LMFDB - Embedded newform 6042.2.a.w.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.326108912.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 11x^{4} + 25x^{3} + 12x^{2} - 32x + 4 $ x^6 - 3x^5 - 11x^4 + 25x^3 + 12x^2 - 32*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.31489$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.90230 q^{5} -1.00000 q^{6} -5.13108 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.90230 q^{5} -1.00000 q^{6} -5.13108 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.90230 q^{10} -2.66785 q^{11} -1.00000 q^{12} +1.34049 q^{13} -5.13108 q^{14} -1.90230 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} +1.90230 q^{20} +5.13108 q^{21} -2.66785 q^{22} -6.57015 q^{23} -1.00000 q^{24} -1.38125 q^{25} +1.34049 q^{26} -1.00000 q^{27} -5.13108 q^{28} +8.57015 q^{29} -1.90230 q^{30} -0.324679 q^{31} +1.00000 q^{32} +2.66785 q^{33} +2.00000 q^{34} -9.76085 q^{35} +1.00000 q^{36} +2.46411 q^{37} -1.00000 q^{38} -1.34049 q^{39} +1.90230 q^{40} +0.384298 q^{41} +5.13108 q^{42} -1.30329 q^{43} -2.66785 q^{44} +1.90230 q^{45} -6.57015 q^{46} +7.72263 q^{47} -1.00000 q^{48} +19.3280 q^{49} -1.38125 q^{50} -2.00000 q^{51} +1.34049 q^{52} -1.00000 q^{53} -1.00000 q^{54} -5.07506 q^{55} -5.13108 q^{56} +1.00000 q^{57} +8.57015 q^{58} +10.5970 q^{59} -1.90230 q^{60} -2.77666 q^{61} -0.324679 q^{62} -5.13108 q^{63} +1.00000 q^{64} +2.55001 q^{65} +2.66785 q^{66} +8.25470 q^{67} +2.00000 q^{68} +6.57015 q^{69} -9.76085 q^{70} -6.61100 q^{71} +1.00000 q^{72} +1.37023 q^{73} +2.46411 q^{74} +1.38125 q^{75} -1.00000 q^{76} +13.6890 q^{77} -1.34049 q^{78} +6.63418 q^{79} +1.90230 q^{80} +1.00000 q^{81} +0.384298 q^{82} -8.71690 q^{83} +5.13108 q^{84} +3.80460 q^{85} -1.30329 q^{86} -8.57015 q^{87} -2.66785 q^{88} -7.71524 q^{89} +1.90230 q^{90} -6.87815 q^{91} -6.57015 q^{92} +0.324679 q^{93} +7.72263 q^{94} -1.90230 q^{95} -1.00000 q^{96} +9.71710 q^{97} +19.3280 q^{98} -2.66785 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9} - q^{10} + 2 q^{11} - 6 q^{12} + 6 q^{13} + q^{14} + q^{15} + 6 q^{16} + 12 q^{17} + 6 q^{18} - 6 q^{19} - q^{20} - q^{21} + 2 q^{22} - 9 q^{23} - 6 q^{24} + 11 q^{25} + 6 q^{26} - 6 q^{27} + q^{28} + 21 q^{29} + q^{30} + 5 q^{31} + 6 q^{32} - 2 q^{33} + 12 q^{34} - 17 q^{35} + 6 q^{36} - 8 q^{37} - 6 q^{38} - 6 q^{39} - q^{40} + 16 q^{41} - q^{42} - 5 q^{43} + 2 q^{44} - q^{45} - 9 q^{46} + 16 q^{47} - 6 q^{48} + 11 q^{49} + 11 q^{50} - 12 q^{51} + 6 q^{52} - 6 q^{53} - 6 q^{54} + 22 q^{55} + q^{56} + 6 q^{57} + 21 q^{58} + 9 q^{59} + q^{60} + 20 q^{61} + 5 q^{62} + q^{63} + 6 q^{64} + 22 q^{65} - 2 q^{66} - 3 q^{67} + 12 q^{68} + 9 q^{69} - 17 q^{70} + 10 q^{71} + 6 q^{72} + 18 q^{73} - 8 q^{74} - 11 q^{75} - 6 q^{76} + 16 q^{77} - 6 q^{78} - 14 q^{79} - q^{80} + 6 q^{81} + 16 q^{82} + 2 q^{83} - q^{84} - 2 q^{85} - 5 q^{86} - 21 q^{87} + 2 q^{88} + 11 q^{89} - q^{90} - 44 q^{91} - 9 q^{92} - 5 q^{93} + 16 q^{94} + q^{95} - 6 q^{96} + 11 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9 - q^10 + 2 * q^11 - 6 * q^12 + 6 * q^13 + q^14 + q^15 + 6 * q^16 + 12 * q^17 + 6 * q^18 - 6 * q^19 - q^20 - q^21 + 2 * q^22 - 9 * q^23 - 6 * q^24 + 11 * q^25 + 6 * q^26 - 6 * q^27 + q^28 + 21 * q^29 + q^30 + 5 * q^31 + 6 * q^32 - 2 * q^33 + 12 * q^34 - 17 * q^35 + 6 * q^36 - 8 * q^37 - 6 * q^38 - 6 * q^39 - q^40 + 16 * q^41 - q^42 - 5 * q^43 + 2 * q^44 - q^45 - 9 * q^46 + 16 * q^47 - 6 * q^48 + 11 * q^49 + 11 * q^50 - 12 * q^51 + 6 * q^52 - 6 * q^53 - 6 * q^54 + 22 * q^55 + q^56 + 6 * q^57 + 21 * q^58 + 9 * q^59 + q^60 + 20 * q^61 + 5 * q^62 + q^63 + 6 * q^64 + 22 * q^65 - 2 * q^66 - 3 * q^67 + 12 * q^68 + 9 * q^69 - 17 * q^70 + 10 * q^71 + 6 * q^72 + 18 * q^73 - 8 * q^74 - 11 * q^75 - 6 * q^76 + 16 * q^77 - 6 * q^78 - 14 * q^79 - q^80 + 6 * q^81 + 16 * q^82 + 2 * q^83 - q^84 - 2 * q^85 - 5 * q^86 - 21 * q^87 + 2 * q^88 + 11 * q^89 - q^90 - 44 * q^91 - 9 * q^92 - 5 * q^93 + 16 * q^94 + q^95 - 6 * q^96 + 11 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.90230	0.850734	0.425367	−	0.905021i	$-0.360145\pi$
$5$	1.90230	0.850734	0.425367	+	0.905021i	$0.360145\pi$
$6$	−1.00000	−0.408248
$7$	−5.13108	−1.93937	−0.969683	−	0.244368i	$-0.921419\pi$
$7$	−5.13108	−1.93937	−0.969683	+	0.244368i	$0.921419\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.90230	0.601560
$11$	−2.66785	−0.804388	−0.402194	−	0.915554i	$-0.631752\pi$
$11$	−2.66785	−0.804388	−0.402194	+	0.915554i	$0.631752\pi$
$12$	−1.00000	−0.288675
$13$	1.34049	0.371785	0.185892	−	0.982570i	$-0.440482\pi$
$13$	1.34049	0.371785	0.185892	+	0.982570i	$0.440482\pi$
$14$	−5.13108	−1.37134
$15$	−1.90230	−0.491172
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.90230	0.425367
$21$	5.13108	1.11969
$22$	−2.66785	−0.568788
$23$	−6.57015	−1.36997	−0.684986	−	0.728556i	$-0.740192\pi$
$23$	−6.57015	−1.36997	−0.684986	+	0.728556i	$0.740192\pi$
$24$	−1.00000	−0.204124
$25$	−1.38125	−0.276251
$26$	1.34049	0.262891
$27$	−1.00000	−0.192450
$28$	−5.13108	−0.969683
$29$	8.57015	1.59144	0.795719	−	0.605666i	$-0.207093\pi$
$29$	8.57015	1.59144	0.795719	+	0.605666i	$0.207093\pi$
$30$	−1.90230	−0.347311
$31$	−0.324679	−0.0583142	−0.0291571	−	0.999575i	$-0.509282\pi$
$31$	−0.324679	−0.0583142	−0.0291571	+	0.999575i	$0.509282\pi$
$32$	1.00000	0.176777
$33$	2.66785	0.464414
$34$	2.00000	0.342997
$35$	−9.76085	−1.64988
$36$	1.00000	0.166667
$37$	2.46411	0.405097	0.202549	−	0.979272i	$-0.435078\pi$
$37$	2.46411	0.405097	0.202549	+	0.979272i	$0.435078\pi$
$38$	−1.00000	−0.162221
$39$	−1.34049	−0.214650
$40$	1.90230	0.300780
$41$	0.384298	0.0600172	0.0300086	−	0.999550i	$-0.490447\pi$
$41$	0.384298	0.0600172	0.0300086	+	0.999550i	$0.490447\pi$
$42$	5.13108	0.791742
$43$	−1.30329	−0.198750	−0.0993752	−	0.995050i	$-0.531684\pi$
$43$	−1.30329	−0.198750	−0.0993752	+	0.995050i	$0.531684\pi$
$44$	−2.66785	−0.402194
$45$	1.90230	0.283578
$46$	−6.57015	−0.968716
$47$	7.72263	1.12646	0.563231	−	0.826300i	$-0.309558\pi$
