LMFDB - Embedded newform 8026.2.a.b.1.7

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:	$1$
Dimension:	$81$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.80063 q^{3} +1.00000 q^{4} -1.23643 q^{5} +2.80063 q^{6} -3.84630 q^{7} -1.00000 q^{8} +4.84350 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.80063 q^{3} +1.00000 q^{4} -1.23643 q^{5} +2.80063 q^{6} -3.84630 q^{7} -1.00000 q^{8} +4.84350 q^{9} +1.23643 q^{10} +5.45511 q^{11} -2.80063 q^{12} +5.51921 q^{13} +3.84630 q^{14} +3.46277 q^{15} +1.00000 q^{16} -0.925219 q^{17} -4.84350 q^{18} -5.29693 q^{19} -1.23643 q^{20} +10.7721 q^{21} -5.45511 q^{22} +4.28337 q^{23} +2.80063 q^{24} -3.47125 q^{25} -5.51921 q^{26} -5.16296 q^{27} -3.84630 q^{28} +1.03322 q^{29} -3.46277 q^{30} -8.51021 q^{31} -1.00000 q^{32} -15.2777 q^{33} +0.925219 q^{34} +4.75567 q^{35} +4.84350 q^{36} +7.51125 q^{37} +5.29693 q^{38} -15.4572 q^{39} +1.23643 q^{40} -11.6074 q^{41} -10.7721 q^{42} +0.608572 q^{43} +5.45511 q^{44} -5.98863 q^{45} -4.28337 q^{46} -5.11644 q^{47} -2.80063 q^{48} +7.79405 q^{49} +3.47125 q^{50} +2.59119 q^{51} +5.51921 q^{52} +4.39713 q^{53} +5.16296 q^{54} -6.74484 q^{55} +3.84630 q^{56} +14.8347 q^{57} -1.03322 q^{58} -7.03594 q^{59} +3.46277 q^{60} +2.18839 q^{61} +8.51021 q^{62} -18.6296 q^{63} +1.00000 q^{64} -6.82409 q^{65} +15.2777 q^{66} +1.02982 q^{67} -0.925219 q^{68} -11.9961 q^{69} -4.75567 q^{70} +2.93912 q^{71} -4.84350 q^{72} -4.45375 q^{73} -7.51125 q^{74} +9.72167 q^{75} -5.29693 q^{76} -20.9820 q^{77} +15.4572 q^{78} -7.09246 q^{79} -1.23643 q^{80} -0.0709871 q^{81} +11.6074 q^{82} +10.2898 q^{83} +10.7721 q^{84} +1.14396 q^{85} -0.608572 q^{86} -2.89367 q^{87} -5.45511 q^{88} +13.4541 q^{89} +5.98863 q^{90} -21.2285 q^{91} +4.28337 q^{92} +23.8339 q^{93} +5.11644 q^{94} +6.54926 q^{95} +2.80063 q^{96} -1.03786 q^{97} -7.79405 q^{98} +26.4219 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) $ 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * 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
$3$	−2.80063	−1.61694	−0.808471	−	0.588536i	$-0.799704\pi$
$3$	−2.80063	−1.61694	−0.808471	+	0.588536i	$0.799704\pi$
$4$	1.00000	0.500000
$5$	−1.23643	−0.552947	−0.276473	−	0.961022i	$-0.589166\pi$
$5$	−1.23643	−0.552947	−0.276473	+	0.961022i	$0.589166\pi$
$6$	2.80063	1.14335
$7$	−3.84630	−1.45377	−0.726883	−	0.686761i	$-0.759032\pi$
$7$	−3.84630	−1.45377	−0.726883	+	0.686761i	$0.759032\pi$
$8$	−1.00000	−0.353553
$9$	4.84350	1.61450
$10$	1.23643	0.390992
$11$	5.45511	1.64478	0.822389	−	0.568925i	$-0.192641\pi$
$11$	5.45511	1.64478	0.822389	+	0.568925i	$0.192641\pi$
$12$	−2.80063	−0.808471
$13$	5.51921	1.53075	0.765376	−	0.643583i	$-0.222553\pi$
$13$	5.51921	1.53075	0.765376	+	0.643583i	$0.222553\pi$
$14$	3.84630	1.02797
$15$	3.46277	0.894082
$16$	1.00000	0.250000
$17$	−0.925219	−0.224399	−0.112199	−	0.993686i	$-0.535789\pi$
$17$	−0.925219	−0.224399	−0.112199	+	0.993686i	$0.535789\pi$
$18$	−4.84350	−1.14162
$19$	−5.29693	−1.21520	−0.607599	−	0.794244i	$-0.707867\pi$
$19$	−5.29693	−1.21520	−0.607599	+	0.794244i	$0.707867\pi$
$20$	−1.23643	−0.276473
$21$	10.7721	2.35066
$22$	−5.45511	−1.16303
$23$	4.28337	0.893145	0.446572	−	0.894748i	$-0.352645\pi$
$23$	4.28337	0.893145	0.446572	+	0.894748i	$0.352645\pi$
$24$	2.80063	0.571675
$25$	−3.47125	−0.694250
$26$	−5.51921	−1.08241
$27$	−5.16296	−0.993612
$28$	−3.84630	−0.726883
$29$	1.03322	0.191865	0.0959323	−	0.995388i	$-0.469417\pi$
$29$	1.03322	0.191865	0.0959323	+	0.995388i	$0.469417\pi$
$30$	−3.46277	−0.632212
$31$	−8.51021	−1.52848	−0.764240	−	0.644932i	$-0.776886\pi$
$31$	−8.51021	−1.52848	−0.764240	+	0.644932i	$0.776886\pi$
$32$	−1.00000	−0.176777
$33$	−15.2777	−2.65951
$34$	0.925219	0.158674
$35$	4.75567	0.803855
$36$	4.84350	0.807251
$37$	7.51125	1.23484	0.617421	−	0.786633i	$-0.288177\pi$
$37$	7.51125	1.23484	0.617421	+	0.786633i	$0.288177\pi$
$38$	5.29693	0.859275
$39$	−15.4572	−2.47514
$40$	1.23643	0.195496
$41$	−11.6074	−1.81277	−0.906386	−	0.422450i	$-0.861170\pi$
$41$	−11.6074	−1.81277	−0.906386	+	0.422450i	$0.861170\pi$
$42$	−10.7721	−1.66216
$43$	0.608572	0.0928063	0.0464031	−	0.998923i	$-0.485224\pi$
$43$	0.608572	0.0928063	0.0464031	+	0.998923i	$0.485224\pi$
$44$	5.45511	0.822389
$45$	−5.98863	−0.892733
$46$	−4.28337	−0.631549
$47$	−5.11644	−0.746309	−0.373155	−	0.927769i	$-0.621724\pi$
$47$	−5.11644	−0.746309	−0.373155	+	0.927769i	$0.621724\pi$
$48$	−2.80063	−0.404235
$49$	7.79405	1.11344
$50$	3.47125	0.490909
$51$	2.59119	0.362839
$52$	5.51921	0.765376
$53$	4.39713	0.603992	0.301996	−	0.953309i	$-0.402347\pi$
$53$	4.39713	0.603992	0.301996	+	0.953309i	$0.402347\pi$
$54$	5.16296	0.702590
$55$	−6.74484	−0.909475
$56$	3.84630	0.513984
$57$	14.8347	1.96491
$58$	−1.03322	−0.135669
$59$	−7.03594	−0.916002	−0.458001	−	0.888952i	$-0.651434\pi$
$59$	−7.03594	−0.916002	−0.458001	+	0.888952i	$0.651434\pi$
$60$	3.46277	0.447041
$61$	2.18839	0.280195	0.140098	−	0.990138i	$-0.455258\pi$
$61$	2.18839	0.280195	0.140098	+	0.990138i	$0.455258\pi$
$62$	8.51021	1.08080
$63$	−18.6296	−2.34711
$64$	1.00000	0.125000
$65$	−6.82409	−0.846424
$66$	15.2777	1.88056
$67$	1.02982	0.125813	0.0629063	−	0.998019i	$-0.479963\pi$
$67$	1.02982	0.125813	0.0629063	+	0.998019i	$0.479963\pi$
$68$	−0.925219	−0.112199
$69$	−11.9961	−1.44416
$70$	−4.75567	−0.568411
$71$	2.93912	0.348809	0.174405	−	0.984674i	$-0.444200\pi$
$71$	2.93912	0.348809	0.174405	+	0.984674i	$0.444200\pi$
$72$	−4.84350	−0.570812
$73$	−4.45375	−0.521272	−0.260636	−	0.965437i	$-0.583932\pi$
