LMFDB - Embedded newform 4011.2.a.k.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.25182 q^{2} +1.00000 q^{3} -0.432954 q^{4} +2.68317 q^{5} +1.25182 q^{6} +1.00000 q^{7} -3.04561 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.25182 q^{2} +1.00000 q^{3} -0.432954 q^{4} +2.68317 q^{5} +1.25182 q^{6} +1.00000 q^{7} -3.04561 q^{8} +1.00000 q^{9} +3.35884 q^{10} +3.43086 q^{11} -0.432954 q^{12} -2.76346 q^{13} +1.25182 q^{14} +2.68317 q^{15} -2.94664 q^{16} -3.33728 q^{17} +1.25182 q^{18} +6.17079 q^{19} -1.16169 q^{20} +1.00000 q^{21} +4.29481 q^{22} -4.18264 q^{23} -3.04561 q^{24} +2.19939 q^{25} -3.45934 q^{26} +1.00000 q^{27} -0.432954 q^{28} +9.73183 q^{29} +3.35884 q^{30} +4.17101 q^{31} +2.40257 q^{32} +3.43086 q^{33} -4.17767 q^{34} +2.68317 q^{35} -0.432954 q^{36} +1.48739 q^{37} +7.72470 q^{38} -2.76346 q^{39} -8.17189 q^{40} +5.50976 q^{41} +1.25182 q^{42} -1.92592 q^{43} -1.48541 q^{44} +2.68317 q^{45} -5.23590 q^{46} +9.79720 q^{47} -2.94664 q^{48} +1.00000 q^{49} +2.75324 q^{50} -3.33728 q^{51} +1.19645 q^{52} -4.17682 q^{53} +1.25182 q^{54} +9.20559 q^{55} -3.04561 q^{56} +6.17079 q^{57} +12.1825 q^{58} +1.49735 q^{59} -1.16169 q^{60} -0.995213 q^{61} +5.22134 q^{62} +1.00000 q^{63} +8.90086 q^{64} -7.41482 q^{65} +4.29481 q^{66} +13.2456 q^{67} +1.44489 q^{68} -4.18264 q^{69} +3.35884 q^{70} +2.66851 q^{71} -3.04561 q^{72} -13.2238 q^{73} +1.86195 q^{74} +2.19939 q^{75} -2.67167 q^{76} +3.43086 q^{77} -3.45934 q^{78} -5.49190 q^{79} -7.90634 q^{80} +1.00000 q^{81} +6.89721 q^{82} -10.8504 q^{83} -0.432954 q^{84} -8.95449 q^{85} -2.41090 q^{86} +9.73183 q^{87} -10.4491 q^{88} +7.23099 q^{89} +3.35884 q^{90} -2.76346 q^{91} +1.81089 q^{92} +4.17101 q^{93} +12.2643 q^{94} +16.5573 q^{95} +2.40257 q^{96} +12.1971 q^{97} +1.25182 q^{98} +3.43086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) $ 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * 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 $

$2$	1.25182	0.885168	0.442584	−	0.896727i	$-0.354062\pi$
$2$	1.25182	0.885168	0.442584	+	0.896727i	$0.354062\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.432954	−0.216477
$5$	2.68317	1.19995	0.599975	−	0.800019i	$-0.295177\pi$
$5$	2.68317	1.19995	0.599975	+	0.800019i	$0.295177\pi$
$6$	1.25182	0.511052
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.04561	−1.07679
$9$	1.00000	0.333333
$10$	3.35884	1.06216
$11$	3.43086	1.03444	0.517222	−	0.855851i	$-0.326966\pi$
$11$	3.43086	1.03444	0.517222	+	0.855851i	$0.326966\pi$
$12$	−0.432954	−0.124983
$13$	−2.76346	−0.766445	−0.383222	−	0.923656i	$-0.625186\pi$
$13$	−2.76346	−0.766445	−0.383222	+	0.923656i	$0.625186\pi$
$14$	1.25182	0.334562
$15$	2.68317	0.692791
$16$	−2.94664	−0.736661
$17$	−3.33728	−0.809410	−0.404705	−	0.914447i	$-0.632626\pi$
$17$	−3.33728	−0.809410	−0.404705	+	0.914447i	$0.632626\pi$
$18$	1.25182	0.295056
$19$	6.17079	1.41568	0.707838	−	0.706374i	$-0.249670\pi$
$19$	6.17079	1.41568	0.707838	+	0.706374i	$0.249670\pi$
$20$	−1.16169	−0.259761
$21$	1.00000	0.218218
$22$	4.29481	0.915658
$23$	−4.18264	−0.872140	−0.436070	−	0.899913i	$-0.643630\pi$
$23$	−4.18264	−0.872140	−0.436070	+	0.899913i	$0.643630\pi$
$24$	−3.04561	−0.621683
$25$	2.19939	0.439878
$26$	−3.45934	−0.678433
$27$	1.00000	0.192450
$28$	−0.432954	−0.0818206
$29$	9.73183	1.80716	0.903578	−	0.428425i	$-0.140931\pi$
$29$	9.73183	1.80716	0.903578	+	0.428425i	$0.140931\pi$
$30$	3.35884	0.613237
$31$	4.17101	0.749135	0.374567	−	0.927200i	$-0.377791\pi$
$31$	4.17101	0.749135	0.374567	+	0.927200i	$0.377791\pi$
$32$	2.40257	0.424718
$33$	3.43086	0.597237
$34$	−4.17767	−0.716464
$35$	2.68317	0.453538
$36$	−0.432954	−0.0721590
$37$	1.48739	0.244526	0.122263	−	0.992498i	$-0.460985\pi$
$37$	1.48739	0.244526	0.122263	+	0.992498i	$0.460985\pi$
$38$	7.72470	1.25311
$39$	−2.76346	−0.442507
$40$	−8.17189	−1.29209
$41$	5.50976	0.860480	0.430240	−	0.902714i	$-0.358429\pi$
$41$	5.50976	0.860480	0.430240	+	0.902714i	$0.358429\pi$
$42$	1.25182	0.193160
$43$	−1.92592	−0.293700	−0.146850	−	0.989159i	$-0.546913\pi$
$43$	−1.92592	−0.293700	−0.146850	+	0.989159i	$0.546913\pi$
$44$	−1.48541	−0.223933
$45$	2.68317	0.399983
$46$	−5.23590	−0.771991
$47$	9.79720	1.42907	0.714534	−	0.699600i	$-0.246639\pi$
$47$	9.79720	1.42907	0.714534	+	0.699600i	$0.246639\pi$
$48$	−2.94664	−0.425311
$49$	1.00000	0.142857
$50$	2.75324	0.389366
$51$	−3.33728	−0.467313
$52$	1.19645	0.165918
$53$	−4.17682	−0.573731	−0.286865	−	0.957971i	$-0.592613\pi$
$53$	−4.17682	−0.573731	−0.286865	+	0.957971i	$0.592613\pi$
$54$	1.25182	0.170351
$55$	9.20559	1.24128
$56$	−3.04561	−0.406987
$57$	6.17079	0.817341
$58$	12.1825	1.59964
$59$	1.49735	0.194938	0.0974689	−	0.995239i	$-0.468925\pi$
$59$	1.49735	0.194938	0.0974689	+	0.995239i	$0.468925\pi$
$60$	−1.16169	−0.149973
$61$	−0.995213	−0.127424	−0.0637120	−	0.997968i	$-0.520294\pi$
$61$	−0.995213	−0.127424	−0.0637120	+	0.997968i	$0.520294\pi$
$62$	5.22134	0.663110
$63$	1.00000	0.125988
$64$	8.90086	1.11261
$65$	−7.41482	−0.919695
$66$	4.29481	0.528655
$67$	13.2456	1.61820	0.809102	−	0.587668i	$-0.199954\pi$
$67$	13.2456	1.61820	0.809102	+	0.587668i	$0.199954\pi$
$68$	1.44489	0.175219
$69$	−4.18264	−0.503530
$70$	3.35884	0.401458
$71$	2.66851	0.316694	0.158347	−	0.987384i	$-0.449384\pi$
$71$	2.66851	0.316694	0.158347	+	0.987384i	$0.449384\pi$
$72$	−3.04561	−0.358929
$73$	−13.2238	−1.54773	−0.773863	−	0.633353i	$-0.781678\pi$
$73$	−13.2238	−1.54773	−0.773863	+	0.633353i	$0.781678\pi$
$74$	1.86195	0.216447
$75$	2.19939	0.253964
