LMFDB - Embedded newform 6034.2.a.n.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.797155 q^{3} +1.00000 q^{4} +1.40867 q^{5} +0.797155 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.36454 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.797155 q^{3} +1.00000 q^{4} +1.40867 q^{5} +0.797155 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.36454 q^{9} -1.40867 q^{10} -4.26652 q^{11} -0.797155 q^{12} +0.799192 q^{13} +1.00000 q^{14} -1.12293 q^{15} +1.00000 q^{16} -3.62976 q^{17} +2.36454 q^{18} -6.70269 q^{19} +1.40867 q^{20} +0.797155 q^{21} +4.26652 q^{22} -4.59211 q^{23} +0.797155 q^{24} -3.01565 q^{25} -0.799192 q^{26} +4.27637 q^{27} -1.00000 q^{28} -6.21178 q^{29} +1.12293 q^{30} -6.61866 q^{31} -1.00000 q^{32} +3.40108 q^{33} +3.62976 q^{34} -1.40867 q^{35} -2.36454 q^{36} +5.42018 q^{37} +6.70269 q^{38} -0.637080 q^{39} -1.40867 q^{40} -4.51614 q^{41} -0.797155 q^{42} +0.780925 q^{43} -4.26652 q^{44} -3.33086 q^{45} +4.59211 q^{46} +11.1285 q^{47} -0.797155 q^{48} +1.00000 q^{49} +3.01565 q^{50} +2.89348 q^{51} +0.799192 q^{52} -3.36589 q^{53} -4.27637 q^{54} -6.01012 q^{55} +1.00000 q^{56} +5.34309 q^{57} +6.21178 q^{58} +5.39532 q^{59} -1.12293 q^{60} -5.80734 q^{61} +6.61866 q^{62} +2.36454 q^{63} +1.00000 q^{64} +1.12580 q^{65} -3.40108 q^{66} -4.88292 q^{67} -3.62976 q^{68} +3.66063 q^{69} +1.40867 q^{70} +9.37398 q^{71} +2.36454 q^{72} -3.99440 q^{73} -5.42018 q^{74} +2.40394 q^{75} -6.70269 q^{76} +4.26652 q^{77} +0.637080 q^{78} +5.28980 q^{79} +1.40867 q^{80} +3.68470 q^{81} +4.51614 q^{82} +14.1032 q^{83} +0.797155 q^{84} -5.11313 q^{85} -0.780925 q^{86} +4.95175 q^{87} +4.26652 q^{88} -13.9685 q^{89} +3.33086 q^{90} -0.799192 q^{91} -4.59211 q^{92} +5.27610 q^{93} -11.1285 q^{94} -9.44188 q^{95} +0.797155 q^{96} -3.54831 q^{97} -1.00000 q^{98} +10.0884 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * 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
$3$	−0.797155	−0.460238	−0.230119	−	0.973163i	$-0.573912\pi$
$3$	−0.797155	−0.460238	−0.230119	+	0.973163i	$0.573912\pi$
$4$	1.00000	0.500000
$5$	1.40867	0.629976	0.314988	−	0.949096i	$-0.397999\pi$
$5$	1.40867	0.629976	0.314988	+	0.949096i	$0.397999\pi$
$6$	0.797155	0.325437
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.36454	−0.788181
$10$	−1.40867	−0.445460
$11$	−4.26652	−1.28640	−0.643202	−	0.765696i	$-0.722394\pi$
$11$	−4.26652	−1.28640	−0.643202	+	0.765696i	$0.722394\pi$
$12$	−0.797155	−0.230119
$13$	0.799192	0.221656	0.110828	−	0.993840i	$-0.464650\pi$
$13$	0.799192	0.221656	0.110828	+	0.993840i	$0.464650\pi$
$14$	1.00000	0.267261
$15$	−1.12293	−0.289939
$16$	1.00000	0.250000
$17$	−3.62976	−0.880345	−0.440173	−	0.897913i	$-0.645083\pi$
$17$	−3.62976	−0.880345	−0.440173	+	0.897913i	$0.645083\pi$
$18$	2.36454	0.557328
$19$	−6.70269	−1.53770	−0.768851	−	0.639427i	$-0.779171\pi$
$19$	−6.70269	−1.53770	−0.768851	+	0.639427i	$0.779171\pi$
$20$	1.40867	0.314988
$21$	0.797155	0.173954
$22$	4.26652	0.909625
$23$	−4.59211	−0.957522	−0.478761	−	0.877945i	$-0.658914\pi$
$23$	−4.59211	−0.957522	−0.478761	+	0.877945i	$0.658914\pi$
$24$	0.797155	0.162719
$25$	−3.01565	−0.603130
$26$	−0.799192	−0.156734
$27$	4.27637	0.822989
$28$	−1.00000	−0.188982
$29$	−6.21178	−1.15350	−0.576749	−	0.816921i	$-0.695679\pi$
$29$	−6.21178	−1.15350	−0.576749	+	0.816921i	$0.695679\pi$
$30$	1.12293	0.205018
$31$	−6.61866	−1.18875	−0.594373	−	0.804189i	$-0.702600\pi$
$31$	−6.61866	−1.18875	−0.594373	+	0.804189i	$0.702600\pi$
$32$	−1.00000	−0.176777
$33$	3.40108	0.592052
$34$	3.62976	0.622498
$35$	−1.40867	−0.238109
$36$	−2.36454	−0.394091
$37$	5.42018	0.891072	0.445536	−	0.895264i	$-0.353013\pi$
$37$	5.42018	0.891072	0.445536	+	0.895264i	$0.353013\pi$
$38$	6.70269	1.08732
$39$	−0.637080	−0.102014
$40$	−1.40867	−0.222730
$41$	−4.51614	−0.705303	−0.352652	−	0.935755i	$-0.614720\pi$
$41$	−4.51614	−0.705303	−0.352652	+	0.935755i	$0.614720\pi$
$42$	−0.797155	−0.123004
$43$	0.780925	0.119090	0.0595450	−	0.998226i	$-0.481035\pi$
$43$	0.780925	0.119090	0.0595450	+	0.998226i	$0.481035\pi$
$44$	−4.26652	−0.643202
$45$	−3.33086	−0.496535
$46$	4.59211	0.677070
$47$	11.1285	1.62325	0.811627	−	0.584176i	$-0.198582\pi$
$47$	11.1285	1.62325	0.811627	+	0.584176i	$0.198582\pi$
$48$	−0.797155	−0.115059
$49$	1.00000	0.142857
$50$	3.01565	0.426477
$51$	2.89348	0.405168
$52$	0.799192	0.110828
$53$	−3.36589	−0.462341	−0.231170	−	0.972913i	$-0.574255\pi$
$53$	−3.36589	−0.462341	−0.231170	+	0.972913i	$0.574255\pi$
$54$	−4.27637	−0.581941
$55$	−6.01012	−0.810404
$56$	1.00000	0.133631
$57$	5.34309	0.707709
$58$	6.21178	0.815646
$59$	5.39532	0.702410	0.351205	−	0.936298i	$-0.385772\pi$
$59$	5.39532	0.702410	0.351205	+	0.936298i	$0.385772\pi$
$60$	−1.12293	−0.144969
$61$	−5.80734	−0.743554	−0.371777	−	0.928322i	$-0.621251\pi$
$61$	−5.80734	−0.743554	−0.371777	+	0.928322i	$0.621251\pi$
$62$	6.61866	0.840571
$63$	2.36454	0.297904
$64$	1.00000	0.125000
$65$	1.12580	0.139638
$66$	−3.40108	−0.418644
$67$	−4.88292	−0.596543	−0.298272	−	0.954481i	$-0.596410\pi$
$67$	−4.88292	−0.596543	−0.298272	+	0.954481i	$0.596410\pi$
$68$	−3.62976	−0.440173
$69$	3.66063	0.440688
$70$	1.40867	0.168368
$71$	9.37398	1.11249	0.556243	−	0.831020i	$-0.312242\pi$
$71$	9.37398	1.11249	0.556243	+	0.831020i	$0.312242\pi$
$72$	2.36454	0.278664
$73$	−3.99440	−0.467510	−0.233755	−	0.972296i	$-0.575101\pi$
$73$	−3.99440	−0.467510	−0.233755	+	0.972296i	$0.575101\pi$
$74$	−5.42018	−0.630083
$75$	2.40394	0.277583
$76$	−6.70269	−0.768851
