LMFDB - Embedded newform 121.8.a.f.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [121,8,Mod(1,121)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("121.1"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(121, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	121.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$37.7985880836$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 742x^{4} + 146056x^{2} - 6022080 $ x^6 - 742x^4 + 146056x^2 - 6022080
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$15.5920$ of defining polynomial
Character	$\chi$	$=$	121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+15.5920 q^{2} -64.5932 q^{3} +115.109 q^{4} -389.261 q^{5} -1007.13 q^{6} -1439.06 q^{7} -200.996 q^{8} +1985.28 q^{9} -6069.34 q^{10} -7435.25 q^{12} +9861.13 q^{13} -22437.8 q^{14} +25143.6 q^{15} -17867.9 q^{16} -12840.8 q^{17} +30954.4 q^{18} +29454.1 q^{19} -44807.5 q^{20} +92953.7 q^{21} -13190.0 q^{23} +12983.0 q^{24} +73399.3 q^{25} +153754. q^{26} +13029.9 q^{27} -165649. q^{28} +80678.5 q^{29} +392038. q^{30} -223348. q^{31} -252868. q^{32} -200212. q^{34} +560172. q^{35} +228523. q^{36} -506577. q^{37} +459248. q^{38} -636962. q^{39} +78240.0 q^{40} -407143. q^{41} +1.44933e6 q^{42} +650348. q^{43} -772791. q^{45} -205658. q^{46} +90177.3 q^{47} +1.15414e6 q^{48} +1.24736e6 q^{49} +1.14444e6 q^{50} +829425. q^{51} +1.13510e6 q^{52} +419636. q^{53} +203161. q^{54} +289246. q^{56} -1.90254e6 q^{57} +1.25793e6 q^{58} +742297. q^{59} +2.89426e6 q^{60} +1.64976e6 q^{61} -3.48244e6 q^{62} -2.85694e6 q^{63} -1.65561e6 q^{64} -3.83856e6 q^{65} -3.27999e6 q^{67} -1.47809e6 q^{68} +851984. q^{69} +8.73417e6 q^{70} +1.13876e6 q^{71} -399033. q^{72} -2.48383e6 q^{73} -7.89853e6 q^{74} -4.74109e6 q^{75} +3.39044e6 q^{76} -9.93148e6 q^{78} +5.02524e6 q^{79} +6.95527e6 q^{80} -5.18344e6 q^{81} -6.34816e6 q^{82} +5.29335e6 q^{83} +1.06998e7 q^{84} +4.99841e6 q^{85} +1.01402e7 q^{86} -5.21128e6 q^{87} -753558. q^{89} -1.20493e7 q^{90} -1.41908e7 q^{91} -1.51829e6 q^{92} +1.44268e7 q^{93} +1.40604e6 q^{94} -1.14654e7 q^{95} +1.63335e7 q^{96} +181489. q^{97} +1.94488e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 16 q^{3} + 716 q^{4} + 240 q^{5} + 3746 q^{9} + 27108 q^{12} - 51264 q^{14} + 88120 q^{15} + 45352 q^{16} + 81900 q^{20} - 55104 q^{23} + 108910 q^{25} + 56928 q^{26} + 73280 q^{27} - 254560 q^{31}+ \cdots + 10649568 q^{97}+O(q^{100}) $ 6 * q - 16 * q^3 + 716 * q^4 + 240 * q^5 + 3746 * q^9 + 27108 * q^12 - 51264 * q^14 + 88120 * q^15 + 45352 * q^16 + 81900 * q^20 - 55104 * q^23 + 108910 * q^25 + 56928 * q^26 + 73280 * q^27 - 254560 * q^31 - 2103776 * q^34 + 2027544 * q^36 - 252272 * q^37 + 2154240 * q^38 + 790240 * q^42 - 1092740 * q^45 + 372072 * q^47 + 7846456 * q^48 + 5017046 * q^49 + 4947636 * q^53 - 9608160 * q^56 + 3784000 * q^58 + 10205904 * q^59 + 18925140 * q^60 + 5409808 * q^64 - 11727568 * q^67 + 7645372 * q^69 + 12576640 * q^70 + 3862176 * q^71 - 5964800 * q^75 - 40017600 * q^78 + 40052040 * q^80 - 11954122 * q^81 + 23841440 * q^82 + 2122368 * q^86 + 3655008 * q^89 - 7026528 * q^91 + 29314212 * q^92 + 19011180 * q^93 + 10649568 * q^97

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 $

$2$	15.5920	1.37815	0.689073	−	0.724692i	$-0.258018\pi$
$2$	15.5920	1.37815	0.689073	+	0.724692i	$0.258018\pi$
$3$	−64.5932	−1.38122	−0.690609	−	0.723228i	$-0.742657\pi$
$3$	−64.5932	−1.38122	−0.690609	+	0.723228i	$0.742657\pi$
$4$	115.109	0.899289
$5$	−389.261	−1.39266	−0.696332	−	0.717720i	$-0.745186\pi$
$5$	−389.261	−1.39266	−0.696332	+	0.717720i	$0.745186\pi$
$6$	−1007.13	−1.90352
$7$	−1439.06	−1.58576	−0.792879	−	0.609379i	$-0.791419\pi$
$7$	−1439.06	−1.58576	−0.792879	+	0.609379i	$0.791419\pi$
$8$	−200.996	−0.138795
$9$	1985.28	0.907763
$10$	−6069.34	−1.91929
$11$	0	0
$11$	0	0
$12$	−7435.25	−1.24211
$13$	9861.13	1.24487	0.622436	−	0.782670i	$-0.286143\pi$
$13$	9861.13	1.24487	0.622436	+	0.782670i	$0.286143\pi$
$14$	−22437.8	−2.18541
$15$	25143.6	1.92357
$16$	−17867.9	−1.09057
$17$	−12840.8	−0.633898	−0.316949	−	0.948443i	$-0.602658\pi$
$17$	−12840.8	−0.633898	−0.316949	+	0.948443i	$0.602658\pi$
$18$	30954.4	1.25103
$19$	29454.1	0.985165	0.492582	−	0.870266i	$-0.336053\pi$
$19$	29454.1	0.985165	0.492582	+	0.870266i	$0.336053\pi$
$20$	−44807.5	−1.25241
$21$	92953.7	2.19028
$22$	0	0
$23$	−13190.0	−0.226046	−0.113023	−	0.993592i	$-0.536053\pi$
$23$	−13190.0	−0.226046	−0.113023	+	0.993592i	$0.536053\pi$
$24$	12983.0	0.191706
$25$	73399.3	0.939511
$26$	153754.	1.71562
$27$	13029.9	0.127399
$28$	−165649.	−1.42606
$29$	80678.5	0.614278	0.307139	−	0.951665i	$-0.400628\pi$
$29$	80678.5	0.614278	0.307139	+	0.951665i	$0.400628\pi$
$30$	392038.	2.65096
$31$	−223348.	−1.34653	−0.673266	−	0.739400i	$-0.735109\pi$
$31$	−223348.	−1.34653	−0.673266	+	0.739400i	$0.735109\pi$
$32$	−252868.	−1.36417
$33$	0	0
$34$	−200212.	−0.873604
$35$	560172.	2.20843
$36$	228523.	0.816341
$37$	−506577.	−1.64414	−0.822072	−	0.569384i	$-0.807182\pi$
$37$	−506577.	−1.64414	−0.822072	+	0.569384i	$0.807182\pi$
$38$	459248.	1.35770
$39$	−636962.	−1.71944
$40$	78240.0	0.193294
$41$	−407143.	−0.922580	−0.461290	−	0.887250i	$-0.652613\pi$
$41$	−407143.	−0.922580	−0.461290	+	0.887250i	$0.652613\pi$
$42$	1.44933e6	3.01852
$43$	650348.	1.24740	0.623700	−	0.781664i	$-0.285629\pi$
$43$	650348.	1.24740	0.623700	+	0.781664i	$0.285629\pi$
$44$	0	0
$45$	−772791.	−1.26421
$46$	−205658.	−0.311525
$47$	90177.3	0.126694	0.0633468	−	0.997992i	$-0.479823\pi$
$47$	90177.3	0.126694	0.0633468	+	0.997992i	$0.479823\pi$
$48$	1.15414e6	1.50631
$49$	1.24736e6	1.51463
$50$	1.14444e6	1.29478
$51$	829425.	0.875551
$52$	1.13510e6	1.11950
$53$	419636.	0.387175	0.193587	−	0.981083i	$-0.437988\pi$
$53$	419636.	0.387175	0.193587	+	0.981083i	$0.437988\pi$
$54$	203161.	0.175575
$55$	0	0
$56$	289246.	0.220095
$57$	−1.90254e6	−1.36073
