LMFDB - Embedded newform 8041.2.a.f.1.15

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			1.15
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)

$f(q)$	$=$	$q-1.63713 q^{2} +2.43295 q^{3} +0.680210 q^{4} -0.845755 q^{5} -3.98306 q^{6} -3.87420 q^{7} +2.16067 q^{8} +2.91923 q^{9} +O(q^{10})$	\(q-1.63713 q^{2} +2.43295 q^{3} +0.680210 q^{4} -0.845755 q^{5} -3.98306 q^{6} -3.87420 q^{7} +2.16067 q^{8} +2.91923 q^{9} +1.38461 q^{10} -1.00000 q^{11} +1.65492 q^{12} -2.62064 q^{13} +6.34259 q^{14} -2.05768 q^{15} -4.89773 q^{16} +1.00000 q^{17} -4.77917 q^{18} -2.62181 q^{19} -0.575291 q^{20} -9.42572 q^{21} +1.63713 q^{22} -3.95001 q^{23} +5.25680 q^{24} -4.28470 q^{25} +4.29034 q^{26} -0.196510 q^{27} -2.63527 q^{28} +1.71401 q^{29} +3.36869 q^{30} -2.45103 q^{31} +3.69690 q^{32} -2.43295 q^{33} -1.63713 q^{34} +3.27662 q^{35} +1.98569 q^{36} +4.87562 q^{37} +4.29225 q^{38} -6.37588 q^{39} -1.82740 q^{40} -1.86636 q^{41} +15.4312 q^{42} -1.00000 q^{43} -0.680210 q^{44} -2.46895 q^{45} +6.46670 q^{46} -11.0548 q^{47} -11.9159 q^{48} +8.00943 q^{49} +7.01463 q^{50} +2.43295 q^{51} -1.78259 q^{52} +7.48366 q^{53} +0.321713 q^{54} +0.845755 q^{55} -8.37088 q^{56} -6.37872 q^{57} -2.80606 q^{58} -10.9808 q^{59} -1.39965 q^{60} +6.67652 q^{61} +4.01266 q^{62} -11.3097 q^{63} +3.74314 q^{64} +2.21642 q^{65} +3.98306 q^{66} +1.15871 q^{67} +0.680210 q^{68} -9.61016 q^{69} -5.36427 q^{70} +0.0350989 q^{71} +6.30750 q^{72} -1.20775 q^{73} -7.98204 q^{74} -10.4244 q^{75} -1.78338 q^{76} +3.87420 q^{77} +10.4382 q^{78} +13.2678 q^{79} +4.14228 q^{80} -9.23579 q^{81} +3.05548 q^{82} +14.7537 q^{83} -6.41147 q^{84} -0.845755 q^{85} +1.63713 q^{86} +4.17009 q^{87} -2.16067 q^{88} +6.13613 q^{89} +4.04201 q^{90} +10.1529 q^{91} -2.68684 q^{92} -5.96321 q^{93} +18.0983 q^{94} +2.21741 q^{95} +8.99437 q^{96} +2.18890 q^{97} -13.1125 q^{98} -2.91923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) $ 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * 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 $

$2$	−1.63713	−1.15763	−0.578815	−	0.815459i	$-0.696484\pi$
$2$	−1.63713	−1.15763	−0.578815	+	0.815459i	$0.696484\pi$
$3$	2.43295	1.40466	0.702331	−	0.711850i	$-0.252143\pi$
$3$	2.43295	1.40466	0.702331	+	0.711850i	$0.252143\pi$
$4$	0.680210	0.340105
$5$	−0.845755	−0.378233	−0.189117	−	0.981955i	$-0.560562\pi$
$5$	−0.845755	−0.378233	−0.189117	+	0.981955i	$0.560562\pi$
$6$	−3.98306	−1.62608
$7$	−3.87420	−1.46431	−0.732155	−	0.681138i	$-0.761485\pi$
$7$	−3.87420	−1.46431	−0.732155	+	0.681138i	$0.761485\pi$
$8$	2.16067	0.763913
$9$	2.91923	0.973077
$10$	1.38461	0.437854
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.65492	0.477733
$13$	−2.62064	−0.726835	−0.363418	−	0.931626i	$-0.618390\pi$
$13$	−2.62064	−0.726835	−0.363418	+	0.931626i	$0.618390\pi$
$14$	6.34259	1.69513
$15$	−2.05768	−0.531290
$16$	−4.89773	−1.22443
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−4.77917	−1.12646
$19$	−2.62181	−0.601484	−0.300742	−	0.953706i	$-0.597234\pi$
$19$	−2.62181	−0.601484	−0.300742	+	0.953706i	$0.597234\pi$
$20$	−0.575291	−0.128639
$21$	−9.42572	−2.05686
$22$	1.63713	0.349038
$23$	−3.95001	−0.823634	−0.411817	−	0.911267i	$-0.635106\pi$
$23$	−3.95001	−0.823634	−0.411817	+	0.911267i	$0.635106\pi$
$24$	5.25680	1.07304
$25$	−4.28470	−0.856940
$26$	4.29034	0.841406
$27$	−0.196510	−0.0378183
$28$	−2.63527	−0.498019
$29$	1.71401	0.318284	0.159142	−	0.987256i	$-0.449127\pi$
$29$	1.71401	0.318284	0.159142	+	0.987256i	$0.449127\pi$
$30$	3.36869	0.615037
$31$	−2.45103	−0.440217	−0.220109	−	0.975475i	$-0.570641\pi$
$31$	−2.45103	−0.440217	−0.220109	+	0.975475i	$0.570641\pi$
$32$	3.69690	0.653527
$33$	−2.43295	−0.423522
$34$	−1.63713	−0.280766
$35$	3.27662	0.553851
$36$	1.98569	0.330948
$37$	4.87562	0.801547	0.400773	−	0.916177i	$-0.368741\pi$
$37$	4.87562	0.801547	0.400773	+	0.916177i	$0.368741\pi$
$38$	4.29225	0.696296
$39$	−6.37588	−1.02096
$40$	−1.82740	−0.288937
$41$	−1.86636	−0.291476	−0.145738	−	0.989323i	$-0.546556\pi$
$41$	−1.86636	−0.291476	−0.145738	+	0.989323i	$0.546556\pi$
$42$	15.4312	2.38108
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−0.680210	−0.102546
$45$	−2.46895	−0.368050
$46$	6.46670	0.953463
$47$	−11.0548	−1.61251	−0.806257	−	0.591566i	$-0.798510\pi$
$47$	−11.0548	−1.61251	−0.806257	+	0.591566i	$0.798510\pi$
$48$	−11.9159	−1.71992
$49$	8.00943	1.14420
$50$	7.01463	0.992018
$51$	2.43295	0.340681
$52$	−1.78259	−0.247200
$53$	7.48366	1.02796	0.513980	−	0.857802i	$-0.328171\pi$
$53$	7.48366	1.02796	0.513980	+	0.857802i	$0.328171\pi$
$54$	0.321713	0.0437796
$55$	0.845755	0.114042
$56$	−8.37088	−1.11861
$57$	−6.37872	−0.844882
$58$	−2.80606	−0.368454
$59$	−10.9808	−1.42958	−0.714791	−	0.699339i	$-0.753478\pi$
$59$	−10.9808	−1.42958	−0.714791	+	0.699339i	$0.753478\pi$
$60$	−1.39965	−0.180694
$61$	6.67652	0.854841	0.427420	−	0.904053i	$-0.359422\pi$
$61$	6.67652	0.854841	0.427420	+	0.904053i	$0.359422\pi$
$62$	4.01266	0.509608
$63$	−11.3097	−1.42489
$64$	3.74314	0.467892
$65$	2.21642	0.274913
$66$	3.98306	0.490281
$67$	1.15871	0.141559	0.0707795	−	0.997492i	$-0.477451\pi$
$67$	1.15871	0.141559	0.0707795	+	0.997492i	$0.477451\pi$
$68$	0.680210	0.0824876
$69$	−9.61016	−1.15693
$70$	−5.36427	−0.641153
$71$	0.0350989	0.00416547	0.00208274	−	0.999998i	$-0.499337\pi$
$71$	0.0350989	0.00416547	0.00208274	+	0.999998i	$0.499337\pi$
$72$	6.30750	0.743346
$73$	−1.20775	−0.141356	−0.0706781	−	0.997499i	$-0.522516\pi$
$73$	−1.20775	−0.141356	−0.0706781	+	0.997499i	$0.522516\pi$
