LMFDB - Embedded newform 2166.2.a.p.1.2

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:	$1$
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			1.2
Root			$-0.347296$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.34730 q^{5} -1.00000 q^{6} +3.57398 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.34730 q^{5} -1.00000 q^{6} +3.57398 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.34730 q^{10} +2.71688 q^{11} +1.00000 q^{12} -5.41147 q^{13} -3.57398 q^{14} -2.34730 q^{15} +1.00000 q^{16} -3.87939 q^{17} -1.00000 q^{18} -2.34730 q^{20} +3.57398 q^{21} -2.71688 q^{22} -8.23442 q^{23} -1.00000 q^{24} +0.509800 q^{25} +5.41147 q^{26} +1.00000 q^{27} +3.57398 q^{28} -3.53209 q^{29} +2.34730 q^{30} -6.53209 q^{31} -1.00000 q^{32} +2.71688 q^{33} +3.87939 q^{34} -8.38919 q^{35} +1.00000 q^{36} -0.389185 q^{37} -5.41147 q^{39} +2.34730 q^{40} +1.94356 q^{41} -3.57398 q^{42} +5.02229 q^{43} +2.71688 q^{44} -2.34730 q^{45} +8.23442 q^{46} +2.98545 q^{47} +1.00000 q^{48} +5.77332 q^{49} -0.509800 q^{50} -3.87939 q^{51} -5.41147 q^{52} -8.30541 q^{53} -1.00000 q^{54} -6.37733 q^{55} -3.57398 q^{56} +3.53209 q^{58} -2.73143 q^{59} -2.34730 q^{60} +6.29086 q^{61} +6.53209 q^{62} +3.57398 q^{63} +1.00000 q^{64} +12.7023 q^{65} -2.71688 q^{66} +14.9368 q^{67} -3.87939 q^{68} -8.23442 q^{69} +8.38919 q^{70} -9.02229 q^{71} -1.00000 q^{72} +10.2909 q^{73} +0.389185 q^{74} +0.509800 q^{75} +9.71007 q^{77} +5.41147 q^{78} -13.0077 q^{79} -2.34730 q^{80} +1.00000 q^{81} -1.94356 q^{82} -8.17024 q^{83} +3.57398 q^{84} +9.10607 q^{85} -5.02229 q^{86} -3.53209 q^{87} -2.71688 q^{88} -11.7246 q^{89} +2.34730 q^{90} -19.3405 q^{91} -8.23442 q^{92} -6.53209 q^{93} -2.98545 q^{94} -1.00000 q^{96} +8.60401 q^{97} -5.77332 q^{98} +2.71688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 3 q^{12} - 6 q^{13} - 3 q^{14} - 6 q^{15} + 3 q^{16} - 6 q^{17} - 3 q^{18} - 6 q^{20} + 3 q^{21} + 6 q^{23} - 3 q^{24} + 3 q^{25} + 6 q^{26} + 3 q^{27} + 3 q^{28} - 6 q^{29} + 6 q^{30} - 15 q^{31} - 3 q^{32} + 6 q^{34} - 21 q^{35} + 3 q^{36} + 3 q^{37} - 6 q^{39} + 6 q^{40} - 9 q^{41} - 3 q^{42} + 9 q^{43} - 6 q^{45} - 6 q^{46} - 9 q^{47} + 3 q^{48} + 24 q^{49} - 3 q^{50} - 6 q^{51} - 6 q^{52} - 27 q^{53} - 3 q^{54} + 12 q^{55} - 3 q^{56} + 6 q^{58} - 18 q^{59} - 6 q^{60} + 3 q^{61} + 15 q^{62} + 3 q^{63} + 3 q^{64} + 12 q^{65} - 12 q^{67} - 6 q^{68} + 6 q^{69} + 21 q^{70} - 21 q^{71} - 3 q^{72} + 15 q^{73} - 3 q^{74} + 3 q^{75} - 21 q^{77} + 6 q^{78} - 15 q^{79} - 6 q^{80} + 3 q^{81} + 9 q^{82} - 3 q^{83} + 3 q^{84} + 15 q^{85} - 9 q^{86} - 6 q^{87} - 3 q^{89} + 6 q^{90} - 15 q^{91} + 6 q^{92} - 15 q^{93} + 9 q^{94} - 3 q^{96} - 12 q^{97} - 24 q^{98}+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 + 3 * q^12 - 6 * q^13 - 3 * q^14 - 6 * q^15 + 3 * q^16 - 6 * q^17 - 3 * q^18 - 6 * q^20 + 3 * q^21 + 6 * q^23 - 3 * q^24 + 3 * q^25 + 6 * q^26 + 3 * q^27 + 3 * q^28 - 6 * q^29 + 6 * q^30 - 15 * q^31 - 3 * q^32 + 6 * q^34 - 21 * q^35 + 3 * q^36 + 3 * q^37 - 6 * q^39 + 6 * q^40 - 9 * q^41 - 3 * q^42 + 9 * q^43 - 6 * q^45 - 6 * q^46 - 9 * q^47 + 3 * q^48 + 24 * q^49 - 3 * q^50 - 6 * q^51 - 6 * q^52 - 27 * q^53 - 3 * q^54 + 12 * q^55 - 3 * q^56 + 6 * q^58 - 18 * q^59 - 6 * q^60 + 3 * q^61 + 15 * q^62 + 3 * q^63 + 3 * q^64 + 12 * q^65 - 12 * q^67 - 6 * q^68 + 6 * q^69 + 21 * q^70 - 21 * q^71 - 3 * q^72 + 15 * q^73 - 3 * q^74 + 3 * q^75 - 21 * q^77 + 6 * q^78 - 15 * q^79 - 6 * q^80 + 3 * q^81 + 9 * q^82 - 3 * q^83 + 3 * q^84 + 15 * q^85 - 9 * q^86 - 6 * q^87 - 3 * q^89 + 6 * q^90 - 15 * q^91 + 6 * q^92 - 15 * q^93 + 9 * q^94 - 3 * q^96 - 12 * q^97 - 24 * q^98

