LMFDB - Embedded newform 6014.2.a.f.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.29017 q^{3} +1.00000 q^{4} +3.44095 q^{5} -1.29017 q^{6} -0.471801 q^{7} -1.00000 q^{8} -1.33547 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.29017 q^{3} +1.00000 q^{4} +3.44095 q^{5} -1.29017 q^{6} -0.471801 q^{7} -1.00000 q^{8} -1.33547 q^{9} -3.44095 q^{10} -1.26627 q^{11} +1.29017 q^{12} +2.78604 q^{13} +0.471801 q^{14} +4.43940 q^{15} +1.00000 q^{16} -6.13698 q^{17} +1.33547 q^{18} +0.199297 q^{19} +3.44095 q^{20} -0.608701 q^{21} +1.26627 q^{22} -8.85670 q^{23} -1.29017 q^{24} +6.84012 q^{25} -2.78604 q^{26} -5.59348 q^{27} -0.471801 q^{28} +6.27296 q^{29} -4.43940 q^{30} +1.00000 q^{31} -1.00000 q^{32} -1.63371 q^{33} +6.13698 q^{34} -1.62344 q^{35} -1.33547 q^{36} -10.0939 q^{37} -0.199297 q^{38} +3.59446 q^{39} -3.44095 q^{40} -12.0441 q^{41} +0.608701 q^{42} -11.3142 q^{43} -1.26627 q^{44} -4.59528 q^{45} +8.85670 q^{46} +1.29479 q^{47} +1.29017 q^{48} -6.77740 q^{49} -6.84012 q^{50} -7.91772 q^{51} +2.78604 q^{52} +7.50149 q^{53} +5.59348 q^{54} -4.35719 q^{55} +0.471801 q^{56} +0.257127 q^{57} -6.27296 q^{58} +3.31010 q^{59} +4.43940 q^{60} +0.0255868 q^{61} -1.00000 q^{62} +0.630075 q^{63} +1.00000 q^{64} +9.58663 q^{65} +1.63371 q^{66} -1.11184 q^{67} -6.13698 q^{68} -11.4266 q^{69} +1.62344 q^{70} +9.58260 q^{71} +1.33547 q^{72} +6.45692 q^{73} +10.0939 q^{74} +8.82490 q^{75} +0.199297 q^{76} +0.597429 q^{77} -3.59446 q^{78} -9.96197 q^{79} +3.44095 q^{80} -3.21011 q^{81} +12.0441 q^{82} +10.0833 q^{83} -0.608701 q^{84} -21.1170 q^{85} +11.3142 q^{86} +8.09316 q^{87} +1.26627 q^{88} -14.9846 q^{89} +4.59528 q^{90} -1.31446 q^{91} -8.85670 q^{92} +1.29017 q^{93} -1.29479 q^{94} +0.685772 q^{95} -1.29017 q^{96} +1.00000 q^{97} +6.77740 q^{98} +1.69107 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.29017	0.744878	0.372439	−	0.928057i	$-0.378522\pi$
$3$	1.29017	0.744878	0.372439	+	0.928057i	$0.378522\pi$
$4$	1.00000	0.500000
$5$	3.44095	1.53884	0.769419	−	0.638744i	$-0.220546\pi$
$5$	3.44095	1.53884	0.769419	+	0.638744i	$0.220546\pi$
$6$	−1.29017	−0.526708
$7$	−0.471801	−0.178324	−0.0891619	−	0.996017i	$-0.528419\pi$
$7$	−0.471801	−0.178324	−0.0891619	+	0.996017i	$0.528419\pi$
$8$	−1.00000	−0.353553
$9$	−1.33547	−0.445157
$10$	−3.44095	−1.08812
$11$	−1.26627	−0.381796	−0.190898	−	0.981610i	$-0.561140\pi$
$11$	−1.26627	−0.381796	−0.190898	+	0.981610i	$0.561140\pi$
$12$	1.29017	0.372439
$13$	2.78604	0.772709	0.386355	−	0.922350i	$-0.373734\pi$
$13$	2.78604	0.772709	0.386355	+	0.922350i	$0.373734\pi$
$14$	0.471801	0.126094
$15$	4.43940	1.14625
$16$	1.00000	0.250000
$17$	−6.13698	−1.48844	−0.744218	−	0.667937i	$-0.767178\pi$
$17$	−6.13698	−1.48844	−0.744218	+	0.667937i	$0.767178\pi$
$18$	1.33547	0.314773
$19$	0.199297	0.0457220	0.0228610	−	0.999739i	$-0.492722\pi$
$19$	0.199297	0.0457220	0.0228610	+	0.999739i	$0.492722\pi$
$20$	3.44095	0.769419
$21$	−0.608701	−0.132830
$22$	1.26627	0.269971
$23$	−8.85670	−1.84675	−0.923375	−	0.383900i	$-0.874581\pi$
$23$	−8.85670	−1.84675	−0.923375	+	0.383900i	$0.874581\pi$
$24$	−1.29017	−0.263354
$25$	6.84012	1.36802
$26$	−2.78604	−0.546388
$27$	−5.59348	−1.07647
$28$	−0.471801	−0.0891619
$29$	6.27296	1.16486	0.582429	−	0.812881i	$-0.302102\pi$
$29$	6.27296	1.16486	0.582429	+	0.812881i	$0.302102\pi$
$30$	−4.43940	−0.810519
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−1.63371	−0.284392
$34$	6.13698	1.05248
$35$	−1.62344	−0.274412
$36$	−1.33547	−0.222578
$37$	−10.0939	−1.65942	−0.829710	−	0.558195i	$-0.811494\pi$
$37$	−10.0939	−1.65942	−0.829710	+	0.558195i	$0.811494\pi$
$38$	−0.199297	−0.0323303
$39$	3.59446	0.575574
$40$	−3.44095	−0.544062
$41$	−12.0441	−1.88097	−0.940486	−	0.339832i	$-0.889630\pi$
$41$	−12.0441	−1.88097	−0.940486	+	0.339832i	$0.889630\pi$
$42$	0.608701	0.0939246
$43$	−11.3142	−1.72540	−0.862698	−	0.505719i	$-0.831227\pi$
$43$	−11.3142	−1.72540	−0.862698	+	0.505719i	$0.831227\pi$
$44$	−1.26627	−0.190898
$45$	−4.59528	−0.685024
$46$	8.85670	1.30585
$47$	1.29479	0.188864	0.0944322	−	0.995531i	$-0.469896\pi$
$47$	1.29479	0.188864	0.0944322	+	0.995531i	$0.469896\pi$
$48$	1.29017	0.186220
$49$	−6.77740	−0.968201
$50$	−6.84012	−0.967339
$51$	−7.91772	−1.10870
$52$	2.78604	0.386355
$53$	7.50149	1.03041	0.515204	−	0.857067i	$-0.327716\pi$
$53$	7.50149	1.03041	0.515204	+	0.857067i	$0.327716\pi$
$54$	5.59348	0.761176
$55$	−4.35719	−0.587523
$56$	0.471801	0.0630470
$57$	0.257127	0.0340573
$58$	−6.27296	−0.823679
$59$	3.31010	0.430939	0.215469	−	0.976511i	$-0.430872\pi$
$59$	3.31010	0.430939	0.215469	+	0.976511i	$0.430872\pi$
$60$	4.43940	0.573124
$61$	0.0255868	0.00327605	0.00163803	−	0.999999i	$-0.499479\pi$
$61$	0.0255868	0.00327605	0.00163803	+	0.999999i	$0.499479\pi$
$62$	−1.00000	−0.127000
$63$	0.630075	0.0793820
$64$	1.00000	0.125000
$65$	9.58663	1.18908
$66$	1.63371	0.201095
$67$	−1.11184	−0.135833	−0.0679163	−	0.997691i	$-0.521635\pi$
$67$	−1.11184	−0.135833	−0.0679163	+	0.997691i	$0.521635\pi$
$68$	−6.13698	−0.744218
$69$	−11.4266	−1.37560
$70$	1.62344	0.194038
$71$	9.58260	1.13725	0.568623	−	0.822598i	$-0.307476\pi$
$71$	9.58260	1.13725	0.568623	+	0.822598i	$0.307476\pi$
$72$	1.33547	0.157387
$73$	6.45692	0.755726	0.377863	−	0.925862i	$-0.376659\pi$
$73$	6.45692	0.755726	0.377863	+	0.925862i	$0.376659\pi$
$74$	10.0939	1.17339
$75$	8.82490	1.01901
$76$	0.199297	0.0228610
$77$	0.597429	0.0680834
$78$	−3.59446	−0.406992
$79$	−9.96197	−1.12081	−0.560404	−	0.828219i	$-0.689354\pi$
