LMFDB - Embedded newform 8018.2.a.j.1.3

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			1.3
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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.07943 q^{3} +1.00000 q^{4} -3.30634 q^{5} -3.07943 q^{6} -2.62160 q^{7} +1.00000 q^{8} +6.48290 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.07943 q^{3} +1.00000 q^{4} -3.30634 q^{5} -3.07943 q^{6} -2.62160 q^{7} +1.00000 q^{8} +6.48290 q^{9} -3.30634 q^{10} +3.59685 q^{11} -3.07943 q^{12} -3.17175 q^{13} -2.62160 q^{14} +10.1816 q^{15} +1.00000 q^{16} +4.85924 q^{17} +6.48290 q^{18} -1.00000 q^{19} -3.30634 q^{20} +8.07304 q^{21} +3.59685 q^{22} -3.16632 q^{23} -3.07943 q^{24} +5.93186 q^{25} -3.17175 q^{26} -10.7254 q^{27} -2.62160 q^{28} -1.52137 q^{29} +10.1816 q^{30} -6.15407 q^{31} +1.00000 q^{32} -11.0763 q^{33} +4.85924 q^{34} +8.66789 q^{35} +6.48290 q^{36} +7.44862 q^{37} -1.00000 q^{38} +9.76720 q^{39} -3.30634 q^{40} +0.725201 q^{41} +8.07304 q^{42} -1.68387 q^{43} +3.59685 q^{44} -21.4347 q^{45} -3.16632 q^{46} -10.0853 q^{47} -3.07943 q^{48} -0.127213 q^{49} +5.93186 q^{50} -14.9637 q^{51} -3.17175 q^{52} +9.64128 q^{53} -10.7254 q^{54} -11.8924 q^{55} -2.62160 q^{56} +3.07943 q^{57} -1.52137 q^{58} -9.95767 q^{59} +10.1816 q^{60} -12.4578 q^{61} -6.15407 q^{62} -16.9956 q^{63} +1.00000 q^{64} +10.4869 q^{65} -11.0763 q^{66} +5.58038 q^{67} +4.85924 q^{68} +9.75047 q^{69} +8.66789 q^{70} +3.62595 q^{71} +6.48290 q^{72} +7.67422 q^{73} +7.44862 q^{74} -18.2668 q^{75} -1.00000 q^{76} -9.42950 q^{77} +9.76720 q^{78} -12.0529 q^{79} -3.30634 q^{80} +13.5793 q^{81} +0.725201 q^{82} -4.32343 q^{83} +8.07304 q^{84} -16.0663 q^{85} -1.68387 q^{86} +4.68497 q^{87} +3.59685 q^{88} -12.5944 q^{89} -21.4347 q^{90} +8.31507 q^{91} -3.16632 q^{92} +18.9511 q^{93} -10.0853 q^{94} +3.30634 q^{95} -3.07943 q^{96} -9.41884 q^{97} -0.127213 q^{98} +23.3180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.07943	−1.77791	−0.888956	−	0.457993i	$-0.848568\pi$
$3$	−3.07943	−1.77791	−0.888956	+	0.457993i	$0.848568\pi$
$4$	1.00000	0.500000
$5$	−3.30634	−1.47864	−0.739319	−	0.673355i	$-0.764853\pi$
$5$	−3.30634	−1.47864	−0.739319	+	0.673355i	$0.764853\pi$
$6$	−3.07943	−1.25717
$7$	−2.62160	−0.990872	−0.495436	−	0.868645i	$-0.664992\pi$
$7$	−2.62160	−0.990872	−0.495436	+	0.868645i	$0.664992\pi$
$8$	1.00000	0.353553
$9$	6.48290	2.16097
$10$	−3.30634	−1.04556
$11$	3.59685	1.08449	0.542245	−	0.840220i	$-0.317574\pi$
$11$	3.59685	1.08449	0.542245	+	0.840220i	$0.317574\pi$
$12$	−3.07943	−0.888956
$13$	−3.17175	−0.879686	−0.439843	−	0.898075i	$-0.644966\pi$
$13$	−3.17175	−0.879686	−0.439843	+	0.898075i	$0.644966\pi$
$14$	−2.62160	−0.700652
$15$	10.1816	2.62889
$16$	1.00000	0.250000
$17$	4.85924	1.17854	0.589269	−	0.807937i	$-0.299416\pi$
$17$	4.85924	1.17854	0.589269	+	0.807937i	$0.299416\pi$
$18$	6.48290	1.52804
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.30634	−0.739319
$21$	8.07304	1.76168
$22$	3.59685	0.766851
$23$	−3.16632	−0.660223	−0.330112	−	0.943942i	$-0.607086\pi$
$23$	−3.16632	−0.660223	−0.330112	+	0.943942i	$0.607086\pi$
$24$	−3.07943	−0.628587
$25$	5.93186	1.18637
$26$	−3.17175	−0.622032
$27$	−10.7254	−2.06410
$28$	−2.62160	−0.495436
$29$	−1.52137	−0.282512	−0.141256	−	0.989973i	$-0.545114\pi$
$29$	−1.52137	−0.282512	−0.141256	+	0.989973i	$0.545114\pi$
$30$	10.1816	1.85890
$31$	−6.15407	−1.10530	−0.552652	−	0.833412i	$-0.686384\pi$
$31$	−6.15407	−1.10530	−0.552652	+	0.833412i	$0.686384\pi$
$32$	1.00000	0.176777
$33$	−11.0763	−1.92813
$34$	4.85924	0.833353
$35$	8.66789	1.46514
$36$	6.48290	1.08048
$37$	7.44862	1.22455	0.612273	−	0.790647i	$-0.290255\pi$
$37$	7.44862	1.22455	0.612273	+	0.790647i	$0.290255\pi$
$38$	−1.00000	−0.162221
$39$	9.76720	1.56400
$40$	−3.30634	−0.522778
$41$	0.725201	0.113257	0.0566287	−	0.998395i	$-0.481965\pi$
$41$	0.725201	0.113257	0.0566287	+	0.998395i	$0.481965\pi$
$42$	8.07304	1.24570
$43$	−1.68387	−0.256789	−0.128394	−	0.991723i	$-0.540982\pi$
$43$	−1.68387	−0.256789	−0.128394	+	0.991723i	$0.540982\pi$
$44$	3.59685	0.542245
$45$	−21.4347	−3.19529
$46$	−3.16632	−0.466848
$47$	−10.0853	−1.47109	−0.735547	−	0.677474i	$-0.763075\pi$
$47$	−10.0853	−1.47109	−0.735547	+	0.677474i	$0.763075\pi$
$48$	−3.07943	−0.444478
$49$	−0.127213	−0.0181732
$50$	5.93186	0.838892
$51$	−14.9637	−2.09534
$52$	−3.17175	−0.439843
$53$	9.64128	1.32433	0.662166	−	0.749357i	$-0.269638\pi$
$53$	9.64128	1.32433	0.662166	+	0.749357i	$0.269638\pi$
$54$	−10.7254	−1.45954
$55$	−11.8924	−1.60357
$56$	−2.62160	−0.350326
$57$	3.07943	0.407881
$58$	−1.52137	−0.199766
$59$	−9.95767	−1.29638	−0.648189	−	0.761479i	$-0.724474\pi$
$59$	−9.95767	−1.29638	−0.648189	+	0.761479i	$0.724474\pi$
$60$	10.1816	1.31444
$61$	−12.4578	−1.59506	−0.797528	−	0.603282i	$-0.793859\pi$
$61$	−12.4578	−1.59506	−0.797528	+	0.603282i	$0.793859\pi$
$62$	−6.15407	−0.781568
$63$	−16.9956	−2.14124
$64$	1.00000	0.125000
$65$	10.4869	1.30074
$66$	−11.0763	−1.36339
$67$	5.58038	0.681752	0.340876	−	0.940108i	$-0.389276\pi$
$67$	5.58038	0.681752	0.340876	+	0.940108i	$0.389276\pi$
$68$	4.85924	0.589269
$69$	9.75047	1.17382
$70$	8.66789	1.03601
$71$	3.62595	0.430321	0.215160	−	0.976579i	$-0.430973\pi$
$71$	3.62595	0.430321	0.215160	+	0.976579i	$0.430973\pi$
$72$	6.48290	0.764018
$73$	7.67422	0.898200	0.449100	−	0.893481i	$-0.351745\pi$
$73$	7.67422	0.898200	0.449100	+	0.893481i	$0.351745\pi$
$74$	7.44862	0.865885
$75$	−18.2668	−2.10926
