LMFDB - Embedded newform 6026.2.a.l.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.372945 q^{3} +1.00000 q^{4} -2.66658 q^{5} -0.372945 q^{6} +3.34934 q^{7} -1.00000 q^{8} -2.86091 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.372945 q^{3} +1.00000 q^{4} -2.66658 q^{5} -0.372945 q^{6} +3.34934 q^{7} -1.00000 q^{8} -2.86091 q^{9} +2.66658 q^{10} -3.14966 q^{11} +0.372945 q^{12} +0.642654 q^{13} -3.34934 q^{14} -0.994488 q^{15} +1.00000 q^{16} -3.11448 q^{17} +2.86091 q^{18} -0.263898 q^{19} -2.66658 q^{20} +1.24912 q^{21} +3.14966 q^{22} -1.00000 q^{23} -0.372945 q^{24} +2.11066 q^{25} -0.642654 q^{26} -2.18580 q^{27} +3.34934 q^{28} +8.24723 q^{29} +0.994488 q^{30} +8.42877 q^{31} -1.00000 q^{32} -1.17465 q^{33} +3.11448 q^{34} -8.93129 q^{35} -2.86091 q^{36} -11.3608 q^{37} +0.263898 q^{38} +0.239674 q^{39} +2.66658 q^{40} -2.02200 q^{41} -1.24912 q^{42} -1.76054 q^{43} -3.14966 q^{44} +7.62885 q^{45} +1.00000 q^{46} -0.148071 q^{47} +0.372945 q^{48} +4.21809 q^{49} -2.11066 q^{50} -1.16153 q^{51} +0.642654 q^{52} -9.49126 q^{53} +2.18580 q^{54} +8.39883 q^{55} -3.34934 q^{56} -0.0984195 q^{57} -8.24723 q^{58} -3.73906 q^{59} -0.994488 q^{60} +5.20249 q^{61} -8.42877 q^{62} -9.58217 q^{63} +1.00000 q^{64} -1.71369 q^{65} +1.17465 q^{66} +5.80138 q^{67} -3.11448 q^{68} -0.372945 q^{69} +8.93129 q^{70} -14.2284 q^{71} +2.86091 q^{72} -4.25808 q^{73} +11.3608 q^{74} +0.787158 q^{75} -0.263898 q^{76} -10.5493 q^{77} -0.239674 q^{78} +5.78002 q^{79} -2.66658 q^{80} +7.76755 q^{81} +2.02200 q^{82} +2.76081 q^{83} +1.24912 q^{84} +8.30502 q^{85} +1.76054 q^{86} +3.07576 q^{87} +3.14966 q^{88} +12.7467 q^{89} -7.62885 q^{90} +2.15247 q^{91} -1.00000 q^{92} +3.14347 q^{93} +0.148071 q^{94} +0.703706 q^{95} -0.372945 q^{96} -3.82614 q^{97} -4.21809 q^{98} +9.01090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) $ 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * 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
$3$	0.372945	0.215320	0.107660	−	0.994188i	$-0.465664\pi$
$3$	0.372945	0.215320	0.107660	+	0.994188i	$0.465664\pi$
$4$	1.00000	0.500000
$5$	−2.66658	−1.19253	−0.596266	−	0.802787i	$-0.703350\pi$
$5$	−2.66658	−1.19253	−0.596266	+	0.802787i	$0.703350\pi$
$6$	−0.372945	−0.152254
$7$	3.34934	1.26593	0.632966	−	0.774179i	$-0.281837\pi$
$7$	3.34934	1.26593	0.632966	+	0.774179i	$0.281837\pi$
$8$	−1.00000	−0.353553
$9$	−2.86091	−0.953637
$10$	2.66658	0.843247
$11$	−3.14966	−0.949659	−0.474829	−	0.880078i	$-0.657490\pi$
$11$	−3.14966	−0.949659	−0.474829	+	0.880078i	$0.657490\pi$
$12$	0.372945	0.107660
$13$	0.642654	0.178240	0.0891200	−	0.996021i	$-0.471595\pi$
$13$	0.642654	0.178240	0.0891200	+	0.996021i	$0.471595\pi$
$14$	−3.34934	−0.895149
$15$	−0.994488	−0.256776
$16$	1.00000	0.250000
$17$	−3.11448	−0.755373	−0.377687	−	0.925934i	$-0.623280\pi$
$17$	−3.11448	−0.755373	−0.377687	+	0.925934i	$0.623280\pi$
$18$	2.86091	0.674323
$19$	−0.263898	−0.0605424	−0.0302712	−	0.999542i	$-0.509637\pi$
$19$	−0.263898	−0.0605424	−0.0302712	+	0.999542i	$0.509637\pi$
$20$	−2.66658	−0.596266
$21$	1.24912	0.272580
$22$	3.14966	0.671510
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.372945	−0.0761271
$25$	2.11066	0.422131
$26$	−0.642654	−0.126035
$27$	−2.18580	−0.420657
$28$	3.34934	0.632966
$29$	8.24723	1.53147	0.765736	−	0.643155i	$-0.222375\pi$
$29$	8.24723	1.53147	0.765736	+	0.643155i	$0.222375\pi$
$30$	0.994488	0.181568
$31$	8.42877	1.51385	0.756926	−	0.653501i	$-0.226700\pi$
$31$	8.42877	1.51385	0.756926	+	0.653501i	$0.226700\pi$
$32$	−1.00000	−0.176777
$33$	−1.17465	−0.204480
$34$	3.11448	0.534129
$35$	−8.93129	−1.50966
$36$	−2.86091	−0.476819
$37$	−11.3608	−1.86771	−0.933854	−	0.357656i	$-0.883576\pi$
$37$	−11.3608	−1.86771	−0.933854	+	0.357656i	$0.883576\pi$
$38$	0.263898	0.0428099
$39$	0.239674	0.0383786
$40$	2.66658	0.421624
$41$	−2.02200	−0.315783	−0.157892	−	0.987456i	$-0.550470\pi$
$41$	−2.02200	−0.315783	−0.157892	+	0.987456i	$0.550470\pi$
$42$	−1.24912	−0.192743
$43$	−1.76054	−0.268480	−0.134240	−	0.990949i	$-0.542859\pi$
$43$	−1.76054	−0.268480	−0.134240	+	0.990949i	$0.542859\pi$
$44$	−3.14966	−0.474829
$45$	7.62885	1.13724
$46$	1.00000	0.147442
$47$	−0.148071	−0.0215984	−0.0107992	−	0.999942i	$-0.503438\pi$
$47$	−0.148071	−0.0215984	−0.0107992	+	0.999942i	$0.503438\pi$
$48$	0.372945	0.0538300
$49$	4.21809	0.602585
$50$	−2.11066	−0.298492
$51$	−1.16153	−0.162647
$52$	0.642654	0.0891200
$53$	−9.49126	−1.30373	−0.651863	−	0.758337i	$-0.726012\pi$
$53$	−9.49126	−1.30373	−0.651863	+	0.758337i	$0.726012\pi$
$54$	2.18580	0.297449
$55$	8.39883	1.13250
$56$	−3.34934	−0.447575
$57$	−0.0984195	−0.0130360
$58$	−8.24723	−1.08291
$59$	−3.73906	−0.486784	−0.243392	−	0.969928i	$-0.578260\pi$
$59$	−3.73906	−0.486784	−0.243392	+	0.969928i	$0.578260\pi$
$60$	−0.994488	−0.128388
$61$	5.20249	0.666111	0.333055	−	0.942907i	$-0.391920\pi$
$61$	5.20249	0.666111	0.333055	+	0.942907i	$0.391920\pi$
$62$	−8.42877	−1.07045
$63$	−9.58217	−1.20724
$64$	1.00000	0.125000
$65$	−1.71369	−0.212557
$66$	1.17465	0.144589
$67$	5.80138	0.708752	0.354376	−	0.935103i	$-0.384693\pi$
$67$	5.80138	0.708752	0.354376	+	0.935103i	$0.384693\pi$
$68$	−3.11448	−0.377687
$69$	−0.372945	−0.0448973
$70$	8.93129	1.06749
$71$	−14.2284	−1.68860	−0.844301	−	0.535870i	$-0.819984\pi$
$71$	−14.2284	−1.68860	−0.844301	+	0.535870i	$0.819984\pi$
$72$	2.86091	0.337162
$73$	−4.25808	−0.498371	−0.249185	−	0.968456i	$-0.580163\pi$
$73$	−4.25808	−0.498371	−0.249185	+	0.968456i	$0.580163\pi$
$74$	11.3608	1.32067
