LMFDB - Embedded newform 8018.2.a.j.1.19

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			1.19
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.764189 q^{3} +1.00000 q^{4} -0.445775 q^{5} -0.764189 q^{6} -0.938446 q^{7} +1.00000 q^{8} -2.41602 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.764189 q^{3} +1.00000 q^{4} -0.445775 q^{5} -0.764189 q^{6} -0.938446 q^{7} +1.00000 q^{8} -2.41602 q^{9} -0.445775 q^{10} +2.33898 q^{11} -0.764189 q^{12} -6.49743 q^{13} -0.938446 q^{14} +0.340656 q^{15} +1.00000 q^{16} +1.93985 q^{17} -2.41602 q^{18} -1.00000 q^{19} -0.445775 q^{20} +0.717150 q^{21} +2.33898 q^{22} +3.50222 q^{23} -0.764189 q^{24} -4.80128 q^{25} -6.49743 q^{26} +4.13886 q^{27} -0.938446 q^{28} -1.31075 q^{29} +0.340656 q^{30} +4.83737 q^{31} +1.00000 q^{32} -1.78742 q^{33} +1.93985 q^{34} +0.418336 q^{35} -2.41602 q^{36} +2.27726 q^{37} -1.00000 q^{38} +4.96526 q^{39} -0.445775 q^{40} -8.03117 q^{41} +0.717150 q^{42} -2.86373 q^{43} +2.33898 q^{44} +1.07700 q^{45} +3.50222 q^{46} +2.15639 q^{47} -0.764189 q^{48} -6.11932 q^{49} -4.80128 q^{50} -1.48241 q^{51} -6.49743 q^{52} +3.08544 q^{53} +4.13886 q^{54} -1.04266 q^{55} -0.938446 q^{56} +0.764189 q^{57} -1.31075 q^{58} +1.71699 q^{59} +0.340656 q^{60} +2.46308 q^{61} +4.83737 q^{62} +2.26730 q^{63} +1.00000 q^{64} +2.89639 q^{65} -1.78742 q^{66} +4.61290 q^{67} +1.93985 q^{68} -2.67636 q^{69} +0.418336 q^{70} +8.01255 q^{71} -2.41602 q^{72} +10.4169 q^{73} +2.27726 q^{74} +3.66909 q^{75} -1.00000 q^{76} -2.19501 q^{77} +4.96526 q^{78} +0.375799 q^{79} -0.445775 q^{80} +4.08518 q^{81} -8.03117 q^{82} +6.21956 q^{83} +0.717150 q^{84} -0.864734 q^{85} -2.86373 q^{86} +1.00166 q^{87} +2.33898 q^{88} +14.0546 q^{89} +1.07700 q^{90} +6.09749 q^{91} +3.50222 q^{92} -3.69666 q^{93} +2.15639 q^{94} +0.445775 q^{95} -0.764189 q^{96} -16.8131 q^{97} -6.11932 q^{98} -5.65101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.764189	−0.441205	−0.220602	−	0.975364i	$-0.570802\pi$
$3$	−0.764189	−0.441205	−0.220602	+	0.975364i	$0.570802\pi$
$4$	1.00000	0.500000
$5$	−0.445775	−0.199357	−0.0996783	−	0.995020i	$-0.531781\pi$
$5$	−0.445775	−0.199357	−0.0996783	+	0.995020i	$0.531781\pi$
$6$	−0.764189	−0.311979
$7$	−0.938446	−0.354699	−0.177350	−	0.984148i	$-0.556752\pi$
$7$	−0.938446	−0.354699	−0.177350	+	0.984148i	$0.556752\pi$
$8$	1.00000	0.353553
$9$	−2.41602	−0.805338
$10$	−0.445775	−0.140966
$11$	2.33898	0.705229	0.352615	−	0.935769i	$-0.385293\pi$
$11$	2.33898	0.705229	0.352615	+	0.935769i	$0.385293\pi$
$12$	−0.764189	−0.220602
$13$	−6.49743	−1.80206	−0.901031	−	0.433755i	$-0.857188\pi$
$13$	−6.49743	−1.80206	−0.901031	+	0.433755i	$0.857188\pi$
$14$	−0.938446	−0.250810
$15$	0.340656	0.0879570
$16$	1.00000	0.250000
$17$	1.93985	0.470482	0.235241	−	0.971937i	$-0.424412\pi$
$17$	1.93985	0.470482	0.235241	+	0.971937i	$0.424412\pi$
$18$	−2.41602	−0.569460
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.445775	−0.0996783
$21$	0.717150	0.156495
$22$	2.33898	0.498672
$23$	3.50222	0.730263	0.365132	−	0.930956i	$-0.381024\pi$
$23$	3.50222	0.730263	0.365132	+	0.930956i	$0.381024\pi$
$24$	−0.764189	−0.155989
$25$	−4.80128	−0.960257
$26$	−6.49743	−1.27425
$27$	4.13886	0.796524
$28$	−0.938446	−0.177350
$29$	−1.31075	−0.243400	−0.121700	−	0.992567i	$-0.538835\pi$
$29$	−1.31075	−0.243400	−0.121700	+	0.992567i	$0.538835\pi$
$30$	0.340656	0.0621950
$31$	4.83737	0.868816	0.434408	−	0.900716i	$-0.356958\pi$
$31$	4.83737	0.868816	0.434408	+	0.900716i	$0.356958\pi$
$32$	1.00000	0.176777
$33$	−1.78742	−0.311150
$34$	1.93985	0.332681
$35$	0.418336	0.0707116
$36$	−2.41602	−0.402669
$37$	2.27726	0.374380	0.187190	−	0.982324i	$-0.440062\pi$
$37$	2.27726	0.374380	0.187190	+	0.982324i	$0.440062\pi$
$38$	−1.00000	−0.162221
$39$	4.96526	0.795078
$40$	−0.445775	−0.0704832
$41$	−8.03117	−1.25426	−0.627129	−	0.778916i	$-0.715770\pi$
$41$	−8.03117	−1.25426	−0.627129	+	0.778916i	$0.715770\pi$
$42$	0.717150	0.110659
$43$	−2.86373	−0.436715	−0.218358	−	0.975869i	$-0.570070\pi$
$43$	−2.86373	−0.436715	−0.218358	+	0.975869i	$0.570070\pi$
$44$	2.33898	0.352615
$45$	1.07700	0.160549
$46$	3.50222	0.516374
$47$	2.15639	0.314542	0.157271	−	0.987556i	$-0.449730\pi$
$47$	2.15639	0.314542	0.157271	+	0.987556i	$0.449730\pi$
$48$	−0.764189	−0.110301
$49$	−6.11932	−0.874188
$50$	−4.80128	−0.679004
$51$	−1.48241	−0.207579
$52$	−6.49743	−0.901031
$53$	3.08544	0.423818	0.211909	−	0.977289i	$-0.432032\pi$
$53$	3.08544	0.423818	0.211909	+	0.977289i	$0.432032\pi$
$54$	4.13886	0.563227
$55$	−1.04266	−0.140592
$56$	−0.938446	−0.125405
$57$	0.764189	0.101219
$58$	−1.31075	−0.172109
$59$	1.71699	0.223534	0.111767	−	0.993734i	$-0.464349\pi$
$59$	1.71699	0.223534	0.111767	+	0.993734i	$0.464349\pi$
$60$	0.340656	0.0439785
$61$	2.46308	0.315365	0.157682	−	0.987490i	$-0.449598\pi$
$61$	2.46308	0.315365	0.157682	+	0.987490i	$0.449598\pi$
$62$	4.83737	0.614346
$63$	2.26730	0.285653
$64$	1.00000	0.125000
$65$	2.89639	0.359253
$66$	−1.78742	−0.220017
$67$	4.61290	0.563555	0.281778	−	0.959480i	$-0.409076\pi$
$67$	4.61290	0.563555	0.281778	+	0.959480i	$0.409076\pi$
$68$	1.93985	0.235241
$69$	−2.67636	−0.322196
$70$	0.418336	0.0500007
$71$	8.01255	0.950915	0.475457	−	0.879739i	$-0.342283\pi$
$71$	8.01255	0.950915	0.475457	+	0.879739i	$0.342283\pi$
$72$	−2.41602	−0.284730
$73$	10.4169	1.21921	0.609605	−	0.792705i	$-0.291328\pi$
$73$	10.4169	1.21921	0.609605	+	0.792705i	$0.291328\pi$
$74$	2.27726	0.264726
$75$	3.66909	0.423670
$76$	−1.00000	−0.114708
$77$	−2.19501	−0.250144
