LMFDB - Embedded newform 8018.2.a.k.1.4

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:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.03421 q^{3} +1.00000 q^{4} -2.36281 q^{5} -3.03421 q^{6} -0.910676 q^{7} +1.00000 q^{8} +6.20641 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.03421 q^{3} +1.00000 q^{4} -2.36281 q^{5} -3.03421 q^{6} -0.910676 q^{7} +1.00000 q^{8} +6.20641 q^{9} -2.36281 q^{10} -2.58908 q^{11} -3.03421 q^{12} +1.05006 q^{13} -0.910676 q^{14} +7.16925 q^{15} +1.00000 q^{16} -6.94941 q^{17} +6.20641 q^{18} +1.00000 q^{19} -2.36281 q^{20} +2.76318 q^{21} -2.58908 q^{22} -2.67837 q^{23} -3.03421 q^{24} +0.582862 q^{25} +1.05006 q^{26} -9.72890 q^{27} -0.910676 q^{28} -5.00623 q^{29} +7.16925 q^{30} -4.06043 q^{31} +1.00000 q^{32} +7.85580 q^{33} -6.94941 q^{34} +2.15175 q^{35} +6.20641 q^{36} +11.7594 q^{37} +1.00000 q^{38} -3.18608 q^{39} -2.36281 q^{40} +7.52605 q^{41} +2.76318 q^{42} -4.17050 q^{43} -2.58908 q^{44} -14.6646 q^{45} -2.67837 q^{46} -3.63153 q^{47} -3.03421 q^{48} -6.17067 q^{49} +0.582862 q^{50} +21.0860 q^{51} +1.05006 q^{52} -9.88112 q^{53} -9.72890 q^{54} +6.11750 q^{55} -0.910676 q^{56} -3.03421 q^{57} -5.00623 q^{58} -3.88658 q^{59} +7.16925 q^{60} -4.39669 q^{61} -4.06043 q^{62} -5.65203 q^{63} +1.00000 q^{64} -2.48108 q^{65} +7.85580 q^{66} +2.21731 q^{67} -6.94941 q^{68} +8.12671 q^{69} +2.15175 q^{70} -8.42951 q^{71} +6.20641 q^{72} +9.64456 q^{73} +11.7594 q^{74} -1.76852 q^{75} +1.00000 q^{76} +2.35781 q^{77} -3.18608 q^{78} +1.16191 q^{79} -2.36281 q^{80} +10.9003 q^{81} +7.52605 q^{82} -12.6221 q^{83} +2.76318 q^{84} +16.4201 q^{85} -4.17050 q^{86} +15.1899 q^{87} -2.58908 q^{88} -14.5109 q^{89} -14.6646 q^{90} -0.956260 q^{91} -2.67837 q^{92} +12.3202 q^{93} -3.63153 q^{94} -2.36281 q^{95} -3.03421 q^{96} -9.67002 q^{97} -6.17067 q^{98} -16.0689 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9}+O(q^{10}) $ 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9} + 17 q^{10} + 21 q^{11} + 13 q^{12} + 13 q^{13} + 22 q^{14} + 8 q^{15} + 49 q^{16} + 24 q^{17} + 66 q^{18} + 49 q^{19} + 17 q^{20} + 6 q^{21} + 21 q^{22} + 22 q^{23} + 13 q^{24} + 96 q^{25} + 13 q^{26} + 31 q^{27} + 22 q^{28} + 33 q^{29} + 8 q^{30} + 21 q^{31} + 49 q^{32} + 20 q^{33} + 24 q^{34} + 18 q^{35} + 66 q^{36} + 48 q^{37} + 49 q^{38} + 4 q^{39} + 17 q^{40} + 37 q^{41} + 6 q^{42} + 43 q^{43} + 21 q^{44} + 47 q^{45} + 22 q^{46} + 7 q^{47} + 13 q^{48} + 87 q^{49} + 96 q^{50} + 12 q^{51} + 13 q^{52} + 23 q^{53} + 31 q^{54} + 31 q^{55} + 22 q^{56} + 13 q^{57} + 33 q^{58} + 37 q^{59} + 8 q^{60} + 61 q^{61} + 21 q^{62} + 45 q^{63} + 49 q^{64} + 36 q^{65} + 20 q^{66} + 43 q^{67} + 24 q^{68} + 18 q^{69} + 18 q^{70} + 14 q^{71} + 66 q^{72} + 90 q^{73} + 48 q^{74} + 53 q^{75} + 49 q^{76} + 46 q^{77} + 4 q^{78} + 16 q^{79} + 17 q^{80} + 97 q^{81} + 37 q^{82} + 11 q^{83} + 6 q^{84} + 88 q^{85} + 43 q^{86} - 35 q^{87} + 21 q^{88} + 46 q^{89} + 47 q^{90} + 27 q^{91} + 22 q^{92} + 9 q^{93} + 7 q^{94} + 17 q^{95} + 13 q^{96} + 34 q^{97} + 87 q^{98} + 84 q^{99}+O(q^{100}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9 + 17 * q^10 + 21 * q^11 + 13 * q^12 + 13 * q^13 + 22 * q^14 + 8 * q^15 + 49 * q^16 + 24 * q^17 + 66 * q^18 + 49 * q^19 + 17 * q^20 + 6 * q^21 + 21 * q^22 + 22 * q^23 + 13 * q^24 + 96 * q^25 + 13 * q^26 + 31 * q^27 + 22 * q^28 + 33 * q^29 + 8 * q^30 + 21 * q^31 + 49 * q^32 + 20 * q^33 + 24 * q^34 + 18 * q^35 + 66 * q^36 + 48 * q^37 + 49 * q^38 + 4 * q^39 + 17 * q^40 + 37 * q^41 + 6 * q^42 + 43 * q^43 + 21 * q^44 + 47 * q^45 + 22 * q^46 + 7 * q^47 + 13 * q^48 + 87 * q^49 + 96 * q^50 + 12 * q^51 + 13 * q^52 + 23 * q^53 + 31 * q^54 + 31 * q^55 + 22 * q^56 + 13 * q^57 + 33 * q^58 + 37 * q^59 + 8 * q^60 + 61 * q^61 + 21 * q^62 + 45 * q^63 + 49 * q^64 + 36 * q^65 + 20 * q^66 + 43 * q^67 + 24 * q^68 + 18 * q^69 + 18 * q^70 + 14 * q^71 + 66 * q^72 + 90 * q^73 + 48 * q^74 + 53 * q^75 + 49 * q^76 + 46 * q^77 + 4 * q^78 + 16 * q^79 + 17 * q^80 + 97 * q^81 + 37 * q^82 + 11 * q^83 + 6 * q^84 + 88 * q^85 + 43 * q^86 - 35 * q^87 + 21 * q^88 + 46 * q^89 + 47 * q^90 + 27 * q^91 + 22 * q^92 + 9 * q^93 + 7 * q^94 + 17 * q^95 + 13 * q^96 + 34 * q^97 + 87 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.03421	−1.75180	−0.875900	−	0.482493i	$-0.839731\pi$
$3$	−3.03421	−1.75180	−0.875900	+	0.482493i	$0.839731\pi$
$4$	1.00000	0.500000
$5$	−2.36281	−1.05668	−0.528340	−	0.849033i	$-0.677185\pi$
$5$	−2.36281	−1.05668	−0.528340	+	0.849033i	$0.677185\pi$
$6$	−3.03421	−1.23871
$7$	−0.910676	−0.344203	−0.172102	−	0.985079i	$-0.555056\pi$
$7$	−0.910676	−0.344203	−0.172102	+	0.985079i	$0.555056\pi$
$8$	1.00000	0.353553
$9$	6.20641	2.06880
$10$	−2.36281	−0.747186
$11$	−2.58908	−0.780637	−0.390319	−	0.920680i	$-0.627635\pi$
$11$	−2.58908	−0.780637	−0.390319	+	0.920680i	$0.627635\pi$
$12$	−3.03421	−0.875900
$13$	1.05006	0.291233	0.145616	−	0.989341i	$-0.453483\pi$
$13$	1.05006	0.291233	0.145616	+	0.989341i	$0.453483\pi$
$14$	−0.910676	−0.243388
$15$	7.16925	1.85109
$16$	1.00000	0.250000
$17$	−6.94941	−1.68548	−0.842740	−	0.538321i	$-0.819059\pi$
$17$	−6.94941	−1.68548	−0.842740	+	0.538321i	$0.819059\pi$
$18$	6.20641	1.46286
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.36281	−0.528340
$21$	2.76318	0.602975
$22$	−2.58908	−0.551994
$23$	−2.67837	−0.558478	−0.279239	−	0.960222i	$-0.590082\pi$
$23$	−2.67837	−0.558478	−0.279239	+	0.960222i	$0.590082\pi$
$24$	−3.03421	−0.619355
$25$	0.582862	0.116572
$26$	1.05006	0.205933
$27$	−9.72890	−1.87233
$28$	−0.910676	−0.172102
$29$	−5.00623	−0.929633	−0.464816	−	0.885407i	$-0.653880\pi$
$29$	−5.00623	−0.929633	−0.464816	+	0.885407i	$0.653880\pi$
$30$	7.16925	1.30892
$31$	−4.06043	−0.729275	−0.364637	−	0.931150i	$-0.618807\pi$
$31$	−4.06043	−0.729275	−0.364637	+	0.931150i	$0.618807\pi$
$32$	1.00000	0.176777
$33$	7.85580	1.36752
$34$	−6.94941	−1.19181
$35$	2.15175	0.363713
$36$	6.20641	1.03440
$37$	11.7594	1.93323	0.966615	−	0.256232i	$-0.0824811\pi$
$37$	11.7594	1.93323	0.966615	+	0.256232i	$0.0824811\pi$
$38$	1.00000	0.162221
