LMFDB - Embedded newform 8018.2.a.j.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.46195 q^{3} +1.00000 q^{4} +2.14418 q^{5} -1.46195 q^{6} +2.84565 q^{7} +1.00000 q^{8} -0.862709 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.46195 q^{3} +1.00000 q^{4} +2.14418 q^{5} -1.46195 q^{6} +2.84565 q^{7} +1.00000 q^{8} -0.862709 q^{9} +2.14418 q^{10} -4.14345 q^{11} -1.46195 q^{12} +5.72765 q^{13} +2.84565 q^{14} -3.13468 q^{15} +1.00000 q^{16} +0.828433 q^{17} -0.862709 q^{18} -1.00000 q^{19} +2.14418 q^{20} -4.16019 q^{21} -4.14345 q^{22} +4.11173 q^{23} -1.46195 q^{24} -0.402477 q^{25} +5.72765 q^{26} +5.64708 q^{27} +2.84565 q^{28} +5.07697 q^{29} -3.13468 q^{30} +3.20401 q^{31} +1.00000 q^{32} +6.05751 q^{33} +0.828433 q^{34} +6.10160 q^{35} -0.862709 q^{36} -1.30300 q^{37} -1.00000 q^{38} -8.37352 q^{39} +2.14418 q^{40} -9.49007 q^{41} -4.16019 q^{42} +1.76733 q^{43} -4.14345 q^{44} -1.84981 q^{45} +4.11173 q^{46} +6.02255 q^{47} -1.46195 q^{48} +1.09774 q^{49} -0.402477 q^{50} -1.21113 q^{51} +5.72765 q^{52} -9.71241 q^{53} +5.64708 q^{54} -8.88433 q^{55} +2.84565 q^{56} +1.46195 q^{57} +5.07697 q^{58} -1.16819 q^{59} -3.13468 q^{60} -0.741864 q^{61} +3.20401 q^{62} -2.45497 q^{63} +1.00000 q^{64} +12.2811 q^{65} +6.05751 q^{66} +12.6141 q^{67} +0.828433 q^{68} -6.01113 q^{69} +6.10160 q^{70} +1.20025 q^{71} -0.862709 q^{72} +14.2635 q^{73} -1.30300 q^{74} +0.588401 q^{75} -1.00000 q^{76} -11.7908 q^{77} -8.37352 q^{78} +0.0154584 q^{79} +2.14418 q^{80} -5.66760 q^{81} -9.49007 q^{82} +5.25605 q^{83} -4.16019 q^{84} +1.77631 q^{85} +1.76733 q^{86} -7.42227 q^{87} -4.14345 q^{88} +15.8470 q^{89} -1.84981 q^{90} +16.2989 q^{91} +4.11173 q^{92} -4.68409 q^{93} +6.02255 q^{94} -2.14418 q^{95} -1.46195 q^{96} -9.00620 q^{97} +1.09774 q^{98} +3.57460 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * 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
$3$	−1.46195	−0.844056	−0.422028	−	0.906583i	$-0.638682\pi$
$3$	−1.46195	−0.844056	−0.422028	+	0.906583i	$0.638682\pi$
$4$	1.00000	0.500000
$5$	2.14418	0.958908	0.479454	−	0.877567i	$-0.340835\pi$
$5$	2.14418	0.958908	0.479454	+	0.877567i	$0.340835\pi$
$6$	−1.46195	−0.596838
$7$	2.84565	1.07556	0.537778	−	0.843087i	$-0.319264\pi$
$7$	2.84565	1.07556	0.537778	+	0.843087i	$0.319264\pi$
$8$	1.00000	0.353553
$9$	−0.862709	−0.287570
$10$	2.14418	0.678050
$11$	−4.14345	−1.24930	−0.624649	−	0.780905i	$-0.714758\pi$
$11$	−4.14345	−1.24930	−0.624649	+	0.780905i	$0.714758\pi$
$12$	−1.46195	−0.422028
$13$	5.72765	1.58856	0.794282	−	0.607549i	$-0.207847\pi$
$13$	5.72765	1.58856	0.794282	+	0.607549i	$0.207847\pi$
$14$	2.84565	0.760533
$15$	−3.13468	−0.809372
$16$	1.00000	0.250000
$17$	0.828433	0.200925	0.100462	−	0.994941i	$-0.467968\pi$
$17$	0.828433	0.200925	0.100462	+	0.994941i	$0.467968\pi$
$18$	−0.862709	−0.203343
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.14418	0.479454
$21$	−4.16019	−0.907829
$22$	−4.14345	−0.883388
$23$	4.11173	0.857355	0.428678	−	0.903458i	$-0.358980\pi$
$23$	4.11173	0.857355	0.428678	+	0.903458i	$0.358980\pi$
$24$	−1.46195	−0.298419
$25$	−0.402477	−0.0804955
$26$	5.72765	1.12328
$27$	5.64708	1.08678
$28$	2.84565	0.537778
$29$	5.07697	0.942770	0.471385	−	0.881928i	$-0.343754\pi$
$29$	5.07697	0.942770	0.471385	+	0.881928i	$0.343754\pi$
$30$	−3.13468	−0.572312
$31$	3.20401	0.575456	0.287728	−	0.957712i	$-0.407100\pi$
$31$	3.20401	0.575456	0.287728	+	0.957712i	$0.407100\pi$
$32$	1.00000	0.176777
$33$	6.05751	1.05448
$34$	0.828433	0.142075
$35$	6.10160	1.03136
$36$	−0.862709	−0.143785
$37$	−1.30300	−0.214211	−0.107106	−	0.994248i	$-0.534158\pi$
$37$	−1.30300	−0.214211	−0.107106	+	0.994248i	$0.534158\pi$
$38$	−1.00000	−0.162221
$39$	−8.37352	−1.34084
$40$	2.14418	0.339025
$41$	−9.49007	−1.48210	−0.741050	−	0.671450i	$-0.765672\pi$
$41$	−9.49007	−1.48210	−0.741050	+	0.671450i	$0.765672\pi$
$42$	−4.16019	−0.641932
$43$	1.76733	0.269515	0.134758	−	0.990879i	$-0.456974\pi$
$43$	1.76733	0.269515	0.134758	+	0.990879i	$0.456974\pi$
$44$	−4.14345	−0.624649
$45$	−1.84981	−0.275753
$46$	4.11173	0.606242
$47$	6.02255	0.878479	0.439239	−	0.898370i	$-0.355248\pi$
$47$	6.02255	0.878479	0.439239	+	0.898370i	$0.355248\pi$
$48$	−1.46195	−0.211014
$49$	1.09774	0.156820
$50$	−0.402477	−0.0569189
$51$	−1.21113	−0.169592
$52$	5.72765	0.794282
$53$	−9.71241	−1.33410	−0.667051	−	0.745012i	$-0.732444\pi$
$53$	−9.71241	−1.33410	−0.667051	+	0.745012i	$0.732444\pi$
$54$	5.64708	0.768470
$55$	−8.88433	−1.19796
$56$	2.84565	0.380266
$57$	1.46195	0.193640
$58$	5.07697	0.666639
$59$	−1.16819	−0.152086	−0.0760430	−	0.997105i	$-0.524229\pi$
$59$	−1.16819	−0.152086	−0.0760430	+	0.997105i	$0.524229\pi$
$60$	−3.13468	−0.404686
$61$	−0.741864	−0.0949860	−0.0474930	−	0.998872i	$-0.515123\pi$
$61$	−0.741864	−0.0949860	−0.0474930	+	0.998872i	$0.515123\pi$
$62$	3.20401	0.406909
$63$	−2.45497	−0.309297
$64$	1.00000	0.125000
$65$	12.2811	1.52329
$66$	6.05751	0.745628
$67$	12.6141	1.54106	0.770528	−	0.637406i	$-0.219992\pi$
$67$	12.6141	1.54106	0.770528	+	0.637406i	$0.219992\pi$
$68$	0.828433	0.100462
$69$	−6.01113	−0.723656
$70$	6.10160	0.729281
$71$	1.20025	0.142444	0.0712219	−	0.997460i	$-0.477310\pi$
$71$	1.20025	0.142444	0.0712219	+	0.997460i	$0.477310\pi$
$72$	−0.862709	−0.101671
$73$	14.2635	1.66942	0.834710	−	0.550690i	$-0.185635\pi$
$73$	14.2635	1.66942	0.834710	+	0.550690i	$0.185635\pi$
$74$	−1.30300	−0.151470
$75$	0.588401	0.0679427
$76$	−1.00000	−0.114708
$77$	−11.7908	−1.34369
$78$	−8.37352	−0.948115
