LMFDB - Embedded newform 5054.2.a.bj.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 15x^{7} + 40x^{6} + 81x^{5} - 162x^{4} - 205x^{3} + 204x^{2} + 210x + 1 $ x^9 - 3x^8 - 15x^7 + 40x^6 + 81x^5 - 162x^4 - 205x^3 + 204x^2 + 210x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.18756$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.18756 q^{3} +1.00000 q^{4} -0.616139 q^{5} +2.18756 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.78540 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.18756 q^{3} +1.00000 q^{4} -0.616139 q^{5} +2.18756 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.78540 q^{9} +0.616139 q^{10} +3.42998 q^{11} -2.18756 q^{12} -6.38112 q^{13} +1.00000 q^{14} +1.34784 q^{15} +1.00000 q^{16} +2.47999 q^{17} -1.78540 q^{18} -0.616139 q^{20} +2.18756 q^{21} -3.42998 q^{22} +2.70527 q^{23} +2.18756 q^{24} -4.62037 q^{25} +6.38112 q^{26} +2.65701 q^{27} -1.00000 q^{28} -6.00017 q^{29} -1.34784 q^{30} +7.72644 q^{31} -1.00000 q^{32} -7.50328 q^{33} -2.47999 q^{34} +0.616139 q^{35} +1.78540 q^{36} -4.26808 q^{37} +13.9591 q^{39} +0.616139 q^{40} +1.28851 q^{41} -2.18756 q^{42} -10.3584 q^{43} +3.42998 q^{44} -1.10005 q^{45} -2.70527 q^{46} +1.53750 q^{47} -2.18756 q^{48} +1.00000 q^{49} +4.62037 q^{50} -5.42512 q^{51} -6.38112 q^{52} +5.11208 q^{53} -2.65701 q^{54} -2.11335 q^{55} +1.00000 q^{56} +6.00017 q^{58} -12.7768 q^{59} +1.34784 q^{60} -5.54592 q^{61} -7.72644 q^{62} -1.78540 q^{63} +1.00000 q^{64} +3.93166 q^{65} +7.50328 q^{66} -4.16481 q^{67} +2.47999 q^{68} -5.91793 q^{69} -0.616139 q^{70} -0.0244707 q^{71} -1.78540 q^{72} +13.0675 q^{73} +4.26808 q^{74} +10.1073 q^{75} -3.42998 q^{77} -13.9591 q^{78} -2.96283 q^{79} -0.616139 q^{80} -11.1685 q^{81} -1.28851 q^{82} +12.9425 q^{83} +2.18756 q^{84} -1.52802 q^{85} +10.3584 q^{86} +13.1257 q^{87} -3.42998 q^{88} +12.4510 q^{89} +1.10005 q^{90} +6.38112 q^{91} +2.70527 q^{92} -16.9020 q^{93} -1.53750 q^{94} +2.18756 q^{96} +1.51714 q^{97} -1.00000 q^{98} +6.12389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} - 9 q^{8} + 12 q^{9}+O(q^{10}) $ 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 - 9 * q^8 + 12 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} - 9 q^{8} + 12 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} - 12 q^{13} + 9 q^{14} + 6 q^{15} + 9 q^{16} + 12 q^{17} - 12 q^{18} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 6 q^{23} + 3 q^{24} + 12 q^{26} - 24 q^{27} - 9 q^{28} + 6 q^{29} - 6 q^{30} - 9 q^{31} - 9 q^{32} + 3 q^{33} - 12 q^{34} - 3 q^{35} + 12 q^{36} - 9 q^{37} + 33 q^{39} - 3 q^{40} - 3 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 18 q^{45} - 6 q^{46} + 21 q^{47} - 3 q^{48} + 9 q^{49} - 39 q^{51} - 12 q^{52} + 24 q^{54} + 24 q^{55} + 9 q^{56} - 6 q^{58} + 9 q^{59} + 6 q^{60} + 6 q^{61} + 9 q^{62} - 12 q^{63} + 9 q^{64} + 3 q^{65} - 3 q^{66} - 27 q^{67} + 12 q^{68} - 6 q^{69} + 3 q^{70} - 9 q^{71} - 12 q^{72} + 51 q^{73} + 9 q^{74} + 3 q^{75} + 3 q^{77} - 33 q^{78} - 24 q^{79} + 3 q^{80} - 3 q^{81} + 3 q^{82} + 9 q^{83} + 3 q^{84} + 6 q^{85} - 21 q^{86} - 3 q^{87} + 3 q^{88} - 9 q^{89} - 18 q^{90} + 12 q^{91} + 6 q^{92} + 3 q^{93} - 21 q^{94} + 3 q^{96} + 12 q^{97} - 9 q^{98} - 15 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 - 9 * q^8 + 12 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 - 12 * q^13 + 9 * q^14 + 6 * q^15 + 9 * q^16 + 12 * q^17 - 12 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 6 * q^23 + 3 * q^24 + 12 * q^26 - 24 * q^27 - 9 * q^28 + 6 * q^29 - 6 * q^30 - 9 * q^31 - 9 * q^32 + 3 * q^33 - 12 * q^34 - 3 * q^35 + 12 * q^36 - 9 * q^37 + 33 * q^39 - 3 * q^40 - 3 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 18 * q^45 - 6 * q^46 + 21 * q^47 - 3 * q^48 + 9 * q^49 - 39 * q^51 - 12 * q^52 + 24 * q^54 + 24 * q^55 + 9 * q^56 - 6 * q^58 + 9 * q^59 + 6 * q^60 + 6 * q^61 + 9 * q^62 - 12 * q^63 + 9 * q^64 + 3 * q^65 - 3 * q^66 - 27 * q^67 + 12 * q^68 - 6 * q^69 + 3 * q^70 - 9 * q^71 - 12 * q^72 + 51 * q^73 + 9 * q^74 + 3 * q^75 + 3 * q^77 - 33 * q^78 - 24 * q^79 + 3 * q^80 - 3 * q^81 + 3 * q^82 + 9 * q^83 + 3 * q^84 + 6 * q^85 - 21 * q^86 - 3 * q^87 + 3 * q^88 - 9 * q^89 - 18 * q^90 + 12 * q^91 + 6 * q^92 + 3 * q^93 - 21 * q^94 + 3 * q^96 + 12 * q^97 - 9 * q^98 - 15 * 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
$3$	−2.18756	−1.26299	−0.631493	−	0.775382i	$-0.717558\pi$
$3$	−2.18756	−1.26299	−0.631493	+	0.775382i	$0.717558\pi$
$4$	1.00000	0.500000
$5$	−0.616139	−0.275546	−0.137773	−	0.990464i	$-0.543994\pi$
$5$	−0.616139	−0.275546	−0.137773	+	0.990464i	$0.543994\pi$
$6$	2.18756	0.893066
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.78540	0.595133
$10$	0.616139	0.194840
$11$	3.42998	1.03418	0.517089	−	0.855931i	$-0.327015\pi$
$11$	3.42998	1.03418	0.517089	+	0.855931i	$0.327015\pi$
$12$	−2.18756	−0.631493
$13$	−6.38112	−1.76980	−0.884902	−	0.465776i	$-0.845775\pi$
$13$	−6.38112	−1.76980	−0.884902	+	0.465776i	$0.845775\pi$
$14$	1.00000	0.267261
$15$	1.34784	0.348010
$16$	1.00000	0.250000
$17$	2.47999	0.601486	0.300743	−	0.953705i	$-0.402765\pi$
$17$	2.47999	0.601486	0.300743	+	0.953705i	$0.402765\pi$
$18$	−1.78540	−0.420823
$19$	0	0
$19$	0	0
$20$	−0.616139	−0.137773
$21$	2.18756	0.477364
$22$	−3.42998	−0.731275
$23$	2.70527	0.564088	0.282044	−	0.959401i	$-0.408988\pi$
$23$	2.70527	0.564088	0.282044	+	0.959401i	$0.408988\pi$
$24$	2.18756	0.446533
$25$	−4.62037	−0.924074
$26$	6.38112	1.25144
$27$	2.65701	0.511341
$28$	−1.00000	−0.188982
$29$	−6.00017	−1.11420	−0.557101	−	0.830444i	$-0.688087\pi$
$29$	−6.00017	−1.11420	−0.557101	+	0.830444i	$0.688087\pi$
$30$	−1.34784	−0.246081
$31$	7.72644	1.38771	0.693855	−	0.720115i	$-0.255911\pi$
$31$	7.72644	1.38771	0.693855	+	0.720115i	$0.255911\pi$
$32$	−1.00000	−0.176777
$33$	−7.50328	−1.30615
$34$	−2.47999	−0.425315
$35$	0.616139	0.104147
$36$	1.78540	0.297567
$37$	−4.26808	−0.701669	−0.350834	−	0.936438i	$-0.614102\pi$
$37$	−4.26808	−0.701669	−0.350834	+	0.936438i	$0.614102\pi$
$38$	0	0
$39$	13.9591	2.23524
