LMFDB - Embedded newform 6042.2.a.w.1.3

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			1.3
Root			$-2.86940$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.38494 q^{5} -1.00000 q^{6} -1.10454 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.38494 q^{5} -1.00000 q^{6} -1.10454 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.38494 q^{10} -2.20104 q^{11} -1.00000 q^{12} +4.90985 q^{13} -1.10454 q^{14} +2.38494 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} -2.38494 q^{20} +1.10454 q^{21} -2.20104 q^{22} -1.81610 q^{23} -1.00000 q^{24} +0.687928 q^{25} +4.90985 q^{26} -1.00000 q^{27} -1.10454 q^{28} +3.81610 q^{29} +2.38494 q^{30} -9.82881 q^{31} +1.00000 q^{32} +2.20104 q^{33} +2.00000 q^{34} +2.63426 q^{35} +1.00000 q^{36} -9.67973 q^{37} -1.00000 q^{38} -4.90985 q^{39} -2.38494 q^{40} +6.27391 q^{41} +1.10454 q^{42} +11.6132 q^{43} -2.20104 q^{44} -2.38494 q^{45} -1.81610 q^{46} +0.638699 q^{47} -1.00000 q^{48} -5.77999 q^{49} +0.687928 q^{50} -2.00000 q^{51} +4.90985 q^{52} -1.00000 q^{53} -1.00000 q^{54} +5.24935 q^{55} -1.10454 q^{56} +1.00000 q^{57} +3.81610 q^{58} -10.5296 q^{59} +2.38494 q^{60} +15.5532 q^{61} -9.82881 q^{62} -1.10454 q^{63} +1.00000 q^{64} -11.7097 q^{65} +2.20104 q^{66} -11.4850 q^{67} +2.00000 q^{68} +1.81610 q^{69} +2.63426 q^{70} +15.4941 q^{71} +1.00000 q^{72} +9.73880 q^{73} -9.67973 q^{74} -0.687928 q^{75} -1.00000 q^{76} +2.43114 q^{77} -4.90985 q^{78} +1.99348 q^{79} -2.38494 q^{80} +1.00000 q^{81} +6.27391 q^{82} -7.21449 q^{83} +1.10454 q^{84} -4.76988 q^{85} +11.6132 q^{86} -3.81610 q^{87} -2.20104 q^{88} +2.04392 q^{89} -2.38494 q^{90} -5.42313 q^{91} -1.81610 q^{92} +9.82881 q^{93} +0.638699 q^{94} +2.38494 q^{95} -1.00000 q^{96} -6.49864 q^{97} -5.77999 q^{98} -2.20104 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.38494	−1.06658	−0.533288	−	0.845934i	$-0.679044\pi$
$5$	−2.38494	−1.06658	−0.533288	+	0.845934i	$0.679044\pi$
$6$	−1.00000	−0.408248
$7$	−1.10454	−0.417477	−0.208738	−	0.977971i	$-0.566936\pi$
$7$	−1.10454	−0.417477	−0.208738	+	0.977971i	$0.566936\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.38494	−0.754184
$11$	−2.20104	−0.663639	−0.331820	−	0.943343i	$-0.607663\pi$
$11$	−2.20104	−0.663639	−0.331820	+	0.943343i	$0.607663\pi$
$12$	−1.00000	−0.288675
$13$	4.90985	1.36175	0.680874	−	0.732401i	$-0.261600\pi$
$13$	4.90985	1.36175	0.680874	+	0.732401i	$0.261600\pi$
$14$	−1.10454	−0.295201
$15$	2.38494	0.615788
$16$	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
$20$	−2.38494	−0.533288
$21$	1.10454	0.241030
$22$	−2.20104	−0.469264
$23$	−1.81610	−0.378684	−0.189342	−	0.981911i	$-0.560635\pi$
$23$	−1.81610	−0.378684	−0.189342	+	0.981911i	$0.560635\pi$
$24$	−1.00000	−0.204124
$25$	0.687928	0.137586
$26$	4.90985	0.962901
$27$	−1.00000	−0.192450
$28$	−1.10454	−0.208738
$29$	3.81610	0.708633	0.354316	−	0.935126i	$-0.384714\pi$
$29$	3.81610	0.708633	0.354316	+	0.935126i	$0.384714\pi$
$30$	2.38494	0.435428
$31$	−9.82881	−1.76531	−0.882653	−	0.470024i	$-0.844245\pi$
$31$	−9.82881	−1.76531	−0.882653	+	0.470024i	$0.844245\pi$
$32$	1.00000	0.176777
$33$	2.20104	0.383152
$34$	2.00000	0.342997
$35$	2.63426	0.445271
$36$	1.00000	0.166667
$37$	−9.67973	−1.59134	−0.795669	−	0.605732i	$-0.792880\pi$
$37$	−9.67973	−1.59134	−0.795669	+	0.605732i	$0.792880\pi$
$38$	−1.00000	−0.162221
$39$	−4.90985	−0.786206
$40$	−2.38494	−0.377092
$41$	6.27391	0.979820	0.489910	−	0.871773i	$-0.337030\pi$
$41$	6.27391	0.979820	0.489910	+	0.871773i	$0.337030\pi$
$42$	1.10454	0.170434
$43$	11.6132	1.77100	0.885499	−	0.464641i	$-0.153816\pi$
$43$	11.6132	1.77100	0.885499	+	0.464641i	$0.153816\pi$
$44$	−2.20104	−0.331820
$45$	−2.38494	−0.355526
$46$	−1.81610	−0.267770
$47$	0.638699	0.0931638	0.0465819	−	0.998914i	$-0.485167\pi$
$47$	0.638699	0.0931638	0.0465819	+	0.998914i	$0.485167\pi$
$48$	−1.00000	−0.144338
$49$	−5.77999	−0.825713
$50$	0.687928	0.0972877
$51$	−2.00000	−0.280056
$52$	4.90985	0.680874
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.00000	−0.136083
$55$	5.24935	0.707822
$56$	−1.10454	−0.147600
$57$	1.00000	0.132453
$58$	3.81610	0.501079
$59$	−10.5296	−1.37084	−0.685418	−	0.728150i	$-0.740380\pi$
$59$	−10.5296	−1.37084	−0.685418	+	0.728150i	$0.740380\pi$
$60$	2.38494	0.307894
$61$	15.5532	1.99139	0.995693	−	0.0927126i	$-0.0295538\pi$
$61$	15.5532	1.99139	0.995693	+	0.0927126i	$0.0295538\pi$
$62$	−9.82881	−1.24826
$63$	−1.10454	−0.139159
$64$	1.00000	0.125000
$65$	−11.7097	−1.45241
$66$	2.20104	0.270930
$67$	−11.4850	−1.40312	−0.701560	−	0.712610i	$-0.747513\pi$
$67$	−11.4850	−1.40312	−0.701560	+	0.712610i	$0.747513\pi$
$68$	2.00000	0.242536
$69$	1.81610	0.218633
$70$	2.63426	0.314854
$71$	15.4941	1.83882	0.919409	−	0.393304i	$-0.128668\pi$
$71$	15.4941	1.83882	0.919409	+	0.393304i	$0.128668\pi$
$72$	1.00000	0.117851
$73$	9.73880	1.13984	0.569920	−	0.821700i	$-0.306974\pi$
$73$	9.73880	1.13984	0.569920	+	0.821700i	$0.306974\pi$
$74$	−9.67973	−1.12525
$75$	−0.687928	−0.0794351
$76$	−1.00000	−0.114708
$77$	2.43114	0.277054
$78$	−4.90985	−0.555931
$79$	1.99348	0.224284	0.112142	−	0.993692i	$-0.464229\pi$
$79$	1.99348	0.224284	0.112142	+	0.993692i	$0.464229\pi$
$80$	−2.38494	−0.266644
$81$	1.00000	0.111111
$82$	6.27391	0.692837
$83$	−7.21449	−0.791893	−0.395946	−	0.918274i	$-0.629583\pi$
$83$	−7.21449	−0.791893	−0.395946	+	0.918274i	$0.629583\pi$
$84$	1.10454	0.120515
$85$	−4.76988	−0.517366
$86$	11.6132	1.25229
$87$	−3.81610	−0.409129