$79$	−9.96197	−1.12081	−0.560404	+	0.828219i	$0.689354\pi$
$80$	3.44095	0.384710
$81$	−3.21011	−0.356679
$82$	12.0441	1.33005
$83$	10.0833	1.10678	0.553391	−	0.832922i	$-0.313334\pi$
$83$	10.0833	1.10678	0.553391	+	0.832922i	$0.313334\pi$
$84$	−0.608701	−0.0664148
$85$	−21.1170	−2.29046
$86$	11.3142	1.22004
$87$	8.09316	0.867678
$88$	1.26627	0.134985
$89$	−14.9846	−1.58837	−0.794183	−	0.607678i	$-0.792101\pi$
$89$	−14.9846	−1.58837	−0.794183	+	0.607678i	$0.792101\pi$
$90$	4.59528	0.484385
$91$	−1.31446	−0.137793
$92$	−8.85670	−0.923375
$93$	1.29017	0.133784
$94$	−1.29479	−0.133547
$95$	0.685772	0.0703587
$96$	−1.29017	−0.131677
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	6.77740	0.684621
$99$	1.69107	0.169959
$100$	6.84012	0.684012
$101$	−11.6069	−1.15493	−0.577465	−	0.816415i	$-0.695958\pi$
$101$	−11.6069	−1.15493	−0.577465	+	0.816415i	$0.695958\pi$
$102$	7.91772	0.783971
$103$	3.52460	0.347289	0.173644	−	0.984808i	$-0.444446\pi$
$103$	3.52460	0.347289	0.173644	+	0.984808i	$0.444446\pi$
$104$	−2.78604	−0.273194
$105$	−2.09451	−0.204403
$106$	−7.50149	−0.728609
$107$	11.4973	1.11148	0.555741	−	0.831355i	$-0.312435\pi$
$107$	11.4973	1.11148	0.555741	+	0.831355i	$0.312435\pi$
$108$	−5.59348	−0.538233
$109$	−11.8256	−1.13269	−0.566345	−	0.824168i	$-0.691643\pi$
$109$	−11.8256	−1.13269	−0.566345	+	0.824168i	$0.691643\pi$
$110$	4.35719	0.415441
$111$	−13.0228	−1.23607
$112$	−0.471801	−0.0445810
$113$	−13.3050	−1.25163	−0.625815	−	0.779971i	$-0.715234\pi$
$113$	−13.3050	−1.25163	−0.625815	+	0.779971i	$0.715234\pi$
$114$	−0.257127	−0.0240821
$115$	−30.4754	−2.84185
$116$	6.27296	0.582429
$117$	−3.72068	−0.343977
$118$	−3.31010	−0.304720
$119$	2.89543	0.265424
$120$	−4.43940	−0.405260
$121$	−9.39655	−0.854232
$122$	−0.0255868	−0.00231652
$123$	−15.5389	−1.40109
$124$	1.00000	0.0898027
$125$	6.33177	0.566330
$126$	−0.630075	−0.0561316
$127$	−5.48629	−0.486830	−0.243415	−	0.969922i	$-0.578268\pi$
$127$	−5.48629	−0.486830	−0.243415	+	0.969922i	$0.578268\pi$
$128$	−1.00000	−0.0883883
$129$	−14.5972	−1.28521
$130$	−9.58663	−0.840803
$131$	16.8902	1.47570	0.737851	−	0.674964i	$-0.235841\pi$
$131$	16.8902	1.47570	0.737851	+	0.674964i	$0.235841\pi$
$132$	−1.63371	−0.142196
$133$	−0.0940286	−0.00815332
$134$	1.11184	0.0960482
$135$	−19.2469	−1.65651
$136$	6.13698	0.526241
$137$	12.3241	1.05292	0.526459	−	0.850201i	$-0.323519\pi$
$137$	12.3241	1.05292	0.526459	+	0.850201i	$0.323519\pi$
$138$	11.4266	0.972698
$139$	17.9081	1.51894	0.759471	−	0.650541i	$-0.225458\pi$
$139$	17.9081	1.51894	0.759471	+	0.650541i	$0.225458\pi$
$140$	−1.62344	−0.137206
$141$	1.67049	0.140681
$142$	−9.58260	−0.804154
$143$	−3.52790	−0.295018
$144$	−1.33547	−0.111289
$145$	21.5849	1.79253
$146$	−6.45692	−0.534379
$147$	−8.74398	−0.721191
$148$	−10.0939	−0.829710
$149$	−19.4597	−1.59420	−0.797099	−	0.603849i	$-0.793633\pi$
$149$	−19.4597	−1.59420	−0.797099	+	0.603849i	$0.793633\pi$
$150$	−8.82490	−0.720550
$151$	−10.0579	−0.818504	−0.409252	−	0.912421i	$-0.634210\pi$
$151$	−10.0579	−0.818504	−0.409252	+	0.912421i	$0.634210\pi$
$152$	−0.199297	−0.0161652
$153$	8.19575	0.662587
$154$	−0.597429	−0.0481422
$155$	3.44095	0.276384
$156$	3.59446	0.287787
$157$	12.0887	0.964785	0.482392	−	0.875955i	$-0.339768\pi$
$157$	12.0887	0.964785	0.482392	+	0.875955i	$0.339768\pi$
$158$	9.96197	0.792532
$159$	9.67817	0.767529
$160$	−3.44095	−0.272031
$161$	4.17860	0.329319
$162$	3.21011	0.252210
$163$	−14.3175	−1.12144	−0.560718	−	0.828007i	$-0.689475\pi$
$163$	−14.3175	−1.12144	−0.560718	+	0.828007i	$0.689475\pi$
$164$	−12.0441	−0.940486
$165$	−5.62150	−0.437633
$166$	−10.0833	−0.782612
$167$	25.4809	1.97177	0.985884	−	0.167428i	$-0.0535462\pi$
$167$	25.4809	1.97177	0.985884	+	0.167428i	$0.0535462\pi$
$168$	0.608701	0.0469623
$169$	−5.23796	−0.402920
$170$	21.1170	1.61960
$171$	−0.266156	−0.0203534
$172$	−11.3142	−0.862698
$173$	−5.89813	−0.448427	−0.224213	−	0.974540i	$-0.571981\pi$
$173$	−5.89813	−0.448427	−0.224213	+	0.974540i	$0.571981\pi$
$174$	−8.09316	−0.613541
$175$	−3.22717	−0.243951
$176$	−1.26627	−0.0954491
$177$	4.27058	0.320997
$178$	14.9846	1.12315
$179$	4.65176	0.347689	0.173844	−	0.984773i	$-0.444381\pi$
$179$	4.65176	0.347689	0.173844	+	0.984773i	$0.444381\pi$
$180$	−4.59528	−0.342512
$181$	19.6081	1.45746	0.728730	−	0.684801i	$-0.240111\pi$
$181$	19.6081	1.45746	0.728730	+	0.684801i	$0.240111\pi$
$182$	1.31446	0.0974340
$183$	0.0330112	0.00244026
$184$	8.85670	0.652925
$185$	−34.7324	−2.55358
$186$	−1.29017	−0.0945996
$187$	7.77110	0.568279
$188$	1.29479	0.0944322
$189$	2.63901	0.191959
$190$	−0.685772	−0.0497511
$191$	−11.0545	−0.799875	−0.399938	−	0.916542i	$-0.630968\pi$
$191$	−11.0545	−0.799875	−0.399938	+	0.916542i	$0.630968\pi$
$192$	1.29017	0.0931098
$193$	−9.57344	−0.689112	−0.344556	−	0.938766i	$-0.611970\pi$
$193$	−9.57344	−0.689112	−0.344556	+	0.938766i	$0.611970\pi$
$194$	−1.00000	−0.0717958
$195$	12.3684	0.885716
$196$	−6.77740	−0.484100
$197$	4.40356	0.313740	0.156870	−	0.987619i	$-0.449860\pi$
$197$	4.40356	0.313740	0.156870	+	0.987619i	$0.449860\pi$
$198$	−1.69107	−0.120179
$199$	−24.0496	−1.70483	−0.852414	−	0.522867i	$-0.824862\pi$
$199$	−24.0496	−1.70483	−0.852414	+	0.522867i	$0.824862\pi$
$200$	−6.84012	−0.483670
$201$	−1.43446	−0.101179
$202$	11.6069	0.816659
$203$	−2.95958	−0.207722
$204$	−7.91772	−0.554352
$205$	−41.4431	−2.89451
$206$	−3.52460	−0.245570
$207$	11.8279	0.822093
$208$	2.78604	0.193177
$209$	−0.252365	−0.0174565
$210$	2.09451	0.144535