$79$	0.0154584	0.00173920	0.000869600	−	1.00000i	$-0.499723\pi$
$79$	0.0154584	0.00173920	0.000869600		1.00000i	$0.499723\pi$
$80$	2.14418	0.239727
$81$	−5.66760	−0.629734
$82$	−9.49007	−1.04800
$83$	5.25605	0.576926	0.288463	−	0.957491i	$-0.406856\pi$
$83$	5.25605	0.576926	0.288463	+	0.957491i	$0.406856\pi$
$84$	−4.16019	−0.453914
$85$	1.77631	0.192668
$86$	1.76733	0.190576
$87$	−7.42227	−0.795750
$88$	−4.14345	−0.441694
$89$	15.8470	1.67978	0.839888	−	0.542759i	$-0.182620\pi$
$89$	15.8470	1.67978	0.839888	+	0.542759i	$0.182620\pi$
$90$	−1.84981	−0.194987
$91$	16.2989	1.70859
$92$	4.11173	0.428678
$93$	−4.68409	−0.485717
$94$	6.02255	0.621178
$95$	−2.14418	−0.219989
$96$	−1.46195	−0.149209
$97$	−9.00620	−0.914441	−0.457221	−	0.889353i	$-0.651155\pi$
$97$	−9.00620	−0.914441	−0.457221	+	0.889353i	$0.651155\pi$
$98$	1.09774	0.110888
$99$	3.57460	0.359261
$100$	−0.402477	−0.0402477
$101$	9.96408	0.991464	0.495732	−	0.868476i	$-0.334900\pi$
$101$	9.96408	0.991464	0.495732	+	0.868476i	$0.334900\pi$
$102$	−1.21113	−0.119919
$103$	−7.91932	−0.780313	−0.390157	−	0.920748i	$-0.627579\pi$
$103$	−7.91932	−0.780313	−0.390157	+	0.920748i	$0.627579\pi$
$104$	5.72765	0.561642
$105$	−8.92022	−0.870524
$106$	−9.71241	−0.943353
$107$	−19.5270	−1.88775	−0.943875	−	0.330302i	$-0.892849\pi$
$107$	−19.5270	−1.88775	−0.943875	+	0.330302i	$0.892849\pi$
$108$	5.64708	0.543390
$109$	2.14391	0.205349	0.102674	−	0.994715i	$-0.467260\pi$
$109$	2.14391	0.205349	0.102674	+	0.994715i	$0.467260\pi$
$110$	−8.88433	−0.847087
$111$	1.90491	0.180806
$112$	2.84565	0.268889
$113$	17.2207	1.61999	0.809993	−	0.586440i	$-0.199471\pi$
$113$	17.2207	1.61999	0.809993	+	0.586440i	$0.199471\pi$
$114$	1.46195	0.136924
$115$	8.81631	0.822125
$116$	5.07697	0.471385
$117$	−4.94130	−0.456823
$118$	−1.16819	−0.107541
$119$	2.35743	0.216106
$120$	−3.13468	−0.286156
$121$	6.16822	0.560747
$122$	−0.741864	−0.0671652
$123$	13.8740	1.25097
$124$	3.20401	0.287728
$125$	−11.5839	−1.03610
$126$	−2.45497	−0.218706
$127$	−0.744794	−0.0660897	−0.0330449	−	0.999454i	$-0.510520\pi$
$127$	−0.744794	−0.0660897	−0.0330449	+	0.999454i	$0.510520\pi$
$128$	1.00000	0.0883883
$129$	−2.58374	−0.227486
$130$	12.2811	1.07713
$131$	0.775074	0.0677185	0.0338592	−	0.999427i	$-0.489220\pi$
$131$	0.775074	0.0677185	0.0338592	+	0.999427i	$0.489220\pi$
$132$	6.05751	0.527239
$133$	−2.84565	−0.246749
$134$	12.6141	1.08969
$135$	12.1084	1.04212
$136$	0.828433	0.0710376
$137$	−10.8225	−0.924630	−0.462315	−	0.886716i	$-0.652981\pi$
$137$	−10.8225	−0.924630	−0.462315	+	0.886716i	$0.652981\pi$
$138$	−6.01113	−0.511702
$139$	−5.75291	−0.487955	−0.243978	−	0.969781i	$-0.578452\pi$
$139$	−5.75291	−0.487955	−0.243978	+	0.969781i	$0.578452\pi$
$140$	6.10160	0.515679
$141$	−8.80465	−0.741485
$142$	1.20025	0.100723
$143$	−23.7323	−1.98459
$144$	−0.862709	−0.0718925
$145$	10.8860	0.904030
$146$	14.2635	1.18046
$147$	−1.60484	−0.132365
$148$	−1.30300	−0.107106
$149$	17.6403	1.44515	0.722574	−	0.691294i	$-0.242959\pi$
$149$	17.6403	1.44515	0.722574	+	0.691294i	$0.242959\pi$
$150$	0.588401	0.0480427
$151$	−11.6954	−0.951755	−0.475877	−	0.879512i	$-0.657869\pi$
$151$	−11.6954	−0.951755	−0.475877	+	0.879512i	$0.657869\pi$
$152$	−1.00000	−0.0811107
$153$	−0.714697	−0.0577798
$154$	−11.7908	−0.950132
$155$	6.86997	0.551810
$156$	−8.37352	−0.670418
$157$	19.0859	1.52322	0.761611	−	0.648034i	$-0.224409\pi$
$157$	19.0859	1.52322	0.761611	+	0.648034i	$0.224409\pi$
$158$	0.0154584	0.00122980
$159$	14.1990	1.12606
$160$	2.14418	0.169513
$161$	11.7006	0.922133
$162$	−5.66760	−0.445289
$163$	−4.38341	−0.343335	−0.171668	−	0.985155i	$-0.554916\pi$
$163$	−4.38341	−0.343335	−0.171668	+	0.985155i	$0.554916\pi$
$164$	−9.49007	−0.741050
$165$	12.9884	1.01115
$166$	5.25605	0.407948
$167$	12.6831	0.981444	0.490722	−	0.871316i	$-0.336733\pi$
$167$	12.6831	0.981444	0.490722	+	0.871316i	$0.336733\pi$
$168$	−4.16019	−0.320966
$169$	19.8060	1.52354
$170$	1.77631	0.136237
$171$	0.862709	0.0659730
$172$	1.76733	0.134758
$173$	14.5957	1.10969	0.554846	−	0.831953i	$-0.312777\pi$
$173$	14.5957	1.10969	0.554846	+	0.831953i	$0.312777\pi$
$174$	−7.42227	−0.562681
$175$	−1.14531	−0.0865774
$176$	−4.14345	−0.312325
$177$	1.70784	0.128369
$178$	15.8470	1.18778
$179$	−7.01955	−0.524666	−0.262333	−	0.964977i	$-0.584492\pi$
$179$	−7.01955	−0.524666	−0.262333	+	0.964977i	$0.584492\pi$
$180$	−1.84981	−0.137877
$181$	6.98602	0.519267	0.259633	−	0.965707i	$-0.416398\pi$
$181$	6.98602	0.519267	0.259633	+	0.965707i	$0.416398\pi$
$182$	16.2989	1.20815
$183$	1.08457	0.0801735
$184$	4.11173	0.303121
$185$	−2.79386	−0.205409
$186$	−4.68409	−0.343454
$187$	−3.43258	−0.251015
$188$	6.02255	0.439239
$189$	16.0696	1.16889
$190$	−2.14418	−0.155555
$191$	−4.48856	−0.324781	−0.162391	−	0.986727i	$-0.551920\pi$
$191$	−4.48856	−0.324781	−0.162391	+	0.986727i	$0.551920\pi$
$192$	−1.46195	−0.105507
$193$	15.3315	1.10358	0.551791	−	0.833982i	$-0.313945\pi$
$193$	15.3315	1.10358	0.551791	+	0.833982i	$0.313945\pi$
$194$	−9.00620	−0.646608
$195$	−17.9544	−1.28574
$196$	1.09774	0.0784099
$197$	−14.0812	−1.00325	−0.501623	−	0.865086i	$-0.667264\pi$
$197$	−14.0812	−1.00325	−0.501623	+	0.865086i	$0.667264\pi$
$198$	3.57460	0.254036
$199$	−7.77841	−0.551397	−0.275699	−	0.961244i	$-0.588909\pi$
$199$	−7.77841	−0.551397	−0.275699	+	0.961244i	$0.588909\pi$
$200$	−0.402477	−0.0284595
$201$	−18.4411	−1.30074
$202$	9.96408	0.701071
$203$	14.4473	1.01400
$204$	−1.21113	−0.0847958
$205$	−20.3484	−1.42120
$206$	−7.91932	−0.551765
