LMFDB - Embedded newform 4029.2.a.e.1.10

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:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} + \cdots + 138 $ x^18 - 6x^17 - 10x^16 + 120x^15 - 56x^14 - 921x^13 + 1181x^12 + 3316x^11 - 6280x^10 - 5249x^9 + 15005x^8 + 1809x^7 - 16711x^6 + 2434x^5 + 8758x^4 - 1858x^3 - 1942x^2 + 318*x + 138
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.498176$ of defining polynomial
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)

$f(q)$	$=$	$q-0.498176 q^{2} +1.00000 q^{3} -1.75182 q^{4} +2.85615 q^{5} -0.498176 q^{6} -0.756391 q^{7} +1.86907 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.498176 q^{2} +1.00000 q^{3} -1.75182 q^{4} +2.85615 q^{5} -0.498176 q^{6} -0.756391 q^{7} +1.86907 q^{8} +1.00000 q^{9} -1.42286 q^{10} -3.09466 q^{11} -1.75182 q^{12} +5.04114 q^{13} +0.376816 q^{14} +2.85615 q^{15} +2.57252 q^{16} +1.00000 q^{17} -0.498176 q^{18} -8.20898 q^{19} -5.00346 q^{20} -0.756391 q^{21} +1.54169 q^{22} -6.58337 q^{23} +1.86907 q^{24} +3.15758 q^{25} -2.51137 q^{26} +1.00000 q^{27} +1.32506 q^{28} -4.48554 q^{29} -1.42286 q^{30} -9.86847 q^{31} -5.01970 q^{32} -3.09466 q^{33} -0.498176 q^{34} -2.16036 q^{35} -1.75182 q^{36} +1.04301 q^{37} +4.08952 q^{38} +5.04114 q^{39} +5.33833 q^{40} -1.24693 q^{41} +0.376816 q^{42} +1.98880 q^{43} +5.42129 q^{44} +2.85615 q^{45} +3.27968 q^{46} +1.38118 q^{47} +2.57252 q^{48} -6.42787 q^{49} -1.57303 q^{50} +1.00000 q^{51} -8.83117 q^{52} -9.43976 q^{53} -0.498176 q^{54} -8.83880 q^{55} -1.41375 q^{56} -8.20898 q^{57} +2.23459 q^{58} -4.23269 q^{59} -5.00346 q^{60} +12.2735 q^{61} +4.91624 q^{62} -0.756391 q^{63} -2.64434 q^{64} +14.3982 q^{65} +1.54169 q^{66} -6.41981 q^{67} -1.75182 q^{68} -6.58337 q^{69} +1.07624 q^{70} +10.9177 q^{71} +1.86907 q^{72} -12.1472 q^{73} -0.519604 q^{74} +3.15758 q^{75} +14.3807 q^{76} +2.34077 q^{77} -2.51137 q^{78} -1.00000 q^{79} +7.34748 q^{80} +1.00000 q^{81} +0.621192 q^{82} +10.5169 q^{83} +1.32506 q^{84} +2.85615 q^{85} -0.990774 q^{86} -4.48554 q^{87} -5.78413 q^{88} +12.6305 q^{89} -1.42286 q^{90} -3.81307 q^{91} +11.5329 q^{92} -9.86847 q^{93} -0.688070 q^{94} -23.4460 q^{95} -5.01970 q^{96} -0.501191 q^{97} +3.20221 q^{98} -3.09466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * 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 $

$2$	−0.498176	−0.352264	−0.176132	−	0.984367i	$-0.556359\pi$
$2$	−0.498176	−0.352264	−0.176132	+	0.984367i	$0.556359\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.75182	−0.875910
$5$	2.85615	1.27731	0.638654	−	0.769494i	$-0.279492\pi$
$5$	2.85615	1.27731	0.638654	+	0.769494i	$0.279492\pi$
$6$	−0.498176	−0.203380
$7$	−0.756391	−0.285889	−0.142944	−	0.989731i	$-0.545657\pi$
$7$	−0.756391	−0.285889	−0.142944	+	0.989731i	$0.545657\pi$
$8$	1.86907	0.660815
$9$	1.00000	0.333333
$10$	−1.42286	−0.449949
$11$	−3.09466	−0.933075	−0.466538	−	0.884501i	$-0.654499\pi$
$11$	−3.09466	−0.933075	−0.466538	+	0.884501i	$0.654499\pi$
$12$	−1.75182	−0.505707
$13$	5.04114	1.39816	0.699080	−	0.715043i	$-0.253593\pi$
$13$	5.04114	1.39816	0.699080	+	0.715043i	$0.253593\pi$
$14$	0.376816	0.100708
$15$	2.85615	0.737454
$16$	2.57252	0.643129
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.498176	−0.117421
$19$	−8.20898	−1.88327	−0.941634	−	0.336638i	$-0.890710\pi$
$19$	−8.20898	−1.88327	−0.941634	+	0.336638i	$0.890710\pi$
$20$	−5.00346	−1.11881
$21$	−0.756391	−0.165058
$22$	1.54169	0.328689
$23$	−6.58337	−1.37273	−0.686364	−	0.727258i	$-0.740794\pi$
$23$	−6.58337	−1.37273	−0.686364	+	0.727258i	$0.740794\pi$
$24$	1.86907	0.381522
$25$	3.15758	0.631516
$26$	−2.51137	−0.492521
$27$	1.00000	0.192450
$28$	1.32506	0.250413
$29$	−4.48554	−0.832944	−0.416472	−	0.909148i	$-0.636734\pi$
$29$	−4.48554	−0.832944	−0.416472	+	0.909148i	$0.636734\pi$
$30$	−1.42286	−0.259778
$31$	−9.86847	−1.77243	−0.886215	−	0.463274i	$-0.846675\pi$
$31$	−9.86847	−1.77243	−0.886215	+	0.463274i	$0.846675\pi$
$32$	−5.01970	−0.887366
$33$	−3.09466	−0.538711
$34$	−0.498176	−0.0854365
$35$	−2.16036	−0.365168
$36$	−1.75182	−0.291970
$37$	1.04301	0.171470	0.0857352	−	0.996318i	$-0.472676\pi$
$37$	1.04301	0.171470	0.0857352	+	0.996318i	$0.472676\pi$
$38$	4.08952	0.663407
$39$	5.04114	0.807228
$40$	5.33833	0.844065
$41$	−1.24693	−0.194738	−0.0973690	−	0.995248i	$-0.531043\pi$
$41$	−1.24693	−0.194738	−0.0973690	+	0.995248i	$0.531043\pi$
$42$	0.376816	0.0581439
$43$	1.98880	0.303290	0.151645	−	0.988435i	$-0.451543\pi$
$43$	1.98880	0.303290	0.151645	+	0.988435i	$0.451543\pi$
$44$	5.42129	0.817290
$45$	2.85615	0.425769
$46$	3.27968	0.483562
$47$	1.38118	0.201466	0.100733	−	0.994914i	$-0.467881\pi$
$47$	1.38118	0.201466	0.100733	+	0.994914i	$0.467881\pi$
$48$	2.57252	0.371311
$49$	−6.42787	−0.918268
$50$	−1.57303	−0.222460
$51$	1.00000	0.140028
$52$	−8.83117	−1.22466
$53$	−9.43976	−1.29665	−0.648325	−	0.761364i	$-0.724530\pi$
$53$	−9.43976	−1.29665	−0.648325	+	0.761364i	$0.724530\pi$
$54$	−0.498176	−0.0677932
$55$	−8.83880	−1.19182
$56$	−1.41375	−0.188920
$57$	−8.20898	−1.08731
$58$	2.23459	0.293416
$59$	−4.23269	−0.551049	−0.275524	−	0.961294i	$-0.588852\pi$
$59$	−4.23269	−0.551049	−0.275524	+	0.961294i	$0.588852\pi$
$60$	−5.00346	−0.645944
$61$	12.2735	1.57146	0.785731	−	0.618569i	$-0.212287\pi$
$61$	12.2735	1.57146	0.785731	+	0.618569i	$0.212287\pi$
$62$	4.91624	0.624363
$63$	−0.756391	−0.0952963
$64$	−2.64434	−0.330542
$65$	14.3982	1.78588
$66$	1.54169	0.189768
$67$	−6.41981	−0.784304	−0.392152	−	0.919900i	$-0.628269\pi$
$67$	−6.41981	−0.784304	−0.392152	+	0.919900i	$0.628269\pi$
