LMFDB - Embedded newform 6014.2.a.l.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.679880 q^{3} +1.00000 q^{4} -4.32143 q^{5} +0.679880 q^{6} +1.08152 q^{7} -1.00000 q^{8} -2.53776 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.679880 q^{3} +1.00000 q^{4} -4.32143 q^{5} +0.679880 q^{6} +1.08152 q^{7} -1.00000 q^{8} -2.53776 q^{9} +4.32143 q^{10} +1.65302 q^{11} -0.679880 q^{12} +0.0968017 q^{13} -1.08152 q^{14} +2.93805 q^{15} +1.00000 q^{16} +4.58686 q^{17} +2.53776 q^{18} -3.34440 q^{19} -4.32143 q^{20} -0.735306 q^{21} -1.65302 q^{22} +3.14777 q^{23} +0.679880 q^{24} +13.6748 q^{25} -0.0968017 q^{26} +3.76501 q^{27} +1.08152 q^{28} -0.744649 q^{29} -2.93805 q^{30} +1.00000 q^{31} -1.00000 q^{32} -1.12386 q^{33} -4.58686 q^{34} -4.67373 q^{35} -2.53776 q^{36} +1.71839 q^{37} +3.34440 q^{38} -0.0658135 q^{39} +4.32143 q^{40} +1.17272 q^{41} +0.735306 q^{42} -8.75600 q^{43} +1.65302 q^{44} +10.9668 q^{45} -3.14777 q^{46} -10.1418 q^{47} -0.679880 q^{48} -5.83031 q^{49} -13.6748 q^{50} -3.11852 q^{51} +0.0968017 q^{52} -10.5620 q^{53} -3.76501 q^{54} -7.14343 q^{55} -1.08152 q^{56} +2.27379 q^{57} +0.744649 q^{58} -0.0616620 q^{59} +2.93805 q^{60} -6.28097 q^{61} -1.00000 q^{62} -2.74465 q^{63} +1.00000 q^{64} -0.418322 q^{65} +1.12386 q^{66} -3.38171 q^{67} +4.58686 q^{68} -2.14010 q^{69} +4.67373 q^{70} -13.5623 q^{71} +2.53776 q^{72} +15.9363 q^{73} -1.71839 q^{74} -9.29720 q^{75} -3.34440 q^{76} +1.78778 q^{77} +0.0658135 q^{78} +3.57644 q^{79} -4.32143 q^{80} +5.05353 q^{81} -1.17272 q^{82} -9.93990 q^{83} -0.735306 q^{84} -19.8218 q^{85} +8.75600 q^{86} +0.506272 q^{87} -1.65302 q^{88} -10.7476 q^{89} -10.9668 q^{90} +0.104693 q^{91} +3.14777 q^{92} -0.679880 q^{93} +10.1418 q^{94} +14.4526 q^{95} +0.679880 q^{96} -1.00000 q^{97} +5.83031 q^{98} -4.19498 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) $ 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * 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
$3$	−0.679880	−0.392529	−0.196264	−	0.980551i	$-0.562881\pi$
$3$	−0.679880	−0.392529	−0.196264	+	0.980551i	$0.562881\pi$
$4$	1.00000	0.500000
$5$	−4.32143	−1.93260	−0.966302	−	0.257413i	$-0.917130\pi$
$5$	−4.32143	−1.93260	−0.966302	+	0.257413i	$0.917130\pi$
$6$	0.679880	0.277560
$7$	1.08152	0.408777	0.204389	−	0.978890i	$-0.434479\pi$
$7$	1.08152	0.408777	0.204389	+	0.978890i	$0.434479\pi$
$8$	−1.00000	−0.353553
$9$	−2.53776	−0.845921
$10$	4.32143	1.36656
$11$	1.65302	0.498405	0.249203	−	0.968451i	$-0.419832\pi$
$11$	1.65302	0.498405	0.249203	+	0.968451i	$0.419832\pi$
$12$	−0.679880	−0.196264
$13$	0.0968017	0.0268480	0.0134240	−	0.999910i	$-0.495727\pi$
$13$	0.0968017	0.0268480	0.0134240	+	0.999910i	$0.495727\pi$
$14$	−1.08152	−0.289049
$15$	2.93805	0.758602
$16$	1.00000	0.250000
$17$	4.58686	1.11248	0.556239	−	0.831023i	$-0.312244\pi$
$17$	4.58686	1.11248	0.556239	+	0.831023i	$0.312244\pi$
$18$	2.53776	0.598157
$19$	−3.34440	−0.767258	−0.383629	−	0.923487i	$-0.625326\pi$
$19$	−3.34440	−0.767258	−0.383629	+	0.923487i	$0.625326\pi$
$20$	−4.32143	−0.966302
$21$	−0.735306	−0.160457
$22$	−1.65302	−0.352426
$23$	3.14777	0.656355	0.328177	−	0.944616i	$-0.393566\pi$
$23$	3.14777	0.656355	0.328177	+	0.944616i	$0.393566\pi$
$24$	0.679880	0.138780
$25$	13.6748	2.73495
$26$	−0.0968017	−0.0189844
$27$	3.76501	0.724577
$28$	1.08152	0.204389
$29$	−0.744649	−0.138278	−0.0691390	−	0.997607i	$-0.522025\pi$
$29$	−0.744649	−0.138278	−0.0691390	+	0.997607i	$0.522025\pi$
$30$	−2.93805	−0.536413
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−1.12386	−0.195638
$34$	−4.58686	−0.786640
$35$	−4.67373	−0.790004
$36$	−2.53776	−0.422961
$37$	1.71839	0.282502	0.141251	−	0.989974i	$-0.454888\pi$
$37$	1.71839	0.282502	0.141251	+	0.989974i	$0.454888\pi$
$38$	3.34440	0.542533
$39$	−0.0658135	−0.0105386
$40$	4.32143	0.683278
$41$	1.17272	0.183147	0.0915737	−	0.995798i	$-0.470810\pi$
$41$	1.17272	0.183147	0.0915737	+	0.995798i	$0.470810\pi$
$42$	0.735306	0.113460
$43$	−8.75600	−1.33528	−0.667639	−	0.744485i	$-0.732695\pi$
$43$	−8.75600	−1.33528	−0.667639	+	0.744485i	$0.732695\pi$
$44$	1.65302	0.249203
$45$	10.9668	1.63483
$46$	−3.14777	−0.464113
$47$	−10.1418	−1.47933	−0.739665	−	0.672975i	$-0.765016\pi$
$47$	−10.1418	−1.47933	−0.739665	+	0.672975i	$0.765016\pi$
$48$	−0.679880	−0.0981322
$49$	−5.83031	−0.832901
$50$	−13.6748	−1.93391
$51$	−3.11852	−0.436679
$52$	0.0968017	0.0134240
$53$	−10.5620	−1.45081	−0.725403	−	0.688324i	$-0.758347\pi$
$53$	−10.5620	−1.45081	−0.725403	+	0.688324i	$0.758347\pi$
$54$	−3.76501	−0.512353
$55$	−7.14343	−0.963219
$56$	−1.08152	−0.144525
$57$	2.27379	0.301171
$58$	0.744649	0.0977773
$59$	−0.0616620	−0.00802771	−0.00401385	−	0.999992i	$-0.501278\pi$
$59$	−0.0616620	−0.00802771	−0.00401385	+	0.999992i	$0.501278\pi$
$60$	2.93805	0.379301
$61$	−6.28097	−0.804196	−0.402098	−	0.915597i	$-0.631719\pi$
$61$	−6.28097	−0.804196	−0.402098	+	0.915597i	$0.631719\pi$
$62$	−1.00000	−0.127000
$63$	−2.74465	−0.345793
$64$	1.00000	0.125000
$65$	−0.418322	−0.0518864
$66$	1.12386	0.138337
$67$	−3.38171	−0.413142	−0.206571	−	0.978432i	$-0.566230\pi$
$67$	−3.38171	−0.413142	−0.206571	+	0.978432i	$0.566230\pi$
$68$	4.58686	0.556239
$69$	−2.14010	−0.257638
$70$	4.67373	0.558617
$71$	−13.5623	−1.60955	−0.804777	−	0.593577i	$-0.797715\pi$
$71$	−13.5623	−1.60955	−0.804777	+	0.593577i	$0.797715\pi$
$72$	2.53776	0.299078
$73$	15.9363	1.86520	0.932602	−	0.360906i	$-0.117532\pi$
$73$	15.9363	1.86520	0.932602	+	0.360906i	$0.117532\pi$
$74$	−1.71839	−0.199759
$75$	−9.29720	−1.07355