$211$	26.1602	1.80094	0.900472	−	0.434913i	$-0.143221\pi$
$211$	26.1602	1.80094	0.900472	+	0.434913i	$0.143221\pi$
$212$	7.50149	0.515204
$213$	12.3632	0.847109
$214$	−11.4973	−0.785937
$215$	−38.9315	−2.65511
$216$	5.59348	0.380588
$217$	−0.471801	−0.0320279
$218$	11.8256	0.800933
$219$	8.33051	0.562923
$220$	−4.35719	−0.293761
$221$	−17.0979	−1.15013
$222$	13.0228	0.874030
$223$	7.87359	0.527255	0.263627	−	0.964625i	$-0.415081\pi$
$223$	7.87359	0.527255	0.263627	+	0.964625i	$0.415081\pi$
$224$	0.471801	0.0315235
$225$	−9.13478	−0.608985
$226$	13.3050	0.885036
$227$	16.0640	1.06621	0.533103	−	0.846050i	$-0.321026\pi$
$227$	16.0640	1.06621	0.533103	+	0.846050i	$0.321026\pi$
$228$	0.257127	0.0170286
$229$	6.17220	0.407870	0.203935	−	0.978984i	$-0.434627\pi$
$229$	6.17220	0.407870	0.203935	+	0.978984i	$0.434627\pi$
$230$	30.4754	2.00949
$231$	0.770783	0.0507138
$232$	−6.27296	−0.411840
$233$	16.8040	1.10087	0.550433	−	0.834879i	$-0.314463\pi$
$233$	16.8040	1.10087	0.550433	+	0.834879i	$0.314463\pi$
$234$	3.72068	0.243228
$235$	4.45530	0.290632
$236$	3.31010	0.215469
$237$	−12.8526	−0.834866
$238$	−2.89543	−0.187683
$239$	−9.83269	−0.636024	−0.318012	−	0.948087i	$-0.603015\pi$
$239$	−9.83269	−0.636024	−0.318012	+	0.948087i	$0.603015\pi$
$240$	4.43940	0.286562
$241$	−5.70154	−0.367269	−0.183634	−	0.982995i	$-0.558786\pi$
$241$	−5.70154	−0.367269	−0.183634	+	0.982995i	$0.558786\pi$
$242$	9.39655	0.604033
$243$	12.6389	0.810783
$244$	0.0255868	0.00163803
$245$	−23.3207	−1.48990
$246$	15.5389	0.990724
$247$	0.555251	0.0353298
$248$	−1.00000	−0.0635001
$249$	13.0091	0.824417
$250$	−6.33177	−0.400456
$251$	27.3903	1.72886	0.864429	−	0.502755i	$-0.167680\pi$
$251$	27.3903	1.72886	0.864429	+	0.502755i	$0.167680\pi$
$252$	0.630075	0.0396910
$253$	11.2150	0.705082
$254$	5.48629	0.344241
$255$	−27.2445	−1.70612
$256$	1.00000	0.0625000
$257$	−31.2864	−1.95159	−0.975795	−	0.218686i	$-0.929823\pi$
$257$	−31.2864	−1.95159	−0.975795	+	0.218686i	$0.929823\pi$
$258$	14.5972	0.908781
$259$	4.76229	0.295914
$260$	9.58663	0.594538
$261$	−8.37734	−0.518545
$262$	−16.8902	−1.04348
$263$	−15.5292	−0.957571	−0.478786	−	0.877932i	$-0.658923\pi$
$263$	−15.5292	−0.957571	−0.478786	+	0.877932i	$0.658923\pi$
$264$	1.63371	0.100548
$265$	25.8122	1.58563
$266$	0.0940286	0.00576527
$267$	−19.3327	−1.18314
$268$	−1.11184	−0.0679163
$269$	−23.8608	−1.45482	−0.727411	−	0.686202i	$-0.759276\pi$
$269$	−23.8608	−1.45482	−0.727411	+	0.686202i	$0.759276\pi$
$270$	19.2469	1.17133
$271$	−17.6105	−1.06976	−0.534881	−	0.844928i	$-0.679643\pi$
$271$	−17.6105	−1.06976	−0.534881	+	0.844928i	$0.679643\pi$
$272$	−6.13698	−0.372109
$273$	−1.69587	−0.102639
$274$	−12.3241	−0.744525
$275$	−8.66148	−0.522307
$276$	−11.4266	−0.687802
$277$	7.66931	0.460804	0.230402	−	0.973096i	$-0.425996\pi$
$277$	7.66931	0.460804	0.230402	+	0.973096i	$0.425996\pi$
$278$	−17.9081	−1.07405
$279$	−1.33547	−0.0799525
$280$	1.62344	0.0970192
$281$	14.5027	0.865161	0.432580	−	0.901595i	$-0.357603\pi$
$281$	14.5027	0.865161	0.432580	+	0.901595i	$0.357603\pi$
$282$	−1.67049	−0.0994765
$283$	−15.6645	−0.931160	−0.465580	−	0.885006i	$-0.654154\pi$
$283$	−15.6645	−0.931160	−0.465580	+	0.885006i	$0.654154\pi$
$284$	9.58260	0.568623
$285$	0.884760	0.0524087
$286$	3.52790	0.208609
$287$	5.68241	0.335422
$288$	1.33547	0.0786933
$289$	20.6625	1.21544
$290$	−21.5849	−1.26751
$291$	1.29017	0.0756309
$292$	6.45692	0.377863
$293$	20.0526	1.17148	0.585742	−	0.810497i	$-0.300803\pi$
$293$	20.0526	1.17148	0.585742	+	0.810497i	$0.300803\pi$
$294$	8.74398	0.509959
$295$	11.3899	0.663145
$296$	10.0939	0.586694
$297$	7.08288	0.410990
$298$	19.4597	1.12727
$299$	−24.6752	−1.42700
$300$	8.82490	0.509506
$301$	5.33804	0.307679
$302$	10.0579	0.578770
$303$	−14.9748	−0.860282
$304$	0.199297	0.0114305
$305$	0.0880429	0.00504132
$306$	−8.19575	−0.468520
$307$	1.68762	0.0963173	0.0481586	−	0.998840i	$-0.484665\pi$
$307$	1.68762	0.0963173	0.0481586	+	0.998840i	$0.484665\pi$
$308$	0.597429	0.0340417
$309$	4.54732	0.258688
$310$	−3.44095	−0.195433
$311$	19.6559	1.11459	0.557293	−	0.830316i	$-0.311840\pi$
$311$	19.6559	1.11459	0.557293	+	0.830316i	$0.311840\pi$
$312$	−3.59446	−0.203496
$313$	5.25654	0.297117	0.148558	−	0.988904i	$-0.452537\pi$
$313$	5.25654	0.297117	0.148558	+	0.988904i	$0.452537\pi$
$314$	−12.0887	−0.682206
$315$	2.16806	0.122156
$316$	−9.96197	−0.560404
$317$	6.43051	0.361173	0.180587	−	0.983559i	$-0.442200\pi$
$317$	6.43051	0.361173	0.180587	+	0.983559i	$0.442200\pi$
$318$	−9.67817	−0.542725
$319$	−7.94329	−0.444739
$320$	3.44095	0.192355
$321$	14.8334	0.827919
$322$	−4.17860	−0.232864
$323$	−1.22308	−0.0680542
$324$	−3.21011	−0.178339
$325$	19.0569	1.05709
$326$	14.3175	0.792975
$327$	−15.2570	−0.843716
$328$	12.0441	0.665024
$329$	−0.610882	−0.0336790
$330$	5.62150	0.309453
$331$	0.797046	0.0438096	0.0219048	−	0.999760i	$-0.493027\pi$
$331$	0.797046	0.0438096	0.0219048	+	0.999760i	$0.493027\pi$
$332$	10.0833	0.553391
$333$	13.4800	0.738702
$334$	−25.4809	−1.39425
$335$	−3.82578	−0.209025
$336$	−0.608701	−0.0332074
$337$	31.4047	1.71072	0.855362	−	0.518030i	$-0.173334\pi$
$337$	31.4047	1.71072	0.855362	+	0.518030i	$0.173334\pi$
$338$	5.23796	0.284908
$339$	−17.1657	−0.932312
$340$	−21.1170	−1.14523
$341$	−1.26627	−0.0685726
$342$	0.266156	0.0143921
$343$	6.50019	0.350977
$344$	11.3142	0.610020
$345$	−39.3184	−2.11683
$346$	5.89813	0.317086
$347$	−4.23015	−0.227086	−0.113543	−	0.993533i	$-0.536220\pi$
$347$	−4.23015	−0.227086	−0.113543	+	0.993533i	$0.536220\pi$