$73$	−4.45375	−0.521272	−0.260636	+	0.965437i	$0.583932\pi$
$74$	−7.51125	−0.873165
$75$	9.72167	1.12256
$76$	−5.29693	−0.607599
$77$	−20.9820	−2.39112
$78$	15.4572	1.75019
$79$	−7.09246	−0.797964	−0.398982	−	0.916959i	$-0.630636\pi$
$79$	−7.09246	−0.797964	−0.398982	+	0.916959i	$0.630636\pi$
$80$	−1.23643	−0.138237
$81$	−0.0709871	−0.00788746
$82$	11.6074	1.28182
$83$	10.2898	1.12946	0.564728	−	0.825277i	$-0.308981\pi$
$83$	10.2898	1.12946	0.564728	+	0.825277i	$0.308981\pi$
$84$	10.7721	1.17533
$85$	1.14396	0.124080
$86$	−0.608572	−0.0656240
$87$	−2.89367	−0.310234
$88$	−5.45511	−0.581517
$89$	13.4541	1.42613	0.713066	−	0.701097i	$-0.247306\pi$
$89$	13.4541	1.42613	0.713066	+	0.701097i	$0.247306\pi$
$90$	5.98863	0.631257
$91$	−21.2285	−2.22536
$92$	4.28337	0.446572
$93$	23.8339	2.47146
$94$	5.11644	0.527720
$95$	6.54926	0.671940
$96$	2.80063	0.285838
$97$	−1.03786	−0.105379	−0.0526893	−	0.998611i	$-0.516779\pi$
$97$	−1.03786	−0.105379	−0.0526893	+	0.998611i	$0.516779\pi$
$98$	−7.79405	−0.787318
$99$	26.4219	2.65550
$100$	−3.47125	−0.347125
$101$	−5.79675	−0.576798	−0.288399	−	0.957510i	$-0.593123\pi$
$101$	−5.79675	−0.576798	−0.288399	+	0.957510i	$0.593123\pi$
$102$	−2.59119	−0.256566
$103$	−10.9988	−1.08375	−0.541874	−	0.840460i	$-0.682285\pi$
$103$	−10.9988	−1.08375	−0.541874	+	0.840460i	$0.682285\pi$
$104$	−5.51921	−0.541203
$105$	−13.3188	−1.29979
$106$	−4.39713	−0.427087
$107$	14.9311	1.44345	0.721724	−	0.692181i	$-0.243350\pi$
$107$	14.9311	1.44345	0.721724	+	0.692181i	$0.243350\pi$
$108$	−5.16296	−0.496806
$109$	7.19347	0.689010	0.344505	−	0.938785i	$-0.388047\pi$
$109$	7.19347	0.689010	0.344505	+	0.938785i	$0.388047\pi$
$110$	6.74484	0.643096
$111$	−21.0362	−1.99667
$112$	−3.84630	−0.363442
$113$	10.4883	0.986661	0.493330	−	0.869842i	$-0.335779\pi$
$113$	10.4883	0.986661	0.493330	+	0.869842i	$0.335779\pi$
$114$	−14.8347	−1.38940
$115$	−5.29607	−0.493861
$116$	1.03322	0.0959323
$117$	26.7323	2.47140
$118$	7.03594	0.647711
$119$	3.55867	0.326223
$120$	−3.46277	−0.316106
$121$	18.7583	1.70530
$122$	−2.18839	−0.198128
$123$	32.5080	2.93115
$124$	−8.51021	−0.764240
$125$	10.4741	0.936830
$126$	18.6296	1.65966
$127$	13.3296	1.18281	0.591406	−	0.806374i	$-0.298573\pi$
$127$	13.3296	1.18281	0.591406	+	0.806374i	$0.298573\pi$
$128$	−1.00000	−0.0883883
$129$	−1.70438	−0.150062
$130$	6.82409	0.598512
$131$	3.47164	0.303319	0.151659	−	0.988433i	$-0.451538\pi$
$131$	3.47164	0.303319	0.151659	+	0.988433i	$0.451538\pi$
$132$	−15.2777	−1.32976
$133$	20.3736	1.76661
$134$	−1.02982	−0.0889629
$135$	6.38362	0.549415
$136$	0.925219	0.0793369
$137$	−3.79192	−0.323965	−0.161983	−	0.986794i	$-0.551789\pi$
$137$	−3.79192	−0.323965	−0.161983	+	0.986794i	$0.551789\pi$
$138$	11.9961	1.02118
$139$	−2.85936	−0.242528	−0.121264	−	0.992620i	$-0.538695\pi$
$139$	−2.85936	−0.242528	−0.121264	+	0.992620i	$0.538695\pi$
$140$	4.75567	0.401927
$141$	14.3292	1.20674
$142$	−2.93912	−0.246645
$143$	30.1079	2.51775
$144$	4.84350	0.403625
$145$	−1.27750	−0.106091
$146$	4.45375	0.368595
$147$	−21.8282	−1.80036
$148$	7.51125	0.617421
$149$	14.6979	1.20410	0.602050	−	0.798459i	$-0.294351\pi$
$149$	14.6979	1.20410	0.602050	+	0.798459i	$0.294351\pi$
$150$	−9.72167	−0.793771
$151$	7.91496	0.644110	0.322055	−	0.946721i	$-0.395626\pi$
$151$	7.91496	0.644110	0.322055	+	0.946721i	$0.395626\pi$
$152$	5.29693	0.429638
$153$	−4.48130	−0.362292
$154$	20.9820	1.69078
$155$	10.5222	0.845167
$156$	−15.4572	−1.23757
$157$	16.9549	1.35315	0.676574	−	0.736375i	$-0.263464\pi$
$157$	16.9549	1.35315	0.676574	+	0.736375i	$0.263464\pi$
$158$	7.09246	0.564246
$159$	−12.3147	−0.976620
$160$	1.23643	0.0977481
$161$	−16.4751	−1.29842
$162$	0.0709871	0.00557727
$163$	12.6317	0.989393	0.494696	−	0.869066i	$-0.335279\pi$
$163$	12.6317	0.989393	0.494696	+	0.869066i	$0.335279\pi$
$164$	−11.6074	−0.906386
$165$	18.8898	1.47057
$166$	−10.2898	−0.798646
$167$	−13.9011	−1.07570	−0.537850	−	0.843041i	$-0.680763\pi$
$167$	−13.9011	−1.07570	−0.537850	+	0.843041i	$0.680763\pi$
$168$	−10.7721	−0.831082
$169$	17.4617	1.34320
$170$	−1.14396	−0.0877381
$171$	−25.6557	−1.96194
$172$	0.608572	0.0464031
$173$	−14.9767	−1.13865	−0.569327	−	0.822111i	$-0.692796\pi$
$173$	−14.9767	−1.13865	−0.569327	+	0.822111i	$0.692796\pi$
$174$	2.89367	0.219368
$175$	13.3515	1.00928
$176$	5.45511	0.411195
$177$	19.7050	1.48112
$178$	−13.4541	−1.00843
$179$	−6.09039	−0.455217	−0.227608	−	0.973753i	$-0.573091\pi$
$179$	−6.09039	−0.455217	−0.227608	+	0.973753i	$0.573091\pi$
$180$	−5.98863	−0.446366
$181$	−12.8030	−0.951636	−0.475818	−	0.879544i	$-0.657848\pi$
$181$	−12.8030	−0.951636	−0.475818	+	0.879544i	$0.657848\pi$
$182$	21.2285	1.57356
$183$	−6.12887	−0.453059
$184$	−4.28337	−0.315774
$185$	−9.28711	−0.682802
$186$	−23.8339	−1.74759
$187$	−5.04717	−0.369086
$188$	−5.11644	−0.373155
$189$	19.8583	1.44448
$190$	−6.54926	−0.475133
$191$	−13.5629	−0.981376	−0.490688	−	0.871335i	$-0.663255\pi$
$191$	−13.5629	−0.981376	−0.490688	+	0.871335i	$0.663255\pi$
$192$	−2.80063	−0.202118
$193$	−19.7813	−1.42389	−0.711943	−	0.702237i	$-0.752185\pi$
$193$	−19.7813	−1.42389	−0.711943	+	0.702237i	$0.752185\pi$
$194$	1.03786	0.0745139
$195$	19.1117	1.36862
$196$	7.79405	0.556718
$197$	20.4538	1.45727	0.728636	−	0.684901i	$-0.240154\pi$
$197$	20.4538	1.45727	0.728636	+	0.684901i	$0.240154\pi$
$198$	−26.4219	−1.87772
$199$	−22.1226	−1.56823	−0.784115	−	0.620616i	$-0.786883\pi$
$199$	−22.1226	−1.56823	−0.784115	+	0.620616i	$0.786883\pi$
$200$	3.47125	0.245455