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
$5$	−2.34730	−1.04974	−0.524871	−	0.851182i	$-0.675887\pi$
$5$	−2.34730	−1.04974	−0.524871	+	0.851182i	$0.675887\pi$
$6$	−1.00000	−0.408248
$7$	3.57398	1.35084	0.675418	−	0.737435i	$-0.263963\pi$
$7$	3.57398	1.35084	0.675418	+	0.737435i	$0.263963\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.34730	0.742280
$11$	2.71688	0.819171	0.409585	−	0.912272i	$-0.365673\pi$
$11$	2.71688	0.819171	0.409585	+	0.912272i	$0.365673\pi$
$12$	1.00000	0.288675
$13$	−5.41147	−1.50087	−0.750436	−	0.660943i	$-0.770157\pi$
$13$	−5.41147	−1.50087	−0.750436	+	0.660943i	$0.770157\pi$
$14$	−3.57398	−0.955186
$15$	−2.34730	−0.606069
$16$	1.00000	0.250000
$17$	−3.87939	−0.940889	−0.470445	−	0.882430i	$-0.655906\pi$
$17$	−3.87939	−0.940889	−0.470445	+	0.882430i	$0.655906\pi$
$18$	−1.00000	−0.235702
$19$	0	0
$19$	0	0
$20$	−2.34730	−0.524871
$21$	3.57398	0.779906
$22$	−2.71688	−0.579241
$23$	−8.23442	−1.71700	−0.858498	−	0.512817i	$-0.828602\pi$
$23$	−8.23442	−1.71700	−0.858498	+	0.512817i	$0.828602\pi$
$24$	−1.00000	−0.204124
$25$	0.509800	0.101960
$26$	5.41147	1.06128
$27$	1.00000	0.192450
$28$	3.57398	0.675418
$29$	−3.53209	−0.655892	−0.327946	−	0.944696i	$-0.606356\pi$
$29$	−3.53209	−0.655892	−0.327946	+	0.944696i	$0.606356\pi$
$30$	2.34730	0.428556
$31$	−6.53209	−1.17320	−0.586599	−	0.809878i	$-0.699533\pi$
$31$	−6.53209	−1.17320	−0.586599	+	0.809878i	$0.699533\pi$
$32$	−1.00000	−0.176777
$33$	2.71688	0.472948
$34$	3.87939	0.665309
$35$	−8.38919	−1.41803
$36$	1.00000	0.166667
$37$	−0.389185	−0.0639817	−0.0319908	−	0.999488i	$-0.510185\pi$
$37$	−0.389185	−0.0639817	−0.0319908	+	0.999488i	$0.510185\pi$
$38$	0	0
$39$	−5.41147	−0.866529
$40$	2.34730	0.371140
$41$	1.94356	0.303534	0.151767	−	0.988416i	$-0.451504\pi$
$41$	1.94356	0.303534	0.151767	+	0.988416i	$0.451504\pi$
$42$	−3.57398	−0.551477
$43$	5.02229	0.765892	0.382946	−	0.923771i	$-0.374910\pi$
$43$	5.02229	0.765892	0.382946	+	0.923771i	$0.374910\pi$
$44$	2.71688	0.409585
$45$	−2.34730	−0.349914
$46$	8.23442	1.21410
$47$	2.98545	0.435473	0.217736	−	0.976008i	$-0.430133\pi$
$47$	2.98545	0.435473	0.217736	+	0.976008i	$0.430133\pi$
$48$	1.00000	0.144338
$49$	5.77332	0.824760
$50$	−0.509800	−0.0720966
$51$	−3.87939	−0.543223
$52$	−5.41147	−0.750436
$53$	−8.30541	−1.14084	−0.570418	−	0.821355i	$-0.693219\pi$
$53$	−8.30541	−1.14084	−0.570418	+	0.821355i	$0.693219\pi$
$54$	−1.00000	−0.136083
$55$	−6.37733	−0.859918
$56$	−3.57398	−0.477593
$57$	0	0
$58$	3.53209	0.463786
$59$	−2.73143	−0.355602	−0.177801	−	0.984066i	$-0.556898\pi$
$59$	−2.73143	−0.355602	−0.177801	+	0.984066i	$0.556898\pi$
$60$	−2.34730	−0.303035
$61$	6.29086	0.805462	0.402731	−	0.915318i	$-0.368061\pi$
$61$	6.29086	0.805462	0.402731	+	0.915318i	$0.368061\pi$
$62$	6.53209	0.829576
$63$	3.57398	0.450279
$64$	1.00000	0.125000
$65$	12.7023	1.57553
$66$	−2.71688	−0.334425
$67$	14.9368	1.82482	0.912408	−	0.409283i	$-0.134221\pi$
$67$	14.9368	1.82482	0.912408	+	0.409283i	$0.134221\pi$
$68$	−3.87939	−0.470445
$69$	−8.23442	−0.991308
$70$	8.38919	1.00270
$71$	−9.02229	−1.07075	−0.535374	−	0.844615i	$-0.679829\pi$
$71$	−9.02229	−1.07075	−0.535374	+	0.844615i	$0.679829\pi$
$72$	−1.00000	−0.117851
$73$	10.2909	1.20445	0.602227	−	0.798325i	$-0.294280\pi$
$73$	10.2909	1.20445	0.602227	+	0.798325i	$0.294280\pi$
$74$	0.389185	0.0452419
$75$	0.509800	0.0588667
$76$	0	0
$77$	9.71007	1.10657
$78$	5.41147	0.612729
$79$	−13.0077	−1.46349	−0.731743	−	0.681581i	$-0.761293\pi$
$79$	−13.0077	−1.46349	−0.731743	+	0.681581i	$0.761293\pi$
$80$	−2.34730	−0.262436