$77$	4.26652	0.486215
$78$	0.637080	0.0721351
$79$	5.28980	0.595149	0.297575	−	0.954699i	$-0.403822\pi$
$79$	5.28980	0.595149	0.297575	+	0.954699i	$0.403822\pi$
$80$	1.40867	0.157494
$81$	3.68470	0.409411
$82$	4.51614	0.498725
$83$	14.1032	1.54803	0.774015	−	0.633168i	$-0.218246\pi$
$83$	14.1032	1.54803	0.774015	+	0.633168i	$0.218246\pi$
$84$	0.797155	0.0869768
$85$	−5.11313	−0.554596
$86$	−0.780925	−0.0842093
$87$	4.95175	0.530883
$88$	4.26652	0.454813
$89$	−13.9685	−1.48066	−0.740328	−	0.672246i	$-0.765330\pi$
$89$	−13.9685	−1.48066	−0.740328	+	0.672246i	$0.765330\pi$
$90$	3.33086	0.351104
$91$	−0.799192	−0.0837781
$92$	−4.59211	−0.478761
$93$	5.27610	0.547106
$94$	−11.1285	−1.14781
$95$	−9.44188	−0.968716
$96$	0.797155	0.0813593
$97$	−3.54831	−0.360277	−0.180138	−	0.983641i	$-0.557655\pi$
$97$	−3.54831	−0.360277	−0.180138	+	0.983641i	$0.557655\pi$
$98$	−1.00000	−0.101015
$99$	10.0884	1.01392
$100$	−3.01565	−0.301565
$101$	9.29483	0.924870	0.462435	−	0.886653i	$-0.346976\pi$
$101$	9.29483	0.924870	0.462435	+	0.886653i	$0.346976\pi$
$102$	−2.89348	−0.286497
$103$	8.45408	0.833005	0.416503	−	0.909134i	$-0.363256\pi$
$103$	8.45408	0.833005	0.416503	+	0.909134i	$0.363256\pi$
$104$	−0.799192	−0.0783672
$105$	1.12293	0.109587
$106$	3.36589	0.326924
$107$	12.0908	1.16886	0.584430	−	0.811444i	$-0.301318\pi$
$107$	12.0908	1.16886	0.584430	+	0.811444i	$0.301318\pi$
$108$	4.27637	0.411494
$109$	−5.51476	−0.528218	−0.264109	−	0.964493i	$-0.585078\pi$
$109$	−5.51476	−0.528218	−0.264109	+	0.964493i	$0.585078\pi$
$110$	6.01012	0.573042
$111$	−4.32072	−0.410105
$112$	−1.00000	−0.0944911
$113$	5.38250	0.506343	0.253171	−	0.967421i	$-0.418526\pi$
$113$	5.38250	0.506343	0.253171	+	0.967421i	$0.418526\pi$
$114$	−5.34309	−0.500426
$115$	−6.46877	−0.603216
$116$	−6.21178	−0.576749
$117$	−1.88972	−0.174705
$118$	−5.39532	−0.496679
$119$	3.62976	0.332739
$120$	1.12293	0.102509
$121$	7.20319	0.654836
$122$	5.80734	0.525772
$123$	3.60007	0.324607
$124$	−6.61866	−0.594373
$125$	−11.2914	−1.00993
$126$	−2.36454	−0.210650
$127$	13.0689	1.15968	0.579839	−	0.814731i	$-0.303115\pi$
$127$	13.0689	1.15968	0.579839	+	0.814731i	$0.303115\pi$
$128$	−1.00000	−0.0883883
$129$	−0.622518	−0.0548097
$130$	−1.12580	−0.0987390
$131$	5.75249	0.502597	0.251299	−	0.967910i	$-0.419142\pi$
$131$	5.75249	0.502597	0.251299	+	0.967910i	$0.419142\pi$
$132$	3.40108	0.296026
$133$	6.70269	0.581197
$134$	4.88292	0.421820
$135$	6.02400	0.518463
$136$	3.62976	0.311249
$137$	7.21273	0.616225	0.308113	−	0.951350i	$-0.400303\pi$
$137$	7.21273	0.616225	0.308113	+	0.951350i	$0.400303\pi$
$138$	−3.66063	−0.311613
$139$	−3.15380	−0.267502	−0.133751	−	0.991015i	$-0.542702\pi$
$139$	−3.15380	−0.267502	−0.133751	+	0.991015i	$0.542702\pi$
$140$	−1.40867	−0.119054
$141$	−8.87112	−0.747083
$142$	−9.37398	−0.786647
$143$	−3.40977	−0.285139
$144$	−2.36454	−0.197045
$145$	−8.75034	−0.726676
$146$	3.99440	0.330579
$147$	−0.797155	−0.0657483
$148$	5.42018	0.445536
$149$	16.0083	1.31145	0.655726	−	0.754999i	$-0.272363\pi$
$149$	16.0083	1.31145	0.655726	+	0.754999i	$0.272363\pi$
$150$	−2.40394	−0.196281
$151$	9.62444	0.783226	0.391613	−	0.920130i	$-0.371917\pi$
$151$	9.62444	0.783226	0.391613	+	0.920130i	$0.371917\pi$
$152$	6.70269	0.543660
$153$	8.58272	0.693871
$154$	−4.26652	−0.343806
$155$	−9.32351	−0.748882
$156$	−0.637080	−0.0510072
$157$	−2.78528	−0.222289	−0.111145	−	0.993804i	$-0.535452\pi$
$157$	−2.78528	−0.222289	−0.111145	+	0.993804i	$0.535452\pi$
$158$	−5.28980	−0.420834
$159$	2.68314	0.212787
$160$	−1.40867	−0.111365
$161$	4.59211	0.361909
$162$	−3.68470	−0.289497
$163$	7.65399	0.599507	0.299753	−	0.954017i	$-0.403096\pi$
$163$	7.65399	0.599507	0.299753	+	0.954017i	$0.403096\pi$
$164$	−4.51614	−0.352652
$165$	4.79100	0.372979
$166$	−14.1032	−1.09462
$167$	8.70855	0.673888	0.336944	−	0.941525i	$-0.390607\pi$
$167$	8.70855	0.673888	0.336944	+	0.941525i	$0.390607\pi$
$168$	−0.797155	−0.0615019
$169$	−12.3613	−0.950869
$170$	5.11313	0.392159
$171$	15.8488	1.21199
$172$	0.780925	0.0595450
$173$	0.799481	0.0607834	0.0303917	−	0.999538i	$-0.490325\pi$
$173$	0.799481	0.0607834	0.0303917	+	0.999538i	$0.490325\pi$
$174$	−4.95175	−0.375391
$175$	3.01565	0.227962
$176$	−4.26652	−0.321601
$177$	−4.30091	−0.323276
$178$	13.9685	1.04698
$179$	−7.40805	−0.553704	−0.276852	−	0.960913i	$-0.589291\pi$
$179$	−7.40805	−0.553704	−0.276852	+	0.960913i	$0.589291\pi$
$180$	−3.33086	−0.248268
$181$	−11.7333	−0.872126	−0.436063	−	0.899916i	$-0.643628\pi$
$181$	−11.7333	−0.872126	−0.436063	+	0.899916i	$0.643628\pi$
$182$	0.799192	0.0592400
$183$	4.62935	0.342211
$184$	4.59211	0.338535
$185$	7.63524	0.561354
$186$	−5.27610	−0.386863
$187$	15.4864	1.13248
$188$	11.1285	0.811627
$189$	−4.27637	−0.311060
$190$	9.44188	0.684986
$191$	8.22734	0.595309	0.297655	−	0.954674i	$-0.403796\pi$
$191$	8.22734	0.595309	0.297655	+	0.954674i	$0.403796\pi$
$192$	−0.797155	−0.0575297
$193$	−18.7582	−1.35024	−0.675121	−	0.737707i	$-0.735909\pi$
$193$	−18.7582	−1.35024	−0.675121	+	0.737707i	$0.735909\pi$
$194$	3.54831	0.254754
$195$	−0.897435	−0.0642667
$196$	1.00000	0.0714286
$197$	−20.4237	−1.45512	−0.727562	−	0.686041i	$-0.759347\pi$
$197$	−20.4237	−1.45512	−0.727562	+	0.686041i	$0.759347\pi$
$198$	−10.0884	−0.716949
$199$	−13.8409	−0.981152	−0.490576	−	0.871398i	$-0.663214\pi$
$199$	−13.8409	−0.981152	−0.490576	+	0.871398i	$0.663214\pi$
$200$	3.01565	0.213239
$201$	3.89244	0.274552
$202$	−9.29483	−0.653982
$203$	6.21178	0.435981
$204$	2.89348	0.202584
