LMFDB - Embedded newform 8038.2.a.d.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8038,2,Mod(1,8038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8038, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8038 = 2 \cdot 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8038.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1837531447$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.67211 q^{3} +1.00000 q^{4} +1.54258 q^{5} -2.67211 q^{6} +1.53058 q^{7} +1.00000 q^{8} +4.14019 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.67211 q^{3} +1.00000 q^{4} +1.54258 q^{5} -2.67211 q^{6} +1.53058 q^{7} +1.00000 q^{8} +4.14019 q^{9} +1.54258 q^{10} -0.242994 q^{11} -2.67211 q^{12} +2.26336 q^{13} +1.53058 q^{14} -4.12195 q^{15} +1.00000 q^{16} -1.48447 q^{17} +4.14019 q^{18} +4.72739 q^{19} +1.54258 q^{20} -4.08988 q^{21} -0.242994 q^{22} -5.72536 q^{23} -2.67211 q^{24} -2.62045 q^{25} +2.26336 q^{26} -3.04673 q^{27} +1.53058 q^{28} +7.61807 q^{29} -4.12195 q^{30} +7.13459 q^{31} +1.00000 q^{32} +0.649308 q^{33} -1.48447 q^{34} +2.36104 q^{35} +4.14019 q^{36} -0.190629 q^{37} +4.72739 q^{38} -6.04795 q^{39} +1.54258 q^{40} -0.786097 q^{41} -4.08988 q^{42} +6.26489 q^{43} -0.242994 q^{44} +6.38658 q^{45} -5.72536 q^{46} -1.31794 q^{47} -2.67211 q^{48} -4.65733 q^{49} -2.62045 q^{50} +3.96666 q^{51} +2.26336 q^{52} -3.84781 q^{53} -3.04673 q^{54} -0.374838 q^{55} +1.53058 q^{56} -12.6321 q^{57} +7.61807 q^{58} -7.45997 q^{59} -4.12195 q^{60} +2.26563 q^{61} +7.13459 q^{62} +6.33690 q^{63} +1.00000 q^{64} +3.49141 q^{65} +0.649308 q^{66} +16.1002 q^{67} -1.48447 q^{68} +15.2988 q^{69} +2.36104 q^{70} +5.96809 q^{71} +4.14019 q^{72} -2.58683 q^{73} -0.190629 q^{74} +7.00213 q^{75} +4.72739 q^{76} -0.371922 q^{77} -6.04795 q^{78} +1.81227 q^{79} +1.54258 q^{80} -4.27938 q^{81} -0.786097 q^{82} +16.5019 q^{83} -4.08988 q^{84} -2.28991 q^{85} +6.26489 q^{86} -20.3564 q^{87} -0.242994 q^{88} +10.2315 q^{89} +6.38658 q^{90} +3.46425 q^{91} -5.72536 q^{92} -19.0644 q^{93} -1.31794 q^{94} +7.29238 q^{95} -2.67211 q^{96} +3.87448 q^{97} -4.65733 q^{98} -1.00604 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9}+O(q^{10}) $ 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9} + 28 q^{10} + 37 q^{11} + 31 q^{12} + 20 q^{13} + 29 q^{14} + 30 q^{15} + 92 q^{16} + 52 q^{17} + 113 q^{18} + 61 q^{19} + 28 q^{20} + 5 q^{21} + 37 q^{22} + 71 q^{23} + 31 q^{24} + 118 q^{25} + 20 q^{26} + 112 q^{27} + 29 q^{28} + 30 q^{29} + 30 q^{30} + 89 q^{31} + 92 q^{32} + 52 q^{33} + 52 q^{34} + 58 q^{35} + 113 q^{36} + 15 q^{37} + 61 q^{38} + 43 q^{39} + 28 q^{40} + 75 q^{41} + 5 q^{42} + 46 q^{43} + 37 q^{44} + 63 q^{45} + 71 q^{46} + 92 q^{47} + 31 q^{48} + 131 q^{49} + 118 q^{50} + 45 q^{51} + 20 q^{52} + 72 q^{53} + 112 q^{54} + 86 q^{55} + 29 q^{56} + 44 q^{57} + 30 q^{58} + 95 q^{59} + 30 q^{60} - 4 q^{61} + 89 q^{62} + 67 q^{63} + 92 q^{64} + 55 q^{65} + 52 q^{66} + 40 q^{67} + 52 q^{68} + 25 q^{69} + 58 q^{70} + 84 q^{71} + 113 q^{72} + 87 q^{73} + 15 q^{74} + 132 q^{75} + 61 q^{76} + 96 q^{77} + 43 q^{78} + 68 q^{79} + 28 q^{80} + 156 q^{81} + 75 q^{82} + 120 q^{83} + 5 q^{84} - 14 q^{85} + 46 q^{86} + 73 q^{87} + 37 q^{88} + 86 q^{89} + 63 q^{90} + 93 q^{91} + 71 q^{92} + 29 q^{93} + 92 q^{94} + 67 q^{95} + 31 q^{96} + 65 q^{97} + 131 q^{98} + 94 q^{99}+O(q^{100}) \) 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9 + 28 * q^10 + 37 * q^11 + 31 * q^12 + 20 * q^13 + 29 * q^14 + 30 * q^15 + 92 * q^16 + 52 * q^17 + 113 * q^18 + 61 * q^19 + 28 * q^20 + 5 * q^21 + 37 * q^22 + 71 * q^23 + 31 * q^24 + 118 * q^25 + 20 * q^26 + 112 * q^27 + 29 * q^28 + 30 * q^29 + 30 * q^30 + 89 * q^31 + 92 * q^32 + 52 * q^33 + 52 * q^34 + 58 * q^35 + 113 * q^36 + 15 * q^37 + 61 * q^38 + 43 * q^39 + 28 * q^40 + 75 * q^41 + 5 * q^42 + 46 * q^43 + 37 * q^44 + 63 * q^45 + 71 * q^46 + 92 * q^47 + 31 * q^48 + 131 * q^49 + 118 * q^50 + 45 * q^51 + 20 * q^52 + 72 * q^53 + 112 * q^54 + 86 * q^55 + 29 * q^56 + 44 * q^57 + 30 * q^58 + 95 * q^59 + 30 * q^60 - 4 * q^61 + 89 * q^62 + 67 * q^63 + 92 * q^64 + 55 * q^65 + 52 * q^66 + 40 * q^67 + 52 * q^68 + 25 * q^69 + 58 * q^70 + 84 * q^71 + 113 * q^72 + 87 * q^73 + 15 * q^74 + 132 * q^75 + 61 * q^76 + 96 * q^77 + 43 * q^78 + 68 * q^79 + 28 * q^80 + 156 * q^81 + 75 * q^82 + 120 * q^83 + 5 * q^84 - 14 * q^85 + 46 * q^86 + 73 * q^87 + 37 * q^88 + 86 * q^89 + 63 * q^90 + 93 * q^91 + 71 * q^92 + 29 * q^93 + 92 * q^94 + 67 * q^95 + 31 * q^96 + 65 * q^97 + 131 * q^98 + 94 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.67211	−1.54275	−0.771373	−	0.636383i	$-0.780430\pi$
$3$	−2.67211	−1.54275	−0.771373	+	0.636383i	$0.780430\pi$
$4$	1.00000	0.500000
$5$	1.54258	0.689863	0.344931	−	0.938628i	$-0.387902\pi$
$5$	1.54258	0.689863	0.344931	+	0.938628i	$0.387902\pi$
$6$	−2.67211	−1.09089
$7$	1.53058	0.578505	0.289252	−	0.957253i	$-0.406593\pi$
$7$	1.53058	0.578505	0.289252	+	0.957253i	$0.406593\pi$
$8$	1.00000	0.353553
$9$	4.14019	1.38006
$10$	1.54258	0.487807
$11$	−0.242994	−0.0732655	−0.0366328	−	0.999329i	$-0.511663\pi$
$11$	−0.242994	−0.0732655	−0.0366328	+	0.999329i	$0.511663\pi$
$12$	−2.67211	−0.771373
$13$	2.26336	0.627742	0.313871	−	0.949466i	$-0.398374\pi$
$13$	2.26336	0.627742	0.313871	+	0.949466i	$0.398374\pi$
$14$	1.53058	0.409065
$15$	−4.12195	−1.06428
$16$	1.00000	0.250000
$17$	−1.48447	−0.360036	−0.180018	−	0.983663i	$-0.557616\pi$
$17$	−1.48447	−0.360036	−0.180018	+	0.983663i	$0.557616\pi$
$18$	4.14019	0.975853
$19$	4.72739	1.08454	0.542269	−	0.840205i	$-0.317565\pi$
$19$	4.72739	1.08454	0.542269	+	0.840205i	$0.317565\pi$
$20$	1.54258	0.344931
$21$	−4.08988	−0.892486
$22$	−0.242994	−0.0518065
$23$	−5.72536	−1.19382	−0.596910	−	0.802308i	$-0.703605\pi$
$23$	−5.72536	−1.19382	−0.596910	+	0.802308i	$0.703605\pi$
$24$	−2.67211	−0.545443
$25$	−2.62045	−0.524089
$26$	2.26336	0.443881
$27$	−3.04673	−0.586343
$28$	1.53058	0.289252
$29$	7.61807	1.41464	0.707320	−	0.706893i	$-0.249904\pi$
$29$	7.61807	1.41464	0.707320	+	0.706893i	$0.249904\pi$
$30$	−4.12195	−0.752562
$31$	7.13459	1.28141	0.640705	−	0.767787i	$-0.278642\pi$
$31$	7.13459	1.28141	0.640705	+	0.767787i	$0.278642\pi$
