LMFDB - Embedded newform 6013.2.a.f.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.94077 q^{2} -1.00614 q^{3} +1.76657 q^{4} -2.69594 q^{5} +1.95267 q^{6} -1.00000 q^{7} +0.453027 q^{8} -1.98769 q^{9} +O(q^{10})$	\(q-1.94077 q^{2} -1.00614 q^{3} +1.76657 q^{4} -2.69594 q^{5} +1.95267 q^{6} -1.00000 q^{7} +0.453027 q^{8} -1.98769 q^{9} +5.23218 q^{10} -2.02239 q^{11} -1.77741 q^{12} -2.17575 q^{13} +1.94077 q^{14} +2.71248 q^{15} -4.41237 q^{16} +4.25543 q^{17} +3.85764 q^{18} +4.60176 q^{19} -4.76257 q^{20} +1.00614 q^{21} +3.92498 q^{22} +3.71760 q^{23} -0.455807 q^{24} +2.26807 q^{25} +4.22262 q^{26} +5.01829 q^{27} -1.76657 q^{28} +4.80924 q^{29} -5.26428 q^{30} +5.14954 q^{31} +7.65732 q^{32} +2.03479 q^{33} -8.25880 q^{34} +2.69594 q^{35} -3.51140 q^{36} -9.38929 q^{37} -8.93094 q^{38} +2.18910 q^{39} -1.22133 q^{40} -7.52063 q^{41} -1.95267 q^{42} +1.39522 q^{43} -3.57269 q^{44} +5.35869 q^{45} -7.21499 q^{46} -4.71182 q^{47} +4.43944 q^{48} +1.00000 q^{49} -4.40179 q^{50} -4.28154 q^{51} -3.84362 q^{52} -6.51423 q^{53} -9.73933 q^{54} +5.45222 q^{55} -0.453027 q^{56} -4.62999 q^{57} -9.33362 q^{58} -4.76787 q^{59} +4.79179 q^{60} +4.31436 q^{61} -9.99406 q^{62} +1.98769 q^{63} -6.03633 q^{64} +5.86568 q^{65} -3.94906 q^{66} +2.95615 q^{67} +7.51753 q^{68} -3.74041 q^{69} -5.23218 q^{70} -13.2270 q^{71} -0.900479 q^{72} -11.7451 q^{73} +18.2224 q^{74} -2.28199 q^{75} +8.12934 q^{76} +2.02239 q^{77} -4.24853 q^{78} -14.4019 q^{79} +11.8955 q^{80} +0.913994 q^{81} +14.5958 q^{82} -2.48225 q^{83} +1.77741 q^{84} -11.4724 q^{85} -2.70779 q^{86} -4.83875 q^{87} -0.916196 q^{88} +2.08095 q^{89} -10.4000 q^{90} +2.17575 q^{91} +6.56741 q^{92} -5.18114 q^{93} +9.14454 q^{94} -12.4060 q^{95} -7.70430 q^{96} +7.38920 q^{97} -1.94077 q^{98} +4.01988 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) $ 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * 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 $

$2$	−1.94077	−1.37233	−0.686164	−	0.727446i	$-0.740707\pi$
$2$	−1.94077	−1.37233	−0.686164	+	0.727446i	$0.740707\pi$
$3$	−1.00614	−0.580892	−0.290446	−	0.956891i	$-0.593804\pi$
$3$	−1.00614	−0.580892	−0.290446	+	0.956891i	$0.593804\pi$
$4$	1.76657	0.883286
$5$	−2.69594	−1.20566	−0.602830	−	0.797870i	$-0.705960\pi$
$5$	−2.69594	−1.20566	−0.602830	+	0.797870i	$0.705960\pi$
$6$	1.95267	0.797175
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.453027	0.160169
$9$	−1.98769	−0.662564
$10$	5.23218	1.65456
$11$	−2.02239	−0.609772	−0.304886	−	0.952389i	$-0.598618\pi$
$11$	−2.02239	−0.609772	−0.304886	+	0.952389i	$0.598618\pi$
$12$	−1.77741	−0.513094
$13$	−2.17575	−0.603444	−0.301722	−	0.953396i	$-0.597562\pi$
$13$	−2.17575	−0.603444	−0.301722	+	0.953396i	$0.597562\pi$
$14$	1.94077	0.518692
$15$	2.71248	0.700358
$16$	−4.41237	−1.10309
$17$	4.25543	1.03209	0.516047	−	0.856560i	$-0.327403\pi$
$17$	4.25543	1.03209	0.516047	+	0.856560i	$0.327403\pi$
$18$	3.85764	0.909256
$19$	4.60176	1.05572	0.527858	−	0.849333i	$-0.322995\pi$
$19$	4.60176	1.05572	0.527858	+	0.849333i	$0.322995\pi$
$20$	−4.76257	−1.06494
$21$	1.00614	0.219557
$22$	3.92498	0.836808
$23$	3.71760	0.775173	0.387587	−	0.921833i	$-0.373309\pi$
$23$	3.71760	0.775173	0.387587	+	0.921833i	$0.373309\pi$
$24$	−0.455807	−0.0930412
$25$	2.26807	0.453614
$26$	4.22262	0.828124
$27$	5.01829	0.965771
$28$	−1.76657	−0.333851
$29$	4.80924	0.893054	0.446527	−	0.894770i	$-0.352661\pi$
$29$	4.80924	0.893054	0.446527	+	0.894770i	$0.352661\pi$
$30$	−5.26428	−0.961122
$31$	5.14954	0.924885	0.462443	−	0.886649i	$-0.346973\pi$
$31$	5.14954	0.924885	0.462443	+	0.886649i	$0.346973\pi$
$32$	7.65732	1.35363
$33$	2.03479	0.354212
$34$	−8.25880	−1.41637
$35$	2.69594	0.455696
$36$	−3.51140	−0.585234
$37$	−9.38929	−1.54359	−0.771795	−	0.635871i	$-0.780641\pi$
$37$	−9.38929	−1.54359	−0.771795	+	0.635871i	$0.780641\pi$
$38$	−8.93094	−1.44879
$39$	2.18910	0.350536
$40$	−1.22133	−0.193110
$41$	−7.52063	−1.17452	−0.587262	−	0.809397i	$-0.699794\pi$
$41$	−7.52063	−1.17452	−0.587262	+	0.809397i	$0.699794\pi$
$42$	−1.95267	−0.301304
$43$	1.39522	0.212769	0.106384	−	0.994325i	$-0.466073\pi$
$43$	1.39522	0.212769	0.106384	+	0.994325i	$0.466073\pi$
$44$	−3.57269	−0.538604
$45$	5.35869	0.798826
$46$	−7.21499	−1.06379
$47$	−4.71182	−0.687290	−0.343645	−	0.939100i	$-0.611662\pi$
$47$	−4.71182	−0.687290	−0.343645	+	0.939100i	$0.611662\pi$
$48$	4.43944	0.640778
$49$	1.00000	0.142857
$50$	−4.40179	−0.622508
$51$	−4.28154	−0.599535
$52$	−3.84362	−0.533014
$53$	−6.51423	−0.894798	−0.447399	−	0.894335i	$-0.647650\pi$
$53$	−6.51423	−0.894798	−0.447399	+	0.894335i	$0.647650\pi$
$54$	−9.73933	−1.32536
$55$	5.45222	0.735177
$56$	−0.453027	−0.0605383
$57$	−4.62999	−0.613257
$58$	−9.33362	−1.22556
$59$	−4.76787	−0.620724	−0.310362	−	0.950619i	$-0.600450\pi$
$59$	−4.76787	−0.620724	−0.310362	+	0.950619i	$0.600450\pi$
$60$	4.79179	0.618617
$61$	4.31436	0.552397	0.276198	−	0.961101i	$-0.410925\pi$
$61$	4.31436	0.552397	0.276198	+	0.961101i	$0.410925\pi$
$62$	−9.99406	−1.26925
$63$	1.98769	0.250426
$64$	−6.03633	−0.754541
$65$	5.86568	0.727548
$66$	−3.94906	−0.486095
$67$	2.95615	0.361151	0.180576	−	0.983561i	$-0.442204\pi$
$67$	2.95615	0.361151	0.180576	+	0.983561i	$0.442204\pi$
$68$	7.51753	0.911634
$69$	−3.74041	−0.450292
$70$	−5.23218	−0.625365
$71$	−13.2270	−1.56976	−0.784880	−	0.619648i	$-0.787276\pi$
$71$	−13.2270	−1.56976	−0.784880	+	0.619648i	$0.787276\pi$
$72$	−0.900479	−0.106122
$73$	−11.7451	−1.37466	−0.687332	−	0.726343i	$-0.741218\pi$
