LMFDB - Embedded newform 2166.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,2,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2166.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2166.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:	$17.2955970778$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.87939 q^{5} +1.00000 q^{6} +1.22668 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.87939 q^{5} +1.00000 q^{6} +1.22668 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.87939 q^{10} -2.12061 q^{11} -1.00000 q^{12} -0.490200 q^{13} -1.22668 q^{14} +3.87939 q^{15} +1.00000 q^{16} -5.53209 q^{17} -1.00000 q^{18} -3.87939 q^{20} -1.22668 q^{21} +2.12061 q^{22} -8.94356 q^{23} +1.00000 q^{24} +10.0496 q^{25} +0.490200 q^{26} -1.00000 q^{27} +1.22668 q^{28} +8.47565 q^{29} -3.87939 q^{30} -2.41147 q^{31} -1.00000 q^{32} +2.12061 q^{33} +5.53209 q^{34} -4.75877 q^{35} +1.00000 q^{36} -1.69459 q^{37} +0.490200 q^{39} +3.87939 q^{40} -1.59627 q^{41} +1.22668 q^{42} -6.63816 q^{43} -2.12061 q^{44} -3.87939 q^{45} +8.94356 q^{46} +2.17024 q^{47} -1.00000 q^{48} -5.49525 q^{49} -10.0496 q^{50} +5.53209 q^{51} -0.490200 q^{52} -8.88713 q^{53} +1.00000 q^{54} +8.22668 q^{55} -1.22668 q^{56} -8.47565 q^{58} +11.4192 q^{59} +3.87939 q^{60} +0.0418891 q^{61} +2.41147 q^{62} +1.22668 q^{63} +1.00000 q^{64} +1.90167 q^{65} -2.12061 q^{66} -4.47565 q^{67} -5.53209 q^{68} +8.94356 q^{69} +4.75877 q^{70} -2.63816 q^{71} -1.00000 q^{72} -15.3628 q^{73} +1.69459 q^{74} -10.0496 q^{75} -2.60132 q^{77} -0.490200 q^{78} +4.66044 q^{79} -3.87939 q^{80} +1.00000 q^{81} +1.59627 q^{82} +12.4807 q^{83} -1.22668 q^{84} +21.4611 q^{85} +6.63816 q^{86} -8.47565 q^{87} +2.12061 q^{88} -8.45605 q^{89} +3.87939 q^{90} -0.601319 q^{91} -8.94356 q^{92} +2.41147 q^{93} -2.17024 q^{94} +1.00000 q^{96} +14.3773 q^{97} +5.49525 q^{98} -2.12061 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 6 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 6 * q^5 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 6 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} + 6 q^{10} - 12 q^{11} - 3 q^{12} + 3 q^{14} + 6 q^{15} + 3 q^{16} - 12 q^{17} - 3 q^{18} - 6 q^{20} + 3 q^{21} + 12 q^{22} - 12 q^{23} + 3 q^{24} + 3 q^{25} - 3 q^{27} - 3 q^{28} + 6 q^{29} - 6 q^{30} + 3 q^{31} - 3 q^{32} + 12 q^{33} + 12 q^{34} - 3 q^{35} + 3 q^{36} - 3 q^{37} + 6 q^{40} + 9 q^{41} - 3 q^{42} - 3 q^{43} - 12 q^{44} - 6 q^{45} + 12 q^{46} - 15 q^{47} - 3 q^{48} - 3 q^{50} + 12 q^{51} + 3 q^{53} + 3 q^{54} + 18 q^{55} + 3 q^{56} - 6 q^{58} + 6 q^{60} - 3 q^{61} - 3 q^{62} - 3 q^{63} + 3 q^{64} - 6 q^{65} - 12 q^{66} + 6 q^{67} - 12 q^{68} + 12 q^{69} + 3 q^{70} + 9 q^{71} - 3 q^{72} + 3 q^{73} + 3 q^{74} - 3 q^{75} + 21 q^{77} - 9 q^{79} - 6 q^{80} + 3 q^{81} - 9 q^{82} + 3 q^{83} + 3 q^{84} + 27 q^{85} + 3 q^{86} - 6 q^{87} + 12 q^{88} - 3 q^{89} + 6 q^{90} + 27 q^{91} - 12 q^{92} - 3 q^{93} + 15 q^{94} + 3 q^{96} + 12 q^{97} - 12 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 6 * q^5 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9 + 6 * q^10 - 12 * q^11 - 3 * q^12 + 3 * q^14 + 6 * q^15 + 3 * q^16 - 12 * q^17 - 3 * q^18 - 6 * q^20 + 3 * q^21 + 12 * q^22 - 12 * q^23 + 3 * q^24 + 3 * q^25 - 3 * q^27 - 3 * q^28 + 6 * q^29 - 6 * q^30 + 3 * q^31 - 3 * q^32 + 12 * q^33 + 12 * q^34 - 3 * q^35 + 3 * q^36 - 3 * q^37 + 6 * q^40 + 9 * q^41 - 3 * q^42 - 3 * q^43 - 12 * q^44 - 6 * q^45 + 12 * q^46 - 15 * q^47 - 3 * q^48 - 3 * q^50 + 12 * q^51 + 3 * q^53 + 3 * q^54 + 18 * q^55 + 3 * q^56 - 6 * q^58 + 6 * q^60 - 3 * q^61 - 3 * q^62 - 3 * q^63 + 3 * q^64 - 6 * q^65 - 12 * q^66 + 6 * q^67 - 12 * q^68 + 12 * q^69 + 3 * q^70 + 9 * q^71 - 3 * q^72 + 3 * q^73 + 3 * q^74 - 3 * q^75 + 21 * q^77 - 9 * q^79 - 6 * q^80 + 3 * q^81 - 9 * q^82 + 3 * q^83 + 3 * q^84 + 27 * q^85 + 3 * q^86 - 6 * q^87 + 12 * q^88 - 3 * q^89 + 6 * q^90 + 27 * q^91 - 12 * q^92 - 3 * q^93 + 15 * q^94 + 3 * q^96 + 12 * q^97 - 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−3.87939	−1.73491	−0.867457	−	0.497512i	$-0.834247\pi$
$5$	−3.87939	−1.73491	−0.867457	+	0.497512i	$0.834247\pi$
$6$	1.00000	0.408248
$7$	1.22668	0.463642	0.231821	−	0.972758i	$-0.425532\pi$
$7$	1.22668	0.463642	0.231821	+	0.972758i	$0.425532\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.87939	1.22677
$11$	−2.12061	−0.639389	−0.319695	−	0.947521i	$-0.603580\pi$
$11$	−2.12061	−0.639389	−0.319695	+	0.947521i	$0.603580\pi$
$12$	−1.00000	−0.288675
$13$	−0.490200	−0.135957	−0.0679785	−	0.997687i	$-0.521655\pi$
$13$	−0.490200	−0.135957	−0.0679785	+	0.997687i	$0.521655\pi$
$14$	−1.22668	−0.327844
$15$	3.87939	1.00165
$16$	1.00000	0.250000
$17$	−5.53209	−1.34173	−0.670864	−	0.741580i	$-0.734077\pi$
$17$	−5.53209	−1.34173	−0.670864	+	0.741580i	$0.734077\pi$
$18$	−1.00000	−0.235702
$19$	0	0
$19$	0	0
$20$	−3.87939	−0.867457
$21$	−1.22668	−0.267684
$22$	2.12061	0.452117
$23$	−8.94356	−1.86486	−0.932431	−	0.361348i	$-0.882317\pi$
$23$	−8.94356	−1.86486	−0.932431	+	0.361348i	$0.882317\pi$
$24$	1.00000	0.204124
$25$	10.0496	2.00993
$26$	0.490200	0.0961361
$27$	−1.00000	−0.192450
$28$	1.22668	0.231821
$29$	8.47565	1.57389	0.786945	−	0.617024i	$-0.211662\pi$
$29$	8.47565	1.57389	0.786945	+	0.617024i	$0.211662\pi$
$30$	−3.87939	−0.708276
$31$	−2.41147	−0.433114	−0.216557	−	0.976270i	$-0.569483\pi$
$31$	−2.41147	−0.433114	−0.216557	+	0.976270i	$0.569483\pi$
$32$	−1.00000	−0.176777
$33$	2.12061	0.369152
$34$	5.53209	0.948745
$35$	−4.75877	−0.804379
$36$	1.00000	0.166667
$37$	−1.69459	−0.278589	−0.139295	−	0.990251i	$-0.544484\pi$
$37$	−1.69459	−0.278589	−0.139295	+	0.990251i	$0.544484\pi$
$38$	0	0
$39$	0.490200	0.0784948
$40$	3.87939	0.613385
$41$	−1.59627	−0.249295	−0.124647	−	0.992201i	$-0.539780\pi$
$41$	−1.59627	−0.249295	−0.124647	+	0.992201i	$0.539780\pi$
$42$	1.22668	0.189281
$43$	−6.63816	−1.01231	−0.506155	−	0.862443i	$-0.668933\pi$
$43$	−6.63816	−1.01231	−0.506155	+	0.862443i	$0.668933\pi$
$44$	−2.12061	−0.319695
