LMFDB - Embedded newform 6026.2.a.h.1.17

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			1.17
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.48980 q^{3} +1.00000 q^{4} +3.56615 q^{5} -1.48980 q^{6} -2.69745 q^{7} -1.00000 q^{8} -0.780502 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.48980 q^{3} +1.00000 q^{4} +3.56615 q^{5} -1.48980 q^{6} -2.69745 q^{7} -1.00000 q^{8} -0.780502 q^{9} -3.56615 q^{10} -4.79381 q^{11} +1.48980 q^{12} +0.746865 q^{13} +2.69745 q^{14} +5.31284 q^{15} +1.00000 q^{16} +4.10189 q^{17} +0.780502 q^{18} +4.65428 q^{19} +3.56615 q^{20} -4.01866 q^{21} +4.79381 q^{22} -1.00000 q^{23} -1.48980 q^{24} +7.71742 q^{25} -0.746865 q^{26} -5.63218 q^{27} -2.69745 q^{28} -6.16822 q^{29} -5.31284 q^{30} -8.26320 q^{31} -1.00000 q^{32} -7.14180 q^{33} -4.10189 q^{34} -9.61952 q^{35} -0.780502 q^{36} -2.87867 q^{37} -4.65428 q^{38} +1.11268 q^{39} -3.56615 q^{40} -5.19872 q^{41} +4.01866 q^{42} +1.25728 q^{43} -4.79381 q^{44} -2.78339 q^{45} +1.00000 q^{46} -6.72119 q^{47} +1.48980 q^{48} +0.276254 q^{49} -7.71742 q^{50} +6.11098 q^{51} +0.746865 q^{52} +2.81932 q^{53} +5.63218 q^{54} -17.0954 q^{55} +2.69745 q^{56} +6.93393 q^{57} +6.16822 q^{58} +5.55324 q^{59} +5.31284 q^{60} -3.81590 q^{61} +8.26320 q^{62} +2.10537 q^{63} +1.00000 q^{64} +2.66343 q^{65} +7.14180 q^{66} -10.3918 q^{67} +4.10189 q^{68} -1.48980 q^{69} +9.61952 q^{70} +9.37733 q^{71} +0.780502 q^{72} -2.73400 q^{73} +2.87867 q^{74} +11.4974 q^{75} +4.65428 q^{76} +12.9311 q^{77} -1.11268 q^{78} -5.86082 q^{79} +3.56615 q^{80} -6.04931 q^{81} +5.19872 q^{82} -2.35445 q^{83} -4.01866 q^{84} +14.6279 q^{85} -1.25728 q^{86} -9.18940 q^{87} +4.79381 q^{88} -2.14139 q^{89} +2.78339 q^{90} -2.01463 q^{91} -1.00000 q^{92} -12.3105 q^{93} +6.72119 q^{94} +16.5979 q^{95} -1.48980 q^{96} -5.78968 q^{97} -0.276254 q^{98} +3.74158 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.48980	0.860135	0.430068	−	0.902797i	$-0.358490\pi$
$3$	1.48980	0.860135	0.430068	+	0.902797i	$0.358490\pi$
$4$	1.00000	0.500000
$5$	3.56615	1.59483	0.797415	−	0.603431i	$-0.206200\pi$
$5$	3.56615	1.59483	0.797415	+	0.603431i	$0.206200\pi$
$6$	−1.48980	−0.608207
$7$	−2.69745	−1.01954	−0.509771	−	0.860310i	$-0.670270\pi$
$7$	−2.69745	−1.01954	−0.509771	+	0.860310i	$0.670270\pi$
$8$	−1.00000	−0.353553
$9$	−0.780502	−0.260167
$10$	−3.56615	−1.12772
$11$	−4.79381	−1.44539	−0.722694	−	0.691169i	$-0.757096\pi$
$11$	−4.79381	−1.44539	−0.722694	+	0.691169i	$0.757096\pi$
$12$	1.48980	0.430068
$13$	0.746865	0.207143	0.103572	−	0.994622i	$-0.466973\pi$
$13$	0.746865	0.207143	0.103572	+	0.994622i	$0.466973\pi$
$14$	2.69745	0.720925
$15$	5.31284	1.37177
$16$	1.00000	0.250000
$17$	4.10189	0.994854	0.497427	−	0.867506i	$-0.334278\pi$
$17$	4.10189	0.994854	0.497427	+	0.867506i	$0.334278\pi$
$18$	0.780502	0.183966
$19$	4.65428	1.06776	0.533882	−	0.845559i	$-0.320733\pi$
$19$	4.65428	1.06776	0.533882	+	0.845559i	$0.320733\pi$
$20$	3.56615	0.797415
$21$	−4.01866	−0.876944
$22$	4.79381	1.02204
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.48980	−0.304104
$25$	7.71742	1.54348
$26$	−0.746865	−0.146472
$27$	−5.63218	−1.08391
$28$	−2.69745	−0.509771
$29$	−6.16822	−1.14541	−0.572705	−	0.819762i	$-0.694106\pi$
$29$	−6.16822	−1.14541	−0.572705	+	0.819762i	$0.694106\pi$
$30$	−5.31284	−0.969988
$31$	−8.26320	−1.48411	−0.742057	−	0.670337i	$-0.766150\pi$
$31$	−8.26320	−1.48411	−0.742057	+	0.670337i	$0.766150\pi$
$32$	−1.00000	−0.176777
$33$	−7.14180	−1.24323
$34$	−4.10189	−0.703468
$35$	−9.61952	−1.62600
$36$	−0.780502	−0.130084
$37$	−2.87867	−0.473251	−0.236625	−	0.971601i	$-0.576041\pi$
$37$	−2.87867	−0.473251	−0.236625	+	0.971601i	$0.576041\pi$
$38$	−4.65428	−0.755024
$39$	1.11268	0.178171
$40$	−3.56615	−0.563858
$41$	−5.19872	−0.811903	−0.405951	−	0.913895i	$-0.633060\pi$
$41$	−5.19872	−0.811903	−0.405951	+	0.913895i	$0.633060\pi$
$42$	4.01866	0.620093
$43$	1.25728	0.191734	0.0958668	−	0.995394i	$-0.469438\pi$
$43$	1.25728	0.191734	0.0958668	+	0.995394i	$0.469438\pi$
$44$	−4.79381	−0.722694
$45$	−2.78339	−0.414923
$46$	1.00000	0.147442
$47$	−6.72119	−0.980387	−0.490193	−	0.871614i	$-0.663074\pi$
$47$	−6.72119	−0.980387	−0.490193	+	0.871614i	$0.663074\pi$
$48$	1.48980	0.215034
$49$	0.276254	0.0394649
$50$	−7.71742	−1.09141
$51$	6.11098	0.855709
$52$	0.746865	0.103572
$53$	2.81932	0.387264	0.193632	−	0.981074i	$-0.437973\pi$
$53$	2.81932	0.387264	0.193632	+	0.981074i	$0.437973\pi$
$54$	5.63218	0.766443
$55$	−17.0954	−2.30515
$56$	2.69745	0.360462
$57$	6.93393	0.918422
$58$	6.16822	0.809927
$59$	5.55324	0.722971	0.361485	−	0.932378i	$-0.382270\pi$
$59$	5.55324	0.722971	0.361485	+	0.932378i	$0.382270\pi$
$60$	5.31284	0.685885
$61$	−3.81590	−0.488576	−0.244288	−	0.969703i	$-0.578554\pi$
$61$	−3.81590	−0.488576	−0.244288	+	0.969703i	$0.578554\pi$
$62$	8.26320	1.04943
$63$	2.10537	0.265252
$64$	1.00000	0.125000
$65$	2.66343	0.330358
$66$	7.14180	0.879095
$67$	−10.3918	−1.26956	−0.634778	−	0.772694i	$-0.718909\pi$
$67$	−10.3918	−1.26956	−0.634778	+	0.772694i	$0.718909\pi$
$68$	4.10189	0.497427
$69$	−1.48980	−0.179351
$70$	9.61952	1.14975
$71$	9.37733	1.11288	0.556442	−	0.830886i	$-0.312166\pi$
$71$	9.37733	1.11288	0.556442	+	0.830886i	$0.312166\pi$
$72$	0.780502	0.0919831
$73$	−2.73400	−0.319991	−0.159995	−	0.987118i	$-0.551148\pi$
$73$	−2.73400	−0.319991	−0.159995	+	0.987118i	$0.551148\pi$
$74$	2.87867	0.334639
$75$	11.4974	1.32761
$76$	4.65428	0.533882
$77$	12.9311	1.47363
$78$	−1.11268	−0.125986
