LMFDB - Embedded newform 8018.2.a.h.1.12

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:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.48981 q^{3} +1.00000 q^{4} +2.56048 q^{5} +1.48981 q^{6} +1.18596 q^{7} -1.00000 q^{8} -0.780452 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.48981 q^{3} +1.00000 q^{4} +2.56048 q^{5} +1.48981 q^{6} +1.18596 q^{7} -1.00000 q^{8} -0.780452 q^{9} -2.56048 q^{10} -5.34165 q^{11} -1.48981 q^{12} -2.66560 q^{13} -1.18596 q^{14} -3.81465 q^{15} +1.00000 q^{16} +7.31002 q^{17} +0.780452 q^{18} -1.00000 q^{19} +2.56048 q^{20} -1.76686 q^{21} +5.34165 q^{22} +8.05997 q^{23} +1.48981 q^{24} +1.55608 q^{25} +2.66560 q^{26} +5.63217 q^{27} +1.18596 q^{28} +0.692148 q^{29} +3.81465 q^{30} +7.91095 q^{31} -1.00000 q^{32} +7.95807 q^{33} -7.31002 q^{34} +3.03663 q^{35} -0.780452 q^{36} +2.80494 q^{37} +1.00000 q^{38} +3.97125 q^{39} -2.56048 q^{40} +7.89946 q^{41} +1.76686 q^{42} -0.167918 q^{43} -5.34165 q^{44} -1.99833 q^{45} -8.05997 q^{46} -7.59864 q^{47} -1.48981 q^{48} -5.59350 q^{49} -1.55608 q^{50} -10.8906 q^{51} -2.66560 q^{52} -10.1692 q^{53} -5.63217 q^{54} -13.6772 q^{55} -1.18596 q^{56} +1.48981 q^{57} -0.692148 q^{58} +8.23414 q^{59} -3.81465 q^{60} -10.9867 q^{61} -7.91095 q^{62} -0.925583 q^{63} +1.00000 q^{64} -6.82523 q^{65} -7.95807 q^{66} -14.9554 q^{67} +7.31002 q^{68} -12.0079 q^{69} -3.03663 q^{70} +6.43514 q^{71} +0.780452 q^{72} +3.97651 q^{73} -2.80494 q^{74} -2.31827 q^{75} -1.00000 q^{76} -6.33498 q^{77} -3.97125 q^{78} +7.54761 q^{79} +2.56048 q^{80} -6.04954 q^{81} -7.89946 q^{82} -1.06719 q^{83} -1.76686 q^{84} +18.7172 q^{85} +0.167918 q^{86} -1.03117 q^{87} +5.34165 q^{88} -0.00516629 q^{89} +1.99833 q^{90} -3.16129 q^{91} +8.05997 q^{92} -11.7858 q^{93} +7.59864 q^{94} -2.56048 q^{95} +1.48981 q^{96} -18.1527 q^{97} +5.59350 q^{98} +4.16890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) $ 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * 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
$3$	−1.48981	−0.860145	−0.430073	−	0.902794i	$-0.641512\pi$
$3$	−1.48981	−0.860145	−0.430073	+	0.902794i	$0.641512\pi$
$4$	1.00000	0.500000
$5$	2.56048	1.14508	0.572542	−	0.819876i	$-0.305957\pi$
$5$	2.56048	1.14508	0.572542	+	0.819876i	$0.305957\pi$
$6$	1.48981	0.608214
$7$	1.18596	0.448250	0.224125	−	0.974560i	$-0.428048\pi$
$7$	1.18596	0.448250	0.224125	+	0.974560i	$0.428048\pi$
$8$	−1.00000	−0.353553
$9$	−0.780452	−0.260151
$10$	−2.56048	−0.809696
$11$	−5.34165	−1.61057	−0.805284	−	0.592889i	$-0.797987\pi$
$11$	−5.34165	−1.61057	−0.805284	+	0.592889i	$0.797987\pi$
$12$	−1.48981	−0.430073
$13$	−2.66560	−0.739305	−0.369652	−	0.929170i	$-0.620523\pi$
$13$	−2.66560	−0.739305	−0.369652	+	0.929170i	$0.620523\pi$
$14$	−1.18596	−0.316961
$15$	−3.81465	−0.984938
$16$	1.00000	0.250000
$17$	7.31002	1.77294	0.886470	−	0.462786i	$-0.153150\pi$
$17$	7.31002	1.77294	0.886470	+	0.462786i	$0.153150\pi$
$18$	0.780452	0.183954
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.56048	0.572542
$21$	−1.76686	−0.385560
$22$	5.34165	1.13884
$23$	8.05997	1.68062	0.840309	−	0.542107i	$-0.182373\pi$
$23$	8.05997	1.68062	0.840309	+	0.542107i	$0.182373\pi$
$24$	1.48981	0.304107
$25$	1.55608	0.311217
$26$	2.66560	0.522767
$27$	5.63217	1.08391
$28$	1.18596	0.224125
$29$	0.692148	0.128529	0.0642643	−	0.997933i	$-0.479530\pi$
$29$	0.692148	0.128529	0.0642643	+	0.997933i	$0.479530\pi$
$30$	3.81465	0.696456
$31$	7.91095	1.42085	0.710424	−	0.703774i	$-0.248503\pi$
$31$	7.91095	1.42085	0.710424	+	0.703774i	$0.248503\pi$
$32$	−1.00000	−0.176777
$33$	7.95807	1.38532
$34$	−7.31002	−1.25366
$35$	3.03663	0.513284
$36$	−0.780452	−0.130075
$37$	2.80494	0.461129	0.230564	−	0.973057i	$-0.425943\pi$
$37$	2.80494	0.461129	0.230564	+	0.973057i	$0.425943\pi$
$38$	1.00000	0.162221
$39$	3.97125	0.635909
$40$	−2.56048	−0.404848
$41$	7.89946	1.23369	0.616844	−	0.787086i	$-0.288411\pi$
$41$	7.89946	1.23369	0.616844	+	0.787086i	$0.288411\pi$
$42$	1.76686	0.272632
$43$	−0.167918	−0.0256072	−0.0128036	−	0.999918i	$-0.504076\pi$
$43$	−0.167918	−0.0256072	−0.0128036	+	0.999918i	$0.504076\pi$
$44$	−5.34165	−0.805284
$45$	−1.99833	−0.297894
$46$	−8.05997	−1.18838
$47$	−7.59864	−1.10838	−0.554188	−	0.832392i	$-0.686971\pi$
$47$	−7.59864	−1.10838	−0.554188	+	0.832392i	$0.686971\pi$
$48$	−1.48981	−0.215036
$49$	−5.59350	−0.799072
$50$	−1.55608	−0.220063
$51$	−10.8906	−1.52499
$52$	−2.66560	−0.369652
$53$	−10.1692	−1.39684	−0.698422	−	0.715686i	$-0.746114\pi$
$53$	−10.1692	−1.39684	−0.698422	+	0.715686i	$0.746114\pi$
$54$	−5.63217	−0.766442
$55$	−13.6772	−1.84424
$56$	−1.18596	−0.158480
$57$	1.48981	0.197331
$58$	−0.692148	−0.0908834
$59$	8.23414	1.07199	0.535997	−	0.844220i	$-0.319936\pi$
$59$	8.23414	1.07199	0.535997	+	0.844220i	$0.319936\pi$
$60$	−3.81465	−0.492469
$61$	−10.9867	−1.40671	−0.703353	−	0.710840i	$-0.748315\pi$
$61$	−10.9867	−1.40671	−0.703353	+	0.710840i	$0.748315\pi$
$62$	−7.91095	−1.00469
$63$	−0.925583	−0.116613
$64$	1.00000	0.125000
$65$	−6.82523	−0.846566
$66$	−7.95807	−0.979571
$67$	−14.9554	−1.82709	−0.913544	−	0.406740i	$-0.866665\pi$
$67$	−14.9554	−1.82709	−0.913544	+	0.406740i	$0.866665\pi$
$68$	7.31002	0.886470
$69$	−12.0079	−1.44558
$70$	−3.03663	−0.362946
$71$	6.43514	0.763711	0.381855	−	0.924222i	$-0.375285\pi$
$71$	6.43514	0.763711	0.381855	+	0.924222i	$0.375285\pi$
$72$	0.780452	0.0919771
$73$	3.97651	0.465415	0.232707	−	0.972547i	$-0.425242\pi$
$73$	3.97651	0.465415	0.232707	+	0.972547i	$0.425242\pi$