$81$	1.00000	0.111111
$82$	−1.94356	−0.214631
$83$	−8.17024	−0.896801	−0.448400	−	0.893833i	$-0.648006\pi$
$83$	−8.17024	−0.896801	−0.448400	+	0.893833i	$0.648006\pi$
$84$	3.57398	0.389953
$85$	9.10607	0.987692
$86$	−5.02229	−0.541567
$87$	−3.53209	−0.378680
$88$	−2.71688	−0.289621
$89$	−11.7246	−1.24281	−0.621404	−	0.783491i	$-0.713437\pi$
$89$	−11.7246	−1.24281	−0.621404	+	0.783491i	$0.713437\pi$
$90$	2.34730	0.247427
$91$	−19.3405	−2.02743
$92$	−8.23442	−0.858498
$93$	−6.53209	−0.677346
$94$	−2.98545	−0.307926
$95$	0	0
$96$	−1.00000	−0.102062
$97$	8.60401	0.873605	0.436802	−	0.899558i	$-0.356111\pi$
$97$	8.60401	0.873605	0.436802	+	0.899558i	$0.356111\pi$
$98$	−5.77332	−0.583193
$99$	2.71688	0.273057
$100$	0.509800	0.0509800
$101$	−1.28581	−0.127943	−0.0639713	−	0.997952i	$-0.520377\pi$
$101$	−1.28581	−0.127943	−0.0639713	+	0.997952i	$0.520377\pi$
$102$	3.87939	0.384116
$103$	−0.736482	−0.0725677	−0.0362839	−	0.999342i	$-0.511552\pi$
$103$	−0.736482	−0.0725677	−0.0362839	+	0.999342i	$0.511552\pi$
$104$	5.41147	0.530639
$105$	−8.38919	−0.818701
$106$	8.30541	0.806692
$107$	−10.0273	−0.969380	−0.484690	−	0.874686i	$-0.661068\pi$
$107$	−10.0273	−0.969380	−0.484690	+	0.874686i	$0.661068\pi$
$108$	1.00000	0.0962250
$109$	−13.9213	−1.33342	−0.666708	−	0.745319i	$-0.732297\pi$
$109$	−13.9213	−1.33342	−0.666708	+	0.745319i	$0.732297\pi$
$110$	6.37733	0.608054
$111$	−0.389185	−0.0369398
$112$	3.57398	0.337709
$113$	0.226682	0.0213244	0.0106622	−	0.999943i	$-0.496606\pi$
$113$	0.226682	0.0213244	0.0106622	+	0.999943i	$0.496606\pi$
$114$	0	0
$115$	19.3286	1.80240
$116$	−3.53209	−0.327946
$117$	−5.41147	−0.500291
$118$	2.73143	0.251448
$119$	−13.8648	−1.27099
$120$	2.34730	0.214278
$121$	−3.61856	−0.328960
$122$	−6.29086	−0.569548
$123$	1.94356	0.175245
$124$	−6.53209	−0.586599
$125$	10.5398	0.942711
$126$	−3.57398	−0.318395
$127$	−8.69459	−0.771520	−0.385760	−	0.922599i	$-0.626061\pi$
$127$	−8.69459	−0.771520	−0.385760	+	0.922599i	$0.626061\pi$
$128$	−1.00000	−0.0883883
$129$	5.02229	0.442188
$130$	−12.7023	−1.11407
$131$	−12.6432	−1.10464	−0.552321	−	0.833631i	$-0.686258\pi$
$131$	−12.6432	−1.10464	−0.552321	+	0.833631i	$0.686258\pi$
$132$	2.71688	0.236474
$133$	0	0
$134$	−14.9368	−1.29034
$135$	−2.34730	−0.202023
$136$	3.87939	0.332655
$137$	21.7939	1.86197	0.930987	−	0.365052i	$-0.118949\pi$
$137$	21.7939	1.86197	0.930987	+	0.365052i	$0.118949\pi$
$138$	8.23442	0.700961
$139$	−11.2267	−0.952235	−0.476117	−	0.879382i	$-0.657956\pi$
$139$	−11.2267	−0.952235	−0.476117	+	0.879382i	$0.657956\pi$
$140$	−8.38919	−0.709016
$141$	2.98545	0.251420
$142$	9.02229	0.757134
$143$	−14.7023	−1.22947
$144$	1.00000	0.0833333
$145$	8.29086	0.688518
$146$	−10.2909	−0.851678
$147$	5.77332	0.476175
$148$	−0.389185	−0.0319908
$149$	−21.9786	−1.80056	−0.900280	−	0.435311i	$-0.856639\pi$
$149$	−21.9786	−1.80056	−0.900280	+	0.435311i	$0.856639\pi$
$150$	−0.509800	−0.0416250
$151$	−2.36184	−0.192204	−0.0961021	−	0.995371i	$-0.530638\pi$
$151$	−2.36184	−0.192204	−0.0961021	+	0.995371i	$0.530638\pi$
$152$	0	0
$153$	−3.87939	−0.313630
$154$	−9.71007	−0.782460
$155$	15.3327	1.23156
$156$	−5.41147	−0.433265
$157$	−14.3550	−1.14566	−0.572828	−	0.819675i	$-0.694154\pi$
$157$	−14.3550	−1.14566	−0.572828	+	0.819675i	$0.694154\pi$
$158$	13.0077	1.03484
$159$	−8.30541	−0.658662
$160$	2.34730	0.185570
$161$	−29.4296	−2.31938
$162$	−1.00000	−0.0785674
$163$	−17.1411	−1.34260	−0.671299	−	0.741186i	$-0.734263\pi$
$163$	−17.1411	−1.34260	−0.671299	+	0.741186i	$0.734263\pi$
$164$	1.94356	0.151767
$165$	−6.37733	−0.496474
$166$	8.17024	0.634134
