LMFDB - Embedded newform 6042.2.a.bf.1.2

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 27 x^{10} + 134 x^{9} + 294 x^{8} - 1313 x^{7} - 1685 x^{6} + 5910 x^{5} + \cdots + 4048 $ x^12 - 5x^11 - 27x^10 + 134x^9 + 294x^8 - 1313x^7 - 1685x^6 + 5910x^5 + 5237x^4 - 12206x^3 - 7876x^2 + 9264*x + 4048
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			1.2
Root			$-2.24876$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.24876 q^{5} -1.00000 q^{6} +1.74785 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.24876 q^{5} -1.00000 q^{6} +1.74785 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.24876 q^{10} +2.18165 q^{11} +1.00000 q^{12} -0.407978 q^{13} -1.74785 q^{14} -3.24876 q^{15} +1.00000 q^{16} -6.01716 q^{17} -1.00000 q^{18} +1.00000 q^{19} -3.24876 q^{20} +1.74785 q^{21} -2.18165 q^{22} -2.93884 q^{23} -1.00000 q^{24} +5.55444 q^{25} +0.407978 q^{26} +1.00000 q^{27} +1.74785 q^{28} -3.77634 q^{29} +3.24876 q^{30} +7.51046 q^{31} -1.00000 q^{32} +2.18165 q^{33} +6.01716 q^{34} -5.67833 q^{35} +1.00000 q^{36} -2.39618 q^{37} -1.00000 q^{38} -0.407978 q^{39} +3.24876 q^{40} -0.830653 q^{41} -1.74785 q^{42} +4.93884 q^{43} +2.18165 q^{44} -3.24876 q^{45} +2.93884 q^{46} +4.42714 q^{47} +1.00000 q^{48} -3.94503 q^{49} -5.55444 q^{50} -6.01716 q^{51} -0.407978 q^{52} +1.00000 q^{53} -1.00000 q^{54} -7.08767 q^{55} -1.74785 q^{56} +1.00000 q^{57} +3.77634 q^{58} -5.76899 q^{59} -3.24876 q^{60} +7.54540 q^{61} -7.51046 q^{62} +1.74785 q^{63} +1.00000 q^{64} +1.32542 q^{65} -2.18165 q^{66} +10.3061 q^{67} -6.01716 q^{68} -2.93884 q^{69} +5.67833 q^{70} +14.1274 q^{71} -1.00000 q^{72} +8.66135 q^{73} +2.39618 q^{74} +5.55444 q^{75} +1.00000 q^{76} +3.81320 q^{77} +0.407978 q^{78} -15.9810 q^{79} -3.24876 q^{80} +1.00000 q^{81} +0.830653 q^{82} -12.5023 q^{83} +1.74785 q^{84} +19.5483 q^{85} -4.93884 q^{86} -3.77634 q^{87} -2.18165 q^{88} +10.7636 q^{89} +3.24876 q^{90} -0.713083 q^{91} -2.93884 q^{92} +7.51046 q^{93} -4.42714 q^{94} -3.24876 q^{95} -1.00000 q^{96} +3.10066 q^{97} +3.94503 q^{98} +2.18165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9} + 7 q^{10} - 5 q^{11} + 12 q^{12} + 10 q^{13} - 5 q^{14} - 7 q^{15} + 12 q^{16} + 6 q^{17} - 12 q^{18} + 12 q^{19} - 7 q^{20} + 5 q^{21} + 5 q^{22} - 12 q^{24} + 21 q^{25} - 10 q^{26} + 12 q^{27} + 5 q^{28} + 7 q^{30} + 2 q^{31} - 12 q^{32} - 5 q^{33} - 6 q^{34} - 17 q^{35} + 12 q^{36} + 16 q^{37} - 12 q^{38} + 10 q^{39} + 7 q^{40} + 7 q^{41} - 5 q^{42} + 24 q^{43} - 5 q^{44} - 7 q^{45} + 4 q^{47} + 12 q^{48} + 29 q^{49} - 21 q^{50} + 6 q^{51} + 10 q^{52} + 12 q^{53} - 12 q^{54} - 2 q^{55} - 5 q^{56} + 12 q^{57} + 2 q^{59} - 7 q^{60} + 29 q^{61} - 2 q^{62} + 5 q^{63} + 12 q^{64} - 17 q^{65} + 5 q^{66} + 36 q^{67} + 6 q^{68} + 17 q^{70} - 3 q^{71} - 12 q^{72} + 7 q^{73} - 16 q^{74} + 21 q^{75} + 12 q^{76} - 35 q^{77} - 10 q^{78} + 40 q^{79} - 7 q^{80} + 12 q^{81} - 7 q^{82} + 24 q^{83} + 5 q^{84} - 22 q^{85} - 24 q^{86} + 5 q^{88} - 45 q^{89} + 7 q^{90} + 71 q^{91} + 2 q^{93} - 4 q^{94} - 7 q^{95} - 12 q^{96} + q^{97} - 29 q^{98} - 5 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9 + 7 * q^10 - 5 * q^11 + 12 * q^12 + 10 * q^13 - 5 * q^14 - 7 * q^15 + 12 * q^16 + 6 * q^17 - 12 * q^18 + 12 * q^19 - 7 * q^20 + 5 * q^21 + 5 * q^22 - 12 * q^24 + 21 * q^25 - 10 * q^26 + 12 * q^27 + 5 * q^28 + 7 * q^30 + 2 * q^31 - 12 * q^32 - 5 * q^33 - 6 * q^34 - 17 * q^35 + 12 * q^36 + 16 * q^37 - 12 * q^38 + 10 * q^39 + 7 * q^40 + 7 * q^41 - 5 * q^42 + 24 * q^43 - 5 * q^44 - 7 * q^45 + 4 * q^47 + 12 * q^48 + 29 * q^49 - 21 * q^50 + 6 * q^51 + 10 * q^52 + 12 * q^53 - 12 * q^54 - 2 * q^55 - 5 * q^56 + 12 * q^57 + 2 * q^59 - 7 * q^60 + 29 * q^61 - 2 * q^62 + 5 * q^63 + 12 * q^64 - 17 * q^65 + 5 * q^66 + 36 * q^67 + 6 * q^68 + 17 * q^70 - 3 * q^71 - 12 * q^72 + 7 * q^73 - 16 * q^74 + 21 * q^75 + 12 * q^76 - 35 * q^77 - 10 * q^78 + 40 * q^79 - 7 * q^80 + 12 * q^81 - 7 * q^82 + 24 * q^83 + 5 * q^84 - 22 * q^85 - 24 * q^86 + 5 * q^88 - 45 * q^89 + 7 * q^90 + 71 * q^91 + 2 * q^93 - 4 * q^94 - 7 * q^95 - 12 * q^96 + q^97 - 29 * q^98 - 5 * 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
$5$	−3.24876	−1.45289	−0.726445	−	0.687225i	$-0.758829\pi$
$5$	−3.24876	−1.45289	−0.726445	+	0.687225i	$0.758829\pi$
$6$	−1.00000	−0.408248
$7$	1.74785	0.660624	0.330312	−	0.943872i	$-0.392846\pi$
$7$	1.74785	0.660624	0.330312	+	0.943872i	$0.392846\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.24876	1.02735
$11$	2.18165	0.657794	0.328897	−	0.944366i	$-0.393323\pi$
$11$	2.18165	0.657794	0.328897	+	0.944366i	$0.393323\pi$
$12$	1.00000	0.288675
$13$	−0.407978	−0.113153	−0.0565764	−	0.998398i	$-0.518018\pi$
$13$	−0.407978	−0.113153	−0.0565764	+	0.998398i	$0.518018\pi$
$14$	−1.74785	−0.467132
$15$	−3.24876	−0.838826
$16$	1.00000	0.250000
$17$	−6.01716	−1.45938	−0.729688	−	0.683780i	$-0.760335\pi$
$17$	−6.01716	−1.45938	−0.729688	+	0.683780i	$0.760335\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.24876	−0.726445
$21$	1.74785	0.381411
$22$	−2.18165	−0.465130
$23$	−2.93884	−0.612790	−0.306395	−	0.951904i	$-0.599123\pi$
$23$	−2.93884	−0.612790	−0.306395	+	0.951904i	$0.599123\pi$
$24$	−1.00000	−0.204124
$25$	5.55444	1.11089
$26$	0.407978	0.0800110
$27$	1.00000	0.192450
$28$	1.74785	0.330312
$29$	−3.77634	−0.701250	−0.350625	−	0.936516i	$-0.614031\pi$
$29$	−3.77634	−0.701250	−0.350625	+	0.936516i	$0.614031\pi$
$30$	3.24876	0.593140
$31$	7.51046	1.34892	0.674459	−	0.738312i	$-0.264377\pi$
$31$	7.51046	1.34892	0.674459	+	0.738312i	$0.264377\pi$
$32$	−1.00000	−0.176777
$33$	2.18165	0.379777
$34$	6.01716	1.03193
$35$	−5.67833	−0.959814
$36$	1.00000	0.166667
$37$	−2.39618	−0.393929	−0.196965	−	0.980411i	$-0.563108\pi$
$37$	−2.39618	−0.393929	−0.196965	+	0.980411i	$0.563108\pi$
$38$	−1.00000	−0.162221
$39$	−0.407978	−0.0653287
$40$	3.24876	0.513674
$41$	−0.830653	−0.129726	−0.0648631	−	0.997894i	$-0.520661\pi$
$41$	−0.830653	−0.129726	−0.0648631	+	0.997894i	$0.520661\pi$
$42$	−1.74785	−0.269699
