LMFDB - Embedded newform 6026.2.a.f.1.3

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:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} - 17 x^{18} + 115 x^{17} + 78 x^{16} - 1083 x^{15} + 248 x^{14} + 5359 x^{13} + \cdots - 18 $ x^20 - 5x^19 - 17x^18 + 115x^17 + 78x^16 - 1083x^15 + 248x^14 + 5359x^13 - 3723x^12 - 14776x^11 + 14837x^10 + 21886x^9 - 28084x^8 - 14682x^7 + 25315x^6 + 2042x^5 - 9137x^4 + 576x^3 + 1159x^2 - 78*x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.60929$ of defining polynomial
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.60929 q^{3} +1.00000 q^{4} +1.96845 q^{5} -2.60929 q^{6} -1.34895 q^{7} +1.00000 q^{8} +3.80840 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.60929 q^{3} +1.00000 q^{4} +1.96845 q^{5} -2.60929 q^{6} -1.34895 q^{7} +1.00000 q^{8} +3.80840 q^{9} +1.96845 q^{10} -0.884748 q^{11} -2.60929 q^{12} +1.44370 q^{13} -1.34895 q^{14} -5.13627 q^{15} +1.00000 q^{16} -5.54898 q^{17} +3.80840 q^{18} +3.27258 q^{19} +1.96845 q^{20} +3.51981 q^{21} -0.884748 q^{22} +1.00000 q^{23} -2.60929 q^{24} -1.12519 q^{25} +1.44370 q^{26} -2.10935 q^{27} -1.34895 q^{28} -2.61505 q^{29} -5.13627 q^{30} +0.00956313 q^{31} +1.00000 q^{32} +2.30856 q^{33} -5.54898 q^{34} -2.65535 q^{35} +3.80840 q^{36} +0.196541 q^{37} +3.27258 q^{38} -3.76703 q^{39} +1.96845 q^{40} +0.972313 q^{41} +3.51981 q^{42} +0.854580 q^{43} -0.884748 q^{44} +7.49666 q^{45} +1.00000 q^{46} +0.398117 q^{47} -2.60929 q^{48} -5.18032 q^{49} -1.12519 q^{50} +14.4789 q^{51} +1.44370 q^{52} -8.43975 q^{53} -2.10935 q^{54} -1.74159 q^{55} -1.34895 q^{56} -8.53910 q^{57} -2.61505 q^{58} -5.87768 q^{59} -5.13627 q^{60} -3.18824 q^{61} +0.00956313 q^{62} -5.13735 q^{63} +1.00000 q^{64} +2.84185 q^{65} +2.30856 q^{66} +5.96088 q^{67} -5.54898 q^{68} -2.60929 q^{69} -2.65535 q^{70} +10.0689 q^{71} +3.80840 q^{72} -1.24831 q^{73} +0.196541 q^{74} +2.93594 q^{75} +3.27258 q^{76} +1.19348 q^{77} -3.76703 q^{78} -3.92466 q^{79} +1.96845 q^{80} -5.92129 q^{81} +0.972313 q^{82} +8.85662 q^{83} +3.51981 q^{84} -10.9229 q^{85} +0.854580 q^{86} +6.82343 q^{87} -0.884748 q^{88} -12.0529 q^{89} +7.49666 q^{90} -1.94748 q^{91} +1.00000 q^{92} -0.0249530 q^{93} +0.398117 q^{94} +6.44192 q^{95} -2.60929 q^{96} -11.8638 q^{97} -5.18032 q^{98} -3.36947 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9} - 6 q^{10} - 3 q^{11} - 5 q^{12} - 13 q^{13} - 12 q^{14} - 10 q^{15} + 20 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} - 6 q^{20} - 8 q^{21} - 3 q^{22} + 20 q^{23} - 5 q^{24} - 14 q^{25} - 13 q^{26} - 5 q^{27} - 12 q^{28} - 27 q^{29} - 10 q^{30} - 27 q^{31} + 20 q^{32} - 12 q^{33} - 14 q^{34} - 23 q^{35} - q^{36} - 19 q^{37} - 21 q^{38} - 35 q^{39} - 6 q^{40} - 17 q^{41} - 8 q^{42} - 27 q^{43} - 3 q^{44} + 4 q^{45} + 20 q^{46} - 28 q^{47} - 5 q^{48} - 10 q^{49} - 14 q^{50} + 6 q^{51} - 13 q^{52} - 47 q^{53} - 5 q^{54} - 4 q^{55} - 12 q^{56} - 16 q^{57} - 27 q^{58} - 16 q^{59} - 10 q^{60} - 9 q^{61} - 27 q^{62} - 9 q^{63} + 20 q^{64} + 9 q^{65} - 12 q^{66} - 8 q^{67} - 14 q^{68} - 5 q^{69} - 23 q^{70} - 30 q^{71} - q^{72} - 26 q^{73} - 19 q^{74} - 18 q^{75} - 21 q^{76} - 50 q^{77} - 35 q^{78} - 35 q^{79} - 6 q^{80} - 60 q^{81} - 17 q^{82} + 2 q^{83} - 8 q^{84} - 62 q^{85} - 27 q^{86} + q^{87} - 3 q^{88} - 25 q^{89} + 4 q^{90} + 22 q^{91} + 20 q^{92} - 21 q^{93} - 28 q^{94} - 14 q^{95} - 5 q^{96} + 2 q^{97} - 10 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9 - 6 * q^10 - 3 * q^11 - 5 * q^12 - 13 * q^13 - 12 * q^14 - 10 * q^15 + 20 * q^16 - 14 * q^17 - q^18 - 21 * q^19 - 6 * q^20 - 8 * q^21 - 3 * q^22 + 20 * q^23 - 5 * q^24 - 14 * q^25 - 13 * q^26 - 5 * q^27 - 12 * q^28 - 27 * q^29 - 10 * q^30 - 27 * q^31 + 20 * q^32 - 12 * q^33 - 14 * q^34 - 23 * q^35 - q^36 - 19 * q^37 - 21 * q^38 - 35 * q^39 - 6 * q^40 - 17 * q^41 - 8 * q^42 - 27 * q^43 - 3 * q^44 + 4 * q^45 + 20 * q^46 - 28 * q^47 - 5 * q^48 - 10 * q^49 - 14 * q^50 + 6 * q^51 - 13 * q^52 - 47 * q^53 - 5 * q^54 - 4 * q^55 - 12 * q^56 - 16 * q^57 - 27 * q^58 - 16 * q^59 - 10 * q^60 - 9 * q^61 - 27 * q^62 - 9 * q^63 + 20 * q^64 + 9 * q^65 - 12 * q^66 - 8 * q^67 - 14 * q^68 - 5 * q^69 - 23 * q^70 - 30 * q^71 - q^72 - 26 * q^73 - 19 * q^74 - 18 * q^75 - 21 * q^76 - 50 * q^77 - 35 * q^78 - 35 * q^79 - 6 * q^80 - 60 * q^81 - 17 * q^82 + 2 * q^83 - 8 * q^84 - 62 * q^85 - 27 * q^86 + q^87 - 3 * q^88 - 25 * q^89 + 4 * q^90 + 22 * q^91 + 20 * q^92 - 21 * q^93 - 28 * q^94 - 14 * q^95 - 5 * q^96 + 2 * q^97 - 10 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.60929	−1.50647	−0.753237	−	0.657749i	$-0.771509\pi$
$3$	−2.60929	−1.50647	−0.753237	+	0.657749i	$0.771509\pi$
$4$	1.00000	0.500000
$5$	1.96845	0.880319	0.440160	−	0.897919i	$-0.354922\pi$
$5$	1.96845	0.880319	0.440160	+	0.897919i	$0.354922\pi$
$6$	−2.60929	−1.06524
$7$	−1.34895	−0.509857	−0.254928	−	0.966960i	$-0.582052\pi$
$7$	−1.34895	−0.509857	−0.254928	+	0.966960i	$0.582052\pi$
$8$	1.00000	0.353553
$9$	3.80840	1.26947
$10$	1.96845	0.622480
$11$	−0.884748	−0.266761	−0.133381	−	0.991065i	$-0.542583\pi$
$11$	−0.884748	−0.266761	−0.133381	+	0.991065i	$0.542583\pi$
$12$	−2.60929	−0.753237
$13$	1.44370	0.400410	0.200205	−	0.979754i	$-0.435839\pi$
$13$	1.44370	0.400410	0.200205	+	0.979754i	$0.435839\pi$
$14$	−1.34895	−0.360523
$15$	−5.13627	−1.32618
$16$	1.00000	0.250000
$17$	−5.54898	−1.34583	−0.672913	−	0.739721i	$-0.734957\pi$
$17$	−5.54898	−1.34583	−0.672913	+	0.739721i	$0.734957\pi$
$18$	3.80840	0.897648
$19$	3.27258	0.750780	0.375390	−	0.926867i	$-0.377509\pi$
$19$	3.27258	0.750780	0.375390	+	0.926867i	$0.377509\pi$
$20$	1.96845	0.440160
$21$	3.51981	0.768086
$22$	−0.884748	−0.188629
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.60929	−0.532619
$25$	−1.12519	−0.225038
$26$	1.44370	0.283132
$27$	−2.10935	−0.405944
$28$	−1.34895	−0.254928
$29$	−2.61505	−0.485603	−0.242801	−	0.970076i	$-0.578066\pi$
$29$	−2.61505	−0.485603	−0.242801	+	0.970076i	$0.578066\pi$
$30$	−5.13627	−0.937750
$31$	0.00956313	0.00171759	0.000858794	−	1.00000i	$-0.499727\pi$
$31$	0.00956313	0.00171759	0.000858794		1.00000i	$0.499727\pi$
$32$	1.00000	0.176777
