LMFDB - Embedded newform 6002.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.59777 q^{3} +1.00000 q^{4} +0.373803 q^{5} +1.59777 q^{6} +0.398412 q^{7} -1.00000 q^{8} -0.447134 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.59777 q^{3} +1.00000 q^{4} +0.373803 q^{5} +1.59777 q^{6} +0.398412 q^{7} -1.00000 q^{8} -0.447134 q^{9} -0.373803 q^{10} +3.67735 q^{11} -1.59777 q^{12} +1.92808 q^{13} -0.398412 q^{14} -0.597250 q^{15} +1.00000 q^{16} -6.55986 q^{17} +0.447134 q^{18} +0.0517994 q^{19} +0.373803 q^{20} -0.636571 q^{21} -3.67735 q^{22} +3.45371 q^{23} +1.59777 q^{24} -4.86027 q^{25} -1.92808 q^{26} +5.50772 q^{27} +0.398412 q^{28} -3.77464 q^{29} +0.597250 q^{30} +0.705533 q^{31} -1.00000 q^{32} -5.87556 q^{33} +6.55986 q^{34} +0.148928 q^{35} -0.447134 q^{36} +10.0485 q^{37} -0.0517994 q^{38} -3.08063 q^{39} -0.373803 q^{40} +7.53179 q^{41} +0.636571 q^{42} -6.24786 q^{43} +3.67735 q^{44} -0.167140 q^{45} -3.45371 q^{46} -2.41214 q^{47} -1.59777 q^{48} -6.84127 q^{49} +4.86027 q^{50} +10.4811 q^{51} +1.92808 q^{52} -1.36534 q^{53} -5.50772 q^{54} +1.37460 q^{55} -0.398412 q^{56} -0.0827634 q^{57} +3.77464 q^{58} -1.26062 q^{59} -0.597250 q^{60} -9.91540 q^{61} -0.705533 q^{62} -0.178144 q^{63} +1.00000 q^{64} +0.720722 q^{65} +5.87556 q^{66} -8.33599 q^{67} -6.55986 q^{68} -5.51823 q^{69} -0.148928 q^{70} +3.12059 q^{71} +0.447134 q^{72} -12.6726 q^{73} -10.0485 q^{74} +7.76559 q^{75} +0.0517994 q^{76} +1.46510 q^{77} +3.08063 q^{78} +10.8981 q^{79} +0.373803 q^{80} -7.45867 q^{81} -7.53179 q^{82} -8.81151 q^{83} -0.636571 q^{84} -2.45209 q^{85} +6.24786 q^{86} +6.03101 q^{87} -3.67735 q^{88} +13.7515 q^{89} +0.167140 q^{90} +0.768171 q^{91} +3.45371 q^{92} -1.12728 q^{93} +2.41214 q^{94} +0.0193627 q^{95} +1.59777 q^{96} +9.40196 q^{97} +6.84127 q^{98} -1.64427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) $ 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.59777	−0.922472	−0.461236	−	0.887277i	$-0.652594\pi$
$3$	−1.59777	−0.922472	−0.461236	+	0.887277i	$0.652594\pi$
$4$	1.00000	0.500000
$5$	0.373803	0.167170	0.0835848	−	0.996501i	$-0.473363\pi$
$5$	0.373803	0.167170	0.0835848	+	0.996501i	$0.473363\pi$
$6$	1.59777	0.652287
$7$	0.398412	0.150586	0.0752928	−	0.997161i	$-0.476011\pi$
$7$	0.398412	0.150586	0.0752928	+	0.997161i	$0.476011\pi$
$8$	−1.00000	−0.353553
$9$	−0.447134	−0.149045
$10$	−0.373803	−0.118207
$11$	3.67735	1.10876	0.554382	−	0.832262i	$-0.312955\pi$
$11$	3.67735	1.10876	0.554382	+	0.832262i	$0.312955\pi$
$12$	−1.59777	−0.461236
$13$	1.92808	0.534753	0.267377	−	0.963592i	$-0.413843\pi$
$13$	1.92808	0.534753	0.267377	+	0.963592i	$0.413843\pi$
$14$	−0.398412	−0.106480
$15$	−0.597250	−0.154209
$16$	1.00000	0.250000
$17$	−6.55986	−1.59100	−0.795499	−	0.605954i	$-0.792791\pi$
$17$	−6.55986	−1.59100	−0.795499	+	0.605954i	$0.792791\pi$
$18$	0.447134	0.105390
$19$	0.0517994	0.0118836	0.00594180	−	0.999982i	$-0.498109\pi$
$19$	0.0517994	0.0118836	0.00594180	+	0.999982i	$0.498109\pi$
$20$	0.373803	0.0835848
$21$	−0.636571	−0.138911
$22$	−3.67735	−0.784015
$23$	3.45371	0.720148	0.360074	−	0.932924i	$-0.382751\pi$
$23$	3.45371	0.720148	0.360074	+	0.932924i	$0.382751\pi$
$24$	1.59777	0.326143
$25$	−4.86027	−0.972054
$26$	−1.92808	−0.378128
$27$	5.50772	1.05996
$28$	0.398412	0.0752928
$29$	−3.77464	−0.700934	−0.350467	−	0.936575i	$-0.613977\pi$
$29$	−3.77464	−0.700934	−0.350467	+	0.936575i	$0.613977\pi$
$30$	0.597250	0.109043
$31$	0.705533	0.126717	0.0633587	−	0.997991i	$-0.479819\pi$
$31$	0.705533	0.126717	0.0633587	+	0.997991i	$0.479819\pi$
$32$	−1.00000	−0.176777
$33$	−5.87556	−1.02280
$34$	6.55986	1.12501
$35$	0.148928	0.0251733
$36$	−0.447134	−0.0745223
$37$	10.0485	1.65196	0.825982	−	0.563696i	$-0.190621\pi$
$37$	10.0485	1.65196	0.825982	+	0.563696i	$0.190621\pi$
$38$	−0.0517994	−0.00840297
$39$	−3.08063	−0.493295
$40$	−0.373803	−0.0591034
$41$	7.53179	1.17627	0.588134	−	0.808764i	$-0.299863\pi$
$41$	7.53179	1.17627	0.588134	+	0.808764i	$0.299863\pi$
$42$	0.636571	0.0982250
$43$	−6.24786	−0.952790	−0.476395	−	0.879231i	$-0.658057\pi$
$43$	−6.24786	−0.952790	−0.476395	+	0.879231i	$0.658057\pi$
$44$	3.67735	0.554382
$45$	−0.167140	−0.0249157
$46$	−3.45371	−0.509222
$47$	−2.41214	−0.351847	−0.175924	−	0.984404i	$-0.556291\pi$
$47$	−2.41214	−0.351847	−0.175924	+	0.984404i	$0.556291\pi$
$48$	−1.59777	−0.230618
$49$	−6.84127	−0.977324
$50$	4.86027	0.687346
$51$	10.4811	1.46765
$52$	1.92808	0.267377
$53$	−1.36534	−0.187544	−0.0937720	−	0.995594i	$-0.529892\pi$
$53$	−1.36534	−0.187544	−0.0937720	+	0.995594i	$0.529892\pi$
$54$	−5.50772	−0.749506
$55$	1.37460	0.185352
$56$	−0.398412	−0.0532401
$57$	−0.0827634	−0.0109623
$58$	3.77464	0.495635
$59$	−1.26062	−0.164118	−0.0820592	−	0.996627i	$-0.526150\pi$
$59$	−1.26062	−0.164118	−0.0820592	+	0.996627i	$0.526150\pi$
$60$	−0.597250	−0.0771047
$61$	−9.91540	−1.26954	−0.634768	−	0.772703i	$-0.718904\pi$
$61$	−9.91540	−1.26954	−0.634768	+	0.772703i	$0.718904\pi$
$62$	−0.705533	−0.0896028
$63$	−0.178144	−0.0224440
$64$	1.00000	0.125000
$65$	0.720722	0.0893945
$66$	5.87556	0.723232
$67$	−8.33599	−1.01840	−0.509201	−	0.860647i	$-0.670059\pi$
$67$	−8.33599	−1.01840	−0.509201	+	0.860647i	$0.670059\pi$
$68$	−6.55986	−0.795499
$69$	−5.51823	−0.664317
$70$	−0.148928	−0.0178002
$71$	3.12059	0.370346	0.185173	−	0.982706i	$-0.440715\pi$
$71$	3.12059	0.370346	0.185173	+	0.982706i	$0.440715\pi$
$72$	0.447134	0.0526952
$73$	−12.6726	−1.48322	−0.741610	−	0.670831i	$-0.765938\pi$
$73$	−12.6726	−1.48322	−0.741610	+	0.670831i	$0.765938\pi$
$74$	−10.0485	−1.16812
$75$	7.76559	0.896693