$74$	−2.80494	−0.326067
$75$	−2.31827	−0.267691
$76$	−1.00000	−0.114708
$77$	−6.33498	−0.721938
$78$	−3.97125	−0.449656
$79$	7.54761	0.849173	0.424586	−	0.905387i	$-0.360420\pi$
$79$	7.54761	0.849173	0.424586	+	0.905387i	$0.360420\pi$
$80$	2.56048	0.286271
$81$	−6.04954	−0.672171
$82$	−7.89946	−0.872349
$83$	−1.06719	−0.117140	−0.0585699	−	0.998283i	$-0.518654\pi$
$83$	−1.06719	−0.117140	−0.0585699	+	0.998283i	$0.518654\pi$
$84$	−1.76686	−0.192780
$85$	18.7172	2.03016
$86$	0.167918	0.0181070
$87$	−1.03117	−0.110553
$88$	5.34165	0.569422
$89$	−0.00516629	−0.000547626 0	−0.000273813	−	1.00000i	$-0.500087\pi$
$89$	−0.00516629	−0.000547626 0	−0.000273813		1.00000i	$0.500087\pi$
$90$	1.99833	0.210643
$91$	−3.16129	−0.331393
$92$	8.05997	0.840309
$93$	−11.7858	−1.22214
$94$	7.59864	0.783740
$95$	−2.56048	−0.262700
$96$	1.48981	0.152054
$97$	−18.1527	−1.84313	−0.921565	−	0.388224i	$-0.873089\pi$
$97$	−18.1527	−1.84313	−0.921565	+	0.388224i	$0.873089\pi$
$98$	5.59350	0.565029
$99$	4.16890	0.418990
$100$	1.55608	0.155608
$101$	−7.40508	−0.736833	−0.368416	−	0.929661i	$-0.620100\pi$
$101$	−7.40508	−0.736833	−0.368416	+	0.929661i	$0.620100\pi$
$102$	10.8906	1.07833
$103$	1.32212	0.130273	0.0651364	−	0.997876i	$-0.479252\pi$
$103$	1.32212	0.130273	0.0651364	+	0.997876i	$0.479252\pi$
$104$	2.66560	0.261384
$105$	−4.52401	−0.441499
$106$	10.1692	0.987718
$107$	5.87570	0.568025	0.284013	−	0.958821i	$-0.408334\pi$
$107$	5.87570	0.568025	0.284013	+	0.958821i	$0.408334\pi$
$108$	5.63217	0.541956
$109$	16.2168	1.55329	0.776645	−	0.629938i	$-0.216920\pi$
$109$	16.2168	1.55329	0.776645	+	0.629938i	$0.216920\pi$
$110$	13.6772	1.30407
$111$	−4.17883	−0.396637
$112$	1.18596	0.112063
$113$	5.67901	0.534236	0.267118	−	0.963664i	$-0.413929\pi$
$113$	5.67901	0.534236	0.267118	+	0.963664i	$0.413929\pi$
$114$	−1.48981	−0.139534
$115$	20.6374	1.92445
$116$	0.692148	0.0642643
$117$	2.08037	0.192331
$118$	−8.23414	−0.758014
$119$	8.66938	0.794721
$120$	3.81465	0.348228
$121$	17.5332	1.59393
$122$	10.9867	0.994692
$123$	−11.7687	−1.06115
$124$	7.91095	0.710424
$125$	−8.81810	−0.788715
$126$	0.925583	0.0824575
$127$	16.7436	1.48575	0.742877	−	0.669428i	$-0.233461\pi$
$127$	16.7436	1.48575	0.742877	+	0.669428i	$0.233461\pi$
$128$	−1.00000	−0.0883883
$129$	0.250166	0.0220259
$130$	6.82523	0.598612
$131$	10.8648	0.949265	0.474633	−	0.880184i	$-0.342581\pi$
$131$	10.8648	0.949265	0.474633	+	0.880184i	$0.342581\pi$
$132$	7.95807	0.692661
$133$	−1.18596	−0.102836
$134$	14.9554	1.29195
$135$	14.4211	1.24117
$136$	−7.31002	−0.626829
$137$	−9.44867	−0.807254	−0.403627	−	0.914924i	$-0.632251\pi$
$137$	−9.44867	−0.807254	−0.403627	+	0.914924i	$0.632251\pi$
$138$	12.0079	1.02218
$139$	−7.66705	−0.650311	−0.325155	−	0.945661i	$-0.605417\pi$
$139$	−7.66705	−0.650311	−0.325155	+	0.945661i	$0.605417\pi$
$140$	3.03663	0.256642
$141$	11.3206	0.953363
$142$	−6.43514	−0.540025
$143$	14.2387	1.19070
$144$	−0.780452	−0.0650376
$145$	1.77223	0.147176
$146$	−3.97651	−0.329098
$147$	8.33328	0.687318
$148$	2.80494	0.230564
$149$	−15.6878	−1.28520	−0.642599	−	0.766203i	$-0.722144\pi$
$149$	−15.6878	−1.28520	−0.642599	+	0.766203i	$0.722144\pi$
$150$	2.31827	0.189286
$151$	16.5332	1.34545	0.672727	−	0.739891i	$-0.265123\pi$
$151$	16.5332	1.34545	0.672727	+	0.739891i	$0.265123\pi$
$152$	1.00000	0.0811107
$153$	−5.70512	−0.461231
$154$	6.33498	0.510487
$155$	20.2559	1.62699
$156$	3.97125	0.317955
$157$	−17.3652	−1.38589	−0.692947	−	0.720989i	$-0.743688\pi$
$157$	−17.3652	−1.38589	−0.692947	+	0.720989i	$0.743688\pi$
$158$	−7.54761	−0.600456
$159$	15.1502	1.20149
$160$	−2.56048	−0.202424
$161$	9.55878	0.753338
$162$	6.04954	0.475297
$163$	−0.344598	−0.0269910	−0.0134955	−	0.999909i	$-0.504296\pi$
$163$	−0.344598	−0.0269910	−0.0134955	+	0.999909i	$0.504296\pi$
$164$	7.89946	0.616844
$165$	20.3765	1.58631
$166$	1.06719	0.0828303
$167$	−5.54833	−0.429343	−0.214671	−	0.976686i	$-0.568868\pi$
$167$	−5.54833	−0.429343	−0.214671	+	0.976686i	$0.568868\pi$
$168$	1.76686	0.136316
$169$	−5.89457	−0.453428
$170$	−18.7172	−1.43554
$171$	0.780452	0.0596826
$172$	−0.167918	−0.0128036
$173$	3.83825	0.291817	0.145908	−	0.989298i	$-0.453390\pi$
$173$	3.83825	0.291817	0.145908	+	0.989298i	$0.453390\pi$
$174$	1.03117	0.0781729
$175$	1.84545	0.139503
$176$	−5.34165	−0.402642
$177$	−12.2673	−0.922070
$178$	0.00516629	0.000387230 0
$179$	−3.52467	−0.263446	−0.131723	−	0.991287i	$-0.542051\pi$
$179$	−3.52467	−0.263446	−0.131723	+	0.991287i	$0.542051\pi$
$180$	−1.99833	−0.148947
$181$	1.35420	0.100657	0.0503286	−	0.998733i	$-0.483973\pi$
$181$	1.35420	0.100657	0.0503286	+	0.998733i	$0.483973\pi$
$182$	3.16129	0.234331
$183$	16.3682	1.20997
$184$	−8.05997	−0.594189
$185$	7.18199	0.528031
$186$	11.7858	0.864180
$187$	−39.0476	−2.85544
$188$	−7.59864	−0.554188
$189$	6.67952	0.485864
$190$	2.56048	0.185757
$191$	12.4182	0.898553	0.449276	−	0.893393i	$-0.351682\pi$
$191$	12.4182	0.898553	0.449276	+	0.893393i	$0.351682\pi$
$192$	−1.48981	−0.107518
$193$	2.38753	0.171858	0.0859292	−	0.996301i	$-0.472614\pi$
$193$	2.38753	0.171858	0.0859292	+	0.996301i	$0.472614\pi$
$194$	18.1527	1.30329
$195$	10.1683	0.728169
$196$	−5.59350	−0.399536
$197$	4.76905	0.339780	0.169890	−	0.985463i	$-0.445659\pi$
$197$	4.76905	0.339780	0.169890	+	0.985463i	$0.445659\pi$
$198$	−4.16890	−0.296271
$199$	−5.97986	−0.423901	−0.211951	−	0.977280i	$-0.567982\pi$
$199$	−5.97986	−0.423901	−0.211951	+	0.977280i	$0.567982\pi$
$200$	−1.55608	−0.110032
$201$	22.2807	1.57156
$202$	7.40508	0.521019