$201$	−2.88414	−0.203432
$202$	5.79675	0.407858
$203$	−3.97409	−0.278926
$204$	2.59119	0.181420
$205$	14.3517	1.00237
$206$	10.9988	0.766326
$207$	20.7465	1.44198
$208$	5.51921	0.382688
$209$	−28.8953	−1.99873
$210$	13.3188	0.919088
$211$	−19.9040	−1.37025	−0.685123	−	0.728428i	$-0.740251\pi$
$211$	−19.9040	−1.37025	−0.685123	+	0.728428i	$0.740251\pi$
$212$	4.39713	0.301996
$213$	−8.23137	−0.564004
$214$	−14.9311	−1.02067
$215$	−0.752454	−0.0513169
$216$	5.16296	0.351295
$217$	32.7329	2.22205
$218$	−7.19347	−0.487203
$219$	12.4733	0.842866
$220$	−6.74484	−0.454737
$221$	−5.10648	−0.343499
$222$	21.0362	1.41186
$223$	−20.0632	−1.34353	−0.671766	−	0.740764i	$-0.734464\pi$
$223$	−20.0632	−1.34353	−0.671766	+	0.740764i	$0.734464\pi$
$224$	3.84630	0.256992
$225$	−16.8130	−1.12087
$226$	−10.4883	−0.697674
$227$	21.9810	1.45893	0.729465	−	0.684018i	$-0.239769\pi$
$227$	21.9810	1.45893	0.729465	+	0.684018i	$0.239769\pi$
$228$	14.8347	0.982453
$229$	−6.84578	−0.452382	−0.226191	−	0.974083i	$-0.572627\pi$
$229$	−6.84578	−0.452382	−0.226191	+	0.974083i	$0.572627\pi$
$230$	5.29607	0.349213
$231$	58.7628	3.86631
$232$	−1.03322	−0.0678343
$233$	0.0119176	0.000780746 0	0.000390373	−	1.00000i	$-0.499876\pi$
$233$	0.0119176	0.000780746 0	0.000390373		1.00000i	$0.499876\pi$
$234$	−26.7323	−1.74755
$235$	6.32610	0.412669
$236$	−7.03594	−0.458001
$237$	19.8633	1.29026
$238$	−3.55867	−0.230675
$239$	−10.4426	−0.675473	−0.337736	−	0.941241i	$-0.609661\pi$
$239$	−10.4426	−0.675473	−0.337736	+	0.941241i	$0.609661\pi$
$240$	3.46277	0.223521
$241$	26.7183	1.72108	0.860538	−	0.509387i	$-0.170128\pi$
$241$	26.7183	1.72108	0.860538	+	0.509387i	$0.170128\pi$
$242$	−18.7583	−1.20583
$243$	15.6877	1.00637
$244$	2.18839	0.140098
$245$	−9.63677	−0.615670
$246$	−32.5080	−2.07263
$247$	−29.2348	−1.86017
$248$	8.51021	0.540399
$249$	−28.8180	−1.82626
$250$	−10.4741	−0.662439
$251$	−14.1931	−0.895863	−0.447932	−	0.894068i	$-0.647839\pi$
$251$	−14.1931	−0.895863	−0.447932	+	0.894068i	$0.647839\pi$
$252$	−18.6296	−1.17355
$253$	23.3663	1.46902
$254$	−13.3296	−0.836374
$255$	−3.20382	−0.200631
$256$	1.00000	0.0625000
$257$	5.05648	0.315415	0.157707	−	0.987486i	$-0.449590\pi$
$257$	5.05648	0.315415	0.157707	+	0.987486i	$0.449590\pi$
$258$	1.70438	0.106110
$259$	−28.8906	−1.79517
$260$	−6.82409	−0.423212
$261$	5.00441	0.309765
$262$	−3.47164	−0.214479
$263$	−15.6721	−0.966383	−0.483191	−	0.875515i	$-0.660522\pi$
$263$	−15.6721	−0.966383	−0.483191	+	0.875515i	$0.660522\pi$
$264$	15.2777	0.940279
$265$	−5.43672	−0.333975
$266$	−20.3736	−1.24918
$267$	−37.6799	−2.30597
$268$	1.02982	0.0629063
$269$	1.34304	0.0818865	0.0409432	−	0.999161i	$-0.486964\pi$
$269$	1.34304	0.0818865	0.0409432	+	0.999161i	$0.486964\pi$
$270$	−6.38362	−0.388495
$271$	−9.94403	−0.604057	−0.302029	−	0.953299i	$-0.597664\pi$
$271$	−9.94403	−0.604057	−0.302029	+	0.953299i	$0.597664\pi$
$272$	−0.925219	−0.0560996
$273$	59.4532	3.59827
$274$	3.79192	0.229078
$275$	−18.9361	−1.14189
$276$	−11.9961	−0.722081
$277$	−6.76637	−0.406552	−0.203276	−	0.979121i	$-0.565159\pi$
$277$	−6.76637	−0.406552	−0.203276	+	0.979121i	$0.565159\pi$
$278$	2.85936	0.171493
$279$	−41.2192	−2.46773
$280$	−4.75567	−0.284206
$281$	−0.380798	−0.0227165	−0.0113582	−	0.999935i	$-0.503616\pi$
$281$	−0.380798	−0.0227165	−0.0113582	+	0.999935i	$0.503616\pi$
$282$	−14.3292	−0.853293
$283$	−15.1377	−0.899841	−0.449921	−	0.893069i	$-0.648548\pi$
$283$	−15.1377	−0.899841	−0.449921	+	0.893069i	$0.648548\pi$
$284$	2.93912	0.174405
$285$	−18.3420	−1.08649
$286$	−30.1079	−1.78032
$287$	44.6456	2.63535
$288$	−4.84350	−0.285406
$289$	−16.1440	−0.949645
$290$	1.27750	0.0750175
$291$	2.90665	0.170391
$292$	−4.45375	−0.260636
$293$	−17.4401	−1.01886	−0.509432	−	0.860511i	$-0.670144\pi$
$293$	−17.4401	−1.01886	−0.509432	+	0.860511i	$0.670144\pi$
$294$	21.8282	1.27305
$295$	8.69942	0.506500
$296$	−7.51125	−0.436583
$297$	−28.1645	−1.63427
$298$	−14.6979	−0.851427
$299$	23.6408	1.36718
$300$	9.72167	0.561281
$301$	−2.34075	−0.134919
$302$	−7.91496	−0.455455
$303$	16.2345	0.932649
$304$	−5.29693	−0.303800
$305$	−2.70579	−0.154933
$306$	4.48130	0.256179
$307$	14.0936	0.804367	0.402183	−	0.915559i	$-0.368251\pi$
$307$	14.0936	0.804367	0.402183	+	0.915559i	$0.368251\pi$
$308$	−20.9820	−1.19556
$309$	30.8037	1.75236
$310$	−10.5222	−0.597624
$311$	26.4641	1.50064	0.750320	−	0.661074i	$-0.229899\pi$
$311$	26.4641	1.50064	0.750320	+	0.661074i	$0.229899\pi$
$312$	15.4572	0.875094
$313$	11.1978	0.632937	0.316469	−	0.948603i	$-0.397503\pi$
$313$	11.1978	0.632937	0.316469	+	0.948603i	$0.397503\pi$
$314$	−16.9549	−0.956820
$315$	23.0341	1.29782
$316$	−7.09246	−0.398982
$317$	26.9532	1.51384	0.756920	−	0.653507i	$-0.226703\pi$
$317$	26.9532	1.51384	0.756920	+	0.653507i	$0.226703\pi$
$318$	12.3147	0.690575
$319$	5.63634	0.315575
$320$	−1.23643	−0.0691183
$321$	−41.8165	−2.33397
$322$	16.4751	0.918124
$323$	4.90082	0.272689
$324$	−0.0709871	−0.00394373
$325$	−19.1586	−1.06273
$326$	−12.6317	−0.699606
$327$	−20.1462	−1.11409
$328$	11.6074	0.640912
$329$	19.6794	1.08496
$330$	−18.8898	−1.03985
$331$	34.4428	1.89315	0.946574	−	0.322486i	$-0.104518\pi$
$331$	34.4428	1.89315	0.946574	+	0.322486i	$0.104518\pi$
$332$	10.2898	0.564728
$333$	36.3808	1.99365
$334$	13.9011	0.760634
$335$	−1.27330	−0.0695676
$336$	10.7721	0.587664
$337$	−6.98989	−0.380764	−0.190382	−	0.981710i	$-0.560973\pi$
$337$	−6.98989	−0.380764	−0.190382	+	0.981710i	$0.560973\pi$
$338$	−17.4617	−0.949789
$339$	−29.3739	−1.59537
