LMFDB - Embedded newform 4011.2.a.k.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.69492 q^{2} +1.00000 q^{3} +0.872752 q^{4} -3.19478 q^{5} -1.69492 q^{6} +1.00000 q^{7} +1.91059 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.69492 q^{2} +1.00000 q^{3} +0.872752 q^{4} -3.19478 q^{5} -1.69492 q^{6} +1.00000 q^{7} +1.91059 q^{8} +1.00000 q^{9} +5.41490 q^{10} -0.178874 q^{11} +0.872752 q^{12} -0.968622 q^{13} -1.69492 q^{14} -3.19478 q^{15} -4.98381 q^{16} +1.15721 q^{17} -1.69492 q^{18} +4.17756 q^{19} -2.78825 q^{20} +1.00000 q^{21} +0.303177 q^{22} +7.71313 q^{23} +1.91059 q^{24} +5.20664 q^{25} +1.64174 q^{26} +1.00000 q^{27} +0.872752 q^{28} +8.99618 q^{29} +5.41490 q^{30} -9.58748 q^{31} +4.62596 q^{32} -0.178874 q^{33} -1.96137 q^{34} -3.19478 q^{35} +0.872752 q^{36} -9.91100 q^{37} -7.08064 q^{38} -0.968622 q^{39} -6.10394 q^{40} -6.08354 q^{41} -1.69492 q^{42} -2.46708 q^{43} -0.156113 q^{44} -3.19478 q^{45} -13.0731 q^{46} +13.2209 q^{47} -4.98381 q^{48} +1.00000 q^{49} -8.82483 q^{50} +1.15721 q^{51} -0.845367 q^{52} -9.95804 q^{53} -1.69492 q^{54} +0.571465 q^{55} +1.91059 q^{56} +4.17756 q^{57} -15.2478 q^{58} +6.39864 q^{59} -2.78825 q^{60} -6.43868 q^{61} +16.2500 q^{62} +1.00000 q^{63} +2.12698 q^{64} +3.09454 q^{65} +0.303177 q^{66} +3.79443 q^{67} +1.00995 q^{68} +7.71313 q^{69} +5.41490 q^{70} +1.48022 q^{71} +1.91059 q^{72} -9.12334 q^{73} +16.7983 q^{74} +5.20664 q^{75} +3.64598 q^{76} -0.178874 q^{77} +1.64174 q^{78} -10.0757 q^{79} +15.9222 q^{80} +1.00000 q^{81} +10.3111 q^{82} +12.8248 q^{83} +0.872752 q^{84} -3.69702 q^{85} +4.18149 q^{86} +8.99618 q^{87} -0.341756 q^{88} +1.00799 q^{89} +5.41490 q^{90} -0.968622 q^{91} +6.73165 q^{92} -9.58748 q^{93} -22.4084 q^{94} -13.3464 q^{95} +4.62596 q^{96} +11.8356 q^{97} -1.69492 q^{98} -0.178874 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) $ 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.69492	−1.19849	−0.599245	−	0.800566i	$-0.704532\pi$
$2$	−1.69492	−1.19849	−0.599245	+	0.800566i	$0.704532\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.872752	0.436376
$5$	−3.19478	−1.42875	−0.714375	−	0.699763i	$-0.753289\pi$
$5$	−3.19478	−1.42875	−0.714375	+	0.699763i	$0.753289\pi$
$6$	−1.69492	−0.691948
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.91059	0.675497
$9$	1.00000	0.333333
$10$	5.41490	1.71234
$11$	−0.178874	−0.0539326	−0.0269663	−	0.999636i	$-0.508585\pi$
$11$	−0.178874	−0.0539326	−0.0269663	+	0.999636i	$0.508585\pi$
$12$	0.872752	0.251942
$13$	−0.968622	−0.268647	−0.134324	−	0.990938i	$-0.542886\pi$
$13$	−0.968622	−0.268647	−0.134324	+	0.990938i	$0.542886\pi$
$14$	−1.69492	−0.452986
$15$	−3.19478	−0.824889
$16$	−4.98381	−1.24595
$17$	1.15721	0.280664	0.140332	−	0.990105i	$-0.455183\pi$
$17$	1.15721	0.280664	0.140332	+	0.990105i	$0.455183\pi$
$18$	−1.69492	−0.399496
$19$	4.17756	0.958399	0.479200	−	0.877706i	$-0.340927\pi$
$19$	4.17756	0.958399	0.479200	+	0.877706i	$0.340927\pi$
$20$	−2.78825	−0.623472
$21$	1.00000	0.218218
$22$	0.303177	0.0646377
$23$	7.71313	1.60830	0.804149	−	0.594427i	$-0.202621\pi$
$23$	7.71313	1.60830	0.804149	+	0.594427i	$0.202621\pi$
$24$	1.91059	0.389998
$25$	5.20664	1.04133
$26$	1.64174	0.321971
$27$	1.00000	0.192450
$28$	0.872752	0.164935
$29$	8.99618	1.67055	0.835274	−	0.549833i	$-0.185309\pi$
$29$	8.99618	1.67055	0.835274	+	0.549833i	$0.185309\pi$
$30$	5.41490	0.988621
$31$	−9.58748	−1.72196	−0.860981	−	0.508637i	$-0.830149\pi$
$31$	−9.58748	−1.72196	−0.860981	+	0.508637i	$0.830149\pi$
$32$	4.62596	0.817763
$33$	−0.178874	−0.0311380
$34$	−1.96137	−0.336372
$35$	−3.19478	−0.540017
$36$	0.872752	0.145459
$37$	−9.91100	−1.62936	−0.814679	−	0.579912i	$-0.803087\pi$
$37$	−9.91100	−1.62936	−0.814679	+	0.579912i	$0.803087\pi$
$38$	−7.08064	−1.14863
$39$	−0.968622	−0.155104
$40$	−6.10394	−0.965117
$41$	−6.08354	−0.950089	−0.475044	−	0.879962i	$-0.657568\pi$
$41$	−6.08354	−0.950089	−0.475044	+	0.879962i	$0.657568\pi$
$42$	−1.69492	−0.261532
$43$	−2.46708	−0.376225	−0.188113	−	0.982147i	$-0.560237\pi$
$43$	−2.46708	−0.376225	−0.188113	+	0.982147i	$0.560237\pi$
$44$	−0.156113	−0.0235349
$45$	−3.19478	−0.476250
$46$	−13.0731	−1.92753
$47$	13.2209	1.92847	0.964235	−	0.265049i	$-0.0853880\pi$
$47$	13.2209	1.92847	0.964235	+	0.265049i	$0.0853880\pi$
$48$	−4.98381	−0.719351
$49$	1.00000	0.142857
$50$	−8.82483	−1.24802
$51$	1.15721	0.162041
$52$	−0.845367	−0.117231
$53$	−9.95804	−1.36784	−0.683921	−	0.729556i	$-0.739727\pi$
$53$	−9.95804	−1.36784	−0.683921	+	0.729556i	$0.739727\pi$
$54$	−1.69492	−0.230649
$55$	0.571465	0.0770563
$56$	1.91059	0.255314
$57$	4.17756	0.553332
$58$	−15.2478	−2.00213
$59$	6.39864	0.833032	0.416516	−	0.909128i	$-0.363251\pi$
$59$	6.39864	0.833032	0.416516	+	0.909128i	$0.363251\pi$
$60$	−2.78825	−0.359962
$61$	−6.43868	−0.824389	−0.412194	−	0.911096i	$-0.635238\pi$
$61$	−6.43868	−0.824389	−0.412194	+	0.911096i	$0.635238\pi$
$62$	16.2500	2.06375
$63$	1.00000	0.125988
$64$	2.12698	0.265872
$65$	3.09454	0.383830
$66$	0.303177	0.0373186
$67$	3.79443	0.463563	0.231781	−	0.972768i	$-0.425545\pi$
$67$	3.79443	0.463563	0.231781	+	0.972768i	$0.425545\pi$
$68$	1.00995	0.122475
$69$	7.71313	0.928552
$70$	5.41490	0.647204
$71$	1.48022	0.175670	0.0878348	−	0.996135i	$-0.472005\pi$
$71$	1.48022	0.175670	0.0878348	+	0.996135i	$0.472005\pi$
$72$	1.91059	0.225166
$73$	−9.12334	−1.06781	−0.533903	−	0.845546i	$-0.679275\pi$
$73$	−9.12334	−1.06781	−0.533903	+	0.845546i	$0.679275\pi$
$74$	16.7983	1.95277
$75$	5.20664	0.601211