$68$	−1.75182	−0.212439
$69$	−6.58337	−0.792545
$70$	1.07624	0.128635
$71$	10.9177	1.29569	0.647846	−	0.761771i	$-0.275670\pi$
$71$	10.9177	1.29569	0.647846	+	0.761771i	$0.275670\pi$
$72$	1.86907	0.220272
$73$	−12.1472	−1.42172	−0.710860	−	0.703334i	$-0.751694\pi$
$73$	−12.1472	−1.42172	−0.710860	+	0.703334i	$0.751694\pi$
$74$	−0.519604	−0.0604028
$75$	3.15758	0.364606
$76$	14.3807	1.64957
$77$	2.34077	0.266756
$78$	−2.51137	−0.284357
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	7.34748	0.821474
$81$	1.00000	0.111111
$82$	0.621192	0.0685991
$83$	10.5169	1.15438	0.577192	−	0.816608i	$-0.304148\pi$
$83$	10.5169	1.15438	0.577192	+	0.816608i	$0.304148\pi$
$84$	1.32506	0.144576
$85$	2.85615	0.309793
$86$	−0.990774	−0.106838
$87$	−4.48554	−0.480901
$88$	−5.78413	−0.616590
$89$	12.6305	1.33883	0.669414	−	0.742890i	$-0.266545\pi$
$89$	12.6305	1.33883	0.669414	+	0.742890i	$0.266545\pi$
$90$	−1.42286	−0.149983
$91$	−3.81307	−0.399718
$92$	11.5329	1.20239
$93$	−9.86847	−1.02331
$94$	−0.688070	−0.0709690
$95$	−23.4460	−2.40551
$96$	−5.01970	−0.512321
$97$	−0.501191	−0.0508883	−0.0254441	−	0.999676i	$-0.508100\pi$
$97$	−0.501191	−0.0508883	−0.0254441	+	0.999676i	$0.508100\pi$
$98$	3.20221	0.323472
$99$	−3.09466	−0.311025
$100$	−5.53151	−0.553151
$101$	−19.1110	−1.90162	−0.950810	−	0.309774i	$-0.899747\pi$
$101$	−19.1110	−1.90162	−0.950810	+	0.309774i	$0.899747\pi$
$102$	−0.498176	−0.0493268
$103$	10.7358	1.05783	0.528913	−	0.848676i	$-0.322600\pi$
$103$	10.7358	1.05783	0.528913	+	0.848676i	$0.322600\pi$
$104$	9.42223	0.923925
$105$	−2.16036	−0.210830
$106$	4.70266	0.456763
$107$	12.6768	1.22551	0.612755	−	0.790273i	$-0.290061\pi$
$107$	12.6768	1.22551	0.612755	+	0.790273i	$0.290061\pi$
$108$	−1.75182	−0.168569
$109$	−4.59018	−0.439659	−0.219830	−	0.975538i	$-0.570550\pi$
$109$	−4.59018	−0.439659	−0.219830	+	0.975538i	$0.570550\pi$
$110$	4.40328	0.419836
$111$	1.04301	0.0989984
$112$	−1.94583	−0.183863
$113$	11.4085	1.07322	0.536611	−	0.843830i	$-0.319704\pi$
$113$	11.4085	1.07322	0.536611	+	0.843830i	$0.319704\pi$
$114$	4.08952	0.383018
$115$	−18.8031	−1.75340
$116$	7.85786	0.729584
$117$	5.04114	0.466053
$118$	2.10862	0.194115
$119$	−0.756391	−0.0693382
$120$	5.33833	0.487321
$121$	−1.42308	−0.129371
$122$	−6.11437	−0.553569
$123$	−1.24693	−0.112432
$124$	17.2878	1.55249
$125$	−5.26223	−0.470668
$126$	0.376816	0.0335694
$127$	−8.19036	−0.726777	−0.363389	−	0.931638i	$-0.618380\pi$
$127$	−8.19036	−0.726777	−0.363389	+	0.931638i	$0.618380\pi$
$128$	11.3567	1.00380
$129$	1.98880	0.175104
$130$	−7.17286	−0.629101
$131$	−19.4588	−1.70012	−0.850062	−	0.526682i	$-0.823436\pi$
$131$	−19.4588	−1.70012	−0.850062	+	0.526682i	$0.823436\pi$
$132$	5.42129	0.471863
$133$	6.20919	0.538405
$134$	3.19819	0.276282
$135$	2.85615	0.245818
$136$	1.86907	0.160271
$137$	−15.4348	−1.31869	−0.659343	−	0.751842i	$-0.729165\pi$
$137$	−15.4348	−1.31869	−0.659343	+	0.751842i	$0.729165\pi$
$138$	3.27968	0.279185
$139$	−21.5734	−1.82983	−0.914917	−	0.403641i	$-0.867744\pi$
$139$	−21.5734	−1.82983	−0.914917	+	0.403641i	$0.867744\pi$
$140$	3.78457	0.319854
$141$	1.38118	0.116316
$142$	−5.43894	−0.456426
$143$	−15.6006	−1.30459
$144$	2.57252	0.214376
$145$	−12.8114	−1.06393
$146$	6.05144	0.500820
$147$	−6.42787	−0.530162
$148$	−1.82717	−0.150193
$149$	10.4486	0.855982	0.427991	−	0.903783i	$-0.359222\pi$
$149$	10.4486	0.855982	0.427991	+	0.903783i	$0.359222\pi$
$150$	−1.57303	−0.128437
$151$	−1.70212	−0.138516	−0.0692582	−	0.997599i	$-0.522063\pi$
$151$	−1.70212	−0.138516	−0.0692582	+	0.997599i	$0.522063\pi$
$152$	−15.3431	−1.24449
$153$	1.00000	0.0808452
$154$	−1.16612	−0.0939684
$155$	−28.1858	−2.26394
$156$	−8.83117	−0.707059
$157$	12.5474	1.00139	0.500695	−	0.865624i	$-0.333078\pi$
$157$	12.5474	1.00139	0.500695	+	0.865624i	$0.333078\pi$
$158$	0.498176	0.0396328
$159$	−9.43976	−0.748621
$160$	−14.3370	−1.13344
$161$	4.97960	0.392448
$162$	−0.498176	−0.0391404
$163$	−13.7615	−1.07789	−0.538944	−	0.842342i	$-0.681176\pi$
$163$	−13.7615	−1.07789	−0.538944	+	0.842342i	$0.681176\pi$
$164$	2.18440	0.170573
$165$	−8.83880	−0.688100
$166$	−5.23929	−0.406648
$167$	4.79940	0.371389	0.185694	−	0.982608i	$-0.440547\pi$
$167$	4.79940	0.371389	0.185694	+	0.982608i	$0.440547\pi$
$168$	−1.41375	−0.109073
$169$	12.4131	0.954852
$170$	−1.42286	−0.109129
$171$	−8.20898	−0.627756
$172$	−3.48403	−0.265654
$173$	1.89544	0.144108	0.0720538	−	0.997401i	$-0.477045\pi$
$173$	1.89544	0.144108	0.0720538	+	0.997401i	$0.477045\pi$
$174$	2.23459	0.169404
$175$	−2.38836	−0.180543
$176$	−7.96106	−0.600088
$177$	−4.23269	−0.318148
$178$	−6.29220	−0.471620
$179$	10.5492	0.788482	0.394241	−	0.919007i	$-0.371008\pi$
$179$	10.5492	0.788482	0.394241	+	0.919007i	$0.371008\pi$
$180$	−5.00346	−0.372936
$181$	22.9160	1.70333	0.851666	−	0.524085i	$-0.175592\pi$
$181$	22.9160	1.70333	0.851666	+	0.524085i	$0.175592\pi$
$182$	1.89958	0.140806
$183$	12.2735	0.907283
$184$	−12.3048	−0.907120
$185$	2.97900	0.219020
$186$	4.91624	0.360476
$187$	−3.09466	−0.226304
$188$	−2.41958	−0.176466
$189$	−0.756391	−0.0550193
$190$	11.6803	0.847375
$191$	1.61316	0.116724	0.0583622	−	0.998295i	$-0.481412\pi$
$191$	1.61316	0.116724	0.0583622	+	0.998295i	$0.481412\pi$
$192$	−2.64434	−0.190839
$193$	10.5234	0.757492	0.378746	−	0.925501i	$-0.376355\pi$
$193$	10.5234	0.757492	0.378746	+	0.925501i	$0.376355\pi$
$194$	0.249682	0.0179261
$195$	14.3982	1.03108
$196$	11.2605	0.804320
$197$	−22.8349	−1.62692	−0.813460	−	0.581621i	$-0.802419\pi$
$197$	−22.8349	−1.62692	−0.813460	+	0.581621i	$0.802419\pi$
$198$	1.54169	0.109563
