LMFDB - Embedded newform 4022.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.50306 q^{3} +1.00000 q^{4} +0.0732871 q^{5} -2.50306 q^{6} -1.25699 q^{7} +1.00000 q^{8} +3.26529 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.50306 q^{3} +1.00000 q^{4} +0.0732871 q^{5} -2.50306 q^{6} -1.25699 q^{7} +1.00000 q^{8} +3.26529 q^{9} +0.0732871 q^{10} -2.84908 q^{11} -2.50306 q^{12} +1.61180 q^{13} -1.25699 q^{14} -0.183442 q^{15} +1.00000 q^{16} -6.27913 q^{17} +3.26529 q^{18} +7.93778 q^{19} +0.0732871 q^{20} +3.14631 q^{21} -2.84908 q^{22} -3.36070 q^{23} -2.50306 q^{24} -4.99463 q^{25} +1.61180 q^{26} -0.664031 q^{27} -1.25699 q^{28} +2.56226 q^{29} -0.183442 q^{30} -2.29991 q^{31} +1.00000 q^{32} +7.13141 q^{33} -6.27913 q^{34} -0.0921209 q^{35} +3.26529 q^{36} +4.83601 q^{37} +7.93778 q^{38} -4.03443 q^{39} +0.0732871 q^{40} -5.31870 q^{41} +3.14631 q^{42} +6.39401 q^{43} -2.84908 q^{44} +0.239303 q^{45} -3.36070 q^{46} +2.78599 q^{47} -2.50306 q^{48} -5.41998 q^{49} -4.99463 q^{50} +15.7170 q^{51} +1.61180 q^{52} -10.7813 q^{53} -0.664031 q^{54} -0.208801 q^{55} -1.25699 q^{56} -19.8687 q^{57} +2.56226 q^{58} -7.89307 q^{59} -0.183442 q^{60} +9.40976 q^{61} -2.29991 q^{62} -4.10443 q^{63} +1.00000 q^{64} +0.118124 q^{65} +7.13141 q^{66} +12.5474 q^{67} -6.27913 q^{68} +8.41201 q^{69} -0.0921209 q^{70} +2.58613 q^{71} +3.26529 q^{72} +14.4787 q^{73} +4.83601 q^{74} +12.5018 q^{75} +7.93778 q^{76} +3.58126 q^{77} -4.03443 q^{78} +7.54999 q^{79} +0.0732871 q^{80} -8.13376 q^{81} -5.31870 q^{82} -3.60097 q^{83} +3.14631 q^{84} -0.460179 q^{85} +6.39401 q^{86} -6.41349 q^{87} -2.84908 q^{88} +2.95236 q^{89} +0.239303 q^{90} -2.02601 q^{91} -3.36070 q^{92} +5.75681 q^{93} +2.78599 q^{94} +0.581737 q^{95} -2.50306 q^{96} +1.08941 q^{97} -5.41998 q^{98} -9.30307 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.50306	−1.44514	−0.722570	−	0.691298i	$-0.757039\pi$
$3$	−2.50306	−1.44514	−0.722570	+	0.691298i	$0.757039\pi$
$4$	1.00000	0.500000
$5$	0.0732871	0.0327750	0.0163875	−	0.999866i	$-0.494783\pi$
$5$	0.0732871	0.0327750	0.0163875	+	0.999866i	$0.494783\pi$
$6$	−2.50306	−1.02187
$7$	−1.25699	−0.475097	−0.237548	−	0.971376i	$-0.576344\pi$
$7$	−1.25699	−0.475097	−0.237548	+	0.971376i	$0.576344\pi$
$8$	1.00000	0.353553
$9$	3.26529	1.08843
$10$	0.0732871	0.0231754
$11$	−2.84908	−0.859030	−0.429515	−	0.903060i	$-0.641315\pi$
$11$	−2.84908	−0.859030	−0.429515	+	0.903060i	$0.641315\pi$
$12$	−2.50306	−0.722570
$13$	1.61180	0.447033	0.223516	−	0.974700i	$-0.428246\pi$
$13$	1.61180	0.447033	0.223516	+	0.974700i	$0.428246\pi$
$14$	−1.25699	−0.335944
$15$	−0.183442	−0.0473644
$16$	1.00000	0.250000
$17$	−6.27913	−1.52291	−0.761457	−	0.648216i	$-0.775516\pi$
$17$	−6.27913	−1.52291	−0.761457	+	0.648216i	$0.775516\pi$
$18$	3.26529	0.769636
$19$	7.93778	1.82105	0.910526	−	0.413452i	$-0.135677\pi$
$19$	7.93778	1.82105	0.910526	+	0.413452i	$0.135677\pi$
$20$	0.0732871	0.0163875
$21$	3.14631	0.686581
$22$	−2.84908	−0.607426
$23$	−3.36070	−0.700754	−0.350377	−	0.936609i	$-0.613946\pi$
$23$	−3.36070	−0.700754	−0.350377	+	0.936609i	$0.613946\pi$
$24$	−2.50306	−0.510934
$25$	−4.99463	−0.998926
$26$	1.61180	0.316100
$27$	−0.664031	−0.127793
$28$	−1.25699	−0.237548
$29$	2.56226	0.475800	0.237900	−	0.971290i	$-0.423541\pi$
$29$	2.56226	0.475800	0.237900	+	0.971290i	$0.423541\pi$
$30$	−0.183442	−0.0334917
$31$	−2.29991	−0.413077	−0.206538	−	0.978439i	$-0.566220\pi$
$31$	−2.29991	−0.413077	−0.206538	+	0.978439i	$0.566220\pi$
$32$	1.00000	0.176777
$33$	7.13141	1.24142
$34$	−6.27913	−1.07686
$35$	−0.0921209	−0.0155713
$36$	3.26529	0.544215
$37$	4.83601	0.795035	0.397517	−	0.917595i	$-0.369872\pi$
$37$	4.83601	0.795035	0.397517	+	0.917595i	$0.369872\pi$
$38$	7.93778	1.28768
$39$	−4.03443	−0.646025
$40$	0.0732871	0.0115877
$41$	−5.31870	−0.830641	−0.415321	−	0.909675i	$-0.636331\pi$
$41$	−5.31870	−0.830641	−0.415321	+	0.909675i	$0.636331\pi$
$42$	3.14631	0.485486
$43$	6.39401	0.975078	0.487539	−	0.873101i	$-0.337895\pi$
$43$	6.39401	0.975078	0.487539	+	0.873101i	$0.337895\pi$
$44$	−2.84908	−0.429515
$45$	0.239303	0.0356732
$46$	−3.36070	−0.495508
$47$	2.78599	0.406379	0.203189	−	0.979139i	$-0.434869\pi$
$47$	2.78599	0.406379	0.203189	+	0.979139i	$0.434869\pi$
$48$	−2.50306	−0.361285
$49$	−5.41998	−0.774283
$50$	−4.99463	−0.706347
$51$	15.7170	2.20082
$52$	1.61180	0.223516
$53$	−10.7813	−1.48092	−0.740461	−	0.672099i	$-0.765393\pi$
$53$	−10.7813	−1.48092	−0.740461	+	0.672099i	$0.765393\pi$
$54$	−0.664031	−0.0903632
$55$	−0.208801	−0.0281547
$56$	−1.25699	−0.167972
$57$	−19.8687	−2.63167
$58$	2.56226	0.336442
$59$	−7.89307	−1.02759	−0.513795	−	0.857913i	$-0.671761\pi$
$59$	−7.89307	−1.02759	−0.513795	+	0.857913i	$0.671761\pi$
$60$	−0.183442	−0.0236822
$61$	9.40976	1.20480	0.602398	−	0.798196i	$-0.294212\pi$
$61$	9.40976	1.20480	0.602398	+	0.798196i	$0.294212\pi$
$62$	−2.29991	−0.292089
$63$	−4.10443	−0.517109
$64$	1.00000	0.125000
$65$	0.118124	0.0146515
$66$	7.13141	0.877815
$67$	12.5474	1.53291	0.766455	−	0.642298i	$-0.222019\pi$
$67$	12.5474	1.53291	0.766455	+	0.642298i	$0.222019\pi$
$68$	−6.27913	−0.761457
$69$	8.41201	1.01269
$70$	−0.0921209	−0.0110106
$71$	2.58613	0.306917	0.153459	−	0.988155i	$-0.450959\pi$
$71$	2.58613	0.306917	0.153459	+	0.988155i	$0.450959\pi$
$72$	3.26529	0.384818
$73$	14.4787	1.69460	0.847300	−	0.531114i	$-0.178227\pi$
$73$	14.4787	1.69460	0.847300	+	0.531114i	$0.178227\pi$
$74$	4.83601	0.562174
$75$	12.5018	1.44359
$76$	7.93778	0.910526
$77$	3.58126	0.408122
$78$	−4.03443	−0.456809
