LMFDB - Embedded newform 4015.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24746 q^{2} +1.22256 q^{3} +3.05108 q^{4} -1.00000 q^{5} -2.74765 q^{6} -0.859995 q^{7} -2.36225 q^{8} -1.50535 q^{9} +O(q^{10})$	\(q-2.24746 q^{2} +1.22256 q^{3} +3.05108 q^{4} -1.00000 q^{5} -2.74765 q^{6} -0.859995 q^{7} -2.36225 q^{8} -1.50535 q^{9} +2.24746 q^{10} +1.00000 q^{11} +3.73012 q^{12} +0.0713076 q^{13} +1.93280 q^{14} -1.22256 q^{15} -0.793082 q^{16} +0.642646 q^{17} +3.38322 q^{18} -0.461346 q^{19} -3.05108 q^{20} -1.05139 q^{21} -2.24746 q^{22} -0.536624 q^{23} -2.88799 q^{24} +1.00000 q^{25} -0.160261 q^{26} -5.50805 q^{27} -2.62391 q^{28} -0.279556 q^{29} +2.74765 q^{30} +7.74233 q^{31} +6.50693 q^{32} +1.22256 q^{33} -1.44432 q^{34} +0.859995 q^{35} -4.59294 q^{36} -7.64995 q^{37} +1.03686 q^{38} +0.0871777 q^{39} +2.36225 q^{40} -6.23400 q^{41} +2.36297 q^{42} +2.55121 q^{43} +3.05108 q^{44} +1.50535 q^{45} +1.20604 q^{46} +9.97981 q^{47} -0.969590 q^{48} -6.26041 q^{49} -2.24746 q^{50} +0.785672 q^{51} +0.217565 q^{52} +8.24852 q^{53} +12.3791 q^{54} -1.00000 q^{55} +2.03153 q^{56} -0.564023 q^{57} +0.628290 q^{58} -8.42064 q^{59} -3.73012 q^{60} +7.56098 q^{61} -17.4006 q^{62} +1.29459 q^{63} -13.0379 q^{64} -0.0713076 q^{65} -2.74765 q^{66} -6.86869 q^{67} +1.96076 q^{68} -0.656054 q^{69} -1.93280 q^{70} +8.05062 q^{71} +3.55602 q^{72} -1.00000 q^{73} +17.1930 q^{74} +1.22256 q^{75} -1.40760 q^{76} -0.859995 q^{77} -0.195928 q^{78} -7.75449 q^{79} +0.793082 q^{80} -2.21787 q^{81} +14.0107 q^{82} -6.01345 q^{83} -3.20789 q^{84} -0.642646 q^{85} -5.73375 q^{86} -0.341773 q^{87} -2.36225 q^{88} -3.80593 q^{89} -3.38322 q^{90} -0.0613242 q^{91} -1.63728 q^{92} +9.46545 q^{93} -22.4292 q^{94} +0.461346 q^{95} +7.95510 q^{96} +6.98693 q^{97} +14.0700 q^{98} -1.50535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 6 q^{2} + 5 q^{3} + 22 q^{4} - 27 q^{5} + 7 q^{6} + 10 q^{7} + 15 q^{8} + 24 q^{9}+O(q^{10}) $ 27 * q + 6 * q^2 + 5 * q^3 + 22 * q^4 - 27 * q^5 + 7 * q^6 + 10 * q^7 + 15 * q^8 + 24 * q^9	\( 27 q + 6 q^{2} + 5 q^{3} + 22 q^{4} - 27 q^{5} + 7 q^{6} + 10 q^{7} + 15 q^{8} + 24 q^{9} - 6 q^{10} + 27 q^{11} + 28 q^{12} + 21 q^{13} + 11 q^{14} - 5 q^{15} + 12 q^{16} + 30 q^{17} + 10 q^{18} + 20 q^{19} - 22 q^{20} - 14 q^{21} + 6 q^{22} + 16 q^{23} + 23 q^{24} + 27 q^{25} + 13 q^{26} + 17 q^{27} + 6 q^{28} - 2 q^{29} - 7 q^{30} - 6 q^{31} + 41 q^{32} + 5 q^{33} + 8 q^{34} - 10 q^{35} + 13 q^{36} + 20 q^{37} + 11 q^{38} - 10 q^{39} - 15 q^{40} + 38 q^{41} - 33 q^{42} + 29 q^{43} + 22 q^{44} - 24 q^{45} + 23 q^{46} + 17 q^{47} + 37 q^{48} + 21 q^{49} + 6 q^{50} + 13 q^{51} + 29 q^{52} + 4 q^{53} + q^{54} - 27 q^{55} + 28 q^{56} + 51 q^{57} - 6 q^{58} + 35 q^{59} - 28 q^{60} - 13 q^{61} + 28 q^{62} + 41 q^{63} - 5 q^{64} - 21 q^{65} + 7 q^{66} + 10 q^{67} + 65 q^{68} - 12 q^{69} - 11 q^{70} + 22 q^{71} - 12 q^{72} - 27 q^{73} - 5 q^{74} + 5 q^{75} + 13 q^{76} + 10 q^{77} - 9 q^{78} - 18 q^{79} - 12 q^{80} + 39 q^{81} + 20 q^{82} + 54 q^{83} - 50 q^{84} - 30 q^{85} + 3 q^{86} + 15 q^{87} + 15 q^{88} + 89 q^{89} - 10 q^{90} - 18 q^{91} + 57 q^{92} + 20 q^{93} - 29 q^{94} - 20 q^{95} + 105 q^{96} + 35 q^{97} + 10 q^{98} + 24 q^{99}+O(q^{100}) \) 27 * q + 6 * q^2 + 5 * q^3 + 22 * q^4 - 27 * q^5 + 7 * q^6 + 10 * q^7 + 15 * q^8 + 24 * q^9 - 6 * q^10 + 27 * q^11 + 28 * q^12 + 21 * q^13 + 11 * q^14 - 5 * q^15 + 12 * q^16 + 30 * q^17 + 10 * q^18 + 20 * q^19 - 22 * q^20 - 14 * q^21 + 6 * q^22 + 16 * q^23 + 23 * q^24 + 27 * q^25 + 13 * q^26 + 17 * q^27 + 6 * q^28 - 2 * q^29 - 7 * q^30 - 6 * q^31 + 41 * q^32 + 5 * q^33 + 8 * q^34 - 10 * q^35 + 13 * q^36 + 20 * q^37 + 11 * q^38 - 10 * q^39 - 15 * q^40 + 38 * q^41 - 33 * q^42 + 29 * q^43 + 22 * q^44 - 24 * q^45 + 23 * q^46 + 17 * q^47 + 37 * q^48 + 21 * q^49 + 6 * q^50 + 13 * q^51 + 29 * q^52 + 4 * q^53 + q^54 - 27 * q^55 + 28 * q^56 + 51 * q^57 - 6 * q^58 + 35 * q^59 - 28 * q^60 - 13 * q^61 + 28 * q^62 + 41 * q^63 - 5 * q^64 - 21 * q^65 + 7 * q^66 + 10 * q^67 + 65 * q^68 - 12 * q^69 - 11 * q^70 + 22 * q^71 - 12 * q^72 - 27 * q^73 - 5 * q^74 + 5 * q^75 + 13 * q^76 + 10 * q^77 - 9 * q^78 - 18 * q^79 - 12 * q^80 + 39 * q^81 + 20 * q^82 + 54 * q^83 - 50 * q^84 - 30 * q^85 + 3 * q^86 + 15 * q^87 + 15 * q^88 + 89 * q^89 - 10 * q^90 - 18 * q^91 + 57 * q^92 + 20 * q^93 - 29 * q^94 - 20 * q^95 + 105 * q^96 + 35 * q^97 + 10 * q^98 + 24 * 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 $

$2$	−2.24746	−1.58919	−0.794597	−	0.607137i	$-0.792318\pi$
$2$	−2.24746	−1.58919	−0.794597	+	0.607137i	$0.792318\pi$
$3$	1.22256	0.705844	0.352922	−	0.935653i	$-0.385188\pi$
$3$	1.22256	0.705844	0.352922	+	0.935653i	$0.385188\pi$
$4$	3.05108	1.52554
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.74765	−1.12172
$7$	−0.859995	−0.325048	−0.162524	−	0.986705i	$-0.551963\pi$
$7$	−0.859995	−0.325048	−0.162524	+	0.986705i	$0.551963\pi$
$8$	−2.36225	−0.835183
$9$	−1.50535	−0.501784
$10$	2.24746	0.710709
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.73012	1.07679
$13$	0.0713076	0.0197772	0.00988858	−	0.999951i	$-0.496852\pi$
$13$	0.0713076	0.0197772	0.00988858	+	0.999951i	$0.496852\pi$
$14$	1.93280	0.516564
$15$	−1.22256	−0.315663
$16$	−0.793082	−0.198271
$17$	0.642646	0.155864	0.0779322	−	0.996959i	$-0.475168\pi$
$17$	0.642646	0.155864	0.0779322	+	0.996959i	$0.475168\pi$
$18$	3.38322	0.797432
$19$	−0.461346	−0.105840	−0.0529200	−	0.998599i	$-0.516853\pi$
$19$	−0.461346	−0.105840	−0.0529200	+	0.998599i	$0.516853\pi$
$20$	−3.05108	−0.682242
$21$	−1.05139	−0.229433
$22$	−2.24746	−0.479160
$23$	−0.536624	−0.111894	−0.0559469	−	0.998434i	$-0.517818\pi$
$23$	−0.536624	−0.111894	−0.0559469	+	0.998434i	$0.517818\pi$
$24$	−2.88799	−0.589509
$25$	1.00000	0.200000
$26$	−0.160261	−0.0314298
$27$	−5.50805	−1.06003
$28$	−2.62391	−0.495873
$29$	−0.279556	−0.0519122	−0.0259561	−	0.999663i	$-0.508263\pi$
$29$	−0.279556	−0.0519122	−0.0259561	+	0.999663i	$0.508263\pi$
$30$	2.74765	0.501650
$31$	7.74233	1.39056	0.695282	−	0.718737i	$-0.255280\pi$
$31$	7.74233	1.39056	0.695282	+	0.718737i	$0.255280\pi$
$32$	6.50693	1.15027
$33$	1.22256	0.212820
$34$	−1.44432	−0.247699
$35$	0.859995	0.145366