$75$	0.787158	0.0908932
$76$	−0.263898	−0.0302712
$77$	−10.5493	−1.20220
$78$	−0.239674	−0.0271378
$79$	5.78002	0.650303	0.325151	−	0.945662i	$-0.394585\pi$
$79$	5.78002	0.650303	0.325151	+	0.945662i	$0.394585\pi$
$80$	−2.66658	−0.298133
$81$	7.76755	0.863062
$82$	2.02200	0.223293
$83$	2.76081	0.303039	0.151519	−	0.988454i	$-0.451583\pi$
$83$	2.76081	0.303039	0.151519	+	0.988454i	$0.451583\pi$
$84$	1.24912	0.136290
$85$	8.30502	0.900806
$86$	1.76054	0.189844
$87$	3.07576	0.329756
$88$	3.14966	0.335755
$89$	12.7467	1.35115	0.675574	−	0.737292i	$-0.263896\pi$
$89$	12.7467	1.35115	0.675574	+	0.737292i	$0.263896\pi$
$90$	−7.62885	−0.804152
$91$	2.15247	0.225640
$92$	−1.00000	−0.104257
$93$	3.14347	0.325962
$94$	0.148071	0.0152724
$95$	0.703706	0.0721987
$96$	−0.372945	−0.0380635
$97$	−3.82614	−0.388486	−0.194243	−	0.980953i	$-0.562225\pi$
$97$	−3.82614	−0.388486	−0.194243	+	0.980953i	$0.562225\pi$
$98$	−4.21809	−0.426092
$99$	9.01090	0.905630
$100$	2.11066	0.211066
$101$	16.4278	1.63463	0.817315	−	0.576191i	$-0.195462\pi$
$101$	16.4278	1.63463	0.817315	+	0.576191i	$0.195462\pi$
$102$	1.16153	0.115009
$103$	18.3341	1.80651	0.903255	−	0.429104i	$-0.141171\pi$
$103$	18.3341	1.80651	0.903255	+	0.429104i	$0.141171\pi$
$104$	−0.642654	−0.0630174
$105$	−3.33088	−0.325061
$106$	9.49126	0.921873
$107$	1.01800	0.0984137	0.0492068	−	0.998789i	$-0.484331\pi$
$107$	1.01800	0.0984137	0.0492068	+	0.998789i	$0.484331\pi$
$108$	−2.18580	−0.210328
$109$	7.29920	0.699137	0.349569	−	0.936911i	$-0.386328\pi$
$109$	7.29920	0.699137	0.349569	+	0.936911i	$0.386328\pi$
$110$	−8.39883	−0.800797
$111$	−4.23696	−0.402154
$112$	3.34934	0.316483
$113$	−18.4414	−1.73482	−0.867410	−	0.497595i	$-0.834217\pi$
$113$	−18.4414	−1.73482	−0.867410	+	0.497595i	$0.834217\pi$
$114$	0.0984195	0.00921783
$115$	2.66658	0.248660
$116$	8.24723	0.765736
$117$	−1.83858	−0.169976
$118$	3.73906	0.344208
$119$	−10.4315	−0.956251
$120$	0.994488	0.0907839
$121$	−1.07963	−0.0981485
$122$	−5.20249	−0.471011
$123$	−0.754095	−0.0679944
$124$	8.42877	0.756926
$125$	7.70467	0.689127
$126$	9.58217	0.853648
$127$	−6.86305	−0.608997	−0.304499	−	0.952513i	$-0.598489\pi$
$127$	−6.86305	−0.608997	−0.304499	+	0.952513i	$0.598489\pi$
$128$	−1.00000	−0.0883883
$129$	−0.656586	−0.0578092
$130$	1.71369	0.150300
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−1.17465	−0.102240
$133$	−0.883885	−0.0766426
$134$	−5.80138	−0.501163
$135$	5.82861	0.501647
$136$	3.11448	0.267065
$137$	11.5250	0.984649	0.492325	−	0.870412i	$-0.336147\pi$
$137$	11.5250	0.984649	0.492325	+	0.870412i	$0.336147\pi$
$138$	0.372945	0.0317472
$139$	−15.1884	−1.28826	−0.644132	−	0.764914i	$-0.722781\pi$
$139$	−15.1884	−1.28826	−0.644132	+	0.764914i	$0.722781\pi$
$140$	−8.93129	−0.754832
$141$	−0.0552225	−0.00465057
$142$	14.2284	1.19402
$143$	−2.02414	−0.169267
$144$	−2.86091	−0.238409
$145$	−21.9919	−1.82633
$146$	4.25808	0.352401
$147$	1.57312	0.129748
$148$	−11.3608	−0.933854
$149$	21.3323	1.74761	0.873804	−	0.486278i	$-0.161646\pi$
$149$	21.3323	1.74761	0.873804	+	0.486278i	$0.161646\pi$
$150$	−0.787158	−0.0642712
$151$	13.0219	1.05971	0.529854	−	0.848089i	$-0.322247\pi$
$151$	13.0219	1.05971	0.529854	+	0.848089i	$0.322247\pi$
$152$	0.263898	0.0214050
$153$	8.91026	0.720352
$154$	10.5493	0.850086
$155$	−22.4760	−1.80532
$156$	0.239674	0.0191893
$157$	19.0971	1.52412	0.762058	−	0.647509i	$-0.224189\pi$
$157$	19.0971	1.52412	0.762058	+	0.647509i	$0.224189\pi$
$158$	−5.78002	−0.459834
$159$	−3.53972	−0.280718
$160$	2.66658	0.210812
$161$	−3.34934	−0.263965
$162$	−7.76755	−0.610277
$163$	−0.0511642	−0.00400749	−0.00200374	−	0.999998i	$-0.500638\pi$
$163$	−0.0511642	−0.00400749	−0.00200374	+	0.999998i	$0.500638\pi$
$164$	−2.02200	−0.157892
$165$	3.13230	0.243849
$166$	−2.76081	−0.214281
$167$	7.81925	0.605072	0.302536	−	0.953138i	$-0.402167\pi$
$167$	7.81925	0.605072	0.302536	+	0.953138i	$0.402167\pi$
$168$	−1.24912	−0.0963717
$169$	−12.5870	−0.968230
$170$	−8.30502	−0.636966
$171$	0.754989	0.0577355
$172$	−1.76054	−0.134240
$173$	−5.91632	−0.449810	−0.224905	−	0.974381i	$-0.572207\pi$
$173$	−5.91632	−0.449810	−0.224905	+	0.974381i	$0.572207\pi$
$174$	−3.07576	−0.233173
$175$	7.06931	0.534389
$176$	−3.14966	−0.237415
$177$	−1.39446	−0.104814
$178$	−12.7467	−0.955406
$179$	6.28387	0.469679	0.234839	−	0.972034i	$-0.424544\pi$
$179$	6.28387	0.469679	0.234839	+	0.972034i	$0.424544\pi$
$180$	7.62885	0.568621
$181$	8.23941	0.612430	0.306215	−	0.951962i	$-0.400937\pi$
$181$	8.23941	0.612430	0.306215	+	0.951962i	$0.400937\pi$
$182$	−2.15247	−0.159551
$183$	1.94024	0.143427
$184$	1.00000	0.0737210
$185$	30.2945	2.22730
$186$	−3.14347	−0.230490
$187$	9.80957	0.717347
$188$	−0.148071	−0.0107992
$189$	−7.32098	−0.532523
$190$	−0.703706	−0.0510522
$191$	8.82014	0.638203	0.319101	−	0.947721i	$-0.396619\pi$
$191$	8.82014	0.638203	0.319101	+	0.947721i	$0.396619\pi$
$192$	0.372945	0.0269150
$193$	−7.10907	−0.511722	−0.255861	−	0.966714i	$-0.582359\pi$
$193$	−7.10907	−0.511722	−0.255861	+	0.966714i	$0.582359\pi$
$194$	3.82614	0.274701
$195$	−0.639112	−0.0457677
$196$	4.21809	0.301292
$197$	−6.06136	−0.431854	−0.215927	−	0.976409i	$-0.569277\pi$
$197$	−6.06136	−0.431854	−0.215927	+	0.976409i	$0.569277\pi$
$198$	−9.01090	−0.640377
$199$	−21.8539	−1.54918	−0.774589	−	0.632465i	$-0.782043\pi$
$199$	−21.8539	−1.54918	−0.774589	+	0.632465i	$0.782043\pi$
$200$	−2.11066	−0.149246
$201$	2.16360	0.152608
$202$	−16.4278	−1.15586
$203$	27.6228	1.93874
$204$	−1.16153	−0.0813234
$205$	5.39183	0.376581
