LMFDB - Embedded newform 6002.2.a.a.1.16

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:	$47$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.48674 q^{3} +1.00000 q^{4} +1.68773 q^{5} -1.48674 q^{6} +3.31084 q^{7} +1.00000 q^{8} -0.789607 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.48674 q^{3} +1.00000 q^{4} +1.68773 q^{5} -1.48674 q^{6} +3.31084 q^{7} +1.00000 q^{8} -0.789607 q^{9} +1.68773 q^{10} -2.31778 q^{11} -1.48674 q^{12} +3.30314 q^{13} +3.31084 q^{14} -2.50921 q^{15} +1.00000 q^{16} -0.160415 q^{17} -0.789607 q^{18} -7.08781 q^{19} +1.68773 q^{20} -4.92235 q^{21} -2.31778 q^{22} -5.83899 q^{23} -1.48674 q^{24} -2.15157 q^{25} +3.30314 q^{26} +5.63416 q^{27} +3.31084 q^{28} -4.95741 q^{29} -2.50921 q^{30} -2.17648 q^{31} +1.00000 q^{32} +3.44593 q^{33} -0.160415 q^{34} +5.58780 q^{35} -0.789607 q^{36} -10.6680 q^{37} -7.08781 q^{38} -4.91090 q^{39} +1.68773 q^{40} +0.999174 q^{41} -4.92235 q^{42} -4.21236 q^{43} -2.31778 q^{44} -1.33264 q^{45} -5.83899 q^{46} -1.35716 q^{47} -1.48674 q^{48} +3.96166 q^{49} -2.15157 q^{50} +0.238495 q^{51} +3.30314 q^{52} -4.42494 q^{53} +5.63416 q^{54} -3.91178 q^{55} +3.31084 q^{56} +10.5377 q^{57} -4.95741 q^{58} -6.99872 q^{59} -2.50921 q^{60} -10.6878 q^{61} -2.17648 q^{62} -2.61426 q^{63} +1.00000 q^{64} +5.57480 q^{65} +3.44593 q^{66} +1.07316 q^{67} -0.160415 q^{68} +8.68105 q^{69} +5.58780 q^{70} +12.9752 q^{71} -0.789607 q^{72} -11.8835 q^{73} -10.6680 q^{74} +3.19882 q^{75} -7.08781 q^{76} -7.67379 q^{77} -4.91090 q^{78} +11.7017 q^{79} +1.68773 q^{80} -6.00770 q^{81} +0.999174 q^{82} -12.9807 q^{83} -4.92235 q^{84} -0.270737 q^{85} -4.21236 q^{86} +7.37038 q^{87} -2.31778 q^{88} -12.4010 q^{89} -1.33264 q^{90} +10.9362 q^{91} -5.83899 q^{92} +3.23586 q^{93} -1.35716 q^{94} -11.9623 q^{95} -1.48674 q^{96} +11.4758 q^{97} +3.96166 q^{98} +1.83014 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * 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
$3$	−1.48674	−0.858369	−0.429185	−	0.903217i	$-0.641199\pi$
$3$	−1.48674	−0.858369	−0.429185	+	0.903217i	$0.641199\pi$
$4$	1.00000	0.500000
$5$	1.68773	0.754776	0.377388	−	0.926055i	$-0.376822\pi$
$5$	1.68773	0.754776	0.377388	+	0.926055i	$0.376822\pi$
$6$	−1.48674	−0.606959
$7$	3.31084	1.25138	0.625690	−	0.780072i	$-0.284818\pi$
$7$	3.31084	1.25138	0.625690	+	0.780072i	$0.284818\pi$
$8$	1.00000	0.353553
$9$	−0.789607	−0.263202
$10$	1.68773	0.533707
$11$	−2.31778	−0.698837	−0.349418	−	0.936967i	$-0.613621\pi$
$11$	−2.31778	−0.698837	−0.349418	+	0.936967i	$0.613621\pi$
$12$	−1.48674	−0.429185
$13$	3.30314	0.916125	0.458062	−	0.888920i	$-0.348544\pi$
$13$	3.30314	0.916125	0.458062	+	0.888920i	$0.348544\pi$
$14$	3.31084	0.884859
$15$	−2.50921	−0.647876
$16$	1.00000	0.250000
$17$	−0.160415	−0.0389064	−0.0194532	−	0.999811i	$-0.506193\pi$
$17$	−0.160415	−0.0389064	−0.0194532	+	0.999811i	$0.506193\pi$
$18$	−0.789607	−0.186112
$19$	−7.08781	−1.62605	−0.813027	−	0.582226i	$-0.802182\pi$
$19$	−7.08781	−1.62605	−0.813027	+	0.582226i	$0.802182\pi$
$20$	1.68773	0.377388
$21$	−4.92235	−1.07415
$22$	−2.31778	−0.494152
$23$	−5.83899	−1.21751	−0.608757	−	0.793357i	$-0.708331\pi$
$23$	−5.83899	−1.21751	−0.608757	+	0.793357i	$0.708331\pi$
$24$	−1.48674	−0.303479
$25$	−2.15157	−0.430314
$26$	3.30314	0.647798
$27$	5.63416	1.08429
$28$	3.31084	0.625690
$29$	−4.95741	−0.920568	−0.460284	−	0.887772i	$-0.652252\pi$
$29$	−4.95741	−0.920568	−0.460284	+	0.887772i	$0.652252\pi$
$30$	−2.50921	−0.458118
$31$	−2.17648	−0.390908	−0.195454	−	0.980713i	$-0.562618\pi$
$31$	−2.17648	−0.390908	−0.195454	+	0.980713i	$0.562618\pi$
$32$	1.00000	0.176777
$33$	3.44593	0.599860
$34$	−0.160415	−0.0275110
$35$	5.58780	0.944511
$36$	−0.789607	−0.131601
$37$	−10.6680	−1.75381	−0.876904	−	0.480665i	$-0.840395\pi$
$37$	−10.6680	−1.75381	−0.876904	+	0.480665i	$0.840395\pi$
$38$	−7.08781	−1.14979
$39$	−4.91090	−0.786373
$40$	1.68773	0.266854
$41$	0.999174	0.156045	0.0780224	−	0.996952i	$-0.475139\pi$
$41$	0.999174	0.156045	0.0780224	+	0.996952i	$0.475139\pi$
$42$	−4.92235	−0.759536
$43$	−4.21236	−0.642379	−0.321189	−	0.947015i	$-0.604083\pi$
$43$	−4.21236	−0.642379	−0.321189	+	0.947015i	$0.604083\pi$
$44$	−2.31778	−0.349418
$45$	−1.33264	−0.198659
$46$	−5.83899	−0.860912
$47$	−1.35716	−0.197962	−0.0989812	−	0.995089i	$-0.531558\pi$
$47$	−1.35716	−0.197962	−0.0989812	+	0.995089i	$0.531558\pi$
$48$	−1.48674	−0.214592
$49$	3.96166	0.565951
$50$	−2.15157	−0.304278
$51$	0.238495	0.0333960
$52$	3.30314	0.458062
$53$	−4.42494	−0.607813	−0.303906	−	0.952702i	$-0.598291\pi$
$53$	−4.42494	−0.607813	−0.303906	+	0.952702i	$0.598291\pi$
$54$	5.63416	0.766712
$55$	−3.91178	−0.527465
$56$	3.31084	0.442430
$57$	10.5377	1.39575
$58$	−4.95741	−0.650940
$59$	−6.99872	−0.911156	−0.455578	−	0.890196i	$-0.650567\pi$
$59$	−6.99872	−0.911156	−0.455578	+	0.890196i	$0.650567\pi$
$60$	−2.50921	−0.323938
$61$	−10.6878	−1.36844	−0.684218	−	0.729278i	$-0.739856\pi$
$61$	−10.6878	−1.36844	−0.684218	+	0.729278i	$0.739856\pi$
$62$	−2.17648	−0.276414
$63$	−2.61426	−0.329366
$64$	1.00000	0.125000
$65$	5.57480	0.691469
$66$	3.44593	0.424165
$67$	1.07316	0.131107	0.0655537	−	0.997849i	$-0.479119\pi$
$67$	1.07316	0.131107	0.0655537	+	0.997849i	$0.479119\pi$
$68$	−0.160415	−0.0194532
$69$	8.68105	1.04508
$70$	5.58780	0.667870
$71$	12.9752	1.53987	0.769934	−	0.638124i	$-0.220289\pi$
$71$	12.9752	1.53987	0.769934	+	0.638124i	$0.220289\pi$
$72$	−0.789607	−0.0930561
$73$	−11.8835	−1.39086	−0.695430	−	0.718594i	$-0.744786\pi$
$73$	−11.8835	−1.39086	−0.695430	+	0.718594i	$0.744786\pi$
$74$	−10.6680	−1.24013
$75$	3.19882	0.369368
$76$	−7.08781	−0.813027
$77$	−7.67379	−0.874510
$78$	−4.91090	−0.556050
$79$	11.7017	1.31654	0.658270	−	0.752782i	$-0.271289\pi$
$79$	11.7017	1.31654	0.658270	+	0.752782i	$0.271289\pi$
$80$	1.68773	0.188694