$47$	7.72263	1.12646	0.563231	+	0.826300i	$0.309558\pi$
$48$	−1.00000	−0.144338
$49$	19.3280	2.76114
$50$	−1.38125	−0.195339
$51$	−2.00000	−0.280056
$52$	1.34049	0.185892
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.00000	−0.136083
$55$	−5.07506	−0.684320
$56$	−5.13108	−0.685669
$57$	1.00000	0.132453
$58$	8.57015	1.12532
$59$	10.5970	1.37961	0.689805	−	0.723995i	$-0.257696\pi$
$59$	10.5970	1.37961	0.689805	+	0.723995i	$0.257696\pi$
$60$	−1.90230	−0.245586
$61$	−2.77666	−0.355515	−0.177757	−	0.984074i	$-0.556884\pi$
$61$	−2.77666	−0.355515	−0.177757	+	0.984074i	$0.556884\pi$
$62$	−0.324679	−0.0412343
$63$	−5.13108	−0.646455
$64$	1.00000	0.125000
$65$	2.55001	0.316290
$66$	2.66785	0.328390
$67$	8.25470	1.00847	0.504236	−	0.863566i	$-0.331774\pi$
$67$	8.25470	1.00847	0.504236	+	0.863566i	$0.331774\pi$
$68$	2.00000	0.242536
$69$	6.57015	0.790953
$70$	−9.76085	−1.16664
$71$	−6.61100	−0.784581	−0.392291	−	0.919841i	$-0.628317\pi$
$71$	−6.61100	−0.784581	−0.392291	+	0.919841i	$0.628317\pi$
$72$	1.00000	0.117851
$73$	1.37023	0.160373	0.0801866	−	0.996780i	$-0.474448\pi$
$73$	1.37023	0.160373	0.0801866	+	0.996780i	$0.474448\pi$
$74$	2.46411	0.286447
$75$	1.38125	0.159494
$76$	−1.00000	−0.114708
$77$	13.6890	1.56000
$78$	−1.34049	−0.151780
$79$	6.63418	0.746404	0.373202	−	0.927750i	$-0.378260\pi$
$79$	6.63418	0.746404	0.373202	+	0.927750i	$0.378260\pi$
$80$	1.90230	0.212684
$81$	1.00000	0.111111
$82$	0.384298	0.0424386
$83$	−8.71690	−0.956804	−0.478402	−	0.878141i	$-0.658784\pi$
$83$	−8.71690	−0.956804	−0.478402	+	0.878141i	$0.658784\pi$
$84$	5.13108	0.559846
$85$	3.80460	0.412667
$86$	−1.30329	−0.140538
$87$	−8.57015	−0.918817
$88$	−2.66785	−0.284394
$89$	−7.71524	−0.817814	−0.408907	−	0.912576i	$-0.634090\pi$
$89$	−7.71524	−0.817814	−0.408907	+	0.912576i	$0.634090\pi$
$90$	1.90230	0.200520
$91$	−6.87815	−0.721026
$92$	−6.57015	−0.684986
$93$	0.324679	0.0336677
$94$	7.72263	0.796528
$95$	−1.90230	−0.195172
$96$	−1.00000	−0.102062
$97$	9.71710	0.986622	0.493311	−	0.869853i	$-0.335786\pi$
$97$	9.71710	0.986622	0.493311	+	0.869853i	$0.335786\pi$
$98$	19.3280	1.95242
$99$	−2.66785	−0.268129
$100$	−1.38125	−0.138125
$101$	−0.269916	−0.0268576	−0.0134288	−	0.999910i	$-0.504275\pi$
$101$	−0.269916	−0.0268576	−0.0134288	+	0.999910i	$0.504275\pi$
$102$	−2.00000	−0.198030
$103$	−0.324679	−0.0319916	−0.0159958	−	0.999872i	$-0.505092\pi$
$103$	−0.324679	−0.0319916	−0.0159958	+	0.999872i	$0.505092\pi$
$104$	1.34049	0.131446
$105$	9.76085	0.952561
$106$	−1.00000	−0.0971286
$107$	12.3682	1.19568	0.597839	−	0.801616i	$-0.296026\pi$
$107$	12.3682	1.19568	0.597839	+	0.801616i	$0.296026\pi$
$108$	−1.00000	−0.0962250
$109$	13.9756	1.33862	0.669308	−	0.742985i	$-0.266591\pi$
$109$	13.9756	1.33862	0.669308	+	0.742985i	$0.266591\pi$
$110$	−5.07506	−0.483888
$111$	−2.46411	−0.233883
$112$	−5.13108	−0.484841
$113$	11.4295	1.07519	0.537597	−	0.843202i	$-0.319332\pi$
$113$	11.4295	1.07519	0.537597	+	0.843202i	$0.319332\pi$
$114$	1.00000	0.0936586
$115$	−12.4984	−1.16548
$116$	8.57015	0.795719
$117$	1.34049	0.123928
$118$	10.5970	0.975532
$119$	−10.2622	−0.940730
$120$	−1.90230	−0.173655
$121$	−3.88256	−0.352960
$122$	−2.77666	−0.251387
$123$	−0.384298	−0.0346510
$124$	−0.324679	−0.0291571
$125$	−12.1391	−1.08575
$126$	−5.13108	−0.457113
$127$	20.1549	1.78846	0.894230	−	0.447607i	$-0.147724\pi$
$127$	20.1549	1.78846	0.894230	+	0.447607i	$0.147724\pi$
$128$	1.00000	0.0883883
$129$	1.30329	0.114749
$130$	2.55001	0.223651
$131$	−2.33971	−0.204422	−0.102211	−	0.994763i	$-0.532592\pi$
$131$	−2.33971	−0.204422	−0.102211	+	0.994763i	$0.532592\pi$
$132$	2.66785	0.232207
$133$	5.13108	0.444921
$134$	8.25470	0.713098
$135$	−1.90230	−0.163724
$136$	2.00000	0.171499
$137$	−0.313433	−0.0267784	−0.0133892	−	0.999910i	$-0.504262\pi$
$137$	−0.313433	−0.0267784	−0.0133892	+	0.999910i	$0.504262\pi$
$138$	6.57015	0.559289
$139$	−5.15617	−0.437341	−0.218670	−	0.975799i	$-0.570172\pi$
$139$	−5.15617	−0.437341	−0.218670	+	0.975799i	$0.570172\pi$
$140$	−9.76085	−0.824942
$141$	−7.72263	−0.650363
$142$	−6.61100	−0.554783
$143$	−3.57623	−0.299059
$144$	1.00000	0.0833333
$145$	16.3030	1.35389
$146$	1.37023	0.113401
$147$	−19.3280	−1.59414
$148$	2.46411	0.202549
$149$	−0.865879	−0.0709356	−0.0354678	−	0.999371i	$-0.511292\pi$
$149$	−0.865879	−0.0709356	−0.0354678	+	0.999371i	$0.511292\pi$
$150$	1.38125	0.112779
$151$	−16.2591	−1.32315	−0.661574	−	0.749880i	$-0.730111\pi$
$151$	−16.2591	−1.32315	−0.661574	+	0.749880i	$0.730111\pi$
$152$	−1.00000	−0.0811107
$153$	2.00000	0.161690
$154$	13.6890	1.10309
$155$	−0.617638	−0.0496099
$156$	−1.34049	−0.107325
$157$	5.23712	0.417968	0.208984	−	0.977919i	$-0.432984\pi$
$157$	5.23712	0.417968	0.208984	+	0.977919i	$0.432984\pi$
$158$	6.63418	0.527787
$159$	1.00000	0.0793052
$160$	1.90230	0.150390
$161$	33.7120	2.65687
$162$	1.00000	0.0785674
$163$	24.7969	1.94224	0.971120	−	0.238593i	$-0.0766861\pi$
$163$	24.7969	1.94224	0.971120	+	0.238593i	$0.0766861\pi$
$164$	0.384298	0.0300086
$165$	5.07506	0.395093
$166$	−8.71690	−0.676563
$167$	22.9840	1.77855	0.889276	−	0.457371i	$-0.151209\pi$
$167$	22.9840	1.77855	0.889276	+	0.457371i	$0.151209\pi$
$168$	5.13108	0.395871
$169$	−11.2031	−0.861776
$170$	3.80460	0.291799
$171$	−1.00000	−0.0764719
$172$	−1.30329	−0.0993752
$173$	5.18133	0.393929	0.196965	−	0.980411i	$-0.436892\pi$
$173$	5.18133	0.393929	0.196965	+	0.980411i	$0.436892\pi$
$174$	−8.57015	−0.649702
$175$	7.08733	0.535752
$176$	−2.66785	−0.201097
$177$	−10.5970	−0.796518
$178$	−7.71524	−0.578282
$179$	15.3419	1.14671	0.573353	−	0.819308i	$-0.305642\pi$
$179$	15.3419	1.14671	0.573353	+	0.819308i	$0.305642\pi$
$180$	1.90230	0.141789
$181$	23.8816	1.77510	0.887551	−	0.460710i	$-0.152405\pi$
$181$	23.8816	1.77510	0.887551	+	0.460710i	$0.152405\pi$
$182$	−6.87815	−0.509842
$183$	2.77666	0.205256
$184$	−6.57015	−0.484358
$185$	4.68748	0.344630
$186$	0.324679	0.0238067
$187$	−5.33571	−0.390185
$188$	7.72263	0.563231
$189$	5.13108	0.373231
$190$	−1.90230	−0.138007
