LMFDB - Embedded newform 6026.2.a.h.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.510961 q^{3} +1.00000 q^{4} +2.36930 q^{5} +0.510961 q^{6} +2.78886 q^{7} -1.00000 q^{8} -2.73892 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.510961 q^{3} +1.00000 q^{4} +2.36930 q^{5} +0.510961 q^{6} +2.78886 q^{7} -1.00000 q^{8} -2.73892 q^{9} -2.36930 q^{10} +0.898516 q^{11} -0.510961 q^{12} +1.36209 q^{13} -2.78886 q^{14} -1.21062 q^{15} +1.00000 q^{16} -4.57925 q^{17} +2.73892 q^{18} +3.53869 q^{19} +2.36930 q^{20} -1.42500 q^{21} -0.898516 q^{22} -1.00000 q^{23} +0.510961 q^{24} +0.613574 q^{25} -1.36209 q^{26} +2.93236 q^{27} +2.78886 q^{28} -9.50770 q^{29} +1.21062 q^{30} -7.83584 q^{31} -1.00000 q^{32} -0.459106 q^{33} +4.57925 q^{34} +6.60763 q^{35} -2.73892 q^{36} -3.08532 q^{37} -3.53869 q^{38} -0.695976 q^{39} -2.36930 q^{40} +6.50322 q^{41} +1.42500 q^{42} -2.06915 q^{43} +0.898516 q^{44} -6.48932 q^{45} +1.00000 q^{46} +2.55882 q^{47} -0.510961 q^{48} +0.777721 q^{49} -0.613574 q^{50} +2.33982 q^{51} +1.36209 q^{52} -0.0206505 q^{53} -2.93236 q^{54} +2.12885 q^{55} -2.78886 q^{56} -1.80813 q^{57} +9.50770 q^{58} -3.00244 q^{59} -1.21062 q^{60} -8.28348 q^{61} +7.83584 q^{62} -7.63845 q^{63} +1.00000 q^{64} +3.22721 q^{65} +0.459106 q^{66} -12.5193 q^{67} -4.57925 q^{68} +0.510961 q^{69} -6.60763 q^{70} -2.24850 q^{71} +2.73892 q^{72} -6.70712 q^{73} +3.08532 q^{74} -0.313512 q^{75} +3.53869 q^{76} +2.50583 q^{77} +0.695976 q^{78} -5.25698 q^{79} +2.36930 q^{80} +6.71844 q^{81} -6.50322 q^{82} -6.21446 q^{83} -1.42500 q^{84} -10.8496 q^{85} +2.06915 q^{86} +4.85806 q^{87} -0.898516 q^{88} -2.45122 q^{89} +6.48932 q^{90} +3.79868 q^{91} -1.00000 q^{92} +4.00381 q^{93} -2.55882 q^{94} +8.38421 q^{95} +0.510961 q^{96} -8.88248 q^{97} -0.777721 q^{98} -2.46096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * 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
$3$	−0.510961	−0.295003	−0.147502	−	0.989062i	$-0.547123\pi$
$3$	−0.510961	−0.295003	−0.147502	+	0.989062i	$0.547123\pi$
$4$	1.00000	0.500000
$5$	2.36930	1.05958	0.529791	−	0.848128i	$-0.322270\pi$
$5$	2.36930	1.05958	0.529791	+	0.848128i	$0.322270\pi$
$6$	0.510961	0.208599
$7$	2.78886	1.05409	0.527044	−	0.849838i	$-0.323300\pi$
$7$	2.78886	1.05409	0.527044	+	0.849838i	$0.323300\pi$
$8$	−1.00000	−0.353553
$9$	−2.73892	−0.912973
$10$	−2.36930	−0.749238
$11$	0.898516	0.270913	0.135456	−	0.990783i	$-0.456750\pi$
$11$	0.898516	0.270913	0.135456	+	0.990783i	$0.456750\pi$
$12$	−0.510961	−0.147502
$13$	1.36209	0.377777	0.188888	−	0.981999i	$-0.439512\pi$
$13$	1.36209	0.377777	0.188888	+	0.981999i	$0.439512\pi$
$14$	−2.78886	−0.745353
$15$	−1.21062	−0.312580
$16$	1.00000	0.250000
$17$	−4.57925	−1.11063	−0.555316	−	0.831640i	$-0.687403\pi$
$17$	−4.57925	−1.11063	−0.555316	+	0.831640i	$0.687403\pi$
$18$	2.73892	0.645569
$19$	3.53869	0.811831	0.405915	−	0.913911i	$-0.366953\pi$
$19$	3.53869	0.811831	0.405915	+	0.913911i	$0.366953\pi$
$20$	2.36930	0.529791
$21$	−1.42500	−0.310960
$22$	−0.898516	−0.191564
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.510961	0.104299
$25$	0.613574	0.122715
$26$	−1.36209	−0.267129
$27$	2.93236	0.564333
$28$	2.78886	0.527044
$29$	−9.50770	−1.76554	−0.882768	−	0.469809i	$-0.844323\pi$
$29$	−9.50770	−1.76554	−0.882768	+	0.469809i	$0.844323\pi$
$30$	1.21062	0.221028
$31$	−7.83584	−1.40736	−0.703679	−	0.710518i	$-0.748461\pi$
$31$	−7.83584	−1.40736	−0.703679	+	0.710518i	$0.748461\pi$
$32$	−1.00000	−0.176777
$33$	−0.459106	−0.0799202
$34$	4.57925	0.785335
$35$	6.60763	1.11689
$36$	−2.73892	−0.456487
$37$	−3.08532	−0.507224	−0.253612	−	0.967306i	$-0.581619\pi$
$37$	−3.08532	−0.507224	−0.253612	+	0.967306i	$0.581619\pi$
$38$	−3.53869	−0.574051
$39$	−0.695976	−0.111445
$40$	−2.36930	−0.374619
$41$	6.50322	1.01563	0.507816	−	0.861465i	$-0.330453\pi$
$41$	6.50322	1.01563	0.507816	+	0.861465i	$0.330453\pi$
$42$	1.42500	0.219882
$43$	−2.06915	−0.315542	−0.157771	−	0.987476i	$-0.550431\pi$
$43$	−2.06915	−0.315542	−0.157771	+	0.987476i	$0.550431\pi$
$44$	0.898516	0.135456
$45$	−6.48932	−0.967370
$46$	1.00000	0.147442
$47$	2.55882	0.373243	0.186621	−	0.982432i	$-0.440246\pi$
$47$	2.55882	0.373243	0.186621	+	0.982432i	$0.440246\pi$
$48$	−0.510961	−0.0737508
$49$	0.777721	0.111103
$50$	−0.613574	−0.0867724
$51$	2.33982	0.327640
$52$	1.36209	0.188888
$53$	−0.0206505	−0.00283657	−0.00141828	−	0.999999i	$-0.500451\pi$
$53$	−0.0206505	−0.00283657	−0.00141828	+	0.999999i	$0.500451\pi$
$54$	−2.93236	−0.399044
$55$	2.12885	0.287054
$56$	−2.78886	−0.372677
$57$	−1.80813	−0.239493
$58$	9.50770	1.24842
$59$	−3.00244	−0.390884	−0.195442	−	0.980715i	$-0.562614\pi$
$59$	−3.00244	−0.390884	−0.195442	+	0.980715i	$0.562614\pi$
$60$	−1.21062	−0.156290
$61$	−8.28348	−1.06059	−0.530295	−	0.847813i	$-0.677919\pi$
$61$	−8.28348	−1.06059	−0.530295	+	0.847813i	$0.677919\pi$
$62$	7.83584	0.995153
$63$	−7.63845	−0.962355
$64$	1.00000	0.125000
$65$	3.22721	0.400286
$66$	0.459106	0.0565121
$67$	−12.5193	−1.52948	−0.764738	−	0.644342i	$-0.777132\pi$
$67$	−12.5193	−1.52948	−0.764738	+	0.644342i	$0.777132\pi$
$68$	−4.57925	−0.555316
$69$	0.510961	0.0615124
$70$	−6.60763	−0.789763
$71$	−2.24850	−0.266848	−0.133424	−	0.991059i	$-0.542597\pi$
$71$	−2.24850	−0.266848	−0.133424	+	0.991059i	$0.542597\pi$
$72$	2.73892	0.322785
$73$	−6.70712	−0.785009	−0.392504	−	0.919750i	$-0.628391\pi$
$73$	−6.70712	−0.785009	−0.392504	+	0.919750i	$0.628391\pi$
$74$	3.08532	0.358662
$75$	−0.313512	−0.0362013
$76$	3.53869	0.405915
$77$	2.50583	0.285566
