LMFDB - Embedded newform 6022.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.50713 q^{3} +1.00000 q^{4} -3.56652 q^{5} -1.50713 q^{6} -0.922198 q^{7} +1.00000 q^{8} -0.728548 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.50713 q^{3} +1.00000 q^{4} -3.56652 q^{5} -1.50713 q^{6} -0.922198 q^{7} +1.00000 q^{8} -0.728548 q^{9} -3.56652 q^{10} +4.12114 q^{11} -1.50713 q^{12} -5.71487 q^{13} -0.922198 q^{14} +5.37522 q^{15} +1.00000 q^{16} +3.94025 q^{17} -0.728548 q^{18} -0.193378 q^{19} -3.56652 q^{20} +1.38988 q^{21} +4.12114 q^{22} +3.84922 q^{23} -1.50713 q^{24} +7.72006 q^{25} -5.71487 q^{26} +5.61942 q^{27} -0.922198 q^{28} -3.42455 q^{29} +5.37522 q^{30} +0.624515 q^{31} +1.00000 q^{32} -6.21111 q^{33} +3.94025 q^{34} +3.28904 q^{35} -0.728548 q^{36} +9.83162 q^{37} -0.193378 q^{38} +8.61307 q^{39} -3.56652 q^{40} -5.91104 q^{41} +1.38988 q^{42} +1.58391 q^{43} +4.12114 q^{44} +2.59838 q^{45} +3.84922 q^{46} -0.856937 q^{47} -1.50713 q^{48} -6.14955 q^{49} +7.72006 q^{50} -5.93848 q^{51} -5.71487 q^{52} +5.29708 q^{53} +5.61942 q^{54} -14.6981 q^{55} -0.922198 q^{56} +0.291446 q^{57} -3.42455 q^{58} +5.09500 q^{59} +5.37522 q^{60} +1.25284 q^{61} +0.624515 q^{62} +0.671865 q^{63} +1.00000 q^{64} +20.3822 q^{65} -6.21111 q^{66} -9.75785 q^{67} +3.94025 q^{68} -5.80129 q^{69} +3.28904 q^{70} +8.77902 q^{71} -0.728548 q^{72} -16.7004 q^{73} +9.83162 q^{74} -11.6352 q^{75} -0.193378 q^{76} -3.80051 q^{77} +8.61307 q^{78} +13.0459 q^{79} -3.56652 q^{80} -6.28358 q^{81} -5.91104 q^{82} +11.4673 q^{83} +1.38988 q^{84} -14.0530 q^{85} +1.58391 q^{86} +5.16126 q^{87} +4.12114 q^{88} -8.63122 q^{89} +2.59838 q^{90} +5.27024 q^{91} +3.84922 q^{92} -0.941227 q^{93} -0.856937 q^{94} +0.689685 q^{95} -1.50713 q^{96} -13.7782 q^{97} -6.14955 q^{98} -3.00245 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) $ 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * 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
$3$	−1.50713	−0.870144	−0.435072	−	0.900396i	$-0.643277\pi$
$3$	−1.50713	−0.870144	−0.435072	+	0.900396i	$0.643277\pi$
$4$	1.00000	0.500000
$5$	−3.56652	−1.59500	−0.797498	−	0.603322i	$-0.793844\pi$
$5$	−3.56652	−1.59500	−0.797498	+	0.603322i	$0.793844\pi$
$6$	−1.50713	−0.615285
$7$	−0.922198	−0.348558	−0.174279	−	0.984696i	$-0.555759\pi$
$7$	−0.922198	−0.348558	−0.174279	+	0.984696i	$0.555759\pi$
$8$	1.00000	0.353553
$9$	−0.728548	−0.242849
$10$	−3.56652	−1.12783
$11$	4.12114	1.24257	0.621286	−	0.783584i	$-0.286611\pi$
$11$	4.12114	1.24257	0.621286	+	0.783584i	$0.286611\pi$
$12$	−1.50713	−0.435072
$13$	−5.71487	−1.58502	−0.792510	−	0.609859i	$-0.791226\pi$
$13$	−5.71487	−1.58502	−0.792510	+	0.609859i	$0.791226\pi$
$14$	−0.922198	−0.246468
$15$	5.37522	1.38788
$16$	1.00000	0.250000
$17$	3.94025	0.955651	0.477825	−	0.878455i	$-0.341425\pi$
$17$	3.94025	0.955651	0.477825	+	0.878455i	$0.341425\pi$
$18$	−0.728548	−0.171720
$19$	−0.193378	−0.0443639	−0.0221819	−	0.999754i	$-0.507061\pi$
$19$	−0.193378	−0.0443639	−0.0221819	+	0.999754i	$0.507061\pi$
$20$	−3.56652	−0.797498
$21$	1.38988	0.303296
$22$	4.12114	0.878630
$23$	3.84922	0.802618	0.401309	−	0.915943i	$-0.368555\pi$
$23$	3.84922	0.802618	0.401309	+	0.915943i	$0.368555\pi$
$24$	−1.50713	−0.307642
$25$	7.72006	1.54401
$26$	−5.71487	−1.12078
$27$	5.61942	1.08146
$28$	−0.922198	−0.174279
$29$	−3.42455	−0.635924	−0.317962	−	0.948104i	$-0.602998\pi$
$29$	−3.42455	−0.635924	−0.317962	+	0.948104i	$0.602998\pi$
$30$	5.37522	0.981377
$31$	0.624515	0.112166	0.0560831	−	0.998426i	$-0.482139\pi$
$31$	0.624515	0.112166	0.0560831	+	0.998426i	$0.482139\pi$
$32$	1.00000	0.176777
$33$	−6.21111	−1.08122
$34$	3.94025	0.675747
$35$	3.28904	0.555949
$36$	−0.728548	−0.121425
$37$	9.83162	1.61631	0.808154	−	0.588971i	$-0.200467\pi$
$37$	9.83162	1.61631	0.808154	+	0.588971i	$0.200467\pi$
$38$	−0.193378	−0.0313700
$39$	8.61307	1.37920
$40$	−3.56652	−0.563916
$41$	−5.91104	−0.923150	−0.461575	−	0.887101i	$-0.652715\pi$
$41$	−5.91104	−0.923150	−0.461575	+	0.887101i	$0.652715\pi$
$42$	1.38988	0.214463
$43$	1.58391	0.241545	0.120772	−	0.992680i	$-0.461463\pi$
$43$	1.58391	0.241545	0.120772	+	0.992680i	$0.461463\pi$
$44$	4.12114	0.621286
$45$	2.59838	0.387344
$46$	3.84922	0.567536
$47$	−0.856937	−0.124997	−0.0624985	−	0.998045i	$-0.519907\pi$
$47$	−0.856937	−0.124997	−0.0624985	+	0.998045i	$0.519907\pi$
$48$	−1.50713	−0.217536
$49$	−6.14955	−0.878507
$50$	7.72006	1.09178
$51$	−5.93848	−0.831554
$52$	−5.71487	−0.792510
$53$	5.29708	0.727610	0.363805	−	0.931475i	$-0.381477\pi$
$53$	5.29708	0.727610	0.363805	+	0.931475i	$0.381477\pi$
$54$	5.61942	0.764706
$55$	−14.6981	−1.98190
$56$	−0.922198	−0.123234
$57$	0.291446	0.0386030
$58$	−3.42455	−0.449666
$59$	5.09500	0.663312	0.331656	−	0.943400i	$-0.392393\pi$
$59$	5.09500	0.663312	0.331656	+	0.943400i	$0.392393\pi$
$60$	5.37522	0.693938
$61$	1.25284	0.160410	0.0802048	−	0.996778i	$-0.474443\pi$
$61$	1.25284	0.160410	0.0802048	+	0.996778i	$0.474443\pi$
$62$	0.624515	0.0793134
$63$	0.671865	0.0846471
$64$	1.00000	0.125000
$65$	20.3822	2.52810
$66$	−6.21111	−0.764535
$67$	−9.75785	−1.19211	−0.596056	−	0.802943i	$-0.703266\pi$
$67$	−9.75785	−1.19211	−0.596056	+	0.802943i	$0.703266\pi$
$68$	3.94025	0.477825
$69$	−5.80129	−0.698393
$70$	3.28904	0.393115
$71$	8.77902	1.04188	0.520939	−	0.853594i	$-0.325582\pi$
$71$	8.77902	1.04188	0.520939	+	0.853594i	$0.325582\pi$
$72$	−0.728548	−0.0858602
$73$	−16.7004	−1.95463	−0.977316	−	0.211788i	$-0.932071\pi$
$73$	−16.7004	−1.95463	−0.977316	+	0.211788i	$0.932071\pi$
