LMFDB - Embedded newform 6046.2.a.d.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, 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("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$1$
Dimension:	$55$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.56981 q^{3} +1.00000 q^{4} +3.21985 q^{5} +1.56981 q^{6} -0.392480 q^{7} -1.00000 q^{8} -0.535687 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.56981 q^{3} +1.00000 q^{4} +3.21985 q^{5} +1.56981 q^{6} -0.392480 q^{7} -1.00000 q^{8} -0.535687 q^{9} -3.21985 q^{10} +1.67931 q^{11} -1.56981 q^{12} -0.362248 q^{13} +0.392480 q^{14} -5.05457 q^{15} +1.00000 q^{16} -4.58600 q^{17} +0.535687 q^{18} -0.0581319 q^{19} +3.21985 q^{20} +0.616120 q^{21} -1.67931 q^{22} -8.13019 q^{23} +1.56981 q^{24} +5.36746 q^{25} +0.362248 q^{26} +5.55037 q^{27} -0.392480 q^{28} +2.16132 q^{29} +5.05457 q^{30} +6.76515 q^{31} -1.00000 q^{32} -2.63620 q^{33} +4.58600 q^{34} -1.26373 q^{35} -0.535687 q^{36} +9.21469 q^{37} +0.0581319 q^{38} +0.568662 q^{39} -3.21985 q^{40} -9.76408 q^{41} -0.616120 q^{42} +6.52135 q^{43} +1.67931 q^{44} -1.72483 q^{45} +8.13019 q^{46} +4.17386 q^{47} -1.56981 q^{48} -6.84596 q^{49} -5.36746 q^{50} +7.19916 q^{51} -0.362248 q^{52} -5.98979 q^{53} -5.55037 q^{54} +5.40713 q^{55} +0.392480 q^{56} +0.0912562 q^{57} -2.16132 q^{58} -9.19439 q^{59} -5.05457 q^{60} -2.92717 q^{61} -6.76515 q^{62} +0.210246 q^{63} +1.00000 q^{64} -1.16639 q^{65} +2.63620 q^{66} -1.85178 q^{67} -4.58600 q^{68} +12.7629 q^{69} +1.26373 q^{70} -1.84731 q^{71} +0.535687 q^{72} +9.05854 q^{73} -9.21469 q^{74} -8.42591 q^{75} -0.0581319 q^{76} -0.659094 q^{77} -0.568662 q^{78} -4.30867 q^{79} +3.21985 q^{80} -7.10598 q^{81} +9.76408 q^{82} +8.28532 q^{83} +0.616120 q^{84} -14.7662 q^{85} -6.52135 q^{86} -3.39287 q^{87} -1.67931 q^{88} +10.4554 q^{89} +1.72483 q^{90} +0.142175 q^{91} -8.13019 q^{92} -10.6200 q^{93} -4.17386 q^{94} -0.187176 q^{95} +1.56981 q^{96} -4.40881 q^{97} +6.84596 q^{98} -0.899584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) $ 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9} + 7 q^{10} - 28 q^{11} - 4 q^{12} + q^{13} - 17 q^{14} - 8 q^{15} + 55 q^{16} - 32 q^{17} - 29 q^{18} - 3 q^{19} - 7 q^{20} - 25 q^{21} + 28 q^{22} - 27 q^{23} + 4 q^{24} + 30 q^{25} - q^{26} - q^{27} + 17 q^{28} - 69 q^{29} + 8 q^{30} - 13 q^{31} - 55 q^{32} - 18 q^{33} + 32 q^{34} - 23 q^{35} + 29 q^{36} + 3 q^{37} + 3 q^{38} - 28 q^{39} + 7 q^{40} - 51 q^{41} + 25 q^{42} + 23 q^{43} - 28 q^{44} - 28 q^{45} + 27 q^{46} - 27 q^{47} - 4 q^{48} + 8 q^{49} - 30 q^{50} - 42 q^{51} + q^{52} - 61 q^{53} + q^{54} + 5 q^{55} - 17 q^{56} - 52 q^{57} + 69 q^{58} - 71 q^{59} - 8 q^{60} - 16 q^{61} + 13 q^{62} + 14 q^{63} + 55 q^{64} - 82 q^{65} + 18 q^{66} + 32 q^{67} - 32 q^{68} - 44 q^{69} + 23 q^{70} - 84 q^{71} - 29 q^{72} - 43 q^{73} - 3 q^{74} - 37 q^{75} - 3 q^{76} - 47 q^{77} + 28 q^{78} - 20 q^{79} - 7 q^{80} - 33 q^{81} + 51 q^{82} + 17 q^{83} - 25 q^{84} + 10 q^{85} - 23 q^{86} - q^{87} + 28 q^{88} - 92 q^{89} + 28 q^{90} - 34 q^{91} - 27 q^{92} - 13 q^{93} + 27 q^{94} - 60 q^{95} + 4 q^{96} - 45 q^{97} - 8 q^{98} - 73 q^{99}+O(q^{100}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9 + 7 * q^10 - 28 * q^11 - 4 * q^12 + q^13 - 17 * q^14 - 8 * q^15 + 55 * q^16 - 32 * q^17 - 29 * q^18 - 3 * q^19 - 7 * q^20 - 25 * q^21 + 28 * q^22 - 27 * q^23 + 4 * q^24 + 30 * q^25 - q^26 - q^27 + 17 * q^28 - 69 * q^29 + 8 * q^30 - 13 * q^31 - 55 * q^32 - 18 * q^33 + 32 * q^34 - 23 * q^35 + 29 * q^36 + 3 * q^37 + 3 * q^38 - 28 * q^39 + 7 * q^40 - 51 * q^41 + 25 * q^42 + 23 * q^43 - 28 * q^44 - 28 * q^45 + 27 * q^46 - 27 * q^47 - 4 * q^48 + 8 * q^49 - 30 * q^50 - 42 * q^51 + q^52 - 61 * q^53 + q^54 + 5 * q^55 - 17 * q^56 - 52 * q^57 + 69 * q^58 - 71 * q^59 - 8 * q^60 - 16 * q^61 + 13 * q^62 + 14 * q^63 + 55 * q^64 - 82 * q^65 + 18 * q^66 + 32 * q^67 - 32 * q^68 - 44 * q^69 + 23 * q^70 - 84 * q^71 - 29 * q^72 - 43 * q^73 - 3 * q^74 - 37 * q^75 - 3 * q^76 - 47 * q^77 + 28 * q^78 - 20 * q^79 - 7 * q^80 - 33 * q^81 + 51 * q^82 + 17 * q^83 - 25 * q^84 + 10 * q^85 - 23 * q^86 - q^87 + 28 * q^88 - 92 * q^89 + 28 * q^90 - 34 * q^91 - 27 * q^92 - 13 * q^93 + 27 * q^94 - 60 * q^95 + 4 * q^96 - 45 * q^97 - 8 * q^98 - 73 * 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
$3$	−1.56981	−0.906332	−0.453166	−	0.891426i	$-0.649706\pi$
$3$	−1.56981	−0.906332	−0.453166	+	0.891426i	$0.649706\pi$
$4$	1.00000	0.500000
$5$	3.21985	1.43996	0.719981	−	0.693993i	$-0.244150\pi$
$5$	3.21985	1.43996	0.719981	+	0.693993i	$0.244150\pi$
$6$	1.56981	0.640873
$7$	−0.392480	−0.148343	−0.0741717	−	0.997245i	$-0.523631\pi$
$7$	−0.392480	−0.148343	−0.0741717	+	0.997245i	$0.523631\pi$
$8$	−1.00000	−0.353553
$9$	−0.535687	−0.178562
$10$	−3.21985	−1.01821
$11$	1.67931	0.506330	0.253165	−	0.967423i	$-0.418528\pi$
$11$	1.67931	0.506330	0.253165	+	0.967423i	$0.418528\pi$
$12$	−1.56981	−0.453166
$13$	−0.362248	−0.100470	−0.0502348	−	0.998737i	$-0.515997\pi$
$13$	−0.362248	−0.100470	−0.0502348	+	0.998737i	$0.515997\pi$
$14$	0.392480	0.104895
$15$	−5.05457	−1.30508
$16$	1.00000	0.250000
$17$	−4.58600	−1.11227	−0.556134	−	0.831093i	$-0.687716\pi$
$17$	−4.58600	−1.11227	−0.556134	+	0.831093i	$0.687716\pi$
$18$	0.535687	0.126263
$19$	−0.0581319	−0.0133364	−0.00666818	−	0.999978i	$-0.502123\pi$
$19$	−0.0581319	−0.0133364	−0.00666818	+	0.999978i	$0.502123\pi$
$20$	3.21985	0.719981
$21$	0.616120	0.134448
$22$	−1.67931	−0.358030
$23$	−8.13019	−1.69526	−0.847630	−	0.530587i	$-0.821971\pi$
$23$	−8.13019	−1.69526	−0.847630	+	0.530587i	$0.821971\pi$
$24$	1.56981	0.320437
$25$	5.36746	1.07349
$26$	0.362248	0.0710428
$27$	5.55037	1.06817
$28$	−0.392480	−0.0741717
$29$	2.16132	0.401347	0.200674	−	0.979658i	$-0.435687\pi$
$29$	2.16132	0.401347	0.200674	+	0.979658i	$0.435687\pi$
$30$	5.05457	0.922834
$31$	6.76515	1.21506	0.607528	−	0.794298i	$-0.292161\pi$
$31$	6.76515	1.21506	0.607528	+	0.794298i	$0.292161\pi$
$32$	−1.00000	−0.176777
$33$	−2.63620	−0.458903
$34$	4.58600	0.786492
$35$	−1.26373	−0.213609
$36$	−0.535687	−0.0892812
$37$	9.21469	1.51489	0.757443	−	0.652901i	$-0.226448\pi$