$207$	−3.54723	−0.246549
$208$	5.72765	0.397141
$209$	4.14345	0.286609
$210$	−8.92022	−0.615554
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−9.71241	−0.667051
$213$	−1.75471	−0.120231
$214$	−19.5270	−1.33484
$215$	3.78948	0.258440
$216$	5.64708	0.384235
$217$	9.11749	0.618935
$218$	2.14391	0.145204
$219$	−20.8525	−1.40908
$220$	−8.88433	−0.598981
$221$	4.74497	0.319182
$222$	1.90491	0.127849
$223$	−25.6890	−1.72026	−0.860130	−	0.510075i	$-0.829618\pi$
$223$	−25.6890	−1.72026	−0.860130	+	0.510075i	$0.829618\pi$
$224$	2.84565	0.190133
$225$	0.347221	0.0231481
$226$	17.2207	1.14550
$227$	−0.630959	−0.0418782	−0.0209391	−	0.999781i	$-0.506666\pi$
$227$	−0.630959	−0.0418782	−0.0209391	+	0.999781i	$0.506666\pi$
$228$	1.46195	0.0968198
$229$	15.0811	0.996588	0.498294	−	0.867008i	$-0.333960\pi$
$229$	15.0811	0.996588	0.498294	+	0.867008i	$0.333960\pi$
$230$	8.81631	0.581330
$231$	17.2376	1.13415
$232$	5.07697	0.333320
$233$	9.27718	0.607768	0.303884	−	0.952709i	$-0.401716\pi$
$233$	9.27718	0.607768	0.303884	+	0.952709i	$0.401716\pi$
$234$	−4.94130	−0.323023
$235$	12.9134	0.842380
$236$	−1.16819	−0.0760430
$237$	−0.0225993	−0.00146798
$238$	2.35743	0.152810
$239$	−3.55667	−0.230062	−0.115031	−	0.993362i	$-0.536697\pi$
$239$	−3.55667	−0.230062	−0.115031	+	0.993362i	$0.536697\pi$
$240$	−3.13468	−0.202343
$241$	22.0482	1.42025	0.710125	−	0.704075i	$-0.248638\pi$
$241$	22.0482	1.42025	0.710125	+	0.704075i	$0.248638\pi$
$242$	6.16822	0.396508
$243$	−8.65550	−0.555250
$244$	−0.741864	−0.0474930
$245$	2.35375	0.150376
$246$	13.8740	0.884573
$247$	−5.72765	−0.364442
$248$	3.20401	0.203455
$249$	−7.68406	−0.486958
$250$	−11.5839	−0.732630
$251$	−20.7095	−1.30717	−0.653587	−	0.756851i	$-0.726737\pi$
$251$	−20.7095	−1.30717	−0.653587	+	0.756851i	$0.726737\pi$
$252$	−2.45497	−0.154649
$253$	−17.0368	−1.07109
$254$	−0.744794	−0.0467325
$255$	−2.59688	−0.162623
$256$	1.00000	0.0625000
$257$	27.8267	1.73578	0.867891	−	0.496754i	$-0.165475\pi$
$257$	27.8267	1.73578	0.867891	+	0.496754i	$0.165475\pi$
$258$	−2.58374	−0.160857
$259$	−3.70787	−0.230396
$260$	12.2811	0.761643
$261$	−4.37995	−0.271112
$262$	0.775074	0.0478842
$263$	−25.6234	−1.58001	−0.790003	−	0.613103i	$-0.789921\pi$
$263$	−25.6234	−1.58001	−0.790003	+	0.613103i	$0.789921\pi$
$264$	6.05751	0.372814
$265$	−20.8252	−1.27928
$266$	−2.84565	−0.174478
$267$	−23.1675	−1.41783
$268$	12.6141	0.770528
$269$	−13.2302	−0.806658	−0.403329	−	0.915055i	$-0.632147\pi$
$269$	−13.2302	−0.806658	−0.403329	+	0.915055i	$0.632147\pi$
$270$	12.1084	0.736892
$271$	16.9638	1.03048	0.515240	−	0.857046i	$-0.327703\pi$
$271$	16.9638	1.03048	0.515240	+	0.857046i	$0.327703\pi$
$272$	0.828433	0.0502311
$273$	−23.8281	−1.44214
$274$	−10.8225	−0.653812
$275$	1.66765	0.100563
$276$	−6.01113	−0.361828
$277$	−5.90568	−0.354838	−0.177419	−	0.984135i	$-0.556775\pi$
$277$	−5.90568	−0.354838	−0.177419	+	0.984135i	$0.556775\pi$
$278$	−5.75291	−0.345037
$279$	−2.76413	−0.165484
$280$	6.10160	0.364640
$281$	−20.4261	−1.21852	−0.609261	−	0.792970i	$-0.708534\pi$
$281$	−20.4261	−1.21852	−0.609261	+	0.792970i	$0.708534\pi$
$282$	−8.80465	−0.524309
$283$	4.60453	0.273711	0.136855	−	0.990591i	$-0.456300\pi$
$283$	4.60453	0.273711	0.136855	+	0.990591i	$0.456300\pi$
$284$	1.20025	0.0712219
$285$	3.13468	0.185683
$286$	−23.7323	−1.40332
$287$	−27.0054	−1.59408
$288$	−0.862709	−0.0508356
$289$	−16.3137	−0.959629
$290$	10.8860	0.639245
$291$	13.1666	0.771839
$292$	14.2635	0.834710
$293$	−16.3422	−0.954723	−0.477362	−	0.878707i	$-0.658407\pi$
$293$	−16.3422	−0.954723	−0.477362	+	0.878707i	$0.658407\pi$
$294$	−1.60484	−0.0935959
$295$	−2.50482	−0.145836
$296$	−1.30300	−0.0757351
$297$	−23.3984	−1.35771
$298$	17.6403	1.02187
$299$	23.5506	1.36196
$300$	0.588401	0.0339713
$301$	5.02920	0.289879
$302$	−11.6954	−0.672992
$303$	−14.5670	−0.836851
$304$	−1.00000	−0.0573539
$305$	−1.59069	−0.0910828
$306$	−0.714697	−0.0408565
$307$	4.35094	0.248321	0.124161	−	0.992262i	$-0.460376\pi$
$307$	4.35094	0.248321	0.124161	+	0.992262i	$0.460376\pi$
$308$	−11.7908	−0.671845
$309$	11.5776	0.658628
$310$	6.86997	0.390188
$311$	−1.44045	−0.0816803	−0.0408402	−	0.999166i	$-0.513003\pi$
$311$	−1.44045	−0.0816803	−0.0408402	+	0.999166i	$0.513003\pi$
$312$	−8.37352	−0.474057
$313$	17.9598	1.01515	0.507575	−	0.861608i	$-0.330542\pi$
$313$	17.9598	1.01515	0.507575	+	0.861608i	$0.330542\pi$
$314$	19.0859	1.07708
$315$	−5.26391	−0.296588
$316$	0.0154584	0.000869600 0
$317$	4.35186	0.244425	0.122212	−	0.992504i	$-0.461001\pi$
$317$	4.35186	0.244425	0.122212	+	0.992504i	$0.461001\pi$
$318$	14.1990	0.796242
$319$	−21.0362	−1.17780
$320$	2.14418	0.119863
$321$	28.5475	1.59337
$322$	11.7006	0.652047
$323$	−0.828433	−0.0460953
$324$	−5.66760	−0.314867
$325$	−2.30525	−0.127872
$326$	−4.38341	−0.242775
$327$	−3.13428	−0.173326
$328$	−9.49007	−0.524001
$329$	17.1381	0.944853
$330$	12.9884	0.714989
$331$	11.8181	0.649582	0.324791	−	0.945786i	$-0.394706\pi$
$331$	11.8181	0.649582	0.324791	+	0.945786i	$0.394706\pi$
$332$	5.25605	0.288463
$333$	1.12411	0.0616007
$334$	12.6831	0.693986
$335$	27.0469	1.47773
$336$	−4.16019	−0.226957
$337$	−19.4839	−1.06135	−0.530677	−	0.847574i	$-0.678062\pi$
$337$	−19.4839	−1.06135	−0.530677	+	0.847574i	$0.678062\pi$
$338$	19.8060	1.07730
$339$	−25.1757	−1.36736
$340$	1.77631	0.0963341
$341$	−13.2757	−0.718917
$342$	0.862709	0.0466500
$343$	−16.7958	−0.906887
$344$	1.76733	0.0952880
$345$	−12.8890	−0.693919
$346$	14.5957	0.784671
$347$	10.4554	0.561274	0.280637	−	0.959814i	$-0.409454\pi$
