LMFDB - Embedded newform 4011.2.a.k.1.13

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			1.13
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)

$f(q)$	$=$	$q+0.267433 q^{2} +1.00000 q^{3} -1.92848 q^{4} +0.0366447 q^{5} +0.267433 q^{6} +1.00000 q^{7} -1.05060 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.267433 q^{2} +1.00000 q^{3} -1.92848 q^{4} +0.0366447 q^{5} +0.267433 q^{6} +1.00000 q^{7} -1.05060 q^{8} +1.00000 q^{9} +0.00980000 q^{10} +4.21101 q^{11} -1.92848 q^{12} +3.67485 q^{13} +0.267433 q^{14} +0.0366447 q^{15} +3.57599 q^{16} -6.13318 q^{17} +0.267433 q^{18} -2.34693 q^{19} -0.0706686 q^{20} +1.00000 q^{21} +1.12616 q^{22} +7.94611 q^{23} -1.05060 q^{24} -4.99866 q^{25} +0.982774 q^{26} +1.00000 q^{27} -1.92848 q^{28} +0.655666 q^{29} +0.00980000 q^{30} +5.37695 q^{31} +3.05755 q^{32} +4.21101 q^{33} -1.64021 q^{34} +0.0366447 q^{35} -1.92848 q^{36} +2.83216 q^{37} -0.627645 q^{38} +3.67485 q^{39} -0.0384991 q^{40} -4.58297 q^{41} +0.267433 q^{42} -4.32631 q^{43} -8.12085 q^{44} +0.0366447 q^{45} +2.12505 q^{46} +0.864954 q^{47} +3.57599 q^{48} +1.00000 q^{49} -1.33680 q^{50} -6.13318 q^{51} -7.08687 q^{52} -7.72969 q^{53} +0.267433 q^{54} +0.154311 q^{55} -1.05060 q^{56} -2.34693 q^{57} +0.175347 q^{58} +14.3507 q^{59} -0.0706686 q^{60} -2.75729 q^{61} +1.43797 q^{62} +1.00000 q^{63} -6.33430 q^{64} +0.134664 q^{65} +1.12616 q^{66} +5.99139 q^{67} +11.8277 q^{68} +7.94611 q^{69} +0.00980000 q^{70} -1.19268 q^{71} -1.05060 q^{72} +13.2813 q^{73} +0.757413 q^{74} -4.99866 q^{75} +4.52600 q^{76} +4.21101 q^{77} +0.982774 q^{78} -3.61434 q^{79} +0.131041 q^{80} +1.00000 q^{81} -1.22564 q^{82} +10.6258 q^{83} -1.92848 q^{84} -0.224749 q^{85} -1.15700 q^{86} +0.655666 q^{87} -4.42411 q^{88} +5.66725 q^{89} +0.00980000 q^{90} +3.67485 q^{91} -15.3239 q^{92} +5.37695 q^{93} +0.231317 q^{94} -0.0860025 q^{95} +3.05755 q^{96} -5.01426 q^{97} +0.267433 q^{98} +4.21101 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.267433	0.189104	0.0945518	−	0.995520i	$-0.469858\pi$
$2$	0.267433	0.189104	0.0945518	+	0.995520i	$0.469858\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.92848	−0.964240
$5$	0.0366447	0.0163880	0.00819401	−	0.999966i	$-0.497392\pi$
$5$	0.0366447	0.0163880	0.00819401	+	0.999966i	$0.497392\pi$
$6$	0.267433	0.109179
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.05060	−0.371445
$9$	1.00000	0.333333
$10$	0.00980000	0.00309903
$11$	4.21101	1.26967	0.634834	−	0.772648i	$-0.281068\pi$
$11$	4.21101	1.26967	0.634834	+	0.772648i	$0.281068\pi$
$12$	−1.92848	−0.556704
$13$	3.67485	1.01922	0.509609	−	0.860406i	$-0.329790\pi$
$13$	3.67485	1.01922	0.509609	+	0.860406i	$0.329790\pi$
$14$	0.267433	0.0714744
$15$	0.0366447	0.00946163
$16$	3.57599	0.893998
$17$	−6.13318	−1.48751	−0.743757	−	0.668450i	$-0.766958\pi$
$17$	−6.13318	−1.48751	−0.743757	+	0.668450i	$0.766958\pi$
$18$	0.267433	0.0630345
$19$	−2.34693	−0.538422	−0.269211	−	0.963081i	$-0.586763\pi$
$19$	−2.34693	−0.538422	−0.269211	+	0.963081i	$0.586763\pi$
$20$	−0.0706686	−0.0158020
$21$	1.00000	0.218218
$22$	1.12616	0.240099
$23$	7.94611	1.65688	0.828439	−	0.560080i	$-0.189229\pi$
$23$	7.94611	1.65688	0.828439	+	0.560080i	$0.189229\pi$
$24$	−1.05060	−0.214454
$25$	−4.99866	−0.999731
$26$	0.982774	0.192738
$27$	1.00000	0.192450
$28$	−1.92848	−0.364448
$29$	0.655666	0.121754	0.0608771	−	0.998145i	$-0.480610\pi$
$29$	0.655666	0.121754	0.0608771	+	0.998145i	$0.480610\pi$
$30$	0.00980000	0.00178923
$31$	5.37695	0.965729	0.482865	−	0.875695i	$-0.339596\pi$
$31$	5.37695	0.965729	0.482865	+	0.875695i	$0.339596\pi$
$32$	3.05755	0.540503
$33$	4.21101	0.733043
$34$	−1.64021	−0.281294
$35$	0.0366447	0.00619409
$36$	−1.92848	−0.321413
$37$	2.83216	0.465604	0.232802	−	0.972524i	$-0.425211\pi$
$37$	2.83216	0.465604	0.232802	+	0.972524i	$0.425211\pi$
$38$	−0.627645	−0.101817
$39$	3.67485	0.588446
$40$	−0.0384991	−0.00608724
$41$	−4.58297	−0.715740	−0.357870	−	0.933771i	$-0.616497\pi$
$41$	−4.58297	−0.715740	−0.357870	+	0.933771i	$0.616497\pi$
$42$	0.267433	0.0412658
$43$	−4.32631	−0.659757	−0.329878	−	0.944023i	$-0.607008\pi$
$43$	−4.32631	−0.659757	−0.329878	+	0.944023i	$0.607008\pi$
$44$	−8.12085	−1.22426
$45$	0.0366447	0.00546267
$46$	2.12505	0.313321
$47$	0.864954	0.126167	0.0630833	−	0.998008i	$-0.479907\pi$
$47$	0.864954	0.126167	0.0630833	+	0.998008i	$0.479907\pi$
$48$	3.57599	0.516150
$49$	1.00000	0.142857
$50$	−1.33680	−0.189053
$51$	−6.13318	−0.858817
$52$	−7.08687	−0.982771
$53$	−7.72969	−1.06175	−0.530877	−	0.847449i	$-0.678137\pi$
$53$	−7.72969	−1.06175	−0.530877	+	0.847449i	$0.678137\pi$
$54$	0.267433	0.0363930
$55$	0.154311	0.0208073
$56$	−1.05060	−0.140393
$57$	−2.34693	−0.310858
$58$	0.175347	0.0230241
$59$	14.3507	1.86831	0.934154	−	0.356870i	$-0.116156\pi$
$59$	14.3507	1.86831	0.934154	+	0.356870i	$0.116156\pi$
$60$	−0.0706686	−0.00912328
$61$	−2.75729	−0.353035	−0.176518	−	0.984297i	$-0.556483\pi$
$61$	−2.75729	−0.353035	−0.176518	+	0.984297i	$0.556483\pi$
$62$	1.43797	0.182623
$63$	1.00000	0.125988
$64$	−6.33430	−0.791787
$65$	0.134664	0.0167030
$66$	1.12616	0.138621
$67$	5.99139	0.731965	0.365983	−	0.930622i	$-0.380733\pi$
$67$	5.99139	0.731965	0.365983	+	0.930622i	$0.380733\pi$
$68$	11.8277	1.43432
$69$	7.94611	0.956599
$70$	0.00980000	0.00117132
$71$	−1.19268	−0.141545	−0.0707726	−	0.997492i	$-0.522546\pi$
$71$	−1.19268	−0.141545	−0.0707726	+	0.997492i	$0.522546\pi$
$72$	−1.05060	−0.123815
$73$	13.2813	1.55445	0.777227	−	0.629220i	$-0.216625\pi$
$73$	13.2813	1.55445	0.777227	+	0.629220i	$0.216625\pi$
$74$	0.757413	0.0880474
