LMFDB - Embedded newform 6042.2.a.v.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2456129013$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.21848308.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 4x^{4} + 9x^{3} + 6x^{2} - 4x - 2 $ x^6 - 3x^5 - 4x^4 + 9x^3 + 6x^2 - 4*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.712460$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.82997 q^{5} -1.00000 q^{6} +1.67867 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.82997 q^{5} -1.00000 q^{6} +1.67867 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.82997 q^{10} +2.01624 q^{11} +1.00000 q^{12} -4.91732 q^{13} -1.67867 q^{14} +1.82997 q^{15} +1.00000 q^{16} -6.76353 q^{17} -1.00000 q^{18} +1.00000 q^{19} +1.82997 q^{20} +1.67867 q^{21} -2.01624 q^{22} -3.81454 q^{23} -1.00000 q^{24} -1.65120 q^{25} +4.91732 q^{26} +1.00000 q^{27} +1.67867 q^{28} +2.88565 q^{29} -1.82997 q^{30} -4.78519 q^{31} -1.00000 q^{32} +2.01624 q^{33} +6.76353 q^{34} +3.07192 q^{35} +1.00000 q^{36} -7.07868 q^{37} -1.00000 q^{38} -4.91732 q^{39} -1.82997 q^{40} -9.22847 q^{41} -1.67867 q^{42} +5.31931 q^{43} +2.01624 q^{44} +1.82997 q^{45} +3.81454 q^{46} -0.326577 q^{47} +1.00000 q^{48} -4.18206 q^{49} +1.65120 q^{50} -6.76353 q^{51} -4.91732 q^{52} -1.00000 q^{53} -1.00000 q^{54} +3.68966 q^{55} -1.67867 q^{56} +1.00000 q^{57} -2.88565 q^{58} -1.93626 q^{59} +1.82997 q^{60} -2.19824 q^{61} +4.78519 q^{62} +1.67867 q^{63} +1.00000 q^{64} -8.99856 q^{65} -2.01624 q^{66} +1.21471 q^{67} -6.76353 q^{68} -3.81454 q^{69} -3.07192 q^{70} +5.02747 q^{71} -1.00000 q^{72} -14.3454 q^{73} +7.07868 q^{74} -1.65120 q^{75} +1.00000 q^{76} +3.38461 q^{77} +4.91732 q^{78} -5.68004 q^{79} +1.82997 q^{80} +1.00000 q^{81} +9.22847 q^{82} +3.63268 q^{83} +1.67867 q^{84} -12.3771 q^{85} -5.31931 q^{86} +2.88565 q^{87} -2.01624 q^{88} -11.9694 q^{89} -1.82997 q^{90} -8.25456 q^{91} -3.81454 q^{92} -4.78519 q^{93} +0.326577 q^{94} +1.82997 q^{95} -1.00000 q^{96} +14.3188 q^{97} +4.18206 q^{98} +2.01624 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} - 7 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 - 7 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} - 7 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + q^{11} + 6 q^{12} - 13 q^{13} + 7 q^{14} + 3 q^{15} + 6 q^{16} - 5 q^{17} - 6 q^{18} + 6 q^{19} + 3 q^{20} - 7 q^{21} - q^{22} + 9 q^{23} - 6 q^{24} - 5 q^{25} + 13 q^{26} + 6 q^{27} - 7 q^{28} - 12 q^{29} - 3 q^{30} - 2 q^{31} - 6 q^{32} + q^{33} + 5 q^{34} - 14 q^{35} + 6 q^{36} - 7 q^{37} - 6 q^{38} - 13 q^{39} - 3 q^{40} - 18 q^{41} + 7 q^{42} - 11 q^{43} + q^{44} + 3 q^{45} - 9 q^{46} - 5 q^{47} + 6 q^{48} + 3 q^{49} + 5 q^{50} - 5 q^{51} - 13 q^{52} - 6 q^{53} - 6 q^{54} + 8 q^{55} + 7 q^{56} + 6 q^{57} + 12 q^{58} + 2 q^{59} + 3 q^{60} - 12 q^{61} + 2 q^{62} - 7 q^{63} + 6 q^{64} - 5 q^{65} - q^{66} - 9 q^{67} - 5 q^{68} + 9 q^{69} + 14 q^{70} + 18 q^{71} - 6 q^{72} - 31 q^{73} + 7 q^{74} - 5 q^{75} + 6 q^{76} + q^{77} + 13 q^{78} - 17 q^{79} + 3 q^{80} + 6 q^{81} + 18 q^{82} - 9 q^{83} - 7 q^{84} - 32 q^{85} + 11 q^{86} - 12 q^{87} - q^{88} + 18 q^{89} - 3 q^{90} + 9 q^{92} - 2 q^{93} + 5 q^{94} + 3 q^{95} - 6 q^{96} - 7 q^{97} - 3 q^{98} + q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 - 7 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + q^11 + 6 * q^12 - 13 * q^13 + 7 * q^14 + 3 * q^15 + 6 * q^16 - 5 * q^17 - 6 * q^18 + 6 * q^19 + 3 * q^20 - 7 * q^21 - q^22 + 9 * q^23 - 6 * q^24 - 5 * q^25 + 13 * q^26 + 6 * q^27 - 7 * q^28 - 12 * q^29 - 3 * q^30 - 2 * q^31 - 6 * q^32 + q^33 + 5 * q^34 - 14 * q^35 + 6 * q^36 - 7 * q^37 - 6 * q^38 - 13 * q^39 - 3 * q^40 - 18 * q^41 + 7 * q^42 - 11 * q^43 + q^44 + 3 * q^45 - 9 * q^46 - 5 * q^47 + 6 * q^48 + 3 * q^49 + 5 * q^50 - 5 * q^51 - 13 * q^52 - 6 * q^53 - 6 * q^54 + 8 * q^55 + 7 * q^56 + 6 * q^57 + 12 * q^58 + 2 * q^59 + 3 * q^60 - 12 * q^61 + 2 * q^62 - 7 * q^63 + 6 * q^64 - 5 * q^65 - q^66 - 9 * q^67 - 5 * q^68 + 9 * q^69 + 14 * q^70 + 18 * q^71 - 6 * q^72 - 31 * q^73 + 7 * q^74 - 5 * q^75 + 6 * q^76 + q^77 + 13 * q^78 - 17 * q^79 + 3 * q^80 + 6 * q^81 + 18 * q^82 - 9 * q^83 - 7 * q^84 - 32 * q^85 + 11 * q^86 - 12 * q^87 - q^88 + 18 * q^89 - 3 * q^90 + 9 * q^92 - 2 * q^93 + 5 * q^94 + 3 * q^95 - 6 * q^96 - 7 * q^97 - 3 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.82997	0.818388	0.409194	−	0.912447i	$-0.365810\pi$
$5$	1.82997	0.818388	0.409194	+	0.912447i	$0.365810\pi$
$6$	−1.00000	−0.408248
$7$	1.67867	0.634478	0.317239	−	0.948346i	$-0.397244\pi$
$7$	1.67867	0.634478	0.317239	+	0.948346i	$0.397244\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.82997	−0.578688
$11$	2.01624	0.607920	0.303960	−	0.952685i	$-0.401691\pi$
$11$	2.01624	0.607920	0.303960	+	0.952685i	$0.401691\pi$
$12$	1.00000	0.288675
$13$	−4.91732	−1.36382	−0.681910	−	0.731436i	$-0.738850\pi$
$13$	−4.91732	−1.36382	−0.681910	+	0.731436i	$0.738850\pi$
$14$	−1.67867	−0.448644
$15$	1.82997	0.472497
$16$	1.00000	0.250000
$17$	−6.76353	−1.64040	−0.820199	−	0.572078i	$-0.806137\pi$
$17$	−6.76353	−1.64040	−0.820199	+	0.572078i	$0.806137\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.82997	0.409194
$21$	1.67867	0.366316
$22$	−2.01624	−0.429864
$23$	−3.81454	−0.795387	−0.397693	−	0.917518i	$-0.630189\pi$
$23$	−3.81454	−0.795387	−0.397693	+	0.917518i	$0.630189\pi$
$24$	−1.00000	−0.204124
$25$	−1.65120	−0.330241
$26$	4.91732	0.964366
$27$	1.00000	0.192450
$28$	1.67867	0.317239
$29$	2.88565	0.535852	0.267926	−	0.963440i	$-0.413662\pi$
$29$	2.88565	0.535852	0.267926	+	0.963440i	$0.413662\pi$
$30$	−1.82997	−0.334106
$31$	−4.78519	−0.859445	−0.429723	−	0.902961i	$-0.641389\pi$
$31$	−4.78519	−0.859445	−0.429723	+	0.902961i	$0.641389\pi$
$32$	−1.00000	−0.176777
$33$	2.01624	0.350983
$34$	6.76353	1.15994
$35$	3.07192	0.519249
$36$	1.00000	0.166667
$37$	−7.07868	−1.16373	−0.581864	−	0.813286i	$-0.697676\pi$
$37$	−7.07868	−1.16373	−0.581864	+	0.813286i	$0.697676\pi$
$38$	−1.00000	−0.162221
$39$	−4.91732	−0.787401
$40$	−1.82997	−0.289344