$88$	−2.20104	−0.234632
$89$	2.04392	0.216655	0.108327	−	0.994115i	$-0.465450\pi$
$89$	2.04392	0.216655	0.108327	+	0.994115i	$0.465450\pi$
$90$	−2.38494	−0.251395
$91$	−5.42313	−0.568498
$92$	−1.81610	−0.189342
$93$	9.82881	1.01920
$94$	0.638699	0.0658768
$95$	2.38494	0.244689
$96$	−1.00000	−0.102062
$97$	−6.49864	−0.659837	−0.329919	−	0.944009i	$-0.607021\pi$
$97$	−6.49864	−0.659837	−0.329919	+	0.944009i	$0.607021\pi$
$98$	−5.77999	−0.583867
$99$	−2.20104	−0.221213
$100$	0.687928	0.0687928
$101$	4.33282	0.431132	0.215566	−	0.976489i	$-0.430840\pi$
$101$	4.33282	0.431132	0.215566	+	0.976489i	$0.430840\pi$
$102$	−2.00000	−0.198030
$103$	−9.82881	−0.968462	−0.484231	−	0.874940i	$-0.660901\pi$
$103$	−9.82881	−0.968462	−0.484231	+	0.874940i	$0.660901\pi$
$104$	4.90985	0.481451
$105$	−2.63426	−0.257077
$106$	−1.00000	−0.0971286
$107$	11.7049	1.13156	0.565778	−	0.824557i	$-0.308576\pi$
$107$	11.7049	1.13156	0.565778	+	0.824557i	$0.308576\pi$
$108$	−1.00000	−0.0962250
$109$	4.32011	0.413792	0.206896	−	0.978363i	$-0.433664\pi$
$109$	4.32011	0.413792	0.206896	+	0.978363i	$0.433664\pi$
$110$	5.24935	0.500506
$111$	9.67973	0.918759
$112$	−1.10454	−0.104369
$113$	15.4084	1.44950	0.724751	−	0.689011i	$-0.241955\pi$
$113$	15.4084	1.44950	0.724751	+	0.689011i	$0.241955\pi$
$114$	1.00000	0.0936586
$115$	4.33130	0.403895
$116$	3.81610	0.354316
$117$	4.90985	0.453916
$118$	−10.5296	−0.969327
$119$	−2.20908	−0.202506
$120$	2.38494	0.217714
$121$	−6.15541	−0.559583
$122$	15.5532	1.40812
$123$	−6.27391	−0.565699
$124$	−9.82881	−0.882653
$125$	10.2840	0.919831
$126$	−1.10454	−0.0984003
$127$	−9.70331	−0.861030	−0.430515	−	0.902583i	$-0.641668\pi$
$127$	−9.70331	−0.861030	−0.430515	+	0.902583i	$0.641668\pi$
$128$	1.00000	0.0883883
$129$	−11.6132	−1.02249
$130$	−11.7097	−1.02701
$131$	10.9318	0.955114	0.477557	−	0.878601i	$-0.341522\pi$
$131$	10.9318	0.955114	0.477557	+	0.878601i	$0.341522\pi$
$132$	2.20104	0.191576
$133$	1.10454	0.0957758
$134$	−11.4850	−0.992156
$135$	2.38494	0.205263
$136$	2.00000	0.171499
$137$	14.4567	1.23512	0.617560	−	0.786523i	$-0.288121\pi$
$137$	14.4567	1.23512	0.617560	+	0.786523i	$0.288121\pi$
$138$	1.81610	0.154597
$139$	11.7871	0.999767	0.499884	−	0.866093i	$-0.333376\pi$
$139$	11.7871	0.999767	0.499884	+	0.866093i	$0.333376\pi$
$140$	2.63426	0.222636
$141$	−0.638699	−0.0537881
$142$	15.4941	1.30024
$143$	−10.8068	−0.903709
$144$	1.00000	0.0833333
$145$	−9.10117	−0.755811
$146$	9.73880	0.805989
$147$	5.77999	0.476726
$148$	−9.67973	−0.795669
$149$	3.06638	0.251207	0.125604	−	0.992081i	$-0.459913\pi$
$149$	3.06638	0.251207	0.125604	+	0.992081i	$0.459913\pi$
$150$	−0.687928	−0.0561691
$151$	−0.247245	−0.0201205	−0.0100602	−	0.999949i	$-0.503202\pi$
$151$	−0.247245	−0.0201205	−0.0100602	+	0.999949i	$0.503202\pi$
$152$	−1.00000	−0.0811107
$153$	2.00000	0.161690
$154$	2.43114	0.195907
$155$	23.4411	1.88283
$156$	−4.90985	−0.393103
$157$	8.60037	0.686384	0.343192	−	0.939265i	$-0.388492\pi$
$157$	8.60037	0.686384	0.343192	+	0.939265i	$0.388492\pi$
$158$	1.99348	0.158593
$159$	1.00000	0.0793052
$160$	−2.38494	−0.188546
$161$	2.00596	0.158092
$162$	1.00000	0.0785674
$163$	−7.95195	−0.622845	−0.311422	−	0.950272i	$-0.600805\pi$
$163$	−7.95195	−0.622845	−0.311422	+	0.950272i	$0.600805\pi$
$164$	6.27391	0.489910
$165$	−5.24935	−0.408661
$166$	−7.21449	−0.559953
$167$	14.9307	1.15537	0.577685	−	0.816260i	$-0.303956\pi$
$167$	14.9307	1.15537	0.577685	+	0.816260i	$0.303956\pi$
$168$	1.10454	0.0852171
$169$	11.1066	0.854357
$170$	−4.76988	−0.365833
$171$	−1.00000	−0.0764719
$172$	11.6132	0.885499
$173$	16.2348	1.23431	0.617153	−	0.786843i	$-0.288286\pi$
$173$	16.2348	1.23431	0.617153	+	0.786843i	$0.288286\pi$
$174$	−3.81610	−0.289298
$175$	−0.759844	−0.0574388
$176$	−2.20104	−0.165910
$177$	10.5296	0.791452
$178$	2.04392	0.153198
$179$	0.967918	0.0723456	0.0361728	−	0.999346i	$-0.488483\pi$
$179$	0.967918	0.0723456	0.0361728	+	0.999346i	$0.488483\pi$
$180$	−2.38494	−0.177763
$181$	−4.67450	−0.347453	−0.173726	−	0.984794i	$-0.555581\pi$
$181$	−4.67450	−0.347453	−0.173726	+	0.984794i	$0.555581\pi$
$182$	−5.42313	−0.401989
$183$	−15.5532	−1.14973
$184$	−1.81610	−0.133885
$185$	23.0855	1.69728
$186$	9.82881	0.720684
$187$	−4.40208	−0.321912
$188$	0.638699	0.0465819
$189$	1.10454	0.0803435
$190$	2.38494	0.173022
$191$	−7.06153	−0.510954	−0.255477	−	0.966815i	$-0.582233\pi$
$191$	−7.06153	−0.510954	−0.255477	+	0.966815i	$0.582233\pi$
$192$	−1.00000	−0.0721688
$193$	8.41280	0.605567	0.302783	−	0.953059i	$-0.402084\pi$
$193$	8.41280	0.605567	0.302783	+	0.953059i	$0.402084\pi$
$194$	−6.49864	−0.466575
$195$	11.7097	0.838548
$196$	−5.77999	−0.412856
$197$	23.9901	1.70922	0.854612	−	0.519266i	$-0.173795\pi$
$197$	23.9901	1.70922	0.854612	+	0.519266i	$0.173795\pi$
$198$	−2.20104	−0.156421
$199$	10.2665	0.727771	0.363885	−	0.931444i	$-0.381450\pi$
$199$	10.2665	0.727771	0.363885	+	0.931444i	$0.381450\pi$
$200$	0.687928	0.0486438
$201$	11.4850	0.810092
$202$	4.33282	0.304856
$203$	−4.21504	−0.295838
$204$	−2.00000	−0.140028
$205$	−14.9629	−1.04505
$206$	−9.82881	−0.684806
$207$	−1.81610	−0.126228
$208$	4.90985	0.340437
$209$	2.20104	0.152249
$210$	−2.63426	−0.181781
$211$	20.0361	1.37934	0.689672	−	0.724122i	$-0.257755\pi$
$211$	20.0361	1.37934	0.689672	+	0.724122i	$0.257755\pi$
$212$	−1.00000	−0.0686803
$213$	−15.4941	−1.06164
$214$	11.7049	0.800131
$215$	−27.6968	−1.88891
$216$	−1.00000	−0.0680414
$217$	10.8563	0.736975
