LMFDB - Embedded newform 6026.2.a.h.1.10

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:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.785811 q^{3} +1.00000 q^{4} -1.42219 q^{5} +0.785811 q^{6} +3.87369 q^{7} -1.00000 q^{8} -2.38250 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.785811 q^{3} +1.00000 q^{4} -1.42219 q^{5} +0.785811 q^{6} +3.87369 q^{7} -1.00000 q^{8} -2.38250 q^{9} +1.42219 q^{10} +4.24761 q^{11} -0.785811 q^{12} +2.46631 q^{13} -3.87369 q^{14} +1.11757 q^{15} +1.00000 q^{16} +1.55090 q^{17} +2.38250 q^{18} -2.53414 q^{19} -1.42219 q^{20} -3.04399 q^{21} -4.24761 q^{22} -1.00000 q^{23} +0.785811 q^{24} -2.97737 q^{25} -2.46631 q^{26} +4.22963 q^{27} +3.87369 q^{28} +4.09137 q^{29} -1.11757 q^{30} -7.27950 q^{31} -1.00000 q^{32} -3.33782 q^{33} -1.55090 q^{34} -5.50912 q^{35} -2.38250 q^{36} -5.04022 q^{37} +2.53414 q^{38} -1.93805 q^{39} +1.42219 q^{40} -6.34949 q^{41} +3.04399 q^{42} -9.30138 q^{43} +4.24761 q^{44} +3.38837 q^{45} +1.00000 q^{46} -5.01571 q^{47} -0.785811 q^{48} +8.00545 q^{49} +2.97737 q^{50} -1.21871 q^{51} +2.46631 q^{52} -6.61052 q^{53} -4.22963 q^{54} -6.04091 q^{55} -3.87369 q^{56} +1.99135 q^{57} -4.09137 q^{58} -1.17415 q^{59} +1.11757 q^{60} +6.46185 q^{61} +7.27950 q^{62} -9.22906 q^{63} +1.00000 q^{64} -3.50756 q^{65} +3.33782 q^{66} +9.88156 q^{67} +1.55090 q^{68} +0.785811 q^{69} +5.50912 q^{70} +6.27474 q^{71} +2.38250 q^{72} -13.0599 q^{73} +5.04022 q^{74} +2.33965 q^{75} -2.53414 q^{76} +16.4539 q^{77} +1.93805 q^{78} -8.91977 q^{79} -1.42219 q^{80} +3.82381 q^{81} +6.34949 q^{82} +14.1085 q^{83} -3.04399 q^{84} -2.20568 q^{85} +9.30138 q^{86} -3.21504 q^{87} -4.24761 q^{88} -11.5983 q^{89} -3.38837 q^{90} +9.55371 q^{91} -1.00000 q^{92} +5.72031 q^{93} +5.01571 q^{94} +3.60403 q^{95} +0.785811 q^{96} -14.5136 q^{97} -8.00545 q^{98} -10.1199 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * 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
$3$	−0.785811	−0.453688	−0.226844	−	0.973931i	$-0.572841\pi$
$3$	−0.785811	−0.453688	−0.226844	+	0.973931i	$0.572841\pi$
$4$	1.00000	0.500000
$5$	−1.42219	−0.636023	−0.318011	−	0.948087i	$-0.603015\pi$
$5$	−1.42219	−0.636023	−0.318011	+	0.948087i	$0.603015\pi$
$6$	0.785811	0.320806
$7$	3.87369	1.46412	0.732058	−	0.681242i	$-0.238560\pi$
$7$	3.87369	1.46412	0.732058	+	0.681242i	$0.238560\pi$
$8$	−1.00000	−0.353553
$9$	−2.38250	−0.794167
$10$	1.42219	0.449736
$11$	4.24761	1.28070	0.640351	−	0.768082i	$-0.278789\pi$
$11$	4.24761	1.28070	0.640351	+	0.768082i	$0.278789\pi$
$12$	−0.785811	−0.226844
$13$	2.46631	0.684031	0.342016	−	0.939694i	$-0.388890\pi$
$13$	2.46631	0.684031	0.342016	+	0.939694i	$0.388890\pi$
$14$	−3.87369	−1.03529
$15$	1.11757	0.288556
$16$	1.00000	0.250000
$17$	1.55090	0.376149	0.188074	−	0.982155i	$-0.439775\pi$
$17$	1.55090	0.376149	0.188074	+	0.982155i	$0.439775\pi$
$18$	2.38250	0.561561
$19$	−2.53414	−0.581371	−0.290686	−	0.956819i	$-0.593883\pi$
$19$	−2.53414	−0.581371	−0.290686	+	0.956819i	$0.593883\pi$
$20$	−1.42219	−0.318011
$21$	−3.04399	−0.664252
$22$	−4.24761	−0.905593
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.785811	0.160403
$25$	−2.97737	−0.595475
$26$	−2.46631	−0.483683
$27$	4.22963	0.813993
$28$	3.87369	0.732058
$29$	4.09137	0.759748	0.379874	−	0.925038i	$-0.375967\pi$
$29$	4.09137	0.759748	0.379874	+	0.925038i	$0.375967\pi$
$30$	−1.11757	−0.204040
$31$	−7.27950	−1.30744	−0.653719	−	0.756738i	$-0.726792\pi$
$31$	−7.27950	−1.30744	−0.653719	+	0.756738i	$0.726792\pi$
$32$	−1.00000	−0.176777
$33$	−3.33782	−0.581040
$34$	−1.55090	−0.265977
$35$	−5.50912	−0.931211
$36$	−2.38250	−0.397083
$37$	−5.04022	−0.828606	−0.414303	−	0.910139i	$-0.635975\pi$
$37$	−5.04022	−0.828606	−0.414303	+	0.910139i	$0.635975\pi$
$38$	2.53414	0.411092
$39$	−1.93805	−0.310337
$40$	1.42219	0.224868
$41$	−6.34949	−0.991624	−0.495812	−	0.868430i	$-0.665129\pi$
$41$	−6.34949	−0.991624	−0.495812	+	0.868430i	$0.665129\pi$
$42$	3.04399	0.469697
$43$	−9.30138	−1.41845	−0.709223	−	0.704984i	$-0.750954\pi$
$43$	−9.30138	−1.41845	−0.709223	+	0.704984i	$0.750954\pi$
$44$	4.24761	0.640351
$45$	3.38837	0.505108
$46$	1.00000	0.147442
$47$	−5.01571	−0.731617	−0.365808	−	0.930690i	$-0.619207\pi$
$47$	−5.01571	−0.731617	−0.365808	+	0.930690i	$0.619207\pi$
$48$	−0.785811	−0.113422
$49$	8.00545	1.14364
$50$	2.97737	0.421064
$51$	−1.21871	−0.170654
$52$	2.46631	0.342016
$53$	−6.61052	−0.908025	−0.454013	−	0.890995i	$-0.650008\pi$
$53$	−6.61052	−0.908025	−0.454013	+	0.890995i	$0.650008\pi$
$54$	−4.22963	−0.575580
$55$	−6.04091	−0.814556
$56$	−3.87369	−0.517643
$57$	1.99135	0.263761
$58$	−4.09137	−0.537223
$59$	−1.17415	−0.152861	−0.0764306	−	0.997075i	$-0.524352\pi$
$59$	−1.17415	−0.152861	−0.0764306	+	0.997075i	$0.524352\pi$
$60$	1.11757	0.144278
$61$	6.46185	0.827355	0.413677	−	0.910424i	$-0.364244\pi$
$61$	6.46185	0.827355	0.413677	+	0.910424i	$0.364244\pi$
$62$	7.27950	0.924498
$63$	−9.22906	−1.16275
$64$	1.00000	0.125000
$65$	−3.50756	−0.435060
$66$	3.33782	0.410857
$67$	9.88156	1.20723	0.603613	−	0.797278i	$-0.293727\pi$
$67$	9.88156	1.20723	0.603613	+	0.797278i	$0.293727\pi$
$68$	1.55090	0.188074
$69$	0.785811	0.0946006
$70$	5.50912	0.658466
$71$	6.27474	0.744674	0.372337	−	0.928098i	$-0.378557\pi$
$71$	6.27474	0.744674	0.372337	+	0.928098i	$0.378557\pi$
$72$	2.38250	0.280780
$73$	−13.0599	−1.52854	−0.764271	−	0.644895i	$-0.776901\pi$
$73$	−13.0599	−1.52854	−0.764271	+	0.644895i	$0.776901\pi$
$74$	5.04022	0.585913
$75$	2.33965	0.270160