$43$	4.93884	0.753166	0.376583	−	0.926383i	$-0.377099\pi$
$43$	4.93884	0.753166	0.376583	+	0.926383i	$0.377099\pi$
$44$	2.18165	0.328897
$45$	−3.24876	−0.484296
$46$	2.93884	0.433308
$47$	4.42714	0.645765	0.322882	−	0.946439i	$-0.395348\pi$
$47$	4.42714	0.645765	0.322882	+	0.946439i	$0.395348\pi$
$48$	1.00000	0.144338
$49$	−3.94503	−0.563576
$50$	−5.55444	−0.785516
$51$	−6.01716	−0.842571
$52$	−0.407978	−0.0565764
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−1.00000	−0.136083
$55$	−7.08767	−0.955701
$56$	−1.74785	−0.233566
$57$	1.00000	0.132453
$58$	3.77634	0.495858
$59$	−5.76899	−0.751058	−0.375529	−	0.926811i	$-0.622539\pi$
$59$	−5.76899	−0.751058	−0.375529	+	0.926811i	$0.622539\pi$
$60$	−3.24876	−0.419413
$61$	7.54540	0.966090	0.483045	−	0.875596i	$-0.339531\pi$
$61$	7.54540	0.966090	0.483045	+	0.875596i	$0.339531\pi$
$62$	−7.51046	−0.953829
$63$	1.74785	0.220208
$64$	1.00000	0.125000
$65$	1.32542	0.164398
$66$	−2.18165	−0.268543
$67$	10.3061	1.25908	0.629542	−	0.776966i	$-0.283242\pi$
$67$	10.3061	1.25908	0.629542	+	0.776966i	$0.283242\pi$
$68$	−6.01716	−0.729688
$69$	−2.93884	−0.353794
$70$	5.67833	0.678691
$71$	14.1274	1.67661	0.838307	−	0.545199i	$-0.183546\pi$
$71$	14.1274	1.67661	0.838307	+	0.545199i	$0.183546\pi$
$72$	−1.00000	−0.117851
$73$	8.66135	1.01373	0.506867	−	0.862024i	$-0.330803\pi$
$73$	8.66135	1.01373	0.506867	+	0.862024i	$0.330803\pi$
$74$	2.39618	0.278550
$75$	5.55444	0.641371
$76$	1.00000	0.114708
$77$	3.81320	0.434554
$78$	0.407978	0.0461944
$79$	−15.9810	−1.79800	−0.898999	−	0.437950i	$-0.855705\pi$
$79$	−15.9810	−1.79800	−0.898999	+	0.437950i	$0.855705\pi$
$80$	−3.24876	−0.363222
$81$	1.00000	0.111111
$82$	0.830653	0.0917303
$83$	−12.5023	−1.37230	−0.686151	−	0.727459i	$-0.740701\pi$
$83$	−12.5023	−1.37230	−0.686151	+	0.727459i	$0.740701\pi$
$84$	1.74785	0.190706
$85$	19.5483	2.12031
$86$	−4.93884	−0.532568
$87$	−3.77634	−0.404867
$88$	−2.18165	−0.232565
$89$	10.7636	1.14094	0.570471	−	0.821318i	$-0.306761\pi$
$89$	10.7636	1.14094	0.570471	+	0.821318i	$0.306761\pi$
$90$	3.24876	0.342449
$91$	−0.713083	−0.0747514
$92$	−2.93884	−0.306395
$93$	7.51046	0.778798
$94$	−4.42714	−0.456624
$95$	−3.24876	−0.333316
$96$	−1.00000	−0.102062
$97$	3.10066	0.314825	0.157412	−	0.987533i	$-0.449685\pi$
$97$	3.10066	0.314825	0.157412	+	0.987533i	$0.449685\pi$
$98$	3.94503	0.398508
$99$	2.18165	0.219265
$100$	5.55444	0.555444
$101$	11.4872	1.14302	0.571512	−	0.820594i	$-0.306357\pi$
$101$	11.4872	1.14302	0.571512	+	0.820594i	$0.306357\pi$
$102$	6.01716	0.595788
$103$	−12.4983	−1.23149	−0.615745	−	0.787946i	$-0.711145\pi$
$103$	−12.4983	−1.23149	−0.615745	+	0.787946i	$0.711145\pi$
$104$	0.407978	0.0400055
$105$	−5.67833	−0.554149
$106$	−1.00000	−0.0971286
$107$	8.11960	0.784951	0.392476	−	0.919762i	$-0.371619\pi$
$107$	8.11960	0.784951	0.392476	+	0.919762i	$0.371619\pi$
$108$	1.00000	0.0962250
$109$	−14.1719	−1.35742	−0.678712	−	0.734404i	$-0.737462\pi$
$109$	−14.1719	−1.35742	−0.678712	+	0.734404i	$0.737462\pi$
$110$	7.08767	0.675783
$111$	−2.39618	−0.227435
$112$	1.74785	0.165156
$113$	7.19062	0.676437	0.338219	−	0.941068i	$-0.390176\pi$
$113$	7.19062	0.676437	0.338219	+	0.941068i	$0.390176\pi$
$114$	−1.00000	−0.0936586
$115$	9.54757	0.890316
$116$	−3.77634	−0.350625
$117$	−0.407978	−0.0377176
$118$	5.76899	0.531079
$119$	−10.5171	−0.964099
$120$	3.24876	0.296570
$121$	−6.24038	−0.567308
$122$	−7.54540	−0.683129
$123$	−0.830653	−0.0748975
$124$	7.51046	0.674459
$125$	−1.80124	−0.161107
$126$	−1.74785	−0.155711
$127$	12.5832	1.11658	0.558289	−	0.829646i	$-0.311458\pi$
$127$	12.5832	1.11658	0.558289	+	0.829646i	$0.311458\pi$
$128$	−1.00000	−0.0883883
$129$	4.93884	0.434840
$130$	−1.32542	−0.116247
$131$	4.57492	0.399713	0.199856	−	0.979825i	$-0.435952\pi$
$131$	4.57492	0.399713	0.199856	+	0.979825i	$0.435952\pi$
$132$	2.18165	0.189889
$133$	1.74785	0.151558
$134$	−10.3061	−0.890307
$135$	−3.24876	−0.279609
$136$	6.01716	0.515967
$137$	−6.01857	−0.514201	−0.257100	−	0.966385i	$-0.582767\pi$
$137$	−6.01857	−0.514201	−0.257100	+	0.966385i	$0.582767\pi$
$138$	2.93884	0.250170
$139$	−11.6706	−0.989885	−0.494942	−	0.868926i	$-0.664811\pi$
$139$	−11.6706	−0.989885	−0.494942	+	0.868926i	$0.664811\pi$
$140$	−5.67833	−0.479907
$141$	4.42714	0.372832
$142$	−14.1274	−1.18554
$143$	−0.890067	−0.0744311
$144$	1.00000	0.0833333
$145$	12.2684	1.01884
$146$	−8.66135	−0.716819
$147$	−3.94503	−0.325381
$148$	−2.39618	−0.196965
$149$	19.6669	1.61117	0.805586	−	0.592478i	$-0.201850\pi$
$149$	19.6669	1.61117	0.805586	+	0.592478i	$0.201850\pi$
$150$	−5.55444	−0.453518
$151$	3.34958	0.272585	0.136293	−	0.990669i	$-0.456481\pi$
$151$	3.34958	0.272585	0.136293	+	0.990669i	$0.456481\pi$
$152$	−1.00000	−0.0811107
$153$	−6.01716	−0.486459
$154$	−3.81320	−0.307276
$155$	−24.3997	−1.95983
$156$	−0.407978	−0.0326644
$157$	13.5586	1.08209	0.541047	−	0.840992i	$-0.318028\pi$
$157$	13.5586	1.08209	0.541047	+	0.840992i	$0.318028\pi$
$158$	15.9810	1.27138
$159$	1.00000	0.0793052
$160$	3.24876	0.256837
$161$	−5.13664	−0.404824
$162$	−1.00000	−0.0785674
$163$	−0.936413	−0.0733455	−0.0366728	−	0.999327i	$-0.511676\pi$
$163$	−0.936413	−0.0733455	−0.0366728	+	0.999327i	$0.511676\pi$
$164$	−0.830653	−0.0648631
$165$	−7.08767	−0.551774
$166$	12.5023	0.970364
$167$	7.89507	0.610939	0.305470	−	0.952202i	$-0.401187\pi$
$167$	7.89507	0.610939	0.305470	+	0.952202i	$0.401187\pi$
$168$	−1.74785	−0.134849
$169$	−12.8336	−0.987196
$170$	−19.5483	−1.49929
$171$	1.00000	0.0764719
$172$	4.93884	0.376583
$173$	−24.7657	−1.88290	−0.941450	−	0.337151i	$-0.890537\pi$
$173$	−24.7657	−1.88290	−0.941450	+	0.337151i	$0.890537\pi$
$174$	3.77634	0.286284
$175$	9.70831	0.733879
$176$	2.18165	0.164448
$177$	−5.76899	−0.433624
$178$	−10.7636	−0.806768
$179$	−11.9371	−0.892220	−0.446110	−	0.894978i	$-0.647191\pi$
$179$	−11.9371	−0.892220	−0.446110	+	0.894978i	$0.647191\pi$
$180$	−3.24876	−0.242148
$181$	−20.9921	−1.56033	−0.780165	−	0.625573i	$-0.784865\pi$
$181$	−20.9921	−1.56033	−0.780165	+	0.625573i	$0.784865\pi$