$76$	3.64598	0.418222
$77$	−0.178874	−0.0203846
$78$	1.64174	0.185890
$79$	−10.0757	−1.13360	−0.566800	−	0.823856i	$-0.691819\pi$
$79$	−10.0757	−1.13360	−0.566800	+	0.823856i	$0.691819\pi$
$80$	15.9222	1.78015
$81$	1.00000	0.111111
$82$	10.3111	1.13867
$83$	12.8248	1.40770	0.703851	−	0.710348i	$-0.251462\pi$
$83$	12.8248	1.40770	0.703851	+	0.710348i	$0.251462\pi$
$84$	0.872752	0.0952251
$85$	−3.69702	−0.400998
$86$	4.18149	0.450902
$87$	8.99618	0.964492
$88$	−0.341756	−0.0364313
$89$	1.00799	0.106846	0.0534232	−	0.998572i	$-0.482987\pi$
$89$	1.00799	0.106846	0.0534232	+	0.998572i	$0.482987\pi$
$90$	5.41490	0.570781
$91$	−0.968622	−0.101539
$92$	6.73165	0.701823
$93$	−9.58748	−0.994175
$94$	−22.4084	−2.31125
$95$	−13.3464	−1.36931
$96$	4.62596	0.472135
$97$	11.8356	1.20173	0.600863	−	0.799352i	$-0.294824\pi$
$97$	11.8356	1.20173	0.600863	+	0.799352i	$0.294824\pi$
$98$	−1.69492	−0.171213
$99$	−0.178874	−0.0179775
$100$	4.54411	0.454411
$101$	0.794845	0.0790900	0.0395450	−	0.999218i	$-0.487409\pi$
$101$	0.794845	0.0790900	0.0395450	+	0.999218i	$0.487409\pi$
$102$	−1.96137	−0.194205
$103$	10.4585	1.03051	0.515254	−	0.857038i	$-0.327698\pi$
$103$	10.4585	1.03051	0.515254	+	0.857038i	$0.327698\pi$
$104$	−1.85064	−0.181471
$105$	−3.19478	−0.311779
$106$	16.8781	1.63934
$107$	−17.9937	−1.73952	−0.869760	−	0.493475i	$-0.835727\pi$
$107$	−17.9937	−1.73952	−0.869760	+	0.493475i	$0.835727\pi$
$108$	0.872752	0.0839806
$109$	12.6765	1.21418	0.607092	−	0.794631i	$-0.292336\pi$
$109$	12.6765	1.21418	0.607092	+	0.794631i	$0.292336\pi$
$110$	−0.968586	−0.0923511
$111$	−9.91100	−0.940711
$112$	−4.98381	−0.470926
$113$	−10.5096	−0.988662	−0.494331	−	0.869274i	$-0.664587\pi$
$113$	−10.5096	−0.988662	−0.494331	+	0.869274i	$0.664587\pi$
$114$	−7.08064	−0.663162
$115$	−24.6418	−2.29786
$116$	7.85143	0.728987
$117$	−0.968622	−0.0895491
$118$	−10.8452	−0.998380
$119$	1.15721	0.106081
$120$	−6.10394	−0.557211
$121$	−10.9680	−0.997091
$122$	10.9130	0.988021
$123$	−6.08354	−0.548534
$124$	−8.36749	−0.751423
$125$	−0.660168	−0.0590472
$126$	−1.69492	−0.150995
$127$	21.1439	1.87622	0.938110	−	0.346336i	$-0.112574\pi$
$127$	21.1439	1.87622	0.938110	+	0.346336i	$0.112574\pi$
$128$	−12.8570	−1.13641
$129$	−2.46708	−0.217214
$130$	−5.24499	−0.460016
$131$	5.48371	0.479114	0.239557	−	0.970882i	$-0.422998\pi$
$131$	5.48371	0.479114	0.239557	+	0.970882i	$0.422998\pi$
$132$	−0.156113	−0.0135879
$133$	4.17756	0.362241
$134$	−6.43125	−0.555575
$135$	−3.19478	−0.274963
$136$	2.21095	0.189588
$137$	−1.77152	−0.151351	−0.0756756	−	0.997132i	$-0.524111\pi$
$137$	−1.77152	−0.151351	−0.0756756	+	0.997132i	$0.524111\pi$
$138$	−13.0731	−1.11286
$139$	2.95471	0.250615	0.125308	−	0.992118i	$-0.460008\pi$
$139$	2.95471	0.250615	0.125308	+	0.992118i	$0.460008\pi$
$140$	−2.78825	−0.235650
$141$	13.2209	1.11340
$142$	−2.50885	−0.210538
$143$	0.173262	0.0144889
$144$	−4.98381	−0.415317
$145$	−28.7408	−2.38680
$146$	15.4633	1.27975
$147$	1.00000	0.0824786
$148$	−8.64985	−0.711013
$149$	2.26364	0.185445	0.0927224	−	0.995692i	$-0.470443\pi$
$149$	2.26364	0.185445	0.0927224	+	0.995692i	$0.470443\pi$
$150$	−8.82483	−0.720545
$151$	6.16105	0.501379	0.250690	−	0.968068i	$-0.419343\pi$
$151$	6.16105	0.501379	0.250690	+	0.968068i	$0.419343\pi$
$152$	7.98163	0.647396
$153$	1.15721	0.0935546
$154$	0.303177	0.0244307
$155$	30.6299	2.46025
$156$	−0.845367	−0.0676835
$157$	14.9405	1.19238	0.596192	−	0.802842i	$-0.296680\pi$
$157$	14.9405	1.19238	0.596192	+	0.802842i	$0.296680\pi$
$158$	17.0774	1.35861
$159$	−9.95804	−0.789724
$160$	−14.7790	−1.16838
$161$	7.71313	0.607880
$162$	−1.69492	−0.133165
$163$	−12.0704	−0.945424	−0.472712	−	0.881217i	$-0.656725\pi$
$163$	−12.0704	−0.945424	−0.472712	+	0.881217i	$0.656725\pi$
$164$	−5.30942	−0.414596
$165$	0.571465	0.0444885
$166$	−21.7370	−1.68712
$167$	−4.38189	−0.339081	−0.169540	−	0.985523i	$-0.554228\pi$
$167$	−4.38189	−0.339081	−0.169540	+	0.985523i	$0.554228\pi$
$168$	1.91059	0.147406
$169$	−12.0618	−0.927829
$170$	6.26615	0.480592
$171$	4.17756	0.319466
$172$	−2.15314	−0.164176
$173$	5.35922	0.407454	0.203727	−	0.979028i	$-0.434694\pi$
$173$	5.35922	0.407454	0.203727	+	0.979028i	$0.434694\pi$
$174$	−15.2478	−1.15593
$175$	5.20664	0.393585
$176$	0.891475	0.0671975
$177$	6.39864	0.480951
$178$	−1.70846	−0.128054
$179$	−1.76224	−0.131716	−0.0658579	−	0.997829i	$-0.520978\pi$
$179$	−1.76224	−0.131716	−0.0658579	+	0.997829i	$0.520978\pi$
$180$	−2.78825	−0.207824
$181$	3.55731	0.264413	0.132206	−	0.991222i	$-0.457794\pi$
$181$	3.55731	0.264413	0.132206	+	0.991222i	$0.457794\pi$
$182$	1.64174	0.121694
$183$	−6.43868	−0.475961
$184$	14.7367	1.08640
$185$	31.6635	2.32795
$186$	16.2500	1.19151
$187$	−0.206994	−0.0151369
$188$	11.5386	0.841538
$189$	1.00000	0.0727393
$190$	22.6211	1.64111
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	2.12698	0.153502
$193$	14.8550	1.06928	0.534642	−	0.845079i	$-0.320446\pi$
$193$	14.8550	1.06928	0.534642	+	0.845079i	$0.320446\pi$
$194$	−20.0605	−1.44026
$195$	3.09454	0.221604
$196$	0.872752	0.0623394
$197$	8.74083	0.622758	0.311379	−	0.950286i	$-0.399209\pi$
$197$	8.74083	0.622758	0.311379	+	0.950286i	$0.399209\pi$
$198$	0.303177	0.0215459
$199$	−16.6557	−1.18069	−0.590346	−	0.807150i	$-0.701009\pi$
$199$	−16.6557	−1.18069	−0.590346	+	0.807150i	$0.701009\pi$
$200$	9.94778	0.703414
$201$	3.79443	0.267638
$202$	−1.34720	−0.0947885
$203$	8.99618	0.631408
$204$	1.00995	0.0707109
$205$	19.4356	1.35744
$206$	−17.7263	−1.23505
$207$	7.71313	0.536100
