LMFDB - Embedded newform 4011.2.a.k.1.14

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			1.14
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)

$f(q)$	$=$	$q+0.374739 q^{2} +1.00000 q^{3} -1.85957 q^{4} +2.21215 q^{5} +0.374739 q^{6} +1.00000 q^{7} -1.44633 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.374739 q^{2} +1.00000 q^{3} -1.85957 q^{4} +2.21215 q^{5} +0.374739 q^{6} +1.00000 q^{7} -1.44633 q^{8} +1.00000 q^{9} +0.828982 q^{10} -6.32950 q^{11} -1.85957 q^{12} +4.55904 q^{13} +0.374739 q^{14} +2.21215 q^{15} +3.17714 q^{16} +2.56328 q^{17} +0.374739 q^{18} +6.99721 q^{19} -4.11366 q^{20} +1.00000 q^{21} -2.37191 q^{22} +4.27336 q^{23} -1.44633 q^{24} -0.106373 q^{25} +1.70845 q^{26} +1.00000 q^{27} -1.85957 q^{28} -0.0635796 q^{29} +0.828982 q^{30} -5.00262 q^{31} +4.08327 q^{32} -6.32950 q^{33} +0.960563 q^{34} +2.21215 q^{35} -1.85957 q^{36} -8.85888 q^{37} +2.62213 q^{38} +4.55904 q^{39} -3.19951 q^{40} +2.72333 q^{41} +0.374739 q^{42} -7.61388 q^{43} +11.7701 q^{44} +2.21215 q^{45} +1.60139 q^{46} +5.03778 q^{47} +3.17714 q^{48} +1.00000 q^{49} -0.0398621 q^{50} +2.56328 q^{51} -8.47786 q^{52} +7.02614 q^{53} +0.374739 q^{54} -14.0018 q^{55} -1.44633 q^{56} +6.99721 q^{57} -0.0238258 q^{58} -7.34998 q^{59} -4.11366 q^{60} +11.5844 q^{61} -1.87468 q^{62} +1.00000 q^{63} -4.82412 q^{64} +10.0853 q^{65} -2.37191 q^{66} +13.5159 q^{67} -4.76660 q^{68} +4.27336 q^{69} +0.828982 q^{70} +5.05351 q^{71} -1.44633 q^{72} -10.5171 q^{73} -3.31977 q^{74} -0.106373 q^{75} -13.0118 q^{76} -6.32950 q^{77} +1.70845 q^{78} -2.58011 q^{79} +7.02833 q^{80} +1.00000 q^{81} +1.02054 q^{82} +12.4383 q^{83} -1.85957 q^{84} +5.67037 q^{85} -2.85322 q^{86} -0.0635796 q^{87} +9.15456 q^{88} +5.05842 q^{89} +0.828982 q^{90} +4.55904 q^{91} -7.94660 q^{92} -5.00262 q^{93} +1.88786 q^{94} +15.4789 q^{95} +4.08327 q^{96} +4.32905 q^{97} +0.374739 q^{98} -6.32950 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.374739	0.264981	0.132490	−	0.991184i	$-0.457703\pi$
$2$	0.374739	0.264981	0.132490	+	0.991184i	$0.457703\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.85957	−0.929785
$5$	2.21215	0.989306	0.494653	−	0.869091i	$-0.335295\pi$
$5$	2.21215	0.989306	0.494653	+	0.869091i	$0.335295\pi$
$6$	0.374739	0.152987
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.44633	−0.511356
$9$	1.00000	0.333333
$10$	0.828982	0.262147
$11$	−6.32950	−1.90842	−0.954208	−	0.299145i	$-0.903299\pi$
$11$	−6.32950	−1.90842	−0.954208	+	0.299145i	$0.903299\pi$
$12$	−1.85957	−0.536812
$13$	4.55904	1.26445	0.632226	−	0.774784i	$-0.282142\pi$
$13$	4.55904	1.26445	0.632226	+	0.774784i	$0.282142\pi$
$14$	0.374739	0.100153
$15$	2.21215	0.571176
$16$	3.17714	0.794286
$17$	2.56328	0.621687	0.310843	−	0.950461i	$-0.399388\pi$
$17$	2.56328	0.621687	0.310843	+	0.950461i	$0.399388\pi$
$18$	0.374739	0.0883269
$19$	6.99721	1.60527	0.802635	−	0.596471i	$-0.203431\pi$
$19$	6.99721	1.60527	0.802635	+	0.596471i	$0.203431\pi$
$20$	−4.11366	−0.919842
$21$	1.00000	0.218218
$22$	−2.37191	−0.505693
$23$	4.27336	0.891056	0.445528	−	0.895268i	$-0.353016\pi$
$23$	4.27336	0.891056	0.445528	+	0.895268i	$0.353016\pi$
$24$	−1.44633	−0.295232
$25$	−0.106373	−0.0212746
$26$	1.70845	0.335055
$27$	1.00000	0.192450
$28$	−1.85957	−0.351426
$29$	−0.0635796	−0.0118064	−0.00590322	−	0.999983i	$-0.501879\pi$
$29$	−0.0635796	−0.0118064	−0.00590322	+	0.999983i	$0.501879\pi$
$30$	0.828982	0.151351
$31$	−5.00262	−0.898497	−0.449248	−	0.893407i	$-0.648308\pi$
$31$	−5.00262	−0.898497	−0.449248	+	0.893407i	$0.648308\pi$
$32$	4.08327	0.721827
$33$	−6.32950	−1.10182
$34$	0.960563	0.164735
$35$	2.21215	0.373922
$36$	−1.85957	−0.309928
$37$	−8.85888	−1.45639	−0.728195	−	0.685370i	$-0.759641\pi$
$37$	−8.85888	−1.45639	−0.728195	+	0.685370i	$0.759641\pi$
$38$	2.62213	0.425366
$39$	4.55904	0.730031
$40$	−3.19951	−0.505887
$41$	2.72333	0.425313	0.212657	−	0.977127i	$-0.431788\pi$
$41$	2.72333	0.425313	0.212657	+	0.977127i	$0.431788\pi$
$42$	0.374739	0.0578236
$43$	−7.61388	−1.16111	−0.580553	−	0.814222i	$-0.697164\pi$
$43$	−7.61388	−1.16111	−0.580553	+	0.814222i	$0.697164\pi$
$44$	11.7701	1.77442
$45$	2.21215	0.329769
$46$	1.60139	0.236113
$47$	5.03778	0.734836	0.367418	−	0.930056i	$-0.380242\pi$
$47$	5.03778	0.734836	0.367418	+	0.930056i	$0.380242\pi$
$48$	3.17714	0.458581
$49$	1.00000	0.142857
$50$	−0.0398621	−0.00563736
$51$	2.56328	0.358931
$52$	−8.47786	−1.17567
$53$	7.02614	0.965114	0.482557	−	0.875864i	$-0.339708\pi$
$53$	7.02614	0.965114	0.482557	+	0.875864i	$0.339708\pi$
$54$	0.374739	0.0509956
$55$	−14.0018	−1.88801
$56$	−1.44633	−0.193274
$57$	6.99721	0.926803
$58$	−0.0238258	−0.00312848
$59$	−7.34998	−0.956885	−0.478443	−	0.878119i	$-0.658799\pi$
$59$	−7.34998	−0.956885	−0.478443	+	0.878119i	$0.658799\pi$
$60$	−4.11366	−0.531071
$61$	11.5844	1.48322	0.741612	−	0.670829i	$-0.234062\pi$
$61$	11.5844	1.48322	0.741612	+	0.670829i	$0.234062\pi$
$62$	−1.87468	−0.238084
$63$	1.00000	0.125988
$64$	−4.82412	−0.603015
$65$	10.0853	1.25093
$66$	−2.37191	−0.291962
$67$	13.5159	1.65123	0.825615	−	0.564234i	$-0.190828\pi$
$67$	13.5159	1.65123	0.825615	+	0.564234i	$0.190828\pi$
$68$	−4.76660	−0.578035
$69$	4.27336	0.514452
$70$	0.828982	0.0990823
$71$	5.05351	0.599741	0.299871	−	0.953980i	$-0.403057\pi$
$71$	5.05351	0.599741	0.299871	+	0.953980i	$0.403057\pi$
$72$	−1.44633	−0.170452
$73$	−10.5171	−1.23093	−0.615465	−	0.788164i	$-0.711032\pi$
$73$	−10.5171	−1.23093	−0.615465	+	0.788164i	$0.711032\pi$
$74$	−3.31977	−0.385916
$75$	−0.106373	−0.0122829