$45$	−3.87939	−0.578305
$46$	8.94356	1.31866
$47$	2.17024	0.316563	0.158281	−	0.987394i	$-0.449405\pi$
$47$	2.17024	0.316563	0.158281	+	0.987394i	$0.449405\pi$
$48$	−1.00000	−0.144338
$49$	−5.49525	−0.785036
$50$	−10.0496	−1.42123
$51$	5.53209	0.774647
$52$	−0.490200	−0.0679785
$53$	−8.88713	−1.22074	−0.610370	−	0.792116i	$-0.708979\pi$
$53$	−8.88713	−1.22074	−0.610370	+	0.792116i	$0.708979\pi$
$54$	1.00000	0.136083
$55$	8.22668	1.10929
$56$	−1.22668	−0.163922
$57$	0	0
$58$	−8.47565	−1.11291
$59$	11.4192	1.48666	0.743328	−	0.668928i	$-0.233246\pi$
$59$	11.4192	1.48666	0.743328	+	0.668928i	$0.233246\pi$
$60$	3.87939	0.500826
$61$	0.0418891	0.00536335	0.00268167	−	0.999996i	$-0.499146\pi$
$61$	0.0418891	0.00536335	0.00268167	+	0.999996i	$0.499146\pi$
$62$	2.41147	0.306258
$63$	1.22668	0.154547
$64$	1.00000	0.125000
$65$	1.90167	0.235874
$66$	−2.12061	−0.261030
$67$	−4.47565	−0.546788	−0.273394	−	0.961902i	$-0.588146\pi$
$67$	−4.47565	−0.546788	−0.273394	+	0.961902i	$0.588146\pi$
$68$	−5.53209	−0.670864
$69$	8.94356	1.07668
$70$	4.75877	0.568782
$71$	−2.63816	−0.313091	−0.156546	−	0.987671i	$-0.550036\pi$
$71$	−2.63816	−0.313091	−0.156546	+	0.987671i	$0.550036\pi$
$72$	−1.00000	−0.117851
$73$	−15.3628	−1.79808	−0.899039	−	0.437869i	$-0.855733\pi$
$73$	−15.3628	−1.79808	−0.899039	+	0.437869i	$0.855733\pi$
$74$	1.69459	0.196992
$75$	−10.0496	−1.16043
$76$	0	0
$77$	−2.60132	−0.296448
$78$	−0.490200	−0.0555042
$79$	4.66044	0.524341	0.262170	−	0.965022i	$-0.415562\pi$
$79$	4.66044	0.524341	0.262170	+	0.965022i	$0.415562\pi$
$80$	−3.87939	−0.433728
$81$	1.00000	0.111111
$82$	1.59627	0.176278
$83$	12.4807	1.36994	0.684968	−	0.728573i	$-0.259816\pi$
$83$	12.4807	1.36994	0.684968	+	0.728573i	$0.259816\pi$
$84$	−1.22668	−0.133842
$85$	21.4611	2.32778
$86$	6.63816	0.715811
$87$	−8.47565	−0.908685
$88$	2.12061	0.226058
$89$	−8.45605	−0.896340	−0.448170	−	0.893948i	$-0.647924\pi$
$89$	−8.45605	−0.896340	−0.448170	+	0.893948i	$0.647924\pi$
$90$	3.87939	0.408923
$91$	−0.601319	−0.0630354
$92$	−8.94356	−0.932431
$93$	2.41147	0.250058
$94$	−2.17024	−0.223844
$95$	0	0
$96$	1.00000	0.102062
$97$	14.3773	1.45980	0.729898	−	0.683556i	$-0.239567\pi$
$97$	14.3773	1.45980	0.729898	+	0.683556i	$0.239567\pi$
$98$	5.49525	0.555104
$99$	−2.12061	−0.213130
$100$	10.0496	1.00496
$101$	5.69459	0.566633	0.283317	−	0.959026i	$-0.408565\pi$
$101$	5.69459	0.566633	0.283317	+	0.959026i	$0.408565\pi$
$102$	−5.53209	−0.547758
$103$	0.313148	0.0308554	0.0154277	−	0.999881i	$-0.495089\pi$
$103$	0.313148	0.0308554	0.0154277	+	0.999881i	$0.495089\pi$
$104$	0.490200	0.0480680
$105$	4.75877	0.464408
$106$	8.88713	0.863194
$107$	16.8280	1.62682	0.813412	−	0.581688i	$-0.197607\pi$
$107$	16.8280	1.62682	0.813412	+	0.581688i	$0.197607\pi$
$108$	−1.00000	−0.0962250
$109$	10.4115	0.997238	0.498619	−	0.866821i	$-0.333841\pi$
$109$	10.4115	0.997238	0.498619	+	0.866821i	$0.333841\pi$
$110$	−8.22668	−0.784383
$111$	1.69459	0.160844
$112$	1.22668	0.115911
$113$	17.3824	1.63520	0.817598	−	0.575789i	$-0.195305\pi$
$113$	17.3824	1.63520	0.817598	+	0.575789i	$0.195305\pi$
$114$	0	0
$115$	34.6955	3.23537
$116$	8.47565	0.786945
$117$	−0.490200	−0.0453190
$118$	−11.4192	−1.05122
$119$	−6.78611	−0.622082
$120$	−3.87939	−0.354138
$121$	−6.50299	−0.591181
$122$	−0.0418891	−0.00379246
$123$	1.59627	0.143931
$124$	−2.41147	−0.216557
$125$	−19.5895	−1.75213
$126$	−1.22668	−0.109281
$127$	1.63041	0.144676	0.0723380	−	0.997380i	$-0.476954\pi$
$127$	1.63041	0.144676	0.0723380	+	0.997380i	$0.476954\pi$
$128$	−1.00000	−0.0883883
$129$	6.63816	0.584457
$130$	−1.90167	−0.166788
$131$	5.96316	0.521004	0.260502	−	0.965473i	$-0.416112\pi$
$131$	5.96316	0.521004	0.260502	+	0.965473i	$0.416112\pi$
$132$	2.12061	0.184576
$133$	0	0
$134$	4.47565	0.386637
$135$	3.87939	0.333884
$136$	5.53209	0.474373
$137$	−0.0196004	−0.00167457	−0.000837286	−	1.00000i	$-0.500267\pi$
$137$	−0.0196004	−0.00167457	−0.000837286		1.00000i	$0.500267\pi$
$138$	−8.94356	−0.761327
$139$	4.49525	0.381282	0.190641	−	0.981660i	$-0.438943\pi$
$139$	4.49525	0.381282	0.190641	+	0.981660i	$0.438943\pi$
$140$	−4.75877	−0.402190
$141$	−2.17024	−0.182768
$142$	2.63816	0.221389
$143$	1.03952	0.0869294
$144$	1.00000	0.0833333
$145$	−32.8803	−2.73056
$146$	15.3628	1.27143
$147$	5.49525	0.453241
$148$	−1.69459	−0.139295
$149$	12.0300	0.985538	0.492769	−	0.870160i	$-0.335985\pi$
$149$	12.0300	0.985538	0.492769	+	0.870160i	$0.335985\pi$
$150$	10.0496	0.820549
$151$	−0.0591253	−0.00481155	−0.00240578	−	0.999997i	$-0.500766\pi$
$151$	−0.0591253	−0.00481155	−0.00240578	+	0.999997i	$0.500766\pi$
$152$	0	0
$153$	−5.53209	−0.447243
$154$	2.60132	0.209620
$155$	9.35504	0.751415
$156$	0.490200	0.0392474
$157$	12.9581	1.03417	0.517085	−	0.855934i	$-0.327017\pi$
$157$	12.9581	1.03417	0.517085	+	0.855934i	$0.327017\pi$
$158$	−4.66044	−0.370765
$159$	8.88713	0.704795
$160$	3.87939	0.306692
$161$	−10.9709	−0.864628
$162$	−1.00000	−0.0785674
$163$	15.0719	1.18052	0.590262	−	0.807212i	$-0.299024\pi$
$163$	15.0719	1.18052	0.590262	+	0.807212i	$0.299024\pi$
$164$	−1.59627	−0.124647
$165$	−8.22668	−0.640446
$166$	−12.4807	−0.968691
$167$	1.94087	0.150189	0.0750947	−	0.997176i	$-0.476074\pi$
$167$	1.94087	0.150189	0.0750947	+	0.997176i	$0.476074\pi$
$168$	1.22668	0.0946405
$169$	−12.7597	−0.981516
$170$	−21.4611	−1.64599
$171$	0	0
$172$	−6.63816	−0.506155
$173$	−16.0719	−1.22193	−0.610963	−	0.791659i	$-0.709217\pi$
$173$	−16.0719	−1.22193	−0.610963	+	0.791659i	$0.709217\pi$
$174$	8.47565	0.642538
$175$	12.3277	0.931886
$176$	−2.12061	−0.159847
$177$	−11.4192	−0.858321
$178$	8.45605	0.633808
$179$	−14.7743	−1.10428	−0.552140	−	0.833752i	$-0.686189\pi$
$179$	−14.7743	−1.10428	−0.552140	+	0.833752i	$0.686189\pi$
$180$	−3.87939	−0.289152
$181$	18.2267	1.35478	0.677389	−	0.735625i	$-0.263111\pi$
$181$	18.2267	1.35478	0.677389	+	0.735625i	$0.263111\pi$
$182$	0.601319	0.0445727
$183$	−0.0418891	−0.00309653
$184$	8.94356	0.659328
$185$	6.57398	0.483328
$186$	−2.41147	−0.176818
$187$	11.7314	0.857887
