LMFDB - Embedded newform 4011.2.a.k.1.10

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			1.10
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)

$f(q)$	$=$	$q-0.667457 q^{2} +1.00000 q^{3} -1.55450 q^{4} -3.08787 q^{5} -0.667457 q^{6} +1.00000 q^{7} +2.37248 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.667457 q^{2} +1.00000 q^{3} -1.55450 q^{4} -3.08787 q^{5} -0.667457 q^{6} +1.00000 q^{7} +2.37248 q^{8} +1.00000 q^{9} +2.06102 q^{10} +3.38261 q^{11} -1.55450 q^{12} +5.44801 q^{13} -0.667457 q^{14} -3.08787 q^{15} +1.52548 q^{16} +3.25641 q^{17} -0.667457 q^{18} -2.41947 q^{19} +4.80010 q^{20} +1.00000 q^{21} -2.25775 q^{22} +3.81625 q^{23} +2.37248 q^{24} +4.53495 q^{25} -3.63631 q^{26} +1.00000 q^{27} -1.55450 q^{28} -2.74166 q^{29} +2.06102 q^{30} -2.56542 q^{31} -5.76314 q^{32} +3.38261 q^{33} -2.17351 q^{34} -3.08787 q^{35} -1.55450 q^{36} -2.44039 q^{37} +1.61489 q^{38} +5.44801 q^{39} -7.32590 q^{40} +7.88451 q^{41} -0.667457 q^{42} -5.47513 q^{43} -5.25828 q^{44} -3.08787 q^{45} -2.54718 q^{46} -7.99578 q^{47} +1.52548 q^{48} +1.00000 q^{49} -3.02688 q^{50} +3.25641 q^{51} -8.46894 q^{52} +4.78771 q^{53} -0.667457 q^{54} -10.4451 q^{55} +2.37248 q^{56} -2.41947 q^{57} +1.82994 q^{58} -7.18848 q^{59} +4.80010 q^{60} +11.6380 q^{61} +1.71231 q^{62} +1.00000 q^{63} +0.795692 q^{64} -16.8228 q^{65} -2.25775 q^{66} -6.11569 q^{67} -5.06209 q^{68} +3.81625 q^{69} +2.06102 q^{70} +15.4248 q^{71} +2.37248 q^{72} -0.602919 q^{73} +1.62885 q^{74} +4.53495 q^{75} +3.76106 q^{76} +3.38261 q^{77} -3.63631 q^{78} -5.66920 q^{79} -4.71048 q^{80} +1.00000 q^{81} -5.26257 q^{82} +4.60337 q^{83} -1.55450 q^{84} -10.0554 q^{85} +3.65441 q^{86} -2.74166 q^{87} +8.02517 q^{88} +0.152886 q^{89} +2.06102 q^{90} +5.44801 q^{91} -5.93236 q^{92} -2.56542 q^{93} +5.33684 q^{94} +7.47100 q^{95} -5.76314 q^{96} +4.77136 q^{97} -0.667457 q^{98} +3.38261 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.667457	−0.471963	−0.235982	−	0.971758i	$-0.575831\pi$
$2$	−0.667457	−0.471963	−0.235982	+	0.971758i	$0.575831\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.55450	−0.777251
$5$	−3.08787	−1.38094	−0.690469	−	0.723362i	$-0.742596\pi$
$5$	−3.08787	−1.38094	−0.690469	+	0.723362i	$0.742596\pi$
$6$	−0.667457	−0.272488
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.37248	0.838797
$9$	1.00000	0.333333
$10$	2.06102	0.651752
$11$	3.38261	1.01990	0.509948	−	0.860205i	$-0.329665\pi$
$11$	3.38261	1.01990	0.509948	+	0.860205i	$0.329665\pi$
$12$	−1.55450	−0.448746
$13$	5.44801	1.51101	0.755503	−	0.655145i	$-0.227392\pi$
$13$	5.44801	1.51101	0.755503	+	0.655145i	$0.227392\pi$
$14$	−0.667457	−0.178385
$15$	−3.08787	−0.797285
$16$	1.52548	0.381370
$17$	3.25641	0.789794	0.394897	−	0.918725i	$-0.370780\pi$
$17$	3.25641	0.789794	0.394897	+	0.918725i	$0.370780\pi$
$18$	−0.667457	−0.157321
$19$	−2.41947	−0.555063	−0.277532	−	0.960716i	$-0.589516\pi$
$19$	−2.41947	−0.555063	−0.277532	+	0.960716i	$0.589516\pi$
$20$	4.80010	1.07334
$21$	1.00000	0.218218
$22$	−2.25775	−0.481353
$23$	3.81625	0.795743	0.397871	−	0.917441i	$-0.369749\pi$
$23$	3.81625	0.795743	0.397871	+	0.917441i	$0.369749\pi$
$24$	2.37248	0.484280
$25$	4.53495	0.906990
$26$	−3.63631	−0.713140
$27$	1.00000	0.192450
$28$	−1.55450	−0.293773
$29$	−2.74166	−0.509114	−0.254557	−	0.967058i	$-0.581930\pi$
$29$	−2.74166	−0.509114	−0.254557	+	0.967058i	$0.581930\pi$
$30$	2.06102	0.376289
$31$	−2.56542	−0.460763	−0.230382	−	0.973100i	$-0.573997\pi$
$31$	−2.56542	−0.460763	−0.230382	+	0.973100i	$0.573997\pi$
$32$	−5.76314	−1.01879
$33$	3.38261	0.588837
$34$	−2.17351	−0.372754
$35$	−3.08787	−0.521945
$36$	−1.55450	−0.259084
$37$	−2.44039	−0.401198	−0.200599	−	0.979673i	$-0.564289\pi$
$37$	−2.44039	−0.401198	−0.200599	+	0.979673i	$0.564289\pi$
$38$	1.61489	0.261969
$39$	5.44801	0.872380
$40$	−7.32590	−1.15833
$41$	7.88451	1.23135	0.615677	−	0.787999i	$-0.288883\pi$
$41$	7.88451	1.23135	0.615677	+	0.787999i	$0.288883\pi$
$42$	−0.667457	−0.102991
$43$	−5.47513	−0.834949	−0.417475	−	0.908689i	$-0.637085\pi$
$43$	−5.47513	−0.834949	−0.417475	+	0.908689i	$0.637085\pi$
$44$	−5.25828	−0.792715
$45$	−3.08787	−0.460313
$46$	−2.54718	−0.375561
$47$	−7.99578	−1.16630	−0.583152	−	0.812363i	$-0.698181\pi$
$47$	−7.99578	−1.16630	−0.583152	+	0.812363i	$0.698181\pi$
$48$	1.52548	0.220184
$49$	1.00000	0.142857
$50$	−3.02688	−0.428066
$51$	3.25641	0.455988
$52$	−8.46894	−1.17443
$53$	4.78771	0.657643	0.328822	−	0.944392i	$-0.393349\pi$
$53$	4.78771	0.657643	0.328822	+	0.944392i	$0.393349\pi$
$54$	−0.667457	−0.0908294
$55$	−10.4451	−1.40841
$56$	2.37248	0.317035
$57$	−2.41947	−0.320466
$58$	1.82994	0.240283
$59$	−7.18848	−0.935860	−0.467930	−	0.883766i	$-0.655000\pi$
$59$	−7.18848	−0.935860	−0.467930	+	0.883766i	$0.655000\pi$
$60$	4.80010	0.619690
$61$	11.6380	1.49009	0.745045	−	0.667014i	$-0.232428\pi$
$61$	11.6380	1.49009	0.745045	+	0.667014i	$0.232428\pi$
$62$	1.71231	0.217463
$63$	1.00000	0.125988
$64$	0.795692	0.0994615
$65$	−16.8228	−2.08661
$66$	−2.25775	−0.277909
$67$	−6.11569	−0.747150	−0.373575	−	0.927600i	$-0.621868\pi$
$67$	−6.11569	−0.747150	−0.373575	+	0.927600i	$0.621868\pi$
$68$	−5.06209	−0.613868
$69$	3.81625	0.459422
$70$	2.06102	0.246339
$71$	15.4248	1.83058	0.915291	−	0.402794i	$-0.131961\pi$
$71$	15.4248	1.83058	0.915291	+	0.402794i	$0.131961\pi$
$72$	2.37248	0.279599
$73$	−0.602919	−0.0705663	−0.0352831	−	0.999377i	$-0.511233\pi$
$73$	−0.602919	−0.0705663	−0.0352831	+	0.999377i	$0.511233\pi$
$74$	1.62885	0.189350