$203$	0.820858	0.0576129
$204$	−10.8906	−0.762493
$205$	20.2264	1.41268
$206$	−1.32212	−0.0921167
$207$	−6.29041	−0.437214
$208$	−2.66560	−0.184826
$209$	5.34165	0.369490
$210$	4.52401	0.312187
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−10.1692	−0.698422
$213$	−9.58717	−0.656902
$214$	−5.87570	−0.401655
$215$	−0.429951	−0.0293224
$216$	−5.63217	−0.383221
$217$	9.38205	0.636895
$218$	−16.2168	−1.09834
$219$	−5.92426	−0.400324
$220$	−13.6772	−0.922118
$221$	−19.4856	−1.31074
$222$	4.17883	0.280465
$223$	14.9130	0.998646	0.499323	−	0.866416i	$-0.333582\pi$
$223$	14.9130	0.998646	0.499323	+	0.866416i	$0.333582\pi$
$224$	−1.18596	−0.0792402
$225$	−1.21445	−0.0809632
$226$	−5.67901	−0.377762
$227$	27.9557	1.85549	0.927744	−	0.373217i	$-0.121745\pi$
$227$	27.9557	1.85549	0.927744	+	0.373217i	$0.121745\pi$
$228$	1.48981	0.0986654
$229$	8.30629	0.548895	0.274447	−	0.961602i	$-0.411505\pi$
$229$	8.30629	0.548895	0.274447	+	0.961602i	$0.411505\pi$
$230$	−20.6374	−1.36079
$231$	9.43794	0.620971
$232$	−0.692148	−0.0454417
$233$	−12.7298	−0.833959	−0.416979	−	0.908916i	$-0.636911\pi$
$233$	−12.7298	−0.833959	−0.416979	+	0.908916i	$0.636911\pi$
$234$	−2.08037	−0.135998
$235$	−19.4562	−1.26918
$236$	8.23414	0.535997
$237$	−11.2445	−0.730412
$238$	−8.66938	−0.561952
$239$	−6.45304	−0.417412	−0.208706	−	0.977978i	$-0.566925\pi$
$239$	−6.45304	−0.417412	−0.208706	+	0.977978i	$0.566925\pi$
$240$	−3.81465	−0.246234
$241$	4.56223	0.293879	0.146940	−	0.989145i	$-0.453058\pi$
$241$	4.56223	0.293879	0.146940	+	0.989145i	$0.453058\pi$
$242$	−17.5332	−1.12708
$243$	−7.88383	−0.505748
$244$	−10.9867	−0.703353
$245$	−14.3221	−0.915004
$246$	11.7687	0.750347
$247$	2.66560	0.169608
$248$	−7.91095	−0.502346
$249$	1.58992	0.100757
$250$	8.81810	0.557706
$251$	−16.6460	−1.05069	−0.525343	−	0.850890i	$-0.676063\pi$
$251$	−16.6460	−1.05069	−0.525343	+	0.850890i	$0.676063\pi$
$252$	−0.925583	−0.0583063
$253$	−43.0535	−2.70675
$254$	−16.7436	−1.05059
$255$	−27.8852	−1.74624
$256$	1.00000	0.0625000
$257$	23.9364	1.49311	0.746555	−	0.665324i	$-0.231706\pi$
$257$	23.9364	1.49311	0.746555	+	0.665324i	$0.231706\pi$
$258$	−0.250166	−0.0155747
$259$	3.32654	0.206701
$260$	−6.82523	−0.423283
$261$	−0.540188	−0.0334368
$262$	−10.8648	−0.671232
$263$	−10.8653	−0.669986	−0.334993	−	0.942221i	$-0.608734\pi$
$263$	−10.8653	−0.669986	−0.334993	+	0.942221i	$0.608734\pi$
$264$	−7.95807	−0.489786
$265$	−26.0380	−1.59950
$266$	1.18596	0.0727158
$267$	0.00769681	0.000471037 0
$268$	−14.9554	−0.913544
$269$	18.2930	1.11535	0.557673	−	0.830061i	$-0.311694\pi$
$269$	18.2930	1.11535	0.557673	+	0.830061i	$0.311694\pi$
$270$	−14.4211	−0.877640
$271$	9.63078	0.585028	0.292514	−	0.956261i	$-0.405508\pi$
$271$	9.63078	0.585028	0.292514	+	0.956261i	$0.405508\pi$
$272$	7.31002	0.443235
$273$	4.70974	0.285046
$274$	9.44867	0.570815
$275$	−8.31205	−0.501236
$276$	−12.0079	−0.722788
$277$	16.5518	0.994498	0.497249	−	0.867608i	$-0.334343\pi$
$277$	16.5518	0.994498	0.497249	+	0.867608i	$0.334343\pi$
$278$	7.66705	0.459839
$279$	−6.17411	−0.369634
$280$	−3.03663	−0.181473
$281$	23.6574	1.41128	0.705642	−	0.708569i	$-0.250659\pi$
$281$	23.6574	1.41128	0.705642	+	0.708569i	$0.250659\pi$
$282$	−11.3206	−0.674130
$283$	23.6434	1.40546	0.702728	−	0.711459i	$-0.251965\pi$
$283$	23.6434	1.40546	0.702728	+	0.711459i	$0.251965\pi$
$284$	6.43514	0.381855
$285$	3.81465	0.225960
$286$	−14.2387	−0.841953
$287$	9.36842	0.553001
$288$	0.780452	0.0459886
$289$	36.4364	2.14332
$290$	−1.77223	−0.104069
$291$	27.0442	1.58536
$292$	3.97651	0.232707
$293$	2.61130	0.152554	0.0762769	−	0.997087i	$-0.475697\pi$
$293$	2.61130	0.152554	0.0762769	+	0.997087i	$0.475697\pi$
$294$	−8.33328	−0.486007
$295$	21.0834	1.22752
$296$	−2.80494	−0.163034
$297$	−30.0851	−1.74572
$298$	15.6878	0.908772
$299$	−21.4847	−1.24249
$300$	−2.31827	−0.133846
$301$	−0.199143	−0.0114784
$302$	−16.5332	−0.951380
$303$	11.0322	0.633783
$304$	−1.00000	−0.0573539
$305$	−28.1314	−1.61080
$306$	5.70512	0.326140
$307$	29.4031	1.67812	0.839061	−	0.544037i	$-0.183105\pi$
$307$	29.4031	1.67812	0.839061	+	0.544037i	$0.183105\pi$
$308$	−6.33498	−0.360969
$309$	−1.96972	−0.112053
$310$	−20.2559	−1.15046
$311$	23.9773	1.35963	0.679814	−	0.733385i	$-0.262061\pi$
$311$	23.9773	1.35963	0.679814	+	0.733385i	$0.262061\pi$
$312$	−3.97125	−0.224828
$313$	12.8980	0.729037	0.364518	−	0.931196i	$-0.381234\pi$
$313$	12.8980	0.729037	0.364518	+	0.931196i	$0.381234\pi$
$314$	17.3652	0.979974
$315$	−2.36994	−0.133531
$316$	7.54761	0.424586
$317$	−10.0261	−0.563122	−0.281561	−	0.959543i	$-0.590852\pi$
$317$	−10.0261	−0.563122	−0.281561	+	0.959543i	$0.590852\pi$
$318$	−15.1502	−0.849581
$319$	−3.69721	−0.207004
$320$	2.56048	0.143135
$321$	−8.75370	−0.488584
$322$	−9.55878	−0.532690
$323$	−7.31002	−0.406740
$324$	−6.04954	−0.336086
$325$	−4.14790	−0.230084
$326$	0.344598	0.0190855
$327$	−24.1601	−1.33606
$328$	−7.89946	−0.436174
$329$	−9.01167	−0.496829
$330$	−20.3765	−1.12169
$331$	−6.58705	−0.362057	−0.181028	−	0.983478i	$-0.557943\pi$
$331$	−6.58705	−0.362057	−0.181028	+	0.983478i	$0.557943\pi$
$332$	−1.06719	−0.0585699
$333$	−2.18912	−0.119963
$334$	5.54833	0.303591
$335$	−38.2930	−2.09217
$336$	−1.76686	−0.0963900
$337$	18.3991	1.00226	0.501132	−	0.865371i	$-0.332917\pi$
$337$	18.3991	1.00226	0.501132	+	0.865371i	$0.332917\pi$
$338$	5.89457	0.320622
$339$	−8.46067	−0.459520
$340$	18.7172	1.01508
$341$	−42.2575	−2.28837
$342$	−0.780452	−0.0422020
$343$	−14.9354	−0.806434
$344$	0.167918	0.00905351
