LMFDB - Embedded newform 8026.2.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, 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("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.90629 q^{3} +1.00000 q^{4} -3.44864 q^{5} +1.90629 q^{6} +0.576337 q^{7} -1.00000 q^{8} +0.633932 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.90629 q^{3} +1.00000 q^{4} -3.44864 q^{5} +1.90629 q^{6} +0.576337 q^{7} -1.00000 q^{8} +0.633932 q^{9} +3.44864 q^{10} -2.52760 q^{11} -1.90629 q^{12} -3.72282 q^{13} -0.576337 q^{14} +6.57409 q^{15} +1.00000 q^{16} -0.135390 q^{17} -0.633932 q^{18} +6.77310 q^{19} -3.44864 q^{20} -1.09866 q^{21} +2.52760 q^{22} +6.42164 q^{23} +1.90629 q^{24} +6.89310 q^{25} +3.72282 q^{26} +4.51041 q^{27} +0.576337 q^{28} +3.64156 q^{29} -6.57409 q^{30} -3.48116 q^{31} -1.00000 q^{32} +4.81834 q^{33} +0.135390 q^{34} -1.98758 q^{35} +0.633932 q^{36} -6.73560 q^{37} -6.77310 q^{38} +7.09676 q^{39} +3.44864 q^{40} +6.30497 q^{41} +1.09866 q^{42} -9.94360 q^{43} -2.52760 q^{44} -2.18620 q^{45} -6.42164 q^{46} -10.9283 q^{47} -1.90629 q^{48} -6.66784 q^{49} -6.89310 q^{50} +0.258093 q^{51} -3.72282 q^{52} +7.21285 q^{53} -4.51041 q^{54} +8.71679 q^{55} -0.576337 q^{56} -12.9115 q^{57} -3.64156 q^{58} +9.89885 q^{59} +6.57409 q^{60} +4.83709 q^{61} +3.48116 q^{62} +0.365358 q^{63} +1.00000 q^{64} +12.8386 q^{65} -4.81834 q^{66} -8.17945 q^{67} -0.135390 q^{68} -12.2415 q^{69} +1.98758 q^{70} -6.36792 q^{71} -0.633932 q^{72} -15.5985 q^{73} +6.73560 q^{74} -13.1402 q^{75} +6.77310 q^{76} -1.45675 q^{77} -7.09676 q^{78} -9.18127 q^{79} -3.44864 q^{80} -10.4999 q^{81} -6.30497 q^{82} -13.4764 q^{83} -1.09866 q^{84} +0.466912 q^{85} +9.94360 q^{86} -6.94185 q^{87} +2.52760 q^{88} -9.66471 q^{89} +2.18620 q^{90} -2.14560 q^{91} +6.42164 q^{92} +6.63609 q^{93} +10.9283 q^{94} -23.3580 q^{95} +1.90629 q^{96} +8.55243 q^{97} +6.66784 q^{98} -1.60233 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * 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
$3$	−1.90629	−1.10060	−0.550298	−	0.834968i	$-0.685486\pi$
$3$	−1.90629	−1.10060	−0.550298	+	0.834968i	$0.685486\pi$
$4$	1.00000	0.500000
$5$	−3.44864	−1.54228	−0.771139	−	0.636667i	$-0.780313\pi$
$5$	−3.44864	−1.54228	−0.771139	+	0.636667i	$0.780313\pi$
$6$	1.90629	0.778239
$7$	0.576337	0.217835	0.108917	−	0.994051i	$-0.465262\pi$
$7$	0.576337	0.217835	0.108917	+	0.994051i	$0.465262\pi$
$8$	−1.00000	−0.353553
$9$	0.633932	0.211311
$10$	3.44864	1.09056
$11$	−2.52760	−0.762101	−0.381051	−	0.924554i	$-0.624438\pi$
$11$	−2.52760	−0.762101	−0.381051	+	0.924554i	$0.624438\pi$
$12$	−1.90629	−0.550298
$13$	−3.72282	−1.03252	−0.516262	−	0.856431i	$-0.672677\pi$
$13$	−3.72282	−1.03252	−0.516262	+	0.856431i	$0.672677\pi$
$14$	−0.576337	−0.154032
$15$	6.57409	1.69742
$16$	1.00000	0.250000
$17$	−0.135390	−0.0328369	−0.0164185	−	0.999865i	$-0.505226\pi$
$17$	−0.135390	−0.0328369	−0.0164185	+	0.999865i	$0.505226\pi$
$18$	−0.633932	−0.149419
$19$	6.77310	1.55386	0.776928	−	0.629589i	$-0.216777\pi$
$19$	6.77310	1.55386	0.776928	+	0.629589i	$0.216777\pi$
$20$	−3.44864	−0.771139
$21$	−1.09866	−0.239748
$22$	2.52760	0.538887
$23$	6.42164	1.33900	0.669502	−	0.742810i	$-0.266507\pi$
$23$	6.42164	1.33900	0.669502	+	0.742810i	$0.266507\pi$
$24$	1.90629	0.389119
$25$	6.89310	1.37862
$26$	3.72282	0.730105
$27$	4.51041	0.868028
$28$	0.576337	0.108917
$29$	3.64156	0.676220	0.338110	−	0.941107i	$-0.390212\pi$
$29$	3.64156	0.676220	0.338110	+	0.941107i	$0.390212\pi$
$30$	−6.57409	−1.20026
$31$	−3.48116	−0.625235	−0.312617	−	0.949879i	$-0.601206\pi$
$31$	−3.48116	−0.625235	−0.312617	+	0.949879i	$0.601206\pi$
$32$	−1.00000	−0.176777
$33$	4.81834	0.838765
$34$	0.135390	0.0232192
$35$	−1.98758	−0.335962
$36$	0.633932	0.105655
$37$	−6.73560	−1.10733	−0.553663	−	0.832741i	$-0.686770\pi$
$37$	−6.73560	−1.10733	−0.553663	+	0.832741i	$0.686770\pi$
$38$	−6.77310	−1.09874
$39$	7.09676	1.13639
$40$	3.44864	0.545278
$41$	6.30497	0.984671	0.492335	−	0.870406i	$-0.336143\pi$
$41$	6.30497	0.984671	0.492335	+	0.870406i	$0.336143\pi$
$42$	1.09866	0.169527
$43$	−9.94360	−1.51638	−0.758192	−	0.652031i	$-0.773917\pi$
$43$	−9.94360	−1.51638	−0.758192	+	0.652031i	$0.773917\pi$
$44$	−2.52760	−0.381051
$45$	−2.18620	−0.325899
$46$	−6.42164	−0.946820
$47$	−10.9283	−1.59405	−0.797025	−	0.603947i	$-0.793594\pi$
$47$	−10.9283	−1.59405	−0.797025	+	0.603947i	$0.793594\pi$
$48$	−1.90629	−0.275149
$49$	−6.66784	−0.952548
$50$	−6.89310	−0.974832
$51$	0.258093	0.0361402
$52$	−3.72282	−0.516262
$53$	7.21285	0.990761	0.495381	−	0.868676i	$-0.335029\pi$
$53$	7.21285	0.990761	0.495381	+	0.868676i	$0.335029\pi$
$54$	−4.51041	−0.613789
$55$	8.71679	1.17537
$56$	−0.576337	−0.0770162
$57$	−12.9115	−1.71017
$58$	−3.64156	−0.478160
$59$	9.89885	1.28872	0.644360	−	0.764722i	$-0.277124\pi$
$59$	9.89885	1.28872	0.644360	+	0.764722i	$0.277124\pi$
$60$	6.57409	0.848712
$61$	4.83709	0.619327	0.309663	−	0.950846i	$-0.399784\pi$
$61$	4.83709	0.619327	0.309663	+	0.950846i	$0.399784\pi$
$62$	3.48116	0.442108
$63$	0.365358	0.0460308
$64$	1.00000	0.125000
$65$	12.8386	1.59244
$66$	−4.81834	−0.593097
$67$	−8.17945	−0.999278	−0.499639	−	0.866234i	$-0.666534\pi$
$67$	−8.17945	−0.999278	−0.499639	+	0.866234i	$0.666534\pi$
$68$	−0.135390	−0.0164185
$69$	−12.2415	−1.47370
$70$	1.98758	0.237561
$71$	−6.36792	−0.755733	−0.377867	−	0.925860i	$-0.623342\pi$
$71$	−6.36792	−0.755733	−0.377867	+	0.925860i	$0.623342\pi$
$72$	−0.633932	−0.0747095
$73$	−15.5985	−1.82567	−0.912833	−	0.408333i	$-0.866110\pi$