$218$	4.32011	0.292595
$219$	−9.73880	−0.658087
$220$	5.24935	0.353911
$221$	9.81970	0.660545
$222$	9.67973	0.649661
$223$	23.9744	1.60544	0.802722	−	0.596354i	$-0.203384\pi$
$223$	23.9744	1.60544	0.802722	+	0.596354i	$0.203384\pi$
$224$	−1.10454	−0.0738002
$225$	0.687928	0.0458619
$226$	15.4084	1.02495
$227$	6.38118	0.423534	0.211767	−	0.977320i	$-0.432078\pi$
$227$	6.38118	0.423534	0.211767	+	0.977320i	$0.432078\pi$
$228$	1.00000	0.0662266
$229$	−18.9043	−1.24923	−0.624617	−	0.780932i	$-0.714745\pi$
$229$	−18.9043	−1.24923	−0.624617	+	0.780932i	$0.714745\pi$
$230$	4.33130	0.285597
$231$	−2.43114	−0.159957
$232$	3.81610	0.250540
$233$	−9.37829	−0.614392	−0.307196	−	0.951646i	$-0.599391\pi$
$233$	−9.37829	−0.614392	−0.307196	+	0.951646i	$0.599391\pi$
$234$	4.90985	0.320967
$235$	−1.52326	−0.0993663
$236$	−10.5296	−0.685418
$237$	−1.99348	−0.129491
$238$	−2.20908	−0.143193
$239$	−5.66751	−0.366601	−0.183300	−	0.983057i	$-0.558678\pi$
$239$	−5.66751	−0.366601	−0.183300	+	0.983057i	$0.558678\pi$
$240$	2.38494	0.153947
$241$	6.88465	0.443479	0.221740	−	0.975106i	$-0.428826\pi$
$241$	6.88465	0.443479	0.221740	+	0.975106i	$0.428826\pi$
$242$	−6.15541	−0.395685
$243$	−1.00000	−0.0641500
$244$	15.5532	0.995693
$245$	13.7849	0.880686
$246$	−6.27391	−0.400010
$247$	−4.90985	−0.312406
$248$	−9.82881	−0.624130
$249$	7.21449	0.457199
$250$	10.2840	0.650419
$251$	24.7618	1.56295	0.781474	−	0.623938i	$-0.214468\pi$
$251$	24.7618	1.56295	0.781474	+	0.623938i	$0.214468\pi$
$252$	−1.10454	−0.0695795
$253$	3.99732	0.251310
$254$	−9.70331	−0.608840
$255$	4.76988	0.298701
$256$	1.00000	0.0625000
$257$	15.5033	0.967068	0.483534	−	0.875325i	$-0.339353\pi$
$257$	15.5033	0.967068	0.483534	+	0.875325i	$0.339353\pi$
$258$	−11.6132	−0.723007
$259$	10.6916	0.664347
$260$	−11.7097	−0.726204
$261$	3.81610	0.236211
$262$	10.9318	0.675367
$263$	5.18444	0.319686	0.159843	−	0.987142i	$-0.448901\pi$
$263$	5.18444	0.319686	0.159843	+	0.987142i	$0.448901\pi$
$264$	2.20104	0.135465
$265$	2.38494	0.146506
$266$	1.10454	0.0677237
$267$	−2.04392	−0.125086
$268$	−11.4850	−0.701560
$269$	−27.0908	−1.65176	−0.825878	−	0.563849i	$-0.809320\pi$
$269$	−27.0908	−1.65176	−0.825878	+	0.563849i	$0.809320\pi$
$270$	2.38494	0.145143
$271$	10.9343	0.664210	0.332105	−	0.943242i	$-0.392241\pi$
$271$	10.9343	0.664210	0.332105	+	0.943242i	$0.392241\pi$
$272$	2.00000	0.121268
$273$	5.42313	0.328223
$274$	14.4567	0.873362
$275$	−1.51416	−0.0913072
$276$	1.81610	0.109317
$277$	22.7961	1.36968	0.684841	−	0.728692i	$-0.259872\pi$
$277$	22.7961	1.36968	0.684841	+	0.728692i	$0.259872\pi$
$278$	11.7871	0.706942
$279$	−9.82881	−0.588436
$280$	2.63426	0.157427
$281$	26.9734	1.60910	0.804550	−	0.593885i	$-0.202407\pi$
$281$	26.9734	1.60910	0.804550	+	0.593885i	$0.202407\pi$
$282$	−0.638699	−0.0380340
$283$	−20.7879	−1.23571	−0.617857	−	0.786290i	$-0.711999\pi$
$283$	−20.7879	−1.23571	−0.617857	+	0.786290i	$0.711999\pi$
$284$	15.4941	0.919409
$285$	−2.38494	−0.141272
$286$	−10.8068	−0.639019
$287$	−6.92978	−0.409052
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	−9.10117	−0.534439
$291$	6.49864	0.380957
$292$	9.73880	0.569920
$293$	−20.6303	−1.20524	−0.602619	−	0.798029i	$-0.705876\pi$
$293$	−20.6303	−1.20524	−0.602619	+	0.798029i	$0.705876\pi$
$294$	5.77999	0.337096
$295$	25.1124	1.46210
$296$	−9.67973	−0.562623
$297$	2.20104	0.127717
$298$	3.06638	0.177630
$299$	−8.91680	−0.515672
$300$	−0.687928	−0.0397175
$301$	−12.8273	−0.739351
$302$	−0.247245	−0.0142273
$303$	−4.33282	−0.248914
$304$	−1.00000	−0.0573539
$305$	−37.0935	−2.12397
$306$	2.00000	0.114332
$307$	−8.09371	−0.461932	−0.230966	−	0.972962i	$-0.574189\pi$
$307$	−8.09371	−0.461932	−0.230966	+	0.972962i	$0.574189\pi$
$308$	2.43114	0.138527
$309$	9.82881	0.559142
$310$	23.4411	1.33137
$311$	21.3215	1.20903	0.604515	−	0.796594i	$-0.293367\pi$
$311$	21.3215	1.20903	0.604515	+	0.796594i	$0.293367\pi$
$312$	−4.90985	−0.277966
$313$	32.4174	1.83234	0.916170	−	0.400789i	$-0.131264\pi$
$313$	32.4174	1.83234	0.916170	+	0.400789i	$0.131264\pi$
$314$	8.60037	0.485347
$315$	2.63426	0.148424
$316$	1.99348	0.112142
$317$	−16.3399	−0.917742	−0.458871	−	0.888503i	$-0.651746\pi$
$317$	−16.3399	−0.917742	−0.458871	+	0.888503i	$0.651746\pi$
$318$	1.00000	0.0560772
$319$	−8.39941	−0.470277
$320$	−2.38494	−0.133322
$321$	−11.7049	−0.653305
$322$	2.00596	0.111788
$323$	−2.00000	−0.111283
$324$	1.00000	0.0555556
$325$	3.37762	0.187357
$326$	−7.95195	−0.440418
$327$	−4.32011	−0.238903
$328$	6.27391	0.346419
$329$	−0.705469	−0.0388937
$330$	−5.24935	−0.288967
$331$	−35.2035	−1.93496	−0.967480	−	0.252947i	$-0.918600\pi$
$331$	−35.2035	−1.93496	−0.967480	+	0.252947i	$0.918600\pi$
$332$	−7.21449	−0.395946
$333$	−9.67973	−0.530446
$334$	14.9307	0.816970
$335$	27.3911	1.49654
$336$	1.10454	0.0602576
$337$	13.5619	0.738766	0.369383	−	0.929277i	$-0.379569\pi$
$337$	13.5619	0.738766	0.369383	+	0.929277i	$0.379569\pi$
$338$	11.1066	0.604122
$339$	−15.4084	−0.836870
$340$	−4.76988	−0.258683
$341$	21.6336	1.17153
$342$	−1.00000	−0.0540738
$343$	14.1160	0.762193
$344$	11.6132	0.626143
$345$	−4.33130	−0.233189
$346$	16.2348	0.872787
$347$	−31.0538	−1.66705	−0.833526	−	0.552480i	$-0.813682\pi$
$347$	−31.0538	−1.66705	−0.833526	+	0.552480i	$0.813682\pi$
$348$	−3.81610	−0.204565
$349$	−11.7266	−0.627710	−0.313855	−	0.949471i	$-0.601621\pi$
$349$	−11.7266	−0.627710	−0.313855	+	0.949471i	$0.601621\pi$
$350$	−0.759844	−0.0406154
