LMFDB - Embedded newform 8026.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.20966 q^{3} +1.00000 q^{4} +0.782750 q^{5} +3.20966 q^{6} +3.68309 q^{7} -1.00000 q^{8} +7.30189 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.20966 q^{3} +1.00000 q^{4} +0.782750 q^{5} +3.20966 q^{6} +3.68309 q^{7} -1.00000 q^{8} +7.30189 q^{9} -0.782750 q^{10} +0.549538 q^{11} -3.20966 q^{12} +1.85501 q^{13} -3.68309 q^{14} -2.51236 q^{15} +1.00000 q^{16} +3.12566 q^{17} -7.30189 q^{18} +3.31393 q^{19} +0.782750 q^{20} -11.8215 q^{21} -0.549538 q^{22} +7.89709 q^{23} +3.20966 q^{24} -4.38730 q^{25} -1.85501 q^{26} -13.8076 q^{27} +3.68309 q^{28} +2.26329 q^{29} +2.51236 q^{30} -8.28334 q^{31} -1.00000 q^{32} -1.76383 q^{33} -3.12566 q^{34} +2.88294 q^{35} +7.30189 q^{36} +5.70022 q^{37} -3.31393 q^{38} -5.95393 q^{39} -0.782750 q^{40} +5.18064 q^{41} +11.8215 q^{42} +9.88270 q^{43} +0.549538 q^{44} +5.71555 q^{45} -7.89709 q^{46} +3.23068 q^{47} -3.20966 q^{48} +6.56518 q^{49} +4.38730 q^{50} -10.0323 q^{51} +1.85501 q^{52} -5.91275 q^{53} +13.8076 q^{54} +0.430151 q^{55} -3.68309 q^{56} -10.6366 q^{57} -2.26329 q^{58} +9.82198 q^{59} -2.51236 q^{60} +11.9837 q^{61} +8.28334 q^{62} +26.8935 q^{63} +1.00000 q^{64} +1.45201 q^{65} +1.76383 q^{66} +4.93168 q^{67} +3.12566 q^{68} -25.3469 q^{69} -2.88294 q^{70} +10.5066 q^{71} -7.30189 q^{72} -9.02798 q^{73} -5.70022 q^{74} +14.0817 q^{75} +3.31393 q^{76} +2.02400 q^{77} +5.95393 q^{78} -0.715813 q^{79} +0.782750 q^{80} +22.4119 q^{81} -5.18064 q^{82} +3.12896 q^{83} -11.8215 q^{84} +2.44661 q^{85} -9.88270 q^{86} -7.26439 q^{87} -0.549538 q^{88} -15.2018 q^{89} -5.71555 q^{90} +6.83216 q^{91} +7.89709 q^{92} +26.5867 q^{93} -3.23068 q^{94} +2.59398 q^{95} +3.20966 q^{96} +11.2136 q^{97} -6.56518 q^{98} +4.01267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.20966	−1.85310	−0.926548	−	0.376177i	$-0.877239\pi$
$3$	−3.20966	−1.85310	−0.926548	+	0.376177i	$0.877239\pi$
$4$	1.00000	0.500000
$5$	0.782750	0.350056	0.175028	−	0.984563i	$-0.443998\pi$
$5$	0.782750	0.350056	0.175028	+	0.984563i	$0.443998\pi$
$6$	3.20966	1.31034
$7$	3.68309	1.39208	0.696039	−	0.718004i	$-0.254944\pi$
$7$	3.68309	1.39208	0.696039	+	0.718004i	$0.254944\pi$
$8$	−1.00000	−0.353553
$9$	7.30189	2.43396
$10$	−0.782750	−0.247527
$11$	0.549538	0.165692	0.0828459	−	0.996562i	$-0.473599\pi$
$11$	0.549538	0.165692	0.0828459	+	0.996562i	$0.473599\pi$
$12$	−3.20966	−0.926548
$13$	1.85501	0.514486	0.257243	−	0.966347i	$-0.417186\pi$
$13$	1.85501	0.514486	0.257243	+	0.966347i	$0.417186\pi$
$14$	−3.68309	−0.984348
$15$	−2.51236	−0.648688
$16$	1.00000	0.250000
$17$	3.12566	0.758083	0.379042	−	0.925380i	$-0.376254\pi$
$17$	3.12566	0.758083	0.379042	+	0.925380i	$0.376254\pi$
$18$	−7.30189	−1.72107
$19$	3.31393	0.760267	0.380133	−	0.924932i	$-0.375878\pi$
$19$	3.31393	0.760267	0.380133	+	0.924932i	$0.375878\pi$
$20$	0.782750	0.175028
$21$	−11.8215	−2.57965
$22$	−0.549538	−0.117162
$23$	7.89709	1.64666	0.823329	−	0.567565i	$-0.192114\pi$
$23$	7.89709	1.64666	0.823329	+	0.567565i	$0.192114\pi$
$24$	3.20966	0.655168
$25$	−4.38730	−0.877461
$26$	−1.85501	−0.363797
$27$	−13.8076	−2.65727
$28$	3.68309	0.696039
$29$	2.26329	0.420283	0.210142	−	0.977671i	$-0.432608\pi$
$29$	2.26329	0.420283	0.210142	+	0.977671i	$0.432608\pi$
$30$	2.51236	0.458692
$31$	−8.28334	−1.48773	−0.743866	−	0.668329i	$-0.767010\pi$
$31$	−8.28334	−1.48773	−0.743866	+	0.668329i	$0.767010\pi$
$32$	−1.00000	−0.176777
$33$	−1.76383	−0.307043
$34$	−3.12566	−0.536046
$35$	2.88294	0.487306
$36$	7.30189	1.21698
$37$	5.70022	0.937110	0.468555	−	0.883434i	$-0.344775\pi$
$37$	5.70022	0.937110	0.468555	+	0.883434i	$0.344775\pi$
$38$	−3.31393	−0.537590
$39$	−5.95393	−0.953392
$40$	−0.782750	−0.123764
$41$	5.18064	0.809080	0.404540	−	0.914520i	$-0.367432\pi$
$41$	5.18064	0.809080	0.404540	+	0.914520i	$0.367432\pi$
$42$	11.8215	1.82409
$43$	9.88270	1.50710	0.753549	−	0.657392i	$-0.228340\pi$
$43$	9.88270	1.50710	0.753549	+	0.657392i	$0.228340\pi$
$44$	0.549538	0.0828459
$45$	5.71555	0.852025
$46$	−7.89709	−1.16436
$47$	3.23068	0.471243	0.235621	−	0.971845i	$-0.424287\pi$
$47$	3.23068	0.471243	0.235621	+	0.971845i	$0.424287\pi$
$48$	−3.20966	−0.463274
$49$	6.56518	0.937882
$50$	4.38730	0.620458
$51$	−10.0323	−1.40480
$52$	1.85501	0.257243
$53$	−5.91275	−0.812179	−0.406089	−	0.913833i	$-0.633108\pi$
$53$	−5.91275	−0.812179	−0.406089	+	0.913833i	$0.633108\pi$
$54$	13.8076	1.87898
$55$	0.430151	0.0580015
$56$	−3.68309	−0.492174
$57$	−10.6366	−1.40885
$58$	−2.26329	−0.297185
$59$	9.82198	1.27871	0.639357	−	0.768910i	$-0.279201\pi$
$59$	9.82198	1.27871	0.639357	+	0.768910i	$0.279201\pi$
$60$	−2.51236	−0.324344
$61$	11.9837	1.53436	0.767180	−	0.641431i	$-0.221659\pi$
$61$	11.9837	1.53436	0.767180	+	0.641431i	$0.221659\pi$
$62$	8.28334	1.05199
$63$	26.8935	3.38827
$64$	1.00000	0.125000
$65$	1.45201	0.180099
$66$	1.76383	0.217112
$67$	4.93168	0.602501	0.301251	−	0.953545i	$-0.402596\pi$
$67$	4.93168	0.602501	0.301251	+	0.953545i	$0.402596\pi$
$68$	3.12566	0.379042
$69$	−25.3469	−3.05141
$70$	−2.88294	−0.344577
$71$	10.5066	1.24690	0.623451	−	0.781863i	$-0.285730\pi$
$71$	10.5066	1.24690	0.623451	+	0.781863i	$0.285730\pi$
$72$	−7.30189	−0.860536
$73$	−9.02798	−1.05665	−0.528323	−	0.849044i	$-0.677179\pi$
$73$	−9.02798	−1.05665	−0.528323	+	0.849044i	$0.677179\pi$
$74$	−5.70022	−0.662637
$75$	14.0817	1.62602
$76$	3.31393	0.380133
$77$	2.02400	0.230656
$78$	5.95393	0.674150
