LMFDB - Embedded newform 8041.2.a.e.1.61

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.61
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.42070 q^{2} -1.43320 q^{3} +3.85979 q^{4} -0.00337016 q^{5} -3.46935 q^{6} -4.65271 q^{7} +4.50200 q^{8} -0.945936 q^{9} +O(q^{10})$	\(q+2.42070 q^{2} -1.43320 q^{3} +3.85979 q^{4} -0.00337016 q^{5} -3.46935 q^{6} -4.65271 q^{7} +4.50200 q^{8} -0.945936 q^{9} -0.00815815 q^{10} -1.00000 q^{11} -5.53186 q^{12} -3.09924 q^{13} -11.2628 q^{14} +0.00483012 q^{15} +3.17842 q^{16} -1.00000 q^{17} -2.28983 q^{18} +1.66965 q^{19} -0.0130081 q^{20} +6.66827 q^{21} -2.42070 q^{22} +0.653083 q^{23} -6.45227 q^{24} -4.99999 q^{25} -7.50233 q^{26} +5.65532 q^{27} -17.9585 q^{28} +6.43985 q^{29} +0.0116923 q^{30} -1.77371 q^{31} -1.31001 q^{32} +1.43320 q^{33} -2.42070 q^{34} +0.0156804 q^{35} -3.65112 q^{36} +7.07156 q^{37} +4.04173 q^{38} +4.44183 q^{39} -0.0151725 q^{40} -3.90367 q^{41} +16.1419 q^{42} +1.00000 q^{43} -3.85979 q^{44} +0.00318796 q^{45} +1.58092 q^{46} +4.49308 q^{47} -4.55531 q^{48} +14.6477 q^{49} -12.1035 q^{50} +1.43320 q^{51} -11.9624 q^{52} +5.29549 q^{53} +13.6898 q^{54} +0.00337016 q^{55} -20.9465 q^{56} -2.39295 q^{57} +15.5890 q^{58} -3.35044 q^{59} +0.0186433 q^{60} +6.18793 q^{61} -4.29362 q^{62} +4.40116 q^{63} -9.52797 q^{64} +0.0104449 q^{65} +3.46935 q^{66} +9.54604 q^{67} -3.85979 q^{68} -0.935999 q^{69} +0.0379575 q^{70} +16.4000 q^{71} -4.25861 q^{72} +12.3859 q^{73} +17.1181 q^{74} +7.16599 q^{75} +6.44452 q^{76} +4.65271 q^{77} +10.7523 q^{78} -3.55372 q^{79} -0.0107118 q^{80} -5.26740 q^{81} -9.44962 q^{82} -5.51588 q^{83} +25.7381 q^{84} +0.00337016 q^{85} +2.42070 q^{86} -9.22960 q^{87} -4.50200 q^{88} -2.24023 q^{89} +0.00771709 q^{90} +14.4199 q^{91} +2.52077 q^{92} +2.54208 q^{93} +10.8764 q^{94} -0.00562700 q^{95} +1.87751 q^{96} +3.26573 q^{97} +35.4577 q^{98} +0.945936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * 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 $

$2$	2.42070	1.71169	0.855847	−	0.517229i	$-0.173036\pi$
$2$	2.42070	1.71169	0.855847	+	0.517229i	$0.173036\pi$
$3$	−1.43320	−0.827459	−0.413729	−	0.910400i	$-0.635774\pi$
$3$	−1.43320	−0.827459	−0.413729	+	0.910400i	$0.635774\pi$
$4$	3.85979	1.92990
$5$	−0.00337016	−0.00150718	−0.000753591	−	1.00000i	$-0.500240\pi$
$5$	−0.00337016	−0.00150718	−0.000753591		1.00000i	$0.500240\pi$
$6$	−3.46935	−1.41636
$7$	−4.65271	−1.75856	−0.879279	−	0.476307i	$-0.841975\pi$
$7$	−4.65271	−1.75856	−0.879279	+	0.476307i	$0.841975\pi$
$8$	4.50200	1.59170
$9$	−0.945936	−0.315312
$10$	−0.00815815	−0.00257983
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−5.53186	−1.59691
$13$	−3.09924	−0.859574	−0.429787	−	0.902930i	$-0.641411\pi$
$13$	−3.09924	−0.859574	−0.429787	+	0.902930i	$0.641411\pi$
$14$	−11.2628	−3.01011
$15$	0.00483012	0.00124713
$16$	3.17842	0.794604
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.28983	−0.539718
$19$	1.66965	0.383045	0.191522	−	0.981488i	$-0.438658\pi$
$19$	1.66965	0.383045	0.191522	+	0.981488i	$0.438658\pi$
$20$	−0.0130081	−0.00290871
$21$	6.66827	1.45513
$22$	−2.42070	−0.516095
$23$	0.653083	0.136177	0.0680886	−	0.997679i	$-0.478310\pi$
$23$	0.653083	0.136177	0.0680886	+	0.997679i	$0.478310\pi$
$24$	−6.45227	−1.31706
$25$	−4.99999	−0.999998
$26$	−7.50233	−1.47133
$27$	5.65532	1.08837
$28$	−17.9585	−3.39384
$29$	6.43985	1.19585	0.597925	−	0.801552i	$-0.295992\pi$
$29$	6.43985	1.19585	0.597925	+	0.801552i	$0.295992\pi$
$30$	0.0116923	0.00213471
$31$	−1.77371	−0.318568	−0.159284	−	0.987233i	$-0.550918\pi$
$31$	−1.77371	−0.318568	−0.159284	+	0.987233i	$0.550918\pi$
$32$	−1.31001	−0.231579
$33$	1.43320	0.249488
$34$	−2.42070	−0.415147
$35$	0.0156804	0.00265047
$36$	−3.65112	−0.608520
$37$	7.07156	1.16256	0.581279	−	0.813705i	$-0.302553\pi$
$37$	7.07156	1.16256	0.581279	+	0.813705i	$0.302553\pi$
$38$	4.04173	0.655656
$39$	4.44183	0.711262
$40$	−0.0151725	−0.00239898
$41$	−3.90367	−0.609651	−0.304826	−	0.952408i	$-0.598598\pi$
$41$	−3.90367	−0.609651	−0.304826	+	0.952408i	$0.598598\pi$
$42$	16.1419	2.49075
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−3.85979	−0.581886
$45$	0.00318796	0.000475233 0
$46$	1.58092	0.233094
$47$	4.49308	0.655384	0.327692	−	0.944785i	$-0.393729\pi$
$47$	4.49308	0.655384	0.327692	+	0.944785i	$0.393729\pi$
$48$	−4.55531	−0.657502
$49$	14.6477	2.09253
$50$	−12.1035	−1.71169
$51$	1.43320	0.200688
$52$	−11.9624	−1.65889
$53$	5.29549	0.727391	0.363695	−	0.931518i	$-0.381515\pi$
$53$	5.29549	0.727391	0.363695	+	0.931518i	$0.381515\pi$
$54$	13.6898	1.86295
$55$	0.00337016	0.000454432 0
$56$	−20.9465	−2.79910
$57$	−2.39295	−0.316954
$58$	15.5890	2.04693
$59$	−3.35044	−0.436190	−0.218095	−	0.975928i	$-0.569984\pi$
$59$	−3.35044	−0.436190	−0.218095	+	0.975928i	$0.569984\pi$
$60$	0.0186433	0.00240683
$61$	6.18793	0.792283	0.396142	−	0.918189i	$-0.370349\pi$
$61$	6.18793	0.792283	0.396142	+	0.918189i	$0.370349\pi$
$62$	−4.29362	−0.545290
$63$	4.40116	0.554495
$64$	−9.52797	−1.19100
$65$	0.0104449	0.00129553
$66$	3.46935	0.427047
$67$	9.54604	1.16623	0.583117	−	0.812388i	$-0.301833\pi$
$67$	9.54604	1.16623	0.583117	+	0.812388i	$0.301833\pi$
$68$	−3.85979	−0.468069
$69$	−0.935999	−0.112681
$70$	0.0379575	0.00453679
$71$	16.4000	1.94632	0.973161	−	0.230124i	$-0.0739131\pi$
$71$	16.4000	1.94632	0.973161	+	0.230124i	$0.0739131\pi$
$72$	−4.25861	−0.501882
$73$	12.3859	1.44966	0.724830	−	0.688928i	$-0.241918\pi$
$73$	12.3859	1.44966	0.724830	+	0.688928i	$0.241918\pi$
$74$	17.1181	1.98994
$75$	7.16599	0.827457
$76$	6.44452	0.739237
$77$	4.65271	0.530225