$167$	14.6186	1.13122	0.565609	−	0.824674i	$-0.308641\pi$
$167$	14.6186	1.13122	0.565609	+	0.824674i	$0.308641\pi$
$168$	−3.57398	−0.275738
$169$	16.2841	1.25262
$170$	−9.10607	−0.698403
$171$	0	0
$172$	5.02229	0.382946
$173$	20.6682	1.57137	0.785687	−	0.618625i	$-0.212310\pi$
$173$	20.6682	1.57137	0.785687	+	0.618625i	$0.212310\pi$
$174$	3.53209	0.267767
$175$	1.82201	0.137731
$176$	2.71688	0.204793
$177$	−2.73143	−0.205307
$178$	11.7246	0.878798
$179$	−5.69459	−0.425634	−0.212817	−	0.977092i	$-0.568264\pi$
$179$	−5.69459	−0.425634	−0.212817	+	0.977092i	$0.568264\pi$
$180$	−2.34730	−0.174957
$181$	22.2199	1.65159	0.825795	−	0.563970i	$-0.190727\pi$
$181$	22.2199	1.65159	0.825795	+	0.563970i	$0.190727\pi$
$182$	19.3405	1.43361
$183$	6.29086	0.465034
$184$	8.23442	0.607050
$185$	0.913534	0.0671643
$186$	6.53209	0.478956
$187$	−10.5398	−0.770749
$188$	2.98545	0.217736
$189$	3.57398	0.259969
$190$	0	0
$191$	6.04694	0.437541	0.218771	−	0.975776i	$-0.429795\pi$
$191$	6.04694	0.437541	0.218771	+	0.975776i	$0.429795\pi$
$192$	1.00000	0.0721688
$193$	−6.29860	−0.453383	−0.226692	−	0.973967i	$-0.572791\pi$
$193$	−6.29860	−0.453383	−0.226692	+	0.973967i	$0.572791\pi$
$194$	−8.60401	−0.617732
$195$	12.7023	0.909633
$196$	5.77332	0.412380
$197$	19.9368	1.42044	0.710218	−	0.703982i	$-0.248597\pi$
$197$	19.9368	1.42044	0.710218	+	0.703982i	$0.248597\pi$
$198$	−2.71688	−0.193080
$199$	12.8821	0.913186	0.456593	−	0.889676i	$-0.349070\pi$
$199$	12.8821	0.913186	0.456593	+	0.889676i	$0.349070\pi$
$200$	−0.509800	−0.0360483
$201$	14.9368	1.05356
$202$	1.28581	0.0904691
$203$	−12.6236	−0.886004
$204$	−3.87939	−0.271611
$205$	−4.56212	−0.318632
$206$	0.736482	0.0513131
$207$	−8.23442	−0.572332
$208$	−5.41147	−0.375218
$209$	0	0
$210$	8.38919	0.578909
$211$	−2.31315	−0.159244	−0.0796218	−	0.996825i	$-0.525371\pi$
$211$	−2.31315	−0.159244	−0.0796218	+	0.996825i	$0.525371\pi$
$212$	−8.30541	−0.570418
$213$	−9.02229	−0.618197
$214$	10.0273	0.685455
$215$	−11.7888	−0.803989
$216$	−1.00000	−0.0680414
$217$	−23.3455	−1.58480
$218$	13.9213	0.942868
$219$	10.2909	0.695392
$220$	−6.37733	−0.429959
$221$	20.9932	1.41215
$222$	0.389185	0.0261204
$223$	−4.07098	−0.272613	−0.136307	−	0.990667i	$-0.543523\pi$
$223$	−4.07098	−0.272613	−0.136307	+	0.990667i	$0.543523\pi$
$224$	−3.57398	−0.238796
$225$	0.509800	0.0339867
$226$	−0.226682	−0.0150786
$227$	0.440570	0.0292417	0.0146208	−	0.999893i	$-0.495346\pi$
$227$	0.440570	0.0292417	0.0146208	+	0.999893i	$0.495346\pi$
$228$	0	0
$229$	−3.38919	−0.223964	−0.111982	−	0.993710i	$-0.535720\pi$
$229$	−3.38919	−0.223964	−0.111982	+	0.993710i	$0.535720\pi$
$230$	−19.3286	−1.27449
$231$	9.71007	0.638876
$232$	3.53209	0.231893
$233$	2.11381	0.138480	0.0692401	−	0.997600i	$-0.477943\pi$
$233$	2.11381	0.138480	0.0692401	+	0.997600i	$0.477943\pi$
$234$	5.41147	0.353759
$235$	−7.00774	−0.457135
$236$	−2.73143	−0.177801
$237$	−13.0077	−0.844944
$238$	13.8648	0.898724
$239$	−4.02910	−0.260621	−0.130310	−	0.991473i	$-0.541597\pi$
$239$	−4.02910	−0.260621	−0.130310	+	0.991473i	$0.541597\pi$
$240$	−2.34730	−0.151517
$241$	10.1771	0.655562	0.327781	−	0.944754i	$-0.393699\pi$
$241$	10.1771	0.655562	0.327781	+	0.944754i	$0.393699\pi$
$242$	3.61856	0.232610
$243$	1.00000	0.0641500
$244$	6.29086	0.402731
$245$	−13.5517	−0.865786
$246$	−1.94356	−0.123917
$247$	0	0
$248$	6.53209	0.414788
$249$	−8.17024	−0.517768
$250$	−10.5398	−0.666597
$251$	2.90941	0.183641	0.0918203	−	0.995776i	$-0.470731\pi$
$251$	2.90941	0.183641	0.0918203	+	0.995776i	$0.470731\pi$
$252$	3.57398	0.225139
$253$	−22.3719	−1.40651
$254$	8.69459	0.545547