$76$	0.0517994	0.00594180
$77$	1.46510	0.166964
$78$	3.08063	0.348812
$79$	10.8981	1.22613	0.613067	−	0.790031i	$-0.289935\pi$
$79$	10.8981	1.22613	0.613067	+	0.790031i	$0.289935\pi$
$80$	0.373803	0.0417924
$81$	−7.45867	−0.828741
$82$	−7.53179	−0.831747
$83$	−8.81151	−0.967188	−0.483594	−	0.875292i	$-0.660669\pi$
$83$	−8.81151	−0.967188	−0.483594	+	0.875292i	$0.660669\pi$
$84$	−0.636571	−0.0694555
$85$	−2.45209	−0.265967
$86$	6.24786	0.673724
$87$	6.03101	0.646592
$88$	−3.67735	−0.392007
$89$	13.7515	1.45765	0.728827	−	0.684698i	$-0.240066\pi$
$89$	13.7515	1.45765	0.728827	+	0.684698i	$0.240066\pi$
$90$	0.167140	0.0176181
$91$	0.768171	0.0805262
$92$	3.45371	0.360074
$93$	−1.12728	−0.116893
$94$	2.41214	0.248794
$95$	0.0193627	0.00198658
$96$	1.59777	0.163072
$97$	9.40196	0.954624	0.477312	−	0.878734i	$-0.341611\pi$
$97$	9.40196	0.954624	0.477312	+	0.878734i	$0.341611\pi$
$98$	6.84127	0.691072
$99$	−1.64427	−0.165255
$100$	−4.86027	−0.486027
$101$	−7.85216	−0.781319	−0.390660	−	0.920535i	$-0.627753\pi$
$101$	−7.85216	−0.781319	−0.390660	+	0.920535i	$0.627753\pi$
$102$	−10.4811	−1.03779
$103$	4.51819	0.445190	0.222595	−	0.974911i	$-0.428547\pi$
$103$	4.51819	0.445190	0.222595	+	0.974911i	$0.428547\pi$
$104$	−1.92808	−0.189064
$105$	−0.237952	−0.0232217
$106$	1.36534	0.132614
$107$	0.359079	0.0347135	0.0173567	−	0.999849i	$-0.494475\pi$
$107$	0.359079	0.0347135	0.0173567	+	0.999849i	$0.494475\pi$
$108$	5.50772	0.529981
$109$	3.90597	0.374124	0.187062	−	0.982348i	$-0.440103\pi$
$109$	3.90597	0.374124	0.187062	+	0.982348i	$0.440103\pi$
$110$	−1.37460	−0.131063
$111$	−16.0552	−1.52389
$112$	0.398412	0.0376464
$113$	−5.24695	−0.493591	−0.246796	−	0.969068i	$-0.579378\pi$
$113$	−5.24695	−0.493591	−0.246796	+	0.969068i	$0.579378\pi$
$114$	0.0827634	0.00775151
$115$	1.29101	0.120387
$116$	−3.77464	−0.350467
$117$	−0.862110	−0.0797021
$118$	1.26062	0.116049
$119$	−2.61353	−0.239582
$120$	0.597250	0.0545213
$121$	2.52293	0.229358
$122$	9.91540	0.897698
$123$	−12.0341	−1.08507
$124$	0.705533	0.0633587
$125$	−3.68580	−0.329668
$126$	0.178144	0.0158703
$127$	10.5093	0.932547	0.466274	−	0.884641i	$-0.345596\pi$
$127$	10.5093	0.932547	0.466274	+	0.884641i	$0.345596\pi$
$128$	−1.00000	−0.0883883
$129$	9.98264	0.878922
$130$	−0.720722	−0.0632115
$131$	−0.826010	−0.0721689	−0.0360844	−	0.999349i	$-0.511489\pi$
$131$	−0.826010	−0.0721689	−0.0360844	+	0.999349i	$0.511489\pi$
$132$	−5.87556	−0.511402
$133$	0.0206375	0.00178950
$134$	8.33599	0.720119
$135$	2.05880	0.177193
$136$	6.55986	0.562503
$137$	1.18957	0.101632	0.0508159	−	0.998708i	$-0.483818\pi$
$137$	1.18957	0.101632	0.0508159	+	0.998708i	$0.483818\pi$
$138$	5.51823	0.469743
$139$	10.1836	0.863762	0.431881	−	0.901931i	$-0.357850\pi$
$139$	10.1836	0.863762	0.431881	+	0.901931i	$0.357850\pi$
$140$	0.148928	0.0125867
$141$	3.85405	0.324569
$142$	−3.12059	−0.261874
$143$	7.09023	0.592915
$144$	−0.447134	−0.0372612
$145$	−1.41097	−0.117175
$146$	12.6726	1.04880
$147$	10.9308	0.901554
$148$	10.0485	0.825982
$149$	16.4388	1.34672	0.673359	−	0.739315i	$-0.264851\pi$
$149$	16.4388	1.34672	0.673359	+	0.739315i	$0.264851\pi$
$150$	−7.76559	−0.634058
$151$	−23.4575	−1.90894	−0.954470	−	0.298305i	$-0.903579\pi$
$151$	−23.4575	−1.90894	−0.954470	+	0.298305i	$0.903579\pi$
$152$	−0.0517994	−0.00420148
$153$	2.93313	0.237130
$154$	−1.46510	−0.118061
$155$	0.263730	0.0211833
$156$	−3.08063	−0.246648
$157$	−9.75430	−0.778478	−0.389239	−	0.921137i	$-0.627262\pi$
$157$	−9.75430	−0.778478	−0.389239	+	0.921137i	$0.627262\pi$
$158$	−10.8981	−0.867008
$159$	2.18150	0.173004
$160$	−0.373803	−0.0295517
$161$	1.37600	0.108444
$162$	7.45867	0.586008
$163$	8.06388	0.631612	0.315806	−	0.948824i	$-0.397725\pi$
$163$	8.06388	0.631612	0.315806	+	0.948824i	$0.397725\pi$
$164$	7.53179	0.588134
$165$	−2.19630	−0.170982
$166$	8.81151	0.683906
$167$	23.4217	1.81243	0.906214	−	0.422819i	$-0.138960\pi$
$167$	23.4217	1.81243	0.906214	+	0.422819i	$0.138960\pi$
$168$	0.636571	0.0491125
$169$	−9.28251	−0.714039
$170$	2.45209	0.188067
$171$	−0.0231613	−0.00177119
$172$	−6.24786	−0.476395
$173$	−0.914248	−0.0695090	−0.0347545	−	0.999396i	$-0.511065\pi$
$173$	−0.914248	−0.0695090	−0.0347545	+	0.999396i	$0.511065\pi$
$174$	−6.03101	−0.457210
$175$	−1.93639	−0.146377
$176$	3.67735	0.277191
$177$	2.01418	0.151395
$178$	−13.7515	−1.03072
$179$	−8.76427	−0.655073	−0.327536	−	0.944839i	$-0.606218\pi$
$179$	−8.76427	−0.655073	−0.327536	+	0.944839i	$0.606218\pi$
$180$	−0.167140	−0.0124579
$181$	17.0757	1.26922	0.634612	−	0.772831i	$-0.281160\pi$
$181$	17.0757	1.26922	0.634612	+	0.772831i	$0.281160\pi$
$182$	−0.768171	−0.0569406
$183$	15.8425	1.17111
$184$	−3.45371	−0.254611
$185$	3.75616	0.276158
$186$	1.12728	0.0826561
$187$	−24.1229	−1.76404
$188$	−2.41214	−0.175924
$189$	2.19434	0.159615
$190$	−0.0193627	−0.00140472
$191$	−21.6593	−1.56722	−0.783608	−	0.621256i	$-0.786623\pi$
$191$	−21.6593	−1.56722	−0.783608	+	0.621256i	$0.786623\pi$
$192$	−1.59777	−0.115309
$193$	−17.2120	−1.23895	−0.619474	−	0.785017i	$-0.712654\pi$
$193$	−17.2120	−1.23895	−0.619474	+	0.785017i	$0.712654\pi$
$194$	−9.40196	−0.675021
$195$	−1.15155	−0.0824640
$196$	−6.84127	−0.488662
$197$	−3.88082	−0.276497	−0.138248	−	0.990398i	$-0.544147\pi$
$197$	−3.88082	−0.276497	−0.138248	+	0.990398i	$0.544147\pi$
$198$	1.64427	0.116853
$199$	7.81861	0.554247	0.277123	−	0.960834i	$-0.410619\pi$
$199$	7.81861	0.554247	0.277123	+	0.960834i	$0.410619\pi$
$200$	4.86027	0.343673
$201$	13.3190	0.939448
$202$	7.85216	0.552476
$203$	−1.50386	−0.105551
$204$	10.4811	0.733826
