LMFDB - Embedded newform 8018.2.a.j.1.14

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			1.14
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.39823 q^{3} +1.00000 q^{4} +0.539425 q^{5} -1.39823 q^{6} +5.05784 q^{7} +1.00000 q^{8} -1.04494 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.39823 q^{3} +1.00000 q^{4} +0.539425 q^{5} -1.39823 q^{6} +5.05784 q^{7} +1.00000 q^{8} -1.04494 q^{9} +0.539425 q^{10} -1.12561 q^{11} -1.39823 q^{12} -2.68807 q^{13} +5.05784 q^{14} -0.754243 q^{15} +1.00000 q^{16} -4.30545 q^{17} -1.04494 q^{18} -1.00000 q^{19} +0.539425 q^{20} -7.07204 q^{21} -1.12561 q^{22} +7.92041 q^{23} -1.39823 q^{24} -4.70902 q^{25} -2.68807 q^{26} +5.65578 q^{27} +5.05784 q^{28} -0.281706 q^{29} -0.754243 q^{30} -6.56253 q^{31} +1.00000 q^{32} +1.57386 q^{33} -4.30545 q^{34} +2.72833 q^{35} -1.04494 q^{36} +1.71537 q^{37} -1.00000 q^{38} +3.75855 q^{39} +0.539425 q^{40} +0.408032 q^{41} -7.07204 q^{42} +5.34809 q^{43} -1.12561 q^{44} -0.563668 q^{45} +7.92041 q^{46} -3.58934 q^{47} -1.39823 q^{48} +18.5817 q^{49} -4.70902 q^{50} +6.02003 q^{51} -2.68807 q^{52} -3.58303 q^{53} +5.65578 q^{54} -0.607181 q^{55} +5.05784 q^{56} +1.39823 q^{57} -0.281706 q^{58} +8.94333 q^{59} -0.754243 q^{60} +13.1010 q^{61} -6.56253 q^{62} -5.28514 q^{63} +1.00000 q^{64} -1.45001 q^{65} +1.57386 q^{66} +7.49995 q^{67} -4.30545 q^{68} -11.0746 q^{69} +2.72833 q^{70} +9.98622 q^{71} -1.04494 q^{72} -7.18763 q^{73} +1.71537 q^{74} +6.58431 q^{75} -1.00000 q^{76} -5.69314 q^{77} +3.75855 q^{78} +16.4632 q^{79} +0.539425 q^{80} -4.77328 q^{81} +0.408032 q^{82} +7.00532 q^{83} -7.07204 q^{84} -2.32247 q^{85} +5.34809 q^{86} +0.393892 q^{87} -1.12561 q^{88} -4.37900 q^{89} -0.563668 q^{90} -13.5958 q^{91} +7.92041 q^{92} +9.17596 q^{93} -3.58934 q^{94} -0.539425 q^{95} -1.39823 q^{96} +12.0690 q^{97} +18.5817 q^{98} +1.17619 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.39823	−0.807271	−0.403635	−	0.914920i	$-0.632254\pi$
$3$	−1.39823	−0.807271	−0.403635	+	0.914920i	$0.632254\pi$
$4$	1.00000	0.500000
$5$	0.539425	0.241238	0.120619	−	0.992699i	$-0.461512\pi$
$5$	0.539425	0.241238	0.120619	+	0.992699i	$0.461512\pi$
$6$	−1.39823	−0.570827
$7$	5.05784	1.91168	0.955842	−	0.293883i	$-0.0949475\pi$
$7$	5.05784	1.91168	0.955842	+	0.293883i	$0.0949475\pi$
$8$	1.00000	0.353553
$9$	−1.04494	−0.348314
$10$	0.539425	0.170581
$11$	−1.12561	−0.339383	−0.169692	−	0.985497i	$-0.554277\pi$
$11$	−1.12561	−0.339383	−0.169692	+	0.985497i	$0.554277\pi$
$12$	−1.39823	−0.403635
$13$	−2.68807	−0.745537	−0.372768	−	0.927924i	$-0.621591\pi$
$13$	−2.68807	−0.745537	−0.372768	+	0.927924i	$0.621591\pi$
$14$	5.05784	1.35176
$15$	−0.754243	−0.194745
$16$	1.00000	0.250000
$17$	−4.30545	−1.04423	−0.522113	−	0.852876i	$-0.674856\pi$
$17$	−4.30545	−1.04423	−0.522113	+	0.852876i	$0.674856\pi$
$18$	−1.04494	−0.246295
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.539425	0.120619
$21$	−7.07204	−1.54325
$22$	−1.12561	−0.239980
$23$	7.92041	1.65152	0.825760	−	0.564022i	$-0.190747\pi$
$23$	7.92041	1.65152	0.825760	+	0.564022i	$0.190747\pi$
$24$	−1.39823	−0.285413
$25$	−4.70902	−0.941804
$26$	−2.68807	−0.527174
$27$	5.65578	1.08845
$28$	5.05784	0.955842
$29$	−0.281706	−0.0523116	−0.0261558	−	0.999658i	$-0.508327\pi$
$29$	−0.281706	−0.0523116	−0.0261558	+	0.999658i	$0.508327\pi$
$30$	−0.754243	−0.137705
$31$	−6.56253	−1.17867	−0.589333	−	0.807890i	$-0.700609\pi$
$31$	−6.56253	−1.17867	−0.589333	+	0.807890i	$0.700609\pi$
$32$	1.00000	0.176777
$33$	1.57386	0.273974
$34$	−4.30545	−0.738379
$35$	2.72833	0.461171
$36$	−1.04494	−0.174157
$37$	1.71537	0.282005	0.141003	−	0.990009i	$-0.454967\pi$
$37$	1.71537	0.282005	0.141003	+	0.990009i	$0.454967\pi$
$38$	−1.00000	−0.162221
$39$	3.75855	0.601850
$40$	0.539425	0.0852907
$41$	0.408032	0.0637239	0.0318620	−	0.999492i	$-0.489856\pi$
$41$	0.408032	0.0637239	0.0318620	+	0.999492i	$0.489856\pi$
$42$	−7.07204	−1.09124
$43$	5.34809	0.815576	0.407788	−	0.913077i	$-0.366300\pi$
$43$	5.34809	0.815576	0.407788	+	0.913077i	$0.366300\pi$
$44$	−1.12561	−0.169692
$45$	−0.563668	−0.0840266
$46$	7.92041	1.16780
$47$	−3.58934	−0.523559	−0.261780	−	0.965128i	$-0.584309\pi$
$47$	−3.58934	−0.523559	−0.261780	+	0.965128i	$0.584309\pi$
$48$	−1.39823	−0.201818
$49$	18.5817	2.65453
$50$	−4.70902	−0.665956
$51$	6.02003	0.842973
$52$	−2.68807	−0.372768
$53$	−3.58303	−0.492167	−0.246084	−	0.969249i	$-0.579144\pi$
$53$	−3.58303	−0.492167	−0.246084	+	0.969249i	$0.579144\pi$
$54$	5.65578	0.769653
$55$	−0.607181	−0.0818723
$56$	5.05784	0.675882
$57$	1.39823	0.185201
$58$	−0.281706	−0.0369899
$59$	8.94333	1.16432	0.582161	−	0.813074i	$-0.302207\pi$
$59$	8.94333	1.16432	0.582161	+	0.813074i	$0.302207\pi$
$60$	−0.754243	−0.0973724
$61$	13.1010	1.67741	0.838703	−	0.544589i	$-0.183314\pi$
$61$	13.1010	1.67741	0.838703	+	0.544589i	$0.183314\pi$
$62$	−6.56253	−0.833443
$63$	−5.28514	−0.665865
$64$	1.00000	0.125000
$65$	−1.45001	−0.179852
$66$	1.57386	0.193729
$67$	7.49995	0.916265	0.458132	−	0.888884i	$-0.348519\pi$
$67$	7.49995	0.916265	0.458132	+	0.888884i	$0.348519\pi$
$68$	−4.30545	−0.522113
$69$	−11.0746	−1.33322
$70$	2.72833	0.326097
$71$	9.98622	1.18515	0.592573	−	0.805517i	$-0.298112\pi$
$71$	9.98622	1.18515	0.592573	+	0.805517i	$0.298112\pi$
$72$	−1.04494	−0.123147
$73$	−7.18763	−0.841248	−0.420624	−	0.907235i	$-0.638189\pi$
$73$	−7.18763	−0.841248	−0.420624	+	0.907235i	$0.638189\pi$
$74$	1.71537	0.199408
$75$	6.58431	0.760291
$76$	−1.00000	−0.114708
$77$	−5.69314	−0.648793