$40$	0.616139	0.0974202
$41$	1.28851	0.201232	0.100616	−	0.994925i	$-0.467919\pi$
$41$	1.28851	0.201232	0.100616	+	0.994925i	$0.467919\pi$
$42$	−2.18756	−0.337547
$43$	−10.3584	−1.57964	−0.789819	−	0.613340i	$-0.789826\pi$
$43$	−10.3584	−1.57964	−0.789819	+	0.613340i	$0.789826\pi$
$44$	3.42998	0.517089
$45$	−1.10005	−0.163986
$46$	−2.70527	−0.398871
$47$	1.53750	0.224267	0.112134	−	0.993693i	$-0.464232\pi$
$47$	1.53750	0.224267	0.112134	+	0.993693i	$0.464232\pi$
$48$	−2.18756	−0.315746
$49$	1.00000	0.142857
$50$	4.62037	0.653419
$51$	−5.42512	−0.759669
$52$	−6.38112	−0.884902
$53$	5.11208	0.702198	0.351099	−	0.936338i	$-0.385808\pi$
$53$	5.11208	0.702198	0.351099	+	0.936338i	$0.385808\pi$
$54$	−2.65701	−0.361573
$55$	−2.11335	−0.284964
$56$	1.00000	0.133631
$57$	0	0
$58$	6.00017	0.787860
$59$	−12.7768	−1.66339	−0.831696	−	0.555232i	$-0.812630\pi$
$59$	−12.7768	−1.66339	−0.831696	+	0.555232i	$0.812630\pi$
$60$	1.34784	0.174005
$61$	−5.54592	−0.710082	−0.355041	−	0.934851i	$-0.615533\pi$
$61$	−5.54592	−0.710082	−0.355041	+	0.934851i	$0.615533\pi$
$62$	−7.72644	−0.981259
$63$	−1.78540	−0.224939
$64$	1.00000	0.125000
$65$	3.93166	0.487662
$66$	7.50328	0.923590
$67$	−4.16481	−0.508813	−0.254406	−	0.967097i	$-0.581880\pi$
$67$	−4.16481	−0.508813	−0.254406	+	0.967097i	$0.581880\pi$
$68$	2.47999	0.300743
$69$	−5.91793	−0.712435
$70$	−0.616139	−0.0736427
$71$	−0.0244707	−0.00290414	−0.00145207	−	0.999999i	$-0.500462\pi$
$71$	−0.0244707	−0.00290414	−0.00145207	+	0.999999i	$0.500462\pi$
$72$	−1.78540	−0.210411
$73$	13.0675	1.52943	0.764715	−	0.644368i	$-0.222880\pi$
$73$	13.0675	1.52943	0.764715	+	0.644368i	$0.222880\pi$
$74$	4.26808	0.496155
$75$	10.1073	1.16709
$76$	0	0
$77$	−3.42998	−0.390883
$78$	−13.9591	−1.58055
$79$	−2.96283	−0.333344	−0.166672	−	0.986012i	$-0.553302\pi$
$79$	−2.96283	−0.333344	−0.166672	+	0.986012i	$0.553302\pi$
$80$	−0.616139	−0.0688865
$81$	−11.1685	−1.24095
$82$	−1.28851	−0.142292
$83$	12.9425	1.42062	0.710312	−	0.703887i	$-0.248554\pi$
$83$	12.9425	1.42062	0.710312	+	0.703887i	$0.248554\pi$
$84$	2.18756	0.238682
$85$	−1.52802	−0.165737
$86$	10.3584	1.11697
$87$	13.1257	1.40722
$88$	−3.42998	−0.365637
$89$	12.4510	1.31980	0.659899	−	0.751354i	$-0.270599\pi$
$89$	12.4510	1.31980	0.659899	+	0.751354i	$0.270599\pi$
$90$	1.10005	0.115956
$91$	6.38112	0.668923
$92$	2.70527	0.282044
$93$	−16.9020	−1.75266
$94$	−1.53750	−0.158581
$95$	0	0
$96$	2.18756	0.223266
$97$	1.51714	0.154042	0.0770211	−	0.997029i	$-0.475459\pi$
$97$	1.51714	0.154042	0.0770211	+	0.997029i	$0.475459\pi$
$98$	−1.00000	−0.101015
$99$	6.12389	0.615474
$100$	−4.62037	−0.462037
$101$	−9.92823	−0.987896	−0.493948	−	0.869491i	$-0.664447\pi$
$101$	−9.92823	−0.987896	−0.493948	+	0.869491i	$0.664447\pi$
$102$	5.42512	0.537167
$103$	−8.34988	−0.822738	−0.411369	−	0.911469i	$-0.634949\pi$
$103$	−8.34988	−0.822738	−0.411369	+	0.911469i	$0.634949\pi$
$104$	6.38112	0.625720
$105$	−1.34784	−0.131536
$106$	−5.11208	−0.496529
$107$	−13.5562	−1.31053	−0.655264	−	0.755400i	$-0.727443\pi$
$107$	−13.5562	−1.31053	−0.655264	+	0.755400i	$0.727443\pi$
$108$	2.65701	0.255671
$109$	−0.558302	−0.0534756	−0.0267378	−	0.999642i	$-0.508512\pi$
$109$	−0.558302	−0.0534756	−0.0267378	+	0.999642i	$0.508512\pi$
$110$	2.11335	0.201500
$111$	9.33667	0.886197
$112$	−1.00000	−0.0944911
$113$	−10.0986	−0.949999	−0.474999	−	0.879986i	$-0.657552\pi$
$113$	−10.0986	−0.949999	−0.474999	+	0.879986i	$0.657552\pi$
$114$	0	0
$115$	−1.66682	−0.155432
$116$	−6.00017	−0.557101
$117$	−11.3929	−1.05327
$118$	12.7768	1.17620
$119$	−2.47999	−0.227340
$120$	−1.34784	−0.123040
$121$	0.764783	0.0695257
$122$	5.54592	0.502104
$123$	−2.81869	−0.254153
$124$	7.72644	0.693855
$125$	5.92749	0.530171
$126$	1.78540	0.159056
$127$	−4.44613	−0.394530	−0.197265	−	0.980350i	$-0.563206\pi$
$127$	−4.44613	−0.394530	−0.197265	+	0.980350i	$0.563206\pi$
$128$	−1.00000	−0.0883883
$129$	22.6595	1.99506
$130$	−3.93166	−0.344829
$131$	7.17183	0.626606	0.313303	−	0.949653i	$-0.398564\pi$
$131$	7.17183	0.626606	0.313303	+	0.949653i	$0.398564\pi$
$132$	−7.50328	−0.653077
$133$	0	0
$134$	4.16481	0.359785
$135$	−1.63709	−0.140898
$136$	−2.47999	−0.212658
$137$	−16.8073	−1.43594	−0.717971	−	0.696073i	$-0.754929\pi$
$137$	−16.8073	−1.43594	−0.717971	+	0.696073i	$0.754929\pi$
$138$	5.91793	0.503768
$139$	−13.5566	−1.14986	−0.574929	−	0.818203i	$-0.694970\pi$
$139$	−13.5566	−1.14986	−0.574929	+	0.818203i	$0.694970\pi$
$140$	0.616139	0.0520733
$141$	−3.36336	−0.283246
$142$	0.0244707	0.00205353
$143$	−21.8871	−1.83029
$144$	1.78540	0.148783
$145$	3.69694	0.307014
$146$	−13.0675	−1.08147
$147$	−2.18756	−0.180427
$148$	−4.26808	−0.350834
$149$	13.5990	1.11408	0.557038	−	0.830487i	$-0.311938\pi$
$149$	13.5990	1.11408	0.557038	+	0.830487i	$0.311938\pi$
$150$	−10.1073	−0.825259
$151$	20.2325	1.64650	0.823250	−	0.567679i	$-0.192159\pi$
$151$	20.2325	1.64650	0.823250	+	0.567679i	$0.192159\pi$
$152$	0	0
$153$	4.42778	0.357964
$154$	3.42998	0.276396
$155$	−4.76056	−0.382378
$156$	13.9591	1.11762
$157$	−11.1097	−0.886648	−0.443324	−	0.896361i	$-0.646201\pi$
$157$	−11.1097	−0.886648	−0.443324	+	0.896361i	$0.646201\pi$
$158$	2.96283	0.235710
$159$	−11.1830	−0.886866
$160$	0.616139	0.0487101
$161$	−2.70527	−0.213205
$162$	11.1685	0.877484
$163$	−10.2803	−0.805215	−0.402608	−	0.915373i	$-0.631896\pi$
$163$	−10.2803	−0.805215	−0.402608	+	0.915373i	$0.631896\pi$
$164$	1.28851	0.100616
$165$	4.62306	0.359905
$166$	−12.9425	−1.00453
$167$	12.6748	0.980806	0.490403	−	0.871496i	$-0.336850\pi$
$167$	12.6748	0.980806	0.490403	+	0.871496i	$0.336850\pi$
$168$	−2.18756	−0.168774
$169$	27.7187	2.13221
$170$	1.52802	0.117194
$171$	0	0
$172$	−10.3584	−0.789819
$173$	−6.24437	−0.474751	−0.237376	−	0.971418i	$-0.576287\pi$
$173$	−6.24437	−0.474751	−0.237376	+	0.971418i	$0.576287\pi$
$174$	−13.1257	−0.995057
$175$	4.62037	0.349267
$176$	3.42998	0.258545
$177$	27.9499	2.10084
$178$	−12.4510	−0.933238
$179$	−17.7976	−1.33026	−0.665128	−	0.746729i	$-0.731623\pi$