$81$	−6.00770	−0.667522
$82$	0.999174	0.110340
$83$	−12.9807	−1.42481	−0.712406	−	0.701767i	$-0.752395\pi$
$83$	−12.9807	−1.42481	−0.712406	+	0.701767i	$0.752395\pi$
$84$	−4.92235	−0.537073
$85$	−0.270737	−0.0293656
$86$	−4.21236	−0.454230
$87$	7.37038	0.790187
$88$	−2.31778	−0.247076
$89$	−12.4010	−1.31450	−0.657249	−	0.753673i	$-0.728280\pi$
$89$	−12.4010	−1.31450	−0.657249	+	0.753673i	$0.728280\pi$
$90$	−1.33264	−0.140473
$91$	10.9362	1.14642
$92$	−5.83899	−0.608757
$93$	3.23586	0.335543
$94$	−1.35716	−0.139981
$95$	−11.9623	−1.22731
$96$	−1.48674	−0.151740
$97$	11.4758	1.16519	0.582597	−	0.812761i	$-0.302037\pi$
$97$	11.4758	1.16519	0.582597	+	0.812761i	$0.302037\pi$
$98$	3.96166	0.400188
$99$	1.83014	0.183936
$100$	−2.15157	−0.215157
$101$	13.3207	1.32546	0.662729	−	0.748859i	$-0.269398\pi$
$101$	13.3207	1.32546	0.662729	+	0.748859i	$0.269398\pi$
$102$	0.238495	0.0236146
$103$	14.2317	1.40229	0.701147	−	0.713017i	$-0.252672\pi$
$103$	14.2317	1.40229	0.701147	+	0.713017i	$0.252672\pi$
$104$	3.30314	0.323899
$105$	−8.30760	−0.810739
$106$	−4.42494	−0.429789
$107$	10.5458	1.01950	0.509750	−	0.860322i	$-0.329738\pi$
$107$	10.5458	1.01950	0.509750	+	0.860322i	$0.329738\pi$
$108$	5.63416	0.542147
$109$	−16.8135	−1.61044	−0.805220	−	0.592977i	$-0.797953\pi$
$109$	−16.8135	−1.61044	−0.805220	+	0.592977i	$0.797953\pi$
$110$	−3.91178	−0.372974
$111$	15.8605	1.50542
$112$	3.31084	0.312845
$113$	2.61225	0.245740	0.122870	−	0.992423i	$-0.460790\pi$
$113$	2.61225	0.245740	0.122870	+	0.992423i	$0.460790\pi$
$114$	10.5377	0.986948
$115$	−9.85463	−0.918949
$116$	−4.95741	−0.460284
$117$	−2.60818	−0.241126
$118$	−6.99872	−0.644284
$119$	−0.531109	−0.0486867
$120$	−2.50921	−0.229059
$121$	−5.62790	−0.511627
$122$	−10.6878	−0.967630
$123$	−1.48551	−0.133944
$124$	−2.17648	−0.195454
$125$	−12.0699	−1.07957
$126$	−2.61426	−0.232897
$127$	21.0944	1.87182	0.935912	−	0.352234i	$-0.114578\pi$
$127$	21.0944	1.87182	0.935912	+	0.352234i	$0.114578\pi$
$128$	1.00000	0.0883883
$129$	6.26268	0.551398
$130$	5.57480	0.488942
$131$	1.92401	0.168101	0.0840507	−	0.996461i	$-0.473214\pi$
$131$	1.92401	0.168101	0.0840507	+	0.996461i	$0.473214\pi$
$132$	3.44593	0.299930
$133$	−23.4666	−2.03481
$134$	1.07316	0.0927069
$135$	9.50893	0.818399
$136$	−0.160415	−0.0137555
$137$	8.53905	0.729541	0.364770	−	0.931098i	$-0.381147\pi$
$137$	8.53905	0.729541	0.364770	+	0.931098i	$0.381147\pi$
$138$	8.68105	0.738980
$139$	−1.87649	−0.159162	−0.0795809	−	0.996828i	$-0.525358\pi$
$139$	−1.87649	−0.159162	−0.0795809	+	0.996828i	$0.525358\pi$
$140$	5.58780	0.472256
$141$	2.01775	0.169925
$142$	12.9752	1.08885
$143$	−7.65594	−0.640222
$144$	−0.789607	−0.0658006
$145$	−8.36677	−0.694823
$146$	−11.8835	−0.983486
$147$	−5.88995	−0.485795
$148$	−10.6680	−0.876904
$149$	−1.93716	−0.158698	−0.0793491	−	0.996847i	$-0.525284\pi$
$149$	−1.93716	−0.158698	−0.0793491	+	0.996847i	$0.525284\pi$
$150$	3.19882	0.261183
$151$	1.62845	0.132521	0.0662606	−	0.997802i	$-0.478893\pi$
$151$	1.62845	0.132521	0.0662606	+	0.997802i	$0.478893\pi$
$152$	−7.08781	−0.574897
$153$	0.126665	0.0102403
$154$	−7.67379	−0.618372
$155$	−3.67332	−0.295048
$156$	−4.91090	−0.393187
$157$	8.18050	0.652875	0.326438	−	0.945219i	$-0.394152\pi$
$157$	8.18050	0.652875	0.326438	+	0.945219i	$0.394152\pi$
$158$	11.7017	0.930934
$159$	6.57874	0.521728
$160$	1.68773	0.133427
$161$	−19.3320	−1.52357
$162$	−6.00770	−0.472009
$163$	19.2206	1.50547	0.752736	−	0.658322i	$-0.228734\pi$
$163$	19.2206	1.50547	0.752736	+	0.658322i	$0.228734\pi$
$164$	0.999174	0.0780224
$165$	5.81580	0.452760
$166$	−12.9807	−1.00749
$167$	−10.2266	−0.791360	−0.395680	−	0.918389i	$-0.629491\pi$
$167$	−10.2266	−0.791360	−0.395680	+	0.918389i	$0.629491\pi$
$168$	−4.92235	−0.379768
$169$	−2.08930	−0.160715
$170$	−0.270737	−0.0207646
$171$	5.59658	0.427982
$172$	−4.21236	−0.321189
$173$	22.2947	1.69504	0.847519	−	0.530765i	$-0.178095\pi$
$173$	22.2947	1.69504	0.847519	+	0.530765i	$0.178095\pi$
$174$	7.37038	0.558747
$175$	−7.12350	−0.538486
$176$	−2.31778	−0.174709
$177$	10.4053	0.782108
$178$	−12.4010	−0.929491
$179$	−24.8595	−1.85809	−0.929043	−	0.369972i	$-0.879367\pi$
$179$	−24.8595	−1.85809	−0.929043	+	0.369972i	$0.879367\pi$
$180$	−1.33264	−0.0993294
$181$	12.5185	0.930495	0.465247	−	0.885181i	$-0.345965\pi$
$181$	12.5185	0.930495	0.465247	+	0.885181i	$0.345965\pi$
$182$	10.9362	0.810642
$183$	15.8900	1.17462
$184$	−5.83899	−0.430456
$185$	−18.0047	−1.32373
$186$	3.23586	0.237265
$187$	0.371807	0.0271892
$188$	−1.35716	−0.0989812
$189$	18.6538	1.35686
$190$	−11.9623	−0.867837
$191$	22.2609	1.61075	0.805373	−	0.592769i	$-0.201965\pi$
$191$	22.2609	1.61075	0.805373	+	0.592769i	$0.201965\pi$
$192$	−1.48674	−0.107296
$193$	−1.00883	−0.0726173	−0.0363087	−	0.999341i	$-0.511560\pi$
$193$	−1.00883	−0.0726173	−0.0363087	+	0.999341i	$0.511560\pi$
$194$	11.4758	0.823916
$195$	−8.28827	−0.593536
$196$	3.96166	0.282976
$197$	19.5141	1.39032	0.695160	−	0.718855i	$-0.255334\pi$
$197$	19.5141	1.39032	0.695160	+	0.718855i	$0.255334\pi$
$198$	1.83014	0.130062
$199$	−24.1448	−1.71158	−0.855791	−	0.517321i	$-0.826929\pi$
$199$	−24.1448	−1.71158	−0.855791	+	0.517321i	$0.826929\pi$
$200$	−2.15157	−0.152139
$201$	−1.59551	−0.112538
$202$	13.3207	0.937241
$203$	−16.4132	−1.15198
$204$	0.238495	0.0166980
$205$	1.68634	0.117779
$206$	14.2317	0.991571
$207$	4.61051	0.320452
$208$	3.30314	0.229031
$209$	16.4280	1.13635
$210$	−8.30760	−0.573279
$211$	2.78620	0.191810	0.0959048	−	0.995391i	$-0.469426\pi$
$211$	2.78620	0.191810	0.0959048	+	0.995391i	$0.469426\pi$
$212$	−4.42494	−0.303906
$213$	−19.2907	−1.32177
$214$	10.5458	0.720896
$215$	−7.10932	−0.484852
$216$	5.63416	0.383356
$217$	−7.20599	−0.489174
$218$	−16.8135	−1.13875
$219$	17.6677	1.19387
$220$	−3.91178	−0.263732
$221$	−0.529873	−0.0356431
$222$	15.8605	1.06449
