LMFDB - Embedded newform 4011.2.a.k.1.4

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			1.4
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.70789 q^{2} +1.00000 q^{3} +0.916895 q^{4} +2.36693 q^{5} -1.70789 q^{6} +1.00000 q^{7} +1.84983 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.70789 q^{2} +1.00000 q^{3} +0.916895 q^{4} +2.36693 q^{5} -1.70789 q^{6} +1.00000 q^{7} +1.84983 q^{8} +1.00000 q^{9} -4.04246 q^{10} -0.746546 q^{11} +0.916895 q^{12} +1.43337 q^{13} -1.70789 q^{14} +2.36693 q^{15} -4.99309 q^{16} -0.954280 q^{17} -1.70789 q^{18} +0.503438 q^{19} +2.17023 q^{20} +1.00000 q^{21} +1.27502 q^{22} +3.97252 q^{23} +1.84983 q^{24} +0.602358 q^{25} -2.44805 q^{26} +1.00000 q^{27} +0.916895 q^{28} -7.00431 q^{29} -4.04246 q^{30} +3.89382 q^{31} +4.82801 q^{32} -0.746546 q^{33} +1.62981 q^{34} +2.36693 q^{35} +0.916895 q^{36} +3.42569 q^{37} -0.859818 q^{38} +1.43337 q^{39} +4.37841 q^{40} +2.77066 q^{41} -1.70789 q^{42} +0.415126 q^{43} -0.684504 q^{44} +2.36693 q^{45} -6.78463 q^{46} -0.842645 q^{47} -4.99309 q^{48} +1.00000 q^{49} -1.02876 q^{50} -0.954280 q^{51} +1.31425 q^{52} +0.595852 q^{53} -1.70789 q^{54} -1.76702 q^{55} +1.84983 q^{56} +0.503438 q^{57} +11.9626 q^{58} +14.5620 q^{59} +2.17023 q^{60} -7.43261 q^{61} -6.65022 q^{62} +1.00000 q^{63} +1.74047 q^{64} +3.39270 q^{65} +1.27502 q^{66} +12.8339 q^{67} -0.874974 q^{68} +3.97252 q^{69} -4.04246 q^{70} +11.9338 q^{71} +1.84983 q^{72} +4.44314 q^{73} -5.85070 q^{74} +0.602358 q^{75} +0.461600 q^{76} -0.746546 q^{77} -2.44805 q^{78} -10.2846 q^{79} -11.8183 q^{80} +1.00000 q^{81} -4.73199 q^{82} -12.8515 q^{83} +0.916895 q^{84} -2.25871 q^{85} -0.708991 q^{86} -7.00431 q^{87} -1.38098 q^{88} +2.33027 q^{89} -4.04246 q^{90} +1.43337 q^{91} +3.64238 q^{92} +3.89382 q^{93} +1.43915 q^{94} +1.19160 q^{95} +4.82801 q^{96} -0.569211 q^{97} -1.70789 q^{98} -0.746546 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) $ 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.70789	−1.20766	−0.603831	−	0.797112i	$-0.706360\pi$
$2$	−1.70789	−1.20766	−0.603831	+	0.797112i	$0.706360\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.916895	0.458447
$5$	2.36693	1.05852	0.529262	−	0.848459i	$-0.322469\pi$
$5$	2.36693	1.05852	0.529262	+	0.848459i	$0.322469\pi$
$6$	−1.70789	−0.697244
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.84983	0.654013
$9$	1.00000	0.333333
$10$	−4.04246	−1.27834
$11$	−0.746546	−0.225092	−0.112546	−	0.993647i	$-0.535901\pi$
$11$	−0.746546	−0.225092	−0.112546	+	0.993647i	$0.535901\pi$
$12$	0.916895	0.264685
$13$	1.43337	0.397547	0.198773	−	0.980046i	$-0.436304\pi$
$13$	1.43337	0.397547	0.198773	+	0.980046i	$0.436304\pi$
$14$	−1.70789	−0.456453
$15$	2.36693	0.611139
$16$	−4.99309	−1.24827
$17$	−0.954280	−0.231447	−0.115723	−	0.993281i	$-0.536919\pi$
$17$	−0.954280	−0.231447	−0.115723	+	0.993281i	$0.536919\pi$
$18$	−1.70789	−0.402554
$19$	0.503438	0.115497	0.0577483	−	0.998331i	$-0.481608\pi$
$19$	0.503438	0.115497	0.0577483	+	0.998331i	$0.481608\pi$
$20$	2.17023	0.485277
$21$	1.00000	0.218218
$22$	1.27502	0.271835
$23$	3.97252	0.828328	0.414164	−	0.910202i	$-0.364074\pi$
$23$	3.97252	0.828328	0.414164	+	0.910202i	$0.364074\pi$
$24$	1.84983	0.377594
$25$	0.602358	0.120472
$26$	−2.44805	−0.480102
$27$	1.00000	0.192450
$28$	0.916895	0.173277
$29$	−7.00431	−1.30067	−0.650334	−	0.759649i	$-0.725371\pi$
$29$	−7.00431	−1.30067	−0.650334	+	0.759649i	$0.725371\pi$
$30$	−4.04246	−0.738049
$31$	3.89382	0.699350	0.349675	−	0.936871i	$-0.386292\pi$
$31$	3.89382	0.699350	0.349675	+	0.936871i	$0.386292\pi$
$32$	4.82801	0.853480
$33$	−0.746546	−0.129957
$34$	1.62981	0.279510
$35$	2.36693	0.400084
$36$	0.916895	0.152816
$37$	3.42569	0.563180	0.281590	−	0.959535i	$-0.409138\pi$
$37$	3.42569	0.563180	0.281590	+	0.959535i	$0.409138\pi$
$38$	−0.859818	−0.139481
$39$	1.43337	0.229524
$40$	4.37841	0.692288
$41$	2.77066	0.432704	0.216352	−	0.976315i	$-0.430584\pi$
$41$	2.77066	0.432704	0.216352	+	0.976315i	$0.430584\pi$
$42$	−1.70789	−0.263533
$43$	0.415126	0.0633062	0.0316531	−	0.999499i	$-0.489923\pi$
$43$	0.415126	0.0633062	0.0316531	+	0.999499i	$0.489923\pi$
$44$	−0.684504	−0.103193
$45$	2.36693	0.352841
$46$	−6.78463	−1.00034
$47$	−0.842645	−0.122912	−0.0614562	−	0.998110i	$-0.519574\pi$
$47$	−0.842645	−0.122912	−0.0614562	+	0.998110i	$0.519574\pi$
$48$	−4.99309	−0.720691
$49$	1.00000	0.142857
$50$	−1.02876	−0.145489
$51$	−0.954280	−0.133626
$52$	1.31425	0.182254
$53$	0.595852	0.0818465	0.0409233	−	0.999162i	$-0.486970\pi$
$53$	0.595852	0.0818465	0.0409233	+	0.999162i	$0.486970\pi$
$54$	−1.70789	−0.232415
$55$	−1.76702	−0.238265
$56$	1.84983	0.247194
$57$	0.503438	0.0666820
$58$	11.9626	1.57077
$59$	14.5620	1.89581	0.947903	−	0.318560i	$-0.103199\pi$
$59$	14.5620	1.89581	0.947903	+	0.318560i	$0.103199\pi$
$60$	2.17023	0.280175
$61$	−7.43261	−0.951648	−0.475824	−	0.879541i	$-0.657850\pi$
$61$	−7.43261	−0.951648	−0.475824	+	0.879541i	$0.657850\pi$
$62$	−6.65022	−0.844579
$63$	1.00000	0.125988
$64$	1.74047	0.217559
$65$	3.39270	0.420812
$66$	1.27502	0.156944
$67$	12.8339	1.56791	0.783955	−	0.620818i	$-0.213199\pi$
$67$	12.8339	1.56791	0.783955	+	0.620818i	$0.213199\pi$
$68$	−0.874974	−0.106106
$69$	3.97252	0.478235
$70$	−4.04246	−0.483166
$71$	11.9338	1.41628	0.708141	−	0.706071i	$-0.249534\pi$
$71$	11.9338	1.41628	0.708141	+	0.706071i	$0.249534\pi$
$72$	1.84983	0.218004
$73$	4.44314	0.520031	0.260015	−	0.965605i	$-0.416272\pi$
$73$	4.44314	0.520031	0.260015	+	0.965605i	$0.416272\pi$
$74$	−5.85070	−0.680131
