LMFDB - Embedded newform 8018.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.65255 q^{3} +1.00000 q^{4} -0.493279 q^{5} -2.65255 q^{6} +4.58344 q^{7} +1.00000 q^{8} +4.03601 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.65255 q^{3} +1.00000 q^{4} -0.493279 q^{5} -2.65255 q^{6} +4.58344 q^{7} +1.00000 q^{8} +4.03601 q^{9} -0.493279 q^{10} +4.03650 q^{11} -2.65255 q^{12} +2.44046 q^{13} +4.58344 q^{14} +1.30845 q^{15} +1.00000 q^{16} -4.68079 q^{17} +4.03601 q^{18} -1.00000 q^{19} -0.493279 q^{20} -12.1578 q^{21} +4.03650 q^{22} -4.29070 q^{23} -2.65255 q^{24} -4.75668 q^{25} +2.44046 q^{26} -2.74807 q^{27} +4.58344 q^{28} +1.38963 q^{29} +1.30845 q^{30} -2.22094 q^{31} +1.00000 q^{32} -10.7070 q^{33} -4.68079 q^{34} -2.26092 q^{35} +4.03601 q^{36} -10.4599 q^{37} -1.00000 q^{38} -6.47343 q^{39} -0.493279 q^{40} +2.05993 q^{41} -12.1578 q^{42} -10.7516 q^{43} +4.03650 q^{44} -1.99088 q^{45} -4.29070 q^{46} -13.4282 q^{47} -2.65255 q^{48} +14.0079 q^{49} -4.75668 q^{50} +12.4160 q^{51} +2.44046 q^{52} -9.73291 q^{53} -2.74807 q^{54} -1.99112 q^{55} +4.58344 q^{56} +2.65255 q^{57} +1.38963 q^{58} -6.44939 q^{59} +1.30845 q^{60} +1.66604 q^{61} -2.22094 q^{62} +18.4988 q^{63} +1.00000 q^{64} -1.20383 q^{65} -10.7070 q^{66} -11.2345 q^{67} -4.68079 q^{68} +11.3813 q^{69} -2.26092 q^{70} +4.89380 q^{71} +4.03601 q^{72} -4.95608 q^{73} -10.4599 q^{74} +12.6173 q^{75} -1.00000 q^{76} +18.5010 q^{77} -6.47343 q^{78} -13.3503 q^{79} -0.493279 q^{80} -4.81865 q^{81} +2.05993 q^{82} -3.60512 q^{83} -12.1578 q^{84} +2.30894 q^{85} -10.7516 q^{86} -3.68606 q^{87} +4.03650 q^{88} +4.46844 q^{89} -1.99088 q^{90} +11.1857 q^{91} -4.29070 q^{92} +5.89116 q^{93} -13.4282 q^{94} +0.493279 q^{95} -2.65255 q^{96} +1.35200 q^{97} +14.0079 q^{98} +16.2913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * 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
$3$	−2.65255	−1.53145	−0.765725	−	0.643168i	$-0.777619\pi$
$3$	−2.65255	−1.53145	−0.765725	+	0.643168i	$0.777619\pi$
$4$	1.00000	0.500000
$5$	−0.493279	−0.220601	−0.110301	−	0.993898i	$-0.535181\pi$
$5$	−0.493279	−0.220601	−0.110301	+	0.993898i	$0.535181\pi$
$6$	−2.65255	−1.08290
$7$	4.58344	1.73238	0.866189	−	0.499717i	$-0.166563\pi$
$7$	4.58344	1.73238	0.866189	+	0.499717i	$0.166563\pi$
$8$	1.00000	0.353553
$9$	4.03601	1.34534
$10$	−0.493279	−0.155989
$11$	4.03650	1.21705	0.608525	−	0.793535i	$-0.291762\pi$
$11$	4.03650	1.21705	0.608525	+	0.793535i	$0.291762\pi$
$12$	−2.65255	−0.765725
$13$	2.44046	0.676861	0.338430	−	0.940991i	$-0.390104\pi$
$13$	2.44046	0.676861	0.338430	+	0.940991i	$0.390104\pi$
$14$	4.58344	1.22498
$15$	1.30845	0.337839
$16$	1.00000	0.250000
$17$	−4.68079	−1.13526	−0.567630	−	0.823284i	$-0.692139\pi$
$17$	−4.68079	−1.13526	−0.567630	+	0.823284i	$0.692139\pi$
$18$	4.03601	0.951297
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.493279	−0.110301
$21$	−12.1578	−2.65305
$22$	4.03650	0.860584
$23$	−4.29070	−0.894672	−0.447336	−	0.894366i	$-0.647627\pi$
$23$	−4.29070	−0.894672	−0.447336	+	0.894366i	$0.647627\pi$
$24$	−2.65255	−0.541449
$25$	−4.75668	−0.951335
$26$	2.44046	0.478613
$27$	−2.74807	−0.528866
$28$	4.58344	0.866189
$29$	1.38963	0.258047	0.129024	−	0.991642i	$-0.458816\pi$
$29$	1.38963	0.258047	0.129024	+	0.991642i	$0.458816\pi$
$30$	1.30845	0.238888
$31$	−2.22094	−0.398893	−0.199447	−	0.979909i	$-0.563914\pi$
$31$	−2.22094	−0.398893	−0.199447	+	0.979909i	$0.563914\pi$
$32$	1.00000	0.176777
$33$	−10.7070	−1.86385
$34$	−4.68079	−0.802750
$35$	−2.26092	−0.382164
$36$	4.03601	0.672669
$37$	−10.4599	−1.71960	−0.859798	−	0.510635i	$-0.829411\pi$
$37$	−10.4599	−1.71960	−0.859798	+	0.510635i	$0.829411\pi$
$38$	−1.00000	−0.162221
$39$	−6.47343	−1.03658
$40$	−0.493279	−0.0779943
$41$	2.05993	0.321707	0.160853	−	0.986978i	$-0.448575\pi$
$41$	2.05993	0.321707	0.160853	+	0.986978i	$0.448575\pi$
$42$	−12.1578	−1.87599
$43$	−10.7516	−1.63961	−0.819805	−	0.572643i	$-0.805918\pi$
$43$	−10.7516	−1.63961	−0.819805	+	0.572643i	$0.805918\pi$
$44$	4.03650	0.608525
$45$	−1.99088	−0.296783
$46$	−4.29070	−0.632629
$47$	−13.4282	−1.95871	−0.979355	−	0.202146i	$-0.935208\pi$
$47$	−13.4282	−1.95871	−0.979355	+	0.202146i	$0.935208\pi$
$48$	−2.65255	−0.382862
$49$	14.0079	2.00113
$50$	−4.75668	−0.672696
$51$	12.4160	1.73859
$52$	2.44046	0.338430
$53$	−9.73291	−1.33692	−0.668459	−	0.743749i	$-0.733046\pi$
$53$	−9.73291	−1.33692	−0.668459	+	0.743749i	$0.733046\pi$
$54$	−2.74807	−0.373965
$55$	−1.99112	−0.268482
$56$	4.58344	0.612488
$57$	2.65255	0.351339
$58$	1.38963	0.182467
$59$	−6.44939	−0.839638	−0.419819	−	0.907608i	$-0.637907\pi$
$59$	−6.44939	−0.839638	−0.419819	+	0.907608i	$0.637907\pi$
$60$	1.30845	0.168920
$61$	1.66604	0.213314	0.106657	−	0.994296i	$-0.465985\pi$
$61$	1.66604	0.213314	0.106657	+	0.994296i	$0.465985\pi$
$62$	−2.22094	−0.282060
$63$	18.4988	2.33063
$64$	1.00000	0.125000
$65$	−1.20383	−0.149316
$66$	−10.7070	−1.31794
$67$	−11.2345	−1.37251	−0.686254	−	0.727362i	$-0.740746\pi$
$67$	−11.2345	−1.37251	−0.686254	+	0.727362i	$0.740746\pi$
$68$	−4.68079	−0.567630
$69$	11.3813	1.37014
$70$	−2.26092	−0.270231
$71$	4.89380	0.580787	0.290394	−	0.956907i	$-0.406214\pi$
$71$	4.89380	0.580787	0.290394	+	0.956907i	$0.406214\pi$
$72$	4.03601	0.475649
$73$	−4.95608	−0.580065	−0.290033	−	0.957017i	$-0.593666\pi$
$73$	−4.95608	−0.580065	−0.290033	+	0.957017i	$0.593666\pi$
$74$	−10.4599	−1.21594
$75$	12.6173	1.45692
$76$	−1.00000	−0.114708
$77$	18.5010	2.10839
$78$	−6.47343	−0.732972
