LMFDB - Embedded newform 4029.2.a.l.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.34067 q^{2} -1.00000 q^{3} -0.202611 q^{4} +1.16053 q^{5} +1.34067 q^{6} -4.05917 q^{7} +2.95297 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.34067 q^{2} -1.00000 q^{3} -0.202611 q^{4} +1.16053 q^{5} +1.34067 q^{6} -4.05917 q^{7} +2.95297 q^{8} +1.00000 q^{9} -1.55588 q^{10} +0.687421 q^{11} +0.202611 q^{12} -5.30961 q^{13} +5.44200 q^{14} -1.16053 q^{15} -3.55373 q^{16} -1.00000 q^{17} -1.34067 q^{18} +7.04145 q^{19} -0.235136 q^{20} +4.05917 q^{21} -0.921603 q^{22} +3.83710 q^{23} -2.95297 q^{24} -3.65317 q^{25} +7.11842 q^{26} -1.00000 q^{27} +0.822434 q^{28} +5.25655 q^{29} +1.55588 q^{30} -6.46598 q^{31} -1.14157 q^{32} -0.687421 q^{33} +1.34067 q^{34} -4.71078 q^{35} -0.202611 q^{36} -10.3188 q^{37} -9.44024 q^{38} +5.30961 q^{39} +3.42700 q^{40} +7.73454 q^{41} -5.44200 q^{42} -11.8132 q^{43} -0.139279 q^{44} +1.16053 q^{45} -5.14428 q^{46} -7.75967 q^{47} +3.55373 q^{48} +9.47688 q^{49} +4.89769 q^{50} +1.00000 q^{51} +1.07579 q^{52} +11.5622 q^{53} +1.34067 q^{54} +0.797771 q^{55} -11.9866 q^{56} -7.04145 q^{57} -7.04729 q^{58} -3.00997 q^{59} +0.235136 q^{60} -11.8368 q^{61} +8.66873 q^{62} -4.05917 q^{63} +8.63792 q^{64} -6.16195 q^{65} +0.921603 q^{66} +11.4342 q^{67} +0.202611 q^{68} -3.83710 q^{69} +6.31559 q^{70} +4.29205 q^{71} +2.95297 q^{72} -2.60512 q^{73} +13.8341 q^{74} +3.65317 q^{75} -1.42668 q^{76} -2.79036 q^{77} -7.11842 q^{78} +1.00000 q^{79} -4.12420 q^{80} +1.00000 q^{81} -10.3694 q^{82} -5.07294 q^{83} -0.822434 q^{84} -1.16053 q^{85} +15.8376 q^{86} -5.25655 q^{87} +2.02993 q^{88} -6.92093 q^{89} -1.55588 q^{90} +21.5526 q^{91} -0.777440 q^{92} +6.46598 q^{93} +10.4031 q^{94} +8.17180 q^{95} +1.14157 q^{96} -7.18674 q^{97} -12.7053 q^{98} +0.687421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * 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 $

$2$	−1.34067	−0.947995	−0.473997	−	0.880526i	$-0.657189\pi$
$2$	−1.34067	−0.947995	−0.473997	+	0.880526i	$0.657189\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.202611	−0.101306
$5$	1.16053	0.519004	0.259502	−	0.965743i	$-0.416442\pi$
$5$	1.16053	0.519004	0.259502	+	0.965743i	$0.416442\pi$
$6$	1.34067	0.547325
$7$	−4.05917	−1.53422	−0.767111	−	0.641514i	$-0.778307\pi$
$7$	−4.05917	−1.53422	−0.767111	+	0.641514i	$0.778307\pi$
$8$	2.95297	1.04403
$9$	1.00000	0.333333
$10$	−1.55588	−0.492013
$11$	0.687421	0.207265	0.103633	−	0.994616i	$-0.466953\pi$
$11$	0.687421	0.207265	0.103633	+	0.994616i	$0.466953\pi$
$12$	0.202611	0.0584888
$13$	−5.30961	−1.47262	−0.736310	−	0.676644i	$-0.763434\pi$
$13$	−5.30961	−1.47262	−0.736310	+	0.676644i	$0.763434\pi$
$14$	5.44200	1.45444
$15$	−1.16053	−0.299647
$16$	−3.55373	−0.888432
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.34067	−0.315998
$19$	7.04145	1.61542	0.807710	−	0.589580i	$-0.200707\pi$
$19$	7.04145	1.61542	0.807710	+	0.589580i	$0.200707\pi$
$20$	−0.235136	−0.0525780
$21$	4.05917	0.885784
$22$	−0.921603	−0.196486
$23$	3.83710	0.800091	0.400045	−	0.916495i	$-0.368994\pi$
$23$	3.83710	0.800091	0.400045	+	0.916495i	$0.368994\pi$
$24$	−2.95297	−0.602772
$25$	−3.65317	−0.730635
$26$	7.11842	1.39604
$27$	−1.00000	−0.192450
$28$	0.822434	0.155425
$29$	5.25655	0.976118	0.488059	−	0.872811i	$-0.337705\pi$
$29$	5.25655	0.976118	0.488059	+	0.872811i	$0.337705\pi$
$30$	1.55588	0.284064
$31$	−6.46598	−1.16132	−0.580662	−	0.814145i	$-0.697206\pi$
$31$	−6.46598	−1.16132	−0.580662	+	0.814145i	$0.697206\pi$
$32$	−1.14157	−0.201804
$33$	−0.687421	−0.119665
$34$	1.34067	0.229923
$35$	−4.71078	−0.796268
$36$	−0.202611	−0.0337685
$37$	−10.3188	−1.69640	−0.848200	−	0.529677i	$-0.822313\pi$
$37$	−10.3188	−1.69640	−0.848200	+	0.529677i	$0.822313\pi$
$38$	−9.44024	−1.53141
$39$	5.30961	0.850218
$40$	3.42700	0.541857
$41$	7.73454	1.20793	0.603966	−	0.797010i	$-0.293586\pi$
$41$	7.73454	1.20793	0.603966	+	0.797010i	$0.293586\pi$
$42$	−5.44200	−0.839719
$43$	−11.8132	−1.80150	−0.900749	−	0.434340i	$-0.856982\pi$
$43$	−11.8132	−1.80150	−0.900749	+	0.434340i	$0.856982\pi$
$44$	−0.139279	−0.0209971
$45$	1.16053	0.173001
$46$	−5.14428	−0.758482
$47$	−7.75967	−1.13186	−0.565932	−	0.824452i	$-0.691484\pi$
$47$	−7.75967	−1.13186	−0.565932	+	0.824452i	$0.691484\pi$
$48$	3.55373	0.512936
$49$	9.47688	1.35384
$50$	4.89769	0.692638
$51$	1.00000	0.140028
$52$	1.07579	0.149185
$53$	11.5622	1.58819	0.794093	−	0.607796i	$-0.207946\pi$
$53$	11.5622	1.58819	0.794093	+	0.607796i	$0.207946\pi$
$54$	1.34067	0.182442
$55$	0.797771	0.107571
$56$	−11.9866	−1.60178
$57$	−7.04145	−0.932663
$58$	−7.04729	−0.925355
$59$	−3.00997	−0.391865	−0.195933	−	0.980617i	$-0.562773\pi$
$59$	−3.00997	−0.391865	−0.195933	+	0.980617i	$0.562773\pi$
$60$	0.235136	0.0303559
$61$	−11.8368	−1.51555	−0.757774	−	0.652517i	$-0.773713\pi$
$61$	−11.8368	−1.51555	−0.757774	+	0.652517i	$0.773713\pi$
$62$	8.66873	1.10093
$63$	−4.05917	−0.511408
$64$	8.63792	1.07974
$65$	−6.16195	−0.764296
$66$	0.921603	0.113441
$67$	11.4342	1.39690	0.698452	−	0.715656i	$-0.253872\pi$
$67$	11.4342	1.39690	0.698452	+	0.715656i	$0.253872\pi$
$68$	0.202611	0.0245702
$69$	−3.83710	−0.461933
$70$	6.31559	0.754858
$71$	4.29205	0.509373	0.254686	−	0.967024i	$-0.418028\pi$
$71$	4.29205	0.509373	0.254686	+	0.967024i	$0.418028\pi$
$72$	2.95297	0.348011
$73$	−2.60512	−0.304907	−0.152453	−	0.988311i	$-0.548717\pi$
$73$	−2.60512	−0.304907	−0.152453	+	0.988311i	$0.548717\pi$
$74$	13.8341	1.60818
$75$	3.65317	0.421832