$75$	−4.99866	−0.577195
$76$	4.52600	0.519168
$77$	4.21101	0.479889
$78$	0.982774	0.111277
$79$	−3.61434	−0.406645	−0.203322	−	0.979112i	$-0.565174\pi$
$79$	−3.61434	−0.406645	−0.203322	+	0.979112i	$0.565174\pi$
$80$	0.131041	0.0146509
$81$	1.00000	0.111111
$82$	−1.22564	−0.135349
$83$	10.6258	1.16633	0.583166	−	0.812353i	$-0.301814\pi$
$83$	10.6258	1.16633	0.583166	+	0.812353i	$0.301814\pi$
$84$	−1.92848	−0.210414
$85$	−0.224749	−0.0243774
$86$	−1.15700	−0.124762
$87$	0.655666	0.0702948
$88$	−4.42411	−0.471612
$89$	5.66725	0.600727	0.300363	−	0.953825i	$-0.402892\pi$
$89$	5.66725	0.600727	0.300363	+	0.953825i	$0.402892\pi$
$90$	0.00980000	0.00103301
$91$	3.67485	0.385229
$92$	−15.3239	−1.59763
$93$	5.37695	0.557564
$94$	0.231317	0.0238585
$95$	−0.0860025	−0.00882367
$96$	3.05755	0.312060
$97$	−5.01426	−0.509121	−0.254560	−	0.967057i	$-0.581931\pi$
$97$	−5.01426	−0.509121	−0.254560	+	0.967057i	$0.581931\pi$
$98$	0.267433	0.0270148
$99$	4.21101	0.423223
$100$	9.63981	0.963981
$101$	−13.2263	−1.31607	−0.658034	−	0.752989i	$-0.728611\pi$
$101$	−13.2263	−1.31607	−0.658034	+	0.752989i	$0.728611\pi$
$102$	−1.64021	−0.162405
$103$	4.22437	0.416240	0.208120	−	0.978103i	$-0.433266\pi$
$103$	4.22437	0.416240	0.208120	+	0.978103i	$0.433266\pi$
$104$	−3.86081	−0.378583
$105$	0.0366447	0.00357616
$106$	−2.06717	−0.200781
$107$	10.1513	0.981362	0.490681	−	0.871339i	$-0.336748\pi$
$107$	10.1513	0.981362	0.490681	+	0.871339i	$0.336748\pi$
$108$	−1.92848	−0.185568
$109$	−4.99943	−0.478858	−0.239429	−	0.970914i	$-0.576960\pi$
$109$	−4.99943	−0.478858	−0.239429	+	0.970914i	$0.576960\pi$
$110$	0.0412679	0.00393474
$111$	2.83216	0.268817
$112$	3.57599	0.337900
$113$	−7.36164	−0.692525	−0.346262	−	0.938138i	$-0.612549\pi$
$113$	−7.36164	−0.692525	−0.346262	+	0.938138i	$0.612549\pi$
$114$	−0.627645	−0.0587844
$115$	0.291183	0.0271529
$116$	−1.26444	−0.117400
$117$	3.67485	0.339740
$118$	3.83786	0.353304
$119$	−6.13318	−0.562228
$120$	−0.0384991	−0.00351447
$121$	6.73263	0.612057
$122$	−0.737390	−0.0667602
$123$	−4.58297	−0.413233
$124$	−10.3693	−0.931194
$125$	−0.366398	−0.0327716
$126$	0.267433	0.0238248
$127$	−10.2969	−0.913702	−0.456851	−	0.889543i	$-0.651023\pi$
$127$	−10.2969	−0.913702	−0.456851	+	0.889543i	$0.651023\pi$
$128$	−7.80909	−0.690233
$129$	−4.32631	−0.380911
$130$	0.0360135	0.00315859
$131$	9.63191	0.841544	0.420772	−	0.907166i	$-0.361759\pi$
$131$	9.63191	0.841544	0.420772	+	0.907166i	$0.361759\pi$
$132$	−8.12085	−0.706830
$133$	−2.34693	−0.203504
$134$	1.60229	0.138417
$135$	0.0366447	0.00315388
$136$	6.44354	0.552529
$137$	11.9259	1.01890	0.509449	−	0.860501i	$-0.329849\pi$
$137$	11.9259	1.01890	0.509449	+	0.860501i	$0.329849\pi$
$138$	2.12505	0.180896
$139$	3.39342	0.287826	0.143913	−	0.989590i	$-0.454031\pi$
$139$	3.39342	0.287826	0.143913	+	0.989590i	$0.454031\pi$
$140$	−0.0706686	−0.00597259
$141$	0.864954	0.0728423
$142$	−0.318962	−0.0267667
$143$	15.4748	1.29407
$144$	3.57599	0.297999
$145$	0.0240267	0.00199531
$146$	3.55185	0.293953
$147$	1.00000	0.0824786
$148$	−5.46176	−0.448954
$149$	−7.09942	−0.581607	−0.290803	−	0.956783i	$-0.593923\pi$
$149$	−7.09942	−0.581607	−0.290803	+	0.956783i	$0.593923\pi$
$150$	−1.33680	−0.109150
$151$	21.5636	1.75482	0.877409	−	0.479743i	$-0.159270\pi$
$151$	21.5636	1.75482	0.877409	+	0.479743i	$0.159270\pi$
$152$	2.46569	0.199994
$153$	−6.13318	−0.495838
$154$	1.12616	0.0907488
$155$	0.197037	0.0158264
$156$	−7.08687	−0.567403
$157$	−0.627072	−0.0500458	−0.0250229	−	0.999687i	$-0.507966\pi$
$157$	−0.627072	−0.0500458	−0.0250229	+	0.999687i	$0.507966\pi$
$158$	−0.966593	−0.0768980
$159$	−7.72969	−0.613004
$160$	0.112043	0.00885777
$161$	7.94611	0.626241
$162$	0.267433	0.0210115
$163$	12.7064	0.995243	0.497621	−	0.867394i	$-0.334207\pi$
$163$	12.7064	0.995243	0.497621	+	0.867394i	$0.334207\pi$
$164$	8.83817	0.690145
$165$	0.154311	0.0120131
$166$	2.84169	0.220558
$167$	16.0450	1.24160	0.620800	−	0.783969i	$-0.286808\pi$
$167$	16.0450	1.24160	0.620800	+	0.783969i	$0.286808\pi$
$168$	−1.05060	−0.0810559
$169$	0.504491	0.0388070
$170$	−0.0601052	−0.00460986
$171$	−2.34693	−0.179474
$172$	8.34321	0.636164
$173$	23.7759	1.80765	0.903824	−	0.427904i	$-0.140748\pi$
$173$	23.7759	1.80765	0.903824	+	0.427904i	$0.140748\pi$
$174$	0.175347	0.0132930
$175$	−4.99866	−0.377863
$176$	15.0586	1.13508
$177$	14.3507	1.07867
$178$	1.51561	0.113600
$179$	3.61530	0.270220	0.135110	−	0.990831i	$-0.456861\pi$
$179$	3.61530	0.270220	0.135110	+	0.990831i	$0.456861\pi$
$180$	−0.0706686	−0.00526733
$181$	17.3032	1.28613	0.643067	−	0.765810i	$-0.277662\pi$
$181$	17.3032	1.28613	0.643067	+	0.765810i	$0.277662\pi$
$182$	0.982774	0.0728481
$183$	−2.75729	−0.203825
$184$	−8.34821	−0.615438
$185$	0.103784	0.00763033
$186$	1.43797	0.105437
$187$	−25.8269	−1.88865
$188$	−1.66805	−0.121655
$189$	1.00000	0.0727393
$190$	−0.0229999	−0.00166859
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−6.33430	−0.457139
$193$	19.8177	1.42651	0.713256	−	0.700903i	$-0.247220\pi$
$193$	19.8177	1.42651	0.713256	+	0.700903i	$0.247220\pi$
$194$	−1.34098	−0.0962765
$195$	0.134664	0.00964347
$196$	−1.92848	−0.137749
$197$	−13.0380	−0.928922	−0.464461	−	0.885594i	$-0.653752\pi$
$197$	−13.0380	−0.928922	−0.464461	+	0.885594i	$0.653752\pi$
$198$	1.12616	0.0800329
$199$	16.7906	1.19025	0.595127	−	0.803632i	$-0.297102\pi$
$199$	16.7906	1.19025	0.595127	+	0.803632i	$0.297102\pi$
$200$	5.25161	0.371345
$201$	5.99139	0.422600
$202$	−3.53715	−0.248873
$203$	0.655666	0.0460188
$204$	11.8277	0.828105
$205$	−0.167942	−0.0117296
$206$	1.12974	0.0787125
$207$	7.94611	0.552293