$199$	−10.5003	−0.744348	−0.372174	−	0.928163i	$-0.621388\pi$
$199$	−10.5003	−0.744348	−0.372174	+	0.928163i	$0.621388\pi$
$200$	5.90173	0.417315
$201$	−6.41981	−0.452818
$202$	9.52067	0.669872
$203$	3.39282	0.238129
$204$	−1.75182	−0.122652
$205$	−3.56142	−0.248740
$206$	−5.34830	−0.372634
$207$	−6.58337	−0.457576
$208$	12.9684	0.899197
$209$	25.4040	1.75723
$210$	1.07624	0.0742677
$211$	25.0147	1.72208	0.861041	−	0.508536i	$-0.169813\pi$
$211$	25.0147	1.72208	0.861041	+	0.508536i	$0.169813\pi$
$212$	16.5368	1.13575
$213$	10.9177	0.748068
$214$	−6.31526	−0.431702
$215$	5.68031	0.387394
$216$	1.86907	0.127174
$217$	7.46442	0.506718
$218$	2.28672	0.154876
$219$	−12.1472	−0.820830
$220$	15.4840	1.04393
$221$	5.04114	0.339104
$222$	−0.519604	−0.0348736
$223$	−24.9534	−1.67100	−0.835502	−	0.549488i	$-0.814823\pi$
$223$	−24.9534	−1.67100	−0.835502	+	0.549488i	$0.814823\pi$
$224$	3.79686	0.253688
$225$	3.15758	0.210505
$226$	−5.68345	−0.378057
$227$	−15.8940	−1.05492	−0.527461	−	0.849579i	$-0.676856\pi$
$227$	−15.8940	−1.05492	−0.527461	+	0.849579i	$0.676856\pi$
$228$	14.3807	0.952382
$229$	25.8547	1.70853	0.854265	−	0.519838i	$-0.174008\pi$
$229$	25.8547	1.70853	0.854265	+	0.519838i	$0.174008\pi$
$230$	9.36725	0.617658
$231$	2.34077	0.154011
$232$	−8.38378	−0.550422
$233$	−9.31335	−0.610138	−0.305069	−	0.952330i	$-0.598680\pi$
$233$	−9.31335	−0.610138	−0.305069	+	0.952330i	$0.598680\pi$
$234$	−2.51137	−0.164174
$235$	3.94485	0.257334
$236$	7.41491	0.482669
$237$	−1.00000	−0.0649570
$238$	0.376816	0.0244253
$239$	−1.62131	−0.104874	−0.0524368	−	0.998624i	$-0.516699\pi$
$239$	−1.62131	−0.104874	−0.0524368	+	0.998624i	$0.516699\pi$
$240$	7.34748	0.474278
$241$	5.66481	0.364903	0.182451	−	0.983215i	$-0.441597\pi$
$241$	5.66481	0.364903	0.182451	+	0.983215i	$0.441597\pi$
$242$	0.708945	0.0455727
$243$	1.00000	0.0641500
$244$	−21.5010	−1.37646
$245$	−18.3590	−1.17291
$246$	0.621192	0.0396057
$247$	−41.3826	−2.63311
$248$	−18.4448	−1.17125
$249$	10.5169	0.666484
$250$	2.62152	0.165799
$251$	−6.90892	−0.436087	−0.218044	−	0.975939i	$-0.569968\pi$
$251$	−6.90892	−0.436087	−0.218044	+	0.975939i	$0.569968\pi$
$252$	1.32506	0.0834710
$253$	20.3733	1.28086
$254$	4.08024	0.256017
$255$	2.85615	0.178859
$256$	−0.368990	−0.0230619
$257$	−11.2290	−0.700449	−0.350224	−	0.936666i	$-0.613895\pi$
$257$	−11.2290	−0.700449	−0.350224	+	0.936666i	$0.613895\pi$
$258$	−0.990774	−0.0616829
$259$	−0.788926	−0.0490214
$260$	−25.2231	−1.56427
$261$	−4.48554	−0.277648
$262$	9.69392	0.598892
$263$	−23.2416	−1.43314	−0.716570	−	0.697515i	$-0.754289\pi$
$263$	−23.2416	−1.43314	−0.716570	+	0.697515i	$0.754289\pi$
$264$	−5.78413	−0.355989
$265$	−26.9613	−1.65622
$266$	−3.09327	−0.189661
$267$	12.6305	0.772972
$268$	11.2463	0.686980
$269$	−2.81692	−0.171751	−0.0858754	−	0.996306i	$-0.527369\pi$
$269$	−2.81692	−0.171751	−0.0858754	+	0.996306i	$0.527369\pi$
$270$	−1.42286	−0.0865928
$271$	−2.75435	−0.167315	−0.0836573	−	0.996495i	$-0.526660\pi$
$271$	−2.75435	−0.167315	−0.0836573	+	0.996495i	$0.526660\pi$
$272$	2.57252	0.155982
$273$	−3.81307	−0.230777
$274$	7.68926	0.464525
$275$	−9.77163	−0.589251
$276$	11.5329	0.694198
$277$	−3.30428	−0.198535	−0.0992675	−	0.995061i	$-0.531650\pi$
$277$	−3.30428	−0.198535	−0.0992675	+	0.995061i	$0.531650\pi$
$278$	10.7474	0.644584
$279$	−9.86847	−0.590810
$280$	−4.03787	−0.241309
$281$	30.3678	1.81159	0.905794	−	0.423717i	$-0.139275\pi$
$281$	30.3678	1.81159	0.905794	+	0.423717i	$0.139275\pi$
$282$	−0.688070	−0.0409740
$283$	6.00193	0.356778	0.178389	−	0.983960i	$-0.442911\pi$
$283$	6.00193	0.356778	0.178389	+	0.983960i	$0.442911\pi$
$284$	−19.1259	−1.13491
$285$	−23.4460	−1.38882
$286$	7.77185	0.459559
$287$	0.943167	0.0556734
$288$	−5.01970	−0.295789
$289$	1.00000	0.0588235
$290$	6.38232	0.374783
$291$	−0.501191	−0.0293804
$292$	21.2797	1.24530
$293$	−12.3230	−0.719918	−0.359959	−	0.932968i	$-0.617209\pi$
$293$	−12.3230	−0.719918	−0.359959	+	0.932968i	$0.617209\pi$
$294$	3.20221	0.186757
$295$	−12.0892	−0.703859
$296$	1.94946	0.113310
$297$	−3.09466	−0.179570
$298$	−5.20524	−0.301531
$299$	−33.1877	−1.91929
$300$	−5.53151	−0.319362
$301$	−1.50431	−0.0867071
$302$	0.847955	0.0487943
$303$	−19.1110	−1.09790
$304$	−21.1177	−1.21118
$305$	35.0549	2.00724
$306$	−0.498176	−0.0284788
$307$	29.1952	1.66626	0.833130	−	0.553077i	$-0.186547\pi$
$307$	29.1952	1.66626	0.833130	+	0.553077i	$0.186547\pi$
$308$	−4.10061	−0.233654
$309$	10.7358	0.610736
$310$	14.0415	0.797504
$311$	8.24065	0.467285	0.233642	−	0.972323i	$-0.424936\pi$
$311$	8.24065	0.467285	0.233642	+	0.972323i	$0.424936\pi$
$312$	9.42223	0.533429
$313$	−21.8703	−1.23618	−0.618091	−	0.786107i	$-0.712093\pi$
$313$	−21.8703	−1.23618	−0.618091	+	0.786107i	$0.712093\pi$
$314$	−6.25080	−0.352753
$315$	−2.16036	−0.121723
$316$	1.75182	0.0985476
$317$	−18.8204	−1.05706	−0.528529	−	0.848915i	$-0.677256\pi$
$317$	−18.8204	−1.05706	−0.528529	+	0.848915i	$0.677256\pi$
$318$	4.70266	0.263712
$319$	13.8812	0.777200
$320$	−7.55261	−0.422204
$321$	12.6768	0.707548
$322$	−2.48072	−0.138245
$323$	−8.20898	−0.456760
$324$	−1.75182	−0.0973234
$325$	15.9178	0.882960
$326$	6.85567	0.379701
$327$	−4.59018	−0.253837
$328$	−2.33060	−0.128686
$329$	−1.04471	−0.0575967
$330$	4.40328	0.242393
$331$	5.16459	0.283872	0.141936	−	0.989876i	$-0.454667\pi$
$331$	5.16459	0.283872	0.141936	+	0.989876i	$0.454667\pi$
$332$	−18.4238	−1.01114
$333$	1.04301	0.0571568
$334$	−2.39095	−0.130827
$335$	−18.3359	−1.00180
$336$	−1.94583	−0.106154
$337$	−11.0581	−0.602375	−0.301187	−	0.953565i	$-0.597383\pi$