$223$	13.0071	0.871022	0.435511	−	0.900183i	$-0.356568\pi$
$223$	13.0071	0.871022	0.435511	+	0.900183i	$0.356568\pi$
$224$	3.31084	0.221215
$225$	1.69889	0.113260
$226$	2.61225	0.173764
$227$	−14.7546	−0.979298	−0.489649	−	0.871920i	$-0.662875\pi$
$227$	−14.7546	−0.979298	−0.489649	+	0.871920i	$0.662875\pi$
$228$	10.5377	0.697877
$229$	−16.9426	−1.11960	−0.559798	−	0.828629i	$-0.689121\pi$
$229$	−16.9426	−1.11960	−0.559798	+	0.828629i	$0.689121\pi$
$230$	−9.85463	−0.649795
$231$	11.4089	0.750652
$232$	−4.95741	−0.325470
$233$	20.3168	1.33100	0.665500	−	0.746398i	$-0.268218\pi$
$233$	20.3168	1.33100	0.665500	+	0.746398i	$0.268218\pi$
$234$	−2.60818	−0.170502
$235$	−2.29052	−0.149417
$236$	−6.99872	−0.455578
$237$	−17.3973	−1.13008
$238$	−0.531109	−0.0344267
$239$	14.3469	0.928025	0.464012	−	0.885829i	$-0.346409\pi$
$239$	14.3469	0.928025	0.464012	+	0.885829i	$0.346409\pi$
$240$	−2.50921	−0.161969
$241$	−13.6488	−0.879195	−0.439598	−	0.898195i	$-0.644879\pi$
$241$	−13.6488	−0.879195	−0.439598	+	0.898195i	$0.644879\pi$
$242$	−5.62790	−0.361775
$243$	−7.97059	−0.511314
$244$	−10.6878	−0.684218
$245$	6.68621	0.427166
$246$	−1.48551	−0.0947127
$247$	−23.4120	−1.48967
$248$	−2.17648	−0.138207
$249$	19.2989	1.22302
$250$	−12.0699	−0.763368
$251$	0.239750	0.0151329	0.00756645	−	0.999971i	$-0.497592\pi$
$251$	0.239750	0.0151329	0.00756645	+	0.999971i	$0.497592\pi$
$252$	−2.61426	−0.164683
$253$	13.5335	0.850843
$254$	21.0944	1.32358
$255$	0.402516	0.0252065
$256$	1.00000	0.0625000
$257$	−24.8828	−1.55215	−0.776073	−	0.630643i	$-0.782791\pi$
$257$	−24.8828	−1.55215	−0.776073	+	0.630643i	$0.782791\pi$
$258$	6.26268	0.389897
$259$	−35.3200	−2.19468
$260$	5.57480	0.345734
$261$	3.91441	0.242296
$262$	1.92401	0.118866
$263$	3.38523	0.208743	0.104371	−	0.994538i	$-0.466717\pi$
$263$	3.38523	0.208743	0.104371	+	0.994538i	$0.466717\pi$
$264$	3.44593	0.212082
$265$	−7.46811	−0.458762
$266$	−23.4666	−1.43883
$267$	18.4370	1.12832
$268$	1.07316	0.0655537
$269$	−6.29253	−0.383663	−0.191831	−	0.981428i	$-0.561443\pi$
$269$	−6.29253	−0.383663	−0.191831	+	0.981428i	$0.561443\pi$
$270$	9.50893	0.578695
$271$	−23.0199	−1.39836	−0.699181	−	0.714945i	$-0.746452\pi$
$271$	−23.0199	−1.39836	−0.699181	+	0.714945i	$0.746452\pi$
$272$	−0.160415	−0.00972660
$273$	−16.2592	−0.984052
$274$	8.53905	0.515863
$275$	4.98686	0.300719
$276$	8.68105	0.522538
$277$	−28.2277	−1.69604	−0.848020	−	0.529965i	$-0.822205\pi$
$277$	−28.2277	−1.69604	−0.848020	+	0.529965i	$0.822205\pi$
$278$	−1.87649	−0.112544
$279$	1.71857	0.102888
$280$	5.58780	0.333935
$281$	2.60585	0.155452	0.0777259	−	0.996975i	$-0.475234\pi$
$281$	2.60585	0.155452	0.0777259	+	0.996975i	$0.475234\pi$
$282$	2.01775	0.120155
$283$	−1.76737	−0.105059	−0.0525295	−	0.998619i	$-0.516728\pi$
$283$	−1.76737	−0.105059	−0.0525295	+	0.998619i	$0.516728\pi$
$284$	12.9752	0.769934
$285$	17.7848	1.05348
$286$	−7.65594	−0.452705
$287$	3.30810	0.195271
$288$	−0.789607	−0.0465281
$289$	−16.9743	−0.998486
$290$	−8.36677	−0.491314
$291$	−17.0616	−1.00017
$292$	−11.8835	−0.695430
$293$	15.7554	0.920438	0.460219	−	0.887805i	$-0.347771\pi$
$293$	15.7554	0.920438	0.460219	+	0.887805i	$0.347771\pi$
$294$	−5.88995	−0.343509
$295$	−11.8119	−0.687718
$296$	−10.6680	−0.620065
$297$	−13.0587	−0.757744
$298$	−1.93716	−0.112217
$299$	−19.2870	−1.11539
$300$	3.19882	0.184684
$301$	−13.9464	−0.803860
$302$	1.62845	0.0937066
$303$	−19.8044	−1.13773
$304$	−7.08781	−0.406514
$305$	−18.0382	−1.03286
$306$	0.126665	0.00724095
$307$	17.3790	0.991874	0.495937	−	0.868359i	$-0.334825\pi$
$307$	17.3790	0.991874	0.495937	+	0.868359i	$0.334825\pi$
$308$	−7.67379	−0.437255
$309$	−21.1589	−1.20369
$310$	−3.67332	−0.208630
$311$	−2.47426	−0.140303	−0.0701513	−	0.997536i	$-0.522348\pi$
$311$	−2.47426	−0.140303	−0.0701513	+	0.997536i	$0.522348\pi$
$312$	−4.91090	−0.278025
$313$	10.6812	0.603738	0.301869	−	0.953349i	$-0.402390\pi$
$313$	10.6812	0.603738	0.301869	+	0.953349i	$0.402390\pi$
$314$	8.18050	0.461652
$315$	−4.41217	−0.248598
$316$	11.7017	0.658270
$317$	−18.7116	−1.05095	−0.525475	−	0.850809i	$-0.676112\pi$
$317$	−18.7116	−1.05095	−0.525475	+	0.850809i	$0.676112\pi$
$318$	6.57874	0.368917
$319$	11.4902	0.643327
$320$	1.68773	0.0943470
$321$	−15.6788	−0.875108
$322$	−19.3320	−1.07733
$323$	1.13699	0.0632639
$324$	−6.00770	−0.333761
$325$	−7.10692	−0.394221
$326$	19.2206	1.06453
$327$	24.9973	1.38235
$328$	0.999174	0.0551701
$329$	−4.49335	−0.247726
$330$	5.81580	0.320149
$331$	10.7200	0.589227	0.294613	−	0.955617i	$-0.404809\pi$
$331$	10.7200	0.589227	0.294613	+	0.955617i	$0.404809\pi$
$332$	−12.9807	−0.712406
$333$	8.42353	0.461607
$334$	−10.2266	−0.559576
$335$	1.81120	0.0989566
$336$	−4.92235	−0.268536
$337$	−25.2109	−1.37333	−0.686663	−	0.726976i	$-0.740925\pi$
$337$	−25.2109	−1.37333	−0.686663	+	0.726976i	$0.740925\pi$
$338$	−2.08930	−0.113643
$339$	−3.88373	−0.210935
$340$	−0.270737	−0.0146828
$341$	5.04461	0.273181
$342$	5.59658	0.302629
$343$	−10.0595	−0.543160
$344$	−4.21236	−0.227115
$345$	14.6513	0.788798
$346$	22.2947	1.19857
$347$	−2.06218	−0.110704	−0.0553519	−	0.998467i	$-0.517628\pi$
$347$	−2.06218	−0.110704	−0.0553519	+	0.998467i	$0.517628\pi$
$348$	7.37038	0.395094
$349$	−19.3457	−1.03555	−0.517775	−	0.855517i	$-0.673239\pi$
$349$	−19.3457	−1.03555	−0.517775	+	0.855517i	$0.673239\pi$
$350$	−7.12350	−0.380767
$351$	18.6104	0.993349
$352$	−2.31778	−0.123538
$353$	21.5612	1.14759	0.573793	−	0.819001i	$-0.305471\pi$
$353$	21.5612	1.14759	0.573793	+	0.819001i	$0.305471\pi$
$354$	10.4053	0.553034
$355$	21.8985	1.16225
$356$	−12.4010	−0.657249
$357$	0.789620	0.0417911
$358$	−24.8595	−1.31387
$359$	−19.4399	−1.02600	−0.513001	−	0.858388i	$-0.671466\pi$
$359$	−19.4399	−1.02600	−0.513001	+	0.858388i	$0.671466\pi$
$360$	−1.33264	−0.0702365
$361$	31.2370	1.64405
$362$	12.5185	0.657959