$179$	−17.7976	−1.33026	−0.665128	+	0.746729i	$0.731623\pi$
$180$	−1.10005	−0.0819932
$181$	5.92757	0.440593	0.220296	−	0.975433i	$-0.429298\pi$
$181$	5.92757	0.440593	0.220296	+	0.975433i	$0.429298\pi$
$182$	−6.38112	−0.473000
$183$	12.1320	0.896823
$184$	−2.70527	−0.199435
$185$	2.62973	0.193342
$186$	16.9020	1.23932
$187$	8.50633	0.622044
$188$	1.53750	0.112134
$189$	−2.65701	−0.193269
$190$	0	0
$191$	16.3567	1.18353	0.591764	−	0.806111i	$-0.298432\pi$
$191$	16.3567	1.18353	0.591764	+	0.806111i	$0.298432\pi$
$192$	−2.18756	−0.157873
$193$	−19.9885	−1.43881	−0.719403	−	0.694593i	$-0.755584\pi$
$193$	−19.9885	−1.43881	−0.719403	+	0.694593i	$0.755584\pi$
$194$	−1.51714	−0.108924
$195$	−8.60072	−0.615911
$196$	1.00000	0.0714286
$197$	−3.44430	−0.245396	−0.122698	−	0.992444i	$-0.539155\pi$
$197$	−3.44430	−0.245396	−0.122698	+	0.992444i	$0.539155\pi$
$198$	−6.12389	−0.435206
$199$	3.13027	0.221899	0.110949	−	0.993826i	$-0.464611\pi$
$199$	3.13027	0.221899	0.110949	+	0.993826i	$0.464611\pi$
$200$	4.62037	0.326710
$201$	9.11076	0.642623
$202$	9.92823	0.698548
$203$	6.00017	0.421129
$204$	−5.42512	−0.379834
$205$	−0.793902	−0.0554485
$206$	8.34988	0.581764
$207$	4.82999	0.335708
$208$	−6.38112	−0.442451
$209$	0	0
$210$	1.34784	0.0930097
$211$	16.6987	1.14959	0.574793	−	0.818299i	$-0.305083\pi$
$211$	16.6987	1.14959	0.574793	+	0.818299i	$0.305083\pi$
$212$	5.11208	0.351099
$213$	0.0535310	0.00366788
$214$	13.5562	0.926684
$215$	6.38221	0.435263
$216$	−2.65701	−0.180786
$217$	−7.72644	−0.524505
$218$	0.558302	0.0378130
$219$	−28.5858	−1.93165
$220$	−2.11335	−0.142482
$221$	−15.8251	−1.06451
$222$	−9.33667	−0.626636
$223$	−14.5844	−0.976641	−0.488320	−	0.872664i	$-0.662390\pi$
$223$	−14.5844	−0.976641	−0.488320	+	0.872664i	$0.662390\pi$
$224$	1.00000	0.0668153
$225$	−8.24921	−0.549947
$226$	10.0986	0.671750
$227$	4.73333	0.314162	0.157081	−	0.987586i	$-0.449792\pi$
$227$	4.73333	0.314162	0.157081	+	0.987586i	$0.449792\pi$
$228$	0	0
$229$	14.8611	0.982051	0.491026	−	0.871145i	$-0.336622\pi$
$229$	14.8611	0.982051	0.491026	+	0.871145i	$0.336622\pi$
$230$	1.66682	0.109907
$231$	7.50328	0.493679
$232$	6.00017	0.393930
$233$	−4.36751	−0.286125	−0.143062	−	0.989714i	$-0.545695\pi$
$233$	−4.36751	−0.286125	−0.143062	+	0.989714i	$0.545695\pi$
$234$	11.3929	0.744774
$235$	−0.947313	−0.0617959
$236$	−12.7768	−0.831696
$237$	6.48135	0.421009
$238$	2.47999	0.160754
$239$	−24.2217	−1.56677	−0.783385	−	0.621537i	$-0.786509\pi$
$239$	−24.2217	−1.56677	−0.783385	+	0.621537i	$0.786509\pi$
$240$	1.34784	0.0870026
$241$	17.1009	1.10157	0.550784	−	0.834648i	$-0.314329\pi$
$241$	17.1009	1.10157	0.550784	+	0.834648i	$0.314329\pi$
$242$	−0.764783	−0.0491621
$243$	16.4608	1.05596
$244$	−5.54592	−0.355041
$245$	−0.616139	−0.0393637
$246$	2.81869	0.179713
$247$	0	0
$248$	−7.72644	−0.490629
$249$	−28.3125	−1.79423
$250$	−5.92749	−0.374887
$251$	27.3096	1.72377	0.861883	−	0.507107i	$-0.169285\pi$
$251$	27.3096	1.72377	0.861883	+	0.507107i	$0.169285\pi$
$252$	−1.78540	−0.112470
$253$	9.27904	0.583368
$254$	4.44613	0.278975
$255$	3.34263	0.209324
$256$	1.00000	0.0625000
$257$	9.96817	0.621797	0.310899	−	0.950443i	$-0.399370\pi$
$257$	9.96817	0.621797	0.310899	+	0.950443i	$0.399370\pi$
$258$	−22.6595	−1.41072
$259$	4.26808	0.265206
$260$	3.93166	0.243831
$261$	−10.7127	−0.663099
$262$	−7.17183	−0.443077
$263$	−24.9314	−1.53734	−0.768669	−	0.639647i	$-0.779080\pi$
$263$	−24.9314	−1.53734	−0.768669	+	0.639647i	$0.779080\pi$
$264$	7.50328	0.461795
$265$	−3.14975	−0.193488
$266$	0	0
$267$	−27.2371	−1.66689
$268$	−4.16481	−0.254406
$269$	25.6665	1.56491	0.782456	−	0.622706i	$-0.213967\pi$
$269$	25.6665	1.56491	0.782456	+	0.622706i	$0.213967\pi$
$270$	1.63709	0.0996299
$271$	18.7964	1.14180	0.570900	−	0.821020i	$-0.306595\pi$
$271$	18.7964	1.14180	0.570900	+	0.821020i	$0.306595\pi$
$272$	2.47999	0.150372
$273$	−13.9591	−0.844841
$274$	16.8073	1.01536
$275$	−15.8478	−0.955658
$276$	−5.91793	−0.356218
$277$	19.8745	1.19414	0.597071	−	0.802188i	$-0.296331\pi$
$277$	19.8745	1.19414	0.597071	+	0.802188i	$0.296331\pi$
$278$	13.5566	0.813073
$279$	13.7948	0.825872
$280$	−0.616139	−0.0368214
$281$	21.2943	1.27031	0.635156	−	0.772384i	$-0.280936\pi$
$281$	21.2943	1.27031	0.635156	+	0.772384i	$0.280936\pi$
$282$	3.36336	0.200285
$283$	−3.77466	−0.224380	−0.112190	−	0.993687i	$-0.535787\pi$
$283$	−3.77466	−0.224380	−0.112190	+	0.993687i	$0.535787\pi$
$284$	−0.0244707	−0.00145207
$285$	0	0
$286$	21.8871	1.29421
$287$	−1.28851	−0.0760584
$288$	−1.78540	−0.105206
$289$	−10.8496	−0.638214
$290$	−3.69694	−0.217092
$291$	−3.31883	−0.194553
$292$	13.0675	0.764715
$293$	16.9584	0.990721	0.495360	−	0.868688i	$-0.335036\pi$
$293$	16.9584	0.990721	0.495360	+	0.868688i	$0.335036\pi$
$294$	2.18756	0.127581
$295$	7.87226	0.458341
$296$	4.26808	0.248077
$297$	9.11349	0.528818
$298$	−13.5990	−0.787770
$299$	−17.2627	−0.998326
$300$	10.1073	0.583546
$301$	10.3584	0.597047
$302$	−20.2325	−1.16425
$303$	21.7186	1.24770
$304$	0	0
$305$	3.41706	0.195660
$306$	−4.42778	−0.253119
$307$	2.68585	0.153289	0.0766447	−	0.997058i	$-0.475579\pi$
$307$	2.68585	0.153289	0.0766447	+	0.997058i	$0.475579\pi$
$308$	−3.42998	−0.195441
$309$	18.2658	1.03911
$310$	4.76056	0.270382
$311$	1.77079	0.100412	0.0502062	−	0.998739i	$-0.484012\pi$
$311$	1.77079	0.100412	0.0502062	+	0.998739i	$0.484012\pi$
$312$	−13.9591	−0.790276
$313$	7.89729	0.446381	0.223191	−	0.974775i	$-0.428353\pi$
$313$	7.89729	0.446381	0.223191	+	0.974775i	$0.428353\pi$
$314$	11.1097	0.626955
$315$	1.10005	0.0619811
$316$	−2.96283	−0.166672
$317$	11.6202	0.652656	0.326328	−	0.945257i	$-0.394189\pi$
$317$	11.6202	0.652656	0.326328	+	0.945257i	$0.394189\pi$
$318$	11.1830	0.627109
$319$	−20.5805	−1.15229
$320$	−0.616139	−0.0344432
$321$	29.6550	1.65518
$322$	2.70527	0.150759
$323$	0	0
$324$	−11.1685	−0.620475
$325$	29.4832	1.63543
$326$	10.2803	0.569373
$327$	1.22132	0.0675389
$328$	−1.28851	−0.0711461
$329$	−1.53750	−0.0847650
$330$	−4.62306	−0.254491
$331$	1.15352	0.0634032	0.0317016	−	0.999497i	$-0.489907\pi$