$37$	9.21469	1.51489	0.757443	+	0.652901i	$0.226448\pi$
$38$	0.0581319	0.00943023
$39$	0.568662	0.0910588
$40$	−3.21985	−0.509104
$41$	−9.76408	−1.52489	−0.762446	−	0.647052i	$-0.776002\pi$
$41$	−9.76408	−1.52489	−0.762446	+	0.647052i	$0.776002\pi$
$42$	−0.616120	−0.0950693
$43$	6.52135	0.994497	0.497249	−	0.867608i	$-0.334344\pi$
$43$	6.52135	0.994497	0.497249	+	0.867608i	$0.334344\pi$
$44$	1.67931	0.253165
$45$	−1.72483	−0.257123
$46$	8.13019	1.19873
$47$	4.17386	0.608820	0.304410	−	0.952541i	$-0.401541\pi$
$47$	4.17386	0.608820	0.304410	+	0.952541i	$0.401541\pi$
$48$	−1.56981	−0.226583
$49$	−6.84596	−0.977994
$50$	−5.36746	−0.759074
$51$	7.19916	1.00808
$52$	−0.362248	−0.0502348
$53$	−5.98979	−0.822760	−0.411380	−	0.911464i	$-0.634953\pi$
$53$	−5.98979	−0.822760	−0.411380	+	0.911464i	$0.634953\pi$
$54$	−5.55037	−0.755309
$55$	5.40713	0.729097
$56$	0.392480	0.0524473
$57$	0.0912562	0.0120872
$58$	−2.16132	−0.283795
$59$	−9.19439	−1.19701	−0.598504	−	0.801120i	$-0.704238\pi$
$59$	−9.19439	−1.19701	−0.598504	+	0.801120i	$0.704238\pi$
$60$	−5.05457	−0.652542
$61$	−2.92717	−0.374785	−0.187393	−	0.982285i	$-0.560004\pi$
$61$	−2.92717	−0.374785	−0.187393	+	0.982285i	$0.560004\pi$
$62$	−6.76515	−0.859175
$63$	0.210246	0.0264886
$64$	1.00000	0.125000
$65$	−1.16639	−0.144673
$66$	2.63620	0.324494
$67$	−1.85178	−0.226231	−0.113116	−	0.993582i	$-0.536083\pi$
$67$	−1.85178	−0.226231	−0.113116	+	0.993582i	$0.536083\pi$
$68$	−4.58600	−0.556134
$69$	12.7629	1.53647
$70$	1.26373	0.151044
$71$	−1.84731	−0.219235	−0.109618	−	0.993974i	$-0.534963\pi$
$71$	−1.84731	−0.219235	−0.109618	+	0.993974i	$0.534963\pi$
$72$	0.535687	0.0631313
$73$	9.05854	1.06022	0.530111	−	0.847928i	$-0.322150\pi$
$73$	9.05854	1.06022	0.530111	+	0.847928i	$0.322150\pi$
$74$	−9.21469	−1.07119
$75$	−8.42591	−0.972941
$76$	−0.0581319	−0.00666818
$77$	−0.659094	−0.0751108
$78$	−0.568662	−0.0643883
$79$	−4.30867	−0.484763	−0.242382	−	0.970181i	$-0.577929\pi$
$79$	−4.30867	−0.484763	−0.242382	+	0.970181i	$0.577929\pi$
$80$	3.21985	0.359991
$81$	−7.10598	−0.789553
$82$	9.76408	1.07826
$83$	8.28532	0.909432	0.454716	−	0.890636i	$-0.349741\pi$
$83$	8.28532	0.909432	0.454716	+	0.890636i	$0.349741\pi$
$84$	0.616120	0.0672242
$85$	−14.7662	−1.60162
$86$	−6.52135	−0.703216
$87$	−3.39287	−0.363754
$88$	−1.67931	−0.179015
$89$	10.4554	1.10827	0.554133	−	0.832428i	$-0.313050\pi$
$89$	10.4554	1.10827	0.554133	+	0.832428i	$0.313050\pi$
$90$	1.72483	0.181814
$91$	0.142175	0.0149040
$92$	−8.13019	−0.847630
$93$	−10.6200	−1.10124
$94$	−4.17386	−0.430501
$95$	−0.187176	−0.0192039
$96$	1.56981	0.160218
$97$	−4.40881	−0.447647	−0.223823	−	0.974630i	$-0.571854\pi$
$97$	−4.40881	−0.447647	−0.223823	+	0.974630i	$0.571854\pi$
$98$	6.84596	0.691546
$99$	−0.899584	−0.0904116
$100$	5.36746	0.536746
$101$	−7.55590	−0.751840	−0.375920	−	0.926652i	$-0.622673\pi$
$101$	−7.55590	−0.751840	−0.375920	+	0.926652i	$0.622673\pi$
$102$	−7.19916	−0.712823
$103$	−14.3475	−1.41370	−0.706852	−	0.707361i	$-0.749885\pi$
$103$	−14.3475	−1.41370	−0.706852	+	0.707361i	$0.749885\pi$
$104$	0.362248	0.0355214
$105$	1.98382	0.193601
$106$	5.98979	0.581779
$107$	−11.9149	−1.15185	−0.575927	−	0.817501i	$-0.695359\pi$
$107$	−11.9149	−1.15185	−0.575927	+	0.817501i	$0.695359\pi$
$108$	5.55037	0.534084
$109$	−7.93077	−0.759630	−0.379815	−	0.925063i	$-0.624012\pi$
$109$	−7.93077	−0.759630	−0.379815	+	0.925063i	$0.624012\pi$
$110$	−5.40713	−0.515549
$111$	−14.4653	−1.37299
$112$	−0.392480	−0.0370858
$113$	3.07418	0.289195	0.144597	−	0.989491i	$-0.453811\pi$
$113$	3.07418	0.289195	0.144597	+	0.989491i	$0.453811\pi$
$114$	−0.0912562	−0.00854692
$115$	−26.1780	−2.44111
$116$	2.16132	0.200674
$117$	0.194052	0.0179401
$118$	9.19439	0.846412
$119$	1.79991	0.164998
$120$	5.05457	0.461417
$121$	−8.17993	−0.743630
$122$	2.92717	0.265013
$123$	15.3278	1.38206
$124$	6.76515	0.607528
$125$	1.18318	0.105827
$126$	−0.210246	−0.0187302
$127$	17.1635	1.52302	0.761508	−	0.648156i	$-0.224460\pi$
$127$	17.1635	1.52302	0.761508	+	0.648156i	$0.224460\pi$
$128$	−1.00000	−0.0883883
$129$	−10.2373	−0.901345
$130$	1.16639	0.102299
$131$	−6.18199	−0.540123	−0.270061	−	0.962843i	$-0.587044\pi$
$131$	−6.18199	−0.540123	−0.270061	+	0.962843i	$0.587044\pi$
$132$	−2.63620	−0.229452
$133$	0.0228156	0.00197836
$134$	1.85178	0.159970
$135$	17.8714	1.53812
$136$	4.58600	0.393246
$137$	−5.88799	−0.503045	−0.251523	−	0.967851i	$-0.580931\pi$
$137$	−5.88799	−0.503045	−0.251523	+	0.967851i	$0.580931\pi$
$138$	−12.7629	−1.08645
$139$	−17.1513	−1.45475	−0.727375	−	0.686240i	$-0.759260\pi$
$139$	−17.1513	−1.45475	−0.727375	+	0.686240i	$0.759260\pi$
$140$	−1.26373	−0.106804
$141$	−6.55218	−0.551793
$142$	1.84731	0.155023
$143$	−0.608327	−0.0508708
$144$	−0.535687	−0.0446406
$145$	6.95914	0.577925
$146$	−9.05854	−0.749690
$147$	10.7469	0.886387
$148$	9.21469	0.757443
$149$	−22.7439	−1.86325	−0.931626	−	0.363418i	$-0.881610\pi$
$149$	−22.7439	−1.86325	−0.931626	+	0.363418i	$0.881610\pi$
$150$	8.42591	0.687973
$151$	10.5564	0.859068	0.429534	−	0.903051i	$-0.358678\pi$
$151$	10.5564	0.859068	0.429534	+	0.903051i	$0.358678\pi$
$152$	0.0581319	0.00471512
$153$	2.45666	0.198609
$154$	0.659094	0.0531113
$155$	21.7828	1.74964
$156$	0.568662	0.0455294
$157$	4.45250	0.355348	0.177674	−	0.984089i	$-0.443143\pi$
$157$	4.45250	0.355348	0.177674	+	0.984089i	$0.443143\pi$
$158$	4.30867	0.342779
$159$	9.40284	0.745694
$160$	−3.21985	−0.254552
$161$	3.19093	0.251481
$162$	7.10598	0.558298
$163$	14.6762	1.14953	0.574764	−	0.818319i	$-0.305094\pi$
$163$	14.6762	1.14953	0.574764	+	0.818319i	$0.305094\pi$
$164$	−9.76408	−0.762446
$165$	−8.48818	−0.660804
$166$	−8.28532	−0.643066
$167$	8.19648	0.634262	0.317131	−	0.948382i	$-0.397280\pi$
$167$	8.19648	0.634262	0.317131	+	0.948382i	$0.397280\pi$
$168$	−0.616120	−0.0475347
$169$	−12.8688	−0.989906
$170$	14.7662	1.13252
$171$	0.0311405	0.00238137
$172$	6.52135	0.497249
$173$	6.90311	0.524834	0.262417	−	0.964955i	$-0.415480\pi$
$173$	6.90311	0.524834	0.262417	+	0.964955i	$0.415480\pi$
$174$	3.39287	0.257213
$175$	−2.10662	−0.159246
$176$	1.67931	0.126583
$177$	14.4335	1.08489
$178$	−10.4554	−0.783662
