LMFDB - Embedded newform 6026.2.a.g.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.780842 q^{3} +1.00000 q^{4} -0.582778 q^{5} +0.780842 q^{6} +2.23605 q^{7} +1.00000 q^{8} -2.39029 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.780842 q^{3} +1.00000 q^{4} -0.582778 q^{5} +0.780842 q^{6} +2.23605 q^{7} +1.00000 q^{8} -2.39029 q^{9} -0.582778 q^{10} -2.03779 q^{11} +0.780842 q^{12} -1.44548 q^{13} +2.23605 q^{14} -0.455058 q^{15} +1.00000 q^{16} -6.79707 q^{17} -2.39029 q^{18} +5.55097 q^{19} -0.582778 q^{20} +1.74600 q^{21} -2.03779 q^{22} -1.00000 q^{23} +0.780842 q^{24} -4.66037 q^{25} -1.44548 q^{26} -4.20896 q^{27} +2.23605 q^{28} +3.89492 q^{29} -0.455058 q^{30} -5.98440 q^{31} +1.00000 q^{32} -1.59119 q^{33} -6.79707 q^{34} -1.30312 q^{35} -2.39029 q^{36} -2.34033 q^{37} +5.55097 q^{38} -1.12869 q^{39} -0.582778 q^{40} -0.200794 q^{41} +1.74600 q^{42} -0.647318 q^{43} -2.03779 q^{44} +1.39301 q^{45} -1.00000 q^{46} +3.73383 q^{47} +0.780842 q^{48} -2.00009 q^{49} -4.66037 q^{50} -5.30744 q^{51} -1.44548 q^{52} -2.03169 q^{53} -4.20896 q^{54} +1.18758 q^{55} +2.23605 q^{56} +4.33443 q^{57} +3.89492 q^{58} -3.34783 q^{59} -0.455058 q^{60} -2.26060 q^{61} -5.98440 q^{62} -5.34479 q^{63} +1.00000 q^{64} +0.842395 q^{65} -1.59119 q^{66} -2.42111 q^{67} -6.79707 q^{68} -0.780842 q^{69} -1.30312 q^{70} +3.20400 q^{71} -2.39029 q^{72} -11.0586 q^{73} -2.34033 q^{74} -3.63901 q^{75} +5.55097 q^{76} -4.55660 q^{77} -1.12869 q^{78} -10.4230 q^{79} -0.582778 q^{80} +3.88432 q^{81} -0.200794 q^{82} -13.5527 q^{83} +1.74600 q^{84} +3.96118 q^{85} -0.647318 q^{86} +3.04132 q^{87} -2.03779 q^{88} +10.8836 q^{89} +1.39301 q^{90} -3.23216 q^{91} -1.00000 q^{92} -4.67287 q^{93} +3.73383 q^{94} -3.23499 q^{95} +0.780842 q^{96} -6.47506 q^{97} -2.00009 q^{98} +4.87090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * 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
$3$	0.780842	0.450819	0.225410	−	0.974264i	$-0.427628\pi$
$3$	0.780842	0.450819	0.225410	+	0.974264i	$0.427628\pi$
$4$	1.00000	0.500000
$5$	−0.582778	−0.260626	−0.130313	−	0.991473i	$-0.541598\pi$
$5$	−0.582778	−0.260626	−0.130313	+	0.991473i	$0.541598\pi$
$6$	0.780842	0.318778
$7$	2.23605	0.845147	0.422573	−	0.906329i	$-0.361127\pi$
$7$	2.23605	0.845147	0.422573	+	0.906329i	$0.361127\pi$
$8$	1.00000	0.353553
$9$	−2.39029	−0.796762
$10$	−0.582778	−0.184291
$11$	−2.03779	−0.614417	−0.307209	−	0.951642i	$-0.599395\pi$
$11$	−2.03779	−0.614417	−0.307209	+	0.951642i	$0.599395\pi$
$12$	0.780842	0.225410
$13$	−1.44548	−0.400904	−0.200452	−	0.979704i	$-0.564241\pi$
$13$	−1.44548	−0.400904	−0.200452	+	0.979704i	$0.564241\pi$
$14$	2.23605	0.597609
$15$	−0.455058	−0.117495
$16$	1.00000	0.250000
$17$	−6.79707	−1.64853	−0.824265	−	0.566204i	$-0.808412\pi$
$17$	−6.79707	−1.64853	−0.824265	+	0.566204i	$0.808412\pi$
$18$	−2.39029	−0.563396
$19$	5.55097	1.27348	0.636740	−	0.771079i	$-0.280282\pi$
$19$	5.55097	1.27348	0.636740	+	0.771079i	$0.280282\pi$
$20$	−0.582778	−0.130313
$21$	1.74600	0.381009
$22$	−2.03779	−0.434459
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.780842	0.159389
$25$	−4.66037	−0.932074
$26$	−1.44548	−0.283482
$27$	−4.20896	−0.810015
$28$	2.23605	0.422573
$29$	3.89492	0.723269	0.361634	−	0.932320i	$-0.382219\pi$
$29$	3.89492	0.723269	0.361634	+	0.932320i	$0.382219\pi$
$30$	−0.455058	−0.0830818
$31$	−5.98440	−1.07483	−0.537415	−	0.843318i	$-0.680599\pi$
$31$	−5.98440	−1.07483	−0.537415	+	0.843318i	$0.680599\pi$
$32$	1.00000	0.176777
$33$	−1.59119	−0.276991
$34$	−6.79707	−1.16569
$35$	−1.30312	−0.220268
$36$	−2.39029	−0.398381
$37$	−2.34033	−0.384747	−0.192374	−	0.981322i	$-0.561619\pi$
$37$	−2.34033	−0.384747	−0.192374	+	0.981322i	$0.561619\pi$
$38$	5.55097	0.900486
$39$	−1.12869	−0.180735
$40$	−0.582778	−0.0921454
$41$	−0.200794	−0.0313587	−0.0156794	−	0.999877i	$-0.504991\pi$
$41$	−0.200794	−0.0313587	−0.0156794	+	0.999877i	$0.504991\pi$
$42$	1.74600	0.269414
$43$	−0.647318	−0.0987151	−0.0493575	−	0.998781i	$-0.515717\pi$
$43$	−0.647318	−0.0987151	−0.0493575	+	0.998781i	$0.515717\pi$
$44$	−2.03779	−0.307209
$45$	1.39301	0.207657
$46$	−1.00000	−0.147442
$47$	3.73383	0.544634	0.272317	−	0.962208i	$-0.412210\pi$
$47$	3.73383	0.544634	0.272317	+	0.962208i	$0.412210\pi$
$48$	0.780842	0.112705
$49$	−2.00009	−0.285727
$50$	−4.66037	−0.659076
$51$	−5.30744	−0.743190
$52$	−1.44548	−0.200452
$53$	−2.03169	−0.279074	−0.139537	−	0.990217i	$-0.544561\pi$
$53$	−2.03169	−0.279074	−0.139537	+	0.990217i	$0.544561\pi$
$54$	−4.20896	−0.572767
$55$	1.18758	0.160133
$56$	2.23605	0.298805
$57$	4.33443	0.574110
$58$	3.89492	0.511428
$59$	−3.34783	−0.435850	−0.217925	−	0.975966i	$-0.569929\pi$
$59$	−3.34783	−0.435850	−0.217925	+	0.975966i	$0.569929\pi$
$60$	−0.455058	−0.0587477
$61$	−2.26060	−0.289440	−0.144720	−	0.989473i	$-0.546228\pi$
$61$	−2.26060	−0.289440	−0.144720	+	0.989473i	$0.546228\pi$
$62$	−5.98440	−0.760020
$63$	−5.34479	−0.673381
$64$	1.00000	0.125000
$65$	0.842395	0.104486
$66$	−1.59119	−0.195862
$67$	−2.42111	−0.295785	−0.147893	−	0.989003i	$-0.547249\pi$
$67$	−2.42111	−0.295785	−0.147893	+	0.989003i	$0.547249\pi$
$68$	−6.79707	−0.824265
$69$	−0.780842	−0.0940024
$70$	−1.30312	−0.155753
$71$	3.20400	0.380245	0.190123	−	0.981760i	$-0.439111\pi$
$71$	3.20400	0.380245	0.190123	+	0.981760i	$0.439111\pi$
$72$	−2.39029	−0.281698
$73$	−11.0586	−1.29431	−0.647156	−	0.762358i	$-0.724042\pi$
$73$	−11.0586	−1.29431	−0.647156	+	0.762358i	$0.724042\pi$
$74$	−2.34033	−0.272057
$75$	−3.63901	−0.420197
$76$	5.55097	0.636740
$77$	−4.55660	−0.519273
$78$	−1.12869	−0.127799
$79$	−10.4230	−1.17268	−0.586342	−	0.810064i	$-0.699433\pi$
$79$	−10.4230	−1.17268	−0.586342	+	0.810064i	$0.699433\pi$
$80$	−0.582778	−0.0651566
$81$	3.88432	0.431591
$82$	−0.200794	−0.0221740