$39$	−3.18608	−0.510182
$40$	−2.36281	−0.373593
$41$	7.52605	1.17537	0.587685	−	0.809089i	$-0.300039\pi$
$41$	7.52605	1.17537	0.587685	+	0.809089i	$0.300039\pi$
$42$	2.76318	0.426368
$43$	−4.17050	−0.635996	−0.317998	−	0.948091i	$-0.603010\pi$
$43$	−4.17050	−0.635996	−0.317998	+	0.948091i	$0.603010\pi$
$44$	−2.58908	−0.390319
$45$	−14.6646	−2.18606
$46$	−2.67837	−0.394903
$47$	−3.63153	−0.529713	−0.264856	−	0.964288i	$-0.585325\pi$
$47$	−3.63153	−0.529713	−0.264856	+	0.964288i	$0.585325\pi$
$48$	−3.03421	−0.437950
$49$	−6.17067	−0.881524
$50$	0.582862	0.0824291
$51$	21.0860	2.95262
$52$	1.05006	0.145616
$53$	−9.88112	−1.35728	−0.678638	−	0.734473i	$-0.737430\pi$
$53$	−9.88112	−1.35728	−0.678638	+	0.734473i	$0.737430\pi$
$54$	−9.72890	−1.32394
$55$	6.11750	0.824883
$56$	−0.910676	−0.121694
$57$	−3.03421	−0.401890
$58$	−5.00623	−0.657350
$59$	−3.88658	−0.505989	−0.252995	−	0.967468i	$-0.581415\pi$
$59$	−3.88658	−0.505989	−0.252995	+	0.967468i	$0.581415\pi$
$60$	7.16925	0.925546
$61$	−4.39669	−0.562938	−0.281469	−	0.959570i	$-0.590822\pi$
$61$	−4.39669	−0.562938	−0.281469	+	0.959570i	$0.590822\pi$
$62$	−4.06043	−0.515675
$63$	−5.65203	−0.712089
$64$	1.00000	0.125000
$65$	−2.48108	−0.307740
$66$	7.85580	0.966983
$67$	2.21731	0.270887	0.135444	−	0.990785i	$-0.456754\pi$
$67$	2.21731	0.270887	0.135444	+	0.990785i	$0.456754\pi$
$68$	−6.94941	−0.842740
$69$	8.12671	0.978341
$70$	2.15175	0.257184
$71$	−8.42951	−1.00040	−0.500200	−	0.865910i	$-0.666740\pi$
$71$	−8.42951	−1.00040	−0.500200	+	0.865910i	$0.666740\pi$
$72$	6.20641	0.731432
$73$	9.64456	1.12881	0.564405	−	0.825498i	$-0.309106\pi$
$73$	9.64456	1.12881	0.564405	+	0.825498i	$0.309106\pi$
$74$	11.7594	1.36700
$75$	−1.76852	−0.204212
$76$	1.00000	0.114708
$77$	2.35781	0.268698
$78$	−3.18608	−0.360753
$79$	1.16191	0.130725	0.0653623	−	0.997862i	$-0.479180\pi$
$79$	1.16191	0.130725	0.0653623	+	0.997862i	$0.479180\pi$
$80$	−2.36281	−0.264170
$81$	10.9003	1.21114
$82$	7.52605	0.831113
$83$	−12.6221	−1.38545	−0.692727	−	0.721200i	$-0.743591\pi$
$83$	−12.6221	−1.38545	−0.692727	+	0.721200i	$0.743591\pi$
$84$	2.76318	0.301488
$85$	16.4201	1.78101
$86$	−4.17050	−0.449717
$87$	15.1899	1.62853
$88$	−2.58908	−0.275997
$89$	−14.5109	−1.53816	−0.769078	−	0.639155i	$-0.779284\pi$
$89$	−14.5109	−1.53816	−0.769078	+	0.639155i	$0.779284\pi$
$90$	−14.6646	−1.54578
$91$	−0.956260	−0.100243
$92$	−2.67837	−0.279239
$93$	12.3202	1.27754
$94$	−3.63153	−0.374563
$95$	−2.36281	−0.242419
$96$	−3.03421	−0.309677
$97$	−9.67002	−0.981842	−0.490921	−	0.871204i	$-0.663340\pi$
$97$	−9.67002	−0.981842	−0.490921	+	0.871204i	$0.663340\pi$
$98$	−6.17067	−0.623332
$99$	−16.0689	−1.61498
$100$	0.582862	0.0582862
$101$	−4.00338	−0.398352	−0.199176	−	0.979964i	$-0.563826\pi$
$101$	−4.00338	−0.398352	−0.199176	+	0.979964i	$0.563826\pi$
$102$	21.0860	2.08782
$103$	−10.1129	−0.996452	−0.498226	−	0.867047i	$-0.666015\pi$
$103$	−10.1129	−0.996452	−0.498226	+	0.867047i	$0.666015\pi$
$104$	1.05006	0.102966
$105$	−6.52886	−0.637152
$106$	−9.88112	−0.959739
$107$	−12.7264	−1.23031	−0.615155	−	0.788406i	$-0.710907\pi$
$107$	−12.7264	−1.23031	−0.615155	+	0.788406i	$0.710907\pi$
$108$	−9.72890	−0.936164
$109$	16.7579	1.60512	0.802559	−	0.596573i	$-0.203471\pi$
$109$	16.7579	1.60512	0.802559	+	0.596573i	$0.203471\pi$
$110$	6.11750	0.583281
$111$	−35.6804	−3.38663
$112$	−0.910676	−0.0860508
$113$	15.8003	1.48637	0.743185	−	0.669086i	$-0.233314\pi$
$113$	15.8003	1.48637	0.743185	+	0.669086i	$0.233314\pi$
$114$	−3.03421	−0.284179
$115$	6.32846	0.590132
$116$	−5.00623	−0.464816
$117$	6.51707	0.602503
$118$	−3.88658	−0.357788
$119$	6.32866	0.580148
$120$	7.16925	0.654460
$121$	−4.29666	−0.390606
$122$	−4.39669	−0.398057
$123$	−22.8356	−2.05901
$124$	−4.06043	−0.364637
$125$	10.4368	0.933500
$126$	−5.65203	−0.503523
$127$	18.5786	1.64859	0.824293	−	0.566164i	$-0.191573\pi$
$127$	18.5786	1.64859	0.824293	+	0.566164i	$0.191573\pi$
$128$	1.00000	0.0883883
$129$	12.6542	1.11414
$130$	−2.48108	−0.217605
$131$	−12.3247	−1.07681	−0.538407	−	0.842685i	$-0.680974\pi$
$131$	−12.3247	−1.07681	−0.538407	+	0.842685i	$0.680974\pi$
$132$	7.85580	0.683760
$133$	−0.910676	−0.0789656
$134$	2.21731	0.191546
$135$	22.9875	1.97845
$136$	−6.94941	−0.595907
$137$	−15.1981	−1.29846	−0.649229	−	0.760593i	$-0.724908\pi$
$137$	−15.1981	−1.29846	−0.649229	+	0.760593i	$0.724908\pi$
$138$	8.12671	0.691792
$139$	−5.61924	−0.476618	−0.238309	−	0.971189i	$-0.576593\pi$
$139$	−5.61924	−0.476618	−0.238309	+	0.971189i	$0.576593\pi$
$140$	2.15175	0.181856
$141$	11.0188	0.927951
$142$	−8.42951	−0.707389
$143$	−2.71868	−0.227347
$144$	6.20641	0.517201
$145$	11.8287	0.982324
$146$	9.64456	0.798189
$147$	18.7231	1.54425
$148$	11.7594	0.966615
$149$	−13.2702	−1.08713	−0.543567	−	0.839366i	$-0.682927\pi$
$149$	−13.2702	−1.08713	−0.543567	+	0.839366i	$0.682927\pi$
$150$	−1.76852	−0.144399
$151$	16.7175	1.36045	0.680224	−	0.733005i	$-0.261883\pi$
$151$	16.7175	1.36045	0.680224	+	0.733005i	$0.261883\pi$
$152$	1.00000	0.0811107
$153$	−43.1309	−3.48693
$154$	2.35781	0.189998
$155$	9.59402	0.770610
$156$	−3.18608	−0.255091
$157$	−1.49056	−0.118960	−0.0594800	−	0.998230i	$-0.518944\pi$
$157$	−1.49056	−0.118960	−0.0594800	+	0.998230i	$0.518944\pi$
$158$	1.16191	0.0924362
$159$	29.9814	2.37768
$160$	−2.36281	−0.186796
$161$	2.43912	0.192230
$162$	10.9003	0.856407
$163$	−4.23873	−0.332003	−0.166001	−	0.986126i	$-0.553086\pi$
$163$	−4.23873	−0.332003	−0.166001	+	0.986126i	$0.553086\pi$
$164$	7.52605	0.587685
$165$	−18.5618	−1.44503
$166$	−12.6221	−0.979664
$167$	2.00713	0.155316	0.0776581	−	0.996980i	$-0.475256\pi$
$167$	2.00713	0.155316	0.0776581	+	0.996980i	$0.475256\pi$
$168$	2.76318	0.213184
$169$	−11.8974	−0.915183
$170$	16.4201	1.25937
$171$	6.20641	0.474616
$172$	−4.17050	−0.317998
$173$	24.5190	1.86415	0.932074	−	0.362268i	$-0.117997\pi$
$173$	24.5190	1.86415	0.932074	+	0.362268i	$0.117997\pi$
$174$	15.1899	1.15154
$175$	−0.530799	−0.0401246
$176$	−2.58908	−0.195159
$177$	11.7927	0.886392
$178$	−14.5109	−1.08764