$78$	3.75855	0.425572
$79$	16.4632	1.85226	0.926129	−	0.377206i	$-0.123115\pi$
$79$	16.4632	1.85226	0.926129	+	0.377206i	$0.123115\pi$
$80$	0.539425	0.0603096
$81$	−4.77328	−0.530364
$82$	0.408032	0.0450596
$83$	7.00532	0.768933	0.384467	−	0.923139i	$-0.374385\pi$
$83$	7.00532	0.768933	0.384467	+	0.923139i	$0.374385\pi$
$84$	−7.07204	−0.771623
$85$	−2.32247	−0.251907
$86$	5.34809	0.576699
$87$	0.393892	0.0422296
$88$	−1.12561	−0.119990
$89$	−4.37900	−0.464173	−0.232086	−	0.972695i	$-0.574555\pi$
$89$	−4.37900	−0.464173	−0.232086	+	0.972695i	$0.574555\pi$
$90$	−0.563668	−0.0594158
$91$	−13.5958	−1.42523
$92$	7.92041	0.825760
$93$	9.17596	0.951503
$94$	−3.58934	−0.370212
$95$	−0.539425	−0.0553439
$96$	−1.39823	−0.142707
$97$	12.0690	1.22542	0.612709	−	0.790309i	$-0.290080\pi$
$97$	12.0690	1.22542	0.612709	+	0.790309i	$0.290080\pi$
$98$	18.5817	1.87704
$99$	1.17619	0.118212
$100$	−4.70902	−0.470902
$101$	1.21217	0.120616	0.0603079	−	0.998180i	$-0.480792\pi$
$101$	1.21217	0.120616	0.0603079	+	0.998180i	$0.480792\pi$
$102$	6.02003	0.596072
$103$	17.1286	1.68773	0.843863	−	0.536558i	$-0.180276\pi$
$103$	17.1286	1.68773	0.843863	+	0.536558i	$0.180276\pi$
$104$	−2.68807	−0.263587
$105$	−3.81484	−0.372290
$106$	−3.58303	−0.348015
$107$	5.75691	0.556541	0.278271	−	0.960503i	$-0.410239\pi$
$107$	5.75691	0.556541	0.278271	+	0.960503i	$0.410239\pi$
$108$	5.65578	0.544227
$109$	1.63885	0.156973	0.0784865	−	0.996915i	$-0.474991\pi$
$109$	1.63885	0.156973	0.0784865	+	0.996915i	$0.474991\pi$
$110$	−0.607181	−0.0578924
$111$	−2.39849	−0.227655
$112$	5.05784	0.477921
$113$	−2.73876	−0.257641	−0.128821	−	0.991668i	$-0.541119\pi$
$113$	−2.73876	−0.257641	−0.128821	+	0.991668i	$0.541119\pi$
$114$	1.39823	0.130957
$115$	4.27247	0.398410
$116$	−0.281706	−0.0261558
$117$	2.80888	0.259681
$118$	8.94333	0.823300
$119$	−21.7763	−1.99623
$120$	−0.754243	−0.0688527
$121$	−9.73301	−0.884819
$122$	13.1010	1.18611
$123$	−0.570524	−0.0514425
$124$	−6.56253	−0.589333
$125$	−5.23729	−0.468438
$126$	−5.28514	−0.470838
$127$	15.1724	1.34633	0.673166	−	0.739492i	$-0.264934\pi$
$127$	15.1724	1.34633	0.673166	+	0.739492i	$0.264934\pi$
$128$	1.00000	0.0883883
$129$	−7.47788	−0.658391
$130$	−1.45001	−0.127175
$131$	17.8014	1.55531	0.777656	−	0.628690i	$-0.216409\pi$
$131$	17.8014	1.55531	0.777656	+	0.628690i	$0.216409\pi$
$132$	1.57386	0.136987
$133$	−5.05784	−0.438570
$134$	7.49995	0.647897
$135$	3.05087	0.262577
$136$	−4.30545	−0.369190
$137$	−6.31444	−0.539479	−0.269740	−	0.962933i	$-0.586938\pi$
$137$	−6.31444	−0.539479	−0.269740	+	0.962933i	$0.586938\pi$
$138$	−11.0746	−0.942731
$139$	−4.18766	−0.355193	−0.177596	−	0.984103i	$-0.556832\pi$
$139$	−4.18766	−0.355193	−0.177596	+	0.984103i	$0.556832\pi$
$140$	2.72833	0.230586
$141$	5.01874	0.422654
$142$	9.98622	0.838025
$143$	3.02571	0.253023
$144$	−1.04494	−0.0870784
$145$	−0.151960	−0.0126196
$146$	−7.18763	−0.594852
$147$	−25.9816	−2.14293
$148$	1.71537	0.141003
$149$	−13.0258	−1.06712	−0.533558	−	0.845763i	$-0.679146\pi$
$149$	−13.0258	−1.06712	−0.533558	+	0.845763i	$0.679146\pi$
$150$	6.58431	0.537607
$151$	−0.626724	−0.0510021	−0.0255010	−	0.999675i	$-0.508118\pi$
$151$	−0.626724	−0.0510021	−0.0255010	+	0.999675i	$0.508118\pi$
$152$	−1.00000	−0.0811107
$153$	4.49895	0.363718
$154$	−5.69314	−0.458766
$155$	−3.54000	−0.284340
$156$	3.75855	0.300925
$157$	−6.57277	−0.524564	−0.262282	−	0.964991i	$-0.584475\pi$
$157$	−6.57277	−0.524564	−0.262282	+	0.964991i	$0.584475\pi$
$158$	16.4632	1.30974
$159$	5.00992	0.397312
$160$	0.539425	0.0426453
$161$	40.0601	3.15718
$162$	−4.77328	−0.375024
$163$	7.39921	0.579551	0.289776	−	0.957095i	$-0.406419\pi$
$163$	7.39921	0.579551	0.289776	+	0.957095i	$0.406419\pi$
$164$	0.408032	0.0318620
$165$	0.848981	0.0660931
$166$	7.00532	0.543718
$167$	−15.1677	−1.17371	−0.586855	−	0.809692i	$-0.699634\pi$
$167$	−15.1677	−1.17371	−0.586855	+	0.809692i	$0.699634\pi$
$168$	−7.07204	−0.545620
$169$	−5.77428	−0.444175
$170$	−2.32247	−0.178125
$171$	1.04494	0.0799086
$172$	5.34809	0.407788
$173$	−15.7761	−1.19944	−0.599719	−	0.800211i	$-0.704721\pi$
$173$	−15.7761	−1.19944	−0.599719	+	0.800211i	$0.704721\pi$
$174$	0.393892	0.0298608
$175$	−23.8175	−1.80043
$176$	−1.12561	−0.0848458
$177$	−12.5049	−0.939923
$178$	−4.37900	−0.328220
$179$	0.905811	0.0677035	0.0338518	−	0.999427i	$-0.489223\pi$
$179$	0.905811	0.0677035	0.0338518	+	0.999427i	$0.489223\pi$
$180$	−0.563668	−0.0420133
$181$	−16.8041	−1.24904	−0.624518	−	0.781010i	$-0.714705\pi$
$181$	−16.8041	−1.24904	−0.624518	+	0.781010i	$0.714705\pi$
$182$	−13.5958	−1.00779
$183$	−18.3182	−1.35412
$184$	7.92041	0.583900
$185$	0.925314	0.0680305
$186$	9.17596	0.672814
$187$	4.84625	0.354393
$188$	−3.58934	−0.261780
$189$	28.6060	2.08078
$190$	−0.539425	−0.0391340
$191$	−9.56666	−0.692219	−0.346109	−	0.938194i	$-0.612497\pi$
$191$	−9.56666	−0.692219	−0.346109	+	0.938194i	$0.612497\pi$
$192$	−1.39823	−0.100909
$193$	19.2576	1.38619	0.693097	−	0.720844i	$-0.256246\pi$
$193$	19.2576	1.38619	0.693097	+	0.720844i	$0.256246\pi$
$194$	12.0690	0.866501
$195$	2.02746	0.145189
$196$	18.5817	1.32727
$197$	14.0935	1.00412	0.502060	−	0.864833i	$-0.332576\pi$
$197$	14.0935	1.00412	0.502060	+	0.864833i	$0.332576\pi$
$198$	1.17619	0.0835884
$199$	1.07616	0.0762872	0.0381436	−	0.999272i	$-0.487856\pi$
$199$	1.07616	0.0762872	0.0381436	+	0.999272i	$0.487856\pi$
$200$	−4.70902	−0.332978
$201$	−10.4867	−0.739674
$202$	1.21217	0.0852882
$203$	−1.42483	−0.100003
$204$	6.02003	0.421487
$205$	0.220103	0.0153727
