LMFDB - Embedded newform 2738.2.a.s.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2738,2,Mod(1,2738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2738, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.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:	$21.8630400734$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{36})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 6x^{4} + 9x^{2} - 3 $ x^6 - 6x^4 + 9x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.684040$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.347296 q^{3} +1.00000 q^{4} -0.852666 q^{5} +0.347296 q^{6} +1.38475 q^{7} +1.00000 q^{8} -2.87939 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.347296 q^{3} +1.00000 q^{4} -0.852666 q^{5} +0.347296 q^{6} +1.38475 q^{7} +1.00000 q^{8} -2.87939 q^{9} -0.852666 q^{10} +0.932013 q^{11} +0.347296 q^{12} -3.64182 q^{13} +1.38475 q^{14} -0.296128 q^{15} +1.00000 q^{16} -4.42664 q^{17} -2.87939 q^{18} -3.82511 q^{19} -0.852666 q^{20} +0.480920 q^{21} +0.932013 q^{22} +1.06323 q^{23} +0.347296 q^{24} -4.27296 q^{25} -3.64182 q^{26} -2.04189 q^{27} +1.38475 q^{28} +1.00895 q^{29} -0.296128 q^{30} -7.33920 q^{31} +1.00000 q^{32} +0.323685 q^{33} -4.42664 q^{34} -1.18073 q^{35} -2.87939 q^{36} -3.82511 q^{38} -1.26479 q^{39} -0.852666 q^{40} +0.243134 q^{41} +0.480920 q^{42} +5.13740 q^{43} +0.932013 q^{44} +2.45515 q^{45} +1.06323 q^{46} -7.79590 q^{47} +0.347296 q^{48} -5.08246 q^{49} -4.27296 q^{50} -1.53736 q^{51} -3.64182 q^{52} +12.9791 q^{53} -2.04189 q^{54} -0.794695 q^{55} +1.38475 q^{56} -1.32845 q^{57} +1.00895 q^{58} -9.76735 q^{59} -0.296128 q^{60} -0.397006 q^{61} -7.33920 q^{62} -3.98724 q^{63} +1.00000 q^{64} +3.10525 q^{65} +0.323685 q^{66} +14.2401 q^{67} -4.42664 q^{68} +0.369254 q^{69} -1.18073 q^{70} -13.6693 q^{71} -2.87939 q^{72} +13.1543 q^{73} -1.48398 q^{75} -3.82511 q^{76} +1.29061 q^{77} -1.26479 q^{78} -3.48554 q^{79} -0.852666 q^{80} +7.92902 q^{81} +0.243134 q^{82} -16.7194 q^{83} +0.480920 q^{84} +3.77445 q^{85} +5.13740 q^{86} +0.350404 q^{87} +0.932013 q^{88} -6.28907 q^{89} +2.45515 q^{90} -5.04303 q^{91} +1.06323 q^{92} -2.54888 q^{93} -7.79590 q^{94} +3.26154 q^{95} +0.347296 q^{96} +7.47277 q^{97} -5.08246 q^{98} -2.68362 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^8 - 6 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} - 12 q^{13} + 6 q^{15} + 6 q^{16} - 12 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 6 q^{22} + 6 q^{23} + 6 q^{25} - 12 q^{26} - 6 q^{27} + 6 q^{29} + 6 q^{30} - 18 q^{31} + 6 q^{32} + 6 q^{33} - 12 q^{34} - 24 q^{35} - 6 q^{36} - 12 q^{38} - 6 q^{39} - 6 q^{40} - 12 q^{41} - 12 q^{42} - 6 q^{44} - 6 q^{45} + 6 q^{46} - 6 q^{47} - 12 q^{49} + 6 q^{50} - 24 q^{51} - 12 q^{52} - 24 q^{53} - 6 q^{54} - 36 q^{55} - 24 q^{57} + 6 q^{58} - 12 q^{59} + 6 q^{60} - 12 q^{61} - 18 q^{62} + 6 q^{63} + 6 q^{64} + 18 q^{65} + 6 q^{66} + 18 q^{67} - 12 q^{68} - 24 q^{69} - 24 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{75} - 12 q^{76} + 30 q^{77} - 6 q^{78} - 12 q^{79} - 6 q^{80} - 18 q^{81} - 12 q^{82} - 6 q^{83} - 12 q^{84} + 18 q^{85} - 6 q^{87} - 6 q^{88} - 6 q^{90} - 12 q^{91} + 6 q^{92} + 36 q^{93} - 6 q^{94} + 18 q^{95} + 12 q^{97} - 12 q^{98} + 12 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 - 12 * q^13 + 6 * q^15 + 6 * q^16 - 12 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 - 12 * q^21 - 6 * q^22 + 6 * q^23 + 6 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^29 + 6 * q^30 - 18 * q^31 + 6 * q^32 + 6 * q^33 - 12 * q^34 - 24 * q^35 - 6 * q^36 - 12 * q^38 - 6 * q^39 - 6 * q^40 - 12 * q^41 - 12 * q^42 - 6 * q^44 - 6 * q^45 + 6 * q^46 - 6 * q^47 - 12 * q^49 + 6 * q^50 - 24 * q^51 - 12 * q^52 - 24 * q^53 - 6 * q^54 - 36 * q^55 - 24 * q^57 + 6 * q^58 - 12 * q^59 + 6 * q^60 - 12 * q^61 - 18 * q^62 + 6 * q^63 + 6 * q^64 + 18 * q^65 + 6 * q^66 + 18 * q^67 - 12 * q^68 - 24 * q^69 - 24 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^75 - 12 * q^76 + 30 * q^77 - 6 * q^78 - 12 * q^79 - 6 * q^80 - 18 * q^81 - 12 * q^82 - 6 * q^83 - 12 * q^84 + 18 * q^85 - 6 * q^87 - 6 * q^88 - 6 * q^90 - 12 * q^91 + 6 * q^92 + 36 * q^93 - 6 * q^94 + 18 * q^95 + 12 * q^97 - 12 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.347296	0.200512	0.100256	−	0.994962i	$-0.468034\pi$
$3$	0.347296	0.200512	0.100256	+	0.994962i	$0.468034\pi$
$4$	1.00000	0.500000
$5$	−0.852666	−0.381324	−0.190662	−	0.981656i	$-0.561063\pi$
$5$	−0.852666	−0.381324	−0.190662	+	0.981656i	$0.561063\pi$
$6$	0.347296	0.141783
$7$	1.38475	0.523388	0.261694	−	0.965151i	$-0.415719\pi$
$7$	1.38475	0.523388	0.261694	+	0.965151i	$0.415719\pi$
$8$	1.00000	0.353553
$9$	−2.87939	−0.959795
$10$	−0.852666	−0.269637
$11$	0.932013	0.281012	0.140506	−	0.990080i	$-0.455127\pi$
$11$	0.932013	0.281012	0.140506	+	0.990080i	$0.455127\pi$
$12$	0.347296	0.100256
$13$	−3.64182	−1.01006	−0.505030	−	0.863102i	$-0.668518\pi$
$13$	−3.64182	−1.01006	−0.505030	+	0.863102i	$0.668518\pi$
$14$	1.38475	0.370091
$15$	−0.296128	−0.0764598
$16$	1.00000	0.250000
$17$	−4.42664	−1.07362	−0.536809	−	0.843704i	$-0.680371\pi$
$17$	−4.42664	−1.07362	−0.536809	+	0.843704i	$0.680371\pi$
$18$	−2.87939	−0.678678
$19$	−3.82511	−0.877540	−0.438770	−	0.898599i	$-0.644586\pi$
$19$	−3.82511	−0.877540	−0.438770	+	0.898599i	$0.644586\pi$
$20$	−0.852666	−0.190662
$21$	0.480920	0.104945
$22$	0.932013	0.198706
$23$	1.06323	0.221698	0.110849	−	0.993837i	$-0.464643\pi$
$23$	1.06323	0.221698	0.110849	+	0.993837i	$0.464643\pi$
$24$	0.347296	0.0708916
$25$	−4.27296	−0.854592
$26$	−3.64182	−0.714220
$27$	−2.04189	−0.392962
$28$	1.38475	0.261694
$29$	1.00895	0.187357	0.0936786	−	0.995602i	$-0.470137\pi$
$29$	1.00895	0.187357	0.0936786	+	0.995602i	$0.470137\pi$
$30$	−0.296128	−0.0540653
$31$	−7.33920	−1.31816	−0.659080	−	0.752073i	$-0.729054\pi$
$31$	−7.33920	−1.31816	−0.659080	+	0.752073i	$0.729054\pi$
$32$	1.00000	0.176777
$33$	0.323685	0.0563463
$34$	−4.42664	−0.759163
$35$	−1.18073	−0.199580
$36$	−2.87939	−0.479898
$37$	0	0
$37$	0	0
$38$	−3.82511	−0.620515
$39$	−1.26479	−0.202529
$40$	−0.852666	−0.134818