$36$	−4.59294	−0.765490
$37$	−7.64995	−1.25764	−0.628822	−	0.777549i	$-0.716462\pi$
$37$	−7.64995	−1.25764	−0.628822	+	0.777549i	$0.716462\pi$
$38$	1.03686	0.168200
$39$	0.0871777	0.0139596
$40$	2.36225	0.373505
$41$	−6.23400	−0.973588	−0.486794	−	0.873517i	$-0.661834\pi$
$41$	−6.23400	−0.973588	−0.486794	+	0.873517i	$0.661834\pi$
$42$	2.36297	0.364614
$43$	2.55121	0.389057	0.194528	−	0.980897i	$-0.437682\pi$
$43$	2.55121	0.389057	0.194528	+	0.980897i	$0.437682\pi$
$44$	3.05108	0.459967
$45$	1.50535	0.224404
$46$	1.20604	0.177821
$47$	9.97981	1.45571	0.727853	−	0.685733i	$-0.240518\pi$
$47$	9.97981	1.45571	0.727853	+	0.685733i	$0.240518\pi$
$48$	−0.969590	−0.139948
$49$	−6.26041	−0.894344
$50$	−2.24746	−0.317839
$51$	0.785672	0.110016
$52$	0.217565	0.0301708
$53$	8.24852	1.13302	0.566511	−	0.824054i	$-0.308293\pi$
$53$	8.24852	1.13302	0.566511	+	0.824054i	$0.308293\pi$
$54$	12.3791	1.68459
$55$	−1.00000	−0.134840
$56$	2.03153	0.271474
$57$	−0.564023	−0.0747066
$58$	0.628290	0.0824985
$59$	−8.42064	−1.09627	−0.548137	−	0.836389i	$-0.684663\pi$
$59$	−8.42064	−1.09627	−0.548137	+	0.836389i	$0.684663\pi$
$60$	−3.73012	−0.481556
$61$	7.56098	0.968084	0.484042	−	0.875045i	$-0.339168\pi$
$61$	7.56098	0.968084	0.484042	+	0.875045i	$0.339168\pi$
$62$	−17.4006	−2.20988
$63$	1.29459	0.163104
$64$	−13.0379	−1.62974
$65$	−0.0713076	−0.00884462
$66$	−2.74765	−0.338213
$67$	−6.86869	−0.839144	−0.419572	−	0.907722i	$-0.637820\pi$
$67$	−6.86869	−0.839144	−0.419572	+	0.907722i	$0.637820\pi$
$68$	1.96076	0.237777
$69$	−0.656054	−0.0789797
$70$	−1.93280	−0.231014
$71$	8.05062	0.955433	0.477716	−	0.878514i	$-0.341465\pi$
$71$	8.05062	0.955433	0.477716	+	0.878514i	$0.341465\pi$
$72$	3.55602	0.419081
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	17.1930	1.99864
$75$	1.22256	0.141169
$76$	−1.40760	−0.161463
$77$	−0.859995	−0.0980055
$78$	−0.195928	−0.0221845
$79$	−7.75449	−0.872448	−0.436224	−	0.899838i	$-0.643685\pi$
$79$	−7.75449	−0.872448	−0.436224	+	0.899838i	$0.643685\pi$
$80$	0.793082	0.0886693
$81$	−2.21787	−0.246430
$82$	14.0107	1.54722
$83$	−6.01345	−0.660062	−0.330031	−	0.943970i	$-0.607059\pi$
$83$	−6.01345	−0.660062	−0.330031	+	0.943970i	$0.607059\pi$
$84$	−3.20789	−0.350009
$85$	−0.642646	−0.0697047
$86$	−5.73375	−0.618287
$87$	−0.341773	−0.0366419
$88$	−2.36225	−0.251817
$89$	−3.80593	−0.403428	−0.201714	−	0.979444i	$-0.564651\pi$
$89$	−3.80593	−0.403428	−0.201714	+	0.979444i	$0.564651\pi$
$90$	−3.38322	−0.356622
$91$	−0.0613242	−0.00642852
$92$	−1.63728	−0.170698
$93$	9.46545	0.981522
$94$	−22.4292	−2.31340
$95$	0.461346	0.0473331
$96$	7.95510	0.811914
$97$	6.98693	0.709415	0.354708	−	0.934977i	$-0.384580\pi$
$97$	6.98693	0.709415	0.354708	+	0.934977i	$0.384580\pi$
$98$	14.0700	1.42129
$99$	−1.50535	−0.151293
$100$	3.05108	0.305108
$101$	9.55698	0.950955	0.475477	−	0.879728i	$-0.342275\pi$
$101$	9.55698	0.950955	0.475477	+	0.879728i	$0.342275\pi$
$102$	−1.76577	−0.174837
$103$	11.6273	1.14567	0.572834	−	0.819671i	$-0.305844\pi$
$103$	11.6273	1.14567	0.572834	+	0.819671i	$0.305844\pi$
$104$	−0.168447	−0.0165175
$105$	1.05139	0.102606
$106$	−18.5382	−1.80059
$107$	15.4417	1.49281	0.746403	−	0.665494i	$-0.231779\pi$
$107$	15.4417	1.49281	0.746403	+	0.665494i	$0.231779\pi$
$108$	−16.8055	−1.61711
$109$	−4.72282	−0.452364	−0.226182	−	0.974085i	$-0.572624\pi$
$109$	−4.72282	−0.452364	−0.226182	+	0.974085i	$0.572624\pi$
$110$	2.24746	0.214287
$111$	−9.35251	−0.887701
$112$	0.682047	0.0644474
$113$	−11.2845	−1.06156	−0.530780	−	0.847510i	$-0.678101\pi$
$113$	−11.2845	−1.06156	−0.530780	+	0.847510i	$0.678101\pi$
$114$	1.26762	0.118723
$115$	0.536624	0.0500405
$116$	−0.852946	−0.0791940
$117$	−0.107343	−0.00992386
$118$	18.9251	1.74219
$119$	−0.552672	−0.0506634
$120$	2.88799	0.263637
$121$	1.00000	0.0909091
$122$	−16.9930	−1.53847
$123$	−7.62143	−0.687201
$124$	23.6224	2.12136
$125$	−1.00000	−0.0894427
$126$	−2.90955	−0.259203
$127$	7.39180	0.655916	0.327958	−	0.944692i	$-0.393640\pi$
$127$	7.39180	0.655916	0.327958	+	0.944692i	$0.393640\pi$
$128$	16.2883	1.43970
$129$	3.11901	0.274613
$130$	0.160261	0.0140558
$131$	17.0155	1.48665	0.743323	−	0.668932i	$-0.233248\pi$
$131$	17.0155	1.48665	0.743323	+	0.668932i	$0.233248\pi$
$132$	3.73012	0.324665
$133$	0.396756	0.0344031
$134$	15.4371	1.33356
$135$	5.50805	0.474058
$136$	−1.51809	−0.130175
$137$	5.88319	0.502635	0.251317	−	0.967905i	$-0.419136\pi$
$137$	5.88319	0.502635	0.251317	+	0.967905i	$0.419136\pi$
$138$	1.47446	0.125514
$139$	0.661608	0.0561168	0.0280584	−	0.999606i	$-0.491068\pi$
$139$	0.661608	0.0561168	0.0280584	+	0.999606i	$0.491068\pi$
$140$	2.62391	0.221761
$141$	12.2009	1.02750
$142$	−18.0934	−1.51837
$143$	0.0713076	0.00596304
$144$	1.19387	0.0994889
$145$	0.279556	0.0232158
$146$	2.24746	0.186001
$147$	−7.65372	−0.631268
$148$	−23.3406	−1.91858
$149$	5.54630	0.454371	0.227185	−	0.973852i	$-0.427048\pi$
$149$	5.54630	0.454371	0.227185	+	0.973852i	$0.427048\pi$
$150$	−2.74765	−0.224345
$151$	14.3971	1.17162	0.585811	−	0.810448i	$-0.300776\pi$
$151$	14.3971	1.17162	0.585811	+	0.810448i	$0.300776\pi$
$152$	1.08982	0.0883958
$153$	−0.967407	−0.0782102
$154$	1.93280	0.155750
$155$	−7.74233	−0.621879
$156$	0.265986	0.0212959
$157$	−14.2112	−1.13418	−0.567088	−	0.823657i	$-0.691930\pi$
$157$	−14.2112	−1.13418	−0.567088	+	0.823657i	$0.691930\pi$
$158$	17.4279	1.38649
$159$	10.0843	0.799737
$160$	−6.50693	−0.514418
$161$	0.461494	0.0363708
$162$	4.98457	0.391625
$163$	8.54217	0.669075	0.334537	−	0.942383i	$-0.391420\pi$
$163$	8.54217	0.669075	0.334537	+	0.942383i	$0.391420\pi$
$164$	−19.0204	−1.48525
$165$	−1.22256	−0.0951760
$166$	13.5150	1.04897
$167$	18.2241	1.41022	0.705110	−	0.709098i	$-0.250898\pi$
$167$	18.2241	1.41022	0.705110	+	0.709098i	$0.250898\pi$
$168$	2.48366	0.191619
$169$	−12.9949	−0.999609
$170$	1.44432	0.110774
$171$	0.694488	0.0531088
$172$	7.78395	0.593521
$173$	10.0370	0.763099	0.381549	−	0.924348i	$-0.375391\pi$
$173$	10.0370	0.763099	0.381549	+	0.924348i	$0.375391\pi$
$174$	0.768121	0.0582311
$175$	−0.859995	−0.0650095
$176$	−0.793082	−0.0597808
$177$	−10.2947	−0.773799
$178$	8.55369	0.641126
$179$	11.6309	0.869337	0.434669	−	0.900591i	$-0.356866\pi$