$83$	−13.5527	−1.48760	−0.743801	−	0.668402i	$-0.766979\pi$
$83$	−13.5527	−1.48760	−0.743801	+	0.668402i	$0.766979\pi$
$84$	1.74600	0.190504
$85$	3.96118	0.429651
$86$	−0.647318	−0.0698021
$87$	3.04132	0.326064
$88$	−2.03779	−0.217229
$89$	10.8836	1.15366	0.576829	−	0.816865i	$-0.304290\pi$
$89$	10.8836	1.15366	0.576829	+	0.816865i	$0.304290\pi$
$90$	1.39301	0.146836
$91$	−3.23216	−0.338823
$92$	−1.00000	−0.104257
$93$	−4.67287	−0.484554
$94$	3.73383	0.385115
$95$	−3.23499	−0.331903
$96$	0.780842	0.0796944
$97$	−6.47506	−0.657442	−0.328721	−	0.944427i	$-0.606618\pi$
$97$	−6.47506	−0.657442	−0.328721	+	0.944427i	$0.606618\pi$
$98$	−2.00009	−0.202039
$99$	4.87090	0.489544
$100$	−4.66037	−0.466037
$101$	8.01590	0.797612	0.398806	−	0.917035i	$-0.369425\pi$
$101$	8.01590	0.797612	0.398806	+	0.917035i	$0.369425\pi$
$102$	−5.30744	−0.525515
$103$	5.28673	0.520917	0.260459	−	0.965485i	$-0.416126\pi$
$103$	5.28673	0.520917	0.260459	+	0.965485i	$0.416126\pi$
$104$	−1.44548	−0.141741
$105$	−1.01753	−0.0993009
$106$	−2.03169	−0.197335
$107$	−19.1047	−1.84692	−0.923460	−	0.383694i	$-0.874652\pi$
$107$	−19.1047	−1.84692	−0.923460	+	0.383694i	$0.874652\pi$
$108$	−4.20896	−0.405008
$109$	7.65897	0.733596	0.366798	−	0.930301i	$-0.380454\pi$
$109$	7.65897	0.733596	0.366798	+	0.930301i	$0.380454\pi$
$110$	1.18758	0.113231
$111$	−1.82742	−0.173452
$112$	2.23605	0.211287
$113$	3.30094	0.310526	0.155263	−	0.987873i	$-0.450377\pi$
$113$	3.30094	0.310526	0.155263	+	0.987873i	$0.450377\pi$
$114$	4.33443	0.405957
$115$	0.582778	0.0543444
$116$	3.89492	0.361634
$117$	3.45511	0.319425
$118$	−3.34783	−0.308193
$119$	−15.1986	−1.39325
$120$	−0.455058	−0.0415409
$121$	−6.84741	−0.622491
$122$	−2.26060	−0.204665
$123$	−0.156788	−0.0141371
$124$	−5.98440	−0.537415
$125$	5.62985	0.503550
$126$	−5.34479	−0.476152
$127$	8.46671	0.751299	0.375650	−	0.926762i	$-0.377420\pi$
$127$	8.46671	0.751299	0.375650	+	0.926762i	$0.377420\pi$
$128$	1.00000	0.0883883
$129$	−0.505453	−0.0445027
$130$	0.842395	0.0738829
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−1.59119	−0.138496
$133$	12.4122	1.07628
$134$	−2.42111	−0.209152
$135$	2.45289	0.211111
$136$	−6.79707	−0.582844
$137$	18.3942	1.57153	0.785763	−	0.618528i	$-0.212271\pi$
$137$	18.3942	1.57153	0.785763	+	0.618528i	$0.212271\pi$
$138$	−0.780842	−0.0664697
$139$	−19.5467	−1.65793	−0.828964	−	0.559302i	$-0.811069\pi$
$139$	−19.5467	−1.65793	−0.828964	+	0.559302i	$0.811069\pi$
$140$	−1.30312	−0.110134
$141$	2.91553	0.245532
$142$	3.20400	0.268874
$143$	2.94559	0.246322
$144$	−2.39029	−0.199190
$145$	−2.26988	−0.188503
$146$	−11.0586	−0.915216
$147$	−1.56175	−0.128811
$148$	−2.34033	−0.192374
$149$	−14.1909	−1.16256	−0.581282	−	0.813702i	$-0.697449\pi$
$149$	−14.1909	−1.16256	−0.581282	+	0.813702i	$0.697449\pi$
$150$	−3.63901	−0.297124
$151$	4.74213	0.385909	0.192955	−	0.981208i	$-0.438193\pi$
$151$	4.74213	0.385909	0.192955	+	0.981208i	$0.438193\pi$
$152$	5.55097	0.450243
$153$	16.2469	1.31349
$154$	−4.55660	−0.367181
$155$	3.48758	0.280129
$156$	−1.12869	−0.0903677
$157$	0.291601	0.0232723	0.0116361	−	0.999932i	$-0.496296\pi$
$157$	0.291601	0.0232723	0.0116361	+	0.999932i	$0.496296\pi$
$158$	−10.4230	−0.829213
$159$	−1.58643	−0.125812
$160$	−0.582778	−0.0460727
$161$	−2.23605	−0.176225
$162$	3.88432	0.305181
$163$	−0.641025	−0.0502090	−0.0251045	−	0.999685i	$-0.507992\pi$
$163$	−0.641025	−0.0502090	−0.0251045	+	0.999685i	$0.507992\pi$
$164$	−0.200794	−0.0156794
$165$	0.927313	0.0721912
$166$	−13.5527	−1.05189
$167$	−2.23413	−0.172882	−0.0864411	−	0.996257i	$-0.527549\pi$
$167$	−2.23413	−0.172882	−0.0864411	+	0.996257i	$0.527549\pi$
$168$	1.74600	0.134707
$169$	−10.9106	−0.839276
$170$	3.96118	0.303809
$171$	−13.2684	−1.01466
$172$	−0.647318	−0.0493575
$173$	8.16688	0.620916	0.310458	−	0.950587i	$-0.399518\pi$
$173$	8.16688	0.620916	0.310458	+	0.950587i	$0.399518\pi$
$174$	3.04132	0.230562
$175$	−10.4208	−0.787739
$176$	−2.03779	−0.153604
$177$	−2.61413	−0.196490
$178$	10.8836	0.815759
$179$	3.72583	0.278481	0.139241	−	0.990259i	$-0.455534\pi$
$179$	3.72583	0.278481	0.139241	+	0.990259i	$0.455534\pi$
$180$	1.39301	0.103829
$181$	−0.206197	−0.0153265	−0.00766326	−	0.999971i	$-0.502439\pi$
$181$	−0.206197	−0.0153265	−0.00766326	+	0.999971i	$0.502439\pi$
$182$	−3.23216	−0.239584
$183$	−1.76517	−0.130485
$184$	−1.00000	−0.0737210
$185$	1.36389	0.100275
$186$	−4.67287	−0.342632
$187$	13.8510	1.01289
$188$	3.73383	0.272317
$189$	−9.41145	−0.684582
$190$	−3.23499	−0.234691
$191$	−14.9192	−1.07951	−0.539757	−	0.841821i	$-0.681484\pi$
$191$	−14.9192	−1.07951	−0.539757	+	0.841821i	$0.681484\pi$
$192$	0.780842	0.0563524
$193$	−16.7401	−1.20498	−0.602490	−	0.798126i	$-0.705825\pi$
$193$	−16.7401	−1.20498	−0.602490	+	0.798126i	$0.705825\pi$
$194$	−6.47506	−0.464882
$195$	0.657777	0.0471044
$196$	−2.00009	−0.142863
$197$	−0.00218456	−0.000155643 0	−7.78216e−5	−	1.00000i	$-0.500025\pi$
$197$	−0.00218456	−0.000155643 0	−7.78216e−5		1.00000i	$0.500025\pi$
$198$	4.87090	0.346160
$199$	23.7153	1.68113	0.840567	−	0.541708i	$-0.182222\pi$
$199$	23.7153	1.68113	0.840567	+	0.541708i	$0.182222\pi$
$200$	−4.66037	−0.329538
$201$	−1.89050	−0.133346
$202$	8.01590	0.563997
$203$	8.70923	0.611268
$204$	−5.30744	−0.371595
$205$	0.117018	0.00817291
$206$	5.28673	0.368344
$207$	2.39029	0.166136
$208$	−1.44548	−0.100226
$209$	−11.3117	−0.782448
$210$	−1.01753	−0.0702164
$211$	−23.0317	−1.58557	−0.792785	−	0.609501i	$-0.791370\pi$
$211$	−23.0317	−1.58557	−0.792785	+	0.609501i	$0.791370\pi$
$212$	−2.03169	−0.139537
$213$	2.50182	0.171422
$214$	−19.1047	−1.30597
$215$	0.377243	0.0257278
$216$	−4.20896	−0.286384
$217$	−13.3814	−0.908390
$218$	7.65897	0.518731
$219$	−8.63502	−0.583501
$220$	1.18758	0.0800667
$221$	9.82503	0.660903
$222$	−1.82742	−0.122649
$223$	0.556575	0.0372710	0.0186355	−	0.999826i	$-0.494068\pi$