$78$	4.96526	0.562205
$79$	0.375799	0.0422807	0.0211403	−	0.999777i	$-0.493270\pi$
$79$	0.375799	0.0422807	0.0211403	+	0.999777i	$0.493270\pi$
$80$	−0.445775	−0.0498391
$81$	4.08518	0.453908
$82$	−8.03117	−0.886894
$83$	6.21956	0.682685	0.341343	−	0.939939i	$-0.389118\pi$
$83$	6.21956	0.682685	0.341343	+	0.939939i	$0.389118\pi$
$84$	0.717150	0.0782475
$85$	−0.864734	−0.0937936
$86$	−2.86373	−0.308804
$87$	1.00166	0.107389
$88$	2.33898	0.249336
$89$	14.0546	1.48978	0.744890	−	0.667187i	$-0.232502\pi$
$89$	14.0546	1.48978	0.744890	+	0.667187i	$0.232502\pi$
$90$	1.07700	0.113526
$91$	6.09749	0.639190
$92$	3.50222	0.365132
$93$	−3.69666	−0.383326
$94$	2.15639	0.222414
$95$	0.445775	0.0457355
$96$	−0.764189	−0.0779947
$97$	−16.8131	−1.70711	−0.853557	−	0.520999i	$-0.825560\pi$
$97$	−16.8131	−1.70711	−0.853557	+	0.520999i	$0.825560\pi$
$98$	−6.11932	−0.618145
$99$	−5.65101	−0.567948
$100$	−4.80128	−0.480128
$101$	−7.61087	−0.757309	−0.378655	−	0.925538i	$-0.623613\pi$
$101$	−7.61087	−0.757309	−0.378655	+	0.925538i	$0.623613\pi$
$102$	−1.48241	−0.146780
$103$	−2.78620	−0.274533	−0.137266	−	0.990534i	$-0.543832\pi$
$103$	−2.78620	−0.274533	−0.137266	+	0.990534i	$0.543832\pi$
$104$	−6.49743	−0.637125
$105$	−0.319687	−0.0311983
$106$	3.08544	0.299685
$107$	3.42104	0.330725	0.165362	−	0.986233i	$-0.447121\pi$
$107$	3.42104	0.330725	0.165362	+	0.986233i	$0.447121\pi$
$108$	4.13886	0.398262
$109$	−9.39884	−0.900246	−0.450123	−	0.892967i	$-0.648620\pi$
$109$	−9.39884	−0.900246	−0.450123	+	0.892967i	$0.648620\pi$
$110$	−1.04266	−0.0994136
$111$	−1.74026	−0.165178
$112$	−0.938446	−0.0886748
$113$	5.98637	0.563151	0.281575	−	0.959539i	$-0.409143\pi$
$113$	5.98637	0.563151	0.281575	+	0.959539i	$0.409143\pi$
$114$	0.764189	0.0715729
$115$	−1.56120	−0.145583
$116$	−1.31075	−0.121700
$117$	15.6979	1.45127
$118$	1.71699	0.158062
$119$	−1.82044	−0.166879
$120$	0.340656	0.0310975
$121$	−5.52917	−0.502652
$122$	2.46308	0.222997
$123$	6.13733	0.553384
$124$	4.83737	0.434408
$125$	4.36917	0.390790
$126$	2.26730	0.201987
$127$	3.86438	0.342908	0.171454	−	0.985192i	$-0.445153\pi$
$127$	3.86438	0.342908	0.171454	+	0.985192i	$0.445153\pi$
$128$	1.00000	0.0883883
$129$	2.18843	0.192681
$130$	2.89639	0.254030
$131$	18.3402	1.60239	0.801197	−	0.598400i	$-0.204197\pi$
$131$	18.3402	1.60239	0.801197	+	0.598400i	$0.204197\pi$
$132$	−1.78742	−0.155575
$133$	0.938446	0.0813736
$134$	4.61290	0.398494
$135$	−1.84500	−0.158792
$136$	1.93985	0.166340
$137$	−11.4988	−0.982412	−0.491206	−	0.871043i	$-0.663444\pi$
$137$	−11.4988	−0.982412	−0.491206	+	0.871043i	$0.663444\pi$
$138$	−2.67636	−0.227827
$139$	4.45298	0.377697	0.188848	−	0.982006i	$-0.439525\pi$
$139$	4.45298	0.377697	0.188848	+	0.982006i	$0.439525\pi$
$140$	0.418336	0.0353558
$141$	−1.64789	−0.138777
$142$	8.01255	0.672398
$143$	−15.1974	−1.27087
$144$	−2.41602	−0.201335
$145$	0.584298	0.0485233
$146$	10.4169	0.862112
$147$	4.67632	0.385696
$148$	2.27726	0.187190
$149$	8.24566	0.675511	0.337755	−	0.941234i	$-0.390332\pi$
$149$	8.24566	0.675511	0.337755	+	0.941234i	$0.390332\pi$
$150$	3.66909	0.299580
$151$	15.8642	1.29101	0.645505	−	0.763756i	$-0.276647\pi$
$151$	15.8642	1.29101	0.645505	+	0.763756i	$0.276647\pi$
$152$	−1.00000	−0.0811107
$153$	−4.68670	−0.378897
$154$	−2.19501	−0.176879
$155$	−2.15638	−0.173204
$156$	4.96526	0.397539
$157$	−0.995625	−0.0794595	−0.0397298	−	0.999210i	$-0.512650\pi$
$157$	−0.995625	−0.0794595	−0.0397298	+	0.999210i	$0.512650\pi$
$158$	0.375799	0.0298969
$159$	−2.35786	−0.186991
$160$	−0.445775	−0.0352416
$161$	−3.28664	−0.259024
$162$	4.08518	0.320962
$163$	7.80212	0.611109	0.305555	−	0.952175i	$-0.401158\pi$
$163$	7.80212	0.611109	0.305555	+	0.952175i	$0.401158\pi$
$164$	−8.03117	−0.627129
$165$	0.796788	0.0620299
$166$	6.21956	0.482731
$167$	23.4783	1.81680	0.908402	−	0.418098i	$-0.137303\pi$
$167$	23.4783	1.81680	0.908402	+	0.418098i	$0.137303\pi$
$168$	0.717150	0.0553293
$169$	29.2166	2.24743
$170$	−0.864734	−0.0663221
$171$	2.41602	0.184757
$172$	−2.86373	−0.218358
$173$	25.8598	1.96609	0.983044	−	0.183372i	$-0.0587013\pi$
$173$	25.8598	1.96609	0.983044	+	0.183372i	$0.0587013\pi$
$174$	1.00166	0.0759355
$175$	4.50575	0.340602
$176$	2.33898	0.176307
$177$	−1.31211	−0.0986241
$178$	14.0546	1.05343
$179$	−8.61773	−0.644120	−0.322060	−	0.946719i	$-0.604375\pi$
$179$	−8.61773	−0.644120	−0.322060	+	0.946719i	$0.604375\pi$
$180$	1.07700	0.0802747
$181$	−14.8729	−1.10549	−0.552746	−	0.833350i	$-0.686420\pi$
$181$	−14.8729	−1.10549	−0.552746	+	0.833350i	$0.686420\pi$
$182$	6.09749	0.451976
$183$	−1.88226	−0.139140
$184$	3.50222	0.258187
$185$	−1.01515	−0.0746351
$186$	−3.69666	−0.271052
$187$	4.53726	0.331797
$188$	2.15639	0.157271
$189$	−3.88410	−0.282526
$190$	0.445775	0.0323399
$191$	26.5713	1.92263	0.961316	−	0.275448i	$-0.0888261\pi$
$191$	26.5713	1.92263	0.961316	+	0.275448i	$0.0888261\pi$
$192$	−0.764189	−0.0551506
$193$	9.14555	0.658311	0.329155	−	0.944276i	$-0.393236\pi$
$193$	9.14555	0.658311	0.329155	+	0.944276i	$0.393236\pi$
$194$	−16.8131	−1.20711
$195$	−2.21339	−0.158504
$196$	−6.11932	−0.437094
$197$	−6.29190	−0.448280	−0.224140	−	0.974557i	$-0.571957\pi$
$197$	−6.29190	−0.448280	−0.224140	+	0.974557i	$0.571957\pi$
$198$	−5.65101	−0.401600
$199$	12.9988	0.921461	0.460730	−	0.887540i	$-0.347588\pi$
$199$	12.9988	0.921461	0.460730	+	0.887540i	$0.347588\pi$
$200$	−4.80128	−0.339502
$201$	−3.52513	−0.248643
$202$	−7.61087	−0.535499
$203$	1.23007	0.0863336
$204$	−1.48241	−0.103789
$205$	3.58009	0.250044
$206$	−2.78620	−0.194124