$337$	−11.0581	−0.602375	−0.301187	+	0.953565i	$0.597383\pi$
$338$	−6.18390	−0.336360
$339$	11.4085	0.619625
$340$	−5.00346	−0.271351
$341$	30.5396	1.65381
$342$	4.08952	0.221136
$343$	10.1567	0.548411
$344$	3.71721	0.200418
$345$	−18.8031	−1.01232
$346$	−0.944263	−0.0507639
$347$	9.46255	0.507976	0.253988	−	0.967207i	$-0.418258\pi$
$347$	9.46255	0.507976	0.253988	+	0.967207i	$0.418258\pi$
$348$	7.85786	0.421226
$349$	−29.6040	−1.58466	−0.792332	−	0.610090i	$-0.791133\pi$
$349$	−29.6040	−1.58466	−0.792332	+	0.610090i	$0.791133\pi$
$350$	1.18983	0.0635988
$351$	5.04114	0.269076
$352$	15.5343	0.827979
$353$	12.9261	0.687989	0.343995	−	0.938972i	$-0.388220\pi$
$353$	12.9261	0.687989	0.343995	+	0.938972i	$0.388220\pi$
$354$	2.10862	0.112072
$355$	31.1826	1.65500
$356$	−22.1263	−1.17269
$357$	−0.756391	−0.0400324
$358$	−5.25534	−0.277754
$359$	−14.0981	−0.744071	−0.372035	−	0.928219i	$-0.621340\pi$
$359$	−14.0981	−0.744071	−0.372035	+	0.928219i	$0.621340\pi$
$360$	5.33833	0.281355
$361$	48.3873	2.54670
$362$	−11.4162	−0.600022
$363$	−1.42308	−0.0746924
$364$	6.67981	0.350117
$365$	−34.6941	−1.81597
$366$	−6.11437	−0.319603
$367$	0.542738	0.0283307	0.0141653	−	0.999900i	$-0.495491\pi$
$367$	0.542738	0.0283307	0.0141653	+	0.999900i	$0.495491\pi$
$368$	−16.9358	−0.882841
$369$	−1.24693	−0.0649127
$370$	−1.48407	−0.0771530
$371$	7.14014	0.370698
$372$	17.2878	0.896330
$373$	23.9650	1.24086	0.620431	−	0.784261i	$-0.286958\pi$
$373$	23.9650	1.24086	0.620431	+	0.784261i	$0.286958\pi$
$374$	1.54169	0.0797187
$375$	−5.26223	−0.271740
$376$	2.58152	0.133131
$377$	−22.6122	−1.16459
$378$	0.376816	0.0193813
$379$	−11.9232	−0.612455	−0.306227	−	0.951958i	$-0.599067\pi$
$379$	−11.9232	−0.612455	−0.306227	+	0.951958i	$0.599067\pi$
$380$	41.0733	2.10701
$381$	−8.19036	−0.419605
$382$	−0.803639	−0.0411178
$383$	6.79995	0.347461	0.173730	−	0.984793i	$-0.444418\pi$
$383$	6.79995	0.347461	0.173730	+	0.984793i	$0.444418\pi$
$384$	11.3567	0.579547
$385$	6.68559	0.340729
$386$	−5.24252	−0.266837
$387$	1.98880	0.101097
$388$	0.877997	0.0445736
$389$	−16.2964	−0.826262	−0.413131	−	0.910672i	$-0.635565\pi$
$389$	−16.2964	−0.826262	−0.413131	+	0.910672i	$0.635565\pi$
$390$	−7.17286	−0.363212
$391$	−6.58337	−0.332935
$392$	−12.0141	−0.606805
$393$	−19.4588	−0.981567
$394$	11.3758	0.573105
$395$	−2.85615	−0.143708
$396$	5.42129	0.272430
$397$	−8.03449	−0.403239	−0.201620	−	0.979464i	$-0.564621\pi$
$397$	−8.03449	−0.403239	−0.201620	+	0.979464i	$0.564621\pi$
$398$	5.23101	0.262207
$399$	6.20919	0.310849
$400$	8.12292	0.406146
$401$	−8.12750	−0.405868	−0.202934	−	0.979192i	$-0.565048\pi$
$401$	−8.12750	−0.405868	−0.202934	+	0.979192i	$0.565048\pi$
$402$	3.19819	0.159511
$403$	−49.7483	−2.47814
$404$	33.4791	1.66565
$405$	2.85615	0.141923
$406$	−1.69022	−0.0838844
$407$	−3.22777	−0.159995
$408$	1.86907	0.0925326
$409$	20.8567	1.03130	0.515649	−	0.856800i	$-0.327551\pi$
$409$	20.8567	1.03130	0.515649	+	0.856800i	$0.327551\pi$
$410$	1.77421	0.0876222
$411$	−15.4348	−0.761344
$412$	−18.8071	−0.926560
$413$	3.20157	0.157539
$414$	3.27968	0.161187
$415$	30.0379	1.47450
$416$	−25.3050	−1.24068
$417$	−21.5734	−1.05646
$418$	−12.6557	−0.619009
$419$	7.34365	0.358761	0.179380	−	0.983780i	$-0.442591\pi$
$419$	7.34365	0.358761	0.179380	+	0.983780i	$0.442591\pi$
$420$	3.78457	0.184668
$421$	28.3207	1.38027	0.690133	−	0.723682i	$-0.257552\pi$
$421$	28.3207	1.38027	0.690133	+	0.723682i	$0.257552\pi$
$422$	−12.4617	−0.606627
$423$	1.38118	0.0671552
$424$	−17.6435	−0.856846
$425$	3.15758	0.153165
$426$	−5.43894	−0.263517
$427$	−9.28356	−0.449263
$428$	−22.2074	−1.07344
$429$	−15.6006	−0.753204
$430$	−2.82980	−0.136465
$431$	10.0788	0.485479	0.242740	−	0.970091i	$-0.421954\pi$
$431$	10.0788	0.485479	0.242740	+	0.970091i	$0.421954\pi$
$432$	2.57252	0.123770
$433$	−27.2421	−1.30917	−0.654587	−	0.755987i	$-0.727157\pi$
$433$	−27.2421	−1.30917	−0.654587	+	0.755987i	$0.727157\pi$
$434$	−3.71860	−0.178498
$435$	−12.8114	−0.614258
$436$	8.04116	0.385102
$437$	54.0428	2.58522
$438$	6.05144	0.289149
$439$	−4.12268	−0.196765	−0.0983824	−	0.995149i	$-0.531367\pi$
$439$	−4.12268	−0.196765	−0.0983824	+	0.995149i	$0.531367\pi$
$440$	−16.5203	−0.787576
$441$	−6.42787	−0.306089
$442$	−2.51137	−0.119454
$443$	−0.536903	−0.0255090	−0.0127545	−	0.999919i	$-0.504060\pi$
$443$	−0.536903	−0.0255090	−0.0127545	+	0.999919i	$0.504060\pi$
$444$	−1.82717	−0.0867137
$445$	36.0745	1.71009
$446$	12.4312	0.588634
$447$	10.4486	0.494201
$448$	2.00015	0.0944983
$449$	−18.1779	−0.857868	−0.428934	−	0.903336i	$-0.641111\pi$
$449$	−18.1779	−0.857868	−0.428934	+	0.903336i	$0.641111\pi$
$450$	−1.57303	−0.0741533
$451$	3.85883	0.181705
$452$	−19.9857	−0.940046
$453$	−1.70212	−0.0799725
$454$	7.91802	0.371611
$455$	−10.8907	−0.510563
$456$	−15.3431	−0.718508
$457$	19.5950	0.916615	0.458308	−	0.888794i	$-0.348456\pi$
$457$	19.5950	0.916615	0.458308	+	0.888794i	$0.348456\pi$
$458$	−12.8802	−0.601853
$459$	1.00000	0.0466760
$460$	32.9396	1.53582
$461$	−39.6358	−1.84603	−0.923013	−	0.384769i	$-0.874281\pi$
$461$	−39.6358	−1.84603	−0.923013	+	0.384769i	$0.874281\pi$
$462$	−1.16612	−0.0542527
$463$	8.82192	0.409989	0.204995	−	0.978763i	$-0.434282\pi$
$463$	8.82192	0.409989	0.204995	+	0.978763i	$0.434282\pi$
$464$	−11.5391	−0.535691
$465$	−28.1858	−1.30709
$466$	4.63969	0.214930
$467$	−41.5160	−1.92113	−0.960566	−	0.278053i	$-0.910311\pi$
$467$	−41.5160	−1.92113	−0.960566	+	0.278053i	$0.910311\pi$
$468$	−8.83117	−0.408221
$469$	4.85588	0.224224
$470$	−1.96523	−0.0906493
$471$	12.5474	0.578152
$472$	−7.91118	−0.364142