$205$	2.81540	0.196636
$206$	−4.51819	−0.314797
$207$	−1.54427	−0.107334
$208$	1.92808	0.133688
$209$	0.190485	0.0131761
$210$	0.237952	0.0164202
$211$	−23.8920	−1.64479	−0.822396	−	0.568916i	$-0.807363\pi$
$211$	−23.8920	−1.64479	−0.822396	+	0.568916i	$0.807363\pi$
$212$	−1.36534	−0.0937720
$213$	−4.98598	−0.341634
$214$	−0.359079	−0.0245461
$215$	−2.33547	−0.159278
$216$	−5.50772	−0.374753
$217$	0.281093	0.0190818
$218$	−3.90597	−0.264546
$219$	20.2480	1.36823
$220$	1.37460	0.0926758
$221$	−12.6479	−0.850792
$222$	16.0552	1.07755
$223$	−21.2389	−1.42226	−0.711131	−	0.703060i	$-0.751817\pi$
$223$	−21.2389	−1.42226	−0.711131	+	0.703060i	$0.751817\pi$
$224$	−0.398412	−0.0266200
$225$	2.17319	0.144879
$226$	5.24695	0.349022
$227$	−2.92250	−0.193973	−0.0969865	−	0.995286i	$-0.530920\pi$
$227$	−2.92250	−0.193973	−0.0969865	+	0.995286i	$0.530920\pi$
$228$	−0.0827634	−0.00548114
$229$	−15.9402	−1.05336	−0.526678	−	0.850065i	$-0.676563\pi$
$229$	−15.9402	−1.05336	−0.526678	+	0.850065i	$0.676563\pi$
$230$	−1.29101	−0.0851264
$231$	−2.34090	−0.154020
$232$	3.77464	0.247818
$233$	−2.42535	−0.158890	−0.0794451	−	0.996839i	$-0.525315\pi$
$233$	−2.42535	−0.158890	−0.0794451	+	0.996839i	$0.525315\pi$
$234$	0.862110	0.0563579
$235$	−0.901666	−0.0588182
$236$	−1.26062	−0.0820592
$237$	−17.4127	−1.13108
$238$	2.61353	0.169410
$239$	23.7583	1.53680	0.768400	−	0.639970i	$-0.221053\pi$
$239$	23.7583	1.53680	0.768400	+	0.639970i	$0.221053\pi$
$240$	−0.597250	−0.0385524
$241$	7.40717	0.477137	0.238569	−	0.971126i	$-0.423322\pi$
$241$	7.40717	0.477137	0.238569	+	0.971126i	$0.423322\pi$
$242$	−2.52293	−0.162180
$243$	−4.60594	−0.295471
$244$	−9.91540	−0.634768
$245$	−2.55728	−0.163379
$246$	12.0341	0.767264
$247$	0.0998734	0.00635479
$248$	−0.705533	−0.0448014
$249$	14.0788	0.892205
$250$	3.68580	0.233110
$251$	2.72576	0.172048	0.0860242	−	0.996293i	$-0.472584\pi$
$251$	2.72576	0.172048	0.0860242	+	0.996293i	$0.472584\pi$
$252$	−0.178144	−0.0112220
$253$	12.7005	0.798474
$254$	−10.5093	−0.659411
$255$	3.91788	0.245347
$256$	1.00000	0.0625000
$257$	−12.2989	−0.767185	−0.383592	−	0.923503i	$-0.625313\pi$
$257$	−12.2989	−0.767185	−0.383592	+	0.923503i	$0.625313\pi$
$258$	−9.98264	−0.621492
$259$	4.00345	0.248762
$260$	0.720722	0.0446973
$261$	1.68777	0.104470
$262$	0.826010	0.0510311
$263$	29.1191	1.79556	0.897780	−	0.440444i	$-0.145179\pi$
$263$	29.1191	1.79556	0.897780	+	0.440444i	$0.145179\pi$
$264$	5.87556	0.361616
$265$	−0.510368	−0.0313517
$266$	−0.0206375	−0.00126537
$267$	−21.9717	−1.34465
$268$	−8.33599	−0.509201
$269$	30.1751	1.83981	0.919905	−	0.392142i	$-0.128266\pi$
$269$	30.1751	1.83981	0.919905	+	0.392142i	$0.128266\pi$
$270$	−2.05880	−0.125295
$271$	9.70043	0.589259	0.294629	−	0.955612i	$-0.404804\pi$
$271$	9.70043	0.589259	0.294629	+	0.955612i	$0.404804\pi$
$272$	−6.55986	−0.397750
$273$	−1.22736	−0.0742832
$274$	−1.18957	−0.0718646
$275$	−17.8729	−1.07778
$276$	−5.51823	−0.332158
$277$	−10.9154	−0.655842	−0.327921	−	0.944705i	$-0.606348\pi$
$277$	−10.9154	−0.655842	−0.327921	+	0.944705i	$0.606348\pi$
$278$	−10.1836	−0.610772
$279$	−0.315468	−0.0188866
$280$	−0.148928	−0.00890012
$281$	14.3811	0.857903	0.428951	−	0.903328i	$-0.358883\pi$
$281$	14.3811	0.857903	0.428951	+	0.903328i	$0.358883\pi$
$282$	−3.85405	−0.229505
$283$	−21.9537	−1.30501	−0.652506	−	0.757783i	$-0.726282\pi$
$283$	−21.9537	−1.30501	−0.652506	+	0.757783i	$0.726282\pi$
$284$	3.12059	0.185173
$285$	−0.0309372	−0.00183256
$286$	−7.09023	−0.419254
$287$	3.00076	0.177129
$288$	0.447134	0.0263476
$289$	26.0317	1.53128
$290$	1.41097	0.0828551
$291$	−15.0222	−0.880615
$292$	−12.6726	−0.741610
$293$	−9.89021	−0.577792	−0.288896	−	0.957360i	$-0.593288\pi$
$293$	−9.89021	−0.577792	−0.288896	+	0.957360i	$0.593288\pi$
$294$	−10.9308	−0.637495
$295$	−0.471222	−0.0274356
$296$	−10.0485	−0.584058
$297$	20.2539	1.17525
$298$	−16.4388	−0.952274
$299$	6.65903	0.385102
$300$	7.76559	0.448347
$301$	−2.48922	−0.143476
$302$	23.4575	1.34983
$303$	12.5459	0.720746
$304$	0.0517994	0.00297090
$305$	−3.70640	−0.212228
$306$	−2.93313	−0.167676
$307$	−6.45061	−0.368156	−0.184078	−	0.982912i	$-0.558930\pi$
$307$	−6.45061	−0.368156	−0.184078	+	0.982912i	$0.558930\pi$
$308$	1.46510	0.0834820
$309$	−7.21902	−0.410676
$310$	−0.263730	−0.0149789
$311$	−7.46794	−0.423468	−0.211734	−	0.977327i	$-0.567911\pi$
$311$	−7.46794	−0.423468	−0.211734	+	0.977327i	$0.567911\pi$
$312$	3.08063	0.174406
$313$	−26.0247	−1.47100	−0.735502	−	0.677522i	$-0.763054\pi$
$313$	−26.0247	−1.47100	−0.735502	+	0.677522i	$0.763054\pi$
$314$	9.75430	0.550467
$315$	−0.0665905	−0.00375195
$316$	10.8981	0.613067
$317$	−23.6850	−1.33028	−0.665142	−	0.746717i	$-0.731629\pi$
$317$	−23.6850	−1.33028	−0.665142	+	0.746717i	$0.731629\pi$
$318$	−2.18150	−0.122332
$319$	−13.8807	−0.777170
$320$	0.373803	0.0208962
$321$	−0.573725	−0.0320222
$322$	−1.37600	−0.0766814
$323$	−0.339796	−0.0189068
$324$	−7.45867	−0.414371
$325$	−9.37099	−0.519809
$326$	−8.06388	−0.446617
$327$	−6.24084	−0.345119
$328$	−7.53179	−0.415873
$329$	−0.961027	−0.0529831
$330$	2.19630	0.120902
$331$	25.6303	1.40877	0.704383	−	0.709820i	$-0.251224\pi$
$331$	25.6303	1.40877	0.704383	+	0.709820i	$0.251224\pi$
$332$	−8.81151	−0.483594
$333$	−4.49303	−0.246216
$334$	−23.4217	−1.28158
$335$	−3.11601	−0.170246
$336$	−0.636571	−0.0347278
$337$	−26.0207	−1.41744	−0.708719	−	0.705491i	$-0.750726\pi$
$337$	−26.0207	−1.41744	−0.708719	+	0.705491i	$0.750726\pi$
$338$	9.28251	0.504902
$339$	8.38341	0.455324
$340$	−2.45209	−0.132983
$341$	2.59449	0.140500
$342$	0.0231613	0.00125242