$191$	−8.40716	−0.608321	−0.304161	−	0.952621i	$-0.598376\pi$
$191$	−8.40716	−0.608321	−0.304161	+	0.952621i	$0.598376\pi$
$192$	−1.00000	−0.0721688
$193$	3.40181	0.244868	0.122434	−	0.992477i	$-0.460930\pi$
$193$	3.40181	0.244868	0.122434	+	0.992477i	$0.460930\pi$
$194$	9.71710	0.697647
$195$	−2.55001	−0.182610
$196$	19.3280	1.38057
$197$	−0.799896	−0.0569902	−0.0284951	−	0.999594i	$-0.509072\pi$
$197$	−0.799896	−0.0569902	−0.0284951	+	0.999594i	$0.509072\pi$
$198$	−2.66785	−0.189596
$199$	7.37946	0.523116	0.261558	−	0.965188i	$-0.415764\pi$
$199$	7.37946	0.523116	0.261558	+	0.965188i	$0.415764\pi$
$200$	−1.38125	−0.0976695
$201$	−8.25470	−0.582242
$202$	−0.269916	−0.0189912
$203$	−43.9741	−3.08638
$204$	−2.00000	−0.140028
$205$	0.731050	0.0510587
$206$	−0.324679	−0.0226215
$207$	−6.57015	−0.456657
$208$	1.34049	0.0929461
$209$	2.66785	0.184539
$210$	9.76085	0.673563
$211$	−14.4248	−0.993047	−0.496524	−	0.868023i	$-0.665390\pi$
$211$	−14.4248	−0.993047	−0.496524	+	0.868023i	$0.665390\pi$
$212$	−1.00000	−0.0686803
$213$	6.61100	0.452978
$214$	12.3682	0.845473
$215$	−2.47925	−0.169084
$216$	−1.00000	−0.0680414
$217$	1.66596	0.113092
$218$	13.9756	0.946544
$219$	−1.37023	−0.0925915
$220$	−5.07506	−0.342160
$221$	2.68098	0.180342
$222$	−2.46411	−0.165380
$223$	−0.730984	−0.0489503	−0.0244752	−	0.999700i	$-0.507791\pi$
$223$	−0.730984	−0.0489503	−0.0244752	+	0.999700i	$0.507791\pi$
$224$	−5.13108	−0.342835
$225$	−1.38125	−0.0920837
$226$	11.4295	0.760277
$227$	11.4983	0.763170	0.381585	−	0.924334i	$-0.375378\pi$
$227$	11.4983	0.763170	0.381585	+	0.924334i	$0.375378\pi$
$228$	1.00000	0.0662266
$229$	8.27057	0.546535	0.273267	−	0.961938i	$-0.411896\pi$
$229$	8.27057	0.546535	0.273267	+	0.961938i	$0.411896\pi$
$230$	−12.4984	−0.824120
$231$	−13.6890	−0.900667
$232$	8.57015	0.562658
$233$	−5.02682	−0.329318	−0.164659	−	0.986351i	$-0.552652\pi$
$233$	−5.02682	−0.329318	−0.164659	+	0.986351i	$0.552652\pi$
$234$	1.34049	0.0876305
$235$	14.6908	0.958319
$236$	10.5970	0.689805
$237$	−6.63418	−0.430936
$238$	−10.2622	−0.665197
$239$	−11.4493	−0.740591	−0.370295	−	0.928914i	$-0.620744\pi$
$239$	−11.4493	−0.740591	−0.370295	+	0.928914i	$0.620744\pi$
$240$	−1.90230	−0.122793
$241$	−23.5700	−1.51828	−0.759139	−	0.650929i	$-0.774379\pi$
$241$	−23.5700	−1.51828	−0.759139	+	0.650929i	$0.774379\pi$
$242$	−3.88256	−0.249581
$243$	−1.00000	−0.0641500
$244$	−2.77666	−0.177757
$245$	36.7676	2.34899
$246$	−0.384298	−0.0245019
$247$	−1.34049	−0.0852932
$248$	−0.324679	−0.0206172
$249$	8.71690	0.552411
$250$	−12.1391	−0.767742
$251$	−9.69354	−0.611851	−0.305925	−	0.952055i	$-0.598966\pi$
$251$	−9.69354	−0.611851	−0.305925	+	0.952055i	$0.598966\pi$
$252$	−5.13108	−0.323228
$253$	17.5282	1.10199
$254$	20.1549	1.26463
$255$	−3.80460	−0.238253
$256$	1.00000	0.0625000
$257$	−20.3404	−1.26880	−0.634399	−	0.773006i	$-0.718752\pi$
$257$	−20.3404	−1.26880	−0.634399	+	0.773006i	$0.718752\pi$
$258$	1.30329	0.0811395
$259$	−12.6435	−0.785632
$260$	2.55001	0.158145
$261$	8.57015	0.530479
$262$	−2.33971	−0.144548
$263$	24.6089	1.51745	0.758724	−	0.651412i	$-0.225823\pi$
$263$	24.6089	1.51745	0.758724	+	0.651412i	$0.225823\pi$
$264$	2.66785	0.164195
$265$	−1.90230	−0.116857
$266$	5.13108	0.314607
$267$	7.71524	0.472165
$268$	8.25470	0.504236
$269$	2.56284	0.156259	0.0781294	−	0.996943i	$-0.475105\pi$
$269$	2.56284	0.156259	0.0781294	+	0.996943i	$0.475105\pi$
$270$	−1.90230	−0.115770
$271$	7.09478	0.430977	0.215489	−	0.976506i	$-0.430866\pi$
$271$	7.09478	0.430977	0.215489	+	0.976506i	$0.430866\pi$
$272$	2.00000	0.121268
$273$	6.87815	0.416285
$274$	−0.313433	−0.0189352
$275$	3.68498	0.222213
$276$	6.57015	0.395477
$277$	−1.21753	−0.0731543	−0.0365772	−	0.999331i	$-0.511645\pi$
$277$	−1.21753	−0.0731543	−0.0365772	+	0.999331i	$0.511645\pi$
$278$	−5.15617	−0.309247
$279$	−0.324679	−0.0194381
$280$	−9.76085	−0.583322
$281$	2.84650	0.169808	0.0849039	−	0.996389i	$-0.472942\pi$
$281$	2.84650	0.169808	0.0849039	+	0.996389i	$0.472942\pi$
$282$	−7.72263	−0.459876
$283$	29.1065	1.73020	0.865100	−	0.501599i	$-0.167255\pi$
$283$	29.1065	1.73020	0.865100	+	0.501599i	$0.167255\pi$
$284$	−6.61100	−0.392291
$285$	1.90230	0.112683
$286$	−3.57623	−0.211467
$287$	−1.97186	−0.116395
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	16.3030	0.957345
$291$	−9.71710	−0.569626
$292$	1.37023	0.0801866
$293$	−15.1512	−0.885144	−0.442572	−	0.896733i	$-0.645934\pi$
$293$	−15.1512	−0.885144	−0.442572	+	0.896733i	$0.645934\pi$
$294$	−19.3280	−1.12723
$295$	20.1586	1.17368
$296$	2.46411	0.143224
$297$	2.66785	0.154805
$298$	−0.865879	−0.0501590
$299$	−8.80721	−0.509334
$300$	1.38125	0.0797468
$301$	6.68730	0.385449
$302$	−16.2591	−0.935607
$303$	0.269916	0.0155062
$304$	−1.00000	−0.0573539
$305$	−5.28204	−0.302448
$306$	2.00000	0.114332
$307$	12.0913	0.690089	0.345044	−	0.938586i	$-0.387864\pi$
$307$	12.0913	0.690089	0.345044	+	0.938586i	$0.387864\pi$
$308$	13.6890	0.780001
$309$	0.324679	0.0184704
$310$	−0.617638	−0.0350795
$311$	−33.8879	−1.92161	−0.960803	−	0.277234i	$-0.910582\pi$
$311$	−33.8879	−1.92161	−0.960803	+	0.277234i	$0.910582\pi$
$312$	−1.34049	−0.0758902
$313$	9.99505	0.564953	0.282477	−	0.959274i	$-0.408844\pi$
$313$	9.99505	0.564953	0.282477	+	0.959274i	$0.408844\pi$
$314$	5.23712	0.295548
$315$	−9.76085	−0.549962
$316$	6.63418	0.373202
$317$	−17.6854	−0.993309	−0.496654	−	0.867948i	$-0.665438\pi$
$317$	−17.6854	−0.993309	−0.496654	+	0.867948i	$0.665438\pi$
$318$	1.00000	0.0560772
$319$	−22.8639	−1.28013
$320$	1.90230	0.106342
$321$	−12.3682	−0.690325
$322$	33.7120	1.87869
$323$	−2.00000	−0.111283
$324$	1.00000	0.0555556
$325$	−1.85156	−0.102706
$326$	24.7969	1.37337
$327$	−13.9756	−0.772850
$328$	0.384298	0.0212193
$329$	−39.6254	−2.18462
$330$	5.07506	0.279373
$331$	−7.78943	−0.428146	−0.214073	−	0.976818i	$-0.568673\pi$
$331$	−7.78943	−0.428146	−0.214073	+	0.976818i	$0.568673\pi$
$332$	−8.71690	−0.478402
$333$	2.46411	0.135032
$334$	22.9840	1.25763