$208$	4.82743	0.334722
$209$	−0.747259	−0.0516890
$210$	5.41490	0.373664
$211$	8.02832	0.552693	0.276346	−	0.961058i	$-0.410876\pi$
$211$	8.02832	0.552693	0.276346	+	0.961058i	$0.410876\pi$
$212$	−8.69090	−0.596893
$213$	1.48022	0.101423
$214$	30.4979	2.08480
$215$	7.88177	0.537532
$216$	1.91059	0.129999
$217$	−9.58748	−0.650840
$218$	−21.4856	−1.45519
$219$	−9.12334	−0.616498
$220$	0.498747	0.0336255
$221$	−1.12090	−0.0753996
$222$	16.7983	1.12743
$223$	24.4454	1.63698	0.818491	−	0.574519i	$-0.194811\pi$
$223$	24.4454	1.63698	0.818491	+	0.574519i	$0.194811\pi$
$224$	4.62596	0.309085
$225$	5.20664	0.347109
$226$	17.8130	1.18490
$227$	12.2179	0.810932	0.405466	−	0.914110i	$-0.367109\pi$
$227$	12.2179	0.810932	0.405466	+	0.914110i	$0.367109\pi$
$228$	3.64598	0.241461
$229$	21.7585	1.43784	0.718920	−	0.695093i	$-0.244637\pi$
$229$	21.7585	1.43784	0.718920	+	0.695093i	$0.244637\pi$
$230$	41.7658	2.75396
$231$	−0.178874	−0.0117691
$232$	17.1881	1.12845
$233$	−18.5689	−1.21649	−0.608246	−	0.793749i	$-0.708127\pi$
$233$	−18.5689	−1.21649	−0.608246	+	0.793749i	$0.708127\pi$
$234$	1.64174	0.107324
$235$	−42.2380	−2.75530
$236$	5.58443	0.363515
$237$	−10.0757	−0.654484
$238$	−1.96137	−0.127137
$239$	13.3161	0.861350	0.430675	−	0.902507i	$-0.358276\pi$
$239$	13.3161	0.861350	0.430675	+	0.902507i	$0.358276\pi$
$240$	15.9222	1.02777
$241$	−3.52478	−0.227051	−0.113525	−	0.993535i	$-0.536214\pi$
$241$	−3.52478	−0.227051	−0.113525	+	0.993535i	$0.536214\pi$
$242$	18.5899	1.19500
$243$	1.00000	0.0641500
$244$	−5.61937	−0.359743
$245$	−3.19478	−0.204107
$246$	10.3111	0.657412
$247$	−4.04648	−0.257471
$248$	−18.3178	−1.16318
$249$	12.8248	0.812737
$250$	1.11893	0.0707674
$251$	16.2615	1.02642	0.513208	−	0.858264i	$-0.328457\pi$
$251$	16.2615	1.02642	0.513208	+	0.858264i	$0.328457\pi$
$252$	0.872752	0.0549782
$253$	−1.37968	−0.0867398
$254$	−35.8373	−2.24863
$255$	−3.69702	−0.231516
$256$	17.5376	1.09610
$257$	−9.93748	−0.619883	−0.309941	−	0.950756i	$-0.600309\pi$
$257$	−9.93748	−0.619883	−0.309941	+	0.950756i	$0.600309\pi$
$258$	4.18149	0.260328
$259$	−9.91100	−0.615840
$260$	2.70076	0.167494
$261$	8.99618	0.556850
$262$	−9.29445	−0.574213
$263$	25.4551	1.56963	0.784815	−	0.619730i	$-0.212758\pi$
$263$	25.4551	1.56963	0.784815	+	0.619730i	$0.212758\pi$
$264$	−0.341756	−0.0210336
$265$	31.8138	1.95430
$266$	−7.08064	−0.434142
$267$	1.00799	0.0616878
$268$	3.31159	0.202288
$269$	4.87389	0.297166	0.148583	−	0.988900i	$-0.452529\pi$
$269$	4.87389	0.297166	0.148583	+	0.988900i	$0.452529\pi$
$270$	5.41490	0.329540
$271$	3.93466	0.239014	0.119507	−	0.992833i	$-0.461869\pi$
$271$	3.93466	0.239014	0.119507	+	0.992833i	$0.461869\pi$
$272$	−5.76729	−0.349693
$273$	−0.968622	−0.0586237
$274$	3.00258	0.181393
$275$	−0.931334	−0.0561615
$276$	6.73165	0.405198
$277$	4.67777	0.281060	0.140530	−	0.990076i	$-0.455119\pi$
$277$	4.67777	0.281060	0.140530	+	0.990076i	$0.455119\pi$
$278$	−5.00799	−0.300360
$279$	−9.58748	−0.573987
$280$	−6.10394	−0.364780
$281$	13.0932	0.781077	0.390539	−	0.920586i	$-0.372289\pi$
$281$	13.0932	0.781077	0.390539	+	0.920586i	$0.372289\pi$
$282$	−22.4084	−1.33440
$283$	23.9878	1.42592	0.712962	−	0.701203i	$-0.247353\pi$
$283$	23.9878	1.42592	0.712962	+	0.701203i	$0.247353\pi$
$284$	1.29186	0.0766580
$285$	−13.3464	−0.790573
$286$	−0.293664	−0.0173647
$287$	−6.08354	−0.359100
$288$	4.62596	0.272588
$289$	−15.6609	−0.921228
$290$	48.7134	2.86055
$291$	11.8356	0.693817
$292$	−7.96241	−0.465965
$293$	10.1748	0.594419	0.297209	−	0.954812i	$-0.403944\pi$
$293$	10.1748	0.594419	0.297209	+	0.954812i	$0.403944\pi$
$294$	−1.69492	−0.0988497
$295$	−20.4423	−1.19019
$296$	−18.9359	−1.10063
$297$	−0.178874	−0.0103793
$298$	−3.83669	−0.222254
$299$	−7.47111	−0.432065
$300$	4.54411	0.262354
$301$	−2.46708	−0.142200
$302$	−10.4425	−0.600897
$303$	0.794845	0.0456626
$304$	−20.8202	−1.19412
$305$	20.5702	1.17785
$306$	−1.96137	−0.112124
$307$	24.8009	1.41546	0.707731	−	0.706482i	$-0.249719\pi$
$307$	24.8009	1.41546	0.707731	+	0.706482i	$0.249719\pi$
$308$	−0.156113	−0.00889536
$309$	10.4585	0.594964
$310$	−51.9152	−2.94859
$311$	−0.518912	−0.0294248	−0.0147124	−	0.999892i	$-0.504683\pi$
$311$	−0.518912	−0.0294248	−0.0147124	+	0.999892i	$0.504683\pi$
$312$	−1.85064	−0.104772
$313$	−21.5545	−1.21833	−0.609166	−	0.793043i	$-0.708496\pi$
$313$	−21.5545	−1.21833	−0.609166	+	0.793043i	$0.708496\pi$
$314$	−25.3230	−1.42906
$315$	−3.19478	−0.180006
$316$	−8.79355	−0.494676
$317$	−0.282729	−0.0158797	−0.00793983	−	0.999968i	$-0.502527\pi$
$317$	−0.282729	−0.0158797	−0.00793983	+	0.999968i	$0.502527\pi$
$318$	16.8781	0.946475
$319$	−1.60919	−0.0900971
$320$	−6.79524	−0.379865
$321$	−17.9937	−1.00431
$322$	−13.0731	−0.728537
$323$	4.83430	0.268988
$324$	0.872752	0.0484862
$325$	−5.04327	−0.279750
$326$	20.4583	1.13308
$327$	12.6765	0.701010
$328$	−11.6232	−0.641782
$329$	13.2209	0.728893
$330$	−0.968586	−0.0533189
$331$	−0.422981	−0.0232491	−0.0116246	−	0.999932i	$-0.503700\pi$
$331$	−0.422981	−0.0232491	−0.0116246	+	0.999932i	$0.503700\pi$
$332$	11.1928	0.614287
$333$	−9.91100	−0.543119
$334$	7.42695	0.406384
$335$	−12.1224	−0.662316
$336$	−4.98381	−0.271889
$337$	−23.5931	−1.28520	−0.642599	−	0.766203i	$-0.722144\pi$
$337$	−23.5931	−1.28520	−0.642599	+	0.766203i	$0.722144\pi$
$338$	20.4437	1.11199
$339$	−10.5096	−0.570805
$340$	−3.22658	−0.174986
$341$	1.71495	0.0928699
$342$	−7.08064	−0.382877
$343$	1.00000	0.0539949
$344$	−4.71358	−0.254139
$345$	−24.6418	−1.32667
$346$	−9.08345	−0.488329