$73$	−15.5985	−1.82567	−0.912833	+	0.408333i	$0.866110\pi$
$74$	6.73560	0.782997
$75$	−13.1402	−1.51730
$76$	6.77310	0.776928
$77$	−1.45675	−0.166012
$78$	−7.09676	−0.803550
$79$	−9.18127	−1.03297	−0.516487	−	0.856295i	$-0.672761\pi$
$79$	−9.18127	−1.03297	−0.516487	+	0.856295i	$0.672761\pi$
$80$	−3.44864	−0.385569
$81$	−10.4999	−1.16666
$82$	−6.30497	−0.696268
$83$	−13.4764	−1.47923	−0.739613	−	0.673032i	$-0.764992\pi$
$83$	−13.4764	−1.47923	−0.739613	+	0.673032i	$0.764992\pi$
$84$	−1.09866	−0.119874
$85$	0.466912	0.0506437
$86$	9.94360	1.07225
$87$	−6.94185	−0.744244
$88$	2.52760	0.269444
$89$	−9.66471	−1.02446	−0.512229	−	0.858849i	$-0.671180\pi$
$89$	−9.66471	−1.02446	−0.512229	+	0.858849i	$0.671180\pi$
$90$	2.18620	0.230446
$91$	−2.14560	−0.224920
$92$	6.42164	0.669502
$93$	6.63609	0.688131
$94$	10.9283	1.12716
$95$	−23.3580	−2.39648
$96$	1.90629	0.194560
$97$	8.55243	0.868368	0.434184	−	0.900824i	$-0.357037\pi$
$97$	8.55243	0.868368	0.434184	+	0.900824i	$0.357037\pi$
$98$	6.66784	0.673553
$99$	−1.60233	−0.161040
$100$	6.89310	0.689310
$101$	14.2863	1.42154	0.710768	−	0.703426i	$-0.248347\pi$
$101$	14.2863	1.42154	0.710768	+	0.703426i	$0.248347\pi$
$102$	−0.258093	−0.0255550
$103$	−4.93742	−0.486498	−0.243249	−	0.969964i	$-0.578213\pi$
$103$	−4.93742	−0.486498	−0.243249	+	0.969964i	$0.578213\pi$
$104$	3.72282	0.365052
$105$	3.78889	0.369758
$106$	−7.21285	−0.700574
$107$	14.1760	1.37045	0.685225	−	0.728331i	$-0.259704\pi$
$107$	14.1760	1.37045	0.685225	+	0.728331i	$0.259704\pi$
$108$	4.51041	0.434014
$109$	1.52598	0.146162	0.0730810	−	0.997326i	$-0.476717\pi$
$109$	1.52598	0.146162	0.0730810	+	0.997326i	$0.476717\pi$
$110$	−8.71679	−0.831113
$111$	12.8400	1.21872
$112$	0.576337	0.0544587
$113$	−9.45088	−0.889064	−0.444532	−	0.895763i	$-0.646630\pi$
$113$	−9.45088	−0.889064	−0.444532	+	0.895763i	$0.646630\pi$
$114$	12.9115	1.20927
$115$	−22.1459	−2.06512
$116$	3.64156	0.338110
$117$	−2.36001	−0.218183
$118$	−9.89885	−0.911263
$119$	−0.0780303	−0.00715303
$120$	−6.57409	−0.600130
$121$	−4.61122	−0.419202
$122$	−4.83709	−0.437930
$123$	−12.0191	−1.08372
$124$	−3.48116	−0.312617
$125$	−6.52862	−0.583938
$126$	−0.365358	−0.0325487
$127$	−2.57457	−0.228457	−0.114228	−	0.993455i	$-0.536440\pi$
$127$	−2.57457	−0.228457	−0.114228	+	0.993455i	$0.536440\pi$
$128$	−1.00000	−0.0883883
$129$	18.9554	1.66893
$130$	−12.8386	−1.12602
$131$	−13.0315	−1.13857	−0.569284	−	0.822141i	$-0.692780\pi$
$131$	−13.0315	−1.13857	−0.569284	+	0.822141i	$0.692780\pi$
$132$	4.81834	0.419383
$133$	3.90359	0.338484
$134$	8.17945	0.706597
$135$	−15.5548	−1.33874
$136$	0.135390	0.0116096
$137$	−22.6525	−1.93533	−0.967667	−	0.252231i	$-0.918836\pi$
$137$	−22.6525	−1.93533	−0.967667	+	0.252231i	$0.918836\pi$
$138$	12.2415	1.04207
$139$	−1.66687	−0.141382	−0.0706911	−	0.997498i	$-0.522520\pi$
$139$	−1.66687	−0.141382	−0.0706911	+	0.997498i	$0.522520\pi$
$140$	−1.98758	−0.167981
$141$	20.8324	1.75440
$142$	6.36792	0.534384
$143$	9.40981	0.786888
$144$	0.633932	0.0528276
$145$	−12.5584	−1.04292
$146$	15.5985	1.29094
$147$	12.7108	1.04837
$148$	−6.73560	−0.553663
$149$	22.7885	1.86691	0.933453	−	0.358699i	$-0.116780\pi$
$149$	22.7885	1.86691	0.933453	+	0.358699i	$0.116780\pi$
$150$	13.1402	1.07290
$151$	1.41340	0.115021	0.0575104	−	0.998345i	$-0.481684\pi$
$151$	1.41340	0.115021	0.0575104	+	0.998345i	$0.481684\pi$
$152$	−6.77310	−0.549371
$153$	−0.0858281	−0.00693879
$154$	1.45675	0.117388
$155$	12.0053	0.964286
$156$	7.09676	0.568196
$157$	5.98332	0.477521	0.238760	−	0.971079i	$-0.423259\pi$
$157$	5.98332	0.477521	0.238760	+	0.971079i	$0.423259\pi$
$158$	9.18127	0.730423
$159$	−13.7498	−1.09043
$160$	3.44864	0.272639
$161$	3.70103	0.291682
$162$	10.4999	0.824952
$163$	−6.36633	−0.498650	−0.249325	−	0.968420i	$-0.580209\pi$
$163$	−6.36633	−0.498650	−0.249325	+	0.968420i	$0.580209\pi$
$164$	6.30497	0.492335
$165$	−16.6167	−1.29361
$166$	13.4764	1.04597
$167$	13.7345	1.06280	0.531402	−	0.847120i	$-0.321665\pi$
$167$	13.7345	1.06280	0.531402	+	0.847120i	$0.321665\pi$
$168$	1.09866	0.0847637
$169$	0.859371	0.0661055
$170$	−0.466912	−0.0358105
$171$	4.29368	0.328346
$172$	−9.94360	−0.758192
$173$	6.27011	0.476708	0.238354	−	0.971178i	$-0.423392\pi$
$173$	6.27011	0.476708	0.238354	+	0.971178i	$0.423392\pi$
$174$	6.94185	0.526260
$175$	3.97275	0.300311
$176$	−2.52760	−0.190525
$177$	−18.8700	−1.41836
$178$	9.66471	0.724401
$179$	−5.74419	−0.429341	−0.214671	−	0.976687i	$-0.568868\pi$
$179$	−5.74419	−0.429341	−0.214671	+	0.976687i	$0.568868\pi$
$180$	−2.18620	−0.162950
$181$	0.803801	0.0597461	0.0298730	−	0.999554i	$-0.490490\pi$
$181$	0.803801	0.0597461	0.0298730	+	0.999554i	$0.490490\pi$
$182$	2.14560	0.159042
$183$	−9.22089	−0.681628
$184$	−6.42164	−0.473410
$185$	23.2286	1.70780
$186$	−6.63609	−0.486582
$187$	0.342213	0.0250251
$188$	−10.9283	−0.797025
$189$	2.59951	0.189087
$190$	23.3580	1.69457
$191$	9.23399	0.668148	0.334074	−	0.942547i	$-0.391576\pi$
$191$	9.23399	0.668148	0.334074	+	0.942547i	$0.391576\pi$
$192$	−1.90629	−0.137574
$193$	16.6869	1.20115	0.600576	−	0.799568i	$-0.294938\pi$
$193$	16.6869	1.20115	0.600576	+	0.799568i	$0.294938\pi$
$194$	−8.55243	−0.614029
$195$	−24.4742	−1.75263
$196$	−6.66784	−0.476274
$197$	13.2031	0.940684	0.470342	−	0.882484i	$-0.344131\pi$
$197$	13.2031	0.940684	0.470342	+	0.882484i	$0.344131\pi$
$198$	1.60233	0.113872
$199$	−14.2637	−1.01113	−0.505563	−	0.862790i	$-0.668715\pi$
$199$	−14.2637	−1.01113	−0.505563	+	0.862790i	$0.668715\pi$
$200$	−6.89310	−0.487416