$75$	4.53495	0.523651
$76$	3.76106	0.431423
$77$	3.38261	0.385484
$78$	−3.63631	−0.411731
$79$	−5.66920	−0.637834	−0.318917	−	0.947783i	$-0.603319\pi$
$79$	−5.66920	−0.637834	−0.318917	+	0.947783i	$0.603319\pi$
$80$	−4.71048	−0.526648
$81$	1.00000	0.111111
$82$	−5.26257	−0.581153
$83$	4.60337	0.505285	0.252643	−	0.967560i	$-0.418700\pi$
$83$	4.60337	0.505285	0.252643	+	0.967560i	$0.418700\pi$
$84$	−1.55450	−0.169610
$85$	−10.0554	−1.09066
$86$	3.65441	0.394065
$87$	−2.74166	−0.293937
$88$	8.02517	0.855486
$89$	0.152886	0.0162059	0.00810293	−	0.999967i	$-0.497421\pi$
$89$	0.152886	0.0162059	0.00810293	+	0.999967i	$0.497421\pi$
$90$	2.06102	0.217251
$91$	5.44801	0.571107
$92$	−5.93236	−0.618492
$93$	−2.56542	−0.266022
$94$	5.33684	0.550453
$95$	7.47100	0.766508
$96$	−5.76314	−0.588198
$97$	4.77136	0.484459	0.242229	−	0.970219i	$-0.422121\pi$
$97$	4.77136	0.484459	0.242229	+	0.970219i	$0.422121\pi$
$98$	−0.667457	−0.0674233
$99$	3.38261	0.339965
$100$	−7.04958	−0.704958
$101$	14.5572	1.44850	0.724248	−	0.689540i	$-0.242187\pi$
$101$	14.5572	1.44850	0.724248	+	0.689540i	$0.242187\pi$
$102$	−2.17351	−0.215210
$103$	−17.7347	−1.74745	−0.873726	−	0.486419i	$-0.838303\pi$
$103$	−17.7347	−1.74745	−0.873726	+	0.486419i	$0.838303\pi$
$104$	12.9253	1.26743
$105$	−3.08787	−0.301345
$106$	−3.19559	−0.310383
$107$	2.98071	0.288156	0.144078	−	0.989566i	$-0.453978\pi$
$107$	2.98071	0.288156	0.144078	+	0.989566i	$0.453978\pi$
$108$	−1.55450	−0.149582
$109$	10.0142	0.959189	0.479594	−	0.877490i	$-0.340784\pi$
$109$	10.0142	0.959189	0.479594	+	0.877490i	$0.340784\pi$
$110$	6.97163	0.664719
$111$	−2.44039	−0.231632
$112$	1.52548	0.144144
$113$	4.26465	0.401185	0.200592	−	0.979675i	$-0.435713\pi$
$113$	4.26465	0.401185	0.200592	+	0.979675i	$0.435713\pi$
$114$	1.61489	0.151248
$115$	−11.7841	−1.09887
$116$	4.26192	0.395709
$117$	5.44801	0.503669
$118$	4.79800	0.441691
$119$	3.25641	0.298514
$120$	−7.32590	−0.668760
$121$	0.442066	0.0401878
$122$	−7.76784	−0.703267
$123$	7.88451	0.710922
$124$	3.98795	0.358128
$125$	1.43602	0.128442
$126$	−0.667457	−0.0594618
$127$	−4.08207	−0.362225	−0.181112	−	0.983462i	$-0.557970\pi$
$127$	−4.08207	−0.362225	−0.181112	+	0.983462i	$0.557970\pi$
$128$	10.9952	0.971847
$129$	−5.47513	−0.482058
$130$	11.2285	0.984802
$131$	−5.40654	−0.472372	−0.236186	−	0.971708i	$-0.575897\pi$
$131$	−5.40654	−0.472372	−0.236186	+	0.971708i	$0.575897\pi$
$132$	−5.25828	−0.457674
$133$	−2.41947	−0.209794
$134$	4.08196	0.352627
$135$	−3.08787	−0.265762
$136$	7.72574	0.662477
$137$	3.15025	0.269144	0.134572	−	0.990904i	$-0.457034\pi$
$137$	3.15025	0.269144	0.134572	+	0.990904i	$0.457034\pi$
$138$	−2.54718	−0.216830
$139$	−0.517691	−0.0439100	−0.0219550	−	0.999759i	$-0.506989\pi$
$139$	−0.517691	−0.0439100	−0.0219550	+	0.999759i	$0.506989\pi$
$140$	4.80010	0.405683
$141$	−7.99578	−0.673366
$142$	−10.2954	−0.863967
$143$	18.4285	1.54107
$144$	1.52548	0.127123
$145$	8.46590	0.703054
$146$	0.402422	0.0333047
$147$	1.00000	0.0824786
$148$	3.79359	0.311831
$149$	−14.3198	−1.17312	−0.586562	−	0.809904i	$-0.699519\pi$
$149$	−14.3198	−1.17312	−0.586562	+	0.809904i	$0.699519\pi$
$150$	−3.02688	−0.247144
$151$	−4.69987	−0.382470	−0.191235	−	0.981544i	$-0.561249\pi$
$151$	−4.69987	−0.382470	−0.191235	+	0.981544i	$0.561249\pi$
$152$	−5.74012	−0.465585
$153$	3.25641	0.263265
$154$	−2.25775	−0.181934
$155$	7.92169	0.636285
$156$	−8.46894	−0.678058
$157$	13.9878	1.11635	0.558175	−	0.829724i	$-0.311502\pi$
$157$	13.9878	1.11635	0.558175	+	0.829724i	$0.311502\pi$
$158$	3.78394	0.301034
$159$	4.78771	0.379690
$160$	17.7958	1.40688
$161$	3.81625	0.300763
$162$	−0.667457	−0.0524404
$163$	9.64387	0.755366	0.377683	−	0.925935i	$-0.376721\pi$
$163$	9.64387	0.755366	0.377683	+	0.925935i	$0.376721\pi$
$164$	−12.2565	−0.957070
$165$	−10.4451	−0.813148
$166$	−3.07255	−0.238476
$167$	7.61005	0.588883	0.294442	−	0.955670i	$-0.404866\pi$
$167$	7.61005	0.588883	0.294442	+	0.955670i	$0.404866\pi$
$168$	2.37248	0.183040
$169$	16.6808	1.28314
$170$	6.71152	0.514750
$171$	−2.41947	−0.185021
$172$	8.51109	0.648965
$173$	11.3520	0.863079	0.431539	−	0.902094i	$-0.357971\pi$
$173$	11.3520	0.863079	0.431539	+	0.902094i	$0.357971\pi$
$174$	1.82994	0.138727
$175$	4.53495	0.342810
$176$	5.16010	0.388957
$177$	−7.18848	−0.540319
$178$	−0.102045	−0.00764857
$179$	−3.53608	−0.264299	−0.132150	−	0.991230i	$-0.542188\pi$
$179$	−3.53608	−0.264299	−0.132150	+	0.991230i	$0.542188\pi$
$180$	4.80010	0.357778
$181$	−5.12094	−0.380636	−0.190318	−	0.981722i	$-0.560952\pi$
$181$	−5.12094	−0.380636	−0.190318	+	0.981722i	$0.560952\pi$
$182$	−3.63631	−0.269541
$183$	11.6380	0.860304
$184$	9.05396	0.667467
$185$	7.53561	0.554029
$186$	1.71231	0.125552
$187$	11.0152	0.805508
$188$	12.4295	0.906511
$189$	1.00000	0.0727393
$190$	−4.98657	−0.361764
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	0.795692	0.0574241
$193$	9.36730	0.674273	0.337136	−	0.941456i	$-0.390542\pi$
$193$	9.36730	0.674273	0.337136	+	0.941456i	$0.390542\pi$
$194$	−3.18468	−0.228647
$195$	−16.8228	−1.20470
$196$	−1.55450	−0.111036
$197$	21.2008	1.51049	0.755247	−	0.655441i	$-0.227517\pi$
$197$	21.2008	1.51049	0.755247	+	0.655441i	$0.227517\pi$
$198$	−2.25775	−0.160451
$199$	−8.78524	−0.622769	−0.311385	−	0.950284i	$-0.600793\pi$
$199$	−8.78524	−0.622769	−0.311385	+	0.950284i	$0.600793\pi$
$200$	10.7591	0.760780
$201$	−6.11569	−0.431367
$202$	−9.71630	−0.683637
$203$	−2.74166	−0.192427
$204$	−5.06209	−0.354417
$205$	−24.3463	−1.70042
$206$	11.8371	0.824733