$363$	8.36722	0.439165
$364$	10.9362	0.573210
$365$	−20.0562	−1.04979
$366$	15.8900	0.830584
$367$	5.43609	0.283762	0.141881	−	0.989884i	$-0.454685\pi$
$367$	5.43609	0.283762	0.141881	+	0.989884i	$0.454685\pi$
$368$	−5.83899	−0.304378
$369$	−0.788955	−0.0410714
$370$	−18.0047	−0.936020
$371$	−14.6503	−0.760605
$372$	3.23586	0.167772
$373$	28.3123	1.46596	0.732978	−	0.680252i	$-0.238130\pi$
$373$	28.3123	1.46596	0.732978	+	0.680252i	$0.238130\pi$
$374$	0.371807	0.0192257
$375$	17.9448	0.926666
$376$	−1.35716	−0.0699903
$377$	−16.3750	−0.843356
$378$	18.6538	0.959447
$379$	−12.5543	−0.644873	−0.322436	−	0.946591i	$-0.604502\pi$
$379$	−12.5543	−0.644873	−0.322436	+	0.946591i	$0.604502\pi$
$380$	−11.9623	−0.613653
$381$	−31.3618	−1.60672
$382$	22.2609	1.13897
$383$	5.28787	0.270198	0.135099	−	0.990832i	$-0.456865\pi$
$383$	5.28787	0.270198	0.135099	+	0.990832i	$0.456865\pi$
$384$	−1.48674	−0.0758698
$385$	−12.9513	−0.660059
$386$	−1.00883	−0.0513482
$387$	3.32611	0.169076
$388$	11.4758	0.582597
$389$	15.1345	0.767352	0.383676	−	0.923468i	$-0.374658\pi$
$389$	15.1345	0.767352	0.383676	+	0.923468i	$0.374658\pi$
$390$	−8.28827	−0.419693
$391$	0.936662	0.0473690
$392$	3.96166	0.200094
$393$	−2.86050	−0.144293
$394$	19.5141	0.983104
$395$	19.7492	0.993692
$396$	1.83014	0.0919678
$397$	5.00396	0.251142	0.125571	−	0.992085i	$-0.459924\pi$
$397$	5.00396	0.251142	0.125571	+	0.992085i	$0.459924\pi$
$398$	−24.1448	−1.21027
$399$	34.8887	1.74662
$400$	−2.15157	−0.107578
$401$	−17.8825	−0.893011	−0.446505	−	0.894781i	$-0.647332\pi$
$401$	−17.8825	−0.893011	−0.446505	+	0.894781i	$0.647332\pi$
$402$	−1.59551	−0.0795767
$403$	−7.18922	−0.358120
$404$	13.3207	0.662729
$405$	−10.1394	−0.503829
$406$	−16.4132	−0.814573
$407$	24.7261	1.22563
$408$	0.238495	0.0118073
$409$	15.5102	0.766931	0.383466	−	0.923555i	$-0.374730\pi$
$409$	15.5102	0.766931	0.383466	+	0.923555i	$0.374730\pi$
$410$	1.68634	0.0832822
$411$	−12.6953	−0.626215
$412$	14.2317	0.701147
$413$	−23.1716	−1.14020
$414$	4.61051	0.226594
$415$	−21.9078	−1.07541
$416$	3.30314	0.161950
$417$	2.78985	0.136620
$418$	16.4280	0.803518
$419$	9.71888	0.474799	0.237399	−	0.971412i	$-0.423705\pi$
$419$	9.71888	0.474799	0.237399	+	0.971412i	$0.423705\pi$
$420$	−8.30760	−0.405370
$421$	−7.27171	−0.354402	−0.177201	−	0.984175i	$-0.556704\pi$
$421$	−7.27171	−0.354402	−0.177201	+	0.984175i	$0.556704\pi$
$422$	2.78620	0.135630
$423$	1.07163	0.0521042
$424$	−4.42494	−0.214894
$425$	0.345144	0.0167419
$426$	−19.2907	−0.934636
$427$	−35.3857	−1.71243
$428$	10.5458	0.509750
$429$	11.3824	0.549547
$430$	−7.10932	−0.342842
$431$	34.3279	1.65352	0.826759	−	0.562556i	$-0.190182\pi$
$431$	34.3279	1.65352	0.826759	+	0.562556i	$0.190182\pi$
$432$	5.63416	0.271073
$433$	−30.9705	−1.48835	−0.744174	−	0.667985i	$-0.767157\pi$
$433$	−30.9705	−1.48835	−0.744174	+	0.667985i	$0.767157\pi$
$434$	−7.20599	−0.345898
$435$	12.4392	0.596414
$436$	−16.8135	−0.805220
$437$	41.3856	1.97974
$438$	17.6677	0.844194
$439$	−33.5538	−1.60144	−0.800718	−	0.599041i	$-0.795548\pi$
$439$	−33.5538	−1.60144	−0.800718	+	0.599041i	$0.795548\pi$
$440$	−3.91178	−0.186487
$441$	−3.12815	−0.148960
$442$	−0.529873	−0.0252035
$443$	6.40125	0.304133	0.152066	−	0.988370i	$-0.451407\pi$
$443$	6.40125	0.304133	0.152066	+	0.988370i	$0.451407\pi$
$444$	15.8605	0.752708
$445$	−20.9295	−0.992151
$446$	13.0071	0.615906
$447$	2.88005	0.136222
$448$	3.31084	0.156422
$449$	−4.36346	−0.205924	−0.102962	−	0.994685i	$-0.532832\pi$
$449$	−4.36346	−0.205924	−0.102962	+	0.994685i	$0.532832\pi$
$450$	1.69889	0.0800866
$451$	−2.31586	−0.109050
$452$	2.61225	0.122870
$453$	−2.42107	−0.113752
$454$	−14.7546	−0.692469
$455$	18.4573	0.865290
$456$	10.5377	0.493474
$457$	−17.3651	−0.812306	−0.406153	−	0.913805i	$-0.633130\pi$
$457$	−17.3651	−0.812306	−0.406153	+	0.913805i	$0.633130\pi$
$458$	−16.9426	−0.791673
$459$	−0.903804	−0.0421860
$460$	−9.85463	−0.459475
$461$	−17.0327	−0.793294	−0.396647	−	0.917971i	$-0.629826\pi$
$461$	−17.0327	−0.793294	−0.396647	+	0.917971i	$0.629826\pi$
$462$	11.4089	0.530791
$463$	6.38016	0.296511	0.148256	−	0.988949i	$-0.452634\pi$
$463$	6.38016	0.296511	0.148256	+	0.988949i	$0.452634\pi$
$464$	−4.95741	−0.230142
$465$	5.46126	0.253260
$466$	20.3168	0.941159
$467$	41.7268	1.93089	0.965444	−	0.260611i	$-0.0839241\pi$
$467$	41.7268	1.93089	0.965444	+	0.260611i	$0.0839241\pi$
$468$	−2.60818	−0.120563
$469$	3.55306	0.164065
$470$	−2.29052	−0.105654
$471$	−12.1623	−0.560408
$472$	−6.99872	−0.322142
$473$	9.76332	0.448918
$474$	−17.3973	−0.799085
$475$	15.2499	0.699713
$476$	−0.531109	−0.0243433
$477$	3.49397	0.159978
$478$	14.3469	0.656212
$479$	−20.4878	−0.936113	−0.468056	−	0.883699i	$-0.655046\pi$
$479$	−20.4878	−0.936113	−0.468056	+	0.883699i	$0.655046\pi$
$480$	−2.50921	−0.114529
$481$	−35.2379	−1.60671
$482$	−13.6488	−0.621685
$483$	28.7416	1.30779
$484$	−5.62790	−0.255814
$485$	19.3681	0.879460
$486$	−7.97059	−0.361553
$487$	−5.52603	−0.250408	−0.125204	−	0.992131i	$-0.539959\pi$
$487$	−5.52603	−0.250408	−0.125204	+	0.992131i	$0.539959\pi$
$488$	−10.6878	−0.483815
$489$	−28.5760	−1.29225
$490$	6.68621	0.302052
$491$	−16.5457	−0.746699	−0.373350	−	0.927691i	$-0.621791\pi$
$491$	−16.5457	−0.746699	−0.373350	+	0.927691i	$0.621791\pi$
$492$	−1.48551	−0.0669720
$493$	0.795244	0.0358160
$494$	−23.4120	−1.05336
$495$	3.08877	0.138830
$496$	−2.17648	−0.0977270
$497$	42.9586	1.92696
$498$	19.2989	0.864802
$499$	6.78916	0.303924	0.151962	−	0.988386i	$-0.451441\pi$
$499$	6.78916	0.303924	0.151962	+	0.988386i	$0.451441\pi$
$500$	−12.0699	−0.539783
$501$	15.2043	0.679279
$502$	0.239750	0.0107006
$503$	13.4895	0.601466	0.300733	−	0.953708i	$-0.402769\pi$
$503$	13.4895	0.601466	0.300733	+	0.953708i	$0.402769\pi$
$504$	−2.61426	−0.116449
$505$	22.4817	1.00042
$506$	13.5335	0.601637