$205$	−6.36175	−0.444324
$206$	−8.45408	−0.589024
$207$	10.8582	0.754701
$208$	0.799192	0.0554140
$209$	28.5972	1.97811
$210$	−1.12293	−0.0774894
$211$	22.7593	1.56681	0.783407	−	0.621509i	$-0.213480\pi$
$211$	22.7593	1.56681	0.783407	+	0.621509i	$0.213480\pi$
$212$	−3.36589	−0.231170
$213$	−7.47251	−0.512008
$214$	−12.0908	−0.826509
$215$	1.10007	0.0750238
$216$	−4.27637	−0.290970
$217$	6.61866	0.449304
$218$	5.51476	0.373507
$219$	3.18416	0.215166
$220$	−6.01012	−0.405202
$221$	−2.90087	−0.195134
$222$	4.32072	0.289988
$223$	−8.70757	−0.583102	−0.291551	−	0.956555i	$-0.594171\pi$
$223$	−8.70757	−0.583102	−0.291551	+	0.956555i	$0.594171\pi$
$224$	1.00000	0.0668153
$225$	7.13063	0.475376
$226$	−5.38250	−0.358038
$227$	−16.8011	−1.11513	−0.557564	−	0.830134i	$-0.688264\pi$
$227$	−16.8011	−1.11513	−0.557564	+	0.830134i	$0.688264\pi$
$228$	5.34309	0.353854
$229$	24.0920	1.59205	0.796023	−	0.605267i	$-0.206934\pi$
$229$	24.0920	1.59205	0.796023	+	0.605267i	$0.206934\pi$
$230$	6.46877	0.426538
$231$	−3.40108	−0.223775
$232$	6.21178	0.407823
$233$	−12.7964	−0.838321	−0.419160	−	0.907912i	$-0.637676\pi$
$233$	−12.7964	−0.838321	−0.419160	+	0.907912i	$0.637676\pi$
$234$	1.88972	0.123535
$235$	15.6763	1.02261
$236$	5.39532	0.351205
$237$	−4.21680	−0.273910
$238$	−3.62976	−0.235282
$239$	2.87318	0.185851	0.0929253	−	0.995673i	$-0.470378\pi$
$239$	2.87318	0.185851	0.0929253	+	0.995673i	$0.470378\pi$
$240$	−1.12293	−0.0724847
$241$	−8.19163	−0.527669	−0.263835	−	0.964568i	$-0.584987\pi$
$241$	−8.19163	−0.527669	−0.263835	+	0.964568i	$0.584987\pi$
$242$	−7.20319	−0.463039
$243$	−15.7664	−1.01141
$244$	−5.80734	−0.371777
$245$	1.40867	0.0899966
$246$	−3.60007	−0.229532
$247$	−5.35674	−0.340841
$248$	6.61866	0.420285
$249$	−11.2425	−0.712462
$250$	11.2914	0.714131
$251$	−14.2956	−0.902332	−0.451166	−	0.892440i	$-0.648992\pi$
$251$	−14.2956	−0.902332	−0.451166	+	0.892440i	$0.648992\pi$
$252$	2.36454	0.148952
$253$	19.5923	1.23176
$254$	−13.0689	−0.820017
$255$	4.07596	0.255246
$256$	1.00000	0.0625000
$257$	8.61994	0.537697	0.268849	−	0.963182i	$-0.413357\pi$
$257$	8.61994	0.537697	0.268849	+	0.963182i	$0.413357\pi$
$258$	0.622518	0.0387563
$259$	−5.42018	−0.336793
$260$	1.12580	0.0698190
$261$	14.6880	0.909165
$262$	−5.75249	−0.355390
$263$	−22.6467	−1.39646	−0.698228	−	0.715875i	$-0.746028\pi$
$263$	−22.6467	−1.39646	−0.698228	+	0.715875i	$0.746028\pi$
$264$	−3.40108	−0.209322
$265$	−4.74143	−0.291264
$266$	−6.70269	−0.410968
$267$	11.1350	0.681454
$268$	−4.88292	−0.298272
$269$	−1.14346	−0.0697182	−0.0348591	−	0.999392i	$-0.511098\pi$
$269$	−1.14346	−0.0697182	−0.0348591	+	0.999392i	$0.511098\pi$
$270$	−6.02400	−0.366609
$271$	−26.5613	−1.61349	−0.806743	−	0.590903i	$-0.798772\pi$
$271$	−26.5613	−1.61349	−0.806743	+	0.590903i	$0.798772\pi$
$272$	−3.62976	−0.220086
$273$	0.637080	0.0385578
$274$	−7.21273	−0.435737
$275$	12.8663	0.775869
$276$	3.66063	0.220344
$277$	−17.7413	−1.06597	−0.532987	−	0.846124i	$-0.678930\pi$
$277$	−17.7413	−1.06597	−0.532987	+	0.846124i	$0.678930\pi$
$278$	3.15380	0.189152
$279$	15.6501	0.936948
$280$	1.40867	0.0841841
$281$	3.28356	0.195881	0.0979404	−	0.995192i	$-0.468775\pi$
$281$	3.28356	0.195881	0.0979404	+	0.995192i	$0.468775\pi$
$282$	8.87112	0.528267
$283$	15.1321	0.899508	0.449754	−	0.893152i	$-0.351512\pi$
$283$	15.1321	0.899508	0.449754	+	0.893152i	$0.351512\pi$
$284$	9.37398	0.556243
$285$	7.52664	0.445840
$286$	3.40977	0.201624
$287$	4.51614	0.266580
$288$	2.36454	0.139332
$289$	−3.82487	−0.224993
$290$	8.75034	0.513838
$291$	2.82856	0.165813
$292$	−3.99440	−0.233755
$293$	3.09226	0.180652	0.0903259	−	0.995912i	$-0.471209\pi$
$293$	3.09226	0.180652	0.0903259	+	0.995912i	$0.471209\pi$
$294$	0.797155	0.0464910
$295$	7.60022	0.442502
$296$	−5.42018	−0.315041
$297$	−18.2452	−1.05870
$298$	−16.0083	−0.927337
$299$	−3.66998	−0.212240
$300$	2.40394	0.138792
$301$	−0.780925	−0.0450118
$302$	−9.62444	−0.553825
$303$	−7.40942	−0.425660
$304$	−6.70269	−0.384426
$305$	−8.18062	−0.468421
$306$	−8.58272	−0.490641
$307$	12.4885	0.712754	0.356377	−	0.934342i	$-0.384012\pi$
$307$	12.4885	0.712754	0.356377	+	0.934342i	$0.384012\pi$
$308$	4.26652	0.243108
$309$	−6.73922	−0.383381
$310$	9.32351	0.529540
$311$	−17.8336	−1.01125	−0.505624	−	0.862754i	$-0.668738\pi$
$311$	−17.8336	−1.01125	−0.505624	+	0.862754i	$0.668738\pi$
$312$	0.637080	0.0360676
$313$	−28.9134	−1.63428	−0.817142	−	0.576437i	$-0.804443\pi$
$313$	−28.9134	−1.63428	−0.817142	+	0.576437i	$0.804443\pi$
$314$	2.78528	0.157182
$315$	3.33086	0.187673
$316$	5.28980	0.297575
$317$	−7.35728	−0.413226	−0.206613	−	0.978423i	$-0.566244\pi$
$317$	−7.35728	−0.413226	−0.206613	+	0.978423i	$0.566244\pi$
$318$	−2.68314	−0.150463
$319$	26.5027	1.48386
$320$	1.40867	0.0787470
$321$	−9.63823	−0.537954
$322$	−4.59211	−0.255908
$323$	24.3291	1.35371
$324$	3.68470	0.204705
$325$	−2.41008	−0.133687
$326$	−7.65399	−0.423915
$327$	4.39612	0.243106
$328$	4.51614	0.249362
$329$	−11.1285	−0.613532
$330$	−4.79100	−0.263736
$331$	−6.60868	−0.363246	−0.181623	−	0.983368i	$-0.558135\pi$
$331$	−6.60868	−0.363246	−0.181623	+	0.983368i	$0.558135\pi$
$332$	14.1032	0.774015
$333$	−12.8162	−0.702326
$334$	−8.70855	−0.476511
$335$	−6.87841	−0.375808
$336$	0.797155	0.0434884
$337$	−13.4528	−0.732821	−0.366411	−	0.930453i	$-0.619413\pi$
$337$	−13.4528	−0.732821	−0.366411	+	0.930453i	$0.619413\pi$
$338$	12.3613	0.672366
$339$	−4.29069	−0.233038
$340$	−5.11313	−0.277298
$341$	28.2387	1.52921
$342$	−15.8488	−0.857005
$343$	−1.00000	−0.0539949