$76$	−2.53414	−0.290686
$77$	16.4539	1.87510
$78$	1.93805	0.219441
$79$	−8.91977	−1.00355	−0.501776	−	0.864998i	$-0.667320\pi$
$79$	−8.91977	−1.00355	−0.501776	+	0.864998i	$0.667320\pi$
$80$	−1.42219	−0.159006
$81$	3.82381	0.424868
$82$	6.34949	0.701184
$83$	14.1085	1.54861	0.774307	−	0.632810i	$-0.218099\pi$
$83$	14.1085	1.54861	0.774307	+	0.632810i	$0.218099\pi$
$84$	−3.04399	−0.332126
$85$	−2.20568	−0.239239
$86$	9.30138	1.00299
$87$	−3.21504	−0.344689
$88$	−4.24761	−0.452797
$89$	−11.5983	−1.22941	−0.614706	−	0.788756i	$-0.710725\pi$
$89$	−11.5983	−1.22941	−0.614706	+	0.788756i	$0.710725\pi$
$90$	−3.38837	−0.357166
$91$	9.55371	1.00150
$92$	−1.00000	−0.104257
$93$	5.72031	0.593169
$94$	5.01571	0.517331
$95$	3.60403	0.369765
$96$	0.785811	0.0802015
$97$	−14.5136	−1.47363	−0.736817	−	0.676092i	$-0.763672\pi$
$97$	−14.5136	−1.47363	−0.736817	+	0.676092i	$0.763672\pi$
$98$	−8.00545	−0.808673
$99$	−10.1199	−1.01709
$100$	−2.97737	−0.297737
$101$	−1.16747	−0.116168	−0.0580840	−	0.998312i	$-0.518499\pi$
$101$	−1.16747	−0.116168	−0.0580840	+	0.998312i	$0.518499\pi$
$102$	1.21871	0.120671
$103$	−3.01876	−0.297447	−0.148724	−	0.988879i	$-0.547516\pi$
$103$	−3.01876	−0.297447	−0.148724	+	0.988879i	$0.547516\pi$
$104$	−2.46631	−0.241842
$105$	4.32913	0.422480
$106$	6.61052	0.642071
$107$	−7.17272	−0.693413	−0.346706	−	0.937974i	$-0.612700\pi$
$107$	−7.17272	−0.693413	−0.346706	+	0.937974i	$0.612700\pi$
$108$	4.22963	0.406996
$109$	−3.99600	−0.382747	−0.191373	−	0.981517i	$-0.561294\pi$
$109$	−3.99600	−0.382747	−0.191373	+	0.981517i	$0.561294\pi$
$110$	6.04091	0.575978
$111$	3.96066	0.375929
$112$	3.87369	0.366029
$113$	13.6826	1.28715	0.643574	−	0.765384i	$-0.277451\pi$
$113$	13.6826	1.28715	0.643574	+	0.765384i	$0.277451\pi$
$114$	−1.99135	−0.186507
$115$	1.42219	0.132620
$116$	4.09137	0.379874
$117$	−5.87599	−0.543235
$118$	1.17415	0.108089
$119$	6.00770	0.550725
$120$	−1.11757	−0.102020
$121$	7.04218	0.640199
$122$	−6.46185	−0.585028
$123$	4.98950	0.449888
$124$	−7.27950	−0.653719
$125$	11.3453	1.01476
$126$	9.22906	0.822190
$127$	14.2216	1.26197	0.630983	−	0.775797i	$-0.282652\pi$
$127$	14.2216	1.26197	0.630983	+	0.775797i	$0.282652\pi$
$128$	−1.00000	−0.0883883
$129$	7.30913	0.643533
$130$	3.50756	0.307634
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−3.33782	−0.290520
$133$	−9.81646	−0.851195
$134$	−9.88156	−0.853637
$135$	−6.01534	−0.517718
$136$	−1.55090	−0.132989
$137$	−16.5255	−1.41187	−0.705935	−	0.708277i	$-0.749473\pi$
$137$	−16.5255	−1.41187	−0.705935	+	0.708277i	$0.749473\pi$
$138$	−0.785811	−0.0668927
$139$	8.60490	0.729858	0.364929	−	0.931035i	$-0.381093\pi$
$139$	8.60490	0.729858	0.364929	+	0.931035i	$0.381093\pi$
$140$	−5.50912	−0.465606
$141$	3.94140	0.331926
$142$	−6.27474	−0.526564
$143$	10.4759	0.876041
$144$	−2.38250	−0.198542
$145$	−5.81870	−0.483217
$146$	13.0599	1.08084
$147$	−6.29078	−0.518854
$148$	−5.04022	−0.414303
$149$	−15.3186	−1.25495	−0.627475	−	0.778637i	$-0.715911\pi$
$149$	−15.3186	−1.25495	−0.627475	+	0.778637i	$0.715911\pi$
$150$	−2.33965	−0.191032
$151$	−13.1238	−1.06800	−0.534001	−	0.845484i	$-0.679312\pi$
$151$	−13.1238	−1.06800	−0.534001	+	0.845484i	$0.679312\pi$
$152$	2.53414	0.205546
$153$	−3.69502	−0.298725
$154$	−16.4539	−1.32589
$155$	10.3528	0.831560
$156$	−1.93805	−0.155169
$157$	−0.761128	−0.0607446	−0.0303723	−	0.999539i	$-0.509669\pi$
$157$	−0.761128	−0.0607446	−0.0303723	+	0.999539i	$0.509669\pi$
$158$	8.91977	0.709618
$159$	5.19462	0.411960
$160$	1.42219	0.112434
$161$	−3.87369	−0.305289
$162$	−3.82381	−0.300427
$163$	19.8011	1.55094	0.775470	−	0.631384i	$-0.217513\pi$
$163$	19.8011	1.55094	0.775470	+	0.631384i	$0.217513\pi$
$164$	−6.34949	−0.495812
$165$	4.74701	0.369555
$166$	−14.1085	−1.09504
$167$	4.08020	0.315735	0.157868	−	0.987460i	$-0.449538\pi$
$167$	4.08020	0.315735	0.157868	+	0.987460i	$0.449538\pi$
$168$	3.04399	0.234849
$169$	−6.91731	−0.532101
$170$	2.20568	0.169168
$171$	6.03759	0.461706
$172$	−9.30138	−0.709223
$173$	2.46367	0.187309	0.0936545	−	0.995605i	$-0.470145\pi$
$173$	2.46367	0.187309	0.0936545	+	0.995605i	$0.470145\pi$
$174$	3.21504	0.243732
$175$	−11.5334	−0.871845
$176$	4.24761	0.320176
$177$	0.922660	0.0693513
$178$	11.5983	0.869326
$179$	10.7958	0.806916	0.403458	−	0.914998i	$-0.367808\pi$
$179$	10.7958	0.806916	0.403458	+	0.914998i	$0.367808\pi$
$180$	3.38837	0.252554
$181$	9.47637	0.704373	0.352187	−	0.935930i	$-0.385438\pi$
$181$	9.47637	0.704373	0.352187	+	0.935930i	$0.385438\pi$
$182$	−9.55371	−0.708168
$183$	−5.07779	−0.375361
$184$	1.00000	0.0737210
$185$	7.16815	0.527013
$186$	−5.72031	−0.419434
$187$	6.58762	0.481734
$188$	−5.01571	−0.365808
$189$	16.3843	1.19178
$190$	−3.60403	−0.261464
$191$	6.80800	0.492610	0.246305	−	0.969192i	$-0.420784\pi$
$191$	6.80800	0.492610	0.246305	+	0.969192i	$0.420784\pi$
$192$	−0.785811	−0.0567110
$193$	−14.7284	−1.06018	−0.530088	−	0.847943i	$-0.677841\pi$
$193$	−14.7284	−1.06018	−0.530088	+	0.847943i	$0.677841\pi$
$194$	14.5136	1.04202
$195$	2.75628	0.197381
$196$	8.00545	0.571818
$197$	−13.0172	−0.927438	−0.463719	−	0.885982i	$-0.653485\pi$
$197$	−13.0172	−0.927438	−0.463719	+	0.885982i	$0.653485\pi$
$198$	10.1199	0.719192
$199$	16.5962	1.17647	0.588236	−	0.808690i	$-0.299823\pi$
$199$	16.5962	1.17647	0.588236	+	0.808690i	$0.299823\pi$
$200$	2.97737	0.210532
$201$	−7.76504	−0.547704
$202$	1.16747	0.0821432
$203$	15.8487	1.11236
$204$	−1.21871	−0.0853271
$205$	9.03018	0.630695
$206$	3.01876	0.210327
$207$	2.38250	0.165595
$208$	2.46631	0.171008