$351$	−4.90985	−0.262069
$352$	−2.20104	−0.117316
$353$	1.57908	0.0840462	0.0420231	−	0.999117i	$-0.486620\pi$
$353$	1.57908	0.0840462	0.0420231	+	0.999117i	$0.486620\pi$
$354$	10.5296	0.559641
$355$	−36.9526	−1.96124
$356$	2.04392	0.108327
$357$	2.20908	0.116917
$358$	0.967918	0.0511561
$359$	2.53561	0.133824	0.0669122	−	0.997759i	$-0.478685\pi$
$359$	2.53561	0.133824	0.0669122	+	0.997759i	$0.478685\pi$
$360$	−2.38494	−0.125697
$361$	1.00000	0.0526316
$362$	−4.67450	−0.245686
$363$	6.15541	0.323075
$364$	−5.42313	−0.284249
$365$	−23.2264	−1.21573
$366$	−15.5532	−0.812980
$367$	−18.9574	−0.989567	−0.494783	−	0.869016i	$-0.664753\pi$
$367$	−18.9574	−0.989567	−0.494783	+	0.869016i	$0.664753\pi$
$368$	−1.81610	−0.0946710
$369$	6.27391	0.326607
$370$	23.0855	1.20016
$371$	1.10454	0.0573449
$372$	9.82881	0.509600
$373$	−3.41264	−0.176700	−0.0883500	−	0.996089i	$-0.528159\pi$
$373$	−3.41264	−0.176700	−0.0883500	+	0.996089i	$0.528159\pi$
$374$	−4.40208	−0.227626
$375$	−10.2840	−0.531065
$376$	0.638699	0.0329384
$377$	18.7365	0.964979
$378$	1.10454	0.0568114
$379$	16.1697	0.830583	0.415291	−	0.909688i	$-0.363680\pi$
$379$	16.1697	0.830583	0.415291	+	0.909688i	$0.363680\pi$
$380$	2.38494	0.122345
$381$	9.70331	0.497116
$382$	−7.06153	−0.361299
$383$	15.7323	0.803882	0.401941	−	0.915666i	$-0.368336\pi$
$383$	15.7323	0.803882	0.401941	+	0.915666i	$0.368336\pi$
$384$	−1.00000	−0.0510310
$385$	−5.79812	−0.295499
$386$	8.41280	0.428200
$387$	11.6132	0.590333
$388$	−6.49864	−0.329919
$389$	32.4421	1.64488	0.822440	−	0.568853i	$-0.192613\pi$
$389$	32.4421	1.64488	0.822440	+	0.568853i	$0.192613\pi$
$390$	11.7097	0.592943
$391$	−3.63221	−0.183689
$392$	−5.77999	−0.291934
$393$	−10.9318	−0.551435
$394$	23.9901	1.20860
$395$	−4.75433	−0.239216
$396$	−2.20104	−0.110607
$397$	−31.1556	−1.56366	−0.781828	−	0.623494i	$-0.785713\pi$
$397$	−31.1556	−1.56366	−0.781828	+	0.623494i	$0.785713\pi$
$398$	10.2665	0.514612
$399$	−1.10454	−0.0552962
$400$	0.687928	0.0343964
$401$	−16.9656	−0.847219	−0.423610	−	0.905845i	$-0.639237\pi$
$401$	−16.9656	−0.847219	−0.423610	+	0.905845i	$0.639237\pi$
$402$	11.4850	0.572822
$403$	−48.2580	−2.40390
$404$	4.33282	0.215566
$405$	−2.38494	−0.118509
$406$	−4.21504	−0.209189
$407$	21.3055	1.05607
$408$	−2.00000	−0.0990148
$409$	35.0516	1.73319	0.866596	−	0.499010i	$-0.166303\pi$
$409$	35.0516	1.73319	0.866596	+	0.499010i	$0.166303\pi$
$410$	−14.9629	−0.738964
$411$	−14.4567	−0.713097
$412$	−9.82881	−0.484231
$413$	11.6303	0.572292
$414$	−1.81610	−0.0892567
$415$	17.2061	0.844614
$416$	4.90985	0.240725
$417$	−11.7871	−0.577216
$418$	2.20104	0.107657
$419$	4.13897	0.202202	0.101101	−	0.994876i	$-0.467763\pi$
$419$	4.13897	0.202202	0.101101	+	0.994876i	$0.467763\pi$
$420$	−2.63426	−0.128539
$421$	31.8131	1.55048	0.775238	−	0.631670i	$-0.217630\pi$
$421$	31.8131	1.55048	0.775238	+	0.631670i	$0.217630\pi$
$422$	20.0361	0.975344
$423$	0.638699	0.0310546
$424$	−1.00000	−0.0485643
$425$	1.37586	0.0667388
$426$	−15.4941	−0.750694
$427$	−17.1792	−0.831358
$428$	11.7049	0.565778
$429$	10.8068	0.521757
$430$	−27.6968	−1.33566
$431$	13.8338	0.666351	0.333175	−	0.942865i	$-0.391880\pi$
$431$	13.8338	0.666351	0.333175	+	0.942865i	$0.391880\pi$
$432$	−1.00000	−0.0481125
$433$	−31.6994	−1.52338	−0.761688	−	0.647944i	$-0.775629\pi$
$433$	−31.6994	−1.52338	−0.761688	+	0.647944i	$0.775629\pi$
$434$	10.8563	0.521120
$435$	9.10117	0.436368
$436$	4.32011	0.206896
$437$	1.81610	0.0868761
$438$	−9.73880	−0.465338
$439$	3.80287	0.181501	0.0907505	−	0.995874i	$-0.471073\pi$
$439$	3.80287	0.181501	0.0907505	+	0.995874i	$0.471073\pi$
$440$	5.24935	0.250253
$441$	−5.77999	−0.275238
$442$	9.81970	0.467076
$443$	−30.5420	−1.45109	−0.725546	−	0.688173i	$-0.758413\pi$
$443$	−30.5420	−1.45109	−0.725546	+	0.688173i	$0.758413\pi$
$444$	9.67973	0.459380
$445$	−4.87462	−0.231079
$446$	23.9744	1.13522
$447$	−3.06638	−0.145035
$448$	−1.10454	−0.0521846
$449$	−33.1525	−1.56456	−0.782281	−	0.622926i	$-0.785944\pi$
$449$	−33.1525	−1.56456	−0.782281	+	0.622926i	$0.785944\pi$
$450$	0.687928	0.0324292
$451$	−13.8091	−0.650247
$452$	15.4084	0.724751
$453$	0.247245	0.0116166
$454$	6.38118	0.299483
$455$	12.9338	0.606347
$456$	1.00000	0.0468293
$457$	−40.6235	−1.90029	−0.950145	−	0.311809i	$-0.899065\pi$
$457$	−40.6235	−1.90029	−0.950145	+	0.311809i	$0.899065\pi$
$458$	−18.9043	−0.883341
$459$	−2.00000	−0.0933520
$460$	4.33130	0.201948
$461$	−4.37693	−0.203854	−0.101927	−	0.994792i	$-0.532501\pi$
$461$	−4.37693	−0.203854	−0.101927	+	0.994792i	$0.532501\pi$
$462$	−2.43114	−0.113107
$463$	22.6231	1.05139	0.525693	−	0.850675i	$-0.323806\pi$
$463$	22.6231	1.05139	0.525693	+	0.850675i	$0.323806\pi$
$464$	3.81610	0.177158
$465$	−23.4411	−1.08706
$466$	−9.37829	−0.434441
$467$	13.5769	0.628264	0.314132	−	0.949379i	$-0.398287\pi$
$467$	13.5769	0.628264	0.314132	+	0.949379i	$0.398287\pi$
$468$	4.90985	0.226958
$469$	12.6857	0.585771
$470$	−1.52326	−0.0702626
$471$	−8.60037	−0.396284
$472$	−10.5296	−0.484663
$473$	−25.5612	−1.17530
$474$	−1.99348	−0.0915637
$475$	−0.687928	−0.0315643
$476$	−2.20908	−0.101253
$477$	−1.00000	−0.0457869
$478$	−5.66751	−0.259226
$479$	−11.3301	−0.517686	−0.258843	−	0.965919i	$-0.583341\pi$
$479$	−11.3301	−0.517686	−0.258843	+	0.965919i	$0.583341\pi$
$480$	2.38494	0.108857
$481$	−47.5260	−2.16700
$482$	6.88465	0.313587
$483$	−2.00596	−0.0912744
$484$	−6.15541	−0.279791
$485$	15.4989	0.703767
$486$	−1.00000	−0.0453609