$58$	1.25793e6	0.846565
$59$	742297.	0.470539	0.235269	−	0.971930i	$-0.424403\pi$
$59$	742297.	0.470539	0.235269	+	0.971930i	$0.424403\pi$
$60$	2.89426e6	1.72985
$61$	1.64976e6	0.930606	0.465303	−	0.885151i	$-0.345945\pi$
$61$	1.64976e6	0.930606	0.465303	+	0.885151i	$0.345945\pi$
$62$	−3.48244e6	−1.85572
$63$	−2.85694e6	−1.43949
$64$	−1.65561e6	−0.789457
$65$	−3.83856e6	−1.73369
$66$	0	0
$67$	−3.27999e6	−1.33233	−0.666164	−	0.745806i	$-0.732065\pi$
$67$	−3.27999e6	−1.33233	−0.666164	+	0.745806i	$0.732065\pi$
$68$	−1.47809e6	−0.570057
$69$	851984.	0.312219
$70$	8.73417e6	3.04354
$71$	1.13876e6	0.377597	0.188799	−	0.982016i	$-0.439541\pi$
$71$	1.13876e6	0.377597	0.188799	+	0.982016i	$0.439541\pi$
$72$	−399033.	−0.125993
$73$	−2.48383e6	−0.747294	−0.373647	−	0.927571i	$-0.621893\pi$
$73$	−2.48383e6	−0.747294	−0.373647	+	0.927571i	$0.621893\pi$
$74$	−7.89853e6	−2.26587
$75$	−4.74109e6	−1.29767
$76$	3.39044e6	0.885948
$77$	0	0
$78$	−9.93148e6	−2.36964
$79$	5.02524e6	1.14673	0.573366	−	0.819299i	$-0.305637\pi$
$79$	5.02524e6	1.14673	0.573366	+	0.819299i	$0.305637\pi$
$80$	6.95527e6	1.51879
$81$	−5.18344e6	−1.08373
$82$	−6.34816e6	−1.27145
$83$	5.29335e6	1.01615	0.508075	−	0.861313i	$-0.330357\pi$
$83$	5.29335e6	1.01615	0.508075	+	0.861313i	$0.330357\pi$
$84$	1.06998e7	1.96969
$85$	4.99841e6	0.882806
$86$	1.01402e7	1.71910
$87$	−5.21128e6	−0.848451
$88$	0	0
$89$	−753558.	−0.113306	−0.0566529	−	0.998394i	$-0.518043\pi$
$89$	−753558.	−0.113306	−0.0566529	+	0.998394i	$0.518043\pi$
$90$	−1.20493e7	−1.74226
$91$	−1.41908e7	−1.97407
$92$	−1.51829e6	−0.203281
$93$	1.44268e7	1.85985
$94$	1.40604e6	0.174602
$95$	−1.14654e7	−1.37200
$96$	1.63335e7	1.88421
$97$	181489.	0.0201906	0.0100953	−	0.999949i	$-0.496787\pi$
$97$	181489.	0.0201906	0.0100953	+	0.999949i	$0.496787\pi$
$98$	1.94488e7	2.08738
$99$	0	0
$100$	8.44891e6	0.844891
$101$	8.33741e6	0.805205	0.402603	−	0.915375i	$-0.368106\pi$
$101$	8.33741e6	0.805205	0.402603	+	0.915375i	$0.368106\pi$
$102$	1.29324e7	1.20664
$103$	5.28744e6	0.476777	0.238388	−	0.971170i	$-0.423381\pi$
$103$	5.28744e6	0.476777	0.238388	+	0.971170i	$0.423381\pi$
$104$	−1.98205e6	−0.172782
$105$	−3.61833e7	−3.05032
$106$	6.54294e6	0.533583
$107$	2.02654e6	0.159923	0.0799615	−	0.996798i	$-0.474520\pi$
$107$	2.02654e6	0.159923	0.0799615	+	0.996798i	$0.474520\pi$
$108$	1.49986e6	0.114569
$109$	−1.81174e7	−1.34000	−0.669998	−	0.742363i	$-0.733705\pi$
$109$	−1.81174e7	−1.34000	−0.669998	+	0.742363i	$0.733705\pi$
$110$	0	0
$111$	3.27214e7	2.27092
$112$	2.57130e7	1.72938
$113$	−60130.6	−0.00392032	−0.00196016	−	0.999998i	$-0.500624\pi$
$113$	−60130.6	−0.00392032	−0.00196016	+	0.999998i	$0.500624\pi$
$114$	−2.96643e7	−1.87528
$115$	5.13435e6	0.314806
$116$	9.28682e6	0.552413
$117$	1.95771e7	1.13005
$118$	1.15739e7	0.648472
$119$	1.84787e7	1.00521
$120$	−5.05377e6	−0.266981
$121$	0	0
$122$	2.57230e7	1.28251
$123$	2.62987e7	1.27428
$124$	−2.57094e7	−1.21092
$125$	1.83955e6	0.0842415
$126$	−4.45453e7	−1.98383
$127$	−753898.	−0.0326587	−0.0163294	−	0.999867i	$-0.505198\pi$
$127$	−753898.	−0.0326587	−0.0163294	+	0.999867i	$0.505198\pi$
$128$	6.55284e6	0.276182
$129$	−4.20080e7	−1.72293
$130$	−5.98506e7	−2.38928
$131$	1.98880e7	0.772932	0.386466	−	0.922304i	$-0.373696\pi$
$131$	1.98880e7	0.772932	0.386466	+	0.922304i	$0.373696\pi$
$132$	0	0
$133$	−4.23864e7	−1.56223
$134$	−5.11415e7	−1.83614
$135$	−5.07203e6	−0.177424
$136$	2.58094e6	0.0879816
$137$	−4.10773e7	−1.36483	−0.682417	−	0.730963i	$-0.739071\pi$
$137$	−4.10773e7	−1.36483	−0.682417	+	0.730963i	$0.739071\pi$
$138$	1.32841e7	0.430284
$139$	−1.67704e7	−0.529654	−0.264827	−	0.964296i	$-0.585315\pi$
$139$	−1.67704e7	−0.529654	−0.264827	+	0.964296i	$0.585315\pi$
$140$	6.44808e7	1.98601
$141$	−5.82484e6	−0.174991
$142$	1.77555e7	0.520385
$143$	0	0
$144$	−3.54727e7	−0.989978
$145$	−3.14050e7	−0.855482
$146$	−3.87277e7	−1.02988
$147$	−8.05711e7	−2.09203
$148$	−5.83116e7	−1.47856
$149$	5.51818e6	0.136661	0.0683303	−	0.997663i	$-0.478233\pi$
$149$	5.51818e6	0.136661	0.0683303	+	0.997663i	$0.478233\pi$
$150$	−7.39229e7	−1.78838
$151$	−4.27356e7	−1.01011	−0.505057	−	0.863086i	$-0.668529\pi$
$151$	−4.27356e7	−1.01011	−0.505057	+	0.863086i	$0.668529\pi$
$152$	−5.92017e6	−0.136736
$153$	−2.54925e7	−0.575429
$154$	0	0
$155$	8.69408e7	1.87527
$156$	−7.33200e7	−1.54627
$157$	1.33235e7	0.274770	0.137385	−	0.990518i	$-0.456130\pi$
$157$	1.33235e7	0.274770	0.137385	+	0.990518i	$0.456130\pi$
$158$	7.83533e7	1.58036
$159$	−2.71056e7	−0.534773
$160$	9.84315e7	1.89983
$161$	1.89813e7	0.358455
$162$	−8.08200e7	−1.49354
$163$	9.03819e6	0.163465	0.0817325	−	0.996654i	$-0.473955\pi$
$163$	9.03819e6	0.163465	0.0817325	+	0.996654i	$0.473955\pi$
$164$	−4.68659e7	−0.829666
$165$	0	0
$166$	8.25337e7	1.40040
$167$	1.12750e8	1.87330	0.936650	−	0.350267i	$-0.113909\pi$
$167$	1.12750e8	1.87330	0.936650	+	0.350267i	$0.113909\pi$
$168$	−1.86833e7	−0.303999
$169$	3.44934e7	0.549708
$170$	7.79349e7	1.21664
$171$	5.84747e7	0.894296
$172$	7.48608e7	1.12177
$173$	−1.05426e8	−1.54805	−0.774027	−	0.633152i	$-0.781761\pi$
$173$	−1.05426e8	−1.54805	−0.774027	+	0.633152i	$0.781761\pi$
$174$	−8.12540e7	−1.16929
$175$	−1.05626e8	−1.48984
$176$	0	0
$177$	−4.79473e7	−0.649917
$178$	−1.17494e7	−0.156152
$179$	1.22007e8	1.59001	0.795006	−	0.606602i	$-0.207468\pi$
$179$	1.22007e8	1.59001	0.795006	+	0.606602i	$0.207468\pi$
$180$	−8.89552e7	−1.13689
$181$	1.37642e8	1.72534	0.862670	−	0.505767i	$-0.168791\pi$
$181$	1.37642e8	1.72534	0.862670	+	0.505767i	$0.168791\pi$
$182$	−2.21262e8	−2.72056
$183$	−1.06563e8	−1.28537
$184$	2.65114e6	0.0313740
$185$	1.97191e8	2.28974
$186$	2.24942e8	2.56315
$187$	0	0
$188$	1.03802e7	0.113934
$189$	−1.87508e7	−0.202025
$190$	−1.78767e8	−1.89082
$191$	−4.03226e7	−0.418728	−0.209364	−	0.977838i	$-0.567139\pi$
$191$	−4.03226e7	−0.418728	−0.209364	+	0.977838i	$0.567139\pi$