$347$	10.4554	0.561274	0.280637	+	0.959814i	$0.409454\pi$
$348$	−7.42227	−0.397875
$349$	30.9932	1.65903	0.829515	−	0.558485i	$-0.188617\pi$
$349$	30.9932	1.65903	0.829515	+	0.558485i	$0.188617\pi$
$350$	−1.14531	−0.0612194
$351$	32.3445	1.72642
$352$	−4.14345	−0.220847
$353$	31.9801	1.70213	0.851064	−	0.525061i	$-0.175958\pi$
$353$	31.9801	1.70213	0.851064	+	0.525061i	$0.175958\pi$
$354$	1.70784	0.0907706
$355$	2.57356	0.136590
$356$	15.8470	0.839888
$357$	−3.44644	−0.182405
$358$	−7.01955	−0.370995
$359$	11.4813	0.605958	0.302979	−	0.952997i	$-0.402019\pi$
$359$	11.4813	0.605958	0.302979	+	0.952997i	$0.402019\pi$
$360$	−1.84981	−0.0974934
$361$	1.00000	0.0526316
$362$	6.98602	0.367177
$363$	−9.01761	−0.473302
$364$	16.2989	0.854295
$365$	30.5836	1.60082
$366$	1.08457	0.0566912
$367$	4.21857	0.220207	0.110104	−	0.993920i	$-0.464882\pi$
$367$	4.21857	0.220207	0.110104	+	0.993920i	$0.464882\pi$
$368$	4.11173	0.214339
$369$	8.18717	0.426207
$370$	−2.79386	−0.145246
$371$	−27.6381	−1.43490
$372$	−4.68409	−0.242859
$373$	18.0156	0.932812	0.466406	−	0.884571i	$-0.345549\pi$
$373$	18.0156	0.932812	0.466406	+	0.884571i	$0.345549\pi$
$374$	−3.43258	−0.177494
$375$	16.9351	0.874523
$376$	6.02255	0.310589
$377$	29.0791	1.49765
$378$	16.0696	0.826532
$379$	11.2182	0.576242	0.288121	−	0.957594i	$-0.406970\pi$
$379$	11.2182	0.576242	0.288121	+	0.957594i	$0.406970\pi$
$380$	−2.14418	−0.109994
$381$	1.08885	0.0557834
$382$	−4.48856	−0.229655
$383$	−1.60731	−0.0821299	−0.0410650	−	0.999156i	$-0.513075\pi$
$383$	−1.60731	−0.0821299	−0.0410650	+	0.999156i	$0.513075\pi$
$384$	−1.46195	−0.0746047
$385$	−25.2817	−1.28848
$386$	15.3315	0.780351
$387$	−1.52469	−0.0775044
$388$	−9.00620	−0.457221
$389$	−17.5609	−0.890375	−0.445187	−	0.895437i	$-0.646863\pi$
$389$	−17.5609	−0.890375	−0.445187	+	0.895437i	$0.646863\pi$
$390$	−17.9544	−0.909155
$391$	3.40629	0.172264
$392$	1.09774	0.0554442
$393$	−1.13312	−0.0571582
$394$	−14.0812	−0.709402
$395$	0.0331455	0.00166773
$396$	3.57460	0.179630
$397$	−0.150873	−0.00757208	−0.00378604	−	0.999993i	$-0.501205\pi$
$397$	−0.150873	−0.00757208	−0.00378604	+	0.999993i	$0.501205\pi$
$398$	−7.77841	−0.389897
$399$	4.16019	0.208270
$400$	−0.402477	−0.0201239
$401$	−5.06306	−0.252837	−0.126418	−	0.991977i	$-0.540348\pi$
$401$	−5.06306	−0.252837	−0.126418	+	0.991977i	$0.540348\pi$
$402$	−18.4411	−0.919760
$403$	18.3514	0.914149
$404$	9.96408	0.495732
$405$	−12.1524	−0.603857
$406$	14.4473	0.717007
$407$	5.39891	0.267614
$408$	−1.21113	−0.0599597
$409$	29.5594	1.46162	0.730809	−	0.682581i	$-0.239143\pi$
$409$	29.5594	1.46162	0.730809	+	0.682581i	$0.239143\pi$
$410$	−20.3484	−1.00494
$411$	15.8219	0.780439
$412$	−7.91932	−0.390157
$413$	−3.32427	−0.163577
$414$	−3.54723	−0.174337
$415$	11.2699	0.553219
$416$	5.72765	0.280821
$417$	8.41045	0.411862
$418$	4.14345	0.202663
$419$	−10.8629	−0.530687	−0.265343	−	0.964154i	$-0.585485\pi$
$419$	−10.8629	−0.530687	−0.265343	+	0.964154i	$0.585485\pi$
$420$	−8.92022	−0.435262
$421$	20.9345	1.02029	0.510143	−	0.860090i	$-0.329593\pi$
$421$	20.9345	1.02029	0.510143	+	0.860090i	$0.329593\pi$
$422$	−1.00000	−0.0486792
$423$	−5.19571	−0.252624
$424$	−9.71241	−0.471676
$425$	−0.333426	−0.0161735
$426$	−1.75471	−0.0850158
$427$	−2.11109	−0.102163
$428$	−19.5270	−0.943875
$429$	34.6953	1.67511
$430$	3.78948	0.182745
$431$	−24.5708	−1.18353	−0.591767	−	0.806109i	$-0.701569\pi$
$431$	−24.5708	−1.18353	−0.591767	+	0.806109i	$0.701569\pi$
$432$	5.64708	0.271695
$433$	−10.2969	−0.494836	−0.247418	−	0.968909i	$-0.579582\pi$
$433$	−10.2969	−0.494836	−0.247418	+	0.968909i	$0.579582\pi$
$434$	9.11749	0.437653
$435$	−15.9147	−0.763051
$436$	2.14391	0.102674
$437$	−4.11173	−0.196691
$438$	−20.8525	−0.996372
$439$	23.3441	1.11415	0.557077	−	0.830461i	$-0.311923\pi$
$439$	23.3441	1.11415	0.557077	+	0.830461i	$0.311923\pi$
$440$	−8.88433	−0.423544
$441$	−0.947029	−0.0450966
$442$	4.74497	0.225695
$443$	−35.5818	−1.69054	−0.845271	−	0.534338i	$-0.820561\pi$
$443$	−35.5818	−1.69054	−0.845271	+	0.534338i	$0.820561\pi$
$444$	1.90491	0.0904031
$445$	33.9788	1.61075
$446$	−25.6890	−1.21641
$447$	−25.7892	−1.21979
$448$	2.84565	0.134444
$449$	25.6489	1.21045	0.605223	−	0.796056i	$-0.293084\pi$
$449$	25.6489	1.21045	0.605223	+	0.796056i	$0.293084\pi$
$450$	0.347221	0.0163682
$451$	39.3217	1.85159
$452$	17.2207	0.809993
$453$	17.0980	0.803334
$454$	−0.630959	−0.0296124
$455$	34.9478	1.63838
$456$	1.46195	0.0684620
$457$	−24.8873	−1.16418	−0.582090	−	0.813124i	$-0.697765\pi$
$457$	−24.8873	−1.16418	−0.582090	+	0.813124i	$0.697765\pi$
$458$	15.0811	0.704694
$459$	4.67823	0.218361
$460$	8.81631	0.411062
$461$	18.8711	0.878915	0.439457	−	0.898263i	$-0.355171\pi$
$461$	18.8711	0.878915	0.439457	+	0.898263i	$0.355171\pi$
$462$	17.2376	0.801965
$463$	−4.38457	−0.203768	−0.101884	−	0.994796i	$-0.532487\pi$
$463$	−4.38457	−0.203768	−0.101884	+	0.994796i	$0.532487\pi$
$464$	5.07697	0.235692
$465$	−10.0435	−0.465758
$466$	9.27718	0.429757
$467$	−9.98957	−0.462262	−0.231131	−	0.972923i	$-0.574243\pi$
$467$	−9.98957	−0.462262	−0.231131	+	0.972923i	$0.574243\pi$
$468$	−4.94130	−0.228412
$469$	35.8953	1.65749
$470$	12.9134	0.595653
$471$	−27.9026	−1.28568
$472$	−1.16819	−0.0537705
$473$	−7.32285	−0.336705
$474$	−0.0225993	−0.00103802
$475$	0.402477	0.0184669
$476$	2.35743	0.108053
$477$	8.37899	0.383648
$478$	−3.55667	−0.162678
$479$	40.2855	1.84069	0.920346	−	0.391106i	$-0.127907\pi$
$479$	40.2855	1.84069	0.920346	+	0.391106i	$0.127907\pi$