$78$	10.7523	1.21746
$79$	−3.55372	−0.399825	−0.199912	−	0.979814i	$-0.564066\pi$
$79$	−3.55372	−0.399825	−0.199912	+	0.979814i	$0.564066\pi$
$80$	−0.0107118	−0.00119761
$81$	−5.26740	−0.585266
$82$	−9.44962	−1.04354
$83$	−5.51588	−0.605447	−0.302723	−	0.953078i	$-0.597896\pi$
$83$	−5.51588	−0.605447	−0.302723	+	0.953078i	$0.597896\pi$
$84$	25.7381	2.80826
$85$	0.00337016	0.000365545 0
$86$	2.42070	0.261031
$87$	−9.22960	−0.989517
$88$	−4.50200	−0.479915
$89$	−2.24023	−0.237464	−0.118732	−	0.992926i	$-0.537883\pi$
$89$	−2.24023	−0.237464	−0.118732	+	0.992926i	$0.537883\pi$
$90$	0.00771709	0.000813453 0
$91$	14.4199	1.51161
$92$	2.52077	0.262808
$93$	2.54208	0.263602
$94$	10.8764	1.12182
$95$	−0.00562700	−0.000577318 0
$96$	1.87751	0.191622
$97$	3.26573	0.331584	0.165792	−	0.986161i	$-0.446982\pi$
$97$	3.26573	0.331584	0.165792	+	0.986161i	$0.446982\pi$
$98$	35.4577	3.58177
$99$	0.945936	0.0950701
$100$	−19.2989	−1.92989
$101$	−15.2915	−1.52156	−0.760779	−	0.649011i	$-0.775183\pi$
$101$	−15.2915	−1.52156	−0.760779	+	0.649011i	$0.775183\pi$
$102$	3.46935	0.343517
$103$	−12.7691	−1.25818	−0.629091	−	0.777332i	$-0.716573\pi$
$103$	−12.7691	−1.25818	−0.629091	+	0.777332i	$0.716573\pi$
$104$	−13.9528	−1.36818
$105$	−0.0224731	−0.00219315
$106$	12.8188	1.24507
$107$	4.18526	0.404604	0.202302	−	0.979323i	$-0.435158\pi$
$107$	4.18526	0.404604	0.202302	+	0.979323i	$0.435158\pi$
$108$	21.8284	2.10043
$109$	−10.5776	−1.01315	−0.506576	−	0.862195i	$-0.669089\pi$
$109$	−10.5776	−1.01315	−0.506576	+	0.862195i	$0.669089\pi$
$110$	0.00815815	0.000777849 0
$111$	−10.1350	−0.961968
$112$	−14.7883	−1.39736
$113$	8.11251	0.763161	0.381580	−	0.924336i	$-0.375380\pi$
$113$	8.11251	0.763161	0.381580	+	0.924336i	$0.375380\pi$
$114$	−5.79261	−0.542528
$115$	−0.00220100	−0.000205244 0
$116$	24.8565	2.30787
$117$	2.93168	0.271034
$118$	−8.11041	−0.746624
$119$	4.65271	0.426513
$120$	0.0217452	0.00198506
$121$	1.00000	0.0909091
$122$	14.9791	1.35615
$123$	5.59475	0.504461
$124$	−6.84615	−0.614803
$125$	0.0337016	0.00301436
$126$	10.6539	0.949125
$127$	−11.6087	−1.03010	−0.515052	−	0.857159i	$-0.672227\pi$
$127$	−11.6087	−1.03010	−0.515052	+	0.857159i	$0.672227\pi$
$128$	−20.4444	−1.80704
$129$	−1.43320	−0.126186
$130$	0.0252841	0.00221756
$131$	22.3800	1.95535	0.977676	−	0.210118i	$-0.0673847\pi$
$131$	22.3800	1.95535	0.977676	+	0.210118i	$0.0673847\pi$
$132$	5.53186	0.481486
$133$	−7.76841	−0.673607
$134$	23.1081	1.99624
$135$	−0.0190593	−0.00164037
$136$	−4.50200	−0.386044
$137$	−19.2588	−1.64539	−0.822694	−	0.568484i	$-0.807530\pi$
$137$	−19.2588	−1.64539	−0.822694	+	0.568484i	$0.807530\pi$
$138$	−2.26577	−0.192875
$139$	10.4945	0.890132	0.445066	−	0.895498i	$-0.353180\pi$
$139$	10.4945	0.890132	0.445066	+	0.895498i	$0.353180\pi$
$140$	0.0605230	0.00511513
$141$	−6.43949	−0.542303
$142$	39.6995	3.33151
$143$	3.09924	0.259171
$144$	−3.00658	−0.250548
$145$	−0.0217033	−0.00180236
$146$	29.9825	2.48137
$147$	−20.9931	−1.73148
$148$	27.2948	2.24362
$149$	19.5834	1.60434	0.802168	−	0.597098i	$-0.203680\pi$
$149$	19.5834	1.60434	0.802168	+	0.597098i	$0.203680\pi$
$150$	17.3467	1.41635
$151$	11.9601	0.973296	0.486648	−	0.873598i	$-0.338220\pi$
$151$	11.9601	0.973296	0.486648	+	0.873598i	$0.338220\pi$
$152$	7.51679	0.609692
$153$	0.945936	0.0764744
$154$	11.2628	0.907584
$155$	0.00597769	0.000480139 0
$156$	17.1445	1.37266
$157$	−14.8675	−1.18655	−0.593277	−	0.804998i	$-0.702166\pi$
$157$	−14.8675	−1.18655	−0.593277	+	0.804998i	$0.702166\pi$
$158$	−8.60249	−0.684377
$159$	−7.58949	−0.601886
$160$	0.00441494	0.000349032 0
$161$	−3.03861	−0.239476
$162$	−12.7508	−1.00180
$163$	−14.2584	−1.11681	−0.558403	−	0.829570i	$-0.688586\pi$
$163$	−14.2584	−1.11681	−0.558403	+	0.829570i	$0.688586\pi$
$164$	−15.0674	−1.17656
$165$	−0.00483012	−0.000376024 0
$166$	−13.3523	−1.03634
$167$	−0.786164	−0.0608352	−0.0304176	−	0.999537i	$-0.509684\pi$
$167$	−0.786164	−0.0608352	−0.0304176	+	0.999537i	$0.509684\pi$
$168$	30.0206	2.31614
$169$	−3.39472	−0.261133
$170$	0.00815815	0.000625702 0
$171$	−1.57939	−0.120779
$172$	3.85979	0.294306
$173$	−8.11629	−0.617070	−0.308535	−	0.951213i	$-0.599839\pi$
$173$	−8.11629	−0.617070	−0.308535	+	0.951213i	$0.599839\pi$
$174$	−22.3421	−1.69375
$175$	23.2635	1.75855
$176$	−3.17842	−0.239582
$177$	4.80185	0.360929
$178$	−5.42292	−0.406465
$179$	20.1131	1.50332	0.751660	−	0.659550i	$-0.229253\pi$
$179$	20.1131	1.50332	0.751660	+	0.659550i	$0.229253\pi$
$180$	0.0123049	0.000917150 0
$181$	7.31744	0.543901	0.271950	−	0.962311i	$-0.412331\pi$
$181$	7.31744	0.543901	0.271950	+	0.962311i	$0.412331\pi$
$182$	34.9061	2.58742
$183$	−8.86855	−0.655582
$184$	2.94018	0.216753
$185$	−0.0238323	−0.00175219
$186$	6.15362	0.451205
$187$	1.00000	0.0731272
$188$	17.3424	1.26482
$189$	−26.3125	−1.91396
$190$	−0.0136213	−0.000988192 0
$191$	3.70145	0.267828	0.133914	−	0.990993i	$-0.457245\pi$
$191$	3.70145	0.267828	0.133914	+	0.990993i	$0.457245\pi$
$192$	13.6555	0.985501
$193$	−4.28658	−0.308555	−0.154277	−	0.988028i	$-0.549305\pi$
$193$	−4.28658	−0.308555	−0.154277	+	0.988028i	$0.549305\pi$
$194$	7.90535	0.567571
$195$	−0.0149697	−0.00107200
$196$	56.5371	4.03836
$197$	14.5531	1.03687	0.518433	−	0.855118i	$-0.326515\pi$
$197$	14.5531	1.03687	0.518433	+	0.855118i	$0.326515\pi$
$198$	2.28983	0.162731
$199$	−14.2291	−1.00867	−0.504336	−	0.863507i	$-0.668263\pi$
$199$	−14.2291	−1.00867	−0.504336	+	0.863507i	$0.668263\pi$
$200$	−22.5100	−1.59169
$201$	−13.6814	−0.965011
$202$	−37.0161	−2.60444
$203$	−29.9628	−2.10297
$204$	5.53186	0.387308
$205$	0.0131560	0.000918855 0