$182$	0.713083	0.0528572
$183$	7.54540	0.557772
$184$	2.93884	0.216654
$185$	7.78460	0.572335
$186$	−7.51046	−0.550693
$187$	−13.1274	−0.959968
$188$	4.42714	0.322882
$189$	1.74785	0.127137
$190$	3.24876	0.235690
$191$	−24.6921	−1.78666	−0.893330	−	0.449401i	$-0.851637\pi$
$191$	−24.6921	−1.78666	−0.893330	+	0.449401i	$0.851637\pi$
$192$	1.00000	0.0721688
$193$	14.5459	1.04704	0.523518	−	0.852015i	$-0.324619\pi$
$193$	14.5459	1.04704	0.523518	+	0.852015i	$0.324619\pi$
$194$	−3.10066	−0.222615
$195$	1.32542	0.0949154
$196$	−3.94503	−0.281788
$197$	9.26034	0.659772	0.329886	−	0.944021i	$-0.392990\pi$
$197$	9.26034	0.659772	0.329886	+	0.944021i	$0.392990\pi$
$198$	−2.18165	−0.155043
$199$	17.8310	1.26400	0.632002	−	0.774967i	$-0.282233\pi$
$199$	17.8310	1.26400	0.632002	+	0.774967i	$0.282233\pi$
$200$	−5.55444	−0.392758
$201$	10.3061	0.726933
$202$	−11.4872	−0.808240
$203$	−6.60047	−0.463262
$204$	−6.01716	−0.421285
$205$	2.69859	0.188478
$206$	12.4983	0.870795
$207$	−2.93884	−0.204263
$208$	−0.407978	−0.0282882
$209$	2.18165	0.150908
$210$	5.67833	0.391842
$211$	21.7283	1.49584	0.747919	−	0.663790i	$-0.231053\pi$
$211$	21.7283	1.49584	0.747919	+	0.663790i	$0.231053\pi$
$212$	1.00000	0.0686803
$213$	14.1274	0.967993
$214$	−8.11960	−0.555044
$215$	−16.0451	−1.09427
$216$	−1.00000	−0.0680414
$217$	13.1271	0.891127
$218$	14.1719	0.959844
$219$	8.66135	0.585280
$220$	−7.08767	−0.477851
$221$	2.45487	0.165132
$222$	2.39618	0.160821
$223$	18.6074	1.24604	0.623021	−	0.782205i	$-0.285905\pi$
$223$	18.6074	1.24604	0.623021	+	0.782205i	$0.285905\pi$
$224$	−1.74785	−0.116783
$225$	5.55444	0.370296
$226$	−7.19062	−0.478313
$227$	23.1012	1.53328	0.766640	−	0.642077i	$-0.221927\pi$
$227$	23.1012	1.53328	0.766640	+	0.642077i	$0.221927\pi$
$228$	1.00000	0.0662266
$229$	8.93999	0.590771	0.295386	−	0.955378i	$-0.404552\pi$
$229$	8.93999	0.590771	0.295386	+	0.955378i	$0.404552\pi$
$230$	−9.54757	−0.629548
$231$	3.81320	0.250890
$232$	3.77634	0.247929
$233$	25.5728	1.67533	0.837665	−	0.546184i	$-0.183920\pi$
$233$	25.5728	1.67533	0.837665	+	0.546184i	$0.183920\pi$
$234$	0.407978	0.0266703
$235$	−14.3827	−0.938224
$236$	−5.76899	−0.375529
$237$	−15.9810	−1.03807
$238$	10.5171	0.681721
$239$	−28.1152	−1.81862	−0.909310	−	0.416120i	$-0.863390\pi$
$239$	−28.1152	−1.81862	−0.909310	+	0.416120i	$0.863390\pi$
$240$	−3.24876	−0.209707
$241$	−18.1251	−1.16754	−0.583771	−	0.811918i	$-0.698424\pi$
$241$	−18.1251	−1.16754	−0.583771	+	0.811918i	$0.698424\pi$
$242$	6.24038	0.401147
$243$	1.00000	0.0641500
$244$	7.54540	0.483045
$245$	12.8165	0.818813
$246$	0.830653	0.0529605
$247$	−0.407978	−0.0259590
$248$	−7.51046	−0.476914
$249$	−12.5023	−0.792299
$250$	1.80124	0.113920
$251$	29.2740	1.84776	0.923879	−	0.382684i	$-0.125000\pi$
$251$	29.2740	1.84776	0.923879	+	0.382684i	$0.125000\pi$
$252$	1.74785	0.110104
$253$	−6.41153	−0.403089
$254$	−12.5832	−0.789540
$255$	19.5483	1.22416
$256$	1.00000	0.0625000
$257$	21.7565	1.35713	0.678567	−	0.734539i	$-0.262601\pi$
$257$	21.7565	1.35713	0.678567	+	0.734539i	$0.262601\pi$
$258$	−4.93884	−0.307479
$259$	−4.18815	−0.260239
$260$	1.32542	0.0821992
$261$	−3.77634	−0.233750
$262$	−4.57492	−0.282640
$263$	3.59983	0.221975	0.110987	−	0.993822i	$-0.464599\pi$
$263$	3.59983	0.221975	0.110987	+	0.993822i	$0.464599\pi$
$264$	−2.18165	−0.134272
$265$	−3.24876	−0.199570
$266$	−1.74785	−0.107167
$267$	10.7636	0.658723
$268$	10.3061	0.629542
$269$	−7.24632	−0.441816	−0.220908	−	0.975295i	$-0.570902\pi$
$269$	−7.24632	−0.441816	−0.220908	+	0.975295i	$0.570902\pi$
$270$	3.24876	0.197713
$271$	12.5373	0.761590	0.380795	−	0.924660i	$-0.375650\pi$
$271$	12.5373	0.761590	0.380795	+	0.924660i	$0.375650\pi$
$272$	−6.01716	−0.364844
$273$	−0.713083	−0.0431577
$274$	6.01857	0.363595
$275$	12.1179	0.730735
$276$	−2.93884	−0.176897
$277$	25.8053	1.55049	0.775245	−	0.631660i	$-0.217626\pi$
$277$	25.8053	1.55049	0.775245	+	0.631660i	$0.217626\pi$
$278$	11.6706	0.699954
$279$	7.51046	0.449639
$280$	5.67833	0.339345
$281$	16.6319	0.992179	0.496089	−	0.868271i	$-0.334769\pi$
$281$	16.6319	0.992179	0.496089	+	0.868271i	$0.334769\pi$
$282$	−4.42714	−0.263632
$283$	27.8760	1.65706	0.828530	−	0.559945i	$-0.189178\pi$
$283$	27.8760	1.65706	0.828530	+	0.559945i	$0.189178\pi$
$284$	14.1274	0.838307
$285$	−3.24876	−0.192440
$286$	0.890067	0.0526308
$287$	−1.45185	−0.0857003
$288$	−1.00000	−0.0589256
$289$	19.2062	1.12978
$290$	−12.2684	−0.720427
$291$	3.10066	0.181764
$292$	8.66135	0.506867
$293$	−8.64623	−0.505118	−0.252559	−	0.967581i	$-0.581272\pi$
$293$	−8.64623	−0.505118	−0.252559	+	0.967581i	$0.581272\pi$
$294$	3.94503	0.230079
$295$	18.7421	1.09120
$296$	2.39618	0.139275
$297$	2.18165	0.126592
$298$	−19.6669	−1.13927
$299$	1.19898	0.0693388
$300$	5.55444	0.320686
$301$	8.63233	0.497559
$302$	−3.34958	−0.192747
$303$	11.4872	0.659925
$304$	1.00000	0.0573539
$305$	−24.5132	−1.40362
$306$	6.01716	0.343978
$307$	16.4014	0.936076	0.468038	−	0.883708i	$-0.344961\pi$
$307$	16.4014	0.936076	0.468038	+	0.883708i	$0.344961\pi$
$308$	3.81320	0.217277
$309$	−12.4983	−0.711001
$310$	24.3997	1.38581
$311$	2.40290	0.136256	0.0681279	−	0.997677i	$-0.478297\pi$
$311$	2.40290	0.136256	0.0681279	+	0.997677i	$0.478297\pi$
$312$	0.407978	0.0230972
$313$	19.3876	1.09585	0.547926	−	0.836527i	$-0.315417\pi$
$313$	19.3876	1.09585	0.547926	+	0.836527i	$0.315417\pi$
$314$	−13.5586	−0.765156
$315$	−5.67833	−0.319938
$316$	−15.9810	−0.898999
$317$	14.1456	0.794494	0.397247	−	0.917712i	$-0.369966\pi$
$317$	14.1456	0.794494	0.397247	+	0.917712i	$0.369966\pi$
$318$	−1.00000	−0.0560772
$319$	−8.23868	−0.461277
$320$	−3.24876	−0.181611
$321$	8.11960	0.453192
$322$	5.13664	0.286254
$323$	−6.01716	−0.334804
$324$	1.00000	0.0555556
$325$	−2.26609	−0.125700
$326$	0.936413	0.0518631
$327$	−14.1719	−0.783709
$328$	0.830653	0.0458651
$329$	7.73796	0.426608
$330$	7.08767	0.390163
$331$	−10.0450	−0.552122	−0.276061	−	0.961140i	$-0.589029\pi$
$331$	−10.0450	−0.552122	−0.276061	+	0.961140i	$0.589029\pi$