$76$	−1.42668	−0.163651
$77$	−2.79036	−0.317991
$78$	−7.11842	−0.806002
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−4.12420	−0.461100
$81$	1.00000	0.111111
$82$	−10.3694	−1.14511
$83$	−5.07294	−0.556828	−0.278414	−	0.960461i	$-0.589809\pi$
$83$	−5.07294	−0.556828	−0.278414	+	0.960461i	$0.589809\pi$
$84$	−0.822434	−0.0897349
$85$	−1.16053	−0.125877
$86$	15.8376	1.70781
$87$	−5.25655	−0.563562
$88$	2.02993	0.216392
$89$	−6.92093	−0.733617	−0.366809	−	0.930296i	$-0.619550\pi$
$89$	−6.92093	−0.733617	−0.366809	+	0.930296i	$0.619550\pi$
$90$	−1.55588	−0.164004
$91$	21.5526	2.25933
$92$	−0.777440	−0.0810537
$93$	6.46598	0.670491
$94$	10.4031	1.07300
$95$	8.17180	0.838409
$96$	1.14157	0.116511
$97$	−7.18674	−0.729703	−0.364851	−	0.931066i	$-0.618880\pi$
$97$	−7.18674	−0.729703	−0.364851	+	0.931066i	$0.618880\pi$
$98$	−12.7053	−1.28343
$99$	0.687421	0.0690884
$100$	0.740174	0.0740174
$101$	14.3632	1.42919	0.714596	−	0.699537i	$-0.246611\pi$
$101$	14.3632	1.42919	0.714596	+	0.699537i	$0.246611\pi$
$102$	−1.34067	−0.132746
$103$	16.2362	1.59980	0.799899	−	0.600135i	$-0.204886\pi$
$103$	16.2362	1.59980	0.799899	+	0.600135i	$0.204886\pi$
$104$	−15.6791	−1.53746
$105$	4.71078	0.459725
$106$	−15.5010	−1.50559
$107$	−17.7659	−1.71750	−0.858749	−	0.512396i	$-0.828758\pi$
$107$	−17.7659	−1.71750	−0.858749	+	0.512396i	$0.828758\pi$
$108$	0.202611	0.0194963
$109$	−12.2214	−1.17060	−0.585299	−	0.810817i	$-0.699023\pi$
$109$	−12.2214	−1.17060	−0.585299	+	0.810817i	$0.699023\pi$
$110$	−1.06955	−0.101977
$111$	10.3188	0.979417
$112$	14.4252	1.36305
$113$	11.5125	1.08300	0.541502	−	0.840700i	$-0.317856\pi$
$113$	11.5125	1.08300	0.541502	+	0.840700i	$0.317856\pi$
$114$	9.44024	0.884160
$115$	4.45307	0.415250
$116$	−1.06504	−0.0988862
$117$	−5.30961	−0.490873
$118$	4.03537	0.371486
$119$	4.05917	0.372104
$120$	−3.42700	−0.312841
$121$	−10.5275	−0.957041
$122$	15.8692	1.43673
$123$	−7.73454	−0.697400
$124$	1.31008	0.117649
$125$	−10.0423	−0.898206
$126$	5.44200	0.484812
$127$	3.35833	0.298004	0.149002	−	0.988837i	$-0.452394\pi$
$127$	3.35833	0.298004	0.149002	+	0.988837i	$0.452394\pi$
$128$	−9.29743	−0.821785
$129$	11.8132	1.04010
$130$	8.26113	0.724549
$131$	14.5046	1.26727	0.633635	−	0.773632i	$-0.281562\pi$
$131$	14.5046	1.26727	0.633635	+	0.773632i	$0.281562\pi$
$132$	0.139279	0.0121227
$133$	−28.5825	−2.47841
$134$	−15.3294	−1.32426
$135$	−1.16053	−0.0998824
$136$	−2.95297	−0.253215
$137$	−16.8949	−1.44343	−0.721716	−	0.692190i	$-0.756646\pi$
$137$	−16.8949	−1.44343	−0.721716	+	0.692190i	$0.756646\pi$
$138$	5.14428	0.437910
$139$	12.1040	1.02665	0.513326	−	0.858194i	$-0.328413\pi$
$139$	12.1040	1.02665	0.513326	+	0.858194i	$0.328413\pi$
$140$	0.954458	0.0806664
$141$	7.75967	0.653482
$142$	−5.75421	−0.482883
$143$	−3.64993	−0.305223
$144$	−3.55373	−0.296144
$145$	6.10038	0.506609
$146$	3.49260	0.289050
$147$	−9.47688	−0.781640
$148$	2.09070	0.171855
$149$	−3.03517	−0.248651	−0.124326	−	0.992241i	$-0.539677\pi$
$149$	−3.03517	−0.248651	−0.124326	+	0.992241i	$0.539677\pi$
$150$	−4.89769	−0.399895
$151$	−11.8078	−0.960903	−0.480452	−	0.877021i	$-0.659527\pi$
$151$	−11.8078	−0.960903	−0.480452	+	0.877021i	$0.659527\pi$
$152$	20.7932	1.68655
$153$	−1.00000	−0.0808452
$154$	3.74094	0.301454
$155$	−7.50395	−0.602732
$156$	−1.07579	−0.0861318
$157$	−8.10733	−0.647036	−0.323518	−	0.946222i	$-0.604866\pi$
$157$	−8.10733	−0.647036	−0.323518	+	0.946222i	$0.604866\pi$
$158$	−1.34067	−0.106658
$159$	−11.5622	−0.916940
$160$	−1.32483	−0.104737
$161$	−15.5755	−1.22752
$162$	−1.34067	−0.105333
$163$	−6.17262	−0.483477	−0.241739	−	0.970341i	$-0.577718\pi$
$163$	−6.17262	−0.483477	−0.241739	+	0.970341i	$0.577718\pi$
$164$	−1.56710	−0.122370
$165$	−0.797771	−0.0621064
$166$	6.80113	0.527870
$167$	−20.3368	−1.57371	−0.786854	−	0.617139i	$-0.788292\pi$
$167$	−20.3368	−1.57371	−0.786854	+	0.617139i	$0.788292\pi$
$168$	11.9866	0.924787
$169$	15.1919	1.16861
$170$	1.55588	0.119331
$171$	7.04145	0.538473
$172$	2.39349	0.182502
$173$	16.1657	1.22906	0.614528	−	0.788895i	$-0.289347\pi$
$173$	16.1657	1.22906	0.614528	+	0.788895i	$0.289347\pi$
$174$	7.04729	0.534254
$175$	14.8289	1.12096
$176$	−2.44291	−0.184141
$177$	3.00997	0.226243
$178$	9.27866	0.695465
$179$	3.23273	0.241625	0.120813	−	0.992675i	$-0.461450\pi$
$179$	3.23273	0.241625	0.120813	+	0.992675i	$0.461450\pi$
$180$	−0.235136	−0.0175260
$181$	−10.3861	−0.771996	−0.385998	−	0.922500i	$-0.626143\pi$
$181$	−10.3861	−0.771996	−0.385998	+	0.922500i	$0.626143\pi$
$182$	−28.8949	−2.14183
$183$	11.8368	0.875002
$184$	11.3308	0.835321
$185$	−11.9753	−0.880438
$186$	−8.66873	−0.635622
$187$	−0.687421	−0.0502692
$188$	1.57220	0.114664
$189$	4.05917	0.295261
$190$	−10.9557	−0.794808
$191$	13.0022	0.940803	0.470401	−	0.882453i	$-0.344109\pi$
$191$	13.0022	0.940803	0.470401	+	0.882453i	$0.344109\pi$
$192$	−8.63792	−0.623388
$193$	3.38016	0.243309	0.121655	−	0.992572i	$-0.461180\pi$
$193$	3.38016	0.243309	0.121655	+	0.992572i	$0.461180\pi$
$194$	9.63503	0.691755
$195$	6.16195	0.441266
$196$	−1.92012	−0.137152
$197$	−3.49753	−0.249189	−0.124594	−	0.992208i	$-0.539763\pi$
$197$	−3.49753	−0.249189	−0.124594	+	0.992208i	$0.539763\pi$
$198$	−0.921603	−0.0654954
$199$	11.2955	0.800715	0.400357	−	0.916359i	$-0.368886\pi$
$199$	11.2955	0.800715	0.400357	+	0.916359i	$0.368886\pi$
$200$	−10.7877	−0.762806
$201$	−11.4342	−0.806503
$202$	−19.2563	−1.35487
$203$	−21.3373	−1.49758
$204$	−0.202611	−0.0141856
$205$	8.97615	0.626922
$206$	−21.7673	−1.51660
$207$	3.83710	0.266697