$206$	−30.9103	−2.15362
$207$	−0.617775	−0.0429383
$208$	−9.85067	−0.683021
$209$	−1.66965	−0.115492
$210$	−0.0544007	−0.00375401
$211$	13.3185	0.916882	0.458441	−	0.888725i	$-0.348408\pi$
$211$	13.3185	0.916882	0.458441	+	0.888725i	$0.348408\pi$
$212$	20.4395	1.40379
$213$	−23.5045	−1.61050
$214$	10.1313	0.692559
$215$	−0.00337016	−0.000229843 0
$216$	25.4603	1.73235
$217$	8.25255	0.560220
$218$	−25.6053	−1.73421
$219$	−17.7515	−1.19953
$220$	0.0130081	0.000877008 0
$221$	3.09924	0.208477
$222$	−24.5337	−1.64660
$223$	12.2899	0.822993	0.411497	−	0.911411i	$-0.365006\pi$
$223$	12.2899	0.822993	0.411497	+	0.911411i	$0.365006\pi$
$224$	6.09509	0.407245
$225$	4.72967	0.315311
$226$	19.6380	1.30630
$227$	8.28733	0.550049	0.275025	−	0.961437i	$-0.411314\pi$
$227$	8.28733	0.550049	0.275025	+	0.961437i	$0.411314\pi$
$228$	−9.23629	−0.611688
$229$	2.24090	0.148083	0.0740413	−	0.997255i	$-0.476410\pi$
$229$	2.24090	0.148083	0.0740413	+	0.997255i	$0.476410\pi$
$230$	−0.00532795	−0.000351315 0
$231$	−6.66827	−0.438740
$232$	28.9922	1.90343
$233$	−10.4121	−0.682117	−0.341058	−	0.940042i	$-0.610785\pi$
$233$	−10.4121	−0.682117	−0.341058	+	0.940042i	$0.610785\pi$
$234$	7.09672	0.463927
$235$	−0.0151424	−0.000987783 0
$236$	−12.9320	−0.841801
$237$	5.09319	0.330838
$238$	11.2628	0.730060
$239$	18.9236	1.22406	0.612032	−	0.790833i	$-0.290352\pi$
$239$	18.9236	1.22406	0.612032	+	0.790833i	$0.290352\pi$
$240$	0.0153521	0.000990976 0
$241$	12.7638	0.822192	0.411096	−	0.911592i	$-0.365146\pi$
$241$	12.7638	0.822192	0.411096	+	0.911592i	$0.365146\pi$
$242$	2.42070	0.155609
$243$	−9.41672	−0.604083
$244$	23.8841	1.52902
$245$	−0.0493651	−0.00315382
$246$	13.5432	0.863483
$247$	−5.17465	−0.329255
$248$	−7.98525	−0.507064
$249$	7.90537	0.500982
$250$	0.0815814	0.00515966
$251$	12.0641	0.761479	0.380739	−	0.924682i	$-0.375669\pi$
$251$	12.0641	0.761479	0.380739	+	0.924682i	$0.375669\pi$
$252$	16.9876	1.07012
$253$	−0.653083	−0.0410590
$254$	−28.1011	−1.76322
$255$	−0.00483012	−0.000302474 0
$256$	−30.4337	−1.90211
$257$	−7.07338	−0.441225	−0.220613	−	0.975362i	$-0.570806\pi$
$257$	−7.07338	−0.441225	−0.220613	+	0.975362i	$0.570806\pi$
$258$	−3.46935	−0.215992
$259$	−32.9019	−2.04443
$260$	0.0403153	0.00250025
$261$	−6.09169	−0.377066
$262$	54.1754	3.34696
$263$	5.45141	0.336148	0.168074	−	0.985774i	$-0.446245\pi$
$263$	5.45141	0.336148	0.168074	+	0.985774i	$0.446245\pi$
$264$	6.45227	0.397110
$265$	−0.0178466	−0.00109631
$266$	−18.8050	−1.15301
$267$	3.21070	0.196491
$268$	36.8457	2.25071
$269$	−0.556012	−0.0339006	−0.0169503	−	0.999856i	$-0.505396\pi$
$269$	−0.556012	−0.0339006	−0.0169503	+	0.999856i	$0.505396\pi$
$270$	−0.0461369	−0.00280781
$271$	3.62552	0.220234	0.110117	−	0.993919i	$-0.464877\pi$
$271$	3.62552	0.220234	0.110117	+	0.993919i	$0.464877\pi$
$272$	−3.17842	−0.192720
$273$	−20.6665	−1.25080
$274$	−46.6198	−2.81640
$275$	4.99999	0.301511
$276$	−3.61276	−0.217463
$277$	17.8843	1.07457	0.537283	−	0.843402i	$-0.319451\pi$
$277$	17.8843	1.07457	0.537283	+	0.843402i	$0.319451\pi$
$278$	25.4041	1.52363
$279$	1.67782	0.100448
$280$	0.0705931	0.00421875
$281$	−32.9929	−1.96819	−0.984096	−	0.177640i	$-0.943154\pi$
$281$	−32.9929	−1.96819	−0.984096	+	0.177640i	$0.943154\pi$
$282$	−15.5881	−0.928257
$283$	6.13948	0.364954	0.182477	−	0.983210i	$-0.441588\pi$
$283$	6.13948	0.364954	0.182477	+	0.983210i	$0.441588\pi$
$284$	63.3006	3.75620
$285$	0.00806462	0.000477707 0
$286$	7.50233	0.443622
$287$	18.1626	1.07211
$288$	1.23918	0.0730196
$289$	1.00000	0.0588235
$290$	−0.0525373	−0.00308510
$291$	−4.68044	−0.274372
$292$	47.8070	2.79769
$293$	6.09142	0.355864	0.177932	−	0.984043i	$-0.443059\pi$
$293$	6.09142	0.355864	0.177932	+	0.984043i	$0.443059\pi$
$294$	−50.8180	−2.96377
$295$	0.0112915	0.000657417 0
$296$	31.8362	1.85044
$297$	−5.65532	−0.328155
$298$	47.4056	2.74613
$299$	−2.02406	−0.117054
$300$	27.6592	1.59691
$301$	−4.65271	−0.268178
$302$	28.9517	1.66598
$303$	21.9157	1.25903
$304$	5.30686	0.304369
$305$	−0.0208543	−0.00119412
$306$	2.28983	0.130901
$307$	18.0884	1.03236	0.516180	−	0.856480i	$-0.327353\pi$
$307$	18.0884	1.03236	0.516180	+	0.856480i	$0.327353\pi$
$308$	17.9585	1.02328
$309$	18.3007	1.04109
$310$	0.0144702	0.000821852 0
$311$	13.9496	0.791009	0.395505	−	0.918464i	$-0.370570\pi$
$311$	13.9496	0.791009	0.395505	+	0.918464i	$0.370570\pi$
$312$	19.9971	1.13211
$313$	12.2987	0.695161	0.347581	−	0.937650i	$-0.387003\pi$
$313$	12.2987	0.695161	0.347581	+	0.937650i	$0.387003\pi$
$314$	−35.9897	−2.03102
$315$	−0.0148326	−0.000835724 0
$316$	−13.7166	−0.771620
$317$	−33.7606	−1.89618	−0.948092	−	0.317995i	$-0.896990\pi$
$317$	−33.7606	−1.89618	−0.948092	+	0.317995i	$0.896990\pi$
$318$	−18.3719	−1.03024
$319$	−6.43985	−0.360562
$320$	0.0321108	0.00179505
$321$	−5.99832	−0.334793
$322$	−7.35555	−0.409909
$323$	−1.66965	−0.0929020
$324$	−20.3311	−1.12950
$325$	15.4962	0.859572
$326$	−34.5154	−1.91163
$327$	15.1599	0.838342
$328$	−17.5743	−0.970381
$329$	−20.9050	−1.15253
$330$	−0.0116923	−0.000643638 0
$331$	−12.7011	−0.698117	−0.349058	−	0.937101i	$-0.613498\pi$
$331$	−12.7011	−0.698117	−0.349058	+	0.937101i	$0.613498\pi$
$332$	−21.2902	−1.16845
$333$	−6.68924	−0.366568
$334$	−1.90307	−0.104131
$335$	−0.0321717	−0.00175773
$336$	21.1945	1.15626
$337$	9.24386	0.503545	0.251772	−	0.967786i	$-0.418987\pi$
$337$	9.24386	0.503545	0.251772	+	0.967786i	$0.418987\pi$
$338$	−8.21761	−0.446979
$339$	−11.6269	−0.631484
$340$	0.0130081	0.000705465 0
$341$	1.77371	0.0960517
$342$	−3.82322	−0.206736
$343$	−35.5825	−1.92128
$344$	4.50200	0.242732
$345$	0.00315447	0.000169831 0