$345$	−30.7459	−1.65531
$346$	−3.83825	−0.206345
$347$	2.53559	0.136117	0.0680587	−	0.997681i	$-0.478319\pi$
$347$	2.53559	0.136117	0.0680587	+	0.997681i	$0.478319\pi$
$348$	−1.03117	−0.0552766
$349$	26.7044	1.42945	0.714726	−	0.699404i	$-0.246551\pi$
$349$	26.7044	1.42945	0.714726	+	0.699404i	$0.246551\pi$
$350$	−1.84545	−0.0986434
$351$	−15.0131	−0.801342
$352$	5.34165	0.284711
$353$	20.0049	1.06475	0.532377	−	0.846508i	$-0.321299\pi$
$353$	20.0049	1.06475	0.532377	+	0.846508i	$0.321299\pi$
$354$	12.2673	0.652002
$355$	16.4771	0.874513
$356$	−0.00516629	−0.000273813 0
$357$	−12.9158	−0.683575
$358$	3.52467	0.186284
$359$	32.6937	1.72551	0.862754	−	0.505624i	$-0.168738\pi$
$359$	32.6937	1.72551	0.862754	+	0.505624i	$0.168738\pi$
$360$	1.99833	0.105321
$361$	1.00000	0.0526316
$362$	−1.35420	−0.0711754
$363$	−26.1213	−1.37101
$364$	−3.16129	−0.165697
$365$	10.1818	0.532939
$366$	−16.3682	−0.855579
$367$	33.9050	1.76983	0.884913	−	0.465756i	$-0.154217\pi$
$367$	33.9050	1.76983	0.884913	+	0.465756i	$0.154217\pi$
$368$	8.05997	0.420155
$369$	−6.16514	−0.320945
$370$	−7.18199	−0.373374
$371$	−12.0602	−0.626136
$372$	−11.7858	−0.611068
$373$	19.4898	1.00914	0.504572	−	0.863369i	$-0.331650\pi$
$373$	19.4898	1.00914	0.504572	+	0.863369i	$0.331650\pi$
$374$	39.0476	2.01910
$375$	13.1373	0.678409
$376$	7.59864	0.391870
$377$	−1.84499	−0.0950218
$378$	−6.67952	−0.343558
$379$	5.68931	0.292240	0.146120	−	0.989267i	$-0.453321\pi$
$379$	5.68931	0.292240	0.146120	+	0.989267i	$0.453321\pi$
$380$	−2.56048	−0.131350
$381$	−24.9449	−1.27796
$382$	−12.4182	−0.635373
$383$	−9.83278	−0.502432	−0.251216	−	0.967931i	$-0.580830\pi$
$383$	−9.83278	−0.502432	−0.251216	+	0.967931i	$0.580830\pi$
$384$	1.48981	0.0760268
$385$	−16.2206	−0.826679
$386$	−2.38753	−0.121522
$387$	0.131052	0.00666173
$388$	−18.1527	−0.921565
$389$	−7.19246	−0.364672	−0.182336	−	0.983236i	$-0.558366\pi$
$389$	−7.19246	−0.364672	−0.182336	+	0.983236i	$0.558366\pi$
$390$	−10.1683	−0.514894
$391$	58.9185	2.97964
$392$	5.59350	0.282515
$393$	−16.1866	−0.816506
$394$	−4.76905	−0.240261
$395$	19.3255	0.972374
$396$	4.16890	0.209495
$397$	30.7708	1.54434	0.772171	−	0.635415i	$-0.219171\pi$
$397$	30.7708	1.54434	0.772171	+	0.635415i	$0.219171\pi$
$398$	5.97986	0.299744
$399$	1.76686	0.0884535
$400$	1.55608	0.0778041
$401$	−12.0806	−0.603274	−0.301637	−	0.953423i	$-0.597533\pi$
$401$	−12.0806	−0.603274	−0.301637	+	0.953423i	$0.597533\pi$
$402$	−22.2807	−1.11126
$403$	−21.0874	−1.05044
$404$	−7.40508	−0.368416
$405$	−15.4898	−0.769692
$406$	−0.820858	−0.0407385
$407$	−14.9830	−0.742679
$408$	10.8906	0.539164
$409$	−16.6931	−0.825420	−0.412710	−	0.910862i	$-0.635418\pi$
$409$	−16.6931	−0.825420	−0.412710	+	0.910862i	$0.635418\pi$
$410$	−20.2264	−0.998912
$411$	14.0768	0.694356
$412$	1.32212	0.0651364
$413$	9.76535	0.480521
$414$	6.29041	0.309157
$415$	−2.73253	−0.134135
$416$	2.66560	0.130692
$417$	11.4225	0.559361
$418$	−5.34165	−0.261269
$419$	10.8596	0.530525	0.265262	−	0.964176i	$-0.414541\pi$
$419$	10.8596	0.530525	0.265262	+	0.964176i	$0.414541\pi$
$420$	−4.52401	−0.220749
$421$	2.11295	0.102979	0.0514894	−	0.998674i	$-0.483603\pi$
$421$	2.11295	0.102979	0.0514894	+	0.998674i	$0.483603\pi$
$422$	−1.00000	−0.0486792
$423$	5.93037	0.288344
$424$	10.1692	0.493859
$425$	11.3750	0.551768
$426$	9.58717	0.464500
$427$	−13.0298	−0.630557
$428$	5.87570	0.284013
$429$	−21.2131	−1.02418
$430$	0.429951	0.0207341
$431$	−22.6846	−1.09268	−0.546338	−	0.837564i	$-0.683979\pi$
$431$	−22.6846	−1.09268	−0.546338	+	0.837564i	$0.683979\pi$
$432$	5.63217	0.270978
$433$	−27.3550	−1.31460	−0.657300	−	0.753629i	$-0.728301\pi$
$433$	−27.3550	−1.31460	−0.657300	+	0.753629i	$0.728301\pi$
$434$	−9.38205	−0.450353
$435$	−2.64030	−0.126593
$436$	16.2168	0.776645
$437$	−8.05997	−0.385560
$438$	5.92426	0.283072
$439$	−27.9973	−1.33624	−0.668119	−	0.744054i	$-0.732900\pi$
$439$	−27.9973	−1.33624	−0.668119	+	0.744054i	$0.732900\pi$
$440$	13.6772	0.652036
$441$	4.36546	0.207879
$442$	19.4856	0.926836
$443$	−38.1213	−1.81120	−0.905598	−	0.424138i	$-0.860577\pi$
$443$	−38.1213	−1.81120	−0.905598	+	0.424138i	$0.860577\pi$
$444$	−4.17883	−0.198319
$445$	−0.0132282	−0.000627077 0
$446$	−14.9130	−0.706150
$447$	23.3720	1.10546
$448$	1.18596	0.0560313
$449$	−2.29685	−0.108395	−0.0541976	−	0.998530i	$-0.517260\pi$
$449$	−2.29685	−0.108395	−0.0541976	+	0.998530i	$0.517260\pi$
$450$	1.21445	0.0572496
$451$	−42.1961	−1.98694
$452$	5.67901	0.267118
$453$	−24.6314	−1.15729
$454$	−27.9557	−1.31203
$455$	−8.09444	−0.379473
$456$	−1.48981	−0.0697670
$457$	−11.9085	−0.557054	−0.278527	−	0.960428i	$-0.589846\pi$
$457$	−11.9085	−0.557054	−0.278527	+	0.960428i	$0.589846\pi$
$458$	−8.30629	−0.388127
$459$	41.1713	1.92171
$460$	20.6374	0.962225
$461$	11.4831	0.534823	0.267412	−	0.963582i	$-0.413832\pi$
$461$	11.4831	0.534823	0.267412	+	0.963582i	$0.413832\pi$
$462$	−9.43794	−0.439093
$463$	21.8369	1.01484	0.507422	−	0.861697i	$-0.330598\pi$
$463$	21.8369	1.01484	0.507422	+	0.861697i	$0.330598\pi$
$464$	0.692148	0.0321321
$465$	−30.1775	−1.39945
$466$	12.7298	0.589698
$467$	−3.78130	−0.174978	−0.0874888	−	0.996166i	$-0.527884\pi$
$467$	−3.78130	−0.174978	−0.0874888	+	0.996166i	$0.527884\pi$
$468$	2.08037	0.0961653
$469$	−17.7364	−0.818992
$470$	19.4562	0.897447
$471$	25.8709	1.19207
$472$	−8.23414	−0.379007
$473$	0.896958	0.0412422
$474$	11.2445	0.516479
$475$	−1.55608	−0.0713980
$476$	8.66938	0.397360
$477$	7.93655	0.363390
$478$	6.45304	0.295155