$335$	15.7029	0.857942
$336$	5.13108	0.279923
$337$	31.7017	1.72690	0.863452	−	0.504431i	$-0.168298\pi$
$337$	31.7017	1.72690	0.863452	+	0.504431i	$0.168298\pi$
$338$	−11.2031	−0.609368
$339$	−11.4295	−0.620764
$340$	3.80460	0.206333
$341$	0.866197	0.0469072
$342$	−1.00000	−0.0540738
$343$	−63.2557	−3.41549
$344$	−1.30329	−0.0702689
$345$	12.4984	0.672891
$346$	5.18133	0.278550
$347$	27.8835	1.49686	0.748431	−	0.663212i	$-0.230807\pi$
$347$	27.8835	1.49686	0.748431	+	0.663212i	$0.230807\pi$
$348$	−8.57015	−0.459408
$349$	−21.2836	−1.13928	−0.569642	−	0.821893i	$-0.692918\pi$
$349$	−21.2836	−1.13928	−0.569642	+	0.821893i	$0.692918\pi$
$350$	7.08733	0.378834
$351$	−1.34049	−0.0715500
$352$	−2.66785	−0.142197
$353$	−19.2908	−1.02674	−0.513372	−	0.858166i	$-0.671604\pi$
$353$	−19.2908	−1.02674	−0.513372	+	0.858166i	$0.671604\pi$
$354$	−10.5970	−0.563224
$355$	−12.5761	−0.667470
$356$	−7.71524	−0.408907
$357$	10.2622	0.543131
$358$	15.3419	0.810844
$359$	−26.8991	−1.41968	−0.709839	−	0.704364i	$-0.751232\pi$
$359$	−26.8991	−1.41968	−0.709839	+	0.704364i	$0.751232\pi$
$360$	1.90230	0.100260
$361$	1.00000	0.0526316
$362$	23.8816	1.25519
$363$	3.88256	0.203782
$364$	−6.87815	−0.360513
$365$	2.60659	0.136435
$366$	2.77666	0.145138
$367$	6.26393	0.326974	0.163487	−	0.986545i	$-0.447726\pi$
$367$	6.26393	0.326974	0.163487	+	0.986545i	$0.447726\pi$
$368$	−6.57015	−0.342493
$369$	0.384298	0.0200057
$370$	4.68748	0.243690
$371$	5.13108	0.266392
$372$	0.324679	0.0168338
$373$	30.5112	1.57981	0.789905	−	0.613229i	$-0.210130\pi$
$373$	30.5112	1.57981	0.789905	+	0.613229i	$0.210130\pi$
$374$	−5.33571	−0.275903
$375$	12.1391	0.626858
$376$	7.72263	0.398264
$377$	11.4882	0.591672
$378$	5.13108	0.263914
$379$	5.21605	0.267931	0.133965	−	0.990986i	$-0.457229\pi$
$379$	5.21605	0.267931	0.133965	+	0.990986i	$0.457229\pi$
$380$	−1.90230	−0.0975859
$381$	−20.1549	−1.03257
$382$	−8.40716	−0.430148
$383$	12.0044	0.613397	0.306698	−	0.951807i	$-0.400776\pi$
$383$	12.0044	0.613397	0.306698	+	0.951807i	$0.400776\pi$
$384$	−1.00000	−0.0510310
$385$	26.0405	1.32715
$386$	3.40181	0.173147
$387$	−1.30329	−0.0662501
$388$	9.71710	0.493311
$389$	−3.56819	−0.180915	−0.0904573	−	0.995900i	$-0.528833\pi$
$389$	−3.56819	−0.180915	−0.0904573	+	0.995900i	$0.528833\pi$
$390$	−2.55001	−0.129125
$391$	−13.1403	−0.664534
$392$	19.3280	0.976209
$393$	2.33971	0.118023
$394$	−0.799896	−0.0402982
$395$	12.6202	0.634991
$396$	−2.66785	−0.134065
$397$	26.5189	1.33094	0.665472	−	0.746423i	$-0.268230\pi$
$397$	26.5189	1.33094	0.665472	+	0.746423i	$0.268230\pi$
$398$	7.37946	0.369899
$399$	−5.13108	−0.256875
$400$	−1.38125	−0.0690627
$401$	12.2592	0.612198	0.306099	−	0.952000i	$-0.400976\pi$
$401$	12.2592	0.612198	0.306099	+	0.952000i	$0.400976\pi$
$402$	−8.25470	−0.411707
$403$	−0.435229	−0.0216803
$404$	−0.269916	−0.0134288
$405$	1.90230	0.0945260
$406$	−43.9741	−2.18240
$407$	−6.57389	−0.325855
$408$	−2.00000	−0.0990148
$409$	11.6073	0.573943	0.286971	−	0.957939i	$-0.407352\pi$
$409$	11.6073	0.573943	0.286971	+	0.957939i	$0.407352\pi$
$410$	0.731050	0.0361040
$411$	0.313433	0.0154605
$412$	−0.324679	−0.0159958
$413$	−54.3740	−2.67557
$414$	−6.57015	−0.322905
$415$	−16.5822	−0.813986
$416$	1.34049	0.0657228
$417$	5.15617	0.252499
$418$	2.66785	0.130489
$419$	23.3121	1.13887	0.569437	−	0.822035i	$-0.307161\pi$
$419$	23.3121	1.13887	0.569437	+	0.822035i	$0.307161\pi$
$420$	9.76085	0.476281
$421$	−3.05766	−0.149021	−0.0745106	−	0.997220i	$-0.523739\pi$
$421$	−3.05766	−0.149021	−0.0745106	+	0.997220i	$0.523739\pi$
$422$	−14.4248	−0.702190
$423$	7.72263	0.375487
$424$	−1.00000	−0.0485643
$425$	−2.76251	−0.134001
$426$	6.61100	0.320304
$427$	14.2472	0.689473
$428$	12.3682	0.597839
$429$	3.57623	0.172662
$430$	−2.47925	−0.119560
$431$	38.8306	1.87041	0.935203	−	0.354112i	$-0.115217\pi$
$431$	38.8306	1.87041	0.935203	+	0.354112i	$0.115217\pi$
$432$	−1.00000	−0.0481125
$433$	−8.75714	−0.420841	−0.210421	−	0.977611i	$-0.567483\pi$
$433$	−8.75714	−0.420841	−0.210421	+	0.977611i	$0.567483\pi$
$434$	1.66596	0.0799684
$435$	−16.3030	−0.781669
$436$	13.9756	0.669308
$437$	6.57015	0.314293
$438$	−1.37023	−0.0654721
$439$	−17.6581	−0.842775	−0.421388	−	0.906881i	$-0.638457\pi$
$439$	−17.6581	−0.842775	−0.421388	+	0.906881i	$0.638457\pi$
$440$	−5.07506	−0.241944
$441$	19.3280	0.920379
$442$	2.68098	0.127521
$443$	9.81957	0.466542	0.233271	−	0.972412i	$-0.425057\pi$
$443$	9.81957	0.466542	0.233271	+	0.972412i	$0.425057\pi$
$444$	−2.46411	−0.116942
$445$	−14.6767	−0.695742
$446$	−0.730984	−0.0346131
$447$	0.865879	0.0409547
$448$	−5.13108	−0.242421
$449$	−9.54939	−0.450664	−0.225332	−	0.974282i	$-0.572347\pi$
$449$	−9.54939	−0.450664	−0.225332	+	0.974282i	$0.572347\pi$
$450$	−1.38125	−0.0651130
$451$	−1.02525	−0.0482771
$452$	11.4295	0.537597
$453$	16.2591	0.763920
$454$	11.4983	0.539643
$455$	−13.0843	−0.613402
$456$	1.00000	0.0468293
$457$	−30.3753	−1.42090	−0.710448	−	0.703750i	$-0.751508\pi$
$457$	−30.3753	−1.42090	−0.710448	+	0.703750i	$0.751508\pi$
$458$	8.27057	0.386458
$459$	−2.00000	−0.0933520
$460$	−12.4984	−0.582741
$461$	18.8697	0.878848	0.439424	−	0.898280i	$-0.355183\pi$
$461$	18.8697	0.878848	0.439424	+	0.898280i	$0.355183\pi$
$462$	−13.6890	−0.636868
$463$	4.27437	0.198647	0.0993235	−	0.995055i	$-0.468332\pi$
$463$	4.27437	0.198647	0.0993235	+	0.995055i	$0.468332\pi$
$464$	8.57015	0.397859
$465$	0.617638	0.0286423
$466$	−5.02682	−0.232863
$467$	9.90534	0.458365	0.229182	−	0.973384i	$-0.426395\pi$
$467$	9.90534	0.458365	0.229182	+	0.973384i	$0.426395\pi$
$468$	1.34049	0.0619641
$469$	−42.3555	−1.95580
$470$	14.6908	0.677634
$471$	−5.23712	−0.241314
$472$	10.5970	0.487766
$473$	3.47699	0.159872
$474$	−6.63418	−0.304718
$475$	1.38125	0.0633763
$476$	−10.2622	−0.470365
$477$	−1.00000	−0.0457869
$478$	−11.4493	−0.523677
$479$	−22.4748	−1.02690	−0.513450	−	0.858120i	$-0.671633\pi$
$479$	−22.4748	−1.02690	−0.513450	+	0.858120i	$0.671633\pi$
$480$	−1.90230	−0.0868277
$481$	3.30311	0.150609