$78$	0.695976	0.0788038
$79$	−5.25698	−0.591457	−0.295728	−	0.955272i	$-0.595562\pi$
$79$	−5.25698	−0.591457	−0.295728	+	0.955272i	$0.595562\pi$
$80$	2.36930	0.264896
$81$	6.71844	0.746493
$82$	−6.50322	−0.718161
$83$	−6.21446	−0.682126	−0.341063	−	0.940041i	$-0.610787\pi$
$83$	−6.21446	−0.682126	−0.341063	+	0.940041i	$0.610787\pi$
$84$	−1.42500	−0.155480
$85$	−10.8496	−1.17681
$86$	2.06915	0.223122
$87$	4.85806	0.520839
$88$	−0.898516	−0.0957821
$89$	−2.45122	−0.259828	−0.129914	−	0.991525i	$-0.541470\pi$
$89$	−2.45122	−0.259828	−0.129914	+	0.991525i	$0.541470\pi$
$90$	6.48932	0.684034
$91$	3.79868	0.398210
$92$	−1.00000	−0.104257
$93$	4.00381	0.415175
$94$	−2.55882	−0.263923
$95$	8.38421	0.860202
$96$	0.510961	0.0521497
$97$	−8.88248	−0.901879	−0.450940	−	0.892555i	$-0.648911\pi$
$97$	−8.88248	−0.901879	−0.450940	+	0.892555i	$0.648911\pi$
$98$	−0.777721	−0.0785617
$99$	−2.46096	−0.247336
$100$	0.613574	0.0613574
$101$	12.4967	1.24347	0.621734	−	0.783229i	$-0.286429\pi$
$101$	12.4967	1.24347	0.621734	+	0.783229i	$0.286429\pi$
$102$	−2.33982	−0.231676
$103$	−8.31273	−0.819078	−0.409539	−	0.912293i	$-0.634310\pi$
$103$	−8.31273	−0.819078	−0.409539	+	0.912293i	$0.634310\pi$
$104$	−1.36209	−0.133564
$105$	−3.37624	−0.329487
$106$	0.0206505	0.00200576
$107$	15.8181	1.52919	0.764597	−	0.644509i	$-0.222938\pi$
$107$	15.8181	1.52919	0.764597	+	0.644509i	$0.222938\pi$
$108$	2.93236	0.282167
$109$	−3.38985	−0.324689	−0.162345	−	0.986734i	$-0.551906\pi$
$109$	−3.38985	−0.324689	−0.162345	+	0.986734i	$0.551906\pi$
$110$	−2.12885	−0.202978
$111$	1.57648	0.149633
$112$	2.78886	0.263522
$113$	−12.8122	−1.20527	−0.602635	−	0.798017i	$-0.705883\pi$
$113$	−12.8122	−1.20527	−0.602635	+	0.798017i	$0.705883\pi$
$114$	1.80813	0.169347
$115$	−2.36930	−0.220938
$116$	−9.50770	−0.882768
$117$	−3.73066	−0.344900
$118$	3.00244	0.276397
$119$	−12.7709	−1.17070
$120$	1.21062	0.110514
$121$	−10.1927	−0.926606
$122$	8.28348	0.749951
$123$	−3.32289	−0.299615
$124$	−7.83584	−0.703679
$125$	−10.3928	−0.929556
$126$	7.63845	0.680487
$127$	10.3367	0.917234	0.458617	−	0.888634i	$-0.348345\pi$
$127$	10.3367	0.917234	0.458617	+	0.888634i	$0.348345\pi$
$128$	−1.00000	−0.0883883
$129$	1.05725	0.0930860
$130$	−3.22721	−0.283045
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−0.459106	−0.0399601
$133$	9.86889	0.855742
$134$	12.5193	1.08150
$135$	6.94764	0.597958
$136$	4.57925	0.392668
$137$	−6.03988	−0.516022	−0.258011	−	0.966142i	$-0.583067\pi$
$137$	−6.03988	−0.516022	−0.258011	+	0.966142i	$0.583067\pi$
$138$	−0.510961	−0.0434959
$139$	7.51656	0.637547	0.318773	−	0.947831i	$-0.396729\pi$
$139$	7.51656	0.637547	0.318773	+	0.947831i	$0.396729\pi$
$140$	6.60763	0.558447
$141$	−1.30746	−0.110108
$142$	2.24850	0.188690
$143$	1.22386	0.102345
$144$	−2.73892	−0.228243
$145$	−22.5266	−1.87073
$146$	6.70712	0.555085
$147$	−0.397385	−0.0327758
$148$	−3.08532	−0.253612
$149$	9.92371	0.812982	0.406491	−	0.913655i	$-0.366752\pi$
$149$	9.92371	0.812982	0.406491	+	0.913655i	$0.366752\pi$
$150$	0.313512	0.0255982
$151$	0.928938	0.0755959	0.0377979	−	0.999285i	$-0.487966\pi$
$151$	0.928938	0.0755959	0.0377979	+	0.999285i	$0.487966\pi$
$152$	−3.53869	−0.287026
$153$	12.5422	1.01398
$154$	−2.50583	−0.201926
$155$	−18.5654	−1.49121
$156$	−0.695976	−0.0557227
$157$	6.44044	0.514003	0.257001	−	0.966411i	$-0.417266\pi$
$157$	6.44044	0.514003	0.257001	+	0.966411i	$0.417266\pi$
$158$	5.25698	0.418223
$159$	0.0105516	0.000836797 0
$160$	−2.36930	−0.187309
$161$	−2.78886	−0.219793
$162$	−6.71844	−0.527850
$163$	−21.0988	−1.65258	−0.826291	−	0.563243i	$-0.809553\pi$
$163$	−21.0988	−1.65258	−0.826291	+	0.563243i	$0.809553\pi$
$164$	6.50322	0.507816
$165$	−1.08776	−0.0846820
$166$	6.21446	0.482336
$167$	7.53014	0.582699	0.291350	−	0.956617i	$-0.405896\pi$
$167$	7.53014	0.582699	0.291350	+	0.956617i	$0.405896\pi$
$168$	1.42500	0.109941
$169$	−11.1447	−0.857285
$170$	10.8496	0.832127
$171$	−9.69218	−0.741180
$172$	−2.06915	−0.157771
$173$	5.61427	0.426845	0.213423	−	0.976960i	$-0.431539\pi$
$173$	5.61427	0.426845	0.213423	+	0.976960i	$0.431539\pi$
$174$	−4.85806	−0.368289
$175$	1.71117	0.129352
$176$	0.898516	0.0677282
$177$	1.53413	0.115312
$178$	2.45122	0.183726
$179$	23.9003	1.78639	0.893196	−	0.449667i	$-0.148458\pi$
$179$	23.9003	1.78639	0.893196	+	0.449667i	$0.148458\pi$
$180$	−6.48932	−0.483685
$181$	−16.2641	−1.20890	−0.604450	−	0.796643i	$-0.706607\pi$
$181$	−16.2641	−1.20890	−0.604450	+	0.796643i	$0.706607\pi$
$182$	−3.79868	−0.281577
$183$	4.23253	0.312878
$184$	1.00000	0.0737210
$185$	−7.31005	−0.537446
$186$	−4.00381	−0.293573
$187$	−4.11453	−0.300884
$188$	2.55882	0.186621
$189$	8.17794	0.594857
$190$	−8.38421	−0.608254
$191$	12.0462	0.871633	0.435816	−	0.900036i	$-0.356460\pi$
$191$	12.0462	0.871633	0.435816	+	0.900036i	$0.356460\pi$
$192$	−0.510961	−0.0368754
$193$	−1.94869	−0.140270	−0.0701350	−	0.997538i	$-0.522343\pi$
$193$	−1.94869	−0.140270	−0.0701350	+	0.997538i	$0.522343\pi$
$194$	8.88248	0.637725
$195$	−1.64898	−0.118086
$196$	0.777721	0.0555515
$197$	−21.5515	−1.53548	−0.767740	−	0.640761i	$-0.778619\pi$
$197$	−21.5515	−1.53548	−0.767740	+	0.640761i	$0.778619\pi$
$198$	2.46096	0.174893
$199$	−8.18967	−0.580550	−0.290275	−	0.956943i	$-0.593747\pi$
$199$	−8.18967	−0.580550	−0.290275	+	0.956943i	$0.593747\pi$
$200$	−0.613574	−0.0433862
$201$	6.39687	0.451200
$202$	−12.4967	−0.879264
$203$	−26.5156	−1.86103
$204$	2.33982	0.163820
$205$	15.4081	1.07615
$206$	8.31273	0.579176
$207$	2.73892	0.190368
$208$	1.36209	0.0944442