$79$	7.54999	0.849441	0.424720	−	0.905325i	$-0.360372\pi$
$79$	7.54999	0.849441	0.424720	+	0.905325i	$0.360372\pi$
$80$	0.0732871	0.00819374
$81$	−8.13376	−0.903751
$82$	−5.31870	−0.587352
$83$	−3.60097	−0.395258	−0.197629	−	0.980277i	$-0.563324\pi$
$83$	−3.60097	−0.395258	−0.197629	+	0.980277i	$0.563324\pi$
$84$	3.14631	0.343291
$85$	−0.460179	−0.0499134
$86$	6.39401	0.689484
$87$	−6.41349	−0.687598
$88$	−2.84908	−0.303713
$89$	2.95236	0.312950	0.156475	−	0.987682i	$-0.449987\pi$
$89$	2.95236	0.312950	0.156475	+	0.987682i	$0.449987\pi$
$90$	0.239303	0.0252248
$91$	−2.02601	−0.212384
$92$	−3.36070	−0.350377
$93$	5.75681	0.596953
$94$	2.78599	0.287353
$95$	0.581737	0.0596849
$96$	−2.50306	−0.255467
$97$	1.08941	0.110613	0.0553065	−	0.998469i	$-0.482386\pi$
$97$	1.08941	0.110613	0.0553065	+	0.998469i	$0.482386\pi$
$98$	−5.41998	−0.547501
$99$	−9.30307	−0.934993
$100$	−4.99463	−0.499463
$101$	−11.4845	−1.14276	−0.571378	−	0.820687i	$-0.693591\pi$
$101$	−11.4845	−1.14276	−0.571378	+	0.820687i	$0.693591\pi$
$102$	15.7170	1.55622
$103$	−0.617715	−0.0608652	−0.0304326	−	0.999537i	$-0.509689\pi$
$103$	−0.617715	−0.0608652	−0.0304326	+	0.999537i	$0.509689\pi$
$104$	1.61180	0.158050
$105$	0.230584	0.0225027
$106$	−10.7813	−1.04717
$107$	17.2253	1.66523	0.832616	−	0.553851i	$-0.186842\pi$
$107$	17.2253	1.66523	0.832616	+	0.553851i	$0.186842\pi$
$108$	−0.664031	−0.0638964
$109$	8.80570	0.843434	0.421717	−	0.906728i	$-0.361428\pi$
$109$	8.80570	0.843434	0.421717	+	0.906728i	$0.361428\pi$
$110$	−0.208801	−0.0199084
$111$	−12.1048	−1.14894
$112$	−1.25699	−0.118774
$113$	4.22222	0.397193	0.198597	−	0.980081i	$-0.436362\pi$
$113$	4.22222	0.397193	0.198597	+	0.980081i	$0.436362\pi$
$114$	−19.8687	−1.86088
$115$	−0.246296	−0.0229672
$116$	2.56226	0.237900
$117$	5.26299	0.486564
$118$	−7.89307	−0.726616
$119$	7.89279	0.723531
$120$	−0.183442	−0.0167459
$121$	−2.88275	−0.262068
$122$	9.40976	0.851920
$123$	13.3130	1.20039
$124$	−2.29991	−0.206538
$125$	−0.732477	−0.0655147
$126$	−4.10443	−0.365651
$127$	4.76056	0.422432	0.211216	−	0.977439i	$-0.432258\pi$
$127$	4.76056	0.422432	0.211216	+	0.977439i	$0.432258\pi$
$128$	1.00000	0.0883883
$129$	−16.0046	−1.40912
$130$	0.118124	0.0103602
$131$	12.1098	1.05804	0.529019	−	0.848610i	$-0.322560\pi$
$131$	12.1098	1.05804	0.529019	+	0.848610i	$0.322560\pi$
$132$	7.13141	0.620709
$133$	−9.97769	−0.865176
$134$	12.5474	1.08393
$135$	−0.0486649	−0.00418841
$136$	−6.27913	−0.538431
$137$	11.2786	0.963596	0.481798	−	0.876282i	$-0.339984\pi$
$137$	11.2786	0.963596	0.481798	+	0.876282i	$0.339984\pi$
$138$	8.41201	0.716078
$139$	−16.4307	−1.39363	−0.696817	−	0.717249i	$-0.745401\pi$
$139$	−16.4307	−1.39363	−0.696817	+	0.717249i	$0.745401\pi$
$140$	−0.0921209	−0.00778564
$141$	−6.97349	−0.587274
$142$	2.58613	0.217023
$143$	−4.59215	−0.384015
$144$	3.26529	0.272107
$145$	0.187781	0.0155943
$146$	14.4787	1.19826
$147$	13.5665	1.11895
$148$	4.83601	0.397517
$149$	−11.6150	−0.951541	−0.475771	−	0.879569i	$-0.657831\pi$
$149$	−11.6150	−0.951541	−0.475771	+	0.879569i	$0.657831\pi$
$150$	12.5018	1.02077
$151$	13.7458	1.11862	0.559309	−	0.828959i	$-0.311066\pi$
$151$	13.7458	1.11862	0.559309	+	0.828959i	$0.311066\pi$
$152$	7.93778	0.643839
$153$	−20.5032	−1.65758
$154$	3.58126	0.288586
$155$	−0.168554	−0.0135386
$156$	−4.03443	−0.323013
$157$	16.9202	1.35038	0.675188	−	0.737645i	$-0.264062\pi$
$157$	16.9202	1.35038	0.675188	+	0.737645i	$0.264062\pi$
$158$	7.54999	0.600645
$159$	26.9861	2.14014
$160$	0.0732871	0.00579385
$161$	4.22435	0.332926
$162$	−8.13376	−0.639048
$163$	4.60136	0.360406	0.180203	−	0.983629i	$-0.442324\pi$
$163$	4.60136	0.360406	0.180203	+	0.983629i	$0.442324\pi$
$164$	−5.31870	−0.415321
$165$	0.522640	0.0406874
$166$	−3.60097	−0.279489
$167$	22.5770	1.74706	0.873532	−	0.486767i	$-0.161824\pi$
$167$	22.5770	1.74706	0.873532	+	0.486767i	$0.161824\pi$
$168$	3.14631	0.242743
$169$	−10.4021	−0.800162
$170$	−0.460179	−0.0352941
$171$	25.9191	1.98209
$172$	6.39401	0.487539
$173$	−0.748496	−0.0569071	−0.0284535	−	0.999595i	$-0.509058\pi$
$173$	−0.748496	−0.0569071	−0.0284535	+	0.999595i	$0.509058\pi$
$174$	−6.41349	−0.486205
$175$	6.27819	0.474586
$176$	−2.84908	−0.214757
$177$	19.7568	1.48501
$178$	2.95236	0.221289
$179$	−7.22728	−0.540192	−0.270096	−	0.962833i	$-0.587055\pi$
$179$	−7.22728	−0.540192	−0.270096	+	0.962833i	$0.587055\pi$
$180$	0.239303	0.0178366
$181$	3.01609	0.224184	0.112092	−	0.993698i	$-0.464245\pi$
$181$	3.01609	0.224184	0.112092	+	0.993698i	$0.464245\pi$
$182$	−2.02601	−0.150178
$183$	−23.5532	−1.74110
$184$	−3.36070	−0.247754
$185$	0.354417	0.0260572
$186$	5.75681	0.422110
$187$	17.8898	1.30823
$188$	2.78599	0.203189
$189$	0.834679	0.0607140
$190$	0.581737	0.0422036
$191$	10.6334	0.769406	0.384703	−	0.923041i	$-0.374304\pi$
$191$	10.6334	0.769406	0.384703	+	0.923041i	$0.374304\pi$
$192$	−2.50306	−0.180642
$193$	−1.43622	−0.103381	−0.0516905	−	0.998663i	$-0.516461\pi$
$193$	−1.43622	−0.103381	−0.0516905	+	0.998663i	$0.516461\pi$
$194$	1.08941	0.0782153
$195$	−0.295671	−0.0211735
$196$	−5.41998	−0.387142
$197$	2.72603	0.194222	0.0971108	−	0.995274i	$-0.469040\pi$
$197$	2.72603	0.194222	0.0971108	+	0.995274i	$0.469040\pi$
$198$	−9.30307	−0.661140
$199$	7.68601	0.544847	0.272423	−	0.962177i	$-0.412175\pi$
$199$	7.68601	0.544847	0.272423	+	0.962177i	$0.412175\pi$
$200$	−4.99463	−0.353174
$201$	−31.4069	−2.21527
$202$	−11.4845	−0.808050
$203$	−3.22073	−0.226051
$204$	15.7170	1.10041
$205$	−0.389792	−0.0272242
$206$	−0.617715	−0.0430382
$207$	−10.9736	−0.762721
