LMFDB - Embedded newform 8018.2.a.h.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.20998 q^{3} +1.00000 q^{4} +0.0448427 q^{5} +1.20998 q^{6} -2.73874 q^{7} -1.00000 q^{8} -1.53595 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.20998 q^{3} +1.00000 q^{4} +0.0448427 q^{5} +1.20998 q^{6} -2.73874 q^{7} -1.00000 q^{8} -1.53595 q^{9} -0.0448427 q^{10} +2.04170 q^{11} -1.20998 q^{12} +1.85754 q^{13} +2.73874 q^{14} -0.0542587 q^{15} +1.00000 q^{16} +1.92176 q^{17} +1.53595 q^{18} -1.00000 q^{19} +0.0448427 q^{20} +3.31382 q^{21} -2.04170 q^{22} -2.83061 q^{23} +1.20998 q^{24} -4.99799 q^{25} -1.85754 q^{26} +5.48840 q^{27} -2.73874 q^{28} +6.47351 q^{29} +0.0542587 q^{30} -7.78208 q^{31} -1.00000 q^{32} -2.47041 q^{33} -1.92176 q^{34} -0.122813 q^{35} -1.53595 q^{36} -2.03660 q^{37} +1.00000 q^{38} -2.24758 q^{39} -0.0448427 q^{40} +4.98252 q^{41} -3.31382 q^{42} -0.0680112 q^{43} +2.04170 q^{44} -0.0688762 q^{45} +2.83061 q^{46} +9.41398 q^{47} -1.20998 q^{48} +0.500717 q^{49} +4.99799 q^{50} -2.32529 q^{51} +1.85754 q^{52} -9.40770 q^{53} -5.48840 q^{54} +0.0915551 q^{55} +2.73874 q^{56} +1.20998 q^{57} -6.47351 q^{58} +3.35189 q^{59} -0.0542587 q^{60} -7.94329 q^{61} +7.78208 q^{62} +4.20658 q^{63} +1.00000 q^{64} +0.0832970 q^{65} +2.47041 q^{66} +1.66761 q^{67} +1.92176 q^{68} +3.42498 q^{69} +0.122813 q^{70} -0.505292 q^{71} +1.53595 q^{72} +0.785797 q^{73} +2.03660 q^{74} +6.04746 q^{75} -1.00000 q^{76} -5.59168 q^{77} +2.24758 q^{78} -13.5898 q^{79} +0.0448427 q^{80} -2.03299 q^{81} -4.98252 q^{82} +14.9815 q^{83} +3.31382 q^{84} +0.0861768 q^{85} +0.0680112 q^{86} -7.83281 q^{87} -2.04170 q^{88} -1.46405 q^{89} +0.0688762 q^{90} -5.08732 q^{91} -2.83061 q^{92} +9.41615 q^{93} -9.41398 q^{94} -0.0448427 q^{95} +1.20998 q^{96} -5.36599 q^{97} -0.500717 q^{98} -3.13595 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) $ 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * 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
$3$	−1.20998	−0.698581	−0.349291	−	0.937014i	$-0.613577\pi$
$3$	−1.20998	−0.698581	−0.349291	+	0.937014i	$0.613577\pi$
$4$	1.00000	0.500000
$5$	0.0448427	0.0200543	0.0100271	−	0.999950i	$-0.496808\pi$
$5$	0.0448427	0.0200543	0.0100271	+	0.999950i	$0.496808\pi$
$6$	1.20998	0.493972
$7$	−2.73874	−1.03515	−0.517574	−	0.855639i	$-0.673165\pi$
$7$	−2.73874	−1.03515	−0.517574	+	0.855639i	$0.673165\pi$
$8$	−1.00000	−0.353553
$9$	−1.53595	−0.511984
$10$	−0.0448427	−0.0141805
$11$	2.04170	0.615594	0.307797	−	0.951452i	$-0.400408\pi$
$11$	2.04170	0.615594	0.307797	+	0.951452i	$0.400408\pi$
$12$	−1.20998	−0.349291
$13$	1.85754	0.515188	0.257594	−	0.966253i	$-0.417070\pi$
$13$	1.85754	0.515188	0.257594	+	0.966253i	$0.417070\pi$
$14$	2.73874	0.731960
$15$	−0.0542587	−0.0140095
$16$	1.00000	0.250000
$17$	1.92176	0.466095	0.233047	−	0.972465i	$-0.425130\pi$
$17$	1.92176	0.466095	0.233047	+	0.972465i	$0.425130\pi$
$18$	1.53595	0.362027
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.0448427	0.0100271
$21$	3.31382	0.723135
$22$	−2.04170	−0.435291
$23$	−2.83061	−0.590223	−0.295111	−	0.955463i	$-0.595357\pi$
$23$	−2.83061	−0.590223	−0.295111	+	0.955463i	$0.595357\pi$
$24$	1.20998	0.246986
$25$	−4.99799	−0.999598
$26$	−1.85754	−0.364293
$27$	5.48840	1.05624
$28$	−2.73874	−0.517574
$29$	6.47351	1.20210	0.601050	−	0.799211i	$-0.294749\pi$
$29$	6.47351	1.20210	0.601050	+	0.799211i	$0.294749\pi$
$30$	0.0542587	0.00990624
$31$	−7.78208	−1.39770	−0.698851	−	0.715267i	$-0.746305\pi$
$31$	−7.78208	−1.39770	−0.698851	+	0.715267i	$0.746305\pi$
$32$	−1.00000	−0.176777
$33$	−2.47041	−0.430043
$34$	−1.92176	−0.329579
$35$	−0.122813	−0.0207591
$36$	−1.53595	−0.255992
$37$	−2.03660	−0.334814	−0.167407	−	0.985888i	$-0.553539\pi$
$37$	−2.03660	−0.334814	−0.167407	+	0.985888i	$0.553539\pi$
$38$	1.00000	0.162221
$39$	−2.24758	−0.359901
$40$	−0.0448427	−0.00709025
$41$	4.98252	0.778138	0.389069	−	0.921209i	$-0.372797\pi$
$41$	4.98252	0.778138	0.389069	+	0.921209i	$0.372797\pi$
$42$	−3.31382	−0.511334
$43$	−0.0680112	−0.0103716	−0.00518580	−	0.999987i	$-0.501651\pi$
$43$	−0.0680112	−0.0103716	−0.00518580	+	0.999987i	$0.501651\pi$
$44$	2.04170	0.307797
$45$	−0.0688762	−0.0102675
$46$	2.83061	0.417351
$47$	9.41398	1.37317	0.686585	−	0.727050i	$-0.259109\pi$
$47$	9.41398	1.37317	0.686585	+	0.727050i	$0.259109\pi$
$48$	−1.20998	−0.174645
$49$	0.500717	0.0715310
$50$	4.99799	0.706822
$51$	−2.32529	−0.325605
$52$	1.85754	0.257594
$53$	−9.40770	−1.29225	−0.646123	−	0.763233i	$-0.723611\pi$
$53$	−9.40770	−1.29225	−0.646123	+	0.763233i	$0.723611\pi$
$54$	−5.48840	−0.746877
$55$	0.0915551	0.0123453
$56$	2.73874	0.365980
$57$	1.20998	0.160266
$58$	−6.47351	−0.850013
$59$	3.35189	0.436379	0.218190	−	0.975906i	$-0.429985\pi$
$59$	3.35189	0.436379	0.218190	+	0.975906i	$0.429985\pi$
$60$	−0.0542587	−0.00700477
$61$	−7.94329	−1.01703	−0.508517	−	0.861052i	$-0.669806\pi$
$61$	−7.94329	−1.01703	−0.508517	+	0.861052i	$0.669806\pi$
$62$	7.78208	0.988325
$63$	4.20658	0.529979
$64$	1.00000	0.125000
$65$	0.0832970	0.0103317
$66$	2.47041	0.304086
$67$	1.66761	0.203731	0.101866	−	0.994798i	$-0.467519\pi$
$67$	1.66761	0.203731	0.101866	+	0.994798i	$0.467519\pi$
$68$	1.92176	0.233047
$69$	3.42498	0.412319
$70$	0.122813	0.0146789
$71$	−0.505292	−0.0599672	−0.0299836	−	0.999550i	$-0.509546\pi$
$71$	−0.505292	−0.0599672	−0.0299836	+	0.999550i	$0.509546\pi$
$72$	1.53595	0.181014
$73$	0.785797	0.0919706	0.0459853	−	0.998942i	$-0.485357\pi$
$73$	0.785797	0.0919706	0.0459853	+	0.998942i	$0.485357\pi$
$74$	2.03660	0.236750
$75$	6.04746	0.698300
$76$	−1.00000	−0.114708
$77$	−5.59168	−0.637231
$78$	2.24758	0.254488
$79$	−13.5898	−1.52897	−0.764484	−	0.644643i	$-0.777006\pi$