$348$	8.09316	0.433839
$349$	−26.9435	−1.44225	−0.721126	−	0.692804i	$-0.756375\pi$
$349$	−26.9435	−1.44225	−0.721126	+	0.692804i	$0.756375\pi$
$350$	3.22717	0.172500
$351$	−15.5837	−0.831795
$352$	1.26627	0.0674927
$353$	21.6494	1.15228	0.576140	−	0.817351i	$-0.304558\pi$
$353$	21.6494	1.15228	0.576140	+	0.817351i	$0.304558\pi$
$354$	−4.27058	−0.226979
$355$	32.9732	1.75004
$356$	−14.9846	−0.794183
$357$	3.73559	0.197708
$358$	−4.65176	−0.245853
$359$	18.3880	0.970479	0.485240	−	0.874381i	$-0.338732\pi$
$359$	18.3880	0.970479	0.485240	+	0.874381i	$0.338732\pi$
$360$	4.59528	0.242193
$361$	−18.9603	−0.997910
$362$	−19.6081	−1.03058
$363$	−12.1231	−0.636298
$364$	−1.31446	−0.0688963
$365$	22.2179	1.16294
$366$	−0.0330112	−0.00172553
$367$	16.7085	0.872177	0.436088	−	0.899904i	$-0.356363\pi$
$367$	16.7085	0.872177	0.436088	+	0.899904i	$0.356363\pi$
$368$	−8.85670	−0.461687
$369$	16.0845	0.837327
$370$	34.7324	1.80565
$371$	−3.53921	−0.183746
$372$	1.29017	0.0668920
$373$	4.02059	0.208178	0.104089	−	0.994568i	$-0.466807\pi$
$373$	4.02059	0.208178	0.104089	+	0.994568i	$0.466807\pi$
$374$	−7.77110	−0.401834
$375$	8.16903	0.421847
$376$	−1.29479	−0.0667737
$377$	17.4767	0.900097
$378$	−2.63901	−0.135736
$379$	−28.8681	−1.48285	−0.741426	−	0.671034i	$-0.765850\pi$
$379$	−28.8681	−1.48285	−0.741426	+	0.671034i	$0.765850\pi$
$380$	0.685772	0.0351794
$381$	−7.07823	−0.362629
$382$	11.0545	0.565597
$383$	−3.18432	−0.162711	−0.0813556	−	0.996685i	$-0.525925\pi$
$383$	−3.18432	−0.162711	−0.0813556	+	0.996685i	$0.525925\pi$
$384$	−1.29017	−0.0658385
$385$	2.05572	0.104769
$386$	9.57344	0.487275
$387$	15.1098	0.768072
$388$	1.00000	0.0507673
$389$	−3.89594	−0.197532	−0.0987660	−	0.995111i	$-0.531490\pi$
$389$	−3.89594	−0.197532	−0.0987660	+	0.995111i	$0.531490\pi$
$390$	−12.3684	−0.626296
$391$	54.3534	2.74877
$392$	6.77740	0.342311
$393$	21.7911	1.09922
$394$	−4.40356	−0.221848
$395$	−34.2786	−1.72474
$396$	1.69107	0.0849796
$397$	26.6704	1.33855	0.669274	−	0.743016i	$-0.266605\pi$
$397$	26.6704	1.33855	0.669274	+	0.743016i	$0.266605\pi$
$398$	24.0496	1.20550
$399$	−0.121313	−0.00607323
$400$	6.84012	0.342006
$401$	1.80624	0.0901992	0.0450996	−	0.998982i	$-0.485639\pi$
$401$	1.80624	0.0901992	0.0450996	+	0.998982i	$0.485639\pi$
$402$	1.43446	0.0715442
$403$	2.78604	0.138783
$404$	−11.6069	−0.577465
$405$	−11.0458	−0.548871
$406$	2.95958	0.146882
$407$	12.7816	0.633560
$408$	7.91772	0.391986
$409$	11.5225	0.569749	0.284875	−	0.958565i	$-0.408048\pi$
$409$	11.5225	0.569749	0.284875	+	0.958565i	$0.408048\pi$
$410$	41.4431	2.04673
$411$	15.9001	0.784295
$412$	3.52460	0.173644
$413$	−1.56171	−0.0768466
$414$	−11.8279	−0.581308
$415$	34.6960	1.70316
$416$	−2.78604	−0.136597
$417$	23.1044	1.13143
$418$	0.252365	0.0123436
$419$	−11.3355	−0.553777	−0.276889	−	0.960902i	$-0.589303\pi$
$419$	−11.3355	−0.553777	−0.276889	+	0.960902i	$0.589303\pi$
$420$	−2.09451	−0.102202
$421$	−20.4346	−0.995923	−0.497962	−	0.867199i	$-0.665918\pi$
$421$	−20.4346	−0.995923	−0.497962	+	0.867199i	$0.665918\pi$
$422$	−26.1602	−1.27346
$423$	−1.72915	−0.0840743
$424$	−7.50149	−0.364304
$425$	−41.9777	−2.03622
$426$	−12.3632	−0.598997
$427$	−0.0120719	−0.000584199 0
$428$	11.4973	0.555741
$429$	−4.55157	−0.219752
$430$	38.9315	1.87744
$431$	39.0145	1.87926	0.939632	−	0.342187i	$-0.111168\pi$
$431$	39.0145	1.87926	0.939632	+	0.342187i	$0.111168\pi$
$432$	−5.59348	−0.269116
$433$	−27.7980	−1.33589	−0.667943	−	0.744213i	$-0.732825\pi$
$433$	−27.7980	−1.33589	−0.667943	+	0.744213i	$0.732825\pi$
$434$	0.471801	0.0226471
$435$	27.8481	1.33522
$436$	−11.8256	−0.566345
$437$	−1.76512	−0.0844370
$438$	−8.33051	−0.398047
$439$	−20.7400	−0.989866	−0.494933	−	0.868931i	$-0.664807\pi$
$439$	−20.7400	−0.989866	−0.494933	+	0.868931i	$0.664807\pi$
$440$	4.35719	0.207721
$441$	9.05102	0.431001
$442$	17.0979	0.813264
$443$	−29.6454	−1.40850	−0.704248	−	0.709954i	$-0.748716\pi$
$443$	−29.6454	−1.40850	−0.704248	+	0.709954i	$0.748716\pi$
$444$	−13.0228	−0.618033
$445$	−51.5613	−2.44424
$446$	−7.87359	−0.372825
$447$	−25.1062	−1.18748
$448$	−0.471801	−0.0222905
$449$	23.2317	1.09637	0.548185	−	0.836357i	$-0.315319\pi$
$449$	23.2317	1.09637	0.548185	+	0.836357i	$0.315319\pi$
$450$	9.13478	0.430618
$451$	15.2511	0.718148
$452$	−13.3050	−0.625815
$453$	−12.9764	−0.609686
$454$	−16.0640	−0.753922
$455$	−4.52298	−0.212040
$456$	−0.257127	−0.0120411
$457$	35.2624	1.64950	0.824752	−	0.565495i	$-0.191315\pi$
$457$	35.2624	1.64950	0.824752	+	0.565495i	$0.191315\pi$
$458$	−6.17220	−0.288408
$459$	34.3271	1.60225
$460$	−30.4754	−1.42093
$461$	−26.6455	−1.24100	−0.620502	−	0.784205i	$-0.713071\pi$
$461$	−26.6455	−1.24100	−0.620502	+	0.784205i	$0.713071\pi$
$462$	−0.770783	−0.0358601
$463$	9.03782	0.420023	0.210011	−	0.977699i	$-0.432650\pi$
$463$	9.03782	0.420023	0.210011	+	0.977699i	$0.432650\pi$
$464$	6.27296	0.291215
$465$	4.43940	0.205872
$466$	−16.8040	−0.778430
$467$	4.41257	0.204189	0.102095	−	0.994775i	$-0.467446\pi$
$467$	4.41257	0.204189	0.102095	+	0.994775i	$0.467446\pi$
$468$	−3.72068	−0.171988
$469$	0.524566	0.0242222
$470$	−4.45530	−0.205508
$471$	15.5965	0.718647
$472$	−3.31010	−0.152360
$473$	14.3269	0.658750
$474$	12.8526	0.590339
$475$	1.36322	0.0625488
$476$	2.89543	0.132712
$477$	−10.0180	−0.458693
$478$	9.83269	0.449737
$479$	−13.8442	−0.632559	−0.316280	−	0.948666i	$-0.602434\pi$
$479$	−13.8442	−0.632559	−0.316280	+	0.948666i	$0.602434\pi$
$480$	−4.43940	−0.202630
$481$	−28.1219	−1.28225
$482$	5.70154	0.259698