$74$	9.83162	1.14290
$75$	−11.6352	−1.34351
$76$	−0.193378	−0.0221819
$77$	−3.80051	−0.433108
$78$	8.61307	0.975238
$79$	13.0459	1.46777	0.733887	−	0.679271i	$-0.237704\pi$
$79$	13.0459	1.46777	0.733887	+	0.679271i	$0.237704\pi$
$80$	−3.56652	−0.398749
$81$	−6.28358	−0.698175
$82$	−5.91104	−0.652766
$83$	11.4673	1.25870	0.629349	−	0.777123i	$-0.283322\pi$
$83$	11.4673	1.25870	0.629349	+	0.777123i	$0.283322\pi$
$84$	1.38988	0.151648
$85$	−14.0530	−1.52426
$86$	1.58391	0.170798
$87$	5.16126	0.553345
$88$	4.12114	0.439315
$89$	−8.63122	−0.914907	−0.457454	−	0.889233i	$-0.651238\pi$
$89$	−8.63122	−0.914907	−0.457454	+	0.889233i	$0.651238\pi$
$90$	2.59838	0.273893
$91$	5.27024	0.552471
$92$	3.84922	0.401309
$93$	−0.941227	−0.0976007
$94$	−0.856937	−0.0883863
$95$	0.689685	0.0707602
$96$	−1.50713	−0.153821
$97$	−13.7782	−1.39897	−0.699484	−	0.714648i	$-0.746587\pi$
$97$	−13.7782	−1.39897	−0.699484	+	0.714648i	$0.746587\pi$
$98$	−6.14955	−0.621198
$99$	−3.00245	−0.301757
$100$	7.72006	0.772006
$101$	4.84226	0.481823	0.240911	−	0.970547i	$-0.422554\pi$
$101$	4.84226	0.481823	0.240911	+	0.970547i	$0.422554\pi$
$102$	−5.93848	−0.587997
$103$	9.07412	0.894100	0.447050	−	0.894509i	$-0.352475\pi$
$103$	9.07412	0.894100	0.447050	+	0.894509i	$0.352475\pi$
$104$	−5.71487	−0.560389
$105$	−4.95702	−0.483756
$106$	5.29708	0.514498
$107$	−4.17743	−0.403848	−0.201924	−	0.979401i	$-0.564719\pi$
$107$	−4.17743	−0.403848	−0.201924	+	0.979401i	$0.564719\pi$
$108$	5.61942	0.540729
$109$	−14.9544	−1.43237	−0.716187	−	0.697909i	$-0.754114\pi$
$109$	−14.9544	−1.43237	−0.716187	+	0.697909i	$0.754114\pi$
$110$	−14.6981	−1.40141
$111$	−14.8176	−1.40642
$112$	−0.922198	−0.0871395
$113$	−18.6006	−1.74980	−0.874898	−	0.484308i	$-0.839071\pi$
$113$	−18.6006	−1.74980	−0.874898	+	0.484308i	$0.839071\pi$
$114$	0.291446	0.0272964
$115$	−13.7283	−1.28017
$116$	−3.42455	−0.317962
$117$	4.16355	0.384921
$118$	5.09500	0.469033
$119$	−3.63369	−0.333100
$120$	5.37522	0.490688
$121$	5.98381	0.543983
$122$	1.25284	0.113427
$123$	8.90874	0.803274
$124$	0.624515	0.0560831
$125$	−9.70116	−0.867698
$126$	0.671865	0.0598545
$127$	−2.63772	−0.234060	−0.117030	−	0.993128i	$-0.537337\pi$
$127$	−2.63772	−0.234060	−0.117030	+	0.993128i	$0.537337\pi$
$128$	1.00000	0.0883883
$129$	−2.38717	−0.210179
$130$	20.3822	1.78764
$131$	10.9896	0.960165	0.480083	−	0.877223i	$-0.340607\pi$
$131$	10.9896	0.960165	0.480083	+	0.877223i	$0.340607\pi$
$132$	−6.21111	−0.540608
$133$	0.178333	0.0154634
$134$	−9.75785	−0.842950
$135$	−20.0418	−1.72492
$136$	3.94025	0.337873
$137$	6.45447	0.551442	0.275721	−	0.961238i	$-0.411083\pi$
$137$	6.45447	0.551442	0.275721	+	0.961238i	$0.411083\pi$
$138$	−5.80129	−0.493839
$139$	−20.3688	−1.72766	−0.863829	−	0.503786i	$-0.831940\pi$
$139$	−20.3688	−1.72766	−0.863829	+	0.503786i	$0.831940\pi$
$140$	3.28904	0.277974
$141$	1.29152	0.108765
$142$	8.77902	0.736719
$143$	−23.5518	−1.96950
$144$	−0.728548	−0.0607123
$145$	12.2137	1.01430
$146$	−16.7004	−1.38213
$147$	9.26820	0.764428
$148$	9.83162	0.808154
$149$	−13.5723	−1.11189	−0.555943	−	0.831220i	$-0.687643\pi$
$149$	−13.5723	−1.11189	−0.555943	+	0.831220i	$0.687643\pi$
$150$	−11.6352	−0.950007
$151$	5.42148	0.441194	0.220597	−	0.975365i	$-0.429199\pi$
$151$	5.42148	0.441194	0.220597	+	0.975365i	$0.429199\pi$
$152$	−0.193378	−0.0156850
$153$	−2.87066	−0.232079
$154$	−3.80051	−0.306254
$155$	−2.22734	−0.178905
$156$	8.61307	0.689598
$157$	−3.92605	−0.313333	−0.156666	−	0.987652i	$-0.550075\pi$
$157$	−3.92605	−0.313333	−0.156666	+	0.987652i	$0.550075\pi$
$158$	13.0459	1.03787
$159$	−7.98341	−0.633126
$160$	−3.56652	−0.281958
$161$	−3.54974	−0.279759
$162$	−6.28358	−0.493684
$163$	−4.78360	−0.374680	−0.187340	−	0.982295i	$-0.559987\pi$
$163$	−4.78360	−0.374680	−0.187340	+	0.982295i	$0.559987\pi$
$164$	−5.91104	−0.461575
$165$	22.1521	1.72454
$166$	11.4673	0.890033
$167$	−5.98614	−0.463222	−0.231611	−	0.972809i	$-0.574400\pi$
$167$	−5.98614	−0.463222	−0.231611	+	0.972809i	$0.574400\pi$
$168$	1.38988	0.107231
$169$	19.6597	1.51229
$170$	−14.0530	−1.07781
$171$	0.140885	0.0107737
$172$	1.58391	0.120772
$173$	−12.5910	−0.957277	−0.478639	−	0.878012i	$-0.658870\pi$
$173$	−12.5910	−0.957277	−0.478639	+	0.878012i	$0.658870\pi$
$174$	5.16126	0.391274
$175$	−7.11943	−0.538178
$176$	4.12114	0.310643
$177$	−7.67885	−0.577177
$178$	−8.63122	−0.646937
$179$	−8.91075	−0.666021	−0.333010	−	0.942923i	$-0.608064\pi$
$179$	−8.91075	−0.666021	−0.333010	+	0.942923i	$0.608064\pi$
$180$	2.59838	0.193672
$181$	4.99765	0.371472	0.185736	−	0.982600i	$-0.440533\pi$
$181$	4.99765	0.371472	0.185736	+	0.982600i	$0.440533\pi$
$182$	5.27024	0.390656
$183$	−1.88820	−0.139579
$184$	3.84922	0.283768
$185$	−35.0647	−2.57801
$186$	−0.941227	−0.0690141
$187$	16.2383	1.18746
$188$	−0.856937	−0.0624985
$189$	−5.18222	−0.376951
$190$	0.689685	0.0500350
$191$	15.6369	1.13145	0.565725	−	0.824594i	$-0.308596\pi$
$191$	15.6369	1.13145	0.565725	+	0.824594i	$0.308596\pi$
$192$	−1.50713	−0.108768
$193$	10.1426	0.730078	0.365039	−	0.930992i	$-0.381056\pi$
$193$	10.1426	0.730078	0.365039	+	0.930992i	$0.381056\pi$
$194$	−13.7782	−0.989220
$195$	−30.7187	−2.19981
$196$	−6.14955	−0.439254
$197$	−12.8716	−0.917061	−0.458530	−	0.888679i	$-0.651624\pi$
$197$	−12.8716	−0.917061	−0.458530	+	0.888679i	$0.651624\pi$
$198$	−3.00245	−0.213375
$199$	−21.5502	−1.52765	−0.763825	−	0.645423i	$-0.776681\pi$
$199$	−21.5502	−1.52765	−0.763825	+	0.645423i	$0.776681\pi$
$200$	7.72006	0.545891
$201$	14.7064	1.03731
$202$	4.84226	0.340700