$507$	3.10624	0.137953
$508$	21.0944	0.935912
$509$	−10.5358	−0.466993	−0.233496	−	0.972358i	$-0.575017\pi$
$509$	−10.5358	−0.466993	−0.233496	+	0.972358i	$0.575017\pi$
$510$	0.402516	0.0178237
$511$	−39.3444	−1.74049
$512$	1.00000	0.0441942
$513$	−39.9338	−1.76312
$514$	−24.8828	−1.09753
$515$	24.0193	1.05842
$516$	6.26268	0.275699
$517$	3.14560	0.138343
$518$	−35.3200	−1.55187
$519$	−33.1465	−1.45497
$520$	5.57480	0.244471
$521$	32.7940	1.43673	0.718365	−	0.695666i	$-0.244891\pi$
$521$	32.7940	1.43673	0.718365	+	0.695666i	$0.244891\pi$
$522$	3.91441	0.171329
$523$	37.5244	1.64083	0.820415	−	0.571769i	$-0.193743\pi$
$523$	37.5244	1.64083	0.820415	+	0.571769i	$0.193743\pi$
$524$	1.92401	0.0840507
$525$	10.5908	0.462220
$526$	3.38523	0.147603
$527$	0.349141	0.0152088
$528$	3.44593	0.149965
$529$	11.0938	0.482338
$530$	−7.46811	−0.324394
$531$	5.52624	0.239818
$532$	−23.4666	−1.01741
$533$	3.30041	0.142956
$534$	18.4370	0.797846
$535$	17.7985	0.769494
$536$	1.07316	0.0463534
$537$	36.9596	1.59492
$538$	−6.29253	−0.271290
$539$	−9.18225	−0.395507
$540$	9.50893	0.409199
$541$	33.7985	1.45311	0.726555	−	0.687108i	$-0.241120\pi$
$541$	33.7985	1.45311	0.726555	+	0.687108i	$0.241120\pi$
$542$	−23.0199	−0.988791
$543$	−18.6118	−0.798708
$544$	−0.160415	−0.00687774
$545$	−28.3766	−1.21552
$546$	−16.2592	−0.695830
$547$	−11.8344	−0.506001	−0.253000	−	0.967466i	$-0.581417\pi$
$547$	−11.8344	−0.506001	−0.253000	+	0.967466i	$0.581417\pi$
$548$	8.53905	0.364770
$549$	8.43918	0.360176
$550$	4.98686	0.212640
$551$	35.1372	1.49689
$552$	8.68105	0.369490
$553$	38.7423	1.64749
$554$	−28.2277	−1.19928
$555$	26.7683	1.13625
$556$	−1.87649	−0.0795809
$557$	−32.3203	−1.36946	−0.684728	−	0.728799i	$-0.740079\pi$
$557$	−32.3203	−1.36946	−0.684728	+	0.728799i	$0.740079\pi$
$558$	1.71857	0.0727527
$559$	−13.9140	−0.588499
$560$	5.58780	0.236128
$561$	−0.552780	−0.0233384
$562$	2.60585	0.109921
$563$	−38.3599	−1.61668	−0.808338	−	0.588719i	$-0.799633\pi$
$563$	−38.3599	−1.61668	−0.808338	+	0.588719i	$0.799633\pi$
$564$	2.01775	0.0849624
$565$	4.40877	0.185478
$566$	−1.76737	−0.0742879
$567$	−19.8905	−0.835323
$568$	12.9752	0.544425
$569$	−17.2929	−0.724957	−0.362478	−	0.931992i	$-0.618069\pi$
$569$	−17.2929	−0.724957	−0.362478	+	0.931992i	$0.618069\pi$
$570$	17.7848	0.744924
$571$	−21.2892	−0.890926	−0.445463	−	0.895300i	$-0.646961\pi$
$571$	−21.2892	−0.890926	−0.445463	+	0.895300i	$0.646961\pi$
$572$	−7.65594	−0.320111
$573$	−33.0962	−1.38261
$574$	3.30810	0.138078
$575$	12.5630	0.523912
$576$	−0.789607	−0.0329003
$577$	−30.2448	−1.25911	−0.629555	−	0.776956i	$-0.716763\pi$
$577$	−30.2448	−1.25911	−0.629555	+	0.776956i	$0.716763\pi$
$578$	−16.9743	−0.706036
$579$	1.49987	0.0623325
$580$	−8.36677	−0.347411
$581$	−42.9769	−1.78298
$582$	−17.0616	−0.707224
$583$	10.2560	0.424762
$584$	−11.8835	−0.491743
$585$	−4.40190	−0.181996
$586$	15.7554	0.650848
$587$	15.2071	0.627666	0.313833	−	0.949478i	$-0.398387\pi$
$587$	15.2071	0.627666	0.313833	+	0.949478i	$0.398387\pi$
$588$	−5.88995	−0.242898
$589$	15.4265	0.635637
$590$	−11.8119	−0.486290
$591$	−29.0123	−1.19341
$592$	−10.6680	−0.438452
$593$	25.5599	1.04962	0.524810	−	0.851219i	$-0.324136\pi$
$593$	25.5599	1.04962	0.524810	+	0.851219i	$0.324136\pi$
$594$	−13.0587	−0.535806
$595$	−0.896368	−0.0367475
$596$	−1.93716	−0.0793491
$597$	35.8971	1.46917
$598$	−19.2870	−0.788703
$599$	−39.7107	−1.62254	−0.811268	−	0.584675i	$-0.801222\pi$
$599$	−39.7107	−1.62254	−0.811268	+	0.584675i	$0.801222\pi$
$600$	3.19882	0.130591
$601$	−14.6387	−0.597124	−0.298562	−	0.954390i	$-0.596507\pi$
$601$	−14.6387	−0.597124	−0.298562	+	0.954390i	$0.596507\pi$
$602$	−13.9464	−0.568415
$603$	−0.847375	−0.0345078
$604$	1.62845	0.0662606
$605$	−9.49837	−0.386164
$606$	−19.8044	−0.804499
$607$	32.3028	1.31113	0.655565	−	0.755139i	$-0.272431\pi$
$607$	32.3028	1.31113	0.655565	+	0.755139i	$0.272431\pi$
$608$	−7.08781	−0.287449
$609$	24.4021	0.988824
$610$	−18.0382	−0.730343
$611$	−4.48289	−0.181358
$612$	0.126665	0.00512013
$613$	−7.30807	−0.295170	−0.147585	−	0.989049i	$-0.547150\pi$
$613$	−7.30807	−0.295170	−0.147585	+	0.989049i	$0.547150\pi$
$614$	17.3790	0.701361
$615$	−2.50714	−0.101098
$616$	−7.67379	−0.309186
$617$	−24.8412	−1.00007	−0.500035	−	0.866005i	$-0.666680\pi$
$617$	−24.8412	−1.00007	−0.500035	+	0.866005i	$0.666680\pi$
$618$	−21.1589	−0.851134
$619$	−0.255873	−0.0102844	−0.00514220	−	0.999987i	$-0.501637\pi$
$619$	−0.255873	−0.0102844	−0.00514220	+	0.999987i	$0.501637\pi$
$620$	−3.67332	−0.147524
$621$	−32.8978	−1.32014
$622$	−2.47426	−0.0992089
$623$	−41.0576	−1.64494
$624$	−4.91090	−0.196593
$625$	−9.61292	−0.384517
$626$	10.6812	0.426907
$627$	−24.4241	−0.975405
$628$	8.18050	0.326438
$629$	1.71131	0.0682344
$630$	−4.41217	−0.175785
$631$	−38.7971	−1.54449	−0.772243	−	0.635327i	$-0.780865\pi$
$631$	−38.7971	−1.54449	−0.772243	+	0.635327i	$0.780865\pi$
$632$	11.7017	0.465467
$633$	−4.14235	−0.164643
$634$	−18.7116	−0.743134
$635$	35.6016	1.41281
$636$	6.57874	0.260864
$637$	13.0859	0.518482
$638$	11.4902	0.454901
$639$	−10.2453	−0.405297
$640$	1.68773	0.0667134
$641$	45.9632	1.81544	0.907718	−	0.419581i	$-0.137823\pi$
$641$	45.9632	1.81544	0.907718	+	0.419581i	$0.137823\pi$
$642$	−15.6788	−0.618795
$643$	5.30287	0.209125	0.104562	−	0.994518i	$-0.466656\pi$
$643$	5.30287	0.209125	0.104562	+	0.994518i	$0.466656\pi$
$644$	−19.3320	−0.761786
$645$	10.5697	0.416182
$646$	1.13699	0.0447343
$647$	−20.2372	−0.795606	−0.397803	−	0.917471i	$-0.630227\pi$
$647$	−20.2372	−0.795606	−0.397803	+	0.917471i	$0.630227\pi$
$648$	−6.00770	−0.236005
$649$	16.2215	0.636749
$650$	−7.10692	−0.278756
$651$	10.7134	0.419892
$652$	19.2206	0.752736
$653$	−6.83969	−0.267658	−0.133829	−	0.991004i	$-0.542727\pi$
$653$	−6.83969	−0.267658	−0.133829	+	0.991004i	$0.542727\pi$
$654$	24.9973	0.977470