$76$	−3.34440	−0.383629
$77$	1.78778	0.203737
$78$	0.0658135	0.00745191
$79$	3.57644	0.402381	0.201190	−	0.979552i	$-0.435519\pi$
$79$	3.57644	0.402381	0.201190	+	0.979552i	$0.435519\pi$
$80$	−4.32143	−0.483151
$81$	5.05353	0.561504
$82$	−1.17272	−0.129505
$83$	−9.93990	−1.09105	−0.545523	−	0.838096i	$-0.683669\pi$
$83$	−9.93990	−1.09105	−0.545523	+	0.838096i	$0.683669\pi$
$84$	−0.735306	−0.0802284
$85$	−19.8218	−2.14998
$86$	8.75600	0.944184
$87$	0.506272	0.0542781
$88$	−1.65302	−0.176213
$89$	−10.7476	−1.13924	−0.569620	−	0.821908i	$-0.692910\pi$
$89$	−10.7476	−1.13924	−0.569620	+	0.821908i	$0.692910\pi$
$90$	−10.9668	−1.15600
$91$	0.104693	0.0109748
$92$	3.14777	0.328177
$93$	−0.679880	−0.0705003
$94$	10.1418	1.04604
$95$	14.4526	1.48280
$96$	0.679880	0.0693900
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	5.83031	0.588950
$99$	−4.19498	−0.421611
$100$	13.6748	1.36748
$101$	10.4652	1.04133	0.520664	−	0.853762i	$-0.325684\pi$
$101$	10.4652	1.04133	0.520664	+	0.853762i	$0.325684\pi$
$102$	3.11852	0.308779
$103$	20.1209	1.98258	0.991288	−	0.131714i	$-0.0420481\pi$
$103$	20.1209	1.98258	0.991288	+	0.131714i	$0.0420481\pi$
$104$	−0.0968017	−0.00949219
$105$	3.17757	0.310099
$106$	10.5620	1.02588
$107$	7.25592	0.701456	0.350728	−	0.936477i	$-0.385934\pi$
$107$	7.25592	0.701456	0.350728	+	0.936477i	$0.385934\pi$
$108$	3.76501	0.362289
$109$	12.8197	1.22790	0.613952	−	0.789343i	$-0.289579\pi$
$109$	12.8197	1.22790	0.613952	+	0.789343i	$0.289579\pi$
$110$	7.14343	0.681099
$111$	−1.16830	−0.110890
$112$	1.08152	0.102194
$113$	−15.6080	−1.46827	−0.734137	−	0.679002i	$-0.762413\pi$
$113$	−15.6080	−1.46827	−0.734137	+	0.679002i	$0.762413\pi$
$114$	−2.27379	−0.212960
$115$	−13.6029	−1.26847
$116$	−0.744649	−0.0691390
$117$	−0.245660	−0.0227113
$118$	0.0616620	0.00567645
$119$	4.96080	0.454756
$120$	−2.93805	−0.268206
$121$	−8.26752	−0.751592
$122$	6.28097	0.568652
$123$	−0.797306	−0.0718906
$124$	1.00000	0.0898027
$125$	−37.4874	−3.35298
$126$	2.74465	0.244513
$127$	−3.03699	−0.269489	−0.134745	−	0.990880i	$-0.543021\pi$
$127$	−3.03699	−0.269489	−0.134745	+	0.990880i	$0.543021\pi$
$128$	−1.00000	−0.0883883
$129$	5.95303	0.524135
$130$	0.418322	0.0366893
$131$	−6.79761	−0.593910	−0.296955	−	0.954891i	$-0.595971\pi$
$131$	−6.79761	−0.593910	−0.296955	+	0.954891i	$0.595971\pi$
$132$	−1.12386	−0.0978192
$133$	−3.61704	−0.313638
$134$	3.38171	0.292136
$135$	−16.2703	−1.40032
$136$	−4.58686	−0.393320
$137$	18.9970	1.62303	0.811513	−	0.584334i	$-0.198644\pi$
$137$	18.9970	1.62303	0.811513	+	0.584334i	$0.198644\pi$
$138$	2.14010	0.182178
$139$	5.38059	0.456375	0.228188	−	0.973617i	$-0.426720\pi$
$139$	5.38059	0.456375	0.228188	+	0.973617i	$0.426720\pi$
$140$	−4.67373	−0.395002
$141$	6.89519	0.580680
$142$	13.5623	1.13813
$143$	0.160015	0.0133812
$144$	−2.53776	−0.211480
$145$	3.21795	0.267236
$146$	−15.9363	−1.31890
$147$	3.96391	0.326938
$148$	1.71839	0.141251
$149$	−11.5122	−0.943113	−0.471557	−	0.881836i	$-0.656308\pi$
$149$	−11.5122	−0.943113	−0.471557	+	0.881836i	$0.656308\pi$
$150$	9.29720	0.759113
$151$	16.9776	1.38162	0.690809	−	0.723038i	$-0.257255\pi$
$151$	16.9776	1.38162	0.690809	+	0.723038i	$0.257255\pi$
$152$	3.34440	0.271267
$153$	−11.6404	−0.941068
$154$	−1.78778	−0.144064
$155$	−4.32143	−0.347106
$156$	−0.0658135	−0.00526930
$157$	−22.7356	−1.81450	−0.907248	−	0.420596i	$-0.861821\pi$
$157$	−22.7356	−1.81450	−0.907248	+	0.420596i	$0.861821\pi$
$158$	−3.57644	−0.284526
$159$	7.18091	0.569484
$160$	4.32143	0.341639
$161$	3.40438	0.268303
$162$	−5.05353	−0.397043
$163$	0.0892650	0.00699178	0.00349589	−	0.999994i	$-0.498887\pi$
$163$	0.0892650	0.00699178	0.00349589	+	0.999994i	$0.498887\pi$
$164$	1.17272	0.0915737
$165$	4.85667	0.378091
$166$	9.93990	0.771486
$167$	23.0416	1.78301	0.891507	−	0.453007i	$-0.149649\pi$
$167$	23.0416	1.78301	0.891507	+	0.453007i	$0.149649\pi$
$168$	0.735306	0.0567301
$169$	−12.9906	−0.999279
$170$	19.8218	1.52026
$171$	8.48729	0.649039
$172$	−8.75600	−0.667639
$173$	1.45385	0.110534	0.0552670	−	0.998472i	$-0.482399\pi$
$173$	1.45385	0.110534	0.0552670	+	0.998472i	$0.482399\pi$
$174$	−0.506272	−0.0383804
$175$	14.7896	1.11799
$176$	1.65302	0.124601
$177$	0.0419227	0.00315111
$178$	10.7476	0.805565
$179$	18.4320	1.37768	0.688838	−	0.724915i	$-0.258121\pi$
$179$	18.4320	1.37768	0.688838	+	0.724915i	$0.258121\pi$
$180$	10.9668	0.817415
$181$	11.0808	0.823626	0.411813	−	0.911268i	$-0.364896\pi$
$181$	11.0808	0.823626	0.411813	+	0.911268i	$0.364896\pi$
$182$	−0.104693	−0.00776038
$183$	4.27031	0.315670
$184$	−3.14777	−0.232056
$185$	−7.42592	−0.545964
$186$	0.679880	0.0498512
$187$	7.58219	0.554465
$188$	−10.1418	−0.739665
$189$	4.07195	0.296191
$190$	−14.4526	−1.04850
$191$	−15.1366	−1.09525	−0.547623	−	0.836725i	$-0.684467\pi$
$191$	−15.1366	−1.09525	−0.547623	+	0.836725i	$0.684467\pi$
$192$	−0.679880	−0.0490661
$193$	21.4969	1.54738	0.773691	−	0.633564i	$-0.218408\pi$
$193$	21.4969	1.54738	0.773691	+	0.633564i	$0.218408\pi$
$194$	1.00000	0.0717958
$195$	0.284409	0.0203669
$196$	−5.83031	−0.416451
$197$	−15.1806	−1.08157	−0.540785	−	0.841161i	$-0.681873\pi$
$197$	−15.1806	−1.08157	−0.540785	+	0.841161i	$0.681873\pi$
$198$	4.19498	0.298124
$199$	13.0278	0.923519	0.461759	−	0.887005i	$-0.347218\pi$
$199$	13.0278	0.923519	0.461759	+	0.887005i	$0.347218\pi$
$200$	−13.6748	−0.966953
$201$	2.29916	0.162170
$202$	−10.4652	−0.736330
$203$	−0.805356	−0.0565249
$204$	−3.11852	−0.218340
$205$	−5.06781	−0.353951
$206$	−20.1209	−1.40189
$207$	−7.98829	−0.555224