$340$	1.14396	0.0620402
$341$	−46.4242	−2.51401
$342$	25.6557	1.38730
$343$	−3.05416	−0.164909
$344$	−0.608572	−0.0328120
$345$	14.8323	0.798545
$346$	14.9767	0.805150
$347$	8.13869	0.436908	0.218454	−	0.975847i	$-0.429899\pi$
$347$	8.13869	0.436908	0.218454	+	0.975847i	$0.429899\pi$
$348$	−2.89367	−0.155117
$349$	29.7341	1.59163	0.795816	−	0.605538i	$-0.207042\pi$
$349$	29.7341	1.59163	0.795816	+	0.605538i	$0.207042\pi$
$350$	−13.3515	−0.713667
$351$	−28.4955	−1.52098
$352$	−5.45511	−0.290759
$353$	−27.2456	−1.45014	−0.725069	−	0.688676i	$-0.758192\pi$
$353$	−27.2456	−1.45014	−0.725069	+	0.688676i	$0.758192\pi$
$354$	−19.7050	−1.04731
$355$	−3.63400	−0.192873
$356$	13.4541	0.713066
$357$	−9.96651	−0.527484
$358$	6.09039	0.321887
$359$	4.36028	0.230127	0.115063	−	0.993358i	$-0.463293\pi$
$359$	4.36028	0.230127	0.115063	+	0.993358i	$0.463293\pi$
$360$	5.98863	0.315629
$361$	9.05744	0.476707
$362$	12.8030	0.672908
$363$	−52.5349	−2.75736
$364$	−21.2285	−1.11268
$365$	5.50673	0.288235
$366$	6.12887	0.320361
$367$	20.1616	1.05243	0.526214	−	0.850352i	$-0.323611\pi$
$367$	20.1616	1.05243	0.526214	+	0.850352i	$0.323611\pi$
$368$	4.28337	0.223286
$369$	−56.2205	−2.92672
$370$	9.28711	0.482814
$371$	−16.9127	−0.878063
$372$	23.8339	1.23573
$373$	−3.09143	−0.160068	−0.0800342	−	0.996792i	$-0.525503\pi$
$373$	−3.09143	−0.160068	−0.0800342	+	0.996792i	$0.525503\pi$
$374$	5.04717	0.260983
$375$	−29.3340	−1.51480
$376$	5.11644	0.263860
$377$	5.70257	0.293697
$378$	−19.8583	−1.02140
$379$	20.7996	1.06840	0.534202	−	0.845357i	$-0.320612\pi$
$379$	20.7996	1.06840	0.534202	+	0.845357i	$0.320612\pi$
$380$	6.54926	0.335970
$381$	−37.3312	−1.91254
$382$	13.5629	0.693938
$383$	−0.393547	−0.0201093	−0.0100547	−	0.999949i	$-0.503201\pi$
$383$	−0.393547	−0.0201093	−0.0100547	+	0.999949i	$0.503201\pi$
$384$	2.80063	0.142919
$385$	25.9427	1.32216
$386$	19.7813	1.00684
$387$	2.94762	0.149836
$388$	−1.03786	−0.0526893
$389$	19.4959	0.988479	0.494240	−	0.869326i	$-0.335447\pi$
$389$	19.4959	0.988479	0.494240	+	0.869326i	$0.335447\pi$
$390$	−19.1117	−0.967760
$391$	−3.96306	−0.200420
$392$	−7.79405	−0.393659
$393$	−9.72276	−0.490448
$394$	−20.4538	−1.03045
$395$	8.76930	0.441231
$396$	26.4219	1.32775
$397$	8.61458	0.432353	0.216177	−	0.976354i	$-0.430641\pi$
$397$	8.61458	0.432353	0.216177	+	0.976354i	$0.430641\pi$
$398$	22.1226	1.10891
$399$	−57.0588	−2.85651
$400$	−3.47125	−0.173563
$401$	10.7587	0.537263	0.268632	−	0.963243i	$-0.413429\pi$
$401$	10.7587	0.537263	0.268632	+	0.963243i	$0.413429\pi$
$402$	2.88414	0.143848
$403$	−46.9696	−2.33972
$404$	−5.79675	−0.288399
$405$	0.0877703	0.00436134
$406$	3.97409	0.197231
$407$	40.9747	2.03104
$408$	−2.59119	−0.128283
$409$	−6.69924	−0.331256	−0.165628	−	0.986188i	$-0.552965\pi$
$409$	−6.69924	−0.331256	−0.165628	+	0.986188i	$0.552965\pi$
$410$	−14.3517	−0.708780
$411$	10.6197	0.523833
$412$	−10.9988	−0.541874
$413$	27.0624	1.33165
$414$	−20.7465	−1.01964
$415$	−12.7226	−0.624529
$416$	−5.51921	−0.270601
$417$	8.00799	0.392153
$418$	28.8953	1.41332
$419$	−11.3316	−0.553586	−0.276793	−	0.960930i	$-0.589272\pi$
$419$	−11.3316	−0.553586	−0.276793	+	0.960930i	$0.589272\pi$
$420$	−13.3188	−0.649893
$421$	12.0179	0.585719	0.292859	−	0.956156i	$-0.405393\pi$
$421$	12.0179	0.585719	0.292859	+	0.956156i	$0.405393\pi$
$422$	19.9040	0.968910
$423$	−24.7815	−1.20492
$424$	−4.39713	−0.213543
$425$	3.21167	0.155789
$426$	8.23137	0.398811
$427$	−8.41722	−0.407338
$428$	14.9311	0.721724
$429$	−84.3210	−4.07105
$430$	0.752454	0.0362865
$431$	−28.7386	−1.38429	−0.692146	−	0.721758i	$-0.743335\pi$
$431$	−28.7386	−1.38429	−0.692146	+	0.721758i	$0.743335\pi$
$432$	−5.16296	−0.248403
$433$	−4.52784	−0.217594	−0.108797	−	0.994064i	$-0.534700\pi$
$433$	−4.52784	−0.217594	−0.108797	+	0.994064i	$0.534700\pi$
$434$	−32.7329	−1.57123
$435$	3.57781	0.171543
$436$	7.19347	0.344505
$437$	−22.6887	−1.08535
$438$	−12.4733	−0.595997
$439$	35.7380	1.70568	0.852841	−	0.522171i	$-0.174878\pi$
$439$	35.7380	1.70568	0.852841	+	0.522171i	$0.174878\pi$
$440$	6.74484	0.321548
$441$	37.7505	1.79764
$442$	5.10648	0.242890
$443$	1.68211	0.0799193	0.0399597	−	0.999201i	$-0.487277\pi$
$443$	1.68211	0.0799193	0.0399597	+	0.999201i	$0.487277\pi$
$444$	−21.0362	−0.998334
$445$	−16.6350	−0.788574
$446$	20.0632	0.950020
$447$	−41.1633	−1.94696
$448$	−3.84630	−0.181721
$449$	−18.9907	−0.896225	−0.448112	−	0.893977i	$-0.647904\pi$
$449$	−18.9907	−0.896225	−0.448112	+	0.893977i	$0.647904\pi$
$450$	16.8130	0.792573
$451$	−63.3197	−2.98161
$452$	10.4883	0.493330
$453$	−22.1668	−1.04149
$454$	−21.9810	−1.03162
$455$	26.2475	1.23050
$456$	−14.8347	−0.694699
$457$	−3.64113	−0.170325	−0.0851624	−	0.996367i	$-0.527141\pi$
$457$	−3.64113	−0.170325	−0.0851624	+	0.996367i	$0.527141\pi$
$458$	6.84578	0.319882
$459$	4.77687	0.222965
$460$	−5.29607	−0.246931
$461$	13.7474	0.640282	0.320141	−	0.947370i	$-0.396270\pi$
$461$	13.7474	0.640282	0.320141	+	0.947370i	$0.396270\pi$
$462$	−58.7628	−2.73389
$463$	−11.0753	−0.514713	−0.257356	−	0.966317i	$-0.582851\pi$
$463$	−11.0753	−0.514713	−0.257356	+	0.966317i	$0.582851\pi$
$464$	1.03322	0.0479661
$465$	−29.4689	−1.36659
$466$	−0.0119176	−0.000552070 0
$467$	2.73692	0.126650	0.0633248	−	0.997993i	$-0.479830\pi$
$467$	2.73692	0.126650	0.0633248	+	0.997993i	$0.479830\pi$
$468$	26.7323	1.23570
$469$	−3.96100	−0.182902
$470$	−6.32610	−0.291801
$471$	−47.4843	−2.18796
$472$	7.03594	0.323855
$473$	3.31983	0.152646
$474$	−19.8633	−0.912353
$475$	18.3870	0.843652
$476$	3.55867	0.163112