$179$	11.6309	0.869337	0.434669	+	0.900591i	$0.356866\pi$
$180$	4.59294	0.342338
$181$	−9.14151	−0.679483	−0.339742	−	0.940519i	$-0.610340\pi$
$181$	−9.14151	−0.679483	−0.339742	+	0.940519i	$0.610340\pi$
$182$	0.137824	0.0102162
$183$	9.24374	0.683317
$184$	1.26764	0.0934518
$185$	7.64995	0.562435
$186$	−21.2732	−1.55983
$187$	0.642646	0.0469949
$188$	30.4492	2.22073
$189$	4.73690	0.344559
$190$	−1.03686	−0.0752215
$191$	−8.38524	−0.606734	−0.303367	−	0.952874i	$-0.598111\pi$
$191$	−8.38524	−0.606734	−0.303367	+	0.952874i	$0.598111\pi$
$192$	−15.9396	−1.15034
$193$	4.01383	0.288922	0.144461	−	0.989511i	$-0.453855\pi$
$193$	4.01383	0.288922	0.144461	+	0.989511i	$0.453855\pi$
$194$	−15.7029	−1.12740
$195$	−0.0871777	−0.00624292
$196$	−19.1010	−1.36436
$197$	19.2667	1.37270	0.686349	−	0.727272i	$-0.259212\pi$
$197$	19.2667	1.37270	0.686349	+	0.727272i	$0.259212\pi$
$198$	3.38322	0.240435
$199$	−21.3749	−1.51523	−0.757613	−	0.652704i	$-0.773634\pi$
$199$	−21.3749	−1.51523	−0.757613	+	0.652704i	$0.773634\pi$
$200$	−2.36225	−0.167037
$201$	−8.39737	−0.592305
$202$	−21.4789	−1.51125
$203$	0.240416	0.0168739
$204$	2.39715	0.167834
$205$	6.23400	0.435402
$206$	−26.1318	−1.82069
$207$	0.807807	0.0561465
$208$	−0.0565528	−0.00392123
$209$	−0.461346	−0.0319120
$210$	−2.36297	−0.163060
$211$	−13.1046	−0.902155	−0.451078	−	0.892485i	$-0.648960\pi$
$211$	−13.1046	−0.902155	−0.451078	+	0.892485i	$0.648960\pi$
$212$	25.1669	1.72847
$213$	9.84235	0.674387
$214$	−34.7046	−2.37236
$215$	−2.55121	−0.173991
$216$	13.0114	0.885315
$217$	−6.65837	−0.451999
$218$	10.6143	0.718894
$219$	−1.22256	−0.0826128
$220$	−3.05108	−0.205704
$221$	0.0458255	0.00308256
$222$	21.0194	1.41073
$223$	6.58249	0.440796	0.220398	−	0.975410i	$-0.429264\pi$
$223$	6.58249	0.440796	0.220398	+	0.975410i	$0.429264\pi$
$224$	−5.59593	−0.373894
$225$	−1.50535	−0.100357
$226$	25.3615	1.68702
$227$	5.05363	0.335421	0.167711	−	0.985836i	$-0.446363\pi$
$227$	5.05363	0.335421	0.167711	+	0.985836i	$0.446363\pi$
$228$	−1.72088	−0.113968
$229$	4.12911	0.272859	0.136430	−	0.990650i	$-0.456437\pi$
$229$	4.12911	0.272859	0.136430	+	0.990650i	$0.456437\pi$
$230$	−1.20604	−0.0795240
$231$	−1.05139	−0.0691767
$232$	0.660381	0.0433562
$233$	26.0036	1.70355	0.851776	−	0.523906i	$-0.175526\pi$
$233$	26.0036	1.70355	0.851776	+	0.523906i	$0.175526\pi$
$234$	0.241249	0.0157709
$235$	−9.97981	−0.651011
$236$	−25.6920	−1.67241
$237$	−9.48032	−0.615813
$238$	1.24211	0.0805139
$239$	11.0079	0.712039	0.356020	−	0.934478i	$-0.384134\pi$
$239$	11.0079	0.712039	0.356020	+	0.934478i	$0.384134\pi$
$240$	0.969590	0.0625867
$241$	18.3788	1.18388	0.591941	−	0.805981i	$-0.298362\pi$
$241$	18.3788	1.18388	0.591941	+	0.805981i	$0.298362\pi$
$242$	−2.24746	−0.144472
$243$	13.8127	0.886085
$244$	23.0691	1.47685
$245$	6.26041	0.399963
$246$	17.1289	1.09210
$247$	−0.0328975	−0.00209322
$248$	−18.2894	−1.16138
$249$	−7.35180	−0.465901
$250$	2.24746	0.142142
$251$	−1.73523	−0.109527	−0.0547634	−	0.998499i	$-0.517440\pi$
$251$	−1.73523	−0.109527	−0.0547634	+	0.998499i	$0.517440\pi$
$252$	3.94991	0.248821
$253$	−0.536624	−0.0337373
$254$	−16.6128	−1.04238
$255$	−0.785672	−0.0492007
$256$	−10.5315	−0.658219
$257$	7.32613	0.456992	0.228496	−	0.973545i	$-0.426619\pi$
$257$	7.32613	0.456992	0.228496	+	0.973545i	$0.426619\pi$
$258$	−7.00985	−0.436414
$259$	6.57892	0.408794
$260$	−0.217565	−0.0134928
$261$	0.420829	0.0260487
$262$	−38.2415	−2.36257
$263$	−0.831217	−0.0512550	−0.0256275	−	0.999672i	$-0.508158\pi$
$263$	−0.831217	−0.0512550	−0.0256275	+	0.999672i	$0.508158\pi$
$264$	−2.88799	−0.177744
$265$	−8.24852	−0.506703
$266$	−0.891692	−0.0546732
$267$	−4.65298	−0.284758
$268$	−20.9569	−1.28015
$269$	−28.1890	−1.71871	−0.859356	−	0.511378i	$-0.829135\pi$
$269$	−28.1890	−1.71871	−0.859356	+	0.511378i	$0.829135\pi$
$270$	−12.3791	−0.753370
$271$	−17.6444	−1.07182	−0.535910	−	0.844275i	$-0.680031\pi$
$271$	−17.6444	−1.07182	−0.535910	+	0.844275i	$0.680031\pi$
$272$	−0.509671	−0.0309033
$273$	−0.0749724	−0.00453753
$274$	−13.2222	−0.798785
$275$	1.00000	0.0603023
$276$	−2.00167	−0.120487
$277$	−3.78003	−0.227120	−0.113560	−	0.993531i	$-0.536225\pi$
$277$	−3.78003	−0.227120	−0.113560	+	0.993531i	$0.536225\pi$
$278$	−1.48694	−0.0891805
$279$	−11.6549	−0.697762
$280$	−2.03153	−0.121407
$281$	5.16747	0.308265	0.154133	−	0.988050i	$-0.450742\pi$
$281$	5.16747	0.308265	0.154133	+	0.988050i	$0.450742\pi$
$282$	−27.4210	−1.63290
$283$	13.2369	0.786855	0.393427	−	0.919356i	$-0.371289\pi$
$283$	13.2369	0.786855	0.393427	+	0.919356i	$0.371289\pi$
$284$	24.5631	1.45755
$285$	0.564023	0.0334098
$286$	−0.160261	−0.00947643
$287$	5.36121	0.316462
$288$	−9.79521	−0.577188
$289$	−16.5870	−0.975706
$290$	−0.628290	−0.0368945
$291$	8.54193	0.500737
$292$	−3.05108	−0.178551
$293$	−15.8083	−0.923529	−0.461764	−	0.887003i	$-0.652783\pi$
$293$	−15.8083	−0.923529	−0.461764	+	0.887003i	$0.652783\pi$
$294$	17.2014	1.00321
$295$	8.42064	0.490269
$296$	18.0711	1.05036
$297$	−5.50805	−0.319610
$298$	−12.4651	−0.722083
$299$	−0.0382654	−0.00221294
$300$	3.73012	0.215359
$301$	−2.19403	−0.126462
$302$	−32.3570	−1.86193
$303$	11.6840	0.671226
$304$	0.365886	0.0209850
$305$	−7.56098	−0.432940
$306$	2.17421	0.124291
$307$	10.0326	0.572590	0.286295	−	0.958142i	$-0.407576\pi$
$307$	10.0326	0.572590	0.286295	+	0.958142i	$0.407576\pi$
$308$	−2.62391	−0.149511
$309$	14.2150	0.808664
$310$	17.4006	0.988287
$311$	4.25696	0.241390	0.120695	−	0.992690i	$-0.461488\pi$
$311$	4.25696	0.241390	0.120695	+	0.992690i	$0.461488\pi$
$312$	−0.205936	−0.0116588
$313$	10.1207	0.572056	0.286028	−	0.958221i	$-0.407665\pi$
$313$	10.1207	0.572056	0.286028	+	0.958221i	$0.407665\pi$
$314$	31.9391	1.80243
$315$	−1.29459	−0.0729421
$316$	−23.6595	−1.33095
$317$	−20.8471	−1.17089	−0.585444	−	0.810713i	$-0.699080\pi$
$317$	−20.8471	−1.17089	−0.585444	+	0.810713i	$0.699080\pi$
$318$	−22.6641	−1.27094
$319$	−0.279556	−0.0156521
$320$	13.0379	0.728841
$321$	18.8784	1.05369
$322$	−1.03719	−0.0578003
$323$	−0.296482	−0.0164967
$324$	−6.76688	−0.375938
$325$	0.0713076	0.00395543
$326$	−19.1982	−1.06329
$327$	−5.77392	−0.319299
$328$	14.7263	0.813124