$209$	3.17957	0.219935
$210$	3.37624	0.232983
$211$	3.83262	0.263849	0.131924	−	0.991260i	$-0.457884\pi$
$211$	3.83262	0.263849	0.131924	+	0.991260i	$0.457884\pi$
$212$	−0.0206505	−0.00141828
$213$	1.14890	0.0787211
$214$	−15.8181	−1.08130
$215$	−4.90243	−0.334343
$216$	−2.93236	−0.199522
$217$	−21.8530	−1.48348
$218$	3.38985	0.229590
$219$	3.42707	0.231580
$220$	2.12885	0.143527
$221$	−6.23737	−0.419571
$222$	−1.57648	−0.105806
$223$	18.0304	1.20741	0.603704	−	0.797209i	$-0.293691\pi$
$223$	18.0304	1.20741	0.603704	+	0.797209i	$0.293691\pi$
$224$	−2.78886	−0.186338
$225$	−1.68053	−0.112035
$226$	12.8122	0.852255
$227$	19.8771	1.31929	0.659643	−	0.751579i	$-0.270707\pi$
$227$	19.8771	1.31929	0.659643	+	0.751579i	$0.270707\pi$
$228$	−1.80813	−0.119746
$229$	12.8990	0.852387	0.426193	−	0.904632i	$-0.359854\pi$
$229$	12.8990	0.852387	0.426193	+	0.904632i	$0.359854\pi$
$230$	2.36930	0.156227
$231$	−1.28038	−0.0842430
$232$	9.50770	0.624211
$233$	13.4158	0.878898	0.439449	−	0.898268i	$-0.355174\pi$
$233$	13.4158	0.878898	0.439449	+	0.898268i	$0.355174\pi$
$234$	3.73066	0.243881
$235$	6.06262	0.395482
$236$	−3.00244	−0.195442
$237$	2.68611	0.174482
$238$	12.7709	0.827813
$239$	−4.38008	−0.283324	−0.141662	−	0.989915i	$-0.545245\pi$
$239$	−4.38008	−0.283324	−0.141662	+	0.989915i	$0.545245\pi$
$240$	−1.21062	−0.0781451
$241$	3.61274	0.232717	0.116359	−	0.993207i	$-0.462878\pi$
$241$	3.61274	0.232717	0.116359	+	0.993207i	$0.462878\pi$
$242$	10.1927	0.655210
$243$	−12.2299	−0.784551
$244$	−8.28348	−0.530295
$245$	1.84265	0.117723
$246$	3.32289	0.211860
$247$	4.82002	0.306691
$248$	7.83584	0.497576
$249$	3.17534	0.201229
$250$	10.3928	0.657295
$251$	−7.04420	−0.444626	−0.222313	−	0.974975i	$-0.571361\pi$
$251$	−7.04420	−0.444626	−0.222313	+	0.974975i	$0.571361\pi$
$252$	−7.63845	−0.481177
$253$	−0.898516	−0.0564892
$254$	−10.3367	−0.648583
$255$	5.54372	0.347162
$256$	1.00000	0.0625000
$257$	−3.26883	−0.203904	−0.101952	−	0.994789i	$-0.532509\pi$
$257$	−3.26883	−0.203904	−0.101952	+	0.994789i	$0.532509\pi$
$258$	−1.05725	−0.0658218
$259$	−8.60452	−0.534659
$260$	3.22721	0.200143
$261$	26.0408	1.61189
$262$	1.00000	0.0617802
$263$	19.8540	1.22425	0.612126	−	0.790760i	$-0.290314\pi$
$263$	19.8540	1.22425	0.612126	+	0.790760i	$0.290314\pi$
$264$	0.459106	0.0282560
$265$	−0.0489273	−0.00300558
$266$	−9.86889	−0.605101
$267$	1.25248	0.0766502
$268$	−12.5193	−0.764738
$269$	19.6024	1.19518	0.597591	−	0.801801i	$-0.296125\pi$
$269$	19.6024	1.19518	0.597591	+	0.801801i	$0.296125\pi$
$270$	−6.94764	−0.422820
$271$	−3.63275	−0.220674	−0.110337	−	0.993894i	$-0.535193\pi$
$271$	−3.63275	−0.220674	−0.110337	+	0.993894i	$0.535193\pi$
$272$	−4.57925	−0.277658
$273$	−1.94098	−0.117473
$274$	6.03988	0.364883
$275$	0.551306	0.0332450
$276$	0.510961	0.0307562
$277$	20.3699	1.22391	0.611956	−	0.790892i	$-0.290383\pi$
$277$	20.3699	1.22391	0.611956	+	0.790892i	$0.290383\pi$
$278$	−7.51656	−0.450813
$279$	21.4617	1.28488
$280$	−6.60763	−0.394882
$281$	−0.960400	−0.0572927	−0.0286463	−	0.999590i	$-0.509120\pi$
$281$	−0.960400	−0.0572927	−0.0286463	+	0.999590i	$0.509120\pi$
$282$	1.30746	0.0778580
$283$	−7.94276	−0.472148	−0.236074	−	0.971735i	$-0.575861\pi$
$283$	−7.94276	−0.472148	−0.236074	+	0.971735i	$0.575861\pi$
$284$	−2.24850	−0.133424
$285$	−4.28400	−0.253762
$286$	−1.22386	−0.0723686
$287$	18.1366	1.07057
$288$	2.73892	0.161392
$289$	3.96954	0.233502
$290$	22.5266	1.32281
$291$	4.53860	0.266057
$292$	−6.70712	−0.392504
$293$	20.7207	1.21052	0.605259	−	0.796029i	$-0.293070\pi$
$293$	20.7207	1.21052	0.605259	+	0.796029i	$0.293070\pi$
$294$	0.397385	0.0231760
$295$	−7.11367	−0.414174
$296$	3.08532	0.179331
$297$	2.63477	0.152885
$298$	−9.92371	−0.574865
$299$	−1.36209	−0.0787719
$300$	−0.313512	−0.0181006
$301$	−5.77056	−0.332610
$302$	−0.928938	−0.0534544
$303$	−6.38532	−0.366827
$304$	3.53869	0.202958
$305$	−19.6260	−1.12378
$306$	−12.5422	−0.716990
$307$	−6.56579	−0.374730	−0.187365	−	0.982290i	$-0.559995\pi$
$307$	−6.56579	−0.374730	−0.187365	+	0.982290i	$0.559995\pi$
$308$	2.50583	0.142783
$309$	4.24748	0.241631
$310$	18.5654	1.05445
$311$	−4.91478	−0.278691	−0.139346	−	0.990244i	$-0.544500\pi$
$311$	−4.91478	−0.278691	−0.139346	+	0.990244i	$0.544500\pi$
$312$	0.695976	0.0394019
$313$	5.15580	0.291423	0.145711	−	0.989327i	$-0.453453\pi$
$313$	5.15580	0.291423	0.145711	+	0.989327i	$0.453453\pi$
$314$	−6.44044	−0.363455
$315$	−18.0978	−1.01969
$316$	−5.25698	−0.295728
$317$	−1.06135	−0.0596112	−0.0298056	−	0.999556i	$-0.509489\pi$
$317$	−1.06135	−0.0596112	−0.0298056	+	0.999556i	$0.509489\pi$
$318$	−0.0105516	−0.000591705 0
$319$	−8.54283	−0.478306
$320$	2.36930	0.132448
$321$	−8.08242	−0.451117
$322$	2.78886	0.155417
$323$	−16.2045	−0.901645
$324$	6.71844	0.373246
$325$	0.835745	0.0463588
$326$	21.0988	1.16855
$327$	1.73208	0.0957844
$328$	−6.50322	−0.359080
$329$	7.13619	0.393431
$330$	1.08776	0.0598792
$331$	15.7680	0.866690	0.433345	−	0.901228i	$-0.357333\pi$
$331$	15.7680	0.866690	0.433345	+	0.901228i	$0.357333\pi$
$332$	−6.21446	−0.341063
$333$	8.45045	0.463082
$334$	−7.53014	−0.412031
$335$	−29.6620	−1.62061
$336$	−1.42500	−0.0777399
$337$	24.4343	1.33102	0.665510	−	0.746389i	$-0.268214\pi$
$337$	24.4343	1.33102	0.665510	+	0.746389i	$0.268214\pi$
$338$	11.1447	0.606192
$339$	6.54653	0.355559
$340$	−10.8496	−0.588403
$341$	−7.04063	−0.381271
$342$	9.69218	0.524093
$343$	−17.3530	−0.936976
$344$	2.06915	0.111561
$345$	1.21062	0.0651775
$346$	−5.61427	−0.301825
$347$	−9.11262	−0.489191	−0.244596	−	0.969625i	$-0.578655\pi$