$79$	−5.86082	−0.659394	−0.329697	−	0.944087i	$-0.606947\pi$
$79$	−5.86082	−0.659394	−0.329697	+	0.944087i	$0.606947\pi$
$80$	3.56615	0.398708
$81$	−6.04931	−0.672145
$82$	5.19872	0.574102
$83$	−2.35445	−0.258434	−0.129217	−	0.991616i	$-0.541246\pi$
$83$	−2.35445	−0.258434	−0.129217	+	0.991616i	$0.541246\pi$
$84$	−4.01866	−0.438472
$85$	14.6279	1.58662
$86$	−1.25728	−0.135576
$87$	−9.18940	−0.985208
$88$	4.79381	0.511022
$89$	−2.14139	−0.226987	−0.113494	−	0.993539i	$-0.536204\pi$
$89$	−2.14139	−0.226987	−0.113494	+	0.993539i	$0.536204\pi$
$90$	2.78339	0.293395
$91$	−2.01463	−0.211191
$92$	−1.00000	−0.104257
$93$	−12.3105	−1.27654
$94$	6.72119	0.693238
$95$	16.5979	1.70290
$96$	−1.48980	−0.152052
$97$	−5.78968	−0.587853	−0.293927	−	0.955828i	$-0.594962\pi$
$97$	−5.78968	−0.587853	−0.293927	+	0.955828i	$0.594962\pi$
$98$	−0.276254	−0.0279059
$99$	3.74158	0.376043
$100$	7.71742	0.771742
$101$	4.56806	0.454539	0.227269	−	0.973832i	$-0.427020\pi$
$101$	4.56806	0.454539	0.227269	+	0.973832i	$0.427020\pi$
$102$	−6.11098	−0.605077
$103$	7.62144	0.750963	0.375481	−	0.926830i	$-0.377477\pi$
$103$	7.62144	0.750963	0.375481	+	0.926830i	$0.377477\pi$
$104$	−0.746865	−0.0732362
$105$	−14.3311	−1.39858
$106$	−2.81932	−0.273837
$107$	−10.1233	−0.978661	−0.489330	−	0.872099i	$-0.662759\pi$
$107$	−10.1233	−0.978661	−0.489330	+	0.872099i	$0.662759\pi$
$108$	−5.63218	−0.541957
$109$	−0.727196	−0.0696527	−0.0348264	−	0.999393i	$-0.511088\pi$
$109$	−0.727196	−0.0696527	−0.0348264	+	0.999393i	$0.511088\pi$
$110$	17.0954	1.62999
$111$	−4.28864	−0.407060
$112$	−2.69745	−0.254885
$113$	13.1529	1.23732	0.618659	−	0.785660i	$-0.287676\pi$
$113$	13.1529	1.23732	0.618659	+	0.785660i	$0.287676\pi$
$114$	−6.93393	−0.649422
$115$	−3.56615	−0.332545
$116$	−6.16822	−0.572705
$117$	−0.582930	−0.0538919
$118$	−5.55324	−0.511217
$119$	−11.0646	−1.01429
$120$	−5.31284	−0.484994
$121$	11.9806	1.08914
$122$	3.81590	0.345476
$123$	−7.74503	−0.698346
$124$	−8.26320	−0.742057
$125$	9.69074	0.866766
$126$	−2.10537	−0.187561
$127$	−9.25234	−0.821012	−0.410506	−	0.911858i	$-0.634648\pi$
$127$	−9.25234	−0.821012	−0.410506	+	0.911858i	$0.634648\pi$
$128$	−1.00000	−0.0883883
$129$	1.87310	0.164917
$130$	−2.66343	−0.233599
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−7.14180	−0.621614
$133$	−12.5547	−1.08863
$134$	10.3918	0.897712
$135$	−20.0852	−1.72866
$136$	−4.10189	−0.351734
$137$	−16.9974	−1.45219	−0.726093	−	0.687597i	$-0.758666\pi$
$137$	−16.9974	−1.45219	−0.726093	+	0.687597i	$0.758666\pi$
$138$	1.48980	0.126820
$139$	−1.64747	−0.139737	−0.0698683	−	0.997556i	$-0.522258\pi$
$139$	−1.64747	−0.139737	−0.0698683	+	0.997556i	$0.522258\pi$
$140$	−9.61952	−0.812998
$141$	−10.0132	−0.843265
$142$	−9.37733	−0.786928
$143$	−3.58033	−0.299402
$144$	−0.780502	−0.0650419
$145$	−21.9968	−1.82674
$146$	2.73400	0.226268
$147$	0.411563	0.0339451
$148$	−2.87867	−0.236625
$149$	5.21941	0.427591	0.213795	−	0.976878i	$-0.431417\pi$
$149$	5.21941	0.427591	0.213795	+	0.976878i	$0.431417\pi$
$150$	−11.4974	−0.938759
$151$	−0.660230	−0.0537288	−0.0268644	−	0.999639i	$-0.508552\pi$
$151$	−0.660230	−0.0537288	−0.0268644	+	0.999639i	$0.508552\pi$
$152$	−4.65428	−0.377512
$153$	−3.20153	−0.258828
$154$	−12.9311	−1.04202
$155$	−29.4678	−2.36691
$156$	1.11268	0.0890856
$157$	9.01181	0.719221	0.359610	−	0.933103i	$-0.382910\pi$
$157$	9.01181	0.719221	0.359610	+	0.933103i	$0.382910\pi$
$158$	5.86082	0.466262
$159$	4.20022	0.333099
$160$	−3.56615	−0.281929
$161$	2.69745	0.212589
$162$	6.04931	0.475279
$163$	6.96678	0.545681	0.272840	−	0.962059i	$-0.412037\pi$
$163$	6.96678	0.545681	0.272840	+	0.962059i	$0.412037\pi$
$164$	−5.19872	−0.405951
$165$	−25.4687	−1.98274
$166$	2.35445	0.182740
$167$	−12.9286	−1.00045	−0.500224	−	0.865896i	$-0.666749\pi$
$167$	−12.9286	−1.00045	−0.500224	+	0.865896i	$0.666749\pi$
$168$	4.01866	0.310046
$169$	−12.4422	−0.957092
$170$	−14.6279	−1.12191
$171$	−3.63268	−0.277798
$172$	1.25728	0.0958668
$173$	−2.74653	−0.208815	−0.104407	−	0.994535i	$-0.533295\pi$
$173$	−2.74653	−0.208815	−0.104407	+	0.994535i	$0.533295\pi$
$174$	9.18940	0.696647
$175$	−20.8174	−1.57365
$176$	−4.79381	−0.361347
$177$	8.27321	0.621853
$178$	2.14139	0.160504
$179$	−15.4429	−1.15425	−0.577127	−	0.816654i	$-0.695826\pi$
$179$	−15.4429	−1.15425	−0.577127	+	0.816654i	$0.695826\pi$
$180$	−2.78339	−0.207462
$181$	18.1904	1.35208	0.676040	−	0.736865i	$-0.263694\pi$
$181$	18.1904	1.35208	0.676040	+	0.736865i	$0.263694\pi$
$182$	2.01463	0.149335
$183$	−5.68492	−0.420242
$184$	1.00000	0.0737210
$185$	−10.2658	−0.754755
$186$	12.3105	0.902649
$187$	−19.6636	−1.43795
$188$	−6.72119	−0.490193
$189$	15.1926	1.10510
$190$	−16.5979	−1.20413
$191$	2.00049	0.144750	0.0723751	−	0.997377i	$-0.476942\pi$
$191$	2.00049	0.144750	0.0723751	+	0.997377i	$0.476942\pi$
$192$	1.48980	0.107517
$193$	−1.38564	−0.0997404	−0.0498702	−	0.998756i	$-0.515881\pi$
$193$	−1.38564	−0.0997404	−0.0498702	+	0.998756i	$0.515881\pi$
$194$	5.78968	0.415675
$195$	3.96798	0.284153
$196$	0.276254	0.0197324
$197$	0.933591	0.0665156	0.0332578	−	0.999447i	$-0.489412\pi$
$197$	0.933591	0.0665156	0.0332578	+	0.999447i	$0.489412\pi$
$198$	−3.74158	−0.265902
$199$	0.0385265	0.00273107	0.00136554	−	0.999999i	$-0.499565\pi$
$199$	0.0385265	0.00273107	0.00136554	+	0.999999i	$0.499565\pi$
$200$	−7.71742	−0.545704
$201$	−15.4816	−1.09199
$202$	−4.56806	−0.321407
$203$	16.6385	1.16779
$204$	6.11098	0.427854
$205$	−18.5394	−1.29485
$206$	−7.62144	−0.531011
$207$	0.780502	0.0542487