$41$	−9.22847	−1.44124	−0.720622	−	0.693328i	$-0.756144\pi$
$41$	−9.22847	−1.44124	−0.720622	+	0.693328i	$0.756144\pi$
$42$	−1.67867	−0.259025
$43$	5.31931	0.811187	0.405593	−	0.914054i	$-0.367065\pi$
$43$	5.31931	0.811187	0.405593	+	0.914054i	$0.367065\pi$
$44$	2.01624	0.303960
$45$	1.82997	0.272796
$46$	3.81454	0.562423
$47$	−0.326577	−0.0476362	−0.0238181	−	0.999716i	$-0.507582\pi$
$47$	−0.326577	−0.0476362	−0.0238181	+	0.999716i	$0.507582\pi$
$48$	1.00000	0.144338
$49$	−4.18206	−0.597438
$50$	1.65120	0.233516
$51$	−6.76353	−0.947084
$52$	−4.91732	−0.681910
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.00000	−0.136083
$55$	3.68966	0.497514
$56$	−1.67867	−0.224322
$57$	1.00000	0.132453
$58$	−2.88565	−0.378904
$59$	−1.93626	−0.252079	−0.126040	−	0.992025i	$-0.540227\pi$
$59$	−1.93626	−0.252079	−0.126040	+	0.992025i	$0.540227\pi$
$60$	1.82997	0.236248
$61$	−2.19824	−0.281456	−0.140728	−	0.990048i	$-0.544944\pi$
$61$	−2.19824	−0.281456	−0.140728	+	0.990048i	$0.544944\pi$
$62$	4.78519	0.607720
$63$	1.67867	0.211493
$64$	1.00000	0.125000
$65$	−8.99856	−1.11613
$66$	−2.01624	−0.248182
$67$	1.21471	0.148401	0.0742004	−	0.997243i	$-0.476360\pi$
$67$	1.21471	0.148401	0.0742004	+	0.997243i	$0.476360\pi$
$68$	−6.76353	−0.820199
$69$	−3.81454	−0.459217
$70$	−3.07192	−0.367165
$71$	5.02747	0.596650	0.298325	−	0.954464i	$-0.403572\pi$
$71$	5.02747	0.596650	0.298325	+	0.954464i	$0.403572\pi$
$72$	−1.00000	−0.117851
$73$	−14.3454	−1.67900	−0.839501	−	0.543358i	$-0.817153\pi$
$73$	−14.3454	−1.67900	−0.839501	+	0.543358i	$0.817153\pi$
$74$	7.07868	0.822879
$75$	−1.65120	−0.190665
$76$	1.00000	0.114708
$77$	3.38461	0.385712
$78$	4.91732	0.556777
$79$	−5.68004	−0.639055	−0.319527	−	0.947577i	$-0.603524\pi$
$79$	−5.68004	−0.639055	−0.319527	+	0.947577i	$0.603524\pi$
$80$	1.82997	0.204597
$81$	1.00000	0.111111
$82$	9.22847	1.01911
$83$	3.63268	0.398738	0.199369	−	0.979924i	$-0.436111\pi$
$83$	3.63268	0.398738	0.199369	+	0.979924i	$0.436111\pi$
$84$	1.67867	0.183158
$85$	−12.3771	−1.34248
$86$	−5.31931	−0.573596
$87$	2.88565	0.309374
$88$	−2.01624	−0.214932
$89$	−11.9694	−1.26876	−0.634379	−	0.773022i	$-0.718744\pi$
$89$	−11.9694	−1.26876	−0.634379	+	0.773022i	$0.718744\pi$
$90$	−1.82997	−0.192896
$91$	−8.25456	−0.865313
$92$	−3.81454	−0.397693
$93$	−4.78519	−0.496201
$94$	0.326577	0.0336839
$95$	1.82997	0.187751
$96$	−1.00000	−0.102062
$97$	14.3188	1.45386	0.726929	−	0.686713i	$-0.240947\pi$
$97$	14.3188	1.45386	0.726929	+	0.686713i	$0.240947\pi$
$98$	4.18206	0.422452
$99$	2.01624	0.202640
$100$	−1.65120	−0.165120
$101$	11.7632	1.17048	0.585241	−	0.810859i	$-0.301000\pi$
$101$	11.7632	1.17048	0.585241	+	0.810859i	$0.301000\pi$
$102$	6.76353	0.669690
$103$	0.462585	0.0455799	0.0227899	−	0.999740i	$-0.492745\pi$
$103$	0.462585	0.0455799	0.0227899	+	0.999740i	$0.492745\pi$
$104$	4.91732	0.482183
$105$	3.07192	0.299789
$106$	1.00000	0.0971286
$107$	−16.0364	−1.55030	−0.775150	−	0.631777i	$-0.782326\pi$
$107$	−16.0364	−1.55030	−0.775150	+	0.631777i	$0.782326\pi$
$108$	1.00000	0.0962250
$109$	−16.5947	−1.58949	−0.794743	−	0.606946i	$-0.792394\pi$
$109$	−16.5947	−1.58949	−0.794743	+	0.606946i	$0.792394\pi$
$110$	−3.68966	−0.351796
$111$	−7.07868	−0.671878
$112$	1.67867	0.158619
$113$	−10.0659	−0.946923	−0.473461	−	0.880815i	$-0.656996\pi$
$113$	−10.0659	−0.946923	−0.473461	+	0.880815i	$0.656996\pi$
$114$	−1.00000	−0.0936586
$115$	−6.98050	−0.650935
$116$	2.88565	0.267926
$117$	−4.91732	−0.454606
$118$	1.93626	0.178247
$119$	−11.3537	−1.04080
$120$	−1.82997	−0.167053
$121$	−6.93477	−0.630434
$122$	2.19824	0.199019
$123$	−9.22847	−0.832103
$124$	−4.78519	−0.429723
$125$	−12.1715	−1.08865
$126$	−1.67867	−0.149548
$127$	−12.4778	−1.10722	−0.553612	−	0.832775i	$-0.686751\pi$
$127$	−12.4778	−1.10722	−0.553612	+	0.832775i	$0.686751\pi$
$128$	−1.00000	−0.0883883
$129$	5.31931	0.468339
$130$	8.99856	0.789226
$131$	1.18571	0.103596	0.0517979	−	0.998658i	$-0.483505\pi$
$131$	1.18571	0.103596	0.0517979	+	0.998658i	$0.483505\pi$
$132$	2.01624	0.175491
$133$	1.67867	0.145559
$134$	−1.21471	−0.104935
$135$	1.82997	0.157499
$136$	6.76353	0.579968
$137$	18.5007	1.58062	0.790310	−	0.612708i	$-0.209920\pi$
$137$	18.5007	1.58062	0.790310	+	0.612708i	$0.209920\pi$
$138$	3.81454	0.324715
$139$	20.6993	1.75570	0.877848	−	0.478939i	$-0.158979\pi$
$139$	20.6993	1.75570	0.877848	+	0.478939i	$0.158979\pi$
$140$	3.07192	0.259625
$141$	−0.326577	−0.0275028
$142$	−5.02747	−0.421896
$143$	−9.91450	−0.829093
$144$	1.00000	0.0833333
$145$	5.28066	0.438535
$146$	14.3454	1.18723
$147$	−4.18206	−0.344931
$148$	−7.07868	−0.581864
$149$	9.67726	0.792792	0.396396	−	0.918080i	$-0.370261\pi$
$149$	9.67726	0.792792	0.396396	+	0.918080i	$0.370261\pi$
$150$	1.65120	0.134820
$151$	15.6367	1.27249	0.636246	−	0.771486i	$-0.280486\pi$
$151$	15.6367	1.27249	0.636246	+	0.771486i	$0.280486\pi$
$152$	−1.00000	−0.0811107
$153$	−6.76353	−0.546799
$154$	−3.38461	−0.272739
$155$	−8.75676	−0.703360
$156$	−4.91732	−0.393701
$157$	−13.0127	−1.03853	−0.519264	−	0.854614i	$-0.673794\pi$
$157$	−13.0127	−1.03853	−0.519264	+	0.854614i	$0.673794\pi$
$158$	5.68004	0.451880
$159$	−1.00000	−0.0793052
$160$	−1.82997	−0.144672
$161$	−6.40336	−0.504655
$162$	−1.00000	−0.0785674
$163$	14.4971	1.13550	0.567752	−	0.823200i	$-0.307813\pi$
$163$	14.4971	1.13550	0.567752	+	0.823200i	$0.307813\pi$
$164$	−9.22847	−0.720622
$165$	3.68966	0.287240
$166$	−3.63268	−0.281951
$167$	13.7105	1.06095	0.530474	−	0.847701i	$-0.322014\pi$
$167$	13.7105	1.06095	0.530474	+	0.847701i	$0.322014\pi$
$168$	−1.67867	−0.129512
$169$	11.1800	0.860003
$170$	12.3771	0.949278
$171$	1.00000	0.0764719
$172$	5.31931	0.405593
$173$	16.9629	1.28966	0.644832	−	0.764324i	$-0.276927\pi$
$173$	16.9629	1.28966	0.644832	+	0.764324i	$0.276927\pi$
$174$	−2.88565	−0.218761
$175$	−2.77183	−0.209531
$176$	2.01624	0.151980
$177$	−1.93626	−0.145538
$178$	11.9694	0.897147
$179$	15.6436	1.16926	0.584630	−	0.811300i	$-0.301240\pi$
$179$	15.6436	1.16926	0.584630	+	0.811300i	$0.301240\pi$
$180$	1.82997	0.136398