$208$	0.0968017	0.00671199
$209$	−5.52837	−0.382405
$210$	−3.17757	−0.219273
$211$	14.6313	1.00726	0.503629	−	0.863920i	$-0.331998\pi$
$211$	14.6313	1.00726	0.503629	+	0.863920i	$0.331998\pi$
$212$	−10.5620	−0.725403
$213$	9.22077	0.631797
$214$	−7.25592	−0.496004
$215$	37.8385	2.58056
$216$	−3.76501	−0.256177
$217$	1.08152	0.0734186
$218$	−12.8197	−0.868260
$219$	−10.8348	−0.732147
$220$	−7.14343	−0.481610
$221$	0.444016	0.0298677
$222$	1.16830	0.0784112
$223$	16.3888	1.09748	0.548739	−	0.835994i	$-0.315108\pi$
$223$	16.3888	1.09748	0.548739	+	0.835994i	$0.315108\pi$
$224$	−1.08152	−0.0722623
$225$	−34.7033	−2.31356
$226$	15.6080	1.03823
$227$	−0.566205	−0.0375803	−0.0187902	−	0.999823i	$-0.505981\pi$
$227$	−0.566205	−0.0375803	−0.0187902	+	0.999823i	$0.505981\pi$
$228$	2.27379	0.150585
$229$	−18.2043	−1.20298	−0.601489	−	0.798881i	$-0.705425\pi$
$229$	−18.2043	−1.20298	−0.601489	+	0.798881i	$0.705425\pi$
$230$	13.6029	0.896946
$231$	−1.21548	−0.0799725
$232$	0.744649	0.0488886
$233$	−7.52804	−0.493178	−0.246589	−	0.969120i	$-0.579310\pi$
$233$	−7.52804	−0.493178	−0.246589	+	0.969120i	$0.579310\pi$
$234$	0.245660	0.0160593
$235$	43.8270	2.85896
$236$	−0.0616620	−0.00401385
$237$	−2.43155	−0.157946
$238$	−4.96080	−0.321561
$239$	−17.7988	−1.15131	−0.575653	−	0.817694i	$-0.695252\pi$
$239$	−17.7988	−1.15131	−0.575653	+	0.817694i	$0.695252\pi$
$240$	2.93805	0.189651
$241$	−10.5890	−0.682097	−0.341049	−	0.940046i	$-0.610782\pi$
$241$	−10.5890	−0.682097	−0.341049	+	0.940046i	$0.610782\pi$
$242$	8.26752	0.531456
$243$	−14.7308	−0.944984
$244$	−6.28097	−0.402098
$245$	25.1953	1.60967
$246$	0.797306	0.0508344
$247$	−0.323743	−0.0205993
$248$	−1.00000	−0.0635001
$249$	6.75794	0.428267
$250$	37.4874	2.37091
$251$	−20.9663	−1.32338	−0.661690	−	0.749778i	$-0.730160\pi$
$251$	−20.9663	−1.32338	−0.661690	+	0.749778i	$0.730160\pi$
$252$	−2.74465	−0.172897
$253$	5.20333	0.327131
$254$	3.03699	0.190558
$255$	13.4765	0.843928
$256$	1.00000	0.0625000
$257$	26.6081	1.65977	0.829884	−	0.557936i	$-0.188406\pi$
$257$	26.6081	1.65977	0.829884	+	0.557936i	$0.188406\pi$
$258$	−5.95303	−0.370619
$259$	1.85848	0.115480
$260$	−0.418322	−0.0259432
$261$	1.88974	0.116972
$262$	6.79761	0.419958
$263$	−2.61922	−0.161508	−0.0807542	−	0.996734i	$-0.525733\pi$
$263$	−2.61922	−0.161508	−0.0807542	+	0.996734i	$0.525733\pi$
$264$	1.12386	0.0691686
$265$	45.6431	2.80383
$266$	3.61704	0.221775
$267$	7.30706	0.447185
$268$	−3.38171	−0.206571
$269$	−9.24059	−0.563409	−0.281704	−	0.959501i	$-0.590900\pi$
$269$	−9.24059	−0.563409	−0.281704	+	0.959501i	$0.590900\pi$
$270$	16.2703	0.990176
$271$	11.1452	0.677023	0.338512	−	0.940962i	$-0.390077\pi$
$271$	11.1452	0.677023	0.338512	+	0.940962i	$0.390077\pi$
$272$	4.58686	0.278119
$273$	−0.0711788	−0.00430794
$274$	−18.9970	−1.14765
$275$	22.6047	1.36312
$276$	−2.14010	−0.128819
$277$	3.69446	0.221978	0.110989	−	0.993822i	$-0.464598\pi$
$277$	3.69446	0.221978	0.110989	+	0.993822i	$0.464598\pi$
$278$	−5.38059	−0.322706
$279$	−2.53776	−0.151932
$280$	4.67373	0.279309
$281$	28.5471	1.70298	0.851488	−	0.524374i	$-0.175700\pi$
$281$	28.5471	1.70298	0.851488	+	0.524374i	$0.175700\pi$
$282$	−6.89519	−0.410603
$283$	0.253596	0.0150747	0.00753735	−	0.999972i	$-0.497601\pi$
$283$	0.253596	0.0150747	0.00753735	+	0.999972i	$0.497601\pi$
$284$	−13.5623	−0.804777
$285$	−9.82603	−0.582044
$286$	−0.160015	−0.00946191
$287$	1.26832	0.0748665
$288$	2.53776	0.149539
$289$	4.03930	0.237606
$290$	−3.21795	−0.188965
$291$	0.679880	0.0398553
$292$	15.9363	0.932602
$293$	20.0182	1.16948	0.584739	−	0.811222i	$-0.301197\pi$
$293$	20.0182	1.16948	0.584739	+	0.811222i	$0.301197\pi$
$294$	−3.96391	−0.231180
$295$	0.266468	0.0155144
$296$	−1.71839	−0.0998795
$297$	6.22365	0.361133
$298$	11.5122	0.666882
$299$	0.304709	0.0176218
$300$	−9.29720	−0.536774
$301$	−9.46982	−0.545831
$302$	−16.9776	−0.976951
$303$	−7.11509	−0.408751
$304$	−3.34440	−0.191814
$305$	27.1428	1.55419
$306$	11.6404	0.665436
$307$	16.3231	0.931609	0.465805	−	0.884888i	$-0.345765\pi$
$307$	16.3231	0.931609	0.465805	+	0.884888i	$0.345765\pi$
$308$	1.78778	0.101868
$309$	−13.6798	−0.778218
$310$	4.32143	0.245441
$311$	−18.0587	−1.02401	−0.512007	−	0.858981i	$-0.671098\pi$
$311$	−18.0587	−1.02401	−0.512007	+	0.858981i	$0.671098\pi$
$312$	0.0658135	0.00372596
$313$	−6.97868	−0.394458	−0.197229	−	0.980357i	$-0.563194\pi$
$313$	−6.97868	−0.394458	−0.197229	+	0.980357i	$0.563194\pi$
$314$	22.7356	1.28304
$315$	11.8608	0.668281
$316$	3.57644	0.201190
$317$	27.8617	1.56487	0.782436	−	0.622731i	$-0.213977\pi$
$317$	27.8617	1.56487	0.782436	+	0.622731i	$0.213977\pi$
$318$	−7.18091	−0.402686
$319$	−1.23092	−0.0689184
$320$	−4.32143	−0.241575
$321$	−4.93315	−0.275342
$322$	−3.40438	−0.189719
$323$	−15.3403	−0.853557
$324$	5.05353	0.280752
$325$	1.32374	0.0734279
$326$	−0.0892650	−0.00494393
$327$	−8.71586	−0.481988
$328$	−1.17272	−0.0647524
$329$	−10.9686	−0.604717
$330$	−4.85667	−0.267351
$331$	11.0248	0.605980	0.302990	−	0.952994i	$-0.402015\pi$
$331$	11.0248	0.605980	0.302990	+	0.952994i	$0.402015\pi$
$332$	−9.93990	−0.545523
$333$	−4.36087	−0.238974
$334$	−23.0416	−1.26078
$335$	14.6138	0.798440
$336$	−0.735306	−0.0401142
$337$	−1.33611	−0.0727828	−0.0363914	−	0.999338i	$-0.511586\pi$
$337$	−1.33611	−0.0727828	−0.0363914	+	0.999338i	$0.511586\pi$
$338$	12.9906	0.706597
$339$	10.6115	0.576340
$340$	−19.8218	−1.07499
$341$	1.65302	0.0895162
$342$	−8.48729	−0.458940
$343$	−13.8763	−0.749248
$344$	8.75600	0.472092
$345$	9.24831	0.497912
$346$	−1.45385	−0.0781593