$487$	1.03793	0.0470333	0.0235166	−	0.999723i	$-0.492514\pi$
$487$	1.03793	0.0470333	0.0235166	+	0.999723i	$0.492514\pi$
$488$	15.5532	0.704061
$489$	7.95195	0.359600
$490$	13.7849	0.622739
$491$	−34.6228	−1.56250	−0.781252	−	0.624216i	$-0.785419\pi$
$491$	−34.6228	−1.56250	−0.781252	+	0.624216i	$0.785419\pi$
$492$	−6.27391	−0.282850
$493$	7.63221	0.343737
$494$	−4.90985	−0.220905
$495$	5.24935	0.235941
$496$	−9.82881	−0.441327
$497$	−17.1139	−0.767664
$498$	7.21449	0.323289
$499$	42.1889	1.88863	0.944317	−	0.329037i	$-0.106724\pi$
$499$	42.1889	1.88863	0.944317	+	0.329037i	$0.106724\pi$
$500$	10.2840	0.459916
$501$	−14.9307	−0.667053
$502$	24.7618	1.10517
$503$	−2.16149	−0.0963763	−0.0481881	−	0.998838i	$-0.515345\pi$
$503$	−2.16149	−0.0963763	−0.0481881	+	0.998838i	$0.515345\pi$
$504$	−1.10454	−0.0492001
$505$	−10.3335	−0.459835
$506$	3.99732	0.177703
$507$	−11.1066	−0.493263
$508$	−9.70331	−0.430515
$509$	−3.03075	−0.134336	−0.0671678	−	0.997742i	$-0.521396\pi$
$509$	−3.03075	−0.134336	−0.0671678	+	0.997742i	$0.521396\pi$
$510$	4.76988	0.211214
$511$	−10.7569	−0.475857
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	15.5033	0.683821
$515$	23.4411	1.03294
$516$	−11.6132	−0.511243
$517$	−1.40580	−0.0618272
$518$	10.6916	0.469764
$519$	−16.2348	−0.712627
$520$	−11.7097	−0.513504
$521$	6.31390	0.276617	0.138309	−	0.990389i	$-0.455833\pi$
$521$	6.31390	0.276617	0.138309	+	0.990389i	$0.455833\pi$
$522$	3.81610	0.167026
$523$	13.8333	0.604886	0.302443	−	0.953167i	$-0.402198\pi$
$523$	13.8333	0.604886	0.302443	+	0.953167i	$0.402198\pi$
$524$	10.9318	0.477557
$525$	0.759844	0.0331623
$526$	5.18444	0.226052
$527$	−19.6576	−0.856300
$528$	2.20104	0.0957881
$529$	−19.7018	−0.856598
$530$	2.38494	0.103595
$531$	−10.5296	−0.456945
$532$	1.10454	0.0478879
$533$	30.8040	1.33427
$534$	−2.04392	−0.0884490
$535$	−27.9155	−1.20689
$536$	−11.4850	−0.496078
$537$	−0.967918	−0.0417687
$538$	−27.0908	−1.16797
$539$	12.7220	0.547976
$540$	2.38494	0.102631
$541$	−10.3589	−0.445365	−0.222683	−	0.974891i	$-0.571481\pi$
$541$	−10.3589	−0.445365	−0.222683	+	0.974891i	$0.571481\pi$
$542$	10.9343	0.469667
$543$	4.67450	0.200602
$544$	2.00000	0.0857493
$545$	−10.3032	−0.441340
$546$	5.42313	0.232088
$547$	3.43593	0.146910	0.0734549	−	0.997299i	$-0.476597\pi$
$547$	3.43593	0.146910	0.0734549	+	0.997299i	$0.476597\pi$
$548$	14.4567	0.617560
$549$	15.5532	0.663795
$550$	−1.51416	−0.0645639
$551$	−3.81610	−0.162572
$552$	1.81610	0.0772985
$553$	−2.20188	−0.0936336
$554$	22.7961	0.968511
$555$	−23.0855	−0.979927
$556$	11.7871	0.499884
$557$	−25.4027	−1.07635	−0.538174	−	0.842834i	$-0.680886\pi$
$557$	−25.4027	−1.07635	−0.538174	+	0.842834i	$0.680886\pi$
$558$	−9.82881	−0.416087
$559$	57.0192	2.41165
$560$	2.63426	0.111318
$561$	4.40208	0.185856
$562$	26.9734	1.13781
$563$	46.6745	1.96710	0.983548	−	0.180647i	$-0.0578193\pi$
$563$	46.6745	1.96710	0.983548	+	0.180647i	$0.0578193\pi$
$564$	−0.638699	−0.0268941
$565$	−36.7481	−1.54600
$566$	−20.7879	−0.873782
$567$	−1.10454	−0.0463863
$568$	15.4941	0.650120
$569$	7.83458	0.328443	0.164221	−	0.986424i	$-0.447489\pi$
$569$	7.83458	0.328443	0.164221	+	0.986424i	$0.447489\pi$
$570$	−2.38494	−0.0998940
$571$	7.84918	0.328478	0.164239	−	0.986421i	$-0.447483\pi$
$571$	7.84918	0.328478	0.164239	+	0.986421i	$0.447483\pi$
$572$	−10.8068	−0.451855
$573$	7.06153	0.295000
$574$	−6.92978	−0.289244
$575$	−1.24935	−0.0521015
$576$	1.00000	0.0416667
$577$	16.2202	0.675254	0.337627	−	0.941280i	$-0.390376\pi$
$577$	16.2202	0.675254	0.337627	+	0.941280i	$0.390376\pi$
$578$	−13.0000	−0.540729
$579$	−8.41280	−0.349624
$580$	−9.10117	−0.377906
$581$	7.96869	0.330597
$582$	6.49864	0.269377
$583$	2.20104	0.0911579
$584$	9.73880	0.402994
$585$	−11.7097	−0.484136
$586$	−20.6303	−0.852231
$587$	30.7439	1.26893	0.634467	−	0.772950i	$-0.281220\pi$
$587$	30.7439	1.26893	0.634467	+	0.772950i	$0.281220\pi$
$588$	5.77999	0.238363
$589$	9.82881	0.404989
$590$	25.1124	1.03386
$591$	−23.9901	−0.986821
$592$	−9.67973	−0.397834
$593$	8.93315	0.366841	0.183420	−	0.983035i	$-0.441283\pi$
$593$	8.93315	0.366841	0.183420	+	0.983035i	$0.441283\pi$
$594$	2.20104	0.0903099
$595$	5.26852	0.215988
$596$	3.06638	0.125604
$597$	−10.2665	−0.420179
$598$	−8.91680	−0.364635
$599$	−7.58452	−0.309895	−0.154947	−	0.987923i	$-0.549521\pi$
$599$	−7.58452	−0.309895	−0.154947	+	0.987923i	$0.549521\pi$
$600$	−0.687928	−0.0280845
$601$	−12.4881	−0.509401	−0.254700	−	0.967020i	$-0.581977\pi$
$601$	−12.4881	−0.509401	−0.254700	+	0.967020i	$0.581977\pi$
$602$	−12.8273	−0.522800
$603$	−11.4850	−0.467707
$604$	−0.247245	−0.0100602
$605$	14.6803	0.596838
$606$	−4.33282	−0.176009
$607$	32.3016	1.31108	0.655540	−	0.755161i	$-0.272441\pi$
$607$	32.3016	1.31108	0.655540	+	0.755161i	$0.272441\pi$
$608$	−1.00000	−0.0405554
$609$	4.21504	0.170802
$610$	−37.0935	−1.50187
$611$	3.13592	0.126866
$612$	2.00000	0.0808452
$613$	20.1092	0.812204	0.406102	−	0.913828i	$-0.366888\pi$
$613$	20.1092	0.812204	0.406102	+	0.913828i	$0.366888\pi$
$614$	−8.09371	−0.326635
$615$	14.9629	0.603362
$616$	2.43114	0.0979534
$617$	3.12388	0.125763	0.0628813	−	0.998021i	$-0.479971\pi$
$617$	3.12388	0.125763	0.0628813	+	0.998021i	$0.479971\pi$
$618$	9.82881	0.395373
$619$	−9.59566	−0.385682	−0.192841	−	0.981230i	$-0.561770\pi$
$619$	−9.59566	−0.385682	−0.192841	+	0.981230i	$0.561770\pi$
$620$	23.4411	0.941417
$621$	1.81610	0.0728778
$622$	21.3215	0.854913
$623$	−2.25759	−0.0904485
$624$	−4.90985	−0.196551