$201$	15.5924	1.09980
$202$	−14.2863	−1.00518
$203$	2.09876	0.147304
$204$	0.258093	0.0180701
$205$	−21.7436	−1.51864
$206$	4.93742	0.344006
$207$	4.07088	0.282946
$208$	−3.72282	−0.258131
$209$	−17.1197	−1.18420
$210$	−3.78889	−0.261458
$211$	−22.5826	−1.55465	−0.777325	−	0.629099i	$-0.783424\pi$
$211$	−22.5826	−1.55465	−0.777325	+	0.629099i	$0.783424\pi$
$212$	7.21285	0.495381
$213$	12.1391	0.831756
$214$	−14.1760	−0.969055
$215$	34.2919	2.33869
$216$	−4.51041	−0.306894
$217$	−2.00632	−0.136198
$218$	−1.52598	−0.103352
$219$	29.7352	2.00932
$220$	8.71679	0.587686
$221$	0.504033	0.0339049
$222$	−12.8400	−0.861763
$223$	−4.37688	−0.293097	−0.146549	−	0.989203i	$-0.546816\pi$
$223$	−4.37688	−0.293097	−0.146549	+	0.989203i	$0.546816\pi$
$224$	−0.576337	−0.0385081
$225$	4.36976	0.291317
$226$	9.45088	0.628663
$227$	9.73531	0.646155	0.323078	−	0.946372i	$-0.395283\pi$
$227$	9.73531	0.646155	0.323078	+	0.946372i	$0.395283\pi$
$228$	−12.9115	−0.855084
$229$	−8.75050	−0.578249	−0.289125	−	0.957291i	$-0.593364\pi$
$229$	−8.75050	−0.578249	−0.289125	+	0.957291i	$0.593364\pi$
$230$	22.1459	1.46026
$231$	2.77699	0.182712
$232$	−3.64156	−0.239080
$233$	−18.2084	−1.19287	−0.596435	−	0.802661i	$-0.703417\pi$
$233$	−18.2084	−1.19287	−0.596435	+	0.802661i	$0.703417\pi$
$234$	2.36001	0.154279
$235$	37.6876	2.45847
$236$	9.89885	0.644360
$237$	17.5021	1.13689
$238$	0.0780303	0.00505795
$239$	−1.38867	−0.0898254	−0.0449127	−	0.998991i	$-0.514301\pi$
$239$	−1.38867	−0.0898254	−0.0449127	+	0.998991i	$0.514301\pi$
$240$	6.57409	0.424356
$241$	25.2339	1.62546	0.812729	−	0.582642i	$-0.197981\pi$
$241$	25.2339	1.62546	0.812729	+	0.582642i	$0.197981\pi$
$242$	4.61122	0.296420
$243$	6.48466	0.415991
$244$	4.83709	0.309663
$245$	22.9950	1.46909
$246$	12.0191	0.766309
$247$	−25.2150	−1.60439
$248$	3.48116	0.221054
$249$	25.6899	1.62803
$250$	6.52862	0.412906
$251$	−12.5201	−0.790263	−0.395132	−	0.918624i	$-0.629301\pi$
$251$	−12.5201	−0.790263	−0.395132	+	0.918624i	$0.629301\pi$
$252$	0.365358	0.0230154
$253$	−16.2314	−1.02046
$254$	2.57457	0.161543
$255$	−0.890068	−0.0557382
$256$	1.00000	0.0625000
$257$	−11.3037	−0.705103	−0.352552	−	0.935792i	$-0.614686\pi$
$257$	−11.3037	−0.705103	−0.352552	+	0.935792i	$0.614686\pi$
$258$	−18.9554	−1.18011
$259$	−3.88197	−0.241214
$260$	12.8386	0.796219
$261$	2.30850	0.142892
$262$	13.0315	0.805089
$263$	−1.84795	−0.113949	−0.0569747	−	0.998376i	$-0.518145\pi$
$263$	−1.84795	−0.113949	−0.0569747	+	0.998376i	$0.518145\pi$
$264$	−4.81834	−0.296548
$265$	−24.8745	−1.52803
$266$	−3.90359	−0.239344
$267$	18.4237	1.12751
$268$	−8.17945	−0.499639
$269$	−29.0587	−1.77174	−0.885870	−	0.463934i	$-0.846437\pi$
$269$	−29.0587	−1.77174	−0.885870	+	0.463934i	$0.846437\pi$
$270$	15.5548	0.946632
$271$	−31.2094	−1.89584	−0.947918	−	0.318516i	$-0.896816\pi$
$271$	−31.2094	−1.89584	−0.947918	+	0.318516i	$0.896816\pi$
$272$	−0.135390	−0.00820923
$273$	4.09012	0.247545
$274$	22.6525	1.36849
$275$	−17.4230	−1.05065
$276$	−12.2415	−0.736851
$277$	0.532600	0.0320008	0.0160004	−	0.999872i	$-0.494907\pi$
$277$	0.532600	0.0320008	0.0160004	+	0.999872i	$0.494907\pi$
$278$	1.66687	0.0999723
$279$	−2.20682	−0.132119
$280$	1.98758	0.118780
$281$	7.65267	0.456520	0.228260	−	0.973600i	$-0.426696\pi$
$281$	7.65267	0.456520	0.228260	+	0.973600i	$0.426696\pi$
$282$	−20.8324	−1.24055
$283$	14.6537	0.871072	0.435536	−	0.900171i	$-0.356559\pi$
$283$	14.6537	0.871072	0.435536	+	0.900171i	$0.356559\pi$
$284$	−6.36792	−0.377867
$285$	44.5270	2.63755
$286$	−9.40981	−0.556414
$287$	3.63379	0.214496
$288$	−0.633932	−0.0373548
$289$	−16.9817	−0.998922
$290$	12.5584	0.737455
$291$	−16.3034	−0.955721
$292$	−15.5985	−0.912833
$293$	−28.3990	−1.65909	−0.829543	−	0.558442i	$-0.811399\pi$
$293$	−28.3990	−1.65909	−0.829543	+	0.558442i	$0.811399\pi$
$294$	−12.7108	−0.741310
$295$	−34.1375	−1.98756
$296$	6.73560	0.391499
$297$	−11.4005	−0.661525
$298$	−22.7885	−1.32010
$299$	−23.9066	−1.38255
$300$	−13.1402	−0.758652
$301$	−5.73086	−0.330321
$302$	−1.41340	−0.0813320
$303$	−27.2337	−1.56454
$304$	6.77310	0.388464
$305$	−16.6814	−0.955173
$306$	0.0858281	0.00490647
$307$	14.7237	0.840326	0.420163	−	0.907449i	$-0.361973\pi$
$307$	14.7237	0.840326	0.420163	+	0.907449i	$0.361973\pi$
$308$	−1.45675	−0.0830061
$309$	9.41213	0.535438
$310$	−12.0053	−0.681853
$311$	7.71615	0.437543	0.218771	−	0.975776i	$-0.429795\pi$
$311$	7.71615	0.437543	0.218771	+	0.975776i	$0.429795\pi$
$312$	−7.09676	−0.401775
$313$	−18.3358	−1.03640	−0.518201	−	0.855259i	$-0.673398\pi$
$313$	−18.3358	−1.03640	−0.518201	+	0.855259i	$0.673398\pi$
$314$	−5.98332	−0.337658
$315$	−1.25999	−0.0709922
$316$	−9.18127	−0.516487
$317$	23.1086	1.29791	0.648954	−	0.760827i	$-0.275207\pi$
$317$	23.1086	1.29791	0.648954	+	0.760827i	$0.275207\pi$
$318$	13.7498	0.771049
$319$	−9.20441	−0.515348
$320$	−3.44864	−0.192785
$321$	−27.0236	−1.50831
$322$	−3.70103	−0.206250
$323$	−0.917011	−0.0510239
$324$	−10.4999	−0.583329
$325$	−25.6618	−1.42346
$326$	6.36633	0.352599
$327$	−2.90895	−0.160865
$328$	−6.30497	−0.348134
$329$	−6.29835	−0.347239
$330$	16.6167	0.914720
$331$	26.9383	1.48067	0.740333	−	0.672241i	$-0.234668\pi$
$331$	26.9383	1.48067	0.740333	+	0.672241i	$0.234668\pi$
$332$	−13.4764	−0.739613
$333$	−4.26991	−0.233989
$334$	−13.7345	−0.751516
$335$	28.2079	1.54116
$336$	−1.09866	−0.0599370
$337$	31.6280	1.72289	0.861444	−	0.507853i	$-0.169561\pi$
$337$	31.6280	1.72289	0.861444	+	0.507853i	$0.169561\pi$
$338$	−0.859371	−0.0467436
$339$	18.0161	0.978500