$76$	−2.67167	−0.306462
$77$	3.43086	0.390983
$78$	−3.45934	−0.391693
$79$	−5.49190	−0.617887	−0.308944	−	0.951080i	$-0.599975\pi$
$79$	−5.49190	−0.617887	−0.308944	+	0.951080i	$0.599975\pi$
$80$	−7.90634	−0.883955
$81$	1.00000	0.111111
$82$	6.89721	0.761670
$83$	−10.8504	−1.19098	−0.595492	−	0.803361i	$-0.703043\pi$
$83$	−10.8504	−1.19098	−0.595492	+	0.803361i	$0.703043\pi$
$84$	−0.432954	−0.0472392
$85$	−8.95449	−0.971251
$86$	−2.41090	−0.259974
$87$	9.73183	1.04336
$88$	−10.4491	−1.11388
$89$	7.23099	0.766483	0.383242	−	0.923648i	$-0.374808\pi$
$89$	7.23099	0.766483	0.383242	+	0.923648i	$0.374808\pi$
$90$	3.35884	0.354052
$91$	−2.76346	−0.289689
$92$	1.81089	0.188798
$93$	4.17101	0.432513
$94$	12.2643	1.26497
$95$	16.5573	1.69874
$96$	2.40257	0.245211
$97$	12.1971	1.23843	0.619213	−	0.785223i	$-0.287452\pi$
$97$	12.1971	1.23843	0.619213	+	0.785223i	$0.287452\pi$
$98$	1.25182	0.126453
$99$	3.43086	0.344815
$100$	−0.952236	−0.0952236
$101$	−4.39393	−0.437212	−0.218606	−	0.975813i	$-0.570151\pi$
$101$	−4.39393	−0.437212	−0.218606	+	0.975813i	$0.570151\pi$
$102$	−4.17767	−0.413651
$103$	0.254549	0.0250814	0.0125407	−	0.999921i	$-0.496008\pi$
$103$	0.254549	0.0250814	0.0125407	+	0.999921i	$0.496008\pi$
$104$	8.41642	0.825298
$105$	2.68317	0.261850
$106$	−5.22862	−0.507848
$107$	1.26279	0.122078	0.0610392	−	0.998135i	$-0.480559\pi$
$107$	1.26279	0.122078	0.0610392	+	0.998135i	$0.480559\pi$
$108$	−0.432954	−0.0416610
$109$	−0.124683	−0.0119424	−0.00597121	−	0.999982i	$-0.501901\pi$
$109$	−0.124683	−0.0119424	−0.00597121	+	0.999982i	$0.501901\pi$
$110$	11.5237	1.09874
$111$	1.48739	0.141177
$112$	−2.94664	−0.278432
$113$	−8.49894	−0.799513	−0.399756	−	0.916621i	$-0.630905\pi$
$113$	−8.49894	−0.799513	−0.399756	+	0.916621i	$0.630905\pi$
$114$	7.72470	0.723485
$115$	−11.2227	−1.04652
$116$	−4.21343	−0.391208
$117$	−2.76346	−0.255482
$118$	1.87440	0.172553
$119$	−3.33728	−0.305928
$120$	−8.17189	−0.745988
$121$	0.770832	0.0700757
$122$	−1.24583	−0.112792
$123$	5.50976	0.496799
$124$	−1.80585	−0.162170
$125$	−7.51450	−0.672118
$126$	1.25182	0.111521
$127$	8.15412	0.723561	0.361780	−	0.932263i	$-0.382169\pi$
$127$	8.15412	0.723561	0.361780	+	0.932263i	$0.382169\pi$
$128$	6.33711	0.560127
$129$	−1.92592	−0.169568
$130$	−9.28199	−0.814085
$131$	−14.4599	−1.26337	−0.631683	−	0.775227i	$-0.717636\pi$
$131$	−14.4599	−1.26337	−0.631683	+	0.775227i	$0.717636\pi$
$132$	−1.48541	−0.129288
$133$	6.17079	0.535076
$134$	16.5810	1.43238
$135$	2.68317	0.230930
$136$	10.1641	0.871562
$137$	−19.2434	−1.64408	−0.822039	−	0.569431i	$-0.807164\pi$
$137$	−19.2434	−1.64408	−0.822039	+	0.569431i	$0.807164\pi$
$138$	−5.23590	−0.445709
$139$	5.83467	0.494890	0.247445	−	0.968902i	$-0.420409\pi$
$139$	5.83467	0.494890	0.247445	+	0.968902i	$0.420409\pi$
$140$	−1.16169	−0.0981806
$141$	9.79720	0.825073
$142$	3.34049	0.280327
$143$	−9.48104	−0.792845
$144$	−2.94664	−0.245554
$145$	26.1121	2.16849
$146$	−16.5537	−1.37000
$147$	1.00000	0.0824786
$148$	−0.643974	−0.0529343
$149$	11.0013	0.901262	0.450631	−	0.892710i	$-0.351199\pi$
$149$	11.0013	0.901262	0.450631	+	0.892710i	$0.351199\pi$
$150$	2.75324	0.224801
$151$	−14.3628	−1.16882	−0.584412	−	0.811457i	$-0.698675\pi$
$151$	−14.3628	−1.16882	−0.584412	+	0.811457i	$0.698675\pi$
$152$	−18.7938	−1.52438
$153$	−3.33728	−0.269803
$154$	4.29481	0.346086
$155$	11.1915	0.898924
$156$	1.19645	0.0957926
$157$	−15.2236	−1.21498	−0.607488	−	0.794329i	$-0.707823\pi$
$157$	−15.2236	−1.21498	−0.607488	+	0.794329i	$0.707823\pi$
$158$	−6.87486	−0.546934
$159$	−4.17682	−0.331244
$160$	6.44650	0.509640
$161$	−4.18264	−0.329638
$162$	1.25182	0.0983520
$163$	22.7967	1.78558	0.892788	−	0.450478i	$-0.148746\pi$
$163$	22.7967	1.78558	0.892788	+	0.450478i	$0.148746\pi$
$164$	−2.38547	−0.186274
$165$	9.20559	0.716654
$166$	−13.5827	−1.05422
$167$	−11.2454	−0.870199	−0.435099	−	0.900382i	$-0.643287\pi$
$167$	−11.2454	−0.870199	−0.435099	+	0.900382i	$0.643287\pi$
$168$	−3.04561	−0.234974
$169$	−5.36331	−0.412563
$170$	−11.2094	−0.859720
$171$	6.17079	0.471892
$172$	0.833833	0.0635792
$173$	2.63501	0.200336	0.100168	−	0.994971i	$-0.468062\pi$
$173$	2.63501	0.200336	0.100168	+	0.994971i	$0.468062\pi$
$174$	12.1825	0.923551
$175$	2.19939	0.166258
$176$	−10.1095	−0.762035
$177$	1.49735	0.112547
$178$	9.05187	0.678467
$179$	−8.70214	−0.650429	−0.325214	−	0.945640i	$-0.605436\pi$
$179$	−8.70214	−0.650429	−0.325214	+	0.945640i	$0.605436\pi$
$180$	−1.16169	−0.0865872
$181$	9.23294	0.686279	0.343140	−	0.939284i	$-0.388510\pi$
$181$	9.23294	0.686279	0.343140	+	0.939284i	$0.388510\pi$
$182$	−3.45934	−0.256423
$183$	−0.995213	−0.0735683
$184$	12.7387	0.939109
$185$	3.99093	0.293419
$186$	5.22134	0.382847
$187$	−11.4498	−0.837290
$188$	−4.24174	−0.309361
$189$	1.00000	0.0727393
$190$	20.7267	1.50367
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	8.90086	0.642364
$193$	13.2817	0.956034	0.478017	−	0.878351i	$-0.341356\pi$
$193$	13.2817	0.956034	0.478017	+	0.878351i	$0.341356\pi$
$194$	15.2685	1.09622
$195$	−7.41482	−0.530986
$196$	−0.432954	−0.0309253
$197$	19.0229	1.35533	0.677663	−	0.735373i	$-0.262993\pi$
$197$	19.0229	1.35533	0.677663	+	0.735373i	$0.262993\pi$
$198$	4.29481	0.305219
$199$	−8.50233	−0.602714	−0.301357	−	0.953511i	$-0.597440\pi$
$199$	−8.50233	−0.602714	−0.301357	+	0.953511i	$0.597440\pi$
$200$	−6.69850	−0.473655
$201$	13.2456	0.934271
$202$	−5.50040	−0.387007
$203$	9.73183	0.683040
$204$	1.44489	0.101163
$205$	14.7836	1.03253
$206$	0.318648	0.0222013