$76$	−1.00000	−0.114708
$77$	−9.42950	−1.07459
$78$	9.76720	1.10592
$79$	−12.0529	−1.35606	−0.678031	−	0.735033i	$-0.737167\pi$
$79$	−12.0529	−1.35606	−0.678031	+	0.735033i	$0.737167\pi$
$80$	−3.30634	−0.369660
$81$	13.5793	1.50882
$82$	0.725201	0.0800851
$83$	−4.32343	−0.474558	−0.237279	−	0.971442i	$-0.576256\pi$
$83$	−4.32343	−0.474558	−0.237279	+	0.971442i	$0.576256\pi$
$84$	8.07304	0.880841
$85$	−16.0663	−1.74263
$86$	−1.68387	−0.181577
$87$	4.68497	0.502281
$88$	3.59685	0.383425
$89$	−12.5944	−1.33501	−0.667504	−	0.744606i	$-0.732637\pi$
$89$	−12.5944	−1.33501	−0.667504	+	0.744606i	$0.732637\pi$
$90$	−21.4347	−2.25941
$91$	8.31507	0.871656
$92$	−3.16632	−0.330112
$93$	18.9511	1.96513
$94$	−10.0853	−1.04022
$95$	3.30634	0.339223
$96$	−3.07943	−0.314293
$97$	−9.41884	−0.956338	−0.478169	−	0.878268i	$-0.658699\pi$
$97$	−9.41884	−0.956338	−0.478169	+	0.878268i	$0.658699\pi$
$98$	−0.127213	−0.0128504
$99$	23.3180	2.34355
$100$	5.93186	0.593186
$101$	−9.38248	−0.933592	−0.466796	−	0.884365i	$-0.654592\pi$
$101$	−9.38248	−0.933592	−0.466796	+	0.884365i	$0.654592\pi$
$102$	−14.9637	−1.48163
$103$	4.29595	0.423292	0.211646	−	0.977346i	$-0.432118\pi$
$103$	4.29595	0.423292	0.211646	+	0.977346i	$0.432118\pi$
$104$	−3.17175	−0.311016
$105$	−26.6922	−2.60489
$106$	9.64128	0.936444
$107$	15.3169	1.48074	0.740369	−	0.672201i	$-0.234651\pi$
$107$	15.3169	1.48074	0.740369	+	0.672201i	$0.234651\pi$
$108$	−10.7254	−1.03205
$109$	−10.9789	−1.05158	−0.525792	−	0.850613i	$-0.676231\pi$
$109$	−10.9789	−1.05158	−0.525792	+	0.850613i	$0.676231\pi$
$110$	−11.8924	−1.13390
$111$	−22.9375	−2.17713
$112$	−2.62160	−0.247718
$113$	−3.89336	−0.366256	−0.183128	−	0.983089i	$-0.558622\pi$
$113$	−3.89336	−0.366256	−0.183128	+	0.983089i	$0.558622\pi$
$114$	3.07943	0.288415
$115$	10.4689	0.976232
$116$	−1.52137	−0.141256
$117$	−20.5622	−1.90097
$118$	−9.95767	−0.916678
$119$	−12.7390	−1.16778
$120$	10.1816	0.929452
$121$	1.93733	0.176121
$122$	−12.4578	−1.12788
$123$	−2.23321	−0.201362
$124$	−6.15407	−0.552652
$125$	−3.08104	−0.275577
$126$	−16.9956	−1.51409
$127$	−21.9029	−1.94357	−0.971785	−	0.235869i	$-0.924206\pi$
$127$	−21.9029	−1.94357	−0.971785	+	0.235869i	$0.924206\pi$
$128$	1.00000	0.0883883
$129$	5.18538	0.456547
$130$	10.4869	0.919760
$131$	18.1070	1.58201	0.791007	−	0.611808i	$-0.209557\pi$
$131$	18.1070	1.58201	0.791007	+	0.611808i	$0.209557\pi$
$132$	−11.0763	−0.964064
$133$	2.62160	0.227322
$134$	5.58038	0.482071
$135$	35.4617	3.05206
$136$	4.85924	0.416676
$137$	16.0615	1.37222	0.686112	−	0.727496i	$-0.259316\pi$
$137$	16.0615	1.37222	0.686112	+	0.727496i	$0.259316\pi$
$138$	9.75047	0.830015
$139$	17.4362	1.47892	0.739461	−	0.673199i	$-0.235080\pi$
$139$	17.4362	1.47892	0.739461	+	0.673199i	$0.235080\pi$
$140$	8.66789	0.732571
$141$	31.0570	2.61547
$142$	3.62595	0.304283
$143$	−11.4083	−0.954011
$144$	6.48290	0.540242
$145$	5.03017	0.417733
$146$	7.67422	0.635123
$147$	0.391742	0.0323104
$148$	7.44862	0.612273
$149$	7.05726	0.578153	0.289077	−	0.957306i	$-0.406652\pi$
$149$	7.05726	0.578153	0.289077	+	0.957306i	$0.406652\pi$
$150$	−18.2668	−1.49147
$151$	−7.40687	−0.602762	−0.301381	−	0.953504i	$-0.597448\pi$
$151$	−7.40687	−0.602762	−0.301381	+	0.953504i	$0.597448\pi$
$152$	−1.00000	−0.0811107
$153$	31.5020	2.54678
$154$	−9.42950	−0.759851
$155$	20.3474	1.63435
$156$	9.76720	0.782002
$157$	−7.77822	−0.620769	−0.310385	−	0.950611i	$-0.600458\pi$
$157$	−7.77822	−0.620769	−0.310385	+	0.950611i	$0.600458\pi$
$158$	−12.0529	−0.958881
$159$	−29.6897	−2.35454
$160$	−3.30634	−0.261389
$161$	8.30083	0.654197
$162$	13.5793	1.06689
$163$	−13.6308	−1.06764	−0.533822	−	0.845597i	$-0.679245\pi$
$163$	−13.6308	−1.06764	−0.533822	+	0.845597i	$0.679245\pi$
$164$	0.725201	0.0566287
$165$	36.6218	2.85101
$166$	−4.32343	−0.335563
$167$	17.3668	1.34388	0.671942	−	0.740604i	$-0.265460\pi$
$167$	17.3668	1.34388	0.671942	+	0.740604i	$0.265460\pi$
$168$	8.07304	0.622849
$169$	−2.93998	−0.226153
$170$	−16.0663	−1.23223
$171$	−6.48290	−0.495760
$172$	−1.68387	−0.128394
$173$	4.48265	0.340810	0.170405	−	0.985374i	$-0.445492\pi$
$173$	4.48265	0.340810	0.170405	+	0.985374i	$0.445492\pi$
$174$	4.68497	0.355166
$175$	−15.5510	−1.17554
$176$	3.59685	0.271123
$177$	30.6640	2.30485
$178$	−12.5944	−0.943993
$179$	−16.8384	−1.25856	−0.629282	−	0.777177i	$-0.716651\pi$
$179$	−16.8384	−1.25856	−0.629282	+	0.777177i	$0.716651\pi$
$180$	−21.4347	−1.59765
$181$	22.8206	1.69624	0.848122	−	0.529801i	$-0.177733\pi$
$181$	22.8206	1.69624	0.848122	+	0.529801i	$0.177733\pi$
$182$	8.31507	0.616354
$183$	38.3629	2.83587
$184$	−3.16632	−0.233424
$185$	−24.6276	−1.81066
$186$	18.9511	1.38956
$187$	17.4780	1.27811
$188$	−10.0853	−0.735547
$189$	28.1176	2.04526
$190$	3.30634	0.239867
$191$	−25.2853	−1.82958	−0.914792	−	0.403926i	$-0.867645\pi$
$191$	−25.2853	−1.82958	−0.914792	+	0.403926i	$0.867645\pi$
$192$	−3.07943	−0.222239
$193$	8.29723	0.597248	0.298624	−	0.954371i	$-0.403472\pi$
$193$	8.29723	0.597248	0.298624	+	0.954371i	$0.403472\pi$
$194$	−9.41884	−0.676233
$195$	−32.2936	−2.31260
$196$	−0.127213	−0.00908661
$197$	−7.81057	−0.556480	−0.278240	−	0.960512i	$-0.589751\pi$
$197$	−7.81057	−0.556480	−0.278240	+	0.960512i	$0.589751\pi$
$198$	23.3180	1.65714
$199$	−17.2026	−1.21946	−0.609730	−	0.792609i	$-0.708722\pi$
$199$	−17.2026	−1.21946	−0.609730	+	0.792609i	$0.708722\pi$
$200$	5.93186	0.419446
$201$	−17.1844	−1.21209
$202$	−9.38248	−0.660149
$203$	3.98843	0.279933