$223$	0.556575	0.0372710	0.0186355	+	0.999826i	$0.494068\pi$
$224$	2.23605	0.149402
$225$	11.1396	0.742641
$226$	3.30094	0.219575
$227$	10.5157	0.697949	0.348975	−	0.937132i	$-0.386530\pi$
$227$	10.5157	0.697949	0.348975	+	0.937132i	$0.386530\pi$
$228$	4.33443	0.287055
$229$	−3.79711	−0.250920	−0.125460	−	0.992099i	$-0.540041\pi$
$229$	−3.79711	−0.250920	−0.125460	+	0.992099i	$0.540041\pi$
$230$	0.582778	0.0384273
$231$	−3.55799	−0.234098
$232$	3.89492	0.255714
$233$	23.3118	1.52721	0.763605	−	0.645684i	$-0.223428\pi$
$233$	23.3118	1.52721	0.763605	+	0.645684i	$0.223428\pi$
$234$	3.45511	0.225868
$235$	−2.17599	−0.141946
$236$	−3.34783	−0.217925
$237$	−8.13875	−0.528669
$238$	−15.1986	−0.985177
$239$	17.5112	1.13271	0.566354	−	0.824162i	$-0.308354\pi$
$239$	17.5112	1.13271	0.566354	+	0.824162i	$0.308354\pi$
$240$	−0.455058	−0.0293739
$241$	6.49610	0.418451	0.209225	−	0.977867i	$-0.432906\pi$
$241$	6.49610	0.418451	0.209225	+	0.977867i	$0.432906\pi$
$242$	−6.84741	−0.440168
$243$	15.6599	1.00458
$244$	−2.26060	−0.144720
$245$	1.16561	0.0744679
$246$	−0.156788	−0.00999645
$247$	−8.02382	−0.510543
$248$	−5.98440	−0.380010
$249$	−10.5825	−0.670640
$250$	5.62985	0.356063
$251$	−5.67930	−0.358474	−0.179237	−	0.983806i	$-0.557363\pi$
$251$	−5.67930	−0.358474	−0.179237	+	0.983806i	$0.557363\pi$
$252$	−5.34479	−0.336690
$253$	2.03779	0.128115
$254$	8.46671	0.531249
$255$	3.09306	0.193695
$256$	1.00000	0.0625000
$257$	10.7507	0.670608	0.335304	−	0.942110i	$-0.391161\pi$
$257$	10.7507	0.670608	0.335304	+	0.942110i	$0.391161\pi$
$258$	−0.505453	−0.0314681
$259$	−5.23308	−0.325168
$260$	0.842395	0.0522431
$261$	−9.30997	−0.576273
$262$	1.00000	0.0617802
$263$	19.2234	1.18537	0.592683	−	0.805436i	$-0.298069\pi$
$263$	19.2234	1.18537	0.592683	+	0.805436i	$0.298069\pi$
$264$	−1.59119	−0.0979312
$265$	1.18402	0.0727340
$266$	12.4122	0.761043
$267$	8.49836	0.520091
$268$	−2.42111	−0.147893
$269$	7.49724	0.457115	0.228557	−	0.973530i	$-0.426599\pi$
$269$	7.49724	0.457115	0.228557	+	0.973530i	$0.426599\pi$
$270$	2.45289	0.149278
$271$	−23.0068	−1.39756	−0.698781	−	0.715336i	$-0.746274\pi$
$271$	−23.0068	−1.39756	−0.698781	+	0.715336i	$0.746274\pi$
$272$	−6.79707	−0.412133
$273$	−2.52381	−0.152748
$274$	18.3942	1.11124
$275$	9.49686	0.572682
$276$	−0.780842	−0.0470012
$277$	−10.2930	−0.618448	−0.309224	−	0.950989i	$-0.600069\pi$
$277$	−10.2930	−0.618448	−0.309224	+	0.950989i	$0.600069\pi$
$278$	−19.5467	−1.17233
$279$	14.3044	0.856384
$280$	−1.30312	−0.0778764
$281$	−16.2713	−0.970665	−0.485332	−	0.874330i	$-0.661301\pi$
$281$	−16.2713	−0.970665	−0.485332	+	0.874330i	$0.661301\pi$
$282$	2.91553	0.173617
$283$	3.89512	0.231541	0.115771	−	0.993276i	$-0.463066\pi$
$283$	3.89512	0.231541	0.115771	+	0.993276i	$0.463066\pi$
$284$	3.20400	0.190123
$285$	−2.52601	−0.149628
$286$	2.94559	0.174176
$287$	−0.448984	−0.0265027
$288$	−2.39029	−0.140849
$289$	29.2001	1.71765
$290$	−2.26988	−0.133292
$291$	−5.05600	−0.296388
$292$	−11.0586	−0.647156
$293$	8.84681	0.516836	0.258418	−	0.966033i	$-0.416799\pi$
$293$	8.84681	0.516836	0.258418	+	0.966033i	$0.416799\pi$
$294$	−1.56175	−0.0910832
$295$	1.95104	0.113594
$296$	−2.34033	−0.136029
$297$	8.57699	0.497687
$298$	−14.1909	−0.822057
$299$	1.44548	0.0835943
$300$	−3.63901	−0.210099
$301$	−1.44743	−0.0834287
$302$	4.74213	0.272879
$303$	6.25916	0.359579
$304$	5.55097	0.318370
$305$	1.31743	0.0754357
$306$	16.2469	0.928775
$307$	−23.0819	−1.31735	−0.658677	−	0.752426i	$-0.728883\pi$
$307$	−23.0819	−1.31735	−0.658677	+	0.752426i	$0.728883\pi$
$308$	−4.55660	−0.259636
$309$	4.12811	0.234840
$310$	3.48758	0.198081
$311$	2.92972	0.166129	0.0830646	−	0.996544i	$-0.473529\pi$
$311$	2.92972	0.166129	0.0830646	+	0.996544i	$0.473529\pi$
$312$	−1.12869	−0.0638996
$313$	20.3598	1.15080	0.575401	−	0.817872i	$-0.304846\pi$
$313$	20.3598	1.15080	0.575401	+	0.817872i	$0.304846\pi$
$314$	0.291601	0.0164560
$315$	3.11483	0.175501
$316$	−10.4230	−0.586342
$317$	17.5499	0.985698	0.492849	−	0.870115i	$-0.335955\pi$
$317$	17.5499	0.985698	0.492849	+	0.870115i	$0.335955\pi$
$318$	−1.58643	−0.0889625
$319$	−7.93704	−0.444389
$320$	−0.582778	−0.0325783
$321$	−14.9178	−0.832628
$322$	−2.23605	−0.124610
$323$	−37.7303	−2.09937
$324$	3.88432	0.215796
$325$	6.73647	0.373672
$326$	−0.641025	−0.0355031
$327$	5.98045	0.330719
$328$	−0.200794	−0.0110870
$329$	8.34902	0.460296
$330$	0.927313	0.0510469
$331$	−3.99852	−0.219779	−0.109889	−	0.993944i	$-0.535050\pi$
$331$	−3.99852	−0.219779	−0.109889	+	0.993944i	$0.535050\pi$
$332$	−13.5527	−0.743801
$333$	5.59405	0.306552
$334$	−2.23413	−0.122246
$335$	1.41097	0.0770894
$336$	1.74600	0.0952522
$337$	3.33485	0.181661	0.0908304	−	0.995866i	$-0.471048\pi$
$337$	3.33485	0.181661	0.0908304	+	0.995866i	$0.471048\pi$
$338$	−10.9106	−0.593458
$339$	2.57751	0.139991
$340$	3.96118	0.214825
$341$	12.1950	0.660394
$342$	−13.2684	−0.717473
$343$	−20.1246	−1.08663
$344$	−0.647318	−0.0349010
$345$	0.455058	0.0244995
$346$	8.16688	0.439054
$347$	2.49829	0.134115	0.0670575	−	0.997749i	$-0.478639\pi$
$347$	2.49829	0.134115	0.0670575	+	0.997749i	$0.478639\pi$
$348$	3.04132	0.163032
$349$	−17.9204	−0.959258	−0.479629	−	0.877471i	$-0.659229\pi$
$349$	−17.9204	−0.959258	−0.479629	+	0.877471i	$0.659229\pi$
$350$	−10.4208	−0.557016
$351$	6.08397	0.324738
$352$	−2.03779	−0.108615
$353$	13.6887	0.728577	0.364288	−	0.931286i	$-0.381312\pi$
$353$	13.6887	0.728577	0.364288	+	0.931286i	$0.381312\pi$
$354$	−2.61413	−0.138939
$355$	−1.86722	−0.0991020
$356$	10.8836	0.576829
$357$	−11.8677	−0.628105
$358$	3.72583	0.196916
$359$	−5.31389	−0.280456	−0.140228	−	0.990119i	$-0.544784\pi$
$359$	−5.31389	−0.280456	−0.140228	+	0.990119i	$0.544784\pi$
$360$	1.39301	0.0734179
$361$	11.8133	0.621752
$362$	−0.206197	−0.0108375