$203$	3.15812	0.221656
$204$	−5.93848	−0.415777
$205$	21.0819	1.47242
$206$	9.07412	0.632224
$207$	−2.80434	−0.194915
$208$	−5.71487	−0.396255
$209$	−0.796937	−0.0551253
$210$	−4.95702	−0.342067
$211$	20.1801	1.38926	0.694629	−	0.719368i	$-0.255569\pi$
$211$	20.1801	1.38926	0.694629	+	0.719368i	$0.255569\pi$
$212$	5.29708	0.363805
$213$	−13.2312	−0.906584
$214$	−4.17743	−0.285563
$215$	−5.64906	−0.385263
$216$	5.61942	0.382353
$217$	−0.575926	−0.0390964
$218$	−14.9544	−1.01284
$219$	25.1697	1.70081
$220$	−14.6981	−0.990948
$221$	−22.5180	−1.51472
$222$	−14.8176	−0.994490
$223$	1.73281	0.116038	0.0580188	−	0.998315i	$-0.481522\pi$
$223$	1.73281	0.116038	0.0580188	+	0.998315i	$0.481522\pi$
$224$	−0.922198	−0.0616170
$225$	−5.62443	−0.374962
$226$	−18.6006	−1.23729
$227$	24.4295	1.62144	0.810720	−	0.585434i	$-0.199076\pi$
$227$	24.4295	1.62144	0.810720	+	0.585434i	$0.199076\pi$
$228$	0.291446	0.0193015
$229$	−17.3783	−1.14839	−0.574194	−	0.818719i	$-0.694685\pi$
$229$	−17.3783	−1.14839	−0.574194	+	0.818719i	$0.694685\pi$
$230$	−13.7283	−0.905218
$231$	5.72788	0.376867
$232$	−3.42455	−0.224833
$233$	−15.0811	−0.987994	−0.493997	−	0.869464i	$-0.664465\pi$
$233$	−15.0811	−0.987994	−0.493997	+	0.869464i	$0.664465\pi$
$234$	4.16355	0.272180
$235$	3.05628	0.199370
$236$	5.09500	0.331656
$237$	−19.6619	−1.27718
$238$	−3.63369	−0.235537
$239$	−15.8363	−1.02437	−0.512184	−	0.858876i	$-0.671163\pi$
$239$	−15.8363	−1.02437	−0.512184	+	0.858876i	$0.671163\pi$
$240$	5.37522	0.346969
$241$	−10.4206	−0.671249	−0.335624	−	0.941996i	$-0.608947\pi$
$241$	−10.4206	−0.671249	−0.335624	+	0.941996i	$0.608947\pi$
$242$	5.98381	0.384654
$243$	−7.38807	−0.473945
$244$	1.25284	0.0802048
$245$	21.9325	1.40122
$246$	8.90874	0.568000
$247$	1.10513	0.0703176
$248$	0.624515	0.0396567
$249$	−17.2827	−1.09525
$250$	−9.70116	−0.613555
$251$	1.54709	0.0976516	0.0488258	−	0.998807i	$-0.484452\pi$
$251$	1.54709	0.0976516	0.0488258	+	0.998807i	$0.484452\pi$
$252$	0.671865	0.0423235
$253$	15.8632	0.997310
$254$	−2.63772	−0.165505
$255$	21.1797	1.32632
$256$	1.00000	0.0625000
$257$	−25.0626	−1.56336	−0.781680	−	0.623680i	$-0.785637\pi$
$257$	−25.0626	−1.56336	−0.781680	+	0.623680i	$0.785637\pi$
$258$	−2.38717	−0.148619
$259$	−9.06671	−0.563378
$260$	20.3822	1.26405
$261$	2.49495	0.154434
$262$	10.9896	0.678940
$263$	−10.2043	−0.629223	−0.314611	−	0.949221i	$-0.601874\pi$
$263$	−10.2043	−0.629223	−0.314611	+	0.949221i	$0.601874\pi$
$264$	−6.21111	−0.382268
$265$	−18.8921	−1.16054
$266$	0.178333	0.0109343
$267$	13.0084	0.796101
$268$	−9.75785	−0.596056
$269$	6.35927	0.387731	0.193866	−	0.981028i	$-0.437897\pi$
$269$	6.35927	0.387731	0.193866	+	0.981028i	$0.437897\pi$
$270$	−20.0418	−1.21970
$271$	−4.97934	−0.302474	−0.151237	−	0.988498i	$-0.548326\pi$
$271$	−4.97934	−0.302474	−0.151237	+	0.988498i	$0.548326\pi$
$272$	3.94025	0.238913
$273$	−7.94296	−0.480730
$274$	6.45447	0.389929
$275$	31.8155	1.91855
$276$	−5.80129	−0.349197
$277$	1.13423	0.0681495	0.0340747	−	0.999419i	$-0.489152\pi$
$277$	1.13423	0.0681495	0.0340747	+	0.999419i	$0.489152\pi$
$278$	−20.3688	−1.22164
$279$	−0.454989	−0.0272395
$280$	3.28904	0.196558
$281$	−1.31710	−0.0785714	−0.0392857	−	0.999228i	$-0.512508\pi$
$281$	−1.31710	−0.0785714	−0.0392857	+	0.999228i	$0.512508\pi$
$282$	1.29152	0.0769088
$283$	21.4304	1.27391	0.636954	−	0.770902i	$-0.280194\pi$
$283$	21.4304	1.27391	0.636954	+	0.770902i	$0.280194\pi$
$284$	8.77902	0.520939
$285$	−1.03945	−0.0615716
$286$	−23.5518	−1.39265
$287$	5.45116	0.321772
$288$	−0.728548	−0.0429301
$289$	−1.47445	−0.0867321
$290$	12.2137	0.717215
$291$	20.7656	1.21730
$292$	−16.7004	−0.977316
$293$	12.0245	0.702480	0.351240	−	0.936286i	$-0.385760\pi$
$293$	12.0245	0.702480	0.351240	+	0.936286i	$0.385760\pi$
$294$	9.26820	0.540532
$295$	−18.1714	−1.05798
$296$	9.83162	0.571452
$297$	23.1584	1.34379
$298$	−13.5723	−0.786222
$299$	−21.9978	−1.27216
$300$	−11.6352	−0.671757
$301$	−1.46068	−0.0841923
$302$	5.42148	0.311971
$303$	−7.29793	−0.419255
$304$	−0.193378	−0.0110910
$305$	−4.46827	−0.255853
$306$	−2.87066	−0.164105
$307$	−1.33546	−0.0762188	−0.0381094	−	0.999274i	$-0.512134\pi$
$307$	−1.33546	−0.0762188	−0.0381094	+	0.999274i	$0.512134\pi$
$308$	−3.80051	−0.216554
$309$	−13.6759	−0.777995
$310$	−2.22734	−0.126505
$311$	1.92034	0.108892	0.0544461	−	0.998517i	$-0.482661\pi$
$311$	1.92034	0.108892	0.0544461	+	0.998517i	$0.482661\pi$
$312$	8.61307	0.487619
$313$	5.11449	0.289088	0.144544	−	0.989498i	$-0.453828\pi$
$313$	5.11449	0.289088	0.144544	+	0.989498i	$0.453828\pi$
$314$	−3.92605	−0.221560
$315$	−2.39622	−0.135012
$316$	13.0459	0.733887
$317$	−13.6829	−0.768510	−0.384255	−	0.923227i	$-0.625542\pi$
$317$	−13.6829	−0.768510	−0.384255	+	0.923227i	$0.625542\pi$
$318$	−7.98341	−0.447688
$319$	−14.1131	−0.790180
$320$	−3.56652	−0.199375
$321$	6.29595	0.351406
$322$	−3.54974	−0.197819
$323$	−0.761956	−0.0423964
$324$	−6.28358	−0.349088
$325$	−44.1191	−2.44729
$326$	−4.78360	−0.264939
$327$	22.5383	1.24637
$328$	−5.91104	−0.326383
$329$	0.790265	0.0435687
$330$	22.1521	1.21943
$331$	10.2940	0.565812	0.282906	−	0.959148i	$-0.408702\pi$
$331$	10.2940	0.565812	0.282906	+	0.959148i	$0.408702\pi$
$332$	11.4673	0.629349
$333$	−7.16281	−0.392519
$334$	−5.98614	−0.327547
$335$	34.8016	1.90141
$336$	1.38988	0.0758240
$337$	−12.5670	−0.684567	−0.342284	−	0.939597i	$-0.611200\pi$
$337$	−12.5670	−0.684567	−0.342284	+	0.939597i	$0.611200\pi$
$338$	19.6597	1.06935
$339$	28.0336	1.52257
$340$	−14.0530	−0.762129
$341$	2.57371	0.139374
$342$	0.140885	0.00761818