$477$	21.2975	0.975146
$478$	10.4426	0.477631
$479$	−38.2165	−1.74616	−0.873079	−	0.487578i	$-0.837880\pi$
$479$	−38.2165	−1.74616	−0.873079	+	0.487578i	$0.837880\pi$
$480$	−3.46277	−0.158053
$481$	41.4562	1.89024
$482$	−26.7183	−1.21698
$483$	46.1407	2.09947
$484$	18.7583	0.852648
$485$	1.28323	0.0582687
$486$	−15.6877	−0.711608
$487$	−40.8930	−1.85304	−0.926520	−	0.376245i	$-0.877215\pi$
$487$	−40.8930	−1.85304	−0.926520	+	0.376245i	$0.877215\pi$
$488$	−2.18839	−0.0990639
$489$	−35.3767	−1.59979
$490$	9.63677	0.435345
$491$	−15.1744	−0.684809	−0.342405	−	0.939553i	$-0.611241\pi$
$491$	−15.1744	−0.684809	−0.342405	+	0.939553i	$0.611241\pi$
$492$	32.5080	1.46557
$493$	−0.955957	−0.0430541
$494$	29.2348	1.31534
$495$	−32.6687	−1.46835
$496$	−8.51021	−0.382120
$497$	−11.3047	−0.507087
$498$	28.8180	1.29136
$499$	5.30531	0.237498	0.118749	−	0.992924i	$-0.462112\pi$
$499$	5.30531	0.237498	0.118749	+	0.992924i	$0.462112\pi$
$500$	10.4741	0.468415
$501$	38.9318	1.73934
$502$	14.1931	0.633471
$503$	1.75647	0.0783173	0.0391587	−	0.999233i	$-0.487532\pi$
$503$	1.75647	0.0783173	0.0391587	+	0.999233i	$0.487532\pi$
$504$	18.6296	0.829828
$505$	7.16725	0.318938
$506$	−23.3663	−1.03876
$507$	−48.9036	−2.17188
$508$	13.3296	0.591406
$509$	−8.28358	−0.367163	−0.183582	−	0.983004i	$-0.558769\pi$
$509$	−8.28358	−0.367163	−0.183582	+	0.983004i	$0.558769\pi$
$510$	3.20382	0.141867
$511$	17.1305	0.757807
$512$	−1.00000	−0.0441942
$513$	27.3478	1.20744
$514$	−5.05648	−0.223032
$515$	13.5993	0.599255
$516$	−1.70438	−0.0750312
$517$	−27.9107	−1.22751
$518$	28.8906	1.26938
$519$	41.9440	1.84114
$520$	6.82409	0.299256
$521$	0.434556	0.0190382	0.00951912	−	0.999955i	$-0.496970\pi$
$521$	0.434556	0.0190382	0.00951912	+	0.999955i	$0.496970\pi$
$522$	−5.00441	−0.219037
$523$	6.57763	0.287620	0.143810	−	0.989605i	$-0.454065\pi$
$523$	6.57763	0.287620	0.143810	+	0.989605i	$0.454065\pi$
$524$	3.47164	0.151659
$525$	−37.3925	−1.63194
$526$	15.6721	0.683336
$527$	7.87381	0.342989
$528$	−15.2777	−0.664878
$529$	−4.65274	−0.202293
$530$	5.43672	0.236156
$531$	−34.0786	−1.47889
$532$	20.3736	0.883307
$533$	−64.0637	−2.77491
$534$	37.6799	1.63057
$535$	−18.4613	−0.798150
$536$	−1.02982	−0.0444815
$537$	17.0569	0.736059
$538$	−1.34304	−0.0579025
$539$	42.5174	1.83136
$540$	6.38362	0.274707
$541$	−23.9392	−1.02923	−0.514613	−	0.857423i	$-0.672064\pi$
$541$	−23.9392	−1.02923	−0.514613	+	0.857423i	$0.672064\pi$
$542$	9.94403	0.427133
$543$	35.8563	1.53874
$544$	0.925219	0.0396684
$545$	−8.89419	−0.380985
$546$	−59.4532	−2.54436
$547$	1.53801	0.0657606	0.0328803	−	0.999459i	$-0.489532\pi$
$547$	1.53801	0.0657606	0.0328803	+	0.999459i	$0.489532\pi$
$548$	−3.79192	−0.161983
$549$	10.5995	0.452375
$550$	18.9361	0.807437
$551$	−5.47290	−0.233153
$552$	11.9961	0.510589
$553$	27.2798	1.16005
$554$	6.76637	0.287476
$555$	26.0097	1.10405
$556$	−2.85936	−0.121264
$557$	−24.2688	−1.02830	−0.514151	−	0.857699i	$-0.671893\pi$
$557$	−24.2688	−1.02830	−0.514151	+	0.857699i	$0.671893\pi$
$558$	41.2192	1.74495
$559$	3.35883	0.142063
$560$	4.75567	0.200964
$561$	14.1352	0.596790
$562$	0.380798	0.0160630
$563$	−37.8806	−1.59647	−0.798237	−	0.602343i	$-0.794234\pi$
$563$	−37.8806	−1.59647	−0.798237	+	0.602343i	$0.794234\pi$
$564$	14.3292	0.603369
$565$	−12.9681	−0.545571
$566$	15.1377	0.636284
$567$	0.273038	0.0114665
$568$	−2.93912	−0.123323
$569$	−12.3800	−0.518996	−0.259498	−	0.965744i	$-0.583557\pi$
$569$	−12.3800	−0.518996	−0.259498	+	0.965744i	$0.583557\pi$
$570$	18.3420	0.768263
$571$	2.98295	0.124832	0.0624162	−	0.998050i	$-0.480119\pi$
$571$	2.98295	0.124832	0.0624162	+	0.998050i	$0.480119\pi$
$572$	30.1079	1.25887
$573$	37.9846	1.58683
$574$	−44.6456	−1.86347
$575$	−14.8687	−0.620066
$576$	4.84350	0.201813
$577$	43.6684	1.81794	0.908970	−	0.416862i	$-0.136870\pi$
$577$	43.6684	1.81794	0.908970	+	0.416862i	$0.136870\pi$
$578$	16.1440	0.671501
$579$	55.3999	2.30234
$580$	−1.27750	−0.0530454
$581$	−39.5778	−1.64197
$582$	−2.90665	−0.120485
$583$	23.9868	0.993433
$584$	4.45375	0.184297
$585$	−33.0525	−1.36655
$586$	17.4401	0.720445
$587$	−23.3238	−0.962678	−0.481339	−	0.876534i	$-0.659849\pi$
$587$	−23.3238	−0.962678	−0.481339	+	0.876534i	$0.659849\pi$
$588$	−21.8282	−0.900181
$589$	45.0780	1.85741
$590$	−8.69942	−0.358149
$591$	−57.2834	−2.35633
$592$	7.51125	0.308711
$593$	33.1698	1.36212	0.681060	−	0.732227i	$-0.261519\pi$
$593$	33.1698	1.36212	0.681060	+	0.732227i	$0.261519\pi$
$594$	28.1645	1.15561
$595$	−4.40004	−0.180384
$596$	14.6979	0.602050
$597$	61.9571	2.53574
$598$	−23.6408	−0.966745
$599$	−17.8008	−0.727322	−0.363661	−	0.931531i	$-0.618473\pi$
$599$	−17.8008	−0.727322	−0.363661	+	0.931531i	$0.618473\pi$
$600$	−9.72167	−0.396886
$601$	24.8313	1.01289	0.506445	−	0.862273i	$-0.330960\pi$
$601$	24.8313	1.01289	0.506445	+	0.862273i	$0.330960\pi$
$602$	2.34075	0.0954019
$603$	4.98794	0.203125
$604$	7.91496	0.322055
$605$	−23.1932	−0.942938
$606$	−16.2345	−0.659482
$607$	19.2021	0.779388	0.389694	−	0.920944i	$-0.372581\pi$
$607$	19.2021	0.779388	0.389694	+	0.920944i	$0.372581\pi$
$608$	5.29693	0.214819
$609$	11.1299	0.451007
$610$	2.70579	0.109554
$611$	−28.2387	−1.14241
$612$	−4.48130	−0.181146
$613$	3.72341	0.150387	0.0751935	−	0.997169i	$-0.476043\pi$
$613$	3.72341	0.150387	0.0751935	+	0.997169i	$0.476043\pi$
$614$	−14.0936	−0.568773
$615$	−40.1937	−1.62077
$616$	20.9820	0.845390
$617$	−41.6998	−1.67877	−0.839386	−	0.543535i	$-0.817085\pi$
$617$	−41.6998	−1.67877	−0.839386	+	0.543535i	$0.817085\pi$