$208$	0.746865	0.0517858
$209$	−22.3117	−1.54333
$210$	14.3311	0.988943
$211$	−1.69707	−0.116831	−0.0584155	−	0.998292i	$-0.518605\pi$
$211$	−1.69707	−0.116831	−0.0584155	+	0.998292i	$0.518605\pi$
$212$	2.81932	0.193632
$213$	13.9703	0.957231
$214$	10.1233	0.692018
$215$	4.48365	0.305783
$216$	5.63218	0.383222
$217$	22.2896	1.51312
$218$	0.727196	0.0492519
$219$	−4.07311	−0.275235
$220$	−17.0954	−1.15257
$221$	3.06356	0.206077
$222$	4.28864	0.287835
$223$	13.8360	0.926529	0.463265	−	0.886220i	$-0.346678\pi$
$223$	13.8360	0.926529	0.463265	+	0.886220i	$0.346678\pi$
$224$	2.69745	0.180231
$225$	−6.02347	−0.401565
$226$	−13.1529	−0.874915
$227$	−10.5000	−0.696910	−0.348455	−	0.937326i	$-0.613294\pi$
$227$	−10.5000	−0.696910	−0.348455	+	0.937326i	$0.613294\pi$
$228$	6.93393	0.459211
$229$	12.3635	0.817005	0.408503	−	0.912757i	$-0.366051\pi$
$229$	12.3635	0.817005	0.408503	+	0.912757i	$0.366051\pi$
$230$	3.56615	0.235145
$231$	19.2647	1.26752
$232$	6.16822	0.404964
$233$	7.47482	0.489692	0.244846	−	0.969562i	$-0.421263\pi$
$233$	7.47482	0.489692	0.244846	+	0.969562i	$0.421263\pi$
$234$	0.582930	0.0381073
$235$	−23.9688	−1.56355
$236$	5.55324	0.361485
$237$	−8.73144	−0.567168
$238$	11.0646	0.717214
$239$	2.73435	0.176870	0.0884350	−	0.996082i	$-0.471813\pi$
$239$	2.73435	0.176870	0.0884350	+	0.996082i	$0.471813\pi$
$240$	5.31284	0.342942
$241$	25.7983	1.66181	0.830907	−	0.556412i	$-0.187822\pi$
$241$	25.7983	1.66181	0.830907	+	0.556412i	$0.187822\pi$
$242$	−11.9806	−0.770141
$243$	7.88431	0.505778
$244$	−3.81590	−0.244288
$245$	0.985164	0.0629398
$246$	7.74503	0.493805
$247$	3.47612	0.221180
$248$	8.26320	0.524714
$249$	−3.50765	−0.222288
$250$	−9.69074	−0.612896
$251$	−16.1788	−1.02120	−0.510599	−	0.859819i	$-0.670577\pi$
$251$	−16.1788	−1.02120	−0.510599	+	0.859819i	$0.670577\pi$
$252$	2.10537	0.132626
$253$	4.79381	0.301384
$254$	9.25234	0.580543
$255$	21.7927	1.36471
$256$	1.00000	0.0625000
$257$	−20.7693	−1.29555	−0.647777	−	0.761830i	$-0.724301\pi$
$257$	−20.7693	−1.29555	−0.647777	+	0.761830i	$0.724301\pi$
$258$	−1.87310	−0.116614
$259$	7.76509	0.482499
$260$	2.66343	0.165179
$261$	4.81431	0.297998
$262$	1.00000	0.0617802
$263$	−11.5028	−0.709296	−0.354648	−	0.935000i	$-0.615399\pi$
$263$	−11.5028	−0.709296	−0.354648	+	0.935000i	$0.615399\pi$
$264$	7.14180	0.439548
$265$	10.0541	0.617620
$266$	12.5547	0.769778
$267$	−3.19024	−0.195240
$268$	−10.3918	−0.634778
$269$	16.5846	1.01118	0.505590	−	0.862774i	$-0.331275\pi$
$269$	16.5846	1.01118	0.505590	+	0.862774i	$0.331275\pi$
$270$	20.0852	1.22235
$271$	−7.01482	−0.426120	−0.213060	−	0.977039i	$-0.568343\pi$
$271$	−7.01482	−0.426120	−0.213060	+	0.977039i	$0.568343\pi$
$272$	4.10189	0.248713
$273$	−3.00140	−0.181653
$274$	16.9974	1.02685
$275$	−36.9958	−2.23093
$276$	−1.48980	−0.0896753
$277$	−28.5911	−1.71787	−0.858936	−	0.512083i	$-0.828874\pi$
$277$	−28.5911	−1.71787	−0.858936	+	0.512083i	$0.828874\pi$
$278$	1.64747	0.0988086
$279$	6.44945	0.386118
$280$	9.61952	0.574876
$281$	−3.76526	−0.224617	−0.112308	−	0.993673i	$-0.535824\pi$
$281$	−3.76526	−0.224617	−0.112308	+	0.993673i	$0.535824\pi$
$282$	10.0132	0.596278
$283$	21.7158	1.29087	0.645436	−	0.763814i	$-0.276676\pi$
$283$	21.7158	1.29087	0.645436	+	0.763814i	$0.276676\pi$
$284$	9.37733	0.556442
$285$	24.7274	1.46473
$286$	3.58033	0.211709
$287$	14.0233	0.827769
$288$	0.780502	0.0459915
$289$	−0.174531	−0.0102665
$290$	21.9968	1.29170
$291$	−8.62545	−0.505633
$292$	−2.73400	−0.159995
$293$	−9.75958	−0.570161	−0.285080	−	0.958504i	$-0.592020\pi$
$293$	−9.75958	−0.570161	−0.285080	+	0.958504i	$0.592020\pi$
$294$	−0.411563	−0.0240028
$295$	19.8037	1.15302
$296$	2.87867	0.167319
$297$	26.9996	1.56668
$298$	−5.21941	−0.302352
$299$	−0.746865	−0.0431923
$300$	11.4974	0.663803
$301$	−3.39146	−0.195480
$302$	0.660230	0.0379920
$303$	6.80548	0.390965
$304$	4.65428	0.266941
$305$	−13.6081	−0.779196
$306$	3.20153	0.183019
$307$	−19.3190	−1.10259	−0.551297	−	0.834309i	$-0.685867\pi$
$307$	−19.3190	−1.10259	−0.551297	+	0.834309i	$0.685867\pi$
$308$	12.9311	0.736816
$309$	11.3544	0.645929
$310$	29.4678	1.67366
$311$	10.5007	0.595440	0.297720	−	0.954653i	$-0.403774\pi$
$311$	10.5007	0.595440	0.297720	+	0.954653i	$0.403774\pi$
$312$	−1.11268	−0.0629930
$313$	6.56310	0.370968	0.185484	−	0.982647i	$-0.440615\pi$
$313$	6.56310	0.370968	0.185484	+	0.982647i	$0.440615\pi$
$314$	−9.01181	−0.508566
$315$	7.50806	0.423031
$316$	−5.86082	−0.329697
$317$	−1.15264	−0.0647385	−0.0323693	−	0.999476i	$-0.510305\pi$
$317$	−1.15264	−0.0647385	−0.0323693	+	0.999476i	$0.510305\pi$
$318$	−4.20022	−0.235537
$319$	29.5693	1.65556
$320$	3.56615	0.199354
$321$	−15.0817	−0.841781
$322$	−2.69745	−0.150323
$323$	19.0913	1.06227
$324$	−6.04931	−0.336073
$325$	5.76388	0.319722
$326$	−6.96678	−0.385855
$327$	−1.08337	−0.0599107
$328$	5.19872	0.287051
$329$	18.1301	0.999545
$330$	25.4687	1.40201
$331$	−21.0778	−1.15854	−0.579271	−	0.815135i	$-0.696663\pi$
$331$	−21.0778	−1.15854	−0.579271	+	0.815135i	$0.696663\pi$
$332$	−2.35445	−0.129217
$333$	2.24681	0.123124
$334$	12.9286	0.707424
$335$	−37.0586	−2.02473
$336$	−4.01866	−0.219236
$337$	17.8366	0.971622	0.485811	−	0.874064i	$-0.338524\pi$
$337$	17.8366	0.971622	0.485811	+	0.874064i	$0.338524\pi$
$338$	12.4422	0.676766
$339$	19.5951	1.06426
$340$	14.6279	0.793311
$341$	39.6122	2.14512
$342$	3.63268	0.196433
$343$	18.1370	0.979305
$344$	−1.25728	−0.0677881
$345$	−5.31284	−0.286034
$346$	2.74653	0.147654