$482$	−23.5700	−1.07358
$483$	−33.7120	−1.53395
$484$	−3.88256	−0.176480
$485$	18.4848	0.839353
$486$	−1.00000	−0.0453609
$487$	11.4485	0.518781	0.259391	−	0.965772i	$-0.416478\pi$
$487$	11.4485	0.518781	0.259391	+	0.965772i	$0.416478\pi$
$488$	−2.77666	−0.125693
$489$	−24.7969	−1.12135
$490$	36.7676	1.66099
$491$	33.0839	1.49305	0.746527	−	0.665355i	$-0.231720\pi$
$491$	33.0839	1.49305	0.746527	+	0.665355i	$0.231720\pi$
$492$	−0.384298	−0.0173255
$493$	17.1403	0.771961
$494$	−1.34049	−0.0603114
$495$	−5.07506	−0.228107
$496$	−0.324679	−0.0145785
$497$	33.9215	1.52159
$498$	8.71690	0.390614
$499$	16.7694	0.750702	0.375351	−	0.926883i	$-0.377522\pi$
$499$	16.7694	0.750702	0.375351	+	0.926883i	$0.377522\pi$
$500$	−12.1391	−0.542875
$501$	−22.9840	−1.02685
$502$	−9.69354	−0.432644
$503$	−22.2214	−0.990804	−0.495402	−	0.868664i	$-0.664979\pi$
$503$	−22.2214	−0.990804	−0.495402	+	0.868664i	$0.664979\pi$
$504$	−5.13108	−0.228556
$505$	−0.513460	−0.0228487
$506$	17.5282	0.779224
$507$	11.2031	0.497547
$508$	20.1549	0.894230
$509$	2.15194	0.0953829	0.0476915	−	0.998862i	$-0.484814\pi$
$509$	2.15194	0.0953829	0.0476915	+	0.998862i	$0.484814\pi$
$510$	−3.80460	−0.168471
$511$	−7.03075	−0.311022
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−20.3404	−0.897175
$515$	−0.617638	−0.0272164
$516$	1.30329	0.0573743
$517$	−20.6028	−0.906112
$518$	−12.6435	−0.555526
$519$	−5.18133	−0.227435
$520$	2.55001	0.111825
$521$	−2.41887	−0.105973	−0.0529864	−	0.998595i	$-0.516874\pi$
$521$	−2.41887	−0.105973	−0.0529864	+	0.998595i	$0.516874\pi$
$522$	8.57015	0.375105
$523$	23.8082	1.04106	0.520529	−	0.853844i	$-0.325735\pi$
$523$	23.8082	1.04106	0.520529	+	0.853844i	$0.325735\pi$
$524$	−2.33971	−0.102211
$525$	−7.08733	−0.309316
$526$	24.6089	1.07300
$527$	−0.649359	−0.0282865
$528$	2.66785	0.116103
$529$	20.1669	0.876822
$530$	−1.90230	−0.0826306
$531$	10.5970	0.459870
$532$	5.13108	0.222460
$533$	0.515147	0.0223135
$534$	7.71524	0.333871
$535$	23.5280	1.01720
$536$	8.25470	0.356549
$537$	−15.3419	−0.662051
$538$	2.56284	0.110492
$539$	−51.5641	−2.22103
$540$	−1.90230	−0.0818620
$541$	−34.1290	−1.46732	−0.733659	−	0.679517i	$-0.762189\pi$
$541$	−34.1290	−1.46732	−0.733659	+	0.679517i	$0.762189\pi$
$542$	7.09478	0.304747
$543$	−23.8816	−1.02486
$544$	2.00000	0.0857493
$545$	26.5857	1.13881
$546$	6.87815	0.294358
$547$	−16.5239	−0.706512	−0.353256	−	0.935527i	$-0.614926\pi$
$547$	−16.5239	−0.706512	−0.353256	+	0.935527i	$0.614926\pi$
$548$	−0.313433	−0.0133892
$549$	−2.77666	−0.118505
$550$	3.68498	0.157128
$551$	−8.57015	−0.365101
$552$	6.57015	0.279644
$553$	−34.0405	−1.44755
$554$	−1.21753	−0.0517279
$555$	−4.68748	−0.198972
$556$	−5.15617	−0.218670
$557$	−20.7811	−0.880524	−0.440262	−	0.897869i	$-0.645114\pi$
$557$	−20.7811	−0.880524	−0.440262	+	0.897869i	$0.645114\pi$
$558$	−0.324679	−0.0137448
$559$	−1.74705	−0.0738923
$560$	−9.76085	−0.412471
$561$	5.33571	0.225274
$562$	2.84650	0.120072
$563$	14.3207	0.603545	0.301772	−	0.953380i	$-0.402422\pi$
$563$	14.3207	0.603545	0.301772	+	0.953380i	$0.402422\pi$
$564$	−7.72263	−0.325181
$565$	21.7423	0.914705
$566$	29.1065	1.22344
$567$	−5.13108	−0.215485
$568$	−6.61100	−0.277391
$569$	−5.30934	−0.222579	−0.111290	−	0.993788i	$-0.535498\pi$
$569$	−5.30934	−0.222579	−0.111290	+	0.993788i	$0.535498\pi$
$570$	1.90230	0.0796786
$571$	−5.07282	−0.212291	−0.106145	−	0.994351i	$-0.533851\pi$
$571$	−5.07282	−0.212291	−0.106145	+	0.994351i	$0.533851\pi$
$572$	−3.57623	−0.149530
$573$	8.40716	0.351214
$574$	−1.97186	−0.0823039
$575$	9.07506	0.378456
$576$	1.00000	0.0416667
$577$	−44.7144	−1.86148	−0.930742	−	0.365676i	$-0.880838\pi$
$577$	−44.7144	−1.86148	−0.930742	+	0.365676i	$0.880838\pi$
$578$	−13.0000	−0.540729
$579$	−3.40181	−0.141374
$580$	16.3030	0.676945
$581$	44.7271	1.85559
$582$	−9.71710	−0.402787
$583$	2.66785	0.110491
$584$	1.37023	0.0567005
$585$	2.55001	0.105430
$586$	−15.1512	−0.625891
$587$	−11.8798	−0.490331	−0.245166	−	0.969481i	$-0.578842\pi$
$587$	−11.8798	−0.490331	−0.245166	+	0.969481i	$0.578842\pi$
$588$	−19.3280	−0.797072
$589$	0.324679	0.0133782
$590$	20.1586	0.829918
$591$	0.799896	0.0329033
$592$	2.46411	0.101274
$593$	33.4059	1.37182	0.685909	−	0.727688i	$-0.259405\pi$
$593$	33.4059	1.37182	0.685909	+	0.727688i	$0.259405\pi$
$594$	2.66785	0.109463
$595$	−19.5217	−0.800312
$596$	−0.865879	−0.0354678
$597$	−7.37946	−0.302021
$598$	−8.80721	−0.360154
$599$	22.0525	0.901041	0.450521	−	0.892766i	$-0.351238\pi$
$599$	22.0525	0.901041	0.450521	+	0.892766i	$0.351238\pi$
$600$	1.38125	0.0563895
$601$	−14.9858	−0.611282	−0.305641	−	0.952147i	$-0.598871\pi$
$601$	−14.9858	−0.611282	−0.305641	+	0.952147i	$0.598871\pi$
$602$	6.68730	0.272554
$603$	8.25470	0.336157
$604$	−16.2591	−0.661574
$605$	−7.38580	−0.300275
$606$	0.269916	0.0109646
$607$	27.6329	1.12158	0.560792	−	0.827957i	$-0.310497\pi$
$607$	27.6329	1.12158	0.560792	+	0.827957i	$0.310497\pi$
$608$	−1.00000	−0.0405554
$609$	43.9741	1.78192
$610$	−5.28204	−0.213863
$611$	10.3521	0.418801
$612$	2.00000	0.0808452
$613$	−14.0034	−0.565591	−0.282796	−	0.959180i	$-0.591262\pi$
$613$	−14.0034	−0.565591	−0.282796	+	0.959180i	$0.591262\pi$
$614$	12.0913	0.487967
$615$	−0.731050	−0.0294788
$616$	13.6890	0.551544
$617$	44.8322	1.80488	0.902438	−	0.430820i	$-0.141775\pi$
$617$	44.8322	1.80488	0.902438	+	0.430820i	$0.141775\pi$
$618$	0.324679	0.0130605
$619$	−16.2152	−0.651745	−0.325872	−	0.945414i	$-0.605658\pi$
$619$	−16.2152	−0.651745	−0.325872	+	0.945414i	$0.605658\pi$
$620$	−0.617638	−0.0248049
$621$	6.57015	0.263651
$622$	−33.8879	−1.35878
$623$	39.5875	1.58604
$624$	−1.34049	−0.0536625
$625$	−16.1859	−0.647434
$626$	9.99505	0.399482
$627$	−2.66785	−0.106544
$628$	5.23712	0.208984
$629$	4.92822	0.196501
$630$	−9.76085	−0.388882
$631$	−9.04256	−0.359979	−0.179989	−	0.983669i	$-0.557606\pi$
$631$	−9.04256	−0.359979	−0.179989	+	0.983669i	$0.557606\pi$
$632$	6.63418	0.263894
$633$	14.4248	0.573336
$634$	−17.6854	−0.702375