$483$	5.39108	0.245303
$484$	−9.39655	−0.427116
$485$	3.44095	0.156245
$486$	−12.6389	−0.573310
$487$	33.2285	1.50573	0.752863	−	0.658177i	$-0.228672\pi$
$487$	33.2285	1.50573	0.752863	+	0.658177i	$0.228672\pi$
$488$	−0.0255868	−0.00115826
$489$	−18.4720	−0.835333
$490$	23.3207	1.05352
$491$	4.56338	0.205942	0.102971	−	0.994684i	$-0.467165\pi$
$491$	4.56338	0.205942	0.102971	+	0.994684i	$0.467165\pi$
$492$	−15.5389	−0.700547
$493$	−38.4970	−1.73382
$494$	−0.555251	−0.0249819
$495$	5.81889	0.261540
$496$	1.00000	0.0449013
$497$	−4.52108	−0.202798
$498$	−13.0091	−0.582951
$499$	1.00002	0.0447670	0.0223835	−	0.999749i	$-0.492875\pi$
$499$	1.00002	0.0447670	0.0223835	+	0.999749i	$0.492875\pi$
$500$	6.33177	0.283165
$501$	32.8746	1.46873
$502$	−27.3903	−1.22249
$503$	−19.2144	−0.856728	−0.428364	−	0.903606i	$-0.640910\pi$
$503$	−19.2144	−0.856728	−0.428364	+	0.903606i	$0.640910\pi$
$504$	−0.630075	−0.0280658
$505$	−39.9388	−1.77725
$506$	−11.2150	−0.498568
$507$	−6.75784	−0.300126
$508$	−5.48629	−0.243415
$509$	16.3721	0.725683	0.362841	−	0.931851i	$-0.381807\pi$
$509$	16.3721	0.725683	0.362841	+	0.931851i	$0.381807\pi$
$510$	27.2445	1.20641
$511$	−3.04638	−0.134764
$512$	−1.00000	−0.0441942
$513$	−1.11477	−0.0492181
$514$	31.2864	1.37998
$515$	12.1280	0.534422
$516$	−14.5972	−0.642605
$517$	−1.63956	−0.0721077
$518$	−4.76229	−0.209243
$519$	−7.60957	−0.334023
$520$	−9.58663	−0.420402
$521$	−35.3626	−1.54926	−0.774631	−	0.632414i	$-0.782064\pi$
$521$	−35.3626	−1.54926	−0.774631	+	0.632414i	$0.782064\pi$
$522$	8.37734	0.366666
$523$	5.08001	0.222133	0.111067	−	0.993813i	$-0.464573\pi$
$523$	5.08001	0.222133	0.111067	+	0.993813i	$0.464573\pi$
$524$	16.8902	0.737851
$525$	−4.16359	−0.181714
$526$	15.5292	0.677105
$527$	−6.13698	−0.267331
$528$	−1.63371	−0.0710979
$529$	55.4411	2.41048
$530$	−25.8122	−1.12121
$531$	−4.42054	−0.191835
$532$	−0.0940286	−0.00407666
$533$	−33.5554	−1.45344
$534$	19.3327	0.836606
$535$	39.5615	1.71039
$536$	1.11184	0.0480241
$537$	6.00154	0.258986
$538$	23.8608	1.02871
$539$	8.58206	0.369655
$540$	−19.2469	−0.828253
$541$	−27.9268	−1.20067	−0.600333	−	0.799750i	$-0.704965\pi$
$541$	−27.9268	−1.20067	−0.600333	+	0.799750i	$0.704965\pi$
$542$	17.6105	0.756435
$543$	25.2977	1.08563
$544$	6.13698	0.263121
$545$	−40.6914	−1.74303
$546$	1.69587	0.0725765
$547$	−35.9585	−1.53747	−0.768737	−	0.639566i	$-0.779114\pi$
$547$	−35.9585	−1.53747	−0.768737	+	0.639566i	$0.779114\pi$
$548$	12.3241	0.526459
$549$	−0.0341704	−0.00145836
$550$	8.66148	0.369327
$551$	1.25018	0.0532596
$552$	11.4266	0.486349
$553$	4.70006	0.199867
$554$	−7.66931	−0.325838
$555$	−44.8106	−1.90211
$556$	17.9081	0.759471
$557$	−0.756924	−0.0320719	−0.0160359	−	0.999871i	$-0.505105\pi$
$557$	−0.756924	−0.0320719	−0.0160359	+	0.999871i	$0.505105\pi$
$558$	1.33547	0.0565350
$559$	−31.5218	−1.33323
$560$	−1.62344	−0.0686029
$561$	10.0260	0.423299
$562$	−14.5027	−0.611761
$563$	−4.40227	−0.185534	−0.0927668	−	0.995688i	$-0.529571\pi$
$563$	−4.40227	−0.185534	−0.0927668	+	0.995688i	$0.529571\pi$
$564$	1.67049	0.0703405
$565$	−45.7819	−1.92606
$566$	15.6645	0.658429
$567$	1.51453	0.0636043
$568$	−9.58260	−0.402077
$569$	16.4597	0.690026	0.345013	−	0.938598i	$-0.387875\pi$
$569$	16.4597	0.690026	0.345013	+	0.938598i	$0.387875\pi$
$570$	−0.884760	−0.0370585
$571$	−1.87173	−0.0783296	−0.0391648	−	0.999233i	$-0.512470\pi$
$571$	−1.87173	−0.0783296	−0.0391648	+	0.999233i	$0.512470\pi$
$572$	−3.52790	−0.147509
$573$	−14.2621	−0.595809
$574$	−5.68241	−0.237179
$575$	−60.5809	−2.52640
$576$	−1.33547	−0.0556446
$577$	−30.1974	−1.25714	−0.628568	−	0.777755i	$-0.716359\pi$
$577$	−30.1974	−1.25714	−0.628568	+	0.777755i	$0.716359\pi$
$578$	−20.6625	−0.859446
$579$	−12.3513	−0.513304
$580$	21.5849	0.896265
$581$	−4.75729	−0.197365
$582$	−1.29017	−0.0534791
$583$	−9.49894	−0.393406
$584$	−6.45692	−0.267189
$585$	−12.8027	−0.529325
$586$	−20.0526	−0.828365
$587$	−2.38661	−0.0985058	−0.0492529	−	0.998786i	$-0.515684\pi$
$587$	−2.38661	−0.0985058	−0.0492529	+	0.998786i	$0.515684\pi$
$588$	−8.74398	−0.360596
$589$	0.199297	0.00821191
$590$	−11.3899	−0.468914
$591$	5.68132	0.233698
$592$	−10.0939	−0.414855
$593$	10.5503	0.433250	0.216625	−	0.976255i	$-0.430495\pi$
$593$	10.5503	0.433250	0.216625	+	0.976255i	$0.430495\pi$
$594$	−7.08288	−0.290614
$595$	9.96302	0.408444
$596$	−19.4597	−0.797099
$597$	−31.0279	−1.26989
$598$	24.6752	1.00904
$599$	−24.0843	−0.984056	−0.492028	−	0.870579i	$-0.663744\pi$
$599$	−24.0843	−0.984056	−0.492028	+	0.870579i	$0.663744\pi$
$600$	−8.82490	−0.360275
$601$	16.6381	0.678681	0.339340	−	0.940664i	$-0.389796\pi$
$601$	16.6381	0.678681	0.339340	+	0.940664i	$0.389796\pi$
$602$	−5.33804	−0.217562
$603$	1.48483	0.0604668
$604$	−10.0579	−0.409252
$605$	−32.3330	−1.31452
$606$	14.9748	0.608312
$607$	−17.2836	−0.701521	−0.350761	−	0.936465i	$-0.614077\pi$
$607$	−17.2836	−0.701521	−0.350761	+	0.936465i	$0.614077\pi$
$608$	−0.199297	−0.00808258
$609$	−3.81836	−0.154728
$610$	−0.0880429	−0.00356475
$611$	3.60734	0.145937
$612$	8.19575	0.331294
$613$	−3.64157	−0.147082	−0.0735408	−	0.997292i	$-0.523430\pi$
$613$	−3.64157	−0.147082	−0.0735408	+	0.997292i	$0.523430\pi$
$614$	−1.68762	−0.0681066
$615$	−53.4685	−2.15606
$616$	−0.597429	−0.0240711
$617$	−20.1288	−0.810355	−0.405178	−	0.914238i	$-0.632790\pi$
$617$	−20.1288	−0.810355	−0.405178	+	0.914238i	$0.632790\pi$
$618$	−4.54732	−0.182920
$619$	−4.87643	−0.196000	−0.0980002	−	0.995186i	$-0.531245\pi$
$619$	−4.87643	−0.196000	−0.0980002	+	0.995186i	$0.531245\pi$