$181$	−13.6802	−1.01684	−0.508421	−	0.861109i	$-0.669770\pi$
$181$	−13.6802	−1.01684	−0.508421	+	0.861109i	$0.669770\pi$
$182$	8.25456	0.611869
$183$	−2.19824	−0.162499
$184$	3.81454	0.281212
$185$	−12.9538	−0.952381
$186$	4.78519	0.350867
$187$	−13.6369	−0.997230
$188$	−0.326577	−0.0238181
$189$	1.67867	0.122105
$190$	−1.82997	−0.132760
$191$	3.79372	0.274504	0.137252	−	0.990536i	$-0.456173\pi$
$191$	3.79372	0.274504	0.137252	+	0.990536i	$0.456173\pi$
$192$	1.00000	0.0721688
$193$	−12.1220	−0.872559	−0.436280	−	0.899811i	$-0.643704\pi$
$193$	−12.1220	−0.872559	−0.436280	+	0.899811i	$0.643704\pi$
$194$	−14.3188	−1.02803
$195$	−8.99856	−0.644400
$196$	−4.18206	−0.298719
$197$	−15.7107	−1.11934	−0.559671	−	0.828715i	$-0.689073\pi$
$197$	−15.7107	−1.11934	−0.559671	+	0.828715i	$0.689073\pi$
$198$	−2.01624	−0.143288
$199$	−9.53375	−0.675830	−0.337915	−	0.941177i	$-0.609722\pi$
$199$	−9.53375	−0.675830	−0.337915	+	0.941177i	$0.609722\pi$
$200$	1.65120	0.116758
$201$	1.21471	0.0856793
$202$	−11.7632	−0.827656
$203$	4.84406	0.339986
$204$	−6.76353	−0.473542
$205$	−16.8878	−1.17950
$206$	−0.462585	−0.0322298
$207$	−3.81454	−0.265129
$208$	−4.91732	−0.340955
$209$	2.01624	0.139466
$210$	−3.07192	−0.211983
$211$	−5.22430	−0.359655	−0.179828	−	0.983698i	$-0.557554\pi$
$211$	−5.22430	−0.359655	−0.179828	+	0.983698i	$0.557554\pi$
$212$	−1.00000	−0.0686803
$213$	5.02747	0.344476
$214$	16.0364	1.09623
$215$	9.73418	0.663866
$216$	−1.00000	−0.0680414
$217$	−8.03276	−0.545299
$218$	16.5947	1.12394
$219$	−14.3454	−0.969372
$220$	3.68966	0.248757
$221$	33.2585	2.23721
$222$	7.07868	0.475090
$223$	8.03389	0.537989	0.268995	−	0.963142i	$-0.413309\pi$
$223$	8.03389	0.537989	0.268995	+	0.963142i	$0.413309\pi$
$224$	−1.67867	−0.112161
$225$	−1.65120	−0.110080
$226$	10.0659	0.669575
$227$	23.5491	1.56301	0.781504	−	0.623900i	$-0.214453\pi$
$227$	23.5491	1.56301	0.781504	+	0.623900i	$0.214453\pi$
$228$	1.00000	0.0662266
$229$	13.4028	0.885680	0.442840	−	0.896601i	$-0.353971\pi$
$229$	13.4028	0.885680	0.442840	+	0.896601i	$0.353971\pi$
$230$	6.98050	0.460281
$231$	3.38461	0.222691
$232$	−2.88565	−0.189452
$233$	1.75466	0.114951	0.0574757	−	0.998347i	$-0.481695\pi$
$233$	1.75466	0.114951	0.0574757	+	0.998347i	$0.481695\pi$
$234$	4.91732	0.321455
$235$	−0.597627	−0.0389849
$236$	−1.93626	−0.126040
$237$	−5.68004	−0.368958
$238$	11.3537	0.735954
$239$	−7.06655	−0.457097	−0.228549	−	0.973533i	$-0.573398\pi$
$239$	−7.06655	−0.457097	−0.228549	+	0.973533i	$0.573398\pi$
$240$	1.82997	0.118124
$241$	22.3701	1.44098	0.720491	−	0.693464i	$-0.243917\pi$
$241$	22.3701	1.44098	0.720491	+	0.693464i	$0.243917\pi$
$242$	6.93477	0.445784
$243$	1.00000	0.0641500
$244$	−2.19824	−0.140728
$245$	−7.65306	−0.488936
$246$	9.22847	0.588386
$247$	−4.91732	−0.312882
$248$	4.78519	0.303860
$249$	3.63268	0.230212
$250$	12.1715	0.769794
$251$	19.4392	1.22699	0.613496	−	0.789698i	$-0.289763\pi$
$251$	19.4392	1.22699	0.613496	+	0.789698i	$0.289763\pi$
$252$	1.67867	0.105746
$253$	−7.69104	−0.483531
$254$	12.4778	0.782926
$255$	−12.3771	−0.775082
$256$	1.00000	0.0625000
$257$	−16.8818	−1.05306	−0.526529	−	0.850157i	$-0.676507\pi$
$257$	−16.8818	−1.05306	−0.526529	+	0.850157i	$0.676507\pi$
$258$	−5.31931	−0.331166
$259$	−11.8828	−0.738359
$260$	−8.99856	−0.558067
$261$	2.88565	0.178617
$262$	−1.18571	−0.0732532
$263$	−11.3054	−0.697121	−0.348561	−	0.937286i	$-0.613329\pi$
$263$	−11.3054	−0.697121	−0.348561	+	0.937286i	$0.613329\pi$
$264$	−2.01624	−0.124091
$265$	−1.82997	−0.112414
$266$	−1.67867	−0.102926
$267$	−11.9694	−0.732518
$268$	1.21471	0.0742004
$269$	22.7265	1.38566	0.692831	−	0.721100i	$-0.256363\pi$
$269$	22.7265	1.38566	0.692831	+	0.721100i	$0.256363\pi$
$270$	−1.82997	−0.111369
$271$	−25.0006	−1.51868	−0.759338	−	0.650696i	$-0.774477\pi$
$271$	−25.0006	−1.51868	−0.759338	+	0.650696i	$0.774477\pi$
$272$	−6.76353	−0.410099
$273$	−8.25456	−0.499589
$274$	−18.5007	−1.11767
$275$	−3.32923	−0.200760
$276$	−3.81454	−0.229608
$277$	18.4958	1.11130	0.555652	−	0.831415i	$-0.312469\pi$
$277$	18.4958	1.11130	0.555652	+	0.831415i	$0.312469\pi$
$278$	−20.6993	−1.24146
$279$	−4.78519	−0.286482
$280$	−3.07192	−0.183582
$281$	−26.7049	−1.59308	−0.796540	−	0.604586i	$-0.793339\pi$
$281$	−26.7049	−1.59308	−0.796540	+	0.604586i	$0.793339\pi$
$282$	0.326577	0.0194474
$283$	−0.720726	−0.0428427	−0.0214214	−	0.999771i	$-0.506819\pi$
$283$	−0.720726	−0.0428427	−0.0214214	+	0.999771i	$0.506819\pi$
$284$	5.02747	0.298325
$285$	1.82997	0.108398
$286$	9.91450	0.586257
$287$	−15.4916	−0.914438
$288$	−1.00000	−0.0589256
$289$	28.7454	1.69090
$290$	−5.28066	−0.310091
$291$	14.3188	0.839385
$292$	−14.3454	−0.839501
$293$	9.39722	0.548992	0.274496	−	0.961588i	$-0.411489\pi$
$293$	9.39722	0.548992	0.274496	+	0.961588i	$0.411489\pi$
$294$	4.18206	0.243903
$295$	−3.54330	−0.206299
$296$	7.07868	0.411440
$297$	2.01624	0.116994
$298$	−9.67726	−0.560589
$299$	18.7573	1.08476
$300$	−1.65120	−0.0953323
$301$	8.92937	0.514680
$302$	−15.6367	−0.899788
$303$	11.7632	0.675778
$304$	1.00000	0.0573539
$305$	−4.02272	−0.230340
$306$	6.76353	0.386645
$307$	−20.7864	−1.18634	−0.593171	−	0.805077i	$-0.702124\pi$
$307$	−20.7864	−1.18634	−0.593171	+	0.805077i	$0.702124\pi$
$308$	3.38461	0.192856
$309$	0.462585	0.0263155
$310$	8.75676	0.497350
$311$	20.5249	1.16386	0.581932	−	0.813238i	$-0.302297\pi$
$311$	20.5249	1.16386	0.581932	+	0.813238i	$0.302297\pi$
$312$	4.91732	0.278388
$313$	−24.1449	−1.36475	−0.682375	−	0.731002i	$-0.739053\pi$
$313$	−24.1449	−1.36475	−0.682375	+	0.731002i	$0.739053\pi$
$314$	13.0127	0.734350
$315$	3.07192	0.173083
$316$	−5.68004	−0.319527
$317$	13.5367	0.760299	0.380150	−	0.924925i	$-0.375872\pi$
$317$	13.5367	0.760299	0.380150	+	0.924925i	$0.375872\pi$
$318$	1.00000	0.0560772
$319$	5.81817	0.325755
$320$	1.82997	0.102299
$321$	−16.0364	−0.895067
$322$	6.40336	0.356845
$323$	−6.76353	−0.376333
$324$	1.00000	0.0555556
$325$	8.11950	0.450389
$326$	−14.4971	−0.802922
$327$	−16.5947	−0.917690
$328$	9.22847	0.509557
$329$	−0.548216	−0.0302241
$330$	−3.68966	−0.203109