$346$	−19.6471	−1.05623
$347$	−9.47927	−0.508874	−0.254437	−	0.967089i	$-0.581890\pi$
$347$	−9.47927	−0.508874	−0.254437	+	0.967089i	$0.581890\pi$
$348$	−35.6243	−1.90967
$349$	18.7488	1.00360	0.501799	−	0.864984i	$-0.332672\pi$
$349$	18.7488	1.00360	0.501799	+	0.864984i	$0.332672\pi$
$350$	56.3140	3.01011
$351$	−17.5272	−0.935531
$352$	1.31001	0.0698237
$353$	−17.3687	−0.924443	−0.462222	−	0.886764i	$-0.652948\pi$
$353$	−17.3687	−0.924443	−0.462222	+	0.886764i	$0.652948\pi$
$354$	11.6238	0.617800
$355$	−0.0552707	−0.00293346
$356$	−8.64681	−0.458280
$357$	−6.66827	−0.352922
$358$	48.6877	2.57323
$359$	−9.93520	−0.524360	−0.262180	−	0.965019i	$-0.584441\pi$
$359$	−9.93520	−0.524360	−0.262180	+	0.965019i	$0.584441\pi$
$360$	0.0143522	0.000756427 0
$361$	−16.2123	−0.853277
$362$	17.7133	0.930992
$363$	−1.43320	−0.0752235
$364$	55.6576	2.91725
$365$	−0.0417425	−0.00218490
$366$	−21.4681	−1.12216
$367$	−32.3738	−1.68990	−0.844950	−	0.534845i	$-0.820370\pi$
$367$	−32.3738	−1.68990	−0.844950	+	0.534845i	$0.820370\pi$
$368$	2.07577	0.108207
$369$	3.69262	0.192230
$370$	−0.0576909	−0.00299921
$371$	−24.6384	−1.27916
$372$	9.81191	0.508724
$373$	32.4726	1.68137	0.840683	−	0.541528i	$-0.182154\pi$
$373$	32.4726	1.68137	0.840683	+	0.541528i	$0.182154\pi$
$374$	2.42070	0.125171
$375$	−0.0483011	−0.00249426
$376$	20.2279	1.04317
$377$	−19.9586	−1.02792
$378$	−63.6948	−3.27611
$379$	22.1365	1.13708	0.568538	−	0.822657i	$-0.307509\pi$
$379$	22.1365	1.13708	0.568538	+	0.822657i	$0.307509\pi$
$380$	−0.0217191	−0.00111416
$381$	16.6376	0.852368
$382$	8.96010	0.458439
$383$	3.88010	0.198264	0.0991320	−	0.995074i	$-0.468393\pi$
$383$	3.88010	0.198264	0.0991320	+	0.995074i	$0.468393\pi$
$384$	29.3009	1.49525
$385$	−0.0156804	−0.000799146 0
$386$	−10.3765	−0.528151
$387$	−0.945936	−0.0480846
$388$	12.6050	0.639923
$389$	10.2080	0.517568	0.258784	−	0.965935i	$-0.416678\pi$
$389$	10.2080	0.517568	0.258784	+	0.965935i	$0.416678\pi$
$390$	−0.0362371	−0.00183494
$391$	−0.653083	−0.0330278
$392$	65.9440	3.33067
$393$	−32.0751	−1.61797
$394$	35.2287	1.77480
$395$	0.0119766	0.000602608 0
$396$	3.65112	0.183476
$397$	−26.7403	−1.34206	−0.671029	−	0.741432i	$-0.734147\pi$
$397$	−26.7403	−1.34206	−0.671029	+	0.741432i	$0.734147\pi$
$398$	−34.4444	−1.72654
$399$	11.1337	0.557382
$400$	−15.8921	−0.794603
$401$	−34.9763	−1.74663	−0.873317	−	0.487153i	$-0.838035\pi$
$401$	−34.9763	−1.74663	−0.873317	+	0.487153i	$0.838035\pi$
$402$	−33.1185	−1.65180
$403$	5.49715	0.273832
$404$	−59.0219	−2.93645
$405$	0.0177520	0.000882103 0
$406$	−72.5309	−3.59965
$407$	−7.07156	−0.350524
$408$	6.45227	0.319435
$409$	−28.6961	−1.41893	−0.709466	−	0.704739i	$-0.751064\pi$
$409$	−28.6961	−1.41893	−0.709466	+	0.704739i	$0.751064\pi$
$410$	0.0318468	0.00157280
$411$	27.6017	1.36149
$412$	−49.2863	−2.42816
$413$	15.5886	0.767065
$414$	−1.49545	−0.0734973
$415$	0.0185894	0.000912518 0
$416$	4.06003	0.199059
$417$	−15.0407	−0.736548
$418$	−4.04173	−0.197688
$419$	−20.2516	−0.989355	−0.494677	−	0.869077i	$-0.664714\pi$
$419$	−20.2516	−0.989355	−0.494677	+	0.869077i	$0.664714\pi$
$420$	−0.0867416	−0.00423256
$421$	18.2477	0.889340	0.444670	−	0.895694i	$-0.353321\pi$
$421$	18.2477	0.889340	0.444670	+	0.895694i	$0.353321\pi$
$422$	32.2401	1.56942
$423$	−4.25017	−0.206650
$424$	23.8403	1.15779
$425$	4.99999	0.242535
$426$	−56.8974	−2.75669
$427$	−28.7906	−1.39328
$428$	16.1542	0.780845
$429$	−4.44183	−0.214454
$430$	−0.00815815	−0.000393421 0
$431$	−12.3184	−0.593358	−0.296679	−	0.954977i	$-0.595879\pi$
$431$	−12.3184	−0.593358	−0.296679	+	0.954977i	$0.595879\pi$
$432$	17.9750	0.864821
$433$	35.0052	1.68224	0.841121	−	0.540847i	$-0.181896\pi$
$433$	35.0052	1.68224	0.841121	+	0.540847i	$0.181896\pi$
$434$	19.9770	0.958925
$435$	0.0311052	0.00149138
$436$	−40.8274	−1.95528
$437$	1.09042	0.0521620
$438$	−42.9710	−2.05323
$439$	−18.4200	−0.879136	−0.439568	−	0.898209i	$-0.644869\pi$
$439$	−18.4200	−0.879136	−0.439568	+	0.898209i	$0.644869\pi$
$440$	0.0151725	0.000723319 0
$441$	−13.8558	−0.659799
$442$	7.50233	0.356849
$443$	−16.7861	−0.797532	−0.398766	−	0.917053i	$-0.630562\pi$
$443$	−16.7861	−0.797532	−0.398766	+	0.917053i	$0.630562\pi$
$444$	−39.1189	−1.85650
$445$	0.00754993	0.000357901 0
$446$	29.7502	1.40871
$447$	−28.0670	−1.32752
$448$	44.3309	2.09444
$449$	4.12689	0.194760	0.0973799	−	0.995247i	$-0.468954\pi$
$449$	4.12689	0.194760	0.0973799	+	0.995247i	$0.468954\pi$
$450$	11.4491	0.539716
$451$	3.90367	0.183817
$452$	31.3126	1.47282
$453$	−17.1412	−0.805362
$454$	20.0611	0.941516
$455$	−0.0485972	−0.00227827
$456$	−10.7731	−0.504495
$457$	30.9452	1.44756	0.723778	−	0.690033i	$-0.242404\pi$
$457$	30.9452	1.44756	0.723778	+	0.690033i	$0.242404\pi$
$458$	5.42454	0.253472
$459$	−5.65532	−0.263968
$460$	−0.00849539	−0.000396099 0
$461$	11.3266	0.527531	0.263765	−	0.964587i	$-0.415036\pi$
$461$	11.3266	0.527531	0.263765	+	0.964587i	$0.415036\pi$
$462$	−16.1419	−0.750988
$463$	18.4214	0.856117	0.428058	−	0.903751i	$-0.359198\pi$
$463$	18.4214	0.856117	0.428058	+	0.903751i	$0.359198\pi$
$464$	20.4685	0.950228
$465$	−0.00856722	−0.000397295 0
$466$	−25.2045	−1.16758
$467$	−19.0954	−0.883630	−0.441815	−	0.897106i	$-0.645665\pi$
$467$	−19.0954	−0.883630	−0.441815	+	0.897106i	$0.645665\pi$
$468$	11.3157	0.523068
$469$	−44.4149	−2.05089
$470$	−0.0366553	−0.00169078
$471$	21.3081	0.981825
$472$	−15.0837	−0.694283
$473$	−1.00000	−0.0459800
$474$	12.3291	0.566294
$475$	−8.34825	−0.383044
$476$	17.9585	0.823126
$477$	−5.00919	−0.229355
$478$	45.8083	2.09522
$479$	2.98698	0.136479	0.0682393	−	0.997669i	$-0.478262\pi$