$655$	3.24721	0.126879
$656$	0.999174	0.0390112
$657$	9.38331	0.366078
$658$	−4.49335	−0.175169
$659$	12.2446	0.476982	0.238491	−	0.971145i	$-0.423347\pi$
$659$	12.2446	0.476982	0.238491	+	0.971145i	$0.423347\pi$
$660$	5.81580	0.226380
$661$	−42.6254	−1.65794	−0.828968	−	0.559296i	$-0.811072\pi$
$661$	−42.6254	−1.65794	−0.828968	+	0.559296i	$0.811072\pi$
$662$	10.7200	0.416646
$663$	0.787783	0.0305949
$664$	−12.9807	−0.503747
$665$	−39.6053	−1.53583
$666$	8.42353	0.326405
$667$	28.9463	1.12080
$668$	−10.2266	−0.395680
$669$	−19.3382	−0.747659
$670$	1.81120	0.0699729
$671$	24.7720	0.956313
$672$	−4.92235	−0.189884
$673$	10.9925	0.423730	0.211865	−	0.977299i	$-0.432046\pi$
$673$	10.9925	0.423730	0.211865	+	0.977299i	$0.432046\pi$
$674$	−25.2109	−0.971089
$675$	−12.1223	−0.466586
$676$	−2.08930	−0.0803575
$677$	19.0557	0.732370	0.366185	−	0.930542i	$-0.380664\pi$
$677$	19.0557	0.732370	0.366185	+	0.930542i	$0.380664\pi$
$678$	−3.88373	−0.149154
$679$	37.9946	1.45810
$680$	−0.270737	−0.0103823
$681$	21.9363	0.840600
$682$	5.04461	0.193168
$683$	2.78166	0.106437	0.0532185	−	0.998583i	$-0.483052\pi$
$683$	2.78166	0.106437	0.0532185	+	0.998583i	$0.483052\pi$
$684$	5.59658	0.213991
$685$	14.4116	0.550640
$686$	−10.0595	−0.384072
$687$	25.1892	0.961026
$688$	−4.21236	−0.160595
$689$	−14.6162	−0.556833
$690$	14.6513	0.557764
$691$	−45.8542	−1.74438	−0.872189	−	0.489169i	$-0.837300\pi$
$691$	−45.8542	−1.74438	−0.872189	+	0.489169i	$0.837300\pi$
$692$	22.2947	0.847519
$693$	6.05929	0.230173
$694$	−2.06218	−0.0782794
$695$	−3.16701	−0.120132
$696$	7.37038	0.279373
$697$	−0.160283	−0.00607114
$698$	−19.3457	−0.732244
$699$	−30.2058	−1.14249
$700$	−7.12350	−0.269243
$701$	−20.0238	−0.756287	−0.378144	−	0.925747i	$-0.623437\pi$
$701$	−20.0238	−0.756287	−0.378144	+	0.925747i	$0.623437\pi$
$702$	18.6104	0.702404
$703$	75.6127	2.85179
$704$	−2.31778	−0.0873546
$705$	3.40541	0.128255
$706$	21.5612	0.811466
$707$	44.1027	1.65865
$708$	10.4053	0.391054
$709$	−23.7840	−0.893225	−0.446613	−	0.894727i	$-0.647370\pi$
$709$	−23.7840	−0.893225	−0.446613	+	0.894727i	$0.647370\pi$
$710$	21.8985	0.821838
$711$	−9.23972	−0.346516
$712$	−12.4010	−0.464745
$713$	12.7085	0.475936
$714$	0.789620	0.0295508
$715$	−12.9212	−0.483224
$716$	−24.8595	−0.929043
$717$	−21.3301	−0.796588
$718$	−19.4399	−0.725492
$719$	9.04791	0.337430	0.168715	−	0.985665i	$-0.446038\pi$
$719$	9.04791	0.337430	0.168715	+	0.985665i	$0.446038\pi$
$720$	−1.33264	−0.0496647
$721$	47.1189	1.75480
$722$	31.2370	1.16252
$723$	20.2922	0.754674
$724$	12.5185	0.465247
$725$	10.6662	0.396133
$726$	8.36722	0.310537
$727$	−19.1531	−0.710350	−0.355175	−	0.934800i	$-0.615579\pi$
$727$	−19.1531	−0.710350	−0.355175	+	0.934800i	$0.615579\pi$
$728$	10.9362	0.405321
$729$	29.8733	1.10642
$730$	−20.0562	−0.742312
$731$	0.675726	0.0249926
$732$	15.8900	0.587311
$733$	28.7310	1.06120	0.530601	−	0.847622i	$-0.321966\pi$
$733$	28.7310	1.06120	0.530601	+	0.847622i	$0.321966\pi$
$734$	5.43609	0.200650
$735$	−9.94065	−0.366666
$736$	−5.83899	−0.215228
$737$	−2.48735	−0.0916226
$738$	−0.788955	−0.0290418
$739$	40.4485	1.48792	0.743961	−	0.668223i	$-0.232945\pi$
$739$	40.4485	1.48792	0.743961	+	0.668223i	$0.232945\pi$
$740$	−18.0047	−0.661866
$741$	34.8075	1.27869
$742$	−14.6503	−0.537829
$743$	13.2169	0.484882	0.242441	−	0.970166i	$-0.422052\pi$
$743$	13.2169	0.484882	0.242441	+	0.970166i	$0.422052\pi$
$744$	3.23586	0.118632
$745$	−3.26940	−0.119782
$746$	28.3123	1.03659
$747$	10.2496	0.375014
$748$	0.371807	0.0135946
$749$	34.9154	1.27578
$750$	17.9448	0.655252
$751$	−29.9097	−1.09142	−0.545710	−	0.837974i	$-0.683740\pi$
$751$	−29.9097	−1.09142	−0.545710	+	0.837974i	$0.683740\pi$
$752$	−1.35716	−0.0494906
$753$	−0.356446	−0.0129896
$754$	−16.3750	−0.596342
$755$	2.74838	0.100024
$756$	18.6538	0.678432
$757$	13.5816	0.493632	0.246816	−	0.969062i	$-0.420616\pi$
$757$	13.5816	0.493632	0.246816	+	0.969062i	$0.420616\pi$
$758$	−12.5543	−0.455994
$759$	−20.1208	−0.730337
$760$	−11.9623	−0.433918
$761$	34.3585	1.24549	0.622747	−	0.782423i	$-0.286017\pi$
$761$	34.3585	1.24549	0.622747	+	0.782423i	$0.286017\pi$
$762$	−31.3618	−1.13612
$763$	−55.6667	−2.01527
$764$	22.2609	0.805373
$765$	0.213776	0.00772910
$766$	5.28787	0.191059
$767$	−23.1177	−0.834732
$768$	−1.48674	−0.0536481
$769$	5.90087	0.212791	0.106395	−	0.994324i	$-0.466069\pi$
$769$	5.90087	0.212791	0.106395	+	0.994324i	$0.466069\pi$
$770$	−12.9513	−0.466732
$771$	36.9942	1.33231
$772$	−1.00883	−0.0363087
$773$	33.8280	1.21671	0.608355	−	0.793665i	$-0.291830\pi$
$773$	33.8280	1.21671	0.608355	+	0.793665i	$0.291830\pi$
$774$	3.32611	0.119555
$775$	4.68285	0.168213
$776$	11.4758	0.411958
$777$	52.5117	1.88385
$778$	15.1345	0.542600
$779$	−7.08195	−0.253737
$780$	−8.28827	−0.296768
$781$	−30.0735	−1.07612
$782$	0.936662	0.0334950
$783$	−27.9308	−0.998167
$784$	3.96166	0.141488
$785$	13.8065	0.492774
$786$	−2.86050	−0.102031
$787$	49.9617	1.78094	0.890471	−	0.455041i	$-0.150375\pi$
$787$	49.9617	1.78094	0.890471	+	0.455041i	$0.150375\pi$
$788$	19.5141	0.695160
$789$	−5.03296	−0.179178
$790$	19.7492	0.702646
$791$	8.64874	0.307514
$792$	1.83014	0.0650310
$793$	−35.3033	−1.25366
$794$	5.00396	0.177584
$795$	11.1031	0.393787
$796$	−24.1448	−0.855791
$797$	−38.3865	−1.35972	−0.679860	−	0.733342i	$-0.737959\pi$
$797$	−38.3865	−1.35972	−0.679860	+	0.733342i	$0.737959\pi$
$798$	34.8887	1.23505
$799$	0.217709	0.00770200
$800$	−2.15157	−0.0760694
$801$	9.79188	0.345979
$802$	−17.8825	−0.631454
$803$	27.5434	0.971984
$804$	−1.59551	−0.0562692
$805$	−32.6271	−1.14995
$806$	−7.18922	−0.253229
$807$	9.35535	0.329324
$808$	13.3207	0.468620
$809$	−24.2513	−0.852630	−0.426315	−	0.904575i	$-0.640189\pi$
$809$	−24.2513	−0.852630	−0.426315	+	0.904575i	$0.640189\pi$
$810$	−10.1394	−0.356261
$811$	11.5252	0.404705	0.202353	−	0.979313i	$-0.435141\pi$