$343$	−5.51453	−0.297757
$344$	6.24786	0.336862
$345$	−2.06273	−0.111054
$346$	0.914248	0.0491503
$347$	−25.9125	−1.39106	−0.695528	−	0.718499i	$-0.744830\pi$
$347$	−25.9125	−1.39106	−0.695528	+	0.718499i	$0.744830\pi$
$348$	6.03101	0.323296
$349$	27.9290	1.49501	0.747504	−	0.664258i	$-0.231252\pi$
$349$	27.9290	1.49501	0.747504	+	0.664258i	$0.231252\pi$
$350$	1.93639	0.103504
$351$	10.6193	0.566818
$352$	−3.67735	−0.196004
$353$	2.49607	0.132853	0.0664263	−	0.997791i	$-0.478840\pi$
$353$	2.49607	0.132853	0.0664263	+	0.997791i	$0.478840\pi$
$354$	−2.01418	−0.107052
$355$	1.16648	0.0619106
$356$	13.7515	0.728827
$357$	4.17581	0.221007
$358$	8.76427	0.463206
$359$	−28.6233	−1.51068	−0.755339	−	0.655334i	$-0.772528\pi$
$359$	−28.6233	−1.51068	−0.755339	+	0.655334i	$0.772528\pi$
$360$	0.167140	0.00880904
$361$	−18.9973	−0.999859
$362$	−17.0757	−0.897477
$363$	−4.03106	−0.211576
$364$	0.768171	0.0402631
$365$	−4.73707	−0.247949
$366$	−15.8425	−0.828102
$367$	−10.7527	−0.561289	−0.280644	−	0.959812i	$-0.590548\pi$
$367$	−10.7527	−0.561289	−0.280644	+	0.959812i	$0.590548\pi$
$368$	3.45371	0.180037
$369$	−3.36772	−0.175316
$370$	−3.75616	−0.195273
$371$	−0.543968	−0.0282414
$372$	−1.12728	−0.0584467
$373$	30.6816	1.58864	0.794318	−	0.607503i	$-0.207829\pi$
$373$	30.6816	1.58864	0.794318	+	0.607503i	$0.207829\pi$
$374$	24.1229	1.24737
$375$	5.88905	0.304109
$376$	2.41214	0.124397
$377$	−7.27782	−0.374827
$378$	−2.19434	−0.112865
$379$	−13.8183	−0.709796	−0.354898	−	0.934905i	$-0.615484\pi$
$379$	−13.8183	−0.709796	−0.354898	+	0.934905i	$0.615484\pi$
$380$	0.0193627	0.000993288 0
$381$	−16.7914	−0.860249
$382$	21.6593	1.10819
$383$	0.639382	0.0326709	0.0163354	−	0.999867i	$-0.494800\pi$
$383$	0.639382	0.0326709	0.0163354	+	0.999867i	$0.494800\pi$
$384$	1.59777	0.0815358
$385$	0.547659	0.0279113
$386$	17.2120	0.876069
$387$	2.79363	0.142008
$388$	9.40196	0.477312
$389$	32.9254	1.66938	0.834692	−	0.550717i	$-0.185646\pi$
$389$	32.9254	1.66938	0.834692	+	0.550717i	$0.185646\pi$
$390$	1.15155	0.0583108
$391$	−22.6558	−1.14575
$392$	6.84127	0.345536
$393$	1.31977	0.0665738
$394$	3.88082	0.195513
$395$	4.07375	0.204973
$396$	−1.64427	−0.0826277
$397$	1.29574	0.0650312	0.0325156	−	0.999471i	$-0.489648\pi$
$397$	1.29574	0.0650312	0.0325156	+	0.999471i	$0.489648\pi$
$398$	−7.81861	−0.391912
$399$	−0.0329740	−0.00165076
$400$	−4.86027	−0.243014
$401$	−19.7778	−0.987654	−0.493827	−	0.869560i	$-0.664402\pi$
$401$	−19.7778	−0.987654	−0.493827	+	0.869560i	$0.664402\pi$
$402$	−13.3190	−0.664290
$403$	1.36032	0.0677626
$404$	−7.85216	−0.390660
$405$	−2.78807	−0.138540
$406$	1.50386	0.0746355
$407$	36.9519	1.83164
$408$	−10.4811	−0.518893
$409$	22.1810	1.09678	0.548390	−	0.836223i	$-0.315241\pi$
$409$	22.1810	1.09678	0.548390	+	0.836223i	$0.315241\pi$
$410$	−2.81540	−0.139043
$411$	−1.90066	−0.0937526
$412$	4.51819	0.222595
$413$	−0.502245	−0.0247139
$414$	1.54427	0.0758967
$415$	−3.29377	−0.161685
$416$	−1.92808	−0.0945319
$417$	−16.2710	−0.796797
$418$	−0.190485	−0.00931691
$419$	−20.0904	−0.981482	−0.490741	−	0.871306i	$-0.663274\pi$
$419$	−20.0904	−0.981482	−0.490741	+	0.871306i	$0.663274\pi$
$420$	−0.237952	−0.0116109
$421$	−35.9570	−1.75244	−0.876218	−	0.481915i	$-0.839941\pi$
$421$	−35.9570	−1.75244	−0.876218	+	0.481915i	$0.839941\pi$
$422$	23.8920	1.16304
$423$	1.07855	0.0524409
$424$	1.36534	0.0663068
$425$	31.8827	1.54654
$426$	4.98598	0.241572
$427$	−3.95041	−0.191174
$428$	0.359079	0.0173567
$429$	−11.3286	−0.546948
$430$	2.33547	0.112626
$431$	−13.3871	−0.644833	−0.322417	−	0.946598i	$-0.604495\pi$
$431$	−13.3871	−0.644833	−0.322417	+	0.946598i	$0.604495\pi$
$432$	5.50772	0.264990
$433$	−5.92414	−0.284696	−0.142348	−	0.989817i	$-0.545465\pi$
$433$	−5.92414	−0.284696	−0.142348	+	0.989817i	$0.545465\pi$
$434$	−0.281093	−0.0134929
$435$	2.25441	0.108091
$436$	3.90597	0.187062
$437$	0.178900	0.00855794
$438$	−20.2480	−0.967485
$439$	−5.36749	−0.256176	−0.128088	−	0.991763i	$-0.540884\pi$
$439$	−5.36749	−0.256176	−0.128088	+	0.991763i	$0.540884\pi$
$440$	−1.37460	−0.0655317
$441$	3.05896	0.145665
$442$	12.6479	0.601601
$443$	−38.8316	−1.84494	−0.922472	−	0.386065i	$-0.873834\pi$
$443$	−38.8316	−1.84494	−0.922472	+	0.386065i	$0.873834\pi$
$444$	−16.0552	−0.761946
$445$	5.14034	0.243675
$446$	21.2389	1.00569
$447$	−26.2654	−1.24231
$448$	0.398412	0.0188232
$449$	−2.29896	−0.108495	−0.0542474	−	0.998528i	$-0.517276\pi$
$449$	−2.29896	−0.108495	−0.0542474	+	0.998528i	$0.517276\pi$
$450$	−2.17319	−0.102445
$451$	27.6971	1.30420
$452$	−5.24695	−0.246796
$453$	37.4796	1.76095
$454$	2.92250	0.137160
$455$	0.287144	0.0134615
$456$	0.0827634	0.00387575
$457$	5.91510	0.276697	0.138348	−	0.990384i	$-0.455821\pi$
$457$	5.91510	0.276697	0.138348	+	0.990384i	$0.455821\pi$
$458$	15.9402	0.744835
$459$	−36.1299	−1.68640
$460$	1.29101	0.0601934
$461$	−24.9692	−1.16293	−0.581467	−	0.813570i	$-0.697521\pi$
$461$	−24.9692	−1.16293	−0.581467	+	0.813570i	$0.697521\pi$
$462$	2.34090	0.108908
$463$	−4.35799	−0.202533	−0.101266	−	0.994859i	$-0.532289\pi$
$463$	−4.35799	−0.202533	−0.101266	+	0.994859i	$0.532289\pi$
$464$	−3.77464	−0.175233
$465$	−0.421380	−0.0195410
$466$	2.42535	0.112352
$467$	−40.4929	−1.87379	−0.936893	−	0.349616i	$-0.886312\pi$
$467$	−40.4929	−1.87379	−0.936893	+	0.349616i	$0.886312\pi$
$468$	−0.862110	−0.0398511
$469$	−3.32116	−0.153357
$470$	0.901666	0.0415907
$471$	15.5851	0.718124
$472$	1.26062	0.0580246
$473$	−22.9756	−1.05642
$474$	17.4127	0.799791
$475$	−0.251759	−0.0115515
$476$	−2.61353	−0.119791
$477$	0.610490	0.0279524
$478$	−23.7583	−1.08668