$41$	0.243134	0.0379711	0.0189856	−	0.999820i	$-0.493956\pi$
$41$	0.243134	0.0379711	0.0189856	+	0.999820i	$0.493956\pi$
$42$	0.480920	0.0742076
$43$	5.13740	0.783447	0.391723	−	0.920083i	$-0.371879\pi$
$43$	5.13740	0.783447	0.391723	+	0.920083i	$0.371879\pi$
$44$	0.932013	0.140506
$45$	2.45515	0.365993
$46$	1.06323	0.156764
$47$	−7.79590	−1.13715	−0.568574	−	0.822632i	$-0.692505\pi$
$47$	−7.79590	−1.13715	−0.568574	+	0.822632i	$0.692505\pi$
$48$	0.347296	0.0501279
$49$	−5.08246	−0.726065
$50$	−4.27296	−0.604288
$51$	−1.53736	−0.215273
$52$	−3.64182	−0.505030
$53$	12.9791	1.78282	0.891409	−	0.453199i	$-0.149717\pi$
$53$	12.9791	1.78282	0.891409	+	0.453199i	$0.149717\pi$
$54$	−2.04189	−0.277866
$55$	−0.794695	−0.107157
$56$	1.38475	0.185046
$57$	−1.32845	−0.175957
$58$	1.00895	0.132481
$59$	−9.76735	−1.27160	−0.635800	−	0.771854i	$-0.719330\pi$
$59$	−9.76735	−1.27160	−0.635800	+	0.771854i	$0.719330\pi$
$60$	−0.296128	−0.0382299
$61$	−0.397006	−0.0508314	−0.0254157	−	0.999677i	$-0.508091\pi$
$61$	−0.397006	−0.0508314	−0.0254157	+	0.999677i	$0.508091\pi$
$62$	−7.33920	−0.932079
$63$	−3.98724	−0.502345
$64$	1.00000	0.125000
$65$	3.10525	0.385159
$66$	0.323685	0.0398428
$67$	14.2401	1.73971	0.869855	−	0.493308i	$-0.164212\pi$
$67$	14.2401	1.73971	0.869855	+	0.493308i	$0.164212\pi$
$68$	−4.42664	−0.536809
$69$	0.369254	0.0444530
$70$	−1.18073	−0.141125
$71$	−13.6693	−1.62224	−0.811122	−	0.584876i	$-0.801143\pi$
$71$	−13.6693	−1.62224	−0.811122	+	0.584876i	$0.801143\pi$
$72$	−2.87939	−0.339339
$73$	13.1543	1.53959	0.769794	−	0.638292i	$-0.220359\pi$
$73$	13.1543	1.53959	0.769794	+	0.638292i	$0.220359\pi$
$74$	0	0
$75$	−1.48398	−0.171356
$76$	−3.82511	−0.438770
$77$	1.29061	0.147079
$78$	−1.26479	−0.143209
$79$	−3.48554	−0.392154	−0.196077	−	0.980589i	$-0.562820\pi$
$79$	−3.48554	−0.392154	−0.196077	+	0.980589i	$0.562820\pi$
$80$	−0.852666	−0.0953309
$81$	7.92902	0.881002
$82$	0.243134	0.0268496
$83$	−16.7194	−1.83519	−0.917594	−	0.397518i	$-0.869872\pi$
$83$	−16.7194	−1.83519	−0.917594	+	0.397518i	$0.869872\pi$
$84$	0.480920	0.0524727
$85$	3.77445	0.409396
$86$	5.13740	0.553980
$87$	0.350404	0.0375673
$88$	0.932013	0.0993529
$89$	−6.28907	−0.666640	−0.333320	−	0.942814i	$-0.608169\pi$
$89$	−6.28907	−0.666640	−0.333320	+	0.942814i	$0.608169\pi$
$90$	2.45515	0.258796
$91$	−5.04303	−0.528653
$92$	1.06323	0.110849
$93$	−2.54888	−0.264306
$94$	−7.79590	−0.804085
$95$	3.26154	0.334627
$96$	0.347296	0.0354458
$97$	7.47277	0.758744	0.379372	−	0.925244i	$-0.376140\pi$
$97$	7.47277	0.758744	0.379372	+	0.925244i	$0.376140\pi$
$98$	−5.08246	−0.513405
$99$	−2.68362	−0.269714
$100$	−4.27296	−0.427296
$101$	4.02880	0.400881	0.200440	−	0.979706i	$-0.435763\pi$
$101$	4.02880	0.400881	0.200440	+	0.979706i	$0.435763\pi$
$102$	−1.53736	−0.152221
$103$	0.233104	0.0229684	0.0114842	−	0.999934i	$-0.496344\pi$
$103$	0.233104	0.0229684	0.0114842	+	0.999934i	$0.496344\pi$
$104$	−3.64182	−0.357110
$105$	−0.410064	−0.0400182
$106$	12.9791	1.26064
$107$	6.44912	0.623460	0.311730	−	0.950171i	$-0.399092\pi$
$107$	6.44912	0.623460	0.311730	+	0.950171i	$0.399092\pi$
$108$	−2.04189	−0.196481
$109$	−13.7765	−1.31955	−0.659773	−	0.751465i	$-0.729347\pi$
$109$	−13.7765	−1.31955	−0.659773	+	0.751465i	$0.729347\pi$
$110$	−0.794695	−0.0757712
$111$	0	0
$112$	1.38475	0.130847
$113$	4.26033	0.400778	0.200389	−	0.979716i	$-0.435779\pi$
$113$	4.26033	0.400778	0.200389	+	0.979716i	$0.435779\pi$
$114$	−1.32845	−0.124420
$115$	−0.906576	−0.0845386
$116$	1.00895	0.0936786
$117$	10.4862	0.969450
$118$	−9.76735	−0.899157
$119$	−6.12981	−0.561919
$120$	−0.296128	−0.0270326
$121$	−10.1314	−0.921032
$122$	−0.397006	−0.0359433
$123$	0.0844395	0.00761365
$124$	−7.33920	−0.659080
$125$	7.90673	0.707200
$126$	−3.98724	−0.355212
$127$	11.5291	1.02304	0.511521	−	0.859271i	$-0.329082\pi$
$127$	11.5291	1.02304	0.511521	+	0.859271i	$0.329082\pi$
$128$	1.00000	0.0883883
$129$	1.78420	0.157090
$130$	3.10525	0.272349
$131$	−10.4534	−0.913315	−0.456657	−	0.889643i	$-0.650953\pi$
$131$	−10.4534	−0.913315	−0.456657	+	0.889643i	$0.650953\pi$
$132$	0.323685	0.0281731
$133$	−5.29684	−0.459294
$134$	14.2401	1.23016
$135$	1.74105	0.149846
$136$	−4.42664	−0.379582
$137$	−6.77895	−0.579165	−0.289582	−	0.957153i	$-0.593516\pi$
$137$	−6.77895	−0.579165	−0.289582	+	0.957153i	$0.593516\pi$
$138$	0.369254	0.0314330
$139$	19.1491	1.62421	0.812104	−	0.583513i	$-0.198322\pi$
$139$	19.1491	1.62421	0.812104	+	0.583513i	$0.198322\pi$
$140$	−1.18073	−0.0997901
$141$	−2.70749	−0.228012
$142$	−13.6693	−1.14710
$143$	−3.39422	−0.283839
$144$	−2.87939	−0.239949
$145$	−0.860296	−0.0714437
$146$	13.1543	1.08865
$147$	−1.76512	−0.145584
$148$	0	0
$149$	4.47583	0.366674	0.183337	−	0.983050i	$-0.441310\pi$
$149$	4.47583	0.366674	0.183337	+	0.983050i	$0.441310\pi$
$150$	−1.48398	−0.121167
$151$	−8.84231	−0.719577	−0.359789	−	0.933034i	$-0.617151\pi$
$151$	−8.84231	−0.719577	−0.359789	+	0.933034i	$0.617151\pi$
$152$	−3.82511	−0.310257
$153$	12.7460	1.03045
$154$	1.29061	0.104000
$155$	6.25788	0.502645
$156$	−1.26479	−0.101264
$157$	−18.4218	−1.47022	−0.735111	−	0.677947i	$-0.762870\pi$
$157$	−18.4218	−1.47022	−0.735111	+	0.677947i	$0.762870\pi$
$158$	−3.48554	−0.277294
$159$	4.50760	0.357476
$160$	−0.852666	−0.0674091
$161$	1.47231	0.116034
$162$	7.92902	0.622962
$163$	−9.23285	−0.723173	−0.361586	−	0.932339i	$-0.617765\pi$
$163$	−9.23285	−0.723173	−0.361586	+	0.932339i	$0.617765\pi$
$164$	0.243134	0.0189856
$165$	−0.275995	−0.0214862
$166$	−16.7194	−1.29767
$167$	−16.3096	−1.26207	−0.631037	−	0.775753i	$-0.717370\pi$
$167$	−16.3096	−1.26207	−0.631037	+	0.775753i	$0.717370\pi$
$168$	0.480920	0.0371038
$169$	0.262857	0.0202198
$170$	3.77445	0.289487
$171$	11.0140	0.842259
$172$	5.13740	0.391723
$173$	−1.92224	−0.146145	−0.0730726	−	0.997327i	$-0.523280\pi$
$173$	−1.92224	−0.146145	−0.0730726	+	0.997327i	$0.523280\pi$
$174$	0.350404	0.0265641
$175$	−5.91700	−0.447283
$176$	0.932013	0.0702531
$177$	−3.39216	−0.254971
$178$	−6.28907	−0.471386
$179$	18.8954	1.41231	0.706154	−	0.708059i	$-0.250429\pi$
$179$	18.8954	1.41231	0.706154	+	0.708059i	$0.250429\pi$