$255$	9.10607	0.570244
$256$	1.00000	0.0625000
$257$	2.55943	0.159653	0.0798264	−	0.996809i	$-0.474563\pi$
$257$	2.55943	0.159653	0.0798264	+	0.996809i	$0.474563\pi$
$258$	−5.02229	−0.312674
$259$	−1.39094	−0.0864288
$260$	12.7023	0.787765
$261$	−3.53209	−0.218631
$262$	12.6432	0.781100
$263$	15.9290	0.982225	0.491113	−	0.871096i	$-0.336590\pi$
$263$	15.9290	0.982225	0.491113	+	0.871096i	$0.336590\pi$
$264$	−2.71688	−0.167212
$265$	19.4953	1.19758
$266$	0	0
$267$	−11.7246	−0.717535
$268$	14.9368	0.912408
$269$	−16.8949	−1.03010	−0.515049	−	0.857161i	$-0.672226\pi$
$269$	−16.8949	−1.03010	−0.515049	+	0.857161i	$0.672226\pi$
$270$	2.34730	0.142852
$271$	−0.622674	−0.0378248	−0.0189124	−	0.999821i	$-0.506020\pi$
$271$	−0.622674	−0.0378248	−0.0189124	+	0.999821i	$0.506020\pi$
$272$	−3.87939	−0.235222
$273$	−19.3405	−1.17054
$274$	−21.7939	−1.31661
$275$	1.38507	0.0835227
$276$	−8.23442	−0.495654
$277$	−27.4766	−1.65091	−0.825454	−	0.564469i	$-0.809081\pi$
$277$	−27.4766	−1.65091	−0.825454	+	0.564469i	$0.809081\pi$
$278$	11.2267	0.673332
$279$	−6.53209	−0.391066
$280$	8.38919	0.501350
$281$	2.48070	0.147986	0.0739932	−	0.997259i	$-0.476426\pi$
$281$	2.48070	0.147986	0.0739932	+	0.997259i	$0.476426\pi$
$282$	−2.98545	−0.177781
$283$	2.28312	0.135717	0.0678587	−	0.997695i	$-0.478383\pi$
$283$	2.28312	0.135717	0.0678587	+	0.997695i	$0.478383\pi$
$284$	−9.02229	−0.535374
$285$	0	0
$286$	14.7023	0.869367
$287$	6.94625	0.410024
$288$	−1.00000	−0.0589256
$289$	−1.95037	−0.114728
$290$	−8.29086	−0.486856
$291$	8.60401	0.504376
$292$	10.2909	0.602227
$293$	2.39599	0.139975	0.0699877	−	0.997548i	$-0.477704\pi$
$293$	2.39599	0.139975	0.0699877	+	0.997548i	$0.477704\pi$
$294$	−5.77332	−0.336707
$295$	6.41147	0.373290
$296$	0.389185	0.0226209
$297$	2.71688	0.157649
$298$	21.9786	1.27319
$299$	44.5604	2.57699
$300$	0.509800	0.0294333
$301$	17.9495	1.03459
$302$	2.36184	0.135909
$303$	−1.28581	−0.0738677
$304$	0	0
$305$	−14.7665	−0.845528
$306$	3.87939	0.221770
$307$	5.23349	0.298691	0.149345	−	0.988785i	$-0.452283\pi$
$307$	5.23349	0.298691	0.149345	+	0.988785i	$0.452283\pi$
$308$	9.71007	0.553283
$309$	−0.736482	−0.0418970
$310$	−15.3327	−0.870842
$311$	−10.9932	−0.623367	−0.311683	−	0.950186i	$-0.600893\pi$
$311$	−10.9932	−0.623367	−0.311683	+	0.950186i	$0.600893\pi$
$312$	5.41147	0.306364
$313$	−30.4516	−1.72123	−0.860613	−	0.509259i	$-0.829920\pi$
$313$	−30.4516	−1.72123	−0.860613	+	0.509259i	$0.829920\pi$
$314$	14.3550	0.810102
$315$	−8.38919	−0.472677
$316$	−13.0077	−0.731743
$317$	−11.3396	−0.636893	−0.318446	−	0.947941i	$-0.603161\pi$
$317$	−11.3396	−0.636893	−0.318446	+	0.947941i	$0.603161\pi$
$318$	8.30541	0.465744
$319$	−9.59627	−0.537288
$320$	−2.34730	−0.131218
$321$	−10.0273	−0.559672
$322$	29.4296	1.64005
$323$	0	0
$324$	1.00000	0.0555556
$325$	−2.75877	−0.153029
$326$	17.1411	0.949360
$327$	−13.9213	−0.769848
$328$	−1.94356	−0.107315
$329$	10.6699	0.588253
$330$	6.37733	0.351060
$331$	−12.9317	−0.710791	−0.355395	−	0.934716i	$-0.615654\pi$
$331$	−12.9317	−0.710791	−0.355395	+	0.934716i	$0.615654\pi$
$332$	−8.17024	−0.448400
$333$	−0.389185	−0.0213272
$334$	−14.6186	−0.799892
$335$	−35.0610	−1.91559
$336$	3.57398	0.194976
$337$	−10.7469	−0.585422	−0.292711	−	0.956201i	$-0.594557\pi$
$337$	−10.7469	−0.585422	−0.292711	+	0.956201i	$0.594557\pi$
$338$	−16.2841	−0.885736
$339$	0.226682	0.0123117
$340$	9.10607	0.493846
$341$	−17.7469	−0.961049
$342$	0	0
$343$	−4.38413	−0.236721
$344$	−5.02229	−0.270784
$345$	19.3286	1.04062
$346$	−20.6682	−1.11113
$347$	22.8033	1.22415	0.612074	−	0.790801i	$-0.290335\pi$