$207$	−4.18264	−0.290713
$208$	8.14292	0.564610
$209$	21.1712	1.46444
$210$	3.35884	0.231782
$211$	8.94488	0.615791	0.307896	−	0.951420i	$-0.400375\pi$
$211$	8.94488	0.615791	0.307896	+	0.951420i	$0.400375\pi$
$212$	1.80837	0.124200
$213$	2.66851	0.182843
$214$	1.58078	0.108060
$215$	−5.16756	−0.352425
$216$	−3.04561	−0.207228
$217$	4.17101	0.283146
$218$	−0.156080	−0.0105711
$219$	−13.2238	−0.893580
$220$	−3.98560	−0.268709
$221$	9.22243	0.620368
$222$	1.86195	0.124966
$223$	16.5895	1.11091	0.555457	−	0.831546i	$-0.312544\pi$
$223$	16.5895	1.11091	0.555457	+	0.831546i	$0.312544\pi$
$224$	2.40257	0.160528
$225$	2.19939	0.146626
$226$	−10.6391	−0.707703
$227$	7.22448	0.479506	0.239753	−	0.970834i	$-0.422934\pi$
$227$	7.22448	0.479506	0.239753	+	0.970834i	$0.422934\pi$
$228$	−2.67167	−0.176936
$229$	−8.12403	−0.536851	−0.268426	−	0.963300i	$-0.586503\pi$
$229$	−8.12403	−0.536851	−0.268426	+	0.963300i	$0.586503\pi$
$230$	−14.0488	−0.926350
$231$	3.43086	0.225734
$232$	−29.6394	−1.94592
$233$	5.62017	0.368190	0.184095	−	0.982908i	$-0.441065\pi$
$233$	5.62017	0.368190	0.184095	+	0.982908i	$0.441065\pi$
$234$	−3.45934	−0.226144
$235$	26.2875	1.71481
$236$	−0.648282	−0.0421996
$237$	−5.49190	−0.356737
$238$	−4.17767	−0.270798
$239$	−27.2373	−1.76183	−0.880917	−	0.473271i	$-0.843073\pi$
$239$	−27.2373	−1.76183	−0.880917	+	0.473271i	$0.843073\pi$
$240$	−7.90634	−0.510352
$241$	−21.5822	−1.39023	−0.695116	−	0.718898i	$-0.744647\pi$
$241$	−21.5822	−1.39023	−0.695116	+	0.718898i	$0.744647\pi$
$242$	0.964941	0.0620288
$243$	1.00000	0.0641500
$244$	0.430882	0.0275844
$245$	2.68317	0.171421
$246$	6.89721	0.439750
$247$	−17.0527	−1.08504
$248$	−12.7033	−0.806658
$249$	−10.8504	−0.687615
$250$	−9.40678	−0.594937
$251$	8.78728	0.554648	0.277324	−	0.960776i	$-0.410552\pi$
$251$	8.78728	0.554648	0.277324	+	0.960776i	$0.410552\pi$
$252$	−0.432954	−0.0272735
$253$	−14.3501	−0.902180
$254$	10.2075	0.640473
$255$	−8.95449	−0.560752
$256$	−9.86882	−0.616801
$257$	7.52897	0.469644	0.234822	−	0.972038i	$-0.424549\pi$
$257$	7.52897	0.469644	0.234822	+	0.972038i	$0.424549\pi$
$258$	−2.41090	−0.150096
$259$	1.48739	0.0924222
$260$	3.21027	0.199093
$261$	9.73183	0.602385
$262$	−18.1011	−1.11829
$263$	12.0926	0.745659	0.372829	−	0.927900i	$-0.378388\pi$
$263$	12.0926	0.745659	0.372829	+	0.927900i	$0.378388\pi$
$264$	−10.4491	−0.643097
$265$	−11.2071	−0.688448
$266$	7.72470	0.473632
$267$	7.23099	0.442529
$268$	−5.73472	−0.350304
$269$	−21.0842	−1.28552	−0.642762	−	0.766066i	$-0.722212\pi$
$269$	−21.0842	−1.28552	−0.642762	+	0.766066i	$0.722212\pi$
$270$	3.35884	0.204412
$271$	3.45210	0.209700	0.104850	−	0.994488i	$-0.466564\pi$
$271$	3.45210	0.209700	0.104850	+	0.994488i	$0.466564\pi$
$272$	9.83378	0.596260
$273$	−2.76346	−0.167252
$274$	−24.0893	−1.45529
$275$	7.54582	0.455030
$276$	1.81089	0.109003
$277$	−8.36136	−0.502385	−0.251193	−	0.967937i	$-0.580823\pi$
$277$	−8.36136	−0.502385	−0.251193	+	0.967937i	$0.580823\pi$
$278$	7.30393	0.438061
$279$	4.17101	0.249712
$280$	−8.17189	−0.488364
$281$	7.71000	0.459940	0.229970	−	0.973198i	$-0.426137\pi$
$281$	7.71000	0.459940	0.229970	+	0.973198i	$0.426137\pi$
$282$	12.2643	0.730329
$283$	−22.9825	−1.36617	−0.683085	−	0.730339i	$-0.739362\pi$
$283$	−22.9825	−1.36617	−0.683085	+	0.730339i	$0.739362\pi$
$284$	−1.15534	−0.0685570
$285$	16.5573	0.980768
$286$	−11.8685	−0.701801
$287$	5.50976	0.325231
$288$	2.40257	0.141573
$289$	−5.86255	−0.344856
$290$	32.6876	1.91948
$291$	12.1971	0.715005
$292$	5.72529	0.335047
$293$	−12.6724	−0.740330	−0.370165	−	0.928966i	$-0.620699\pi$
$293$	−12.6724	−0.740330	−0.370165	+	0.928966i	$0.620699\pi$
$294$	1.25182	0.0730075
$295$	4.01763	0.233915
$296$	−4.53003	−0.263303
$297$	3.43086	0.199079
$298$	13.7716	0.797769
$299$	11.5585	0.668447
$300$	−0.952236	−0.0549773
$301$	−1.92592	−0.111008
$302$	−17.9795	−1.03461
$303$	−4.39393	−0.252425
$304$	−18.1831	−1.04287
$305$	−2.67033	−0.152902
$306$	−4.17767	−0.238821
$307$	24.7208	1.41089	0.705447	−	0.708763i	$-0.250746\pi$
$307$	24.7208	1.41089	0.705447	+	0.708763i	$0.250746\pi$
$308$	−1.48541	−0.0846389
$309$	0.254549	0.0144808
$310$	14.0097	0.795699
$311$	14.5667	0.826001	0.413000	−	0.910731i	$-0.364481\pi$
$311$	14.5667	0.826001	0.413000	+	0.910731i	$0.364481\pi$
$312$	8.41642	0.476486
$313$	−16.5443	−0.935141	−0.467570	−	0.883956i	$-0.654871\pi$
$313$	−16.5443	−0.935141	−0.467570	+	0.883956i	$0.654871\pi$
$314$	−19.0572	−1.07546
$315$	2.68317	0.151179
$316$	2.37774	0.133758
$317$	−11.8616	−0.666213	−0.333106	−	0.942889i	$-0.608097\pi$
$317$	−11.8616	−0.666213	−0.333106	+	0.942889i	$0.608097\pi$
$318$	−5.22862	−0.293206
$319$	33.3886	1.86940
$320$	23.8825	1.33507
$321$	1.26279	0.0704820
$322$	−5.23590	−0.291785
$323$	−20.5937	−1.14586
$324$	−0.432954	−0.0240530
$325$	−6.07792	−0.337142
$326$	28.5373	1.58053
$327$	−0.124683	−0.00689496
$328$	−16.7806	−0.926554
$329$	9.79720	0.540137
$330$	11.5237	0.634359
$331$	14.5922	0.802061	0.401030	−	0.916065i	$-0.368652\pi$
$331$	14.5922	0.802061	0.401030	+	0.916065i	$0.368652\pi$
$332$	4.69772	0.257821
$333$	1.48739	0.0815087
$334$	−14.0772	−0.770272
$335$	35.5401	1.94176
$336$	−2.94664	−0.160753
$337$	−29.7849	−1.62249	−0.811244	−	0.584708i	$-0.801209\pi$
$337$	−29.7849	−1.62249	−0.811244	+	0.584708i	$0.801209\pi$
$338$	−6.71389	−0.365187
$339$	−8.49894	−0.461599
$340$	3.87688	0.210253
$341$	14.3102	0.774938
$342$	7.72470	0.417704
$343$	1.00000	0.0539949
$344$	5.86560	0.316252
$345$	−11.2227	−0.604211
$346$	3.29855	0.177331