$473$	−6.15467	−0.282992
$474$	0.498176	0.0228820
$475$	−25.9205	−1.18931
$476$	1.32506	0.0607341
$477$	−9.43976	−0.432217
$478$	0.807696	0.0369431
$479$	−38.0995	−1.74081	−0.870405	−	0.492337i	$-0.836143\pi$
$479$	−38.0995	−1.74081	−0.870405	+	0.492337i	$0.836143\pi$
$480$	−14.3370	−0.654392
$481$	5.25797	0.239743
$482$	−2.82207	−0.128542
$483$	4.97960	0.226580
$484$	2.49298	0.113317
$485$	−1.43148	−0.0650000
$486$	−0.498176	−0.0225977
$487$	−29.4577	−1.33486	−0.667428	−	0.744674i	$-0.732605\pi$
$487$	−29.4577	−1.33486	−0.667428	+	0.744674i	$0.732605\pi$
$488$	22.9400	1.03845
$489$	−13.7615	−0.622319
$490$	9.14599	0.413174
$491$	−2.63871	−0.119083	−0.0595417	−	0.998226i	$-0.518964\pi$
$491$	−2.63871	−0.119083	−0.0595417	+	0.998226i	$0.518964\pi$
$492$	2.18440	0.0984804
$493$	−4.48554	−0.202019
$494$	20.6158	0.927550
$495$	−8.83880	−0.397275
$496$	−25.3868	−1.13990
$497$	−8.25805	−0.370424
$498$	−5.23929	−0.234778
$499$	12.9128	0.578056	0.289028	−	0.957321i	$-0.406668\pi$
$499$	12.9128	0.578056	0.289028	+	0.957321i	$0.406668\pi$
$500$	9.21848	0.412263
$501$	4.79940	0.214421
$502$	3.44186	0.153618
$503$	10.2105	0.455262	0.227631	−	0.973748i	$-0.426902\pi$
$503$	10.2105	0.455262	0.227631	+	0.973748i	$0.426902\pi$
$504$	−1.41375	−0.0629732
$505$	−54.5840	−2.42895
$506$	−10.1495	−0.451200
$507$	12.4131	0.551284
$508$	14.3480	0.636592
$509$	−5.72746	−0.253865	−0.126933	−	0.991911i	$-0.540513\pi$
$509$	−5.72746	−0.253865	−0.126933	+	0.991911i	$0.540513\pi$
$510$	−1.42286	−0.0630055
$511$	9.18801	0.406454
$512$	−22.5297	−0.995680
$513$	−8.20898	−0.362435
$514$	5.59405	0.246743
$515$	30.6629	1.35117
$516$	−3.48403	−0.153376
$517$	−4.27428	−0.187982
$518$	0.393024	0.0172685
$519$	1.89544	0.0832006
$520$	26.9113	1.18014
$521$	−13.9185	−0.609779	−0.304889	−	0.952388i	$-0.598620\pi$
$521$	−13.9185	−0.609779	−0.304889	+	0.952388i	$0.598620\pi$
$522$	2.23459	0.0978054
$523$	−20.3354	−0.889204	−0.444602	−	0.895728i	$-0.646655\pi$
$523$	−20.3354	−0.889204	−0.444602	+	0.895728i	$0.646655\pi$
$524$	34.0883	1.48916
$525$	−2.38836	−0.104237
$526$	11.5784	0.504844
$527$	−9.86847	−0.429877
$528$	−7.96106	−0.346461
$529$	20.3408	0.884382
$530$	13.4315	0.583427
$531$	−4.23269	−0.183683
$532$	−10.8774	−0.471595
$533$	−6.28595	−0.272275
$534$	−6.29220	−0.272290
$535$	36.2067	1.56535
$536$	−11.9991	−0.518280
$537$	10.5492	0.455230
$538$	1.40332	0.0605016
$539$	19.8921	0.856813
$540$	−5.00346	−0.215315
$541$	20.9548	0.900915	0.450458	−	0.892798i	$-0.351261\pi$
$541$	20.9548	0.900915	0.450458	+	0.892798i	$0.351261\pi$
$542$	1.37215	0.0589389
$543$	22.9160	0.983419
$544$	−5.01970	−0.215218
$545$	−13.1102	−0.561580
$546$	1.89958	0.0812945
$547$	−21.7698	−0.930810	−0.465405	−	0.885098i	$-0.654091\pi$
$547$	−21.7698	−0.930810	−0.465405	+	0.885098i	$0.654091\pi$
$548$	27.0390	1.15505
$549$	12.2735	0.523820
$550$	4.86799	0.207572
$551$	36.8217	1.56866
$552$	−12.3048	−0.523726
$553$	0.756391	0.0321650
$554$	1.64611	0.0699367
$555$	2.97900	0.126451
$556$	37.7928	1.60277
$557$	35.3114	1.49619	0.748095	−	0.663591i	$-0.230969\pi$
$557$	35.3114	1.49619	0.748095	+	0.663591i	$0.230969\pi$
$558$	4.91624	0.208121
$559$	10.0258	0.424047
$560$	−5.55757	−0.234850
$561$	−3.09466	−0.130657
$562$	−15.1285	−0.638157
$563$	40.1865	1.69366	0.846829	−	0.531865i	$-0.178509\pi$
$563$	40.1865	1.69366	0.846829	+	0.531865i	$0.178509\pi$
$564$	−2.41958	−0.101883
$565$	32.5844	1.37084
$566$	−2.99002	−0.125680
$567$	−0.756391	−0.0317654
$568$	20.4059	0.856213
$569$	−21.3059	−0.893188	−0.446594	−	0.894737i	$-0.647363\pi$
$569$	−21.3059	−0.893188	−0.446594	+	0.894737i	$0.647363\pi$
$570$	11.6803	0.489232
$571$	18.0301	0.754535	0.377267	−	0.926104i	$-0.376864\pi$
$571$	18.0301	0.754535	0.377267	+	0.926104i	$0.376864\pi$
$572$	27.3295	1.14270
$573$	1.61316	0.0673908
$574$	−0.469864	−0.0196117
$575$	−20.7875	−0.866899
$576$	−2.64434	−0.110181
$577$	24.3933	1.01551	0.507753	−	0.861503i	$-0.330476\pi$
$577$	24.3933	1.01551	0.507753	+	0.861503i	$0.330476\pi$
$578$	−0.498176	−0.0207214
$579$	10.5234	0.437338
$580$	22.4432	0.931904
$581$	−7.95492	−0.330026
$582$	0.249682	0.0103496
$583$	29.2128	1.20987
$584$	−22.7039	−0.939494
$585$	14.3982	0.595294
$586$	6.13903	0.253601
$587$	14.5194	0.599282	0.299641	−	0.954052i	$-0.403133\pi$
$587$	14.5194	0.599282	0.299641	+	0.954052i	$0.403133\pi$
$588$	11.2605	0.464374
$589$	81.0101	3.33796
$590$	6.02254	0.247944
$591$	−22.8349	−0.939302
$592$	2.68317	0.110278
$593$	0.664199	0.0272754	0.0136377	−	0.999907i	$-0.495659\pi$
$593$	0.664199	0.0272754	0.0136377	+	0.999907i	$0.495659\pi$
$594$	1.54169	0.0632561
$595$	−2.16036	−0.0885663
$596$	−18.3041	−0.749763
$597$	−10.5003	−0.429750
$598$	16.5333	0.676098
$599$	−17.1628	−0.701255	−0.350627	−	0.936515i	$-0.614032\pi$
$599$	−17.1628	−0.701255	−0.350627	+	0.936515i	$0.614032\pi$
$600$	5.90173	0.240937
$601$	46.9213	1.91396	0.956980	−	0.290153i	$-0.0937062\pi$
$601$	46.9213	1.91396	0.956980	+	0.290153i	$0.0937062\pi$
$602$	0.749412	0.0305438
$603$	−6.41981	−0.261435
$604$	2.98181	0.121328
$605$	−4.06453	−0.165247
$606$	9.52067	0.386751
$607$	31.1314	1.26358	0.631792	−	0.775138i	$-0.282320\pi$
$607$	31.1314	1.26358	0.631792	+	0.775138i	$0.282320\pi$
$608$	41.2066	1.67115
$609$	3.39282	0.137484
$610$	−17.4635	−0.707078
$611$	6.96271	0.281681
$612$	−1.75182	−0.0708131
$613$	12.9706	0.523877	0.261939	−	0.965085i	$-0.415638\pi$
$613$	12.9706	0.523877	0.261939	+	0.965085i	$0.415638\pi$
$614$	−14.5444	−0.586963
$615$	−3.56142	−0.143610
$616$	4.37506	0.176276
$617$	−0.295273	−0.0118872	−0.00594362	−	0.999982i	$-0.501892\pi$