$33$	2.30856	0.401869
$34$	−5.54898	−0.951643
$35$	−2.65535	−0.448837
$36$	3.80840	0.634733
$37$	0.196541	0.0323112	0.0161556	−	0.999869i	$-0.494857\pi$
$37$	0.196541	0.0323112	0.0161556	+	0.999869i	$0.494857\pi$
$38$	3.27258	0.530882
$39$	−3.76703	−0.603207
$40$	1.96845	0.311240
$41$	0.972313	0.151850	0.0759249	−	0.997114i	$-0.475809\pi$
$41$	0.972313	0.151850	0.0759249	+	0.997114i	$0.475809\pi$
$42$	3.51981	0.543119
$43$	0.854580	0.130322	0.0651611	−	0.997875i	$-0.479244\pi$
$43$	0.854580	0.130322	0.0651611	+	0.997875i	$0.479244\pi$
$44$	−0.884748	−0.133381
$45$	7.49666	1.11754
$46$	1.00000	0.147442
$47$	0.398117	0.0580714	0.0290357	−	0.999578i	$-0.490756\pi$
$47$	0.398117	0.0580714	0.0290357	+	0.999578i	$0.490756\pi$
$48$	−2.60929	−0.376619
$49$	−5.18032	−0.740046
$50$	−1.12519	−0.159126
$51$	14.4789	2.02745
$52$	1.44370	0.200205
$53$	−8.43975	−1.15929	−0.579644	−	0.814870i	$-0.696808\pi$
$53$	−8.43975	−1.15929	−0.579644	+	0.814870i	$0.696808\pi$
$54$	−2.10935	−0.287046
$55$	−1.74159	−0.234835
$56$	−1.34895	−0.180262
$57$	−8.53910	−1.13103
$58$	−2.61505	−0.343373
$59$	−5.87768	−0.765209	−0.382605	−	0.923912i	$-0.624973\pi$
$59$	−5.87768	−0.765209	−0.382605	+	0.923912i	$0.624973\pi$
$60$	−5.13627	−0.663090
$61$	−3.18824	−0.408212	−0.204106	−	0.978949i	$-0.565429\pi$
$61$	−3.18824	−0.408212	−0.204106	+	0.978949i	$0.565429\pi$
$62$	0.00956313	0.00121452
$63$	−5.13735	−0.647246
$64$	1.00000	0.125000
$65$	2.84185	0.352489
$66$	2.30856	0.284165
$67$	5.96088	0.728238	0.364119	−	0.931352i	$-0.381370\pi$
$67$	5.96088	0.728238	0.364119	+	0.931352i	$0.381370\pi$
$68$	−5.54898	−0.672913
$69$	−2.60929	−0.314122
$70$	−2.65535	−0.317376
$71$	10.0689	1.19496	0.597479	−	0.801885i	$-0.296169\pi$
$71$	10.0689	1.19496	0.597479	+	0.801885i	$0.296169\pi$
$72$	3.80840	0.448824
$73$	−1.24831	−0.146103	−0.0730517	−	0.997328i	$-0.523274\pi$
$73$	−1.24831	−0.146103	−0.0730517	+	0.997328i	$0.523274\pi$
$74$	0.196541	0.0228474
$75$	2.93594	0.339013
$76$	3.27258	0.375390
$77$	1.19348	0.136010
$78$	−3.76703	−0.426532
$79$	−3.92466	−0.441558	−0.220779	−	0.975324i	$-0.570860\pi$
$79$	−3.92466	−0.441558	−0.220779	+	0.975324i	$0.570860\pi$
$80$	1.96845	0.220080
$81$	−5.92129	−0.657922
$82$	0.972313	0.107374
$83$	8.85662	0.972141	0.486070	−	0.873920i	$-0.338430\pi$
$83$	8.85662	0.972141	0.486070	+	0.873920i	$0.338430\pi$
$84$	3.51981	0.384043
$85$	−10.9229	−1.18476
$86$	0.854580	0.0921518
$87$	6.82343	0.731548
$88$	−0.884748	−0.0943144
$89$	−12.0529	−1.27760	−0.638800	−	0.769373i	$-0.720569\pi$
$89$	−12.0529	−1.27760	−0.638800	+	0.769373i	$0.720569\pi$
$90$	7.49666	0.790217
$91$	−1.94748	−0.204152
$92$	1.00000	0.104257
$93$	−0.0249530	−0.00258750
$94$	0.398117	0.0410627
$95$	6.44192	0.660927
$96$	−2.60929	−0.266310
$97$	−11.8638	−1.20459	−0.602293	−	0.798275i	$-0.705746\pi$
$97$	−11.8638	−1.20459	−0.602293	+	0.798275i	$0.705746\pi$
$98$	−5.18032	−0.523292
$99$	−3.36947	−0.338645
$100$	−1.12519	−0.112519
$101$	−3.32813	−0.331161	−0.165581	−	0.986196i	$-0.552950\pi$
$101$	−3.32813	−0.331161	−0.165581	+	0.986196i	$0.552950\pi$
$102$	14.4789	1.43363
$103$	11.1799	1.10159	0.550795	−	0.834640i	$-0.314325\pi$
$103$	11.1799	1.10159	0.550795	+	0.834640i	$0.314325\pi$
$104$	1.44370	0.141566
$105$	6.92859	0.676161
$106$	−8.43975	−0.819741
$107$	−15.5851	−1.50667	−0.753334	−	0.657638i	$-0.771556\pi$
$107$	−15.5851	−1.50667	−0.753334	+	0.657638i	$0.771556\pi$
$108$	−2.10935	−0.202972
$109$	−14.2870	−1.36845	−0.684223	−	0.729273i	$-0.739858\pi$
$109$	−14.2870	−1.36845	−0.684223	+	0.729273i	$0.739858\pi$
$110$	−1.74159	−0.166054
$111$	−0.512833	−0.0486760
$112$	−1.34895	−0.127464
$113$	19.5707	1.84106	0.920528	−	0.390676i	$-0.127759\pi$
$113$	19.5707	1.84106	0.920528	+	0.390676i	$0.127759\pi$
$114$	−8.53910	−0.799760
$115$	1.96845	0.183559
$116$	−2.61505	−0.242801
$117$	5.49818	0.508307
$118$	−5.87768	−0.541085
$119$	7.48533	0.686179
$120$	−5.13627	−0.468875
$121$	−10.2172	−0.928838
$122$	−3.18824	−0.288649
$123$	−2.53705	−0.228758
$124$	0.00956313	0.000858794 0
$125$	−12.0572	−1.07842
$126$	−5.13735	−0.457672
$127$	14.0421	1.24603	0.623016	−	0.782209i	$-0.285907\pi$
$127$	14.0421	1.24603	0.623016	+	0.782209i	$0.285907\pi$
$128$	1.00000	0.0883883
$129$	−2.22985	−0.196327
$130$	2.84185	0.249247
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	2.30856	0.200935
$133$	−4.41455	−0.382790
$134$	5.96088	0.514942
$135$	−4.15215	−0.357361
$136$	−5.54898	−0.475822
$137$	21.2209	1.81302	0.906512	−	0.422180i	$-0.138735\pi$
$137$	21.2209	1.81302	0.906512	+	0.422180i	$0.138735\pi$
$138$	−2.60929	−0.222118
$139$	16.3126	1.38362	0.691809	−	0.722080i	$-0.256814\pi$
$139$	16.3126	1.38362	0.691809	+	0.722080i	$0.256814\pi$
$140$	−2.65535	−0.224418
$141$	−1.03880	−0.0874831
$142$	10.0689	0.844963
$143$	−1.27731	−0.106814
$144$	3.80840	0.317367
$145$	−5.14761	−0.427486
$146$	−1.24831	−0.103311
$147$	13.5170	1.11486
$148$	0.196541	0.0161556
$149$	10.7357	0.879506	0.439753	−	0.898119i	$-0.355066\pi$
$149$	10.7357	0.879506	0.439753	+	0.898119i	$0.355066\pi$
$150$	2.93594	0.239719
$151$	−14.2271	−1.15779	−0.578893	−	0.815403i	$-0.696515\pi$
$151$	−14.2271	−1.15779	−0.578893	+	0.815403i	$0.696515\pi$
$152$	3.27258	0.265441
$153$	−21.1327	−1.70848
$154$	1.19348	0.0961737
$155$	0.0188246	0.00151203
$156$	−3.76703	−0.301604
$157$	−17.1748	−1.37070	−0.685348	−	0.728216i	$-0.740350\pi$
$157$	−17.1748	−1.37070	−0.685348	+	0.728216i	$0.740350\pi$
$158$	−3.92466	−0.312229
$159$	22.0218	1.74644
$160$	1.96845	0.155620
$161$	−1.34895	−0.106312
$162$	−5.92129	−0.465221
$163$	−25.4019	−1.98963	−0.994816	−	0.101696i	$-0.967573\pi$
$163$	−25.4019	−1.98963	−0.994816	+	0.101696i	$0.967573\pi$
$164$	0.972313	0.0759249
$165$	4.54430	0.353773
$166$	8.85662	0.687407
$167$	17.5780	1.36022	0.680112	−	0.733109i	$-0.261931\pi$
$167$	17.5780	1.36022	0.680112	+	0.733109i	$0.261931\pi$
$168$	3.51981	0.271560
$169$	−10.9157	−0.839672
$170$	−10.9229	−0.837750
$171$	12.4633	0.953090
$172$	0.854580	0.0651611
$173$	−23.8555	−1.81370	−0.906850	−	0.421455i	$-0.861520\pi$
$173$	−23.8555	−1.81370	−0.906850	+	0.421455i	$0.861520\pi$
$174$	6.82343	0.517283
$175$	1.51783	0.114737