$208$	13.1412	0.911180
$209$	−9.88294	−0.683617
$210$	0.00980000	0.000676264 0
$211$	20.6776	1.42350	0.711751	−	0.702432i	$-0.247903\pi$
$211$	20.6776	1.42350	0.711751	+	0.702432i	$0.247903\pi$
$212$	14.9065	1.02379
$213$	−1.19268	−0.0817212
$214$	2.71479	0.185579
$215$	−0.158537	−0.0108121
$216$	−1.05060	−0.0714846
$217$	5.37695	0.365011
$218$	−1.33701	−0.0905538
$219$	13.2813	0.897465
$220$	−0.297586	−0.0200633
$221$	−22.5385	−1.51610
$222$	0.757413	0.0508342
$223$	−6.32946	−0.423852	−0.211926	−	0.977286i	$-0.567974\pi$
$223$	−6.32946	−0.423852	−0.211926	+	0.977286i	$0.567974\pi$
$224$	3.05755	0.204291
$225$	−4.99866	−0.333244
$226$	−1.96874	−0.130959
$227$	−11.9167	−0.790939	−0.395469	−	0.918479i	$-0.629418\pi$
$227$	−11.9167	−0.790939	−0.395469	+	0.918479i	$0.629418\pi$
$228$	4.52600	0.299742
$229$	−14.2608	−0.942380	−0.471190	−	0.882032i	$-0.656175\pi$
$229$	−14.2608	−0.942380	−0.471190	+	0.882032i	$0.656175\pi$
$230$	0.0778719	0.00513472
$231$	4.21101	0.277064
$232$	−0.688846	−0.0452249
$233$	−26.3606	−1.72694	−0.863469	−	0.504402i	$-0.831713\pi$
$233$	−26.3606	−1.72694	−0.863469	+	0.504402i	$0.831713\pi$
$234$	0.982774	0.0642460
$235$	0.0316960	0.00206762
$236$	−27.6751	−1.80150
$237$	−3.61434	−0.234777
$238$	−1.64021	−0.106319
$239$	11.9887	0.775485	0.387743	−	0.921768i	$-0.373255\pi$
$239$	11.9887	0.775485	0.387743	+	0.921768i	$0.373255\pi$
$240$	0.131041	0.00845868
$241$	−21.3657	−1.37629	−0.688144	−	0.725575i	$-0.741574\pi$
$241$	−21.3657	−1.37629	−0.688144	+	0.725575i	$0.741574\pi$
$242$	1.80053	0.115742
$243$	1.00000	0.0641500
$244$	5.31738	0.340411
$245$	0.0366447	0.00234115
$246$	−1.22564	−0.0781438
$247$	−8.62459	−0.548770
$248$	−5.64905	−0.358715
$249$	10.6258	0.673382
$250$	−0.0979869	−0.00619723
$251$	16.5587	1.04518	0.522589	−	0.852585i	$-0.324966\pi$
$251$	16.5587	1.04518	0.522589	+	0.852585i	$0.324966\pi$
$252$	−1.92848	−0.121483
$253$	33.4612	2.10368
$254$	−2.75373	−0.172784
$255$	−0.224749	−0.0140743
$256$	10.5802	0.661262
$257$	10.0707	0.628194	0.314097	−	0.949391i	$-0.398298\pi$
$257$	10.0707	0.628194	0.314097	+	0.949391i	$0.398298\pi$
$258$	−1.15700	−0.0720316
$259$	2.83216	0.175982
$260$	−0.259696	−0.0161057
$261$	0.655666	0.0405847
$262$	2.57589	0.159139
$263$	12.8443	0.792016	0.396008	−	0.918247i	$-0.370395\pi$
$263$	12.8443	0.792016	0.396008	+	0.918247i	$0.370395\pi$
$264$	−4.42411	−0.272285
$265$	−0.283252	−0.0174000
$266$	−0.627645	−0.0384834
$267$	5.66725	0.346830
$268$	−11.5543	−0.705790
$269$	8.94286	0.545256	0.272628	−	0.962120i	$-0.412107\pi$
$269$	8.94286	0.545256	0.272628	+	0.962120i	$0.412107\pi$
$270$	0.00980000	0.000596409 0
$271$	−19.9862	−1.21408	−0.607039	−	0.794672i	$-0.707643\pi$
$271$	−19.9862	−1.21408	−0.607039	+	0.794672i	$0.707643\pi$
$272$	−21.9322	−1.32984
$273$	3.67485	0.222412
$274$	3.18937	0.192677
$275$	−21.0494	−1.26933
$276$	−15.3239	−0.922391
$277$	3.96109	0.237999	0.118999	−	0.992894i	$-0.462031\pi$
$277$	3.96109	0.237999	0.118999	+	0.992894i	$0.462031\pi$
$278$	0.907511	0.0544289
$279$	5.37695	0.321910
$280$	−0.0384991	−0.00230076
$281$	22.9409	1.36854	0.684269	−	0.729230i	$-0.260121\pi$
$281$	22.9409	1.36854	0.684269	+	0.729230i	$0.260121\pi$
$282$	0.231317	0.0137747
$283$	26.1902	1.55685	0.778423	−	0.627740i	$-0.216020\pi$
$283$	26.1902	1.55685	0.778423	+	0.627740i	$0.216020\pi$
$284$	2.30006	0.136484
$285$	−0.0860025	−0.00509435
$286$	4.13848	0.244713
$287$	−4.58297	−0.270524
$288$	3.05755	0.180168
$289$	20.6159	1.21270
$290$	0.00642553	0.000377320 0
$291$	−5.01426	−0.293941
$292$	−25.6127	−1.49887
$293$	−25.4951	−1.48944	−0.744719	−	0.667378i	$-0.767416\pi$
$293$	−25.4951	−1.48944	−0.744719	+	0.667378i	$0.767416\pi$
$294$	0.267433	0.0155970
$295$	0.525879	0.0306179
$296$	−2.97548	−0.172946
$297$	4.21101	0.244348
$298$	−1.89862	−0.109984
$299$	29.2007	1.68872
$300$	9.63981	0.556555
$301$	−4.32631	−0.249365
$302$	5.76680	0.331842
$303$	−13.2263	−0.759832
$304$	−8.39259	−0.481348
$305$	−0.101040	−0.00578555
$306$	−1.64021	−0.0937648
$307$	−24.6943	−1.40938	−0.704688	−	0.709518i	$-0.748913\pi$
$307$	−24.6943	−1.40938	−0.704688	+	0.709518i	$0.748913\pi$
$308$	−8.12085	−0.462729
$309$	4.22437	0.240316
$310$	0.0526941	0.00299283
$311$	1.07377	0.0608877	0.0304438	−	0.999536i	$-0.490308\pi$
$311$	1.07377	0.0608877	0.0304438	+	0.999536i	$0.490308\pi$
$312$	−3.86081	−0.218575
$313$	16.7660	0.947672	0.473836	−	0.880613i	$-0.342869\pi$
$313$	16.7660	0.947672	0.473836	+	0.880613i	$0.342869\pi$
$314$	−0.167700	−0.00946384
$315$	0.0366447	0.00206470
$316$	6.97018	0.392103
$317$	−8.52857	−0.479012	−0.239506	−	0.970895i	$-0.576986\pi$
$317$	−8.52857	−0.479012	−0.239506	+	0.970895i	$0.576986\pi$
$318$	−2.06717	−0.115921
$319$	2.76102	0.154587
$320$	−0.232119	−0.0129758
$321$	10.1513	0.566589
$322$	2.12505	0.118424
$323$	14.3941	0.800910
$324$	−1.92848	−0.107138
$325$	−18.3693	−1.01895
$326$	3.39811	0.188204
$327$	−4.99943	−0.276469
$328$	4.81489	0.265858
$329$	0.864954	0.0476865
$330$	0.0412679	0.00227173
$331$	−23.1783	−1.27399	−0.636997	−	0.770867i	$-0.719823\pi$
$331$	−23.1783	−1.27399	−0.636997	+	0.770867i	$0.719823\pi$
$332$	−20.4916	−1.12462
$333$	2.83216	0.155201
$334$	4.29096	0.234791
$335$	0.219553	0.0119955
$336$	3.57599	0.195086
$337$	−27.0922	−1.47580	−0.737902	−	0.674908i	$-0.764183\pi$
$337$	−27.0922	−1.47580	−0.737902	+	0.674908i	$0.764183\pi$
$338$	0.134917	0.00733854
$339$	−7.36164	−0.399829
$340$	0.433423	0.0235057
$341$	22.6424	1.22616
$342$	−0.627645	−0.0339392
$343$	1.00000	0.0539949
$344$	4.54524	0.245063
$345$	0.291183	0.0156768
$346$	6.35845	0.341833