$74$	−7.98204	−0.927894
$75$	−10.4244	−1.20371
$76$	−1.78338	−0.204568
$77$	3.87420	0.441506
$78$	10.4382	1.18189
$79$	13.2678	1.49274	0.746371	−	0.665530i	$-0.231794\pi$
$79$	13.2678	1.49274	0.746371	+	0.665530i	$0.231794\pi$
$80$	4.14228	0.463121
$81$	−9.23579	−1.02620
$82$	3.05548	0.337422
$83$	14.7537	1.61943	0.809713	−	0.586827i	$-0.199623\pi$
$83$	14.7537	1.61943	0.809713	+	0.586827i	$0.199623\pi$
$84$	−6.41147	−0.699549
$85$	−0.845755	−0.0917350
$86$	1.63713	0.176537
$87$	4.17009	0.447081
$88$	−2.16067	−0.230329
$89$	6.13613	0.650429	0.325214	−	0.945640i	$-0.394564\pi$
$89$	6.13613	0.650429	0.325214	+	0.945640i	$0.394564\pi$
$90$	4.04201	0.426065
$91$	10.1529	1.06431
$92$	−2.68684	−0.280122
$93$	−5.96321	−0.618357
$94$	18.0983	1.86669
$95$	2.21741	0.227501
$96$	8.99437	0.917984
$97$	2.18890	0.222249	0.111125	−	0.993806i	$-0.464555\pi$
$97$	2.18890	0.222249	0.111125	+	0.993806i	$0.464555\pi$
$98$	−13.1125	−1.32456
$99$	−2.91923	−0.293394
$100$	−2.91450	−0.291450
$101$	−9.91588	−0.986667	−0.493333	−	0.869840i	$-0.664222\pi$
$101$	−9.91588	−0.986667	−0.493333	+	0.869840i	$0.664222\pi$
$102$	−3.98306	−0.394382
$103$	8.63342	0.850676	0.425338	−	0.905035i	$-0.360155\pi$
$103$	8.63342	0.850676	0.425338	+	0.905035i	$0.360155\pi$
$104$	−5.66235	−0.555239
$105$	7.97185	0.777973
$106$	−12.2518	−1.19000
$107$	−5.62942	−0.544217	−0.272108	−	0.962267i	$-0.587721\pi$
$107$	−5.62942	−0.544217	−0.272108	+	0.962267i	$0.587721\pi$
$108$	−0.133668	−0.0128622
$109$	17.8720	1.71182	0.855912	−	0.517121i	$-0.172996\pi$
$109$	17.8720	1.71182	0.855912	+	0.517121i	$0.172996\pi$
$110$	−1.38461	−0.132018
$111$	11.8621	1.12590
$112$	18.9748	1.79295
$113$	−10.8897	−1.02441	−0.512206	−	0.858863i	$-0.671172\pi$
$113$	−10.8897	−1.02441	−0.512206	+	0.858863i	$0.671172\pi$
$114$	10.4428	0.978060
$115$	3.34074	0.311526
$116$	1.16589	0.108250
$117$	−7.65026	−0.707266
$118$	17.9771	1.65492
$119$	−3.87420	−0.355147
$120$	−4.44597	−0.405859
$121$	1.00000	0.0909091
$122$	−10.9304	−0.989588
$123$	−4.54075	−0.409426
$124$	−1.66721	−0.149720
$125$	7.85258	0.702356
$126$	18.5155	1.64949
$127$	2.49379	0.221288	0.110644	−	0.993860i	$-0.464709\pi$
$127$	2.49379	0.221288	0.110644	+	0.993860i	$0.464709\pi$
$128$	−13.5218	−1.19517
$129$	−2.43295	−0.214209
$130$	−3.62858	−0.318247
$131$	−9.33054	−0.815213	−0.407607	−	0.913158i	$-0.633636\pi$
$131$	−9.33054	−0.815213	−0.407607	+	0.913158i	$0.633636\pi$
$132$	−1.65492	−0.144042
$133$	10.1574	0.880759
$134$	−1.89696	−0.163873
$135$	0.166199	0.0143041
$136$	2.16067	0.185276
$137$	12.6923	1.08437	0.542187	−	0.840258i	$-0.317597\pi$
$137$	12.6923	1.08437	0.542187	+	0.840258i	$0.317597\pi$
$138$	15.7331	1.33929
$139$	1.59703	0.135459	0.0677293	−	0.997704i	$-0.478425\pi$
$139$	1.59703	0.135459	0.0677293	+	0.997704i	$0.478425\pi$
$140$	2.22879	0.188367
$141$	−26.8958	−2.26504
$142$	−0.0574616	−0.00482207
$143$	2.62064	0.219149
$144$	−14.2976	−1.19147
$145$	−1.44963	−0.120385
$146$	1.97725	0.163638
$147$	19.4865	1.60722
$148$	3.31645	0.272610
$149$	−9.81765	−0.804293	−0.402147	−	0.915575i	$-0.631736\pi$
$149$	−9.81765	−0.804293	−0.402147	+	0.915575i	$0.631736\pi$
$150$	17.0662	1.39345
$151$	16.9882	1.38248	0.691240	−	0.722625i	$-0.257065\pi$
$151$	16.9882	1.38248	0.691240	+	0.722625i	$0.257065\pi$
$152$	−5.66487	−0.459482
$153$	2.91923	0.236006
$154$	−6.34259	−0.511100
$155$	2.07297	0.166505
$156$	−4.33694	−0.347233
$157$	−15.6665	−1.25032	−0.625160	−	0.780497i	$-0.714966\pi$
$157$	−15.6665	−1.25032	−0.625160	+	0.780497i	$0.714966\pi$
$158$	−21.7211	−1.72804
$159$	18.2074	1.44394
$160$	−3.12667	−0.247185
$161$	15.3031	1.20606
$162$	15.1202	1.18796
$163$	6.37042	0.498970	0.249485	−	0.968379i	$-0.419739\pi$
$163$	6.37042	0.498970	0.249485	+	0.968379i	$0.419739\pi$
$164$	−1.26952	−0.0991326
$165$	2.05768	0.160190
$166$	−24.1537	−1.87469
$167$	17.4873	1.35321	0.676605	−	0.736346i	$-0.263450\pi$
$167$	17.4873	1.35321	0.676605	+	0.736346i	$0.263450\pi$
$168$	−20.3659	−1.57126
$169$	−6.13224	−0.471711
$170$	1.38461	0.106195
$171$	−7.65366	−0.585290
$172$	−0.680210	−0.0518655
$173$	3.90226	0.296683	0.148342	−	0.988936i	$-0.452607\pi$
$173$	3.90226	0.296683	0.148342	+	0.988936i	$0.452607\pi$
$174$	−6.82700	−0.517554
$175$	16.5998	1.25483
$176$	4.89773	0.369181
$177$	−26.7158	−2.00808
$178$	−10.0457	−0.752955
$179$	1.74368	0.130329	0.0651643	−	0.997875i	$-0.479243\pi$
$179$	1.74368	0.130329	0.0651643	+	0.997875i	$0.479243\pi$
$180$	−1.67941	−0.125176
$181$	−24.8846	−1.84965	−0.924827	−	0.380387i	$-0.875791\pi$
$181$	−24.8846	−1.84965	−0.924827	+	0.380387i	$0.875791\pi$
$182$	−16.6217	−1.23208
$183$	16.2436	1.20076
$184$	−8.53468	−0.629185
$185$	−4.12358	−0.303171
$186$	9.76259	0.715828
$187$	−1.00000	−0.0731272
$188$	−7.51961	−0.548424
$189$	0.761318	0.0553777
$190$	−3.63019	−0.263362
$191$	19.8240	1.43441	0.717207	−	0.696860i	$-0.245420\pi$
$191$	19.8240	1.43441	0.717207	+	0.696860i	$0.245420\pi$
$192$	9.10686	0.657231
$193$	−1.79519	−0.129221	−0.0646104	−	0.997911i	$-0.520580\pi$
$193$	−1.79519	−0.129221	−0.0646104	+	0.997911i	$0.520580\pi$
$194$	−3.58352	−0.257282
$195$	5.39243	0.386160
$196$	5.44810	0.389150
$197$	−17.3346	−1.23504	−0.617521	−	0.786554i	$-0.711863\pi$
$197$	−17.3346	−1.23504	−0.617521	+	0.786554i	$0.711863\pi$
$198$	4.77917	0.339641
$199$	−3.69735	−0.262098	−0.131049	−	0.991376i	$-0.541835\pi$
$199$	−3.69735	−0.262098	−0.131049	+	0.991376i	$0.541835\pi$
$200$	−9.25784	−0.654628
$201$	2.81908	0.198843
$202$	16.2336	1.14219