$208$	1.61180	0.111758
$209$	−22.6154	−1.56434
$210$	0.230584	0.0159118
$211$	13.3045	0.915917	0.457959	−	0.888974i	$-0.348581\pi$
$211$	13.3045	0.915917	0.457959	+	0.888974i	$0.348581\pi$
$212$	−10.7813	−0.740461
$213$	−6.47323	−0.443538
$214$	17.2253	1.17750
$215$	0.468598	0.0319581
$216$	−0.664031	−0.0451816
$217$	2.89096	0.196251
$218$	8.80570	0.596398
$219$	−36.2409	−2.44893
$220$	−0.208801	−0.0140773
$221$	−10.1207	−0.680792
$222$	−12.1048	−0.812421
$223$	5.60413	0.375281	0.187640	−	0.982238i	$-0.439916\pi$
$223$	5.60413	0.375281	0.187640	+	0.982238i	$0.439916\pi$
$224$	−1.25699	−0.0839860
$225$	−16.3089	−1.08726
$226$	4.22222	0.280858
$227$	26.0194	1.72697	0.863483	−	0.504378i	$-0.168278\pi$
$227$	26.0194	1.72697	0.863483	+	0.504378i	$0.168278\pi$
$228$	−19.8687	−1.31584
$229$	19.0513	1.25894	0.629472	−	0.777023i	$-0.283271\pi$
$229$	19.0513	1.25894	0.629472	+	0.777023i	$0.283271\pi$
$230$	−0.246296	−0.0162402
$231$	−8.96409	−0.589794
$232$	2.56226	0.168221
$233$	5.11960	0.335396	0.167698	−	0.985838i	$-0.446367\pi$
$233$	5.11960	0.335396	0.167698	+	0.985838i	$0.446367\pi$
$234$	5.26299	0.344053
$235$	0.204177	0.0133191
$236$	−7.89307	−0.513795
$237$	−18.8981	−1.22756
$238$	7.89279	0.511614
$239$	−22.9400	−1.48386	−0.741932	−	0.670475i	$-0.766090\pi$
$239$	−22.9400	−1.48386	−0.741932	+	0.670475i	$0.766090\pi$
$240$	−0.183442	−0.0118411
$241$	16.2412	1.04619	0.523093	−	0.852275i	$-0.324778\pi$
$241$	16.2412	1.04619	0.523093	+	0.852275i	$0.324778\pi$
$242$	−2.88275	−0.185310
$243$	22.3513	1.43384
$244$	9.40976	0.602398
$245$	−0.397215	−0.0253771
$246$	13.3130	0.848806
$247$	12.7941	0.814070
$248$	−2.29991	−0.146045
$249$	9.01343	0.571203
$250$	−0.732477	−0.0463259
$251$	8.76594	0.553301	0.276651	−	0.960971i	$-0.410776\pi$
$251$	8.76594	0.553301	0.276651	+	0.960971i	$0.410776\pi$
$252$	−4.10443	−0.258555
$253$	9.57489	0.601968
$254$	4.76056	0.298704
$255$	1.15185	0.0721319
$256$	1.00000	0.0625000
$257$	4.66192	0.290802	0.145401	−	0.989373i	$-0.453553\pi$
$257$	4.66192	0.290802	0.145401	+	0.989373i	$0.453553\pi$
$258$	−16.0046	−0.996401
$259$	−6.07880	−0.377718
$260$	0.118124	0.00732575
$261$	8.36653	0.517875
$262$	12.1098	0.748145
$263$	−3.88618	−0.239632	−0.119816	−	0.992796i	$-0.538231\pi$
$263$	−3.88618	−0.239632	−0.119816	+	0.992796i	$0.538231\pi$
$264$	7.13141	0.438908
$265$	−0.790128	−0.0485372
$266$	−9.97769	−0.611772
$267$	−7.38993	−0.452257
$268$	12.5474	0.766455
$269$	12.1564	0.741187	0.370593	−	0.928795i	$-0.379154\pi$
$269$	12.1564	0.741187	0.370593	+	0.928795i	$0.379154\pi$
$270$	−0.0486649	−0.00296165
$271$	4.52991	0.275172	0.137586	−	0.990490i	$-0.456066\pi$
$271$	4.52991	0.275172	0.137586	+	0.990490i	$0.456066\pi$
$272$	−6.27913	−0.380728
$273$	5.07122	0.306924
$274$	11.2786	0.681365
$275$	14.2301	0.858107
$276$	8.41201	0.506344
$277$	0.700840	0.0421094	0.0210547	−	0.999778i	$-0.493298\pi$
$277$	0.700840	0.0421094	0.0210547	+	0.999778i	$0.493298\pi$
$278$	−16.4307	−0.985448
$279$	−7.50988	−0.449605
$280$	−0.0921209	−0.00550528
$281$	−11.0037	−0.656424	−0.328212	−	0.944604i	$-0.606446\pi$
$281$	−11.0037	−0.656424	−0.328212	+	0.944604i	$0.606446\pi$
$282$	−6.97349	−0.415266
$283$	18.9431	1.12605	0.563027	−	0.826439i	$-0.309637\pi$
$283$	18.9431	1.12605	0.563027	+	0.826439i	$0.309637\pi$
$284$	2.58613	0.153459
$285$	−1.45612	−0.0862531
$286$	−4.59215	−0.271539
$287$	6.68554	0.394635
$288$	3.26529	0.192409
$289$	22.4275	1.31927
$290$	0.187781	0.0110269
$291$	−2.72686	−0.159851
$292$	14.4787	0.847300
$293$	14.8903	0.869898	0.434949	−	0.900455i	$-0.356766\pi$
$293$	14.8903	0.869898	0.434949	+	0.900455i	$0.356766\pi$
$294$	13.5665	0.791215
$295$	−0.578460	−0.0336792
$296$	4.83601	0.281087
$297$	1.89188	0.109778
$298$	−11.6150	−0.672841
$299$	−5.41677	−0.313260
$300$	12.5018	0.721794
$301$	−8.03719	−0.463256
$302$	13.7458	0.790983
$303$	28.7465	1.65144
$304$	7.93778	0.455263
$305$	0.689614	0.0394872
$306$	−20.5032	−1.17209
$307$	21.9660	1.25367	0.626833	−	0.779153i	$-0.284351\pi$
$307$	21.9660	1.25367	0.626833	+	0.779153i	$0.284351\pi$
$308$	3.58126	0.204061
$309$	1.54617	0.0879588
$310$	−0.168554	−0.00957321
$311$	−0.789869	−0.0447894	−0.0223947	−	0.999749i	$-0.507129\pi$
$311$	−0.789869	−0.0447894	−0.0223947	+	0.999749i	$0.507129\pi$
$312$	−4.03443	−0.228404
$313$	−7.71109	−0.435857	−0.217928	−	0.975965i	$-0.569930\pi$
$313$	−7.71109	−0.435857	−0.217928	+	0.975965i	$0.569930\pi$
$314$	16.9202	0.954860
$315$	−0.300801	−0.0169482
$316$	7.54999	0.424720
$317$	8.45844	0.475073	0.237537	−	0.971379i	$-0.423660\pi$
$317$	8.45844	0.475073	0.237537	+	0.971379i	$0.423660\pi$
$318$	26.9861	1.51331
$319$	−7.30009	−0.408727
$320$	0.0732871	0.00409687
$321$	−43.1159	−2.40649
$322$	4.22435	0.235414
$323$	−49.8424	−2.77330
$324$	−8.13376	−0.451875
$325$	−8.05034	−0.446553
$326$	4.60136	0.254846
$327$	−22.0412	−1.21888
$328$	−5.31870	−0.293676
$329$	−3.50196	−0.193069
$330$	0.522640	0.0287704
$331$	−12.6610	−0.695911	−0.347955	−	0.937511i	$-0.613124\pi$
$331$	−12.6610	−0.695911	−0.347955	+	0.937511i	$0.613124\pi$
$332$	−3.60097	−0.197629
$333$	15.7910	0.865339
$334$	22.5770	1.23536
$335$	0.919563	0.0502411
$336$	3.14631	0.171645
$337$	−9.53440	−0.519372	−0.259686	−	0.965693i	$-0.583619\pi$
$337$	−9.53440	−0.519372	−0.259686	+	0.965693i	$0.583619\pi$
$338$	−10.4021	−0.565800
$339$	−10.5685	−0.574000
$340$	−0.460179	−0.0249567
$341$	6.55263	0.354845
$342$	25.9191	1.40155
$343$	15.6118	0.842956
$344$	6.39401	0.344742
$345$	0.616492	0.0331908
$346$	−0.748496	−0.0402394