$176$	−0.884748	−0.0666904
$177$	15.3366	1.15277
$178$	−12.0529	−0.903400
$179$	−5.23433	−0.391232	−0.195616	−	0.980681i	$-0.562671\pi$
$179$	−5.23433	−0.391232	−0.195616	+	0.980681i	$0.562671\pi$
$180$	7.49666	0.558768
$181$	5.35539	0.398063	0.199032	−	0.979993i	$-0.436220\pi$
$181$	5.35539	0.398063	0.199032	+	0.979993i	$0.436220\pi$
$182$	−1.94748	−0.144357
$183$	8.31903	0.614961
$184$	1.00000	0.0737210
$185$	0.386882	0.0284442
$186$	−0.0249530	−0.00182964
$187$	4.90945	0.359015
$188$	0.398117	0.0290357
$189$	2.84541	0.206973
$190$	6.44192	0.467346
$191$	−21.3304	−1.54342	−0.771708	−	0.635977i	$-0.780597\pi$
$191$	−21.3304	−1.54342	−0.771708	+	0.635977i	$0.780597\pi$
$192$	−2.60929	−0.188309
$193$	−6.75035	−0.485901	−0.242950	−	0.970039i	$-0.578115\pi$
$193$	−6.75035	−0.485901	−0.242950	+	0.970039i	$0.578115\pi$
$194$	−11.8638	−0.851771
$195$	−7.41522	−0.531015
$196$	−5.18032	−0.370023
$197$	−8.50166	−0.605718	−0.302859	−	0.953035i	$-0.597941\pi$
$197$	−8.50166	−0.605718	−0.302859	+	0.953035i	$0.597941\pi$
$198$	−3.36947	−0.239458
$199$	19.1622	1.35837	0.679186	−	0.733966i	$-0.262333\pi$
$199$	19.1622	1.35837	0.679186	+	0.733966i	$0.262333\pi$
$200$	−1.12519	−0.0795628
$201$	−15.5537	−1.09707
$202$	−3.32813	−0.234166
$203$	3.52758	0.247588
$204$	14.4789	1.01373
$205$	1.91395	0.133676
$206$	11.1799	0.778942
$207$	3.80840	0.264702
$208$	1.44370	0.100102
$209$	−2.89540	−0.200279
$210$	6.92859	0.478118
$211$	3.60438	0.248135	0.124068	−	0.992274i	$-0.460406\pi$
$211$	3.60438	0.248135	0.124068	+	0.992274i	$0.460406\pi$
$212$	−8.43975	−0.579644
$213$	−26.2727	−1.80017
$214$	−15.5851	−1.06538
$215$	1.68220	0.114725
$216$	−2.10935	−0.143523
$217$	−0.0129002	−0.000875724 0
$218$	−14.2870	−0.967637
$219$	3.25720	0.220101
$220$	−1.74159	−0.117418
$221$	−8.01106	−0.538882
$222$	−0.512833	−0.0344191
$223$	−24.8829	−1.66628	−0.833140	−	0.553062i	$-0.813459\pi$
$223$	−24.8829	−1.66628	−0.833140	+	0.553062i	$0.813459\pi$
$224$	−1.34895	−0.0901308
$225$	−4.28516	−0.285678
$226$	19.5707	1.30182
$227$	−21.3260	−1.41546	−0.707728	−	0.706485i	$-0.750280\pi$
$227$	−21.3260	−1.41546	−0.707728	+	0.706485i	$0.750280\pi$
$228$	−8.53910	−0.565516
$229$	−13.0327	−0.861228	−0.430614	−	0.902536i	$-0.641703\pi$
$229$	−13.0327	−0.861228	−0.430614	+	0.902536i	$0.641703\pi$
$230$	1.96845	0.129796
$231$	−3.11415	−0.204896
$232$	−2.61505	−0.171687
$233$	8.14547	0.533628	0.266814	−	0.963748i	$-0.414029\pi$
$233$	8.14547	0.533628	0.266814	+	0.963748i	$0.414029\pi$
$234$	5.49818	0.359427
$235$	0.783676	0.0511214
$236$	−5.87768	−0.382605
$237$	10.2406	0.665196
$238$	7.48533	0.485202
$239$	2.17004	0.140368	0.0701842	−	0.997534i	$-0.477641\pi$
$239$	2.17004	0.140368	0.0701842	+	0.997534i	$0.477641\pi$
$240$	−5.13627	−0.331545
$241$	−0.678804	−0.0437256	−0.0218628	−	0.999761i	$-0.506960\pi$
$241$	−0.678804	−0.0437256	−0.0218628	+	0.999761i	$0.506960\pi$
$242$	−10.2172	−0.656788
$243$	21.7784	1.39709
$244$	−3.18824	−0.204106
$245$	−10.1972	−0.651477
$246$	−2.53705	−0.161756
$247$	4.72461	0.300620
$248$	0.00956313	0.000607259 0
$249$	−23.1095	−1.46451
$250$	−12.0572	−0.762561
$251$	6.18774	0.390566	0.195283	−	0.980747i	$-0.437437\pi$
$251$	6.18774	0.390566	0.195283	+	0.980747i	$0.437437\pi$
$252$	−5.13735	−0.323623
$253$	−0.884748	−0.0556236
$254$	14.0421	0.881077
$255$	28.5011	1.78481
$256$	1.00000	0.0625000
$257$	28.0117	1.74732	0.873662	−	0.486533i	$-0.161739\pi$
$257$	28.0117	1.74732	0.873662	+	0.486533i	$0.161739\pi$
$258$	−2.22985	−0.138824
$259$	−0.265125	−0.0164741
$260$	2.84185	0.176244
$261$	−9.95916	−0.616456
$262$	−1.00000	−0.0617802
$263$	−21.4613	−1.32336	−0.661679	−	0.749787i	$-0.730156\pi$
$263$	−21.4613	−1.32336	−0.661679	+	0.749787i	$0.730156\pi$
$264$	2.30856	0.142082
$265$	−16.6133	−1.02054
$266$	−4.41455	−0.270674
$267$	31.4494	1.92467
$268$	5.96088	0.364119
$269$	−16.3066	−0.994230	−0.497115	−	0.867685i	$-0.665607\pi$
$269$	−16.3066	−0.994230	−0.497115	+	0.867685i	$0.665607\pi$
$270$	−4.15215	−0.252692
$271$	−17.8805	−1.08616	−0.543082	−	0.839680i	$-0.682743\pi$
$271$	−17.8805	−1.08616	−0.543082	+	0.839680i	$0.682743\pi$
$272$	−5.54898	−0.336457
$273$	5.08155	0.307549
$274$	21.2209	1.28200
$275$	0.995507	0.0600314
$276$	−2.60929	−0.157061
$277$	27.5343	1.65438	0.827189	−	0.561924i	$-0.189939\pi$
$277$	27.5343	1.65438	0.827189	+	0.561924i	$0.189939\pi$
$278$	16.3126	0.978366
$279$	0.0364202	0.00218042
$280$	−2.65535	−0.158688
$281$	−12.3493	−0.736697	−0.368349	−	0.929688i	$-0.620077\pi$
$281$	−12.3493	−0.736697	−0.368349	+	0.929688i	$0.620077\pi$
$282$	−1.03880	−0.0618599
$283$	−7.44523	−0.442573	−0.221287	−	0.975209i	$-0.571026\pi$
$283$	−7.44523	−0.442573	−0.221287	+	0.975209i	$0.571026\pi$
$284$	10.0689	0.597479
$285$	−16.8088	−0.995669
$286$	−1.27731	−0.0755288
$287$	−1.31161	−0.0774217
$288$	3.80840	0.224412
$289$	13.7912	0.811249
$290$	−5.14761	−0.302278
$291$	30.9561	1.81468
$292$	−1.24831	−0.0730517
$293$	15.0365	0.878441	0.439221	−	0.898379i	$-0.355255\pi$
$293$	15.0365	0.878441	0.439221	+	0.898379i	$0.355255\pi$
$294$	13.5170	0.788326
$295$	−11.5700	−0.673629
$296$	0.196541	0.0114237
$297$	1.86624	0.108290
$298$	10.7357	0.621905
$299$	1.44370	0.0834912
$300$	2.93594	0.169507
$301$	−1.15279	−0.0664457
$302$	−14.2271	−0.818679
$303$	8.68405	0.498886
$304$	3.27258	0.187695
$305$	−6.27590	−0.359357
$306$	−21.1327	−1.20808
$307$	−18.1330	−1.03491	−0.517453	−	0.855711i	$-0.673120\pi$
$307$	−18.1330	−1.03491	−0.517453	+	0.855711i	$0.673120\pi$
$308$	1.19348	0.0680051
$309$	−29.1717	−1.65952
$310$	0.0188246	0.00106916
$311$	16.2125	0.919324	0.459662	−	0.888094i	$-0.347971\pi$
$311$	16.2125	0.919324	0.459662	+	0.888094i	$0.347971\pi$
$312$	−3.76703	−0.213266
$313$	−17.4957	−0.988917	−0.494459	−	0.869201i	$-0.664634\pi$
$313$	−17.4957	−0.988917	−0.494459	+	0.869201i	$0.664634\pi$
$314$	−17.1748	−0.969229
$315$	−10.1126	−0.569783
$316$	−3.92466	−0.220779
$317$	31.0367	1.74320	0.871599	−	0.490220i	$-0.163084\pi$
$317$	31.0367	1.74320	0.871599	+	0.490220i	$0.163084\pi$
$318$	22.0218	1.23492
$319$	2.31366	0.129540
$320$	1.96845	0.110040
$321$	40.6661	2.26976
$322$	−1.34895	−0.0751743