$347$	−30.1746	−1.61986	−0.809929	−	0.586529i	$-0.800494\pi$
$347$	−30.1746	−1.61986	−0.809929	+	0.586529i	$0.800494\pi$
$348$	−9.18940	−0.492604
$349$	−19.9201	−1.06630	−0.533148	−	0.846022i	$-0.678991\pi$
$349$	−19.9201	−1.06630	−0.533148	+	0.846022i	$0.678991\pi$
$350$	20.8174	1.11274
$351$	−4.20648	−0.224525
$352$	4.79381	0.255511
$353$	−3.43107	−0.182617	−0.0913087	−	0.995823i	$-0.529105\pi$
$353$	−3.43107	−0.182617	−0.0913087	+	0.995823i	$0.529105\pi$
$354$	−8.27321	−0.439716
$355$	33.4410	1.77486
$356$	−2.14139	−0.113494
$357$	−16.4841	−0.872430
$358$	15.4429	0.816181
$359$	−0.142270	−0.00750874	−0.00375437	−	0.999993i	$-0.501195\pi$
$359$	−0.142270	−0.00750874	−0.00375437	+	0.999993i	$0.501195\pi$
$360$	2.78339	0.146697
$361$	2.66231	0.140121
$362$	−18.1904	−0.956065
$363$	17.8486	0.936811
$364$	−2.01463	−0.105596
$365$	−9.74986	−0.510331
$366$	5.68492	0.297156
$367$	−12.4235	−0.648500	−0.324250	−	0.945971i	$-0.605112\pi$
$367$	−12.4235	−0.648500	−0.324250	+	0.945971i	$0.605112\pi$
$368$	−1.00000	−0.0521286
$369$	4.05761	0.211231
$370$	10.2658	0.533692
$371$	−7.60499	−0.394831
$372$	−12.3105	−0.638270
$373$	−34.9365	−1.80894	−0.904470	−	0.426536i	$-0.859734\pi$
$373$	−34.9365	−1.80894	−0.904470	+	0.426536i	$0.859734\pi$
$374$	19.6636	1.01678
$375$	14.4372	0.745536
$376$	6.72119	0.346619
$377$	−4.60683	−0.237264
$378$	−15.1926	−0.781421
$379$	−21.9430	−1.12714	−0.563569	−	0.826069i	$-0.690572\pi$
$379$	−21.9430	−1.12714	−0.563569	+	0.826069i	$0.690572\pi$
$380$	16.5979	0.851452
$381$	−13.7841	−0.706181
$382$	−2.00049	−0.102354
$383$	−25.5463	−1.30535	−0.652676	−	0.757637i	$-0.726354\pi$
$383$	−25.5463	−1.30535	−0.652676	+	0.757637i	$0.726354\pi$
$384$	−1.48980	−0.0760259
$385$	46.1141	2.35019
$386$	1.38564	0.0705271
$387$	−0.981311	−0.0498829
$388$	−5.78968	−0.293927
$389$	1.15731	0.0586779	0.0293389	−	0.999570i	$-0.490660\pi$
$389$	1.15731	0.0586779	0.0293389	+	0.999570i	$0.490660\pi$
$390$	−3.96798	−0.200926
$391$	−4.10189	−0.207441
$392$	−0.276254	−0.0139529
$393$	−1.48980	−0.0751504
$394$	−0.933591	−0.0470336
$395$	−20.9006	−1.05162
$396$	3.74158	0.188021
$397$	21.3912	1.07360	0.536798	−	0.843711i	$-0.319634\pi$
$397$	21.3912	1.07360	0.536798	+	0.843711i	$0.319634\pi$
$398$	−0.0385265	−0.00193116
$399$	−18.7040	−0.936369
$400$	7.71742	0.385871
$401$	32.6522	1.63057	0.815286	−	0.579059i	$-0.196580\pi$
$401$	32.6522	1.63057	0.815286	+	0.579059i	$0.196580\pi$
$402$	15.4816	0.772154
$403$	−6.17150	−0.307424
$404$	4.56806	0.227269
$405$	−21.5727	−1.07196
$406$	−16.6385	−0.825754
$407$	13.7998	0.684031
$408$	−6.11098	−0.302539
$409$	−9.95033	−0.492012	−0.246006	−	0.969268i	$-0.579118\pi$
$409$	−9.95033	−0.492012	−0.246006	+	0.969268i	$0.579118\pi$
$410$	18.5394	0.915596
$411$	−25.3227	−1.24908
$412$	7.62144	0.375481
$413$	−14.9796	−0.737099
$414$	−0.780502	−0.0383596
$415$	−8.39630	−0.412158
$416$	−0.746865	−0.0366181
$417$	−2.45440	−0.120192
$418$	22.3117	1.09130
$419$	−13.7916	−0.673763	−0.336881	−	0.941547i	$-0.609372\pi$
$419$	−13.7916	−0.673763	−0.336881	+	0.941547i	$0.609372\pi$
$420$	−14.3311	−0.699288
$421$	8.50368	0.414444	0.207222	−	0.978294i	$-0.433558\pi$
$421$	8.50368	0.414444	0.207222	+	0.978294i	$0.433558\pi$
$422$	1.69707	0.0826121
$423$	5.24591	0.255065
$424$	−2.81932	−0.136918
$425$	31.6560	1.53554
$426$	−13.9703	−0.676864
$427$	10.2932	0.498124
$428$	−10.1233	−0.489330
$429$	−5.33396	−0.257526
$430$	−4.48365	−0.216221
$431$	−22.1517	−1.06701	−0.533505	−	0.845797i	$-0.679126\pi$
$431$	−22.1517	−1.06701	−0.533505	+	0.845797i	$0.679126\pi$
$432$	−5.63218	−0.270979
$433$	33.6565	1.61743	0.808714	−	0.588202i	$-0.200164\pi$
$433$	33.6565	1.61743	0.808714	+	0.588202i	$0.200164\pi$
$434$	−22.2896	−1.06993
$435$	−32.7708	−1.57124
$436$	−0.727196	−0.0348264
$437$	−4.65428	−0.222644
$438$	4.07311	0.194621
$439$	−15.3656	−0.733360	−0.366680	−	0.930347i	$-0.619506\pi$
$439$	−15.3656	−0.733360	−0.366680	+	0.930347i	$0.619506\pi$
$440$	17.0954	0.814993
$441$	−0.215617	−0.0102675
$442$	−3.06356	−0.145719
$443$	22.7407	1.08044	0.540222	−	0.841523i	$-0.318340\pi$
$443$	22.7407	1.08044	0.540222	+	0.841523i	$0.318340\pi$
$444$	−4.28864	−0.203530
$445$	−7.63653	−0.362006
$446$	−13.8360	−0.655155
$447$	7.77587	0.367786
$448$	−2.69745	−0.127443
$449$	14.9135	0.703813	0.351907	−	0.936035i	$-0.385533\pi$
$449$	14.9135	0.703813	0.351907	+	0.936035i	$0.385533\pi$
$450$	6.02347	0.283949
$451$	24.9216	1.17351
$452$	13.1529	0.618659
$453$	−0.983610	−0.0462140
$454$	10.5000	0.492790
$455$	−7.18449	−0.336814
$456$	−6.93393	−0.324711
$457$	−22.3010	−1.04320	−0.521599	−	0.853191i	$-0.674664\pi$
$457$	−22.3010	−1.04320	−0.521599	+	0.853191i	$0.674664\pi$
$458$	−12.3635	−0.577710
$459$	−23.1026	−1.07834
$460$	−3.56615	−0.166273
$461$	1.90159	0.0885657	0.0442829	−	0.999019i	$-0.485900\pi$
$461$	1.90159	0.0885657	0.0442829	+	0.999019i	$0.485900\pi$
$462$	−19.2647	−0.896274
$463$	−29.3617	−1.36455	−0.682277	−	0.731094i	$-0.739010\pi$
$463$	−29.3617	−1.36455	−0.682277	+	0.731094i	$0.739010\pi$
$464$	−6.16822	−0.286353
$465$	−43.9011	−2.03586
$466$	−7.47482	−0.346264
$467$	24.7902	1.14715	0.573577	−	0.819152i	$-0.305556\pi$
$467$	24.7902	1.14715	0.573577	+	0.819152i	$0.305556\pi$
$468$	−0.582930	−0.0269460
$469$	28.0313	1.29437
$470$	23.9688	1.10560
$471$	13.4258	0.618627
$472$	−5.55324	−0.255609
$473$	−6.02716	−0.277129
$474$	8.73144	0.401048
$475$	35.9190	1.64808
$476$	−11.0646	−0.507147
$477$	−2.20049	−0.100753
$478$	−2.73435	−0.125066
$479$	−15.1463	−0.692052	−0.346026	−	0.938225i	$-0.612469\pi$