$75$	0.602358	0.0695543
$76$	0.461600	0.0529491
$77$	−0.746546	−0.0850768
$78$	−2.44805	−0.277187
$79$	−10.2846	−1.15711	−0.578557	−	0.815642i	$-0.696384\pi$
$79$	−10.2846	−1.15711	−0.578557	+	0.815642i	$0.696384\pi$
$80$	−11.8183	−1.32133
$81$	1.00000	0.111111
$82$	−4.73199	−0.522561
$83$	−12.8515	−1.41063	−0.705316	−	0.708893i	$-0.749195\pi$
$83$	−12.8515	−1.41063	−0.705316	+	0.708893i	$0.749195\pi$
$84$	0.916895	0.100041
$85$	−2.25871	−0.244992
$86$	−0.708991	−0.0764524
$87$	−7.00431	−0.750940
$88$	−1.38098	−0.147213
$89$	2.33027	0.247008	0.123504	−	0.992344i	$-0.460587\pi$
$89$	2.33027	0.247008	0.123504	+	0.992344i	$0.460587\pi$
$90$	−4.04246	−0.426113
$91$	1.43337	0.150258
$92$	3.64238	0.379745
$93$	3.89382	0.403770
$94$	1.43915	0.148437
$95$	1.19160	0.122256
$96$	4.82801	0.492757
$97$	−0.569211	−0.0577946	−0.0288973	−	0.999582i	$-0.509200\pi$
$97$	−0.569211	−0.0577946	−0.0288973	+	0.999582i	$0.509200\pi$
$98$	−1.70789	−0.172523
$99$	−0.746546	−0.0750307
$100$	0.552298	0.0552298
$101$	10.1044	1.00542	0.502711	−	0.864454i	$-0.332336\pi$
$101$	10.1044	1.00542	0.502711	+	0.864454i	$0.332336\pi$
$102$	1.62981	0.161375
$103$	11.2842	1.11187	0.555933	−	0.831227i	$-0.312361\pi$
$103$	11.2842	1.11187	0.555933	+	0.831227i	$0.312361\pi$
$104$	2.65149	0.260000
$105$	2.36693	0.230989
$106$	−1.01765	−0.0988429
$107$	12.7716	1.23468	0.617340	−	0.786696i	$-0.288210\pi$
$107$	12.7716	1.23468	0.617340	+	0.786696i	$0.288210\pi$
$108$	0.916895	0.0882282
$109$	4.78205	0.458037	0.229019	−	0.973422i	$-0.426448\pi$
$109$	4.78205	0.458037	0.229019	+	0.973422i	$0.426448\pi$
$110$	3.01788	0.287744
$111$	3.42569	0.325152
$112$	−4.99309	−0.471803
$113$	16.2874	1.53219	0.766095	−	0.642727i	$-0.222197\pi$
$113$	16.2874	1.53219	0.766095	+	0.642727i	$0.222197\pi$
$114$	−0.859818	−0.0805294
$115$	9.40268	0.876804
$116$	−6.42221	−0.596287
$117$	1.43337	0.132516
$118$	−24.8702	−2.28949
$119$	−0.954280	−0.0874787
$120$	4.37841	0.399692
$121$	−10.4427	−0.949334
$122$	12.6941	1.14927
$123$	2.77066	0.249822
$124$	3.57022	0.320615
$125$	−10.4089	−0.931001
$126$	−1.70789	−0.152151
$127$	15.7156	1.39454	0.697268	−	0.716811i	$-0.254399\pi$
$127$	15.7156	1.39454	0.697268	+	0.716811i	$0.254399\pi$
$128$	−12.6286	−1.11622
$129$	0.415126	0.0365498
$130$	−5.79436	−0.508199
$131$	4.13018	0.360856	0.180428	−	0.983588i	$-0.442252\pi$
$131$	4.13018	0.360856	0.180428	+	0.983588i	$0.442252\pi$
$132$	−0.684504	−0.0595784
$133$	0.503438	0.0436536
$134$	−21.9189	−1.89350
$135$	2.36693	0.203713
$136$	−1.76525	−0.151369
$137$	−13.2408	−1.13124	−0.565618	−	0.824667i	$-0.691362\pi$
$137$	−13.2408	−1.13124	−0.565618	+	0.824667i	$0.691362\pi$
$138$	−6.78463	−0.577546
$139$	−23.2299	−1.97033	−0.985167	−	0.171598i	$-0.945107\pi$
$139$	−23.2299	−1.97033	−0.985167	+	0.171598i	$0.945107\pi$
$140$	2.17023	0.183418
$141$	−0.842645	−0.0709635
$142$	−20.3817	−1.71039
$143$	−1.07008	−0.0894846
$144$	−4.99309	−0.416091
$145$	−16.5787	−1.37679
$146$	−7.58841	−0.628021
$147$	1.00000	0.0824786
$148$	3.14099	0.258188
$149$	−14.7076	−1.20489	−0.602445	−	0.798160i	$-0.705807\pi$
$149$	−14.7076	−1.20489	−0.602445	+	0.798160i	$0.705807\pi$
$150$	−1.02876	−0.0839980
$151$	−9.96036	−0.810562	−0.405281	−	0.914192i	$-0.632826\pi$
$151$	−9.96036	−0.810562	−0.405281	+	0.914192i	$0.632826\pi$
$152$	0.931274	0.0755363
$153$	−0.954280	−0.0771490
$154$	1.27502	0.102744
$155$	9.21640	0.740279
$156$	1.31425	0.105224
$157$	9.69702	0.773906	0.386953	−	0.922099i	$-0.373527\pi$
$157$	9.69702	0.773906	0.386953	+	0.922099i	$0.373527\pi$
$158$	17.5651	1.39740
$159$	0.595852	0.0472541
$160$	11.4276	0.903428
$161$	3.97252	0.313078
$162$	−1.70789	−0.134185
$163$	−20.3135	−1.59108	−0.795539	−	0.605902i	$-0.792812\pi$
$163$	−20.3135	−1.59108	−0.795539	+	0.605902i	$0.792812\pi$
$164$	2.54040	0.198372
$165$	−1.76702	−0.137562
$166$	21.9489	1.70357
$167$	1.08305	0.0838091	0.0419045	−	0.999122i	$-0.486657\pi$
$167$	1.08305	0.0838091	0.0419045	+	0.999122i	$0.486657\pi$
$168$	1.84983	0.142717
$169$	−10.9454	−0.841957
$170$	3.85764	0.295867
$171$	0.503438	0.0384989
$172$	0.380627	0.0290225
$173$	20.2032	1.53602	0.768010	−	0.640437i	$-0.221247\pi$
$173$	20.2032	1.53602	0.768010	+	0.640437i	$0.221247\pi$
$174$	11.9626	0.906882
$175$	0.602358	0.0455340
$176$	3.72757	0.280976
$177$	14.5620	1.09454
$178$	−3.97984	−0.298302
$179$	4.86978	0.363985	0.181992	−	0.983300i	$-0.441745\pi$
$179$	4.86978	0.363985	0.181992	+	0.983300i	$0.441745\pi$
$180$	2.17023	0.161759
$181$	9.52144	0.707723	0.353861	−	0.935298i	$-0.384868\pi$
$181$	9.52144	0.707723	0.353861	+	0.935298i	$0.384868\pi$
$182$	−2.44805	−0.181461
$183$	−7.43261	−0.549434
$184$	7.34847	0.541737
$185$	8.10836	0.596139
$186$	−6.65022	−0.487618
$187$	0.712414	0.0520969
$188$	−0.772617	−0.0563489
$189$	1.00000	0.0727393
$190$	−2.03513	−0.147644
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	1.74047	0.125607
$193$	−4.40259	−0.316905	−0.158453	−	0.987367i	$-0.550651\pi$
$193$	−4.40259	−0.316905	−0.158453	+	0.987367i	$0.550651\pi$
$194$	0.972150	0.0697963
$195$	3.39270	0.242956
$196$	0.916895	0.0654925
$197$	24.3950	1.73807	0.869036	−	0.494748i	$-0.164740\pi$
$197$	24.3950	1.73807	0.869036	+	0.494748i	$0.164740\pi$
$198$	1.27502	0.0906117
$199$	−0.175370	−0.0124316	−0.00621582	−	0.999981i	$-0.501979\pi$
$199$	−0.175370	−0.0124316	−0.00621582	+	0.999981i	$0.501979\pi$
$200$	1.11426	0.0787899
$201$	12.8339	0.905233
$202$	−17.2572	−1.21421
$203$	−7.00431	−0.491606
$204$	−0.874974	−0.0612604
$205$	6.55796	0.458028
$206$	−19.2722	−1.34276