$188$	2.17024	0.158281
$189$	−1.22668	−0.0892280
$190$	0	0
$191$	1.29086	0.0934033	0.0467017	−	0.998909i	$-0.485129\pi$
$191$	1.29086	0.0934033	0.0467017	+	0.998909i	$0.485129\pi$
$192$	−1.00000	−0.0721688
$193$	9.12061	0.656516	0.328258	−	0.944588i	$-0.393538\pi$
$193$	9.12061	0.656516	0.328258	+	0.944588i	$0.393538\pi$
$194$	−14.3773	−1.03223
$195$	−1.90167	−0.136182
$196$	−5.49525	−0.392518
$197$	18.6236	1.32688	0.663439	−	0.748231i	$-0.269096\pi$
$197$	18.6236	1.32688	0.663439	+	0.748231i	$0.269096\pi$
$198$	2.12061	0.150706
$199$	8.43107	0.597663	0.298832	−	0.954306i	$-0.403403\pi$
$199$	8.43107	0.597663	0.298832	+	0.954306i	$0.403403\pi$
$200$	−10.0496	−0.710616
$201$	4.47565	0.315688
$202$	−5.69459	−0.400670
$203$	10.3969	0.729721
$204$	5.53209	0.387324
$205$	6.19253	0.432505
$206$	−0.313148	−0.0218181
$207$	−8.94356	−0.621621
$208$	−0.490200	−0.0339892
$209$	0	0
$210$	−4.75877	−0.328386
$211$	1.46791	0.101055	0.0505276	−	0.998723i	$-0.483910\pi$
$211$	1.46791	0.101055	0.0505276	+	0.998723i	$0.483910\pi$
$212$	−8.88713	−0.610370
$213$	2.63816	0.180763
$214$	−16.8280	−1.15034
$215$	25.7520	1.75627
$216$	1.00000	0.0680414
$217$	−2.95811	−0.200810
$218$	−10.4115	−0.705154
$219$	15.3628	1.03812
$220$	8.22668	0.554643
$221$	2.71183	0.182417
$222$	−1.69459	−0.113734
$223$	−26.2686	−1.75907	−0.879537	−	0.475831i	$-0.842147\pi$
$223$	−26.2686	−1.75907	−0.879537	+	0.475831i	$0.842147\pi$
$224$	−1.22668	−0.0819611
$225$	10.0496	0.669975
$226$	−17.3824	−1.15626
$227$	−18.3678	−1.21912	−0.609558	−	0.792742i	$-0.708653\pi$
$227$	−18.3678	−1.21912	−0.609558	+	0.792742i	$0.708653\pi$
$228$	0	0
$229$	3.87164	0.255845	0.127923	−	0.991784i	$-0.459169\pi$
$229$	3.87164	0.255845	0.127923	+	0.991784i	$0.459169\pi$
$230$	−34.6955	−2.28776
$231$	2.60132	0.171154
$232$	−8.47565	−0.556454
$233$	16.4466	1.07745	0.538725	−	0.842482i	$-0.318906\pi$
$233$	16.4466	1.07745	0.538725	+	0.842482i	$0.318906\pi$
$234$	0.490200	0.0320454
$235$	−8.41921	−0.549209
$236$	11.4192	0.743328
$237$	−4.66044	−0.302728
$238$	6.78611	0.439878
$239$	3.30541	0.213809	0.106905	−	0.994269i	$-0.465906\pi$
$239$	3.30541	0.213809	0.106905	+	0.994269i	$0.465906\pi$
$240$	3.87939	0.250413
$241$	−3.01548	−0.194244	−0.0971221	−	0.995272i	$-0.530964\pi$
$241$	−3.01548	−0.194244	−0.0971221	+	0.995272i	$0.530964\pi$
$242$	6.50299	0.418028
$243$	−1.00000	−0.0641500
$244$	0.0418891	0.00268167
$245$	21.3182	1.36197
$246$	−1.59627	−0.101774
$247$	0	0
$248$	2.41147	0.153129
$249$	−12.4807	−0.790933
$250$	19.5895	1.23895
$251$	−3.53478	−0.223113	−0.111557	−	0.993758i	$-0.535584\pi$
$251$	−3.53478	−0.223113	−0.111557	+	0.993758i	$0.535584\pi$
$252$	1.22668	0.0772737
$253$	18.9659	1.19237
$254$	−1.63041	−0.102301
$255$	−21.4611	−1.34395
$256$	1.00000	0.0625000
$257$	4.70233	0.293324	0.146662	−	0.989187i	$-0.453147\pi$
$257$	4.70233	0.293324	0.146662	+	0.989187i	$0.453147\pi$
$258$	−6.63816	−0.413274
$259$	−2.07873	−0.129166
$260$	1.90167	0.117937
$261$	8.47565	0.524630
$262$	−5.96316	−0.368405
$263$	21.0624	1.29876	0.649382	−	0.760462i	$-0.275028\pi$
$263$	21.0624	1.29876	0.649382	+	0.760462i	$0.275028\pi$
$264$	−2.12061	−0.130515
$265$	34.4766	2.11788
$266$	0	0
$267$	8.45605	0.517502
$268$	−4.47565	−0.273394
$269$	−10.0787	−0.614511	−0.307255	−	0.951627i	$-0.599411\pi$
$269$	−10.0787	−0.614511	−0.307255	+	0.951627i	$0.599411\pi$
$270$	−3.87939	−0.236092
$271$	−9.76382	−0.593110	−0.296555	−	0.955016i	$-0.595838\pi$
$271$	−9.76382	−0.593110	−0.296555	+	0.955016i	$0.595838\pi$
$272$	−5.53209	−0.335432
$273$	0.601319	0.0363935
$274$	0.0196004	0.00118410
$275$	−21.3114	−1.28513
$276$	8.94356	0.538339
$277$	16.8571	1.01284	0.506422	−	0.862286i	$-0.330968\pi$
$277$	16.8571	1.01284	0.506422	+	0.862286i	$0.330968\pi$
$278$	−4.49525	−0.269607
$279$	−2.41147	−0.144371
$280$	4.75877	0.284391
$281$	11.7246	0.699432	0.349716	−	0.936856i	$-0.386278\pi$
$281$	11.7246	0.699432	0.349716	+	0.936856i	$0.386278\pi$
$282$	2.17024	0.129236
$283$	−21.5449	−1.28071	−0.640355	−	0.768079i	$-0.721213\pi$
$283$	−21.5449	−1.28071	−0.640355	+	0.768079i	$0.721213\pi$
$284$	−2.63816	−0.156546
$285$	0	0
$286$	−1.03952	−0.0614684
$287$	−1.95811	−0.115584
$288$	−1.00000	−0.0589256
$289$	13.6040	0.800236
$290$	32.8803	1.93080
$291$	−14.3773	−0.842814
$292$	−15.3628	−0.899039
$293$	11.1206	0.649673	0.324837	−	0.945770i	$-0.394691\pi$
$293$	11.1206	0.649673	0.324837	+	0.945770i	$0.394691\pi$
$294$	−5.49525	−0.320490
$295$	−44.2995	−2.57922
$296$	1.69459	0.0984962
$297$	2.12061	0.123051
$298$	−12.0300	−0.696881
$299$	4.38413	0.253541
$300$	−10.0496	−0.580216
$301$	−8.14290	−0.469349
$302$	0.0591253	0.00340228
$303$	−5.69459	−0.327146
$304$	0	0
$305$	−0.162504	−0.00930494
$306$	5.53209	0.316248
$307$	−25.0401	−1.42912	−0.714558	−	0.699576i	$-0.753372\pi$
$307$	−25.0401	−1.42912	−0.714558	+	0.699576i	$0.753372\pi$
$308$	−2.60132	−0.148224
$309$	−0.313148	−0.0178144
$310$	−9.35504	−0.531330
$311$	0.0564370	0.00320025	0.00160012	−	0.999999i	$-0.499491\pi$
$311$	0.0564370	0.00320025	0.00160012	+	0.999999i	$0.499491\pi$
$312$	−0.490200	−0.0277521
$313$	13.7638	0.777977	0.388989	−	0.921243i	$-0.372825\pi$
$313$	13.7638	0.777977	0.388989	+	0.921243i	$0.372825\pi$
$314$	−12.9581	−0.731269
$315$	−4.75877	−0.268126
$316$	4.66044	0.262170
$317$	−10.9040	−0.612432	−0.306216	−	0.951962i	$-0.599063\pi$
$317$	−10.9040	−0.612432	−0.306216	+	0.951962i	$0.599063\pi$
$318$	−8.88713	−0.498365
$319$	−17.9736	−1.00633
$320$	−3.87939	−0.216864
$321$	−16.8280	−0.939247
$322$	10.9709	0.611385
$323$	0	0
$324$	1.00000	0.0555556
$325$	−4.92633	−0.273263
$326$	−15.0719	−0.834756
$327$	−10.4115	−0.575756
$328$	1.59627	0.0881391
$329$	2.66220	0.146772
$330$	8.22668	0.452864
$331$	−8.59121	−0.472216	−0.236108	−	0.971727i	$-0.575872\pi$
$331$	−8.59121	−0.472216	−0.236108	+	0.971727i	$0.575872\pi$
$332$	12.4807	0.684968
$333$	−1.69459	−0.0928631
$334$	−1.94087	−0.106200
$335$	17.3628	0.948630
$336$	−1.22668	−0.0669210
$337$	2.31046	0.125859	0.0629294	−	0.998018i	$-0.479956\pi$