$79$	−13.5898	−1.52897	−0.764484	+	0.644643i	$0.777006\pi$
$80$	0.0448427	0.00501357
$81$	−2.03299	−0.225888
$82$	−4.98252	−0.550227
$83$	14.9815	1.64443	0.822216	−	0.569175i	$-0.192737\pi$
$83$	14.9815	1.64443	0.822216	+	0.569175i	$0.192737\pi$
$84$	3.31382	0.361567
$85$	0.0861768	0.00934719
$86$	0.0680112	0.00733383
$87$	−7.83281	−0.839765
$88$	−2.04170	−0.217645
$89$	−1.46405	−0.155189	−0.0775947	−	0.996985i	$-0.524724\pi$
$89$	−1.46405	−0.155189	−0.0775947	+	0.996985i	$0.524724\pi$
$90$	0.0688762	0.00726019
$91$	−5.08732	−0.533296
$92$	−2.83061	−0.295111
$93$	9.41615	0.976409
$94$	−9.41398	−0.970978
$95$	−0.0448427	−0.00460076
$96$	1.20998	0.123493
$97$	−5.36599	−0.544834	−0.272417	−	0.962179i	$-0.587823\pi$
$97$	−5.36599	−0.544834	−0.272417	+	0.962179i	$0.587823\pi$
$98$	−0.500717	−0.0505800
$99$	−3.13595	−0.315174
$100$	−4.99799	−0.499799
$101$	−0.764511	−0.0760717	−0.0380359	−	0.999276i	$-0.512110\pi$
$101$	−0.764511	−0.0760717	−0.0380359	+	0.999276i	$0.512110\pi$
$102$	2.32529	0.230238
$103$	3.72634	0.367167	0.183583	−	0.983004i	$-0.441230\pi$
$103$	3.72634	0.367167	0.183583	+	0.983004i	$0.441230\pi$
$104$	−1.85754	−0.182147
$105$	0.148601	0.0145019
$106$	9.40770	0.913756
$107$	−7.50454	−0.725492	−0.362746	−	0.931888i	$-0.618161\pi$
$107$	−7.50454	−0.725492	−0.362746	+	0.931888i	$0.618161\pi$
$108$	5.48840	0.528122
$109$	−6.89890	−0.660794	−0.330397	−	0.943842i	$-0.607183\pi$
$109$	−6.89890	−0.660794	−0.330397	+	0.943842i	$0.607183\pi$
$110$	−0.0915551	−0.00872944
$111$	2.46424	0.233895
$112$	−2.73874	−0.258787
$113$	−12.1419	−1.14221	−0.571106	−	0.820877i	$-0.693485\pi$
$113$	−12.1419	−1.14221	−0.571106	+	0.820877i	$0.693485\pi$
$114$	−1.20998	−0.113325
$115$	−0.126932	−0.0118365
$116$	6.47351	0.601050
$117$	−2.85309	−0.263768
$118$	−3.35189	−0.308567
$119$	−5.26320	−0.482477
$120$	0.0542587	0.00495312
$121$	−6.83148	−0.621044
$122$	7.94329	0.719151
$123$	−6.02874	−0.543593
$124$	−7.78208	−0.698851
$125$	−0.448337	−0.0401005
$126$	−4.20658	−0.374752
$127$	11.5438	1.02435	0.512175	−	0.858881i	$-0.328840\pi$
$127$	11.5438	1.02435	0.512175	+	0.858881i	$0.328840\pi$
$128$	−1.00000	−0.0883883
$129$	0.0822920	0.00724541
$130$	−0.0832970	−0.00730563
$131$	−2.66428	−0.232779	−0.116389	−	0.993204i	$-0.537132\pi$
$131$	−2.66428	−0.232779	−0.116389	+	0.993204i	$0.537132\pi$
$132$	−2.47041	−0.215021
$133$	2.73874	0.237479
$134$	−1.66761	−0.144060
$135$	0.246115	0.0211822
$136$	−1.92176	−0.164789
$137$	−11.1215	−0.950178	−0.475089	−	0.879938i	$-0.657584\pi$
$137$	−11.1215	−0.950178	−0.475089	+	0.879938i	$0.657584\pi$
$138$	−3.42498	−0.291553
$139$	12.2154	1.03610	0.518049	−	0.855351i	$-0.326659\pi$
$139$	12.2154	1.03610	0.518049	+	0.855351i	$0.326659\pi$
$140$	−0.122813	−0.0103796
$141$	−11.3907	−0.959271
$142$	0.505292	0.0424032
$143$	3.79252	0.317147
$144$	−1.53595	−0.127996
$145$	0.290290	0.0241072
$146$	−0.785797	−0.0650330
$147$	−0.605857	−0.0499702
$148$	−2.03660	−0.167407
$149$	9.17304	0.751484	0.375742	−	0.926724i	$-0.377388\pi$
$149$	9.17304	0.751484	0.375742	+	0.926724i	$0.377388\pi$
$150$	−6.04746	−0.493773
$151$	9.99988	0.813779	0.406889	−	0.913477i	$-0.366613\pi$
$151$	9.99988	0.813779	0.406889	+	0.913477i	$0.366613\pi$
$152$	1.00000	0.0811107
$153$	−2.95173	−0.238633
$154$	5.59168	0.450590
$155$	−0.348969	−0.0280299
$156$	−2.24758	−0.179950
$157$	−5.68658	−0.453839	−0.226919	−	0.973914i	$-0.572865\pi$
$157$	−5.68658	−0.453839	−0.226919	+	0.973914i	$0.572865\pi$
$158$	13.5898	1.08114
$159$	11.3831	0.902739
$160$	−0.0448427	−0.00354513
$161$	7.75231	0.610968
$162$	2.03299	0.159727
$163$	5.80869	0.454972	0.227486	−	0.973781i	$-0.426949\pi$
$163$	5.80869	0.454972	0.227486	+	0.973781i	$0.426949\pi$
$164$	4.98252	0.389069
$165$	−0.110780	−0.00862419
$166$	−14.9815	−1.16279
$167$	−2.21510	−0.171410	−0.0857048	−	0.996321i	$-0.527314\pi$
$167$	−2.21510	−0.171410	−0.0857048	+	0.996321i	$0.527314\pi$
$168$	−3.31382	−0.255667
$169$	−9.54956	−0.734581
$170$	−0.0861768	−0.00660946
$171$	1.53595	0.117457
$172$	−0.0680112	−0.00518580
$173$	−10.3281	−0.785228	−0.392614	−	0.919703i	$-0.628429\pi$
$173$	−10.3281	−0.785228	−0.392614	+	0.919703i	$0.628429\pi$
$174$	7.83281	0.593803
$175$	13.6882	1.03473
$176$	2.04170	0.153899
$177$	−4.05572	−0.304847
$178$	1.46405	0.109735
$179$	−8.87410	−0.663282	−0.331641	−	0.943406i	$-0.607602\pi$
$179$	−8.87410	−0.663282	−0.331641	+	0.943406i	$0.607602\pi$
$180$	−0.0688762	−0.00513373
$181$	5.73170	0.426034	0.213017	−	0.977048i	$-0.431671\pi$
$181$	5.73170	0.426034	0.213017	+	0.977048i	$0.431671\pi$
$182$	5.08732	0.377097
$183$	9.61121	0.710481
$184$	2.83061	0.208675
$185$	−0.0913265	−0.00671446
$186$	−9.41615	−0.690425
$187$	3.92365	0.286925
$188$	9.41398	0.686585
$189$	−15.0313	−1.09337
$190$	0.0448427	0.00325323
$191$	−7.40545	−0.535839	−0.267920	−	0.963441i	$-0.586336\pi$
$191$	−7.40545	−0.535839	−0.267920	+	0.963441i	$0.586336\pi$
$192$	−1.20998	−0.0873227
$193$	4.31071	0.310292	0.155146	−	0.987892i	$-0.450415\pi$
$193$	4.31071	0.310292	0.155146	+	0.987892i	$0.450415\pi$
$194$	5.36599	0.385256
$195$	−0.100788	−0.00721755
$196$	0.500717	0.0357655
$197$	6.81519	0.485562	0.242781	−	0.970081i	$-0.421940\pi$
$197$	6.81519	0.485562	0.242781	+	0.970081i	$0.421940\pi$
$198$	3.13595	0.222862
$199$	4.23326	0.300088	0.150044	−	0.988679i	$-0.452058\pi$
$199$	4.23326	0.300088	0.150044	+	0.988679i	$0.452058\pi$
$200$	4.99799	0.353411
$201$	−2.01778	−0.142323
$202$	0.764511	0.0537908
$203$	−17.7293	−1.24435
$204$	−2.32529	−0.162803
$205$	0.223429	0.0156050
$206$	−3.72634	−0.259626
$207$	4.34768	0.302185
$208$	1.85754	0.128797
$209$	−2.04170	−0.141227
$210$	−0.148601	−0.0102544
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−9.40770	−0.646123
$213$	0.611393	0.0418919
$214$	7.50454	0.513000