$207$	−8.46141	−0.588109
$208$	−6.49743	−0.450515
$209$	−2.33898	−0.161791
$210$	−0.319687	−0.0220605
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	3.08544	0.211909
$213$	−6.12310	−0.419548
$214$	3.42104	0.233858
$215$	1.27658	0.0870620
$216$	4.13886	0.281614
$217$	−4.53961	−0.308169
$218$	−9.39884	−0.636570
$219$	−7.96051	−0.537922
$220$	−1.04266	−0.0702960
$221$	−12.6040	−0.847837
$222$	−1.74026	−0.116799
$223$	−7.52754	−0.504081	−0.252041	−	0.967717i	$-0.581102\pi$
$223$	−7.52754	−0.504081	−0.252041	+	0.967717i	$0.581102\pi$
$224$	−0.938446	−0.0627026
$225$	11.6000	0.773332
$226$	5.98637	0.398208
$227$	14.5955	0.968741	0.484370	−	0.874863i	$-0.339049\pi$
$227$	14.5955	0.968741	0.484370	+	0.874863i	$0.339049\pi$
$228$	0.764189	0.0506096
$229$	0.825160	0.0545281	0.0272641	−	0.999628i	$-0.491321\pi$
$229$	0.825160	0.0545281	0.0272641	+	0.999628i	$0.491321\pi$
$230$	−1.56120	−0.102943
$231$	1.67740	0.110365
$232$	−1.31075	−0.0860547
$233$	−3.32946	−0.218120	−0.109060	−	0.994035i	$-0.534784\pi$
$233$	−3.32946	−0.218120	−0.109060	+	0.994035i	$0.534784\pi$
$234$	15.6979	1.02620
$235$	−0.961264	−0.0627059
$236$	1.71699	0.111767
$237$	−0.287181	−0.0186544
$238$	−1.82044	−0.118002
$239$	25.7371	1.66479	0.832397	−	0.554179i	$-0.186968\pi$
$239$	25.7371	1.66479	0.832397	+	0.554179i	$0.186968\pi$
$240$	0.340656	0.0219893
$241$	−16.2372	−1.04593	−0.522964	−	0.852355i	$-0.675174\pi$
$241$	−16.2372	−1.04593	−0.522964	+	0.852355i	$0.675174\pi$
$242$	−5.52917	−0.355429
$243$	−15.5384	−0.996790
$244$	2.46308	0.157682
$245$	2.72784	0.174275
$246$	6.13733	0.391302
$247$	6.49743	0.413421
$248$	4.83737	0.307173
$249$	−4.75292	−0.301204
$250$	4.36917	0.276330
$251$	21.4672	1.35499	0.677497	−	0.735525i	$-0.263065\pi$
$251$	21.4672	1.35499	0.677497	+	0.735525i	$0.263065\pi$
$252$	2.26730	0.142826
$253$	8.19162	0.515003
$254$	3.86438	0.242473
$255$	0.660820	0.0413822
$256$	1.00000	0.0625000
$257$	−13.1660	−0.821273	−0.410636	−	0.911799i	$-0.634693\pi$
$257$	−13.1660	−0.821273	−0.410636	+	0.911799i	$0.634693\pi$
$258$	2.18843	0.136246
$259$	−2.13709	−0.132792
$260$	2.89639	0.179626
$261$	3.16678	0.196019
$262$	18.3402	1.13306
$263$	−20.5440	−1.26680	−0.633399	−	0.773826i	$-0.718341\pi$
$263$	−20.5440	−1.26680	−0.633399	+	0.773826i	$0.718341\pi$
$264$	−1.78742	−0.110008
$265$	−1.37541	−0.0844909
$266$	0.938446	0.0575398
$267$	−10.7403	−0.657298
$268$	4.61290	0.281778
$269$	15.2113	0.927450	0.463725	−	0.885979i	$-0.346513\pi$
$269$	15.2113	0.927450	0.463725	+	0.885979i	$0.346513\pi$
$270$	−1.84500	−0.112283
$271$	−28.2783	−1.71779	−0.858893	−	0.512156i	$-0.828847\pi$
$271$	−28.2783	−1.71779	−0.858893	+	0.512156i	$0.828847\pi$
$272$	1.93985	0.117620
$273$	−4.65963	−0.282014
$274$	−11.4988	−0.694670
$275$	−11.2301	−0.677201
$276$	−2.67636	−0.161098
$277$	4.85219	0.291540	0.145770	−	0.989319i	$-0.453434\pi$
$277$	4.85219	0.291540	0.145770	+	0.989319i	$0.453434\pi$
$278$	4.45298	0.267072
$279$	−11.6871	−0.699691
$280$	0.418336	0.0250003
$281$	17.6581	1.05339	0.526697	−	0.850053i	$-0.323430\pi$
$281$	17.6581	1.05339	0.526697	+	0.850053i	$0.323430\pi$
$282$	−1.64789	−0.0981303
$283$	−16.3055	−0.969259	−0.484630	−	0.874719i	$-0.661046\pi$
$283$	−16.3055	−0.969259	−0.484630	+	0.874719i	$0.661046\pi$
$284$	8.01255	0.475457
$285$	−0.340656	−0.0201787
$286$	−15.1974	−0.898638
$287$	7.53682	0.444884
$288$	−2.41602	−0.142365
$289$	−13.2370	−0.778647
$290$	0.584298	0.0343111
$291$	12.8484	0.753187
$292$	10.4169	0.609605
$293$	−13.4661	−0.786699	−0.393350	−	0.919389i	$-0.628684\pi$
$293$	−13.4661	−0.786699	−0.393350	+	0.919389i	$0.628684\pi$
$294$	4.67632	0.272728
$295$	−0.765393	−0.0445629
$296$	2.27726	0.132363
$297$	9.68071	0.561732
$298$	8.24566	0.477658
$299$	−22.7554	−1.31598
$300$	3.66909	0.211835
$301$	2.68746	0.154903
$302$	15.8642	0.912882
$303$	5.81614	0.334128
$304$	−1.00000	−0.0573539
$305$	−1.09798	−0.0628700
$306$	−4.68670	−0.267921
$307$	22.3795	1.27727	0.638633	−	0.769511i	$-0.279500\pi$
$307$	22.3795	1.27727	0.638633	+	0.769511i	$0.279500\pi$
$308$	−2.19501	−0.125072
$309$	2.12919	0.121125
$310$	−2.15638	−0.122474
$311$	−2.35198	−0.133369	−0.0666844	−	0.997774i	$-0.521242\pi$
$311$	−2.35198	−0.133369	−0.0666844	+	0.997774i	$0.521242\pi$
$312$	4.96526	0.281103
$313$	−6.37098	−0.360109	−0.180054	−	0.983657i	$-0.557627\pi$
$313$	−6.37098	−0.360109	−0.180054	+	0.983657i	$0.557627\pi$
$314$	−0.995625	−0.0561864
$315$	−1.01071	−0.0569468
$316$	0.375799	0.0211403
$317$	17.7481	0.996831	0.498415	−	0.866938i	$-0.333915\pi$
$317$	17.7481	0.996831	0.498415	+	0.866938i	$0.333915\pi$
$318$	−2.35786	−0.132222
$319$	−3.06581	−0.171652
$320$	−0.445775	−0.0249196
$321$	−2.61432	−0.145917
$322$	−3.28664	−0.183158
$323$	−1.93985	−0.107936
$324$	4.08518	0.226954
$325$	31.1960	1.73044
$326$	7.80212	0.432119
$327$	7.18249	0.397193
$328$	−8.03117	−0.443447
$329$	−2.02365	−0.111568
$330$	0.796788	0.0438617
$331$	33.0567	1.81696	0.908481	−	0.417926i	$-0.137243\pi$
$331$	33.0567	1.81696	0.908481	+	0.417926i	$0.137243\pi$
$332$	6.21956	0.341343
$333$	−5.50190	−0.301502
$334$	23.4783	1.28467
$335$	−2.05631	−0.112348
$336$	0.717150	0.0391237
$337$	14.7689	0.804512	0.402256	−	0.915527i	$-0.368226\pi$
$337$	14.7689	0.804512	0.402256	+	0.915527i	$0.368226\pi$
$338$	29.2166	1.58917
$339$	−4.57472	−0.248465
$340$	−0.864734	−0.0468968
$341$	11.3145	0.612715
$342$	2.41602	0.130643
$343$	12.3118	0.664773
$344$	−2.86373	−0.154402
$345$	1.19305	0.0642318
$346$	25.8598	1.39023
$347$	4.30574	0.231144	0.115572	−	0.993299i	$-0.463130\pi$