$204$	−14.9637	−1.04767
$205$	−2.39776	−0.167467
$206$	4.29595	0.299313
$207$	−20.5270	−1.42672
$208$	−3.17175	−0.219921
$209$	−3.59685	−0.248799
$210$	−26.6922	−1.84194
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	9.64128	0.662166
$213$	−11.1659	−0.765072
$214$	15.3169	1.04704
$215$	5.56746	0.379697
$216$	−10.7254	−0.729769
$217$	16.1335	1.09521
$218$	−10.9789	−0.743583
$219$	−23.6323	−1.59692
$220$	−11.8924	−0.801785
$221$	−15.4123	−1.03674
$222$	−22.9375	−1.53947
$223$	28.9438	1.93822	0.969112	−	0.246623i	$-0.0793208\pi$
$223$	28.9438	1.93822	0.969112	+	0.246623i	$0.0793208\pi$
$224$	−2.62160	−0.175163
$225$	38.4557	2.56371
$226$	−3.89336	−0.258982
$227$	5.79137	0.384387	0.192193	−	0.981357i	$-0.438440\pi$
$227$	5.79137	0.384387	0.192193	+	0.981357i	$0.438440\pi$
$228$	3.07943	0.203940
$229$	−18.6651	−1.23342	−0.616712	−	0.787189i	$-0.711536\pi$
$229$	−18.6651	−1.23342	−0.616712	+	0.787189i	$0.711536\pi$
$230$	10.4689	0.690300
$231$	29.0375	1.91053
$232$	−1.52137	−0.0998830
$233$	21.7720	1.42633	0.713165	−	0.700996i	$-0.247261\pi$
$233$	21.7720	1.42633	0.713165	+	0.700996i	$0.247261\pi$
$234$	−20.5622	−1.34419
$235$	33.3454	2.17522
$236$	−9.95767	−0.648189
$237$	37.1162	2.41096
$238$	−12.7390	−0.825746
$239$	−8.04048	−0.520096	−0.260048	−	0.965596i	$-0.583738\pi$
$239$	−8.04048	−0.520096	−0.260048	+	0.965596i	$0.583738\pi$
$240$	10.1816	0.657222
$241$	19.9326	1.28397	0.641986	−	0.766716i	$-0.278111\pi$
$241$	19.9326	1.28397	0.641986	+	0.766716i	$0.278111\pi$
$242$	1.93733	0.124536
$243$	−9.64055	−0.618442
$244$	−12.4578	−0.797528
$245$	0.420607	0.0268716
$246$	−2.23321	−0.142384
$247$	3.17175	0.201814
$248$	−6.15407	−0.390784
$249$	13.3137	0.843721
$250$	−3.08104	−0.194862
$251$	22.5793	1.42519	0.712597	−	0.701573i	$-0.247519\pi$
$251$	22.5793	1.42519	0.712597	+	0.701573i	$0.247519\pi$
$252$	−16.9956	−1.07062
$253$	−11.3888	−0.716006
$254$	−21.9029	−1.37431
$255$	49.4750	3.09825
$256$	1.00000	0.0625000
$257$	−6.05765	−0.377866	−0.188933	−	0.981990i	$-0.560503\pi$
$257$	−6.05765	−0.377866	−0.188933	+	0.981990i	$0.560503\pi$
$258$	5.18538	0.322828
$259$	−19.5273	−1.21337
$260$	10.4869	0.650369
$261$	−9.86292	−0.610499
$262$	18.1070	1.11865
$263$	7.77313	0.479312	0.239656	−	0.970858i	$-0.422965\pi$
$263$	7.77313	0.479312	0.239656	+	0.970858i	$0.422965\pi$
$264$	−11.0763	−0.681696
$265$	−31.8773	−1.95821
$266$	2.62160	0.160741
$267$	38.7837	2.37353
$268$	5.58038	0.340876
$269$	17.7961	1.08505	0.542525	−	0.840040i	$-0.317469\pi$
$269$	17.7961	1.08505	0.542525	+	0.840040i	$0.317469\pi$
$270$	35.4617	2.15813
$271$	7.28986	0.442827	0.221414	−	0.975180i	$-0.428933\pi$
$271$	7.28986	0.442827	0.221414	+	0.975180i	$0.428933\pi$
$272$	4.85924	0.294635
$273$	−25.6057	−1.54973
$274$	16.0615	0.970309
$275$	21.3360	1.28661
$276$	9.75047	0.586909
$277$	8.85228	0.531882	0.265941	−	0.963989i	$-0.414317\pi$
$277$	8.85228	0.531882	0.265941	+	0.963989i	$0.414317\pi$
$278$	17.4362	1.04576
$279$	−39.8963	−2.38853
$280$	8.66789	0.518006
$281$	26.7309	1.59463	0.797316	−	0.603563i	$-0.206253\pi$
$281$	26.7309	1.59463	0.797316	+	0.603563i	$0.206253\pi$
$282$	31.0570	1.84942
$283$	10.0108	0.595083	0.297541	−	0.954709i	$-0.403833\pi$
$283$	10.0108	0.595083	0.297541	+	0.954709i	$0.403833\pi$
$284$	3.62595	0.215160
$285$	−10.1816	−0.603108
$286$	−11.4083	−0.674588
$287$	−1.90119	−0.112224
$288$	6.48290	0.382009
$289$	6.61221	0.388954
$290$	5.03017	0.295382
$291$	29.0047	1.70028
$292$	7.67422	0.449100
$293$	30.3026	1.77029	0.885147	−	0.465311i	$-0.154058\pi$
$293$	30.3026	1.77029	0.885147	+	0.465311i	$0.154058\pi$
$294$	0.391742	0.0228469
$295$	32.9234	1.91688
$296$	7.44862	0.432942
$297$	−38.5775	−2.23850
$298$	7.05726	0.408816
$299$	10.0428	0.580789
$300$	−18.2668	−1.05463
$301$	4.41445	0.254444
$302$	−7.40687	−0.426217
$303$	28.8927	1.65984
$304$	−1.00000	−0.0573539
$305$	41.1896	2.35851
$306$	31.5020	1.80085
$307$	31.1710	1.77902	0.889512	−	0.456911i	$-0.151044\pi$
$307$	31.1710	1.77902	0.889512	+	0.456911i	$0.151044\pi$
$308$	−9.42950	−0.537296
$309$	−13.2291	−0.752576
$310$	20.3474	1.15566
$311$	−12.8925	−0.731066	−0.365533	−	0.930798i	$-0.619113\pi$
$311$	−12.8925	−0.731066	−0.365533	+	0.930798i	$0.619113\pi$
$312$	9.76720	0.552959
$313$	−23.8586	−1.34857	−0.674285	−	0.738471i	$-0.735548\pi$
$313$	−23.8586	−1.34857	−0.674285	+	0.738471i	$0.735548\pi$
$314$	−7.77822	−0.438950
$315$	56.1931	3.16612
$316$	−12.0529	−0.678031
$317$	−16.6396	−0.934571	−0.467286	−	0.884106i	$-0.654768\pi$
$317$	−16.6396	−0.934571	−0.467286	+	0.884106i	$0.654768\pi$
$318$	−29.6897	−1.66491
$319$	−5.47215	−0.306382
$320$	−3.30634	−0.184830
$321$	−47.1673	−2.63262
$322$	8.30083	0.462587
$323$	−4.85924	−0.270375
$324$	13.5793	0.754408
$325$	−18.8144	−1.04363
$326$	−13.6308	−0.754939
$327$	33.8087	1.86962
$328$	0.725201	0.0400425
$329$	26.4397	1.45767
$330$	36.6218	2.01597
$331$	−2.23202	−0.122683	−0.0613414	−	0.998117i	$-0.519538\pi$
$331$	−2.23202	−0.122683	−0.0613414	+	0.998117i	$0.519538\pi$
$332$	−4.32343	−0.237279
$333$	48.2887	2.64620
$334$	17.3668	0.950270
$335$	−18.4506	−1.00806
$336$	8.07304	0.440420
$337$	9.48518	0.516691	0.258345	−	0.966053i	$-0.416823\pi$
$337$	9.48518	0.516691	0.258345	+	0.966053i	$0.416823\pi$
$338$	−2.93998	−0.159914
$339$	11.9893	0.651171
$340$	−16.0663	−0.871316
$341$	−22.1353	−1.19869
$342$	−6.48290	−0.350555
$343$	18.6847	1.00888
$344$	−1.68387	−0.0907885
$345$	−32.2383	−1.73565
$346$	4.48265	0.240989