$215$	−0.00304980	−0.000207995 0
$216$	−5.48840	−0.373439
$217$	21.3131	1.44683
$218$	6.89890	0.467252
$219$	−0.950797	−0.0642489
$220$	0.0915551	0.00617264
$221$	3.56974	0.240127
$222$	−2.46424	−0.165389
$223$	−7.55745	−0.506084	−0.253042	−	0.967455i	$-0.581431\pi$
$223$	−7.55745	−0.506084	−0.253042	+	0.967455i	$0.581431\pi$
$224$	2.73874	0.182990
$225$	7.67667	0.511778
$226$	12.1419	0.807665
$227$	26.5914	1.76493	0.882466	−	0.470377i	$-0.155882\pi$
$227$	26.5914	1.76493	0.882466	+	0.470377i	$0.155882\pi$
$228$	1.20998	0.0801328
$229$	26.9239	1.77918	0.889591	−	0.456757i	$-0.150989\pi$
$229$	26.9239	1.77918	0.889591	+	0.456757i	$0.150989\pi$
$230$	0.126932	0.00836966
$231$	6.76581	0.445158
$232$	−6.47351	−0.425007
$233$	−17.6009	−1.15307	−0.576536	−	0.817072i	$-0.695596\pi$
$233$	−17.6009	−1.15307	−0.576536	+	0.817072i	$0.695596\pi$
$234$	2.85309	0.186512
$235$	0.422148	0.0275379
$236$	3.35189	0.218190
$237$	16.4433	1.06811
$238$	5.26320	0.341163
$239$	−13.1897	−0.853169	−0.426584	−	0.904448i	$-0.640283\pi$
$239$	−13.1897	−0.853169	−0.426584	+	0.904448i	$0.640283\pi$
$240$	−0.0542587	−0.00350238
$241$	2.57390	0.165800	0.0828999	−	0.996558i	$-0.473582\pi$
$241$	2.57390	0.165800	0.0828999	+	0.996558i	$0.473582\pi$
$242$	6.83148	0.439144
$243$	−14.0053	−0.898443
$244$	−7.94329	−0.508517
$245$	0.0224535	0.00143450
$246$	6.02874	0.384378
$247$	−1.85754	−0.118192
$248$	7.78208	0.494162
$249$	−18.1273	−1.14877
$250$	0.448337	0.0283553
$251$	3.43499	0.216815	0.108407	−	0.994107i	$-0.465425\pi$
$251$	3.43499	0.216815	0.108407	+	0.994107i	$0.465425\pi$
$252$	4.20658	0.264990
$253$	−5.77924	−0.363338
$254$	−11.5438	−0.724325
$255$	−0.104272	−0.00652977
$256$	1.00000	0.0625000
$257$	−20.6341	−1.28712	−0.643561	−	0.765395i	$-0.722544\pi$
$257$	−20.6341	−1.28712	−0.643561	+	0.765395i	$0.722544\pi$
$258$	−0.0822920	−0.00512328
$259$	5.57772	0.346582
$260$	0.0832970	0.00516586
$261$	−9.94300	−0.615456
$262$	2.66428	0.164599
$263$	18.0576	1.11348	0.556741	−	0.830686i	$-0.312052\pi$
$263$	18.0576	1.11348	0.556741	+	0.830686i	$0.312052\pi$
$264$	2.47041	0.152043
$265$	−0.421866	−0.0259150
$266$	−2.73874	−0.167923
$267$	1.77147	0.108412
$268$	1.66761	0.101866
$269$	30.3245	1.84892	0.924460	−	0.381280i	$-0.124517\pi$
$269$	30.3245	1.84892	0.924460	+	0.381280i	$0.124517\pi$
$270$	−0.246115	−0.0149781
$271$	7.46687	0.453580	0.226790	−	0.973944i	$-0.427177\pi$
$271$	7.46687	0.453580	0.226790	+	0.973944i	$0.427177\pi$
$272$	1.92176	0.116524
$273$	6.15555	0.372551
$274$	11.1215	0.671877
$275$	−10.2044	−0.615347
$276$	3.42498	0.206159
$277$	31.8582	1.91417	0.957087	−	0.289800i	$-0.0935888\pi$
$277$	31.8582	1.91417	0.957087	+	0.289800i	$0.0935888\pi$
$278$	−12.2154	−0.732632
$279$	11.9529	0.715601
$280$	0.122813	0.00733946
$281$	−3.05766	−0.182405	−0.0912024	−	0.995832i	$-0.529071\pi$
$281$	−3.05766	−0.182405	−0.0912024	+	0.995832i	$0.529071\pi$
$282$	11.3907	0.678307
$283$	17.5142	1.04111	0.520556	−	0.853828i	$-0.325725\pi$
$283$	17.5142	1.04111	0.520556	+	0.853828i	$0.325725\pi$
$284$	−0.505292	−0.0299836
$285$	0.0542587	0.00321401
$286$	−3.79252	−0.224257
$287$	−13.6458	−0.805488
$288$	1.53595	0.0905068
$289$	−13.3068	−0.782755
$290$	−0.290290	−0.0170464
$291$	6.49273	0.380611
$292$	0.785797	0.0459853
$293$	25.1596	1.46984	0.734919	−	0.678154i	$-0.237220\pi$
$293$	25.1596	1.46984	0.734919	+	0.678154i	$0.237220\pi$
$294$	0.605857	0.0353343
$295$	0.150308	0.00875127
$296$	2.03660	0.118375
$297$	11.2056	0.650218
$298$	−9.17304	−0.531380
$299$	−5.25796	−0.304076
$300$	6.04746	0.349150
$301$	0.186265	0.0107361
$302$	−9.99988	−0.575429
$303$	0.925042	0.0531423
$304$	−1.00000	−0.0573539
$305$	−0.356198	−0.0203959
$306$	2.95173	0.168739
$307$	7.27043	0.414945	0.207473	−	0.978241i	$-0.433476\pi$
$307$	7.27043	0.414945	0.207473	+	0.978241i	$0.433476\pi$
$308$	−5.59168	−0.318616
$309$	−4.50879	−0.256496
$310$	0.348969	0.0198201
$311$	2.71336	0.153861	0.0769304	−	0.997036i	$-0.475488\pi$
$311$	2.71336	0.153861	0.0769304	+	0.997036i	$0.475488\pi$
$312$	2.24758	0.127244
$313$	−20.8311	−1.17744	−0.588722	−	0.808336i	$-0.700369\pi$
$313$	−20.8311	−1.17744	−0.588722	+	0.808336i	$0.700369\pi$
$314$	5.68658	0.320913
$315$	0.188634	0.0106283
$316$	−13.5898	−0.764484
$317$	16.4333	0.922983	0.461492	−	0.887145i	$-0.347314\pi$
$317$	16.4333	0.922983	0.461492	+	0.887145i	$0.347314\pi$
$318$	−11.3831	−0.638333
$319$	13.2169	0.740006
$320$	0.0448427	0.00250678
$321$	9.08034	0.506815
$322$	−7.75231	−0.432020
$323$	−1.92176	−0.106930
$324$	−2.03299	−0.112944
$325$	−9.28395	−0.514981
$326$	−5.80869	−0.321714
$327$	8.34752	0.461619
$328$	−4.98252	−0.275113
$329$	−25.7825	−1.42143
$330$	0.110780	0.00609822
$331$	−12.7091	−0.698557	−0.349278	−	0.937019i	$-0.613573\pi$
$331$	−12.7091	−0.698557	−0.349278	+	0.937019i	$0.613573\pi$
$332$	14.9815	0.822216
$333$	3.12812	0.171420
$334$	2.21510	0.121205
$335$	0.0747803	0.00408568
$336$	3.31382	0.180784
$337$	−7.40878	−0.403582	−0.201791	−	0.979429i	$-0.564676\pi$
$337$	−7.40878	−0.403582	−0.201791	+	0.979429i	$0.564676\pi$
$338$	9.54956	0.519427
$339$	14.6914	0.797927
$340$	0.0861768	0.00467360
$341$	−15.8886	−0.860418
$342$	−1.53595	−0.0830548
$343$	17.7999	0.961103
$344$	0.0680112	0.00366692
$345$	0.153585	0.00826875
$346$	10.3281	0.555240
$347$	15.7189	0.843834	0.421917	−	0.906635i	$-0.361357\pi$
$347$	15.7189	0.843834	0.421917	+	0.906635i	$0.361357\pi$
$348$	−7.83281	−0.419882
$349$	−2.98915	−0.160005	−0.0800027	−	0.996795i	$-0.525493\pi$
$349$	−2.98915	−0.160005	−0.0800027	+	0.996795i	$0.525493\pi$
$350$	−13.6882	−0.731666
$351$	10.1949	0.544164
$352$	−2.04170	−0.108823
$353$	−0.786860	−0.0418803	−0.0209402	−	0.999781i	$-0.506666\pi$
$353$	−0.786860	−0.0418803	−0.0209402	+	0.999781i	$0.506666\pi$