$363$	−5.34674	−0.280631
$364$	−3.23216	−0.169411
$365$	6.44471	0.337332
$366$	−1.76517	−0.0922670
$367$	−27.1291	−1.41613	−0.708063	−	0.706149i	$-0.750431\pi$
$367$	−27.1291	−1.41613	−0.708063	+	0.706149i	$0.750431\pi$
$368$	−1.00000	−0.0521286
$369$	0.479954	0.0249854
$370$	1.36389	0.0709053
$371$	−4.54295	−0.235858
$372$	−4.67287	−0.242277
$373$	−25.4178	−1.31609	−0.658043	−	0.752981i	$-0.728615\pi$
$373$	−25.4178	−1.31609	−0.658043	+	0.752981i	$0.728615\pi$
$374$	13.8510	0.716218
$375$	4.39603	0.227010
$376$	3.73383	0.192557
$377$	−5.63003	−0.289961
$378$	−9.41145	−0.484072
$379$	24.5895	1.26308	0.631538	−	0.775345i	$-0.282424\pi$
$379$	24.5895	1.26308	0.631538	+	0.775345i	$0.282424\pi$
$380$	−3.23499	−0.165951
$381$	6.61117	0.338700
$382$	−14.9192	−0.763331
$383$	22.9743	1.17393	0.586965	−	0.809612i	$-0.300322\pi$
$383$	22.9743	1.17393	0.586965	+	0.809612i	$0.300322\pi$
$384$	0.780842	0.0398472
$385$	2.65549	0.135336
$386$	−16.7401	−0.852050
$387$	1.54727	0.0786524
$388$	−6.47506	−0.328721
$389$	10.6712	0.541053	0.270527	−	0.962713i	$-0.412802\pi$
$389$	10.6712	0.541053	0.270527	+	0.962713i	$0.412802\pi$
$390$	0.657777	0.0333079
$391$	6.79707	0.343742
$392$	−2.00009	−0.101020
$393$	0.780842	0.0393883
$394$	−0.00218456	−0.000110056 0
$395$	6.07432	0.305632
$396$	4.87090	0.244772
$397$	7.75041	0.388982	0.194491	−	0.980904i	$-0.437695\pi$
$397$	7.75041	0.388982	0.194491	+	0.980904i	$0.437695\pi$
$398$	23.7153	1.18874
$399$	9.69200	0.485207
$400$	−4.66037	−0.233018
$401$	18.5898	0.928332	0.464166	−	0.885748i	$-0.346354\pi$
$401$	18.5898	0.928332	0.464166	+	0.885748i	$0.346354\pi$
$402$	−1.89050	−0.0942897
$403$	8.65034	0.430904
$404$	8.01590	0.398806
$405$	−2.26370	−0.112484
$406$	8.70923	0.432232
$407$	4.76910	0.236395
$408$	−5.30744	−0.262757
$409$	−6.01995	−0.297667	−0.148834	−	0.988862i	$-0.547552\pi$
$409$	−6.01995	−0.297667	−0.148834	+	0.988862i	$0.547552\pi$
$410$	0.117018	0.00577912
$411$	14.3630	0.708474
$412$	5.28673	0.260459
$413$	−7.48591	−0.368357
$414$	2.39029	0.117476
$415$	7.89822	0.387708
$416$	−1.44548	−0.0708705
$417$	−15.2629	−0.747426
$418$	−11.3117	−0.553274
$419$	−16.8148	−0.821456	−0.410728	−	0.911758i	$-0.634725\pi$
$419$	−16.8148	−0.821456	−0.410728	+	0.911758i	$0.634725\pi$
$420$	−1.01753	−0.0496505
$421$	−24.2106	−1.17995	−0.589976	−	0.807421i	$-0.700863\pi$
$421$	−24.2106	−1.17995	−0.589976	+	0.807421i	$0.700863\pi$
$422$	−23.0317	−1.12117
$423$	−8.92491	−0.433944
$424$	−2.03169	−0.0986675
$425$	31.6768	1.53655
$426$	2.50182	0.121214
$427$	−5.05481	−0.244619
$428$	−19.1047	−0.923460
$429$	2.30004	0.111047
$430$	0.377243	0.0181923
$431$	−28.3786	−1.36695	−0.683474	−	0.729975i	$-0.739532\pi$
$431$	−28.3786	−1.36695	−0.683474	+	0.729975i	$0.739532\pi$
$432$	−4.20896	−0.202504
$433$	−25.7007	−1.23510	−0.617548	−	0.786533i	$-0.711874\pi$
$433$	−25.7007	−1.23510	−0.617548	+	0.786533i	$0.711874\pi$
$434$	−13.3814	−0.642328
$435$	−1.77241	−0.0849808
$436$	7.65897	0.366798
$437$	−5.55097	−0.265539
$438$	−8.63502	−0.412597
$439$	23.8969	1.14054	0.570268	−	0.821459i	$-0.306839\pi$
$439$	23.8969	1.14054	0.570268	+	0.821459i	$0.306839\pi$
$440$	1.18758	0.0566157
$441$	4.78078	0.227656
$442$	9.82503	0.467329
$443$	2.86881	0.136301	0.0681507	−	0.997675i	$-0.478290\pi$
$443$	2.86881	0.136301	0.0681507	+	0.997675i	$0.478290\pi$
$444$	−1.82742	−0.0867258
$445$	−6.34272	−0.300674
$446$	0.556575	0.0263546
$447$	−11.0809	−0.524106
$448$	2.23605	0.105643
$449$	3.09948	0.146274	0.0731368	−	0.997322i	$-0.476699\pi$
$449$	3.09948	0.146274	0.0731368	+	0.997322i	$0.476699\pi$
$450$	11.1396	0.525126
$451$	0.409176	0.0192673
$452$	3.30094	0.155263
$453$	3.70286	0.173975
$454$	10.5157	0.493525
$455$	1.88364	0.0883062
$456$	4.33443	0.202978
$457$	−21.5324	−1.00724	−0.503622	−	0.863924i	$-0.668000\pi$
$457$	−21.5324	−1.00724	−0.503622	+	0.863924i	$0.668000\pi$
$458$	−3.79711	−0.177427
$459$	28.6086	1.33534
$460$	0.582778	0.0271722
$461$	6.99176	0.325639	0.162819	−	0.986656i	$-0.447941\pi$
$461$	6.99176	0.325639	0.162819	+	0.986656i	$0.447941\pi$
$462$	−3.55799	−0.165533
$463$	−11.3750	−0.528643	−0.264322	−	0.964435i	$-0.585148\pi$
$463$	−11.3750	−0.528643	−0.264322	+	0.964435i	$0.585148\pi$
$464$	3.89492	0.180817
$465$	2.72325	0.126288
$466$	23.3118	1.07990
$467$	−5.87265	−0.271754	−0.135877	−	0.990726i	$-0.543385\pi$
$467$	−5.87265	−0.271754	−0.135877	+	0.990726i	$0.543385\pi$
$468$	3.45511	0.159713
$469$	−5.41371	−0.249982
$470$	−2.17599	−0.100371
$471$	0.227694	0.0104916
$472$	−3.34783	−0.154096
$473$	1.31910	0.0606522
$474$	−8.13875	−0.373825
$475$	−25.8696	−1.18698
$476$	−15.1986	−0.696625
$477$	4.85632	0.222355
$478$	17.5112	0.800945
$479$	−13.9318	−0.636559	−0.318279	−	0.947997i	$-0.603105\pi$
$479$	−13.9318	−0.636559	−0.318279	+	0.947997i	$0.603105\pi$
$480$	−0.455058	−0.0207705
$481$	3.38289	0.154247
$482$	6.49610	0.295889
$483$	−1.74600	−0.0794458
$484$	−6.84741	−0.311246
$485$	3.77352	0.171347
$486$	15.6599	0.710349
$487$	2.51562	0.113994	0.0569968	−	0.998374i	$-0.481848\pi$
$487$	2.51562	0.113994	0.0569968	+	0.998374i	$0.481848\pi$
$488$	−2.26060	−0.102332
$489$	−0.500540	−0.0226352
$490$	1.16561	0.0526568
$491$	−15.2333	−0.687471	−0.343735	−	0.939067i	$-0.611692\pi$
$491$	−15.2333	−0.687471	−0.343735	+	0.939067i	$0.611692\pi$
$492$	−0.156788	−0.00706856
$493$	−26.4740	−1.19233
$494$	−8.02382	−0.361009
$495$	−2.83866	−0.127588
$496$	−5.98440	−0.268708
$497$	7.16431	0.321363
$498$	−10.5825	−0.474214
$499$	−12.3510	−0.552907	−0.276453	−	0.961027i	$-0.589159\pi$
$499$	−12.3510	−0.552907	−0.276453	+	0.961027i	$0.589159\pi$
$500$	5.62985	0.251775
$501$	−1.74450	−0.0779386
$502$	−5.67930	−0.253479
$503$	36.5056	1.62770	0.813852	−	0.581072i	$-0.197367\pi$
$503$	36.5056	1.62770	0.813852	+	0.581072i	$0.197367\pi$
$504$	−5.34479	−0.238076