$32$	1.00000	0.176777
$33$	0.649308	0.113030
$34$	−1.48447	−0.254584
$35$	2.36104	0.399089
$36$	4.14019	0.690032
$37$	−0.190629	−0.0313391	−0.0156696	−	0.999877i	$-0.504988\pi$
$37$	−0.190629	−0.0313391	−0.0156696	+	0.999877i	$0.504988\pi$
$38$	4.72739	0.766884
$39$	−6.04795	−0.968447
$40$	1.54258	0.243903
$41$	−0.786097	−0.122768	−0.0613839	−	0.998114i	$-0.519551\pi$
$41$	−0.786097	−0.122768	−0.0613839	+	0.998114i	$0.519551\pi$
$42$	−4.08988	−0.631083
$43$	6.26489	0.955387	0.477693	−	0.878527i	$-0.341473\pi$
$43$	6.26489	0.955387	0.477693	+	0.878527i	$0.341473\pi$
$44$	−0.242994	−0.0366328
$45$	6.38658	0.952055
$46$	−5.72536	−0.844158
$47$	−1.31794	−0.192241	−0.0961207	−	0.995370i	$-0.530643\pi$
$47$	−1.31794	−0.192241	−0.0961207	+	0.995370i	$0.530643\pi$
$48$	−2.67211	−0.385686
$49$	−4.65733	−0.665332
$50$	−2.62045	−0.370587
$51$	3.96666	0.555444
$52$	2.26336	0.313871
$53$	−3.84781	−0.528538	−0.264269	−	0.964449i	$-0.585131\pi$
$53$	−3.84781	−0.528538	−0.264269	+	0.964449i	$0.585131\pi$
$54$	−3.04673	−0.414607
$55$	−0.374838	−0.0505432
$56$	1.53058	0.204532
$57$	−12.6321	−1.67317
$58$	7.61807	1.00030
$59$	−7.45997	−0.971206	−0.485603	−	0.874179i	$-0.661400\pi$
$59$	−7.45997	−0.971206	−0.485603	+	0.874179i	$0.661400\pi$
$60$	−4.12195	−0.532142
$61$	2.26563	0.290085	0.145042	−	0.989425i	$-0.453668\pi$
$61$	2.26563	0.290085	0.145042	+	0.989425i	$0.453668\pi$
$62$	7.13459	0.906094
$63$	6.33690	0.798374
$64$	1.00000	0.125000
$65$	3.49141	0.433056
$66$	0.649308	0.0799243
$67$	16.1002	1.96695	0.983476	−	0.181038i	$-0.0579458\pi$
$67$	16.1002	1.96695	0.983476	+	0.181038i	$0.0579458\pi$
$68$	−1.48447	−0.180018
$69$	15.2988	1.84176
$70$	2.36104	0.282199
$71$	5.96809	0.708282	0.354141	−	0.935192i	$-0.384773\pi$
$71$	5.96809	0.708282	0.354141	+	0.935192i	$0.384773\pi$
$72$	4.14019	0.487927
$73$	−2.58683	−0.302766	−0.151383	−	0.988475i	$-0.548373\pi$
$73$	−2.58683	−0.302766	−0.151383	+	0.988475i	$0.548373\pi$
$74$	−0.190629	−0.0221601
$75$	7.00213	0.808536
$76$	4.72739	0.542269
$77$	−0.371922	−0.0423844
$78$	−6.04795	−0.684795
$79$	1.81227	0.203897	0.101948	−	0.994790i	$-0.467492\pi$
$79$	1.81227	0.203897	0.101948	+	0.994790i	$0.467492\pi$
$80$	1.54258	0.172466
$81$	−4.27938	−0.475486
$82$	−0.786097	−0.0868099
$83$	16.5019	1.81132	0.905658	−	0.424009i	$-0.139377\pi$
$83$	16.5019	1.81132	0.905658	+	0.424009i	$0.139377\pi$
$84$	−4.08988	−0.446243
$85$	−2.28991	−0.248375
$86$	6.26489	0.675560
$87$	−20.3564	−2.18243
$88$	−0.242994	−0.0259033
$89$	10.2315	1.08453	0.542266	−	0.840207i	$-0.317567\pi$
$89$	10.2315	1.08453	0.542266	+	0.840207i	$0.317567\pi$
$90$	6.38658	0.673205
$91$	3.46425	0.363152
$92$	−5.72536	−0.596910
$93$	−19.0644	−1.97689
$94$	−1.31794	−0.135935
$95$	7.29238	0.748182
$96$	−2.67211	−0.272722
$97$	3.87448	0.393394	0.196697	−	0.980464i	$-0.436979\pi$
$97$	3.87448	0.393394	0.196697	+	0.980464i	$0.436979\pi$
$98$	−4.65733	−0.470461
$99$	−1.00604	−0.101111
$100$	−2.62045	−0.262045
$101$	−3.08877	−0.307345	−0.153672	−	0.988122i	$-0.549110\pi$
$101$	−3.08877	−0.307345	−0.153672	+	0.988122i	$0.549110\pi$
$102$	3.96666	0.392758
$103$	−16.1878	−1.59503	−0.797515	−	0.603299i	$-0.793852\pi$
$103$	−16.1878	−1.59503	−0.797515	+	0.603299i	$0.793852\pi$
$104$	2.26336	0.221940
$105$	−6.30897	−0.615693
$106$	−3.84781	−0.373733
$107$	1.97161	0.190603	0.0953016	−	0.995448i	$-0.469618\pi$
$107$	1.97161	0.190603	0.0953016	+	0.995448i	$0.469618\pi$
$108$	−3.04673	−0.293172
$109$	−16.5660	−1.58674	−0.793368	−	0.608742i	$-0.791674\pi$
$109$	−16.5660	−1.58674	−0.793368	+	0.608742i	$0.791674\pi$
$110$	−0.374838	−0.0357394
$111$	0.509381	0.0483483
$112$	1.53058	0.144626
$113$	10.8064	1.01658	0.508289	−	0.861187i	$-0.330278\pi$
$113$	10.8064	1.01658	0.508289	+	0.861187i	$0.330278\pi$
$114$	−12.6321	−1.18311
$115$	−8.83182	−0.823572
$116$	7.61807	0.707320
$117$	9.37074	0.866325
$118$	−7.45997	−0.686746
$119$	−2.27209	−0.208282
$120$	−4.12195	−0.376281
$121$	−10.9410	−0.994632
$122$	2.26563	0.205121
$123$	2.10054	0.189399
$124$	7.13459	0.640705
$125$	−11.7552	−1.05141
$126$	6.33690	0.564536
$127$	−10.3670	−0.919921	−0.459960	−	0.887939i	$-0.652136\pi$
$127$	−10.3670	−0.919921	−0.459960	+	0.887939i	$0.652136\pi$
$128$	1.00000	0.0883883
$129$	−16.7405	−1.47392
$130$	3.49141	0.306217
$131$	−2.35300	−0.205583	−0.102791	−	0.994703i	$-0.532777\pi$
$131$	−2.35300	−0.205583	−0.102791	+	0.994703i	$0.532777\pi$
$132$	0.649308	0.0565150
$133$	7.23565	0.627410
$134$	16.1002	1.39085
$135$	−4.69982	−0.404496
$136$	−1.48447	−0.127292
$137$	11.5805	0.989391	0.494696	−	0.869066i	$-0.335280\pi$
$137$	11.5805	0.989391	0.494696	+	0.869066i	$0.335280\pi$
$138$	15.2988	1.30232
$139$	1.66475	0.141202	0.0706011	−	0.997505i	$-0.477508\pi$
$139$	1.66475	0.141202	0.0706011	+	0.997505i	$0.477508\pi$
$140$	2.36104	0.199544
$141$	3.52169	0.296580
$142$	5.96809	0.500831
$143$	−0.549983	−0.0459919
$144$	4.14019	0.345016
$145$	11.7515	0.975908
$146$	−2.58683	−0.214088
$147$	12.4449	1.02644
$148$	−0.190629	−0.0156696
$149$	16.1436	1.32253	0.661267	−	0.750151i	$-0.270019\pi$
$149$	16.1436	1.32253	0.661267	+	0.750151i	$0.270019\pi$
$150$	7.00213	0.571721
$151$	−22.7807	−1.85387	−0.926935	−	0.375222i	$-0.877567\pi$
$151$	−22.7807	−1.85387	−0.926935	+	0.375222i	$0.877567\pi$
$152$	4.72739	0.383442
$153$	−6.14597	−0.496873
$154$	−0.371922	−0.0299703
$155$	11.0057	0.883997
$156$	−6.04795	−0.484223
$157$	2.41265	0.192550	0.0962752	−	0.995355i	$-0.469307\pi$
$157$	2.41265	0.192550	0.0962752	+	0.995355i	$0.469307\pi$
$158$	1.81227	0.144177
$159$	10.2818	0.815400
$160$	1.54258	0.121952
$161$	−8.76311	−0.690630
$162$	−4.27938	−0.336220
$163$	12.4319	0.973743	0.486872	−	0.873474i	$-0.338138\pi$
$163$	12.4319	0.973743	0.486872	+	0.873474i	$0.338138\pi$
$164$	−0.786097	−0.0613839
$165$	1.00161	0.0779753
$166$	16.5019	1.28079
$167$	−6.10802	−0.472653	−0.236326	−	0.971674i	$-0.575943\pi$
$167$	−6.10802	−0.472653	−0.236326	+	0.971674i	$0.575943\pi$
$168$	−4.08988	−0.315541
$169$	−7.87722	−0.605940
$170$	−2.28991	−0.175628
$171$	19.5723	1.49673
$172$	6.26489	0.477693
$173$	−5.94113	−0.451696	−0.225848	−	0.974163i	$-0.572515\pi$