$329$	−8.58259	−0.473174
$330$	2.74765	0.151253
$331$	−27.5444	−1.51397	−0.756987	−	0.653430i	$-0.773330\pi$
$331$	−27.5444	−1.51397	−0.756987	+	0.653430i	$0.773330\pi$
$332$	−18.3475	−1.00695
$333$	11.5159	0.631065
$334$	−40.9579	−2.24111
$335$	6.86869	0.375277
$336$	0.833842	0.0454898
$337$	18.1958	0.991190	0.495595	−	0.868554i	$-0.334950\pi$
$337$	18.1958	0.991190	0.495595	+	0.868554i	$0.334950\pi$
$338$	29.2056	1.58857
$339$	−13.7960	−0.749296
$340$	−1.96076	−0.106337
$341$	7.74233	0.419271
$342$	−1.56083	−0.0844002
$343$	11.4039	0.615752
$344$	−6.02662	−0.324933
$345$	0.656054	0.0353208
$346$	−22.5578	−1.21271
$347$	−18.4659	−0.991304	−0.495652	−	0.868521i	$-0.665071\pi$
$347$	−18.4659	−0.991304	−0.495652	+	0.868521i	$0.665071\pi$
$348$	−1.04278	−0.0558987
$349$	5.31882	0.284710	0.142355	−	0.989816i	$-0.454533\pi$
$349$	5.31882	0.284710	0.142355	+	0.989816i	$0.454533\pi$
$350$	1.93280	0.103313
$351$	−0.392766	−0.0209643
$352$	6.50693	0.346820
$353$	−0.136018	−0.00723953	−0.00361977	−	0.999993i	$-0.501152\pi$
$353$	−0.136018	−0.00723953	−0.00361977	+	0.999993i	$0.501152\pi$
$354$	23.1370	1.22972
$355$	−8.05062	−0.427282
$356$	−11.6122	−0.615445
$357$	−0.675674	−0.0357605
$358$	−26.1401	−1.38155
$359$	36.7409	1.93911	0.969556	−	0.244868i	$-0.0787446\pi$
$359$	36.7409	1.93911	0.969556	+	0.244868i	$0.0787446\pi$
$360$	−3.55602	−0.187419
$361$	−18.7872	−0.988798
$362$	20.5452	1.07983
$363$	1.22256	0.0641677
$364$	−0.187105	−0.00980695
$365$	1.00000	0.0523424
$366$	−20.7749	−1.08592
$367$	22.6994	1.18490	0.592451	−	0.805607i	$-0.298160\pi$
$367$	22.6994	1.18490	0.592451	+	0.805607i	$0.298160\pi$
$368$	0.425587	0.0221853
$369$	9.38436	0.488530
$370$	−17.1930	−0.893819
$371$	−7.09369	−0.368286
$372$	28.8798	1.49735
$373$	25.7216	1.33182	0.665908	−	0.746034i	$-0.268044\pi$
$373$	25.7216	1.33182	0.665908	+	0.746034i	$0.268044\pi$
$374$	−1.44432	−0.0746840
$375$	−1.22256	−0.0631326
$376$	−23.5749	−1.21578
$377$	−0.0199344	−0.00102668
$378$	−10.6460	−0.547571
$379$	5.38522	0.276620	0.138310	−	0.990389i	$-0.455833\pi$
$379$	5.38522	0.276620	0.138310	+	0.990389i	$0.455833\pi$
$380$	1.40760	0.0722085
$381$	9.03691	0.462975
$382$	18.8455	0.964219
$383$	14.7662	0.754516	0.377258	−	0.926108i	$-0.376867\pi$
$383$	14.7662	0.754516	0.377258	+	0.926108i	$0.376867\pi$
$384$	19.9134	1.01620
$385$	0.859995	0.0438294
$386$	−9.02093	−0.459153
$387$	−3.84047	−0.195222
$388$	21.3177	1.08224
$389$	13.9474	0.707161	0.353581	−	0.935404i	$-0.384964\pi$
$389$	13.9474	0.707161	0.353581	+	0.935404i	$0.384964\pi$
$390$	0.195928	0.00992122
$391$	−0.344859	−0.0174403
$392$	14.7887	0.746941
$393$	20.8024	1.04934
$394$	−43.3012	−2.18148
$395$	7.75449	0.390171
$396$	−4.59294	−0.230804
$397$	1.16856	0.0586485	0.0293242	−	0.999570i	$-0.490664\pi$
$397$	1.16856	0.0586485	0.0293242	+	0.999570i	$0.490664\pi$
$398$	48.0392	2.40799
$399$	0.485057	0.0242832
$400$	−0.793082	−0.0396541
$401$	34.0927	1.70251	0.851255	−	0.524752i	$-0.175842\pi$
$401$	34.0927	1.70251	0.851255	+	0.524752i	$0.175842\pi$
$402$	18.8728	0.941288
$403$	0.552087	0.0275014
$404$	29.1591	1.45072
$405$	2.21787	0.110207
$406$	−0.540326	−0.0268159
$407$	−7.64995	−0.379194
$408$	−1.85596	−0.0918835
$409$	22.7630	1.12556	0.562779	−	0.826608i	$-0.309732\pi$
$409$	22.7630	1.12556	0.562779	+	0.826608i	$0.309732\pi$
$410$	−14.0107	−0.691938
$411$	7.19254	0.354782
$412$	35.4757	1.74776
$413$	7.24171	0.356341
$414$	−1.81552	−0.0892277
$415$	6.01345	0.295189
$416$	0.463993	0.0227491
$417$	0.808854	0.0396097
$418$	1.03686	0.0507144
$419$	0.465011	0.0227173	0.0113586	−	0.999935i	$-0.496384\pi$
$419$	0.465011	0.0227173	0.0113586	+	0.999935i	$0.496384\pi$
$420$	3.20789	0.156529
$421$	−7.23446	−0.352586	−0.176293	−	0.984338i	$-0.556411\pi$
$421$	−7.23446	−0.352586	−0.176293	+	0.984338i	$0.556411\pi$
$422$	29.4520	1.43370
$423$	−15.0231	−0.730449
$424$	−19.4851	−0.946280
$425$	0.642646	0.0311729
$426$	−22.1203	−1.07173
$427$	−6.50240	−0.314673
$428$	47.1139	2.27733
$429$	0.0871777	0.00420898
$430$	5.73375	0.276506
$431$	5.86889	0.282695	0.141347	−	0.989960i	$-0.454857\pi$
$431$	5.86889	0.282695	0.141347	+	0.989960i	$0.454857\pi$
$432$	4.36834	0.210172
$433$	39.5826	1.90222	0.951110	−	0.308852i	$-0.0999449\pi$
$433$	39.5826	1.90222	0.951110	+	0.308852i	$0.0999449\pi$
$434$	14.9644	0.718315
$435$	0.341773	0.0163868
$436$	−14.4097	−0.690099
$437$	0.247570	0.0118429
$438$	2.74765	0.131288
$439$	−21.1476	−1.00932	−0.504659	−	0.863319i	$-0.668382\pi$
$439$	−21.1476	−1.00932	−0.504659	+	0.863319i	$0.668382\pi$
$440$	2.36225	0.112616
$441$	9.42411	0.448767
$442$	−0.102991	−0.00489878
$443$	39.7047	1.88643	0.943214	−	0.332186i	$-0.107786\pi$
$443$	39.7047	1.88643	0.943214	+	0.332186i	$0.107786\pi$
$444$	−28.5352	−1.35422
$445$	3.80593	0.180419
$446$	−14.7939	−0.700511
$447$	6.78068	0.320715
$448$	11.2125	0.529742
$449$	24.2271	1.14335	0.571673	−	0.820482i	$-0.306295\pi$
$449$	24.2271	1.14335	0.571673	+	0.820482i	$0.306295\pi$
$450$	3.38322	0.159486
$451$	−6.23400	−0.293548
$452$	−34.4300	−1.61945
$453$	17.6013	0.826982
$454$	−11.3578	−0.533049
$455$	0.0613242	0.00287492
$456$	1.33237	0.0623937
$457$	10.1588	0.475209	0.237604	−	0.971362i	$-0.423638\pi$
$457$	10.1588	0.475209	0.237604	+	0.971362i	$0.423638\pi$
$458$	−9.28000	−0.433626
$459$	−3.53973	−0.165220
$460$	1.63728	0.0763386
$461$	−6.32705	−0.294680	−0.147340	−	0.989086i	$-0.547071\pi$
$461$	−6.32705	−0.294680	−0.147340	+	0.989086i	$0.547071\pi$
$462$	2.36297	0.109935
$463$	25.5143	1.18575	0.592876	−	0.805294i	$-0.297993\pi$
$463$	25.5143	1.18575	0.592876	+	0.805294i	$0.297993\pi$
$464$	0.221711	0.0102927
$465$	−9.46545	−0.438950
$466$	−58.4421	−2.70728
$467$	−4.98064	−0.230476	−0.115238	−	0.993338i	$-0.536763\pi$
$467$	−4.98064	−0.230476	−0.115238	+	0.993338i	$0.536763\pi$
$468$	−0.327511	−0.0151392
$469$	5.90704	0.272762
$470$	22.4292	1.03458
$471$	−17.3740	−0.800551
$472$	19.8917	0.915589
$473$	2.55121	0.117305
$474$	21.3066	0.978646
$475$	−0.461346	−0.0211680
$476$	−1.68625	−0.0772889
$477$	−12.4169	−0.568532
$478$	−24.7397	−1.13157
$479$	−10.6244	−0.485443	−0.242722	−	0.970096i	$-0.578040\pi$
$479$	−10.6244	−0.485443	−0.242722	+	0.970096i	$0.578040\pi$