$207$	3.81625	0.265248
$208$	8.31082	0.576252
$209$	−8.18411	−0.566107
$210$	2.06102	0.142224
$211$	2.26025	0.155602	0.0778012	−	0.996969i	$-0.475210\pi$
$211$	2.26025	0.155602	0.0778012	+	0.996969i	$0.475210\pi$
$212$	−7.44251	−0.511154
$213$	15.4248	1.05689
$214$	−1.98949	−0.135999
$215$	16.9065	1.15301
$216$	2.37248	0.161427
$217$	−2.56542	−0.174152
$218$	−6.68406	−0.452702
$219$	−0.602919	−0.0407415
$220$	16.2369	1.09469
$221$	17.7409	1.19338
$222$	1.62885	0.109322
$223$	10.8614	0.727336	0.363668	−	0.931529i	$-0.381524\pi$
$223$	10.8614	0.727336	0.363668	+	0.931529i	$0.381524\pi$
$224$	−5.76314	−0.385066
$225$	4.53495	0.302330
$226$	−2.84647	−0.189344
$227$	15.5064	1.02919	0.514597	−	0.857432i	$-0.327942\pi$
$227$	15.5064	1.02919	0.514597	+	0.857432i	$0.327942\pi$
$228$	3.76106	0.249082
$229$	−10.2988	−0.680562	−0.340281	−	0.940324i	$-0.610522\pi$
$229$	−10.2988	−0.680562	−0.340281	+	0.940324i	$0.610522\pi$
$230$	7.86537	0.518627
$231$	3.38261	0.222560
$232$	−6.50453	−0.427043
$233$	−15.9728	−1.04641	−0.523206	−	0.852206i	$-0.675264\pi$
$233$	−15.9728	−1.04641	−0.523206	+	0.852206i	$0.675264\pi$
$234$	−3.63631	−0.237713
$235$	24.6899	1.61059
$236$	11.1745	0.727398
$237$	−5.66920	−0.368254
$238$	−2.17351	−0.140888
$239$	−9.28681	−0.600714	−0.300357	−	0.953827i	$-0.597106\pi$
$239$	−9.28681	−0.600714	−0.300357	+	0.953827i	$0.597106\pi$
$240$	−4.71048	−0.304060
$241$	28.5878	1.84150	0.920752	−	0.390149i	$-0.127577\pi$
$241$	28.5878	1.84150	0.920752	+	0.390149i	$0.127577\pi$
$242$	−0.295060	−0.0189672
$243$	1.00000	0.0641500
$244$	−18.0912	−1.15817
$245$	−3.08787	−0.197277
$246$	−5.26257	−0.335529
$247$	−13.1813	−0.838705
$248$	−6.08640	−0.386487
$249$	4.60337	0.291726
$250$	−0.958482	−0.0606197
$251$	−10.2397	−0.646322	−0.323161	−	0.946344i	$-0.604746\pi$
$251$	−10.2397	−0.646322	−0.323161	+	0.946344i	$0.604746\pi$
$252$	−1.55450	−0.0979244
$253$	12.9089	0.811575
$254$	2.72460	0.170957
$255$	−10.0554	−0.629691
$256$	−8.93020	−0.558138
$257$	23.6781	1.47700	0.738500	−	0.674254i	$-0.235535\pi$
$257$	23.6781	1.47700	0.738500	+	0.674254i	$0.235535\pi$
$258$	3.65441	0.227514
$259$	−2.44039	−0.151638
$260$	26.1510	1.62182
$261$	−2.74166	−0.169705
$262$	3.60863	0.222942
$263$	22.9556	1.41551	0.707753	−	0.706460i	$-0.249709\pi$
$263$	22.9556	1.41551	0.707753	+	0.706460i	$0.249709\pi$
$264$	8.02517	0.493915
$265$	−14.7838	−0.908164
$266$	1.61489	0.0990151
$267$	0.152886	0.00935645
$268$	9.50684	0.580723
$269$	27.0414	1.64874	0.824370	−	0.566051i	$-0.191529\pi$
$269$	27.0414	1.64874	0.824370	+	0.566051i	$0.191529\pi$
$270$	2.06102	0.125430
$271$	3.95819	0.240443	0.120222	−	0.992747i	$-0.461640\pi$
$271$	3.95819	0.240443	0.120222	+	0.992747i	$0.461640\pi$
$272$	4.96758	0.301204
$273$	5.44801	0.329729
$274$	−2.10266	−0.127026
$275$	15.3400	0.925035
$276$	−5.93236	−0.357086
$277$	1.44990	0.0871160	0.0435580	−	0.999051i	$-0.486131\pi$
$277$	1.44990	0.0871160	0.0435580	+	0.999051i	$0.486131\pi$
$278$	0.345537	0.0207239
$279$	−2.56542	−0.153588
$280$	−7.32590	−0.437806
$281$	−18.6067	−1.10998	−0.554991	−	0.831856i	$-0.687278\pi$
$281$	−18.6067	−1.10998	−0.554991	+	0.831856i	$0.687278\pi$
$282$	5.33684	0.317804
$283$	−28.3029	−1.68243	−0.841215	−	0.540701i	$-0.818159\pi$
$283$	−28.3029	−1.68243	−0.841215	+	0.540701i	$0.818159\pi$
$284$	−23.9778	−1.42282
$285$	7.47100	0.442544
$286$	−12.3002	−0.727328
$287$	7.88451	0.465408
$288$	−5.76314	−0.339596
$289$	−6.39582	−0.376225
$290$	−5.65062	−0.331816
$291$	4.77136	0.279702
$292$	0.937238	0.0548477
$293$	9.35124	0.546305	0.273153	−	0.961971i	$-0.411934\pi$
$293$	9.35124	0.546305	0.273153	+	0.961971i	$0.411934\pi$
$294$	−0.667457	−0.0389269
$295$	22.1971	1.29236
$296$	−5.78977	−0.336523
$297$	3.38261	0.196279
$298$	9.55785	0.553672
$299$	20.7910	1.20237
$300$	−7.04958	−0.407008
$301$	−5.47513	−0.315581
$302$	3.13696	0.180512
$303$	14.5572	0.836290
$304$	−3.69084	−0.211684
$305$	−35.9366	−2.05772
$306$	−2.17351	−0.124251
$307$	−0.546078	−0.0311663	−0.0155832	−	0.999879i	$-0.504960\pi$
$307$	−0.546078	−0.0311663	−0.0155832	+	0.999879i	$0.504960\pi$
$308$	−5.25828	−0.299618
$309$	−17.7347	−1.00889
$310$	−5.28738	−0.300303
$311$	11.3455	0.643343	0.321672	−	0.946851i	$-0.395755\pi$
$311$	11.3455	0.643343	0.321672	+	0.946851i	$0.395755\pi$
$312$	12.9253	0.731750
$313$	23.5566	1.33150	0.665749	−	0.746176i	$-0.268112\pi$
$313$	23.5566	1.33150	0.665749	+	0.746176i	$0.268112\pi$
$314$	−9.33626	−0.526876
$315$	−3.08787	−0.173982
$316$	8.81277	0.495757
$317$	−9.58214	−0.538186	−0.269093	−	0.963114i	$-0.586724\pi$
$317$	−9.58214	−0.538186	−0.269093	+	0.963114i	$0.586724\pi$
$318$	−3.19559	−0.179200
$319$	−9.27398	−0.519243
$320$	−2.45699	−0.137350
$321$	2.98071	0.166367
$322$	−2.54718	−0.141949
$323$	−7.87876	−0.438386
$324$	−1.55450	−0.0863612
$325$	24.7065	1.37047
$326$	−6.43687	−0.356505
$327$	10.0142	0.553788
$328$	18.7058	1.03286
$329$	−7.99578	−0.440822
$330$	6.97163	0.383776
$331$	−3.58708	−0.197164	−0.0985818	−	0.995129i	$-0.531431\pi$
$331$	−3.58708	−0.197164	−0.0985818	+	0.995129i	$0.531431\pi$
$332$	−7.15594	−0.392733
$333$	−2.44039	−0.133733
$334$	−5.07938	−0.277931
$335$	18.8845	1.03177
$336$	1.52548	0.0832216
$337$	−4.45757	−0.242819	−0.121410	−	0.992602i	$-0.538741\pi$
$337$	−4.45757	−0.242819	−0.121410	+	0.992602i	$0.538741\pi$
$338$	−11.1337	−0.605596
$339$	4.26465	0.231624
$340$	15.6311	0.847714
$341$	−8.67782	−0.469930
$342$	1.61489	0.0873232
$343$	1.00000	0.0539949
$344$	−12.9896	−0.700353
$345$	−11.7841	−0.634434
$346$	−7.57699	−0.407341