$331$	1.15352	0.0634032	0.0317016	+	0.999497i	$0.489907\pi$
$332$	12.9425	0.710312
$333$	−7.62023	−0.417586
$334$	−12.6748	−0.693534
$335$	2.56610	0.140201
$336$	2.18756	0.119341
$337$	7.31544	0.398497	0.199249	−	0.979949i	$-0.436150\pi$
$337$	7.31544	0.398497	0.199249	+	0.979949i	$0.436150\pi$
$338$	−27.7187	−1.50770
$339$	22.0913	1.19983
$340$	−1.52802	−0.0828685
$341$	26.5016	1.43514
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	10.3584	0.558486
$345$	3.64627	0.196309
$346$	6.24437	0.335700
$347$	−31.3704	−1.68405	−0.842025	−	0.539439i	$-0.818636\pi$
$347$	−31.3704	−1.68405	−0.842025	+	0.539439i	$0.818636\pi$
$348$	13.1257	0.703611
$349$	−2.33966	−0.125239	−0.0626197	−	0.998037i	$-0.519946\pi$
$349$	−2.33966	−0.125239	−0.0626197	+	0.998037i	$0.519946\pi$
$350$	−4.62037	−0.246969
$351$	−16.9547	−0.904974
$352$	−3.42998	−0.182819
$353$	−6.64960	−0.353923	−0.176961	−	0.984218i	$-0.556627\pi$
$353$	−6.64960	−0.353923	−0.176961	+	0.984218i	$0.556627\pi$
$354$	−27.9499	−1.48552
$355$	0.0150774	0.000800223 0
$356$	12.4510	0.659899
$357$	5.42512	0.287128
$358$	17.7976	0.940633
$359$	23.2605	1.22764	0.613821	−	0.789445i	$-0.289631\pi$
$359$	23.2605	1.22764	0.613821	+	0.789445i	$0.289631\pi$
$360$	1.10005	0.0579780
$361$	0	0
$362$	−5.92757	−0.311546
$363$	−1.67301	−0.0878100
$364$	6.38112	0.334462
$365$	−8.05138	−0.421428
$366$	−12.1320	−0.634150
$367$	10.6463	0.555733	0.277866	−	0.960620i	$-0.410373\pi$
$367$	10.6463	0.555733	0.277866	+	0.960620i	$0.410373\pi$
$368$	2.70527	0.141022
$369$	2.30051	0.119760
$370$	−2.62973	−0.136713
$371$	−5.11208	−0.265406
$372$	−16.9020	−0.876329
$373$	28.8794	1.49532	0.747659	−	0.664083i	$-0.231178\pi$
$373$	28.8794	1.49532	0.747659	+	0.664083i	$0.231178\pi$
$374$	−8.50633	−0.439852
$375$	−12.9667	−0.669598
$376$	−1.53750	−0.0792904
$377$	38.2878	1.97192
$378$	2.65701	0.136662
$379$	33.1311	1.70183	0.850916	−	0.525302i	$-0.176048\pi$
$379$	33.1311	1.70183	0.850916	+	0.525302i	$0.176048\pi$
$380$	0	0
$381$	9.72616	0.498286
$382$	−16.3567	−0.836880
$383$	3.65421	0.186722	0.0933608	−	0.995632i	$-0.470239\pi$
$383$	3.65421	0.186722	0.0933608	+	0.995632i	$0.470239\pi$
$384$	2.18756	0.111633
$385$	2.11335	0.107706
$386$	19.9885	1.01739
$387$	−18.4938	−0.940095
$388$	1.51714	0.0770211
$389$	−9.25078	−0.469033	−0.234517	−	0.972112i	$-0.575351\pi$
$389$	−9.25078	−0.469033	−0.234517	+	0.972112i	$0.575351\pi$
$390$	8.60072	0.435515
$391$	6.70905	0.339291
$392$	−1.00000	−0.0505076
$393$	−15.6888	−0.791395
$394$	3.44430	0.173521
$395$	1.82552	0.0918517
$396$	6.12389	0.307737
$397$	19.2309	0.965172	0.482586	−	0.875849i	$-0.339698\pi$
$397$	19.2309	0.965172	0.482586	+	0.875849i	$0.339698\pi$
$398$	−3.13027	−0.156906
$399$	0	0
$400$	−4.62037	−0.231019
$401$	29.5430	1.47531	0.737654	−	0.675179i	$-0.235933\pi$
$401$	29.5430	1.47531	0.737654	+	0.675179i	$0.235933\pi$
$402$	−9.11076	−0.454403
$403$	−49.3034	−2.45597
$404$	−9.92823	−0.493948
$405$	6.88138	0.341939
$406$	−6.00017	−0.297783
$407$	−14.6395	−0.725651
$408$	5.42512	0.268583
$409$	39.8965	1.97276	0.986378	−	0.164494i	$-0.0525991\pi$
$409$	39.8965	1.97276	0.986378	+	0.164494i	$0.0525991\pi$
$410$	0.793902	0.0392080
$411$	36.7668	1.81357
$412$	−8.34988	−0.411369
$413$	12.7768	0.628703
$414$	−4.82999	−0.237381
$415$	−7.97439	−0.391447
$416$	6.38112	0.312860
$417$	29.6559	1.45225
$418$	0	0
$419$	−34.5562	−1.68818	−0.844090	−	0.536201i	$-0.819859\pi$
$419$	−34.5562	−1.68818	−0.844090	+	0.536201i	$0.819859\pi$
$420$	−1.34784	−0.0657678
$421$	28.8651	1.40680	0.703399	−	0.710795i	$-0.251665\pi$
$421$	28.8651	1.40680	0.703399	+	0.710795i	$0.251665\pi$
$422$	−16.6987	−0.812880
$423$	2.74505	0.133469
$424$	−5.11208	−0.248265
$425$	−11.4585	−0.555818
$426$	−0.0535310	−0.00259358
$427$	5.54592	0.268386
$428$	−13.5562	−0.655264
$429$	47.8793	2.31164
$430$	−6.38221	−0.307777
$431$	19.4879	0.938699	0.469350	−	0.883012i	$-0.344488\pi$
$431$	19.4879	0.938699	0.469350	+	0.883012i	$0.344488\pi$
$432$	2.65701	0.127835
$433$	1.44225	0.0693102	0.0346551	−	0.999399i	$-0.488967\pi$
$433$	1.44225	0.0693102	0.0346551	+	0.999399i	$0.488967\pi$
$434$	7.72644	0.370881
$435$	−8.08726	−0.387754
$436$	−0.558302	−0.0267378
$437$	0	0
$438$	28.5858	1.36588
$439$	−16.5525	−0.790006	−0.395003	−	0.918680i	$-0.629256\pi$
$439$	−16.5525	−0.790006	−0.395003	+	0.918680i	$0.629256\pi$
$440$	2.11335	0.100750
$441$	1.78540	0.0850190
$442$	15.8251	0.752725
$443$	3.08768	0.146700	0.0733500	−	0.997306i	$-0.476631\pi$
$443$	3.08768	0.146700	0.0733500	+	0.997306i	$0.476631\pi$
$444$	9.33667	0.443099
$445$	−7.67152	−0.363665
$446$	14.5844	0.690589
$447$	−29.7486	−1.40706
$448$	−1.00000	−0.0472456
$449$	17.9081	0.845135	0.422568	−	0.906331i	$-0.361129\pi$
$449$	17.9081	0.845135	0.422568	+	0.906331i	$0.361129\pi$
$450$	8.24921	0.388871
$451$	4.41957	0.208109
$452$	−10.0986	−0.474999
$453$	−44.2598	−2.07951
$454$	−4.73333	−0.222146
$455$	−3.93166	−0.184319
$456$	0	0
$457$	31.2954	1.46394	0.731970	−	0.681337i	$-0.238601\pi$
$457$	31.2954	1.46394	0.731970	+	0.681337i	$0.238601\pi$
$458$	−14.8611	−0.694415
$459$	6.58936	0.307565
$460$	−1.66682	−0.0777161
$461$	−11.6085	−0.540660	−0.270330	−	0.962768i	$-0.587133\pi$
$461$	−11.6085	−0.540660	−0.270330	+	0.962768i	$0.587133\pi$
$462$	−7.50328	−0.349084
$463$	4.15132	0.192928	0.0964640	−	0.995336i	$-0.469247\pi$
$463$	4.15132	0.192928	0.0964640	+	0.995336i	$0.469247\pi$
$464$	−6.00017	−0.278551
$465$	10.4140	0.482937
$466$	4.36751	0.202321
$467$	−24.9196	−1.15314	−0.576570	−	0.817047i	$-0.695609\pi$
$467$	−24.9196	−1.15314	−0.576570	+	0.817047i	$0.695609\pi$
$468$	−11.3929	−0.526635
$469$	4.16481	0.192313
$470$	0.947313	0.0436963
$471$	24.3030	1.11982
$472$	12.7768	0.588098
$473$	−35.5291	−1.63363
$474$	−6.48135	−0.297698
$475$	0	0
$476$	−2.47999	−0.113670
$477$	9.12710	0.417901
$478$	24.2217	1.10787
$479$	−18.9778	−0.867117	−0.433559	−	0.901125i	$-0.642742\pi$
$479$	−18.9778	−0.867117	−0.433559	+	0.901125i	$0.642742\pi$
$480$	−1.34784	−0.0615201
$481$	27.2352	1.24182