$208$	18.8689	1.30832
$209$	4.84044	0.334820
$210$	−6.31559	−0.435817
$211$	18.1639	1.25046	0.625228	−	0.780442i	$-0.285006\pi$
$211$	18.1639	1.25046	0.625228	+	0.780442i	$0.285006\pi$
$212$	−2.34262	−0.160892
$213$	−4.29205	−0.294086
$214$	23.8182	1.62818
$215$	−13.7096	−0.934985
$216$	−2.95297	−0.200924
$217$	26.2465	1.78173
$218$	16.3848	1.10972
$219$	2.60512	0.176038
$220$	−0.161637	−0.0108976
$221$	5.30961	0.357163
$222$	−13.8341	−0.928482
$223$	4.09022	0.273901	0.136951	−	0.990578i	$-0.456270\pi$
$223$	4.09022	0.273901	0.136951	+	0.990578i	$0.456270\pi$
$224$	4.63384	0.309612
$225$	−3.65317	−0.243545
$226$	−15.4344	−1.02668
$227$	24.9126	1.65351	0.826755	−	0.562562i	$-0.190184\pi$
$227$	24.9126	1.65351	0.826755	+	0.562562i	$0.190184\pi$
$228$	1.42668	0.0944840
$229$	27.3467	1.80712	0.903560	−	0.428461i	$-0.140944\pi$
$229$	27.3467	1.80712	0.903560	+	0.428461i	$0.140944\pi$
$230$	−5.97008	−0.393655
$231$	2.79036	0.183592
$232$	15.5224	1.01910
$233$	12.8636	0.842723	0.421361	−	0.906893i	$-0.361552\pi$
$233$	12.8636	0.842723	0.421361	+	0.906893i	$0.361552\pi$
$234$	7.11842	0.465345
$235$	−9.00532	−0.587442
$236$	0.609854	0.0396981
$237$	−1.00000	−0.0649570
$238$	−5.44200	−0.352752
$239$	9.75104	0.630742	0.315371	−	0.948968i	$-0.397871\pi$
$239$	9.75104	0.630742	0.315371	+	0.948968i	$0.397871\pi$
$240$	4.12420	0.266216
$241$	−3.15488	−0.203224	−0.101612	−	0.994824i	$-0.532400\pi$
$241$	−3.15488	−0.203224	−0.101612	+	0.994824i	$0.532400\pi$
$242$	14.1138	0.907270
$243$	−1.00000	−0.0641500
$244$	2.39827	0.153534
$245$	10.9982	0.702648
$246$	10.3694	0.661132
$247$	−37.3873	−2.37890
$248$	−19.0938	−1.21246
$249$	5.07294	0.321485
$250$	13.4633	0.851495
$251$	6.60429	0.416859	0.208430	−	0.978037i	$-0.433165\pi$
$251$	6.60429	0.416859	0.208430	+	0.978037i	$0.433165\pi$
$252$	0.822434	0.0518085
$253$	2.63770	0.165831
$254$	−4.50241	−0.282506
$255$	1.16053	0.0726751
$256$	−4.81108	−0.300692
$257$	−13.9554	−0.870514	−0.435257	−	0.900306i	$-0.643343\pi$
$257$	−13.9554	−0.870514	−0.435257	+	0.900306i	$0.643343\pi$
$258$	−15.8376	−0.986005
$259$	41.8858	2.60265
$260$	1.24848	0.0774275
$261$	5.25655	0.325373
$262$	−19.4458	−1.20137
$263$	25.7056	1.58508	0.792538	−	0.609823i	$-0.208759\pi$
$263$	25.7056	1.58508	0.792538	+	0.609823i	$0.208759\pi$
$264$	−2.02993	−0.124934
$265$	13.4182	0.824275
$266$	38.3196	2.34952
$267$	6.92093	0.423554
$268$	−2.31669	−0.141514
$269$	15.0361	0.916767	0.458383	−	0.888755i	$-0.348429\pi$
$269$	15.0361	0.916767	0.458383	+	0.888755i	$0.348429\pi$
$270$	1.55588	0.0946880
$271$	11.8915	0.722357	0.361178	−	0.932497i	$-0.382375\pi$
$271$	11.8915	0.722357	0.361178	+	0.932497i	$0.382375\pi$
$272$	3.55373	0.215476
$273$	−21.5526	−1.30442
$274$	22.6505	1.36837
$275$	−2.51127	−0.151435
$276$	0.777440	0.0467964
$277$	30.7994	1.85056	0.925278	−	0.379289i	$-0.123831\pi$
$277$	30.7994	1.85056	0.925278	+	0.379289i	$0.123831\pi$
$278$	−16.2275	−0.973261
$279$	−6.46598	−0.387108
$280$	−13.9108	−0.831329
$281$	9.74076	0.581085	0.290543	−	0.956862i	$-0.406164\pi$
$281$	9.74076	0.581085	0.290543	+	0.956862i	$0.406164\pi$
$282$	−10.4031	−0.619498
$283$	26.2209	1.55867	0.779335	−	0.626607i	$-0.215557\pi$
$283$	26.2209	1.55867	0.779335	+	0.626607i	$0.215557\pi$
$284$	−0.869617	−0.0516023
$285$	−8.17180	−0.484056
$286$	4.89335	0.289350
$287$	−31.3958	−1.85324
$288$	−1.14157	−0.0672678
$289$	1.00000	0.0588235
$290$	−8.17858	−0.480263
$291$	7.18674	0.421294
$292$	0.527827	0.0308888
$293$	−25.6696	−1.49963	−0.749816	−	0.661647i	$-0.769858\pi$
$293$	−25.6696	−1.49963	−0.749816	+	0.661647i	$0.769858\pi$
$294$	12.7053	0.740990
$295$	−3.49316	−0.203380
$296$	−30.4711	−1.77110
$297$	−0.687421	−0.0398882
$298$	4.06916	0.235720
$299$	−20.3735	−1.17823
$300$	−0.740174	−0.0427340
$301$	47.9519	2.76390
$302$	15.8303	0.910931
$303$	−14.3632	−0.825144
$304$	−25.0234	−1.43519
$305$	−13.7370	−0.786576
$306$	1.34067	0.0766408
$307$	15.0301	0.857811	0.428906	−	0.903349i	$-0.358899\pi$
$307$	15.0301	0.857811	0.428906	+	0.903349i	$0.358899\pi$
$308$	0.565358	0.0322143
$309$	−16.2362	−0.923644
$310$	10.0603	0.571387
$311$	−23.4034	−1.32709	−0.663543	−	0.748138i	$-0.730948\pi$
$311$	−23.4034	−1.32709	−0.663543	+	0.748138i	$0.730948\pi$
$312$	15.6791	0.887655
$313$	−5.99411	−0.338807	−0.169404	−	0.985547i	$-0.554184\pi$
$313$	−5.99411	−0.338807	−0.169404	+	0.985547i	$0.554184\pi$
$314$	10.8692	0.613387
$315$	−4.71078	−0.265423
$316$	−0.202611	−0.0113978
$317$	2.48476	0.139558	0.0697789	−	0.997562i	$-0.477771\pi$
$317$	2.48476	0.139558	0.0697789	+	0.997562i	$0.477771\pi$
$318$	15.5010	0.869254
$319$	3.61346	0.202315
$320$	10.0246	0.560390
$321$	17.7659	0.991598
$322$	20.8815	1.16368
$323$	−7.04145	−0.391797
$324$	−0.202611	−0.0112562
$325$	19.3969	1.07595
$326$	8.27544	0.458334
$327$	12.2214	0.675845
$328$	22.8399	1.26112
$329$	31.4978	1.73653
$330$	1.06955	0.0588766
$331$	−13.2932	−0.730660	−0.365330	−	0.930878i	$-0.619044\pi$
$331$	−13.2932	−0.730660	−0.365330	+	0.930878i	$0.619044\pi$
$332$	1.02783	0.0564098
$333$	−10.3188	−0.565466
$334$	27.2649	1.49187
$335$	13.2697	0.724999
$336$	−14.4252	−0.786958
$337$	−16.1094	−0.877535	−0.438768	−	0.898601i	$-0.644585\pi$
$337$	−16.1094	−0.877535	−0.438768	+	0.898601i	$0.644585\pi$
$338$	−20.3673	−1.10784
$339$	−11.5125	−0.625273
$340$	0.235136	0.0127520
$341$	−4.44485	−0.240702
$342$	−9.44024	−0.510470
$343$	−10.0541	−0.542869
$344$	−34.8840	−1.88082
$345$	−4.45307	−0.239745
$346$	−21.6728	−1.16514
$347$	8.63515	0.463559	0.231780	−	0.972768i	$-0.425545\pi$