$347$	8.25148	0.442963	0.221481	−	0.975165i	$-0.428911\pi$
$347$	8.25148	0.442963	0.221481	+	0.975165i	$0.428911\pi$
$348$	4.26192	0.228463
$349$	−13.8205	−0.739793	−0.369896	−	0.929073i	$-0.620607\pi$
$349$	−13.8205	−0.739793	−0.369896	+	0.929073i	$0.620607\pi$
$350$	−3.02688	−0.161794
$351$	5.44801	0.290793
$352$	−19.4945	−1.03906
$353$	−8.82099	−0.469494	−0.234747	−	0.972057i	$-0.575426\pi$
$353$	−8.82099	−0.469494	−0.234747	+	0.972057i	$0.575426\pi$
$354$	4.79800	0.255011
$355$	−47.6297	−2.52792
$356$	−0.237661	−0.0125960
$357$	3.25641	0.172347
$358$	2.36018	0.124740
$359$	−19.4495	−1.02651	−0.513253	−	0.858238i	$-0.671560\pi$
$359$	−19.4495	−1.02651	−0.513253	+	0.858238i	$0.671560\pi$
$360$	−7.32590	−0.386109
$361$	−13.1462	−0.691905
$362$	3.41800	0.179646
$363$	0.442066	0.0232024
$364$	−8.46894	−0.443893
$365$	1.86174	0.0974477
$366$	−7.76784	−0.406032
$367$	0.638828	0.0333466	0.0166733	−	0.999861i	$-0.494692\pi$
$367$	0.638828	0.0333466	0.0166733	+	0.999861i	$0.494692\pi$
$368$	5.82160	0.303472
$369$	7.88451	0.410451
$370$	−5.02969	−0.261481
$371$	4.78771	0.248566
$372$	3.98795	0.206766
$373$	−10.5405	−0.545766	−0.272883	−	0.962047i	$-0.587977\pi$
$373$	−10.5405	−0.545766	−0.272883	+	0.962047i	$0.587977\pi$
$374$	−7.35214	−0.380170
$375$	1.43602	0.0741558
$376$	−18.9698	−0.978293
$377$	−14.9366	−0.769274
$378$	−0.667457	−0.0343303
$379$	5.64807	0.290122	0.145061	−	0.989423i	$-0.453662\pi$
$379$	5.64807	0.290122	0.145061	+	0.989423i	$0.453662\pi$
$380$	−11.6137	−0.595769
$381$	−4.08207	−0.209131
$382$	−0.667457	−0.0341501
$383$	−6.62269	−0.338404	−0.169202	−	0.985581i	$-0.554119\pi$
$383$	−6.62269	−0.338404	−0.169202	+	0.985581i	$0.554119\pi$
$384$	10.9952	0.561096
$385$	−10.4451	−0.532330
$386$	−6.25226	−0.318232
$387$	−5.47513	−0.278316
$388$	−7.41709	−0.376546
$389$	−12.8099	−0.649488	−0.324744	−	0.945802i	$-0.605278\pi$
$389$	−12.8099	−0.649488	−0.324744	+	0.945802i	$0.605278\pi$
$390$	11.2285	0.568575
$391$	12.4273	0.628473
$392$	2.37248	0.119828
$393$	−5.40654	−0.272724
$394$	−14.1506	−0.712897
$395$	17.5057	0.880810
$396$	−5.25828	−0.264238
$397$	−8.72778	−0.438035	−0.219017	−	0.975721i	$-0.570285\pi$
$397$	−8.72778	−0.438035	−0.219017	+	0.975721i	$0.570285\pi$
$398$	5.86377	0.293924
$399$	−2.41947	−0.121125
$400$	6.91796	0.345898
$401$	25.0406	1.25047	0.625234	−	0.780437i	$-0.285004\pi$
$401$	25.0406	1.25047	0.625234	+	0.780437i	$0.285004\pi$
$402$	4.08196	0.203589
$403$	−13.9764	−0.696216
$404$	−22.6292	−1.12584
$405$	−3.08787	−0.153438
$406$	1.82994	0.0908184
$407$	−8.25489	−0.409180
$408$	7.72574	0.382481
$409$	−5.72950	−0.283305	−0.141653	−	0.989916i	$-0.545242\pi$
$409$	−5.72950	−0.283305	−0.141653	+	0.989916i	$0.545242\pi$
$410$	16.2501	0.802537
$411$	3.15025	0.155390
$412$	27.5686	1.35821
$413$	−7.18848	−0.353722
$414$	−2.54718	−0.125187
$415$	−14.2146	−0.697767
$416$	−31.3977	−1.53940
$417$	−0.517691	−0.0253514
$418$	5.46254	0.267182
$419$	6.07304	0.296687	0.148344	−	0.988936i	$-0.452606\pi$
$419$	6.07304	0.296687	0.148344	+	0.988936i	$0.452606\pi$
$420$	4.80010	0.234221
$421$	8.67038	0.422568	0.211284	−	0.977425i	$-0.432235\pi$
$421$	8.67038	0.422568	0.211284	+	0.977425i	$0.432235\pi$
$422$	−1.50862	−0.0734386
$423$	−7.99578	−0.388768
$424$	11.3587	0.551629
$425$	14.7676	0.716335
$426$	−10.2954	−0.498812
$427$	11.6380	0.563201
$428$	−4.63351	−0.223969
$429$	18.4285	0.889737
$430$	−11.2843	−0.544180
$431$	−3.52565	−0.169824	−0.0849122	−	0.996388i	$-0.527061\pi$
$431$	−3.52565	−0.169824	−0.0849122	+	0.996388i	$0.527061\pi$
$432$	1.52548	0.0733946
$433$	−28.4726	−1.36831	−0.684153	−	0.729338i	$-0.739828\pi$
$433$	−28.4726	−1.36831	−0.684153	+	0.729338i	$0.739828\pi$
$434$	1.71231	0.0821934
$435$	8.46590	0.405909
$436$	−15.5671	−0.745530
$437$	−9.23328	−0.441688
$438$	0.402422	0.0192285
$439$	−21.7932	−1.04013	−0.520066	−	0.854126i	$-0.674093\pi$
$439$	−21.7932	−1.04013	−0.520066	+	0.854126i	$0.674093\pi$
$440$	−24.7807	−1.18137
$441$	1.00000	0.0476190
$442$	−11.8413	−0.563234
$443$	−28.8685	−1.37159	−0.685793	−	0.727797i	$-0.740544\pi$
$443$	−28.8685	−1.37159	−0.685793	+	0.727797i	$0.740544\pi$
$444$	3.79359	0.180036
$445$	−0.472091	−0.0223793
$446$	−7.24955	−0.343276
$447$	−14.3198	−0.677304
$448$	0.795692	0.0375929
$449$	3.56074	0.168042	0.0840208	−	0.996464i	$-0.473224\pi$
$449$	3.56074	0.168042	0.0840208	+	0.996464i	$0.473224\pi$
$450$	−3.02688	−0.142689
$451$	26.6702	1.25585
$452$	−6.62941	−0.311821
$453$	−4.69987	−0.220819
$454$	−10.3498	−0.485742
$455$	−16.8228	−0.788663
$456$	−5.74012	−0.268806
$457$	21.6075	1.01076	0.505378	−	0.862898i	$-0.331353\pi$
$457$	21.6075	1.01076	0.505378	+	0.862898i	$0.331353\pi$
$458$	6.87399	0.321200
$459$	3.25641	0.151996
$460$	18.3184	0.854099
$461$	21.4463	0.998854	0.499427	−	0.866356i	$-0.333544\pi$
$461$	21.4463	0.998854	0.499427	+	0.866356i	$0.333544\pi$
$462$	−2.25775	−0.105040
$463$	−16.2899	−0.757057	−0.378529	−	0.925590i	$-0.623570\pi$
$463$	−16.2899	−0.757057	−0.378529	+	0.925590i	$0.623570\pi$
$464$	−4.18234	−0.194160
$465$	7.92169	0.367359
$466$	10.6611	0.493868
$467$	20.1213	0.931105	0.465552	−	0.885020i	$-0.345856\pi$
$467$	20.1213	0.931105	0.465552	+	0.885020i	$0.345856\pi$
$468$	−8.46894	−0.391477
$469$	−6.11569	−0.282396
$470$	−16.4795	−0.760141
$471$	13.9878	0.644524
$472$	−17.0545	−0.784996
$473$	−18.5202	−0.851561
$474$	3.78394	0.173802
$475$	−10.9721	−0.503437
$476$	−5.06209	−0.232020
$477$	4.78771	0.219214
$478$	6.19855	0.283515
$479$	−6.59382	−0.301279	−0.150640	−	0.988589i	$-0.548133\pi$