$625$	−27.9664	−1.11866
$626$	32.4174	1.29566
$627$	−2.20104	−0.0879012
$628$	8.60037	0.343192
$629$	−19.3595	−0.771912
$630$	2.63426	0.104951
$631$	23.9764	0.954484	0.477242	−	0.878772i	$-0.341636\pi$
$631$	23.9764	0.954484	0.477242	+	0.878772i	$0.341636\pi$
$632$	1.99348	0.0792965
$633$	−20.0361	−0.796365
$634$	−16.3399	−0.648942
$635$	23.1418	0.918354
$636$	1.00000	0.0396526
$637$	−28.3789	−1.12441
$638$	−8.39941	−0.332536
$639$	15.4941	0.612939
$640$	−2.38494	−0.0942729
$641$	10.0976	0.398831	0.199415	−	0.979915i	$-0.436096\pi$
$641$	10.0976	0.398831	0.199415	+	0.979915i	$0.436096\pi$
$642$	−11.7049	−0.461956
$643$	−16.8719	−0.665361	−0.332681	−	0.943040i	$-0.607953\pi$
$643$	−16.8719	−0.665361	−0.332681	+	0.943040i	$0.607953\pi$
$644$	2.00596	0.0790459
$645$	27.6968	1.09056
$646$	−2.00000	−0.0786889
$647$	−33.8495	−1.33076	−0.665380	−	0.746505i	$-0.731731\pi$
$647$	−33.8495	−1.33076	−0.665380	+	0.746505i	$0.731731\pi$
$648$	1.00000	0.0392837
$649$	23.1761	0.909740
$650$	3.37762	0.132481
$651$	−10.8563	−0.425493
$652$	−7.95195	−0.311422
$653$	12.4913	0.488824	0.244412	−	0.969671i	$-0.421405\pi$
$653$	12.4913	0.488824	0.244412	+	0.969671i	$0.421405\pi$
$654$	−4.32011	−0.168930
$655$	−26.0716	−1.01870
$656$	6.27391	0.244955
$657$	9.73880	0.379947
$658$	−0.705469	−0.0275020
$659$	−12.2272	−0.476302	−0.238151	−	0.971228i	$-0.576541\pi$
$659$	−12.2272	−0.476302	−0.238151	+	0.971228i	$0.576541\pi$
$660$	−5.24935	−0.204331
$661$	−0.582572	−0.0226594	−0.0113297	−	0.999936i	$-0.503606\pi$
$661$	−0.582572	−0.0226594	−0.0113297	+	0.999936i	$0.503606\pi$
$662$	−35.2035	−1.36822
$663$	−9.81970	−0.381366
$664$	−7.21449	−0.279976
$665$	−2.63426	−0.102152
$666$	−9.67973	−0.375082
$667$	−6.93045	−0.268348
$668$	14.9307	0.577685
$669$	−23.9744	−0.926903
$670$	27.3911	1.05821
$671$	−34.2333	−1.32156
$672$	1.10454	0.0426086
$673$	−15.0244	−0.579149	−0.289574	−	0.957156i	$-0.593514\pi$
$673$	−15.0244	−0.579149	−0.289574	+	0.957156i	$0.593514\pi$
$674$	13.5619	0.522386
$675$	−0.687928	−0.0264784
$676$	11.1066	0.427179
$677$	18.5869	0.714353	0.357176	−	0.934037i	$-0.383740\pi$
$677$	18.5869	0.714353	0.357176	+	0.934037i	$0.383740\pi$
$678$	−15.4084	−0.591756
$679$	7.17801	0.275467
$680$	−4.76988	−0.182916
$681$	−6.38118	−0.244527
$682$	21.6336	0.828395
$683$	−47.2626	−1.80845	−0.904227	−	0.427051i	$-0.859552\pi$
$683$	−47.2626	−1.80845	−0.904227	+	0.427051i	$0.859552\pi$
$684$	−1.00000	−0.0382360
$685$	−34.4784	−1.31735
$686$	14.1160	0.538952
$687$	18.9043	0.721245
$688$	11.6132	0.442750
$689$	−4.90985	−0.187050
$690$	−4.33130	−0.164890
$691$	2.36784	0.0900771	0.0450385	−	0.998985i	$-0.485659\pi$
$691$	2.36784	0.0900771	0.0450385	+	0.998985i	$0.485659\pi$
$692$	16.2348	0.617153
$693$	2.43114	0.0923514
$694$	−31.0538	−1.17878
$695$	−28.1115	−1.06633
$696$	−3.81610	−0.144649
$697$	12.5478	0.475282
$698$	−11.7266	−0.443858
$699$	9.37829	0.354719
$700$	−0.759844	−0.0287194
$701$	20.5316	0.775468	0.387734	−	0.921771i	$-0.373258\pi$
$701$	20.5316	0.775468	0.387734	+	0.921771i	$0.373258\pi$
$702$	−4.90985	−0.185310
$703$	9.67973	0.365078
$704$	−2.20104	−0.0829549
$705$	1.52326	0.0573692
$706$	1.57908	0.0594296
$707$	−4.78577	−0.179987
$708$	10.5296	0.395726
$709$	0.376178	0.0141277	0.00706384	−	0.999975i	$-0.497751\pi$
$709$	0.376178	0.0141277	0.00706384	+	0.999975i	$0.497751\pi$
$710$	−36.9526	−1.38681
$711$	1.99348	0.0747615
$712$	2.04392	0.0765991
$713$	17.8502	0.668493
$714$	2.20908	0.0826728
$715$	25.7735	0.963875
$716$	0.967918	0.0361728
$717$	5.66751	0.211657
$718$	2.53561	0.0946281
$719$	0.114221	0.00425974	0.00212987	−	0.999998i	$-0.499322\pi$
$719$	0.114221	0.00425974	0.00212987	+	0.999998i	$0.499322\pi$
$720$	−2.38494	−0.0888814
$721$	10.8563	0.404310
$722$	1.00000	0.0372161
$723$	−6.88465	−0.256043
$724$	−4.67450	−0.173726
$725$	2.62520	0.0974977
$726$	6.15541	0.228449
$727$	21.8349	0.809812	0.404906	−	0.914358i	$-0.367304\pi$
$727$	21.8349	0.809812	0.404906	+	0.914358i	$0.367304\pi$
$728$	−5.42313	−0.200995
$729$	1.00000	0.0370370
$730$	−23.2264	−0.859649
$731$	23.2264	0.859061
$732$	−15.5532	−0.574864
$733$	43.1688	1.59448	0.797238	−	0.603665i	$-0.206293\pi$
$733$	43.1688	1.59448	0.797238	+	0.603665i	$0.206293\pi$
$734$	−18.9574	−0.699729
$735$	−13.7849	−0.508464
$736$	−1.81610	−0.0669425
$737$	25.2791	0.931166
$738$	6.27391	0.230946
$739$	3.59241	0.132149	0.0660744	−	0.997815i	$-0.478953\pi$
$739$	3.59241	0.132149	0.0660744	+	0.997815i	$0.478953\pi$
$740$	23.0855	0.848642
$741$	4.90985	0.180368
$742$	1.10454	0.0405489
$743$	−29.4243	−1.07947	−0.539736	−	0.841834i	$-0.681476\pi$
$743$	−29.4243	−1.07947	−0.539736	+	0.841834i	$0.681476\pi$
$744$	9.82881	0.360342
$745$	−7.31312	−0.267932
$746$	−3.41264	−0.124946
$747$	−7.21449	−0.263964
$748$	−4.40208	−0.160956
$749$	−12.9285	−0.472399
$750$	−10.2840	−0.375519
$751$	38.7191	1.41288	0.706440	−	0.707773i	$-0.250300\pi$
$751$	38.7191	1.41288	0.706440	+	0.707773i	$0.250300\pi$
$752$	0.638699	0.0232910
$753$	−24.7618	−0.902369
$754$	18.7365	0.682343
$755$	0.589663	0.0214600
$756$	1.10454	0.0401717
$757$	−46.8836	−1.70401	−0.852007	−	0.523530i	$-0.824615\pi$
$757$	−46.8836	−1.70401	−0.852007	+	0.523530i	$0.824615\pi$
$758$	16.1697	0.587311
$759$	−3.99732	−0.145094
$760$	2.38494	0.0865108
$761$	−15.3864	−0.557757	−0.278879	−	0.960326i	$-0.589963\pi$
$761$	−15.3864	−0.557757	−0.278879	+	0.960326i	$0.589963\pi$
$762$	9.70331	0.351514
$763$	−4.77174	−0.172748