$811$	11.5252	0.404705	0.202353	+	0.979313i	$0.435141\pi$
$812$	−16.4132	−0.575990
$813$	34.2246	1.20031
$814$	24.7261	0.866648
$815$	32.4391	1.13629
$816$	0.238495	0.00834901
$817$	29.8564	1.04454
$818$	15.5102	0.542302
$819$	−8.63527	−0.301741
$820$	1.68634	0.0588894
$821$	−23.4539	−0.818547	−0.409274	−	0.912412i	$-0.634218\pi$
$821$	−23.4539	−0.818547	−0.409274	+	0.912412i	$0.634218\pi$
$822$	−12.6953	−0.442801
$823$	−15.5346	−0.541502	−0.270751	−	0.962649i	$-0.587272\pi$
$823$	−15.5346	−0.541502	−0.270751	+	0.962649i	$0.587272\pi$
$824$	14.2317	0.495786
$825$	−7.41416	−0.258128
$826$	−23.1716	−0.806244
$827$	−9.69671	−0.337188	−0.168594	−	0.985686i	$-0.553923\pi$
$827$	−9.69671	−0.337188	−0.168594	+	0.985686i	$0.553923\pi$
$828$	4.61051	0.160226
$829$	14.0499	0.487975	0.243987	−	0.969778i	$-0.421544\pi$
$829$	14.0499	0.487975	0.243987	+	0.969778i	$0.421544\pi$
$830$	−21.9078	−0.760432
$831$	41.9672	1.45583
$832$	3.30314	0.114516
$833$	−0.635510	−0.0220191
$834$	2.78985	0.0966047
$835$	−17.2598	−0.597299
$836$	16.4280	0.568173
$837$	−12.2626	−0.423859
$838$	9.71888	0.335733
$839$	10.0400	0.346620	0.173310	−	0.984867i	$-0.444554\pi$
$839$	10.0400	0.346620	0.173310	+	0.984867i	$0.444554\pi$
$840$	−8.30760	−0.286640
$841$	−4.42407	−0.152554
$842$	−7.27171	−0.250600
$843$	−3.87422	−0.133435
$844$	2.78620	0.0959048
$845$	−3.52617	−0.121304
$846$	1.07163	0.0368432
$847$	−18.6331	−0.640240
$848$	−4.42494	−0.151953
$849$	2.62761	0.0901794
$850$	0.345144	0.0118383
$851$	62.2903	2.13529
$852$	−19.2907	−0.660887
$853$	−25.7210	−0.880670	−0.440335	−	0.897833i	$-0.645140\pi$
$853$	−25.7210	−0.880670	−0.440335	+	0.897833i	$0.645140\pi$
$854$	−35.3857	−1.21087
$855$	9.44552	0.323030
$856$	10.5458	0.360448
$857$	2.76797	0.0945522	0.0472761	−	0.998882i	$-0.484946\pi$
$857$	2.76797	0.0945522	0.0472761	+	0.998882i	$0.484946\pi$
$858$	11.3824	0.388588
$859$	16.5569	0.564916	0.282458	−	0.959280i	$-0.408850\pi$
$859$	16.5569	0.564916	0.282458	+	0.959280i	$0.408850\pi$
$860$	−7.10932	−0.242426
$861$	−4.91829	−0.167615
$862$	34.3279	1.16921
$863$	10.0848	0.343292	0.171646	−	0.985159i	$-0.445092\pi$
$863$	10.0848	0.343292	0.171646	+	0.985159i	$0.445092\pi$
$864$	5.63416	0.191678
$865$	37.6275	1.27937
$866$	−30.9705	−1.05242
$867$	25.2363	0.857070
$868$	−7.20599	−0.244587
$869$	−27.1219	−0.920046
$870$	12.4392	0.421729
$871$	3.54479	0.120111
$872$	−16.8135	−0.569376
$873$	−9.06140	−0.306682
$874$	41.3856	1.39989
$875$	−39.9616	−1.35095
$876$	17.6677	0.596936
$877$	−1.96376	−0.0663114	−0.0331557	−	0.999450i	$-0.510556\pi$
$877$	−1.96376	−0.0663114	−0.0331557	+	0.999450i	$0.510556\pi$
$878$	−33.5538	−1.13239
$879$	−23.4241	−0.790075
$880$	−3.91178	−0.131866
$881$	6.77880	0.228384	0.114192	−	0.993459i	$-0.463572\pi$
$881$	6.77880	0.228384	0.114192	+	0.993459i	$0.463572\pi$
$882$	−3.12815	−0.105330
$883$	−32.8470	−1.10539	−0.552694	−	0.833384i	$-0.686400\pi$
$883$	−32.8470	−1.10539	−0.552694	+	0.833384i	$0.686400\pi$
$884$	−0.529873	−0.0178216
$885$	17.5613	0.590316
$886$	6.40125	0.215054
$887$	16.1701	0.542940	0.271470	−	0.962447i	$-0.412490\pi$
$887$	16.1701	0.542940	0.271470	+	0.962447i	$0.412490\pi$
$888$	15.8605	0.532245
$889$	69.8401	2.34236
$890$	−20.9295	−0.701557
$891$	13.9245	0.466489
$892$	13.0071	0.435511
$893$	9.61931	0.321898
$894$	2.88005	0.0963233
$895$	−41.9561	−1.40244
$896$	3.31084	0.110607
$897$	28.6747	0.957420
$898$	−4.36346	−0.145611
$899$	10.7897	0.359857
$900$	1.69889	0.0566298
$901$	0.709828	0.0236478
$902$	−2.31586	−0.0771098
$903$	20.7347	0.690008
$904$	2.61225	0.0868821
$905$	21.1279	0.702315
$906$	−2.42107	−0.0804348
$907$	7.29410	0.242197	0.121098	−	0.992641i	$-0.461358\pi$
$907$	7.29410	0.242197	0.121098	+	0.992641i	$0.461358\pi$
$908$	−14.7546	−0.489649
$909$	−10.5181	−0.348864
$910$	18.4573	0.611853
$911$	32.5861	1.07963	0.539813	−	0.841785i	$-0.318495\pi$
$911$	32.5861	1.07963	0.539813	+	0.841785i	$0.318495\pi$
$912$	10.5377	0.348939
$913$	30.0863	0.995711
$914$	−17.3651	−0.574387
$915$	26.8180	0.886577
$916$	−16.9426	−0.559798
$917$	6.37009	0.210359
$918$	−0.903804	−0.0298300
$919$	−9.08716	−0.299758	−0.149879	−	0.988704i	$-0.547888\pi$
$919$	−9.08716	−0.299758	−0.149879	+	0.988704i	$0.547888\pi$
$920$	−9.85463	−0.324898
$921$	−25.8381	−0.851394
$922$	−17.0327	−0.560943
$923$	42.8587	1.41071
$924$	11.4089	0.375326
$925$	22.9529	0.754688
$926$	6.38016	0.209665
$927$	−11.2375	−0.369087
$928$	−4.95741	−0.162735
$929$	33.5709	1.10142	0.550712	−	0.834695i	$-0.314356\pi$
$929$	33.5709	1.10142	0.550712	+	0.834695i	$0.314356\pi$
$930$	5.46126	0.179082
$931$	−28.0795	−0.920267
$932$	20.3168	0.665500
$933$	3.67858	0.120431
$934$	41.7268	1.36534
$935$	0.627509	0.0205218
$936$	−2.60818	−0.0852510
$937$	−22.3052	−0.728678	−0.364339	−	0.931266i	$-0.618705\pi$
$937$	−22.3052	−0.728678	−0.364339	+	0.931266i	$0.618705\pi$
$938$	3.55306	0.116012
$939$	−15.8802	−0.518230
$940$	−2.29052	−0.0747086
$941$	−24.7125	−0.805603	−0.402802	−	0.915287i	$-0.631964\pi$
$941$	−24.7125	−0.805603	−0.402802	+	0.915287i	$0.631964\pi$
$942$	−12.1623	−0.396268
$943$	−5.83416	−0.189987
$944$	−6.99872	−0.227789
$945$	31.4826	1.02413
$946$	9.76332	0.317433
$947$	−21.6139	−0.702357	−0.351178	−	0.936309i	$-0.614219\pi$
$947$	−21.6139	−0.702357	−0.351178	+	0.936309i	$0.614219\pi$
$948$	−17.3973	−0.565038
$949$	−39.2528	−1.27420
$950$	15.2499	0.494772
$951$	27.8193	0.902103
$952$	−0.531109	−0.0172133
$953$	6.82598	0.221115	0.110558	−	0.993870i	$-0.464736\pi$
$953$	6.82598	0.221115	0.110558	+	0.993870i	$0.464736\pi$
$954$	3.49397	0.113121
$955$	37.5705	1.21575
$956$	14.3469	0.464012
$957$	−17.0829	−0.552212
$958$	−20.4878	−0.661932
$959$	28.2714	0.912932
$960$	−2.50921	−0.0809845
$961$	−26.2629	−0.847191
$962$	−35.2379	−1.13611
$963$	−8.32704	−0.268335
$964$	−13.6488	−0.439598