$479$	−6.59382	−0.301279	−0.150640	+	0.988589i	$0.548133\pi$
$480$	17.7958	0.812265
$481$	−13.2953	−0.606212
$482$	−19.0811	−0.869122
$483$	3.81625	0.173645
$484$	−0.687192	−0.0312360
$485$	−14.7334	−0.669007
$486$	−0.667457	−0.0302765
$487$	40.4016	1.83077	0.915385	−	0.402578i	$-0.131886\pi$
$487$	40.4016	1.83077	0.915385	+	0.402578i	$0.131886\pi$
$488$	27.6108	1.24988
$489$	9.64387	0.436111
$490$	2.06102	0.0931074
$491$	6.34604	0.286393	0.143196	−	0.989694i	$-0.454262\pi$
$491$	6.34604	0.286393	0.143196	+	0.989694i	$0.454262\pi$
$492$	−12.2565	−0.552565
$493$	−8.92796	−0.402095
$494$	8.79793	0.395838
$495$	−10.4451	−0.469471
$496$	−3.91349	−0.175721
$497$	15.4248	0.691895
$498$	−3.07255	−0.137684
$499$	10.8364	0.485102	0.242551	−	0.970139i	$-0.422016\pi$
$499$	10.8364	0.485102	0.242551	+	0.970139i	$0.422016\pi$
$500$	−2.23230	−0.0998313
$501$	7.61005	0.339992
$502$	6.83454	0.305040
$503$	32.9473	1.46905	0.734523	−	0.678584i	$-0.237406\pi$
$503$	32.9473	1.46905	0.734523	+	0.678584i	$0.237406\pi$
$504$	2.37248	0.105678
$505$	−44.9508	−2.00028
$506$	−8.61613	−0.383034
$507$	16.6808	0.740822
$508$	6.34558	0.281540
$509$	23.6706	1.04918	0.524590	−	0.851355i	$-0.324219\pi$
$509$	23.6706	1.04918	0.524590	+	0.851355i	$0.324219\pi$
$510$	6.71152	0.297191
$511$	−0.602919	−0.0266716
$512$	−16.0299	−0.708427
$513$	−2.41947	−0.106822
$514$	−15.8041	−0.697089
$515$	54.7624	2.41312
$516$	8.51109	0.374680
$517$	−27.0466	−1.18951
$518$	1.62885	0.0715678
$519$	11.3520	0.498299
$520$	−39.9116	−1.75024
$521$	−11.0945	−0.486061	−0.243030	−	0.970019i	$-0.578141\pi$
$521$	−11.0945	−0.486061	−0.243030	+	0.970019i	$0.578141\pi$
$522$	1.82994	0.0800943
$523$	22.1200	0.967238	0.483619	−	0.875279i	$-0.339322\pi$
$523$	22.1200	0.967238	0.483619	+	0.875279i	$0.339322\pi$
$524$	8.40448	0.367151
$525$	4.53495	0.197921
$526$	−15.3219	−0.668067
$527$	−8.35405	−0.363908
$528$	5.16010	0.224565
$529$	−8.43624	−0.366793
$530$	9.86758	0.428620
$531$	−7.18848	−0.311953
$532$	3.76106	0.163063
$533$	42.9549	1.86058
$534$	−0.102045	−0.00441590
$535$	−9.20404	−0.397925
$536$	−14.5093	−0.626707
$537$	−3.53608	−0.152593
$538$	−18.0489	−0.778145
$539$	3.38261	0.145699
$540$	4.80010	0.206563
$541$	19.2252	0.826554	0.413277	−	0.910605i	$-0.364384\pi$
$541$	19.2252	0.826554	0.413277	+	0.910605i	$0.364384\pi$
$542$	−2.64192	−0.113480
$543$	−5.12094	−0.219760
$544$	−18.7671	−0.804634
$545$	−30.9226	−1.32458
$546$	−3.63631	−0.155620
$547$	−2.34687	−0.100345	−0.0501725	−	0.998741i	$-0.515977\pi$
$547$	−2.34687	−0.100345	−0.0501725	+	0.998741i	$0.515977\pi$
$548$	−4.89707	−0.209192
$549$	11.6380	0.496697
$550$	−10.2388	−0.436582
$551$	6.63335	0.282590
$552$	9.05396	0.385362
$553$	−5.66920	−0.241079
$554$	−0.967745	−0.0411156
$555$	7.53561	0.319869
$556$	0.804752	0.0341291
$557$	10.0338	0.425147	0.212573	−	0.977145i	$-0.431816\pi$
$557$	10.0338	0.425147	0.212573	+	0.977145i	$0.431816\pi$
$558$	1.71231	0.0724877
$559$	−29.8286	−1.26161
$560$	−4.71048	−0.199054
$561$	11.0152	0.465060
$562$	12.4192	0.523871
$563$	23.3001	0.981983	0.490992	−	0.871164i	$-0.336635\pi$
$563$	23.3001	0.981983	0.490992	+	0.871164i	$0.336635\pi$
$564$	12.4295	0.523374
$565$	−13.1687	−0.554011
$566$	18.8909	0.794045
$567$	1.00000	0.0419961
$568$	36.5949	1.53549
$569$	13.8704	0.581477	0.290738	−	0.956803i	$-0.406099\pi$
$569$	13.8704	0.581477	0.290738	+	0.956803i	$0.406099\pi$
$570$	−4.98657	−0.208864
$571$	−3.38015	−0.141455	−0.0707275	−	0.997496i	$-0.522532\pi$
$571$	−3.38015	−0.141455	−0.0707275	+	0.997496i	$0.522532\pi$
$572$	−28.6472	−1.19780
$573$	1.00000	0.0417756
$574$	−5.26257	−0.219655
$575$	17.3065	0.721731
$576$	0.795692	0.0331538
$577$	1.31753	0.0548496	0.0274248	−	0.999624i	$-0.491269\pi$
$577$	1.31753	0.0548496	0.0274248	+	0.999624i	$0.491269\pi$
$578$	4.26893	0.177564
$579$	9.36730	0.389292
$580$	−13.1602	−0.546450
$581$	4.60337	0.190980
$582$	−3.18468	−0.132009
$583$	16.1950	0.670728
$584$	−1.43041	−0.0591908
$585$	−16.8228	−0.695536
$586$	−6.24155	−0.257836
$587$	19.2731	0.795487	0.397744	−	0.917497i	$-0.369793\pi$
$587$	19.2731	0.795487	0.397744	+	0.917497i	$0.369793\pi$
$588$	−1.55450	−0.0641066
$589$	6.20694	0.255753
$590$	−14.8156	−0.609948
$591$	21.2008	0.872084
$592$	−3.72276	−0.153005
$593$	17.8721	0.733920	0.366960	−	0.930237i	$-0.380399\pi$
$593$	17.8721	0.733920	0.366960	+	0.930237i	$0.380399\pi$
$594$	−2.25775	−0.0926365
$595$	−10.0554	−0.412230
$596$	22.2602	0.911812
$597$	−8.78524	−0.359556
$598$	−13.8771	−0.567476
$599$	14.1308	0.577370	0.288685	−	0.957424i	$-0.406782\pi$
$599$	14.1308	0.577370	0.288685	+	0.957424i	$0.406782\pi$
$600$	10.7591	0.439237
$601$	11.9782	0.488601	0.244301	−	0.969700i	$-0.421442\pi$
$601$	11.9782	0.488601	0.244301	+	0.969700i	$0.421442\pi$
$602$	3.65441	0.148943
$603$	−6.11569	−0.249050
$604$	7.30596	0.297275
$605$	−1.36504	−0.0554968
$606$	−9.71630	−0.394698
$607$	−20.7704	−0.843043	−0.421522	−	0.906818i	$-0.638504\pi$
$607$	−20.7704	−0.843043	−0.421522	+	0.906818i	$0.638504\pi$
$608$	13.9437	0.565493
$609$	−2.74166	−0.111098
$610$	23.9861	0.971169
$611$	−43.5611	−1.76229
$612$	−5.06209	−0.204623
$613$	11.9465	0.482514	0.241257	−	0.970461i	$-0.422440\pi$
$613$	11.9465	0.482514	0.241257	+	0.970461i	$0.422440\pi$
$614$	0.364484	0.0147094
$615$	−24.3463	−0.981739
$616$	8.02517	0.323343
$617$	−21.9687	−0.884425	−0.442213	−	0.896910i	$-0.645806\pi$
$617$	−21.9687	−0.884425	−0.442213	+	0.896910i	$0.645806\pi$
$618$	11.8371	0.476160
$619$	44.9141	1.80525	0.902625	−	0.430428i	$-0.141638\pi$