$173$	−5.94113	−0.451696	−0.225848	+	0.974163i	$0.572515\pi$
$174$	−20.3564	−1.54321
$175$	−4.01080	−0.303188
$176$	−0.242994	−0.0183164
$177$	19.9339	1.49832
$178$	10.2315	0.766880
$179$	17.5073	1.30855	0.654277	−	0.756255i	$-0.272973\pi$
$179$	17.5073	1.30855	0.654277	+	0.756255i	$0.272973\pi$
$180$	6.38658	0.476028
$181$	−14.2484	−1.05907	−0.529536	−	0.848287i	$-0.677634\pi$
$181$	−14.2484	−1.05907	−0.529536	+	0.848287i	$0.677634\pi$
$182$	3.46425	0.256787
$183$	−6.05403	−0.447527
$184$	−5.72536	−0.422079
$185$	−0.294060	−0.0216197
$186$	−19.0644	−1.39787
$187$	0.360717	0.0263782
$188$	−1.31794	−0.0961207
$189$	−4.66326	−0.339202
$190$	7.29238	0.529045
$191$	21.1591	1.53102	0.765508	−	0.643427i	$-0.222488\pi$
$191$	21.1591	1.53102	0.765508	+	0.643427i	$0.222488\pi$
$192$	−2.67211	−0.192843
$193$	23.0206	1.65706	0.828531	−	0.559943i	$-0.189177\pi$
$193$	23.0206	1.65706	0.828531	+	0.559943i	$0.189177\pi$
$194$	3.87448	0.278171
$195$	−9.32945	−0.668096
$196$	−4.65733	−0.332666
$197$	−4.98388	−0.355087	−0.177543	−	0.984113i	$-0.556815\pi$
$197$	−4.98388	−0.355087	−0.177543	+	0.984113i	$0.556815\pi$
$198$	−1.00604	−0.0714964
$199$	−9.49186	−0.672860	−0.336430	−	0.941708i	$-0.609220\pi$
$199$	−9.49186	−0.672860	−0.336430	+	0.941708i	$0.609220\pi$
$200$	−2.62045	−0.185293
$201$	−43.0216	−3.03451
$202$	−3.08877	−0.217325
$203$	11.6601	0.818376
$204$	3.96666	0.277722
$205$	−1.21262	−0.0846929
$206$	−16.1878	−1.12786
$207$	−23.7041	−1.64755
$208$	2.26336	0.156936
$209$	−1.14873	−0.0794592
$210$	−6.30897	−0.435361
$211$	5.28526	0.363852	0.181926	−	0.983312i	$-0.441767\pi$
$211$	5.28526	0.363852	0.181926	+	0.983312i	$0.441767\pi$
$212$	−3.84781	−0.264269
$213$	−15.9474	−1.09270
$214$	1.97161	0.134777
$215$	9.66409	0.659086
$216$	−3.04673	−0.207304
$217$	10.9201	0.741302
$218$	−16.5660	−1.12199
$219$	6.91231	0.467091
$220$	−0.374838	−0.0252716
$221$	−3.35988	−0.226010
$222$	0.509381	0.0341874
$223$	5.79143	0.387823	0.193911	−	0.981019i	$-0.437883\pi$
$223$	5.79143	0.387823	0.193911	+	0.981019i	$0.437883\pi$
$224$	1.53058	0.102266
$225$	−10.8492	−0.723277
$226$	10.8064	0.718829
$227$	−0.143720	−0.00953905	−0.00476952	−	0.999989i	$-0.501518\pi$
$227$	−0.143720	−0.00953905	−0.00476952	+	0.999989i	$0.501518\pi$
$228$	−12.6321	−0.836583
$229$	−20.0353	−1.32397	−0.661986	−	0.749516i	$-0.730286\pi$
$229$	−20.0353	−1.32397	−0.661986	+	0.749516i	$0.730286\pi$
$230$	−8.83182	−0.582353
$231$	0.993818	0.0653884
$232$	7.61807	0.500151
$233$	18.4254	1.20709	0.603546	−	0.797329i	$-0.293754\pi$
$233$	18.4254	1.20709	0.603546	+	0.797329i	$0.293754\pi$
$234$	9.37074	0.612584
$235$	−2.03303	−0.132620
$236$	−7.45997	−0.485603
$237$	−4.84261	−0.314561
$238$	−2.27209	−0.147278
$239$	17.9629	1.16192	0.580961	−	0.813931i	$-0.302677\pi$
$239$	17.9629	1.16192	0.580961	+	0.813931i	$0.302677\pi$
$240$	−4.12195	−0.266071
$241$	−22.0437	−1.41996	−0.709981	−	0.704221i	$-0.751297\pi$
$241$	−22.0437	−1.41996	−0.709981	+	0.704221i	$0.751297\pi$
$242$	−10.9410	−0.703311
$243$	20.5752	1.31990
$244$	2.26563	0.145042
$245$	−7.18430	−0.458988
$246$	2.10054	0.133926
$247$	10.6998	0.680810
$248$	7.13459	0.453047
$249$	−44.0949	−2.79440
$250$	−11.7552	−0.743461
$251$	2.84013	0.179268	0.0896338	−	0.995975i	$-0.471430\pi$
$251$	2.84013	0.179268	0.0896338	+	0.995975i	$0.471430\pi$
$252$	6.33690	0.399187
$253$	1.39123	0.0874658
$254$	−10.3670	−0.650482
$255$	6.11889	0.383180
$256$	1.00000	0.0625000
$257$	−15.5053	−0.967191	−0.483596	−	0.875291i	$-0.660669\pi$
$257$	−15.5053	−0.967191	−0.483596	+	0.875291i	$0.660669\pi$
$258$	−16.7405	−1.04222
$259$	−0.291772	−0.0181298
$260$	3.49141	0.216528
$261$	31.5403	1.95229
$262$	−2.35300	−0.145369
$263$	16.8989	1.04203	0.521017	−	0.853547i	$-0.325553\pi$
$263$	16.8989	1.04203	0.521017	+	0.853547i	$0.325553\pi$
$264$	0.649308	0.0399622
$265$	−5.93556	−0.364619
$266$	7.23565	0.443646
$267$	−27.3396	−1.67316
$268$	16.1002	0.983476
$269$	−10.7604	−0.656073	−0.328037	−	0.944665i	$-0.606387\pi$
$269$	−10.7604	−0.656073	−0.328037	+	0.944665i	$0.606387\pi$
$270$	−4.69982	−0.286022
$271$	−2.92423	−0.177634	−0.0888172	−	0.996048i	$-0.528309\pi$
$271$	−2.92423	−0.177634	−0.0888172	+	0.996048i	$0.528309\pi$
$272$	−1.48447	−0.0900089
$273$	−9.25687	−0.560251
$274$	11.5805	0.699605
$275$	0.636753	0.0383977
$276$	15.2988	0.920880
$277$	16.7942	1.00907	0.504533	−	0.863392i	$-0.331665\pi$
$277$	16.7942	1.00907	0.504533	+	0.863392i	$0.331665\pi$
$278$	1.66475	0.0998450
$279$	29.5386	1.76843
$280$	2.36104	0.141099
$281$	−7.84228	−0.467831	−0.233916	−	0.972257i	$-0.575154\pi$
$281$	−7.84228	−0.467831	−0.233916	+	0.972257i	$0.575154\pi$
$282$	3.52169	0.209714
$283$	22.5405	1.33990	0.669948	−	0.742408i	$-0.266316\pi$
$283$	22.5405	1.33990	0.669948	+	0.742408i	$0.266316\pi$
$284$	5.96809	0.354141
$285$	−19.4861	−1.15425
$286$	−0.549983	−0.0325212
$287$	−1.20318	−0.0710217
$288$	4.14019	0.243963
$289$	−14.7964	−0.870374
$290$	11.7515	0.690071
$291$	−10.3531	−0.606907
$292$	−2.58683	−0.151383
$293$	31.0174	1.81206	0.906028	−	0.423218i	$-0.139100\pi$
$293$	31.0174	1.81206	0.906028	+	0.423218i	$0.139100\pi$
$294$	12.4449	0.725802
$295$	−11.5076	−0.669999
$296$	−0.190629	−0.0110801
$297$	0.740337	0.0429587
$298$	16.1436	0.935172
$299$	−12.9585	−0.749411
$300$	7.00213	0.404268
$301$	9.58891	0.552696
$302$	−22.7807	−1.31088
$303$	8.25356	0.474154
$304$	4.72739	0.271134
$305$	3.49492	0.200119
$306$	−6.14597	−0.351342
$307$	14.6953	0.838704	0.419352	−	0.907824i	$-0.362257\pi$
$307$	14.6953	0.838704	0.419352	+	0.907824i	$0.362257\pi$
$308$	−0.371922	−0.0211922
$309$	43.2556	2.46073
$310$	11.0057	0.625080
$311$	13.2704	0.752495	0.376248	−	0.926519i	$-0.377214\pi$
$311$	13.2704	0.752495	0.376248	+	0.926519i	$0.377214\pi$
$312$	−6.04795	−0.342398
$313$	11.7200	0.662453	0.331226	−	0.943551i	$-0.392538\pi$
$313$	11.7200	0.662453	0.331226	+	0.943551i	$0.392538\pi$
$314$	2.41265	0.136154
$315$	9.77517	0.550769
$316$	1.81227	0.101948
$317$	−21.0946	−1.18479	−0.592394	−	0.805648i	$-0.701817\pi$
$317$	−21.0946	−1.18479	−0.592394	+	0.805648i	$0.701817\pi$
$318$	10.2818	0.576575
$319$	−1.85115	−0.103644
$320$	1.54258	0.0862329
$321$	−5.26838	−0.294052