$620$	3.44095	0.138192
$621$	49.5398	1.98796
$622$	−19.6559	−0.788131
$623$	7.06975	0.283244
$624$	3.59446	0.143894
$625$	−12.4133	−0.496533
$626$	−5.25654	−0.210093
$627$	−0.325593	−0.0130029
$628$	12.0887	0.482392
$629$	61.9458	2.46994
$630$	−2.16806	−0.0863775
$631$	22.3219	0.888621	0.444311	−	0.895873i	$-0.353449\pi$
$631$	22.3219	0.888621	0.444311	+	0.895873i	$0.353449\pi$
$632$	9.96197	0.396266
$633$	33.7511	1.34148
$634$	−6.43051	−0.255388
$635$	−18.8780	−0.749152
$636$	9.67817	0.383764
$637$	−18.8821	−0.748138
$638$	7.94329	0.314478
$639$	−12.7973	−0.506253
$640$	−3.44095	−0.136015
$641$	−48.3940	−1.91145	−0.955724	−	0.294265i	$-0.904925\pi$
$641$	−48.3940	−1.91145	−0.955724	+	0.294265i	$0.904925\pi$
$642$	−14.8334	−0.585427
$643$	−11.1245	−0.438708	−0.219354	−	0.975645i	$-0.570395\pi$
$643$	−11.1245	−0.438708	−0.219354	+	0.975645i	$0.570395\pi$
$644$	4.17860	0.164660
$645$	−50.2281	−1.97773
$646$	1.22308	0.0481216
$647$	17.7073	0.696145	0.348072	−	0.937468i	$-0.386836\pi$
$647$	17.7073	0.696145	0.348072	+	0.937468i	$0.386836\pi$
$648$	3.21011	0.126105
$649$	−4.19150	−0.164531
$650$	−19.0569	−0.747472
$651$	−0.608701	−0.0238569
$652$	−14.3175	−0.560718
$653$	−10.0485	−0.393229	−0.196615	−	0.980481i	$-0.562995\pi$
$653$	−10.0485	−0.393229	−0.196615	+	0.980481i	$0.562995\pi$
$654$	15.2570	0.596597
$655$	58.1182	2.27087
$656$	−12.0441	−0.470243
$657$	−8.62303	−0.336416
$658$	0.610882	0.0238147
$659$	7.32179	0.285216	0.142608	−	0.989779i	$-0.454451\pi$
$659$	7.32179	0.285216	0.142608	+	0.989779i	$0.454451\pi$
$660$	−5.62150	−0.218816
$661$	−21.6422	−0.841784	−0.420892	−	0.907111i	$-0.638283\pi$
$661$	−21.6422	−0.841784	−0.420892	+	0.907111i	$0.638283\pi$
$662$	−0.797046	−0.0309781
$663$	−22.0591	−0.856705
$664$	−10.0833	−0.391306
$665$	−0.323548	−0.0125466
$666$	−13.4800	−0.522341
$667$	−55.5577	−2.15120
$668$	25.4809	0.985884
$669$	10.1582	0.392741
$670$	3.82578	0.147803
$671$	−0.0323999	−0.00125079
$672$	0.608701	0.0234812
$673$	−36.5825	−1.41015	−0.705077	−	0.709131i	$-0.749087\pi$
$673$	−36.5825	−1.41015	−0.705077	+	0.709131i	$0.749087\pi$
$674$	−31.4047	−1.20967
$675$	−38.2601	−1.47263
$676$	−5.23796	−0.201460
$677$	−31.5485	−1.21251	−0.606253	−	0.795272i	$-0.707328\pi$
$677$	−31.5485	−1.21251	−0.606253	+	0.795272i	$0.707328\pi$
$678$	17.1657	0.659244
$679$	−0.471801	−0.0181060
$680$	21.1170	0.809801
$681$	20.7253	0.794194
$682$	1.26627	0.0484882
$683$	−28.7700	−1.10085	−0.550427	−	0.834883i	$-0.685535\pi$
$683$	−28.7700	−1.10085	−0.550427	+	0.834883i	$0.685535\pi$
$684$	−0.266156	−0.0101767
$685$	42.4065	1.62027
$686$	−6.50019	−0.248178
$687$	7.96316	0.303814
$688$	−11.3142	−0.431349
$689$	20.8995	0.796206
$690$	39.3184	1.49683
$691$	39.5645	1.50511	0.752553	−	0.658532i	$-0.228822\pi$
$691$	39.5645	1.50511	0.752553	+	0.658532i	$0.228822\pi$
$692$	−5.89813	−0.224213
$693$	−0.797849	−0.0303078
$694$	4.23015	0.160574
$695$	61.6207	2.33741
$696$	−8.09316	−0.306770
$697$	73.9144	2.79971
$698$	26.9435	1.01983
$699$	21.6800	0.820011
$700$	−3.22717	−0.121976
$701$	−17.0589	−0.644306	−0.322153	−	0.946688i	$-0.604407\pi$
$701$	−17.0589	−0.644306	−0.322153	+	0.946688i	$0.604407\pi$
$702$	15.5837	0.588168
$703$	−2.01168	−0.0758720
$704$	−1.26627	−0.0477245
$705$	5.74808	0.216485
$706$	−21.6494	−0.814785
$707$	5.47615	0.205952
$708$	4.27058	0.160498
$709$	−41.1720	−1.54625	−0.773123	−	0.634256i	$-0.781306\pi$
$709$	−41.1720	−1.54625	−0.773123	+	0.634256i	$0.781306\pi$
$710$	−32.9732	−1.23746
$711$	13.3039	0.498936
$712$	14.9846	0.561573
$713$	−8.85670	−0.331686
$714$	−3.73559	−0.139801
$715$	−12.1393	−0.453984
$716$	4.65176	0.173844
$717$	−12.6858	−0.473760
$718$	−18.3880	−0.686232
$719$	3.04579	0.113589	0.0567944	−	0.998386i	$-0.481912\pi$
$719$	3.04579	0.113589	0.0567944	+	0.998386i	$0.481912\pi$
$720$	−4.59528	−0.171256
$721$	−1.66291	−0.0619299
$722$	18.9603	0.705629
$723$	−7.35594	−0.273570
$724$	19.6081	0.728730
$725$	42.9078	1.59356
$726$	12.1231	0.449931
$727$	−19.5605	−0.725459	−0.362729	−	0.931895i	$-0.618155\pi$
$727$	−19.5605	−0.725459	−0.362729	+	0.931895i	$0.618155\pi$
$728$	1.31446	0.0487170
$729$	25.9366	0.960613
$730$	−22.2179	−0.822323
$731$	69.4349	2.56814
$732$	0.0330112	0.00122013
$733$	18.6750	0.689778	0.344889	−	0.938644i	$-0.387917\pi$
$733$	18.6750	0.689778	0.344889	+	0.938644i	$0.387917\pi$
$734$	−16.7085	−0.616722
$735$	−30.0876	−1.10980
$736$	8.85670	0.326462
$737$	1.40789	0.0518604
$738$	−16.0845	−0.592080
$739$	15.7944	0.581007	0.290503	−	0.956874i	$-0.406177\pi$
$739$	15.7944	0.581007	0.290503	+	0.956874i	$0.406177\pi$
$740$	−34.7324	−1.27679
$741$	0.716367	0.0263164
$742$	3.53921	0.129928
$743$	−6.20690	−0.227709	−0.113855	−	0.993497i	$-0.536320\pi$
$743$	−6.20690	−0.227709	−0.113855	+	0.993497i	$0.536320\pi$
$744$	−1.29017	−0.0472998
$745$	−66.9597	−2.45321
$746$	−4.02059	−0.147204
$747$	−13.4659	−0.492691
$748$	7.77110	0.284140
$749$	−5.42441	−0.198204
$750$	−8.16903	−0.298291
$751$	−40.7464	−1.48686	−0.743428	−	0.668816i	$-0.766802\pi$
$751$	−40.7464	−1.48686	−0.743428	+	0.668816i	$0.766802\pi$
$752$	1.29479	0.0472161
$753$	35.3380	1.28779
$754$	−17.4767	−0.636465
$755$	−34.6089	−1.25955
$756$	2.63901	0.0959797
$757$	21.2023	0.770611	0.385306	−	0.922789i	$-0.374096\pi$
$757$	21.2023	0.770611	0.385306	+	0.922789i	$0.374096\pi$
$758$	28.8681	1.04854
$759$	14.4692	0.525200
$760$	−0.685772	−0.0248756
$761$	23.8568	0.864809	0.432405	−	0.901680i	$-0.357665\pi$
$761$	23.8568	0.864809	0.432405	+	0.901680i	$0.357665\pi$