$203$	−6.64041	−0.466066
$204$	1.65492	0.115867
$205$	1.57848	0.110246
$206$	−14.1341	−0.984768
$207$	−11.5310	−0.801459
$208$	12.8352	0.889962
$209$	2.62181	0.181354
$210$	−13.0510	−0.900604
$211$	−10.1171	−0.696491	−0.348245	−	0.937403i	$-0.613222\pi$
$211$	−10.1171	−0.696491	−0.348245	+	0.937403i	$0.613222\pi$
$212$	5.09046	0.349615
$213$	0.0853938	0.00585109
$214$	9.21612	0.630001
$215$	0.845755	0.0576800
$216$	−0.424593	−0.0288899
$217$	9.49576	0.644614
$218$	−29.2588	−1.98166
$219$	−2.93838	−0.198558
$220$	0.575291	0.0387861
$221$	−2.62064	−0.176283
$222$	−19.4199	−1.30338
$223$	−7.69486	−0.515286	−0.257643	−	0.966240i	$-0.582946\pi$
$223$	−7.69486	−0.515286	−0.257643	+	0.966240i	$0.582946\pi$
$224$	−14.3225	−0.956965
$225$	−12.5080	−0.833868
$226$	17.8278	1.18589
$227$	16.4146	1.08948	0.544738	−	0.838606i	$-0.316629\pi$
$227$	16.4146	1.08948	0.544738	+	0.838606i	$0.316629\pi$
$228$	−4.33887	−0.287349
$229$	−6.46419	−0.427166	−0.213583	−	0.976925i	$-0.568513\pi$
$229$	−6.46419	−0.427166	−0.213583	+	0.976925i	$0.568513\pi$
$230$	−5.46924	−0.360631
$231$	9.42572	0.620167
$232$	3.70341	0.243141
$233$	−29.0628	−1.90397	−0.951984	−	0.306147i	$-0.900960\pi$
$233$	−29.0628	−1.90397	−0.951984	+	0.306147i	$0.900960\pi$
$234$	12.5245	0.818752
$235$	9.34968	0.609906
$236$	−7.46927	−0.486208
$237$	32.2798	2.09680
$238$	6.34259	0.411129
$239$	20.7937	1.34504	0.672518	−	0.740081i	$-0.265213\pi$
$239$	20.7937	1.34504	0.672518	+	0.740081i	$0.265213\pi$
$240$	10.0780	0.650529
$241$	−0.551022	−0.0354944	−0.0177472	−	0.999843i	$-0.505649\pi$
$241$	−0.551022	−0.0354944	−0.0177472	+	0.999843i	$0.505649\pi$
$242$	−1.63713	−0.105239
$243$	−21.8806	−1.40364
$244$	4.54144	0.290736
$245$	−6.77401	−0.432776
$246$	7.43383	0.473963
$247$	6.87082	0.437180
$248$	−5.29587	−0.336288
$249$	35.8949	2.27475
$250$	−12.8557	−0.813068
$251$	10.2710	0.648297	0.324149	−	0.946006i	$-0.394922\pi$
$251$	10.2710	0.648297	0.324149	+	0.946006i	$0.394922\pi$
$252$	−7.69296	−0.484611
$253$	3.95001	0.248335
$254$	−4.08267	−0.256170
$255$	−2.05768	−0.128857
$256$	14.6508	0.915674
$257$	6.71762	0.419034	0.209517	−	0.977805i	$-0.432811\pi$
$257$	6.71762	0.419034	0.209517	+	0.977805i	$0.432811\pi$
$258$	3.98306	0.247975
$259$	−18.8891	−1.17371
$260$	1.50763	0.0934994
$261$	5.00359	0.309714
$262$	15.2754	0.943714
$263$	−20.6438	−1.27295	−0.636475	−	0.771297i	$-0.719608\pi$
$263$	−20.6438	−1.27295	−0.636475	+	0.771297i	$0.719608\pi$
$264$	−5.25680	−0.323534
$265$	−6.32934	−0.388809
$266$	−16.6291	−1.01959
$267$	14.9289	0.913633
$268$	0.788167	0.0481449
$269$	−5.55172	−0.338495	−0.169247	−	0.985574i	$-0.554134\pi$
$269$	−5.55172	−0.338495	−0.169247	+	0.985574i	$0.554134\pi$
$270$	−0.272090	−0.0165589
$271$	24.5539	1.49154	0.745771	−	0.666202i	$-0.232081\pi$
$271$	24.5539	1.49154	0.745771	+	0.666202i	$0.232081\pi$
$272$	−4.89773	−0.296969
$273$	24.7014	1.49500
$274$	−20.7789	−1.25530
$275$	4.28470	0.258377
$276$	−6.53693	−0.393477
$277$	−10.4075	−0.625323	−0.312662	−	0.949865i	$-0.601221\pi$
$277$	−10.4075	−0.625323	−0.312662	+	0.949865i	$0.601221\pi$
$278$	−2.61456	−0.156811
$279$	−7.15511	−0.428365
$280$	7.07971	0.423094
$281$	29.2867	1.74710	0.873549	−	0.486736i	$-0.161813\pi$
$281$	29.2867	1.74710	0.873549	+	0.486736i	$0.161813\pi$
$282$	44.0321	2.62207
$283$	10.8379	0.644249	0.322124	−	0.946697i	$-0.395603\pi$
$283$	10.8379	0.644249	0.322124	+	0.946697i	$0.395603\pi$
$284$	0.0238746	0.00141670
$285$	5.39483	0.319562
$286$	−4.29034	−0.253693
$287$	7.23065	0.426812
$288$	10.7921	0.635931
$289$	1.00000	0.0588235
$290$	2.37324	0.139362
$291$	5.32548	0.312185
$292$	−0.821522	−0.0480759
$293$	26.7147	1.56069	0.780345	−	0.625350i	$-0.215044\pi$
$293$	26.7147	1.56069	0.780345	+	0.625350i	$0.215044\pi$
$294$	−31.9020	−1.86057
$295$	9.28708	0.540715
$296$	10.5346	0.612312
$297$	0.196510	0.0114027
$298$	16.0728	0.931073
$299$	10.3516	0.598646
$300$	−7.09081	−0.409388
$301$	3.87420	0.223305
$302$	−27.8120	−1.60040
$303$	−24.1248	−1.38593
$304$	12.8409	0.736477
$305$	−5.64670	−0.323329
$306$	−4.77917	−0.273207
$307$	16.8328	0.960696	0.480348	−	0.877078i	$-0.340510\pi$
$307$	16.8328	0.960696	0.480348	+	0.877078i	$0.340510\pi$
$308$	2.63527	0.150158
$309$	21.0047	1.19491
$310$	−3.39373	−0.192751
$311$	−15.9737	−0.905784	−0.452892	−	0.891565i	$-0.649608\pi$
$311$	−15.9737	−0.905784	−0.452892	+	0.891565i	$0.649608\pi$
$312$	−13.7762	−0.779924
$313$	−0.0916412	−0.00517987	−0.00258993	−	0.999997i	$-0.500824\pi$
$313$	−0.0916412	−0.00517987	−0.00258993	+	0.999997i	$0.500824\pi$
$314$	25.6481	1.44741
$315$	9.56522	0.538939
$316$	9.02488	0.507689
$317$	12.2892	0.690230	0.345115	−	0.938560i	$-0.387840\pi$
$317$	12.2892	0.690230	0.345115	+	0.938560i	$0.387840\pi$
$318$	−29.8079	−1.67154
$319$	−1.71401	−0.0959661
$320$	−3.16578	−0.176972
$321$	−13.6961	−0.764441
$322$	−25.0533	−1.39617
$323$	−2.62181	−0.145881
$324$	−6.28228	−0.349015
$325$	11.2287	0.622854
$326$	−10.4292	−0.577622
$327$	43.4816	2.40454
$328$	−4.03259	−0.222663
$329$	42.8286	2.36122
$330$	−3.36869	−0.185440
$331$	−0.777632	−0.0427425	−0.0213713	−	0.999772i	$-0.506803\pi$
$331$	−0.777632	−0.0427425	−0.0213713	+	0.999772i	$0.506803\pi$
$332$	10.0356	0.550775
$333$	14.2330	0.779966
$334$	−28.6291	−1.56652
$335$	−0.979985	−0.0535423
$336$	46.1647	2.51849
$337$	15.9165	0.867029	0.433514	−	0.901147i	$-0.357273\pi$
$337$	15.9165	0.867029	0.433514	+	0.901147i	$0.357273\pi$
$338$	10.0393	0.546066
$339$	−26.4939	−1.43895
$340$	−0.575291	−0.0311995
$341$	2.45103	0.132730