$322$	−8.76311	−0.488349
$323$	−7.01765	−0.390472
$324$	−4.27938	−0.237743
$325$	−5.93100	−0.328993
$326$	12.4319	0.688540
$327$	44.2663	2.44793
$328$	−0.786097	−0.0434050
$329$	−2.01721	−0.111213
$330$	1.00161	0.0551368
$331$	−7.80058	−0.428759	−0.214379	−	0.976750i	$-0.568773\pi$
$331$	−7.80058	−0.428759	−0.214379	+	0.976750i	$0.568773\pi$
$332$	16.5019	0.905658
$333$	−0.789239	−0.0432500
$334$	−6.10802	−0.334216
$335$	24.8358	1.35693
$336$	−4.08988	−0.223121
$337$	17.4264	0.949277	0.474639	−	0.880181i	$-0.342579\pi$
$337$	17.4264	0.949277	0.474639	+	0.880181i	$0.342579\pi$
$338$	−7.87722	−0.428464
$339$	−28.8758	−1.56832
$340$	−2.28991	−0.124188
$341$	−1.73366	−0.0938832
$342$	19.5723	1.05835
$343$	−17.8425	−0.963403
$344$	6.26489	0.337780
$345$	23.5996	1.27056
$346$	−5.94113	−0.319397
$347$	5.48709	0.294562	0.147281	−	0.989095i	$-0.452948\pi$
$347$	5.48709	0.294562	0.147281	+	0.989095i	$0.452948\pi$
$348$	−20.3564	−1.09122
$349$	12.9415	0.692741	0.346371	−	0.938098i	$-0.387414\pi$
$349$	12.9415	0.692741	0.346371	+	0.938098i	$0.387414\pi$
$350$	−4.01080	−0.214386
$351$	−6.89583	−0.368072
$352$	−0.242994	−0.0129516
$353$	−26.9966	−1.43688	−0.718441	−	0.695588i	$-0.755144\pi$
$353$	−26.9966	−1.43688	−0.718441	+	0.695588i	$0.755144\pi$
$354$	19.9339	1.05947
$355$	9.20625	0.488617
$356$	10.2315	0.542266
$357$	6.07129	0.321327
$358$	17.5073	0.925288
$359$	14.3007	0.754762	0.377381	−	0.926058i	$-0.376825\pi$
$359$	14.3007	0.754762	0.377381	+	0.926058i	$0.376825\pi$
$360$	6.38658	0.336602
$361$	3.34821	0.176221
$362$	−14.2484	−0.748877
$363$	29.2355	1.53446
$364$	3.46425	0.181576
$365$	−3.99040	−0.208867
$366$	−6.05403	−0.316449
$367$	29.0059	1.51410	0.757048	−	0.653359i	$-0.226641\pi$
$367$	29.0059	1.51410	0.757048	+	0.653359i	$0.226641\pi$
$368$	−5.72536	−0.298455
$369$	−3.25460	−0.169427
$370$	−0.294060	−0.0152874
$371$	−5.88939	−0.305762
$372$	−19.0644	−0.988445
$373$	−21.6104	−1.11894	−0.559472	−	0.828849i	$-0.688996\pi$
$373$	−21.6104	−1.11894	−0.559472	+	0.828849i	$0.688996\pi$
$374$	0.360717	0.0186522
$375$	31.4111	1.62206
$376$	−1.31794	−0.0679676
$377$	17.2424	0.888029
$378$	−4.66326	−0.239852
$379$	−18.4146	−0.945894	−0.472947	−	0.881091i	$-0.656810\pi$
$379$	−18.4146	−0.945894	−0.472947	+	0.881091i	$0.656810\pi$
$380$	7.29238	0.374091
$381$	27.7018	1.41920
$382$	21.1591	1.08259
$383$	13.7101	0.700556	0.350278	−	0.936646i	$-0.386087\pi$
$383$	13.7101	0.700556	0.350278	+	0.936646i	$0.386087\pi$
$384$	−2.67211	−0.136361
$385$	−0.573720	−0.0292395
$386$	23.0206	1.17172
$387$	25.9379	1.31850
$388$	3.87448	0.196697
$389$	−9.24988	−0.468988	−0.234494	−	0.972118i	$-0.575343\pi$
$389$	−9.24988	−0.468988	−0.234494	+	0.972118i	$0.575343\pi$
$390$	−9.32945	−0.472415
$391$	8.49910	0.429818
$392$	−4.65733	−0.235230
$393$	6.28749	0.317162
$394$	−4.98388	−0.251084
$395$	2.79558	0.140661
$396$	−1.00604	−0.0505556
$397$	12.0435	0.604447	0.302223	−	0.953237i	$-0.402271\pi$
$397$	12.0435	0.604447	0.302223	+	0.953237i	$0.402271\pi$
$398$	−9.49186	−0.475784
$399$	−19.3345	−0.967934
$400$	−2.62045	−0.131022
$401$	17.7224	0.885014	0.442507	−	0.896765i	$-0.354089\pi$
$401$	17.7224	0.885014	0.442507	+	0.896765i	$0.354089\pi$
$402$	−43.0216	−2.14572
$403$	16.1481	0.804395
$404$	−3.08877	−0.153672
$405$	−6.60128	−0.328020
$406$	11.6601	0.578679
$407$	0.0463216	0.00229608
$408$	3.96666	0.196379
$409$	31.5590	1.56049	0.780246	−	0.625473i	$-0.215094\pi$
$409$	31.5590	1.56049	0.780246	+	0.625473i	$0.215094\pi$
$410$	−1.21262	−0.0598870
$411$	−30.9445	−1.52638
$412$	−16.1878	−0.797515
$413$	−11.4181	−0.561847
$414$	−23.7041	−1.16499
$415$	25.4555	1.24956
$416$	2.26336	0.110970
$417$	−4.44840	−0.217839
$418$	−1.14873	−0.0561861
$419$	−16.1235	−0.787685	−0.393842	−	0.919178i	$-0.628854\pi$
$419$	−16.1235	−0.787685	−0.393842	+	0.919178i	$0.628854\pi$
$420$	−6.30897	−0.307846
$421$	10.0250	0.488590	0.244295	−	0.969701i	$-0.421444\pi$
$421$	10.0250	0.488590	0.244295	+	0.969701i	$0.421444\pi$
$422$	5.28526	0.257282
$423$	−5.45653	−0.265306
$424$	−3.84781	−0.186866
$425$	3.88996	0.188691
$426$	−15.9474	−0.772654
$427$	3.46773	0.167815
$428$	1.97161	0.0953016
$429$	1.46962	0.0709537
$430$	9.66409	0.466044
$431$	16.0663	0.773884	0.386942	−	0.922104i	$-0.373531\pi$
$431$	16.0663	0.773884	0.386942	+	0.922104i	$0.373531\pi$
$432$	−3.04673	−0.146586
$433$	28.1134	1.35105	0.675523	−	0.737339i	$-0.263918\pi$
$433$	28.1134	1.35105	0.675523	+	0.737339i	$0.263918\pi$
$434$	10.9201	0.524179
$435$	−31.4013	−1.50558
$436$	−16.5660	−0.793368
$437$	−27.0660	−1.29474
$438$	6.91231	0.330283
$439$	−9.34301	−0.445918	−0.222959	−	0.974828i	$-0.571572\pi$
$439$	−9.34301	−0.445918	−0.222959	+	0.974828i	$0.571572\pi$
$440$	−0.374838	−0.0178697
$441$	−19.2822	−0.918202
$442$	−3.35988	−0.159813
$443$	5.51180	0.261873	0.130937	−	0.991391i	$-0.458202\pi$
$443$	5.51180	0.261873	0.130937	+	0.991391i	$0.458202\pi$
$444$	0.509381	0.0241742
$445$	15.7828	0.748178
$446$	5.79143	0.274232
$447$	−43.1375	−2.04033
$448$	1.53058	0.0723131
$449$	29.0429	1.37062	0.685311	−	0.728251i	$-0.259666\pi$
$449$	29.0429	1.37062	0.685311	+	0.728251i	$0.259666\pi$
$450$	−10.8492	−0.511434
$451$	0.191017	0.00899465
$452$	10.8064	0.508289
$453$	60.8727	2.86005
$454$	−0.143720	−0.00674512
$455$	5.34388	0.250525
$456$	−12.6321	−0.591553
$457$	−32.0699	−1.50017	−0.750083	−	0.661343i	$-0.769987\pi$
$457$	−32.0699	−1.50017	−0.750083	+	0.661343i	$0.769987\pi$
$458$	−20.0353	−0.936190
$459$	4.52276	0.211104
$460$	−8.83182	−0.411786
$461$	15.1934	0.707627	0.353813	−	0.935316i	$-0.384885\pi$
$461$	15.1934	0.707627	0.353813	+	0.935316i	$0.384885\pi$
$462$	0.993818	0.0462366
$463$	11.7465	0.545906	0.272953	−	0.962027i	$-0.412000\pi$
$463$	11.7465	0.545906	0.272953	+	0.962027i	$0.412000\pi$
$464$	7.61807	0.353660
$465$	−29.4084	−1.36378
$466$	18.4254	0.853542
$467$	39.0470	1.80688	0.903439	−	0.428717i	$-0.141034\pi$
$467$	39.0470	1.80688	0.903439	+	0.428717i	$0.141034\pi$
$468$	9.37074	0.433162
$469$	24.6426	1.13789
$470$	−2.03303	−0.0937767
$471$	−6.44687	−0.297056
$472$	−7.45997	−0.343373
$473$	−1.52233	−0.0699969
$474$	−4.84261	−0.222428
$475$	−12.3879	−0.568394
$476$	−2.27209	−0.104141