$347$	−9.11262	−0.489191	−0.244596	+	0.969625i	$0.578655\pi$
$348$	4.85806	0.260419
$349$	−12.3863	−0.663021	−0.331511	−	0.943451i	$-0.607558\pi$
$349$	−12.3863	−0.663021	−0.331511	+	0.943451i	$0.607558\pi$
$350$	−1.71117	−0.0914659
$351$	3.99415	0.213192
$352$	−0.898516	−0.0478911
$353$	−5.10072	−0.271484	−0.135742	−	0.990744i	$-0.543342\pi$
$353$	−5.10072	−0.271484	−0.135742	+	0.990744i	$0.543342\pi$
$354$	−1.53413	−0.0815379
$355$	−5.32737	−0.282748
$356$	−2.45122	−0.129914
$357$	6.52541	0.345362
$358$	−23.9003	−1.26317
$359$	−14.3929	−0.759627	−0.379814	−	0.925063i	$-0.624012\pi$
$359$	−14.3929	−0.759627	−0.379814	+	0.925063i	$0.624012\pi$
$360$	6.48932	0.342017
$361$	−6.47769	−0.340931
$362$	16.2641	0.854822
$363$	5.20805	0.273352
$364$	3.79868	0.199105
$365$	−15.8912	−0.831781
$366$	−4.23253	−0.221238
$367$	4.65866	0.243180	0.121590	−	0.992580i	$-0.461201\pi$
$367$	4.65866	0.243180	0.121590	+	0.992580i	$0.461201\pi$
$368$	−1.00000	−0.0521286
$369$	−17.8118	−0.927245
$370$	7.31005	0.380031
$371$	−0.0575914	−0.00299000
$372$	4.00381	0.207588
$373$	2.02497	0.104849	0.0524246	−	0.998625i	$-0.483305\pi$
$373$	2.02497	0.104849	0.0524246	+	0.998625i	$0.483305\pi$
$374$	4.11453	0.212757
$375$	5.31029	0.274222
$376$	−2.55882	−0.131961
$377$	−12.9504	−0.666979
$378$	−8.17794	−0.420628
$379$	13.2463	0.680418	0.340209	−	0.940350i	$-0.389502\pi$
$379$	13.2463	0.680418	0.340209	+	0.940350i	$0.389502\pi$
$380$	8.38421	0.430101
$381$	−5.28165	−0.270587
$382$	−12.0462	−0.616337
$383$	−19.7135	−1.00731	−0.503657	−	0.863904i	$-0.668012\pi$
$383$	−19.7135	−1.00731	−0.503657	+	0.863904i	$0.668012\pi$
$384$	0.510961	0.0260749
$385$	5.93707	0.302581
$386$	1.94869	0.0991858
$387$	5.66723	0.288082
$388$	−8.88248	−0.450940
$389$	22.6822	1.15003	0.575016	−	0.818142i	$-0.304996\pi$
$389$	22.6822	1.15003	0.575016	+	0.818142i	$0.304996\pi$
$390$	1.64898	0.0834991
$391$	4.57925	0.231583
$392$	−0.777721	−0.0392809
$393$	0.510961	0.0257746
$394$	21.5515	1.08575
$395$	−12.4554	−0.626697
$396$	−2.46096	−0.123668
$397$	11.7673	0.590584	0.295292	−	0.955407i	$-0.404583\pi$
$397$	11.7673	0.590584	0.295292	+	0.955407i	$0.404583\pi$
$398$	8.18967	0.410511
$399$	−5.04262	−0.252447
$400$	0.613574	0.0306787
$401$	−16.1699	−0.807484	−0.403742	−	0.914873i	$-0.632291\pi$
$401$	−16.1699	−0.807484	−0.403742	+	0.914873i	$0.632291\pi$
$402$	−6.39687	−0.319047
$403$	−10.6731	−0.531667
$404$	12.4967	0.621734
$405$	15.9180	0.790971
$406$	26.5156	1.31595
$407$	−2.77221	−0.137413
$408$	−2.33982	−0.115838
$409$	39.9690	1.97634	0.988169	−	0.153367i	$-0.0490116\pi$
$409$	39.9690	1.97634	0.988169	+	0.153367i	$0.0490116\pi$
$410$	−15.4081	−0.760951
$411$	3.08614	0.152228
$412$	−8.31273	−0.409539
$413$	−8.37336	−0.412026
$414$	−2.73892	−0.134611
$415$	−14.7239	−0.722768
$416$	−1.36209	−0.0667821
$417$	−3.84067	−0.188078
$418$	−3.17957	−0.155518
$419$	−30.0864	−1.46982	−0.734908	−	0.678167i	$-0.762775\pi$
$419$	−30.0864	−1.46982	−0.734908	+	0.678167i	$0.762775\pi$
$420$	−3.37624	−0.164744
$421$	−31.6647	−1.54324	−0.771622	−	0.636082i	$-0.780554\pi$
$421$	−31.6647	−1.54324	−0.771622	+	0.636082i	$0.780554\pi$
$422$	−3.83262	−0.186569
$423$	−7.00841	−0.340761
$424$	0.0206505	0.00100288
$425$	−2.80971	−0.136291
$426$	−1.14890	−0.0556642
$427$	−23.1014	−1.11796
$428$	15.8181	0.764597
$429$	−0.625346	−0.0301920
$430$	4.90243	0.236416
$431$	−20.4046	−0.982853	−0.491426	−	0.870919i	$-0.663524\pi$
$431$	−20.4046	−0.982853	−0.491426	+	0.870919i	$0.663524\pi$
$432$	2.93236	0.141083
$433$	−8.53681	−0.410253	−0.205126	−	0.978735i	$-0.565761\pi$
$433$	−8.53681	−0.410253	−0.205126	+	0.978735i	$0.565761\pi$
$434$	21.8530	1.04898
$435$	11.5102	0.551872
$436$	−3.38985	−0.162345
$437$	−3.53869	−0.169278
$438$	−3.42707	−0.163752
$439$	−19.1651	−0.914700	−0.457350	−	0.889287i	$-0.651201\pi$
$439$	−19.1651	−0.914700	−0.457350	+	0.889287i	$0.651201\pi$
$440$	−2.12885	−0.101489
$441$	−2.13012	−0.101434
$442$	6.23737	0.296681
$443$	23.9265	1.13678	0.568392	−	0.822758i	$-0.307566\pi$
$443$	23.9265	1.13678	0.568392	+	0.822758i	$0.307566\pi$
$444$	1.57648	0.0748164
$445$	−5.80766	−0.275310
$446$	−18.0304	−0.853766
$447$	−5.07063	−0.239832
$448$	2.78886	0.131761
$449$	23.2056	1.09514	0.547571	−	0.836759i	$-0.315553\pi$
$449$	23.2056	1.09514	0.547571	+	0.836759i	$0.315553\pi$
$450$	1.68053	0.0792209
$451$	5.84325	0.275148
$452$	−12.8122	−0.602635
$453$	−0.474651	−0.0223010
$454$	−19.8771	−0.932876
$455$	9.00022	0.421937
$456$	1.80813	0.0846735
$457$	−4.56956	−0.213755	−0.106877	−	0.994272i	$-0.534085\pi$
$457$	−4.56956	−0.213755	−0.106877	+	0.994272i	$0.534085\pi$
$458$	−12.8990	−0.602728
$459$	−13.4280	−0.626766
$460$	−2.36930	−0.110469
$461$	−22.1990	−1.03391	−0.516955	−	0.856012i	$-0.672935\pi$
$461$	−22.1990	−1.03391	−0.516955	+	0.856012i	$0.672935\pi$
$462$	1.28038	0.0595688
$463$	−21.1625	−0.983507	−0.491753	−	0.870735i	$-0.663644\pi$
$463$	−21.1625	−0.983507	−0.491753	+	0.870735i	$0.663644\pi$
$464$	−9.50770	−0.441384
$465$	9.48621	0.439913
$466$	−13.4158	−0.621475
$467$	−1.89152	−0.0875292	−0.0437646	−	0.999042i	$-0.513935\pi$
$467$	−1.89152	−0.0875292	−0.0437646	+	0.999042i	$0.513935\pi$
$468$	−3.73066	−0.172450
$469$	−34.9145	−1.61220
$470$	−6.06262	−0.279648
$471$	−3.29081	−0.151633
$472$	3.00244	0.138198
$473$	−1.85916	−0.0854845
$474$	−2.68611	−0.123377
$475$	2.17125	0.0996236
$476$	−12.7709	−0.585352
$477$	0.0565601	0.00258971
$478$	4.38008	0.200340
$479$	−9.85969	−0.450501	−0.225250	−	0.974301i	$-0.572320\pi$