$206$	−18.3341	−1.27740
$207$	2.86091	0.198847
$208$	0.642654	0.0445600
$209$	0.831190	0.0574946
$210$	3.33088	0.229853
$211$	8.20266	0.564694	0.282347	−	0.959312i	$-0.408887\pi$
$211$	8.20266	0.564694	0.282347	+	0.959312i	$0.408887\pi$
$212$	−9.49126	−0.651863
$213$	−5.30641	−0.363589
$214$	−1.01800	−0.0695890
$215$	4.69463	0.320171
$216$	2.18580	0.148725
$217$	28.2308	1.91643
$218$	−7.29920	−0.494365
$219$	−1.58803	−0.107309
$220$	8.39883	0.566249
$221$	−2.00153	−0.134638
$222$	4.23696	0.284366
$223$	5.14663	0.344644	0.172322	−	0.985041i	$-0.444873\pi$
$223$	5.14663	0.344644	0.172322	+	0.985041i	$0.444873\pi$
$224$	−3.34934	−0.223787
$225$	−6.03840	−0.402560
$226$	18.4414	1.22670
$227$	−24.7569	−1.64317	−0.821585	−	0.570086i	$-0.806910\pi$
$227$	−24.7569	−1.64317	−0.821585	+	0.570086i	$0.806910\pi$
$228$	−0.0984195	−0.00651799
$229$	25.1048	1.65897	0.829486	−	0.558528i	$-0.188634\pi$
$229$	25.1048	1.65897	0.829486	+	0.558528i	$0.188634\pi$
$230$	−2.66658	−0.175829
$231$	−3.93431	−0.258858
$232$	−8.24723	−0.541457
$233$	−7.49513	−0.491022	−0.245511	−	0.969394i	$-0.578956\pi$
$233$	−7.49513	−0.491022	−0.245511	+	0.969394i	$0.578956\pi$
$234$	1.83858	0.120191
$235$	0.394844	0.0257568
$236$	−3.73906	−0.243392
$237$	2.15563	0.140023
$238$	10.4315	0.676172
$239$	−18.7569	−1.21328	−0.606641	−	0.794976i	$-0.707483\pi$
$239$	−18.7569	−1.21328	−0.606641	+	0.794976i	$0.707483\pi$
$240$	−0.994488	−0.0641939
$241$	−21.4904	−1.38432	−0.692159	−	0.721745i	$-0.743340\pi$
$241$	−21.4904	−1.38432	−0.692159	+	0.721745i	$0.743340\pi$
$242$	1.07963	0.0694014
$243$	9.45426	0.606491
$244$	5.20249	0.333055
$245$	−11.2479	−0.718601
$246$	0.754095	0.0480793
$247$	−0.169595	−0.0107911
$248$	−8.42877	−0.535227
$249$	1.02963	0.0652502
$250$	−7.70467	−0.487286
$251$	−3.62925	−0.229076	−0.114538	−	0.993419i	$-0.536539\pi$
$251$	−3.62925	−0.229076	−0.114538	+	0.993419i	$0.536539\pi$
$252$	−9.58217	−0.603620
$253$	3.14966	0.198018
$254$	6.86305	0.430626
$255$	3.09732	0.193961
$256$	1.00000	0.0625000
$257$	−21.7861	−1.35898	−0.679489	−	0.733686i	$-0.737798\pi$
$257$	−21.7861	−1.35898	−0.679489	+	0.733686i	$0.737798\pi$
$258$	0.656586	0.0408773
$259$	−38.0513	−2.36439
$260$	−1.71369	−0.106278
$261$	−23.5946	−1.46047
$262$	−1.00000	−0.0617802
$263$	4.41684	0.272354	0.136177	−	0.990685i	$-0.456518\pi$
$263$	4.41684	0.272354	0.136177	+	0.990685i	$0.456518\pi$
$264$	1.17465	0.0722947
$265$	25.3092	1.55473
$266$	0.883885	0.0541945
$267$	4.75382	0.290929
$268$	5.80138	0.354376
$269$	22.9534	1.39949	0.699747	−	0.714390i	$-0.253296\pi$
$269$	22.9534	1.39949	0.699747	+	0.714390i	$0.253296\pi$
$270$	−5.82861	−0.354718
$271$	15.9775	0.970563	0.485282	−	0.874358i	$-0.338717\pi$
$271$	15.9775	0.970563	0.485282	+	0.874358i	$0.338717\pi$
$272$	−3.11448	−0.188843
$273$	0.802752	0.0485848
$274$	−11.5250	−0.696252
$275$	−6.64785	−0.400880
$276$	−0.372945	−0.0224486
$277$	16.4329	0.987355	0.493678	−	0.869645i	$-0.335652\pi$
$277$	16.4329	0.987355	0.493678	+	0.869645i	$0.335652\pi$
$278$	15.1884	0.910940
$279$	−24.1140	−1.44367
$280$	8.93129	0.533747
$281$	7.52356	0.448818	0.224409	−	0.974495i	$-0.427955\pi$
$281$	7.52356	0.448818	0.224409	+	0.974495i	$0.427955\pi$
$282$	0.0552225	0.00328845
$283$	28.4605	1.69180	0.845902	−	0.533338i	$-0.179063\pi$
$283$	28.4605	1.69180	0.845902	+	0.533338i	$0.179063\pi$
$284$	−14.2284	−0.844301
$285$	0.262444	0.0155458
$286$	2.02414	0.119690
$287$	−6.77237	−0.399760
$288$	2.86091	0.168581
$289$	−7.29999	−0.429411
$290$	21.9919	1.29141
$291$	−1.42694	−0.0836487
$292$	−4.25808	−0.249185
$293$	15.6896	0.916599	0.458299	−	0.888798i	$-0.348459\pi$
$293$	15.6896	0.916599	0.458299	+	0.888798i	$0.348459\pi$
$294$	−1.57312	−0.0917460
$295$	9.97051	0.580505
$296$	11.3608	0.660334
$297$	6.88452	0.399481
$298$	−21.3323	−1.23575
$299$	−0.642654	−0.0371656
$300$	0.787158	0.0454466
$301$	−5.89666	−0.339878
$302$	−13.0219	−0.749327
$303$	6.12668	0.351968
$304$	−0.263898	−0.0151356
$305$	−13.8729	−0.794358
$306$	−8.91026	−0.509366
$307$	25.3152	1.44481	0.722406	−	0.691469i	$-0.243036\pi$
$307$	25.3152	1.44481	0.722406	+	0.691469i	$0.243036\pi$
$308$	−10.5493	−0.601102
$309$	6.83760	0.388978
$310$	22.4760	1.27655
$311$	−23.3532	−1.32424	−0.662119	−	0.749399i	$-0.730343\pi$
$311$	−23.3532	−1.32424	−0.662119	+	0.749399i	$0.730343\pi$
$312$	−0.239674	−0.0135689
$313$	23.9573	1.35415	0.677073	−	0.735916i	$-0.263248\pi$
$313$	23.9573	1.35415	0.677073	+	0.735916i	$0.263248\pi$
$314$	−19.0971	−1.07771
$315$	25.5516	1.43967
$316$	5.78002	0.325151
$317$	18.3402	1.03009	0.515043	−	0.857164i	$-0.327776\pi$
$317$	18.3402	1.03009	0.515043	+	0.857164i	$0.327776\pi$
$318$	3.53972	0.198498
$319$	−25.9760	−1.45438
$320$	−2.66658	−0.149066
$321$	0.379658	0.0211904
$322$	3.34934	0.186652
$323$	0.821906	0.0457321
$324$	7.76755	0.431531
$325$	1.35642	0.0752407
$326$	0.0511642	0.00283372
$327$	2.72220	0.150538
$328$	2.02200	0.111646
$329$	−0.495942	−0.0273422
$330$	−3.13230	−0.172427
$331$	33.1619	1.82275	0.911373	−	0.411582i	$-0.135024\pi$
$331$	33.1619	1.82275	0.911373	+	0.411582i	$0.135024\pi$
$332$	2.76081	0.151519
$333$	32.5023	1.78112
$334$	−7.81925	−0.427850
$335$	−15.4699	−0.845209
$336$	1.24912	0.0681451
$337$	22.6883	1.23591	0.617956	−	0.786213i	$-0.287961\pi$
$337$	22.6883	1.23591	0.617956	+	0.786213i	$0.287961\pi$
$338$	12.5870	0.684642
$339$	−6.87762	−0.373541
$340$	8.30502	0.450403
$341$	−26.5478	−1.43764
$342$	−0.754989	−0.0408251
$343$	−9.31756	−0.503101
$344$	1.76054	0.0949222
$345$	0.994488	0.0535414
$346$	5.91632	0.318064