$76$	−13.0118	−1.49256
$77$	−6.32950	−0.721313
$78$	1.70845	0.193444
$79$	−2.58011	−0.290285	−0.145143	−	0.989411i	$-0.546364\pi$
$79$	−2.58011	−0.290285	−0.145143	+	0.989411i	$0.546364\pi$
$80$	7.02833	0.785791
$81$	1.00000	0.111111
$82$	1.02054	0.112700
$83$	12.4383	1.36529	0.682643	−	0.730752i	$-0.260830\pi$
$83$	12.4383	1.36529	0.682643	+	0.730752i	$0.260830\pi$
$84$	−1.85957	−0.202896
$85$	5.67037	0.615038
$86$	−2.85322	−0.307671
$87$	−0.0635796	−0.00681645
$88$	9.15456	0.975880
$89$	5.05842	0.536192	0.268096	−	0.963392i	$-0.413606\pi$
$89$	5.05842	0.536192	0.268096	+	0.963392i	$0.413606\pi$
$90$	0.828982	0.0873823
$91$	4.55904	0.477918
$92$	−7.94660	−0.828491
$93$	−5.00262	−0.518747
$94$	1.88786	0.194717
$95$	15.4789	1.58810
$96$	4.08327	0.416747
$97$	4.32905	0.439548	0.219774	−	0.975551i	$-0.429468\pi$
$97$	4.32905	0.439548	0.219774	+	0.975551i	$0.429468\pi$
$98$	0.374739	0.0378544
$99$	−6.32950	−0.636138
$100$	0.197808	0.0197808
$101$	7.69948	0.766126	0.383063	−	0.923722i	$-0.374869\pi$
$101$	7.69948	0.766126	0.383063	+	0.923722i	$0.374869\pi$
$102$	0.960563	0.0951099
$103$	1.63058	0.160666	0.0803328	−	0.996768i	$-0.474402\pi$
$103$	1.63058	0.160666	0.0803328	+	0.996768i	$0.474402\pi$
$104$	−6.59390	−0.646585
$105$	2.21215	0.215884
$106$	2.63297	0.255737
$107$	11.3241	1.09474	0.547372	−	0.836889i	$-0.315628\pi$
$107$	11.3241	1.09474	0.547372	+	0.836889i	$0.315628\pi$
$108$	−1.85957	−0.178937
$109$	8.15072	0.780698	0.390349	−	0.920667i	$-0.372354\pi$
$109$	8.15072	0.780698	0.390349	+	0.920667i	$0.372354\pi$
$110$	−5.24704	−0.500285
$111$	−8.85888	−0.840847
$112$	3.17714	0.300212
$113$	−8.47599	−0.797354	−0.398677	−	0.917091i	$-0.630530\pi$
$113$	−8.47599	−0.797354	−0.398677	+	0.917091i	$0.630530\pi$
$114$	2.62213	0.245585
$115$	9.45332	0.881527
$116$	0.118231	0.0109775
$117$	4.55904	0.421484
$118$	−2.75433	−0.253556
$119$	2.56328	0.234976
$120$	−3.19951	−0.292074
$121$	29.0625	2.64205
$122$	4.34111	0.393026
$123$	2.72333	0.245555
$124$	9.30272	0.835409
$125$	−11.2961	−1.01035
$126$	0.374739	0.0333844
$127$	8.44291	0.749187	0.374594	−	0.927189i	$-0.377782\pi$
$127$	8.44291	0.749187	0.374594	+	0.927189i	$0.377782\pi$
$128$	−9.97432	−0.881614
$129$	−7.61388	−0.670365
$130$	3.77936	0.331472
$131$	6.32258	0.552406	0.276203	−	0.961099i	$-0.410924\pi$
$131$	6.32258	0.552406	0.276203	+	0.961099i	$0.410924\pi$
$132$	11.7701	1.02446
$133$	6.99721	0.606735
$134$	5.06494	0.437544
$135$	2.21215	0.190392
$136$	−3.70736	−0.317903
$137$	15.7015	1.34147	0.670734	−	0.741698i	$-0.265979\pi$
$137$	15.7015	1.34147	0.670734	+	0.741698i	$0.265979\pi$
$138$	1.60139	0.136320
$139$	−12.5947	−1.06827	−0.534134	−	0.845400i	$-0.679362\pi$
$139$	−12.5947	−1.06827	−0.534134	+	0.845400i	$0.679362\pi$
$140$	−4.11366	−0.347667
$141$	5.03778	0.424258
$142$	1.89375	0.158920
$143$	−28.8565	−2.41310
$144$	3.17714	0.264762
$145$	−0.140648	−0.0116802
$146$	−3.94116	−0.326173
$147$	1.00000	0.0824786
$148$	16.4737	1.35413
$149$	6.65425	0.545137	0.272569	−	0.962136i	$-0.412127\pi$
$149$	6.65425	0.545137	0.272569	+	0.962136i	$0.412127\pi$
$150$	−0.0398621	−0.00325473
$151$	15.0194	1.22226	0.611131	−	0.791529i	$-0.290715\pi$
$151$	15.0194	1.22226	0.611131	+	0.791529i	$0.290715\pi$
$152$	−10.1203	−0.820864
$153$	2.56328	0.207229
$154$	−2.37191	−0.191134
$155$	−11.0666	−0.888888
$156$	−8.47786	−0.678772
$157$	−17.0038	−1.35705	−0.678525	−	0.734577i	$-0.737381\pi$
$157$	−17.0038	−1.35705	−0.678525	+	0.734577i	$0.737381\pi$
$158$	−0.966869	−0.0769200
$159$	7.02614	0.557209
$160$	9.03282	0.714107
$161$	4.27336	0.336788
$162$	0.374739	0.0294423
$163$	−17.2742	−1.35302	−0.676511	−	0.736432i	$-0.736509\pi$
$163$	−17.2742	−1.35302	−0.676511	+	0.736432i	$0.736509\pi$
$164$	−5.06423	−0.395450
$165$	−14.0018	−1.09004
$166$	4.66114	0.361775
$167$	12.6297	0.977318	0.488659	−	0.872475i	$-0.337486\pi$
$167$	12.6297	0.977318	0.488659	+	0.872475i	$0.337486\pi$
$168$	−1.44633	−0.111587
$169$	7.78489	0.598838
$170$	2.12491	0.162973
$171$	6.99721	0.535090
$172$	14.1586	1.07958
$173$	17.3937	1.32242	0.661210	−	0.750201i	$-0.270043\pi$
$173$	17.3937	1.32242	0.661210	+	0.750201i	$0.270043\pi$
$174$	−0.0238258	−0.00180623
$175$	−0.106373	−0.00804104
$176$	−20.1097	−1.51583
$177$	−7.34998	−0.552458
$178$	1.89559	0.142081
$179$	−11.8097	−0.882696	−0.441348	−	0.897336i	$-0.645500\pi$
$179$	−11.8097	−0.882696	−0.441348	+	0.897336i	$0.645500\pi$
$180$	−4.11366	−0.306614
$181$	0.820114	0.0609586	0.0304793	−	0.999535i	$-0.490297\pi$
$181$	0.820114	0.0609586	0.0304793	+	0.999535i	$0.490297\pi$
$182$	1.70845	0.126639
$183$	11.5844	0.856340
$184$	−6.18070	−0.455647
$185$	−19.5972	−1.44081
$186$	−1.87468	−0.137458
$187$	−16.2243	−1.18644
$188$	−9.36811	−0.683240
$189$	1.00000	0.0727393
$190$	5.80055	0.420816
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−4.82412	−0.348151
$193$	2.09572	0.150854	0.0754268	−	0.997151i	$-0.475968\pi$
$193$	2.09572	0.150854	0.0754268	+	0.997151i	$0.475968\pi$
$194$	1.62227	0.116472
$195$	10.0853	0.722224
$196$	−1.85957	−0.132826
$197$	−16.7066	−1.19029	−0.595146	−	0.803617i	$-0.702906\pi$
$197$	−16.7066	−1.19029	−0.595146	+	0.803617i	$0.702906\pi$
$198$	−2.37191	−0.168564
$199$	−8.86297	−0.628279	−0.314140	−	0.949377i	$-0.601716\pi$
$199$	−8.86297	−0.628279	−0.314140	+	0.949377i	$0.601716\pi$
$200$	0.153851	0.0108789
$201$	13.5159	0.953338
$202$	2.88530	0.203009
$203$	−0.0635796	−0.00446242
$204$	−4.76660	−0.333729
$205$	6.02443	0.420765
$206$	0.611042	0.0425733
$207$	4.27336	0.297019
$208$	14.4847	1.00434