$343$	12.1265	0.654769
$344$	1.58391	0.0853989
$345$	20.6904	1.11393
$346$	−12.5910	−0.676897
$347$	−22.3001	−1.19713	−0.598566	−	0.801073i	$-0.704263\pi$
$347$	−22.3001	−1.19713	−0.598566	+	0.801073i	$0.704263\pi$
$348$	5.16126	0.276673
$349$	18.8017	1.00643	0.503215	−	0.864161i	$-0.332150\pi$
$349$	18.8017	1.00643	0.503215	+	0.864161i	$0.332150\pi$
$350$	−7.11943	−0.380549
$351$	−32.1142	−1.71413
$352$	4.12114	0.219658
$353$	−30.9842	−1.64912	−0.824562	−	0.565771i	$-0.808578\pi$
$353$	−30.9842	−1.64912	−0.824562	+	0.565771i	$0.808578\pi$
$354$	−7.67885	−0.408126
$355$	−31.3105	−1.66179
$356$	−8.63122	−0.457454
$357$	5.47646	0.289845
$358$	−8.91075	−0.470948
$359$	26.2829	1.38716	0.693580	−	0.720380i	$-0.256032\pi$
$359$	26.2829	1.38716	0.693580	+	0.720380i	$0.256032\pi$
$360$	2.59838	0.136947
$361$	−18.9626	−0.998032
$362$	4.99765	0.262671
$363$	−9.01841	−0.473344
$364$	5.27024	0.276236
$365$	59.5622	3.11763
$366$	−1.88820	−0.0986975
$367$	−0.534827	−0.0279178	−0.0139589	−	0.999903i	$-0.504443\pi$
$367$	−0.534827	−0.0279178	−0.0139589	+	0.999903i	$0.504443\pi$
$368$	3.84922	0.200654
$369$	4.30648	0.224186
$370$	−35.0647	−1.82293
$371$	−4.88496	−0.253614
$372$	−0.941227	−0.0488003
$373$	13.5494	0.701560	0.350780	−	0.936458i	$-0.385916\pi$
$373$	13.5494	0.701560	0.350780	+	0.936458i	$0.385916\pi$
$374$	16.2383	0.839664
$375$	14.6209	0.755022
$376$	−0.856937	−0.0441931
$377$	19.5709	1.00795
$378$	−5.18222	−0.266545
$379$	−13.6924	−0.703332	−0.351666	−	0.936126i	$-0.614385\pi$
$379$	−13.6924	−0.703332	−0.351666	+	0.936126i	$0.614385\pi$
$380$	0.689685	0.0353801
$381$	3.97540	0.203666
$382$	15.6369	0.800056
$383$	−14.0356	−0.717183	−0.358592	−	0.933495i	$-0.616743\pi$
$383$	−14.0356	−0.717183	−0.358592	+	0.933495i	$0.616743\pi$
$384$	−1.50713	−0.0769106
$385$	13.5546	0.690806
$386$	10.1426	0.516243
$387$	−1.15396	−0.0586589
$388$	−13.7782	−0.699484
$389$	−13.1625	−0.667363	−0.333682	−	0.942686i	$-0.608291\pi$
$389$	−13.1625	−0.667363	−0.333682	+	0.942686i	$0.608291\pi$
$390$	−30.7187	−1.55550
$391$	15.1669	0.767022
$392$	−6.14955	−0.310599
$393$	−16.5628	−0.835482
$394$	−12.8716	−0.648460
$395$	−46.5283	−2.34109
$396$	−3.00245	−0.150879
$397$	−5.00742	−0.251315	−0.125658	−	0.992074i	$-0.540104\pi$
$397$	−5.00742	−0.251315	−0.125658	+	0.992074i	$0.540104\pi$
$398$	−21.5502	−1.08021
$399$	−0.268771	−0.0134554
$400$	7.72006	0.386003
$401$	9.76329	0.487555	0.243778	−	0.969831i	$-0.421613\pi$
$401$	9.76329	0.487555	0.243778	+	0.969831i	$0.421613\pi$
$402$	14.7064	0.733488
$403$	−3.56902	−0.177785
$404$	4.84226	0.240911
$405$	22.4105	1.11359
$406$	3.15812	0.156735
$407$	40.5175	2.00838
$408$	−5.93848	−0.293999
$409$	−13.1775	−0.651584	−0.325792	−	0.945441i	$-0.605631\pi$
$409$	−13.1775	−0.651584	−0.325792	+	0.945441i	$0.605631\pi$
$410$	21.0819	1.04116
$411$	−9.72775	−0.479834
$412$	9.07412	0.447050
$413$	−4.69860	−0.231203
$414$	−2.80434	−0.137826
$415$	−40.8983	−2.00762
$416$	−5.71487	−0.280194
$417$	30.6985	1.50331
$418$	−0.796937	−0.0389795
$419$	−7.24685	−0.354032	−0.177016	−	0.984208i	$-0.556644\pi$
$419$	−7.24685	−0.354032	−0.177016	+	0.984208i	$0.556644\pi$
$420$	−4.95702	−0.241878
$421$	−4.82758	−0.235282	−0.117641	−	0.993056i	$-0.537533\pi$
$421$	−4.82758	−0.235282	−0.117641	+	0.993056i	$0.537533\pi$
$422$	20.1801	0.982354
$423$	0.624319	0.0303554
$424$	5.29708	0.257249
$425$	30.4190	1.47554
$426$	−13.2312	−0.641052
$427$	−1.15537	−0.0559120
$428$	−4.17743	−0.201924
$429$	35.4957	1.71375
$430$	−5.64906	−0.272422
$431$	6.02693	0.290307	0.145154	−	0.989409i	$-0.453632\pi$
$431$	6.02693	0.290307	0.145154	+	0.989409i	$0.453632\pi$
$432$	5.61942	0.270364
$433$	−8.64718	−0.415557	−0.207779	−	0.978176i	$-0.566623\pi$
$433$	−8.64718	−0.415557	−0.207779	+	0.978176i	$0.566623\pi$
$434$	−0.575926	−0.0276453
$435$	−18.4077	−0.882583
$436$	−14.9544	−0.716187
$437$	−0.744353	−0.0356072
$438$	25.1697	1.20266
$439$	16.1851	0.772472	0.386236	−	0.922400i	$-0.373775\pi$
$439$	16.1851	0.772472	0.386236	+	0.922400i	$0.373775\pi$
$440$	−14.6981	−0.700706
$441$	4.48024	0.213345
$442$	−22.5180	−1.07107
$443$	3.80804	0.180926	0.0904628	−	0.995900i	$-0.471165\pi$
$443$	3.80804	0.180926	0.0904628	+	0.995900i	$0.471165\pi$
$444$	−14.8176	−0.703211
$445$	30.7834	1.45927
$446$	1.73281	0.0820510
$447$	20.4553	0.967501
$448$	−0.922198	−0.0435698
$449$	3.81082	0.179844	0.0899218	−	0.995949i	$-0.471338\pi$
$449$	3.81082	0.179844	0.0899218	+	0.995949i	$0.471338\pi$
$450$	−5.62443	−0.265138
$451$	−24.3603	−1.14708
$452$	−18.6006	−0.874898
$453$	−8.17090	−0.383902
$454$	24.4295	1.14653
$455$	−18.7964	−0.881190
$456$	0.291446	0.0136482
$457$	14.2825	0.668108	0.334054	−	0.942554i	$-0.391583\pi$
$457$	14.2825	0.668108	0.334054	+	0.942554i	$0.391583\pi$
$458$	−17.3783	−0.812033
$459$	22.1419	1.03350
$460$	−13.7283	−0.640086
$461$	3.88374	0.180884	0.0904419	−	0.995902i	$-0.471172\pi$
$461$	3.88374	0.180884	0.0904419	+	0.995902i	$0.471172\pi$
$462$	5.72788	0.266485
$463$	−29.7470	−1.38246	−0.691230	−	0.722635i	$-0.742931\pi$
$463$	−29.7470	−1.38246	−0.691230	+	0.722635i	$0.742931\pi$
$464$	−3.42455	−0.158981
$465$	3.35690	0.155673
$466$	−15.0811	−0.698617
$467$	−31.3336	−1.44994	−0.724972	−	0.688778i	$-0.758147\pi$
$467$	−31.3336	−1.44994	−0.724972	+	0.688778i	$0.758147\pi$
$468$	4.16355	0.192460
$469$	8.99868	0.415520
$470$	3.05628	0.140976
$471$	5.91708	0.272645
$472$	5.09500	0.234516
$473$	6.52753	0.300136
$474$	−19.6619	−0.903100
$475$	−1.49289	−0.0684984
$476$	−3.63369	−0.166550
$477$	−3.85918	−0.176700