$479$	2.98698	0.136479	0.0682393	+	0.997669i	$0.478262\pi$
$480$	−0.00632750	−0.000288809 0
$481$	−21.9164	−0.999304
$482$	30.8975	1.40734
$483$	4.35493	0.198156
$484$	3.85979	0.175445
$485$	−0.0110060	−0.000499758 0
$486$	−22.7951	−1.03400
$487$	30.5470	1.38421	0.692107	−	0.721795i	$-0.256682\pi$
$487$	30.5470	1.38421	0.692107	+	0.721795i	$0.256682\pi$
$488$	27.8581	1.26108
$489$	20.4352	0.924112
$490$	−0.119498	−0.00539838
$491$	12.7753	0.576539	0.288270	−	0.957549i	$-0.406920\pi$
$491$	12.7753	0.576539	0.288270	+	0.957549i	$0.406920\pi$
$492$	21.5946	0.973558
$493$	−6.43985	−0.290036
$494$	−12.5263	−0.563584
$495$	−0.00318796	−0.000143288 0
$496$	−5.63759	−0.253135
$497$	−76.3045	−3.42272
$498$	19.1365	0.857528
$499$	13.8077	0.618115	0.309058	−	0.951043i	$-0.399986\pi$
$499$	13.8077	0.618115	0.309058	+	0.951043i	$0.399986\pi$
$500$	0.130081	0.00581740
$501$	1.12673	0.0503386
$502$	29.2036	1.30342
$503$	9.87009	0.440086	0.220043	−	0.975490i	$-0.429380\pi$
$503$	9.87009	0.440086	0.220043	+	0.975490i	$0.429380\pi$
$504$	19.8141	0.882588
$505$	0.0515347	0.00229326
$506$	−1.58092	−0.0702804
$507$	4.86532	0.216076
$508$	−44.8071	−1.98799
$509$	34.2672	1.51887	0.759434	−	0.650585i	$-0.225476\pi$
$509$	34.2672	1.51887	0.759434	+	0.650585i	$0.225476\pi$
$510$	−0.0116923	−0.000517742 0
$511$	−57.6280	−2.54931
$512$	−32.7822	−1.44878
$513$	9.44242	0.416893
$514$	−17.1225	−0.755242
$515$	0.0430341	0.00189631
$516$	−5.53186	−0.243526
$517$	−4.49308	−0.197606
$518$	−79.6457	−3.49943
$519$	11.6323	0.510600
$520$	0.0470231	0.00206210
$521$	33.3367	1.46051	0.730254	−	0.683176i	$-0.239402\pi$
$521$	33.3367	1.46051	0.730254	+	0.683176i	$0.239402\pi$
$522$	−14.7462	−0.645422
$523$	11.5885	0.506731	0.253366	−	0.967371i	$-0.418462\pi$
$523$	11.5885	0.506731	0.253366	+	0.967371i	$0.418462\pi$
$524$	86.3823	3.77363
$525$	−33.3412	−1.45513
$526$	13.1962	0.575383
$527$	1.77371	0.0772640
$528$	4.55531	0.198244
$529$	−22.5735	−0.981456
$530$	−0.0432014	−0.00187655
$531$	3.16930	0.137536
$532$	−29.9845	−1.29999
$533$	12.0984	0.524040
$534$	7.77213	0.336333
$535$	−0.0141050	−0.000609812 0
$536$	42.9763	1.85629
$537$	−28.8261	−1.24394
$538$	−1.34594	−0.0580275
$539$	−14.6477	−0.630921
$540$	−0.0735651	−0.00316574
$541$	−28.1828	−1.21167	−0.605836	−	0.795590i	$-0.707161\pi$
$541$	−28.1828	−1.21167	−0.605836	+	0.795590i	$0.707161\pi$
$542$	8.77629	0.376974
$543$	−10.4874	−0.450055
$544$	1.31001	0.0561662
$545$	0.0356483	0.00152700
$546$	−50.0275	−2.14098
$547$	38.3248	1.63865	0.819325	−	0.573329i	$-0.194348\pi$
$547$	38.3248	1.63865	0.819325	+	0.573329i	$0.194348\pi$
$548$	−74.3349	−3.17543
$549$	−5.85339	−0.249816
$550$	12.1035	0.516094
$551$	10.7523	0.458064
$552$	−4.21387	−0.179354
$553$	16.5344	0.703115
$554$	43.2927	1.83933
$555$	0.0341565	0.00144986
$556$	40.5066	1.71786
$557$	5.60272	0.237395	0.118697	−	0.992930i	$-0.462128\pi$
$557$	5.60272	0.237395	0.118697	+	0.992930i	$0.462128\pi$
$558$	4.06149	0.171937
$559$	−3.09924	−0.131084
$560$	0.0498388	0.00210607
$561$	−1.43320	−0.0605098
$562$	−79.8659	−3.36894
$563$	17.7650	0.748706	0.374353	−	0.927286i	$-0.377865\pi$
$563$	17.7650	0.748706	0.374353	+	0.927286i	$0.377865\pi$
$564$	−24.8551	−1.04659
$565$	−0.0273405	−0.00115022
$566$	14.8618	0.624690
$567$	24.5077	1.02923
$568$	73.8329	3.09796
$569$	37.6858	1.57987	0.789936	−	0.613189i	$-0.210114\pi$
$569$	37.6858	1.57987	0.789936	+	0.613189i	$0.210114\pi$
$570$	0.0195220	0.000817688 0
$571$	41.7821	1.74852	0.874262	−	0.485454i	$-0.161346\pi$
$571$	41.7821	1.74852	0.874262	+	0.485454i	$0.161346\pi$
$572$	11.9624	0.500174
$573$	−5.30492	−0.221616
$574$	43.9663	1.83512
$575$	−3.26541	−0.136177
$576$	9.01285	0.375536
$577$	−26.7934	−1.11542	−0.557711	−	0.830035i	$-0.688320\pi$
$577$	−26.7934	−1.11542	−0.557711	+	0.830035i	$0.688320\pi$
$578$	2.42070	0.100688
$579$	6.14353	0.255316
$580$	−0.0837704	−0.00347838
$581$	25.6638	1.06471
$582$	−11.3299	−0.469641
$583$	−5.29549	−0.219317
$584$	55.7613	2.30742
$585$	−0.00988024	−0.000408498 0
$586$	14.7455	0.609131
$587$	38.8365	1.60295	0.801477	−	0.598026i	$-0.204048\pi$
$587$	38.8365	1.60295	0.801477	+	0.598026i	$0.204048\pi$
$588$	−81.0290	−3.34158
$589$	−2.96148	−0.122026
$590$	0.0273334	0.00112530
$591$	−20.8575	−0.857964
$592$	22.4764	0.923773
$593$	−17.5814	−0.721983	−0.360991	−	0.932569i	$-0.617562\pi$
$593$	−17.5814	−0.721983	−0.360991	+	0.932569i	$0.617562\pi$
$594$	−13.6898	−0.561701
$595$	−0.0156804	−0.000642833 0
$596$	75.5880	3.09620
$597$	20.3931	0.834635
$598$	−4.89964	−0.200361
$599$	30.7979	1.25837	0.629185	−	0.777256i	$-0.283389\pi$
$599$	30.7979	1.25837	0.629185	+	0.777256i	$0.283389\pi$
$600$	32.2613	1.31706
$601$	−0.256449	−0.0104608	−0.00523038	−	0.999986i	$-0.501665\pi$
$601$	−0.256449	−0.0104608	−0.00523038	+	0.999986i	$0.501665\pi$
$602$	−11.2628	−0.459038
$603$	−9.02994	−0.367728
$604$	46.1633	1.87836
$605$	−0.00337016	−0.000137017 0
$606$	53.0515	2.15507
$607$	−10.4276	−0.423242	−0.211621	−	0.977352i	$-0.567874\pi$
$607$	−10.4276	−0.423242	−0.211621	+	0.977352i	$0.567874\pi$
$608$	−2.18726	−0.0887051
$609$	42.9426	1.74012
$610$	−0.0504821	−0.00204396
$611$	−13.9251	−0.563351
$612$	3.65112	0.147588
$613$	27.9080	1.12719	0.563596	−	0.826050i	$-0.309417\pi$
$613$	27.9080	1.12719	0.563596	+	0.826050i	$0.309417\pi$
$614$	43.7866	1.76709
$615$	−0.0188552	−0.000760315 0
$616$	20.9465	0.843959
$617$	34.6786	1.39611	0.698055	−	0.716044i	$-0.254049\pi$
$617$	34.6786	1.39611	0.698055	+	0.716044i	$0.254049\pi$
$618$	44.3006	1.78203
$619$	7.99806	0.321469	0.160735	−	0.986998i	$-0.448614\pi$