$354$	4.05572	0.215559
$355$	−0.0226587	−0.00120260
$356$	−1.46405	−0.0775947
$357$	6.36836	0.337050
$358$	8.87410	0.469011
$359$	−15.5405	−0.820195	−0.410097	−	0.912042i	$-0.634505\pi$
$359$	−15.5405	−0.820195	−0.410097	+	0.912042i	$0.634505\pi$
$360$	0.0688762	0.00363010
$361$	1.00000	0.0526316
$362$	−5.73170	−0.301252
$363$	8.26594	0.433850
$364$	−5.08732	−0.266648
$365$	0.0352372	0.00184440
$366$	−9.61121	−0.502386
$367$	−17.0403	−0.889495	−0.444748	−	0.895656i	$-0.646707\pi$
$367$	−17.0403	−0.889495	−0.444748	+	0.895656i	$0.646707\pi$
$368$	−2.83061	−0.147556
$369$	−7.65291	−0.398394
$370$	0.0913265	0.00474784
$371$	25.7653	1.33767
$372$	9.41615	0.488205
$373$	16.6854	0.863940	0.431970	−	0.901888i	$-0.357819\pi$
$373$	16.6854	0.863940	0.431970	+	0.901888i	$0.357819\pi$
$374$	−3.92365	−0.202887
$375$	0.542478	0.0280134
$376$	−9.41398	−0.485489
$377$	12.0248	0.619308
$378$	15.0313	0.773128
$379$	20.9333	1.07527	0.537636	−	0.843177i	$-0.319318\pi$
$379$	20.9333	1.07527	0.537636	+	0.843177i	$0.319318\pi$
$380$	−0.0448427	−0.00230038
$381$	−13.9678	−0.715592
$382$	7.40545	0.378896
$383$	27.8816	1.42468	0.712341	−	0.701834i	$-0.247635\pi$
$383$	27.8816	1.42468	0.712341	+	0.701834i	$0.247635\pi$
$384$	1.20998	0.0617465
$385$	−0.250746	−0.0127792
$386$	−4.31071	−0.219410
$387$	0.104462	0.00531010
$388$	−5.36599	−0.272417
$389$	−16.9170	−0.857726	−0.428863	−	0.903370i	$-0.641086\pi$
$389$	−16.9170	−0.857726	−0.428863	+	0.903370i	$0.641086\pi$
$390$	0.100788	0.00510358
$391$	−5.43975	−0.275100
$392$	−0.500717	−0.0252900
$393$	3.22372	0.162615
$394$	−6.81519	−0.343344
$395$	−0.609402	−0.0306623
$396$	−3.13595	−0.157587
$397$	−4.90896	−0.246374	−0.123187	−	0.992384i	$-0.539311\pi$
$397$	−4.90896	−0.246374	−0.123187	+	0.992384i	$0.539311\pi$
$398$	−4.23326	−0.212194
$399$	−3.31382	−0.165899
$400$	−4.99799	−0.249899
$401$	−3.24262	−0.161929	−0.0809644	−	0.996717i	$-0.525800\pi$
$401$	−3.24262	−0.161929	−0.0809644	+	0.996717i	$0.525800\pi$
$402$	2.01778	0.100638
$403$	−14.4555	−0.720080
$404$	−0.764511	−0.0380359
$405$	−0.0911650	−0.00453002
$406$	17.7293	0.879889
$407$	−4.15811	−0.206110
$408$	2.32529	0.115119
$409$	−10.5525	−0.521786	−0.260893	−	0.965368i	$-0.584017\pi$
$409$	−10.5525	−0.521786	−0.260893	+	0.965368i	$0.584017\pi$
$410$	−0.223429	−0.0110344
$411$	13.4568	0.663776
$412$	3.72634	0.183583
$413$	−9.17998	−0.451717
$414$	−4.34768	−0.213677
$415$	0.671811	0.0329779
$416$	−1.85754	−0.0910733
$417$	−14.7804	−0.723798
$418$	2.04170	0.0998626
$419$	−31.7266	−1.54994	−0.774972	−	0.631996i	$-0.782236\pi$
$419$	−31.7266	−1.54994	−0.774972	+	0.631996i	$0.782236\pi$
$420$	0.148601	0.00725097
$421$	23.7832	1.15912	0.579562	−	0.814928i	$-0.303224\pi$
$421$	23.7832	1.15912	0.579562	+	0.814928i	$0.303224\pi$
$422$	−1.00000	−0.0486792
$423$	−14.4594	−0.703041
$424$	9.40770	0.456878
$425$	−9.60493	−0.465908
$426$	−0.611393	−0.0296221
$427$	21.7546	1.05278
$428$	−7.50454	−0.362746
$429$	−4.58887	−0.221553
$430$	0.00304980	0.000147075 0
$431$	−3.13657	−0.151083	−0.0755417	−	0.997143i	$-0.524069\pi$
$431$	−3.13657	−0.151083	−0.0755417	+	0.997143i	$0.524069\pi$
$432$	5.48840	0.264061
$433$	24.2943	1.16751	0.583754	−	0.811931i	$-0.301583\pi$
$433$	24.2943	1.16751	0.583754	+	0.811931i	$0.301583\pi$
$434$	−21.3131	−1.02306
$435$	−0.351244	−0.0168409
$436$	−6.89890	−0.330397
$437$	2.83061	0.135406
$438$	0.950797	0.0454309
$439$	−6.37754	−0.304383	−0.152192	−	0.988351i	$-0.548633\pi$
$439$	−6.37754	−0.304383	−0.152192	+	0.988351i	$0.548633\pi$
$440$	−0.0915551	−0.00436472
$441$	−0.769077	−0.0366227
$442$	−3.56974	−0.169795
$443$	15.8222	0.751735	0.375867	−	0.926673i	$-0.377345\pi$
$443$	15.8222	0.751735	0.375867	+	0.926673i	$0.377345\pi$
$444$	2.46424	0.116948
$445$	−0.0656521	−0.00311221
$446$	7.55745	0.357856
$447$	−11.0992	−0.524973
$448$	−2.73874	−0.129393
$449$	0.375322	0.0177125	0.00885626	−	0.999961i	$-0.497181\pi$
$449$	0.375322	0.0177125	0.00885626	+	0.999961i	$0.497181\pi$
$450$	−7.67667	−0.361882
$451$	10.1728	0.479017
$452$	−12.1419	−0.571106
$453$	−12.0996	−0.568491
$454$	−26.5914	−1.24799
$455$	−0.228129	−0.0106949
$456$	−1.20998	−0.0566624
$457$	9.07588	0.424552	0.212276	−	0.977210i	$-0.431912\pi$
$457$	9.07588	0.424552	0.212276	+	0.977210i	$0.431912\pi$
$458$	−26.9239	−1.25807
$459$	10.5474	0.492310
$460$	−0.126932	−0.00591824
$461$	−36.3391	−1.69248	−0.846240	−	0.532801i	$-0.821139\pi$
$461$	−36.3391	−1.69248	−0.846240	+	0.532801i	$0.821139\pi$
$462$	−6.76581	−0.314774
$463$	−28.6466	−1.33132	−0.665660	−	0.746255i	$-0.731850\pi$
$463$	−28.6466	−1.33132	−0.665660	+	0.746255i	$0.731850\pi$
$464$	6.47351	0.300525
$465$	0.422245	0.0195812
$466$	17.6009	0.815345
$467$	−5.09899	−0.235953	−0.117977	−	0.993016i	$-0.537641\pi$
$467$	−5.09899	−0.235953	−0.117977	+	0.993016i	$0.537641\pi$
$468$	−2.85309	−0.131884
$469$	−4.56717	−0.210892
$470$	−0.422148	−0.0194722
$471$	6.88064	0.317043
$472$	−3.35189	−0.154283
$473$	−0.138858	−0.00638470
$474$	−16.4433	−0.755267
$475$	4.99799	0.229323
$476$	−5.26320	−0.241239
$477$	14.4498	0.661610
$478$	13.1897	0.603281
$479$	8.74345	0.399498	0.199749	−	0.979847i	$-0.435987\pi$
$479$	8.74345	0.399498	0.199749	+	0.979847i	$0.435987\pi$
$480$	0.0542587	0.00247656
$481$	−3.78305	−0.172492
$482$	−2.57390	−0.117238
$483$	−9.38013	−0.426811
$484$	−6.83148	−0.310522
$485$	−0.240626	−0.0109262
$486$	14.0053	0.635295
$487$	−1.45780	−0.0660594	−0.0330297	−	0.999454i	$-0.510516\pi$
$487$	−1.45780	−0.0660594	−0.0330297	+	0.999454i	$0.510516\pi$
$488$	7.94329	0.359576
$489$	−7.02840	−0.317835
$490$	−0.0224535	−0.00101435
$491$	18.2117	0.821884	0.410942	−	0.911662i	$-0.365200\pi$
$491$	18.2117	0.821884	0.410942	+	0.911662i	$0.365200\pi$