$79$	−0.715813	−0.0805353	−0.0402676	−	0.999189i	$-0.512821\pi$
$79$	−0.715813	−0.0805353	−0.0402676	+	0.999189i	$0.512821\pi$
$80$	0.782750	0.0875141
$81$	22.4119	2.49022
$82$	−5.18064	−0.572106
$83$	3.12896	0.343448	0.171724	−	0.985145i	$-0.445066\pi$
$83$	3.12896	0.343448	0.171724	+	0.985145i	$0.445066\pi$
$84$	−11.8215	−1.28983
$85$	2.44661	0.265372
$86$	−9.88270	−1.06568
$87$	−7.26439	−0.778825
$88$	−0.549538	−0.0585809
$89$	−15.2018	−1.61139	−0.805696	−	0.592329i	$-0.798209\pi$
$89$	−15.2018	−1.61139	−0.805696	+	0.592329i	$0.798209\pi$
$90$	−5.71555	−0.602472
$91$	6.83216	0.716205
$92$	7.89709	0.823329
$93$	26.5867	2.75691
$94$	−3.23068	−0.333219
$95$	2.59398	0.266136
$96$	3.20966	0.327584
$97$	11.2136	1.13857	0.569283	−	0.822141i	$-0.307221\pi$
$97$	11.2136	1.13857	0.569283	+	0.822141i	$0.307221\pi$
$98$	−6.56518	−0.663183
$99$	4.01267	0.403288
$100$	−4.38730	−0.438730
$101$	16.5490	1.64669	0.823345	−	0.567541i	$-0.192105\pi$
$101$	16.5490	1.64669	0.823345	+	0.567541i	$0.192105\pi$
$102$	10.0323	0.993344
$103$	10.5638	1.04089	0.520443	−	0.853896i	$-0.325767\pi$
$103$	10.5638	1.04089	0.520443	+	0.853896i	$0.325767\pi$
$104$	−1.85501	−0.181898
$105$	−9.25325	−0.903025
$106$	5.91275	0.574297
$107$	−1.36504	−0.131964	−0.0659818	−	0.997821i	$-0.521018\pi$
$107$	−1.36504	−0.131964	−0.0659818	+	0.997821i	$0.521018\pi$
$108$	−13.8076	−1.32864
$109$	9.14686	0.876111	0.438055	−	0.898948i	$-0.355667\pi$
$109$	9.14686	0.876111	0.438055	+	0.898948i	$0.355667\pi$
$110$	−0.430151	−0.0410133
$111$	−18.2957	−1.73655
$112$	3.68309	0.348020
$113$	−13.9762	−1.31477	−0.657386	−	0.753554i	$-0.728338\pi$
$113$	−13.9762	−1.31477	−0.657386	+	0.753554i	$0.728338\pi$
$114$	10.6366	0.996206
$115$	6.18145	0.576423
$116$	2.26329	0.210142
$117$	13.5451	1.25224
$118$	−9.82198	−0.904187
$119$	11.5121	1.05531
$120$	2.51236	0.229346
$121$	−10.6980	−0.972546
$122$	−11.9837	−1.08496
$123$	−16.6281	−1.49930
$124$	−8.28334	−0.743866
$125$	−7.34791	−0.657217
$126$	−26.8935	−2.39587
$127$	−8.57264	−0.760699	−0.380349	−	0.924843i	$-0.624196\pi$
$127$	−8.57264	−0.760699	−0.380349	+	0.924843i	$0.624196\pi$
$128$	−1.00000	−0.0883883
$129$	−31.7201	−2.79280
$130$	−1.45201	−0.127349
$131$	−0.282017	−0.0246400	−0.0123200	−	0.999924i	$-0.503922\pi$
$131$	−0.282017	−0.0246400	−0.0123200	+	0.999924i	$0.503922\pi$
$132$	−1.76383	−0.153521
$133$	12.2055	1.05835
$134$	−4.93168	−0.426033
$135$	−10.8079	−0.930195
$136$	−3.12566	−0.268023
$137$	16.1549	1.38021	0.690104	−	0.723710i	$-0.257565\pi$
$137$	16.1549	1.38021	0.690104	+	0.723710i	$0.257565\pi$
$138$	25.3469	2.15768
$139$	−12.7992	−1.08561	−0.542805	−	0.839859i	$-0.682638\pi$
$139$	−12.7992	−1.08561	−0.542805	+	0.839859i	$0.682638\pi$
$140$	2.88294	0.243653
$141$	−10.3694	−0.873258
$142$	−10.5066	−0.881693
$143$	1.01940	0.0852462
$144$	7.30189	0.608491
$145$	1.77159	0.147123
$146$	9.02798	0.747161
$147$	−21.0720	−1.73799
$148$	5.70022	0.468555
$149$	16.0813	1.31743	0.658715	−	0.752393i	$-0.271100\pi$
$149$	16.0813	1.31743	0.658715	+	0.752393i	$0.271100\pi$
$150$	−14.0817	−1.14977
$151$	22.8757	1.86160	0.930801	−	0.365526i	$-0.119111\pi$
$151$	22.8757	1.86160	0.930801	+	0.365526i	$0.119111\pi$
$152$	−3.31393	−0.268795
$153$	22.8232	1.84515
$154$	−2.02400	−0.163098
$155$	−6.48378	−0.520790
$156$	−5.95393	−0.476696
$157$	3.50970	0.280104	0.140052	−	0.990144i	$-0.455273\pi$
$157$	3.50970	0.280104	0.140052	+	0.990144i	$0.455273\pi$
$158$	0.715813	0.0569470
$159$	18.9779	1.50505
$160$	−0.782750	−0.0618818
$161$	29.0857	2.29228
$162$	−22.4119	−1.76085
$163$	−13.6789	−1.07141	−0.535707	−	0.844404i	$-0.679955\pi$
$163$	−13.6789	−1.07141	−0.535707	+	0.844404i	$0.679955\pi$
$164$	5.18064	0.404540
$165$	−1.38064	−0.107482
$166$	−3.12896	−0.242854
$167$	−13.3214	−1.03084	−0.515421	−	0.856937i	$-0.672364\pi$
$167$	−13.3214	−1.03084	−0.515421	+	0.856937i	$0.672364\pi$
$168$	11.8215	0.912046
$169$	−9.55895	−0.735304
$170$	−2.44661	−0.187646
$171$	24.1979	1.85046
$172$	9.88270	0.753549
$173$	−24.5230	−1.86445	−0.932225	−	0.361878i	$-0.882136\pi$
$173$	−24.5230	−1.86445	−0.932225	+	0.361878i	$0.882136\pi$
$174$	7.26439	0.550712
$175$	−16.1588	−1.22149
$176$	0.549538	0.0414230
$177$	−31.5252	−2.36958
$178$	15.2018	1.13943
$179$	2.33260	0.174347	0.0871734	−	0.996193i	$-0.472217\pi$
$179$	2.33260	0.174347	0.0871734	+	0.996193i	$0.472217\pi$
$180$	5.71555	0.426012
$181$	5.42925	0.403553	0.201776	−	0.979432i	$-0.435329\pi$
$181$	5.42925	0.403553	0.201776	+	0.979432i	$0.435329\pi$
$182$	−6.83216	−0.506433
$183$	−38.4637	−2.84332
$184$	−7.89709	−0.582181
$185$	4.46184	0.328041
$186$	−26.5867	−1.94943
$187$	1.71767	0.125608
$188$	3.23068	0.235621
$189$	−50.8547	−3.69913
$190$	−2.59398	−0.188187
$191$	−23.7318	−1.71717	−0.858586	−	0.512670i	$-0.828657\pi$
$191$	−23.7318	−1.71717	−0.858586	+	0.512670i	$0.828657\pi$
$192$	−3.20966	−0.231637
$193$	−23.5289	−1.69365	−0.846823	−	0.531875i	$-0.821488\pi$
$193$	−23.5289	−1.69365	−0.846823	+	0.531875i	$0.821488\pi$
$194$	−11.2136	−0.805088
$195$	−4.66044	−0.333741
$196$	6.56518	0.468941
$197$	−23.3475	−1.66344	−0.831720	−	0.555195i	$-0.812644\pi$
$197$	−23.3475	−1.66344	−0.831720	+	0.555195i	$0.812644\pi$
$198$	−4.01267	−0.285168
$199$	21.9835	1.55837	0.779186	−	0.626793i	$-0.215633\pi$
$199$	21.9835	1.55837	0.779186	+	0.626793i	$0.215633\pi$
$200$	4.38730	0.310229
$201$	−15.8290	−1.11649
$202$	−16.5490	−1.16439
$203$	8.33592	0.585067
$204$	−10.0323	−0.702400
$205$	4.05514	0.283224
$206$	−10.5638	−0.736018