$480$	−3.13468	−0.143078
$481$	−7.46311	−0.340288
$482$	22.0482	1.00427
$483$	−17.1056	−0.778332
$484$	6.16822	0.280374
$485$	−19.3109	−0.876865
$486$	−8.65550	−0.392621
$487$	14.0124	0.634964	0.317482	−	0.948264i	$-0.397163\pi$
$487$	14.0124	0.634964	0.317482	+	0.948264i	$0.397163\pi$
$488$	−0.741864	−0.0335826
$489$	6.40832	0.289794
$490$	2.35375	0.106332
$491$	−12.7909	−0.577243	−0.288622	−	0.957443i	$-0.593197\pi$
$491$	−12.7909	−0.577243	−0.288622	+	0.957443i	$0.593197\pi$
$492$	13.8740	0.625487
$493$	4.20593	0.189426
$494$	−5.72765	−0.257699
$495$	7.66459	0.344498
$496$	3.20401	0.143864
$497$	3.41550	0.153206
$498$	−7.68406	−0.344331
$499$	2.40267	0.107558	0.0537791	−	0.998553i	$-0.482873\pi$
$499$	2.40267	0.107558	0.0537791	+	0.998553i	$0.482873\pi$
$500$	−11.5839	−0.518048
$501$	−18.5420	−0.828394
$502$	−20.7095	−0.924312
$503$	−32.3328	−1.44165	−0.720824	−	0.693118i	$-0.756237\pi$
$503$	−32.3328	−1.44165	−0.720824	+	0.693118i	$0.756237\pi$
$504$	−2.45497	−0.109353
$505$	21.3648	0.950722
$506$	−17.0368	−0.757377
$507$	−28.9553	−1.28595
$508$	−0.744794	−0.0330449
$509$	30.9450	1.37161	0.685807	−	0.727783i	$-0.259449\pi$
$509$	30.9450	1.37161	0.685807	+	0.727783i	$0.259449\pi$
$510$	−2.59688	−0.114992
$511$	40.5890	1.79555
$512$	1.00000	0.0441942
$513$	−5.64708	−0.249325
$514$	27.8267	1.22738
$515$	−16.9805	−0.748249
$516$	−2.58374	−0.113743
$517$	−24.9542	−1.09748
$518$	−3.70787	−0.162915
$519$	−21.3382	−0.936642
$520$	12.2811	0.538563
$521$	27.0458	1.18490	0.592450	−	0.805608i	$-0.298161\pi$
$521$	27.0458	1.18490	0.592450	+	0.805608i	$0.298161\pi$
$522$	−4.37995	−0.191705
$523$	−12.6584	−0.553514	−0.276757	−	0.960940i	$-0.589260\pi$
$523$	−12.6584	−0.553514	−0.276757	+	0.960940i	$0.589260\pi$
$524$	0.775074	0.0338592
$525$	1.67438	0.0730761
$526$	−25.6234	−1.11723
$527$	2.65430	0.115623
$528$	6.05751	0.263619
$529$	−6.09367	−0.264942
$530$	−20.8252	−0.904588
$531$	1.00781	0.0437353
$532$	−2.84565	−0.123375
$533$	−54.3558	−2.35441
$534$	−23.1675	−1.00255
$535$	−41.8696	−1.81018
$536$	12.6141	0.544846
$537$	10.2622	0.442847
$538$	−13.2302	−0.570393
$539$	−4.54843	−0.195915
$540$	12.1084	0.521061
$541$	12.2683	0.527455	0.263727	−	0.964597i	$-0.415048\pi$
$541$	12.2683	0.527455	0.263727	+	0.964597i	$0.415048\pi$
$542$	16.9638	0.728660
$543$	−10.2132	−0.438290
$544$	0.828433	0.0355188
$545$	4.59693	0.196911
$546$	−23.8281	−1.01975
$547$	−15.9475	−0.681867	−0.340933	−	0.940087i	$-0.610743\pi$
$547$	−15.9475	−0.681867	−0.340933	+	0.940087i	$0.610743\pi$
$548$	−10.8225	−0.462315
$549$	0.640013	0.0273151
$550$	1.66765	0.0711087
$551$	−5.07697	−0.216286
$552$	−6.01113	−0.255851
$553$	0.0439891	0.00187061
$554$	−5.90568	−0.250908
$555$	4.08448	0.173377
$556$	−5.75291	−0.243978
$557$	−4.10858	−0.174086	−0.0870431	−	0.996205i	$-0.527742\pi$
$557$	−4.10858	−0.174086	−0.0870431	+	0.996205i	$0.527742\pi$
$558$	−2.76413	−0.117015
$559$	10.1226	0.428142
$560$	6.10160	0.257840
$561$	5.01824	0.211870
$562$	−20.4261	−0.861625
$563$	19.4469	0.819591	0.409796	−	0.912177i	$-0.365600\pi$
$563$	19.4469	0.819591	0.409796	+	0.912177i	$0.365600\pi$
$564$	−8.80465	−0.370743
$565$	36.9243	1.55342
$566$	4.60453	0.193543
$567$	−16.1280	−0.677314
$568$	1.20025	0.0503615
$569$	−27.9325	−1.17099	−0.585496	−	0.810675i	$-0.699100\pi$
$569$	−27.9325	−1.17099	−0.585496	+	0.810675i	$0.699100\pi$
$570$	3.13468	0.131297
$571$	40.9053	1.71184	0.855918	−	0.517112i	$-0.172993\pi$
$571$	40.9053	1.71184	0.855918	+	0.517112i	$0.172993\pi$
$572$	−23.7323	−0.992296
$573$	6.56204	0.274133
$574$	−27.0054	−1.12719
$575$	−1.65488	−0.0690132
$576$	−0.862709	−0.0359462
$577$	29.0254	1.20834	0.604172	−	0.796854i	$-0.293504\pi$
$577$	29.0254	1.20834	0.604172	+	0.796854i	$0.293504\pi$
$578$	−16.3137	−0.678560
$579$	−22.4138	−0.931485
$580$	10.8860	0.452015
$581$	14.9569	0.620516
$582$	13.1666	0.545773
$583$	40.2429	1.66669
$584$	14.2635	0.590229
$585$	−10.5950	−0.438051
$586$	−16.3422	−0.675091
$587$	−36.9891	−1.52670	−0.763351	−	0.645984i	$-0.776447\pi$
$587$	−36.9891	−1.52670	−0.763351	+	0.645984i	$0.776447\pi$
$588$	−1.60484	−0.0661823
$589$	−3.20401	−0.132019
$590$	−2.50482	−0.103122
$591$	20.5860	0.846796
$592$	−1.30300	−0.0535528
$593$	14.0042	0.575084	0.287542	−	0.957768i	$-0.407162\pi$
$593$	14.0042	0.575084	0.287542	+	0.957768i	$0.407162\pi$
$594$	−23.3984	−0.960049
$595$	5.05477	0.207225
$596$	17.6403	0.722574
$597$	11.3716	0.465410
$598$	23.5506	0.963054
$599$	−21.9668	−0.897540	−0.448770	−	0.893647i	$-0.648138\pi$
$599$	−21.9668	−0.897540	−0.448770	+	0.893647i	$0.648138\pi$
$600$	0.588401	0.0240214
$601$	−0.402585	−0.0164218	−0.00821089	−	0.999966i	$-0.502614\pi$
$601$	−0.402585	−0.0164218	−0.00821089	+	0.999966i	$0.502614\pi$
$602$	5.02920	0.204975
$603$	−10.8823	−0.443161
$604$	−11.6954	−0.475877
$605$	13.2258	0.537705
$606$	−14.5670	−0.591743
$607$	−17.8165	−0.723150	−0.361575	−	0.932343i	$-0.617761\pi$
$607$	−17.8165	−0.723150	−0.361575	+	0.932343i	$0.617761\pi$
$608$	−1.00000	−0.0405554
$609$	−21.1212	−0.855874
$610$	−1.59069	−0.0644053
$611$	34.4950	1.39552
$612$	−0.714697	−0.0288899
$613$	0.241320	0.00974684	0.00487342	−	0.999988i	$-0.498449\pi$
$613$	0.241320	0.00974684	0.00487342	+	0.999988i	$0.498449\pi$
$614$	4.35094	0.175590
$615$	29.7484	1.19957
$616$	−11.7908	−0.475066
$617$	−22.2070	−0.894020	−0.447010	−	0.894529i	$-0.647511\pi$
$617$	−22.2070	−0.894020	−0.447010	+	0.894529i	$0.647511\pi$
$618$	11.5776	0.465720
$619$	−43.9613	−1.76695	−0.883476	−	0.468476i	$-0.844803\pi$