$618$	−30.8037	−1.23910
$619$	29.7518	1.19583	0.597914	−	0.801560i	$-0.295997\pi$
$619$	29.7518	1.19583	0.597914	+	0.801560i	$0.295997\pi$
$620$	10.5222	0.422584
$621$	−22.1149	−0.887439
$622$	−26.4641	−1.06111
$623$	−51.7485	−2.07326
$624$	−15.4572	−0.618785
$625$	4.40584	0.176233
$626$	−11.1978	−0.447554
$627$	80.9250	3.23183
$628$	16.9549	0.676574
$629$	−6.94955	−0.277097
$630$	−23.0341	−0.917701
$631$	−34.7101	−1.38179	−0.690894	−	0.722956i	$-0.742783\pi$
$631$	−34.7101	−1.38179	−0.690894	+	0.722956i	$0.742783\pi$
$632$	7.09246	0.282123
$633$	55.7436	2.21561
$634$	−26.9532	−1.07045
$635$	−16.4811	−0.654031
$636$	−12.3147	−0.488310
$637$	43.0170	1.70440
$638$	−5.63634	−0.223145
$639$	14.2356	0.563153
$640$	1.23643	0.0488740
$641$	15.0162	0.593103	0.296551	−	0.955017i	$-0.404163\pi$
$641$	15.0162	0.593103	0.296551	+	0.955017i	$0.404163\pi$
$642$	41.8165	1.65037
$643$	−5.81298	−0.229242	−0.114621	−	0.993409i	$-0.536565\pi$
$643$	−5.81298	−0.229242	−0.114621	+	0.993409i	$0.536565\pi$
$644$	−16.4751	−0.649212
$645$	2.10734	0.0829765
$646$	−4.90082	−0.192820
$647$	−29.5891	−1.16327	−0.581635	−	0.813450i	$-0.697587\pi$
$647$	−29.5891	−1.16327	−0.581635	+	0.813450i	$0.697587\pi$
$648$	0.0709871	0.00278864
$649$	−38.3819	−1.50662
$650$	19.1586	0.751460
$651$	−91.6725	−3.59293
$652$	12.6317	0.494696
$653$	−36.1148	−1.41328	−0.706642	−	0.707572i	$-0.749791\pi$
$653$	−36.1148	−1.41328	−0.706642	+	0.707572i	$0.749791\pi$
$654$	20.1462	0.787779
$655$	−4.29243	−0.167719
$656$	−11.6074	−0.453193
$657$	−21.5717	−0.841594
$658$	−19.6794	−0.767182
$659$	−44.2165	−1.72243	−0.861216	−	0.508239i	$-0.830297\pi$
$659$	−44.2165	−1.72243	−0.861216	+	0.508239i	$0.830297\pi$
$660$	18.8898	0.735284
$661$	6.67665	0.259692	0.129846	−	0.991534i	$-0.458552\pi$
$661$	6.67665	0.259692	0.129846	+	0.991534i	$0.458552\pi$
$662$	−34.4428	−1.33866
$663$	14.3013	0.555417
$664$	−10.2898	−0.399323
$665$	−25.1904	−0.976843
$666$	−36.3808	−1.40973
$667$	4.42567	0.171363
$668$	−13.9011	−0.537850
$669$	56.1895	2.17241
$670$	1.27330	0.0491917
$671$	11.9379	0.460859
$672$	−10.7721	−0.415541
$673$	−7.23279	−0.278804	−0.139402	−	0.990236i	$-0.544518\pi$
$673$	−7.23279	−0.278804	−0.139402	+	0.990236i	$0.544518\pi$
$674$	6.98989	0.269241
$675$	17.9219	0.689816
$676$	17.4617	0.671602
$677$	39.4832	1.51746	0.758731	−	0.651404i	$-0.225820\pi$
$677$	39.4832	1.51746	0.758731	+	0.651404i	$0.225820\pi$
$678$	29.3739	1.12810
$679$	3.99192	0.153196
$680$	−1.14396	−0.0438690
$681$	−61.5606	−2.35901
$682$	46.4242	1.77767
$683$	35.7742	1.36886	0.684430	−	0.729079i	$-0.260051\pi$
$683$	35.7742	1.36886	0.684430	+	0.729079i	$0.260051\pi$
$684$	−25.6557	−0.980970
$685$	4.68842	0.179135
$686$	3.05416	0.116608
$687$	19.1725	0.731475
$688$	0.608572	0.0232016
$689$	24.2687	0.924563
$690$	−14.8323	−0.564656
$691$	−31.9976	−1.21725	−0.608623	−	0.793460i	$-0.708278\pi$
$691$	−31.9976	−1.21725	−0.608623	+	0.793460i	$0.708278\pi$
$692$	−14.9767	−0.569327
$693$	−101.626	−3.86047
$694$	−8.13869	−0.308940
$695$	3.53538	0.134105
$696$	2.89367	0.109684
$697$	10.7394	0.406784
$698$	−29.7341	−1.12545
$699$	−0.0333766	−0.00126242
$700$	13.3515	0.504639
$701$	−29.2797	−1.10588	−0.552939	−	0.833222i	$-0.686494\pi$
$701$	−29.2797	−1.10588	−0.552939	+	0.833222i	$0.686494\pi$
$702$	28.4955	1.07549
$703$	−39.7866	−1.50058
$704$	5.45511	0.205597
$705$	−17.7170	−0.667262
$706$	27.2456	1.02540
$707$	22.2961	0.838529
$708$	19.7050	0.740561
$709$	−43.9164	−1.64931	−0.824657	−	0.565633i	$-0.808632\pi$
$709$	−43.9164	−1.64931	−0.824657	+	0.565633i	$0.808632\pi$
$710$	3.63400	0.136382
$711$	−34.3523	−1.28831
$712$	−13.4541	−0.504214
$713$	−36.4524	−1.36515
$714$	9.96651	0.372987
$715$	−37.2262	−1.39218
$716$	−6.09039	−0.227608
$717$	29.2457	1.09220
$718$	−4.36028	−0.162724
$719$	14.4883	0.540321	0.270160	−	0.962815i	$-0.412923\pi$
$719$	14.4883	0.540321	0.270160	+	0.962815i	$0.412923\pi$
$720$	−5.98863	−0.223183
$721$	42.3049	1.57552
$722$	−9.05744	−0.337083
$723$	−74.8279	−2.78288
$724$	−12.8030	−0.475818
$725$	−3.58657	−0.133202
$726$	52.5349	1.94975
$727$	28.9414	1.07338	0.536689	−	0.843780i	$-0.319675\pi$
$727$	28.9414	1.07338	0.536689	+	0.843780i	$0.319675\pi$
$728$	21.2285	0.786782
$729$	−43.7224	−1.61935
$730$	−5.50673	−0.203813
$731$	−0.563062	−0.0208256
$732$	−6.12887	−0.226530
$733$	24.2113	0.894266	0.447133	−	0.894468i	$-0.352445\pi$
$733$	24.2113	0.894266	0.447133	+	0.894468i	$0.352445\pi$
$734$	−20.1616	−0.744179
$735$	26.9890	0.995503
$736$	−4.28337	−0.157887
$737$	5.61779	0.206934
$738$	56.2205	2.06951
$739$	53.1928	1.95673	0.978364	−	0.206890i	$-0.0663343\pi$
$739$	53.1928	1.95673	0.978364	+	0.206890i	$0.0663343\pi$
$740$	−9.28711	−0.341401
$741$	81.8758	3.00778
$742$	16.9127	0.620884
$743$	−39.9281	−1.46482	−0.732410	−	0.680863i	$-0.761605\pi$
$743$	−39.9281	−1.46482	−0.732410	+	0.680863i	$0.761605\pi$
$744$	−23.8339	−0.873794
$745$	−18.1729	−0.665802
$746$	3.09143	0.113185
$747$	49.8388	1.82351
$748$	−5.04717	−0.184543
$749$	−57.4297	−2.09844
$750$	29.3340	1.07112
$751$	−15.1485	−0.552776	−0.276388	−	0.961046i	$-0.589138\pi$
$751$	−15.1485	−0.552776	−0.276388	+	0.961046i	$0.589138\pi$
$752$	−5.11644	−0.186577
$753$	39.7497	1.44856
$754$	−5.70257	−0.207675
$755$	−9.78626	−0.356158
$756$	19.8583	0.722240
$757$	−30.1660	−1.09640	−0.548200	−	0.836347i	$-0.684687\pi$
$757$	−30.1660	−1.09640	−0.548200	+	0.836347i	$0.684687\pi$
$758$	−20.7996	−0.755476
$759$	−65.4402	−2.37533
$760$	−6.54926	−0.237567
$761$	29.9350	1.08514	0.542571	−	0.840010i	$-0.317451\pi$