$492$	−6.02874	−0.271796
$493$	12.4405	0.560293
$494$	1.85754	0.0835745
$495$	−0.140624	−0.00632059
$496$	−7.78208	−0.349426
$497$	1.38387	0.0620749
$498$	18.1273	0.812303
$499$	6.37347	0.285316	0.142658	−	0.989772i	$-0.454435\pi$
$499$	6.37347	0.285316	0.142658	+	0.989772i	$0.454435\pi$
$500$	−0.448337	−0.0200502
$501$	2.68022	0.119744
$502$	−3.43499	−0.153311
$503$	39.2616	1.75059	0.875293	−	0.483593i	$-0.160668\pi$
$503$	39.2616	1.75059	0.875293	+	0.483593i	$0.160668\pi$
$504$	−4.20658	−0.187376
$505$	−0.0342828	−0.00152556
$506$	5.77924	0.256919
$507$	11.5548	0.513165
$508$	11.5438	0.512175
$509$	34.9816	1.55053	0.775266	−	0.631634i	$-0.217616\pi$
$509$	34.9816	1.55053	0.775266	+	0.631634i	$0.217616\pi$
$510$	0.104272	0.00461725
$511$	−2.15210	−0.0952031
$512$	−1.00000	−0.0441942
$513$	−5.48840	−0.242319
$514$	20.6341	0.910132
$515$	0.167099	0.00736326
$516$	0.0822920	0.00362270
$517$	19.2205	0.845316
$518$	−5.57772	−0.245071
$519$	12.4967	0.548546
$520$	−0.0832970	−0.00365281
$521$	24.5132	1.07394	0.536971	−	0.843601i	$-0.319568\pi$
$521$	24.5132	1.07394	0.536971	+	0.843601i	$0.319568\pi$
$522$	9.94300	0.435193
$523$	−18.4689	−0.807588	−0.403794	−	0.914850i	$-0.632309\pi$
$523$	−18.4689	−0.807588	−0.403794	+	0.914850i	$0.632309\pi$
$524$	−2.66428	−0.116389
$525$	−16.5624	−0.722844
$526$	−18.0576	−0.787351
$527$	−14.9553	−0.651462
$528$	−2.47041	−0.107511
$529$	−14.9876	−0.651637
$530$	0.421866	0.0183247
$531$	−5.14835	−0.223419
$532$	2.73874	0.118740
$533$	9.25521	0.400888
$534$	−1.77147	−0.0766592
$535$	−0.336524	−0.0145492
$536$	−1.66761	−0.0720299
$537$	10.7375	0.463356
$538$	−30.3245	−1.30738
$539$	1.02231	0.0440341
$540$	0.246115	0.0105911
$541$	28.7139	1.23451	0.617253	−	0.786765i	$-0.288246\pi$
$541$	28.7139	1.23451	0.617253	+	0.786765i	$0.288246\pi$
$542$	−7.46687	−0.320729
$543$	−6.93524	−0.297619
$544$	−1.92176	−0.0823947
$545$	−0.309365	−0.0132517
$546$	−6.15555	−0.263433
$547$	31.2204	1.33489	0.667444	−	0.744660i	$-0.267389\pi$
$547$	31.2204	1.33489	0.667444	+	0.744660i	$0.267389\pi$
$548$	−11.1215	−0.475089
$549$	12.2005	0.520705
$550$	10.2044	0.435116
$551$	−6.47351	−0.275781
$552$	−3.42498	−0.145777
$553$	37.2189	1.58271
$554$	−31.8582	−1.35353
$555$	0.110503	0.00469059
$556$	12.2154	0.518049
$557$	17.2103	0.729224	0.364612	−	0.931160i	$-0.381202\pi$
$557$	17.2103	0.729224	0.364612	+	0.931160i	$0.381202\pi$
$558$	−11.9529	−0.506007
$559$	−0.126333	−0.00534333
$560$	−0.122813	−0.00518978
$561$	−4.74753	−0.200441
$562$	3.05766	0.128980
$563$	−7.12262	−0.300183	−0.150091	−	0.988672i	$-0.547957\pi$
$563$	−7.12262	−0.300183	−0.150091	+	0.988672i	$0.547957\pi$
$564$	−11.3907	−0.479635
$565$	−0.544474	−0.0229062
$566$	−17.5142	−0.736177
$567$	5.56785	0.233828
$568$	0.505292	0.0212016
$569$	−30.1132	−1.26241	−0.631205	−	0.775616i	$-0.717439\pi$
$569$	−30.1132	−1.26241	−0.631205	+	0.775616i	$0.717439\pi$
$570$	−0.0542587	−0.00227265
$571$	8.50857	0.356072	0.178036	−	0.984024i	$-0.443026\pi$
$571$	8.50857	0.356072	0.178036	+	0.984024i	$0.443026\pi$
$572$	3.79252	0.158573
$573$	8.96043	0.374327
$574$	13.6458	0.569566
$575$	14.1474	0.589986
$576$	−1.53595	−0.0639980
$577$	−8.70274	−0.362300	−0.181150	−	0.983456i	$-0.557982\pi$
$577$	−8.70274	−0.362300	−0.181150	+	0.983456i	$0.557982\pi$
$578$	13.3068	0.553492
$579$	−5.21587	−0.216764
$580$	0.290290	0.0120536
$581$	−41.0305	−1.70223
$582$	−6.49273	−0.269133
$583$	−19.2076	−0.795499
$584$	−0.785797	−0.0325165
$585$	−0.127940	−0.00528967
$586$	−25.1596	−1.03933
$587$	46.2495	1.90892	0.954461	−	0.298334i	$-0.0964311\pi$
$587$	46.2495	1.90892	0.954461	+	0.298334i	$0.0964311\pi$
$588$	−0.605857	−0.0249851
$589$	7.78208	0.320655
$590$	−0.150308	−0.00618808
$591$	−8.24623	−0.339204
$592$	−2.03660	−0.0837036
$593$	26.3507	1.08209	0.541047	−	0.840993i	$-0.318028\pi$
$593$	26.3507	1.08209	0.541047	+	0.840993i	$0.318028\pi$
$594$	−11.2056	−0.459773
$595$	−0.236016	−0.00967572
$596$	9.17304	0.375742
$597$	−5.12216	−0.209636
$598$	5.25796	0.215014
$599$	−17.9714	−0.734291	−0.367146	−	0.930163i	$-0.619665\pi$
$599$	−17.9714	−0.734291	−0.367146	+	0.930163i	$0.619665\pi$
$600$	−6.04746	−0.246886
$601$	23.9345	0.976308	0.488154	−	0.872757i	$-0.337670\pi$
$601$	23.9345	0.976308	0.488154	+	0.872757i	$0.337670\pi$
$602$	−0.186265	−0.00759160
$603$	−2.56137	−0.104307
$604$	9.99988	0.406889
$605$	−0.306342	−0.0124546
$606$	−0.925042	−0.0375773
$607$	17.5506	0.712358	0.356179	−	0.934418i	$-0.384079\pi$
$607$	17.5506	0.712358	0.356179	+	0.934418i	$0.384079\pi$
$608$	1.00000	0.0405554
$609$	21.4520	0.869281
$610$	0.356198	0.0144220
$611$	17.4868	0.707441
$612$	−2.95173	−0.119317
$613$	25.7385	1.03957	0.519783	−	0.854298i	$-0.326013\pi$
$613$	25.7385	1.03957	0.519783	+	0.854298i	$0.326013\pi$
$614$	−7.27043	−0.293411
$615$	−0.270345	−0.0109014
$616$	5.59168	0.225295
$617$	29.7041	1.19584	0.597921	−	0.801555i	$-0.295994\pi$
$617$	29.7041	1.19584	0.597921	+	0.801555i	$0.295994\pi$
$618$	4.50879	0.181370
$619$	−16.0381	−0.644624	−0.322312	−	0.946633i	$-0.604460\pi$
$619$	−16.0381	−0.644624	−0.322312	+	0.946633i	$0.604460\pi$
$620$	−0.348969	−0.0140149
$621$	−15.5355	−0.623419
$622$	−2.71336	−0.108796
$623$	4.00967	0.160644
$624$	−2.24758	−0.0899752
$625$	24.9698	0.998794
$626$	20.8311	0.832579
$627$	2.47041	0.0986586
$628$	−5.68658	−0.226919
$629$	−3.91385	−0.156055
$630$	−0.188634	−0.00751537
$631$	−25.1387	−1.00075	−0.500377	−	0.865807i	$-0.666805\pi$
$631$	−25.1387	−1.00075	−0.500377	+	0.865807i	$0.666805\pi$
$632$	13.5898	0.540572
$633$	−1.20998	−0.0480923
$634$	−16.4333	−0.652648
$635$	0.517657	0.0205426
$636$	11.3831	0.451370
$637$	0.930100	0.0368519
$638$	−13.2169	−0.523263
$639$	0.776105	0.0307022
$640$	−0.0448427	−0.00177256