$347$	−33.1370	−1.77889	−0.889445	−	0.457042i	$-0.848909\pi$
$347$	−33.1370	−1.77889	−0.889445	+	0.457042i	$0.848909\pi$
$348$	−4.21343	−0.225864
$349$	5.84753	0.313011	0.156505	−	0.987677i	$-0.449977\pi$
$349$	5.84753	0.313011	0.156505	+	0.987677i	$0.449977\pi$
$350$	2.75324	0.147167
$351$	−2.76346	−0.147502
$352$	8.24289	0.439347
$353$	−16.3398	−0.869681	−0.434841	−	0.900507i	$-0.643195\pi$
$353$	−16.3398	−0.869681	−0.434841	+	0.900507i	$0.643195\pi$
$354$	1.87440	0.0996234
$355$	7.16006	0.380017
$356$	−3.13069	−0.165926
$357$	−3.33728	−0.176628
$358$	−10.8935	−0.575739
$359$	−0.865284	−0.0456679	−0.0228340	−	0.999739i	$-0.507269\pi$
$359$	−0.865284	−0.0456679	−0.0228340	+	0.999739i	$0.507269\pi$
$360$	−8.17189	−0.430697
$361$	19.0787	1.00414
$362$	11.5580	0.607472
$363$	0.770832	0.0404582
$364$	1.19645	0.0627110
$365$	−35.4816	−1.85719
$366$	−1.24583	−0.0651203
$367$	−28.2857	−1.47650	−0.738252	−	0.674526i	$-0.764348\pi$
$367$	−28.2857	−1.47650	−0.738252	+	0.674526i	$0.764348\pi$
$368$	12.3247	0.642471
$369$	5.50976	0.286827
$370$	4.99591	0.259725
$371$	−4.17682	−0.216850
$372$	−1.80585	−0.0936292
$373$	11.9631	0.619428	0.309714	−	0.950830i	$-0.399767\pi$
$373$	11.9631	0.619428	0.309714	+	0.950830i	$0.399767\pi$
$374$	−14.3330	−0.741142
$375$	−7.51450	−0.388047
$376$	−29.8385	−1.53880
$377$	−26.8935	−1.38508
$378$	1.25182	0.0643865
$379$	23.5944	1.21196	0.605981	−	0.795479i	$-0.292781\pi$
$379$	23.5944	1.21196	0.605981	+	0.795479i	$0.292781\pi$
$380$	−7.16854	−0.367738
$381$	8.15412	0.417748
$382$	1.25182	0.0640485
$383$	11.7231	0.599021	0.299511	−	0.954093i	$-0.403177\pi$
$383$	11.7231	0.599021	0.299511	+	0.954093i	$0.403177\pi$
$384$	6.33711	0.323389
$385$	9.20559	0.469160
$386$	16.6262	0.846251
$387$	−1.92592	−0.0978999
$388$	−5.28077	−0.268091
$389$	−0.734867	−0.0372593	−0.0186296	−	0.999826i	$-0.505930\pi$
$389$	−0.734867	−0.0372593	−0.0186296	+	0.999826i	$0.505930\pi$
$390$	−9.28199	−0.470012
$391$	13.9586	0.705919
$392$	−3.04561	−0.153827
$393$	−14.4599	−0.729405
$394$	23.8132	1.19969
$395$	−14.7357	−0.741433
$396$	−1.48541	−0.0746445
$397$	−38.7757	−1.94610	−0.973048	−	0.230604i	$-0.925930\pi$
$397$	−38.7757	−1.94610	−0.973048	+	0.230604i	$0.925930\pi$
$398$	−10.6434	−0.533503
$399$	6.17079	0.308926
$400$	−6.48082	−0.324041
$401$	30.9142	1.54378	0.771891	−	0.635755i	$-0.219311\pi$
$401$	30.9142	1.54378	0.771891	+	0.635755i	$0.219311\pi$
$402$	16.5810	0.826987
$403$	−11.5264	−0.574170
$404$	1.90237	0.0946464
$405$	2.68317	0.133328
$406$	12.1825	0.604606
$407$	5.10305	0.252949
$408$	10.1641	0.503197
$409$	−0.340540	−0.0168386	−0.00841930	−	0.999965i	$-0.502680\pi$
$409$	−0.340540	−0.0168386	−0.00841930	+	0.999965i	$0.502680\pi$
$410$	18.5064	0.913965
$411$	−19.2434	−0.949209
$412$	−0.110208	−0.00542955
$413$	1.49735	0.0736796
$414$	−5.23590	−0.257330
$415$	−29.1134	−1.42912
$416$	−6.63939	−0.325523
$417$	5.83467	0.285725
$418$	26.5024	1.29628
$419$	−10.6161	−0.518629	−0.259314	−	0.965793i	$-0.583497\pi$
$419$	−10.6161	−0.518629	−0.259314	+	0.965793i	$0.583497\pi$
$420$	−1.16169	−0.0566846
$421$	4.91047	0.239322	0.119661	−	0.992815i	$-0.461819\pi$
$421$	4.91047	0.239322	0.119661	+	0.992815i	$0.461819\pi$
$422$	11.1974	0.545079
$423$	9.79720	0.476356
$424$	12.7210	0.617786
$425$	−7.33999	−0.356042
$426$	3.34049	0.161847
$427$	−0.995213	−0.0481618
$428$	−0.546729	−0.0264272
$429$	−9.48104	−0.457749
$430$	−6.46884	−0.311955
$431$	−24.6217	−1.18599	−0.592993	−	0.805208i	$-0.702054\pi$
$431$	−24.6217	−1.18599	−0.592993	+	0.805208i	$0.702054\pi$
$432$	−2.94664	−0.141770
$433$	0.781997	0.0375804	0.0187902	−	0.999823i	$-0.494019\pi$
$433$	0.781997	0.0375804	0.0187902	+	0.999823i	$0.494019\pi$
$434$	5.22134	0.250632
$435$	26.1121	1.25198
$436$	0.0539818	0.00258526
$437$	−25.8102	−1.23467
$438$	−16.5537	−0.790969
$439$	19.7137	0.940884	0.470442	−	0.882431i	$-0.344094\pi$
$439$	19.7137	0.940884	0.470442	+	0.882431i	$0.344094\pi$
$440$	−28.0367	−1.33660
$441$	1.00000	0.0476190
$442$	11.5448	0.549130
$443$	−21.5931	−1.02592	−0.512960	−	0.858413i	$-0.671451\pi$
$443$	−21.5931	−1.02592	−0.512960	+	0.858413i	$0.671451\pi$
$444$	−0.643974	−0.0305616
$445$	19.4020	0.919741
$446$	20.7670	0.983345
$447$	11.0013	0.520344
$448$	8.90086	0.420526
$449$	7.37093	0.347856	0.173928	−	0.984758i	$-0.444354\pi$
$449$	7.37093	0.347856	0.173928	+	0.984758i	$0.444354\pi$
$450$	2.75324	0.129789
$451$	18.9032	0.890119
$452$	3.67965	0.173076
$453$	−14.3628	−0.674821
$454$	9.04373	0.424443
$455$	−7.41482	−0.347612
$456$	−18.7938	−0.880103
$457$	−1.88860	−0.0883451	−0.0441726	−	0.999024i	$-0.514065\pi$
$457$	−1.88860	−0.0883451	−0.0441726	+	0.999024i	$0.514065\pi$
$458$	−10.1698	−0.475204
$459$	−3.33728	−0.155771
$460$	4.85892	0.226548
$461$	−1.58801	−0.0739611	−0.0369806	−	0.999316i	$-0.511774\pi$
$461$	−1.58801	−0.0739611	−0.0369806	+	0.999316i	$0.511774\pi$
$462$	4.29481	0.199813
$463$	−11.9725	−0.556408	−0.278204	−	0.960522i	$-0.589739\pi$
$463$	−11.9725	−0.556408	−0.278204	+	0.960522i	$0.589739\pi$
$464$	−28.6762	−1.33126
$465$	11.1915	0.518994
$466$	7.03543	0.325910
$467$	−17.2158	−0.796652	−0.398326	−	0.917244i	$-0.630409\pi$
$467$	−17.2158	−0.796652	−0.398326	+	0.917244i	$0.630409\pi$
$468$	1.19645	0.0553059
$469$	13.2456	0.611624
$470$	32.9072	1.51790
$471$	−15.2236	−0.701466
$472$	−4.56034	−0.209906
$473$	−6.60756	−0.303816
$474$	−6.87486	−0.315773
$475$	13.5720	0.622726
$476$	1.44489	0.0662264
$477$	−4.17682	−0.191244
$478$	−34.0961	−1.55952
$479$	19.9777	0.912806	0.456403	−	0.889773i	$-0.349138\pi$