$635$	38.3407	1.52151
$636$	1.00000	0.0396526
$637$	25.9089	1.02655
$638$	−22.8639	−0.905191
$639$	−6.61100	−0.261527
$640$	1.90230	0.0751950
$641$	45.7383	1.80655	0.903277	−	0.429058i	$-0.141154\pi$
$641$	45.7383	1.80655	0.903277	+	0.429058i	$0.141154\pi$
$642$	−12.3682	−0.488134
$643$	−16.4816	−0.649969	−0.324985	−	0.945719i	$-0.605359\pi$
$643$	−16.4816	−0.649969	−0.324985	+	0.945719i	$0.605359\pi$
$644$	33.7120	1.32844
$645$	2.47925	0.0976206
$646$	−2.00000	−0.0786889
$647$	−33.4796	−1.31622	−0.658109	−	0.752922i	$-0.728644\pi$
$647$	−33.4796	−1.31622	−0.658109	+	0.752922i	$0.728644\pi$
$648$	1.00000	0.0392837
$649$	−28.2712	−1.10974
$650$	−1.85156	−0.0726240
$651$	−1.66596	−0.0652939
$652$	24.7969	0.971120
$653$	13.2903	0.520090	0.260045	−	0.965596i	$-0.416263\pi$
$653$	13.2903	0.520090	0.260045	+	0.965596i	$0.416263\pi$
$654$	−13.9756	−0.546488
$655$	−4.45084	−0.173909
$656$	0.384298	0.0150043
$657$	1.37023	0.0534577
$658$	−39.6254	−1.54476
$659$	−41.0667	−1.59973	−0.799866	−	0.600178i	$-0.795096\pi$
$659$	−41.0667	−1.59973	−0.799866	+	0.600178i	$0.795096\pi$
$660$	5.07506	0.197546
$661$	14.1573	0.550656	0.275328	−	0.961350i	$-0.411213\pi$
$661$	14.1573	0.550656	0.275328	+	0.961350i	$0.411213\pi$
$662$	−7.78943	−0.302745
$663$	−2.68098	−0.104121
$664$	−8.71690	−0.338281
$665$	9.76085	0.378509
$666$	2.46411	0.0954824
$667$	−56.3072	−2.18022
$668$	22.9840	0.889276
$669$	0.730984	0.0282615
$670$	15.7029	0.606657
$671$	7.40771	0.285972
$672$	5.13108	0.197936
$673$	−44.9765	−1.73372	−0.866859	−	0.498554i	$-0.833865\pi$
$673$	−44.9765	−1.73372	−0.866859	+	0.498554i	$0.833865\pi$
$674$	31.7017	1.22111
$675$	1.38125	0.0531645
$676$	−11.2031	−0.430888
$677$	16.4046	0.630479	0.315240	−	0.949012i	$-0.397915\pi$
$677$	16.4046	0.630479	0.315240	+	0.949012i	$0.397915\pi$
$678$	−11.4295	−0.438946
$679$	−49.8592	−1.91342
$680$	3.80460	0.145900
$681$	−11.4983	−0.440617
$682$	0.866197	0.0331684
$683$	−5.26321	−0.201391	−0.100696	−	0.994917i	$-0.532107\pi$
$683$	−5.26321	−0.201391	−0.100696	+	0.994917i	$0.532107\pi$
$684$	−1.00000	−0.0382360
$685$	−0.596243	−0.0227813
$686$	−63.2557	−2.41511
$687$	−8.27057	−0.315542
$688$	−1.30329	−0.0496876
$689$	−1.34049	−0.0510685
$690$	12.4984	0.475806
$691$	−11.5733	−0.440270	−0.220135	−	0.975469i	$-0.570650\pi$
$691$	−11.5733	−0.440270	−0.220135	+	0.975469i	$0.570650\pi$
$692$	5.18133	0.196965
$693$	13.6890	0.520001
$694$	27.8835	1.05844
$695$	−9.80859	−0.372061
$696$	−8.57015	−0.324851
$697$	0.768596	0.0291126
$698$	−21.2836	−0.805596
$699$	5.02682	0.190132
$700$	7.08733	0.267876
$701$	15.2994	0.577850	0.288925	−	0.957352i	$-0.406702\pi$
$701$	15.2994	0.577850	0.288925	+	0.957352i	$0.406702\pi$
$702$	−1.34049	−0.0505935
$703$	−2.46411	−0.0929357
$704$	−2.66785	−0.100548
$705$	−14.6908	−0.553286
$706$	−19.2908	−0.726017
$707$	1.38496	0.0520867
$708$	−10.5970	−0.398259
$709$	26.1588	0.982413	0.491206	−	0.871043i	$-0.336556\pi$
$709$	26.1588	0.982413	0.491206	+	0.871043i	$0.336556\pi$
$710$	−12.5761	−0.471973
$711$	6.63418	0.248801
$712$	−7.71524	−0.289141
$713$	2.13319	0.0798887
$714$	10.2622	0.384052
$715$	−6.80305	−0.254420
$716$	15.3419	0.573353
$717$	11.4493	0.427580
$718$	−26.8991	−1.00386
$719$	14.5807	0.543770	0.271885	−	0.962330i	$-0.412353\pi$
$719$	14.5807	0.543770	0.271885	+	0.962330i	$0.412353\pi$
$720$	1.90230	0.0708945
$721$	1.66596	0.0620434
$722$	1.00000	0.0372161
$723$	23.5700	0.876578
$724$	23.8816	0.887551
$725$	−11.8376	−0.439636
$726$	3.88256	0.144095
$727$	18.5195	0.686849	0.343425	−	0.939180i	$-0.388413\pi$
$727$	18.5195	0.686849	0.343425	+	0.939180i	$0.388413\pi$
$728$	−6.87815	−0.254921
$729$	1.00000	0.0370370
$730$	2.60659	0.0964741
$731$	−2.60659	−0.0964081
$732$	2.77666	0.102628
$733$	−35.2262	−1.30111	−0.650555	−	0.759459i	$-0.725464\pi$
$733$	−35.2262	−1.30111	−0.650555	+	0.759459i	$0.725464\pi$
$734$	6.26393	0.231206
$735$	−36.7676	−1.35619
$736$	−6.57015	−0.242179
$737$	−22.0223	−0.811203
$738$	0.384298	0.0141462
$739$	−6.86858	−0.252665	−0.126332	−	0.991988i	$-0.540321\pi$
$739$	−6.86858	−0.252665	−0.126332	+	0.991988i	$0.540321\pi$
$740$	4.68748	0.172315
$741$	1.34049	0.0492441
$742$	5.13108	0.188368
$743$	8.80608	0.323064	0.161532	−	0.986867i	$-0.448357\pi$
$743$	8.80608	0.323064	0.161532	+	0.986867i	$0.448357\pi$
$744$	0.324679	0.0119033
$745$	−1.64716	−0.0603474
$746$	30.5112	1.11709
$747$	−8.71690	−0.318935
$748$	−5.33571	−0.195093
$749$	−63.4622	−2.31886
$750$	12.1391	0.443256
$751$	2.76188	0.100783	0.0503913	−	0.998730i	$-0.483953\pi$
$751$	2.76188	0.100783	0.0503913	+	0.998730i	$0.483953\pi$
$752$	7.72263	0.281615
$753$	9.69354	0.353252
$754$	11.4882	0.418375
$755$	−30.9297	−1.12565
$756$	5.13108	0.186615
$757$	−8.02004	−0.291493	−0.145747	−	0.989322i	$-0.546558\pi$
$757$	−8.02004	−0.291493	−0.145747	+	0.989322i	$0.546558\pi$
$758$	5.21605	0.189456
$759$	−17.5282	−0.636233
$760$	−1.90230	−0.0690037
$761$	−11.4645	−0.415588	−0.207794	−	0.978173i	$-0.566628\pi$
$761$	−11.4645	−0.415588	−0.207794	+	0.978173i	$0.566628\pi$
$762$	−20.1549	−0.730136
$763$	−71.7097	−2.59606
$764$	−8.40716	−0.304161
$765$	3.80460	0.137556
$766$	12.0044	0.433737
$767$	14.2051	0.512918
$768$	−1.00000	−0.0360844
$769$	−36.3408	−1.31048	−0.655241	−	0.755420i	$-0.727433\pi$
$769$	−36.3408	−1.31048	−0.655241	+	0.755420i	$0.727433\pi$
$770$	26.0405	0.938435
$771$	20.3404	0.732540
$772$	3.40181	0.122434
$773$	−15.1599	−0.545264	−0.272632	−	0.962118i	$-0.587894\pi$
$773$	−15.1599	−0.545264	−0.272632	+	0.962118i	$0.587894\pi$
$774$	−1.30329	−0.0468459
$775$	0.448465	0.0161093
$776$	9.71710	0.348823
$777$	12.6435	0.453585
$778$	−3.56819	−0.127926
$779$	−0.384298	−0.0137689
$780$	−2.55001	−0.0913050
$781$	17.6372	0.631108
$782$	−13.1403	−0.469896
$783$	−8.57015	−0.306272
$784$	19.3280	0.690284
$785$	9.96257	0.355579
$786$	2.33971	0.0834548
$787$	1.39695	0.0497958	0.0248979	−	0.999690i	$-0.492074\pi$
$787$	1.39695	0.0497958	0.0248979	+	0.999690i	$0.492074\pi$
$788$	−0.799896	−0.0284951