$207$	57.6637	4.00790
$208$	1.85501	0.128622
$209$	1.82113	0.125970
$210$	9.25325	0.638535
$211$	−25.6473	−1.76563	−0.882816	−	0.469719i	$-0.844355\pi$
$211$	−25.6473	−1.76563	−0.882816	+	0.469719i	$0.844355\pi$
$212$	−5.91275	−0.406089
$213$	−33.7225	−2.31063
$214$	1.36504	0.0933123
$215$	7.73569	0.527569
$216$	13.8076	0.939488
$217$	−30.5083	−2.07104
$218$	−9.14686	−0.619504
$219$	28.9767	1.95807
$220$	0.430151	0.0290008
$221$	5.79811	0.390023
$222$	18.2957	1.22793
$223$	24.3373	1.62974	0.814872	−	0.579641i	$-0.196807\pi$
$223$	24.3373	1.62974	0.814872	+	0.579641i	$0.196807\pi$
$224$	−3.68309	−0.246087
$225$	−32.0356	−2.13571
$226$	13.9762	0.929685
$227$	14.7671	0.980127	0.490064	−	0.871687i	$-0.336974\pi$
$227$	14.7671	0.980127	0.490064	+	0.871687i	$0.336974\pi$
$228$	−10.6366	−0.704424
$229$	−16.1720	−1.06867	−0.534337	−	0.845272i	$-0.679439\pi$
$229$	−16.1720	−1.06867	−0.534337	+	0.845272i	$0.679439\pi$
$230$	−6.18145	−0.407592
$231$	−6.49634	−0.427428
$232$	−2.26329	−0.148592
$233$	13.8134	0.904947	0.452474	−	0.891778i	$-0.350542\pi$
$233$	13.8134	0.904947	0.452474	+	0.891778i	$0.350542\pi$
$234$	−13.5451	−0.885468
$235$	2.52881	0.164962
$236$	9.82198	0.639357
$237$	2.29751	0.149240
$238$	−11.5121	−0.746218
$239$	−2.12729	−0.137603	−0.0688013	−	0.997630i	$-0.521917\pi$
$239$	−2.12729	−0.137603	−0.0688013	+	0.997630i	$0.521917\pi$
$240$	−2.51236	−0.162172
$241$	−0.461568	−0.0297322	−0.0148661	−	0.999889i	$-0.504732\pi$
$241$	−0.461568	−0.0297322	−0.0148661	+	0.999889i	$0.504732\pi$
$242$	10.6980	0.687694
$243$	−30.5119	−1.95734
$244$	11.9837	0.767180
$245$	5.13889	0.328312
$246$	16.6281	1.06017
$247$	6.14736	0.391147
$248$	8.28334	0.525993
$249$	−10.0429	−0.636442
$250$	7.34791	0.464723
$251$	2.76735	0.174674	0.0873368	−	0.996179i	$-0.472164\pi$
$251$	2.76735	0.174674	0.0873368	+	0.996179i	$0.472164\pi$
$252$	26.8935	1.69413
$253$	4.33975	0.272838
$254$	8.57264	0.537895
$255$	−7.85277	−0.491759
$256$	1.00000	0.0625000
$257$	25.8185	1.61051	0.805256	−	0.592927i	$-0.202028\pi$
$257$	25.8185	1.61051	0.805256	+	0.592927i	$0.202028\pi$
$258$	31.7201	1.97481
$259$	20.9944	1.30453
$260$	1.45201	0.0900496
$261$	16.5263	1.02295
$262$	0.282017	0.0174231
$263$	4.23051	0.260864	0.130432	−	0.991457i	$-0.458364\pi$
$263$	4.23051	0.260864	0.130432	+	0.991457i	$0.458364\pi$
$264$	1.76383	0.108556
$265$	−4.62821	−0.284308
$266$	−12.2055	−0.748367
$267$	48.7927	2.98606
$268$	4.93168	0.301251
$269$	−8.72954	−0.532250	−0.266125	−	0.963939i	$-0.585743\pi$
$269$	−8.72954	−0.532250	−0.266125	+	0.963939i	$0.585743\pi$
$270$	10.8079	0.657747
$271$	2.32728	0.141372	0.0706860	−	0.997499i	$-0.477481\pi$
$271$	2.32728	0.141372	0.0706860	+	0.997499i	$0.477481\pi$
$272$	3.12566	0.189521
$273$	−21.9289	−1.32720
$274$	−16.1549	−0.975954
$275$	−2.41099	−0.145388
$276$	−25.3469	−1.52571
$277$	−21.0416	−1.26427	−0.632133	−	0.774860i	$-0.717820\pi$
$277$	−21.0416	−1.26427	−0.632133	+	0.774860i	$0.717820\pi$
$278$	12.7992	0.767642
$279$	−60.4841	−3.62109
$280$	−2.88294	−0.172289
$281$	−7.60360	−0.453593	−0.226796	−	0.973942i	$-0.572825\pi$
$281$	−7.60360	−0.453593	−0.226796	+	0.973942i	$0.572825\pi$
$282$	10.3694	0.617487
$283$	−31.4835	−1.87150	−0.935751	−	0.352661i	$-0.885277\pi$
$283$	−31.4835	−1.87150	−0.935751	+	0.352661i	$0.885277\pi$
$284$	10.5066	0.623451
$285$	−8.32577	−0.493176
$286$	−1.01940	−0.0602782
$287$	19.0808	1.12630
$288$	−7.30189	−0.430268
$289$	−7.23027	−0.425310
$290$	−1.77159	−0.104031
$291$	−35.9917	−2.10987
$292$	−9.02798	−0.528323
$293$	−12.3202	−0.719753	−0.359876	−	0.933000i	$-0.617181\pi$
$293$	−12.3202	−0.719753	−0.359876	+	0.933000i	$0.617181\pi$
$294$	21.0720	1.22894
$295$	7.68815	0.447622
$296$	−5.70022	−0.331318
$297$	−7.58779	−0.440288
$298$	−16.0813	−0.931563
$299$	14.6492	0.847182
$300$	14.0817	0.813009
$301$	36.3989	2.09800
$302$	−22.8757	−1.31635
$303$	−53.1167	−3.05148
$304$	3.31393	0.190067
$305$	9.38027	0.537113
$306$	−22.8232	−1.30472
$307$	14.1499	0.807579	0.403789	−	0.914852i	$-0.367693\pi$
$307$	14.1499	0.807579	0.403789	+	0.914852i	$0.367693\pi$
$308$	2.02400	0.115328
$309$	−33.9063	−1.92886
$310$	6.48378	0.368254
$311$	28.6334	1.62365	0.811824	−	0.583902i	$-0.198475\pi$
$311$	28.6334	1.62365	0.811824	+	0.583902i	$0.198475\pi$
$312$	5.95393	0.337075
$313$	−28.0211	−1.58384	−0.791922	−	0.610622i	$-0.790920\pi$
$313$	−28.0211	−1.58384	−0.791922	+	0.610622i	$0.790920\pi$
$314$	−3.50970	−0.198064
$315$	21.0509	1.18609
$316$	−0.715813	−0.0402676
$317$	3.58660	0.201443	0.100722	−	0.994915i	$-0.467885\pi$
$317$	3.58660	0.201443	0.100722	+	0.994915i	$0.467885\pi$
$318$	−18.9779	−1.06423
$319$	1.24377	0.0696375
$320$	0.782750	0.0437570
$321$	4.38131	0.244541
$322$	−29.0857	−1.62088
$323$	10.3582	0.576346
$324$	22.4119	1.24511
$325$	−8.13847	−0.451441
$326$	13.6789	0.757605
$327$	−29.3583	−1.62352
$328$	−5.18064	−0.286053
$329$	11.8989	0.656007
$330$	1.38064	0.0760015
$331$	−26.9428	−1.48091	−0.740454	−	0.672107i	$-0.765389\pi$
$331$	−26.9428	−1.48091	−0.740454	+	0.672107i	$0.765389\pi$
$332$	3.12896	0.171724
$333$	41.6224	2.28089
$334$	13.3214	0.728915
$335$	3.86028	0.210909
$336$	−11.8215	−0.644914
$337$	−14.1130	−0.768786	−0.384393	−	0.923170i	$-0.625589\pi$
$337$	−14.1130	−0.768786	−0.384393	+	0.923170i	$0.625589\pi$
$338$	9.55895	0.519938
$339$	44.8589	2.43640
$340$	2.44661	0.132686
$341$	−4.55201	−0.246505
$342$	−24.1979	−1.30847
$343$	−1.60149	−0.0864726
$344$	−9.88270	−0.532840
$345$	−19.8403	−1.06817
$346$	24.5230	1.31837