$479$	26.3865	1.20563	0.602814	−	0.797881i	$-0.294046\pi$
$479$	26.3865	1.20563	0.602814	+	0.797881i	$0.294046\pi$
$480$	3.81465	0.174114
$481$	−7.47684	−0.340915
$482$	−4.56223	−0.207804
$483$	−14.2408	−0.647980
$484$	17.5332	0.796966
$485$	−46.4798	−2.11054
$486$	7.88383	0.357618
$487$	39.5653	1.79287	0.896437	−	0.443172i	$-0.146147\pi$
$487$	39.5653	1.79287	0.896437	+	0.443172i	$0.146147\pi$
$488$	10.9867	0.497346
$489$	0.513387	0.0232162
$490$	14.3221	0.647006
$491$	13.7876	0.622226	0.311113	−	0.950373i	$-0.399298\pi$
$491$	13.7876	0.622226	0.311113	+	0.950373i	$0.399298\pi$
$492$	−11.7687	−0.530575
$493$	5.05961	0.227873
$494$	−2.66560	−0.119931
$495$	10.6744	0.479779
$496$	7.91095	0.355212
$497$	7.63181	0.342333
$498$	−1.58992	−0.0712461
$499$	5.30972	0.237696	0.118848	−	0.992912i	$-0.462080\pi$
$499$	5.30972	0.237696	0.118848	+	0.992912i	$0.462080\pi$
$500$	−8.81810	−0.394357
$501$	8.26599	0.369297
$502$	16.6460	0.742948
$503$	−22.3195	−0.995177	−0.497589	−	0.867413i	$-0.665781\pi$
$503$	−22.3195	−0.995177	−0.497589	+	0.867413i	$0.665781\pi$
$504$	0.925583	0.0412288
$505$	−18.9606	−0.843735
$506$	43.0535	1.91396
$507$	8.78182	0.390014
$508$	16.7436	0.742877
$509$	−6.77631	−0.300355	−0.150177	−	0.988659i	$-0.547984\pi$
$509$	−6.77631	−0.300355	−0.150177	+	0.988659i	$0.547984\pi$
$510$	27.8852	1.23478
$511$	4.71597	0.208622
$512$	−1.00000	−0.0441942
$513$	−5.63217	−0.248667
$514$	−23.9364	−1.05579
$515$	3.38528	0.149173
$516$	0.250166	0.0110130
$517$	40.5893	1.78511
$518$	−3.32654	−0.146160
$519$	−5.71828	−0.251005
$520$	6.82523	0.299306
$521$	−38.0767	−1.66817	−0.834086	−	0.551634i	$-0.814004\pi$
$521$	−38.0767	−1.66817	−0.834086	+	0.551634i	$0.814004\pi$
$522$	0.540188	0.0236434
$523$	−24.9667	−1.09172	−0.545859	−	0.837877i	$-0.683797\pi$
$523$	−24.9667	−1.09172	−0.545859	+	0.837877i	$0.683797\pi$
$524$	10.8648	0.474633
$525$	−2.74938	−0.119993
$526$	10.8653	0.473752
$527$	57.8292	2.51908
$528$	7.95807	0.346331
$529$	41.9630	1.82448
$530$	26.0380	1.13102
$531$	−6.42635	−0.278880
$532$	−1.18596	−0.0514178
$533$	−21.0568	−0.912071
$534$	−0.00769681	−0.000333074 0
$535$	15.0446	0.650436
$536$	14.9554	0.645973
$537$	5.25110	0.226602
$538$	−18.2930	−0.788668
$539$	29.8785	1.28696
$540$	14.4211	0.620585
$541$	−37.4666	−1.61081	−0.805407	−	0.592722i	$-0.798053\pi$
$541$	−37.4666	−1.61081	−0.805407	+	0.592722i	$0.798053\pi$
$542$	−9.63078	−0.413677
$543$	−2.01751	−0.0865798
$544$	−7.31002	−0.313415
$545$	41.5230	1.77865
$546$	−4.70974	−0.201558
$547$	−4.39317	−0.187839	−0.0939193	−	0.995580i	$-0.529940\pi$
$547$	−4.39317	−0.187839	−0.0939193	+	0.995580i	$0.529940\pi$
$548$	−9.44867	−0.403627
$549$	8.57461	0.365956
$550$	8.31205	0.354427
$551$	−0.692148	−0.0294865
$552$	12.0079	0.511088
$553$	8.95115	0.380642
$554$	−16.5518	−0.703217
$555$	−10.6998	−0.454183
$556$	−7.66705	−0.325155
$557$	−10.2976	−0.436323	−0.218161	−	0.975913i	$-0.570006\pi$
$557$	−10.2976	−0.436323	−0.218161	+	0.975913i	$0.570006\pi$
$558$	6.17411	0.261371
$559$	0.447602	0.0189315
$560$	3.03663	0.128321
$561$	58.1737	2.45609
$562$	−23.6574	−0.997928
$563$	13.3216	0.561440	0.280720	−	0.959790i	$-0.409427\pi$
$563$	13.3216	0.561440	0.280720	+	0.959790i	$0.409427\pi$
$564$	11.3206	0.476682
$565$	14.5410	0.611745
$566$	−23.6434	−0.993807
$567$	−7.17450	−0.301301
$568$	−6.43514	−0.270012
$569$	1.82806	0.0766364	0.0383182	−	0.999266i	$-0.487800\pi$
$569$	1.82806	0.0766364	0.0383182	+	0.999266i	$0.487800\pi$
$570$	−3.81465	−0.159778
$571$	−42.2327	−1.76739	−0.883693	−	0.468068i	$-0.844950\pi$
$571$	−42.2327	−1.76739	−0.883693	+	0.468068i	$0.844950\pi$
$572$	14.2387	0.595351
$573$	−18.5009	−0.772886
$574$	−9.36842	−0.391030
$575$	12.5420	0.523036
$576$	−0.780452	−0.0325188
$577$	11.7320	0.488408	0.244204	−	0.969724i	$-0.421473\pi$
$577$	11.7320	0.488408	0.244204	+	0.969724i	$0.421473\pi$
$578$	−36.4364	−1.51555
$579$	−3.55698	−0.147823
$580$	1.77223	0.0735880
$581$	−1.26565	−0.0525079
$582$	−27.0442	−1.12102
$583$	54.3202	2.24971
$584$	−3.97651	−0.164549
$585$	5.32676	0.220235
$586$	−2.61130	−0.107872
$587$	35.7707	1.47641	0.738207	−	0.674574i	$-0.235673\pi$
$587$	35.7707	1.47641	0.738207	+	0.674574i	$0.235673\pi$
$588$	8.33328	0.343659
$589$	−7.91095	−0.325965
$590$	−21.0834	−0.867990
$591$	−7.10500	−0.292260
$592$	2.80494	0.115282
$593$	26.1988	1.07586	0.537928	−	0.842991i	$-0.319207\pi$
$593$	26.1988	1.07586	0.537928	+	0.842991i	$0.319207\pi$
$594$	30.0851	1.23441
$595$	22.1978	0.910022
$596$	−15.6878	−0.642599
$597$	8.90889	0.364617
$598$	21.4847	0.878573
$599$	37.8115	1.54493	0.772467	−	0.635054i	$-0.219022\pi$
$599$	37.8115	1.54493	0.772467	+	0.635054i	$0.219022\pi$
$600$	2.31827	0.0946432
$601$	15.0546	0.614091	0.307046	−	0.951695i	$-0.400660\pi$
$601$	15.0546	0.614091	0.307046	+	0.951695i	$0.400660\pi$
$602$	0.199143	0.00811648
$603$	11.6719	0.475318
$604$	16.5332	0.672727
$605$	44.8936	1.82519
$606$	−11.0322	−0.448152
$607$	28.7281	1.16604	0.583019	−	0.812459i	$-0.301871\pi$
$607$	28.7281	1.16604	0.583019	+	0.812459i	$0.301871\pi$
$608$	1.00000	0.0405554
$609$	−1.22293	−0.0495555
$610$	28.1314	1.13901
$611$	20.2549	0.819427
$612$	−5.70512	−0.230616
$613$	19.3823	0.782843	0.391421	−	0.920212i	$-0.371983\pi$
$613$	19.3823	0.782843	0.391421	+	0.920212i	$0.371983\pi$
$614$	−29.4031	−1.18661
$615$	−30.1336	−1.21511
$616$	6.33498	0.255243
$617$	1.94915	0.0784698	0.0392349	−	0.999230i	$-0.487508\pi$
$617$	1.94915	0.0784698	0.0392349	+	0.999230i	$0.487508\pi$
$618$	1.96972	0.0792337
$619$	46.7281	1.87816	0.939080	−	0.343698i	$-0.111680\pi$