$179$	11.1188	0.831056	0.415528	−	0.909580i	$-0.363597\pi$
$179$	11.1188	0.831056	0.415528	+	0.909580i	$0.363597\pi$
$180$	−14.6646	−1.09303
$181$	−13.9432	−1.03639	−0.518195	−	0.855263i	$-0.673396\pi$
$181$	−13.9432	−1.03639	−0.518195	+	0.855263i	$0.673396\pi$
$182$	−0.956260	−0.0708827
$183$	13.3405	0.986155
$184$	−2.67837	−0.197452
$185$	−27.7852	−2.04281
$186$	12.3202	0.903360
$187$	17.9926	1.31575
$188$	−3.63153	−0.264856
$189$	8.85988	0.644461
$190$	−2.36281	−0.171416
$191$	10.1792	0.736538	0.368269	−	0.929719i	$-0.379951\pi$
$191$	10.1792	0.736538	0.368269	+	0.929719i	$0.379951\pi$
$192$	−3.03421	−0.218975
$193$	−7.94880	−0.572167	−0.286083	−	0.958205i	$-0.592353\pi$
$193$	−7.94880	−0.572167	−0.286083	+	0.958205i	$0.592353\pi$
$194$	−9.67002	−0.694267
$195$	7.52811	0.539099
$196$	−6.17067	−0.440762
$197$	16.1314	1.14932	0.574659	−	0.818393i	$-0.305135\pi$
$197$	16.1314	1.14932	0.574659	+	0.818393i	$0.305135\pi$
$198$	−16.0689	−1.14197
$199$	−16.3876	−1.16169	−0.580844	−	0.814015i	$-0.697277\pi$
$199$	−16.3876	−1.16169	−0.580844	+	0.814015i	$0.697277\pi$
$200$	0.582862	0.0412146
$201$	−6.72776	−0.474540
$202$	−4.00338	−0.281677
$203$	4.55905	0.319983
$204$	21.0860	1.47631
$205$	−17.7826	−1.24199
$206$	−10.1129	−0.704598
$207$	−16.6230	−1.15538
$208$	1.05006	0.0728082
$209$	−2.58908	−0.179090
$210$	−6.52886	−0.450534
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−9.88112	−0.678638
$213$	25.5769	1.75250
$214$	−12.7264	−0.869961
$215$	9.85410	0.672044
$216$	−9.72890	−0.661968
$217$	3.69774	0.251019
$218$	16.7579	1.13499
$219$	−29.2636	−1.97745
$220$	6.11750	0.412442
$221$	−7.29727	−0.490867
$222$	−35.6804	−2.39471
$223$	7.77640	0.520746	0.260373	−	0.965508i	$-0.416154\pi$
$223$	7.77640	0.520746	0.260373	+	0.965508i	$0.416154\pi$
$224$	−0.910676	−0.0608471
$225$	3.61748	0.241165
$226$	15.8003	1.05102
$227$	28.3738	1.88324	0.941618	−	0.336684i	$-0.109305\pi$
$227$	28.3738	1.88324	0.941618	+	0.336684i	$0.109305\pi$
$228$	−3.03421	−0.200945
$229$	−3.05247	−0.201713	−0.100856	−	0.994901i	$-0.532158\pi$
$229$	−3.05247	−0.201713	−0.100856	+	0.994901i	$0.532158\pi$
$230$	6.32846	0.417287
$231$	−7.15409	−0.470705
$232$	−5.00623	−0.328675
$233$	11.9028	0.779776	0.389888	−	0.920862i	$-0.372514\pi$
$233$	11.9028	0.779776	0.389888	+	0.920862i	$0.372514\pi$
$234$	6.51707	0.426034
$235$	8.58060	0.559737
$236$	−3.88658	−0.252995
$237$	−3.52546	−0.229003
$238$	6.32866	0.410226
$239$	−20.2360	−1.30896	−0.654479	−	0.756080i	$-0.727112\pi$
$239$	−20.2360	−1.30896	−0.654479	+	0.756080i	$0.727112\pi$
$240$	7.16925	0.462773
$241$	−3.43996	−0.221587	−0.110794	−	0.993843i	$-0.535339\pi$
$241$	−3.43996	−0.221587	−0.110794	+	0.993843i	$0.535339\pi$
$242$	−4.29666	−0.276200
$243$	−3.88698	−0.249350
$244$	−4.39669	−0.281469
$245$	14.5801	0.931489
$246$	−22.8356	−1.45594
$247$	1.05006	0.0668134
$248$	−4.06043	−0.257838
$249$	38.2980	2.42704
$250$	10.4368	0.660084
$251$	−3.09152	−0.195135	−0.0975677	−	0.995229i	$-0.531106\pi$
$251$	−3.09152	−0.195135	−0.0975677	+	0.995229i	$0.531106\pi$
$252$	−5.65203	−0.356044
$253$	6.93450	0.435968
$254$	18.5786	1.16573
$255$	−49.8221	−3.11998
$256$	1.00000	0.0625000
$257$	1.39542	0.0870438	0.0435219	−	0.999052i	$-0.486142\pi$
$257$	1.39542	0.0870438	0.0435219	+	0.999052i	$0.486142\pi$
$258$	12.6542	0.787814
$259$	−10.7090	−0.665424
$260$	−2.48108	−0.153870
$261$	−31.0707	−1.92323
$262$	−12.3247	−0.761422
$263$	0.380081	0.0234368	0.0117184	−	0.999931i	$-0.496270\pi$
$263$	0.380081	0.0234368	0.0117184	+	0.999931i	$0.496270\pi$
$264$	7.85580	0.483491
$265$	23.3472	1.43421
$266$	−0.910676	−0.0558371
$267$	44.0292	2.69454
$268$	2.21731	0.135444
$269$	25.9442	1.58184	0.790921	−	0.611918i	$-0.209602\pi$
$269$	25.9442	1.58184	0.790921	+	0.611918i	$0.209602\pi$
$270$	22.9875	1.39898
$271$	17.3474	1.05378	0.526890	−	0.849934i	$-0.323358\pi$
$271$	17.3474	1.05378	0.526890	+	0.849934i	$0.323358\pi$
$272$	−6.94941	−0.421370
$273$	2.90149	0.175606
$274$	−15.1981	−0.918148
$275$	−1.50908	−0.0910007
$276$	8.12671	0.489171
$277$	20.9489	1.25870	0.629350	−	0.777122i	$-0.283321\pi$
$277$	20.9489	1.25870	0.629350	+	0.777122i	$0.283321\pi$
$278$	−5.61924	−0.337020
$279$	−25.2007	−1.50873
$280$	2.15175	0.128592
$281$	−22.1216	−1.31966	−0.659831	−	0.751414i	$-0.729372\pi$
$281$	−22.1216	−1.31966	−0.659831	+	0.751414i	$0.729372\pi$
$282$	11.0188	0.656160
$283$	27.0872	1.61017	0.805084	−	0.593161i	$-0.202120\pi$
$283$	27.0872	1.61017	0.805084	+	0.593161i	$0.202120\pi$
$284$	−8.42951	−0.500200
$285$	7.16925	0.424670
$286$	−2.71868	−0.160759
$287$	−6.85379	−0.404566
$288$	6.20641	0.365716
$289$	31.2943	1.84084
$290$	11.8287	0.694608
$291$	29.3408	1.71999
$292$	9.64456	0.564405
$293$	−4.88144	−0.285177	−0.142588	−	0.989782i	$-0.545542\pi$
$293$	−4.88144	−0.285177	−0.142588	+	0.989782i	$0.545542\pi$
$294$	18.7231	1.09195
$295$	9.18323	0.534669
$296$	11.7594	0.683500
$297$	25.1889	1.46161
$298$	−13.2702	−0.768719
$299$	−2.81243	−0.162647
$300$	−1.76852	−0.102106
$301$	3.79798	0.218912
$302$	16.7175	0.961981
$303$	12.1471	0.697832
$304$	1.00000	0.0573539
$305$	10.3885	0.594845
$306$	−43.1309	−2.46563
$307$	−26.1448	−1.49216	−0.746081	−	0.665856i	$-0.768067\pi$
$307$	−26.1448	−1.49216	−0.746081	+	0.665856i	$0.768067\pi$
$308$	2.35781	0.134349
$309$	30.6846	1.74558
$310$	9.59402	0.544904
$311$	−29.3891	−1.66650	−0.833252	−	0.552894i	$-0.813524\pi$
$311$	−29.3891	−1.66650	−0.833252	+	0.552894i	$0.813524\pi$
$312$	−3.18608	−0.180377
$313$	26.1009	1.47531	0.737654	−	0.675179i	$-0.235934\pi$
$313$	26.1009	1.47531	0.737654	+	0.675179i	$0.235934\pi$
$314$	−1.49056	−0.0841174
$315$	13.3547	0.752450
$316$	1.16191	0.0653623
$317$	31.1569	1.74995	0.874974	−	0.484170i	$-0.160878\pi$
$317$	31.1569	1.74995	0.874974	+	0.484170i	$0.160878\pi$
$318$	29.9814	1.68127
$319$	12.9615	0.725706
$320$	−2.36281	−0.132085
$321$	38.6146	2.15526
$322$	2.43912	0.135927
$323$	−6.94941	−0.386676
$324$	10.9003	0.605571
$325$	0.612037	0.0339497
$326$	−4.23873	−0.234761
$327$	−50.8470	−2.81185
$328$	7.52605	0.415556
$329$	3.30715	0.182329
$330$	−18.5618	−1.02179