$344$	−0.780925	−0.0421046
$345$	5.15661	0.277623
$346$	−0.799481	−0.0429803
$347$	−13.0592	−0.701052	−0.350526	−	0.936553i	$-0.613997\pi$
$347$	−13.0592	−0.701052	−0.350526	+	0.936553i	$0.613997\pi$
$348$	4.95175	0.265442
$349$	−32.8893	−1.76052	−0.880262	−	0.474488i	$-0.842633\pi$
$349$	−32.8893	−1.76052	−0.880262	+	0.474488i	$0.842633\pi$
$350$	−3.01565	−0.161193
$351$	3.41764	0.182420
$352$	4.26652	0.227406
$353$	33.8962	1.80411	0.902056	−	0.431620i	$-0.142058\pi$
$353$	33.8962	1.80411	0.902056	+	0.431620i	$0.142058\pi$
$354$	4.30091	0.228591
$355$	13.2048	0.700840
$356$	−13.9685	−0.740328
$357$	−2.89348	−0.153139
$358$	7.40805	0.391528
$359$	−20.3577	−1.07444	−0.537219	−	0.843442i	$-0.680525\pi$
$359$	−20.3577	−1.07444	−0.537219	+	0.843442i	$0.680525\pi$
$360$	3.33086	0.175552
$361$	25.9261	1.36453
$362$	11.7333	0.616686
$363$	−5.74206	−0.301380
$364$	−0.799192	−0.0418890
$365$	−5.62680	−0.294520
$366$	−4.62935	−0.241980
$367$	23.4757	1.22542	0.612710	−	0.790308i	$-0.290079\pi$
$367$	23.4757	1.22542	0.612710	+	0.790308i	$0.290079\pi$
$368$	−4.59211	−0.239380
$369$	10.6786	0.555907
$370$	−7.63524	−0.396937
$371$	3.36589	0.174748
$372$	5.27610	0.273553
$373$	7.31132	0.378566	0.189283	−	0.981923i	$-0.439384\pi$
$373$	7.31132	0.378566	0.189283	+	0.981923i	$0.439384\pi$
$374$	−15.4864	−0.800784
$375$	9.00100	0.464810
$376$	−11.1285	−0.573907
$377$	−4.96440	−0.255680
$378$	4.27637	0.219953
$379$	−15.8034	−0.811766	−0.405883	−	0.913925i	$-0.633036\pi$
$379$	−15.8034	−0.811766	−0.405883	+	0.913925i	$0.633036\pi$
$380$	−9.44188	−0.484358
$381$	−10.4180	−0.533728
$382$	−8.22734	−0.420947
$383$	13.1987	0.674424	0.337212	−	0.941429i	$-0.390516\pi$
$383$	13.1987	0.674424	0.337212	+	0.941429i	$0.390516\pi$
$384$	0.797155	0.0406797
$385$	6.01012	0.306304
$386$	18.7582	0.954765
$387$	−1.84653	−0.0938644
$388$	−3.54831	−0.180138
$389$	33.1194	1.67922	0.839609	−	0.543191i	$-0.182784\pi$
$389$	33.1194	1.67922	0.839609	+	0.543191i	$0.182784\pi$
$390$	0.897435	0.0454434
$391$	16.6682	0.842949
$392$	−1.00000	−0.0505076
$393$	−4.58563	−0.231314
$394$	20.4237	1.02893
$395$	7.45159	0.374930
$396$	10.0884	0.506960
$397$	−17.0911	−0.857777	−0.428888	−	0.903358i	$-0.641095\pi$
$397$	−17.0911	−0.857777	−0.428888	+	0.903358i	$0.641095\pi$
$398$	13.8409	0.693779
$399$	−5.34309	−0.267489
$400$	−3.01565	−0.150782
$401$	−20.1721	−1.00735	−0.503673	−	0.863894i	$-0.668018\pi$
$401$	−20.1721	−1.00735	−0.503673	+	0.863894i	$0.668018\pi$
$402$	−3.89244	−0.194137
$403$	−5.28958	−0.263493
$404$	9.29483	0.462435
$405$	5.19052	0.257919
$406$	−6.21178	−0.308285
$407$	−23.1253	−1.14628
$408$	−2.89348	−0.143249
$409$	32.3193	1.59809	0.799043	−	0.601274i	$-0.205340\pi$
$409$	32.3193	1.59809	0.799043	+	0.601274i	$0.205340\pi$
$410$	6.36175	0.314185
$411$	−5.74967	−0.283610
$412$	8.45408	0.416503
$413$	−5.39532	−0.265486
$414$	−10.8582	−0.533654
$415$	19.8668	0.975222
$416$	−0.799192	−0.0391836
$417$	2.51407	0.123114
$418$	−28.5972	−1.39873
$419$	−22.7045	−1.10919	−0.554594	−	0.832121i	$-0.687126\pi$
$419$	−22.7045	−1.10919	−0.554594	+	0.832121i	$0.687126\pi$
$420$	1.12293	0.0547933
$421$	16.2815	0.793513	0.396756	−	0.917924i	$-0.370136\pi$
$421$	16.2815	0.793513	0.396756	+	0.917924i	$0.370136\pi$
$422$	−22.7593	−1.10790
$423$	−26.3137	−1.27942
$424$	3.36589	0.163462
$425$	10.9461	0.530962
$426$	7.47251	0.362044
$427$	5.80734	0.281037
$428$	12.0908	0.584430
$429$	2.71811	0.131232
$430$	−1.10007	−0.0530499
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	4.27637	0.205747
$433$	5.04478	0.242437	0.121218	−	0.992626i	$-0.461320\pi$
$433$	5.04478	0.242437	0.121218	+	0.992626i	$0.461320\pi$
$434$	−6.61866	−0.317706
$435$	6.97538	0.334444
$436$	−5.51476	−0.264109
$437$	30.7795	1.47238
$438$	−3.18416	−0.152145
$439$	12.8675	0.614132	0.307066	−	0.951688i	$-0.400653\pi$
$439$	12.8675	0.614132	0.307066	+	0.951688i	$0.400653\pi$
$440$	6.01012	0.286521
$441$	−2.36454	−0.112597
$442$	2.90087	0.137980
$443$	7.97797	0.379045	0.189522	−	0.981876i	$-0.439306\pi$
$443$	7.97797	0.379045	0.189522	+	0.981876i	$0.439306\pi$
$444$	−4.32072	−0.205052
$445$	−19.6770	−0.932778
$446$	8.70757	0.412315
$447$	−12.7611	−0.603580
$448$	−1.00000	−0.0472456
$449$	33.4115	1.57679	0.788394	−	0.615171i	$-0.210913\pi$
$449$	33.4115	1.57679	0.788394	+	0.615171i	$0.210913\pi$
$450$	−7.13063	−0.336141
$451$	19.2682	0.907305
$452$	5.38250	0.253171
$453$	−7.67218	−0.360470
$454$	16.8011	0.788515
$455$	−1.12580	−0.0527782
$456$	−5.34309	−0.250213
$457$	14.1064	0.659871	0.329935	−	0.944004i	$-0.392973\pi$
$457$	14.1064	0.659871	0.329935	+	0.944004i	$0.392973\pi$
$458$	−24.0920	−1.12575
$459$	−15.5222	−0.724514
$460$	−6.46877	−0.301608
$461$	12.0170	0.559688	0.279844	−	0.960046i	$-0.409717\pi$
$461$	12.0170	0.559688	0.279844	+	0.960046i	$0.409717\pi$
$462$	3.40108	0.158233
$463$	−11.9976	−0.557575	−0.278787	−	0.960353i	$-0.589932\pi$
$463$	−11.9976	−0.557575	−0.278787	+	0.960353i	$0.589932\pi$
$464$	−6.21178	−0.288375
$465$	7.43228	0.344664
$466$	12.7964	0.592782
$467$	11.6270	0.538035	0.269018	−	0.963135i	$-0.413301\pi$
$467$	11.6270	0.538035	0.269018	+	0.963135i	$0.413301\pi$
$468$	−1.88972	−0.0873525
$469$	4.88292	0.225472
$470$	−15.6763	−0.723095
$471$	2.22030	0.102306
$472$	−5.39532	−0.248340
$473$	−3.33183	−0.153198
$474$	4.21680	0.193684
$475$	20.2130	0.927435
$476$	3.62976	0.166370
$477$	7.95880	0.364408
$478$	−2.87318	−0.131416
$479$	2.99665	0.136921	0.0684603	−	0.997654i	$-0.478191\pi$