$192$	1.06941e8	1.09041
$193$	6.10954e7	0.611727	0.305864	−	0.952075i	$-0.401055\pi$
$193$	6.10954e7	0.611727	0.305864	+	0.952075i	$0.401055\pi$
$194$	2.82977e6	0.0278257
$195$	2.47944e8	2.39460
$196$	1.43583e8	1.36209
$197$	2.17459e7	0.202650	0.101325	−	0.994853i	$-0.467692\pi$
$197$	2.17459e7	0.202650	0.101325	+	0.994853i	$0.467692\pi$
$198$	0	0
$199$	7.90058e7	0.710679	0.355339	−	0.934737i	$-0.384365\pi$
$199$	7.90058e7	0.710679	0.355339	+	0.934737i	$0.384365\pi$
$200$	−1.47530e7	−0.130399
$201$	2.11865e8	1.84023
$202$	1.29997e8	1.10969
$203$	−1.16101e8	−0.974096
$204$	9.54743e7	0.787373
$205$	1.58485e8	1.28484
$206$	8.24415e7	0.657068
$207$	−2.61858e7	−0.205196
$208$	−1.76197e8	−1.35762
$209$	0	0
$210$	−5.64168e8	−4.20379
$211$	−1.28026e8	−0.938231	−0.469115	−	0.883137i	$-0.655427\pi$
$211$	−1.28026e8	−0.938231	−0.469115	+	0.883137i	$0.655427\pi$
$212$	4.83038e7	0.348182
$213$	−7.35563e7	−0.521544
$214$	3.15977e7	0.220397
$215$	−2.53155e8	−1.73721
$216$	−2.61896e6	−0.0176824
$217$	3.21412e8	2.13527
$218$	−2.82486e8	−1.84671
$219$	1.60438e8	1.03218
$220$	0	0
$221$	−1.26624e8	−0.789122
$222$	5.10191e8	3.12966
$223$	−1.16676e7	−0.0704554	−0.0352277	−	0.999379i	$-0.511216\pi$
$223$	−1.16676e7	−0.0704554	−0.0352277	+	0.999379i	$0.511216\pi$
$224$	3.63893e8	2.16324
$225$	1.45718e8	0.852853
$226$	−937554.	−0.00540277
$227$	2.86492e7	0.162563	0.0812815	−	0.996691i	$-0.474099\pi$
$227$	2.86492e7	0.162563	0.0812815	+	0.996691i	$0.474099\pi$
$228$	−2.18999e8	−1.22369
$229$	2.83733e8	1.56130	0.780648	−	0.624971i	$-0.214889\pi$
$229$	2.83733e8	1.56130	0.780648	+	0.624971i	$0.214889\pi$
$230$	8.00546e7	0.433849
$231$	0	0
$232$	−1.62161e7	−0.0852584
$233$	−5.42579e7	−0.281007	−0.140504	−	0.990080i	$-0.544872\pi$
$233$	−5.42579e7	−0.281007	−0.140504	+	0.990080i	$0.544872\pi$
$234$	3.05245e8	1.55737
$235$	−3.51025e7	−0.176441
$236$	8.54450e7	0.423150
$237$	−3.24596e8	−1.58389
$238$	2.88118e8	1.38533
$239$	−4.07069e8	−1.92875	−0.964374	−	0.264542i	$-0.914779\pi$
$239$	−4.07069e8	−1.92875	−0.964374	+	0.264542i	$0.914779\pi$
$240$	−4.49263e8	−2.09779
$241$	−6.67562e7	−0.307207	−0.153604	−	0.988133i	$-0.549088\pi$
$241$	−6.67562e7	−0.307207	−0.153604	+	0.988133i	$0.549088\pi$
$242$	0	0
$243$	3.06319e8	1.36947
$244$	1.89902e8	0.836884
$245$	−4.85550e8	−2.10937
$246$	4.10048e8	1.75615
$247$	2.90451e8	1.22640
$248$	4.48921e7	0.186891
$249$	−3.41915e8	−1.40352
$250$	2.86821e7	0.116097
$251$	−2.64371e8	−1.05525	−0.527625	−	0.849477i	$-0.676917\pi$
$251$	−2.64371e8	−1.05525	−0.527625	+	0.849477i	$0.676917\pi$
$252$	−3.28860e8	−1.29452
$253$	0	0
$254$	−1.17547e7	−0.0450086
$255$	−3.22863e8	−1.21935
$256$	3.14090e8	1.17008
$257$	1.78743e8	0.656846	0.328423	−	0.944531i	$-0.393483\pi$
$257$	1.78743e8	0.656846	0.328423	+	0.944531i	$0.393483\pi$
$258$	−6.54987e8	−2.37445
$259$	7.28997e8	2.60721
$260$	−4.41852e8	−1.55909
$261$	1.60169e8	0.557618
$262$	3.10093e8	1.06521
$263$	3.84126e8	1.30205	0.651027	−	0.759055i	$-0.274338\pi$
$263$	3.84126e8	1.30205	0.651027	+	0.759055i	$0.274338\pi$
$264$	0	0
$265$	−1.63348e8	−0.539204
$266$	−6.60887e8	−2.15299
$267$	4.86747e7	0.156500
$268$	−3.77557e8	−1.19815
$269$	5.57804e8	1.74723	0.873613	−	0.486622i	$-0.161771\pi$
$269$	5.57804e8	1.74723	0.873613	+	0.486622i	$0.161771\pi$
$270$	−7.90828e7	−0.244517
$271$	3.89377e8	1.18844	0.594220	−	0.804303i	$-0.297461\pi$
$271$	3.89377e8	1.18844	0.594220	+	0.804303i	$0.297461\pi$
$272$	2.29437e8	0.691309
$273$	9.16629e8	2.72662
$274$	−6.40475e8	−1.88094
$275$	0	0
$276$	9.80710e7	0.280775
$277$	1.48403e8	0.419530	0.209765	−	0.977752i	$-0.432730\pi$
$277$	1.48403e8	0.419530	0.209765	+	0.977752i	$0.432730\pi$
$278$	−2.61483e8	−0.729940
$279$	−4.43408e8	−1.22233
$280$	−1.12592e8	−0.306518
$281$	7.06377e8	1.89917	0.949587	−	0.313504i	$-0.101503\pi$
$281$	7.06377e8	1.89917	0.949587	+	0.313504i	$0.101503\pi$
$282$	−9.08206e7	−0.241164
$283$	−4.47929e7	−0.117478	−0.0587390	−	0.998273i	$-0.518708\pi$
$283$	−4.47929e7	−0.117478	−0.0587390	+	0.998273i	$0.518708\pi$
$284$	1.31082e8	0.339569
$285$	7.40584e8	1.89503
$286$	0	0
$287$	5.85905e8	1.46299
$288$	−5.02012e8	−1.23834
$289$	−2.45454e8	−0.598174
$290$	−4.89665e8	−1.17898
$291$	−1.17230e7	−0.0278877
$292$	−2.85911e8	−0.672033
$293$	−3.16321e8	−0.734669	−0.367334	−	0.930089i	$-0.619730\pi$
$293$	−3.16321e8	−0.734669	−0.367334	+	0.930089i	$0.619730\pi$
$294$	−1.25626e9	−2.88313
$295$	−2.88947e8	−0.655302
$296$	1.01820e8	0.228198
$297$	0	0
$298$	8.60391e7	0.188339
$299$	−1.30068e8	−0.281399
$300$	−5.45742e8	−1.16698
$301$	−9.35892e8	−1.97808
$302$	−6.66331e8	−1.39209
$303$	−5.38540e8	−1.11216
$304$	−5.26283e8	−1.07439
$305$	−6.42187e8	−1.29602
$306$	−3.97477e8	−0.793026
$307$	−5.44406e8	−1.07384	−0.536918	−	0.843634i	$-0.680412\pi$
$307$	−5.44406e8	−1.07384	−0.536918	+	0.843634i	$0.680412\pi$
$308$	0	0
$309$	−3.41532e8	−0.658532
$310$	1.35558e9	2.58439
$311$	9.41155e8	1.77419	0.887095	−	0.461588i	$-0.152720\pi$
$311$	9.41155e8	1.77419	0.887095	+	0.461588i	$0.152720\pi$
$312$	1.28027e8	0.238649
$313$	−6.24562e8	−1.15125	−0.575626	−	0.817713i	$-0.695241\pi$
$313$	−6.24562e8	−1.15125	−0.575626	+	0.817713i	$0.695241\pi$
$314$	2.07739e8	0.378673
$315$	1.11210e9	2.00473
$316$	5.78450e8	1.03124
$317$	−7.63633e8	−1.34641	−0.673205	−	0.739456i	$-0.735083\pi$
$317$	−7.63633e8	−1.34641	−0.673205	+	0.739456i	$0.735083\pi$
$318$	−4.22629e8	−0.736995
$319$	0	0
$320$	6.44465e8	1.09945
$321$	−1.30900e8	−0.220889
$322$	2.95955e8	0.494003
$323$	−3.78213e8	−0.624494
$324$	−5.96661e8	−0.974586
$325$	7.23800e8	1.16957
$326$	1.40923e8	0.225279
$327$	1.17026e9	1.85083
$328$	8.18343e7	0.128049
$329$	−1.29771e8	−0.200905
$330$	0	0
$331$	8.81946e8	1.33673	0.668365	−	0.743833i	$-0.266994\pi$
$331$	8.81946e8	1.33673	0.668365	+	0.743833i	$0.266994\pi$
$332$	6.09313e8	0.913812
$333$	−1.00570e9	−1.49249
$334$	1.75799e9	2.58168
$335$	1.27677e9	1.85548