$337$	2.31046	0.125859	0.0629294	+	0.998018i	$0.479956\pi$
$338$	12.7597	0.694036
$339$	−17.3824	−0.944081
$340$	21.4611	1.16389
$341$	5.11381	0.276928
$342$	0	0
$343$	−15.3277	−0.827618
$344$	6.63816	0.357905
$345$	−34.6955	−1.86794
$346$	16.0719	0.864032
$347$	−3.28581	−0.176391	−0.0881957	−	0.996103i	$-0.528110\pi$
$347$	−3.28581	−0.176391	−0.0881957	+	0.996103i	$0.528110\pi$
$348$	−8.47565	−0.454343
$349$	29.3482	1.57097	0.785487	−	0.618878i	$-0.212412\pi$
$349$	29.3482	1.57097	0.785487	+	0.618878i	$0.212412\pi$
$350$	−12.3277	−0.658943
$351$	0.490200	0.0261649
$352$	2.12061	0.113029
$353$	−7.73917	−0.411914	−0.205957	−	0.978561i	$-0.566031\pi$
$353$	−7.73917	−0.411914	−0.205957	+	0.978561i	$0.566031\pi$
$354$	11.4192	0.606924
$355$	10.2344	0.543187
$356$	−8.45605	−0.448170
$357$	6.78611	0.359159
$358$	14.7743	0.780843
$359$	2.86753	0.151342	0.0756711	−	0.997133i	$-0.475890\pi$
$359$	2.86753	0.151342	0.0756711	+	0.997133i	$0.475890\pi$
$360$	3.87939	0.204462
$361$	0	0
$362$	−18.2267	−0.957973
$363$	6.50299	0.341319
$364$	−0.601319	−0.0315177
$365$	59.5981	3.11951
$366$	0.0418891	0.00218958
$367$	−22.9659	−1.19881	−0.599404	−	0.800447i	$-0.704596\pi$
$367$	−22.9659	−1.19881	−0.599404	+	0.800447i	$0.704596\pi$
$368$	−8.94356	−0.466215
$369$	−1.59627	−0.0830983
$370$	−6.57398	−0.341765
$371$	−10.9017	−0.565987
$372$	2.41147	0.125029
$373$	23.1908	1.20077	0.600387	−	0.799710i	$-0.295013\pi$
$373$	23.1908	1.20077	0.600387	+	0.799710i	$0.295013\pi$
$374$	−11.7314	−0.606618
$375$	19.5895	1.01160
$376$	−2.17024	−0.111922
$377$	−4.15476	−0.213981
$378$	1.22668	0.0630937
$379$	33.5185	1.72173	0.860864	−	0.508835i	$-0.169924\pi$
$379$	33.5185	1.72173	0.860864	+	0.508835i	$0.169924\pi$
$380$	0	0
$381$	−1.63041	−0.0835287
$382$	−1.29086	−0.0660461
$383$	−6.72967	−0.343870	−0.171935	−	0.985108i	$-0.555002\pi$
$383$	−6.72967	−0.343870	−0.171935	+	0.985108i	$0.555002\pi$
$384$	1.00000	0.0510310
$385$	10.0915	0.514311
$386$	−9.12061	−0.464227
$387$	−6.63816	−0.337436
$388$	14.3773	0.729898
$389$	−19.0223	−0.964468	−0.482234	−	0.876042i	$-0.660175\pi$
$389$	−19.0223	−0.964468	−0.482234	+	0.876042i	$0.660175\pi$
$390$	1.90167	0.0962950
$391$	49.4766	2.50214
$392$	5.49525	0.277552
$393$	−5.96316	−0.300802
$394$	−18.6236	−0.938244
$395$	−18.0797	−0.909686
$396$	−2.12061	−0.106565
$397$	−26.9145	−1.35080	−0.675399	−	0.737452i	$-0.736029\pi$
$397$	−26.9145	−1.35080	−0.675399	+	0.737452i	$0.736029\pi$
$398$	−8.43107	−0.422612
$399$	0	0
$400$	10.0496	0.502481
$401$	5.70140	0.284714	0.142357	−	0.989815i	$-0.454532\pi$
$401$	5.70140	0.284714	0.142357	+	0.989815i	$0.454532\pi$
$402$	−4.47565	−0.223225
$403$	1.18210	0.0588848
$404$	5.69459	0.283317
$405$	−3.87939	−0.192768
$406$	−10.3969	−0.515991
$407$	3.59358	0.178127
$408$	−5.53209	−0.273879
$409$	0.807467	0.0399267	0.0199633	−	0.999801i	$-0.493645\pi$
$409$	0.807467	0.0399267	0.0199633	+	0.999801i	$0.493645\pi$
$410$	−6.19253	−0.305827
$411$	0.0196004	0.000966814 0
$412$	0.313148	0.0154277
$413$	14.0077	0.689276
$414$	8.94356	0.439552
$415$	−48.4175	−2.37672
$416$	0.490200	0.0240340
$417$	−4.49525	−0.220133
$418$	0	0
$419$	−19.1215	−0.934149	−0.467074	−	0.884218i	$-0.654692\pi$
$419$	−19.1215	−0.934149	−0.467074	+	0.884218i	$0.654692\pi$
$420$	4.75877	0.232204
$421$	28.0232	1.36577	0.682884	−	0.730527i	$-0.260725\pi$
$421$	28.0232	1.36577	0.682884	+	0.730527i	$0.260725\pi$
$422$	−1.46791	−0.0714568
$423$	2.17024	0.105521
$424$	8.88713	0.431597
$425$	−55.5954	−2.69678
$426$	−2.63816	−0.127819
$427$	0.0513845	0.00248667
$428$	16.8280	0.813412
$429$	−1.03952	−0.0501887
$430$	−25.7520	−1.24187
$431$	9.03684	0.435289	0.217645	−	0.976028i	$-0.430163\pi$
$431$	9.03684	0.435289	0.217645	+	0.976028i	$0.430163\pi$
$432$	−1.00000	−0.0481125
$433$	−1.46286	−0.0703005	−0.0351503	−	0.999382i	$-0.511191\pi$
$433$	−1.46286	−0.0703005	−0.0351503	+	0.999382i	$0.511191\pi$
$434$	2.95811	0.141994
$435$	32.8803	1.57649
$436$	10.4115	0.498619
$437$	0	0
$438$	−15.3628	−0.734062
$439$	5.41653	0.258517	0.129258	−	0.991611i	$-0.458740\pi$
$439$	5.41653	0.258517	0.129258	+	0.991611i	$0.458740\pi$
$440$	−8.22668	−0.392192
$441$	−5.49525	−0.261679
$442$	−2.71183	−0.128989
$443$	−28.4662	−1.35247	−0.676234	−	0.736687i	$-0.736389\pi$
$443$	−28.4662	−1.35247	−0.676234	+	0.736687i	$0.736389\pi$
$444$	1.69459	0.0804218
$445$	32.8043	1.55507
$446$	26.2686	1.24385
$447$	−12.0300	−0.569001
$448$	1.22668	0.0579553
$449$	22.7648	1.07434	0.537168	−	0.843476i	$-0.319494\pi$
$449$	22.7648	1.07434	0.537168	+	0.843476i	$0.319494\pi$
$450$	−10.0496	−0.473744
$451$	3.38507	0.159397
$452$	17.3824	0.817598
$453$	0.0591253	0.00277795
$454$	18.3678	0.862045
$455$	2.33275	0.109361
$456$	0	0
$457$	−1.13011	−0.0528643	−0.0264322	−	0.999651i	$-0.508415\pi$
$457$	−1.13011	−0.0528643	−0.0264322	+	0.999651i	$0.508415\pi$
$458$	−3.87164	−0.180910
$459$	5.53209	0.258216
$460$	34.6955	1.61769
$461$	−12.9831	−0.604683	−0.302341	−	0.953200i	$-0.597768\pi$
$461$	−12.9831	−0.604683	−0.302341	+	0.953200i	$0.597768\pi$
$462$	−2.60132	−0.121024
$463$	−30.6245	−1.42324	−0.711622	−	0.702563i	$-0.752039\pi$
$463$	−30.6245	−1.42324	−0.711622	+	0.702563i	$0.752039\pi$
$464$	8.47565	0.393472
$465$	−9.35504	−0.433829
$466$	−16.4466	−0.761872
$467$	11.0574	0.511674	0.255837	−	0.966720i	$-0.417649\pi$
$467$	11.0574	0.511674	0.255837	+	0.966720i	$0.417649\pi$
$468$	−0.490200	−0.0226595
$469$	−5.49020	−0.253514
$470$	8.41921	0.388349
$471$	−12.9581	−0.597078
$472$	−11.4192	−0.525612
$473$	14.0770	0.647260
$474$	4.66044	0.214061
$475$	0	0
$476$	−6.78611	−0.311041
$477$	−8.88713	−0.406914
$478$	−3.30541	−0.151186
$479$	−17.6382	−0.805908	−0.402954	−	0.915220i	$-0.632017\pi$
$479$	−17.6382	−0.805908	−0.402954	+	0.915220i	$0.632017\pi$
$480$	−3.87939	−0.177069
$481$	0.830689	0.0378762
$482$	3.01548	0.137351
$483$	10.9709	0.499193
$484$	−6.50299	−0.295591
$485$	−55.7752	−2.53262
$486$	1.00000	0.0453609
$487$	15.2935	0.693017	0.346508	−	0.938047i	$-0.387367\pi$