$209$	−10.7640	−0.744564
$210$	−4.32913	−0.298738
$211$	−4.82200	−0.331960	−0.165980	−	0.986129i	$-0.553079\pi$
$211$	−4.82200	−0.331960	−0.165980	+	0.986129i	$0.553079\pi$
$212$	−6.61052	−0.454013
$213$	−4.93076	−0.337850
$214$	7.17272	0.490317
$215$	13.2283	0.902165
$216$	−4.22963	−0.287790
$217$	−28.1985	−1.91424
$218$	3.99600	0.270643
$219$	10.2626	0.693482
$220$	−6.04091	−0.407278
$221$	3.82500	0.257297
$222$	−3.96066	−0.265822
$223$	−23.8010	−1.59383	−0.796915	−	0.604091i	$-0.793536\pi$
$223$	−23.8010	−1.59383	−0.796915	+	0.604091i	$0.793536\pi$
$224$	−3.87369	−0.258822
$225$	7.09360	0.472906
$226$	−13.6826	−0.910151
$227$	−6.05338	−0.401777	−0.200889	−	0.979614i	$-0.564383\pi$
$227$	−6.05338	−0.401777	−0.200889	+	0.979614i	$0.564383\pi$
$228$	1.99135	0.131881
$229$	−25.9038	−1.71177	−0.855885	−	0.517167i	$-0.826987\pi$
$229$	−25.9038	−1.71177	−0.855885	+	0.517167i	$0.826987\pi$
$230$	−1.42219	−0.0937765
$231$	−12.9297	−0.850710
$232$	−4.09137	−0.268611
$233$	10.7270	0.702746	0.351373	−	0.936236i	$-0.385715\pi$
$233$	10.7270	0.702746	0.351373	+	0.936236i	$0.385715\pi$
$234$	5.87599	0.384125
$235$	7.13330	0.465325
$236$	−1.17415	−0.0764306
$237$	7.00925	0.455300
$238$	−6.00770	−0.389422
$239$	−24.0030	−1.55263	−0.776314	−	0.630347i	$-0.782913\pi$
$239$	−24.0030	−1.55263	−0.776314	+	0.630347i	$0.782913\pi$
$240$	1.11757	0.0721390
$241$	6.77771	0.436591	0.218295	−	0.975883i	$-0.429950\pi$
$241$	6.77771	0.436591	0.218295	+	0.975883i	$0.429950\pi$
$242$	−7.04218	−0.452689
$243$	−15.6937	−1.00675
$244$	6.46185	0.413677
$245$	−11.3853	−0.727379
$246$	−4.98950	−0.318119
$247$	−6.24997	−0.397676
$248$	7.27950	0.462249
$249$	−11.0867	−0.702588
$250$	−11.3453	−0.717543
$251$	11.3933	0.719136	0.359568	−	0.933119i	$-0.382924\pi$
$251$	11.3933	0.719136	0.359568	+	0.933119i	$0.382924\pi$
$252$	−9.22906	−0.581376
$253$	−4.24761	−0.267045
$254$	−14.2216	−0.892345
$255$	1.73324	0.108540
$256$	1.00000	0.0625000
$257$	9.94455	0.620324	0.310162	−	0.950684i	$-0.399617\pi$
$257$	9.94455	0.620324	0.310162	+	0.950684i	$0.399617\pi$
$258$	−7.30913	−0.455046
$259$	−19.5242	−1.21318
$260$	−3.50756	−0.217530
$261$	−9.74768	−0.603366
$262$	1.00000	0.0617802
$263$	9.89205	0.609970	0.304985	−	0.952357i	$-0.401349\pi$
$263$	9.89205	0.609970	0.304985	+	0.952357i	$0.401349\pi$
$264$	3.33782	0.205429
$265$	9.40142	0.577525
$266$	9.81646	0.601886
$267$	9.11404	0.557770
$268$	9.88156	0.603613
$269$	4.93260	0.300746	0.150373	−	0.988629i	$-0.451953\pi$
$269$	4.93260	0.300746	0.150373	+	0.988629i	$0.451953\pi$
$270$	6.01534	0.366082
$271$	28.7211	1.74468	0.872342	−	0.488895i	$-0.162600\pi$
$271$	28.7211	1.74468	0.872342	+	0.488895i	$0.162600\pi$
$272$	1.55090	0.0940371
$273$	−7.50742	−0.454370
$274$	16.5255	0.998343
$275$	−12.6467	−0.762626
$276$	0.785811	0.0473003
$277$	−25.9935	−1.56180	−0.780898	−	0.624658i	$-0.785238\pi$
$277$	−25.9935	−1.56180	−0.780898	+	0.624658i	$0.785238\pi$
$278$	−8.60490	−0.516088
$279$	17.3434	1.03832
$280$	5.50912	0.329233
$281$	32.0766	1.91353	0.956763	−	0.290867i	$-0.0939439\pi$
$281$	32.0766	1.91353	0.956763	+	0.290867i	$0.0939439\pi$
$282$	−3.94140	−0.234707
$283$	−30.7274	−1.82655	−0.913277	−	0.407340i	$-0.866456\pi$
$283$	−30.7274	−1.82655	−0.913277	+	0.407340i	$0.866456\pi$
$284$	6.27474	0.372337
$285$	−2.83209	−0.167758
$286$	−10.4759	−0.619454
$287$	−24.5959	−1.45185
$288$	2.38250	0.140390
$289$	−14.5947	−0.858512
$290$	5.81870	0.341686
$291$	11.4050	0.668570
$292$	−13.0599	−0.764271
$293$	−13.4226	−0.784156	−0.392078	−	0.919932i	$-0.628244\pi$
$293$	−13.4226	−0.784156	−0.392078	+	0.919932i	$0.628244\pi$
$294$	6.29078	0.366885
$295$	1.66986	0.0972232
$296$	5.04022	0.292957
$297$	17.9658	1.04248
$298$	15.3186	0.887383
$299$	−2.46631	−0.142630
$300$	2.33965	0.135080
$301$	−36.0306	−2.07677
$302$	13.1238	0.755192
$303$	0.917415	0.0527041
$304$	−2.53414	−0.145343
$305$	−9.18998	−0.526217
$306$	3.69502	0.211230
$307$	13.7714	0.785976	0.392988	−	0.919544i	$-0.371441\pi$
$307$	13.7714	0.785976	0.392988	+	0.919544i	$0.371441\pi$
$308$	16.4539	0.937549
$309$	2.37218	0.134948
$310$	−10.3528	−0.588002
$311$	17.4388	0.988864	0.494432	−	0.869216i	$-0.335376\pi$
$311$	17.4388	0.988864	0.494432	+	0.869216i	$0.335376\pi$
$312$	1.93805	0.109721
$313$	−14.0667	−0.795099	−0.397549	−	0.917581i	$-0.630139\pi$
$313$	−14.0667	−0.795099	−0.397549	+	0.917581i	$0.630139\pi$
$314$	0.761128	0.0429529
$315$	13.1255	0.739537
$316$	−8.91977	−0.501776
$317$	6.19260	0.347811	0.173905	−	0.984762i	$-0.444361\pi$
$317$	6.19260	0.347811	0.173905	+	0.984762i	$0.444361\pi$
$318$	−5.19462	−0.291300
$319$	17.3785	0.973011
$320$	−1.42219	−0.0795029
$321$	5.63640	0.314593
$322$	3.87369	0.215872
$323$	−3.93020	−0.218682
$324$	3.82381	0.212434
$325$	−7.34313	−0.407324
$326$	−19.8011	−1.09668
$327$	3.14010	0.173648
$328$	6.34949	0.350592
$329$	−19.4293	−1.07117
$330$	−4.74701	−0.261315
$331$	−18.1773	−0.999114	−0.499557	−	0.866281i	$-0.666504\pi$
$331$	−18.1773	−0.999114	−0.499557	+	0.866281i	$0.666504\pi$
$332$	14.1085	0.774307
$333$	12.0083	0.658052
$334$	−4.08020	−0.223259
$335$	−14.0535	−0.767823
$336$	−3.04399	−0.166063
$337$	23.9544	1.30488	0.652440	−	0.757841i	$-0.273745\pi$
$337$	23.9544	1.30488	0.652440	+	0.757841i	$0.273745\pi$
$338$	6.91731	0.376252
$339$	−10.7519	−0.583964
$340$	−2.20568	−0.119620
$341$	−30.9205	−1.67444
$342$	−6.03759	−0.326475
$343$	3.89481	0.210300
$344$	9.30138	0.501497
$345$	−1.11757	−0.0601681
$346$	−2.46367	−0.132448
$347$	−32.0717	−1.72170	−0.860849	−	0.508861i	$-0.830067\pi$