$480$	−7.95510	−0.363099
$481$	−0.545499	−0.0248726
$482$	−41.3056	−1.88142
$483$	0.564204	0.0256721
$484$	3.05108	0.138685
$485$	−6.98693	−0.317260
$486$	−31.0435	−1.40816
$487$	−8.01662	−0.363268	−0.181634	−	0.983366i	$-0.558139\pi$
$487$	−8.01662	−0.363268	−0.181634	+	0.983366i	$0.558139\pi$
$488$	−17.8609	−0.808527
$489$	10.4433	0.472263
$490$	−14.0700	−0.635619
$491$	16.4600	0.742829	0.371415	−	0.928467i	$-0.378873\pi$
$491$	16.4600	0.742829	0.371415	+	0.928467i	$0.378873\pi$
$492$	−23.2536	−1.04835
$493$	−0.179655	−0.00809126
$494$	0.0739358	0.00332653
$495$	1.50535	0.0676605
$496$	−6.14031	−0.275708
$497$	−6.92349	−0.310561
$498$	16.5229	0.740408
$499$	12.9890	0.581468	0.290734	−	0.956804i	$-0.406100\pi$
$499$	12.9890	0.581468	0.290734	+	0.956804i	$0.406100\pi$
$500$	−3.05108	−0.136448
$501$	22.2800	0.995396
$502$	3.89986	0.174059
$503$	−0.348556	−0.0155413	−0.00777066	−	0.999970i	$-0.502474\pi$
$503$	−0.348556	−0.0155413	−0.00777066	+	0.999970i	$0.502474\pi$
$504$	−3.05816	−0.136221
$505$	−9.55698	−0.425280
$506$	1.20604	0.0536151
$507$	−15.8870	−0.705568
$508$	22.5530	1.00063
$509$	31.8493	1.41170	0.705848	−	0.708363i	$-0.250566\pi$
$509$	31.8493	1.41170	0.705848	+	0.708363i	$0.250566\pi$
$510$	1.76577	0.0781894
$511$	0.859995	0.0380439
$512$	−8.90745	−0.393658
$513$	2.54112	0.112193
$514$	−16.4652	−0.726249
$515$	−11.6273	−0.512358
$516$	9.51634	0.418933
$517$	9.97981	0.438912
$518$	−14.7859	−0.649653
$519$	12.2708	0.538629
$520$	0.168447	0.00738687
$521$	16.7944	0.735774	0.367887	−	0.929870i	$-0.380081\pi$
$521$	16.7944	0.735774	0.367887	+	0.929870i	$0.380081\pi$
$522$	−0.945797	−0.0413964
$523$	−10.4212	−0.455689	−0.227844	−	0.973698i	$-0.573168\pi$
$523$	−10.4212	−0.455689	−0.227844	+	0.973698i	$0.573168\pi$
$524$	51.9155	2.26794
$525$	−1.05139	−0.0458866
$526$	1.86813	0.0814542
$527$	4.97557	0.216739
$528$	−0.969590	−0.0421960
$529$	−22.7120	−0.987480
$530$	18.5382	0.805249
$531$	12.6760	0.550092
$532$	1.21053	0.0524832
$533$	−0.444532	−0.0192548
$534$	10.4574	0.452535
$535$	−15.4417	−0.667604
$536$	16.2256	0.700839
$537$	14.2195	0.613617
$538$	63.3536	2.73137
$539$	−6.26041	−0.269655
$540$	16.8055	0.723194
$541$	−32.6950	−1.40567	−0.702833	−	0.711355i	$-0.748082\pi$
$541$	−32.6950	−1.40567	−0.702833	+	0.711355i	$0.748082\pi$
$542$	39.6551	1.70333
$543$	−11.1760	−0.479609
$544$	4.18165	0.179287
$545$	4.72282	0.202303
$546$	0.168497	0.00721102
$547$	10.5831	0.452502	0.226251	−	0.974069i	$-0.427353\pi$
$547$	10.5831	0.452502	0.226251	+	0.974069i	$0.427353\pi$
$548$	17.9501	0.766789
$549$	−11.3819	−0.485769
$550$	−2.24746	−0.0958320
$551$	0.128972	0.00549439
$552$	1.54977	0.0659625
$553$	6.66882	0.283587
$554$	8.49546	0.360937
$555$	9.35251	0.396992
$556$	2.01862	0.0856084
$557$	5.40645	0.229078	0.114539	−	0.993419i	$-0.463461\pi$
$557$	5.40645	0.229078	0.114539	+	0.993419i	$0.463461\pi$
$558$	26.1940	1.10888
$559$	0.181921	0.00769444
$560$	−0.682047	−0.0288217
$561$	0.785672	0.0331711
$562$	−11.6137	−0.489893
$563$	38.2607	1.61250	0.806248	−	0.591577i	$-0.201495\pi$
$563$	38.2607	1.61250	0.806248	+	0.591577i	$0.201495\pi$
$564$	37.2259	1.56749
$565$	11.2845	0.474744
$566$	−29.7495	−1.25046
$567$	1.90735	0.0801014
$568$	−19.0176	−0.797961
$569$	11.5660	0.484870	0.242435	−	0.970168i	$-0.422054\pi$
$569$	11.5660	0.484870	0.242435	+	0.970168i	$0.422054\pi$
$570$	−1.26762	−0.0530947
$571$	27.2883	1.14198	0.570990	−	0.820957i	$-0.306559\pi$
$571$	27.2883	1.14198	0.570990	+	0.820957i	$0.306559\pi$
$572$	0.217565	0.00909685
$573$	−10.2514	−0.428260
$574$	−12.0491	−0.502920
$575$	−0.536624	−0.0223788
$576$	19.6266	0.817776
$577$	−7.03095	−0.292702	−0.146351	−	0.989233i	$-0.546753\pi$
$577$	−7.03095	−0.292702	−0.146351	+	0.989233i	$0.546753\pi$
$578$	37.2786	1.55059
$579$	4.90714	0.203934
$580$	0.852946	0.0354166
$581$	5.17154	0.214552
$582$	−19.1977	−0.795768
$583$	8.24852	0.341619
$584$	2.36225	0.0977508
$585$	0.107343	0.00443808
$586$	35.5284	1.46767
$587$	22.4414	0.926255	0.463128	−	0.886292i	$-0.346727\pi$
$587$	22.4414	0.926255	0.463128	+	0.886292i	$0.346727\pi$
$588$	−23.3521	−0.963023
$589$	−3.57190	−0.147177
$590$	−18.9251	−0.779132
$591$	23.5547	0.968912
$592$	6.06704	0.249354
$593$	−21.8690	−0.898051	−0.449025	−	0.893519i	$-0.648229\pi$
$593$	−21.8690	−0.898051	−0.449025	+	0.893519i	$0.648229\pi$
$594$	12.3791	0.507922
$595$	0.552672	0.0226573
$596$	16.9222	0.693160
$597$	−26.1320	−1.06951
$598$	0.0859999	0.00351680
$599$	32.8233	1.34112	0.670562	−	0.741854i	$-0.266053\pi$
$599$	32.8233	1.34112	0.670562	+	0.741854i	$0.266053\pi$
$600$	−2.88799	−0.117902
$601$	−21.6870	−0.884632	−0.442316	−	0.896859i	$-0.645843\pi$
$601$	−21.6870	−0.884632	−0.442316	+	0.896859i	$0.645843\pi$
$602$	4.93100	0.200973
$603$	10.3398	0.421069
$604$	43.9267	1.78735
$605$	−1.00000	−0.0406558
$606$	−26.2592	−1.06671
$607$	15.8862	0.644801	0.322400	−	0.946603i	$-0.395510\pi$
$607$	15.8862	0.644801	0.322400	+	0.946603i	$0.395510\pi$
$608$	−3.00195	−0.121745
$609$	0.293923	0.0119104
$610$	16.9930	0.688026
$611$	0.711636	0.0287897
$612$	−2.95163	−0.119313
$613$	−5.92468	−0.239295	−0.119648	−	0.992816i	$-0.538177\pi$
$613$	−5.92468	−0.239295	−0.119648	+	0.992816i	$0.538177\pi$
$614$	−22.5478	−0.909956
$615$	7.62143	0.307326
$616$	2.03153	0.0818526
$617$	32.2369	1.29781	0.648904	−	0.760870i	$-0.275228\pi$
$617$	32.2369	1.29781	0.648904	+	0.760870i	$0.275228\pi$
$618$	−31.9477	−1.28512
$619$	39.4372	1.58511	0.792557	−	0.609797i	$-0.208749\pi$
$619$	39.4372	1.58511	0.792557	+	0.609797i	$0.208749\pi$
$620$	−23.6224	−0.948700
$621$	2.95575	0.118610
$622$	−9.56736	−0.383616
$623$	3.27308	0.131133
$624$	−0.0691391	−0.00276778
$625$	1.00000	0.0400000
$626$	−22.7459	−0.909109
$627$	−0.564023	−0.0225249
$628$	−43.3594	−1.73023
$629$	−4.91620	−0.196022
$630$	2.90955	0.115919
$631$	−35.2379	−1.40280	−0.701399	−	0.712769i	$-0.747441\pi$
$631$	−35.2379	−1.40280	−0.701399	+	0.712769i	$0.747441\pi$
$632$	18.3181	0.728654
$633$	−16.0211	−0.636781
$634$	46.8529	1.86077
$635$	−7.39180	−0.293335
$636$	30.7680	1.22003
$637$	−0.446414	−0.0176876
$638$	0.628290	0.0248742
$639$	−12.1190	−0.479420
$640$	−16.2883	−0.643852