$477$	−15.9307	−0.729417
$478$	17.9629	0.821604
$479$	11.0464	0.504725	0.252362	−	0.967633i	$-0.418793\pi$
$479$	11.0464	0.504725	0.252362	+	0.967633i	$0.418793\pi$
$480$	−4.12195	−0.188140
$481$	−0.431460	−0.0196729
$482$	−22.0437	−1.00407
$483$	23.4160	1.06547
$484$	−10.9410	−0.497316
$485$	5.97670	0.271388
$486$	20.5752	0.933309
$487$	−33.7729	−1.53039	−0.765197	−	0.643796i	$-0.777358\pi$
$487$	−33.7729	−1.53039	−0.765197	+	0.643796i	$0.777358\pi$
$488$	2.26563	0.102560
$489$	−33.2195	−1.50224
$490$	−7.18430	−0.324554
$491$	28.0685	1.26671	0.633356	−	0.773861i	$-0.281677\pi$
$491$	28.0685	1.26671	0.633356	+	0.773861i	$0.281677\pi$
$492$	2.10054	0.0946997
$493$	−11.3088	−0.509321
$494$	10.6998	0.481405
$495$	−1.55190	−0.0697528
$496$	7.13459	0.320352
$497$	9.13463	0.409744
$498$	−44.0949	−1.97594
$499$	3.28146	0.146898	0.0734491	−	0.997299i	$-0.476599\pi$
$499$	3.28146	0.146898	0.0734491	+	0.997299i	$0.476599\pi$
$500$	−11.7552	−0.525706
$501$	16.3213	0.729183
$502$	2.84013	0.126761
$503$	25.2809	1.12722	0.563609	−	0.826042i	$-0.309413\pi$
$503$	25.2809	1.12722	0.563609	+	0.826042i	$0.309413\pi$
$504$	6.33690	0.282268
$505$	−4.76468	−0.212026
$506$	1.39123	0.0618477
$507$	21.0488	0.934811
$508$	−10.3670	−0.459960
$509$	−19.3461	−0.857501	−0.428750	−	0.903423i	$-0.641046\pi$
$509$	−19.3461	−0.857501	−0.428750	+	0.903423i	$0.641046\pi$
$510$	6.11889	0.270949
$511$	−3.95935	−0.175151
$512$	1.00000	0.0441942
$513$	−14.4031	−0.635911
$514$	−15.5053	−0.683908
$515$	−24.9710	−1.10035
$516$	−16.7405	−0.736959
$517$	0.320252	0.0140847
$518$	−0.291772	−0.0128197
$519$	15.8754	0.696852
$520$	3.49141	0.153108
$521$	25.3534	1.11075	0.555376	−	0.831600i	$-0.312575\pi$
$521$	25.3534	1.11075	0.555376	+	0.831600i	$0.312575\pi$
$522$	31.5403	1.38048
$523$	9.07012	0.396609	0.198304	−	0.980140i	$-0.436457\pi$
$523$	9.07012	0.396609	0.198304	+	0.980140i	$0.436457\pi$
$524$	−2.35300	−0.102791
$525$	10.7173	0.467742
$526$	16.8989	0.736829
$527$	−10.5910	−0.461353
$528$	0.649308	0.0282575
$529$	9.77971	0.425205
$530$	−5.93556	−0.257824
$531$	−30.8857	−1.34033
$532$	7.23565	0.313705
$533$	−1.77922	−0.0770665
$534$	−27.3396	−1.18310
$535$	3.04137	0.131490
$536$	16.1002	0.695423
$537$	−46.7814	−2.01877
$538$	−10.7604	−0.463914
$539$	1.13170	0.0487459
$540$	−4.69982	−0.202248
$541$	−20.6935	−0.889683	−0.444841	−	0.895609i	$-0.646740\pi$
$541$	−20.6935	−0.889683	−0.444841	+	0.895609i	$0.646740\pi$
$542$	−2.92423	−0.125607
$543$	38.0732	1.63388
$544$	−1.48447	−0.0636459
$545$	−25.5544	−1.09463
$546$	−9.25687	−0.396157
$547$	−6.35946	−0.271911	−0.135956	−	0.990715i	$-0.543410\pi$
$547$	−6.35946	−0.271911	−0.135956	+	0.990715i	$0.543410\pi$
$548$	11.5805	0.494696
$549$	9.38017	0.400336
$550$	0.636753	0.0271512
$551$	36.0136	1.53423
$552$	15.2988	0.651160
$553$	2.77383	0.117955
$554$	16.7942	0.713518
$555$	0.785762	0.0333537
$556$	1.66475	0.0706011
$557$	−0.833740	−0.0353267	−0.0176633	−	0.999844i	$-0.505623\pi$
$557$	−0.833740	−0.0353267	−0.0176633	+	0.999844i	$0.505623\pi$
$558$	29.5386	1.25047
$559$	14.1797	0.599736
$560$	2.36104	0.0997722
$561$	−0.963876	−0.0406949
$562$	−7.84228	−0.330807
$563$	31.4592	1.32585	0.662924	−	0.748687i	$-0.269315\pi$
$563$	31.4592	1.32585	0.662924	+	0.748687i	$0.269315\pi$
$564$	3.52169	0.148290
$565$	16.6697	0.701299
$566$	22.5405	0.947450
$567$	−6.54993	−0.275071
$568$	5.96809	0.250415
$569$	0.772276	0.0323755	0.0161877	−	0.999869i	$-0.494847\pi$
$569$	0.772276	0.0323755	0.0161877	+	0.999869i	$0.494847\pi$
$570$	−19.4861	−0.816182
$571$	−12.5757	−0.526276	−0.263138	−	0.964758i	$-0.584757\pi$
$571$	−12.5757	−0.526276	−0.263138	+	0.964758i	$0.584757\pi$
$572$	−0.549983	−0.0229959
$573$	−56.5394	−2.36197
$574$	−1.20318	−0.0502200
$575$	15.0030	0.625668
$576$	4.14019	0.172508
$577$	18.9705	0.789752	0.394876	−	0.918734i	$-0.370788\pi$
$577$	18.9705	0.789752	0.394876	+	0.918734i	$0.370788\pi$
$578$	−14.7964	−0.615448
$579$	−61.5138	−2.55643
$580$	11.7515	0.487954
$581$	25.2574	1.04786
$582$	−10.3531	−0.429148
$583$	0.934997	0.0387236
$584$	−2.58683	−0.107044
$585$	14.4551	0.597645
$586$	31.0174	1.28132
$587$	28.6600	1.18293	0.591463	−	0.806332i	$-0.298551\pi$
$587$	28.6600	1.18293	0.591463	+	0.806332i	$0.298551\pi$
$588$	12.4449	0.513219
$589$	33.7280	1.38974
$590$	−11.5076	−0.473761
$591$	13.3175	0.547808
$592$	−0.190629	−0.00783479
$593$	20.6639	0.848565	0.424283	−	0.905530i	$-0.360526\pi$
$593$	20.6639	0.848565	0.424283	+	0.905530i	$0.360526\pi$
$594$	0.740337	0.0303764
$595$	−3.50489	−0.143686
$596$	16.1436	0.661267
$597$	25.3633	1.03805
$598$	−12.9585	−0.529914
$599$	−31.2557	−1.27707	−0.638537	−	0.769591i	$-0.720460\pi$
$599$	−31.2557	−1.27707	−0.638537	+	0.769591i	$0.720460\pi$
$600$	7.00213	0.285861
$601$	9.92625	0.404900	0.202450	−	0.979293i	$-0.435110\pi$
$601$	9.92625	0.404900	0.202450	+	0.979293i	$0.435110\pi$
$602$	9.58891	0.390815
$603$	66.6579	2.71452
$604$	−22.7807	−0.926935
$605$	−16.8773	−0.686160
$606$	8.25356	0.335278
$607$	−5.74153	−0.233042	−0.116521	−	0.993188i	$-0.537174\pi$
$607$	−5.74153	−0.233042	−0.116521	+	0.993188i	$0.537174\pi$
$608$	4.72739	0.191721
$609$	−31.1570	−1.26255
$610$	3.49492	0.141505
$611$	−2.98297	−0.120678
$612$	−6.14597	−0.248436
$613$	−19.5719	−0.790502	−0.395251	−	0.918573i	$-0.629342\pi$
$613$	−19.5719	−0.790502	−0.395251	+	0.918573i	$0.629342\pi$
$614$	14.6953	0.593054
$615$	3.24025	0.130660
$616$	−0.371922	−0.0149852
$617$	10.8255	0.435820	0.217910	−	0.975969i	$-0.430076\pi$
$617$	10.8255	0.435820	0.217910	+	0.975969i	$0.430076\pi$
$618$	43.2556	1.74000
$619$	25.4720	1.02380	0.511902	−	0.859044i	$-0.328941\pi$
$619$	25.4720	1.02380	0.511902	+	0.859044i	$0.328941\pi$
$620$	11.0057	0.441999
$621$	17.4436	0.699988
$622$	13.2704	0.532095
$623$	15.6601	0.627407
$624$	−6.04795	−0.242112
$625$	−5.03104	−0.201242
$626$	11.7200	0.468425
$627$	3.06953	0.122585
$628$	2.41265	0.0962752
$629$	0.282982	0.0112832
$630$	9.77517	0.389452
$631$	−31.2230	−1.24297	−0.621485	−	0.783426i	$-0.713470\pi$
$631$	−31.2230	−1.24297	−0.621485	+	0.783426i	$0.713470\pi$
$632$	1.81227	0.0720884
$633$	−14.1228	−0.561331
$634$	−21.0946	−0.837772
$635$	−15.9919	−0.634619