$619$	46.7281	1.87816	0.939080	+	0.343698i	$0.111680\pi$
$620$	20.2559	0.813495
$621$	45.3951	1.82164
$622$	−23.9773	−0.961402
$623$	−0.00612700	−0.000245473 0
$624$	3.97125	0.158977
$625$	−30.3590	−1.21436
$626$	−12.8980	−0.515507
$627$	−7.95807	−0.317815
$628$	−17.3652	−0.692947
$629$	20.5041	0.817553
$630$	2.36994	0.0944207
$631$	−36.8191	−1.46574	−0.732872	−	0.680367i	$-0.761821\pi$
$631$	−36.8191	−1.46574	−0.732872	+	0.680367i	$0.761821\pi$
$632$	−7.54761	−0.300228
$633$	−1.48981	−0.0592148
$634$	10.0261	0.398188
$635$	42.8717	1.70131
$636$	15.1502	0.600744
$637$	14.9101	0.590758
$638$	3.69721	0.146374
$639$	−5.02232	−0.198680
$640$	−2.56048	−0.101212
$641$	−22.8265	−0.901591	−0.450796	−	0.892627i	$-0.648860\pi$
$641$	−22.8265	−0.901591	−0.450796	+	0.892627i	$0.648860\pi$
$642$	8.75370	0.345481
$643$	−21.9255	−0.864659	−0.432329	−	0.901716i	$-0.642308\pi$
$643$	−21.9255	−0.864659	−0.432329	+	0.901716i	$0.642308\pi$
$644$	9.55878	0.376669
$645$	0.640547	0.0252215
$646$	7.31002	0.287609
$647$	−31.3755	−1.23350	−0.616749	−	0.787160i	$-0.711551\pi$
$647$	−31.3755	−1.23350	−0.616749	+	0.787160i	$0.711551\pi$
$648$	6.04954	0.237648
$649$	−43.9839	−1.72652
$650$	4.14790	0.162694
$651$	−13.9775	−0.547822
$652$	−0.344598	−0.0134955
$653$	2.89701	0.113369	0.0566844	−	0.998392i	$-0.481947\pi$
$653$	2.89701	0.113369	0.0566844	+	0.998392i	$0.481947\pi$
$654$	24.1601	0.944734
$655$	27.8192	1.08699
$656$	7.89946	0.308422
$657$	−3.10347	−0.121078
$658$	9.01167	0.351311
$659$	−37.2064	−1.44936	−0.724678	−	0.689087i	$-0.758012\pi$
$659$	−37.2064	−1.44936	−0.724678	+	0.689087i	$0.758012\pi$
$660$	20.3765	0.793155
$661$	7.64430	0.297329	0.148664	−	0.988888i	$-0.452503\pi$
$661$	7.64430	0.297329	0.148664	+	0.988888i	$0.452503\pi$
$662$	6.58705	0.256013
$663$	29.0299	1.12743
$664$	1.06719	0.0414151
$665$	−3.03663	−0.117755
$666$	2.18912	0.0848265
$667$	5.57868	0.216008
$668$	−5.54833	−0.214671
$669$	−22.2176	−0.858981
$670$	38.2930	1.47939
$671$	58.6873	2.26560
$672$	1.76686	0.0681580
$673$	7.98037	0.307621	0.153810	−	0.988100i	$-0.450846\pi$
$673$	7.98037	0.307621	0.153810	+	0.988100i	$0.450846\pi$
$674$	−18.3991	−0.708707
$675$	8.76413	0.337331
$676$	−5.89457	−0.226714
$677$	17.8814	0.687237	0.343618	−	0.939109i	$-0.388347\pi$
$677$	17.8814	0.687237	0.343618	+	0.939109i	$0.388347\pi$
$678$	8.46067	0.324930
$679$	−21.5284	−0.826183
$680$	−18.7172	−0.717772
$681$	−41.6489	−1.59599
$682$	42.2575	1.61812
$683$	3.90274	0.149334	0.0746670	−	0.997209i	$-0.476211\pi$
$683$	3.90274	0.149334	0.0746670	+	0.997209i	$0.476211\pi$
$684$	0.780452	0.0298413
$685$	−24.1932	−0.924374
$686$	14.9354	0.570235
$687$	−12.3748	−0.472129
$688$	−0.167918	−0.00640180
$689$	27.1070	1.03269
$690$	30.7459	1.17048
$691$	41.8017	1.59021	0.795107	−	0.606470i	$-0.207415\pi$
$691$	41.8017	1.59021	0.795107	+	0.606470i	$0.207415\pi$
$692$	3.83825	0.145908
$693$	4.94414	0.187812
$694$	−2.53559	−0.0962495
$695$	−19.6314	−0.744660
$696$	1.03117	0.0390865
$697$	57.7452	2.18725
$698$	−26.7044	−1.01078
$699$	18.9651	0.717325
$700$	1.84545	0.0697514
$701$	−32.9285	−1.24369	−0.621846	−	0.783140i	$-0.713617\pi$
$701$	−32.9285	−1.24369	−0.621846	+	0.783140i	$0.713617\pi$
$702$	15.0131	0.566634
$703$	−2.80494	−0.105790
$704$	−5.34165	−0.201321
$705$	28.9861	1.09168
$706$	−20.0049	−0.752894
$707$	−8.78211	−0.330285
$708$	−12.2673	−0.461035
$709$	−30.7827	−1.15607	−0.578035	−	0.816012i	$-0.696180\pi$
$709$	−30.7827	−1.15607	−0.578035	+	0.816012i	$0.696180\pi$
$710$	−16.4771	−0.618374
$711$	−5.89055	−0.220913
$712$	0.00516629	0.000193615 0
$713$	63.7620	2.38790
$714$	12.9158	0.483361
$715$	36.4580	1.36345
$716$	−3.52467	−0.131723
$717$	9.61383	0.359035
$718$	−32.6937	−1.22012
$719$	16.9480	0.632054	0.316027	−	0.948750i	$-0.397651\pi$
$719$	16.9480	0.632054	0.316027	+	0.948750i	$0.397651\pi$
$720$	−1.99833	−0.0744735
$721$	1.56798	0.0583948
$722$	−1.00000	−0.0372161
$723$	−6.79688	−0.252779
$724$	1.35420	0.0503286
$725$	1.07704	0.0400002
$726$	26.1213	0.969452
$727$	30.4378	1.12888	0.564438	−	0.825476i	$-0.309093\pi$
$727$	30.4378	1.12888	0.564438	+	0.825476i	$0.309093\pi$
$728$	3.16129	0.117165
$729$	29.8941	1.10719
$730$	−10.1818	−0.376845
$731$	−1.22748	−0.0454000
$732$	16.3682	0.604986
$733$	17.5293	0.647459	0.323729	−	0.946150i	$-0.395063\pi$
$733$	17.5293	0.647459	0.323729	+	0.946150i	$0.395063\pi$
$734$	−33.9050	−1.25146
$735$	21.3372	0.787036
$736$	−8.05997	−0.297094
$737$	79.8863	2.94265
$738$	6.16514	0.226942
$739$	−42.0549	−1.54701	−0.773507	−	0.633787i	$-0.781499\pi$
$739$	−42.0549	−1.54701	−0.773507	+	0.633787i	$0.781499\pi$
$740$	7.18199	0.264015
$741$	−3.97125	−0.145888
$742$	12.0602	0.442745
$743$	−44.9609	−1.64945	−0.824727	−	0.565531i	$-0.808671\pi$
$743$	−44.9609	−1.64945	−0.824727	+	0.565531i	$0.808671\pi$
$744$	11.7858	0.432090
$745$	−40.1685	−1.47166
$746$	−19.4898	−0.713573
$747$	0.832893	0.0304740
$748$	−39.0476	−1.42772
$749$	6.96833	0.254617
$750$	−13.1373	−0.479708
$751$	33.5745	1.22515	0.612575	−	0.790412i	$-0.290134\pi$
$751$	33.5745	1.22515	0.612575	+	0.790412i	$0.290134\pi$
$752$	−7.59864	−0.277094
$753$	24.7995	0.903743
$754$	1.84499	0.0671906
$755$	42.3331	1.54066
$756$	6.67952	0.242932
$757$	1.45024	0.0527099	0.0263549	−	0.999653i	$-0.491610\pi$
$757$	1.45024	0.0527099	0.0263549	+	0.999653i	$0.491610\pi$
$758$	−5.68931	−0.206645
$759$	64.1418	2.32820
$760$	2.56048	0.0928785
$761$	28.0399	1.01645	0.508224	−	0.861225i	$-0.330302\pi$
$761$	28.0399	1.01645	0.508224	+	0.861225i	$0.330302\pi$