$347$	8.63515	0.463559	0.231780	+	0.972768i	$0.425545\pi$
$348$	1.06504	0.0570920
$349$	−19.7336	−1.05631	−0.528157	−	0.849147i	$-0.677117\pi$
$349$	−19.7336	−1.05631	−0.528157	+	0.849147i	$0.677117\pi$
$350$	−19.8806	−1.06266
$351$	5.30961	0.283406
$352$	−0.784741	−0.0418268
$353$	20.0675	1.06809	0.534043	−	0.845457i	$-0.320672\pi$
$353$	20.0675	1.06809	0.534043	+	0.845457i	$0.320672\pi$
$354$	−4.03537	−0.214478
$355$	4.98105	0.264366
$356$	1.40226	0.0743195
$357$	−4.05917	−0.214834
$358$	−4.33401	−0.229060
$359$	0.383076	0.0202180	0.0101090	−	0.999949i	$-0.496782\pi$
$359$	0.383076	0.0202180	0.0101090	+	0.999949i	$0.496782\pi$
$360$	3.42700	0.180619
$361$	30.5820	1.60958
$362$	13.9244	0.731848
$363$	10.5275	0.552548
$364$	−4.36680	−0.228883
$365$	−3.02332	−0.158248
$366$	−15.8692	−0.829498
$367$	29.8216	1.55667	0.778337	−	0.627846i	$-0.216063\pi$
$367$	29.8216	1.55667	0.778337	+	0.627846i	$0.216063\pi$
$368$	−13.6360	−0.710826
$369$	7.73454	0.402644
$370$	16.0548	0.834651
$371$	−46.9328	−2.43663
$372$	−1.31008	−0.0679245
$373$	−3.20080	−0.165731	−0.0828655	−	0.996561i	$-0.526407\pi$
$373$	−3.20080	−0.165731	−0.0828655	+	0.996561i	$0.526407\pi$
$374$	0.921603	0.0476549
$375$	10.0423	0.518580
$376$	−22.9141	−1.18170
$377$	−27.9102	−1.43745
$378$	−5.44200	−0.279906
$379$	−7.99675	−0.410765	−0.205383	−	0.978682i	$-0.565844\pi$
$379$	−7.99675	−0.410765	−0.205383	+	0.978682i	$0.565844\pi$
$380$	−1.65570	−0.0849356
$381$	−3.35833	−0.172053
$382$	−17.4316	−0.891876
$383$	35.3913	1.80841	0.904205	−	0.427099i	$-0.140464\pi$
$383$	35.3913	1.80841	0.904205	+	0.427099i	$0.140464\pi$
$384$	9.29743	0.474458
$385$	−3.23829	−0.165039
$386$	−4.53167	−0.230656
$387$	−11.8132	−0.600499
$388$	1.45611	0.0739230
$389$	7.34691	0.372503	0.186252	−	0.982502i	$-0.440366\pi$
$389$	7.34691	0.372503	0.186252	+	0.982502i	$0.440366\pi$
$390$	−8.26113	−0.418318
$391$	−3.83710	−0.194051
$392$	27.9849	1.41345
$393$	−14.5046	−0.731658
$394$	4.68903	0.236230
$395$	1.16053	0.0583925
$396$	−0.139279	−0.00699904
$397$	3.24085	0.162653	0.0813267	−	0.996687i	$-0.474084\pi$
$397$	3.24085	0.162653	0.0813267	+	0.996687i	$0.474084\pi$
$398$	−15.1435	−0.759073
$399$	28.5825	1.43091
$400$	12.9824	0.649119
$401$	12.8012	0.639263	0.319632	−	0.947542i	$-0.396441\pi$
$401$	12.8012	0.639263	0.319632	+	0.947542i	$0.396441\pi$
$402$	15.3294	0.764561
$403$	34.3318	1.71019
$404$	−2.91015	−0.144785
$405$	1.16053	0.0576671
$406$	28.6062	1.41970
$407$	−7.09335	−0.351605
$408$	2.95297	0.146194
$409$	27.0191	1.33601	0.668004	−	0.744158i	$-0.267149\pi$
$409$	27.0191	1.33601	0.668004	+	0.744158i	$0.267149\pi$
$410$	−12.0340	−0.594319
$411$	16.8949	0.833365
$412$	−3.28963	−0.162069
$413$	12.2180	0.601208
$414$	−5.14428	−0.252827
$415$	−5.88729	−0.288996
$416$	6.06130	0.297180
$417$	−12.1040	−0.592738
$418$	−6.48942	−0.317408
$419$	11.2668	0.550420	0.275210	−	0.961384i	$-0.411253\pi$
$419$	11.2668	0.550420	0.275210	+	0.961384i	$0.411253\pi$
$420$	−0.954458	−0.0465728
$421$	−18.5205	−0.902633	−0.451317	−	0.892364i	$-0.649046\pi$
$421$	−18.5205	−0.902633	−0.451317	+	0.892364i	$0.649046\pi$
$422$	−24.3518	−1.18543
$423$	−7.75967	−0.377288
$424$	34.1427	1.65812
$425$	3.65317	0.177205
$426$	5.75421	0.278792
$427$	48.0477	2.32519
$428$	3.59958	0.173992
$429$	3.64993	0.176221
$430$	18.3800	0.886361
$431$	3.19388	0.153844	0.0769219	−	0.997037i	$-0.475491\pi$
$431$	3.19388	0.153844	0.0769219	+	0.997037i	$0.475491\pi$
$432$	3.55373	0.170979
$433$	28.2453	1.35738	0.678692	−	0.734423i	$-0.262547\pi$
$433$	28.2453	1.35738	0.678692	+	0.734423i	$0.262547\pi$
$434$	−35.1879	−1.68907
$435$	−6.10038	−0.292491
$436$	2.47619	0.118588
$437$	27.0188	1.29248
$438$	−3.49260	−0.166883
$439$	−18.6279	−0.889061	−0.444530	−	0.895764i	$-0.646629\pi$
$439$	−18.6279	−0.889061	−0.444530	+	0.895764i	$0.646629\pi$
$440$	2.35579	0.112308
$441$	9.47688	0.451280
$442$	−7.11842	−0.338589
$443$	−19.3894	−0.921220	−0.460610	−	0.887603i	$-0.652369\pi$
$443$	−19.3894	−0.921220	−0.460610	+	0.887603i	$0.652369\pi$
$444$	−2.09070	−0.0992204
$445$	−8.03194	−0.380750
$446$	−5.48362	−0.259657
$447$	3.03517	0.143559
$448$	−35.0628	−1.65656
$449$	−4.85756	−0.229243	−0.114621	−	0.993409i	$-0.536565\pi$
$449$	−4.85756	−0.229243	−0.114621	+	0.993409i	$0.536565\pi$
$450$	4.89769	0.230879
$451$	5.31688	0.250362
$452$	−2.33256	−0.109714
$453$	11.8078	0.554778
$454$	−33.3996	−1.56752
$455$	25.0124	1.17260
$456$	−20.7932	−0.973730
$457$	40.2164	1.88124	0.940622	−	0.339457i	$-0.110243\pi$
$457$	40.2164	1.88124	0.940622	+	0.339457i	$0.110243\pi$
$458$	−36.6628	−1.71314
$459$	1.00000	0.0466760
$460$	−0.902241	−0.0420672
$461$	−7.02805	−0.327329	−0.163665	−	0.986516i	$-0.552331\pi$
$461$	−7.02805	−0.327329	−0.163665	+	0.986516i	$0.552331\pi$
$462$	−3.74094	−0.174044
$463$	−3.27707	−0.152298	−0.0761492	−	0.997096i	$-0.524263\pi$
$463$	−3.27707	−0.152298	−0.0761492	+	0.997096i	$0.524263\pi$
$464$	−18.6804	−0.867214
$465$	7.50395	0.347987
$466$	−17.2458	−0.798897
$467$	25.2454	1.16822	0.584108	−	0.811676i	$-0.301444\pi$
$467$	25.2454	1.16822	0.584108	+	0.811676i	$0.301444\pi$
$468$	1.07579	0.0497282
$469$	−46.4132	−2.14316
$470$	12.0731	0.556892
$471$	8.10733	0.373566
$472$	−8.88836	−0.409120
$473$	−8.12065	−0.373388
$474$	1.34067	0.0615789
$475$	−25.7236	−1.18028
$476$	−0.822434	−0.0376962
$477$	11.5622	0.529395
$478$	−13.0729	−0.597941
$479$	29.0095	1.32548	0.662740	−	0.748850i	$-0.269394\pi$
$479$	29.0095	1.32548	0.662740	+	0.748850i	$0.269394\pi$