$73$	−11.7451	−1.37466	−0.687332	+	0.726343i	$0.741218\pi$
$74$	18.2224	2.11831
$75$	−2.28199	−0.263501
$76$	8.12934	0.932500
$77$	2.02239	0.230472
$78$	−4.24853	−0.481051
$79$	−14.4019	−1.62034	−0.810170	−	0.586196i	$-0.800625\pi$
$79$	−14.4019	−1.62034	−0.810170	+	0.586196i	$0.800625\pi$
$80$	11.8955	1.32995
$81$	0.913994	0.101555
$82$	14.5958	1.61183
$83$	−2.48225	−0.272462	−0.136231	−	0.990677i	$-0.543499\pi$
$83$	−2.48225	−0.272462	−0.136231	+	0.990677i	$0.543499\pi$
$84$	1.77741	0.193931
$85$	−11.4724	−1.24435
$86$	−2.70779	−0.291989
$87$	−4.83875	−0.518768
$88$	−0.916196	−0.0976668
$89$	2.08095	0.220580	0.110290	−	0.993899i	$-0.464822\pi$
$89$	2.08095	0.220580	0.110290	+	0.993899i	$0.464822\pi$
$90$	−10.4000	−1.09625
$91$	2.17575	0.228081
$92$	6.56741	0.684700
$93$	−5.18114	−0.537259
$94$	9.14454	0.943188
$95$	−12.4060	−1.27283
$96$	−7.70430	−0.786316
$97$	7.38920	0.750260	0.375130	−	0.926972i	$-0.377598\pi$
$97$	7.38920	0.750260	0.375130	+	0.926972i	$0.377598\pi$
$98$	−1.94077	−0.196047
$99$	4.01988	0.404013
$100$	4.00671	0.400671
$101$	12.9712	1.29068	0.645341	−	0.763894i	$-0.276715\pi$
$101$	12.9712	1.29068	0.645341	+	0.763894i	$0.276715\pi$
$102$	8.30947	0.822760
$103$	−14.4207	−1.42092	−0.710458	−	0.703740i	$-0.751512\pi$
$103$	−14.4207	−1.42092	−0.710458	+	0.703740i	$0.751512\pi$
$104$	−0.985674	−0.0966533
$105$	−2.71248	−0.264711
$106$	12.6426	1.22796
$107$	−10.5866	−1.02345	−0.511724	−	0.859150i	$-0.670993\pi$
$107$	−10.5866	−1.02345	−0.511724	+	0.859150i	$0.670993\pi$
$108$	8.86518	0.853052
$109$	9.28338	0.889186	0.444593	−	0.895733i	$-0.353348\pi$
$109$	9.28338	0.889186	0.444593	+	0.895733i	$0.353348\pi$
$110$	−10.5815	−1.00891
$111$	9.44690	0.896660
$112$	4.41237	0.416929
$113$	12.3511	1.16189	0.580946	−	0.813942i	$-0.302683\pi$
$113$	12.3511	1.16189	0.580946	+	0.813942i	$0.302683\pi$
$114$	8.98573	0.841591
$115$	−10.0224	−0.934594
$116$	8.49588	0.788823
$117$	4.32472	0.399821
$118$	9.25332	0.851837
$119$	−4.25543	−0.390095
$120$	1.22883	0.112176
$121$	−6.90996	−0.628178
$122$	−8.37316	−0.758070
$123$	7.56677	0.682273
$124$	9.09704	0.816939
$125$	7.36511	0.658755
$126$	−3.85764	−0.343666
$127$	9.55798	0.848134	0.424067	−	0.905631i	$-0.360602\pi$
$127$	9.55798	0.848134	0.424067	+	0.905631i	$0.360602\pi$
$128$	−3.59953	−0.318157
$129$	−1.40378	−0.123596
$130$	−11.3839	−0.998436
$131$	−5.64714	−0.493393	−0.246696	−	0.969093i	$-0.579345\pi$
$131$	−5.64714	−0.493393	−0.246696	+	0.969093i	$0.579345\pi$
$132$	3.59461	0.312871
$133$	−4.60176	−0.399023
$134$	−5.73720	−0.495619
$135$	−13.5290	−1.16439
$136$	1.92783	0.165310
$137$	22.6928	1.93877	0.969387	−	0.245539i	$-0.0789650\pi$
$137$	22.6928	1.93877	0.969387	+	0.245539i	$0.0789650\pi$
$138$	7.25926	0.617949
$139$	−18.4366	−1.56377	−0.781887	−	0.623420i	$-0.785743\pi$
$139$	−18.4366	−1.56377	−0.781887	+	0.623420i	$0.785743\pi$
$140$	4.76257	0.402510
$141$	4.74073	0.399242
$142$	25.6706	2.15423
$143$	4.40021	0.367964
$144$	8.77042	0.730869
$145$	−12.9654	−1.07672
$146$	22.7946	1.88649
$147$	−1.00614	−0.0829846
$148$	−16.5869	−1.36343
$149$	−3.42609	−0.280676	−0.140338	−	0.990104i	$-0.544819\pi$
$149$	−3.42609	−0.280676	−0.140338	+	0.990104i	$0.544819\pi$
$150$	4.42880	0.361610
$151$	17.8329	1.45122	0.725610	−	0.688106i	$-0.241558\pi$
$151$	17.8329	1.45122	0.725610	+	0.688106i	$0.241558\pi$
$152$	2.08472	0.169093
$153$	−8.45849	−0.683828
$154$	−3.92498	−0.316284
$155$	−13.8828	−1.11510
$156$	3.86720	0.309624
$157$	−22.0449	−1.75937	−0.879685	−	0.475556i	$-0.842247\pi$
$157$	−22.0449	−1.75937	−0.879685	+	0.475556i	$0.842247\pi$
$158$	27.9507	2.22364
$159$	6.55419	0.519781
$160$	−20.6436	−1.63202
$161$	−3.71760	−0.292988
$162$	−1.77385	−0.139367
$163$	9.68461	0.758557	0.379279	−	0.925282i	$-0.376172\pi$
$163$	9.68461	0.758557	0.379279	+	0.925282i	$0.376172\pi$
$164$	−13.2857	−1.03744
$165$	−5.48567	−0.427059
$166$	4.81746	0.373907
$167$	−9.33002	−0.721979	−0.360989	−	0.932570i	$-0.617561\pi$
$167$	−9.33002	−0.721979	−0.360989	+	0.932570i	$0.617561\pi$
$168$	0.455807	0.0351662
$169$	−8.26611	−0.635855
$170$	22.2652	1.70766
$171$	−9.14688	−0.699479
$172$	2.46475	0.187936
$173$	20.7325	1.57626	0.788130	−	0.615509i	$-0.211050\pi$
$173$	20.7325	1.57626	0.788130	+	0.615509i	$0.211050\pi$
$174$	9.39088	0.711921
$175$	−2.26807	−0.171450
$176$	8.92351	0.672635
$177$	4.79712	0.360574
$178$	−4.03863	−0.302708
$179$	−20.9050	−1.56251	−0.781257	−	0.624209i	$-0.785421\pi$
$179$	−20.9050	−1.56251	−0.781257	+	0.624209i	$0.785421\pi$
$180$	9.46652	0.705592
$181$	−3.15181	−0.234272	−0.117136	−	0.993116i	$-0.537371\pi$
$181$	−3.15181	−0.234272	−0.117136	+	0.993116i	$0.537371\pi$
$182$	−4.22262	−0.313002
$183$	−4.34083	−0.320883
$184$	1.68417	0.124159
$185$	25.3129	1.86104
$186$	10.0554	0.737296
$187$	−8.60612	−0.629342
$188$	−8.32378	−0.607074
$189$	−5.01829	−0.365027
$190$	24.0772	1.74675
$191$	−11.2964	−0.817376	−0.408688	−	0.912674i	$-0.634013\pi$
$191$	−11.2964	−0.817376	−0.408688	+	0.912674i	$0.634013\pi$
$192$	6.07336	0.438307
$193$	−22.5463	−1.62292	−0.811459	−	0.584410i	$-0.801326\pi$
$193$	−22.5463	−1.62292	−0.811459	+	0.584410i	$0.801326\pi$
$194$	−14.3407	−1.02960
$195$	−5.90167	−0.422627
$196$	1.76657	0.126184
$197$	−23.1505	−1.64941	−0.824703	−	0.565567i	$-0.808658\pi$
$197$	−23.1505	−1.64941	−0.824703	+	0.565567i	$0.808658\pi$
$198$	−7.80165	−0.554439
$199$	−6.68588	−0.473949	−0.236975	−	0.971516i	$-0.576156\pi$
$199$	−6.68588	−0.473949	−0.236975	+	0.971516i	$0.576156\pi$