$209$	−44.2888	−3.06352
$210$	0.828982	0.0572052
$211$	14.2019	0.977699	0.488849	−	0.872368i	$-0.337417\pi$
$211$	14.2019	0.977699	0.488849	+	0.872368i	$0.337417\pi$
$212$	−13.0656	−0.897349
$213$	5.05351	0.346261
$214$	4.24359	0.290086
$215$	−16.8431	−1.14869
$216$	−1.44633	−0.0984105
$217$	−5.00262	−0.339600
$218$	3.05440	0.206870
$219$	−10.5171	−0.710677
$220$	26.0374	1.75544
$221$	11.6861	0.786093
$222$	−3.31977	−0.222808
$223$	−14.2913	−0.957019	−0.478509	−	0.878082i	$-0.658823\pi$
$223$	−14.2913	−0.957019	−0.478509	+	0.878082i	$0.658823\pi$
$224$	4.08327	0.272825
$225$	−0.106373	−0.00709153
$226$	−3.17629	−0.211283
$227$	−1.31225	−0.0870972	−0.0435486	−	0.999051i	$-0.513866\pi$
$227$	−1.31225	−0.0870972	−0.0435486	+	0.999051i	$0.513866\pi$
$228$	−13.0118	−0.861727
$229$	−6.40781	−0.423440	−0.211720	−	0.977330i	$-0.567906\pi$
$229$	−6.40781	−0.423440	−0.211720	+	0.977330i	$0.567906\pi$
$230$	3.54253	0.233588
$231$	−6.32950	−0.416450
$232$	0.0919573	0.00603730
$233$	12.3995	0.812321	0.406161	−	0.913802i	$-0.366867\pi$
$233$	12.3995	0.812321	0.406161	+	0.913802i	$0.366867\pi$
$234$	1.70845	0.111685
$235$	11.1444	0.726977
$236$	13.6678	0.889698
$237$	−2.58011	−0.167596
$238$	0.960563	0.0622640
$239$	3.23944	0.209542	0.104771	−	0.994496i	$-0.466589\pi$
$239$	3.23944	0.209542	0.104771	+	0.994496i	$0.466589\pi$
$240$	7.02833	0.453677
$241$	10.4232	0.671416	0.335708	−	0.941966i	$-0.391025\pi$
$241$	10.4232	0.671416	0.335708	+	0.941966i	$0.391025\pi$
$242$	10.8909	0.700092
$243$	1.00000	0.0641500
$244$	−21.5419	−1.37908
$245$	2.21215	0.141329
$246$	1.02054	0.0650673
$247$	31.9006	2.02978
$248$	7.23545	0.459452
$249$	12.4383	0.788248
$250$	−4.23309	−0.267724
$251$	−25.6099	−1.61648	−0.808241	−	0.588852i	$-0.799580\pi$
$251$	−25.6099	−1.61648	−0.808241	+	0.588852i	$0.799580\pi$
$252$	−1.85957	−0.117142
$253$	−27.0482	−1.70051
$254$	3.16389	0.198520
$255$	5.67037	0.355093
$256$	5.91047	0.369405
$257$	10.2664	0.640398	0.320199	−	0.947350i	$-0.396250\pi$
$257$	10.2664	0.640398	0.320199	+	0.947350i	$0.396250\pi$
$258$	−2.85322	−0.177634
$259$	−8.85888	−0.550464
$260$	−18.7543	−1.16310
$261$	−0.0635796	−0.00393548
$262$	2.36932	0.146377
$263$	1.64960	0.101719	0.0508593	−	0.998706i	$-0.483804\pi$
$263$	1.64960	0.101719	0.0508593	+	0.998706i	$0.483804\pi$
$264$	9.15456	0.563424
$265$	15.5429	0.954793
$266$	2.62213	0.160773
$267$	5.05842	0.309571
$268$	−25.1338	−1.53529
$269$	21.2555	1.29597	0.647987	−	0.761652i	$-0.275611\pi$
$269$	21.2555	1.29597	0.647987	+	0.761652i	$0.275611\pi$
$270$	0.828982	0.0504502
$271$	−27.9876	−1.70013	−0.850063	−	0.526680i	$-0.823437\pi$
$271$	−27.9876	−1.70013	−0.850063	+	0.526680i	$0.823437\pi$
$272$	8.14391	0.493797
$273$	4.55904	0.275926
$274$	5.88396	0.355463
$275$	0.673287	0.0406007
$276$	−7.94660	−0.478329
$277$	−24.8728	−1.49446	−0.747231	−	0.664564i	$-0.768617\pi$
$277$	−24.8728	−1.49446	−0.747231	+	0.664564i	$0.768617\pi$
$278$	−4.71973	−0.283070
$279$	−5.00262	−0.299499
$280$	−3.19951	−0.191207
$281$	−0.0524246	−0.00312739	−0.00156370	−	0.999999i	$-0.500498\pi$
$281$	−0.0524246	−0.00312739	−0.00156370	+	0.999999i	$0.500498\pi$
$282$	1.88786	0.112420
$283$	15.2309	0.905382	0.452691	−	0.891667i	$-0.350464\pi$
$283$	15.2309	0.905382	0.452691	+	0.891667i	$0.350464\pi$
$284$	−9.39735	−0.557630
$285$	15.4789	0.916891
$286$	−10.8137	−0.639425
$287$	2.72333	0.160753
$288$	4.08327	0.240609
$289$	−10.4296	−0.613505
$290$	−0.0527063	−0.00309502
$291$	4.32905	0.253773
$292$	19.5572	1.14450
$293$	26.3296	1.53819	0.769097	−	0.639132i	$-0.220706\pi$
$293$	26.3296	1.53819	0.769097	+	0.639132i	$0.220706\pi$
$294$	0.374739	0.0218553
$295$	−16.2593	−0.946652
$296$	12.8129	0.744734
$297$	−6.32950	−0.367275
$298$	2.49361	0.144451
$299$	19.4824	1.12670
$300$	0.197808	0.0114204
$301$	−7.61388	−0.438857
$302$	5.62836	0.323876
$303$	7.69948	0.442323
$304$	22.2311	1.27504
$305$	25.6264	1.46736
$306$	0.960563	0.0549117
$307$	14.0095	0.799562	0.399781	−	0.916611i	$-0.369086\pi$
$307$	14.0095	0.799562	0.399781	+	0.916611i	$0.369086\pi$
$308$	11.7701	0.670666
$309$	1.63058	0.0927603
$310$	−4.14708	−0.235538
$311$	−31.6760	−1.79618	−0.898091	−	0.439809i	$-0.855046\pi$
$311$	−31.6760	−1.79618	−0.898091	+	0.439809i	$0.855046\pi$
$312$	−6.59390	−0.373306
$313$	−16.6443	−0.940789	−0.470395	−	0.882456i	$-0.655888\pi$
$313$	−16.6443	−0.940789	−0.470395	+	0.882456i	$0.655888\pi$
$314$	−6.37199	−0.359592
$315$	2.21215	0.124641
$316$	4.79790	0.269903
$317$	18.9319	1.06332	0.531661	−	0.846957i	$-0.321568\pi$
$317$	18.9319	1.06332	0.531661	+	0.846957i	$0.321568\pi$
$318$	2.63297	0.147650
$319$	0.402427	0.0225316
$320$	−10.6717	−0.596566
$321$	11.3241	0.632051
$322$	1.60139	0.0892422
$323$	17.9358	0.997975
$324$	−1.85957	−0.103309
$325$	−0.484959	−0.0269007
$326$	−6.47334	−0.358525
$327$	8.15072	0.450736
$328$	−3.93885	−0.217486
$329$	5.03778	0.277742
$330$	−5.24704	−0.288840
$331$	−15.3365	−0.842972	−0.421486	−	0.906835i	$-0.638491\pi$
$331$	−15.3365	−0.842972	−0.421486	+	0.906835i	$0.638491\pi$
$332$	−23.1300	−1.26942
$333$	−8.85888	−0.485463
$334$	4.73286	0.258971
$335$	29.8993	1.63357
$336$	3.17714	0.173327
$337$	7.12311	0.388021	0.194010	−	0.980999i	$-0.437850\pi$
$337$	7.12311	0.388021	0.194010	+	0.980999i	$0.437850\pi$
$338$	2.91730	0.158680
$339$	−8.47599	−0.460352
$340$	−10.5445	−0.571854
$341$	31.6641	1.71470
$342$	2.62213	0.141789
$343$	1.00000	0.0539949
$344$	11.0122	0.593739
$345$	9.45332	0.508950
$346$	6.51811	0.350416
$347$	−25.2988	−1.35811	−0.679055	−	0.734087i	$-0.737610\pi$