$347$	−32.0717	−1.72170	−0.860849	+	0.508861i	$0.830067\pi$
$348$	−3.21504	−0.172344
$349$	0.128543	0.00688074	0.00344037	−	0.999994i	$-0.498905\pi$
$349$	0.128543	0.00688074	0.00344037	+	0.999994i	$0.498905\pi$
$350$	11.5334	0.616487
$351$	10.4316	0.556796
$352$	−4.24761	−0.226398
$353$	5.01443	0.266891	0.133446	−	0.991056i	$-0.457396\pi$
$353$	5.01443	0.266891	0.133446	+	0.991056i	$0.457396\pi$
$354$	−0.922660	−0.0490388
$355$	−8.92387	−0.473630
$356$	−11.5983	−0.614706
$357$	−4.72092	−0.249858
$358$	−10.7958	−0.570575
$359$	−23.3707	−1.23346	−0.616730	−	0.787175i	$-0.711543\pi$
$359$	−23.3707	−1.23346	−0.616730	+	0.787175i	$0.711543\pi$
$360$	−3.38837	−0.178583
$361$	−12.5781	−0.662007
$362$	−9.47637	−0.498067
$363$	−5.53383	−0.290451
$364$	9.55371	0.500751
$365$	18.5736	0.972188
$366$	5.07779	0.265420
$367$	25.8392	1.34880	0.674398	−	0.738368i	$-0.264403\pi$
$367$	25.8392	1.34880	0.674398	+	0.738368i	$0.264403\pi$
$368$	−1.00000	−0.0521286
$369$	15.1277	0.787515
$370$	−7.16815	−0.372654
$371$	−25.6071	−1.32945
$372$	5.72031	0.296584
$373$	−2.83438	−0.146758	−0.0733792	−	0.997304i	$-0.523378\pi$
$373$	−2.83438	−0.146758	−0.0733792	+	0.997304i	$0.523378\pi$
$374$	−6.58762	−0.340638
$375$	−8.91530	−0.460384
$376$	5.01571	0.258666
$377$	10.0906	0.519691
$378$	−16.3843	−0.842716
$379$	−33.9194	−1.74232	−0.871160	−	0.490999i	$-0.836632\pi$
$379$	−33.9194	−1.74232	−0.871160	+	0.490999i	$0.836632\pi$
$380$	3.60403	0.184883
$381$	−11.1755	−0.572539
$382$	−6.80800	−0.348328
$383$	29.3851	1.50151	0.750753	−	0.660583i	$-0.229691\pi$
$383$	29.3851	1.50151	0.750753	+	0.660583i	$0.229691\pi$
$384$	0.785811	0.0401008
$385$	−23.4006	−1.19260
$386$	14.7284	0.749657
$387$	22.1605	1.12648
$388$	−14.5136	−0.736817
$389$	11.5197	0.584070	0.292035	−	0.956408i	$-0.405668\pi$
$389$	11.5197	0.584070	0.292035	+	0.956408i	$0.405668\pi$
$390$	−2.75628	−0.139570
$391$	−1.55090	−0.0784324
$392$	−8.00545	−0.404336
$393$	0.785811	0.0396389
$394$	13.0172	0.655798
$395$	12.6856	0.638282
$396$	−10.1199	−0.508546
$397$	−30.2065	−1.51602	−0.758010	−	0.652243i	$-0.773828\pi$
$397$	−30.2065	−1.51602	−0.758010	+	0.652243i	$0.773828\pi$
$398$	−16.5962	−0.831891
$399$	7.71389	0.386177
$400$	−2.97737	−0.148869
$401$	−3.54033	−0.176796	−0.0883978	−	0.996085i	$-0.528175\pi$
$401$	−3.54033	−0.176796	−0.0883978	+	0.996085i	$0.528175\pi$
$402$	7.76504	0.387285
$403$	−17.9535	−0.894328
$404$	−1.16747	−0.0580840
$405$	−5.43819	−0.270226
$406$	−15.8487	−0.786556
$407$	−21.4089	−1.06120
$408$	1.21871	0.0603354
$409$	−24.7495	−1.22378	−0.611891	−	0.790942i	$-0.709591\pi$
$409$	−24.7495	−1.22378	−0.611891	+	0.790942i	$0.709591\pi$
$410$	−9.03018	−0.445969
$411$	12.9859	0.640549
$412$	−3.01876	−0.148724
$413$	−4.54829	−0.223807
$414$	−2.38250	−0.117094
$415$	−20.0650	−0.984954
$416$	−2.46631	−0.120921
$417$	−6.76183	−0.331128
$418$	10.7640	0.526486
$419$	30.3852	1.48441	0.742206	−	0.670171i	$-0.233779\pi$
$419$	30.3852	1.48441	0.742206	+	0.670171i	$0.233779\pi$
$420$	4.32913	0.211240
$421$	−23.4771	−1.14420	−0.572102	−	0.820183i	$-0.693872\pi$
$421$	−23.4771	−1.14420	−0.572102	+	0.820183i	$0.693872\pi$
$422$	4.82200	0.234731
$423$	11.9499	0.581026
$424$	6.61052	0.321035
$425$	−4.61761	−0.223987
$426$	4.93076	0.238896
$427$	25.0312	1.21134
$428$	−7.17272	−0.346706
$429$	−8.23210	−0.397449
$430$	−13.2283	−0.637927
$431$	16.7750	0.808025	0.404013	−	0.914753i	$-0.367615\pi$
$431$	16.7750	0.808025	0.404013	+	0.914753i	$0.367615\pi$
$432$	4.22963	0.203498
$433$	33.2177	1.59634	0.798170	−	0.602433i	$-0.205802\pi$
$433$	33.2177	1.59634	0.798170	+	0.602433i	$0.205802\pi$
$434$	28.1985	1.35357
$435$	4.57240	0.219230
$436$	−3.99600	−0.191373
$437$	2.53414	0.121224
$438$	−10.2626	−0.490366
$439$	−4.02949	−0.192317	−0.0961585	−	0.995366i	$-0.530656\pi$
$439$	−4.02949	−0.192317	−0.0961585	+	0.995366i	$0.530656\pi$
$440$	6.04091	0.287989
$441$	−19.0730	−0.908238
$442$	−3.82500	−0.181937
$443$	−23.2202	−1.10323	−0.551613	−	0.834100i	$-0.685988\pi$
$443$	−23.2202	−1.10323	−0.551613	+	0.834100i	$0.685988\pi$
$444$	3.96066	0.187965
$445$	16.4949	0.781934
$446$	23.8010	1.12701
$447$	12.0375	0.569356
$448$	3.87369	0.183015
$449$	15.7458	0.743092	0.371546	−	0.928415i	$-0.378828\pi$
$449$	15.7458	0.743092	0.371546	+	0.928415i	$0.378828\pi$
$450$	−7.09360	−0.334395
$451$	−26.9702	−1.26998
$452$	13.6826	0.643574
$453$	10.3129	0.484540
$454$	6.05338	0.284099
$455$	−13.5872	−0.636978
$456$	−1.99135	−0.0932537
$457$	22.8637	1.06952	0.534760	−	0.845004i	$-0.320402\pi$
$457$	22.8637	1.06952	0.534760	+	0.845004i	$0.320402\pi$
$458$	25.9038	1.21040
$459$	6.55973	0.306182
$460$	1.42219	0.0663100
$461$	−1.40109	−0.0652555	−0.0326277	−	0.999468i	$-0.510388\pi$
$461$	−1.40109	−0.0652555	−0.0326277	+	0.999468i	$0.510388\pi$
$462$	12.9297	0.601543
$463$	−38.6071	−1.79423	−0.897113	−	0.441802i	$-0.854339\pi$
$463$	−38.6071	−1.79423	−0.897113	+	0.441802i	$0.854339\pi$
$464$	4.09137	0.189937
$465$	−8.13537	−0.377269
$466$	−10.7270	−0.496916
$467$	−33.5864	−1.55420	−0.777098	−	0.629380i	$-0.783309\pi$
$467$	−33.5864	−1.55420	−0.777098	+	0.629380i	$0.783309\pi$
$468$	−5.87599	−0.271618
$469$	38.2781	1.76752
$470$	−7.13330	−0.329034
$471$	0.598103	0.0275591
$472$	1.17415	0.0540446
$473$	−39.5086	−1.81661
$474$	−7.00925	−0.321946
$475$	7.54508	0.346192
$476$	6.00770	0.275363
$477$	15.7496	0.721124
$478$	24.0030	1.09787
$479$	16.2242	0.741304	0.370652	−	0.928772i	$-0.379134\pi$
$479$	16.2242	0.741304	0.370652	+	0.928772i	$0.379134\pi$