$479$	19.9777	0.912806	0.456403	+	0.889773i	$0.349138\pi$
$480$	6.44650	0.294241
$481$	−4.11035	−0.187416
$482$	−27.0170	−1.23059
$483$	−4.18264	−0.190317
$484$	−0.333735	−0.0151698
$485$	32.7268	1.48605
$486$	1.25182	0.0567836
$487$	13.1596	0.596319	0.298160	−	0.954516i	$-0.403627\pi$
$487$	13.1596	0.596319	0.298160	+	0.954516i	$0.403627\pi$
$488$	3.03104	0.137209
$489$	22.7967	1.03090
$490$	3.35884	0.151737
$491$	−27.3455	−1.23408	−0.617042	−	0.786930i	$-0.711669\pi$
$491$	−27.3455	−1.23408	−0.617042	+	0.786930i	$0.711669\pi$
$492$	−2.38547	−0.107545
$493$	−32.4779	−1.46273
$494$	−21.3469	−0.960441
$495$	9.20559	0.413760
$496$	−12.2905	−0.551858
$497$	2.66851	0.119699
$498$	−13.5827	−0.608655
$499$	−33.7148	−1.50928	−0.754640	−	0.656139i	$-0.772189\pi$
$499$	−33.7148	−1.50928	−0.754640	+	0.656139i	$0.772189\pi$
$500$	3.25343	0.145498
$501$	−11.2454	−0.502409
$502$	11.0001	0.490957
$503$	−18.9661	−0.845657	−0.422829	−	0.906210i	$-0.638963\pi$
$503$	−18.9661	−0.845657	−0.422829	+	0.906210i	$0.638963\pi$
$504$	−3.04561	−0.135662
$505$	−11.7897	−0.524633
$506$	−17.9636	−0.798582
$507$	−5.36331	−0.238193
$508$	−3.53036	−0.156634
$509$	41.9863	1.86101	0.930505	−	0.366280i	$-0.119369\pi$
$509$	41.9863	1.86101	0.930505	+	0.366280i	$0.119369\pi$
$510$	−11.2094	−0.496360
$511$	−13.2238	−0.584985
$512$	−25.0282	−1.10610
$513$	6.17079	0.272447
$514$	9.42489	0.415714
$515$	0.682997	0.0300964
$516$	0.833833	0.0367075
$517$	33.6129	1.47829
$518$	1.86195	0.0818092
$519$	2.63501	0.115664
$520$	22.5827	0.990315
$521$	14.5419	0.637094	0.318547	−	0.947907i	$-0.396805\pi$
$521$	14.5419	0.637094	0.318547	+	0.947907i	$0.396805\pi$
$522$	12.1825	0.533212
$523$	38.8988	1.70093	0.850463	−	0.526035i	$-0.176322\pi$
$523$	38.8988	1.70093	0.850463	+	0.526035i	$0.176322\pi$
$524$	6.26047	0.273490
$525$	2.19939	0.0959893
$526$	15.1377	0.660033
$527$	−13.9198	−0.606357
$528$	−10.1095	−0.439961
$529$	−5.50556	−0.239372
$530$	−14.0293	−0.609392
$531$	1.49735	0.0649793
$532$	−2.67167	−0.115832
$533$	−15.2260	−0.659511
$534$	9.05187	0.391713
$535$	3.38827	0.146488
$536$	−40.3409	−1.74246
$537$	−8.70214	−0.375525
$538$	−26.3935	−1.13791
$539$	3.43086	0.147778
$540$	−1.16169	−0.0499911
$541$	−39.0109	−1.67721	−0.838605	−	0.544740i	$-0.816628\pi$
$541$	−39.0109	−1.67721	−0.838605	+	0.544740i	$0.816628\pi$
$542$	4.32140	0.185620
$543$	9.23294	0.396223
$544$	−8.01805	−0.343771
$545$	−0.334544	−0.0143303
$546$	−3.45934	−0.148046
$547$	−22.1690	−0.947878	−0.473939	−	0.880558i	$-0.657168\pi$
$547$	−22.1690	−0.947878	−0.473939	+	0.880558i	$0.657168\pi$
$548$	8.33153	0.355905
$549$	−0.995213	−0.0424747
$550$	9.44598	0.402778
$551$	60.0531	2.55835
$552$	12.7387	0.542195
$553$	−5.49190	−0.233539
$554$	−10.4669	−0.444695
$555$	3.99093	0.169406
$556$	−2.52614	−0.107132
$557$	25.7847	1.09253	0.546267	−	0.837611i	$-0.316048\pi$
$557$	25.7847	1.09253	0.546267	+	0.837611i	$0.316048\pi$
$558$	5.22134	0.221037
$559$	5.32219	0.225104
$560$	−7.90634	−0.334104
$561$	−11.4498	−0.483409
$562$	9.65151	0.407124
$563$	37.2550	1.57011	0.785056	−	0.619425i	$-0.212634\pi$
$563$	37.2550	1.57011	0.785056	+	0.619425i	$0.212634\pi$
$564$	−4.24174	−0.178609
$565$	−22.8041	−0.959375
$566$	−28.7699	−1.20929
$567$	1.00000	0.0419961
$568$	−8.12725	−0.341012
$569$	−9.05853	−0.379753	−0.189877	−	0.981808i	$-0.560809\pi$
$569$	−9.05853	−0.379753	−0.189877	+	0.981808i	$0.560809\pi$
$570$	20.7267	0.868145
$571$	−17.8893	−0.748645	−0.374323	−	0.927299i	$-0.622125\pi$
$571$	−17.8893	−0.748645	−0.374323	+	0.927299i	$0.622125\pi$
$572$	4.10486	0.171633
$573$	1.00000	0.0417756
$574$	6.89721	0.287884
$575$	−9.19925	−0.383635
$576$	8.90086	0.370869
$577$	16.2686	0.677272	0.338636	−	0.940917i	$-0.390034\pi$
$577$	16.2686	0.677272	0.338636	+	0.940917i	$0.390034\pi$
$578$	−7.33883	−0.305255
$579$	13.2817	0.551967
$580$	−11.3054	−0.469429
$581$	−10.8504	−0.450150
$582$	15.2685	0.632900
$583$	−14.3301	−0.593493
$584$	40.2745	1.66657
$585$	−7.41482	−0.306565
$586$	−15.8635	−0.655317
$587$	−39.2575	−1.62033	−0.810165	−	0.586202i	$-0.800622\pi$
$587$	−39.2575	−1.62033	−0.810165	+	0.586202i	$0.800622\pi$
$588$	−0.432954	−0.0178547
$589$	25.7384	1.06053
$590$	5.02934	0.207055
$591$	19.0229	0.782497
$592$	−4.38282	−0.180133
$593$	29.1082	1.19533	0.597665	−	0.801746i	$-0.296095\pi$
$593$	29.1082	1.19533	0.597665	+	0.801746i	$0.296095\pi$
$594$	4.29481	0.176218
$595$	−8.95449	−0.367098
$596$	−4.76306	−0.195103
$597$	−8.50233	−0.347977
$598$	14.4692	0.591688
$599$	36.1601	1.47746	0.738731	−	0.674000i	$-0.235425\pi$
$599$	36.1601	1.47746	0.738731	+	0.674000i	$0.235425\pi$
$600$	−6.69850	−0.273465
$601$	−16.3215	−0.665768	−0.332884	−	0.942968i	$-0.608022\pi$
$601$	−16.3215	−0.665768	−0.332884	+	0.942968i	$0.608022\pi$
$602$	−2.41090	−0.0982608
$603$	13.2456	0.539401
$604$	6.21841	0.253024
$605$	2.06827	0.0840872
$606$	−5.50040	−0.223438
$607$	−24.1067	−0.978461	−0.489230	−	0.872155i	$-0.662722\pi$
$607$	−24.1067	−0.978461	−0.489230	+	0.872155i	$0.662722\pi$
$608$	14.8258	0.601264
$609$	9.73183	0.394354
$610$	−3.34276	−0.135344
$611$	−27.0741	−1.09530
$612$	1.44489	0.0584062
$613$	−16.7549	−0.676725	−0.338362	−	0.941016i	$-0.609873\pi$
$613$	−16.7549	−0.676725	−0.338362	+	0.941016i	$0.609873\pi$
$614$	30.9460	1.24888
$615$	14.7836	0.596133
$616$	−10.4491	−0.421006
$617$	−12.9829	−0.522672	−0.261336	−	0.965248i	$-0.584163\pi$
$617$	−12.9829	−0.522672	−0.261336	+	0.965248i	$0.584163\pi$
$618$	0.318648	0.0128179
$619$	11.0250	0.443133	0.221567	−	0.975145i	$-0.428883\pi$