$487$	15.2935	0.693017	0.346508	+	0.938047i	$0.387367\pi$
$488$	−0.0418891	−0.00189623
$489$	−15.0719	−0.681576
$490$	−21.3182	−0.963058
$491$	−1.77837	−0.0802568	−0.0401284	−	0.999195i	$-0.512777\pi$
$491$	−1.77837	−0.0802568	−0.0401284	+	0.999195i	$0.512777\pi$
$492$	1.59627	0.0719653
$493$	−46.8881	−2.11173
$494$	0	0
$495$	8.22668	0.369762
$496$	−2.41147	−0.108278
$497$	−3.23618	−0.145162
$498$	12.4807	0.559274
$499$	−0.107822	−0.00482675	−0.00241338	−	0.999997i	$-0.500768\pi$
$499$	−0.107822	−0.00482675	−0.00241338	+	0.999997i	$0.500768\pi$
$500$	−19.5895	−0.876067
$501$	−1.94087	−0.0867119
$502$	3.53478	0.157765
$503$	−23.6901	−1.05629	−0.528146	−	0.849154i	$-0.677113\pi$
$503$	−23.6901	−1.05629	−0.528146	+	0.849154i	$0.677113\pi$
$504$	−1.22668	−0.0546407
$505$	−22.0915	−0.983060
$506$	−18.9659	−0.843135
$507$	12.7597	0.566678
$508$	1.63041	0.0723380
$509$	3.57398	0.158414	0.0792069	−	0.996858i	$-0.474761\pi$
$509$	3.57398	0.158414	0.0792069	+	0.996858i	$0.474761\pi$
$510$	21.4611	0.950314
$511$	−18.8452	−0.833664
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−4.70233	−0.207411
$515$	−1.21482	−0.0535315
$516$	6.63816	0.292229
$517$	−4.60225	−0.202407
$518$	2.07873	0.0913340
$519$	16.0719	0.705479
$520$	−1.90167	−0.0833939
$521$	−34.1215	−1.49489	−0.747446	−	0.664322i	$-0.768720\pi$
$521$	−34.1215	−1.49489	−0.747446	+	0.664322i	$0.768720\pi$
$522$	−8.47565	−0.370969
$523$	−17.0669	−0.746282	−0.373141	−	0.927775i	$-0.621719\pi$
$523$	−17.0669	−0.746282	−0.373141	+	0.927775i	$0.621719\pi$
$524$	5.96316	0.260502
$525$	−12.3277	−0.538025
$526$	−21.0624	−0.918365
$527$	13.3405	0.581121
$528$	2.12061	0.0922879
$529$	56.9873	2.47771
$530$	−34.4766	−1.49757
$531$	11.4192	0.495552
$532$	0	0
$533$	0.782490	0.0338934
$534$	−8.45605	−0.365929
$535$	−65.2823	−2.82240
$536$	4.47565	0.193319
$537$	14.7743	0.637556
$538$	10.0787	0.434525
$539$	11.6533	0.501944
$540$	3.87939	0.166942
$541$	26.3746	1.13393	0.566967	−	0.823740i	$-0.308117\pi$
$541$	26.3746	1.13393	0.566967	+	0.823740i	$0.308117\pi$
$542$	9.76382	0.419392
$543$	−18.2267	−0.782182
$544$	5.53209	0.237186
$545$	−40.3901	−1.73012
$546$	−0.601319	−0.0257341
$547$	34.8958	1.49204	0.746018	−	0.665925i	$-0.231963\pi$
$547$	34.8958	1.49204	0.746018	+	0.665925i	$0.231963\pi$
$548$	−0.0196004	−0.000837286 0
$549$	0.0418891	0.00178778
$550$	21.3114	0.908721
$551$	0	0
$552$	−8.94356	−0.380663
$553$	5.71688	0.243107
$554$	−16.8571	−0.716189
$555$	−6.57398	−0.279050
$556$	4.49525	0.190641
$557$	−32.5921	−1.38097	−0.690487	−	0.723345i	$-0.742604\pi$
$557$	−32.5921	−1.38097	−0.690487	+	0.723345i	$0.742604\pi$
$558$	2.41147	0.102086
$559$	3.25402	0.137630
$560$	−4.75877	−0.201095
$561$	−11.7314	−0.495301
$562$	−11.7246	−0.494573
$563$	4.79561	0.202111	0.101055	−	0.994881i	$-0.467778\pi$
$563$	4.79561	0.202111	0.101055	+	0.994881i	$0.467778\pi$
$564$	−2.17024	−0.0913838
$565$	−67.4329	−2.83693
$566$	21.5449	0.905599
$567$	1.22668	0.0515158
$568$	2.63816	0.110695
$569$	32.7006	1.37088	0.685440	−	0.728129i	$-0.259610\pi$
$569$	32.7006	1.37088	0.685440	+	0.728129i	$0.259610\pi$
$570$	0	0
$571$	−10.9531	−0.458371	−0.229186	−	0.973383i	$-0.573606\pi$
$571$	−10.9531	−0.458371	−0.229186	+	0.973383i	$0.573606\pi$
$572$	1.03952	0.0434647
$573$	−1.29086	−0.0539264
$574$	1.95811	0.0817300
$575$	−89.8795	−3.74823
$576$	1.00000	0.0416667
$577$	−18.3027	−0.761952	−0.380976	−	0.924585i	$-0.624412\pi$
$577$	−18.3027	−0.761952	−0.380976	+	0.924585i	$0.624412\pi$
$578$	−13.6040	−0.565852
$579$	−9.12061	−0.379040
$580$	−32.8803	−1.36528
$581$	15.3099	0.635160
$582$	14.3773	0.595959
$583$	18.8462	0.780529
$584$	15.3628	0.635716
$585$	1.90167	0.0786245
$586$	−11.1206	−0.459388
$587$	−5.68416	−0.234611	−0.117305	−	0.993096i	$-0.537426\pi$
$587$	−5.68416	−0.234611	−0.117305	+	0.993096i	$0.537426\pi$
$588$	5.49525	0.226620
$589$	0	0
$590$	44.2995	1.82378
$591$	−18.6236	−0.766073
$592$	−1.69459	−0.0696473
$593$	−10.5098	−0.431586	−0.215793	−	0.976439i	$-0.569234\pi$
$593$	−10.5098	−0.431586	−0.215793	+	0.976439i	$0.569234\pi$
$594$	−2.12061	−0.0870099
$595$	26.3259	1.07926
$596$	12.0300	0.492769
$597$	−8.43107	−0.345061
$598$	−4.38413	−0.179281
$599$	44.7110	1.82684	0.913421	−	0.407016i	$-0.133431\pi$
$599$	44.7110	1.82684	0.913421	+	0.407016i	$0.133431\pi$
$600$	10.0496	0.410274
$601$	−32.8726	−1.34090	−0.670450	−	0.741955i	$-0.733899\pi$
$601$	−32.8726	−1.34090	−0.670450	+	0.741955i	$0.733899\pi$
$602$	8.14290	0.331880
$603$	−4.47565	−0.182263
$604$	−0.0591253	−0.00240578
$605$	25.2276	1.02565
$606$	5.69459	0.231327
$607$	−29.9486	−1.21558	−0.607788	−	0.794099i	$-0.707943\pi$
$607$	−29.9486	−1.21558	−0.607788	+	0.794099i	$0.707943\pi$
$608$	0	0
$609$	−10.3969	−0.421305
$610$	0.162504	0.00657959
$611$	−1.06385	−0.0430389
$612$	−5.53209	−0.223621
$613$	5.84018	0.235883	0.117941	−	0.993021i	$-0.462370\pi$
$613$	5.84018	0.235883	0.117941	+	0.993021i	$0.462370\pi$
$614$	25.0401	1.01054
$615$	−6.19253	−0.249707
$616$	2.60132	0.104810
$617$	−12.5716	−0.506114	−0.253057	−	0.967451i	$-0.581436\pi$
$617$	−12.5716	−0.506114	−0.253057	+	0.967451i	$0.581436\pi$
$618$	0.313148	0.0125967
$619$	8.28581	0.333035	0.166517	−	0.986039i	$-0.446748\pi$
$619$	8.28581	0.333035	0.166517	+	0.986039i	$0.446748\pi$
$620$	9.35504	0.375707
$621$	8.94356	0.358893
$622$	−0.0564370	−0.00226292
$623$	−10.3729	−0.415581
$624$	0.490200	0.0196237
$625$	25.7469	1.02988
$626$	−13.7638	−0.550113
$627$	0	0
$628$	12.9581	0.517085
$629$	9.37464	0.373791
$630$	4.75877	0.189594
$631$	6.82800	0.271818	0.135909	−	0.990721i	$-0.456604\pi$
$631$	6.82800	0.271818	0.135909	+	0.990721i	$0.456604\pi$
$632$	−4.66044	−0.185383
$633$	−1.46791	−0.0583442
$634$	10.9040	0.433055
$635$	−6.32501	−0.251000
$636$	8.88713	0.352397
$637$	2.69377	0.106731
$638$	17.9736	0.711581
$639$	−2.63816	−0.104364
$640$	3.87939	0.153346
$641$	−38.7110	−1.52899	−0.764496	−	0.644628i	$-0.777012\pi$
$641$	−38.7110	−1.52899	−0.764496	+	0.644628i	$0.777012\pi$
$642$	16.8280	0.664148