$619$	7.99806	0.321469	0.160735	+	0.986998i	$0.448614\pi$
$620$	0.0230726	0.000926619 0
$621$	3.69339	0.148211
$622$	33.7678	1.35397
$623$	10.4231	0.417594
$624$	14.1180	0.565172
$625$	24.9998	0.999993
$626$	29.7714	1.18990
$627$	2.39295	0.0955652
$628$	−57.3854	−2.28993
$629$	−7.07156	−0.281962
$630$	−0.0359054	−0.00143050
$631$	−13.0325	−0.518817	−0.259409	−	0.965768i	$-0.583528\pi$
$631$	−13.0325	−0.518817	−0.259409	+	0.965768i	$0.583528\pi$
$632$	−15.9989	−0.636400
$633$	−19.0881	−0.758682
$634$	−81.7243	−3.24569
$635$	0.0391231	0.00155255
$636$	−29.2939	−1.16158
$637$	−45.3967	−1.79868
$638$	−15.5890	−0.617173
$639$	−15.5134	−0.613699
$640$	0.0689008	0.00272354
$641$	−13.1262	−0.518455	−0.259227	−	0.965816i	$-0.583468\pi$
$641$	−13.1262	−0.518455	−0.259227	+	0.965816i	$0.583468\pi$
$642$	−14.5201	−0.573064
$643$	3.02639	0.119349	0.0596747	−	0.998218i	$-0.480994\pi$
$643$	3.02639	0.119349	0.0596747	+	0.998218i	$0.480994\pi$
$644$	−11.7284	−0.462163
$645$	0.00483012	0.000190186 0
$646$	−4.04173	−0.159020
$647$	−35.3023	−1.38788	−0.693939	−	0.720034i	$-0.744126\pi$
$647$	−35.3023	−1.38788	−0.693939	+	0.720034i	$0.744126\pi$
$648$	−23.7138	−0.931568
$649$	3.35044	0.131516
$650$	37.5116	1.47132
$651$	−11.8276	−0.463559
$652$	−55.0346	−2.15532
$653$	30.3200	1.18651	0.593257	−	0.805013i	$-0.297842\pi$
$653$	30.3200	1.18651	0.593257	+	0.805013i	$0.297842\pi$
$654$	36.6975	1.43498
$655$	−0.0754243	−0.00294707
$656$	−12.4075	−0.484431
$657$	−11.7163	−0.457095
$658$	−50.6048	−1.97278
$659$	−23.3034	−0.907771	−0.453886	−	0.891060i	$-0.649963\pi$
$659$	−23.3034	−0.907771	−0.453886	+	0.891060i	$0.649963\pi$
$660$	−0.0186433	−0.000725688 0
$661$	34.6028	1.34589	0.672946	−	0.739692i	$-0.265029\pi$
$661$	34.6028	1.34589	0.672946	+	0.739692i	$0.265029\pi$
$662$	−30.7456	−1.19496
$663$	−4.44183	−0.172506
$664$	−24.8325	−0.963689
$665$	0.0261808	0.00101525
$666$	−16.1927	−0.627453
$667$	4.20576	0.162848
$668$	−3.03443	−0.117406
$669$	−17.6139	−0.680993
$670$	−0.0778780	−0.00300869
$671$	−6.18793	−0.238882
$672$	−8.73548	−0.336979
$673$	22.7540	0.877101	0.438551	−	0.898706i	$-0.355492\pi$
$673$	22.7540	0.877101	0.438551	+	0.898706i	$0.355492\pi$
$674$	22.3766	0.861915
$675$	−28.2765	−1.08836
$676$	−13.1029	−0.503959
$677$	−4.19826	−0.161352	−0.0806761	−	0.996740i	$-0.525708\pi$
$677$	−4.19826	−0.161352	−0.0806761	+	0.996740i	$0.525708\pi$
$678$	−28.1451	−1.08091
$679$	−15.1945	−0.583110
$680$	0.0151725	0.000581838 0
$681$	−11.8774	−0.455143
$682$	4.29362	0.164411
$683$	14.5718	0.557574	0.278787	−	0.960353i	$-0.410068\pi$
$683$	14.5718	0.557574	0.278787	+	0.960353i	$0.410068\pi$
$684$	−6.09610	−0.233090
$685$	0.0649052	0.00247990
$686$	−86.1346	−3.28864
$687$	−3.21166	−0.122532
$688$	3.17842	0.121176
$689$	−16.4120	−0.625246
$690$	0.00763602	0.000290698 0
$691$	35.5067	1.35074	0.675369	−	0.737480i	$-0.263984\pi$
$691$	35.5067	1.35074	0.675369	+	0.737480i	$0.263984\pi$
$692$	−31.3272	−1.19088
$693$	−4.40116	−0.167186
$694$	−22.9465	−0.871036
$695$	−0.0353682	−0.00134159
$696$	−41.5517	−1.57501
$697$	3.90367	0.147862
$698$	45.3852	1.71785
$699$	14.9226	0.564424
$700$	89.7923	3.39383
$701$	−14.5349	−0.548974	−0.274487	−	0.961591i	$-0.588508\pi$
$701$	−14.5349	−0.548974	−0.274487	+	0.961591i	$0.588508\pi$
$702$	−42.4281	−1.60134
$703$	11.8071	0.445312
$704$	9.52797	0.359099
$705$	0.0217021	0.000817349 0
$706$	−42.0445	−1.58236
$707$	71.1468	2.67575
$708$	18.5341	0.696556
$709$	10.9317	0.410548	0.205274	−	0.978705i	$-0.434191\pi$
$709$	10.9317	0.410548	0.205274	+	0.978705i	$0.434191\pi$
$710$	−0.133794	−0.00502119
$711$	3.36159	0.126069
$712$	−10.0855	−0.377971
$713$	−1.15838	−0.0433817
$714$	−16.1419	−0.604095
$715$	−0.0104449	−0.000390618 0
$716$	77.6323	2.90125
$717$	−27.1213	−1.01286
$718$	−24.0502	−0.897544
$719$	−47.8088	−1.78297	−0.891484	−	0.453051i	$-0.850335\pi$
$719$	−47.8088	−1.78297	−0.891484	+	0.453051i	$0.850335\pi$
$720$	0.0101327	0.000377622 0
$721$	59.4111	2.21259
$722$	−39.2450	−1.46055
$723$	−18.2932	−0.680330
$724$	28.2438	1.04967
$725$	−32.1992	−1.19585
$726$	−3.46935	−0.128760
$727$	6.58111	0.244080	0.122040	−	0.992525i	$-0.461056\pi$
$727$	6.58111	0.244080	0.122040	+	0.992525i	$0.461056\pi$
$728$	64.9182	2.40603
$729$	29.2982	1.08512
$730$	−0.101046	−0.00373988
$731$	−1.00000	−0.0369863
$732$	−34.2308	−1.26521
$733$	−11.8219	−0.436653	−0.218326	−	0.975876i	$-0.570060\pi$
$733$	−11.8219	−0.436653	−0.218326	+	0.975876i	$0.570060\pi$
$734$	−78.3674	−2.89259
$735$	0.0707501	0.00260966
$736$	−0.855544	−0.0315358
$737$	−9.54604	−0.351633
$738$	8.93874	0.329039
$739$	31.6473	1.16417	0.582083	−	0.813130i	$-0.302238\pi$
$739$	31.6473	1.16417	0.582083	+	0.813130i	$0.302238\pi$
$740$	−0.0919877	−0.00338154
$741$	7.41632	0.272445
$742$	−59.6421	−2.18953
$743$	−16.9663	−0.622435	−0.311217	−	0.950339i	$-0.600737\pi$
$743$	−16.9663	−0.622435	−0.311217	+	0.950339i	$0.600737\pi$
$744$	11.4445	0.419574
$745$	−0.0659993	−0.00241803
$746$	78.6064	2.87798
$747$	5.21767	0.190905
$748$	3.85979	0.141128
$749$	−19.4728	−0.711521
$750$	−0.116923	−0.00426941
$751$	−33.3407	−1.21662	−0.608310	−	0.793699i	$-0.708152\pi$
$751$	−33.3407	−1.21662	−0.608310	+	0.793699i	$0.708152\pi$
$752$	14.2809	0.520771
$753$	−17.2903	−0.630092
$754$	−48.3139	−1.75949
$755$	−0.0403073	−0.00146693
$756$	−101.561	−3.69374
$757$	29.2280	1.06231	0.531154	−	0.847275i	$-0.321758\pi$
$757$	29.2280	1.06231	0.531154	+	0.847275i	$0.321758\pi$
$758$	53.5858	1.94632
$759$	0.935999	0.0339746
$760$	−0.0253328	−0.000918917 0
$761$	−1.57659	−0.0571512	−0.0285756	−	0.999592i	$-0.509097\pi$