$200$	1.02750	0.0726551
$201$	−2.97429	−0.209790
$202$	−25.1741	−1.77124
$203$	−4.80924	−0.337543
$204$	−7.56365	−0.529562
$205$	20.2751	1.41608
$206$	27.9872	1.94996
$207$	−7.38944	−0.513602
$208$	9.60020	0.665654
$209$	−9.30653	−0.643746
$210$	5.26428	0.363270
$211$	−12.3048	−0.847100	−0.423550	−	0.905873i	$-0.639216\pi$
$211$	−12.3048	−0.847100	−0.423550	+	0.905873i	$0.639216\pi$
$212$	−11.5079	−0.790363
$213$	13.3082	0.911862
$214$	20.5462	1.40451
$215$	−3.76142	−0.256527
$216$	2.27342	0.154687
$217$	−5.14954	−0.349574
$218$	−18.0169	−1.22026
$219$	11.8172	0.798532
$220$	9.63175	0.649372
$221$	−9.25875	−0.622811
$222$	−18.3342	−1.23051
$223$	−15.3174	−1.02573	−0.512866	−	0.858469i	$-0.671416\pi$
$223$	−15.3174	−1.02573	−0.512866	+	0.858469i	$0.671416\pi$
$224$	−7.65732	−0.511626
$225$	−4.50822	−0.300548
$226$	−23.9706	−1.59450
$227$	13.8232	0.917478	0.458739	−	0.888571i	$-0.348301\pi$
$227$	13.8232	0.917478	0.458739	+	0.888571i	$0.348301\pi$
$228$	−8.17922	−0.541682
$229$	7.44973	0.492292	0.246146	−	0.969233i	$-0.420836\pi$
$229$	7.44973	0.492292	0.246146	+	0.969233i	$0.420836\pi$
$230$	19.4512	1.28257
$231$	−2.03479	−0.133880
$232$	2.17872	0.143040
$233$	−9.57488	−0.627271	−0.313636	−	0.949543i	$-0.601547\pi$
$233$	−9.57488	−0.627271	−0.313636	+	0.949543i	$0.601547\pi$
$234$	−8.39327	−0.548685
$235$	12.7028	0.828637
$236$	−8.42279	−0.548277
$237$	14.4902	0.941243
$238$	8.25880	0.535338
$239$	25.6135	1.65680	0.828400	−	0.560137i	$-0.189251\pi$
$239$	25.6135	1.65680	0.828400	+	0.560137i	$0.189251\pi$
$240$	−11.9684	−0.772559
$241$	11.3040	0.728152	0.364076	−	0.931369i	$-0.381385\pi$
$241$	11.3040	0.728152	0.364076	+	0.931369i	$0.381385\pi$
$242$	13.4106	0.862067
$243$	−15.9745	−1.02476
$244$	7.62163	0.487925
$245$	−2.69594	−0.172237
$246$	−14.6853	−0.936303
$247$	−10.0123	−0.637066
$248$	2.33288	0.148138
$249$	2.49748	0.158271
$250$	−14.2940	−0.904029
$251$	−6.26583	−0.395496	−0.197748	−	0.980253i	$-0.563363\pi$
$251$	−6.26583	−0.395496	−0.197748	+	0.980253i	$0.563363\pi$
$252$	3.51140	0.221198
$253$	−7.51842	−0.472679
$254$	−18.5498	−1.16392
$255$	11.5428	0.722835
$256$	19.0585	1.19116
$257$	0.495227	0.0308914	0.0154457	−	0.999881i	$-0.495083\pi$
$257$	0.495227	0.0308914	0.0154457	+	0.999881i	$0.495083\pi$
$258$	2.72440	0.169614
$259$	9.38929	0.583422
$260$	10.3622	0.642634
$261$	−9.55930	−0.591706
$262$	10.9598	0.677097
$263$	11.9267	0.735429	0.367715	−	0.929939i	$-0.380140\pi$
$263$	11.9267	0.735429	0.367715	+	0.929939i	$0.380140\pi$
$264$	0.921817	0.0567339
$265$	17.5619	1.07882
$266$	8.93094	0.547591
$267$	−2.09371	−0.128133
$268$	5.22226	0.319000
$269$	15.3707	0.937167	0.468584	−	0.883419i	$-0.344764\pi$
$269$	15.3707	0.937167	0.468584	+	0.883419i	$0.344764\pi$
$270$	26.2566	1.59793
$271$	−12.9522	−0.786790	−0.393395	−	0.919369i	$-0.628700\pi$
$271$	−12.9522	−0.786790	−0.393395	+	0.919369i	$0.628700\pi$
$272$	−18.7765	−1.13849
$273$	−2.18910	−0.132490
$274$	−44.0413	−2.66063
$275$	−4.58691	−0.276601
$276$	−6.60770	−0.397737
$277$	−1.46366	−0.0879428	−0.0439714	−	0.999033i	$-0.514001\pi$
$277$	−1.46366	−0.0879428	−0.0439714	+	0.999033i	$0.514001\pi$
$278$	35.7812	2.14601
$279$	−10.2357	−0.612796
$280$	1.22133	0.0729886
$281$	17.0323	1.01606	0.508032	−	0.861338i	$-0.330373\pi$
$281$	17.0323	1.01606	0.508032	+	0.861338i	$0.330373\pi$
$282$	−9.20065	−0.547891
$283$	18.2911	1.08729	0.543647	−	0.839314i	$-0.317043\pi$
$283$	18.2911	1.08729	0.543647	+	0.839314i	$0.317043\pi$
$284$	−23.3665	−1.38655
$285$	12.4822	0.739379
$286$	−8.53977	−0.504967
$287$	7.52063	0.443929
$288$	−15.2204	−0.896870
$289$	1.10869	0.0652172
$290$	25.1628	1.47761
$291$	−7.43453	−0.435820
$292$	−20.7486	−1.21422
$293$	28.2990	1.65324	0.826622	−	0.562757i	$-0.190259\pi$
$293$	28.2990	1.65324	0.826622	+	0.562757i	$0.190259\pi$
$294$	1.95267	0.113882
$295$	12.8539	0.748381
$296$	−4.25361	−0.247236
$297$	−10.1489	−0.588900
$298$	6.64923	0.385180
$299$	−8.08857	−0.467774
$300$	−4.03129	−0.232747
$301$	−1.39522	−0.0804190
$302$	−34.6095	−1.99155
$303$	−13.0508	−0.749748
$304$	−20.3046	−1.16455
$305$	−11.6312	−0.666002
$306$	16.4159	0.938437
$307$	−1.55813	−0.0889273	−0.0444637	−	0.999011i	$-0.514158\pi$
$307$	−1.55813	−0.0889273	−0.0444637	+	0.999011i	$0.514158\pi$
$308$	3.57269	0.203573
$309$	14.5092	0.825399
$310$	26.9433	1.53028
$311$	15.3696	0.871529	0.435765	−	0.900061i	$-0.356478\pi$
$311$	15.3696	0.871529	0.435765	+	0.900061i	$0.356478\pi$
$312$	0.991721	0.0561452
$313$	−20.2720	−1.14584	−0.572920	−	0.819611i	$-0.694189\pi$
$313$	−20.2720	−1.14584	−0.572920	+	0.819611i	$0.694189\pi$
$314$	42.7839	2.41444
$315$	−5.35869	−0.301928
$316$	−25.4420	−1.43122
$317$	22.2825	1.25151	0.625754	−	0.780021i	$-0.284792\pi$
$317$	22.2825	1.25151	0.625754	+	0.780021i	$0.284792\pi$
$318$	−12.7202	−0.713311
$319$	−9.72615	−0.544560
$320$	16.2735	0.909719
$321$	10.6516	0.594513
$322$	7.21499	0.402076
$323$	19.5825	1.08960
$324$	1.61464	0.0897021
$325$	−4.93475	−0.273731
$326$	−18.7956	−1.04099
$327$	−9.34033	−0.516522
$328$	−3.40705	−0.188123
$329$	4.71182	0.259771
$330$	10.6464	0.586065
$331$	31.6438	1.73930	0.869650	−	0.493670i	$-0.164345\pi$
$331$	31.6438	1.73930	0.869650	+	0.493670i	$0.164345\pi$
$332$	−4.38507	−0.240662
$333$	18.6630	1.02273
$334$	18.1074	0.990792
$335$	−7.96960	−0.435426
$336$	−4.43944	−0.242191
$337$	−6.16689	−0.335932	−0.167966	−	0.985793i	$-0.553720\pi$
$337$	−6.16689	−0.335932	−0.167966	+	0.985793i	$0.553720\pi$
$338$	16.0426	0.872602
$339$	−12.4269	−0.674935