$180$	2.45515	0.182996
$181$	6.85363	0.509426	0.254713	−	0.967017i	$-0.418019\pi$
$181$	6.85363	0.509426	0.254713	+	0.967017i	$0.418019\pi$
$182$	−5.04303	−0.373814
$183$	−0.137879	−0.0101923
$184$	1.06323	0.0783820
$185$	0	0
$186$	−2.54888	−0.186893
$187$	−4.12569	−0.301700
$188$	−7.79590	−0.568574
$189$	−2.82751	−0.205671
$190$	3.26154	0.236617
$191$	21.1777	1.53236	0.766181	−	0.642625i	$-0.222155\pi$
$191$	21.1777	1.53236	0.766181	+	0.642625i	$0.222155\pi$
$192$	0.347296	0.0250640
$193$	−7.67587	−0.552521	−0.276261	−	0.961083i	$-0.589095\pi$
$193$	−7.67587	−0.552521	−0.276261	+	0.961083i	$0.589095\pi$
$194$	7.47277	0.536513
$195$	1.07844	0.0772290
$196$	−5.08246	−0.363033
$197$	−11.3622	−0.809523	−0.404762	−	0.914422i	$-0.632646\pi$
$197$	−11.3622	−0.809523	−0.404762	+	0.914422i	$0.632646\pi$
$198$	−2.68362	−0.190717
$199$	−24.8783	−1.76358	−0.881788	−	0.471646i	$-0.843660\pi$
$199$	−24.8783	−1.76358	−0.881788	+	0.471646i	$0.843660\pi$
$200$	−4.27296	−0.302144
$201$	4.94555	0.348832
$202$	4.02880	0.283465
$203$	1.39715	0.0980605
$204$	−1.53736	−0.107637
$205$	−0.207312	−0.0144793
$206$	0.233104	0.0162411
$207$	−3.06144	−0.212785
$208$	−3.64182	−0.252515
$209$	−3.56505	−0.246600
$210$	−0.410064	−0.0282971
$211$	13.1296	0.903879	0.451939	−	0.892049i	$-0.350732\pi$
$211$	13.1296	0.903879	0.451939	+	0.892049i	$0.350732\pi$
$212$	12.9791	0.891409
$213$	−4.74729	−0.325279
$214$	6.44912	0.440853
$215$	−4.38049	−0.298747
$216$	−2.04189	−0.138933
$217$	−10.1630	−0.689909
$218$	−13.7765	−0.933059
$219$	4.56842	0.308705
$220$	−0.794695	−0.0535783
$221$	16.1210	1.08442
$222$	0	0
$223$	1.40208	0.0938902	0.0469451	−	0.998897i	$-0.485051\pi$
$223$	1.40208	0.0938902	0.0469451	+	0.998897i	$0.485051\pi$
$224$	1.38475	0.0925228
$225$	12.3035	0.820233
$226$	4.26033	0.283393
$227$	−3.00615	−0.199525	−0.0997627	−	0.995011i	$-0.531808\pi$
$227$	−3.00615	−0.199525	−0.0997627	+	0.995011i	$0.531808\pi$
$228$	−1.32845	−0.0879785
$229$	9.28299	0.613437	0.306719	−	0.951800i	$-0.400769\pi$
$229$	9.28299	0.613437	0.306719	+	0.951800i	$0.400769\pi$
$230$	−0.906576	−0.0597778
$231$	0.448224	0.0294910
$232$	1.00895	0.0662407
$233$	27.4216	1.79645	0.898225	−	0.439536i	$-0.144857\pi$
$233$	27.4216	1.79645	0.898225	+	0.439536i	$0.144857\pi$
$234$	10.4862	0.685505
$235$	6.64729	0.433622
$236$	−9.76735	−0.635800
$237$	−1.21051	−0.0786314
$238$	−6.12981	−0.397337
$239$	−0.739736	−0.0478495	−0.0239248	−	0.999714i	$-0.507616\pi$
$239$	−0.739736	−0.0478495	−0.0239248	+	0.999714i	$0.507616\pi$
$240$	−0.296128	−0.0191150
$241$	−0.923265	−0.0594727	−0.0297364	−	0.999558i	$-0.509467\pi$
$241$	−0.923265	−0.0594727	−0.0297364	+	0.999558i	$0.509467\pi$
$242$	−10.1314	−0.651268
$243$	8.87939	0.569613
$244$	−0.397006	−0.0254157
$245$	4.33363	0.276866
$246$	0.0844395	0.00538367
$247$	13.9304	0.886368
$248$	−7.33920	−0.466040
$249$	−5.80658	−0.367977
$250$	7.90673	0.500066
$251$	−9.83141	−0.620553	−0.310277	−	0.950646i	$-0.600422\pi$
$251$	−9.83141	−0.620553	−0.310277	+	0.950646i	$0.600422\pi$
$252$	−3.98724	−0.251173
$253$	0.990940	0.0622999
$254$	11.5291	0.723400
$255$	1.31085	0.0820887
$256$	1.00000	0.0625000
$257$	−5.17095	−0.322555	−0.161278	−	0.986909i	$-0.551561\pi$
$257$	−5.17095	−0.322555	−0.161278	+	0.986909i	$0.551561\pi$
$258$	1.78420	0.111080
$259$	0	0
$260$	3.10525	0.192580
$261$	−2.90515	−0.179824
$262$	−10.4534	−0.645811
$263$	20.5241	1.26557	0.632785	−	0.774327i	$-0.281912\pi$
$263$	20.5241	1.26557	0.632785	+	0.774327i	$0.281912\pi$
$264$	0.323685	0.0199214
$265$	−11.0668	−0.679831
$266$	−5.29684	−0.324770
$267$	−2.18417	−0.133669
$268$	14.2401	0.869855
$269$	16.5164	1.00702	0.503512	−	0.863988i	$-0.332041\pi$
$269$	16.5164	1.00702	0.503512	+	0.863988i	$0.332041\pi$
$270$	1.74105	0.105957
$271$	−10.6339	−0.645961	−0.322980	−	0.946406i	$-0.604685\pi$
$271$	−10.6339	−0.645961	−0.322980	+	0.946406i	$0.604685\pi$
$272$	−4.42664	−0.268405
$273$	−1.75142	−0.106001
$274$	−6.77895	−0.409531
$275$	−3.98245	−0.240151
$276$	0.369254	0.0222265
$277$	−6.55413	−0.393799	−0.196900	−	0.980424i	$-0.563087\pi$
$277$	−6.55413	−0.393799	−0.196900	+	0.980424i	$0.563087\pi$
$278$	19.1491	1.14849
$279$	21.1324	1.26516
$280$	−1.18073	−0.0705623
$281$	−24.7267	−1.47507	−0.737537	−	0.675307i	$-0.764011\pi$
$281$	−24.7267	−1.47507	−0.737537	+	0.675307i	$0.764011\pi$
$282$	−2.70749	−0.161229
$283$	−19.7140	−1.17188	−0.585938	−	0.810356i	$-0.699274\pi$
$283$	−19.7140	−1.17188	−0.585938	+	0.810356i	$0.699274\pi$
$284$	−13.6693	−0.811122
$285$	1.13272	0.0670966
$286$	−3.39422	−0.200705
$287$	0.336681	0.0198736
$288$	−2.87939	−0.169669
$289$	2.59517	0.152657
$290$	−0.860296	−0.0505183
$291$	2.59526	0.152137
$292$	13.1543	0.769794
$293$	1.17264	0.0685065	0.0342533	−	0.999413i	$-0.489095\pi$
$293$	1.17264	0.0685065	0.0342533	+	0.999413i	$0.489095\pi$
$294$	−1.76512	−0.102944
$295$	8.32828	0.484891
$296$	0	0
$297$	−1.90307	−0.110427
$298$	4.47583	0.259278
$299$	−3.87208	−0.223928
$300$	−1.48398	−0.0856779
$301$	7.11404	0.410047
$302$	−8.84231	−0.508818
$303$	1.39919	0.0803812
$304$	−3.82511	−0.219385
$305$	0.338514	0.0193832
$306$	12.7460	0.728641
$307$	−18.7364	−1.06934	−0.534671	−	0.845060i	$-0.679565\pi$
$307$	−18.7364	−1.06934	−0.534671	+	0.845060i	$0.679565\pi$
$308$	1.29061	0.0735393
$309$	0.0809561	0.00460543
$310$	6.25788	0.355424
$311$	32.8406	1.86222	0.931110	−	0.364738i	$-0.118841\pi$
$311$	32.8406	1.86222	0.931110	+	0.364738i	$0.118841\pi$
$312$	−1.26479	−0.0716047
$313$	21.5524	1.21821	0.609107	−	0.793088i	$-0.291528\pi$
$313$	21.5524	1.21821	0.609107	+	0.793088i	$0.291528\pi$
$314$	−18.4218	−1.03960
$315$	3.39978	0.191556
$316$	−3.48554	−0.196077
$317$	−17.6229	−0.989801	−0.494901	−	0.868950i	$-0.664796\pi$
$317$	−17.6229	−0.989801	−0.494901	+	0.868950i	$0.664796\pi$
$318$	4.50760	0.252774
$319$	0.940353	0.0526497
$320$	−0.852666	−0.0476655
$321$	2.23976	0.125011
$322$	1.47231	0.0820484
$323$	16.9324	0.942144
$324$	7.92902	0.440501
$325$	15.5614	0.863189
$326$	−9.23285	−0.511360
$327$	−4.78451	−0.264584
$328$	0.243134	0.0134248
$329$	−10.7954	−0.595170