$347$	−25.2988	−1.35811	−0.679055	+	0.734087i	$0.737610\pi$
$348$	0.118231	0.00633784
$349$	12.7472	0.682340	0.341170	−	0.940002i	$-0.389177\pi$
$349$	12.7472	0.682340	0.341170	+	0.940002i	$0.389177\pi$
$350$	−0.0398621	−0.00213072
$351$	4.55904	0.243344
$352$	−25.8450	−1.37754
$353$	3.75985	0.200116	0.100058	−	0.994982i	$-0.468097\pi$
$353$	3.75985	0.200116	0.100058	+	0.994982i	$0.468097\pi$
$354$	−2.75433	−0.146391
$355$	11.1791	0.593327
$356$	−9.40650	−0.498543
$357$	2.56328	0.135663
$358$	−4.42555	−0.233897
$359$	−16.3196	−0.861315	−0.430658	−	0.902515i	$-0.641718\pi$
$359$	−16.3196	−0.861315	−0.430658	+	0.902515i	$0.641718\pi$
$360$	−3.19951	−0.168629
$361$	29.9609	1.57689
$362$	0.307329	0.0161529
$363$	29.0625	1.52539
$364$	−8.47786	−0.444361
$365$	−23.2654	−1.21777
$366$	4.34111	0.226914
$367$	−19.0109	−0.992359	−0.496179	−	0.868220i	$-0.665264\pi$
$367$	−19.0109	−0.992359	−0.496179	+	0.868220i	$0.665264\pi$
$368$	13.5771	0.707753
$369$	2.72333	0.141771
$370$	−7.34385	−0.381788
$371$	7.02614	0.364779
$372$	9.30272	0.482323
$373$	17.3981	0.900839	0.450420	−	0.892817i	$-0.351274\pi$
$373$	17.3981	0.900839	0.450420	+	0.892817i	$0.351274\pi$
$374$	−6.07988	−0.314383
$375$	−11.2961	−0.583327
$376$	−7.28631	−0.375763
$377$	−0.289862	−0.0149287
$378$	0.374739	0.0192745
$379$	4.78051	0.245558	0.122779	−	0.992434i	$-0.460819\pi$
$379$	4.78051	0.245558	0.122779	+	0.992434i	$0.460819\pi$
$380$	−28.7841	−1.47659
$381$	8.44291	0.432543
$382$	0.374739	0.0191733
$383$	−19.8744	−1.01553	−0.507767	−	0.861494i	$-0.669529\pi$
$383$	−19.8744	−1.01553	−0.507767	+	0.861494i	$0.669529\pi$
$384$	−9.97432	−0.509000
$385$	−14.0018	−0.713599
$386$	0.785351	0.0399733
$387$	−7.61388	−0.387035
$388$	−8.05017	−0.408686
$389$	31.2105	1.58243	0.791216	−	0.611536i	$-0.209448\pi$
$389$	31.2105	1.58243	0.791216	+	0.611536i	$0.209448\pi$
$390$	3.77936	0.191376
$391$	10.9538	0.553958
$392$	−1.44633	−0.0730509
$393$	6.32258	0.318932
$394$	−6.26061	−0.315405
$395$	−5.70760	−0.287181
$396$	11.7701	0.591472
$397$	−38.8357	−1.94911	−0.974555	−	0.224150i	$-0.928039\pi$
$397$	−38.8357	−1.94911	−0.974555	+	0.224150i	$0.928039\pi$
$398$	−3.32131	−0.166482
$399$	6.99721	0.350298
$400$	−0.337962	−0.0168981
$401$	2.86206	0.142924	0.0714622	−	0.997443i	$-0.477233\pi$
$401$	2.86206	0.142924	0.0714622	+	0.997443i	$0.477233\pi$
$402$	5.06494	0.252616
$403$	−22.8072	−1.13611
$404$	−14.3177	−0.712333
$405$	2.21215	0.109923
$406$	−0.0238258	−0.00118245
$407$	56.0722	2.77940
$408$	−3.70736	−0.183542
$409$	4.45987	0.220527	0.110263	−	0.993902i	$-0.464831\pi$
$409$	4.45987	0.220527	0.110263	+	0.993902i	$0.464831\pi$
$410$	2.25759	0.111495
$411$	15.7015	0.774497
$412$	−3.03217	−0.149384
$413$	−7.34998	−0.361669
$414$	1.60139	0.0787043
$415$	27.5155	1.35068
$416$	18.6158	0.912715
$417$	−12.5947	−0.616765
$418$	−16.5968	−0.811774
$419$	−5.05225	−0.246818	−0.123409	−	0.992356i	$-0.539383\pi$
$419$	−5.05225	−0.246818	−0.123409	+	0.992356i	$0.539383\pi$
$420$	−4.11366	−0.200726
$421$	6.74545	0.328753	0.164376	−	0.986398i	$-0.447439\pi$
$421$	6.74545	0.328753	0.164376	+	0.986398i	$0.447439\pi$
$422$	5.32201	0.259071
$423$	5.03778	0.244945
$424$	−10.1621	−0.493517
$425$	−0.272664	−0.0132261
$426$	1.89375	0.0917524
$427$	11.5844	0.560606
$428$	−21.0580	−1.01788
$429$	−28.8565	−1.39320
$430$	−6.31177	−0.304381
$431$	−20.5490	−0.989810	−0.494905	−	0.868947i	$-0.664797\pi$
$431$	−20.5490	−0.989810	−0.494905	+	0.868947i	$0.664797\pi$
$432$	3.17714	0.152860
$433$	16.3736	0.786867	0.393433	−	0.919353i	$-0.371287\pi$
$433$	16.3736	0.786867	0.393433	+	0.919353i	$0.371287\pi$
$434$	−1.87468	−0.0899874
$435$	−0.140648	−0.00674355
$436$	−15.1568	−0.725881
$437$	29.9015	1.43038
$438$	−3.94116	−0.188316
$439$	34.8782	1.66465	0.832323	−	0.554291i	$-0.187010\pi$
$439$	34.8782	1.66465	0.832323	+	0.554291i	$0.187010\pi$
$440$	20.2513	0.965443
$441$	1.00000	0.0476190
$442$	4.37925	0.208300
$443$	31.7842	1.51011	0.755056	−	0.655660i	$-0.227609\pi$
$443$	31.7842	1.51011	0.755056	+	0.655660i	$0.227609\pi$
$444$	16.4737	0.781807
$445$	11.1900	0.530458
$446$	−5.35553	−0.253592
$447$	6.65425	0.314735
$448$	−4.82412	−0.227918
$449$	24.7062	1.16596	0.582980	−	0.812487i	$-0.301887\pi$
$449$	24.7062	1.16596	0.582980	+	0.812487i	$0.301887\pi$
$450$	−0.0398621	−0.00187912
$451$	−17.2373	−0.811674
$452$	15.7617	0.741368
$453$	15.0194	0.705673
$454$	−0.491753	−0.0230791
$455$	10.0853	0.472807
$456$	−10.1203	−0.473926
$457$	15.4417	0.722334	0.361167	−	0.932501i	$-0.382378\pi$
$457$	15.4417	0.722334	0.361167	+	0.932501i	$0.382378\pi$
$458$	−2.40126	−0.112203
$459$	2.56328	0.119644
$460$	−17.5791	−0.819631
$461$	−27.9539	−1.30194	−0.650972	−	0.759102i	$-0.725638\pi$
$461$	−27.9539	−1.30194	−0.650972	+	0.759102i	$0.725638\pi$
$462$	−2.37191	−0.110351
$463$	3.29158	0.152973	0.0764863	−	0.997071i	$-0.475630\pi$
$463$	3.29158	0.152973	0.0764863	+	0.997071i	$0.475630\pi$
$464$	−0.202002	−0.00937769
$465$	−11.0666	−0.513199
$466$	4.64660	0.215250
$467$	−8.57384	−0.396750	−0.198375	−	0.980126i	$-0.563566\pi$
$467$	−8.57384	−0.396750	−0.198375	+	0.980126i	$0.563566\pi$
$468$	−8.47786	−0.391889
$469$	13.5159	0.624106
$470$	4.17623	0.192635
$471$	−17.0038	−0.783494
$472$	10.6305	0.489309
$473$	48.1921	2.21587
$474$	−0.966869	−0.0444098
$475$	−0.744313	−0.0341514
$476$	−4.76660	−0.218477
$477$	7.02614	0.321705
$478$	1.21395	0.0555246
$479$	−22.6910	−1.03678	−0.518388	−	0.855145i	$-0.673468\pi$
$479$	−22.6910	−1.03678	−0.518388	+	0.855145i	$0.673468\pi$
$480$	9.03282	0.412290