$761$	−1.57659	−0.0571512	−0.0285756	+	0.999592i	$0.509097\pi$
$762$	40.2746	1.45899
$763$	49.2146	1.78169
$764$	14.2868	0.516879
$765$	−0.00318796	−0.000115261 0
$766$	9.39257	0.339367
$767$	10.3838	0.374937
$768$	43.6176	1.57392
$769$	−17.5026	−0.631159	−0.315580	−	0.948899i	$-0.602199\pi$
$769$	−17.5026	−0.631159	−0.315580	+	0.948899i	$0.602199\pi$
$770$	−0.0379575	−0.00136789
$771$	10.1376	0.365096
$772$	−16.5453	−0.595479
$773$	−33.3925	−1.20105	−0.600523	−	0.799607i	$-0.705041\pi$
$773$	−33.3925	−1.20105	−0.600523	+	0.799607i	$0.705041\pi$
$774$	−2.28983	−0.0823062
$775$	8.86853	0.318567
$776$	14.7023	0.527782
$777$	47.1550	1.69168
$778$	24.7106	0.885919
$779$	−6.51778	−0.233524
$780$	−0.0577799	−0.00206885
$781$	−16.4000	−0.586838
$782$	−1.58092	−0.0565335
$783$	36.4194	1.30152
$784$	46.5565	1.66273
$785$	0.0501058	0.00178835
$786$	−77.6442	−2.76948
$787$	42.3363	1.50913	0.754563	−	0.656227i	$-0.227849\pi$
$787$	42.3363	1.50913	0.754563	+	0.656227i	$0.227849\pi$
$788$	56.1720	2.00105
$789$	−7.81296	−0.278149
$790$	0.0289918	0.00103148
$791$	−37.7452	−1.34206
$792$	4.25861	0.151323
$793$	−19.1779	−0.681026
$794$	−64.7303	−2.29719
$795$	0.0255778	0.000907152 0
$796$	−54.9213	−1.94663
$797$	48.0573	1.70228	0.851138	−	0.524942i	$-0.175913\pi$
$797$	48.0573	1.70228	0.851138	+	0.524942i	$0.175913\pi$
$798$	26.9513	0.954067
$799$	−4.49308	−0.158954
$800$	6.55003	0.231578
$801$	2.11911	0.0748751
$802$	−84.6672	−2.98970
$803$	−12.3859	−0.437089
$804$	−52.8073	−1.86237
$805$	0.0102406	0.000360933 0
$806$	13.3069	0.468717
$807$	0.796876	0.0280514
$808$	−68.8422	−2.42186
$809$	15.3168	0.538512	0.269256	−	0.963069i	$-0.413222\pi$
$809$	15.3168	0.538512	0.269256	+	0.963069i	$0.413222\pi$
$810$	0.0429722	0.00150989
$811$	30.8082	1.08182	0.540911	−	0.841080i	$-0.318079\pi$
$811$	30.8082	1.08182	0.540911	+	0.841080i	$0.318079\pi$
$812$	−115.650	−4.05852
$813$	−5.19609	−0.182235
$814$	−17.1181	−0.599990
$815$	0.0480532	0.00168323
$816$	4.55531	0.159468
$817$	1.66965	0.0584138
$818$	−69.4648	−2.42878
$819$	−13.6403	−0.476629
$820$	0.0507795	0.00177330
$821$	33.1298	1.15624	0.578118	−	0.815953i	$-0.303787\pi$
$821$	33.1298	1.15624	0.578118	+	0.815953i	$0.303787\pi$
$822$	66.8155	2.33046
$823$	−27.0510	−0.942937	−0.471468	−	0.881883i	$-0.656276\pi$
$823$	−27.0510	−0.942937	−0.471468	+	0.881883i	$0.656276\pi$
$824$	−57.4867	−2.00265
$825$	−7.16599	−0.249488
$826$	37.7354	1.31298
$827$	13.6442	0.474454	0.237227	−	0.971454i	$-0.423762\pi$
$827$	13.6442	0.474454	0.237227	+	0.971454i	$0.423762\pi$
$828$	−2.38448	−0.0828665
$829$	0.905397	0.0314457	0.0157229	−	0.999876i	$-0.494995\pi$
$829$	0.905397	0.0314457	0.0157229	+	0.999876i	$0.494995\pi$
$830$	0.0449994	0.00156195
$831$	−25.6319	−0.889159
$832$	29.5295	1.02375
$833$	−14.6477	−0.507513
$834$	−36.4091	−1.26074
$835$	0.00264950	9.16897e−5 0
$836$	−6.44452	−0.222888
$837$	−10.0309	−0.346718
$838$	−49.0230	−1.69347
$839$	−51.9197	−1.79247	−0.896233	−	0.443583i	$-0.853707\pi$
$839$	−51.9197	−1.79247	−0.896233	+	0.443583i	$0.853707\pi$
$840$	−0.101174	−0.00349084
$841$	12.4717	0.430058
$842$	44.1723	1.52228
$843$	47.2854	1.62860
$844$	51.4066	1.76949
$845$	0.0114408	0.000393574 0
$846$	−10.2884	−0.353722
$847$	−4.65271	−0.159869
$848$	16.8313	0.577988
$849$	−8.79910	−0.301984
$850$	12.1035	0.415146
$851$	4.61832	0.158314
$852$	−90.7225	−3.10810
$853$	12.9546	0.443558	0.221779	−	0.975097i	$-0.428814\pi$
$853$	12.9546	0.443558	0.221779	+	0.975097i	$0.428814\pi$
$854$	−69.6935	−2.38486
$855$	0.00532278	0.000182035 0
$856$	18.8421	0.644008
$857$	−28.7265	−0.981278	−0.490639	−	0.871363i	$-0.663237\pi$
$857$	−28.7265	−0.981278	−0.490639	+	0.871363i	$0.663237\pi$
$858$	−10.7523	−0.367079
$859$	−42.5297	−1.45110	−0.725548	−	0.688172i	$-0.758413\pi$
$859$	−42.5297	−1.45110	−0.725548	+	0.688172i	$0.758413\pi$
$860$	−0.0130081	−0.000443573 0
$861$	−26.0307	−0.887125
$862$	−29.8193	−1.01565
$863$	35.7652	1.21746	0.608730	−	0.793377i	$-0.291679\pi$
$863$	35.7652	1.21746	0.608730	+	0.793377i	$0.291679\pi$
$864$	−7.40852	−0.252043
$865$	0.0273532	0.000930036 0
$866$	84.7371	2.87948
$867$	−1.43320	−0.0486740
$868$	31.8531	1.08117
$869$	3.55372	0.120552
$870$	0.0752965	0.00255279
$871$	−29.5854	−1.00246
$872$	−47.6205	−1.61263
$873$	−3.08917	−0.104553
$874$	2.63959	0.0892854
$875$	−0.156804	−0.00530093
$876$	−68.5170	−2.31498
$877$	−41.1818	−1.39061	−0.695305	−	0.718715i	$-0.744731\pi$
$877$	−41.1818	−1.39061	−0.695305	+	0.718715i	$0.744731\pi$
$878$	−44.5892	−1.50481
$879$	−8.73022	−0.294463
$880$	0.0107118	0.000361094 0
$881$	−6.97043	−0.234840	−0.117420	−	0.993082i	$-0.537462\pi$
$881$	−6.97043	−0.234840	−0.117420	+	0.993082i	$0.537462\pi$
$882$	−33.5407	−1.12937
$883$	2.80643	0.0944440	0.0472220	−	0.998884i	$-0.484963\pi$
$883$	2.80643	0.0944440	0.0472220	+	0.998884i	$0.484963\pi$
$884$	11.9624	0.402340
$885$	−0.0161830	−0.000543986 0
$886$	−40.6342	−1.36513
$887$	−8.02323	−0.269394	−0.134697	−	0.990887i	$-0.543006\pi$
$887$	−8.02323	−0.269394	−0.134697	+	0.990887i	$0.543006\pi$
$888$	−45.6276	−1.53116
$889$	54.0118	1.81150
$890$	0.0182761	0.000612617 0
$891$	5.26740	0.176464
$892$	47.4365	1.58829
$893$	7.50190	0.251041
$894$	−67.9417	−2.27231
$895$	−0.0677843	−0.00226578
$896$	95.1216	3.17779
$897$	2.90088	0.0968577
$898$	9.98996	0.333369
$899$	−11.4224	−0.380959
$900$	18.2555	0.608518
$901$	−5.29549	−0.176418
$902$	9.44962	0.314638
$903$	6.66827	0.221906
$904$	36.5226	1.21472
$905$	−0.0246609	−0.000819757 0
$906$	−41.4936	−1.37853
$907$	31.9899	1.06221	0.531104	−	0.847307i	$-0.321778\pi$
$907$	31.9899	1.06221	0.531104	+	0.847307i	$0.321778\pi$