$480$	1.32483	0.0604698
$481$	54.7888	2.49815
$482$	4.22964	0.192655
$483$	15.5755	0.708708
$484$	2.13298	0.0969536
$485$	−8.34042	−0.378719
$486$	1.34067	0.0608139
$487$	27.0840	1.22729	0.613647	−	0.789581i	$-0.289702\pi$
$487$	27.0840	1.22729	0.613647	+	0.789581i	$0.289702\pi$
$488$	−34.9537	−1.58228
$489$	6.17262	0.279136
$490$	−14.7449	−0.666107
$491$	31.1323	1.40498	0.702491	−	0.711693i	$-0.252071\pi$
$491$	31.1323	1.40498	0.702491	+	0.711693i	$0.252071\pi$
$492$	1.56710	0.0706505
$493$	−5.25655	−0.236743
$494$	50.1240	2.25518
$495$	0.797771	0.0358572
$496$	22.9783	1.03176
$497$	−17.4222	−0.781491
$498$	−6.80113	−0.304766
$499$	−38.9804	−1.74500	−0.872501	−	0.488613i	$-0.837503\pi$
$499$	−38.9804	−1.74500	−0.872501	+	0.488613i	$0.837503\pi$
$500$	2.03467	0.0909934
$501$	20.3368	0.908581
$502$	−8.85416	−0.395181
$503$	−5.89255	−0.262736	−0.131368	−	0.991334i	$-0.541937\pi$
$503$	−5.89255	−0.262736	−0.131368	+	0.991334i	$0.541937\pi$
$504$	−11.9866	−0.533926
$505$	16.6689	0.741756
$506$	−3.53628	−0.157207
$507$	−15.1919	−0.674697
$508$	−0.680436	−0.0301895
$509$	−8.30520	−0.368122	−0.184061	−	0.982915i	$-0.558924\pi$
$509$	−8.30520	−0.368122	−0.184061	+	0.982915i	$0.558924\pi$
$510$	−1.55588	−0.0688956
$511$	10.5746	0.467795
$512$	25.0449	1.10684
$513$	−7.04145	−0.310888
$514$	18.7096	0.825243
$515$	18.8425	0.830302
$516$	−2.39349	−0.105367
$517$	−5.33416	−0.234596
$518$	−56.1549	−2.46730
$519$	−16.1657	−0.709596
$520$	−18.1960	−0.797949
$521$	−36.7470	−1.60992	−0.804958	−	0.593332i	$-0.797812\pi$
$521$	−36.7470	−1.60992	−0.804958	+	0.593332i	$0.797812\pi$
$522$	−7.04729	−0.308452
$523$	−32.8646	−1.43707	−0.718534	−	0.695492i	$-0.755186\pi$
$523$	−32.8646	−1.43707	−0.718534	+	0.695492i	$0.755186\pi$
$524$	−2.93879	−0.128382
$525$	−14.8289	−0.647185
$526$	−34.4627	−1.50264
$527$	6.46598	0.281662
$528$	2.44291	0.106314
$529$	−8.27665	−0.359854
$530$	−17.9894	−0.781408
$531$	−3.00997	−0.130622
$532$	5.79113	0.251077
$533$	−41.0674	−1.77883
$534$	−9.27866	−0.401527
$535$	−20.6179	−0.891389
$536$	33.7647	1.45841
$537$	−3.23273	−0.139502
$538$	−20.1584	−0.869090
$539$	6.51460	0.280604
$540$	0.235136	0.0101186
$541$	−1.61268	−0.0693346	−0.0346673	−	0.999399i	$-0.511037\pi$
$541$	−1.61268	−0.0693346	−0.0346673	+	0.999399i	$0.511037\pi$
$542$	−15.9425	−0.684790
$543$	10.3861	0.445712
$544$	1.14157	0.0489445
$545$	−14.1833	−0.607545
$546$	28.8949	1.23659
$547$	−29.1427	−1.24605	−0.623025	−	0.782202i	$-0.714097\pi$
$547$	−29.1427	−1.24605	−0.623025	+	0.782202i	$0.714097\pi$
$548$	3.42310	0.146228
$549$	−11.8368	−0.505183
$550$	3.36677	0.143560
$551$	37.0138	1.57684
$552$	−11.3308	−0.482273
$553$	−4.05917	−0.172614
$554$	−41.2917	−1.75432
$555$	11.9753	0.508321
$556$	−2.45242	−0.104006
$557$	25.6246	1.08575	0.542874	−	0.839814i	$-0.317336\pi$
$557$	25.6246	1.08575	0.542874	+	0.839814i	$0.317336\pi$
$558$	8.66873	0.366976
$559$	62.7235	2.65292
$560$	16.7408	0.707430
$561$	0.687421	0.0290229
$562$	−13.0591	−0.550866
$563$	18.2169	0.767749	0.383874	−	0.923385i	$-0.374590\pi$
$563$	18.2169	0.767749	0.383874	+	0.923385i	$0.374590\pi$
$564$	−1.57220	−0.0662014
$565$	13.3606	0.562083
$566$	−35.1535	−1.47761
$567$	−4.05917	−0.170469
$568$	12.6743	0.531801
$569$	14.7930	0.620154	0.310077	−	0.950711i	$-0.399645\pi$
$569$	14.7930	0.620154	0.310077	+	0.950711i	$0.399645\pi$
$570$	10.9557	0.458883
$571$	−0.378441	−0.0158372	−0.00791862	−	0.999969i	$-0.502521\pi$
$571$	−0.378441	−0.0158372	−0.00791862	+	0.999969i	$0.502521\pi$
$572$	0.739518	0.0309208
$573$	−13.0022	−0.543173
$574$	42.0914	1.75686
$575$	−14.0176	−0.584574
$576$	8.63792	0.359913
$577$	14.4007	0.599509	0.299754	−	0.954016i	$-0.403095\pi$
$577$	14.4007	0.599509	0.299754	+	0.954016i	$0.403095\pi$
$578$	−1.34067	−0.0557644
$579$	−3.38016	−0.140475
$580$	−1.23601	−0.0513223
$581$	20.5919	0.854298
$582$	−9.63503	−0.399385
$583$	7.94808	0.329176
$584$	−7.69285	−0.318332
$585$	−6.16195	−0.254765
$586$	34.4143	1.42164
$587$	23.9942	0.990347	0.495173	−	0.868794i	$-0.335105\pi$
$587$	23.9942	0.990347	0.495173	+	0.868794i	$0.335105\pi$
$588$	1.92012	0.0791845
$589$	−45.5299	−1.87603
$590$	4.68316	0.192803
$591$	3.49753	0.143869
$592$	36.6702	1.50713
$593$	−24.4590	−1.00441	−0.502205	−	0.864748i	$-0.667478\pi$
$593$	−24.4590	−1.00441	−0.502205	+	0.864748i	$0.667478\pi$
$594$	0.921603	0.0378138
$595$	4.71078	0.193123
$596$	0.614960	0.0251897
$597$	−11.2955	−0.462293
$598$	27.3141	1.11696
$599$	43.5632	1.77995	0.889973	−	0.456013i	$-0.150723\pi$
$599$	43.5632	1.77995	0.889973	+	0.456013i	$0.150723\pi$
$600$	10.7877	0.440406
$601$	16.2585	0.663197	0.331598	−	0.943421i	$-0.392412\pi$
$601$	16.2585	0.663197	0.331598	+	0.943421i	$0.392412\pi$
$602$	−64.2875	−2.62016
$603$	11.4342	0.465635
$604$	2.39239	0.0973449
$605$	−12.2174	−0.496708
$606$	19.2563	0.782233
$607$	−17.9372	−0.728047	−0.364023	−	0.931390i	$-0.618597\pi$
$607$	−17.9372	−0.728047	−0.364023	+	0.931390i	$0.618597\pi$
$608$	−8.03833	−0.325997
$609$	21.3373	0.864629
$610$	18.4167	0.745670
$611$	41.2008	1.66681
$612$	0.202611	0.00819007
$613$	−33.0964	−1.33675	−0.668374	−	0.743825i	$-0.733010\pi$
$613$	−33.0964	−1.33675	−0.668374	+	0.743825i	$0.733010\pi$
$614$	−20.1503	−0.813201
$615$	−8.97615	−0.361953
$616$	−8.23984	−0.331993
$617$	38.5578	1.55228	0.776140	−	0.630561i	$-0.217175\pi$
$617$	38.5578	1.55228	0.776140	+	0.630561i	$0.217175\pi$
$618$	21.7673	0.875610
$619$	26.6029	1.06926	0.534631	−	0.845086i	$-0.320451\pi$
$619$	26.6029	1.06926	0.534631	+	0.845086i	$0.320451\pi$