$179$	−2.11519	−0.158097	−0.0790485	−	0.996871i	$-0.525188\pi$
$179$	−2.11519	−0.158097	−0.0790485	+	0.996871i	$0.525188\pi$
$180$	−1.72483	−0.128562
$181$	−0.602093	−0.0447532	−0.0223766	−	0.999750i	$-0.507123\pi$
$181$	−0.602093	−0.0447532	−0.0223766	+	0.999750i	$0.507123\pi$
$182$	−0.142175	−0.0105387
$183$	4.59510	0.339680
$184$	8.13019	0.599365
$185$	29.6700	2.18138
$186$	10.6200	0.778698
$187$	−7.70130	−0.563175
$188$	4.17386	0.304410
$189$	−2.17841	−0.158456
$190$	0.187176	0.0135792
$191$	−2.17469	−0.157355	−0.0786775	−	0.996900i	$-0.525070\pi$
$191$	−2.17469	−0.157355	−0.0786775	+	0.996900i	$0.525070\pi$
$192$	−1.56981	−0.113291
$193$	3.18221	0.229060	0.114530	−	0.993420i	$-0.463464\pi$
$193$	3.18221	0.229060	0.114530	+	0.993420i	$0.463464\pi$
$194$	4.40881	0.316534
$195$	1.83101	0.131121
$196$	−6.84596	−0.488997
$197$	8.71983	0.621262	0.310631	−	0.950531i	$-0.399460\pi$
$197$	8.71983	0.621262	0.310631	+	0.950531i	$0.399460\pi$
$198$	0.899584	0.0639306
$199$	−14.5965	−1.03472	−0.517360	−	0.855768i	$-0.673085\pi$
$199$	−14.5965	−1.03472	−0.517360	+	0.855768i	$0.673085\pi$
$200$	−5.36746	−0.379537
$201$	2.90695	0.205041
$202$	7.55590	0.531631
$203$	−0.848275	−0.0595372
$204$	7.19916	0.504042
$205$	−31.4389	−2.19579
$206$	14.3475	0.999640
$207$	4.35524	0.302710
$208$	−0.362248	−0.0251174
$209$	−0.0976213	−0.00675261
$210$	−1.98382	−0.136896
$211$	−7.32711	−0.504419	−0.252210	−	0.967673i	$-0.581157\pi$
$211$	−7.32711	−0.504419	−0.252210	+	0.967673i	$0.581157\pi$
$212$	−5.98979	−0.411380
$213$	2.89993	0.198700
$214$	11.9149	0.814483
$215$	20.9978	1.43204
$216$	−5.55037	−0.377655
$217$	−2.65518	−0.180246
$218$	7.93077	0.537139
$219$	−14.2202	−0.960913
$220$	5.40713	0.364548
$221$	1.66127	0.111749
$222$	14.4653	0.970851
$223$	−0.857158	−0.0573996	−0.0286998	−	0.999588i	$-0.509137\pi$
$223$	−0.857158	−0.0573996	−0.0286998	+	0.999588i	$0.509137\pi$
$224$	0.392480	0.0262237
$225$	−2.87528	−0.191685
$226$	−3.07418	−0.204492
$227$	−8.19637	−0.544012	−0.272006	−	0.962295i	$-0.587687\pi$
$227$	−8.19637	−0.544012	−0.272006	+	0.962295i	$0.587687\pi$
$228$	0.0912562	0.00604359
$229$	−12.8077	−0.846358	−0.423179	−	0.906046i	$-0.639086\pi$
$229$	−12.8077	−0.846358	−0.423179	+	0.906046i	$0.639086\pi$
$230$	26.1780	1.72613
$231$	1.03465	0.0680753
$232$	−2.16132	−0.141898
$233$	−10.1910	−0.667636	−0.333818	−	0.942638i	$-0.608337\pi$
$233$	−10.1910	−0.667636	−0.333818	+	0.942638i	$0.608337\pi$
$234$	−0.194052	−0.0126856
$235$	13.4392	0.876678
$236$	−9.19439	−0.598504
$237$	6.76380	0.439356
$238$	−1.79991	−0.116671
$239$	13.0752	0.845767	0.422883	−	0.906184i	$-0.361018\pi$
$239$	13.0752	0.845767	0.422883	+	0.906184i	$0.361018\pi$
$240$	−5.05457	−0.326271
$241$	−3.55567	−0.229041	−0.114521	−	0.993421i	$-0.536533\pi$
$241$	−3.55567	−0.229041	−0.114521	+	0.993421i	$0.536533\pi$
$242$	8.17993	0.525826
$243$	−5.49605	−0.352572
$244$	−2.92717	−0.187393
$245$	−22.0430	−1.40828
$246$	−15.3278	−0.977263
$247$	0.0210582	0.00133990
$248$	−6.76515	−0.429587
$249$	−13.0064	−0.824248
$250$	−1.18318	−0.0748307
$251$	16.4175	1.03626	0.518130	−	0.855302i	$-0.326628\pi$
$251$	16.4175	1.03626	0.518130	+	0.855302i	$0.326628\pi$
$252$	0.210246	0.0132443
$253$	−13.6531	−0.858362
$254$	−17.1635	−1.07693
$255$	23.1802	1.45160
$256$	1.00000	0.0625000
$257$	8.65186	0.539688	0.269844	−	0.962904i	$-0.413028\pi$
$257$	8.65186	0.539688	0.269844	+	0.962904i	$0.413028\pi$
$258$	10.2373	0.637347
$259$	−3.61658	−0.224723
$260$	−1.16639	−0.0723363
$261$	−1.15779	−0.0716656
$262$	6.18199	0.381925
$263$	8.51855	0.525276	0.262638	−	0.964894i	$-0.415407\pi$
$263$	8.51855	0.525276	0.262638	+	0.964894i	$0.415407\pi$
$264$	2.63620	0.162247
$265$	−19.2862	−1.18474
$266$	−0.0228156	−0.00139891
$267$	−16.4130	−1.00446
$268$	−1.85178	−0.113116
$269$	−14.5021	−0.884211	−0.442106	−	0.896963i	$-0.645768\pi$
$269$	−14.5021	−0.884211	−0.442106	+	0.896963i	$0.645768\pi$
$270$	−17.8714	−1.08762
$271$	29.0419	1.76417	0.882083	−	0.471093i	$-0.156140\pi$
$271$	29.0419	1.76417	0.882083	+	0.471093i	$0.156140\pi$
$272$	−4.58600	−0.278067
$273$	−0.223188	−0.0135080
$274$	5.88799	0.355707
$275$	9.01362	0.543542
$276$	12.7629	0.768234
$277$	11.6227	0.698339	0.349170	−	0.937059i	$-0.386464\pi$
$277$	11.6227	0.698339	0.349170	+	0.937059i	$0.386464\pi$
$278$	17.1513	1.02866
$279$	−3.62400	−0.216963
$280$	1.26373	0.0755222
$281$	−7.55577	−0.450740	−0.225370	−	0.974273i	$-0.572359\pi$
$281$	−7.55577	−0.450740	−0.225370	+	0.974273i	$0.572359\pi$
$282$	6.55218	0.390177
$283$	4.38234	0.260503	0.130251	−	0.991481i	$-0.458422\pi$
$283$	4.38234	0.260503	0.130251	+	0.991481i	$0.458422\pi$
$284$	−1.84731	−0.109618
$285$	0.293832	0.0174051
$286$	0.608327	0.0359711
$287$	3.83220	0.226208
$288$	0.535687	0.0315657
$289$	4.03137	0.237139
$290$	−6.95914	−0.408655
$291$	6.92101	0.405717
$292$	9.05854	0.530111
$293$	−22.2063	−1.29731	−0.648653	−	0.761084i	$-0.724667\pi$
$293$	−22.2063	−1.29731	−0.648653	+	0.761084i	$0.724667\pi$
$294$	−10.7469	−0.626771
$295$	−29.6046	−1.72365
$296$	−9.21469	−0.535593
$297$	9.32077	0.540846
$298$	22.7439	1.31752
$299$	2.94515	0.170322
$300$	−8.42591	−0.486470
$301$	−2.55950	−0.147527
$302$	−10.5564	−0.607453
$303$	11.8614	0.681417
$304$	−0.0581319	−0.00333409
$305$	−9.42505	−0.539677
$306$	−2.45666	−0.140438
$307$	32.5016	1.85496	0.927482	−	0.373869i	$-0.121969\pi$
$307$	32.5016	1.85496	0.927482	+	0.373869i	$0.121969\pi$
$308$	−0.659094	−0.0375554
$309$	22.5229	1.28129
$310$	−21.7828	−1.23718
$311$	3.73478	0.211780	0.105890	−	0.994378i	$-0.466231\pi$
$311$	3.73478	0.211780	0.105890	+	0.994378i	$0.466231\pi$
$312$	−0.568662	−0.0321942
$313$	5.27230	0.298008	0.149004	−	0.988837i	$-0.452393\pi$
$313$	5.27230	0.298008	0.149004	+	0.988837i	$0.452393\pi$
$314$	−4.45250	−0.251269
$315$	0.676963	0.0381425
$316$	−4.30867	−0.242382
$317$	−20.8764	−1.17253	−0.586267	−	0.810118i	$-0.699403\pi$
$317$	−20.8764	−1.17253	−0.586267	+	0.810118i	$0.699403\pi$
$318$	−9.40284	−0.527285
$319$	3.62952	0.203214
$320$	3.21985	0.179995
$321$	18.7041	1.04396
$322$	−3.19093	−0.177824
$323$	0.266593	0.0148336
$324$	−7.10598	−0.394777
$325$	−1.94436	−0.107853
$326$	−14.6762	−0.812839