$336$	−1.66089e9	−2.38865
$337$	9.78415e7	0.139257	0.0696287	−	0.997573i	$-0.477819\pi$
$337$	9.78415e7	0.139257	0.0696287	+	0.997573i	$0.477819\pi$
$338$	5.37819e8	0.757579
$339$	3.88403e6	0.00541481
$340$	5.75361e8	0.793898
$341$	0	0
$342$	9.11734e8	1.23247
$343$	−6.09904e8	−0.816079
$344$	−1.30717e8	−0.173133
$345$	−3.31644e8	−0.434816
$346$	−1.64380e9	−2.13345
$347$	−1.30435e9	−1.67587	−0.837934	−	0.545771i	$-0.816237\pi$
$347$	−1.30435e9	−1.67587	−0.837934	+	0.545771i	$0.816237\pi$
$348$	−5.99865e8	−0.763003
$349$	1.43808e9	1.81090	0.905449	−	0.424455i	$-0.139534\pi$
$349$	1.43808e9	1.81090	0.905449	+	0.424455i	$0.139534\pi$
$350$	−1.64692e9	−2.05321
$351$	1.28489e8	0.158596
$352$	0	0
$353$	−7.29341e8	−0.882509	−0.441254	−	0.897382i	$-0.645466\pi$
$353$	−7.29341e8	−0.882509	−0.441254	+	0.897382i	$0.645466\pi$
$354$	−7.47592e8	−0.895681
$355$	−4.43276e8	−0.525866
$356$	−8.67413e7	−0.101895
$357$	−1.19360e9	−1.38841
$358$	1.90233e9	2.19127
$359$	−8.57786e8	−0.978472	−0.489236	−	0.872151i	$-0.662724\pi$
$359$	−8.57786e8	−0.978472	−0.489236	+	0.872151i	$0.662724\pi$
$360$	1.55328e8	0.175465
$361$	−2.63249e7	−0.0294504
$362$	2.14610e9	2.37777
$363$	0	0
$364$	−1.63349e9	−1.77526
$365$	9.66858e8	1.04073
$366$	−1.66153e9	−1.77143
$367$	6.22191e8	0.657041	0.328520	−	0.944497i	$-0.393450\pi$
$367$	6.22191e8	0.657041	0.328520	+	0.944497i	$0.393450\pi$
$368$	2.35677e8	0.246519
$369$	−8.08293e8	−0.837484
$370$	3.07459e9	3.15560
$371$	−6.03883e8	−0.613965
$372$	1.66065e9	1.67255
$373$	−4.62049e8	−0.461007	−0.230504	−	0.973071i	$-0.574037\pi$
$373$	−4.62049e8	−0.461007	−0.230504	+	0.973071i	$0.574037\pi$
$374$	0	0
$375$	−1.18822e8	−0.116356
$376$	−1.81253e7	−0.0175844
$377$	7.95581e8	0.764697
$378$	−2.92362e8	−0.278420
$379$	6.34924e8	0.599080	0.299540	−	0.954084i	$-0.403167\pi$
$379$	6.34924e8	0.599080	0.299540	+	0.954084i	$0.403167\pi$
$380$	−1.31977e9	−1.23383
$381$	4.86967e7	0.0451088
$382$	−6.28709e8	−0.577069
$383$	1.44381e9	1.31315	0.656574	−	0.754261i	$-0.272005\pi$
$383$	1.44381e9	1.31315	0.656574	+	0.754261i	$0.272005\pi$
$384$	−4.23269e8	−0.381467
$385$	0	0
$386$	9.52597e8	0.843050
$387$	1.29112e9	1.13234
$388$	2.08911e7	0.0181572
$389$	−6.22024e8	−0.535777	−0.267888	−	0.963450i	$-0.586326\pi$
$389$	−6.22024e8	−0.535777	−0.267888	+	0.963450i	$0.586326\pi$
$390$	3.86594e9	3.30011
$391$	1.69370e8	0.143290
$392$	−2.50715e8	−0.210223
$393$	−1.28463e9	−1.06759
$394$	3.39062e8	0.279281
$395$	−1.95613e9	−1.59701
$396$	0	0
$397$	−1.41277e9	−1.13319	−0.566596	−	0.823996i	$-0.691740\pi$
$397$	−1.41277e9	−1.13319	−0.566596	+	0.823996i	$0.691740\pi$
$398$	1.23186e9	0.979420
$399$	2.73787e9	2.15778
$400$	−1.31149e9	−1.02460
$401$	−1.23117e9	−0.953482	−0.476741	−	0.879044i	$-0.658182\pi$
$401$	−1.23117e9	−0.953482	−0.476741	+	0.879044i	$0.658182\pi$
$402$	3.30339e9	2.53611
$403$	−2.20247e9	−1.67626
$404$	9.59711e8	0.724112
$405$	2.01771e9	1.50927
$406$	−1.81025e9	−1.34245
$407$	0	0
$408$	−1.66711e8	−0.121522
$409$	−7.95236e8	−0.574731	−0.287365	−	0.957821i	$-0.592779\pi$
$409$	−7.95236e8	−0.574731	−0.287365	+	0.957821i	$0.592779\pi$
$410$	2.47109e9	1.77070
$411$	2.65331e9	1.88513
$412$	6.08632e8	0.428760
$413$	−1.06821e9	−0.746161
$414$	−4.08288e8	−0.282791
$415$	−2.06050e9	−1.41515
$416$	−2.49356e9	−1.69822
$417$	1.08325e9	0.731567
$418$	0	0
$419$	1.16169e9	0.771507	0.385753	−	0.922602i	$-0.373942\pi$
$419$	1.16169e9	0.771507	0.385753	+	0.922602i	$0.373942\pi$
$420$	−4.16502e9	−2.74312
$421$	−6.33220e8	−0.413587	−0.206794	−	0.978385i	$-0.566303\pi$
$421$	−6.33220e8	−0.413587	−0.206794	+	0.978385i	$0.566303\pi$
$422$	−1.99618e9	−1.29302
$423$	1.79027e8	0.115008
$424$	−8.43452e7	−0.0537378
$425$	−9.42502e8	−0.595554
$426$	−1.14689e9	−0.718765
$427$	−2.37411e9	−1.47572
$428$	2.33272e8	0.143817
$429$	0	0
$430$	−3.94718e9	−2.39413
$431$	−1.21482e9	−0.730871	−0.365435	−	0.930837i	$-0.619080\pi$
$431$	−1.21482e9	−0.730871	−0.365435	+	0.930837i	$0.619080\pi$
$432$	−2.32816e8	−0.138938
$433$	−1.35284e9	−0.800825	−0.400413	−	0.916335i	$-0.631133\pi$
$433$	−1.35284e9	−0.800825	−0.400413	+	0.916335i	$0.631133\pi$
$434$	5.01145e9	2.94272
$435$	2.02855e9	1.18161
$436$	−2.08548e9	−1.20504
$437$	−3.88500e8	−0.222693
$438$	2.50155e9	1.42249
$439$	1.75117e9	0.987877	0.493939	−	0.869497i	$-0.335557\pi$
$439$	1.75117e9	0.987877	0.493939	+	0.869497i	$0.335557\pi$
$440$	0	0
$441$	2.47636e9	1.37492
$442$	−1.97432e9	−1.08753
$443$	1.52217e9	0.831862	0.415931	−	0.909396i	$-0.363456\pi$
$443$	1.52217e9	0.831862	0.415931	+	0.909396i	$0.363456\pi$
$444$	3.76653e9	2.04221
$445$	2.93331e8	0.157797
$446$	−1.81920e8	−0.0970978
$447$	−3.56436e8	−0.188758
$448$	2.38253e9	1.25189
$449$	6.70359e8	0.349498	0.174749	−	0.984613i	$-0.444089\pi$
$449$	6.70359e8	0.349498	0.174749	+	0.984613i	$0.444089\pi$
$450$	2.27203e9	1.17536
$451$	0	0
$452$	−6.92157e6	−0.00352550
$453$	2.76043e9	1.39519
$454$	4.46696e8	0.224036
$455$	5.52393e9	2.74921
$456$	3.82403e8	0.188862
$457$	1.52084e9	0.745379	0.372690	−	0.927956i	$-0.378436\pi$
$457$	1.52084e9	0.745379	0.372690	+	0.927956i	$0.378436\pi$
$458$	4.42395e9	2.15169
$459$	−1.67314e8	−0.0807582
$460$	5.91010e8	0.283102
$461$	−3.40772e9	−1.61998	−0.809992	−	0.586441i	$-0.800529\pi$
$461$	−3.40772e9	−1.61998	−0.809992	+	0.586441i	$0.800529\pi$
$462$	0	0
$463$	−2.44774e9	−1.14612	−0.573062	−	0.819512i	$-0.694245\pi$
$463$	−2.44774e9	−1.14612	−0.573062	+	0.819512i	$0.694245\pi$
$464$	−1.44155e9	−0.669912
$465$	−5.61578e9	−2.59015
$466$	−8.45987e8	−0.387269
$467$	−1.88810e9	−0.857861	−0.428930	−	0.903338i	$-0.641109\pi$
$467$	−1.88810e9	−0.857861	−0.428930	+	0.903338i	$0.641109\pi$
$468$	2.25350e9	1.01624
$469$	4.72012e9	2.11275
$470$	−5.47317e8	−0.243162
$471$	−8.60606e8	−0.379517
$472$	−1.49199e8	−0.0653083
$473$	0	0
$474$	−5.06109e9	−2.18283
$475$	2.16191e9	0.925573
$476$	2.12706e9	0.903973
$477$	8.33093e8	0.351463