$347$	26.6329	1.42973	0.714865	−	0.699262i	$-0.246488\pi$
$347$	26.6329	1.42973	0.714865	+	0.699262i	$0.246488\pi$
$348$	0.506272	0.0271390
$349$	4.43519	0.237410	0.118705	−	0.992930i	$-0.462126\pi$
$349$	4.43519	0.237410	0.118705	+	0.992930i	$0.462126\pi$
$350$	−14.7896	−0.790537
$351$	0.364460	0.0194534
$352$	−1.65302	−0.0881064
$353$	−7.65347	−0.407353	−0.203676	−	0.979038i	$-0.565289\pi$
$353$	−7.65347	−0.407353	−0.203676	+	0.979038i	$0.565289\pi$
$354$	−0.0419227	−0.00222817
$355$	58.6088	3.11063
$356$	−10.7476	−0.569620
$357$	−3.37275	−0.178505
$358$	−18.4320	−0.974164
$359$	−17.6190	−0.929893	−0.464947	−	0.885339i	$-0.653927\pi$
$359$	−17.6190	−0.929893	−0.464947	+	0.885339i	$0.653927\pi$
$360$	−10.9668	−0.578000
$361$	−7.81500	−0.411316
$362$	−11.0808	−0.582392
$363$	5.62092	0.295022
$364$	0.104693	0.00548742
$365$	−68.8677	−3.60470
$366$	−4.27031	−0.223212
$367$	23.6797	1.23607	0.618035	−	0.786151i	$-0.287929\pi$
$367$	23.6797	1.23607	0.618035	+	0.786151i	$0.287929\pi$
$368$	3.14777	0.164089
$369$	−2.97607	−0.154928
$370$	7.42592	0.386055
$371$	−11.4231	−0.593057
$372$	−0.679880	−0.0352501
$373$	−27.0414	−1.40015	−0.700076	−	0.714068i	$-0.746851\pi$
$373$	−27.0414	−1.40015	−0.700076	+	0.714068i	$0.746851\pi$
$374$	−7.58219	−0.392066
$375$	25.4870	1.31614
$376$	10.1418	0.523022
$377$	−0.0720833	−0.00371248
$378$	−4.07195	−0.209439
$379$	28.9055	1.48477	0.742387	−	0.669971i	$-0.233694\pi$
$379$	28.9055	1.48477	0.742387	+	0.669971i	$0.233694\pi$
$380$	14.4526	0.741402
$381$	2.06479	0.105782
$382$	15.1366	0.774455
$383$	−22.3144	−1.14021	−0.570106	−	0.821571i	$-0.693098\pi$
$383$	−22.3144	−1.14021	−0.570106	+	0.821571i	$0.693098\pi$
$384$	0.679880	0.0346950
$385$	−7.72578	−0.393742
$386$	−21.4969	−1.09416
$387$	22.2207	1.12954
$388$	−1.00000	−0.0507673
$389$	−16.0875	−0.815670	−0.407835	−	0.913056i	$-0.633716\pi$
$389$	−16.0875	−0.815670	−0.407835	+	0.913056i	$0.633716\pi$
$390$	−0.284409	−0.0144016
$391$	14.4384	0.730180
$392$	5.83031	0.294475
$393$	4.62156	0.233127
$394$	15.1806	0.764785
$395$	−15.4553	−0.777642
$396$	−4.19498	−0.210806
$397$	1.73829	0.0872422	0.0436211	−	0.999048i	$-0.486111\pi$
$397$	1.73829	0.0872422	0.0436211	+	0.999048i	$0.486111\pi$
$398$	−13.0278	−0.653027
$399$	2.45916	0.123112
$400$	13.6748	0.683739
$401$	8.36205	0.417581	0.208790	−	0.977960i	$-0.433047\pi$
$401$	8.36205	0.417581	0.208790	+	0.977960i	$0.433047\pi$
$402$	−2.29916	−0.114672
$403$	0.0968017	0.00482204
$404$	10.4652	0.520664
$405$	−21.8385	−1.08516
$406$	0.805356	0.0399691
$407$	2.84054	0.140800
$408$	3.11852	0.154390
$409$	21.8022	1.07805	0.539025	−	0.842289i	$-0.318793\pi$
$409$	21.8022	1.07805	0.539025	+	0.842289i	$0.318793\pi$
$410$	5.06781	0.250281
$411$	−12.9157	−0.637085
$412$	20.1209	0.991288
$413$	−0.0666889	−0.00328155
$414$	7.98829	0.392603
$415$	42.9546	2.10856
$416$	−0.0968017	−0.00474609
$417$	−3.65815	−0.179140
$418$	5.52837	0.270401
$419$	1.83467	0.0896297	0.0448148	−	0.998995i	$-0.485730\pi$
$419$	1.83467	0.0896297	0.0448148	+	0.998995i	$0.485730\pi$
$420$	3.17757	0.155050
$421$	10.8477	0.528685	0.264343	−	0.964429i	$-0.414845\pi$
$421$	10.8477	0.528685	0.264343	+	0.964429i	$0.414845\pi$
$422$	−14.6313	−0.712239
$423$	25.7374	1.25140
$424$	10.5620	0.512938
$425$	62.7243	3.04258
$426$	−9.22077	−0.446748
$427$	−6.79302	−0.328737
$428$	7.25592	0.350728
$429$	−0.108791	−0.00525249
$430$	−37.8385	−1.82473
$431$	−31.1173	−1.49887	−0.749433	−	0.662080i	$-0.769674\pi$
$431$	−31.1173	−1.49887	−0.749433	+	0.662080i	$0.769674\pi$
$432$	3.76501	0.181144
$433$	4.31878	0.207547	0.103774	−	0.994601i	$-0.466908\pi$
$433$	4.31878	0.207547	0.103774	+	0.994601i	$0.466908\pi$
$434$	−1.08152	−0.0519148
$435$	−2.18782	−0.104898
$436$	12.8197	0.613952
$437$	−10.5274	−0.503593
$438$	10.8348	0.517706
$439$	−9.06024	−0.432422	−0.216211	−	0.976347i	$-0.569370\pi$
$439$	−9.06024	−0.432422	−0.216211	+	0.976347i	$0.569370\pi$
$440$	7.14343	0.340549
$441$	14.7959	0.704569
$442$	−0.444016	−0.0211197
$443$	−6.25780	−0.297317	−0.148659	−	0.988889i	$-0.547496\pi$
$443$	−6.25780	−0.297317	−0.148659	+	0.988889i	$0.547496\pi$
$444$	−1.16830	−0.0554451
$445$	46.4449	2.20170
$446$	−16.3888	−0.776035
$447$	7.82689	0.370199
$448$	1.08152	0.0510972
$449$	30.9961	1.46279	0.731397	−	0.681952i	$-0.238869\pi$
$449$	30.9961	1.46279	0.731397	+	0.681952i	$0.238869\pi$
$450$	34.7033	1.63593
$451$	1.93853	0.0912816
$452$	−15.6080	−0.734137
$453$	−11.5427	−0.542325
$454$	0.566205	0.0265733
$455$	−0.452425	−0.0212100
$456$	−2.27379	−0.106480
$457$	−3.04660	−0.142514	−0.0712570	−	0.997458i	$-0.522701\pi$
$457$	−3.04660	−0.142514	−0.0712570	+	0.997458i	$0.522701\pi$
$458$	18.2043	0.850633
$459$	17.2696	0.806076
$460$	−13.6029	−0.634237
$461$	34.4896	1.60634	0.803170	−	0.595750i	$-0.203145\pi$
$461$	34.4896	1.60634	0.803170	+	0.595750i	$0.203145\pi$
$462$	1.21548	0.0565491
$463$	−22.0155	−1.02315	−0.511574	−	0.859240i	$-0.670937\pi$
$463$	−22.0155	−1.02315	−0.511574	+	0.859240i	$0.670937\pi$
$464$	−0.744649	−0.0345695
$465$	2.93805	0.136249
$466$	7.52804	0.348730
$467$	−21.8257	−1.00997	−0.504987	−	0.863127i	$-0.668503\pi$
$467$	−21.8257	−1.00997	−0.504987	+	0.863127i	$0.668503\pi$
$468$	−0.245660	−0.0113556
$469$	−3.65740	−0.168883
$470$	−43.8270	−2.02159
$471$	15.4575	0.712242
$472$	0.0616620	0.00283822
$473$	−14.4739	−0.665509
$474$	2.43155	0.111685
$475$	−45.7339	−2.09842
$476$	4.96080	0.227378
$477$	26.8039	1.22727
$478$	17.7988	0.814096
$479$	12.8202	0.585771	0.292886	−	0.956147i	$-0.405384\pi$
$479$	12.8202	0.585771	0.292886	+	0.956147i	$0.405384\pi$