$347$	18.1699	0.975412	0.487706	−	0.873008i	$-0.337834\pi$
$347$	18.1699	0.975412	0.487706	+	0.873008i	$0.337834\pi$
$348$	4.68497	0.251140
$349$	8.80359	0.471245	0.235623	−	0.971845i	$-0.424287\pi$
$349$	8.80359	0.471245	0.235623	+	0.971845i	$0.424287\pi$
$350$	−15.5510	−0.831234
$351$	34.0182	1.81576
$352$	3.59685	0.191713
$353$	−34.1955	−1.82004	−0.910020	−	0.414564i	$-0.863934\pi$
$353$	−34.1955	−1.82004	−0.910020	+	0.414564i	$0.863934\pi$
$354$	30.6640	1.62977
$355$	−11.9886	−0.636289
$356$	−12.5944	−0.667504
$357$	39.2288	2.07621
$358$	−16.8384	−0.889939
$359$	−26.0976	−1.37738	−0.688690	−	0.725056i	$-0.741814\pi$
$359$	−26.0976	−1.37738	−0.688690	+	0.725056i	$0.741814\pi$
$360$	−21.4347	−1.12971
$361$	1.00000	0.0526316
$362$	22.8206	1.19943
$363$	−5.96586	−0.313127
$364$	8.31507	0.435828
$365$	−25.3736	−1.32811
$366$	38.3629	2.00526
$367$	−5.06346	−0.264310	−0.132155	−	0.991229i	$-0.542190\pi$
$367$	−5.06346	−0.264310	−0.132155	+	0.991229i	$0.542190\pi$
$368$	−3.16632	−0.165056
$369$	4.70141	0.244746
$370$	−24.6276	−1.28033
$371$	−25.2756	−1.31224
$372$	18.9511	0.982566
$373$	−13.6706	−0.707839	−0.353919	−	0.935276i	$-0.615151\pi$
$373$	−13.6706	−0.707839	−0.353919	+	0.935276i	$0.615151\pi$
$374$	17.4780	0.903764
$375$	9.48785	0.489951
$376$	−10.0853	−0.520110
$377$	4.82542	0.248522
$378$	28.1176	1.44621
$379$	−9.76421	−0.501554	−0.250777	−	0.968045i	$-0.580686\pi$
$379$	−9.76421	−0.501554	−0.250777	+	0.968045i	$0.580686\pi$
$380$	3.30634	0.169611
$381$	67.4486	3.45549
$382$	−25.2853	−1.29371
$383$	−5.82604	−0.297697	−0.148848	−	0.988860i	$-0.547557\pi$
$383$	−5.82604	−0.297697	−0.148848	+	0.988860i	$0.547557\pi$
$384$	−3.07943	−0.157147
$385$	31.1771	1.58893
$386$	8.29723	0.422318
$387$	−10.9164	−0.554912
$388$	−9.41884	−0.478169
$389$	24.5023	1.24231	0.621157	−	0.783686i	$-0.286663\pi$
$389$	24.5023	1.24231	0.621157	+	0.783686i	$0.286663\pi$
$390$	−32.2936	−1.63525
$391$	−15.3859	−0.778099
$392$	−0.127213	−0.00642520
$393$	−55.7592	−2.81268
$394$	−7.81057	−0.393491
$395$	39.8511	2.00513
$396$	23.3180	1.17178
$397$	10.2721	0.515540	0.257770	−	0.966206i	$-0.417012\pi$
$397$	10.2721	0.515540	0.257770	+	0.966206i	$0.417012\pi$
$398$	−17.2026	−0.862289
$399$	−8.07304	−0.404158
$400$	5.93186	0.296593
$401$	23.9630	1.19665	0.598327	−	0.801252i	$-0.295832\pi$
$401$	23.9630	1.19665	0.598327	+	0.801252i	$0.295832\pi$
$402$	−17.1844	−0.857080
$403$	19.5192	0.972321
$404$	−9.38248	−0.466796
$405$	−44.8979	−2.23099
$406$	3.98843	0.197943
$407$	26.7916	1.32801
$408$	−14.9637	−0.740814
$409$	32.3667	1.60043	0.800215	−	0.599714i	$-0.204719\pi$
$409$	32.3667	1.60043	0.800215	+	0.599714i	$0.204719\pi$
$410$	−2.39776	−0.118417
$411$	−49.4602	−2.43969
$412$	4.29595	0.211646
$413$	26.1050	1.28455
$414$	−20.5270	−1.00884
$415$	14.2947	0.701699
$416$	−3.17175	−0.155508
$417$	−53.6937	−2.62939
$418$	−3.59685	−0.175928
$419$	−3.17751	−0.155232	−0.0776158	−	0.996983i	$-0.524731\pi$
$419$	−3.17751	−0.155232	−0.0776158	+	0.996983i	$0.524731\pi$
$420$	−26.6922	−1.30245
$421$	−10.6423	−0.518673	−0.259336	−	0.965787i	$-0.583504\pi$
$421$	−10.6423	−0.518673	−0.259336	+	0.965787i	$0.583504\pi$
$422$	−1.00000	−0.0486792
$423$	−65.3821	−3.17899
$424$	9.64128	0.468222
$425$	28.8243	1.39819
$426$	−11.1659	−0.540988
$427$	32.6593	1.58050
$428$	15.3169	0.740369
$429$	35.1311	1.69615
$430$	5.56746	0.268487
$431$	20.6701	0.995642	0.497821	−	0.867280i	$-0.334134\pi$
$431$	20.6701	0.995642	0.497821	+	0.867280i	$0.334134\pi$
$432$	−10.7254	−0.516025
$433$	22.9944	1.10504	0.552521	−	0.833499i	$-0.313666\pi$
$433$	22.9944	1.10504	0.552521	+	0.833499i	$0.313666\pi$
$434$	16.1335	0.774434
$435$	−15.4901	−0.742692
$436$	−10.9789	−0.525792
$437$	3.16632	0.151466
$438$	−23.6323	−1.12919
$439$	15.2381	0.727277	0.363639	−	0.931540i	$-0.381534\pi$
$439$	15.2381	0.727277	0.363639	+	0.931540i	$0.381534\pi$
$440$	−11.8924	−0.566948
$441$	−0.824707	−0.0392718
$442$	−15.4123	−0.733089
$443$	16.2175	0.770517	0.385259	−	0.922809i	$-0.374112\pi$
$443$	16.2175	0.770517	0.385259	+	0.922809i	$0.374112\pi$
$444$	−22.9375	−1.08857
$445$	41.6414	1.97399
$446$	28.9438	1.37053
$447$	−21.7323	−1.02790
$448$	−2.62160	−0.123859
$449$	−26.3657	−1.24427	−0.622136	−	0.782909i	$-0.713735\pi$
$449$	−26.3657	−1.24427	−0.622136	+	0.782909i	$0.713735\pi$
$450$	38.4557	1.81282
$451$	2.60844	0.122827
$452$	−3.89336	−0.183128
$453$	22.8090	1.07166
$454$	5.79137	0.271802
$455$	−27.4924	−1.28886
$456$	3.07943	0.144208
$457$	−28.5587	−1.33592	−0.667960	−	0.744197i	$-0.732832\pi$
$457$	−28.5587	−1.33592	−0.667960	+	0.744197i	$0.732832\pi$
$458$	−18.6651	−0.872162
$459$	−52.1171	−2.43262
$460$	10.4689	0.488116
$461$	−28.1105	−1.30924	−0.654618	−	0.755960i	$-0.727170\pi$
$461$	−28.1105	−1.30924	−0.654618	+	0.755960i	$0.727170\pi$
$462$	29.0375	1.35095
$463$	−6.56312	−0.305014	−0.152507	−	0.988302i	$-0.548735\pi$
$463$	−6.56312	−0.305014	−0.152507	+	0.988302i	$0.548735\pi$
$464$	−1.52137	−0.0706280
$465$	−62.6586	−2.90572
$466$	21.7720	1.00857
$467$	−36.3201	−1.68070	−0.840348	−	0.542048i	$-0.817649\pi$
$467$	−36.3201	−1.68070	−0.840348	+	0.542048i	$0.817649\pi$
$468$	−20.5622	−0.950487
$469$	−14.6295	−0.675528
$470$	33.3454	1.53811
$471$	23.9525	1.10367
$472$	−9.95767	−0.458339
$473$	−6.05664	−0.278485
$474$	37.1162	1.70481
$475$	−5.93186	−0.272172
$476$	−12.7390	−0.583890
$477$	62.5035	2.86184
$478$	−8.04048	−0.367763
$479$	14.6465	0.669216	0.334608	−	0.942357i	$-0.391396\pi$
$479$	14.6465	0.669216	0.334608	+	0.942357i	$0.391396\pi$