$342$	12.5301	0.677549
$343$	−3.91073	−0.211159
$344$	−2.16067	−0.116496
$345$	8.12784	0.437588
$346$	−6.38852	−0.343449
$347$	27.0736	1.45339	0.726694	−	0.686961i	$-0.241056\pi$
$347$	27.0736	1.45339	0.726694	+	0.686961i	$0.241056\pi$
$348$	2.83654	0.152055
$349$	14.2785	0.764309	0.382154	−	0.924098i	$-0.375182\pi$
$349$	14.2785	0.764309	0.382154	+	0.924098i	$0.375182\pi$
$350$	−27.1761	−1.45262
$351$	0.514982	0.0274877
$352$	−3.69690	−0.197046
$353$	−14.9611	−0.796300	−0.398150	−	0.917320i	$-0.630348\pi$
$353$	−14.9611	−0.796300	−0.398150	+	0.917320i	$0.630348\pi$
$354$	43.7373	2.32461
$355$	−0.0296851	−0.00157552
$356$	4.17386	0.221214
$357$	−9.42572	−0.498862
$358$	−2.85464	−0.150872
$359$	10.5818	0.558489	0.279244	−	0.960220i	$-0.409916\pi$
$359$	10.5818	0.558489	0.279244	+	0.960220i	$0.409916\pi$
$360$	−5.33460	−0.281158
$361$	−12.1261	−0.638217
$362$	40.7394	2.14121
$363$	2.43295	0.127697
$364$	6.90610	0.361978
$365$	1.02146	0.0534656
$366$	−26.5930	−1.39004
$367$	23.8293	1.24388	0.621940	−	0.783065i	$-0.286345\pi$
$367$	23.8293	1.24388	0.621940	+	0.783065i	$0.286345\pi$
$368$	19.3461	1.00849
$369$	−5.44833	−0.283629
$370$	6.75085	0.350960
$371$	−28.9932	−1.50525
$372$	−4.05624	−0.210306
$373$	−17.0676	−0.883728	−0.441864	−	0.897082i	$-0.645683\pi$
$373$	−17.0676	−0.883728	−0.441864	+	0.897082i	$0.645683\pi$
$374$	1.63713	0.0846542
$375$	19.1049	0.986573
$376$	−23.8859	−1.23182
$377$	−4.49180	−0.231340
$378$	−1.24638	−0.0641069
$379$	−24.8816	−1.27808	−0.639041	−	0.769173i	$-0.720669\pi$
$379$	−24.8816	−1.27808	−0.639041	+	0.769173i	$0.720669\pi$
$380$	1.50830	0.0773743
$381$	6.06726	0.310835
$382$	−32.4545	−1.66052
$383$	−9.58495	−0.489768	−0.244884	−	0.969552i	$-0.578750\pi$
$383$	−9.58495	−0.489768	−0.244884	+	0.969552i	$0.578750\pi$
$384$	−32.8979	−1.67881
$385$	−3.27662	−0.166992
$386$	2.93897	0.149590
$387$	−2.91923	−0.148393
$388$	1.48891	0.0755881
$389$	25.4411	1.28992	0.644958	−	0.764218i	$-0.276875\pi$
$389$	25.4411	1.28992	0.644958	+	0.764218i	$0.276875\pi$
$390$	−8.82814	−0.447030
$391$	−3.95001	−0.199761
$392$	17.3058	0.874073
$393$	−22.7007	−1.14510
$394$	28.3792	1.42972
$395$	−11.2213	−0.564604
$396$	−1.98569	−0.0997847
$397$	32.3934	1.62578	0.812890	−	0.582417i	$-0.197893\pi$
$397$	32.3934	1.62578	0.812890	+	0.582417i	$0.197893\pi$
$398$	6.05306	0.303413
$399$	24.7124	1.23717
$400$	20.9853	1.04927
$401$	−1.54876	−0.0773411	−0.0386706	−	0.999252i	$-0.512312\pi$
$401$	−1.54876	−0.0773411	−0.0386706	+	0.999252i	$0.512312\pi$
$402$	−4.61521	−0.230186
$403$	6.42326	0.319965
$404$	−6.74488	−0.335570
$405$	7.81121	0.388142
$406$	10.8713	0.539531
$407$	−4.87562	−0.241675
$408$	5.25680	0.260251
$409$	−28.6654	−1.41741	−0.708706	−	0.705504i	$-0.750721\pi$
$409$	−28.6654	−1.41741	−0.708706	+	0.705504i	$0.750721\pi$
$410$	−2.58419	−0.127624
$411$	30.8796	1.52318
$412$	5.87254	0.289319
$413$	42.5419	2.09335
$414$	18.8778	0.927792
$415$	−12.4780	−0.612520
$416$	−9.68826	−0.475006
$417$	3.88550	0.190274
$418$	−4.29225	−0.209941
$419$	15.0051	0.733045	0.366522	−	0.930409i	$-0.380548\pi$
$419$	15.0051	0.733045	0.366522	+	0.930409i	$0.380548\pi$
$420$	5.42254	0.264593
$421$	−14.8129	−0.721934	−0.360967	−	0.932579i	$-0.617553\pi$
$421$	−14.8129	−0.721934	−0.360967	+	0.932579i	$0.617553\pi$
$422$	16.5631	0.806278
$423$	−32.2716	−1.56910
$424$	16.1698	0.785273
$425$	−4.28470	−0.207838
$426$	−0.139801	−0.00677339
$427$	−25.8662	−1.25175
$428$	−3.82919	−0.185091
$429$	6.37588	0.307830
$430$	−1.38461	−0.0667721
$431$	35.7660	1.72279	0.861393	−	0.507939i	$-0.169593\pi$
$431$	35.7660	1.72279	0.861393	+	0.507939i	$0.169593\pi$
$432$	0.962453	0.0463060
$433$	6.88559	0.330900	0.165450	−	0.986218i	$-0.447092\pi$
$433$	6.88559	0.330900	0.165450	+	0.986218i	$0.447092\pi$
$434$	−15.5458	−0.746224
$435$	−3.52688	−0.169101
$436$	12.1567	0.582200
$437$	10.3562	0.495403
$438$	4.81053	0.229856
$439$	22.1009	1.05482	0.527409	−	0.849612i	$-0.323164\pi$
$439$	22.1009	1.05482	0.527409	+	0.849612i	$0.323164\pi$
$440$	1.82740	0.0871179
$441$	23.3814	1.11340
$442$	4.29034	0.204071
$443$	−16.0866	−0.764296	−0.382148	−	0.924101i	$-0.624815\pi$
$443$	−16.0866	−0.764296	−0.382148	+	0.924101i	$0.624815\pi$
$444$	8.06874	0.382925
$445$	−5.18966	−0.246014
$446$	12.5975	0.596510
$447$	−23.8858	−1.12976
$448$	−14.5017	−0.685139
$449$	31.6324	1.49282	0.746412	−	0.665484i	$-0.231775\pi$
$449$	31.6324	1.49282	0.746412	+	0.665484i	$0.231775\pi$
$450$	20.4773	0.965310
$451$	1.86636	0.0878834
$452$	−7.40725	−0.348408
$453$	41.3314	1.94192
$454$	−26.8729	−1.26121
$455$	−8.58686	−0.402558
$456$	−13.7823	−0.645417
$457$	−26.8172	−1.25445	−0.627227	−	0.778837i	$-0.715810\pi$
$457$	−26.8172	−1.25445	−0.627227	+	0.778837i	$0.715810\pi$
$458$	10.5828	0.494500
$459$	−0.196510	−0.00917229
$460$	2.27241	0.105951
$461$	−35.2947	−1.64384	−0.821918	−	0.569605i	$-0.807096\pi$
$461$	−35.2947	−1.64384	−0.821918	+	0.569605i	$0.807096\pi$
$462$	−15.4312	−0.717923
$463$	−39.9130	−1.85491	−0.927457	−	0.373931i	$-0.878010\pi$
$463$	−39.9130	−1.85491	−0.927457	+	0.373931i	$0.878010\pi$
$464$	−8.39476	−0.389717
$465$	5.04342	0.233883
$466$	47.5797	2.20409
$467$	25.4539	1.17787	0.588934	−	0.808181i	$-0.299548\pi$
$467$	25.4539	1.17787	0.588934	+	0.808181i	$0.299548\pi$
$468$	−5.20378	−0.240545
$469$	−4.48908	−0.207286
$470$	−15.3067	−0.706045
$471$	−38.1157	−1.75628
$472$	−23.7260	−1.09208
$473$	1.00000	0.0459800
$474$	−52.8464	−2.42732
$475$	11.2337	0.515436
$476$	−2.63527	−0.120787
$477$	21.8465	1.00028