$479$	2.99665	0.136921	0.0684603	+	0.997654i	$0.478191\pi$
$480$	1.12293	0.0512544
$481$	4.33176	0.197511
$482$	8.19163	0.373118
$483$	−3.66063	−0.166564
$484$	7.20319	0.327418
$485$	−4.99840	−0.226966
$486$	15.7664	0.715178
$487$	−18.3844	−0.833079	−0.416539	−	0.909118i	$-0.636757\pi$
$487$	−18.3844	−0.833079	−0.416539	+	0.909118i	$0.636757\pi$
$488$	5.80734	0.262886
$489$	−6.10142	−0.275916
$490$	−1.40867	−0.0636372
$491$	21.2906	0.960832	0.480416	−	0.877041i	$-0.340486\pi$
$491$	21.2906	0.960832	0.480416	+	0.877041i	$0.340486\pi$
$492$	3.60007	0.162304
$493$	22.5472	1.01548
$494$	5.35674	0.241011
$495$	14.2112	0.638745
$496$	−6.61866	−0.297187
$497$	−9.37398	−0.420480
$498$	11.2425	0.503787
$499$	39.7003	1.77723	0.888614	−	0.458655i	$-0.151669\pi$
$499$	39.7003	1.77723	0.888614	+	0.458655i	$0.151669\pi$
$500$	−11.2914	−0.504967
$501$	−6.94207	−0.310149
$502$	14.2956	0.638045
$503$	−24.7499	−1.10354	−0.551772	−	0.833995i	$-0.686048\pi$
$503$	−24.7499	−1.10354	−0.551772	+	0.833995i	$0.686048\pi$
$504$	−2.36454	−0.105325
$505$	13.0933	0.582646
$506$	−19.5923	−0.870986
$507$	9.85387	0.437626
$508$	13.0689	0.579839
$509$	16.9879	0.752977	0.376489	−	0.926421i	$-0.377131\pi$
$509$	16.9879	0.752977	0.376489	+	0.926421i	$0.377131\pi$
$510$	−4.07596	−0.180486
$511$	3.99440	0.176702
$512$	−1.00000	−0.0441942
$513$	−28.6632	−1.26551
$514$	−8.61994	−0.380209
$515$	11.9090	0.524774
$516$	−0.622518	−0.0274048
$517$	−47.4798	−2.08816
$518$	5.42018	0.238149
$519$	−0.637310	−0.0279748
$520$	−1.12580	−0.0493695
$521$	−0.356556	−0.0156210	−0.00781050	−	0.999969i	$-0.502486\pi$
$521$	−0.356556	−0.0156210	−0.00781050	+	0.999969i	$0.502486\pi$
$522$	−14.6880	−0.642877
$523$	0.463689	0.0202757	0.0101379	−	0.999949i	$-0.496773\pi$
$523$	0.463689	0.0202757	0.0101379	+	0.999949i	$0.496773\pi$
$524$	5.75249	0.251299
$525$	−2.40394	−0.104917
$526$	22.6467	0.987444
$527$	24.0241	1.04651
$528$	3.40108	0.148013
$529$	−1.91250	−0.0831523
$530$	4.74143	0.205955
$531$	−12.7575	−0.553627
$532$	6.70269	0.290599
$533$	−3.60927	−0.156335
$534$	−11.1350	−0.481861
$535$	17.0319	0.736354
$536$	4.88292	0.210910
$537$	5.90537	0.254835
$538$	1.14346	0.0492982
$539$	−4.26652	−0.183772
$540$	6.02400	0.259232
$541$	−18.7910	−0.807888	−0.403944	−	0.914784i	$-0.632361\pi$
$541$	−18.7910	−0.807888	−0.403944	+	0.914784i	$0.632361\pi$
$542$	26.5613	1.14091
$543$	9.35323	0.401385
$544$	3.62976	0.155624
$545$	−7.76848	−0.332765
$546$	−0.637080	−0.0272645
$547$	22.4507	0.959923	0.479962	−	0.877290i	$-0.340651\pi$
$547$	22.4507	0.959923	0.479962	+	0.877290i	$0.340651\pi$
$548$	7.21273	0.308113
$549$	13.7317	0.586055
$550$	−12.8663	−0.548622
$551$	41.6356	1.77374
$552$	−3.66063	−0.155807
$553$	−5.28980	−0.224945
$554$	17.7413	0.753757
$555$	−6.08647	−0.258356
$556$	−3.15380	−0.133751
$557$	26.9804	1.14320	0.571599	−	0.820533i	$-0.306323\pi$
$557$	26.9804	1.14320	0.571599	+	0.820533i	$0.306323\pi$
$558$	−15.6501	−0.662522
$559$	0.624109	0.0263970
$560$	−1.40867	−0.0595272
$561$	−12.3451	−0.521210
$562$	−3.28356	−0.138509
$563$	9.44939	0.398244	0.199122	−	0.979975i	$-0.436191\pi$
$563$	9.44939	0.398244	0.199122	+	0.979975i	$0.436191\pi$
$564$	−8.87112	−0.373541
$565$	7.58216	0.318984
$566$	−15.1321	−0.636048
$567$	−3.68470	−0.154743
$568$	−9.37398	−0.393323
$569$	−22.8688	−0.958710	−0.479355	−	0.877621i	$-0.659129\pi$
$569$	−22.8688	−0.958710	−0.479355	+	0.877621i	$0.659129\pi$
$570$	−7.52664	−0.315256
$571$	33.7728	1.41335	0.706674	−	0.707539i	$-0.250195\pi$
$571$	33.7728	1.41335	0.706674	+	0.707539i	$0.250195\pi$
$572$	−3.40977	−0.142570
$573$	−6.55847	−0.273984
$574$	−4.51614	−0.188500
$575$	13.8482	0.577510
$576$	−2.36454	−0.0985226
$577$	30.0463	1.25084	0.625422	−	0.780286i	$-0.284927\pi$
$577$	30.0463	1.25084	0.625422	+	0.780286i	$0.284927\pi$
$578$	3.82487	0.159094
$579$	14.9532	0.621432
$580$	−8.75034	−0.363338
$581$	−14.1032	−0.585100
$582$	−2.82856	−0.117247
$583$	14.3606	0.594757
$584$	3.99440	0.165290
$585$	−2.66200	−0.110060
$586$	−3.09226	−0.127740
$587$	−3.46068	−0.142838	−0.0714189	−	0.997446i	$-0.522753\pi$
$587$	−3.46068	−0.142838	−0.0714189	+	0.997446i	$0.522753\pi$
$588$	−0.797155	−0.0328741
$589$	44.3628	1.82794
$590$	−7.60022	−0.312896
$591$	16.2808	0.669703
$592$	5.42018	0.222768
$593$	10.4962	0.431029	0.215514	−	0.976501i	$-0.430857\pi$
$593$	10.4962	0.431029	0.215514	+	0.976501i	$0.430857\pi$
$594$	18.2452	0.748611
$595$	5.11313	0.209618
$596$	16.0083	0.655726
$597$	11.0333	0.451563
$598$	3.66998	0.150077
$599$	6.44694	0.263415	0.131707	−	0.991289i	$-0.457954\pi$
$599$	6.44694	0.263415	0.131707	+	0.991289i	$0.457954\pi$
$600$	−2.40394	−0.0981405
$601$	−8.45631	−0.344940	−0.172470	−	0.985015i	$-0.555175\pi$
$601$	−8.45631	−0.344940	−0.172470	+	0.985015i	$0.555175\pi$
$602$	0.780925	0.0318281
$603$	11.5459	0.470184
$604$	9.62444	0.391613
$605$	10.1469	0.412531
$606$	7.40942	0.300987
$607$	−25.4777	−1.03411	−0.517053	−	0.855953i	$-0.672971\pi$
$607$	−25.4777	−1.03411	−0.517053	+	0.855953i	$0.672971\pi$
$608$	6.70269	0.271830
$609$	−4.95175	−0.200655
$610$	8.18062	0.331224
$611$	8.89378	0.359804
$612$	8.58272	0.346936
$613$	−37.4831	−1.51393	−0.756964	−	0.653456i	$-0.773318\pi$
$613$	−37.4831	−1.51393	−0.756964	+	0.653456i	$0.773318\pi$
$614$	−12.4885	−0.503993
$615$	5.07131	0.204495
$616$	−4.26652	−0.171903
$617$	44.3768	1.78654	0.893271	−	0.449518i	$-0.148404\pi$
$617$	44.3768	1.78654	0.893271	+	0.449518i	$0.148404\pi$
$618$	6.73922	0.271091
$619$	23.0916	0.928131	0.464066	−	0.885801i	$-0.346390\pi$