$761$	29.9350	1.08514	0.542571	+	0.840010i	$0.317451\pi$
$762$	37.3312	1.35237
$763$	−27.6683	−1.00166
$764$	−13.5629	−0.490688
$765$	5.54080	0.200328
$766$	0.393547	0.0142194
$767$	−38.8328	−1.40217
$768$	−2.80063	−0.101059
$769$	31.8820	1.14969	0.574847	−	0.818261i	$-0.305061\pi$
$769$	31.8820	1.14969	0.574847	+	0.818261i	$0.305061\pi$
$770$	−25.9427	−0.934911
$771$	−14.1613	−0.510007
$772$	−19.7813	−0.711943
$773$	−32.3107	−1.16214	−0.581068	−	0.813855i	$-0.697365\pi$
$773$	−32.3107	−1.16214	−0.581068	+	0.813855i	$0.697365\pi$
$774$	−2.94762	−0.105950
$775$	29.5411	1.06115
$776$	1.03786	0.0372569
$777$	80.9116	2.90269
$778$	−19.4959	−0.698960
$779$	61.4836	2.20288
$780$	19.1117	0.684310
$781$	16.0332	0.573714
$782$	3.96306	0.141719
$783$	−5.33449	−0.190639
$784$	7.79405	0.278359
$785$	−20.9635	−0.748218
$786$	9.72276	0.346799
$787$	−19.1836	−0.683820	−0.341910	−	0.939733i	$-0.611074\pi$
$787$	−19.1836	−0.683820	−0.341910	+	0.939733i	$0.611074\pi$
$788$	20.4538	0.728636
$789$	43.8917	1.56258
$790$	−8.76930	−0.311998
$791$	−40.3414	−1.43437
$792$	−26.4219	−0.938860
$793$	12.0782	0.428909
$794$	−8.61458	−0.305720
$795$	15.2262	0.540019
$796$	−22.1226	−0.784115
$797$	14.6308	0.518249	0.259125	−	0.965844i	$-0.416566\pi$
$797$	14.6308	0.518249	0.259125	+	0.965844i	$0.416566\pi$
$798$	57.0588	2.01986
$799$	4.73383	0.167471
$800$	3.47125	0.122727
$801$	65.1650	2.30249
$802$	−10.7587	−0.379903
$803$	−24.2957	−0.857377
$804$	−2.88414	−0.101716
$805$	20.3703	0.717959
$806$	46.9696	1.65444
$807$	−3.76135	−0.132406
$808$	5.79675	0.203929
$809$	1.02572	0.0360626	0.0180313	−	0.999837i	$-0.494260\pi$
$809$	1.02572	0.0360626	0.0180313	+	0.999837i	$0.494260\pi$
$810$	−0.0877703	−0.00308393
$811$	−4.06177	−0.142628	−0.0713140	−	0.997454i	$-0.522719\pi$
$811$	−4.06177	−0.142628	−0.0713140	+	0.997454i	$0.522719\pi$
$812$	−3.97409	−0.139463
$813$	27.8495	0.976725
$814$	−40.9747	−1.43616
$815$	−15.6182	−0.547081
$816$	2.59119	0.0907099
$817$	−3.22356	−0.112778
$818$	6.69924	0.234233
$819$	−102.821	−3.59284
$820$	14.3517	0.501183
$821$	−44.1586	−1.54114	−0.770572	−	0.637353i	$-0.780030\pi$
$821$	−44.1586	−1.54114	−0.770572	+	0.637353i	$0.780030\pi$
$822$	−10.6197	−0.370406
$823$	37.6817	1.31350	0.656751	−	0.754107i	$-0.271930\pi$
$823$	37.6817	1.31350	0.656751	+	0.754107i	$0.271930\pi$
$824$	10.9988	0.383163
$825$	53.0328	1.84637
$826$	−27.0624	−0.941620
$827$	−23.2229	−0.807538	−0.403769	−	0.914861i	$-0.632300\pi$
$827$	−23.2229	−0.807538	−0.403769	+	0.914861i	$0.632300\pi$
$828$	20.7465	0.720991
$829$	11.7718	0.408852	0.204426	−	0.978882i	$-0.434467\pi$
$829$	11.7718	0.408852	0.204426	+	0.978882i	$0.434467\pi$
$830$	12.7226	0.441609
$831$	18.9501	0.657371
$832$	5.51921	0.191344
$833$	−7.21120	−0.249853
$834$	−8.00799	−0.277294
$835$	17.1877	0.594804
$836$	−28.8953	−0.999366
$837$	43.9379	1.51872
$838$	11.3316	0.391444
$839$	0.314486	0.0108573	0.00542863	−	0.999985i	$-0.498272\pi$
$839$	0.314486	0.0108573	0.00542863	+	0.999985i	$0.498272\pi$
$840$	13.3188	0.459544
$841$	−27.9325	−0.963188
$842$	−12.0179	−0.414166
$843$	1.06647	0.0367312
$844$	−19.9040	−0.685123
$845$	−21.5900	−0.742720
$846$	24.7815	0.852005
$847$	−72.1500	−2.47910
$848$	4.39713	0.150998
$849$	42.3950	1.45499
$850$	−3.21167	−0.110159
$851$	32.1735	1.10289
$852$	−8.23137	−0.282002
$853$	−41.6667	−1.42664	−0.713321	−	0.700837i	$-0.752810\pi$
$853$	−41.6667	−1.42664	−0.713321	+	0.700837i	$0.752810\pi$
$854$	8.41722	0.288031
$855$	31.7214	1.08485
$856$	−14.9311	−0.510336
$857$	41.9023	1.43136	0.715678	−	0.698431i	$-0.246118\pi$
$857$	41.9023	1.43136	0.715678	+	0.698431i	$0.246118\pi$
$858$	84.3210	2.87867
$859$	25.1952	0.859651	0.429825	−	0.902912i	$-0.358575\pi$
$859$	25.1952	0.859651	0.429825	+	0.902912i	$0.358575\pi$
$860$	−0.752454	−0.0256585
$861$	−125.036	−4.26120
$862$	28.7386	0.978842
$863$	−37.6309	−1.28097	−0.640486	−	0.767970i	$-0.721267\pi$
$863$	−37.6309	−1.28097	−0.640486	+	0.767970i	$0.721267\pi$
$864$	5.16296	0.175648
$865$	18.5175	0.629615
$866$	4.52784	0.153862
$867$	45.2132	1.53552
$868$	32.7329	1.11103
$869$	−38.6902	−1.31247
$870$	−3.57781	−0.121299
$871$	5.68379	0.192588
$872$	−7.19347	−0.243602
$873$	−5.02687	−0.170134
$874$	22.6887	0.767457
$875$	−40.2865	−1.36193
$876$	12.4733	0.421433
$877$	33.5158	1.13175	0.565873	−	0.824492i	$-0.308539\pi$
$877$	33.5158	1.13175	0.565873	+	0.824492i	$0.308539\pi$
$878$	−35.7380	−1.20610
$879$	48.8433	1.64744
$880$	−6.74484	−0.227369
$881$	−41.3688	−1.39375	−0.696875	−	0.717193i	$-0.745427\pi$
$881$	−41.3688	−1.39375	−0.696875	+	0.717193i	$0.745427\pi$
$882$	−37.7505	−1.27113
$883$	13.9044	0.467920	0.233960	−	0.972246i	$-0.424832\pi$
$883$	13.9044	0.467920	0.233960	+	0.972246i	$0.424832\pi$
$884$	−5.10648	−0.171749
$885$	−24.3638	−0.818981
$886$	−1.68211	−0.0565115
$887$	30.9119	1.03792	0.518959	−	0.854799i	$-0.326320\pi$
$887$	30.9119	1.03792	0.518959	+	0.854799i	$0.326320\pi$
$888$	21.0362	0.705929
$889$	−51.2697	−1.71953
$890$	16.6350	0.557606
$891$	−0.387243	−0.0129731
$892$	−20.0632	−0.671766
$893$	27.1014	0.906914
$894$	41.1633	1.37671
$895$	7.53031	0.251711
$896$	3.84630	0.128496
$897$	−66.2091	−2.21066
$898$	18.9907	0.633727
$899$	−8.79294	−0.293261
$900$	−16.8130	−0.560434
$901$	−4.06831	−0.135535
$902$	63.3197	2.10832
$903$	6.55557	0.218156
$904$	−10.4883	−0.348837
$905$	15.8299	0.526204
$906$	22.1668	0.736444
$907$	3.15396	0.104726	0.0523628	−	0.998628i	$-0.483325\pi$
$907$	3.15396	0.104726	0.0523628	+	0.998628i	$0.483325\pi$