$481$	−40.3880	−1.84153
$482$	3.90597	0.177912
$483$	4.27336	0.194444
$484$	−54.0438	−2.45654
$485$	9.57653	0.434848
$486$	0.374739	0.0169985
$487$	−29.5622	−1.33959	−0.669796	−	0.742545i	$-0.733618\pi$
$487$	−29.5622	−1.33959	−0.669796	+	0.742545i	$0.733618\pi$
$488$	−16.7548	−0.758456
$489$	−17.2742	−0.781168
$490$	0.828982	0.0374496
$491$	−17.0079	−0.767555	−0.383777	−	0.923426i	$-0.625377\pi$
$491$	−17.0079	−0.767555	−0.383777	+	0.923426i	$0.625377\pi$
$492$	−5.06423	−0.228313
$493$	−0.162972	−0.00733991
$494$	11.9544	0.537854
$495$	−14.0018	−0.629335
$496$	−15.8940	−0.713663
$497$	5.05351	0.226681
$498$	4.66114	0.208871
$499$	−19.6260	−0.878578	−0.439289	−	0.898346i	$-0.644770\pi$
$499$	−19.6260	−0.878578	−0.439289	+	0.898346i	$0.644770\pi$
$500$	21.0059	0.939411
$501$	12.6297	0.564255
$502$	−9.59703	−0.428337
$503$	−16.6861	−0.743996	−0.371998	−	0.928234i	$-0.621327\pi$
$503$	−16.6861	−0.743996	−0.371998	+	0.928234i	$0.621327\pi$
$504$	−1.44633	−0.0644248
$505$	17.0324	0.757933
$506$	−10.1360	−0.450601
$507$	7.78489	0.345739
$508$	−15.7002	−0.696583
$509$	−16.3072	−0.722804	−0.361402	−	0.932410i	$-0.617702\pi$
$509$	−16.3072	−0.722804	−0.361402	+	0.932410i	$0.617702\pi$
$510$	2.12491	0.0940927
$511$	−10.5171	−0.465248
$512$	22.1635	0.979499
$513$	6.99721	0.308934
$514$	3.84721	0.169693
$515$	3.60709	0.158947
$516$	14.1586	0.623296
$517$	−31.8866	−1.40237
$518$	−3.31977	−0.145862
$519$	17.3937	0.763499
$520$	−14.5867	−0.639670
$521$	−3.38337	−0.148228	−0.0741142	−	0.997250i	$-0.523613\pi$
$521$	−3.38337	−0.148228	−0.0741142	+	0.997250i	$0.523613\pi$
$522$	−0.0238258	−0.00104283
$523$	−26.5815	−1.16233	−0.581164	−	0.813786i	$-0.697403\pi$
$523$	−26.5815	−1.16233	−0.581164	+	0.813786i	$0.697403\pi$
$524$	−11.7573	−0.513619
$525$	−0.106373	−0.00464249
$526$	0.618170	0.0269535
$527$	−12.8231	−0.558584
$528$	−20.1097	−0.875163
$529$	−4.73844	−0.206019
$530$	5.82454	0.253002
$531$	−7.34998	−0.318962
$532$	−13.0118	−0.564133
$533$	12.4158	0.537788
$534$	1.89559	0.0820303
$535$	25.0507	1.08304
$536$	−19.5485	−0.844367
$537$	−11.8097	−0.509625
$538$	7.96529	0.343408
$539$	−6.32950	−0.272631
$540$	−4.11366	−0.177024
$541$	−19.4885	−0.837877	−0.418939	−	0.908015i	$-0.637598\pi$
$541$	−19.4885	−0.837877	−0.418939	+	0.908015i	$0.637598\pi$
$542$	−10.4881	−0.450501
$543$	0.820114	0.0351944
$544$	10.4666	0.448750
$545$	18.0307	0.772348
$546$	1.70845	0.0731151
$547$	−28.7341	−1.22858	−0.614290	−	0.789080i	$-0.710557\pi$
$547$	−28.7341	−1.22858	−0.614290	+	0.789080i	$0.710557\pi$
$548$	−29.1980	−1.24728
$549$	11.5844	0.494408
$550$	0.252307	0.0107584
$551$	−0.444880	−0.0189525
$552$	−6.18070	−0.263068
$553$	−2.58011	−0.109717
$554$	−9.32083	−0.396004
$555$	−19.5972	−0.831855
$556$	23.4207	0.993259
$557$	−38.9597	−1.65078	−0.825389	−	0.564565i	$-0.809044\pi$
$557$	−38.9597	−1.65078	−0.825389	+	0.564565i	$0.809044\pi$
$558$	−1.87468	−0.0793615
$559$	−34.7120	−1.46816
$560$	7.02833	0.297001
$561$	−16.2243	−0.684990
$562$	−0.0196456	−0.000828699 0
$563$	−32.4058	−1.36574	−0.682870	−	0.730540i	$-0.739269\pi$
$563$	−32.4058	−1.36574	−0.682870	+	0.730540i	$0.739269\pi$
$564$	−9.36811	−0.394469
$565$	−18.7502	−0.788826
$566$	5.70761	0.239909
$567$	1.00000	0.0419961
$568$	−7.30906	−0.306681
$569$	−4.83169	−0.202555	−0.101277	−	0.994858i	$-0.532293\pi$
$569$	−4.83169	−0.202555	−0.101277	+	0.994858i	$0.532293\pi$
$570$	5.80055	0.242959
$571$	−41.0403	−1.71748	−0.858742	−	0.512408i	$-0.828753\pi$
$571$	−41.0403	−1.71748	−0.858742	+	0.512408i	$0.828753\pi$
$572$	53.6606	2.24366
$573$	1.00000	0.0417756
$574$	1.02054	0.0425965
$575$	−0.454569	−0.0189568
$576$	−4.82412	−0.201005
$577$	−0.674918	−0.0280972	−0.0140486	−	0.999901i	$-0.504472\pi$
$577$	−0.674918	−0.0280972	−0.0140486	+	0.999901i	$0.504472\pi$
$578$	−3.90838	−0.162567
$579$	2.09572	0.0870953
$580$	0.261545	0.0108601
$581$	12.4383	0.516029
$582$	1.62227	0.0672451
$583$	−44.4719	−1.84184
$584$	15.2112	0.629443
$585$	10.0853	0.416976
$586$	9.86675	0.407592
$587$	5.62866	0.232320	0.116160	−	0.993231i	$-0.462942\pi$
$587$	5.62866	0.232320	0.116160	+	0.993231i	$0.462942\pi$
$588$	−1.85957	−0.0766874
$589$	−35.0043	−1.44233
$590$	−6.09299	−0.250845
$591$	−16.7066	−0.687216
$592$	−28.1459	−1.15679
$593$	9.88308	0.405849	0.202925	−	0.979194i	$-0.434955\pi$
$593$	9.88308	0.405849	0.202925	+	0.979194i	$0.434955\pi$
$594$	−2.37191	−0.0973208
$595$	5.67037	0.232463
$596$	−12.3740	−0.506860
$597$	−8.86297	−0.362737
$598$	7.30083	0.298553
$599$	−28.9970	−1.18479	−0.592393	−	0.805649i	$-0.701817\pi$
$599$	−28.9970	−1.18479	−0.592393	+	0.805649i	$0.701817\pi$
$600$	0.153851	0.00628093
$601$	−12.6051	−0.514171	−0.257086	−	0.966389i	$-0.582762\pi$
$601$	−12.6051	−0.514171	−0.257086	+	0.966389i	$0.582762\pi$
$602$	−2.85322	−0.116289
$603$	13.5159	0.550410
$604$	−27.9296	−1.13644
$605$	64.2908	2.61379
$606$	2.88530	0.117207
$607$	24.9897	1.01430	0.507151	−	0.861857i	$-0.330699\pi$
$607$	24.9897	1.01430	0.507151	+	0.861857i	$0.330699\pi$
$608$	28.5715	1.15873
$609$	−0.0635796	−0.00257638
$610$	9.60321	0.388823
$611$	22.9675	0.929164
$612$	−4.76660	−0.192678
$613$	1.47558	0.0595980	0.0297990	−	0.999556i	$-0.490513\pi$
$613$	1.47558	0.0595980	0.0297990	+	0.999556i	$0.490513\pi$
$614$	5.24990	0.211869
$615$	6.02443	0.242929
$616$	9.15456	0.368848
$617$	18.7847	0.756243	0.378122	−	0.925756i	$-0.376570\pi$
$617$	18.7847	0.756243	0.378122	+	0.925756i	$0.376570\pi$
$618$	0.611042	0.0245797
$619$	−26.3716	−1.05996	−0.529982	−	0.848009i	$-0.677801\pi$
$619$	−26.3716	−1.05996	−0.529982	+	0.848009i	$0.677801\pi$