$762$	7.07823	0.256417
$763$	5.57934	0.201986
$764$	−11.0545	−0.399938
$765$	28.2011	1.01961
$766$	3.18432	0.115054
$767$	9.22209	0.332990
$768$	1.29017	0.0465549
$769$	0.568229	0.0204908	0.0102454	−	0.999948i	$-0.496739\pi$
$769$	0.568229	0.0204908	0.0102454	+	0.999948i	$0.496739\pi$
$770$	−2.05572	−0.0740831
$771$	−40.3646	−1.45370
$772$	−9.57344	−0.344556
$773$	20.2250	0.727441	0.363720	−	0.931508i	$-0.381506\pi$
$773$	20.2250	0.727441	0.363720	+	0.931508i	$0.381506\pi$
$774$	−15.1098	−0.543109
$775$	6.84012	0.245704
$776$	−1.00000	−0.0358979
$777$	6.14414	0.220420
$778$	3.89594	0.139676
$779$	−2.40036	−0.0860018
$780$	12.3684	0.442858
$781$	−12.1342	−0.434196
$782$	−54.3534	−1.94367
$783$	−35.0876	−1.25393
$784$	−6.77740	−0.242050
$785$	41.5967	1.48465
$786$	−21.7911	−0.777264
$787$	34.9627	1.24629	0.623143	−	0.782108i	$-0.285855\pi$
$787$	34.9627	1.24629	0.623143	+	0.782108i	$0.285855\pi$
$788$	4.40356	0.156870
$789$	−20.0353	−0.713274
$790$	34.2786	1.21958
$791$	6.27731	0.223195
$792$	−1.69107	−0.0600896
$793$	0.0712860	0.00253144
$794$	−26.6704	−0.946497
$795$	33.3021	1.18110
$796$	−24.0496	−0.852414
$797$	16.5613	0.586630	0.293315	−	0.956016i	$-0.405242\pi$
$797$	16.5613	0.586630	0.293315	+	0.956016i	$0.405242\pi$
$798$	0.121313	0.00429442
$799$	−7.94609	−0.281113
$800$	−6.84012	−0.241835
$801$	20.0115	0.707072
$802$	−1.80624	−0.0637805
$803$	−8.17624	−0.288533
$804$	−1.43446	−0.0505894
$805$	14.3783	0.506770
$806$	−2.78604	−0.0981342
$807$	−30.7845	−1.08366
$808$	11.6069	0.408330
$809$	−42.2217	−1.48443	−0.742217	−	0.670159i	$-0.766226\pi$
$809$	−42.2217	−1.48443	−0.742217	+	0.670159i	$0.766226\pi$
$810$	11.0458	0.388111
$811$	7.36874	0.258751	0.129376	−	0.991596i	$-0.458703\pi$
$811$	7.36874	0.258751	0.129376	+	0.991596i	$0.458703\pi$
$812$	−2.95958	−0.103861
$813$	−22.7205	−0.796842
$814$	−12.7816	−0.447995
$815$	−49.2659	−1.72571
$816$	−7.91772	−0.277176
$817$	−2.25489	−0.0788885
$818$	−11.5225	−0.402873
$819$	1.75542	0.0613393
$820$	−41.4431	−1.44726
$821$	5.79294	0.202175	0.101088	−	0.994878i	$-0.467768\pi$
$821$	5.79294	0.202175	0.101088	+	0.994878i	$0.467768\pi$
$822$	−15.9001	−0.554580
$823$	18.2326	0.635550	0.317775	−	0.948166i	$-0.397064\pi$
$823$	18.2326	0.635550	0.317775	+	0.948166i	$0.397064\pi$
$824$	−3.52460	−0.122785
$825$	−11.1747	−0.389055
$826$	1.56171	0.0543388
$827$	−9.47815	−0.329587	−0.164794	−	0.986328i	$-0.552696\pi$
$827$	−9.47815	−0.329587	−0.164794	+	0.986328i	$0.552696\pi$
$828$	11.8279	0.411047
$829$	−25.6825	−0.891991	−0.445995	−	0.895035i	$-0.647150\pi$
$829$	−25.6825	−0.891991	−0.445995	+	0.895035i	$0.647150\pi$
$830$	−34.6960	−1.20431
$831$	9.89468	0.343243
$832$	2.78604	0.0965887
$833$	41.5928	1.44110
$834$	−23.1044	−0.800040
$835$	87.6783	3.03423
$836$	−0.252365	−0.00872824
$837$	−5.59348	−0.193339
$838$	11.3355	0.391579
$839$	−18.5064	−0.638913	−0.319457	−	0.947601i	$-0.603500\pi$
$839$	−18.5064	−0.638913	−0.319457	+	0.947601i	$0.603500\pi$
$840$	2.09451	0.0722674
$841$	10.3500	0.356895
$842$	20.4346	0.704224
$843$	18.7110	0.644439
$844$	26.1602	0.900472
$845$	−18.0236	−0.620029
$846$	1.72915	0.0594495
$847$	4.43330	0.152330
$848$	7.50149	0.257602
$849$	−20.2099	−0.693600
$850$	41.9777	1.43982
$851$	89.3983	3.06453
$852$	12.3632	0.423555
$853$	−28.0672	−0.961003	−0.480501	−	0.876994i	$-0.659545\pi$
$853$	−28.0672	−0.961003	−0.480501	+	0.876994i	$0.659545\pi$
$854$	0.0120719	0.000413091 0
$855$	−0.915828	−0.0313207
$856$	−11.4973	−0.392968
$857$	−48.2179	−1.64709	−0.823546	−	0.567250i	$-0.808007\pi$
$857$	−48.2179	−1.64709	−0.823546	+	0.567250i	$0.808007\pi$
$858$	4.55157	0.155388
$859$	−4.71597	−0.160907	−0.0804534	−	0.996758i	$-0.525637\pi$
$859$	−4.71597	−0.160907	−0.0804534	+	0.996758i	$0.525637\pi$
$860$	−38.9315	−1.32755
$861$	7.33126	0.249849
$862$	−39.0145	−1.32884
$863$	−21.6746	−0.737812	−0.368906	−	0.929467i	$-0.620268\pi$
$863$	−21.6746	−0.737812	−0.368906	+	0.929467i	$0.620268\pi$
$864$	5.59348	0.190294
$865$	−20.2952	−0.690056
$866$	27.7980	0.944614
$867$	26.6581	0.905355
$868$	−0.471801	−0.0160140
$869$	12.6146	0.427921
$870$	−27.8481	−0.944140
$871$	−3.09763	−0.104959
$872$	11.8256	0.400466
$873$	−1.33547	−0.0451988
$874$	1.76512	0.0597060
$875$	−2.98733	−0.100990
$876$	8.33051	0.281462
$877$	−45.0404	−1.52090	−0.760452	−	0.649394i	$-0.775023\pi$
$877$	−45.0404	−1.52090	−0.760452	+	0.649394i	$0.775023\pi$
$878$	20.7400	0.699941
$879$	25.8712	0.872613
$880$	−4.35719	−0.146881
$881$	−2.86285	−0.0964520	−0.0482260	−	0.998836i	$-0.515357\pi$
$881$	−2.86285	−0.0964520	−0.0482260	+	0.998836i	$0.515357\pi$
$882$	−9.05102	−0.304764
$883$	−55.3321	−1.86207	−0.931036	−	0.364928i	$-0.881094\pi$
$883$	−55.3321	−1.86207	−0.931036	+	0.364928i	$0.881094\pi$
$884$	−17.0979	−0.575064
$885$	14.6949	0.493962
$886$	29.6454	0.995957
$887$	40.9133	1.37373	0.686867	−	0.726783i	$-0.258985\pi$
$887$	40.9133	1.37373	0.686867	+	0.726783i	$0.258985\pi$
$888$	13.0228	0.437015
$889$	2.58844	0.0868133
$890$	51.5613	1.72834
$891$	4.06488	0.136179
$892$	7.87359	0.263627
$893$	0.258048	0.00863525
$894$	25.1062	0.839677
$895$	16.0065	0.535037
$896$	0.471801	0.0157617
$897$	−31.8351	−1.06294
$898$	−23.2317	−0.775250
$899$	6.27296	0.209215
$900$	−9.13478	−0.304493
$901$	−46.0365	−1.53370
$902$	−15.2511	−0.507807
$903$	6.88696	0.229184
$904$	13.3050	0.442518
$905$	67.4705	2.24280
$906$	12.9764	0.431113
$907$	−19.6984	−0.654074	−0.327037	−	0.945012i	$-0.606050\pi$
$907$	−19.6984	−0.654074	−0.327037	+	0.945012i	$0.606050\pi$