$206$	17.1286	1.19340
$207$	−8.27636	−0.575247
$208$	−2.68807	−0.186384
$209$	1.12561	0.0778598
$210$	−3.81484	−0.263249
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−3.58303	−0.246084
$213$	−13.9631	−0.956734
$214$	5.75691	0.393534
$215$	2.88489	0.196748
$216$	5.65578	0.384827
$217$	−33.1922	−2.25324
$218$	1.63885	0.110997
$219$	10.0500	0.679115
$220$	−0.607181	−0.0409361
$221$	11.5734	0.778509
$222$	−2.39849	−0.160976
$223$	9.95413	0.666578	0.333289	−	0.942825i	$-0.391842\pi$
$223$	9.95413	0.666578	0.333289	+	0.942825i	$0.391842\pi$
$224$	5.05784	0.337941
$225$	4.92065	0.328043
$226$	−2.73876	−0.182180
$227$	25.9588	1.72295	0.861474	−	0.507801i	$-0.169542\pi$
$227$	25.9588	1.72295	0.861474	+	0.507801i	$0.169542\pi$
$228$	1.39823	0.0926003
$229$	−4.86224	−0.321306	−0.160653	−	0.987011i	$-0.551360\pi$
$229$	−4.86224	−0.321306	−0.160653	+	0.987011i	$0.551360\pi$
$230$	4.27247	0.281718
$231$	7.96034	0.523752
$232$	−0.281706	−0.0184949
$233$	3.48455	0.228280	0.114140	−	0.993465i	$-0.463589\pi$
$233$	3.48455	0.228280	0.114140	+	0.993465i	$0.463589\pi$
$234$	2.80888	0.183622
$235$	−1.93618	−0.126303
$236$	8.94333	0.582161
$237$	−23.0195	−1.49527
$238$	−21.7763	−1.41155
$239$	−23.5249	−1.52170	−0.760848	−	0.648930i	$-0.775217\pi$
$239$	−23.5249	−1.52170	−0.760848	+	0.648930i	$0.775217\pi$
$240$	−0.754243	−0.0486862
$241$	14.2840	0.920116	0.460058	−	0.887889i	$-0.347829\pi$
$241$	14.2840	0.920116	0.460058	+	0.887889i	$0.347829\pi$
$242$	−9.73301	−0.625662
$243$	−10.2932	−0.660307
$244$	13.1010	0.838703
$245$	10.0235	0.640375
$246$	−0.570524	−0.0363753
$247$	2.68807	0.171038
$248$	−6.56253	−0.416721
$249$	−9.79507	−0.620738
$250$	−5.23729	−0.331235
$251$	−5.37276	−0.339126	−0.169563	−	0.985519i	$-0.554236\pi$
$251$	−5.37276	−0.339126	−0.169563	+	0.985519i	$0.554236\pi$
$252$	−5.28514	−0.332933
$253$	−8.91526	−0.560498
$254$	15.1724	0.952000
$255$	3.24736	0.203358
$256$	1.00000	0.0625000
$257$	−2.19233	−0.136754	−0.0683770	−	0.997660i	$-0.521782\pi$
$257$	−2.19233	−0.136754	−0.0683770	+	0.997660i	$0.521782\pi$
$258$	−7.47788	−0.465552
$259$	8.67606	0.539104
$260$	−1.45001	−0.0899260
$261$	0.294367	0.0182208
$262$	17.8014	1.09977
$263$	31.8437	1.96357	0.981785	−	0.189998i	$-0.0608481\pi$
$263$	31.8437	1.96357	0.981785	+	0.189998i	$0.0608481\pi$
$264$	1.57386	0.0968645
$265$	−1.93278	−0.118730
$266$	−5.05784	−0.310116
$267$	6.12287	0.374713
$268$	7.49995	0.458132
$269$	17.6913	1.07866	0.539330	−	0.842095i	$-0.318678\pi$
$269$	17.6913	1.07866	0.539330	+	0.842095i	$0.318678\pi$
$270$	3.05087	0.185670
$271$	8.78563	0.533689	0.266845	−	0.963740i	$-0.414019\pi$
$271$	8.78563	0.533689	0.266845	+	0.963740i	$0.414019\pi$
$272$	−4.30545	−0.261056
$273$	19.0101	1.15055
$274$	−6.31444	−0.381469
$275$	5.30050	0.319632
$276$	−11.0746	−0.666612
$277$	−21.3490	−1.28274	−0.641368	−	0.767233i	$-0.721633\pi$
$277$	−21.3490	−1.28274	−0.641368	+	0.767233i	$0.721633\pi$
$278$	−4.18766	−0.251159
$279$	6.85746	0.410546
$280$	2.72833	0.163049
$281$	0.534356	0.0318770	0.0159385	−	0.999873i	$-0.494926\pi$
$281$	0.534356	0.0318770	0.0159385	+	0.999873i	$0.494926\pi$
$282$	5.01874	0.298862
$283$	−11.9700	−0.711541	−0.355771	−	0.934573i	$-0.615782\pi$
$283$	−11.9700	−0.711541	−0.355771	+	0.934573i	$0.615782\pi$
$284$	9.98622	0.592573
$285$	0.754243	0.0446775
$286$	3.02571	0.178914
$287$	2.06376	0.121820
$288$	−1.04494	−0.0615737
$289$	1.53693	0.0904077
$290$	−0.151960	−0.00892338
$291$	−16.8752	−0.989244
$292$	−7.18763	−0.420624
$293$	−16.8883	−0.986625	−0.493313	−	0.869852i	$-0.664214\pi$
$293$	−16.8883	−0.986625	−0.493313	+	0.869852i	$0.664214\pi$
$294$	−25.9816	−1.51528
$295$	4.82426	0.280879
$296$	1.71537	0.0997039
$297$	−6.36618	−0.369403
$298$	−13.0258	−0.754565
$299$	−21.2906	−1.23127
$300$	6.58431	0.380145
$301$	27.0498	1.55912
$302$	−0.626724	−0.0360639
$303$	−1.69490	−0.0973696
$304$	−1.00000	−0.0573539
$305$	7.06699	0.404655
$306$	4.49895	0.257188
$307$	−19.8836	−1.13482	−0.567408	−	0.823437i	$-0.692054\pi$
$307$	−19.8836	−1.13482	−0.567408	+	0.823437i	$0.692054\pi$
$308$	−5.69314	−0.324397
$309$	−23.9497	−1.36245
$310$	−3.54000	−0.201058
$311$	8.70171	0.493428	0.246714	−	0.969088i	$-0.420649\pi$
$311$	8.70171	0.493428	0.246714	+	0.969088i	$0.420649\pi$
$312$	3.75855	0.212786
$313$	−23.2841	−1.31610	−0.658049	−	0.752975i	$-0.728618\pi$
$313$	−23.2841	−1.31610	−0.658049	+	0.752975i	$0.728618\pi$
$314$	−6.57277	−0.370923
$315$	−2.85094	−0.160632
$316$	16.4632	0.926129
$317$	−1.08251	−0.0607997	−0.0303998	−	0.999538i	$-0.509678\pi$
$317$	−1.08251	−0.0607997	−0.0303998	+	0.999538i	$0.509678\pi$
$318$	5.00992	0.280942
$319$	0.317091	0.0177537
$320$	0.539425	0.0301548
$321$	−8.04951	−0.449280
$322$	40.0601	2.23246
$323$	4.30545	0.239562
$324$	−4.77328	−0.265182
$325$	12.6582	0.702149
$326$	7.39921	0.409804
$327$	−2.29149	−0.126720
$328$	0.408032	0.0225298
$329$	−18.1543	−1.00088
$330$	0.848981	0.0467349
$331$	29.4757	1.62013	0.810064	−	0.586341i	$-0.199432\pi$
$331$	29.4757	1.62013	0.810064	+	0.586341i	$0.199432\pi$
$332$	7.00532	0.384467
$333$	−1.79246	−0.0982262
$334$	−15.1677	−0.829938
$335$	4.04566	0.221038
$336$	−7.07204	−0.385812
$337$	−8.97516	−0.488908	−0.244454	−	0.969661i	$-0.578609\pi$
$337$	−8.97516	−0.488908	−0.244454	+	0.969661i	$0.578609\pi$
$338$	−5.77428	−0.314079
$339$	3.82943	0.207986
$340$	−2.32247	−0.125954
$341$	7.38683	0.400019
$342$	1.04494	0.0565039
$343$	58.5785	3.16294
$344$	5.34809	0.288350
$345$	−5.97391	−0.321625
$346$	−15.7761	−0.848131