$478$	−15.8363	−0.724338
$479$	−30.2103	−1.38034	−0.690172	−	0.723646i	$-0.742465\pi$
$479$	−30.2103	−1.38034	−0.690172	+	0.723646i	$0.742465\pi$
$480$	5.37522	0.245344
$481$	−56.1864	−2.56188
$482$	−10.4206	−0.474645
$483$	5.34994	0.243431
$484$	5.98381	0.271991
$485$	49.1403	2.23135
$486$	−7.38807	−0.335130
$487$	0.369644	0.0167502	0.00837509	−	0.999965i	$-0.497334\pi$
$487$	0.369644	0.0167502	0.00837509	+	0.999965i	$0.497334\pi$
$488$	1.25284	0.0567133
$489$	7.20952	0.326026
$490$	21.9325	0.990809
$491$	32.9093	1.48518	0.742588	−	0.669749i	$-0.233598\pi$
$491$	32.9093	1.48518	0.742588	+	0.669749i	$0.233598\pi$
$492$	8.90874	0.401637
$493$	−13.4936	−0.607721
$494$	1.10513	0.0497221
$495$	10.7083	0.481302
$496$	0.624515	0.0280415
$497$	−8.09600	−0.363155
$498$	−17.2827	−0.774457
$499$	−13.9236	−0.623306	−0.311653	−	0.950196i	$-0.600883\pi$
$499$	−13.9236	−0.623306	−0.311653	+	0.950196i	$0.600883\pi$
$500$	−9.70116	−0.433849
$501$	9.02192	0.403070
$502$	1.54709	0.0690501
$503$	−31.5770	−1.40795	−0.703974	−	0.710226i	$-0.748593\pi$
$503$	−31.5770	−1.40795	−0.703974	+	0.710226i	$0.748593\pi$
$504$	0.671865	0.0299273
$505$	−17.2700	−0.768505
$506$	15.8632	0.705204
$507$	−29.6298	−1.31591
$508$	−2.63772	−0.117030
$509$	23.9453	1.06136	0.530679	−	0.847573i	$-0.321937\pi$
$509$	23.9453	1.06136	0.530679	+	0.847573i	$0.321937\pi$
$510$	21.1797	0.937853
$511$	15.4011	0.681303
$512$	1.00000	0.0441942
$513$	−1.08667	−0.0479777
$514$	−25.0626	−1.10546
$515$	−32.3630	−1.42609
$516$	−2.38717	−0.105089
$517$	−3.53156	−0.155318
$518$	−9.06671	−0.398368
$519$	18.9763	0.832969
$520$	20.3822	0.893818
$521$	−2.01680	−0.0883578	−0.0441789	−	0.999024i	$-0.514067\pi$
$521$	−2.01680	−0.0883578	−0.0441789	+	0.999024i	$0.514067\pi$
$522$	2.49495	0.109201
$523$	−21.6320	−0.945902	−0.472951	−	0.881089i	$-0.656811\pi$
$523$	−21.6320	−0.945902	−0.472951	+	0.881089i	$0.656811\pi$
$524$	10.9896	0.480083
$525$	10.7299	0.468293
$526$	−10.2043	−0.444928
$527$	2.46074	0.107192
$528$	−6.21111	−0.270304
$529$	−8.18351	−0.355805
$530$	−18.8921	−0.820622
$531$	−3.71195	−0.161085
$532$	0.178333	0.00773170
$533$	33.7808	1.46321
$534$	13.0084	0.562929
$535$	14.8989	0.644135
$536$	−9.75785	−0.421475
$537$	13.4297	0.579534
$538$	6.35927	0.274167
$539$	−25.3432	−1.09161
$540$	−20.0418	−0.862461
$541$	10.8130	0.464888	0.232444	−	0.972610i	$-0.425328\pi$
$541$	10.8130	0.464888	0.232444	+	0.972610i	$0.425328\pi$
$542$	−4.97934	−0.213881
$543$	−7.53213	−0.323235
$544$	3.94025	0.168937
$545$	53.3352	2.28463
$546$	−7.94296	−0.339927
$547$	13.8141	0.590647	0.295323	−	0.955397i	$-0.404573\pi$
$547$	13.8141	0.590647	0.295323	+	0.955397i	$0.404573\pi$
$548$	6.45447	0.275721
$549$	−0.912752	−0.0389553
$550$	31.8155	1.35662
$551$	0.662232	0.0282120
$552$	−5.80129	−0.246919
$553$	−12.0309	−0.511605
$554$	1.13423	0.0481889
$555$	52.8472	2.24324
$556$	−20.3688	−0.863829
$557$	5.99339	0.253948	0.126974	−	0.991906i	$-0.459473\pi$
$557$	5.99339	0.253948	0.126974	+	0.991906i	$0.459473\pi$
$558$	−0.454989	−0.0192612
$559$	−9.05186	−0.382853
$560$	3.28904	0.138987
$561$	−24.4733	−1.03326
$562$	−1.31710	−0.0555584
$563$	−11.2991	−0.476201	−0.238101	−	0.971240i	$-0.576525\pi$
$563$	−11.2991	−0.476201	−0.238101	+	0.971240i	$0.576525\pi$
$564$	1.29152	0.0543827
$565$	66.3393	2.79092
$566$	21.4304	0.900788
$567$	5.79470	0.243355
$568$	8.77902	0.368359
$569$	8.38653	0.351582	0.175791	−	0.984428i	$-0.443752\pi$
$569$	8.38653	0.351582	0.175791	+	0.984428i	$0.443752\pi$
$570$	−1.03945	−0.0435377
$571$	27.4157	1.14731	0.573656	−	0.819097i	$-0.305525\pi$
$571$	27.4157	1.14731	0.573656	+	0.819097i	$0.305525\pi$
$572$	−23.5518	−0.984750
$573$	−23.5670	−0.984524
$574$	5.45116	0.227527
$575$	29.7162	1.23925
$576$	−0.728548	−0.0303561
$577$	8.90548	0.370740	0.185370	−	0.982669i	$-0.440652\pi$
$577$	8.90548	0.370740	0.185370	+	0.982669i	$0.440652\pi$
$578$	−1.47445	−0.0613289
$579$	−15.2862	−0.635273
$580$	12.2137	0.507148
$581$	−10.5751	−0.438729
$582$	20.7656	0.860764
$583$	21.8300	0.904107
$584$	−16.7004	−0.691067
$585$	−14.8494	−0.613947
$586$	12.0245	0.496728
$587$	25.7945	1.06465	0.532326	−	0.846540i	$-0.321318\pi$
$587$	25.7945	1.06465	0.532326	+	0.846540i	$0.321318\pi$
$588$	9.26820	0.382214
$589$	−0.120767	−0.00497613
$590$	−18.1714	−0.748105
$591$	19.3992	0.797975
$592$	9.83162	0.404077
$593$	39.2695	1.61260	0.806302	−	0.591504i	$-0.201466\pi$
$593$	39.2695	1.61260	0.806302	+	0.591504i	$0.201466\pi$
$594$	23.1584	0.950202
$595$	12.9596	0.531293
$596$	−13.5723	−0.555943
$597$	32.4790	1.32928
$598$	−21.9978	−0.899556
$599$	2.66400	0.108848	0.0544241	−	0.998518i	$-0.482668\pi$
$599$	2.66400	0.108848	0.0544241	+	0.998518i	$0.482668\pi$
$600$	−11.6352	−0.475004
$601$	43.6170	1.77918	0.889588	−	0.456764i	$-0.150992\pi$
$601$	43.6170	1.77918	0.889588	+	0.456764i	$0.150992\pi$
$602$	−1.46068	−0.0595330
$603$	7.10906	0.289503
$604$	5.42148	0.220597
$605$	−21.3414	−0.867651
$606$	−7.29793	−0.296458
$607$	3.09530	0.125634	0.0628172	−	0.998025i	$-0.479991\pi$
$607$	3.09530	0.125634	0.0628172	+	0.998025i	$0.479991\pi$
$608$	−0.193378	−0.00784250
$609$	−4.75971	−0.192873
$610$	−4.46827	−0.180915
$611$	4.89728	0.198123
$612$	−2.87066	−0.116039
$613$	36.1691	1.46086	0.730429	−	0.682989i	$-0.239320\pi$
$613$	36.1691	1.46086	0.730429	+	0.682989i	$0.239320\pi$
$614$	−1.33546	−0.0538948
$615$	−31.7732	−1.28122
$616$	−3.80051	−0.153127
$617$	11.3648	0.457528	0.228764	−	0.973482i	$-0.426532\pi$
$617$	11.3648	0.457528	0.228764	+	0.973482i	$0.426532\pi$
$618$	−13.6759	−0.550126