$340$	0.466912	0.0253218
$341$	8.79900	0.476492
$342$	−4.29368	−0.232176
$343$	−7.87727	−0.425333
$344$	9.94360	0.536123
$345$	42.2165	2.27286
$346$	−6.27011	−0.337083
$347$	21.8096	1.17080	0.585399	−	0.810745i	$-0.300938\pi$
$347$	21.8096	1.17080	0.585399	+	0.810745i	$0.300938\pi$
$348$	−6.94185	−0.372122
$349$	−22.8499	−1.22313	−0.611564	−	0.791195i	$-0.709459\pi$
$349$	−22.8499	−1.22313	−0.611564	+	0.791195i	$0.709459\pi$
$350$	−3.97275	−0.212352
$351$	−16.7914	−0.896260
$352$	2.52760	0.134722
$353$	−1.94798	−0.103680	−0.0518402	−	0.998655i	$-0.516509\pi$
$353$	−1.94798	−0.103680	−0.0518402	+	0.998655i	$0.516509\pi$
$354$	18.8700	1.00293
$355$	21.9606	1.16555
$356$	−9.66471	−0.512229
$357$	0.148748	0.00787259
$358$	5.74419	0.303590
$359$	37.4144	1.97466	0.987328	−	0.158692i	$-0.0507277\pi$
$359$	37.4144	1.97466	0.987328	+	0.158692i	$0.0507277\pi$
$360$	2.18620	0.115223
$361$	26.8749	1.41447
$362$	−0.803801	−0.0422469
$363$	8.79030	0.461371
$364$	−2.14560	−0.112460
$365$	53.7936	2.81568
$366$	9.22089	0.481984
$367$	−34.5696	−1.80452	−0.902259	−	0.431194i	$-0.858093\pi$
$367$	−34.5696	−1.80452	−0.902259	+	0.431194i	$0.858093\pi$
$368$	6.42164	0.334751
$369$	3.99692	0.208071
$370$	−23.2286	−1.20760
$371$	4.15703	0.215822
$372$	6.63609	0.344065
$373$	−31.4079	−1.62624	−0.813120	−	0.582096i	$-0.802233\pi$
$373$	−31.4079	−1.62624	−0.813120	+	0.582096i	$0.802233\pi$
$374$	−0.342213	−0.0176954
$375$	12.4454	0.642679
$376$	10.9283	0.563582
$377$	−13.5568	−0.698213
$378$	−2.59951	−0.133704
$379$	6.35859	0.326619	0.163309	−	0.986575i	$-0.447783\pi$
$379$	6.35859	0.326619	0.163309	+	0.986575i	$0.447783\pi$
$380$	−23.3580	−1.19824
$381$	4.90788	0.251438
$382$	−9.23399	−0.472452
$383$	29.1724	1.49064	0.745320	−	0.666707i	$-0.232297\pi$
$383$	29.1724	1.49064	0.745320	+	0.666707i	$0.232297\pi$
$384$	1.90629	0.0972798
$385$	5.02381	0.256037
$386$	−16.6869	−0.849342
$387$	−6.30356	−0.320428
$388$	8.55243	0.434184
$389$	−1.97966	−0.100373	−0.0501864	−	0.998740i	$-0.515982\pi$
$389$	−1.97966	−0.100373	−0.0501864	+	0.998740i	$0.515982\pi$
$390$	24.4742	1.23930
$391$	−0.869427	−0.0439688
$392$	6.66784	0.336777
$393$	24.8418	1.25310
$394$	−13.2031	−0.665164
$395$	31.6629	1.59313
$396$	−1.60233	−0.0805200
$397$	−9.74853	−0.489265	−0.244632	−	0.969616i	$-0.578667\pi$
$397$	−9.74853	−0.489265	−0.244632	+	0.969616i	$0.578667\pi$
$398$	14.2637	0.714974
$399$	−7.44136	−0.372534
$400$	6.89310	0.344655
$401$	−18.9600	−0.946819	−0.473410	−	0.880842i	$-0.656977\pi$
$401$	−18.9600	−0.946819	−0.473410	+	0.880842i	$0.656977\pi$
$402$	−15.5924	−0.777677
$403$	12.9597	0.645570
$404$	14.2863	0.710768
$405$	36.2104	1.79931
$406$	−2.09876	−0.104160
$407$	17.0249	0.843894
$408$	−0.258093	−0.0127775
$409$	25.0401	1.23815	0.619076	−	0.785331i	$-0.287507\pi$
$409$	25.0401	1.23815	0.619076	+	0.785331i	$0.287507\pi$
$410$	21.7436	1.07384
$411$	43.1822	2.13002
$412$	−4.93742	−0.243249
$413$	5.70507	0.280728
$414$	−4.07088	−0.200073
$415$	46.4752	2.28138
$416$	3.72282	0.182526
$417$	3.17754	0.155605
$418$	17.1197	0.837353
$419$	30.8403	1.50665	0.753324	−	0.657650i	$-0.228449\pi$
$419$	30.8403	1.50665	0.753324	+	0.657650i	$0.228449\pi$
$420$	3.78889	0.184879
$421$	−3.22509	−0.157181	−0.0785905	−	0.996907i	$-0.525042\pi$
$421$	−3.22509	−0.157181	−0.0785905	+	0.996907i	$0.525042\pi$
$422$	22.5826	1.09930
$423$	−6.92776	−0.336839
$424$	−7.21285	−0.350287
$425$	−0.933258	−0.0452697
$426$	−12.1391	−0.588141
$427$	2.78779	0.134911
$428$	14.1760	0.685225
$429$	−17.9378	−0.866045
$430$	−34.2919	−1.65370
$431$	−19.5169	−0.940095	−0.470048	−	0.882641i	$-0.655763\pi$
$431$	−19.5169	−0.940095	−0.470048	+	0.882641i	$0.655763\pi$
$432$	4.51041	0.217007
$433$	−20.0509	−0.963584	−0.481792	−	0.876286i	$-0.660014\pi$
$433$	−20.0509	−0.963584	−0.481792	+	0.876286i	$0.660014\pi$
$434$	2.00632	0.0963064
$435$	23.9399	1.14783
$436$	1.52598	0.0730810
$437$	43.4944	2.08062
$438$	−29.7352	−1.42080
$439$	6.16608	0.294291	0.147145	−	0.989115i	$-0.452991\pi$
$439$	6.16608	0.294291	0.147145	+	0.989115i	$0.452991\pi$
$440$	−8.71679	−0.415557
$441$	−4.22695	−0.201283
$442$	−0.504033	−0.0239744
$443$	−32.8649	−1.56146	−0.780729	−	0.624869i	$-0.785152\pi$
$443$	−32.8649	−1.56146	−0.780729	+	0.624869i	$0.785152\pi$
$444$	12.8400	0.609359
$445$	33.3301	1.58000
$446$	4.37688	0.207251
$447$	−43.4414	−2.05471
$448$	0.576337	0.0272293
$449$	7.43141	0.350710	0.175355	−	0.984505i	$-0.443893\pi$
$449$	7.43141	0.350710	0.175355	+	0.984505i	$0.443893\pi$
$450$	−4.36976	−0.205992
$451$	−15.9365	−0.750419
$452$	−9.45088	−0.444532
$453$	−2.69435	−0.126591
$454$	−9.73531	−0.456901
$455$	7.39938	0.346888
$456$	12.9115	0.604635
$457$	10.0225	0.468830	0.234415	−	0.972137i	$-0.424682\pi$
$457$	10.0225	0.468830	0.234415	+	0.972137i	$0.424682\pi$
$458$	8.75050	0.408884
$459$	−0.610665	−0.0285034
$460$	−22.1459	−1.03256
$461$	20.9585	0.976134	0.488067	−	0.872806i	$-0.337702\pi$
$461$	20.9585	0.976134	0.488067	+	0.872806i	$0.337702\pi$
$462$	−2.77699	−0.129197
$463$	14.7467	0.685337	0.342669	−	0.939456i	$-0.388669\pi$
$463$	14.7467	0.685337	0.342669	+	0.939456i	$0.388669\pi$
$464$	3.64156	0.169055
$465$	−22.8855	−1.06129
$466$	18.2084	0.843486
$467$	15.5836	0.721125	0.360563	−	0.932735i	$-0.382585\pi$
$467$	15.5836	0.721125	0.360563	+	0.932735i	$0.382585\pi$
$468$	−2.36001	−0.109092
$469$	−4.71411	−0.217678
$470$	−37.6876	−1.73840
$471$	−11.4059	−0.525557
$472$	−9.89885	−0.455631
$473$	25.1335	1.15564
$474$	−17.5021	−0.803900
$475$	46.6877	2.14218