$641$	−40.7984	−1.61144	−0.805721	−	0.592295i	$-0.798222\pi$
$641$	−40.7984	−1.61144	−0.805721	+	0.592295i	$0.798222\pi$
$642$	−9.08034	−0.358372
$643$	38.1025	1.50261	0.751307	−	0.659953i	$-0.229424\pi$
$643$	38.1025	1.50261	0.751307	+	0.659953i	$0.229424\pi$
$644$	7.75231	0.305484
$645$	0.00369020	0.000145301 0
$646$	1.92176	0.0756106
$647$	−45.5527	−1.79086	−0.895431	−	0.445200i	$-0.853133\pi$
$647$	−45.5527	−1.79086	−0.895431	+	0.445200i	$0.853133\pi$
$648$	2.03299	0.0798636
$649$	6.84354	0.268633
$650$	9.28395	0.364147
$651$	−25.7884	−1.01073
$652$	5.80869	0.227486
$653$	10.2061	0.399397	0.199699	−	0.979857i	$-0.436004\pi$
$653$	10.2061	0.399397	0.199699	+	0.979857i	$0.436004\pi$
$654$	−8.34752	−0.326414
$655$	−0.119473	−0.00466821
$656$	4.98252	0.194535
$657$	−1.20695	−0.0470875
$658$	25.7825	1.00511
$659$	44.5937	1.73712	0.868561	−	0.495582i	$-0.165045\pi$
$659$	44.5937	1.73712	0.868561	+	0.495582i	$0.165045\pi$
$660$	−0.110780	−0.00431209
$661$	16.1901	0.629724	0.314862	−	0.949138i	$-0.398042\pi$
$661$	16.1901	0.629724	0.314862	+	0.949138i	$0.398042\pi$
$662$	12.7091	0.493954
$663$	−4.31931	−0.167748
$664$	−14.9815	−0.581395
$665$	0.122813	0.00476247
$666$	−3.12812	−0.121212
$667$	−18.3240	−0.709507
$668$	−2.21510	−0.0857048
$669$	9.14435	0.353541
$670$	−0.0747803	−0.00288901
$671$	−16.2178	−0.626080
$672$	−3.31382	−0.127833
$673$	15.3128	0.590263	0.295132	−	0.955457i	$-0.404636\pi$
$673$	15.3128	0.590263	0.295132	+	0.955457i	$0.404636\pi$
$674$	7.40878	0.285375
$675$	−27.4310	−1.05582
$676$	−9.54956	−0.367291
$677$	35.7116	1.37251	0.686255	−	0.727361i	$-0.259253\pi$
$677$	35.7116	1.37251	0.686255	+	0.727361i	$0.259253\pi$
$678$	−14.6914	−0.564220
$679$	14.6961	0.563984
$680$	−0.0861768	−0.00330473
$681$	−32.1750	−1.23295
$682$	15.8886	0.608407
$683$	−1.49599	−0.0572423	−0.0286212	−	0.999590i	$-0.509112\pi$
$683$	−1.49599	−0.0572423	−0.0286212	+	0.999590i	$0.509112\pi$
$684$	1.53595	0.0587286
$685$	−0.498720	−0.0190551
$686$	−17.7999	−0.679602
$687$	−32.5774	−1.24290
$688$	−0.0680112	−0.00259290
$689$	−17.4751	−0.665750
$690$	−0.153585	−0.00584689
$691$	−38.4899	−1.46422	−0.732112	−	0.681184i	$-0.761465\pi$
$691$	−38.4899	−1.46422	−0.732112	+	0.681184i	$0.761465\pi$
$692$	−10.3281	−0.392614
$693$	8.58855	0.326252
$694$	−15.7189	−0.596680
$695$	0.547772	0.0207782
$696$	7.83281	0.296902
$697$	9.57519	0.362686
$698$	2.98915	0.113141
$699$	21.2967	0.805515
$700$	13.6882	0.517366
$701$	−36.3287	−1.37211	−0.686057	−	0.727548i	$-0.740660\pi$
$701$	−36.3287	−1.37211	−0.686057	+	0.727548i	$0.740660\pi$
$702$	−10.1949	−0.384782
$703$	2.03660	0.0768117
$704$	2.04170	0.0769493
$705$	−0.510790	−0.0192375
$706$	0.786860	0.0296139
$707$	2.09380	0.0787455
$708$	−4.05572	−0.152423
$709$	−30.9061	−1.16070	−0.580352	−	0.814366i	$-0.697085\pi$
$709$	−30.9061	−1.16070	−0.580352	+	0.814366i	$0.697085\pi$
$710$	0.0226587	0.000850365 0
$711$	20.8732	0.782807
$712$	1.46405	0.0548677
$713$	22.0280	0.824956
$714$	−6.36836	−0.238330
$715$	0.170067	0.00636015
$716$	−8.87410	−0.331641
$717$	15.9592	0.596008
$718$	15.5405	0.579965
$719$	44.5382	1.66100	0.830498	−	0.557022i	$-0.188056\pi$
$719$	44.5382	1.66100	0.830498	+	0.557022i	$0.188056\pi$
$720$	−0.0688762	−0.00256687
$721$	−10.2055	−0.380072
$722$	−1.00000	−0.0372161
$723$	−3.11437	−0.115825
$724$	5.73170	0.213017
$725$	−32.3545	−1.20162
$726$	−8.26594	−0.306778
$727$	11.7787	0.436847	0.218424	−	0.975854i	$-0.429909\pi$
$727$	11.7787	0.436847	0.218424	+	0.975854i	$0.429909\pi$
$728$	5.08732	0.188549
$729$	23.0451	0.853524
$730$	−0.0352372	−0.00130419
$731$	−0.130701	−0.00483415
$732$	9.61121	0.355240
$733$	−12.6876	−0.468627	−0.234313	−	0.972161i	$-0.575284\pi$
$733$	−12.6876	−0.468627	−0.234313	+	0.972161i	$0.575284\pi$
$734$	17.0403	0.628968
$735$	−0.0271682	−0.00100212
$736$	2.83061	0.104338
$737$	3.40476	0.125416
$738$	7.65291	0.281707
$739$	17.7407	0.652603	0.326301	−	0.945266i	$-0.394198\pi$
$739$	17.7407	0.652603	0.326301	+	0.945266i	$0.394198\pi$
$740$	−0.0913265	−0.00335723
$741$	2.24758	0.0825669
$742$	−25.7653	−0.945873
$743$	20.1383	0.738804	0.369402	−	0.929270i	$-0.379563\pi$
$743$	20.1383	0.738804	0.369402	+	0.929270i	$0.379563\pi$
$744$	−9.41615	−0.345213
$745$	0.411344	0.0150705
$746$	−16.6854	−0.610898
$747$	−23.0109	−0.841923
$748$	3.92365	0.143463
$749$	20.5530	0.750991
$750$	−0.542478	−0.0198085
$751$	26.2753	0.958801	0.479400	−	0.877596i	$-0.340854\pi$
$751$	26.2753	0.958801	0.479400	+	0.877596i	$0.340854\pi$
$752$	9.41398	0.343292
$753$	−4.15626	−0.151463
$754$	−12.0248	−0.437917
$755$	0.448422	0.0163197
$756$	−15.0313	−0.546684
$757$	−13.6533	−0.496237	−0.248119	−	0.968730i	$-0.579812\pi$
$757$	−13.6533	−0.496237	−0.248119	+	0.968730i	$0.579812\pi$
$758$	−20.9333	−0.760332
$759$	6.99276	0.253821
$760$	0.0448427	0.00162662
$761$	−20.3777	−0.738692	−0.369346	−	0.929292i	$-0.620418\pi$
$761$	−20.3777	−0.738692	−0.369346	+	0.929292i	$0.620418\pi$
$762$	13.9678	0.506000
$763$	18.8943	0.684020
$764$	−7.40545	−0.267920
$765$	−0.132363	−0.00478561
$766$	−27.8816	−1.00740
$767$	6.22627	0.224817
$768$	−1.20998	−0.0436613
$769$	18.4729	0.666148	0.333074	−	0.942901i	$-0.391914\pi$
$769$	18.4729	0.666148	0.333074	+	0.942901i	$0.391914\pi$
$770$	0.250746	0.00903626
$771$	24.9668	0.899159
$772$	4.31071	0.155146
$773$	12.9924	0.467304	0.233652	−	0.972320i	$-0.424932\pi$
$773$	12.9924	0.467304	0.233652	+	0.972320i	$0.424932\pi$
$774$	−0.104462	−0.00375480
$775$	38.8947	1.39714
$776$	5.36599	0.192628
$777$	−6.74892	−0.242116
$778$	16.9170	0.606504
$779$	−4.98252	−0.178517
$780$	−0.100788	−0.00360877
$781$	−1.03165	−0.0369154
$782$	5.43975	0.194525
$783$	35.5292	1.26971
$784$	0.500717	0.0178827
$785$	−0.255002	−0.00910140
$786$	−3.22372	−0.114986