$330$	−0.275995	−0.0151930
$331$	−7.10238	−0.390382	−0.195191	−	0.980765i	$-0.562533\pi$
$331$	−7.10238	−0.390382	−0.195191	+	0.980765i	$0.562533\pi$
$332$	−16.7194	−0.917594
$333$	0	0
$334$	−16.3096	−0.892421
$335$	−12.1421	−0.663392
$336$	0.480920	0.0262363
$337$	1.01995	0.0555603	0.0277802	−	0.999614i	$-0.491156\pi$
$337$	1.01995	0.0555603	0.0277802	+	0.999614i	$0.491156\pi$
$338$	0.262857	0.0142975
$339$	1.47960	0.0803607
$340$	3.77445	0.204698
$341$	−6.84023	−0.370419
$342$	11.0140	0.595567
$343$	−16.7312	−0.903402
$344$	5.13740	0.276990
$345$	−0.314850	−0.0169510
$346$	−1.92224	−0.103340
$347$	4.98492	0.267605	0.133802	−	0.991008i	$-0.457281\pi$
$347$	4.98492	0.267605	0.133802	+	0.991008i	$0.457281\pi$
$348$	0.350404	0.0187836
$349$	−25.7294	−1.37726	−0.688631	−	0.725111i	$-0.741788\pi$
$349$	−25.7294	−1.37726	−0.688631	+	0.725111i	$0.741788\pi$
$350$	−5.91700	−0.316277
$351$	7.43619	0.396915
$352$	0.932013	0.0496764
$353$	26.8221	1.42760	0.713799	−	0.700351i	$-0.246973\pi$
$353$	26.8221	1.42760	0.713799	+	0.700351i	$0.246973\pi$
$354$	−3.39216	−0.180292
$355$	11.6553	0.618600
$356$	−6.28907	−0.333320
$357$	−2.12886	−0.112671
$358$	18.8954	0.998652
$359$	19.9335	1.05205	0.526024	−	0.850470i	$-0.323682\pi$
$359$	19.9335	1.05205	0.526024	+	0.850470i	$0.323682\pi$
$360$	2.45515	0.129398
$361$	−4.36854	−0.229923
$362$	6.85363	0.360219
$363$	−3.51858	−0.184678
$364$	−5.04303	−0.264326
$365$	−11.2162	−0.587082
$366$	−0.137879	−0.00720704
$367$	14.8345	0.774357	0.387178	−	0.922005i	$-0.373450\pi$
$367$	14.8345	0.774357	0.387178	+	0.922005i	$0.373450\pi$
$368$	1.06323	0.0554245
$369$	−0.700076	−0.0364445
$370$	0	0
$371$	17.9729	0.933106
$372$	−2.54888	−0.132153
$373$	2.70556	0.140088	0.0700442	−	0.997544i	$-0.477686\pi$
$373$	2.70556	0.140088	0.0700442	+	0.997544i	$0.477686\pi$
$374$	−4.12569	−0.213334
$375$	2.74598	0.141802
$376$	−7.79590	−0.402043
$377$	−3.67441	−0.189242
$378$	−2.82751	−0.145432
$379$	20.1282	1.03392	0.516959	−	0.856010i	$-0.327064\pi$
$379$	20.1282	1.03392	0.516959	+	0.856010i	$0.327064\pi$
$380$	3.26154	0.167313
$381$	4.00402	0.205132
$382$	21.1777	1.08354
$383$	26.9133	1.37521	0.687603	−	0.726087i	$-0.258663\pi$
$383$	26.9133	1.37521	0.687603	+	0.726087i	$0.258663\pi$
$384$	0.347296	0.0177229
$385$	−1.10046	−0.0560845
$386$	−7.67587	−0.390691
$387$	−14.7926	−0.751948
$388$	7.47277	0.379372
$389$	−0.971540	−0.0492590	−0.0246295	−	0.999697i	$-0.507841\pi$
$389$	−0.971540	−0.0492590	−0.0246295	+	0.999697i	$0.507841\pi$
$390$	1.07844	0.0546091
$391$	−4.70652	−0.238019
$392$	−5.08246	−0.256703
$393$	−3.63041	−0.183130
$394$	−11.3622	−0.572419
$395$	2.97200	0.149537
$396$	−2.68362	−0.134857
$397$	−22.1881	−1.11359	−0.556794	−	0.830651i	$-0.687969\pi$
$397$	−22.1881	−1.11359	−0.556794	+	0.830651i	$0.687969\pi$
$398$	−24.8783	−1.24704
$399$	−1.83957	−0.0920938
$400$	−4.27296	−0.213648
$401$	23.0731	1.15222	0.576108	−	0.817374i	$-0.304571\pi$
$401$	23.0731	1.15222	0.576108	+	0.817374i	$0.304571\pi$
$402$	4.94555	0.246661
$403$	26.7281	1.33142
$404$	4.02880	0.200440
$405$	−6.76080	−0.335947
$406$	1.39715	0.0693392
$407$	0	0
$408$	−1.53736	−0.0761105
$409$	14.5116	0.717553	0.358777	−	0.933423i	$-0.383194\pi$
$409$	14.5116	0.717553	0.358777	+	0.933423i	$0.383194\pi$
$410$	−0.207312	−0.0102384
$411$	−2.35431	−0.116129
$412$	0.233104	0.0114842
$413$	−13.5254	−0.665540
$414$	−3.06144	−0.150461
$415$	14.2560	0.699801
$416$	−3.64182	−0.178555
$417$	6.65042	0.325672
$418$	−3.56505	−0.174372
$419$	16.9612	0.828610	0.414305	−	0.910138i	$-0.364025\pi$
$419$	16.9612	0.828610	0.414305	+	0.910138i	$0.364025\pi$
$420$	−0.410064	−0.0200091
$421$	−15.7920	−0.769654	−0.384827	−	0.922989i	$-0.625739\pi$
$421$	−15.7920	−0.769654	−0.384827	+	0.922989i	$0.625739\pi$
$422$	13.1296	0.639139
$423$	22.4474	1.09143
$424$	12.9791	0.630322
$425$	18.9149	0.917506
$426$	−4.74729	−0.230007
$427$	−0.549756	−0.0266046
$428$	6.44912	0.311730
$429$	−1.17880	−0.0569131
$430$	−4.38049	−0.211246
$431$	37.4886	1.80576	0.902882	−	0.429888i	$-0.141447\pi$
$431$	37.4886	1.80576	0.902882	+	0.429888i	$0.141447\pi$
$432$	−2.04189	−0.0982404
$433$	16.0229	0.770014	0.385007	−	0.922914i	$-0.374199\pi$
$433$	16.0229	0.770014	0.385007	+	0.922914i	$0.374199\pi$
$434$	−10.1630	−0.487839
$435$	−0.298778	−0.0143253
$436$	−13.7765	−0.659773
$437$	−4.06695	−0.194549
$438$	4.56842	0.218288
$439$	−30.3278	−1.44747	−0.723733	−	0.690080i	$-0.757575\pi$
$439$	−30.3278	−1.44747	−0.723733	+	0.690080i	$0.757575\pi$
$440$	−0.794695	−0.0378856
$441$	14.6343	0.696874
$442$	16.1210	0.766800
$443$	−24.5626	−1.16700	−0.583502	−	0.812112i	$-0.698318\pi$
$443$	−24.5626	−1.16700	−0.583502	+	0.812112i	$0.698318\pi$
$444$	0	0
$445$	5.36247	0.254206
$446$	1.40208	0.0663904
$447$	1.55444	0.0735224
$448$	1.38475	0.0654235
$449$	−26.5382	−1.25241	−0.626207	−	0.779657i	$-0.715393\pi$
$449$	−26.5382	−1.25241	−0.626207	+	0.779657i	$0.715393\pi$
$450$	12.3035	0.579993
$451$	0.226604	0.0106704
$452$	4.26033	0.200389
$453$	−3.07090	−0.144284
$454$	−3.00615	−0.141086
$455$	4.30002	0.201588
$456$	−1.32845	−0.0622102
$457$	−23.6890	−1.10812	−0.554062	−	0.832476i	$-0.686923\pi$
$457$	−23.6890	−1.10812	−0.554062	+	0.832476i	$0.686923\pi$
$458$	9.28299	0.433766
$459$	9.03871	0.421891
$460$	−0.906576	−0.0422693
$461$	17.8807	0.832788	0.416394	−	0.909184i	$-0.363294\pi$
$461$	17.8807	0.832788	0.416394	+	0.909184i	$0.363294\pi$
$462$	0.448224	0.0208533
$463$	−11.6114	−0.539629	−0.269814	−	0.962912i	$-0.586962\pi$
$463$	−11.6114	−0.539629	−0.269814	+	0.962912i	$0.586962\pi$
$464$	1.00895	0.0468393
$465$	2.17334	0.100786
$466$	27.4216	1.27028
$467$	−6.92332	−0.320373	−0.160187	−	0.987087i	$-0.551210\pi$
$467$	−6.92332	−0.320373	−0.160187	+	0.987087i	$0.551210\pi$
$468$	10.4862	0.484725
$469$	19.7191	0.910543
$470$	6.64729	0.306617
$471$	−6.39783	−0.294797
$472$	−9.76735	−0.449579
$473$	4.78813	0.220158
$474$	−1.21051	−0.0556008
$475$	16.3445	0.749939
$476$	−6.12981	−0.280960
$477$	−37.3719	−1.71114
$478$	−0.739736	−0.0338347
$479$	30.8026	1.40741	0.703703	−	0.710494i	$-0.251529\pi$
$479$	30.8026	1.40741	0.703703	+	0.710494i	$0.251529\pi$