$347$	−14.8371	−0.796499	−0.398249	−	0.917277i	$-0.630382\pi$
$347$	−14.8371	−0.796499	−0.398249	+	0.917277i	$0.630382\pi$
$348$	−1.26444	−0.0677811
$349$	−1.37342	−0.0735174	−0.0367587	−	0.999324i	$-0.511703\pi$
$349$	−1.37342	−0.0735174	−0.0367587	+	0.999324i	$0.511703\pi$
$350$	−1.33680	−0.0714552
$351$	3.67485	0.196149
$352$	12.8754	0.686259
$353$	14.2193	0.756814	0.378407	−	0.925639i	$-0.376472\pi$
$353$	14.2193	0.756814	0.378407	+	0.925639i	$0.376472\pi$
$354$	3.83786	0.203980
$355$	−0.0437055	−0.00231965
$356$	−10.9292	−0.579245
$357$	−6.13318	−0.324602
$358$	0.966849	0.0510996
$359$	−8.99023	−0.474486	−0.237243	−	0.971450i	$-0.576244\pi$
$359$	−8.99023	−0.474486	−0.237243	+	0.971450i	$0.576244\pi$
$360$	−0.0384991	−0.00202908
$361$	−13.4919	−0.710102
$362$	4.62743	0.243212
$363$	6.73263	0.353371
$364$	−7.08687	−0.371453
$365$	0.486688	0.0254744
$366$	−0.737390	−0.0385440
$367$	−12.6860	−0.662205	−0.331103	−	0.943595i	$-0.607421\pi$
$367$	−12.6860	−0.662205	−0.331103	+	0.943595i	$0.607421\pi$
$368$	28.4152	1.48125
$369$	−4.58297	−0.238580
$370$	0.0277552	0.00144292
$371$	−7.72969	−0.401305
$372$	−10.3693	−0.537625
$373$	−2.18856	−0.113319	−0.0566596	−	0.998394i	$-0.518045\pi$
$373$	−2.18856	−0.113319	−0.0566596	+	0.998394i	$0.518045\pi$
$374$	−6.90696	−0.357150
$375$	−0.366398	−0.0189207
$376$	−0.908725	−0.0468639
$377$	2.40947	0.124094
$378$	0.267433	0.0137553
$379$	−9.11653	−0.468285	−0.234142	−	0.972202i	$-0.575228\pi$
$379$	−9.11653	−0.468285	−0.234142	+	0.972202i	$0.575228\pi$
$380$	0.165854	0.00850813
$381$	−10.2969	−0.527526
$382$	0.267433	0.0136831
$383$	33.7306	1.72355	0.861777	−	0.507287i	$-0.169352\pi$
$383$	33.7306	1.72355	0.861777	+	0.507287i	$0.169352\pi$
$384$	−7.80909	−0.398506
$385$	0.154311	0.00786444
$386$	5.29992	0.269759
$387$	−4.32631	−0.219919
$388$	9.66989	0.490914
$389$	−23.5193	−1.19248	−0.596238	−	0.802808i	$-0.703339\pi$
$389$	−23.5193	−1.19248	−0.596238	+	0.802808i	$0.703339\pi$
$390$	0.0360135	0.00182361
$391$	−48.7349	−2.46463
$392$	−1.05060	−0.0530635
$393$	9.63191	0.485866
$394$	−3.48680	−0.175662
$395$	−0.132446	−0.00666410
$396$	−8.12085	−0.408088
$397$	−25.2570	−1.26761	−0.633806	−	0.773492i	$-0.718508\pi$
$397$	−25.2570	−1.26761	−0.633806	+	0.773492i	$0.718508\pi$
$398$	4.49036	0.225081
$399$	−2.34693	−0.117493
$400$	−17.8752	−0.893758
$401$	−13.7575	−0.687018	−0.343509	−	0.939149i	$-0.611616\pi$
$401$	−13.7575	−0.687018	−0.343509	+	0.939149i	$0.611616\pi$
$402$	1.60229	0.0799152
$403$	19.7595	0.984289
$404$	25.5067	1.26900
$405$	0.0366447	0.00182089
$406$	0.175347	0.00870231
$407$	11.9263	0.591163
$408$	6.44354	0.319003
$409$	−15.5548	−0.769133	−0.384567	−	0.923097i	$-0.625649\pi$
$409$	−15.5548	−0.769133	−0.384567	+	0.923097i	$0.625649\pi$
$410$	−0.0449132	−0.00221810
$411$	11.9259	0.588260
$412$	−8.14662	−0.401355
$413$	14.3507	0.706154
$414$	2.12505	0.104440
$415$	0.389379	0.0191139
$416$	11.2360	0.550891
$417$	3.39342	0.166176
$418$	−2.64302	−0.129274
$419$	15.7108	0.767523	0.383762	−	0.923432i	$-0.374628\pi$
$419$	15.7108	0.767523	0.383762	+	0.923432i	$0.374628\pi$
$420$	−0.0706686	−0.00344828
$421$	8.26573	0.402847	0.201424	−	0.979504i	$-0.435443\pi$
$421$	8.26573	0.402847	0.201424	+	0.979504i	$0.435443\pi$
$422$	5.52986	0.269189
$423$	0.864954	0.0420555
$424$	8.12084	0.394383
$425$	30.6577	1.48712
$426$	−0.318962	−0.0154538
$427$	−2.75729	−0.133435
$428$	−19.5765	−0.946268
$429$	15.4748	0.747131
$430$	−0.0423979	−0.00204461
$431$	8.61526	0.414982	0.207491	−	0.978237i	$-0.433470\pi$
$431$	8.61526	0.414982	0.207491	+	0.978237i	$0.433470\pi$
$432$	3.57599	0.172050
$433$	0.464944	0.0223438	0.0111719	−	0.999938i	$-0.496444\pi$
$433$	0.464944	0.0223438	0.0111719	+	0.999938i	$0.496444\pi$
$434$	1.43797	0.0690249
$435$	0.0240267	0.00115199
$436$	9.64130	0.461734
$437$	−18.6489	−0.892099
$438$	3.55185	0.169714
$439$	−6.82086	−0.325542	−0.162771	−	0.986664i	$-0.552043\pi$
$439$	−6.82086	−0.325542	−0.162771	+	0.986664i	$0.552043\pi$
$440$	−0.162120	−0.00772878
$441$	1.00000	0.0476190
$442$	−6.02753	−0.286700
$443$	3.32999	0.158213	0.0791064	−	0.996866i	$-0.474793\pi$
$443$	3.32999	0.158213	0.0791064	+	0.996866i	$0.474793\pi$
$444$	−5.46176	−0.259204
$445$	0.207675	0.00984473
$446$	−1.69271	−0.0801520
$447$	−7.09942	−0.335791
$448$	−6.33430	−0.299267
$449$	−2.88002	−0.135916	−0.0679582	−	0.997688i	$-0.521648\pi$
$449$	−2.88002	−0.135916	−0.0679582	+	0.997688i	$0.521648\pi$
$450$	−1.33680	−0.0630176
$451$	−19.2990	−0.908753
$452$	14.1968	0.667760
$453$	21.5636	1.01314
$454$	−3.18691	−0.149569
$455$	0.134664	0.00631313
$456$	2.46569	0.115467
$457$	−28.5041	−1.33336	−0.666682	−	0.745343i	$-0.732286\pi$
$457$	−28.5041	−1.33336	−0.666682	+	0.745343i	$0.732286\pi$
$458$	−3.81381	−0.178207
$459$	−6.13318	−0.286272
$460$	−0.561540	−0.0261820
$461$	−38.4580	−1.79117	−0.895584	−	0.444892i	$-0.853242\pi$
$461$	−38.4580	−1.79117	−0.895584	+	0.444892i	$0.853242\pi$
$462$	1.12616	0.0523938
$463$	−38.1266	−1.77189	−0.885946	−	0.463789i	$-0.846489\pi$
$463$	−38.1266	−1.77189	−0.885946	+	0.463789i	$0.846489\pi$
$464$	2.34466	0.108848
$465$	0.197037	0.00913737
$466$	−7.04968	−0.326570
$467$	2.71734	0.125743	0.0628716	−	0.998022i	$-0.479974\pi$
$467$	2.71734	0.125743	0.0628716	+	0.998022i	$0.479974\pi$
$468$	−7.08687	−0.327590
$469$	5.99139	0.276657
$470$	0.00847655	0.000390994 0
$471$	−0.627072	−0.0288940
$472$	−15.0770	−0.693973
$473$	−18.2182	−0.837672
$474$	−0.966593	−0.0443971
$475$	11.7315	0.538277
$476$	11.8277	0.542122
$477$	−7.72969	−0.353918
$478$	3.20617	0.146647
$479$	−16.9258	−0.773358	−0.386679	−	0.922214i	$-0.626378\pi$