$347$	−23.2997	−1.25079	−0.625397	−	0.780306i	$-0.715063\pi$
$347$	−23.2997	−1.25079	−0.625397	+	0.780306i	$0.715063\pi$
$348$	3.07576	0.164878
$349$	22.2842	1.19285	0.596424	−	0.802670i	$-0.296588\pi$
$349$	22.2842	1.19285	0.596424	+	0.802670i	$0.296588\pi$
$350$	−7.06931	−0.377870
$351$	−1.40471	−0.0749779
$352$	3.14966	0.167878
$353$	13.2432	0.704865	0.352432	−	0.935837i	$-0.385355\pi$
$353$	13.2432	0.704865	0.352432	+	0.935837i	$0.385355\pi$
$354$	1.39446	0.0741149
$355$	37.9412	2.01371
$356$	12.7467	0.675574
$357$	−3.89036	−0.205900
$358$	−6.28387	−0.332113
$359$	28.2912	1.49315	0.746577	−	0.665299i	$-0.231696\pi$
$359$	28.2912	1.49315	0.746577	+	0.665299i	$0.231696\pi$
$360$	−7.62885	−0.402076
$361$	−18.9304	−0.996335
$362$	−8.23941	−0.433054
$363$	−0.402644	−0.0211333
$364$	2.15247	0.112820
$365$	11.3545	0.594323
$366$	−1.94024	−0.101418
$367$	32.3605	1.68921	0.844603	−	0.535394i	$-0.179837\pi$
$367$	32.3605	1.68921	0.844603	+	0.535394i	$0.179837\pi$
$368$	−1.00000	−0.0521286
$369$	5.78476	0.301143
$370$	−30.2945	−1.57494
$371$	−31.7895	−1.65043
$372$	3.14347	0.162981
$373$	30.1838	1.56286	0.781428	−	0.623995i	$-0.214491\pi$
$373$	30.1838	1.56286	0.781428	+	0.623995i	$0.214491\pi$
$374$	−9.80957	−0.507241
$375$	2.87342	0.148383
$376$	0.148071	0.00763620
$377$	5.30012	0.272970
$378$	7.32098	0.376551
$379$	−27.3705	−1.40593	−0.702965	−	0.711225i	$-0.748141\pi$
$379$	−27.3705	−1.40593	−0.702965	+	0.711225i	$0.748141\pi$
$380$	0.703706	0.0360993
$381$	−2.55954	−0.131129
$382$	−8.82014	−0.451277
$383$	−4.70135	−0.240228	−0.120114	−	0.992760i	$-0.538326\pi$
$383$	−4.70135	−0.240228	−0.120114	+	0.992760i	$0.538326\pi$
$384$	−0.372945	−0.0190318
$385$	28.1305	1.43367
$386$	7.10907	0.361842
$387$	5.03676	0.256033
$388$	−3.82614	−0.194243
$389$	25.4451	1.29012	0.645059	−	0.764133i	$-0.276833\pi$
$389$	25.4451	1.29012	0.645059	+	0.764133i	$0.276833\pi$
$390$	0.639112	0.0323627
$391$	3.11448	0.157506
$392$	−4.21809	−0.213046
$393$	0.372945	0.0188126
$394$	6.06136	0.305367
$395$	−15.4129	−0.775506
$396$	9.01090	0.452815
$397$	−22.2238	−1.11538	−0.557689	−	0.830050i	$-0.688312\pi$
$397$	−22.2238	−1.11538	−0.557689	+	0.830050i	$0.688312\pi$
$398$	21.8539	1.09543
$399$	−0.329640	−0.0165027
$400$	2.11066	0.105533
$401$	25.6445	1.28063	0.640313	−	0.768114i	$-0.278805\pi$
$401$	25.6445	1.28063	0.640313	+	0.768114i	$0.278805\pi$
$402$	−2.16360	−0.107910
$403$	5.41678	0.269829
$404$	16.4278	0.817315
$405$	−20.7128	−1.02923
$406$	−27.6228	−1.37090
$407$	35.7827	1.77368
$408$	1.16153	0.0575043
$409$	−13.3226	−0.658761	−0.329381	−	0.944197i	$-0.606840\pi$
$409$	−13.3226	−0.658761	−0.329381	+	0.944197i	$0.606840\pi$
$410$	−5.39183	−0.266283
$411$	4.29820	0.212015
$412$	18.3341	0.903255
$413$	−12.5234	−0.616236
$414$	−2.86091	−0.140606
$415$	−7.36193	−0.361383
$416$	−0.642654	−0.0315087
$417$	−5.66444	−0.277389
$418$	−0.831190	−0.0406548
$419$	11.9710	0.584820	0.292410	−	0.956293i	$-0.405543\pi$
$419$	11.9710	0.584820	0.292410	+	0.956293i	$0.405543\pi$
$420$	−3.33088	−0.162530
$421$	27.0823	1.31991	0.659955	−	0.751305i	$-0.270575\pi$
$421$	27.0823	1.31991	0.659955	+	0.751305i	$0.270575\pi$
$422$	−8.20266	−0.399299
$423$	0.423619	0.0205971
$424$	9.49126	0.460936
$425$	−6.57360	−0.318866
$426$	5.30641	0.257097
$427$	17.4249	0.843251
$428$	1.01800	0.0492068
$429$	−0.754894	−0.0364466
$430$	−4.69463	−0.226395
$431$	−36.5228	−1.75924	−0.879622	−	0.475674i	$-0.842204\pi$
$431$	−36.5228	−1.75924	−0.879622	+	0.475674i	$0.842204\pi$
$432$	−2.18580	−0.105164
$433$	−2.46789	−0.118599	−0.0592997	−	0.998240i	$-0.518887\pi$
$433$	−2.46789	−0.118599	−0.0592997	+	0.998240i	$0.518887\pi$
$434$	−28.2308	−1.35512
$435$	−8.20177	−0.393245
$436$	7.29920	0.349569
$437$	0.263898	0.0126240
$438$	1.58803	0.0758790
$439$	6.81768	0.325390	0.162695	−	0.986676i	$-0.447981\pi$
$439$	6.81768	0.325390	0.162695	+	0.986676i	$0.447981\pi$
$440$	−8.39883	−0.400398
$441$	−12.0676	−0.574647
$442$	2.00153	0.0952033
$443$	−13.8361	−0.657371	−0.328686	−	0.944439i	$-0.606606\pi$
$443$	−13.8361	−0.657371	−0.328686	+	0.944439i	$0.606606\pi$
$444$	−4.23696	−0.201077
$445$	−33.9901	−1.61129
$446$	−5.14663	−0.243700
$447$	7.95576	0.376295
$448$	3.34934	0.158242
$449$	−15.1134	−0.713245	−0.356623	−	0.934249i	$-0.616072\pi$
$449$	−15.1134	−0.713245	−0.356623	+	0.934249i	$0.616072\pi$
$450$	6.03840	0.284653
$451$	6.36861	0.299886
$452$	−18.4414	−0.867410
$453$	4.85646	0.228176
$454$	24.7569	1.16190
$455$	−5.73973	−0.269083
$456$	0.0984195	0.00460891
$457$	−27.9887	−1.30926	−0.654628	−	0.755951i	$-0.727175\pi$
$457$	−27.9887	−1.30926	−0.654628	+	0.755951i	$0.727175\pi$
$458$	−25.1048	−1.17307
$459$	6.80763	0.317753
$460$	2.66658	0.124330
$461$	34.7688	1.61935	0.809673	−	0.586882i	$-0.199645\pi$
$461$	34.7688	1.61935	0.809673	+	0.586882i	$0.199645\pi$
$462$	3.93431	0.183040
$463$	−1.10173	−0.0512015	−0.0256008	−	0.999672i	$-0.508150\pi$
$463$	−1.10173	−0.0512015	−0.0256008	+	0.999672i	$0.508150\pi$
$464$	8.24723	0.382868
$465$	−8.38231	−0.388720
$466$	7.49513	0.347205
$467$	−19.7907	−0.915807	−0.457903	−	0.889002i	$-0.651399\pi$
$467$	−19.7907	−0.915807	−0.457903	+	0.889002i	$0.651399\pi$
$468$	−1.83858	−0.0849882
$469$	19.4308	0.897232
$470$	−0.394844	−0.0182128
$471$	7.12217	0.328172
$472$	3.73906	0.172104
$473$	5.54512	0.254965
$474$	−2.15563	−0.0990113
$475$	−0.556998	−0.0255568
$476$	−10.4315	−0.478126
$477$	27.1537	1.24328
$478$	18.7569	0.857919
$479$	23.6862	1.08225	0.541125	−	0.840942i	$-0.317998\pi$