$347$	10.5888	0.568438	0.284219	−	0.958759i	$-0.408266\pi$
$347$	10.5888	0.568438	0.284219	+	0.958759i	$0.408266\pi$
$348$	−7.26439	−0.389412
$349$	−6.62086	−0.354406	−0.177203	−	0.984174i	$-0.556705\pi$
$349$	−6.62086	−0.354406	−0.177203	+	0.984174i	$0.556705\pi$
$350$	16.1588	0.863727
$351$	−25.6132	−1.36713
$352$	−0.549538	−0.0292905
$353$	−16.3008	−0.867606	−0.433803	−	0.901008i	$-0.642829\pi$
$353$	−16.3008	−0.867606	−0.433803	+	0.901008i	$0.642829\pi$
$354$	31.5252	1.67554
$355$	8.22402	0.436486
$356$	−15.2018	−0.805696
$357$	−36.9498	−1.95559
$358$	−2.33260	−0.123282
$359$	−13.0918	−0.690959	−0.345479	−	0.938426i	$-0.612284\pi$
$359$	−13.0918	−0.690959	−0.345479	+	0.938426i	$0.612284\pi$
$360$	−5.71555	−0.301236
$361$	−8.01789	−0.421994
$362$	−5.42925	−0.285355
$363$	34.3369	1.80222
$364$	6.83216	0.358103
$365$	−7.06665	−0.369885
$366$	38.4637	2.01053
$367$	32.4923	1.69608	0.848041	−	0.529930i	$-0.177782\pi$
$367$	32.4923	1.69608	0.848041	+	0.529930i	$0.177782\pi$
$368$	7.89709	0.411664
$369$	37.8285	1.96927
$370$	−4.46184	−0.231960
$371$	−21.7772	−1.13062
$372$	26.5867	1.37845
$373$	−21.3657	−1.10628	−0.553138	−	0.833090i	$-0.686570\pi$
$373$	−21.3657	−1.10628	−0.553138	+	0.833090i	$0.686570\pi$
$374$	−1.71767	−0.0888184
$375$	23.5843	1.21789
$376$	−3.23068	−0.166609
$377$	4.19842	0.216230
$378$	50.8547	2.61568
$379$	−23.9452	−1.22998	−0.614992	−	0.788533i	$-0.710841\pi$
$379$	−23.9452	−1.22998	−0.614992	+	0.788533i	$0.710841\pi$
$380$	2.59398	0.133068
$381$	27.5152	1.40965
$382$	23.7318	1.21422
$383$	−33.1575	−1.69427	−0.847134	−	0.531379i	$-0.821674\pi$
$383$	−33.1575	−1.69427	−0.847134	+	0.531379i	$0.821674\pi$
$384$	3.20966	0.163792
$385$	1.58428	0.0807426
$386$	23.5289	1.19759
$387$	72.1624	3.66822
$388$	11.2136	0.569283
$389$	3.37601	0.171170	0.0855852	−	0.996331i	$-0.472724\pi$
$389$	3.37601	0.171170	0.0855852	+	0.996331i	$0.472724\pi$
$390$	4.66044	0.235991
$391$	24.6836	1.24830
$392$	−6.56518	−0.331592
$393$	0.905178	0.0456602
$394$	23.3475	1.17623
$395$	−0.560303	−0.0281919
$396$	4.01267	0.201644
$397$	−1.27092	−0.0637855	−0.0318927	−	0.999491i	$-0.510153\pi$
$397$	−1.27092	−0.0637855	−0.0318927	+	0.999491i	$0.510153\pi$
$398$	−21.9835	−1.10193
$399$	−39.1755	−1.96123
$400$	−4.38730	−0.219365
$401$	−16.1782	−0.807901	−0.403950	−	0.914781i	$-0.632363\pi$
$401$	−16.1782	−0.807901	−0.403950	+	0.914781i	$0.632363\pi$
$402$	15.8290	0.789479
$403$	−15.3656	−0.765417
$404$	16.5490	0.823345
$405$	17.5429	0.871716
$406$	−8.33592	−0.413705
$407$	3.13249	0.155272
$408$	10.0323	0.496672
$409$	−31.6416	−1.56458	−0.782288	−	0.622916i	$-0.785948\pi$
$409$	−31.6416	−1.56458	−0.782288	+	0.622916i	$0.785948\pi$
$410$	−4.05514	−0.200269
$411$	−51.8517	−2.55766
$412$	10.5638	0.520443
$413$	36.1753	1.78007
$414$	−57.6637	−2.83402
$415$	2.44919	0.120226
$416$	−1.85501	−0.0909492
$417$	41.0809	2.01174
$418$	−1.82113	−0.0890743
$419$	20.8654	1.01934	0.509670	−	0.860370i	$-0.329767\pi$
$419$	20.8654	1.01934	0.509670	+	0.860370i	$0.329767\pi$
$420$	−9.25325	−0.451512
$421$	−19.0679	−0.929313	−0.464656	−	0.885491i	$-0.653822\pi$
$421$	−19.0679	−0.929313	−0.464656	+	0.885491i	$0.653822\pi$
$422$	25.6473	1.24849
$423$	23.5901	1.14699
$424$	5.91275	0.287149
$425$	−13.7132	−0.665188
$426$	33.7225	1.63386
$427$	44.1372	2.13595
$428$	−1.36504	−0.0659818
$429$	−3.27191	−0.157969
$430$	−7.73569	−0.373048
$431$	−20.7949	−1.00166	−0.500829	−	0.865546i	$-0.666971\pi$
$431$	−20.7949	−1.00166	−0.500829	+	0.865546i	$0.666971\pi$
$432$	−13.8076	−0.664318
$433$	−29.5988	−1.42243	−0.711213	−	0.702976i	$-0.751854\pi$
$433$	−29.5988	−1.42243	−0.711213	+	0.702976i	$0.751854\pi$
$434$	30.5083	1.46445
$435$	−5.68620	−0.272633
$436$	9.14686	0.438055
$437$	26.1704	1.25190
$438$	−28.9767	−1.38456
$439$	14.4377	0.689072	0.344536	−	0.938773i	$-0.388036\pi$
$439$	14.4377	0.689072	0.344536	+	0.938773i	$0.388036\pi$
$440$	−0.430151	−0.0205066
$441$	47.9382	2.28277
$442$	−5.79811	−0.275788
$443$	16.7829	0.797381	0.398691	−	0.917085i	$-0.369465\pi$
$443$	16.7829	0.797381	0.398691	+	0.917085i	$0.369465\pi$
$444$	−18.2957	−0.868277
$445$	−11.8992	−0.564078
$446$	−24.3373	−1.15240
$447$	−51.6154	−2.44132
$448$	3.68309	0.174010
$449$	12.1606	0.573895	0.286948	−	0.957946i	$-0.407359\pi$
$449$	12.1606	0.573895	0.286948	+	0.957946i	$0.407359\pi$
$450$	32.0356	1.51017
$451$	2.84696	0.134058
$452$	−13.9762	−0.657386
$453$	−73.4233	−3.44973
$454$	−14.7671	−0.693055
$455$	5.34787	0.250712
$456$	10.6366	0.498103
$457$	40.0035	1.87129	0.935643	−	0.352947i	$-0.114820\pi$
$457$	40.0035	1.87129	0.935643	+	0.352947i	$0.114820\pi$
$458$	16.1720	0.755666
$459$	−43.1578	−2.01443
$460$	6.18145	0.288211
$461$	30.6589	1.42793	0.713963	−	0.700183i	$-0.246898\pi$
$461$	30.6589	1.42793	0.713963	+	0.700183i	$0.246898\pi$
$462$	6.49634	0.302237
$463$	−22.7227	−1.05601	−0.528007	−	0.849240i	$-0.677061\pi$
$463$	−22.7227	−1.05601	−0.528007	+	0.849240i	$0.677061\pi$
$464$	2.26329	0.105071
$465$	20.8107	0.965074
$466$	−13.8134	−0.639894
$467$	−0.0185245	−0.000857210 0	−0.000428605	−	1.00000i	$-0.500136\pi$
$467$	−0.0185245	−0.000857210 0	−0.000428605		1.00000i	$0.500136\pi$
$468$	13.5451	0.626120
$469$	18.1639	0.838729
$470$	−2.52881	−0.116645
$471$	−11.2649	−0.519060
$472$	−9.82198	−0.452093
$473$	5.43092	0.249714
$474$	−2.29751	−0.105528
$475$	−14.5392	−0.667104
$476$	11.5121	0.527656
$477$	−43.1743	−1.97681
$478$	2.12729	0.0972998
$479$	15.1158	0.690657	0.345328	−	0.938482i	$-0.387768\pi$
