i	$0.534789\pi$
$812$	−8.87993	−0.311625
$813$	4.22973	0.148343
$814$	−3.84276	−0.134689
$815$	−0.402377	−0.0140946
$816$	−7.74687	−0.271195
$817$	5.04965	0.176665
$818$	36.0745	1.26132
$819$	−1.95567	−0.0683365
$820$	−4.66118	−0.162775
$821$	24.7755	0.864669	0.432335	−	0.901713i	$-0.357690\pi$
$821$	24.7755	0.864669	0.432335	+	0.901713i	$0.357690\pi$
$822$	16.2746	0.567644
$823$	−38.1392	−1.32945	−0.664724	−	0.747089i	$-0.731451\pi$
$823$	−38.1392	−1.32945	−0.664724	+	0.747089i	$0.731451\pi$
$824$	−12.4613	−0.434111
$825$	15.2538	0.531068
$826$	−8.24623	−0.286923
$827$	−32.3481	−1.12485	−0.562427	−	0.826847i	$-0.690132\pi$
$827$	−32.3481	−1.12485	−0.562427	+	0.826847i	$0.690132\pi$
$828$	−0.514862	−0.0178927
$829$	−7.38566	−0.256515	−0.128257	−	0.991741i	$-0.540938\pi$
$829$	−7.38566	−0.256515	−0.128257	+	0.991741i	$0.540938\pi$
$830$	1.13521	0.0394036
$831$	−54.5980	−1.89398
$832$	0.977747	0.0338973
$833$	33.4380	1.15856
$834$	23.0376	0.797726
$835$	−10.3629	−0.358622
$836$	1.61961	0.0560153
$837$	−27.2627	−0.942338
$838$	26.0297	0.899181
$839$	−25.2978	−0.873379	−0.436689	−	0.899612i	$-0.643849\pi$
$839$	−25.2978	−0.873379	−0.436689	+	0.899612i	$0.643849\pi$
$840$	3.03806	0.104823
$841$	−23.7752	−0.819836
$842$	6.92411	0.238621
$843$	31.8298	1.09628
$844$	2.60305	0.0896008
$845$	−5.02385	−0.172826
$846$	5.13647	0.176595
$847$	31.6916	1.08894
$848$	−7.30545	−0.250870
$849$	4.00205	0.137350
$850$	−19.9416	−0.683992
$851$	2.27934	0.0781347
$852$	−23.7930	−0.815134
$853$	−23.0071	−0.787749	−0.393875	−	0.919164i	$-0.628866\pi$
$853$	−23.0071	−0.787749	−0.393875	+	0.919164i	$0.628866\pi$
$854$	−17.3269	−0.592915
$855$	0.206316	0.00705585
$856$	−9.14975	−0.312732
$857$	7.07329	0.241619	0.120809	−	0.992676i	$-0.461451\pi$
$857$	7.07329	0.241619	0.120809	+	0.992676i	$0.461451\pi$
$858$	−3.09041	−0.105505
$859$	24.0269	0.819788	0.409894	−	0.912133i	$-0.365566\pi$
$859$	24.0269	0.819788	0.409894	+	0.912133i	$0.365566\pi$
$860$	2.19256	0.0747657
$861$	−81.3880	−2.77370
$862$	24.4652	0.833289
$863$	25.1840	0.857274	0.428637	−	0.903477i	$-0.358994\pi$
$863$	25.1840	0.857274	0.428637	+	0.903477i	$0.358994\pi$
$864$	4.65913	0.158507
$865$	6.68780	0.227392
$866$	−33.9020	−1.15204
$867$	−0.139434	−0.00473541
$868$	22.7322	0.771581
$869$	24.6438	0.835983
$870$	−1.78753	−0.0606029
$871$	−3.57300	−0.121067
$872$	−0.730774	−0.0247471
$873$	−3.79322	−0.128381
$874$	−0.960672	−0.0324952
$875$	15.9228	0.538289
$876$	−2.44148	−0.0824900
$877$	5.28800	0.178563	0.0892815	−	0.996006i	$-0.471543\pi$
$877$	5.28800	0.178563	0.0892815	+	0.996006i	$0.471543\pi$
$878$	−29.6623	−1.00105
$879$	−24.5363	−0.827590
$880$	0.703236	0.0237061
$881$	−46.6569	−1.57191	−0.785956	−	0.618282i	$-0.787829\pi$
$881$	−46.6569	−1.57191	−0.785956	+	0.618282i	$0.787829\pi$
$882$	4.16638	0.140289
$883$	45.7308	1.53896	0.769482	−	0.638669i	$-0.220515\pi$
$883$	45.7308	1.53896	0.769482	+	0.638669i	$0.220515\pi$
$884$	4.04016	0.135885
$885$	−1.65997	−0.0557991
$886$	−9.71238	−0.326294
$887$	−38.7344	−1.30057	−0.650287	−	0.759688i	$-0.725352\pi$