$619$	11.0250	0.443133	0.221567	+	0.975145i	$0.428883\pi$
$620$	−4.84541	−0.194596
$621$	−4.18264	−0.167843
$622$	18.2348	0.731150
$623$	7.23099	0.289703
$624$	8.14292	0.325978
$625$	−31.1596	−1.24639
$626$	−20.7105	−0.827757
$627$	21.1712	0.845494
$628$	6.59112	0.263014
$629$	−4.96386	−0.197922
$630$	3.35884	0.133819
$631$	−16.6214	−0.661687	−0.330843	−	0.943686i	$-0.607333\pi$
$631$	−16.6214	−0.661687	−0.330843	+	0.943686i	$0.607333\pi$
$632$	16.7262	0.665333
$633$	8.94488	0.355527
$634$	−14.8485	−0.589710
$635$	21.8789	0.868236
$636$	1.80837	0.0717066
$637$	−2.76346	−0.109492
$638$	41.7964	1.65474
$639$	2.66851	0.105565
$640$	17.0035	0.672124
$641$	24.7991	0.979505	0.489753	−	0.871861i	$-0.337087\pi$
$641$	24.7991	0.979505	0.489753	+	0.871861i	$0.337087\pi$
$642$	1.58078	0.0623884
$643$	−42.7738	−1.68683	−0.843416	−	0.537261i	$-0.819459\pi$
$643$	−42.7738	−1.68683	−0.843416	+	0.537261i	$0.819459\pi$
$644$	1.81089	0.0713590
$645$	−5.16756	−0.203472
$646$	−25.7795	−1.01428
$647$	−0.417646	−0.0164194	−0.00820968	−	0.999966i	$-0.502613\pi$
$647$	−0.417646	−0.0164194	−0.00820968	+	0.999966i	$0.502613\pi$
$648$	−3.04561	−0.119643
$649$	5.13719	0.201652
$650$	−7.60844	−0.298428
$651$	4.17101	0.163475
$652$	−9.86992	−0.386536
$653$	−14.5037	−0.567576	−0.283788	−	0.958887i	$-0.591591\pi$
$653$	−14.5037	−0.567576	−0.283788	+	0.958887i	$0.591591\pi$
$654$	−0.156080	−0.00610320
$655$	−38.7983	−1.51598
$656$	−16.2353	−0.633882
$657$	−13.2238	−0.515909
$658$	12.2643	0.478112
$659$	−40.8182	−1.59005	−0.795026	−	0.606575i	$-0.792543\pi$
$659$	−40.8182	−1.59005	−0.795026	+	0.606575i	$0.792543\pi$
$660$	−3.98560	−0.155139
$661$	46.9856	1.82753	0.913763	−	0.406248i	$-0.133163\pi$
$661$	46.9856	1.82753	0.913763	+	0.406248i	$0.133163\pi$
$662$	18.2668	0.709959
$663$	9.22243	0.358170
$664$	33.0461	1.28244
$665$	16.5573	0.642064
$666$	1.86195	0.0721489
$667$	−40.7047	−1.57609
$668$	4.86876	0.188378
$669$	16.5895	0.641386
$670$	44.4897	1.71879
$671$	−3.41444	−0.131813
$672$	2.40257	0.0926811
$673$	−29.3174	−1.13010	−0.565051	−	0.825056i	$-0.691143\pi$
$673$	−29.3174	−1.13010	−0.565051	+	0.825056i	$0.691143\pi$
$674$	−37.2853	−1.43617
$675$	2.19939	0.0846546
$676$	2.32207	0.0893103
$677$	−10.7849	−0.414499	−0.207249	−	0.978288i	$-0.566451\pi$
$677$	−10.7849	−0.414499	−0.207249	+	0.978288i	$0.566451\pi$
$678$	−10.6391	−0.408593
$679$	12.1971	0.468081
$680$	27.2719	1.04583
$681$	7.22448	0.276843
$682$	17.9137	0.685951
$683$	−4.51668	−0.172826	−0.0864130	−	0.996259i	$-0.527540\pi$
$683$	−4.51668	−0.172826	−0.0864130	+	0.996259i	$0.527540\pi$
$684$	−2.67167	−0.102154
$685$	−51.6334	−1.97281
$686$	1.25182	0.0477946
$687$	−8.12403	−0.309951
$688$	5.67499	0.216357
$689$	11.5425	0.439733
$690$	−14.0488	−0.534828
$691$	−33.2726	−1.26575	−0.632875	−	0.774254i	$-0.718125\pi$
$691$	−33.2726	−1.26575	−0.632875	+	0.774254i	$0.718125\pi$
$692$	−1.14084	−0.0433681
$693$	3.43086	0.130328
$694$	−41.4815	−1.57462
$695$	15.6554	0.593843
$696$	−29.6394	−1.12348
$697$	−18.3876	−0.696481
$698$	7.32003	0.277067
$699$	5.62017	0.212574
$700$	−0.952236	−0.0359911
$701$	23.2673	0.878794	0.439397	−	0.898293i	$-0.355192\pi$
$701$	23.2673	0.878794	0.439397	+	0.898293i	$0.355192\pi$
$702$	−3.45934	−0.130564
$703$	9.17840	0.346170
$704$	30.5377	1.15093
$705$	26.2875	0.990046
$706$	−20.4545	−0.769814
$707$	−4.39393	−0.165251
$708$	−0.648282	−0.0243639
$709$	−33.6648	−1.26431	−0.632154	−	0.774842i	$-0.717829\pi$
$709$	−33.6648	−1.26431	−0.632154	+	0.774842i	$0.717829\pi$
$710$	8.96309	0.336379
$711$	−5.49190	−0.205962
$712$	−22.0228	−0.825339
$713$	−17.4458	−0.653350
$714$	−4.17767	−0.156345
$715$	−25.4392	−0.951373
$716$	3.76763	0.140803
$717$	−27.2373	−1.01719
$718$	−1.08318	−0.0404238
$719$	50.0100	1.86506	0.932529	−	0.361096i	$-0.117597\pi$
$719$	50.0100	1.86506	0.932529	+	0.361096i	$0.117597\pi$
$720$	−7.90634	−0.294652
$721$	0.254549	0.00947988
$722$	23.8830	0.888834
$723$	−21.5822	−0.802651
$724$	−3.99744	−0.148564
$725$	21.4041	0.794928
$726$	0.964941	0.0358123
$727$	45.6221	1.69203	0.846015	−	0.533160i	$-0.178996\pi$
$727$	45.6221	1.69203	0.846015	+	0.533160i	$0.178996\pi$
$728$	8.41642	0.311933
$729$	1.00000	0.0370370
$730$	−44.4165	−1.64393
$731$	6.42733	0.237723
$732$	0.430882	0.0159258
$733$	35.3601	1.30605	0.653027	−	0.757335i	$-0.273499\pi$
$733$	35.3601	1.30605	0.653027	+	0.757335i	$0.273499\pi$
$734$	−35.4086	−1.30695
$735$	2.68317	0.0989702
$736$	−10.0491	−0.370414
$737$	45.4438	1.67394
$738$	6.89721	0.253890
$739$	−45.8510	−1.68666	−0.843329	−	0.537398i	$-0.819407\pi$
$739$	−45.8510	−1.68666	−0.843329	+	0.537398i	$0.819407\pi$
$740$	−1.72789	−0.0635185
$741$	−17.0527	−0.626447
$742$	−5.22862	−0.191949
$743$	−30.8225	−1.13077	−0.565384	−	0.824828i	$-0.691272\pi$
$743$	−30.8225	−1.13077	−0.565384	+	0.824828i	$0.691272\pi$
$744$	−12.7033	−0.465724
$745$	29.5184	1.08147
$746$	14.9757	0.548298
$747$	−10.8504	−0.396995
$748$	4.95722	0.181254
$749$	1.26279	0.0461413
$750$	−9.40678	−0.343487
$751$	−4.91225	−0.179251	−0.0896253	−	0.995976i	$-0.528567\pi$
$751$	−4.91225	−0.179251	−0.0896253	+	0.995976i	$0.528567\pi$
$752$	−28.8689	−1.05274
$753$	8.78728	0.320226
$754$	−33.6657	−1.22603
$755$	−38.5377	−1.40253
$756$	−0.432954	−0.0157464
$757$	−23.1150	−0.840129	−0.420064	−	0.907494i	$-0.637992\pi$
$757$	−23.1150	−0.840129	−0.420064	+	0.907494i	$0.637992\pi$
$758$	29.5358	1.07279
$759$	−14.3501	−0.520874
$760$	−50.4271	−1.82918
$761$	−39.4976	−1.43179	−0.715894	−	0.698209i	$-0.753981\pi$