$478$	−6.34700e9	−2.65810
$479$	9.59217e8	0.398788	0.199394	−	0.979919i	$-0.436103\pi$
$479$	9.59217e8	0.398788	0.199394	+	0.979919i	$0.436103\pi$
$480$	−6.35800e9	−2.62408
$481$	−4.99543e9	−2.04675
$482$	−1.04086e9	−0.423377
$483$	−1.22606e9	−0.495104
$484$	0	0
$485$	−7.06468e7	−0.0281188
$486$	4.77611e9	1.88733
$487$	−2.73997e8	−0.107497	−0.0537483	−	0.998555i	$-0.517117\pi$
$487$	−2.73997e8	−0.107497	−0.0537483	+	0.998555i	$0.517117\pi$
$488$	−3.31595e8	−0.129163
$489$	−5.83805e8	−0.225781
$490$	−7.57067e9	−2.90702
$491$	2.81112e9	1.07175	0.535875	−	0.844297i	$-0.319982\pi$
$491$	2.81112e9	1.07175	0.535875	+	0.844297i	$0.319982\pi$
$492$	3.02721e9	1.14595
$493$	−1.03597e9	−0.389389
$494$	4.52870e9	1.69017
$495$	0	0
$496$	3.99076e9	1.46849
$497$	−1.63875e9	−0.598778
$498$	−5.33111e9	−1.93426
$499$	1.54321e9	0.555997	0.277998	−	0.960582i	$-0.410329\pi$
$499$	1.54321e9	0.555997	0.277998	+	0.960582i	$0.410329\pi$
$500$	2.11748e8	0.0757574
$501$	−7.28285e9	−2.58744
$502$	−4.12206e9	−1.45429
$503$	3.21540e9	1.12654	0.563270	−	0.826273i	$-0.309543\pi$
$503$	3.21540e9	1.12654	0.563270	+	0.826273i	$0.309543\pi$
$504$	5.74234e8	0.199794
$505$	−3.24543e9	−1.12138
$506$	0	0
$507$	−2.22804e9	−0.759267
$508$	−8.67804e7	−0.0293696
$509$	4.19858e9	1.41120	0.705602	−	0.708608i	$-0.250677\pi$
$509$	4.19858e9	1.41120	0.705602	+	0.708608i	$0.250677\pi$
$510$	−5.03406e9	−1.68044
$511$	3.57439e9	1.18503
$512$	4.05851e9	1.33635
$513$	3.83784e8	0.125509
$514$	2.78695e9	0.905230
$515$	−2.05819e9	−0.663989
$516$	−4.83550e9	−1.54941
$517$	0	0
$518$	1.13665e10	3.59313
$519$	6.80980e9	2.13820
$520$	7.71535e8	0.240627
$521$	−9.90828e8	−0.306949	−0.153475	−	0.988153i	$-0.549046\pi$
$521$	−9.90828e8	−0.306949	−0.153475	+	0.988153i	$0.549046\pi$
$522$	2.49735e9	0.768480
$523$	−4.37918e9	−1.33856	−0.669279	−	0.743011i	$-0.733397\pi$
$523$	−4.37918e9	−1.33856	−0.669279	+	0.743011i	$0.733397\pi$
$524$	2.28929e9	0.695089
$525$	6.82273e9	2.05779
$526$	5.98928e9	1.79442
$527$	2.86796e9	0.853564
$528$	0	0
$529$	−3.23085e9	−0.948903
$530$	−2.54691e9	−0.743102
$531$	1.47367e9	0.427138
$532$	−4.87906e9	−1.40490
$533$	−4.01489e9	−1.14849
$534$	7.58934e8	0.215680
$535$	−7.88852e8	−0.222719
$536$	6.59266e8	0.184920
$537$	−7.88084e9	−2.19615
$538$	8.69726e9	2.40793
$539$	0	0
$540$	−5.83836e8	−0.159556
$541$	−6.03111e9	−1.63759	−0.818797	−	0.574082i	$-0.805359\pi$
$541$	−6.03111e9	−1.63759	−0.818797	+	0.574082i	$0.805359\pi$
$542$	6.07114e9	1.63784
$543$	−8.89071e9	−2.38307
$544$	3.24701e9	0.864744
$545$	7.05240e9	1.86616
$546$	1.42920e10	3.75768
$547$	3.34376e8	0.0873532	0.0436766	−	0.999046i	$-0.486093\pi$
$547$	3.34376e8	0.0873532	0.0436766	+	0.999046i	$0.486093\pi$
$548$	−4.72836e9	−1.22738
$549$	3.27523e9	0.844770
$550$	0	0
$551$	2.37632e9	0.605165
$552$	−1.71245e8	−0.0433344
$553$	−7.23164e9	−1.81844
$554$	2.31389e9	0.578175
$555$	−1.27372e10	−3.16263
$556$	−1.93042e9	−0.476312
$557$	−7.42994e9	−1.82176	−0.910882	−	0.412667i	$-0.864597\pi$
$557$	−7.42994e9	−1.82176	−0.910882	+	0.412667i	$0.864597\pi$
$558$	−6.91360e9	−1.68455
$559$	6.41316e9	1.55286
$560$	−1.00091e10	−2.40844
$561$	0	0
$562$	1.10138e10	2.61734
$563$	−1.22416e8	−0.0289107	−0.0144554	−	0.999896i	$-0.504601\pi$
$563$	−1.22416e8	−0.0289107	−0.0144554	+	0.999896i	$0.504601\pi$
$564$	−6.70491e8	−0.157368
$565$	2.34065e7	0.00545968
$566$	−6.98409e8	−0.161902
$567$	7.45931e9	1.71853
$568$	−2.28887e8	−0.0524085
$569$	4.51809e8	0.102816	0.0514081	−	0.998678i	$-0.483629\pi$
$569$	4.51809e8	0.102816	0.0514081	+	0.998678i	$0.483629\pi$
$570$	1.15471e10	2.61164
$571$	5.21292e9	1.17180	0.585902	−	0.810382i	$-0.300740\pi$
$571$	5.21292e9	1.17180	0.585902	+	0.810382i	$0.300740\pi$
$572$	0	0
$573$	2.60457e9	0.578355
$574$	9.13541e9	2.01621
$575$	−9.68136e8	−0.212373
$576$	−3.28685e9	−0.716639
$577$	8.38244e9	1.81658	0.908291	−	0.418339i	$-0.137388\pi$
$577$	8.38244e9	1.81658	0.908291	+	0.418339i	$0.137388\pi$
$578$	−3.82710e9	−0.824371
$579$	−3.94635e9	−0.844929
$580$	−3.61500e9	−0.769325
$581$	−7.61748e9	−1.61137
$582$	−1.82784e8	−0.0384333
$583$	0	0
$584$	4.99240e8	0.103720
$585$	−7.62060e9	−1.57378
$586$	−4.93206e9	−1.01248
$587$	1.27671e9	0.260531	0.130266	−	0.991479i	$-0.458417\pi$
$587$	1.27671e9	0.260531	0.130266	+	0.991479i	$0.458417\pi$
$588$	−9.27446e9	−1.88134
$589$	−6.57853e9	−1.32656
$590$	−4.50525e9	−0.903103
$591$	−1.40464e9	−0.279904
$592$	9.05146e9	1.79305
$593$	−1.01389e9	−0.199663	−0.0998317	−	0.995004i	$-0.531830\pi$
$593$	−1.01389e9	−0.199663	−0.0998317	+	0.995004i	$0.531830\pi$
$594$	0	0
$595$	−7.19303e9	−1.39992
$596$	6.35192e8	0.122897
$597$	−5.10324e9	−0.981602
$598$	−2.02802e9	−0.387809
$599$	5.68301e9	1.08040	0.540200	−	0.841537i	$-0.318349\pi$
$599$	5.68301e9	1.08040	0.540200	+	0.841537i	$0.318349\pi$
$600$	9.52941e8	0.180110
$601$	−3.02010e9	−0.567494	−0.283747	−	0.958899i	$-0.591578\pi$
$601$	−3.02010e9	−0.567494	−0.283747	+	0.958899i	$0.591578\pi$
$602$	−1.45924e10	−2.72608
$603$	−6.51169e9	−1.20944
$604$	−4.91925e9	−0.908384
$605$	0	0
$606$	−8.39689e9	−1.53272
$607$	−4.85699e9	−0.881469	−0.440735	−	0.897637i	$-0.645282\pi$
$607$	−4.85699e9	−0.881469	−0.440735	+	0.897637i	$0.645282\pi$
$608$	−7.44800e9	−1.34393
$609$	7.49936e9	1.34544
$610$	−1.00129e10	−1.78611
$611$	8.89250e8	0.157717
$612$	−2.93441e9	−0.517477
$613$	1.31805e8	0.0231111	0.0115556	−	0.999933i	$-0.496322\pi$
$613$	1.31805e8	0.0231111	0.0115556	+	0.999933i	$0.496322\pi$
$614$	−8.48835e9	−1.47990
$615$	−1.02371e10	−1.77465
$616$	0	0
$617$	−9.20525e8	−0.157775	−0.0788874	−	0.996884i	$-0.525137\pi$
$617$	−9.20525e8	−0.157775	−0.0788874	+	0.996884i	$0.525137\pi$
$618$	−5.32516e9	−0.907555
$619$	−3.58891e9	−0.608198	−0.304099	−	0.952640i	$-0.598355\pi$
$619$	−3.58891e9	−0.608198	−0.304099	+	0.952640i	$0.598355\pi$
$620$	1.00077e10	1.68641
$621$	−1.71864e8	−0.0287982
$622$	1.46744e10	2.44509
$623$	1.08442e9	0.179675