$331$	19.8754	1.09245	0.546224	−	0.837639i	$-0.316065\pi$
$331$	19.8754	1.09245	0.546224	+	0.837639i	$0.316065\pi$
$332$	3.63268	0.199369
$333$	−7.07868	−0.387909
$334$	−13.7105	−0.750204
$335$	2.22289	0.121450
$336$	1.67867	0.0915790
$337$	−24.2650	−1.32180	−0.660899	−	0.750475i	$-0.729825\pi$
$337$	−24.2650	−1.32180	−0.660899	+	0.750475i	$0.729825\pi$
$338$	−11.1800	−0.608114
$339$	−10.0659	−0.546706
$340$	−12.3771	−0.671241
$341$	−9.64810	−0.522474
$342$	−1.00000	−0.0540738
$343$	−18.7710	−1.01354
$344$	−5.31931	−0.286798
$345$	−6.98050	−0.375818
$346$	−16.9629	−0.911930
$347$	26.6638	1.43139	0.715694	−	0.698414i	$-0.246110\pi$
$347$	26.6638	1.43139	0.715694	+	0.698414i	$0.246110\pi$
$348$	2.88565	0.154687
$349$	12.8924	0.690113	0.345056	−	0.938582i	$-0.387860\pi$
$349$	12.8924	0.690113	0.345056	+	0.938582i	$0.387860\pi$
$350$	2.77183	0.148160
$351$	−4.91732	−0.262467
$352$	−2.01624	−0.107466
$353$	6.26395	0.333396	0.166698	−	0.986008i	$-0.446689\pi$
$353$	6.26395	0.333396	0.166698	+	0.986008i	$0.446689\pi$
$354$	1.93626	0.102911
$355$	9.20012	0.488292
$356$	−11.9694	−0.634379
$357$	−11.3537	−0.600904
$358$	−15.6436	−0.826792
$359$	8.33428	0.439866	0.219933	−	0.975515i	$-0.429416\pi$
$359$	8.33428	0.439866	0.219933	+	0.975515i	$0.429416\pi$
$360$	−1.82997	−0.0964480
$361$	1.00000	0.0526316
$362$	13.6802	0.719015
$363$	−6.93477	−0.363981
$364$	−8.25456	−0.432657
$365$	−26.2517	−1.37408
$366$	2.19824	0.114904
$367$	−9.60416	−0.501333	−0.250667	−	0.968074i	$-0.580650\pi$
$367$	−9.60416	−0.501333	−0.250667	+	0.968074i	$0.580650\pi$
$368$	−3.81454	−0.198847
$369$	−9.22847	−0.480415
$370$	12.9538	0.673435
$371$	−1.67867	−0.0871522
$372$	−4.78519	−0.248100
$373$	−14.6242	−0.757213	−0.378607	−	0.925558i	$-0.623597\pi$
$373$	−14.6242	−0.757213	−0.378607	+	0.925558i	$0.623597\pi$
$374$	13.6369	0.705148
$375$	−12.1715	−0.628534
$376$	0.326577	0.0168419
$377$	−14.1897	−0.730805
$378$	−1.67867	−0.0863415
$379$	29.1960	1.49970	0.749848	−	0.661610i	$-0.230127\pi$
$379$	29.1960	1.49970	0.749848	+	0.661610i	$0.230127\pi$
$380$	1.82997	0.0938756
$381$	−12.4778	−0.639256
$382$	−3.79372	−0.194104
$383$	13.4192	0.685688	0.342844	−	0.939392i	$-0.388610\pi$
$383$	13.4192	0.685688	0.342844	+	0.939392i	$0.388610\pi$
$384$	−1.00000	−0.0510310
$385$	6.19373	0.315662
$386$	12.1220	0.616992
$387$	5.31931	0.270396
$388$	14.3188	0.726929
$389$	17.8705	0.906072	0.453036	−	0.891492i	$-0.350341\pi$
$389$	17.8705	0.906072	0.453036	+	0.891492i	$0.350341\pi$
$390$	8.99856	0.455660
$391$	25.7998	1.30475
$392$	4.18206	0.211226
$393$	1.18571	0.0598110
$394$	15.7107	0.791495
$395$	−10.3943	−0.522995
$396$	2.01624	0.101320
$397$	−6.69808	−0.336167	−0.168084	−	0.985773i	$-0.553758\pi$
$397$	−6.69808	−0.336167	−0.168084	+	0.985773i	$0.553758\pi$
$398$	9.53375	0.477884
$399$	1.67867	0.0840386
$400$	−1.65120	−0.0825602
$401$	−16.2790	−0.812936	−0.406468	−	0.913665i	$-0.633240\pi$
$401$	−16.2790	−0.812936	−0.406468	+	0.913665i	$0.633240\pi$
$402$	−1.21471	−0.0605844
$403$	23.5303	1.17213
$404$	11.7632	0.585241
$405$	1.82997	0.0909320
$406$	−4.84406	−0.240406
$407$	−14.2723	−0.707453
$408$	6.76353	0.334845
$409$	−36.0746	−1.78377	−0.891887	−	0.452259i	$-0.850618\pi$
$409$	−36.0746	−1.78377	−0.891887	+	0.452259i	$0.850618\pi$
$410$	16.8878	0.834031
$411$	18.5007	0.912571
$412$	0.462585	0.0227899
$413$	−3.25034	−0.159939
$414$	3.81454	0.187474
$415$	6.64770	0.326323
$416$	4.91732	0.241091
$417$	20.6993	1.01365
$418$	−2.01624	−0.0986176
$419$	13.0160	0.635873	0.317937	−	0.948112i	$-0.397010\pi$
$419$	13.0160	0.635873	0.317937	+	0.948112i	$0.397010\pi$
$420$	3.07192	0.149894
$421$	−11.2940	−0.550438	−0.275219	−	0.961382i	$-0.588750\pi$
$421$	−11.2940	−0.550438	−0.275219	+	0.961382i	$0.588750\pi$
$422$	5.22430	0.254315
$423$	−0.326577	−0.0158787
$424$	1.00000	0.0485643
$425$	11.1680	0.541726
$426$	−5.02747	−0.243582
$427$	−3.69012	−0.178578
$428$	−16.0364	−0.775150
$429$	−9.91450	−0.478677
$430$	−9.73418	−0.469424
$431$	−6.00406	−0.289206	−0.144603	−	0.989490i	$-0.546190\pi$
$431$	−6.00406	−0.289206	−0.144603	+	0.989490i	$0.546190\pi$
$432$	1.00000	0.0481125
$433$	−12.1053	−0.581741	−0.290871	−	0.956762i	$-0.593945\pi$
$433$	−12.1053	−0.581741	−0.290871	+	0.956762i	$0.593945\pi$
$434$	8.03276	0.385585
$435$	5.28066	0.253188
$436$	−16.5947	−0.794743
$437$	−3.81454	−0.182474
$438$	14.3454	0.685450
$439$	15.4987	0.739711	0.369856	−	0.929089i	$-0.379407\pi$
$439$	15.4987	0.739711	0.369856	+	0.929089i	$0.379407\pi$
$440$	−3.68966	−0.175898
$441$	−4.18206	−0.199146
$442$	−33.2585	−1.58194
$443$	−15.4339	−0.733287	−0.366643	−	0.930362i	$-0.619493\pi$
$443$	−15.4339	−0.733287	−0.366643	+	0.930362i	$0.619493\pi$
$444$	−7.07868	−0.335939
$445$	−21.9037	−1.03834
$446$	−8.03389	−0.380416
$447$	9.67726	0.457719
$448$	1.67867	0.0793097
$449$	23.3945	1.10406	0.552028	−	0.833825i	$-0.313854\pi$
$449$	23.3945	1.10406	0.552028	+	0.833825i	$0.313854\pi$
$450$	1.65120	0.0778385
$451$	−18.6068	−0.876161
$452$	−10.0659	−0.473461
$453$	15.6367	0.734674
$454$	−23.5491	−1.10521
$455$	−15.1056	−0.708162
$456$	−1.00000	−0.0468293
$457$	−7.37685	−0.345074	−0.172537	−	0.985003i	$-0.555196\pi$
$457$	−7.37685	−0.345074	−0.172537	+	0.985003i	$0.555196\pi$
$458$	−13.4028	−0.626270
$459$	−6.76353	−0.315695
$460$	−6.98050	−0.325468
$461$	19.0342	0.886511	0.443256	−	0.896395i	$-0.353823\pi$
$461$	19.0342	0.886511	0.443256	+	0.896395i	$0.353823\pi$
$462$	−3.38461	−0.157466
$463$	18.9218	0.879372	0.439686	−	0.898152i	$-0.355090\pi$
$463$	18.9218	0.879372	0.439686	+	0.898152i	$0.355090\pi$
$464$	2.88565	0.133963
$465$	−8.75676	−0.406085
$466$	−1.75466	−0.0812830
$467$	−6.93699	−0.321006	−0.160503	−	0.987035i	$-0.551312\pi$
$467$	−6.93699	−0.321006	−0.160503	+	0.987035i	$0.551312\pi$
$468$	−4.91732	−0.227303
$469$	2.03910	0.0941571
$470$	0.597627	0.0275665
$471$	−13.0127	−0.599594
$472$	1.93626	0.0891235
$473$	10.7250	0.493136
$474$	5.68004	0.260893
$475$	−1.65120	−0.0757625
$476$	−11.3537	−0.520398
$477$	−1.00000	−0.0457869
$478$	7.06655	0.323217
$479$	−36.7045	−1.67707	−0.838535	−	0.544848i	$-0.816587\pi$