$641$	−0.328509	−0.0129753	−0.00648766	−	0.999979i	$-0.502065\pi$
$641$	−0.328509	−0.0129753	−0.00648766	+	0.999979i	$0.502065\pi$
$642$	−42.4285	−1.67452
$643$	−22.6038	−0.891407	−0.445704	−	0.895181i	$-0.647046\pi$
$643$	−22.6038	−0.891407	−0.445704	+	0.895181i	$0.647046\pi$
$644$	1.40805	0.0554851
$645$	−3.11901	−0.122811
$646$	0.666332	0.0262165
$647$	−30.0140	−1.17997	−0.589985	−	0.807414i	$-0.700866\pi$
$647$	−30.0140	−1.17997	−0.589985	+	0.807414i	$0.700866\pi$
$648$	5.23916	0.205814
$649$	−8.42064	−0.330539
$650$	−0.160261	−0.00628595
$651$	−8.14024	−0.319041
$652$	26.0628	1.02070
$653$	−16.7095	−0.653895	−0.326948	−	0.945042i	$-0.606020\pi$
$653$	−16.7095	−0.653895	−0.326948	+	0.945042i	$0.606020\pi$
$654$	12.9767	0.507427
$655$	−17.0155	−0.664849
$656$	4.94408	0.193034
$657$	1.50535	0.0587293
$658$	19.2890	0.751965
$659$	−13.7725	−0.536500	−0.268250	−	0.963349i	$-0.586445\pi$
$659$	−13.7725	−0.536500	−0.268250	+	0.963349i	$0.586445\pi$
$660$	−3.73012	−0.145195
$661$	−24.7066	−0.960976	−0.480488	−	0.877001i	$-0.659541\pi$
$661$	−24.7066	−0.960976	−0.480488	+	0.877001i	$0.659541\pi$
$662$	61.9048	2.40600
$663$	0.0560243	0.00217581
$664$	14.2053	0.551273
$665$	−0.396756	−0.0153855
$666$	−25.8814	−1.00288
$667$	0.150016	0.00580865
$668$	55.6030	2.15135
$669$	8.04748	0.311134
$670$	−15.4371	−0.596387
$671$	7.56098	0.291888
$672$	−6.84135	−0.263911
$673$	−21.7108	−0.836889	−0.418445	−	0.908242i	$-0.637425\pi$
$673$	−21.7108	−0.836889	−0.418445	+	0.908242i	$0.637425\pi$
$674$	−40.8944	−1.57519
$675$	−5.50805	−0.212005
$676$	−39.6485	−1.52494
$677$	−22.5239	−0.865663	−0.432831	−	0.901475i	$-0.642485\pi$
$677$	−22.5239	−0.865663	−0.432831	+	0.901475i	$0.642485\pi$
$678$	31.0060	1.19078
$679$	−6.00873	−0.230594
$680$	1.51809	0.0582162
$681$	6.17835	0.236755
$682$	−17.4006	−0.666303
$683$	7.59318	0.290545	0.145272	−	0.989392i	$-0.453594\pi$
$683$	7.59318	0.290545	0.145272	+	0.989392i	$0.453594\pi$
$684$	2.11894	0.0810196
$685$	−5.88319	−0.224785
$686$	−25.6298	−0.978550
$687$	5.04807	0.192596
$688$	−2.02332	−0.0771385
$689$	0.588182	0.0224080
$690$	−1.47446	−0.0561316
$691$	30.0421	1.14286	0.571428	−	0.820652i	$-0.306390\pi$
$691$	30.0421	1.14286	0.571428	+	0.820652i	$0.306390\pi$
$692$	30.6237	1.16414
$693$	1.29459	0.0491776
$694$	41.5015	1.57537
$695$	−0.661608	−0.0250962
$696$	0.807355	0.0306027
$697$	−4.00625	−0.151748
$698$	−11.9538	−0.452460
$699$	31.7909	1.20244
$700$	−2.62391	−0.0991745
$701$	3.36090	0.126939	0.0634696	−	0.997984i	$-0.479783\pi$
$701$	3.36090	0.126939	0.0634696	+	0.997984i	$0.479783\pi$
$702$	0.882726	0.0333163
$703$	3.52927	0.133109
$704$	−13.0379	−0.491384
$705$	−12.2009	−0.459513
$706$	0.305696	0.0115050
$707$	−8.21895	−0.309106
$708$	−31.4100	−1.18046
$709$	5.74636	0.215809	0.107904	−	0.994161i	$-0.465586\pi$
$709$	5.74636	0.215809	0.107904	+	0.994161i	$0.465586\pi$
$710$	18.0934	0.679035
$711$	11.6732	0.437780
$712$	8.99058	0.336936
$713$	−4.15472	−0.155596
$714$	1.51855	0.0568303
$715$	−0.0713076	−0.00266675
$716$	35.4869	1.32621
$717$	13.4578	0.502589
$718$	−82.5738	−3.08163
$719$	−30.7718	−1.14760	−0.573798	−	0.818997i	$-0.694530\pi$
$719$	−30.7718	−1.14760	−0.573798	+	0.818997i	$0.694530\pi$
$720$	−1.19387	−0.0444928
$721$	−9.99939	−0.372397
$722$	42.2234	1.57139
$723$	22.4692	0.835637
$724$	−27.8914	−1.03658
$725$	−0.279556	−0.0103824
$726$	−2.74765	−0.101975
$727$	4.60124	0.170650	0.0853252	−	0.996353i	$-0.472807\pi$
$727$	4.60124	0.170650	0.0853252	+	0.996353i	$0.472807\pi$
$728$	0.144863	0.00536899
$729$	23.5404	0.871868
$730$	−2.24746	−0.0831822
$731$	1.63953	0.0606401
$732$	28.2033	1.04243
$733$	32.0888	1.18523	0.592613	−	0.805487i	$-0.298096\pi$
$733$	32.0888	1.18523	0.592613	+	0.805487i	$0.298096\pi$
$734$	−51.0161	−1.88304
$735$	7.65372	0.282312
$736$	−3.49177	−0.128709
$737$	−6.86869	−0.253011
$738$	−21.0910	−0.776370
$739$	−16.2257	−0.596872	−0.298436	−	0.954430i	$-0.596465\pi$
$739$	−16.2257	−0.596872	−0.298436	+	0.954430i	$0.596465\pi$
$740$	23.3406	0.858017
$741$	−0.0402191	−0.00147749
$742$	15.9428	0.585278
$743$	14.2724	0.523602	0.261801	−	0.965122i	$-0.415684\pi$
$743$	14.2724	0.523602	0.261801	+	0.965122i	$0.415684\pi$
$744$	−22.3598	−0.819750
$745$	−5.54630	−0.203201
$746$	−57.8084	−2.11651
$747$	9.05236	0.331208
$748$	1.96076	0.0716925
$749$	−13.2798	−0.485233
$750$	2.74765	0.100330
$751$	17.8087	0.649847	0.324924	−	0.945740i	$-0.394661\pi$
$751$	17.8087	0.649847	0.324924	+	0.945740i	$0.394661\pi$
$752$	−7.91481	−0.288624
$753$	−2.12142	−0.0773088
$754$	0.0448018	0.00163159
$755$	−14.3971	−0.523965
$756$	14.4526	0.525638
$757$	−41.4802	−1.50762	−0.753812	−	0.657091i	$-0.771787\pi$
$757$	−41.4802	−1.50762	−0.753812	+	0.657091i	$0.771787\pi$
$758$	−12.1031	−0.439603
$759$	−0.656054	−0.0238133
$760$	−1.08982	−0.0395318
$761$	50.8275	1.84250	0.921248	−	0.388976i	$-0.127171\pi$
$761$	50.8275	1.84250	0.921248	+	0.388976i	$0.127171\pi$
$762$	−20.3101	−0.735757
$763$	4.06160	0.147040
$764$	−25.5840	−0.925597
$765$	0.967407	0.0349767
$766$	−33.1864	−1.19907
$767$	−0.600455	−0.0216812
$768$	−12.8754	−0.464600
$769$	−46.1316	−1.66355	−0.831775	−	0.555113i	$-0.812675\pi$
$769$	−46.1316	−1.66355	−0.831775	+	0.555113i	$0.812675\pi$
$770$	−1.93280	−0.0696535
$771$	8.95663	0.322565
$772$	12.2465	0.440761
$773$	−23.6584	−0.850934	−0.425467	−	0.904974i	$-0.639890\pi$
$773$	−23.6584	−0.850934	−0.425467	+	0.904974i	$0.639890\pi$
$774$	8.63131	0.310246
$775$	7.74233	0.278113
$776$	−16.5049	−0.592492
$777$	8.04311	0.288545
$778$	−31.3462	−1.12382
$779$	2.87603	0.103045
$780$	−0.265986	−0.00952382
$781$	8.05062	0.288074
$782$	0.775057	0.0277160
$783$	1.53981	0.0550282
$784$	4.96502	0.177322
$785$	14.2112	0.507219
$786$	−46.7525	−1.66761
$787$	−38.2443	−1.36326	−0.681632	−	0.731695i	$-0.738729\pi$
$787$	−38.2443	−1.36326	−0.681632	+	0.731695i	$0.738729\pi$
$788$	58.7843	2.09410
$789$	−1.01621	−0.0361781
$790$	−17.4279	−0.620057
$791$	9.70464	0.345057
$792$	3.55602	0.126358
$793$	0.539155	0.0191459
$794$	−2.62630	−0.0932038
$795$	−10.0843	−0.357653
$796$	−65.2164	−2.31153
$797$	−39.4195	−1.39631	−0.698155	−	0.715947i	$-0.745995\pi$
$797$	−39.4195	−1.39631	−0.698155	+	0.715947i	$0.745995\pi$