$619$	44.9141	1.80525	0.902625	+	0.430428i	$0.141638\pi$
$620$	−12.3143	−0.494553
$621$	3.81625	0.153141
$622$	−7.57262	−0.303634
$623$	0.152886	0.00612524
$624$	8.31082	0.332699
$625$	−27.1090	−1.08436
$626$	−15.7230	−0.628418
$627$	−8.18411	−0.326842
$628$	−21.7441	−0.867683
$629$	−7.94690	−0.316864
$630$	2.06102	0.0821130
$631$	2.72164	0.108347	0.0541734	−	0.998532i	$-0.482748\pi$
$631$	2.72164	0.108347	0.0541734	+	0.998532i	$0.482748\pi$
$632$	−13.4500	−0.535013
$633$	2.26025	0.0898370
$634$	6.39566	0.254004
$635$	12.6049	0.500210
$636$	−7.44251	−0.295115
$637$	5.44801	0.215858
$638$	6.18998	0.245064
$639$	15.4248	0.610194
$640$	−33.9517	−1.34206
$641$	−21.3447	−0.843067	−0.421533	−	0.906813i	$-0.638508\pi$
$641$	−21.3447	−0.843067	−0.421533	+	0.906813i	$0.638508\pi$
$642$	−1.98949	−0.0785190
$643$	−32.7446	−1.29132	−0.645660	−	0.763625i	$-0.723418\pi$
$643$	−32.7446	−1.29132	−0.645660	+	0.763625i	$0.723418\pi$
$644$	−5.93236	−0.233768
$645$	16.9065	0.665692
$646$	5.25873	0.206902
$647$	−25.0467	−0.984689	−0.492344	−	0.870401i	$-0.663860\pi$
$647$	−25.0467	−0.984689	−0.492344	+	0.870401i	$0.663860\pi$
$648$	2.37248	0.0931997
$649$	−24.3158	−0.954480
$650$	−16.4905	−0.646810
$651$	−2.56542	−0.100547
$652$	−14.9914	−0.587109
$653$	−21.0387	−0.823309	−0.411655	−	0.911340i	$-0.635049\pi$
$653$	−21.0387	−0.823309	−0.411655	+	0.911340i	$0.635049\pi$
$654$	−6.68406	−0.261368
$655$	16.6947	0.652316
$656$	12.0276	0.469600
$657$	−0.602919	−0.0235221
$658$	5.33684	0.208052
$659$	42.1066	1.64024	0.820121	−	0.572190i	$-0.193906\pi$
$659$	42.1066	1.64024	0.820121	+	0.572190i	$0.193906\pi$
$660$	16.2369	0.632020
$661$	−15.7775	−0.613672	−0.306836	−	0.951762i	$-0.599270\pi$
$661$	−15.7775	−0.613672	−0.306836	+	0.951762i	$0.599270\pi$
$662$	2.39422	0.0930540
$663$	17.7409	0.689001
$664$	10.9214	0.423832
$665$	7.47100	0.289713
$666$	1.62885	0.0631168
$667$	−10.4629	−0.405124
$668$	−11.8298	−0.457710
$669$	10.8614	0.419928
$670$	−12.6046	−0.486956
$671$	39.3667	1.51974
$672$	−5.76314	−0.222318
$673$	−28.9199	−1.11478	−0.557391	−	0.830250i	$-0.688197\pi$
$673$	−28.9199	−1.11478	−0.557391	+	0.830250i	$0.688197\pi$
$674$	2.97524	0.114602
$675$	4.53495	0.174550
$676$	−25.9304	−0.997323
$677$	44.9752	1.72854	0.864268	−	0.503031i	$-0.167782\pi$
$677$	44.9752	1.72854	0.864268	+	0.503031i	$0.167782\pi$
$678$	−2.84647	−0.109318
$679$	4.77136	0.183108
$680$	−23.8561	−0.914840
$681$	15.5064	0.594205
$682$	5.79207	0.221790
$683$	−41.4891	−1.58754	−0.793768	−	0.608220i	$-0.791884\pi$
$683$	−41.4891	−1.58754	−0.793768	+	0.608220i	$0.791884\pi$
$684$	3.76106	0.143808
$685$	−9.72757	−0.371671
$686$	−0.667457	−0.0254836
$687$	−10.2988	−0.392923
$688$	−8.35219	−0.318424
$689$	26.0835	0.993703
$690$	7.86537	0.299429
$691$	10.2203	0.388798	0.194399	−	0.980923i	$-0.437724\pi$
$691$	10.2203	0.388798	0.194399	+	0.980923i	$0.437724\pi$
$692$	−17.6467	−0.670828
$693$	3.38261	0.128495
$694$	−5.50751	−0.209062
$695$	1.59856	0.0606370
$696$	−6.50453	−0.246553
$697$	25.6752	0.972516
$698$	9.22457	0.349155
$699$	−15.9728	−0.604146
$700$	−7.04958	−0.266449
$701$	−0.664532	−0.0250990	−0.0125495	−	0.999921i	$-0.503995\pi$
$701$	−0.664532	−0.0250990	−0.0125495	+	0.999921i	$0.503995\pi$
$702$	−3.63631	−0.137244
$703$	5.90444	0.222690
$704$	2.69152	0.101440
$705$	24.6899	0.929877
$706$	5.88763	0.221584
$707$	14.5572	0.547480
$708$	11.1745	0.419963
$709$	32.1354	1.20687	0.603435	−	0.797412i	$-0.293798\pi$
$709$	32.1354	1.20687	0.603435	+	0.797412i	$0.293798\pi$
$710$	31.7907	1.19308
$711$	−5.66920	−0.212611
$712$	0.362718	0.0135934
$713$	−9.79028	−0.366649
$714$	−2.17351	−0.0813416
$715$	−56.9049	−2.12812
$716$	5.49685	0.205427
$717$	−9.28681	−0.346822
$718$	12.9817	0.484473
$719$	27.6666	1.03179	0.515895	−	0.856652i	$-0.327460\pi$
$719$	27.6666	1.03179	0.515895	+	0.856652i	$0.327460\pi$
$720$	−4.71048	−0.175549
$721$	−17.7347	−0.660474
$722$	8.77451	0.326554
$723$	28.5878	1.06319
$724$	7.96050	0.295850
$725$	−12.4333	−0.461761
$726$	−0.295060	−0.0109507
$727$	−4.97543	−0.184529	−0.0922643	−	0.995735i	$-0.529410\pi$
$727$	−4.97543	−0.184529	−0.0922643	+	0.995735i	$0.529410\pi$
$728$	12.9253	0.479043
$729$	1.00000	0.0370370
$730$	−1.24263	−0.0459917
$731$	−17.8292	−0.659438
$732$	−18.0912	−0.668672
$733$	31.6841	1.17028	0.585140	−	0.810932i	$-0.301040\pi$
$733$	31.6841	1.17028	0.585140	+	0.810932i	$0.301040\pi$
$734$	−0.426390	−0.0157384
$735$	−3.08787	−0.113898
$736$	−21.9936	−0.810694
$737$	−20.6870	−0.762015
$738$	−5.26257	−0.193718
$739$	−13.4057	−0.493138	−0.246569	−	0.969125i	$-0.579303\pi$
$739$	−13.4057	−0.493138	−0.246569	+	0.969125i	$0.579303\pi$
$740$	−11.7141	−0.430619
$741$	−13.1813	−0.484226
$742$	−3.19559	−0.117314
$743$	52.4454	1.92403	0.962017	−	0.272990i	$-0.0880126\pi$
$743$	52.4454	1.92403	0.962017	+	0.272990i	$0.0880126\pi$
$744$	−6.08640	−0.223138
$745$	44.2177	1.62001
$746$	7.03532	0.257581
$747$	4.60337	0.168428
$748$	−17.1231	−0.626082
$749$	2.98071	0.108913
$750$	−0.958482	−0.0349988
$751$	39.7434	1.45026	0.725129	−	0.688613i	$-0.241780\pi$
$751$	39.7434	1.45026	0.725129	+	0.688613i	$0.241780\pi$
$752$	−12.1974	−0.444793
$753$	−10.2397	−0.373154
$754$	9.96954	0.363069
$755$	14.5126	0.528168
$756$	−1.55450	−0.0565367
$757$	−34.7249	−1.26210	−0.631049	−	0.775743i	$-0.717375\pi$
$757$	−34.7249	−1.26210	−0.631049	+	0.775743i	$0.717375\pi$
$758$	−3.76984	−0.136927
$759$	12.9089	0.468563
$760$	17.7248	0.642945
$761$	−42.6721	−1.54686	−0.773430	−	0.633881i	$-0.781461\pi$