$479$	−36.7045	−1.67707	−0.838535	+	0.544848i	$0.816587\pi$
$480$	−1.82997	−0.0835264
$481$	34.8081	1.58711
$482$	−22.3701	−1.01893
$483$	−6.40336	−0.291363
$484$	−6.93477	−0.315217
$485$	26.2031	1.18982
$486$	−1.00000	−0.0453609
$487$	−22.6007	−1.02414	−0.512068	−	0.858945i	$-0.671121\pi$
$487$	−22.6007	−1.02414	−0.512068	+	0.858945i	$0.671121\pi$
$488$	2.19824	0.0995097
$489$	14.4971	0.655583
$490$	7.65306	0.345730
$491$	−20.2104	−0.912081	−0.456040	−	0.889959i	$-0.650733\pi$
$491$	−20.2104	−0.912081	−0.456040	+	0.889959i	$0.650733\pi$
$492$	−9.22847	−0.416051
$493$	−19.5172	−0.879010
$494$	4.91732	0.221241
$495$	3.68966	0.165838
$496$	−4.78519	−0.214861
$497$	8.43946	0.378562
$498$	−3.63268	−0.162784
$499$	−16.5662	−0.741605	−0.370802	−	0.928712i	$-0.620917\pi$
$499$	−16.5662	−0.741605	−0.370802	+	0.928712i	$0.620917\pi$
$500$	−12.1715	−0.544327
$501$	13.7105	0.612539
$502$	−19.4392	−0.867614
$503$	30.5255	1.36106	0.680532	−	0.732719i	$-0.261749\pi$
$503$	30.5255	1.36106	0.680532	+	0.732719i	$0.261749\pi$
$504$	−1.67867	−0.0747739
$505$	21.5263	0.957909
$506$	7.69104	0.341908
$507$	11.1800	0.496523
$508$	−12.4778	−0.553612
$509$	26.8982	1.19224	0.596122	−	0.802894i	$-0.296707\pi$
$509$	26.8982	1.19224	0.596122	+	0.802894i	$0.296707\pi$
$510$	12.3771	0.548066
$511$	−24.0812	−1.06529
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	16.8818	0.744624
$515$	0.846518	0.0373020
$516$	5.31931	0.234169
$517$	−0.658459	−0.0289590
$518$	11.8828	0.522099
$519$	16.9629	0.744588
$520$	8.99856	0.394613
$521$	35.6978	1.56395	0.781975	−	0.623310i	$-0.214212\pi$
$521$	35.6978	1.56395	0.781975	+	0.623310i	$0.214212\pi$
$522$	−2.88565	−0.126301
$523$	−8.47989	−0.370800	−0.185400	−	0.982663i	$-0.559358\pi$
$523$	−8.47989	−0.370800	−0.185400	+	0.982663i	$0.559358\pi$
$524$	1.18571	0.0517979
$525$	−2.77183	−0.120973
$526$	11.3054	0.492939
$527$	32.3648	1.40983
$528$	2.01624	0.0877456
$529$	−8.44927	−0.367360
$530$	1.82997	0.0794889
$531$	−1.93626	−0.0840264
$532$	1.67867	0.0727796
$533$	45.3793	1.96560
$534$	11.9694	0.517968
$535$	−29.3462	−1.26875
$536$	−1.21471	−0.0524676
$537$	15.6436	0.675073
$538$	−22.7265	−0.979811
$539$	−8.43205	−0.363194
$540$	1.82997	0.0787494
$541$	−21.2796	−0.914880	−0.457440	−	0.889240i	$-0.651234\pi$
$541$	−21.2796	−0.914880	−0.457440	+	0.889240i	$0.651234\pi$
$542$	25.0006	1.07387
$543$	−13.6802	−0.587073
$544$	6.76353	0.289984
$545$	−30.3679	−1.30082
$546$	8.25456	0.353263
$547$	12.0951	0.517148	0.258574	−	0.965991i	$-0.416747\pi$
$547$	12.0951	0.517148	0.258574	+	0.965991i	$0.416747\pi$
$548$	18.5007	0.790310
$549$	−2.19824	−0.0938186
$550$	3.32923	0.141959
$551$	2.88565	0.122933
$552$	3.81454	0.162358
$553$	−9.53492	−0.405466
$554$	−18.4958	−0.785810
$555$	−12.9538	−0.549857
$556$	20.6993	0.877848
$557$	37.4678	1.58756	0.793781	−	0.608204i	$-0.208110\pi$
$557$	37.4678	1.58756	0.793781	+	0.608204i	$0.208110\pi$
$558$	4.78519	0.202573
$559$	−26.1567	−1.10631
$560$	3.07192	0.129812
$561$	−13.6369	−0.575751
$562$	26.7049	1.12648
$563$	−14.7701	−0.622487	−0.311243	−	0.950330i	$-0.600745\pi$
$563$	−14.7701	−0.622487	−0.311243	+	0.950330i	$0.600745\pi$
$564$	−0.326577	−0.0137514
$565$	−18.4204	−0.774950
$566$	0.720726	0.0302944
$567$	1.67867	0.0704975
$568$	−5.02747	−0.210948
$569$	−31.5765	−1.32376	−0.661879	−	0.749611i	$-0.730241\pi$
$569$	−31.5765	−1.32376	−0.661879	+	0.749611i	$0.730241\pi$
$570$	−1.82997	−0.0766491
$571$	28.1232	1.17692	0.588459	−	0.808527i	$-0.299735\pi$
$571$	28.1232	1.17692	0.588459	+	0.808527i	$0.299735\pi$
$572$	−9.91450	−0.414546
$573$	3.79372	0.158485
$574$	15.4916	0.646605
$575$	6.29859	0.262669
$576$	1.00000	0.0416667
$577$	−0.531062	−0.0221084	−0.0110542	−	0.999939i	$-0.503519\pi$
$577$	−0.531062	−0.0221084	−0.0110542	+	0.999939i	$0.503519\pi$
$578$	−28.7454	−1.19565
$579$	−12.1220	−0.503772
$580$	5.28066	0.219267
$581$	6.09807	0.252991
$582$	−14.3188	−0.593535
$583$	−2.01624	−0.0835042
$584$	14.3454	0.593617
$585$	−8.99856	−0.372045
$586$	−9.39722	−0.388196
$587$	−35.1264	−1.44982	−0.724910	−	0.688844i	$-0.758119\pi$
$587$	−35.1264	−1.44982	−0.724910	+	0.688844i	$0.758119\pi$
$588$	−4.18206	−0.172465
$589$	−4.78519	−0.197170
$590$	3.54330	0.145875
$591$	−15.7107	−0.646253
$592$	−7.07868	−0.290932
$593$	−11.4375	−0.469681	−0.234840	−	0.972034i	$-0.575457\pi$
$593$	−11.4375	−0.469681	−0.234840	+	0.972034i	$0.575457\pi$
$594$	−2.01624	−0.0827274
$595$	−20.7770	−0.851775
$596$	9.67726	0.396396
$597$	−9.53375	−0.390190
$598$	−18.7573	−0.767044
$599$	−19.3478	−0.790530	−0.395265	−	0.918567i	$-0.629347\pi$
$599$	−19.3478	−0.790530	−0.395265	+	0.918567i	$0.629347\pi$
$600$	1.65120	0.0674101
$601$	9.78644	0.399197	0.199599	−	0.979878i	$-0.436036\pi$
$601$	9.78644	0.399197	0.199599	+	0.979878i	$0.436036\pi$
$602$	−8.92937	−0.363934
$603$	1.21471	0.0494670
$604$	15.6367	0.636246
$605$	−12.6904	−0.515939
$606$	−11.7632	−0.477848
$607$	−41.3958	−1.68021	−0.840103	−	0.542427i	$-0.817505\pi$
$607$	−41.3958	−1.68021	−0.840103	+	0.542427i	$0.817505\pi$
$608$	−1.00000	−0.0405554
$609$	4.84406	0.196291
$610$	4.02272	0.162875
$611$	1.60589	0.0649672
$612$	−6.76353	−0.273400
$613$	−41.7485	−1.68621	−0.843103	−	0.537753i	$-0.819273\pi$
$613$	−41.7485	−1.68621	−0.843103	+	0.537753i	$0.819273\pi$
$614$	20.7864	0.838870
$615$	−16.8878	−0.680983
$616$	−3.38461	−0.136370
$617$	−27.7405	−1.11679	−0.558395	−	0.829576i	$-0.688582\pi$
$617$	−27.7405	−1.11679	−0.558395	+	0.829576i	$0.688582\pi$
$618$	−0.462585	−0.0186079
$619$	−6.81231	−0.273810	−0.136905	−	0.990584i	$-0.543716\pi$
$619$	−6.81231	−0.273810	−0.136905	+	0.990584i	$0.543716\pi$
$620$	−8.75676	−0.351680
$621$	−3.81454	−0.153072
$622$	−20.5249	−0.822975
$623$	−20.0927	−0.804999
$624$	−4.91732	−0.196850
$625$	−14.0175	−0.560700
$626$	24.1449	0.965024
$627$	2.01624	0.0805209
$628$	−13.0127	−0.519264
$629$	47.8769	1.90898
$630$	−3.07192	−0.122388
$631$	21.5675	0.858590	0.429295	−	0.903164i	$-0.358762\pi$
$631$	21.5675	0.858590	0.429295	+	0.903164i	$0.358762\pi$
$632$	5.68004	0.225940