$347$	−4.11913	−0.221127	−0.110563	−	0.993869i	$-0.535266\pi$
$347$	−4.11913	−0.221127	−0.110563	+	0.993869i	$0.535266\pi$
$348$	−6.41349	−0.343799
$349$	−32.4434	−1.73666	−0.868328	−	0.495991i	$-0.834805\pi$
$349$	−32.4434	−1.73666	−0.868328	+	0.495991i	$0.834805\pi$
$350$	6.27819	0.335583
$351$	−1.07029	−0.0571276
$352$	−2.84908	−0.151856
$353$	−1.98124	−0.105451	−0.0527254	−	0.998609i	$-0.516791\pi$
$353$	−1.98124	−0.105451	−0.0527254	+	0.998609i	$0.516791\pi$
$354$	19.7568	1.05006
$355$	0.189530	0.0100592
$356$	2.95236	0.156475
$357$	−19.7561	−1.04560
$358$	−7.22728	−0.381974
$359$	−1.52429	−0.0804490	−0.0402245	−	0.999191i	$-0.512807\pi$
$359$	−1.52429	−0.0804490	−0.0402245	+	0.999191i	$0.512807\pi$
$360$	0.239303	0.0126124
$361$	44.0084	2.31623
$362$	3.01609	0.158522
$363$	7.21567	0.378725
$364$	−2.02601	−0.106192
$365$	1.06110	0.0555405
$366$	−23.5532	−1.23114
$367$	−28.7275	−1.49956	−0.749782	−	0.661685i	$-0.769841\pi$
$367$	−28.7275	−1.49956	−0.749782	+	0.661685i	$0.769841\pi$
$368$	−3.36070	−0.175188
$369$	−17.3671	−0.904094
$370$	0.354417	0.0184252
$371$	13.5519	0.703581
$372$	5.75681	0.298477
$373$	−7.34260	−0.380185	−0.190093	−	0.981766i	$-0.560879\pi$
$373$	−7.34260	−0.380185	−0.190093	+	0.981766i	$0.560879\pi$
$374$	17.8898	0.925057
$375$	1.83343	0.0946780
$376$	2.78599	0.143677
$377$	4.12986	0.212698
$378$	0.834679	0.0429313
$379$	−13.9457	−0.716342	−0.358171	−	0.933656i	$-0.616600\pi$
$379$	−13.9457	−0.716342	−0.358171	+	0.933656i	$0.616600\pi$
$380$	0.581737	0.0298425
$381$	−11.9160	−0.610473
$382$	10.6334	0.544052
$383$	−6.06270	−0.309789	−0.154895	−	0.987931i	$-0.549504\pi$
$383$	−6.06270	−0.309789	−0.154895	+	0.987931i	$0.549504\pi$
$384$	−2.50306	−0.127734
$385$	0.262460	0.0133762
$386$	−1.43622	−0.0731015
$387$	20.8783	1.06130
$388$	1.08941	0.0553065
$389$	30.2018	1.53129	0.765645	−	0.643263i	$-0.222420\pi$
$389$	30.2018	1.53129	0.765645	+	0.643263i	$0.222420\pi$
$390$	−0.295671	−0.0149719
$391$	21.1023	1.06719
$392$	−5.41998	−0.273750
$393$	−30.3115	−1.52901
$394$	2.72603	0.137335
$395$	0.553317	0.0278404
$396$	−9.30307	−0.467497
$397$	−17.9251	−0.899636	−0.449818	−	0.893120i	$-0.648511\pi$
$397$	−17.9251	−0.899636	−0.449818	+	0.893120i	$0.648511\pi$
$398$	7.68601	0.385265
$399$	24.9747	1.25030
$400$	−4.99463	−0.249731
$401$	−26.5773	−1.32721	−0.663603	−	0.748085i	$-0.730974\pi$
$401$	−26.5773	−1.32721	−0.663603	+	0.748085i	$0.730974\pi$
$402$	−31.4069	−1.56643
$403$	−3.70700	−0.184659
$404$	−11.4845	−0.571378
$405$	−0.596099	−0.0296204
$406$	−3.22073	−0.159842
$407$	−13.7782	−0.682958
$408$	15.7170	0.778108
$409$	−3.04631	−0.150630	−0.0753151	−	0.997160i	$-0.523996\pi$
$409$	−3.04631	−0.150630	−0.0753151	+	0.997160i	$0.523996\pi$
$410$	−0.389792	−0.0192504
$411$	−28.2310	−1.39253
$412$	−0.617715	−0.0304326
$413$	9.92149	0.488205
$414$	−10.9736	−0.539325
$415$	−0.263904	−0.0129546
$416$	1.61180	0.0790250
$417$	41.1269	2.01400
$418$	−22.6154	−1.10615
$419$	16.8127	0.821352	0.410676	−	0.911781i	$-0.365293\pi$
$419$	16.8127	0.821352	0.410676	+	0.911781i	$0.365293\pi$
$420$	0.230584	0.0112513
$421$	−40.3056	−1.96438	−0.982188	−	0.187899i	$-0.939832\pi$
$421$	−40.3056	−1.96438	−0.982188	+	0.187899i	$0.939832\pi$
$422$	13.3045	0.647651
$423$	9.09707	0.442315
$424$	−10.7813	−0.523585
$425$	31.3619	1.52128
$426$	−6.47323	−0.313629
$427$	−11.8280	−0.572395
$428$	17.2253	0.832616
$429$	11.4944	0.554955
$430$	0.468598	0.0225978
$431$	16.8867	0.813405	0.406702	−	0.913561i	$-0.366679\pi$
$431$	16.8867	0.813405	0.406702	+	0.913561i	$0.366679\pi$
$432$	−0.664031	−0.0319482
$433$	−1.01520	−0.0487873	−0.0243937	−	0.999702i	$-0.507766\pi$
$433$	−1.01520	−0.0487873	−0.0243937	+	0.999702i	$0.507766\pi$
$434$	2.89096	0.138771
$435$	−0.470026	−0.0225360
$436$	8.80570	0.421717
$437$	−26.6765	−1.27611
$438$	−36.2409	−1.73166
$439$	29.8989	1.42700	0.713499	−	0.700657i	$-0.247109\pi$
$439$	29.8989	1.42700	0.713499	+	0.700657i	$0.247109\pi$
$440$	−0.208801	−0.00995418
$441$	−17.6978	−0.842753
$442$	−10.1207	−0.481393
$443$	15.6699	0.744500	0.372250	−	0.928132i	$-0.378586\pi$
$443$	15.6699	0.744500	0.372250	+	0.928132i	$0.378586\pi$
$444$	−12.1048	−0.574468
$445$	0.216370	0.0102569
$446$	5.60413	0.265363
$447$	29.0731	1.37511
$448$	−1.25699	−0.0593871
$449$	−7.05157	−0.332784	−0.166392	−	0.986060i	$-0.553212\pi$
$449$	−7.05157	−0.332784	−0.166392	+	0.986060i	$0.553212\pi$
$450$	−16.3089	−0.768809
$451$	15.1534	0.713546
$452$	4.22222	0.198597
$453$	−34.4065	−1.61656
$454$	26.0194	1.22115
$455$	−0.148480	−0.00696087
$456$	−19.8687	−0.930438
$457$	−31.4584	−1.47156	−0.735781	−	0.677220i	$-0.763185\pi$
$457$	−31.4584	−1.47156	−0.735781	+	0.677220i	$0.763185\pi$
$458$	19.0513	0.890208
$459$	4.16954	0.194617
$460$	−0.246296	−0.0114836
$461$	−10.7377	−0.500103	−0.250051	−	0.968233i	$-0.580448\pi$
$461$	−10.7377	−0.500103	−0.250051	+	0.968233i	$0.580448\pi$
$462$	−8.96409	−0.417047
$463$	13.4944	0.627139	0.313569	−	0.949565i	$-0.398475\pi$
$463$	13.4944	0.627139	0.313569	+	0.949565i	$0.398475\pi$
$464$	2.56226	0.118950
$465$	0.421900	0.0195651
$466$	5.11960	0.237161
$467$	−10.4824	−0.485068	−0.242534	−	0.970143i	$-0.577979\pi$
$467$	−10.4824	−0.485068	−0.242534	+	0.970143i	$0.577979\pi$
$468$	5.26299	0.243282
$469$	−15.7719	−0.728280
$470$	0.204177	0.00941799
$471$	−42.3521	−1.95148
$472$	−7.89307	−0.363308
$473$	−18.2171	−0.837621
$474$	−18.8981	−0.868016
$475$	−39.6463	−1.81910
$476$	7.89279	0.361766
$477$	−35.2040	−1.61188
$478$	−22.9400	−1.04925
$479$	33.1021	1.51247	0.756236	−	0.654299i	$-0.227036\pi$