$479$	−9.85969	−0.450501	−0.225250	+	0.974301i	$0.572320\pi$
$480$	1.21062	0.0552569
$481$	−4.20250	−0.191617
$482$	−3.61274	−0.164556
$483$	1.42500	0.0648396
$484$	−10.1927	−0.463303
$485$	−21.0452	−0.955615
$486$	12.2299	0.554761
$487$	−32.8919	−1.49047	−0.745237	−	0.666799i	$-0.767664\pi$
$487$	−32.8919	−1.49047	−0.745237	+	0.666799i	$0.767664\pi$
$488$	8.28348	0.374976
$489$	10.7806	0.487517
$490$	−1.84265	−0.0832426
$491$	−21.7901	−0.983372	−0.491686	−	0.870773i	$-0.663619\pi$
$491$	−21.7901	−0.983372	−0.491686	+	0.870773i	$0.663619\pi$
$492$	−3.32289	−0.149808
$493$	43.5382	1.96086
$494$	−4.82002	−0.216863
$495$	−5.83076	−0.262073
$496$	−7.83584	−0.351840
$497$	−6.27075	−0.281282
$498$	−3.17534	−0.142291
$499$	11.1791	0.500443	0.250222	−	0.968189i	$-0.419497\pi$
$499$	11.1791	0.500443	0.250222	+	0.968189i	$0.419497\pi$
$500$	−10.3928	−0.464778
$501$	−3.84760	−0.171898
$502$	7.04420	0.314398
$503$	−38.2699	−1.70637	−0.853185	−	0.521609i	$-0.825332\pi$
$503$	−38.2699	−1.70637	−0.853185	+	0.521609i	$0.825332\pi$
$504$	7.63845	0.340244
$505$	29.6084	1.31756
$506$	0.898516	0.0399439
$507$	5.69450	0.252902
$508$	10.3367	0.458617
$509$	13.0436	0.578148	0.289074	−	0.957307i	$-0.406653\pi$
$509$	13.0436	0.578148	0.289074	+	0.957307i	$0.406653\pi$
$510$	−5.54372	−0.245480
$511$	−18.7052	−0.827469
$512$	−1.00000	−0.0441942
$513$	10.3767	0.458143
$514$	3.26883	0.144182
$515$	−19.6953	−0.867881
$516$	1.05725	0.0465430
$517$	2.29915	0.101116
$518$	8.60452	0.378061
$519$	−2.86867	−0.125921
$520$	−3.22721	−0.141522
$521$	12.1415	0.531927	0.265963	−	0.963983i	$-0.414310\pi$
$521$	12.1415	0.531927	0.265963	+	0.963983i	$0.414310\pi$
$522$	−26.0408	−1.13978
$523$	−5.14171	−0.224831	−0.112416	−	0.993661i	$-0.535859\pi$
$523$	−5.14171	−0.224831	−0.112416	+	0.993661i	$0.535859\pi$
$524$	−1.00000	−0.0436852
$525$	−0.874340	−0.0381593
$526$	−19.8540	−0.865677
$527$	35.8823	1.56306
$528$	−0.459106	−0.0199800
$529$	1.00000	0.0434783
$530$	0.0489273	0.00212526
$531$	8.22343	0.356866
$532$	9.86889	0.427871
$533$	8.85800	0.383683
$534$	−1.25248	−0.0541999
$535$	37.4778	1.62031
$536$	12.5193	0.540751
$537$	−12.2121	−0.526992
$538$	−19.6024	−0.845121
$539$	0.698795	0.0300992
$540$	6.94764	0.298979
$541$	1.01304	0.0435539	0.0217769	−	0.999763i	$-0.493068\pi$
$541$	1.01304	0.0435539	0.0217769	+	0.999763i	$0.493068\pi$
$542$	3.63275	0.156040
$543$	8.31032	0.356630
$544$	4.57925	0.196334
$545$	−8.03157	−0.344035
$546$	1.94098	0.0830662
$547$	−27.2628	−1.16567	−0.582837	−	0.812589i	$-0.698057\pi$
$547$	−27.2628	−1.16567	−0.582837	+	0.812589i	$0.698057\pi$
$548$	−6.03988	−0.258011
$549$	22.6878	0.968291
$550$	−0.551306	−0.0235078
$551$	−33.6448	−1.43332
$552$	−0.510961	−0.0217479
$553$	−14.6610	−0.623448
$554$	−20.3699	−0.865436
$555$	3.73515	0.158548
$556$	7.51656	0.318773
$557$	3.16273	0.134009	0.0670046	−	0.997753i	$-0.478656\pi$
$557$	3.16273	0.134009	0.0670046	+	0.997753i	$0.478656\pi$
$558$	−21.4617	−0.908548
$559$	−2.81838	−0.119205
$560$	6.60763	0.279223
$561$	2.10236	0.0887619
$562$	0.960400	0.0405120
$563$	−19.7409	−0.831978	−0.415989	−	0.909370i	$-0.636565\pi$
$563$	−19.7409	−0.831978	−0.415989	+	0.909370i	$0.636565\pi$
$564$	−1.30746	−0.0550539
$565$	−30.3559	−1.27708
$566$	7.94276	0.333859
$567$	18.7368	0.786870
$568$	2.24850	0.0943451
$569$	9.48894	0.397797	0.198898	−	0.980020i	$-0.436264\pi$
$569$	9.48894	0.397797	0.198898	+	0.980020i	$0.436264\pi$
$570$	4.28400	0.179437
$571$	45.8540	1.91893	0.959465	−	0.281826i	$-0.0909402\pi$
$571$	45.8540	1.91893	0.959465	+	0.281826i	$0.0909402\pi$
$572$	1.22386	0.0511723
$573$	−6.15514	−0.257135
$574$	−18.1366	−0.757005
$575$	−0.613574	−0.0255878
$576$	−2.73892	−0.114122
$577$	10.6861	0.444870	0.222435	−	0.974948i	$-0.428599\pi$
$577$	10.6861	0.444870	0.222435	+	0.974948i	$0.428599\pi$
$578$	−3.96954	−0.165111
$579$	0.995705	0.0413801
$580$	−22.5266	−0.935365
$581$	−17.3312	−0.719021
$582$	−4.53860	−0.188131
$583$	−0.0185548	−0.000768463 0
$584$	6.70712	0.277543
$585$	−8.83906	−0.365450
$586$	−20.7207	−0.855965
$587$	−2.26704	−0.0935706	−0.0467853	−	0.998905i	$-0.514898\pi$
$587$	−2.26704	−0.0935706	−0.0467853	+	0.998905i	$0.514898\pi$
$588$	−0.397385	−0.0163879
$589$	−27.7286	−1.14254
$590$	7.11367	0.292865
$591$	11.0120	0.452972
$592$	−3.08532	−0.126806
$593$	−19.8737	−0.816115	−0.408057	−	0.912956i	$-0.633794\pi$
$593$	−19.8737	−0.816115	−0.408057	+	0.912956i	$0.633794\pi$
$594$	−2.63477	−0.108106
$595$	−30.2580	−1.24046
$596$	9.92371	0.406491
$597$	4.18460	0.171264
$598$	1.36209	0.0557002
$599$	−30.7323	−1.25569	−0.627843	−	0.778340i	$-0.716062\pi$
$599$	−30.7323	−1.25569	−0.627843	+	0.778340i	$0.716062\pi$
$600$	0.313512	0.0127991
$601$	−22.8624	−0.932576	−0.466288	−	0.884633i	$-0.654409\pi$
$601$	−22.8624	−0.932576	−0.466288	+	0.884633i	$0.654409\pi$
$602$	5.77056	0.235191
$603$	34.2893	1.39637
$604$	0.928938	0.0377979
$605$	−24.1495	−0.981816
$606$	6.38532	0.259386
$607$	−24.2688	−0.985042	−0.492521	−	0.870301i	$-0.663925\pi$
$607$	−24.2688	−0.985042	−0.492521	+	0.870301i	$0.663925\pi$
$608$	−3.53869	−0.143513
$609$	13.5484	0.549010
$610$	19.6260	0.794635
$611$	3.48536	0.141003
$612$	12.5422	0.506988
$613$	−27.8346	−1.12423	−0.562115	−	0.827059i	$-0.690012\pi$
$613$	−27.8346	−1.12423	−0.562115	+	0.827059i	$0.690012\pi$
$614$	6.56579	0.264974
$615$	−7.87292	−0.317467
$616$	−2.50583	−0.100963
$617$	−18.6085	−0.749150	−0.374575	−	0.927197i	$-0.622211\pi$
$617$	−18.6085	−0.749150	−0.374575	+	0.927197i	$0.622211\pi$
$618$	−4.24748	−0.170859
$619$	−43.8186	−1.76122	−0.880610	−	0.473842i	$-0.842867\pi$