$620$	20.5790	0.826474
$621$	4.27336	0.171484
$622$	−11.8703	−0.475954
$623$	5.05842	0.202661
$624$	14.4847	0.579853
$625$	−24.4568	−0.978273
$626$	−6.23726	−0.249291
$627$	−44.2888	−1.76872
$628$	31.6198	1.26177
$629$	−22.7078	−0.905419
$630$	0.828982	0.0330274
$631$	−40.7343	−1.62161	−0.810804	−	0.585318i	$-0.800970\pi$
$631$	−40.7343	−1.62161	−0.810804	+	0.585318i	$0.800970\pi$
$632$	3.73170	0.148439
$633$	14.2019	0.564475
$634$	7.09454	0.281760
$635$	18.6770	0.741175
$636$	−13.0656	−0.518085
$637$	4.55904	0.180636
$638$	0.150805	0.00597044
$639$	5.05351	0.199914
$640$	−22.0647	−0.872186
$641$	−21.0665	−0.832078	−0.416039	−	0.909347i	$-0.636582\pi$
$641$	−21.0665	−0.832078	−0.416039	+	0.909347i	$0.636582\pi$
$642$	4.24359	0.167481
$643$	44.9919	1.77431	0.887153	−	0.461475i	$-0.152680\pi$
$643$	44.9919	1.77431	0.887153	+	0.461475i	$0.152680\pi$
$644$	−7.94660	−0.313140
$645$	−16.8431	−0.663196
$646$	6.72125	0.264444
$647$	10.7484	0.422564	0.211282	−	0.977425i	$-0.432236\pi$
$647$	10.7484	0.422564	0.211282	+	0.977425i	$0.432236\pi$
$648$	−1.44633	−0.0568173
$649$	46.5217	1.82613
$650$	−0.181733	−0.00712816
$651$	−5.00262	−0.196068
$652$	32.1227	1.25802
$653$	38.7139	1.51499	0.757496	−	0.652840i	$-0.226423\pi$
$653$	38.7139	1.51499	0.757496	+	0.652840i	$0.226423\pi$
$654$	3.05440	0.119436
$655$	13.9865	0.546499
$656$	8.65241	0.337820
$657$	−10.5171	−0.410310
$658$	1.88786	0.0735963
$659$	−23.4296	−0.912686	−0.456343	−	0.889804i	$-0.650841\pi$
$659$	−23.4296	−0.912686	−0.456343	+	0.889804i	$0.650841\pi$
$660$	26.0374	1.01350
$661$	−4.18325	−0.162709	−0.0813547	−	0.996685i	$-0.525925\pi$
$661$	−4.18325	−0.162709	−0.0813547	+	0.996685i	$0.525925\pi$
$662$	−5.74720	−0.223371
$663$	11.6861	0.453851
$664$	−17.9900	−0.698147
$665$	15.4789	0.600246
$666$	−3.31977	−0.128639
$667$	−0.271698	−0.0105202
$668$	−23.4859	−0.908696
$669$	−14.2913	−0.552535
$670$	11.2044	0.432865
$671$	−73.3231	−2.83061
$672$	4.08327	0.157515
$673$	15.1840	0.585299	0.292650	−	0.956220i	$-0.405463\pi$
$673$	15.1840	0.585299	0.292650	+	0.956220i	$0.405463\pi$
$674$	2.66931	0.102818
$675$	−0.106373	−0.00409430
$676$	−14.4765	−0.556790
$677$	41.3753	1.59018	0.795090	−	0.606491i	$-0.207423\pi$
$677$	41.3753	1.59018	0.795090	+	0.606491i	$0.207423\pi$
$678$	−3.17629	−0.121985
$679$	4.32905	0.166134
$680$	−8.20125	−0.314504
$681$	−1.31225	−0.0502856
$682$	11.8658	0.454364
$683$	39.6578	1.51746	0.758732	−	0.651403i	$-0.225819\pi$
$683$	39.6578	1.51746	0.758732	+	0.651403i	$0.225819\pi$
$684$	−13.0118	−0.497518
$685$	34.7341	1.32712
$686$	0.374739	0.0143076
$687$	−6.40781	−0.244473
$688$	−24.1904	−0.922250
$689$	32.0325	1.22034
$690$	3.54253	0.134862
$691$	30.8414	1.17326	0.586631	−	0.809854i	$-0.300454\pi$
$691$	30.8414	1.17326	0.586631	+	0.809854i	$0.300454\pi$
$692$	−32.3448	−1.22957
$693$	−6.32950	−0.240438
$694$	−9.48046	−0.359873
$695$	−27.8614	−1.05684
$696$	0.0919573	0.00348563
$697$	6.98067	0.264412
$698$	4.77687	0.180807
$699$	12.3995	0.468994
$700$	0.197808	0.00747644
$701$	0.947585	0.0357898	0.0178949	−	0.999840i	$-0.494304\pi$
$701$	0.947585	0.0357898	0.0178949	+	0.999840i	$0.494304\pi$
$702$	1.70845	0.0644814
$703$	−61.9874	−2.33790
$704$	30.5343	1.15080
$705$	11.1444	0.419721
$706$	1.40896	0.0530270
$707$	7.69948	0.289569
$708$	13.6678	0.513667
$709$	−32.6066	−1.22457	−0.612283	−	0.790639i	$-0.709749\pi$
$709$	−32.6066	−1.22457	−0.612283	+	0.790639i	$0.709749\pi$
$710$	4.18927	0.157220
$711$	−2.58011	−0.0967617
$712$	−7.31617	−0.274185
$713$	−21.3780	−0.800611
$714$	0.960563	0.0359482
$715$	−63.8350	−2.38729
$716$	21.9609	0.820717
$717$	3.23944	0.120979
$718$	−6.11560	−0.228232
$719$	−35.4458	−1.32191	−0.660953	−	0.750427i	$-0.729848\pi$
$719$	−35.4458	−1.32191	−0.660953	+	0.750427i	$0.729848\pi$
$720$	7.02833	0.261930
$721$	1.63058	0.0607259
$722$	11.2275	0.417845
$723$	10.4232	0.387642
$724$	−1.52506	−0.0566784
$725$	0.00676315	0.000251177 0
$726$	10.8909	0.404199
$727$	−21.5361	−0.798728	−0.399364	−	0.916792i	$-0.630769\pi$
$727$	−21.5361	−0.798728	−0.399364	+	0.916792i	$0.630769\pi$
$728$	−6.59390	−0.244386
$729$	1.00000	0.0370370
$730$	−8.71845	−0.322684
$731$	−19.5165	−0.721845
$732$	−21.5419	−0.796212
$733$	4.57409	0.168948	0.0844739	−	0.996426i	$-0.473079\pi$
$733$	4.57409	0.168948	0.0844739	+	0.996426i	$0.473079\pi$
$734$	−7.12412	−0.262956
$735$	2.21215	0.0815965
$736$	17.4493	0.643188
$737$	−85.5489	−3.15123
$738$	1.02054	0.0375666
$739$	1.70747	0.0628103	0.0314051	−	0.999507i	$-0.490002\pi$
$739$	1.70747	0.0628103	0.0314051	+	0.999507i	$0.490002\pi$
$740$	36.4424	1.33965
$741$	31.9006	1.17190
$742$	2.63297	0.0966594
$743$	27.2385	0.999284	0.499642	−	0.866232i	$-0.333465\pi$
$743$	27.2385	0.999284	0.499642	+	0.866232i	$0.333465\pi$
$744$	7.23545	0.265265
$745$	14.7202	0.539307
$746$	6.51975	0.238705
$747$	12.4383	0.455095
$748$	30.1702	1.10313
$749$	11.3241	0.413774
$750$	−4.23309	−0.154571
$751$	−2.31422	−0.0844469	−0.0422235	−	0.999108i	$-0.513444\pi$
$751$	−2.31422	−0.0844469	−0.0422235	+	0.999108i	$0.513444\pi$
$752$	16.0057	0.583670
$753$	−25.6099	−0.933276
$754$	−0.108623	−0.00395581
$755$	33.2252	1.20919
$756$	−1.85957	−0.0676319
$757$	8.25345	0.299977	0.149988	−	0.988688i	$-0.452076\pi$
$757$	8.25345	0.299977	0.149988	+	0.988688i	$0.452076\pi$
$758$	1.79144	0.0650682
$759$	−27.0482	−0.981787
$760$	−22.3876	−0.812085
$761$	−21.9197	−0.794590	−0.397295	−	0.917691i	$-0.630051\pi$
$761$	−21.9197	−0.794590	−0.397295	+	0.917691i	$0.630051\pi$
$762$	3.16389	0.114616