$480$	−0.296128	−0.0135163
$481$	0	0
$482$	−0.923265	−0.0420536
$483$	0.511327	0.0232662
$484$	−10.1314	−0.460516
$485$	−6.37177	−0.289327
$486$	8.87939	0.402777
$487$	−26.1340	−1.18425	−0.592123	−	0.805848i	$-0.701710\pi$
$487$	−26.1340	−1.18425	−0.592123	+	0.805848i	$0.701710\pi$
$488$	−0.397006	−0.0179716
$489$	−3.20654	−0.145005
$490$	4.33363	0.195774
$491$	9.44253	0.426135	0.213068	−	0.977037i	$-0.431655\pi$
$491$	9.44253	0.426135	0.213068	+	0.977037i	$0.431655\pi$
$492$	0.0844395	0.00380683
$493$	−4.46626	−0.201150
$494$	13.9304	0.626756
$495$	2.28823	0.102848
$496$	−7.33920	−0.329540
$497$	−18.9286	−0.849063
$498$	−5.80658	−0.260199
$499$	13.6466	0.610905	0.305453	−	0.952207i	$-0.401192\pi$
$499$	13.6466	0.610905	0.305453	+	0.952207i	$0.401192\pi$
$500$	7.90673	0.353600
$501$	−5.66426	−0.253061
$502$	−9.83141	−0.438797
$503$	19.9911	0.891359	0.445679	−	0.895193i	$-0.352962\pi$
$503$	19.9911	0.891359	0.445679	+	0.895193i	$0.352962\pi$
$504$	−3.98724	−0.177606
$505$	−3.43522	−0.152865
$506$	0.990940	0.0440526
$507$	0.0912892	0.00405430
$508$	11.5291	0.511521
$509$	−24.3826	−1.08074	−0.540369	−	0.841428i	$-0.681715\pi$
$509$	−24.3826	−1.08074	−0.540369	+	0.841428i	$0.681715\pi$
$510$	1.31085	0.0580455
$511$	18.2154	0.805802
$512$	1.00000	0.0441942
$513$	7.81045	0.344840
$514$	−5.17095	−0.228081
$515$	−0.198760	−0.00875840
$516$	1.78420	0.0785451
$517$	−7.26588	−0.319553
$518$	0	0
$519$	−0.667587	−0.0293038
$520$	3.10525	0.136174
$521$	14.7563	0.646485	0.323243	−	0.946316i	$-0.395227\pi$
$521$	14.7563	0.646485	0.323243	+	0.946316i	$0.395227\pi$
$522$	−2.90515	−0.127155
$523$	−9.39526	−0.410826	−0.205413	−	0.978675i	$-0.565854\pi$
$523$	−9.39526	−0.410826	−0.205413	+	0.978675i	$0.565854\pi$
$524$	−10.4534	−0.456657
$525$	−2.05495	−0.0896855
$526$	20.5241	0.894893
$527$	32.4880	1.41520
$528$	0.323685	0.0140866
$529$	−21.8696	−0.950850
$530$	−11.0668	−0.480713
$531$	28.1240	1.22048
$532$	−5.29684	−0.229647
$533$	−0.885450	−0.0383531
$534$	−2.18417	−0.0945183
$535$	−5.49894	−0.237740
$536$	14.2401	0.615080
$537$	6.56230	0.283184
$538$	16.5164	0.712074
$539$	−4.73691	−0.204033
$540$	1.74105	0.0749228
$541$	−43.1558	−1.85541	−0.927707	−	0.373309i	$-0.878223\pi$
$541$	−43.1558	−1.85541	−0.927707	+	0.373309i	$0.878223\pi$
$542$	−10.6339	−0.456763
$543$	2.38024	0.102146
$544$	−4.42664	−0.189791
$545$	11.7467	0.503174
$546$	−1.75142	−0.0749541
$547$	−24.3769	−1.04228	−0.521140	−	0.853471i	$-0.674493\pi$
$547$	−24.3769	−1.04228	−0.521140	+	0.853471i	$0.674493\pi$
$548$	−6.77895	−0.289582
$549$	1.14313	0.0487878
$550$	−3.98245	−0.169812
$551$	−3.85934	−0.164413
$552$	0.369254	0.0157165
$553$	−4.82661	−0.205248
$554$	−6.55413	−0.278458
$555$	0	0
$556$	19.1491	0.812104
$557$	30.6168	1.29728	0.648638	−	0.761097i	$-0.275339\pi$
$557$	30.6168	1.29728	0.648638	+	0.761097i	$0.275339\pi$
$558$	21.1324	0.894605
$559$	−18.7095	−0.791328
$560$	−1.18073	−0.0498951
$561$	−1.43284	−0.0604944
$562$	−24.7267	−1.04303
$563$	−3.52981	−0.148764	−0.0743819	−	0.997230i	$-0.523698\pi$
$563$	−3.52981	−0.148764	−0.0743819	+	0.997230i	$0.523698\pi$
$564$	−2.70749	−0.114006
$565$	−3.63264	−0.152826
$566$	−19.7140	−0.828642
$567$	10.9797	0.461106
$568$	−13.6693	−0.573550
$569$	36.4633	1.52862	0.764310	−	0.644849i	$-0.223080\pi$
$569$	36.4633	1.52862	0.764310	+	0.644849i	$0.223080\pi$
$570$	1.13272	0.0474444
$571$	−38.6717	−1.61836	−0.809180	−	0.587561i	$-0.800088\pi$
$571$	−38.6717	−1.61836	−0.809180	+	0.587561i	$0.800088\pi$
$572$	−3.39422	−0.141920
$573$	7.35493	0.307256
$574$	0.336681	0.0140528
$575$	−4.54312	−0.189461
$576$	−2.87939	−0.119974
$577$	43.3780	1.80585	0.902925	−	0.429798i	$-0.141415\pi$
$577$	43.3780	1.80585	0.902925	+	0.429798i	$0.141415\pi$
$578$	2.59517	0.107945
$579$	−2.66580	−0.110787
$580$	−0.860296	−0.0357218
$581$	−23.1522	−0.960516
$582$	2.59526	0.107577
$583$	12.0967	0.500994
$584$	13.1543	0.544327
$585$	−8.94123	−0.369674
$586$	1.17264	0.0484414
$587$	−0.0111176	−0.000458874 0	−0.000229437	−	1.00000i	$-0.500073\pi$
$587$	−0.0111176	−0.000458874 0	−0.000229437		1.00000i	$0.500073\pi$
$588$	−1.76512	−0.0727922
$589$	28.0732	1.15674
$590$	8.32828	0.342870
$591$	−3.94605	−0.162319
$592$	0	0
$593$	−36.1152	−1.48307	−0.741537	−	0.670912i	$-0.765903\pi$
$593$	−36.1152	−1.48307	−0.741537	+	0.670912i	$0.765903\pi$
$594$	−1.90307	−0.0780838
$595$	5.22668	0.214273
$596$	4.47583	0.183337
$597$	−8.64014	−0.353617
$598$	−3.87208	−0.158341
$599$	−16.0475	−0.655682	−0.327841	−	0.944733i	$-0.606321\pi$
$599$	−16.0475	−0.655682	−0.327841	+	0.944733i	$0.606321\pi$
$600$	−1.48398	−0.0605834
$601$	−19.8156	−0.808294	−0.404147	−	0.914694i	$-0.632432\pi$
$601$	−19.8156	−0.808294	−0.404147	+	0.914694i	$0.632432\pi$
$602$	7.11404	0.289947
$603$	−41.0028	−1.66976
$604$	−8.84231	−0.359789
$605$	8.63866	0.351211
$606$	1.39919	0.0568381
$607$	14.6638	0.595186	0.297593	−	0.954693i	$-0.403816\pi$
$607$	14.6638	0.595186	0.297593	+	0.954693i	$0.403816\pi$
$608$	−3.82511	−0.155129
$609$	0.485224	0.0196623
$610$	0.338514	0.0137060
$611$	28.3913	1.14859
$612$	12.7460	0.515227
$613$	7.12885	0.287931	0.143966	−	0.989583i	$-0.454015\pi$
$613$	7.12885	0.287931	0.143966	+	0.989583i	$0.454015\pi$
$614$	−18.7364	−0.756140
$615$	−0.0719986	−0.00290327
$616$	1.29061	0.0520001
$617$	−1.64722	−0.0663146	−0.0331573	−	0.999450i	$-0.510556\pi$
$617$	−1.64722	−0.0663146	−0.0331573	+	0.999450i	$0.510556\pi$
$618$	0.0809561	0.00325653
$619$	−12.5749	−0.505427	−0.252713	−	0.967541i	$-0.581323\pi$
$619$	−12.5749	−0.505427	−0.252713	+	0.967541i	$0.581323\pi$
$620$	6.25788	0.251323
$621$	−2.17099	−0.0871188
$622$	32.8406	1.31679
$623$	−8.70882	−0.348911
$624$	−1.26479	−0.0506322
$625$	14.6230	0.584920
$626$	21.5524	0.861407
$627$	−1.23813	−0.0494461
$628$	−18.4218	−0.735111
$629$	0	0
$630$	3.39978	0.135451
$631$	−22.5892	−0.899260	−0.449630	−	0.893215i	$-0.648444\pi$
$631$	−22.5892	−0.899260	−0.449630	+	0.893215i	$0.648444\pi$
$632$	−3.48554	−0.138647
$633$	4.55986	0.181238
$634$	−17.6229	−0.699895
$635$	−9.83047	−0.390110
$636$	4.50760	0.178738
$637$	18.5094	0.733369
$638$	0.940353	0.0372289