$79$	−13.3503	−1.50202	−0.751011	−	0.660289i	$-0.770434\pi$
$79$	−13.3503	−1.50202	−0.751011	+	0.660289i	$0.770434\pi$
$80$	−0.493279	−0.0551503
$81$	−4.81865	−0.535405
$82$	2.05993	0.227481
$83$	−3.60512	−0.395714	−0.197857	−	0.980231i	$-0.563398\pi$
$83$	−3.60512	−0.395714	−0.197857	+	0.980231i	$0.563398\pi$
$84$	−12.1578	−1.32652
$85$	2.30894	0.250439
$86$	−10.7516	−1.15938
$87$	−3.68606	−0.395187
$88$	4.03650	0.430292
$89$	4.46844	0.473654	0.236827	−	0.971552i	$-0.423893\pi$
$89$	4.46844	0.473654	0.236827	+	0.971552i	$0.423893\pi$
$90$	−1.99088	−0.209857
$91$	11.1857	1.17258
$92$	−4.29070	−0.447336
$93$	5.89116	0.610885
$94$	−13.4282	−1.38502
$95$	0.493279	0.0506094
$96$	−2.65255	−0.270725
$97$	1.35200	0.137275	0.0686374	−	0.997642i	$-0.478135\pi$
$97$	1.35200	0.137275	0.0686374	+	0.997642i	$0.478135\pi$
$98$	14.0079	1.41501
$99$	16.2913	1.63734
$100$	−4.75668	−0.475668
$101$	−7.48325	−0.744611	−0.372306	−	0.928110i	$-0.621433\pi$
$101$	−7.48325	−0.744611	−0.372306	+	0.928110i	$0.621433\pi$
$102$	12.4160	1.22937
$103$	−9.80771	−0.966383	−0.483191	−	0.875515i	$-0.660522\pi$
$103$	−9.80771	−0.966383	−0.483191	+	0.875515i	$0.660522\pi$
$104$	2.44046	0.239306
$105$	5.99719	0.585265
$106$	−9.73291	−0.945344
$107$	−8.86286	−0.856805	−0.428402	−	0.903588i	$-0.640923\pi$
$107$	−8.86286	−0.856805	−0.428402	+	0.903588i	$0.640923\pi$
$108$	−2.74807	−0.264433
$109$	−6.37398	−0.610516	−0.305258	−	0.952270i	$-0.598743\pi$
$109$	−6.37398	−0.610516	−0.305258	+	0.952270i	$0.598743\pi$
$110$	−1.99112	−0.189846
$111$	27.7454	2.63347
$112$	4.58344	0.433094
$113$	18.9102	1.77892	0.889461	−	0.457011i	$-0.151080\pi$
$113$	18.9102	1.77892	0.889461	+	0.457011i	$0.151080\pi$
$114$	2.65255	0.248434
$115$	2.11651	0.197366
$116$	1.38963	0.129024
$117$	9.84971	0.910606
$118$	−6.44939	−0.593714
$119$	−21.4541	−1.96670
$120$	1.30845	0.119444
$121$	5.29331	0.481210
$122$	1.66604	0.150836
$123$	−5.46406	−0.492678
$124$	−2.22094	−0.199447
$125$	4.81276	0.430467
$126$	18.4988	1.64801
$127$	5.97251	0.529975	0.264987	−	0.964252i	$-0.414632\pi$
$127$	5.97251	0.529975	0.264987	+	0.964252i	$0.414632\pi$
$128$	1.00000	0.0883883
$129$	28.5192	2.51098
$130$	−1.20383	−0.105583
$131$	15.0408	1.31412	0.657060	−	0.753839i	$-0.271800\pi$
$131$	15.0408	1.31412	0.657060	+	0.753839i	$0.271800\pi$
$132$	−10.7070	−0.931925
$133$	−4.58344	−0.397435
$134$	−11.2345	−0.970509
$135$	1.35557	0.116668
$136$	−4.68079	−0.401375
$137$	−6.37138	−0.544344	−0.272172	−	0.962249i	$-0.587742\pi$
$137$	−6.37138	−0.544344	−0.272172	+	0.962249i	$0.587742\pi$
$138$	11.3813	0.968839
$139$	21.3173	1.80811	0.904056	−	0.427413i	$-0.140575\pi$
$139$	21.3173	1.80811	0.904056	+	0.427413i	$0.140575\pi$
$140$	−2.26092	−0.191082
$141$	35.6191	2.99967
$142$	4.89380	0.410678
$143$	9.85090	0.823773
$144$	4.03601	0.336334
$145$	−0.685474	−0.0569255
$146$	−4.95608	−0.410168
$147$	−37.1567	−3.06463
$148$	−10.4599	−0.859798
$149$	18.8471	1.54401	0.772006	−	0.635616i	$-0.219254\pi$
$149$	18.8471	1.54401	0.772006	+	0.635616i	$0.219254\pi$
$150$	12.6173	1.03020
$151$	9.45927	0.769785	0.384892	−	0.922961i	$-0.374239\pi$
$151$	9.45927	0.769785	0.384892	+	0.922961i	$0.374239\pi$
$152$	−1.00000	−0.0811107
$153$	−18.8917	−1.52731
$154$	18.5010	1.49086
$155$	1.09554	0.0879962
$156$	−6.47343	−0.518289
$157$	−4.32073	−0.344832	−0.172416	−	0.985024i	$-0.555157\pi$
$157$	−4.32073	−0.344832	−0.172416	+	0.985024i	$0.555157\pi$
$158$	−13.3503	−1.06209
$159$	25.8170	2.04742
$160$	−0.493279	−0.0389971
$161$	−19.6661	−1.54991
$162$	−4.81865	−0.378589
$163$	3.80102	0.297719	0.148859	−	0.988858i	$-0.452440\pi$
$163$	3.80102	0.297719	0.148859	+	0.988858i	$0.452440\pi$
$164$	2.05993	0.160853
$165$	5.28154	0.411167
$166$	−3.60512	−0.279812
$167$	20.3512	1.57482	0.787412	−	0.616427i	$-0.211421\pi$
$167$	20.3512	1.57482	0.787412	+	0.616427i	$0.211421\pi$
$168$	−12.1578	−0.937994
$169$	−7.04417	−0.541859
$170$	2.30894	0.177087
$171$	−4.03601	−0.308642
$172$	−10.7516	−0.819805
$173$	−11.5756	−0.880080	−0.440040	−	0.897978i	$-0.645036\pi$
$173$	−11.5756	−0.880080	−0.440040	+	0.897978i	$0.645036\pi$
$174$	−3.68606	−0.279439
$175$	−21.8019	−1.64807
$176$	4.03650	0.304262
$177$	17.1073	1.28586
$178$	4.46844	0.334924
$179$	−17.3658	−1.29798	−0.648992	−	0.760796i	$-0.724809\pi$
$179$	−17.3658	−1.29798	−0.648992	+	0.760796i	$0.724809\pi$
$180$	−1.99088	−0.148391
$181$	14.6197	1.08667	0.543337	−	0.839515i	$-0.317161\pi$
$181$	14.6197	1.08667	0.543337	+	0.839515i	$0.317161\pi$
$182$	11.1857	0.829139
$183$	−4.41925	−0.326680
$184$	−4.29070	−0.316314
$185$	5.15964	0.379345
$186$	5.89116	0.431961
$187$	−18.8940	−1.38167
$188$	−13.4282	−0.979355
$189$	−12.5956	−0.916197
$190$	0.493279	0.0357862
$191$	−15.3076	−1.10762	−0.553809	−	0.832644i	$-0.686826\pi$
$191$	−15.3076	−1.10762	−0.553809	+	0.832644i	$0.686826\pi$
$192$	−2.65255	−0.191431
$193$	−19.0457	−1.37094	−0.685471	−	0.728099i	$-0.740404\pi$
$193$	−19.0457	−1.37094	−0.685471	+	0.728099i	$0.740404\pi$
$194$	1.35200	0.0970680
$195$	3.19321	0.228670
$196$	14.0079	1.00057
$197$	−4.43777	−0.316178	−0.158089	−	0.987425i	$-0.550533\pi$
$197$	−4.43777	−0.316178	−0.158089	+	0.987425i	$0.550533\pi$
$198$	16.2913	1.15778
$199$	18.7974	1.33251	0.666256	−	0.745723i	$-0.267896\pi$
$199$	18.7974	1.33251	0.666256	+	0.745723i	$0.267896\pi$
$200$	−4.75668	−0.336348
$201$	29.7999	2.10193
$202$	−7.48325	−0.526520
$203$	6.36928	0.447036
$204$	12.4160	0.869296
$205$	−1.01612	−0.0709689
$206$	−9.80771	−0.683336