$332$	−12.5023	−0.686151
$333$	−2.39618	−0.131310
$334$	−7.89507	−0.431999
$335$	−33.4819	−1.82931
$336$	1.74785	0.0953529
$337$	7.81274	0.425587	0.212794	−	0.977097i	$-0.431744\pi$
$337$	7.81274	0.425587	0.212794	+	0.977097i	$0.431744\pi$
$338$	12.8336	0.698053
$339$	7.19062	0.390541
$340$	19.5483	1.06016
$341$	16.3852	0.887309
$342$	−1.00000	−0.0540738
$343$	−19.1302	−1.03294
$344$	−4.93884	−0.266284
$345$	9.54757	0.514024
$346$	24.7657	1.33141
$347$	27.1607	1.45806	0.729032	−	0.684480i	$-0.239971\pi$
$347$	27.1607	1.45806	0.729032	+	0.684480i	$0.239971\pi$
$348$	−3.77634	−0.202433
$349$	25.0347	1.34008	0.670039	−	0.742326i	$-0.266277\pi$
$349$	25.0347	1.34008	0.670039	+	0.742326i	$0.266277\pi$
$350$	−9.70831	−0.518931
$351$	−0.407978	−0.0217762
$352$	−2.18165	−0.116283
$353$	−33.8071	−1.79937	−0.899684	−	0.436542i	$-0.856203\pi$
$353$	−33.8071	−1.79937	−0.899684	+	0.436542i	$0.856203\pi$
$354$	5.76899	0.306618
$355$	−45.8965	−2.43593
$356$	10.7636	0.570471
$357$	−10.5171	−0.556623
$358$	11.9371	0.630895
$359$	−4.93541	−0.260481	−0.130240	−	0.991482i	$-0.541575\pi$
$359$	−4.93541	−0.260481	−0.130240	+	0.991482i	$0.541575\pi$
$360$	3.24876	0.171225
$361$	1.00000	0.0526316
$362$	20.9921	1.10332
$363$	−6.24038	−0.327535
$364$	−0.713083	−0.0373757
$365$	−28.1386	−1.47284
$366$	−7.54540	−0.394405
$367$	−4.60875	−0.240575	−0.120287	−	0.992739i	$-0.538382\pi$
$367$	−4.60875	−0.240575	−0.120287	+	0.992739i	$0.538382\pi$
$368$	−2.93884	−0.153197
$369$	−0.830653	−0.0432421
$370$	−7.78460	−0.404702
$371$	1.74785	0.0907437
$372$	7.51046	0.389399
$373$	5.49294	0.284414	0.142207	−	0.989837i	$-0.454580\pi$
$373$	5.49294	0.284414	0.142207	+	0.989837i	$0.454580\pi$
$374$	13.1274	0.678800
$375$	−1.80124	−0.0930154
$376$	−4.42714	−0.228312
$377$	1.54066	0.0793483
$378$	−1.74785	−0.0898995
$379$	14.9288	0.766840	0.383420	−	0.923574i	$-0.374746\pi$
$379$	14.9288	0.766840	0.383420	+	0.923574i	$0.374746\pi$
$380$	−3.24876	−0.166658
$381$	12.5832	0.644657
$382$	24.6921	1.26336
$383$	−13.6160	−0.695745	−0.347872	−	0.937542i	$-0.613096\pi$
$383$	−13.6160	−0.695745	−0.347872	+	0.937542i	$0.613096\pi$
$384$	−1.00000	−0.0510310
$385$	−12.3882	−0.631359
$386$	−14.5459	−0.740366
$387$	4.93884	0.251055
$388$	3.10066	0.157412
$389$	13.7622	0.697769	0.348885	−	0.937166i	$-0.386561\pi$
$389$	13.7622	0.697769	0.348885	+	0.937166i	$0.386561\pi$
$390$	−1.32542	−0.0671154
$391$	17.6835	0.894291
$392$	3.94503	0.199254
$393$	4.57492	0.230774
$394$	−9.26034	−0.466529
$395$	51.9183	2.61229
$396$	2.18165	0.109632
$397$	21.9797	1.10313	0.551564	−	0.834133i	$-0.314031\pi$
$397$	21.9797	1.10313	0.551564	+	0.834133i	$0.314031\pi$
$398$	−17.8310	−0.893786
$399$	1.74785	0.0875018
$400$	5.55444	0.277722
$401$	5.94465	0.296862	0.148431	−	0.988923i	$-0.452578\pi$
$401$	5.94465	0.296862	0.148431	+	0.988923i	$0.452578\pi$
$402$	−10.3061	−0.514019
$403$	−3.06410	−0.152634
$404$	11.4872	0.571512
$405$	−3.24876	−0.161432
$406$	6.60047	0.327576
$407$	−5.22763	−0.259124
$408$	6.01716	0.297894
$409$	32.8534	1.62450	0.812248	−	0.583312i	$-0.198243\pi$
$409$	32.8534	1.62450	0.812248	+	0.583312i	$0.198243\pi$
$410$	−2.69859	−0.133274
$411$	−6.01857	−0.296874
$412$	−12.4983	−0.615745
$413$	−10.0833	−0.496167
$414$	2.93884	0.144436
$415$	40.6169	1.99380
$416$	0.407978	0.0200028
$417$	−11.6706	−0.571510
$418$	−2.18165	−0.106708
$419$	5.50423	0.268899	0.134450	−	0.990920i	$-0.457073\pi$
$419$	5.50423	0.268899	0.134450	+	0.990920i	$0.457073\pi$
$420$	−5.67833	−0.277074
$421$	−13.7951	−0.672331	−0.336166	−	0.941803i	$-0.609130\pi$
$421$	−13.7951	−0.672331	−0.336166	+	0.941803i	$0.609130\pi$
$422$	−21.7283	−1.05772
$423$	4.42714	0.215255
$424$	−1.00000	−0.0485643
$425$	−33.4219	−1.62120
$426$	−14.1274	−0.684475
$427$	13.1882	0.638222
$428$	8.11960	0.392476
$429$	−0.890067	−0.0429728
$430$	16.0451	0.773763
$431$	−5.01852	−0.241734	−0.120867	−	0.992669i	$-0.538567\pi$
$431$	−5.01852	−0.241734	−0.120867	+	0.992669i	$0.538567\pi$
$432$	1.00000	0.0481125
$433$	31.1100	1.49505	0.747526	−	0.664233i	$-0.231242\pi$
$433$	31.1100	1.49505	0.747526	+	0.664233i	$0.231242\pi$
$434$	−13.1271	−0.630122
$435$	12.2684	0.588226
$436$	−14.1719	−0.678712
$437$	−2.93884	−0.140584
$438$	−8.66135	−0.413855
$439$	−23.7636	−1.13418	−0.567088	−	0.823658i	$-0.691930\pi$
$439$	−23.7636	−1.13418	−0.567088	+	0.823658i	$0.691930\pi$
$440$	7.08767	0.337891
$441$	−3.94503	−0.187859
$442$	−2.45487	−0.116766
$443$	−7.40902	−0.352013	−0.176007	−	0.984389i	$-0.556318\pi$
$443$	−7.40902	−0.352013	−0.176007	+	0.984389i	$0.556318\pi$
$444$	−2.39618	−0.113718
$445$	−34.9684	−1.65766
$446$	−18.6074	−0.881085
$447$	19.6669	0.930211
$448$	1.74785	0.0825780
$449$	−17.6881	−0.834755	−0.417377	−	0.908733i	$-0.637051\pi$
$449$	−17.6881	−0.834755	−0.417377	+	0.908733i	$0.637051\pi$
$450$	−5.55444	−0.261839
$451$	−1.81220	−0.0853331
$452$	7.19062	0.338219
$453$	3.34958	0.157377
$454$	−23.1012	−1.08419
$455$	2.31663	0.108606
$456$	−1.00000	−0.0468293
$457$	17.1310	0.801355	0.400677	−	0.916219i	$-0.368775\pi$
$457$	17.1310	0.801355	0.400677	+	0.916219i	$0.368775\pi$
$458$	−8.93999	−0.417738
$459$	−6.01716	−0.280857
$460$	9.54757	0.445158
$461$	26.0070	1.21127	0.605633	−	0.795744i	$-0.292920\pi$
$461$	26.0070	1.21127	0.605633	+	0.795744i	$0.292920\pi$
$462$	−3.81320	−0.177406
$463$	−31.3255	−1.45582	−0.727910	−	0.685673i	$-0.759508\pi$
$463$	−31.3255	−1.45582	−0.727910	+	0.685673i	$0.759508\pi$
$464$	−3.77634	−0.175312
$465$	−24.3997	−1.13151
$466$	−25.5728	−1.18464
$467$	−15.4157	−0.713355	−0.356678	−	0.934228i	$-0.616091\pi$
$467$	−15.4157	−0.713355	−0.356678	+	0.934228i	$0.616091\pi$
$468$	−0.407978	−0.0188588
$469$	18.0134	0.831782
$470$	14.3827	0.663425
$471$	13.5586	0.624747
$472$	5.76899	0.265539
$473$	10.7748	0.495427
$474$	15.9810	0.734030
$475$	5.55444	0.254855
$476$	−10.5171	−0.482049
$477$	1.00000	0.0457869
$478$	28.1152	1.28596
$479$	3.53117	0.161343	0.0806716	−	0.996741i	$-0.474294\pi$