$789$	−24.6089	−0.876100
$790$	12.6202	0.449007
$791$	−58.6455	−2.08520
$792$	−2.66785	−0.0947980
$793$	−3.72208	−0.132175
$794$	26.5189	0.941120
$795$	1.90230	0.0674676
$796$	7.37946	0.261558
$797$	17.6466	0.625076	0.312538	−	0.949905i	$-0.398821\pi$
$797$	17.6466	0.625076	0.312538	+	0.949905i	$0.398821\pi$
$798$	−5.13108	−0.181638
$799$	15.4453	0.546414
$800$	−1.38125	−0.0488347
$801$	−7.71524	−0.272605
$802$	12.2592	0.432889
$803$	−3.65557	−0.129002
$804$	−8.25470	−0.291121
$805$	64.1303	2.26029
$806$	−0.435229	−0.0153303
$807$	−2.56284	−0.0902161
$808$	−0.269916	−0.00949560
$809$	30.7678	1.08174	0.540869	−	0.841107i	$-0.318095\pi$
$809$	30.7678	1.08174	0.540869	+	0.841107i	$0.318095\pi$
$810$	1.90230	0.0668400
$811$	−1.07135	−0.0376201	−0.0188101	−	0.999823i	$-0.505988\pi$
$811$	−1.07135	−0.0376201	−0.0188101	+	0.999823i	$0.505988\pi$
$812$	−43.9741	−1.54319
$813$	−7.09478	−0.248825
$814$	−6.57389	−0.230415
$815$	47.1711	1.65233
$816$	−2.00000	−0.0700140
$817$	1.30329	0.0455965
$818$	11.6073	0.405839
$819$	−6.87815	−0.240342
$820$	0.731050	0.0255294
$821$	48.0013	1.67526	0.837628	−	0.546241i	$-0.183942\pi$
$821$	48.0013	1.67526	0.837628	+	0.546241i	$0.183942\pi$
$822$	0.313433	0.0109322
$823$	−20.7821	−0.724418	−0.362209	−	0.932097i	$-0.617977\pi$
$823$	−20.7821	−0.724418	−0.362209	+	0.932097i	$0.617977\pi$
$824$	−0.324679	−0.0113107
$825$	−3.68498	−0.128295
$826$	−54.3740	−1.89191
$827$	26.7819	0.931299	0.465650	−	0.884969i	$-0.345821\pi$
$827$	26.7819	0.931299	0.465650	+	0.884969i	$0.345821\pi$
$828$	−6.57015	−0.228329
$829$	−21.8413	−0.758580	−0.379290	−	0.925278i	$-0.623832\pi$
$829$	−21.8413	−0.758580	−0.379290	+	0.925278i	$0.623832\pi$
$830$	−16.5822	−0.575575
$831$	1.21753	0.0422357
$832$	1.34049	0.0464731
$833$	38.6559	1.33935
$834$	5.15617	0.178544
$835$	43.7224	1.51308
$836$	2.66785	0.0922696
$837$	0.324679	0.0112226
$838$	23.3121	0.805305
$839$	40.5346	1.39941	0.699706	−	0.714431i	$-0.253314\pi$
$839$	40.5346	1.39941	0.699706	+	0.714431i	$0.253314\pi$
$840$	9.76085	0.336781
$841$	44.4475	1.53267
$842$	−3.05766	−0.105374
$843$	−2.84650	−0.0980386
$844$	−14.4248	−0.496524
$845$	−21.3116	−0.733143
$846$	7.72263	0.265509
$847$	19.9217	0.684519
$848$	−1.00000	−0.0343401
$849$	−29.1065	−0.998932
$850$	−2.76251	−0.0947533
$851$	−16.1896	−0.554972
$852$	6.61100	0.226489
$853$	39.0949	1.33858	0.669291	−	0.743000i	$-0.266598\pi$
$853$	39.0949	1.33858	0.669291	+	0.743000i	$0.266598\pi$
$854$	14.2472	0.487531
$855$	−1.90230	−0.0650573
$856$	12.3682	0.422736
$857$	0.234785	0.00802010	0.00401005	−	0.999992i	$-0.498724\pi$
$857$	0.234785	0.00802010	0.00401005	+	0.999992i	$0.498724\pi$
$858$	3.57623	0.122090
$859$	−40.9277	−1.39644	−0.698218	−	0.715886i	$-0.746023\pi$
$859$	−40.9277	−1.39644	−0.698218	+	0.715886i	$0.746023\pi$
$860$	−2.47925	−0.0845419
$861$	1.97186	0.0672009
$862$	38.8306	1.32258
$863$	−31.1592	−1.06067	−0.530336	−	0.847788i	$-0.677934\pi$
$863$	−31.1592	−1.06067	−0.530336	+	0.847788i	$0.677934\pi$
$864$	−1.00000	−0.0340207
$865$	9.85645	0.335129
$866$	−8.75714	−0.297580
$867$	13.0000	0.441503
$868$	1.66596	0.0565462
$869$	−17.6990	−0.600398
$870$	−16.3030	−0.552723
$871$	11.0653	0.374934
$872$	13.9756	0.473272
$873$	9.71710	0.328874
$874$	6.57015	0.222239
$875$	62.2865	2.10567
$876$	−1.37023	−0.0462957
$877$	−8.29732	−0.280180	−0.140090	−	0.990139i	$-0.544739\pi$
$877$	−8.29732	−0.280180	−0.140090	+	0.990139i	$0.544739\pi$
$878$	−17.6581	−0.595932
$879$	15.1512	0.511038
$880$	−5.07506	−0.171080
$881$	−33.6225	−1.13277	−0.566385	−	0.824141i	$-0.691658\pi$
$881$	−33.6225	−1.13277	−0.566385	+	0.824141i	$0.691658\pi$
$882$	19.3280	0.650806
$883$	−31.5163	−1.06061	−0.530304	−	0.847807i	$-0.677922\pi$
$883$	−31.5163	−1.06061	−0.530304	+	0.847807i	$0.677922\pi$
$884$	2.68098	0.0901710
$885$	−20.1586	−0.677626
$886$	9.81957	0.329895
$887$	−7.47429	−0.250962	−0.125481	−	0.992096i	$-0.540047\pi$
$887$	−7.47429	−0.250962	−0.125481	+	0.992096i	$0.540047\pi$
$888$	−2.46411	−0.0826902
$889$	−103.417	−3.46848
$890$	−14.6767	−0.491964
$891$	−2.66785	−0.0893764
$892$	−0.730984	−0.0244752
$893$	−7.72263	−0.258428
$894$	0.865879	0.0289593
$895$	29.1849	0.975543
$896$	−5.13108	−0.171417
$897$	8.80721	0.294064
$898$	−9.54939	−0.318667
$899$	−2.78255	−0.0928033
$900$	−1.38125	−0.0460418
$901$	−2.00000	−0.0666297
$902$	−1.02525	−0.0341371
$903$	−6.68730	−0.222539
$904$	11.4295	0.380139
$905$	45.4299	1.51014
$906$	16.2591	0.540173
$907$	−5.87585	−0.195104	−0.0975522	−	0.995230i	$-0.531101\pi$
$907$	−5.87585	−0.195104	−0.0975522	+	0.995230i	$0.531101\pi$
$908$	11.4983	0.381585
$909$	−0.269916	−0.00895253
$910$	−13.0843	−0.433740
$911$	47.8523	1.58542	0.792708	−	0.609602i	$-0.208671\pi$
$911$	47.8523	1.58542	0.792708	+	0.609602i	$0.208671\pi$
$912$	1.00000	0.0331133
$913$	23.2554	0.769642
$914$	−30.3753	−1.00472
$915$	5.28204	0.174619
$916$	8.27057	0.273267
$917$	12.0053	0.396448
$918$	−2.00000	−0.0660098
$919$	−8.92207	−0.294312	−0.147156	−	0.989113i	$-0.547012\pi$
$919$	−8.92207	−0.294312	−0.147156	+	0.989113i	$0.547012\pi$
$920$	−12.4984	−0.412060
$921$	−12.0913	−0.398423
$922$	18.8697	0.621440
$923$	−8.86197	−0.291695
$924$	−13.6890	−0.450334
$925$	−3.40357	−0.111909
$926$	4.27437	0.140465
$927$	−0.324679	−0.0106639
$928$	8.57015	0.281329
$929$	9.71934	0.318881	0.159441	−	0.987208i	$-0.449031\pi$
$929$	9.71934	0.318881	0.159441	+	0.987208i	$0.449031\pi$
$930$	0.617638	0.0202531
$931$	−19.3280	−0.633448
$932$	−5.02682	−0.164659
$933$	33.8879	1.10944
$934$	9.90534	0.324113
$935$	−10.1501	−0.331944
$936$	1.34049	0.0438152
$937$	−25.5560	−0.834879	−0.417440	−	0.908705i	$-0.637073\pi$
$937$	−25.5560	−0.834879	−0.417440	+	0.908705i	$0.637073\pi$
$938$	−42.3555	−1.38296
$939$	−9.99505	−0.326176
$940$	14.6908	0.479160
$941$	−11.4145	−0.372101	−0.186051	−	0.982540i	$-0.559569\pi$
$941$	−11.4145	−0.372101	−0.186051	+	0.982540i	$0.559569\pi$
$942$	−5.23712	−0.170635
$943$	−2.52490	−0.0822219
$944$	10.5970	0.344903
$945$	9.76085	0.317520