$620$	1.52038	0.0610601
$621$	−3.83710	−0.153978
$622$	31.3762	1.25807
$623$	28.0932	1.12553
$624$	−18.8689	−0.755360
$625$	6.61155	0.264462
$626$	8.03611	0.321187
$627$	−4.84044	−0.193309
$628$	1.64264	0.0655483
$629$	10.3188	0.411437
$630$	6.31559	0.251619
$631$	−36.5603	−1.45544	−0.727720	−	0.685874i	$-0.759420\pi$
$631$	−36.5603	−1.45544	−0.727720	+	0.685874i	$0.759420\pi$
$632$	2.95297	0.117463
$633$	−18.1639	−0.721951
$634$	−3.33123	−0.132300
$635$	3.89744	0.154665
$636$	2.34262	0.0928911
$637$	−50.3185	−1.99369
$638$	−4.84445	−0.191794
$639$	4.29205	0.169791
$640$	−10.7899	−0.426510
$641$	29.8352	1.17842	0.589210	−	0.807980i	$-0.299439\pi$
$641$	29.8352	1.17842	0.589210	+	0.807980i	$0.299439\pi$
$642$	−23.8182	−0.940030
$643$	15.3169	0.604040	0.302020	−	0.953302i	$-0.402339\pi$
$643$	15.3169	0.604040	0.302020	+	0.953302i	$0.402339\pi$
$644$	3.15576	0.124354
$645$	13.7096	0.539814
$646$	9.44024	0.371421
$647$	29.3369	1.15335	0.576676	−	0.816973i	$-0.304349\pi$
$647$	29.3369	1.15335	0.576676	+	0.816973i	$0.304349\pi$
$648$	2.95297	0.116004
$649$	−2.06912	−0.0812200
$650$	−26.0048	−1.01999
$651$	−26.2465	−1.02868
$652$	1.25064	0.0489790
$653$	−3.36570	−0.131710	−0.0658550	−	0.997829i	$-0.520977\pi$
$653$	−3.36570	−0.131710	−0.0658550	+	0.997829i	$0.520977\pi$
$654$	−16.3848	−0.640698
$655$	16.8330	0.657718
$656$	−27.4864	−1.07317
$657$	−2.60512	−0.101636
$658$	−42.2281	−1.64622
$659$	−18.9760	−0.739199	−0.369599	−	0.929191i	$-0.620505\pi$
$659$	−18.9760	−0.739199	−0.369599	+	0.929191i	$0.620505\pi$
$660$	0.161637	0.00629173
$661$	−20.1214	−0.782632	−0.391316	−	0.920256i	$-0.627980\pi$
$661$	−20.1214	−0.782632	−0.391316	+	0.920256i	$0.627980\pi$
$662$	17.8218	0.692662
$663$	−5.30961	−0.206208
$664$	−14.9802	−0.581346
$665$	−33.1708	−1.28631
$666$	13.8341	0.536059
$667$	20.1699	0.780983
$668$	4.12046	0.159426
$669$	−4.09022	−0.158137
$670$	−17.7902	−0.687296
$671$	−8.13687	−0.314120
$672$	−4.63384	−0.178754
$673$	−24.6487	−0.950138	−0.475069	−	0.879949i	$-0.657577\pi$
$673$	−24.6487	−0.950138	−0.475069	+	0.879949i	$0.657577\pi$
$674$	21.5974	0.831899
$675$	3.65317	0.140611
$676$	−3.07806	−0.118387
$677$	−9.69623	−0.372656	−0.186328	−	0.982488i	$-0.559659\pi$
$677$	−9.69623	−0.372656	−0.186328	+	0.982488i	$0.559659\pi$
$678$	15.4344	0.592755
$679$	29.1722	1.11953
$680$	−3.42700	−0.131420
$681$	−24.9126	−0.954654
$682$	5.95906	0.228184
$683$	26.7129	1.02214	0.511070	−	0.859539i	$-0.329249\pi$
$683$	26.7129	1.02214	0.511070	+	0.859539i	$0.329249\pi$
$684$	−1.42668	−0.0545504
$685$	−19.6070	−0.749147
$686$	13.4792	0.514637
$687$	−27.3467	−1.04334
$688$	41.9809	1.60051
$689$	−61.3906	−2.33879
$690$	5.97008	0.227277
$691$	−33.3456	−1.26853	−0.634263	−	0.773117i	$-0.718696\pi$
$691$	−33.3456	−1.26853	−0.634263	+	0.773117i	$0.718696\pi$
$692$	−3.27535	−0.124510
$693$	−2.79036	−0.105997
$694$	−11.5769	−0.439452
$695$	14.0471	0.532837
$696$	−15.5224	−0.588377
$697$	−7.73454	−0.292967
$698$	26.4561	1.00138
$699$	−12.8636	−0.486546
$700$	−3.00449	−0.113559
$701$	−13.9025	−0.525091	−0.262546	−	0.964920i	$-0.584562\pi$
$701$	−13.9025	−0.525091	−0.262546	+	0.964920i	$0.584562\pi$
$702$	−7.11842	−0.268667
$703$	−72.6593	−2.74040
$704$	5.93789	0.223793
$705$	9.00532	0.339160
$706$	−26.9039	−1.01254
$707$	−58.3027	−2.19270
$708$	−0.609854	−0.0229197
$709$	−42.8187	−1.60809	−0.804045	−	0.594568i	$-0.797323\pi$
$709$	−42.8187	−1.60809	−0.804045	+	0.594568i	$0.797323\pi$
$710$	−6.67793	−0.250618
$711$	1.00000	0.0375029
$712$	−20.4373	−0.765920
$713$	−24.8106	−0.929165
$714$	5.44200	0.203662
$715$	−4.23585	−0.158412
$716$	−0.654987	−0.0244780
$717$	−9.75104	−0.364159
$718$	−0.513578	−0.0191666
$719$	13.6744	0.509970	0.254985	−	0.966945i	$-0.417929\pi$
$719$	13.6744	0.509970	0.254985	+	0.966945i	$0.417929\pi$
$720$	−4.12420	−0.153700
$721$	−65.9054	−2.45445
$722$	−41.0003	−1.52587
$723$	3.15488	0.117331
$724$	2.10435	0.0782075
$725$	−19.2031	−0.713185
$726$	−14.1138	−0.523813
$727$	30.0101	1.11301	0.556506	−	0.830843i	$-0.312142\pi$
$727$	30.0101	1.11301	0.556506	+	0.830843i	$0.312142\pi$
$728$	63.6442	2.35881
$729$	1.00000	0.0370370
$730$	4.05327	0.150018
$731$	11.8132	0.436927
$732$	−2.39827	−0.0886426
$733$	−15.6798	−0.579145	−0.289573	−	0.957156i	$-0.593513\pi$
$733$	−15.6798	−0.579145	−0.289573	+	0.957156i	$0.593513\pi$
$734$	−39.9808	−1.47572
$735$	−10.9982	−0.405674
$736$	−4.38033	−0.161461
$737$	7.86008	0.289530
$738$	−10.3694	−0.381705
$739$	18.9572	0.697353	0.348676	−	0.937243i	$-0.386631\pi$
$739$	18.9572	0.697353	0.348676	+	0.937243i	$0.386631\pi$
$740$	2.42632	0.0891933
$741$	37.3873	1.37346
$742$	62.9213	2.30991
$743$	−35.7120	−1.31015	−0.655074	−	0.755565i	$-0.727362\pi$
$743$	−35.7120	−1.31015	−0.655074	+	0.755565i	$0.727362\pi$
$744$	19.0938	0.700014
$745$	−3.52240	−0.129051
$746$	4.29121	0.157112
$747$	−5.07294	−0.185609
$748$	0.139279	0.00509255
$749$	72.1150	2.63503
$750$	−13.4633	−0.491611
$751$	−16.8921	−0.616402	−0.308201	−	0.951321i	$-0.599727\pi$
$751$	−16.8921	−0.616402	−0.308201	+	0.951321i	$0.599727\pi$
$752$	27.5757	1.00558
$753$	−6.60429	−0.240674
$754$	37.4183	1.36270
$755$	−13.7033	−0.498713
$756$	−0.822434	−0.0299116
$757$	−7.57701	−0.275391	−0.137696	−	0.990475i	$-0.543970\pi$
$757$	−7.57701	−0.275391	−0.137696	+	0.990475i	$0.543970\pi$
$758$	10.7210	0.389403
$759$	−2.63770	−0.0957426
$760$	24.1311	0.875326
$761$	−0.126198	−0.00457466	−0.00228733	−	0.999997i	$-0.500728\pi$
$761$	−0.126198	−0.00457466	−0.00228733	+	0.999997i	$0.500728\pi$