$478$	−34.0422	−1.55705
$479$	3.81947	0.174516	0.0872580	−	0.996186i	$-0.472190\pi$
$479$	3.81947	0.174516	0.0872580	+	0.996186i	$0.472190\pi$
$480$	−7.60703	−0.347212
$481$	−12.7772	−0.582592
$482$	0.902097	0.0410894
$483$	37.2317	1.69410
$484$	0.680210	0.0309186
$485$	−1.85127	−0.0840620
$486$	35.8216	1.62490
$487$	10.5345	0.477365	0.238683	−	0.971098i	$-0.423284\pi$
$487$	10.5345	0.477365	0.238683	+	0.971098i	$0.423284\pi$
$488$	14.4258	0.653024
$489$	15.4989	0.700884
$490$	11.0900	0.500994
$491$	9.55561	0.431239	0.215619	−	0.976478i	$-0.430823\pi$
$491$	9.55561	0.431239	0.215619	+	0.976478i	$0.430823\pi$
$492$	−3.08867	−0.139248
$493$	1.71401	0.0771951
$494$	−11.2485	−0.506092
$495$	2.46895	0.110971
$496$	12.0045	0.539017
$497$	−0.135980	−0.00609955
$498$	−58.7648	−2.63331
$499$	2.58587	0.115759	0.0578796	−	0.998324i	$-0.481566\pi$
$499$	2.58587	0.115759	0.0578796	+	0.998324i	$0.481566\pi$
$500$	5.34141	0.238875
$501$	42.5458	1.90080
$502$	−16.8149	−0.750488
$503$	13.3484	0.595175	0.297587	−	0.954695i	$-0.403818\pi$
$503$	13.3484	0.595175	0.297587	+	0.954695i	$0.403818\pi$
$504$	−24.4365	−1.08849
$505$	8.38640	0.373190
$506$	−6.46670	−0.287480
$507$	−14.9194	−0.662594
$508$	1.69630	0.0752613
$509$	9.59632	0.425349	0.212675	−	0.977123i	$-0.431783\pi$
$509$	9.59632	0.425349	0.212675	+	0.977123i	$0.431783\pi$
$510$	3.36869	0.149168
$511$	4.67906	0.206989
$512$	3.05836	0.135162
$513$	0.515211	0.0227471
$514$	−10.9976	−0.485086
$515$	−7.30176	−0.321754
$516$	−1.65492	−0.0728536
$517$	11.0548	0.486191
$518$	30.9240	1.35872
$519$	9.49398	0.416740
$520$	4.78896	0.210010
$521$	−21.3244	−0.934238	−0.467119	−	0.884194i	$-0.654708\pi$
$521$	−21.3244	−0.934238	−0.467119	+	0.884194i	$0.654708\pi$
$522$	−8.19155	−0.358534
$523$	−12.2284	−0.534709	−0.267355	−	0.963598i	$-0.586150\pi$
$523$	−12.2284	−0.534709	−0.267355	+	0.963598i	$0.586150\pi$
$524$	−6.34673	−0.277258
$525$	40.3864	1.76261
$526$	33.7967	1.47360
$527$	−2.45103	−0.106768
$528$	11.9159	0.518574
$529$	−7.39742	−0.321627
$530$	10.3620	0.450096
$531$	−32.0555	−1.39109
$532$	6.90918	0.299551
$533$	4.89106	0.211855
$534$	−24.4406	−1.05765
$535$	4.76111	0.205841
$536$	2.50359	0.108139
$537$	4.24228	0.183068
$538$	9.08892	0.391851
$539$	−8.00943	−0.344990
$540$	0.113050	0.00486491
$541$	−9.20936	−0.395941	−0.197971	−	0.980208i	$-0.563435\pi$
$541$	−9.20936	−0.395941	−0.197971	+	0.980208i	$0.563435\pi$
$542$	−40.1980	−1.72665
$543$	−60.5428	−2.59814
$544$	3.69690	0.158503
$545$	−15.1153	−0.647469
$546$	−40.4396	−1.73065
$547$	41.8768	1.79052	0.895262	−	0.445540i	$-0.146988\pi$
$547$	41.8768	1.79052	0.895262	+	0.445540i	$0.146988\pi$
$548$	8.63341	0.368801
$549$	19.4903	0.831825
$550$	−7.01463	−0.299105
$551$	−4.49380	−0.191442
$552$	−20.7644	−0.883793
$553$	−51.4020	−2.18584
$554$	17.0384	0.723893
$555$	−10.0324	−0.425854
$556$	1.08632	0.0460702
$557$	43.4935	1.84288	0.921439	−	0.388522i	$-0.127014\pi$
$557$	43.4935	1.84288	0.921439	+	0.388522i	$0.127014\pi$
$558$	11.7139	0.495888
$559$	2.62064	0.110841
$560$	−16.0480	−0.678153
$561$	−2.43295	−0.102719
$562$	−47.9463	−2.02249
$563$	−8.31284	−0.350344	−0.175172	−	0.984538i	$-0.556048\pi$
$563$	−8.31284	−0.350344	−0.175172	+	0.984538i	$0.556048\pi$
$564$	−18.2948	−0.770351
$565$	9.20998	0.387467
$566$	−17.7432	−0.745801
$567$	35.7813	1.50267
$568$	0.0758373	0.00318206
$569$	16.4926	0.691405	0.345703	−	0.938344i	$-0.387641\pi$
$569$	16.4926	0.691405	0.345703	+	0.938344i	$0.387641\pi$
$570$	−8.83207	−0.369935
$571$	35.9085	1.50273	0.751363	−	0.659889i	$-0.229397\pi$
$571$	35.9085	1.50273	0.751363	+	0.659889i	$0.229397\pi$
$572$	1.78259	0.0745337
$573$	48.2307	2.01487
$574$	−11.8376	−0.494090
$575$	16.9246	0.705805
$576$	10.9271	0.455295
$577$	−20.9996	−0.874223	−0.437112	−	0.899407i	$-0.643999\pi$
$577$	−20.9996	−0.874223	−0.437112	+	0.899407i	$0.643999\pi$
$578$	−1.63713	−0.0680958
$579$	−4.36761	−0.181512
$580$	−0.986054	−0.0409437
$581$	−57.1587	−2.37134
$582$	−8.71853	−0.361395
$583$	−7.48366	−0.309942
$584$	−2.60955	−0.107984
$585$	6.47024	0.267512
$586$	−43.7356	−1.80670
$587$	35.3678	1.45979	0.729893	−	0.683561i	$-0.239570\pi$
$587$	35.3678	1.45979	0.729893	+	0.683561i	$0.239570\pi$
$588$	13.2549	0.546624
$589$	6.42612	0.264784
$590$	−15.2042	−0.625947
$591$	−42.1743	−1.73482
$592$	−23.8795	−0.981441
$593$	−28.4298	−1.16747	−0.583735	−	0.811944i	$-0.698409\pi$
$593$	−28.4298	−1.16747	−0.583735	+	0.811944i	$0.698409\pi$
$594$	−0.321713	−0.0132000
$595$	3.27662	0.134328
$596$	−6.67807	−0.273544
$597$	−8.99546	−0.368160
$598$	−16.9469	−0.693010
$599$	−22.0650	−0.901553	−0.450777	−	0.892637i	$-0.648853\pi$
$599$	−22.0650	−0.901553	−0.450777	+	0.892637i	$0.648853\pi$
$600$	−22.5238	−0.919531
$601$	−7.25461	−0.295922	−0.147961	−	0.988993i	$-0.547271\pi$
$601$	−7.25461	−0.295922	−0.147961	+	0.988993i	$0.547271\pi$
$602$	−6.34259	−0.258505
$603$	3.38254	0.137748
$604$	11.5555	0.470189
$605$	−0.845755	−0.0343848
$606$	39.4955	1.60440
$607$	−23.8972	−0.969959	−0.484980	−	0.874525i	$-0.661173\pi$
$607$	−23.8972	−0.969959	−0.484980	+	0.874525i	$0.661173\pi$
$608$	−9.69258	−0.393086
$609$	−16.1558	−0.654665
$610$	9.24441	0.374295
$611$	28.9708	1.17203
$612$	1.98569	0.0802668
$613$	−12.3652	−0.499426	−0.249713	−	0.968320i	$-0.580336\pi$
$613$	−12.3652	−0.499426	−0.249713	+	0.968320i	$0.580336\pi$
$614$	−27.5575	−1.11213
$615$	3.84036	0.154858
$616$	8.37088	0.337272
$617$	−17.6973	−0.712467	−0.356234	−	0.934397i	$-0.615939\pi$
$617$	−17.6973	−0.712467	−0.356234	+	0.934397i	$0.615939\pi$