$207$	3.97252	0.276109
$208$	−7.15697	−0.496247
$209$	−0.375840	−0.0259974
$210$	−4.04246	−0.278956
$211$	−14.1014	−0.970783	−0.485391	−	0.874297i	$-0.661323\pi$
$211$	−14.1014	−0.970783	−0.485391	+	0.874297i	$0.661323\pi$
$212$	0.546333	0.0375223
$213$	11.9338	0.817691
$214$	−21.8126	−1.49108
$215$	0.982575	0.0670110
$216$	1.84983	0.125865
$217$	3.89382	0.264330
$218$	−8.16722	−0.553154
$219$	4.44314	0.300240
$220$	−1.62017	−0.109232
$221$	−1.36784	−0.0920109
$222$	−5.85070	−0.392674
$223$	−3.29267	−0.220493	−0.110247	−	0.993904i	$-0.535164\pi$
$223$	−3.29267	−0.220493	−0.110247	+	0.993904i	$0.535164\pi$
$224$	4.82801	0.322585
$225$	0.602358	0.0401572
$226$	−27.8171	−1.85037
$227$	1.78164	0.118252	0.0591259	−	0.998251i	$-0.481169\pi$
$227$	1.78164	0.118252	0.0591259	+	0.998251i	$0.481169\pi$
$228$	0.461600	0.0305702
$229$	−22.0061	−1.45420	−0.727102	−	0.686529i	$-0.759133\pi$
$229$	−22.0061	−1.45420	−0.727102	+	0.686529i	$0.759133\pi$
$230$	−16.0588	−1.05888
$231$	−0.746546	−0.0491191
$232$	−12.9568	−0.850653
$233$	21.8651	1.43243	0.716216	−	0.697879i	$-0.245873\pi$
$233$	21.8651	1.43243	0.716216	+	0.697879i	$0.245873\pi$
$234$	−2.44805	−0.160034
$235$	−1.99448	−0.130106
$236$	13.3518	0.869127
$237$	−10.2846	−0.668060
$238$	1.62981	0.105645
$239$	19.9407	1.28986	0.644930	−	0.764242i	$-0.276887\pi$
$239$	19.9407	1.28986	0.644930	+	0.764242i	$0.276887\pi$
$240$	−11.8183	−0.762868
$241$	12.3395	0.794854	0.397427	−	0.917634i	$-0.369903\pi$
$241$	12.3395	0.794854	0.397427	+	0.917634i	$0.369903\pi$
$242$	17.8349	1.14647
$243$	1.00000	0.0641500
$244$	−6.81492	−0.436280
$245$	2.36693	0.151218
$246$	−4.73199	−0.301701
$247$	0.721616	0.0459153
$248$	7.20289	0.457384
$249$	−12.8515	−0.814428
$250$	17.7773	1.12433
$251$	22.6131	1.42733	0.713664	−	0.700488i	$-0.247034\pi$
$251$	22.6131	1.42733	0.713664	+	0.700488i	$0.247034\pi$
$252$	0.916895	0.0577589
$253$	−2.96567	−0.186450
$254$	−26.8406	−1.68413
$255$	−2.25871	−0.141446
$256$	18.0873	1.13045
$257$	−15.4648	−0.964669	−0.482335	−	0.875987i	$-0.660211\pi$
$257$	−15.4648	−0.964669	−0.482335	+	0.875987i	$0.660211\pi$
$258$	−0.708991	−0.0441398
$259$	3.42569	0.212862
$260$	3.11075	0.192920
$261$	−7.00431	−0.433556
$262$	−7.05390	−0.435792
$263$	−18.9232	−1.16686	−0.583428	−	0.812165i	$-0.698289\pi$
$263$	−18.9232	−1.16686	−0.583428	+	0.812165i	$0.698289\pi$
$264$	−1.38098	−0.0849935
$265$	1.41034	0.0866364
$266$	−0.859818	−0.0527188
$267$	2.33027	0.142610
$268$	11.7673	0.718804
$269$	13.1886	0.804124	0.402062	−	0.915613i	$-0.368294\pi$
$269$	13.1886	0.804124	0.402062	+	0.915613i	$0.368294\pi$
$270$	−4.04246	−0.246016
$271$	−24.8772	−1.51118	−0.755590	−	0.655044i	$-0.772650\pi$
$271$	−24.8772	−1.51118	−0.755590	+	0.655044i	$0.772650\pi$
$272$	4.76481	0.288909
$273$	1.43337	0.0867518
$274$	22.6138	1.36615
$275$	−0.449688	−0.0271172
$276$	3.64238	0.219246
$277$	5.52870	0.332187	0.166094	−	0.986110i	$-0.446885\pi$
$277$	5.52870	0.332187	0.166094	+	0.986110i	$0.446885\pi$
$278$	39.6741	2.37950
$279$	3.89382	0.233117
$280$	4.37841	0.261660
$281$	10.0736	0.600940	0.300470	−	0.953791i	$-0.402856\pi$
$281$	10.0736	0.600940	0.300470	+	0.953791i	$0.402856\pi$
$282$	1.43915	0.0856999
$283$	−30.4246	−1.80855	−0.904276	−	0.426947i	$-0.859589\pi$
$283$	−30.4246	−1.80855	−0.904276	+	0.426947i	$0.859589\pi$
$284$	10.9420	0.649291
$285$	1.19160	0.0705845
$286$	1.82758	0.108067
$287$	2.77066	0.163547
$288$	4.82801	0.284493
$289$	−16.0893	−0.946432
$290$	28.3146	1.66269
$291$	−0.569211	−0.0333677
$292$	4.07389	0.238407
$293$	−14.6843	−0.857867	−0.428934	−	0.903336i	$-0.641111\pi$
$293$	−14.6843	−0.857867	−0.428934	+	0.903336i	$0.641111\pi$
$294$	−1.70789	−0.0996063
$295$	34.4671	2.00675
$296$	6.33693	0.368327
$297$	−0.746546	−0.0433190
$298$	25.1189	1.45510
$299$	5.69411	0.329299
$300$	0.552298	0.0318870
$301$	0.415126	0.0239275
$302$	17.0112	0.978885
$303$	10.1044	0.580481
$304$	−2.51372	−0.144171
$305$	−17.5925	−1.00734
$306$	1.62981	0.0931699
$307$	15.3466	0.875875	0.437938	−	0.899005i	$-0.355709\pi$
$307$	15.3466	0.875875	0.437938	+	0.899005i	$0.355709\pi$
$308$	−0.684504	−0.0390032
$309$	11.2842	0.641936
$310$	−15.7406	−0.894006
$311$	−3.49075	−0.197942	−0.0989712	−	0.995090i	$-0.531555\pi$
$311$	−3.49075	−0.197942	−0.0989712	+	0.995090i	$0.531555\pi$
$312$	2.65149	0.150111
$313$	7.15230	0.404272	0.202136	−	0.979357i	$-0.435212\pi$
$313$	7.15230	0.404272	0.202136	+	0.979357i	$0.435212\pi$
$314$	−16.5615	−0.934617
$315$	2.36693	0.133361
$316$	−9.42994	−0.530475
$317$	−13.5085	−0.758713	−0.379357	−	0.925251i	$-0.623855\pi$
$317$	−13.5085	−0.758713	−0.379357	+	0.925251i	$0.623855\pi$
$318$	−1.01765	−0.0570670
$319$	5.22904	0.292770
$320$	4.11957	0.230291
$321$	12.7716	0.712843
$322$	−6.78463	−0.378093
$323$	−0.480421	−0.0267313
$324$	0.916895	0.0509386
$325$	0.863404	0.0478930
$326$	34.6933	1.92148
$327$	4.78205	0.264448
$328$	5.12524	0.282994
$329$	−0.842645	−0.0464565
$330$	3.01788	0.166129
$331$	−21.5798	−1.18614	−0.593068	−	0.805153i	$-0.702083\pi$
$331$	−21.5798	−1.18614	−0.593068	+	0.805153i	$0.702083\pi$
$332$	−11.7834	−0.646700
$333$	3.42569	0.187727
$334$	−1.84974	−0.101213
$335$	30.3769	1.65967
$336$	−4.99309	−0.272396
$337$	22.3815	1.21920	0.609600	−	0.792709i	$-0.291330\pi$
$337$	22.3815	1.21920	0.609600	+	0.792709i	$0.291330\pi$
$338$	18.6936	1.01680
$339$	16.2874	0.884610
$340$	−2.07100	−0.112316
$341$	−2.90691	−0.157418
$342$	−0.859818	−0.0464937
$343$	1.00000	0.0539949
$344$	0.767912	0.0414030
$345$	9.40268	0.506223
$346$	−34.5049	−1.85499