$479$	33.1021	1.51247	0.756236	+	0.654299i	$0.227036\pi$
$480$	−0.183442	−0.00837293
$481$	7.79468	0.355407
$482$	16.2412	0.739766
$483$	−10.5738	−0.481124
$484$	−2.88275	−0.131034
$485$	0.0798398	0.00362534
$486$	22.3513	1.01388
$487$	17.3503	0.786218	0.393109	−	0.919492i	$-0.371400\pi$
$487$	17.3503	0.786218	0.393109	+	0.919492i	$0.371400\pi$
$488$	9.40976	0.425960
$489$	−11.5175	−0.520838
$490$	−0.397215	−0.0179443
$491$	−32.5188	−1.46755	−0.733776	−	0.679391i	$-0.762244\pi$
$491$	−32.5188	−1.46755	−0.733776	+	0.679391i	$0.762244\pi$
$492$	13.3130	0.600196
$493$	−16.0888	−0.724603
$494$	12.7941	0.575635
$495$	−0.681794	−0.0306444
$496$	−2.29991	−0.103269
$497$	−3.25073	−0.145815
$498$	9.01343	0.403901
$499$	−36.3677	−1.62804	−0.814022	−	0.580835i	$-0.802726\pi$
$499$	−36.3677	−1.62804	−0.814022	+	0.580835i	$0.802726\pi$
$500$	−0.732477	−0.0327574
$501$	−56.5116	−2.52475
$502$	8.76594	0.391243
$503$	−22.4027	−0.998886	−0.499443	−	0.866347i	$-0.666462\pi$
$503$	−22.4027	−0.998886	−0.499443	+	0.866347i	$0.666462\pi$
$504$	−4.10443	−0.182826
$505$	−0.841669	−0.0374538
$506$	9.57489	0.425656
$507$	26.0370	1.15635
$508$	4.76056	0.211216
$509$	16.7812	0.743814	0.371907	−	0.928270i	$-0.378704\pi$
$509$	16.7812	0.743814	0.371907	+	0.928270i	$0.378704\pi$
$510$	1.15185	0.0510050
$511$	−18.1995	−0.805099
$512$	1.00000	0.0441942
$513$	−5.27093	−0.232717
$514$	4.66192	0.205628
$515$	−0.0452705	−0.00199486
$516$	−16.0046	−0.704562
$517$	−7.93751	−0.349091
$518$	−6.07880	−0.267087
$519$	1.87353	0.0822387
$520$	0.118124	0.00518008
$521$	−33.1730	−1.45334	−0.726668	−	0.686989i	$-0.758932\pi$
$521$	−33.1730	−1.45334	−0.726668	+	0.686989i	$0.758932\pi$
$522$	8.36653	0.366193
$523$	−8.17339	−0.357397	−0.178699	−	0.983904i	$-0.557189\pi$
$523$	−8.17339	−0.357397	−0.178699	+	0.983904i	$0.557189\pi$
$524$	12.1098	0.529019
$525$	−15.7146	−0.685844
$526$	−3.88618	−0.169446
$527$	14.4415	0.629080
$528$	7.13141	0.310355
$529$	−11.7057	−0.508944
$530$	−0.790128	−0.0343210
$531$	−25.7732	−1.11846
$532$	−9.97769	−0.432588
$533$	−8.57268	−0.371324
$534$	−7.38993	−0.319794
$535$	1.26239	0.0545779
$536$	12.5474	0.541966
$537$	18.0903	0.780653
$538$	12.1564	0.524098
$539$	15.4420	0.665132
$540$	−0.0486649	−0.00209420
$541$	−6.26310	−0.269272	−0.134636	−	0.990895i	$-0.542986\pi$
$541$	−6.26310	−0.269272	−0.134636	+	0.990895i	$0.542986\pi$
$542$	4.52991	0.194576
$543$	−7.54943	−0.323977
$544$	−6.27913	−0.269216
$545$	0.645344	0.0276435
$546$	5.07122	0.217028
$547$	16.7450	0.715963	0.357982	−	0.933729i	$-0.383465\pi$
$547$	16.7450	0.715963	0.357982	+	0.933729i	$0.383465\pi$
$548$	11.2786	0.481798
$549$	30.7256	1.31134
$550$	14.2301	0.606773
$551$	20.3387	0.866457
$552$	8.41201	0.358039
$553$	−9.49025	−0.403566
$554$	0.700840	0.0297759
$555$	−0.887125	−0.0376563
$556$	−16.4307	−0.696817
$557$	39.1167	1.65743	0.828713	−	0.559673i	$-0.189073\pi$
$557$	39.1167	1.65743	0.828713	+	0.559673i	$0.189073\pi$
$558$	−7.50988	−0.317918
$559$	10.3059	0.435892
$560$	−0.0921209	−0.00389282
$561$	−44.7790	−1.89057
$562$	−11.0037	−0.464162
$563$	−12.8152	−0.540096	−0.270048	−	0.962847i	$-0.587040\pi$
$563$	−12.8152	−0.540096	−0.270048	+	0.962847i	$0.587040\pi$
$564$	−6.97349	−0.293637
$565$	0.309434	0.0130180
$566$	18.9431	0.796240
$567$	10.2240	0.429369
$568$	2.58613	0.108512
$569$	3.48635	0.146155	0.0730777	−	0.997326i	$-0.476718\pi$
$569$	3.48635	0.146155	0.0730777	+	0.997326i	$0.476718\pi$
$570$	−1.45612	−0.0609901
$571$	−20.4225	−0.854654	−0.427327	−	0.904097i	$-0.640545\pi$
$571$	−20.4225	−0.854654	−0.427327	+	0.904097i	$0.640545\pi$
$572$	−4.59215	−0.192007
$573$	−26.6160	−1.11190
$574$	6.68554	0.279049
$575$	16.7854	0.700001
$576$	3.26529	0.136054
$577$	−12.8232	−0.533838	−0.266919	−	0.963719i	$-0.586006\pi$
$577$	−12.8232	−0.533838	−0.266919	+	0.963719i	$0.586006\pi$
$578$	22.4275	0.932862
$579$	3.59493	0.149400
$580$	0.187781	0.00779717
$581$	4.52637	0.187786
$582$	−2.72686	−0.113032
$583$	30.7167	1.27216
$584$	14.4787	0.599132
$585$	0.385709	0.0159471
$586$	14.8903	0.615111
$587$	8.20589	0.338693	0.169347	−	0.985557i	$-0.445834\pi$
$587$	8.20589	0.338693	0.169347	+	0.985557i	$0.445834\pi$
$588$	13.5665	0.559474
$589$	−18.2562	−0.752234
$590$	−0.578460	−0.0238148
$591$	−6.82341	−0.280677
$592$	4.83601	0.198759
$593$	−9.57242	−0.393092	−0.196546	−	0.980495i	$-0.562973\pi$
$593$	−9.57242	−0.393092	−0.196546	+	0.980495i	$0.562973\pi$
$594$	1.89188	0.0776247
$595$	0.578439	0.0237137
$596$	−11.6150	−0.475771
$597$	−19.2385	−0.787380
$598$	−5.41677	−0.221508
$599$	−34.6804	−1.41700	−0.708502	−	0.705709i	$-0.750629\pi$
$599$	−34.6804	−1.41700	−0.708502	+	0.705709i	$0.750629\pi$
$600$	12.5018	0.510385
$601$	22.7332	0.927306	0.463653	−	0.886017i	$-0.346538\pi$
$601$	22.7332	0.927306	0.463653	+	0.886017i	$0.346538\pi$
$602$	−8.03719	−0.327572
$603$	40.9709	1.66846
$604$	13.7458	0.559309
$605$	−0.211268	−0.00858926
$606$	28.7465	1.16775
$607$	13.7497	0.558084	0.279042	−	0.960279i	$-0.409983\pi$
$607$	13.7497	0.558084	0.279042	+	0.960279i	$0.409983\pi$
$608$	7.93778	0.321920
$609$	8.06167	0.326675
$610$	0.689614	0.0279216
$611$	4.49046	0.181665
$612$	−20.5032	−0.828792
$613$	−21.1720	−0.855127	−0.427564	−	0.903985i	$-0.640628\pi$
$613$	−21.1720	−0.855127	−0.427564	+	0.903985i	$0.640628\pi$
$614$	21.9660	0.886476
$615$	0.975671	0.0393428
$616$	3.58126	0.144293
$617$	40.0853	1.61377	0.806887	−	0.590706i	$-0.201151\pi$
$617$	40.0853	1.61377	0.806887	+	0.590706i	$0.201151\pi$
$618$	1.54617	0.0621963
$619$	8.25566	0.331823	0.165911	−	0.986141i	$-0.446943\pi$