$479$	6.16146	0.281524	0.140762	−	0.990043i	$-0.455045\pi$
$479$	6.16146	0.281524	0.140762	+	0.990043i	$0.455045\pi$
$480$	0.597250	0.0272606
$481$	19.3743	0.883394
$482$	−7.40717	−0.337387
$483$	−2.19853	−0.100037
$484$	2.52293	0.114679
$485$	3.51448	0.159584
$486$	4.60594	0.208930
$487$	−7.85545	−0.355964	−0.177982	−	0.984034i	$-0.556957\pi$
$487$	−7.85545	−0.355964	−0.177982	+	0.984034i	$0.556957\pi$
$488$	9.91540	0.448849
$489$	−12.8842	−0.582644
$490$	2.55728	0.115526
$491$	−23.6342	−1.06660	−0.533299	−	0.845927i	$-0.679048\pi$
$491$	−23.6342	−1.06660	−0.533299	+	0.845927i	$0.679048\pi$
$492$	−12.0341	−0.542537
$493$	24.7611	1.11518
$494$	−0.0998734	−0.00449352
$495$	−0.614632	−0.0276257
$496$	0.705533	0.0316794
$497$	1.24328	0.0557688
$498$	−14.0788	−0.630884
$499$	−8.48110	−0.379666	−0.189833	−	0.981816i	$-0.560795\pi$
$499$	−8.48110	−0.379666	−0.189833	+	0.981816i	$0.560795\pi$
$500$	−3.68580	−0.164834
$501$	−37.4225	−1.67191
$502$	−2.72576	−0.121657
$503$	−14.6700	−0.654101	−0.327051	−	0.945007i	$-0.606055\pi$
$503$	−14.6700	−0.654101	−0.327051	+	0.945007i	$0.606055\pi$
$504$	0.178144	0.00793514
$505$	−2.93516	−0.130613
$506$	−12.7005	−0.564606
$507$	14.8313	0.658681
$508$	10.5093	0.466274
$509$	−6.68312	−0.296224	−0.148112	−	0.988971i	$-0.547320\pi$
$509$	−6.68312	−0.296224	−0.148112	+	0.988971i	$0.547320\pi$
$510$	−3.91788	−0.173486
$511$	−5.04893	−0.223352
$512$	−1.00000	−0.0441942
$513$	0.285297	0.0125962
$514$	12.2989	0.542481
$515$	1.68891	0.0744223
$516$	9.98264	0.439461
$517$	−8.87030	−0.390115
$518$	−4.00345	−0.175901
$519$	1.46076	0.0641201
$520$	−0.720722	−0.0316057
$521$	9.19072	0.402653	0.201326	−	0.979524i	$-0.435475\pi$
$521$	9.19072	0.402653	0.201326	+	0.979524i	$0.435475\pi$
$522$	−1.68777	−0.0738717
$523$	30.0993	1.31615	0.658076	−	0.752952i	$-0.271371\pi$
$523$	30.0993	1.31615	0.658076	+	0.752952i	$0.271371\pi$
$524$	−0.826010	−0.0360844
$525$	3.09391	0.135029
$526$	−29.1191	−1.26965
$527$	−4.62819	−0.201607
$528$	−5.87556	−0.255701
$529$	−11.0719	−0.481387
$530$	0.510368	0.0221690
$531$	0.563665	0.0244610
$532$	0.0206375	0.000894749 0
$533$	14.5219	0.629013
$534$	21.9717	0.950808
$535$	0.134225	0.00580304
$536$	8.33599	0.360060
$537$	14.0033	0.604286
$538$	−30.1751	−1.30094
$539$	−25.1578	−1.08362
$540$	2.05880	0.0885967
$541$	−28.5534	−1.22761	−0.613803	−	0.789459i	$-0.710361\pi$
$541$	−28.5534	−1.22761	−0.613803	+	0.789459i	$0.710361\pi$
$542$	−9.70043	−0.416669
$543$	−27.2830	−1.17082
$544$	6.55986	0.281251
$545$	1.46006	0.0625422
$546$	1.22736	0.0525261
$547$	−15.6193	−0.667832	−0.333916	−	0.942603i	$-0.608370\pi$
$547$	−15.6193	−0.667832	−0.333916	+	0.942603i	$0.608370\pi$
$548$	1.18957	0.0508159
$549$	4.43351	0.189218
$550$	17.8729	0.762105
$551$	−0.195524	−0.00832961
$552$	5.51823	0.234871
$553$	4.34195	0.184638
$554$	10.9154	0.463751
$555$	−6.00148	−0.254749
$556$	10.1836	0.431881
$557$	9.53629	0.404066	0.202033	−	0.979379i	$-0.435245\pi$
$557$	9.53629	0.404066	0.202033	+	0.979379i	$0.435245\pi$
$558$	0.315468	0.0133548
$559$	−12.0464	−0.509508
$560$	0.148928	0.00629334
$561$	38.5428	1.62728
$562$	−14.3811	−0.606629
$563$	0.185083	0.00780032	0.00390016	−	0.999992i	$-0.498759\pi$
$563$	0.185083	0.00780032	0.00390016	+	0.999992i	$0.498759\pi$
$564$	3.85405	0.162285
$565$	−1.96132	−0.0825135
$566$	21.9537	0.922783
$567$	−2.97162	−0.124796
$568$	−3.12059	−0.130937
$569$	35.0989	1.47142	0.735711	−	0.677295i	$-0.236848\pi$
$569$	35.0989	1.47142	0.735711	+	0.677295i	$0.236848\pi$
$570$	0.0309372	0.00129582
$571$	−45.7097	−1.91289	−0.956446	−	0.291910i	$-0.905709\pi$
$571$	−45.7097	−1.91289	−0.956446	+	0.291910i	$0.905709\pi$
$572$	7.09023	0.296458
$573$	34.6066	1.44571
$574$	−3.00076	−0.125249
$575$	−16.7860	−0.700023
$576$	−0.447134	−0.0186306
$577$	−6.40613	−0.266691	−0.133345	−	0.991070i	$-0.542572\pi$
$577$	−6.40613	−0.266691	−0.133345	+	0.991070i	$0.542572\pi$
$578$	−26.0317	−1.08278
$579$	27.5008	1.14290
$580$	−1.41097	−0.0585874
$581$	−3.51061	−0.145645
$582$	15.0222	0.622689
$583$	−5.02084	−0.207942
$584$	12.6726	0.524398
$585$	−0.322259	−0.0133238
$586$	9.89021	0.408561
$587$	−39.9071	−1.64714	−0.823571	−	0.567214i	$-0.808021\pi$
$587$	−39.9071	−1.64714	−0.823571	+	0.567214i	$0.808021\pi$
$588$	10.9308	0.450777
$589$	0.0365462	0.00150586
$590$	0.471222	0.0193999
$591$	6.20065	0.255061
$592$	10.0485	0.412991
$593$	3.25624	0.133718	0.0668590	−	0.997762i	$-0.478702\pi$
$593$	3.25624	0.133718	0.0668590	+	0.997762i	$0.478702\pi$
$594$	−20.2539	−0.831026
$595$	−0.976943	−0.0400508
$596$	16.4388	0.673359
$597$	−12.4923	−0.511277
$598$	−6.65903	−0.272308
$599$	6.07518	0.248225	0.124113	−	0.992268i	$-0.460392\pi$
$599$	6.07518	0.248225	0.124113	+	0.992268i	$0.460392\pi$
$600$	−7.76559	−0.317029
$601$	9.63572	0.393049	0.196525	−	0.980499i	$-0.437034\pi$
$601$	9.63572	0.393049	0.196525	+	0.980499i	$0.437034\pi$
$602$	2.48922	0.101453
$603$	3.72730	0.151787
$604$	−23.4575	−0.954470
$605$	0.943079	0.0383416
$606$	−12.5459	−0.509644
$607$	−21.1397	−0.858034	−0.429017	−	0.903297i	$-0.641140\pi$
$607$	−21.1397	−0.858034	−0.429017	+	0.903297i	$0.641140\pi$
$608$	−0.0517994	−0.00210074
$609$	2.40283	0.0973675
$610$	3.70640	0.150068
$611$	−4.65081	−0.188151
$612$	2.93313	0.118565
$613$	33.5186	1.35381	0.676903	−	0.736072i	$-0.263322\pi$
$613$	33.5186	1.35381	0.676903	+	0.736072i	$0.263322\pi$
$614$	6.45061	0.260325
$615$	−4.49836	−0.181392
$616$	−1.46510	−0.0590307
$617$	−18.8008	−0.756893	−0.378446	−	0.925623i	$-0.623542\pi$
$617$	−18.8008	−0.756893	−0.378446	+	0.925623i	$0.623542\pi$
$618$	7.21902	0.290391