$327$	12.4498	0.688477
$328$	9.76408	0.539131
$329$	−1.63816	−0.0903144
$330$	8.48818	0.467259
$331$	−23.1876	−1.27451	−0.637253	−	0.770655i	$-0.719929\pi$
$331$	−23.1876	−1.27451	−0.637253	+	0.770655i	$0.719929\pi$
$332$	8.28532	0.454716
$333$	−4.93619	−0.270502
$334$	−8.19648	−0.448491
$335$	−5.96247	−0.325764
$336$	0.616120	0.0336121
$337$	−22.4781	−1.22446	−0.612229	−	0.790681i	$-0.709727\pi$
$337$	−22.4781	−1.22446	−0.612229	+	0.790681i	$0.709727\pi$
$338$	12.8688	0.699969
$339$	−4.82589	−0.262107
$340$	−14.7662	−0.800812
$341$	11.3608	0.615220
$342$	−0.0311405	−0.00168389
$343$	5.43426	0.293422
$344$	−6.52135	−0.351608
$345$	41.0946	2.21246
$346$	−6.90311	−0.371114
$347$	28.8635	1.54947	0.774737	−	0.632283i	$-0.217882\pi$
$347$	28.8635	1.54947	0.774737	+	0.632283i	$0.217882\pi$
$348$	−3.39287	−0.181877
$349$	−27.0565	−1.44830	−0.724149	−	0.689643i	$-0.757767\pi$
$349$	−27.0565	−1.44830	−0.724149	+	0.689643i	$0.757767\pi$
$350$	2.10662	0.112604
$351$	−2.01061	−0.107319
$352$	−1.67931	−0.0895074
$353$	8.46640	0.450621	0.225311	−	0.974287i	$-0.427660\pi$
$353$	8.46640	0.450621	0.225311	+	0.974287i	$0.427660\pi$
$354$	−14.4335	−0.767130
$355$	−5.94807	−0.315691
$356$	10.4554	0.554133
$357$	−2.82552	−0.149543
$358$	2.11519	0.111791
$359$	−18.3013	−0.965907	−0.482954	−	0.875646i	$-0.660436\pi$
$359$	−18.3013	−0.965907	−0.482954	+	0.875646i	$0.660436\pi$
$360$	1.72483	0.0909068
$361$	−18.9966	−0.999822
$362$	0.602093	0.0316453
$363$	12.8410	0.673975
$364$	0.142175	0.00745200
$365$	29.1672	1.52668
$366$	−4.59510	−0.240190
$367$	−29.2445	−1.52655	−0.763276	−	0.646072i	$-0.776411\pi$
$367$	−29.2445	−1.52655	−0.763276	+	0.646072i	$0.776411\pi$
$368$	−8.13019	−0.423815
$369$	5.23049	0.272288
$370$	−29.6700	−1.54247
$371$	2.35087	0.122051
$372$	−10.6200	−0.550622
$373$	−21.1393	−1.09455	−0.547276	−	0.836952i	$-0.684335\pi$
$373$	−21.1393	−1.09455	−0.547276	+	0.836952i	$0.684335\pi$
$374$	7.70130	0.398225
$375$	−1.85737	−0.0959141
$376$	−4.17386	−0.215250
$377$	−0.782935	−0.0403232
$378$	2.17841	0.112045
$379$	−10.6973	−0.549483	−0.274741	−	0.961518i	$-0.588592\pi$
$379$	−10.6973	−0.549483	−0.274741	+	0.961518i	$0.588592\pi$
$380$	−0.187176	−0.00960193
$381$	−26.9435	−1.38036
$382$	2.17469	0.111267
$383$	−1.80409	−0.0921848	−0.0460924	−	0.998937i	$-0.514677\pi$
$383$	−1.80409	−0.0921848	−0.0460924	+	0.998937i	$0.514677\pi$
$384$	1.56981	0.0801092
$385$	−2.12219	−0.108157
$386$	−3.18221	−0.161970
$387$	−3.49341	−0.177580
$388$	−4.40881	−0.223823
$389$	−2.67027	−0.135388	−0.0676941	−	0.997706i	$-0.521564\pi$
$389$	−2.67027	−0.135388	−0.0676941	+	0.997706i	$0.521564\pi$
$390$	−1.83101	−0.0927168
$391$	37.2850	1.88558
$392$	6.84596	0.345773
$393$	9.70457	0.489531
$394$	−8.71983	−0.439299
$395$	−13.8733	−0.698041
$396$	−0.899584	−0.0452058
$397$	−34.9087	−1.75202	−0.876008	−	0.482296i	$-0.839803\pi$
$397$	−34.9087	−1.75202	−0.876008	+	0.482296i	$0.839803\pi$
$398$	14.5965	0.731658
$399$	−0.0358162	−0.00179305
$400$	5.36746	0.268373
$401$	−11.8072	−0.589623	−0.294811	−	0.955555i	$-0.595257\pi$
$401$	−11.8072	−0.589623	−0.294811	+	0.955555i	$0.595257\pi$
$402$	−2.90695	−0.144986
$403$	−2.45067	−0.122076
$404$	−7.55590	−0.375920
$405$	−22.8802	−1.13693
$406$	0.848275	0.0420992
$407$	15.4743	0.767033
$408$	−7.19916	−0.356411
$409$	−24.6663	−1.21967	−0.609834	−	0.792529i	$-0.708764\pi$
$409$	−24.6663	−1.21967	−0.609834	+	0.792529i	$0.708764\pi$
$410$	31.4389	1.55266
$411$	9.24305	0.455926
$412$	−14.3475	−0.706852
$413$	3.60861	0.177568
$414$	−4.35524	−0.214048
$415$	26.6775	1.30955
$416$	0.362248	0.0177607
$417$	26.9243	1.31849
$418$	0.0976213	0.00477481
$419$	−18.1521	−0.886789	−0.443395	−	0.896326i	$-0.646226\pi$
$419$	−18.1521	−0.886789	−0.443395	+	0.896326i	$0.646226\pi$
$420$	1.98382	0.0968003
$421$	3.74235	0.182391	0.0911956	−	0.995833i	$-0.470931\pi$
$421$	3.74235	0.182391	0.0911956	+	0.995833i	$0.470931\pi$
$422$	7.32711	0.356678
$423$	−2.23588	−0.108712
$424$	5.98979	0.290890
$425$	−24.6152	−1.19401
$426$	−2.89993	−0.140502
$427$	1.14885	0.0555969
$428$	−11.9149	−0.575927
$429$	0.954959	0.0461059
$430$	−20.9978	−1.01260
$431$	38.8121	1.86951	0.934756	−	0.355289i	$-0.115618\pi$
$431$	38.8121	1.86951	0.934756	+	0.355289i	$0.115618\pi$
$432$	5.55037	0.267042
$433$	29.9264	1.43817	0.719086	−	0.694922i	$-0.244561\pi$
$433$	29.9264	1.43817	0.719086	+	0.694922i	$0.244561\pi$
$434$	2.65518	0.127453
$435$	−10.9246	−0.523792
$436$	−7.93077	−0.379815
$437$	0.472623	0.0226086
$438$	14.2202	0.679468
$439$	−7.76587	−0.370645	−0.185322	−	0.982678i	$-0.559333\pi$
$439$	−7.76587	−0.370645	−0.185322	+	0.982678i	$0.559333\pi$
$440$	−5.40713	−0.257775
$441$	3.66729	0.174633
$442$	−1.66127	−0.0790186
$443$	−16.6728	−0.792147	−0.396073	−	0.918219i	$-0.629627\pi$
$443$	−16.6728	−0.792147	−0.396073	+	0.918219i	$0.629627\pi$
$444$	−14.4653	−0.686495
$445$	33.6647	1.59586
$446$	0.857158	0.0405876
$447$	35.7037	1.68873
$448$	−0.392480	−0.0185429
$449$	−3.10801	−0.146676	−0.0733381	−	0.997307i	$-0.523365\pi$
$449$	−3.10801	−0.146676	−0.0733381	+	0.997307i	$0.523365\pi$
$450$	2.87528	0.135542
$451$	−16.3969	−0.772099
$452$	3.07418	0.144597
$453$	−16.5716	−0.778601
$454$	8.19637	0.384675
$455$	0.457783	0.0214612
$456$	−0.0912562	−0.00427346
$457$	29.1268	1.36250	0.681248	−	0.732053i	$-0.261438\pi$
$457$	29.1268	1.36250	0.681248	+	0.732053i	$0.261438\pi$
$458$	12.8077	0.598465
$459$	−25.4540	−1.18809
$460$	−26.1780	−1.22056
$461$	−31.8375	−1.48282	−0.741409	−	0.671053i	$-0.765842\pi$
$461$	−31.8375	−1.48282	−0.741409	+	0.671053i	$0.765842\pi$
$462$	−1.03465	−0.0481365
$463$	−10.1786	−0.473039	−0.236520	−	0.971627i	$-0.576007\pi$
$463$	−10.1786	−0.473039	−0.236520	+	0.971627i	$0.576007\pi$
$464$	2.16132	0.100337
$465$	−34.1949	−1.58575
$466$	10.1910	0.472090
$467$	−4.70596	−0.217766	−0.108883	−	0.994055i	$-0.534727\pi$
$467$	−4.70596	−0.217766	−0.108883	+	0.994055i	$0.534727\pi$
$468$	0.194052	0.00897005
$469$	0.726787	0.0335599
$470$	−13.4392	−0.619905
$471$	−6.98959	−0.322063
$472$	9.19439	0.423206
$473$	10.9514	0.503544
$474$	−6.76380	−0.310672
$475$	−0.312021	−0.0143165
$476$	1.79991	0.0824988
$477$	3.20865	0.146914