$619$	8.25566	0.331823	0.165911	+	0.986141i	$0.446943\pi$
$620$	−0.168554	−0.00676929
$621$	2.23161	0.0895513
$622$	−0.789869	−0.0316709
$623$	−3.71108	−0.148681
$624$	−4.03443	−0.161506
$625$	24.9195	0.996779
$626$	−7.71109	−0.308197
$627$	56.6075	2.26069
$628$	16.9202	0.675188
$629$	−30.3659	−1.21077
$630$	−0.300801	−0.0119842
$631$	−11.9847	−0.477103	−0.238552	−	0.971130i	$-0.576673\pi$
$631$	−11.9847	−0.477103	−0.238552	+	0.971130i	$0.576673\pi$
$632$	7.54999	0.300323
$633$	−33.3018	−1.32363
$634$	8.45844	0.335928
$635$	0.348888	0.0138452
$636$	26.9861	1.07007
$637$	−8.73593	−0.346130
$638$	−7.30009	−0.289013
$639$	8.44446	0.334058
$640$	0.0732871	0.00289693
$641$	1.26732	0.0500561	0.0250280	−	0.999687i	$-0.492032\pi$
$641$	1.26732	0.0500561	0.0250280	+	0.999687i	$0.492032\pi$
$642$	−43.1159	−1.70165
$643$	−30.7094	−1.21106	−0.605531	−	0.795822i	$-0.707039\pi$
$643$	−30.7094	−1.21106	−0.605531	+	0.795822i	$0.707039\pi$
$644$	4.22435	0.166463
$645$	−1.17293	−0.0461840
$646$	−49.8424	−1.96102
$647$	−28.7450	−1.13008	−0.565042	−	0.825062i	$-0.691140\pi$
$647$	−28.7450	−1.13008	−0.565042	+	0.825062i	$0.691140\pi$
$648$	−8.13376	−0.319524
$649$	22.4880	0.882731
$650$	−8.05034	−0.315760
$651$	−7.23624	−0.283611
$652$	4.60136	0.180203
$653$	3.32212	0.130005	0.0650024	−	0.997885i	$-0.479295\pi$
$653$	3.32212	0.130005	0.0650024	+	0.997885i	$0.479295\pi$
$654$	−22.0412	−0.861878
$655$	0.887491	0.0346771
$656$	−5.31870	−0.207660
$657$	47.2770	1.84445
$658$	−3.50196	−0.136521
$659$	13.7205	0.534475	0.267237	−	0.963631i	$-0.413889\pi$
$659$	13.7205	0.534475	0.267237	+	0.963631i	$0.413889\pi$
$660$	0.522640	0.0203437
$661$	−30.3360	−1.17993	−0.589966	−	0.807428i	$-0.700859\pi$
$661$	−30.3360	−1.17993	−0.589966	+	0.807428i	$0.700859\pi$
$662$	−12.6610	−0.492083
$663$	25.3327	0.983840
$664$	−3.60097	−0.139745
$665$	−0.731236	−0.0283561
$666$	15.7910	0.611887
$667$	−8.61099	−0.333419
$668$	22.5770	0.873532
$669$	−14.0275	−0.542333
$670$	0.919563	0.0355258
$671$	−26.8092	−1.03496
$672$	3.14631	0.121372
$673$	11.1832	0.431082	0.215541	−	0.976495i	$-0.430849\pi$
$673$	11.1832	0.431082	0.215541	+	0.976495i	$0.430849\pi$
$674$	−9.53440	−0.367252
$675$	3.31659	0.127656
$676$	−10.4021	−0.400081
$677$	9.03682	0.347313	0.173657	−	0.984806i	$-0.444442\pi$
$677$	9.03682	0.347313	0.173657	+	0.984806i	$0.444442\pi$
$678$	−10.5685	−0.405879
$679$	−1.36938	−0.0525519
$680$	−0.460179	−0.0176471
$681$	−65.1279	−2.49571
$682$	6.55263	0.250913
$683$	34.0205	1.30176	0.650880	−	0.759181i	$-0.274400\pi$
$683$	34.0205	1.30176	0.650880	+	0.759181i	$0.274400\pi$
$684$	25.9191	0.991043
$685$	0.826576	0.0315818
$686$	15.6118	0.596060
$687$	−47.6864	−1.81935
$688$	6.39401	0.243769
$689$	−17.3773	−0.662021
$690$	0.616492	0.0234694
$691$	−23.4507	−0.892106	−0.446053	−	0.895007i	$-0.647171\pi$
$691$	−23.4507	−0.892106	−0.446053	+	0.895007i	$0.647171\pi$
$692$	−0.748496	−0.0284535
$693$	11.6938	0.444212
$694$	−4.11913	−0.156360
$695$	−1.20416	−0.0456763
$696$	−6.41349	−0.243103
$697$	33.3968	1.26499
$698$	−32.4434	−1.22800
$699$	−12.8147	−0.484695
$700$	6.27819	0.237293
$701$	18.4243	0.695876	0.347938	−	0.937518i	$-0.386882\pi$
$701$	18.4243	0.695876	0.347938	+	0.937518i	$0.386882\pi$
$702$	−1.07029	−0.0403953
$703$	38.3872	1.44780
$704$	−2.84908	−0.107379
$705$	−0.511067	−0.0192479
$706$	−1.98124	−0.0745649
$707$	14.4359	0.542919
$708$	19.7568	0.742506
$709$	−28.8670	−1.08412	−0.542061	−	0.840339i	$-0.682356\pi$
$709$	−28.8670	−1.08412	−0.542061	+	0.840339i	$0.682356\pi$
$710$	0.189530	0.00711293
$711$	24.6529	0.924556
$712$	2.95236	0.110645
$713$	7.72931	0.289465
$714$	−19.7561	−0.739353
$715$	−0.336545	−0.0125861
$716$	−7.22728	−0.270096
$717$	57.4201	2.14439
$718$	−1.52429	−0.0568860
$719$	9.34232	0.348410	0.174205	−	0.984709i	$-0.444264\pi$
$719$	9.34232	0.348410	0.174205	+	0.984709i	$0.444264\pi$
$720$	0.239303	0.00891831
$721$	0.776460	0.0289169
$722$	44.0084	1.63782
$723$	−40.6526	−1.51189
$724$	3.01609	0.112092
$725$	−12.7976	−0.475289
$726$	7.21567	0.267799
$727$	−3.57659	−0.132649	−0.0663243	−	0.997798i	$-0.521127\pi$
$727$	−3.57659	−0.132649	−0.0663243	+	0.997798i	$0.521127\pi$
$728$	−2.02601	−0.0750890
$729$	−31.5454	−1.16835
$730$	1.06110	0.0392730
$731$	−40.1489	−1.48496
$732$	−23.5532	−0.870550
$733$	22.2760	0.822784	0.411392	−	0.911459i	$-0.365043\pi$
$733$	22.2760	0.822784	0.411392	+	0.911459i	$0.365043\pi$
$734$	−28.7275	−1.06035
$735$	0.994250	0.0366735
$736$	−3.36070	−0.123877
$737$	−35.7486	−1.31682
$738$	−17.3671	−0.639291
$739$	−20.8011	−0.765180	−0.382590	−	0.923918i	$-0.624968\pi$
$739$	−20.8011	−0.765180	−0.382590	+	0.923918i	$0.624968\pi$
$740$	0.354417	0.0130286
$741$	−32.0244	−1.17645
$742$	13.5519	0.497507
$743$	37.3805	1.37136	0.685678	−	0.727905i	$-0.259506\pi$
$743$	37.3805	1.37136	0.685678	+	0.727905i	$0.259506\pi$
$744$	5.75681	0.211055
$745$	−0.851232	−0.0311867
$746$	−7.34260	−0.268832
$747$	−11.7582	−0.430210
$748$	17.8898	0.654114
$749$	−21.6520	−0.791146
$750$	1.83343	0.0669474
$751$	−20.7970	−0.758893	−0.379446	−	0.925214i	$-0.623885\pi$
$751$	−20.7970	−0.758893	−0.379446	+	0.925214i	$0.623885\pi$
$752$	2.78599	0.101595
$753$	−21.9416	−0.799598
$754$	4.12986	0.150400
$755$	1.00739	0.0366627
$756$	0.834679	0.0303570
$757$	−34.7018	−1.26126	−0.630629	−	0.776085i	$-0.717203\pi$
$757$	−34.7018	−1.26126	−0.630629	+	0.776085i	$0.717203\pi$
$758$	−13.9457	−0.506530
$759$	−23.9665	−0.869928
$760$	0.581737	0.0211018
$761$	40.3675	1.46332	0.731660	−	0.681670i	$-0.238746\pi$