$479$	23.6862	1.08225	0.541125	+	0.840942i	$0.317998\pi$
$480$	0.994488	0.0453920
$481$	−7.30107	−0.332900
$482$	21.4904	0.978861
$483$	−1.24912	−0.0568369
$484$	−1.07963	−0.0490742
$485$	10.2027	0.463281
$486$	−9.45426	−0.428854
$487$	−21.7382	−0.985052	−0.492526	−	0.870298i	$-0.663926\pi$
$487$	−21.7382	−0.985052	−0.492526	+	0.870298i	$0.663926\pi$
$488$	−5.20249	−0.235506
$489$	−0.0190814	−0.000862892 0
$490$	11.2479	0.508128
$491$	2.54218	0.114727	0.0573635	−	0.998353i	$-0.481731\pi$
$491$	2.54218	0.114727	0.0573635	+	0.998353i	$0.481731\pi$
$492$	−0.754095	−0.0339972
$493$	−25.6859	−1.15683
$494$	0.169595	0.00763045
$495$	−24.0283	−1.07999
$496$	8.42877	0.378463
$497$	−47.6558	−2.13765
$498$	−1.02963	−0.0461389
$499$	34.6773	1.55237	0.776185	−	0.630505i	$-0.217152\pi$
$499$	34.6773	1.55237	0.776185	+	0.630505i	$0.217152\pi$
$500$	7.70467	0.344563
$501$	2.91615	0.130284
$502$	3.62925	0.161981
$503$	−0.127885	−0.00570212	−0.00285106	−	0.999996i	$-0.500908\pi$
$503$	−0.127885	−0.00570212	−0.00285106	+	0.999996i	$0.500908\pi$
$504$	9.58217	0.426824
$505$	−43.8061	−1.94935
$506$	−3.14966	−0.140020
$507$	−4.69426	−0.208479
$508$	−6.86305	−0.304499
$509$	−2.20831	−0.0978815	−0.0489407	−	0.998802i	$-0.515585\pi$
$509$	−2.20831	−0.0978815	−0.0489407	+	0.998802i	$0.515585\pi$
$510$	−3.09732	−0.137151
$511$	−14.2618	−0.630903
$512$	−1.00000	−0.0441942
$513$	0.576828	0.0254676
$514$	21.7861	0.960942
$515$	−48.8893	−2.15432
$516$	−0.656586	−0.0289046
$517$	0.466375	0.0205111
$518$	38.0513	1.67188
$519$	−2.20646	−0.0968530
$520$	1.71369	0.0751502
$521$	31.5433	1.38194	0.690969	−	0.722885i	$-0.257184\pi$
$521$	31.5433	1.38194	0.690969	+	0.722885i	$0.257184\pi$
$522$	23.5946	1.03271
$523$	−1.43055	−0.0625538	−0.0312769	−	0.999511i	$-0.509957\pi$
$523$	−1.43055	−0.0625538	−0.0312769	+	0.999511i	$0.509957\pi$
$524$	1.00000	0.0436852
$525$	2.63646	0.115065
$526$	−4.41684	−0.192583
$527$	−26.2513	−1.14352
$528$	−1.17465	−0.0511201
$529$	1.00000	0.0434783
$530$	−25.3092	−1.09936
$531$	10.6971	0.464216
$532$	−0.883885	−0.0383213
$533$	−1.29945	−0.0562852
$534$	−4.75382	−0.205718
$535$	−2.71458	−0.117361
$536$	−5.80138	−0.250582
$537$	2.34354	0.101131
$538$	−22.9534	−0.989592
$539$	−13.2856	−0.572250
$540$	5.82861	0.250823
$541$	−26.2537	−1.12874	−0.564368	−	0.825523i	$-0.690880\pi$
$541$	−26.2537	−1.12874	−0.564368	+	0.825523i	$0.690880\pi$
$542$	−15.9775	−0.686292
$543$	3.07285	0.131868
$544$	3.11448	0.133532
$545$	−19.4639	−0.833743
$546$	−0.802752	−0.0343546
$547$	−28.5549	−1.22092	−0.610459	−	0.792048i	$-0.709015\pi$
$547$	−28.5549	−1.22092	−0.610459	+	0.792048i	$0.709015\pi$
$548$	11.5250	0.492325
$549$	−14.8839	−0.635228
$550$	6.64785	0.283465
$551$	−2.17643	−0.0927190
$552$	0.372945	0.0158736
$553$	19.3593	0.823239
$554$	−16.4329	−0.698165
$555$	11.2982	0.479582
$556$	−15.1884	−0.644132
$557$	36.3515	1.54026	0.770132	−	0.637885i	$-0.220190\pi$
$557$	36.3515	1.54026	0.770132	+	0.637885i	$0.220190\pi$
$558$	24.1140	1.02083
$559$	−1.13142	−0.0478540
$560$	−8.93129	−0.377416
$561$	3.65843	0.154459
$562$	−7.52356	−0.317362
$563$	6.27585	0.264496	0.132248	−	0.991217i	$-0.457781\pi$
$563$	6.27585	0.264496	0.132248	+	0.991217i	$0.457781\pi$
$564$	−0.0552225	−0.00232529
$565$	49.1754	2.06883
$566$	−28.4605	−1.19629
$567$	26.0162	1.09258
$568$	14.2284	0.597011
$569$	30.1215	1.26276	0.631379	−	0.775475i	$-0.282489\pi$
$569$	30.1215	1.26276	0.631379	+	0.775475i	$0.282489\pi$
$570$	−0.262444	−0.0109925
$571$	18.0098	0.753686	0.376843	−	0.926277i	$-0.377010\pi$
$571$	18.0098	0.753686	0.376843	+	0.926277i	$0.377010\pi$
$572$	−2.02414	−0.0846336
$573$	3.28943	0.137418
$574$	6.77237	0.282673
$575$	−2.11066	−0.0880204
$576$	−2.86091	−0.119205
$577$	38.5114	1.60325	0.801625	−	0.597827i	$-0.203969\pi$
$577$	38.5114	1.60325	0.801625	+	0.597827i	$0.203969\pi$
$578$	7.29999	0.303640
$579$	−2.65129	−0.110184
$580$	−21.9919	−0.913165
$581$	9.24691	0.383626
$582$	1.42694	0.0591485
$583$	29.8943	1.23809
$584$	4.25808	0.176201
$585$	4.90271	0.202702
$586$	−15.6896	−0.648133
$587$	28.4959	1.17615	0.588075	−	0.808806i	$-0.299886\pi$
$587$	28.4959	1.17615	0.588075	+	0.808806i	$0.299886\pi$
$588$	1.57312	0.0648742
$589$	−2.22434	−0.0916522
$590$	−9.97051	−0.410479
$591$	−2.26055	−0.0929868
$592$	−11.3608	−0.466927
$593$	−0.996844	−0.0409355	−0.0204677	−	0.999791i	$-0.506516\pi$
$593$	−0.996844	−0.0409355	−0.0204677	+	0.999791i	$0.506516\pi$
$594$	−6.88452	−0.282475
$595$	27.8164	1.14036
$596$	21.3323	0.873804
$597$	−8.15028	−0.333569
$598$	0.642654	0.0262801
$599$	14.8959	0.608630	0.304315	−	0.952571i	$-0.401572\pi$
$599$	14.8959	0.608630	0.304315	+	0.952571i	$0.401572\pi$
$600$	−0.787158	−0.0321356
$601$	1.70680	0.0696217	0.0348108	−	0.999394i	$-0.488917\pi$
$601$	1.70680	0.0696217	0.0348108	+	0.999394i	$0.488917\pi$
$602$	5.89666	0.240330
$603$	−16.5972	−0.675892
$604$	13.0219	0.529854
$605$	2.87893	0.117045
$606$	−6.12668	−0.248879
$607$	5.75840	0.233726	0.116863	−	0.993148i	$-0.462716\pi$
$607$	5.75840	0.233726	0.116863	+	0.993148i	$0.462716\pi$
$608$	0.263898	0.0107025
$609$	10.3018	0.417449
$610$	13.8729	0.561696
$611$	−0.0951586	−0.00384971
$612$	8.91026	0.360176
$613$	16.4947	0.666214	0.333107	−	0.942889i	$-0.391903\pi$
$613$	16.4947	0.666214	0.333107	+	0.942889i	$0.391903\pi$
$614$	−25.3152	−1.02164
$615$	2.01085	0.0810855
$616$	10.5493	0.425043
$617$	−28.4796	−1.14654	−0.573272	−	0.819365i	$-0.694326\pi$
$617$	−28.4796	−1.14654	−0.573272	+	0.819365i	$0.694326\pi$
$618$	−6.83760	−0.275049
$619$	−32.0452	−1.28801	−0.644003	−	0.765023i	$-0.722728\pi$