$207$	−17.3173	−1.20364
$208$	2.44046	0.169215
$209$	−4.03650	−0.279210
$210$	5.99719	0.413845
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−9.73291	−0.668459
$213$	−12.9810	−0.889446
$214$	−8.86286	−0.605853
$215$	5.30356	0.361700
$216$	−2.74807	−0.186983
$217$	−10.1796	−0.691033
$218$	−6.37398	−0.431700
$219$	13.1462	0.888341
$220$	−1.99112	−0.134241
$221$	−11.4233	−0.768413
$222$	27.7454	1.86215
$223$	−25.8881	−1.73360	−0.866799	−	0.498657i	$-0.833827\pi$
$223$	−25.8881	−1.73360	−0.866799	+	0.498657i	$0.833827\pi$
$224$	4.58344	0.306244
$225$	−19.1980	−1.27987
$226$	18.9102	1.25789
$227$	−2.28881	−0.151914	−0.0759568	−	0.997111i	$-0.524201\pi$
$227$	−2.28881	−0.151914	−0.0759568	+	0.997111i	$0.524201\pi$
$228$	2.65255	0.175669
$229$	10.2166	0.675132	0.337566	−	0.941302i	$-0.390396\pi$
$229$	10.2166	0.675132	0.337566	+	0.941302i	$0.390396\pi$
$230$	2.11651	0.139559
$231$	−49.0749	−3.22889
$232$	1.38963	0.0912336
$233$	23.2763	1.52488	0.762439	−	0.647060i	$-0.224002\pi$
$233$	23.2763	1.52488	0.762439	+	0.647060i	$0.224002\pi$
$234$	9.84971	0.643896
$235$	6.62387	0.432094
$236$	−6.44939	−0.419819
$237$	35.4122	2.30027
$238$	−21.4541	−1.39067
$239$	−0.402276	−0.0260211	−0.0130105	−	0.999915i	$-0.504142\pi$
$239$	−0.402276	−0.0260211	−0.0130105	+	0.999915i	$0.504142\pi$
$240$	1.30845	0.0844598
$241$	−21.8822	−1.40956	−0.704778	−	0.709428i	$-0.748953\pi$
$241$	−21.8822	−1.40956	−0.704778	+	0.709428i	$0.748953\pi$
$242$	5.29331	0.340267
$243$	21.0259	1.34881
$244$	1.66604	0.106657
$245$	−6.90982	−0.441452
$246$	−5.46406	−0.348376
$247$	−2.44046	−0.155283
$248$	−2.22094	−0.141030
$249$	9.56276	0.606015
$250$	4.81276	0.304386
$251$	12.6960	0.801365	0.400683	−	0.916217i	$-0.368773\pi$
$251$	12.6960	0.801365	0.400683	+	0.916217i	$0.368773\pi$
$252$	18.4988	1.16532
$253$	−17.3194	−1.08886
$254$	5.97251	0.374749
$255$	−6.12457	−0.383535
$256$	1.00000	0.0625000
$257$	−7.66234	−0.477964	−0.238982	−	0.971024i	$-0.576814\pi$
$257$	−7.66234	−0.477964	−0.238982	+	0.971024i	$0.576814\pi$
$258$	28.5192	1.77553
$259$	−47.9423	−2.97899
$260$	−1.20383	−0.0746581
$261$	5.60856	0.347161
$262$	15.0408	0.929223
$263$	17.3997	1.07291	0.536455	−	0.843929i	$-0.319763\pi$
$263$	17.3997	1.07291	0.536455	+	0.843929i	$0.319763\pi$
$264$	−10.7070	−0.658970
$265$	4.80104	0.294926
$266$	−4.58344	−0.281029
$267$	−11.8528	−0.725377
$268$	−11.2345	−0.686254
$269$	12.0472	0.734528	0.367264	−	0.930117i	$-0.380294\pi$
$269$	12.0472	0.734528	0.367264	+	0.930117i	$0.380294\pi$
$270$	1.35557	0.0824971
$271$	11.7571	0.714192	0.357096	−	0.934068i	$-0.383767\pi$
$271$	11.7571	0.714192	0.357096	+	0.934068i	$0.383767\pi$
$272$	−4.68079	−0.283815
$273$	−29.6706	−1.79575
$274$	−6.37138	−0.384909
$275$	−19.2003	−1.15782
$276$	11.3813	0.685072
$277$	3.46448	0.208160	0.104080	−	0.994569i	$-0.466810\pi$
$277$	3.46448	0.208160	0.104080	+	0.994569i	$0.466810\pi$
$278$	21.3173	1.27853
$279$	−8.96375	−0.536646
$280$	−2.26092	−0.135116
$281$	−7.18959	−0.428895	−0.214448	−	0.976735i	$-0.568795\pi$
$281$	−7.18959	−0.428895	−0.214448	+	0.976735i	$0.568795\pi$
$282$	35.6191	2.12108
$283$	−10.8753	−0.646470	−0.323235	−	0.946319i	$-0.604770\pi$
$283$	−10.8753	−0.646470	−0.323235	+	0.946319i	$0.604770\pi$
$284$	4.89380	0.290394
$285$	−1.30845	−0.0775057
$286$	9.85090	0.582496
$287$	9.44156	0.557318
$288$	4.03601	0.237824
$289$	4.90984	0.288814
$290$	−0.685474	−0.0402524
$291$	−3.58625	−0.210230
$292$	−4.95608	−0.290033
$293$	−16.2866	−0.951476	−0.475738	−	0.879587i	$-0.657819\pi$
$293$	−16.2866	−0.951476	−0.475738	+	0.879587i	$0.657819\pi$
$294$	−37.1567	−2.16702
$295$	3.18135	0.185225
$296$	−10.4599	−0.607969
$297$	−11.0926	−0.643657
$298$	18.8471	1.09178
$299$	−10.4713	−0.605568
$300$	12.6173	0.728461
$301$	−49.2795	−2.84042
$302$	9.45927	0.544320
$303$	19.8497	1.14033
$304$	−1.00000	−0.0573539
$305$	−0.821821	−0.0470574
$306$	−18.8917	−1.07997
$307$	1.39011	0.0793375	0.0396688	−	0.999213i	$-0.487370\pi$
$307$	1.39011	0.0793375	0.0396688	+	0.999213i	$0.487370\pi$
$308$	18.5010	1.05420
$309$	26.0154	1.47997
$310$	1.09554	0.0622227
$311$	15.1712	0.860282	0.430141	−	0.902762i	$-0.358464\pi$
$311$	15.1712	0.860282	0.430141	+	0.902762i	$0.358464\pi$
$312$	−6.47343	−0.366486
$313$	−3.41373	−0.192955	−0.0964776	−	0.995335i	$-0.530758\pi$
$313$	−3.41373	−0.192955	−0.0964776	+	0.995335i	$0.530758\pi$
$314$	−4.32073	−0.243833
$315$	−9.12508	−0.514140
$316$	−13.3503	−0.751011
$317$	−10.8980	−0.612092	−0.306046	−	0.952017i	$-0.599006\pi$
$317$	−10.8980	−0.612092	−0.306046	+	0.952017i	$0.599006\pi$
$318$	25.8170	1.44775
$319$	5.60923	0.314057
$320$	−0.493279	−0.0275751
$321$	23.5092	1.31215
$322$	−19.6661	−1.09595
$323$	4.68079	0.260446
$324$	−4.81865	−0.267703
$325$	−11.6085	−0.643922
$326$	3.80102	0.210519
$327$	16.9073	0.934975
$328$	2.05993	0.113741
$329$	−61.5476	−3.39323
$330$	5.28154	0.290739
$331$	−19.3329	−1.06263	−0.531317	−	0.847173i	$-0.678303\pi$
$331$	−19.3329	−1.06263	−0.531317	+	0.847173i	$0.678303\pi$
$332$	−3.60512	−0.197857
$333$	−42.2162	−2.31344
$334$	20.3512	1.11357
$335$	5.54172	0.302777
$336$	−12.1578	−0.663262
$337$	−0.675010	−0.0367701	−0.0183851	−	0.999831i	$-0.505852\pi$
$337$	−0.675010	−0.0367701	−0.0183851	+	0.999831i	$0.505852\pi$
$338$	−7.04417	−0.383152
$339$	−50.1602	−2.72433
$340$	2.30894	0.125220
$341$	−8.96483	−0.485473
$342$	−4.03601	−0.218243
$343$	32.1204	1.73434
$344$	−10.7516	−0.579690
$345$	−5.61414	−0.302255
$346$	−11.5756	−0.622310