$482$	−17.1009	−0.778926
$483$	5.91793	0.269275
$484$	0.764783	0.0347629
$485$	−0.934769	−0.0424457
$486$	−16.4608	−0.746677
$487$	−36.1508	−1.63815	−0.819074	−	0.573687i	$-0.805512\pi$
$487$	−36.1508	−1.63815	−0.819074	+	0.573687i	$0.805512\pi$
$488$	5.54592	0.251052
$489$	22.4887	1.01698
$490$	0.616139	0.0278343
$491$	3.08754	0.139339	0.0696693	−	0.997570i	$-0.477806\pi$
$491$	3.08754	0.139339	0.0696693	+	0.997570i	$0.477806\pi$
$492$	−2.81869	−0.127076
$493$	−14.8804	−0.670178
$494$	0	0
$495$	−3.77317	−0.169591
$496$	7.72644	0.346927
$497$	0.0244707	0.00109766
$498$	28.3125	1.26871
$499$	30.9593	1.38593	0.692964	−	0.720972i	$-0.256304\pi$
$499$	30.9593	1.38593	0.692964	+	0.720972i	$0.256304\pi$
$500$	5.92749	0.265085
$501$	−27.7268	−1.23874
$502$	−27.3096	−1.21889
$503$	3.79268	0.169107	0.0845536	−	0.996419i	$-0.473054\pi$
$503$	3.79268	0.169107	0.0845536	+	0.996419i	$0.473054\pi$
$504$	1.78540	0.0795280
$505$	6.11717	0.272211
$506$	−9.27904	−0.412504
$507$	−60.6362	−2.69295
$508$	−4.44613	−0.197265
$509$	−36.0268	−1.59686	−0.798430	−	0.602087i	$-0.794336\pi$
$509$	−36.0268	−1.59686	−0.798430	+	0.602087i	$0.794336\pi$
$510$	−3.34263	−0.148014
$511$	−13.0675	−0.578071
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−9.96817	−0.439677
$515$	5.14469	0.226702
$516$	22.6595	0.997530
$517$	5.27359	0.231932
$518$	−4.26808	−0.187529
$519$	13.6599	0.599604
$520$	−3.93166	−0.172415
$521$	−7.91028	−0.346555	−0.173278	−	0.984873i	$-0.555436\pi$
$521$	−7.91028	−0.346555	−0.173278	+	0.984873i	$0.555436\pi$
$522$	10.7127	0.468882
$523$	33.0876	1.44682	0.723409	−	0.690420i	$-0.242574\pi$
$523$	33.0876	1.44682	0.723409	+	0.690420i	$0.242574\pi$
$524$	7.17183	0.313303
$525$	−10.1073	−0.441120
$526$	24.9314	1.08706
$527$	19.1615	0.834688
$528$	−7.50328	−0.326538
$529$	−15.6815	−0.681804
$530$	3.14975	0.136817
$531$	−22.8116	−0.989939
$532$	0	0
$533$	−8.22215	−0.356141
$534$	27.2371	1.17867
$535$	8.35251	0.361111
$536$	4.16481	0.179892
$537$	38.9333	1.68009
$538$	−25.6665	−1.10656
$539$	3.42998	0.147740
$540$	−1.63709	−0.0704490
$541$	9.32192	0.400781	0.200390	−	0.979716i	$-0.435779\pi$
$541$	9.32192	0.400781	0.200390	+	0.979716i	$0.435779\pi$
$542$	−18.7964	−0.807374
$543$	−12.9669	−0.556462
$544$	−2.47999	−0.106329
$545$	0.343992	0.0147350
$546$	13.9591	0.597393
$547$	27.3456	1.16921	0.584607	−	0.811317i	$-0.301249\pi$
$547$	27.3456	1.16921	0.584607	+	0.811317i	$0.301249\pi$
$548$	−16.8073	−0.717971
$549$	−9.90167	−0.422593
$550$	15.8478	0.675752
$551$	0	0
$552$	5.91793	0.251884
$553$	2.96283	0.125992
$554$	−19.8745	−0.844386
$555$	−5.75269	−0.244188
$556$	−13.5566	−0.574929
$557$	−16.4963	−0.698970	−0.349485	−	0.936942i	$-0.613643\pi$
$557$	−16.4963	−0.698970	−0.349485	+	0.936942i	$0.613643\pi$
$558$	−13.7948	−0.583980
$559$	66.0981	2.79565
$560$	0.616139	0.0260366
$561$	−18.6081	−0.785633
$562$	−21.2943	−0.898246
$563$	35.4681	1.49480	0.747401	−	0.664373i	$-0.231301\pi$
$563$	35.4681	1.49480	0.747401	+	0.664373i	$0.231301\pi$
$564$	−3.36336	−0.141623
$565$	6.22216	0.261768
$566$	3.77466	0.158661
$567$	11.1685	0.469035
$568$	0.0244707	0.00102677
$569$	43.3131	1.81578	0.907889	−	0.419210i	$-0.137693\pi$
$569$	43.3131	1.81578	0.907889	+	0.419210i	$0.137693\pi$
$570$	0	0
$571$	1.18471	0.0495787	0.0247893	−	0.999693i	$-0.492108\pi$
$571$	1.18471	0.0495787	0.0247893	+	0.999693i	$0.492108\pi$
$572$	−21.8871	−0.915147
$573$	−35.7811	−1.49478
$574$	1.28851	0.0537814
$575$	−12.4994	−0.521260
$576$	1.78540	0.0743916
$577$	12.9555	0.539343	0.269671	−	0.962952i	$-0.413085\pi$
$577$	12.9555	0.539343	0.269671	+	0.962952i	$0.413085\pi$
$578$	10.8496	0.451286
$579$	43.7260	1.81719
$580$	3.69694	0.153507
$581$	−12.9425	−0.536946
$582$	3.31883	0.137570
$583$	17.5343	0.726198
$584$	−13.0675	−0.540735
$585$	7.01958	0.290224
$586$	−16.9584	−0.700545
$587$	36.4405	1.50406	0.752030	−	0.659129i	$-0.229075\pi$
$587$	36.4405	1.50406	0.752030	+	0.659129i	$0.229075\pi$
$588$	−2.18756	−0.0902133
$589$	0	0
$590$	−7.87226	−0.324096
$591$	7.53460	0.309932
$592$	−4.26808	−0.175417
$593$	31.6814	1.30100	0.650500	−	0.759506i	$-0.274559\pi$
$593$	31.6814	1.30100	0.650500	+	0.759506i	$0.274559\pi$
$594$	−9.11349	−0.373931
$595$	1.52802	0.0626427
$596$	13.5990	0.557038
$597$	−6.84763	−0.280255
$598$	17.2627	0.705923
$599$	−5.21417	−0.213045	−0.106523	−	0.994310i	$-0.533972\pi$
$599$	−5.21417	−0.213045	−0.106523	+	0.994310i	$0.533972\pi$
$600$	−10.1073	−0.412630
$601$	8.43231	0.343961	0.171981	−	0.985100i	$-0.444983\pi$
$601$	8.43231	0.343961	0.171981	+	0.985100i	$0.444983\pi$
$602$	−10.3584	−0.422176
$603$	−7.43585	−0.302811
$604$	20.2325	0.823250
$605$	−0.471213	−0.0191575
$606$	−21.7186	−0.882256
$607$	−18.8481	−0.765022	−0.382511	−	0.923951i	$-0.624941\pi$
$607$	−18.8481	−0.765022	−0.382511	+	0.923951i	$0.624941\pi$
$608$	0	0
$609$	−13.1257	−0.531880
$610$	−3.41706	−0.138353
$611$	−9.81096	−0.396909
$612$	4.42778	0.178982
$613$	14.8192	0.598542	0.299271	−	0.954168i	$-0.403256\pi$
$613$	14.8192	0.598542	0.299271	+	0.954168i	$0.403256\pi$
$614$	−2.68585	−0.108392
$615$	1.73671	0.0700307
$616$	3.42998	0.138198
$617$	14.2858	0.575123	0.287562	−	0.957762i	$-0.407155\pi$
$617$	14.2858	0.575123	0.287562	+	0.957762i	$0.407155\pi$
$618$	−18.2658	−0.734760
$619$	−27.8881	−1.12092	−0.560459	−	0.828182i	$-0.689375\pi$
$619$	−27.8881	−1.12092	−0.560459	+	0.828182i	$0.689375\pi$
$620$	−4.76056	−0.191189
$621$	7.18793	0.288442
$622$	−1.77079	−0.0710023
$623$	−12.4510	−0.498837
$624$	13.9591	0.558810
$625$	19.4497	0.777988
$626$	−7.89729	−0.315639
$627$	0	0
$628$	−11.1097	−0.443324
$629$	−10.5848	−0.422044
$630$	−1.10005	−0.0438272
$631$	26.3781	1.05010	0.525048	−	0.851073i	$-0.324047\pi$
$631$	26.3781	1.05010	0.525048	+	0.851073i	$0.324047\pi$
$632$	2.96283	0.117855
$633$	−36.5293	−1.45191
$634$	−11.6202	−0.461498
$635$	2.73944	0.108711
$636$	−11.1830	−0.443433
$637$	−6.38112	−0.252829
$638$	20.5805	0.814789
$639$	−0.0436899	−0.00172835
$640$	0.616139	0.0243550
$641$	−39.1472	−1.54622	−0.773110	−	0.634272i	$-0.781300\pi$