$347$	−28.9627	−1.55480	−0.777401	−	0.629006i	$-0.783462\pi$
$347$	−28.9627	−1.55480	−0.777401	+	0.629006i	$0.783462\pi$
$348$	7.85143	0.420881
$349$	−24.0451	−1.28711	−0.643553	−	0.765401i	$-0.722540\pi$
$349$	−24.0451	−1.28711	−0.643553	+	0.765401i	$0.722540\pi$
$350$	−8.82483	−0.471707
$351$	−0.968622	−0.0517012
$352$	−0.827466	−0.0441041
$353$	−17.6996	−0.942053	−0.471027	−	0.882119i	$-0.656116\pi$
$353$	−17.6996	−0.942053	−0.471027	+	0.882119i	$0.656116\pi$
$354$	−10.8452	−0.576415
$355$	−4.72898	−0.250988
$356$	0.879723	0.0466252
$357$	1.15721	0.0612458
$358$	2.98685	0.157860
$359$	11.6975	0.617368	0.308684	−	0.951165i	$-0.400111\pi$
$359$	11.6975	0.617368	0.308684	+	0.951165i	$0.400111\pi$
$360$	−6.10394	−0.321706
$361$	−1.54795	−0.0814712
$362$	−6.02935	−0.316896
$363$	−10.9680	−0.575671
$364$	−0.845367	−0.0443093
$365$	29.1471	1.52563
$366$	10.9130	0.570434
$367$	10.9879	0.573562	0.286781	−	0.957996i	$-0.407415\pi$
$367$	10.9879	0.573562	0.286781	+	0.957996i	$0.407415\pi$
$368$	−38.4408	−2.00386
$369$	−6.08354	−0.316696
$370$	−53.6671	−2.79002
$371$	−9.95804	−0.516996
$372$	−8.36749	−0.433834
$373$	20.6908	1.07133	0.535665	−	0.844430i	$-0.320061\pi$
$373$	20.6908	1.07133	0.535665	+	0.844430i	$0.320061\pi$
$374$	0.350839	0.0181414
$375$	−0.660168	−0.0340909
$376$	25.2598	1.30268
$377$	−8.71390	−0.448789
$378$	−1.69492	−0.0871773
$379$	23.9848	1.23202	0.616008	−	0.787740i	$-0.288749\pi$
$379$	23.9848	1.23202	0.616008	+	0.787740i	$0.288749\pi$
$380$	−11.6481	−0.597535
$381$	21.1439	1.08324
$382$	−1.69492	−0.0867196
$383$	37.7897	1.93097	0.965483	−	0.260467i	$-0.0838766\pi$
$383$	37.7897	1.93097	0.965483	+	0.260467i	$0.0838766\pi$
$384$	−12.8570	−0.656105
$385$	0.571465	0.0291245
$386$	−25.1780	−1.28153
$387$	−2.46708	−0.125408
$388$	10.3296	0.524405
$389$	−0.685224	−0.0347422	−0.0173711	−	0.999849i	$-0.505530\pi$
$389$	−0.685224	−0.0347422	−0.0173711	+	0.999849i	$0.505530\pi$
$390$	−5.24499	−0.265590
$391$	8.92568	0.451391
$392$	1.91059	0.0964996
$393$	5.48371	0.276617
$394$	−14.8150	−0.746369
$395$	32.1895	1.61963
$396$	−0.156113	−0.00784497
$397$	35.3763	1.77548	0.887742	−	0.460341i	$-0.152273\pi$
$397$	35.3763	1.77548	0.887742	+	0.460341i	$0.152273\pi$
$398$	28.2301	1.41505
$399$	4.17756	0.209140
$400$	−25.9489	−1.29744
$401$	−12.8880	−0.643598	−0.321799	−	0.946808i	$-0.604287\pi$
$401$	−12.8880	−0.643598	−0.321799	+	0.946808i	$0.604287\pi$
$402$	−6.43125	−0.320761
$403$	9.28664	0.462601
$404$	0.693702	0.0345130
$405$	−3.19478	−0.158750
$406$	−15.2478	−0.756736
$407$	1.77282	0.0878756
$408$	2.21095	0.109458
$409$	36.3215	1.79598	0.897992	−	0.440012i	$-0.145026\pi$
$409$	36.3215	1.79598	0.897992	+	0.440012i	$0.145026\pi$
$410$	−32.9417	−1.62688
$411$	−1.77152	−0.0873826
$412$	9.12768	0.449689
$413$	6.39864	0.314857
$414$	−13.0731	−0.642509
$415$	−40.9724	−2.01125
$416$	−4.48081	−0.219690
$417$	2.95471	0.144693
$418$	1.26654	0.0619487
$419$	20.5767	1.00524	0.502618	−	0.864509i	$-0.332370\pi$
$419$	20.5767	1.00524	0.502618	+	0.864509i	$0.332370\pi$
$420$	−2.78825	−0.136053
$421$	−12.7929	−0.623488	−0.311744	−	0.950166i	$-0.600913\pi$
$421$	−12.7929	−0.623488	−0.311744	+	0.950166i	$0.600913\pi$
$422$	−13.6074	−0.662396
$423$	13.2209	0.642823
$424$	−19.0258	−0.923973
$425$	6.02515	0.292263
$426$	−2.50885	−0.121554
$427$	−6.43868	−0.311590
$428$	−15.7041	−0.759085
$429$	0.173262	0.00836515
$430$	−13.3590	−0.644227
$431$	−2.96231	−0.142690	−0.0713448	−	0.997452i	$-0.522729\pi$
$431$	−2.96231	−0.142690	−0.0713448	+	0.997452i	$0.522729\pi$
$432$	−4.98381	−0.239784
$433$	−26.5229	−1.27461	−0.637304	−	0.770613i	$-0.719950\pi$
$433$	−26.5229	−1.27461	−0.637304	+	0.770613i	$0.719950\pi$
$434$	16.2500	0.780025
$435$	−28.7408	−1.37802
$436$	11.0634	0.529841
$437$	32.2221	1.54139
$438$	15.4633	0.738866
$439$	16.1379	0.770218	0.385109	−	0.922871i	$-0.374164\pi$
$439$	16.1379	0.770218	0.385109	+	0.922871i	$0.374164\pi$
$440$	1.09184	0.0520513
$441$	1.00000	0.0476190
$442$	1.89983	0.0903655
$443$	36.9973	1.75779	0.878896	−	0.477013i	$-0.158280\pi$
$443$	36.9973	1.75779	0.878896	+	0.477013i	$0.158280\pi$
$444$	−8.64985	−0.410504
$445$	−3.22030	−0.152657
$446$	−41.4329	−1.96191
$447$	2.26364	0.107067
$448$	2.12698	0.100490
$449$	−17.3082	−0.816823	−0.408412	−	0.912798i	$-0.633917\pi$
$449$	−17.3082	−0.816823	−0.408412	+	0.912798i	$0.633917\pi$
$450$	−8.82483	−0.416007
$451$	1.08819	0.0512408
$452$	−9.17230	−0.431429
$453$	6.16105	0.289471
$454$	−20.7084	−0.971893
$455$	3.09454	0.145074
$456$	7.98163	0.373774
$457$	15.6196	0.730656	0.365328	−	0.930879i	$-0.380957\pi$
$457$	15.6196	0.730656	0.365328	+	0.930879i	$0.380957\pi$
$458$	−36.8789	−1.72324
$459$	1.15721	0.0540137
$460$	−21.5062	−1.00273
$461$	33.4802	1.55933	0.779664	−	0.626199i	$-0.215390\pi$
$461$	33.4802	1.55933	0.779664	+	0.626199i	$0.215390\pi$
$462$	0.303177	0.0141051
$463$	26.4003	1.22692	0.613462	−	0.789724i	$-0.289776\pi$
$463$	26.4003	1.22692	0.613462	+	0.789724i	$0.289776\pi$
$464$	−44.8352	−2.08142
$465$	30.6299	1.42043
$466$	31.4729	1.45795
$467$	−11.3812	−0.526659	−0.263329	−	0.964706i	$-0.584821\pi$
$467$	−11.3812	−0.526659	−0.263329	+	0.964706i	$0.584821\pi$
$468$	−0.845367	−0.0390771
$469$	3.79443	0.175210
$470$	71.5900	3.30220
$471$	14.9405	0.688423
$472$	12.2252	0.562711
$473$	0.441296	0.0202908
$474$	17.0774	0.784392
$475$	21.7511	0.998008
$476$	1.00995	0.0462912
$477$	−9.95804	−0.455947
$478$	−22.5698	−1.03232
$479$	37.0786	1.69416	0.847082	−	0.531463i	$-0.178357\pi$
$479$	37.0786	1.69416	0.847082	+	0.531463i	$0.178357\pi$