$633$	−5.22430	−0.207647
$634$	−13.5367	−0.537613
$635$	−22.8340	−0.906139
$636$	−1.00000	−0.0396526
$637$	20.5646	0.814797
$638$	−5.81817	−0.230343
$639$	5.02747	0.198883
$640$	−1.82997	−0.0723360
$641$	−10.7407	−0.424231	−0.212115	−	0.977245i	$-0.568035\pi$
$641$	−10.7407	−0.424231	−0.212115	+	0.977245i	$0.568035\pi$
$642$	16.0364	0.632908
$643$	−35.4056	−1.39626	−0.698131	−	0.715970i	$-0.745985\pi$
$643$	−35.4056	−1.39626	−0.698131	+	0.715970i	$0.745985\pi$
$644$	−6.40336	−0.252328
$645$	9.73418	0.383283
$646$	6.76353	0.266108
$647$	29.3106	1.15232	0.576160	−	0.817337i	$-0.304550\pi$
$647$	29.3106	1.15232	0.576160	+	0.817337i	$0.304550\pi$
$648$	−1.00000	−0.0392837
$649$	−3.90396	−0.153244
$650$	−8.11950	−0.318473
$651$	−8.03276	−0.314829
$652$	14.4971	0.567752
$653$	1.99591	0.0781059	0.0390529	−	0.999237i	$-0.487566\pi$
$653$	1.99591	0.0781059	0.0390529	+	0.999237i	$0.487566\pi$
$654$	16.5947	0.648905
$655$	2.16981	0.0847815
$656$	−9.22847	−0.360311
$657$	−14.3454	−0.559667
$658$	0.548216	0.0213717
$659$	−0.418966	−0.0163206	−0.00816031	−	0.999967i	$-0.502598\pi$
$659$	−0.418966	−0.0163206	−0.00816031	+	0.999967i	$0.502598\pi$
$660$	3.68966	0.143620
$661$	−18.6749	−0.726368	−0.363184	−	0.931717i	$-0.618310\pi$
$661$	−18.6749	−0.726368	−0.363184	+	0.931717i	$0.618310\pi$
$662$	−19.8754	−0.772478
$663$	33.2585	1.29165
$664$	−3.63268	−0.140975
$665$	3.07192	0.119124
$666$	7.07868	0.274293
$667$	−11.0074	−0.426209
$668$	13.7105	0.530474
$669$	8.03389	0.310608
$670$	−2.22289	−0.0858778
$671$	−4.43218	−0.171103
$672$	−1.67867	−0.0647561
$673$	2.96407	0.114256	0.0571282	−	0.998367i	$-0.481806\pi$
$673$	2.96407	0.114256	0.0571282	+	0.998367i	$0.481806\pi$
$674$	24.2650	0.934652
$675$	−1.65120	−0.0635549
$676$	11.1800	0.430002
$677$	−39.6440	−1.52364	−0.761822	−	0.647786i	$-0.775695\pi$
$677$	−39.6440	−1.52364	−0.761822	+	0.647786i	$0.775695\pi$
$678$	10.0659	0.386580
$679$	24.0366	0.922441
$680$	12.3771	0.474639
$681$	23.5491	0.902403
$682$	9.64810	0.369445
$683$	−38.9148	−1.48904	−0.744518	−	0.667603i	$-0.767320\pi$
$683$	−38.9148	−1.48904	−0.744518	+	0.667603i	$0.767320\pi$
$684$	1.00000	0.0382360
$685$	33.8557	1.29356
$686$	18.7710	0.716680
$687$	13.4028	0.511348
$688$	5.31931	0.202797
$689$	4.91732	0.187335
$690$	6.98050	0.265743
$691$	−43.8421	−1.66783	−0.833916	−	0.551892i	$-0.813906\pi$
$691$	−43.8421	−1.66783	−0.833916	+	0.551892i	$0.813906\pi$
$692$	16.9629	0.644832
$693$	3.38461	0.128571
$694$	−26.6638	−1.01214
$695$	37.8792	1.43684
$696$	−2.88565	−0.109380
$697$	62.4171	2.36421
$698$	−12.8924	−0.487983
$699$	1.75466	0.0663673
$700$	−2.77183	−0.104765
$701$	45.6227	1.72315	0.861573	−	0.507634i	$-0.169480\pi$
$701$	45.6227	1.72315	0.861573	+	0.507634i	$0.169480\pi$
$702$	4.91732	0.185592
$703$	−7.07868	−0.266977
$704$	2.01624	0.0759900
$705$	−0.597627	−0.0225079
$706$	−6.26395	−0.235747
$707$	19.7465	0.742645
$708$	−1.93626	−0.0727690
$709$	−12.8780	−0.483645	−0.241822	−	0.970321i	$-0.577745\pi$
$709$	−12.8780	−0.483645	−0.241822	+	0.970321i	$0.577745\pi$
$710$	−9.20012	−0.345274
$711$	−5.68004	−0.213018
$712$	11.9694	0.448574
$713$	18.2533	0.683592
$714$	11.3537	0.424903
$715$	−18.1433	−0.678519
$716$	15.6436	0.584630
$717$	−7.06655	−0.263905
$718$	−8.33428	−0.311032
$719$	−13.4057	−0.499947	−0.249974	−	0.968253i	$-0.580422\pi$
$719$	−13.4057	−0.499947	−0.249974	+	0.968253i	$0.580422\pi$
$720$	1.82997	0.0681990
$721$	0.776528	0.0289194
$722$	−1.00000	−0.0372161
$723$	22.3701	0.831951
$724$	−13.6802	−0.508421
$725$	−4.76480	−0.176960
$726$	6.93477	0.257373
$727$	−2.26162	−0.0838789	−0.0419395	−	0.999120i	$-0.513354\pi$
$727$	−2.26162	−0.0838789	−0.0419395	+	0.999120i	$0.513354\pi$
$728$	8.25456	0.305934
$729$	1.00000	0.0370370
$730$	26.2517	0.971618
$731$	−35.9773	−1.33067
$732$	−2.19824	−0.0812493
$733$	25.3470	0.936214	0.468107	−	0.883672i	$-0.344936\pi$
$733$	25.3470	0.936214	0.468107	+	0.883672i	$0.344936\pi$
$734$	9.60416	0.354496
$735$	−7.65306	−0.282287
$736$	3.81454	0.140606
$737$	2.44916	0.0902158
$738$	9.22847	0.339705
$739$	−38.5157	−1.41682	−0.708412	−	0.705799i	$-0.750588\pi$
$739$	−38.5157	−1.41682	−0.708412	+	0.705799i	$0.750588\pi$
$740$	−12.9538	−0.476190
$741$	−4.91732	−0.180642
$742$	1.67867	0.0616259
$743$	−38.5507	−1.41429	−0.707144	−	0.707070i	$-0.750017\pi$
$743$	−38.5507	−1.41429	−0.707144	+	0.707070i	$0.750017\pi$
$744$	4.78519	0.175434
$745$	17.7091	0.648811
$746$	14.6242	0.535431
$747$	3.63268	0.132913
$748$	−13.6369	−0.498615
$749$	−26.9199	−0.983632
$750$	12.1715	0.444441
$751$	14.7174	0.537044	0.268522	−	0.963274i	$-0.413465\pi$
$751$	14.7174	0.537044	0.268522	+	0.963274i	$0.413465\pi$
$752$	−0.326577	−0.0119091
$753$	19.4392	0.708404
$754$	14.1897	0.516757
$755$	28.6146	1.04139
$756$	1.67867	0.0610527
$757$	37.2544	1.35403	0.677017	−	0.735967i	$-0.263272\pi$
$757$	37.2544	1.35403	0.677017	+	0.735967i	$0.263272\pi$
$758$	−29.1960	−1.06045
$759$	−7.69104	−0.279167
$760$	−1.82997	−0.0663800
$761$	5.30595	0.192341	0.0961703	−	0.995365i	$-0.469341\pi$
$761$	5.30595	0.192341	0.0961703	+	0.995365i	$0.469341\pi$
$762$	12.4778	0.452022
$763$	−27.8571	−1.00849
$764$	3.79372	0.137252
$765$	−12.3771	−0.447494
$766$	−13.4192	−0.484855
$767$	9.52120	0.343791
$768$	1.00000	0.0360844
$769$	−28.1883	−1.01649	−0.508247	−	0.861211i	$-0.669706\pi$
$769$	−28.1883	−1.01649	−0.508247	+	0.861211i	$0.669706\pi$
$770$	−6.19373	−0.223207
$771$	−16.8818	−0.607983
$772$	−12.1220	−0.436280
$773$	−49.9900	−1.79802	−0.899008	−	0.437932i	$-0.855711\pi$
$773$	−49.9900	−1.79802	−0.899008	+	0.437932i	$0.855711\pi$
$774$	−5.31931	−0.191199
$775$	7.90133	0.283824
$776$	−14.3188	−0.514016
$777$	−11.8828	−0.426292
$778$	−17.8705	−0.640690
$779$	−9.22847	−0.330644
$780$	−8.99856	−0.322200
$781$	10.1366	0.362716
$782$	−25.7998	−0.922598
$783$	2.88565	0.103125
$784$	−4.18206	−0.149359
$785$	−23.8129	−0.849918
$786$	−1.18571	−0.0422928
$787$	−26.3721	−0.940065	−0.470032	−	0.882649i	$-0.655758\pi$
$787$	−26.3721	−0.940065	−0.470032	+	0.882649i	$0.655758\pi$
$788$	−15.7107	−0.559671