$761$	−42.6721	−1.54686	−0.773430	+	0.633881i	$0.781461\pi$
$762$	2.72460	0.0987020
$763$	10.0142	0.362539
$764$	−1.55450	−0.0562399
$765$	−10.0554	−0.363552
$766$	4.42036	0.159714
$767$	−39.1629	−1.41409
$768$	−8.93020	−0.322241
$769$	27.9809	1.00902	0.504509	−	0.863406i	$-0.331673\pi$
$769$	27.9809	1.00902	0.504509	+	0.863406i	$0.331673\pi$
$770$	6.97163	0.251240
$771$	23.6781	0.852746
$772$	−14.5615	−0.524079
$773$	24.4508	0.879433	0.439716	−	0.898137i	$-0.355079\pi$
$773$	24.4508	0.879433	0.439716	+	0.898137i	$0.355079\pi$
$774$	3.65441	0.131355
$775$	−11.6340	−0.417907
$776$	11.3199	0.406362
$777$	−2.44039	−0.0875485
$778$	8.55005	0.306534
$779$	−19.0763	−0.683479
$780$	26.1510	0.936356
$781$	52.1760	1.86700
$782$	−8.29466	−0.296616
$783$	−2.74166	−0.0979790
$784$	1.52548	0.0544814
$785$	−43.1926	−1.54161
$786$	3.60863	0.128716
$787$	−0.895713	−0.0319287	−0.0159644	−	0.999873i	$-0.505082\pi$
$787$	−0.895713	−0.0319287	−0.0159644	+	0.999873i	$0.505082\pi$
$788$	−32.9567	−1.17403
$789$	22.9556	0.817243
$790$	−11.6843	−0.415710
$791$	4.26465	0.151634
$792$	8.02517	0.285162
$793$	63.4038	2.25154
$794$	5.82542	0.206736
$795$	−14.7838	−0.524329
$796$	13.6567	0.484048
$797$	41.4695	1.46893	0.734463	−	0.678649i	$-0.237434\pi$
$797$	41.4695	1.46893	0.734463	+	0.678649i	$0.237434\pi$
$798$	1.61489	0.0571664
$799$	−26.0375	−0.921141
$800$	−26.1356	−0.924031
$801$	0.152886	0.00540195
$802$	−16.7135	−0.590175
$803$	−2.03944	−0.0719703
$804$	9.50684	0.335281
$805$	−11.7841	−0.415334
$806$	9.32867	0.328588
$807$	27.0414	0.951901
$808$	34.5366	1.21499
$809$	34.5365	1.21424	0.607120	−	0.794610i	$-0.292325\pi$
$809$	34.5365	1.21424	0.607120	+	0.794610i	$0.292325\pi$
$810$	2.06102	0.0724169
$811$	−53.1637	−1.86683	−0.933414	−	0.358801i	$-0.883186\pi$
$811$	−53.1637	−1.86683	−0.933414	+	0.358801i	$0.883186\pi$
$812$	4.26192	0.149564
$813$	3.95819	0.138820
$814$	5.50978	0.193118
$815$	−29.7790	−1.04311
$816$	4.96758	0.173900
$817$	13.2469	0.463450
$818$	3.82419	0.133710
$819$	5.44801	0.190369
$820$	37.8464	1.32165
$821$	−15.2289	−0.531491	−0.265745	−	0.964043i	$-0.585618\pi$
$821$	−15.2289	−0.531491	−0.265745	+	0.964043i	$0.585618\pi$
$822$	−2.10266	−0.0733385
$823$	51.5387	1.79653	0.898264	−	0.439457i	$-0.144829\pi$
$823$	51.5387	1.79653	0.898264	+	0.439457i	$0.144829\pi$
$824$	−42.0751	−1.46576
$825$	15.3400	0.534069
$826$	4.79800	0.166944
$827$	7.11862	0.247539	0.123769	−	0.992311i	$-0.460502\pi$
$827$	7.11862	0.247539	0.123769	+	0.992311i	$0.460502\pi$
$828$	−5.93236	−0.206164
$829$	1.66078	0.0576813	0.0288406	−	0.999584i	$-0.490818\pi$
$829$	1.66078	0.0576813	0.0288406	+	0.999584i	$0.490818\pi$
$830$	9.48763	0.329320
$831$	1.44990	0.0502965
$832$	4.33494	0.150287
$833$	3.25641	0.112828
$834$	0.345537	0.0119650
$835$	−23.4988	−0.813211
$836$	12.7222	0.440007
$837$	−2.56542	−0.0886739
$838$	−4.05349	−0.140026
$839$	−2.24558	−0.0775260	−0.0387630	−	0.999248i	$-0.512342\pi$
$839$	−2.24558	−0.0775260	−0.0387630	+	0.999248i	$0.512342\pi$
$840$	−7.32590	−0.252768
$841$	−21.4833	−0.740803
$842$	−5.78710	−0.199437
$843$	−18.6067	−0.640849
$844$	−3.51357	−0.120942
$845$	−51.5083	−1.77194
$846$	5.33684	0.183484
$847$	0.442066	0.0151896
$848$	7.30355	0.250805
$849$	−28.3029	−0.971352
$850$	−9.85675	−0.338084
$851$	−9.31313	−0.319250
$852$	−23.9778	−0.821466
$853$	52.9448	1.81280	0.906398	−	0.422425i	$-0.138821\pi$
$853$	52.9448	1.81280	0.906398	+	0.422425i	$0.138821\pi$
$854$	−7.76784	−0.265810
$855$	7.47100	0.255503
$856$	7.07166	0.241704
$857$	−32.5834	−1.11303	−0.556514	−	0.830838i	$-0.687861\pi$
$857$	−32.5834	−1.11303	−0.556514	+	0.830838i	$0.687861\pi$
$858$	−12.3002	−0.419923
$859$	−40.1398	−1.36955	−0.684776	−	0.728754i	$-0.740100\pi$
$859$	−40.1398	−1.36955	−0.684776	+	0.728754i	$0.740100\pi$
$860$	−26.2812	−0.896180
$861$	7.88451	0.268703
$862$	2.35322	0.0801509
$863$	−2.78104	−0.0946679	−0.0473339	−	0.998879i	$-0.515072\pi$
$863$	−2.78104	−0.0946679	−0.0473339	+	0.998879i	$0.515072\pi$
$864$	−5.76314	−0.196066
$865$	−35.0536	−1.19186
$866$	19.0042	0.645790
$867$	−6.39582	−0.217213
$868$	3.98795	0.135360
$869$	−19.1767	−0.650525
$870$	−5.65062	−0.191574
$871$	−33.3183	−1.12895
$872$	23.7585	0.804565
$873$	4.77136	0.161486
$874$	6.16282	0.208460
$875$	1.43602	0.0485464
$876$	0.937238	0.0316663
$877$	−11.7384	−0.396378	−0.198189	−	0.980164i	$-0.563506\pi$
$877$	−11.7384	−0.396378	−0.198189	+	0.980164i	$0.563506\pi$
$878$	14.5460	0.490904
$879$	9.35124	0.315409
$880$	−15.9337	−0.537126
$881$	−44.2002	−1.48914	−0.744571	−	0.667543i	$-0.767346\pi$
$881$	−44.2002	−1.48914	−0.744571	+	0.667543i	$0.767346\pi$
$882$	−0.667457	−0.0224744
$883$	−58.0283	−1.95281	−0.976404	−	0.215951i	$-0.930715\pi$
$883$	−58.0283	−1.95281	−0.976404	+	0.215951i	$0.930715\pi$
$884$	−27.5783	−0.927559
$885$	22.1971	0.746147
$886$	19.2685	0.647338
$887$	−42.0717	−1.41263	−0.706314	−	0.707899i	$-0.749643\pi$
$887$	−42.0717	−1.41263	−0.706314	+	0.707899i	$0.749643\pi$
$888$	−5.78977	−0.194292
$889$	−4.08207	−0.136908
$890$	0.315101	0.0105622
$891$	3.38261	0.113322
$892$	−16.8841	−0.565323
$893$	19.3455	0.647373
$894$	9.55785	0.319662
$895$	10.9190	0.364981
$896$	10.9952	0.367324
$897$	20.7910	0.694190
$898$	−2.37664	−0.0793095
$899$	7.03351	0.234581
$900$	−7.04958	−0.234986
$901$	15.5907	0.519403
$902$	−17.8012	−0.592716
$903$	−5.47513	−0.182201
$904$	10.1178	0.336512
$905$	15.8128	0.525635
$906$	3.13696	0.104219
$907$	44.1502	1.46598	0.732992	−	0.680237i	$-0.238123\pi$
$907$	44.1502	1.46598	0.732992	+	0.680237i	$0.238123\pi$