$618$	−34.3875	−1.38327
$619$	−29.0528	−1.16773	−0.583864	−	0.811851i	$-0.698460\pi$
$619$	−29.0528	−1.16773	−0.583864	+	0.811851i	$0.698460\pi$
$620$	1.41005	0.0566291
$621$	0.776216	0.0311485
$622$	26.1511	1.04856
$623$	−23.7726	−0.952429
$624$	31.2274	1.25010
$625$	14.7821	0.591285
$626$	0.150029	0.00599637
$627$	6.37872	0.254742
$628$	−10.6565	−0.425240
$629$	4.87562	0.194404
$630$	−15.6596	−0.623891
$631$	44.2663	1.76221	0.881107	−	0.472918i	$-0.156799\pi$
$631$	44.2663	1.76221	0.881107	+	0.472918i	$0.156799\pi$
$632$	28.6673	1.14033
$633$	−24.6144	−0.978334
$634$	−20.1191	−0.799030
$635$	−2.10914	−0.0836985
$636$	12.3848	0.491090
$637$	−20.9898	−0.831648
$638$	2.80606	0.111093
$639$	0.102462	0.00405333
$640$	11.4362	0.452054
$641$	15.2424	0.602037	0.301018	−	0.953618i	$-0.402673\pi$
$641$	15.2424	0.602037	0.301018	+	0.953618i	$0.402673\pi$
$642$	22.4223	0.884939
$643$	28.7525	1.13389	0.566943	−	0.823757i	$-0.308126\pi$
$643$	28.7525	1.13389	0.566943	+	0.823757i	$0.308126\pi$
$644$	10.4093	0.410186
$645$	2.05768	0.0810209
$646$	4.29225	0.168876
$647$	−9.57816	−0.376556	−0.188278	−	0.982116i	$-0.560291\pi$
$647$	−9.57816	−0.376556	−0.188278	+	0.982116i	$0.560291\pi$
$648$	−19.9555	−0.783927
$649$	10.9808	0.431035
$650$	−18.3828	−0.721034
$651$	23.1027	0.905466
$652$	4.33323	0.169702
$653$	−43.1104	−1.68704	−0.843519	−	0.537099i	$-0.819520\pi$
$653$	−43.1104	−1.68704	−0.843519	+	0.537099i	$0.819520\pi$
$654$	−71.1852	−2.78356
$655$	7.89135	0.308341
$656$	9.14093	0.356894
$657$	−3.52569	−0.137550
$658$	−70.1163	−2.73342
$659$	−21.8623	−0.851635	−0.425818	−	0.904809i	$-0.640013\pi$
$659$	−21.8623	−0.851635	−0.425818	+	0.904809i	$0.640013\pi$
$660$	1.39965	0.0544814
$661$	39.8761	1.55100	0.775501	−	0.631347i	$-0.217498\pi$
$661$	39.8761	1.55100	0.775501	+	0.631347i	$0.217498\pi$
$662$	1.27309	0.0494800
$663$	−6.37588	−0.247619
$664$	31.8779	1.23710
$665$	−8.59068	−0.333132
$666$	−23.3014	−0.902912
$667$	−6.77035	−0.262149
$668$	11.8951	0.460234
$669$	−18.7212	−0.723803
$670$	1.60437	0.0619821
$671$	−6.67652	−0.257744
$672$	−34.8460	−1.34421
$673$	−27.0256	−1.04176	−0.520881	−	0.853629i	$-0.674397\pi$
$673$	−27.0256	−1.04176	−0.520881	+	0.853629i	$0.674397\pi$
$674$	−26.0575	−1.00370
$675$	0.841985	0.0324080
$676$	−4.17121	−0.160431
$677$	−36.7762	−1.41343	−0.706713	−	0.707501i	$-0.749823\pi$
$677$	−36.7762	−1.41343	−0.706713	+	0.707501i	$0.749823\pi$
$678$	43.3742	1.66577
$679$	−8.48024	−0.325442
$680$	−1.82740	−0.0700776
$681$	39.9359	1.53035
$682$	−4.01266	−0.153653
$683$	27.3843	1.04783	0.523916	−	0.851770i	$-0.324471\pi$
$683$	27.3843	1.04783	0.523916	+	0.851770i	$0.324471\pi$
$684$	−5.20610	−0.199060
$685$	−10.7345	−0.410146
$686$	6.40239	0.244444
$687$	−15.7270	−0.600024
$688$	4.89773	0.186724
$689$	−19.6120	−0.747158
$690$	−13.3064	−0.506565
$691$	6.67746	0.254023	0.127011	−	0.991901i	$-0.459462\pi$
$691$	6.67746	0.254023	0.127011	+	0.991901i	$0.459462\pi$
$692$	2.65436	0.100903
$693$	11.3097	0.429619
$694$	−44.3232	−1.68248
$695$	−1.35070	−0.0512349
$696$	9.01021	0.341531
$697$	−1.86636	−0.0706934
$698$	−23.3758	−0.884786
$699$	−70.7083	−2.67443
$700$	11.2913	0.426773
$701$	2.40710	0.0909150	0.0454575	−	0.998966i	$-0.485525\pi$
$701$	2.40710	0.0909150	0.0454575	+	0.998966i	$0.485525\pi$
$702$	−0.843094	−0.0318205
$703$	−12.7829	−0.482118
$704$	−3.74314	−0.141075
$705$	22.7473	0.856712
$706$	24.4934	0.921820
$707$	38.4161	1.44479
$708$	−18.1723	−0.682958
$709$	19.2831	0.724193	0.362097	−	0.932141i	$-0.382061\pi$
$709$	19.2831	0.724193	0.362097	+	0.932141i	$0.382061\pi$
$710$	0.0485985	0.00182387
$711$	38.7317	1.45255
$712$	13.2582	0.496871
$713$	9.68158	0.362578
$714$	15.4312	0.577497
$715$	−2.21642	−0.0828894
$716$	1.18607	0.0443255
$717$	50.5901	1.88932
$718$	−17.3239	−0.646523
$719$	−17.8611	−0.666108	−0.333054	−	0.942908i	$-0.608079\pi$
$719$	−17.8611	−0.666108	−0.333054	+	0.942908i	$0.608079\pi$
$720$	12.0923	0.450652
$721$	−33.4476	−1.24565
$722$	19.8521	0.738818
$723$	−1.34061	−0.0498577
$724$	−16.9267	−0.629077
$725$	−7.34401	−0.272750
$726$	−3.98306	−0.147825
$727$	−12.7677	−0.473527	−0.236764	−	0.971567i	$-0.576087\pi$
$727$	−12.7677	−0.473527	−0.236764	+	0.971567i	$0.576087\pi$
$728$	21.9371	0.813042
$729$	−25.5271	−0.945448
$730$	−1.67226	−0.0618933
$731$	−1.00000	−0.0369863
$732$	11.0491	0.408385
$733$	−26.3725	−0.974090	−0.487045	−	0.873377i	$-0.661925\pi$
$733$	−26.3725	−0.974090	−0.487045	+	0.873377i	$0.661925\pi$
$734$	−39.0118	−1.43995
$735$	−16.4808	−0.607904
$736$	−14.6028	−0.538267
$737$	−1.15871	−0.0426816
$738$	8.91965	0.328337
$739$	17.2462	0.634413	0.317207	−	0.948356i	$-0.397255\pi$
$739$	17.2462	0.634413	0.317207	+	0.948356i	$0.397255\pi$
$740$	−2.80490	−0.103110
$741$	16.7163	0.614090
$742$	47.4658	1.74252
$743$	41.7878	1.53304	0.766522	−	0.642218i	$-0.221985\pi$
$743$	41.7878	1.53304	0.766522	+	0.642218i	$0.221985\pi$
$744$	−12.8846	−0.472371
$745$	8.30332	0.304210
$746$	27.9420	1.02303
$747$	43.0693	1.57582
$748$	−0.680210	−0.0248710
$749$	21.8095	0.796902
$750$	−31.2773	−1.14209
$751$	11.8554	0.432611	0.216306	−	0.976326i	$-0.430599\pi$
$751$	11.8554	0.432611	0.216306	+	0.976326i	$0.430599\pi$
$752$	54.1436	1.97442
$753$	24.9887	0.910639
$754$	7.35369	0.267806
$755$	−14.3679	−0.522900
$756$	0.517856	0.0188343
$757$	34.9422	1.27000	0.634998	−	0.772514i	$-0.281001\pi$
$757$	34.9422	1.27000	0.634998	+	0.772514i	$0.281001\pi$
$758$	40.7345	1.47954
$759$	9.61016	0.348827
$760$	4.79109	0.173791