$619$	−43.9613	−1.76695	−0.883476	+	0.468476i	$0.844803\pi$
$620$	6.86997	0.275905
$621$	23.2193	0.931757
$622$	−1.44045	−0.0577567
$623$	45.0950	1.80669
$624$	−8.37352	−0.335209
$625$	−22.8256	−0.913025
$626$	17.9598	0.717819
$627$	−6.05751	−0.241914
$628$	19.0859	0.761611
$629$	−1.07945	−0.0430403
$630$	−5.26391	−0.209719
$631$	17.9004	0.712603	0.356301	−	0.934371i	$-0.384038\pi$
$631$	17.9004	0.712603	0.356301	+	0.934371i	$0.384038\pi$
$632$	0.0154584	0.000614900 0
$633$	1.46195	0.0581072
$634$	4.35186	0.172834
$635$	−1.59697	−0.0633740
$636$	14.1990	0.563028
$637$	6.28746	0.249118
$638$	−21.0362	−0.832831
$639$	−1.03547	−0.0409625
$640$	2.14418	0.0847563
$641$	19.7232	0.779021	0.389511	−	0.921022i	$-0.372644\pi$
$641$	19.7232	0.779021	0.389511	+	0.921022i	$0.372644\pi$
$642$	28.5475	1.12668
$643$	29.3895	1.15901	0.579505	−	0.814969i	$-0.303246\pi$
$643$	29.3895	1.15901	0.579505	+	0.814969i	$0.303246\pi$
$644$	11.7006	0.461067
$645$	−5.54002	−0.218138
$646$	−0.828433	−0.0325943
$647$	−18.7284	−0.736290	−0.368145	−	0.929768i	$-0.620007\pi$
$647$	−18.7284	−0.736290	−0.368145	+	0.929768i	$0.620007\pi$
$648$	−5.66760	−0.222645
$649$	4.84036	0.190001
$650$	−2.30525	−0.0904193
$651$	−13.3293	−0.522416
$652$	−4.38341	−0.171668
$653$	−28.2590	−1.10586	−0.552930	−	0.833228i	$-0.686490\pi$
$653$	−28.2590	−1.10586	−0.552930	+	0.833228i	$0.686490\pi$
$654$	−3.13428	−0.122560
$655$	1.66190	0.0649358
$656$	−9.49007	−0.370525
$657$	−12.3053	−0.480075
$658$	17.1381	0.668112
$659$	−14.9519	−0.582442	−0.291221	−	0.956656i	$-0.594061\pi$
$659$	−14.9519	−0.582442	−0.291221	+	0.956656i	$0.594061\pi$
$660$	12.9884	0.505574
$661$	33.3340	1.29654	0.648272	−	0.761409i	$-0.275492\pi$
$661$	33.3340	1.29654	0.648272	+	0.761409i	$0.275492\pi$
$662$	11.8181	0.459324
$663$	−6.93690	−0.269407
$664$	5.25605	0.203974
$665$	−6.10160	−0.236610
$666$	1.12411	0.0435583
$667$	20.8751	0.808289
$668$	12.6831	0.490722
$669$	37.5559	1.45200
$670$	27.0469	1.04491
$671$	3.07388	0.118666
$672$	−4.16019	−0.160483
$673$	−15.6909	−0.604839	−0.302419	−	0.953175i	$-0.597794\pi$
$673$	−15.6909	−0.604839	−0.302419	+	0.953175i	$0.597794\pi$
$674$	−19.4839	−0.750490
$675$	−2.27282	−0.0874809
$676$	19.8060	0.761768
$677$	2.12121	0.0815246	0.0407623	−	0.999169i	$-0.487021\pi$
$677$	2.12121	0.0815246	0.0407623	+	0.999169i	$0.487021\pi$
$678$	−25.1757	−0.966868
$679$	−25.6285	−0.983532
$680$	1.77631	0.0681185
$681$	0.922429	0.0353476
$682$	−13.2757	−0.508351
$683$	44.9510	1.72000	0.860001	−	0.510293i	$-0.170463\pi$
$683$	44.9510	1.72000	0.860001	+	0.510293i	$0.170463\pi$
$684$	0.862709	0.0329865
$685$	−23.2055	−0.886635
$686$	−16.7958	−0.641266
$687$	−22.0478	−0.841176
$688$	1.76733	0.0673788
$689$	−55.6293	−2.11931
$690$	−12.8890	−0.490675
$691$	−30.8647	−1.17415	−0.587074	−	0.809534i	$-0.699720\pi$
$691$	−30.8647	−1.17415	−0.587074	+	0.809534i	$0.699720\pi$
$692$	14.5957	0.554846
$693$	10.1721	0.386405
$694$	10.4554	0.396880
$695$	−12.3353	−0.467904
$696$	−7.42227	−0.281340
$697$	−7.86189	−0.297790
$698$	30.9932	1.17311
$699$	−13.5628	−0.512990
$700$	−1.14531	−0.0432887
$701$	−13.8059	−0.521441	−0.260721	−	0.965414i	$-0.583960\pi$
$701$	−13.8059	−0.521441	−0.260721	+	0.965414i	$0.583960\pi$
$702$	32.3445	1.22076
$703$	1.30300	0.0491434
$704$	−4.14345	−0.156162
$705$	−18.8788	−0.711016
$706$	31.9801	1.20359
$707$	28.3543	1.06637
$708$	1.70784	0.0641845
$709$	38.8522	1.45913	0.729563	−	0.683914i	$-0.239724\pi$
$709$	38.8522	1.45913	0.729563	+	0.683914i	$0.239724\pi$
$710$	2.57356	0.0965841
$711$	−0.0133361	−0.000500142 0
$712$	15.8470	0.593891
$713$	13.1740	0.493370
$714$	−3.44644	−0.128980
$715$	−50.8863	−1.90304
$716$	−7.01955	−0.262333
$717$	5.19967	0.194185
$718$	11.4813	0.428477
$719$	−5.04037	−0.187974	−0.0939870	−	0.995573i	$-0.529961\pi$
$719$	−5.04037	−0.187974	−0.0939870	+	0.995573i	$0.529961\pi$
$720$	−1.84981	−0.0689383
$721$	−22.5356	−0.839271
$722$	1.00000	0.0372161
$723$	−32.2333	−1.19877
$724$	6.98602	0.259633
$725$	−2.04337	−0.0758887
$726$	−9.01761	−0.334675
$727$	21.3845	0.793106	0.396553	−	0.918012i	$-0.370206\pi$
$727$	21.3845	0.793106	0.396553	+	0.918012i	$0.370206\pi$
$728$	16.2989	0.604077
$729$	29.6567	1.09840
$730$	30.5836	1.13195
$731$	1.46411	0.0541522
$732$	1.08457	0.0400867
$733$	38.8646	1.43550	0.717748	−	0.696303i	$-0.245173\pi$
$733$	38.8646	1.43550	0.717748	+	0.696303i	$0.245173\pi$
$734$	4.21857	0.155710
$735$	−3.44106	−0.126926
$736$	4.11173	0.151560
$737$	−52.2659	−1.92524
$738$	8.18717	0.301374
$739$	−13.4327	−0.494129	−0.247064	−	0.968999i	$-0.579466\pi$
$739$	−13.4327	−0.494129	−0.247064	+	0.968999i	$0.579466\pi$
$740$	−2.79386	−0.102704
$741$	8.37352	0.307609
$742$	−27.6381	−1.01463
$743$	2.75446	0.101051	0.0505257	−	0.998723i	$-0.483910\pi$
$743$	2.75446	0.101051	0.0505257	+	0.998723i	$0.483910\pi$
$744$	−4.68409	−0.171727
$745$	37.8240	1.38576
$746$	18.0156	0.659598
$747$	−4.53444	−0.165906
$748$	−3.43258	−0.125507
$749$	−55.5672	−2.03038
$750$	16.9351	0.618381
$751$	33.9990	1.24064	0.620320	−	0.784349i	$-0.287003\pi$
$751$	33.9990	1.24064	0.620320	+	0.784349i	$0.287003\pi$
$752$	6.02255	0.219620
$753$	30.2763	1.10333
$754$	29.0791	1.05900
$755$	−25.0770	−0.912645
$756$	16.0696	0.584447
$757$	−22.4250	−0.815049	−0.407524	−	0.913194i	$-0.633608\pi$
$757$	−22.4250	−0.815049	−0.407524	+	0.913194i	$0.633608\pi$
$758$	11.2182	0.407464
$759$	24.9069	0.904062
$760$	−2.14418	−0.0777777
$761$	−38.2175	−1.38538	−0.692691	−	0.721235i	$-0.743575\pi$
$761$	−38.2175	−1.38538	−0.692691	+	0.721235i	$0.743575\pi$