$323$	−18.1595	−1.01042
$324$	−5.92129	−0.328961
$325$	−1.62443	−0.0901073
$326$	−25.4019	−1.40688
$327$	37.2789	2.06153
$328$	0.972313	0.0536870
$329$	−0.537042	−0.0296081
$330$	4.54430	0.250156
$331$	−27.5601	−1.51484	−0.757421	−	0.652927i	$-0.773541\pi$
$331$	−27.5601	−1.51484	−0.757421	+	0.652927i	$0.773541\pi$
$332$	8.85662	0.486070
$333$	0.748507	0.0410179
$334$	17.5780	0.961823
$335$	11.7337	0.641082
$336$	3.51981	0.192022
$337$	−11.8872	−0.647537	−0.323768	−	0.946136i	$-0.604950\pi$
$337$	−11.8872	−0.647537	−0.323768	+	0.946136i	$0.604950\pi$
$338$	−10.9157	−0.593738
$339$	−51.0657	−2.77351
$340$	−10.9229	−0.592379
$341$	−0.00846095	−0.000458186 0
$342$	12.4633	0.673937
$343$	16.4307	0.887174
$344$	0.854580	0.0460759
$345$	−5.13627	−0.276527
$346$	−23.8555	−1.28248
$347$	−33.0355	−1.77344	−0.886718	−	0.462310i	$-0.847021\pi$
$347$	−33.0355	−1.77344	−0.886718	+	0.462310i	$0.847021\pi$
$348$	6.82343	0.365774
$349$	−14.0113	−0.750008	−0.375004	−	0.927023i	$-0.622359\pi$
$349$	−14.0113	−0.750008	−0.375004	+	0.927023i	$0.622359\pi$
$350$	1.51783	0.0811313
$351$	−3.04526	−0.162544
$352$	−0.884748	−0.0471572
$353$	−26.7435	−1.42341	−0.711706	−	0.702478i	$-0.752077\pi$
$353$	−26.7435	−1.42341	−0.711706	+	0.702478i	$0.752077\pi$
$354$	15.3366	0.815130
$355$	19.8202	1.05194
$356$	−12.0529	−0.638800
$357$	−19.5314	−1.03371
$358$	−5.23433	−0.276643
$359$	−21.3220	−1.12533	−0.562665	−	0.826685i	$-0.690224\pi$
$359$	−21.3220	−1.12533	−0.562665	+	0.826685i	$0.690224\pi$
$360$	7.49666	0.395109
$361$	−8.29025	−0.436329
$362$	5.35539	0.281473
$363$	26.6597	1.39927
$364$	−1.94748	−0.102076
$365$	−2.45724	−0.128618
$366$	8.31903	0.434843
$367$	−0.122241	−0.00638094	−0.00319047	−	0.999995i	$-0.501016\pi$
$367$	−0.122241	−0.00638094	−0.00319047	+	0.999995i	$0.501016\pi$
$368$	1.00000	0.0521286
$369$	3.70296	0.192768
$370$	0.386882	0.0201131
$371$	11.3848	0.591071
$372$	−0.0249530	−0.00129375
$373$	14.6001	0.755965	0.377982	−	0.925813i	$-0.376618\pi$
$373$	14.6001	0.755965	0.377982	+	0.925813i	$0.376618\pi$
$374$	4.90945	0.253862
$375$	31.4606	1.62462
$376$	0.398117	0.0205313
$377$	−3.77534	−0.194440
$378$	2.84541	0.146352
$379$	−27.3526	−1.40501	−0.702505	−	0.711679i	$-0.747935\pi$
$379$	−27.3526	−1.40501	−0.702505	+	0.711679i	$0.747935\pi$
$380$	6.44192	0.330463
$381$	−36.6398	−1.87711
$382$	−21.3304	−1.09136
$383$	−11.0961	−0.566987	−0.283493	−	0.958974i	$-0.591493\pi$
$383$	−11.0961	−0.566987	−0.283493	+	0.958974i	$0.591493\pi$
$384$	−2.60929	−0.133155
$385$	2.34932	0.119732
$386$	−6.75035	−0.343584
$387$	3.25458	0.165440
$388$	−11.8638	−0.602293
$389$	−5.39645	−0.273611	−0.136805	−	0.990598i	$-0.543684\pi$
$389$	−5.39645	−0.273611	−0.136805	+	0.990598i	$0.543684\pi$
$390$	−7.41522	−0.375484
$391$	−5.54898	−0.280624
$392$	−5.18032	−0.261646
$393$	2.60929	0.131621
$394$	−8.50166	−0.428307
$395$	−7.72551	−0.388712
$396$	−3.36947	−0.169322
$397$	−1.39104	−0.0698145	−0.0349073	−	0.999391i	$-0.511114\pi$
$397$	−1.39104	−0.0698145	−0.0349073	+	0.999391i	$0.511114\pi$
$398$	19.1622	0.960515
$399$	11.5189	0.576664
$400$	−1.12519	−0.0562594
$401$	−9.69422	−0.484106	−0.242053	−	0.970263i	$-0.577821\pi$
$401$	−9.69422	−0.484106	−0.242053	+	0.970263i	$0.577821\pi$
$402$	−15.5537	−0.775747
$403$	0.0138063	0.000687739 0
$404$	−3.32813	−0.165581
$405$	−11.6558	−0.579181
$406$	3.52758	0.175071
$407$	−0.173889	−0.00861938
$408$	14.4789	0.716813
$409$	−22.7002	−1.12245	−0.561227	−	0.827662i	$-0.689670\pi$
$409$	−22.7002	−1.12245	−0.561227	+	0.827662i	$0.689670\pi$
$410$	1.91395	0.0945235
$411$	−55.3715	−2.73127
$412$	11.1799	0.550795
$413$	7.92873	0.390147
$414$	3.80840	0.187173
$415$	17.4339	0.855794
$416$	1.44370	0.0707831
$417$	−42.5644	−2.08439
$418$	−2.89540	−0.141619
$419$	−16.0169	−0.782475	−0.391237	−	0.920290i	$-0.627953\pi$
$419$	−16.0169	−0.782475	−0.391237	+	0.920290i	$0.627953\pi$
$420$	6.92859	0.338081
$421$	−14.1655	−0.690386	−0.345193	−	0.938532i	$-0.612187\pi$
$421$	−14.1655	−0.690386	−0.345193	+	0.938532i	$0.612187\pi$
$422$	3.60438	0.175458
$423$	1.51619	0.0737197
$424$	−8.43975	−0.409870
$425$	6.24365	0.302862
$426$	−26.2727	−1.27292
$427$	4.30078	0.208130
$428$	−15.5851	−0.753334
$429$	3.33287	0.160912
$430$	1.68220	0.0811230
$431$	−1.15372	−0.0555726	−0.0277863	−	0.999614i	$-0.508846\pi$
$431$	−1.15372	−0.0555726	−0.0277863	+	0.999614i	$0.508846\pi$
$432$	−2.10935	−0.101486
$433$	33.2565	1.59821	0.799103	−	0.601195i	$-0.205308\pi$
$433$	33.2565	1.59821	0.799103	+	0.601195i	$0.205308\pi$
$434$	−0.0129002	−0.000619230 0
$435$	13.4316	0.643996
$436$	−14.2870	−0.684223
$437$	3.27258	0.156549
$438$	3.25720	0.155635
$439$	−25.8103	−1.23186	−0.615930	−	0.787801i	$-0.711219\pi$
$439$	−25.8103	−1.23186	−0.615930	+	0.787801i	$0.711219\pi$
$440$	−1.74159	−0.0830268
$441$	−19.7287	−0.939464
$442$	−8.01106	−0.381047
$443$	29.3389	1.39393	0.696966	−	0.717104i	$-0.254533\pi$
$443$	29.3389	1.39393	0.696966	+	0.717104i	$0.254533\pi$
$444$	−0.512833	−0.0243380
$445$	−23.7255	−1.12470
$446$	−24.8829	−1.17824
$447$	−28.0127	−1.32495
$448$	−1.34895	−0.0637321
$449$	−35.4152	−1.67134	−0.835672	−	0.549229i	$-0.814922\pi$
$449$	−35.4152	−1.67134	−0.835672	+	0.549229i	$0.814922\pi$
$450$	−4.28516	−0.202005
$451$	−0.860252	−0.0405077
$452$	19.5707	0.920528
$453$	37.1227	1.74418
$454$	−21.3260	−1.00088
$455$	−3.83353	−0.179719
$456$	−8.53910	−0.399880
$457$	23.1647	1.08360	0.541799	−	0.840508i	$-0.317743\pi$
$457$	23.1647	1.08360	0.541799	+	0.840508i	$0.317743\pi$
$458$	−13.0327	−0.608980
$459$	11.7047	0.546330
$460$	1.96845	0.0917797
$461$	−29.7400	−1.38513	−0.692564	−	0.721357i	$-0.743519\pi$
$461$	−29.7400	−1.38513	−0.692564	+	0.721357i	$0.743519\pi$
$462$	−3.11415	−0.144883
$463$	−19.1384	−0.889438	−0.444719	−	0.895670i	$-0.646696\pi$
$463$	−19.1384	−0.889438	−0.444719	+	0.895670i	$0.646696\pi$
$464$	−2.61505	−0.121401
$465$	−0.0491188	−0.00227783
$466$	8.14547	0.377332
$467$	15.0273	0.695380	0.347690	−	0.937609i	$-0.386966\pi$
$467$	15.0273	0.695380	0.347690	+	0.937609i	$0.386966\pi$
$468$	5.49818	0.254153
$469$	−8.04096	−0.371297
$470$	0.783676	0.0361483
$471$	44.8140	2.06492