$619$	23.0916	0.928131	0.464066	+	0.885801i	$0.346390\pi$
$620$	−9.32351	−0.374441
$621$	−19.6376	−0.788029
$622$	17.8336	0.715060
$623$	13.9685	0.559635
$624$	−0.637080	−0.0255036
$625$	−0.827608	−0.0331043
$626$	28.9134	1.15561
$627$	−22.7964	−0.910400
$628$	−2.78528	−0.111145
$629$	−19.6739	−0.784451
$630$	−3.33086	−0.132705
$631$	−0.164653	−0.00655472	−0.00327736	−	0.999995i	$-0.501043\pi$
$631$	−0.164653	−0.00655472	−0.00327736	+	0.999995i	$0.501043\pi$
$632$	−5.28980	−0.210417
$633$	−18.1427	−0.721107
$634$	7.35728	0.292195
$635$	18.4098	0.730570
$636$	2.68314	0.106393
$637$	0.799192	0.0316651
$638$	−26.5027	−1.04925
$639$	−22.1652	−0.876841
$640$	−1.40867	−0.0556826
$641$	5.09320	0.201169	0.100585	−	0.994928i	$-0.467929\pi$
$641$	5.09320	0.201169	0.100585	+	0.994928i	$0.467929\pi$
$642$	9.63823	0.380391
$643$	−27.0878	−1.06824	−0.534119	−	0.845409i	$-0.679357\pi$
$643$	−27.0878	−1.06824	−0.534119	+	0.845409i	$0.679357\pi$
$644$	4.59211	0.180955
$645$	−0.876923	−0.0345288
$646$	−24.3291	−0.957217
$647$	9.90929	0.389574	0.194787	−	0.980846i	$-0.437598\pi$
$647$	9.90929	0.389574	0.194787	+	0.980846i	$0.437598\pi$
$648$	−3.68470	−0.144749
$649$	−23.0192	−0.903584
$650$	2.41008	0.0945312
$651$	−5.27610	−0.206787
$652$	7.65399	0.299753
$653$	10.1183	0.395961	0.197980	−	0.980206i	$-0.436562\pi$
$653$	10.1183	0.395961	0.197980	+	0.980206i	$0.436562\pi$
$654$	−4.39612	−0.171902
$655$	8.10335	0.316624
$656$	−4.51614	−0.176326
$657$	9.44494	0.368482
$658$	11.1285	0.433833
$659$	−22.7802	−0.887392	−0.443696	−	0.896177i	$-0.646333\pi$
$659$	−22.7802	−0.887392	−0.443696	+	0.896177i	$0.646333\pi$
$660$	4.79100	0.186489
$661$	−29.7642	−1.15769	−0.578846	−	0.815437i	$-0.696497\pi$
$661$	−29.7642	−1.15769	−0.578846	+	0.815437i	$0.696497\pi$
$662$	6.60868	0.256854
$663$	2.31244	0.0898079
$664$	−14.1032	−0.547311
$665$	9.44188	0.366140
$666$	12.8162	0.496619
$667$	28.5252	1.10450
$668$	8.70855	0.336944
$669$	6.94128	0.268365
$670$	6.87841	0.265736
$671$	24.7771	0.956510
$672$	−0.797155	−0.0307509
$673$	5.64016	0.217412	0.108706	−	0.994074i	$-0.465329\pi$
$673$	5.64016	0.217412	0.108706	+	0.994074i	$0.465329\pi$
$674$	13.4528	0.518183
$675$	−12.8960	−0.496369
$676$	−12.3613	−0.475434
$677$	−31.1155	−1.19586	−0.597932	−	0.801547i	$-0.704011\pi$
$677$	−31.1155	−1.19586	−0.597932	+	0.801547i	$0.704011\pi$
$678$	4.29069	0.164783
$679$	3.54831	0.136172
$680$	5.11313	0.196079
$681$	13.3931	0.513224
$682$	−28.2387	−1.08131
$683$	−0.451659	−0.0172822	−0.00864112	−	0.999963i	$-0.502751\pi$
$683$	−0.451659	−0.0172822	−0.00864112	+	0.999963i	$0.502751\pi$
$684$	15.8488	0.605994
$685$	10.1604	0.388207
$686$	1.00000	0.0381802
$687$	−19.2051	−0.732719
$688$	0.780925	0.0297725
$689$	−2.68999	−0.102481
$690$	−5.15661	−0.196309
$691$	−40.4771	−1.53982	−0.769910	−	0.638152i	$-0.779699\pi$
$691$	−40.4771	−1.53982	−0.769910	+	0.638152i	$0.779699\pi$
$692$	0.799481	0.0303917
$693$	−10.0884	−0.383226
$694$	13.0592	0.495719
$695$	−4.44266	−0.168520
$696$	−4.95175	−0.187696
$697$	16.3925	0.620910
$698$	32.8893	1.24488
$699$	10.2007	0.385827
$700$	3.01565	0.113981
$701$	9.36340	0.353651	0.176825	−	0.984242i	$-0.443417\pi$
$701$	9.36340	0.353651	0.176825	+	0.984242i	$0.443417\pi$
$702$	−3.41764	−0.128991
$703$	−36.3298	−1.37020
$704$	−4.26652	−0.160801
$705$	−12.4965	−0.470644
$706$	−33.8962	−1.27570
$707$	−9.29483	−0.349568
$708$	−4.30091	−0.161638
$709$	42.8899	1.61076	0.805381	−	0.592757i	$-0.201961\pi$
$709$	42.8899	1.61076	0.805381	+	0.592757i	$0.201961\pi$
$710$	−13.2048	−0.495569
$711$	−12.5080	−0.469086
$712$	13.9685	0.523491
$713$	30.3936	1.13825
$714$	2.89348	0.108286
$715$	−4.80324	−0.179631
$716$	−7.40805	−0.276852
$717$	−2.29037	−0.0855354
$718$	20.3577	0.759743
$719$	42.3347	1.57882	0.789409	−	0.613867i	$-0.210387\pi$
$719$	42.3347	1.57882	0.789409	+	0.613867i	$0.210387\pi$
$720$	−3.33086	−0.124134
$721$	−8.45408	−0.314846
$722$	−25.9261	−0.964869
$723$	6.53000	0.242853
$724$	−11.7333	−0.436063
$725$	18.7325	0.695709
$726$	5.74206	0.213108
$727$	50.0598	1.85661	0.928307	−	0.371814i	$-0.121264\pi$
$727$	50.0598	1.85661	0.928307	+	0.371814i	$0.121264\pi$
$728$	0.799192	0.0296200
$729$	1.51418	0.0560806
$730$	5.62680	0.208257
$731$	−2.83457	−0.104840
$732$	4.62935	0.171106
$733$	−42.7236	−1.57803	−0.789016	−	0.614372i	$-0.789409\pi$
$733$	−42.7236	−1.57803	−0.789016	+	0.614372i	$0.789409\pi$
$734$	−23.4757	−0.866503
$735$	−1.12293	−0.0414198
$736$	4.59211	0.169268
$737$	20.8331	0.767395
$738$	−10.6786	−0.393085
$739$	−17.5227	−0.644583	−0.322292	−	0.946640i	$-0.604453\pi$
$739$	−17.5227	−0.644583	−0.322292	+	0.946640i	$0.604453\pi$
$740$	7.63524	0.280677
$741$	4.27015	0.156868
$742$	−3.36589	−0.123566
$743$	−19.0604	−0.699259	−0.349629	−	0.936888i	$-0.613693\pi$
$743$	−19.0604	−0.699259	−0.349629	+	0.936888i	$0.613693\pi$
$744$	−5.27610	−0.193431
$745$	22.5504	0.826184
$746$	−7.31132	−0.267686
$747$	−33.3477	−1.22013
$748$	15.4864	0.566240
$749$	−12.0908	−0.441788
$750$	−9.00100	−0.328670
$751$	39.7034	1.44880	0.724398	−	0.689382i	$-0.242118\pi$
$751$	39.7034	1.44880	0.724398	+	0.689382i	$0.242118\pi$
$752$	11.1285	0.405813
$753$	11.3958	0.415287
$754$	4.96440	0.180793
$755$	13.5577	0.493414
$756$	−4.27637	−0.155530
$757$	29.3432	1.06650	0.533248	−	0.845959i	$-0.320971\pi$
$757$	29.3432	1.06650	0.533248	+	0.845959i	$0.320971\pi$
$758$	15.8034	0.574005
$759$	−15.6181	−0.566902
$760$	9.44188	0.342493
$761$	8.77351	0.318039	0.159020	−	0.987275i	$-0.449167\pi$
$761$	8.77351	0.318039	0.159020	+	0.987275i	$0.449167\pi$