$480$	−14.7790	−0.674564
$481$	9.60001	0.437723
$482$	5.97421	0.272118
$483$	7.71313	0.350960
$484$	−9.57235	−0.435107
$485$	−37.8123	−1.71697
$486$	−1.69492	−0.0768831
$487$	−40.9537	−1.85579	−0.927895	−	0.372842i	$-0.878383\pi$
$487$	−40.9537	−1.85579	−0.927895	+	0.372842i	$0.878383\pi$
$488$	−12.3017	−0.556872
$489$	−12.0704	−0.545841
$490$	5.41490	0.244620
$491$	29.7166	1.34109	0.670545	−	0.741869i	$-0.266060\pi$
$491$	29.7166	1.34109	0.670545	+	0.741869i	$0.266060\pi$
$492$	−5.30942	−0.239367
$493$	10.4104	0.468862
$494$	6.85846	0.308577
$495$	0.571465	0.0256854
$496$	47.7822	2.14548
$497$	1.48022	0.0663969
$498$	−21.7370	−0.974056
$499$	−7.30354	−0.326951	−0.163476	−	0.986547i	$-0.552271\pi$
$499$	−7.30354	−0.326951	−0.163476	+	0.986547i	$0.552271\pi$
$500$	−0.576163	−0.0257668
$501$	−4.38189	−0.195768
$502$	−27.5619	−1.23015
$503$	15.9423	0.710833	0.355417	−	0.934708i	$-0.384339\pi$
$503$	15.9423	0.710833	0.355417	+	0.934708i	$0.384339\pi$
$504$	1.91059	0.0851046
$505$	−2.53936	−0.113000
$506$	2.33845	0.103957
$507$	−12.0618	−0.535682
$508$	18.4534	0.818738
$509$	1.39748	0.0619423	0.0309711	−	0.999520i	$-0.490140\pi$
$509$	1.39748	0.0619423	0.0309711	+	0.999520i	$0.490140\pi$
$510$	6.26615	0.277470
$511$	−9.12334	−0.403593
$512$	−4.01084	−0.177256
$513$	4.17756	0.184444
$514$	16.8432	0.742923
$515$	−33.4127	−1.47234
$516$	−2.15314	−0.0947869
$517$	−2.36488	−0.104007
$518$	16.7983	0.738077
$519$	5.35922	0.235244
$520$	5.91241	0.259276
$521$	−20.3562	−0.891821	−0.445910	−	0.895078i	$-0.647120\pi$
$521$	−20.3562	−0.891821	−0.445910	+	0.895078i	$0.647120\pi$
$522$	−15.2478	−0.667378
$523$	−1.41174	−0.0617311	−0.0308655	−	0.999524i	$-0.509826\pi$
$523$	−1.41174	−0.0617311	−0.0308655	+	0.999524i	$0.509826\pi$
$524$	4.78592	0.209074
$525$	5.20664	0.227236
$526$	−43.1444	−1.88119
$527$	−11.0947	−0.483292
$528$	0.891475	0.0387965
$529$	36.4924	1.58662
$530$	−53.9218	−2.34221
$531$	6.39864	0.277677
$532$	3.64598	0.158073
$533$	5.89265	0.255239
$534$	−1.70846	−0.0739321
$535$	57.4861	2.48534
$536$	7.24961	0.313135
$537$	−1.76224	−0.0760462
$538$	−8.26085	−0.356151
$539$	−0.178874	−0.00770466
$540$	−2.78825	−0.119987
$541$	19.9966	0.859719	0.429860	−	0.902896i	$-0.358563\pi$
$541$	19.9966	0.859719	0.429860	+	0.902896i	$0.358563\pi$
$542$	−6.66893	−0.286455
$543$	3.55731	0.152659
$544$	5.35319	0.229516
$545$	−40.4985	−1.73477
$546$	1.64174	0.0702598
$547$	−1.54673	−0.0661335	−0.0330667	−	0.999453i	$-0.510527\pi$
$547$	−1.54673	−0.0661335	−0.0330667	+	0.999453i	$0.510527\pi$
$548$	−1.54610	−0.0660460
$549$	−6.43868	−0.274796
$550$	1.57854	0.0673090
$551$	37.5821	1.60105
$552$	14.7367	0.627234
$553$	−10.0757	−0.428460
$554$	−7.92844	−0.336847
$555$	31.6635	1.34404
$556$	2.57873	0.109362
$557$	−6.48564	−0.274805	−0.137403	−	0.990515i	$-0.543875\pi$
$557$	−6.48564	−0.274805	−0.137403	+	0.990515i	$0.543875\pi$
$558$	16.2500	0.687918
$559$	2.38966	0.101072
$560$	15.9222	0.672835
$561$	−0.206994	−0.00873931
$562$	−22.1920	−0.936113
$563$	29.6857	1.25110	0.625551	−	0.780183i	$-0.284874\pi$
$563$	29.6857	1.25110	0.625551	+	0.780183i	$0.284874\pi$
$564$	11.5386	0.485862
$565$	33.5760	1.41255
$566$	−40.6573	−1.70895
$567$	1.00000	0.0419961
$568$	2.82810	0.118664
$569$	−7.83485	−0.328454	−0.164227	−	0.986423i	$-0.552513\pi$
$569$	−7.83485	−0.328454	−0.164227	+	0.986423i	$0.552513\pi$
$570$	22.6211	0.947493
$571$	4.12086	0.172453	0.0862263	−	0.996276i	$-0.472519\pi$
$571$	4.12086	0.172453	0.0862263	+	0.996276i	$0.472519\pi$
$572$	0.151214	0.00632259
$573$	1.00000	0.0417756
$574$	10.3111	0.430377
$575$	40.1595	1.67477
$576$	2.12698	0.0886241
$577$	−25.9609	−1.08077	−0.540383	−	0.841419i	$-0.681721\pi$
$577$	−25.9609	−1.08077	−0.540383	+	0.841419i	$0.681721\pi$
$578$	26.5439	1.10408
$579$	14.8550	0.617352
$580$	−25.0836	−1.04154
$581$	12.8248	0.532061
$582$	−20.0605	−0.831532
$583$	1.78124	0.0737713
$584$	−17.4310	−0.721300
$585$	3.09454	0.127943
$586$	−17.2455	−0.712405
$587$	29.3923	1.21315	0.606576	−	0.795026i	$-0.292543\pi$
$587$	29.3923	1.21315	0.606576	+	0.795026i	$0.292543\pi$
$588$	0.872752	0.0359917
$589$	−40.0523	−1.65033
$590$	34.6480	1.42644
$591$	8.74083	0.359550
$592$	49.3945	2.03010
$593$	5.64446	0.231790	0.115895	−	0.993261i	$-0.463026\pi$
$593$	5.64446	0.231790	0.115895	+	0.993261i	$0.463026\pi$
$594$	0.303177	0.0124395
$595$	−3.69702	−0.151563
$596$	1.97560	0.0809237
$597$	−16.6557	−0.681673
$598$	12.6629	0.517825
$599$	−33.8230	−1.38197	−0.690986	−	0.722868i	$-0.742823\pi$
$599$	−33.8230	−1.38197	−0.690986	+	0.722868i	$0.742823\pi$
$600$	9.94778	0.406116
$601$	−14.1987	−0.579176	−0.289588	−	0.957151i	$-0.593518\pi$
$601$	−14.1987	−0.579176	−0.289588	+	0.957151i	$0.593518\pi$
$602$	4.18149	0.170425
$603$	3.79443	0.154521
$604$	5.37707	0.218790
$605$	35.0404	1.42459
$606$	−1.34720	−0.0547262
$607$	−18.3519	−0.744881	−0.372441	−	0.928056i	$-0.621479\pi$
$607$	−18.3519	−0.744881	−0.372441	+	0.928056i	$0.621479\pi$
$608$	19.3253	0.783743
$609$	8.99618	0.364544
$610$	−34.8648	−1.41163
$611$	−12.8061	−0.518078
$612$	1.00995	0.0408250
$613$	−21.1714	−0.855104	−0.427552	−	0.903991i	$-0.640624\pi$
$613$	−21.1714	−0.855104	−0.427552	+	0.903991i	$0.640624\pi$
$614$	−42.0355	−1.69642
$615$	19.4356	0.783718
$616$	−0.341756	−0.0137698
$617$	24.9284	1.00358	0.501791	−	0.864989i	$-0.332675\pi$
$617$	24.9284	1.00358	0.501791	+	0.864989i	$0.332675\pi$
$618$	−17.7263	−0.713057
$619$	22.8769	0.919498	0.459749	−	0.888049i	$-0.347939\pi$
$619$	22.8769	0.919498	0.459749	+	0.888049i	$0.347939\pi$