$331$	14.6088	0.802971	0.401485	−	0.915865i	$-0.368494\pi$
$331$	14.6088	0.802971	0.401485	+	0.915865i	$0.368494\pi$
$332$	−12.6221	−0.692727
$333$	72.9835	3.99947
$334$	2.00713	0.109825
$335$	−5.23907	−0.286241
$336$	2.76318	0.150744
$337$	−6.84697	−0.372978	−0.186489	−	0.982457i	$-0.559711\pi$
$337$	−6.84697	−0.372978	−0.186489	+	0.982457i	$0.559711\pi$
$338$	−11.8974	−0.647132
$339$	−47.9414	−2.60382
$340$	16.4201	0.890507
$341$	10.5128	0.569299
$342$	6.20641	0.335604
$343$	11.9942	0.647627
$344$	−4.17050	−0.224858
$345$	−19.2019	−1.03379
$346$	24.5190	1.31815
$347$	21.5763	1.15828	0.579139	−	0.815229i	$-0.303389\pi$
$347$	21.5763	1.15828	0.579139	+	0.815229i	$0.303389\pi$
$348$	15.1899	0.814265
$349$	24.9422	1.33513	0.667564	−	0.744553i	$-0.267337\pi$
$349$	24.9422	1.33513	0.667564	+	0.744553i	$0.267337\pi$
$350$	−0.530799	−0.0283724
$351$	−10.2159	−0.545284
$352$	−2.58908	−0.137998
$353$	11.0871	0.590106	0.295053	−	0.955481i	$-0.404663\pi$
$353$	11.0871	0.590106	0.295053	+	0.955481i	$0.404663\pi$
$354$	11.7927	0.626774
$355$	19.9173	1.05710
$356$	−14.5109	−0.769078
$357$	−19.2025	−1.01630
$358$	11.1188	0.587646
$359$	18.3464	0.968289	0.484144	−	0.874988i	$-0.339131\pi$
$359$	18.3464	0.968289	0.484144	+	0.874988i	$0.339131\pi$
$360$	−14.6646	−0.772890
$361$	1.00000	0.0526316
$362$	−13.9432	−0.732838
$363$	13.0370	0.684263
$364$	−0.956260	−0.0501217
$365$	−22.7882	−1.19279
$366$	13.3405	0.697317
$367$	−30.9530	−1.61574	−0.807868	−	0.589364i	$-0.799378\pi$
$367$	−30.9530	−1.61574	−0.807868	+	0.589364i	$0.799378\pi$
$368$	−2.67837	−0.139619
$369$	46.7097	2.43161
$370$	−27.7852	−1.44448
$371$	8.99850	0.467179
$372$	12.3202	0.638772
$373$	25.5602	1.32346	0.661730	−	0.749743i	$-0.269823\pi$
$373$	25.5602	1.32346	0.661730	+	0.749743i	$0.269823\pi$
$374$	17.9926	0.930375
$375$	−31.6676	−1.63531
$376$	−3.63153	−0.187282
$377$	−5.25681	−0.270740
$378$	8.85988	0.455703
$379$	17.2753	0.887370	0.443685	−	0.896183i	$-0.353671\pi$
$379$	17.2753	0.887370	0.443685	+	0.896183i	$0.353671\pi$
$380$	−2.36281	−0.121209
$381$	−56.3714	−2.88799
$382$	10.1792	0.520811
$383$	15.0278	0.767884	0.383942	−	0.923357i	$-0.374566\pi$
$383$	15.0278	0.767884	0.383942	+	0.923357i	$0.374566\pi$
$384$	−3.03421	−0.154839
$385$	−5.57106	−0.283928
$386$	−7.94880	−0.404583
$387$	−25.8838	−1.31575
$388$	−9.67002	−0.490921
$389$	15.4618	0.783943	0.391972	−	0.919977i	$-0.371793\pi$
$389$	15.4618	0.783943	0.391972	+	0.919977i	$0.371793\pi$
$390$	7.52811	0.381200
$391$	18.6131	0.941303
$392$	−6.17067	−0.311666
$393$	37.3957	1.88636
$394$	16.1314	0.812691
$395$	−2.74536	−0.138134
$396$	−16.0689	−0.807492
$397$	−3.95890	−0.198691	−0.0993456	−	0.995053i	$-0.531675\pi$
$397$	−3.95890	−0.198691	−0.0993456	+	0.995053i	$0.531675\pi$
$398$	−16.3876	−0.821437
$399$	2.76318	0.138332
$400$	0.582862	0.0291431
$401$	−15.3809	−0.768084	−0.384042	−	0.923316i	$-0.625468\pi$
$401$	−15.3809	−0.768084	−0.384042	+	0.923316i	$0.625468\pi$
$402$	−6.72776	−0.335550
$403$	−4.26368	−0.212389
$404$	−4.00338	−0.199176
$405$	−25.7553	−1.27979
$406$	4.55905	0.226262
$407$	−30.4460	−1.50915
$408$	21.0860	1.04391
$409$	31.4216	1.55370	0.776849	−	0.629687i	$-0.216817\pi$
$409$	31.4216	1.55370	0.776849	+	0.629687i	$0.216817\pi$
$410$	−17.7826	−0.878220
$411$	46.1140	2.27464
$412$	−10.1129	−0.498226
$413$	3.53941	0.174163
$414$	−16.6230	−0.816977
$415$	29.8236	1.46398
$416$	1.05006	0.0514832
$417$	17.0499	0.834939
$418$	−2.58908	−0.126636
$419$	−30.9088	−1.50999	−0.754997	−	0.655728i	$-0.772362\pi$
$419$	−30.9088	−1.50999	−0.754997	+	0.655728i	$0.772362\pi$
$420$	−6.52886	−0.318576
$421$	−17.2296	−0.839720	−0.419860	−	0.907589i	$-0.637921\pi$
$421$	−17.2296	−0.839720	−0.419860	+	0.907589i	$0.637921\pi$
$422$	1.00000	0.0486792
$423$	−22.5387	−1.09587
$424$	−9.88112	−0.479870
$425$	−4.05055	−0.196481
$426$	25.5769	1.23920
$427$	4.00396	0.193765
$428$	−12.7264	−0.615155
$429$	8.24903	0.398267
$430$	9.85410	0.475207
$431$	16.7323	0.805968	0.402984	−	0.915207i	$-0.367973\pi$
$431$	16.7323	0.805968	0.402984	+	0.915207i	$0.367973\pi$
$432$	−9.72890	−0.468082
$433$	−28.0923	−1.35003	−0.675016	−	0.737803i	$-0.735863\pi$
$433$	−28.0923	−1.35003	−0.675016	+	0.737803i	$0.735863\pi$
$434$	3.69774	0.177497
$435$	−35.8909	−1.72084
$436$	16.7579	0.802559
$437$	−2.67837	−0.128124
$438$	−29.2636	−1.39827
$439$	−31.9247	−1.52368	−0.761842	−	0.647763i	$-0.775705\pi$
$439$	−31.9247	−1.52368	−0.761842	+	0.647763i	$0.775705\pi$
$440$	6.11750	0.291640
$441$	−38.2977	−1.82370
$442$	−7.29727	−0.347096
$443$	17.1102	0.812929	0.406464	−	0.913667i	$-0.366762\pi$
$443$	17.1102	0.812929	0.406464	+	0.913667i	$0.366762\pi$
$444$	−35.6804	−1.69332
$445$	34.2866	1.62534
$446$	7.77640	0.368223
$447$	40.2644	1.90444
$448$	−0.910676	−0.0430254
$449$	36.4897	1.72205	0.861027	−	0.508560i	$-0.169822\pi$
$449$	36.4897	1.72205	0.861027	+	0.508560i	$0.169822\pi$
$450$	3.61748	0.170530
$451$	−19.4855	−0.917538
$452$	15.8003	0.743185
$453$	−50.7242	−2.38323
$454$	28.3738	1.33165
$455$	2.25946	0.105925
$456$	−3.03421	−0.142090
$457$	38.3793	1.79531	0.897655	−	0.440700i	$-0.145270\pi$
$457$	38.3793	1.79531	0.897655	+	0.440700i	$0.145270\pi$
$458$	−3.05247	−0.142633
$459$	67.6102	3.15577
$460$	6.32846	0.295066
$461$	16.1523	0.752290	0.376145	−	0.926561i	$-0.377249\pi$
$461$	16.1523	0.752290	0.376145	+	0.926561i	$0.377249\pi$
$462$	−7.15409	−0.332838
$463$	−23.1686	−1.07674	−0.538368	−	0.842710i	$-0.680959\pi$
$463$	−23.1686	−1.07674	−0.538368	+	0.842710i	$0.680959\pi$
$464$	−5.00623	−0.232408
$465$	−29.1102	−1.34995
$466$	11.9028	0.551385
$467$	−0.418164	−0.0193503	−0.00967516	−	0.999953i	$-0.503080\pi$
$467$	−0.418164	−0.0193503	−0.00967516	+	0.999953i	$0.503080\pi$
$468$	6.51707	0.301252
$469$	−2.01925	−0.0932402
$470$	8.58060	0.395794
$471$	4.52268	0.208394
$472$	−3.88658	−0.178894
$473$	10.7978	0.496482
$474$	−3.52546	−0.161930
$475$	0.582862	0.0267435
$476$	6.32866	0.290074
$477$	−61.3263	−2.80794
$478$	−20.2360	−0.925573
$479$	−21.9725	−1.00395	−0.501975	−	0.864882i	$-0.667393\pi$