$762$	10.4180	0.377403
$763$	5.51476	0.199648
$764$	8.22734	0.297655
$765$	12.0902	0.437122
$766$	−13.1987	−0.476890
$767$	4.31189	0.155693
$768$	−0.797155	−0.0287649
$769$	−2.17784	−0.0785349	−0.0392675	−	0.999229i	$-0.512502\pi$
$769$	−2.17784	−0.0785349	−0.0392675	+	0.999229i	$0.512502\pi$
$770$	−6.01012	−0.216590
$771$	−6.87143	−0.247469
$772$	−18.7582	−0.675121
$773$	16.9098	0.608204	0.304102	−	0.952639i	$-0.401644\pi$
$773$	16.9098	0.608204	0.304102	+	0.952639i	$0.401644\pi$
$774$	1.84653	0.0663722
$775$	19.9596	0.716969
$776$	3.54831	0.127377
$777$	4.32072	0.155005
$778$	−33.1194	−1.18739
$779$	30.2703	1.08455
$780$	−0.897435	−0.0321333
$781$	−39.9943	−1.43111
$782$	−16.6682	−0.596055
$783$	−26.5639	−0.949316
$784$	1.00000	0.0357143
$785$	−3.92354	−0.140037
$786$	4.58563	0.163564
$787$	−0.623669	−0.0222314	−0.0111157	−	0.999938i	$-0.503538\pi$
$787$	−0.623669	−0.0222314	−0.0111157	+	0.999938i	$0.503538\pi$
$788$	−20.4237	−0.727562
$789$	18.0530	0.642702
$790$	−7.45159	−0.265116
$791$	−5.38250	−0.191380
$792$	−10.0884	−0.358475
$793$	−4.64118	−0.164813
$794$	17.0911	0.606540
$795$	3.77966	0.134051
$796$	−13.8409	−0.490576
$797$	35.5372	1.25879	0.629396	−	0.777084i	$-0.283302\pi$
$797$	35.5372	1.25879	0.629396	+	0.777084i	$0.283302\pi$
$798$	5.34309	0.189143
$799$	−40.3936	−1.42902
$800$	3.01565	0.106619
$801$	33.0291	1.16702
$802$	20.1721	0.712301
$803$	17.0422	0.601406
$804$	3.89244	0.137276
$805$	6.46877	0.227994
$806$	5.28958	0.186318
$807$	0.911518	0.0320870
$808$	−9.29483	−0.326991
$809$	15.9061	0.559227	0.279614	−	0.960113i	$-0.409794\pi$
$809$	15.9061	0.559227	0.279614	+	0.960113i	$0.409794\pi$
$810$	−5.19052	−0.182376
$811$	21.1041	0.741064	0.370532	−	0.928820i	$-0.379175\pi$
$811$	21.1041	0.741064	0.370532	+	0.928820i	$0.379175\pi$
$812$	6.21178	0.217991
$813$	21.1735	0.742587
$814$	23.1253	0.810541
$815$	10.7819	0.377675
$816$	2.89348	0.101292
$817$	−5.23430	−0.183125
$818$	−32.3193	−1.13002
$819$	1.88972	0.0660323
$820$	−6.36175	−0.222162
$821$	14.3095	0.499405	0.249702	−	0.968323i	$-0.419667\pi$
$821$	14.3095	0.499405	0.249702	+	0.968323i	$0.419667\pi$
$822$	5.74967	0.200543
$823$	−45.2039	−1.57571	−0.787854	−	0.615862i	$-0.788808\pi$
$823$	−45.2039	−1.57571	−0.787854	+	0.615862i	$0.788808\pi$
$824$	−8.45408	−0.294512
$825$	−10.2565	−0.357084
$826$	5.39532	0.187727
$827$	−1.63444	−0.0568352	−0.0284176	−	0.999596i	$-0.509047\pi$
$827$	−1.63444	−0.0568352	−0.0284176	+	0.999596i	$0.509047\pi$
$828$	10.8582	0.377350
$829$	−6.78874	−0.235783	−0.117891	−	0.993026i	$-0.537613\pi$
$829$	−6.78874	−0.235783	−0.117891	+	0.993026i	$0.537613\pi$
$830$	−19.8668	−0.689586
$831$	14.1426	0.490601
$832$	0.799192	0.0277070
$833$	−3.62976	−0.125764
$834$	−2.51407	−0.0870550
$835$	12.2675	0.424533
$836$	28.5972	0.989054
$837$	−28.3039	−0.978325
$838$	22.7045	0.784314
$839$	−13.8355	−0.477656	−0.238828	−	0.971062i	$-0.576763\pi$
$839$	−13.8355	−0.477656	−0.238828	+	0.971062i	$0.576763\pi$
$840$	−1.12293	−0.0387447
$841$	9.58617	0.330558
$842$	−16.2815	−0.561098
$843$	−2.61751	−0.0901518
$844$	22.7593	0.783407
$845$	−17.4130	−0.599025
$846$	26.3137	0.904685
$847$	−7.20319	−0.247505
$848$	−3.36589	−0.115585
$849$	−12.0626	−0.413988
$850$	−10.9461	−0.375447
$851$	−24.8901	−0.853221
$852$	−7.47251	−0.256004
$853$	−34.3220	−1.17516	−0.587582	−	0.809165i	$-0.699920\pi$
$853$	−34.3220	−1.17516	−0.587582	+	0.809165i	$0.699920\pi$
$854$	−5.80734	−0.198723
$855$	22.3257	0.763524
$856$	−12.0908	−0.413254
$857$	1.08984	0.0372282	0.0186141	−	0.999827i	$-0.494075\pi$
$857$	1.08984	0.0372282	0.0186141	+	0.999827i	$0.494075\pi$
$858$	−2.71811	−0.0927949
$859$	54.4606	1.85817	0.929086	−	0.369863i	$-0.120595\pi$
$859$	54.4606	1.85817	0.929086	+	0.369863i	$0.120595\pi$
$860$	1.10007	0.0375119
$861$	−3.60007	−0.122690
$862$	−1.00000	−0.0340601
$863$	1.23710	0.0421113	0.0210557	−	0.999778i	$-0.493297\pi$
$863$	1.23710	0.0421113	0.0210557	+	0.999778i	$0.493297\pi$
$864$	−4.27637	−0.145485
$865$	1.12620	0.0382921
$866$	−5.04478	−0.171429
$867$	3.04902	0.103550
$868$	6.61866	0.224652
$869$	−22.5691	−0.765603
$870$	−6.97538	−0.236488
$871$	−3.90239	−0.132227
$872$	5.51476	0.186753
$873$	8.39014	0.283963
$874$	−30.7795	−1.04113
$875$	11.2914	0.381719
$876$	3.18416	0.107583
$877$	−55.8532	−1.88603	−0.943014	−	0.332753i	$-0.892022\pi$
$877$	−55.8532	−1.88603	−0.943014	+	0.332753i	$0.892022\pi$
$878$	−12.8675	−0.434257
$879$	−2.46501	−0.0831428
$880$	−6.01012	−0.202601
$881$	3.74474	0.126164	0.0630818	−	0.998008i	$-0.479907\pi$
$881$	3.74474	0.126164	0.0630818	+	0.998008i	$0.479907\pi$
$882$	2.36454	0.0796183
$883$	31.3669	1.05558	0.527789	−	0.849375i	$-0.323021\pi$
$883$	31.3669	1.05558	0.527789	+	0.849375i	$0.323021\pi$
$884$	−2.90087	−0.0975669
$885$	−6.05856	−0.203656
$886$	−7.97797	−0.268025
$887$	−9.21818	−0.309516	−0.154758	−	0.987952i	$-0.549460\pi$
$887$	−9.21818	−0.309516	−0.154758	+	0.987952i	$0.549460\pi$
$888$	4.32072	0.144994
$889$	−13.0689	−0.438317
$890$	19.6770	0.659574
$891$	−15.7208	−0.526668
$892$	−8.70757	−0.291551
$893$	−74.5907	−2.49608
$894$	12.7611	0.426796
$895$	−10.4355	−0.348820
$896$	1.00000	0.0334077
$897$	2.92554	0.0976810
$898$	−33.4115	−1.11496
$899$	41.1137	1.37122
$900$	7.13063	0.237688
$901$	12.2174	0.407019
$902$	−19.2682	−0.641561
$903$	0.622518	0.0207161
$904$	−5.38250	−0.179019
$905$	−16.5283	−0.549419
$906$	7.67218	0.254891
$907$	−55.8219	−1.85353	−0.926767	−	0.375637i	$-0.877424\pi$
$907$	−55.8219	−1.85353	−0.926767	+	0.375637i	$0.877424\pi$