$619$	−7.84278	−0.315228	−0.157614	−	0.987501i	$-0.550380\pi$
$619$	−7.84278	−0.315228	−0.157614	+	0.987501i	$0.550380\pi$
$620$	−2.22734	−0.0894523
$621$	21.6304	0.867997
$622$	1.92034	0.0769984
$623$	7.95969	0.318898
$624$	8.61307	0.344799
$625$	−4.00095	−0.160038
$626$	5.11449	0.204416
$627$	1.20109	0.0479669
$628$	−3.92605	−0.156666
$629$	38.7390	1.54463
$630$	−2.39622	−0.0954677
$631$	−35.4182	−1.40998	−0.704988	−	0.709220i	$-0.749048\pi$
$631$	−35.4182	−1.40998	−0.704988	+	0.709220i	$0.749048\pi$
$632$	13.0459	0.518937
$633$	−30.4142	−1.20885
$634$	−13.6829	−0.543419
$635$	9.40748	0.373324
$636$	−7.98341	−0.316563
$637$	35.1439	1.39245
$638$	−14.1131	−0.558742
$639$	−6.39593	−0.253019
$640$	−3.56652	−0.140979
$641$	−50.4755	−1.99366	−0.996831	−	0.0795447i	$-0.974653\pi$
$641$	−50.4755	−1.99366	−0.996831	+	0.0795447i	$0.974653\pi$
$642$	6.29595	0.248481
$643$	0.660332	0.0260409	0.0130205	−	0.999915i	$-0.495855\pi$
$643$	0.660332	0.0260409	0.0130205	+	0.999915i	$0.495855\pi$
$644$	−3.54974	−0.139880
$645$	8.51389	0.335234
$646$	−0.761956	−0.0299788
$647$	−11.3781	−0.447318	−0.223659	−	0.974667i	$-0.571800\pi$
$647$	−11.3781	−0.447318	−0.223659	+	0.974667i	$0.571800\pi$
$648$	−6.28358	−0.246842
$649$	20.9972	0.824213
$650$	−44.1191	−1.73049
$651$	0.867998	0.0340195
$652$	−4.78360	−0.187340
$653$	−31.1590	−1.21934	−0.609672	−	0.792653i	$-0.708699\pi$
$653$	−31.1590	−1.21934	−0.609672	+	0.792653i	$0.708699\pi$
$654$	22.5383	0.881318
$655$	−39.1946	−1.53146
$656$	−5.91104	−0.230788
$657$	12.1670	0.474681
$658$	0.790265	0.0308078
$659$	−45.5586	−1.77471	−0.887355	−	0.461086i	$-0.847460\pi$
$659$	−45.5586	−1.77471	−0.887355	+	0.461086i	$0.847460\pi$
$660$	22.1521	0.862268
$661$	14.0926	0.548139	0.274069	−	0.961710i	$-0.411630\pi$
$661$	14.0926	0.548139	0.274069	+	0.961710i	$0.411630\pi$
$662$	10.2940	0.400089
$663$	33.9376	1.31803
$664$	11.4673	0.445017
$665$	−0.636027	−0.0246641
$666$	−7.16281	−0.277553
$667$	−13.1819	−0.510404
$668$	−5.98614	−0.231611
$669$	−2.61158	−0.100969
$670$	34.8016	1.34450
$671$	5.16312	0.199320
$672$	1.38988	0.0536156
$673$	−25.1862	−0.970855	−0.485427	−	0.874277i	$-0.661336\pi$
$673$	−25.1862	−0.970855	−0.485427	+	0.874277i	$0.661336\pi$
$674$	−12.5670	−0.484062
$675$	43.3823	1.66978
$676$	19.6597	0.756143
$677$	−44.9556	−1.72779	−0.863893	−	0.503676i	$-0.831981\pi$
$677$	−44.9556	−1.72779	−0.863893	+	0.503676i	$0.831981\pi$
$678$	28.0336	1.07662
$679$	12.7063	0.487622
$680$	−14.0530	−0.538907
$681$	−36.8185	−1.41089
$682$	2.57371	0.0985526
$683$	−3.58072	−0.137012	−0.0685062	−	0.997651i	$-0.521823\pi$
$683$	−3.58072	−0.137012	−0.0685062	+	0.997651i	$0.521823\pi$
$684$	0.140885	0.00538687
$685$	−23.0200	−0.879548
$686$	12.1265	0.462992
$687$	26.1914	0.999263
$688$	1.58391	0.0603861
$689$	−30.2721	−1.15328
$690$	20.6904	0.787671
$691$	−25.6418	−0.975460	−0.487730	−	0.872994i	$-0.662175\pi$
$691$	−25.6418	−0.975460	−0.487730	+	0.872994i	$0.662175\pi$
$692$	−12.5910	−0.478639
$693$	2.76885	0.105180
$694$	−22.3001	−0.846500
$695$	72.6457	2.75561
$696$	5.16126	0.195637
$697$	−23.2910	−0.882209
$698$	18.8017	0.711653
$699$	22.7292	0.859697
$700$	−7.11943	−0.269089
$701$	−6.51753	−0.246164	−0.123082	−	0.992397i	$-0.539278\pi$
$701$	−6.51753	−0.246164	−0.123082	+	0.992397i	$0.539278\pi$
$702$	−32.1142	−1.21207
$703$	−1.90122	−0.0717058
$704$	4.12114	0.155321
$705$	−4.60622	−0.173480
$706$	−30.9842	−1.16611
$707$	−4.46552	−0.167943
$708$	−7.67885	−0.288589
$709$	−11.4129	−0.428621	−0.214311	−	0.976766i	$-0.568750\pi$
$709$	−11.4129	−0.428621	−0.214311	+	0.976766i	$0.568750\pi$
$710$	−31.3105	−1.17506
$711$	−9.50454	−0.356448
$712$	−8.63122	−0.323469
$713$	2.40389	0.0900265
$714$	5.47646	0.204951
$715$	83.9979	3.14134
$716$	−8.91075	−0.333010
$717$	23.8675	0.891348
$718$	26.2829	0.980870
$719$	26.0000	0.969636	0.484818	−	0.874615i	$-0.338886\pi$
$719$	26.0000	0.969636	0.484818	+	0.874615i	$0.338886\pi$
$720$	2.59838	0.0968359
$721$	−8.36814	−0.311646
$722$	−18.9626	−0.705715
$723$	15.7052	0.584083
$724$	4.99765	0.185736
$725$	−26.4378	−0.981874
$726$	−9.01841	−0.334704
$727$	0.217365	0.00806163	0.00403081	−	0.999992i	$-0.498717\pi$
$727$	0.217365	0.00806163	0.00403081	+	0.999992i	$0.498717\pi$
$728$	5.27024	0.195328
$729$	29.9855	1.11058
$730$	59.5622	2.20450
$731$	6.24101	0.230832
$732$	−1.88820	−0.0697897
$733$	26.3310	0.972557	0.486279	−	0.873804i	$-0.338354\pi$
$733$	26.3310	0.972557	0.486279	+	0.873804i	$0.338354\pi$
$734$	−0.534827	−0.0197408
$735$	−33.0552	−1.21926
$736$	3.84922	0.141884
$737$	−40.2135	−1.48128
$738$	4.30648	0.158524
$739$	39.9591	1.46992	0.734959	−	0.678111i	$-0.237201\pi$
$739$	39.9591	1.46992	0.734959	+	0.678111i	$0.237201\pi$
$740$	−35.0647	−1.28900
$741$	−1.66558	−0.0611865
$742$	−4.88496	−0.179333
$743$	−2.16269	−0.0793415	−0.0396707	−	0.999213i	$-0.512631\pi$
$743$	−2.16269	−0.0793415	−0.0396707	+	0.999213i	$0.512631\pi$
$744$	−0.941227	−0.0345071
$745$	48.4059	1.77345
$746$	13.5494	0.496078
$747$	−8.35446	−0.305674
$748$	16.2383	0.593732
$749$	3.85242	0.140764
$750$	14.6209	0.533881
$751$	−21.5216	−0.785335	−0.392667	−	0.919681i	$-0.628448\pi$
$751$	−21.5216	−0.785335	−0.392667	+	0.919681i	$0.628448\pi$
$752$	−0.856937	−0.0312493
$753$	−2.33168	−0.0849710
$754$	19.5709	0.712729
$755$	−19.3358	−0.703703
$756$	−5.18222	−0.188476
$757$	47.6932	1.73344	0.866719	−	0.498797i	$-0.166225\pi$
$757$	47.6932	1.73344	0.866719	+	0.498797i	$0.166225\pi$
$758$	−13.6924	−0.497331
$759$	−23.9079	−0.867803
$760$	0.689685	0.0250175
$761$	−11.4066	−0.413488	−0.206744	−	0.978395i	$-0.566287\pi$