$887$	−38.7344	−1.30057	−0.650287	+	0.759688i	$0.725352\pi$
$888$	4.27330	0.143402
$889$	−57.1427	−1.91651
$890$	1.26009	0.0422384
$891$	−17.3303	−0.580588
$892$	3.63020	0.121548
$893$	9.58404	0.320718
$894$	24.3018	0.812775
$895$	−9.72178	−0.324963
$896$	−3.88487	−0.129784
$897$	1.83308	0.0612047
$898$	19.8899	0.663735
$899$	−13.3751	−0.446085
$900$	−2.48473	−0.0828243
$901$	−30.1869	−1.00567
$902$	−18.8393	−0.627280
$903$	38.2839	1.27401
$904$	−7.99067	−0.265766
$905$	−7.95665	−0.264488
$906$	3.29074	0.109328
$907$	−7.20642	−0.239285	−0.119643	−	0.992817i	$-0.538175\pi$
$907$	−7.20642	−0.239285	−0.119643	+	0.992817i	$0.538175\pi$
$908$	−21.1315	−0.701274
$909$	−9.17745	−0.304397
$910$	−1.58442	−0.0525229
$911$	−34.1436	−1.13123	−0.565614	−	0.824670i	$-0.691361\pi$
$911$	−34.1436	−1.13123	−0.565614	+	0.824670i	$0.691361\pi$
$912$	−1.80107	−0.0596392
$913$	4.58822	0.151848
$914$	−17.0791	−0.564928
$915$	−3.48790	−0.115307
$916$	−12.4428	−0.411120
$917$	−3.88487	−0.128290
$918$	19.2521	0.635412
$919$	−21.0377	−0.693968	−0.346984	−	0.937871i	$-0.612794\pi$
$919$	−21.0377	−0.693968	−0.346984	+	0.937871i	$0.612794\pi$
$920$	−0.417125	−0.0137522
$921$	−18.3768	−0.605537
$922$	−5.49174	−0.180861
$923$	12.4086	0.408433
$924$	12.2791	0.403952
$925$	11.0001	0.361681
$926$	−33.2142	−1.09149
$927$	−6.41587	−0.210725
$928$	2.28577	0.0750342
$929$	48.5099	1.59156	0.795780	−	0.605586i	$-0.207061\pi$
$929$	48.5099	1.59156	0.795780	+	0.605586i	$0.207061\pi$
$930$	4.57599	0.150053
$931$	7.77398	0.254782
$932$	3.95732	0.129626
$933$	2.11407	0.0692117
$934$	22.6811	0.742147
$935$	2.90585	0.0950315
$936$	0.503405	0.0164543
$937$	57.5722	1.88080	0.940402	−	0.340066i	$-0.110449\pi$
$937$	57.5722	1.88080	0.940402	+	0.340066i	$0.110449\pi$
$938$	14.1966	0.463535
$939$	−60.2687	−1.96680
$940$	4.16140	0.135730
$941$	−52.8017	−1.72129	−0.860643	−	0.509208i	$-0.829938\pi$
$941$	−52.8017	−1.72129	−0.860643	+	0.509208i	$0.829938\pi$
$942$	19.0364	0.620239
$943$	11.1745	0.363893
$944$	2.12265	0.0690865
$945$	−7.55001	−0.245602
$946$	8.86177	0.288121
$947$	−45.4444	−1.47674	−0.738372	−	0.674394i	$-0.764405\pi$
$947$	−45.4444	−1.47674	−0.738372	+	0.674394i	$0.764405\pi$
$948$	−27.4048	−0.890067
$949$	1.27329	0.0413326
$950$	−4.63621	−0.150419
$951$	61.3182	1.98838
$952$	−16.0527	−0.520272
$953$	−41.4845	−1.34381	−0.671907	−	0.740635i	$-0.734525\pi$
$953$	−41.4845	−1.34381	−0.671907	+	0.740635i	$0.734525\pi$
$954$	−3.76130	−0.121777
$955$	4.04898	0.131022
$956$	4.03460	0.130488
$957$	−7.22474	−0.233543
$958$	31.5210	1.01840
$959$	33.7236	1.08899
$960$	−0.782024	−0.0252397
$961$	3.23966	0.104505
$962$	−2.22862	−0.0718535
$963$	−4.71086	−0.151805
$964$	10.6775	0.343898
$965$	−5.55128	−0.178702
$966$	−7.28334	−0.234338
$967$	4.12333	0.132597	0.0662987	−	0.997800i	$-0.478881\pi$
$967$	4.12333	0.132597	0.0662987	+	0.997800i	$0.478881\pi$
$968$	−8.15770	−0.262198
$969$	−7.44221	−0.239078
$970$	−3.07315	−0.0986728
$971$	−53.6877	−1.72292	−0.861461	−	0.507824i	$-0.830450\pi$
$971$	−53.6877	−1.72292	−0.861461	+	0.507824i	$0.830450\pi$