$641$	−39.1472	−1.54622	−0.773110	+	0.634272i	$0.781300\pi$
$642$	−29.6550	−1.17039
$643$	−6.20232	−0.244596	−0.122298	−	0.992493i	$-0.539026\pi$
$643$	−6.20232	−0.244596	−0.122298	+	0.992493i	$0.539026\pi$
$644$	−2.70527	−0.106603
$645$	−13.9614	−0.549731
$646$	0	0
$647$	−2.11530	−0.0831610	−0.0415805	−	0.999135i	$-0.513239\pi$
$647$	−2.11530	−0.0831610	−0.0415805	+	0.999135i	$0.513239\pi$
$648$	11.1685	0.438742
$649$	−43.8240	−1.72024
$650$	−29.4832	−1.15642
$651$	16.9020	0.662442
$652$	−10.2803	−0.402608
$653$	−20.2029	−0.790602	−0.395301	−	0.918552i	$-0.629360\pi$
$653$	−20.2029	−0.790602	−0.395301	+	0.918552i	$0.629360\pi$
$654$	−1.22132	−0.0477572
$655$	−4.41885	−0.172659
$656$	1.28851	0.0503079
$657$	23.3306	0.910215
$658$	1.53750	0.0599379
$659$	23.3082	0.907958	0.453979	−	0.891012i	$-0.350004\pi$
$659$	23.3082	0.907958	0.453979	+	0.891012i	$0.350004\pi$
$660$	4.62306	0.179953
$661$	28.4307	1.10583	0.552914	−	0.833238i	$-0.313516\pi$
$661$	28.4307	1.10583	0.552914	+	0.833238i	$0.313516\pi$
$662$	−1.15352	−0.0448329
$663$	34.6184	1.34447
$664$	−12.9425	−0.502267
$665$	0	0
$666$	7.62023	0.295278
$667$	−16.2321	−0.628509
$668$	12.6748	0.490403
$669$	31.9041	1.23348
$670$	−2.56610	−0.0991372
$671$	−19.0224	−0.734351
$672$	−2.18756	−0.0843868
$673$	9.48697	0.365696	0.182848	−	0.983141i	$-0.441468\pi$
$673$	9.48697	0.365696	0.182848	+	0.983141i	$0.441468\pi$
$674$	−7.31544	−0.281780
$675$	−12.2764	−0.472517
$676$	27.7187	1.06610
$677$	−43.2866	−1.66364	−0.831820	−	0.555045i	$-0.812701\pi$
$677$	−43.2866	−1.66364	−0.831820	+	0.555045i	$0.812701\pi$
$678$	−22.0913	−0.848411
$679$	−1.51714	−0.0582225
$680$	1.52802	0.0585969
$681$	−10.3544	−0.396782
$682$	−26.5016	−1.01480
$683$	16.3891	0.627110	0.313555	−	0.949570i	$-0.398480\pi$
$683$	16.3891	0.627110	0.313555	+	0.949570i	$0.398480\pi$
$684$	0	0
$685$	10.3556	0.395668
$686$	1.00000	0.0381802
$687$	−32.5096	−1.24032
$688$	−10.3584	−0.394910
$689$	−32.6208	−1.24275
$690$	−3.64627	−0.138811
$691$	41.4257	1.57591	0.787953	−	0.615735i	$-0.211141\pi$
$691$	41.4257	1.57591	0.787953	+	0.615735i	$0.211141\pi$
$692$	−6.24437	−0.237376
$693$	−6.12389	−0.232627
$694$	31.3704	1.19080
$695$	8.35277	0.316839
$696$	−13.1257	−0.497528
$697$	3.19550	0.121038
$698$	2.33966	0.0885576
$699$	9.55416	0.361372
$700$	4.62037	0.174634
$701$	46.1088	1.74150	0.870752	−	0.491722i	$-0.163632\pi$
$701$	46.1088	1.74150	0.870752	+	0.491722i	$0.163632\pi$
$702$	16.9547	0.639913
$703$	0	0
$704$	3.42998	0.129272
$705$	2.07230	0.0780473
$706$	6.64960	0.250261
$707$	9.92823	0.373390
$708$	27.9499	1.05042
$709$	−27.0329	−1.01524	−0.507622	−	0.861580i	$-0.669475\pi$
$709$	−27.0329	−1.01524	−0.507622	+	0.861580i	$0.669475\pi$
$710$	−0.0150774	−0.000565843 0
$711$	−5.28983	−0.198384
$712$	−12.4510	−0.466619
$713$	20.9021	0.782791
$714$	−5.42512	−0.203030
$715$	13.4855	0.504330
$716$	−17.7976	−0.665128
$717$	52.9862	1.97881
$718$	−23.2605	−0.868075
$719$	−47.8432	−1.78425	−0.892125	−	0.451789i	$-0.850786\pi$
$719$	−47.8432	−1.78425	−0.892125	+	0.451789i	$0.850786\pi$
$720$	−1.10005	−0.0409966
$721$	8.34988	0.310966
$722$	0	0
$723$	−37.4092	−1.39126
$724$	5.92757	0.220296
$725$	27.7230	1.02961
$726$	1.67301	0.0620911
$727$	4.90682	0.181984	0.0909919	−	0.995852i	$-0.470996\pi$
$727$	4.90682	0.181984	0.0909919	+	0.995852i	$0.470996\pi$
$728$	−6.38112	−0.236500
$729$	−2.50327	−0.0927136
$730$	8.05138	0.297995
$731$	−25.6887	−0.950131
$732$	12.1320	0.448412
$733$	52.5699	1.94172	0.970858	−	0.239657i	$-0.0770349\pi$
$733$	52.5699	1.94172	0.970858	+	0.239657i	$0.0770349\pi$
$734$	−10.6463	−0.392962
$735$	1.34784	0.0497158
$736$	−2.70527	−0.0997177
$737$	−14.2852	−0.526203
$738$	−2.30051	−0.0846828
$739$	25.2192	0.927702	0.463851	−	0.885913i	$-0.346467\pi$
$739$	25.2192	0.927702	0.463851	+	0.885913i	$0.346467\pi$
$740$	2.62973	0.0966709
$741$	0	0
$742$	5.11208	0.187670
$743$	−5.58183	−0.204777	−0.102389	−	0.994744i	$-0.532649\pi$
$743$	−5.58183	−0.204777	−0.102389	+	0.994744i	$0.532649\pi$
$744$	16.9020	0.619658
$745$	−8.37889	−0.306979
$746$	−28.8794	−1.05735
$747$	23.1075	0.845461
$748$	8.50633	0.311022
$749$	13.5562	0.495333
$750$	12.9667	0.473477
$751$	−25.7524	−0.939718	−0.469859	−	0.882742i	$-0.655695\pi$
$751$	−25.7524	−0.939718	−0.469859	+	0.882742i	$0.655695\pi$
$752$	1.53750	0.0560668
$753$	−59.7413	−2.17709
$754$	−38.2878	−1.39436
$755$	−12.4661	−0.453686
$756$	−2.65701	−0.0966344
$757$	−45.3483	−1.64821	−0.824106	−	0.566435i	$-0.808322\pi$
$757$	−45.3483	−1.64821	−0.824106	+	0.566435i	$0.808322\pi$
$758$	−33.1311	−1.20338
$759$	−20.2984	−0.736786
$760$	0	0
$761$	−24.9534	−0.904560	−0.452280	−	0.891876i	$-0.649389\pi$
$761$	−24.9534	−0.904560	−0.452280	+	0.891876i	$0.649389\pi$
$762$	−9.72616	−0.352342
$763$	0.558302	0.0202119
$764$	16.3567	0.591764
$765$	−2.72813	−0.0986356
$766$	−3.65421	−0.132032
$767$	81.5300	2.94388
$768$	−2.18756	−0.0789366
$769$	12.9261	0.466126	0.233063	−	0.972462i	$-0.425125\pi$
$769$	12.9261	0.466126	0.233063	+	0.972462i	$0.425125\pi$
$770$	−2.11335	−0.0761597
$771$	−21.8059	−0.785321
$772$	−19.9885	−0.719403
$773$	−14.0205	−0.504281	−0.252141	−	0.967691i	$-0.581135\pi$
$773$	−14.0205	−0.504281	−0.252141	+	0.967691i	$0.581135\pi$
$774$	18.4938	0.664748
$775$	−35.6990	−1.28235
$776$	−1.51714	−0.0544621
$777$	−9.33667	−0.334951
$778$	9.25078	0.331657
$779$	0	0
$780$	−8.60072	−0.307955
$781$	−0.0839340	−0.00300340
$782$	−6.70905	−0.239915
$783$	−15.9425	−0.569738
$784$	1.00000	0.0357143
$785$	6.84511	0.244312
$786$	15.6888	0.559600
$787$	4.13771	0.147494	0.0737468	−	0.997277i	$-0.476504\pi$
$787$	4.13771	0.147494	0.0737468	+	0.997277i	$0.476504\pi$
$788$	−3.44430	−0.122698
$789$	54.5389	1.94164
$790$	−1.82552	−0.0649489
$791$	10.0986	0.359066
$792$	−6.12389	−0.217603
$793$	35.3892	1.25671
$794$	−19.2309	−0.682480
$795$	6.89026	0.244372
$796$	3.13027	0.110949
$797$	−53.5733	−1.89767	−0.948833	−	0.315780i	$-0.897734\pi$
$797$	−53.5733	−1.89767	−0.948833	+	0.315780i	$0.897734\pi$
$798$	0	0