$965$	−1.70264	−0.0548098
$966$	28.7416	0.924745
$967$	26.1463	0.840809	0.420405	−	0.907337i	$-0.361888\pi$
$967$	26.1463	0.840809	0.420405	+	0.907337i	$0.361888\pi$
$968$	−5.62790	−0.180888
$969$	−1.69041	−0.0543038
$970$	19.3681	0.621872
$971$	17.8019	0.571290	0.285645	−	0.958335i	$-0.407792\pi$
$971$	17.8019	0.571290	0.285645	+	0.958335i	$0.407792\pi$
$972$	−7.97059	−0.255657
$973$	−6.21276	−0.199172
$974$	−5.52603	−0.177065
$975$	10.5661	0.338387
$976$	−10.6878	−0.342109
$977$	17.2501	0.551879	0.275939	−	0.961175i	$-0.411011\pi$
$977$	17.2501	0.551879	0.275939	+	0.961175i	$0.411011\pi$
$978$	−28.5760	−0.913759
$979$	28.7427	0.918619
$980$	6.68621	0.213583
$981$	13.2760	0.423872
$982$	−16.5457	−0.527996
$983$	−2.13626	−0.0681362	−0.0340681	−	0.999420i	$-0.510846\pi$
$983$	−2.13626	−0.0681362	−0.0340681	+	0.999420i	$0.510846\pi$
$984$	−1.48551	−0.0473563
$985$	32.9345	1.04938
$986$	0.795244	0.0253257
$987$	6.68043	0.212641
$988$	−23.4120	−0.744835
$989$	24.5959	0.782104
$990$	3.08877	0.0981677
$991$	−12.9047	−0.409933	−0.204966	−	0.978769i	$-0.565708\pi$
$991$	−12.9047	−0.409933	−0.204966	+	0.978769i	$0.565708\pi$
$992$	−2.17648	−0.0691034
$993$	−15.9379	−0.505774
$994$	42.9586	1.36257
$995$	−40.7500	−1.29186
$996$	19.2989	0.611508
$997$	−19.5128	−0.617975	−0.308988	−	0.951066i	$-0.599990\pi$
$997$	−19.5128	−0.617975	−0.308988	+	0.951066i	$0.599990\pi$
$998$	6.78916	0.214907
$999$	−60.1052	−1.90164

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.a.1.16	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.a.1.16	✓	47	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.48674 q^{3} +1.00000 q^{4} +1.68773 q^{5} -1.48674 q^{6} +3.31084 q^{7} +1.00000 q^{8} -0.789607 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.48674 q^{3} +1.00000 q^{4} +1.68773 q^{5} -1.48674 q^{6} +3.31084 q^{7} +1.00000 q^{8} -0.789607 q^{9} +1.68773 q^{10} -2.31778 q^{11} -1.48674 q^{12} +3.30314 q^{13} +3.31084 q^{14} -2.50921 q^{15} +1.00000 q^{16} -0.160415 q^{17} -0.789607 q^{18} -7.08781 q^{19} +1.68773 q^{20} -4.92235 q^{21} -2.31778 q^{22} -5.83899 q^{23} -1.48674 q^{24} -2.15157 q^{25} +3.30314 q^{26} +5.63416 q^{27} +3.31084 q^{28} -4.95741 q^{29} -2.50921 q^{30} -2.17648 q^{31} +1.00000 q^{32} +3.44593 q^{33} -0.160415 q^{34} +5.58780 q^{35} -0.789607 q^{36} -10.6680 q^{37} -7.08781 q^{38} -4.91090 q^{39} +1.68773 q^{40} +0.999174 q^{41} -4.92235 q^{42} -4.21236 q^{43} -2.31778 q^{44} -1.33264 q^{45} -5.83899 q^{46} -1.35716 q^{47} -1.48674 q^{48} +3.96166 q^{49} -2.15157 q^{50} +0.238495 q^{51} +3.30314 q^{52} -4.42494 q^{53} +5.63416 q^{54} -3.91178 q^{55} +3.31084 q^{56} +10.5377 q^{57} -4.95741 q^{58} -6.99872 q^{59} -2.50921 q^{60} -10.6878 q^{61} -2.17648 q^{62} -2.61426 q^{63} +1.00000 q^{64} +5.57480 q^{65} +3.44593 q^{66} +1.07316 q^{67} -0.160415 q^{68} +8.68105 q^{69} +5.58780 q^{70} +12.9752 q^{71} -0.789607 q^{72} -11.8835 q^{73} -10.6680 q^{74} +3.19882 q^{75} -7.08781 q^{76} -7.67379 q^{77} -4.91090 q^{78} +11.7017 q^{79} +1.68773 q^{80} -6.00770 q^{81} +0.999174 q^{82} -12.9807 q^{83} -4.92235 q^{84} -0.270737 q^{85} -4.21236 q^{86} +7.37038 q^{87} -2.31778 q^{88} -12.4010 q^{89} -1.33264 q^{90} +10.9362 q^{91} -5.83899 q^{92} +3.23586 q^{93} -1.35716 q^{94} -11.9623 q^{95} -1.48674 q^{96} +11.4758 q^{97} +3.96166 q^{98} +1.83014 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9	\( 47 q + 47 q^{2} - 13 q^{3} + 47 q^{4} - 14 q^{5} - 13 q^{6} - 17 q^{7} + 47 q^{8} + 12 q^{9} - 14 q^{10} - 30 q^{11} - 13 q^{12} - 39 q^{13} - 17 q^{14} - 18 q^{15} + 47 q^{16} - 26 q^{17} + 12 q^{18} - 23 q^{19} - 14 q^{20} - 39 q^{21} - 30 q^{22} - 25 q^{23} - 13 q^{24} - 19 q^{25} - 39 q^{26} - 46 q^{27} - 17 q^{28} - 53 q^{29} - 18 q^{30} - 23 q^{31} + 47 q^{32} - 26 q^{33} - 26 q^{34} - 31 q^{35} + 12 q^{36} - 83 q^{37} - 23 q^{38} - 9 q^{39} - 14 q^{40} - 48 q^{41} - 39 q^{42} - 78 q^{43} - 30 q^{44} - 27 q^{45} - 25 q^{46} - 15 q^{47} - 13 q^{48} - 12 q^{49} - 19 q^{50} - 47 q^{51} - 39 q^{52} - 76 q^{53} - 46 q^{54} - 39 q^{55} - 17 q^{56} - 44 q^{57} - 53 q^{58} - 33 q^{59} - 18 q^{60} - 33 q^{61} - 23 q^{62} - 7 q^{63} + 47 q^{64} - 67 q^{65} - 26 q^{66} - 85 q^{67} - 26 q^{68} - 33 q^{69} - 31 q^{70} - 17 q^{71} + 12 q^{72} - 59 q^{73} - 83 q^{74} - 21 q^{75} - 23 q^{76} - 59 q^{77} - 9 q^{78} - 49 q^{79} - 14 q^{80} - 41 q^{81} - 48 q^{82} - 30 q^{83} - 39 q^{84} - 84 q^{85} - 78 q^{86} + 9 q^{87} - 30 q^{88} - 50 q^{89} - 27 q^{90} - 42 q^{91} - 25 q^{92} - 43 q^{93} - 15 q^{94} + 8 q^{95} - 13 q^{96} - 49 q^{97} - 12 q^{98} - 49 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 - 13 * q^3 + 47 * q^4 - 14 * q^5 - 13 * q^6 - 17 * q^7 + 47 * q^8 + 12 * q^9 - 14 * q^10 - 30 * q^11 - 13 * q^12 - 39 * q^13 - 17 * q^14 - 18 * q^15 + 47 * q^16 - 26 * q^17 + 12 * q^18 - 23 * q^19 - 14 * q^20 - 39 * q^21 - 30 * q^22 - 25 * q^23 - 13 * q^24 - 19 * q^25 - 39 * q^26 - 46 * q^27 - 17 * q^28 - 53 * q^29 - 18 * q^30 - 23 * q^31 + 47 * q^32 - 26 * q^33 - 26 * q^34 - 31 * q^35 + 12 * q^36 - 83 * q^37 - 23 * q^38 - 9 * q^39 - 14 * q^40 - 48 * q^41 - 39 * q^42 - 78 * q^43 - 30 * q^44 - 27 * q^45 - 25 * q^46 - 15 * q^47 - 13 * q^48 - 12 * q^49 - 19 * q^50 - 47 * q^51 - 39 * q^52 - 76 * q^53 - 46 * q^54 - 39 * q^55 - 17 * q^56 - 44 * q^57 - 53 * q^58 - 33 * q^59 - 18 * q^60 - 33 * q^61 - 23 * q^62 - 7 * q^63 + 47 * q^64 - 67 * q^65 - 26 * q^66 - 85 * q^67 - 26 * q^68 - 33 * q^69 - 31 * q^70 - 17 * q^71 + 12 * q^72 - 59 * q^73 - 83 * q^74 - 21 * q^75 - 23 * q^76 - 59 * q^77 - 9 * q^78 - 49 * q^79 - 14 * q^80 - 41 * q^81 - 48 * q^82 - 30 * q^83 - 39 * q^84 - 84 * q^85 - 78 * q^86 + 9 * q^87 - 30 * q^88 - 50 * q^89 - 27 * q^90 - 42 * q^91 - 25 * q^92 - 43 * q^93 - 15 * q^94 + 8 * q^95 - 13 * q^96 - 49 * q^97 - 12 * q^98 - 49 * q^99

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