$617$	−0.295273	−0.0118872	−0.00594362	+	0.999982i	$0.501892\pi$
$618$	−5.34830	−0.215140
$619$	−35.1842	−1.41417	−0.707087	−	0.707126i	$-0.749991\pi$
$619$	−35.1842	−1.41417	−0.707087	+	0.707126i	$0.749991\pi$
$620$	49.3765	1.98301
$621$	−6.58337	−0.264182
$622$	−4.10530	−0.164607
$623$	−9.55357	−0.382756
$624$	12.9684	0.519152
$625$	−30.8176	−1.23270
$626$	10.8953	0.435462
$627$	25.4040	1.01454
$628$	−21.9807	−0.877127
$629$	1.04301	0.0415877
$630$	1.07624	0.0428785
$631$	33.7146	1.34216	0.671078	−	0.741386i	$-0.265831\pi$
$631$	33.7146	1.34216	0.671078	+	0.741386i	$0.265831\pi$
$632$	−1.86907	−0.0743475
$633$	25.0147	0.994244
$634$	9.37587	0.372363
$635$	−23.3929	−0.928318
$636$	16.5368	0.655725
$637$	−32.4038	−1.28389
$638$	−6.91530	−0.273779
$639$	10.9177	0.431898
$640$	32.4365	1.28217
$641$	−0.806833	−0.0318680	−0.0159340	−	0.999873i	$-0.505072\pi$
$641$	−0.806833	−0.0318680	−0.0159340	+	0.999873i	$0.505072\pi$
$642$	−6.31526	−0.249244
$643$	8.48465	0.334602	0.167301	−	0.985906i	$-0.446495\pi$
$643$	8.48465	0.334602	0.167301	+	0.985906i	$0.446495\pi$
$644$	−8.72337	−0.343749
$645$	5.68031	0.223662
$646$	4.08952	0.160900
$647$	−12.7770	−0.502314	−0.251157	−	0.967946i	$-0.580811\pi$
$647$	−12.7770	−0.502314	−0.251157	+	0.967946i	$0.580811\pi$
$648$	1.86907	0.0734239
$649$	13.0987	0.514170
$650$	−7.92986	−0.311035
$651$	7.46442	0.292554
$652$	24.1078	0.944133
$653$	−43.5862	−1.70566	−0.852830	−	0.522189i	$-0.825116\pi$
$653$	−43.5862	−1.70566	−0.852830	+	0.522189i	$0.825116\pi$
$654$	2.28672	0.0894177
$655$	−55.5772	−2.17158
$656$	−3.20775	−0.125242
$657$	−12.1472	−0.473907
$658$	0.520450	0.0202892
$659$	−0.586014	−0.0228279	−0.0114139	−	0.999935i	$-0.503633\pi$
$659$	−0.586014	−0.0228279	−0.0114139	+	0.999935i	$0.503633\pi$
$660$	15.4840	0.602714
$661$	−5.05895	−0.196770	−0.0983851	−	0.995148i	$-0.531368\pi$
$661$	−5.05895	−0.196770	−0.0983851	+	0.995148i	$0.531368\pi$
$662$	−2.57288	−0.0999977
$663$	5.04114	0.195782
$664$	19.6569	0.762835
$665$	17.7344	0.687709
$666$	−0.519604	−0.0201343
$667$	29.5300	1.14341
$668$	−8.40769	−0.325303
$669$	−24.9534	−0.964754
$670$	9.13451	0.352897
$671$	−37.9823	−1.46629
$672$	3.79686	0.146467
$673$	13.9844	0.539057	0.269529	−	0.962992i	$-0.413132\pi$
$673$	13.9844	0.539057	0.269529	+	0.962992i	$0.413132\pi$
$674$	5.50890	0.212195
$675$	3.15758	0.121535
$676$	−21.7455	−0.836364
$677$	−25.0947	−0.964467	−0.482233	−	0.876043i	$-0.660174\pi$
$677$	−25.0947	−0.964467	−0.482233	+	0.876043i	$0.660174\pi$
$678$	−5.68345	−0.218271
$679$	0.379097	0.0145484
$680$	5.33833	0.204716
$681$	−15.8940	−0.609060
$682$	−15.2141	−0.582577
$683$	17.1295	0.655441	0.327721	−	0.944775i	$-0.393720\pi$
$683$	17.1295	0.655441	0.327721	+	0.944775i	$0.393720\pi$
$684$	14.3807	0.549858
$685$	−44.0841	−1.68437
$686$	−5.05984	−0.193185
$687$	25.8547	0.986420
$688$	5.11623	0.195054
$689$	−47.5871	−1.81292
$690$	9.36725	0.356605
$691$	−2.02087	−0.0768774	−0.0384387	−	0.999261i	$-0.512238\pi$
$691$	−2.02087	−0.0768774	−0.0384387	+	0.999261i	$0.512238\pi$
$692$	−3.32047	−0.126225
$693$	2.34077	0.0889186
$694$	−4.71402	−0.178942
$695$	−61.6169	−2.33726
$696$	−8.38378	−0.317786
$697$	−1.24693	−0.0472309
$698$	14.7480	0.558220
$699$	−9.31335	−0.352263
$700$	4.18398	0.158140
$701$	31.3512	1.18412	0.592060	−	0.805894i	$-0.298315\pi$
$701$	31.3512	1.18412	0.592060	+	0.805894i	$0.298315\pi$
$702$	−2.51137	−0.0947857
$703$	−8.56207	−0.322925
$704$	8.18332	0.308420
$705$	3.94485	0.148572
$706$	−6.43950	−0.242354
$707$	14.4554	0.543652
$708$	7.41491	0.278669
$709$	43.1336	1.61992	0.809959	−	0.586487i	$-0.199489\pi$
$709$	43.1336	1.61992	0.809959	+	0.586487i	$0.199489\pi$
$710$	−15.5344	−0.582996
$711$	−1.00000	−0.0375029
$712$	23.6072	0.884717
$713$	64.9678	2.43306
$714$	0.376816	0.0141020
$715$	−44.5576	−1.66636
$716$	−18.4802	−0.690639
$717$	−1.62131	−0.0605487
$718$	7.02335	0.262109
$719$	−22.6425	−0.844422	−0.422211	−	0.906498i	$-0.638746\pi$
$719$	−22.6425	−0.844422	−0.422211	+	0.906498i	$0.638746\pi$
$720$	7.34748	0.273825
$721$	−8.12043	−0.302421
$722$	−24.1054	−0.897110
$723$	5.66481	0.210677
$724$	−40.1447	−1.49197
$725$	−14.1634	−0.526017
$726$	0.708945	0.0263114
$727$	−13.2087	−0.489885	−0.244942	−	0.969538i	$-0.578769\pi$
$727$	−13.2087	−0.489885	−0.244942	+	0.969538i	$0.578769\pi$
$728$	−7.12689	−0.264140
$729$	1.00000	0.0370370
$730$	17.2838	0.639702
$731$	1.98880	0.0735585
$732$	−21.5010	−0.794699
$733$	0.226491	0.00836564	0.00418282	−	0.999991i	$-0.498669\pi$
$733$	0.226491	0.00836564	0.00418282	+	0.999991i	$0.498669\pi$
$734$	−0.270379	−0.00997987
$735$	−18.3590	−0.677180
$736$	33.0466	1.21811
$737$	19.8671	0.731815
$738$	0.621192	0.0228664
$739$	33.9425	1.24860	0.624298	−	0.781186i	$-0.285385\pi$
$739$	33.9425	1.24860	0.624298	+	0.781186i	$0.285385\pi$
$740$	−5.21867	−0.191842
$741$	−41.3826	−1.52023
$742$	−3.55705	−0.130583
$743$	27.6666	1.01499	0.507494	−	0.861655i	$-0.330572\pi$
$743$	27.6666	1.01499	0.507494	+	0.861655i	$0.330572\pi$
$744$	−18.4448	−0.676221
$745$	29.8427	1.09335
$746$	−11.9388	−0.437111
$747$	10.5169	0.384795
$748$	5.42129	0.198222
$749$	−9.58859	−0.350359
$750$	2.62152	0.0957243
$751$	6.83317	0.249346	0.124673	−	0.992198i	$-0.460212\pi$
$751$	6.83317	0.249346	0.124673	+	0.992198i	$0.460212\pi$
$752$	3.55310	0.129568
$753$	−6.90892	−0.251775
$754$	11.2649	0.410243
$755$	−4.86150	−0.176928
$756$	1.32506	0.0481920
$757$	−29.0212	−1.05479	−0.527397	−	0.849619i	$-0.676832\pi$
$757$	−29.0212	−1.05479	−0.527397	+	0.849619i	$0.676832\pi$
$758$	5.93987	0.215746
$759$	20.3733	0.739504