$762$	4.50241	0.163105
$763$	49.6088	1.79596
$764$	−2.63438	−0.0953086
$765$	−1.16053	−0.0419590
$766$	−47.4479	−1.71436
$767$	15.9818	0.577069
$768$	4.81108	0.173605
$769$	−12.5225	−0.451572	−0.225786	−	0.974177i	$-0.572495\pi$
$769$	−12.5225	−0.451572	−0.225786	+	0.974177i	$0.572495\pi$
$770$	4.34147	0.156456
$771$	13.9554	0.502592
$772$	−0.684858	−0.0246486
$773$	−21.5135	−0.773786	−0.386893	−	0.922125i	$-0.626452\pi$
$773$	−21.5135	−0.773786	−0.386893	+	0.922125i	$0.626452\pi$
$774$	15.8376	0.569270
$775$	23.6213	0.848504
$776$	−21.2222	−0.761833
$777$	−41.8858	−1.50264
$778$	−9.84976	−0.353131
$779$	54.4624	1.95132
$780$	−1.24848	−0.0447028
$781$	2.95044	0.105575
$782$	5.14428	0.183959
$783$	−5.25655	−0.187854
$784$	−33.6782	−1.20279
$785$	−9.40879	−0.335814
$786$	19.4458	0.693609
$787$	38.3753	1.36793	0.683966	−	0.729514i	$-0.260254\pi$
$787$	38.3753	1.36793	0.683966	+	0.729514i	$0.260254\pi$
$788$	0.708639	0.0252442
$789$	−25.7056	−0.915144
$790$	−1.55588	−0.0553558
$791$	−46.7312	−1.66157
$792$	2.02993	0.0721305
$793$	62.8488	2.23183
$794$	−4.34490	−0.154195
$795$	−13.4182	−0.475895
$796$	−2.28859	−0.0811169
$797$	4.11999	0.145938	0.0729688	−	0.997334i	$-0.476753\pi$
$797$	4.11999	0.145938	0.0729688	+	0.997334i	$0.476753\pi$
$798$	−38.3196	−1.35650
$799$	7.75967	0.274517
$800$	4.17036	0.147445
$801$	−6.92093	−0.244539
$802$	−17.1622	−0.606018
$803$	−1.79082	−0.0631965
$804$	2.31669	0.0817033
$805$	−18.0758	−0.637087
$806$	−46.0275	−1.62125
$807$	−15.0361	−0.529296
$808$	42.4141	1.49212
$809$	23.4514	0.824506	0.412253	−	0.911069i	$-0.364742\pi$
$809$	23.4514	0.824506	0.412253	+	0.911069i	$0.364742\pi$
$810$	−1.55588	−0.0546681
$811$	40.7618	1.43134	0.715670	−	0.698439i	$-0.246121\pi$
$811$	40.7618	1.43134	0.715670	+	0.698439i	$0.246121\pi$
$812$	4.32317	0.151713
$813$	−11.8915	−0.417053
$814$	9.50983	0.333319
$815$	−7.16351	−0.250927
$816$	−3.55373	−0.124405
$817$	−83.1822	−2.91018
$818$	−36.2236	−1.26653
$819$	21.5526	0.753109
$820$	−1.81867	−0.0635107
$821$	1.43536	0.0500944	0.0250472	−	0.999686i	$-0.492026\pi$
$821$	1.43536	0.0500944	0.0250472	+	0.999686i	$0.492026\pi$
$822$	−22.6505	−0.790026
$823$	16.6844	0.581581	0.290790	−	0.956787i	$-0.406082\pi$
$823$	16.6844	0.581581	0.290790	+	0.956787i	$0.406082\pi$
$824$	47.9449	1.67024
$825$	2.51127	0.0874311
$826$	−16.3803	−0.569943
$827$	40.9466	1.42385	0.711926	−	0.702255i	$-0.247823\pi$
$827$	40.9466	1.42385	0.711926	+	0.702255i	$0.247823\pi$
$828$	−0.777440	−0.0270179
$829$	−27.7083	−0.962349	−0.481174	−	0.876625i	$-0.659790\pi$
$829$	−27.7083	−0.962349	−0.481174	+	0.876625i	$0.659790\pi$
$830$	7.89290	0.273967
$831$	−30.7994	−1.06842
$832$	−45.8640	−1.59005
$833$	−9.47688	−0.328354
$834$	16.2275	0.561912
$835$	−23.6014	−0.816761
$836$	−0.980727	−0.0339192
$837$	6.46598	0.223497
$838$	−15.1051	−0.521796
$839$	−29.8701	−1.03123	−0.515616	−	0.856820i	$-0.672437\pi$
$839$	−29.8701	−1.03123	−0.515616	+	0.856820i	$0.672437\pi$
$840$	13.9108	0.479968
$841$	−1.36864	−0.0471945
$842$	24.8298	0.855692
$843$	−9.74076	−0.335490
$844$	−3.68021	−0.126678
$845$	17.6307	0.606513
$846$	10.4031	0.357667
$847$	42.7327	1.46831
$848$	−41.0888	−1.41099
$849$	−26.2209	−0.899899
$850$	−4.89769	−0.167989
$851$	−39.5943	−1.35727
$852$	0.869617	0.0297926
$853$	−0.862347	−0.0295262	−0.0147631	−	0.999891i	$-0.504699\pi$
$853$	−0.862347	−0.0295262	−0.0147631	+	0.999891i	$0.504699\pi$
$854$	−64.4159	−2.20427
$855$	8.17180	0.279470
$856$	−52.4623	−1.79312
$857$	40.0791	1.36908	0.684539	−	0.728977i	$-0.260004\pi$
$857$	40.0791	1.36908	0.684539	+	0.728977i	$0.260004\pi$
$858$	−4.89335	−0.167056
$859$	14.4423	0.492764	0.246382	−	0.969173i	$-0.420758\pi$
$859$	14.4423	0.492764	0.246382	+	0.969173i	$0.420758\pi$
$860$	2.77771	0.0947192
$861$	31.3958	1.06997
$862$	−4.28193	−0.145843
$863$	44.0445	1.49929	0.749646	−	0.661840i	$-0.230224\pi$
$863$	44.0445	1.49929	0.749646	+	0.661840i	$0.230224\pi$
$864$	1.14157	0.0388371
$865$	18.7608	0.637885
$866$	−37.8676	−1.28679
$867$	−1.00000	−0.0339618
$868$	−5.31784	−0.180499
$869$	0.687421	0.0233192
$870$	8.17858	0.277280
$871$	−60.7109	−2.05711
$872$	−36.0894	−1.22214
$873$	−7.18674	−0.243234
$874$	−36.2232	−1.22527
$875$	40.7632	1.37805
$876$	−0.527827	−0.0178336
$877$	−19.0013	−0.641630	−0.320815	−	0.947142i	$-0.603957\pi$
$877$	−19.0013	−0.641630	−0.320815	+	0.947142i	$0.603957\pi$
$878$	24.9738	0.842825
$879$	25.6696	0.865813
$880$	−2.83506	−0.0955699
$881$	−35.1472	−1.18414	−0.592070	−	0.805886i	$-0.701689\pi$
$881$	−35.1472	−1.18414	−0.592070	+	0.805886i	$0.701689\pi$
$882$	−12.7053	−0.427811
$883$	−7.42449	−0.249854	−0.124927	−	0.992166i	$-0.539870\pi$
$883$	−7.42449	−0.249854	−0.124927	+	0.992166i	$0.539870\pi$
$884$	−1.07579	−0.0361826
$885$	3.49316	0.117421
$886$	25.9948	0.873312
$887$	−49.0405	−1.64662	−0.823309	−	0.567593i	$-0.807875\pi$
$887$	−49.0405	−1.64662	−0.823309	+	0.567593i	$0.807875\pi$
$888$	30.4711	1.02254
$889$	−13.6320	−0.457204
$890$	10.7682	0.360949
$891$	0.687421	0.0230295
$892$	−0.828724	−0.0277477
$893$	−54.6393	−1.82844
$894$	−4.06916	−0.136093
$895$	3.75167	0.125405
$896$	37.7399	1.26080
$897$	20.3735	0.680251
$898$	6.51238	0.217321
$899$	−33.9888	−1.13359
$900$	0.740174	0.0246725
$901$	−11.5622	−0.385192
$902$	−7.12817	−0.237342
$903$	−47.9519	−1.59574
$904$	33.9960	1.13069
$905$	−12.0534	−0.400669
$906$	−15.8303	−0.525926
$907$	−27.6460	−0.917970	−0.458985	−	0.888444i	$-0.651787\pi$
$907$	−27.6460	−0.917970	−0.458985	+	0.888444i	$0.651787\pi$