$478$	−13.0752	−0.598047
$479$	38.3724	1.75328	0.876641	−	0.481146i	$-0.159779\pi$
$479$	38.3724	1.75328	0.876641	+	0.481146i	$0.159779\pi$
$480$	5.05457	0.230708
$481$	−3.33801	−0.152200
$482$	3.55567	0.161957
$483$	−5.00917	−0.227925
$484$	−8.17993	−0.371815
$485$	−14.1957	−0.644595
$486$	5.49605	0.249306
$487$	−36.1492	−1.63808	−0.819038	−	0.573739i	$-0.805492\pi$
$487$	−36.1492	−1.63808	−0.819038	+	0.573739i	$0.805492\pi$
$488$	2.92717	0.132507
$489$	−23.0389	−1.04185
$490$	22.0430	0.995801
$491$	−32.5319	−1.46814	−0.734071	−	0.679073i	$-0.762382\pi$
$491$	−32.5319	−1.46814	−0.734071	+	0.679073i	$0.762382\pi$
$492$	15.3278	0.691029
$493$	−9.91182	−0.446406
$494$	−0.0210582	−0.000947452 0
$495$	−2.89653	−0.130189
$496$	6.76515	0.303764
$497$	0.725032	0.0325221
$498$	13.0064	0.582831
$499$	27.9442	1.25095	0.625477	−	0.780243i	$-0.284905\pi$
$499$	27.9442	1.25095	0.625477	+	0.780243i	$0.284905\pi$
$500$	1.18318	0.0529133
$501$	−12.8669	−0.574852
$502$	−16.4175	−0.732747
$503$	−38.4821	−1.71583	−0.857916	−	0.513789i	$-0.828241\pi$
$503$	−38.4821	−1.71583	−0.857916	+	0.513789i	$0.828241\pi$
$504$	−0.210246	−0.00936512
$505$	−24.3289	−1.08262
$506$	13.6531	0.606954
$507$	20.2016	0.897183
$508$	17.1635	0.761508
$509$	37.1734	1.64768	0.823842	−	0.566819i	$-0.191826\pi$
$509$	37.1734	1.64768	0.823842	+	0.566819i	$0.191826\pi$
$510$	−23.1802	−1.02644
$511$	−3.55529	−0.157277
$512$	−1.00000	−0.0441942
$513$	−0.322653	−0.0142455
$514$	−8.65186	−0.381617
$515$	−46.1970	−2.03568
$516$	−10.2373	−0.450672
$517$	7.00920	0.308264
$518$	3.61658	0.158903
$519$	−10.8366	−0.475674
$520$	1.16639	0.0511495
$521$	−16.6579	−0.729798	−0.364899	−	0.931047i	$-0.618896\pi$
$521$	−16.6579	−0.729798	−0.364899	+	0.931047i	$0.618896\pi$
$522$	1.15779	0.0506752
$523$	2.84780	0.124526	0.0622629	−	0.998060i	$-0.480168\pi$
$523$	2.84780	0.124526	0.0622629	+	0.998060i	$0.480168\pi$
$524$	−6.18199	−0.270061
$525$	3.30700	0.144329
$526$	−8.51855	−0.371426
$527$	−31.0250	−1.35147
$528$	−2.63620	−0.114726
$529$	43.0999	1.87391
$530$	19.2862	0.837741
$531$	4.92531	0.213740
$532$	0.0228156	0.000989181 0
$533$	3.53702	0.153205
$534$	16.4130	0.710258
$535$	−38.3641	−1.65863
$536$	1.85178	0.0799848
$537$	3.32046	0.143288
$538$	14.5021	0.625232
$539$	−11.4965	−0.495188
$540$	17.8714	0.769062
$541$	37.6082	1.61690	0.808452	−	0.588561i	$-0.200306\pi$
$541$	37.6082	1.61690	0.808452	+	0.588561i	$0.200306\pi$
$542$	−29.0419	−1.24745
$543$	0.945174	0.0405613
$544$	4.58600	0.196623
$545$	−25.5359	−1.09384
$546$	0.223188	0.00955158
$547$	31.5187	1.34764	0.673821	−	0.738894i	$-0.264652\pi$
$547$	31.5187	1.34764	0.673821	+	0.738894i	$0.264652\pi$
$548$	−5.88799	−0.251523
$549$	1.56805	0.0669225
$550$	−9.01362	−0.384342
$551$	−0.125642	−0.00535252
$552$	−12.7629	−0.543224
$553$	1.69107	0.0719114
$554$	−11.6227	−0.493801
$555$	−46.5763	−1.97705
$556$	−17.1513	−0.727375
$557$	−16.4976	−0.699024	−0.349512	−	0.936932i	$-0.613653\pi$
$557$	−16.4976	−0.699024	−0.349512	+	0.936932i	$0.613653\pi$
$558$	3.62400	0.153416
$559$	−2.36235	−0.0999168
$560$	−1.26373	−0.0534022
$561$	12.0896	0.510423
$562$	7.55577	0.318721
$563$	−16.4986	−0.695332	−0.347666	−	0.937618i	$-0.613026\pi$
$563$	−16.4986	−0.695332	−0.347666	+	0.937618i	$0.613026\pi$
$564$	−6.55218	−0.275897
$565$	9.89843	0.416430
$566$	−4.38234	−0.184203
$567$	2.78895	0.117125
$568$	1.84731	0.0775114
$569$	38.6256	1.61927	0.809635	−	0.586934i	$-0.199665\pi$
$569$	38.6256	1.61927	0.809635	+	0.586934i	$0.199665\pi$
$570$	−0.293832	−0.0123072
$571$	−8.22685	−0.344283	−0.172142	−	0.985072i	$-0.555069\pi$
$571$	−8.22685	−0.344283	−0.172142	+	0.985072i	$0.555069\pi$
$572$	−0.608327	−0.0254354
$573$	3.41386	0.142616
$574$	−3.83220	−0.159953
$575$	−43.6385	−1.81985
$576$	−0.535687	−0.0223203
$577$	−1.64497	−0.0684810	−0.0342405	−	0.999414i	$-0.510901\pi$
$577$	−1.64497	−0.0684810	−0.0342405	+	0.999414i	$0.510901\pi$
$578$	−4.03137	−0.167683
$579$	−4.99547	−0.207605
$580$	6.95914	0.288963
$581$	−3.25182	−0.134908
$582$	−6.92101	−0.286885
$583$	−10.0587	−0.416588
$584$	−9.05854	−0.374845
$585$	0.624819	0.0258331
$586$	22.2063	0.917334
$587$	−24.2432	−1.00063	−0.500313	−	0.865845i	$-0.666782\pi$
$587$	−24.2432	−1.00063	−0.500313	+	0.865845i	$0.666782\pi$
$588$	10.7469	0.443194
$589$	−0.393271	−0.0162044
$590$	29.6046	1.21880
$591$	−13.6885	−0.563070
$592$	9.21469	0.378722
$593$	−35.2820	−1.44886	−0.724429	−	0.689349i	$-0.757897\pi$
$593$	−35.2820	−1.44886	−0.724429	+	0.689349i	$0.757897\pi$
$594$	−9.32077	−0.382436
$595$	5.79545	0.237590
$596$	−22.7439	−0.931626
$597$	22.9138	0.937800
$598$	−2.94515	−0.120436
$599$	−25.6829	−1.04937	−0.524687	−	0.851295i	$-0.675818\pi$
$599$	−25.6829	−1.04937	−0.524687	+	0.851295i	$0.675818\pi$
$600$	8.42591	0.343986
$601$	22.6608	0.924353	0.462176	−	0.886788i	$-0.347069\pi$
$601$	22.6608	0.924353	0.462176	+	0.886788i	$0.347069\pi$
$602$	2.55950	0.104317
$603$	0.991976	0.0403964
$604$	10.5564	0.429534
$605$	−26.3382	−1.07080
$606$	−11.8614	−0.481835
$607$	6.18701	0.251123	0.125561	−	0.992086i	$-0.459927\pi$
$607$	6.18701	0.251123	0.125561	+	0.992086i	$0.459927\pi$
$608$	0.0581319	0.00235756
$609$	1.33163	0.0539605
$610$	9.42505	0.381609
$611$	−1.51197	−0.0611679
$612$	2.45666	0.0993046
$613$	−22.5436	−0.910528	−0.455264	−	0.890357i	$-0.650455\pi$
$613$	−22.5436	−0.910528	−0.455264	+	0.890357i	$0.650455\pi$
$614$	−32.5016	−1.31166
$615$	49.3532	1.99011
$616$	0.659094	0.0265557
$617$	−30.3248	−1.22083	−0.610415	−	0.792081i	$-0.708998\pi$
$617$	−30.3248	−1.22083	−0.610415	+	0.792081i	$0.708998\pi$
$618$	−22.5229	−0.906005
$619$	−20.4382	−0.821479	−0.410739	−	0.911753i	$-0.634729\pi$
$619$	−20.4382	−0.821479	−0.410739	+	0.911753i	$0.634729\pi$
$620$	21.7828	0.874818
$621$	−45.1255	−1.81082
$622$	−3.73478	−0.149751
$623$	−4.10351	−0.164404
$624$	0.568662	0.0227647
$625$	−23.0277	−0.921106
$626$	−5.27230	−0.210724
$627$	0.153247	0.00612010
$628$	4.45250	0.177674
$629$	−42.2586	−1.68496
$630$	−0.676963	−0.0269708
$631$	8.75301	0.348452	0.174226	−	0.984706i	$-0.444258\pi$
$631$	8.75301	0.348452	0.174226	+	0.984706i	$0.444258\pi$
$632$	4.30867	0.171390
$633$	11.5022	0.457171