$643$	−12.6013	−0.496948	−0.248474	−	0.968639i	$-0.579929\pi$
$643$	−12.6013	−0.496948	−0.248474	+	0.968639i	$0.579929\pi$
$644$	−10.9709	−0.432314
$645$	−25.7520	−1.01398
$646$	0	0
$647$	8.41241	0.330726	0.165363	−	0.986233i	$-0.447120\pi$
$647$	8.41241	0.330726	0.165363	+	0.986233i	$0.447120\pi$
$648$	−1.00000	−0.0392837
$649$	−24.2158	−0.950552
$650$	4.92633	0.193226
$651$	2.95811	0.115938
$652$	15.0719	0.590262
$653$	26.3800	1.03233	0.516165	−	0.856489i	$-0.327359\pi$
$653$	26.3800	1.03233	0.516165	+	0.856489i	$0.327359\pi$
$654$	10.4115	0.407121
$655$	−23.1334	−0.903897
$656$	−1.59627	−0.0623237
$657$	−15.3628	−0.599359
$658$	−2.66220	−0.103783
$659$	−32.0069	−1.24681	−0.623406	−	0.781898i	$-0.714252\pi$
$659$	−32.0069	−1.24681	−0.623406	+	0.781898i	$0.714252\pi$
$660$	−8.22668	−0.320223
$661$	40.5280	1.57636	0.788178	−	0.615448i	$-0.211025\pi$
$661$	40.5280	1.57636	0.788178	+	0.615448i	$0.211025\pi$
$662$	8.59121	0.333907
$663$	−2.71183	−0.105319
$664$	−12.4807	−0.484345
$665$	0	0
$666$	1.69459	0.0656641
$667$	−75.8025	−2.93509
$668$	1.94087	0.0750947
$669$	26.2686	1.01560
$670$	−17.3628	−0.670783
$671$	−0.0888306	−0.00342927
$672$	1.22668	0.0473203
$673$	4.56118	0.175821	0.0879104	−	0.996128i	$-0.471981\pi$
$673$	4.56118	0.175821	0.0879104	+	0.996128i	$0.471981\pi$
$674$	−2.31046	−0.0889956
$675$	−10.0496	−0.386810
$676$	−12.7597	−0.490758
$677$	−33.4415	−1.28526	−0.642631	−	0.766176i	$-0.722157\pi$
$677$	−33.4415	−1.28526	−0.642631	+	0.766176i	$0.722157\pi$
$678$	17.3824	0.667566
$679$	17.6364	0.676823
$680$	−21.4611	−0.822996
$681$	18.3678	0.703857
$682$	−5.11381	−0.195818
$683$	26.4825	1.01332	0.506662	−	0.862145i	$-0.330879\pi$
$683$	26.4825	1.01332	0.506662	+	0.862145i	$0.330879\pi$
$684$	0	0
$685$	0.0760373	0.00290524
$686$	15.3277	0.585214
$687$	−3.87164	−0.147712
$688$	−6.63816	−0.253077
$689$	4.35647	0.165968
$690$	34.6955	1.32084
$691$	33.4005	1.27062	0.635308	−	0.772259i	$-0.280873\pi$
$691$	33.4005	1.27062	0.635308	+	0.772259i	$0.280873\pi$
$692$	−16.0719	−0.610963
$693$	−2.60132	−0.0988159
$694$	3.28581	0.124728
$695$	−17.4388	−0.661492
$696$	8.47565	0.321269
$697$	8.83069	0.334486
$698$	−29.3482	−1.11085
$699$	−16.4466	−0.622066
$700$	12.3277	0.465943
$701$	18.8794	0.713065	0.356532	−	0.934283i	$-0.383959\pi$
$701$	18.8794	0.713065	0.356532	+	0.934283i	$0.383959\pi$
$702$	−0.490200	−0.0185014
$703$	0	0
$704$	−2.12061	−0.0799237
$705$	8.41921	0.317086
$706$	7.73917	0.291268
$707$	6.98545	0.262715
$708$	−11.4192	−0.429160
$709$	−0.213067	−0.00800191	−0.00400096	−	0.999992i	$-0.501274\pi$
$709$	−0.213067	−0.00800191	−0.00400096	+	0.999992i	$0.501274\pi$
$710$	−10.2344	−0.384091
$711$	4.66044	0.174780
$712$	8.45605	0.316904
$713$	21.5672	0.807697
$714$	−6.78611	−0.253964
$715$	−4.03272	−0.150815
$716$	−14.7743	−0.552140
$717$	−3.30541	−0.123443
$718$	−2.86753	−0.107015
$719$	−12.9659	−0.483545	−0.241772	−	0.970333i	$-0.577729\pi$
$719$	−12.9659	−0.483545	−0.241772	+	0.970333i	$0.577729\pi$
$720$	−3.87939	−0.144576
$721$	0.384133	0.0143059
$722$	0	0
$723$	3.01548	0.112147
$724$	18.2267	0.677389
$725$	85.1772	3.16340
$726$	−6.50299	−0.241349
$727$	25.7246	0.954073	0.477037	−	0.878883i	$-0.341711\pi$
$727$	25.7246	0.954073	0.477037	+	0.878883i	$0.341711\pi$
$728$	0.601319	0.0222864
$729$	1.00000	0.0370370
$730$	−59.5981	−2.20583
$731$	36.7229	1.35824
$732$	−0.0418891	−0.00154826
$733$	8.51991	0.314690	0.157345	−	0.987544i	$-0.449707\pi$
$733$	8.51991	0.314690	0.157345	+	0.987544i	$0.449707\pi$
$734$	22.9659	0.847685
$735$	−21.3182	−0.786334
$736$	8.94356	0.329664
$737$	9.49113	0.349610
$738$	1.59627	0.0587594
$739$	−13.3054	−0.489447	−0.244724	−	0.969593i	$-0.578697\pi$
$739$	−13.3054	−0.489447	−0.244724	+	0.969593i	$0.578697\pi$
$740$	6.57398	0.241664
$741$	0	0
$742$	10.9017	0.400213
$743$	26.9564	0.988933	0.494466	−	0.869197i	$-0.335363\pi$
$743$	26.9564	0.988933	0.494466	+	0.869197i	$0.335363\pi$
$744$	−2.41147	−0.0884089
$745$	−46.6691	−1.70982
$746$	−23.1908	−0.849075
$747$	12.4807	0.456645
$748$	11.7314	0.428944
$749$	20.6426	0.754264
$750$	−19.5895	−0.715306
$751$	−18.4397	−0.672876	−0.336438	−	0.941706i	$-0.609222\pi$
$751$	−18.4397	−0.672876	−0.336438	+	0.941706i	$0.609222\pi$
$752$	2.17024	0.0791407
$753$	3.53478	0.128814
$754$	4.15476	0.151308
$755$	0.229370	0.00834763
$756$	−1.22668	−0.0446140
$757$	29.9162	1.08732	0.543662	−	0.839304i	$-0.317037\pi$
$757$	29.9162	1.08732	0.543662	+	0.839304i	$0.317037\pi$
$758$	−33.5185	−1.21745
$759$	−18.9659	−0.688417
$760$	0	0
$761$	−28.6691	−1.03925	−0.519627	−	0.854393i	$-0.673929\pi$
$761$	−28.6691	−1.03925	−0.519627	+	0.854393i	$0.673929\pi$
$762$	1.63041	0.0590637
$763$	12.7716	0.462362
$764$	1.29086	0.0467017
$765$	21.4611	0.775928
$766$	6.72967	0.243153
$767$	−5.59770	−0.202121
$768$	−1.00000	−0.0360844
$769$	−9.76146	−0.352007	−0.176004	−	0.984390i	$-0.556317\pi$
$769$	−9.76146	−0.352007	−0.176004	+	0.984390i	$0.556317\pi$
$770$	−10.0915	−0.363673
$771$	−4.70233	−0.169350
$772$	9.12061	0.328258
$773$	3.89662	0.140152	0.0700759	−	0.997542i	$-0.477676\pi$
$773$	3.89662	0.140152	0.0700759	+	0.997542i	$0.477676\pi$
$774$	6.63816	0.238604
$775$	−24.2344	−0.870526
$776$	−14.3773	−0.516116
$777$	2.07873	0.0745739
$778$	19.0223	0.681982
$779$	0	0
$780$	−1.90167	−0.0680908
$781$	5.59451	0.200187
$782$	−49.4766	−1.76928
$783$	−8.47565	−0.302895
$784$	−5.49525	−0.196259
$785$	−50.2695	−1.79420
$786$	5.96316	0.212699
$787$	2.94087	0.104831	0.0524154	−	0.998625i	$-0.483308\pi$
$787$	2.94087	0.104831	0.0524154	+	0.998625i	$0.483308\pi$
$788$	18.6236	0.663439
$789$	−21.0624	−0.749842
$790$	18.0797	0.643245
$791$	21.3226	0.758146
$792$	2.12061	0.0753528
$793$	−0.0205340	−0.000729184 0
$794$	26.9145	0.955159
$795$	−34.4766	−1.22276
$796$	8.43107	0.298832
$797$	−8.26950	−0.292921	−0.146460	−	0.989217i	$-0.546788\pi$
$797$	−8.26950	−0.292921	−0.146460	+	0.989217i	$0.546788\pi$
$798$	0	0
$799$	−12.0060	−0.424741
$800$	−10.0496	−0.355308
$801$	−8.45605	−0.298780
$802$	−5.70140	−0.201323