$480$	−1.11757	−0.0510100
$481$	−12.4307	−0.566793
$482$	−6.77771	−0.308716
$483$	3.04399	0.138506
$484$	7.04218	0.320099
$485$	20.6411	0.937265
$486$	15.6937	0.711880
$487$	−1.66642	−0.0755125	−0.0377562	−	0.999287i	$-0.512021\pi$
$487$	−1.66642	−0.0755125	−0.0377562	+	0.999287i	$0.512021\pi$
$488$	−6.46185	−0.292514
$489$	−15.5599	−0.703644
$490$	11.3853	0.514334
$491$	5.78439	0.261046	0.130523	−	0.991445i	$-0.458334\pi$
$491$	5.78439	0.261046	0.130523	+	0.991445i	$0.458334\pi$
$492$	4.98950	0.224944
$493$	6.34530	0.285778
$494$	6.24997	0.281200
$495$	14.3925	0.646893
$496$	−7.27950	−0.326859
$497$	24.3064	1.09029
$498$	11.0867	0.496805
$499$	−26.4914	−1.18592	−0.592959	−	0.805232i	$-0.702041\pi$
$499$	−26.4914	−1.18592	−0.592959	+	0.805232i	$0.702041\pi$
$500$	11.3453	0.507379
$501$	−3.20627	−0.143245
$502$	−11.3933	−0.508506
$503$	−16.6310	−0.741539	−0.370769	−	0.928725i	$-0.620906\pi$
$503$	−16.6310	−0.741539	−0.370769	+	0.928725i	$0.620906\pi$
$504$	9.22906	0.411095
$505$	1.66037	0.0738855
$506$	4.24761	0.188829
$507$	5.43570	0.241408
$508$	14.2216	0.630983
$509$	−12.7565	−0.565422	−0.282711	−	0.959205i	$-0.591234\pi$
$509$	−12.7565	−0.565422	−0.282711	+	0.959205i	$0.591234\pi$
$510$	−1.73324	−0.0767493
$511$	−50.5899	−2.23796
$512$	−1.00000	−0.0441942
$513$	−10.7185	−0.473232
$514$	−9.94455	−0.438635
$515$	4.29325	0.189183
$516$	7.30913	0.321766
$517$	−21.3048	−0.936983
$518$	19.5242	0.857845
$519$	−1.93598	−0.0849799
$520$	3.50756	0.153817
$521$	−12.7609	−0.559063	−0.279532	−	0.960137i	$-0.590179\pi$
$521$	−12.7609	−0.559063	−0.279532	+	0.960137i	$0.590179\pi$
$522$	9.74768	0.426644
$523$	−6.25629	−0.273569	−0.136784	−	0.990601i	$-0.543677\pi$
$523$	−6.25629	−0.273569	−0.136784	+	0.990601i	$0.543677\pi$
$524$	−1.00000	−0.0436852
$525$	9.06309	0.395546
$526$	−9.89205	−0.431314
$527$	−11.2898	−0.491791
$528$	−3.33782	−0.145260
$529$	1.00000	0.0434783
$530$	−9.40142	−0.408372
$531$	2.79741	0.121397
$532$	−9.81646	−0.425598
$533$	−15.6598	−0.678302
$534$	−9.11404	−0.394403
$535$	10.2010	0.441026
$536$	−9.88156	−0.426819
$537$	−8.48346	−0.366088
$538$	−4.93260	−0.212659
$539$	34.0040	1.46466
$540$	−6.01534	−0.258859
$541$	−3.89662	−0.167529	−0.0837643	−	0.996486i	$-0.526694\pi$
$541$	−3.89662	−0.167529	−0.0837643	+	0.996486i	$0.526694\pi$
$542$	−28.7211	−1.23368
$543$	−7.44664	−0.319566
$544$	−1.55090	−0.0664943
$545$	5.68307	0.243436
$546$	7.50742	0.321288
$547$	4.45583	0.190517	0.0952587	−	0.995453i	$-0.469632\pi$
$547$	4.45583	0.190517	0.0952587	+	0.995453i	$0.469632\pi$
$548$	−16.5255	−0.705935
$549$	−15.3954	−0.657058
$550$	12.6467	0.539258
$551$	−10.3681	−0.441695
$552$	−0.785811	−0.0334463
$553$	−34.5524	−1.46932
$554$	25.9935	1.10436
$555$	−5.63281	−0.239099
$556$	8.60490	0.364929
$557$	43.4169	1.83963	0.919817	−	0.392348i	$-0.128337\pi$
$557$	43.4169	1.83963	0.919817	+	0.392348i	$0.128337\pi$
$558$	−17.3434	−0.734205
$559$	−22.9401	−0.970262
$560$	−5.50912	−0.232803
$561$	−5.17662	−0.218557
$562$	−32.0766	−1.35307
$563$	−16.3347	−0.688424	−0.344212	−	0.938892i	$-0.611854\pi$
$563$	−16.3347	−0.688424	−0.344212	+	0.938892i	$0.611854\pi$
$564$	3.94140	0.165963
$565$	−19.4592	−0.818655
$566$	30.7274	1.29157
$567$	14.8123	0.622056
$568$	−6.27474	−0.263282
$569$	23.3598	0.979293	0.489647	−	0.871921i	$-0.337126\pi$
$569$	23.3598	0.979293	0.489647	+	0.871921i	$0.337126\pi$
$570$	2.83209	0.118623
$571$	−4.00674	−0.167677	−0.0838384	−	0.996479i	$-0.526718\pi$
$571$	−4.00674	−0.167677	−0.0838384	+	0.996479i	$0.526718\pi$
$572$	10.4759	0.438020
$573$	−5.34980	−0.223491
$574$	24.5959	1.02661
$575$	2.97737	0.124165
$576$	−2.38250	−0.0992709
$577$	−0.942727	−0.0392463	−0.0196231	−	0.999807i	$-0.506247\pi$
$577$	−0.942727	−0.0392463	−0.0196231	+	0.999807i	$0.506247\pi$
$578$	14.5947	0.607060
$579$	11.5738	0.480989
$580$	−5.81870	−0.241608
$581$	54.6521	2.26735
$582$	−11.4050	−0.472751
$583$	−28.0789	−1.16291
$584$	13.0599	0.540421
$585$	8.35677	0.345510
$586$	13.4226	0.554482
$587$	−1.48796	−0.0614145	−0.0307073	−	0.999528i	$-0.509776\pi$
$587$	−1.48796	−0.0614145	−0.0307073	+	0.999528i	$0.509776\pi$
$588$	−6.29078	−0.259427
$589$	18.4473	0.760106
$590$	−1.66986	−0.0687472
$591$	10.2291	0.420768
$592$	−5.04022	−0.207152
$593$	1.86374	0.0765345	0.0382673	−	0.999268i	$-0.487816\pi$
$593$	1.86374	0.0765345	0.0382673	+	0.999268i	$0.487816\pi$
$594$	−17.9658	−0.737146
$595$	−8.54410	−0.350274
$596$	−15.3186	−0.627475
$597$	−13.0415	−0.533751
$598$	2.46631	0.100855
$599$	−11.8117	−0.482614	−0.241307	−	0.970449i	$-0.577576\pi$
$599$	−11.8117	−0.482614	−0.241307	+	0.970449i	$0.577576\pi$
$600$	−2.33965	−0.0955160
$601$	41.3786	1.68787	0.843934	−	0.536447i	$-0.180234\pi$
$601$	41.3786	1.68787	0.843934	+	0.536447i	$0.180234\pi$
$602$	36.0306	1.46850
$603$	−23.5428	−0.958738
$604$	−13.1238	−0.534001
$605$	−10.0153	−0.407181
$606$	−0.917415	−0.0372674
$607$	−2.96436	−0.120320	−0.0601598	−	0.998189i	$-0.519161\pi$
$607$	−2.96436	−0.120320	−0.0601598	+	0.998189i	$0.519161\pi$
$608$	2.53414	0.102773
$609$	−12.4541	−0.504664
$610$	9.18998	0.372091
$611$	−12.3703	−0.500449
$612$	−3.69502	−0.149362
$613$	−46.7489	−1.88817	−0.944086	−	0.329700i	$-0.893052\pi$
$613$	−46.7489	−1.88817	−0.944086	+	0.329700i	$0.893052\pi$
$614$	−13.7714	−0.555769
$615$	−7.09602	−0.286139
$616$	−16.4539	−0.662947
$617$	−7.73953	−0.311582	−0.155791	−	0.987790i	$-0.549793\pi$
$617$	−7.73953	−0.311582	−0.155791	+	0.987790i	$0.549793\pi$
$618$	−2.37218	−0.0954229