$347$	23.8265	1.27907	0.639536	−	0.768761i	$-0.279127\pi$
$347$	23.8265	1.27907	0.639536	+	0.768761i	$0.279127\pi$
$348$	−6.42221	−0.344267
$349$	−2.98546	−0.159808	−0.0799039	−	0.996803i	$-0.525461\pi$
$349$	−2.98546	−0.159808	−0.0799039	+	0.996803i	$0.525461\pi$
$350$	−1.02876	−0.0549896
$351$	1.43337	0.0765079
$352$	−3.60433	−0.192112
$353$	−13.4246	−0.714520	−0.357260	−	0.934005i	$-0.616289\pi$
$353$	−13.4246	−0.714520	−0.357260	+	0.934005i	$0.616289\pi$
$354$	−24.8702	−1.32184
$355$	28.2465	1.49917
$356$	2.13661	0.113240
$357$	−0.954280	−0.0505058
$358$	−8.31706	−0.439570
$359$	−23.1991	−1.22440	−0.612200	−	0.790703i	$-0.709715\pi$
$359$	−23.1991	−1.22440	−0.612200	+	0.790703i	$0.709715\pi$
$360$	4.37841	0.230763
$361$	−18.7465	−0.986661
$362$	−16.2616	−0.854690
$363$	−10.4427	−0.548098
$364$	1.31425	0.0688856
$365$	10.5166	0.550464
$366$	12.6941	0.663531
$367$	10.3364	0.539553	0.269777	−	0.962923i	$-0.413050\pi$
$367$	10.3364	0.539553	0.269777	+	0.962923i	$0.413050\pi$
$368$	−19.8352	−1.03398
$369$	2.77066	0.144235
$370$	−13.8482	−0.719934
$371$	0.595852	0.0309351
$372$	3.57022	0.185107
$373$	19.7210	1.02112	0.510558	−	0.859843i	$-0.329439\pi$
$373$	19.7210	1.02112	0.510558	+	0.859843i	$0.329439\pi$
$374$	−1.21673	−0.0629154
$375$	−10.4089	−0.537514
$376$	−1.55875	−0.0803863
$377$	−10.0398	−0.517076
$378$	−1.70789	−0.0878445
$379$	19.7899	1.01654	0.508270	−	0.861198i	$-0.330285\pi$
$379$	19.7899	1.01654	0.508270	+	0.861198i	$0.330285\pi$
$380$	1.09257	0.0560479
$381$	15.7156	0.805136
$382$	−1.70789	−0.0873833
$383$	−17.7405	−0.906498	−0.453249	−	0.891384i	$-0.649735\pi$
$383$	−17.7405	−0.906498	−0.453249	+	0.891384i	$0.649735\pi$
$384$	−12.6286	−0.644448
$385$	−1.76702	−0.0900558
$386$	7.51915	0.382715
$387$	0.415126	0.0211021
$388$	−0.521906	−0.0264958
$389$	21.7958	1.10509	0.552547	−	0.833482i	$-0.313656\pi$
$389$	21.7958	1.10509	0.552547	+	0.833482i	$0.313656\pi$
$390$	−5.79436	−0.293409
$391$	−3.79090	−0.191714
$392$	1.84983	0.0934304
$393$	4.13018	0.208340
$394$	−41.6641	−2.09900
$395$	−24.3430	−1.22483
$396$	−0.684504	−0.0343976
$397$	33.3843	1.67551	0.837755	−	0.546046i	$-0.183868\pi$
$397$	33.3843	1.67551	0.837755	+	0.546046i	$0.183868\pi$
$398$	0.299513	0.0150132
$399$	0.503438	0.0252034
$400$	−3.00763	−0.150381
$401$	24.7226	1.23459	0.617294	−	0.786733i	$-0.288229\pi$
$401$	24.7226	1.23459	0.617294	+	0.786733i	$0.288229\pi$
$402$	−21.9189	−1.09322
$403$	5.58130	0.278024
$404$	9.26464	0.460933
$405$	2.36693	0.117614
$406$	11.9626	0.593694
$407$	−2.55743	−0.126767
$408$	−1.76525	−0.0873930
$409$	2.23356	0.110443	0.0552213	−	0.998474i	$-0.482414\pi$
$409$	2.23356	0.110443	0.0552213	+	0.998474i	$0.482414\pi$
$410$	−11.2003	−0.553143
$411$	−13.2408	−0.653120
$412$	10.3464	0.509732
$413$	14.5620	0.716547
$414$	−6.78463	−0.333447
$415$	−30.4185	−1.49319
$416$	6.92035	0.339298
$417$	−23.2299	−1.13757
$418$	0.641894	0.0313961
$419$	5.99881	0.293061	0.146530	−	0.989206i	$-0.453189\pi$
$419$	5.99881	0.293061	0.146530	+	0.989206i	$0.453189\pi$
$420$	2.17023	0.105896
$421$	−20.0574	−0.977539	−0.488769	−	0.872413i	$-0.662554\pi$
$421$	−20.0574	−0.977539	−0.488769	+	0.872413i	$0.662554\pi$
$422$	24.0837	1.17238
$423$	−0.842645	−0.0409708
$424$	1.10222	0.0535287
$425$	−0.574818	−0.0278828
$426$	−20.3817	−0.987494
$427$	−7.43261	−0.359689
$428$	11.7102	0.566036
$429$	−1.07008	−0.0516639
$430$	−1.67813	−0.0809267
$431$	30.8562	1.48629	0.743145	−	0.669130i	$-0.233333\pi$
$431$	30.8562	1.48629	0.743145	+	0.669130i	$0.233333\pi$
$432$	−4.99309	−0.240230
$433$	35.7742	1.71920	0.859600	−	0.510968i	$-0.170713\pi$
$433$	35.7742	1.71920	0.859600	+	0.510968i	$0.170713\pi$
$434$	−6.65022	−0.319221
$435$	−16.5787	−0.794888
$436$	4.38464	0.209986
$437$	1.99992	0.0956691
$438$	−7.58841	−0.362588
$439$	−19.9489	−0.952107	−0.476053	−	0.879416i	$-0.657933\pi$
$439$	−19.9489	−0.952107	−0.476053	+	0.879416i	$0.657933\pi$
$440$	−3.26869	−0.155828
$441$	1.00000	0.0476190
$442$	2.33612	0.111118
$443$	11.6104	0.551627	0.275814	−	0.961211i	$-0.411053\pi$
$443$	11.6104	0.551627	0.275814	+	0.961211i	$0.411053\pi$
$444$	3.14099	0.149065
$445$	5.51558	0.261463
$446$	5.62352	0.266281
$447$	−14.7076	−0.695644
$448$	1.74047	0.0822294
$449$	38.5350	1.81858	0.909290	−	0.416162i	$-0.136625\pi$
$449$	38.5350	1.81858	0.909290	+	0.416162i	$0.136625\pi$
$450$	−1.02876	−0.0484963
$451$	−2.06843	−0.0973984
$452$	14.9338	0.702428
$453$	−9.96036	−0.467978
$454$	−3.04285	−0.142808
$455$	3.39270	0.159052
$456$	0.931274	0.0436109
$457$	25.1155	1.17486	0.587428	−	0.809277i	$-0.300141\pi$
$457$	25.1155	1.17486	0.587428	+	0.809277i	$0.300141\pi$
$458$	37.5841	1.75619
$459$	−0.954280	−0.0445420
$460$	8.62126	0.401968
$461$	26.6182	1.23973	0.619867	−	0.784707i	$-0.287186\pi$
$461$	26.6182	1.23973	0.619867	+	0.784707i	$0.287186\pi$
$462$	1.27502	0.0593193
$463$	11.1856	0.519838	0.259919	−	0.965630i	$-0.416304\pi$
$463$	11.1856	0.519838	0.259919	+	0.965630i	$0.416304\pi$
$464$	34.9732	1.62359
$465$	9.21640	0.427400
$466$	−37.3433	−1.72989
$467$	−14.3359	−0.663387	−0.331694	−	0.943387i	$-0.607620\pi$
$467$	−14.3359	−0.663387	−0.331694	+	0.943387i	$0.607620\pi$
$468$	1.31425	0.0607514
$469$	12.8339	0.592614
$470$	3.40636	0.157124
$471$	9.69702	0.446815
$472$	26.9371	1.23988
$473$	−0.309911	−0.0142497
$474$	17.5651	0.806790
$475$	0.303250	0.0139141
$476$	−0.874974	−0.0401044
$477$	0.595852	0.0272822
$478$	−34.0566	−1.55771
$479$	−26.0704	−1.19119	−0.595593	−	0.803286i	$-0.703083\pi$
$479$	−26.0704	−1.19119	−0.595593	+	0.803286i	$0.703083\pi$