$636$	10.2818	0.407700
$637$	−10.5412	−0.417657
$638$	−1.85115	−0.0732876
$639$	24.7090	0.977474
$640$	1.54258	0.0609758
$641$	37.3744	1.47620	0.738101	−	0.674690i	$-0.235723\pi$
$641$	37.3744	1.47620	0.738101	+	0.674690i	$0.235723\pi$
$642$	−5.26838	−0.207926
$643$	−13.2381	−0.522061	−0.261030	−	0.965331i	$-0.584062\pi$
$643$	−13.2381	−0.522061	−0.261030	+	0.965331i	$0.584062\pi$
$644$	−8.76311	−0.345315
$645$	−25.8236	−1.01680
$646$	−7.01765	−0.276106
$647$	14.1610	0.556728	0.278364	−	0.960476i	$-0.410208\pi$
$647$	14.1610	0.556728	0.278364	+	0.960476i	$0.410208\pi$
$648$	−4.27938	−0.168110
$649$	1.81273	0.0711559
$650$	−5.93100	−0.232633
$651$	−29.1796	−1.14364
$652$	12.4319	0.486872
$653$	−19.6330	−0.768298	−0.384149	−	0.923271i	$-0.625505\pi$
$653$	−19.6330	−0.768298	−0.384149	+	0.923271i	$0.625505\pi$
$654$	44.2663	1.73095
$655$	−3.62970	−0.141824
$656$	−0.786097	−0.0306919
$657$	−10.7100	−0.417836
$658$	−2.01721	−0.0786392
$659$	−31.9992	−1.24651	−0.623256	−	0.782018i	$-0.714190\pi$
$659$	−31.9992	−1.24651	−0.623256	+	0.782018i	$0.714190\pi$
$660$	1.00161	0.0389876
$661$	24.0835	0.936740	0.468370	−	0.883532i	$-0.344841\pi$
$661$	24.0835	0.936740	0.468370	+	0.883532i	$0.344841\pi$
$662$	−7.80058	−0.303178
$663$	8.97797	0.348675
$664$	16.5019	0.640397
$665$	11.1616	0.432827
$666$	−0.789239	−0.0305824
$667$	−43.6162	−1.68882
$668$	−6.10802	−0.236326
$669$	−15.4754	−0.598312
$670$	24.8358	0.959493
$671$	−0.550536	−0.0212532
$672$	−4.08988	−0.157771
$673$	−40.5342	−1.56248	−0.781239	−	0.624232i	$-0.785412\pi$
$673$	−40.5342	−1.56248	−0.781239	+	0.624232i	$0.785412\pi$
$674$	17.4264	0.671240
$675$	7.98378	0.307296
$676$	−7.87722	−0.302970
$677$	−13.7315	−0.527745	−0.263872	−	0.964558i	$-0.585000\pi$
$677$	−13.7315	−0.527745	−0.263872	+	0.964558i	$0.585000\pi$
$678$	−28.8758	−1.10897
$679$	5.93020	0.227580
$680$	−2.28991	−0.0878139
$681$	0.384037	0.0147163
$682$	−1.73366	−0.0663854
$683$	41.1233	1.57354	0.786769	−	0.617247i	$-0.211752\pi$
$683$	41.1233	1.57354	0.786769	+	0.617247i	$0.211752\pi$
$684$	19.5723	0.748366
$685$	17.8639	0.682544
$686$	−17.8425	−0.681228
$687$	53.5367	2.04255
$688$	6.26489	0.238847
$689$	−8.70898	−0.331786
$690$	23.5996	0.898423
$691$	21.7571	0.827678	0.413839	−	0.910350i	$-0.364188\pi$
$691$	21.7571	0.827678	0.413839	+	0.910350i	$0.364188\pi$
$692$	−5.94113	−0.225848
$693$	−1.53983	−0.0584933
$694$	5.48709	0.208287
$695$	2.56801	0.0974102
$696$	−20.3564	−0.771606
$697$	1.16693	0.0442008
$698$	12.9415	0.489842
$699$	−49.2349	−1.86223
$700$	−4.01080	−0.151594
$701$	−34.9552	−1.32024	−0.660120	−	0.751160i	$-0.729495\pi$
$701$	−34.9552	−1.32024	−0.660120	+	0.751160i	$0.729495\pi$
$702$	−6.89583	−0.260266
$703$	−0.901175	−0.0339885
$704$	−0.242994	−0.00915819
$705$	5.43249	0.204599
$706$	−26.9966	−1.01603
$707$	−4.72761	−0.177800
$708$	19.9339	0.749162
$709$	−8.07009	−0.303079	−0.151539	−	0.988451i	$-0.548423\pi$
$709$	−8.07009	−0.303079	−0.151539	+	0.988451i	$0.548423\pi$
$710$	9.20625	0.345505
$711$	7.50317	0.281391
$712$	10.2315	0.383440
$713$	−40.8481	−1.52977
$714$	6.07129	0.227212
$715$	−0.848393	−0.0317281
$716$	17.5073	0.654277
$717$	−47.9989	−1.79255
$718$	14.3007	0.533697
$719$	15.2286	0.567930	0.283965	−	0.958835i	$-0.408350\pi$
$719$	15.2286	0.567930	0.283965	+	0.958835i	$0.408350\pi$
$720$	6.38658	0.238014
$721$	−24.7767	−0.922732
$722$	3.34821	0.124607
$723$	58.9034	2.19064
$724$	−14.2484	−0.529536
$725$	−19.9627	−0.741397
$726$	29.2355	1.08503
$727$	−38.2184	−1.41744	−0.708720	−	0.705490i	$-0.750727\pi$
$727$	−38.2184	−1.41744	−0.708720	+	0.705490i	$0.750727\pi$
$728$	3.46425	0.128394
$729$	−42.1411	−1.56078
$730$	−3.99040	−0.147691
$731$	−9.30001	−0.343973
$732$	−6.05403	−0.223764
$733$	−30.3110	−1.11956	−0.559782	−	0.828640i	$-0.689115\pi$
$733$	−30.3110	−1.11956	−0.559782	+	0.828640i	$0.689115\pi$
$734$	29.0059	1.07063
$735$	19.1973	0.708102
$736$	−5.72536	−0.211039
$737$	−3.91225	−0.144110
$738$	−3.25460	−0.119803
$739$	−32.0927	−1.18055	−0.590275	−	0.807202i	$-0.700981\pi$
$739$	−32.0927	−1.18055	−0.590275	+	0.807202i	$0.700981\pi$
$740$	−0.294060	−0.0108099
$741$	−28.5910	−1.05032
$742$	−5.88939	−0.216206
$743$	−29.4066	−1.07882	−0.539411	−	0.842043i	$-0.681353\pi$
$743$	−29.4066	−1.07882	−0.539411	+	0.842043i	$0.681353\pi$
$744$	−19.0644	−0.698936
$745$	24.9028	0.912367
$746$	−21.6104	−0.791212
$747$	68.3210	2.49973
$748$	0.360717	0.0131891
$749$	3.01771	0.110265
$750$	31.4111	1.14697
$751$	−21.0248	−0.767205	−0.383603	−	0.923498i	$-0.625317\pi$
$751$	−21.0248	−0.767205	−0.383603	+	0.923498i	$0.625317\pi$
$752$	−1.31794	−0.0480604
$753$	−7.58916	−0.276564
$754$	17.2424	0.627932
$755$	−35.1411	−1.27892
$756$	−4.66326	−0.169601
$757$	47.0354	1.70953	0.854766	−	0.519014i	$-0.173701\pi$
$757$	47.0354	1.70953	0.854766	+	0.519014i	$0.173701\pi$
$758$	−18.4146	−0.668848
$759$	−3.71752	−0.134938
$760$	7.29238	0.264522
$761$	−4.77882	−0.173232	−0.0866160	−	0.996242i	$-0.527605\pi$
$761$	−4.77882	−0.173232	−0.0866160	+	0.996242i	$0.527605\pi$
$762$	27.7018	1.00353
$763$	−25.3556	−0.917934
$764$	21.1591	0.765508
$765$	−9.48066	−0.342774
$766$	13.7101	0.495368
$767$	−16.8846	−0.609667
$768$	−2.67211	−0.0964216
$769$	34.0944	1.22948	0.614738	−	0.788732i	$-0.289262\pi$
$769$	34.0944	1.22948	0.614738	+	0.788732i	$0.289262\pi$
$770$	−0.573720	−0.0206754
$771$	41.4318	1.49213
$772$	23.0206	0.828531
$773$	−11.3643	−0.408746	−0.204373	−	0.978893i	$-0.565515\pi$
$773$	−11.3643	−0.408746	−0.204373	+	0.978893i	$0.565515\pi$
$774$	25.9379	0.932317
$775$	−18.6958	−0.671573
$776$	3.87448	0.139086
$777$	0.779649	0.0279697
$778$	−9.24988	−0.331624
$779$	−3.71619	−0.133146
$780$	−9.32945	−0.334048
$781$	−1.45021	−0.0518926
$782$	8.49910	0.303927
$783$	−23.2102	−0.829464
$784$	−4.65733	−0.166333
$785$	3.72171	0.132833
$786$	6.28749	0.224267
$787$	28.9099	1.03053	0.515263	−	0.857032i	$-0.327694\pi$
$787$	28.9099	1.03053	0.515263	+	0.857032i	$0.327694\pi$
$788$	−4.98388	−0.177543
$789$	−45.1559	−1.60759
$790$	2.79558	0.0994623
$791$	16.5400	0.588095
$792$	−1.00604	−0.0357482
$793$	5.12794	0.182098
$794$	12.0435	0.427408
$795$	15.8605	0.562514
$796$	−9.49186	−0.336430