$347$	26.4970	1.42244	0.711218	−	0.702971i	$-0.248144\pi$
$347$	26.4970	1.42244	0.711218	+	0.702971i	$0.248144\pi$
$348$	0.393892	0.0211148
$349$	−4.60150	−0.246312	−0.123156	−	0.992387i	$-0.539302\pi$
$349$	−4.60150	−0.246312	−0.123156	+	0.992387i	$0.539302\pi$
$350$	−23.8175	−1.27310
$351$	−15.2031	−0.811483
$352$	−1.12561	−0.0599950
$353$	−3.77583	−0.200967	−0.100484	−	0.994939i	$-0.532039\pi$
$353$	−3.77583	−0.200967	−0.100484	+	0.994939i	$0.532039\pi$
$354$	−12.5049	−0.664626
$355$	5.38682	0.285903
$356$	−4.37900	−0.232086
$357$	30.4484	1.61150
$358$	0.905811	0.0478736
$359$	−21.5307	−1.13635	−0.568173	−	0.822909i	$-0.692350\pi$
$359$	−21.5307	−1.13635	−0.568173	+	0.822909i	$0.692350\pi$
$360$	−0.563668	−0.0297079
$361$	1.00000	0.0526316
$362$	−16.8041	−0.883203
$363$	13.6090	0.714289
$364$	−13.5958	−0.712615
$365$	−3.87719	−0.202941
$366$	−18.3182	−0.957508
$367$	−21.8841	−1.14234	−0.571170	−	0.820832i	$-0.693510\pi$
$367$	−21.8841	−1.14234	−0.571170	+	0.820832i	$0.693510\pi$
$368$	7.92041	0.412880
$369$	−0.426370	−0.0221959
$370$	0.925314	0.0481048
$371$	−18.1224	−0.940867
$372$	9.17596	0.475751
$373$	13.7549	0.712203	0.356102	−	0.934447i	$-0.384106\pi$
$373$	13.7549	0.712203	0.356102	+	0.934447i	$0.384106\pi$
$374$	4.84625	0.250593
$375$	7.32296	0.378156
$376$	−3.58934	−0.185106
$377$	0.757247	0.0390002
$378$	28.6060	1.47133
$379$	−5.18809	−0.266494	−0.133247	−	0.991083i	$-0.542540\pi$
$379$	−5.18809	−0.266494	−0.133247	+	0.991083i	$0.542540\pi$
$380$	−0.539425	−0.0276719
$381$	−21.2145	−1.08685
$382$	−9.56666	−0.489473
$383$	32.9761	1.68500	0.842499	−	0.538697i	$-0.181083\pi$
$383$	32.9761	1.68500	0.842499	+	0.538697i	$0.181083\pi$
$384$	−1.39823	−0.0713533
$385$	−3.07102	−0.156514
$386$	19.2576	0.980188
$387$	−5.58844	−0.284076
$388$	12.0690	0.612709
$389$	11.2758	0.571707	0.285854	−	0.958273i	$-0.407723\pi$
$389$	11.2758	0.571707	0.285854	+	0.958273i	$0.407723\pi$
$390$	2.02746	0.102664
$391$	−34.1010	−1.72456
$392$	18.5817	0.938519
$393$	−24.8905	−1.25556
$394$	14.0935	0.710020
$395$	8.88069	0.446836
$396$	1.17619	0.0591059
$397$	−15.9178	−0.798893	−0.399446	−	0.916757i	$-0.630798\pi$
$397$	−15.9178	−0.798893	−0.399446	+	0.916757i	$0.630798\pi$
$398$	1.07616	0.0539432
$399$	7.07204	0.354045
$400$	−4.70902	−0.235451
$401$	30.8843	1.54229	0.771143	−	0.636662i	$-0.219685\pi$
$401$	30.8843	1.54229	0.771143	+	0.636662i	$0.219685\pi$
$402$	−10.4867	−0.523028
$403$	17.6406	0.878739
$404$	1.21217	0.0603079
$405$	−2.57483	−0.127944
$406$	−1.42483	−0.0707129
$407$	−1.93083	−0.0957078
$408$	6.02003	0.298036
$409$	35.8549	1.77291	0.886455	−	0.462814i	$-0.153160\pi$
$409$	35.8549	1.77291	0.886455	+	0.462814i	$0.153160\pi$
$410$	0.220103	0.0108701
$411$	8.82907	0.435506
$412$	17.1286	0.843863
$413$	45.2339	2.22581
$414$	−8.27636	−0.406761
$415$	3.77885	0.185496
$416$	−2.68807	−0.131794
$417$	5.85533	0.286737
$418$	1.12561	0.0550552
$419$	−25.3099	−1.23647	−0.618234	−	0.785994i	$-0.712152\pi$
$419$	−25.3099	−1.23647	−0.618234	+	0.785994i	$0.712152\pi$
$420$	−3.81484	−0.186145
$421$	35.4253	1.72653	0.863263	−	0.504755i	$-0.168417\pi$
$421$	35.4253	1.72653	0.863263	+	0.504755i	$0.168417\pi$
$422$	−1.00000	−0.0486792
$423$	3.75065	0.182363
$424$	−3.58303	−0.174007
$425$	20.2745	0.983456
$426$	−13.9631	−0.676513
$427$	66.2625	3.20667
$428$	5.75691	0.278271
$429$	−4.23065	−0.204258
$430$	2.88489	0.139122
$431$	31.1751	1.50165	0.750825	−	0.660501i	$-0.229656\pi$
$431$	31.1751	1.50165	0.750825	+	0.660501i	$0.229656\pi$
$432$	5.65578	0.272114
$433$	−28.5507	−1.37206	−0.686030	−	0.727574i	$-0.740648\pi$
$433$	−28.5507	−1.37206	−0.686030	+	0.727574i	$0.740648\pi$
$434$	−33.1922	−1.59328
$435$	0.212475	0.0101874
$436$	1.63885	0.0784865
$437$	−7.92041	−0.378885
$438$	10.0500	0.480207
$439$	−25.6159	−1.22258	−0.611291	−	0.791406i	$-0.709350\pi$
$439$	−25.6159	−1.22258	−0.611291	+	0.791406i	$0.709350\pi$
$440$	−0.607181	−0.0289462
$441$	−19.4168	−0.924610
$442$	11.5734	0.550489
$443$	16.4574	0.781915	0.390957	−	0.920409i	$-0.372144\pi$
$443$	16.4574	0.781915	0.390957	+	0.920409i	$0.372144\pi$
$444$	−2.39849	−0.113827
$445$	−2.36214	−0.111976
$446$	9.95413	0.471342
$447$	18.2131	0.861452
$448$	5.05784	0.238960
$449$	−6.37899	−0.301043	−0.150522	−	0.988607i	$-0.548095\pi$
$449$	−6.37899	−0.301043	−0.150522	+	0.988607i	$0.548095\pi$
$450$	4.92065	0.231962
$451$	−0.459284	−0.0216268
$452$	−2.73876	−0.128821
$453$	0.876307	0.0411725
$454$	25.9588	1.21831
$455$	−7.33393	−0.343820
$456$	1.39823	0.0654783
$457$	−17.7167	−0.828750	−0.414375	−	0.910106i	$-0.636000\pi$
$457$	−17.7167	−0.828750	−0.414375	+	0.910106i	$0.636000\pi$
$458$	−4.86224	−0.227198
$459$	−24.3507	−1.13659
$460$	4.27247	0.199205
$461$	−11.1057	−0.517242	−0.258621	−	0.965979i	$-0.583268\pi$
$461$	−11.1057	−0.517242	−0.258621	+	0.965979i	$0.583268\pi$
$462$	7.96034	0.370348
$463$	−20.2349	−0.940397	−0.470199	−	0.882561i	$-0.655818\pi$
$463$	−20.2349	−0.940397	−0.470199	+	0.882561i	$0.655818\pi$
$464$	−0.281706	−0.0130779
$465$	4.94975	0.229539
$466$	3.48455	0.161418
$467$	−33.9185	−1.56956	−0.784781	−	0.619773i	$-0.787225\pi$
$467$	−33.9185	−1.56956	−0.784781	+	0.619773i	$0.787225\pi$
$468$	2.80888	0.129840
$469$	37.9335	1.75161
$470$	−1.93618	−0.0893094
$471$	9.19027	0.423465
$472$	8.94333	0.411650
$473$	−6.01984	−0.276793
$474$	−23.0195	−1.05732
$475$	4.70902	0.216065
$476$	−21.7763	−0.998114
$477$	3.74406	0.171429
$478$	−23.5249	−1.07600
$479$	15.7058	0.717614	0.358807	−	0.933412i	$-0.383184\pi$
$479$	15.7058	0.717614	0.358807	+	0.933412i	$0.383184\pi$