$789$	−11.3054	−0.402483
$790$	10.3943	0.369813
$791$	−16.8974	−0.600801
$792$	−2.01624	−0.0716440
$793$	10.8095	0.383855
$794$	6.69808	0.237706
$795$	−1.82997	−0.0649024
$796$	−9.53375	−0.337915
$797$	−15.8357	−0.560929	−0.280464	−	0.959864i	$-0.590488\pi$
$797$	−15.8357	−0.560929	−0.280464	+	0.959864i	$0.590488\pi$
$798$	−1.67867	−0.0594243
$799$	2.20882	0.0781423
$800$	1.65120	0.0583789
$801$	−11.9694	−0.422919
$802$	16.2790	0.574833
$803$	−28.9238	−1.02070
$804$	1.21471	0.0428396
$805$	−11.7180	−0.413004
$806$	−23.5303	−0.828820
$807$	22.7265	0.800012
$808$	−11.7632	−0.413828
$809$	25.9199	0.911295	0.455648	−	0.890160i	$-0.349408\pi$
$809$	25.9199	0.911295	0.455648	+	0.890160i	$0.349408\pi$
$810$	−1.82997	−0.0642986
$811$	26.0318	0.914100	0.457050	−	0.889441i	$-0.348906\pi$
$811$	26.0318	0.914100	0.457050	+	0.889441i	$0.348906\pi$
$812$	4.84406	0.169993
$813$	−25.0006	−0.876809
$814$	14.2723	0.500245
$815$	26.5293	0.929282
$816$	−6.76353	−0.236771
$817$	5.31931	0.186099
$818$	36.0746	1.26132
$819$	−8.25456	−0.288438
$820$	−16.8878	−0.589749
$821$	45.8717	1.60093	0.800466	−	0.599378i	$-0.204585\pi$
$821$	45.8717	1.60093	0.800466	+	0.599378i	$0.204585\pi$
$822$	−18.5007	−0.645285
$823$	−29.3130	−1.02179	−0.510893	−	0.859644i	$-0.670685\pi$
$823$	−29.3130	−1.02179	−0.510893	+	0.859644i	$0.670685\pi$
$824$	−0.462585	−0.0161149
$825$	−3.32923	−0.115909
$826$	3.25034	0.113094
$827$	24.2294	0.842540	0.421270	−	0.906935i	$-0.361584\pi$
$827$	24.2294	0.842540	0.421270	+	0.906935i	$0.361584\pi$
$828$	−3.81454	−0.132564
$829$	56.8385	1.97408	0.987042	−	0.160465i	$-0.0512994\pi$
$829$	56.8385	1.97408	0.987042	+	0.160465i	$0.0512994\pi$
$830$	−6.64770	−0.230745
$831$	18.4958	0.641612
$832$	−4.91732	−0.170477
$833$	28.2855	0.980036
$834$	−20.6993	−0.716760
$835$	25.0898	0.868268
$836$	2.01624	0.0697332
$837$	−4.78519	−0.165400
$838$	−13.0160	−0.449630
$839$	−52.6638	−1.81816	−0.909078	−	0.416627i	$-0.863212\pi$
$839$	−52.6638	−1.81816	−0.909078	+	0.416627i	$0.863212\pi$
$840$	−3.07192	−0.105991
$841$	−20.6730	−0.712863
$842$	11.2940	0.389218
$843$	−26.7049	−0.919765
$844$	−5.22430	−0.179828
$845$	20.4592	0.703816
$846$	0.326577	0.0112280
$847$	−11.6412	−0.399996
$848$	−1.00000	−0.0343401
$849$	−0.720726	−0.0247353
$850$	−11.1680	−0.383058
$851$	27.0019	0.925613
$852$	5.02747	0.172238
$853$	−33.1659	−1.13558	−0.567789	−	0.823174i	$-0.692201\pi$
$853$	−33.1659	−1.13558	−0.567789	+	0.823174i	$0.692201\pi$
$854$	3.69012	0.126273
$855$	1.82997	0.0625837
$856$	16.0364	0.548114
$857$	−13.4674	−0.460037	−0.230019	−	0.973186i	$-0.573879\pi$
$857$	−13.4674	−0.460037	−0.230019	+	0.973186i	$0.573879\pi$
$858$	9.91450	0.338476
$859$	54.8632	1.87191	0.935954	−	0.352122i	$-0.114540\pi$
$859$	54.8632	1.87191	0.935954	+	0.352122i	$0.114540\pi$
$860$	9.73418	0.331933
$861$	−15.4916	−0.527951
$862$	6.00406	0.204499
$863$	8.17369	0.278236	0.139118	−	0.990276i	$-0.455573\pi$
$863$	8.17369	0.278236	0.139118	+	0.990276i	$0.455573\pi$
$864$	−1.00000	−0.0340207
$865$	31.0416	1.05545
$866$	12.1053	0.411353
$867$	28.7454	0.976244
$868$	−8.03276	−0.272650
$869$	−11.4523	−0.388494
$870$	−5.28066	−0.179031
$871$	−5.97314	−0.202392
$872$	16.5947	0.561968
$873$	14.3188	0.484619
$874$	3.81454	0.129029
$875$	−20.4320	−0.690726
$876$	−14.3454	−0.484686
$877$	−19.2098	−0.648668	−0.324334	−	0.945943i	$-0.605140\pi$
$877$	−19.2098	−0.648668	−0.324334	+	0.945943i	$0.605140\pi$
$878$	−15.4987	−0.523055
$879$	9.39722	0.316960
$880$	3.68966	0.124379
$881$	13.5303	0.455846	0.227923	−	0.973679i	$-0.426807\pi$
$881$	13.5303	0.455846	0.227923	+	0.973679i	$0.426807\pi$
$882$	4.18206	0.140817
$883$	−21.3701	−0.719160	−0.359580	−	0.933114i	$-0.617080\pi$
$883$	−21.3701	−0.719160	−0.359580	+	0.933114i	$0.617080\pi$
$884$	33.2585	1.11860
$885$	−3.54330	−0.119107
$886$	15.4339	0.518512
$887$	−8.86929	−0.297802	−0.148901	−	0.988852i	$-0.547574\pi$
$887$	−8.86929	−0.297802	−0.148901	+	0.988852i	$0.547574\pi$
$888$	7.07868	0.237545
$889$	−20.9461	−0.702509
$890$	21.9037	0.734215
$891$	2.01624	0.0675466
$892$	8.03389	0.268995
$893$	−0.326577	−0.0109285
$894$	−9.67726	−0.323656
$895$	28.6274	0.956908
$896$	−1.67867	−0.0560805
$897$	18.7573	0.626289
$898$	−23.3945	−0.780686
$899$	−13.8084	−0.460535
$900$	−1.65120	−0.0550402
$901$	6.76353	0.225326
$902$	18.6068	0.619539
$903$	8.92937	0.297151
$904$	10.0659	0.334788
$905$	−25.0344	−0.832171
$906$	−15.6367	−0.519493
$907$	−39.8019	−1.32160	−0.660800	−	0.750562i	$-0.729783\pi$
$907$	−39.8019	−1.32160	−0.660800	+	0.750562i	$0.729783\pi$
$908$	23.5491	0.781504
$909$	11.7632	0.390161
$910$	15.1056	0.500746
$911$	−37.1868	−1.23205	−0.616026	−	0.787726i	$-0.711259\pi$
$911$	−37.1868	−1.23205	−0.616026	+	0.787726i	$0.711259\pi$
$912$	1.00000	0.0331133
$913$	7.32436	0.242401
$914$	7.37685	0.244004
$915$	−4.02272	−0.132987
$916$	13.4028	0.442840
$917$	1.99041	0.0657292
$918$	6.76353	0.223230
$919$	−28.2951	−0.933370	−0.466685	−	0.884424i	$-0.654552\pi$
$919$	−28.2951	−0.933370	−0.466685	+	0.884424i	$0.654552\pi$
$920$	6.98050	0.230140
$921$	−20.7864	−0.684934
$922$	−19.0342	−0.626858
$923$	−24.7217	−0.813723
$924$	3.38461	0.111345
$925$	11.6883	0.384310
$926$	−18.9218	−0.621810
$927$	0.462585	0.0151933
$928$	−2.88565	−0.0947261
$929$	−6.76250	−0.221870	−0.110935	−	0.993828i	$-0.535385\pi$
$929$	−6.76250	−0.221870	−0.110935	+	0.993828i	$0.535385\pi$
$930$	8.75676	0.287145
$931$	−4.18206	−0.137062
$932$	1.75466	0.0574757
$933$	20.5249	0.671957
$934$	6.93699	0.226985
$935$	−24.9552	−0.816121
$936$	4.91732	0.160728
$937$	−7.29075	−0.238178	−0.119089	−	0.992884i	$-0.537997\pi$
$937$	−7.29075	−0.238178	−0.119089	+	0.992884i	$0.537997\pi$
$938$	−2.03910	−0.0665791
$939$	−24.1449	−0.787939
$940$	−0.597627	−0.0194925
$941$	−48.1838	−1.57075	−0.785373	−	0.619022i	$-0.787529\pi$
$941$	−48.1838	−1.57075	−0.785373	+	0.619022i	$0.787529\pi$
$942$	13.0127	0.423977
$943$	35.2024	1.14635
$944$	−1.93626	−0.0630198
$945$	3.07192	0.0999295
$946$	−10.7250	−0.348700
$947$	55.7561	1.81183	0.905915	−	0.423460i	$-0.139185\pi$