$619$	−1.07015	−0.0430131	−0.0215066	−	0.999769i	$-0.506846\pi$
$619$	−1.07015	−0.0430131	−0.0215066	+	0.999769i	$0.506846\pi$
$620$	10.3528	0.415780
$621$	−4.22963	−0.169729
$622$	−17.4388	−0.699233
$623$	−44.9280	−1.80000
$624$	−1.93805	−0.0775843
$625$	−1.24837	−0.0499346
$626$	14.0667	0.562220
$627$	8.45850	0.337800
$628$	−0.761128	−0.0303723
$629$	−7.81687	−0.311679
$630$	−13.1255	−0.522932
$631$	−8.86536	−0.352924	−0.176462	−	0.984307i	$-0.556465\pi$
$631$	−8.86536	−0.352924	−0.176462	+	0.984307i	$0.556465\pi$
$632$	8.91977	0.354809
$633$	3.78918	0.150607
$634$	−6.19260	−0.245939
$635$	−20.2259	−0.802639
$636$	5.19462	0.205980
$637$	19.7439	0.782283
$638$	−17.3785	−0.688022
$639$	−14.9496	−0.591395
$640$	1.42219	0.0562170
$641$	−21.3470	−0.843157	−0.421578	−	0.906792i	$-0.638524\pi$
$641$	−21.3470	−0.843157	−0.421578	+	0.906792i	$0.638524\pi$
$642$	−5.63640	−0.222451
$643$	−24.2440	−0.956092	−0.478046	−	0.878335i	$-0.658655\pi$
$643$	−24.2440	−0.956092	−0.478046	+	0.878335i	$0.658655\pi$
$644$	−3.87369	−0.152645
$645$	−10.3950	−0.409302
$646$	3.93020	0.154632
$647$	−40.1279	−1.57759	−0.788796	−	0.614656i	$-0.789295\pi$
$647$	−40.1279	−1.57759	−0.788796	+	0.614656i	$0.789295\pi$
$648$	−3.82381	−0.150214
$649$	−4.98733	−0.195770
$650$	7.34313	0.288021
$651$	22.1587	0.868468
$652$	19.8011	0.775470
$653$	42.4364	1.66066	0.830331	−	0.557270i	$-0.188151\pi$
$653$	42.4364	1.66066	0.830331	+	0.557270i	$0.188151\pi$
$654$	−3.14010	−0.122788
$655$	1.42219	0.0555696
$656$	−6.34949	−0.247906
$657$	31.1152	1.21392
$658$	19.4293	0.757433
$659$	37.0603	1.44366	0.721832	−	0.692068i	$-0.243300\pi$
$659$	37.0603	1.44366	0.721832	+	0.692068i	$0.243300\pi$
$660$	4.74701	0.184777
$661$	−47.4400	−1.84520	−0.922601	−	0.385755i	$-0.873941\pi$
$661$	−47.4400	−1.84520	−0.922601	+	0.385755i	$0.873941\pi$
$662$	18.1773	0.706480
$663$	−3.00573	−0.116733
$664$	−14.1085	−0.547518
$665$	13.9609	0.541380
$666$	−12.0083	−0.465313
$667$	−4.09137	−0.158418
$668$	4.08020	0.157868
$669$	18.7031	0.723102
$670$	14.0535	0.542933
$671$	27.4474	1.05960
$672$	3.04399	0.117424
$673$	−10.1492	−0.391223	−0.195612	−	0.980681i	$-0.562669\pi$
$673$	−10.1492	−0.391223	−0.195612	+	0.980681i	$0.562669\pi$
$674$	−23.9544	−0.922689
$675$	−12.5932	−0.484712
$676$	−6.91731	−0.266051
$677$	−6.88451	−0.264593	−0.132297	−	0.991210i	$-0.542235\pi$
$677$	−6.88451	−0.264593	−0.132297	+	0.991210i	$0.542235\pi$
$678$	10.7519	0.412925
$679$	−56.2212	−2.15757
$680$	2.20568	0.0845838
$681$	4.75682	0.182282
$682$	30.9205	1.18401
$683$	−43.2779	−1.65598	−0.827991	−	0.560741i	$-0.810516\pi$
$683$	−43.2779	−1.65598	−0.827991	+	0.560741i	$0.810516\pi$
$684$	6.03759	0.230853
$685$	23.5024	0.897981
$686$	−3.89481	−0.148705
$687$	20.3555	0.776610
$688$	−9.30138	−0.354612
$689$	−16.3036	−0.621118
$690$	1.11757	0.0425453
$691$	−10.0098	−0.380792	−0.190396	−	0.981707i	$-0.560977\pi$
$691$	−10.0098	−0.380792	−0.190396	+	0.981707i	$0.560977\pi$
$692$	2.46367	0.0936545
$693$	−39.2015	−1.48914
$694$	32.0717	1.21742
$695$	−12.2378	−0.464206
$696$	3.21504	0.121866
$697$	−9.84743	−0.372998
$698$	−0.128543	−0.00486542
$699$	−8.42936	−0.318828
$700$	−11.5334	−0.435922
$701$	−22.1761	−0.837581	−0.418790	−	0.908083i	$-0.637546\pi$
$701$	−22.1761	−0.837581	−0.418790	+	0.908083i	$0.637546\pi$
$702$	−10.4316	−0.393715
$703$	12.7726	0.481728
$704$	4.24761	0.160088
$705$	−5.60543	−0.211113
$706$	−5.01443	−0.188721
$707$	−4.52243	−0.170084
$708$	0.922660	0.0346757
$709$	−49.8074	−1.87056	−0.935278	−	0.353915i	$-0.884850\pi$
$709$	−49.8074	−1.87056	−0.935278	+	0.353915i	$0.884850\pi$
$710$	8.92387	0.334907
$711$	21.2513	0.796988
$712$	11.5983	0.434663
$713$	7.27950	0.272619
$714$	4.72092	0.176676
$715$	−14.8988	−0.557182
$716$	10.7958	0.403458
$717$	18.8619	0.704409
$718$	23.3707	0.872187
$719$	−7.28751	−0.271778	−0.135889	−	0.990724i	$-0.543389\pi$
$719$	−7.28751	−0.271778	−0.135889	+	0.990724i	$0.543389\pi$
$720$	3.38837	0.126277
$721$	−11.6937	−0.435498
$722$	12.5781	0.468110
$723$	−5.32600	−0.198076
$724$	9.47637	0.352187
$725$	−12.1815	−0.452411
$726$	5.53383	0.205380
$727$	−0.170838	−0.00633602	−0.00316801	−	0.999995i	$-0.501008\pi$
$727$	−0.170838	−0.00633602	−0.00316801	+	0.999995i	$0.501008\pi$
$728$	−9.55371	−0.354084
$729$	0.860836	0.0318828
$730$	−18.5736	−0.687441
$731$	−14.4255	−0.533547
$732$	−5.07779	−0.187681
$733$	−43.1216	−1.59273	−0.796367	−	0.604814i	$-0.793247\pi$
$733$	−43.1216	−1.59273	−0.796367	+	0.604814i	$0.793247\pi$
$734$	−25.8392	−0.953743
$735$	8.94668	0.330003
$736$	1.00000	0.0368605
$737$	41.9730	1.54610
$738$	−15.1277	−0.556857
$739$	9.57554	0.352242	0.176121	−	0.984369i	$-0.443645\pi$
$739$	9.57554	0.352242	0.176121	+	0.984369i	$0.443645\pi$
$740$	7.16815	0.263506
$741$	4.91130	0.180421
$742$	25.6071	0.940066
$743$	13.1943	0.484053	0.242027	−	0.970270i	$-0.422188\pi$
$743$	13.1943	0.484053	0.242027	+	0.970270i	$0.422188\pi$
$744$	−5.72031	−0.209717
$745$	21.7860	0.798176
$746$	2.83438	0.103774
$747$	−33.6136	−1.22986
$748$	6.58762	0.240867
$749$	−27.7849	−1.01524
$750$	8.91530	0.325541
$751$	10.1773	0.371374	0.185687	−	0.982609i	$-0.440549\pi$
$751$	10.1773	0.371374	0.185687	+	0.982609i	$0.440549\pi$
$752$	−5.01571	−0.182904
$753$	−8.95295	−0.326264
$754$	−10.0906	−0.367477
$755$	18.6646	0.679274
$756$	16.3843	0.595890
$757$	41.7124	1.51606	0.758031	−	0.652218i	$-0.226161\pi$
$757$	41.7124	1.51606	0.758031	+	0.652218i	$0.226161\pi$
$758$	33.9194	1.23201
$759$	3.33782	0.121155
$760$	−3.60403	−0.130732
$761$	25.8827	0.938246	0.469123	−	0.883133i	$-0.344570\pi$