$479$	−15.1463	−0.692052	−0.346026	+	0.938225i	$0.612469\pi$
$480$	−5.31284	−0.242497
$481$	−2.14998	−0.0980307
$482$	−25.7983	−1.17508
$483$	4.01866	0.182855
$484$	11.9806	0.544572
$485$	−20.6469	−0.937526
$486$	−7.88431	−0.357639
$487$	−21.9472	−0.994522	−0.497261	−	0.867601i	$-0.665661\pi$
$487$	−21.9472	−0.994522	−0.497261	+	0.867601i	$0.665661\pi$
$488$	3.81590	0.172738
$489$	10.3791	0.469359
$490$	−0.985164	−0.0445052
$491$	−2.23531	−0.100878	−0.0504390	−	0.998727i	$-0.516062\pi$
$491$	−2.23531	−0.100878	−0.0504390	+	0.998727i	$0.516062\pi$
$492$	−7.74503	−0.349173
$493$	−25.3013	−1.13952
$494$	−3.47612	−0.156398
$495$	13.3430	0.599724
$496$	−8.26320	−0.371029
$497$	−25.2949	−1.13463
$498$	3.50765	0.157181
$499$	−10.8109	−0.483961	−0.241980	−	0.970281i	$-0.577797\pi$
$499$	−10.8109	−0.483961	−0.241980	+	0.970281i	$0.577797\pi$
$500$	9.69074	0.433383
$501$	−19.2611	−0.860521
$502$	16.1788	0.722097
$503$	37.7272	1.68217	0.841086	−	0.540901i	$-0.181917\pi$
$503$	37.7272	1.68217	0.841086	+	0.540901i	$0.181917\pi$
$504$	−2.10537	−0.0937806
$505$	16.2904	0.724912
$506$	−4.79381	−0.213111
$507$	−18.5364	−0.823228
$508$	−9.25234	−0.410506
$509$	−1.72412	−0.0764205	−0.0382102	−	0.999270i	$-0.512166\pi$
$509$	−1.72412	−0.0764205	−0.0382102	+	0.999270i	$0.512166\pi$
$510$	−21.7927	−0.964996
$511$	7.37484	0.326244
$512$	−1.00000	−0.0441942
$513$	−26.2138	−1.15737
$514$	20.7693	0.916096
$515$	27.1792	1.19766
$516$	1.87310	0.0824584
$517$	32.2201	1.41704
$518$	−7.76509	−0.341178
$519$	−4.09178	−0.179609
$520$	−2.66343	−0.116799
$521$	44.3691	1.94384	0.971922	−	0.235302i	$-0.0756080\pi$
$521$	44.3691	1.94384	0.971922	+	0.235302i	$0.0756080\pi$
$522$	−4.81431	−0.210717
$523$	2.24719	0.0982626	0.0491313	−	0.998792i	$-0.484355\pi$
$523$	2.24719	0.0982626	0.0491313	+	0.998792i	$0.484355\pi$
$524$	−1.00000	−0.0436852
$525$	−31.0137	−1.35355
$526$	11.5028	0.501548
$527$	−33.8947	−1.47648
$528$	−7.14180	−0.310807
$529$	1.00000	0.0434783
$530$	−10.0541	−0.436723
$531$	−4.33432	−0.188093
$532$	−12.5547	−0.544315
$533$	−3.88274	−0.168180
$534$	3.19024	0.138055
$535$	−36.1014	−1.56080
$536$	10.3918	0.448856
$537$	−23.0068	−0.992815
$538$	−16.5846	−0.715013
$539$	−1.32431	−0.0570420
$540$	−20.0852	−0.864330
$541$	29.7587	1.27943	0.639714	−	0.768613i	$-0.279053\pi$
$541$	29.7587	1.27943	0.639714	+	0.768613i	$0.279053\pi$
$542$	7.01482	0.301312
$543$	27.1000	1.16297
$544$	−4.10189	−0.175867
$545$	−2.59329	−0.111084
$546$	3.00140	0.128448
$547$	23.6462	1.01104	0.505520	−	0.862815i	$-0.331301\pi$
$547$	23.6462	1.01104	0.505520	+	0.862815i	$0.331301\pi$
$548$	−16.9974	−0.726093
$549$	2.97832	0.127112
$550$	36.9958	1.57751
$551$	−28.7086	−1.22303
$552$	1.48980	0.0634100
$553$	15.8093	0.672279
$554$	28.5911	1.21472
$555$	−15.2939	−0.649191
$556$	−1.64747	−0.0698683
$557$	35.2034	1.49162	0.745808	−	0.666161i	$-0.232064\pi$
$557$	35.2034	1.49162	0.745808	+	0.666161i	$0.232064\pi$
$558$	−6.44945	−0.273027
$559$	0.939020	0.0397163
$560$	−9.61952	−0.406499
$561$	−29.2949	−1.23683
$562$	3.76526	0.158828
$563$	−9.43221	−0.397520	−0.198760	−	0.980048i	$-0.563691\pi$
$563$	−9.43221	−0.397520	−0.198760	+	0.980048i	$0.563691\pi$
$564$	−10.0132	−0.421633
$565$	46.9051	1.97331
$566$	−21.7158	−0.912784
$567$	16.3177	0.685280
$568$	−9.37733	−0.393464
$569$	1.53518	0.0643581	0.0321791	−	0.999482i	$-0.489755\pi$
$569$	1.53518	0.0643581	0.0321791	+	0.999482i	$0.489755\pi$
$570$	−24.7274	−1.03572
$571$	−33.2809	−1.39276	−0.696382	−	0.717671i	$-0.745208\pi$
$571$	−33.2809	−1.39276	−0.696382	+	0.717671i	$0.745208\pi$
$572$	−3.58033	−0.149701
$573$	2.98032	0.124505
$574$	−14.0233	−0.585321
$575$	−7.71742	−0.321839
$576$	−0.780502	−0.0325209
$577$	−20.4334	−0.850652	−0.425326	−	0.905040i	$-0.639840\pi$
$577$	−20.4334	−0.850652	−0.425326	+	0.905040i	$0.639840\pi$
$578$	0.174531	0.00725951
$579$	−2.06432	−0.0857902
$580$	−21.9968	−0.913368
$581$	6.35101	0.263484
$582$	8.62545	0.357537
$583$	−13.5153	−0.559746
$584$	2.73400	0.113134
$585$	−2.07882	−0.0859485
$586$	9.75958	0.403165
$587$	−6.44000	−0.265807	−0.132904	−	0.991129i	$-0.542430\pi$
$587$	−6.44000	−0.265807	−0.132904	+	0.991129i	$0.542430\pi$
$588$	0.411563	0.0169726
$589$	−38.4592	−1.58468
$590$	−19.8037	−0.815305
$591$	1.39086	0.0572124
$592$	−2.87867	−0.118313
$593$	43.3150	1.77873	0.889367	−	0.457194i	$-0.151146\pi$
$593$	43.3150	1.77873	0.889367	+	0.457194i	$0.151146\pi$
$594$	−26.9996	−1.10781
$595$	−39.4582	−1.61763
$596$	5.21941	0.213795
$597$	0.0573967	0.00234909
$598$	0.746865	0.0305416
$599$	40.6066	1.65914	0.829571	−	0.558401i	$-0.188585\pi$
$599$	40.6066	1.65914	0.829571	+	0.558401i	$0.188585\pi$
$600$	−11.4974	−0.469379
$601$	42.2059	1.72162	0.860808	−	0.508929i	$-0.169959\pi$
$601$	42.2059	1.72162	0.860808	+	0.508929i	$0.169959\pi$
$602$	3.39146	0.138226
$603$	8.11080	0.330297
$604$	−0.660230	−0.0268644
$605$	42.7246	1.73700
$606$	−6.80548	−0.276454
$607$	−26.3401	−1.06911	−0.534556	−	0.845133i	$-0.679521\pi$
$607$	−26.3401	−1.06911	−0.534556	+	0.845133i	$0.679521\pi$
$608$	−4.65428	−0.188756
$609$	24.7880	1.00446
$610$	13.6081	0.550975
$611$	−5.01983	−0.203080
$612$	−3.20153	−0.129414
$613$	18.7395	0.756883	0.378442	−	0.925625i	$-0.376460\pi$
$613$	18.7395	0.756883	0.378442	+	0.925625i	$0.376460\pi$
$614$	19.3190	0.779652
$615$	−27.6200	−1.11374
$616$	−12.9311	−0.521008
$617$	−0.893218	−0.0359596	−0.0179798	−	0.999838i	$-0.505723\pi$
$617$	−0.893218	−0.0359596	−0.0179798	+	0.999838i	$0.505723\pi$
$618$	−11.3544	−0.456741