$762$	1.08885	0.0394448
$763$	6.10081	0.220864
$764$	−4.48856	−0.162391
$765$	−1.53244	−0.0554055
$766$	−1.60731	−0.0580746
$767$	−6.69101	−0.241598
$768$	−1.46195	−0.0527535
$769$	−18.3195	−0.660618	−0.330309	−	0.943873i	$-0.607153\pi$
$769$	−18.3195	−0.660618	−0.330309	+	0.943873i	$0.607153\pi$
$770$	−25.2817	−0.911090
$771$	−40.6812	−1.46510
$772$	15.3315	0.551791
$773$	−12.4872	−0.449133	−0.224566	−	0.974459i	$-0.572097\pi$
$773$	−12.4872	−0.449133	−0.224566	+	0.974459i	$0.572097\pi$
$774$	−1.52469	−0.0548039
$775$	−1.28954	−0.0463216
$776$	−9.00620	−0.323304
$777$	5.42072	0.194467
$778$	−17.5609	−0.629590
$779$	9.49007	0.340017
$780$	−17.9544	−0.642870
$781$	−4.97319	−0.177955
$782$	3.40629	0.121809
$783$	28.6701	1.02458
$784$	1.09774	0.0392049
$785$	40.9237	1.46063
$786$	−1.13312	−0.0404169
$787$	33.3598	1.18915	0.594575	−	0.804040i	$-0.297320\pi$
$787$	33.3598	1.18915	0.594575	+	0.804040i	$0.297320\pi$
$788$	−14.0812	−0.501623
$789$	37.4600	1.33361
$790$	0.0331455	0.00117927
$791$	49.0041	1.74238
$792$	3.57460	0.127018
$793$	−4.24914	−0.150891
$794$	−0.150873	−0.00535427
$795$	30.4453	1.07978
$796$	−7.77841	−0.275699
$797$	−19.1245	−0.677424	−0.338712	−	0.940890i	$-0.609991\pi$
$797$	−19.1245	−0.677424	−0.338712	+	0.940890i	$0.609991\pi$
$798$	4.16019	0.147269
$799$	4.98928	0.176508
$800$	−0.402477	−0.0142297
$801$	−13.6713	−0.483053
$802$	−5.06306	−0.178783
$803$	−59.1003	−2.08560
$804$	−18.4411	−0.650369
$805$	25.0881	0.884241
$806$	18.3514	0.646401
$807$	19.3418	0.680864
$808$	9.96408	0.350535
$809$	−49.0298	−1.72380	−0.861898	−	0.507081i	$-0.830725\pi$
$809$	−49.0298	−1.72380	−0.861898	+	0.507081i	$0.830725\pi$
$810$	−12.1524	−0.426991
$811$	9.58531	0.336586	0.168293	−	0.985737i	$-0.446175\pi$
$811$	9.58531	0.336586	0.168293	+	0.985737i	$0.446175\pi$
$812$	14.4473	0.507001
$813$	−24.8003	−0.869783
$814$	5.39891	0.189232
$815$	−9.39884	−0.329227
$816$	−1.21113	−0.0423979
$817$	−1.76733	−0.0618310
$818$	29.5594	1.03352
$819$	−14.0612	−0.491339
$820$	−20.3484	−0.710599
$821$	25.8400	0.901823	0.450912	−	0.892569i	$-0.351099\pi$
$821$	25.8400	0.901823	0.450912	+	0.892569i	$0.351099\pi$
$822$	15.8219	0.551854
$823$	−22.3393	−0.778700	−0.389350	−	0.921090i	$-0.627300\pi$
$823$	−22.3393	−0.778700	−0.389350	+	0.921090i	$0.627300\pi$
$824$	−7.91932	−0.275882
$825$	−2.43801	−0.0848807
$826$	−3.32427	−0.115666
$827$	12.8864	0.448104	0.224052	−	0.974577i	$-0.428072\pi$
$827$	12.8864	0.448104	0.224052	+	0.974577i	$0.428072\pi$
$828$	−3.54723	−0.123275
$829$	17.9879	0.624747	0.312374	−	0.949959i	$-0.398876\pi$
$829$	17.9879	0.624747	0.312374	+	0.949959i	$0.398876\pi$
$830$	11.2699	0.391185
$831$	8.63379	0.299503
$832$	5.72765	0.198571
$833$	0.909403	0.0315089
$834$	8.41045	0.291230
$835$	27.1948	0.941115
$836$	4.14345	0.143304
$837$	18.0933	0.625395
$838$	−10.8629	−0.375252
$839$	15.2591	0.526802	0.263401	−	0.964686i	$-0.415156\pi$
$839$	15.2591	0.526802	0.263401	+	0.964686i	$0.415156\pi$
$840$	−8.92022	−0.307777
$841$	−3.22436	−0.111185
$842$	20.9345	0.721450
$843$	29.8619	1.02850
$844$	−1.00000	−0.0344214
$845$	42.4676	1.46093
$846$	−5.19571	−0.178632
$847$	17.5526	0.603115
$848$	−9.71241	−0.333526
$849$	−6.73158	−0.231027
$850$	−0.333426	−0.0114364
$851$	−5.35757	−0.183655
$852$	−1.75471	−0.0601153
$853$	20.0870	0.687764	0.343882	−	0.939013i	$-0.388258\pi$
$853$	20.0870	0.687764	0.343882	+	0.939013i	$0.388258\pi$
$854$	−2.11109	−0.0722399
$855$	1.84981	0.0632621
$856$	−19.5270	−0.667421
$857$	−49.4204	−1.68817	−0.844085	−	0.536210i	$-0.819856\pi$
$857$	−49.4204	−1.68817	−0.844085	+	0.536210i	$0.819856\pi$
$858$	34.6953	1.18448
$859$	−14.5429	−0.496198	−0.248099	−	0.968735i	$-0.579806\pi$
$859$	−14.5429	−0.496198	−0.248099	+	0.968735i	$0.579806\pi$
$860$	3.78948	0.129220
$861$	39.4805	1.34549
$862$	−24.5708	−0.836884
$863$	−4.16415	−0.141749	−0.0708747	−	0.997485i	$-0.522579\pi$
$863$	−4.16415	−0.141749	−0.0708747	+	0.997485i	$0.522579\pi$
$864$	5.64708	0.192118
$865$	31.2959	1.06409
$866$	−10.2969	−0.349902
$867$	23.8498	0.809981
$868$	9.11749	0.309468
$869$	−0.0640510	−0.00217278
$870$	−15.9147	−0.539559
$871$	72.2491	2.44807
$872$	2.14391	0.0726018
$873$	7.76973	0.262966
$874$	−4.11173	−0.139081
$875$	−32.9638	−1.11438
$876$	−20.8525	−0.704542
$877$	−17.1129	−0.577860	−0.288930	−	0.957350i	$-0.593300\pi$
$877$	−17.1129	−0.577860	−0.288930	+	0.957350i	$0.593300\pi$
$878$	23.3441	0.787826
$879$	23.8915	0.805840
$880$	−8.88433	−0.299491
$881$	33.3241	1.12272	0.561358	−	0.827573i	$-0.310279\pi$
$881$	33.3241	1.12272	0.561358	+	0.827573i	$0.310279\pi$
$882$	−0.947029	−0.0318881
$883$	−14.1100	−0.474839	−0.237420	−	0.971407i	$-0.576302\pi$
$883$	−14.1100	−0.474839	−0.237420	+	0.971407i	$0.576302\pi$
$884$	4.74497	0.159591
$885$	3.66192	0.123094
$886$	−35.5818	−1.19539
$887$	−2.02756	−0.0680787	−0.0340394	−	0.999420i	$-0.510837\pi$
$887$	−2.02756	−0.0680787	−0.0340394	+	0.999420i	$0.510837\pi$
$888$	1.90491	0.0639247
$889$	−2.11942	−0.0710832
$890$	33.9788	1.13897
$891$	23.4835	0.786726
$892$	−25.6890	−0.860130
$893$	−6.02255	−0.201537
$894$	−25.7892	−0.862518
$895$	−15.0512	−0.503106
$896$	2.84565	0.0950666
$897$	−34.4297	−1.14957
$898$	25.6489	0.855915
$899$	16.2666	0.542523
$900$	0.347221	0.0115740
$901$	−8.04608	−0.268054
$902$	39.3217	1.30927
$903$	−7.35243	−0.244674
$904$	17.2207	0.572751
$905$	14.9793	0.497929
$906$	17.0980	0.568043
$907$	−24.9178	−0.827383	−0.413692	−	0.910417i	$-0.635761\pi$
$907$	−24.9178	−0.827383	−0.413692	+	0.910417i	$0.635761\pi$