$479$	15.1158	0.690657	0.345328	+	0.938482i	$0.387768\pi$
$480$	2.51236	0.114673
$481$	10.5739	0.482130
$482$	0.461568	0.0210239
$483$	−93.3552	−4.24781
$484$	−10.6980	−0.486273
$485$	8.77743	0.398563
$486$	30.5119	1.38405
$487$	−35.9757	−1.63021	−0.815107	−	0.579311i	$-0.803322\pi$
$487$	−35.9757	−1.63021	−0.815107	+	0.579311i	$0.803322\pi$
$488$	−11.9837	−0.542479
$489$	43.9046	1.98543
$490$	−5.13889	−0.232151
$491$	28.2846	1.27647	0.638234	−	0.769843i	$-0.279665\pi$
$491$	28.2846	1.27647	0.638234	+	0.769843i	$0.279665\pi$
$492$	−16.6281	−0.749651
$493$	7.07428	0.318609
$494$	−6.14736	−0.276583
$495$	3.14091	0.141174
$496$	−8.28334	−0.371933
$497$	38.6967	1.73578
$498$	10.0429	0.450033
$499$	24.4164	1.09303	0.546515	−	0.837450i	$-0.315954\pi$
$499$	24.4164	1.09303	0.546515	+	0.837450i	$0.315954\pi$
$500$	−7.34791	−0.328609
$501$	42.7571	1.91025
$502$	−2.76735	−0.123513
$503$	7.40394	0.330125	0.165063	−	0.986283i	$-0.447217\pi$
$503$	7.40394	0.330125	0.165063	+	0.986283i	$0.447217\pi$
$504$	−26.8935	−1.19793
$505$	12.9538	0.576434
$506$	−4.33975	−0.192925
$507$	30.6809	1.36259
$508$	−8.57264	−0.380349
$509$	34.2281	1.51714	0.758568	−	0.651594i	$-0.225900\pi$
$509$	34.2281	1.51714	0.758568	+	0.651594i	$0.225900\pi$
$510$	7.85277	0.347726
$511$	−33.2509	−1.47093
$512$	−1.00000	−0.0441942
$513$	−45.7574	−2.02024
$514$	−25.8185	−1.13880
$515$	8.26884	0.364369
$516$	−31.7201	−1.39640
$517$	1.77538	0.0780811
$518$	−20.9944	−0.922442
$519$	78.7105	3.45501
$520$	−1.45201	−0.0636747
$521$	29.6953	1.30097	0.650487	−	0.759517i	$-0.274565\pi$
$521$	29.6953	1.30097	0.650487	+	0.759517i	$0.274565\pi$
$522$	−16.5263	−0.723337
$523$	16.3763	0.716085	0.358042	−	0.933705i	$-0.383444\pi$
$523$	16.3763	0.716085	0.358042	+	0.933705i	$0.383444\pi$
$524$	−0.282017	−0.0123200
$525$	51.8643	2.26355
$526$	−4.23051	−0.184459
$527$	−25.8909	−1.12782
$528$	−1.76383	−0.0767607
$529$	39.3640	1.71148
$530$	4.62821	0.201036
$531$	71.7190	3.11234
$532$	12.2055	0.529176
$533$	9.61012	0.416260
$534$	−48.7927	−2.11147
$535$	−1.06849	−0.0461947
$536$	−4.93168	−0.213016
$537$	−7.48685	−0.323081
$538$	8.72954	0.376357
$539$	3.60781	0.155400
$540$	−10.8079	−0.465098
$541$	28.2698	1.21541	0.607707	−	0.794161i	$-0.292089\pi$
$541$	28.2698	1.21541	0.607707	+	0.794161i	$0.292089\pi$
$542$	−2.32728	−0.0999651
$543$	−17.4260	−0.747822
$544$	−3.12566	−0.134011
$545$	7.15971	0.306688
$546$	21.9289	0.938470
$547$	−22.6859	−0.969980	−0.484990	−	0.874520i	$-0.661177\pi$
$547$	−22.6859	−0.969980	−0.484990	+	0.874520i	$0.661177\pi$
$548$	16.1549	0.690104
$549$	87.5040	3.73458
$550$	2.41099	0.102805
$551$	7.50039	0.319527
$552$	25.3469	1.07884
$553$	−2.63641	−0.112111
$554$	21.0416	0.893971
$555$	−14.3210	−0.607892
$556$	−12.7992	−0.542805
$557$	24.0055	1.01714	0.508572	−	0.861019i	$-0.330173\pi$
$557$	24.0055	1.01714	0.508572	+	0.861019i	$0.330173\pi$
$558$	60.4841	2.56049
$559$	18.3325	0.775381
$560$	2.88294	0.121826
$561$	−5.51312	−0.232764
$562$	7.60360	0.320739
$563$	32.9160	1.38724	0.693622	−	0.720339i	$-0.256014\pi$
$563$	32.9160	1.38724	0.693622	+	0.720339i	$0.256014\pi$
$564$	−10.3694	−0.436629
$565$	−10.9399	−0.460245
$566$	31.4835	1.32335
$567$	82.5453	3.46658
$568$	−10.5066	−0.440846
$569$	−26.1106	−1.09461	−0.547307	−	0.836932i	$-0.684347\pi$
$569$	−26.1106	−1.09461	−0.547307	+	0.836932i	$0.684347\pi$
$570$	8.32577	0.348728
$571$	12.8757	0.538832	0.269416	−	0.963024i	$-0.413169\pi$
$571$	12.8757	0.538832	0.269416	+	0.963024i	$0.413169\pi$
$572$	1.01940	0.0426231
$573$	76.1709	3.18208
$574$	−19.0808	−0.796416
$575$	−34.6469	−1.44488
$576$	7.30189	0.304245
$577$	−45.3291	−1.88707	−0.943537	−	0.331267i	$-0.892524\pi$
$577$	−45.3291	−1.88707	−0.943537	+	0.331267i	$0.892524\pi$
$578$	7.23027	0.300739
$579$	75.5196	3.13849
$580$	1.77159	0.0735614
$581$	11.5243	0.478107
$582$	35.9917	1.49191
$583$	−3.24928	−0.134571
$584$	9.02798	0.373581
$585$	10.6024	0.438355
$586$	12.3202	0.508942
$587$	22.4814	0.927906	0.463953	−	0.885860i	$-0.346431\pi$
$587$	22.4814	0.927906	0.463953	+	0.885860i	$0.346431\pi$
$588$	−21.0720	−0.868993
$589$	−27.4504	−1.13107
$590$	−7.68815	−0.316516
$591$	74.9374	3.08251
$592$	5.70022	0.234278
$593$	−18.9349	−0.777564	−0.388782	−	0.921330i	$-0.627104\pi$
$593$	−18.9349	−0.777564	−0.388782	+	0.921330i	$0.627104\pi$
$594$	7.58779	0.311331
$595$	9.01108	0.369418
$596$	16.0813	0.658715
$597$	−70.5596	−2.88781
$598$	−14.6492	−0.599048
$599$	−1.93559	−0.0790860	−0.0395430	−	0.999218i	$-0.512590\pi$
$599$	−1.93559	−0.0790860	−0.0395430	+	0.999218i	$0.512590\pi$
$600$	−14.0817	−0.574884
$601$	−6.91768	−0.282178	−0.141089	−	0.989997i	$-0.545060\pi$
$601$	−6.91768	−0.282178	−0.141089	+	0.989997i	$0.545060\pi$
$602$	−36.3989	−1.48351
$603$	36.0106	1.46647
$604$	22.8757	0.930801
$605$	−8.37386	−0.340446
$606$	53.1167	2.15772
$607$	−1.68822	−0.0685228	−0.0342614	−	0.999413i	$-0.510908\pi$
$607$	−1.68822	−0.0685228	−0.0342614	+	0.999413i	$0.510908\pi$
$608$	−3.31393	−0.134397
$609$	−26.7554	−1.08419
$610$	−9.38027	−0.379796
$611$	5.99293	0.242448
$612$	22.8232	0.922574
$613$	26.5738	1.07330	0.536652	−	0.843803i	$-0.319689\pi$
$613$	26.5738	1.07330	0.536652	+	0.843803i	$0.319689\pi$
$614$	−14.1499	−0.571044
$615$	−13.0156	−0.524840
$616$	−2.02400	−0.0815492
$617$	−34.9124	−1.40552	−0.702760	−	0.711427i	$-0.748049\pi$
$617$	−34.9124	−1.40552	−0.702760	+	0.711427i	$0.748049\pi$
$618$	33.9063	1.36391
$619$	−19.0394	−0.765259	−0.382629	−	0.923902i	$-0.624981\pi$