$480$	11.4276	0.521594
$481$	4.91029	0.223890
$482$	−21.0745	−0.959915
$483$	3.97252	0.180756
$484$	−9.57483	−0.435219
$485$	−1.34728	−0.0611769
$486$	−1.70789	−0.0774715
$487$	−31.3411	−1.42020	−0.710100	−	0.704100i	$-0.751351\pi$
$487$	−31.3411	−1.42020	−0.710100	+	0.704100i	$0.751351\pi$
$488$	−13.7490	−0.622390
$489$	−20.3135	−0.918609
$490$	−4.04246	−0.182620
$491$	−31.5245	−1.42268	−0.711339	−	0.702849i	$-0.751911\pi$
$491$	−31.5245	−1.42268	−0.711339	+	0.702849i	$0.751911\pi$
$492$	2.54040	0.114530
$493$	6.68407	0.301035
$494$	−1.23244	−0.0554502
$495$	−1.76702	−0.0794217
$496$	−19.4422	−0.872981
$497$	11.9338	0.535304
$498$	21.9489	0.983554
$499$	−5.94417	−0.266098	−0.133049	−	0.991109i	$-0.542477\pi$
$499$	−5.94417	−0.266098	−0.133049	+	0.991109i	$0.542477\pi$
$500$	−9.54387	−0.426815
$501$	1.08305	0.0483872
$502$	−38.6208	−1.72373
$503$	3.59264	0.160188	0.0800941	−	0.996787i	$-0.474478\pi$
$503$	3.59264	0.160188	0.0800941	+	0.996787i	$0.474478\pi$
$504$	1.84983	0.0823978
$505$	23.9163	1.06426
$506$	5.06504	0.225169
$507$	−10.9454	−0.486104
$508$	14.4096	0.639321
$509$	−15.2981	−0.678076	−0.339038	−	0.940773i	$-0.610101\pi$
$509$	−15.2981	−0.678076	−0.339038	+	0.940773i	$0.610101\pi$
$510$	3.85764	0.170819
$511$	4.44314	0.196553
$512$	−5.63399	−0.248989
$513$	0.503438	0.0222273
$514$	26.4123	1.16499
$515$	26.7089	1.17694
$516$	0.380627	0.0167562
$517$	0.629073	0.0276666
$518$	−5.85070	−0.257065
$519$	20.2032	0.886822
$520$	6.27590	0.275216
$521$	16.0166	0.701702	0.350851	−	0.936431i	$-0.385892\pi$
$521$	16.0166	0.701702	0.350851	+	0.936431i	$0.385892\pi$
$522$	11.9626	0.523589
$523$	−28.2136	−1.23369	−0.616847	−	0.787083i	$-0.711590\pi$
$523$	−28.2136	−1.23369	−0.616847	+	0.787083i	$0.711590\pi$
$524$	3.78694	0.165433
$525$	0.602358	0.0262890
$526$	32.3188	1.40917
$527$	−3.71579	−0.161862
$528$	3.72757	0.162222
$529$	−7.21909	−0.313873
$530$	−2.40871	−0.104628
$531$	14.5620	0.631935
$532$	0.461600	0.0200129
$533$	3.97139	0.172020
$534$	−3.97984	−0.172225
$535$	30.2296	1.30694
$536$	23.7405	1.02543
$537$	4.86978	0.210147
$538$	−22.5247	−0.971110
$539$	−0.746546	−0.0321560
$540$	2.17023	0.0933916
$541$	7.82222	0.336303	0.168152	−	0.985761i	$-0.446220\pi$
$541$	7.82222	0.336303	0.168152	+	0.985761i	$0.446220\pi$
$542$	42.4875	1.82500
$543$	9.52144	0.408604
$544$	−4.60727	−0.197535
$545$	11.3188	0.484843
$546$	−2.44805	−0.104767
$547$	32.3132	1.38161	0.690806	−	0.723040i	$-0.257256\pi$
$547$	32.3132	1.38161	0.690806	+	0.723040i	$0.257256\pi$
$548$	−12.1404	−0.518612
$549$	−7.43261	−0.317216
$550$	0.768018	0.0327484
$551$	−3.52624	−0.150223
$552$	7.34847	0.312772
$553$	−10.2846	−0.437348
$554$	−9.44241	−0.401170
$555$	8.10836	0.344181
$556$	−21.2994	−0.903294
$557$	17.0617	0.722929	0.361464	−	0.932386i	$-0.382277\pi$
$557$	17.0617	0.722929	0.361464	+	0.932386i	$0.382277\pi$
$558$	−6.65022	−0.281526
$559$	0.595031	0.0251671
$560$	−11.8183	−0.499414
$561$	0.712414	0.0300781
$562$	−17.2046	−0.725733
$563$	−7.44612	−0.313817	−0.156908	−	0.987613i	$-0.550153\pi$
$563$	−7.44612	−0.313817	−0.156908	+	0.987613i	$0.550153\pi$
$564$	−0.772617	−0.0325330
$565$	38.5511	1.62186
$566$	51.9619	2.18412
$567$	1.00000	0.0419961
$568$	22.0755	0.926266
$569$	−27.4004	−1.14868	−0.574341	−	0.818616i	$-0.694742\pi$
$569$	−27.4004	−1.14868	−0.574341	+	0.818616i	$0.694742\pi$
$570$	−2.03513	−0.0852422
$571$	0.577266	0.0241578	0.0120789	−	0.999927i	$-0.496155\pi$
$571$	0.577266	0.0241578	0.0120789	+	0.999927i	$0.496155\pi$
$572$	−0.981151	−0.0410240
$573$	1.00000	0.0417756
$574$	−4.73199	−0.197509
$575$	2.39288	0.0997899
$576$	1.74047	0.0725195
$577$	−22.4514	−0.934663	−0.467331	−	0.884082i	$-0.654785\pi$
$577$	−22.4514	−0.934663	−0.467331	+	0.884082i	$0.654785\pi$
$578$	27.4789	1.14297
$579$	−4.40259	−0.182965
$580$	−15.2009	−0.631184
$581$	−12.8515	−0.533168
$582$	0.972150	0.0402969
$583$	−0.444831	−0.0184230
$584$	8.21904	0.340106
$585$	3.39270	0.140271
$586$	25.0792	1.03601
$587$	22.8094	0.941445	0.470722	−	0.882281i	$-0.343993\pi$
$587$	22.8094	0.941445	0.470722	+	0.882281i	$0.343993\pi$
$588$	0.916895	0.0378121
$589$	1.96030	0.0807727
$590$	−58.8661	−2.42348
$591$	24.3950	1.00348
$592$	−17.1048	−0.703002
$593$	−11.4661	−0.470856	−0.235428	−	0.971892i	$-0.575649\pi$
$593$	−11.4661	−0.470856	−0.235428	+	0.971892i	$0.575649\pi$
$594$	1.27502	0.0523147
$595$	−2.25871	−0.0925982
$596$	−13.4853	−0.552379
$597$	−0.175370	−0.00717741
$598$	−9.72492	−0.397682
$599$	16.6536	0.680447	0.340224	−	0.940345i	$-0.389497\pi$
$599$	16.6536	0.680447	0.340224	+	0.940345i	$0.389497\pi$
$600$	1.11426	0.0454894
$601$	37.9878	1.54956	0.774778	−	0.632234i	$-0.217862\pi$
$601$	37.9878	1.54956	0.774778	+	0.632234i	$0.217862\pi$
$602$	−0.708991	−0.0288963
$603$	12.8339	0.522636
$604$	−9.13260	−0.371600
$605$	−24.7171	−1.00489
$606$	−17.2572	−0.701025
$607$	−37.2374	−1.51142	−0.755711	−	0.654906i	$-0.772708\pi$
$607$	−37.2374	−1.51142	−0.755711	+	0.654906i	$0.772708\pi$
$608$	2.43061	0.0985741
$609$	−7.00431	−0.283829
$610$	30.0460	1.21653
$611$	−1.20783	−0.0488634
$612$	−0.874974	−0.0353687
$613$	−38.2344	−1.54427	−0.772137	−	0.635456i	$-0.780812\pi$
$613$	−38.2344	−1.54427	−0.772137	+	0.635456i	$0.780812\pi$
$614$	−26.2103	−1.05776
$615$	6.55796	0.264442
$616$	−1.38098	−0.0556413
$617$	6.80928	0.274131	0.137066	−	0.990562i	$-0.456233\pi$
$617$	6.80928	0.274131	0.137066	+	0.990562i	$0.456233\pi$
$618$	−19.2722	−0.775242
$619$	23.9525	0.962734	0.481367	−	0.876519i	$-0.340140\pi$
$619$	23.9525	0.962734	0.481367	+	0.876519i	$0.340140\pi$