$505$	−4.67150	−0.207879
$506$	2.03779	0.0905909
$507$	−8.51945	−0.378362
$508$	8.46671	0.375650
$509$	17.9077	0.793746	0.396873	−	0.917874i	$-0.370095\pi$
$509$	17.9077	0.793746	0.396873	+	0.917874i	$0.370095\pi$
$510$	3.09306	0.136963
$511$	−24.7276	−1.09388
$512$	1.00000	0.0441942
$513$	−23.3638	−1.03154
$514$	10.7507	0.474191
$515$	−3.08099	−0.135765
$516$	−0.505453	−0.0222513
$517$	−7.60876	−0.334633
$518$	−5.23308	−0.229928
$519$	6.37705	0.279921
$520$	0.842395	0.0369415
$521$	−30.5575	−1.33875	−0.669374	−	0.742926i	$-0.733437\pi$
$521$	−30.5575	−1.33875	−0.669374	+	0.742926i	$0.733437\pi$
$522$	−9.30997	−0.407486
$523$	−9.50702	−0.415713	−0.207856	−	0.978159i	$-0.566649\pi$
$523$	−9.50702	−0.415713	−0.207856	+	0.978159i	$0.566649\pi$
$524$	1.00000	0.0436852
$525$	−8.13701	−0.355128
$526$	19.2234	0.838181
$527$	40.6764	1.77189
$528$	−1.59119	−0.0692478
$529$	1.00000	0.0434783
$530$	1.18402	0.0514307
$531$	8.00227	0.347269
$532$	12.4122	0.538139
$533$	0.290243	0.0125718
$534$	8.49836	0.367760
$535$	11.1338	0.481356
$536$	−2.42111	−0.104576
$537$	2.90928	0.125545
$538$	7.49724	0.323229
$539$	4.07576	0.175555
$540$	2.45289	0.105556
$541$	19.3362	0.831328	0.415664	−	0.909518i	$-0.363549\pi$
$541$	19.3362	0.831328	0.415664	+	0.909518i	$0.363549\pi$
$542$	−23.0068	−0.988225
$543$	−0.161008	−0.00690949
$544$	−6.79707	−0.291422
$545$	−4.46348	−0.191195
$546$	−2.52381	−0.108009
$547$	38.8357	1.66049	0.830247	−	0.557395i	$-0.188199\pi$
$547$	38.8357	1.66049	0.830247	+	0.557395i	$0.188199\pi$
$548$	18.3942	0.785763
$549$	5.40348	0.230615
$550$	9.49686	0.404948
$551$	21.6206	0.921068
$552$	−0.780842	−0.0332349
$553$	−23.3064	−0.991090
$554$	−10.2930	−0.437309
$555$	1.06498	0.0452060
$556$	−19.5467	−0.828964
$557$	26.5243	1.12387	0.561936	−	0.827181i	$-0.310057\pi$
$557$	26.5243	1.12387	0.561936	+	0.827181i	$0.310057\pi$
$558$	14.3044	0.605555
$559$	0.935686	0.0395753
$560$	−1.30312	−0.0550669
$561$	10.8155	0.456629
$562$	−16.2713	−0.686364
$563$	−13.1506	−0.554231	−0.277116	−	0.960837i	$-0.589378\pi$
$563$	−13.1506	−0.554231	−0.277116	+	0.960837i	$0.589378\pi$
$564$	2.91553	0.122766
$565$	−1.92372	−0.0809313
$566$	3.89512	0.163724
$567$	8.68553	0.364758
$568$	3.20400	0.134437
$569$	4.72680	0.198158	0.0990788	−	0.995080i	$-0.468410\pi$
$569$	4.72680	0.198158	0.0990788	+	0.995080i	$0.468410\pi$
$570$	−2.52601	−0.105803
$571$	−15.9441	−0.667241	−0.333621	−	0.942707i	$-0.608270\pi$
$571$	−15.9441	−0.667241	−0.333621	+	0.942707i	$0.608270\pi$
$572$	2.94559	0.123161
$573$	−11.6495	−0.486666
$574$	−0.448984	−0.0187402
$575$	4.66037	0.194351
$576$	−2.39029	−0.0995952
$577$	−0.530305	−0.0220769	−0.0110384	−	0.999939i	$-0.503514\pi$
$577$	−0.530305	−0.0220769	−0.0110384	+	0.999939i	$0.503514\pi$
$578$	29.2001	1.21456
$579$	−13.0714	−0.543229
$580$	−2.26988	−0.0942514
$581$	−30.3045	−1.25724
$582$	−5.05600	−0.209578
$583$	4.14016	0.171468
$584$	−11.0586	−0.457608
$585$	−2.01356	−0.0832506
$586$	8.84681	0.365458
$587$	−22.8899	−0.944766	−0.472383	−	0.881393i	$-0.656606\pi$
$587$	−22.8899	−0.944766	−0.472383	+	0.881393i	$0.656606\pi$
$588$	−1.56175	−0.0644056
$589$	−33.2192	−1.36878
$590$	1.95104	0.0803231
$591$	−0.00170579	−7.01670e−5 0
$592$	−2.34033	−0.0961868
$593$	−6.69573	−0.274961	−0.137480	−	0.990504i	$-0.543900\pi$
$593$	−6.69573	−0.274961	−0.137480	+	0.990504i	$0.543900\pi$
$594$	8.57699	0.351918
$595$	8.85740	0.363118
$596$	−14.1909	−0.581282
$597$	18.5179	0.757888
$598$	1.44548	0.0591101
$599$	−12.3807	−0.505863	−0.252932	−	0.967484i	$-0.581395\pi$
$599$	−12.3807	−0.505863	−0.252932	+	0.967484i	$0.581395\pi$
$600$	−3.63901	−0.148562
$601$	3.66647	0.149558	0.0747792	−	0.997200i	$-0.476175\pi$
$601$	3.66647	0.149558	0.0747792	+	0.997200i	$0.476175\pi$
$602$	−1.44743	−0.0589930
$603$	5.78713	0.235670
$604$	4.74213	0.192955
$605$	3.99052	0.162238
$606$	6.25916	0.254261
$607$	39.9451	1.62132	0.810660	−	0.585517i	$-0.199108\pi$
$607$	39.9451	1.62132	0.810660	+	0.585517i	$0.199108\pi$
$608$	5.55097	0.225122
$609$	6.80054	0.275572
$610$	1.31743	0.0533411
$611$	−5.39717	−0.218346
$612$	16.2469	0.656743
$613$	27.1688	1.09734	0.548669	−	0.836040i	$-0.315135\pi$
$613$	27.1688	1.09734	0.548669	+	0.836040i	$0.315135\pi$
$614$	−23.0819	−0.931509
$615$	0.0913728	0.00368451
$616$	−4.55660	−0.183591
$617$	0.0990333	0.00398693	0.00199347	−	0.999998i	$-0.499365\pi$
$617$	0.0990333	0.00398693	0.00199347	+	0.999998i	$0.499365\pi$
$618$	4.12811	0.166057
$619$	−7.03408	−0.282724	−0.141362	−	0.989958i	$-0.545148\pi$
$619$	−7.03408	−0.282724	−0.141362	+	0.989958i	$0.545148\pi$
$620$	3.48758	0.140065
$621$	4.20896	0.168900
$622$	2.92972	0.117471
$623$	24.3362	0.975011
$624$	−1.12869	−0.0451839
$625$	20.0209	0.800836
$626$	20.3598	0.813740
$627$	−8.83267	−0.352743
$628$	0.291601	0.0116361
$629$	15.9073	0.634268
$630$	3.11483	0.124098
$631$	38.7784	1.54374	0.771872	−	0.635778i	$-0.219321\pi$
$631$	38.7784	1.54374	0.771872	+	0.635778i	$0.219321\pi$
$632$	−10.4230	−0.414606
$633$	−17.9842	−0.714806
$634$	17.5499	0.696994
$635$	−4.93422	−0.195808
$636$	−1.58643	−0.0629060
$637$	2.89109	0.114549
$638$	−7.93704	−0.314230
$639$	−7.65848	−0.302965
$640$	−0.582778	−0.0230363
$641$	5.29394	0.209098	0.104549	−	0.994520i	$-0.466660\pi$
$641$	5.29394	0.209098	0.104549	+	0.994520i	$0.466660\pi$
$642$	−14.9178	−0.588757
$643$	7.81932	0.308364	0.154182	−	0.988042i	$-0.450726\pi$
$643$	7.81932	0.308364	0.154182	+	0.988042i	$0.450726\pi$
$644$	−2.23605	−0.0881127
$645$	0.294567	0.0115986
$646$	−37.7303	−1.48448
$647$	−1.33527	−0.0524949	−0.0262475	−	0.999655i	$-0.508356\pi$
$647$	−1.33527	−0.0524949	−0.0262475	+	0.999655i	$0.508356\pi$
$648$	3.88432	0.152591
$649$	6.82218	0.267794
$650$	6.73647	0.264226
$651$	−10.4488	−0.409520
$652$	−0.641025	−0.0251045
$653$	−12.0142	−0.470151	−0.235076	−	0.971977i	$-0.575534\pi$