$480$	−2.93805	−0.134103
$481$	0.166343	0.00758460
$482$	10.5890	0.482316
$483$	−2.31457	−0.105317
$484$	−8.26752	−0.375796
$485$	4.32143	0.196226
$486$	14.7308	0.668204
$487$	−4.26987	−0.193486	−0.0967431	−	0.995309i	$-0.530843\pi$
$487$	−4.26987	−0.193486	−0.0967431	+	0.995309i	$0.530843\pi$
$488$	6.28097	0.284326
$489$	−0.0606895	−0.00274447
$490$	−25.1953	−1.13821
$491$	38.3770	1.73193	0.865965	−	0.500104i	$-0.166705\pi$
$491$	38.3770	1.73193	0.865965	+	0.500104i	$0.166705\pi$
$492$	−0.797306	−0.0359453
$493$	−3.41560	−0.153831
$494$	0.323743	0.0145659
$495$	18.1283	0.814808
$496$	1.00000	0.0449013
$497$	−14.6680	−0.657949
$498$	−6.75794	−0.302831
$499$	−16.0419	−0.718133	−0.359067	−	0.933312i	$-0.616905\pi$
$499$	−16.0419	−0.718133	−0.359067	+	0.933312i	$0.616905\pi$
$500$	−37.4874	−1.67649
$501$	−15.6655	−0.699884
$502$	20.9663	0.935771
$503$	−5.45218	−0.243101	−0.121550	−	0.992585i	$-0.538787\pi$
$503$	−5.45218	−0.243101	−0.121550	+	0.992585i	$0.538787\pi$
$504$	2.74465	0.122256
$505$	−45.2247	−2.01247
$506$	−5.20333	−0.231316
$507$	8.83207	0.392246
$508$	−3.03699	−0.134745
$509$	29.2174	1.29504	0.647519	−	0.762049i	$-0.275807\pi$
$509$	29.2174	1.29504	0.647519	+	0.762049i	$0.275807\pi$
$510$	−13.4765	−0.596747
$511$	17.2355	0.762453
$512$	−1.00000	−0.0441942
$513$	−12.5917	−0.555937
$514$	−26.6081	−1.17363
$515$	−86.9513	−3.83153
$516$	5.95303	0.262067
$517$	−16.7646	−0.737306
$518$	−1.85848	−0.0816570
$519$	−0.988442	−0.0433878
$520$	0.418322	0.0183446
$521$	8.31800	0.364418	0.182209	−	0.983260i	$-0.441675\pi$
$521$	8.31800	0.364418	0.182209	+	0.983260i	$0.441675\pi$
$522$	−1.88974	−0.0827119
$523$	−10.1205	−0.442540	−0.221270	−	0.975213i	$-0.571020\pi$
$523$	−10.1205	−0.442540	−0.221270	+	0.975213i	$0.571020\pi$
$524$	−6.79761	−0.296955
$525$	−10.0551	−0.438842
$526$	2.61922	0.114204
$527$	4.58686	0.199807
$528$	−1.12386	−0.0489096
$529$	−13.0916	−0.569198
$530$	−45.6431	−1.98261
$531$	0.156484	0.00679081
$532$	−3.61704	−0.156819
$533$	0.113521	0.00491713
$534$	−7.30706	−0.316207
$535$	−31.3560	−1.35564
$536$	3.38171	0.146068
$537$	−12.5316	−0.540777
$538$	9.24059	0.398390
$539$	−9.63763	−0.415122
$540$	−16.2703	−0.700160
$541$	28.9142	1.24312	0.621558	−	0.783368i	$-0.286500\pi$
$541$	28.9142	1.24312	0.621558	+	0.783368i	$0.286500\pi$
$542$	−11.1452	−0.478728
$543$	−7.53358	−0.323297
$544$	−4.58686	−0.196660
$545$	−55.3995	−2.37305
$546$	0.0711788	0.00304617
$547$	−9.26357	−0.396081	−0.198041	−	0.980194i	$-0.563458\pi$
$547$	−9.26357	−0.396081	−0.198041	+	0.980194i	$0.563458\pi$
$548$	18.9970	0.811513
$549$	15.9396	0.680286
$550$	−22.6047	−0.963868
$551$	2.49040	0.106095
$552$	2.14010	0.0910889
$553$	3.86800	0.164484
$554$	−3.69446	−0.156962
$555$	5.04873	0.214307
$556$	5.38059	0.228188
$557$	−1.94480	−0.0824040	−0.0412020	−	0.999151i	$-0.513119\pi$
$557$	−1.94480	−0.0824040	−0.0412020	+	0.999151i	$0.513119\pi$
$558$	2.53776	0.107432
$559$	−0.847596	−0.0358495
$560$	−4.67373	−0.197501
$561$	−5.15498	−0.217643
$562$	−28.5471	−1.20419
$563$	−23.9145	−1.00788	−0.503938	−	0.863740i	$-0.668116\pi$
$563$	−23.9145	−1.00788	−0.503938	+	0.863740i	$0.668116\pi$
$564$	6.89519	0.290340
$565$	67.4487	2.83759
$566$	−0.253596	−0.0106594
$567$	5.46551	0.229530
$568$	13.5623	0.569063
$569$	−2.93700	−0.123126	−0.0615628	−	0.998103i	$-0.519608\pi$
$569$	−2.93700	−0.123126	−0.0615628	+	0.998103i	$0.519608\pi$
$570$	9.82603	0.411567
$571$	2.73373	0.114403	0.0572015	−	0.998363i	$-0.481782\pi$
$571$	2.73373	0.114403	0.0572015	+	0.998363i	$0.481782\pi$
$572$	0.160015	0.00669058
$573$	10.2911	0.429915
$574$	−1.26832	−0.0529386
$575$	43.0450	1.79510
$576$	−2.53776	−0.105740
$577$	−6.94880	−0.289283	−0.144641	−	0.989484i	$-0.546203\pi$
$577$	−6.94880	−0.289283	−0.144641	+	0.989484i	$0.546203\pi$
$578$	−4.03930	−0.168013
$579$	−14.6153	−0.607392
$580$	3.21795	0.133618
$581$	−10.7502	−0.445995
$582$	−0.679880	−0.0281819
$583$	−17.4593	−0.723090
$584$	−15.9363	−0.659449
$585$	1.06160	0.0438918
$586$	−20.0182	−0.826945
$587$	30.8438	1.27306	0.636529	−	0.771252i	$-0.280369\pi$
$587$	30.8438	1.27306	0.636529	+	0.771252i	$0.280369\pi$
$588$	3.96391	0.163469
$589$	−3.34440	−0.137804
$590$	−0.266468	−0.0109703
$591$	10.3210	0.424547
$592$	1.71839	0.0706255
$593$	−1.44918	−0.0595108	−0.0297554	−	0.999557i	$-0.509473\pi$
$593$	−1.44918	−0.0595108	−0.0297554	+	0.999557i	$0.509473\pi$
$594$	−6.22365	−0.255360
$595$	−21.4377	−0.878862
$596$	−11.5122	−0.471557
$597$	−8.85736	−0.362508
$598$	−0.304709	−0.0124605
$599$	12.5259	0.511796	0.255898	−	0.966704i	$-0.417629\pi$
$599$	12.5259	0.511796	0.255898	+	0.966704i	$0.417629\pi$
$600$	9.29720	0.379557
$601$	36.7711	1.49993	0.749963	−	0.661480i	$-0.230071\pi$
$601$	36.7711	1.49993	0.749963	+	0.661480i	$0.230071\pi$
$602$	9.46982	0.385961
$603$	8.58199	0.349486
$604$	16.9776	0.690809
$605$	35.7275	1.45253
$606$	7.11509	0.289031
$607$	5.34813	0.217074	0.108537	−	0.994092i	$-0.465383\pi$
$607$	5.34813	0.217074	0.108537	+	0.994092i	$0.465383\pi$
$608$	3.34440	0.135633
$609$	0.547545	0.0221876
$610$	−27.1428	−1.09898
$611$	−0.981741	−0.0397170
$612$	−11.6404	−0.470534
$613$	39.3594	1.58971	0.794855	−	0.606799i	$-0.207547\pi$
$613$	39.3594	1.58971	0.794855	+	0.606799i	$0.207547\pi$
$614$	−16.3231	−0.658747
$615$	3.44550	0.138936
$616$	−1.78778	−0.0720318
$617$	11.5981	0.466922	0.233461	−	0.972366i	$-0.424995\pi$
$617$	11.5981	0.466922	0.233461	+	0.972366i	$0.424995\pi$
$618$	13.6798	0.550283
$619$	24.8548	0.999000	0.499500	−	0.866314i	$-0.333517\pi$