$634$	20.8764	0.829106
$635$	55.2640	2.19308
$636$	9.40284	0.372847
$637$	2.47994	0.0982587
$638$	−3.62952	−0.143694
$639$	0.989581	0.0391472
$640$	−3.21985	−0.127276
$641$	−36.8830	−1.45679	−0.728395	−	0.685157i	$-0.759733\pi$
$641$	−36.8830	−1.45679	−0.728395	+	0.685157i	$0.759733\pi$
$642$	−18.7041	−0.738192
$643$	5.90055	0.232695	0.116347	−	0.993209i	$-0.462881\pi$
$643$	5.90055	0.232695	0.116347	+	0.993209i	$0.462881\pi$
$644$	3.19093	0.125740
$645$	−32.9626	−1.29790
$646$	−0.266593	−0.0104889
$647$	−8.33322	−0.327613	−0.163806	−	0.986493i	$-0.552377\pi$
$647$	−8.33322	−0.327613	−0.163806	+	0.986493i	$0.552377\pi$
$648$	7.10598	0.279149
$649$	−15.4402	−0.606081
$650$	1.94436	0.0762639
$651$	4.16814	0.163362
$652$	14.6762	0.574764
$653$	0.813052	0.0318172	0.0159086	−	0.999873i	$-0.494936\pi$
$653$	0.813052	0.0318172	0.0159086	+	0.999873i	$0.494936\pi$
$654$	−12.4498	−0.486827
$655$	−19.9051	−0.777757
$656$	−9.76408	−0.381223
$657$	−4.85254	−0.189316
$658$	1.63816	0.0638620
$659$	−13.0638	−0.508895	−0.254447	−	0.967087i	$-0.581894\pi$
$659$	−13.0638	−0.508895	−0.254447	+	0.967087i	$0.581894\pi$
$660$	−8.48818	−0.330402
$661$	−16.8032	−0.653567	−0.326783	−	0.945099i	$-0.605965\pi$
$661$	−16.8032	−0.653567	−0.326783	+	0.945099i	$0.605965\pi$
$662$	23.1876	0.901212
$663$	−2.60788	−0.101282
$664$	−8.28532	−0.321533
$665$	0.0734628	0.00284877
$666$	4.93619	0.191274
$667$	−17.5719	−0.680388
$668$	8.19648	0.317131
$669$	1.34558	0.0520230
$670$	5.96247	0.230350
$671$	−4.91561	−0.189765
$672$	−0.616120	−0.0237673
$673$	−26.3404	−1.01535	−0.507674	−	0.861549i	$-0.669494\pi$
$673$	−26.3404	−1.01535	−0.507674	+	0.861549i	$0.669494\pi$
$674$	22.4781	0.865822
$675$	29.7914	1.14667
$676$	−12.8688	−0.494953
$677$	−34.0165	−1.30736	−0.653679	−	0.756772i	$-0.726776\pi$
$677$	−34.0165	−1.30736	−0.653679	+	0.756772i	$0.726776\pi$
$678$	4.82589	0.185337
$679$	1.73037	0.0664054
$680$	14.7662	0.566260
$681$	12.8668	0.493056
$682$	−11.3608	−0.435026
$683$	4.92075	0.188287	0.0941436	−	0.995559i	$-0.469989\pi$
$683$	4.92075	0.188287	0.0941436	+	0.995559i	$0.469989\pi$
$684$	0.0311405	0.00119069
$685$	−18.9585	−0.724366
$686$	−5.43426	−0.207481
$687$	20.1057	0.767081
$688$	6.52135	0.248624
$689$	2.16979	0.0826624
$690$	−41.0946	−1.56444
$691$	−13.7762	−0.524072	−0.262036	−	0.965058i	$-0.584394\pi$
$691$	−13.7762	−0.524072	−0.262036	+	0.965058i	$0.584394\pi$
$692$	6.90311	0.262417
$693$	0.353068	0.0134120
$694$	−28.8635	−1.09564
$695$	−55.2246	−2.09479
$696$	3.39287	0.128606
$697$	44.7780	1.69609
$698$	27.0565	1.02410
$699$	15.9980	0.605100
$700$	−2.10662	−0.0796228
$701$	−28.8437	−1.08941	−0.544706	−	0.838627i	$-0.683359\pi$
$701$	−28.8437	−1.08941	−0.544706	+	0.838627i	$0.683359\pi$
$702$	2.01061	0.0758857
$703$	−0.535667	−0.0202031
$704$	1.67931	0.0632913
$705$	−21.0971	−0.794562
$706$	−8.46640	−0.318637
$707$	2.96554	0.111531
$708$	14.4335	0.542443
$709$	−18.1863	−0.683000	−0.341500	−	0.939882i	$-0.610935\pi$
$709$	−18.1863	−0.683000	−0.341500	+	0.939882i	$0.610935\pi$
$710$	5.94807	0.223227
$711$	2.30810	0.0865605
$712$	−10.4554	−0.391831
$713$	−55.0019	−2.05984
$714$	2.82552	0.105743
$715$	−1.95872	−0.0732521
$716$	−2.11519	−0.0790485
$717$	−20.5257	−0.766546
$718$	18.3013	0.683000
$719$	18.3349	0.683776	0.341888	−	0.939741i	$-0.388934\pi$
$719$	18.3349	0.683776	0.341888	+	0.939741i	$0.388934\pi$
$720$	−1.72483	−0.0642808
$721$	5.63111	0.209714
$722$	18.9966	0.706981
$723$	5.58174	0.207587
$724$	−0.602093	−0.0223766
$725$	11.6008	0.430843
$726$	−12.8410	−0.476572
$727$	29.1758	1.08207	0.541036	−	0.840999i	$-0.318032\pi$
$727$	29.1758	1.08207	0.541036	+	0.840999i	$0.318032\pi$
$728$	−0.142175	−0.00526936
$729$	29.9457	1.10910
$730$	−29.1672	−1.07953
$731$	−29.9069	−1.10615
$732$	4.59510	0.169840
$733$	18.7870	0.693915	0.346958	−	0.937881i	$-0.387215\pi$
$733$	18.7870	0.693915	0.346958	+	0.937881i	$0.387215\pi$
$734$	29.2445	1.07944
$735$	34.6034	1.27636
$736$	8.13019	0.299683
$737$	−3.10971	−0.114548
$738$	−5.23049	−0.192537
$739$	23.5667	0.866916	0.433458	−	0.901174i	$-0.357293\pi$
$739$	23.5667	0.866916	0.433458	+	0.901174i	$0.357293\pi$
$740$	29.6700	1.09069
$741$	−0.0330574	−0.00121439
$742$	−2.35087	−0.0863031
$743$	−22.0716	−0.809729	−0.404865	−	0.914377i	$-0.632681\pi$
$743$	−22.0716	−0.809729	−0.404865	+	0.914377i	$0.632681\pi$
$744$	10.6200	0.389349
$745$	−73.2320	−2.68301
$746$	21.1393	0.773965
$747$	−4.43834	−0.162390
$748$	−7.70130	−0.281587
$749$	4.67634	0.170870
$750$	1.85737	0.0678215
$751$	3.48819	0.127286	0.0636430	−	0.997973i	$-0.479728\pi$
$751$	3.48819	0.127286	0.0636430	+	0.997973i	$0.479728\pi$
$752$	4.17386	0.152205
$753$	−25.7723	−0.939196
$754$	0.782935	0.0285128
$755$	33.9901	1.23703
$756$	−2.17841	−0.0792279
$757$	41.0340	1.49141	0.745703	−	0.666278i	$-0.232114\pi$
$757$	41.0340	1.49141	0.745703	+	0.666278i	$0.232114\pi$
$758$	10.6973	0.388543
$759$	21.4328	0.777961
$760$	0.187176	0.00678959
$761$	−15.1678	−0.549832	−0.274916	−	0.961468i	$-0.588650\pi$
$761$	−15.1678	−0.549832	−0.274916	+	0.961468i	$0.588650\pi$
$762$	26.9435	0.976060
$763$	3.11267	0.112686
$764$	−2.17469	−0.0786775
$765$	7.91009	0.285990
$766$	1.80409	0.0651845
$767$	3.33065	0.120263
$768$	−1.56981	−0.0566457
$769$	−21.2175	−0.765124	−0.382562	−	0.923930i	$-0.624958\pi$
$769$	−21.2175	−0.765124	−0.382562	+	0.923930i	$0.624958\pi$
$770$	2.12219	0.0764783
$771$	−13.5818	−0.489137
$772$	3.18221	0.114530
$773$	13.4189	0.482644	0.241322	−	0.970445i	$-0.422419\pi$
$773$	13.4189	0.482644	0.241322	+	0.970445i	$0.422419\pi$
$774$	3.49341	0.125568
$775$	36.3117	1.30435
$776$	4.40881	0.158267
$777$	5.67736	0.203674
$778$	2.67027	0.0957340
$779$	0.567604	0.0203365
$780$	1.83101	0.0655607
$781$	−3.10220	−0.111006
$782$	−37.2850	−1.33331
$783$	11.9961	0.428707
$784$	−6.84596	−0.244499
$785$	14.3364	0.511688
$786$	−9.70457	−0.346150
$787$	36.0027	1.28336	0.641678	−	0.766974i	$-0.278238\pi$
$787$	36.0027	1.28336	0.641678	+	0.766974i	$0.278238\pi$
$788$	8.71983	0.310631
$789$	−13.3725	−0.476075
$790$	13.8733	0.493589
$791$	−1.20656	−0.0429002
$792$	0.899584	0.0319653
$793$	1.06036	0.0376545
$794$	34.9087	1.23886