$347$	6.04174	0.324338	0.162169	−	0.986763i	$-0.448151\pi$
$347$	6.04174	0.324338	0.162169	+	0.986763i	$0.448151\pi$
$348$	−3.68606	−0.197593
$349$	16.7575	0.897009	0.448504	−	0.893781i	$-0.351957\pi$
$349$	16.7575	0.897009	0.448504	+	0.893781i	$0.351957\pi$
$350$	−21.8019	−1.16536
$351$	−6.70655	−0.357969
$352$	4.03650	0.215146
$353$	27.8179	1.48060	0.740298	−	0.672279i	$-0.234685\pi$
$353$	27.8179	1.48060	0.740298	+	0.672279i	$0.234685\pi$
$354$	17.1073	0.909243
$355$	−2.41401	−0.128122
$356$	4.46844	0.236827
$357$	56.9082	3.01190
$358$	−17.3658	−0.917813
$359$	5.88838	0.310777	0.155388	−	0.987853i	$-0.450337\pi$
$359$	5.88838	0.310777	0.155388	+	0.987853i	$0.450337\pi$
$360$	−1.99088	−0.104929
$361$	1.00000	0.0526316
$362$	14.6197	0.768394
$363$	−14.0408	−0.736949
$364$	11.1857	0.586289
$365$	2.44473	0.127963
$366$	−4.41925	−0.230998
$367$	−21.5222	−1.12345	−0.561724	−	0.827325i	$-0.689862\pi$
$367$	−21.5222	−1.12345	−0.561724	+	0.827325i	$0.689862\pi$
$368$	−4.29070	−0.223668
$369$	8.31390	0.432804
$370$	5.15964	0.268237
$371$	−44.6102	−2.31605
$372$	5.89116	0.305442
$373$	3.26018	0.168806	0.0844030	−	0.996432i	$-0.473102\pi$
$373$	3.26018	0.168806	0.0844030	+	0.996432i	$0.473102\pi$
$374$	−18.8940	−0.976986
$375$	−12.7661	−0.659238
$376$	−13.4282	−0.692509
$377$	3.39133	0.174662
$378$	−12.5956	−0.647849
$379$	−8.18080	−0.420219	−0.210110	−	0.977678i	$-0.567382\pi$
$379$	−8.18080	−0.420219	−0.210110	+	0.977678i	$0.567382\pi$
$380$	0.493279	0.0253047
$381$	−15.8424	−0.811629
$382$	−15.3076	−0.783204
$383$	−4.79739	−0.245135	−0.122568	−	0.992460i	$-0.539113\pi$
$383$	−4.79739	−0.245135	−0.122568	+	0.992460i	$0.539113\pi$
$384$	−2.65255	−0.135362
$385$	−9.12618	−0.465113
$386$	−19.0457	−0.969403
$387$	−43.3937	−2.20583
$388$	1.35200	0.0686374
$389$	−22.2192	−1.12656	−0.563278	−	0.826267i	$-0.690460\pi$
$389$	−22.2192	−1.12656	−0.563278	+	0.826267i	$0.690460\pi$
$390$	3.19321	0.161694
$391$	20.0839	1.01568
$392$	14.0079	0.707507
$393$	−39.8964	−2.01251
$394$	−4.43777	−0.223571
$395$	6.58541	0.331348
$396$	16.2913	0.818671
$397$	−5.56615	−0.279357	−0.139679	−	0.990197i	$-0.544607\pi$
$397$	−5.56615	−0.279357	−0.139679	+	0.990197i	$0.544607\pi$
$398$	18.7974	0.942228
$399$	12.1578	0.608651
$400$	−4.75668	−0.237834
$401$	−27.6585	−1.38120	−0.690600	−	0.723237i	$-0.742653\pi$
$401$	−27.6585	−1.38120	−0.690600	+	0.723237i	$0.742653\pi$
$402$	29.7999	1.48629
$403$	−5.42011	−0.269995
$404$	−7.48325	−0.372306
$405$	2.37694	0.118111
$406$	6.36928	0.316102
$407$	−42.2213	−2.09283
$408$	12.4160	0.614685
$409$	16.4844	0.815101	0.407550	−	0.913183i	$-0.366383\pi$
$409$	16.4844	0.815101	0.407550	+	0.913183i	$0.366383\pi$
$410$	−1.01612	−0.0501826
$411$	16.9004	0.833635
$412$	−9.80771	−0.483191
$413$	−29.5604	−1.45457
$414$	−17.3173	−0.851099
$415$	1.77833	0.0872948
$416$	2.44046	0.119653
$417$	−56.5453	−2.76903
$418$	−4.03650	−0.197432
$419$	−13.2846	−0.648995	−0.324498	−	0.945886i	$-0.605195\pi$
$419$	−13.2846	−0.648995	−0.324498	+	0.945886i	$0.605195\pi$
$420$	5.99719	0.292633
$421$	−29.1566	−1.42101	−0.710504	−	0.703693i	$-0.751533\pi$
$421$	−29.1566	−1.42101	−0.710504	+	0.703693i	$0.751533\pi$
$422$	1.00000	0.0486792
$423$	−54.1965	−2.63513
$424$	−9.73291	−0.472672
$425$	22.2650	1.08001
$426$	−12.9810	−0.628933
$427$	7.63619	0.369541
$428$	−8.86286	−0.428402
$429$	−26.1300	−1.26157
$430$	5.30356	0.255760
$431$	24.4471	1.17758	0.588789	−	0.808287i	$-0.299605\pi$
$431$	24.4471	1.17758	0.588789	+	0.808287i	$0.299605\pi$
$432$	−2.74807	−0.132217
$433$	−10.8922	−0.523444	−0.261722	−	0.965143i	$-0.584290\pi$
$433$	−10.8922	−0.523444	−0.261722	+	0.965143i	$0.584290\pi$
$434$	−10.1796	−0.488634
$435$	1.81825	0.0871786
$436$	−6.37398	−0.305258
$437$	4.29070	0.205252
$438$	13.1462	0.628152
$439$	11.7953	0.562960	0.281480	−	0.959567i	$-0.409175\pi$
$439$	11.7953	0.562960	0.281480	+	0.959567i	$0.409175\pi$
$440$	−1.99112	−0.0949229
$441$	56.5362	2.69220
$442$	−11.4233	−0.543350
$443$	6.61302	0.314194	0.157097	−	0.987583i	$-0.449786\pi$
$443$	6.61302	0.314194	0.157097	+	0.987583i	$0.449786\pi$
$444$	27.7454	1.31674
$445$	−2.20419	−0.104489
$446$	−25.8881	−1.22584
$447$	−49.9927	−2.36458
$448$	4.58344	0.216547
$449$	34.9493	1.64936	0.824680	−	0.565600i	$-0.191355\pi$
$449$	34.9493	1.64936	0.824680	+	0.565600i	$0.191355\pi$
$450$	−19.1980	−0.905002
$451$	8.31490	0.391533
$452$	18.9102	0.889461
$453$	−25.0912	−1.17889
$454$	−2.28881	−0.107419
$455$	−5.51767	−0.258672
$456$	2.65255	0.124217
$457$	25.1123	1.17470	0.587351	−	0.809332i	$-0.300171\pi$
$457$	25.1123	1.17470	0.587351	+	0.809332i	$0.300171\pi$
$458$	10.2166	0.477390
$459$	12.8632	0.600401
$460$	2.11651	0.0986828
$461$	−7.38999	−0.344186	−0.172093	−	0.985081i	$-0.555053\pi$
$461$	−7.38999	−0.344186	−0.172093	+	0.985081i	$0.555053\pi$
$462$	−49.0749	−2.28317
$463$	4.69829	0.218348	0.109174	−	0.994023i	$-0.465179\pi$
$463$	4.69829	0.218348	0.109174	+	0.994023i	$0.465179\pi$
$464$	1.38963	0.0645119
$465$	−2.90598	−0.134762
$466$	23.2763	1.07825
$467$	−2.01598	−0.0932883	−0.0466442	−	0.998912i	$-0.514853\pi$
$467$	−2.01598	−0.0932883	−0.0466442	+	0.998912i	$0.514853\pi$
$468$	9.84971	0.455303
$469$	−51.4925	−2.37770
$470$	6.62387	0.305536
$471$	11.4609	0.528093
$472$	−6.44939	−0.296857
$473$	−43.3990	−1.99549
$474$	35.4122	1.62654
$475$	4.75668	0.218251
$476$	−21.4541	−0.983349
$477$	−39.2821	−1.79861
$478$	−0.402276	−0.0183997
$479$	20.4146	0.932767	0.466384	−	0.884583i	$-0.345557\pi$