$653$	−12.0142	−0.470151	−0.235076	+	0.971977i	$0.575534\pi$
$654$	5.98045	0.233854
$655$	−0.582778	−0.0227710
$656$	−0.200794	−0.00783968
$657$	26.4332	1.03126
$658$	8.34902	0.325479
$659$	−26.5107	−1.03271	−0.516355	−	0.856374i	$-0.672712\pi$
$659$	−26.5107	−1.03271	−0.516355	+	0.856374i	$0.672712\pi$
$660$	0.927313	0.0360956
$661$	8.00663	0.311422	0.155711	−	0.987803i	$-0.450233\pi$
$661$	8.00663	0.311422	0.155711	+	0.987803i	$0.450233\pi$
$662$	−3.99852	−0.155407
$663$	7.67180	0.297948
$664$	−13.5527	−0.525946
$665$	−7.23359	−0.280506
$666$	5.59405	0.216765
$667$	−3.89492	−0.150812
$668$	−2.23413	−0.0864411
$669$	0.434597	0.0168025
$670$	1.41097	0.0545105
$671$	4.60663	0.177837
$672$	1.74600	0.0673535
$673$	−12.2370	−0.471702	−0.235851	−	0.971789i	$-0.575788\pi$
$673$	−12.2370	−0.471702	−0.235851	+	0.971789i	$0.575788\pi$
$674$	3.33485	0.128454
$675$	19.6153	0.754994
$676$	−10.9106	−0.419638
$677$	−30.0314	−1.15420	−0.577100	−	0.816674i	$-0.695816\pi$
$677$	−30.0314	−1.15420	−0.577100	+	0.816674i	$0.695816\pi$
$678$	2.57751	0.0989888
$679$	−14.4785	−0.555636
$680$	3.96118	0.151904
$681$	8.21107	0.314649
$682$	12.1950	0.466969
$683$	23.0734	0.882880	0.441440	−	0.897291i	$-0.354468\pi$
$683$	23.0734	0.882880	0.441440	+	0.897291i	$0.354468\pi$
$684$	−13.2684	−0.507330
$685$	−10.7198	−0.409581
$686$	−20.1246	−0.768362
$687$	−2.96494	−0.113120
$688$	−0.647318	−0.0246788
$689$	2.93677	0.111882
$690$	0.455058	0.0173238
$691$	−28.3483	−1.07842	−0.539210	−	0.842171i	$-0.681277\pi$
$691$	−28.3483	−1.07842	−0.539210	+	0.842171i	$0.681277\pi$
$692$	8.16688	0.310458
$693$	10.8916	0.413737
$694$	2.49829	0.0948337
$695$	11.3914	0.432100
$696$	3.04132	0.115281
$697$	1.36481	0.0516958
$698$	−17.9204	−0.678298
$699$	18.2029	0.688496
$700$	−10.4208	−0.393870
$701$	−37.1926	−1.40475	−0.702373	−	0.711809i	$-0.747876\pi$
$701$	−37.1926	−1.40475	−0.702373	+	0.711809i	$0.747876\pi$
$702$	6.08397	0.229625
$703$	−12.9911	−0.489968
$704$	−2.03779	−0.0768022
$705$	−1.69911	−0.0639921
$706$	13.6887	0.515182
$707$	17.9239	0.674099
$708$	−2.61413	−0.0982449
$709$	−18.7108	−0.702699	−0.351350	−	0.936244i	$-0.614277\pi$
$709$	−18.7108	−0.702699	−0.351350	+	0.936244i	$0.614277\pi$
$710$	−1.86722	−0.0700757
$711$	24.9140	0.934350
$712$	10.8836	0.407880
$713$	5.98440	0.224118
$714$	−11.8677	−0.444137
$715$	−1.71663	−0.0641981
$716$	3.72583	0.139241
$717$	13.6735	0.510646
$718$	−5.31389	−0.198313
$719$	−2.73210	−0.101890	−0.0509451	−	0.998701i	$-0.516223\pi$
$719$	−2.73210	−0.101890	−0.0509451	+	0.998701i	$0.516223\pi$
$720$	1.39301	0.0519143
$721$	11.8214	0.440252
$722$	11.8133	0.439645
$723$	5.07243	0.188646
$724$	−0.206197	−0.00766326
$725$	−18.1518	−0.674140
$726$	−5.34674	−0.198436
$727$	−25.0463	−0.928916	−0.464458	−	0.885595i	$-0.653751\pi$
$727$	−25.0463	−0.928916	−0.464458	+	0.885595i	$0.653751\pi$
$728$	−3.23216	−0.119792
$729$	0.574972	0.0212953
$730$	6.44471	0.238530
$731$	4.39986	0.162735
$732$	−1.76517	−0.0652426
$733$	38.9057	1.43702	0.718508	−	0.695518i	$-0.244825\pi$
$733$	38.9057	1.43702	0.718508	+	0.695518i	$0.244825\pi$
$734$	−27.1291	−1.00135
$735$	0.910155	0.0335716
$736$	−1.00000	−0.0368605
$737$	4.93371	0.181736
$738$	0.479954	0.0176674
$739$	46.0402	1.69362	0.846808	−	0.531899i	$-0.178521\pi$
$739$	46.0402	1.69362	0.846808	+	0.531899i	$0.178521\pi$
$740$	1.36389	0.0501376
$741$	−6.26534	−0.230163
$742$	−4.54295	−0.166777
$743$	3.31851	0.121744	0.0608721	−	0.998146i	$-0.480612\pi$
$743$	3.31851	0.121744	0.0608721	+	0.998146i	$0.480612\pi$
$744$	−4.67287	−0.171316
$745$	8.27015	0.302995
$746$	−25.4178	−0.930613
$747$	32.3948	1.18526
$748$	13.8510	0.506443
$749$	−42.7190	−1.56092
$750$	4.39603	0.160520
$751$	8.93101	0.325897	0.162949	−	0.986635i	$-0.447900\pi$
$751$	8.93101	0.325897	0.162949	+	0.986635i	$0.447900\pi$
$752$	3.73383	0.136159
$753$	−4.43463	−0.161607
$754$	−5.63003	−0.205034
$755$	−2.76361	−0.100578
$756$	−9.41145	−0.342291
$757$	−26.0352	−0.946264	−0.473132	−	0.880991i	$-0.656877\pi$
$757$	−26.0352	−0.946264	−0.473132	+	0.880991i	$0.656877\pi$
$758$	24.5895	0.893130
$759$	1.59119	0.0577567
$760$	−3.23499	−0.117345
$761$	21.1912	0.768182	0.384091	−	0.923295i	$-0.374515\pi$
$761$	21.1912	0.768182	0.384091	+	0.923295i	$0.374515\pi$
$762$	6.61117	0.239497
$763$	17.1258	0.619997
$764$	−14.9192	−0.539757
$765$	−9.46836	−0.342329
$766$	22.9743	0.830095
$767$	4.83922	0.174734
$768$	0.780842	0.0281762
$769$	−0.179007	−0.00645517	−0.00322758	−	0.999995i	$-0.501027\pi$
$769$	−0.179007	−0.00645517	−0.00322758	+	0.999995i	$0.501027\pi$
$770$	2.65549	0.0956972
$771$	8.39457	0.302323
$772$	−16.7401	−0.602490
$773$	−38.6848	−1.39140	−0.695698	−	0.718335i	$-0.744905\pi$
$773$	−38.6848	−1.39140	−0.695698	+	0.718335i	$0.744905\pi$
$774$	1.54727	0.0556156
$775$	27.8895	1.00182
$776$	−6.47506	−0.232441
$777$	−4.08621	−0.146592
$778$	10.6712	0.382582
$779$	−1.11460	−0.0399347
$780$	0.657777	0.0235522
$781$	−6.52909	−0.233629
$782$	6.79707	0.243063
$783$	−16.3936	−0.585859
$784$	−2.00009	−0.0714317
$785$	−0.169939	−0.00606537
$786$	0.780842	0.0278517
$787$	−14.2678	−0.508592	−0.254296	−	0.967126i	$-0.581844\pi$
$787$	−14.2678	−0.508592	−0.254296	+	0.967126i	$0.581844\pi$
$788$	−0.00218456	−7.78216e−5 0
$789$	15.0105	0.534386
$790$	6.07432	0.216115
$791$	7.38106	0.262440
$792$	4.87090	0.173080
$793$	3.26765	0.116038
$794$	7.75041	0.275052
$795$	0.924536	0.0327899
$796$	23.7153	0.840567
$797$	−33.5863	−1.18969	−0.594844	−	0.803841i	$-0.702786\pi$
$797$	−33.5863	−1.18969	−0.594844	+	0.803841i	$0.702786\pi$
$798$	9.69200	0.343093
$799$	−25.3791	−0.897847
$800$	−4.66037	−0.164769
$801$	−26.0149	−0.919191
$802$	18.5898	0.656430
$803$	22.5351	0.795247
$804$	−1.89050	−0.0666729
$805$	1.30312	0.0459290
$806$	8.65034	0.304695
$807$	5.85416	0.206076
$808$	8.01590	0.281998