$624$	1.13812e10	1.87517
$625$	−6.45038e9	−1.05683
$626$	−9.73814e9	−1.58659
$627$	0	0
$628$	1.53365e9	0.247097
$629$	6.50483e9	1.04222
$630$	1.73398e10	2.76281
$631$	−7.93335e8	−0.125705	−0.0628527	−	0.998023i	$-0.520020\pi$
$631$	−7.93335e8	−0.125705	−0.0628527	+	0.998023i	$0.520020\pi$
$632$	−1.01005e9	−0.159160
$633$	8.26961e9	1.29590
$634$	−1.19065e10	−1.85555
$635$	2.93463e8	0.0454826
$636$	−3.12010e9	−0.480915
$637$	1.23004e10	1.88552
$638$	0	0
$639$	2.26076e9	0.342769
$640$	−2.55077e9	−0.384628
$641$	1.14377e9	0.171529	0.0857644	−	0.996315i	$-0.472667\pi$
$641$	1.14377e9	0.171529	0.0857644	+	0.996315i	$0.472667\pi$
$642$	−2.04099e9	−0.304417
$643$	−9.62821e9	−1.42826	−0.714130	−	0.700014i	$-0.753177\pi$
$643$	−9.62821e9	−1.42826	−0.714130	+	0.700014i	$0.753177\pi$
$644$	2.18491e9	0.322354
$645$	1.63521e10	2.39946
$646$	−5.89709e9	−0.860644
$647$	5.15908e9	0.748871	0.374436	−	0.927253i	$-0.377837\pi$
$647$	5.15908e9	0.748871	0.374436	+	0.927253i	$0.377837\pi$
$648$	1.04185e9	0.150416
$649$	0	0
$650$	1.12855e10	1.61184
$651$	−2.07611e10	−2.94928
$652$	1.04038e9	0.147002
$653$	6.05908e9	0.851550	0.425775	−	0.904829i	$-0.360001\pi$
$653$	6.05908e9	0.851550	0.425775	+	0.904829i	$0.360001\pi$
$654$	1.82466e10	2.55071
$655$	−7.74162e9	−1.07643
$656$	7.27479e9	1.00614
$657$	−4.93109e9	−0.678366
$658$	−2.02338e9	−0.276877
$659$	1.32325e10	1.80112	0.900560	−	0.434731i	$-0.143157\pi$
$659$	1.32325e10	1.80112	0.900560	+	0.434731i	$0.143157\pi$
$660$	0	0
$661$	−3.66685e9	−0.493841	−0.246921	−	0.969036i	$-0.579419\pi$
$661$	−3.66685e9	−0.493841	−0.246921	+	0.969036i	$0.579419\pi$
$662$	1.37513e10	1.84221
$663$	8.17907e9	1.08995
$664$	−1.06394e9	−0.141036
$665$	1.64994e10	2.17566
$666$	−1.56808e10	−2.05687
$667$	−1.06415e9	−0.138855
$668$	1.29785e10	1.68464
$669$	7.53646e8	0.0973142
$670$	1.99074e10	2.55713
$671$	0	0
$672$	−2.35050e10	−2.98791
$673$	6.66087e9	0.842323	0.421161	−	0.906986i	$-0.361623\pi$
$673$	6.66087e9	0.842323	0.421161	+	0.906986i	$0.361623\pi$
$674$	1.52554e9	0.191917
$675$	9.56384e8	0.119693
$676$	3.97050e9	0.494347
$677$	8.60317e9	1.06561	0.532805	−	0.846238i	$-0.321138\pi$
$677$	8.60317e9	1.06561	0.532805	+	0.846238i	$0.321138\pi$
$678$	6.05596e7	0.00746240
$679$	−2.61175e8	−0.0320175
$680$	−1.00466e9	−0.122529
$681$	−1.85054e9	−0.224535
$682$	0	0
$683$	4.20048e9	0.504459	0.252230	−	0.967667i	$-0.418836\pi$
$683$	4.20048e9	0.504459	0.252230	+	0.967667i	$0.418836\pi$
$684$	6.73096e9	0.804231
$685$	1.59898e10	1.90075
$686$	−9.50960e9	−1.12468
$687$	−1.83272e10	−2.15649
$688$	−1.16203e10	−1.36038
$689$	4.13808e9	0.481983
$690$	−5.17098e9	−0.599240
$691$	1.28017e10	1.47603	0.738015	−	0.674785i	$-0.235764\pi$
$691$	1.28017e10	1.47603	0.738015	+	0.674785i	$0.235764\pi$
$692$	−1.21355e10	−1.39215
$693$	0	0
$694$	−2.03373e10	−2.30959
$695$	6.52807e9	0.737629
$696$	1.04745e9	0.117760
$697$	5.22803e9	0.584821
$698$	2.24225e10	2.49568
$699$	3.50469e9	0.388132
$700$	−1.21585e10	−1.33979
$701$	1.71594e10	1.88144	0.940720	−	0.339185i	$-0.110151\pi$
$701$	1.71594e10	1.88144	0.940720	+	0.339185i	$0.110151\pi$
$702$	2.00340e9	0.218569
$703$	−1.49208e10	−1.61975
$704$	0	0
$705$	2.26738e9	0.243704
$706$	−1.13718e10	−1.21623
$707$	−1.19981e10	−1.27686
$708$	−5.51917e9	−0.584463
$709$	9.67564e9	1.01957	0.509786	−	0.860301i	$-0.329725\pi$
$709$	9.67564e9	1.01957	0.509786	+	0.860301i	$0.329725\pi$
$710$	−6.91154e9	−0.724721
$711$	9.97649e9	1.04096
$712$	1.51462e8	0.0157262
$713$	2.94596e9	0.304379
$714$	−1.86105e10	−1.91344
$715$	0	0
$716$	1.40441e10	1.42988
$717$	2.62939e10	2.66402
$718$	−1.33746e10	−1.34848
$719$	6.51076e9	0.653252	0.326626	−	0.945154i	$-0.394088\pi$
$719$	6.51076e9	0.653252	0.326626	+	0.945154i	$0.394088\pi$
$720$	1.38081e10	1.37871
$721$	−7.60896e9	−0.756053
$722$	−4.10457e8	−0.0405870
$723$	4.31199e9	0.424320
$724$	1.58438e10	1.55158
$725$	5.92174e9	0.577120
$726$	0	0
$727$	6.05817e9	0.584751	0.292376	−	0.956304i	$-0.405554\pi$
$727$	6.05817e9	0.584751	0.292376	+	0.956304i	$0.405554\pi$
$728$	2.85230e9	0.273990
$729$	−8.44990e9	−0.807803
$730$	1.50752e10	1.43428
$731$	−8.35095e9	−0.790724
$732$	−1.22664e10	−1.15592
$733$	−2.86680e9	−0.268865	−0.134432	−	0.990923i	$-0.542921\pi$
$733$	−2.86680e9	−0.268865	−0.134432	+	0.990923i	$0.542921\pi$
$734$	9.70117e9	0.905499
$735$	3.13632e10	2.91350
$736$	3.33532e9	0.308365
$737$	0	0
$738$	−1.26029e10	−1.15418
$739$	−1.49594e9	−0.136351	−0.0681755	−	0.997673i	$-0.521718\pi$
$739$	−1.49594e9	−0.136351	−0.0681755	+	0.997673i	$0.521718\pi$
$740$	2.26984e10	2.05914
$741$	−1.87612e10	−1.69393
$742$	−9.41571e9	−0.846135
$743$	−3.76813e9	−0.337027	−0.168514	−	0.985699i	$-0.553897\pi$
$743$	−3.76813e9	−0.337027	−0.168514	+	0.985699i	$0.553897\pi$
$744$	−2.89973e9	−0.258138
$745$	−2.14801e9	−0.190322
$746$	−7.20425e9	−0.635335
$747$	1.05088e10	0.922423
$748$	0	0
$749$	−2.91632e9	−0.253599
$750$	−1.85267e9	−0.160355
$751$	−2.88994e9	−0.248971	−0.124486	−	0.992221i	$-0.539728\pi$
$751$	−2.88994e9	−0.248971	−0.124486	+	0.992221i	$0.539728\pi$
$752$	−1.61128e9	−0.138168
$753$	1.70766e10	1.45753
$754$	1.24047e10	1.05387
$755$	1.66353e10	1.40675
$756$	−2.15839e9	−0.181679
$757$	−1.56667e10	−1.31263	−0.656316	−	0.754487i	$-0.727886\pi$
$757$	−1.56667e10	−1.31263	−0.656316	+	0.754487i	$0.727886\pi$
$758$	9.89971e9	0.825620
$759$	0	0
$760$	2.30449e9	0.190427
$761$	−2.21136e10	−1.81892	−0.909459	−	0.415793i	$-0.863504\pi$
$761$	−2.21136e10	−1.81892	−0.909459	+	0.415793i	$0.863504\pi$
$762$	7.59276e8	0.0621666
$763$	2.60721e10	2.12491
$764$	−4.64150e9	−0.376558
$765$	9.92322e9	0.801379
$766$	2.25118e10	1.80971
$767$	7.31989e9	0.585761
$768$	−2.02881e10	−1.61613
$769$	2.52031e9	0.199854	0.0999269	−	0.994995i	$-0.468139\pi$
$769$	2.52031e9	0.199854	0.0999269	+	0.994995i	$0.468139\pi$
$770$	0	0
$771$	−1.15456e10	−0.907247
$772$	7.03263e9	0.550120