$760$	−43.8223	−1.58960
$761$	42.2415	1.53125	0.765627	−	0.643284i	$-0.222429\pi$
$761$	42.2415	1.53125	0.765627	+	0.643284i	$0.222429\pi$
$762$	4.08024	0.147812
$763$	3.47197	0.125694
$764$	−2.82597	−0.102240
$765$	2.85615	0.103264
$766$	−3.38757	−0.122398
$767$	−21.3376	−0.770455
$768$	−0.368990	−0.0133148
$769$	−40.4857	−1.45995	−0.729976	−	0.683473i	$-0.760469\pi$
$769$	−40.4857	−1.45995	−0.729976	+	0.683473i	$0.760469\pi$
$770$	−3.33060	−0.120027
$771$	−11.2290	−0.404404
$772$	−18.4351	−0.663495
$773$	−5.15197	−0.185304	−0.0926518	−	0.995699i	$-0.529534\pi$
$773$	−5.15197	−0.185304	−0.0926518	+	0.995699i	$0.529534\pi$
$774$	−0.990774	−0.0356126
$775$	−31.1605	−1.11932
$776$	−0.936761	−0.0336277
$777$	−0.788926	−0.0283025
$778$	8.11849	0.291062
$779$	10.2360	0.366744
$780$	−25.2231	−0.903133
$781$	−33.7866	−1.20898
$782$	3.27968	0.117281
$783$	−4.48554	−0.160300
$784$	−16.5358	−0.590564
$785$	35.8371	1.27908
$786$	9.69392	0.345771
$787$	29.0477	1.03544	0.517719	−	0.855551i	$-0.326781\pi$
$787$	29.0477	1.03544	0.517719	+	0.855551i	$0.326781\pi$
$788$	40.0026	1.42504
$789$	−23.2416	−0.827424
$790$	1.42286	0.0506233
$791$	−8.62929	−0.306822
$792$	−5.78413	−0.205530
$793$	61.8724	2.19715
$794$	4.00259	0.142047
$795$	−26.9613	−0.956220
$796$	18.3947	0.651982
$797$	12.0837	0.428026	0.214013	−	0.976831i	$-0.431347\pi$
$797$	12.0837	0.428026	0.214013	+	0.976831i	$0.431347\pi$
$798$	−3.09327	−0.109501
$799$	1.38118	0.0488626
$800$	−15.8501	−0.560386
$801$	12.6305	0.446276
$802$	4.04893	0.142973
$803$	37.5914	1.32657
$804$	11.2463	0.396628
$805$	14.2225	0.501276
$806$	24.7834	0.872959
$807$	−2.81692	−0.0991604
$808$	−35.7198	−1.25662
$809$	33.9408	1.19329	0.596647	−	0.802504i	$-0.296499\pi$
$809$	33.9408	1.19329	0.596647	+	0.802504i	$0.296499\pi$
$810$	−1.42286	−0.0499944
$811$	−11.7197	−0.411533	−0.205767	−	0.978601i	$-0.565969\pi$
$811$	−11.7197	−0.411533	−0.205767	+	0.978601i	$0.565969\pi$
$812$	−5.94362	−0.208580
$813$	−2.75435	−0.0965992
$814$	1.60800	0.0563603
$815$	−39.3050	−1.37679
$816$	2.57252	0.0900561
$817$	−16.3260	−0.571176
$818$	−10.3903	−0.363289
$819$	−3.81307	−0.133239
$820$	6.23897	0.217874
$821$	−36.2211	−1.26412	−0.632062	−	0.774918i	$-0.717791\pi$
$821$	−36.2211	−1.26412	−0.632062	+	0.774918i	$0.717791\pi$
$822$	7.68926	0.268194
$823$	29.9621	1.04441	0.522207	−	0.852819i	$-0.325109\pi$
$823$	29.9621	1.04441	0.522207	+	0.852819i	$0.325109\pi$
$824$	20.0659	0.699027
$825$	−9.77163	−0.340204
$826$	−1.59494	−0.0554952
$827$	−12.5922	−0.437872	−0.218936	−	0.975739i	$-0.570259\pi$
$827$	−12.5922	−0.437872	−0.218936	+	0.975739i	$0.570259\pi$
$828$	11.5329	0.400796
$829$	−41.1088	−1.42777	−0.713884	−	0.700264i	$-0.753066\pi$
$829$	−41.1088	−1.42777	−0.713884	+	0.700264i	$0.753066\pi$
$830$	−14.9642	−0.519415
$831$	−3.30428	−0.114624
$832$	−13.3305	−0.462151
$833$	−6.42787	−0.222713
$834$	10.7474	0.372151
$835$	13.7078	0.474378
$836$	−44.5032	−1.53918
$837$	−9.86847	−0.341104
$838$	−3.65843	−0.126378
$839$	30.2778	1.04531	0.522653	−	0.852546i	$-0.324942\pi$
$839$	30.2778	1.04531	0.522653	+	0.852546i	$0.324942\pi$
$840$	−4.03787	−0.139320
$841$	−8.87991	−0.306204
$842$	−14.1087	−0.486218
$843$	30.3678	1.04592
$844$	−43.8212	−1.50839
$845$	35.4536	1.21964
$846$	−0.688070	−0.0236563
$847$	1.07640	0.0369857
$848$	−24.2839	−0.833913
$849$	6.00193	0.205986
$850$	−1.57303	−0.0539545
$851$	−6.86654	−0.235382
$852$	−19.1259	−0.655241
$853$	22.4121	0.767375	0.383687	−	0.923463i	$-0.374654\pi$
$853$	22.4121	0.767375	0.383687	+	0.923463i	$0.374654\pi$
$854$	4.62485	0.158259
$855$	−23.4460	−0.801838
$856$	23.6937	0.809835
$857$	−23.4844	−0.802211	−0.401105	−	0.916032i	$-0.631374\pi$
$857$	−23.4844	−0.802211	−0.401105	+	0.916032i	$0.631374\pi$
$858$	7.77185	0.265327
$859$	6.46987	0.220749	0.110375	−	0.993890i	$-0.464795\pi$
$859$	6.46987	0.220749	0.110375	+	0.993890i	$0.464795\pi$
$860$	−9.95089	−0.339323
$861$	0.943167	0.0321431
$862$	−5.02102	−0.171017
$863$	−39.9582	−1.36019	−0.680097	−	0.733122i	$-0.738062\pi$
$863$	−39.9582	−1.36019	−0.680097	+	0.733122i	$0.738062\pi$
$864$	−5.01970	−0.170774
$865$	5.41365	0.184070
$866$	13.5714	0.461174
$867$	1.00000	0.0339618
$868$	−13.0763	−0.443839
$869$	3.09466	0.104979
$870$	6.38232	0.216381
$871$	−32.3631	−1.09658
$872$	−8.57935	−0.290533
$873$	−0.501191	−0.0169628
$874$	−26.9228	−0.910678
$875$	3.98030	0.134559
$876$	21.2797	0.718974
$877$	−29.7482	−1.00452	−0.502262	−	0.864715i	$-0.667499\pi$
$877$	−29.7482	−1.00452	−0.502262	+	0.864715i	$0.667499\pi$
$878$	2.05382	0.0693131
$879$	−12.3230	−0.415645
$880$	−22.7380	−0.766497
$881$	−56.3411	−1.89818	−0.949090	−	0.315006i	$-0.897993\pi$
$881$	−56.3411	−1.89818	−0.949090	+	0.315006i	$0.897993\pi$
$882$	3.20221	0.107824
$883$	43.4108	1.46089	0.730445	−	0.682972i	$-0.239313\pi$
$883$	43.4108	1.46089	0.730445	+	0.682972i	$0.239313\pi$
$884$	−8.83117	−0.297024
$885$	−12.0892	−0.406373
$886$	0.267472	0.00898590
$887$	49.8542	1.67394	0.836971	−	0.547248i	$-0.184325\pi$
$887$	49.8542	1.67394	0.836971	+	0.547248i	$0.184325\pi$
$888$	1.94946	0.0654197
$889$	6.19511	0.207777
$890$	−17.9715	−0.602404
$891$	−3.09466	−0.103675
$892$	43.7139	1.46365
$893$	−11.3381	−0.379414
$894$	−5.20524	−0.174089
$895$	30.1300	1.00713
$896$	−8.59014	−0.286976
$897$	−33.1877	−1.10810
$898$	9.05580	0.302196
$899$	44.2655	1.47634
$900$	−5.53151	−0.184384
$901$	−9.43976	−0.314484
$902$	−1.92238	−0.0640081
$903$	−1.50431	−0.0500604
$904$	21.3233	0.709202
$905$	65.4515	2.17568
$906$	0.847955	0.0281714
$907$	8.44868	0.280534	0.140267	−	0.990114i	$-0.455204\pi$