$619$	24.8548	0.999000	0.499500	+	0.866314i	$0.333517\pi$
$620$	−4.32143	−0.173553
$621$	11.8514	0.475580
$622$	18.0587	0.724088
$623$	−11.6237	−0.465696
$624$	−0.0658135	−0.00263465
$625$	93.6256	3.74502
$626$	6.97868	0.278924
$627$	3.75863	0.150105
$628$	−22.7356	−0.907248
$629$	7.88203	0.314277
$630$	−11.8608	−0.472546
$631$	3.59247	0.143014	0.0715069	−	0.997440i	$-0.477219\pi$
$631$	3.59247	0.143014	0.0715069	+	0.997440i	$0.477219\pi$
$632$	−3.57644	−0.142263
$633$	−9.94750	−0.395378
$634$	−27.8617	−1.10653
$635$	13.1241	0.520815
$636$	7.18091	0.284742
$637$	−0.564384	−0.0223617
$638$	1.23092	0.0487327
$639$	34.4180	1.36156
$640$	4.32143	0.170820
$641$	−17.6666	−0.697790	−0.348895	−	0.937162i	$-0.613443\pi$
$641$	−17.6666	−0.697790	−0.348895	+	0.937162i	$0.613443\pi$
$642$	4.93315	0.194696
$643$	41.9074	1.65267	0.826333	−	0.563182i	$-0.190423\pi$
$643$	41.9074	1.65267	0.826333	+	0.563182i	$0.190423\pi$
$644$	3.40438	0.134151
$645$	−25.7256	−1.01294
$646$	15.3403	0.603556
$647$	32.1170	1.26265	0.631324	−	0.775519i	$-0.282512\pi$
$647$	32.1170	1.26265	0.631324	+	0.775519i	$0.282512\pi$
$648$	−5.05353	−0.198522
$649$	−0.101929	−0.00400105
$650$	−1.32374	−0.0519214
$651$	−0.735306	−0.0288189
$652$	0.0892650	0.00349589
$653$	−35.7847	−1.40036	−0.700181	−	0.713965i	$-0.746897\pi$
$653$	−35.7847	−1.40036	−0.700181	+	0.713965i	$0.746897\pi$
$654$	8.71586	0.340817
$655$	29.3754	1.14779
$656$	1.17272	0.0457868
$657$	−40.4426	−1.57782
$658$	10.9686	0.427599
$659$	−36.0585	−1.40464	−0.702319	−	0.711862i	$-0.747852\pi$
$659$	−36.0585	−1.40464	−0.702319	+	0.711862i	$0.747852\pi$
$660$	4.85667	0.189046
$661$	−28.1361	−1.09437	−0.547183	−	0.837013i	$-0.684300\pi$
$661$	−28.1361	−1.09437	−0.547183	+	0.837013i	$0.684300\pi$
$662$	−11.0248	−0.428492
$663$	−0.301878	−0.0117240
$664$	9.93990	0.385743
$665$	15.6308	0.606137
$666$	4.36087	0.168980
$667$	−2.34398	−0.0907594
$668$	23.0416	0.891507
$669$	−11.1424	−0.430792
$670$	−14.6138	−0.564582
$671$	−10.3826	−0.400815
$672$	0.735306	0.0283650
$673$	46.4593	1.79087	0.895437	−	0.445187i	$-0.146863\pi$
$673$	46.4593	1.79087	0.895437	+	0.445187i	$0.146863\pi$
$674$	1.33611	0.0514652
$675$	51.4857	1.98169
$676$	−12.9906	−0.499640
$677$	−34.5889	−1.32936	−0.664679	−	0.747129i	$-0.731432\pi$
$677$	−34.5889	−1.32936	−0.664679	+	0.747129i	$0.731432\pi$
$678$	−10.6115	−0.407534
$679$	−1.08152	−0.0415051
$680$	19.8218	0.760132
$681$	0.384951	0.0147514
$682$	−1.65302	−0.0632975
$683$	−14.3554	−0.549296	−0.274648	−	0.961545i	$-0.588561\pi$
$683$	−14.3554	−0.549296	−0.274648	+	0.961545i	$0.588561\pi$
$684$	8.48729	0.324520
$685$	−82.0944	−3.13667
$686$	13.8763	0.529799
$687$	12.3768	0.472203
$688$	−8.75600	−0.333819
$689$	−1.02242	−0.0389512
$690$	−9.24831	−0.352077
$691$	26.6753	1.01478	0.507389	−	0.861717i	$-0.330611\pi$
$691$	26.6753	1.01478	0.507389	+	0.861717i	$0.330611\pi$
$692$	1.45385	0.0552670
$693$	−4.53697	−0.172345
$694$	−26.6329	−1.01097
$695$	−23.2518	−0.881992
$696$	−0.506272	−0.0191902
$697$	5.37908	0.203747
$698$	−4.43519	−0.167874
$699$	5.11816	0.193587
$700$	14.7896	0.558994
$701$	−28.0857	−1.06078	−0.530392	−	0.847753i	$-0.677955\pi$
$701$	−28.0857	−1.06078	−0.530392	+	0.847753i	$0.677955\pi$
$702$	−0.364460	−0.0137556
$703$	−5.74699	−0.216752
$704$	1.65302	0.0623006
$705$	−29.7971	−1.12222
$706$	7.65347	0.288042
$707$	11.3184	0.425671
$708$	0.0419227	0.00157555
$709$	2.63526	0.0989693	0.0494847	−	0.998775i	$-0.484242\pi$
$709$	2.63526	0.0989693	0.0494847	+	0.998775i	$0.484242\pi$
$710$	−58.6088	−2.19955
$711$	−9.07615	−0.340382
$712$	10.7476	0.402782
$713$	3.14777	0.117885
$714$	3.37275	0.126222
$715$	−0.691496	−0.0258605
$716$	18.4320	0.688838
$717$	12.1010	0.451921
$718$	17.6190	0.657534
$719$	40.3182	1.50362	0.751808	−	0.659382i	$-0.229182\pi$
$719$	40.3182	1.50362	0.751808	+	0.659382i	$0.229182\pi$
$720$	10.9668	0.408707
$721$	21.7613	0.810432
$722$	7.81500	0.290844
$723$	7.19925	0.267743
$724$	11.0808	0.411813
$725$	−10.1829	−0.378184
$726$	−5.62092	−0.208612
$727$	−29.5129	−1.09457	−0.547286	−	0.836946i	$-0.684339\pi$
$727$	−29.5129	−1.09457	−0.547286	+	0.836946i	$0.684339\pi$
$728$	−0.104693	−0.00388019
$729$	−5.14540	−0.190570
$730$	68.8677	2.54891
$731$	−40.1626	−1.48547
$732$	4.27031	0.157835
$733$	−0.961614	−0.0355180	−0.0177590	−	0.999842i	$-0.505653\pi$
$733$	−0.961614	−0.0355180	−0.0177590	+	0.999842i	$0.505653\pi$
$734$	−23.6797	−0.874033
$735$	−17.1298	−0.631841
$736$	−3.14777	−0.116028
$737$	−5.59005	−0.205912
$738$	2.97607	0.109551
$739$	8.41867	0.309686	0.154843	−	0.987939i	$-0.450513\pi$
$739$	8.41867	0.309686	0.154843	+	0.987939i	$0.450513\pi$
$740$	−7.42592	−0.272982
$741$	0.220107	0.00808582
$742$	11.4231	0.419355
$743$	47.2371	1.73296	0.866480	−	0.499211i	$-0.166377\pi$
$743$	47.2371	1.73296	0.866480	+	0.499211i	$0.166377\pi$
$744$	0.679880	0.0249256
$745$	49.7490	1.82266
$746$	27.0414	0.990057
$747$	25.2251	0.922939
$748$	7.58219	0.277232
$749$	7.84744	0.286739
$750$	−25.4870	−0.930652
$751$	45.2812	1.65233	0.826167	−	0.563425i	$-0.190517\pi$
$751$	45.2812	1.65233	0.826167	+	0.563425i	$0.190517\pi$
$752$	−10.1418	−0.369833
$753$	14.2545	0.519465
$754$	0.0720833	0.00262512
$755$	−73.3675	−2.67012
$756$	4.07195	0.148095
$757$	9.95947	0.361983	0.180992	−	0.983485i	$-0.442069\pi$
$757$	9.95947	0.361983	0.180992	+	0.983485i	$0.442069\pi$
$758$	−28.9055	−1.04989
$759$	−3.53764	−0.128408
$760$	−14.4526	−0.524251
$761$	29.2027	1.05860	0.529299	−	0.848435i	$-0.322455\pi$
$761$	29.2027	1.05860	0.529299	+	0.848435i	$0.322455\pi$