$764$	−7.06153	−0.255477
$765$	−4.76988	−0.172455
$766$	15.7323	0.568431
$767$	−51.6987	−1.86673
$768$	−1.00000	−0.0360844
$769$	−37.2868	−1.34460	−0.672299	−	0.740280i	$-0.734693\pi$
$769$	−37.2868	−1.34460	−0.672299	+	0.740280i	$0.734693\pi$
$770$	−5.79812	−0.208950
$771$	−15.5033	−0.558337
$772$	8.41280	0.302783
$773$	8.41931	0.302822	0.151411	−	0.988471i	$-0.451618\pi$
$773$	8.41931	0.302822	0.151411	+	0.988471i	$0.451618\pi$
$774$	11.6132	0.417428
$775$	−6.76151	−0.242881
$776$	−6.49864	−0.233288
$777$	−10.6916	−0.383561
$778$	32.4421	1.16311
$779$	−6.27391	−0.224786
$780$	11.7097	0.419274
$781$	−34.1033	−1.22031
$782$	−3.63221	−0.129888
$783$	−3.81610	−0.136376
$784$	−5.77999	−0.206428
$785$	−20.5114	−0.732082
$786$	−10.9318	−0.389924
$787$	−23.5958	−0.841100	−0.420550	−	0.907269i	$-0.638163\pi$
$787$	−23.5958	−0.841100	−0.420550	+	0.907269i	$0.638163\pi$
$788$	23.9901	0.854612
$789$	−5.18444	−0.184571
$790$	−4.75433	−0.169152
$791$	−17.0192	−0.605133
$792$	−2.20104	−0.0782106
$793$	76.3640	2.71177
$794$	−31.1556	−1.10567
$795$	−2.38494	−0.0845850
$796$	10.2665	0.363885
$797$	30.9716	1.09707	0.548535	−	0.836127i	$-0.315186\pi$
$797$	30.9716	1.09707	0.548535	+	0.836127i	$0.315186\pi$
$798$	−1.10454	−0.0391003
$799$	1.27740	0.0451911
$800$	0.687928	0.0243219
$801$	2.04392	0.0722183
$802$	−16.9656	−0.599075
$803$	−21.4355	−0.756443
$804$	11.4850	0.405046
$805$	−4.78409	−0.168617
$806$	−48.2580	−1.69982
$807$	27.0908	0.953642
$808$	4.33282	0.152428
$809$	21.7732	0.765505	0.382753	−	0.923851i	$-0.374976\pi$
$809$	21.7732	0.765505	0.382753	+	0.923851i	$0.374976\pi$
$810$	−2.38494	−0.0837982
$811$	2.91874	0.102491	0.0512455	−	0.998686i	$-0.483681\pi$
$811$	2.91874	0.102491	0.0512455	+	0.998686i	$0.483681\pi$
$812$	−4.21504	−0.147919
$813$	−10.9343	−0.383482
$814$	21.3055	0.746757
$815$	18.9649	0.664312
$816$	−2.00000	−0.0700140
$817$	−11.6132	−0.406295
$818$	35.0516	1.22555
$819$	−5.42313	−0.189499
$820$	−14.9629	−0.522526
$821$	1.15676	0.0403711	0.0201856	−	0.999796i	$-0.493574\pi$
$821$	1.15676	0.0403711	0.0201856	+	0.999796i	$0.493574\pi$
$822$	−14.4567	−0.504236
$823$	−44.0206	−1.53446	−0.767230	−	0.641372i	$-0.778366\pi$
$823$	−44.0206	−1.53446	−0.767230	+	0.641372i	$0.778366\pi$
$824$	−9.82881	−0.342403
$825$	1.51416	0.0527162
$826$	11.6303	0.404672
$827$	1.89561	0.0659170	0.0329585	−	0.999457i	$-0.489507\pi$
$827$	1.89561	0.0659170	0.0329585	+	0.999457i	$0.489507\pi$
$828$	−1.81610	−0.0631140
$829$	−43.8907	−1.52439	−0.762194	−	0.647349i	$-0.775878\pi$
$829$	−43.8907	−1.52439	−0.762194	+	0.647349i	$0.775878\pi$
$830$	17.2061	0.597232
$831$	−22.7961	−0.790786
$832$	4.90985	0.170218
$833$	−11.5600	−0.400530
$834$	−11.7871	−0.408153
$835$	−35.6087	−1.23229
$836$	2.20104	0.0761246
$837$	9.82881	0.339733
$838$	4.13897	0.142978
$839$	−16.7954	−0.579843	−0.289921	−	0.957050i	$-0.593629\pi$
$839$	−16.7954	−0.579843	−0.289921	+	0.957050i	$0.593629\pi$
$840$	−2.63426	−0.0908906
$841$	−14.4373	−0.497839
$842$	31.8131	1.09635
$843$	−26.9734	−0.929014
$844$	20.0361	0.689672
$845$	−26.4887	−0.911237
$846$	0.638699	0.0219589
$847$	6.79890	0.233613
$848$	−1.00000	−0.0343401
$849$	20.7879	0.713440
$850$	1.37586	0.0471915
$851$	17.5794	0.602614
$852$	−15.4941	−0.530821
$853$	−51.2616	−1.75516	−0.877581	−	0.479428i	$-0.840844\pi$
$853$	−51.2616	−1.75516	−0.877581	+	0.479428i	$0.840844\pi$
$854$	−17.1792	−0.587859
$855$	2.38494	0.0815631
$856$	11.7049	0.400066
$857$	3.46866	0.118487	0.0592436	−	0.998244i	$-0.481131\pi$
$857$	3.46866	0.118487	0.0592436	+	0.998244i	$0.481131\pi$
$858$	10.8068	0.368938
$859$	35.7601	1.22012	0.610060	−	0.792355i	$-0.291145\pi$
$859$	35.7601	1.22012	0.610060	+	0.792355i	$0.291145\pi$
$860$	−27.6968	−0.944453
$861$	6.92978	0.236166
$862$	13.8338	0.471181
$863$	−22.1748	−0.754837	−0.377419	−	0.926043i	$-0.623188\pi$
$863$	−22.1748	−0.754837	−0.377419	+	0.926043i	$0.623188\pi$
$864$	−1.00000	−0.0340207
$865$	−38.7189	−1.31648
$866$	−31.6994	−1.07719
$867$	13.0000	0.441503
$868$	10.8563	0.368487
$869$	−4.38774	−0.148844
$870$	9.10117	0.308559
$871$	−56.3898	−1.91070
$872$	4.32011	0.146297
$873$	−6.49864	−0.219946
$874$	1.81610	0.0614307
$875$	−11.3591	−0.384008
$876$	−9.73880	−0.329044
$877$	−10.5972	−0.357841	−0.178921	−	0.983863i	$-0.557261\pi$
$877$	−10.5972	−0.357841	−0.178921	+	0.983863i	$0.557261\pi$
$878$	3.80287	0.128341
$879$	20.6303	0.695844
$880$	5.24935	0.176956
$881$	45.6928	1.53943	0.769715	−	0.638388i	$-0.220398\pi$
$881$	45.6928	1.53943	0.769715	+	0.638388i	$0.220398\pi$
$882$	−5.77999	−0.194622
$883$	−52.2979	−1.75997	−0.879983	−	0.475005i	$-0.842446\pi$
$883$	−52.2979	−1.75997	−0.879983	+	0.475005i	$0.842446\pi$
$884$	9.81970	0.330272
$885$	−25.1124	−0.844144
$886$	−30.5420	−1.02608
$887$	15.0352	0.504831	0.252415	−	0.967619i	$-0.418775\pi$
$887$	15.0352	0.504831	0.252415	+	0.967619i	$0.418775\pi$
$888$	9.67973	0.324830
$889$	10.7177	0.359460
$890$	−4.87462	−0.163398
$891$	−2.20104	−0.0737377
$892$	23.9744	0.802722
$893$	−0.638699	−0.0213732
$894$	−3.06638	−0.102555
$895$	−2.30842	−0.0771621
$896$	−1.10454	−0.0369001
$897$	8.91680	0.297723
$898$	−33.1525	−1.10631
$899$	−37.5078	−1.25095
$900$	0.687928	0.0229309
$901$	−2.00000	−0.0666297
$902$	−13.8091	−0.459794
$903$	12.8273	0.426865
$904$	15.4084	0.512476
$905$	11.1484	0.370585
$906$	0.247245	0.00821415
$907$	−27.0153	−0.897028	−0.448514	−	0.893776i	$-0.648047\pi$
$907$	−27.0153	−0.897028	−0.448514	+	0.893776i	$0.648047\pi$