$639$	39.3591	1.55702
$640$	−0.852666	−0.0337046
$641$	−30.9877	−1.22394	−0.611971	−	0.790880i	$-0.709623\pi$
$641$	−30.9877	−1.22394	−0.611971	+	0.790880i	$0.709623\pi$
$642$	2.23976	0.0883961
$643$	1.06342	0.0419370	0.0209685	−	0.999780i	$-0.493325\pi$
$643$	1.06342	0.0419370	0.0209685	+	0.999780i	$0.493325\pi$
$644$	1.47231	0.0580170
$645$	−1.52133	−0.0599022
$646$	16.9324	0.666196
$647$	13.3504	0.524860	0.262430	−	0.964951i	$-0.415476\pi$
$647$	13.3504	0.524860	0.262430	+	0.964951i	$0.415476\pi$
$648$	7.92902	0.311481
$649$	−9.10329	−0.357336
$650$	15.5614	0.610367
$651$	−3.52957	−0.138335
$652$	−9.23285	−0.361586
$653$	9.32342	0.364854	0.182427	−	0.983219i	$-0.441605\pi$
$653$	9.32342	0.364854	0.182427	+	0.983219i	$0.441605\pi$
$654$	−4.78451	−0.187089
$655$	8.91322	0.348268
$656$	0.243134	0.00949278
$657$	−37.8762	−1.47769
$658$	−10.7954	−0.420849
$659$	18.9782	0.739285	0.369643	−	0.929174i	$-0.379480\pi$
$659$	18.9782	0.739285	0.369643	+	0.929174i	$0.379480\pi$
$660$	−0.275995	−0.0107431
$661$	21.5786	0.839311	0.419655	−	0.907683i	$-0.362151\pi$
$661$	21.5786	0.839311	0.419655	+	0.907683i	$0.362151\pi$
$662$	−7.10238	−0.276042
$663$	5.59878	0.217439
$664$	−16.7194	−0.648837
$665$	4.51643	0.175140
$666$	0	0
$667$	1.07274	0.0415367
$668$	−16.3096	−0.631037
$669$	0.486937	0.0188261
$670$	−12.1421	−0.469089
$671$	−0.370015	−0.0142843
$672$	0.480920	0.0185519
$673$	−41.3812	−1.59513	−0.797564	−	0.603234i	$-0.793878\pi$
$673$	−41.3812	−1.59513	−0.797564	+	0.603234i	$0.793878\pi$
$674$	1.01995	0.0392871
$675$	8.72491	0.335822
$676$	0.262857	0.0101099
$677$	4.58087	0.176057	0.0880287	−	0.996118i	$-0.471943\pi$
$677$	4.58087	0.176057	0.0880287	+	0.996118i	$0.471943\pi$
$678$	1.47960	0.0568236
$679$	10.3479	0.397118
$680$	3.77445	0.144743
$681$	−1.04403	−0.0400072
$682$	−6.84023	−0.261926
$683$	−35.9910	−1.37716	−0.688579	−	0.725161i	$-0.741765\pi$
$683$	−35.9910	−1.37716	−0.688579	+	0.725161i	$0.741765\pi$
$684$	11.0140	0.421129
$685$	5.78018	0.220849
$686$	−16.7312	−0.638801
$687$	3.22395	0.123001
$688$	5.13740	0.195862
$689$	−47.2676	−1.80075
$690$	−0.314850	−0.0119862
$691$	35.9929	1.36923	0.684617	−	0.728903i	$-0.259969\pi$
$691$	35.9929	1.36923	0.684617	+	0.728903i	$0.259969\pi$
$692$	−1.92224	−0.0730726
$693$	−3.71616	−0.141165
$694$	4.98492	0.189225
$695$	−16.3278	−0.619349
$696$	0.350404	0.0132820
$697$	−1.07627	−0.0407665
$698$	−25.7294	−0.973872
$699$	9.52343	0.360209
$700$	−5.91700	−0.223642
$701$	6.31783	0.238621	0.119311	−	0.992857i	$-0.461932\pi$
$701$	6.31783	0.238621	0.119311	+	0.992857i	$0.461932\pi$
$702$	7.43619	0.280661
$703$	0	0
$704$	0.932013	0.0351266
$705$	2.30858	0.0869462
$706$	26.8221	1.00946
$707$	5.57890	0.209816
$708$	−3.39216	−0.127485
$709$	−15.4046	−0.578533	−0.289267	−	0.957249i	$-0.593411\pi$
$709$	−15.4046	−0.578533	−0.289267	+	0.957249i	$0.593411\pi$
$710$	11.6553	0.437416
$711$	10.0362	0.376387
$712$	−6.28907	−0.235693
$713$	−7.80323	−0.292233
$714$	−2.12886	−0.0796707
$715$	2.89414	0.108235
$716$	18.8954	0.706154
$717$	−0.256908	−0.00959439
$718$	19.9335	0.743911
$719$	−2.98275	−0.111238	−0.0556188	−	0.998452i	$-0.517713\pi$
$719$	−2.98275	−0.111238	−0.0556188	+	0.998452i	$0.517713\pi$
$720$	2.45515	0.0914981
$721$	0.322792	0.0120214
$722$	−4.36854	−0.162580
$723$	−0.320647	−0.0119250
$724$	6.85363	0.254713
$725$	−4.31120	−0.160114
$726$	−3.51858	−0.130587
$727$	17.6206	0.653510	0.326755	−	0.945109i	$-0.394045\pi$
$727$	17.6206	0.653510	0.326755	+	0.945109i	$0.394045\pi$
$728$	−5.04303	−0.186907
$729$	−20.7033	−0.766788
$730$	−11.2162	−0.415129
$731$	−22.7415	−0.841123
$732$	−0.137879	−0.00509615
$733$	19.2423	0.710731	0.355365	−	0.934727i	$-0.384356\pi$
$733$	19.2423	0.710731	0.355365	+	0.934727i	$0.384356\pi$
$734$	14.8345	0.547553
$735$	1.50506	0.0555148
$736$	1.06323	0.0391910
$737$	13.2720	0.488880
$738$	−0.700076	−0.0257702
$739$	−33.3412	−1.22648	−0.613238	−	0.789898i	$-0.710133\pi$
$739$	−33.3412	−1.22648	−0.613238	+	0.789898i	$0.710133\pi$
$740$	0	0
$741$	4.83796	0.177727
$742$	17.9729	0.659805
$743$	36.6381	1.34412	0.672061	−	0.740496i	$-0.265409\pi$
$743$	36.6381	1.34412	0.672061	+	0.740496i	$0.265409\pi$
$744$	−2.54888	−0.0934464
$745$	−3.81638	−0.139822
$746$	2.70556	0.0990575
$747$	48.1415	1.76141
$748$	−4.12569	−0.150850
$749$	8.93045	0.326312
$750$	2.74598	0.100269
$751$	−18.9642	−0.692015	−0.346008	−	0.938232i	$-0.612463\pi$
$751$	−18.9642	−0.692015	−0.346008	+	0.938232i	$0.612463\pi$
$752$	−7.79590	−0.284287
$753$	−3.41441	−0.124428
$754$	−3.67441	−0.133814
$755$	7.53954	0.274392
$756$	−2.82751	−0.102836
$757$	44.0159	1.59978	0.799892	−	0.600144i	$-0.204890\pi$
$757$	44.0159	1.59978	0.799892	+	0.600144i	$0.204890\pi$
$758$	20.1282	0.731090
$759$	0.344150	0.0124918
$760$	3.26154	0.118308
$761$	−8.20965	−0.297600	−0.148800	−	0.988867i	$-0.547541\pi$
$761$	−8.20965	−0.297600	−0.148800	+	0.988867i	$0.547541\pi$
$762$	4.00402	0.145050
$763$	−19.0770	−0.690634
$764$	21.1777	0.766181
$765$	−10.8681	−0.392936
$766$	26.9133	0.972417
$767$	35.5709	1.28439
$768$	0.347296	0.0125320
$769$	53.9091	1.94401	0.972006	−	0.234957i	$-0.0754950\pi$
$769$	53.9091	1.94401	0.972006	+	0.234957i	$0.0754950\pi$
$770$	−1.10046	−0.0396577
$771$	−1.79585	−0.0646761
$772$	−7.67587	−0.276261
$773$	−2.70225	−0.0971932	−0.0485966	−	0.998818i	$-0.515475\pi$
$773$	−2.70225	−0.0971932	−0.0485966	+	0.998818i	$0.515475\pi$
$774$	−14.7926	−0.531708
$775$	31.3601	1.12649
$776$	7.47277	0.268257
$777$	0	0
$778$	−0.971540	−0.0348314
$779$	−0.930013	−0.0333212
$780$	1.07844	0.0386145
$781$	−12.7399	−0.455871
$782$	−4.70652	−0.168305
$783$	−2.06016	−0.0736242
$784$	−5.08246	−0.181516
$785$	15.7077	0.560630
$786$	−3.63041	−0.129493
$787$	−9.68715	−0.345310	−0.172655	−	0.984982i	$-0.555235\pi$
$787$	−9.68715	−0.345310	−0.172655	+	0.984982i	$0.555235\pi$
$788$	−11.3622	−0.404762
$789$	7.12795	0.253762
$790$	2.97200	0.105739
$791$	5.89951	0.209762
$792$	−2.68362	−0.0953584
$793$	1.44583	0.0513428
$794$	−22.1881	−0.787426
$795$	−3.84348	−0.136314
$796$	−24.8783	−0.881788
$797$	30.7045	1.08761	0.543805	−	0.839212i	$-0.316983\pi$