$480$	10.1816	0.464726
$481$	−23.6252	−1.07722
$482$	19.9326	0.907906
$483$	−25.5618	−1.16310
$484$	1.93733	0.0880603
$485$	31.1418	1.41408
$486$	−9.64055	−0.437304
$487$	−13.9606	−0.632616	−0.316308	−	0.948657i	$-0.602443\pi$
$487$	−13.9606	−0.632616	−0.316308	+	0.948657i	$0.602443\pi$
$488$	−12.4578	−0.563938
$489$	41.9751	1.89818
$490$	0.420607	0.0190011
$491$	−8.28220	−0.373770	−0.186885	−	0.982382i	$-0.559839\pi$
$491$	−8.28220	−0.373770	−0.186885	+	0.982382i	$0.559839\pi$
$492$	−2.23321	−0.100681
$493$	−7.39272	−0.332951
$494$	3.17175	0.142704
$495$	−77.0973	−3.46526
$496$	−6.15407	−0.276326
$497$	−9.50579	−0.426393
$498$	13.3137	0.596601
$499$	−8.79475	−0.393707	−0.196854	−	0.980433i	$-0.563072\pi$
$499$	−8.79475	−0.393707	−0.196854	+	0.980433i	$0.563072\pi$
$500$	−3.08104	−0.137788
$501$	−53.4799	−2.38931
$502$	22.5793	1.00776
$503$	16.2843	0.726079	0.363039	−	0.931774i	$-0.381739\pi$
$503$	16.2843	0.726079	0.363039	+	0.931774i	$0.381739\pi$
$504$	−16.9956	−0.757043
$505$	31.0216	1.38044
$506$	−11.3888	−0.506293
$507$	9.05348	0.402079
$508$	−21.9029	−0.971785
$509$	14.8423	0.657875	0.328938	−	0.944352i	$-0.393309\pi$
$509$	14.8423	0.657875	0.328938	+	0.944352i	$0.393309\pi$
$510$	49.4750	2.19079
$511$	−20.1187	−0.890001
$512$	1.00000	0.0441942
$513$	10.7254	0.473537
$514$	−6.05765	−0.267191
$515$	−14.2038	−0.625896
$516$	5.18538	0.228274
$517$	−36.2753	−1.59539
$518$	−19.5273	−0.857981
$519$	−13.8040	−0.605930
$520$	10.4869	0.459880
$521$	−9.87276	−0.432533	−0.216267	−	0.976334i	$-0.569388\pi$
$521$	−9.87276	−0.432533	−0.216267	+	0.976334i	$0.569388\pi$
$522$	−9.86292	−0.431688
$523$	−8.67971	−0.379537	−0.189769	−	0.981829i	$-0.560774\pi$
$523$	−8.67971	−0.379537	−0.189769	+	0.981829i	$0.560774\pi$
$524$	18.1070	0.791007
$525$	47.8881	2.09001
$526$	7.77313	0.338924
$527$	−29.9041	−1.30264
$528$	−11.0763	−0.482032
$529$	−12.9744	−0.564105
$530$	−31.8773	−1.38466
$531$	−64.5547	−2.80143
$532$	2.62160	0.113661
$533$	−2.30016	−0.0996310
$534$	38.7837	1.67834
$535$	−50.6427	−2.18948
$536$	5.58038	0.241036
$537$	51.8528	2.23761
$538$	17.7961	0.767246
$539$	−0.457564	−0.0197087
$540$	35.4617	1.52603
$541$	38.0847	1.63739	0.818695	−	0.574229i	$-0.194698\pi$
$541$	38.0847	1.63739	0.818695	+	0.574229i	$0.194698\pi$
$542$	7.28986	0.313126
$543$	−70.2746	−3.01577
$544$	4.85924	0.208338
$545$	36.2998	1.55491
$546$	−25.6057	−1.09582
$547$	−12.2235	−0.522637	−0.261319	−	0.965253i	$-0.584157\pi$
$547$	−12.2235	−0.522637	−0.261319	+	0.965253i	$0.584157\pi$
$548$	16.0615	0.686112
$549$	−80.7627	−3.44687
$550$	21.3360	0.909770
$551$	1.52137	0.0648127
$552$	9.75047	0.415008
$553$	31.5980	1.34368
$554$	8.85228	0.376097
$555$	75.8392	3.21919
$556$	17.4362	0.739461
$557$	−7.54648	−0.319755	−0.159877	−	0.987137i	$-0.551110\pi$
$557$	−7.54648	−0.319755	−0.159877	+	0.987137i	$0.551110\pi$
$558$	−39.8963	−1.68894
$559$	5.34084	0.225893
$560$	8.66789	0.366285
$561$	−53.8222	−2.27237
$562$	26.7309	1.12757
$563$	18.6248	0.784941	0.392471	−	0.919765i	$-0.371621\pi$
$563$	18.6248	0.784941	0.392471	+	0.919765i	$0.371621\pi$
$564$	31.0570	1.30774
$565$	12.8727	0.541561
$566$	10.0108	0.420787
$567$	−35.5996	−1.49504
$568$	3.62595	0.152141
$569$	8.28382	0.347276	0.173638	−	0.984810i	$-0.444448\pi$
$569$	8.28382	0.347276	0.173638	+	0.984810i	$0.444448\pi$
$570$	−10.1816	−0.426462
$571$	−18.6107	−0.778832	−0.389416	−	0.921062i	$-0.627323\pi$
$571$	−18.6107	−0.778832	−0.389416	+	0.921062i	$0.627323\pi$
$572$	−11.4083	−0.477006
$573$	77.8645	3.25284
$574$	−1.90119	−0.0793541
$575$	−18.7822	−0.783270
$576$	6.48290	0.270121
$577$	−18.5544	−0.772430	−0.386215	−	0.922409i	$-0.626218\pi$
$577$	−18.5544	−0.772430	−0.386215	+	0.922409i	$0.626218\pi$
$578$	6.61221	0.275032
$579$	−25.5508	−1.06185
$580$	5.03017	0.208866
$581$	11.3343	0.470226
$582$	29.0047	1.20228
$583$	34.6782	1.43623
$584$	7.67422	0.317562
$585$	67.9855	2.81085
$586$	30.3026	1.25179
$587$	−1.44658	−0.0597066	−0.0298533	−	0.999554i	$-0.509504\pi$
$587$	−1.44658	−0.0597066	−0.0298533	+	0.999554i	$0.509504\pi$
$588$	0.391742	0.0161552
$589$	6.15407	0.253574
$590$	32.9234	1.35544
$591$	24.0521	0.989372
$592$	7.44862	0.306136
$593$	−18.4786	−0.758826	−0.379413	−	0.925227i	$-0.623874\pi$
$593$	−18.4786	−0.758826	−0.379413	+	0.925227i	$0.623874\pi$
$594$	−38.5775	−1.58286
$595$	42.1194	1.72673
$596$	7.05726	0.289077
$597$	52.9743	2.16809
$598$	10.0428	0.410680
$599$	−28.5876	−1.16806	−0.584028	−	0.811733i	$-0.698524\pi$
$599$	−28.5876	−1.16806	−0.584028	+	0.811733i	$0.698524\pi$
$600$	−18.2668	−0.745737
$601$	8.46071	0.345119	0.172560	−	0.984999i	$-0.444796\pi$
$601$	8.46071	0.345119	0.172560	+	0.984999i	$0.444796\pi$
$602$	4.41445	0.179919
$603$	36.1771	1.47324
$604$	−7.40687	−0.301381
$605$	−6.40545	−0.260419
$606$	28.8927	1.17369
$607$	−12.9877	−0.527156	−0.263578	−	0.964638i	$-0.584903\pi$
$607$	−12.9877	−0.527156	−0.263578	+	0.964638i	$0.584903\pi$
$608$	−1.00000	−0.0405554
$609$	−12.2821	−0.497696
$610$	41.1896	1.66772
$611$	31.9881	1.29410
$612$	31.5020	1.27339
$613$	40.1813	1.62291	0.811453	−	0.584417i	$-0.198677\pi$
$613$	40.1813	1.62291	0.811453	+	0.584417i	$0.198677\pi$
$614$	31.1710	1.25796
$615$	7.38374	0.297741
$616$	−9.42950	−0.379925
$617$	31.7165	1.27686	0.638428	−	0.769681i	$-0.279585\pi$
$617$	31.7165	1.27686	0.638428	+	0.769681i	$0.279585\pi$
$618$	−13.2291	−0.532151
$619$	13.8137	0.555218	0.277609	−	0.960694i	$-0.410458\pi$