$479$	20.4146	0.932767	0.466384	+	0.884583i	$0.345557\pi$
$480$	1.30845	0.0597221
$481$	−25.5269	−1.16393
$482$	−21.8822	−0.996706
$483$	52.1654	2.37361
$484$	5.29331	0.240605
$485$	−0.666913	−0.0302830
$486$	21.0259	0.953754
$487$	0.688755	0.0312105	0.0156052	−	0.999878i	$-0.495032\pi$
$487$	0.688755	0.0312105	0.0156052	+	0.999878i	$0.495032\pi$
$488$	1.66604	0.0754180
$489$	−10.0824	−0.455941
$490$	−6.90982	−0.312154
$491$	−20.2738	−0.914945	−0.457472	−	0.889224i	$-0.651245\pi$
$491$	−20.2738	−0.914945	−0.457472	+	0.889224i	$0.651245\pi$
$492$	−5.46406	−0.246339
$493$	−6.50456	−0.292951
$494$	−2.44046	−0.109801
$495$	−8.03618	−0.361199
$496$	−2.22094	−0.0997233
$497$	22.4304	1.00614
$498$	9.56276	0.428518
$499$	26.6168	1.19153	0.595765	−	0.803159i	$-0.296849\pi$
$499$	26.6168	1.19153	0.595765	+	0.803159i	$0.296849\pi$
$500$	4.81276	0.215233
$501$	−53.9826	−2.41176
$502$	12.6960	0.566651
$503$	29.7428	1.32616	0.663082	−	0.748547i	$-0.269248\pi$
$503$	29.7428	1.32616	0.663082	+	0.748547i	$0.269248\pi$
$504$	18.4988	0.824003
$505$	3.69133	0.164262
$506$	−17.3194	−0.769940
$507$	18.6850	0.829830
$508$	5.97251	0.264987
$509$	23.4891	1.04114	0.520568	−	0.853820i	$-0.325720\pi$
$509$	23.4891	1.04114	0.520568	+	0.853820i	$0.325720\pi$
$510$	−6.12457	−0.271200
$511$	−22.7159	−1.00489
$512$	1.00000	0.0441942
$513$	2.74807	0.121330
$514$	−7.66234	−0.337971
$515$	4.83794	0.213185
$516$	28.5192	1.25549
$517$	−54.2031	−2.38385
$518$	−47.9423	−2.10646
$519$	30.7050	1.34780
$520$	−1.20383	−0.0527913
$521$	−1.48551	−0.0650816	−0.0325408	−	0.999470i	$-0.510360\pi$
$521$	−1.48551	−0.0650816	−0.0325408	+	0.999470i	$0.510360\pi$
$522$	5.60856	0.245480
$523$	−7.77922	−0.340162	−0.170081	−	0.985430i	$-0.554403\pi$
$523$	−7.77922	−0.340162	−0.170081	+	0.985430i	$0.554403\pi$
$524$	15.0408	0.657060
$525$	57.8307	2.52394
$526$	17.3997	0.758662
$527$	10.3958	0.452847
$528$	−10.7070	−0.465963
$529$	−4.58993	−0.199562
$530$	4.80104	0.208544
$531$	−26.0298	−1.12960
$532$	−4.58344	−0.198717
$533$	5.02717	0.217751
$534$	−11.8528	−0.512919
$535$	4.37186	0.189012
$536$	−11.2345	−0.485255
$537$	46.0637	1.98780
$538$	12.0472	0.519390
$539$	56.5430	2.43548
$540$	1.35557	0.0583342
$541$	0.0348489	0.00149827	0.000749137	−	1.00000i	$-0.499762\pi$
$541$	0.0348489	0.00149827	0.000749137		1.00000i	$0.499762\pi$
$542$	11.7571	0.505010
$543$	−38.7795	−1.66419
$544$	−4.68079	−0.200687
$545$	3.14415	0.134681
$546$	−29.6706	−1.26978
$547$	32.7454	1.40009	0.700046	−	0.714097i	$-0.253163\pi$
$547$	32.7454	1.40009	0.700046	+	0.714097i	$0.253163\pi$
$548$	−6.37138	−0.272172
$549$	6.72415	0.286980
$550$	−19.2003	−0.818704
$551$	−1.38963	−0.0592002
$552$	11.3813	0.484419
$553$	−61.1902	−2.60207
$554$	3.46448	0.147192
$555$	−13.6862	−0.580947
$556$	21.3173	0.904056
$557$	2.05412	0.0870358	0.0435179	−	0.999053i	$-0.486143\pi$
$557$	2.05412	0.0870358	0.0435179	+	0.999053i	$0.486143\pi$
$558$	−8.96375	−0.379466
$559$	−26.2389	−1.10979
$560$	−2.26092	−0.0955411
$561$	50.1173	2.11595
$562$	−7.18959	−0.303275
$563$	7.03369	0.296435	0.148217	−	0.988955i	$-0.452647\pi$
$563$	7.03369	0.296435	0.148217	+	0.988955i	$0.452647\pi$
$564$	35.6191	1.49983
$565$	−9.32800	−0.392432
$566$	−10.8753	−0.457123
$567$	−22.0860	−0.927524
$568$	4.89380	0.205339
$569$	29.8747	1.25241	0.626207	−	0.779657i	$-0.284607\pi$
$569$	29.8747	1.25241	0.626207	+	0.779657i	$0.284607\pi$
$570$	−1.30845	−0.0548048
$571$	−43.3395	−1.81370	−0.906850	−	0.421454i	$-0.861520\pi$
$571$	−43.3395	−1.81370	−0.906850	+	0.421454i	$0.861520\pi$
$572$	9.85090	0.411887
$573$	40.6041	1.69626
$574$	9.44156	0.394083
$575$	20.4094	0.851133
$576$	4.03601	0.168167
$577$	20.9706	0.873018	0.436509	−	0.899700i	$-0.356215\pi$
$577$	20.9706	0.873018	0.436509	+	0.899700i	$0.356215\pi$
$578$	4.90984	0.204222
$579$	50.5198	2.09953
$580$	−0.685474	−0.0284628
$581$	−16.5239	−0.685525
$582$	−3.58625	−0.148655
$583$	−39.2869	−1.62710
$584$	−4.95608	−0.205084
$585$	−4.85866	−0.200881
$586$	−16.2866	−0.672795
$587$	10.5193	0.434176	0.217088	−	0.976152i	$-0.430344\pi$
$587$	10.5193	0.434176	0.217088	+	0.976152i	$0.430344\pi$
$588$	−37.1567	−1.53232
$589$	2.22094	0.0915123
$590$	3.18135	0.130974
$591$	11.7714	0.484210
$592$	−10.4599	−0.429899
$593$	−37.2131	−1.52816	−0.764079	−	0.645123i	$-0.776806\pi$
$593$	−37.2131	−1.52816	−0.764079	+	0.645123i	$0.776806\pi$
$594$	−11.0926	−0.455134
$595$	10.5829	0.433856
$596$	18.8471	0.772006
$597$	−49.8610	−2.04067
$598$	−10.4713	−0.428202
$599$	37.9765	1.55168	0.775840	−	0.630930i	$-0.217327\pi$
$599$	37.9765	1.55168	0.775840	+	0.630930i	$0.217327\pi$
$600$	12.6173	0.515100
$601$	−2.31560	−0.0944552	−0.0472276	−	0.998884i	$-0.515039\pi$
$601$	−2.31560	−0.0944552	−0.0472276	+	0.998884i	$0.515039\pi$
$602$	−49.2795	−2.00848
$603$	−45.3424	−1.84649
$604$	9.45927	0.384892
$605$	−2.61108	−0.106155
$606$	19.8497	0.806338
$607$	3.13929	0.127420	0.0637099	−	0.997968i	$-0.479707\pi$
$607$	3.13929	0.127420	0.0637099	+	0.997968i	$0.479707\pi$
$608$	−1.00000	−0.0405554
$609$	−16.8948	−0.684613
$610$	−0.821821	−0.0332746
$611$	−32.7710	−1.32577
$612$	−18.8917	−0.763653
$613$	−29.7028	−1.19968	−0.599842	−	0.800118i	$-0.704770\pi$
$613$	−29.7028	−1.19968	−0.599842	+	0.800118i	$0.704770\pi$
$614$	1.39011	0.0561001
$615$	2.69531	0.108685
$616$	18.5010	0.745428
$617$	30.8289	1.24112	0.620562	−	0.784157i	$-0.286904\pi$
$617$	30.8289	1.24112	0.620562	+	0.784157i	$0.286904\pi$
$618$	26.0154	1.04649
$619$	30.8413	1.23962	0.619809	−	0.784753i	$-0.287210\pi$