$479$	−16.9258	−0.773358	−0.386679	+	0.922214i	$0.626378\pi$
$480$	0.112043	0.00511404
$481$	10.4078	0.474553
$482$	−5.71389	−0.260261
$483$	7.94611	0.361560
$484$	−12.9837	−0.590170
$485$	−0.183746	−0.00834348
$486$	0.267433	0.0121310
$487$	−10.4167	−0.472025	−0.236012	−	0.971750i	$-0.575841\pi$
$487$	−10.4167	−0.472025	−0.236012	+	0.971750i	$0.575841\pi$
$488$	2.89682	0.131133
$489$	12.7064	0.574604
$490$	0.00980000	0.000442719 0
$491$	30.9367	1.39615	0.698077	−	0.716023i	$-0.254039\pi$
$491$	30.9367	1.39615	0.698077	+	0.716023i	$0.254039\pi$
$492$	8.83817	0.398456
$493$	−4.02132	−0.181111
$494$	−2.30650	−0.103774
$495$	0.154311	0.00693578
$496$	19.2279	0.863360
$497$	−1.19268	−0.0534991
$498$	2.84169	0.127339
$499$	−41.8597	−1.87390	−0.936948	−	0.349469i	$-0.886362\pi$
$499$	−41.8597	−1.87390	−0.936948	+	0.349469i	$0.886362\pi$
$500$	0.706591	0.0315997
$501$	16.0450	0.716838
$502$	4.42835	0.197647
$503$	−11.1414	−0.496769	−0.248384	−	0.968662i	$-0.579900\pi$
$503$	−11.1414	−0.496769	−0.248384	+	0.968662i	$0.579900\pi$
$504$	−1.05060	−0.0467976
$505$	−0.484675	−0.0215677
$506$	8.94861	0.397814
$507$	0.504491	0.0224052
$508$	19.8574	0.881028
$509$	21.0956	0.935048	0.467524	−	0.883980i	$-0.345146\pi$
$509$	21.0956	0.935048	0.467524	+	0.883980i	$0.345146\pi$
$510$	−0.0601052	−0.00266150
$511$	13.2813	0.587529
$512$	18.4477	0.815280
$513$	−2.34693	−0.103619
$514$	2.69324	0.118794
$515$	0.154801	0.00682135
$516$	8.34321	0.367289
$517$	3.64233	0.160190
$518$	0.757413	0.0332788
$519$	23.7759	1.04365
$520$	−0.141478	−0.00620423
$521$	36.2127	1.58651	0.793253	−	0.608892i	$-0.208386\pi$
$521$	36.2127	1.58651	0.793253	+	0.608892i	$0.208386\pi$
$522$	0.175347	0.00767472
$523$	−36.5981	−1.60032	−0.800162	−	0.599784i	$-0.795253\pi$
$523$	−36.5981	−1.60032	−0.800162	+	0.599784i	$0.795253\pi$
$524$	−18.5749	−0.811450
$525$	−4.99866	−0.218159
$526$	3.43500	0.149773
$527$	−32.9778	−1.43654
$528$	15.0586	0.655339
$529$	40.1406	1.74524
$530$	−0.0757509	−0.00329041
$531$	14.3507	0.622769
$532$	4.52600	0.196227
$533$	−16.8417	−0.729496
$534$	1.51561	0.0655868
$535$	0.371991	0.0160826
$536$	−6.29458	−0.271885
$537$	3.61530	0.156012
$538$	2.39161	0.103110
$539$	4.21101	0.181381
$540$	−0.0706686	−0.00304109
$541$	−20.5769	−0.884668	−0.442334	−	0.896850i	$-0.645849\pi$
$541$	−20.5769	−0.884668	−0.442334	+	0.896850i	$0.645849\pi$
$542$	−5.34498	−0.229586
$543$	17.3032	0.742550
$544$	−18.7525	−0.804006
$545$	−0.183203	−0.00784754
$546$	0.982774	0.0420589
$547$	17.8080	0.761415	0.380707	−	0.924696i	$-0.375681\pi$
$547$	17.8080	0.761415	0.380707	+	0.924696i	$0.375681\pi$
$548$	−22.9988	−0.982461
$549$	−2.75729	−0.117678
$550$	−5.62930	−0.240034
$551$	−1.53880	−0.0655551
$552$	−8.34821	−0.355324
$553$	−3.61434	−0.153697
$554$	1.05933	0.0450064
$555$	0.103784	0.00440538
$556$	−6.54414	−0.277533
$557$	10.6223	0.450083	0.225042	−	0.974349i	$-0.427748\pi$
$557$	10.6223	0.450083	0.225042	+	0.974349i	$0.427748\pi$
$558$	1.43797	0.0608743
$559$	−15.8985	−0.672436
$560$	0.131041	0.00553751
$561$	−25.8269	−1.09041
$562$	6.13514	0.258795
$563$	−20.8929	−0.880531	−0.440266	−	0.897868i	$-0.645116\pi$
$563$	−20.8929	−0.880531	−0.440266	+	0.897868i	$0.645116\pi$
$564$	−1.66805	−0.0702374
$565$	−0.269765	−0.0113491
$566$	7.00412	0.294405
$567$	1.00000	0.0419961
$568$	1.25304	0.0525762
$569$	32.3679	1.35693	0.678466	−	0.734632i	$-0.262645\pi$
$569$	32.3679	1.35693	0.678466	+	0.734632i	$0.262645\pi$
$570$	−0.0229999	−0.000963359 0
$571$	−10.6157	−0.444252	−0.222126	−	0.975018i	$-0.571300\pi$
$571$	−10.6157	−0.444252	−0.222126	+	0.975018i	$0.571300\pi$
$572$	−29.8429	−1.24779
$573$	1.00000	0.0417756
$574$	−1.22564	−0.0511571
$575$	−39.7199	−1.65643
$576$	−6.33430	−0.263929
$577$	−26.4032	−1.09918	−0.549591	−	0.835434i	$-0.685216\pi$
$577$	−26.4032	−1.09918	−0.549591	+	0.835434i	$0.685216\pi$
$578$	5.51337	0.229326
$579$	19.8177	0.823598
$580$	−0.0463350	−0.00192396
$581$	10.6258	0.440832
$582$	−1.34098	−0.0555853
$583$	−32.5498	−1.34808
$584$	−13.9534	−0.577394
$585$	0.134664	0.00556766
$586$	−6.81822	−0.281658
$587$	−4.00195	−0.165178	−0.0825890	−	0.996584i	$-0.526319\pi$
$587$	−4.00195	−0.165178	−0.0825890	+	0.996584i	$0.526319\pi$
$588$	−1.92848	−0.0795292
$589$	−12.6193	−0.519970
$590$	0.140637	0.00578995
$591$	−13.0380	−0.536313
$592$	10.1278	0.416250
$593$	18.0150	0.739788	0.369894	−	0.929074i	$-0.379394\pi$
$593$	18.0150	0.739788	0.369894	+	0.929074i	$0.379394\pi$
$594$	1.12616	0.0462070
$595$	−0.224749	−0.00921380
$596$	13.6911	0.560809
$597$	16.7906	0.687193
$598$	7.80923	0.319343
$599$	31.5041	1.28722	0.643611	−	0.765352i	$-0.277435\pi$
$599$	31.5041	1.28722	0.643611	+	0.765352i	$0.277435\pi$
$600$	5.25161	0.214396
$601$	−25.0229	−1.02071	−0.510353	−	0.859965i	$-0.670485\pi$
$601$	−25.0229	−1.02071	−0.510353	+	0.859965i	$0.670485\pi$
$602$	−1.15700	−0.0471557
$603$	5.99139	0.243988
$604$	−41.5849	−1.69207
$605$	0.246715	0.0100304
$606$	−3.53715	−0.143687
$607$	18.2033	0.738847	0.369424	−	0.929261i	$-0.379555\pi$
$607$	18.2033	0.738847	0.369424	+	0.929261i	$0.379555\pi$
$608$	−7.17584	−0.291019
$609$	0.655666	0.0265689
$610$	−0.0270215	−0.00109407
$611$	3.17857	0.128591
$612$	11.8277	0.478107
$613$	25.0112	1.01019	0.505096	−	0.863063i	$-0.331457\pi$
$613$	25.0112	1.01019	0.505096	+	0.863063i	$0.331457\pi$
$614$	−6.60405	−0.266518
$615$	−0.167942	−0.00677207
$616$	−4.42411	−0.178252
$617$	12.0619	0.485592	0.242796	−	0.970077i	$-0.421935\pi$
$617$	12.0619	0.485592	0.242796	+	0.970077i	$0.421935\pi$
$618$	1.12974	0.0454447
$619$	7.25308	0.291526	0.145763	−	0.989320i	$-0.453436\pi$