$762$	−2.06479	−0.0747993
$763$	13.8648	0.501940
$764$	−15.1366	−0.547623
$765$	50.3031	1.81871
$766$	22.3144	0.806252
$767$	−0.00596899	−0.000215528 0
$768$	−0.679880	−0.0245331
$769$	25.7358	0.928058	0.464029	−	0.885820i	$-0.346403\pi$
$769$	25.7358	0.928058	0.464029	+	0.885820i	$0.346403\pi$
$770$	7.72578	0.278418
$771$	−18.0903	−0.651507
$772$	21.4969	0.773691
$773$	−45.8964	−1.65078	−0.825389	−	0.564565i	$-0.809044\pi$
$773$	−45.8964	−1.65078	−0.825389	+	0.564565i	$0.809044\pi$
$774$	−22.2207	−0.798705
$775$	13.6748	0.491212
$776$	1.00000	0.0358979
$777$	−1.26354	−0.0453294
$778$	16.0875	0.576766
$779$	−3.92203	−0.140521
$780$	0.284409	0.0101835
$781$	−22.4189	−0.802210
$782$	−14.4384	−0.516315
$783$	−2.80362	−0.100193
$784$	−5.83031	−0.208225
$785$	98.2502	3.50670
$786$	−4.62156	−0.164846
$787$	−11.8052	−0.420810	−0.210405	−	0.977614i	$-0.567478\pi$
$787$	−11.8052	−0.420810	−0.210405	+	0.977614i	$0.567478\pi$
$788$	−15.1806	−0.540785
$789$	1.78076	0.0633967
$790$	15.4553	0.549876
$791$	−16.8804	−0.600197
$792$	4.19498	0.149062
$793$	−0.608009	−0.0215910
$794$	−1.73829	−0.0616895
$795$	−31.0318	−1.10059
$796$	13.0278	0.461759
$797$	11.7356	0.415696	0.207848	−	0.978161i	$-0.433354\pi$
$797$	11.7356	0.415696	0.207848	+	0.978161i	$0.433354\pi$
$798$	−2.45916	−0.0870532
$799$	−46.5189	−1.64572
$800$	−13.6748	−0.483476
$801$	27.2748	0.963708
$802$	−8.36205	−0.295274
$803$	26.3431	0.929628
$804$	2.29916	0.0810851
$805$	−14.7118	−0.518523
$806$	−0.0968017	−0.00340969
$807$	6.28249	0.221154
$808$	−10.4652	−0.368165
$809$	26.1854	0.920628	0.460314	−	0.887756i	$-0.347737\pi$
$809$	26.1854	0.920628	0.460314	+	0.887756i	$0.347737\pi$
$810$	21.8385	0.767327
$811$	44.5978	1.56604	0.783020	−	0.621997i	$-0.213678\pi$
$811$	44.5978	1.56604	0.783020	+	0.621997i	$0.213678\pi$
$812$	−0.805356	−0.0282624
$813$	−7.57740	−0.265751
$814$	−2.84054	−0.0995609
$815$	−0.385753	−0.0135123
$816$	−3.11852	−0.109170
$817$	29.2836	1.02450
$818$	−21.8022	−0.762297
$819$	−0.265687	−0.00928385
$820$	−5.06781	−0.176976
$821$	3.40981	0.119003	0.0595015	−	0.998228i	$-0.481049\pi$
$821$	3.40981	0.119003	0.0595015	+	0.998228i	$0.481049\pi$
$822$	12.9157	0.450487
$823$	−10.4335	−0.363689	−0.181844	−	0.983327i	$-0.558207\pi$
$823$	−10.4335	−0.363689	−0.181844	+	0.983327i	$0.558207\pi$
$824$	−20.1209	−0.700946
$825$	−15.3685	−0.535062
$826$	0.0666889	0.00232040
$827$	51.1374	1.77822	0.889110	−	0.457694i	$-0.151324\pi$
$827$	51.1374	1.77822	0.889110	+	0.457694i	$0.151324\pi$
$828$	−7.98829	−0.277612
$829$	−41.9900	−1.45837	−0.729186	−	0.684316i	$-0.760101\pi$
$829$	−41.9900	−1.45837	−0.729186	+	0.684316i	$0.760101\pi$
$830$	−42.9546	−1.49098
$831$	−2.51179	−0.0871329
$832$	0.0968017	0.00335599
$833$	−26.7428	−0.926584
$834$	3.65815	0.126671
$835$	−99.5728	−3.44586
$836$	−5.52837	−0.191203
$837$	3.76501	0.130138
$838$	−1.83467	−0.0633777
$839$	2.04492	0.0705983	0.0352992	−	0.999377i	$-0.488762\pi$
$839$	2.04492	0.0705983	0.0352992	+	0.999377i	$0.488762\pi$
$840$	−3.17757	−0.109637
$841$	−28.4455	−0.980879
$842$	−10.8477	−0.373837
$843$	−19.4086	−0.668467
$844$	14.6313	0.503629
$845$	56.1381	1.93121
$846$	−25.7374	−0.884871
$847$	−8.94151	−0.307234
$848$	−10.5620	−0.362702
$849$	−0.172415	−0.00591726
$850$	−62.7243	−2.15143
$851$	5.40910	0.185422
$852$	9.22077	0.315898
$853$	−38.8461	−1.33007	−0.665033	−	0.746814i	$-0.731583\pi$
$853$	−38.8461	−1.33007	−0.665033	+	0.746814i	$0.731583\pi$
$854$	6.79302	0.232452
$855$	−36.6773	−1.25434
$856$	−7.25592	−0.248002
$857$	7.25299	0.247757	0.123879	−	0.992297i	$-0.460467\pi$
$857$	7.25299	0.247757	0.123879	+	0.992297i	$0.460467\pi$
$858$	0.108791	0.00371407
$859$	−16.0418	−0.547340	−0.273670	−	0.961824i	$-0.588238\pi$
$859$	−16.0418	−0.547340	−0.273670	+	0.961824i	$0.588238\pi$
$860$	37.8385	1.29028
$861$	−0.862305	−0.0293873
$862$	31.1173	1.05986
$863$	−38.3455	−1.30530	−0.652648	−	0.757662i	$-0.726342\pi$
$863$	−38.3455	−1.30530	−0.652648	+	0.757662i	$0.726342\pi$
$864$	−3.76501	−0.128088
$865$	−6.28270	−0.213618
$866$	−4.31878	−0.146758
$867$	−2.74624	−0.0932673
$868$	1.08152	0.0367093
$869$	5.91193	0.200549
$870$	2.18782	0.0741741
$871$	−0.327356	−0.0110920
$872$	−12.8197	−0.434130
$873$	2.53776	0.0858903
$874$	10.5274	0.356094
$875$	−40.5435	−1.37062
$876$	−10.8348	−0.366073
$877$	36.6528	1.23768	0.618838	−	0.785518i	$-0.287604\pi$
$877$	36.6528	1.23768	0.618838	+	0.785518i	$0.287604\pi$
$878$	9.06024	0.305768
$879$	−13.6100	−0.459053
$880$	−7.14343	−0.240805
$881$	53.9224	1.81669	0.908346	−	0.418219i	$-0.137345\pi$
$881$	53.9224	1.81669	0.908346	+	0.418219i	$0.137345\pi$
$882$	−14.7959	−0.498205
$883$	−27.4985	−0.925397	−0.462698	−	0.886516i	$-0.653119\pi$
$883$	−27.4985	−0.925397	−0.462698	+	0.886516i	$0.653119\pi$
$884$	0.444016	0.0149339
$885$	−0.181166	−0.00608984
$886$	6.25780	0.210235
$887$	−15.8311	−0.531558	−0.265779	−	0.964034i	$-0.585629\pi$
$887$	−15.8311	−0.531558	−0.265779	+	0.964034i	$0.585629\pi$
$888$	1.16830	0.0392056
$889$	−3.28457	−0.110161
$890$	−46.4449	−1.55684
$891$	8.35361	0.279856
$892$	16.3888	0.548739
$893$	33.9181	1.13503
$894$	−7.82689	−0.261770
$895$	−79.6528	−2.66250
$896$	−1.08152	−0.0361312
$897$	−0.207166	−0.00691706
$898$	−30.9961	−1.03435
$899$	−0.744649	−0.0248355
$900$	−34.7033	−1.15678
$901$	−48.4466	−1.61399
$902$	−1.93853	−0.0645458
$903$	6.43834	0.214254
$904$	15.6080	0.519113
$905$	−47.8847	−1.59174
$906$	11.5427	0.383481
$907$	26.8204	0.890555	0.445278	−	0.895393i	$-0.353105\pi$
$907$	26.8204	0.890555	0.445278	+	0.895393i	$0.353105\pi$