$908$	−0.630959	−0.0209391
$909$	−8.59611	−0.285115
$910$	34.9478	1.15851
$911$	−10.1240	−0.335423	−0.167712	−	0.985836i	$-0.553638\pi$
$911$	−10.1240	−0.335423	−0.167712	+	0.985836i	$0.553638\pi$
$912$	1.46195	0.0484099
$913$	−21.7782	−0.720753
$914$	−24.8873	−0.823199
$915$	2.32551	0.0768790
$916$	15.0811	0.498294
$917$	2.20559	0.0728350
$918$	4.67823	0.154404
$919$	15.2836	0.504160	0.252080	−	0.967706i	$-0.418885\pi$
$919$	15.2836	0.504160	0.252080	+	0.967706i	$0.418885\pi$
$920$	8.81631	0.290665
$921$	−6.36084	−0.209597
$922$	18.8711	0.621486
$923$	6.87463	0.226281
$924$	17.2376	0.567075
$925$	0.524427	0.0172430
$926$	−4.38457	−0.144086
$927$	6.83207	0.224395
$928$	5.07697	0.166660
$929$	28.5284	0.935985	0.467993	−	0.883732i	$-0.344977\pi$
$929$	28.5284	0.935985	0.467993	+	0.883732i	$0.344977\pi$
$930$	−10.0435	−0.329341
$931$	−1.09774	−0.0359769
$932$	9.27718	0.303884
$933$	2.10586	0.0689427
$934$	−9.98957	−0.326869
$935$	−7.36007	−0.240700
$936$	−4.94130	−0.161511
$937$	−50.1429	−1.63810	−0.819048	−	0.573725i	$-0.805498\pi$
$937$	−50.1429	−1.63810	−0.819048	+	0.573725i	$0.805498\pi$
$938$	35.8953	1.17202
$939$	−26.2563	−0.856843
$940$	12.9134	0.421190
$941$	−19.0410	−0.620720	−0.310360	−	0.950619i	$-0.600450\pi$
$941$	−19.0410	−0.620720	−0.310360	+	0.950619i	$0.600450\pi$
$942$	−27.9026	−0.909116
$943$	−39.0206	−1.27069
$944$	−1.16819	−0.0380215
$945$	34.4562	1.12086
$946$	−7.32285	−0.238086
$947$	−51.1006	−1.66054	−0.830272	−	0.557358i	$-0.811815\pi$
$947$	−51.1006	−1.66054	−0.830272	+	0.557358i	$0.811815\pi$
$948$	−0.0225993	−0.000733991 0
$949$	81.6965	2.65198
$950$	0.402477	0.0130581
$951$	−6.36219	−0.206308
$952$	2.35743	0.0764048
$953$	−30.2817	−0.980922	−0.490461	−	0.871463i	$-0.663172\pi$
$953$	−30.2817	−0.980922	−0.490461	+	0.871463i	$0.663172\pi$
$954$	8.37899	0.271280
$955$	−9.62430	−0.311435
$956$	−3.55667	−0.115031
$957$	30.7538	0.994130
$958$	40.2855	1.30157
$959$	−30.7971	−0.994491
$960$	−3.13468	−0.101171
$961$	−20.7344	−0.668850
$962$	−7.46311	−0.240620
$963$	16.8462	0.542860
$964$	22.0482	0.710125
$965$	32.8735	1.05823
$966$	−17.1056	−0.550364
$967$	−19.5173	−0.627635	−0.313818	−	0.949483i	$-0.601608\pi$
$967$	−19.5173	−0.627635	−0.313818	+	0.949483i	$0.601608\pi$
$968$	6.16822	0.198254
$969$	1.21113	0.0389070
$970$	−19.3109	−0.620037
$971$	−22.1916	−0.712163	−0.356081	−	0.934455i	$-0.615887\pi$
$971$	−22.1916	−0.712163	−0.356081	+	0.934455i	$0.615887\pi$
$972$	−8.65550	−0.277625
$973$	−16.3708	−0.524823
$974$	14.0124	0.448988
$975$	3.37015	0.107931
$976$	−0.741864	−0.0237465
$977$	25.5094	0.816118	0.408059	−	0.912956i	$-0.366206\pi$
$977$	25.5094	0.816118	0.408059	+	0.912956i	$0.366206\pi$
$978$	6.40832	0.204915
$979$	−65.6612	−2.09854
$980$	2.35375	0.0751879
$981$	−1.84957	−0.0590522
$982$	−12.7909	−0.408173
$983$	−4.81931	−0.153712	−0.0768560	−	0.997042i	$-0.524488\pi$
$983$	−4.81931	−0.153712	−0.0768560	+	0.997042i	$0.524488\pi$
$984$	13.8740	0.442286
$985$	−30.1928	−0.962021
$986$	4.20593	0.133944
$987$	−25.0550	−0.797509
$988$	−5.72765	−0.182221
$989$	7.26678	0.231070
$990$	7.66459	0.243597
$991$	21.3126	0.677016	0.338508	−	0.940963i	$-0.390078\pi$
$991$	21.3126	0.677016	0.338508	+	0.940963i	$0.390078\pi$
$992$	3.20401	0.101727
$993$	−17.2775	−0.548283
$994$	3.41550	0.108333
$995$	−16.6783	−0.528739
$996$	−7.68406	−0.243479
$997$	−51.5769	−1.63346	−0.816728	−	0.577023i	$-0.804214\pi$
$997$	−51.5769	−1.63346	−0.816728	+	0.577023i	$0.804214\pi$
$998$	2.40267	0.0760552
$999$	−7.35812	−0.232801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.13	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.13	✓	47	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.46195 q^{3} +1.00000 q^{4} +2.14418 q^{5} -1.46195 q^{6} +2.84565 q^{7} +1.00000 q^{8} -0.862709 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.46195 q^{3} +1.00000 q^{4} +2.14418 q^{5} -1.46195 q^{6} +2.84565 q^{7} +1.00000 q^{8} -0.862709 q^{9} +2.14418 q^{10} -4.14345 q^{11} -1.46195 q^{12} +5.72765 q^{13} +2.84565 q^{14} -3.13468 q^{15} +1.00000 q^{16} +0.828433 q^{17} -0.862709 q^{18} -1.00000 q^{19} +2.14418 q^{20} -4.16019 q^{21} -4.14345 q^{22} +4.11173 q^{23} -1.46195 q^{24} -0.402477 q^{25} +5.72765 q^{26} +5.64708 q^{27} +2.84565 q^{28} +5.07697 q^{29} -3.13468 q^{30} +3.20401 q^{31} +1.00000 q^{32} +6.05751 q^{33} +0.828433 q^{34} +6.10160 q^{35} -0.862709 q^{36} -1.30300 q^{37} -1.00000 q^{38} -8.37352 q^{39} +2.14418 q^{40} -9.49007 q^{41} -4.16019 q^{42} +1.76733 q^{43} -4.14345 q^{44} -1.84981 q^{45} +4.11173 q^{46} +6.02255 q^{47} -1.46195 q^{48} +1.09774 q^{49} -0.402477 q^{50} -1.21113 q^{51} +5.72765 q^{52} -9.71241 q^{53} +5.64708 q^{54} -8.88433 q^{55} +2.84565 q^{56} +1.46195 q^{57} +5.07697 q^{58} -1.16819 q^{59} -3.13468 q^{60} -0.741864 q^{61} +3.20401 q^{62} -2.45497 q^{63} +1.00000 q^{64} +12.2811 q^{65} +6.05751 q^{66} +12.6141 q^{67} +0.828433 q^{68} -6.01113 q^{69} +6.10160 q^{70} +1.20025 q^{71} -0.862709 q^{72} +14.2635 q^{73} -1.30300 q^{74} +0.588401 q^{75} -1.00000 q^{76} -11.7908 q^{77} -8.37352 q^{78} +0.0154584 q^{79} +2.14418 q^{80} -5.66760 q^{81} -9.49007 q^{82} +5.25605 q^{83} -4.16019 q^{84} +1.77631 q^{85} +1.76733 q^{86} -7.42227 q^{87} -4.14345 q^{88} +15.8470 q^{89} -1.84981 q^{90} +16.2989 q^{91} +4.11173 q^{92} -4.68409 q^{93} +6.02255 q^{94} -2.14418 q^{95} -1.46195 q^{96} -9.00620 q^{97} +1.09774 q^{98} +3.57460 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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