$619$	−19.0394	−0.765259	−0.382629	+	0.923902i	$0.624981\pi$
$620$	−6.48378	−0.260395
$621$	−109.040	−4.37562
$622$	−28.6334	−1.14809
$623$	−55.9898	−2.24318
$624$	−5.95393	−0.238348
$625$	16.1849	0.647398
$626$	28.0211	1.11995
$627$	−5.84519	−0.233435
$628$	3.50970	0.140052
$629$	17.8169	0.710407
$630$	−21.0509	−0.838689
$631$	11.9093	0.474102	0.237051	−	0.971497i	$-0.423819\pi$
$631$	11.9093	0.474102	0.237051	+	0.971497i	$0.423819\pi$
$632$	0.715813	0.0284735
$633$	82.3190	3.27189
$634$	−3.58660	−0.142442
$635$	−6.71023	−0.266287
$636$	18.9779	0.752523
$637$	12.1784	0.482528
$638$	−1.24377	−0.0492411
$639$	76.7179	3.03491
$640$	−0.782750	−0.0309409
$641$	13.2306	0.522578	0.261289	−	0.965261i	$-0.415852\pi$
$641$	13.2306	0.522578	0.261289	+	0.965261i	$0.415852\pi$
$642$	−4.38131	−0.172917
$643$	−18.9380	−0.746843	−0.373421	−	0.927662i	$-0.621815\pi$
$643$	−18.9380	−0.746843	−0.373421	+	0.927662i	$0.621815\pi$
$644$	29.0857	1.14614
$645$	−24.8289	−0.977637
$646$	−10.3582	−0.407538
$647$	−12.3407	−0.485164	−0.242582	−	0.970131i	$-0.577994\pi$
$647$	−12.3407	−0.485164	−0.242582	+	0.970131i	$0.577994\pi$
$648$	−22.4119	−0.880424
$649$	5.39755	0.211872
$650$	8.13847	0.319217
$651$	97.9212	3.83783
$652$	−13.6789	−0.535707
$653$	25.9893	1.01704	0.508519	−	0.861051i	$-0.330193\pi$
$653$	25.9893	1.01704	0.508519	+	0.861051i	$0.330193\pi$
$654$	29.3583	1.14800
$655$	−0.220749	−0.00862538
$656$	5.18064	0.202270
$657$	−65.9213	−2.57184
$658$	−11.8989	−0.463867
$659$	46.8958	1.82680	0.913401	−	0.407060i	$-0.133446\pi$
$659$	46.8958	1.82680	0.913401	+	0.407060i	$0.133446\pi$
$660$	−1.38064	−0.0537412
$661$	29.4504	1.14549	0.572743	−	0.819735i	$-0.305879\pi$
$661$	29.4504	1.14549	0.572743	+	0.819735i	$0.305879\pi$
$662$	26.9428	1.04716
$663$	−18.6100	−0.722751
$664$	−3.12896	−0.121427
$665$	9.55385	0.370483
$666$	−41.6224	−1.61283
$667$	17.8734	0.692062
$668$	−13.3214	−0.515421
$669$	−78.1143	−3.02007
$670$	−3.86028	−0.149135
$671$	6.58552	0.254231
$672$	11.8215	0.456023
$673$	−44.1895	−1.70338	−0.851690	−	0.524045i	$-0.824422\pi$
$673$	−44.1895	−1.70338	−0.851690	+	0.524045i	$0.824422\pi$
$674$	14.1130	0.543614
$675$	60.5781	2.33165
$676$	−9.55895	−0.367652
$677$	31.4559	1.20895	0.604475	−	0.796624i	$-0.293383\pi$
$677$	31.4559	1.20895	0.604475	+	0.796624i	$0.293383\pi$
$678$	−44.8589	−1.72280
$679$	41.3007	1.58497
$680$	−2.44661	−0.0938231
$681$	−47.3973	−1.81627
$682$	4.55201	0.174305
$683$	14.4856	0.554276	0.277138	−	0.960830i	$-0.410614\pi$
$683$	14.4856	0.554276	0.277138	+	0.960830i	$0.410614\pi$
$684$	24.1979	0.925231
$685$	12.6453	0.483151
$686$	1.60149	0.0611453
$687$	51.9064	1.98035
$688$	9.88270	0.376775
$689$	−10.9682	−0.417855
$690$	19.8403	0.755308
$691$	3.67573	0.139831	0.0699156	−	0.997553i	$-0.477727\pi$
$691$	3.67573	0.139831	0.0699156	+	0.997553i	$0.477727\pi$
$692$	−24.5230	−0.932225
$693$	14.7790	0.561409
$694$	−10.5888	−0.401947
$695$	−10.0185	−0.380025
$696$	7.26439	0.275356
$697$	16.1929	0.613350
$698$	6.62086	0.250603
$699$	−44.3363	−1.67695
$700$	−16.1588	−0.610747
$701$	45.4580	1.71692	0.858462	−	0.512877i	$-0.171420\pi$
$701$	45.4580	1.71692	0.858462	+	0.512877i	$0.171420\pi$
$702$	25.6132	0.966707
$703$	18.8901	0.712454
$704$	0.549538	0.0207115
$705$	−8.11662	−0.305690
$706$	16.3008	0.613490
$707$	60.9516	2.29232
$708$	−31.5252	−1.18479
$709$	−5.86207	−0.220155	−0.110077	−	0.993923i	$-0.535110\pi$
$709$	−5.86207	−0.220155	−0.110077	+	0.993923i	$0.535110\pi$
$710$	−8.22402	−0.308642
$711$	−5.22679	−0.196020
$712$	15.2018	0.569713
$713$	−65.4143	−2.44978
$714$	36.9498	1.38281
$715$	0.797932	0.0298410
$716$	2.33260	0.0871734
$717$	6.82786	0.254991
$718$	13.0918	0.488581
$719$	16.2986	0.607835	0.303918	−	0.952698i	$-0.401705\pi$
$719$	16.2986	0.607835	0.303918	+	0.952698i	$0.401705\pi$
$720$	5.71555	0.213006
$721$	38.9076	1.44899
$722$	8.01789	0.298395
$723$	1.48147	0.0550966
$724$	5.42925	0.201776
$725$	−9.92975	−0.368782
$726$	−34.3369	−1.27436
$727$	−37.1845	−1.37910	−0.689549	−	0.724239i	$-0.742191\pi$
$727$	−37.1845	−1.37910	−0.689549	+	0.724239i	$0.742191\pi$
$728$	−6.83216	−0.253217
$729$	30.6967	1.13692
$730$	7.06665	0.261549
$731$	30.8899	1.14251
$732$	−38.4637	−1.42166
$733$	−17.0712	−0.630539	−0.315269	−	0.949002i	$-0.602095\pi$
$733$	−17.0712	−0.630539	−0.315269	+	0.949002i	$0.602095\pi$
$734$	−32.4923	−1.19931
$735$	−16.4941	−0.608393
$736$	−7.89709	−0.291091
$737$	2.71015	0.0998296
$738$	−37.8285	−1.39248
$739$	31.5854	1.16189	0.580944	−	0.813944i	$-0.302684\pi$
$739$	31.5854	1.16189	0.580944	+	0.813944i	$0.302684\pi$
$740$	4.46184	0.164021
$741$	−19.7309	−0.724833
$742$	21.7772	0.799467
$743$	−37.6920	−1.38278	−0.691392	−	0.722480i	$-0.743002\pi$
$743$	−37.6920	−1.38278	−0.691392	+	0.722480i	$0.743002\pi$
$744$	−26.5867	−0.974715
$745$	12.5876	0.461174
$746$	21.3657	0.782255
$747$	22.8473	0.835940
$748$	1.71767	0.0628041
$749$	−5.02758	−0.183704
$750$	−23.5843	−0.861176
$751$	18.9434	0.691254	0.345627	−	0.938372i	$-0.387666\pi$
$751$	18.9434	0.691254	0.345627	+	0.938372i	$0.387666\pi$
$752$	3.23068	0.117811
$753$	−8.88224	−0.323687
$754$	−4.19842	−0.152898
$755$	17.9060	0.651666
$756$	−50.8547	−1.84957
$757$	−10.9197	−0.396883	−0.198441	−	0.980113i	$-0.563588\pi$
$757$	−10.9197	−0.396883	−0.198441	+	0.980113i	$0.563588\pi$
$758$	23.9452	0.869730
$759$	−13.9291	−0.505594
$760$	−2.59398	−0.0940934
$761$	15.4318	0.559403	0.279701	−	0.960087i	$-0.409765\pi$
$761$	15.4318	0.559403	0.279701	+	0.960087i	$0.409765\pi$