$761$	40.3675	1.46332	0.731660	+	0.681670i	$0.238746\pi$
$762$	−11.9160	−0.431669
$763$	−11.0687	−0.400712
$764$	10.6334	0.384703
$765$	−1.50262	−0.0543273
$766$	−6.06270	−0.219054
$767$	−12.7221	−0.459367
$768$	−2.50306	−0.0903212
$769$	45.9918	1.65851	0.829253	−	0.558873i	$-0.188766\pi$
$769$	45.9918	1.65851	0.829253	+	0.558873i	$0.188766\pi$
$770$	0.262460	0.00945840
$771$	−11.6690	−0.420250
$772$	−1.43622	−0.0516905
$773$	30.8849	1.11085	0.555426	−	0.831566i	$-0.312555\pi$
$773$	30.8849	1.11085	0.555426	+	0.831566i	$0.312555\pi$
$774$	20.8783	0.750455
$775$	11.4872	0.412633
$776$	1.08941	0.0391076
$777$	15.2156	0.545856
$778$	30.2018	1.08279
$779$	−42.2187	−1.51264
$780$	−0.295671	−0.0105867
$781$	−7.36809	−0.263651
$782$	21.1023	0.754615
$783$	−1.70142	−0.0608039
$784$	−5.41998	−0.193571
$785$	1.24003	0.0442585
$786$	−30.3115	−1.08117
$787$	−1.28596	−0.0458397	−0.0229198	−	0.999737i	$-0.507296\pi$
$787$	−1.28596	−0.0458397	−0.0229198	+	0.999737i	$0.507296\pi$
$788$	2.72603	0.0971108
$789$	9.72733	0.346302
$790$	0.553317	0.0196861
$791$	−5.30728	−0.188705
$792$	−9.30307	−0.330570
$793$	15.1667	0.538584
$794$	−17.9251	−0.636138
$795$	1.97773	0.0701430
$796$	7.68601	0.272423
$797$	35.7631	1.26680	0.633398	−	0.773827i	$-0.281660\pi$
$797$	35.7631	1.26680	0.633398	+	0.773827i	$0.281660\pi$
$798$	24.9747	0.884095
$799$	−17.4936	−0.618880
$800$	−4.99463	−0.176587
$801$	9.64032	0.340624
$802$	−26.5773	−0.938476
$803$	−41.2509	−1.45571
$804$	−31.4069	−1.10763
$805$	0.309590	0.0109116
$806$	−3.70700	−0.130573
$807$	−30.4281	−1.07112
$808$	−11.4845	−0.404025
$809$	−42.2133	−1.48414	−0.742070	−	0.670323i	$-0.766156\pi$
$809$	−42.2133	−1.48414	−0.742070	+	0.670323i	$0.766156\pi$
$810$	−0.596099	−0.0209448
$811$	31.1810	1.09491	0.547456	−	0.836835i	$-0.315596\pi$
$811$	31.1810	1.09491	0.547456	+	0.836835i	$0.315596\pi$
$812$	−3.22073	−0.113026
$813$	−11.3386	−0.397663
$814$	−13.7782	−0.482924
$815$	0.337220	0.0118123
$816$	15.7170	0.550206
$817$	50.7543	1.77567
$818$	−3.04631	−0.106512
$819$	−6.61551	−0.231165
$820$	−0.389792	−0.0136121
$821$	−41.4792	−1.44764	−0.723818	−	0.689991i	$-0.757614\pi$
$821$	−41.4792	−1.44764	−0.723818	+	0.689991i	$0.757614\pi$
$822$	−28.2310	−0.984668
$823$	−11.6353	−0.405581	−0.202790	−	0.979222i	$-0.565001\pi$
$823$	−11.6353	−0.405581	−0.202790	+	0.979222i	$0.565001\pi$
$824$	−0.617715	−0.0215191
$825$	−35.6187	−1.24008
$826$	9.92149	0.345213
$827$	−10.3859	−0.361154	−0.180577	−	0.983561i	$-0.557797\pi$
$827$	−10.3859	−0.361154	−0.180577	+	0.983561i	$0.557797\pi$
$828$	−10.9736	−0.381360
$829$	30.3121	1.05278	0.526391	−	0.850242i	$-0.323545\pi$
$829$	30.3121	1.05278	0.526391	+	0.850242i	$0.323545\pi$
$830$	−0.263904	−0.00916026
$831$	−1.75424	−0.0608540
$832$	1.61180	0.0558791
$833$	34.0328	1.17917
$834$	41.1269	1.42411
$835$	1.65460	0.0572599
$836$	−22.6154	−0.782169
$837$	1.52721	0.0527882
$838$	16.8127	0.580784
$839$	32.2012	1.11171	0.555854	−	0.831280i	$-0.312391\pi$
$839$	32.2012	1.11171	0.555854	+	0.831280i	$0.312391\pi$
$840$	0.230584	0.00795590
$841$	−22.4348	−0.773614
$842$	−40.3056	−1.38902
$843$	27.5428	0.948624
$844$	13.3045	0.457959
$845$	−0.762339	−0.0262253
$846$	9.09707	0.312764
$847$	3.62357	0.124507
$848$	−10.7813	−0.370231
$849$	−47.4157	−1.62730
$850$	31.3619	1.07571
$851$	−16.2523	−0.557123
$852$	−6.47323	−0.221769
$853$	−27.4465	−0.939749	−0.469874	−	0.882733i	$-0.655701\pi$
$853$	−27.4465	−0.939749	−0.469874	+	0.882733i	$0.655701\pi$
$854$	−11.8280	−0.404744
$855$	1.89954	0.0649628
$856$	17.2253	0.588748
$857$	11.0342	0.376922	0.188461	−	0.982081i	$-0.439650\pi$
$857$	11.0342	0.376922	0.188461	+	0.982081i	$0.439650\pi$
$858$	11.4944	0.392412
$859$	−41.5261	−1.41685	−0.708426	−	0.705785i	$-0.750595\pi$
$859$	−41.5261	−1.41685	−0.708426	+	0.705785i	$0.750595\pi$
$860$	0.468598	0.0159791
$861$	−16.7343	−0.570303
$862$	16.8867	0.575164
$863$	−4.04033	−0.137535	−0.0687673	−	0.997633i	$-0.521907\pi$
$863$	−4.04033	−0.137535	−0.0687673	+	0.997633i	$0.521907\pi$
$864$	−0.664031	−0.0225908
$865$	−0.0548550	−0.00186513
$866$	−1.01520	−0.0344978
$867$	−56.1373	−1.90652
$868$	2.89096	0.0981256
$869$	−21.5105	−0.729695
$870$	−0.470026	−0.0159354
$871$	20.2239	0.685261
$872$	8.80570	0.298199
$873$	3.55725	0.120395
$874$	−26.6765	−0.902345
$875$	0.920714	0.0311258
$876$	−36.2409	−1.22447
$877$	−34.6942	−1.17154	−0.585770	−	0.810477i	$-0.699208\pi$
$877$	−34.6942	−1.17154	−0.585770	+	0.810477i	$0.699208\pi$
$878$	29.8989	1.00904
$879$	−37.2711	−1.25712
$880$	−0.208801	−0.00703867
$881$	38.5988	1.30043	0.650213	−	0.759752i	$-0.274679\pi$
$881$	38.5988	1.30043	0.650213	+	0.759752i	$0.274679\pi$
$882$	−17.6978	−0.595916
$883$	−33.9606	−1.14287	−0.571433	−	0.820649i	$-0.693612\pi$
$883$	−33.9606	−1.14287	−0.571433	+	0.820649i	$0.693612\pi$
$884$	−10.1207	−0.340396
$885$	1.44792	0.0486712
$886$	15.6699	0.526441
$887$	−20.7795	−0.697707	−0.348853	−	0.937177i	$-0.613429\pi$
$887$	−20.7795	−0.697707	−0.348853	+	0.937177i	$0.613429\pi$
$888$	−12.1048	−0.406210
$889$	−5.98397	−0.200696
$890$	0.216370	0.00725274
$891$	23.1737	0.776349
$892$	5.60413	0.187640
$893$	22.1146	0.740037
$894$	29.0731	0.972350
$895$	−0.529666	−0.0177048
$896$	−1.25699	−0.0419930
$897$	13.5585	0.452704
$898$	−7.05157	−0.235314
$899$	−5.89298	−0.196542
$900$	−16.3089	−0.543630
$901$	67.6971	2.25532
$902$	15.1534	0.504553
$903$	20.1175	0.669470
$904$	4.22222	0.140429
$905$	0.221040	0.00734762
$906$	−34.4065	−1.14308
$907$	−14.3691	−0.477118	−0.238559	−	0.971128i	$-0.576675\pi$
$907$	−14.3691	−0.477118	−0.238559	+	0.971128i	$0.576675\pi$