$479$	3.53117	0.161343	0.0806716	+	0.996741i	$0.474294\pi$
$480$	3.24876	0.148285
$481$	0.977587	0.0445741
$482$	18.1251	0.825577
$483$	−5.13664	−0.233725
$484$	−6.24038	−0.283654
$485$	−10.0733	−0.457405
$486$	−1.00000	−0.0453609
$487$	2.01551	0.0913317	0.0456658	−	0.998957i	$-0.485459\pi$
$487$	2.01551	0.0913317	0.0456658	+	0.998957i	$0.485459\pi$
$488$	−7.54540	−0.341564
$489$	−0.936413	−0.0423461
$490$	−12.8165	−0.578989
$491$	−35.9321	−1.62159	−0.810797	−	0.585328i	$-0.800966\pi$
$491$	−35.9321	−1.62159	−0.810797	+	0.585328i	$0.800966\pi$
$492$	−0.830653	−0.0374487
$493$	22.7229	1.02339
$494$	0.407978	0.0183558
$495$	−7.08767	−0.318567
$496$	7.51046	0.337229
$497$	24.6925	1.10761
$498$	12.5023	0.560240
$499$	−40.1073	−1.79545	−0.897724	−	0.440559i	$-0.854780\pi$
$499$	−40.1073	−1.79545	−0.897724	+	0.440559i	$0.854780\pi$
$500$	−1.80124	−0.0805537
$501$	7.89507	0.352726
$502$	−29.2740	−1.30656
$503$	−43.9849	−1.96119	−0.980594	−	0.196048i	$-0.937189\pi$
$503$	−43.9849	−1.96119	−0.980594	+	0.196048i	$0.937189\pi$
$504$	−1.74785	−0.0778553
$505$	−37.3193	−1.66069
$506$	6.41153	0.285027
$507$	−12.8336	−0.569958
$508$	12.5832	0.558289
$509$	17.6572	0.782642	0.391321	−	0.920254i	$-0.372018\pi$
$509$	17.6572	0.782642	0.391321	+	0.920254i	$0.372018\pi$
$510$	−19.5483	−0.865614
$511$	15.1387	0.669697
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−21.7565	−0.959639
$515$	40.6038	1.78922
$516$	4.93884	0.217420
$517$	9.65849	0.424780
$518$	4.18815	0.184017
$519$	−24.7657	−1.08709
$520$	−1.32542	−0.0581236
$521$	23.7669	1.04125	0.520623	−	0.853787i	$-0.325700\pi$
$521$	23.7669	1.04125	0.520623	+	0.853787i	$0.325700\pi$
$522$	3.77634	0.165286
$523$	19.0522	0.833096	0.416548	−	0.909114i	$-0.363240\pi$
$523$	19.0522	0.833096	0.416548	+	0.909114i	$0.363240\pi$
$524$	4.57492	0.199856
$525$	9.70831	0.423705
$526$	−3.59983	−0.156960
$527$	−45.1916	−1.96858
$528$	2.18165	0.0949443
$529$	−14.3632	−0.624489
$530$	3.24876	0.141117
$531$	−5.76899	−0.250353
$532$	1.74785	0.0757788
$533$	0.338888	0.0146789
$534$	−10.7636	−0.465788
$535$	−26.3786	−1.14045
$536$	−10.3061	−0.445154
$537$	−11.9371	−0.515123
$538$	7.24632	0.312411
$539$	−8.60669	−0.370717
$540$	−3.24876	−0.139804
$541$	−41.1198	−1.76788	−0.883940	−	0.467601i	$-0.845119\pi$
$541$	−41.1198	−1.76788	−0.883940	+	0.467601i	$0.845119\pi$
$542$	−12.5373	−0.538525
$543$	−20.9921	−0.900857
$544$	6.01716	0.257984
$545$	46.0412	1.97219
$546$	0.713083	0.0305171
$547$	−15.1552	−0.647990	−0.323995	−	0.946059i	$-0.605026\pi$
$547$	−15.1552	−0.647990	−0.323995	+	0.946059i	$0.605026\pi$
$548$	−6.01857	−0.257100
$549$	7.54540	0.322030
$550$	−12.1179	−0.516707
$551$	−3.77634	−0.160878
$552$	2.93884	0.125085
$553$	−27.9323	−1.18780
$554$	−25.8053	−1.09636
$555$	7.78460	0.330438
$556$	−11.6706	−0.494942
$557$	38.7809	1.64320	0.821599	−	0.570066i	$-0.193082\pi$
$557$	38.7809	1.64320	0.821599	+	0.570066i	$0.193082\pi$
$558$	−7.51046	−0.317943
$559$	−2.01494	−0.0852227
$560$	−5.67833	−0.239953
$561$	−13.1274	−0.554238
$562$	−16.6319	−0.701576
$563$	29.6278	1.24866	0.624332	−	0.781159i	$-0.285371\pi$
$563$	29.6278	1.24866	0.624332	+	0.781159i	$0.285371\pi$
$564$	4.42714	0.186416
$565$	−23.3606	−0.982788
$566$	−27.8760	−1.17172
$567$	1.74785	0.0734027
$568$	−14.1274	−0.592772
$569$	35.2342	1.47710	0.738548	−	0.674201i	$-0.235512\pi$
$569$	35.2342	1.47710	0.738548	+	0.674201i	$0.235512\pi$
$570$	3.24876	0.136076
$571$	−21.1451	−0.884893	−0.442446	−	0.896795i	$-0.645889\pi$
$571$	−21.1451	−0.884893	−0.442446	+	0.896795i	$0.645889\pi$
$572$	−0.890067	−0.0372156
$573$	−24.6921	−1.03153
$574$	1.45185	0.0605992
$575$	−16.3236	−0.680741
$576$	1.00000	0.0416667
$577$	43.0911	1.79390	0.896952	−	0.442128i	$-0.145776\pi$
$577$	43.0911	1.79390	0.896952	+	0.442128i	$0.145776\pi$
$578$	−19.2062	−0.798873
$579$	14.5459	0.604506
$580$	12.2684	0.509419
$581$	−21.8521	−0.906576
$582$	−3.10066	−0.128527
$583$	2.18165	0.0903549
$584$	−8.66135	−0.358409
$585$	1.32542	0.0547995
$586$	8.64623	0.357173
$587$	−20.7025	−0.854483	−0.427241	−	0.904138i	$-0.640515\pi$
$587$	−20.7025	−0.854483	−0.427241	+	0.904138i	$0.640515\pi$
$588$	−3.94503	−0.162690
$589$	7.51046	0.309463
$590$	−18.7421	−0.771598
$591$	9.26034	0.380920
$592$	−2.39618	−0.0984823
$593$	39.5016	1.62214	0.811068	−	0.584952i	$-0.198887\pi$
$593$	39.5016	1.62214	0.811068	+	0.584952i	$0.198887\pi$
$594$	−2.18165	−0.0895144
$595$	34.1674	1.40073
$596$	19.6669	0.805586
$597$	17.8310	0.729773
$598$	−1.19898	−0.0490300
$599$	16.0582	0.656121	0.328061	−	0.944657i	$-0.393605\pi$
$599$	16.0582	0.656121	0.328061	+	0.944657i	$0.393605\pi$
$600$	−5.55444	−0.226759
$601$	−44.3032	−1.80717	−0.903584	−	0.428412i	$-0.859073\pi$
$601$	−44.3032	−1.80717	−0.903584	+	0.428412i	$0.859073\pi$
$602$	−8.63233	−0.351828
$603$	10.3061	0.419695
$604$	3.34958	0.136293
$605$	20.2735	0.824235
$606$	−11.4872	−0.466637
$607$	−10.9166	−0.443091	−0.221546	−	0.975150i	$-0.571110\pi$
$607$	−10.9166	−0.443091	−0.221546	+	0.975150i	$0.571110\pi$
$608$	−1.00000	−0.0405554
$609$	−6.60047	−0.267465
$610$	24.5132	0.992510
$611$	−1.80617	−0.0730700
$612$	−6.01716	−0.243229
$613$	13.9452	0.563242	0.281621	−	0.959526i	$-0.409128\pi$
$613$	13.9452	0.563242	0.281621	+	0.959526i	$0.409128\pi$
$614$	−16.4014	−0.661906
$615$	2.69859	0.108818
$616$	−3.81320	−0.153638
$617$	17.7879	0.716112	0.358056	−	0.933700i	$-0.383440\pi$
$617$	17.7879	0.716112	0.358056	+	0.933700i	$0.383440\pi$
$618$	12.4983	0.502754
$619$	−13.4215	−0.539456	−0.269728	−	0.962937i	$-0.586934\pi$
$619$	−13.4215	−0.539456	−0.269728	+	0.962937i	$0.586934\pi$
$620$	−24.3997	−0.979914
$621$	−2.93884	−0.117931
$622$	−2.40290	−0.0963473
$623$	18.8132	0.753734
$624$	−0.407978	−0.0163322
$625$	−21.9204	−0.876816
$626$	−19.3876	−0.774885
$627$	2.18165	0.0871269
$628$	13.5586	0.541047
$629$	14.4182	0.574890
$630$	5.67833	0.226230
$631$	39.8076	1.58471	0.792357	−	0.610057i	$-0.208854\pi$
$631$	39.8076	1.58471	0.792357	+	0.610057i	$0.208854\pi$
$632$	15.9810	0.635688
$633$	21.7283	0.863622