$799$	3.81298	0.134894
$800$	4.62037	0.163355
$801$	22.2299	0.785456
$802$	−29.5430	−1.04320
$803$	44.8212	1.58170
$804$	9.11076	0.321312
$805$	1.66682	0.0587478
$806$	49.3034	1.73664
$807$	−56.1468	−1.97646
$808$	9.92823	0.349274
$809$	30.7139	1.07984	0.539922	−	0.841715i	$-0.318454\pi$
$809$	30.7139	1.07984	0.539922	+	0.841715i	$0.318454\pi$
$810$	−6.88138	−0.241787
$811$	43.6163	1.53158	0.765788	−	0.643093i	$-0.222349\pi$
$811$	43.6163	1.53158	0.765788	+	0.643093i	$0.222349\pi$
$812$	6.00017	0.210565
$813$	−41.1181	−1.44208
$814$	14.6395	0.513113
$815$	6.33410	0.221874
$816$	−5.42512	−0.189917
$817$	0	0
$818$	−39.8965	−1.39495
$819$	11.3929	0.398098
$820$	−0.793902	−0.0277243
$821$	−43.0095	−1.50104	−0.750521	−	0.660847i	$-0.770197\pi$
$821$	−43.0095	−1.50104	−0.750521	+	0.660847i	$0.770197\pi$
$822$	−36.7668	−1.28239
$823$	−3.41982	−0.119207	−0.0596037	−	0.998222i	$-0.518984\pi$
$823$	−3.41982	−0.119207	−0.0596037	+	0.998222i	$0.518984\pi$
$824$	8.34988	0.290882
$825$	34.6679	1.20698
$826$	−12.7768	−0.444560
$827$	27.6387	0.961093	0.480547	−	0.876969i	$-0.340438\pi$
$827$	27.6387	0.961093	0.480547	+	0.876969i	$0.340438\pi$
$828$	4.82999	0.167854
$829$	−25.7042	−0.892745	−0.446373	−	0.894847i	$-0.647284\pi$
$829$	−25.7042	−0.892745	−0.446373	+	0.894847i	$0.647284\pi$
$830$	7.97439	0.276795
$831$	−43.4765	−1.50818
$832$	−6.38112	−0.221226
$833$	2.47999	0.0859266
$834$	−29.6559	−1.02690
$835$	−7.80944	−0.270257
$836$	0	0
$837$	20.5292	0.709593
$838$	34.5562	1.19372
$839$	−36.9844	−1.27684	−0.638422	−	0.769686i	$-0.720413\pi$
$839$	−36.9844	−1.27684	−0.638422	+	0.769686i	$0.720413\pi$
$840$	1.34784	0.0465049
$841$	7.00200	0.241448
$842$	−28.8651	−0.994757
$843$	−46.5825	−1.60439
$844$	16.6987	0.574793
$845$	−17.0786	−0.587521
$846$	−2.74505	−0.0943766
$847$	−0.764783	−0.0262783
$848$	5.11208	0.175550
$849$	8.25727	0.283389
$850$	11.4585	0.393023
$851$	−11.5463	−0.395803
$852$	0.0535310	0.00183394
$853$	−39.1925	−1.34193	−0.670963	−	0.741491i	$-0.734119\pi$
$853$	−39.1925	−1.34193	−0.670963	+	0.741491i	$0.734119\pi$
$854$	−5.54592	−0.189777
$855$	0	0
$856$	13.5562	0.463342
$857$	5.62471	0.192136	0.0960682	−	0.995375i	$-0.469373\pi$
$857$	5.62471	0.192136	0.0960682	+	0.995375i	$0.469373\pi$
$858$	−47.8793	−1.63457
$859$	−23.0096	−0.785076	−0.392538	−	0.919736i	$-0.628403\pi$
$859$	−23.0096	−0.785076	−0.392538	+	0.919736i	$0.628403\pi$
$860$	6.38221	0.217631
$861$	2.81869	0.0960607
$862$	−19.4879	−0.663760
$863$	−10.3667	−0.352888	−0.176444	−	0.984311i	$-0.556459\pi$
$863$	−10.3667	−0.352888	−0.176444	+	0.984311i	$0.556459\pi$
$864$	−2.65701	−0.0903932
$865$	3.84740	0.130816
$866$	−1.44225	−0.0490097
$867$	23.7342	0.806055
$868$	−7.72644	−0.262252
$869$	−10.1625	−0.344738
$870$	8.08726	0.274184
$871$	26.5762	0.900499
$872$	0.558302	0.0189065
$873$	2.70870	0.0916756
$874$	0	0
$875$	−5.92749	−0.200386
$876$	−28.5858	−0.965825
$877$	37.9086	1.28008	0.640040	−	0.768341i	$-0.278918\pi$
$877$	37.9086	1.28008	0.640040	+	0.768341i	$0.278918\pi$
$878$	16.5525	0.558619
$879$	−37.0975	−1.25127
$880$	−2.11335	−0.0712409
$881$	26.1648	0.881514	0.440757	−	0.897626i	$-0.354710\pi$
$881$	26.1648	0.881514	0.440757	+	0.897626i	$0.354710\pi$
$882$	−1.78540	−0.0601175
$883$	−9.63158	−0.324128	−0.162064	−	0.986780i	$-0.551815\pi$
$883$	−9.63158	−0.324128	−0.162064	+	0.986780i	$0.551815\pi$
$884$	−15.8251	−0.532257
$885$	−17.2210	−0.578878
$886$	−3.08768	−0.103733
$887$	−1.96127	−0.0658531	−0.0329266	−	0.999458i	$-0.510483\pi$
$887$	−1.96127	−0.0658531	−0.0329266	+	0.999458i	$0.510483\pi$
$888$	−9.33667	−0.313318
$889$	4.44613	0.149119
$890$	7.67152	0.257150
$891$	−38.3079	−1.28336
$892$	−14.5844	−0.488320
$893$	0	0
$894$	29.7486	0.994942
$895$	10.9658	0.366546
$896$	1.00000	0.0334077
$897$	37.7631	1.26087
$898$	−17.9081	−0.597601
$899$	−46.3599	−1.54619
$900$	−8.24921	−0.274974
$901$	12.6779	0.422363
$902$	−4.41957	−0.147156
$903$	−22.6595	−0.754062
$904$	10.0986	0.335875
$905$	−3.65221	−0.121403
$906$	44.2598	1.47043
$907$	43.4844	1.44387	0.721937	−	0.691958i	$-0.243252\pi$
$907$	43.4844	1.44387	0.721937	+	0.691958i	$0.243252\pi$
$908$	4.73333	0.157081
$909$	−17.7259	−0.587930
$910$	3.93166	0.130333
$911$	4.93846	0.163618	0.0818092	−	0.996648i	$-0.473930\pi$
$911$	4.93846	0.163618	0.0818092	+	0.996648i	$0.473930\pi$
$912$	0	0
$913$	44.3926	1.46918
$914$	−31.2954	−1.03516
$915$	−7.47500	−0.247116
$916$	14.8611	0.491026
$917$	−7.17183	−0.236835
$918$	−6.58936	−0.217481
$919$	1.25165	0.0412883	0.0206441	−	0.999787i	$-0.493428\pi$
$919$	1.25165	0.0412883	0.0206441	+	0.999787i	$0.493428\pi$
$920$	1.66682	0.0549536
$921$	−5.87544	−0.193602
$922$	11.6085	0.382304
$923$	0.156150	0.00513975
$924$	7.50328	0.246840
$925$	19.7201	0.648394
$926$	−4.15132	−0.136421
$927$	−14.9079	−0.489639
$928$	6.00017	0.196965
$929$	−38.7110	−1.27007	−0.635034	−	0.772484i	$-0.719014\pi$
$929$	−38.7110	−1.27007	−0.635034	+	0.772484i	$0.719014\pi$
$930$	−10.4140	−0.341488
$931$	0	0
$932$	−4.36751	−0.143062
$933$	−3.87371	−0.126819
$934$	24.9196	0.815394
$935$	−5.24108	−0.171402
$936$	11.3929	0.372387
$937$	18.5473	0.605913	0.302957	−	0.953004i	$-0.402026\pi$
$937$	18.5473	0.605913	0.302957	+	0.953004i	$0.402026\pi$
$938$	−4.16481	−0.135986
$939$	−17.2758	−0.563773
$940$	−0.947313	−0.0308979
$941$	−24.6283	−0.802859	−0.401429	−	0.915890i	$-0.631487\pi$
$941$	−24.6283	−0.802859	−0.401429	+	0.915890i	$0.631487\pi$
$942$	−24.3030	−0.791835
$943$	3.48577	0.113512
$944$	−12.7768	−0.415848
$945$	1.63709	0.0532544
$946$	35.5291	1.15515
$947$	20.7160	0.673178	0.336589	−	0.941652i	$-0.390727\pi$
$947$	20.7160	0.673178	0.336589	+	0.941652i	$0.390727\pi$
$948$	6.48135	0.210505
$949$	−83.3851	−2.70679
$950$	0	0
$951$	−25.4199	−0.824296
$952$	2.47999	0.0803770
$953$	42.6761	1.38242	0.691208	−	0.722656i	$-0.257079\pi$
$953$	42.6761	1.38242	0.691208	+	0.722656i	$0.257079\pi$
$954$	−9.12710	−0.295501
$955$	−10.0780	−0.326116
$956$	−24.2217	−0.783385
$957$	45.0209	1.45532
$958$	18.9778	0.613144
$959$	16.8073	0.542735