$797$	30.7045	1.08761	0.543805	+	0.839212i	$0.316983\pi$
$798$	−1.83957	−0.0651201
$799$	34.5097	1.22086
$800$	−4.27296	−0.151072
$801$	18.1087	0.639838
$802$	23.0731	0.814739
$803$	12.2599	0.432644
$804$	4.94555	0.174416
$805$	−1.25538	−0.0442465
$806$	26.7281	0.941455
$807$	5.73610	0.201920
$808$	4.02880	0.141733
$809$	13.0713	0.459562	0.229781	−	0.973242i	$-0.426199\pi$
$809$	13.0713	0.459562	0.229781	+	0.973242i	$0.426199\pi$
$810$	−6.76080	−0.237550
$811$	−45.4480	−1.59589	−0.797947	−	0.602727i	$-0.794081\pi$
$811$	−45.4480	−1.59589	−0.797947	+	0.602727i	$0.794081\pi$
$812$	1.39715	0.0490302
$813$	−3.69310	−0.129523
$814$	0	0
$815$	7.87254	0.275763
$816$	−1.53736	−0.0538183
$817$	−19.6511	−0.687506
$818$	14.5116	0.507387
$819$	14.5208	0.507398
$820$	−0.207312	−0.00723964
$821$	−28.3186	−0.988327	−0.494164	−	0.869369i	$-0.664526\pi$
$821$	−28.3186	−0.988327	−0.494164	+	0.869369i	$0.664526\pi$
$822$	−2.35431	−0.0821158
$823$	24.7006	0.861009	0.430504	−	0.902588i	$-0.358336\pi$
$823$	24.7006	0.861009	0.430504	+	0.902588i	$0.358336\pi$
$824$	0.233104	0.00812056
$825$	−1.38309	−0.0481531
$826$	−13.5254	−0.470608
$827$	−12.4489	−0.432892	−0.216446	−	0.976295i	$-0.569447\pi$
$827$	−12.4489	−0.432892	−0.216446	+	0.976295i	$0.569447\pi$
$828$	−3.06144	−0.106392
$829$	−10.8367	−0.376376	−0.188188	−	0.982133i	$-0.560261\pi$
$829$	−10.8367	−0.376376	−0.188188	+	0.982133i	$0.560261\pi$
$830$	14.2560	0.494834
$831$	−2.27622	−0.0789614
$832$	−3.64182	−0.126257
$833$	22.4982	0.779517
$834$	6.65042	0.230285
$835$	13.9066	0.481259
$836$	−3.56505	−0.123300
$837$	14.9858	0.517986
$838$	16.9612	0.585916
$839$	−25.2252	−0.870870	−0.435435	−	0.900220i	$-0.643405\pi$
$839$	−25.2252	−0.870870	−0.435435	+	0.900220i	$0.643405\pi$
$840$	−0.410064	−0.0141486
$841$	−27.9820	−0.964897
$842$	−15.7920	−0.544228
$843$	−8.58751	−0.295769
$844$	13.1296	0.451939
$845$	−0.224129	−0.00771027
$846$	22.4474	0.771757
$847$	−14.0294	−0.482057
$848$	12.9791	0.445705
$849$	−6.84660	−0.234975
$850$	18.9149	0.648775
$851$	0	0
$852$	−4.74729	−0.162639
$853$	10.8973	0.373116	0.186558	−	0.982444i	$-0.440267\pi$
$853$	10.8973	0.373116	0.186558	+	0.982444i	$0.440267\pi$
$854$	−0.549756	−0.0188123
$855$	−9.39123	−0.321173
$856$	6.44912	0.220426
$857$	−18.7526	−0.640575	−0.320288	−	0.947320i	$-0.603780\pi$
$857$	−18.7526	−0.640575	−0.320288	+	0.947320i	$0.603780\pi$
$858$	−1.17880	−0.0402436
$859$	38.8889	1.32687	0.663436	−	0.748233i	$-0.269098\pi$
$859$	38.8889	1.32687	0.663436	+	0.748233i	$0.269098\pi$
$860$	−4.38049	−0.149373
$861$	0.116928	0.00398489
$862$	37.4886	1.27687
$863$	28.2772	0.962567	0.481283	−	0.876565i	$-0.340171\pi$
$863$	28.2772	0.962567	0.481283	+	0.876565i	$0.340171\pi$
$864$	−2.04189	−0.0694665
$865$	1.63903	0.0557286
$866$	16.0229	0.544482
$867$	0.901294	0.0306096
$868$	−10.1630	−0.344954
$869$	−3.24856	−0.110200
$870$	−0.298778	−0.0101295
$871$	−51.8600	−1.75721
$872$	−13.7765	−0.466530
$873$	−21.5170	−0.728239
$874$	−4.06695	−0.137567
$875$	10.9489	0.370140
$876$	4.56842	0.154353
$877$	0.751276	0.0253688	0.0126844	−	0.999920i	$-0.495962\pi$
$877$	0.751276	0.0253688	0.0126844	+	0.999920i	$0.495962\pi$
$878$	−30.3278	−1.02351
$879$	0.407254	0.0137364
$880$	−0.794695	−0.0267892
$881$	−53.3417	−1.79713	−0.898563	−	0.438844i	$-0.855388\pi$
$881$	−53.3417	−1.79713	−0.898563	+	0.438844i	$0.855388\pi$
$882$	14.6343	0.492764
$883$	−24.1390	−0.812342	−0.406171	−	0.913797i	$-0.633136\pi$
$883$	−24.1390	−0.812342	−0.406171	+	0.913797i	$0.633136\pi$
$884$	16.1210	0.542209
$885$	2.89238	0.0972264
$886$	−24.5626	−0.825196
$887$	−47.2073	−1.58506	−0.792532	−	0.609830i	$-0.791238\pi$
$887$	−47.2073	−1.58506	−0.792532	+	0.609830i	$0.791238\pi$
$888$	0	0
$889$	15.9650	0.535448
$890$	5.36247	0.179751
$891$	7.38994	0.247572
$892$	1.40208	0.0469451
$893$	29.8202	0.997893
$894$	1.55444	0.0519882
$895$	−16.1114	−0.538546
$896$	1.38475	0.0462614
$897$	−1.34476	−0.0449002
$898$	−26.5382	−0.885590
$899$	−7.40488	−0.246967
$900$	12.3035	0.410117
$901$	−57.4539	−1.91407
$902$	0.226604	0.00754508
$903$	2.47068	0.0822191
$904$	4.26033	0.141696
$905$	−5.84385	−0.194256
$906$	−3.07090	−0.102024
$907$	−21.4562	−0.712442	−0.356221	−	0.934402i	$-0.615935\pi$
$907$	−21.4562	−0.712442	−0.356221	+	0.934402i	$0.615935\pi$
$908$	−3.00615	−0.0997627
$909$	−11.6005	−0.384763
$910$	4.30002	0.142544
$911$	21.0056	0.695946	0.347973	−	0.937505i	$-0.386870\pi$
$911$	21.0056	0.695946	0.347973	+	0.937505i	$0.386870\pi$
$912$	−1.32845	−0.0439893
$913$	−15.5827	−0.515711
$914$	−23.6890	−0.783562
$915$	0.117565	0.00388656
$916$	9.28299	0.306719
$917$	−14.4753	−0.478018
$918$	9.03871	0.298322
$919$	−44.9184	−1.48172	−0.740860	−	0.671659i	$-0.765582\pi$
$919$	−44.9184	−1.48172	−0.740860	+	0.671659i	$0.765582\pi$
$920$	−0.906576	−0.0298889
$921$	−6.50708	−0.214416
$922$	17.8807	0.588870
$923$	49.7811	1.63856
$924$	0.448224	0.0147455
$925$	0	0
$926$	−11.6114	−0.381575
$927$	−0.671196	−0.0220450
$928$	1.00895	0.0331204
$929$	−34.8985	−1.14498	−0.572492	−	0.819910i	$-0.694023\pi$
$929$	−34.8985	−1.14498	−0.572492	+	0.819910i	$0.694023\pi$
$930$	2.17334	0.0712666
$931$	19.4409	0.637151
$932$	27.4216	0.898225
$933$	11.4054	0.373397
$934$	−6.92332	−0.226538
$935$	3.51783	0.115045
$936$	10.4862	0.342752
$937$	11.4287	0.373360	0.186680	−	0.982421i	$-0.440227\pi$
$937$	11.4287	0.373360	0.186680	+	0.982421i	$0.440227\pi$
$938$	19.7191	0.643851
$939$	7.48507	0.244266
$940$	6.64729	0.216811
$941$	−35.4596	−1.15595	−0.577975	−	0.816055i	$-0.696157\pi$
$941$	−35.4596	−1.15595	−0.577975	+	0.816055i	$0.696157\pi$
$942$	−6.39783	−0.208453
$943$	0.258506	0.00841812
$944$	−9.76735	−0.317900
$945$	2.41092	0.0784274
$946$	4.78813	0.155675
$947$	−33.9871	−1.10443	−0.552217	−	0.833700i	$-0.686218\pi$
$947$	−33.9871	−1.10443	−0.552217	+	0.833700i	$0.686218\pi$
$948$	−1.21051	−0.0393157
$949$	−47.9054	−1.55508
$950$	16.3445	0.530287
$951$	−6.12037	−0.198467
$952$	−6.12981	−0.198668
$953$	20.0088	0.648147	0.324074	−	0.946032i	$-0.394947\pi$
$953$	20.0088	0.648147	0.324074	+	0.946032i	$0.394947\pi$
$954$	−37.3719	−1.20996