$634$	−14.1456	−0.561792
$635$	−40.8798	−1.62227
$636$	1.00000	0.0396526
$637$	1.60949	0.0637701
$638$	8.23868	0.326172
$639$	14.1274	0.558871
$640$	3.24876	0.128418
$641$	−36.8871	−1.45695	−0.728477	−	0.685070i	$-0.759771\pi$
$641$	−36.8871	−1.45695	−0.728477	+	0.685070i	$0.759771\pi$
$642$	−8.11960	−0.320455
$643$	1.31593	0.0518953	0.0259476	−	0.999663i	$-0.491740\pi$
$643$	1.31593	0.0518953	0.0259476	+	0.999663i	$0.491740\pi$
$644$	−5.13664	−0.202412
$645$	−16.0451	−0.631775
$646$	6.01716	0.236742
$647$	−46.5452	−1.82988	−0.914940	−	0.403591i	$-0.867762\pi$
$647$	−46.5452	−1.82988	−0.914940	+	0.403591i	$0.867762\pi$
$648$	−1.00000	−0.0392837
$649$	−12.5859	−0.494041
$650$	2.26609	0.0888833
$651$	13.1271	0.514493
$652$	−0.936413	−0.0366728
$653$	32.3899	1.26752	0.633758	−	0.773531i	$-0.281511\pi$
$653$	32.3899	1.26752	0.633758	+	0.773531i	$0.281511\pi$
$654$	14.1719	0.554166
$655$	−14.8628	−0.580738
$656$	−0.830653	−0.0324316
$657$	8.66135	0.337912
$658$	−7.73796	−0.301657
$659$	11.6606	0.454234	0.227117	−	0.973867i	$-0.427070\pi$
$659$	11.6606	0.454234	0.227117	+	0.973867i	$0.427070\pi$
$660$	−7.08767	−0.275887
$661$	14.5638	0.566467	0.283234	−	0.959051i	$-0.408593\pi$
$661$	14.5638	0.566467	0.283234	+	0.959051i	$0.408593\pi$
$662$	10.0450	0.390409
$663$	2.45487	0.0953392
$664$	12.5023	0.485182
$665$	−5.67833	−0.220196
$666$	2.39618	0.0928500
$667$	11.0981	0.429719
$668$	7.89507	0.305470
$669$	18.6074	0.719403
$670$	33.4819	1.29352
$671$	16.4615	0.635488
$672$	−1.74785	−0.0674247
$673$	26.1405	1.00764	0.503821	−	0.863808i	$-0.331927\pi$
$673$	26.1405	1.00764	0.503821	+	0.863808i	$0.331927\pi$
$674$	−7.81274	−0.300936
$675$	5.55444	0.213790
$676$	−12.8336	−0.493598
$677$	13.0109	0.500050	0.250025	−	0.968239i	$-0.419561\pi$
$677$	13.0109	0.500050	0.250025	+	0.968239i	$0.419561\pi$
$678$	−7.19062	−0.276154
$679$	5.41948	0.207981
$680$	−19.5483	−0.749643
$681$	23.1012	0.885240
$682$	−16.3852	−0.627423
$683$	41.9766	1.60619	0.803095	−	0.595851i	$-0.203185\pi$
$683$	41.9766	1.60619	0.803095	+	0.595851i	$0.203185\pi$
$684$	1.00000	0.0382360
$685$	19.5529	0.747077
$686$	19.1302	0.730396
$687$	8.93999	0.341082
$688$	4.93884	0.188291
$689$	−0.407978	−0.0155427
$690$	−9.54757	−0.363470
$691$	11.0901	0.421887	0.210944	−	0.977498i	$-0.432346\pi$
$691$	11.0901	0.421887	0.210944	+	0.977498i	$0.432346\pi$
$692$	−24.7657	−0.941450
$693$	3.81320	0.144851
$694$	−27.1607	−1.03101
$695$	37.9149	1.43819
$696$	3.77634	0.143142
$697$	4.99817	0.189319
$698$	−25.0347	−0.947578
$699$	25.5728	0.967253
$700$	9.70831	0.366940
$701$	−45.3658	−1.71344	−0.856722	−	0.515779i	$-0.827503\pi$
$701$	−45.3658	−1.71344	−0.856722	+	0.515779i	$0.827503\pi$
$702$	0.407978	0.0153981
$703$	−2.39618	−0.0903735
$704$	2.18165	0.0822242
$705$	−14.3827	−0.541684
$706$	33.8071	1.27235
$707$	20.0779	0.755109
$708$	−5.76899	−0.216812
$709$	−8.74917	−0.328582	−0.164291	−	0.986412i	$-0.552534\pi$
$709$	−8.74917	−0.328582	−0.164291	+	0.986412i	$0.552534\pi$
$710$	45.8965	1.72247
$711$	−15.9810	−0.599333
$712$	−10.7636	−0.403384
$713$	−22.0720	−0.826603
$714$	10.5171	0.393592
$715$	2.89161	0.108140
$716$	−11.9371	−0.446110
$717$	−28.1152	−1.04998
$718$	4.93541	0.184188
$719$	−22.6833	−0.845943	−0.422971	−	0.906143i	$-0.639013\pi$
$719$	−22.6833	−0.845943	−0.422971	+	0.906143i	$0.639013\pi$
$720$	−3.24876	−0.121074
$721$	−21.8450	−0.813552
$722$	−1.00000	−0.0372161
$723$	−18.1251	−0.674081
$724$	−20.9921	−0.780165
$725$	−20.9755	−0.779009
$726$	6.24038	0.231602
$727$	29.5252	1.09503	0.547515	−	0.836796i	$-0.315574\pi$
$727$	29.5252	1.09503	0.547515	+	0.836796i	$0.315574\pi$
$728$	0.713083	0.0264286
$729$	1.00000	0.0370370
$730$	28.1386	1.04146
$731$	−29.7178	−1.09915
$732$	7.54540	0.278886
$733$	−47.4832	−1.75383	−0.876917	−	0.480642i	$-0.840404\pi$
$733$	−47.4832	−1.75383	−0.876917	+	0.480642i	$0.840404\pi$
$734$	4.60875	0.170112
$735$	12.8165	0.472742
$736$	2.93884	0.108327
$737$	22.4842	0.828218
$738$	0.830653	0.0305768
$739$	8.17785	0.300827	0.150414	−	0.988623i	$-0.451939\pi$
$739$	8.17785	0.300827	0.150414	+	0.988623i	$0.451939\pi$
$740$	7.78460	0.286168
$741$	−0.407978	−0.0149874
$742$	−1.74785	−0.0641655
$743$	31.6100	1.15966	0.579829	−	0.814738i	$-0.303119\pi$
$743$	31.6100	1.15966	0.579829	+	0.814738i	$0.303119\pi$
$744$	−7.51046	−0.275347
$745$	−63.8929	−2.34086
$746$	−5.49294	−0.201111
$747$	−12.5023	−0.457434
$748$	−13.1274	−0.479984
$749$	14.1918	0.518558
$750$	1.80124	0.0657718
$751$	−7.18580	−0.262214	−0.131107	−	0.991368i	$-0.541853\pi$
$751$	−7.18580	−0.262214	−0.131107	+	0.991368i	$0.541853\pi$
$752$	4.42714	0.161441
$753$	29.2740	1.06680
$754$	−1.54066	−0.0561077
$755$	−10.8820	−0.396036
$756$	1.74785	0.0635686
$757$	11.4279	0.415354	0.207677	−	0.978197i	$-0.433410\pi$
$757$	11.4279	0.415354	0.207677	+	0.978197i	$0.433410\pi$
$758$	−14.9288	−0.542238
$759$	−6.41153	−0.232724
$760$	3.24876	0.117845
$761$	−3.49304	−0.126622	−0.0633112	−	0.997994i	$-0.520166\pi$
$761$	−3.49304	−0.126622	−0.0633112	+	0.997994i	$0.520166\pi$
$762$	−12.5832	−0.455841
$763$	−24.7704	−0.896747
$764$	−24.6921	−0.893330
$765$	19.5483	0.706771
$766$	13.6160	0.491966
$767$	2.35362	0.0849843
$768$	1.00000	0.0360844
$769$	3.09065	0.111452	0.0557258	−	0.998446i	$-0.482253\pi$
$769$	3.09065	0.111452	0.0557258	+	0.998446i	$0.482253\pi$
$770$	12.3882	0.446438
$771$	21.7565	0.783542
$772$	14.5459	0.523518
$773$	7.58208	0.272708	0.136354	−	0.990660i	$-0.456461\pi$
$773$	7.58208	0.272708	0.136354	+	0.990660i	$0.456461\pi$
$774$	−4.93884	−0.177523
$775$	41.7164	1.49850
$776$	−3.10066	−0.111307
$777$	−4.18815	−0.150249
$778$	−13.7622	−0.493397
$779$	−0.830653	−0.0297612
$780$	1.32542	0.0474577
$781$	30.8211	1.10287
$782$	−17.6835	−0.632359
$783$	−3.77634	−0.134956
$784$	−3.94503	−0.140894
$785$	−44.0486	−1.57216
$786$	−4.57492	−0.163182
$787$	27.9345	0.995759	0.497880	−	0.867246i	$-0.334112\pi$
$787$	27.9345	0.995759	0.497880	+	0.867246i	$0.334112\pi$
$788$	9.26034	0.329886
$789$	3.59983	0.128157
$790$	−51.9183	−1.84717