$763$	8.15072	0.295076
$764$	−1.85957	−0.0672769
$765$	5.67037	0.205013
$766$	−7.44772	−0.269097
$767$	−33.5089	−1.20994
$768$	5.91047	0.213276
$769$	30.4684	1.09872	0.549359	−	0.835586i	$-0.314872\pi$
$769$	30.4684	1.09872	0.549359	+	0.835586i	$0.314872\pi$
$770$	−5.24704	−0.189090
$771$	10.2664	0.369734
$772$	−3.89715	−0.140261
$773$	11.6157	0.417787	0.208894	−	0.977938i	$-0.433014\pi$
$773$	11.6157	0.417787	0.208894	+	0.977938i	$0.433014\pi$
$774$	−2.85322	−0.102557
$775$	0.532143	0.0191151
$776$	−6.26125	−0.224766
$777$	−8.85888	−0.317810
$778$	11.6958	0.419314
$779$	19.0557	0.682742
$780$	−18.7543	−0.671513
$781$	−31.9862	−1.14456
$782$	4.10483	0.146788
$783$	−0.0635796	−0.00227215
$784$	3.17714	0.113469
$785$	−37.6150	−1.34254
$786$	2.36932	0.0845109
$787$	−36.7910	−1.31146	−0.655728	−	0.754997i	$-0.727638\pi$
$787$	−36.7910	−1.31146	−0.655728	+	0.754997i	$0.727638\pi$
$788$	31.0670	1.10672
$789$	1.64960	0.0587273
$790$	−2.13886	−0.0760974
$791$	−8.47599	−0.301371
$792$	9.15456	0.325293
$793$	52.8136	1.87547
$794$	−14.5533	−0.516477
$795$	15.5429	0.551250
$796$	16.4813	0.584165
$797$	−47.1590	−1.67046	−0.835228	−	0.549904i	$-0.814664\pi$
$797$	−47.1590	−1.67046	−0.835228	+	0.549904i	$0.814664\pi$
$798$	2.62213	0.0928224
$799$	12.9133	0.456838
$800$	−0.434349	−0.0153566
$801$	5.05842	0.178731
$802$	1.07253	0.0378722
$803$	66.5677	2.34912
$804$	−25.1338	−0.886400
$805$	9.45332	0.333186
$806$	−8.54674	−0.301046
$807$	21.2555	0.748231
$808$	−11.1360	−0.391763
$809$	35.2590	1.23964	0.619820	−	0.784744i	$-0.287206\pi$
$809$	35.2590	1.23964	0.619820	+	0.784744i	$0.287206\pi$
$810$	0.828982	0.0291274
$811$	30.0191	1.05411	0.527056	−	0.849830i	$-0.323296\pi$
$811$	30.0191	1.05411	0.527056	+	0.849830i	$0.323296\pi$
$812$	0.118231	0.00414909
$813$	−27.9876	−0.981569
$814$	21.0125	0.736487
$815$	−38.2133	−1.33855
$816$	8.14391	0.285094
$817$	−53.2759	−1.86389
$818$	1.67129	0.0584353
$819$	4.55904	0.159306
$820$	−11.2029	−0.391221
$821$	−18.3327	−0.639815	−0.319907	−	0.947449i	$-0.603652\pi$
$821$	−18.3327	−0.639815	−0.319907	+	0.947449i	$0.603652\pi$
$822$	5.88396	0.205227
$823$	14.7232	0.513218	0.256609	−	0.966515i	$-0.417395\pi$
$823$	14.7232	0.513218	0.256609	+	0.966515i	$0.417395\pi$
$824$	−2.35836	−0.0821573
$825$	0.673287	0.0234409
$826$	−2.75433	−0.0958353
$827$	20.0413	0.696905	0.348452	−	0.937326i	$-0.386707\pi$
$827$	20.0413	0.696905	0.348452	+	0.937326i	$0.386707\pi$
$828$	−7.94660	−0.276164
$829$	−24.0890	−0.836645	−0.418323	−	0.908298i	$-0.637382\pi$
$829$	−24.0890	−0.836645	−0.418323	+	0.908298i	$0.637382\pi$
$830$	10.3112	0.357906
$831$	−24.8728	−0.862828
$832$	−21.9934	−0.762484
$833$	2.56328	0.0888124
$834$	−4.71973	−0.163431
$835$	27.9389	0.966866
$836$	82.3581	2.84842
$837$	−5.00262	−0.172916
$838$	−1.89328	−0.0654022
$839$	−18.2048	−0.628501	−0.314251	−	0.949340i	$-0.601753\pi$
$839$	−18.2048	−0.628501	−0.314251	+	0.949340i	$0.601753\pi$
$840$	−3.19951	−0.110394
$841$	−28.9960	−0.999861
$842$	2.52779	0.0871132
$843$	−0.0524246	−0.00180560
$844$	−26.4094	−0.909050
$845$	17.2214	0.592433
$846$	1.88786	0.0649058
$847$	29.0625	0.998601
$848$	22.3230	0.766576
$849$	15.2309	0.522723
$850$	−0.102178	−0.00350467
$851$	−37.8571	−1.29773
$852$	−9.39735	−0.321948
$853$	27.9152	0.955798	0.477899	−	0.878415i	$-0.341398\pi$
$853$	27.9152	0.955798	0.477899	+	0.878415i	$0.341398\pi$
$854$	4.34111	0.148550
$855$	15.4789	0.529367
$856$	−16.3784	−0.559804
$857$	4.66788	0.159452	0.0797258	−	0.996817i	$-0.474596\pi$
$857$	4.66788	0.159452	0.0797258	+	0.996817i	$0.474596\pi$
$858$	−10.8137	−0.369172
$859$	−20.9150	−0.713610	−0.356805	−	0.934179i	$-0.616134\pi$
$859$	−20.9150	−0.713610	−0.356805	+	0.934179i	$0.616134\pi$
$860$	31.3209	1.06803
$861$	2.72333	0.0928109
$862$	−7.70052	−0.262281
$863$	−11.4896	−0.391111	−0.195556	−	0.980693i	$-0.562651\pi$
$863$	−11.4896	−0.391111	−0.195556	+	0.980693i	$0.562651\pi$
$864$	4.08327	0.138916
$865$	38.4776	1.30828
$866$	6.13585	0.208505
$867$	−10.4296	−0.354207
$868$	9.30272	0.315755
$869$	16.3308	0.553985
$870$	−0.0527063	−0.00178691
$871$	61.6196	2.08790
$872$	−11.7887	−0.399214
$873$	4.32905	0.146516
$874$	11.2053	0.379025
$875$	−11.2961	−0.381877
$876$	19.5572	0.660777
$877$	−37.3467	−1.26111	−0.630553	−	0.776146i	$-0.717172\pi$
$877$	−37.3467	−1.26111	−0.630553	+	0.776146i	$0.717172\pi$
$878$	13.0702	0.441099
$879$	26.3296	0.888076
$880$	−44.4858	−1.49962
$881$	−35.6192	−1.20004	−0.600020	−	0.799985i	$-0.704841\pi$
$881$	−35.6192	−1.20004	−0.600020	+	0.799985i	$0.704841\pi$
$882$	0.374739	0.0126181
$883$	2.71885	0.0914966	0.0457483	−	0.998953i	$-0.485433\pi$
$883$	2.71885	0.0914966	0.0457483	+	0.998953i	$0.485433\pi$
$884$	−21.7311	−0.730898
$885$	−16.2593	−0.546550
$886$	11.9108	0.400151
$887$	−34.2773	−1.15092	−0.575460	−	0.817830i	$-0.695177\pi$
$887$	−34.2773	−1.15092	−0.575460	+	0.817830i	$0.695177\pi$
$888$	12.8129	0.429972
$889$	8.44291	0.283166
$890$	4.19334	0.140561
$891$	−6.32950	−0.212046
$892$	26.5757	0.889822
$893$	35.2504	1.17961
$894$	2.49361	0.0833987
$895$	−26.1248	−0.873256
$896$	−9.97432	−0.333219
$897$	19.4824	0.650499
$898$	9.25840	0.308957
$899$	0.318065	0.0106080
$900$	0.197808	0.00659360
$901$	18.0100	0.599999
$902$	−6.45951	−0.215078
$903$	−7.61388	−0.253374
$904$	12.2591	0.407732
$905$	1.81422	0.0603066
$906$	5.62836	0.186990
$907$	54.2215	1.80039	0.900197	−	0.435482i	$-0.143422\pi$
$907$	54.2215	1.80039	0.900197	+	0.435482i	$0.143422\pi$
$908$	2.44022	0.0809817
$909$	7.69948	0.255375
$910$	3.77936	0.125285