$908$	16.0640	0.533103
$909$	15.5007	0.514125
$910$	4.52298	0.149935
$911$	−9.14964	−0.303141	−0.151571	−	0.988446i	$-0.548433\pi$
$911$	−9.14964	−0.303141	−0.151571	+	0.988446i	$0.548433\pi$
$912$	0.257127	0.00851432
$913$	−12.7682	−0.422565
$914$	−35.2624	−1.16638
$915$	0.113590	0.00375517
$916$	6.17220	0.203935
$917$	−7.96880	−0.263153
$918$	−34.3271	−1.13296
$919$	−10.9580	−0.361471	−0.180736	−	0.983532i	$-0.557848\pi$
$919$	−10.9580	−0.361471	−0.180736	+	0.983532i	$0.557848\pi$
$920$	30.4754	1.00475
$921$	2.17730	0.0717446
$922$	26.6455	0.877522
$923$	26.6976	0.878761
$924$	0.770783	0.0253569
$925$	−69.0432	−2.27013
$926$	−9.03782	−0.297001
$927$	−4.70699	−0.154598
$928$	−6.27296	−0.205920
$929$	32.9394	1.08071	0.540353	−	0.841438i	$-0.318291\pi$
$929$	32.9394	1.08071	0.540353	+	0.841438i	$0.318291\pi$
$930$	−4.43940	−0.145574
$931$	−1.35072	−0.0442680
$932$	16.8040	0.550433
$933$	25.3594	0.830231
$934$	−4.41257	−0.144384
$935$	26.7400	0.874490
$936$	3.72068	0.121614
$937$	9.57467	0.312791	0.156395	−	0.987695i	$-0.450013\pi$
$937$	9.57467	0.312791	0.156395	+	0.987695i	$0.450013\pi$
$938$	−0.524566	−0.0171277
$939$	6.78181	0.221316
$940$	4.45530	0.145316
$941$	33.7294	1.09955	0.549774	−	0.835313i	$-0.314714\pi$
$941$	33.7294	1.09955	0.549774	+	0.835313i	$0.314714\pi$
$942$	−15.5965	−0.508160
$943$	106.671	3.47368
$944$	3.31010	0.107735
$945$	9.08068	0.295395
$946$	−14.3269	−0.465807
$947$	35.2388	1.14511	0.572553	−	0.819868i	$-0.305953\pi$
$947$	35.2388	1.14511	0.572553	+	0.819868i	$0.305953\pi$
$948$	−12.8526	−0.417433
$949$	17.9893	0.583956
$950$	−1.36322	−0.0442287
$951$	8.29643	0.269030
$952$	−2.89543	−0.0938414
$953$	33.8182	1.09548	0.547739	−	0.836649i	$-0.315489\pi$
$953$	33.8182	1.09548	0.547739	+	0.836649i	$0.315489\pi$
$954$	10.0180	0.324345
$955$	−38.0379	−1.23088
$956$	−9.83269	−0.318012
$957$	−10.2482	−0.331276
$958$	13.8442	0.447287
$959$	−5.81451	−0.187760
$960$	4.43940	0.143281
$961$	1.00000	0.0322581
$962$	28.1219	0.906687
$963$	−15.3542	−0.494784
$964$	−5.70154	−0.183634
$965$	−32.9417	−1.06043
$966$	−5.39108	−0.173455
$967$	−57.0271	−1.83387	−0.916934	−	0.399040i	$-0.869344\pi$
$967$	−57.0271	−1.83387	−0.916934	+	0.399040i	$0.869344\pi$
$968$	9.39655	0.302016
$969$	−1.57798	−0.0506921
$970$	−3.44095	−0.110482
$971$	−43.4182	−1.39336	−0.696679	−	0.717383i	$-0.745340\pi$
$971$	−43.4182	−1.39336	−0.696679	+	0.717383i	$0.745340\pi$
$972$	12.6389	0.405392
$973$	−8.44904	−0.270864
$974$	−33.2285	−1.06471
$975$	24.5866	0.787400
$976$	0.0255868	0.000819014 0
$977$	−48.6912	−1.55777	−0.778884	−	0.627168i	$-0.784214\pi$
$977$	−48.6912	−1.55777	−0.778884	+	0.627168i	$0.784214\pi$
$978$	18.4720	0.590669
$979$	18.9747	0.606433
$980$	−23.3207	−0.744952
$981$	15.7928	0.504225
$982$	−4.56338	−0.145623
$983$	36.4312	1.16198	0.580988	−	0.813912i	$-0.302666\pi$
$983$	36.4312	1.16198	0.580988	+	0.813912i	$0.302666\pi$
$984$	15.5389	0.495362
$985$	15.1524	0.482796
$986$	38.4970	1.22599
$987$	−0.788140	−0.0250868
$988$	0.555251	0.0176649
$989$	100.206	3.18638
$990$	−5.81889	−0.184937
$991$	−59.3951	−1.88675	−0.943373	−	0.331733i	$-0.892367\pi$
$991$	−59.3951	−1.88675	−0.943373	+	0.331733i	$0.892367\pi$
$992$	−1.00000	−0.0317500
$993$	1.02832	0.0326328
$994$	4.52108	0.143400
$995$	−82.7533	−2.62346
$996$	13.0091	0.412208
$997$	−16.0191	−0.507331	−0.253666	−	0.967292i	$-0.581636\pi$
$997$	−16.0191	−0.507331	−0.253666	+	0.967292i	$0.581636\pi$
$998$	−1.00002	−0.0316550
$999$	56.4598	1.78631

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.f.1.16	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.f.1.16	✓	22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.29017 q^{3} +1.00000 q^{4} +3.44095 q^{5} -1.29017 q^{6} -0.471801 q^{7} -1.00000 q^{8} -1.33547 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.29017 q^{3} +1.00000 q^{4} +3.44095 q^{5} -1.29017 q^{6} -0.471801 q^{7} -1.00000 q^{8} -1.33547 q^{9} -3.44095 q^{10} -1.26627 q^{11} +1.29017 q^{12} +2.78604 q^{13} +0.471801 q^{14} +4.43940 q^{15} +1.00000 q^{16} -6.13698 q^{17} +1.33547 q^{18} +0.199297 q^{19} +3.44095 q^{20} -0.608701 q^{21} +1.26627 q^{22} -8.85670 q^{23} -1.29017 q^{24} +6.84012 q^{25} -2.78604 q^{26} -5.59348 q^{27} -0.471801 q^{28} +6.27296 q^{29} -4.43940 q^{30} +1.00000 q^{31} -1.00000 q^{32} -1.63371 q^{33} +6.13698 q^{34} -1.62344 q^{35} -1.33547 q^{36} -10.0939 q^{37} -0.199297 q^{38} +3.59446 q^{39} -3.44095 q^{40} -12.0441 q^{41} +0.608701 q^{42} -11.3142 q^{43} -1.26627 q^{44} -4.59528 q^{45} +8.85670 q^{46} +1.29479 q^{47} +1.29017 q^{48} -6.77740 q^{49} -6.84012 q^{50} -7.91772 q^{51} +2.78604 q^{52} +7.50149 q^{53} +5.59348 q^{54} -4.35719 q^{55} +0.471801 q^{56} +0.257127 q^{57} -6.27296 q^{58} +3.31010 q^{59} +4.43940 q^{60} +0.0255868 q^{61} -1.00000 q^{62} +0.630075 q^{63} +1.00000 q^{64} +9.58663 q^{65} +1.63371 q^{66} -1.11184 q^{67} -6.13698 q^{68} -11.4266 q^{69} +1.62344 q^{70} +9.58260 q^{71} +1.33547 q^{72} +6.45692 q^{73} +10.0939 q^{74} +8.82490 q^{75} +0.199297 q^{76} +0.597429 q^{77} -3.59446 q^{78} -9.96197 q^{79} +3.44095 q^{80} -3.21011 q^{81} +12.0441 q^{82} +10.0833 q^{83} -0.608701 q^{84} -21.1170 q^{85} +11.3142 q^{86} +8.09316 q^{87} +1.26627 q^{88} -14.9846 q^{89} +4.59528 q^{90} -1.31446 q^{91} -8.85670 q^{92} +1.29017 q^{93} -1.29479 q^{94} +0.685772 q^{95} -1.29017 q^{96} +1.00000 q^{97} +6.77740 q^{98} +1.69107 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

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