$619$	−32.0452	−1.28801	−0.644003	+	0.765023i	$0.722728\pi$
$620$	−22.4760	−0.902658
$621$	2.18580	0.0877130
$622$	23.3532	0.936377
$623$	42.6931	1.71046
$624$	0.239674	0.00959466
$625$	−31.0984	−1.24394
$626$	−23.9573	−0.957526
$627$	0.309988	0.0123797
$628$	19.0971	0.762058
$629$	35.3831	1.41082
$630$	−25.5516	−1.01800
$631$	−29.2285	−1.16357	−0.581783	−	0.813344i	$-0.697645\pi$
$631$	−29.2285	−1.16357	−0.581783	+	0.813344i	$0.697645\pi$
$632$	−5.78002	−0.229917
$633$	3.05914	0.121590
$634$	−18.3402	−0.728381
$635$	18.3009	0.726248
$636$	−3.53972	−0.140359
$637$	2.71077	0.107405
$638$	25.9760	1.02840
$639$	40.7062	1.61031
$640$	2.66658	0.105406
$641$	3.39538	0.134110	0.0670548	−	0.997749i	$-0.478640\pi$
$641$	3.39538	0.134110	0.0670548	+	0.997749i	$0.478640\pi$
$642$	−0.379658	−0.0149839
$643$	44.4694	1.75370	0.876852	−	0.480761i	$-0.159640\pi$
$643$	44.4694	1.75370	0.876852	+	0.480761i	$0.159640\pi$
$644$	−3.34934	−0.131983
$645$	1.75084	0.0689393
$646$	−0.821906	−0.0323375
$647$	27.0705	1.06425	0.532125	−	0.846666i	$-0.321394\pi$
$647$	27.0705	1.06425	0.532125	+	0.846666i	$0.321394\pi$
$648$	−7.76755	−0.305138
$649$	11.7768	0.462279
$650$	−1.35642	−0.0532032
$651$	10.5285	0.412646
$652$	−0.0511642	−0.00200374
$653$	−23.6357	−0.924937	−0.462468	−	0.886636i	$-0.653036\pi$
$653$	−23.6357	−0.924937	−0.462468	+	0.886636i	$0.653036\pi$
$654$	−2.72220	−0.106447
$655$	−2.66658	−0.104192
$656$	−2.02200	−0.0789458
$657$	12.1820	0.475265
$658$	0.495942	0.0193338
$659$	−40.8700	−1.59207	−0.796035	−	0.605251i	$-0.793073\pi$
$659$	−40.8700	−1.59207	−0.796035	+	0.605251i	$0.793073\pi$
$660$	3.13230	0.121925
$661$	7.49141	0.291382	0.145691	−	0.989330i	$-0.453459\pi$
$661$	7.49141	0.291382	0.145691	+	0.989330i	$0.453459\pi$
$662$	−33.1619	−1.28888
$663$	−0.746462	−0.0289902
$664$	−2.76081	−0.107140
$665$	2.35695	0.0913987
$666$	−32.5023	−1.25944
$667$	−8.24723	−0.319334
$668$	7.81925	0.302536
$669$	1.91941	0.0742087
$670$	15.4699	0.597653
$671$	−16.3861	−0.632578
$672$	−1.24912	−0.0481859
$673$	7.18704	0.277040	0.138520	−	0.990360i	$-0.455765\pi$
$673$	7.18704	0.277040	0.138520	+	0.990360i	$0.455765\pi$
$674$	−22.6883	−0.873921
$675$	−4.61347	−0.177572
$676$	−12.5870	−0.484115
$677$	25.2307	0.969694	0.484847	−	0.874599i	$-0.338875\pi$
$677$	25.2307	0.969694	0.484847	+	0.874599i	$0.338875\pi$
$678$	6.87762	0.264133
$679$	−12.8150	−0.491796
$680$	−8.30502	−0.318483
$681$	−9.23294	−0.353807
$682$	26.5478	1.01657
$683$	−38.0767	−1.45697	−0.728483	−	0.685064i	$-0.759774\pi$
$683$	−38.0767	−1.45697	−0.728483	+	0.685064i	$0.759774\pi$
$684$	0.754989	0.0288677
$685$	−30.7324	−1.17423
$686$	9.31756	0.355746
$687$	9.36271	0.357210
$688$	−1.76054	−0.0671201
$689$	−6.09960	−0.232376
$690$	−0.994488	−0.0378595
$691$	−11.3114	−0.430305	−0.215152	−	0.976581i	$-0.569025\pi$
$691$	−11.3114	−0.430305	−0.215152	+	0.976581i	$0.569025\pi$
$692$	−5.91632	−0.224905
$693$	30.1806	1.14647
$694$	23.2997	0.884445
$695$	40.5011	1.53630
$696$	−3.07576	−0.116587
$697$	6.29748	0.238534
$698$	−22.2842	−0.843471
$699$	−2.79527	−0.105727
$700$	7.06931	0.267195
$701$	4.62190	0.174567	0.0872834	−	0.996184i	$-0.472181\pi$
$701$	4.62190	0.174567	0.0872834	+	0.996184i	$0.472181\pi$
$702$	1.40471	0.0530174
$703$	2.99810	0.113075
$704$	−3.14966	−0.118707
$705$	0.147255	0.00554595
$706$	−13.2432	−0.498415
$707$	55.0224	2.06933
$708$	−1.39446	−0.0524072
$709$	25.1846	0.945829	0.472914	−	0.881108i	$-0.343202\pi$
$709$	25.1846	0.945829	0.472914	+	0.881108i	$0.343202\pi$
$710$	−37.9412	−1.42391
$711$	−16.5361	−0.620153
$712$	−12.7467	−0.477703
$713$	−8.42877	−0.315660
$714$	3.89036	0.145593
$715$	5.39754	0.201857
$716$	6.28387	0.234839
$717$	−6.99528	−0.261244
$718$	−28.2912	−1.05582
$719$	−10.4039	−0.388000	−0.194000	−	0.981002i	$-0.562146\pi$
$719$	−10.4039	−0.388000	−0.194000	+	0.981002i	$0.562146\pi$
$720$	7.62885	0.284311
$721$	61.4071	2.28692
$722$	18.9304	0.704515
$723$	−8.01474	−0.298071
$724$	8.23941	0.306215
$725$	17.4071	0.646482
$726$	0.402644	0.0149435
$727$	16.1748	0.599890	0.299945	−	0.953957i	$-0.403032\pi$
$727$	16.1748	0.599890	0.299945	+	0.953957i	$0.403032\pi$
$728$	−2.15247	−0.0797757
$729$	−19.7767	−0.732472
$730$	−11.3545	−0.420249
$731$	5.48318	0.202803
$732$	1.94024	0.0717134
$733$	−18.2603	−0.674461	−0.337231	−	0.941422i	$-0.609490\pi$
$733$	−18.2603	−0.674461	−0.337231	+	0.941422i	$0.609490\pi$
$734$	−32.3605	−1.19445
$735$	−4.19484	−0.154729
$736$	1.00000	0.0368605
$737$	−18.2724	−0.673072
$738$	−5.78476	−0.212940
$739$	−47.7774	−1.75752	−0.878761	−	0.477263i	$-0.841629\pi$
$739$	−47.7774	−1.75752	−0.878761	+	0.477263i	$0.841629\pi$
$740$	30.2945	1.11365
$741$	−0.0632497	−0.00232353
$742$	31.7895	1.16703
$743$	34.8801	1.27963	0.639814	−	0.768530i	$-0.279011\pi$
$743$	34.8801	1.27963	0.639814	+	0.768530i	$0.279011\pi$
$744$	−3.14347	−0.115245
$745$	−56.8842	−2.08408
$746$	−30.1838	−1.10511
$747$	−7.89844	−0.288989
$748$	9.80957	0.358673
$749$	3.40963	0.124585
$750$	−2.87342	−0.104922
$751$	−36.0545	−1.31565	−0.657823	−	0.753172i	$-0.728523\pi$
$751$	−36.0545	−1.31565	−0.657823	+	0.753172i	$0.728523\pi$
$752$	−0.148071	−0.00539961
$753$	−1.35351	−0.0493246
$754$	−5.30012	−0.193019
$755$	−34.7240	−1.26374
$756$	−7.32098	−0.266262
$757$	−47.7211	−1.73445	−0.867227	−	0.497913i	$-0.834100\pi$
$757$	−47.7211	−1.73445	−0.867227	+	0.497913i	$0.834100\pi$
$758$	27.3705	0.994142
$759$	1.17465	0.0426371
$760$	−0.703706	−0.0255261
$761$	16.8366	0.610327	0.305164	−	0.952300i	$-0.401289\pi$