$908$	21.9810	0.729465
$909$	−28.0766	−0.931241
$910$	−26.2475	−0.870097
$911$	3.81135	0.126276	0.0631378	−	0.998005i	$-0.479889\pi$
$911$	3.81135	0.126276	0.0631378	+	0.998005i	$0.479889\pi$
$912$	14.8347	0.491226
$913$	56.1322	1.85771
$914$	3.64113	0.120438
$915$	7.57789	0.250517
$916$	−6.84578	−0.226191
$917$	−13.3530	−0.440954
$918$	−4.77687	−0.157660
$919$	−47.7975	−1.57669	−0.788347	−	0.615231i	$-0.789063\pi$
$919$	−47.7975	−1.57669	−0.788347	+	0.615231i	$0.789063\pi$
$920$	5.29607	0.174606
$921$	−39.4710	−1.30061
$922$	−13.7474	−0.452748
$923$	16.2216	0.533941
$924$	58.7628	1.93315
$925$	−26.0734	−0.857289
$926$	11.0753	0.363957
$927$	−53.2730	−1.74971
$928$	−1.03322	−0.0339172
$929$	−15.0823	−0.494836	−0.247418	−	0.968909i	$-0.579582\pi$
$929$	−15.0823	−0.494836	−0.247418	+	0.968909i	$0.579582\pi$
$930$	29.4689	0.966323
$931$	−41.2845	−1.35305
$932$	0.0119176	0.000390373 0
$933$	−74.1160	−2.42645
$934$	−2.73692	−0.0895548
$935$	6.24046	0.204085
$936$	−26.7323	−0.873773
$937$	−25.4199	−0.830433	−0.415217	−	0.909723i	$-0.636294\pi$
$937$	−25.4199	−0.830433	−0.415217	+	0.909723i	$0.636294\pi$
$938$	3.96100	0.129331
$939$	−31.3609	−1.02342
$940$	6.32610	0.206335
$941$	−17.2881	−0.563575	−0.281787	−	0.959477i	$-0.590927\pi$
$941$	−17.2881	−0.563575	−0.281787	+	0.959477i	$0.590927\pi$
$942$	47.4843	1.54712
$943$	−49.7188	−1.61907
$944$	−7.03594	−0.229000
$945$	−24.5533	−0.798720
$946$	−3.31983	−0.107937
$947$	4.51303	0.146654	0.0733269	−	0.997308i	$-0.476638\pi$
$947$	4.51303	0.146654	0.0733269	+	0.997308i	$0.476638\pi$
$948$	19.8633	0.645131
$949$	−24.5812	−0.797938
$950$	−18.3870	−0.596552
$951$	−75.4857	−2.44779
$952$	−3.55867	−0.115337
$953$	−48.5293	−1.57202	−0.786008	−	0.618216i	$-0.787856\pi$
$953$	−48.5293	−1.57202	−0.786008	+	0.618216i	$0.787856\pi$
$954$	−21.2975	−0.689532
$955$	16.7695	0.542649
$956$	−10.4426	−0.337736
$957$	−15.7853	−0.510266
$958$	38.2165	1.23472
$959$	14.5849	0.470970
$960$	3.46277	0.111760
$961$	41.4237	1.33625
$962$	−41.4562	−1.33660
$963$	72.3190	2.33045
$964$	26.7183	0.860538
$965$	24.4581	0.787333
$966$	−46.1407	−1.48455
$967$	25.2066	0.810589	0.405294	−	0.914186i	$-0.367169\pi$
$967$	25.2066	0.810589	0.405294	+	0.914186i	$0.367169\pi$
$968$	−18.7583	−0.602913
$969$	−13.7254	−0.440922
$970$	−1.28323	−0.0412022
$971$	−58.2235	−1.86848	−0.934240	−	0.356645i	$-0.883921\pi$
$971$	−58.2235	−1.86848	−0.934240	+	0.356645i	$0.883921\pi$
$972$	15.6877	0.503183
$973$	10.9980	0.352578
$974$	40.8930	1.31030
$975$	53.6559	1.71837
$976$	2.18839	0.0700488
$977$	−1.69829	−0.0543330	−0.0271665	−	0.999631i	$-0.508648\pi$
$977$	−1.69829	−0.0543330	−0.0271665	+	0.999631i	$0.508648\pi$
$978$	35.3767	1.13122
$979$	73.3936	2.34567
$980$	−9.63677	−0.307835
$981$	34.8416	1.11241
$982$	15.1744	0.484233
$983$	−35.5243	−1.13305	−0.566525	−	0.824045i	$-0.691712\pi$
$983$	−35.5243	−1.13305	−0.566525	+	0.824045i	$0.691712\pi$
$984$	−32.5080	−1.03632
$985$	−25.2896	−0.805794
$986$	0.955957	0.0304439
$987$	−55.1146	−1.75432
$988$	−29.2348	−0.930084
$989$	2.60674	0.0828894
$990$	32.6687	1.03828
$991$	−23.9050	−0.759368	−0.379684	−	0.925116i	$-0.623967\pi$
$991$	−23.9050	−0.759368	−0.379684	+	0.925116i	$0.623967\pi$
$992$	8.51021	0.270200
$993$	−96.4614	−3.06111
$994$	11.3047	0.358565
$995$	27.3530	0.867147
$996$	−28.8180	−0.913132
$997$	33.8658	1.07254	0.536271	−	0.844046i	$-0.319833\pi$
$997$	33.8658	1.07254	0.536271	+	0.844046i	$0.319833\pi$
$998$	−5.30531	−0.167937
$999$	−38.7803	−1.22695

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.b.1.7	✓	81

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.b.1.7	✓	81	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.80063 q^{3} +1.00000 q^{4} -1.23643 q^{5} +2.80063 q^{6} -3.84630 q^{7} -1.00000 q^{8} +4.84350 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.80063 q^{3} +1.00000 q^{4} -1.23643 q^{5} +2.80063 q^{6} -3.84630 q^{7} -1.00000 q^{8} +4.84350 q^{9} +1.23643 q^{10} +5.45511 q^{11} -2.80063 q^{12} +5.51921 q^{13} +3.84630 q^{14} +3.46277 q^{15} +1.00000 q^{16} -0.925219 q^{17} -4.84350 q^{18} -5.29693 q^{19} -1.23643 q^{20} +10.7721 q^{21} -5.45511 q^{22} +4.28337 q^{23} +2.80063 q^{24} -3.47125 q^{25} -5.51921 q^{26} -5.16296 q^{27} -3.84630 q^{28} +1.03322 q^{29} -3.46277 q^{30} -8.51021 q^{31} -1.00000 q^{32} -15.2777 q^{33} +0.925219 q^{34} +4.75567 q^{35} +4.84350 q^{36} +7.51125 q^{37} +5.29693 q^{38} -15.4572 q^{39} +1.23643 q^{40} -11.6074 q^{41} -10.7721 q^{42} +0.608572 q^{43} +5.45511 q^{44} -5.98863 q^{45} -4.28337 q^{46} -5.11644 q^{47} -2.80063 q^{48} +7.79405 q^{49} +3.47125 q^{50} +2.59119 q^{51} +5.51921 q^{52} +4.39713 q^{53} +5.16296 q^{54} -6.74484 q^{55} +3.84630 q^{56} +14.8347 q^{57} -1.03322 q^{58} -7.03594 q^{59} +3.46277 q^{60} +2.18839 q^{61} +8.51021 q^{62} -18.6296 q^{63} +1.00000 q^{64} -6.82409 q^{65} +15.2777 q^{66} +1.02982 q^{67} -0.925219 q^{68} -11.9961 q^{69} -4.75567 q^{70} +2.93912 q^{71} -4.84350 q^{72} -4.45375 q^{73} -7.51125 q^{74} +9.72167 q^{75} -5.29693 q^{76} -20.9820 q^{77} +15.4572 q^{78} -7.09246 q^{79} -1.23643 q^{80} -0.0709871 q^{81} +11.6074 q^{82} +10.2898 q^{83} +10.7721 q^{84} +1.14396 q^{85} -0.608572 q^{86} -2.89367 q^{87} -5.45511 q^{88} +13.4541 q^{89} +5.98863 q^{90} -21.2285 q^{91} +4.28337 q^{92} +23.8339 q^{93} +5.11644 q^{94} +6.54926 q^{95} +2.80063 q^{96} -1.03786 q^{97} -7.79405 q^{98} +26.4219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * q^99

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