$347$	4.30574	0.231144	0.115572	+	0.993299i	$0.463130\pi$
$348$	1.00166	0.0536945
$349$	−18.1302	−0.970486	−0.485243	−	0.874379i	$-0.661269\pi$
$349$	−18.1302	−0.970486	−0.485243	+	0.874379i	$0.661269\pi$
$350$	4.50575	0.240842
$351$	−26.8919	−1.43539
$352$	2.33898	0.124668
$353$	2.85803	0.152118	0.0760589	−	0.997103i	$-0.475766\pi$
$353$	2.85803	0.152118	0.0760589	+	0.997103i	$0.475766\pi$
$354$	−1.31211	−0.0697378
$355$	−3.57179	−0.189571
$356$	14.0546	0.744890
$357$	1.39116	0.0736280
$358$	−8.61773	−0.455461
$359$	−6.66319	−0.351670	−0.175835	−	0.984420i	$-0.556262\pi$
$359$	−6.66319	−0.351670	−0.175835	+	0.984420i	$0.556262\pi$
$360$	1.07700	0.0567628
$361$	1.00000	0.0526316
$362$	−14.8729	−0.781701
$363$	4.22533	0.221772
$364$	6.09749	0.319595
$365$	−4.64361	−0.243058
$366$	−1.88226	−0.0983871
$367$	−36.3545	−1.89769	−0.948844	−	0.315746i	$-0.897745\pi$
$367$	−36.3545	−1.89769	−0.948844	+	0.315746i	$0.897745\pi$
$368$	3.50222	0.182566
$369$	19.4034	1.01010
$370$	−1.01515	−0.0527750
$371$	−2.89552	−0.150328
$372$	−3.69666	−0.191663
$373$	−15.6955	−0.812681	−0.406340	−	0.913722i	$-0.633195\pi$
$373$	−15.6955	−0.812681	−0.406340	+	0.913722i	$0.633195\pi$
$374$	4.53726	0.234616
$375$	−3.33887	−0.172418
$376$	2.15639	0.111207
$377$	8.51648	0.438621
$378$	−3.88410	−0.199776
$379$	−28.0313	−1.43987	−0.719934	−	0.694042i	$-0.755828\pi$
$379$	−28.0313	−1.43987	−0.719934	+	0.694042i	$0.755828\pi$
$380$	0.445775	0.0228678
$381$	−2.95311	−0.151293
$382$	26.5713	1.35951
$383$	8.23090	0.420579	0.210290	−	0.977639i	$-0.432559\pi$
$383$	8.23090	0.420579	0.210290	+	0.977639i	$0.432559\pi$
$384$	−0.764189	−0.0389974
$385$	0.978479	0.0498679
$386$	9.14555	0.465496
$387$	6.91882	0.351704
$388$	−16.8131	−0.853557
$389$	−5.79423	−0.293779	−0.146890	−	0.989153i	$-0.546926\pi$
$389$	−5.79423	−0.293779	−0.146890	+	0.989153i	$0.546926\pi$
$390$	−2.21339	−0.112079
$391$	6.79376	0.343575
$392$	−6.11932	−0.309072
$393$	−14.0154	−0.706984
$394$	−6.29190	−0.316982
$395$	−0.167522	−0.00842893
$396$	−5.65101	−0.283974
$397$	−1.96987	−0.0988648	−0.0494324	−	0.998777i	$-0.515741\pi$
$397$	−1.96987	−0.0988648	−0.0494324	+	0.998777i	$0.515741\pi$
$398$	12.9988	0.651571
$399$	−0.717150	−0.0359024
$400$	−4.80128	−0.240064
$401$	−15.0980	−0.753957	−0.376978	−	0.926222i	$-0.623037\pi$
$401$	−15.0980	−0.753957	−0.376978	+	0.926222i	$0.623037\pi$
$402$	−3.52513	−0.175817
$403$	−31.4304	−1.56566
$404$	−7.61087	−0.378655
$405$	−1.82107	−0.0904896
$406$	1.23007	0.0610471
$407$	5.32647	0.264024
$408$	−1.48241	−0.0733901
$409$	−10.4789	−0.518147	−0.259074	−	0.965858i	$-0.583417\pi$
$409$	−10.4789	−0.518147	−0.259074	+	0.965858i	$0.583417\pi$
$410$	3.58009	0.176808
$411$	8.78729	0.433445
$412$	−2.78620	−0.137266
$413$	−1.61131	−0.0792872
$414$	−8.46141	−0.415856
$415$	−2.77252	−0.136098
$416$	−6.49743	−0.318563
$417$	−3.40292	−0.166642
$418$	−2.33898	−0.114403
$419$	3.20378	0.156515	0.0782574	−	0.996933i	$-0.475064\pi$
$419$	3.20378	0.156515	0.0782574	+	0.996933i	$0.475064\pi$
$420$	−0.319687	−0.0155992
$421$	3.79862	0.185133	0.0925667	−	0.995706i	$-0.470493\pi$
$421$	3.79862	0.185133	0.0925667	+	0.995706i	$0.470493\pi$
$422$	−1.00000	−0.0486792
$423$	−5.20987	−0.253312
$424$	3.08544	0.149842
$425$	−9.31375	−0.451783
$426$	−6.12310	−0.296665
$427$	−2.31147	−0.111860
$428$	3.42104	0.165362
$429$	11.6137	0.560712
$430$	1.27658	0.0615621
$431$	27.0164	1.30134	0.650668	−	0.759362i	$-0.274489\pi$
$431$	27.0164	1.30134	0.650668	+	0.759362i	$0.274489\pi$
$432$	4.13886	0.199131
$433$	−13.8771	−0.666891	−0.333445	−	0.942769i	$-0.608211\pi$
$433$	−13.8771	−0.666891	−0.333445	+	0.942769i	$0.608211\pi$
$434$	−4.53961	−0.217908
$435$	−0.446514	−0.0214087
$436$	−9.39884	−0.450123
$437$	−3.50222	−0.167534
$438$	−7.96051	−0.380368
$439$	3.16248	0.150937	0.0754684	−	0.997148i	$-0.475955\pi$
$439$	3.16248	0.150937	0.0754684	+	0.997148i	$0.475955\pi$
$440$	−1.04266	−0.0497068
$441$	14.7844	0.704018
$442$	−12.6040	−0.599511
$443$	5.99833	0.284989	0.142495	−	0.989796i	$-0.454488\pi$
$443$	5.99833	0.284989	0.142495	+	0.989796i	$0.454488\pi$
$444$	−1.74026	−0.0825891
$445$	−6.26517	−0.296997
$446$	−7.52754	−0.356439
$447$	−6.30124	−0.298038
$448$	−0.938446	−0.0443374
$449$	37.6856	1.77850	0.889248	−	0.457426i	$-0.151229\pi$
$449$	37.6856	1.77850	0.889248	+	0.457426i	$0.151229\pi$
$450$	11.6000	0.546828
$451$	−18.7847	−0.884539
$452$	5.98637	0.281575
$453$	−12.1232	−0.569599
$454$	14.5955	0.685003
$455$	−2.71811	−0.127427
$456$	0.764189	0.0357864
$457$	30.0152	1.40405	0.702026	−	0.712151i	$-0.252279\pi$
$457$	30.0152	1.40405	0.702026	+	0.712151i	$0.252279\pi$
$458$	0.825160	0.0385572
$459$	8.02875	0.374750
$460$	−1.56120	−0.0727914
$461$	20.8735	0.972177	0.486089	−	0.873910i	$-0.338423\pi$
$461$	20.8735	0.972177	0.486089	+	0.873910i	$0.338423\pi$
$462$	1.67740	0.0780397
$463$	1.49128	0.0693056	0.0346528	−	0.999399i	$-0.488967\pi$
$463$	1.49128	0.0693056	0.0346528	+	0.999399i	$0.488967\pi$
$464$	−1.31075	−0.0608499
$465$	1.64788	0.0764185
$466$	−3.32946	−0.154234
$467$	30.5393	1.41319	0.706595	−	0.707618i	$-0.250230\pi$
$467$	30.5393	1.41319	0.706595	+	0.707618i	$0.250230\pi$
$468$	15.6979	0.725635
$469$	−4.32896	−0.199893
$470$	−0.961264	−0.0443398
$471$	0.760846	0.0350579
$472$	1.71699	0.0790311
$473$	−6.69822	−0.307984
$474$	−0.287181	−0.0131907
$475$	4.80128	0.220298
$476$	−1.82044	−0.0834397
$477$	−7.45448	−0.341317
$478$	25.7371	1.17719
$479$	−9.83352	−0.449305	−0.224652	−	0.974439i	$-0.572125\pi$
$479$	−9.83352	−0.449305	−0.224652	+	0.974439i	$0.572125\pi$