$946$	3.47699	0.113047
$947$	−32.0983	−1.04305	−0.521527	−	0.853235i	$-0.674637\pi$
$947$	−32.0983	−1.04305	−0.521527	+	0.853235i	$0.674637\pi$
$948$	−6.63418	−0.215468
$949$	1.83678	0.0596243
$950$	1.38125	0.0448138
$951$	17.6854	0.573487
$952$	−10.2622	−0.332598
$953$	4.13932	0.134086	0.0670428	−	0.997750i	$-0.478644\pi$
$953$	4.13932	0.134086	0.0670428	+	0.997750i	$0.478644\pi$
$954$	−1.00000	−0.0323762
$955$	−15.9929	−0.517520
$956$	−11.4493	−0.370295
$957$	22.8639	0.739085
$958$	−22.4748	−0.726128
$959$	1.60825	0.0519330
$960$	−1.90230	−0.0613965
$961$	−30.8946	−0.996599
$962$	3.30311	0.106497
$963$	12.3682	0.398560
$964$	−23.5700	−0.759139
$965$	6.47126	0.208317
$966$	−33.7120	−1.08466
$967$	−17.3518	−0.557997	−0.278999	−	0.960292i	$-0.590002\pi$
$967$	−17.3518	−0.557997	−0.278999	+	0.960292i	$0.590002\pi$
$968$	−3.88256	−0.124790
$969$	2.00000	0.0642493
$970$	18.4848	0.593512
$971$	44.7205	1.43515	0.717575	−	0.696481i	$-0.245252\pi$
$971$	44.7205	1.43515	0.717575	+	0.696481i	$0.245252\pi$
$972$	−1.00000	−0.0320750
$973$	26.4567	0.848164
$974$	11.4485	0.366834
$975$	1.85156	0.0592973
$976$	−2.77666	−0.0888786
$977$	−52.9149	−1.69290	−0.846449	−	0.532470i	$-0.821264\pi$
$977$	−52.9149	−1.69290	−0.846449	+	0.532470i	$0.821264\pi$
$978$	−24.7969	−0.792916
$979$	20.5831	0.657840
$980$	36.7676	1.17450
$981$	13.9756	0.446205
$982$	33.0839	1.05575
$983$	−1.59842	−0.0509818	−0.0254909	−	0.999675i	$-0.508115\pi$
$983$	−1.59842	−0.0509818	−0.0254909	+	0.999675i	$0.508115\pi$
$984$	−0.384298	−0.0122510
$985$	−1.52164	−0.0484835
$986$	17.1403	0.545859
$987$	39.6254	1.26129
$988$	−1.34049	−0.0426466
$989$	8.56284	0.272282
$990$	−5.07506	−0.161296
$991$	−20.4253	−0.648832	−0.324416	−	0.945914i	$-0.605168\pi$
$991$	−20.4253	−0.648832	−0.324416	+	0.945914i	$0.605168\pi$
$992$	−0.324679	−0.0103086
$993$	7.78943	0.247190
$994$	33.9215	1.07593
$995$	14.0379	0.445033
$996$	8.71690	0.276206
$997$	22.6298	0.716693	0.358346	−	0.933589i	$-0.383341\pi$
$997$	22.6298	0.716693	0.358346	+	0.933589i	$0.383341\pi$
$998$	16.7694	0.530826
$999$	−2.46411	−0.0779610

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.w.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.w.1.5	✓	6	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.90230 q^{5} -1.00000 q^{6} -5.13108 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.90230 q^{5} -1.00000 q^{6} -5.13108 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.90230 q^{10} -2.66785 q^{11} -1.00000 q^{12} +1.34049 q^{13} -5.13108 q^{14} -1.90230 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} +1.90230 q^{20} +5.13108 q^{21} -2.66785 q^{22} -6.57015 q^{23} -1.00000 q^{24} -1.38125 q^{25} +1.34049 q^{26} -1.00000 q^{27} -5.13108 q^{28} +8.57015 q^{29} -1.90230 q^{30} -0.324679 q^{31} +1.00000 q^{32} +2.66785 q^{33} +2.00000 q^{34} -9.76085 q^{35} +1.00000 q^{36} +2.46411 q^{37} -1.00000 q^{38} -1.34049 q^{39} +1.90230 q^{40} +0.384298 q^{41} +5.13108 q^{42} -1.30329 q^{43} -2.66785 q^{44} +1.90230 q^{45} -6.57015 q^{46} +7.72263 q^{47} -1.00000 q^{48} +19.3280 q^{49} -1.38125 q^{50} -2.00000 q^{51} +1.34049 q^{52} -1.00000 q^{53} -1.00000 q^{54} -5.07506 q^{55} -5.13108 q^{56} +1.00000 q^{57} +8.57015 q^{58} +10.5970 q^{59} -1.90230 q^{60} -2.77666 q^{61} -0.324679 q^{62} -5.13108 q^{63} +1.00000 q^{64} +2.55001 q^{65} +2.66785 q^{66} +8.25470 q^{67} +2.00000 q^{68} +6.57015 q^{69} -9.76085 q^{70} -6.61100 q^{71} +1.00000 q^{72} +1.37023 q^{73} +2.46411 q^{74} +1.38125 q^{75} -1.00000 q^{76} +13.6890 q^{77} -1.34049 q^{78} +6.63418 q^{79} +1.90230 q^{80} +1.00000 q^{81} +0.384298 q^{82} -8.71690 q^{83} +5.13108 q^{84} +3.80460 q^{85} -1.30329 q^{86} -8.57015 q^{87} -2.66785 q^{88} -7.71524 q^{89} +1.90230 q^{90} -6.87815 q^{91} -6.57015 q^{92} +0.324679 q^{93} +7.72263 q^{94} -1.90230 q^{95} -1.00000 q^{96} +9.71710 q^{97} +19.3280 q^{98} -2.66785 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9} - q^{10} + 2 q^{11} - 6 q^{12} + 6 q^{13} + q^{14} + q^{15} + 6 q^{16} + 12 q^{17} + 6 q^{18} - 6 q^{19} - q^{20} - q^{21} + 2 q^{22} - 9 q^{23} - 6 q^{24} + 11 q^{25} + 6 q^{26} - 6 q^{27} + q^{28} + 21 q^{29} + q^{30} + 5 q^{31} + 6 q^{32} - 2 q^{33} + 12 q^{34} - 17 q^{35} + 6 q^{36} - 8 q^{37} - 6 q^{38} - 6 q^{39} - q^{40} + 16 q^{41} - q^{42} - 5 q^{43} + 2 q^{44} - q^{45} - 9 q^{46} + 16 q^{47} - 6 q^{48} + 11 q^{49} + 11 q^{50} - 12 q^{51} + 6 q^{52} - 6 q^{53} - 6 q^{54} + 22 q^{55} + q^{56} + 6 q^{57} + 21 q^{58} + 9 q^{59} + q^{60} + 20 q^{61} + 5 q^{62} + q^{63} + 6 q^{64} + 22 q^{65} - 2 q^{66} - 3 q^{67} + 12 q^{68} + 9 q^{69} - 17 q^{70} + 10 q^{71} + 6 q^{72} + 18 q^{73} - 8 q^{74} - 11 q^{75} - 6 q^{76} + 16 q^{77} - 6 q^{78} - 14 q^{79} - q^{80} + 6 q^{81} + 16 q^{82} + 2 q^{83} - q^{84} - 2 q^{85} - 5 q^{86} - 21 q^{87} + 2 q^{88} + 11 q^{89} - q^{90} - 44 q^{91} - 9 q^{92} - 5 q^{93} + 16 q^{94} + q^{95} - 6 q^{96} + 11 q^{98} + 2 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9 - q^10 + 2 * q^11 - 6 * q^12 + 6 * q^13 + q^14 + q^15 + 6 * q^16 + 12 * q^17 + 6 * q^18 - 6 * q^19 - q^20 - q^21 + 2 * q^22 - 9 * q^23 - 6 * q^24 + 11 * q^25 + 6 * q^26 - 6 * q^27 + q^28 + 21 * q^29 + q^30 + 5 * q^31 + 6 * q^32 - 2 * q^33 + 12 * q^34 - 17 * q^35 + 6 * q^36 - 8 * q^37 - 6 * q^38 - 6 * q^39 - q^40 + 16 * q^41 - q^42 - 5 * q^43 + 2 * q^44 - q^45 - 9 * q^46 + 16 * q^47 - 6 * q^48 + 11 * q^49 + 11 * q^50 - 12 * q^51 + 6 * q^52 - 6 * q^53 - 6 * q^54 + 22 * q^55 + q^56 + 6 * q^57 + 21 * q^58 + 9 * q^59 + q^60 + 20 * q^61 + 5 * q^62 + q^63 + 6 * q^64 + 22 * q^65 - 2 * q^66 - 3 * q^67 + 12 * q^68 + 9 * q^69 - 17 * q^70 + 10 * q^71 + 6 * q^72 + 18 * q^73 - 8 * q^74 - 11 * q^75 - 6 * q^76 + 16 * q^77 - 6 * q^78 - 14 * q^79 - q^80 + 6 * q^81 + 16 * q^82 + 2 * q^83 - q^84 - 2 * q^85 - 5 * q^86 - 21 * q^87 + 2 * q^88 + 11 * q^89 - q^90 - 44 * q^91 - 9 * q^92 - 5 * q^93 + 16 * q^94 + q^95 - 6 * q^96 + 11 * q^98 + 2 * q^99

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