$620$	26.7323	1.07360
$621$	7.71313	0.309517
$622$	0.879515	0.0352653
$623$	1.00799	0.0403841
$624$	4.82743	0.193252
$625$	−23.9241	−0.956964
$626$	36.5331	1.46016
$627$	−0.747259	−0.0298426
$628$	13.0394	0.520328
$629$	−11.4691	−0.457302
$630$	5.41490	0.215735
$631$	19.3627	0.770818	0.385409	−	0.922746i	$-0.374060\pi$
$631$	19.3627	0.770818	0.385409	+	0.922746i	$0.374060\pi$
$632$	−19.2505	−0.765743
$633$	8.02832	0.319097
$634$	0.479203	0.0190316
$635$	−67.5503	−2.68065
$636$	−8.69090	−0.344616
$637$	−0.968622	−0.0383782
$638$	2.72744	0.107980
$639$	1.48022	0.0585565
$640$	41.0753	1.62364
$641$	−4.07089	−0.160790	−0.0803952	−	0.996763i	$-0.525618\pi$
$641$	−4.07089	−0.160790	−0.0803952	+	0.996763i	$0.525618\pi$
$642$	30.4979	1.20366
$643$	−10.8678	−0.428585	−0.214292	−	0.976770i	$-0.568745\pi$
$643$	−10.8678	−0.428585	−0.214292	+	0.976770i	$0.568745\pi$
$644$	6.73165	0.265264
$645$	7.88177	0.310344
$646$	−8.19375	−0.322379
$647$	7.05376	0.277312	0.138656	−	0.990341i	$-0.455722\pi$
$647$	7.05376	0.277312	0.138656	+	0.990341i	$0.455722\pi$
$648$	1.91059	0.0750552
$649$	−1.14455	−0.0449276
$650$	8.54793	0.335277
$651$	−9.58748	−0.375763
$652$	−10.5344	−0.412560
$653$	−22.6639	−0.886906	−0.443453	−	0.896298i	$-0.646247\pi$
$653$	−22.6639	−0.886906	−0.443453	+	0.896298i	$0.646247\pi$
$654$	−21.4856	−0.840152
$655$	−17.5193	−0.684535
$656$	30.3192	1.18377
$657$	−9.12334	−0.355935
$658$	−22.4084	−0.873570
$659$	21.9135	0.853627	0.426814	−	0.904340i	$-0.359636\pi$
$659$	21.9135	0.853627	0.426814	+	0.904340i	$0.359636\pi$
$660$	0.498747	0.0194137
$661$	−45.5899	−1.77324	−0.886621	−	0.462497i	$-0.846954\pi$
$661$	−45.5899	−1.77324	−0.886621	+	0.462497i	$0.846954\pi$
$662$	0.716918	0.0278638
$663$	−1.12090	−0.0435320
$664$	24.5029	0.950899
$665$	−13.3464	−0.517552
$666$	16.7983	0.650923
$667$	69.3887	2.68674
$668$	−3.82430	−0.147967
$669$	24.4454	0.945112
$670$	20.5464	0.793778
$671$	1.15171	0.0444614
$672$	4.62596	0.178450
$673$	13.0520	0.503118	0.251559	−	0.967842i	$-0.419057\pi$
$673$	13.0520	0.503118	0.251559	+	0.967842i	$0.419057\pi$
$674$	39.9884	1.54029
$675$	5.20664	0.200404
$676$	−10.5269	−0.404882
$677$	−46.9328	−1.80377	−0.901886	−	0.431974i	$-0.857817\pi$
$677$	−46.9328	−1.80377	−0.901886	+	0.431974i	$0.857817\pi$
$678$	17.8130	0.684103
$679$	11.8356	0.454210
$680$	−7.06351	−0.270873
$681$	12.2179	0.468192
$682$	−2.90671	−0.111304
$683$	6.38942	0.244484	0.122242	−	0.992500i	$-0.460992\pi$
$683$	6.38942	0.244484	0.122242	+	0.992500i	$0.460992\pi$
$684$	3.64598	0.139407
$685$	5.65962	0.216243
$686$	−1.69492	−0.0647123
$687$	21.7585	0.830138
$688$	12.2954	0.468759
$689$	9.64557	0.367467
$690$	41.7658	1.59000
$691$	−13.3845	−0.509171	−0.254585	−	0.967050i	$-0.581939\pi$
$691$	−13.3845	−0.509171	−0.254585	+	0.967050i	$0.581939\pi$
$692$	4.67727	0.177803
$693$	−0.178874	−0.00679487
$694$	49.0895	1.86341
$695$	−9.43965	−0.358067
$696$	17.1881	0.651511
$697$	−7.03991	−0.266655
$698$	40.7546	1.54258
$699$	−18.5689	−0.702342
$700$	4.54411	0.171751
$701$	12.0061	0.453464	0.226732	−	0.973957i	$-0.427196\pi$
$701$	12.0061	0.453464	0.226732	+	0.973957i	$0.427196\pi$
$702$	1.64174	0.0619633
$703$	−41.4038	−1.56158
$704$	−0.380462	−0.0143392
$705$	−42.2380	−1.59077
$706$	29.9993	1.12904
$707$	0.794845	0.0298932
$708$	5.58443	0.209876
$709$	44.3775	1.66663	0.833316	−	0.552797i	$-0.186440\pi$
$709$	44.3775	1.66663	0.833316	+	0.552797i	$0.186440\pi$
$710$	8.01524	0.300806
$711$	−10.0757	−0.377866
$712$	1.92585	0.0721744
$713$	−73.9495	−2.76943
$714$	−1.96137	−0.0734025
$715$	−0.553533	−0.0207010
$716$	−1.53800	−0.0574776
$717$	13.3161	0.497301
$718$	−19.8262	−0.739909
$719$	−13.5952	−0.507014	−0.253507	−	0.967334i	$-0.581584\pi$
$719$	−13.5952	−0.507014	−0.253507	+	0.967334i	$0.581584\pi$
$720$	15.9222	0.593385
$721$	10.4585	0.389495
$722$	2.62366	0.0976424
$723$	−3.52478	−0.131088
$724$	3.10465	0.115383
$725$	46.8399	1.73959
$726$	18.5899	0.689935
$727$	24.5090	0.908987	0.454493	−	0.890750i	$-0.349820\pi$
$727$	24.5090	0.908987	0.454493	+	0.890750i	$0.349820\pi$
$728$	−1.85064	−0.0685894
$729$	1.00000	0.0370370
$730$	−49.4020	−1.82845
$731$	−2.85491	−0.105593
$732$	−5.61937	−0.207698
$733$	−42.7639	−1.57952	−0.789761	−	0.613415i	$-0.789795\pi$
$733$	−42.7639	−1.57952	−0.789761	+	0.613415i	$0.789795\pi$
$734$	−18.6236	−0.687408
$735$	−3.19478	−0.117841
$736$	35.6807	1.31521
$737$	−0.678725	−0.0250012
$738$	10.3111	0.379557
$739$	−43.1066	−1.58570	−0.792851	−	0.609415i	$-0.791404\pi$
$739$	−43.1066	−1.58570	−0.792851	+	0.609415i	$0.791404\pi$
$740$	27.6344	1.01586
$741$	−4.04648	−0.148651
$742$	16.8781	0.619614
$743$	11.9467	0.438282	0.219141	−	0.975693i	$-0.429675\pi$
$743$	11.9467	0.438282	0.219141	+	0.975693i	$0.429675\pi$
$744$	−18.3178	−0.671563
$745$	−7.23185	−0.264954
$746$	−35.0693	−1.28398
$747$	12.8248	0.469234
$748$	−0.180655	−0.00660539
$749$	−17.9937	−0.657477
$750$	1.11893	0.0408576
$751$	−29.1450	−1.06352	−0.531758	−	0.846897i	$-0.678468\pi$
$751$	−29.1450	−1.06352	−0.531758	+	0.846897i	$0.678468\pi$
$752$	−65.8905	−2.40278
$753$	16.2615	0.592602
$754$	14.7694	0.537868
$755$	−19.6832	−0.716346
$756$	0.872752	0.0317417
$757$	−31.9925	−1.16279	−0.581393	−	0.813623i	$-0.697492\pi$
$757$	−31.9925	−1.16279	−0.581393	+	0.813623i	$0.697492\pi$
$758$	−40.6523	−1.47656
$759$	−1.37968	−0.0500792
$760$	−25.4996	−0.924967
$761$	2.23114	0.0808789	0.0404395	−	0.999182i	$-0.487124\pi$
$761$	2.23114	0.0808789	0.0404395	+	0.999182i	$0.487124\pi$
$762$	−35.8373	−1.29825