$619$	16.3533	0.657295	0.328647	−	0.944453i	$-0.393407\pi$
$619$	16.3533	0.657295	0.328647	+	0.944453i	$0.393407\pi$
$620$	−29.4678	−1.18346
$621$	5.63218	0.226012
$622$	−10.5007	−0.421040
$623$	5.77631	0.231423
$624$	1.11268	0.0445428
$625$	−4.02848	−0.161139
$626$	−6.56310	−0.262314
$627$	−33.2399	−1.32748
$628$	9.01181	0.359610
$629$	−11.8080	−0.470815
$630$	−7.50806	−0.299128
$631$	−8.13369	−0.323797	−0.161899	−	0.986807i	$-0.551762\pi$
$631$	−8.13369	−0.323797	−0.161899	+	0.986807i	$0.551762\pi$
$632$	5.86082	0.233131
$633$	−2.52829	−0.100491
$634$	1.15264	0.0457770
$635$	−32.9952	−1.30938
$636$	4.20022	0.166549
$637$	0.206325	0.00817488
$638$	−29.5693	−1.17066
$639$	−7.31903	−0.289536
$640$	−3.56615	−0.140964
$641$	−40.5643	−1.60219	−0.801096	−	0.598535i	$-0.795750\pi$
$641$	−40.5643	−1.60219	−0.801096	+	0.598535i	$0.795750\pi$
$642$	15.0817	0.595229
$643$	30.9504	1.22056	0.610282	−	0.792184i	$-0.291056\pi$
$643$	30.9504	1.22056	0.610282	+	0.792184i	$0.291056\pi$
$644$	2.69745	0.106295
$645$	6.67974	0.263014
$646$	−19.0913	−0.751138
$647$	25.9875	1.02167	0.510837	−	0.859678i	$-0.329336\pi$
$647$	25.9875	1.02167	0.510837	+	0.859678i	$0.329336\pi$
$648$	6.04931	0.237639
$649$	−26.6212	−1.04497
$650$	−5.76388	−0.226078
$651$	33.2070	1.30148
$652$	6.96678	0.272840
$653$	5.55371	0.217334	0.108667	−	0.994078i	$-0.465342\pi$
$653$	5.55371	0.217334	0.108667	+	0.994078i	$0.465342\pi$
$654$	1.08337	0.0423633
$655$	−3.56615	−0.139341
$656$	−5.19872	−0.202976
$657$	2.13389	0.0832511
$658$	−18.1301	−0.706785
$659$	−1.49785	−0.0583480	−0.0291740	−	0.999574i	$-0.509288\pi$
$659$	−1.49785	−0.0583480	−0.0291740	+	0.999574i	$0.509288\pi$
$660$	−25.4687	−0.991369
$661$	10.6508	0.414269	0.207135	−	0.978312i	$-0.433586\pi$
$661$	10.6508	0.414269	0.207135	+	0.978312i	$0.433586\pi$
$662$	21.0778	0.819213
$663$	4.56408	0.177254
$664$	2.35445	0.0913702
$665$	−44.7719	−1.73618
$666$	−2.24681	−0.0870622
$667$	6.16822	0.238835
$668$	−12.9286	−0.500224
$669$	20.6129	0.796940
$670$	37.0586	1.43170
$671$	18.2927	0.706182
$672$	4.01866	0.155023
$673$	19.9996	0.770928	0.385464	−	0.922723i	$-0.374041\pi$
$673$	19.9996	0.770928	0.385464	+	0.922723i	$0.374041\pi$
$674$	−17.8366	−0.687040
$675$	−43.4660	−1.67301
$676$	−12.4422	−0.478546
$677$	−10.3796	−0.398921	−0.199460	−	0.979906i	$-0.563919\pi$
$677$	−10.3796	−0.398921	−0.199460	+	0.979906i	$0.563919\pi$
$678$	−19.5951	−0.752546
$679$	15.6174	0.599341
$680$	−14.6279	−0.560956
$681$	−15.6429	−0.599436
$682$	−39.6122	−1.51683
$683$	25.7090	0.983729	0.491864	−	0.870672i	$-0.336316\pi$
$683$	25.7090	0.983729	0.491864	+	0.870672i	$0.336316\pi$
$684$	−3.63268	−0.138899
$685$	−60.6152	−2.31599
$686$	−18.1370	−0.692474
$687$	18.4192	0.702735
$688$	1.25728	0.0479334
$689$	2.10565	0.0802190
$690$	5.31284	0.202256
$691$	−40.2532	−1.53130	−0.765651	−	0.643256i	$-0.777583\pi$
$691$	−40.2532	−1.53130	−0.765651	+	0.643256i	$0.777583\pi$
$692$	−2.74653	−0.104407
$693$	−10.0927	−0.383391
$694$	30.1746	1.14541
$695$	−5.87512	−0.222856
$696$	9.18940	0.348323
$697$	−21.3245	−0.807724
$698$	19.9201	0.753986
$699$	11.1360	0.421201
$700$	−20.8174	−0.786823
$701$	13.1463	0.496528	0.248264	−	0.968692i	$-0.420140\pi$
$701$	13.1463	0.496528	0.248264	+	0.968692i	$0.420140\pi$
$702$	4.20648	0.158763
$703$	−13.3981	−0.505321
$704$	−4.79381	−0.180673
$705$	−35.7086	−1.34487
$706$	3.43107	0.129130
$707$	−12.3221	−0.463421
$708$	8.27321	0.310926
$709$	−14.6856	−0.551529	−0.275765	−	0.961225i	$-0.588931\pi$
$709$	−14.6856	−0.551529	−0.275765	+	0.961225i	$0.588931\pi$
$710$	−33.4410	−1.25502
$711$	4.57438	0.171553
$712$	2.14139	0.0802521
$713$	8.26320	0.309459
$714$	16.4841	0.616901
$715$	−12.7680	−0.477496
$716$	−15.4429	−0.577127
$717$	4.07362	0.152132
$718$	0.142270	0.00530948
$719$	21.4588	0.800279	0.400139	−	0.916454i	$-0.368962\pi$
$719$	21.4588	0.800279	0.400139	+	0.916454i	$0.368962\pi$
$720$	−2.78339	−0.103731
$721$	−20.5585	−0.765638
$722$	−2.66231	−0.0990808
$723$	38.4342	1.42938
$724$	18.1904	0.676040
$725$	−47.6028	−1.76792
$726$	−17.8486	−0.662425
$727$	−11.1963	−0.415248	−0.207624	−	0.978209i	$-0.566573\pi$
$727$	−11.1963	−0.415248	−0.207624	+	0.978209i	$0.566573\pi$
$728$	2.01463	0.0746673
$729$	29.8939	1.10718
$730$	9.74986	0.360858
$731$	5.15723	0.190747
$732$	−5.68492	−0.210121
$733$	−7.95722	−0.293906	−0.146953	−	0.989143i	$-0.546947\pi$
$733$	−7.95722	−0.293906	−0.146953	+	0.989143i	$0.546947\pi$
$734$	12.4235	0.458559
$735$	1.46769	0.0541367
$736$	1.00000	0.0368605
$737$	49.8161	1.83500
$738$	−4.05761	−0.149363
$739$	−11.5665	−0.425481	−0.212741	−	0.977109i	$-0.568239\pi$
$739$	−11.5665	−0.425481	−0.212741	+	0.977109i	$0.568239\pi$
$740$	−10.2658	−0.377378
$741$	5.17871	0.190245
$742$	7.60499	0.279188
$743$	−7.81447	−0.286685	−0.143343	−	0.989673i	$-0.545785\pi$
$743$	−7.81447	−0.286685	−0.143343	+	0.989673i	$0.545785\pi$
$744$	12.3105	0.451325
$745$	18.6132	0.681935
$746$	34.9365	1.27911
$747$	1.83765	0.0672361
$748$	−19.6636	−0.718974
$749$	27.3072	0.997785
$750$	−14.4372	−0.527174
$751$	11.0866	0.404555	0.202277	−	0.979328i	$-0.435166\pi$
$751$	11.0866	0.404555	0.202277	+	0.979328i	$0.435166\pi$
$752$	−6.72119	−0.245097
$753$	−24.1032	−0.878369
$754$	4.60683	0.167771
$755$	−2.35448	−0.0856883
$756$	15.1926	0.552548
$757$	−27.4416	−0.997381	−0.498690	−	0.866780i	$-0.666186\pi$
$757$	−27.4416	−0.997381	−0.498690	+	0.866780i	$0.666186\pi$
$758$	21.9430	0.797007
$759$	7.14180	0.259231
$760$	−16.5979	−0.602067