$761$	−39.4976	−1.43179	−0.715894	+	0.698209i	$0.753981\pi$
$762$	10.2075	0.369777
$763$	−0.124683	−0.00451381
$764$	−0.432954	−0.0156637
$765$	−8.95449	−0.323750
$766$	14.6751	0.530235
$767$	−4.13785	−0.149409
$768$	−9.86882	−0.356110
$769$	45.3104	1.63393	0.816967	−	0.576684i	$-0.195654\pi$
$769$	45.3104	1.63393	0.816967	+	0.576684i	$0.195654\pi$
$770$	11.5237	0.415286
$771$	7.52897	0.271149
$772$	−5.75034	−0.206959
$773$	−1.24011	−0.0446037	−0.0223019	−	0.999751i	$-0.507099\pi$
$773$	−1.24011	−0.0446037	−0.0223019	+	0.999751i	$0.507099\pi$
$774$	−2.41090	−0.0866578
$775$	9.17367	0.329528
$776$	−37.1476	−1.33352
$777$	1.48739	0.0533600
$778$	−0.919920	−0.0329807
$779$	33.9996	1.21816
$780$	3.21027	0.114946
$781$	9.15530	0.327602
$782$	17.4737	0.624857
$783$	9.73183	0.347787
$784$	−2.94664	−0.105237
$785$	−40.8475	−1.45791
$786$	−18.1011	−0.645646
$787$	14.3994	0.513282	0.256641	−	0.966507i	$-0.417384\pi$
$787$	14.3994	0.513282	0.256641	+	0.966507i	$0.417384\pi$
$788$	−8.23604	−0.293397
$789$	12.0926	0.430506
$790$	−18.4464	−0.656293
$791$	−8.49894	−0.302187
$792$	−10.4491	−0.371292
$793$	2.75023	0.0976635
$794$	−48.5401	−1.72262
$795$	−11.2071	−0.397476
$796$	3.68112	0.130474
$797$	−7.16087	−0.253651	−0.126825	−	0.991925i	$-0.540479\pi$
$797$	−7.16087	−0.253651	−0.126825	+	0.991925i	$0.540479\pi$
$798$	7.72470	0.273452
$799$	−32.6960	−1.15670
$800$	5.28419	0.186824
$801$	7.23099	0.255494
$802$	38.6989	1.36651
$803$	−45.3690	−1.60104
$804$	−5.73472	−0.202248
$805$	−11.2227	−0.395549
$806$	−14.4289	−0.508237
$807$	−21.0842	−0.742198
$808$	13.3822	0.470785
$809$	21.6524	0.761256	0.380628	−	0.924728i	$-0.375708\pi$
$809$	21.6524	0.761256	0.380628	+	0.924728i	$0.375708\pi$
$810$	3.35884	0.118017
$811$	−48.8170	−1.71420	−0.857099	−	0.515151i	$-0.827736\pi$
$811$	−48.8170	−1.71420	−0.857099	+	0.515151i	$0.827736\pi$
$812$	−4.21343	−0.147863
$813$	3.45210	0.121070
$814$	6.38808	0.223902
$815$	61.1674	2.14260
$816$	9.83378	0.344251
$817$	−11.8844	−0.415784
$818$	−0.426293	−0.0149050
$819$	−2.76346	−0.0965629
$820$	−6.40063	−0.223520
$821$	34.2477	1.19525	0.597626	−	0.801775i	$-0.296111\pi$
$821$	34.2477	1.19525	0.597626	+	0.801775i	$0.296111\pi$
$822$	−24.0893	−0.840210
$823$	7.22481	0.251841	0.125921	−	0.992040i	$-0.459812\pi$
$823$	7.22481	0.251841	0.125921	+	0.992040i	$0.459812\pi$
$824$	−0.775257	−0.0270073
$825$	7.54582	0.262712
$826$	1.87440	0.0652188
$827$	−42.2275	−1.46839	−0.734197	−	0.678937i	$-0.762441\pi$
$827$	−42.2275	−1.46839	−0.734197	+	0.678937i	$0.762441\pi$
$828$	1.81089	0.0629327
$829$	7.50994	0.260831	0.130416	−	0.991459i	$-0.458369\pi$
$829$	7.50994	0.260831	0.130416	+	0.991459i	$0.458369\pi$
$830$	−36.4447	−1.26501
$831$	−8.36136	−0.290052
$832$	−24.5971	−0.852752
$833$	−3.33728	−0.115630
$834$	7.30393	0.252915
$835$	−30.1734	−1.04419
$836$	−9.16614	−0.317017
$837$	4.17101	0.144171
$838$	−13.2894	−0.459074
$839$	45.1943	1.56028	0.780140	−	0.625605i	$-0.215148\pi$
$839$	45.1943	1.56028	0.780140	+	0.625605i	$0.215148\pi$
$840$	−8.17189	−0.281957
$841$	65.7085	2.26581
$842$	6.14702	0.211840
$843$	7.71000	0.265547
$844$	−3.87272	−0.133305
$845$	−14.3907	−0.495054
$846$	12.2643	0.421655
$847$	0.770832	0.0264861
$848$	12.3076	0.422645
$849$	−22.9825	−0.788758
$850$	−9.18833	−0.315157
$851$	−6.22123	−0.213261
$852$	−1.15534	−0.0395814
$853$	−26.4063	−0.904136	−0.452068	−	0.891984i	$-0.649314\pi$
$853$	−26.4063	−0.904136	−0.452068	+	0.891984i	$0.649314\pi$
$854$	−1.24583	−0.0426313
$855$	16.5573	0.566247
$856$	−3.84597	−0.131452
$857$	−51.4323	−1.75689	−0.878447	−	0.477840i	$-0.841420\pi$
$857$	−51.4323	−1.75689	−0.878447	+	0.477840i	$0.841420\pi$
$858$	−11.8685	−0.405185
$859$	−16.6947	−0.569615	−0.284808	−	0.958585i	$-0.591930\pi$
$859$	−16.6947	−0.569615	−0.284808	+	0.958585i	$0.591930\pi$
$860$	2.23732	0.0762918
$861$	5.50976	0.187772
$862$	−30.8219	−1.04980
$863$	−46.2713	−1.57509	−0.787546	−	0.616255i	$-0.788649\pi$
$863$	−46.2713	−1.57509	−0.787546	+	0.616255i	$0.788649\pi$
$864$	2.40257	0.0817371
$865$	7.07017	0.240393
$866$	0.978917	0.0332650
$867$	−5.86255	−0.199102
$868$	−1.80585	−0.0612947
$869$	−18.8420	−0.639170
$870$	32.6876	1.10821
$871$	−36.6035	−1.24026
$872$	0.379735	0.0128595
$873$	12.1971	0.412809
$874$	−32.3096	−1.09289
$875$	−7.51450	−0.254037
$876$	5.72529	0.193440
$877$	−7.56468	−0.255441	−0.127720	−	0.991810i	$-0.540766\pi$
$877$	−7.56468	−0.255441	−0.127720	+	0.991810i	$0.540766\pi$
$878$	24.6780	0.832841
$879$	−12.6724	−0.427430
$880$	−27.1256	−0.914403
$881$	22.3155	0.751827	0.375914	−	0.926655i	$-0.377329\pi$
$881$	22.3155	0.751827	0.375914	+	0.926655i	$0.377329\pi$
$882$	1.25182	0.0421509
$883$	−25.0888	−0.844304	−0.422152	−	0.906525i	$-0.638725\pi$
$883$	−25.0888	−0.844304	−0.422152	+	0.906525i	$0.638725\pi$
$884$	−3.99289	−0.134295
$885$	4.01763	0.135051
$886$	−27.0306	−0.908112
$887$	28.3069	0.950452	0.475226	−	0.879864i	$-0.342366\pi$
$887$	28.3069	0.950452	0.475226	+	0.879864i	$0.342366\pi$
$888$	−4.53003	−0.152018
$889$	8.15412	0.273480
$890$	24.2877	0.814126
$891$	3.43086	0.114938
$892$	−7.18248	−0.240487
$893$	60.4565	2.02310
$894$	13.7716	0.460592
$895$	−23.3493	−0.780482
$896$	6.33711	0.211708
$897$	11.5585	0.385928
$898$	9.22705	0.307911
$899$	40.5915	1.35380
$900$	−0.952236	−0.0317412
$901$	13.9392	0.464383
$902$	23.6634	0.787905
$903$	−1.92592	−0.0640905
$904$	25.8845	0.860905
$905$	24.7735	0.823500
$906$	−17.9795	−0.597330
$907$	−14.6331	−0.485883	−0.242942	−	0.970041i	$-0.578112\pi$