$480$	−0.754243	−0.0344263
$481$	−4.61104	−0.210245
$482$	14.2840	0.650620
$483$	−56.0135	−2.54870
$484$	−9.73301	−0.442410
$485$	6.51031	0.295618
$486$	−10.2932	−0.466908
$487$	−17.2930	−0.783618	−0.391809	−	0.920046i	$-0.628151\pi$
$487$	−17.2930	−0.783618	−0.391809	+	0.920046i	$0.628151\pi$
$488$	13.1010	0.593053
$489$	−10.3458	−0.467855
$490$	10.0235	0.452814
$491$	25.0354	1.12983	0.564917	−	0.825148i	$-0.308908\pi$
$491$	25.0354	1.12983	0.564917	+	0.825148i	$0.308908\pi$
$492$	−0.570524	−0.0257212
$493$	1.21287	0.0546251
$494$	2.68807	0.120942
$495$	0.634468	0.0285172
$496$	−6.56253	−0.294667
$497$	50.5087	2.26562
$498$	−9.79507	−0.438928
$499$	32.2250	1.44259	0.721295	−	0.692628i	$-0.243547\pi$
$499$	32.2250	1.44259	0.721295	+	0.692628i	$0.243547\pi$
$500$	−5.23729	−0.234219
$501$	21.2080	0.947501
$502$	−5.37276	−0.239798
$503$	−15.4035	−0.686808	−0.343404	−	0.939188i	$-0.611580\pi$
$503$	−15.4035	−0.686808	−0.343404	+	0.939188i	$0.611580\pi$
$504$	−5.28514	−0.235419
$505$	0.653877	0.0290971
$506$	−8.91526	−0.396332
$507$	8.07379	0.358570
$508$	15.1724	0.673166
$509$	−29.0628	−1.28818	−0.644092	−	0.764948i	$-0.722765\pi$
$509$	−29.0628	−1.28818	−0.644092	+	0.764948i	$0.722765\pi$
$510$	3.24736	0.143795
$511$	−36.3538	−1.60820
$512$	1.00000	0.0441942
$513$	−5.65578	−0.249709
$514$	−2.19233	−0.0966997
$515$	9.23958	0.407144
$516$	−7.47788	−0.329195
$517$	4.04019	0.177687
$518$	8.67606	0.381204
$519$	22.0587	0.968272
$520$	−1.45001	−0.0635873
$521$	−19.6781	−0.862113	−0.431057	−	0.902325i	$-0.641859\pi$
$521$	−19.6781	−0.862113	−0.431057	+	0.902325i	$0.641859\pi$
$522$	0.294367	0.0128841
$523$	28.6016	1.25066	0.625330	−	0.780360i	$-0.284964\pi$
$523$	28.6016	1.25066	0.625330	+	0.780360i	$0.284964\pi$
$524$	17.8014	0.777656
$525$	33.3024	1.45344
$526$	31.8437	1.38845
$527$	28.2547	1.23079
$528$	1.57386	0.0684935
$529$	39.7329	1.72752
$530$	−1.93278	−0.0839545
$531$	−9.34525	−0.405549
$532$	−5.05784	−0.219285
$533$	−1.09682	−0.0475085
$534$	6.12287	0.264962
$535$	3.10542	0.134259
$536$	7.49995	0.323948
$537$	−1.26654	−0.0546551
$538$	17.6913	0.762728
$539$	−20.9157	−0.900904
$540$	3.05087	0.131288
$541$	−17.0969	−0.735052	−0.367526	−	0.930013i	$-0.619795\pi$
$541$	−17.0969	−0.735052	−0.367526	+	0.930013i	$0.619795\pi$
$542$	8.78563	0.377375
$543$	23.4960	1.00831
$544$	−4.30545	−0.184595
$545$	0.884035	0.0378679
$546$	19.0101	0.813559
$547$	−20.2406	−0.865426	−0.432713	−	0.901532i	$-0.642444\pi$
$547$	−20.2406	−0.865426	−0.432713	+	0.901532i	$0.642444\pi$
$548$	−6.31444	−0.269740
$549$	−13.6897	−0.584264
$550$	5.30050	0.226014
$551$	0.281706	0.0120011
$552$	−11.0746	−0.471366
$553$	83.2684	3.54093
$554$	−21.3490	−0.907031
$555$	−1.29381	−0.0549190
$556$	−4.18766	−0.177596
$557$	11.4566	0.485431	0.242716	−	0.970097i	$-0.421962\pi$
$557$	11.4566	0.485431	0.242716	+	0.970097i	$0.421962\pi$
$558$	6.85746	0.290300
$559$	−14.3760	−0.608042
$560$	2.72833	0.115293
$561$	−6.77619	−0.286091
$562$	0.534356	0.0225405
$563$	−13.9464	−0.587772	−0.293886	−	0.955840i	$-0.594949\pi$
$563$	−13.9464	−0.587772	−0.293886	+	0.955840i	$0.594949\pi$
$564$	5.01874	0.211327
$565$	−1.47736	−0.0621530
$566$	−11.9700	−0.503136
$567$	−24.1425	−1.01389
$568$	9.98622	0.419013
$569$	34.4070	1.44242	0.721208	−	0.692718i	$-0.243587\pi$
$569$	34.4070	1.44242	0.721208	+	0.692718i	$0.243587\pi$
$570$	0.754243	0.0315918
$571$	46.0927	1.92892	0.964461	−	0.264226i	$-0.0851165\pi$
$571$	46.0927	1.92892	0.964461	+	0.264226i	$0.0851165\pi$
$572$	3.02571	0.126511
$573$	13.3764	0.558808
$574$	2.06376	0.0861397
$575$	−37.2974	−1.55541
$576$	−1.04494	−0.0435392
$577$	−20.1814	−0.840162	−0.420081	−	0.907487i	$-0.637998\pi$
$577$	−20.1814	−0.840162	−0.420081	+	0.907487i	$0.637998\pi$
$578$	1.53693	0.0639279
$579$	−26.9267	−1.11903
$580$	−0.151960	−0.00630978
$581$	35.4318	1.46996
$582$	−16.8752	−0.699501
$583$	4.03308	0.167033
$584$	−7.18763	−0.297426
$585$	1.51518	0.0626449
$586$	−16.8883	−0.697649
$587$	−31.7581	−1.31080	−0.655399	−	0.755283i	$-0.727499\pi$
$587$	−31.7581	−1.31080	−0.655399	+	0.755283i	$0.727499\pi$
$588$	−25.9816	−1.07146
$589$	6.56253	0.270405
$590$	4.82426	0.198612
$591$	−19.7060	−0.810597
$592$	1.71537	0.0705013
$593$	11.8103	0.484992	0.242496	−	0.970152i	$-0.422034\pi$
$593$	11.8103	0.484992	0.242496	+	0.970152i	$0.422034\pi$
$594$	−6.36618	−0.261207
$595$	−11.7467	−0.481567
$596$	−13.0258	−0.533558
$597$	−1.50473	−0.0615844
$598$	−21.2906	−0.870638
$599$	−16.9161	−0.691173	−0.345586	−	0.938387i	$-0.612320\pi$
$599$	−16.9161	−0.691173	−0.345586	+	0.938387i	$0.612320\pi$
$600$	6.58431	0.268803
$601$	26.4584	1.07926	0.539629	−	0.841903i	$-0.318564\pi$
$601$	26.4584	1.07926	0.539629	+	0.841903i	$0.318564\pi$
$602$	27.0498	1.10247
$603$	−7.83700	−0.319147
$604$	−0.626724	−0.0255010
$605$	−5.25023	−0.213452
$606$	−1.69490	−0.0688507
$607$	32.0869	1.30237	0.651184	−	0.758920i	$-0.274273\pi$
$607$	32.0869	1.30237	0.651184	+	0.758920i	$0.274273\pi$
$608$	−1.00000	−0.0405554
$609$	1.99224	0.0807296
$610$	7.06699	0.286134
$611$	9.64840	0.390332
$612$	4.49895	0.181859
$613$	−16.5732	−0.669385	−0.334693	−	0.942327i	$-0.608632\pi$
$613$	−16.5732	−0.669385	−0.334693	+	0.942327i	$0.608632\pi$
$614$	−19.8836	−0.802436
$615$	−0.307755	−0.0124099
$616$	−5.69314	−0.229383
$617$	−46.6098	−1.87644	−0.938220	−	0.346038i	$-0.887527\pi$
$617$	−46.6098	−1.87644	−0.938220	+	0.346038i	$0.887527\pi$
$618$	−23.9497	−0.963399
$619$	6.72091	0.270136	0.135068	−	0.990836i	$-0.456875\pi$