$619$	−43.8186	−1.76122	−0.880610	+	0.473842i	$0.842867\pi$
$620$	−18.5654	−0.745606
$621$	−2.93236	−0.117672
$622$	4.91478	0.197065
$623$	−6.83609	−0.273882
$624$	−0.695976	−0.0278614
$625$	−27.6914	−1.10766
$626$	−5.15580	−0.206067
$627$	−1.62463	−0.0648817
$628$	6.44044	0.257001
$629$	14.1285	0.563339
$630$	18.0978	0.721033
$631$	36.3020	1.44516	0.722579	−	0.691288i	$-0.242956\pi$
$631$	36.3020	1.44516	0.722579	+	0.691288i	$0.242956\pi$
$632$	5.25698	0.209112
$633$	−1.95832	−0.0778362
$634$	1.06135	0.0421515
$635$	24.4907	0.971885
$636$	0.0105516	0.000418399 0
$637$	1.05933	0.0419722
$638$	8.54283	0.338214
$639$	6.15847	0.243625
$640$	−2.36930	−0.0936547
$641$	5.87055	0.231873	0.115936	−	0.993257i	$-0.463013\pi$
$641$	5.87055	0.231873	0.115936	+	0.993257i	$0.463013\pi$
$642$	8.08242	0.318988
$643$	24.4460	0.964057	0.482028	−	0.876156i	$-0.339900\pi$
$643$	24.4460	0.964057	0.482028	+	0.876156i	$0.339900\pi$
$644$	−2.78886	−0.109896
$645$	2.50495	0.0986323
$646$	16.2045	0.637559
$647$	−6.93673	−0.272711	−0.136356	−	0.990660i	$-0.543539\pi$
$647$	−6.93673	−0.272711	−0.136356	+	0.990660i	$0.543539\pi$
$648$	−6.71844	−0.263925
$649$	−2.69774	−0.105895
$650$	−0.835745	−0.0327806
$651$	11.1660	0.437632
$652$	−21.0988	−0.826291
$653$	38.2599	1.49723	0.748613	−	0.663008i	$-0.230720\pi$
$653$	38.2599	1.49723	0.748613	+	0.663008i	$0.230720\pi$
$654$	−1.73208	−0.0677298
$655$	−2.36930	−0.0925761
$656$	6.50322	0.253908
$657$	18.3703	0.716692
$658$	−7.13619	−0.278198
$659$	−35.4568	−1.38120	−0.690599	−	0.723237i	$-0.742653\pi$
$659$	−35.4568	−1.38120	−0.690599	+	0.723237i	$0.742653\pi$
$660$	−1.08776	−0.0423410
$661$	33.2645	1.29384	0.646920	−	0.762558i	$-0.276057\pi$
$661$	33.2645	1.29384	0.646920	+	0.762558i	$0.276057\pi$
$662$	−15.7680	−0.612842
$663$	3.18705	0.123775
$664$	6.21446	0.241168
$665$	23.3824	0.906729
$666$	−8.45045	−0.327448
$667$	9.50770	0.368140
$668$	7.53014	0.291350
$669$	−9.21285	−0.356189
$670$	29.6620	1.14594
$671$	−7.44284	−0.287328
$672$	1.42500	0.0549704
$673$	−17.5508	−0.676535	−0.338267	−	0.941050i	$-0.609841\pi$
$673$	−17.5508	−0.676535	−0.338267	+	0.941050i	$0.609841\pi$
$674$	−24.4343	−0.941174
$675$	1.79922	0.0692520
$676$	−11.1447	−0.428642
$677$	42.2559	1.62403	0.812013	−	0.583639i	$-0.198372\pi$
$677$	42.2559	1.62403	0.812013	+	0.583639i	$0.198372\pi$
$678$	−6.54653	−0.251418
$679$	−24.7720	−0.950661
$680$	10.8496	0.416064
$681$	−10.1564	−0.389194
$682$	7.04063	0.269600
$683$	−21.5436	−0.824344	−0.412172	−	0.911106i	$-0.635230\pi$
$683$	−21.5436	−0.824344	−0.412172	+	0.911106i	$0.635230\pi$
$684$	−9.69218	−0.370590
$685$	−14.3103	−0.546768
$686$	17.3530	0.662542
$687$	−6.59086	−0.251457
$688$	−2.06915	−0.0788856
$689$	−0.0281280	−0.00107159
$690$	−1.21062	−0.0460874
$691$	−16.9878	−0.646248	−0.323124	−	0.946357i	$-0.604733\pi$
$691$	−16.9878	−0.646248	−0.323124	+	0.946357i	$0.604733\pi$
$692$	5.61427	0.213423
$693$	−6.86327	−0.260714
$694$	9.11262	0.345910
$695$	17.8090	0.675533
$696$	−4.85806	−0.184144
$697$	−29.7799	−1.12799
$698$	12.3863	0.468827
$699$	−6.85494	−0.259278
$700$	1.71117	0.0646761
$701$	2.96122	0.111844	0.0559218	−	0.998435i	$-0.482190\pi$
$701$	2.96122	0.111844	0.0559218	+	0.998435i	$0.482190\pi$
$702$	−3.99415	−0.150750
$703$	−10.9180	−0.411780
$704$	0.898516	0.0338641
$705$	−3.09776	−0.116668
$706$	5.10072	0.191968
$707$	34.8515	1.31072
$708$	1.53413	0.0576560
$709$	0.271298	0.0101888	0.00509440	−	0.999987i	$-0.498378\pi$
$709$	0.271298	0.0101888	0.00509440	+	0.999987i	$0.498378\pi$
$710$	5.32737	0.199933
$711$	14.3985	0.539984
$712$	2.45122	0.0918632
$713$	7.83584	0.293455
$714$	−6.52541	−0.244208
$715$	2.89970	0.108443
$716$	23.9003	0.893196
$717$	2.23805	0.0835815
$718$	14.3929	0.537138
$719$	−27.9379	−1.04191	−0.520953	−	0.853585i	$-0.674423\pi$
$719$	−27.9379	−1.04191	−0.520953	+	0.853585i	$0.674423\pi$
$720$	−6.48932	−0.241843
$721$	−23.1830	−0.863381
$722$	6.47769	0.241074
$723$	−1.84597	−0.0686524
$724$	−16.2641	−0.604450
$725$	−5.83368	−0.216657
$726$	−5.20805	−0.193289
$727$	−22.5350	−0.835778	−0.417889	−	0.908498i	$-0.637230\pi$
$727$	−22.5350	−0.835778	−0.417889	+	0.908498i	$0.637230\pi$
$728$	−3.79868	−0.140789
$729$	−13.9063	−0.515048
$730$	15.8912	0.588158
$731$	9.47515	0.350451
$732$	4.23253	0.156439
$733$	−48.9736	−1.80888	−0.904440	−	0.426600i	$-0.859711\pi$
$733$	−48.9736	−1.80888	−0.904440	+	0.426600i	$0.859711\pi$
$734$	−4.65866	−0.171954
$735$	−0.941524	−0.0347286
$736$	1.00000	0.0368605
$737$	−11.2488	−0.414355
$738$	17.8118	0.655662
$739$	−3.91778	−0.144118	−0.0720589	−	0.997400i	$-0.522957\pi$
$739$	−3.91778	−0.144118	−0.0720589	+	0.997400i	$0.522957\pi$
$740$	−7.31005	−0.268723
$741$	−2.46284	−0.0904748
$742$	0.0575914	0.00211425
$743$	1.74544	0.0640340	0.0320170	−	0.999487i	$-0.489807\pi$
$743$	1.74544	0.0640340	0.0320170	+	0.999487i	$0.489807\pi$
$744$	−4.00381	−0.146787
$745$	23.5122	0.861421
$746$	−2.02497	−0.0741395
$747$	17.0209	0.622762
$748$	−4.11453	−0.150442
$749$	44.1144	1.61191
$750$	−5.31029	−0.193904
$751$	17.7952	0.649355	0.324677	−	0.945825i	$-0.394744\pi$
$751$	17.7952	0.649355	0.324677	+	0.945825i	$0.394744\pi$
$752$	2.55882	0.0933107
$753$	3.59931	0.131166
$754$	12.9504	0.471625
$755$	2.20093	0.0801001
$756$	8.17794	0.297429
$757$	42.4155	1.54162	0.770809	−	0.637067i	$-0.219852\pi$
$757$	42.4155	1.54162	0.770809	+	0.637067i	$0.219852\pi$
$758$	−13.2463	−0.481128
$759$	0.459106	0.0166645
$760$	−8.38421	−0.304127
$761$	−8.81019	−0.319369	−0.159685	−	0.987168i	$-0.551048\pi$