$798$	−1.09015	−0.0385908
$799$	6.41348	0.226893
$800$	6.50693	0.230055
$801$	5.72927	0.202434
$802$	−76.6221	−2.70562
$803$	−1.00000	−0.0352892
$804$	−25.6210	−0.903584
$805$	−0.461494	−0.0162655
$806$	−1.24079	−0.0437051
$807$	−34.4627	−1.21314
$808$	−22.5760	−0.794221
$809$	−13.9827	−0.491605	−0.245803	−	0.969320i	$-0.579052\pi$
$809$	−13.9827	−0.491605	−0.245803	+	0.969320i	$0.579052\pi$
$810$	−4.98457	−0.175140
$811$	−6.38765	−0.224301	−0.112150	−	0.993691i	$-0.535774\pi$
$811$	−6.38765	−0.224301	−0.112150	+	0.993691i	$0.535774\pi$
$812$	0.733529	0.0257418
$813$	−21.5713	−0.756538
$814$	17.1930	0.602613
$815$	−8.54217	−0.299219
$816$	−0.623102	−0.0218129
$817$	−1.17699	−0.0411778
$818$	−51.1589	−1.78873
$819$	0.0923144	0.00322573
$820$	19.0204	0.664222
$821$	35.7166	1.24652	0.623260	−	0.782015i	$-0.285808\pi$
$821$	35.7166	1.24652	0.623260	+	0.782015i	$0.285808\pi$
$822$	−16.1650	−0.563818
$823$	15.5084	0.540590	0.270295	−	0.962778i	$-0.412879\pi$
$823$	15.5084	0.540590	0.270295	+	0.962778i	$0.412879\pi$
$824$	−27.4665	−0.956843
$825$	1.22256	0.0425640
$826$	−16.2755	−0.566295
$827$	56.0305	1.94837	0.974186	−	0.225746i	$-0.0724821\pi$
$827$	56.0305	1.94837	0.974186	+	0.225746i	$0.0724821\pi$
$828$	2.46468	0.0856537
$829$	29.2489	1.01586	0.507928	−	0.861399i	$-0.330411\pi$
$829$	29.2489	1.01586	0.507928	+	0.861399i	$0.330411\pi$
$830$	−13.5150	−0.469112
$831$	−4.62130	−0.160311
$832$	−0.929701	−0.0322316
$833$	−4.02322	−0.139396
$834$	−1.81787	−0.0629476
$835$	−18.2241	−0.630670
$836$	−1.40760	−0.0486830
$837$	−42.6452	−1.47403
$838$	−1.04509	−0.0361022
$839$	1.51935	0.0524536	0.0262268	−	0.999656i	$-0.491651\pi$
$839$	1.51935	0.0524536	0.0262268	+	0.999656i	$0.491651\pi$
$840$	−2.48366	−0.0856944
$841$	−28.9218	−0.997305
$842$	16.2592	0.560328
$843$	6.31753	0.217587
$844$	−39.9830	−1.37627
$845$	12.9949	0.447039
$846$	33.7639	1.16083
$847$	−0.859995	−0.0295498
$848$	−6.54176	−0.224645
$849$	16.1829	0.555397
$850$	−1.44432	−0.0495398
$851$	4.10515	0.140723
$852$	30.0298	1.02880
$853$	−21.1396	−0.723806	−0.361903	−	0.932216i	$-0.617873\pi$
$853$	−21.1396	−0.723806	−0.361903	+	0.932216i	$0.617873\pi$
$854$	14.6139	0.500077
$855$	−0.694488	−0.0237510
$856$	−36.4773	−1.24677
$857$	−7.70313	−0.263134	−0.131567	−	0.991307i	$-0.542001\pi$
$857$	−7.70313	−0.263134	−0.131567	+	0.991307i	$0.542001\pi$
$858$	−0.195928	−0.00668888
$859$	48.3463	1.64955	0.824777	−	0.565458i	$-0.191301\pi$
$859$	48.3463	1.64955	0.824777	+	0.565458i	$0.191301\pi$
$860$	−7.78395	−0.265431
$861$	6.55440	0.223373
$862$	−13.1901	−0.449257
$863$	−40.4780	−1.37789	−0.688944	−	0.724815i	$-0.741925\pi$
$863$	−40.4780	−1.37789	−0.688944	+	0.724815i	$0.741925\pi$
$864$	−35.8405	−1.21932
$865$	−10.0370	−0.341268
$866$	−88.9604	−3.02300
$867$	−20.2786	−0.688697
$868$	−20.3152	−0.689543
$869$	−7.75449	−0.263053
$870$	−0.768121	−0.0260417
$871$	−0.489789	−0.0165959
$872$	11.1565	0.377807
$873$	−10.5178	−0.355973
$874$	−0.556403	−0.0188206
$875$	0.859995	0.0290731
$876$	−3.73012	−0.126029
$877$	36.5169	1.23309	0.616545	−	0.787320i	$-0.288532\pi$
$877$	36.5169	1.23309	0.616545	+	0.787320i	$0.288532\pi$
$878$	47.5283	1.60400
$879$	−19.3265	−0.651868
$880$	0.793082	0.0267348
$881$	2.26731	0.0763878	0.0381939	−	0.999270i	$-0.487840\pi$
$881$	2.26731	0.0763878	0.0381939	+	0.999270i	$0.487840\pi$
$882$	−21.1803	−0.713178
$883$	−12.6029	−0.424121	−0.212060	−	0.977257i	$-0.568017\pi$
$883$	−12.6029	−0.424121	−0.212060	+	0.977257i	$0.568017\pi$
$884$	0.139817	0.00470256
$885$	10.2947	0.346053
$886$	−89.2348	−2.99790
$887$	−1.70436	−0.0572267	−0.0286133	−	0.999591i	$-0.509109\pi$
$887$	−1.70436	−0.0572267	−0.0286133	+	0.999591i	$0.509109\pi$
$888$	22.0930	0.741392
$889$	−6.35691	−0.213204
$890$	−8.55369	−0.286720
$891$	−2.21787	−0.0743013
$892$	20.0837	0.672452
$893$	−4.60415	−0.154072
$894$	−15.2393	−0.509679
$895$	−11.6309	−0.388779
$896$	−14.0079	−0.467970
$897$	−0.0467816	−0.00156199
$898$	−54.4493	−1.81700
$899$	−2.16441	−0.0721872
$900$	−4.59294	−0.153098
$901$	5.30088	0.176598
$902$	14.0107	0.466504
$903$	−2.68233	−0.0892625
$904$	26.6569	0.886596
$905$	9.14151	0.303874
$906$	−39.5583	−1.31424
$907$	55.8348	1.85397	0.926983	−	0.375104i	$-0.122393\pi$
$907$	55.8348	1.85397	0.926983	+	0.375104i	$0.122393\pi$
$908$	15.4190	0.511698
$909$	−14.3866	−0.477173
$910$	−0.137824	−0.00456881
$911$	−21.4578	−0.710927	−0.355464	−	0.934690i	$-0.615677\pi$
$911$	−21.4578	−0.710927	−0.355464	+	0.934690i	$0.615677\pi$
$912$	0.447317	0.0148121
$913$	−6.01345	−0.199016
$914$	−22.8315	−0.755199
$915$	−9.24374	−0.305588
$916$	12.5982	0.416257
$917$	−14.6332	−0.483231
$918$	7.95539	0.262567
$919$	−30.3109	−0.999866	−0.499933	−	0.866064i	$-0.666642\pi$
$919$	−30.3109	−0.999866	−0.499933	+	0.866064i	$0.666642\pi$
$920$	−1.26764	−0.0417929
$921$	12.2654	0.404159
$922$	14.2198	0.468304
$923$	0.574070	0.0188957
$924$	−3.20789	−0.105532
$925$	−7.64995	−0.251529
$926$	−57.3424	−1.88439
$927$	−17.5031	−0.574878
$928$	−1.81905	−0.0597132
$929$	14.2844	0.468655	0.234327	−	0.972158i	$-0.424711\pi$
$929$	14.2844	0.468655	0.234327	+	0.972158i	$0.424711\pi$
$930$	21.2732	0.697577
$931$	2.88822	0.0946575
$932$	79.3390	2.59883
$933$	5.20439	0.170384
$934$	11.1938	0.366272
$935$	−0.642646	−0.0210168
$936$	0.253571	0.00828823
$937$	8.64737	0.282497	0.141249	−	0.989974i	$-0.454888\pi$
$937$	8.64737	0.282497	0.141249	+	0.989974i	$0.454888\pi$
$938$	−13.2758	−0.433471
$939$	12.3732	0.403783
$940$	−30.4492	−0.993143
$941$	−58.8146	−1.91730	−0.958651	−	0.284583i	$-0.908145\pi$
$941$	−58.8146	−1.91730	−0.958651	+	0.284583i	$0.908145\pi$
$942$	39.0474	1.27223
$943$	3.34532	0.108938
$944$	6.67826	0.217359
$945$	−4.73690	−0.154091
$946$	−5.73375	−0.186420
$947$	−45.7365	−1.48624	−0.743119	−	0.669159i	$-0.766654\pi$
$947$	−45.7365	−1.48624	−0.743119	+	0.669159i	$0.766654\pi$
$948$	−28.9252	−0.939446
$949$	−0.0713076	−0.00231474
$950$	1.03686	0.0336401
$951$	−25.4867	−0.826464
$952$	1.30555	0.0423132
$953$	9.27383	0.300409	0.150204	−	0.988655i	$-0.452007\pi$
$953$	9.27383	0.300409	0.150204	+	0.988655i	$0.452007\pi$
$954$	27.9065	0.903507
$955$	8.38524	0.271340
$956$	33.5858	1.08624
$957$	−0.341773	−0.0110480