$472$	−5.87768	−0.270542
$473$	−0.756088	−0.0347650
$474$	10.2406	0.470365
$475$	−3.68226	−0.168954
$476$	7.48533	0.343089
$477$	−32.1419	−1.47168
$478$	2.17004	0.0992555
$479$	13.3169	0.608466	0.304233	−	0.952598i	$-0.401600\pi$
$479$	13.3169	0.608466	0.304233	+	0.952598i	$0.401600\pi$
$480$	−5.13627	−0.234438
$481$	0.283746	0.0129377
$482$	−0.678804	−0.0309187
$483$	3.51981	0.160157
$484$	−10.2172	−0.464419
$485$	−23.3533	−1.06042
$486$	21.7784	0.987889
$487$	−24.5091	−1.11062	−0.555308	−	0.831645i	$-0.687399\pi$
$487$	−24.5091	−1.11062	−0.555308	+	0.831645i	$0.687399\pi$
$488$	−3.18824	−0.144325
$489$	66.2810	2.99733
$490$	−10.1972	−0.460664
$491$	15.7221	0.709528	0.354764	−	0.934956i	$-0.384561\pi$
$491$	15.7221	0.709528	0.354764	+	0.934956i	$0.384561\pi$
$492$	−2.53705	−0.114379
$493$	14.5109	0.653537
$494$	4.72461	0.212570
$495$	−6.63265	−0.298115
$496$	0.00956313	0.000429397 0
$497$	−13.5825	−0.609257
$498$	−23.1095	−1.03556
$499$	22.6939	1.01592	0.507959	−	0.861381i	$-0.330400\pi$
$499$	22.6939	1.01592	0.507959	+	0.861381i	$0.330400\pi$
$500$	−12.0572	−0.539212
$501$	−45.8660	−2.04914
$502$	6.18774	0.276172
$503$	19.4711	0.868172	0.434086	−	0.900871i	$-0.357071\pi$
$503$	19.4711	0.868172	0.434086	+	0.900871i	$0.357071\pi$
$504$	−5.13735	−0.228836
$505$	−6.55127	−0.291528
$506$	−0.884748	−0.0393318
$507$	28.4823	1.26494
$508$	14.0421	0.623016
$509$	30.0380	1.33141	0.665705	−	0.746215i	$-0.268131\pi$
$509$	30.0380	1.33141	0.665705	+	0.746215i	$0.268131\pi$
$510$	28.5011	1.26205
$511$	1.68391	0.0744918
$512$	1.00000	0.0441942
$513$	−6.90300	−0.304775
$514$	28.0117	1.23555
$515$	22.0072	0.969751
$516$	−2.22985	−0.0981636
$517$	−0.352233	−0.0154912
$518$	−0.265125	−0.0116489
$519$	62.2459	2.73229
$520$	2.84185	0.124624
$521$	35.9980	1.57710	0.788551	−	0.614970i	$-0.210832\pi$
$521$	35.9980	1.57710	0.788551	+	0.614970i	$0.210832\pi$
$522$	−9.95916	−0.435901
$523$	31.9049	1.39510	0.697552	−	0.716535i	$-0.254273\pi$
$523$	31.9049	1.39510	0.697552	+	0.716535i	$0.254273\pi$
$524$	−1.00000	−0.0436852
$525$	−3.96045	−0.172848
$526$	−21.4613	−0.935756
$527$	−0.0530656	−0.00231158
$528$	2.30856	0.100467
$529$	1.00000	0.0434783
$530$	−16.6133	−0.721634
$531$	−22.3846	−0.971407
$532$	−4.41455	−0.191395
$533$	1.40373	0.0608022
$534$	31.4494	1.36095
$535$	−30.6786	−1.32635
$536$	5.96088	0.257471
$537$	13.6579	0.589381
$538$	−16.3066	−0.703027
$539$	4.58328	0.197416
$540$	−4.15215	−0.178680
$541$	10.7489	0.462130	0.231065	−	0.972938i	$-0.425779\pi$
$541$	10.7489	0.462130	0.231065	+	0.972938i	$0.425779\pi$
$542$	−17.8805	−0.768033
$543$	−13.9738	−0.599672
$544$	−5.54898	−0.237911
$545$	−28.1233	−1.20467
$546$	5.08155	0.217470
$547$	22.1144	0.945541	0.472771	−	0.881185i	$-0.343254\pi$
$547$	22.1144	0.945541	0.472771	+	0.881185i	$0.343254\pi$
$548$	21.2209	0.906512
$549$	−12.1421	−0.518211
$550$	0.995507	0.0424486
$551$	−8.55795	−0.364581
$552$	−2.60929	−0.111059
$553$	5.29418	0.225131
$554$	27.5343	1.16982
$555$	−1.00949	−0.0428504
$556$	16.3126	0.691809
$557$	−37.4829	−1.58820	−0.794100	−	0.607787i	$-0.792058\pi$
$557$	−37.4829	−1.58820	−0.794100	+	0.607787i	$0.792058\pi$
$558$	0.0364202	0.00154179
$559$	1.23376	0.0521823
$560$	−2.65535	−0.112209
$561$	−12.8102	−0.540846
$562$	−12.3493	−0.520923
$563$	−10.4092	−0.438694	−0.219347	−	0.975647i	$-0.570393\pi$
$563$	−10.4092	−0.438694	−0.219347	+	0.975647i	$0.570393\pi$
$564$	−1.03880	−0.0437415
$565$	38.5240	1.62072
$566$	−7.44523	−0.312946
$567$	7.98755	0.335446
$568$	10.0689	0.422481
$569$	−6.78514	−0.284448	−0.142224	−	0.989835i	$-0.545425\pi$
$569$	−6.78514	−0.284448	−0.142224	+	0.989835i	$0.545425\pi$
$570$	−16.8088	−0.704044
$571$	21.6027	0.904043	0.452022	−	0.892007i	$-0.350703\pi$
$571$	21.6027	0.904043	0.452022	+	0.892007i	$0.350703\pi$
$572$	−1.27731	−0.0534070
$573$	55.6573	2.32512
$574$	−1.31161	−0.0547454
$575$	−1.12519	−0.0469236
$576$	3.80840	0.158683
$577$	34.0725	1.41846	0.709228	−	0.704979i	$-0.249044\pi$
$577$	34.0725	1.41846	0.709228	+	0.704979i	$0.249044\pi$
$578$	13.7912	0.573640
$579$	17.6136	0.731997
$580$	−5.14761	−0.213743
$581$	−11.9472	−0.495652
$582$	30.9561	1.28317
$583$	7.46705	0.309253
$584$	−1.24831	−0.0516553
$585$	10.8229	0.447472
$586$	15.0365	0.621152
$587$	−12.5422	−0.517674	−0.258837	−	0.965921i	$-0.583339\pi$
$587$	−12.5422	−0.517674	−0.258837	+	0.965921i	$0.583339\pi$
$588$	13.5170	0.557430
$589$	0.0312961	0.00128953
$590$	−11.5700	−0.476327
$591$	22.1833	0.912499
$592$	0.196541	0.00807779
$593$	16.1365	0.662645	0.331323	−	0.943518i	$-0.392505\pi$
$593$	16.1365	0.662645	0.331323	+	0.943518i	$0.392505\pi$
$594$	1.86624	0.0765728
$595$	14.7345	0.604056
$596$	10.7357	0.439753
$597$	−49.9998	−2.04635
$598$	1.44370	0.0590372
$599$	−28.5994	−1.16854	−0.584271	−	0.811559i	$-0.698619\pi$
$599$	−28.5994	−1.16854	−0.584271	+	0.811559i	$0.698619\pi$
$600$	2.93594	0.119859
$601$	24.9348	1.01711	0.508556	−	0.861029i	$-0.330179\pi$
$601$	24.9348	1.01711	0.508556	+	0.861029i	$0.330179\pi$
$602$	−1.15279	−0.0469842
$603$	22.7014	0.924473
$604$	−14.2271	−0.578893
$605$	−20.1121	−0.817674
$606$	8.68405	0.352766
$607$	−43.0144	−1.74590	−0.872951	−	0.487808i	$-0.837797\pi$
$607$	−43.0144	−1.74590	−0.872951	+	0.487808i	$0.837797\pi$
$608$	3.27258	0.132720
$609$	−9.20449	−0.372985
$610$	−6.27590	−0.254104
$611$	0.574761	0.0232523
$612$	−21.1327	−0.854241
$613$	−31.7872	−1.28387	−0.641936	−	0.766759i	$-0.721868\pi$
$613$	−31.7872	−1.28387	−0.641936	+	0.766759i	$0.721868\pi$
$614$	−18.1330	−0.731790
$615$	−4.99406	−0.201380
$616$	1.19348	0.0480868
$617$	−10.8386	−0.436345	−0.218173	−	0.975910i	$-0.570010\pi$
$617$	−10.8386	−0.436345	−0.218173	+	0.975910i	$0.570010\pi$
$618$	−29.1717	−1.17346
$619$	14.8769	0.597951	0.298976	−	0.954261i	$-0.403355\pi$
$619$	14.8769	0.597951	0.298976	+	0.954261i	$0.403355\pi$
$620$	0.0188246	0.000756013 0
$621$	−2.10935	−0.0846452
$622$	16.2125	0.650060
$623$	16.2587	0.651393
$624$	−3.76703	−0.150802
$625$	−18.1080	−0.724320
$626$	−17.4957	−0.699270
$627$	7.55495	0.301716
$628$	−17.1748	−0.685348
$629$	−1.09060	−0.0434852
$630$	−10.1126	−0.402898