$476$	−0.0780303	−0.00357651
$477$	4.57245	0.209358
$478$	1.38867	0.0635161
$479$	−17.5807	−0.803285	−0.401642	−	0.915797i	$-0.631560\pi$
$479$	−17.5807	−0.803285	−0.401642	+	0.915797i	$0.631560\pi$
$480$	−6.57409	−0.300065
$481$	25.0754	1.14334
$482$	−25.2339	−1.14937
$483$	−7.05522	−0.321024
$484$	−4.61122	−0.209601
$485$	−29.4942	−1.33926
$486$	−6.48466	−0.294150
$487$	−29.7599	−1.34855	−0.674275	−	0.738481i	$-0.735544\pi$
$487$	−29.7599	−1.34855	−0.674275	+	0.738481i	$0.735544\pi$
$488$	−4.83709	−0.218965
$489$	12.1361	0.548812
$490$	−22.9950	−1.03881
$491$	−16.2093	−0.731515	−0.365757	−	0.930710i	$-0.619190\pi$
$491$	−16.2093	−0.731515	−0.365757	+	0.930710i	$0.619190\pi$
$492$	−12.0191	−0.541862
$493$	−0.493031	−0.0222050
$494$	25.2150	1.13448
$495$	5.52585	0.248368
$496$	−3.48116	−0.156309
$497$	−3.67007	−0.164625
$498$	−25.6899	−1.15119
$499$	−11.6837	−0.523036	−0.261518	−	0.965199i	$-0.584223\pi$
$499$	−11.6837	−0.523036	−0.261518	+	0.965199i	$0.584223\pi$
$500$	−6.52862	−0.291969
$501$	−26.1818	−1.16972
$502$	12.5201	0.558801
$503$	11.3788	0.507354	0.253677	−	0.967289i	$-0.418360\pi$
$503$	11.3788	0.507354	0.253677	+	0.967289i	$0.418360\pi$
$504$	−0.365358	−0.0162743
$505$	−49.2682	−2.19240
$506$	16.2314	0.721572
$507$	−1.63821	−0.0727554
$508$	−2.57457	−0.114228
$509$	35.1372	1.55743	0.778713	−	0.627380i	$-0.215873\pi$
$509$	35.1372	1.55743	0.778713	+	0.627380i	$0.215873\pi$
$510$	0.890068	0.0394129
$511$	−8.98999	−0.397694
$512$	−1.00000	−0.0441942
$513$	30.5494	1.34879
$514$	11.3037	0.498583
$515$	17.0274	0.750315
$516$	18.9554	0.834463
$517$	27.6223	1.21483
$518$	3.88197	0.170564
$519$	−11.9526	−0.524663
$520$	−12.8386	−0.563012
$521$	12.1360	0.531687	0.265843	−	0.964016i	$-0.414350\pi$
$521$	12.1360	0.531687	0.265843	+	0.964016i	$0.414350\pi$
$522$	−2.30850	−0.101040
$523$	35.2299	1.54050	0.770248	−	0.637744i	$-0.220132\pi$
$523$	35.2299	1.54050	0.770248	+	0.637744i	$0.220132\pi$
$524$	−13.0315	−0.569284
$525$	−7.57320	−0.330521
$526$	1.84795	0.0805744
$527$	0.471315	0.0205308
$528$	4.81834	0.209691
$529$	18.2375	0.792934
$530$	24.8745	1.08048
$531$	6.27519	0.272320
$532$	3.90359	0.169242
$533$	−23.4723	−1.01670
$534$	−18.4237	−0.797272
$535$	−48.8880	−2.11361
$536$	8.17945	0.353298
$537$	10.9501	0.472531
$538$	29.0587	1.25281
$539$	16.8537	0.725938
$540$	−15.5548	−0.669370
$541$	−4.01099	−0.172446	−0.0862229	−	0.996276i	$-0.527480\pi$
$541$	−4.01099	−0.172446	−0.0862229	+	0.996276i	$0.527480\pi$
$542$	31.2094	1.34056
$543$	−1.53228	−0.0657563
$544$	0.135390	0.00580481
$545$	−5.26254	−0.225422
$546$	−4.09012	−0.175041
$547$	17.6519	0.754741	0.377370	−	0.926062i	$-0.376828\pi$
$547$	17.6519	0.754741	0.377370	+	0.926062i	$0.376828\pi$
$548$	−22.6525	−0.967667
$549$	3.06639	0.130870
$550$	17.4230	0.742921
$551$	24.6646	1.05075
$552$	12.2415	0.521033
$553$	−5.29150	−0.225018
$554$	−0.532600	−0.0226280
$555$	−44.2804	−1.87960
$556$	−1.66687	−0.0706911
$557$	−4.11543	−0.174376	−0.0871882	−	0.996192i	$-0.527788\pi$
$557$	−4.11543	−0.174376	−0.0871882	+	0.996192i	$0.527788\pi$
$558$	2.20682	0.0934220
$559$	37.0182	1.56570
$560$	−1.98758	−0.0839904
$561$	−0.652356	−0.0275425
$562$	−7.65267	−0.322808
$563$	17.6904	0.745561	0.372780	−	0.927920i	$-0.378404\pi$
$563$	17.6904	0.745561	0.372780	+	0.927920i	$0.378404\pi$
$564$	20.8324	0.877202
$565$	32.5927	1.37118
$566$	−14.6537	−0.615941
$567$	−6.05149	−0.254139
$568$	6.36792	0.267192
$569$	16.5578	0.694140	0.347070	−	0.937839i	$-0.387177\pi$
$569$	16.5578	0.694140	0.347070	+	0.937839i	$0.387177\pi$
$570$	−44.5270	−1.86503
$571$	−37.2586	−1.55922	−0.779611	−	0.626264i	$-0.784583\pi$
$571$	−37.2586	−1.55922	−0.779611	+	0.626264i	$0.784583\pi$
$572$	9.40981	0.393444
$573$	−17.6026	−0.735361
$574$	−3.63379	−0.151671
$575$	44.2650	1.84598
$576$	0.633932	0.0264138
$577$	30.6031	1.27402	0.637012	−	0.770854i	$-0.280170\pi$
$577$	30.6031	1.27402	0.637012	+	0.770854i	$0.280170\pi$
$578$	16.9817	0.706344
$579$	−31.8101	−1.32198
$580$	−12.5584	−0.521459
$581$	−7.76694	−0.322227
$582$	16.3034	0.675797
$583$	−18.2312	−0.755061
$584$	15.5985	0.645470
$585$	8.13882	0.336499
$586$	28.3990	1.17315
$587$	9.23380	0.381120	0.190560	−	0.981676i	$-0.438970\pi$
$587$	9.23380	0.381120	0.190560	+	0.981676i	$0.438970\pi$
$588$	12.7108	0.524185
$589$	−23.5783	−0.971525
$590$	34.1375	1.40542
$591$	−25.1690	−1.03531
$592$	−6.73560	−0.276831
$593$	−34.1880	−1.40393	−0.701966	−	0.712210i	$-0.747694\pi$
$593$	−34.1880	−1.40393	−0.701966	+	0.712210i	$0.747694\pi$
$594$	11.4005	0.467769
$595$	0.269098	0.0110320
$596$	22.7885	0.933453
$597$	27.1907	1.11284
$598$	23.9066	0.977614
$599$	30.1903	1.23354	0.616770	−	0.787143i	$-0.288441\pi$
$599$	30.1903	1.23354	0.616770	+	0.787143i	$0.288441\pi$
$600$	13.1402	0.536448
$601$	14.5291	0.592654	0.296327	−	0.955087i	$-0.404238\pi$
$601$	14.5291	0.592654	0.296327	+	0.955087i	$0.404238\pi$
$602$	5.73086	0.233572
$603$	−5.18521	−0.211158
$604$	1.41340	0.0575104
$605$	15.9024	0.646525
$606$	27.2337	1.10629
$607$	15.5597	0.631548	0.315774	−	0.948834i	$-0.397736\pi$
$607$	15.5597	0.631548	0.315774	+	0.948834i	$0.397736\pi$
$608$	−6.77310	−0.274686
$609$	−4.00084	−0.162122
$610$	16.6814	0.675410
$611$	40.6839	1.64589
$612$	−0.0858281	−0.00346940
$613$	6.46085	0.260951	0.130476	−	0.991452i	$-0.458350\pi$
$613$	6.46085	0.260951	0.130476	+	0.991452i	$0.458350\pi$
$614$	−14.7237	−0.594200
$615$	41.4495	1.67140
$616$	1.45675	0.0586942
$617$	−26.6566	−1.07315	−0.536577	−	0.843851i	$-0.680283\pi$
$617$	−26.6566	−1.07315	−0.536577	+	0.843851i	$0.680283\pi$