$763$	12.6765	0.458918
$764$	0.872752	0.0315751
$765$	−3.69702	−0.133666
$766$	−64.0506	−2.31424
$767$	−6.19786	−0.223792
$768$	17.5376	0.632834
$769$	−40.0967	−1.44592	−0.722962	−	0.690887i	$-0.757220\pi$
$769$	−40.0967	−1.44592	−0.722962	+	0.690887i	$0.757220\pi$
$770$	−0.968586	−0.0349054
$771$	−9.93748	−0.357890
$772$	12.9647	0.466610
$773$	−0.410909	−0.0147794	−0.00738968	−	0.999973i	$-0.502352\pi$
$773$	−0.410909	−0.0147794	−0.00738968	+	0.999973i	$0.502352\pi$
$774$	4.18149	0.150301
$775$	−49.9185	−1.79313
$776$	22.6131	0.811763
$777$	−9.91100	−0.355555
$778$	1.16140	0.0416382
$779$	−25.4144	−0.910564
$780$	2.70076	0.0967028
$781$	−0.264773	−0.00947432
$782$	−15.1283	−0.540987
$783$	8.99618	0.321497
$784$	−4.98381	−0.177993
$785$	−47.7317	−1.70362
$786$	−9.29445	−0.331522
$787$	30.9713	1.10401	0.552003	−	0.833842i	$-0.313864\pi$
$787$	30.9713	1.10401	0.552003	+	0.833842i	$0.313864\pi$
$788$	7.62858	0.271757
$789$	25.4551	0.906227
$790$	−54.5587	−1.94111
$791$	−10.5096	−0.373679
$792$	−0.341756	−0.0121438
$793$	6.23665	0.221470
$794$	−59.9599	−2.12790
$795$	31.8138	1.12832
$796$	−14.5363	−0.515226
$797$	7.69123	0.272437	0.136219	−	0.990679i	$-0.456505\pi$
$797$	7.69123	0.272437	0.136219	+	0.990679i	$0.456505\pi$
$798$	−7.08064	−0.250652
$799$	15.2993	0.541251
$800$	24.0857	0.851559
$801$	1.00799	0.0356155
$802$	21.8442	0.771345
$803$	1.63193	0.0575896
$804$	3.31159	0.116791
$805$	−24.6418	−0.868508
$806$	−15.7401	−0.554422
$807$	4.87389	0.171569
$808$	1.51863	0.0534251
$809$	25.3170	0.890097	0.445048	−	0.895507i	$-0.353186\pi$
$809$	25.3170	0.890097	0.445048	+	0.895507i	$0.353186\pi$
$810$	5.41490	0.190260
$811$	20.6664	0.725695	0.362848	−	0.931848i	$-0.381805\pi$
$811$	20.6664	0.725695	0.362848	+	0.931848i	$0.381805\pi$
$812$	7.85143	0.275531
$813$	3.93466	0.137995
$814$	−3.00479	−0.105318
$815$	38.5622	1.35077
$816$	−5.76729	−0.201896
$817$	−10.3064	−0.360574
$818$	−61.5620	−2.15247
$819$	−0.968622	−0.0338464
$820$	16.9624	0.592354
$821$	−2.83580	−0.0989703	−0.0494851	−	0.998775i	$-0.515758\pi$
$821$	−2.83580	−0.0989703	−0.0494851	+	0.998775i	$0.515758\pi$
$822$	3.00258	0.104727
$823$	3.26713	0.113885	0.0569426	−	0.998377i	$-0.481865\pi$
$823$	3.26713	0.113885	0.0569426	+	0.998377i	$0.481865\pi$
$824$	19.9820	0.696105
$825$	−0.931334	−0.0324249
$826$	−10.8452	−0.377352
$827$	−0.182407	−0.00634291	−0.00317145	−	0.999995i	$-0.501010\pi$
$827$	−0.182407	−0.00634291	−0.00317145	+	0.999995i	$0.501010\pi$
$828$	6.73165	0.233941
$829$	−25.7093	−0.892920	−0.446460	−	0.894804i	$-0.647315\pi$
$829$	−25.7093	−0.892920	−0.446460	+	0.894804i	$0.647315\pi$
$830$	69.4449	2.41047
$831$	4.67777	0.162270
$832$	−2.06024	−0.0714259
$833$	1.15721	0.0400948
$834$	−5.00799	−0.173413
$835$	13.9992	0.484462
$836$	−0.652172	−0.0225558
$837$	−9.58748	−0.331392
$838$	−34.8758	−1.20476
$839$	−45.9768	−1.58730	−0.793648	−	0.608377i	$-0.791821\pi$
$839$	−45.9768	−1.58730	−0.793648	+	0.608377i	$0.791821\pi$
$840$	−6.10394	−0.210606
$841$	51.9313	1.79073
$842$	21.6829	0.747244
$843$	13.0932	0.450955
$844$	7.00674	0.241182
$845$	38.5347	1.32564
$846$	−22.4084	−0.770417
$847$	−10.9680	−0.376865
$848$	49.6289	1.70427
$849$	23.9878	0.823258
$850$	−10.2122	−0.350274
$851$	−76.4448	−2.62049
$852$	1.29186	0.0442585
$853$	−32.5376	−1.11406	−0.557032	−	0.830491i	$-0.688060\pi$
$853$	−32.5376	−1.11406	−0.557032	+	0.830491i	$0.688060\pi$
$854$	10.9130	0.373437
$855$	−13.3464	−0.456438
$856$	−34.3787	−1.17504
$857$	18.6358	0.636586	0.318293	−	0.947992i	$-0.396890\pi$
$857$	18.6358	0.636586	0.318293	+	0.947992i	$0.396890\pi$
$858$	−0.293664	−0.0100255
$859$	26.5232	0.904961	0.452481	−	0.891774i	$-0.350539\pi$
$859$	26.5232	0.904961	0.452481	+	0.891774i	$0.350539\pi$
$860$	6.87883	0.234566
$861$	−6.08354	−0.207326
$862$	5.02088	0.171012
$863$	−2.58434	−0.0879720	−0.0439860	−	0.999032i	$-0.514006\pi$
$863$	−2.58434	−0.0879720	−0.0439860	+	0.999032i	$0.514006\pi$
$864$	4.62596	0.157378
$865$	−17.1216	−0.582150
$866$	44.9541	1.52760
$867$	−15.6609	−0.531871
$868$	−8.36749	−0.284011
$869$	1.80228	0.0611380
$870$	48.7134	1.65154
$871$	−3.67536	−0.124535
$872$	24.2196	0.820178
$873$	11.8356	0.400576
$874$	−54.6139	−1.84734
$875$	−0.660168	−0.0223177
$876$	−7.96241	−0.269025
$877$	1.73776	0.0586801	0.0293400	−	0.999569i	$-0.490659\pi$
$877$	1.73776	0.0586801	0.0293400	+	0.999569i	$0.490659\pi$
$878$	−27.3524	−0.923098
$879$	10.1748	0.343188
$880$	−2.84807	−0.0960084
$881$	8.98841	0.302827	0.151414	−	0.988470i	$-0.451617\pi$
$881$	8.98841	0.302827	0.151414	+	0.988470i	$0.451617\pi$
$882$	−1.69492	−0.0570709
$883$	6.10168	0.205338	0.102669	−	0.994716i	$-0.467262\pi$
$883$	6.10168	0.205338	0.102669	+	0.994716i	$0.467262\pi$
$884$	−0.978263	−0.0329026
$885$	−20.4423	−0.687159
$886$	−62.7074	−2.10670
$887$	34.7175	1.16570	0.582850	−	0.812580i	$-0.301938\pi$
$887$	34.7175	1.16570	0.582850	+	0.812580i	$0.301938\pi$
$888$	−18.9359	−0.635447
$889$	21.1439	0.709145
$890$	5.45815	0.182958
$891$	−0.178874	−0.00599251
$892$	21.3347	0.714340
$893$	55.2313	1.84824
$894$	−3.83669	−0.128318
$895$	5.62997	0.188189
$896$	−12.8570	−0.429522
$897$	−7.47111	−0.249453
$898$	29.3360	0.978954
$899$	−86.2507	−2.87662
$900$	4.54411	0.151470
$901$	−11.5235	−0.383903
$902$	−1.84439	−0.0614115
$903$	−2.46708	−0.0820991
$904$	−20.0796	−0.667839
$905$	−11.3648	−0.377780
$906$	−10.4425	−0.346928
$907$	−38.3305	−1.27274	−0.636372	−	0.771383i	$-0.719566\pi$
$907$	−38.3305	−1.27274	−0.636372	+	0.771383i	$0.719566\pi$
$908$	10.6632	0.353871