$773$	1.83618e10	1.42984	0.714920	−	0.699206i	$-0.246463\pi$
$773$	1.83618e10	1.42984	0.714920	+	0.699206i	$0.246463\pi$
$774$	2.01311e10	1.56054
$775$	−1.63936e10	−1.26508
$776$	−3.64787e7	−0.00280235
$777$	−4.70883e10	−3.60113
$778$	−9.69857e9	−0.738379
$779$	−1.19921e10	−0.908893
$780$	2.85406e10	2.15344
$781$	0	0
$782$	2.64080e9	0.197475
$783$	1.05123e9	0.0782586
$784$	−2.22877e10	−1.65181
$785$	−5.18631e9	−0.382662
$786$	−2.00299e10	−1.47129
$787$	−9.31123e9	−0.680919	−0.340460	−	0.940259i	$-0.610583\pi$
$787$	−9.31123e9	−0.680919	−0.340460	+	0.940259i	$0.610583\pi$
$788$	2.50315e9	0.182241
$789$	−2.48119e10	−1.79842
$790$	−3.04999e10	−2.20092
$791$	8.65318e7	0.00621667
$792$	0	0
$793$	1.62685e10	1.15849
$794$	−2.20278e10	−1.56170
$795$	1.05512e10	0.744758
$796$	9.09428e9	0.639106
$797$	2.55129e10	1.78507	0.892536	−	0.450975i	$-0.148924\pi$
$797$	2.55129e10	1.78507	0.892536	+	0.450975i	$0.148924\pi$
$798$	4.26888e10	2.97374
$799$	−1.15794e9	−0.0803108
$800$	−1.85603e10	−1.28165
$801$	−1.49602e9	−0.102855
$802$	−1.91963e10	−1.31404
$803$	0	0
$804$	2.43876e10	1.65490
$805$	−7.38867e9	−0.499207
$806$	−3.43408e10	−2.31013
$807$	−3.60304e10	−2.41330
$808$	−1.67579e9	−0.111758
$809$	2.63626e9	0.175052	0.0875262	−	0.996162i	$-0.472104\pi$
$809$	2.63626e9	0.175052	0.0875262	+	0.996162i	$0.472104\pi$
$810$	3.14601e10	2.08000
$811$	−6.63519e9	−0.436798	−0.218399	−	0.975860i	$-0.570083\pi$
$811$	−6.63519e9	−0.436798	−0.218399	+	0.975860i	$0.570083\pi$
$812$	−1.33643e10	−0.875994
$813$	−2.51511e10	−1.64149
$814$	0	0
$815$	−3.51822e9	−0.227652
$816$	−1.48201e10	−0.954848
$817$	1.91554e10	1.22890
$818$	−1.23993e10	−0.792063
$819$	−2.81727e10	−1.79199
$820$	1.82431e10	1.15544
$821$	−7.40469e9	−0.466988	−0.233494	−	0.972358i	$-0.575016\pi$
$821$	−7.40469e9	−0.466988	−0.233494	+	0.972358i	$0.575016\pi$
$822$	4.13703e10	2.59799
$823$	1.98304e10	1.24003	0.620014	−	0.784591i	$-0.287127\pi$
$823$	1.98304e10	1.24003	0.620014	+	0.784591i	$0.287127\pi$
$824$	−1.06275e9	−0.0661741
$825$	0	0
$826$	−1.66555e10	−1.02832
$827$	2.15969e10	1.32777	0.663883	−	0.747836i	$-0.268907\pi$
$827$	2.15969e10	1.32777	0.663883	+	0.747836i	$0.268907\pi$
$828$	−3.01422e9	−0.184531
$829$	−2.10732e10	−1.28466	−0.642332	−	0.766426i	$-0.722033\pi$
$829$	−2.10732e10	−1.28466	−0.642332	+	0.766426i	$0.722033\pi$
$830$	−3.21272e10	−1.95029
$831$	−9.58582e9	−0.579463
$832$	−1.63262e10	−0.982773
$833$	−1.60171e10	−0.960121
$834$	1.68900e10	1.00821
$835$	−4.38890e10	−2.60888
$836$	0	0
$837$	−2.91020e9	−0.171547
$838$	1.81130e10	1.06325
$839$	2.03583e10	1.19007	0.595037	−	0.803698i	$-0.297137\pi$
$839$	2.03583e10	1.19007	0.595037	+	0.803698i	$0.297137\pi$
$840$	7.27270e9	0.423368
$841$	−1.07409e10	−0.622663
$842$	−9.87314e9	−0.569984
$843$	−4.56272e10	−2.62317
$844$	−1.47369e10	−0.843741
$845$	−1.34269e10	−0.765559
$846$	2.79138e9	0.158498
$847$	0	0
$848$	−7.49800e9	−0.422240
$849$	2.89332e9	0.162263
$850$	−1.46954e10	−0.820760
$851$	6.68176e9	0.371653
$852$	−8.46699e9	−0.469019
$853$	−2.39686e10	−1.32227	−0.661136	−	0.750267i	$-0.729925\pi$
$853$	−2.39686e10	−1.32227	−0.661136	+	0.750267i	$0.729925\pi$
$854$	−3.70170e10	−2.03375
$855$	−2.27619e10	−1.24545
$856$	−4.07326e8	−0.0221965
$857$	−2.47593e9	−0.134371	−0.0671855	−	0.997741i	$-0.521402\pi$
$857$	−2.47593e9	−0.134371	−0.0671855	+	0.997741i	$0.521402\pi$
$858$	0	0
$859$	3.61781e9	0.194746	0.0973732	−	0.995248i	$-0.468956\pi$
$859$	3.61781e9	0.194746	0.0973732	+	0.995248i	$0.468956\pi$
$860$	−2.91404e10	−1.56225
$861$	−3.78455e10	−2.02071
$862$	−1.89414e10	−1.00725
$863$	1.29188e10	0.684205	0.342102	−	0.939663i	$-0.388861\pi$
$863$	1.29188e10	0.684205	0.342102	+	0.939663i	$0.388861\pi$
$864$	−3.29484e9	−0.173794
$865$	4.10382e10	2.15592
$866$	−2.10934e10	−1.10366
$867$	1.58546e10	0.826208
$868$	3.69975e10	1.92023
$869$	0	0
$870$	3.16290e10	1.62843
$871$	−3.23444e10	−1.65858
$872$	3.64153e9	0.185984
$873$	3.60307e8	0.0183283
$874$	−6.05748e9	−0.306903
$875$	−2.64723e9	−0.133587
$876$	1.84679e10	0.928225
$877$	3.10954e10	1.55667	0.778336	−	0.627847i	$-0.216064\pi$
$877$	3.10954e10	1.55667	0.778336	+	0.627847i	$0.216064\pi$
$878$	2.73042e10	1.36144
$879$	2.04322e10	1.01474
$880$	0	0
$881$	2.34971e10	1.15771	0.578853	−	0.815432i	$-0.303500\pi$
$881$	2.34971e10	1.15771	0.578853	+	0.815432i	$0.303500\pi$
$882$	3.86113e10	1.89485
$883$	3.60114e9	0.176026	0.0880132	−	0.996119i	$-0.471948\pi$
$883$	3.60114e9	0.176026	0.0880132	+	0.996119i	$0.471948\pi$
$884$	−1.45756e10	−0.709649
$885$	1.86640e10	0.905115
$886$	2.37337e10	1.14643
$887$	2.15527e10	1.03698	0.518489	−	0.855084i	$-0.326495\pi$
$887$	2.15527e10	1.03698	0.518489	+	0.855084i	$0.326495\pi$
$888$	−6.57688e9	−0.315192
$889$	1.08491e9	0.0517889
$890$	4.57360e9	0.217467
$891$	0	0
$892$	−1.34304e9	−0.0633597
$893$	2.65609e9	0.124814
$894$	−5.55754e9	−0.260137
$895$	−4.74927e10	−2.21435
$896$	−9.42996e9	−0.437957
$897$	8.40152e9	0.388673
$898$	1.04522e10	0.481660
$899$	−1.80194e10	−0.827144
$900$	1.67734e10	0.766961
$901$	−5.38844e9	−0.245429
$902$	0	0
$903$	6.04522e10	2.73215
$904$	1.20860e7	0.000544119 0
$905$	−5.35785e10	−2.40282
$906$	4.30404e10	1.92277
$907$	2.06001e10	0.916737	0.458368	−	0.888762i	$-0.348434\pi$
$907$	2.06001e10	0.916737	0.458368	+	0.888762i	$0.348434\pi$
$908$	3.29778e9	0.146191
$909$	1.65521e10	0.730935
$910$	8.61288e10	3.78882
$911$	4.29148e10	1.88058	0.940292	−	0.340369i	$-0.110552\pi$
$911$	4.29148e10	1.88058	0.940292	+	0.340369i	$0.110552\pi$
$912$	3.39943e10	1.48397
$913$	0	0
$914$	2.37129e10	1.02724
$915$	4.14809e10	1.79009
$916$	3.26602e10	1.40406
$917$	−2.86201e10	−1.22568
$918$	−2.60875e9	−0.111297
$919$	3.61363e10	1.53582	0.767908	−	0.640560i	$-0.221298\pi$
$919$	3.61363e10	1.53582	0.767908	+	0.640560i	$0.221298\pi$
$920$	−1.03199e9	−0.0436934
$921$	3.51649e10	1.48320
$922$	−5.31330e10	−2.23258
$923$	1.12295e10	0.470061
$924$	0	0