$340$	−20.2668	−1.09912
$341$	−10.4144	−0.563969
$342$	17.7520	0.959916
$343$	−1.00000	−0.0539949
$344$	0.632072	0.0340790
$345$	10.0839	0.542899
$346$	−40.2368	−2.16315
$347$	36.2494	1.94597	0.972985	−	0.230868i	$-0.0741566\pi$
$347$	36.2494	1.94597	0.972985	+	0.230868i	$0.0741566\pi$
$348$	−8.54801	−0.458221
$349$	−36.4882	−1.95317	−0.976585	−	0.215130i	$-0.930982\pi$
$349$	−36.4882	−1.95317	−0.976585	+	0.215130i	$0.930982\pi$
$350$	4.40179	0.235286
$351$	−10.9185	−0.582789
$352$	−15.4860	−0.825409
$353$	28.2780	1.50508	0.752542	−	0.658544i	$-0.228827\pi$
$353$	28.2780	1.50508	0.752542	+	0.658544i	$0.228827\pi$
$354$	−9.31009	−0.494826
$355$	35.6592	1.89260
$356$	3.67614	0.194835
$357$	4.28154	0.226603
$358$	40.5717	2.14428
$359$	7.17949	0.378919	0.189459	−	0.981889i	$-0.439326\pi$
$359$	7.17949	0.378919	0.189459	+	0.981889i	$0.439326\pi$
$360$	2.42763	0.127947
$361$	2.17619	0.114536
$362$	6.11693	0.321498
$363$	6.95235	0.364904
$364$	3.84362	0.201460
$365$	31.6641	1.65738
$366$	8.42453	0.440357
$367$	−14.9381	−0.779764	−0.389882	−	0.920865i	$-0.627484\pi$
$367$	−14.9381	−0.779764	−0.389882	+	0.920865i	$0.627484\pi$
$368$	−16.4034	−0.855087
$369$	14.9487	0.778198
$370$	−49.1265	−2.55396
$371$	6.51423	0.338202
$372$	−9.15286	−0.474554
$373$	−3.95267	−0.204661	−0.102331	−	0.994750i	$-0.532630\pi$
$373$	−3.95267	−0.204661	−0.102331	+	0.994750i	$0.532630\pi$
$374$	16.7025	0.863664
$375$	−7.41029	−0.382666
$376$	−2.13458	−0.110083
$377$	−10.4637	−0.538909
$378$	9.73933	0.500937
$379$	−9.67783	−0.497117	−0.248558	−	0.968617i	$-0.579957\pi$
$379$	−9.67783	−0.497117	−0.248558	+	0.968617i	$0.579957\pi$
$380$	−21.9162	−1.12428
$381$	−9.61662	−0.492674
$382$	21.9236	1.12171
$383$	−23.6796	−1.20997	−0.604986	−	0.796236i	$-0.706821\pi$
$383$	−23.6796	−1.20997	−0.604986	+	0.796236i	$0.706821\pi$
$384$	3.62162	0.184815
$385$	−5.45222	−0.277871
$386$	43.7571	2.22718
$387$	−2.77326	−0.140973
$388$	13.0536	0.662694
$389$	−32.9020	−1.66820	−0.834100	−	0.551614i	$-0.814012\pi$
$389$	−32.9020	−1.66820	−0.834100	+	0.551614i	$0.814012\pi$
$390$	11.4538	0.579984
$391$	15.8200	0.800051
$392$	0.453027	0.0228813
$393$	5.68179	0.286608
$394$	44.9297	2.26353
$395$	38.8266	1.95358
$396$	7.10141	0.356859
$397$	−28.2862	−1.41964	−0.709821	−	0.704382i	$-0.751224\pi$
$397$	−28.2862	−1.41964	−0.709821	+	0.704382i	$0.751224\pi$
$398$	12.9757	0.650414
$399$	4.62999	0.231790
$400$	−10.0076	−0.500378
$401$	15.4810	0.773086	0.386543	−	0.922271i	$-0.373669\pi$
$401$	15.4810	0.773086	0.386543	+	0.922271i	$0.373669\pi$
$402$	5.77240	0.287901
$403$	−11.2041	−0.558117
$404$	22.9146	1.14004
$405$	−2.46407	−0.122441
$406$	9.33362	0.463220
$407$	18.9888	0.941239
$408$	−1.93965	−0.0960272
$409$	11.8534	0.586114	0.293057	−	0.956095i	$-0.405327\pi$
$409$	11.8534	0.586114	0.293057	+	0.956095i	$0.405327\pi$
$410$	−39.3493	−1.94332
$411$	−22.8320	−1.12622
$412$	−25.4753	−1.25508
$413$	4.76787	0.234611
$414$	14.3412	0.704830
$415$	6.69198	0.328496
$416$	−16.6604	−0.816843
$417$	18.5497	0.908385
$418$	18.0618	0.883432
$419$	33.4850	1.63585	0.817923	−	0.575327i	$-0.195125\pi$
$419$	33.4850	1.63585	0.817923	+	0.575327i	$0.195125\pi$
$420$	−4.79179	−0.233815
$421$	−0.175204	−0.00853890	−0.00426945	−	0.999991i	$-0.501359\pi$
$421$	−0.175204	−0.00853890	−0.00426945	+	0.999991i	$0.501359\pi$
$422$	23.8808	1.16250
$423$	9.36565	0.455374
$424$	−2.95112	−0.143319
$425$	9.65162	0.468172
$426$	−25.8281	−1.25137
$427$	−4.31436	−0.208786
$428$	−18.7021	−0.903998
$429$	−4.42720	−0.213747
$430$	7.30003	0.352039
$431$	−26.3999	−1.27164	−0.635819	−	0.771839i	$-0.719337\pi$
$431$	−26.3999	−1.27164	−0.635819	+	0.771839i	$0.719337\pi$
$432$	−22.1425	−1.06533
$433$	−25.4869	−1.22482	−0.612412	−	0.790539i	$-0.709801\pi$
$433$	−25.4869	−1.22482	−0.612412	+	0.790539i	$0.709801\pi$
$434$	9.99406	0.479730
$435$	13.0450	0.625458
$436$	16.3998	0.785406
$437$	17.1075	0.818362
$438$	−22.9344	−1.09585
$439$	−3.72762	−0.177909	−0.0889547	−	0.996036i	$-0.528353\pi$
$439$	−3.72762	−0.177909	−0.0889547	+	0.996036i	$0.528353\pi$
$440$	2.47001	0.117753
$441$	−1.98769	−0.0946520
$442$	17.9691	0.854702
$443$	−9.68542	−0.460168	−0.230084	−	0.973171i	$-0.573900\pi$
$443$	−9.68542	−0.460168	−0.230084	+	0.973171i	$0.573900\pi$
$444$	16.6886	0.792008
$445$	−5.61010	−0.265944
$446$	29.7276	1.40764
$447$	3.44711	0.163043
$448$	6.03633	0.285190
$449$	7.71234	0.363968	0.181984	−	0.983302i	$-0.441748\pi$
$449$	7.71234	0.363968	0.181984	+	0.983302i	$0.441748\pi$
$450$	8.74941	0.412451
$451$	15.2096	0.716193
$452$	21.8191	1.02628
$453$	−17.9423	−0.843003
$454$	−26.8276	−1.25908
$455$	−5.86568	−0.274987
$456$	−2.09751	−0.0982250
$457$	−6.57310	−0.307477	−0.153738	−	0.988112i	$-0.549131\pi$
$457$	−6.57310	−0.307477	−0.153738	+	0.988112i	$0.549131\pi$
$458$	−14.4582	−0.675587
$459$	21.3550	0.996766
$460$	−17.7053	−0.825515
$461$	−33.6509	−1.56728	−0.783640	−	0.621215i	$-0.786639\pi$
$461$	−33.6509	−1.56728	−0.783640	+	0.621215i	$0.786639\pi$
$462$	3.94906	0.183727
$463$	7.41113	0.344424	0.172212	−	0.985060i	$-0.444909\pi$
$463$	7.41113	0.344424	0.172212	+	0.985060i	$0.444909\pi$
$464$	−21.2201	−0.985120
$465$	13.9680	0.647751
$466$	18.5826	0.860823
$467$	8.07476	0.373655	0.186828	−	0.982393i	$-0.440179\pi$
$467$	8.07476	0.373655	0.186828	+	0.982393i	$0.440179\pi$
$468$	7.63993	0.353156
$469$	−2.95615	−0.136502
$470$	−24.6531	−1.13716
$471$	22.1801	1.02201
$472$	−2.15997	−0.0994209
$473$	−2.82167	−0.129740
$474$	−28.1222	−1.29169
$475$	10.4371	0.478888