$479$	−21.9725	−1.00395	−0.501975	+	0.864882i	$0.667393\pi$
$480$	7.16925	0.327230
$481$	12.3480	0.563020
$482$	−3.43996	−0.156686
$483$	−7.40080	−0.336748
$484$	−4.29666	−0.195303
$485$	22.8484	1.03749
$486$	−3.88698	−0.176317
$487$	14.1038	0.639103	0.319551	−	0.947569i	$-0.396468\pi$
$487$	14.1038	0.639103	0.319551	+	0.947569i	$0.396468\pi$
$488$	−4.39669	−0.199029
$489$	12.8612	0.581603
$490$	14.5801	0.658662
$491$	−38.1665	−1.72243	−0.861216	−	0.508240i	$-0.830296\pi$
$491$	−38.1665	−1.72243	−0.861216	+	0.508240i	$0.830296\pi$
$492$	−22.8356	−1.02951
$493$	34.7903	1.56688
$494$	1.05006	0.0472442
$495$	37.9677	1.70652
$496$	−4.06043	−0.182319
$497$	7.67656	0.344341
$498$	38.2980	1.71618
$499$	5.23940	0.234548	0.117274	−	0.993100i	$-0.462584\pi$
$499$	5.23940	0.234548	0.117274	+	0.993100i	$0.462584\pi$
$500$	10.4368	0.466750
$501$	−6.09004	−0.272083
$502$	−3.09152	−0.137982
$503$	−19.4906	−0.869042	−0.434521	−	0.900662i	$-0.643082\pi$
$503$	−19.4906	−0.869042	−0.434521	+	0.900662i	$0.643082\pi$
$504$	−5.65203	−0.251761
$505$	9.45923	0.420930
$506$	6.93450	0.308276
$507$	36.0991	1.60322
$508$	18.5786	0.824293
$509$	−18.0249	−0.798938	−0.399469	−	0.916747i	$-0.630806\pi$
$509$	−18.0249	−0.798938	−0.399469	+	0.916747i	$0.630806\pi$
$510$	−49.8221	−2.20616
$511$	−8.78307	−0.388540
$512$	1.00000	0.0441942
$513$	−9.72890	−0.429542
$514$	1.39542	0.0615493
$515$	23.8948	1.05293
$516$	12.6542	0.557069
$517$	9.40232	0.413513
$518$	−10.7090	−0.470526
$519$	−74.3958	−3.26561
$520$	−2.48108	−0.108803
$521$	−9.94968	−0.435903	−0.217952	−	0.975960i	$-0.569937\pi$
$521$	−9.94968	−0.435903	−0.217952	+	0.975960i	$0.569937\pi$
$522$	−31.0707	−1.35993
$523$	37.0334	1.61936	0.809678	−	0.586874i	$-0.199642\pi$
$523$	37.0334	1.61936	0.809678	+	0.586874i	$0.199642\pi$
$524$	−12.3247	−0.538407
$525$	1.61055	0.0702903
$526$	0.380081	0.0165723
$527$	28.2176	1.22918
$528$	7.85580	0.341880
$529$	−15.8264	−0.688103
$530$	23.3472	1.01414
$531$	−24.1217	−1.04679
$532$	−0.910676	−0.0394828
$533$	7.90276	0.342307
$534$	44.0292	1.90533
$535$	30.0701	1.30004
$536$	2.21731	0.0957730
$537$	−33.7367	−1.45584
$538$	25.9442	1.11853
$539$	15.9764	0.688150
$540$	22.9875	0.989226
$541$	−20.2633	−0.871189	−0.435594	−	0.900143i	$-0.643462\pi$
$541$	−20.2633	−0.871189	−0.435594	+	0.900143i	$0.643462\pi$
$542$	17.3474	0.745135
$543$	42.3065	1.81555
$544$	−6.94941	−0.297954
$545$	−39.5958	−1.69610
$546$	2.90149	0.124172
$547$	−33.5502	−1.43450	−0.717252	−	0.696814i	$-0.754600\pi$
$547$	−33.5502	−1.43450	−0.717252	+	0.696814i	$0.754600\pi$
$548$	−15.1981	−0.649229
$549$	−27.2876	−1.16461
$550$	−1.50908	−0.0643472
$551$	−5.00623	−0.213272
$552$	8.12671	0.345896
$553$	−1.05812	−0.0449958
$554$	20.9489	0.890035
$555$	84.3059	3.57859
$556$	−5.61924	−0.238309
$557$	−11.8573	−0.502410	−0.251205	−	0.967934i	$-0.580827\pi$
$557$	−11.8573	−0.502410	−0.251205	+	0.967934i	$0.580827\pi$
$558$	−25.2007	−1.06683
$559$	−4.37926	−0.185223
$560$	2.15175	0.0909282
$561$	−54.5932	−2.30493
$562$	−22.1216	−0.933141
$563$	−32.3966	−1.36535	−0.682677	−	0.730720i	$-0.739185\pi$
$563$	−32.3966	−1.36535	−0.682677	+	0.730720i	$0.739185\pi$
$564$	11.0188	0.463975
$565$	−37.3331	−1.57062
$566$	27.0872	1.13856
$567$	−9.92662	−0.416879
$568$	−8.42951	−0.353695
$569$	7.55517	0.316729	0.158365	−	0.987381i	$-0.449378\pi$
$569$	7.55517	0.316729	0.158365	+	0.987381i	$0.449378\pi$
$570$	7.16925	0.300287
$571$	5.20601	0.217865	0.108932	−	0.994049i	$-0.465257\pi$
$571$	5.20601	0.217865	0.108932	+	0.994049i	$0.465257\pi$
$572$	−2.71868	−0.113674
$573$	−30.8857	−1.29027
$574$	−6.85379	−0.286072
$575$	−1.56112	−0.0651031
$576$	6.20641	0.258600
$577$	−43.3334	−1.80399	−0.901997	−	0.431743i	$-0.857899\pi$
$577$	−43.3334	−1.80399	−0.901997	+	0.431743i	$0.857899\pi$
$578$	31.2943	1.30167
$579$	24.1183	1.00232
$580$	11.8287	0.491162
$581$	11.4946	0.476878
$582$	29.3408	1.21622
$583$	25.5830	1.05954
$584$	9.64456	0.399095
$585$	−15.3986	−0.636653
$586$	−4.88144	−0.201650
$587$	2.11116	0.0871367	0.0435684	−	0.999050i	$-0.486127\pi$
$587$	2.11116	0.0871367	0.0435684	+	0.999050i	$0.486127\pi$
$588$	18.7231	0.772127
$589$	−4.06043	−0.167307
$590$	9.18323	0.378068
$591$	−48.9461	−2.01338
$592$	11.7594	0.483308
$593$	4.93288	0.202569	0.101285	−	0.994857i	$-0.467705\pi$
$593$	4.93288	0.202569	0.101285	+	0.994857i	$0.467705\pi$
$594$	25.1889	1.03351
$595$	−14.9534	−0.613030
$596$	−13.2702	−0.543567
$597$	49.7234	2.03504
$598$	−2.81243	−0.115009
$599$	−24.3111	−0.993324	−0.496662	−	0.867944i	$-0.665441\pi$
$599$	−24.3111	−0.993324	−0.496662	+	0.867944i	$0.665441\pi$
$600$	−1.76852	−0.0721997
$601$	23.1821	0.945616	0.472808	−	0.881165i	$-0.343240\pi$
$601$	23.1821	0.945616	0.472808	+	0.881165i	$0.343240\pi$
$602$	3.79798	0.154794
$603$	13.7615	0.560412
$604$	16.7175	0.680224
$605$	10.1522	0.412745
$606$	12.1471	0.493442
$607$	−11.1679	−0.453289	−0.226645	−	0.973978i	$-0.572776\pi$
$607$	−11.1679	−0.453289	−0.226645	+	0.973978i	$0.572776\pi$
$608$	1.00000	0.0405554
$609$	−13.8331	−0.560545
$610$	10.3885	0.420619
$611$	−3.81330	−0.154270
$612$	−43.1309	−1.74346
$613$	22.3005	0.900709	0.450355	−	0.892850i	$-0.351298\pi$
$613$	22.3005	0.900709	0.450355	+	0.892850i	$0.351298\pi$
$614$	−26.1448	−1.05512
$615$	53.9561	2.17572
$616$	2.35781	0.0949990
$617$	30.9891	1.24758	0.623788	−	0.781594i	$-0.285593\pi$
$617$	30.9891	1.24758	0.623788	+	0.781594i	$0.285593\pi$
$618$	30.6846	1.23431
$619$	29.9793	1.20497	0.602484	−	0.798131i	$-0.294178\pi$
$619$	29.9793	1.20497	0.602484	+	0.798131i	$0.294178\pi$
$620$	9.59402	0.385305
$621$	26.0576	1.04565
$622$	−29.3891	−1.17840
$623$	13.2148	0.529438
$624$	−3.18608	−0.127545
$625$	−27.5746	−1.10298
$626$	26.1009	1.04320
$627$	7.85580	0.313731
$628$	−1.49056	−0.0594800
$629$	−81.7208	−3.25842
$630$	13.3547	0.532062
$631$	−8.35909	−0.332770	−0.166385	−	0.986061i	$-0.553209\pi$
$631$	−8.35909	−0.332770	−0.166385	+	0.986061i	$0.553209\pi$
$632$	1.16191	0.0462181
$633$	−3.03421	−0.120599
$634$	31.1569	1.23740
$635$	−43.8977	−1.74203
$636$	29.9814	1.18884