$618$	−9.41213	−0.378611
$619$	28.2228	1.13437	0.567185	−	0.823591i	$-0.308033\pi$
$619$	28.2228	1.13437	0.567185	+	0.823591i	$0.308033\pi$
$620$	12.0053	0.482143
$621$	28.9642	1.16229
$622$	−7.71615	−0.309390
$623$	−5.57013	−0.223162
$624$	7.09676	0.284098
$625$	−11.9507	−0.478026
$626$	18.3358	0.732847
$627$	32.6351	1.30332
$628$	5.98332	0.238760
$629$	0.911933	0.0363612
$630$	1.25999	0.0501991
$631$	−21.6497	−0.861859	−0.430929	−	0.902386i	$-0.641814\pi$
$631$	−21.6497	−0.861859	−0.430929	+	0.902386i	$0.641814\pi$
$632$	9.18127	0.365211
$633$	43.0489	1.71104
$634$	−23.1086	−0.917760
$635$	8.87877	0.352343
$636$	−13.7498	−0.545214
$637$	24.8231	0.983529
$638$	9.20441	0.364406
$639$	−4.03683	−0.159694
$640$	3.44864	0.136319
$641$	−26.2100	−1.03523	−0.517616	−	0.855613i	$-0.673180\pi$
$641$	−26.2100	−1.03523	−0.517616	+	0.855613i	$0.673180\pi$
$642$	27.0236	1.06654
$643$	36.2107	1.42801	0.714005	−	0.700141i	$-0.246879\pi$
$643$	36.2107	1.42801	0.714005	+	0.700141i	$0.246879\pi$
$644$	3.70103	0.145841
$645$	−65.3702	−2.57395
$646$	0.917011	0.0360793
$647$	−38.4441	−1.51139	−0.755697	−	0.654922i	$-0.772702\pi$
$647$	−38.4441	−1.51139	−0.755697	+	0.654922i	$0.772702\pi$
$648$	10.4999	0.412476
$649$	−25.0204	−0.982135
$650$	25.6618	1.00654
$651$	3.82462	0.149899
$652$	−6.36633	−0.249325
$653$	−35.7652	−1.39960	−0.699800	−	0.714338i	$-0.746728\pi$
$653$	−35.7652	−1.39960	−0.699800	+	0.714338i	$0.746728\pi$
$654$	2.90895	0.113749
$655$	44.9410	1.75599
$656$	6.30497	0.246168
$657$	−9.88838	−0.385782
$658$	6.29835	0.245535
$659$	−35.9164	−1.39910	−0.699551	−	0.714582i	$-0.746617\pi$
$659$	−35.9164	−1.39910	−0.699551	+	0.714582i	$0.746617\pi$
$660$	−16.6167	−0.646805
$661$	1.88757	0.0734179	0.0367089	−	0.999326i	$-0.488313\pi$
$661$	1.88757	0.0734179	0.0367089	+	0.999326i	$0.488313\pi$
$662$	−26.9383	−1.04699
$663$	−0.960832	−0.0373156
$664$	13.4764	0.522986
$665$	−13.4621	−0.522036
$666$	4.26991	0.165456
$667$	23.3848	0.905462
$668$	13.7345	0.531402
$669$	8.34359	0.322582
$670$	−28.2079	−1.08977
$671$	−12.2263	−0.471990
$672$	1.09866	0.0423819
$673$	15.5489	0.599365	0.299683	−	0.954039i	$-0.403119\pi$
$673$	15.5489	0.599365	0.299683	+	0.954039i	$0.403119\pi$
$674$	−31.6280	−1.21827
$675$	31.0907	1.19668
$676$	0.859371	0.0330527
$677$	−37.5728	−1.44404	−0.722021	−	0.691871i	$-0.756786\pi$
$677$	−37.5728	−1.44404	−0.722021	+	0.691871i	$0.756786\pi$
$678$	−18.0161	−0.691904
$679$	4.92908	0.189161
$680$	−0.466912	−0.0179052
$681$	−18.5583	−0.711156
$682$	−8.79900	−0.336931
$683$	19.2955	0.738322	0.369161	−	0.929365i	$-0.379645\pi$
$683$	19.2955	0.738322	0.369161	+	0.929365i	$0.379645\pi$
$684$	4.29368	0.164173
$685$	78.1203	2.98482
$686$	7.87727	0.300756
$687$	16.6810	0.636418
$688$	−9.94360	−0.379096
$689$	−26.8521	−1.02298
$690$	−42.2165	−1.60715
$691$	52.0548	1.98026	0.990129	−	0.140161i	$-0.0447621\pi$
$691$	52.0548	1.98026	0.990129	+	0.140161i	$0.0447621\pi$
$692$	6.27011	0.238354
$693$	−0.923480	−0.0350801
$694$	−21.8096	−0.827880
$695$	5.74844	0.218051
$696$	6.94185	0.263130
$697$	−0.853631	−0.0323336
$698$	22.8499	0.864882
$699$	34.7104	1.31287
$700$	3.97275	0.150156
$701$	36.1598	1.36574	0.682868	−	0.730541i	$-0.260732\pi$
$701$	36.1598	1.36574	0.682868	+	0.730541i	$0.260732\pi$
$702$	16.7914	0.633751
$703$	−45.6209	−1.72062
$704$	−2.52760	−0.0952627
$705$	−71.8434	−2.70578
$706$	1.94798	0.0733131
$707$	8.23370	0.309660
$708$	−18.8700	−0.709180
$709$	9.49204	0.356481	0.178240	−	0.983987i	$-0.442960\pi$
$709$	9.49204	0.356481	0.178240	+	0.983987i	$0.442960\pi$
$710$	−21.9606	−0.824168
$711$	−5.82030	−0.218278
$712$	9.66471	0.362200
$713$	−22.3548	−0.837193
$714$	−0.148748	−0.00556676
$715$	−32.4510	−1.21360
$716$	−5.74419	−0.214671
$717$	2.64720	0.0988614
$718$	−37.4144	−1.39629
$719$	−13.8502	−0.516526	−0.258263	−	0.966075i	$-0.583150\pi$
$719$	−13.8502	−0.516526	−0.258263	+	0.966075i	$0.583150\pi$
$720$	−2.18620	−0.0814749
$721$	−2.84561	−0.105976
$722$	−26.8749	−1.00018
$723$	−48.1030	−1.78897
$724$	0.803801	0.0298730
$725$	25.1016	0.932250
$726$	−8.79030	−0.326239
$727$	−23.7377	−0.880382	−0.440191	−	0.897904i	$-0.645089\pi$
$727$	−23.7377	−0.880382	−0.440191	+	0.897904i	$0.645089\pi$
$728$	2.14560	0.0795211
$729$	19.1382	0.708821
$730$	−53.7936	−1.99099
$731$	1.34627	0.0497934
$732$	−9.22089	−0.340814
$733$	12.1388	0.448358	0.224179	−	0.974548i	$-0.428030\pi$
$733$	12.1388	0.448358	0.224179	+	0.974548i	$0.428030\pi$
$734$	34.5696	1.27599
$735$	−43.8350	−1.61688
$736$	−6.42164	−0.236705
$737$	20.6744	0.761551
$738$	−3.99692	−0.147129
$739$	32.6045	1.19938	0.599689	−	0.800233i	$-0.295291\pi$
$739$	32.6045	1.19938	0.599689	+	0.800233i	$0.295291\pi$
$740$	23.2286	0.853901
$741$	48.0671	1.76579
$742$	−4.15703	−0.152609
$743$	39.2689	1.44064	0.720318	−	0.693644i	$-0.243996\pi$
$743$	39.2689	1.44064	0.720318	+	0.693644i	$0.243996\pi$
$744$	−6.63609	−0.243291
$745$	−78.5893	−2.87929
$746$	31.4079	1.14993
$747$	−8.54311	−0.312576
$748$	0.342213	0.0125125
$749$	8.17017	0.298532
$750$	−12.4454	−0.454443
$751$	−20.7734	−0.758031	−0.379015	−	0.925390i	$-0.623737\pi$
$751$	−20.7734	−0.758031	−0.379015	+	0.925390i	$0.623737\pi$
$752$	−10.9283	−0.398512
$753$	23.8670	0.869760
$754$	13.5568	0.493711
$755$	−4.87430	−0.177394
$756$	2.59951	0.0945433
$757$	27.2570	0.990672	0.495336	−	0.868701i	$-0.335045\pi$
$757$	27.2570	0.990672	0.495336	+	0.868701i	$0.335045\pi$
$758$	−6.35859	−0.230954
$759$	30.9417	1.12311
$760$	23.3580	0.847283