$762$	24.9449	0.903657
$763$	19.2325	0.696263
$764$	12.4182	0.449276
$765$	−14.6079	−0.528149
$766$	9.83278	0.355273
$767$	−21.9489	−0.792530
$768$	−1.48981	−0.0537591
$769$	27.9784	1.00893	0.504464	−	0.863433i	$-0.331690\pi$
$769$	27.9784	1.00893	0.504464	+	0.863433i	$0.331690\pi$
$770$	16.2206	0.584550
$771$	−35.6608	−1.28429
$772$	2.38753	0.0859292
$773$	−44.1176	−1.58680	−0.793400	−	0.608701i	$-0.791691\pi$
$773$	−44.1176	−1.58680	−0.793400	+	0.608701i	$0.791691\pi$
$774$	−0.131052	−0.00471055
$775$	12.3101	0.442191
$776$	18.1527	0.651645
$777$	−4.95592	−0.177793
$778$	7.19246	0.257862
$779$	−7.89946	−0.283027
$780$	10.1683	0.364085
$781$	−34.3743	−1.23001
$782$	−58.9185	−2.10692
$783$	3.89829	0.139314
$784$	−5.59350	−0.199768
$785$	−44.4633	−1.58696
$786$	16.1866	0.577357
$787$	29.0291	1.03477	0.517387	−	0.855752i	$-0.326905\pi$
$787$	29.0291	1.03477	0.517387	+	0.855752i	$0.326905\pi$
$788$	4.76905	0.169890
$789$	16.1874	0.576285
$790$	−19.3255	−0.687572
$791$	6.73507	0.239471
$792$	−4.16890	−0.148135
$793$	29.2863	1.03999
$794$	−30.7708	−1.09201
$795$	38.7918	1.37580
$796$	−5.97986	−0.211951
$797$	−31.4203	−1.11296	−0.556481	−	0.830860i	$-0.687849\pi$
$797$	−31.4203	−1.11296	−0.556481	+	0.830860i	$0.687849\pi$
$798$	−1.76686	−0.0625461
$799$	−55.5462	−1.96508
$800$	−1.55608	−0.0550158
$801$	0.00403204	0.000142465 0
$802$	12.0806	0.426579
$803$	−21.2411	−0.749583
$804$	22.2807	0.785780
$805$	24.4751	0.862634
$806$	21.0874	0.742773
$807$	−27.2532	−0.959359
$808$	7.40508	0.260510
$809$	−33.7316	−1.18594	−0.592970	−	0.805225i	$-0.702045\pi$
$809$	−33.7316	−1.18594	−0.592970	+	0.805225i	$0.702045\pi$
$810$	15.4898	0.544255
$811$	1.21043	0.0425038	0.0212519	−	0.999774i	$-0.493235\pi$
$811$	1.21043	0.0425038	0.0212519	+	0.999774i	$0.493235\pi$
$812$	0.820858	0.0288065
$813$	−14.3481	−0.503209
$814$	14.9830	0.525154
$815$	−0.882338	−0.0309070
$816$	−10.8906	−0.381246
$817$	0.167918	0.00587470
$818$	16.6931	0.583660
$819$	2.46724	0.0862122
$820$	20.2264	0.706338
$821$	52.6882	1.83883	0.919416	−	0.393286i	$-0.128662\pi$
$821$	52.6882	1.83883	0.919416	+	0.393286i	$0.128662\pi$
$822$	−14.0768	−0.490984
$823$	−5.12702	−0.178717	−0.0893584	−	0.996000i	$-0.528482\pi$
$823$	−5.12702	−0.178717	−0.0893584	+	0.996000i	$0.528482\pi$
$824$	−1.32212	−0.0460584
$825$	12.3834	0.431135
$826$	−9.76535	−0.339780
$827$	−34.3304	−1.19378	−0.596892	−	0.802322i	$-0.703598\pi$
$827$	−34.3304	−1.19378	−0.596892	+	0.802322i	$0.703598\pi$
$828$	−6.29041	−0.218607
$829$	−42.2041	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$829$	−42.2041	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$830$	2.73253	0.0948476
$831$	−24.6590	−0.855413
$832$	−2.66560	−0.0924131
$833$	−40.8886	−1.41671
$834$	−11.4225	−0.395528
$835$	−14.2064	−0.491633
$836$	5.34165	0.184745
$837$	44.5558	1.54007
$838$	−10.8596	−0.375138
$839$	−0.166221	−0.00573859	−0.00286930	−	0.999996i	$-0.500913\pi$
$839$	−0.166221	−0.00573859	−0.00286930	+	0.999996i	$0.500913\pi$
$840$	4.52401	0.156093
$841$	−28.5209	−0.983480
$842$	−2.11295	−0.0728171
$843$	−35.2452	−1.21391
$844$	1.00000	0.0344214
$845$	−15.0930	−0.519213
$846$	−5.93037	−0.203890
$847$	20.7937	0.714480
$848$	−10.1692	−0.349211
$849$	−35.2243	−1.20890
$850$	−11.3750	−0.390159
$851$	22.6077	0.774981
$852$	−9.58717	−0.328451
$853$	−25.6919	−0.879675	−0.439838	−	0.898077i	$-0.644964\pi$
$853$	−25.6919	−0.879675	−0.439838	+	0.898077i	$0.644964\pi$
$854$	13.0298	0.445871
$855$	1.99833	0.0683416
$856$	−5.87570	−0.200827
$857$	21.6362	0.739078	0.369539	−	0.929215i	$-0.379516\pi$
$857$	21.6362	0.739078	0.369539	+	0.929215i	$0.379516\pi$
$858$	21.2131	0.724202
$859$	9.01938	0.307737	0.153869	−	0.988091i	$-0.450827\pi$
$859$	9.01938	0.307737	0.153869	+	0.988091i	$0.450827\pi$
$860$	−0.429951	−0.0146612
$861$	−13.9572	−0.475661
$862$	22.6846	0.772639
$863$	41.5277	1.41362	0.706809	−	0.707404i	$-0.250134\pi$
$863$	41.5277	1.41362	0.706809	+	0.707404i	$0.250134\pi$
$864$	−5.63217	−0.191610
$865$	9.82778	0.334154
$866$	27.3550	0.929562
$867$	−54.2835	−1.84356
$868$	9.38205	0.318448
$869$	−40.3167	−1.36765
$870$	2.64030	0.0895145
$871$	39.8650	1.35077
$872$	−16.2168	−0.549171
$873$	14.1673	0.479491
$874$	8.05997	0.272632
$875$	−10.4579	−0.353541
$876$	−5.92426	−0.200162
$877$	−56.0208	−1.89169	−0.945844	−	0.324623i	$-0.894763\pi$
$877$	−56.0208	−1.89169	−0.945844	+	0.324623i	$0.894763\pi$
$878$	27.9973	0.944863
$879$	−3.89035	−0.131218
$880$	−13.6772	−0.461059
$881$	18.2483	0.614801	0.307401	−	0.951580i	$-0.400541\pi$
$881$	18.2483	0.614801	0.307401	+	0.951580i	$0.400541\pi$
$882$	−4.36546	−0.146993
$883$	34.9422	1.17590	0.587949	−	0.808898i	$-0.299936\pi$
$883$	34.9422	1.17590	0.587949	+	0.808898i	$0.299936\pi$
$884$	−19.4856	−0.655372
$885$	−31.4104	−1.05585
$886$	38.1213	1.28071
$887$	24.6021	0.826059	0.413029	−	0.910718i	$-0.364471\pi$
$887$	24.6021	0.826059	0.413029	+	0.910718i	$0.364471\pi$
$888$	4.17883	0.140232
$889$	19.8572	0.665989
$890$	0.0132282	0.000443410 0
$891$	32.3145	1.08258
$892$	14.9130	0.499323
$893$	7.59864	0.254279
$894$	−23.3720	−0.781676
$895$	−9.02486	−0.301668
$896$	−1.18596	−0.0396201
$897$	32.0082	1.06872
$898$	2.29685	0.0766470
$899$	5.47554	0.182620
$900$	−1.21445	−0.0404816
$901$	−74.3369	−2.47652
$902$	42.1961	1.40498
$903$	0.296687	0.00987312
$904$	−5.67901	−0.188881
$905$	3.46742	0.115261
$906$	24.6314	0.818325
$907$	57.3231	1.90338	0.951691	−	0.307058i	$-0.0993445\pi$
$907$	57.3231	1.90338	0.951691	+	0.307058i	$0.0993445\pi$