$637$	−6.47954	−0.256729
$638$	12.9615	0.513151
$639$	−52.3170	−2.06963
$640$	−2.36281	−0.0933982
$641$	35.2506	1.39232	0.696158	−	0.717889i	$-0.254891\pi$
$641$	35.2506	1.39232	0.696158	+	0.717889i	$0.254891\pi$
$642$	38.6146	1.52400
$643$	−25.2508	−0.995794	−0.497897	−	0.867236i	$-0.665894\pi$
$643$	−25.2508	−0.995794	−0.497897	+	0.867236i	$0.665894\pi$
$644$	2.43912	0.0961149
$645$	−29.8994	−1.17729
$646$	−6.94941	−0.273421
$647$	−33.8829	−1.33207	−0.666037	−	0.745919i	$-0.732011\pi$
$647$	−33.8829	−1.33207	−0.666037	+	0.745919i	$0.732011\pi$
$648$	10.9003	0.428203
$649$	10.0627	0.394994
$650$	0.612037	0.0240061
$651$	−11.2197	−0.439735
$652$	−4.23873	−0.166001
$653$	16.0224	0.627006	0.313503	−	0.949587i	$-0.398497\pi$
$653$	16.0224	0.627006	0.313503	+	0.949587i	$0.398497\pi$
$654$	−50.8470	−1.98828
$655$	29.1209	1.13785
$656$	7.52605	0.293843
$657$	59.8581	2.33529
$658$	3.30715	0.128926
$659$	−1.51890	−0.0591680	−0.0295840	−	0.999562i	$-0.509418\pi$
$659$	−1.51890	−0.0591680	−0.0295840	+	0.999562i	$0.509418\pi$
$660$	−18.5618	−0.722515
$661$	26.0230	1.01218	0.506088	−	0.862482i	$-0.331091\pi$
$661$	26.0230	1.01218	0.506088	+	0.862482i	$0.331091\pi$
$662$	14.6088	0.567786
$663$	22.1414	0.859901
$664$	−12.6221	−0.489832
$665$	2.15175	0.0834414
$666$	72.9835	2.82805
$667$	13.4085	0.519179
$668$	2.00713	0.0776581
$669$	−23.5952	−0.912243
$670$	−5.23907	−0.202403
$671$	11.3834	0.439450
$672$	2.76318	0.106592
$673$	5.35669	0.206485	0.103243	−	0.994656i	$-0.467078\pi$
$673$	5.35669	0.206485	0.103243	+	0.994656i	$0.467078\pi$
$674$	−6.84697	−0.263735
$675$	−5.67061	−0.218262
$676$	−11.8974	−0.457592
$677$	5.17924	0.199054	0.0995271	−	0.995035i	$-0.468267\pi$
$677$	5.17924	0.199054	0.0995271	+	0.995035i	$0.468267\pi$
$678$	−47.9414	−1.84118
$679$	8.80625	0.337953
$680$	16.4201	0.629683
$681$	−86.0920	−3.29905
$682$	10.5128	0.402555
$683$	23.8710	0.913400	0.456700	−	0.889621i	$-0.349031\pi$
$683$	23.8710	0.913400	0.456700	+	0.889621i	$0.349031\pi$
$684$	6.20641	0.237308
$685$	35.9101	1.37205
$686$	11.9942	0.457941
$687$	9.26182	0.353360
$688$	−4.17050	−0.158999
$689$	−10.3757	−0.395284
$690$	−19.2019	−0.731002
$691$	21.9300	0.834256	0.417128	−	0.908848i	$-0.363037\pi$
$691$	21.9300	0.834256	0.417128	+	0.908848i	$0.363037\pi$
$692$	24.5190	0.932074
$693$	14.6336	0.555883
$694$	21.5763	0.819026
$695$	13.2772	0.503633
$696$	15.1899	0.575772
$697$	−52.3016	−1.98106
$698$	24.9422	0.944078
$699$	−36.1155	−1.36601
$700$	−0.530799	−0.0200623
$701$	6.66772	0.251836	0.125918	−	0.992041i	$-0.459812\pi$
$701$	6.66772	0.251836	0.125918	+	0.992041i	$0.459812\pi$
$702$	−10.2159	−0.385574
$703$	11.7594	0.443514
$704$	−2.58908	−0.0975796
$705$	−26.0353	−0.980547
$706$	11.0871	0.417268
$707$	3.64579	0.137114
$708$	11.7927	0.443196
$709$	−22.6850	−0.851952	−0.425976	−	0.904734i	$-0.640069\pi$
$709$	−22.6850	−0.851952	−0.425976	+	0.904734i	$0.640069\pi$
$710$	19.9173	0.747484
$711$	7.21126	0.270443
$712$	−14.5109	−0.543820
$713$	10.8753	0.407284
$714$	−19.2025	−0.718635
$715$	6.42371	0.240233
$716$	11.1188	0.415528
$717$	61.4002	2.29303
$718$	18.3464	0.684683
$719$	−31.0980	−1.15976	−0.579880	−	0.814702i	$-0.696901\pi$
$719$	−31.0980	−1.15976	−0.579880	+	0.814702i	$0.696901\pi$
$720$	−14.6646	−0.546516
$721$	9.20956	0.342982
$722$	1.00000	0.0372161
$723$	10.4375	0.388176
$724$	−13.9432	−0.518195
$725$	−2.91794	−0.108370
$726$	13.0370	0.483847
$727$	−48.7651	−1.80860	−0.904298	−	0.426901i	$-0.859605\pi$
$727$	−48.7651	−1.80860	−0.904298	+	0.426901i	$0.859605\pi$
$728$	−0.956260	−0.0354414
$729$	−20.9069	−0.774331
$730$	−22.7882	−0.843431
$731$	28.9825	1.07196
$732$	13.3405	0.493077
$733$	−20.8528	−0.770216	−0.385108	−	0.922872i	$-0.625836\pi$
$733$	−20.8528	−0.770216	−0.385108	+	0.922872i	$0.625836\pi$
$734$	−30.9530	−1.14250
$735$	−44.2391	−1.63178
$736$	−2.67837	−0.0987259
$737$	−5.74078	−0.211464
$738$	46.7097	1.71941
$739$	25.1585	0.925472	0.462736	−	0.886496i	$-0.346868\pi$
$739$	25.1585	0.925472	0.462736	+	0.886496i	$0.346868\pi$
$740$	−27.7852	−1.02140
$741$	−3.18608	−0.117044
$742$	8.99850	0.330345
$743$	−6.74667	−0.247511	−0.123756	−	0.992313i	$-0.539494\pi$
$743$	−6.74667	−0.247511	−0.123756	+	0.992313i	$0.539494\pi$
$744$	12.3202	0.451680
$745$	31.3548	1.14875
$746$	25.5602	0.935827
$747$	−78.3378	−2.86623
$748$	17.9926	0.657874
$749$	11.5897	0.423477
$750$	−31.6676	−1.15634
$751$	25.2166	0.920168	0.460084	−	0.887875i	$-0.347819\pi$
$751$	25.2166	0.920168	0.460084	+	0.887875i	$0.347819\pi$
$752$	−3.63153	−0.132428
$753$	9.38032	0.341838
$754$	−5.25681	−0.191442
$755$	−39.5001	−1.43756
$756$	8.85988	0.322231
$757$	3.97812	0.144587	0.0722936	−	0.997383i	$-0.476968\pi$
$757$	3.97812	0.144587	0.0722936	+	0.997383i	$0.476968\pi$
$758$	17.2753	0.627466
$759$	−21.0407	−0.763729
$760$	−2.36281	−0.0857081
$761$	29.4659	1.06814	0.534069	−	0.845441i	$-0.320662\pi$
$761$	29.4659	1.06814	0.534069	+	0.845441i	$0.320662\pi$
$762$	−56.3714	−2.04212
$763$	−15.2610	−0.552487
$764$	10.1792	0.368269
$765$	101.910	3.68456
$766$	15.0278	0.542976
$767$	−4.08112	−0.147361
$768$	−3.03421	−0.109487
$769$	45.7660	1.65036	0.825182	−	0.564867i	$-0.191073\pi$
$769$	45.7660	1.65036	0.825182	+	0.564867i	$0.191073\pi$
$770$	−5.57106	−0.200767
$771$	−4.23399	−0.152483
$772$	−7.94880	−0.286083
$773$	−36.6781	−1.31922	−0.659610	−	0.751608i	$-0.729278\pi$
$773$	−36.6781	−1.31922	−0.659610	+	0.751608i	$0.729278\pi$
$774$	−25.8838	−0.930375
$775$	−2.36667	−0.0850133
$776$	−9.67002	−0.347133
$777$	32.4933	1.16569
$778$	15.4618	0.554332
$779$	7.52605	0.269649
$780$	7.52811	0.269549
$781$	21.8247	0.780949
$782$	18.6131	0.665602
$783$	48.7051	1.74058
$784$	−6.17067	−0.220381
$785$	3.52192	0.125703
$786$	37.3957	1.33386
$787$	44.6333	1.59101	0.795503	−	0.605949i	$-0.207207\pi$
$787$	44.6333	1.59101	0.795503	+	0.605949i	$0.207207\pi$
$788$	16.1314	0.574659
$789$	−1.15324	−0.0410565
$790$	−2.74536	−0.0976755
$791$	−14.3890	−0.511613
$792$	−16.0689	−0.570983
$793$	−4.61676	−0.163946
$794$	−3.95890	−0.140496
$795$	−70.8402	−2.51244
$796$	−16.3876	−0.580844