$762$	−27.5152	−0.996771
$763$	33.6887	1.21961
$764$	−23.7318	−0.858586
$765$	17.8649	0.645906
$766$	33.1575	1.19803
$767$	18.2198	0.657880
$768$	−3.20966	−0.115818
$769$	−50.4697	−1.81998	−0.909991	−	0.414628i	$-0.863912\pi$
$769$	−50.4697	−1.81998	−0.909991	+	0.414628i	$0.863912\pi$
$770$	−1.58428	−0.0570937
$771$	−82.8684	−2.98443
$772$	−23.5289	−0.846823
$773$	−37.2515	−1.33984	−0.669921	−	0.742432i	$-0.733672\pi$
$773$	−37.2515	−1.33984	−0.669921	+	0.742432i	$0.733672\pi$
$774$	−72.1624	−2.59383
$775$	36.3415	1.30543
$776$	−11.2136	−0.402544
$777$	−67.3849	−2.41742
$778$	−3.37601	−0.121036
$779$	17.1683	0.615117
$780$	−4.66044	−0.166870
$781$	5.77376	0.206601
$782$	−24.6836	−0.882684
$783$	−31.2506	−1.11681
$784$	6.56518	0.234471
$785$	2.74721	0.0980523
$786$	−0.905178	−0.0322866
$787$	27.7001	0.987402	0.493701	−	0.869632i	$-0.335644\pi$
$787$	27.7001	0.987402	0.493701	+	0.869632i	$0.335644\pi$
$788$	−23.3475	−0.831720
$789$	−13.5785	−0.483406
$790$	0.560303	0.0199347
$791$	−51.4758	−1.83027
$792$	−4.01267	−0.142584
$793$	22.2299	0.789408
$794$	1.27092	0.0451032
$795$	14.8549	0.526851
$796$	21.9835	0.779186
$797$	44.0822	1.56147	0.780736	−	0.624861i	$-0.214844\pi$
$797$	44.0822	1.56147	0.780736	+	0.624861i	$0.214844\pi$
$798$	39.1755	1.38680
$799$	10.0980	0.357241
$800$	4.38730	0.155115
$801$	−111.002	−3.92207
$802$	16.1782	0.571272
$803$	−4.96122	−0.175078
$804$	−15.8290	−0.558246
$805$	22.7668	0.802426
$806$	15.3656	0.541232
$807$	28.0188	0.986309
$808$	−16.5490	−0.582193
$809$	−28.6487	−1.00724	−0.503618	−	0.863927i	$-0.667998\pi$
$809$	−28.6487	−1.00724	−0.503618	+	0.863927i	$0.667998\pi$
$810$	−17.5429	−0.616396
$811$	−24.6951	−0.867162	−0.433581	−	0.901115i	$-0.642750\pi$
$811$	−24.6951	−0.867162	−0.433581	+	0.901115i	$0.642750\pi$
$812$	8.33592	0.292533
$813$	−7.46976	−0.261976
$814$	−3.13249	−0.109794
$815$	−10.7072	−0.375056
$816$	−10.0323	−0.351200
$817$	32.7506	1.14580
$818$	31.6416	1.10632
$819$	49.8877	1.74322
$820$	4.05514	0.141612
$821$	10.3393	0.360846	0.180423	−	0.983589i	$-0.442253\pi$
$821$	10.3393	0.360846	0.180423	+	0.983589i	$0.442253\pi$
$822$	51.8517	1.80854
$823$	−5.17797	−0.180493	−0.0902463	−	0.995919i	$-0.528765\pi$
$823$	−5.17797	−0.180493	−0.0902463	+	0.995919i	$0.528765\pi$
$824$	−10.5638	−0.368009
$825$	7.73844	0.269418
$826$	−36.1753	−1.25870
$827$	13.2557	0.460945	0.230472	−	0.973079i	$-0.425973\pi$
$827$	13.2557	0.460945	0.230472	+	0.973079i	$0.425973\pi$
$828$	57.6637	2.00395
$829$	14.1901	0.492843	0.246421	−	0.969163i	$-0.420745\pi$
$829$	14.1901	0.492843	0.246421	+	0.969163i	$0.420745\pi$
$830$	−2.44919	−0.0850127
$831$	67.5362	2.34281
$832$	1.85501	0.0643108
$833$	20.5205	0.710993
$834$	−41.0809	−1.42251
$835$	−10.4273	−0.360853
$836$	1.82113	0.0629850
$837$	114.373	3.95331
$838$	−20.8654	−0.720783
$839$	−10.4311	−0.360123	−0.180061	−	0.983655i	$-0.557630\pi$
$839$	−10.4311	−0.360123	−0.180061	+	0.983655i	$0.557630\pi$
$840$	9.25325	0.319267
$841$	−23.8775	−0.823362
$842$	19.0679	0.657123
$843$	24.4050	0.840551
$844$	−25.6473	−0.882816
$845$	−7.48227	−0.257398
$846$	−23.5901	−0.811043
$847$	−39.4018	−1.35386
$848$	−5.91275	−0.203045
$849$	101.051	3.46807
$850$	13.7132	0.470359
$851$	45.0151	1.54310
$852$	−33.7225	−1.15531
$853$	42.5761	1.45778	0.728890	−	0.684631i	$-0.240037\pi$
$853$	42.5761	1.45778	0.728890	+	0.684631i	$0.240037\pi$
$854$	−44.1372	−1.51035
$855$	18.9409	0.647766
$856$	1.36504	0.0466562
$857$	−44.5875	−1.52308	−0.761539	−	0.648119i	$-0.775556\pi$
$857$	−44.5875	−1.52308	−0.761539	+	0.648119i	$0.775556\pi$
$858$	3.27191	0.111701
$859$	−10.1871	−0.347579	−0.173790	−	0.984783i	$-0.555601\pi$
$859$	−10.1871	−0.347579	−0.173790	+	0.984783i	$0.555601\pi$
$860$	7.73569	0.263785
$861$	−61.2427	−2.08715
$862$	20.7949	0.708279
$863$	−12.1795	−0.414594	−0.207297	−	0.978278i	$-0.566467\pi$
$863$	−12.1795	−0.414594	−0.207297	+	0.978278i	$0.566467\pi$
$864$	13.8076	0.469744
$865$	−19.1954	−0.652663
$866$	29.5988	1.00581
$867$	23.2067	0.788140
$868$	−30.5083	−1.03552
$869$	−0.393366	−0.0133440
$870$	5.68620	0.192780
$871$	9.14831	0.309979
$872$	−9.14686	−0.309752
$873$	81.8804	2.77123
$874$	−26.1704	−0.885226
$875$	−27.0630	−0.914898
$876$	28.9767	0.979033
$877$	−48.5790	−1.64040	−0.820198	−	0.572079i	$-0.806137\pi$
$877$	−48.5790	−1.64040	−0.820198	+	0.572079i	$0.806137\pi$
$878$	−14.4377	−0.487248
$879$	39.5435	1.33377
$880$	0.430151	0.0145004
$881$	−39.6411	−1.33554	−0.667772	−	0.744366i	$-0.732752\pi$
$881$	−39.6411	−1.33554	−0.667772	+	0.744366i	$0.732752\pi$
$882$	−47.9382	−1.61416
$883$	−47.9544	−1.61380	−0.806898	−	0.590691i	$-0.798855\pi$
$883$	−47.9544	−1.61380	−0.806898	+	0.590691i	$0.798855\pi$
$884$	5.79811	0.195012
$885$	−24.6763	−0.829486
$886$	−16.7829	−0.563834
$887$	−17.5672	−0.589850	−0.294925	−	0.955520i	$-0.595295\pi$
$887$	−17.5672	−0.589850	−0.294925	+	0.955520i	$0.595295\pi$
$888$	18.2957	0.613965
$889$	−31.5738	−1.05895
$890$	11.8992	0.398863
$891$	12.3162	0.412609
$892$	24.3373	0.814872
$893$	10.7062	0.358270
$894$	51.6154	1.72628
$895$	1.82584	0.0610312
$896$	−3.68309	−0.123044
$897$	−47.0187	−1.56991
$898$	−12.1606	−0.405805
$899$	−18.7476	−0.625268
$900$	−32.0356	−1.06785
$901$	−18.4812	−0.615699
$902$	−2.84696	−0.0947933
$903$	−116.828	−3.88779
$904$	13.9762	0.464842
$905$	4.24974	0.141266
$906$	73.4233	2.43933
$907$	−28.6013	−0.949689	−0.474844	−	0.880070i	$-0.657496\pi$
$907$	−28.6013	−0.949689	−0.474844	+	0.880070i	$0.657496\pi$