$619$	30.8413	1.23962	0.619809	+	0.784753i	$0.287210\pi$
$620$	1.09554	0.0439981
$621$	11.7911	0.473162
$622$	15.1712	0.608311
$623$	20.4808	0.820548
$624$	−6.47343	−0.259145
$625$	21.4093	0.856374
$626$	−3.41373	−0.136440
$627$	10.7070	0.427597
$628$	−4.32073	−0.172416
$629$	48.9606	1.95219
$630$	−9.12508	−0.363552
$631$	26.0425	1.03674	0.518368	−	0.855158i	$-0.326540\pi$
$631$	26.0425	1.03674	0.518368	+	0.855158i	$0.326540\pi$
$632$	−13.3503	−0.531045
$633$	−2.65255	−0.105429
$634$	−10.8980	−0.432814
$635$	−2.94611	−0.116913
$636$	25.8170	1.02371
$637$	34.1858	1.35449
$638$	5.60923	0.222072
$639$	19.7514	0.781354
$640$	−0.493279	−0.0194986
$641$	−8.62806	−0.340788	−0.170394	−	0.985376i	$-0.554504\pi$
$641$	−8.62806	−0.340788	−0.170394	+	0.985376i	$0.554504\pi$
$642$	23.5092	0.927833
$643$	37.8314	1.49193	0.745963	−	0.665987i	$-0.231989\pi$
$643$	37.8314	1.49193	0.745963	+	0.665987i	$0.231989\pi$
$644$	−19.6661	−0.774955
$645$	−14.0679	−0.553925
$646$	4.68079	0.184163
$647$	4.08856	0.160738	0.0803690	−	0.996765i	$-0.474390\pi$
$647$	4.08856	0.160738	0.0803690	+	0.996765i	$0.474390\pi$
$648$	−4.81865	−0.189294
$649$	−26.0329	−1.02188
$650$	−11.6085	−0.455321
$651$	27.0018	1.05828
$652$	3.80102	0.148859
$653$	12.1388	0.475026	0.237513	−	0.971384i	$-0.423668\pi$
$653$	12.1388	0.475026	0.237513	+	0.971384i	$0.423668\pi$
$654$	16.9073	0.661127
$655$	−7.41930	−0.289896
$656$	2.05993	0.0804267
$657$	−20.0028	−0.780383
$658$	−61.5476	−2.39937
$659$	−13.1869	−0.513687	−0.256844	−	0.966453i	$-0.582683\pi$
$659$	−13.1869	−0.513687	−0.256844	+	0.966453i	$0.582683\pi$
$660$	5.28154	0.205584
$661$	−17.2381	−0.670485	−0.335243	−	0.942132i	$-0.608818\pi$
$661$	−17.2381	−0.670485	−0.335243	+	0.942132i	$0.608818\pi$
$662$	−19.3329	−0.751396
$663$	30.3008	1.17679
$664$	−3.60512	−0.139906
$665$	2.26092	0.0876745
$666$	−42.2162	−1.63585
$667$	−5.96247	−0.230868
$668$	20.3512	0.787412
$669$	68.6695	2.65492
$670$	5.54172	0.214095
$671$	6.72496	0.259614
$672$	−12.1578	−0.468997
$673$	−19.0146	−0.732958	−0.366479	−	0.930426i	$-0.619437\pi$
$673$	−19.0146	−0.732958	−0.366479	+	0.930426i	$0.619437\pi$
$674$	−0.675010	−0.0260004
$675$	13.0717	0.503129
$676$	−7.04417	−0.270930
$677$	23.5121	0.903642	0.451821	−	0.892109i	$-0.350775\pi$
$677$	23.5121	0.903642	0.451821	+	0.892109i	$0.350775\pi$
$678$	−50.1602	−1.92639
$679$	6.19681	0.237812
$680$	2.30894	0.0885437
$681$	6.07118	0.232648
$682$	−8.96483	−0.343281
$683$	16.7930	0.642567	0.321283	−	0.946983i	$-0.395886\pi$
$683$	16.7930	0.642567	0.321283	+	0.946983i	$0.395886\pi$
$684$	−4.03601	−0.154321
$685$	3.14287	0.120083
$686$	32.1204	1.22636
$687$	−27.1000	−1.03393
$688$	−10.7516	−0.409902
$689$	−23.7527	−0.904908
$690$	−5.61414	−0.213727
$691$	6.35916	0.241914	0.120957	−	0.992658i	$-0.461404\pi$
$691$	6.35916	0.241914	0.120957	+	0.992658i	$0.461404\pi$
$692$	−11.5756	−0.440040
$693$	74.6704	2.83650
$694$	6.04174	0.229341
$695$	−10.5154	−0.398872
$696$	−3.68606	−0.139720
$697$	−9.64210	−0.365221
$698$	16.7575	0.634281
$699$	−61.7414	−2.33527
$700$	−21.8019	−0.824036
$701$	39.4626	1.49048	0.745242	−	0.666795i	$-0.232334\pi$
$701$	39.4626	1.49048	0.745242	+	0.666795i	$0.232334\pi$
$702$	−6.70655	−0.253122
$703$	10.4599	0.394502
$704$	4.03650	0.152131
$705$	−17.5701	−0.661730
$706$	27.8179	1.04694
$707$	−34.2990	−1.28995
$708$	17.1073	0.642932
$709$	−28.8569	−1.08375	−0.541873	−	0.840461i	$-0.682284\pi$
$709$	−28.8569	−1.08375	−0.541873	+	0.840461i	$0.682284\pi$
$710$	−2.41401	−0.0905961
$711$	−53.8819	−2.02073
$712$	4.46844	0.167462
$713$	9.52939	0.356878
$714$	56.9082	2.12973
$715$	−4.85924	−0.181725
$716$	−17.3658	−0.648992
$717$	1.06706	0.0398500
$718$	5.88838	0.219753
$719$	17.2793	0.644408	0.322204	−	0.946670i	$-0.395576\pi$
$719$	17.2793	0.644408	0.322204	+	0.946670i	$0.395576\pi$
$720$	−1.99088	−0.0741957
$721$	−44.9531	−1.67414
$722$	1.00000	0.0372161
$723$	58.0436	2.15866
$724$	14.6197	0.543337
$725$	−6.61001	−0.245490
$726$	−14.0408	−0.521101
$727$	26.1338	0.969250	0.484625	−	0.874722i	$-0.338956\pi$
$727$	26.1338	0.969250	0.484625	+	0.874722i	$0.338956\pi$
$728$	11.1857	0.414569
$729$	−41.3163	−1.53023
$730$	2.44473	0.0904835
$731$	50.3262	1.86138
$732$	−4.41925	−0.163340
$733$	41.3417	1.52699	0.763495	−	0.645813i	$-0.223482\pi$
$733$	41.3417	1.52699	0.763495	+	0.645813i	$0.223482\pi$
$734$	−21.5222	−0.794398
$735$	18.3286	0.676062
$736$	−4.29070	−0.158157
$737$	−45.3478	−1.67041
$738$	8.31390	0.306039
$739$	−29.1603	−1.07268	−0.536339	−	0.844003i	$-0.680193\pi$
$739$	−29.1603	−1.07268	−0.536339	+	0.844003i	$0.680193\pi$
$740$	5.15964	0.189672
$741$	6.47343	0.237807
$742$	−44.6102	−1.63769
$743$	18.7176	0.686682	0.343341	−	0.939211i	$-0.388441\pi$
$743$	18.7176	0.686682	0.343341	+	0.939211i	$0.388441\pi$
$744$	5.89116	0.215980
$745$	−9.29686	−0.340611
$746$	3.26018	0.119364
$747$	−14.5503	−0.532368
$748$	−18.8940	−0.690834
$749$	−40.6224	−1.48431
$750$	−12.7661	−0.466152
$751$	38.0560	1.38868	0.694342	−	0.719646i	$-0.255696\pi$
$751$	38.0560	1.38868	0.694342	+	0.719646i	$0.255696\pi$
$752$	−13.4282	−0.489678
$753$	−33.6768	−1.22725
$754$	3.39133	0.123505
$755$	−4.66606	−0.169815
$756$	−12.5956	−0.458098
$757$	−46.1330	−1.67673	−0.838366	−	0.545108i	$-0.816488\pi$
$757$	−46.1330	−1.67673	−0.838366	+	0.545108i	$0.816488\pi$
$758$	−8.18080	−0.297140
$759$	45.9405	1.66753
$760$	0.493279	0.0178931
$761$	1.18056	0.0427952	0.0213976	−	0.999771i	$-0.493188\pi$
$761$	1.18056	0.0427952	0.0213976	+	0.999771i	$0.493188\pi$