$761$	25.8827	0.938246	0.469123	+	0.883133i	$0.344570\pi$
$762$	11.1755	0.404846
$763$	−15.4792	−0.560386
$764$	6.80800	0.246305
$765$	5.25502	0.189996
$766$	−29.3851	−1.06173
$767$	−2.89582	−0.104562
$768$	−0.785811	−0.0283555
$769$	−11.2893	−0.407101	−0.203551	−	0.979064i	$-0.565248\pi$
$769$	−11.2893	−0.407101	−0.203551	+	0.979064i	$0.565248\pi$
$770$	23.4006	0.843299
$771$	−7.81454	−0.281434
$772$	−14.7284	−0.530088
$773$	15.5274	0.558483	0.279242	−	0.960221i	$-0.409917\pi$
$773$	15.5274	0.558483	0.279242	+	0.960221i	$0.409917\pi$
$774$	−22.1605	−0.796544
$775$	21.6738	0.778546
$776$	14.5136	0.521008
$777$	15.3424	0.550404
$778$	−11.5197	−0.413000
$779$	16.0905	0.576502
$780$	2.75628	0.0986907
$781$	26.6526	0.953706
$782$	1.55090	0.0554601
$783$	17.3050	0.618429
$784$	8.00545	0.285909
$785$	1.08247	0.0386350
$786$	−0.785811	−0.0280290
$787$	34.8319	1.24162	0.620811	−	0.783960i	$-0.286803\pi$
$787$	34.8319	1.24162	0.620811	+	0.783960i	$0.286803\pi$
$788$	−13.0172	−0.463719
$789$	−7.77328	−0.276736
$790$	−12.6856	−0.451334
$791$	53.0020	1.88453
$792$	10.1199	0.359596
$793$	15.9369	0.565937
$794$	30.2065	1.07199
$795$	−7.38774	−0.262016
$796$	16.5962	0.588236
$797$	−3.51665	−0.124566	−0.0622830	−	0.998059i	$-0.519838\pi$
$797$	−3.51665	−0.124566	−0.0622830	+	0.998059i	$0.519838\pi$
$798$	−7.71389	−0.273069
$799$	−7.77887	−0.275197
$800$	2.97737	0.105266
$801$	27.6328	0.976359
$802$	3.54033	0.125013
$803$	−55.4732	−1.95761
$804$	−7.76504	−0.273852
$805$	5.50912	0.194171
$806$	17.9535	0.632385
$807$	−3.87609	−0.136445
$808$	1.16747	0.0410716
$809$	−11.4465	−0.402437	−0.201218	−	0.979546i	$-0.564490\pi$
$809$	−11.4465	−0.402437	−0.201218	+	0.979546i	$0.564490\pi$
$810$	5.43819	0.191078
$811$	12.3087	0.432217	0.216109	−	0.976369i	$-0.430663\pi$
$811$	12.3087	0.432217	0.216109	+	0.976369i	$0.430663\pi$
$812$	15.8487	0.556179
$813$	−22.5694	−0.791543
$814$	21.4089	0.750380
$815$	−28.1609	−0.986434
$816$	−1.21871	−0.0426635
$817$	23.5710	0.824644
$818$	24.7495	0.865345
$819$	−22.7617	−0.795359
$820$	9.03018	0.315348
$821$	39.0355	1.36235	0.681174	−	0.732122i	$-0.261470\pi$
$821$	39.0355	1.36235	0.681174	+	0.732122i	$0.261470\pi$
$822$	−12.9859	−0.452936
$823$	−3.40609	−0.118729	−0.0593644	−	0.998236i	$-0.518907\pi$
$823$	−3.40609	−0.118729	−0.0593644	+	0.998236i	$0.518907\pi$
$824$	3.01876	0.105164
$825$	9.93794	0.345995
$826$	4.54829	0.158255
$827$	40.6519	1.41361	0.706803	−	0.707411i	$-0.250137\pi$
$827$	40.6519	1.41361	0.706803	+	0.707411i	$0.250137\pi$
$828$	2.38250	0.0827976
$829$	−30.8370	−1.07101	−0.535507	−	0.844530i	$-0.679880\pi$
$829$	−30.8370	−1.07101	−0.535507	+	0.844530i	$0.679880\pi$
$830$	20.0650	0.696468
$831$	20.4260	0.708569
$832$	2.46631	0.0855039
$833$	12.4157	0.430177
$834$	6.76183	0.234143
$835$	−5.80282	−0.200815
$836$	−10.7640	−0.372282
$837$	−30.7896	−1.06424
$838$	−30.3852	−1.04964
$839$	39.4504	1.36198	0.680989	−	0.732294i	$-0.261550\pi$
$839$	39.4504	1.36198	0.680989	+	0.732294i	$0.261550\pi$
$840$	−4.32913	−0.149369
$841$	−12.2607	−0.422784
$842$	23.4771	0.809074
$843$	−25.2061	−0.868145
$844$	−4.82200	−0.165980
$845$	9.83774	0.338428
$846$	−11.9499	−0.410847
$847$	27.2792	0.937325
$848$	−6.61052	−0.227006
$849$	24.1459	0.828686
$850$	4.61761	0.158383
$851$	5.04022	0.172776
$852$	−4.93076	−0.168925
$853$	24.7081	0.845988	0.422994	−	0.906132i	$-0.360979\pi$
$853$	24.7081	0.845988	0.422994	+	0.906132i	$0.360979\pi$
$854$	−25.0312	−0.856549
$855$	−8.58660	−0.293655
$856$	7.17272	0.245158
$857$	34.1846	1.16772	0.583861	−	0.811854i	$-0.301541\pi$
$857$	34.1846	1.16772	0.583861	+	0.811854i	$0.301541\pi$
$858$	8.23210	0.281039
$859$	−27.2217	−0.928793	−0.464396	−	0.885628i	$-0.653729\pi$
$859$	−27.2217	−0.928793	−0.464396	+	0.885628i	$0.653729\pi$
$860$	13.2283	0.451082
$861$	19.3278	0.658689
$862$	−16.7750	−0.571360
$863$	−21.5808	−0.734618	−0.367309	−	0.930099i	$-0.619721\pi$
$863$	−21.5808	−0.734618	−0.367309	+	0.930099i	$0.619721\pi$
$864$	−4.22963	−0.143895
$865$	−3.50380	−0.119133
$866$	−33.2177	−1.12878
$867$	11.4687	0.389497
$868$	−28.1985	−0.957120
$869$	−37.8877	−1.28525
$870$	−4.57240	−0.155019
$871$	24.3710	0.825780
$872$	3.99600	0.135321
$873$	34.5787	1.17031
$874$	−2.53414	−0.0857185
$875$	43.9483	1.48572
$876$	10.2626	0.346741
$877$	−18.4620	−0.623416	−0.311708	−	0.950178i	$-0.600901\pi$
$877$	−18.4620	−0.623416	−0.311708	+	0.950178i	$0.600901\pi$
$878$	4.02949	0.135989
$879$	10.5476	0.355763
$880$	−6.04091	−0.203639
$881$	−31.8132	−1.07181	−0.535907	−	0.844277i	$-0.680030\pi$
$881$	−31.8132	−1.07181	−0.535907	+	0.844277i	$0.680030\pi$
$882$	19.0730	0.642221
$883$	15.6302	0.526000	0.263000	−	0.964796i	$-0.415288\pi$
$883$	15.6302	0.526000	0.263000	+	0.964796i	$0.415288\pi$
$884$	3.82500	0.128649
$885$	−1.31220	−0.0441090
$886$	23.2202	0.780099
$887$	6.66364	0.223743	0.111872	−	0.993723i	$-0.464315\pi$
$887$	6.66364	0.223743	0.111872	+	0.993723i	$0.464315\pi$
$888$	−3.96066	−0.132911
$889$	55.0902	1.84767
$890$	−16.4949	−0.552911
$891$	16.2421	0.544129
$892$	−23.8010	−0.796915
$893$	12.7105	0.425341
$894$	−12.0375	−0.402595
$895$	−15.3537	−0.513217
$896$	−3.87369	−0.129411
$897$	1.93805	0.0647097
$898$	−15.7458	−0.525445
$899$	−29.7831	−0.993322
$900$	7.09360	0.236453
$901$	−10.2523	−0.341552
$902$	26.9702	0.898008
$903$	28.3133	0.942207
$904$	−13.6826	−0.455075
$905$	−13.4772	−0.447997
$906$	−10.3129	−0.342622
$907$	50.1996	1.66685	0.833425	−	0.552633i	$-0.186377\pi$
$907$	50.1996	1.66685	0.833425	+	0.552633i	$0.186377\pi$