$631$	27.3244	1.08777	0.543884	−	0.839161i	$-0.316953\pi$
$631$	27.3244	1.08777	0.543884	+	0.839161i	$0.316953\pi$
$632$	−3.92466	−0.156114
$633$	−9.40486	−0.373810
$634$	31.0367	1.23263
$635$	27.6411	1.09691
$636$	22.0218	0.873219
$637$	−7.47882	−0.296322
$638$	2.31366	0.0915987
$639$	38.3464	1.51696
$640$	1.96845	0.0778100
$641$	−28.0509	−1.10794	−0.553971	−	0.832536i	$-0.686888\pi$
$641$	−28.0509	−1.10794	−0.553971	+	0.832536i	$0.686888\pi$
$642$	40.6661	1.60496
$643$	22.9437	0.904813	0.452406	−	0.891812i	$-0.350566\pi$
$643$	22.9437	0.904813	0.452406	+	0.891812i	$0.350566\pi$
$644$	−1.34895	−0.0531562
$645$	−4.38935	−0.172831
$646$	−18.1595	−0.714475
$647$	−2.91384	−0.114555	−0.0572774	−	0.998358i	$-0.518242\pi$
$647$	−2.91384	−0.114555	−0.0572774	+	0.998358i	$0.518242\pi$
$648$	−5.92129	−0.232610
$649$	5.20027	0.204128
$650$	−1.62443	−0.0637155
$651$	0.0336604	0.00131926
$652$	−25.4019	−0.994816
$653$	4.64981	0.181961	0.0909806	−	0.995853i	$-0.471000\pi$
$653$	4.64981	0.181961	0.0909806	+	0.995853i	$0.471000\pi$
$654$	37.2789	1.45772
$655$	−1.96845	−0.0769139
$656$	0.972313	0.0379625
$657$	−4.75405	−0.185473
$658$	−0.537042	−0.0209361
$659$	19.4421	0.757356	0.378678	−	0.925529i	$-0.376379\pi$
$659$	19.4421	0.757356	0.378678	+	0.925529i	$0.376379\pi$
$660$	4.54430	0.176887
$661$	−7.17810	−0.279196	−0.139598	−	0.990208i	$-0.544581\pi$
$661$	−7.17810	−0.279196	−0.139598	+	0.990208i	$0.544581\pi$
$662$	−27.5601	−1.07116
$663$	20.9032	0.811812
$664$	8.85662	0.343704
$665$	−8.68985	−0.336978
$666$	0.748507	0.0290041
$667$	−2.61505	−0.101255
$668$	17.5780	0.680112
$669$	64.9266	2.51021
$670$	11.7337	0.453313
$671$	2.82078	0.108895
$672$	3.51981	0.135780
$673$	−28.9795	−1.11708	−0.558539	−	0.829478i	$-0.688638\pi$
$673$	−28.9795	−1.11708	−0.558539	+	0.829478i	$0.688638\pi$
$674$	−11.8872	−0.457878
$675$	2.37341	0.0913527
$676$	−10.9157	−0.419836
$677$	17.2100	0.661433	0.330716	−	0.943730i	$-0.392710\pi$
$677$	17.2100	0.661433	0.330716	+	0.943730i	$0.392710\pi$
$678$	−51.0657	−1.96116
$679$	16.0037	0.614166
$680$	−10.9229	−0.418875
$681$	55.6457	2.13235
$682$	−0.00846095	−0.000323987 0
$683$	11.1734	0.427539	0.213770	−	0.976884i	$-0.431426\pi$
$683$	11.1734	0.427539	0.213770	+	0.976884i	$0.431426\pi$
$684$	12.4633	0.476545
$685$	41.7724	1.59604
$686$	16.4307	0.627327
$687$	34.0062	1.29742
$688$	0.854580	0.0325806
$689$	−12.1844	−0.464190
$690$	−5.13627	−0.195534
$691$	−45.5960	−1.73455	−0.867277	−	0.497826i	$-0.834132\pi$
$691$	−45.5960	−1.73455	−0.867277	+	0.497826i	$0.834132\pi$
$692$	−23.8555	−0.906850
$693$	4.54526	0.172660
$694$	−33.0355	−1.25401
$695$	32.1106	1.21803
$696$	6.82343	0.258641
$697$	−5.39535	−0.204364
$698$	−14.0113	−0.530336
$699$	−21.2539	−0.803897
$700$	1.51783	0.0573685
$701$	8.92964	0.337268	0.168634	−	0.985679i	$-0.446064\pi$
$701$	8.92964	0.337268	0.168634	+	0.985679i	$0.446064\pi$
$702$	−3.04526	−0.114936
$703$	0.643196	0.0242586
$704$	−0.884748	−0.0333452
$705$	−2.04484	−0.0770130
$706$	−26.7435	−1.00650
$707$	4.48949	0.168845
$708$	15.3366	0.576384
$709$	18.9861	0.713037	0.356518	−	0.934288i	$-0.383964\pi$
$709$	18.9861	0.713037	0.356518	+	0.934288i	$0.383964\pi$
$710$	19.8202	0.743837
$711$	−14.9467	−0.560543
$712$	−12.0529	−0.451700
$713$	0.00956313	0.000358142 0
$714$	−19.5314	−0.730944
$715$	−2.51432	−0.0940304
$716$	−5.23433	−0.195616
$717$	−5.66228	−0.211462
$718$	−21.3220	−0.795729
$719$	29.6193	1.10461	0.552307	−	0.833641i	$-0.313748\pi$
$719$	29.6193	1.10461	0.552307	+	0.833641i	$0.313748\pi$
$720$	7.49666	0.279384
$721$	−15.0812	−0.561653
$722$	−8.29025	−0.308531
$723$	1.77120	0.0658715
$724$	5.35539	0.199032
$725$	2.94242	0.109279
$726$	26.6597	0.989434
$727$	1.33421	0.0494832	0.0247416	−	0.999694i	$-0.492124\pi$
$727$	1.33421	0.0494832	0.0247416	+	0.999694i	$0.492124\pi$
$728$	−1.94748	−0.0721785
$729$	−39.0624	−1.44675
$730$	−2.45724	−0.0909464
$731$	−4.74205	−0.175391
$732$	8.31903	0.307480
$733$	26.4335	0.976342	0.488171	−	0.872748i	$-0.337664\pi$
$733$	26.4335	0.976342	0.488171	+	0.872748i	$0.337664\pi$
$734$	−0.122241	−0.00451200
$735$	26.6075	0.981434
$736$	1.00000	0.0368605
$737$	−5.27388	−0.194266
$738$	3.70296	0.136308
$739$	8.91917	0.328097	0.164049	−	0.986452i	$-0.447545\pi$
$739$	8.91917	0.328097	0.164049	+	0.986452i	$0.447545\pi$
$740$	0.386882	0.0142221
$741$	−12.3279	−0.452876
$742$	11.3848	0.417950
$743$	53.5061	1.96295	0.981475	−	0.191592i	$-0.0613651\pi$
$743$	53.5061	1.96295	0.981475	+	0.191592i	$0.0613651\pi$
$744$	−0.0249530	−0.000914820 0
$745$	21.1328	0.774246
$746$	14.6001	0.534548
$747$	33.7295	1.23410
$748$	4.90945	0.179507
$749$	21.0236	0.768185
$750$	31.4606	1.14878
$751$	25.7268	0.938785	0.469393	−	0.882990i	$-0.344473\pi$
$751$	25.7268	0.938785	0.469393	+	0.882990i	$0.344473\pi$
$752$	0.398117	0.0145178
$753$	−16.1456	−0.588379
$754$	−3.77534	−0.137490
$755$	−28.0054	−1.01922
$756$	2.84541	0.103487
$757$	29.6510	1.07769	0.538843	−	0.842406i	$-0.318862\pi$
$757$	29.6510	1.07769	0.538843	+	0.842406i	$0.318862\pi$
$758$	−27.3526	−0.993492
$759$	2.30856	0.0837956
$760$	6.44192	0.233673
$761$	23.2164	0.841592	0.420796	−	0.907155i	$-0.361751\pi$
$761$	23.2164	0.841592	0.420796	+	0.907155i	$0.361751\pi$
$762$	−36.6398	−1.32732
$763$	19.2725	0.697711
$764$	−21.3304	−0.771708
$765$	−41.5988	−1.50401
$766$	−11.0961	−0.400920
$767$	−8.48560	−0.306397
$768$	−2.60929	−0.0941547
$769$	−44.0445	−1.58828	−0.794142	−	0.607732i	$-0.792079\pi$
$769$	−44.0445	−1.58828	−0.794142	+	0.607732i	$0.792079\pi$
$770$	2.34932	0.0846636
$771$	−73.0908	−2.63230
$772$	−6.75035	−0.242950
$773$	12.4498	0.447788	0.223894	−	0.974614i	$-0.428123\pi$
$773$	12.4498	0.447788	0.223894	+	0.974614i	$0.428123\pi$
$774$	3.25458	0.116984
$775$	−0.0107603	−0.000386522 0
$776$	−11.8638	−0.425885
$777$	0.691788	0.0248178
$778$	−5.39645	−0.193472
$779$	3.18197	0.114006
$780$	−7.41522	−0.265508
$781$	−8.90843	−0.318769
$782$	−5.54898	−0.198431
$783$	5.51605	0.197128
$784$	−5.18032	−0.185012
$785$	−33.8078	−1.20665
$786$	2.60929	0.0930703
$787$	24.7208	0.881200	0.440600	−	0.897703i	$-0.354766\pi$
$787$	24.7208	0.881200	0.440600	+	0.897703i	$0.354766\pi$