$347$	22.8033	1.22415	0.612074	+	0.790801i	$0.290335\pi$
$348$	−3.53209	−0.189340
$349$	−25.3628	−1.35764	−0.678819	−	0.734305i	$-0.737508\pi$
$349$	−25.3628	−1.35764	−0.678819	+	0.734305i	$0.737508\pi$
$350$	−1.82201	−0.0973908
$351$	−5.41147	−0.288843
$352$	−2.71688	−0.144810
$353$	−12.1925	−0.648943	−0.324472	−	0.945895i	$-0.605186\pi$
$353$	−12.1925	−0.648943	−0.324472	+	0.945895i	$0.605186\pi$
$354$	2.73143	0.145174
$355$	21.1780	1.12401
$356$	−11.7246	−0.621404
$357$	−13.8648	−0.733805
$358$	5.69459	0.300969
$359$	29.1634	1.53919	0.769594	−	0.638534i	$-0.220459\pi$
$359$	29.1634	1.53919	0.769594	+	0.638534i	$0.220459\pi$
$360$	2.34730	0.123713
$361$	0	0
$362$	−22.2199	−1.16785
$363$	−3.61856	−0.189925
$364$	−19.3405	−1.01372
$365$	−24.1557	−1.26437
$366$	−6.29086	−0.328828
$367$	13.9923	0.730390	0.365195	−	0.930931i	$-0.381002\pi$
$367$	13.9923	0.730390	0.365195	+	0.930931i	$0.381002\pi$
$368$	−8.23442	−0.429249
$369$	1.94356	0.101178
$370$	−0.913534	−0.0474923
$371$	−29.6833	−1.54108
$372$	−6.53209	−0.338673
$373$	6.82026	0.353140	0.176570	−	0.984288i	$-0.443500\pi$
$373$	6.82026	0.353140	0.176570	+	0.984288i	$0.443500\pi$
$374$	10.5398	0.545002
$375$	10.5398	0.544274
$376$	−2.98545	−0.153963
$377$	19.1138	0.984411
$378$	−3.57398	−0.183826
$379$	−31.9341	−1.64034	−0.820171	−	0.572118i	$-0.806122\pi$
$379$	−31.9341	−1.64034	−0.820171	+	0.572118i	$0.806122\pi$
$380$	0	0
$381$	−8.69459	−0.445437
$382$	−6.04694	−0.309388
$383$	36.8188	1.88135	0.940677	−	0.339303i	$-0.110191\pi$
$383$	36.8188	1.88135	0.940677	+	0.339303i	$0.110191\pi$
$384$	−1.00000	−0.0510310
$385$	−22.7924	−1.16161
$386$	6.29860	0.320590
$387$	5.02229	0.255297
$388$	8.60401	0.436802
$389$	−3.35504	−0.170107	−0.0850536	−	0.996376i	$-0.527106\pi$
$389$	−3.35504	−0.170107	−0.0850536	+	0.996376i	$0.527106\pi$
$390$	−12.7023	−0.643208
$391$	31.9445	1.61550
$392$	−5.77332	−0.291597
$393$	−12.6432	−0.637765
$394$	−19.9368	−1.00440
$395$	30.5330	1.53628
$396$	2.71688	0.136528
$397$	6.88444	0.345520	0.172760	−	0.984964i	$-0.444731\pi$
$397$	6.88444	0.345520	0.172760	+	0.984964i	$0.444731\pi$
$398$	−12.8821	−0.645720
$399$	0	0
$400$	0.509800	0.0254900
$401$	5.03003	0.251188	0.125594	−	0.992082i	$-0.459916\pi$
$401$	5.03003	0.251188	0.125594	+	0.992082i	$0.459916\pi$
$402$	−14.9368	−0.744978
$403$	35.3482	1.76082
$404$	−1.28581	−0.0639713
$405$	−2.34730	−0.116638
$406$	12.6236	0.626499
$407$	−1.05737	−0.0524119
$408$	3.87939	0.192058
$409$	10.4088	0.514681	0.257341	−	0.966321i	$-0.417154\pi$
$409$	10.4088	0.514681	0.257341	+	0.966321i	$0.417154\pi$
$410$	4.56212	0.225307
$411$	21.7939	1.07501
$412$	−0.736482	−0.0362839
$413$	−9.76207	−0.480360
$414$	8.23442	0.404700
$415$	19.1780	0.941410
$416$	5.41147	0.265319
$417$	−11.2267	−0.549773
$418$	0	0
$419$	−6.22256	−0.303992	−0.151996	−	0.988381i	$-0.548570\pi$
$419$	−6.22256	−0.303992	−0.151996	+	0.988381i	$0.548570\pi$
$420$	−8.38919	−0.409350
$421$	26.6195	1.29735	0.648677	−	0.761064i	$-0.275323\pi$
$421$	26.6195	1.29735	0.648677	+	0.761064i	$0.275323\pi$
$422$	2.31315	0.112602
$423$	2.98545	0.145158
$424$	8.30541	0.403346
$425$	−1.97771	−0.0959331
$426$	9.02229	0.437131
$427$	22.4834	1.08805
$428$	−10.0273	−0.484690
$429$	−14.7023	−0.709835
$430$	11.7888	0.568506
$431$	13.7324	0.661465	0.330732	−	0.943725i	$-0.392704\pi$
$431$	13.7324	0.661465	0.330732	+	0.943725i	$0.392704\pi$
$432$	1.00000	0.0481125
$433$	24.6946	1.18675	0.593373	−	0.804927i	$-0.297796\pi$
$433$	24.6946	1.18675	0.593373	+	0.804927i	$0.297796\pi$
$434$	23.3455	1.12062
$435$	8.29086	0.397516
$436$	−13.9213	−0.666708
$437$	0	0