$761$	−11.4066	−0.413488	−0.206744	+	0.978395i	$0.566287\pi$
$762$	3.97540	0.144013
$763$	13.7909	0.499265
$764$	15.6369	0.565725
$765$	10.2383	0.370165
$766$	−14.0356	−0.507125
$767$	−29.1173	−1.05136
$768$	−1.50713	−0.0543840
$769$	−5.29015	−0.190768	−0.0953838	−	0.995441i	$-0.530408\pi$
$769$	−5.29015	−0.190768	−0.0953838	+	0.995441i	$0.530408\pi$
$770$	13.5546	0.488474
$771$	37.7726	1.36035
$772$	10.1426	0.365039
$773$	26.1710	0.941306	0.470653	−	0.882318i	$-0.344018\pi$
$773$	26.1710	0.941306	0.470653	+	0.882318i	$0.344018\pi$
$774$	−1.15396	−0.0414781
$775$	4.82129	0.173186
$776$	−13.7782	−0.494610
$777$	13.6647	0.490220
$778$	−13.1625	−0.471897
$779$	1.14306	0.0409545
$780$	−30.7187	−1.09991
$781$	36.1796	1.29461
$782$	15.1669	0.542367
$783$	−19.2440	−0.687725
$784$	−6.14955	−0.219627
$785$	14.0023	0.499765
$786$	−16.5628	−0.590775
$787$	46.1059	1.64350	0.821749	−	0.569849i	$-0.192998\pi$
$787$	46.1059	1.64350	0.821749	+	0.569849i	$0.192998\pi$
$788$	−12.8716	−0.458530
$789$	15.3792	0.547514
$790$	−46.5283	−1.65540
$791$	17.1534	0.609905
$792$	−3.00245	−0.106687
$793$	−7.15981	−0.254252
$794$	−5.00742	−0.177707
$795$	28.4730	1.00983
$796$	−21.5502	−0.763825
$797$	−31.0104	−1.09845	−0.549223	−	0.835676i	$-0.685076\pi$
$797$	−31.0104	−1.09845	−0.549223	+	0.835676i	$0.685076\pi$
$798$	−0.268771	−0.00951439
$799$	−3.37654	−0.119453
$800$	7.72006	0.272945
$801$	6.28825	0.222184
$802$	9.76329	0.344754
$803$	−68.8246	−2.42877
$804$	14.7064	0.518655
$805$	12.6602	0.446215
$806$	−3.56902	−0.125713
$807$	−9.58427	−0.337382
$808$	4.84226	0.170350
$809$	21.5386	0.757258	0.378629	−	0.925548i	$-0.376396\pi$
$809$	21.5386	0.757258	0.378629	+	0.925548i	$0.376396\pi$
$810$	22.4105	0.787425
$811$	−2.97699	−0.104536	−0.0522682	−	0.998633i	$-0.516645\pi$
$811$	−2.97699	−0.104536	−0.0522682	+	0.998633i	$0.516645\pi$
$812$	3.15812	0.110828
$813$	7.50454	0.263196
$814$	40.5175	1.42014
$815$	17.0608	0.597614
$816$	−5.93848	−0.207888
$817$	−0.306294	−0.0107159
$818$	−13.1775	−0.460740
$819$	−3.83962	−0.134167
$820$	21.0819	0.736210
$821$	40.1108	1.39988	0.699938	−	0.714204i	$-0.253211\pi$
$821$	40.1108	1.39988	0.699938	+	0.714204i	$0.253211\pi$
$822$	−9.72775	−0.339294
$823$	−23.4621	−0.817838	−0.408919	−	0.912571i	$-0.634094\pi$
$823$	−23.4621	−0.817838	−0.408919	+	0.912571i	$0.634094\pi$
$824$	9.07412	0.316112
$825$	−47.9502	−1.66941
$826$	−4.69860	−0.163485
$827$	−37.7262	−1.31187	−0.655934	−	0.754818i	$-0.727725\pi$
$827$	−37.7262	−1.31187	−0.655934	+	0.754818i	$0.727725\pi$
$828$	−2.80434	−0.0974575
$829$	9.65782	0.335430	0.167715	−	0.985836i	$-0.446361\pi$
$829$	9.65782	0.335430	0.167715	+	0.985836i	$0.446361\pi$
$830$	−40.8983	−1.41960
$831$	−1.70944	−0.0592999
$832$	−5.71487	−0.198127
$833$	−24.2308	−0.839546
$834$	30.6985	1.06300
$835$	21.3497	0.738837
$836$	−0.796937	−0.0275626
$837$	3.50941	0.121303
$838$	−7.24685	−0.250338
$839$	21.9948	0.759344	0.379672	−	0.925121i	$-0.376037\pi$
$839$	21.9948	0.759344	0.379672	+	0.925121i	$0.376037\pi$
$840$	−4.95702	−0.171033
$841$	−17.2724	−0.595601
$842$	−4.82758	−0.166369
$843$	1.98504	0.0683685
$844$	20.1801	0.694629
$845$	−70.1168	−2.41209
$846$	0.624319	0.0214645
$847$	−5.51826	−0.189610
$848$	5.29708	0.181903
$849$	−32.2985	−1.10848
$850$	30.4190	1.04336
$851$	37.8441	1.29728
$852$	−13.2312	−0.453292
$853$	10.8589	0.371801	0.185901	−	0.982569i	$-0.440480\pi$
$853$	10.8589	0.371801	0.185901	+	0.982569i	$0.440480\pi$
$854$	−1.15537	−0.0395358
$855$	−0.502469	−0.0171841
$856$	−4.17743	−0.142782
$857$	−28.8532	−0.985605	−0.492803	−	0.870141i	$-0.664028\pi$
$857$	−28.8532	−0.985605	−0.492803	+	0.870141i	$0.664028\pi$
$858$	35.4957	1.21180
$859$	−28.9967	−0.989356	−0.494678	−	0.869076i	$-0.664714\pi$
$859$	−28.9967	−0.989356	−0.494678	+	0.869076i	$0.664714\pi$
$860$	−5.64906	−0.192631
$861$	−8.21562	−0.279988
$862$	6.02693	0.205278
$863$	11.6636	0.397032	0.198516	−	0.980098i	$-0.436388\pi$
$863$	11.6636	0.397032	0.198516	+	0.980098i	$0.436388\pi$
$864$	5.61942	0.191177
$865$	44.9061	1.52685
$866$	−8.64718	−0.293843
$867$	2.22219	0.0754694
$868$	−0.575926	−0.0195482
$869$	53.7639	1.82381
$870$	−18.4077	−0.624081
$871$	55.7649	1.88952
$872$	−14.9544	−0.506420
$873$	10.0381	0.339738
$874$	−0.744353	−0.0251781
$875$	8.94639	0.302443
$876$	25.1697	0.850406
$877$	45.3406	1.53104	0.765521	−	0.643411i	$-0.222481\pi$
$877$	45.3406	1.53104	0.765521	+	0.643411i	$0.222481\pi$
$878$	16.1851	0.546220
$879$	−18.1226	−0.611259
$880$	−14.6981	−0.495474
$881$	−41.1425	−1.38612	−0.693062	−	0.720878i	$-0.743739\pi$
$881$	−41.1425	−1.38612	−0.693062	+	0.720878i	$0.743739\pi$
$882$	4.48024	0.150858
$883$	24.7240	0.832030	0.416015	−	0.909358i	$-0.363426\pi$
$883$	24.7240	0.832030	0.416015	+	0.909358i	$0.363426\pi$
$884$	−22.5180	−0.757362
$885$	27.3868	0.920596
$886$	3.80804	0.127934
$887$	20.1857	0.677770	0.338885	−	0.940828i	$-0.389950\pi$
$887$	20.1857	0.677770	0.338885	+	0.940828i	$0.389950\pi$
$888$	−14.8176	−0.497245
$889$	2.43250	0.0815834
$890$	30.7834	1.03186
$891$	−25.8955	−0.867532
$892$	1.73281	0.0580188
$893$	0.165712	0.00554536
$894$	20.4553	0.684126
$895$	31.7804	1.06230
$896$	−0.922198	−0.0308085
$897$	33.1536	1.10697
$898$	3.81082	0.127169
$899$	−2.13868	−0.0713291
$900$	−5.62443	−0.187481
$901$	20.8718	0.695341
$902$	−24.3603	−0.811108
$903$	2.20144	0.0732595
$904$	−18.6006	−0.618646
$905$	−17.8242	−0.592497
$906$	−8.17090	−0.271460
$907$	−39.3712	−1.30730	−0.653649	−	0.756798i	$-0.726763\pi$
$907$	−39.3712	−1.30730	−0.653649	+	0.756798i	$0.726763\pi$