$788$	−8.50166	−0.302859
$789$	55.9987	1.99361
$790$	−7.72551	−0.274861
$791$	−26.4000	−0.938675
$792$	−3.36947	−0.119729
$793$	−4.60285	−0.163452
$794$	−1.39104	−0.0493663
$795$	43.3488	1.53742
$796$	19.1622	0.679186
$797$	34.7405	1.23057	0.615285	−	0.788305i	$-0.289041\pi$
$797$	34.7405	1.23057	0.615285	+	0.788305i	$0.289041\pi$
$798$	11.5189	0.407763
$799$	−2.20915	−0.0781540
$800$	−1.12519	−0.0397814
$801$	−45.9021	−1.62187
$802$	−9.69422	−0.342315
$803$	1.10444	0.0389748
$804$	−15.5537	−0.548536
$805$	−2.65535	−0.0935889
$806$	0.0138063	0.000486305 0
$807$	42.5486	1.49778
$808$	−3.32813	−0.117083
$809$	−9.35337	−0.328847	−0.164423	−	0.986390i	$-0.552576\pi$
$809$	−9.35337	−0.328847	−0.164423	+	0.986390i	$0.552576\pi$
$810$	−11.6558	−0.409543
$811$	2.71430	0.0953120	0.0476560	−	0.998864i	$-0.484825\pi$
$811$	2.71430	0.0953120	0.0476560	+	0.998864i	$0.484825\pi$
$812$	3.52758	0.123794
$813$	46.6554	1.63628
$814$	−0.173889	−0.00609482
$815$	−50.0025	−1.75151
$816$	14.4789	0.506863
$817$	2.79668	0.0978434
$818$	−22.7002	−0.793695
$819$	−7.41679	−0.259164
$820$	1.91395	0.0668382
$821$	−26.6800	−0.931140	−0.465570	−	0.885011i	$-0.654151\pi$
$821$	−26.6800	−0.931140	−0.465570	+	0.885011i	$0.654151\pi$
$822$	−55.3715	−1.93130
$823$	22.8462	0.796370	0.398185	−	0.917305i	$-0.369640\pi$
$823$	22.8462	0.796370	0.398185	+	0.917305i	$0.369640\pi$
$824$	11.1799	0.389471
$825$	−2.59757	−0.0904357
$826$	7.92873	0.275876
$827$	−31.2978	−1.08833	−0.544165	−	0.838978i	$-0.683153\pi$
$827$	−31.2978	−1.08833	−0.544165	+	0.838978i	$0.683153\pi$
$828$	3.80840	0.132351
$829$	32.9132	1.14312	0.571561	−	0.820560i	$-0.306338\pi$
$829$	32.9132	1.14312	0.571561	+	0.820560i	$0.306338\pi$
$830$	17.4339	0.605138
$831$	−71.8451	−2.49228
$832$	1.44370	0.0500512
$833$	28.7455	0.995974
$834$	−42.5644	−1.47388
$835$	34.6014	1.19743
$836$	−2.89540	−0.100140
$837$	−0.0201720	−0.000697245 0
$838$	−16.0169	−0.553293
$839$	48.5591	1.67645	0.838223	−	0.545327i	$-0.183595\pi$
$839$	48.5591	1.67645	0.838223	+	0.545327i	$0.183595\pi$
$840$	6.92859	0.239059
$841$	−22.1615	−0.764190
$842$	−14.1655	−0.488176
$843$	32.2229	1.10982
$844$	3.60438	0.124068
$845$	−21.4871	−0.739180
$846$	1.51619	0.0521277
$847$	13.7826	0.473574
$848$	−8.43975	−0.289822
$849$	19.4268	0.666725
$850$	6.24365	0.214155
$851$	0.196541	0.00673735
$852$	−26.2727	−0.900087
$853$	25.3157	0.866793	0.433397	−	0.901203i	$-0.357315\pi$
$853$	25.3157	0.866793	0.433397	+	0.901203i	$0.357315\pi$
$854$	4.30078	0.147170
$855$	24.5334	0.839024
$856$	−15.5851	−0.532688
$857$	−14.6324	−0.499833	−0.249917	−	0.968267i	$-0.580403\pi$
$857$	−14.6324	−0.499833	−0.249917	+	0.968267i	$0.580403\pi$
$858$	3.33287	0.113782
$859$	18.2949	0.624214	0.312107	−	0.950047i	$-0.398965\pi$
$859$	18.2949	0.624214	0.312107	+	0.950047i	$0.398965\pi$
$860$	1.68220	0.0573626
$861$	3.42236	0.116634
$862$	−1.15372	−0.0392958
$863$	−30.3293	−1.03242	−0.516210	−	0.856462i	$-0.672658\pi$
$863$	−30.3293	−1.03242	−0.516210	+	0.856462i	$0.672658\pi$
$864$	−2.10935	−0.0717615
$865$	−46.9584	−1.59663
$866$	33.2565	1.13010
$867$	−35.9853	−1.22213
$868$	−0.0129002	−0.000437862 0
$869$	3.47233	0.117791
$870$	13.4316	0.455374
$871$	8.60572	0.291594
$872$	−14.2870	−0.483818
$873$	−45.1821	−1.52918
$874$	3.27258	0.110697
$875$	16.2645	0.549842
$876$	3.25720	0.110051
$877$	46.9002	1.58371	0.791854	−	0.610711i	$-0.209116\pi$
$877$	46.9002	1.58371	0.791854	+	0.610711i	$0.209116\pi$
$878$	−25.8103	−0.871056
$879$	−39.2346	−1.32335
$880$	−1.74159	−0.0587088
$881$	57.5304	1.93825	0.969125	−	0.246571i	$-0.0793040\pi$
$881$	57.5304	1.93825	0.969125	+	0.246571i	$0.0793040\pi$
$882$	−19.7287	−0.664301
$883$	13.6267	0.458573	0.229287	−	0.973359i	$-0.426361\pi$
$883$	13.6267	0.458573	0.229287	+	0.973359i	$0.426361\pi$
$884$	−8.01106	−0.269441
$885$	30.1894	1.01480
$886$	29.3389	0.985659
$887$	0.478063	0.0160518	0.00802589	−	0.999968i	$-0.497445\pi$
$887$	0.478063	0.0160518	0.00802589	+	0.999968i	$0.497445\pi$
$888$	−0.512833	−0.0172096
$889$	−18.9421	−0.635297
$890$	−23.7255	−0.795280
$891$	5.23885	0.175508
$892$	−24.8829	−0.833140
$893$	1.30287	0.0435989
$894$	−28.0127	−0.936884
$895$	−10.3035	−0.344409
$896$	−1.34895	−0.0450654
$897$	−3.76703	−0.125777
$898$	−35.4152	−1.18182
$899$	−0.0250081	−0.000834066 0
$900$	−4.28516	−0.142839
$901$	46.8320	1.56020
$902$	−0.860252	−0.0286433
$903$	3.00796	0.100099
$904$	19.5707	0.650912
$905$	10.5418	0.350423
$906$	37.1227	1.23332
$907$	−18.8090	−0.624541	−0.312271	−	0.949993i	$-0.601090\pi$
$907$	−18.8090	−0.624541	−0.312271	+	0.949993i	$0.601090\pi$
$908$	−21.3260	−0.707728
$909$	−12.6748	−0.420398
$910$	−3.83353	−0.127080
$911$	0.0873908	0.00289539	0.00144769	−	0.999999i	$-0.499539\pi$
$911$	0.0873908	0.00289539	0.00144769	+	0.999999i	$0.499539\pi$
$912$	−8.53910	−0.282758
$913$	−7.83588	−0.259330
$914$	23.1647	0.766220
$915$	16.3756	0.541362
$916$	−13.0327	−0.430614
$917$	1.34895	0.0445464
$918$	11.7047	0.386314
$919$	−14.6206	−0.482289	−0.241145	−	0.970489i	$-0.577523\pi$
$919$	−14.6206	−0.482289	−0.241145	+	0.970489i	$0.577523\pi$
$920$	1.96845	0.0648980
$921$	47.3144	1.55906
$922$	−29.7400	−0.979433
$923$	14.5364	0.478473
$924$	−3.11415	−0.102448
$925$	−0.221146	−0.00727123
$926$	−19.1384	−0.628927
$927$	42.5776	1.39843
$928$	−2.61505	−0.0858433
$929$	−49.4323	−1.62182	−0.810911	−	0.585170i	$-0.801028\pi$
$929$	−49.4323	−1.62182	−0.810911	+	0.585170i	$0.801028\pi$
$930$	−0.0491188	−0.00161067
$931$	−16.9530	−0.555612
$932$	8.14547	0.266814
$933$	−42.3030	−1.38494
$934$	15.0273	0.491708
$935$	9.66403	0.316048
$936$	5.49818	0.179714
$937$	−39.6153	−1.29418	−0.647088	−	0.762415i	$-0.724014\pi$
$937$	−39.6153	−1.29418	−0.647088	+	0.762415i	$0.724014\pi$
$938$	−8.04096	−0.262547
$939$	45.6515	1.48978
$940$	0.783676	0.0255607
$941$	−12.9518	−0.422215	−0.211108	−	0.977463i	$-0.567707\pi$
$941$	−12.9518	−0.422215	−0.211108	+	0.977463i	$0.567707\pi$
$942$	44.8140	1.46012
$943$	0.972313	0.0316629
$944$	−5.87768	−0.191302
$945$	5.60107	0.182203
$946$	−0.756088	−0.0245825
$947$	26.8177	0.871457	0.435729	−	0.900078i	$-0.356491\pi$
$947$	26.8177	0.871457	0.435729	+	0.900078i	$0.356491\pi$