$907$	−14.6331	−0.485883	−0.242942	+	0.970041i	$0.578112\pi$
$908$	−3.12787	−0.103802
$909$	−4.39393	−0.145737
$910$	−9.28199	−0.307695
$911$	21.8824	0.724997	0.362498	−	0.931984i	$-0.381924\pi$
$911$	21.8824	0.724997	0.362498	+	0.931984i	$0.381924\pi$
$912$	−18.1831	−0.602103
$913$	−37.2262	−1.23201
$914$	−2.36419	−0.0782003
$915$	−2.67033	−0.0882782
$916$	3.51733	0.116216
$917$	−14.4599	−0.477508
$918$	−4.17767	−0.137884
$919$	−22.5338	−0.743321	−0.371661	−	0.928369i	$-0.621211\pi$
$919$	−22.5338	−0.743321	−0.371661	+	0.928369i	$0.621211\pi$
$920$	34.1801	1.12688
$921$	24.7208	0.814580
$922$	−1.98790	−0.0654680
$923$	−7.37431	−0.242728
$924$	−1.48541	−0.0488663
$925$	3.27136	0.107562
$926$	−14.9873	−0.492515
$927$	0.254549	0.00836047
$928$	23.3814	0.767532
$929$	22.6208	0.742163	0.371082	−	0.928600i	$-0.378987\pi$
$929$	22.6208	0.742163	0.371082	+	0.928600i	$0.378987\pi$
$930$	14.0097	0.459397
$931$	6.17079	0.202240
$932$	−2.43328	−0.0797046
$933$	14.5667	0.476892
$934$	−21.5510	−0.705171
$935$	−30.7216	−1.00471
$936$	8.41642	0.275099
$937$	28.4614	0.929792	0.464896	−	0.885365i	$-0.346092\pi$
$937$	28.4614	0.929792	0.464896	+	0.885365i	$0.346092\pi$
$938$	16.5810	0.541390
$939$	−16.5443	−0.539904
$940$	−11.3813	−0.371217
$941$	11.5931	0.377924	0.188962	−	0.981984i	$-0.439488\pi$
$941$	11.5931	0.377924	0.188962	+	0.981984i	$0.439488\pi$
$942$	−19.0572	−0.620916
$943$	−23.0453	−0.750459
$944$	−4.41214	−0.143603
$945$	2.68317	0.0872835
$946$	−8.27146	−0.268928
$947$	40.1537	1.30482	0.652410	−	0.757866i	$-0.273758\pi$
$947$	40.1537	1.30482	0.652410	+	0.757866i	$0.273758\pi$
$948$	2.37774	0.0772255
$949$	36.5433	1.18625
$950$	16.9896	0.551217
$951$	−11.8616	−0.384638
$952$	10.1641	0.329419
$953$	44.0046	1.42545	0.712725	−	0.701444i	$-0.247461\pi$
$953$	44.0046	1.42545	0.712725	+	0.701444i	$0.247461\pi$
$954$	−5.22862	−0.169283
$955$	2.68317	0.0868253
$956$	11.7925	0.381396
$957$	33.3886	1.07930
$958$	25.0085	0.807987
$959$	−19.2434	−0.621403
$960$	23.8825	0.770805
$961$	−13.6027	−0.438797
$962$	−5.14540	−0.165895
$963$	1.26279	0.0406928
$964$	9.34410	0.300953
$965$	35.6369	1.14719
$966$	−5.23590	−0.168462
$967$	22.8299	0.734159	0.367079	−	0.930190i	$-0.380358\pi$
$967$	22.8299	0.734159	0.367079	+	0.930190i	$0.380358\pi$
$968$	−2.34766	−0.0754566
$969$	−20.5937	−0.661564
$970$	40.9680	1.31540
$971$	−7.93330	−0.254592	−0.127296	−	0.991865i	$-0.540630\pi$
$971$	−7.93330	−0.254592	−0.127296	+	0.991865i	$0.540630\pi$
$972$	−0.432954	−0.0138870
$973$	5.83467	0.187051
$974$	16.4734	0.527843
$975$	−6.07792	−0.194649
$976$	2.93254	0.0938683
$977$	29.5293	0.944725	0.472363	−	0.881404i	$-0.343401\pi$
$977$	29.5293	0.944725	0.472363	+	0.881404i	$0.343401\pi$
$978$	28.5373	0.912522
$979$	24.8085	0.792884
$980$	−1.16169	−0.0371088
$981$	−0.124683	−0.00398081
$982$	−34.2316	−1.09237
$983$	−20.6231	−0.657776	−0.328888	−	0.944369i	$-0.606674\pi$
$983$	−20.6231	−0.657776	−0.328888	+	0.944369i	$0.606674\pi$
$984$	−16.7806	−0.534946
$985$	51.0416	1.62632
$986$	−40.6563	−1.29476
$987$	9.79720	0.311848
$988$	7.38304	0.234886
$989$	8.05541	0.256147
$990$	11.5237	0.366248
$991$	−36.7638	−1.16784	−0.583920	−	0.811811i	$-0.698482\pi$
$991$	−36.7638	−1.16784	−0.583920	+	0.811811i	$0.698482\pi$
$992$	10.0211	0.318171
$993$	14.5922	0.463070
$994$	3.34049	0.105954
$995$	−22.8132	−0.723226
$996$	4.69772	0.148853
$997$	8.50062	0.269217	0.134609	−	0.990899i	$-0.457022\pi$
$997$	8.50062	0.269217	0.134609	+	0.990899i	$0.457022\pi$
$998$	−42.2047	−1.33597
$999$	1.48739	0.0470591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.16	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.16	✓	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q+1.25182 q^{2} +1.00000 q^{3} -0.432954 q^{4} +2.68317 q^{5} +1.25182 q^{6} +1.00000 q^{7} -3.04561 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.25182 q^{2} +1.00000 q^{3} -0.432954 q^{4} +2.68317 q^{5} +1.25182 q^{6} +1.00000 q^{7} -3.04561 q^{8} +1.00000 q^{9} +3.35884 q^{10} +3.43086 q^{11} -0.432954 q^{12} -2.76346 q^{13} +1.25182 q^{14} +2.68317 q^{15} -2.94664 q^{16} -3.33728 q^{17} +1.25182 q^{18} +6.17079 q^{19} -1.16169 q^{20} +1.00000 q^{21} +4.29481 q^{22} -4.18264 q^{23} -3.04561 q^{24} +2.19939 q^{25} -3.45934 q^{26} +1.00000 q^{27} -0.432954 q^{28} +9.73183 q^{29} +3.35884 q^{30} +4.17101 q^{31} +2.40257 q^{32} +3.43086 q^{33} -4.17767 q^{34} +2.68317 q^{35} -0.432954 q^{36} +1.48739 q^{37} +7.72470 q^{38} -2.76346 q^{39} -8.17189 q^{40} +5.50976 q^{41} +1.25182 q^{42} -1.92592 q^{43} -1.48541 q^{44} +2.68317 q^{45} -5.23590 q^{46} +9.79720 q^{47} -2.94664 q^{48} +1.00000 q^{49} +2.75324 q^{50} -3.33728 q^{51} +1.19645 q^{52} -4.17682 q^{53} +1.25182 q^{54} +9.20559 q^{55} -3.04561 q^{56} +6.17079 q^{57} +12.1825 q^{58} +1.49735 q^{59} -1.16169 q^{60} -0.995213 q^{61} +5.22134 q^{62} +1.00000 q^{63} +8.90086 q^{64} -7.41482 q^{65} +4.29481 q^{66} +13.2456 q^{67} +1.44489 q^{68} -4.18264 q^{69} +3.35884 q^{70} +2.66851 q^{71} -3.04561 q^{72} -13.2238 q^{73} +1.86195 q^{74} +2.19939 q^{75} -2.67167 q^{76} +3.43086 q^{77} -3.45934 q^{78} -5.49190 q^{79} -7.90634 q^{80} +1.00000 q^{81} +6.89721 q^{82} -10.8504 q^{83} -0.432954 q^{84} -8.95449 q^{85} -2.41090 q^{86} +9.73183 q^{87} -10.4491 q^{88} +7.23099 q^{89} +3.35884 q^{90} -2.76346 q^{91} +1.81089 q^{92} +4.17101 q^{93} +12.2643 q^{94} +16.5573 q^{95} +2.40257 q^{96} +12.1971 q^{97} +1.25182 q^{98} +3.43086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

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