$476$	−7.51753	−0.344565
$477$	12.9483	0.592861
$478$	−49.7098	−2.27367
$479$	24.6190	1.12487	0.562435	−	0.826842i	$-0.309865\pi$
$479$	24.6190	1.12487	0.562435	+	0.826842i	$0.309865\pi$
$480$	20.7703	0.948029
$481$	20.4288	0.931471
$482$	−21.9383	−0.999264
$483$	3.74041	0.170194
$484$	−12.2069	−0.554861
$485$	−19.9208	−0.904557
$486$	31.0027	1.40631
$487$	7.25667	0.328831	0.164416	−	0.986391i	$-0.447426\pi$
$487$	7.25667	0.328831	0.164416	+	0.986391i	$0.447426\pi$
$488$	1.95452	0.0884770
$489$	−9.74403	−0.440640
$490$	5.23218	0.236366
$491$	−38.0416	−1.71679	−0.858396	−	0.512988i	$-0.828539\pi$
$491$	−38.0416	−1.71679	−0.858396	+	0.512988i	$0.828539\pi$
$492$	13.3673	0.602642
$493$	20.4654	0.921716
$494$	19.4315	0.874264
$495$	−10.8373	−0.487102
$496$	−22.7217	−1.02023
$497$	13.2270	0.593314
$498$	−4.84702	−0.217200
$499$	−29.9037	−1.33867	−0.669337	−	0.742959i	$-0.733422\pi$
$499$	−29.9037	−1.33867	−0.669337	+	0.742959i	$0.733422\pi$
$500$	13.0110	0.581870
$501$	9.38726	0.419392
$502$	12.1605	0.542750
$503$	6.59371	0.293999	0.146999	−	0.989137i	$-0.453038\pi$
$503$	6.59371	0.293999	0.146999	+	0.989137i	$0.453038\pi$
$504$	0.900479	0.0401105
$505$	−34.9695	−1.55612
$506$	14.5915	0.648671
$507$	8.31683	0.369363
$508$	16.8849	0.749145
$509$	−5.11035	−0.226512	−0.113256	−	0.993566i	$-0.536128\pi$
$509$	−5.11035	−0.226512	−0.113256	+	0.993566i	$0.536128\pi$
$510$	−22.4018	−0.991968
$511$	11.7451	0.519574
$512$	−29.7890	−1.31650
$513$	23.0930	1.01958
$514$	−0.961119	−0.0423932
$515$	38.8773	1.71314
$516$	−2.47988	−0.109170
$517$	9.52912	0.419090
$518$	−18.2224	−0.800647
$519$	−20.8596	−0.915637
$520$	2.65731	0.116531
$521$	−34.3032	−1.50285	−0.751426	−	0.659817i	$-0.770634\pi$
$521$	−34.3032	−1.50285	−0.751426	+	0.659817i	$0.770634\pi$
$522$	18.5524	0.812015
$523$	11.4171	0.499234	0.249617	−	0.968345i	$-0.419695\pi$
$523$	11.4171	0.499234	0.249617	+	0.968345i	$0.419695\pi$
$524$	−9.97609	−0.435807
$525$	2.28199	0.0995940
$526$	−23.1469	−1.00925
$527$	21.9135	0.954568
$528$	−8.97825	−0.390728
$529$	−9.17946	−0.399107
$530$	−34.0836	−1.48050
$531$	9.47705	0.411269
$532$	−8.12934	−0.352452
$533$	16.3630	0.708761
$534$	4.06341	0.175841
$535$	28.5409	1.23393
$536$	1.33922	0.0578454
$537$	21.0333	0.907653
$538$	−29.8309	−1.28610
$539$	−2.02239	−0.0871103
$540$	−23.9000	−1.02849
$541$	4.42397	0.190201	0.0951006	−	0.995468i	$-0.469683\pi$
$541$	4.42397	0.190201	0.0951006	+	0.995468i	$0.469683\pi$
$542$	25.1372	1.07974
$543$	3.17115	0.136087
$544$	32.5852	1.39708
$545$	−25.0274	−1.07206
$546$	4.24853	0.181820
$547$	0.655746	0.0280377	0.0140188	−	0.999902i	$-0.495538\pi$
$547$	0.655746	0.0280377	0.0140188	+	0.999902i	$0.495538\pi$
$548$	40.0884	1.71249
$549$	−8.57561	−0.365998
$550$	8.90212	0.379588
$551$	22.1310	0.942812
$552$	−1.69451	−0.0721230
$553$	14.4019	0.612431
$554$	2.84062	0.120686
$555$	−25.4682	−1.08107
$556$	−32.5697	−1.38126
$557$	39.4366	1.67098	0.835492	−	0.549503i	$-0.185183\pi$
$557$	39.4366	1.67098	0.835492	+	0.549503i	$0.185183\pi$
$558$	19.8651	0.840957
$559$	−3.03564	−0.128394
$560$	−11.8955	−0.502675
$561$	8.65892	0.365580
$562$	−33.0558	−1.39437
$563$	19.3254	0.814469	0.407235	−	0.913324i	$-0.366493\pi$
$563$	19.3254	0.814469	0.407235	+	0.913324i	$0.366493\pi$
$564$	8.37485	0.352645
$565$	−33.2977	−1.40085
$566$	−35.4988	−1.49213
$567$	−0.913994	−0.0383842
$568$	−5.99221	−0.251427
$569$	30.3006	1.27027	0.635133	−	0.772402i	$-0.280945\pi$
$569$	30.3006	1.27027	0.635133	+	0.772402i	$0.280945\pi$
$570$	−24.2250	−1.01467
$571$	41.6271	1.74204	0.871020	−	0.491247i	$-0.163459\pi$
$571$	41.6271	1.74204	0.871020	+	0.491247i	$0.163459\pi$
$572$	7.77328	0.325017
$573$	11.3657	0.474807
$574$	−14.5958	−0.609216
$575$	8.43178	0.351629
$576$	11.9984	0.499932
$577$	−24.6434	−1.02592	−0.512959	−	0.858413i	$-0.671451\pi$
$577$	−24.6434	−1.02592	−0.512959	+	0.858413i	$0.671451\pi$
$578$	−2.15171	−0.0894994
$579$	22.6846	0.942741
$580$	−22.9043	−0.951051
$581$	2.48225	0.102981
$582$	14.4287	0.598088
$583$	13.1743	0.545623
$584$	−5.32087	−0.220179
$585$	−11.6592	−0.482047
$586$	−54.9217	−2.26879
$587$	18.7950	0.775754	0.387877	−	0.921711i	$-0.373209\pi$
$587$	18.7950	0.775754	0.387877	+	0.921711i	$0.373209\pi$
$588$	−1.77741	−0.0732992
$589$	23.6970	0.976416
$590$	−24.9464	−1.02702
$591$	23.2925	0.958127
$592$	41.4290	1.70272
$593$	41.3186	1.69675	0.848376	−	0.529394i	$-0.177581\pi$
$593$	41.3186	1.69675	0.848376	+	0.529394i	$0.177581\pi$
$594$	19.6967	0.808165
$595$	11.4724	0.470321
$596$	−6.05243	−0.247917
$597$	6.72690	0.275314
$598$	15.6980	0.641940
$599$	4.49731	0.183755	0.0918776	−	0.995770i	$-0.470713\pi$
$599$	4.49731	0.183755	0.0918776	+	0.995770i	$0.470713\pi$
$600$	−1.03380	−0.0422048
$601$	13.5385	0.552246	0.276123	−	0.961122i	$-0.410950\pi$
$601$	13.5385	0.552246	0.276123	+	0.961122i	$0.410950\pi$
$602$	2.70779	0.110361
$603$	−5.87592	−0.239286
$604$	31.5031	1.28184
$605$	18.6288	0.757368
$606$	25.3285	1.02890
$607$	43.7191	1.77450	0.887252	−	0.461286i	$-0.152612\pi$
$607$	43.7191	1.77450	0.887252	+	0.461286i	$0.152612\pi$
$608$	35.2371	1.42905
$609$	4.83875	0.196076
$610$	22.5735	0.913974
$611$	10.2517	0.414741
$612$	−14.9425	−0.604016
$613$	−7.44788	−0.300817	−0.150409	−	0.988624i	$-0.548059\pi$
$613$	−7.44788	−0.300817	−0.150409	+	0.988624i	$0.548059\pi$
$614$	3.02397	0.122038
$615$	−20.3995	−0.822588
$616$	0.916196	0.0369146
$617$	34.2474	1.37875	0.689374	−	0.724406i	$-0.257886\pi$
$617$	34.2474	1.37875	0.689374	+	0.724406i	$0.257886\pi$