$619$	7.25308	0.291526	0.145763	+	0.989320i	$0.453436\pi$
$620$	−0.379982	−0.0152604
$621$	7.94611	0.318866
$622$	0.287160	0.0115141
$623$	5.66725	0.227053
$624$	13.1412	0.526070
$625$	24.9799	0.999194
$626$	4.48379	0.179208
$627$	−9.88294	−0.394687
$628$	1.20930	0.0482561
$629$	−17.3702	−0.692593
$630$	0.00980000	0.000390441 0
$631$	1.44365	0.0574707	0.0287353	−	0.999587i	$-0.490852\pi$
$631$	1.44365	0.0574707	0.0287353	+	0.999587i	$0.490852\pi$
$632$	3.79724	0.151046
$633$	20.6776	0.821859
$634$	−2.28082	−0.0905829
$635$	−0.377327	−0.0149738
$636$	14.9065	0.591083
$637$	3.67485	0.145603
$638$	0.738387	0.0292330
$639$	−1.19268	−0.0471818
$640$	−0.286162	−0.0113115
$641$	−3.76749	−0.148807	−0.0744034	−	0.997228i	$-0.523705\pi$
$641$	−3.76749	−0.148807	−0.0744034	+	0.997228i	$0.523705\pi$
$642$	2.71479	0.107144
$643$	11.2248	0.442663	0.221331	−	0.975199i	$-0.428960\pi$
$643$	11.2248	0.442663	0.221331	+	0.975199i	$0.428960\pi$
$644$	−15.3239	−0.603846
$645$	−0.158537	−0.00624237
$646$	3.84946	0.151455
$647$	−2.48957	−0.0978753	−0.0489376	−	0.998802i	$-0.515584\pi$
$647$	−2.48957	−0.0978753	−0.0489376	+	0.998802i	$0.515584\pi$
$648$	−1.05060	−0.0412716
$649$	60.4312	2.37213
$650$	−4.91255	−0.192686
$651$	5.37695	0.210739
$652$	−24.5041	−0.959653
$653$	−11.7159	−0.458478	−0.229239	−	0.973370i	$-0.573624\pi$
$653$	−11.7159	−0.458478	−0.229239	+	0.973370i	$0.573624\pi$
$654$	−1.33701	−0.0522813
$655$	0.352959	0.0137912
$656$	−16.3887	−0.639871
$657$	13.2813	0.518152
$658$	0.231317	0.00901768
$659$	−10.3913	−0.404789	−0.202395	−	0.979304i	$-0.564872\pi$
$659$	−10.3913	−0.404789	−0.202395	+	0.979304i	$0.564872\pi$
$660$	−0.297586	−0.0115835
$661$	−8.51175	−0.331069	−0.165534	−	0.986204i	$-0.552935\pi$
$661$	−8.51175	−0.331069	−0.165534	+	0.986204i	$0.552935\pi$
$662$	−6.19863	−0.240917
$663$	−22.5385	−0.875322
$664$	−11.1635	−0.433228
$665$	−0.0860025	−0.00333503
$666$	0.757413	0.0293491
$667$	5.20999	0.201732
$668$	−30.9425	−1.19720
$669$	−6.32946	−0.244711
$670$	0.0587157	0.00226838
$671$	−11.6110	−0.448238
$672$	3.05755	0.117947
$673$	−48.9911	−1.88847	−0.944234	−	0.329276i	$-0.893195\pi$
$673$	−48.9911	−1.88847	−0.944234	+	0.329276i	$0.893195\pi$
$674$	−7.24533	−0.279080
$675$	−4.99866	−0.192398
$676$	−0.972900	−0.0374192
$677$	−18.0265	−0.692814	−0.346407	−	0.938084i	$-0.612598\pi$
$677$	−18.0265	−0.692814	−0.346407	+	0.938084i	$0.612598\pi$
$678$	−1.96874	−0.0756091
$679$	−5.01426	−0.192429
$680$	0.236122	0.00905486
$681$	−11.9167	−0.456649
$682$	6.05532	0.231870
$683$	20.7620	0.794435	0.397218	−	0.917724i	$-0.369976\pi$
$683$	20.7620	0.794435	0.397218	+	0.917724i	$0.369976\pi$
$684$	4.52600	0.173056
$685$	0.437021	0.0166977
$686$	0.267433	0.0102106
$687$	−14.2608	−0.544083
$688$	−15.4709	−0.589821
$689$	−28.4054	−1.08216
$690$	0.0778719	0.00296453
$691$	19.1142	0.727139	0.363569	−	0.931567i	$-0.381558\pi$
$691$	19.1142	0.727139	0.363569	+	0.931567i	$0.381558\pi$
$692$	−45.8513	−1.74301
$693$	4.21101	0.159963
$694$	−3.96793	−0.150621
$695$	0.124351	0.00471690
$696$	−0.688846	−0.0261106
$697$	28.1082	1.06467
$698$	−0.367297	−0.0139024
$699$	−26.3606	−0.997048
$700$	9.63981	0.364351
$701$	−21.3527	−0.806480	−0.403240	−	0.915094i	$-0.632116\pi$
$701$	−21.3527	−0.806480	−0.403240	+	0.915094i	$0.632116\pi$
$702$	0.982774	0.0370924
$703$	−6.64687	−0.250692
$704$	−26.6738	−1.00531
$705$	0.0316960	0.00119374
$706$	3.80269	0.143116
$707$	−13.2263	−0.497427
$708$	−27.6751	−1.04009
$709$	−15.3704	−0.577247	−0.288624	−	0.957443i	$-0.593198\pi$
$709$	−15.3704	−0.577247	−0.288624	+	0.957443i	$0.593198\pi$
$710$	−0.0116883	−0.000438653 0
$711$	−3.61434	−0.135548
$712$	−5.95403	−0.223137
$713$	42.7258	1.60009
$714$	−1.64021	−0.0613834
$715$	0.567071	0.0212072
$716$	−6.97203	−0.260557
$717$	11.9887	0.447727
$718$	−2.40428	−0.0897270
$719$	14.7253	0.549160	0.274580	−	0.961564i	$-0.411461\pi$
$719$	14.7253	0.549160	0.274580	+	0.961564i	$0.411461\pi$
$720$	0.131041	0.00488362
$721$	4.22437	0.157324
$722$	−3.60819	−0.134283
$723$	−21.3657	−0.794600
$724$	−33.3688	−1.24014
$725$	−3.27745	−0.121721
$726$	1.80053	0.0668238
$727$	−14.4233	−0.534932	−0.267466	−	0.963567i	$-0.586186\pi$
$727$	−14.4233	−0.534932	−0.267466	+	0.963567i	$0.586186\pi$
$728$	−3.86081	−0.143091
$729$	1.00000	0.0370370
$730$	0.130156	0.00481731
$731$	26.5341	0.981398
$732$	5.31738	0.196536
$733$	46.9877	1.73553	0.867765	−	0.496974i	$-0.165556\pi$
$733$	46.9877	1.73553	0.867765	+	0.496974i	$0.165556\pi$
$734$	−3.39266	−0.125225
$735$	0.0366447	0.00135166
$736$	24.2956	0.895547
$737$	25.2298	0.929353
$738$	−1.22564	−0.0451163
$739$	−44.4069	−1.63353	−0.816767	−	0.576968i	$-0.804236\pi$
$739$	−44.4069	−1.63353	−0.816767	+	0.576968i	$0.804236\pi$
$740$	−0.200145	−0.00735747
$741$	−8.62459	−0.316832
$742$	−2.06717	−0.0758883
$743$	−29.2619	−1.07352	−0.536758	−	0.843736i	$-0.680351\pi$
$743$	−29.2619	−1.07352	−0.536758	+	0.843736i	$0.680351\pi$
$744$	−5.64905	−0.207104
$745$	−0.260156	−0.00953139
$746$	−0.585292	−0.0214291
$747$	10.6258	0.388777
$748$	49.8066	1.82111
$749$	10.1513	0.370920
$750$	−0.0979869	−0.00357797
$751$	−15.1751	−0.553749	−0.276874	−	0.960906i	$-0.589299\pi$
$751$	−15.1751	−0.553749	−0.276874	+	0.960906i	$0.589299\pi$
$752$	3.09307	0.112793
$753$	16.5587	0.603433
$754$	0.644372	0.0234666
$755$	0.790191	0.0287580
$756$	−1.92848	−0.0701381
$757$	−37.9744	−1.38020	−0.690101	−	0.723713i	$-0.742434\pi$
$757$	−37.9744	−1.38020	−0.690101	+	0.723713i	$0.742434\pi$
$758$	−2.43806	−0.0885543
$759$	33.4612	1.21456
$760$	0.0903546	0.00327751
$761$	−24.0175	−0.870632	−0.435316	−	0.900278i	$-0.643363\pi$