$438$	−10.2909	−0.491716
$439$	−18.1411	−0.865830	−0.432915	−	0.901435i	$-0.642515\pi$
$439$	−18.1411	−0.865830	−0.432915	+	0.901435i	$0.642515\pi$
$440$	6.37733	0.304027
$441$	5.77332	0.274920
$442$	−20.9932	−0.998544
$443$	−12.8625	−0.611115	−0.305557	−	0.952174i	$-0.598843\pi$
$443$	−12.8625	−0.611115	−0.305557	+	0.952174i	$0.598843\pi$
$444$	−0.389185	−0.0184699
$445$	27.5212	1.30463
$446$	4.07098	0.192767
$447$	−21.9786	−1.03955
$448$	3.57398	0.168855
$449$	21.9317	1.03502	0.517511	−	0.855677i	$-0.326859\pi$
$449$	21.9317	1.03502	0.517511	+	0.855677i	$0.326859\pi$
$450$	−0.509800	−0.0240322
$451$	5.28043	0.248646
$452$	0.226682	0.0106622
$453$	−2.36184	−0.110969
$454$	−0.440570	−0.0206770
$455$	45.3979	2.12828
$456$	0	0
$457$	30.8452	1.44288	0.721440	−	0.692477i	$-0.243481\pi$
$457$	30.8452	1.44288	0.721440	+	0.692477i	$0.243481\pi$
$458$	3.38919	0.158366
$459$	−3.87939	−0.181074
$460$	19.3286	0.901202
$461$	−12.3200	−0.573798	−0.286899	−	0.957961i	$-0.592624\pi$
$461$	−12.3200	−0.573798	−0.286899	+	0.957961i	$0.592624\pi$
$462$	−9.71007	−0.451754
$463$	12.2094	0.567421	0.283711	−	0.958910i	$-0.408435\pi$
$463$	12.2094	0.567421	0.283711	+	0.958910i	$0.408435\pi$
$464$	−3.53209	−0.163973
$465$	15.3327	0.711039
$466$	−2.11381	−0.0979202
$467$	−26.7401	−1.23738	−0.618692	−	0.785633i	$-0.712337\pi$
$467$	−26.7401	−1.23738	−0.618692	+	0.785633i	$0.712337\pi$
$468$	−5.41147	−0.250145
$469$	53.3836	2.46503
$470$	7.00774	0.323243
$471$	−14.3550	−0.661445
$472$	2.73143	0.125724
$473$	13.6450	0.627396
$474$	13.0077	0.597465
$475$	0	0
$476$	−13.8648	−0.635494
$477$	−8.30541	−0.380278
$478$	4.02910	0.184287
$479$	7.73648	0.353489	0.176744	−	0.984257i	$-0.443443\pi$
$479$	7.73648	0.353489	0.176744	+	0.984257i	$0.443443\pi$
$480$	2.34730	0.107139
$481$	2.10607	0.0960284
$482$	−10.1771	−0.463552
$483$	−29.4296	−1.33910
$484$	−3.61856	−0.164480
$485$	−20.1962	−0.917060
$486$	−1.00000	−0.0453609
$487$	−13.3919	−0.606844	−0.303422	−	0.952856i	$-0.598129\pi$
$487$	−13.3919	−0.606844	−0.303422	+	0.952856i	$0.598129\pi$
$488$	−6.29086	−0.284774
$489$	−17.1411	−0.775150
$490$	13.5517	0.612203
$491$	−20.2472	−0.913744	−0.456872	−	0.889532i	$-0.651030\pi$
$491$	−20.2472	−0.913744	−0.456872	+	0.889532i	$0.651030\pi$
$492$	1.94356	0.0876226
$493$	13.7023	0.617122
$494$	0	0
$495$	−6.37733	−0.286639
$496$	−6.53209	−0.293299
$497$	−32.2455	−1.44641
$498$	8.17024	0.366117
$499$	−4.73742	−0.212076	−0.106038	−	0.994362i	$-0.533816\pi$
$499$	−4.73742	−0.212076	−0.106038	+	0.994362i	$0.533816\pi$
$500$	10.5398	0.471356
$501$	14.6186	0.653109
$502$	−2.90941	−0.129854
$503$	8.59896	0.383408	0.191704	−	0.981453i	$-0.438599\pi$
$503$	8.59896	0.383408	0.191704	+	0.981453i	$0.438599\pi$
$504$	−3.57398	−0.159198
$505$	3.01817	0.134307
$506$	22.3719	0.994554
$507$	16.2841	0.723200
$508$	−8.69459	−0.385760
$509$	−5.36278	−0.237701	−0.118850	−	0.992912i	$-0.537921\pi$
$509$	−5.36278	−0.237701	−0.118850	+	0.992912i	$0.537921\pi$
$510$	−9.10607	−0.403223
$511$	36.7793	1.62702
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−2.55943	−0.112892
$515$	1.72874	0.0761774
$516$	5.02229	0.221094
$517$	8.11112	0.356727
$518$	1.39094	0.0611144
$519$	20.6682	0.907233
$520$	−12.7023	−0.557034
$521$	23.7151	1.03898	0.519489	−	0.854477i	$-0.326122\pi$
$521$	23.7151	1.03898	0.519489	+	0.854477i	$0.326122\pi$
$522$	3.53209	0.154595
$523$	31.3158	1.36935	0.684673	−	0.728850i	$-0.259945\pi$
$523$	31.3158	1.36935	0.684673	+	0.728850i	$0.259945\pi$
$524$	−12.6432	−0.552321
$525$	1.82201	0.0795192
$526$	−15.9290	−0.694538
$527$	25.3405	1.10385
$528$	2.71688	0.118237