$619$	−39.8438	−1.60146	−0.800728	−	0.599028i	$-0.795554\pi$
$619$	−39.8438	−1.60146	−0.800728	+	0.599028i	$0.795554\pi$
$620$	0.263730	0.0105917
$621$	19.0221	0.763329
$622$	7.46794	0.299437
$623$	5.47875	0.219502
$624$	−3.08063	−0.123324
$625$	22.9236	0.916944
$626$	26.0247	1.04016
$627$	−0.304350	−0.0121546
$628$	−9.75430	−0.389239
$629$	−65.9168	−2.62827
$630$	0.0665905	0.00265303
$631$	−28.0231	−1.11558	−0.557792	−	0.829981i	$-0.688351\pi$
$631$	−28.0231	−1.11558	−0.557792	+	0.829981i	$0.688351\pi$
$632$	−10.8981	−0.433504
$633$	38.1739	1.51727
$634$	23.6850	0.940652
$635$	3.92840	0.155894
$636$	2.18150	0.0865020
$637$	−13.1905	−0.522627
$638$	13.8807	0.549542
$639$	−1.39532	−0.0551980
$640$	−0.373803	−0.0147759
$641$	−15.7649	−0.622676	−0.311338	−	0.950299i	$-0.600777\pi$
$641$	−15.7649	−0.622676	−0.311338	+	0.950299i	$0.600777\pi$
$642$	0.573725	0.0226431
$643$	−43.0963	−1.69955	−0.849776	−	0.527143i	$-0.823263\pi$
$643$	−43.0963	−1.69955	−0.849776	+	0.527143i	$0.823263\pi$
$644$	1.37600	0.0542220
$645$	3.73154	0.146929
$646$	0.339796	0.0133691
$647$	−14.0227	−0.551288	−0.275644	−	0.961260i	$-0.588891\pi$
$647$	−14.0227	−0.551288	−0.275644	+	0.961260i	$0.588891\pi$
$648$	7.45867	0.293004
$649$	−4.63574	−0.181969
$650$	9.37099	0.367561
$651$	−0.449122	−0.0176025
$652$	8.06388	0.315806
$653$	−10.0906	−0.394875	−0.197437	−	0.980316i	$-0.563262\pi$
$653$	−10.0906	−0.394875	−0.197437	+	0.980316i	$0.563262\pi$
$654$	6.24084	0.244036
$655$	−0.308765	−0.0120644
$656$	7.53179	0.294067
$657$	5.66637	0.221066
$658$	0.961027	0.0374647
$659$	−28.3266	−1.10345	−0.551724	−	0.834027i	$-0.686030\pi$
$659$	−28.3266	−1.10345	−0.551724	+	0.834027i	$0.686030\pi$
$660$	−2.19630	−0.0854909
$661$	−44.1576	−1.71753	−0.858767	−	0.512367i	$-0.828769\pi$
$661$	−44.1576	−1.71753	−0.858767	+	0.512367i	$0.828769\pi$
$662$	−25.6303	−0.996148
$663$	20.2085	0.784832
$664$	8.81151	0.341953
$665$	0.00771435	0.000299150 0
$666$	4.49303	0.174101
$667$	−13.0365	−0.504776
$668$	23.4217	0.906214
$669$	33.9349	1.31200
$670$	3.11601	0.120382
$671$	−36.4624	−1.40762
$672$	0.636571	0.0245562
$673$	−35.1435	−1.35468	−0.677342	−	0.735668i	$-0.736868\pi$
$673$	−35.1435	−1.35468	−0.677342	+	0.735668i	$0.736868\pi$
$674$	26.0207	1.00228
$675$	−26.7690	−1.03034
$676$	−9.28251	−0.357019
$677$	37.4090	1.43774	0.718872	−	0.695143i	$-0.244659\pi$
$677$	37.4090	1.43774	0.718872	+	0.695143i	$0.244659\pi$
$678$	−8.38341	−0.321963
$679$	3.74585	0.143753
$680$	2.45209	0.0940334
$681$	4.66948	0.178935
$682$	−2.59449	−0.0993483
$683$	−7.28168	−0.278626	−0.139313	−	0.990248i	$-0.544489\pi$
$683$	−7.28168	−0.278626	−0.139313	+	0.990248i	$0.544489\pi$
$684$	−0.0231613	−0.000885593 0
$685$	0.444665	0.0169898
$686$	5.51453	0.210546
$687$	25.4687	0.971691
$688$	−6.24786	−0.238197
$689$	−2.63249	−0.100290
$690$	2.06273	0.0785267
$691$	21.9578	0.835315	0.417658	−	0.908604i	$-0.362851\pi$
$691$	21.9578	0.835315	0.417658	+	0.908604i	$0.362851\pi$
$692$	−0.914248	−0.0347545
$693$	−0.655097	−0.0248851
$694$	25.9125	0.983625
$695$	3.80666	0.144395
$696$	−6.03101	−0.228605
$697$	−49.4074	−1.87144
$698$	−27.9290	−1.05713
$699$	3.87516	0.146572
$700$	−1.93639	−0.0731887
$701$	48.8467	1.84492	0.922458	−	0.386098i	$-0.126177\pi$
$701$	48.8467	1.84492	0.922458	+	0.386098i	$0.126177\pi$
$702$	−10.6193	−0.400801
$703$	0.520507	0.0196313
$704$	3.67735	0.138595
$705$	1.44065	0.0542581
$706$	−2.49607	−0.0939410
$707$	−3.12840	−0.117655
$708$	2.01418	0.0756974
$709$	31.1783	1.17093	0.585463	−	0.810699i	$-0.300913\pi$
$709$	31.1783	1.17093	0.585463	+	0.810699i	$0.300913\pi$
$710$	−1.16648	−0.0437774
$711$	−4.87292	−0.182749
$712$	−13.7515	−0.515358
$713$	2.43671	0.0912553
$714$	−4.17581	−0.156276
$715$	2.65035	0.0991174
$716$	−8.76427	−0.327536
$717$	−37.9604	−1.41766
$718$	28.6233	1.06821
$719$	−1.84751	−0.0689005	−0.0344503	−	0.999406i	$-0.510968\pi$
$719$	−1.84751	−0.0689005	−0.0344503	+	0.999406i	$0.510968\pi$
$720$	−0.167140	−0.00622893
$721$	1.80010	0.0670392
$722$	18.9973	0.707007
$723$	−11.8349	−0.440146
$724$	17.0757	0.634612
$725$	18.3458	0.681346
$726$	4.03106	0.149607
$727$	−12.7001	−0.471019	−0.235510	−	0.971872i	$-0.575676\pi$
$727$	−12.7001	−0.471019	−0.235510	+	0.971872i	$0.575676\pi$
$728$	−0.768171	−0.0284703
$729$	29.7352	1.10131
$730$	4.73707	0.175327
$731$	40.9851	1.51589
$732$	15.8425	0.585556
$733$	−40.9636	−1.51303	−0.756513	−	0.653979i	$-0.773099\pi$
$733$	−40.9636	−1.51303	−0.756513	+	0.653979i	$0.773099\pi$
$734$	10.7527	0.396891
$735$	4.08595	0.150713
$736$	−3.45371	−0.127305
$737$	−30.6544	−1.12917
$738$	3.36772	0.123967
$739$	−41.7795	−1.53688	−0.768442	−	0.639919i	$-0.778968\pi$
$739$	−41.7795	−1.53688	−0.768442	+	0.639919i	$0.778968\pi$
$740$	3.75616	0.138079
$741$	−0.159575	−0.00586212
$742$	0.543968	0.0199697
$743$	4.55608	0.167146	0.0835731	−	0.996502i	$-0.473367\pi$
$743$	4.55608	0.167146	0.0835731	+	0.996502i	$0.473367\pi$
$744$	1.12728	0.0413280
$745$	6.14487	0.225130
$746$	−30.6816	−1.12333
$747$	3.93992	0.144154
$748$	−24.1229	−0.882021
$749$	0.143061	0.00522735
$750$	−5.88905	−0.215038
$751$	−40.0084	−1.45993	−0.729963	−	0.683487i	$-0.760463\pi$
$751$	−40.0084	−1.45993	−0.729963	+	0.683487i	$0.760463\pi$
$752$	−2.41214	−0.0879618
$753$	−4.35513	−0.158710
$754$	7.27782	0.265042
$755$	−8.76846	−0.319117
$756$	2.19434	0.0798075
$757$	−28.2055	−1.02515	−0.512573	−	0.858644i	$-0.671308\pi$
$757$	−28.2055	−1.02515	−0.512573	+	0.858644i	$0.671308\pi$
$758$	13.8183	0.501901
$759$	−20.2925	−0.736570
$760$	−0.0193627	−0.000702361 0
$761$	19.8495	0.719545	0.359772	−	0.933040i	$-0.382854\pi$