$909$	0.794845	0.0263633
$910$	−5.24499	−0.173870
$911$	20.4262	0.676749	0.338375	−	0.941011i	$-0.390123\pi$
$911$	20.4262	0.676749	0.338375	+	0.941011i	$0.390123\pi$
$912$	−20.8202	−0.689425
$913$	−2.29402	−0.0759210
$914$	−26.4740	−0.875683
$915$	20.5702	0.680029
$916$	18.9898	0.627439
$917$	5.48371	0.181088
$918$	−1.96137	−0.0647349
$919$	48.5489	1.60148	0.800740	−	0.599012i	$-0.204440\pi$
$919$	48.5489	1.60148	0.800740	+	0.599012i	$0.204440\pi$
$920$	−47.0804	−1.55220
$921$	24.8009	0.817218
$922$	−56.7462	−1.86884
$923$	−1.43377	−0.0471932
$924$	−0.156113	−0.00513574
$925$	−51.6030	−1.69670
$926$	−44.7463	−1.47046
$927$	10.4585	0.343502
$928$	41.6160	1.36611
$929$	−41.7733	−1.37054	−0.685269	−	0.728290i	$-0.740315\pi$
$929$	−41.7733	−1.37054	−0.685269	+	0.728290i	$0.740315\pi$
$930$	−51.9152	−1.70237
$931$	4.17756	0.136914
$932$	−16.2061	−0.530848
$933$	−0.518912	−0.0169884
$934$	19.2902	0.631195
$935$	0.661302	0.0216269
$936$	−1.85064	−0.0604902
$937$	4.66576	0.152424	0.0762118	−	0.997092i	$-0.475717\pi$
$937$	4.66576	0.152424	0.0762118	+	0.997092i	$0.475717\pi$
$938$	−6.43125	−0.209988
$939$	−21.5545	−0.703404
$940$	−36.8633	−1.20235
$941$	32.9361	1.07369	0.536843	−	0.843682i	$-0.319617\pi$
$941$	32.9361	1.07369	0.536843	+	0.843682i	$0.319617\pi$
$942$	−25.3230	−0.825067
$943$	−46.9231	−1.52803
$944$	−31.8896	−1.03792
$945$	−3.19478	−0.103926
$946$	−0.747962	−0.0243183
$947$	35.1780	1.14313	0.571566	−	0.820556i	$-0.306336\pi$
$947$	35.1780	1.14313	0.571566	+	0.820556i	$0.306336\pi$
$948$	−8.79355	−0.285601
$949$	8.83707	0.286863
$950$	−36.8663	−1.19610
$951$	−0.282729	−0.00916813
$952$	2.21095	0.0716573
$953$	28.3478	0.918275	0.459137	−	0.888365i	$-0.348159\pi$
$953$	28.3478	0.918275	0.459137	+	0.888365i	$0.348159\pi$
$954$	16.8781	0.546448
$955$	−3.19478	−0.103381
$956$	11.6217	0.375872
$957$	−1.60919	−0.0520176
$958$	−62.8452	−2.03044
$959$	−1.77152	−0.0572053
$960$	−6.79524	−0.219315
$961$	60.9197	1.96515
$962$	−16.2712	−0.524606
$963$	−17.9937	−0.579840
$964$	−3.07626	−0.0990795
$965$	−47.4584	−1.52774
$966$	−13.0731	−0.420621
$967$	−30.5810	−0.983418	−0.491709	−	0.870760i	$-0.663628\pi$
$967$	−30.5810	−0.983418	−0.491709	+	0.870760i	$0.663628\pi$
$968$	−20.9554	−0.673532
$969$	4.83430	0.155300
$970$	64.0888	2.05777
$971$	−39.2820	−1.26062	−0.630309	−	0.776344i	$-0.717072\pi$
$971$	−39.2820	−1.26062	−0.630309	+	0.776344i	$0.717072\pi$
$972$	0.872752	0.0279935
$973$	2.95471	0.0947236
$974$	69.4132	2.22414
$975$	−5.04327	−0.161514
$976$	32.0891	1.02715
$977$	11.7466	0.375806	0.187903	−	0.982188i	$-0.439831\pi$
$977$	11.7466	0.375806	0.187903	+	0.982188i	$0.439831\pi$
$978$	20.4583	0.654184
$979$	−0.180303	−0.00576251
$980$	−2.78825	−0.0890675
$981$	12.6765	0.404728
$982$	−50.3672	−1.60728
$983$	−50.8285	−1.62118	−0.810588	−	0.585617i	$-0.800852\pi$
$983$	−50.8285	−1.62118	−0.810588	+	0.585617i	$0.800852\pi$
$984$	−11.6232	−0.370533
$985$	−27.9251	−0.889766
$986$	−17.6448	−0.561926
$987$	13.2209	0.420827
$988$	−3.53157	−0.112354
$989$	−19.0289	−0.605083
$990$	−0.968586	−0.0307837
$991$	−26.0321	−0.826938	−0.413469	−	0.910518i	$-0.635683\pi$
$991$	−26.0321	−0.826938	−0.413469	+	0.910518i	$0.635683\pi$
$992$	−44.3513	−1.40816
$993$	−0.422981	−0.0134229
$994$	−2.50885	−0.0795759
$995$	53.2114	1.68691
$996$	11.1928	0.354659
$997$	−53.0935	−1.68149	−0.840745	−	0.541432i	$-0.817882\pi$
$997$	−53.0935	−1.68149	−0.840745	+	0.541432i	$0.817882\pi$
$998$	12.3789	0.391848
$999$	−9.91100	−0.313570

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.5	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.5	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-1.69492 q^{2} +1.00000 q^{3} +0.872752 q^{4} -3.19478 q^{5} -1.69492 q^{6} +1.00000 q^{7} +1.91059 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.69492 q^{2} +1.00000 q^{3} +0.872752 q^{4} -3.19478 q^{5} -1.69492 q^{6} +1.00000 q^{7} +1.91059 q^{8} +1.00000 q^{9} +5.41490 q^{10} -0.178874 q^{11} +0.872752 q^{12} -0.968622 q^{13} -1.69492 q^{14} -3.19478 q^{15} -4.98381 q^{16} +1.15721 q^{17} -1.69492 q^{18} +4.17756 q^{19} -2.78825 q^{20} +1.00000 q^{21} +0.303177 q^{22} +7.71313 q^{23} +1.91059 q^{24} +5.20664 q^{25} +1.64174 q^{26} +1.00000 q^{27} +0.872752 q^{28} +8.99618 q^{29} +5.41490 q^{30} -9.58748 q^{31} +4.62596 q^{32} -0.178874 q^{33} -1.96137 q^{34} -3.19478 q^{35} +0.872752 q^{36} -9.91100 q^{37} -7.08064 q^{38} -0.968622 q^{39} -6.10394 q^{40} -6.08354 q^{41} -1.69492 q^{42} -2.46708 q^{43} -0.156113 q^{44} -3.19478 q^{45} -13.0731 q^{46} +13.2209 q^{47} -4.98381 q^{48} +1.00000 q^{49} -8.82483 q^{50} +1.15721 q^{51} -0.845367 q^{52} -9.95804 q^{53} -1.69492 q^{54} +0.571465 q^{55} +1.91059 q^{56} +4.17756 q^{57} -15.2478 q^{58} +6.39864 q^{59} -2.78825 q^{60} -6.43868 q^{61} +16.2500 q^{62} +1.00000 q^{63} +2.12698 q^{64} +3.09454 q^{65} +0.303177 q^{66} +3.79443 q^{67} +1.00995 q^{68} +7.71313 q^{69} +5.41490 q^{70} +1.48022 q^{71} +1.91059 q^{72} -9.12334 q^{73} +16.7983 q^{74} +5.20664 q^{75} +3.64598 q^{76} -0.178874 q^{77} +1.64174 q^{78} -10.0757 q^{79} +15.9222 q^{80} +1.00000 q^{81} +10.3111 q^{82} +12.8248 q^{83} +0.872752 q^{84} -3.69702 q^{85} +4.18149 q^{86} +8.99618 q^{87} -0.341756 q^{88} +1.00799 q^{89} +5.41490 q^{90} -0.968622 q^{91} +6.73165 q^{92} -9.58748 q^{93} -22.4084 q^{94} -13.3464 q^{95} +4.62596 q^{96} +11.8356 q^{97} -1.69492 q^{98} -0.178874 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

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