$787$	−2.57559	−0.0918098	−0.0459049	−	0.998946i	$-0.514617\pi$
$787$	−2.57559	−0.0918098	−0.0459049	+	0.998946i	$0.514617\pi$
$788$	6.81519	0.242781
$789$	−21.8494	−0.777858
$790$	0.609402	0.0216815
$791$	33.2535	1.18236
$792$	3.13595	0.111431
$793$	−14.7549	−0.523964
$794$	4.90896	0.174212
$795$	0.510449	0.0181038
$796$	4.23326	0.150044
$797$	43.2715	1.53276	0.766378	−	0.642390i	$-0.222057\pi$
$797$	43.2715	1.53276	0.766378	+	0.642390i	$0.222057\pi$
$798$	3.31382	0.117308
$799$	18.0914	0.640028
$800$	4.99799	0.176706
$801$	2.24872	0.0794545
$802$	3.24262	0.114501
$803$	1.60436	0.0566166
$804$	−2.01778	−0.0711615
$805$	0.347635	0.0122525
$806$	14.4555	0.509173
$807$	−36.6920	−1.29162
$808$	0.764511	0.0268954
$809$	7.86728	0.276599	0.138299	−	0.990390i	$-0.455836\pi$
$809$	7.86728	0.276599	0.138299	+	0.990390i	$0.455836\pi$
$810$	0.0911650	0.00320321
$811$	42.8850	1.50590	0.752949	−	0.658079i	$-0.228631\pi$
$811$	42.8850	1.50590	0.752949	+	0.658079i	$0.228631\pi$
$812$	−17.7293	−0.622176
$813$	−9.03475	−0.316863
$814$	4.15811	0.145742
$815$	0.260477	0.00912413
$816$	−2.32529	−0.0814013
$817$	0.0680112	0.00237941
$818$	10.5525	0.368958
$819$	7.81388	0.273039
$820$	0.223429	0.00780249
$821$	15.1335	0.528161	0.264081	−	0.964501i	$-0.414932\pi$
$821$	15.1335	0.528161	0.264081	+	0.964501i	$0.414932\pi$
$822$	−13.4568	−0.469361
$823$	12.2086	0.425564	0.212782	−	0.977100i	$-0.431748\pi$
$823$	12.2086	0.425564	0.212782	+	0.977100i	$0.431748\pi$
$824$	−3.72634	−0.129813
$825$	12.3471	0.429870
$826$	9.17998	0.319412
$827$	−26.0440	−0.905638	−0.452819	−	0.891602i	$-0.649582\pi$
$827$	−26.0440	−0.905638	−0.452819	+	0.891602i	$0.649582\pi$
$828$	4.34768	0.151092
$829$	46.0399	1.59903	0.799516	−	0.600644i	$-0.205089\pi$
$829$	46.0399	1.59903	0.799516	+	0.600644i	$0.205089\pi$
$830$	−0.671811	−0.0233189
$831$	−38.5478	−1.33721
$832$	1.85754	0.0643985
$833$	0.962257	0.0333402
$834$	14.7804	0.511803
$835$	−0.0993310	−0.00343749
$836$	−2.04170	−0.0706135
$837$	−42.7112	−1.47631
$838$	31.7266	1.09598
$839$	51.6147	1.78194	0.890968	−	0.454066i	$-0.150027\pi$
$839$	51.6147	1.78194	0.890968	+	0.454066i	$0.150027\pi$
$840$	−0.148601	−0.00512721
$841$	12.9063	0.445045
$842$	−23.7832	−0.819625
$843$	3.69970	0.127425
$844$	1.00000	0.0344214
$845$	−0.428228	−0.0147315
$846$	14.4594	0.497125
$847$	18.7097	0.642872
$848$	−9.40770	−0.323062
$849$	−21.1918	−0.727301
$850$	9.60493	0.329446
$851$	5.76481	0.197615
$852$	0.611393	0.0209460
$853$	46.8320	1.60350	0.801748	−	0.597662i	$-0.203904\pi$
$853$	46.8320	1.60350	0.801748	+	0.597662i	$0.203904\pi$
$854$	−21.7546	−0.744428
$855$	0.0688762	0.00235552
$856$	7.50454	0.256500
$857$	1.40124	0.0478654	0.0239327	−	0.999714i	$-0.492381\pi$
$857$	1.40124	0.0478654	0.0239327	+	0.999714i	$0.492381\pi$
$858$	4.58887	0.156662
$859$	27.1497	0.926337	0.463169	−	0.886270i	$-0.346712\pi$
$859$	27.1497	0.926337	0.463169	+	0.886270i	$0.346712\pi$
$860$	−0.00304980	−0.000103997 0
$861$	16.5112	0.562699
$862$	3.13657	0.106832
$863$	−5.29111	−0.180111	−0.0900557	−	0.995937i	$-0.528705\pi$
$863$	−5.29111	−0.180111	−0.0900557	+	0.995937i	$0.528705\pi$
$864$	−5.48840	−0.186719
$865$	−0.463138	−0.0157472
$866$	−24.2943	−0.825552
$867$	16.1010	0.546818
$868$	21.3131	0.723414
$869$	−27.7462	−0.941224
$870$	0.351244	0.0119083
$871$	3.09765	0.104960
$872$	6.89890	0.233626
$873$	8.24191	0.278946
$874$	−2.83061	−0.0957468
$875$	1.22788	0.0415099
$876$	−0.950797	−0.0321245
$877$	39.3548	1.32892	0.664458	−	0.747326i	$-0.268663\pi$
$877$	39.3548	1.32892	0.664458	+	0.747326i	$0.268663\pi$
$878$	6.37754	0.215231
$879$	−30.4426	−1.02680
$880$	0.0915551	0.00308632
$881$	−28.8075	−0.970548	−0.485274	−	0.874362i	$-0.661280\pi$
$881$	−28.8075	−0.970548	−0.485274	+	0.874362i	$0.661280\pi$
$882$	0.769077	0.0258962
$883$	6.50521	0.218918	0.109459	−	0.993991i	$-0.465088\pi$
$883$	6.50521	0.218918	0.109459	+	0.993991i	$0.465088\pi$
$884$	3.56974	0.120063
$885$	−0.181869	−0.00611347
$886$	−15.8222	−0.531557
$887$	0.656669	0.0220488	0.0110244	−	0.999939i	$-0.496491\pi$
$887$	0.656669	0.0220488	0.0110244	+	0.999939i	$0.496491\pi$
$888$	−2.46424	−0.0826944
$889$	−31.6156	−1.06035
$890$	0.0656521	0.00220066
$891$	−4.15076	−0.139056
$892$	−7.55745	−0.253042
$893$	−9.41398	−0.315027
$894$	11.0992	0.371212
$895$	−0.397939	−0.0133016
$896$	2.73874	0.0914950
$897$	6.36202	0.212422
$898$	−0.375322	−0.0125246
$899$	−50.3773	−1.68018
$900$	7.67667	0.255889
$901$	−18.0793	−0.602310
$902$	−10.1728	−0.338716
$903$	−0.225377	−0.00750007
$904$	12.1419	0.403833
$905$	0.257025	0.00854380
$906$	12.0996	0.401984
$907$	52.6931	1.74965	0.874823	−	0.484444i	$-0.160978\pi$
$907$	52.6931	1.74965	0.874823	+	0.484444i	$0.160978\pi$
$908$	26.5914	0.882466
$909$	1.17425	0.0389475
$910$	0.228129	0.00756240
$911$	−47.8000	−1.58368	−0.791842	−	0.610725i	$-0.790878\pi$
$911$	−47.8000	−1.58368	−0.791842	+	0.610725i	$0.790878\pi$
$912$	1.20998	0.0400664
$913$	30.5876	1.01230
$914$	−9.07588	−0.300203
$915$	0.430992	0.0142482
$916$	26.9239	0.889591
$917$	7.29677	0.240960
$918$	−10.5474	−0.348116
$919$	56.6714	1.86942	0.934709	−	0.355414i	$-0.115660\pi$
$919$	56.6714	1.86942	0.934709	+	0.355414i	$0.115660\pi$
$920$	0.126932	0.00418483
$921$	−8.79706	−0.289873
$922$	36.3391	1.19676
$923$	−0.938599	−0.0308944
$924$	6.76581	0.222579
$925$	10.1789	0.334680
$926$	28.6466	0.941385
$927$	−5.72347	−0.187983
$928$	−6.47351	−0.212503
$929$	8.23766	0.270269	0.135134	−	0.990827i	$-0.456853\pi$
$929$	8.23766	0.270269	0.135134	+	0.990827i	$0.456853\pi$
$930$	−0.422245	−0.0138460
$931$	−0.500717	−0.0164103
$932$	−17.6009	−0.576536
$933$	−3.28311	−0.107484
$934$	5.09899	0.166844
$935$	0.175947	0.00575408
$936$	2.85309	0.0932561
$937$	−1.85542	−0.0606138	−0.0303069	−	0.999541i	$-0.509648\pi$