$947$	55.7561	1.81183	0.905915	+	0.423460i	$0.139185\pi$
$948$	−5.68004	−0.184479
$949$	70.5409	2.28986
$950$	1.65120	0.0535722
$951$	13.5367	0.438959
$952$	11.3537	0.367977
$953$	−41.9583	−1.35916	−0.679582	−	0.733600i	$-0.737839\pi$
$953$	−41.9583	−1.35916	−0.679582	+	0.733600i	$0.737839\pi$
$954$	1.00000	0.0323762
$955$	6.94240	0.224651
$956$	−7.06655	−0.228549
$957$	5.81817	0.188075
$958$	36.7045	1.18587
$959$	31.0565	1.00287
$960$	1.82997	0.0590621
$961$	−8.10197	−0.261354
$962$	−34.8081	−1.12226
$963$	−16.0364	−0.516767
$964$	22.3701	0.720491
$965$	−22.1829	−0.714092
$966$	6.40336	0.206025
$967$	−9.67191	−0.311028	−0.155514	−	0.987834i	$-0.549703\pi$
$967$	−9.67191	−0.311028	−0.155514	+	0.987834i	$0.549703\pi$
$968$	6.93477	0.222892
$969$	−6.76353	−0.217276
$970$	−26.2031	−0.841330
$971$	−14.9967	−0.481267	−0.240634	−	0.970616i	$-0.577355\pi$
$971$	−14.9967	−0.481267	−0.240634	+	0.970616i	$0.577355\pi$
$972$	1.00000	0.0320750
$973$	34.7474	1.11395
$974$	22.6007	0.724174
$975$	8.11950	0.260032
$976$	−2.19824	−0.0703640
$977$	43.2068	1.38231	0.691154	−	0.722708i	$-0.257103\pi$
$977$	43.2068	1.38231	0.691154	+	0.722708i	$0.257103\pi$
$978$	−14.4971	−0.463567
$979$	−24.1333	−0.771303
$980$	−7.65306	−0.244468
$981$	−16.5947	−0.529828
$982$	20.2104	0.644938
$983$	−40.9851	−1.30722	−0.653611	−	0.756831i	$-0.726747\pi$
$983$	−40.9851	−1.30722	−0.653611	+	0.756831i	$0.726747\pi$
$984$	9.22847	0.294193
$985$	−28.7502	−0.916056
$986$	19.5172	0.621554
$987$	−0.548216	−0.0174499
$988$	−4.91732	−0.156441
$989$	−20.2907	−0.645207
$990$	−3.68966	−0.117265
$991$	1.62421	0.0515946	0.0257973	−	0.999667i	$-0.491788\pi$
$991$	1.62421	0.0515946	0.0257973	+	0.999667i	$0.491788\pi$
$992$	4.78519	0.151930
$993$	19.8754	0.630725
$994$	−8.43946	−0.267683
$995$	−17.4465	−0.553091
$996$	3.63268	0.115106
$997$	−15.8446	−0.501804	−0.250902	−	0.968013i	$-0.580727\pi$
$997$	−15.8446	−0.501804	−0.250902	+	0.968013i	$0.580727\pi$
$998$	16.5662	0.524394
$999$	−7.07868	−0.223959

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.v.1.5	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.82997 q^{5} -1.00000 q^{6} +1.67867 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.82997 q^{5} -1.00000 q^{6} +1.67867 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.82997 q^{10} +2.01624 q^{11} +1.00000 q^{12} -4.91732 q^{13} -1.67867 q^{14} +1.82997 q^{15} +1.00000 q^{16} -6.76353 q^{17} -1.00000 q^{18} +1.00000 q^{19} +1.82997 q^{20} +1.67867 q^{21} -2.01624 q^{22} -3.81454 q^{23} -1.00000 q^{24} -1.65120 q^{25} +4.91732 q^{26} +1.00000 q^{27} +1.67867 q^{28} +2.88565 q^{29} -1.82997 q^{30} -4.78519 q^{31} -1.00000 q^{32} +2.01624 q^{33} +6.76353 q^{34} +3.07192 q^{35} +1.00000 q^{36} -7.07868 q^{37} -1.00000 q^{38} -4.91732 q^{39} -1.82997 q^{40} -9.22847 q^{41} -1.67867 q^{42} +5.31931 q^{43} +2.01624 q^{44} +1.82997 q^{45} +3.81454 q^{46} -0.326577 q^{47} +1.00000 q^{48} -4.18206 q^{49} +1.65120 q^{50} -6.76353 q^{51} -4.91732 q^{52} -1.00000 q^{53} -1.00000 q^{54} +3.68966 q^{55} -1.67867 q^{56} +1.00000 q^{57} -2.88565 q^{58} -1.93626 q^{59} +1.82997 q^{60} -2.19824 q^{61} +4.78519 q^{62} +1.67867 q^{63} +1.00000 q^{64} -8.99856 q^{65} -2.01624 q^{66} +1.21471 q^{67} -6.76353 q^{68} -3.81454 q^{69} -3.07192 q^{70} +5.02747 q^{71} -1.00000 q^{72} -14.3454 q^{73} +7.07868 q^{74} -1.65120 q^{75} +1.00000 q^{76} +3.38461 q^{77} +4.91732 q^{78} -5.68004 q^{79} +1.82997 q^{80} +1.00000 q^{81} +9.22847 q^{82} +3.63268 q^{83} +1.67867 q^{84} -12.3771 q^{85} -5.31931 q^{86} +2.88565 q^{87} -2.01624 q^{88} -11.9694 q^{89} -1.82997 q^{90} -8.25456 q^{91} -3.81454 q^{92} -4.78519 q^{93} +0.326577 q^{94} +1.82997 q^{95} -1.00000 q^{96} +14.3188 q^{97} +4.18206 q^{98} +2.01624 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} - 7 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 - 7 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} - 6 q^{6} - 7 q^{7} - 6 q^{8} + 6 q^{9} - 3 q^{10} + q^{11} + 6 q^{12} - 13 q^{13} + 7 q^{14} + 3 q^{15} + 6 q^{16} - 5 q^{17} - 6 q^{18} + 6 q^{19} + 3 q^{20} - 7 q^{21} - q^{22} + 9 q^{23} - 6 q^{24} - 5 q^{25} + 13 q^{26} + 6 q^{27} - 7 q^{28} - 12 q^{29} - 3 q^{30} - 2 q^{31} - 6 q^{32} + q^{33} + 5 q^{34} - 14 q^{35} + 6 q^{36} - 7 q^{37} - 6 q^{38} - 13 q^{39} - 3 q^{40} - 18 q^{41} + 7 q^{42} - 11 q^{43} + q^{44} + 3 q^{45} - 9 q^{46} - 5 q^{47} + 6 q^{48} + 3 q^{49} + 5 q^{50} - 5 q^{51} - 13 q^{52} - 6 q^{53} - 6 q^{54} + 8 q^{55} + 7 q^{56} + 6 q^{57} + 12 q^{58} + 2 q^{59} + 3 q^{60} - 12 q^{61} + 2 q^{62} - 7 q^{63} + 6 q^{64} - 5 q^{65} - q^{66} - 9 q^{67} - 5 q^{68} + 9 q^{69} + 14 q^{70} + 18 q^{71} - 6 q^{72} - 31 q^{73} + 7 q^{74} - 5 q^{75} + 6 q^{76} + q^{77} + 13 q^{78} - 17 q^{79} + 3 q^{80} + 6 q^{81} + 18 q^{82} - 9 q^{83} - 7 q^{84} - 32 q^{85} + 11 q^{86} - 12 q^{87} - q^{88} + 18 q^{89} - 3 q^{90} + 9 q^{92} - 2 q^{93} + 5 q^{94} + 3 q^{95} - 6 q^{96} - 7 q^{97} - 3 q^{98} + q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 - 6 * q^6 - 7 * q^7 - 6 * q^8 + 6 * q^9 - 3 * q^10 + q^11 + 6 * q^12 - 13 * q^13 + 7 * q^14 + 3 * q^15 + 6 * q^16 - 5 * q^17 - 6 * q^18 + 6 * q^19 + 3 * q^20 - 7 * q^21 - q^22 + 9 * q^23 - 6 * q^24 - 5 * q^25 + 13 * q^26 + 6 * q^27 - 7 * q^28 - 12 * q^29 - 3 * q^30 - 2 * q^31 - 6 * q^32 + q^33 + 5 * q^34 - 14 * q^35 + 6 * q^36 - 7 * q^37 - 6 * q^38 - 13 * q^39 - 3 * q^40 - 18 * q^41 + 7 * q^42 - 11 * q^43 + q^44 + 3 * q^45 - 9 * q^46 - 5 * q^47 + 6 * q^48 + 3 * q^49 + 5 * q^50 - 5 * q^51 - 13 * q^52 - 6 * q^53 - 6 * q^54 + 8 * q^55 + 7 * q^56 + 6 * q^57 + 12 * q^58 + 2 * q^59 + 3 * q^60 - 12 * q^61 + 2 * q^62 - 7 * q^63 + 6 * q^64 - 5 * q^65 - q^66 - 9 * q^67 - 5 * q^68 + 9 * q^69 + 14 * q^70 + 18 * q^71 - 6 * q^72 - 31 * q^73 + 7 * q^74 - 5 * q^75 + 6 * q^76 + q^77 + 13 * q^78 - 17 * q^79 + 3 * q^80 + 6 * q^81 + 18 * q^82 - 9 * q^83 - 7 * q^84 - 32 * q^85 + 11 * q^86 - 12 * q^87 - q^88 + 18 * q^89 - 3 * q^90 + 9 * q^92 - 2 * q^93 + 5 * q^94 + 3 * q^95 - 6 * q^96 - 7 * q^97 - 3 * q^98 + q^99

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