$619$	6.72091	0.270136	0.135068	+	0.990836i	$0.456875\pi$
$620$	−3.54000	−0.142170
$621$	44.7960	1.79760
$622$	8.70171	0.348907
$623$	−22.1483	−0.887352
$624$	3.75855	0.150463
$625$	20.7200	0.828799
$626$	−23.2841	−0.930621
$627$	−1.57386	−0.0628540
$628$	−6.57277	−0.262282
$629$	−7.38545	−0.294477
$630$	−2.85094	−0.113584
$631$	18.7172	0.745120	0.372560	−	0.928008i	$-0.378480\pi$
$631$	18.7172	0.745120	0.372560	+	0.928008i	$0.378480\pi$
$632$	16.4632	0.654872
$633$	1.39823	0.0555748
$634$	−1.08251	−0.0429919
$635$	8.18437	0.324787
$636$	5.00992	0.198656
$637$	−49.9490	−1.97905
$638$	0.317091	0.0125537
$639$	−10.4350	−0.412803
$640$	0.539425	0.0213227
$641$	−32.6567	−1.28986	−0.644930	−	0.764241i	$-0.723114\pi$
$641$	−32.6567	−1.28986	−0.644930	+	0.764241i	$0.723114\pi$
$642$	−8.04951	−0.317689
$643$	23.2928	0.918577	0.459289	−	0.888287i	$-0.348104\pi$
$643$	23.2928	0.918577	0.459289	+	0.888287i	$0.348104\pi$
$644$	40.0601	1.57859
$645$	−4.03376	−0.158829
$646$	4.30545	0.169396
$647$	−44.0611	−1.73222	−0.866110	−	0.499854i	$-0.833387\pi$
$647$	−44.0611	−1.73222	−0.866110	+	0.499854i	$0.833387\pi$
$648$	−4.77328	−0.187512
$649$	−10.0667	−0.395151
$650$	12.6582	0.496495
$651$	46.4105	1.81897
$652$	7.39921	0.289776
$653$	30.8368	1.20674	0.603368	−	0.797463i	$-0.293825\pi$
$653$	30.8368	1.20674	0.603368	+	0.797463i	$0.293825\pi$
$654$	−2.29149	−0.0896043
$655$	9.60251	0.375201
$656$	0.408032	0.0159310
$657$	7.51065	0.293018
$658$	−18.1543	−0.707728
$659$	−43.5281	−1.69562	−0.847808	−	0.530304i	$-0.822078\pi$
$659$	−43.5281	−1.69562	−0.847808	+	0.530304i	$0.822078\pi$
$660$	0.848981	0.0330465
$661$	44.1234	1.71620	0.858101	−	0.513482i	$-0.171645\pi$
$661$	44.1234	1.71620	0.858101	+	0.513482i	$0.171645\pi$
$662$	29.4757	1.14560
$663$	−16.1823	−0.628467
$664$	7.00532	0.271859
$665$	−2.72833	−0.105800
$666$	−1.79246	−0.0694564
$667$	−2.23123	−0.0863936
$668$	−15.1677	−0.586855
$669$	−13.9182	−0.538109
$670$	4.04566	0.156298
$671$	−14.7465	−0.569283
$672$	−7.07204	−0.272810
$673$	23.0409	0.888163	0.444081	−	0.895986i	$-0.353530\pi$
$673$	23.0409	0.888163	0.444081	+	0.895986i	$0.353530\pi$
$674$	−8.97516	−0.345710
$675$	−26.6332	−1.02511
$676$	−5.77428	−0.222088
$677$	33.9101	1.30327	0.651636	−	0.758532i	$-0.274083\pi$
$677$	33.9101	1.30327	0.651636	+	0.758532i	$0.274083\pi$
$678$	3.82943	0.147069
$679$	61.0429	2.34261
$680$	−2.32247	−0.0890627
$681$	−36.2965	−1.39089
$682$	7.38683	0.282856
$683$	−37.2066	−1.42367	−0.711836	−	0.702346i	$-0.752136\pi$
$683$	−37.2066	−1.42367	−0.711836	+	0.702346i	$0.752136\pi$
$684$	1.04494	0.0399543
$685$	−3.40617	−0.130143
$686$	58.5785	2.23654
$687$	6.79855	0.259381
$688$	5.34809	0.203894
$689$	9.63144	0.366929
$690$	−5.97391	−0.227423
$691$	37.3225	1.41982	0.709908	−	0.704295i	$-0.248737\pi$
$691$	37.3225	1.41982	0.709908	+	0.704295i	$0.248737\pi$
$692$	−15.7761	−0.599719
$693$	5.94899	0.225984
$694$	26.4970	1.00581
$695$	−2.25893	−0.0856861
$696$	0.393892	0.0149304
$697$	−1.75676	−0.0665422
$698$	−4.60150	−0.174169
$699$	−4.87221	−0.184284
$700$	−23.8175	−0.900215
$701$	38.9177	1.46990	0.734951	−	0.678120i	$-0.237205\pi$
$701$	38.9177	1.46990	0.734951	+	0.678120i	$0.237205\pi$
$702$	−15.2031	−0.573805
$703$	−1.71537	−0.0646964
$704$	−1.12561	−0.0424229
$705$	2.70724	0.101960
$706$	−3.77583	−0.142105
$707$	6.13097	0.230579
$708$	−12.5049	−0.469962
$709$	−41.1852	−1.54674	−0.773371	−	0.633954i	$-0.781431\pi$
$709$	−41.1852	−1.54674	−0.773371	+	0.633954i	$0.781431\pi$
$710$	5.38682	0.202164
$711$	−17.2031	−0.645167
$712$	−4.37900	−0.164110
$713$	−51.9780	−1.94659
$714$	30.4484	1.13950
$715$	1.63215	0.0610388
$716$	0.905811	0.0338518
$717$	32.8933	1.22842
$718$	−21.5307	−0.803518
$719$	−18.1056	−0.675226	−0.337613	−	0.941285i	$-0.609619\pi$
$719$	−18.1056	−0.675226	−0.337613	+	0.941285i	$0.609619\pi$
$720$	−0.563668	−0.0210067
$721$	86.6334	3.22640
$722$	1.00000	0.0372161
$723$	−19.9724	−0.742783
$724$	−16.8041	−0.624518
$725$	1.32656	0.0492673
$726$	13.6090	0.505078
$727$	−25.9544	−0.962594	−0.481297	−	0.876557i	$-0.659834\pi$
$727$	−25.9544	−0.962594	−0.481297	+	0.876557i	$0.659834\pi$
$728$	−13.5958	−0.503895
$729$	28.7121	1.06341
$730$	−3.87719	−0.143501
$731$	−23.0259	−0.851645
$732$	−18.3182	−0.677061
$733$	9.40335	0.347321	0.173660	−	0.984806i	$-0.444441\pi$
$733$	9.40335	0.347321	0.173660	+	0.984806i	$0.444441\pi$
$734$	−21.8841	−0.807757
$735$	−14.0151	−0.516956
$736$	7.92041	0.291950
$737$	−8.44199	−0.310965
$738$	−0.426370	−0.0156949
$739$	37.2029	1.36853	0.684266	−	0.729232i	$-0.260123\pi$
$739$	37.2029	1.36853	0.684266	+	0.729232i	$0.260123\pi$
$740$	0.925314	0.0340152
$741$	−3.75855	−0.138074
$742$	−18.1224	−0.665294
$743$	−30.6366	−1.12395	−0.561975	−	0.827154i	$-0.689958\pi$
$743$	−30.6366	−1.12395	−0.561975	+	0.827154i	$0.689958\pi$
$744$	9.17596	0.336407
$745$	−7.02646	−0.257430
$746$	13.7549	0.503604
$747$	−7.32014	−0.267830
$748$	4.84625	0.177196
$749$	29.1175	1.06393
$750$	7.32296	0.267397
$751$	−47.7664	−1.74302	−0.871511	−	0.490376i	$-0.836860\pi$
$751$	−47.7664	−1.74302	−0.871511	+	0.490376i	$0.836860\pi$
$752$	−3.58934	−0.130890
$753$	7.51238	0.273766
$754$	0.757247	0.0275773
$755$	−0.338071	−0.0123037
$756$	28.6060	1.04039
$757$	35.6625	1.29617	0.648087	−	0.761566i	$-0.275569\pi$
$757$	35.6625	1.29617	0.648087	+	0.761566i	$0.275569\pi$
$758$	−5.18809	−0.188440
$759$	12.4656	0.452474
$760$	−0.539425	−0.0195670
$761$	−19.2845	−0.699061	−0.349531	−	0.936925i	$-0.613659\pi$
$761$	−19.2845	−0.699061	−0.349531	+	0.936925i	$0.613659\pi$