$618$	−28.1590	−1.13272
$619$	4.01692	0.161454	0.0807268	−	0.996736i	$-0.474276\pi$
$619$	4.01692	0.161454	0.0807268	+	0.996736i	$0.474276\pi$
$620$	−24.5250	−0.984950
$621$	18.6560	0.748640
$622$	−29.8288	−1.19602
$623$	−2.08095	−0.0833713
$624$	−9.65910	−0.386674
$625$	−31.1962	−1.24785
$626$	39.3432	1.57247
$627$	9.36363	0.373947
$628$	−38.9438	−1.55403
$629$	−39.9555	−1.59313
$630$	10.4000	0.414344
$631$	−31.2128	−1.24256	−0.621281	−	0.783588i	$-0.713387\pi$
$631$	−31.2128	−1.24256	−0.621281	+	0.783588i	$0.713387\pi$
$632$	−6.52445	−0.259529
$633$	12.3803	0.492074
$634$	−43.2450	−1.71748
$635$	−25.7677	−1.02256
$636$	11.5785	0.459116
$637$	−2.17575	−0.0862063
$638$	18.8762	0.747315
$639$	26.2913	1.04007
$640$	9.70411	0.383589
$641$	26.2583	1.03714	0.518569	−	0.855036i	$-0.326465\pi$
$641$	26.2583	1.03714	0.518569	+	0.855036i	$0.326465\pi$
$642$	−20.6722	−0.815868
$643$	19.0350	0.750667	0.375334	−	0.926890i	$-0.377528\pi$
$643$	19.0350	0.750667	0.375334	+	0.926890i	$0.377528\pi$
$644$	−6.56741	−0.258792
$645$	3.78449	0.149014
$646$	−38.0050	−1.49529
$647$	−45.7092	−1.79702	−0.898508	−	0.438958i	$-0.855348\pi$
$647$	−45.7092	−1.79702	−0.898508	+	0.438958i	$0.855348\pi$
$648$	0.414064	0.0162660
$649$	9.64247	0.378500
$650$	9.57720	0.375649
$651$	5.18114	0.203065
$652$	17.1086	0.670024
$653$	2.17489	0.0851100	0.0425550	−	0.999094i	$-0.486450\pi$
$653$	2.17489	0.0851100	0.0425550	+	0.999094i	$0.486450\pi$
$654$	18.1274	0.708838
$655$	15.2243	0.594864
$656$	33.1838	1.29561
$657$	23.3457	0.910803
$658$	−9.14454	−0.356491
$659$	−6.16136	−0.240012	−0.120006	−	0.992773i	$-0.538291\pi$
$659$	−6.16136	−0.240012	−0.120006	+	0.992773i	$0.538291\pi$
$660$	−9.69084	−0.377215
$661$	−14.4603	−0.562441	−0.281221	−	0.959643i	$-0.590739\pi$
$661$	−14.4603	−0.562441	−0.281221	+	0.959643i	$0.590739\pi$
$662$	−61.4132	−2.38689
$663$	9.31556	0.361786
$664$	−1.12453	−0.0436401
$665$	12.4060	0.481086
$666$	−36.2206	−1.40352
$667$	17.8788	0.692272
$668$	−16.4822	−0.637714
$669$	15.4114	0.595840
$670$	15.4671	0.597547
$671$	−8.72529	−0.336836
$672$	7.70430	0.297200
$673$	−2.86679	−0.110507	−0.0552533	−	0.998472i	$-0.517597\pi$
$673$	−2.86679	−0.110507	−0.0552533	+	0.998472i	$0.517597\pi$
$674$	11.9685	0.461009
$675$	11.3818	0.438087
$676$	−14.6027	−0.561642
$677$	−31.6877	−1.21786	−0.608929	−	0.793225i	$-0.708401\pi$
$677$	−31.6877	−1.21786	−0.608929	+	0.793225i	$0.708401\pi$
$678$	24.1176	0.926232
$679$	−7.38920	−0.283571
$680$	−5.19730	−0.199307
$681$	−13.9080	−0.532956
$682$	20.2118	0.773951
$683$	37.1977	1.42333	0.711665	−	0.702519i	$-0.247942\pi$
$683$	37.1977	1.42333	0.711665	+	0.702519i	$0.247942\pi$
$684$	−16.1586	−0.617841
$685$	−61.1782	−2.33750
$686$	1.94077	0.0740988
$687$	−7.49544	−0.285969
$688$	−6.15621	−0.234703
$689$	14.1733	0.539961
$690$	−19.5705	−0.745036
$691$	25.4335	0.967537	0.483769	−	0.875196i	$-0.339268\pi$
$691$	25.4335	0.967537	0.483769	+	0.875196i	$0.339268\pi$
$692$	36.6254	1.39229
$693$	−4.01988	−0.152703
$694$	−70.3516	−2.67051
$695$	49.7040	1.88538
$696$	−2.19209	−0.0830908
$697$	−32.0035	−1.21222
$698$	70.8151	2.68039
$699$	9.63363	0.364377
$700$	−4.00671	−0.151439
$701$	47.2791	1.78571	0.892853	−	0.450347i	$-0.148700\pi$
$701$	47.2791	1.78571	0.892853	+	0.450347i	$0.148700\pi$
$702$	21.1903	0.799778
$703$	−43.2073	−1.62959
$704$	12.2078	0.460098
$705$	−12.7807	−0.481349
$706$	−54.8809	−2.06547
$707$	−12.9712	−0.487832
$708$	8.47446	0.318490
$709$	43.4179	1.63059	0.815297	−	0.579043i	$-0.196574\pi$
$709$	43.4179	1.63059	0.815297	+	0.579043i	$0.196574\pi$
$710$	−69.2062	−2.59726
$711$	28.6265	1.07358
$712$	0.942725	0.0353301
$713$	19.1439	0.716946
$714$	−8.30947	−0.310974
$715$	−11.8627	−0.443639
$716$	−36.9302	−1.38015
$717$	−25.7707	−0.962423
$718$	−13.9337	−0.520001
$719$	11.2475	0.419460	0.209730	−	0.977759i	$-0.432742\pi$
$719$	11.2475	0.419460	0.209730	+	0.977759i	$0.432742\pi$
$720$	−23.6445	−0.881178
$721$	14.4207	0.537056
$722$	−4.22347	−0.157181
$723$	−11.3733	−0.422978
$724$	−5.56790	−0.206929
$725$	10.9077	0.405102
$726$	−13.4929	−0.500768
$727$	26.5938	0.986309	0.493155	−	0.869942i	$-0.335844\pi$
$727$	26.5938	0.986309	0.493155	+	0.869942i	$0.335844\pi$
$728$	0.985674	0.0365315
$729$	13.3305	0.493722
$730$	−61.4527	−2.27447
$731$	5.93725	0.219597
$732$	−7.66839	−0.283432
$733$	−0.193593	−0.00715053	−0.00357526	−	0.999994i	$-0.501138\pi$
$733$	−0.193593	−0.00715053	−0.00357526	+	0.999994i	$0.501138\pi$
$734$	28.9914	1.07009
$735$	2.71248	0.100051
$736$	28.4668	1.04930
$737$	−5.97848	−0.220220
$738$	−29.0119	−1.06794
$739$	32.0182	1.17781	0.588904	−	0.808203i	$-0.299560\pi$
$739$	32.0182	1.17781	0.588904	+	0.808203i	$0.299560\pi$
$740$	44.7171	1.64384
$741$	10.0737	0.370067
$742$	−12.6426	−0.464124
$743$	38.6762	1.41889	0.709447	−	0.704759i	$-0.248945\pi$
$743$	38.6762	1.41889	0.709447	+	0.704759i	$0.248945\pi$
$744$	−2.34720	−0.0860524
$745$	9.23651	0.338400
$746$	7.67120	0.280863
$747$	4.93394	0.180524
$748$	−15.2033	−0.555889
$749$	10.5866	0.386827
$750$	14.3816	0.525144
$751$	−6.44297	−0.235107	−0.117554	−	0.993067i	$-0.537505\pi$
$751$	−6.44297	−0.235107	−0.117554	+	0.993067i	$0.537505\pi$
$752$	20.7903	0.758144
$753$	6.30427	0.229741
$754$	20.3076	0.739560
$755$	−48.0763	−1.74968
$756$	−8.86518	−0.322423
$757$	22.2234	0.807724	0.403862	−	0.914820i	$-0.367668\pi$
$757$	22.2234	0.807724	0.403862	+	0.914820i	$0.367668\pi$
$758$	18.7824	0.682208
$759$	7.56455	0.274576
$760$	−5.62028	−0.203869