$908$	−5.04758	−0.167510
$909$	14.3632	0.476397
$910$	−33.5333	−1.11162
$911$	−33.8793	−1.12247	−0.561236	−	0.827656i	$-0.689674\pi$
$911$	−33.8793	−1.12247	−0.561236	+	0.827656i	$0.689674\pi$
$912$	25.0234	0.828607
$913$	−3.48725	−0.115411
$914$	−53.9168	−1.78341
$915$	13.7370	0.454130
$916$	−5.54075	−0.183071
$917$	−58.8765	−1.94427
$918$	−1.34067	−0.0442486
$919$	0.763246	0.0251772	0.0125886	−	0.999921i	$-0.495993\pi$
$919$	0.763246	0.0251772	0.0125886	+	0.999921i	$0.495993\pi$
$920$	13.1498	0.433535
$921$	−15.0301	−0.495258
$922$	9.42228	0.310306
$923$	−22.7891	−0.750112
$924$	−0.565358	−0.0185989
$925$	37.6964	1.23945
$926$	4.39346	0.144378
$927$	16.2362	0.533266
$928$	−6.00074	−0.196984
$929$	−36.2828	−1.19040	−0.595199	−	0.803578i	$-0.702927\pi$
$929$	−36.2828	−1.19040	−0.595199	+	0.803578i	$0.702927\pi$
$930$	−10.0603	−0.329890
$931$	66.7310	2.18702
$932$	−2.60631	−0.0853725
$933$	23.4034	0.766193
$934$	−33.8456	−1.10746
$935$	−0.797771	−0.0260899
$936$	−15.6791	−0.512488
$937$	20.3153	0.663672	0.331836	−	0.943337i	$-0.392332\pi$
$937$	20.3153	0.663672	0.331836	+	0.943337i	$0.392332\pi$
$938$	62.2247	2.03171
$939$	5.99411	0.195610
$940$	1.82458	0.0595112
$941$	2.62083	0.0854366	0.0427183	−	0.999087i	$-0.486398\pi$
$941$	2.62083	0.0854366	0.0427183	+	0.999087i	$0.486398\pi$
$942$	−10.8692	−0.354139
$943$	29.6782	0.966456
$944$	10.6966	0.348145
$945$	4.71078	0.153242
$946$	10.8871	0.353970
$947$	−27.0615	−0.879381	−0.439690	−	0.898149i	$-0.644912\pi$
$947$	−27.0615	−0.879381	−0.439690	+	0.898149i	$0.644912\pi$
$948$	0.202611	0.00658051
$949$	13.8322	0.449012
$950$	34.4868	1.11890
$951$	−2.48476	−0.0805737
$952$	11.9866	0.388488
$953$	−45.7337	−1.48146	−0.740730	−	0.671803i	$-0.765520\pi$
$953$	−45.7337	−1.48146	−0.740730	+	0.671803i	$0.765520\pi$
$954$	−15.5010	−0.501864
$955$	15.0894	0.488280
$956$	−1.97567	−0.0638977
$957$	−3.61346	−0.116807
$958$	−38.8921	−1.25655
$959$	68.5794	2.21455
$960$	−10.0246	−0.323541
$961$	10.8089	0.348674
$962$	−73.4535	−2.36824
$963$	−17.7659	−0.572500
$964$	0.639214	0.0205877
$965$	3.92277	0.126279
$966$	−20.8815	−0.671851
$967$	52.2890	1.68150	0.840751	−	0.541423i	$-0.182114\pi$
$967$	52.2890	1.68150	0.840751	+	0.541423i	$0.182114\pi$
$968$	−31.0872	−0.999182
$969$	7.04145	0.226204
$970$	11.1817	0.359023
$971$	43.9402	1.41011	0.705055	−	0.709153i	$-0.250922\pi$
$971$	43.9402	1.41011	0.705055	+	0.709153i	$0.250922\pi$
$972$	0.202611	0.00649876
$973$	−49.1324	−1.57511
$974$	−36.3106	−1.16347
$975$	−19.3969	−0.621199
$976$	42.0648	1.34646
$977$	1.90620	0.0609848	0.0304924	−	0.999535i	$-0.490292\pi$
$977$	1.90620	0.0609848	0.0304924	+	0.999535i	$0.490292\pi$
$978$	−8.27544	−0.264619
$979$	−4.75759	−0.152053
$980$	−2.22836	−0.0711822
$981$	−12.2214	−0.390199
$982$	−41.7381	−1.33192
$983$	5.52324	0.176164	0.0880819	−	0.996113i	$-0.471926\pi$
$983$	5.52324	0.176164	0.0880819	+	0.996113i	$0.471926\pi$
$984$	−22.8399	−0.728108
$985$	−4.05898	−0.129330
$986$	7.04729	0.224431
$987$	−31.4978	−1.00259
$988$	7.57509	0.240996
$989$	−45.3285	−1.44136
$990$	−1.06955	−0.0339924
$991$	−0.489112	−0.0155372	−0.00776858	−	0.999970i	$-0.502473\pi$
$991$	−0.489112	−0.0155372	−0.00776858	+	0.999970i	$0.502473\pi$
$992$	7.38139	0.234359
$993$	13.2932	0.421847
$994$	23.3573	0.740850
$995$	13.1087	0.415574
$996$	−1.02783	−0.0325682
$997$	−29.4566	−0.932900	−0.466450	−	0.884547i	$-0.654467\pi$
$997$	−29.4566	−0.932900	−0.466450	+	0.884547i	$0.654467\pi$
$998$	52.2597	1.65425
$999$	10.3188	0.326472

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.11	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.11	✓	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.34067 q^{2} -1.00000 q^{3} -0.202611 q^{4} +1.16053 q^{5} +1.34067 q^{6} -4.05917 q^{7} +2.95297 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.34067 q^{2} -1.00000 q^{3} -0.202611 q^{4} +1.16053 q^{5} +1.34067 q^{6} -4.05917 q^{7} +2.95297 q^{8} +1.00000 q^{9} -1.55588 q^{10} +0.687421 q^{11} +0.202611 q^{12} -5.30961 q^{13} +5.44200 q^{14} -1.16053 q^{15} -3.55373 q^{16} -1.00000 q^{17} -1.34067 q^{18} +7.04145 q^{19} -0.235136 q^{20} +4.05917 q^{21} -0.921603 q^{22} +3.83710 q^{23} -2.95297 q^{24} -3.65317 q^{25} +7.11842 q^{26} -1.00000 q^{27} +0.822434 q^{28} +5.25655 q^{29} +1.55588 q^{30} -6.46598 q^{31} -1.14157 q^{32} -0.687421 q^{33} +1.34067 q^{34} -4.71078 q^{35} -0.202611 q^{36} -10.3188 q^{37} -9.44024 q^{38} +5.30961 q^{39} +3.42700 q^{40} +7.73454 q^{41} -5.44200 q^{42} -11.8132 q^{43} -0.139279 q^{44} +1.16053 q^{45} -5.14428 q^{46} -7.75967 q^{47} +3.55373 q^{48} +9.47688 q^{49} +4.89769 q^{50} +1.00000 q^{51} +1.07579 q^{52} +11.5622 q^{53} +1.34067 q^{54} +0.797771 q^{55} -11.9866 q^{56} -7.04145 q^{57} -7.04729 q^{58} -3.00997 q^{59} +0.235136 q^{60} -11.8368 q^{61} +8.66873 q^{62} -4.05917 q^{63} +8.63792 q^{64} -6.16195 q^{65} +0.921603 q^{66} +11.4342 q^{67} +0.202611 q^{68} -3.83710 q^{69} +6.31559 q^{70} +4.29205 q^{71} +2.95297 q^{72} -2.60512 q^{73} +13.8341 q^{74} +3.65317 q^{75} -1.42668 q^{76} -2.79036 q^{77} -7.11842 q^{78} +1.00000 q^{79} -4.12420 q^{80} +1.00000 q^{81} -10.3694 q^{82} -5.07294 q^{83} -0.822434 q^{84} -1.16053 q^{85} +15.8376 q^{86} -5.25655 q^{87} +2.02993 q^{88} -6.92093 q^{89} -1.55588 q^{90} +21.5526 q^{91} -0.777440 q^{92} +6.46598 q^{93} +10.4031 q^{94} +8.17180 q^{95} +1.14157 q^{96} -7.18674 q^{97} -12.7053 q^{98} +0.687421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

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