$908$	6.38118	0.211767
$909$	4.33282	0.143711
$910$	12.9338	0.428752
$911$	−32.2754	−1.06933	−0.534666	−	0.845064i	$-0.679562\pi$
$911$	−32.2754	−1.06933	−0.534666	+	0.845064i	$0.679562\pi$
$912$	1.00000	0.0331133
$913$	15.8794	0.525531
$914$	−40.6235	−1.34371
$915$	37.0935	1.22627
$916$	−18.9043	−0.624617
$917$	−12.0746	−0.398738
$918$	−2.00000	−0.0660098
$919$	−15.5981	−0.514535	−0.257267	−	0.966340i	$-0.582822\pi$
$919$	−15.5981	−0.514535	−0.257267	+	0.966340i	$0.582822\pi$
$920$	4.33130	0.142799
$921$	8.09371	0.266697
$922$	−4.37693	−0.144146
$923$	76.0740	2.50401
$924$	−2.43114	−0.0799786
$925$	−6.65895	−0.218945
$926$	22.6231	0.743442
$927$	−9.82881	−0.322821
$928$	3.81610	0.125270
$929$	4.31147	0.141455	0.0707275	−	0.997496i	$-0.477468\pi$
$929$	4.31147	0.141455	0.0707275	+	0.997496i	$0.477468\pi$
$930$	−23.4411	−0.768664
$931$	5.77999	0.189432
$932$	−9.37829	−0.307196
$933$	−21.3215	−0.698034
$934$	13.5769	0.444250
$935$	10.4987	0.343344
$936$	4.90985	0.160484
$937$	27.8446	0.909644	0.454822	−	0.890582i	$-0.349703\pi$
$937$	27.8446	0.909644	0.454822	+	0.890582i	$0.349703\pi$
$938$	12.6857	0.414202
$939$	−32.4174	−1.05790
$940$	−1.52326	−0.0496832
$941$	35.1809	1.14686	0.573432	−	0.819253i	$-0.305611\pi$
$941$	35.1809	1.14686	0.573432	+	0.819253i	$0.305611\pi$
$942$	−8.60037	−0.280215
$943$	−11.3941	−0.371042
$944$	−10.5296	−0.342709
$945$	−2.63426	−0.0856925
$946$	−25.5612	−0.831066
$947$	−18.5143	−0.601634	−0.300817	−	0.953682i	$-0.597259\pi$
$947$	−18.5143	−0.601634	−0.300817	+	0.953682i	$0.597259\pi$
$948$	−1.99348	−0.0647453
$949$	47.8161	1.55218
$950$	−0.687928	−0.0223193
$951$	16.3399	0.529859
$952$	−2.20908	−0.0715967
$953$	−14.5079	−0.469956	−0.234978	−	0.972001i	$-0.575502\pi$
$953$	−14.5079	−0.469956	−0.234978	+	0.972001i	$0.575502\pi$
$954$	−1.00000	−0.0323762
$955$	16.8413	0.544972
$956$	−5.66751	−0.183300
$957$	8.39941	0.271514
$958$	−11.3301	−0.366059
$959$	−15.9680	−0.515634
$960$	2.38494	0.0769735
$961$	65.6056	2.11631
$962$	−47.5260	−1.53230
$963$	11.7049	0.377186
$964$	6.88465	0.221740
$965$	−20.0640	−0.645883
$966$	−2.00596	−0.0645407
$967$	43.8000	1.40851	0.704256	−	0.709946i	$-0.251281\pi$
$967$	43.8000	1.40851	0.704256	+	0.709946i	$0.251281\pi$
$968$	−6.15541	−0.197842
$969$	2.00000	0.0642493
$970$	15.4989	0.497638
$971$	−14.0089	−0.449566	−0.224783	−	0.974409i	$-0.572167\pi$
$971$	−14.0089	−0.449566	−0.224783	+	0.974409i	$0.572167\pi$
$972$	−1.00000	−0.0320750
$973$	−13.0193	−0.417380
$974$	1.03793	0.0332576
$975$	−3.37762	−0.108171
$976$	15.5532	0.497846
$977$	0.0999362	0.00319724	0.00159862	−	0.999999i	$-0.499491\pi$
$977$	0.0999362	0.00319724	0.00159862	+	0.999999i	$0.499491\pi$
$978$	7.95195	0.254275
$979$	−4.49875	−0.143781
$980$	13.7849	0.440343
$981$	4.32011	0.137931
$982$	−34.6228	−1.10486
$983$	43.7507	1.39543	0.697715	−	0.716375i	$-0.254200\pi$
$983$	43.7507	1.39543	0.697715	+	0.716375i	$0.254200\pi$
$984$	−6.27391	−0.200005
$985$	−57.2149	−1.82302
$986$	7.63221	0.243059
$987$	0.705469	0.0224553
$988$	−4.90985	−0.156203
$989$	−21.0908	−0.670649
$990$	5.24935	0.166835
$991$	−31.4639	−0.999482	−0.499741	−	0.866175i	$-0.666572\pi$
$991$	−31.4639	−0.999482	−0.499741	+	0.866175i	$0.666572\pi$
$992$	−9.82881	−0.312065
$993$	35.2035	1.11715
$994$	−17.1139	−0.542820
$995$	−24.4849	−0.776223
$996$	7.21449	0.228600
$997$	4.04906	0.128235	0.0641174	−	0.997942i	$-0.479577\pi$
$997$	4.04906	0.128235	0.0641174	+	0.997942i	$0.479577\pi$
$998$	42.1889	1.33547
$999$	9.67973	0.306253

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.w.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.w.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.38494 q^{5} -1.00000 q^{6} -1.10454 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.38494 q^{5} -1.00000 q^{6} -1.10454 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.38494 q^{10} -2.20104 q^{11} -1.00000 q^{12} +4.90985 q^{13} -1.10454 q^{14} +2.38494 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} -1.00000 q^{19} -2.38494 q^{20} +1.10454 q^{21} -2.20104 q^{22} -1.81610 q^{23} -1.00000 q^{24} +0.687928 q^{25} +4.90985 q^{26} -1.00000 q^{27} -1.10454 q^{28} +3.81610 q^{29} +2.38494 q^{30} -9.82881 q^{31} +1.00000 q^{32} +2.20104 q^{33} +2.00000 q^{34} +2.63426 q^{35} +1.00000 q^{36} -9.67973 q^{37} -1.00000 q^{38} -4.90985 q^{39} -2.38494 q^{40} +6.27391 q^{41} +1.10454 q^{42} +11.6132 q^{43} -2.20104 q^{44} -2.38494 q^{45} -1.81610 q^{46} +0.638699 q^{47} -1.00000 q^{48} -5.77999 q^{49} +0.687928 q^{50} -2.00000 q^{51} +4.90985 q^{52} -1.00000 q^{53} -1.00000 q^{54} +5.24935 q^{55} -1.10454 q^{56} +1.00000 q^{57} +3.81610 q^{58} -10.5296 q^{59} +2.38494 q^{60} +15.5532 q^{61} -9.82881 q^{62} -1.10454 q^{63} +1.00000 q^{64} -11.7097 q^{65} +2.20104 q^{66} -11.4850 q^{67} +2.00000 q^{68} +1.81610 q^{69} +2.63426 q^{70} +15.4941 q^{71} +1.00000 q^{72} +9.73880 q^{73} -9.67973 q^{74} -0.687928 q^{75} -1.00000 q^{76} +2.43114 q^{77} -4.90985 q^{78} +1.99348 q^{79} -2.38494 q^{80} +1.00000 q^{81} +6.27391 q^{82} -7.21449 q^{83} +1.10454 q^{84} -4.76988 q^{85} +11.6132 q^{86} -3.81610 q^{87} -2.20104 q^{88} +2.04392 q^{89} -2.38494 q^{90} -5.42313 q^{91} -1.81610 q^{92} +9.82881 q^{93} +0.638699 q^{94} +2.38494 q^{95} -1.00000 q^{96} -6.49864 q^{97} -5.77999 q^{98} -2.20104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 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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