$761$	−27.3015	−0.989680	−0.494840	−	0.868984i	$-0.664773\pi$
$761$	−27.3015	−0.989680	−0.494840	+	0.868984i	$0.664773\pi$
$762$	13.7841	0.499346
$763$	1.96158	0.0710138
$764$	2.00049	0.0723751
$765$	−11.4171	−0.412788
$766$	25.5463	0.923024
$767$	4.14752	0.149758
$768$	1.48980	0.0537584
$769$	−36.1673	−1.30423	−0.652113	−	0.758122i	$-0.726117\pi$
$769$	−36.1673	−1.30423	−0.652113	+	0.758122i	$0.726117\pi$
$770$	−46.1141	−1.66184
$771$	−30.9421	−1.11435
$772$	−1.38564	−0.0498702
$773$	28.7322	1.03343	0.516713	−	0.856159i	$-0.327155\pi$
$773$	28.7322	1.03343	0.516713	+	0.856159i	$0.327155\pi$
$774$	0.981311	0.0352725
$775$	−63.7706	−2.29071
$776$	5.78968	0.207837
$777$	11.5684	0.415014
$778$	−1.15731	−0.0414915
$779$	−24.1963	−0.866921
$780$	3.96798	0.142076
$781$	−44.9531	−1.60855
$782$	4.10189	0.146683
$783$	34.7406	1.24153
$784$	0.276254	0.00986622
$785$	32.1375	1.14704
$786$	1.48980	0.0531393
$787$	46.7334	1.66587	0.832934	−	0.553373i	$-0.186660\pi$
$787$	46.7334	1.66587	0.832934	+	0.553373i	$0.186660\pi$
$788$	0.933591	0.0332578
$789$	−17.1369	−0.610090
$790$	20.9006	0.743609
$791$	−35.4792	−1.26150
$792$	−3.74158	−0.132951
$793$	−2.84997	−0.101205
$794$	−21.3912	−0.759147
$795$	14.9786	0.531236
$796$	0.0385265	0.00136554
$797$	12.0369	0.426369	0.213185	−	0.977012i	$-0.431616\pi$
$797$	12.0369	0.426369	0.213185	+	0.977012i	$0.431616\pi$
$798$	18.7040	0.662113
$799$	−27.5696	−0.975341
$800$	−7.71742	−0.272852
$801$	1.67136	0.0590547
$802$	−32.6522	−1.15299
$803$	13.1063	0.462510
$804$	−15.4816	−0.545995
$805$	9.61952	0.339044
$806$	6.17150	0.217382
$807$	24.7077	0.869752
$808$	−4.56806	−0.160704
$809$	49.6868	1.74690	0.873448	−	0.486918i	$-0.161879\pi$
$809$	49.6868	1.74690	0.873448	+	0.486918i	$0.161879\pi$
$810$	21.5727	0.757989
$811$	−26.9745	−0.947204	−0.473602	−	0.880739i	$-0.657046\pi$
$811$	−26.9745	−0.947204	−0.473602	+	0.880739i	$0.657046\pi$
$812$	16.6385	0.583897
$813$	−10.4507	−0.366521
$814$	−13.7998	−0.483683
$815$	24.8446	0.870268
$816$	6.11098	0.213927
$817$	5.85174	0.204726
$818$	9.95033	0.347905
$819$	1.57243	0.0549450
$820$	−18.5394	−0.647424
$821$	17.6996	0.617720	0.308860	−	0.951107i	$-0.400053\pi$
$821$	17.6996	0.617720	0.308860	+	0.951107i	$0.400053\pi$
$822$	25.3227	0.883230
$823$	49.8018	1.73598	0.867991	−	0.496580i	$-0.165411\pi$
$823$	49.8018	1.73598	0.867991	+	0.496580i	$0.165411\pi$
$824$	−7.62144	−0.265505
$825$	−55.1163	−1.91890
$826$	14.9796	0.521207
$827$	−4.66362	−0.162170	−0.0810850	−	0.996707i	$-0.525839\pi$
$827$	−4.66362	−0.162170	−0.0810850	+	0.996707i	$0.525839\pi$
$828$	0.780502	0.0271243
$829$	−8.20300	−0.284902	−0.142451	−	0.989802i	$-0.545498\pi$
$829$	−8.20300	−0.284902	−0.142451	+	0.989802i	$0.545498\pi$
$830$	8.39630	0.291440
$831$	−42.5949	−1.47760
$832$	0.746865	0.0258929
$833$	1.13316	0.0392618
$834$	2.45440	0.0849888
$835$	−46.1055	−1.59555
$836$	−22.3117	−0.771667
$837$	46.5399	1.60865
$838$	13.7916	0.476422
$839$	27.2736	0.941589	0.470795	−	0.882243i	$-0.343967\pi$
$839$	27.2736	0.941589	0.470795	+	0.882243i	$0.343967\pi$
$840$	14.3311	0.494471
$841$	9.04696	0.311964
$842$	−8.50368	−0.293056
$843$	−5.60948	−0.193201
$844$	−1.69707	−0.0584155
$845$	−44.3707	−1.52640
$846$	−5.24591	−0.180358
$847$	−32.3171	−1.11043
$848$	2.81932	0.0968159
$849$	32.3522	1.11032
$850$	−31.6560	−1.08579
$851$	2.87867	0.0986796
$852$	13.9703	0.478615
$853$	−53.4894	−1.83144	−0.915722	−	0.401813i	$-0.868380\pi$
$853$	−53.4894	−1.83144	−0.915722	+	0.401813i	$0.868380\pi$
$854$	−10.2932	−0.352227
$855$	−12.9547	−0.443040
$856$	10.1233	0.346009
$857$	−45.9350	−1.56911	−0.784554	−	0.620060i	$-0.787108\pi$
$857$	−45.9350	−1.56911	−0.784554	+	0.620060i	$0.787108\pi$
$858$	5.33396	0.182099
$859$	3.53685	0.120676	0.0603379	−	0.998178i	$-0.480782\pi$
$859$	3.53685	0.120676	0.0603379	+	0.998178i	$0.480782\pi$
$860$	4.48365	0.152891
$861$	20.8919	0.711993
$862$	22.1517	0.754491
$863$	50.0558	1.70392	0.851959	−	0.523608i	$-0.175414\pi$
$863$	50.0558	1.70392	0.851959	+	0.523608i	$0.175414\pi$
$864$	5.63218	0.191611
$865$	−9.79454	−0.333025
$866$	−33.6565	−1.14369
$867$	−0.260015	−0.00883058
$868$	22.2896	0.756558
$869$	28.0956	0.953079
$870$	32.7708	1.11103
$871$	−7.76125	−0.262980
$872$	0.727196	0.0246260
$873$	4.51886	0.152940
$874$	4.65428	0.157433
$875$	−26.1403	−0.883704
$876$	−4.07311	−0.137618
$877$	20.8561	0.704261	0.352131	−	0.935951i	$-0.385457\pi$
$877$	20.8561	0.704261	0.352131	+	0.935951i	$0.385457\pi$
$878$	15.3656	0.518564
$879$	−14.5398	−0.490415
$880$	−17.0954	−0.576287
$881$	9.62865	0.324398	0.162199	−	0.986758i	$-0.448141\pi$
$881$	9.62865	0.324398	0.162199	+	0.986758i	$0.448141\pi$
$882$	0.215617	0.00726020
$883$	16.4198	0.552570	0.276285	−	0.961076i	$-0.410897\pi$
$883$	16.4198	0.552570	0.276285	+	0.961076i	$0.410897\pi$
$884$	3.06356	0.103039
$885$	29.5035	0.991749
$886$	−22.7407	−0.763989
$887$	48.5468	1.63004	0.815022	−	0.579431i	$-0.196725\pi$
$887$	48.5468	1.63004	0.815022	+	0.579431i	$0.196725\pi$
$888$	4.28864	0.143917
$889$	24.9577	0.837056
$890$	7.63653	0.255977
$891$	28.9992	0.971510
$892$	13.8360	0.463265
$893$	−31.2823	−1.04682
$894$	−7.77587	−0.260064
$895$	−55.0716	−1.84084
$896$	2.69745	0.0901156
$897$	−1.11268	−0.0371512
$898$	−14.9135	−0.497671
$899$	50.9692	1.69992
$900$	−6.02347	−0.200782
$901$	11.5645	0.385270
$902$	−24.9216	−0.829800
$903$	−5.05259	−0.168140
$904$	−13.1529	−0.437458
$905$	64.8696	2.15634
$906$	0.983610	0.0326783
$907$	−23.4932	−0.780079	−0.390040	−	0.920798i	$-0.627539\pi$