$480$	0.340656	0.0155488
$481$	−14.7964	−0.674656
$482$	−16.2372	−0.739583
$483$	2.51162	0.114283
$484$	−5.52917	−0.251326
$485$	7.49487	0.340324
$486$	−15.5384	−0.704837
$487$	35.4027	1.60425	0.802125	−	0.597156i	$-0.203703\pi$
$487$	35.4027	1.60425	0.802125	+	0.597156i	$0.203703\pi$
$488$	2.46308	0.111498
$489$	−5.96229	−0.269624
$490$	2.72784	0.123231
$491$	40.3906	1.82280	0.911400	−	0.411521i	$-0.135002\pi$
$491$	40.3906	1.82280	0.911400	+	0.411521i	$0.135002\pi$
$492$	6.13733	0.276692
$493$	−2.54265	−0.114515
$494$	6.49743	0.292333
$495$	2.51908	0.113224
$496$	4.83737	0.217204
$497$	−7.51935	−0.337289
$498$	−4.75292	−0.212983
$499$	−39.7386	−1.77894	−0.889472	−	0.456989i	$-0.848928\pi$
$499$	−39.7386	−1.77894	−0.889472	+	0.456989i	$0.848928\pi$
$500$	4.36917	0.195395
$501$	−17.9418	−0.801582
$502$	21.4672	0.958126
$503$	−15.4051	−0.686878	−0.343439	−	0.939175i	$-0.611592\pi$
$503$	−15.4051	−0.686878	−0.343439	+	0.939175i	$0.611592\pi$
$504$	2.26730	0.100994
$505$	3.39273	0.150975
$506$	8.19162	0.364162
$507$	−22.3270	−0.991576
$508$	3.86438	0.171454
$509$	14.8372	0.657649	0.328824	−	0.944391i	$-0.393348\pi$
$509$	14.8372	0.657649	0.328824	+	0.944391i	$0.393348\pi$
$510$	0.660820	0.0292616
$511$	−9.77574	−0.432453
$512$	1.00000	0.0441942
$513$	−4.13886	−0.182735
$514$	−13.1660	−0.580728
$515$	1.24202	0.0547299
$516$	2.18843	0.0963404
$517$	5.04375	0.221824
$518$	−2.13709	−0.0938983
$519$	−19.7618	−0.867447
$520$	2.89639	0.127015
$521$	2.03437	0.0891275	0.0445637	−	0.999007i	$-0.485810\pi$
$521$	2.03437	0.0891275	0.0445637	+	0.999007i	$0.485810\pi$
$522$	3.16678	0.138606
$523$	−25.5625	−1.11777	−0.558885	−	0.829245i	$-0.688771\pi$
$523$	−25.5625	−1.11777	−0.558885	+	0.829245i	$0.688771\pi$
$524$	18.3402	0.801197
$525$	−3.44324	−0.150275
$526$	−20.5440	−0.895761
$527$	9.38374	0.408762
$528$	−1.78742	−0.0777876
$529$	−10.7345	−0.466716
$530$	−1.37541	−0.0597441
$531$	−4.14829	−0.180020
$532$	0.938446	0.0406868
$533$	52.1819	2.26025
$534$	−10.7403	−0.464780
$535$	−1.52501	−0.0659321
$536$	4.61290	0.199247
$537$	6.58558	0.284189
$538$	15.2113	0.655806
$539$	−14.3130	−0.616503
$540$	−1.84500	−0.0793961
$541$	38.6920	1.66350	0.831749	−	0.555152i	$-0.187340\pi$
$541$	38.6920	1.66350	0.831749	+	0.555152i	$0.187340\pi$
$542$	−28.2783	−1.21466
$543$	11.3657	0.487748
$544$	1.93985	0.0831702
$545$	4.18977	0.179470
$546$	−4.65963	−0.199414
$547$	−9.98396	−0.426883	−0.213442	−	0.976956i	$-0.568467\pi$
$547$	−9.98396	−0.426883	−0.213442	+	0.976956i	$0.568467\pi$
$548$	−11.4988	−0.491206
$549$	−5.95083	−0.253975
$550$	−11.2301	−0.478854
$551$	1.31075	0.0558397
$552$	−2.67636	−0.113913
$553$	−0.352667	−0.0149969
$554$	4.85219	0.206150
$555$	0.775764	0.0329293
$556$	4.45298	0.188848
$557$	3.96418	0.167968	0.0839839	−	0.996467i	$-0.473236\pi$
$557$	3.96418	0.167968	0.0839839	+	0.996467i	$0.473236\pi$
$558$	−11.6871	−0.494756
$559$	18.6069	0.786988
$560$	0.418336	0.0176779
$561$	−3.46732	−0.146391
$562$	17.6581	0.744862
$563$	−22.5379	−0.949858	−0.474929	−	0.880024i	$-0.657526\pi$
$563$	−22.5379	−0.949858	−0.474929	+	0.880024i	$0.657526\pi$
$564$	−1.64789	−0.0693886
$565$	−2.66857	−0.112268
$566$	−16.3055	−0.685370
$567$	−3.83372	−0.161001
$568$	8.01255	0.336199
$569$	14.9334	0.626040	0.313020	−	0.949747i	$-0.398659\pi$
$569$	14.9334	0.626040	0.313020	+	0.949747i	$0.398659\pi$
$570$	−0.340656	−0.0142685
$571$	−1.25242	−0.0524120	−0.0262060	−	0.999657i	$-0.508343\pi$
$571$	−1.25242	−0.0524120	−0.0262060	+	0.999657i	$0.508343\pi$
$572$	−15.1974	−0.635433
$573$	−20.3055	−0.848274
$574$	7.53682	0.314581
$575$	−16.8152	−0.701240
$576$	−2.41602	−0.100667
$577$	6.93416	0.288673	0.144336	−	0.989529i	$-0.453895\pi$
$577$	6.93416	0.288673	0.144336	+	0.989529i	$0.453895\pi$
$578$	−13.2370	−0.550587
$579$	−6.98893	−0.290450
$580$	0.584298	0.0242616
$581$	−5.83672	−0.242148
$582$	12.8484	0.532584
$583$	7.21679	0.298889
$584$	10.4169	0.431056
$585$	−6.99772	−0.289320
$586$	−13.4661	−0.556280
$587$	18.2346	0.752624	0.376312	−	0.926493i	$-0.377192\pi$
$587$	18.2346	0.752624	0.376312	+	0.926493i	$0.377192\pi$
$588$	4.67632	0.192848
$589$	−4.83737	−0.199320
$590$	−0.765393	−0.0315107
$591$	4.80820	0.197783
$592$	2.27726	0.0935949
$593$	13.8580	0.569082	0.284541	−	0.958664i	$-0.408159\pi$
$593$	13.8580	0.569082	0.284541	+	0.958664i	$0.408159\pi$
$594$	9.68071	0.397204
$595$	0.811506	0.0332685
$596$	8.24566	0.337755
$597$	−9.93354	−0.406553
$598$	−22.7554	−0.930538
$599$	−25.1617	−1.02808	−0.514040	−	0.857766i	$-0.671852\pi$
$599$	−25.1617	−1.02808	−0.514040	+	0.857766i	$0.671852\pi$
$600$	3.66909	0.149790
$601$	−9.12976	−0.372411	−0.186205	−	0.982511i	$-0.559619\pi$
$601$	−9.12976	−0.372411	−0.186205	+	0.982511i	$0.559619\pi$
$602$	2.68746	0.109533
$603$	−11.1448	−0.453853
$604$	15.8642	0.645505
$605$	2.46476	0.100207
$606$	5.81614	0.236265
$607$	45.7800	1.85815	0.929076	−	0.369889i	$-0.120604\pi$
$607$	45.7800	1.85815	0.929076	+	0.369889i	$0.120604\pi$
$608$	−1.00000	−0.0405554
$609$	−0.940002	−0.0380908
$610$	−1.09798	−0.0444558
$611$	−14.0110	−0.566823
$612$	−4.68670	−0.189448
$613$	36.8334	1.48769	0.743844	−	0.668353i	$-0.233001\pi$
$613$	36.8334	1.48769	0.743844	+	0.668353i	$0.233001\pi$
$614$	22.3795	0.903163
$615$	−2.73587	−0.110321
$616$	−2.19501	−0.0884394
$617$	−9.04274	−0.364047	−0.182023	−	0.983294i	$-0.558265\pi$
$617$	−9.04274	−0.364047	−0.182023	+	0.983294i	$0.558265\pi$
$618$	2.12919	0.0856484
$619$	−6.06037	−0.243587	−0.121793	−	0.992555i	$-0.538865\pi$
$619$	−6.06037	−0.243587	−0.121793	+	0.992555i	$0.538865\pi$