$972$	5.29460	0.169824
$973$	47.7375	1.53039
$974$	−19.0074	−0.609038
$975$	8.84645	0.283313
$976$	4.46010	0.142764
$977$	36.0983	1.15489	0.577444	−	0.816430i	$-0.304050\pi$
$977$	36.0983	1.15489	0.577444	+	0.816430i	$0.304050\pi$
$978$	1.80851	0.0578298
$979$	5.09297	0.162772
$980$	3.37547	0.107825
$981$	−0.376248	−0.0120127
$982$	7.30630	0.233153
$983$	24.5344	0.782525	0.391262	−	0.920279i	$-0.372038\pi$
$983$	24.5344	0.782525	0.391262	+	0.920279i	$0.372038\pi$
$984$	20.9500	0.667861
$985$	−7.13197	−0.227244
$986$	9.44507	0.300792
$987$	72.6615	2.31284
$988$	0.939295	0.0298830
$989$	−5.25637	−0.167143
$990$	0.362070	0.0115073
$991$	−31.5850	−1.00333	−0.501665	−	0.865062i	$-0.667279\pi$
$991$	−31.5850	−1.00333	−0.501665	+	0.865062i	$0.667279\pi$
$992$	−5.85147	−0.185784
$993$	20.9821	0.665847
$994$	−49.3028	−1.56379
$995$	5.54323	0.175732
$996$	−5.10227	−0.161672
$997$	−14.6108	−0.462727	−0.231364	−	0.972867i	$-0.574319\pi$
$997$	−14.6108	−0.462727	−0.231364	+	0.972867i	$0.574319\pi$
$998$	−17.9443	−0.568018
$999$	−10.6197	−0.335993

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.g.1.4	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.g.1.4	✓	21	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.87480 q^{3} +1.00000 q^{4} +0.417125 q^{5} -1.87480 q^{6} -3.88487 q^{7} +1.00000 q^{8} +0.514862 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.87480 q^{3} +1.00000 q^{4} +0.417125 q^{5} -1.87480 q^{6} -3.88487 q^{7} +1.00000 q^{8} +0.514862 q^{9} +0.417125 q^{10} +1.68591 q^{11} -1.87480 q^{12} +0.977747 q^{13} -3.88487 q^{14} -0.782024 q^{15} +1.00000 q^{16} +4.13211 q^{17} +0.514862 q^{18} +0.960672 q^{19} +0.417125 q^{20} +7.28334 q^{21} +1.68591 q^{22} -1.00000 q^{23} -1.87480 q^{24} -4.82601 q^{25} +0.977747 q^{26} +4.65913 q^{27} -3.88487 q^{28} +2.28577 q^{29} -0.782024 q^{30} -5.85147 q^{31} +1.00000 q^{32} -3.16074 q^{33} +4.13211 q^{34} -1.62048 q^{35} +0.514862 q^{36} -2.27934 q^{37} +0.960672 q^{38} -1.83308 q^{39} +0.417125 q^{40} -11.1745 q^{41} +7.28334 q^{42} +5.25637 q^{43} +1.68591 q^{44} +0.214762 q^{45} -1.00000 q^{46} +9.97639 q^{47} -1.87480 q^{48} +8.09223 q^{49} -4.82601 q^{50} -7.74687 q^{51} +0.977747 q^{52} -7.30545 q^{53} +4.65913 q^{54} +0.703236 q^{55} -3.88487 q^{56} -1.80107 q^{57} +2.28577 q^{58} +2.12265 q^{59} -0.782024 q^{60} +4.46010 q^{61} -5.85147 q^{62} -2.00017 q^{63} +1.00000 q^{64} +0.407843 q^{65} -3.16074 q^{66} -3.65432 q^{67} +4.13211 q^{68} +1.87480 q^{69} -1.62048 q^{70} +12.6910 q^{71} +0.514862 q^{72} +1.30227 q^{73} -2.27934 q^{74} +9.04778 q^{75} +0.960672 q^{76} -6.54955 q^{77} -1.83308 q^{78} +14.6175 q^{79} +0.417125 q^{80} -10.2795 q^{81} -11.1745 q^{82} +2.72150 q^{83} +7.28334 q^{84} +1.72361 q^{85} +5.25637 q^{86} -4.28536 q^{87} +1.68591 q^{88} +3.02090 q^{89} +0.214762 q^{90} -3.79842 q^{91} -1.00000 q^{92} +10.9703 q^{93} +9.97639 q^{94} +0.400720 q^{95} -1.87480 q^{96} -7.36745 q^{97} +8.09223 q^{98} +0.868013 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * q^99

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