$907$	−23.4932	−0.780079	−0.390040	+	0.920798i	$0.627539\pi$
$908$	−10.5000	−0.348455
$909$	−3.56538	−0.118256
$910$	7.18449	0.238163
$911$	−0.163661	−0.00542232	−0.00271116	−	0.999996i	$-0.500863\pi$
$911$	−0.163661	−0.00542232	−0.00271116	+	0.999996i	$0.500863\pi$
$912$	6.93393	0.229605
$913$	11.2868	0.373537
$914$	22.3010	0.737653
$915$	−20.2733	−0.670214
$916$	12.3635	0.408503
$917$	2.69745	0.0890778
$918$	23.1026	0.762499
$919$	−13.7266	−0.452799	−0.226400	−	0.974034i	$-0.572696\pi$
$919$	−13.7266	−0.452799	−0.226400	+	0.974034i	$0.572696\pi$
$920$	3.56615	0.117572
$921$	−28.7814	−0.948381
$922$	−1.90159	−0.0626254
$923$	7.00360	0.230526
$924$	19.2647	0.633761
$925$	−22.2159	−0.730456
$926$	29.3617	0.964885
$927$	−5.94855	−0.195376
$928$	6.16822	0.202482
$929$	−0.724085	−0.0237565	−0.0118782	−	0.999929i	$-0.503781\pi$
$929$	−0.724085	−0.0237565	−0.0118782	+	0.999929i	$0.503781\pi$
$930$	43.9011	1.43957
$931$	1.28576	0.0421392
$932$	7.47482	0.244846
$933$	15.6439	0.512159
$934$	−24.7902	−0.811160
$935$	−70.1235	−2.29328
$936$	0.582930	0.0190537
$937$	14.3312	0.468181	0.234091	−	0.972215i	$-0.424789\pi$
$937$	14.3312	0.468181	0.234091	+	0.972215i	$0.424789\pi$
$938$	−28.0313	−0.915255
$939$	9.77769	0.319083
$940$	−23.9688	−0.781775
$941$	45.7456	1.49126	0.745632	−	0.666358i	$-0.232148\pi$
$941$	45.7456	1.49126	0.745632	+	0.666358i	$0.232148\pi$
$942$	−13.4258	−0.437435
$943$	5.19872	0.169293
$944$	5.55324	0.180743
$945$	54.1789	1.76244
$946$	6.02716	0.195960
$947$	34.3980	1.11778	0.558892	−	0.829240i	$-0.311227\pi$
$947$	34.3980	1.11778	0.558892	+	0.829240i	$0.311227\pi$
$948$	−8.73144	−0.283584
$949$	−2.04193	−0.0662839
$950$	−35.9190	−1.16537
$951$	−1.71720	−0.0556839
$952$	11.0646	0.358607
$953$	−47.9522	−1.55333	−0.776663	−	0.629917i	$-0.783089\pi$
$953$	−47.9522	−1.55333	−0.776663	+	0.629917i	$0.783089\pi$
$954$	2.20049	0.0712434
$955$	7.13404	0.230852
$956$	2.73435	0.0884350
$957$	44.0522	1.42401
$958$	15.1463	0.489354
$959$	45.8497	1.48056
$960$	5.31284	0.171471
$961$	37.2805	1.20260
$962$	2.14998	0.0693182
$963$	7.90129	0.254616
$964$	25.7983	0.830907
$965$	−4.94139	−0.159069
$966$	−4.01866	−0.129298
$967$	−53.9920	−1.73627	−0.868133	−	0.496332i	$-0.834680\pi$
$967$	−53.9920	−1.73627	−0.868133	+	0.496332i	$0.834680\pi$
$968$	−11.9806	−0.385071
$969$	28.4422	0.913695
$970$	20.6469	0.662931
$971$	31.6232	1.01484	0.507418	−	0.861700i	$-0.330600\pi$
$971$	31.6232	1.01484	0.507418	+	0.861700i	$0.330600\pi$
$972$	7.88431	0.252889
$973$	4.44397	0.142467
$974$	21.9472	0.703234
$975$	8.58701	0.275004
$976$	−3.81590	−0.122144
$977$	33.5811	1.07435	0.537177	−	0.843469i	$-0.319491\pi$
$977$	33.5811	1.07435	0.537177	+	0.843469i	$0.319491\pi$
$978$	−10.3791	−0.331887
$979$	10.2654	0.328084
$980$	0.985164	0.0314699
$981$	0.567578	0.0181214
$982$	2.23531	0.0713315
$983$	−14.6335	−0.466735	−0.233368	−	0.972389i	$-0.574975\pi$
$983$	−14.6335	−0.466735	−0.233368	+	0.972389i	$0.574975\pi$
$984$	7.74503	0.246903
$985$	3.32933	0.106081
$986$	25.3013	0.805759
$987$	27.0102	0.859744
$988$	3.47612	0.110590
$989$	−1.25728	−0.0399792
$990$	−13.3430	−0.424069
$991$	54.6984	1.73755	0.868777	−	0.495204i	$-0.164907\pi$
$991$	54.6984	1.73755	0.868777	+	0.495204i	$0.164907\pi$
$992$	8.26320	0.262357
$993$	−31.4017	−0.996503
$994$	25.2949	0.802306
$995$	0.137391	0.00435560
$996$	−3.50765	−0.111144
$997$	3.56303	0.112842	0.0564212	−	0.998407i	$-0.482031\pi$
$997$	3.56303	0.112842	0.0564212	+	0.998407i	$0.482031\pi$
$998$	10.8109	0.342212
$999$	16.2132	0.512964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.17	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.48980 q^{3} +1.00000 q^{4} +3.56615 q^{5} -1.48980 q^{6} -2.69745 q^{7} -1.00000 q^{8} -0.780502 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.48980 q^{3} +1.00000 q^{4} +3.56615 q^{5} -1.48980 q^{6} -2.69745 q^{7} -1.00000 q^{8} -0.780502 q^{9} -3.56615 q^{10} -4.79381 q^{11} +1.48980 q^{12} +0.746865 q^{13} +2.69745 q^{14} +5.31284 q^{15} +1.00000 q^{16} +4.10189 q^{17} +0.780502 q^{18} +4.65428 q^{19} +3.56615 q^{20} -4.01866 q^{21} +4.79381 q^{22} -1.00000 q^{23} -1.48980 q^{24} +7.71742 q^{25} -0.746865 q^{26} -5.63218 q^{27} -2.69745 q^{28} -6.16822 q^{29} -5.31284 q^{30} -8.26320 q^{31} -1.00000 q^{32} -7.14180 q^{33} -4.10189 q^{34} -9.61952 q^{35} -0.780502 q^{36} -2.87867 q^{37} -4.65428 q^{38} +1.11268 q^{39} -3.56615 q^{40} -5.19872 q^{41} +4.01866 q^{42} +1.25728 q^{43} -4.79381 q^{44} -2.78339 q^{45} +1.00000 q^{46} -6.72119 q^{47} +1.48980 q^{48} +0.276254 q^{49} -7.71742 q^{50} +6.11098 q^{51} +0.746865 q^{52} +2.81932 q^{53} +5.63218 q^{54} -17.0954 q^{55} +2.69745 q^{56} +6.93393 q^{57} +6.16822 q^{58} +5.55324 q^{59} +5.31284 q^{60} -3.81590 q^{61} +8.26320 q^{62} +2.10537 q^{63} +1.00000 q^{64} +2.66343 q^{65} +7.14180 q^{66} -10.3918 q^{67} +4.10189 q^{68} -1.48980 q^{69} +9.61952 q^{70} +9.37733 q^{71} +0.780502 q^{72} -2.73400 q^{73} +2.87867 q^{74} +11.4974 q^{75} +4.65428 q^{76} +12.9311 q^{77} -1.11268 q^{78} -5.86082 q^{79} +3.56615 q^{80} -6.04931 q^{81} +5.19872 q^{82} -2.35445 q^{83} -4.01866 q^{84} +14.6279 q^{85} -1.25728 q^{86} -9.18940 q^{87} +4.79381 q^{88} -2.14139 q^{89} +2.78339 q^{90} -2.01463 q^{91} -1.00000 q^{92} -12.3105 q^{93} +6.72119 q^{94} +16.5979 q^{95} -1.48980 q^{96} -5.78968 q^{97} -0.276254 q^{98} +3.74158 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 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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