$761$	−8.81019	−0.319369	−0.159685	+	0.987168i	$0.551048\pi$
$762$	5.28165	0.191334
$763$	−9.45382	−0.342251
$764$	12.0462	0.435816
$765$	29.7162	1.07439
$766$	19.7135	0.712278
$767$	−4.08960	−0.147667
$768$	−0.510961	−0.0184377
$769$	−44.1256	−1.59121	−0.795604	−	0.605817i	$-0.792846\pi$
$769$	−44.1256	−1.59121	−0.795604	+	0.605817i	$0.792846\pi$
$770$	−5.93707	−0.213957
$771$	1.67024	0.0601523
$772$	−1.94869	−0.0701350
$773$	13.3700	0.480885	0.240443	−	0.970663i	$-0.422707\pi$
$773$	13.3700	0.480885	0.240443	+	0.970663i	$0.422707\pi$
$774$	−5.66723	−0.203704
$775$	−4.80787	−0.172704
$776$	8.88248	0.318862
$777$	4.39657	0.157726
$778$	−22.6822	−0.813195
$779$	23.0129	0.824522
$780$	−1.64898	−0.0590428
$781$	−2.02032	−0.0722926
$782$	−4.57925	−0.163754
$783$	−27.8800	−0.996351
$784$	0.777721	0.0277758
$785$	15.2593	0.544628
$786$	−0.510961	−0.0182254
$787$	−26.7837	−0.954734	−0.477367	−	0.878704i	$-0.658409\pi$
$787$	−26.7837	−0.954734	−0.477367	+	0.878704i	$0.658409\pi$
$788$	−21.5515	−0.767740
$789$	−10.1446	−0.361159
$790$	12.4554	0.443142
$791$	−35.7314	−1.27046
$792$	2.46096	0.0874465
$793$	−11.2829	−0.400667
$794$	−11.7673	−0.417606
$795$	0.0249999	0.000886655 0
$796$	−8.18967	−0.290275
$797$	−23.4686	−0.831299	−0.415650	−	0.909525i	$-0.636446\pi$
$797$	−23.4686	−0.831299	−0.415650	+	0.909525i	$0.636446\pi$
$798$	5.04262	0.178507
$799$	−11.7175	−0.414535
$800$	−0.613574	−0.0216931
$801$	6.71368	0.237216
$802$	16.1699	0.570977
$803$	−6.02645	−0.212669
$804$	6.39687	0.225600
$805$	−6.60763	−0.232888
$806$	10.6731	0.375946
$807$	−10.0161	−0.352583
$808$	−12.4967	−0.439632
$809$	30.1944	1.06158	0.530789	−	0.847504i	$-0.321895\pi$
$809$	30.1944	1.06158	0.530789	+	0.847504i	$0.321895\pi$
$810$	−15.9180	−0.559301
$811$	34.2559	1.20289	0.601443	−	0.798916i	$-0.294593\pi$
$811$	34.2559	1.20289	0.601443	+	0.798916i	$0.294593\pi$
$812$	−26.5156	−0.930516
$813$	1.85619	0.0650995
$814$	2.77221	0.0971660
$815$	−49.9893	−1.75105
$816$	2.33982	0.0819100
$817$	−7.32207	−0.256167
$818$	−39.9690	−1.39748
$819$	−10.4043	−0.363555
$820$	15.4081	0.538073
$821$	−25.4104	−0.886829	−0.443415	−	0.896317i	$-0.646233\pi$
$821$	−25.4104	−0.886829	−0.443415	+	0.896317i	$0.646233\pi$
$822$	−3.08614	−0.107642
$823$	−18.8329	−0.656474	−0.328237	−	0.944595i	$-0.606454\pi$
$823$	−18.8329	−0.656474	−0.328237	+	0.944595i	$0.606454\pi$
$824$	8.31273	0.289588
$825$	−0.281696	−0.00980739
$826$	8.37336	0.291347
$827$	55.5970	1.93330	0.966649	−	0.256105i	$-0.0824391\pi$
$827$	55.5970	1.93330	0.966649	+	0.256105i	$0.0824391\pi$
$828$	2.73892	0.0951840
$829$	−26.6216	−0.924607	−0.462304	−	0.886722i	$-0.652977\pi$
$829$	−26.6216	−0.924607	−0.462304	+	0.886722i	$0.652977\pi$
$830$	14.7239	0.511074
$831$	−10.4082	−0.361058
$832$	1.36209	0.0472221
$833$	−3.56138	−0.123395
$834$	3.84067	0.132991
$835$	17.8411	0.617418
$836$	3.17957	0.109968
$837$	−22.9775	−0.794219
$838$	30.0864	1.03932
$839$	−40.8399	−1.40995	−0.704975	−	0.709232i	$-0.749042\pi$
$839$	−40.8399	−1.40995	−0.704975	+	0.709232i	$0.749042\pi$
$840$	3.37624	0.116491
$841$	61.3964	2.11712
$842$	31.6647	1.09124
$843$	0.490727	0.0169015
$844$	3.83262	0.131924
$845$	−26.4051	−0.908364
$846$	7.00841	0.240954
$847$	−28.4259	−0.976725
$848$	−0.0206505	−0.000709142 0
$849$	4.05844	0.139285
$850$	2.80971	0.0963722
$851$	3.08532	0.105764
$852$	1.14890	0.0393606
$853$	35.7169	1.22292	0.611461	−	0.791275i	$-0.290582\pi$
$853$	35.7169	1.22292	0.611461	+	0.791275i	$0.290582\pi$
$854$	23.1014	0.790515
$855$	−22.9637	−0.785341
$856$	−15.8181	−0.540651
$857$	7.36730	0.251662	0.125831	−	0.992052i	$-0.459840\pi$
$857$	7.36730	0.251662	0.125831	+	0.992052i	$0.459840\pi$
$858$	0.625346	0.0213490
$859$	−3.24579	−0.110745	−0.0553724	−	0.998466i	$-0.517635\pi$
$859$	−3.24579	−0.110745	−0.0553724	+	0.998466i	$0.517635\pi$
$860$	−4.90243	−0.167172
$861$	−9.26707	−0.315821
$862$	20.4046	0.694982
$863$	16.0169	0.545222	0.272611	−	0.962124i	$-0.412113\pi$
$863$	16.0169	0.545222	0.272611	+	0.962124i	$0.412113\pi$
$864$	−2.93236	−0.0997610
$865$	13.3019	0.452277
$866$	8.53681	0.290093
$867$	−2.02828	−0.0688840
$868$	−21.8530	−0.741740
$869$	−4.72348	−0.160233
$870$	−11.5102	−0.390232
$871$	−17.0525	−0.577800
$872$	3.38985	0.114795
$873$	24.3284	0.823391
$874$	3.53869	0.119698
$875$	−28.9839	−0.979834
$876$	3.42707	0.115790
$877$	47.0961	1.59032	0.795161	−	0.606399i	$-0.207387\pi$
$877$	47.0961	1.59032	0.795161	+	0.606399i	$0.207387\pi$
$878$	19.1651	0.646791
$879$	−10.5875	−0.357107
$880$	2.12885	0.0717636
$881$	30.9668	1.04330	0.521649	−	0.853160i	$-0.325317\pi$
$881$	30.9668	1.04330	0.521649	+	0.853160i	$0.325317\pi$
$882$	2.13012	0.0717247
$883$	4.05885	0.136591	0.0682955	−	0.997665i	$-0.478244\pi$
$883$	4.05885	0.136591	0.0682955	+	0.997665i	$0.478244\pi$
$884$	−6.23737	−0.209785
$885$	3.63480	0.122183
$886$	−23.9265	−0.803827
$887$	−33.6774	−1.13078	−0.565388	−	0.824825i	$-0.691273\pi$
$887$	−33.6774	−1.13078	−0.565388	+	0.824825i	$0.691273\pi$
$888$	−1.57648	−0.0529032
$889$	28.8276	0.966846
$890$	5.80766	0.194673
$891$	6.03662	0.202234
$892$	18.0304	0.603704
$893$	9.05488	0.303010
$894$	5.07063	0.169587
$895$	56.6269	1.89283
$896$	−2.78886	−0.0931692
$897$	0.695976	0.0232380
$898$	−23.2056	−0.774382
$899$	74.5008	2.48474
$900$	−1.68053	−0.0560176
$901$	0.0945640	0.00315038
$902$	−5.84325	−0.194559
$903$	2.94853	0.0981209
$904$	12.8122	0.426128
$905$	−38.5345	−1.28093
$906$	0.474651	0.0157692
$907$	22.6180	0.751020	0.375510	−	0.926818i	$-0.377468\pi$