$762$	−15.8424	−0.573909
$763$	−29.2147	−1.05764
$764$	−15.3076	−0.553809
$765$	9.31890	0.336925
$766$	−4.79739	−0.173337
$767$	−15.7394	−0.568318
$768$	−2.65255	−0.0957156
$769$	−15.0823	−0.543881	−0.271940	−	0.962314i	$-0.587665\pi$
$769$	−15.0823	−0.543881	−0.271940	+	0.962314i	$0.587665\pi$
$770$	−9.12618	−0.328885
$771$	20.3247	0.731977
$772$	−19.0457	−0.685471
$773$	−53.9110	−1.93904	−0.969521	−	0.245008i	$-0.921209\pi$
$773$	−53.9110	−1.93904	−0.969521	+	0.245008i	$0.921209\pi$
$774$	−43.3937	−1.55976
$775$	10.5643	0.379481
$776$	1.35200	0.0485340
$777$	127.169	4.56217
$778$	−22.2192	−0.796596
$779$	−2.05993	−0.0738046
$780$	3.19321	0.114335
$781$	19.7538	0.706847
$782$	20.0839	0.718197
$783$	−3.81880	−0.136473
$784$	14.0079	0.500283
$785$	2.13133	0.0760703
$786$	−39.8964	−1.42306
$787$	49.8778	1.77795	0.888975	−	0.457956i	$-0.151418\pi$
$787$	49.8778	1.77795	0.888975	+	0.457956i	$0.151418\pi$
$788$	−4.43777	−0.158089
$789$	−46.1535	−1.64311
$790$	6.58541	0.234298
$791$	86.6738	3.08176
$792$	16.2913	0.578888
$793$	4.06589	0.144384
$794$	−5.56615	−0.197535
$795$	−12.7350	−0.451664
$796$	18.7974	0.666256
$797$	−12.6486	−0.448037	−0.224018	−	0.974585i	$-0.571918\pi$
$797$	−12.6486	−0.448037	−0.224018	+	0.974585i	$0.571918\pi$
$798$	12.1578	0.430381
$799$	62.8549	2.22364
$800$	−4.75668	−0.168174
$801$	18.0347	0.637224
$802$	−27.6585	−0.976656
$803$	−20.0052	−0.705968
$804$	29.7999	1.05096
$805$	9.70090	0.341912
$806$	−5.42011	−0.190915
$807$	−31.9557	−1.12489
$808$	−7.48325	−0.263260
$809$	27.2989	0.959779	0.479890	−	0.877329i	$-0.340677\pi$
$809$	27.2989	0.959779	0.479890	+	0.877329i	$0.340677\pi$
$810$	2.37694	0.0835170
$811$	−40.8261	−1.43360	−0.716800	−	0.697279i	$-0.754394\pi$
$811$	−40.8261	−1.43360	−0.716800	+	0.697279i	$0.754394\pi$
$812$	6.36928	0.223518
$813$	−31.1862	−1.09375
$814$	−42.2213	−1.47986
$815$	−1.87496	−0.0656771
$816$	12.4160	0.434648
$817$	10.7516	0.376152
$818$	16.4844	0.576363
$819$	45.1456	1.57751
$820$	−1.01612	−0.0354844
$821$	−47.2275	−1.64825	−0.824126	−	0.566407i	$-0.808333\pi$
$821$	−47.2275	−1.64825	−0.824126	+	0.566407i	$0.808333\pi$
$822$	16.9004	0.589469
$823$	27.3554	0.953548	0.476774	−	0.879026i	$-0.341806\pi$
$823$	27.3554	0.953548	0.476774	+	0.879026i	$0.341806\pi$
$824$	−9.80771	−0.341668
$825$	50.9297	1.77315
$826$	−29.5604	−1.02854
$827$	43.8252	1.52395	0.761976	−	0.647606i	$-0.224230\pi$
$827$	43.8252	1.52395	0.761976	+	0.647606i	$0.224230\pi$
$828$	−17.3173	−0.601818
$829$	17.7185	0.615390	0.307695	−	0.951485i	$-0.400442\pi$
$829$	17.7185	0.615390	0.307695	+	0.951485i	$0.400442\pi$
$830$	1.77833	0.0617268
$831$	−9.18970	−0.318787
$832$	2.44046	0.0846076
$833$	−65.5683	−2.27181
$834$	−56.5453	−1.95800
$835$	−10.0388	−0.347408
$836$	−4.03650	−0.139605
$837$	6.10331	0.210961
$838$	−13.2846	−0.458909
$839$	9.43320	0.325670	0.162835	−	0.986653i	$-0.447936\pi$
$839$	9.43320	0.325670	0.162835	+	0.986653i	$0.447936\pi$
$840$	5.99719	0.206923
$841$	−27.0689	−0.933411
$842$	−29.1566	−1.00480
$843$	19.0707	0.656831
$844$	1.00000	0.0344214
$845$	3.47474	0.119535
$846$	−54.1965	−1.86332
$847$	24.2616	0.833638
$848$	−9.73291	−0.334230
$849$	28.8473	0.990036
$850$	22.2650	0.763684
$851$	44.8802	1.53847
$852$	−12.9810	−0.444723
$853$	−6.82954	−0.233839	−0.116919	−	0.993141i	$-0.537302\pi$
$853$	−6.82954	−0.233839	−0.116919	+	0.993141i	$0.537302\pi$
$854$	7.63619	0.261305
$855$	1.99088	0.0680866
$856$	−8.86286	−0.302926
$857$	−27.9253	−0.953911	−0.476956	−	0.878927i	$-0.658260\pi$
$857$	−27.9253	−0.953911	−0.476956	+	0.878927i	$0.658260\pi$
$858$	−26.1300	−0.892063
$859$	−18.3277	−0.625334	−0.312667	−	0.949863i	$-0.601222\pi$
$859$	−18.3277	−0.625334	−0.312667	+	0.949863i	$0.601222\pi$
$860$	5.30356	0.180850
$861$	−25.0442	−0.853504
$862$	24.4471	0.832673
$863$	−7.11568	−0.242220	−0.121110	−	0.992639i	$-0.538645\pi$
$863$	−7.11568	−0.242220	−0.121110	+	0.992639i	$0.538645\pi$
$864$	−2.74807	−0.0934913
$865$	5.71002	0.194147
$866$	−10.8922	−0.370131
$867$	−13.0236	−0.442304
$868$	−10.1796	−0.345517
$869$	−53.8883	−1.82804
$870$	1.81825	0.0616446
$871$	−27.4172	−0.928997
$872$	−6.37398	−0.215850
$873$	5.45669	0.184681
$874$	4.29070	0.145135
$875$	22.0590	0.745731
$876$	13.1462	0.444170
$877$	−43.9302	−1.48342	−0.741709	−	0.670721i	$-0.765985\pi$
$877$	−43.9302	−1.48342	−0.741709	+	0.670721i	$0.765985\pi$
$878$	11.7953	0.398073
$879$	43.2011	1.45714
$880$	−1.99112	−0.0671206
$881$	−34.1460	−1.15041	−0.575204	−	0.818010i	$-0.695077\pi$
$881$	−34.1460	−1.15041	−0.575204	+	0.818010i	$0.695077\pi$
$882$	56.5362	1.90367
$883$	−15.8423	−0.533136	−0.266568	−	0.963816i	$-0.585890\pi$
$883$	−15.8423	−0.533136	−0.266568	+	0.963816i	$0.585890\pi$
$884$	−11.4233	−0.384206
$885$	−8.43867	−0.283663
$886$	6.61302	0.222169
$887$	32.0912	1.07752	0.538759	−	0.842460i	$-0.318893\pi$
$887$	32.0912	1.07752	0.538759	+	0.842460i	$0.318893\pi$
$888$	27.7454	0.931074
$889$	27.3747	0.918117
$890$	−2.20419	−0.0738846
$891$	−19.4504	−0.651615
$892$	−25.8881	−0.866799
$893$	13.4282	0.449359
$894$	−49.9927	−1.67201
$895$	8.56620	0.286336
$896$	4.58344	0.153122
$897$	27.7755	0.927397
$898$	34.9493	1.16627
$899$	−3.08628	−0.102933
$900$	−19.1980	−0.639933
$901$	45.5578	1.51775
$902$	8.31490	0.276856
$903$	130.716	4.34997
$904$	18.9102	0.628944
$905$	−7.21159	−0.239721
$906$	−25.0912	−0.833599
$907$	−18.8797	−0.626891	−0.313445	−	0.949606i	$-0.601483\pi$
$907$	−18.8797	−0.626891	−0.313445	+	0.949606i	$0.601483\pi$