$791$	12.5681	0.446871
$792$	−2.18165	−0.0775217
$793$	−3.07836	−0.109316
$794$	−21.9797	−0.780029
$795$	−3.24876	−0.115222
$796$	17.8310	0.632002
$797$	−55.2861	−1.95833	−0.979166	−	0.203060i	$-0.934912\pi$
$797$	−55.2861	−1.95833	−0.979166	+	0.203060i	$0.934912\pi$
$798$	−1.74785	−0.0618731
$799$	−26.6388	−0.942413
$800$	−5.55444	−0.196379
$801$	10.7636	0.380314
$802$	−5.94465	−0.209913
$803$	18.8961	0.666828
$804$	10.3061	0.363466
$805$	16.6877	0.588164
$806$	3.06410	0.107928
$807$	−7.24632	−0.255083
$808$	−11.4872	−0.404120
$809$	42.9161	1.50885	0.754426	−	0.656386i	$-0.227916\pi$
$809$	42.9161	1.50885	0.754426	+	0.656386i	$0.227916\pi$
$810$	3.24876	0.114150
$811$	−5.66680	−0.198988	−0.0994942	−	0.995038i	$-0.531722\pi$
$811$	−5.66680	−0.198988	−0.0994942	+	0.995038i	$0.531722\pi$
$812$	−6.60047	−0.231631
$813$	12.5373	0.439704
$814$	5.22763	0.183228
$815$	3.04218	0.106563
$816$	−6.01716	−0.210643
$817$	4.93884	0.172788
$818$	−32.8534	−1.14869
$819$	−0.713083	−0.0249171
$820$	2.69859	0.0942389
$821$	17.6674	0.616597	0.308298	−	0.951290i	$-0.400240\pi$
$821$	17.6674	0.616597	0.308298	+	0.951290i	$0.400240\pi$
$822$	6.01857	0.209922
$823$	4.81945	0.167996	0.0839978	−	0.996466i	$-0.473231\pi$
$823$	4.81945	0.167996	0.0839978	+	0.996466i	$0.473231\pi$
$824$	12.4983	0.435397
$825$	12.1179	0.421890
$826$	10.0833	0.350843
$827$	1.51550	0.0526990	0.0263495	−	0.999653i	$-0.491612\pi$
$827$	1.51550	0.0526990	0.0263495	+	0.999653i	$0.491612\pi$
$828$	−2.93884	−0.102132
$829$	−27.4138	−0.952122	−0.476061	−	0.879412i	$-0.657936\pi$
$829$	−27.4138	−0.952122	−0.476061	+	0.879412i	$0.657936\pi$
$830$	−40.6169	−1.40983
$831$	25.8053	0.895176
$832$	−0.407978	−0.0141441
$833$	23.7379	0.822469
$834$	11.6706	0.404119
$835$	−25.6492	−0.887627
$836$	2.18165	0.0754541
$837$	7.51046	0.259599
$838$	−5.50423	−0.190141
$839$	7.58401	0.261829	0.130915	−	0.991394i	$-0.458209\pi$
$839$	7.58401	0.261829	0.130915	+	0.991394i	$0.458209\pi$
$840$	5.67833	0.195921
$841$	−14.7392	−0.508249
$842$	13.7951	0.475410
$843$	16.6319	0.572835
$844$	21.7283	0.747919
$845$	41.6931	1.43429
$846$	−4.42714	−0.152208
$847$	−10.9072	−0.374777
$848$	1.00000	0.0343401
$849$	27.8760	0.956704
$850$	33.4219	1.14636
$851$	7.04197	0.241396
$852$	14.1274	0.483997
$853$	−39.9336	−1.36730	−0.683649	−	0.729811i	$-0.739608\pi$
$853$	−39.9336	−1.36730	−0.683649	+	0.729811i	$0.739608\pi$
$854$	−13.1882	−0.451291
$855$	−3.24876	−0.111105
$856$	−8.11960	−0.277522
$857$	−39.8240	−1.36036	−0.680181	−	0.733044i	$-0.738099\pi$
$857$	−39.8240	−1.36036	−0.680181	+	0.733044i	$0.738099\pi$
$858$	0.890067	0.0303864
$859$	31.6880	1.08118	0.540591	−	0.841286i	$-0.318201\pi$
$859$	31.6880	1.08118	0.540591	+	0.841286i	$0.318201\pi$
$860$	−16.0451	−0.547133
$861$	−1.45185	−0.0494791
$862$	5.01852	0.170931
$863$	4.31879	0.147013	0.0735066	−	0.997295i	$-0.476581\pi$
$863$	4.31879	0.147013	0.0735066	+	0.997295i	$0.476581\pi$
$864$	−1.00000	−0.0340207
$865$	80.4578	2.73565
$866$	−31.1100	−1.05716
$867$	19.2062	0.652277
$868$	13.1271	0.445564
$869$	−34.8649	−1.18271
$870$	−12.2684	−0.415939
$871$	−4.20464	−0.142469
$872$	14.1719	0.479922
$873$	3.10066	0.104942
$874$	2.93884	0.0994076
$875$	−3.14829	−0.106431
$876$	8.66135	0.292640
$877$	−30.5443	−1.03141	−0.515704	−	0.856767i	$-0.672470\pi$
$877$	−30.5443	−1.03141	−0.515704	+	0.856767i	$0.672470\pi$
$878$	23.7636	0.801983
$879$	−8.64623	−0.291630
$880$	−7.08767	−0.238925
$881$	30.0275	1.01165	0.505826	−	0.862636i	$-0.331188\pi$
$881$	30.0275	1.01165	0.505826	+	0.862636i	$0.331188\pi$
$882$	3.94503	0.132836
$883$	−37.7261	−1.26959	−0.634793	−	0.772682i	$-0.718915\pi$
$883$	−37.7261	−1.26959	−0.634793	+	0.772682i	$0.718915\pi$
$884$	2.45487	0.0825662
$885$	18.7421	0.630007
$886$	7.40902	0.248911
$887$	−2.43268	−0.0816816	−0.0408408	−	0.999166i	$-0.513004\pi$
$887$	−2.43268	−0.0816816	−0.0408408	+	0.999166i	$0.513004\pi$
$888$	2.39618	0.0804104
$889$	21.9935	0.737639
$890$	34.9684	1.17214
$891$	2.18165	0.0730882
$892$	18.6074	0.623021
$893$	4.42714	0.148149
$894$	−19.6669	−0.657759
$895$	38.7807	1.29630
$896$	−1.74785	−0.0583915
$897$	1.19898	0.0400328
$898$	17.6881	0.590261
$899$	−28.3621	−0.945928
$900$	5.55444	0.185148
$901$	−6.01716	−0.200461
$902$	1.81220	0.0603396
$903$	8.63233	0.287266
$904$	−7.19062	−0.239157
$905$	68.1983	2.26699
$906$	−3.34958	−0.111282
$907$	−21.4817	−0.713290	−0.356645	−	0.934240i	$-0.616079\pi$
$907$	−21.4817	−0.713290	−0.356645	+	0.934240i	$0.616079\pi$
$908$	23.1012	0.766640
$909$	11.4872	0.381008
$910$	−2.31663	−0.0767957
$911$	−23.8015	−0.788578	−0.394289	−	0.918987i	$-0.629009\pi$
$911$	−23.8015	−0.788578	−0.394289	+	0.918987i	$0.629009\pi$
$912$	1.00000	0.0331133
$913$	−27.2756	−0.902692
$914$	−17.1310	−0.566644
$915$	−24.5132	−0.810381
$916$	8.93999	0.295386
$917$	7.99626	0.264060
$918$	6.01716	0.198596
$919$	7.90419	0.260735	0.130368	−	0.991466i	$-0.458384\pi$
$919$	7.90419	0.260735	0.130368	+	0.991466i	$0.458384\pi$
$920$	−9.54757	−0.314774
$921$	16.4014	0.540444
$922$	−26.0070	−0.856494
$923$	−5.76367	−0.189713
$924$	3.81320	0.125445
$925$	−13.3094	−0.437611
$926$	31.3255	1.02942
$927$	−12.4983	−0.410497
$928$	3.77634	0.123965
$929$	−24.0102	−0.787751	−0.393875	−	0.919164i	$-0.628866\pi$
$929$	−24.0102	−0.787751	−0.393875	+	0.919164i	$0.628866\pi$
$930$	24.3997	0.800097
$931$	−3.94503	−0.129293
$932$	25.5728	0.837665
$933$	2.40290	0.0786673
$934$	15.4157	0.504418
$935$	42.6477	1.39473
$936$	0.407978	0.0133352
$937$	−23.4463	−0.765956	−0.382978	−	0.923758i	$-0.625101\pi$
$937$	−23.4463	−0.765956	−0.382978	+	0.923758i	$0.625101\pi$
$938$	−18.0134	−0.588158
$939$	19.3876	0.632691
$940$	−14.3827	−0.469112
$941$	16.8223	0.548391	0.274195	−	0.961674i	$-0.411589\pi$
$941$	16.8223	0.548391	0.274195	+	0.961674i	$0.411589\pi$
$942$	−13.5586	−0.441763
$943$	2.44115	0.0794949
$944$	−5.76899	−0.187765
$945$	−5.67833	−0.184716
$946$	−10.7748	−0.350320
$947$	8.07763	0.262488	0.131244	−	0.991350i	$-0.458103\pi$