$907$	22.6180	0.751020	0.375510	+	0.926818i	$0.377468\pi$
$908$	19.8771	0.659643
$909$	−34.2274	−1.13525
$910$	−9.00022	−0.298354
$911$	−36.0075	−1.19298	−0.596490	−	0.802620i	$-0.703439\pi$
$911$	−36.0075	−1.19298	−0.596490	+	0.802620i	$0.703439\pi$
$912$	−1.80813	−0.0598732
$913$	−5.58379	−0.184797
$914$	4.56956	0.151148
$915$	10.0281	0.331520
$916$	12.8990	0.426193
$917$	−2.78886	−0.0920962
$918$	13.4280	0.443191
$919$	−34.7315	−1.14569	−0.572843	−	0.819665i	$-0.694159\pi$
$919$	−34.7315	−1.14569	−0.572843	+	0.819665i	$0.694159\pi$
$920$	2.36930	0.0781134
$921$	3.35486	0.110546
$922$	22.1990	0.731085
$923$	−3.06267	−0.100809
$924$	−1.28038	−0.0421215
$925$	−1.89307	−0.0622439
$926$	21.1625	0.695444
$927$	22.7679	0.747796
$928$	9.50770	0.312106
$929$	15.8472	0.519930	0.259965	−	0.965618i	$-0.416289\pi$
$929$	15.8472	0.519930	0.259965	+	0.965618i	$0.416289\pi$
$930$	−9.48621	−0.311065
$931$	2.75211	0.0901969
$932$	13.4158	0.439449
$933$	2.51126	0.0822149
$934$	1.89152	0.0618925
$935$	−9.74855	−0.318812
$936$	3.73066	0.121941
$937$	−6.50109	−0.212381	−0.106191	−	0.994346i	$-0.533865\pi$
$937$	−6.50109	−0.212381	−0.106191	+	0.994346i	$0.533865\pi$
$938$	34.9145	1.14000
$939$	−2.63441	−0.0859707
$940$	6.06262	0.197741
$941$	−30.9520	−1.00901	−0.504503	−	0.863410i	$-0.668324\pi$
$941$	−30.9520	−1.00901	−0.504503	+	0.863410i	$0.668324\pi$
$942$	3.29081	0.107220
$943$	−6.50322	−0.211774
$944$	−3.00244	−0.0977210
$945$	19.3760	0.630300
$946$	1.85916	0.0604466
$947$	−3.25183	−0.105670	−0.0528351	−	0.998603i	$-0.516826\pi$
$947$	−3.25183	−0.105670	−0.0528351	+	0.998603i	$0.516826\pi$
$948$	2.68611	0.0872408
$949$	−9.13572	−0.296558
$950$	−2.17125	−0.0704445
$951$	0.542307	0.0175855
$952$	12.7709	0.413906
$953$	36.9112	1.19567	0.597836	−	0.801618i	$-0.296027\pi$
$953$	36.9112	1.19567	0.597836	+	0.801618i	$0.296027\pi$
$954$	−0.0565601	−0.00183120
$955$	28.5410	0.923567
$956$	−4.38008	−0.141662
$957$	4.36505	0.141102
$958$	9.85969	0.318552
$959$	−16.8444	−0.543933
$960$	−1.21062	−0.0390725
$961$	30.4004	0.980658
$962$	4.20250	0.135494
$963$	−43.3245	−1.39611
$964$	3.61274	0.116359
$965$	−4.61703	−0.148628
$966$	−1.42500	−0.0458485
$967$	41.6289	1.33870	0.669348	−	0.742949i	$-0.266574\pi$
$967$	41.6289	1.33870	0.669348	+	0.742949i	$0.266574\pi$
$968$	10.1927	0.327605
$969$	8.27988	0.265988
$970$	21.0452	0.675722
$971$	42.7414	1.37164	0.685819	−	0.727773i	$-0.259444\pi$
$971$	42.7414	1.37164	0.685819	+	0.727773i	$0.259444\pi$
$972$	−12.2299	−0.392276
$973$	20.9626	0.672031
$974$	32.8919	1.05392
$975$	−0.427033	−0.0136760
$976$	−8.28348	−0.265148
$977$	21.1898	0.677921	0.338960	−	0.940801i	$-0.389925\pi$
$977$	21.1898	0.677921	0.338960	+	0.940801i	$0.389925\pi$
$978$	−10.7806	−0.344727
$979$	−2.20246	−0.0703908
$980$	1.84265	0.0588614
$981$	9.28454	0.296432
$982$	21.7901	0.695349
$983$	−3.06058	−0.0976173	−0.0488087	−	0.998808i	$-0.515542\pi$
$983$	−3.06058	−0.0976173	−0.0488087	+	0.998808i	$0.515542\pi$
$984$	3.32289	0.105930
$985$	−51.0619	−1.62697
$986$	−43.5382	−1.38654
$987$	−3.64631	−0.116063
$988$	4.82002	0.153345
$989$	2.06915	0.0657951
$990$	5.83076	0.185314
$991$	−29.5613	−0.939044	−0.469522	−	0.882921i	$-0.655574\pi$
$991$	−29.5613	−0.939044	−0.469522	+	0.882921i	$0.655574\pi$
$992$	7.83584	0.248788
$993$	−8.05685	−0.255676
$994$	6.27075	0.198896
$995$	−19.4038	−0.615141
$996$	3.17534	0.100615
$997$	35.0113	1.10882	0.554410	−	0.832244i	$-0.312944\pi$
$997$	35.0113	1.10882	0.554410	+	0.832244i	$0.312944\pi$
$998$	−11.1791	−0.353867
$999$	−9.04728	−0.286243

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.13	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.13	✓	24	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.510961 q^{3} +1.00000 q^{4} +2.36930 q^{5} +0.510961 q^{6} +2.78886 q^{7} -1.00000 q^{8} -2.73892 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.510961 q^{3} +1.00000 q^{4} +2.36930 q^{5} +0.510961 q^{6} +2.78886 q^{7} -1.00000 q^{8} -2.73892 q^{9} -2.36930 q^{10} +0.898516 q^{11} -0.510961 q^{12} +1.36209 q^{13} -2.78886 q^{14} -1.21062 q^{15} +1.00000 q^{16} -4.57925 q^{17} +2.73892 q^{18} +3.53869 q^{19} +2.36930 q^{20} -1.42500 q^{21} -0.898516 q^{22} -1.00000 q^{23} +0.510961 q^{24} +0.613574 q^{25} -1.36209 q^{26} +2.93236 q^{27} +2.78886 q^{28} -9.50770 q^{29} +1.21062 q^{30} -7.83584 q^{31} -1.00000 q^{32} -0.459106 q^{33} +4.57925 q^{34} +6.60763 q^{35} -2.73892 q^{36} -3.08532 q^{37} -3.53869 q^{38} -0.695976 q^{39} -2.36930 q^{40} +6.50322 q^{41} +1.42500 q^{42} -2.06915 q^{43} +0.898516 q^{44} -6.48932 q^{45} +1.00000 q^{46} +2.55882 q^{47} -0.510961 q^{48} +0.777721 q^{49} -0.613574 q^{50} +2.33982 q^{51} +1.36209 q^{52} -0.0206505 q^{53} -2.93236 q^{54} +2.12885 q^{55} -2.78886 q^{56} -1.80813 q^{57} +9.50770 q^{58} -3.00244 q^{59} -1.21062 q^{60} -8.28348 q^{61} +7.83584 q^{62} -7.63845 q^{63} +1.00000 q^{64} +3.22721 q^{65} +0.459106 q^{66} -12.5193 q^{67} -4.57925 q^{68} +0.510961 q^{69} -6.60763 q^{70} -2.24850 q^{71} +2.73892 q^{72} -6.70712 q^{73} +3.08532 q^{74} -0.313512 q^{75} +3.53869 q^{76} +2.50583 q^{77} +0.695976 q^{78} -5.25698 q^{79} +2.36930 q^{80} +6.71844 q^{81} -6.50322 q^{82} -6.21446 q^{83} -1.42500 q^{84} -10.8496 q^{85} +2.06915 q^{86} +4.85806 q^{87} -0.898516 q^{88} -2.45122 q^{89} +6.48932 q^{90} +3.79868 q^{91} -1.00000 q^{92} +4.00381 q^{93} -2.55882 q^{94} +8.38421 q^{95} +0.510961 q^{96} -8.88248 q^{97} -0.777721 q^{98} -2.46096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

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