$948$	10.2406	0.332598
$949$	−1.80218	−0.0585012
$950$	−3.68226	−0.119468
$951$	−80.9839	−2.62608
$952$	7.48533	0.242601
$953$	27.7929	0.900299	0.450150	−	0.892953i	$-0.351371\pi$
$953$	27.7929	0.900299	0.450150	+	0.892953i	$0.351371\pi$
$954$	−32.1419	−1.04063
$955$	−41.9880	−1.35870
$956$	2.17004	0.0701842
$957$	−6.03701	−0.195149
$958$	13.3169	0.430251
$959$	−28.6260	−0.924382
$960$	−5.13627	−0.165772
$961$	−30.9999	−0.999997
$962$	0.283746	0.00914834
$963$	−59.3543	−1.91267
$964$	−0.678804	−0.0218628
$965$	−13.2878	−0.427748
$966$	3.51981	0.113248
$967$	−6.44774	−0.207345	−0.103673	−	0.994611i	$-0.533059\pi$
$967$	−6.44774	−0.207345	−0.103673	+	0.994611i	$0.533059\pi$
$968$	−10.2172	−0.328394
$969$	47.3833	1.52217
$970$	−23.3533	−0.749830
$971$	−13.6641	−0.438502	−0.219251	−	0.975669i	$-0.570361\pi$
$971$	−13.6641	−0.438502	−0.219251	+	0.975669i	$0.570361\pi$
$972$	21.7784	0.698543
$973$	−22.0050	−0.705447
$974$	−24.5091	−0.785323
$975$	4.23862	0.135744
$976$	−3.18824	−0.102053
$977$	−53.6395	−1.71608	−0.858041	−	0.513582i	$-0.828318\pi$
$977$	−53.6395	−1.71608	−0.858041	+	0.513582i	$0.828318\pi$
$978$	66.2810	2.11943
$979$	10.6637	0.340814
$980$	−10.1972	−0.325739
$981$	−54.4105	−1.73719
$982$	15.7221	0.501712
$983$	−8.72323	−0.278228	−0.139114	−	0.990276i	$-0.544425\pi$
$983$	−8.72323	−0.278228	−0.139114	+	0.990276i	$0.544425\pi$
$984$	−2.53705	−0.0808781
$985$	−16.7351	−0.533225
$986$	14.5109	0.462121
$987$	1.40130	0.0446038
$988$	4.72461	0.150310
$989$	0.854580	0.0271741
$990$	−6.63265	−0.210799
$991$	−51.0191	−1.62067	−0.810337	−	0.585964i	$-0.800716\pi$
$991$	−51.0191	−1.62067	−0.810337	+	0.585964i	$0.800716\pi$
$992$	0.00956313	0.000303630 0
$993$	71.9124	2.28207
$994$	−13.5825	−0.430810
$995$	37.7199	1.19580
$996$	−23.1095	−0.732253
$997$	56.1019	1.77676	0.888382	−	0.459105i	$-0.151830\pi$
$997$	56.1019	1.77676	0.888382	+	0.459105i	$0.151830\pi$
$998$	22.6939	0.718362
$999$	−0.414574	−0.0131165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.f.1.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.f.1.3	✓	20	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.60929 q^{3} +1.00000 q^{4} +1.96845 q^{5} -2.60929 q^{6} -1.34895 q^{7} +1.00000 q^{8} +3.80840 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.60929 q^{3} +1.00000 q^{4} +1.96845 q^{5} -2.60929 q^{6} -1.34895 q^{7} +1.00000 q^{8} +3.80840 q^{9} +1.96845 q^{10} -0.884748 q^{11} -2.60929 q^{12} +1.44370 q^{13} -1.34895 q^{14} -5.13627 q^{15} +1.00000 q^{16} -5.54898 q^{17} +3.80840 q^{18} +3.27258 q^{19} +1.96845 q^{20} +3.51981 q^{21} -0.884748 q^{22} +1.00000 q^{23} -2.60929 q^{24} -1.12519 q^{25} +1.44370 q^{26} -2.10935 q^{27} -1.34895 q^{28} -2.61505 q^{29} -5.13627 q^{30} +0.00956313 q^{31} +1.00000 q^{32} +2.30856 q^{33} -5.54898 q^{34} -2.65535 q^{35} +3.80840 q^{36} +0.196541 q^{37} +3.27258 q^{38} -3.76703 q^{39} +1.96845 q^{40} +0.972313 q^{41} +3.51981 q^{42} +0.854580 q^{43} -0.884748 q^{44} +7.49666 q^{45} +1.00000 q^{46} +0.398117 q^{47} -2.60929 q^{48} -5.18032 q^{49} -1.12519 q^{50} +14.4789 q^{51} +1.44370 q^{52} -8.43975 q^{53} -2.10935 q^{54} -1.74159 q^{55} -1.34895 q^{56} -8.53910 q^{57} -2.61505 q^{58} -5.87768 q^{59} -5.13627 q^{60} -3.18824 q^{61} +0.00956313 q^{62} -5.13735 q^{63} +1.00000 q^{64} +2.84185 q^{65} +2.30856 q^{66} +5.96088 q^{67} -5.54898 q^{68} -2.60929 q^{69} -2.65535 q^{70} +10.0689 q^{71} +3.80840 q^{72} -1.24831 q^{73} +0.196541 q^{74} +2.93594 q^{75} +3.27258 q^{76} +1.19348 q^{77} -3.76703 q^{78} -3.92466 q^{79} +1.96845 q^{80} -5.92129 q^{81} +0.972313 q^{82} +8.85662 q^{83} +3.51981 q^{84} -10.9229 q^{85} +0.854580 q^{86} +6.82343 q^{87} -0.884748 q^{88} -12.0529 q^{89} +7.49666 q^{90} -1.94748 q^{91} +1.00000 q^{92} -0.0249530 q^{93} +0.398117 q^{94} +6.44192 q^{95} -2.60929 q^{96} -11.8638 q^{97} -5.18032 q^{98} -3.36947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9} - 6 q^{10} - 3 q^{11} - 5 q^{12} - 13 q^{13} - 12 q^{14} - 10 q^{15} + 20 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} - 6 q^{20} - 8 q^{21} - 3 q^{22} + 20 q^{23} - 5 q^{24} - 14 q^{25} - 13 q^{26} - 5 q^{27} - 12 q^{28} - 27 q^{29} - 10 q^{30} - 27 q^{31} + 20 q^{32} - 12 q^{33} - 14 q^{34} - 23 q^{35} - q^{36} - 19 q^{37} - 21 q^{38} - 35 q^{39} - 6 q^{40} - 17 q^{41} - 8 q^{42} - 27 q^{43} - 3 q^{44} + 4 q^{45} + 20 q^{46} - 28 q^{47} - 5 q^{48} - 10 q^{49} - 14 q^{50} + 6 q^{51} - 13 q^{52} - 47 q^{53} - 5 q^{54} - 4 q^{55} - 12 q^{56} - 16 q^{57} - 27 q^{58} - 16 q^{59} - 10 q^{60} - 9 q^{61} - 27 q^{62} - 9 q^{63} + 20 q^{64} + 9 q^{65} - 12 q^{66} - 8 q^{67} - 14 q^{68} - 5 q^{69} - 23 q^{70} - 30 q^{71} - q^{72} - 26 q^{73} - 19 q^{74} - 18 q^{75} - 21 q^{76} - 50 q^{77} - 35 q^{78} - 35 q^{79} - 6 q^{80} - 60 q^{81} - 17 q^{82} + 2 q^{83} - 8 q^{84} - 62 q^{85} - 27 q^{86} + q^{87} - 3 q^{88} - 25 q^{89} + 4 q^{90} + 22 q^{91} + 20 q^{92} - 21 q^{93} - 28 q^{94} - 14 q^{95} - 5 q^{96} + 2 q^{97} - 10 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9 - 6 * q^10 - 3 * q^11 - 5 * q^12 - 13 * q^13 - 12 * q^14 - 10 * q^15 + 20 * q^16 - 14 * q^17 - q^18 - 21 * q^19 - 6 * q^20 - 8 * q^21 - 3 * q^22 + 20 * q^23 - 5 * q^24 - 14 * q^25 - 13 * q^26 - 5 * q^27 - 12 * q^28 - 27 * q^29 - 10 * q^30 - 27 * q^31 + 20 * q^32 - 12 * q^33 - 14 * q^34 - 23 * q^35 - q^36 - 19 * q^37 - 21 * q^38 - 35 * q^39 - 6 * q^40 - 17 * q^41 - 8 * q^42 - 27 * q^43 - 3 * q^44 + 4 * q^45 + 20 * q^46 - 28 * q^47 - 5 * q^48 - 10 * q^49 - 14 * q^50 + 6 * q^51 - 13 * q^52 - 47 * q^53 - 5 * q^54 - 4 * q^55 - 12 * q^56 - 16 * q^57 - 27 * q^58 - 16 * q^59 - 10 * q^60 - 9 * q^61 - 27 * q^62 - 9 * q^63 + 20 * q^64 + 9 * q^65 - 12 * q^66 - 8 * q^67 - 14 * q^68 - 5 * q^69 - 23 * q^70 - 30 * q^71 - q^72 - 26 * q^73 - 19 * q^74 - 18 * q^75 - 21 * q^76 - 50 * q^77 - 35 * q^78 - 35 * q^79 - 6 * q^80 - 60 * q^81 - 17 * q^82 + 2 * q^83 - 8 * q^84 - 62 * q^85 - 27 * q^86 + q^87 - 3 * q^88 - 25 * q^89 + 4 * q^90 + 22 * q^91 + 20 * q^92 - 21 * q^93 - 28 * q^94 - 14 * q^95 - 5 * q^96 + 2 * q^97 - 10 * q^98 - 5 * q^99

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