$619$	13.8137	0.555218	0.277609	+	0.960694i	$0.410458\pi$
$620$	20.3474	0.817173
$621$	33.9600	1.36277
$622$	−12.8925	−0.516942
$623$	33.0176	1.32282
$624$	9.76720	0.391001
$625$	−19.4723	−0.778894
$626$	−23.8586	−0.953583
$627$	11.0763	0.442343
$628$	−7.77822	−0.310385
$629$	36.1946	1.44317
$630$	56.1931	2.23879
$631$	−22.1676	−0.882479	−0.441240	−	0.897389i	$-0.645461\pi$
$631$	−22.1676	−0.882479	−0.441240	+	0.897389i	$0.645461\pi$
$632$	−12.0529	−0.479441
$633$	3.07943	0.122396
$634$	−16.6396	−0.660841
$635$	72.4184	2.87384
$636$	−29.6897	−1.17727
$637$	0.403487	0.0159867
$638$	−5.47215	−0.216644
$639$	23.5067	0.929910
$640$	−3.30634	−0.130694
$641$	9.67713	0.382224	0.191112	−	0.981568i	$-0.438791\pi$
$641$	9.67713	0.382224	0.191112	+	0.981568i	$0.438791\pi$
$642$	−47.1673	−1.86154
$643$	9.36419	0.369288	0.184644	−	0.982806i	$-0.440887\pi$
$643$	9.36419	0.369288	0.184644	+	0.982806i	$0.440887\pi$
$644$	8.30083	0.327098
$645$	−17.1446	−0.675068
$646$	−4.85924	−0.191184
$647$	−21.7018	−0.853187	−0.426594	−	0.904443i	$-0.640287\pi$
$647$	−21.7018	−0.853187	−0.426594	+	0.904443i	$0.640287\pi$
$648$	13.5793	0.533447
$649$	−35.8163	−1.40591
$650$	−18.8144	−0.737961
$651$	−49.6821	−1.94719
$652$	−13.6308	−0.533822
$653$	17.5043	0.684997	0.342498	−	0.939518i	$-0.388727\pi$
$653$	17.5043	0.684997	0.342498	+	0.939518i	$0.388727\pi$
$654$	33.8087	1.32202
$655$	−59.8677	−2.33923
$656$	0.725201	0.0283144
$657$	49.7513	1.94098
$658$	26.4397	1.03073
$659$	−19.7418	−0.769031	−0.384516	−	0.923118i	$-0.625632\pi$
$659$	−19.7418	−0.769031	−0.384516	+	0.923118i	$0.625632\pi$
$660$	36.6218	1.42550
$661$	6.51672	0.253471	0.126735	−	0.991937i	$-0.459550\pi$
$661$	6.51672	0.253471	0.126735	+	0.991937i	$0.459550\pi$
$662$	−2.23202	−0.0867498
$663$	47.4612	1.84324
$664$	−4.32343	−0.167781
$665$	−8.66789	−0.336126
$666$	48.2887	1.87115
$667$	4.81715	0.186521
$668$	17.3668	0.671942
$669$	−89.1306	−3.44599
$670$	−18.4506	−0.712809
$671$	−44.8088	−1.72982
$672$	8.07304	0.311424
$673$	−4.78895	−0.184601	−0.0923003	−	0.995731i	$-0.529422\pi$
$673$	−4.78895	−0.184601	−0.0923003	+	0.995731i	$0.529422\pi$
$674$	9.48518	0.365355
$675$	−63.6214	−2.44879
$676$	−2.93998	−0.113076
$677$	−4.03118	−0.154931	−0.0774654	−	0.996995i	$-0.524683\pi$
$677$	−4.03118	−0.154931	−0.0774654	+	0.996995i	$0.524683\pi$
$678$	11.9893	0.460448
$679$	24.6924	0.947608
$680$	−16.0663	−0.616114
$681$	−17.8341	−0.683405
$682$	−22.1353	−0.847603
$683$	−5.79267	−0.221650	−0.110825	−	0.993840i	$-0.535349\pi$
$683$	−5.79267	−0.221650	−0.110825	+	0.993840i	$0.535349\pi$
$684$	−6.48290	−0.247880
$685$	−53.1046	−2.02902
$686$	18.6847	0.713385
$687$	57.4779	2.19292
$688$	−1.68387	−0.0641971
$689$	−30.5797	−1.16500
$690$	−32.2383	−1.22729
$691$	39.8481	1.51589	0.757947	−	0.652316i	$-0.226203\pi$
$691$	39.8481	1.51589	0.757947	+	0.652316i	$0.226203\pi$
$692$	4.48265	0.170405
$693$	−61.1306	−2.32216
$694$	18.1699	0.689721
$695$	−57.6501	−2.18679
$696$	4.68497	0.177583
$697$	3.52393	0.133478
$698$	8.80359	0.333221
$699$	−67.0454	−2.53589
$700$	−15.5510	−0.587771
$701$	44.3959	1.67681	0.838405	−	0.545049i	$-0.183489\pi$
$701$	44.3959	1.67681	0.838405	+	0.545049i	$0.183489\pi$
$702$	34.0182	1.28394
$703$	−7.44862	−0.280930
$704$	3.59685	0.135561
$705$	−102.685	−3.86734
$706$	−34.1955	−1.28696
$707$	24.5971	0.925070
$708$	30.6640	1.15242
$709$	32.1101	1.20592	0.602960	−	0.797772i	$-0.293988\pi$
$709$	32.1101	1.20592	0.602960	+	0.797772i	$0.293988\pi$
$710$	−11.9886	−0.449924
$711$	−78.1381	−2.93041
$712$	−12.5944	−0.471997
$713$	19.4858	0.729748
$714$	39.2288	1.46810
$715$	37.7197	1.41064
$716$	−16.8384	−0.629282
$717$	24.7601	0.924684
$718$	−26.0976	−0.973955
$719$	−14.8190	−0.552655	−0.276328	−	0.961063i	$-0.589118\pi$
$719$	−14.8190	−0.552655	−0.276328	+	0.961063i	$0.589118\pi$
$720$	−21.4347	−0.798823
$721$	−11.2623	−0.419428
$722$	1.00000	0.0372161
$723$	−61.3811	−2.28279
$724$	22.8206	0.848122
$725$	−9.02457	−0.335164
$726$	−5.96586	−0.221414
$727$	−4.99472	−0.185244	−0.0926219	−	0.995701i	$-0.529525\pi$
$727$	−4.99472	−0.185244	−0.0926219	+	0.995701i	$0.529525\pi$
$728$	8.31507	0.308177
$729$	−11.0506	−0.409281
$730$	−25.3736	−0.939118
$731$	−8.18235	−0.302635
$732$	38.3629	1.41793
$733$	4.68036	0.172873	0.0864365	−	0.996257i	$-0.472452\pi$
$733$	4.68036	0.172873	0.0864365	+	0.996257i	$0.472452\pi$
$734$	−5.06346	−0.186896
$735$	−1.29523	−0.0477754
$736$	−3.16632	−0.116712
$737$	20.0718	0.739353
$738$	4.70141	0.173061
$739$	−12.1592	−0.447285	−0.223642	−	0.974671i	$-0.571795\pi$
$739$	−12.1592	−0.447285	−0.223642	+	0.974671i	$0.571795\pi$
$740$	−24.6276	−0.905330
$741$	−9.76720	−0.358807
$742$	−25.2756	−0.927896
$743$	26.9877	0.990082	0.495041	−	0.868869i	$-0.335153\pi$
$743$	26.9877	0.990082	0.495041	+	0.868869i	$0.335153\pi$
$744$	18.9511	0.694779
$745$	−23.3337	−0.854879
$746$	−13.6706	−0.500517
$747$	−28.0284	−1.02550
$748$	17.4780	0.639057
$749$	−40.1547	−1.46722
$750$	9.48785	0.346447
$751$	3.99780	0.145882	0.0729409	−	0.997336i	$-0.476762\pi$
$751$	3.99780	0.145882	0.0729409	+	0.997336i	$0.476762\pi$
$752$	−10.0853	−0.367773
$753$	−69.5315	−2.53387
$754$	4.82542	0.175731
$755$	24.4896	0.891268
$756$	28.1176	1.02263
$757$	15.2875	0.555633	0.277816	−	0.960634i	$-0.410389\pi$
$757$	15.2875	0.555633	0.277816	+	0.960634i	$0.410389\pi$
$758$	−9.76421	−0.354652
$759$	35.0710	1.27300
$760$	3.30634	0.119933
$761$	−0.265766	−0.00963401	−0.00481700	−	0.999988i	$-0.501533\pi$