$908$	14.7671	0.490064
$909$	120.839	4.00799
$910$	−5.34787	−0.177280
$911$	−27.2648	−0.903323	−0.451662	−	0.892189i	$-0.649169\pi$
$911$	−27.2648	−0.903323	−0.451662	+	0.892189i	$0.649169\pi$
$912$	−10.6366	−0.352212
$913$	1.71948	0.0569066
$914$	−40.0035	−1.32320
$915$	−30.1074	−0.995322
$916$	−16.1720	−0.534337
$917$	−1.03870	−0.0343008
$918$	43.1578	1.42442
$919$	−36.0279	−1.18845	−0.594225	−	0.804299i	$-0.702541\pi$
$919$	−36.0279	−1.18845	−0.594225	+	0.804299i	$0.702541\pi$
$920$	−6.18145	−0.203796
$921$	−45.4164	−1.49652
$922$	−30.6589	−1.00970
$923$	19.4898	0.641514
$924$	−6.49634	−0.213714
$925$	−25.0086	−0.822277
$926$	22.7227	0.746715
$927$	77.1360	2.53348
$928$	−2.26329	−0.0742962
$929$	37.1401	1.21853	0.609263	−	0.792968i	$-0.291465\pi$
$929$	37.1401	1.21853	0.609263	+	0.792968i	$0.291465\pi$
$930$	−20.8107	−0.682410
$931$	21.7565	0.713041
$932$	13.8134	0.452474
$933$	−91.9032	−3.00878
$934$	0.0185245	0.000606139 0
$935$	1.34450	0.0439700
$936$	−13.5451	−0.442734
$937$	−60.4717	−1.97552	−0.987761	−	0.155972i	$-0.950149\pi$
$937$	−60.4717	−1.97552	−0.987761	+	0.155972i	$0.950149\pi$
$938$	−18.1639	−0.593071
$939$	89.9380	2.93502
$940$	2.52881	0.0824808
$941$	−3.53331	−0.115183	−0.0575913	−	0.998340i	$-0.518342\pi$
$941$	−3.53331	−0.115183	−0.0575913	+	0.998340i	$0.518342\pi$
$942$	11.2649	0.367031
$943$	40.9120	1.33228
$944$	9.82198	0.319678
$945$	−39.8065	−1.29490
$946$	−5.43092	−0.176574
$947$	−50.0470	−1.62631	−0.813154	−	0.582048i	$-0.802251\pi$
$947$	−50.0470	−1.62631	−0.813154	+	0.582048i	$0.802251\pi$
$948$	2.29751	0.0746198
$949$	−16.7470	−0.543629
$950$	14.5392	0.471714
$951$	−11.5117	−0.373294
$952$	−11.5121	−0.373109
$953$	5.71122	0.185004	0.0925022	−	0.995712i	$-0.470513\pi$
$953$	5.71122	0.185004	0.0925022	+	0.995712i	$0.470513\pi$
$954$	43.1743	1.39782
$955$	−18.5761	−0.601107
$956$	−2.12729	−0.0688013
$957$	−3.99206	−0.129045
$958$	−15.1158	−0.488368
$959$	59.5001	1.92136
$960$	−2.51236	−0.0810860
$961$	37.6137	1.21335
$962$	−10.5739	−0.340917
$963$	−9.96739	−0.321195
$964$	−0.461568	−0.0148661
$965$	−18.4172	−0.592872
$966$	93.3552	3.00365
$967$	22.6192	0.727384	0.363692	−	0.931519i	$-0.381516\pi$
$967$	22.6192	0.727384	0.363692	+	0.931519i	$0.381516\pi$
$968$	10.6980	0.343847
$969$	−33.2463	−1.06802
$970$	−8.77743	−0.281826
$971$	29.0737	0.933020	0.466510	−	0.884516i	$-0.345511\pi$
$971$	29.0737	0.933020	0.466510	+	0.884516i	$0.345511\pi$
$972$	−30.5119	−0.978668
$973$	−47.1405	−1.51125
$974$	35.9757	1.15273
$975$	26.1217	0.836564
$976$	11.9837	0.383590
$977$	−9.37258	−0.299855	−0.149928	−	0.988697i	$-0.547904\pi$
$977$	−9.37258	−0.299855	−0.149928	+	0.988697i	$0.547904\pi$
$978$	−43.9046	−1.40391
$979$	−8.35399	−0.266995
$980$	5.13889	0.164156
$981$	66.7894	2.13242
$982$	−28.2846	−0.902598
$983$	22.8203	0.727854	0.363927	−	0.931427i	$-0.381436\pi$
$983$	22.8203	0.727854	0.363927	+	0.931427i	$0.381436\pi$
$984$	16.6281	0.530083
$985$	−18.2753	−0.582298
$986$	−7.07428	−0.225291
$987$	−38.1913	−1.21564
$988$	6.14736	0.195573
$989$	78.0446	2.48167
$990$	−3.14091	−0.0998248
$991$	41.7126	1.32505	0.662523	−	0.749042i	$-0.269486\pi$
$991$	41.7126	1.32505	0.662523	+	0.749042i	$0.269486\pi$
$992$	8.28334	0.262996
$993$	86.4770	2.74426
$994$	−38.6967	−1.22739
$995$	17.2076	0.545518
$996$	−10.0429	−0.318221
$997$	−18.5983	−0.589013	−0.294506	−	0.955650i	$-0.595155\pi$
$997$	−18.5983	−0.589013	−0.294506	+	0.955650i	$0.595155\pi$
$998$	−24.4164	−0.772888
$999$	−78.7063	−2.49016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.3	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.3	✓	86	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.20966 q^{3} +1.00000 q^{4} +0.782750 q^{5} +3.20966 q^{6} +3.68309 q^{7} -1.00000 q^{8} +7.30189 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.20966 q^{3} +1.00000 q^{4} +0.782750 q^{5} +3.20966 q^{6} +3.68309 q^{7} -1.00000 q^{8} +7.30189 q^{9} -0.782750 q^{10} +0.549538 q^{11} -3.20966 q^{12} +1.85501 q^{13} -3.68309 q^{14} -2.51236 q^{15} +1.00000 q^{16} +3.12566 q^{17} -7.30189 q^{18} +3.31393 q^{19} +0.782750 q^{20} -11.8215 q^{21} -0.549538 q^{22} +7.89709 q^{23} +3.20966 q^{24} -4.38730 q^{25} -1.85501 q^{26} -13.8076 q^{27} +3.68309 q^{28} +2.26329 q^{29} +2.51236 q^{30} -8.28334 q^{31} -1.00000 q^{32} -1.76383 q^{33} -3.12566 q^{34} +2.88294 q^{35} +7.30189 q^{36} +5.70022 q^{37} -3.31393 q^{38} -5.95393 q^{39} -0.782750 q^{40} +5.18064 q^{41} +11.8215 q^{42} +9.88270 q^{43} +0.549538 q^{44} +5.71555 q^{45} -7.89709 q^{46} +3.23068 q^{47} -3.20966 q^{48} +6.56518 q^{49} +4.38730 q^{50} -10.0323 q^{51} +1.85501 q^{52} -5.91275 q^{53} +13.8076 q^{54} +0.430151 q^{55} -3.68309 q^{56} -10.6366 q^{57} -2.26329 q^{58} +9.82198 q^{59} -2.51236 q^{60} +11.9837 q^{61} +8.28334 q^{62} +26.8935 q^{63} +1.00000 q^{64} +1.45201 q^{65} +1.76383 q^{66} +4.93168 q^{67} +3.12566 q^{68} -25.3469 q^{69} -2.88294 q^{70} +10.5066 q^{71} -7.30189 q^{72} -9.02798 q^{73} -5.70022 q^{74} +14.0817 q^{75} +3.31393 q^{76} +2.02400 q^{77} +5.95393 q^{78} -0.715813 q^{79} +0.782750 q^{80} +22.4119 q^{81} -5.18064 q^{82} +3.12896 q^{83} -11.8215 q^{84} +2.44661 q^{85} -9.88270 q^{86} -7.26439 q^{87} -0.549538 q^{88} -15.2018 q^{89} -5.71555 q^{90} +6.83216 q^{91} +7.89709 q^{92} +26.5867 q^{93} -3.23068 q^{94} +2.59398 q^{95} +3.20966 q^{96} +11.2136 q^{97} -6.56518 q^{98} +4.01267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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