$925$	−3.71824e10	−1.54469
$926$	−3.81650e10	−1.57953
$927$	1.04970e10	0.432800
$928$	−2.04010e10	−0.837978
$929$	3.97214e9	0.162544	0.0812718	−	0.996692i	$-0.474102\pi$
$929$	3.97214e9	0.162544	0.0812718	+	0.996692i	$0.474102\pi$
$930$	−8.75610e10	−3.56961
$931$	3.67400e10	1.49216
$932$	−6.24558e9	−0.252707
$933$	−6.07922e10	−2.45054
$934$	−2.94392e10	−1.18226
$935$	0	0
$936$	−3.93492e9	−0.156845
$937$	4.24319e10	1.68502	0.842508	−	0.538683i	$-0.181078\pi$
$937$	4.24319e10	1.68502	0.842508	+	0.538683i	$0.181078\pi$
$938$	7.35959e10	2.91168
$939$	4.03424e10	1.59013
$940$	−4.04061e9	−0.158672
$941$	−3.36588e10	−1.31684	−0.658422	−	0.752649i	$-0.728776\pi$
$941$	−3.36588e10	−1.31684	−0.658422	+	0.752649i	$0.728776\pi$
$942$	−1.34185e10	−0.523030
$943$	5.37022e9	0.208546
$944$	−1.32633e10	−0.513155
$945$	7.29898e9	0.281352
$946$	0	0
$947$	−5.02050e10	−1.92098	−0.960488	−	0.278321i	$-0.910222\pi$
$947$	−5.02050e10	−1.92098	−0.960488	+	0.278321i	$0.910222\pi$
$948$	−3.73639e10	−1.42437
$949$	−2.44934e10	−0.930286
$950$	3.37084e10	1.27558
$951$	4.93254e10	1.85968
$952$	−3.71414e9	−0.139518
$953$	−2.06716e10	−0.773659	−0.386829	−	0.922151i	$-0.626430\pi$
$953$	−2.06716e10	−0.773659	−0.386829	+	0.922151i	$0.626430\pi$
$954$	1.29896e10	0.484367
$955$	1.56960e10	0.583147
$956$	−4.68573e10	−1.73450
$957$	0	0
$958$	1.49561e10	0.549589
$959$	5.91128e10	2.16430
$960$	−4.16280e10	−1.51858
$961$	2.23718e10	0.813148
$962$	−7.78884e10	−2.82072
$963$	4.02324e9	0.145172
$964$	−7.68423e9	−0.276268
$965$	−2.37821e10	−0.851930
$966$	−1.91167e10	−0.682326
$967$	1.61592e10	0.574683	0.287341	−	0.957828i	$-0.407229\pi$
$967$	1.61592e10	0.574683	0.287341	+	0.957828i	$0.407229\pi$
$968$	0	0
$969$	2.44300e10	0.862562
$970$	−1.10152e9	−0.0387518
$971$	4.59426e10	1.61045	0.805226	−	0.592968i	$-0.202044\pi$
$971$	4.59426e10	1.61045	0.805226	+	0.592968i	$0.202044\pi$
$972$	3.52600e10	1.23155
$973$	2.41337e10	0.839903
$974$	−4.27215e9	−0.148146
$975$	−4.67525e10	−1.61543
$976$	−2.94777e10	−1.01489
$977$	2.52292e10	0.865510	0.432755	−	0.901512i	$-0.357542\pi$
$977$	2.52292e10	0.865510	0.432755	+	0.901512i	$0.357542\pi$
$978$	−9.10266e9	−0.311159
$979$	0	0
$980$	−5.58912e10	−1.89693
$981$	−3.59681e10	−1.21640
$982$	4.38308e10	1.47703
$983$	2.35014e10	0.789145	0.394573	−	0.918865i	$-0.370893\pi$
$983$	2.35014e10	0.789145	0.394573	+	0.918865i	$0.370893\pi$
$984$	−5.28593e9	−0.176864
$985$	−8.46485e9	−0.282223
$986$	−1.61528e10	−0.536635
$987$	8.38231e9	0.277494
$988$	3.34335e10	1.10289
$989$	−8.57808e9	−0.281970
$990$	0	0
$991$	−2.08437e10	−0.680326	−0.340163	−	0.940367i	$-0.610482\pi$
$991$	−2.08437e10	−0.680326	−0.340163	+	0.940367i	$0.610482\pi$
$992$	5.64775e10	1.83690
$993$	−5.69677e10	−1.84632
$994$	−2.55514e10	−0.825205
$995$	−3.07539e10	−0.989736
$996$	−3.93574e10	−1.26217
$997$	3.10340e10	0.991757	0.495878	−	0.868392i	$-0.334846\pi$
$997$	3.10340e10	0.991757	0.495878	+	0.868392i	$0.334846\pi$
$998$	2.40616e10	0.766246
$999$	−6.60065e9	−0.209463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.8.a.f.1.5	yes	6
11.10	odd	2	inner	121.8.a.f.1.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.8.a.f.1.2	✓	6	11.10	odd	2	inner
121.8.a.f.1.5	yes	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	121.a (trivial)

\(f(q)\)	\(=\)	\(q+15.5920 q^{2} -64.5932 q^{3} +115.109 q^{4} -389.261 q^{5} -1007.13 q^{6} -1439.06 q^{7} -200.996 q^{8} +1985.28 q^{9} -6069.34 q^{10} -7435.25 q^{12} +9861.13 q^{13} -22437.8 q^{14} +25143.6 q^{15} -17867.9 q^{16} -12840.8 q^{17} +30954.4 q^{18} +29454.1 q^{19} -44807.5 q^{20} +92953.7 q^{21} -13190.0 q^{23} +12983.0 q^{24} +73399.3 q^{25} +153754. q^{26} +13029.9 q^{27} -165649. q^{28} +80678.5 q^{29} +392038. q^{30} -223348. q^{31} -252868. q^{32} -200212. q^{34} +560172. q^{35} +228523. q^{36} -506577. q^{37} +459248. q^{38} -636962. q^{39} +78240.0 q^{40} -407143. q^{41} +1.44933e6 q^{42} +650348. q^{43} -772791. q^{45} -205658. q^{46} +90177.3 q^{47} +1.15414e6 q^{48} +1.24736e6 q^{49} +1.14444e6 q^{50} +829425. q^{51} +1.13510e6 q^{52} +419636. q^{53} +203161. q^{54} +289246. q^{56} -1.90254e6 q^{57} +1.25793e6 q^{58} +742297. q^{59} +2.89426e6 q^{60} +1.64976e6 q^{61} -3.48244e6 q^{62} -2.85694e6 q^{63} -1.65561e6 q^{64} -3.83856e6 q^{65} -3.27999e6 q^{67} -1.47809e6 q^{68} +851984. q^{69} +8.73417e6 q^{70} +1.13876e6 q^{71} -399033. q^{72} -2.48383e6 q^{73} -7.89853e6 q^{74} -4.74109e6 q^{75} +3.39044e6 q^{76} -9.93148e6 q^{78} +5.02524e6 q^{79} +6.95527e6 q^{80} -5.18344e6 q^{81} -6.34816e6 q^{82} +5.29335e6 q^{83} +1.06998e7 q^{84} +4.99841e6 q^{85} +1.01402e7 q^{86} -5.21128e6 q^{87} -753558. q^{89} -1.20493e7 q^{90} -1.41908e7 q^{91} -1.51829e6 q^{92} +1.44268e7 q^{93} +1.40604e6 q^{94} -1.14654e7 q^{95} +1.63335e7 q^{96} +181489. q^{97} +1.94488e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 16 q^{3} + 716 q^{4} + 240 q^{5} + 3746 q^{9} + 27108 q^{12} - 51264 q^{14} + 88120 q^{15} + 45352 q^{16} + 81900 q^{20} - 55104 q^{23} + 108910 q^{25} + 56928 q^{26} + 73280 q^{27} - 254560 q^{31}+ \cdots + 10649568 q^{97}+O(q^{100}) \) 6 * q - 16 * q^3 + 716 * q^4 + 240 * q^5 + 3746 * q^9 + 27108 * q^12 - 51264 * q^14 + 88120 * q^15 + 45352 * q^16 + 81900 * q^20 - 55104 * q^23 + 108910 * q^25 + 56928 * q^26 + 73280 * q^27 - 254560 * q^31 - 2103776 * q^34 + 2027544 * q^36 - 252272 * q^37 + 2154240 * q^38 + 790240 * q^42 - 1092740 * q^45 + 372072 * q^47 + 7846456 * q^48 + 5017046 * q^49 + 4947636 * q^53 - 9608160 * q^56 + 3784000 * q^58 + 10205904 * q^59 + 18925140 * q^60 + 5409808 * q^64 - 11727568 * q^67 + 7645372 * q^69 + 12576640 * q^70 + 3862176 * q^71 - 5964800 * q^75 - 40017600 * q^78 + 40052040 * q^80 - 11954122 * q^81 + 23841440 * q^82 + 2122368 * q^86 + 3655008 * q^89 - 7026528 * q^91 + 29314212 * q^92 + 19011180 * q^93 + 10649568 * q^97

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