$908$	31.9874	1.06154
$909$	14.4648	0.479766
$910$	−0.117639	−0.00389971
$911$	−9.95945	−0.329971	−0.164986	−	0.986296i	$-0.552758\pi$
$911$	−9.95945	−0.329971	−0.164986	+	0.986296i	$0.552758\pi$
$912$	−7.60579	−0.251853
$913$	5.51588	0.182549
$914$	74.9091	2.47777
$915$	0.0298884	0.000988081 0
$916$	8.64940	0.285784
$917$	−104.128	−3.43860
$918$	−13.6898	−0.451832
$919$	37.7441	1.24506	0.622531	−	0.782595i	$-0.286104\pi$
$919$	37.7441	1.24506	0.622531	+	0.782595i	$0.286104\pi$
$920$	−0.00990889	−0.000326686 0
$921$	−25.9243	−0.854236
$922$	27.4182	0.902971
$923$	−50.8275	−1.67301
$924$	−25.7381	−0.846722
$925$	−35.3577	−1.16255
$926$	44.5928	1.46541
$927$	12.0788	0.396720
$928$	−8.43626	−0.276934
$929$	−27.1521	−0.890830	−0.445415	−	0.895324i	$-0.646944\pi$
$929$	−27.1521	−0.890830	−0.445415	+	0.895324i	$0.646944\pi$
$930$	−0.0207387	−0.000680048 0
$931$	24.4566	0.801532
$932$	−40.1884	−1.31642
$933$	−19.9926	−0.654527
$934$	−46.2243	−1.51250
$935$	−0.00337016	−0.000110216 0
$936$	13.1984	0.431404
$937$	−18.1323	−0.592357	−0.296179	−	0.955133i	$-0.595712\pi$
$937$	−18.1323	−0.592357	−0.296179	+	0.955133i	$0.595712\pi$
$938$	−107.515	−3.51050
$939$	−17.6264	−0.575217
$940$	−0.0584466	−0.00190632
$941$	−22.8385	−0.744512	−0.372256	−	0.928130i	$-0.621416\pi$
$941$	−22.8385	−0.744512	−0.372256	+	0.928130i	$0.621416\pi$
$942$	51.5805	1.68058
$943$	−2.54942	−0.0830206
$944$	−10.6491	−0.346598
$945$	0.0886775	0.00288468
$946$	−2.42070	−0.0787038
$947$	−12.0461	−0.391446	−0.195723	−	0.980659i	$-0.562705\pi$
$947$	−12.0461	−0.391446	−0.195723	+	0.980659i	$0.562705\pi$
$948$	19.6587	0.638484
$949$	−38.3868	−1.24609
$950$	−20.2086	−0.655654
$951$	48.3857	1.56901
$952$	20.9465	0.678880
$953$	−2.81368	−0.0911440	−0.0455720	−	0.998961i	$-0.514511\pi$
$953$	−2.81368	−0.0911440	−0.0455720	+	0.998961i	$0.514511\pi$
$954$	−12.1258	−0.392586
$955$	−0.0124745	−0.000403665 0
$956$	73.0411	2.36232
$957$	9.22960	0.298351
$958$	7.23059	0.233610
$959$	89.6055	2.89351
$960$	−0.0460212	−0.00148533
$961$	−27.8540	−0.898515
$962$	−53.0532	−1.71050
$963$	−3.95899	−0.127577
$964$	49.2658	1.58675
$965$	0.0144465	0.000465048 0
$966$	10.5420	0.339183
$967$	−29.9527	−0.963213	−0.481607	−	0.876388i	$-0.659947\pi$
$967$	−29.9527	−0.963213	−0.481607	+	0.876388i	$0.659947\pi$
$968$	4.50200	0.144700
$969$	2.39295	0.0768726
$970$	−0.0266423	−0.000855433 0
$971$	31.9834	1.02640	0.513198	−	0.858270i	$-0.328461\pi$
$971$	31.9834	1.02640	0.513198	+	0.858270i	$0.328461\pi$
$972$	−36.3466	−1.16582
$973$	−48.8279	−1.56535
$974$	73.9450	2.36935
$975$	−22.2091	−0.711260
$976$	19.6678	0.629552
$977$	−47.4165	−1.51699	−0.758495	−	0.651679i	$-0.774065\pi$
$977$	−47.4165	−1.51699	−0.758495	+	0.651679i	$0.774065\pi$
$978$	49.4675	1.58180
$979$	2.24023	0.0715980
$980$	−0.190539	−0.00608655
$981$	10.0058	0.319459
$982$	30.9251	0.986859
$983$	31.6488	1.00944	0.504719	−	0.863283i	$-0.331596\pi$
$983$	31.6488	1.00944	0.504719	+	0.863283i	$0.331596\pi$
$984$	25.1876	0.802950
$985$	−0.0490463	−0.00156275
$986$	−15.5890	−0.496453
$987$	29.9611	0.953672
$988$	−19.9731	−0.635429
$989$	0.653083	0.0207668
$990$	−0.00771709	−0.000245265 0
$991$	35.2906	1.12104	0.560522	−	0.828140i	$-0.310601\pi$
$991$	35.2906	1.12104	0.560522	+	0.828140i	$0.310601\pi$
$992$	2.32357	0.0737736
$993$	18.2032	0.577663
$994$	−184.710	−5.85865
$995$	0.0479543	0.00152025
$996$	30.5131	0.966844
$997$	60.2902	1.90941	0.954704	−	0.297557i	$-0.0961717\pi$
$997$	60.2902	1.90941	0.954704	+	0.297557i	$0.0961717\pi$
$998$	33.4242	1.05802
$999$	39.9919	1.26529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.61	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.61	✓	66	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q+2.42070 q^{2} -1.43320 q^{3} +3.85979 q^{4} -0.00337016 q^{5} -3.46935 q^{6} -4.65271 q^{7} +4.50200 q^{8} -0.945936 q^{9} +O(q^{10})\)	\(q+2.42070 q^{2} -1.43320 q^{3} +3.85979 q^{4} -0.00337016 q^{5} -3.46935 q^{6} -4.65271 q^{7} +4.50200 q^{8} -0.945936 q^{9} -0.00815815 q^{10} -1.00000 q^{11} -5.53186 q^{12} -3.09924 q^{13} -11.2628 q^{14} +0.00483012 q^{15} +3.17842 q^{16} -1.00000 q^{17} -2.28983 q^{18} +1.66965 q^{19} -0.0130081 q^{20} +6.66827 q^{21} -2.42070 q^{22} +0.653083 q^{23} -6.45227 q^{24} -4.99999 q^{25} -7.50233 q^{26} +5.65532 q^{27} -17.9585 q^{28} +6.43985 q^{29} +0.0116923 q^{30} -1.77371 q^{31} -1.31001 q^{32} +1.43320 q^{33} -2.42070 q^{34} +0.0156804 q^{35} -3.65112 q^{36} +7.07156 q^{37} +4.04173 q^{38} +4.44183 q^{39} -0.0151725 q^{40} -3.90367 q^{41} +16.1419 q^{42} +1.00000 q^{43} -3.85979 q^{44} +0.00318796 q^{45} +1.58092 q^{46} +4.49308 q^{47} -4.55531 q^{48} +14.6477 q^{49} -12.1035 q^{50} +1.43320 q^{51} -11.9624 q^{52} +5.29549 q^{53} +13.6898 q^{54} +0.00337016 q^{55} -20.9465 q^{56} -2.39295 q^{57} +15.5890 q^{58} -3.35044 q^{59} +0.0186433 q^{60} +6.18793 q^{61} -4.29362 q^{62} +4.40116 q^{63} -9.52797 q^{64} +0.0104449 q^{65} +3.46935 q^{66} +9.54604 q^{67} -3.85979 q^{68} -0.935999 q^{69} +0.0379575 q^{70} +16.4000 q^{71} -4.25861 q^{72} +12.3859 q^{73} +17.1181 q^{74} +7.16599 q^{75} +6.44452 q^{76} +4.65271 q^{77} +10.7523 q^{78} -3.55372 q^{79} -0.0107118 q^{80} -5.26740 q^{81} -9.44962 q^{82} -5.51588 q^{83} +25.7381 q^{84} +0.00337016 q^{85} +2.42070 q^{86} -9.22960 q^{87} -4.50200 q^{88} -2.24023 q^{89} +0.00771709 q^{90} +14.4199 q^{91} +2.52077 q^{92} +2.54208 q^{93} +10.8764 q^{94} -0.00562700 q^{95} +1.87751 q^{96} +3.26573 q^{97} +35.4577 q^{98} +0.945936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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