$911$	1.52738	0.0506045	0.0253023	−	0.999680i	$-0.491945\pi$
$911$	1.52738	0.0506045	0.0253023	+	0.999680i	$0.491945\pi$
$912$	22.2311	0.736146
$913$	−78.7285	−2.60553
$914$	5.78663	0.191405
$915$	25.6264	0.847182
$916$	11.9158	0.393708
$917$	6.32258	0.208790
$918$	0.960563	0.0317033
$919$	−40.5433	−1.33740	−0.668700	−	0.743532i	$-0.733149\pi$
$919$	−40.5433	−1.33740	−0.668700	+	0.743532i	$0.733149\pi$
$920$	−13.6727	−0.450774
$921$	14.0095	0.461628
$922$	−10.4754	−0.344990
$923$	23.0392	0.758344
$924$	11.7701	0.387209
$925$	0.942345	0.0309841
$926$	1.23348	0.0405348
$927$	1.63058	0.0535552
$928$	−0.259613	−0.00852220
$929$	44.2203	1.45082	0.725410	−	0.688317i	$-0.241650\pi$
$929$	44.2203	1.45082	0.725410	+	0.688317i	$0.241650\pi$
$930$	−4.14708	−0.135988
$931$	6.99721	0.229324
$932$	−23.0578	−0.755284
$933$	−31.6760	−1.03703
$934$	−3.21296	−0.105131
$935$	−35.8906	−1.17375
$936$	−6.59390	−0.215528
$937$	0.562772	0.0183850	0.00919248	−	0.999958i	$-0.497074\pi$
$937$	0.562772	0.0183850	0.00919248	+	0.999958i	$0.497074\pi$
$938$	5.06494	0.165376
$939$	−16.6443	−0.543165
$940$	−20.7237	−0.675933
$941$	−26.8987	−0.876871	−0.438436	−	0.898763i	$-0.644467\pi$
$941$	−26.8987	−0.876871	−0.438436	+	0.898763i	$0.644467\pi$
$942$	−6.37199	−0.207611
$943$	11.6378	0.378978
$944$	−23.3519	−0.760040
$945$	2.21215	0.0719614
$946$	18.0595	0.587164
$947$	4.54863	0.147811	0.0739053	−	0.997265i	$-0.476454\pi$
$947$	4.54863	0.147811	0.0739053	+	0.997265i	$0.476454\pi$
$948$	4.79790	0.155828
$949$	−47.9478	−1.55645
$950$	−0.278924	−0.00904947
$951$	18.9319	0.613909
$952$	−3.70736	−0.120156
$953$	−25.7251	−0.833317	−0.416658	−	0.909063i	$-0.636799\pi$
$953$	−25.7251	−0.833317	−0.416658	+	0.909063i	$0.636799\pi$
$954$	2.63297	0.0852456
$955$	2.21215	0.0715836
$956$	−6.02397	−0.194829
$957$	0.402427	0.0130086
$958$	−8.50320	−0.274726
$959$	15.7015	0.507027
$960$	−10.6717	−0.344428
$961$	−5.97382	−0.192704
$962$	−15.1350	−0.487971
$963$	11.3241	0.364915
$964$	−19.3826	−0.624272
$965$	4.63607	0.149240
$966$	1.60139	0.0515240
$967$	−43.1787	−1.38853	−0.694266	−	0.719719i	$-0.744271\pi$
$967$	−43.1787	−1.38853	−0.694266	+	0.719719i	$0.744271\pi$
$968$	−42.0341	−1.35103
$969$	17.9358	0.576181
$970$	3.58870	0.115226
$971$	−14.9225	−0.478887	−0.239443	−	0.970910i	$-0.576965\pi$
$971$	−14.9225	−0.478887	−0.239443	+	0.970910i	$0.576965\pi$
$972$	−1.85957	−0.0596457
$973$	−12.5947	−0.403767
$974$	−11.0781	−0.354966
$975$	−0.484959	−0.0155311
$976$	36.8051	1.17810
$977$	−27.6515	−0.884651	−0.442326	−	0.896855i	$-0.645846\pi$
$977$	−27.6515	−0.884651	−0.442326	+	0.896855i	$0.645846\pi$
$978$	−6.47334	−0.206995
$979$	−32.0173	−1.02328
$980$	−4.11366	−0.131406
$981$	8.15072	0.260233
$982$	−6.37352	−0.203387
$983$	7.91614	0.252486	0.126243	−	0.991999i	$-0.459708\pi$
$983$	7.91614	0.252486	0.126243	+	0.991999i	$0.459708\pi$
$984$	−3.93885	−0.125566
$985$	−36.9575	−1.17756
$986$	−0.0610722	−0.00194494
$987$	5.03778	0.160354
$988$	−59.3214	−1.88726
$989$	−32.5368	−1.03461
$990$	−5.24704	−0.166762
$991$	6.64819	0.211187	0.105593	−	0.994409i	$-0.466326\pi$
$991$	6.64819	0.211187	0.105593	+	0.994409i	$0.466326\pi$
$992$	−20.4270	−0.648559
$993$	−15.3365	−0.486690
$994$	1.89375	0.0600661
$995$	−19.6063	−0.621560
$996$	−23.1300	−0.732901
$997$	61.9069	1.96061	0.980306	−	0.197486i	$-0.0632776\pi$
$997$	61.9069	1.96061	0.980306	+	0.197486i	$0.0632776\pi$
$998$	−7.35462	−0.232806
$999$	−8.85888	−0.280282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.14	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.14	✓	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)

\(f(q)\)	\(=\)	\(q+0.374739 q^{2} +1.00000 q^{3} -1.85957 q^{4} +2.21215 q^{5} +0.374739 q^{6} +1.00000 q^{7} -1.44633 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.374739 q^{2} +1.00000 q^{3} -1.85957 q^{4} +2.21215 q^{5} +0.374739 q^{6} +1.00000 q^{7} -1.44633 q^{8} +1.00000 q^{9} +0.828982 q^{10} -6.32950 q^{11} -1.85957 q^{12} +4.55904 q^{13} +0.374739 q^{14} +2.21215 q^{15} +3.17714 q^{16} +2.56328 q^{17} +0.374739 q^{18} +6.99721 q^{19} -4.11366 q^{20} +1.00000 q^{21} -2.37191 q^{22} +4.27336 q^{23} -1.44633 q^{24} -0.106373 q^{25} +1.70845 q^{26} +1.00000 q^{27} -1.85957 q^{28} -0.0635796 q^{29} +0.828982 q^{30} -5.00262 q^{31} +4.08327 q^{32} -6.32950 q^{33} +0.960563 q^{34} +2.21215 q^{35} -1.85957 q^{36} -8.85888 q^{37} +2.62213 q^{38} +4.55904 q^{39} -3.19951 q^{40} +2.72333 q^{41} +0.374739 q^{42} -7.61388 q^{43} +11.7701 q^{44} +2.21215 q^{45} +1.60139 q^{46} +5.03778 q^{47} +3.17714 q^{48} +1.00000 q^{49} -0.0398621 q^{50} +2.56328 q^{51} -8.47786 q^{52} +7.02614 q^{53} +0.374739 q^{54} -14.0018 q^{55} -1.44633 q^{56} +6.99721 q^{57} -0.0238258 q^{58} -7.34998 q^{59} -4.11366 q^{60} +11.5844 q^{61} -1.87468 q^{62} +1.00000 q^{63} -4.82412 q^{64} +10.0853 q^{65} -2.37191 q^{66} +13.5159 q^{67} -4.76660 q^{68} +4.27336 q^{69} +0.828982 q^{70} +5.05351 q^{71} -1.44633 q^{72} -10.5171 q^{73} -3.31977 q^{74} -0.106373 q^{75} -13.0118 q^{76} -6.32950 q^{77} +1.70845 q^{78} -2.58011 q^{79} +7.02833 q^{80} +1.00000 q^{81} +1.02054 q^{82} +12.4383 q^{83} -1.85957 q^{84} +5.67037 q^{85} -2.85322 q^{86} -0.0635796 q^{87} +9.15456 q^{88} +5.05842 q^{89} +0.828982 q^{90} +4.55904 q^{91} -7.94660 q^{92} -5.00262 q^{93} +1.88786 q^{94} +15.4789 q^{95} +4.08327 q^{96} +4.32905 q^{97} +0.374739 q^{98} -6.32950 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 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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