$908$	−24.1047	−0.799942
$909$	14.5572	0.482832
$910$	11.2285	0.372220
$911$	49.6877	1.64623	0.823113	−	0.567878i	$-0.192235\pi$
$911$	49.6877	1.64623	0.823113	+	0.567878i	$0.192235\pi$
$912$	−3.69084	−0.122216
$913$	15.5714	0.515338
$914$	−14.4221	−0.477040
$915$	−35.9366	−1.18803
$916$	16.0095	0.528967
$917$	−5.40654	−0.178540
$918$	−2.17351	−0.0717365
$919$	26.5819	0.876856	0.438428	−	0.898766i	$-0.355535\pi$
$919$	26.5819	0.876856	0.438428	+	0.898766i	$0.355535\pi$
$920$	−27.9575	−0.921730
$921$	−0.546078	−0.0179939
$922$	−14.3145	−0.471422
$923$	84.0343	2.76602
$924$	−5.25828	−0.172985
$925$	−11.0670	−0.363882
$926$	10.8728	0.357303
$927$	−17.7347	−0.582484
$928$	15.8006	0.518680
$929$	−52.1297	−1.71032	−0.855160	−	0.518365i	$-0.826541\pi$
$929$	−52.1297	−1.71032	−0.855160	+	0.518365i	$0.826541\pi$
$930$	−5.28738	−0.173380
$931$	−2.41947	−0.0792948
$932$	24.8297	0.813324
$933$	11.3455	0.371434
$934$	−13.4301	−0.439447
$935$	−34.0134	−1.11236
$936$	12.9253	0.422476
$937$	−36.5170	−1.19296	−0.596479	−	0.802629i	$-0.703434\pi$
$937$	−36.5170	−1.19296	−0.596479	+	0.802629i	$0.703434\pi$
$938$	4.08196	0.133281
$939$	23.5566	0.768740
$940$	−38.3805	−1.25184
$941$	−38.4973	−1.25498	−0.627488	−	0.778626i	$-0.715917\pi$
$941$	−38.4973	−1.25498	−0.627488	+	0.778626i	$0.715917\pi$
$942$	−9.33626	−0.304192
$943$	30.0892	0.979840
$944$	−10.9659	−0.356908
$945$	−3.08787	−0.100448
$946$	12.3615	0.401906
$947$	48.1836	1.56576	0.782879	−	0.622174i	$-0.213751\pi$
$947$	48.1836	1.56576	0.782879	+	0.622174i	$0.213751\pi$
$948$	8.81277	0.286226
$949$	−3.28471	−0.106626
$950$	7.32343	0.237604
$951$	−9.58214	−0.310722
$952$	7.72574	0.250393
$953$	−31.7010	−1.02690	−0.513448	−	0.858121i	$-0.671632\pi$
$953$	−31.7010	−1.02690	−0.513448	+	0.858121i	$0.671632\pi$
$954$	−3.19559	−0.103461
$955$	−3.08787	−0.0999212
$956$	14.4364	0.466905
$957$	−9.27398	−0.299785
$958$	4.40109	0.142193
$959$	3.15025	0.101727
$960$	−2.45699	−0.0792992
$961$	−24.4186	−0.787697
$962$	8.87402	0.286110
$963$	2.98071	0.0960519
$964$	−44.4398	−1.43131
$965$	−28.9250	−0.931129
$966$	−2.54718	−0.0819542
$967$	18.0366	0.580019	0.290009	−	0.957024i	$-0.406342\pi$
$967$	18.0366	0.580019	0.290009	+	0.957024i	$0.406342\pi$
$968$	1.04879	0.0337094
$969$	−7.87876	−0.253102
$970$	9.83388	0.315747
$971$	22.3712	0.717925	0.358963	−	0.933352i	$-0.383131\pi$
$971$	22.3712	0.717925	0.358963	+	0.933352i	$0.383131\pi$
$972$	−1.55450	−0.0498607
$973$	−0.517691	−0.0165964
$974$	−26.9663	−0.864056
$975$	24.7065	0.791240
$976$	17.7535	0.568275
$977$	16.6502	0.532688	0.266344	−	0.963878i	$-0.414184\pi$
$977$	16.6502	0.532688	0.266344	+	0.963878i	$0.414184\pi$
$978$	−6.43687	−0.205828
$979$	0.517153	0.0165283
$980$	4.80010	0.153334
$981$	10.0142	0.319730
$982$	−4.23571	−0.135167
$983$	11.1289	0.354958	0.177479	−	0.984125i	$-0.443206\pi$
$983$	11.1289	0.354958	0.177479	+	0.984125i	$0.443206\pi$
$984$	18.7058	0.596319
$985$	−65.4653	−2.08590
$986$	5.95903	0.189774
$987$	−7.99578	−0.254509
$988$	20.4903	0.651884
$989$	−20.8945	−0.664405
$990$	6.97163	0.221573
$991$	−29.1450	−0.925822	−0.462911	−	0.886405i	$-0.653195\pi$
$991$	−29.1450	−0.925822	−0.462911	+	0.886405i	$0.653195\pi$
$992$	14.7849	0.469420
$993$	−3.58708	−0.113832
$994$	−10.2954	−0.326549
$995$	27.1277	0.860006
$996$	−7.15594	−0.226745
$997$	38.2625	1.21179	0.605893	−	0.795546i	$-0.292816\pi$
$997$	38.2625	1.21179	0.605893	+	0.795546i	$0.292816\pi$
$998$	−7.23280	−0.228950
$999$	−2.44039	−0.0772105

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.10	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-0.667457 q^{2} +1.00000 q^{3} -1.55450 q^{4} -3.08787 q^{5} -0.667457 q^{6} +1.00000 q^{7} +2.37248 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.667457 q^{2} +1.00000 q^{3} -1.55450 q^{4} -3.08787 q^{5} -0.667457 q^{6} +1.00000 q^{7} +2.37248 q^{8} +1.00000 q^{9} +2.06102 q^{10} +3.38261 q^{11} -1.55450 q^{12} +5.44801 q^{13} -0.667457 q^{14} -3.08787 q^{15} +1.52548 q^{16} +3.25641 q^{17} -0.667457 q^{18} -2.41947 q^{19} +4.80010 q^{20} +1.00000 q^{21} -2.25775 q^{22} +3.81625 q^{23} +2.37248 q^{24} +4.53495 q^{25} -3.63631 q^{26} +1.00000 q^{27} -1.55450 q^{28} -2.74166 q^{29} +2.06102 q^{30} -2.56542 q^{31} -5.76314 q^{32} +3.38261 q^{33} -2.17351 q^{34} -3.08787 q^{35} -1.55450 q^{36} -2.44039 q^{37} +1.61489 q^{38} +5.44801 q^{39} -7.32590 q^{40} +7.88451 q^{41} -0.667457 q^{42} -5.47513 q^{43} -5.25828 q^{44} -3.08787 q^{45} -2.54718 q^{46} -7.99578 q^{47} +1.52548 q^{48} +1.00000 q^{49} -3.02688 q^{50} +3.25641 q^{51} -8.46894 q^{52} +4.78771 q^{53} -0.667457 q^{54} -10.4451 q^{55} +2.37248 q^{56} -2.41947 q^{57} +1.82994 q^{58} -7.18848 q^{59} +4.80010 q^{60} +11.6380 q^{61} +1.71231 q^{62} +1.00000 q^{63} +0.795692 q^{64} -16.8228 q^{65} -2.25775 q^{66} -6.11569 q^{67} -5.06209 q^{68} +3.81625 q^{69} +2.06102 q^{70} +15.4248 q^{71} +2.37248 q^{72} -0.602919 q^{73} +1.62885 q^{74} +4.53495 q^{75} +3.76106 q^{76} +3.38261 q^{77} -3.63631 q^{78} -5.66920 q^{79} -4.71048 q^{80} +1.00000 q^{81} -5.26257 q^{82} +4.60337 q^{83} -1.55450 q^{84} -10.0554 q^{85} +3.65441 q^{86} -2.74166 q^{87} +8.02517 q^{88} +0.152886 q^{89} +2.06102 q^{90} +5.44801 q^{91} -5.93236 q^{92} -2.56542 q^{93} +5.33684 q^{94} +7.47100 q^{95} -5.76314 q^{96} +4.77136 q^{97} -0.667457 q^{98} +3.38261 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 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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