$795$	30.2758	1.07377
$796$	−14.5965	−0.517360
$797$	43.8252	1.55237	0.776185	−	0.630506i	$-0.217152\pi$
$797$	43.8252	1.55237	0.776185	+	0.630506i	$0.217152\pi$
$798$	0.0358162	0.00126788
$799$	−19.1413	−0.677171
$800$	−5.36746	−0.189768
$801$	−5.60080	−0.197895
$802$	11.8072	0.416926
$803$	15.2121	0.536823
$804$	2.90695	0.102520
$805$	10.2743	0.362123
$806$	2.45067	0.0863210
$807$	22.7657	0.801389
$808$	7.55590	0.265816
$809$	5.65651	0.198872	0.0994361	−	0.995044i	$-0.468296\pi$
$809$	5.65651	0.198872	0.0994361	+	0.995044i	$0.468296\pi$
$810$	22.8802	0.803929
$811$	7.20040	0.252840	0.126420	−	0.991977i	$-0.459651\pi$
$811$	7.20040	0.252840	0.126420	+	0.991977i	$0.459651\pi$
$812$	−0.848275	−0.0297686
$813$	−45.5903	−1.59892
$814$	−15.4743	−0.542374
$815$	47.2552	1.65528
$816$	7.19916	0.252021
$817$	−0.379098	−0.0132630
$818$	24.6663	0.862435
$819$	−0.0761614	−0.00266130
$820$	−31.4389	−1.09789
$821$	12.5488	0.437955	0.218978	−	0.975730i	$-0.429728\pi$
$821$	12.5488	0.437955	0.218978	+	0.975730i	$0.429728\pi$
$822$	−9.24305	−0.322388
$823$	−12.6351	−0.440432	−0.220216	−	0.975451i	$-0.570676\pi$
$823$	−12.6351	−0.440432	−0.220216	+	0.975451i	$0.570676\pi$
$824$	14.3475	0.499820
$825$	−14.1497	−0.492629
$826$	−3.60861	−0.125560
$827$	−19.4236	−0.675424	−0.337712	−	0.941250i	$-0.609653\pi$
$827$	−19.4236	−0.675424	−0.337712	+	0.941250i	$0.609653\pi$
$828$	4.35524	0.151355
$829$	11.1139	0.386000	0.193000	−	0.981199i	$-0.438178\pi$
$829$	11.1139	0.386000	0.193000	+	0.981199i	$0.438178\pi$
$830$	−26.6775	−0.925991
$831$	−18.2454	−0.632927
$832$	−0.362248	−0.0125587
$833$	31.3956	1.08779
$834$	−26.9243	−0.932311
$835$	26.3915	0.913314
$836$	−0.0976213	−0.00337630
$837$	37.5491	1.29789
$838$	18.1521	0.627055
$839$	19.4818	0.672585	0.336292	−	0.941758i	$-0.390827\pi$
$839$	19.4818	0.672585	0.336292	+	0.941758i	$0.390827\pi$
$840$	−1.98382	−0.0684482
$841$	−24.3287	−0.838920
$842$	−3.74235	−0.128970
$843$	11.8612	0.408520
$844$	−7.32711	−0.252210
$845$	−41.4356	−1.42543
$846$	2.23588	0.0768713
$847$	3.21046	0.110313
$848$	−5.98979	−0.205690
$849$	−6.87945	−0.236102
$850$	24.6152	0.844293
$851$	−74.9172	−2.56813
$852$	2.89993	0.0993500
$853$	−3.38983	−0.116066	−0.0580328	−	0.998315i	$-0.518483\pi$
$853$	−3.38983	−0.116066	−0.0580328	+	0.998315i	$0.518483\pi$
$854$	−1.14885	−0.0393129
$855$	0.100268	0.00342909
$856$	11.9149	0.407242
$857$	−13.8695	−0.473772	−0.236886	−	0.971537i	$-0.576127\pi$
$857$	−13.8695	−0.473772	−0.236886	+	0.971537i	$0.576127\pi$
$858$	−0.954959	−0.0326018
$859$	−2.49909	−0.0852679	−0.0426339	−	0.999091i	$-0.513575\pi$
$859$	−2.49909	−0.0852679	−0.0426339	+	0.999091i	$0.513575\pi$
$860$	20.9978	0.716019
$861$	−6.01584	−0.205019
$862$	−38.8121	−1.32195
$863$	17.9315	0.610395	0.305197	−	0.952289i	$-0.401278\pi$
$863$	17.9315	0.610395	0.305197	+	0.952289i	$0.401278\pi$
$864$	−5.55037	−0.188827
$865$	22.2270	0.755741
$866$	−29.9264	−1.01694
$867$	−6.32850	−0.214927
$868$	−2.65518	−0.0901228
$869$	−7.23558	−0.245450
$870$	10.9246	0.370377
$871$	0.670805	0.0227294
$872$	7.93077	0.268570
$873$	2.36174	0.0799329
$874$	−0.472623	−0.0159867
$875$	−0.464373	−0.0156987
$876$	−14.2202	−0.480457
$877$	−39.0885	−1.31993	−0.659963	−	0.751298i	$-0.729428\pi$
$877$	−39.0885	−1.31993	−0.659963	+	0.751298i	$0.729428\pi$
$878$	7.76587	0.262085
$879$	34.8598	1.17579
$880$	5.40713	0.182274
$881$	−16.2279	−0.546731	−0.273366	−	0.961910i	$-0.588137\pi$
$881$	−16.2279	−0.546731	−0.273366	+	0.961910i	$0.588137\pi$
$882$	−3.66729	−0.123484
$883$	−35.1000	−1.18121	−0.590604	−	0.806961i	$-0.701110\pi$
$883$	−35.1000	−1.18121	−0.590604	+	0.806961i	$0.701110\pi$
$884$	1.66127	0.0558746
$885$	46.4737	1.56219
$886$	16.6728	0.560132
$887$	−45.1525	−1.51607	−0.758036	−	0.652213i	$-0.773841\pi$
$887$	−45.1525	−1.51607	−0.758036	+	0.652213i	$0.773841\pi$
$888$	14.4653	0.485425
$889$	−6.73633	−0.225929
$890$	−33.6647	−1.12844
$891$	−11.9331	−0.399775
$892$	−0.857158	−0.0286998
$893$	−0.242634	−0.00811945
$894$	−35.7037	−1.19411
$895$	−6.81062	−0.227654
$896$	0.392480	0.0131118
$897$	−4.62333	−0.154368
$898$	3.10801	0.103716
$899$	14.6217	0.487660
$900$	−2.87528	−0.0958427
$901$	27.4691	0.915130
$902$	16.3969	0.545957
$903$	4.01794	0.133709
$904$	−3.07418	−0.102246
$905$	−1.93865	−0.0644430
$906$	16.5716	0.550554
$907$	−11.3824	−0.377947	−0.188973	−	0.981982i	$-0.560516\pi$
$907$	−11.3824	−0.377947	−0.188973	+	0.981982i	$0.560516\pi$
$908$	−8.19637	−0.272006
$909$	4.04760	0.134250
$910$	−0.457783	−0.0151754
$911$	28.0752	0.930172	0.465086	−	0.885266i	$-0.346023\pi$
$911$	28.0752	0.930172	0.465086	+	0.885266i	$0.346023\pi$
$912$	0.0912562	0.00302179
$913$	13.9136	0.460473
$914$	−29.1268	−0.963430
$915$	14.7956	0.489126
$916$	−12.8077	−0.423179
$917$	2.42631	0.0801237
$918$	25.4540	0.840106
$919$	−43.2555	−1.42687	−0.713434	−	0.700722i	$-0.752861\pi$
$919$	−43.2555	−1.42687	−0.713434	+	0.700722i	$0.752861\pi$
$920$	26.1780	0.863064
$921$	−51.0214	−1.68121
$922$	31.8375	1.04851
$923$	0.669185	0.0220265
$924$	1.03465	0.0340376
$925$	49.4595	1.62622
$926$	10.1786	0.334489
$927$	7.68579	0.252434
$928$	−2.16132	−0.0709489
$929$	−13.8021	−0.452833	−0.226417	−	0.974031i	$-0.572701\pi$
$929$	−13.8021	−0.452833	−0.226417	+	0.974031i	$0.572701\pi$
$930$	34.1949	1.12130
$931$	0.397968	0.0130429
$932$	−10.1910	−0.333818
$933$	−5.86291	−0.191943
$934$	4.70596	0.153984
$935$	−24.7971	−0.810951
$936$	−0.194052	−0.00634278
$937$	28.5978	0.934248	0.467124	−	0.884192i	$-0.345290\pi$
$937$	28.5978	0.934248	0.467124	+	0.884192i	$0.345290\pi$
$938$	−0.726787	−0.0237304
$939$	−8.27653	−0.270094
$940$	13.4392	0.438339
$941$	−36.2785	−1.18265	−0.591323	−	0.806435i	$-0.701394\pi$
$941$	−36.2785	−1.18265	−0.591323	+	0.806435i	$0.701394\pi$
$942$	6.98959	0.227733
$943$	79.3837	2.58509
$944$	−9.19439	−0.299252
$945$	−7.01415	−0.228170
$946$	−10.9514	−0.356059
$947$	−3.02186	−0.0981971	−0.0490986	−	0.998794i	$-0.515635\pi$
$947$	−3.02186	−0.0981971	−0.0490986	+	0.998794i	$0.515635\pi$
$948$	6.76380	0.219678
$949$	−3.28144	−0.106520
$950$	0.312021	0.0101233
$951$	32.7720	1.06270
$952$	−1.79991	−0.0583354
$953$	10.1397	0.328457	0.164228	−	0.986422i	$-0.447487\pi$