$809$	−1.84233	−0.0647730	−0.0323865	−	0.999475i	$-0.510311\pi$
$809$	−1.84233	−0.0647730	−0.0323865	+	0.999475i	$0.510311\pi$
$810$	−2.26370	−0.0795382
$811$	39.0207	1.37020	0.685101	−	0.728448i	$-0.259758\pi$
$811$	39.0207	1.37020	0.685101	+	0.728448i	$0.259758\pi$
$812$	8.70923	0.305634
$813$	−17.9646	−0.630048
$814$	4.76910	0.167157
$815$	0.373576	0.0130858
$816$	−5.30744	−0.185797
$817$	−3.59324	−0.125712
$818$	−6.01995	−0.210483
$819$	7.72580	0.269961
$820$	0.117018	0.00408645
$821$	27.5194	0.960435	0.480217	−	0.877149i	$-0.340558\pi$
$821$	27.5194	0.960435	0.480217	+	0.877149i	$0.340558\pi$
$822$	14.3630	0.500967
$823$	−13.2866	−0.463143	−0.231571	−	0.972818i	$-0.574387\pi$
$823$	−13.2866	−0.463143	−0.231571	+	0.972818i	$0.574387\pi$
$824$	5.28673	0.184172
$825$	7.41555	0.258176
$826$	−7.48591	−0.260468
$827$	45.1548	1.57019	0.785093	−	0.619377i	$-0.212615\pi$
$827$	45.1548	1.57019	0.785093	+	0.619377i	$0.212615\pi$
$828$	2.39029	0.0830682
$829$	40.6293	1.41111	0.705556	−	0.708654i	$-0.250697\pi$
$829$	40.6293	1.41111	0.705556	+	0.708654i	$0.250697\pi$
$830$	7.89822	0.274151
$831$	−8.03723	−0.278808
$832$	−1.44548	−0.0501130
$833$	13.5947	0.471029
$834$	−15.2629	−0.528510
$835$	1.30200	0.0450577
$836$	−11.3117	−0.391224
$837$	25.1881	0.870629
$838$	−16.8148	−0.580857
$839$	5.04568	0.174196	0.0870982	−	0.996200i	$-0.472241\pi$
$839$	5.04568	0.174196	0.0870982	+	0.996200i	$0.472241\pi$
$840$	−1.01753	−0.0351082
$841$	−13.8296	−0.476883
$842$	−24.2106	−0.834352
$843$	−12.7053	−0.437595
$844$	−23.0317	−0.792785
$845$	6.35845	0.218737
$846$	−8.92491	−0.306845
$847$	−15.3111	−0.526097
$848$	−2.03169	−0.0697685
$849$	3.04148	0.104383
$850$	31.6768	1.08651
$851$	2.34033	0.0802253
$852$	2.50182	0.0857110
$853$	49.6104	1.69863	0.849314	−	0.527889i	$-0.177016\pi$
$853$	49.6104	1.69863	0.849314	+	0.527889i	$0.177016\pi$
$854$	−5.05481	−0.172972
$855$	7.73254	0.264447
$856$	−19.1047	−0.652985
$857$	−10.6220	−0.362842	−0.181421	−	0.983406i	$-0.558070\pi$
$857$	−10.6220	−0.362842	−0.181421	+	0.983406i	$0.558070\pi$
$858$	2.30004	0.0785221
$859$	−1.80902	−0.0617230	−0.0308615	−	0.999524i	$-0.509825\pi$
$859$	−1.80902	−0.0617230	−0.0308615	+	0.999524i	$0.509825\pi$
$860$	0.377243	0.0128639
$861$	−0.350586	−0.0119479
$862$	−28.3786	−0.966578
$863$	39.7428	1.35286	0.676430	−	0.736507i	$-0.263526\pi$
$863$	39.7428	1.35286	0.676430	+	0.736507i	$0.263526\pi$
$864$	−4.20896	−0.143192
$865$	−4.75948	−0.161827
$866$	−25.7007	−0.873345
$867$	22.8007	0.774352
$868$	−13.3814	−0.454195
$869$	21.2400	0.720517
$870$	−1.77241	−0.0600905
$871$	3.49966	0.118582
$872$	7.65897	0.259365
$873$	15.4772	0.523825
$874$	−5.55097	−0.187764
$875$	12.5886	0.425573
$876$	−8.63502	−0.291750
$877$	35.7835	1.20832	0.604162	−	0.796862i	$-0.293508\pi$
$877$	35.7835	1.20832	0.604162	+	0.796862i	$0.293508\pi$
$878$	23.8969	0.806480
$879$	6.90797	0.233000
$880$	1.18758	0.0400333
$881$	−14.1341	−0.476189	−0.238094	−	0.971242i	$-0.576523\pi$
$881$	−14.1341	−0.476189	−0.238094	+	0.971242i	$0.576523\pi$
$882$	4.78078	0.160977
$883$	−15.0436	−0.506256	−0.253128	−	0.967433i	$-0.581459\pi$
$883$	−15.0436	−0.506256	−0.253128	+	0.967433i	$0.581459\pi$
$884$	9.82503	0.330451
$885$	1.52346	0.0512104
$886$	2.86881	0.0963796
$887$	4.90021	0.164533	0.0822664	−	0.996610i	$-0.473784\pi$
$887$	4.90021	0.164533	0.0822664	+	0.996610i	$0.473784\pi$
$888$	−1.82742	−0.0613244
$889$	18.9320	0.634958
$890$	−6.34272	−0.212608
$891$	−7.91544	−0.265177
$892$	0.556575	0.0186355
$893$	20.7264	0.693581
$894$	−11.0809	−0.370599
$895$	−2.17133	−0.0725796
$896$	2.23605	0.0747011
$897$	1.12869	0.0376859
$898$	3.09948	0.103431
$899$	−23.3088	−0.777391
$900$	11.1396	0.371320
$901$	13.8095	0.460062
$902$	0.409176	0.0136241
$903$	−1.13022	−0.0376113
$904$	3.30094	0.109788
$905$	0.120167	0.00399450
$906$	3.70286	0.123019
$907$	−28.9204	−0.960287	−0.480143	−	0.877190i	$-0.659415\pi$
$907$	−28.9204	−0.960287	−0.480143	+	0.877190i	$0.659415\pi$
$908$	10.5157	0.348975
$909$	−19.1603	−0.635507
$910$	1.88364	0.0624419
$911$	8.44873	0.279919	0.139959	−	0.990157i	$-0.455303\pi$
$911$	8.44873	0.279919	0.139959	+	0.990157i	$0.455303\pi$
$912$	4.33443	0.143527
$913$	27.6176	0.914008
$914$	−21.5324	−0.712229
$915$	1.02870	0.0340079
$916$	−3.79711	−0.125460
$917$	2.23605	0.0738408
$918$	28.6086	0.944225
$919$	−22.7229	−0.749558	−0.374779	−	0.927114i	$-0.622281\pi$
$919$	−22.7229	−0.749558	−0.374779	+	0.927114i	$0.622281\pi$
$920$	0.582778	0.0192136
$921$	−18.0233	−0.593888
$922$	6.99176	0.230261
$923$	−4.63132	−0.152442
$924$	−3.55799	−0.117049
$925$	10.9068	0.358613
$926$	−11.3750	−0.373807
$927$	−12.6368	−0.415047
$928$	3.89492	0.127857
$929$	−35.0096	−1.14863	−0.574314	−	0.818635i	$-0.694731\pi$
$929$	−35.0096	−1.14863	−0.574314	+	0.818635i	$0.694731\pi$
$930$	2.72325	0.0892989
$931$	−11.1024	−0.363867
$932$	23.3118	0.763605
$933$	2.28765	0.0748943
$934$	−5.87265	−0.192159
$935$	−8.07207	−0.263985
$936$	3.45511	0.112934
$937$	12.0948	0.395120	0.197560	−	0.980291i	$-0.436698\pi$
$937$	12.0948	0.395120	0.197560	+	0.980291i	$0.436698\pi$
$938$	−5.41371	−0.176764
$939$	15.8978	0.518804
$940$	−2.17599	−0.0709731
$941$	52.6296	1.71568	0.857838	−	0.513921i	$-0.171807\pi$
$941$	52.6296	1.71568	0.857838	+	0.513921i	$0.171807\pi$
$942$	0.227694	0.00741868
$943$	0.200794	0.00653874
$944$	−3.34783	−0.108963
$945$	5.48479	0.178420
$946$	1.31910	0.0428876
$947$	41.6068	1.35204	0.676020	−	0.736883i	$-0.263703\pi$
$947$	41.6068	1.35204	0.676020	+	0.736883i	$0.263703\pi$
$948$	−8.13875	−0.264334
$949$	15.9850	0.518895
$950$	−25.8696	−0.839320
$951$	13.7037	0.444372
$952$	−15.1986	−0.492589
$953$	17.1090	0.554213	0.277107	−	0.960839i	$-0.410624\pi$
$953$	17.1090	0.554213	0.277107	+	0.960839i	$0.410624\pi$
$954$	4.85632	0.157229
$955$	8.69457	0.281350