$797$	29.7961	1.05543	0.527717	−	0.849421i	$-0.323048\pi$
$797$	29.7961	1.05543	0.527717	+	0.849421i	$0.323048\pi$
$798$	2.76318	0.0978155
$799$	25.2370	0.892820
$800$	0.582862	0.0206073
$801$	−90.0608	−3.18214
$802$	−15.3809	−0.543118
$803$	−24.9705	−0.881191
$804$	−6.72776	−0.237270
$805$	−5.76318	−0.203125
$806$	−4.26368	−0.150182
$807$	−78.7199	−2.77107
$808$	−4.00338	−0.140839
$809$	−12.7228	−0.447310	−0.223655	−	0.974668i	$-0.571799\pi$
$809$	−12.7228	−0.447310	−0.223655	+	0.974668i	$0.571799\pi$
$810$	−25.7553	−0.904948
$811$	8.98407	0.315473	0.157737	−	0.987481i	$-0.449580\pi$
$811$	8.98407	0.315473	0.157737	+	0.987481i	$0.449580\pi$
$812$	4.55905	0.159991
$813$	−52.6356	−1.84601
$814$	−30.4460	−1.06713
$815$	10.0153	0.350821
$816$	21.0860	0.738156
$817$	−4.17050	−0.145907
$818$	31.4216	1.09863
$819$	−5.93494	−0.207384
$820$	−17.7826	−0.620995
$821$	45.9577	1.60394	0.801968	−	0.597368i	$-0.203787\pi$
$821$	45.9577	1.60394	0.801968	+	0.597368i	$0.203787\pi$
$822$	46.1140	1.60841
$823$	8.30418	0.289466	0.144733	−	0.989471i	$-0.453768\pi$
$823$	8.30418	0.289466	0.144733	+	0.989471i	$0.453768\pi$
$824$	−10.1129	−0.352299
$825$	4.57885	0.159415
$826$	3.53941	0.123152
$827$	−6.80218	−0.236535	−0.118267	−	0.992982i	$-0.537734\pi$
$827$	−6.80218	−0.236535	−0.118267	+	0.992982i	$0.537734\pi$
$828$	−16.6230	−0.577690
$829$	−38.5737	−1.33972	−0.669860	−	0.742487i	$-0.733646\pi$
$829$	−38.5737	−1.33972	−0.669860	+	0.742487i	$0.733646\pi$
$830$	29.8236	1.03519
$831$	−63.5634	−2.20499
$832$	1.05006	0.0364041
$833$	42.8825	1.48579
$834$	17.0499	0.590391
$835$	−4.74246	−0.164120
$836$	−2.58908	−0.0895452
$837$	39.5035	1.36544
$838$	−30.9088	−1.06773
$839$	6.10326	0.210708	0.105354	−	0.994435i	$-0.466402\pi$
$839$	6.10326	0.210708	0.105354	+	0.994435i	$0.466402\pi$
$840$	−6.52886	−0.225267
$841$	−3.93771	−0.135783
$842$	−17.2296	−0.593771
$843$	67.1214	2.31178
$844$	1.00000	0.0344214
$845$	28.1112	0.967056
$846$	−22.5387	−0.774898
$847$	3.91287	0.134448
$848$	−9.88112	−0.339319
$849$	−82.1882	−2.82069
$850$	−4.05055	−0.138933
$851$	−31.4959	−1.07967
$852$	25.5769	0.876250
$853$	30.4819	1.04368	0.521841	−	0.853043i	$-0.325245\pi$
$853$	30.4819	1.04368	0.521841	+	0.853043i	$0.325245\pi$
$854$	4.00396	0.137013
$855$	−14.6646	−0.501517
$856$	−12.7264	−0.434980
$857$	−25.7582	−0.879885	−0.439942	−	0.898026i	$-0.645001\pi$
$857$	−25.7582	−0.879885	−0.439942	+	0.898026i	$0.645001\pi$
$858$	8.24903	0.281617
$859$	−51.9348	−1.77199	−0.885996	−	0.463694i	$-0.846524\pi$
$859$	−51.9348	−1.77199	−0.885996	+	0.463694i	$0.846524\pi$
$860$	9.85410	0.336022
$861$	20.7958	0.708719
$862$	16.7323	0.569906
$863$	−35.0782	−1.19408	−0.597039	−	0.802212i	$-0.703656\pi$
$863$	−35.0782	−1.19408	−0.597039	+	0.802212i	$0.703656\pi$
$864$	−9.72890	−0.330984
$865$	−57.9338	−1.96981
$866$	−28.0923	−0.954616
$867$	−94.9535	−3.22479
$868$	3.69774	0.125509
$869$	−3.00827	−0.102048
$870$	−35.8909	−1.21681
$871$	2.32829	0.0788912
$872$	16.7579	0.567495
$873$	−60.0161	−2.03124
$874$	−2.67837	−0.0905971
$875$	−9.50459	−0.321314
$876$	−29.2636	−0.988725
$877$	−37.0689	−1.25173	−0.625865	−	0.779932i	$-0.715254\pi$
$877$	−37.0689	−1.25173	−0.625865	+	0.779932i	$0.715254\pi$
$878$	−31.9247	−1.07741
$879$	14.8113	0.499572
$880$	6.11750	0.206221
$881$	−33.5121	−1.12905	−0.564526	−	0.825416i	$-0.690941\pi$
$881$	−33.5121	−1.12905	−0.564526	+	0.825416i	$0.690941\pi$
$882$	−38.2977	−1.28955
$883$	1.16658	0.0392587	0.0196293	−	0.999807i	$-0.493751\pi$
$883$	1.16658	0.0392587	0.0196293	+	0.999807i	$0.493751\pi$
$884$	−7.29727	−0.245434
$885$	−27.8638	−0.936632
$886$	17.1102	0.574827
$887$	48.9961	1.64513	0.822565	−	0.568672i	$-0.192543\pi$
$887$	48.9961	1.64513	0.822565	+	0.568672i	$0.192543\pi$
$888$	−35.6804	−1.19736
$889$	−16.9191	−0.567448
$890$	34.2866	1.14929
$891$	−28.2217	−0.945462
$892$	7.77640	0.260373
$893$	−3.63153	−0.121524
$894$	40.2644	1.34664
$895$	−26.2715	−0.878161
$896$	−0.910676	−0.0304236
$897$	8.53350	0.284925
$898$	36.4897	1.21768
$899$	20.3274	0.677958
$900$	3.61748	0.120583
$901$	68.6680	2.28766
$902$	−19.4855	−0.648797
$903$	−11.5238	−0.383490
$904$	15.8003	0.525511
$905$	32.9451	1.09513
$906$	−50.7242	−1.68520
$907$	−51.0143	−1.69390	−0.846951	−	0.531672i	$-0.821564\pi$
$907$	−51.0143	−1.69390	−0.846951	+	0.531672i	$0.821564\pi$
$908$	28.3738	0.941618
$909$	−24.8466	−0.824111
$910$	2.25946	0.0749004
$911$	−18.1151	−0.600179	−0.300089	−	0.953911i	$-0.597016\pi$
$911$	−18.1151	−0.600179	−0.300089	+	0.953911i	$0.597016\pi$
$912$	−3.03421	−0.100473
$913$	32.6796	1.08154
$914$	38.3793	1.26948
$915$	−31.5209	−1.04205
$916$	−3.05247	−0.100856
$917$	11.2238	0.370643
$918$	67.6102	2.23147
$919$	1.04587	0.0345002	0.0172501	−	0.999851i	$-0.494509\pi$
$919$	1.04587	0.0345002	0.0172501	+	0.999851i	$0.494509\pi$
$920$	6.32846	0.208643
$921$	79.3286	2.61397
$922$	16.1523	0.531949
$923$	−8.85146	−0.291349
$924$	−7.15409	−0.235352
$925$	6.85410	0.225361
$926$	−23.1686	−0.761368
$927$	−62.7647	−2.06146
$928$	−5.00623	−0.164337
$929$	13.1686	0.432047	0.216024	−	0.976388i	$-0.430691\pi$
$929$	13.1686	0.432047	0.216024	+	0.976388i	$0.430691\pi$
$930$	−29.1102	−0.954562
$931$	−6.17067	−0.202236
$932$	11.9028	0.389888
$933$	89.1726	2.91938
$934$	−0.418164	−0.0136827
$935$	−42.5130	−1.39032
$936$	6.51707	0.213017
$937$	−46.0935	−1.50581	−0.752905	−	0.658129i	$-0.771348\pi$
$937$	−46.0935	−1.50581	−0.752905	+	0.658129i	$0.771348\pi$
$938$	−2.01925	−0.0659308
$939$	−79.1954	−2.58444
$940$	8.58060	0.279868
$941$	17.7339	0.578109	0.289055	−	0.957313i	$-0.406659\pi$
$941$	17.7339	0.578109	0.289055	+	0.957313i	$0.406659\pi$
$942$	4.52268	0.147357
$943$	−20.1575	−0.656419
$944$	−3.88658	−0.126497
$945$	−20.9342	−0.680989
$946$	10.7978	0.351066
$947$	−52.2508	−1.69792	−0.848961	−	0.528455i	$-0.822772\pi$
$947$	−52.2508	−1.69792	−0.848961	+	0.528455i	$0.822772\pi$
$948$	−3.52546	−0.114502
$949$	10.1273	0.328747
$950$	0.582862	0.0189105
$951$	−94.5366	−3.06556
$952$	6.32866	0.205113
$953$	−35.6729	−1.15556	−0.577779	−	0.816193i	$-0.696080\pi$