$797$	4.08869	0.144829	0.0724145	−	0.997375i	$-0.476930\pi$
$797$	4.08869	0.144829	0.0724145	+	0.997375i	$0.476930\pi$
$798$	−19.3345	−0.684433
$799$	1.95644	0.0692138
$800$	−2.62045	−0.0926467
$801$	42.3602	1.49672
$802$	17.7224	0.625799
$803$	0.628585	0.0221823
$804$	−43.0216	−1.51725
$805$	−13.5178	−0.476440
$806$	16.1481	0.568793
$807$	28.7530	1.01215
$808$	−3.08877	−0.108663
$809$	−35.5127	−1.24856	−0.624280	−	0.781201i	$-0.714607\pi$
$809$	−35.5127	−1.24856	−0.624280	+	0.781201i	$0.714607\pi$
$810$	−6.60128	−0.231945
$811$	39.9971	1.40449	0.702245	−	0.711936i	$-0.252181\pi$
$811$	39.9971	1.40449	0.702245	+	0.711936i	$0.252181\pi$
$812$	11.6601	0.409188
$813$	7.81388	0.274045
$814$	0.0463216	0.00162357
$815$	19.1772	0.671749
$816$	3.96666	0.138861
$817$	29.6166	1.03615
$818$	31.5590	1.10343
$819$	14.3427	0.501173
$820$	−1.21262	−0.0423465
$821$	48.2818	1.68505	0.842523	−	0.538661i	$-0.181070\pi$
$821$	48.2818	1.68505	0.842523	+	0.538661i	$0.181070\pi$
$822$	−30.9445	−1.07931
$823$	−12.0786	−0.421035	−0.210517	−	0.977590i	$-0.567515\pi$
$823$	−12.0786	−0.421035	−0.210517	+	0.977590i	$0.567515\pi$
$824$	−16.1878	−0.563928
$825$	−1.70148	−0.0592378
$826$	−11.4181	−0.397286
$827$	−3.75611	−0.130613	−0.0653063	−	0.997865i	$-0.520802\pi$
$827$	−3.75611	−0.130613	−0.0653063	+	0.997865i	$0.520802\pi$
$828$	−23.7041	−0.823774
$829$	−25.7300	−0.893641	−0.446821	−	0.894624i	$-0.647444\pi$
$829$	−25.7300	−0.893641	−0.446821	+	0.894624i	$0.647444\pi$
$830$	25.4555	0.883572
$831$	−44.8761	−1.55673
$832$	2.26336	0.0784678
$833$	6.91364	0.239543
$834$	−4.44840	−0.154035
$835$	−9.42211	−0.326066
$836$	−1.14873	−0.0397296
$837$	−21.7371	−0.751346
$838$	−16.1235	−0.556977
$839$	−31.2929	−1.08035	−0.540176	−	0.841552i	$-0.681642\pi$
$839$	−31.2929	−1.08035	−0.540176	+	0.841552i	$0.681642\pi$
$840$	−6.30897	−0.217680
$841$	29.0350	1.00121
$842$	10.0250	0.345485
$843$	20.9555	0.721745
$844$	5.28526	0.181926
$845$	−12.1512	−0.418015
$846$	−5.45653	−0.187599
$847$	−16.7460	−0.575399
$848$	−3.84781	−0.132134
$849$	−60.2309	−2.06712
$850$	3.88996	0.133425
$851$	1.09142	0.0374133
$852$	−15.9474	−0.546349
$853$	−15.0589	−0.515606	−0.257803	−	0.966197i	$-0.582999\pi$
$853$	−15.0589	−0.515606	−0.257803	+	0.966197i	$0.582999\pi$
$854$	3.46773	0.118663
$855$	30.1919	1.03254
$856$	1.97161	0.0673884
$857$	−25.9501	−0.886438	−0.443219	−	0.896413i	$-0.646164\pi$
$857$	−25.9501	−0.886438	−0.443219	+	0.896413i	$0.646164\pi$
$858$	1.46962	0.0501719
$859$	10.3571	0.353380	0.176690	−	0.984267i	$-0.443461\pi$
$859$	10.3571	0.353380	0.176690	+	0.984267i	$0.443461\pi$
$860$	9.66409	0.329543
$861$	3.21505	0.109568
$862$	16.0663	0.547219
$863$	−37.7296	−1.28433	−0.642165	−	0.766567i	$-0.721963\pi$
$863$	−37.7296	−1.28433	−0.642165	+	0.766567i	$0.721963\pi$
$864$	−3.04673	−0.103652
$865$	−9.16467	−0.311608
$866$	28.1134	0.955333
$867$	39.5376	1.34277
$868$	10.9201	0.370651
$869$	−0.440372	−0.0149386
$870$	−31.4013	−1.06460
$871$	36.4405	1.23474
$872$	−16.5660	−0.560996
$873$	16.0411	0.542909
$874$	−27.0660	−0.915521
$875$	−17.9922	−0.608247
$876$	6.91231	0.233545
$877$	−23.2710	−0.785806	−0.392903	−	0.919580i	$-0.628529\pi$
$877$	−23.2710	−0.785806	−0.392903	+	0.919580i	$0.628529\pi$
$878$	−9.34301	−0.315311
$879$	−82.8820	−2.79554
$880$	−0.374838	−0.0126358
$881$	27.7617	0.935314	0.467657	−	0.883910i	$-0.345098\pi$
$881$	27.7617	0.935314	0.467657	+	0.883910i	$0.345098\pi$
$882$	−19.2822	−0.649267
$883$	−22.5632	−0.759311	−0.379655	−	0.925128i	$-0.623957\pi$
$883$	−22.5632	−0.759311	−0.379655	+	0.925128i	$0.623957\pi$
$884$	−3.35988	−0.113005
$885$	30.7496	1.03364
$886$	5.51180	0.185172
$887$	−18.2737	−0.613572	−0.306786	−	0.951778i	$-0.599254\pi$
$887$	−18.2737	−0.613572	−0.306786	+	0.951778i	$0.599254\pi$
$888$	0.509381	0.0170937
$889$	−15.8675	−0.532178
$890$	15.7828	0.529042
$891$	1.03986	0.0348368
$892$	5.79143	0.193911
$893$	−6.23042	−0.208493
$894$	−43.1375	−1.44273
$895$	27.0064	0.902723
$896$	1.53058	0.0511331
$897$	34.6267	1.15615
$898$	29.0429	0.969175
$899$	54.3518	1.81273
$900$	−10.8492	−0.361638
$901$	5.71195	0.190293
$902$	0.191017	0.00636017
$903$	−25.6227	−0.852669
$904$	10.8064	0.359414
$905$	−21.9792	−0.730615
$906$	60.8727	2.02236
$907$	−34.5036	−1.14567	−0.572837	−	0.819670i	$-0.694157\pi$
$907$	−34.5036	−1.14567	−0.572837	+	0.819670i	$0.694157\pi$
$908$	−0.143720	−0.00476952
$909$	−12.7881	−0.424155
$910$	5.34388	0.177148
$911$	−14.8868	−0.493223	−0.246611	−	0.969114i	$-0.579317\pi$
$911$	−14.8868	−0.493223	−0.246611	+	0.969114i	$0.579317\pi$
$912$	−12.6321	−0.418291
$913$	−4.00986	−0.132707
$914$	−32.0699	−1.06078
$915$	−9.33883	−0.308732
$916$	−20.0353	−0.661986
$917$	−3.60146	−0.118931
$918$	4.52276	0.149273
$919$	−43.4869	−1.43450	−0.717250	−	0.696816i	$-0.754599\pi$
$919$	−43.4869	−1.43450	−0.717250	+	0.696816i	$0.754599\pi$
$920$	−8.83182	−0.291177
$921$	−39.2675	−1.29391
$922$	15.1934	0.500368
$923$	13.5079	0.444618
$924$	0.993818	0.0326942
$925$	0.499532	0.0164245
$926$	11.7465	0.386014
$927$	−67.0206	−2.20124
$928$	7.61807	0.250075
$929$	−19.1943	−0.629745	−0.314872	−	0.949134i	$-0.601962\pi$
$929$	−19.1943	−0.629745	−0.314872	+	0.949134i	$0.601962\pi$
$930$	−29.4084	−0.964340
$931$	−22.0170	−0.721578
$932$	18.4254	0.603546
$933$	−35.4600	−1.16091
$934$	39.0470	1.27766
$935$	0.556434	0.0181973
$936$	9.37074	0.306292
$937$	51.8095	1.69254	0.846271	−	0.532753i	$-0.178842\pi$
$937$	51.8095	1.69254	0.846271	+	0.532753i	$0.178842\pi$
$938$	24.6426	0.804610
$939$	−31.3171	−1.02200
$940$	−2.03303	−0.0663101
$941$	−24.9201	−0.812372	−0.406186	−	0.913790i	$-0.633141\pi$
$941$	−24.9201	−0.812372	−0.406186	+	0.913790i	$0.633141\pi$
$942$	−6.44687	−0.210050
$943$	4.50069	0.146563
$944$	−7.45997	−0.242801
$945$	−7.19345	−0.234003
$946$	−1.52233	−0.0494953
$947$	−46.6989	−1.51751	−0.758755	−	0.651377i	$-0.774192\pi$
$947$	−46.6989	−1.51751	−0.758755	+	0.651377i	$0.774192\pi$
$948$	−4.84261	−0.157281
$949$	−5.85492	−0.190059
$950$	−12.3879	−0.401915
$951$	56.3671	1.82783
$952$	−2.27209	−0.0736389
$953$	−11.9124	−0.385881	−0.192941	−	0.981210i	$-0.561802\pi$
$953$	−11.9124	−0.385881	−0.192941	+	0.981210i	$0.561802\pi$