$620$	−2.15638	−0.0866021
$621$	14.4952	0.581672
$622$	−2.35198	−0.0943059
$623$	−13.1894	−0.528424
$624$	4.96526	0.198770
$625$	22.0588	0.882350
$626$	−6.37098	−0.254635
$627$	1.78742	0.0713828
$628$	−0.995625	−0.0397298
$629$	4.41754	0.176139
$630$	−1.01071	−0.0402675
$631$	−7.79035	−0.310129	−0.155064	−	0.987904i	$-0.549559\pi$
$631$	−7.79035	−0.310129	−0.155064	+	0.987904i	$0.549559\pi$
$632$	0.375799	0.0149485
$633$	0.764189	0.0303738
$634$	17.7481	0.704866
$635$	−1.72264	−0.0683610
$636$	−2.35786	−0.0934953
$637$	39.7598	1.57534
$638$	−3.06581	−0.121377
$639$	−19.3584	−0.765808
$640$	−0.445775	−0.0176208
$641$	−28.5563	−1.12791	−0.563953	−	0.825807i	$-0.690720\pi$
$641$	−28.5563	−1.12791	−0.563953	+	0.825807i	$0.690720\pi$
$642$	−2.61432	−0.103179
$643$	−22.4503	−0.885353	−0.442677	−	0.896681i	$-0.645971\pi$
$643$	−22.4503	−0.885353	−0.442677	+	0.896681i	$0.645971\pi$
$644$	−3.28664	−0.129512
$645$	−0.975548	−0.0384122
$646$	−1.93985	−0.0763222
$647$	−17.4199	−0.684848	−0.342424	−	0.939545i	$-0.611248\pi$
$647$	−17.4199	−0.684848	−0.342424	+	0.939545i	$0.611248\pi$
$648$	4.08518	0.160481
$649$	4.01602	0.157642
$650$	31.1960	1.22361
$651$	3.46912	0.135965
$652$	7.80212	0.305555
$653$	−10.3451	−0.404835	−0.202417	−	0.979299i	$-0.564880\pi$
$653$	−10.3451	−0.404835	−0.202417	+	0.979299i	$0.564880\pi$
$654$	7.18249	0.280858
$655$	−8.17562	−0.319448
$656$	−8.03117	−0.313564
$657$	−25.1675	−0.981877
$658$	−2.02365	−0.0788903
$659$	27.4899	1.07085	0.535427	−	0.844582i	$-0.320151\pi$
$659$	27.4899	1.07085	0.535427	+	0.844582i	$0.320151\pi$
$660$	0.796788	0.0310149
$661$	−7.29822	−0.283868	−0.141934	−	0.989876i	$-0.545332\pi$
$661$	−7.29822	−0.283868	−0.141934	+	0.989876i	$0.545332\pi$
$662$	33.0567	1.28479
$663$	9.63184	0.374070
$664$	6.21956	0.241366
$665$	−0.418336	−0.0162224
$666$	−5.50190	−0.213194
$667$	−4.59052	−0.177746
$668$	23.4783	0.908402
$669$	5.75246	0.222403
$670$	−2.05631	−0.0794423
$671$	5.76109	0.222404
$672$	0.717150	0.0276647
$673$	39.0761	1.50627	0.753137	−	0.657863i	$-0.228540\pi$
$673$	39.0761	1.50627	0.753137	+	0.657863i	$0.228540\pi$
$674$	14.7689	0.568876
$675$	−19.8718	−0.764868
$676$	29.2166	1.12371
$677$	14.2293	0.546878	0.273439	−	0.961889i	$-0.411839\pi$
$677$	14.2293	0.546878	0.273439	+	0.961889i	$0.411839\pi$
$678$	−4.57472	−0.175691
$679$	15.7782	0.605512
$680$	−0.864734	−0.0331610
$681$	−11.1538	−0.427413
$682$	11.3145	0.433255
$683$	−31.5817	−1.20844	−0.604220	−	0.796817i	$-0.706515\pi$
$683$	−31.5817	−1.20844	−0.604220	+	0.796817i	$0.706515\pi$
$684$	2.41602	0.0923787
$685$	5.12589	0.195850
$686$	12.3118	0.470066
$687$	−0.630578	−0.0240581
$688$	−2.86373	−0.109179
$689$	−20.0474	−0.763746
$690$	1.19305	0.0454187
$691$	31.9590	1.21578	0.607889	−	0.794022i	$-0.292016\pi$
$691$	31.9590	1.21578	0.607889	+	0.794022i	$0.292016\pi$
$692$	25.8598	0.983044
$693$	5.30317	0.201451
$694$	4.30574	0.163444
$695$	−1.98503	−0.0752963
$696$	1.00166	0.0379678
$697$	−15.5792	−0.590105
$698$	−18.1302	−0.686237
$699$	2.54434	0.0962357
$700$	4.50575	0.170301
$701$	30.4045	1.14836	0.574180	−	0.818729i	$-0.305321\pi$
$701$	30.4045	1.14836	0.574180	+	0.818729i	$0.305321\pi$
$702$	−26.8919	−1.01497
$703$	−2.27726	−0.0858886
$704$	2.33898	0.0881536
$705$	0.734587	0.0276661
$706$	2.85803	0.107564
$707$	7.14239	0.268617
$708$	−1.31211	−0.0493121
$709$	−29.4007	−1.10417	−0.552083	−	0.833789i	$-0.686167\pi$
$709$	−29.4007	−1.10417	−0.552083	+	0.833789i	$0.686167\pi$
$710$	−3.57179	−0.134047
$711$	−0.907936	−0.0340502
$712$	14.0546	0.526717
$713$	16.9415	0.634465
$714$	1.39116	0.0520629
$715$	6.77460	0.253356
$716$	−8.61773	−0.322060
$717$	−19.6680	−0.734515
$718$	−6.66319	−0.248668
$719$	−41.7483	−1.55695	−0.778475	−	0.627675i	$-0.784007\pi$
$719$	−41.7483	−1.55695	−0.778475	+	0.627675i	$0.784007\pi$
$720$	1.07700	0.0401374
$721$	2.61470	0.0973766
$722$	1.00000	0.0372161
$723$	12.4083	0.461468
$724$	−14.8729	−0.552746
$725$	6.29327	0.233726
$726$	4.22533	0.156817
$727$	−9.25790	−0.343356	−0.171678	−	0.985153i	$-0.554919\pi$
$727$	−9.25790	−0.343356	−0.171678	+	0.985153i	$0.554919\pi$
$728$	6.09749	0.225988
$729$	−0.381235	−0.0141198
$730$	−4.64361	−0.171868
$731$	−5.55520	−0.205466
$732$	−1.88226	−0.0695702
$733$	−33.9445	−1.25377	−0.626884	−	0.779113i	$-0.715670\pi$
$733$	−33.9445	−1.25377	−0.626884	+	0.779113i	$0.715670\pi$
$734$	−36.3545	−1.34187
$735$	−2.08458	−0.0768910
$736$	3.50222	0.129094
$737$	10.7895	0.397435
$738$	19.4034	0.714250
$739$	23.5189	0.865156	0.432578	−	0.901597i	$-0.357604\pi$
$739$	23.5189	0.865156	0.432578	+	0.901597i	$0.357604\pi$
$740$	−1.01515	−0.0373175
$741$	−4.96526	−0.182403
$742$	−2.89552	−0.106298
$743$	7.21153	0.264565	0.132283	−	0.991212i	$-0.457769\pi$
$743$	7.21153	0.264565	0.132283	+	0.991212i	$0.457769\pi$
$744$	−3.69666	−0.135526
$745$	−3.67571	−0.134667
$746$	−15.6955	−0.574652
$747$	−15.0266	−0.549793
$748$	4.53726	0.165899
$749$	−3.21046	−0.117308
$750$	−3.33887	−0.121918
$751$	−21.2134	−0.774087	−0.387043	−	0.922062i	$-0.626504\pi$
$751$	−21.2134	−0.774087	−0.387043	+	0.922062i	$0.626504\pi$
$752$	2.15639	0.0786354
$753$	−16.4050	−0.597830
$754$	8.51648	0.310152
$755$	−7.07186	−0.257371
$756$	−3.88410	−0.141263
$757$	30.4940	1.10832	0.554162	−	0.832409i	$-0.313039\pi$
$757$	30.4940	1.10832	0.554162	+	0.832409i	$0.313039\pi$
$758$	−28.0313	−1.01814
$759$	−6.25995	−0.227222
$760$	0.445775	0.0161700
$761$	26.2626	0.952019	0.476009	−	0.879440i	$-0.342083\pi$
$761$	26.2626	0.952019	0.476009	+	0.879440i	$0.342083\pi$