$620$	8.45046	0.339379
$621$	3.97252	0.159412
$622$	5.96183	0.239048
$623$	2.33027	0.0933602
$624$	−7.15697	−0.286508
$625$	−27.6490	−1.10596
$626$	−12.2154	−0.488224
$627$	−0.375840	−0.0150096
$628$	8.89114	0.354795
$629$	−3.26907	−0.130346
$630$	−4.04246	−0.161055
$631$	−28.9444	−1.15226	−0.576129	−	0.817359i	$-0.695437\pi$
$631$	−28.9444	−1.15226	−0.576129	+	0.817359i	$0.695437\pi$
$632$	−19.0248	−0.756766
$633$	−14.1014	−0.560482
$634$	23.0711	0.916269
$635$	37.1978	1.47615
$636$	0.546333	0.0216635
$637$	1.43337	0.0567924
$638$	−8.93063	−0.353567
$639$	11.9338	0.472094
$640$	−29.8909	−1.18154
$641$	6.98089	0.275729	0.137864	−	0.990451i	$-0.455976\pi$
$641$	6.98089	0.275729	0.137864	+	0.990451i	$0.455976\pi$
$642$	−21.8126	−0.860873
$643$	−41.2065	−1.62503	−0.812513	−	0.582943i	$-0.801901\pi$
$643$	−41.2065	−1.62503	−0.812513	+	0.582943i	$0.801901\pi$
$644$	3.64238	0.143530
$645$	0.982575	0.0386888
$646$	0.820507	0.0322824
$647$	−23.8577	−0.937944	−0.468972	−	0.883213i	$-0.655376\pi$
$647$	−23.8577	−0.937944	−0.468972	+	0.883213i	$0.655376\pi$
$648$	1.84983	0.0726681
$649$	−10.8712	−0.426731
$650$	−1.47460	−0.0578386
$651$	3.89382	0.152611
$652$	−18.6254	−0.729426
$653$	39.5460	1.54755	0.773777	−	0.633459i	$-0.218365\pi$
$653$	39.5460	1.54755	0.773777	+	0.633459i	$0.218365\pi$
$654$	−8.16722	−0.319364
$655$	9.77585	0.381974
$656$	−13.8342	−0.540133
$657$	4.44314	0.173344
$658$	1.43915	0.0561038
$659$	0.428389	0.0166876	0.00834382	−	0.999965i	$-0.497344\pi$
$659$	0.428389	0.0166876	0.00834382	+	0.999965i	$0.497344\pi$
$660$	−1.62017	−0.0630652
$661$	37.8857	1.47358	0.736791	−	0.676121i	$-0.236340\pi$
$661$	37.8857	1.47358	0.736791	+	0.676121i	$0.236340\pi$
$662$	36.8560	1.43245
$663$	−1.36784	−0.0531225
$664$	−23.7730	−0.922571
$665$	1.19160	0.0462084
$666$	−5.85070	−0.226710
$667$	−27.8247	−1.07738
$668$	0.993044	0.0384220
$669$	−3.29267	−0.127302
$670$	−51.8805	−2.00432
$671$	5.54878	0.214208
$672$	4.82801	0.186245
$673$	29.6589	1.14327	0.571633	−	0.820509i	$-0.306310\pi$
$673$	29.6589	1.14327	0.571633	+	0.820509i	$0.306310\pi$
$674$	−38.2252	−1.47238
$675$	0.602358	0.0231848
$676$	−10.0358	−0.385993
$677$	−11.6409	−0.447396	−0.223698	−	0.974659i	$-0.571813\pi$
$677$	−11.6409	−0.447396	−0.223698	+	0.974659i	$0.571813\pi$
$678$	−27.8171	−1.06831
$679$	−0.569211	−0.0218443
$680$	−4.17823	−0.160228
$681$	1.78164	0.0682727
$682$	4.96470	0.190108
$683$	−7.68360	−0.294005	−0.147002	−	0.989136i	$-0.546962\pi$
$683$	−7.68360	−0.294005	−0.147002	+	0.989136i	$0.546962\pi$
$684$	0.461600	0.0176497
$685$	−31.3400	−1.19744
$686$	−1.70789	−0.0652076
$687$	−22.0061	−0.839586
$688$	−2.07276	−0.0790234
$689$	0.854078	0.0325378
$690$	−16.0588	−0.611346
$691$	34.3930	1.30837	0.654185	−	0.756335i	$-0.273012\pi$
$691$	34.3930	1.30837	0.654185	+	0.756335i	$0.273012\pi$
$692$	18.5242	0.704185
$693$	−0.746546	−0.0283589
$694$	−40.6930	−1.54469
$695$	−54.9835	−2.08564
$696$	−12.9568	−0.491125
$697$	−2.64399	−0.100148
$698$	5.09884	0.192994
$699$	21.8651	0.827015
$700$	0.552298	0.0208749
$701$	25.5989	0.966857	0.483428	−	0.875384i	$-0.339391\pi$
$701$	25.5989	0.966857	0.483428	+	0.875384i	$0.339391\pi$
$702$	−2.44805	−0.0923956
$703$	1.72462	0.0650454
$704$	−1.29934	−0.0489707
$705$	−1.99448	−0.0751165
$706$	22.9278	0.862899
$707$	10.1044	0.380014
$708$	13.3518	0.501791
$709$	−45.9736	−1.72658	−0.863288	−	0.504712i	$-0.831599\pi$
$709$	−45.9736	−1.72658	−0.863288	+	0.504712i	$0.831599\pi$
$710$	−48.2419	−1.81049
$711$	−10.2846	−0.385704
$712$	4.31059	0.161546
$713$	15.4683	0.579291
$714$	1.62981	0.0609940
$715$	−2.53280	−0.0947215
$716$	4.46508	0.166868
$717$	19.9407	0.744701
$718$	39.6215	1.47866
$719$	8.85492	0.330233	0.165116	−	0.986274i	$-0.447200\pi$
$719$	8.85492	0.330233	0.165116	+	0.986274i	$0.447200\pi$
$720$	−11.8183	−0.440442
$721$	11.2842	0.420246
$722$	32.0171	1.19155
$723$	12.3395	0.458909
$724$	8.73015	0.324454
$725$	−4.21910	−0.156693
$726$	17.8349	0.661917
$727$	−17.0445	−0.632147	−0.316073	−	0.948735i	$-0.602365\pi$
$727$	−17.0445	−0.632147	−0.316073	+	0.948735i	$0.602365\pi$
$728$	2.65149	0.0982709
$729$	1.00000	0.0370370
$730$	−17.9612	−0.664775
$731$	−0.396147	−0.0146520
$732$	−6.81492	−0.251887
$733$	−18.3332	−0.677153	−0.338576	−	0.940939i	$-0.609945\pi$
$733$	−18.3332	−0.677153	−0.338576	+	0.940939i	$0.609945\pi$
$734$	−17.6534	−0.651598
$735$	2.36693	0.0873055
$736$	19.1794	0.706961
$737$	−9.58109	−0.352924
$738$	−4.73199	−0.174187
$739$	24.4925	0.900971	0.450486	−	0.892784i	$-0.351251\pi$
$739$	24.4925	0.900971	0.450486	+	0.892784i	$0.351251\pi$
$740$	7.43451	0.273298
$741$	0.721616	0.0265092
$742$	−1.01765	−0.0373591
$743$	−38.3160	−1.40568	−0.702839	−	0.711349i	$-0.748085\pi$
$743$	−38.3160	−1.40568	−0.702839	+	0.711349i	$0.748085\pi$
$744$	7.20289	0.264071
$745$	−34.8118	−1.27540
$746$	−33.6814	−1.23316
$747$	−12.8515	−0.470210
$748$	0.653208	0.0238837
$749$	12.7716	0.466665
$750$	17.7773	0.649135
$751$	19.2324	0.701799	0.350899	−	0.936413i	$-0.385876\pi$
$751$	19.2324	0.701799	0.350899	+	0.936413i	$0.385876\pi$
$752$	4.20741	0.153428
$753$	22.6131	0.824068
$754$	17.1469	0.624453
$755$	−23.5755	−0.857999
$756$	0.916895	0.0333471
$757$	−27.0104	−0.981711	−0.490856	−	0.871241i	$-0.663316\pi$
$757$	−27.0104	−0.981711	−0.490856	+	0.871241i	$0.663316\pi$
$758$	−33.7990	−1.22764
$759$	−2.96567	−0.107647
$760$	2.20426	0.0799569
$761$	−15.8137	−0.573248	−0.286624	−	0.958043i	$-0.592533\pi$
$761$	−15.8137	−0.573248	−0.286624	+	0.958043i	$0.592533\pi$
$762$	−26.8406	−0.972332