$958$	23.8780	0.771464
$959$	−5.05952	−0.163380
$960$	15.9396	0.514448
$961$	28.9437	0.933667
$962$	1.22599	0.0395274
$963$	−23.2452	−0.749066
$964$	56.0751	1.80606
$965$	−4.01383	−0.129210
$966$	−1.26802	−0.0407980
$967$	−5.96818	−0.191924	−0.0959619	−	0.995385i	$-0.530593\pi$
$967$	−5.96818	−0.191924	−0.0959619	+	0.995385i	$0.530593\pi$
$968$	−2.36225	−0.0759257
$969$	−0.362467	−0.0116441
$970$	15.7029	0.504188
$971$	−25.6950	−0.824591	−0.412296	−	0.911050i	$-0.635273\pi$
$971$	−25.6950	−0.824591	−0.412296	+	0.911050i	$0.635273\pi$
$972$	42.1436	1.35176
$973$	−0.568979	−0.0182406
$974$	18.0170	0.577303
$975$	0.0871777	0.00279192
$976$	−5.99648	−0.191943
$977$	38.4673	1.23068	0.615339	−	0.788263i	$-0.289019\pi$
$977$	38.4673	1.23068	0.615339	+	0.788263i	$0.289019\pi$
$978$	−23.4709	−0.750517
$979$	−3.80593	−0.121638
$980$	19.1010	0.610159
$981$	7.10950	0.226989
$982$	−36.9932	−1.18050
$983$	30.9164	0.986080	0.493040	−	0.870007i	$-0.335886\pi$
$983$	30.9164	0.986080	0.493040	+	0.870007i	$0.335886\pi$
$984$	18.0038	0.573939
$985$	−19.2667	−0.613889
$986$	0.403768	0.0128586
$987$	−10.4927	−0.333987
$988$	−0.100373	−0.00319328
$989$	−1.36904	−0.0435330
$990$	−3.38322	−0.107526
$991$	−31.7310	−1.00797	−0.503984	−	0.863713i	$-0.668133\pi$
$991$	−31.7310	−1.00797	−0.503984	+	0.863713i	$0.668133\pi$
$992$	50.3788	1.59953
$993$	−33.6746	−1.06863
$994$	15.5603	0.493542
$995$	21.3749	0.677629
$996$	−22.4309	−0.710751
$997$	−31.5413	−0.998924	−0.499462	−	0.866336i	$-0.666469\pi$
$997$	−31.5413	−0.998924	−0.499462	+	0.866336i	$0.666469\pi$
$998$	−29.1923	−0.924066
$999$	42.1363	1.33313

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.e.1.3	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.e.1.3	✓	27	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.24746 q^{2} +1.22256 q^{3} +3.05108 q^{4} -1.00000 q^{5} -2.74765 q^{6} -0.859995 q^{7} -2.36225 q^{8} -1.50535 q^{9} +O(q^{10})\)	\(q-2.24746 q^{2} +1.22256 q^{3} +3.05108 q^{4} -1.00000 q^{5} -2.74765 q^{6} -0.859995 q^{7} -2.36225 q^{8} -1.50535 q^{9} +2.24746 q^{10} +1.00000 q^{11} +3.73012 q^{12} +0.0713076 q^{13} +1.93280 q^{14} -1.22256 q^{15} -0.793082 q^{16} +0.642646 q^{17} +3.38322 q^{18} -0.461346 q^{19} -3.05108 q^{20} -1.05139 q^{21} -2.24746 q^{22} -0.536624 q^{23} -2.88799 q^{24} +1.00000 q^{25} -0.160261 q^{26} -5.50805 q^{27} -2.62391 q^{28} -0.279556 q^{29} +2.74765 q^{30} +7.74233 q^{31} +6.50693 q^{32} +1.22256 q^{33} -1.44432 q^{34} +0.859995 q^{35} -4.59294 q^{36} -7.64995 q^{37} +1.03686 q^{38} +0.0871777 q^{39} +2.36225 q^{40} -6.23400 q^{41} +2.36297 q^{42} +2.55121 q^{43} +3.05108 q^{44} +1.50535 q^{45} +1.20604 q^{46} +9.97981 q^{47} -0.969590 q^{48} -6.26041 q^{49} -2.24746 q^{50} +0.785672 q^{51} +0.217565 q^{52} +8.24852 q^{53} +12.3791 q^{54} -1.00000 q^{55} +2.03153 q^{56} -0.564023 q^{57} +0.628290 q^{58} -8.42064 q^{59} -3.73012 q^{60} +7.56098 q^{61} -17.4006 q^{62} +1.29459 q^{63} -13.0379 q^{64} -0.0713076 q^{65} -2.74765 q^{66} -6.86869 q^{67} +1.96076 q^{68} -0.656054 q^{69} -1.93280 q^{70} +8.05062 q^{71} +3.55602 q^{72} -1.00000 q^{73} +17.1930 q^{74} +1.22256 q^{75} -1.40760 q^{76} -0.859995 q^{77} -0.195928 q^{78} -7.75449 q^{79} +0.793082 q^{80} -2.21787 q^{81} +14.0107 q^{82} -6.01345 q^{83} -3.20789 q^{84} -0.642646 q^{85} -5.73375 q^{86} -0.341773 q^{87} -2.36225 q^{88} -3.80593 q^{89} -3.38322 q^{90} -0.0613242 q^{91} -1.63728 q^{92} +9.46545 q^{93} -22.4292 q^{94} +0.461346 q^{95} +7.95510 q^{96} +6.98693 q^{97} +14.0700 q^{98} -1.50535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 6 q^{2} + 5 q^{3} + 22 q^{4} - 27 q^{5} + 7 q^{6} + 10 q^{7} + 15 q^{8} + 24 q^{9}+O(q^{10}) \) 27 * q + 6 * q^2 + 5 * q^3 + 22 * q^4 - 27 * q^5 + 7 * q^6 + 10 * q^7 + 15 * q^8 + 24 * q^9	\( 27 q + 6 q^{2} + 5 q^{3} + 22 q^{4} - 27 q^{5} + 7 q^{6} + 10 q^{7} + 15 q^{8} + 24 q^{9} - 6 q^{10} + 27 q^{11} + 28 q^{12} + 21 q^{13} + 11 q^{14} - 5 q^{15} + 12 q^{16} + 30 q^{17} + 10 q^{18} + 20 q^{19} - 22 q^{20} - 14 q^{21} + 6 q^{22} + 16 q^{23} + 23 q^{24} + 27 q^{25} + 13 q^{26} + 17 q^{27} + 6 q^{28} - 2 q^{29} - 7 q^{30} - 6 q^{31} + 41 q^{32} + 5 q^{33} + 8 q^{34} - 10 q^{35} + 13 q^{36} + 20 q^{37} + 11 q^{38} - 10 q^{39} - 15 q^{40} + 38 q^{41} - 33 q^{42} + 29 q^{43} + 22 q^{44} - 24 q^{45} + 23 q^{46} + 17 q^{47} + 37 q^{48} + 21 q^{49} + 6 q^{50} + 13 q^{51} + 29 q^{52} + 4 q^{53} + q^{54} - 27 q^{55} + 28 q^{56} + 51 q^{57} - 6 q^{58} + 35 q^{59} - 28 q^{60} - 13 q^{61} + 28 q^{62} + 41 q^{63} - 5 q^{64} - 21 q^{65} + 7 q^{66} + 10 q^{67} + 65 q^{68} - 12 q^{69} - 11 q^{70} + 22 q^{71} - 12 q^{72} - 27 q^{73} - 5 q^{74} + 5 q^{75} + 13 q^{76} + 10 q^{77} - 9 q^{78} - 18 q^{79} - 12 q^{80} + 39 q^{81} + 20 q^{82} + 54 q^{83} - 50 q^{84} - 30 q^{85} + 3 q^{86} + 15 q^{87} + 15 q^{88} + 89 q^{89} - 10 q^{90} - 18 q^{91} + 57 q^{92} + 20 q^{93} - 29 q^{94} - 20 q^{95} + 105 q^{96} + 35 q^{97} + 10 q^{98} + 24 q^{99}+O(q^{100}) \) 27 * q + 6 * q^2 + 5 * q^3 + 22 * q^4 - 27 * q^5 + 7 * q^6 + 10 * q^7 + 15 * q^8 + 24 * q^9 - 6 * q^10 + 27 * q^11 + 28 * q^12 + 21 * q^13 + 11 * q^14 - 5 * q^15 + 12 * q^16 + 30 * q^17 + 10 * q^18 + 20 * q^19 - 22 * q^20 - 14 * q^21 + 6 * q^22 + 16 * q^23 + 23 * q^24 + 27 * q^25 + 13 * q^26 + 17 * q^27 + 6 * q^28 - 2 * q^29 - 7 * q^30 - 6 * q^31 + 41 * q^32 + 5 * q^33 + 8 * q^34 - 10 * q^35 + 13 * q^36 + 20 * q^37 + 11 * q^38 - 10 * q^39 - 15 * q^40 + 38 * q^41 - 33 * q^42 + 29 * q^43 + 22 * q^44 - 24 * q^45 + 23 * q^46 + 17 * q^47 + 37 * q^48 + 21 * q^49 + 6 * q^50 + 13 * q^51 + 29 * q^52 + 4 * q^53 + q^54 - 27 * q^55 + 28 * q^56 + 51 * q^57 - 6 * q^58 + 35 * q^59 - 28 * q^60 - 13 * q^61 + 28 * q^62 + 41 * q^63 - 5 * q^64 - 21 * q^65 + 7 * q^66 + 10 * q^67 + 65 * q^68 - 12 * q^69 - 11 * q^70 + 22 * q^71 - 12 * q^72 - 27 * q^73 - 5 * q^74 + 5 * q^75 + 13 * q^76 + 10 * q^77 - 9 * q^78 - 18 * q^79 - 12 * q^80 + 39 * q^81 + 20 * q^82 + 54 * q^83 - 50 * q^84 - 30 * q^85 + 3 * q^86 + 15 * q^87 + 15 * q^88 + 89 * q^89 - 10 * q^90 - 18 * q^91 + 57 * q^92 + 20 * q^93 - 29 * q^94 - 20 * q^95 + 105 * q^96 + 35 * q^97 + 10 * q^98 + 24 * q^99

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