$907$	8.44868	0.280534	0.140267	+	0.990114i	$0.455204\pi$
$908$	27.8435	0.924018
$909$	−19.1110	−0.633873
$910$	5.42548	0.179853
$911$	11.0579	0.366365	0.183183	−	0.983079i	$-0.441360\pi$
$911$	11.0579	0.366365	0.183183	+	0.983079i	$0.441360\pi$
$912$	−21.1177	−0.699278
$913$	−32.5464	−1.07713
$914$	−9.76176	−0.322890
$915$	35.0549	1.15888
$916$	−45.2929	−1.49652
$917$	14.7185	0.486047
$918$	−0.498176	−0.0164423
$919$	14.4775	0.477569	0.238785	−	0.971073i	$-0.423251\pi$
$919$	14.4775	0.477569	0.238785	+	0.971073i	$0.423251\pi$
$920$	−35.1442	−1.15867
$921$	29.1952	0.962016
$922$	19.7456	0.650288
$923$	55.0376	1.81159
$924$	−4.10061	−0.134900
$925$	3.29340	0.108286
$926$	−4.39487	−0.144424
$927$	10.7358	0.352609
$928$	22.5161	0.739127
$929$	25.2650	0.828918	0.414459	−	0.910068i	$-0.363971\pi$
$929$	25.2650	0.828918	0.414459	+	0.910068i	$0.363971\pi$
$930$	14.0415	0.460439
$931$	52.7663	1.72934
$932$	16.3153	0.534426
$933$	8.24065	0.269787
$934$	20.6823	0.676745
$935$	−8.83880	−0.289060
$936$	9.42223	0.307975
$937$	−27.5949	−0.901485	−0.450743	−	0.892654i	$-0.648841\pi$
$937$	−27.5949	−0.901485	−0.450743	+	0.892654i	$0.648841\pi$
$938$	−2.41908	−0.0789859
$939$	−21.8703	−0.713709
$940$	−6.91067	−0.225401
$941$	49.9818	1.62936	0.814680	−	0.579911i	$-0.196913\pi$
$941$	49.9818	1.62936	0.814680	+	0.579911i	$0.196913\pi$
$942$	−6.25080	−0.203662
$943$	8.20901	0.267322
$944$	−10.8887	−0.354396
$945$	−2.16036	−0.0702766
$946$	3.06611	0.0996878
$947$	−34.9318	−1.13513	−0.567566	−	0.823328i	$-0.692115\pi$
$947$	−34.9318	−1.13513	−0.567566	+	0.823328i	$0.692115\pi$
$948$	1.75182	0.0568965
$949$	−61.2356	−1.98779
$950$	12.9130	0.418952
$951$	−18.8204	−0.610293
$952$	−1.41375	−0.0458198
$953$	10.4551	0.338673	0.169336	−	0.985558i	$-0.445838\pi$
$953$	10.4551	0.338673	0.169336	+	0.985558i	$0.445838\pi$
$954$	4.70266	0.152254
$955$	4.60743	0.149093
$956$	2.84024	0.0918598
$957$	13.8812	0.448716
$958$	18.9803	0.613224
$959$	11.6748	0.376997
$960$	−7.55261	−0.243760
$961$	66.3868	2.14151
$962$	−2.61940	−0.0844528
$963$	12.6768	0.408503
$964$	−9.92373	−0.319622
$965$	30.0564	0.967551
$966$	−2.48072	−0.0798158
$967$	−2.18023	−0.0701116	−0.0350558	−	0.999385i	$-0.511161\pi$
$967$	−2.18023	−0.0701116	−0.0350558	+	0.999385i	$0.511161\pi$
$968$	−2.65983	−0.0854903
$969$	−8.20898	−0.263710
$970$	0.713128	0.0228971
$971$	10.6232	0.340914	0.170457	−	0.985365i	$-0.445476\pi$
$971$	10.6232	0.340914	0.170457	+	0.985365i	$0.445476\pi$
$972$	−1.75182	−0.0561897
$973$	16.3179	0.523129
$974$	14.6751	0.470222
$975$	15.9178	0.509777
$976$	31.5738	1.01065
$977$	28.9126	0.924996	0.462498	−	0.886620i	$-0.346953\pi$
$977$	28.9126	0.924996	0.462498	+	0.886620i	$0.346953\pi$
$978$	6.85567	0.219220
$979$	−39.0870	−1.24923
$980$	32.1616	1.02736
$981$	−4.59018	−0.146553
$982$	1.31454	0.0419488
$983$	33.8387	1.07929	0.539644	−	0.841894i	$-0.318559\pi$
$983$	33.8387	1.07929	0.539644	+	0.841894i	$0.318559\pi$
$984$	−2.33060	−0.0742968
$985$	−65.2198	−2.07808
$986$	2.23459	0.0711639
$987$	−1.04471	−0.0332535
$988$	72.4949	2.30637
$989$	−13.0930	−0.416334
$990$	4.40328	0.139945
$991$	39.2996	1.24839	0.624196	−	0.781268i	$-0.285427\pi$
$991$	39.2996	1.24839	0.624196	+	0.781268i	$0.285427\pi$
$992$	49.5368	1.57279
$993$	5.16459	0.163893
$994$	4.11396	0.130487
$995$	−29.9905	−0.950762
$996$	−18.4238	−0.583780
$997$	−54.7310	−1.73335	−0.866674	−	0.498874i	$-0.833747\pi$
$997$	−54.7310	−1.73335	−0.866674	+	0.498874i	$0.833747\pi$
$998$	−6.43284	−0.203628
$999$	1.04301	0.0329995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.10	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.10	✓	18	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)

\(f(q)\)	\(=\)	\(q-0.498176 q^{2} +1.00000 q^{3} -1.75182 q^{4} +2.85615 q^{5} -0.498176 q^{6} -0.756391 q^{7} +1.86907 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.498176 q^{2} +1.00000 q^{3} -1.75182 q^{4} +2.85615 q^{5} -0.498176 q^{6} -0.756391 q^{7} +1.86907 q^{8} +1.00000 q^{9} -1.42286 q^{10} -3.09466 q^{11} -1.75182 q^{12} +5.04114 q^{13} +0.376816 q^{14} +2.85615 q^{15} +2.57252 q^{16} +1.00000 q^{17} -0.498176 q^{18} -8.20898 q^{19} -5.00346 q^{20} -0.756391 q^{21} +1.54169 q^{22} -6.58337 q^{23} +1.86907 q^{24} +3.15758 q^{25} -2.51137 q^{26} +1.00000 q^{27} +1.32506 q^{28} -4.48554 q^{29} -1.42286 q^{30} -9.86847 q^{31} -5.01970 q^{32} -3.09466 q^{33} -0.498176 q^{34} -2.16036 q^{35} -1.75182 q^{36} +1.04301 q^{37} +4.08952 q^{38} +5.04114 q^{39} +5.33833 q^{40} -1.24693 q^{41} +0.376816 q^{42} +1.98880 q^{43} +5.42129 q^{44} +2.85615 q^{45} +3.27968 q^{46} +1.38118 q^{47} +2.57252 q^{48} -6.42787 q^{49} -1.57303 q^{50} +1.00000 q^{51} -8.83117 q^{52} -9.43976 q^{53} -0.498176 q^{54} -8.83880 q^{55} -1.41375 q^{56} -8.20898 q^{57} +2.23459 q^{58} -4.23269 q^{59} -5.00346 q^{60} +12.2735 q^{61} +4.91624 q^{62} -0.756391 q^{63} -2.64434 q^{64} +14.3982 q^{65} +1.54169 q^{66} -6.41981 q^{67} -1.75182 q^{68} -6.58337 q^{69} +1.07624 q^{70} +10.9177 q^{71} +1.86907 q^{72} -12.1472 q^{73} -0.519604 q^{74} +3.15758 q^{75} +14.3807 q^{76} +2.34077 q^{77} -2.51137 q^{78} -1.00000 q^{79} +7.34748 q^{80} +1.00000 q^{81} +0.621192 q^{82} +10.5169 q^{83} +1.32506 q^{84} +2.85615 q^{85} -0.990774 q^{86} -4.48554 q^{87} -5.78413 q^{88} +12.6305 q^{89} -1.42286 q^{90} -3.81307 q^{91} +11.5329 q^{92} -9.86847 q^{93} -0.688070 q^{94} -23.4460 q^{95} -5.01970 q^{96} -0.501191 q^{97} +3.20221 q^{98} -3.09466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

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