$761$	−24.0175	−0.870632	−0.435316	+	0.900278i	$0.643363\pi$
$762$	−2.75373	−0.0997571
$763$	−4.99943	−0.180991
$764$	−1.92848	−0.0697699
$765$	−0.224749	−0.00812581
$766$	9.02068	0.325930
$767$	52.7368	1.90421
$768$	10.5802	0.381780
$769$	−45.6309	−1.64549	−0.822747	−	0.568408i	$-0.807559\pi$
$769$	−45.6309	−1.64549	−0.822747	+	0.568408i	$0.807559\pi$
$770$	0.0412679	0.00148719
$771$	10.0707	0.362688
$772$	−38.2181	−1.37550
$773$	−43.7331	−1.57297	−0.786486	−	0.617608i	$-0.788102\pi$
$773$	−43.7331	−1.57297	−0.786486	+	0.617608i	$0.788102\pi$
$774$	−1.15700	−0.0415874
$775$	−26.8775	−0.965470
$776$	5.26800	0.189110
$777$	2.83216	0.101603
$778$	−6.28983	−0.225501
$779$	10.7559	0.385370
$780$	−0.259696	−0.00929862
$781$	−5.02240	−0.179716
$782$	−13.0333	−0.466070
$783$	0.655666	0.0234316
$784$	3.57599	0.127714
$785$	−0.0229789	−0.000820152 0
$786$	2.57589	0.0918789
$787$	54.5160	1.94329	0.971643	−	0.236453i	$-0.0759849\pi$
$787$	54.5160	1.94329	0.971643	+	0.236453i	$0.0759849\pi$
$788$	25.1436	0.895703
$789$	12.8443	0.457271
$790$	−0.0354205	−0.00126021
$791$	−7.36164	−0.261750
$792$	−4.42411	−0.157204
$793$	−10.1326	−0.359820
$794$	−6.75455	−0.239710
$795$	−0.283252	−0.0100459
$796$	−32.3803	−1.14769
$797$	15.0004	0.531341	0.265671	−	0.964064i	$-0.414407\pi$
$797$	15.0004	0.531341	0.265671	+	0.964064i	$0.414407\pi$
$798$	−0.627645	−0.0222184
$799$	−5.30492	−0.187675
$800$	−15.2836	−0.540358
$801$	5.66725	0.200242
$802$	−3.67921	−0.129918
$803$	55.9276	1.97364
$804$	−11.5543	−0.407488
$805$	0.291183	0.0102628
$806$	5.28433	0.186133
$807$	8.94286	0.314804
$808$	13.8956	0.488846
$809$	−37.2954	−1.31124	−0.655619	−	0.755092i	$-0.727592\pi$
$809$	−37.2954	−1.31124	−0.655619	+	0.755092i	$0.727592\pi$
$810$	0.00980000	0.000344337 0
$811$	−13.2116	−0.463922	−0.231961	−	0.972725i	$-0.574514\pi$
$811$	−13.2116	−0.463922	−0.231961	+	0.972725i	$0.574514\pi$
$812$	−1.26444	−0.0443731
$813$	−19.9862	−0.700948
$814$	3.18947	0.111791
$815$	0.465623	0.0163101
$816$	−21.9322	−0.767781
$817$	10.1535	0.355227
$818$	−4.15985	−0.145446
$819$	3.67485	0.128410
$820$	0.323872	0.0113101
$821$	39.6529	1.38390	0.691948	−	0.721947i	$-0.256753\pi$
$821$	39.6529	1.38390	0.691948	+	0.721947i	$0.256753\pi$
$822$	3.18937	0.111242
$823$	40.4695	1.41068	0.705340	−	0.708869i	$-0.250794\pi$
$823$	40.4695	1.41068	0.705340	+	0.708869i	$0.250794\pi$
$824$	−4.43815	−0.154610
$825$	−21.0494	−0.732846
$826$	3.83786	0.133536
$827$	−13.5595	−0.471509	−0.235755	−	0.971813i	$-0.575756\pi$
$827$	−13.5595	−0.471509	−0.235755	+	0.971813i	$0.575756\pi$
$828$	−15.3239	−0.532542
$829$	31.5008	1.09407	0.547034	−	0.837110i	$-0.315757\pi$
$829$	31.5008	1.09407	0.547034	+	0.837110i	$0.315757\pi$
$830$	0.104133	0.00361450
$831$	3.96109	0.137409
$832$	−23.2776	−0.807005
$833$	−6.13318	−0.212502
$834$	0.907511	0.0314245
$835$	0.587965	0.0203474
$836$	19.0590	0.659171
$837$	5.37695	0.185855
$838$	4.20158	0.145141
$839$	44.2048	1.52612	0.763059	−	0.646329i	$-0.223696\pi$
$839$	44.2048	1.52612	0.763059	+	0.646329i	$0.223696\pi$
$840$	−0.0384991	−0.00132835
$841$	−28.5701	−0.985176
$842$	2.21053	0.0761798
$843$	22.9409	0.790126
$844$	−39.8762	−1.37260
$845$	0.0184869	0.000635970 0
$846$	0.231317	0.00795285
$847$	6.73263	0.231336
$848$	−27.6413	−0.949206
$849$	26.1902	0.898845
$850$	8.19886	0.281219
$851$	22.5047	0.771449
$852$	2.30006	0.0787988
$853$	−51.8361	−1.77483	−0.887417	−	0.460968i	$-0.847502\pi$
$853$	−51.8361	−1.77483	−0.887417	+	0.460968i	$0.847502\pi$
$854$	−0.737390	−0.0252330
$855$	−0.0860025	−0.00294122
$856$	−10.6650	−0.364522
$857$	35.3180	1.20644	0.603219	−	0.797575i	$-0.293884\pi$
$857$	35.3180	1.20644	0.603219	+	0.797575i	$0.293884\pi$
$858$	4.13848	0.141285
$859$	19.7377	0.673443	0.336722	−	0.941604i	$-0.390682\pi$
$859$	19.7377	0.673443	0.336722	+	0.941604i	$0.390682\pi$
$860$	0.305735	0.0104255
$861$	−4.58297	−0.156187
$862$	2.30400	0.0784746
$863$	21.7609	0.740751	0.370376	−	0.928882i	$-0.379229\pi$
$863$	21.7609	0.740751	0.370376	+	0.928882i	$0.379229\pi$
$864$	3.05755	0.104020
$865$	0.871261	0.0296238
$866$	0.124341	0.00422529
$867$	20.6159	0.700152
$868$	−10.3693	−0.351958
$869$	−15.2200	−0.516304
$870$	0.00642553	0.000217846 0
$871$	22.0174	0.746033
$872$	5.25242	0.177869
$873$	−5.01426	−0.169707
$874$	−4.98733	−0.168699
$875$	−0.366398	−0.0123865
$876$	−25.6127	−0.865371
$877$	−19.5863	−0.661383	−0.330692	−	0.943739i	$-0.607282\pi$
$877$	−19.5863	−0.661383	−0.330692	+	0.943739i	$0.607282\pi$
$878$	−1.82412	−0.0615611
$879$	−25.4951	−0.859927
$880$	0.551817	0.0186017
$881$	41.4956	1.39802	0.699012	−	0.715110i	$-0.253624\pi$
$881$	41.4956	1.39802	0.699012	+	0.715110i	$0.253624\pi$
$882$	0.267433	0.00900493
$883$	16.6033	0.558746	0.279373	−	0.960183i	$-0.409873\pi$
$883$	16.6033	0.558746	0.279373	+	0.960183i	$0.409873\pi$
$884$	43.4650	1.46189
$885$	0.525879	0.0176772
$886$	0.890550	0.0299186
$887$	−54.1516	−1.81823	−0.909116	−	0.416544i	$-0.863241\pi$
$887$	−54.1516	−1.81823	−0.909116	+	0.416544i	$0.863241\pi$
$888$	−2.97548	−0.0998506
$889$	−10.2969	−0.345347
$890$	0.0555390	0.00186167
$891$	4.21101	0.141074
$892$	12.2062	0.408695
$893$	−2.02998	−0.0679308
$894$	−1.89862	−0.0634992
$895$	0.132482	0.00442837
$896$	−7.80909	−0.260883
$897$	29.2007	0.974983
$898$	−0.770211	−0.0257023
$899$	3.52549	0.117582
$900$	9.63981	0.321327
$901$	47.4076	1.57937
$902$	−5.16118	−0.171848
$903$	−4.32631	−0.143971
$904$	7.73417	0.257235
$905$	0.634070	0.0210772
$906$	5.76680	0.191589
$907$	−23.2742	−0.772807	−0.386404	−	0.922330i	$-0.626283\pi$
$907$	−23.2742	−0.772807	−0.386404	+	0.922330i	$0.626283\pi$