$762$	−21.2145	−0.768522
$763$	8.28901	0.300082
$764$	−9.56666	−0.346109
$765$	2.42685	0.0877428
$766$	32.9761	1.19147
$767$	−24.0403	−0.868045
$768$	−1.39823	−0.0504544
$769$	33.9307	1.22357	0.611787	−	0.791023i	$-0.290451\pi$
$769$	33.9307	1.22357	0.611787	+	0.791023i	$0.290451\pi$
$770$	−3.07102	−0.110672
$771$	3.06540	0.110398
$772$	19.2576	0.693097
$773$	7.83486	0.281801	0.140900	−	0.990024i	$-0.455000\pi$
$773$	7.83486	0.281801	0.140900	+	0.990024i	$0.455000\pi$
$774$	−5.58844	−0.200872
$775$	30.9031	1.11007
$776$	12.0690	0.433251
$777$	−12.1312	−0.435203
$778$	11.2758	0.404258
$779$	−0.408032	−0.0146193
$780$	2.02746	0.0725947
$781$	−11.2406	−0.402219
$782$	−34.1010	−1.21945
$783$	−1.59327	−0.0569388
$784$	18.5817	0.663633
$785$	−3.54552	−0.126545
$786$	−24.8905	−0.887814
$787$	22.4427	0.799994	0.399997	−	0.916516i	$-0.369011\pi$
$787$	22.4427	0.799994	0.399997	+	0.916516i	$0.369011\pi$
$788$	14.0935	0.502060
$789$	−44.5250	−1.58513
$790$	8.88069	0.315961
$791$	−13.8522	−0.492529
$792$	1.17619	0.0417942
$793$	−35.2163	−1.25057
$794$	−15.9178	−0.564902
$795$	2.70248	0.0958469
$796$	1.07616	0.0381436
$797$	23.3320	0.826461	0.413230	−	0.910627i	$-0.364400\pi$
$797$	23.3320	0.826461	0.413230	+	0.910627i	$0.364400\pi$
$798$	7.07204	0.250348
$799$	15.4537	0.546714
$800$	−4.70902	−0.166489
$801$	4.57580	0.161678
$802$	30.8843	1.09056
$803$	8.09044	0.285505
$804$	−10.4867	−0.369837
$805$	21.6095	0.761633
$806$	17.6406	0.621362
$807$	−24.7366	−0.870771
$808$	1.21217	0.0426441
$809$	15.6008	0.548496	0.274248	−	0.961659i	$-0.411571\pi$
$809$	15.6008	0.548496	0.274248	+	0.961659i	$0.411571\pi$
$810$	−2.57483	−0.0904702
$811$	−33.6213	−1.18060	−0.590301	−	0.807183i	$-0.700991\pi$
$811$	−33.6213	−1.18060	−0.590301	+	0.807183i	$0.700991\pi$
$812$	−1.42483	−0.0500016
$813$	−12.2844	−0.430832
$814$	−1.93083	−0.0676756
$815$	3.99132	0.139810
$816$	6.02003	0.210743
$817$	−5.34809	−0.187106
$818$	35.8549	1.25364
$819$	14.2068	0.496427
$820$	0.220103	0.00768633
$821$	44.3042	1.54623	0.773114	−	0.634268i	$-0.218698\pi$
$821$	44.3042	1.54623	0.773114	+	0.634268i	$0.218698\pi$
$822$	8.82907	0.307949
$823$	15.8968	0.554128	0.277064	−	0.960852i	$-0.410639\pi$
$823$	15.8968	0.554128	0.277064	+	0.960852i	$0.410639\pi$
$824$	17.1286	0.596701
$825$	−7.41135	−0.258030
$826$	45.2339	1.57389
$827$	−50.4230	−1.75338	−0.876689	−	0.481057i	$-0.840253\pi$
$827$	−50.4230	−1.75338	−0.876689	+	0.481057i	$0.840253\pi$
$828$	−8.27636	−0.287623
$829$	−14.0581	−0.488258	−0.244129	−	0.969743i	$-0.578502\pi$
$829$	−14.0581	−0.488258	−0.244129	+	0.969743i	$0.578502\pi$
$830$	3.77885	0.131166
$831$	29.8509	1.03552
$832$	−2.68807	−0.0931921
$833$	−80.0028	−2.77193
$834$	5.85533	0.202753
$835$	−8.18183	−0.283144
$836$	1.12561	0.0389299
$837$	−37.1162	−1.28292
$838$	−25.3099	−0.874315
$839$	38.3912	1.32541	0.662706	−	0.748880i	$-0.269408\pi$
$839$	38.3912	1.32541	0.662706	+	0.748880i	$0.269408\pi$
$840$	−3.81484	−0.131624
$841$	−28.9206	−0.997263
$842$	35.4253	1.22084
$843$	−0.747155	−0.0257334
$844$	−1.00000	−0.0344214
$845$	−3.11479	−0.107152
$846$	3.75065	0.128950
$847$	−49.2280	−1.69149
$848$	−3.58303	−0.123042
$849$	16.7368	0.574407
$850$	20.2745	0.695409
$851$	13.5864	0.465737
$852$	−13.9631	−0.478367
$853$	−42.4341	−1.45292	−0.726458	−	0.687211i	$-0.758835\pi$
$853$	−42.4341	−1.45292	−0.726458	+	0.687211i	$0.758835\pi$
$854$	66.2625	2.26746
$855$	0.563668	0.0192770
$856$	5.75691	0.196767
$857$	20.3091	0.693746	0.346873	−	0.937912i	$-0.387244\pi$
$857$	20.3091	0.693746	0.346873	+	0.937912i	$0.387244\pi$
$858$	−4.23065	−0.144432
$859$	10.8351	0.369690	0.184845	−	0.982768i	$-0.440822\pi$
$859$	10.8351	0.369690	0.184845	+	0.982768i	$0.440822\pi$
$860$	2.88489	0.0983741
$861$	−2.88562	−0.0983417
$862$	31.1751	1.06183
$863$	2.34439	0.0798040	0.0399020	−	0.999204i	$-0.487295\pi$
$863$	2.34439	0.0798040	0.0399020	+	0.999204i	$0.487295\pi$
$864$	5.65578	0.192413
$865$	−8.51005	−0.289351
$866$	−28.5507	−0.970192
$867$	−2.14899	−0.0729835
$868$	−33.1922	−1.12662
$869$	−18.5311	−0.628626
$870$	0.212475	0.00720358
$871$	−20.1604	−0.683109
$872$	1.63885	0.0554983
$873$	−12.6114	−0.426830
$874$	−7.92041	−0.267912
$875$	−26.4894	−0.895504
$876$	10.0500	0.339558
$877$	8.53605	0.288242	0.144121	−	0.989560i	$-0.453965\pi$
$877$	8.53605	0.288242	0.144121	+	0.989560i	$0.453965\pi$
$878$	−25.6159	−0.864496
$879$	23.6138	0.796474
$880$	−0.607181	−0.0204681
$881$	11.7352	0.395369	0.197685	−	0.980266i	$-0.436658\pi$
$881$	11.7352	0.395369	0.197685	+	0.980266i	$0.436658\pi$
$882$	−19.4168	−0.653798
$883$	−37.5958	−1.26520	−0.632600	−	0.774479i	$-0.718012\pi$
$883$	−37.5958	−1.26520	−0.632600	+	0.774479i	$0.718012\pi$
$884$	11.5734	0.389254
$885$	−6.74544	−0.226746
$886$	16.4574	0.552897
$887$	−41.5645	−1.39560	−0.697800	−	0.716292i	$-0.745838\pi$
$887$	−41.5645	−1.39560	−0.697800	+	0.716292i	$0.745838\pi$
$888$	−2.39849	−0.0804880
$889$	76.7394	2.57376
$890$	−2.36214	−0.0791792
$891$	5.37283	0.179997
$892$	9.95413	0.333289
$893$	3.58934	0.120113
$894$	18.2131	0.609139
$895$	0.488618	0.0163327
$896$	5.05784	0.168971
$897$	29.7693	0.993967
$898$	−6.37899	−0.212870
$899$	1.84871	0.0616579
$900$	4.92065	0.164022
$901$	15.4266	0.513934
$902$	−0.459284	−0.0152925
$903$	−37.8219	−1.25863
$904$	−2.73876	−0.0910900
$905$	−9.06455	−0.301316
$906$	0.876307	0.0291133
$907$	−21.7421	−0.721934	−0.360967	−	0.932579i	$-0.617553\pi$
$907$	−21.7421	−0.721934	−0.360967	+	0.932579i	$0.617553\pi$
$908$	25.9588	0.861474
$909$	−1.26665	−0.0420121