$761$	16.8366	0.610327	0.305164	+	0.952300i	$0.401289\pi$
$762$	2.55954	0.0927224
$763$	24.4475	0.885060
$764$	8.82014	0.319101
$765$	−23.7599	−0.859042
$766$	4.70135	0.169867
$767$	−2.40292	−0.0867645
$768$	0.372945	0.0134575
$769$	18.6237	0.671589	0.335794	−	0.941935i	$-0.390995\pi$
$769$	18.6237	0.671589	0.335794	+	0.941935i	$0.390995\pi$
$770$	−28.1305	−1.01375
$771$	−8.12500	−0.292615
$772$	−7.10907	−0.255861
$773$	49.4999	1.78039	0.890193	−	0.455583i	$-0.150569\pi$
$773$	49.4999	1.78039	0.890193	+	0.455583i	$0.150569\pi$
$774$	−5.03676	−0.181043
$775$	17.7902	0.639044
$776$	3.82614	0.137350
$777$	−14.1910	−0.509100
$778$	−25.4451	−0.912251
$779$	0.533602	0.0191183
$780$	−0.639112	−0.0228839
$781$	44.8147	1.60359
$782$	−3.11448	−0.111374
$783$	−18.0268	−0.644225
$784$	4.21809	0.150646
$785$	−50.9240	−1.81756
$786$	−0.372945	−0.0133025
$787$	−13.5743	−0.483871	−0.241936	−	0.970292i	$-0.577782\pi$
$787$	−13.5743	−0.483871	−0.241936	+	0.970292i	$0.577782\pi$
$788$	−6.06136	−0.215927
$789$	1.64724	0.0586432
$790$	15.4129	0.548366
$791$	−61.7665	−2.19616
$792$	−9.01090	−0.320189
$793$	3.34340	0.118728
$794$	22.2238	0.788692
$795$	9.43895	0.334765
$796$	−21.8539	−0.774589
$797$	−9.25510	−0.327832	−0.163916	−	0.986474i	$-0.552413\pi$
$797$	−9.25510	−0.327832	−0.163916	+	0.986474i	$0.552413\pi$
$798$	0.329640	0.0116691
$799$	0.461166	0.0163149
$800$	−2.11066	−0.0746229
$801$	−36.4672	−1.28851
$802$	−25.6445	−0.905539
$803$	13.4115	0.473282
$804$	2.16360	0.0763042
$805$	8.93129	0.314787
$806$	−5.41678	−0.190798
$807$	8.56036	0.301339
$808$	−16.4278	−0.577929
$809$	−13.0959	−0.460426	−0.230213	−	0.973140i	$-0.573942\pi$
$809$	−13.0959	−0.460426	−0.230213	+	0.973140i	$0.573942\pi$
$810$	20.7128	0.727774
$811$	−27.1252	−0.952496	−0.476248	−	0.879311i	$-0.658003\pi$
$811$	−27.1252	−0.952496	−0.476248	+	0.879311i	$0.658003\pi$
$812$	27.6228	0.969370
$813$	5.95872	0.208982
$814$	−35.7827	−1.25418
$815$	0.136433	0.00477905
$816$	−1.16153	−0.0406617
$817$	0.464604	0.0162544
$818$	13.3226	0.465815
$819$	−6.15802	−0.215179
$820$	5.39183	0.188291
$821$	33.7355	1.17738	0.588688	−	0.808360i	$-0.299645\pi$
$821$	33.7355	1.17738	0.588688	+	0.808360i	$0.299645\pi$
$822$	−4.29820	−0.149917
$823$	37.8037	1.31775	0.658877	−	0.752251i	$-0.271032\pi$
$823$	37.8037	1.31775	0.658877	+	0.752251i	$0.271032\pi$
$824$	−18.3341	−0.638698
$825$	−2.47928	−0.0863175
$826$	12.5234	0.435745
$827$	−42.9560	−1.49373	−0.746864	−	0.664977i	$-0.768441\pi$
$827$	−42.9560	−1.49373	−0.746864	+	0.664977i	$0.768441\pi$
$828$	2.86091	0.0994236
$829$	−34.3874	−1.19432	−0.597162	−	0.802121i	$-0.703705\pi$
$829$	−34.3874	−1.19432	−0.597162	+	0.802121i	$0.703705\pi$
$830$	7.36193	0.255536
$831$	6.12855	0.212597
$832$	0.642654	0.0222800
$833$	−13.1372	−0.455176
$834$	5.66444	0.196144
$835$	−20.8507	−0.721567
$836$	0.831190	0.0287473
$837$	−18.4236	−0.636812
$838$	−11.9710	−0.413530
$839$	−28.8928	−0.997490	−0.498745	−	0.866749i	$-0.666206\pi$
$839$	−28.8928	−0.997490	−0.498745	+	0.866749i	$0.666206\pi$
$840$	3.33088	0.114926
$841$	39.0168	1.34541
$842$	−27.0823	−0.933317
$843$	2.80587	0.0966394
$844$	8.20266	0.282347
$845$	33.5642	1.15465
$846$	−0.423619	−0.0145643
$847$	−3.61606	−0.124249
$848$	−9.49126	−0.325931
$849$	10.6142	0.364279
$850$	6.57360	0.225473
$851$	11.3608	0.389444
$852$	−5.30641	−0.181795
$853$	−45.5351	−1.55909	−0.779546	−	0.626345i	$-0.784550\pi$
$853$	−45.5351	−1.55909	−0.779546	+	0.626345i	$0.784550\pi$
$854$	−17.4249	−0.596269
$855$	−2.01324	−0.0688514
$856$	−1.01800	−0.0347945
$857$	−22.7173	−0.776010	−0.388005	−	0.921657i	$-0.626836\pi$
$857$	−22.7173	−0.776010	−0.388005	+	0.921657i	$0.626836\pi$
$858$	0.754894	0.0257716
$859$	40.1664	1.37046	0.685230	−	0.728327i	$-0.259702\pi$
$859$	40.1664	1.37046	0.685230	+	0.728327i	$0.259702\pi$
$860$	4.69463	0.160086
$861$	−2.52572	−0.0860763
$862$	36.5228	1.24397
$863$	36.2600	1.23430	0.617152	−	0.786844i	$-0.288286\pi$
$863$	36.2600	1.23430	0.617152	+	0.786844i	$0.288286\pi$
$864$	2.18580	0.0743623
$865$	15.7764	0.536412
$866$	2.46789	0.0838624
$867$	−2.72250	−0.0924608
$868$	28.2308	0.958217
$869$	−18.2051	−0.617566
$870$	8.20177	0.278066
$871$	3.72828	0.126328
$872$	−7.29920	−0.247182
$873$	10.9462	0.370474
$874$	−0.263898	−0.00892649
$875$	25.8056	0.872388
$876$	−1.58803	−0.0536545
$877$	−11.5298	−0.389335	−0.194667	−	0.980869i	$-0.562363\pi$
$877$	−11.5298	−0.389335	−0.194667	+	0.980869i	$0.562363\pi$
$878$	−6.81768	−0.230086
$879$	5.85137	0.197362
$880$	8.39883	0.283124
$881$	19.3724	0.652673	0.326337	−	0.945254i	$-0.394186\pi$
$881$	19.3724	0.652673	0.326337	+	0.945254i	$0.394186\pi$
$882$	12.0676	0.406337
$883$	−47.8898	−1.61162	−0.805810	−	0.592174i	$-0.798270\pi$
$883$	−47.8898	−1.61162	−0.805810	+	0.592174i	$0.798270\pi$
$884$	−2.00153	−0.0673189
$885$	3.71845	0.124994
$886$	13.8361	0.464832
$887$	37.1370	1.24694	0.623470	−	0.781847i	$-0.285722\pi$
$887$	37.1370	1.24694	0.623470	+	0.781847i	$0.285722\pi$
$888$	4.23696	0.142183
$889$	−22.9867	−0.770949
$890$	33.9901	1.13935
$891$	−24.4652	−0.819614
$892$	5.14663	0.172322
$893$	0.0390758	0.00130762
$894$	−7.95576	−0.266081
$895$	−16.7565	−0.560107
$896$	−3.34934	−0.111894
$897$	−0.239674	−0.00800250
$898$	15.1134	0.504340
$899$	69.5140	2.31842
$900$	−6.03840	−0.201280
$901$	29.5604	0.984799
$902$	−6.36861	−0.212052
$903$	−2.19913	−0.0731825
$904$	18.4414	0.613351
$905$	−21.9710	−0.730342
$906$	−4.85646	−0.161345
$907$	19.3501	0.642510	0.321255	−	0.946993i	$-0.395895\pi$
$907$	19.3501	0.642510	0.321255	+	0.946993i	$0.395895\pi$