$908$	27.9557	0.927744
$909$	5.77930	0.191687
$910$	8.09444	0.268328
$911$	−4.53763	−0.150338	−0.0751692	−	0.997171i	$-0.523950\pi$
$911$	−4.53763	−0.150338	−0.0751692	+	0.997171i	$0.523950\pi$
$912$	1.48981	0.0493327
$913$	5.70058	0.188662
$914$	11.9085	0.393897
$915$	41.9105	1.38552
$916$	8.30629	0.274447
$917$	12.8852	0.425508
$918$	−41.1713	−1.35886
$919$	9.51366	0.313827	0.156913	−	0.987612i	$-0.449846\pi$
$919$	9.51366	0.313827	0.156913	+	0.987612i	$0.449846\pi$
$920$	−20.6374	−0.680396
$921$	−43.8051	−1.44343
$922$	−11.4831	−0.378177
$923$	−17.1535	−0.564615
$924$	9.43794	0.310485
$925$	4.36471	0.143511
$926$	−21.8369	−0.717604
$927$	−1.03185	−0.0338905
$928$	−0.692148	−0.0227209
$929$	−31.6366	−1.03796	−0.518981	−	0.854786i	$-0.673688\pi$
$929$	−31.6366	−1.03796	−0.518981	+	0.854786i	$0.673688\pi$
$930$	30.1775	0.989559
$931$	5.59350	0.183320
$932$	−12.7298	−0.416979
$933$	−35.7217	−1.16948
$934$	3.78130	0.123728
$935$	−99.9808	−3.26972
$936$	−2.08037	−0.0679991
$937$	−10.7955	−0.352672	−0.176336	−	0.984330i	$-0.556425\pi$
$937$	−10.7955	−0.352672	−0.176336	+	0.984330i	$0.556425\pi$
$938$	17.7364	0.579115
$939$	−19.2156	−0.627077
$940$	−19.4562	−0.634591
$941$	42.8059	1.39543	0.697716	−	0.716375i	$-0.254200\pi$
$941$	42.8059	1.39543	0.697716	+	0.716375i	$0.254200\pi$
$942$	−25.8709	−0.842920
$943$	63.6693	2.07336
$944$	8.23414	0.267998
$945$	17.1028	0.556355
$946$	−0.896958	−0.0291626
$947$	40.5621	1.31809	0.659046	−	0.752103i	$-0.270960\pi$
$947$	40.5621	1.31809	0.659046	+	0.752103i	$0.270960\pi$
$948$	−11.2445	−0.365206
$949$	−10.5998	−0.344084
$950$	1.55608	0.0504860
$951$	14.9370	0.484367
$952$	−8.66938	−0.280976
$953$	37.3969	1.21141	0.605703	−	0.795691i	$-0.292892\pi$
$953$	37.3969	1.21141	0.605703	+	0.795691i	$0.292892\pi$
$954$	−7.93655	−0.256955
$955$	31.7967	1.02892
$956$	−6.45304	−0.208706
$957$	5.50816	0.178054
$958$	−26.3865	−0.852508
$959$	−11.2057	−0.361852
$960$	−3.81465	−0.123117
$961$	31.5831	1.01881
$962$	7.47684	0.241063
$963$	−4.58570	−0.147772
$964$	4.56223	0.146940
$965$	6.11324	0.196792
$966$	14.2408	0.458191
$967$	−44.4057	−1.42799	−0.713996	−	0.700150i	$-0.753117\pi$
$967$	−44.4057	−1.42799	−0.713996	+	0.700150i	$0.753117\pi$
$968$	−17.5332	−0.563540
$969$	10.8906	0.349856
$970$	46.4798	1.49238
$971$	4.57619	0.146857	0.0734285	−	0.997300i	$-0.476606\pi$
$971$	4.57619	0.146857	0.0734285	+	0.997300i	$0.476606\pi$
$972$	−7.88383	−0.252874
$973$	−9.09280	−0.291502
$974$	−39.5653	−1.26775
$975$	6.17960	0.197905
$976$	−10.9867	−0.351677
$977$	−44.2948	−1.41712	−0.708559	−	0.705652i	$-0.750654\pi$
$977$	−44.2948	−1.41712	−0.708559	+	0.705652i	$0.750654\pi$
$978$	−0.513387	−0.0164163
$979$	0.0275965	0.000881989 0
$980$	−14.3221	−0.457502
$981$	−12.6565	−0.404089
$982$	−13.7876	−0.439981
$983$	−24.8037	−0.791115	−0.395558	−	0.918441i	$-0.629449\pi$
$983$	−24.8037	−0.791115	−0.395558	+	0.918441i	$0.629449\pi$
$984$	11.7687	0.375173
$985$	12.2111	0.389077
$986$	−5.05961	−0.161131
$987$	13.4257	0.427345
$988$	2.66560	0.0848041
$989$	−1.35341	−0.0430360
$990$	−10.6744	−0.339255
$991$	−4.33975	−0.137857	−0.0689284	−	0.997622i	$-0.521958\pi$
$991$	−4.33975	−0.137857	−0.0689284	+	0.997622i	$0.521958\pi$
$992$	−7.91095	−0.251173
$993$	9.81348	0.311421
$994$	−7.63181	−0.242066
$995$	−15.3114	−0.485402
$996$	1.58992	0.0503786
$997$	16.8537	0.533764	0.266882	−	0.963729i	$-0.414007\pi$
$997$	16.8537	0.533764	0.266882	+	0.963729i	$0.414007\pi$
$998$	−5.30972	−0.168076
$999$	15.7979	0.499823

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.h.1.12	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.h.1.12	✓	41	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.48981 q^{3} +1.00000 q^{4} +2.56048 q^{5} +1.48981 q^{6} +1.18596 q^{7} -1.00000 q^{8} -0.780452 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.48981 q^{3} +1.00000 q^{4} +2.56048 q^{5} +1.48981 q^{6} +1.18596 q^{7} -1.00000 q^{8} -0.780452 q^{9} -2.56048 q^{10} -5.34165 q^{11} -1.48981 q^{12} -2.66560 q^{13} -1.18596 q^{14} -3.81465 q^{15} +1.00000 q^{16} +7.31002 q^{17} +0.780452 q^{18} -1.00000 q^{19} +2.56048 q^{20} -1.76686 q^{21} +5.34165 q^{22} +8.05997 q^{23} +1.48981 q^{24} +1.55608 q^{25} +2.66560 q^{26} +5.63217 q^{27} +1.18596 q^{28} +0.692148 q^{29} +3.81465 q^{30} +7.91095 q^{31} -1.00000 q^{32} +7.95807 q^{33} -7.31002 q^{34} +3.03663 q^{35} -0.780452 q^{36} +2.80494 q^{37} +1.00000 q^{38} +3.97125 q^{39} -2.56048 q^{40} +7.89946 q^{41} +1.76686 q^{42} -0.167918 q^{43} -5.34165 q^{44} -1.99833 q^{45} -8.05997 q^{46} -7.59864 q^{47} -1.48981 q^{48} -5.59350 q^{49} -1.55608 q^{50} -10.8906 q^{51} -2.66560 q^{52} -10.1692 q^{53} -5.63217 q^{54} -13.6772 q^{55} -1.18596 q^{56} +1.48981 q^{57} -0.692148 q^{58} +8.23414 q^{59} -3.81465 q^{60} -10.9867 q^{61} -7.91095 q^{62} -0.925583 q^{63} +1.00000 q^{64} -6.82523 q^{65} -7.95807 q^{66} -14.9554 q^{67} +7.31002 q^{68} -12.0079 q^{69} -3.03663 q^{70} +6.43514 q^{71} +0.780452 q^{72} +3.97651 q^{73} -2.80494 q^{74} -2.31827 q^{75} -1.00000 q^{76} -6.33498 q^{77} -3.97125 q^{78} +7.54761 q^{79} +2.56048 q^{80} -6.04954 q^{81} -7.89946 q^{82} -1.06719 q^{83} -1.76686 q^{84} +18.7172 q^{85} +0.167918 q^{86} -1.03117 q^{87} +5.34165 q^{88} -0.00516629 q^{89} +1.99833 q^{90} -3.16129 q^{91} +8.05997 q^{92} -11.7858 q^{93} +7.59864 q^{94} -2.56048 q^{95} +1.48981 q^{96} -18.1527 q^{97} +5.59350 q^{98} +4.16890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * q^99

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