$761$	19.8495	0.719545	0.359772	+	0.933040i	$0.382854\pi$
$762$	16.7914	0.608288
$763$	1.55619	0.0563377
$764$	−21.6593	−0.783608
$765$	1.09641	0.0396409
$766$	−0.639382	−0.0231018
$767$	−2.43057	−0.0877629
$768$	−1.59777	−0.0576545
$769$	45.9680	1.65765	0.828825	−	0.559508i	$-0.189010\pi$
$769$	45.9680	1.65765	0.828825	+	0.559508i	$0.189010\pi$
$770$	−0.547659	−0.0197363
$771$	19.6508	0.707707
$772$	−17.2120	−0.619474
$773$	42.8945	1.54281	0.771404	−	0.636346i	$-0.219555\pi$
$773$	42.8945	1.54281	0.771404	+	0.636346i	$0.219555\pi$
$774$	−2.79363	−0.100415
$775$	−3.42908	−0.123176
$776$	−9.40196	−0.337511
$777$	−6.39659	−0.229476
$778$	−32.9254	−1.18043
$779$	0.390142	0.0139783
$780$	−1.15155	−0.0412320
$781$	11.4755	0.410626
$782$	22.6558	0.810171
$783$	−20.7897	−0.742963
$784$	−6.84127	−0.244331
$785$	−3.64618	−0.130138
$786$	−1.31977	−0.0470748
$787$	−32.3714	−1.15392	−0.576958	−	0.816774i	$-0.695760\pi$
$787$	−32.3714	−1.15392	−0.576958	+	0.816774i	$0.695760\pi$
$788$	−3.88082	−0.138248
$789$	−46.5256	−1.65635
$790$	−4.07375	−0.144937
$791$	−2.09045	−0.0743277
$792$	1.64427	0.0584266
$793$	−19.1177	−0.678889
$794$	−1.29574	−0.0459840
$795$	0.815450	0.0289210
$796$	7.81861	0.277123
$797$	−6.44983	−0.228465	−0.114232	−	0.993454i	$-0.536441\pi$
$797$	−6.44983	−0.228465	−0.114232	+	0.993454i	$0.536441\pi$
$798$	0.0329740	0.00116727
$799$	15.8233	0.559788
$800$	4.86027	0.171837
$801$	−6.14875	−0.217255
$802$	19.7778	0.698377
$803$	−46.6018	−1.64454
$804$	13.3190	0.469724
$805$	0.514352	0.0181285
$806$	−1.36032	−0.0479154
$807$	−48.2129	−1.69717
$808$	7.85216	0.276238
$809$	−20.7450	−0.729355	−0.364677	−	0.931134i	$-0.618821\pi$
$809$	−20.7450	−0.729355	−0.364677	+	0.931134i	$0.618821\pi$
$810$	2.78807	0.0979628
$811$	3.44480	0.120963	0.0604817	−	0.998169i	$-0.480736\pi$
$811$	3.44480	0.120963	0.0604817	+	0.998169i	$0.480736\pi$
$812$	−1.50386	−0.0527753
$813$	−15.4990	−0.543575
$814$	−36.9519	−1.29516
$815$	3.01430	0.105586
$816$	10.4811	0.366913
$817$	−0.323635	−0.0113226
$818$	−22.1810	−0.775541
$819$	−0.343475	−0.0120020
$820$	2.81540	0.0983181
$821$	25.3199	0.883671	0.441836	−	0.897096i	$-0.354327\pi$
$821$	25.3199	0.883671	0.441836	+	0.897096i	$0.354327\pi$
$822$	1.90066	0.0662931
$823$	24.5968	0.857391	0.428695	−	0.903449i	$-0.358973\pi$
$823$	24.5968	0.857391	0.428695	+	0.903449i	$0.358973\pi$
$824$	−4.51819	−0.157398
$825$	28.5568	0.994221
$826$	0.502245	0.0174754
$827$	−19.2282	−0.668630	−0.334315	−	0.942461i	$-0.608505\pi$
$827$	−19.2282	−0.668630	−0.334315	+	0.942461i	$0.608505\pi$
$828$	−1.54427	−0.0536671
$829$	−12.2055	−0.423914	−0.211957	−	0.977279i	$-0.567984\pi$
$829$	−12.2055	−0.423914	−0.211957	+	0.977279i	$0.567984\pi$
$830$	3.29377	0.114328
$831$	17.4403	0.604996
$832$	1.92808	0.0668442
$833$	44.8777	1.55492
$834$	16.2710	0.563420
$835$	8.75511	0.302983
$836$	0.190485	0.00658805
$837$	3.88588	0.134316
$838$	20.0904	0.694012
$839$	44.7209	1.54394	0.771968	−	0.635661i	$-0.219273\pi$
$839$	44.7209	1.54394	0.771968	+	0.635661i	$0.219273\pi$
$840$	0.237952	0.00821012
$841$	−14.7521	−0.508692
$842$	35.9570	1.23916
$843$	−22.9776	−0.791391
$844$	−23.8920	−0.822396
$845$	−3.46983	−0.119366
$846$	−1.07855	−0.0370813
$847$	1.00517	0.0345379
$848$	−1.36534	−0.0468860
$849$	35.0769	1.20384
$850$	−31.8827	−1.09357
$851$	34.7046	1.18966
$852$	−4.98598	−0.170817
$853$	−31.2113	−1.06865	−0.534327	−	0.845278i	$-0.679435\pi$
$853$	−31.2113	−1.06865	−0.534327	+	0.845278i	$0.679435\pi$
$854$	3.95041	0.135180
$855$	−0.00865774	−0.000296088 0
$856$	−0.359079	−0.0122731
$857$	29.0720	0.993079	0.496539	−	0.868014i	$-0.334604\pi$
$857$	29.0720	0.993079	0.496539	+	0.868014i	$0.334604\pi$
$858$	11.3286	0.386751
$859$	26.5897	0.907227	0.453614	−	0.891198i	$-0.350135\pi$
$859$	26.5897	0.907227	0.453614	+	0.891198i	$0.350135\pi$
$860$	−2.33547	−0.0796388
$861$	−4.79452	−0.163397
$862$	13.3871	0.455966
$863$	26.2425	0.893307	0.446653	−	0.894707i	$-0.352616\pi$
$863$	26.2425	0.893307	0.446653	+	0.894707i	$0.352616\pi$
$864$	−5.50772	−0.187377
$865$	−0.341748	−0.0116198
$866$	5.92414	0.201311
$867$	−41.5927	−1.41256
$868$	0.281093	0.00954091
$869$	40.0763	1.35949
$870$	−2.25441	−0.0764316
$871$	−16.0725	−0.544594
$872$	−3.90597	−0.132273
$873$	−4.20393	−0.142282
$874$	−0.178900	−0.00605138
$875$	−1.46847	−0.0496432
$876$	20.2480	0.684115
$877$	2.05062	0.0692445	0.0346223	−	0.999400i	$-0.488977\pi$
$877$	2.05062	0.0692445	0.0346223	+	0.999400i	$0.488977\pi$
$878$	5.36749	0.181144
$879$	15.8023	0.532997
$880$	1.37460	0.0463379
$881$	20.4402	0.688649	0.344325	−	0.938851i	$-0.388108\pi$
$881$	20.4402	0.688649	0.344325	+	0.938851i	$0.388108\pi$
$882$	−3.05896	−0.103001
$883$	−12.7597	−0.429398	−0.214699	−	0.976680i	$-0.568877\pi$
$883$	−12.7597	−0.429398	−0.214699	+	0.976680i	$0.568877\pi$
$884$	−12.6479	−0.425396
$885$	0.752905	0.0253086
$886$	38.8316	1.30457
$887$	−17.9443	−0.602512	−0.301256	−	0.953543i	$-0.597406\pi$
$887$	−17.9443	−0.602512	−0.301256	+	0.953543i	$0.597406\pi$
$888$	16.0552	0.538777
$889$	4.18702	0.140428
$890$	−5.14034	−0.172305
$891$	−27.4282	−0.918878
$892$	−21.2389	−0.711131
$893$	−0.124947	−0.00418121
$894$	26.2654	0.878446
$895$	−3.27611	−0.109508
$896$	−0.398412	−0.0133100
$897$	−10.6396	−0.355246
$898$	2.29896	0.0767174
$899$	−2.66314	−0.0888206
$900$	2.17319	0.0724397
$901$	8.95644	0.298382
$902$	−27.6971	−0.922211
$903$	3.97720	0.132353
$904$	5.24695	0.174511
$905$	6.38293	0.212176
$906$	−37.4796	−1.24518
$907$	53.9235	1.79050	0.895250	−	0.445564i	$-0.146997\pi$