$908$	22.9811	0.762655
$909$	−13.2263	−0.438689
$910$	0.0360135	0.00119384
$911$	−7.39986	−0.245168	−0.122584	−	0.992458i	$-0.539118\pi$
$911$	−7.39986	−0.245168	−0.122584	+	0.992458i	$0.539118\pi$
$912$	−8.39259	−0.277907
$913$	44.7453	1.48085
$914$	−7.62292	−0.252144
$915$	−0.101040	−0.00334029
$916$	27.5017	0.908681
$917$	9.63191	0.318074
$918$	−1.64021	−0.0541351
$919$	29.6846	0.979205	0.489602	−	0.871946i	$-0.337142\pi$
$919$	29.6846	0.979205	0.489602	+	0.871946i	$0.337142\pi$
$920$	−0.305918	−0.0100858
$921$	−24.6943	−0.813703
$922$	−10.2849	−0.338716
$923$	−4.38292	−0.144266
$924$	−8.12085	−0.267156
$925$	−14.1570	−0.465479
$926$	−10.1963	−0.335071
$927$	4.22437	0.138747
$928$	2.00473	0.0658085
$929$	31.3943	1.03001	0.515006	−	0.857186i	$-0.327790\pi$
$929$	31.3943	1.03001	0.515006	+	0.857186i	$0.327790\pi$
$930$	0.0526941	0.00172791
$931$	−2.34693	−0.0769174
$932$	50.8358	1.66518
$933$	1.07377	0.0351535
$934$	0.726705	0.0237785
$935$	−0.946420	−0.0309512
$936$	−3.86081	−0.126194
$937$	−24.3789	−0.796424	−0.398212	−	0.917293i	$-0.630369\pi$
$937$	−24.3789	−0.796424	−0.398212	+	0.917293i	$0.630369\pi$
$938$	1.60229	0.0523168
$939$	16.7660	0.547139
$940$	−0.0611251	−0.00199368
$941$	19.0967	0.622534	0.311267	−	0.950323i	$-0.399247\pi$
$941$	19.0967	0.622534	0.311267	+	0.950323i	$0.399247\pi$
$942$	−0.167700	−0.00546395
$943$	−36.4168	−1.18589
$944$	51.3182	1.67026
$945$	0.0366447	0.00119205
$946$	−4.87213	−0.158407
$947$	−44.7314	−1.45358	−0.726788	−	0.686862i	$-0.758988\pi$
$947$	−44.7314	−1.45358	−0.726788	+	0.686862i	$0.758988\pi$
$948$	6.97018	0.226381
$949$	48.8066	1.58433
$950$	3.13738	0.101790
$951$	−8.52857	−0.276558
$952$	6.44354	0.208836
$953$	53.7769	1.74201	0.871003	−	0.491279i	$-0.163470\pi$
$953$	53.7769	1.74201	0.871003	+	0.491279i	$0.163470\pi$
$954$	−2.06717	−0.0669272
$955$	0.0366447	0.00118580
$956$	−23.1200	−0.747754
$957$	2.76102	0.0892511
$958$	−4.52650	−0.146245
$959$	11.9259	0.385107
$960$	−0.232119	−0.00749160
$961$	−2.08839	−0.0673675
$962$	2.78337	0.0897396
$963$	10.1513	0.327121
$964$	41.2034	1.32707
$965$	0.726216	0.0233777
$966$	2.12505	0.0683723
$967$	−41.8692	−1.34642	−0.673212	−	0.739450i	$-0.735086\pi$
$967$	−41.8692	−1.34642	−0.673212	+	0.739450i	$0.735086\pi$
$968$	−7.07333	−0.227345
$969$	14.3941	0.462406
$970$	−0.0491397	−0.00157778
$971$	−47.7692	−1.53299	−0.766494	−	0.642252i	$-0.778000\pi$
$971$	−47.7692	−1.53299	−0.766494	+	0.642252i	$0.778000\pi$
$972$	−1.92848	−0.0618560
$973$	3.39342	0.108788
$974$	−2.78576	−0.0892615
$975$	−18.3693	−0.588288
$976$	−9.86006	−0.315613
$977$	−11.5904	−0.370810	−0.185405	−	0.982662i	$-0.559360\pi$
$977$	−11.5904	−0.370810	−0.185405	+	0.982662i	$0.559360\pi$
$978$	3.39811	0.108660
$979$	23.8648	0.762724
$980$	−0.0706686	−0.00225743
$981$	−4.99943	−0.159619
$982$	8.27349	0.264018
$983$	13.5233	0.431327	0.215664	−	0.976468i	$-0.430809\pi$
$983$	13.5233	0.431327	0.215664	+	0.976468i	$0.430809\pi$
$984$	4.81489	0.153493
$985$	−0.477775	−0.0152232
$986$	−1.07543	−0.0342488
$987$	0.864954	0.0275318
$988$	16.6324	0.529146
$989$	−34.3774	−1.09314
$990$	0.0412679	0.00131158
$991$	16.6636	0.529336	0.264668	−	0.964340i	$-0.414738\pi$
$991$	16.6636	0.529336	0.264668	+	0.964340i	$0.414738\pi$
$992$	16.4403	0.521979
$993$	−23.1783	−0.735540
$994$	−0.318962	−0.0101169
$995$	0.615287	0.0195059
$996$	−20.4916	−0.649302
$997$	26.5837	0.841914	0.420957	−	0.907081i	$-0.361694\pi$
$997$	26.5837	0.841914	0.420957	+	0.907081i	$0.361694\pi$
$998$	−11.1946	−0.354360
$999$	2.83216	0.0896056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.13	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+0.267433 q^{2} +1.00000 q^{3} -1.92848 q^{4} +0.0366447 q^{5} +0.267433 q^{6} +1.00000 q^{7} -1.05060 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.267433 q^{2} +1.00000 q^{3} -1.92848 q^{4} +0.0366447 q^{5} +0.267433 q^{6} +1.00000 q^{7} -1.05060 q^{8} +1.00000 q^{9} +0.00980000 q^{10} +4.21101 q^{11} -1.92848 q^{12} +3.67485 q^{13} +0.267433 q^{14} +0.0366447 q^{15} +3.57599 q^{16} -6.13318 q^{17} +0.267433 q^{18} -2.34693 q^{19} -0.0706686 q^{20} +1.00000 q^{21} +1.12616 q^{22} +7.94611 q^{23} -1.05060 q^{24} -4.99866 q^{25} +0.982774 q^{26} +1.00000 q^{27} -1.92848 q^{28} +0.655666 q^{29} +0.00980000 q^{30} +5.37695 q^{31} +3.05755 q^{32} +4.21101 q^{33} -1.64021 q^{34} +0.0366447 q^{35} -1.92848 q^{36} +2.83216 q^{37} -0.627645 q^{38} +3.67485 q^{39} -0.0384991 q^{40} -4.58297 q^{41} +0.267433 q^{42} -4.32631 q^{43} -8.12085 q^{44} +0.0366447 q^{45} +2.12505 q^{46} +0.864954 q^{47} +3.57599 q^{48} +1.00000 q^{49} -1.33680 q^{50} -6.13318 q^{51} -7.08687 q^{52} -7.72969 q^{53} +0.267433 q^{54} +0.154311 q^{55} -1.05060 q^{56} -2.34693 q^{57} +0.175347 q^{58} +14.3507 q^{59} -0.0706686 q^{60} -2.75729 q^{61} +1.43797 q^{62} +1.00000 q^{63} -6.33430 q^{64} +0.134664 q^{65} +1.12616 q^{66} +5.99139 q^{67} +11.8277 q^{68} +7.94611 q^{69} +0.00980000 q^{70} -1.19268 q^{71} -1.05060 q^{72} +13.2813 q^{73} +0.757413 q^{74} -4.99866 q^{75} +4.52600 q^{76} +4.21101 q^{77} +0.982774 q^{78} -3.61434 q^{79} +0.131041 q^{80} +1.00000 q^{81} -1.22564 q^{82} +10.6258 q^{83} -1.92848 q^{84} -0.224749 q^{85} -1.15700 q^{86} +0.655666 q^{87} -4.42411 q^{88} +5.66725 q^{89} +0.00980000 q^{90} +3.67485 q^{91} -15.3239 q^{92} +5.37695 q^{93} +0.231317 q^{94} -0.0860025 q^{95} +3.05755 q^{96} -5.01426 q^{97} +0.267433 q^{98} +4.21101 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 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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