$937$	−1.85542	−0.0606138	−0.0303069	+	0.999541i	$0.509648\pi$
$938$	4.56717	0.149123
$939$	25.2052	0.822540
$940$	0.422148	0.0137690
$941$	−1.27161	−0.0414534	−0.0207267	−	0.999785i	$-0.506598\pi$
$941$	−1.27161	−0.0414534	−0.0207267	+	0.999785i	$0.506598\pi$
$942$	−6.88064	−0.224184
$943$	−14.1036	−0.459275
$944$	3.35189	0.109095
$945$	−0.674045	−0.0219267
$946$	0.138858	0.00451466
$947$	52.9885	1.72190	0.860948	−	0.508694i	$-0.169871\pi$
$947$	52.9885	1.72190	0.860948	+	0.508694i	$0.169871\pi$
$948$	16.4433	0.534054
$949$	1.45965	0.0473821
$950$	−4.99799	−0.162156
$951$	−19.8839	−0.644779
$952$	5.26320	0.170581
$953$	49.7872	1.61277	0.806383	−	0.591394i	$-0.201422\pi$
$953$	49.7872	1.61277	0.806383	+	0.591394i	$0.201422\pi$
$954$	−14.4498	−0.467829
$955$	−0.332080	−0.0107459
$956$	−13.1897	−0.426584
$957$	−15.9922	−0.516954
$958$	−8.74345	−0.282488
$959$	30.4591	0.983574
$960$	−0.0542587	−0.00175119
$961$	29.5607	0.953573
$962$	3.78305	0.121971
$963$	11.5266	0.371440
$964$	2.57390	0.0828999
$965$	0.193304	0.00622268
$966$	9.38013	0.301801
$967$	−15.6632	−0.503696	−0.251848	−	0.967767i	$-0.581038\pi$
$967$	−15.6632	−0.503696	−0.251848	+	0.967767i	$0.581038\pi$
$968$	6.83148	0.219572
$969$	2.32529	0.0746990
$970$	0.240626	0.00772602
$971$	29.8628	0.958343	0.479171	−	0.877721i	$-0.340937\pi$
$971$	29.8628	0.958343	0.479171	+	0.877721i	$0.340937\pi$
$972$	−14.0053	−0.449221
$973$	−33.4549	−1.07251
$974$	1.45780	0.0467111
$975$	11.2334	0.359756
$976$	−7.94329	−0.254258
$977$	−40.6488	−1.30047	−0.650235	−	0.759733i	$-0.725329\pi$
$977$	−40.6488	−1.30047	−0.650235	+	0.759733i	$0.725329\pi$
$978$	7.02840	0.224743
$979$	−2.98915	−0.0955337
$980$	0.0224535	0.000717250 0
$981$	10.5964	0.338316
$982$	−18.2117	−0.581159
$983$	47.9337	1.52885	0.764424	−	0.644714i	$-0.223023\pi$
$983$	47.9337	1.52885	0.764424	+	0.644714i	$0.223023\pi$
$984$	6.02874	0.192189
$985$	0.305611	0.00973758
$986$	−12.4405	−0.396187
$987$	31.1962	0.992987
$988$	−1.85754	−0.0590961
$989$	0.192513	0.00612156
$990$	0.140624	0.00446933
$991$	6.70873	0.213110	0.106555	−	0.994307i	$-0.466018\pi$
$991$	6.70873	0.213110	0.106555	+	0.994307i	$0.466018\pi$
$992$	7.78208	0.247081
$993$	15.3778	0.487999
$994$	−1.38387	−0.0438936
$995$	0.189831	0.00601804
$996$	−18.1273	−0.574385
$997$	−42.5743	−1.34834	−0.674170	−	0.738576i	$-0.735499\pi$
$997$	−42.5743	−1.34834	−0.674170	+	0.738576i	$0.735499\pi$
$998$	−6.37347	−0.201749
$999$	−11.1777	−0.353646

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.h.1.14	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.h.1.14	✓	41	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.20998 q^{3} +1.00000 q^{4} +0.0448427 q^{5} +1.20998 q^{6} -2.73874 q^{7} -1.00000 q^{8} -1.53595 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.20998 q^{3} +1.00000 q^{4} +0.0448427 q^{5} +1.20998 q^{6} -2.73874 q^{7} -1.00000 q^{8} -1.53595 q^{9} -0.0448427 q^{10} +2.04170 q^{11} -1.20998 q^{12} +1.85754 q^{13} +2.73874 q^{14} -0.0542587 q^{15} +1.00000 q^{16} +1.92176 q^{17} +1.53595 q^{18} -1.00000 q^{19} +0.0448427 q^{20} +3.31382 q^{21} -2.04170 q^{22} -2.83061 q^{23} +1.20998 q^{24} -4.99799 q^{25} -1.85754 q^{26} +5.48840 q^{27} -2.73874 q^{28} +6.47351 q^{29} +0.0542587 q^{30} -7.78208 q^{31} -1.00000 q^{32} -2.47041 q^{33} -1.92176 q^{34} -0.122813 q^{35} -1.53595 q^{36} -2.03660 q^{37} +1.00000 q^{38} -2.24758 q^{39} -0.0448427 q^{40} +4.98252 q^{41} -3.31382 q^{42} -0.0680112 q^{43} +2.04170 q^{44} -0.0688762 q^{45} +2.83061 q^{46} +9.41398 q^{47} -1.20998 q^{48} +0.500717 q^{49} +4.99799 q^{50} -2.32529 q^{51} +1.85754 q^{52} -9.40770 q^{53} -5.48840 q^{54} +0.0915551 q^{55} +2.73874 q^{56} +1.20998 q^{57} -6.47351 q^{58} +3.35189 q^{59} -0.0542587 q^{60} -7.94329 q^{61} +7.78208 q^{62} +4.20658 q^{63} +1.00000 q^{64} +0.0832970 q^{65} +2.47041 q^{66} +1.66761 q^{67} +1.92176 q^{68} +3.42498 q^{69} +0.122813 q^{70} -0.505292 q^{71} +1.53595 q^{72} +0.785797 q^{73} +2.03660 q^{74} +6.04746 q^{75} -1.00000 q^{76} -5.59168 q^{77} +2.24758 q^{78} -13.5898 q^{79} +0.0448427 q^{80} -2.03299 q^{81} -4.98252 q^{82} +14.9815 q^{83} +3.31382 q^{84} +0.0861768 q^{85} +0.0680112 q^{86} -7.83281 q^{87} -2.04170 q^{88} -1.46405 q^{89} +0.0688762 q^{90} -5.08732 q^{91} -2.83061 q^{92} +9.41615 q^{93} -9.41398 q^{94} -0.0448427 q^{95} +1.20998 q^{96} -5.36599 q^{97} -0.500717 q^{98} -3.13595 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9	\( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 41 * q - 41 * q^2 + 8 * q^3 + 41 * q^4 - 9 * q^5 - 8 * q^6 + 7 * q^7 - 41 * q^8 + 43 * q^9 + 9 * q^10 - 9 * q^11 + 8 * q^12 + 13 * q^13 - 7 * q^14 + 26 * q^15 + 41 * q^16 - 16 * q^17 - 43 * q^18 - 41 * q^19 - 9 * q^20 + 2 * q^21 + 9 * q^22 + 10 * q^23 - 8 * q^24 + 60 * q^25 - 13 * q^26 + 47 * q^27 + 7 * q^28 - 14 * q^29 - 26 * q^30 + 49 * q^31 - 41 * q^32 + 12 * q^33 + 16 * q^34 - 8 * q^35 + 43 * q^36 + 54 * q^37 + 41 * q^38 + 16 * q^39 + 9 * q^40 - 18 * q^41 - 2 * q^42 + 29 * q^43 - 9 * q^44 - 13 * q^45 - 10 * q^46 - 8 * q^47 + 8 * q^48 + 44 * q^49 - 60 * q^50 - 16 * q^51 + 13 * q^52 + 7 * q^53 - 47 * q^54 + 19 * q^55 - 7 * q^56 - 8 * q^57 + 14 * q^58 - 5 * q^59 + 26 * q^60 - 6 * q^61 - 49 * q^62 + 24 * q^63 + 41 * q^64 - 26 * q^65 - 12 * q^66 + 66 * q^67 - 16 * q^68 + 12 * q^69 + 8 * q^70 + 27 * q^71 - 43 * q^72 - q^73 - 54 * q^74 + 62 * q^75 - 41 * q^76 - 8 * q^77 - 16 * q^78 + 87 * q^79 - 9 * q^80 + 73 * q^81 + 18 * q^82 - 41 * q^83 + 2 * q^84 + 14 * q^85 - 29 * q^86 + 35 * q^87 + 9 * q^88 - 4 * q^89 + 13 * q^90 + 39 * q^91 + 10 * q^92 + 17 * q^93 + 8 * q^94 + 9 * q^95 - 8 * q^96 + 64 * q^97 - 44 * q^98 + 40 * q^99

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