$908$	−0.566205	−0.0187902
$909$	−26.5583	−0.880882
$910$	0.452425	0.0149977
$911$	56.3949	1.86845	0.934223	−	0.356690i	$-0.116095\pi$
$911$	56.3949	1.86845	0.934223	+	0.356690i	$0.116095\pi$
$912$	2.27379	0.0752927
$913$	−16.4309	−0.543783
$914$	3.04660	0.100773
$915$	−18.4538	−0.610065
$916$	−18.2043	−0.601489
$917$	−7.35178	−0.242777
$918$	−17.2696	−0.569982
$919$	32.5803	1.07473	0.537363	−	0.843351i	$-0.319421\pi$
$919$	32.5803	1.07473	0.537363	+	0.843351i	$0.319421\pi$
$920$	13.6029	0.448473
$921$	−11.0978	−0.365683
$922$	−34.4896	−1.13585
$923$	−1.31286	−0.0432132
$924$	−1.21548	−0.0399863
$925$	23.4986	0.772630
$926$	22.0155	0.723474
$927$	−51.0622	−1.67710
$928$	0.744649	0.0244443
$929$	31.2744	1.02608	0.513039	−	0.858365i	$-0.328520\pi$
$929$	31.2744	1.02608	0.513039	+	0.858365i	$0.328520\pi$
$930$	−2.93805	−0.0963426
$931$	19.4989	0.639050
$932$	−7.52804	−0.246589
$933$	12.2777	0.401955
$934$	21.8257	0.714160
$935$	−32.7659	−1.07156
$936$	0.245660	0.00802964
$937$	−38.9057	−1.27099	−0.635496	−	0.772104i	$-0.719204\pi$
$937$	−38.9057	−1.27099	−0.635496	+	0.772104i	$0.719204\pi$
$938$	3.65740	0.119418
$939$	4.74467	0.154836
$940$	43.8270	1.42948
$941$	−0.485708	−0.0158336	−0.00791682	−	0.999969i	$-0.502520\pi$
$941$	−0.485708	−0.0158336	−0.00791682	+	0.999969i	$0.502520\pi$
$942$	−15.4575	−0.503631
$943$	3.69144	0.120210
$944$	−0.0616620	−0.00200693
$945$	−17.5967	−0.572419
$946$	14.4739	0.470586
$947$	−3.96591	−0.128875	−0.0644374	−	0.997922i	$-0.520525\pi$
$947$	−3.96591	−0.128875	−0.0644374	+	0.997922i	$0.520525\pi$
$948$	−2.43155	−0.0789730
$949$	1.54266	0.0500769
$950$	45.7339	1.48380
$951$	−18.9426	−0.614257
$952$	−4.96080	−0.160780
$953$	−26.2459	−0.850188	−0.425094	−	0.905149i	$-0.639759\pi$
$953$	−26.2459	−0.850188	−0.425094	+	0.905149i	$0.639759\pi$
$954$	−26.8039	−0.867810
$955$	65.4117	2.11667
$956$	−17.7988	−0.575653
$957$	0.836880	0.0270525
$958$	−12.8202	−0.414203
$959$	20.5457	0.663456
$960$	2.93805	0.0948253
$961$	1.00000	0.0322581
$962$	−0.166343	−0.00536312
$963$	−18.4138	−0.593377
$964$	−10.5890	−0.341049
$965$	−92.8974	−2.99047
$966$	2.31457	0.0744701
$967$	49.6838	1.59772	0.798861	−	0.601515i	$-0.205436\pi$
$967$	49.6838	1.59772	0.798861	+	0.601515i	$0.205436\pi$
$968$	8.26752	0.265728
$969$	10.4296	0.335046
$970$	−4.32143	−0.138753
$971$	−32.9642	−1.05787	−0.528936	−	0.848661i	$-0.677409\pi$
$971$	−32.9642	−1.05787	−0.528936	+	0.848661i	$0.677409\pi$
$972$	−14.7308	−0.472492
$973$	5.81923	0.186556
$974$	4.26987	0.136815
$975$	−0.899985	−0.0288226
$976$	−6.28097	−0.201049
$977$	−50.2951	−1.60908	−0.804541	−	0.593897i	$-0.797589\pi$
$977$	−50.2951	−1.60908	−0.804541	+	0.593897i	$0.797589\pi$
$978$	0.0606895	0.00194064
$979$	−17.7660	−0.567803
$980$	25.1953	0.804834
$981$	−32.5334	−1.03871
$982$	−38.3770	−1.22466
$983$	−23.6758	−0.755141	−0.377570	−	0.925981i	$-0.623240\pi$
$983$	−23.6758	−0.755141	−0.377570	+	0.925981i	$0.623240\pi$
$984$	0.797306	0.0254172
$985$	65.6017	2.09025
$986$	3.41560	0.108775
$987$	7.45731	0.237369
$988$	−0.323743	−0.0102997
$989$	−27.5618	−0.876416
$990$	−18.1283	−0.576156
$991$	−20.1320	−0.639515	−0.319758	−	0.947499i	$-0.603602\pi$
$991$	−20.1320	−0.639515	−0.319758	+	0.947499i	$0.603602\pi$
$992$	−1.00000	−0.0317500
$993$	−7.49556	−0.237865
$994$	14.6680	0.465240
$995$	−56.2989	−1.78480
$996$	6.75794	0.214134
$997$	61.4720	1.94684	0.973419	−	0.229033i	$-0.0735565\pi$
$997$	61.4720	1.94684	0.973419	+	0.229033i	$0.0735565\pi$
$998$	16.0419	0.507797
$999$	6.46977	0.204695

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.l.1.18	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.l.1.18	✓	38	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.679880 q^{3} +1.00000 q^{4} -4.32143 q^{5} +0.679880 q^{6} +1.08152 q^{7} -1.00000 q^{8} -2.53776 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.679880 q^{3} +1.00000 q^{4} -4.32143 q^{5} +0.679880 q^{6} +1.08152 q^{7} -1.00000 q^{8} -2.53776 q^{9} +4.32143 q^{10} +1.65302 q^{11} -0.679880 q^{12} +0.0968017 q^{13} -1.08152 q^{14} +2.93805 q^{15} +1.00000 q^{16} +4.58686 q^{17} +2.53776 q^{18} -3.34440 q^{19} -4.32143 q^{20} -0.735306 q^{21} -1.65302 q^{22} +3.14777 q^{23} +0.679880 q^{24} +13.6748 q^{25} -0.0968017 q^{26} +3.76501 q^{27} +1.08152 q^{28} -0.744649 q^{29} -2.93805 q^{30} +1.00000 q^{31} -1.00000 q^{32} -1.12386 q^{33} -4.58686 q^{34} -4.67373 q^{35} -2.53776 q^{36} +1.71839 q^{37} +3.34440 q^{38} -0.0658135 q^{39} +4.32143 q^{40} +1.17272 q^{41} +0.735306 q^{42} -8.75600 q^{43} +1.65302 q^{44} +10.9668 q^{45} -3.14777 q^{46} -10.1418 q^{47} -0.679880 q^{48} -5.83031 q^{49} -13.6748 q^{50} -3.11852 q^{51} +0.0968017 q^{52} -10.5620 q^{53} -3.76501 q^{54} -7.14343 q^{55} -1.08152 q^{56} +2.27379 q^{57} +0.744649 q^{58} -0.0616620 q^{59} +2.93805 q^{60} -6.28097 q^{61} -1.00000 q^{62} -2.74465 q^{63} +1.00000 q^{64} -0.418322 q^{65} +1.12386 q^{66} -3.38171 q^{67} +4.58686 q^{68} -2.14010 q^{69} +4.67373 q^{70} -13.5623 q^{71} +2.53776 q^{72} +15.9363 q^{73} -1.71839 q^{74} -9.29720 q^{75} -3.34440 q^{76} +1.78778 q^{77} +0.0658135 q^{78} +3.57644 q^{79} -4.32143 q^{80} +5.05353 q^{81} -1.17272 q^{82} -9.93990 q^{83} -0.735306 q^{84} -19.8218 q^{85} +8.75600 q^{86} +0.506272 q^{87} -1.65302 q^{88} -10.7476 q^{89} -10.9668 q^{90} +0.104693 q^{91} +3.14777 q^{92} -0.679880 q^{93} +10.1418 q^{94} +14.4526 q^{95} +0.679880 q^{96} -1.00000 q^{97} +5.83031 q^{98} -4.19498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * q^99

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