$762$	−2.95311	−0.106980
$763$	8.82030	0.319316
$764$	26.5713	0.961316
$765$	2.08921	0.0755356
$766$	8.23090	0.297394
$767$	−11.1560	−0.402822
$768$	−0.764189	−0.0275753
$769$	−9.83722	−0.354739	−0.177370	−	0.984144i	$-0.556759\pi$
$769$	−9.83722	−0.354739	−0.177370	+	0.984144i	$0.556759\pi$
$770$	0.978479	0.0352619
$771$	10.0613	0.362349
$772$	9.14555	0.329155
$773$	−18.2383	−0.655986	−0.327993	−	0.944680i	$-0.606372\pi$
$773$	−18.2383	−0.655986	−0.327993	+	0.944680i	$0.606372\pi$
$774$	6.91882	0.248692
$775$	−23.2256	−0.834287
$776$	−16.8131	−0.603556
$777$	1.63314	0.0585886
$778$	−5.79423	−0.207733
$779$	8.03117	0.287746
$780$	−2.21339	−0.0792520
$781$	18.7412	0.670613
$782$	6.79376	0.242944
$783$	−5.42500	−0.193874
$784$	−6.11932	−0.218547
$785$	0.443825	0.0158408
$786$	−14.0154	−0.499913
$787$	−15.5519	−0.554366	−0.277183	−	0.960817i	$-0.589401\pi$
$787$	−15.5519	−0.554366	−0.277183	+	0.960817i	$0.589401\pi$
$788$	−6.29190	−0.224140
$789$	15.6995	0.558917
$790$	−0.167522	−0.00596015
$791$	−5.61789	−0.199749
$792$	−5.65101	−0.200800
$793$	−16.0037	−0.568307
$794$	−1.96987	−0.0699080
$795$	1.05107	0.0372778
$796$	12.9988	0.460730
$797$	35.2201	1.24756	0.623780	−	0.781600i	$-0.285596\pi$
$797$	35.2201	1.24756	0.623780	+	0.781600i	$0.285596\pi$
$798$	−0.717150	−0.0253868
$799$	4.18306	0.147986
$800$	−4.80128	−0.169751
$801$	−33.9560	−1.19978
$802$	−15.0980	−0.533128
$803$	24.3650	0.859823
$804$	−3.52513	−0.124322
$805$	1.46510	0.0516381
$806$	−31.4304	−1.10709
$807$	−11.6243	−0.409195
$808$	−7.61087	−0.267749
$809$	−12.6627	−0.445197	−0.222599	−	0.974910i	$-0.571454\pi$
$809$	−12.6627	−0.445197	−0.222599	+	0.974910i	$0.571454\pi$
$810$	−1.82107	−0.0639858
$811$	−18.1668	−0.637922	−0.318961	−	0.947768i	$-0.603334\pi$
$811$	−18.1668	−0.637922	−0.318961	+	0.947768i	$0.603334\pi$
$812$	1.23007	0.0431668
$813$	21.6100	0.757895
$814$	5.32647	0.186693
$815$	−3.47799	−0.121829
$816$	−1.48241	−0.0518947
$817$	2.86373	0.100189
$818$	−10.4789	−0.366386
$819$	−14.7316	−0.514764
$820$	3.58009	0.125022
$821$	−55.2483	−1.92818	−0.964090	−	0.265577i	$-0.914438\pi$
$821$	−55.2483	−1.92818	−0.964090	+	0.265577i	$0.914438\pi$
$822$	8.78729	0.306492
$823$	−5.05842	−0.176326	−0.0881628	−	0.996106i	$-0.528100\pi$
$823$	−5.05842	−0.176326	−0.0881628	+	0.996106i	$0.528100\pi$
$824$	−2.78620	−0.0970620
$825$	8.58193	0.298784
$826$	−1.61131	−0.0560645
$827$	−1.79636	−0.0624657	−0.0312328	−	0.999512i	$-0.509943\pi$
$827$	−1.79636	−0.0624657	−0.0312328	+	0.999512i	$0.509943\pi$
$828$	−8.46141	−0.294054
$829$	18.1787	0.631373	0.315686	−	0.948864i	$-0.397765\pi$
$829$	18.1787	0.631373	0.315686	+	0.948864i	$0.397765\pi$
$830$	−2.77252	−0.0962357
$831$	−3.70799	−0.128629
$832$	−6.49743	−0.225258
$833$	−11.8705	−0.411290
$834$	−3.40292	−0.117833
$835$	−10.4660	−0.362192
$836$	−2.33898	−0.0808953
$837$	20.0212	0.692033
$838$	3.20378	0.110673
$839$	54.9632	1.89754	0.948770	−	0.315967i	$-0.102329\pi$
$839$	54.9632	1.89754	0.948770	+	0.315967i	$0.102329\pi$
$840$	−0.319687	−0.0110303
$841$	−27.2819	−0.940757
$842$	3.79862	0.130909
$843$	−13.4941	−0.464762
$844$	−1.00000	−0.0344214
$845$	−13.0240	−0.448039
$846$	−5.20987	−0.179119
$847$	5.18883	0.178290
$848$	3.08544	0.105955
$849$	12.4605	0.427642
$850$	−9.31375	−0.319459
$851$	7.97547	0.273396
$852$	−6.12310	−0.209774
$853$	−49.1043	−1.68130	−0.840650	−	0.541579i	$-0.817827\pi$
$853$	−49.1043	−1.68130	−0.840650	+	0.541579i	$0.817827\pi$
$854$	−2.31147	−0.0790967
$855$	−1.07700	−0.0368326
$856$	3.42104	0.116929
$857$	−3.95413	−0.135070	−0.0675352	−	0.997717i	$-0.521513\pi$
$857$	−3.95413	−0.135070	−0.0675352	+	0.997717i	$0.521513\pi$
$858$	11.6137	0.396483
$859$	−25.5395	−0.871397	−0.435698	−	0.900093i	$-0.643499\pi$
$859$	−25.5395	−0.871397	−0.435698	+	0.900093i	$0.643499\pi$
$860$	1.27658	0.0435310
$861$	−5.75955	−0.196285
$862$	27.0164	0.920184
$863$	−42.8897	−1.45998	−0.729990	−	0.683457i	$-0.760476\pi$
$863$	−42.8897	−1.45998	−0.729990	+	0.683457i	$0.760476\pi$
$864$	4.13886	0.140807
$865$	−11.5277	−0.391952
$866$	−13.8771	−0.471563
$867$	10.1156	0.343543
$868$	−4.53961	−0.154084
$869$	0.878986	0.0298176
$870$	−0.446514	−0.0151382
$871$	−29.9720	−1.01556
$872$	−9.39884	−0.318285
$873$	40.6208	1.37480
$874$	−3.50222	−0.118464
$875$	−4.10023	−0.138613
$876$	−7.96051	−0.268961
$877$	13.6457	0.460782	0.230391	−	0.973098i	$-0.425999\pi$
$877$	13.6457	0.460782	0.230391	+	0.973098i	$0.425999\pi$
$878$	3.16248	0.106728
$879$	10.2907	0.347095
$880$	−1.04266	−0.0351480
$881$	−25.6699	−0.864840	−0.432420	−	0.901672i	$-0.642340\pi$
$881$	−25.6699	−0.864840	−0.432420	+	0.901672i	$0.642340\pi$
$882$	14.7844	0.497816
$883$	38.5043	1.29577	0.647887	−	0.761737i	$-0.275653\pi$
$883$	38.5043	1.29577	0.647887	+	0.761737i	$0.275653\pi$
$884$	−12.6040	−0.423918
$885$	0.584905	0.0196614
$886$	5.99833	0.201518
$887$	−37.6529	−1.26426	−0.632131	−	0.774862i	$-0.717819\pi$
$887$	−37.6529	−1.26426	−0.632131	+	0.774862i	$0.717819\pi$
$888$	−1.74026	−0.0583993
$889$	−3.62651	−0.121629
$890$	−6.26517	−0.210009
$891$	9.55515	0.320109
$892$	−7.52754	−0.252041
$893$	−2.15639	−0.0721608
$894$	−6.30124	−0.210745
$895$	3.84157	0.128409
$896$	−0.938446	−0.0313513
$897$	17.3894	0.580616
$898$	37.6856	1.25759
$899$	−6.34056	−0.211470
$900$	11.6000	0.386666
$901$	5.98528	0.199399
$902$	−18.7847	−0.625464
$903$	−2.05373	−0.0683437
$904$	5.98637	0.199104
$905$	6.62995	0.220387
$906$	−12.1232	−0.402768
$907$	45.6997	1.51743	0.758716	−	0.651421i	$-0.225827\pi$
$907$	45.6997	1.51743	0.758716	+	0.651421i	$0.225827\pi$