$763$	4.78205	0.173122
$764$	0.916895	0.0331721
$765$	−2.25871	−0.0816640
$766$	30.2989	1.09474
$767$	20.8727	0.753671
$768$	18.0873	0.652668
$769$	17.4587	0.629576	0.314788	−	0.949162i	$-0.398067\pi$
$769$	17.4587	0.629576	0.314788	+	0.949162i	$0.398067\pi$
$770$	3.01788	0.108757
$771$	−15.4648	−0.556952
$772$	−4.03671	−0.145284
$773$	−35.2203	−1.26679	−0.633394	−	0.773830i	$-0.718339\pi$
$773$	−35.2203	−1.26679	−0.633394	+	0.773830i	$0.718339\pi$
$774$	−0.708991	−0.0254841
$775$	2.34547	0.0842518
$776$	−1.05294	−0.0377984
$777$	3.42569	0.122896
$778$	−37.2249	−1.33458
$779$	1.39486	0.0499759
$780$	3.11075	0.111383
$781$	−8.90914	−0.318794
$782$	6.47444	0.231525
$783$	−7.00431	−0.250313
$784$	−4.99309	−0.178325
$785$	22.9522	0.819198
$786$	−7.05390	−0.251604
$787$	42.1517	1.50255	0.751273	−	0.659992i	$-0.229440\pi$
$787$	42.1517	1.50255	0.751273	+	0.659992i	$0.229440\pi$
$788$	22.3677	0.796815
$789$	−18.9232	−0.673685
$790$	41.5753	1.47918
$791$	16.2874	0.579113
$792$	−1.38098	−0.0490710
$793$	−10.6537	−0.378324
$794$	−57.0168	−2.02345
$795$	1.41034	0.0500196
$796$	−0.160796	−0.00569925
$797$	−31.0489	−1.09981	−0.549904	−	0.835228i	$-0.685336\pi$
$797$	−31.0489	−1.09981	−0.549904	+	0.835228i	$0.685336\pi$
$798$	−0.859818	−0.0304372
$799$	0.804119	0.0284477
$800$	2.90819	0.102820
$801$	2.33027	0.0823359
$802$	−42.2235	−1.49096
$803$	−3.31701	−0.117055
$804$	11.7673	0.415002
$805$	9.40268	0.331401
$806$	−9.53226	−0.335759
$807$	13.1886	0.464261
$808$	18.6913	0.657559
$809$	16.4521	0.578425	0.289213	−	0.957265i	$-0.406607\pi$
$809$	16.4521	0.578425	0.289213	+	0.957265i	$0.406607\pi$
$810$	−4.04246	−0.142038
$811$	−7.60557	−0.267068	−0.133534	−	0.991044i	$-0.542633\pi$
$811$	−7.60557	−0.267068	−0.133534	+	0.991044i	$0.542633\pi$
$812$	−6.42221	−0.225375
$813$	−24.8772	−0.872481
$814$	4.36782	0.153092
$815$	−48.0807	−1.68419
$816$	4.76481	0.166802
$817$	0.208990	0.00731165
$818$	−3.81468	−0.133377
$819$	1.43337	0.0500862
$820$	6.01296	0.209982
$821$	26.2294	0.915412	0.457706	−	0.889104i	$-0.348671\pi$
$821$	26.2294	0.915412	0.457706	+	0.889104i	$0.348671\pi$
$822$	22.6138	0.788748
$823$	18.7004	0.651856	0.325928	−	0.945395i	$-0.394323\pi$
$823$	18.7004	0.651856	0.325928	+	0.945395i	$0.394323\pi$
$824$	20.8738	0.727175
$825$	−0.449688	−0.0156561
$826$	−24.8702	−0.865346
$827$	7.57979	0.263575	0.131787	−	0.991278i	$-0.457928\pi$
$827$	7.57979	0.263575	0.131787	+	0.991278i	$0.457928\pi$
$828$	3.64238	0.126582
$829$	30.0250	1.04281	0.521406	−	0.853309i	$-0.325408\pi$
$829$	30.0250	1.04281	0.521406	+	0.853309i	$0.325408\pi$
$830$	51.9515	1.80326
$831$	5.52870	0.191788
$832$	2.49474	0.0864896
$833$	−0.954280	−0.0330638
$834$	39.6741	1.37380
$835$	2.56351	0.0887139
$836$	−0.344606	−0.0119184
$837$	3.89382	0.134590
$838$	−10.2453	−0.353918
$839$	−50.6858	−1.74987	−0.874934	−	0.484241i	$-0.839096\pi$
$839$	−50.6858	−1.74987	−0.874934	+	0.484241i	$0.839096\pi$
$840$	4.37841	0.151070
$841$	20.0603	0.691735
$842$	34.2559	1.18054
$843$	10.0736	0.346953
$844$	−12.9295	−0.445053
$845$	−25.9071	−0.891231
$846$	1.43915	0.0494789
$847$	−10.4427	−0.358814
$848$	−2.97514	−0.102167
$849$	−30.4246	−1.04417
$850$	0.981727	0.0336729
$851$	13.6086	0.466497
$852$	10.9420	0.374868
$853$	−56.1334	−1.92197	−0.960986	−	0.276598i	$-0.910793\pi$
$853$	−56.1334	−1.92197	−0.960986	+	0.276598i	$0.910793\pi$
$854$	12.6941	0.434383
$855$	1.19160	0.0407520
$856$	23.6253	0.807496
$857$	−41.2925	−1.41053	−0.705263	−	0.708946i	$-0.749171\pi$
$857$	−41.2925	−1.41053	−0.705263	+	0.708946i	$0.749171\pi$
$858$	1.82758	0.0623926
$859$	−26.9755	−0.920392	−0.460196	−	0.887817i	$-0.652221\pi$
$859$	−26.9755	−0.920392	−0.460196	+	0.887817i	$0.652221\pi$
$860$	0.900917	0.0307210
$861$	2.77066	0.0944239
$862$	−52.6991	−1.79494
$863$	−11.9250	−0.405933	−0.202966	−	0.979186i	$-0.565058\pi$
$863$	−11.9250	−0.405933	−0.202966	+	0.979186i	$0.565058\pi$
$864$	4.82801	0.164252
$865$	47.8196	1.62591
$866$	−61.0985	−2.07621
$867$	−16.0893	−0.546423
$868$	3.57022	0.121181
$869$	7.67796	0.260457
$870$	28.3146	0.959956
$871$	18.3958	0.623317
$872$	8.84596	0.299562
$873$	−0.569211	−0.0192649
$874$	−3.41565	−0.115536
$875$	−10.4089	−0.351885
$876$	4.07389	0.137644
$877$	−24.2848	−0.820038	−0.410019	−	0.912077i	$-0.634478\pi$
$877$	−24.2848	−0.820038	−0.410019	+	0.912077i	$0.634478\pi$
$878$	34.0705	1.14982
$879$	−14.6843	−0.495290
$880$	8.82291	0.297420
$881$	−20.8148	−0.701267	−0.350633	−	0.936513i	$-0.614034\pi$
$881$	−20.8148	−0.701267	−0.350633	+	0.936513i	$0.614034\pi$
$882$	−1.70789	−0.0575077
$883$	−5.60631	−0.188667	−0.0943337	−	0.995541i	$-0.530072\pi$
$883$	−5.60631	−0.188667	−0.0943337	+	0.995541i	$0.530072\pi$
$884$	−1.25417	−0.0421821
$885$	34.4671	1.15860
$886$	−19.8293	−0.666179
$887$	−22.1866	−0.744953	−0.372476	−	0.928042i	$-0.621491\pi$
$887$	−22.1866	−0.744953	−0.372476	+	0.928042i	$0.621491\pi$
$888$	6.33693	0.212653
$889$	15.7156	0.527085
$890$	−9.42001	−0.315759
$891$	−0.746546	−0.0250102
$892$	−3.01903	−0.101084
$893$	−0.424220	−0.0141960
$894$	25.1189	0.840103
$895$	11.5264	0.385286
$896$	−12.6286	−0.421890
$897$	5.69411	0.190121
$898$	−65.8137	−2.19623
$899$	−27.2735	−0.909622
$900$	0.552298	0.0184099
$901$	−0.568609	−0.0189431
$902$	3.53265	0.117624
$903$	0.415126	0.0138145
$904$	30.1289	1.00207
$905$	22.5366	0.749141
$906$	17.0112	0.565160
$907$	−0.353016	−0.0117217	−0.00586086	−	0.999983i	$-0.501866\pi$
$907$	−0.353016	−0.0117217	−0.00586086	+	0.999983i	$0.501866\pi$
$908$	1.63358	0.0542122
$909$	10.1044	0.335141
$910$	−5.79436	−0.192081