$803$	32.5785	1.14967
$804$	4.47565	0.157844
$805$	42.5604	1.50006
$806$	−1.18210	−0.0416378
$807$	10.0787	0.354788
$808$	−5.69459	−0.200335
$809$	−2.09059	−0.0735011	−0.0367505	−	0.999324i	$-0.511701\pi$
$809$	−2.09059	−0.0735011	−0.0367505	+	0.999324i	$0.511701\pi$
$810$	3.87939	0.136308
$811$	−0.864837	−0.0303685	−0.0151843	−	0.999885i	$-0.504833\pi$
$811$	−0.864837	−0.0303685	−0.0151843	+	0.999885i	$0.504833\pi$
$812$	10.3969	0.364861
$813$	9.76382	0.342432
$814$	−3.59358	−0.125955
$815$	−58.4698	−2.04811
$816$	5.53209	0.193662
$817$	0	0
$818$	−0.807467	−0.0282324
$819$	−0.601319	−0.0210118
$820$	6.19253	0.216253
$821$	22.7656	0.794524	0.397262	−	0.917705i	$-0.369960\pi$
$821$	22.7656	0.794524	0.397262	+	0.917705i	$0.369960\pi$
$822$	−0.0196004	−0.000683641 0
$823$	−33.1162	−1.15436	−0.577179	−	0.816618i	$-0.695846\pi$
$823$	−33.1162	−1.15436	−0.577179	+	0.816618i	$0.695846\pi$
$824$	−0.313148	−0.0109090
$825$	21.3114	0.741967
$826$	−14.0077	−0.487392
$827$	26.5149	0.922012	0.461006	−	0.887397i	$-0.347489\pi$
$827$	26.5149	0.922012	0.461006	+	0.887397i	$0.347489\pi$
$828$	−8.94356	−0.310810
$829$	3.15745	0.109663	0.0548314	−	0.998496i	$-0.482538\pi$
$829$	3.15745	0.109663	0.0548314	+	0.998496i	$0.482538\pi$
$830$	48.4175	1.68059
$831$	−16.8571	−0.584766
$832$	−0.490200	−0.0169946
$833$	30.4002	1.05331
$834$	4.49525	0.155658
$835$	−7.52940	−0.260566
$836$	0	0
$837$	2.41147	0.0833527
$838$	19.1215	0.660543
$839$	42.1189	1.45410	0.727052	−	0.686582i	$-0.240890\pi$
$839$	42.1189	1.45410	0.727052	+	0.686582i	$0.240890\pi$
$840$	−4.75877	−0.164193
$841$	42.8367	1.47713
$842$	−28.0232	−0.965744
$843$	−11.7246	−0.403817
$844$	1.46791	0.0505276
$845$	49.4998	1.70285
$846$	−2.17024	−0.0746145
$847$	−7.97710	−0.274096
$848$	−8.88713	−0.305185
$849$	21.5449	0.739418
$850$	55.5954	1.90691
$851$	15.1557	0.519531
$852$	2.63816	0.0903817
$853$	56.5235	1.93533	0.967664	−	0.252241i	$-0.0811677\pi$
$853$	56.5235	1.93533	0.967664	+	0.252241i	$0.0811677\pi$
$854$	−0.0513845	−0.00175834
$855$	0	0
$856$	−16.8280	−0.575169
$857$	−13.1916	−0.450616	−0.225308	−	0.974288i	$-0.572339\pi$
$857$	−13.1916	−0.450616	−0.225308	+	0.974288i	$0.572339\pi$
$858$	1.03952	0.0354888
$859$	−21.7510	−0.742136	−0.371068	−	0.928606i	$-0.621008\pi$
$859$	−21.7510	−0.742136	−0.371068	+	0.928606i	$0.621008\pi$
$860$	25.7520	0.878135
$861$	1.95811	0.0667322
$862$	−9.03684	−0.307796
$863$	46.9100	1.59684	0.798418	−	0.602104i	$-0.205671\pi$
$863$	46.9100	1.59684	0.798418	+	0.602104i	$0.205671\pi$
$864$	1.00000	0.0340207
$865$	62.3492	2.11994
$866$	1.46286	0.0497100
$867$	−13.6040	−0.462016
$868$	−2.95811	−0.100405
$869$	−9.88301	−0.335258
$870$	−32.8803	−1.11475
$871$	2.19396	0.0743396
$872$	−10.4115	−0.352577
$873$	14.3773	0.486599
$874$	0	0
$875$	−24.0300	−0.812363
$876$	15.3628	0.519060
$877$	2.67467	0.0903171	0.0451586	−	0.998980i	$-0.485621\pi$
$877$	2.67467	0.0903171	0.0451586	+	0.998980i	$0.485621\pi$
$878$	−5.41653	−0.182799
$879$	−11.1206	−0.375089
$880$	8.22668	0.277321
$881$	−27.1097	−0.913349	−0.456674	−	0.889634i	$-0.650960\pi$
$881$	−27.1097	−0.913349	−0.456674	+	0.889634i	$0.650960\pi$
$882$	5.49525	0.185035
$883$	−43.4243	−1.46134	−0.730671	−	0.682729i	$-0.760793\pi$
$883$	−43.4243	−1.46134	−0.730671	+	0.682729i	$0.760793\pi$
$884$	2.71183	0.0912087
$885$	44.2995	1.48911
$886$	28.4662	0.956339
$887$	21.4371	0.719786	0.359893	−	0.932994i	$-0.382813\pi$
$887$	21.4371	0.719786	0.359893	+	0.932994i	$0.382813\pi$
$888$	−1.69459	−0.0568668
$889$	2.00000	0.0670778
$890$	−32.8043	−1.09960
$891$	−2.12061	−0.0710433
$892$	−26.2686	−0.879537
$893$	0	0
$894$	12.0300	0.402344
$895$	57.3150	1.91583
$896$	−1.22668	−0.0409806
$897$	−4.38413	−0.146382
$898$	−22.7648	−0.759670
$899$	−20.4388	−0.681673
$900$	10.0496	0.334988
$901$	49.1644	1.63790
$902$	−3.38507	−0.112710
$903$	8.14290	0.270979
$904$	−17.3824	−0.578129
$905$	−70.7083	−2.35042
$906$	−0.0591253	−0.00196431
$907$	16.3791	0.543858	0.271929	−	0.962317i	$-0.412338\pi$
$907$	16.3791	0.543858	0.271929	+	0.962317i	$0.412338\pi$
$908$	−18.3678	−0.609558
$909$	5.69459	0.188878
$910$	−2.33275	−0.0773299
$911$	−28.4502	−0.942596	−0.471298	−	0.881974i	$-0.656214\pi$
$911$	−28.4502	−0.942596	−0.471298	+	0.881974i	$0.656214\pi$
$912$	0	0
$913$	−26.4668	−0.875922
$914$	1.13011	0.0373807
$915$	0.162504	0.00537221
$916$	3.87164	0.127923
$917$	7.31490	0.241559
$918$	−5.53209	−0.182586
$919$	−51.2535	−1.69070	−0.845349	−	0.534215i	$-0.820607\pi$
$919$	−51.2535	−1.69070	−0.845349	+	0.534215i	$0.820607\pi$
$920$	−34.6955	−1.14388
$921$	25.0401	0.825100
$922$	12.9831	0.427575
$923$	1.29322	0.0425670
$924$	2.60132	0.0855771
$925$	−17.0300	−0.559944
$926$	30.6245	1.00638
$927$	0.313148	0.0102851
$928$	−8.47565	−0.278227
$929$	51.5536	1.69142	0.845709	−	0.533645i	$-0.179178\pi$
$929$	51.5536	1.69142	0.845709	+	0.533645i	$0.179178\pi$
$930$	9.35504	0.306764
$931$	0	0
$932$	16.4466	0.538725
$933$	−0.0564370	−0.00184766
$934$	−11.0574	−0.361808
$935$	−45.5107	−1.48836
$936$	0.490200	0.0160227
$937$	−14.4638	−0.472511	−0.236256	−	0.971691i	$-0.575920\pi$
$937$	−14.4638	−0.472511	−0.236256	+	0.971691i	$0.575920\pi$
$938$	5.49020	0.179261
$939$	−13.7638	−0.449165
$940$	−8.41921	−0.274605
$941$	13.1803	0.429667	0.214834	−	0.976651i	$-0.431079\pi$
$941$	13.1803	0.429667	0.214834	+	0.976651i	$0.431079\pi$
$942$	12.9581	0.422198
$943$	14.2763	0.464901
$944$	11.4192	0.371664
$945$	4.75877	0.154803
$946$	−14.0770	−0.457682
$947$	−42.8266	−1.39168	−0.695838	−	0.718199i	$-0.744967\pi$
$947$	−42.8266	−1.39168	−0.695838	+	0.718199i	$0.744967\pi$
$948$	−4.66044	−0.151364
$949$	7.53083	0.244461
$950$	0	0
$951$	10.9040	0.353588
$952$	6.78611	0.219939
$953$	32.2175	1.04363	0.521814	−	0.853059i	$-0.325256\pi$
$953$	32.2175	1.04363	0.521814	+	0.853059i	$0.325256\pi$
$954$	8.88713	0.287731
$955$	−5.00774	−0.162047
$956$	3.30541	0.106905
$957$	17.9736	0.581004
$958$	17.6382	0.569863
$959$	−0.0240434	−0.000776402 0
$960$	3.87939	0.125207
$961$	−25.1848	−0.812413