$953$	−35.6729	−1.15556	−0.577779	+	0.816193i	$0.696080\pi$
$954$	−61.3263	−1.98551
$955$	−24.0514	−0.778285
$956$	−20.2360	−0.654479
$957$	−39.3279	−1.27129
$958$	−21.9725	−0.709899
$959$	13.8405	0.446933
$960$	7.16925	0.231386
$961$	−14.5129	−0.468158
$962$	12.3480	0.398116
$963$	−78.9854	−2.54527
$964$	−3.43996	−0.110794
$965$	18.7815	0.604597
$966$	−7.40080	−0.238117
$967$	−21.9800	−0.706828	−0.353414	−	0.935467i	$-0.614979\pi$
$967$	−21.9800	−0.706828	−0.353414	+	0.935467i	$0.614979\pi$
$968$	−4.29666	−0.138100
$969$	21.0860	0.677378
$970$	22.8484	0.733618
$971$	4.39012	0.140886	0.0704428	−	0.997516i	$-0.477559\pi$
$971$	4.39012	0.140886	0.0704428	+	0.997516i	$0.477559\pi$
$972$	−3.88698	−0.124675
$973$	5.11731	0.164053
$974$	14.1038	0.451914
$975$	−1.85705	−0.0594731
$976$	−4.39669	−0.140735
$977$	6.60029	0.211162	0.105581	−	0.994411i	$-0.466330\pi$
$977$	6.60029	0.211162	0.105581	+	0.994411i	$0.466330\pi$
$978$	12.8612	0.411255
$979$	37.5700	1.20074
$980$	14.5801	0.465744
$981$	104.007	3.32067
$982$	−38.1665	−1.21794
$983$	−2.40973	−0.0768583	−0.0384292	−	0.999261i	$-0.512235\pi$
$983$	−2.40973	−0.0768583	−0.0384292	+	0.999261i	$0.512235\pi$
$984$	−22.8356	−0.727972
$985$	−38.1155	−1.21446
$986$	34.7903	1.10795
$987$	−10.0346	−0.319404
$988$	1.05006	0.0334067
$989$	11.1701	0.355189
$990$	37.9677	1.20669
$991$	48.7811	1.54958	0.774792	−	0.632217i	$-0.217855\pi$
$991$	48.7811	1.54958	0.774792	+	0.632217i	$0.217855\pi$
$992$	−4.06043	−0.128919
$993$	−44.3260	−1.40664
$994$	7.67656	0.243486
$995$	38.7208	1.22753
$996$	38.2980	1.21352
$997$	−4.50713	−0.142742	−0.0713711	−	0.997450i	$-0.522737\pi$
$997$	−4.50713	−0.142742	−0.0713711	+	0.997450i	$0.522737\pi$
$998$	5.23940	0.165850
$999$	−114.406	−3.61964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.k.1.4	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.k.1.4	✓	49	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.03421 q^{3} +1.00000 q^{4} -2.36281 q^{5} -3.03421 q^{6} -0.910676 q^{7} +1.00000 q^{8} +6.20641 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.03421 q^{3} +1.00000 q^{4} -2.36281 q^{5} -3.03421 q^{6} -0.910676 q^{7} +1.00000 q^{8} +6.20641 q^{9} -2.36281 q^{10} -2.58908 q^{11} -3.03421 q^{12} +1.05006 q^{13} -0.910676 q^{14} +7.16925 q^{15} +1.00000 q^{16} -6.94941 q^{17} +6.20641 q^{18} +1.00000 q^{19} -2.36281 q^{20} +2.76318 q^{21} -2.58908 q^{22} -2.67837 q^{23} -3.03421 q^{24} +0.582862 q^{25} +1.05006 q^{26} -9.72890 q^{27} -0.910676 q^{28} -5.00623 q^{29} +7.16925 q^{30} -4.06043 q^{31} +1.00000 q^{32} +7.85580 q^{33} -6.94941 q^{34} +2.15175 q^{35} +6.20641 q^{36} +11.7594 q^{37} +1.00000 q^{38} -3.18608 q^{39} -2.36281 q^{40} +7.52605 q^{41} +2.76318 q^{42} -4.17050 q^{43} -2.58908 q^{44} -14.6646 q^{45} -2.67837 q^{46} -3.63153 q^{47} -3.03421 q^{48} -6.17067 q^{49} +0.582862 q^{50} +21.0860 q^{51} +1.05006 q^{52} -9.88112 q^{53} -9.72890 q^{54} +6.11750 q^{55} -0.910676 q^{56} -3.03421 q^{57} -5.00623 q^{58} -3.88658 q^{59} +7.16925 q^{60} -4.39669 q^{61} -4.06043 q^{62} -5.65203 q^{63} +1.00000 q^{64} -2.48108 q^{65} +7.85580 q^{66} +2.21731 q^{67} -6.94941 q^{68} +8.12671 q^{69} +2.15175 q^{70} -8.42951 q^{71} +6.20641 q^{72} +9.64456 q^{73} +11.7594 q^{74} -1.76852 q^{75} +1.00000 q^{76} +2.35781 q^{77} -3.18608 q^{78} +1.16191 q^{79} -2.36281 q^{80} +10.9003 q^{81} +7.52605 q^{82} -12.6221 q^{83} +2.76318 q^{84} +16.4201 q^{85} -4.17050 q^{86} +15.1899 q^{87} -2.58908 q^{88} -14.5109 q^{89} -14.6646 q^{90} -0.956260 q^{91} -2.67837 q^{92} +12.3202 q^{93} -3.63153 q^{94} -2.36281 q^{95} -3.03421 q^{96} -9.67002 q^{97} -6.17067 q^{98} -16.0689 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9}+O(q^{10}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9} + 17 q^{10} + 21 q^{11} + 13 q^{12} + 13 q^{13} + 22 q^{14} + 8 q^{15} + 49 q^{16} + 24 q^{17} + 66 q^{18} + 49 q^{19} + 17 q^{20} + 6 q^{21} + 21 q^{22} + 22 q^{23} + 13 q^{24} + 96 q^{25} + 13 q^{26} + 31 q^{27} + 22 q^{28} + 33 q^{29} + 8 q^{30} + 21 q^{31} + 49 q^{32} + 20 q^{33} + 24 q^{34} + 18 q^{35} + 66 q^{36} + 48 q^{37} + 49 q^{38} + 4 q^{39} + 17 q^{40} + 37 q^{41} + 6 q^{42} + 43 q^{43} + 21 q^{44} + 47 q^{45} + 22 q^{46} + 7 q^{47} + 13 q^{48} + 87 q^{49} + 96 q^{50} + 12 q^{51} + 13 q^{52} + 23 q^{53} + 31 q^{54} + 31 q^{55} + 22 q^{56} + 13 q^{57} + 33 q^{58} + 37 q^{59} + 8 q^{60} + 61 q^{61} + 21 q^{62} + 45 q^{63} + 49 q^{64} + 36 q^{65} + 20 q^{66} + 43 q^{67} + 24 q^{68} + 18 q^{69} + 18 q^{70} + 14 q^{71} + 66 q^{72} + 90 q^{73} + 48 q^{74} + 53 q^{75} + 49 q^{76} + 46 q^{77} + 4 q^{78} + 16 q^{79} + 17 q^{80} + 97 q^{81} + 37 q^{82} + 11 q^{83} + 6 q^{84} + 88 q^{85} + 43 q^{86} - 35 q^{87} + 21 q^{88} + 46 q^{89} + 47 q^{90} + 27 q^{91} + 22 q^{92} + 9 q^{93} + 7 q^{94} + 17 q^{95} + 13 q^{96} + 34 q^{97} + 87 q^{98} + 84 q^{99}+O(q^{100}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9 + 17 * q^10 + 21 * q^11 + 13 * q^12 + 13 * q^13 + 22 * q^14 + 8 * q^15 + 49 * q^16 + 24 * q^17 + 66 * q^18 + 49 * q^19 + 17 * q^20 + 6 * q^21 + 21 * q^22 + 22 * q^23 + 13 * q^24 + 96 * q^25 + 13 * q^26 + 31 * q^27 + 22 * q^28 + 33 * q^29 + 8 * q^30 + 21 * q^31 + 49 * q^32 + 20 * q^33 + 24 * q^34 + 18 * q^35 + 66 * q^36 + 48 * q^37 + 49 * q^38 + 4 * q^39 + 17 * q^40 + 37 * q^41 + 6 * q^42 + 43 * q^43 + 21 * q^44 + 47 * q^45 + 22 * q^46 + 7 * q^47 + 13 * q^48 + 87 * q^49 + 96 * q^50 + 12 * q^51 + 13 * q^52 + 23 * q^53 + 31 * q^54 + 31 * q^55 + 22 * q^56 + 13 * q^57 + 33 * q^58 + 37 * q^59 + 8 * q^60 + 61 * q^61 + 21 * q^62 + 45 * q^63 + 49 * q^64 + 36 * q^65 + 20 * q^66 + 43 * q^67 + 24 * q^68 + 18 * q^69 + 18 * q^70 + 14 * q^71 + 66 * q^72 + 90 * q^73 + 48 * q^74 + 53 * q^75 + 49 * q^76 + 46 * q^77 + 4 * q^78 + 16 * q^79 + 17 * q^80 + 97 * q^81 + 37 * q^82 + 11 * q^83 + 6 * q^84 + 88 * q^85 + 43 * q^86 - 35 * q^87 + 21 * q^88 + 46 * q^89 + 47 * q^90 + 27 * q^91 + 22 * q^92 + 9 * q^93 + 7 * q^94 + 17 * q^95 + 13 * q^96 + 34 * q^97 + 87 * q^98 + 84 * q^99

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