$947$	8.07763	0.262488	0.131244	+	0.991350i	$0.458103\pi$
$948$	−15.9810	−0.519037
$949$	−3.53364	−0.114707
$950$	−5.55444	−0.180210
$951$	14.1456	0.458701
$952$	10.5171	0.340860
$953$	1.83317	0.0593823	0.0296912	−	0.999559i	$-0.490548\pi$
$953$	1.83317	0.0593823	0.0296912	+	0.999559i	$0.490548\pi$
$954$	−1.00000	−0.0323762
$955$	80.2188	2.59582
$956$	−28.1152	−0.909310
$957$	−8.23868	−0.266319
$958$	−3.53117	−0.114087
$959$	−10.5195	−0.339694
$960$	−3.24876	−0.104853
$961$	25.4070	0.819579
$962$	−0.977587	−0.0315187
$963$	8.11960	0.261650
$964$	−18.1251	−0.583771
$965$	−47.2561	−1.52123
$966$	5.13664	0.165269
$967$	−23.7526	−0.763833	−0.381916	−	0.924197i	$-0.624736\pi$
$967$	−23.7526	−0.763833	−0.381916	+	0.924197i	$0.624736\pi$
$968$	6.24038	0.200574
$969$	−6.01716	−0.193299
$970$	10.0733	0.323434
$971$	50.9223	1.63418	0.817088	−	0.576513i	$-0.195587\pi$
$971$	50.9223	1.63418	0.817088	+	0.576513i	$0.195587\pi$
$972$	1.00000	0.0320750
$973$	−20.3984	−0.653942
$974$	−2.01551	−0.0645812
$975$	−2.26609	−0.0725729
$976$	7.54540	0.241522
$977$	−3.58048	−0.114550	−0.0572749	−	0.998358i	$-0.518241\pi$
$977$	−3.58048	−0.114550	−0.0572749	+	0.998358i	$0.518241\pi$
$978$	0.936413	0.0299432
$979$	23.4825	0.750505
$980$	12.8165	0.409407
$981$	−14.1719	−0.452475
$982$	35.9321	1.14664
$983$	−11.7563	−0.374967	−0.187484	−	0.982268i	$-0.560033\pi$
$983$	−11.7563	−0.374967	−0.187484	+	0.982268i	$0.560033\pi$
$984$	0.830653	0.0264803
$985$	−30.0846	−0.958576
$986$	−22.7229	−0.723644
$987$	7.73796	0.246302
$988$	−0.407978	−0.0129795
$989$	−14.5144	−0.461532
$990$	7.08767	0.225261
$991$	−15.1045	−0.479809	−0.239905	−	0.970796i	$-0.577116\pi$
$991$	−15.1045	−0.479809	−0.239905	+	0.970796i	$0.577116\pi$
$992$	−7.51046	−0.238457
$993$	−10.0450	−0.318768
$994$	−24.6925	−0.783199
$995$	−57.9285	−1.83646
$996$	−12.5023	−0.396150
$997$	−21.0458	−0.666526	−0.333263	−	0.942834i	$-0.608150\pi$
$997$	−21.0458	−0.666526	−0.333263	+	0.942834i	$0.608150\pi$
$998$	40.1073	1.26957
$999$	−2.39618	−0.0758117

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bf.1.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bf.1.2	✓	12	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.24876 q^{5} -1.00000 q^{6} +1.74785 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.24876 q^{5} -1.00000 q^{6} +1.74785 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.24876 q^{10} +2.18165 q^{11} +1.00000 q^{12} -0.407978 q^{13} -1.74785 q^{14} -3.24876 q^{15} +1.00000 q^{16} -6.01716 q^{17} -1.00000 q^{18} +1.00000 q^{19} -3.24876 q^{20} +1.74785 q^{21} -2.18165 q^{22} -2.93884 q^{23} -1.00000 q^{24} +5.55444 q^{25} +0.407978 q^{26} +1.00000 q^{27} +1.74785 q^{28} -3.77634 q^{29} +3.24876 q^{30} +7.51046 q^{31} -1.00000 q^{32} +2.18165 q^{33} +6.01716 q^{34} -5.67833 q^{35} +1.00000 q^{36} -2.39618 q^{37} -1.00000 q^{38} -0.407978 q^{39} +3.24876 q^{40} -0.830653 q^{41} -1.74785 q^{42} +4.93884 q^{43} +2.18165 q^{44} -3.24876 q^{45} +2.93884 q^{46} +4.42714 q^{47} +1.00000 q^{48} -3.94503 q^{49} -5.55444 q^{50} -6.01716 q^{51} -0.407978 q^{52} +1.00000 q^{53} -1.00000 q^{54} -7.08767 q^{55} -1.74785 q^{56} +1.00000 q^{57} +3.77634 q^{58} -5.76899 q^{59} -3.24876 q^{60} +7.54540 q^{61} -7.51046 q^{62} +1.74785 q^{63} +1.00000 q^{64} +1.32542 q^{65} -2.18165 q^{66} +10.3061 q^{67} -6.01716 q^{68} -2.93884 q^{69} +5.67833 q^{70} +14.1274 q^{71} -1.00000 q^{72} +8.66135 q^{73} +2.39618 q^{74} +5.55444 q^{75} +1.00000 q^{76} +3.81320 q^{77} +0.407978 q^{78} -15.9810 q^{79} -3.24876 q^{80} +1.00000 q^{81} +0.830653 q^{82} -12.5023 q^{83} +1.74785 q^{84} +19.5483 q^{85} -4.93884 q^{86} -3.77634 q^{87} -2.18165 q^{88} +10.7636 q^{89} +3.24876 q^{90} -0.713083 q^{91} -2.93884 q^{92} +7.51046 q^{93} -4.42714 q^{94} -3.24876 q^{95} -1.00000 q^{96} +3.10066 q^{97} +3.94503 q^{98} +2.18165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 7 q^{5} - 12 q^{6} + 5 q^{7} - 12 q^{8} + 12 q^{9} + 7 q^{10} - 5 q^{11} + 12 q^{12} + 10 q^{13} - 5 q^{14} - 7 q^{15} + 12 q^{16} + 6 q^{17} - 12 q^{18} + 12 q^{19} - 7 q^{20} + 5 q^{21} + 5 q^{22} - 12 q^{24} + 21 q^{25} - 10 q^{26} + 12 q^{27} + 5 q^{28} + 7 q^{30} + 2 q^{31} - 12 q^{32} - 5 q^{33} - 6 q^{34} - 17 q^{35} + 12 q^{36} + 16 q^{37} - 12 q^{38} + 10 q^{39} + 7 q^{40} + 7 q^{41} - 5 q^{42} + 24 q^{43} - 5 q^{44} - 7 q^{45} + 4 q^{47} + 12 q^{48} + 29 q^{49} - 21 q^{50} + 6 q^{51} + 10 q^{52} + 12 q^{53} - 12 q^{54} - 2 q^{55} - 5 q^{56} + 12 q^{57} + 2 q^{59} - 7 q^{60} + 29 q^{61} - 2 q^{62} + 5 q^{63} + 12 q^{64} - 17 q^{65} + 5 q^{66} + 36 q^{67} + 6 q^{68} + 17 q^{70} - 3 q^{71} - 12 q^{72} + 7 q^{73} - 16 q^{74} + 21 q^{75} + 12 q^{76} - 35 q^{77} - 10 q^{78} + 40 q^{79} - 7 q^{80} + 12 q^{81} - 7 q^{82} + 24 q^{83} + 5 q^{84} - 22 q^{85} - 24 q^{86} + 5 q^{88} - 45 q^{89} + 7 q^{90} + 71 q^{91} + 2 q^{93} - 4 q^{94} - 7 q^{95} - 12 q^{96} + q^{97} - 29 q^{98} - 5 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 7 * q^5 - 12 * q^6 + 5 * q^7 - 12 * q^8 + 12 * q^9 + 7 * q^10 - 5 * q^11 + 12 * q^12 + 10 * q^13 - 5 * q^14 - 7 * q^15 + 12 * q^16 + 6 * q^17 - 12 * q^18 + 12 * q^19 - 7 * q^20 + 5 * q^21 + 5 * q^22 - 12 * q^24 + 21 * q^25 - 10 * q^26 + 12 * q^27 + 5 * q^28 + 7 * q^30 + 2 * q^31 - 12 * q^32 - 5 * q^33 - 6 * q^34 - 17 * q^35 + 12 * q^36 + 16 * q^37 - 12 * q^38 + 10 * q^39 + 7 * q^40 + 7 * q^41 - 5 * q^42 + 24 * q^43 - 5 * q^44 - 7 * q^45 + 4 * q^47 + 12 * q^48 + 29 * q^49 - 21 * q^50 + 6 * q^51 + 10 * q^52 + 12 * q^53 - 12 * q^54 - 2 * q^55 - 5 * q^56 + 12 * q^57 + 2 * q^59 - 7 * q^60 + 29 * q^61 - 2 * q^62 + 5 * q^63 + 12 * q^64 - 17 * q^65 + 5 * q^66 + 36 * q^67 + 6 * q^68 + 17 * q^70 - 3 * q^71 - 12 * q^72 + 7 * q^73 - 16 * q^74 + 21 * q^75 + 12 * q^76 - 35 * q^77 - 10 * q^78 + 40 * q^79 - 7 * q^80 + 12 * q^81 - 7 * q^82 + 24 * q^83 + 5 * q^84 - 22 * q^85 - 24 * q^86 + 5 * q^88 - 45 * q^89 + 7 * q^90 + 71 * q^91 + 2 * q^93 - 4 * q^94 - 7 * q^95 - 12 * q^96 + q^97 - 29 * q^98 - 5 * q^99

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