$908$	24.4295	0.810720
$909$	−3.52781	−0.117010
$910$	−18.7964	−0.623095
$911$	42.9277	1.42226	0.711128	−	0.703062i	$-0.248185\pi$
$911$	42.9277	1.42226	0.711128	+	0.703062i	$0.248185\pi$
$912$	0.291446	0.00965075
$913$	47.2583	1.56402
$914$	14.2825	0.472424
$915$	6.73428	0.222629
$916$	−17.3783	−0.574194
$917$	−10.1346	−0.334674
$918$	22.1419	0.730792
$919$	−7.35104	−0.242488	−0.121244	−	0.992623i	$-0.538688\pi$
$919$	−7.35104	−0.242488	−0.121244	+	0.992623i	$0.538688\pi$
$920$	−13.7283	−0.452609
$921$	2.01272	0.0663213
$922$	3.88374	0.127904
$923$	−50.1709	−1.65140
$924$	5.72788	0.188433
$925$	75.9007	2.49560
$926$	−29.7470	−0.977547
$927$	−6.61093	−0.217131
$928$	−3.42455	−0.112416
$929$	−1.91351	−0.0627801	−0.0313900	−	0.999507i	$-0.509993\pi$
$929$	−1.91351	−0.0627801	−0.0313900	+	0.999507i	$0.509993\pi$
$930$	3.35690	0.110077
$931$	1.18919	0.0389740
$932$	−15.0811	−0.493997
$933$	−2.89420	−0.0947519
$934$	−31.3336	−1.02527
$935$	−57.9143	−1.89400
$936$	4.16355	0.136090
$937$	0.291045	0.00950802	0.00475401	−	0.999989i	$-0.498487\pi$
$937$	0.291045	0.00950802	0.00475401	+	0.999989i	$0.498487\pi$
$938$	8.99868	0.293817
$939$	−7.70822	−0.251548
$940$	3.05628	0.0996849
$941$	−3.11226	−0.101457	−0.0507283	−	0.998712i	$-0.516154\pi$
$941$	−3.11226	−0.101457	−0.0507283	+	0.998712i	$0.516154\pi$
$942$	5.91708	0.192789
$943$	−22.7529	−0.740937
$944$	5.09500	0.165828
$945$	18.4825	0.601235
$946$	6.52753	0.212228
$947$	5.76120	0.187214	0.0936069	−	0.995609i	$-0.470160\pi$
$947$	5.76120	0.187214	0.0936069	+	0.995609i	$0.470160\pi$
$948$	−19.6619	−0.638588
$949$	95.4405	3.09813
$950$	−1.49289	−0.0484357
$951$	20.6220	0.668715
$952$	−3.63369	−0.117769
$953$	−33.0633	−1.07103	−0.535513	−	0.844527i	$-0.679882\pi$
$953$	−33.0633	−1.07103	−0.535513	+	0.844527i	$0.679882\pi$
$954$	−3.85918	−0.124945
$955$	−55.7695	−1.80466
$956$	−15.8363	−0.512184
$957$	21.2703	0.687571
$958$	−30.2103	−0.976050
$959$	−5.95230	−0.192210
$960$	5.37522	0.173485
$961$	−30.6100	−0.987419
$962$	−56.1864	−1.81152
$963$	3.04346	0.0980740
$964$	−10.4206	−0.335624
$965$	−36.1737	−1.16447
$966$	5.34994	0.172131
$967$	−11.4624	−0.368607	−0.184304	−	0.982869i	$-0.559003\pi$
$967$	−11.4624	−0.368607	−0.184304	+	0.982869i	$0.559003\pi$
$968$	5.98381	0.192327
$969$	1.14837	0.0368910
$970$	49.1403	1.57780
$971$	18.2763	0.586513	0.293257	−	0.956034i	$-0.405261\pi$
$971$	18.2763	0.586513	0.293257	+	0.956034i	$0.405261\pi$
$972$	−7.38807	−0.236972
$973$	18.7841	0.602189
$974$	0.369644	0.0118442
$975$	66.4934	2.12949
$976$	1.25284	0.0401024
$977$	−51.3542	−1.64296	−0.821482	−	0.570234i	$-0.806853\pi$
$977$	−51.3542	−1.64296	−0.821482	+	0.570234i	$0.806853\pi$
$978$	7.20952	0.230535
$979$	−35.5705	−1.13684
$980$	21.9325	0.700608
$981$	10.8950	0.347851
$982$	32.9093	1.05018
$983$	−61.7982	−1.97106	−0.985528	−	0.169513i	$-0.945781\pi$
$983$	−61.7982	−1.97106	−0.985528	+	0.169513i	$0.945781\pi$
$984$	8.90874	0.284000
$985$	45.9067	1.46271
$986$	−13.4936	−0.429723
$987$	−1.19104	−0.0379111
$988$	1.10513	0.0351588
$989$	6.09683	0.193868
$990$	10.7083	0.340332
$991$	48.6265	1.54467	0.772336	−	0.635214i	$-0.219088\pi$
$991$	48.6265	1.54467	0.772336	+	0.635214i	$0.219088\pi$
$992$	0.624515	0.0198284
$993$	−15.5145	−0.492338
$994$	−8.09600	−0.256789
$995$	76.8591	2.43660
$996$	−17.2827	−0.547624
$997$	−25.9324	−0.821288	−0.410644	−	0.911796i	$-0.634696\pi$
$997$	−25.9324	−0.821288	−0.410644	+	0.911796i	$0.634696\pi$
$998$	−13.9236	−0.440744
$999$	55.2480	1.74797

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.b.1.20	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.b.1.20	✓	54	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.50713 q^{3} +1.00000 q^{4} -3.56652 q^{5} -1.50713 q^{6} -0.922198 q^{7} +1.00000 q^{8} -0.728548 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.50713 q^{3} +1.00000 q^{4} -3.56652 q^{5} -1.50713 q^{6} -0.922198 q^{7} +1.00000 q^{8} -0.728548 q^{9} -3.56652 q^{10} +4.12114 q^{11} -1.50713 q^{12} -5.71487 q^{13} -0.922198 q^{14} +5.37522 q^{15} +1.00000 q^{16} +3.94025 q^{17} -0.728548 q^{18} -0.193378 q^{19} -3.56652 q^{20} +1.38988 q^{21} +4.12114 q^{22} +3.84922 q^{23} -1.50713 q^{24} +7.72006 q^{25} -5.71487 q^{26} +5.61942 q^{27} -0.922198 q^{28} -3.42455 q^{29} +5.37522 q^{30} +0.624515 q^{31} +1.00000 q^{32} -6.21111 q^{33} +3.94025 q^{34} +3.28904 q^{35} -0.728548 q^{36} +9.83162 q^{37} -0.193378 q^{38} +8.61307 q^{39} -3.56652 q^{40} -5.91104 q^{41} +1.38988 q^{42} +1.58391 q^{43} +4.12114 q^{44} +2.59838 q^{45} +3.84922 q^{46} -0.856937 q^{47} -1.50713 q^{48} -6.14955 q^{49} +7.72006 q^{50} -5.93848 q^{51} -5.71487 q^{52} +5.29708 q^{53} +5.61942 q^{54} -14.6981 q^{55} -0.922198 q^{56} +0.291446 q^{57} -3.42455 q^{58} +5.09500 q^{59} +5.37522 q^{60} +1.25284 q^{61} +0.624515 q^{62} +0.671865 q^{63} +1.00000 q^{64} +20.3822 q^{65} -6.21111 q^{66} -9.75785 q^{67} +3.94025 q^{68} -5.80129 q^{69} +3.28904 q^{70} +8.77902 q^{71} -0.728548 q^{72} -16.7004 q^{73} +9.83162 q^{74} -11.6352 q^{75} -0.193378 q^{76} -3.80051 q^{77} +8.61307 q^{78} +13.0459 q^{79} -3.56652 q^{80} -6.28358 q^{81} -5.91104 q^{82} +11.4673 q^{83} +1.38988 q^{84} -14.0530 q^{85} +1.58391 q^{86} +5.16126 q^{87} +4.12114 q^{88} -8.63122 q^{89} +2.59838 q^{90} +5.27024 q^{91} +3.84922 q^{92} -0.941227 q^{93} -0.856937 q^{94} +0.689685 q^{95} -1.50713 q^{96} -13.7782 q^{97} -6.14955 q^{98} -3.00245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * q^99

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