$761$	−9.61514	−0.348549	−0.174274	−	0.984697i	$-0.555758\pi$
$761$	−9.61514	−0.348549	−0.174274	+	0.984697i	$0.555758\pi$
$762$	18.6636	0.676111
$763$	−9.28338	−0.336081
$764$	−19.9558	−0.721977
$765$	22.8035	0.824464
$766$	45.9566	1.66048
$767$	10.3737	0.374572
$768$	−19.1754	−0.691934
$769$	0.885299	0.0319247	0.0159623	−	0.999873i	$-0.494919\pi$
$769$	0.885299	0.0319247	0.0159623	+	0.999873i	$0.494919\pi$
$770$	10.5815	0.381330
$771$	−0.498265	−0.0179446
$772$	−39.8297	−1.43350
$773$	−21.5410	−0.774777	−0.387388	−	0.921917i	$-0.626623\pi$
$773$	−21.5410	−0.774777	−0.387388	+	0.921917i	$0.626623\pi$
$774$	5.38225	0.193461
$775$	11.6795	0.419541
$776$	3.34751	0.120169
$777$	−9.44690	−0.338906
$778$	63.8552	2.28932
$779$	−34.6081	−1.23996
$780$	−10.4257	−0.373301
$781$	26.7502	0.957196
$782$	−30.7029	−1.09793
$783$	24.1342	0.862486
$784$	−4.41237	−0.157584
$785$	59.4315	2.12120
$786$	−11.0270	−0.393321
$787$	−18.6566	−0.665035	−0.332518	−	0.943097i	$-0.607898\pi$
$787$	−18.6566	−0.665035	−0.332518	+	0.943097i	$0.607898\pi$
$788$	−40.8971	−1.45690
$789$	−11.9998	−0.427205
$790$	−75.3533	−2.68095
$791$	−12.3511	−0.439154
$792$	1.82111	0.0647105
$793$	−9.38696	−0.333341
$794$	54.8968	1.94821
$795$	−17.6697	−0.626679
$796$	−11.8111	−0.418633
$797$	−45.5609	−1.61385	−0.806925	−	0.590654i	$-0.798870\pi$
$797$	−45.5609	−1.61385	−0.806925	+	0.590654i	$0.798870\pi$
$798$	−8.98573	−0.318091
$799$	−20.0508	−0.709348
$800$	17.3673	0.614028
$801$	−4.13628	−0.146148
$802$	−30.0451	−1.06093
$803$	23.7532	0.838232
$804$	−5.25430	−0.185305
$805$	10.0224	0.353243
$806$	21.7446	0.765920
$807$	−15.4650	−0.544393
$808$	5.87631	0.206728
$809$	−41.3357	−1.45329	−0.726643	−	0.687015i	$-0.758921\pi$
$809$	−41.3357	−1.45329	−0.726643	+	0.687015i	$0.758921\pi$
$810$	4.78218	0.168029
$811$	−31.6949	−1.11296	−0.556480	−	0.830861i	$-0.687848\pi$
$811$	−31.6949	−1.11296	−0.556480	+	0.830861i	$0.687848\pi$
$812$	−8.49588	−0.298147
$813$	13.0317	0.457041
$814$	−36.8528	−1.29169
$815$	−26.1091	−0.914562
$816$	18.8917	0.661342
$817$	6.42046	0.224623
$818$	−23.0047	−0.804342
$819$	−4.32472	−0.151118
$820$	35.8175	1.25080
$821$	0.652440	0.0227703	0.0113852	−	0.999935i	$-0.496376\pi$
$821$	0.652440	0.0227703	0.0113852	+	0.999935i	$0.496376\pi$
$822$	44.3115	1.54554
$823$	−14.8392	−0.517261	−0.258631	−	0.965976i	$-0.583271\pi$
$823$	−14.8392	−0.517261	−0.258631	+	0.965976i	$0.583271\pi$
$824$	−6.53298	−0.227587
$825$	4.61505	0.160676
$826$	−9.25332	−0.321964
$827$	34.3976	1.19612	0.598060	−	0.801451i	$-0.295938\pi$
$827$	34.3976	1.19612	0.598060	+	0.801451i	$0.295938\pi$
$828$	−13.0540	−0.453657
$829$	−3.43057	−0.119149	−0.0595743	−	0.998224i	$-0.518974\pi$
$829$	−3.43057	−0.119149	−0.0595743	+	0.998224i	$0.518974\pi$
$830$	−12.9876	−0.450805
$831$	1.47264	0.0510853
$832$	13.1335	0.455323
$833$	4.25543	0.147442
$834$	−36.0007	−1.24660
$835$	25.1531	0.870460
$836$	−16.4407	−0.568612
$837$	25.8419	0.893227
$838$	−64.9865	−2.24492
$839$	−21.7907	−0.752298	−0.376149	−	0.926559i	$-0.622752\pi$
$839$	−21.7907	−0.752298	−0.376149	+	0.926559i	$0.622752\pi$
$840$	−1.22883	−0.0423985
$841$	−5.87117	−0.202454
$842$	0.340029	0.0117182
$843$	−17.1368	−0.590224
$844$	−21.7374	−0.748232
$845$	22.2849	0.766624
$846$	−18.1765	−0.624922
$847$	6.90996	0.237429
$848$	28.7431	0.987044
$849$	−18.4034	−0.631601
$850$	−18.7315	−0.642486
$851$	−34.9056	−1.19655
$852$	23.5099	0.805435
$853$	3.04118	0.104128	0.0520640	−	0.998644i	$-0.483420\pi$
$853$	3.04118	0.104128	0.0520640	+	0.998644i	$0.483420\pi$
$854$	8.37316	0.286524
$855$	24.6594	0.843334
$856$	−4.79603	−0.163925
$857$	−38.4348	−1.31291	−0.656454	−	0.754366i	$-0.727944\pi$
$857$	−38.4348	−1.31291	−0.656454	+	0.754366i	$0.727944\pi$
$858$	8.59216	0.293332
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	−6.64482	−0.226586
$861$	−7.56677	−0.257875
$862$	51.2360	1.74510
$863$	−19.2785	−0.656248	−0.328124	−	0.944635i	$-0.606416\pi$
$863$	−19.2785	−0.656248	−0.328124	+	0.944635i	$0.606416\pi$
$864$	38.4266	1.30730
$865$	−55.8934	−1.90043
$866$	49.4642	1.68086
$867$	−1.11549	−0.0378842
$868$	−9.09704	−0.308774
$869$	29.1262	0.988038
$870$	−25.3172	−0.858334
$871$	−6.43185	−0.217935
$872$	4.20562	0.142420
$873$	−14.6875	−0.497095
$874$	−33.2016	−1.12306
$875$	−7.36511	−0.248986
$876$	20.8759	0.705333
$877$	58.3871	1.97159	0.985796	−	0.167945i	$-0.0537131\pi$
$877$	58.3871	1.97159	0.985796	+	0.167945i	$0.0537131\pi$
$878$	7.23443	0.244150
$879$	−28.4726	−0.960357
$880$	−24.0572	−0.810968
$881$	−41.1591	−1.38668	−0.693342	−	0.720609i	$-0.743862\pi$
$881$	−41.1591	−1.38668	−0.693342	+	0.720609i	$0.743862\pi$
$882$	3.85764	0.129894
$883$	20.0031	0.673159	0.336579	−	0.941655i	$-0.390730\pi$
$883$	20.0031	0.673159	0.336579	+	0.941655i	$0.390730\pi$
$884$	−16.3563	−0.550121
$885$	−12.9327	−0.434729
$886$	18.7971	0.631502
$887$	−11.3587	−0.381387	−0.190694	−	0.981650i	$-0.561074\pi$
$887$	−11.3587	−0.381387	−0.190694	+	0.981650i	$0.561074\pi$
$888$	4.27970	0.143617
$889$	−9.55798	−0.320564
$890$	10.8879	0.364963
$891$	−1.84845	−0.0619254
$892$	−27.0594	−0.906015
$893$	−21.6827	−0.725583
$894$	−6.69003	−0.223748
$895$	56.3586	1.88386
$896$	3.59953	0.120252
$897$	8.13819	0.271726
$898$	−14.9678	−0.499484
$899$	24.7654	0.825973
$900$	−7.96411	−0.265470
$901$	−27.7208	−0.923515
$902$	−29.5183	−0.982852
$903$	1.40378	0.0467148
$904$	5.59538	0.186100
$905$	8.49708	0.282452
$906$	34.8218	1.15688
$907$	44.4438	1.47573	0.737866	−	0.674947i	$-0.235833\pi$