$908$	−24.7569	−0.821585
$909$	−46.9986	−1.55884
$910$	5.73973	0.190270
$911$	38.2539	1.26741	0.633704	−	0.773576i	$-0.281534\pi$
$911$	38.2539	1.26741	0.633704	+	0.773576i	$0.281534\pi$
$912$	−0.0984195	−0.00325899
$913$	−8.69563	−0.287783
$914$	27.9887	0.925783
$915$	−5.17382	−0.171041
$916$	25.1048	0.829486
$917$	3.34934	0.110605
$918$	−6.80763	−0.224685
$919$	24.1599	0.796962	0.398481	−	0.917177i	$-0.369538\pi$
$919$	24.1599	0.796962	0.398481	+	0.917177i	$0.369538\pi$
$920$	−2.66658	−0.0879146
$921$	9.44116	0.311097
$922$	−34.7688	−1.14505
$923$	−9.14394	−0.300976
$924$	−3.93431	−0.129429
$925$	−23.9788	−0.788417
$926$	1.10173	0.0362050
$927$	−52.4522	−1.72276
$928$	−8.24723	−0.270729
$929$	−54.5778	−1.79064	−0.895320	−	0.445424i	$-0.853053\pi$
$929$	−54.5778	−1.79064	−0.895320	+	0.445424i	$0.853053\pi$
$930$	8.38231	0.274867
$931$	−1.11315	−0.0364819
$932$	−7.49513	−0.245511
$933$	−8.70945	−0.285135
$934$	19.7907	0.647573
$935$	−26.1580	−0.855458
$936$	1.83858	0.0600957
$937$	−23.1848	−0.757415	−0.378708	−	0.925516i	$-0.623631\pi$
$937$	−23.1848	−0.757415	−0.378708	+	0.925516i	$0.623631\pi$
$938$	−19.4308	−0.634439
$939$	8.93475	0.291575
$940$	0.394844	0.0128784
$941$	−46.5073	−1.51610	−0.758048	−	0.652199i	$-0.773847\pi$
$941$	−46.5073	−1.51610	−0.758048	+	0.652199i	$0.773847\pi$
$942$	−7.12217	−0.232053
$943$	2.02200	0.0658454
$944$	−3.73906	−0.121696
$945$	19.5220	0.635051
$946$	−5.54512	−0.180287
$947$	40.1595	1.30501	0.652504	−	0.757786i	$-0.273719\pi$
$947$	40.1595	1.30501	0.652504	+	0.757786i	$0.273719\pi$
$948$	2.15563	0.0700116
$949$	−2.73647	−0.0888296
$950$	0.556998	0.0180714
$951$	6.83987	0.221798
$952$	10.4315	0.338086
$953$	53.9001	1.74600	0.872998	−	0.487724i	$-0.162173\pi$
$953$	53.9001	1.74600	0.872998	+	0.487724i	$0.162173\pi$
$954$	−27.1537	−0.879132
$955$	−23.5196	−0.761077
$956$	−18.7569	−0.606641
$957$	−9.68761	−0.313156
$958$	−23.6862	−0.765267
$959$	38.6012	1.24650
$960$	−0.994488	−0.0320970
$961$	40.0441	1.29175
$962$	7.30107	0.235396
$963$	−2.91241	−0.0938510
$964$	−21.4904	−0.692159
$965$	18.9569	0.610245
$966$	1.24912	0.0401898
$967$	42.3787	1.36281	0.681404	−	0.731908i	$-0.261370\pi$
$967$	42.3787	1.36281	0.681404	+	0.731908i	$0.261370\pi$
$968$	1.07963	0.0347007
$969$	0.306526	0.00984703
$970$	−10.2027	−0.327589
$971$	31.3681	1.00665	0.503326	−	0.864097i	$-0.332110\pi$
$971$	31.3681	1.00665	0.503326	+	0.864097i	$0.332110\pi$
$972$	9.45426	0.303246
$973$	−50.8712	−1.63085
$974$	21.7382	0.696537
$975$	0.505870	0.0162008
$976$	5.20249	0.166528
$977$	14.4098	0.461011	0.230505	−	0.973071i	$-0.425962\pi$
$977$	14.4098	0.461011	0.230505	+	0.973071i	$0.425962\pi$
$978$	0.0190814	0.000610157 0
$979$	−40.1478	−1.28313
$980$	−11.2479	−0.359300
$981$	−20.8824	−0.666723
$982$	−2.54218	−0.0811242
$983$	10.4402	0.332992	0.166496	−	0.986042i	$-0.446755\pi$
$983$	10.4402	0.332992	0.166496	+	0.986042i	$0.446755\pi$
$984$	0.754095	0.0240397
$985$	16.1631	0.515000
$986$	25.6859	0.818005
$987$	−0.184959	−0.00588731
$988$	−0.169595	−0.00539554
$989$	1.76054	0.0559820
$990$	24.0283	0.763670
$991$	30.2499	0.960920	0.480460	−	0.877017i	$-0.340470\pi$
$991$	30.2499	0.960920	0.480460	+	0.877017i	$0.340470\pi$
$992$	−8.42877	−0.267614
$993$	12.3676	0.392473
$994$	47.6558	1.51155
$995$	58.2751	1.84744
$996$	1.02963	0.0326251
$997$	−27.4843	−0.870438	−0.435219	−	0.900325i	$-0.643329\pi$
$997$	−27.4843	−0.870438	−0.435219	+	0.900325i	$0.643329\pi$
$998$	−34.6773	−1.09769
$999$	24.8324	0.785664

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.19	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.19	✓	36	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.372945 q^{3} +1.00000 q^{4} -2.66658 q^{5} -0.372945 q^{6} +3.34934 q^{7} -1.00000 q^{8} -2.86091 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.372945 q^{3} +1.00000 q^{4} -2.66658 q^{5} -0.372945 q^{6} +3.34934 q^{7} -1.00000 q^{8} -2.86091 q^{9} +2.66658 q^{10} -3.14966 q^{11} +0.372945 q^{12} +0.642654 q^{13} -3.34934 q^{14} -0.994488 q^{15} +1.00000 q^{16} -3.11448 q^{17} +2.86091 q^{18} -0.263898 q^{19} -2.66658 q^{20} +1.24912 q^{21} +3.14966 q^{22} -1.00000 q^{23} -0.372945 q^{24} +2.11066 q^{25} -0.642654 q^{26} -2.18580 q^{27} +3.34934 q^{28} +8.24723 q^{29} +0.994488 q^{30} +8.42877 q^{31} -1.00000 q^{32} -1.17465 q^{33} +3.11448 q^{34} -8.93129 q^{35} -2.86091 q^{36} -11.3608 q^{37} +0.263898 q^{38} +0.239674 q^{39} +2.66658 q^{40} -2.02200 q^{41} -1.24912 q^{42} -1.76054 q^{43} -3.14966 q^{44} +7.62885 q^{45} +1.00000 q^{46} -0.148071 q^{47} +0.372945 q^{48} +4.21809 q^{49} -2.11066 q^{50} -1.16153 q^{51} +0.642654 q^{52} -9.49126 q^{53} +2.18580 q^{54} +8.39883 q^{55} -3.34934 q^{56} -0.0984195 q^{57} -8.24723 q^{58} -3.73906 q^{59} -0.994488 q^{60} +5.20249 q^{61} -8.42877 q^{62} -9.58217 q^{63} +1.00000 q^{64} -1.71369 q^{65} +1.17465 q^{66} +5.80138 q^{67} -3.11448 q^{68} -0.372945 q^{69} +8.93129 q^{70} -14.2284 q^{71} +2.86091 q^{72} -4.25808 q^{73} +11.3608 q^{74} +0.787158 q^{75} -0.263898 q^{76} -10.5493 q^{77} -0.239674 q^{78} +5.78002 q^{79} -2.66658 q^{80} +7.76755 q^{81} +2.02200 q^{82} +2.76081 q^{83} +1.24912 q^{84} +8.30502 q^{85} +1.76054 q^{86} +3.07576 q^{87} +3.14966 q^{88} +12.7467 q^{89} -7.62885 q^{90} +2.15247 q^{91} -1.00000 q^{92} +3.14347 q^{93} +0.148071 q^{94} +0.703706 q^{95} -0.372945 q^{96} -3.82614 q^{97} -4.21809 q^{98} +9.01090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

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