$908$	−2.28881	−0.0759568
$909$	−30.2025	−1.00175
$910$	−5.51767	−0.182909
$911$	−11.3024	−0.374466	−0.187233	−	0.982315i	$-0.559952\pi$
$911$	−11.3024	−0.374466	−0.187233	+	0.982315i	$0.559952\pi$
$912$	2.65255	0.0878346
$913$	−14.5521	−0.481603
$914$	25.1123	0.830640
$915$	2.17992	0.0720660
$916$	10.2166	0.337566
$917$	68.9385	2.27655
$918$	12.8632	0.424547
$919$	−4.95636	−0.163495	−0.0817476	−	0.996653i	$-0.526050\pi$
$919$	−4.95636	−0.163495	−0.0817476	+	0.996653i	$0.526050\pi$
$920$	2.11651	0.0697793
$921$	−3.68732	−0.121501
$922$	−7.38999	−0.243376
$923$	11.9431	0.393112
$924$	−49.0749	−1.61445
$925$	49.7543	1.63591
$926$	4.69829	0.154395
$927$	−39.5840	−1.30011
$928$	1.38963	0.0456168
$929$	31.1800	1.02298	0.511492	−	0.859288i	$-0.329093\pi$
$929$	31.1800	1.02298	0.511492	+	0.859288i	$0.329093\pi$
$930$	−2.90598	−0.0952910
$931$	−14.0079	−0.459091
$932$	23.2763	0.762439
$933$	−40.2424	−1.31748
$934$	−2.01598	−0.0659648
$935$	9.32002	0.304797
$936$	9.84971	0.321948
$937$	54.3952	1.77702	0.888508	−	0.458862i	$-0.151743\pi$
$937$	54.3952	1.77702	0.888508	+	0.458862i	$0.151743\pi$
$938$	−51.4925	−1.68129
$939$	9.05507	0.295501
$940$	6.62387	0.216047
$941$	13.9215	0.453827	0.226914	−	0.973915i	$-0.427136\pi$
$941$	13.9215	0.453827	0.226914	+	0.973915i	$0.427136\pi$
$942$	11.4609	0.373418
$943$	−8.83853	−0.287822
$944$	−6.44939	−0.209910
$945$	6.21315	0.202114
$946$	−43.3990	−1.41102
$947$	−1.85823	−0.0603844	−0.0301922	−	0.999544i	$-0.509612\pi$
$947$	−1.85823	−0.0603844	−0.0301922	+	0.999544i	$0.509612\pi$
$948$	35.4122	1.15014
$949$	−12.0951	−0.392624
$950$	4.75668	0.154327
$951$	28.9074	0.937388
$952$	−21.4541	−0.695333
$953$	29.5529	0.957312	0.478656	−	0.878002i	$-0.341124\pi$
$953$	29.5529	0.957312	0.478656	+	0.878002i	$0.341124\pi$
$954$	−39.2821	−1.27181
$955$	7.55091	0.244342
$956$	−0.402276	−0.0130105
$957$	−14.8788	−0.480962
$958$	20.4146	0.659566
$959$	−29.2028	−0.943009
$960$	1.30845	0.0422299
$961$	−26.0674	−0.840884
$962$	−25.5269	−0.823021
$963$	−35.7706	−1.15269
$964$	−21.8822	−0.704778
$965$	9.39487	0.302431
$966$	52.1654	1.67839
$967$	2.98987	0.0961479	0.0480739	−	0.998844i	$-0.484692\pi$
$967$	2.98987	0.0961479	0.0480739	+	0.998844i	$0.484692\pi$
$968$	5.29331	0.170133
$969$	−12.4160	−0.398860
$970$	−0.666913	−0.0214133
$971$	23.4291	0.751876	0.375938	−	0.926645i	$-0.377321\pi$
$971$	23.4291	0.751876	0.375938	+	0.926645i	$0.377321\pi$
$972$	21.0259	0.674406
$973$	97.7067	3.13233
$974$	0.688755	0.0220691
$975$	30.7920	0.986133
$976$	1.66604	0.0533286
$977$	10.6097	0.339435	0.169717	−	0.985493i	$-0.445715\pi$
$977$	10.6097	0.339435	0.169717	+	0.985493i	$0.445715\pi$
$978$	−10.0824	−0.322399
$979$	18.0369	0.576460
$980$	−6.90982	−0.220726
$981$	−25.7254	−0.821350
$982$	−20.2738	−0.646964
$983$	−0.972248	−0.0310099	−0.0155049	−	0.999880i	$-0.504936\pi$
$983$	−0.972248	−0.0310099	−0.0155049	+	0.999880i	$0.504936\pi$
$984$	−5.46406	−0.174188
$985$	2.18906	0.0697491
$986$	−6.50456	−0.207148
$987$	163.258	5.19656
$988$	−2.44046	−0.0776413
$989$	46.1320	1.46691
$990$	−8.03618	−0.255407
$991$	−51.2320	−1.62744	−0.813719	−	0.581258i	$-0.802561\pi$
$991$	−51.2320	−1.62744	−0.813719	+	0.581258i	$0.802561\pi$
$992$	−2.22094	−0.0705150
$993$	51.2815	1.62737
$994$	22.4304	0.711450
$995$	−9.27236	−0.293954
$996$	9.56276	0.303008
$997$	36.0219	1.14082	0.570412	−	0.821359i	$-0.306784\pi$
$997$	36.0219	1.14082	0.570412	+	0.821359i	$0.306784\pi$
$998$	26.6168	0.842539
$999$	28.7445	0.909436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.e.1.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.e.1.4	✓	32	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.65255 q^{3} +1.00000 q^{4} -0.493279 q^{5} -2.65255 q^{6} +4.58344 q^{7} +1.00000 q^{8} +4.03601 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.65255 q^{3} +1.00000 q^{4} -0.493279 q^{5} -2.65255 q^{6} +4.58344 q^{7} +1.00000 q^{8} +4.03601 q^{9} -0.493279 q^{10} +4.03650 q^{11} -2.65255 q^{12} +2.44046 q^{13} +4.58344 q^{14} +1.30845 q^{15} +1.00000 q^{16} -4.68079 q^{17} +4.03601 q^{18} -1.00000 q^{19} -0.493279 q^{20} -12.1578 q^{21} +4.03650 q^{22} -4.29070 q^{23} -2.65255 q^{24} -4.75668 q^{25} +2.44046 q^{26} -2.74807 q^{27} +4.58344 q^{28} +1.38963 q^{29} +1.30845 q^{30} -2.22094 q^{31} +1.00000 q^{32} -10.7070 q^{33} -4.68079 q^{34} -2.26092 q^{35} +4.03601 q^{36} -10.4599 q^{37} -1.00000 q^{38} -6.47343 q^{39} -0.493279 q^{40} +2.05993 q^{41} -12.1578 q^{42} -10.7516 q^{43} +4.03650 q^{44} -1.99088 q^{45} -4.29070 q^{46} -13.4282 q^{47} -2.65255 q^{48} +14.0079 q^{49} -4.75668 q^{50} +12.4160 q^{51} +2.44046 q^{52} -9.73291 q^{53} -2.74807 q^{54} -1.99112 q^{55} +4.58344 q^{56} +2.65255 q^{57} +1.38963 q^{58} -6.44939 q^{59} +1.30845 q^{60} +1.66604 q^{61} -2.22094 q^{62} +18.4988 q^{63} +1.00000 q^{64} -1.20383 q^{65} -10.7070 q^{66} -11.2345 q^{67} -4.68079 q^{68} +11.3813 q^{69} -2.26092 q^{70} +4.89380 q^{71} +4.03601 q^{72} -4.95608 q^{73} -10.4599 q^{74} +12.6173 q^{75} -1.00000 q^{76} +18.5010 q^{77} -6.47343 q^{78} -13.3503 q^{79} -0.493279 q^{80} -4.81865 q^{81} +2.05993 q^{82} -3.60512 q^{83} -12.1578 q^{84} +2.30894 q^{85} -10.7516 q^{86} -3.68606 q^{87} +4.03650 q^{88} +4.46844 q^{89} -1.99088 q^{90} +11.1857 q^{91} -4.29070 q^{92} +5.89116 q^{93} -13.4282 q^{94} +0.493279 q^{95} -2.65255 q^{96} +1.35200 q^{97} +14.0079 q^{98} +16.2913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * q^99

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