$761$	−0.265766	−0.00963401	−0.00481700	+	0.999988i	$0.501533\pi$
$762$	67.4486	2.44340
$763$	28.7822	1.04199
$764$	−25.2853	−0.914792
$765$	−104.156	−3.76577
$766$	−5.82604	−0.210503
$767$	31.5833	1.14041
$768$	−3.07943	−0.111119
$769$	−10.7293	−0.386910	−0.193455	−	0.981109i	$-0.561969\pi$
$769$	−10.7293	−0.386910	−0.193455	+	0.981109i	$0.561969\pi$
$770$	31.1771	1.12354
$771$	18.6541	0.671812
$772$	8.29723	0.298624
$773$	38.6791	1.39119	0.695595	−	0.718434i	$-0.255141\pi$
$773$	38.6791	1.39119	0.695595	+	0.718434i	$0.255141\pi$
$774$	−10.9164	−0.392382
$775$	−36.5051	−1.31130
$776$	−9.41884	−0.338117
$777$	60.1330	2.15726
$778$	24.5023	0.878449
$779$	−0.725201	−0.0259830
$780$	−32.2936	−1.15630
$781$	13.0420	0.466679
$782$	−15.3859	−0.550199
$783$	16.3173	0.583132
$784$	−0.127213	−0.00454331
$785$	25.7174	0.917893
$786$	−55.7592	−1.98886
$787$	−13.5007	−0.481249	−0.240625	−	0.970618i	$-0.577352\pi$
$787$	−13.5007	−0.481249	−0.240625	+	0.970618i	$0.577352\pi$
$788$	−7.81057	−0.278240
$789$	−23.9368	−0.852173
$790$	39.8511	1.41784
$791$	10.2068	0.362913
$792$	23.3180	0.828570
$793$	39.5130	1.40315
$794$	10.2721	0.364542
$795$	98.1640	3.48152
$796$	−17.2026	−0.609730
$797$	3.90496	0.138321	0.0691604	−	0.997606i	$-0.477968\pi$
$797$	3.90496	0.138321	0.0691604	+	0.997606i	$0.477968\pi$
$798$	−8.07304	−0.285783
$799$	−49.0070	−1.73374
$800$	5.93186	0.209723
$801$	−81.6485	−2.88491
$802$	23.9630	0.846162
$803$	27.6030	0.974090
$804$	−17.1844	−0.606047
$805$	−27.4453	−0.967320
$806$	19.5192	0.687534
$807$	−54.8020	−1.92912
$808$	−9.38248	−0.330075
$809$	45.8869	1.61330	0.806649	−	0.591031i	$-0.201279\pi$
$809$	45.8869	1.61330	0.806649	+	0.591031i	$0.201279\pi$
$810$	−44.8979	−1.57755
$811$	11.0177	0.386882	0.193441	−	0.981112i	$-0.438035\pi$
$811$	11.0177	0.386882	0.193441	+	0.981112i	$0.438035\pi$
$812$	3.98843	0.139967
$813$	−22.4486	−0.787307
$814$	26.7916	0.939044
$815$	45.0679	1.57866
$816$	−14.9637	−0.523834
$817$	1.68387	0.0589113
$818$	32.3667	1.13167
$819$	53.9058	1.88362
$820$	−2.39776	−0.0837334
$821$	40.4816	1.41282	0.706408	−	0.707805i	$-0.250314\pi$
$821$	40.4816	1.41282	0.706408	+	0.707805i	$0.250314\pi$
$822$	−49.4602	−1.72512
$823$	36.1537	1.26024	0.630119	−	0.776499i	$-0.283006\pi$
$823$	36.1537	1.26024	0.630119	+	0.776499i	$0.283006\pi$
$824$	4.29595	0.149656
$825$	−65.7028	−2.28748
$826$	26.1050	0.908311
$827$	−35.6799	−1.24071	−0.620356	−	0.784321i	$-0.713012\pi$
$827$	−35.6799	−1.24071	−0.620356	+	0.784321i	$0.713012\pi$
$828$	−20.5270	−0.713361
$829$	−24.3085	−0.844267	−0.422134	−	0.906534i	$-0.638719\pi$
$829$	−24.3085	−0.844267	−0.422134	+	0.906534i	$0.638719\pi$
$830$	14.2947	0.496176
$831$	−27.2600	−0.945639
$832$	−3.17175	−0.109961
$833$	−0.618156	−0.0214178
$834$	−53.6937	−1.85926
$835$	−57.4205	−1.98712
$836$	−3.59685	−0.124400
$837$	66.0047	2.28146
$838$	−3.17751	−0.109765
$839$	−17.3791	−0.599992	−0.299996	−	0.953940i	$-0.596985\pi$
$839$	−17.3791	−0.599992	−0.299996	+	0.953940i	$0.596985\pi$
$840$	−26.6922	−0.920968
$841$	−26.6854	−0.920187
$842$	−10.6423	−0.366757
$843$	−82.3160	−2.83511
$844$	−1.00000	−0.0344214
$845$	9.72057	0.334398
$846$	−65.3821	−2.24788
$847$	−5.07889	−0.174513
$848$	9.64128	0.331083
$849$	−30.8277	−1.05800
$850$	28.8243	0.988666
$851$	−23.5847	−0.808474
$852$	−11.1659	−0.382536
$853$	39.1600	1.34081	0.670406	−	0.741994i	$-0.266120\pi$
$853$	39.1600	1.34081	0.670406	+	0.741994i	$0.266120\pi$
$854$	32.6593	1.11758
$855$	21.4347	0.733050
$856$	15.3169	0.523520
$857$	12.8771	0.439872	0.219936	−	0.975514i	$-0.429415\pi$
$857$	12.8771	0.439872	0.219936	+	0.975514i	$0.429415\pi$
$858$	35.1311	1.19936
$859$	−16.2199	−0.553415	−0.276708	−	0.960954i	$-0.589243\pi$
$859$	−16.2199	−0.553415	−0.276708	+	0.960954i	$0.589243\pi$
$860$	5.56746	0.189849
$861$	5.85458	0.199524
$862$	20.6701	0.704025
$863$	7.60759	0.258965	0.129483	−	0.991582i	$-0.458668\pi$
$863$	7.60759	0.258965	0.129483	+	0.991582i	$0.458668\pi$
$864$	−10.7254	−0.364885
$865$	−14.8212	−0.503935
$866$	22.9944	0.781382
$867$	−20.3619	−0.691525
$868$	16.1335	0.547607
$869$	−43.3526	−1.47064
$870$	−15.4901	−0.525163
$871$	−17.6996	−0.599727
$872$	−10.9789	−0.371791
$873$	−61.0614	−2.06662
$874$	3.16632	0.107102
$875$	8.07725	0.273061
$876$	−23.6323	−0.798460
$877$	−53.5343	−1.80772	−0.903862	−	0.427824i	$-0.859280\pi$
$877$	−53.5343	−1.80772	−0.903862	+	0.427824i	$0.859280\pi$
$878$	15.2381	0.514263
$879$	−93.3147	−3.14743
$880$	−11.8924	−0.400892
$881$	29.2387	0.985078	0.492539	−	0.870290i	$-0.336069\pi$
$881$	29.2387	0.985078	0.492539	+	0.870290i	$0.336069\pi$
$882$	−0.824707	−0.0277693
$883$	−49.5773	−1.66841	−0.834205	−	0.551454i	$-0.814073\pi$
$883$	−49.5773	−1.66841	−0.834205	+	0.551454i	$0.814073\pi$
$884$	−15.4123	−0.518372
$885$	−101.385	−3.40803
$886$	16.2175	0.544838
$887$	1.61986	0.0543896	0.0271948	−	0.999630i	$-0.491343\pi$
$887$	1.61986	0.0543896	0.0271948	+	0.999630i	$0.491343\pi$
$888$	−22.9375	−0.769733
$889$	57.4207	1.92583
$890$	41.6414	1.39582
$891$	48.8428	1.63630
$892$	28.9438	0.969112
$893$	10.0853	0.337492
$894$	−21.7323	−0.726838
$895$	55.6735	1.86096
$896$	−2.62160	−0.0875815
$897$	−30.9261	−1.03259
$898$	−26.3657	−0.879833
$899$	9.36264	0.312262
$900$	38.4557	1.28186
$901$	46.8493	1.56078
$902$	2.60844	0.0868516
$903$	−13.5940	−0.452380
$904$	−3.89336	−0.129491
$905$	−75.4527	−2.50813
$906$	22.8090	0.757777
$907$	21.0380	0.698557	0.349278	−	0.937019i	$-0.386427\pi$
$907$	21.0380	0.698557	0.349278	+	0.937019i	$0.386427\pi$