$761$	−34.0045	−1.23266	−0.616331	−	0.787487i	$-0.711382\pi$
$761$	−34.0045	−1.23266	−0.616331	+	0.787487i	$0.711382\pi$
$762$	−9.93293	−0.359832
$763$	−69.2396	−2.50664
$764$	13.4845	0.487851
$765$	−2.46895	−0.0892652
$766$	15.6919	0.566970
$767$	28.7768	1.03907
$768$	35.6446	1.28621
$769$	3.01205	0.108617	0.0543087	−	0.998524i	$-0.482704\pi$
$769$	3.01205	0.108617	0.0543087	+	0.998524i	$0.482704\pi$
$770$	5.36427	0.193315
$771$	16.3436	0.588601
$772$	−1.22111	−0.0439487
$773$	−31.5204	−1.13371	−0.566854	−	0.823818i	$-0.691840\pi$
$773$	−31.5204	−1.13371	−0.566854	+	0.823818i	$0.691840\pi$
$774$	4.77917	0.171784
$775$	10.5019	0.377240
$776$	4.72950	0.169779
$777$	−45.9562	−1.64867
$778$	−41.6506	−1.49325
$779$	4.89324	0.175318
$780$	3.66799	0.131335
$781$	−0.0350989	−0.00125594
$782$	6.46670	0.231249
$783$	−0.336820	−0.0120369
$784$	−39.2281	−1.40100
$785$	13.2500	0.472912
$786$	37.1641	1.32560
$787$	−45.2525	−1.61308	−0.806538	−	0.591182i	$-0.798662\pi$
$787$	−45.2525	−1.61308	−0.806538	+	0.591182i	$0.798662\pi$
$788$	−11.7912	−0.420044
$789$	−50.2252	−1.78807
$790$	18.3708	0.653602
$791$	42.1887	1.50006
$792$	−6.30750	−0.224127
$793$	−17.4968	−0.621328
$794$	−53.0324	−1.88205
$795$	−15.3990	−0.546145
$796$	−2.51498	−0.0891410
$797$	−8.02977	−0.284429	−0.142215	−	0.989836i	$-0.545422\pi$
$797$	−8.02977	−0.284429	−0.142215	+	0.989836i	$0.545422\pi$
$798$	−40.4576	−1.43218
$799$	−11.0548	−0.391092
$800$	−15.8401	−0.560033
$801$	17.9128	0.632917
$802$	2.53552	0.0895324
$803$	1.20775	0.0426205
$804$	1.91757	0.0676274
$805$	−12.9427	−0.456170
$806$	−10.5157	−0.370401
$807$	−13.5070	−0.475471
$808$	−21.4250	−0.753728
$809$	−28.1847	−0.990921	−0.495460	−	0.868631i	$-0.665001\pi$
$809$	−28.1847	−0.990921	−0.495460	+	0.868631i	$0.665001\pi$
$810$	−12.7880	−0.449325
$811$	1.36881	0.0480655	0.0240328	−	0.999711i	$-0.492349\pi$
$811$	1.36881	0.0480655	0.0240328	+	0.999711i	$0.492349\pi$
$812$	−4.51688	−0.158511
$813$	59.7383	2.09511
$814$	7.98204	0.279771
$815$	−5.38782	−0.188727
$816$	−11.9159	−0.417141
$817$	2.62181	0.0917255
$818$	46.9291	1.64084
$819$	29.6386	1.03566
$820$	1.07370	0.0374952
$821$	5.79694	0.202315	0.101157	−	0.994870i	$-0.467745\pi$
$821$	5.79694	0.202315	0.101157	+	0.994870i	$0.467745\pi$
$822$	−50.5541	−1.76328
$823$	6.84846	0.238722	0.119361	−	0.992851i	$-0.461915\pi$
$823$	6.84846	0.238722	0.119361	+	0.992851i	$0.461915\pi$
$824$	18.6540	0.649843
$825$	10.4244	0.362933
$826$	−69.6468	−2.42332
$827$	−9.16263	−0.318616	−0.159308	−	0.987229i	$-0.550926\pi$
$827$	−9.16263	−0.318616	−0.159308	+	0.987229i	$0.550926\pi$
$828$	−7.84350	−0.272580
$829$	0.556611	0.0193319	0.00966594	−	0.999953i	$-0.496923\pi$
$829$	0.556611	0.0193319	0.00966594	+	0.999953i	$0.496923\pi$
$830$	20.4281	0.709071
$831$	−25.3208	−0.878368
$832$	−9.80942	−0.340081
$833$	8.00943	0.277510
$834$	−6.36108	−0.220266
$835$	−14.7900	−0.511829
$836$	1.78338	0.0616795
$837$	0.481650	0.0166483
$838$	−24.5653	−0.848594
$839$	−4.24612	−0.146592	−0.0732961	−	0.997310i	$-0.523352\pi$
$839$	−4.24612	−0.146592	−0.0732961	+	0.997310i	$0.523352\pi$
$840$	17.2246	0.594304
$841$	−26.0622	−0.898696
$842$	24.2506	0.835732
$843$	71.2530	2.45408
$844$	−6.88176	−0.236880
$845$	5.18637	0.178417
$846$	52.8330	1.81643
$847$	−3.87420	−0.133119
$848$	−36.6530	−1.25867
$849$	26.3681	0.904952
$850$	7.01463	0.240600
$851$	−19.2587	−0.660181
$852$	0.0580857	0.00198998
$853$	−28.3864	−0.971932	−0.485966	−	0.873978i	$-0.661532\pi$
$853$	−28.3864	−0.971932	−0.485966	+	0.873978i	$0.661532\pi$
$854$	42.3464	1.44906
$855$	6.47312	0.221376
$856$	−12.1633	−0.415735
$857$	−41.1126	−1.40438	−0.702189	−	0.711990i	$-0.747794\pi$
$857$	−41.1126	−1.40438	−0.702189	+	0.711990i	$0.747794\pi$
$858$	−10.4382	−0.356354
$859$	−12.3422	−0.421110	−0.210555	−	0.977582i	$-0.567527\pi$
$859$	−12.3422	−0.421110	−0.210555	+	0.977582i	$0.567527\pi$
$860$	0.575291	0.0196173
$861$	17.5918	0.599527
$862$	−58.5537	−1.99435
$863$	35.6803	1.21457	0.607285	−	0.794484i	$-0.292259\pi$
$863$	35.6803	1.21457	0.607285	+	0.794484i	$0.292259\pi$
$864$	−0.726478	−0.0247153
$865$	−3.30035	−0.112215
$866$	−11.2726	−0.383060
$867$	2.43295	0.0826272
$868$	6.45912	0.219237
$869$	−13.2678	−0.450079
$870$	5.77397	0.195756
$871$	−3.03656	−0.102890
$872$	38.6155	1.30769
$873$	6.38990	0.216265
$874$	−16.9544	−0.573493
$875$	−30.4225	−1.02847
$876$	−1.99872	−0.0675305
$877$	32.8785	1.11023	0.555114	−	0.831775i	$-0.312675\pi$
$877$	32.8785	1.11023	0.555114	+	0.831775i	$0.312675\pi$
$878$	−36.1821	−1.22109
$879$	64.9954	2.19224
$880$	−4.14228	−0.139636
$881$	−46.8268	−1.57764	−0.788818	−	0.614627i	$-0.789307\pi$
$881$	−46.8268	−1.57764	−0.788818	+	0.614627i	$0.789307\pi$
$882$	−38.2784	−1.28890
$883$	−10.6941	−0.359885	−0.179942	−	0.983677i	$-0.557591\pi$
$883$	−10.6941	−0.359885	−0.179942	+	0.983677i	$0.557591\pi$
$884$	−1.78259	−0.0599549
$885$	22.5950	0.759522
$886$	26.3359	0.884771
$887$	−8.57671	−0.287978	−0.143989	−	0.989579i	$-0.545993\pi$
$887$	−8.57671	−0.287978	−0.143989	+	0.989579i	$0.545993\pi$
$888$	25.6302	0.860092
$889$	−9.66145	−0.324035
$890$	8.49618	0.284793
$891$	9.23579	0.309411
$892$	−5.23413	−0.175251
$893$	28.9837	0.969901
$894$	39.1043	1.30784
$895$	−1.47472	−0.0492946
$896$	52.3863	1.75010
$897$	25.1848	0.840896
$898$	−51.7865	−1.72814
$899$	−4.20108	−0.140114
$900$	−8.50808	−0.283603
$901$	7.48366	0.249317
$902$	−3.05548	−0.101736
$903$	9.42572	0.313668
$904$	−23.5290	−0.782562
$905$	21.0462	0.699601
$906$	−67.6650	−2.24802