$907$	44.4438	1.47573	0.737866	+	0.674947i	$0.235833\pi$
$908$	24.4197	0.810396
$909$	−25.7827	−0.855160
$910$	11.3839	0.377373
$911$	4.91339	0.162788	0.0813939	−	0.996682i	$-0.474063\pi$
$911$	4.91339	0.162788	0.0813939	+	0.996682i	$0.474063\pi$
$912$	20.4292	0.676479
$913$	5.02006	0.166140
$914$	12.7569	0.421959
$915$	11.7026	0.386876
$916$	13.1605	0.434835
$917$	5.64714	0.186485
$918$	−41.4451	−1.36789
$919$	−38.8976	−1.28311	−0.641557	−	0.767075i	$-0.721711\pi$
$919$	−38.8976	−1.28311	−0.641557	+	0.767075i	$0.721711\pi$
$920$	−4.54042	−0.149693
$921$	1.56769	0.0516572
$922$	65.3086	2.15082
$923$	28.7787	0.947263
$924$	−3.59461	−0.118254
$925$	−21.2956	−0.700194
$926$	−14.3833	−0.472663
$927$	28.6639	0.941448
$928$	36.8259	1.20887
$929$	25.8716	0.848819	0.424410	−	0.905470i	$-0.360482\pi$
$929$	25.8716	0.848819	0.424410	+	0.905470i	$0.360482\pi$
$930$	−27.1086	−0.888928
$931$	4.60176	0.150817
$932$	−16.9147	−0.554060
$933$	−15.4639	−0.506265
$934$	−15.6712	−0.512778
$935$	23.2016	0.758772
$936$	1.95922	0.0640390
$937$	−1.69529	−0.0553827	−0.0276913	−	0.999617i	$-0.508816\pi$
$937$	−1.69529	−0.0553827	−0.0276913	+	0.999617i	$0.508816\pi$
$938$	5.73720	0.187326
$939$	20.3963	0.665610
$940$	22.4404	0.731924
$941$	41.6980	1.35932	0.679658	−	0.733529i	$-0.262128\pi$
$941$	41.6980	1.35932	0.679658	+	0.733529i	$0.262128\pi$
$942$	−43.0464	−1.40253
$943$	−27.9587	−0.910460
$944$	21.0376	0.684715
$945$	13.5290	0.440098
$946$	5.47620	0.178047
$947$	3.70152	0.120283	0.0601416	−	0.998190i	$-0.480845\pi$
$947$	3.70152	0.120283	0.0601416	+	0.998190i	$0.480845\pi$
$948$	25.5981	0.831387
$949$	25.5545	0.829534
$950$	−20.2560	−0.657191
$951$	−22.4192	−0.726991
$952$	−1.92783	−0.0624812
$953$	42.9699	1.39193	0.695966	−	0.718075i	$-0.254976\pi$
$953$	42.9699	1.39193	0.695966	+	0.718075i	$0.254976\pi$
$954$	−25.1296	−0.813600
$955$	30.4542	0.985476
$956$	45.2481	1.46343
$957$	9.78582	0.316331
$958$	−47.7797	−1.54369
$959$	−22.6928	−0.732787
$960$	−16.3734	−0.528449
$961$	−4.48220	−0.144587
$962$	−39.6474	−1.27828
$963$	21.0430	0.678100
$964$	19.9693	0.643167
$965$	60.7834	1.95669
$966$	−7.25926	−0.233563
$967$	25.3561	0.815397	0.407698	−	0.913117i	$-0.366332\pi$
$967$	25.3561	0.815397	0.407698	+	0.913117i	$0.366332\pi$
$968$	−3.13040	−0.100615
$969$	−19.7026	−0.632939
$970$	38.6616	1.24135
$971$	−56.8790	−1.82533	−0.912667	−	0.408703i	$-0.865981\pi$
$971$	−56.8790	−1.82533	−0.912667	+	0.408703i	$0.865981\pi$
$972$	−28.2201	−0.905160
$973$	18.4366	0.591051
$974$	−14.0835	−0.451264
$975$	4.96503	0.159008
$976$	−19.0365	−0.609344
$977$	−34.8058	−1.11354	−0.556769	−	0.830668i	$-0.687959\pi$
$977$	−34.8058	−1.11354	−0.556769	+	0.830668i	$0.687959\pi$
$978$	18.9109	0.604703
$979$	−4.20847	−0.134503
$980$	−4.76257	−0.152135
$981$	−18.4525	−0.589143
$982$	73.8298	2.35600
$983$	8.96076	0.285804	0.142902	−	0.989737i	$-0.454357\pi$
$983$	8.96076	0.285804	0.142902	+	0.989737i	$0.454357\pi$
$984$	3.42795	0.109279
$985$	62.4123	1.98862
$986$	−39.7186	−1.26490
$987$	−4.74073	−0.150899
$988$	−17.6874	−0.562712
$989$	5.18686	0.164933
$990$	21.0327	0.668464
$991$	−29.2013	−0.927610	−0.463805	−	0.885937i	$-0.653516\pi$
$991$	−29.2013	−0.927610	−0.463805	+	0.885937i	$0.653516\pi$
$992$	39.4317	1.25196
$993$	−31.8379	−1.01035
$994$	−25.6706	−0.814221
$995$	18.0247	0.571421
$996$	4.41197	0.139799
$997$	−21.3778	−0.677043	−0.338522	−	0.940959i	$-0.609927\pi$
$997$	−21.3778	−0.677043	−0.338522	+	0.940959i	$0.609927\pi$
$998$	58.0361	1.83710
$999$	−47.1182	−1.49075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.18	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.18	✓	110	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.94077 q^{2} -1.00614 q^{3} +1.76657 q^{4} -2.69594 q^{5} +1.95267 q^{6} -1.00000 q^{7} +0.453027 q^{8} -1.98769 q^{9} +O(q^{10})\)	\(q-1.94077 q^{2} -1.00614 q^{3} +1.76657 q^{4} -2.69594 q^{5} +1.95267 q^{6} -1.00000 q^{7} +0.453027 q^{8} -1.98769 q^{9} +5.23218 q^{10} -2.02239 q^{11} -1.77741 q^{12} -2.17575 q^{13} +1.94077 q^{14} +2.71248 q^{15} -4.41237 q^{16} +4.25543 q^{17} +3.85764 q^{18} +4.60176 q^{19} -4.76257 q^{20} +1.00614 q^{21} +3.92498 q^{22} +3.71760 q^{23} -0.455807 q^{24} +2.26807 q^{25} +4.22262 q^{26} +5.01829 q^{27} -1.76657 q^{28} +4.80924 q^{29} -5.26428 q^{30} +5.14954 q^{31} +7.65732 q^{32} +2.03479 q^{33} -8.25880 q^{34} +2.69594 q^{35} -3.51140 q^{36} -9.38929 q^{37} -8.93094 q^{38} +2.18910 q^{39} -1.22133 q^{40} -7.52063 q^{41} -1.95267 q^{42} +1.39522 q^{43} -3.57269 q^{44} +5.35869 q^{45} -7.21499 q^{46} -4.71182 q^{47} +4.43944 q^{48} +1.00000 q^{49} -4.40179 q^{50} -4.28154 q^{51} -3.84362 q^{52} -6.51423 q^{53} -9.73933 q^{54} +5.45222 q^{55} -0.453027 q^{56} -4.62999 q^{57} -9.33362 q^{58} -4.76787 q^{59} +4.79179 q^{60} +4.31436 q^{61} -9.99406 q^{62} +1.98769 q^{63} -6.03633 q^{64} +5.86568 q^{65} -3.94906 q^{66} +2.95615 q^{67} +7.51753 q^{68} -3.74041 q^{69} -5.23218 q^{70} -13.2270 q^{71} -0.900479 q^{72} -11.7451 q^{73} +18.2224 q^{74} -2.28199 q^{75} +8.12934 q^{76} +2.02239 q^{77} -4.24853 q^{78} -14.4019 q^{79} +11.8955 q^{80} +0.913994 q^{81} +14.5958 q^{82} -2.48225 q^{83} +1.77741 q^{84} -11.4724 q^{85} -2.70779 q^{86} -4.83875 q^{87} -0.916196 q^{88} +2.08095 q^{89} -10.4000 q^{90} +2.17575 q^{91} +6.56741 q^{92} -5.18114 q^{93} +9.14454 q^{94} -12.4060 q^{95} -7.70430 q^{96} +7.38920 q^{97} -1.94077 q^{98} +4.01988 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

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