$908$	−16.8011	−0.557564
$909$	−21.9780	−0.728965
$910$	1.12580	0.0373198
$911$	−52.2580	−1.73139	−0.865693	−	0.500576i	$-0.833122\pi$
$911$	−52.2580	−1.73139	−0.865693	+	0.500576i	$0.833122\pi$
$912$	5.34309	0.176927
$913$	−60.1717	−1.99139
$914$	−14.1064	−0.466599
$915$	6.52123	0.215585
$916$	24.0920	0.796023
$917$	−5.75249	−0.189964
$918$	15.5222	0.512309
$919$	−26.2785	−0.866847	−0.433423	−	0.901190i	$-0.642694\pi$
$919$	−26.2785	−0.866847	−0.433423	+	0.901190i	$0.642694\pi$
$920$	6.46877	0.213269
$921$	−9.95524	−0.328036
$922$	−12.0170	−0.395759
$923$	7.49161	0.246589
$924$	−3.40108	−0.111887
$925$	−16.3454	−0.537432
$926$	11.9976	0.394265
$927$	−19.9900	−0.656559
$928$	6.21178	0.203912
$929$	59.5011	1.95217	0.976084	−	0.217396i	$-0.0697561\pi$
$929$	59.5011	1.95217	0.976084	+	0.217396i	$0.0697561\pi$
$930$	−7.43228	−0.243714
$931$	−6.70269	−0.219672
$932$	−12.7964	−0.419160
$933$	14.2161	0.465415
$934$	−11.6270	−0.380448
$935$	21.8153	0.713435
$936$	1.88972	0.0617676
$937$	28.4226	0.928527	0.464263	−	0.885697i	$-0.346319\pi$
$937$	28.4226	0.928527	0.464263	+	0.885697i	$0.346319\pi$
$938$	−4.88292	−0.159433
$939$	23.0485	0.752159
$940$	15.6763	0.511306
$941$	−5.91289	−0.192755	−0.0963773	−	0.995345i	$-0.530726\pi$
$941$	−5.91289	−0.192755	−0.0963773	+	0.995345i	$0.530726\pi$
$942$	−2.22030	−0.0723413
$943$	20.7386	0.675343
$944$	5.39532	0.175603
$945$	−6.02400	−0.195961
$946$	3.33183	0.108327
$947$	10.4490	0.339547	0.169774	−	0.985483i	$-0.445696\pi$
$947$	10.4490	0.339547	0.169774	+	0.985483i	$0.445696\pi$
$948$	−4.21680	−0.136955
$949$	−3.19229	−0.103626
$950$	−20.2130	−0.655795
$951$	5.86490	0.190182
$952$	−3.62976	−0.117641
$953$	22.5565	0.730677	0.365338	−	0.930875i	$-0.380953\pi$
$953$	22.5565	0.730677	0.365338	+	0.930875i	$0.380953\pi$
$954$	−7.95880	−0.257676
$955$	11.5896	0.375031
$956$	2.87318	0.0929253
$957$	−21.1267	−0.682931
$958$	−2.99665	−0.0968174
$959$	−7.21273	−0.232911
$960$	−1.12293	−0.0362424
$961$	12.8067	0.413119
$962$	−4.33176	−0.139662
$963$	−28.5892	−0.921274
$964$	−8.19163	−0.263835
$965$	−26.4241	−0.850620
$966$	3.66063	0.117779
$967$	−55.7314	−1.79220	−0.896101	−	0.443851i	$-0.853612\pi$
$967$	−55.7314	−1.79220	−0.896101	+	0.443851i	$0.853612\pi$
$968$	−7.20319	−0.231519
$969$	−19.3941	−0.623028
$970$	4.99840	0.160489
$971$	9.35061	0.300075	0.150038	−	0.988680i	$-0.452061\pi$
$971$	9.35061	0.300075	0.150038	+	0.988680i	$0.452061\pi$
$972$	−15.7664	−0.505707
$973$	3.15380	0.101106
$974$	18.3844	0.589076
$975$	1.92121	0.0615280
$976$	−5.80734	−0.185888
$977$	−59.4553	−1.90214	−0.951072	−	0.308969i	$-0.900016\pi$
$977$	−59.4553	−1.90214	−0.951072	+	0.308969i	$0.900016\pi$
$978$	6.10142	0.195102
$979$	59.5968	1.90472
$980$	1.40867	0.0449983
$981$	13.0399	0.416332
$982$	−21.2906	−0.679411
$983$	−4.33086	−0.138133	−0.0690665	−	0.997612i	$-0.522002\pi$
$983$	−4.33086	−0.138133	−0.0690665	+	0.997612i	$0.522002\pi$
$984$	−3.60007	−0.114766
$985$	−28.7702	−0.916694
$986$	−22.5472	−0.718050
$987$	8.87112	0.282371
$988$	−5.35674	−0.170420
$989$	−3.58609	−0.114031
$990$	−14.2112	−0.451661
$991$	−50.8695	−1.61592	−0.807961	−	0.589236i	$-0.799429\pi$
$991$	−50.8695	−1.61592	−0.807961	+	0.589236i	$0.799429\pi$
$992$	6.61866	0.210143
$993$	5.26814	0.167179
$994$	9.37398	0.297324
$995$	−19.4972	−0.618103
$996$	−11.2425	−0.356231
$997$	−34.9720	−1.10757	−0.553787	−	0.832658i	$-0.686818\pi$
$997$	−34.9720	−1.10757	−0.553787	+	0.832658i	$0.686818\pi$
$998$	−39.7003	−1.25669
$999$	23.1787	0.733342

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.9	✓	24	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.797155 q^{3} +1.00000 q^{4} +1.40867 q^{5} +0.797155 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.36454 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.797155 q^{3} +1.00000 q^{4} +1.40867 q^{5} +0.797155 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.36454 q^{9} -1.40867 q^{10} -4.26652 q^{11} -0.797155 q^{12} +0.799192 q^{13} +1.00000 q^{14} -1.12293 q^{15} +1.00000 q^{16} -3.62976 q^{17} +2.36454 q^{18} -6.70269 q^{19} +1.40867 q^{20} +0.797155 q^{21} +4.26652 q^{22} -4.59211 q^{23} +0.797155 q^{24} -3.01565 q^{25} -0.799192 q^{26} +4.27637 q^{27} -1.00000 q^{28} -6.21178 q^{29} +1.12293 q^{30} -6.61866 q^{31} -1.00000 q^{32} +3.40108 q^{33} +3.62976 q^{34} -1.40867 q^{35} -2.36454 q^{36} +5.42018 q^{37} +6.70269 q^{38} -0.637080 q^{39} -1.40867 q^{40} -4.51614 q^{41} -0.797155 q^{42} +0.780925 q^{43} -4.26652 q^{44} -3.33086 q^{45} +4.59211 q^{46} +11.1285 q^{47} -0.797155 q^{48} +1.00000 q^{49} +3.01565 q^{50} +2.89348 q^{51} +0.799192 q^{52} -3.36589 q^{53} -4.27637 q^{54} -6.01012 q^{55} +1.00000 q^{56} +5.34309 q^{57} +6.21178 q^{58} +5.39532 q^{59} -1.12293 q^{60} -5.80734 q^{61} +6.61866 q^{62} +2.36454 q^{63} +1.00000 q^{64} +1.12580 q^{65} -3.40108 q^{66} -4.88292 q^{67} -3.62976 q^{68} +3.66063 q^{69} +1.40867 q^{70} +9.37398 q^{71} +2.36454 q^{72} -3.99440 q^{73} -5.42018 q^{74} +2.40394 q^{75} -6.70269 q^{76} +4.26652 q^{77} +0.637080 q^{78} +5.28980 q^{79} +1.40867 q^{80} +3.68470 q^{81} +4.51614 q^{82} +14.1032 q^{83} +0.797155 q^{84} -5.11313 q^{85} -0.780925 q^{86} +4.95175 q^{87} +4.26652 q^{88} -13.9685 q^{89} +3.33086 q^{90} -0.799192 q^{91} -4.59211 q^{92} +5.27610 q^{93} -11.1285 q^{94} -9.44188 q^{95} +0.797155 q^{96} -3.54831 q^{97} -1.00000 q^{98} +10.0884 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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