$954$	−15.9307	−0.515775
$955$	32.6395	1.05619
$956$	17.9629	0.580961
$957$	4.94648	0.159897
$958$	11.0464	0.356894
$959$	17.7249	0.572368
$960$	−4.12195	−0.133035
$961$	19.9023	0.642011
$962$	−0.431460	−0.0139108
$963$	8.16287	0.263045
$964$	−22.0437	−0.709981
$965$	35.5112	1.14315
$966$	23.4160	0.753399
$967$	55.8604	1.79635	0.898175	−	0.439637i	$-0.144893\pi$
$967$	55.8604	1.79635	0.898175	+	0.439637i	$0.144893\pi$
$968$	−10.9410	−0.351656
$969$	18.7520	0.602399
$970$	5.97670	0.191900
$971$	0.470325	0.0150935	0.00754673	−	0.999972i	$-0.497598\pi$
$971$	0.470325	0.0150935	0.00754673	+	0.999972i	$0.497598\pi$
$972$	20.5752	0.659949
$973$	2.54803	0.0816861
$974$	−33.7729	−1.08215
$975$	15.8483	0.507552
$976$	2.26563	0.0725212
$977$	−39.5221	−1.26442	−0.632212	−	0.774795i	$-0.717853\pi$
$977$	−39.5221	−1.26442	−0.632212	+	0.774795i	$0.717853\pi$
$978$	−33.2195	−1.06224
$979$	−2.48618	−0.0794588
$980$	−7.18430	−0.229494
$981$	−68.5865	−2.18980
$982$	28.0685	0.895701
$983$	1.34196	0.0428018	0.0214009	−	0.999771i	$-0.493187\pi$
$983$	1.34196	0.0428018	0.0214009	+	0.999771i	$0.493187\pi$
$984$	2.10054	0.0669628
$985$	−7.68803	−0.244961
$986$	−11.3088	−0.360144
$987$	5.39023	0.171573
$988$	10.6998	0.340405
$989$	−35.8687	−1.14056
$990$	−1.55190	−0.0493227
$991$	−14.8177	−0.470699	−0.235350	−	0.971911i	$-0.575624\pi$
$991$	−14.8177	−0.470699	−0.235350	+	0.971911i	$0.575624\pi$
$992$	7.13459	0.226523
$993$	20.8440	0.661466
$994$	9.13463	0.289733
$995$	−14.6420	−0.464181
$996$	−44.0949	−1.39720
$997$	−12.8721	−0.407664	−0.203832	−	0.979006i	$-0.565340\pi$
$997$	−12.8721	−0.407664	−0.203832	+	0.979006i	$0.565340\pi$
$998$	3.28146	0.103873
$999$	0.580793	0.0183755

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8038.2.a.d.1.7	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8038.2.a.d.1.7	✓	92	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:	\( N \)	\(=\)	\( 8038 = 2 \cdot 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.67211 q^{3} +1.00000 q^{4} +1.54258 q^{5} -2.67211 q^{6} +1.53058 q^{7} +1.00000 q^{8} +4.14019 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.67211 q^{3} +1.00000 q^{4} +1.54258 q^{5} -2.67211 q^{6} +1.53058 q^{7} +1.00000 q^{8} +4.14019 q^{9} +1.54258 q^{10} -0.242994 q^{11} -2.67211 q^{12} +2.26336 q^{13} +1.53058 q^{14} -4.12195 q^{15} +1.00000 q^{16} -1.48447 q^{17} +4.14019 q^{18} +4.72739 q^{19} +1.54258 q^{20} -4.08988 q^{21} -0.242994 q^{22} -5.72536 q^{23} -2.67211 q^{24} -2.62045 q^{25} +2.26336 q^{26} -3.04673 q^{27} +1.53058 q^{28} +7.61807 q^{29} -4.12195 q^{30} +7.13459 q^{31} +1.00000 q^{32} +0.649308 q^{33} -1.48447 q^{34} +2.36104 q^{35} +4.14019 q^{36} -0.190629 q^{37} +4.72739 q^{38} -6.04795 q^{39} +1.54258 q^{40} -0.786097 q^{41} -4.08988 q^{42} +6.26489 q^{43} -0.242994 q^{44} +6.38658 q^{45} -5.72536 q^{46} -1.31794 q^{47} -2.67211 q^{48} -4.65733 q^{49} -2.62045 q^{50} +3.96666 q^{51} +2.26336 q^{52} -3.84781 q^{53} -3.04673 q^{54} -0.374838 q^{55} +1.53058 q^{56} -12.6321 q^{57} +7.61807 q^{58} -7.45997 q^{59} -4.12195 q^{60} +2.26563 q^{61} +7.13459 q^{62} +6.33690 q^{63} +1.00000 q^{64} +3.49141 q^{65} +0.649308 q^{66} +16.1002 q^{67} -1.48447 q^{68} +15.2988 q^{69} +2.36104 q^{70} +5.96809 q^{71} +4.14019 q^{72} -2.58683 q^{73} -0.190629 q^{74} +7.00213 q^{75} +4.72739 q^{76} -0.371922 q^{77} -6.04795 q^{78} +1.81227 q^{79} +1.54258 q^{80} -4.27938 q^{81} -0.786097 q^{82} +16.5019 q^{83} -4.08988 q^{84} -2.28991 q^{85} +6.26489 q^{86} -20.3564 q^{87} -0.242994 q^{88} +10.2315 q^{89} +6.38658 q^{90} +3.46425 q^{91} -5.72536 q^{92} -19.0644 q^{93} -1.31794 q^{94} +7.29238 q^{95} -2.67211 q^{96} +3.87448 q^{97} -4.65733 q^{98} -1.00604 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9}+O(q^{10}) \) 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9} + 28 q^{10} + 37 q^{11} + 31 q^{12} + 20 q^{13} + 29 q^{14} + 30 q^{15} + 92 q^{16} + 52 q^{17} + 113 q^{18} + 61 q^{19} + 28 q^{20} + 5 q^{21} + 37 q^{22} + 71 q^{23} + 31 q^{24} + 118 q^{25} + 20 q^{26} + 112 q^{27} + 29 q^{28} + 30 q^{29} + 30 q^{30} + 89 q^{31} + 92 q^{32} + 52 q^{33} + 52 q^{34} + 58 q^{35} + 113 q^{36} + 15 q^{37} + 61 q^{38} + 43 q^{39} + 28 q^{40} + 75 q^{41} + 5 q^{42} + 46 q^{43} + 37 q^{44} + 63 q^{45} + 71 q^{46} + 92 q^{47} + 31 q^{48} + 131 q^{49} + 118 q^{50} + 45 q^{51} + 20 q^{52} + 72 q^{53} + 112 q^{54} + 86 q^{55} + 29 q^{56} + 44 q^{57} + 30 q^{58} + 95 q^{59} + 30 q^{60} - 4 q^{61} + 89 q^{62} + 67 q^{63} + 92 q^{64} + 55 q^{65} + 52 q^{66} + 40 q^{67} + 52 q^{68} + 25 q^{69} + 58 q^{70} + 84 q^{71} + 113 q^{72} + 87 q^{73} + 15 q^{74} + 132 q^{75} + 61 q^{76} + 96 q^{77} + 43 q^{78} + 68 q^{79} + 28 q^{80} + 156 q^{81} + 75 q^{82} + 120 q^{83} + 5 q^{84} - 14 q^{85} + 46 q^{86} + 73 q^{87} + 37 q^{88} + 86 q^{89} + 63 q^{90} + 93 q^{91} + 71 q^{92} + 29 q^{93} + 92 q^{94} + 67 q^{95} + 31 q^{96} + 65 q^{97} + 131 q^{98} + 94 q^{99}+O(q^{100}) \) 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9 + 28 * q^10 + 37 * q^11 + 31 * q^12 + 20 * q^13 + 29 * q^14 + 30 * q^15 + 92 * q^16 + 52 * q^17 + 113 * q^18 + 61 * q^19 + 28 * q^20 + 5 * q^21 + 37 * q^22 + 71 * q^23 + 31 * q^24 + 118 * q^25 + 20 * q^26 + 112 * q^27 + 29 * q^28 + 30 * q^29 + 30 * q^30 + 89 * q^31 + 92 * q^32 + 52 * q^33 + 52 * q^34 + 58 * q^35 + 113 * q^36 + 15 * q^37 + 61 * q^38 + 43 * q^39 + 28 * q^40 + 75 * q^41 + 5 * q^42 + 46 * q^43 + 37 * q^44 + 63 * q^45 + 71 * q^46 + 92 * q^47 + 31 * q^48 + 131 * q^49 + 118 * q^50 + 45 * q^51 + 20 * q^52 + 72 * q^53 + 112 * q^54 + 86 * q^55 + 29 * q^56 + 44 * q^57 + 30 * q^58 + 95 * q^59 + 30 * q^60 - 4 * q^61 + 89 * q^62 + 67 * q^63 + 92 * q^64 + 55 * q^65 + 52 * q^66 + 40 * q^67 + 52 * q^68 + 25 * q^69 + 58 * q^70 + 84 * q^71 + 113 * q^72 + 87 * q^73 + 15 * q^74 + 132 * q^75 + 61 * q^76 + 96 * q^77 + 43 * q^78 + 68 * q^79 + 28 * q^80 + 156 * q^81 + 75 * q^82 + 120 * q^83 + 5 * q^84 - 14 * q^85 + 46 * q^86 + 73 * q^87 + 37 * q^88 + 86 * q^89 + 63 * q^90 + 93 * q^91 + 71 * q^92 + 29 * q^93 + 92 * q^94 + 67 * q^95 + 31 * q^96 + 65 * q^97 + 131 * q^98 + 94 * q^99

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