$907$	53.9235	1.79050	0.895250	+	0.445564i	$0.146997\pi$
$908$	−2.92250	−0.0969865
$909$	3.51097	0.116451
$910$	−0.287144	−0.00951874
$911$	−18.5141	−0.613399	−0.306699	−	0.951806i	$-0.599225\pi$
$911$	−18.5141	−0.613399	−0.306699	+	0.951806i	$0.599225\pi$
$912$	−0.0827634	−0.00274057
$913$	−32.4030	−1.07238
$914$	−5.91510	−0.195654
$915$	5.92198	0.195774
$916$	−15.9402	−0.526678
$917$	−0.329093	−0.0108676
$918$	36.1299	1.19246
$919$	42.4600	1.40063	0.700313	−	0.713836i	$-0.253044\pi$
$919$	42.4600	1.40063	0.700313	+	0.713836i	$0.253044\pi$
$920$	−1.29101	−0.0425632
$921$	10.3066	0.339613
$922$	24.9692	0.822318
$923$	6.01675	0.198044
$924$	−2.34090	−0.0770098
$925$	−48.8385	−1.60580
$926$	4.35799	0.143212
$927$	−2.02023	−0.0663532
$928$	3.77464	0.123909
$929$	−52.0968	−1.70924	−0.854620	−	0.519254i	$-0.826210\pi$
$929$	−52.0968	−1.70924	−0.854620	+	0.519254i	$0.826210\pi$
$930$	0.421380	0.0138176
$931$	−0.354373	−0.0116141
$932$	−2.42535	−0.0794451
$933$	11.9320	0.390637
$934$	40.4929	1.32497
$935$	−9.01721	−0.294894
$936$	0.862110	0.0281789
$937$	−7.27137	−0.237545	−0.118773	−	0.992921i	$-0.537896\pi$
$937$	−7.27137	−0.237545	−0.118773	+	0.992921i	$0.537896\pi$
$938$	3.32116	0.108440
$939$	41.5815	1.35696
$940$	−0.901666	−0.0294091
$941$	35.3320	1.15179	0.575895	−	0.817524i	$-0.304654\pi$
$941$	35.3320	1.15179	0.575895	+	0.817524i	$0.304654\pi$
$942$	−15.5851	−0.507790
$943$	26.0126	0.847087
$944$	−1.26062	−0.0410296
$945$	0.820252	0.0266828
$946$	22.9756	0.747001
$947$	3.37705	0.109739	0.0548696	−	0.998494i	$-0.482526\pi$
$947$	3.37705	0.109739	0.0548696	+	0.998494i	$0.482526\pi$
$948$	−17.4127	−0.565538
$949$	−24.4339	−0.793157
$950$	0.251759	0.00816814
$951$	37.8432	1.22715
$952$	2.61353	0.0847049
$953$	43.6879	1.41519	0.707595	−	0.706618i	$-0.249780\pi$
$953$	43.6879	1.41519	0.707595	+	0.706618i	$0.249780\pi$
$954$	−0.610490	−0.0197653
$955$	−8.09632	−0.261991
$956$	23.7583	0.768400
$957$	22.1782	0.716918
$958$	−6.16146	−0.199068
$959$	0.473939	0.0153043
$960$	−0.597250	−0.0192762
$961$	−30.5022	−0.983943
$962$	−19.3743	−0.624654
$963$	−0.160556	−0.00517386
$964$	7.40717	0.238569
$965$	−6.43390	−0.207115
$966$	2.19853	0.0707365
$967$	14.6782	0.472020	0.236010	−	0.971751i	$-0.424160\pi$
$967$	14.6782	0.472020	0.236010	+	0.971751i	$0.424160\pi$
$968$	−2.52293	−0.0810901
$969$	0.542916	0.0174410
$970$	−3.51448	−0.112843
$971$	31.9087	1.02400	0.512000	−	0.858985i	$-0.328905\pi$
$971$	31.9087	1.02400	0.512000	+	0.858985i	$0.328905\pi$
$972$	−4.60594	−0.147736
$973$	4.05727	0.130070
$974$	7.85545	0.251705
$975$	14.9727	0.479510
$976$	−9.91540	−0.317384
$977$	11.7237	0.375075	0.187538	−	0.982257i	$-0.439949\pi$
$977$	11.7237	0.375075	0.187538	+	0.982257i	$0.439949\pi$
$978$	12.8842	0.411992
$979$	50.5690	1.61619
$980$	−2.55728	−0.0816895
$981$	−1.74649	−0.0557612
$982$	23.6342	0.754199
$983$	−55.6677	−1.77552	−0.887762	−	0.460303i	$-0.847741\pi$
$983$	−55.6677	−1.77552	−0.887762	+	0.460303i	$0.847741\pi$
$984$	12.0341	0.383632
$985$	−1.45066	−0.0462219
$986$	−24.7611	−0.788555
$987$	1.53550	0.0488755
$988$	0.0998734	0.00317740
$989$	−21.5783	−0.686150
$990$	0.614632	0.0195343
$991$	5.98304	0.190058	0.0950288	−	0.995475i	$-0.469706\pi$
$991$	5.98304	0.190058	0.0950288	+	0.995475i	$0.469706\pi$
$992$	−0.705533	−0.0224007
$993$	−40.9512	−1.29955
$994$	−1.24328	−0.0394345
$995$	2.92262	0.0926532
$996$	14.0788	0.446102
$997$	17.5408	0.555523	0.277762	−	0.960650i	$-0.410407\pi$
$997$	17.5408	0.555523	0.277762	+	0.960650i	$0.410407\pi$
$998$	8.48110	0.268465
$999$	55.3444	1.75102

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.b.1.19	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.b.1.19	✓	56	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.59777 q^{3} +1.00000 q^{4} +0.373803 q^{5} +1.59777 q^{6} +0.398412 q^{7} -1.00000 q^{8} -0.447134 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.59777 q^{3} +1.00000 q^{4} +0.373803 q^{5} +1.59777 q^{6} +0.398412 q^{7} -1.00000 q^{8} -0.447134 q^{9} -0.373803 q^{10} +3.67735 q^{11} -1.59777 q^{12} +1.92808 q^{13} -0.398412 q^{14} -0.597250 q^{15} +1.00000 q^{16} -6.55986 q^{17} +0.447134 q^{18} +0.0517994 q^{19} +0.373803 q^{20} -0.636571 q^{21} -3.67735 q^{22} +3.45371 q^{23} +1.59777 q^{24} -4.86027 q^{25} -1.92808 q^{26} +5.50772 q^{27} +0.398412 q^{28} -3.77464 q^{29} +0.597250 q^{30} +0.705533 q^{31} -1.00000 q^{32} -5.87556 q^{33} +6.55986 q^{34} +0.148928 q^{35} -0.447134 q^{36} +10.0485 q^{37} -0.0517994 q^{38} -3.08063 q^{39} -0.373803 q^{40} +7.53179 q^{41} +0.636571 q^{42} -6.24786 q^{43} +3.67735 q^{44} -0.167140 q^{45} -3.45371 q^{46} -2.41214 q^{47} -1.59777 q^{48} -6.84127 q^{49} +4.86027 q^{50} +10.4811 q^{51} +1.92808 q^{52} -1.36534 q^{53} -5.50772 q^{54} +1.37460 q^{55} -0.398412 q^{56} -0.0827634 q^{57} +3.77464 q^{58} -1.26062 q^{59} -0.597250 q^{60} -9.91540 q^{61} -0.705533 q^{62} -0.178144 q^{63} +1.00000 q^{64} +0.720722 q^{65} +5.87556 q^{66} -8.33599 q^{67} -6.55986 q^{68} -5.51823 q^{69} -0.148928 q^{70} +3.12059 q^{71} +0.447134 q^{72} -12.6726 q^{73} -10.0485 q^{74} +7.76559 q^{75} +0.0517994 q^{76} +1.46510 q^{77} +3.08063 q^{78} +10.8981 q^{79} +0.373803 q^{80} -7.45867 q^{81} -7.53179 q^{82} -8.81151 q^{83} -0.636571 q^{84} -2.45209 q^{85} +6.24786 q^{86} +6.03101 q^{87} -3.67735 q^{88} +13.7515 q^{89} +0.167140 q^{90} +0.768171 q^{91} +3.45371 q^{92} -1.12728 q^{93} +2.41214 q^{94} +0.0193627 q^{95} +1.59777 q^{96} +9.40196 q^{97} +6.84127 q^{98} -1.64427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

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