$907$	29.1636	0.968363	0.484181	−	0.874968i	$-0.339118\pi$
$907$	29.1636	0.968363	0.484181	+	0.874968i	$0.339118\pi$
$908$	11.1654	0.370536
$909$	−28.9467	−0.960102
$910$	14.0578	0.466013
$911$	49.4381	1.63796	0.818979	−	0.573824i	$-0.194541\pi$
$911$	49.4381	1.63796	0.818979	+	0.573824i	$0.194541\pi$
$912$	31.2413	1.03450
$913$	−14.7537	−0.488275
$914$	43.9033	1.45219
$915$	−13.7381	−0.454168
$916$	−4.39701	−0.145281
$917$	36.1484	1.19372
$918$	0.321713	0.0106181
$919$	30.5070	1.00633	0.503166	−	0.864190i	$-0.332169\pi$
$919$	30.5070	1.00633	0.503166	+	0.864190i	$0.332169\pi$
$920$	7.21825	0.237979
$921$	40.9532	1.34945
$922$	57.7821	1.90295
$923$	−0.0919817	−0.00302761
$924$	6.41147	0.210922
$925$	−20.8906	−0.686877
$926$	65.3429	2.14730
$927$	25.2029	0.827773
$928$	6.33653	0.208007
$929$	55.4503	1.81927	0.909633	−	0.415412i	$-0.136363\pi$
$929$	55.4503	1.81927	0.909633	+	0.415412i	$0.136363\pi$
$930$	−8.25675	−0.270750
$931$	−20.9992	−0.688221
$932$	−19.7688	−0.647549
$933$	−38.8631	−1.27232
$934$	−41.6715	−1.36353
$935$	0.845755	0.0276591
$936$	−16.5297	−0.540290
$937$	44.0046	1.43757	0.718785	−	0.695233i	$-0.244699\pi$
$937$	44.0046	1.43757	0.718785	+	0.695233i	$0.244699\pi$
$938$	7.34922	0.239961
$939$	−0.222958	−0.00727597
$940$	6.35975	0.207432
$941$	41.9263	1.36676	0.683380	−	0.730063i	$-0.260509\pi$
$941$	41.9263	1.36676	0.683380	+	0.730063i	$0.260509\pi$
$942$	62.4005	2.03312
$943$	7.37214	0.240070
$944$	53.7811	1.75043
$945$	−0.643889	−0.0209457
$946$	−1.63713	−0.0532278
$947$	−10.1075	−0.328450	−0.164225	−	0.986423i	$-0.552512\pi$
$947$	−10.1075	−0.328450	−0.164225	+	0.986423i	$0.552512\pi$
$948$	21.9571	0.713132
$949$	3.16507	0.102743
$950$	−18.3910	−0.596683
$951$	29.8990	0.969540
$952$	−8.37088	−0.271302
$953$	35.7920	1.15942	0.579709	−	0.814824i	$-0.303166\pi$
$953$	35.7920	1.15942	0.579709	+	0.814824i	$0.303166\pi$
$954$	−35.7657	−1.15796
$955$	−16.7662	−0.542543
$956$	14.1441	0.457453
$957$	−4.17009	−0.134800
$958$	−6.25299	−0.202025
$959$	−49.1724	−1.58786
$960$	−7.70217	−0.248586
$961$	−24.9925	−0.806209
$962$	20.9181	0.674426
$963$	−16.4336	−0.529565
$964$	−0.374811	−0.0120718
$965$	1.51829	0.0488756
$966$	−60.9533	−1.96114
$967$	−53.8150	−1.73058	−0.865288	−	0.501276i	$-0.832864\pi$
$967$	−53.8150	−1.73058	−0.865288	+	0.501276i	$0.832864\pi$
$968$	2.16067	0.0694467
$969$	−6.37872	−0.204914
$970$	3.03078	0.0973126
$971$	32.7000	1.04939	0.524696	−	0.851290i	$-0.324179\pi$
$971$	32.7000	1.04939	0.524696	+	0.851290i	$0.324179\pi$
$972$	−14.8834	−0.477387
$973$	−6.18723	−0.198353
$974$	−17.2464	−0.552612
$975$	27.3187	0.874900
$976$	−32.6998	−1.04670
$977$	−17.2342	−0.551370	−0.275685	−	0.961248i	$-0.588905\pi$
$977$	−17.2342	−0.551370	−0.275685	+	0.961248i	$0.588905\pi$
$978$	−25.3738	−0.811364
$979$	−6.13613	−0.196112
$980$	−4.60775	−0.147189
$981$	52.1724	1.66574
$982$	−15.6438	−0.499214
$983$	53.6607	1.71151	0.855756	−	0.517380i	$-0.173093\pi$
$983$	53.6607	1.71151	0.855756	+	0.517380i	$0.173093\pi$
$984$	−9.81109	−0.312766
$985$	14.6609	0.467134
$986$	−2.80606	−0.0893633
$987$	104.200	3.31672
$988$	4.67360	0.148687
$989$	3.95001	0.125603
$990$	−4.04201	−0.128463
$991$	12.9770	0.412228	0.206114	−	0.978528i	$-0.433918\pi$
$991$	12.9770	0.412228	0.206114	+	0.978528i	$0.433918\pi$
$992$	−9.06121	−0.287694
$993$	−1.89194	−0.0600388
$994$	0.222618	0.00706101
$995$	3.12705	0.0991342
$996$	24.4161	0.773653
$997$	50.3198	1.59364	0.796821	−	0.604215i	$-0.206513\pi$
$997$	50.3198	1.59364	0.796821	+	0.604215i	$0.206513\pi$
$998$	−4.23341	−0.134006
$999$	−0.958106	−0.0303131

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.15	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-1.63713 q^{2} +2.43295 q^{3} +0.680210 q^{4} -0.845755 q^{5} -3.98306 q^{6} -3.87420 q^{7} +2.16067 q^{8} +2.91923 q^{9} +O(q^{10})\)	\(q-1.63713 q^{2} +2.43295 q^{3} +0.680210 q^{4} -0.845755 q^{5} -3.98306 q^{6} -3.87420 q^{7} +2.16067 q^{8} +2.91923 q^{9} +1.38461 q^{10} -1.00000 q^{11} +1.65492 q^{12} -2.62064 q^{13} +6.34259 q^{14} -2.05768 q^{15} -4.89773 q^{16} +1.00000 q^{17} -4.77917 q^{18} -2.62181 q^{19} -0.575291 q^{20} -9.42572 q^{21} +1.63713 q^{22} -3.95001 q^{23} +5.25680 q^{24} -4.28470 q^{25} +4.29034 q^{26} -0.196510 q^{27} -2.63527 q^{28} +1.71401 q^{29} +3.36869 q^{30} -2.45103 q^{31} +3.69690 q^{32} -2.43295 q^{33} -1.63713 q^{34} +3.27662 q^{35} +1.98569 q^{36} +4.87562 q^{37} +4.29225 q^{38} -6.37588 q^{39} -1.82740 q^{40} -1.86636 q^{41} +15.4312 q^{42} -1.00000 q^{43} -0.680210 q^{44} -2.46895 q^{45} +6.46670 q^{46} -11.0548 q^{47} -11.9159 q^{48} +8.00943 q^{49} +7.01463 q^{50} +2.43295 q^{51} -1.78259 q^{52} +7.48366 q^{53} +0.321713 q^{54} +0.845755 q^{55} -8.37088 q^{56} -6.37872 q^{57} -2.80606 q^{58} -10.9808 q^{59} -1.39965 q^{60} +6.67652 q^{61} +4.01266 q^{62} -11.3097 q^{63} +3.74314 q^{64} +2.21642 q^{65} +3.98306 q^{66} +1.15871 q^{67} +0.680210 q^{68} -9.61016 q^{69} -5.36427 q^{70} +0.0350989 q^{71} +6.30750 q^{72} -1.20775 q^{73} -7.98204 q^{74} -10.4244 q^{75} -1.78338 q^{76} +3.87420 q^{77} +10.4382 q^{78} +13.2678 q^{79} +4.14228 q^{80} -9.23579 q^{81} +3.05548 q^{82} +14.7537 q^{83} -6.41147 q^{84} -0.845755 q^{85} +1.63713 q^{86} +4.17009 q^{87} -2.16067 q^{88} +6.13613 q^{89} +4.04201 q^{90} +10.1529 q^{91} -2.68684 q^{92} -5.96321 q^{93} +18.0983 q^{94} +2.21741 q^{95} +8.99437 q^{96} +2.18890 q^{97} -13.1125 q^{98} -2.91923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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