$953$	10.1397	0.328457	0.164228	+	0.986422i	$0.447487\pi$
$954$	−3.20865	−0.103884
$955$	−7.00219	−0.226585
$956$	13.0752	0.422883
$957$	−5.69767	−0.184180
$958$	−38.3724	−1.23976
$959$	2.31092	0.0746234
$960$	−5.05457	−0.163136
$961$	14.7673	0.476363
$962$	3.33801	0.107622
$963$	6.38264	0.205678
$964$	−3.55567	−0.114521
$965$	10.2462	0.329838
$966$	5.00917	0.161167
$967$	59.5731	1.91574	0.957871	−	0.287198i	$-0.0927237\pi$
$967$	59.5731	1.91574	0.957871	+	0.287198i	$0.0927237\pi$
$968$	8.17993	0.262913
$969$	−0.418500	−0.0134442
$970$	14.1957	0.455797
$971$	28.0566	0.900379	0.450189	−	0.892933i	$-0.351357\pi$
$971$	28.0566	0.900379	0.450189	+	0.892933i	$0.351357\pi$
$972$	−5.49605	−0.176286
$973$	6.73152	0.215803
$974$	36.1492	1.15829
$975$	3.05227	0.0977510
$976$	−2.92717	−0.0936963
$977$	−16.8215	−0.538169	−0.269084	−	0.963117i	$-0.586721\pi$
$977$	−16.8215	−0.538169	−0.269084	+	0.963117i	$0.586721\pi$
$978$	23.0389	0.736702
$979$	17.5578	0.561148
$980$	−22.0430	−0.704138
$981$	4.24841	0.135641
$982$	32.5319	1.03813
$983$	−11.8981	−0.379490	−0.189745	−	0.981833i	$-0.560766\pi$
$983$	−11.8981	−0.379490	−0.189745	+	0.981833i	$0.560766\pi$
$984$	−15.3278	−0.488632
$985$	28.0766	0.894595
$986$	9.91182	0.315657
$987$	2.57160	0.0818549
$988$	0.0210582	0.000669950 0
$989$	−53.0198	−1.68593
$990$	2.89653	0.0920577
$991$	29.3812	0.933323	0.466662	−	0.884436i	$-0.345457\pi$
$991$	29.3812	0.933323	0.466662	+	0.884436i	$0.345457\pi$
$992$	−6.76515	−0.214794
$993$	36.4002	1.15513
$994$	−0.725032	−0.0229966
$995$	−46.9987	−1.48996
$996$	−13.0064	−0.412124
$997$	46.1867	1.46275	0.731374	−	0.681977i	$-0.238879\pi$
$997$	46.1867	1.46275	0.731374	+	0.681977i	$0.238879\pi$
$998$	−27.9442	−0.884558
$999$	51.1449	1.61815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.d.1.15	✓	55

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.d.1.15	✓	55	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.56981 q^{3} +1.00000 q^{4} +3.21985 q^{5} +1.56981 q^{6} -0.392480 q^{7} -1.00000 q^{8} -0.535687 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.56981 q^{3} +1.00000 q^{4} +3.21985 q^{5} +1.56981 q^{6} -0.392480 q^{7} -1.00000 q^{8} -0.535687 q^{9} -3.21985 q^{10} +1.67931 q^{11} -1.56981 q^{12} -0.362248 q^{13} +0.392480 q^{14} -5.05457 q^{15} +1.00000 q^{16} -4.58600 q^{17} +0.535687 q^{18} -0.0581319 q^{19} +3.21985 q^{20} +0.616120 q^{21} -1.67931 q^{22} -8.13019 q^{23} +1.56981 q^{24} +5.36746 q^{25} +0.362248 q^{26} +5.55037 q^{27} -0.392480 q^{28} +2.16132 q^{29} +5.05457 q^{30} +6.76515 q^{31} -1.00000 q^{32} -2.63620 q^{33} +4.58600 q^{34} -1.26373 q^{35} -0.535687 q^{36} +9.21469 q^{37} +0.0581319 q^{38} +0.568662 q^{39} -3.21985 q^{40} -9.76408 q^{41} -0.616120 q^{42} +6.52135 q^{43} +1.67931 q^{44} -1.72483 q^{45} +8.13019 q^{46} +4.17386 q^{47} -1.56981 q^{48} -6.84596 q^{49} -5.36746 q^{50} +7.19916 q^{51} -0.362248 q^{52} -5.98979 q^{53} -5.55037 q^{54} +5.40713 q^{55} +0.392480 q^{56} +0.0912562 q^{57} -2.16132 q^{58} -9.19439 q^{59} -5.05457 q^{60} -2.92717 q^{61} -6.76515 q^{62} +0.210246 q^{63} +1.00000 q^{64} -1.16639 q^{65} +2.63620 q^{66} -1.85178 q^{67} -4.58600 q^{68} +12.7629 q^{69} +1.26373 q^{70} -1.84731 q^{71} +0.535687 q^{72} +9.05854 q^{73} -9.21469 q^{74} -8.42591 q^{75} -0.0581319 q^{76} -0.659094 q^{77} -0.568662 q^{78} -4.30867 q^{79} +3.21985 q^{80} -7.10598 q^{81} +9.76408 q^{82} +8.28532 q^{83} +0.616120 q^{84} -14.7662 q^{85} -6.52135 q^{86} -3.39287 q^{87} -1.67931 q^{88} +10.4554 q^{89} +1.72483 q^{90} +0.142175 q^{91} -8.13019 q^{92} -10.6200 q^{93} -4.17386 q^{94} -0.187176 q^{95} +1.56981 q^{96} -4.40881 q^{97} +6.84596 q^{98} -0.899584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9}+O(q^{10}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9	\( 55 q - 55 q^{2} - 4 q^{3} + 55 q^{4} - 7 q^{5} + 4 q^{6} + 17 q^{7} - 55 q^{8} + 29 q^{9} + 7 q^{10} - 28 q^{11} - 4 q^{12} + q^{13} - 17 q^{14} - 8 q^{15} + 55 q^{16} - 32 q^{17} - 29 q^{18} - 3 q^{19} - 7 q^{20} - 25 q^{21} + 28 q^{22} - 27 q^{23} + 4 q^{24} + 30 q^{25} - q^{26} - q^{27} + 17 q^{28} - 69 q^{29} + 8 q^{30} - 13 q^{31} - 55 q^{32} - 18 q^{33} + 32 q^{34} - 23 q^{35} + 29 q^{36} + 3 q^{37} + 3 q^{38} - 28 q^{39} + 7 q^{40} - 51 q^{41} + 25 q^{42} + 23 q^{43} - 28 q^{44} - 28 q^{45} + 27 q^{46} - 27 q^{47} - 4 q^{48} + 8 q^{49} - 30 q^{50} - 42 q^{51} + q^{52} - 61 q^{53} + q^{54} + 5 q^{55} - 17 q^{56} - 52 q^{57} + 69 q^{58} - 71 q^{59} - 8 q^{60} - 16 q^{61} + 13 q^{62} + 14 q^{63} + 55 q^{64} - 82 q^{65} + 18 q^{66} + 32 q^{67} - 32 q^{68} - 44 q^{69} + 23 q^{70} - 84 q^{71} - 29 q^{72} - 43 q^{73} - 3 q^{74} - 37 q^{75} - 3 q^{76} - 47 q^{77} + 28 q^{78} - 20 q^{79} - 7 q^{80} - 33 q^{81} + 51 q^{82} + 17 q^{83} - 25 q^{84} + 10 q^{85} - 23 q^{86} - q^{87} + 28 q^{88} - 92 q^{89} + 28 q^{90} - 34 q^{91} - 27 q^{92} - 13 q^{93} + 27 q^{94} - 60 q^{95} + 4 q^{96} - 45 q^{97} - 8 q^{98} - 73 q^{99}+O(q^{100}) \) 55 * q - 55 * q^2 - 4 * q^3 + 55 * q^4 - 7 * q^5 + 4 * q^6 + 17 * q^7 - 55 * q^8 + 29 * q^9 + 7 * q^10 - 28 * q^11 - 4 * q^12 + q^13 - 17 * q^14 - 8 * q^15 + 55 * q^16 - 32 * q^17 - 29 * q^18 - 3 * q^19 - 7 * q^20 - 25 * q^21 + 28 * q^22 - 27 * q^23 + 4 * q^24 + 30 * q^25 - q^26 - q^27 + 17 * q^28 - 69 * q^29 + 8 * q^30 - 13 * q^31 - 55 * q^32 - 18 * q^33 + 32 * q^34 - 23 * q^35 + 29 * q^36 + 3 * q^37 + 3 * q^38 - 28 * q^39 + 7 * q^40 - 51 * q^41 + 25 * q^42 + 23 * q^43 - 28 * q^44 - 28 * q^45 + 27 * q^46 - 27 * q^47 - 4 * q^48 + 8 * q^49 - 30 * q^50 - 42 * q^51 + q^52 - 61 * q^53 + q^54 + 5 * q^55 - 17 * q^56 - 52 * q^57 + 69 * q^58 - 71 * q^59 - 8 * q^60 - 16 * q^61 + 13 * q^62 + 14 * q^63 + 55 * q^64 - 82 * q^65 + 18 * q^66 + 32 * q^67 - 32 * q^68 - 44 * q^69 + 23 * q^70 - 84 * q^71 - 29 * q^72 - 43 * q^73 - 3 * q^74 - 37 * q^75 - 3 * q^76 - 47 * q^77 + 28 * q^78 - 20 * q^79 - 7 * q^80 - 33 * q^81 + 51 * q^82 + 17 * q^83 - 25 * q^84 + 10 * q^85 - 23 * q^86 - q^87 + 28 * q^88 - 92 * q^89 + 28 * q^90 - 34 * q^91 - 27 * q^92 - 13 * q^93 + 27 * q^94 - 60 * q^95 + 4 * q^96 - 45 * q^97 - 8 * q^98 - 73 * q^99

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