$908$	5.79137	0.192193
$909$	−60.8257	−2.01746
$910$	−27.4924	−0.911365
$911$	17.7870	0.589308	0.294654	−	0.955604i	$-0.404796\pi$
$911$	17.7870	0.589308	0.294654	+	0.955604i	$0.404796\pi$
$912$	3.07943	0.101970
$913$	−15.5507	−0.514654
$914$	−28.5587	−0.944639
$915$	−126.841	−4.19322
$916$	−18.6651	−0.616712
$917$	−47.4692	−1.56757
$918$	−52.1171	−1.72012
$919$	30.1580	0.994821	0.497410	−	0.867515i	$-0.334284\pi$
$919$	30.1580	0.994821	0.497410	+	0.867515i	$0.334284\pi$
$920$	10.4689	0.345150
$921$	−95.9891	−3.16295
$922$	−28.1105	−0.925769
$923$	−11.5006	−0.378547
$924$	29.0375	0.955264
$925$	44.1842	1.45277
$926$	−6.56312	−0.215677
$927$	27.8502	0.914721
$928$	−1.52137	−0.0499415
$929$	6.92159	0.227090	0.113545	−	0.993533i	$-0.463779\pi$
$929$	6.92159	0.227090	0.113545	+	0.993533i	$0.463779\pi$
$930$	−62.6586	−2.05465
$931$	0.127213	0.00416922
$932$	21.7720	0.713165
$933$	39.7016	1.29977
$934$	−36.3201	−1.18843
$935$	−57.7880	−1.88987
$936$	−20.5622	−0.672096
$937$	16.4258	0.536606	0.268303	−	0.963335i	$-0.413537\pi$
$937$	16.4258	0.536606	0.268303	+	0.963335i	$0.413537\pi$
$938$	−14.6295	−0.477671
$939$	73.4710	2.39764
$940$	33.3454	1.08761
$941$	2.02529	0.0660224	0.0330112	−	0.999455i	$-0.489490\pi$
$941$	2.02529	0.0660224	0.0330112	+	0.999455i	$0.489490\pi$
$942$	23.9525	0.780415
$943$	−2.29622	−0.0747752
$944$	−9.95767	−0.324095
$945$	−92.9663	−3.02420
$946$	−6.05664	−0.196918
$947$	−40.3818	−1.31223	−0.656117	−	0.754659i	$-0.727802\pi$
$947$	−40.3818	−1.31223	−0.656117	+	0.754659i	$0.727802\pi$
$948$	37.1162	1.20548
$949$	−24.3407	−0.790134
$950$	−5.93186	−0.192455
$951$	51.2404	1.66158
$952$	−12.7390	−0.412873
$953$	53.8358	1.74391	0.871956	−	0.489584i	$-0.162851\pi$
$953$	53.8358	1.74391	0.871956	+	0.489584i	$0.162851\pi$
$954$	62.5035	2.02362
$955$	83.6019	2.70529
$956$	−8.04048	−0.260048
$957$	16.8511	0.544719
$958$	14.6465	0.473207
$959$	−42.1068	−1.35970
$960$	10.1816	0.328611
$961$	6.87262	0.221697
$962$	−23.6252	−0.761707
$963$	99.2978	3.19983
$964$	19.9326	0.641986
$965$	−27.4334	−0.883114
$966$	−25.5618	−0.822438
$967$	−19.1912	−0.617147	−0.308574	−	0.951200i	$-0.599852\pi$
$967$	−19.1912	−0.617147	−0.308574	+	0.951200i	$0.599852\pi$
$968$	1.93733	0.0622680
$969$	14.9637	0.480703
$970$	31.1418	0.999904
$971$	−16.0719	−0.515771	−0.257885	−	0.966175i	$-0.583026\pi$
$971$	−16.0719	−0.515771	−0.257885	+	0.966175i	$0.583026\pi$
$972$	−9.64055	−0.309221
$973$	−45.7108	−1.46542
$974$	−13.9606	−0.447327
$975$	57.9376	1.85549
$976$	−12.4578	−0.398764
$977$	−12.7285	−0.407220	−0.203610	−	0.979052i	$-0.565268\pi$
$977$	−12.7285	−0.407220	−0.203610	+	0.979052i	$0.565268\pi$
$978$	41.9751	1.34221
$979$	−45.3003	−1.44780
$980$	0.420607	0.0134358
$981$	−71.1750	−2.27244
$982$	−8.28220	−0.264296
$983$	−45.5321	−1.45225	−0.726124	−	0.687564i	$-0.758680\pi$
$983$	−45.5321	−1.45225	−0.726124	+	0.687564i	$0.758680\pi$
$984$	−2.23321	−0.0711921
$985$	25.8244	0.822833
$986$	−7.39272	−0.235432
$987$	−81.4191	−2.59160
$988$	3.17175	0.100907
$989$	5.33169	0.169538
$990$	−77.0973	−2.45031
$991$	4.29645	0.136481	0.0682405	−	0.997669i	$-0.478261\pi$
$991$	4.29645	0.136481	0.0682405	+	0.997669i	$0.478261\pi$
$992$	−6.15407	−0.195392
$993$	6.87335	0.218119
$994$	−9.50579	−0.301505
$995$	56.8776	1.80314
$996$	13.3137	0.421861
$997$	55.3690	1.75355	0.876777	−	0.480898i	$-0.159689\pi$
$997$	55.3690	1.75355	0.876777	+	0.480898i	$0.159689\pi$
$998$	−8.79475	−0.278393
$999$	−79.8892	−2.52758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.3	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.07943 q^{3} +1.00000 q^{4} -3.30634 q^{5} -3.07943 q^{6} -2.62160 q^{7} +1.00000 q^{8} +6.48290 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.07943 q^{3} +1.00000 q^{4} -3.30634 q^{5} -3.07943 q^{6} -2.62160 q^{7} +1.00000 q^{8} +6.48290 q^{9} -3.30634 q^{10} +3.59685 q^{11} -3.07943 q^{12} -3.17175 q^{13} -2.62160 q^{14} +10.1816 q^{15} +1.00000 q^{16} +4.85924 q^{17} +6.48290 q^{18} -1.00000 q^{19} -3.30634 q^{20} +8.07304 q^{21} +3.59685 q^{22} -3.16632 q^{23} -3.07943 q^{24} +5.93186 q^{25} -3.17175 q^{26} -10.7254 q^{27} -2.62160 q^{28} -1.52137 q^{29} +10.1816 q^{30} -6.15407 q^{31} +1.00000 q^{32} -11.0763 q^{33} +4.85924 q^{34} +8.66789 q^{35} +6.48290 q^{36} +7.44862 q^{37} -1.00000 q^{38} +9.76720 q^{39} -3.30634 q^{40} +0.725201 q^{41} +8.07304 q^{42} -1.68387 q^{43} +3.59685 q^{44} -21.4347 q^{45} -3.16632 q^{46} -10.0853 q^{47} -3.07943 q^{48} -0.127213 q^{49} +5.93186 q^{50} -14.9637 q^{51} -3.17175 q^{52} +9.64128 q^{53} -10.7254 q^{54} -11.8924 q^{55} -2.62160 q^{56} +3.07943 q^{57} -1.52137 q^{58} -9.95767 q^{59} +10.1816 q^{60} -12.4578 q^{61} -6.15407 q^{62} -16.9956 q^{63} +1.00000 q^{64} +10.4869 q^{65} -11.0763 q^{66} +5.58038 q^{67} +4.85924 q^{68} +9.75047 q^{69} +8.66789 q^{70} +3.62595 q^{71} +6.48290 q^{72} +7.67422 q^{73} +7.44862 q^{74} -18.2668 q^{75} -1.00000 q^{76} -9.42950 q^{77} +9.76720 q^{78} -12.0529 q^{79} -3.30634 q^{80} +13.5793 q^{81} +0.725201 q^{82} -4.32343 q^{83} +8.07304 q^{84} -16.0663 q^{85} -1.68387 q^{86} +4.68497 q^{87} +3.59685 q^{88} -12.5944 q^{89} -21.4347 q^{90} +8.31507 q^{91} -3.16632 q^{92} +18.9511 q^{93} -10.0853 q^{94} +3.30634 q^{95} -3.07943 q^{96} -9.41884 q^{97} -0.127213 q^{98} +23.3180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 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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