$761$	52.8286	1.91504	0.957518	−	0.288373i	$-0.0931142\pi$
$761$	52.8286	1.91504	0.957518	+	0.288373i	$0.0931142\pi$
$762$	−4.90788	−0.177794
$763$	0.879476	0.0318392
$764$	9.23399	0.334074
$765$	0.295990	0.0107015
$766$	−29.1724	−1.05404
$767$	−36.8516	−1.33063
$768$	−1.90629	−0.0687872
$769$	36.6265	1.32078	0.660392	−	0.750921i	$-0.270390\pi$
$769$	36.6265	1.32078	0.660392	+	0.750921i	$0.270390\pi$
$770$	−5.02381	−0.181045
$771$	21.5480	0.776034
$772$	16.6869	0.600576
$773$	−39.6994	−1.42789	−0.713944	−	0.700202i	$-0.753093\pi$
$773$	−39.6994	−1.42789	−0.713944	+	0.700202i	$0.753093\pi$
$774$	6.30356	0.226577
$775$	−23.9960	−0.861962
$776$	−8.55243	−0.307014
$777$	7.40015	0.265479
$778$	1.97966	0.0709744
$779$	42.7042	1.53004
$780$	−24.4742	−0.876315
$781$	16.0956	0.575945
$782$	0.869427	0.0310907
$783$	16.4249	0.586978
$784$	−6.66784	−0.238137
$785$	−20.6343	−0.736470
$786$	−24.8418	−0.886078
$787$	31.9123	1.13755	0.568775	−	0.822493i	$-0.307417\pi$
$787$	31.9123	1.13755	0.568775	+	0.822493i	$0.307417\pi$
$788$	13.2031	0.470342
$789$	3.52272	0.125412
$790$	−31.6629	−1.12652
$791$	−5.44689	−0.193669
$792$	1.60233	0.0569362
$793$	−18.0076	−0.639469
$794$	9.74853	0.345962
$795$	47.4180	1.68174
$796$	−14.2637	−0.505563
$797$	−16.7485	−0.593262	−0.296631	−	0.954992i	$-0.595863\pi$
$797$	−16.7485	−0.593262	−0.296631	+	0.954992i	$0.595863\pi$
$798$	7.44136	0.263421
$799$	1.47958	0.0523437
$800$	−6.89310	−0.243708
$801$	−6.12676	−0.216479
$802$	18.9600	0.669502
$803$	39.4268	1.39134
$804$	15.5924	0.549901
$805$	−12.7635	−0.449854
$806$	−12.9597	−0.456487
$807$	55.3942	1.94997
$808$	−14.2863	−0.502589
$809$	−21.8531	−0.768314	−0.384157	−	0.923268i	$-0.625508\pi$
$809$	−21.8531	−0.768314	−0.384157	+	0.923268i	$0.625508\pi$
$810$	−36.2104	−1.27231
$811$	21.7456	0.763591	0.381796	−	0.924247i	$-0.375306\pi$
$811$	21.7456	0.763591	0.381796	+	0.924247i	$0.375306\pi$
$812$	2.09876	0.0736521
$813$	59.4941	2.08655
$814$	−17.0249	−0.596723
$815$	21.9552	0.769056
$816$	0.258093	0.00903505
$817$	−67.3490	−2.35624
$818$	−25.0401	−0.875505
$819$	−1.36016	−0.0475279
$820$	−21.7436	−0.759318
$821$	5.37457	0.187574	0.0937869	−	0.995592i	$-0.470103\pi$
$821$	5.37457	0.187574	0.0937869	+	0.995592i	$0.470103\pi$
$822$	−43.1822	−1.50615
$823$	−49.4288	−1.72298	−0.861489	−	0.507776i	$-0.830468\pi$
$823$	−49.4288	−1.72298	−0.861489	+	0.507776i	$0.830468\pi$
$824$	4.93742	0.172003
$825$	33.2133	1.15634
$826$	−5.70507	−0.198505
$827$	2.33601	0.0812311	0.0406156	−	0.999175i	$-0.487068\pi$
$827$	2.33601	0.0812311	0.0406156	+	0.999175i	$0.487068\pi$
$828$	4.07088	0.141473
$829$	−46.0698	−1.60007	−0.800035	−	0.599953i	$-0.795186\pi$
$829$	−46.0698	−1.60007	−0.800035	+	0.599953i	$0.795186\pi$
$830$	−46.4752	−1.61318
$831$	−1.01529	−0.0352200
$832$	−3.72282	−0.129065
$833$	0.902759	0.0312788
$834$	−3.17754	−0.110029
$835$	−47.3652	−1.63914
$836$	−17.1197	−0.592098
$837$	−15.7014	−0.542721
$838$	−30.8403	−1.06536
$839$	−28.3472	−0.978653	−0.489327	−	0.872101i	$-0.662757\pi$
$839$	−28.3472	−0.978653	−0.489327	+	0.872101i	$0.662757\pi$
$840$	−3.78889	−0.130729
$841$	−15.7391	−0.542727
$842$	3.22509	0.111144
$843$	−14.5882	−0.502444
$844$	−22.5826	−0.777325
$845$	−2.96366	−0.101953
$846$	6.92776	0.238181
$847$	−2.65761	−0.0913167
$848$	7.21285	0.247690
$849$	−27.9341	−0.958698
$850$	0.933258	0.0320105
$851$	−43.2536	−1.48271
$852$	12.1391	0.415878
$853$	−29.7236	−1.01772	−0.508858	−	0.860851i	$-0.669932\pi$
$853$	−29.7236	−1.01772	−0.508858	+	0.860851i	$0.669932\pi$
$854$	−2.78779	−0.0953964
$855$	−14.8074	−0.506401
$856$	−14.1760	−0.484527
$857$	−39.5164	−1.34985	−0.674927	−	0.737884i	$-0.735825\pi$
$857$	−39.5164	−1.34985	−0.674927	+	0.737884i	$0.735825\pi$
$858$	17.9378	0.612386
$859$	42.8183	1.46094	0.730471	−	0.682944i	$-0.239301\pi$
$859$	42.8183	1.46094	0.730471	+	0.682944i	$0.239301\pi$
$860$	34.2919	1.16934
$861$	−6.92704	−0.236073
$862$	19.5169	0.664748
$863$	22.7744	0.775248	0.387624	−	0.921818i	$-0.373296\pi$
$863$	22.7744	0.775248	0.387624	+	0.921818i	$0.373296\pi$
$864$	−4.51041	−0.153447
$865$	−21.6234	−0.735216
$866$	20.0509	0.681357
$867$	32.3719	1.09941
$868$	−2.00632	−0.0680989
$869$	23.2066	0.787231
$870$	−23.9399	−0.811640
$871$	30.4506	1.03178
$872$	−1.52598	−0.0516761
$873$	5.42165	0.183495
$874$	−43.4944	−1.47122
$875$	−3.76269	−0.127202
$876$	29.7352	1.00466
$877$	17.2325	0.581901	0.290951	−	0.956738i	$-0.406028\pi$
$877$	17.2325	0.581901	0.290951	+	0.956738i	$0.406028\pi$
$878$	−6.16608	−0.208095
$879$	54.1366	1.82598
$880$	8.71679	0.293843
$881$	12.4888	0.420760	0.210380	−	0.977620i	$-0.432530\pi$
$881$	12.4888	0.420760	0.210380	+	0.977620i	$0.432530\pi$
$882$	4.22695	0.142329
$883$	−12.8737	−0.433234	−0.216617	−	0.976257i	$-0.569502\pi$
$883$	−12.8737	−0.433234	−0.216617	+	0.976257i	$0.569502\pi$
$884$	0.504033	0.0169525
$885$	65.0760	2.18750
$886$	32.8649	1.10412
$887$	−49.5840	−1.66487	−0.832434	−	0.554124i	$-0.813053\pi$
$887$	−49.5840	−1.66487	−0.832434	+	0.554124i	$0.813053\pi$
$888$	−12.8400	−0.430882
$889$	−1.48382	−0.0497658
$890$	−33.3301	−1.11723
$891$	26.5397	0.889112
$892$	−4.37688	−0.146549
$893$	−74.0182	−2.47692
$894$	43.4414	1.45290
$895$	19.8096	0.662163
$896$	−0.576337	−0.0192541
$897$	45.5729	1.52163
$898$	−7.43141	−0.247989
$899$	−12.6768	−0.422796
$900$	4.36976	0.145659
$901$	−0.976549	−0.0325336
$902$	15.9365	0.530626
$903$	10.9247	0.363550
$904$	9.45088	0.314331
$905$	−2.77202	−0.0921451
$906$	2.69435	0.0895137
$907$	14.9870	0.497635	0.248818	−	0.968550i	$-0.419958\pi$