$910$	−7.33393	−0.243118
$911$	−39.8011	−1.31867	−0.659335	−	0.751849i	$-0.729162\pi$
$911$	−39.8011	−1.31867	−0.659335	+	0.751849i	$0.729162\pi$
$912$	1.39823	0.0463002
$913$	−7.88523	−0.260963
$914$	−17.7167	−0.586015
$915$	−9.88131	−0.326666
$916$	−4.86224	−0.160653
$917$	90.0364	2.97326
$918$	−24.3507	−0.803692
$919$	36.8996	1.21721	0.608603	−	0.793475i	$-0.291730\pi$
$919$	36.8996	1.21721	0.608603	+	0.793475i	$0.291730\pi$
$920$	4.27247	0.140859
$921$	27.8019	0.916104
$922$	−11.1057	−0.365745
$923$	−26.8437	−0.883570
$924$	7.96034	0.261876
$925$	−8.07771	−0.265594
$926$	−20.2349	−0.664961
$927$	−17.8983	−0.587858
$928$	−0.281706	−0.00924747
$929$	−15.8960	−0.521532	−0.260766	−	0.965402i	$-0.583975\pi$
$929$	−15.8960	−0.521532	−0.260766	+	0.965402i	$0.583975\pi$
$930$	4.94975	0.162309
$931$	−18.5817	−0.608991
$932$	3.48455	0.114140
$933$	−12.1670	−0.398330
$934$	−33.9185	−1.10985
$935$	2.61419	0.0854931
$936$	2.80888	0.0918110
$937$	22.0247	0.719515	0.359758	−	0.933046i	$-0.382859\pi$
$937$	22.0247	0.719515	0.359758	+	0.933046i	$0.382859\pi$
$938$	37.9335	1.23857
$939$	32.5567	1.06245
$940$	−1.93618	−0.0631513
$941$	14.5777	0.475220	0.237610	−	0.971361i	$-0.423636\pi$
$941$	14.5777	0.475220	0.237610	+	0.971361i	$0.423636\pi$
$942$	9.19027	0.299435
$943$	3.23178	0.105241
$944$	8.94333	0.291081
$945$	15.4308	0.501964
$946$	−6.01984	−0.195722
$947$	−18.5352	−0.602314	−0.301157	−	0.953575i	$-0.597373\pi$
$947$	−18.5352	−0.602314	−0.301157	+	0.953575i	$0.597373\pi$
$948$	−23.0195	−0.747637
$949$	19.3208	0.627181
$950$	4.70902	0.152781
$951$	1.51360	0.0490818
$952$	−21.7763	−0.705774
$953$	−45.5710	−1.47619	−0.738094	−	0.674698i	$-0.764274\pi$
$953$	−45.5710	−1.47619	−0.738094	+	0.674698i	$0.764274\pi$
$954$	3.74406	0.121218
$955$	−5.16050	−0.166990
$956$	−23.5249	−0.760848
$957$	−0.443367	−0.0143320
$958$	15.7058	0.507430
$959$	−31.9374	−1.03131
$960$	−0.754243	−0.0243431
$961$	12.0669	0.389254
$962$	−4.61104	−0.148666
$963$	−6.01563	−0.193851
$964$	14.2840	0.460058
$965$	10.3881	0.334403
$966$	−56.0135	−1.80220
$967$	−5.76318	−0.185331	−0.0926657	−	0.995697i	$-0.529539\pi$
$967$	−5.76318	−0.185331	−0.0926657	+	0.995697i	$0.529539\pi$
$968$	−9.73301	−0.312831
$969$	−6.02003	−0.193391
$970$	6.51031	0.209033
$971$	−5.30424	−0.170221	−0.0851106	−	0.996372i	$-0.527124\pi$
$971$	−5.30424	−0.170221	−0.0851106	+	0.996372i	$0.527124\pi$
$972$	−10.2932	−0.330154
$973$	−21.1805	−0.679016
$974$	−17.2930	−0.554102
$975$	−17.6991	−0.566825
$976$	13.1010	0.419352
$977$	−61.5062	−1.96776	−0.983879	−	0.178834i	$-0.942768\pi$
$977$	−61.5062	−1.96776	−0.983879	+	0.178834i	$0.942768\pi$
$978$	−10.3458	−0.330823
$979$	4.92903	0.157532
$980$	10.0235	0.320188
$981$	−1.71250	−0.0546758
$982$	25.0354	0.798913
$983$	−9.58788	−0.305806	−0.152903	−	0.988241i	$-0.548862\pi$
$983$	−9.58788	−0.305806	−0.152903	+	0.988241i	$0.548862\pi$
$984$	−0.570524	−0.0181877
$985$	7.60239	0.242232
$986$	1.21287	0.0386258
$987$	25.3840	0.807981
$988$	2.68807	0.0855189
$989$	42.3590	1.34694
$990$	0.634468	0.0201647
$991$	11.9546	0.379752	0.189876	−	0.981808i	$-0.439191\pi$
$991$	11.9546	0.379752	0.189876	+	0.981808i	$0.439191\pi$
$992$	−6.56253	−0.208361
$993$	−41.2139	−1.30788
$994$	50.5087	1.60204
$995$	0.580510	0.0184034
$996$	−9.79507	−0.310369
$997$	−36.0288	−1.14104	−0.570522	−	0.821283i	$-0.693259\pi$
$997$	−36.0288	−1.14104	−0.570522	+	0.821283i	$0.693259\pi$
$998$	32.2250	1.02007
$999$	9.70175	0.306950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.14	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.14	✓	47	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.39823 q^{3} +1.00000 q^{4} +0.539425 q^{5} -1.39823 q^{6} +5.05784 q^{7} +1.00000 q^{8} -1.04494 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.39823 q^{3} +1.00000 q^{4} +0.539425 q^{5} -1.39823 q^{6} +5.05784 q^{7} +1.00000 q^{8} -1.04494 q^{9} +0.539425 q^{10} -1.12561 q^{11} -1.39823 q^{12} -2.68807 q^{13} +5.05784 q^{14} -0.754243 q^{15} +1.00000 q^{16} -4.30545 q^{17} -1.04494 q^{18} -1.00000 q^{19} +0.539425 q^{20} -7.07204 q^{21} -1.12561 q^{22} +7.92041 q^{23} -1.39823 q^{24} -4.70902 q^{25} -2.68807 q^{26} +5.65578 q^{27} +5.05784 q^{28} -0.281706 q^{29} -0.754243 q^{30} -6.56253 q^{31} +1.00000 q^{32} +1.57386 q^{33} -4.30545 q^{34} +2.72833 q^{35} -1.04494 q^{36} +1.71537 q^{37} -1.00000 q^{38} +3.75855 q^{39} +0.539425 q^{40} +0.408032 q^{41} -7.07204 q^{42} +5.34809 q^{43} -1.12561 q^{44} -0.563668 q^{45} +7.92041 q^{46} -3.58934 q^{47} -1.39823 q^{48} +18.5817 q^{49} -4.70902 q^{50} +6.02003 q^{51} -2.68807 q^{52} -3.58303 q^{53} +5.65578 q^{54} -0.607181 q^{55} +5.05784 q^{56} +1.39823 q^{57} -0.281706 q^{58} +8.94333 q^{59} -0.754243 q^{60} +13.1010 q^{61} -6.56253 q^{62} -5.28514 q^{63} +1.00000 q^{64} -1.45001 q^{65} +1.57386 q^{66} +7.49995 q^{67} -4.30545 q^{68} -11.0746 q^{69} +2.72833 q^{70} +9.98622 q^{71} -1.04494 q^{72} -7.18763 q^{73} +1.71537 q^{74} +6.58431 q^{75} -1.00000 q^{76} -5.69314 q^{77} +3.75855 q^{78} +16.4632 q^{79} +0.539425 q^{80} -4.77328 q^{81} +0.408032 q^{82} +7.00532 q^{83} -7.07204 q^{84} -2.32247 q^{85} +5.34809 q^{86} +0.393892 q^{87} -1.12561 q^{88} -4.37900 q^{89} -0.563668 q^{90} -13.5958 q^{91} +7.92041 q^{92} +9.17596 q^{93} -3.58934 q^{94} -0.539425 q^{95} -1.39823 q^{96} +12.0690 q^{97} +18.5817 q^{98} +1.17619 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 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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