$956$	17.5112	0.566354
$957$	−6.19757	−0.200339
$958$	−13.9318	−0.450115
$959$	41.1304	1.32817
$960$	−0.455058	−0.0146869
$961$	4.81307	0.155260
$962$	3.38289	0.109069
$963$	45.6657	1.47156
$964$	6.49610	0.209225
$965$	9.75578	0.314050
$966$	−1.74600	−0.0561767
$967$	47.6000	1.53071	0.765357	−	0.643606i	$-0.222563\pi$
$967$	47.6000	1.53071	0.765357	+	0.643606i	$0.222563\pi$
$968$	−6.84741	−0.220084
$969$	−29.4614	−0.946437
$970$	3.77352	0.121161
$971$	5.90534	0.189512	0.0947558	−	0.995501i	$-0.469793\pi$
$971$	5.90534	0.189512	0.0947558	+	0.995501i	$0.469793\pi$
$972$	15.6599	0.502292
$973$	−43.7073	−1.40119
$974$	2.51562	0.0806057
$975$	5.26012	0.168459
$976$	−2.26060	−0.0723600
$977$	−34.4414	−1.10188	−0.550938	−	0.834546i	$-0.685730\pi$
$977$	−34.4414	−1.10188	−0.550938	+	0.834546i	$0.685730\pi$
$978$	−0.500540	−0.0160055
$979$	−22.1785	−0.708827
$980$	1.16561	0.0372340
$981$	−18.3071	−0.584501
$982$	−15.2333	−0.486115
$983$	26.7940	0.854597	0.427299	−	0.904111i	$-0.359465\pi$
$983$	26.7940	0.854597	0.427299	+	0.904111i	$0.359465\pi$
$984$	−0.156788	−0.00499822
$985$	0.00127311	4.05647e−5 0
$986$	−26.4740	−0.843105
$987$	6.51926	0.207510
$988$	−8.02382	−0.255272
$989$	0.647318	0.0205835
$990$	−2.83866	−0.0902185
$991$	6.01857	0.191186	0.0955931	−	0.995420i	$-0.469525\pi$
$991$	6.01857	0.191186	0.0955931	+	0.995420i	$0.469525\pi$
$992$	−5.98440	−0.190005
$993$	−3.12221	−0.0990805
$994$	7.16431	0.227238
$995$	−13.8208	−0.438148
$996$	−10.5825	−0.335320
$997$	9.31712	0.295076	0.147538	−	0.989056i	$-0.452865\pi$
$997$	9.31712	0.295076	0.147538	+	0.989056i	$0.452865\pi$
$998$	−12.3510	−0.390964
$999$	9.85034	0.311651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.g.1.13	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.g.1.13	✓	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.780842 q^{3} +1.00000 q^{4} -0.582778 q^{5} +0.780842 q^{6} +2.23605 q^{7} +1.00000 q^{8} -2.39029 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.780842 q^{3} +1.00000 q^{4} -0.582778 q^{5} +0.780842 q^{6} +2.23605 q^{7} +1.00000 q^{8} -2.39029 q^{9} -0.582778 q^{10} -2.03779 q^{11} +0.780842 q^{12} -1.44548 q^{13} +2.23605 q^{14} -0.455058 q^{15} +1.00000 q^{16} -6.79707 q^{17} -2.39029 q^{18} +5.55097 q^{19} -0.582778 q^{20} +1.74600 q^{21} -2.03779 q^{22} -1.00000 q^{23} +0.780842 q^{24} -4.66037 q^{25} -1.44548 q^{26} -4.20896 q^{27} +2.23605 q^{28} +3.89492 q^{29} -0.455058 q^{30} -5.98440 q^{31} +1.00000 q^{32} -1.59119 q^{33} -6.79707 q^{34} -1.30312 q^{35} -2.39029 q^{36} -2.34033 q^{37} +5.55097 q^{38} -1.12869 q^{39} -0.582778 q^{40} -0.200794 q^{41} +1.74600 q^{42} -0.647318 q^{43} -2.03779 q^{44} +1.39301 q^{45} -1.00000 q^{46} +3.73383 q^{47} +0.780842 q^{48} -2.00009 q^{49} -4.66037 q^{50} -5.30744 q^{51} -1.44548 q^{52} -2.03169 q^{53} -4.20896 q^{54} +1.18758 q^{55} +2.23605 q^{56} +4.33443 q^{57} +3.89492 q^{58} -3.34783 q^{59} -0.455058 q^{60} -2.26060 q^{61} -5.98440 q^{62} -5.34479 q^{63} +1.00000 q^{64} +0.842395 q^{65} -1.59119 q^{66} -2.42111 q^{67} -6.79707 q^{68} -0.780842 q^{69} -1.30312 q^{70} +3.20400 q^{71} -2.39029 q^{72} -11.0586 q^{73} -2.34033 q^{74} -3.63901 q^{75} +5.55097 q^{76} -4.55660 q^{77} -1.12869 q^{78} -10.4230 q^{79} -0.582778 q^{80} +3.88432 q^{81} -0.200794 q^{82} -13.5527 q^{83} +1.74600 q^{84} +3.96118 q^{85} -0.647318 q^{86} +3.04132 q^{87} -2.03779 q^{88} +10.8836 q^{89} +1.39301 q^{90} -3.23216 q^{91} -1.00000 q^{92} -4.67287 q^{93} +3.73383 q^{94} -3.23499 q^{95} +0.780842 q^{96} -6.47506 q^{97} -2.00009 q^{98} +4.87090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} + 21 q^{4} - 13 q^{5} - 18 q^{7} + 21 q^{8} + 7 q^{9} - 13 q^{10} - 4 q^{11} - 4 q^{13} - 18 q^{14} - 16 q^{15} + 21 q^{16} - 12 q^{17} + 7 q^{18} - 18 q^{19} - 13 q^{20} - 24 q^{21} - 4 q^{22} - 21 q^{23} + 2 q^{25} - 4 q^{26} - 9 q^{27} - 18 q^{28} - 16 q^{29} - 16 q^{30} - 7 q^{31} + 21 q^{32} - 15 q^{33} - 12 q^{34} + 7 q^{36} - 44 q^{37} - 18 q^{38} - 14 q^{39} - 13 q^{40} - 23 q^{41} - 24 q^{42} - 18 q^{43} - 4 q^{44} - 36 q^{45} - 21 q^{46} + 2 q^{47} - 13 q^{49} + 2 q^{50} - 26 q^{51} - 4 q^{52} - 39 q^{53} - 9 q^{54} - 32 q^{55} - 18 q^{56} - 22 q^{57} - 16 q^{58} - 27 q^{59} - 16 q^{60} - 34 q^{61} - 7 q^{62} - 28 q^{63} + 21 q^{64} - 25 q^{65} - 15 q^{66} - 19 q^{67} - 12 q^{68} - 24 q^{71} + 7 q^{72} - 8 q^{73} - 44 q^{74} + 50 q^{75} - 18 q^{76} - 16 q^{77} - 14 q^{78} - 27 q^{79} - 13 q^{80} + 33 q^{81} - 23 q^{82} + 7 q^{83} - 24 q^{84} - 22 q^{85} - 18 q^{86} - 15 q^{87} - 4 q^{88} - 12 q^{89} - 36 q^{90} - 20 q^{91} - 21 q^{92} - 43 q^{93} + 2 q^{94} - 14 q^{95} - 52 q^{97} - 13 q^{98} - 30 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 + 21 * q^4 - 13 * q^5 - 18 * q^7 + 21 * q^8 + 7 * q^9 - 13 * q^10 - 4 * q^11 - 4 * q^13 - 18 * q^14 - 16 * q^15 + 21 * q^16 - 12 * q^17 + 7 * q^18 - 18 * q^19 - 13 * q^20 - 24 * q^21 - 4 * q^22 - 21 * q^23 + 2 * q^25 - 4 * q^26 - 9 * q^27 - 18 * q^28 - 16 * q^29 - 16 * q^30 - 7 * q^31 + 21 * q^32 - 15 * q^33 - 12 * q^34 + 7 * q^36 - 44 * q^37 - 18 * q^38 - 14 * q^39 - 13 * q^40 - 23 * q^41 - 24 * q^42 - 18 * q^43 - 4 * q^44 - 36 * q^45 - 21 * q^46 + 2 * q^47 - 13 * q^49 + 2 * q^50 - 26 * q^51 - 4 * q^52 - 39 * q^53 - 9 * q^54 - 32 * q^55 - 18 * q^56 - 22 * q^57 - 16 * q^58 - 27 * q^59 - 16 * q^60 - 34 * q^61 - 7 * q^62 - 28 * q^63 + 21 * q^64 - 25 * q^65 - 15 * q^66 - 19 * q^67 - 12 * q^68 - 24 * q^71 + 7 * q^72 - 8 * q^73 - 44 * q^74 + 50 * q^75 - 18 * q^76 - 16 * q^77 - 14 * q^78 - 27 * q^79 - 13 * q^80 + 33 * q^81 - 23 * q^82 + 7 * q^83 - 24 * q^84 - 22 * q^85 - 18 * q^86 - 15 * q^87 - 4 * q^88 - 12 * q^89 - 36 * q^90 - 20 * q^91 - 21 * q^92 - 43 * q^93 + 2 * q^94 - 14 * q^95 - 52 * q^97 - 13 * q^98 - 30 * q^99

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