$955$	−18.0575	−0.584326
$956$	−0.739736	−0.0239248
$957$	0.326581	0.0105569
$958$	30.8026	0.995186
$959$	−9.38718	−0.303128
$960$	−0.296128	−0.00955748
$961$	22.8639	0.737544
$962$	0	0
$963$	−18.5695	−0.598394
$964$	−0.923265	−0.0297364
$965$	6.54495	0.210689
$966$	0.511327	0.0164517
$967$	−21.4849	−0.690909	−0.345455	−	0.938435i	$-0.612275\pi$
$967$	−21.4849	−0.690909	−0.345455	+	0.938435i	$0.612275\pi$
$968$	−10.1314	−0.325634
$969$	5.88056	0.188911
$970$	−6.37177	−0.204585
$971$	0.876347	0.0281233	0.0140617	−	0.999901i	$-0.495524\pi$
$971$	0.876347	0.0281233	0.0140617	+	0.999901i	$0.495524\pi$
$972$	8.87939	0.284806
$973$	26.5168	0.850090
$974$	−26.1340	−0.837388
$975$	5.40440	0.173079
$976$	−0.397006	−0.0127079
$977$	−14.5504	−0.465509	−0.232754	−	0.972536i	$-0.574774\pi$
$977$	−14.5504	−0.465509	−0.232754	+	0.972536i	$0.574774\pi$
$978$	−3.20654	−0.102534
$979$	−5.86149	−0.187334
$980$	4.33363	0.138433
$981$	39.6677	1.26649
$982$	9.44253	0.301323
$983$	13.7478	0.438488	0.219244	−	0.975670i	$-0.429641\pi$
$983$	13.7478	0.438488	0.219244	+	0.975670i	$0.429641\pi$
$984$	0.0844395	0.00269183
$985$	9.68816	0.308690
$986$	−4.46626	−0.142235
$987$	−3.74920	−0.119338
$988$	13.9304	0.443184
$989$	5.46222	0.173688
$990$	2.28823	0.0727248
$991$	47.5583	1.51074	0.755370	−	0.655299i	$-0.227457\pi$
$991$	47.5583	1.51074	0.755370	+	0.655299i	$0.227457\pi$
$992$	−7.33920	−0.233020
$993$	−2.46663	−0.0782761
$994$	−18.9286	−0.600379
$995$	21.2129	0.672493
$996$	−5.80658	−0.183988
$997$	−53.8882	−1.70666	−0.853328	−	0.521375i	$-0.825419\pi$
$997$	−53.8882	−1.70666	−0.853328	+	0.521375i	$0.825419\pi$
$998$	13.6466	0.431975
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.s.1.3		6
37.17	odd	36		74.2.h.a.67.2	yes	12
37.24	odd	36		74.2.h.a.21.2	✓	12
37.36	even	2		2738.2.a.r.1.4		6
111.17	even	36		666.2.bj.c.289.1		12
111.98	even	36		666.2.bj.c.613.1		12
148.91	even	36		592.2.bq.b.289.1		12
148.135	even	36		592.2.bq.b.465.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.21.2	✓	12	37.24	odd	36
74.2.h.a.67.2	yes	12	37.17	odd	36
592.2.bq.b.289.1		12	148.91	even	36
592.2.bq.b.465.1		12	148.135	even	36
666.2.bj.c.289.1		12	111.17	even	36
666.2.bj.c.613.1		12	111.98	even	36
2738.2.a.r.1.4		6	37.36	even	2
2738.2.a.s.1.3		6	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:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.347296 q^{3} +1.00000 q^{4} -0.852666 q^{5} +0.347296 q^{6} +1.38475 q^{7} +1.00000 q^{8} -2.87939 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.347296 q^{3} +1.00000 q^{4} -0.852666 q^{5} +0.347296 q^{6} +1.38475 q^{7} +1.00000 q^{8} -2.87939 q^{9} -0.852666 q^{10} +0.932013 q^{11} +0.347296 q^{12} -3.64182 q^{13} +1.38475 q^{14} -0.296128 q^{15} +1.00000 q^{16} -4.42664 q^{17} -2.87939 q^{18} -3.82511 q^{19} -0.852666 q^{20} +0.480920 q^{21} +0.932013 q^{22} +1.06323 q^{23} +0.347296 q^{24} -4.27296 q^{25} -3.64182 q^{26} -2.04189 q^{27} +1.38475 q^{28} +1.00895 q^{29} -0.296128 q^{30} -7.33920 q^{31} +1.00000 q^{32} +0.323685 q^{33} -4.42664 q^{34} -1.18073 q^{35} -2.87939 q^{36} -3.82511 q^{38} -1.26479 q^{39} -0.852666 q^{40} +0.243134 q^{41} +0.480920 q^{42} +5.13740 q^{43} +0.932013 q^{44} +2.45515 q^{45} +1.06323 q^{46} -7.79590 q^{47} +0.347296 q^{48} -5.08246 q^{49} -4.27296 q^{50} -1.53736 q^{51} -3.64182 q^{52} +12.9791 q^{53} -2.04189 q^{54} -0.794695 q^{55} +1.38475 q^{56} -1.32845 q^{57} +1.00895 q^{58} -9.76735 q^{59} -0.296128 q^{60} -0.397006 q^{61} -7.33920 q^{62} -3.98724 q^{63} +1.00000 q^{64} +3.10525 q^{65} +0.323685 q^{66} +14.2401 q^{67} -4.42664 q^{68} +0.369254 q^{69} -1.18073 q^{70} -13.6693 q^{71} -2.87939 q^{72} +13.1543 q^{73} -1.48398 q^{75} -3.82511 q^{76} +1.29061 q^{77} -1.26479 q^{78} -3.48554 q^{79} -0.852666 q^{80} +7.92902 q^{81} +0.243134 q^{82} -16.7194 q^{83} +0.480920 q^{84} +3.77445 q^{85} +5.13740 q^{86} +0.350404 q^{87} +0.932013 q^{88} -6.28907 q^{89} +2.45515 q^{90} -5.04303 q^{91} +1.06323 q^{92} -2.54888 q^{93} -7.79590 q^{94} +3.26154 q^{95} +0.347296 q^{96} +7.47277 q^{97} -5.08246 q^{98} -2.68362 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^8 - 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} - 12 q^{13} + 6 q^{15} + 6 q^{16} - 12 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 6 q^{22} + 6 q^{23} + 6 q^{25} - 12 q^{26} - 6 q^{27} + 6 q^{29} + 6 q^{30} - 18 q^{31} + 6 q^{32} + 6 q^{33} - 12 q^{34} - 24 q^{35} - 6 q^{36} - 12 q^{38} - 6 q^{39} - 6 q^{40} - 12 q^{41} - 12 q^{42} - 6 q^{44} - 6 q^{45} + 6 q^{46} - 6 q^{47} - 12 q^{49} + 6 q^{50} - 24 q^{51} - 12 q^{52} - 24 q^{53} - 6 q^{54} - 36 q^{55} - 24 q^{57} + 6 q^{58} - 12 q^{59} + 6 q^{60} - 12 q^{61} - 18 q^{62} + 6 q^{63} + 6 q^{64} + 18 q^{65} + 6 q^{66} + 18 q^{67} - 12 q^{68} - 24 q^{69} - 24 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{75} - 12 q^{76} + 30 q^{77} - 6 q^{78} - 12 q^{79} - 6 q^{80} - 18 q^{81} - 12 q^{82} - 6 q^{83} - 12 q^{84} + 18 q^{85} - 6 q^{87} - 6 q^{88} - 6 q^{90} - 12 q^{91} + 6 q^{92} + 36 q^{93} - 6 q^{94} + 18 q^{95} + 12 q^{97} - 12 q^{98} + 12 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 - 12 * q^13 + 6 * q^15 + 6 * q^16 - 12 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 - 12 * q^21 - 6 * q^22 + 6 * q^23 + 6 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^29 + 6 * q^30 - 18 * q^31 + 6 * q^32 + 6 * q^33 - 12 * q^34 - 24 * q^35 - 6 * q^36 - 12 * q^38 - 6 * q^39 - 6 * q^40 - 12 * q^41 - 12 * q^42 - 6 * q^44 - 6 * q^45 + 6 * q^46 - 6 * q^47 - 12 * q^49 + 6 * q^50 - 24 * q^51 - 12 * q^52 - 24 * q^53 - 6 * q^54 - 36 * q^55 - 24 * q^57 + 6 * q^58 - 12 * q^59 + 6 * q^60 - 12 * q^61 - 18 * q^62 + 6 * q^63 + 6 * q^64 + 18 * q^65 + 6 * q^66 + 18 * q^67 - 12 * q^68 - 24 * q^69 - 24 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^75 - 12 * q^76 + 30 * q^77 - 6 * q^78 - 12 * q^79 - 6 * q^80 - 18 * q^81 - 12 * q^82 - 6 * q^83 - 12 * q^84 + 18 * q^85 - 6 * q^87 - 6 * q^88 - 6 * q^90 - 12 * q^91 + 6 * q^92 + 36 * q^93 - 6 * q^94 + 18 * q^95 + 12 * q^97 - 12 * q^98 + 12 * q^99

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