$960$	1.34784	0.0435013
$961$	28.6979	0.925738
$962$	−27.2352	−0.878097
$963$	−24.2033	−0.779939
$964$	17.1009	0.550784
$965$	12.3157	0.396457
$966$	−5.91793	−0.190406
$967$	46.5740	1.49772	0.748860	−	0.662728i	$-0.230602\pi$
$967$	46.5740	1.49772	0.748860	+	0.662728i	$0.230602\pi$
$968$	−0.764783	−0.0245811
$969$	0	0
$970$	0.934769	0.0300136
$971$	−16.9447	−0.543782	−0.271891	−	0.962328i	$-0.587649\pi$
$971$	−16.9447	−0.543782	−0.271891	+	0.962328i	$0.587649\pi$
$972$	16.4608	0.527980
$973$	13.5566	0.434606
$974$	36.1508	1.15835
$975$	−64.4960	−2.06553
$976$	−5.54592	−0.177520
$977$	−10.1186	−0.323723	−0.161862	−	0.986813i	$-0.551750\pi$
$977$	−10.1186	−0.323723	−0.161862	+	0.986813i	$0.551750\pi$
$978$	−22.4887	−0.719110
$979$	42.7066	1.36491
$980$	−0.616139	−0.0196818
$981$	−0.996792	−0.0318251
$982$	−3.08754	−0.0985273
$983$	−36.8594	−1.17563	−0.587816	−	0.808995i	$-0.700012\pi$
$983$	−36.8594	−1.17563	−0.587816	+	0.808995i	$0.700012\pi$
$984$	2.81869	0.0898565
$985$	2.12217	0.0676179
$986$	14.8804	0.473887
$987$	3.36336	0.107057
$988$	0	0
$989$	−28.0222	−0.891055
$990$	3.77317	0.119919
$991$	−50.6580	−1.60921	−0.804603	−	0.593813i	$-0.797622\pi$
$991$	−50.6580	−1.60921	−0.804603	+	0.593813i	$0.797622\pi$
$992$	−7.72644	−0.245315
$993$	−2.52339	−0.0800774
$994$	−0.0244707	−0.000776163 0
$995$	−1.92868	−0.0611432
$996$	−28.3125	−0.897114
$997$	−19.9246	−0.631019	−0.315510	−	0.948922i	$-0.602175\pi$
$997$	−19.9246	−0.631019	−0.315510	+	0.948922i	$0.602175\pi$
$998$	−30.9593	−0.979999
$999$	−11.3403	−0.358792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bj.1.3		9
19.14	odd	18		266.2.u.c.253.1	yes	18
19.15	odd	18		266.2.u.c.225.1	✓	18
19.18	odd	2		5054.2.a.bk.1.7		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.c.225.1	✓	18	19.15	odd	18
266.2.u.c.253.1	yes	18	19.14	odd	18
5054.2.a.bj.1.3		9	1.1	even	1	trivial
5054.2.a.bk.1.7		9	19.18	odd	2

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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.18756 q^{3} +1.00000 q^{4} -0.616139 q^{5} +2.18756 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.78540 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.18756 q^{3} +1.00000 q^{4} -0.616139 q^{5} +2.18756 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.78540 q^{9} +0.616139 q^{10} +3.42998 q^{11} -2.18756 q^{12} -6.38112 q^{13} +1.00000 q^{14} +1.34784 q^{15} +1.00000 q^{16} +2.47999 q^{17} -1.78540 q^{18} -0.616139 q^{20} +2.18756 q^{21} -3.42998 q^{22} +2.70527 q^{23} +2.18756 q^{24} -4.62037 q^{25} +6.38112 q^{26} +2.65701 q^{27} -1.00000 q^{28} -6.00017 q^{29} -1.34784 q^{30} +7.72644 q^{31} -1.00000 q^{32} -7.50328 q^{33} -2.47999 q^{34} +0.616139 q^{35} +1.78540 q^{36} -4.26808 q^{37} +13.9591 q^{39} +0.616139 q^{40} +1.28851 q^{41} -2.18756 q^{42} -10.3584 q^{43} +3.42998 q^{44} -1.10005 q^{45} -2.70527 q^{46} +1.53750 q^{47} -2.18756 q^{48} +1.00000 q^{49} +4.62037 q^{50} -5.42512 q^{51} -6.38112 q^{52} +5.11208 q^{53} -2.65701 q^{54} -2.11335 q^{55} +1.00000 q^{56} +6.00017 q^{58} -12.7768 q^{59} +1.34784 q^{60} -5.54592 q^{61} -7.72644 q^{62} -1.78540 q^{63} +1.00000 q^{64} +3.93166 q^{65} +7.50328 q^{66} -4.16481 q^{67} +2.47999 q^{68} -5.91793 q^{69} -0.616139 q^{70} -0.0244707 q^{71} -1.78540 q^{72} +13.0675 q^{73} +4.26808 q^{74} +10.1073 q^{75} -3.42998 q^{77} -13.9591 q^{78} -2.96283 q^{79} -0.616139 q^{80} -11.1685 q^{81} -1.28851 q^{82} +12.9425 q^{83} +2.18756 q^{84} -1.52802 q^{85} +10.3584 q^{86} +13.1257 q^{87} -3.42998 q^{88} +12.4510 q^{89} +1.10005 q^{90} +6.38112 q^{91} +2.70527 q^{92} -16.9020 q^{93} -1.53750 q^{94} +2.18756 q^{96} +1.51714 q^{97} -1.00000 q^{98} +6.12389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} - 9 q^{8} + 12 q^{9}+O(q^{10}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 - 9 * q^8 + 12 * q^9	\( 9 q - 9 q^{2} - 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} - 9 q^{8} + 12 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} - 12 q^{13} + 9 q^{14} + 6 q^{15} + 9 q^{16} + 12 q^{17} - 12 q^{18} + 3 q^{20} + 3 q^{21} + 3 q^{22} + 6 q^{23} + 3 q^{24} + 12 q^{26} - 24 q^{27} - 9 q^{28} + 6 q^{29} - 6 q^{30} - 9 q^{31} - 9 q^{32} + 3 q^{33} - 12 q^{34} - 3 q^{35} + 12 q^{36} - 9 q^{37} + 33 q^{39} - 3 q^{40} - 3 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 18 q^{45} - 6 q^{46} + 21 q^{47} - 3 q^{48} + 9 q^{49} - 39 q^{51} - 12 q^{52} + 24 q^{54} + 24 q^{55} + 9 q^{56} - 6 q^{58} + 9 q^{59} + 6 q^{60} + 6 q^{61} + 9 q^{62} - 12 q^{63} + 9 q^{64} + 3 q^{65} - 3 q^{66} - 27 q^{67} + 12 q^{68} - 6 q^{69} + 3 q^{70} - 9 q^{71} - 12 q^{72} + 51 q^{73} + 9 q^{74} + 3 q^{75} + 3 q^{77} - 33 q^{78} - 24 q^{79} + 3 q^{80} - 3 q^{81} + 3 q^{82} + 9 q^{83} + 3 q^{84} + 6 q^{85} - 21 q^{86} - 3 q^{87} + 3 q^{88} - 9 q^{89} - 18 q^{90} + 12 q^{91} + 6 q^{92} + 3 q^{93} - 21 q^{94} + 3 q^{96} + 12 q^{97} - 9 q^{98} - 15 q^{99}+O(q^{100}) \) 9 * q - 9 * q^2 - 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 - 9 * q^8 + 12 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 - 12 * q^13 + 9 * q^14 + 6 * q^15 + 9 * q^16 + 12 * q^17 - 12 * q^18 + 3 * q^20 + 3 * q^21 + 3 * q^22 + 6 * q^23 + 3 * q^24 + 12 * q^26 - 24 * q^27 - 9 * q^28 + 6 * q^29 - 6 * q^30 - 9 * q^31 - 9 * q^32 + 3 * q^33 - 12 * q^34 - 3 * q^35 + 12 * q^36 - 9 * q^37 + 33 * q^39 - 3 * q^40 - 3 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 18 * q^45 - 6 * q^46 + 21 * q^47 - 3 * q^48 + 9 * q^49 - 39 * q^51 - 12 * q^52 + 24 * q^54 + 24 * q^55 + 9 * q^56 - 6 * q^58 + 9 * q^59 + 6 * q^60 + 6 * q^61 + 9 * q^62 - 12 * q^63 + 9 * q^64 + 3 * q^65 - 3 * q^66 - 27 * q^67 + 12 * q^68 - 6 * q^69 + 3 * q^70 - 9 * q^71 - 12 * q^72 + 51 * q^73 + 9 * q^74 + 3 * q^75 + 3 * q^77 - 33 * q^78 - 24 * q^79 + 3 * q^80 - 3 * q^81 + 3 * q^82 + 9 * q^83 + 3 * q^84 + 6 * q^85 - 21 * q^86 - 3 * q^87 + 3 * q^88 - 9 * q^89 - 18 * q^90 + 12 * q^91 + 6 * q^92 + 3 * q^93 - 21 * q^94 + 3 * q^96 + 12 * q^97 - 9 * q^98 - 15 * q^99

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