$908$	−6.05338	−0.200889
$909$	2.78151	0.0922568
$910$	13.5872	0.450411
$911$	−0.523949	−0.0173592	−0.00867960	−	0.999962i	$-0.502763\pi$
$911$	−0.523949	−0.0173592	−0.00867960	+	0.999962i	$0.502763\pi$
$912$	1.99135	0.0659403
$913$	59.9276	1.98331
$914$	−22.8637	−0.756265
$915$	7.22159	0.238738
$916$	−25.9038	−0.855885
$917$	−3.87369	−0.127920
$918$	−6.55973	−0.216503
$919$	5.86338	0.193415	0.0967076	−	0.995313i	$-0.469169\pi$
$919$	5.86338	0.193415	0.0967076	+	0.995313i	$0.469169\pi$
$920$	−1.42219	−0.0468882
$921$	−10.8217	−0.356588
$922$	1.40109	0.0461426
$923$	15.4754	0.509380
$924$	−12.9297	−0.425355
$925$	15.0066	0.493414
$926$	38.6071	1.26871
$927$	7.19220	0.236223
$928$	−4.09137	−0.134306
$929$	−31.0110	−1.01744	−0.508719	−	0.860933i	$-0.669881\pi$
$929$	−31.0110	−1.01744	−0.508719	+	0.860933i	$0.669881\pi$
$930$	8.13537	0.266769
$931$	−20.2869	−0.664877
$932$	10.7270	0.351373
$933$	−13.7036	−0.448636
$934$	33.5864	1.09898
$935$	−9.36885	−0.306394
$936$	5.87599	0.192063
$937$	39.6895	1.29660	0.648300	−	0.761385i	$-0.275480\pi$
$937$	39.6895	1.29660	0.648300	+	0.761385i	$0.275480\pi$
$938$	−38.2781	−1.24982
$939$	11.0538	0.360727
$940$	7.13330	0.232663
$941$	−39.2170	−1.27844	−0.639219	−	0.769025i	$-0.720742\pi$
$941$	−39.2170	−1.27844	−0.639219	+	0.769025i	$0.720742\pi$
$942$	−0.598103	−0.0194872
$943$	6.34949	0.206768
$944$	−1.17415	−0.0382153
$945$	−23.3015	−0.757999
$946$	39.5086	1.28454
$947$	39.1458	1.27207	0.636033	−	0.771662i	$-0.280574\pi$
$947$	39.1458	1.27207	0.636033	+	0.771662i	$0.280574\pi$
$948$	7.00925	0.227650
$949$	−32.2097	−1.04557
$950$	−7.54508	−0.244795
$951$	−4.86621	−0.157798
$952$	−6.00770	−0.194711
$953$	−16.8460	−0.545694	−0.272847	−	0.962057i	$-0.587965\pi$
$953$	−16.8460	−0.545694	−0.272847	+	0.962057i	$0.587965\pi$
$954$	−15.7496	−0.509911
$955$	−9.68228	−0.313311
$956$	−24.0030	−0.776314
$957$	−13.6562	−0.441444
$958$	−16.2242	−0.524181
$959$	−64.0147	−2.06714
$960$	1.11757	0.0360695
$961$	21.9911	0.709392
$962$	12.4307	0.400783
$963$	17.0890	0.550686
$964$	6.77771	0.218295
$965$	20.9466	0.674296
$966$	−3.04399	−0.0979387
$967$	10.1989	0.327973	0.163987	−	0.986463i	$-0.447565\pi$
$967$	10.1989	0.327973	0.163987	+	0.986463i	$0.447565\pi$
$968$	−7.04218	−0.226344
$969$	3.08839	0.0992135
$970$	−20.6411	−0.662746
$971$	4.67632	0.150070	0.0750351	−	0.997181i	$-0.476093\pi$
$971$	4.67632	0.150070	0.0750351	+	0.997181i	$0.476093\pi$
$972$	−15.6937	−0.503375
$973$	33.3327	1.06860
$974$	1.66642	0.0533954
$975$	5.77031	0.184798
$976$	6.46185	0.206839
$977$	−38.5977	−1.23485	−0.617425	−	0.786630i	$-0.711824\pi$
$977$	−38.5977	−1.23485	−0.617425	+	0.786630i	$0.711824\pi$
$978$	15.5599	0.497551
$979$	−49.2649	−1.57451
$980$	−11.3853	−0.363689
$981$	9.52046	0.303965
$982$	−5.78439	−0.184587
$983$	−20.1571	−0.642910	−0.321455	−	0.946925i	$-0.604172\pi$
$983$	−20.1571	−0.642910	−0.321455	+	0.946925i	$0.604172\pi$
$984$	−4.98950	−0.159059
$985$	18.5130	0.589872
$986$	−6.34530	−0.202076
$987$	15.2678	0.485978
$988$	−6.24997	−0.198838
$989$	9.30138	0.295767
$990$	−14.3925	−0.457423
$991$	33.4154	1.06148	0.530738	−	0.847536i	$-0.321915\pi$
$991$	33.4154	1.06148	0.530738	+	0.847536i	$0.321915\pi$
$992$	7.27950	0.231124
$993$	14.2839	0.453286
$994$	−24.3064	−0.770951
$995$	−23.6029	−0.748263
$996$	−11.0867	−0.351294
$997$	−17.8866	−0.566474	−0.283237	−	0.959050i	$-0.591408\pi$
$997$	−17.8866	−0.566474	−0.283237	+	0.959050i	$0.591408\pi$
$998$	26.4914	0.838571
$999$	−21.3182	−0.674479

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.10	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.10	✓	24	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.785811 q^{3} +1.00000 q^{4} -1.42219 q^{5} +0.785811 q^{6} +3.87369 q^{7} -1.00000 q^{8} -2.38250 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.785811 q^{3} +1.00000 q^{4} -1.42219 q^{5} +0.785811 q^{6} +3.87369 q^{7} -1.00000 q^{8} -2.38250 q^{9} +1.42219 q^{10} +4.24761 q^{11} -0.785811 q^{12} +2.46631 q^{13} -3.87369 q^{14} +1.11757 q^{15} +1.00000 q^{16} +1.55090 q^{17} +2.38250 q^{18} -2.53414 q^{19} -1.42219 q^{20} -3.04399 q^{21} -4.24761 q^{22} -1.00000 q^{23} +0.785811 q^{24} -2.97737 q^{25} -2.46631 q^{26} +4.22963 q^{27} +3.87369 q^{28} +4.09137 q^{29} -1.11757 q^{30} -7.27950 q^{31} -1.00000 q^{32} -3.33782 q^{33} -1.55090 q^{34} -5.50912 q^{35} -2.38250 q^{36} -5.04022 q^{37} +2.53414 q^{38} -1.93805 q^{39} +1.42219 q^{40} -6.34949 q^{41} +3.04399 q^{42} -9.30138 q^{43} +4.24761 q^{44} +3.38837 q^{45} +1.00000 q^{46} -5.01571 q^{47} -0.785811 q^{48} +8.00545 q^{49} +2.97737 q^{50} -1.21871 q^{51} +2.46631 q^{52} -6.61052 q^{53} -4.22963 q^{54} -6.04091 q^{55} -3.87369 q^{56} +1.99135 q^{57} -4.09137 q^{58} -1.17415 q^{59} +1.11757 q^{60} +6.46185 q^{61} +7.27950 q^{62} -9.22906 q^{63} +1.00000 q^{64} -3.50756 q^{65} +3.33782 q^{66} +9.88156 q^{67} +1.55090 q^{68} +0.785811 q^{69} +5.50912 q^{70} +6.27474 q^{71} +2.38250 q^{72} -13.0599 q^{73} +5.04022 q^{74} +2.33965 q^{75} -2.53414 q^{76} +16.4539 q^{77} +1.93805 q^{78} -8.91977 q^{79} -1.42219 q^{80} +3.82381 q^{81} +6.34949 q^{82} +14.1085 q^{83} -3.04399 q^{84} -2.20568 q^{85} +9.30138 q^{86} -3.21504 q^{87} -4.24761 q^{88} -11.5983 q^{89} -3.38837 q^{90} +9.55371 q^{91} -1.00000 q^{92} +5.72031 q^{93} +5.01571 q^{94} +3.60403 q^{95} +0.785811 q^{96} -14.5136 q^{97} -8.00545 q^{98} -10.1199 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

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