$907$	14.9870	0.497635	0.248818	+	0.968550i	$0.419958\pi$
$908$	9.73531	0.323078
$909$	9.05651	0.300386
$910$	−7.39938	−0.245287
$911$	11.9578	0.396179	0.198090	−	0.980184i	$-0.436526\pi$
$911$	11.9578	0.396179	0.198090	+	0.980184i	$0.436526\pi$
$912$	−12.9115	−0.427542
$913$	34.0630	1.12732
$914$	−10.0225	−0.331513
$915$	31.7995	1.05126
$916$	−8.75050	−0.289125
$917$	−7.51054	−0.248020
$918$	0.610665	0.0201549
$919$	19.4404	0.641281	0.320640	−	0.947201i	$-0.396102\pi$
$919$	19.4404	0.641281	0.320640	+	0.947201i	$0.396102\pi$
$920$	22.1459	0.730129
$921$	−28.0676	−0.924859
$922$	−20.9585	−0.690231
$923$	23.7066	0.780312
$924$	2.77699	0.0913561
$925$	−46.4292	−1.52658
$926$	−14.7467	−0.484607
$927$	−3.12998	−0.102802
$928$	−3.64156	−0.119540
$929$	14.3654	0.471312	0.235656	−	0.971837i	$-0.424276\pi$
$929$	14.3654	0.471312	0.235656	+	0.971837i	$0.424276\pi$
$930$	22.8855	0.750444
$931$	−45.1619	−1.48012
$932$	−18.2084	−0.596435
$933$	−14.7092	−0.481558
$934$	−15.5836	−0.509913
$935$	−1.18017	−0.0385956
$936$	2.36001	0.0771394
$937$	19.2693	0.629502	0.314751	−	0.949174i	$-0.398079\pi$
$937$	19.2693	0.629502	0.314751	+	0.949174i	$0.398079\pi$
$938$	4.71411	0.153921
$939$	34.9533	1.14066
$940$	37.6876	1.22923
$941$	−14.4648	−0.471539	−0.235769	−	0.971809i	$-0.575761\pi$
$941$	−14.4648	−0.471539	−0.235769	+	0.971809i	$0.575761\pi$
$942$	11.4059	0.371625
$943$	40.4883	1.31848
$944$	9.89885	0.322180
$945$	−8.96478	−0.291624
$946$	−25.1335	−0.817160
$947$	25.5035	0.828751	0.414376	−	0.910106i	$-0.364000\pi$
$947$	25.5035	0.828751	0.414376	+	0.910106i	$0.364000\pi$
$948$	17.5021	0.568443
$949$	58.0704	1.88504
$950$	−46.6877	−1.51475
$951$	−44.0516	−1.42847
$952$	0.0780303	0.00252898
$953$	2.16988	0.0702893	0.0351446	−	0.999382i	$-0.488811\pi$
$953$	2.16988	0.0702893	0.0351446	+	0.999382i	$0.488811\pi$
$954$	−4.57245	−0.148039
$955$	−31.8447	−1.03047
$956$	−1.38867	−0.0449127
$957$	17.5463	0.567190
$958$	17.5807	0.568008
$959$	−13.0555	−0.421583
$960$	6.57409	0.212178
$961$	−18.8815	−0.609081
$962$	−25.0754	−0.808463
$963$	8.98664	0.289591
$964$	25.2339	0.812729
$965$	−57.5472	−1.85251
$966$	7.05522	0.226998
$967$	−33.1569	−1.06625	−0.533127	−	0.846035i	$-0.678983\pi$
$967$	−33.1569	−1.06625	−0.533127	+	0.846035i	$0.678983\pi$
$968$	4.61122	0.148210
$969$	1.74809	0.0561567
$970$	29.4942	0.947003
$971$	−4.59929	−0.147598	−0.0737992	−	0.997273i	$-0.523512\pi$
$971$	−4.59929	−0.147598	−0.0737992	+	0.997273i	$0.523512\pi$
$972$	6.48466	0.207995
$973$	−0.960679	−0.0307980
$974$	29.7599	0.953568
$975$	48.9187	1.56665
$976$	4.83709	0.154832
$977$	2.37261	0.0759067	0.0379533	−	0.999280i	$-0.487916\pi$
$977$	2.37261	0.0759067	0.0379533	+	0.999280i	$0.487916\pi$
$978$	−12.1361	−0.388068
$979$	24.4286	0.780740
$980$	22.9950	0.734547
$981$	0.967364	0.0308856
$982$	16.2093	0.517259
$983$	12.2578	0.390963	0.195482	−	0.980707i	$-0.437373\pi$
$983$	12.2578	0.390963	0.195482	+	0.980707i	$0.437373\pi$
$984$	12.0191	0.383154
$985$	−45.5328	−1.45080
$986$	0.493031	0.0157013
$987$	12.0065	0.382170
$988$	−25.2150	−0.802197
$989$	−63.8542	−2.03045
$990$	−5.52585	−0.175623
$991$	45.5090	1.44564	0.722821	−	0.691035i	$-0.242845\pi$
$991$	45.5090	1.44564	0.722821	+	0.691035i	$0.242845\pi$
$992$	3.48116	0.110527
$993$	−51.3522	−1.62961
$994$	3.67007	0.116407
$995$	49.1903	1.55944
$996$	25.6899	0.814015
$997$	28.4724	0.901730	0.450865	−	0.892592i	$-0.351115\pi$
$997$	28.4724	0.901730	0.450865	+	0.892592i	$0.351115\pi$
$998$	11.6837	0.369842
$999$	−30.3803	−0.961189

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.18	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.18	✓	86	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.90629 q^{3} +1.00000 q^{4} -3.44864 q^{5} +1.90629 q^{6} +0.576337 q^{7} -1.00000 q^{8} +0.633932 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.90629 q^{3} +1.00000 q^{4} -3.44864 q^{5} +1.90629 q^{6} +0.576337 q^{7} -1.00000 q^{8} +0.633932 q^{9} +3.44864 q^{10} -2.52760 q^{11} -1.90629 q^{12} -3.72282 q^{13} -0.576337 q^{14} +6.57409 q^{15} +1.00000 q^{16} -0.135390 q^{17} -0.633932 q^{18} +6.77310 q^{19} -3.44864 q^{20} -1.09866 q^{21} +2.52760 q^{22} +6.42164 q^{23} +1.90629 q^{24} +6.89310 q^{25} +3.72282 q^{26} +4.51041 q^{27} +0.576337 q^{28} +3.64156 q^{29} -6.57409 q^{30} -3.48116 q^{31} -1.00000 q^{32} +4.81834 q^{33} +0.135390 q^{34} -1.98758 q^{35} +0.633932 q^{36} -6.73560 q^{37} -6.77310 q^{38} +7.09676 q^{39} +3.44864 q^{40} +6.30497 q^{41} +1.09866 q^{42} -9.94360 q^{43} -2.52760 q^{44} -2.18620 q^{45} -6.42164 q^{46} -10.9283 q^{47} -1.90629 q^{48} -6.66784 q^{49} -6.89310 q^{50} +0.258093 q^{51} -3.72282 q^{52} +7.21285 q^{53} -4.51041 q^{54} +8.71679 q^{55} -0.576337 q^{56} -12.9115 q^{57} -3.64156 q^{58} +9.89885 q^{59} +6.57409 q^{60} +4.83709 q^{61} +3.48116 q^{62} +0.365358 q^{63} +1.00000 q^{64} +12.8386 q^{65} -4.81834 q^{66} -8.17945 q^{67} -0.135390 q^{68} -12.2415 q^{69} +1.98758 q^{70} -6.36792 q^{71} -0.633932 q^{72} -15.5985 q^{73} +6.73560 q^{74} -13.1402 q^{75} +6.77310 q^{76} -1.45675 q^{77} -7.09676 q^{78} -9.18127 q^{79} -3.44864 q^{80} -10.4999 q^{81} -6.30497 q^{82} -13.4764 q^{83} -1.09866 q^{84} +0.466912 q^{85} +9.94360 q^{86} -6.94185 q^{87} +2.52760 q^{88} -9.66471 q^{89} +2.18620 q^{90} -2.14560 q^{91} +6.42164 q^{92} +6.63609 q^{93} +10.9283 q^{94} -23.3580 q^{95} +1.90629 q^{96} +8.55243 q^{97} +6.66784 q^{98} -1.60233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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