$908$	26.0194	0.863483
$909$	−37.5004	−1.24381
$910$	−0.148480	−0.00492208
$911$	5.21961	0.172934	0.0864668	−	0.996255i	$-0.472442\pi$
$911$	5.21961	0.172934	0.0864668	+	0.996255i	$0.472442\pi$
$912$	−19.8687	−0.657919
$913$	10.2594	0.339538
$914$	−31.4584	−1.04055
$915$	−1.72614	−0.0570645
$916$	19.0513	0.629472
$917$	−15.2219	−0.502670
$918$	4.16954	0.137615
$919$	29.2774	0.965773	0.482887	−	0.875683i	$-0.339588\pi$
$919$	29.2774	0.965773	0.482887	+	0.875683i	$0.339588\pi$
$920$	−0.246296	−0.00812012
$921$	−54.9822	−1.81172
$922$	−10.7377	−0.353626
$923$	4.16833	0.137202
$924$	−8.96409	−0.294897
$925$	−24.1541	−0.794181
$926$	13.4944	0.443454
$927$	−2.01702	−0.0662475
$928$	2.56226	0.0841104
$929$	20.6112	0.676230	0.338115	−	0.941105i	$-0.390211\pi$
$929$	20.6112	0.676230	0.338115	+	0.941105i	$0.390211\pi$
$930$	0.421900	0.0138346
$931$	−43.0226	−1.41001
$932$	5.11960	0.167698
$933$	1.97709	0.0647269
$934$	−10.4824	−0.342995
$935$	1.31109	0.0428771
$936$	5.26299	0.172026
$937$	−29.3351	−0.958337	−0.479169	−	0.877723i	$-0.659062\pi$
$937$	−29.3351	−0.958337	−0.479169	+	0.877723i	$0.659062\pi$
$938$	−15.7719	−0.514972
$939$	19.3013	0.629874
$940$	0.204177	0.00665953
$941$	−30.5178	−0.994853	−0.497426	−	0.867506i	$-0.665722\pi$
$941$	−30.5178	−0.994853	−0.497426	+	0.867506i	$0.665722\pi$
$942$	−42.3521	−1.37991
$943$	17.8745	0.582075
$944$	−7.89307	−0.256898
$945$	0.0611712	0.00198990
$946$	−18.2171	−0.592287
$947$	−44.7324	−1.45361	−0.726805	−	0.686844i	$-0.758995\pi$
$947$	−44.7324	−1.45361	−0.726805	+	0.686844i	$0.758995\pi$
$948$	−18.8981	−0.613780
$949$	23.3367	0.757542
$950$	−39.6463	−1.28629
$951$	−21.1719	−0.686547
$952$	7.89279	0.255807
$953$	30.2784	0.980813	0.490406	−	0.871494i	$-0.336848\pi$
$953$	30.2784	0.980813	0.490406	+	0.871494i	$0.336848\pi$
$954$	−35.2040	−1.13977
$955$	0.779290	0.0252172
$956$	−22.9400	−0.741932
$957$	18.2725	0.590667
$958$	33.1021	1.06948
$959$	−14.1771	−0.457801
$960$	−0.183442	−0.00592055
$961$	−25.7104	−0.829368
$962$	7.79468	0.251310
$963$	56.2456	1.81249
$964$	16.2412	0.523093
$965$	−0.105256	−0.00338831
$966$	−10.5738	−0.340206
$967$	−50.2270	−1.61519	−0.807596	−	0.589737i	$-0.799232\pi$
$967$	−50.2270	−1.61519	−0.807596	+	0.589737i	$0.799232\pi$
$968$	−2.88275	−0.0926549
$969$	124.758	4.00781
$970$	0.0798398	0.00256350
$971$	29.1281	0.934766	0.467383	−	0.884055i	$-0.345197\pi$
$971$	29.1281	0.934766	0.467383	+	0.884055i	$0.345197\pi$
$972$	22.3513	0.716920
$973$	20.6532	0.662110
$974$	17.3503	0.555940
$975$	20.1505	0.645331
$976$	9.40976	0.301199
$977$	−47.1583	−1.50873	−0.754363	−	0.656457i	$-0.772054\pi$
$977$	−47.1583	−1.50873	−0.754363	+	0.656457i	$0.772054\pi$
$978$	−11.5175	−0.368288
$979$	−8.41152	−0.268833
$980$	−0.397215	−0.0126886
$981$	28.7532	0.918018
$982$	−32.5188	−1.03772
$983$	−18.0619	−0.576086	−0.288043	−	0.957618i	$-0.593005\pi$
$983$	−18.0619	−0.576086	−0.288043	+	0.957618i	$0.593005\pi$
$984$	13.3130	0.424403
$985$	0.199783	0.00636561
$986$	−16.0888	−0.512372
$987$	8.76559	0.279012
$988$	12.7941	0.407035
$989$	−21.4883	−0.683289
$990$	−0.681794	−0.0216688
$991$	−1.35471	−0.0430337	−0.0215169	−	0.999768i	$-0.506850\pi$
$991$	−1.35471	−0.0430337	−0.0215169	+	0.999768i	$0.506850\pi$
$992$	−2.29991	−0.0730223
$993$	31.6912	1.00569
$994$	−3.25073	−0.103107
$995$	0.563285	0.0178573
$996$	9.01343	0.285601
$997$	56.2921	1.78279	0.891395	−	0.453227i	$-0.149727\pi$
$997$	56.2921	1.78279	0.891395	+	0.453227i	$0.149727\pi$
$998$	−36.3677	−1.15120
$999$	−3.21126	−0.101600

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.6	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.6	✓	50	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.50306 q^{3} +1.00000 q^{4} +0.0732871 q^{5} -2.50306 q^{6} -1.25699 q^{7} +1.00000 q^{8} +3.26529 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.50306 q^{3} +1.00000 q^{4} +0.0732871 q^{5} -2.50306 q^{6} -1.25699 q^{7} +1.00000 q^{8} +3.26529 q^{9} +0.0732871 q^{10} -2.84908 q^{11} -2.50306 q^{12} +1.61180 q^{13} -1.25699 q^{14} -0.183442 q^{15} +1.00000 q^{16} -6.27913 q^{17} +3.26529 q^{18} +7.93778 q^{19} +0.0732871 q^{20} +3.14631 q^{21} -2.84908 q^{22} -3.36070 q^{23} -2.50306 q^{24} -4.99463 q^{25} +1.61180 q^{26} -0.664031 q^{27} -1.25699 q^{28} +2.56226 q^{29} -0.183442 q^{30} -2.29991 q^{31} +1.00000 q^{32} +7.13141 q^{33} -6.27913 q^{34} -0.0921209 q^{35} +3.26529 q^{36} +4.83601 q^{37} +7.93778 q^{38} -4.03443 q^{39} +0.0732871 q^{40} -5.31870 q^{41} +3.14631 q^{42} +6.39401 q^{43} -2.84908 q^{44} +0.239303 q^{45} -3.36070 q^{46} +2.78599 q^{47} -2.50306 q^{48} -5.41998 q^{49} -4.99463 q^{50} +15.7170 q^{51} +1.61180 q^{52} -10.7813 q^{53} -0.664031 q^{54} -0.208801 q^{55} -1.25699 q^{56} -19.8687 q^{57} +2.56226 q^{58} -7.89307 q^{59} -0.183442 q^{60} +9.40976 q^{61} -2.29991 q^{62} -4.10443 q^{63} +1.00000 q^{64} +0.118124 q^{65} +7.13141 q^{66} +12.5474 q^{67} -6.27913 q^{68} +8.41201 q^{69} -0.0921209 q^{70} +2.58613 q^{71} +3.26529 q^{72} +14.4787 q^{73} +4.83601 q^{74} +12.5018 q^{75} +7.93778 q^{76} +3.58126 q^{77} -4.03443 q^{78} +7.54999 q^{79} +0.0732871 q^{80} -8.13376 q^{81} -5.31870 q^{82} -3.60097 q^{83} +3.14631 q^{84} -0.460179 q^{85} +6.39401 q^{86} -6.41349 q^{87} -2.84908 q^{88} +2.95236 q^{89} +0.239303 q^{90} -2.02601 q^{91} -3.36070 q^{92} +5.75681 q^{93} +2.78599 q^{94} +0.581737 q^{95} -2.50306 q^{96} +1.08941 q^{97} -5.41998 q^{98} -9.30307 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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