$962$	−0.830689	−0.0267825
$963$	16.8280	0.542275
$964$	−3.01548	−0.0971221
$965$	−35.3824	−1.13900
$966$	−10.9709	−0.352983
$967$	34.5485	1.11100	0.555502	−	0.831515i	$-0.312526\pi$
$967$	34.5485	1.11100	0.555502	+	0.831515i	$0.312526\pi$
$968$	6.50299	0.209014
$969$	0	0
$970$	55.7752	1.79083
$971$	1.18716	0.0380977	0.0190488	−	0.999819i	$-0.493936\pi$
$971$	1.18716	0.0380977	0.0190488	+	0.999819i	$0.493936\pi$
$972$	−1.00000	−0.0320750
$973$	5.51424	0.176779
$974$	−15.2935	−0.490037
$975$	4.92633	0.157769
$976$	0.0418891	0.00134084
$977$	−20.8827	−0.668096	−0.334048	−	0.942556i	$-0.608415\pi$
$977$	−20.8827	−0.668096	−0.334048	+	0.942556i	$0.608415\pi$
$978$	15.0719	0.481947
$979$	17.9320	0.573110
$980$	21.3182	0.680985
$981$	10.4115	0.332413
$982$	1.77837	0.0567501
$983$	35.0966	1.11941	0.559703	−	0.828693i	$-0.310915\pi$
$983$	35.0966	1.11941	0.559703	+	0.828693i	$0.310915\pi$
$984$	−1.59627	−0.0508871
$985$	−72.2481	−2.30202
$986$	46.8881	1.49322
$987$	−2.66220	−0.0847387
$988$	0	0
$989$	59.3688	1.88782
$990$	−8.22668	−0.261461
$991$	49.7357	1.57991	0.789953	−	0.613168i	$-0.210105\pi$
$991$	49.7357	1.57991	0.789953	+	0.613168i	$0.210105\pi$
$992$	2.41147	0.0765644
$993$	8.59121	0.272634
$994$	3.23618	0.102645
$995$	−32.7074	−1.03689
$996$	−12.4807	−0.395466
$997$	41.8334	1.32488	0.662438	−	0.749117i	$-0.269522\pi$
$997$	41.8334	1.32488	0.662438	+	0.749117i	$0.269522\pi$
$998$	0.107822	0.00341303
$999$	1.69459	0.0536145

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.2.a.n.1.1		3
3.2	odd	2		6498.2.a.bt.1.3		3
19.2	odd	18		114.2.i.b.61.1	yes	6
19.10	odd	18		114.2.i.b.43.1	✓	6
19.18	odd	2		2166.2.a.t.1.1		3
57.2	even	18		342.2.u.d.289.1		6
57.29	even	18		342.2.u.d.271.1		6
57.56	even	2		6498.2.a.bo.1.3		3
76.59	even	18		912.2.bo.c.289.1		6
76.67	even	18		912.2.bo.c.385.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.b.43.1	✓	6	19.10	odd	18
114.2.i.b.61.1	yes	6	19.2	odd	18
342.2.u.d.271.1		6	57.29	even	18
342.2.u.d.289.1		6	57.2	even	18
912.2.bo.c.289.1		6	76.59	even	18
912.2.bo.c.385.1		6	76.67	even	18
2166.2.a.n.1.1		3	1.1	even	1	trivial
2166.2.a.t.1.1		3	19.18	odd	2
6498.2.a.bo.1.3		3	57.56	even	2
6498.2.a.bt.1.3		3	3.2	odd	2

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:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.87939 q^{5} +1.00000 q^{6} +1.22668 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.87939 q^{5} +1.00000 q^{6} +1.22668 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.87939 q^{10} -2.12061 q^{11} -1.00000 q^{12} -0.490200 q^{13} -1.22668 q^{14} +3.87939 q^{15} +1.00000 q^{16} -5.53209 q^{17} -1.00000 q^{18} -3.87939 q^{20} -1.22668 q^{21} +2.12061 q^{22} -8.94356 q^{23} +1.00000 q^{24} +10.0496 q^{25} +0.490200 q^{26} -1.00000 q^{27} +1.22668 q^{28} +8.47565 q^{29} -3.87939 q^{30} -2.41147 q^{31} -1.00000 q^{32} +2.12061 q^{33} +5.53209 q^{34} -4.75877 q^{35} +1.00000 q^{36} -1.69459 q^{37} +0.490200 q^{39} +3.87939 q^{40} -1.59627 q^{41} +1.22668 q^{42} -6.63816 q^{43} -2.12061 q^{44} -3.87939 q^{45} +8.94356 q^{46} +2.17024 q^{47} -1.00000 q^{48} -5.49525 q^{49} -10.0496 q^{50} +5.53209 q^{51} -0.490200 q^{52} -8.88713 q^{53} +1.00000 q^{54} +8.22668 q^{55} -1.22668 q^{56} -8.47565 q^{58} +11.4192 q^{59} +3.87939 q^{60} +0.0418891 q^{61} +2.41147 q^{62} +1.22668 q^{63} +1.00000 q^{64} +1.90167 q^{65} -2.12061 q^{66} -4.47565 q^{67} -5.53209 q^{68} +8.94356 q^{69} +4.75877 q^{70} -2.63816 q^{71} -1.00000 q^{72} -15.3628 q^{73} +1.69459 q^{74} -10.0496 q^{75} -2.60132 q^{77} -0.490200 q^{78} +4.66044 q^{79} -3.87939 q^{80} +1.00000 q^{81} +1.59627 q^{82} +12.4807 q^{83} -1.22668 q^{84} +21.4611 q^{85} +6.63816 q^{86} -8.47565 q^{87} +2.12061 q^{88} -8.45605 q^{89} +3.87939 q^{90} -0.601319 q^{91} -8.94356 q^{92} +2.41147 q^{93} -2.17024 q^{94} +1.00000 q^{96} +14.3773 q^{97} +5.49525 q^{98} -2.12061 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 6 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 6 * q^5 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 6 q^{5} + 3 q^{6} - 3 q^{7} - 3 q^{8} + 3 q^{9} + 6 q^{10} - 12 q^{11} - 3 q^{12} + 3 q^{14} + 6 q^{15} + 3 q^{16} - 12 q^{17} - 3 q^{18} - 6 q^{20} + 3 q^{21} + 12 q^{22} - 12 q^{23} + 3 q^{24} + 3 q^{25} - 3 q^{27} - 3 q^{28} + 6 q^{29} - 6 q^{30} + 3 q^{31} - 3 q^{32} + 12 q^{33} + 12 q^{34} - 3 q^{35} + 3 q^{36} - 3 q^{37} + 6 q^{40} + 9 q^{41} - 3 q^{42} - 3 q^{43} - 12 q^{44} - 6 q^{45} + 12 q^{46} - 15 q^{47} - 3 q^{48} - 3 q^{50} + 12 q^{51} + 3 q^{53} + 3 q^{54} + 18 q^{55} + 3 q^{56} - 6 q^{58} + 6 q^{60} - 3 q^{61} - 3 q^{62} - 3 q^{63} + 3 q^{64} - 6 q^{65} - 12 q^{66} + 6 q^{67} - 12 q^{68} + 12 q^{69} + 3 q^{70} + 9 q^{71} - 3 q^{72} + 3 q^{73} + 3 q^{74} - 3 q^{75} + 21 q^{77} - 9 q^{79} - 6 q^{80} + 3 q^{81} - 9 q^{82} + 3 q^{83} + 3 q^{84} + 27 q^{85} + 3 q^{86} - 6 q^{87} + 12 q^{88} - 3 q^{89} + 6 q^{90} + 27 q^{91} - 12 q^{92} - 3 q^{93} + 15 q^{94} + 3 q^{96} + 12 q^{97} - 12 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 - 6 * q^5 + 3 * q^6 - 3 * q^7 - 3 * q^8 + 3 * q^9 + 6 * q^10 - 12 * q^11 - 3 * q^12 + 3 * q^14 + 6 * q^15 + 3 * q^16 - 12 * q^17 - 3 * q^18 - 6 * q^20 + 3 * q^21 + 12 * q^22 - 12 * q^23 + 3 * q^24 + 3 * q^25 - 3 * q^27 - 3 * q^28 + 6 * q^29 - 6 * q^30 + 3 * q^31 - 3 * q^32 + 12 * q^33 + 12 * q^34 - 3 * q^35 + 3 * q^36 - 3 * q^37 + 6 * q^40 + 9 * q^41 - 3 * q^42 - 3 * q^43 - 12 * q^44 - 6 * q^45 + 12 * q^46 - 15 * q^47 - 3 * q^48 - 3 * q^50 + 12 * q^51 + 3 * q^53 + 3 * q^54 + 18 * q^55 + 3 * q^56 - 6 * q^58 + 6 * q^60 - 3 * q^61 - 3 * q^62 - 3 * q^63 + 3 * q^64 - 6 * q^65 - 12 * q^66 + 6 * q^67 - 12 * q^68 + 12 * q^69 + 3 * q^70 + 9 * q^71 - 3 * q^72 + 3 * q^73 + 3 * q^74 - 3 * q^75 + 21 * q^77 - 9 * q^79 - 6 * q^80 + 3 * q^81 - 9 * q^82 + 3 * q^83 + 3 * q^84 + 27 * q^85 + 3 * q^86 - 6 * q^87 + 12 * q^88 - 3 * q^89 + 6 * q^90 + 27 * q^91 - 12 * q^92 - 3 * q^93 + 15 * q^94 + 3 * q^96 + 12 * q^97 - 12 * q^99

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