$911$	2.60705	0.0863755	0.0431877	−	0.999067i	$-0.486249\pi$
$911$	2.60705	0.0863755	0.0431877	+	0.999067i	$0.486249\pi$
$912$	−2.51372	−0.0832374
$913$	9.59421	0.317522
$914$	−42.8946	−1.41883
$915$	−17.5925	−0.581589
$916$	−20.1773	−0.666676
$917$	4.13018	0.136391
$918$	1.62981	0.0537916
$919$	−9.64557	−0.318178	−0.159089	−	0.987264i	$-0.550856\pi$
$919$	−9.64557	−0.318178	−0.159089	+	0.987264i	$0.550856\pi$
$920$	17.3933	0.573441
$921$	15.3466	0.505687
$922$	−45.4611	−1.49718
$923$	17.1056	0.563038
$924$	−0.684504	−0.0225185
$925$	2.06349	0.0678471
$926$	−19.1038	−0.627789
$927$	11.2842	0.370622
$928$	−33.8169	−1.11009
$929$	−38.1951	−1.25314	−0.626570	−	0.779365i	$-0.715542\pi$
$929$	−38.1951	−1.25314	−0.626570	+	0.779365i	$0.715542\pi$
$930$	−15.7406	−0.516155
$931$	0.503438	0.0164995
$932$	20.0480	0.656695
$933$	−3.49075	−0.114282
$934$	24.4842	0.801148
$935$	1.68623	0.0551457
$936$	2.65149	0.0866668
$937$	−1.80104	−0.0588373	−0.0294186	−	0.999567i	$-0.509366\pi$
$937$	−1.80104	−0.0588373	−0.0294186	+	0.999567i	$0.509366\pi$
$938$	−21.9189	−0.715677
$939$	7.15230	0.233407
$940$	−1.82873	−0.0596466
$941$	−15.8526	−0.516781	−0.258390	−	0.966041i	$-0.583192\pi$
$941$	−15.8526	−0.516781	−0.258390	+	0.966041i	$0.583192\pi$
$942$	−16.5615	−0.539602
$943$	11.0065	0.358421
$944$	−72.7092	−2.36648
$945$	2.36693	0.0769962
$946$	0.529294	0.0172088
$947$	−3.13169	−0.101766	−0.0508832	−	0.998705i	$-0.516204\pi$
$947$	−3.13169	−0.101766	−0.0508832	+	0.998705i	$0.516204\pi$
$948$	−9.42994	−0.306270
$949$	6.36869	0.206736
$950$	−0.517918	−0.0168035
$951$	−13.5085	−0.438043
$952$	−1.76525	−0.0572122
$953$	−58.3557	−1.89033	−0.945163	−	0.326599i	$-0.894097\pi$
$953$	−58.3557	−1.89033	−0.945163	+	0.326599i	$0.894097\pi$
$954$	−1.01765	−0.0329476
$955$	2.36693	0.0765921
$956$	18.2836	0.591333
$957$	5.22904	0.169031
$958$	44.5254	1.43855
$959$	−13.2408	−0.427567
$960$	4.11957	0.132958
$961$	−15.8382	−0.510909
$962$	−8.38625	−0.270384
$963$	12.7716	0.411560
$964$	11.3140	0.364399
$965$	−10.4206	−0.335452
$966$	−6.78463	−0.218292
$967$	−51.0738	−1.64242	−0.821211	−	0.570625i	$-0.806701\pi$
$967$	−51.0738	−1.64242	−0.821211	+	0.570625i	$0.806701\pi$
$968$	−19.3171	−0.620876
$969$	−0.480421	−0.0154334
$970$	2.30101	0.0738810
$971$	−14.8890	−0.477811	−0.238905	−	0.971043i	$-0.576789\pi$
$971$	−14.8890	−0.477811	−0.238905	+	0.971043i	$0.576789\pi$
$972$	0.916895	0.0294094
$973$	−23.2299	−0.744716
$974$	53.5272	1.71512
$975$	0.863404	0.0276511
$976$	37.1117	1.18792
$977$	15.5786	0.498402	0.249201	−	0.968452i	$-0.419832\pi$
$977$	15.5786	0.498402	0.249201	+	0.968452i	$0.419832\pi$
$978$	34.6933	1.10937
$979$	−1.73965	−0.0555995
$980$	2.17023	0.0693253
$981$	4.78205	0.152679
$982$	53.8404	1.71811
$983$	−0.245331	−0.00782483	−0.00391242	−	0.999992i	$-0.501245\pi$
$983$	−0.245331	−0.00782483	−0.00391242	+	0.999992i	$0.501245\pi$
$984$	5.12524	0.163387
$985$	57.7413	1.83979
$986$	−11.4157	−0.363549
$987$	−0.842645	−0.0268217
$988$	0.661646	0.0210497
$989$	1.64910	0.0524382
$990$	3.01788	0.0959146
$991$	5.33448	0.169455	0.0847276	−	0.996404i	$-0.472998\pi$
$991$	5.33448	0.169455	0.0847276	+	0.996404i	$0.472998\pi$
$992$	18.7994	0.596881
$993$	−21.5798	−0.684816
$994$	−20.3817	−0.646467
$995$	−0.415088	−0.0131592
$996$	−11.7834	−0.373372
$997$	10.2018	0.323096	0.161548	−	0.986865i	$-0.448351\pi$
$997$	10.2018	0.323096	0.161548	+	0.986865i	$0.448351\pi$
$998$	10.1520	0.321356
$999$	3.42569	0.108384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.4	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.4	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-1.70789 q^{2} +1.00000 q^{3} +0.916895 q^{4} +2.36693 q^{5} -1.70789 q^{6} +1.00000 q^{7} +1.84983 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.70789 q^{2} +1.00000 q^{3} +0.916895 q^{4} +2.36693 q^{5} -1.70789 q^{6} +1.00000 q^{7} +1.84983 q^{8} +1.00000 q^{9} -4.04246 q^{10} -0.746546 q^{11} +0.916895 q^{12} +1.43337 q^{13} -1.70789 q^{14} +2.36693 q^{15} -4.99309 q^{16} -0.954280 q^{17} -1.70789 q^{18} +0.503438 q^{19} +2.17023 q^{20} +1.00000 q^{21} +1.27502 q^{22} +3.97252 q^{23} +1.84983 q^{24} +0.602358 q^{25} -2.44805 q^{26} +1.00000 q^{27} +0.916895 q^{28} -7.00431 q^{29} -4.04246 q^{30} +3.89382 q^{31} +4.82801 q^{32} -0.746546 q^{33} +1.62981 q^{34} +2.36693 q^{35} +0.916895 q^{36} +3.42569 q^{37} -0.859818 q^{38} +1.43337 q^{39} +4.37841 q^{40} +2.77066 q^{41} -1.70789 q^{42} +0.415126 q^{43} -0.684504 q^{44} +2.36693 q^{45} -6.78463 q^{46} -0.842645 q^{47} -4.99309 q^{48} +1.00000 q^{49} -1.02876 q^{50} -0.954280 q^{51} +1.31425 q^{52} +0.595852 q^{53} -1.70789 q^{54} -1.76702 q^{55} +1.84983 q^{56} +0.503438 q^{57} +11.9626 q^{58} +14.5620 q^{59} +2.17023 q^{60} -7.43261 q^{61} -6.65022 q^{62} +1.00000 q^{63} +1.74047 q^{64} +3.39270 q^{65} +1.27502 q^{66} +12.8339 q^{67} -0.874974 q^{68} +3.97252 q^{69} -4.04246 q^{70} +11.9338 q^{71} +1.84983 q^{72} +4.44314 q^{73} -5.85070 q^{74} +0.602358 q^{75} +0.461600 q^{76} -0.746546 q^{77} -2.44805 q^{78} -10.2846 q^{79} -11.8183 q^{80} +1.00000 q^{81} -4.73199 q^{82} -12.8515 q^{83} +0.916895 q^{84} -2.25871 q^{85} -0.708991 q^{86} -7.00431 q^{87} -1.38098 q^{88} +2.33027 q^{89} -4.04246 q^{90} +1.43337 q^{91} +3.64238 q^{92} +3.89382 q^{93} +1.43915 q^{94} +1.19160 q^{95} +4.82801 q^{96} -0.569211 q^{97} -1.70789 q^{98} -0.746546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 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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