$908$	14.5955	0.484370
$909$	18.3880	0.609890
$910$	−2.71811	−0.0901043
$911$	28.6733	0.949988	0.474994	−	0.879989i	$-0.342450\pi$
$911$	28.6733	0.949988	0.474994	+	0.879989i	$0.342450\pi$
$912$	0.764189	0.0253048
$913$	14.5474	0.481450
$914$	30.0152	0.992815
$915$	0.839063	0.0277386
$916$	0.825160	0.0272641
$917$	−17.2113	−0.568368
$918$	8.02875	0.264988
$919$	−8.74883	−0.288597	−0.144299	−	0.989534i	$-0.546093\pi$
$919$	−8.74883	−0.288597	−0.144299	+	0.989534i	$0.546093\pi$
$920$	−1.56120	−0.0514713
$921$	−17.1022	−0.563536
$922$	20.8735	0.687433
$923$	−52.0610	−1.71361
$924$	1.67740	0.0551824
$925$	−10.9338	−0.359501
$926$	1.49128	0.0490065
$927$	6.73151	0.221092
$928$	−1.31075	−0.0430274
$929$	36.8764	1.20987	0.604937	−	0.796273i	$-0.293198\pi$
$929$	36.8764	1.20987	0.604937	+	0.796273i	$0.293198\pi$
$930$	1.64788	0.0540361
$931$	6.11932	0.200553
$932$	−3.32946	−0.109060
$933$	1.79736	0.0588429
$934$	30.5393	0.999276
$935$	−2.02260	−0.0661460
$936$	15.6979	0.513101
$937$	−3.28529	−0.107326	−0.0536629	−	0.998559i	$-0.517090\pi$
$937$	−3.28529	−0.107326	−0.0536629	+	0.998559i	$0.517090\pi$
$938$	−4.32896	−0.141345
$939$	4.86863	0.158882
$940$	−0.961264	−0.0313530
$941$	−60.3501	−1.96736	−0.983678	−	0.179938i	$-0.942410\pi$
$941$	−60.3501	−1.96736	−0.983678	+	0.179938i	$0.942410\pi$
$942$	0.760846	0.0247897
$943$	−28.1269	−0.915938
$944$	1.71699	0.0558834
$945$	1.73143	0.0563235
$946$	−6.69822	−0.217778
$947$	−28.3231	−0.920379	−0.460189	−	0.887821i	$-0.652218\pi$
$947$	−28.3231	−0.920379	−0.460189	+	0.887821i	$0.652218\pi$
$948$	−0.287181	−0.00932722
$949$	−67.6833	−2.19709
$950$	4.80128	0.155774
$951$	−13.5629	−0.439807
$952$	−1.82044	−0.0590008
$953$	11.0443	0.357761	0.178880	−	0.983871i	$-0.442753\pi$
$953$	11.0443	0.357761	0.178880	+	0.983871i	$0.442753\pi$
$954$	−7.45448	−0.241348
$955$	−11.8448	−0.383289
$956$	25.7371	0.832397
$957$	2.34286	0.0757339
$958$	−9.83352	−0.317706
$959$	10.7910	0.348461
$960$	0.340656	0.0109946
$961$	−7.59990	−0.245158
$962$	−14.7964	−0.477054
$963$	−8.26529	−0.266345
$964$	−16.2372	−0.522964
$965$	−4.07685	−0.131239
$966$	2.51162	0.0808100
$967$	−33.5523	−1.07897	−0.539484	−	0.841996i	$-0.681381\pi$
$967$	−33.5523	−1.07897	−0.539484	+	0.841996i	$0.681381\pi$
$968$	−5.52917	−0.177714
$969$	1.48241	0.0476218
$970$	7.49487	0.240646
$971$	−25.7436	−0.826151	−0.413076	−	0.910697i	$-0.635545\pi$
$971$	−25.7436	−0.826151	−0.413076	+	0.910697i	$0.635545\pi$
$972$	−15.5384	−0.498395
$973$	−4.17888	−0.133969
$974$	35.4027	1.13438
$975$	−23.8396	−0.763479
$976$	2.46308	0.0788412
$977$	61.1818	1.95738	0.978689	−	0.205349i	$-0.0658329\pi$
$977$	61.1818	1.95738	0.978689	+	0.205349i	$0.0658329\pi$
$978$	−5.96229	−0.190653
$979$	32.8733	1.05064
$980$	2.72784	0.0871376
$981$	22.7077	0.725002
$982$	40.3906	1.28891
$983$	9.78730	0.312166	0.156083	−	0.987744i	$-0.450113\pi$
$983$	9.78730	0.312166	0.156083	+	0.987744i	$0.450113\pi$
$984$	6.13733	0.195651
$985$	2.80477	0.0893675
$986$	−2.54265	−0.0809743
$987$	1.54645	0.0492242
$988$	6.49743	0.206711
$989$	−10.0294	−0.318917
$990$	2.51908	0.0800616
$991$	−23.9720	−0.761497	−0.380748	−	0.924679i	$-0.624334\pi$
$991$	−23.9720	−0.761497	−0.380748	+	0.924679i	$0.624334\pi$
$992$	4.83737	0.153586
$993$	−25.2616	−0.801652
$994$	−7.51935	−0.238499
$995$	−5.79454	−0.183699
$996$	−4.75292	−0.150602
$997$	37.4057	1.18465	0.592325	−	0.805699i	$-0.298210\pi$
$997$	37.4057	1.18465	0.592325	+	0.805699i	$0.298210\pi$
$998$	−39.7386	−1.25790
$999$	9.42527	0.298202

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.19	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.764189 q^{3} +1.00000 q^{4} -0.445775 q^{5} -0.764189 q^{6} -0.938446 q^{7} +1.00000 q^{8} -2.41602 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.764189 q^{3} +1.00000 q^{4} -0.445775 q^{5} -0.764189 q^{6} -0.938446 q^{7} +1.00000 q^{8} -2.41602 q^{9} -0.445775 q^{10} +2.33898 q^{11} -0.764189 q^{12} -6.49743 q^{13} -0.938446 q^{14} +0.340656 q^{15} +1.00000 q^{16} +1.93985 q^{17} -2.41602 q^{18} -1.00000 q^{19} -0.445775 q^{20} +0.717150 q^{21} +2.33898 q^{22} +3.50222 q^{23} -0.764189 q^{24} -4.80128 q^{25} -6.49743 q^{26} +4.13886 q^{27} -0.938446 q^{28} -1.31075 q^{29} +0.340656 q^{30} +4.83737 q^{31} +1.00000 q^{32} -1.78742 q^{33} +1.93985 q^{34} +0.418336 q^{35} -2.41602 q^{36} +2.27726 q^{37} -1.00000 q^{38} +4.96526 q^{39} -0.445775 q^{40} -8.03117 q^{41} +0.717150 q^{42} -2.86373 q^{43} +2.33898 q^{44} +1.07700 q^{45} +3.50222 q^{46} +2.15639 q^{47} -0.764189 q^{48} -6.11932 q^{49} -4.80128 q^{50} -1.48241 q^{51} -6.49743 q^{52} +3.08544 q^{53} +4.13886 q^{54} -1.04266 q^{55} -0.938446 q^{56} +0.764189 q^{57} -1.31075 q^{58} +1.71699 q^{59} +0.340656 q^{60} +2.46308 q^{61} +4.83737 q^{62} +2.26730 q^{63} +1.00000 q^{64} +2.89639 q^{65} -1.78742 q^{66} +4.61290 q^{67} +1.93985 q^{68} -2.67636 q^{69} +0.418336 q^{70} +8.01255 q^{71} -2.41602 q^{72} +10.4169 q^{73} +2.27726 q^{74} +3.66909 q^{75} -1.00000 q^{76} -2.19501 q^{77} +4.96526 q^{78} +0.375799 q^{79} -0.445775 q^{80} +4.08518 q^{81} -8.03117 q^{82} +6.21956 q^{83} +0.717150 q^{84} -0.864734 q^{85} -2.86373 q^{86} +1.00166 q^{87} +2.33898 q^{88} +14.0546 q^{89} +1.07700 q^{90} +6.09749 q^{91} +3.50222 q^{92} -3.69666 q^{93} +2.15639 q^{94} +0.445775 q^{95} -0.764189 q^{96} -16.8131 q^{97} -6.11932 q^{98} -5.65101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 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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