$529$	44.8057	1.94807
$530$	−19.4953	−0.846820
$531$	−2.73143	−0.118534
$532$	0	0
$533$	−10.5175	−0.455565
$534$	11.7246	0.507374
$535$	23.5371	1.01760
$536$	−14.9368	−0.645170
$537$	−5.69459	−0.245740
$538$	16.8949	0.728389
$539$	15.6854	0.675619
$540$	−2.34730	−0.101012
$541$	9.58946	0.412283	0.206142	−	0.978522i	$-0.433909\pi$
$541$	9.58946	0.412283	0.206142	+	0.978522i	$0.433909\pi$
$542$	0.622674	0.0267461
$543$	22.2199	0.953546
$544$	3.87939	0.166327
$545$	32.6774	1.39974
$546$	19.3405	0.827697
$547$	−10.2754	−0.439343	−0.219672	−	0.975574i	$-0.570499\pi$
$547$	−10.2754	−0.439343	−0.219672	+	0.975574i	$0.570499\pi$
$548$	21.7939	0.930987
$549$	6.29086	0.268487
$550$	−1.38507	−0.0590594
$551$	0	0
$552$	8.23442	0.350480
$553$	−46.4894	−1.97693
$554$	27.4766	1.16737
$555$	0.913534	0.0387773
$556$	−11.2267	−0.476117
$557$	−16.6774	−0.706642	−0.353321	−	0.935502i	$-0.614948\pi$
$557$	−16.6774	−0.706642	−0.353321	+	0.935502i	$0.614948\pi$
$558$	6.53209	0.276525
$559$	−27.1780	−1.14951
$560$	−8.38919	−0.354508
$561$	−10.5398	−0.444992
$562$	−2.48070	−0.104642
$563$	−3.43107	−0.144603	−0.0723013	−	0.997383i	$-0.523034\pi$
$563$	−3.43107	−0.144603	−0.0723013	+	0.997383i	$0.523034\pi$
$564$	2.98545	0.125710
$565$	−0.532089	−0.0223851
$566$	−2.28312	−0.0959666
$567$	3.57398	0.150093
$568$	9.02229	0.378567
$569$	43.5681	1.82647	0.913235	−	0.407433i	$-0.133576\pi$
$569$	43.5681	1.82647	0.913235	+	0.407433i	$0.133576\pi$
$570$	0	0
$571$	−8.14115	−0.340696	−0.170348	−	0.985384i	$-0.554489\pi$
$571$	−8.14115	−0.340696	−0.170348	+	0.985384i	$0.554489\pi$
$572$	−14.7023	−0.614735
$573$	6.04694	0.252615
$574$	−6.94625	−0.289931
$575$	−4.19791	−0.175065
$576$	1.00000	0.0416667
$577$	35.0496	1.45914	0.729568	−	0.683909i	$-0.239721\pi$
$577$	35.0496	1.45914	0.729568	+	0.683909i	$0.239721\pi$
$578$	1.95037	0.0811247
$579$	−6.29860	−0.261761
$580$	8.29086	0.344259
$581$	−29.2003	−1.21143
$582$	−8.60401	−0.356648
$583$	−22.5648	−0.934539
$584$	−10.2909	−0.425839
$585$	12.7023	0.525177
$586$	−2.39599	−0.0989775
$587$	9.76651	0.403107	0.201554	−	0.979478i	$-0.435401\pi$
$587$	9.76651	0.403107	0.201554	+	0.979478i	$0.435401\pi$
$588$	5.77332	0.238088
$589$	0	0
$590$	−6.41147	−0.263956
$591$	19.9368	0.820089
$592$	−0.389185	−0.0159954
$593$	−32.6973	−1.34272	−0.671358	−	0.741133i	$-0.734289\pi$
$593$	−32.6973	−1.34272	−0.671358	+	0.741133i	$0.734289\pi$
$594$	−2.71688	−0.111475
$595$	32.5449	1.33421
$596$	−21.9786	−0.900280
$597$	12.8821	0.527228
$598$	−44.5604	−1.82221
$599$	8.84430	0.361368	0.180684	−	0.983541i	$-0.442169\pi$
$599$	8.84430	0.361368	0.180684	+	0.983541i	$0.442169\pi$
$600$	−0.509800	−0.0208125
$601$	21.8152	0.889861	0.444930	−	0.895565i	$-0.353228\pi$
$601$	21.8152	0.889861	0.444930	+	0.895565i	$0.353228\pi$
$602$	−17.9495	−0.731569
$603$	14.9368	0.608272
$604$	−2.36184	−0.0961021
$605$	8.49382	0.345323
$606$	1.28581	0.0522323
$607$	26.5963	1.07951	0.539755	−	0.841822i	$-0.318517\pi$
$607$	26.5963	1.07951	0.539755	+	0.841822i	$0.318517\pi$
$608$	0	0
$609$	−12.6236	−0.511534
$610$	14.7665	0.597879
$611$	−16.1557	−0.653590
$612$	−3.87939	−0.156815
$613$	−15.1411	−0.611545	−0.305773	−	0.952105i	$-0.598915\pi$
$613$	−15.1411	−0.611545	−0.305773	+	0.952105i	$0.598915\pi$
$614$	−5.23349	−0.211206
$615$	−4.56212	−0.183962
$616$	−9.71007	−0.391230
$617$	−29.3892	−1.18316	−0.591582	−	0.806245i	$-0.701496\pi$
$617$	−29.3892	−1.18316	−0.591582	+	0.806245i	$0.701496\pi$
$618$	0.736482	0.0296256
$619$	31.4439	1.26384	0.631918	−	0.775035i	$-0.282268\pi$
$619$	31.4439	1.26384	0.631918	+	0.775035i	$0.282268\pi$
$620$	15.3327	0.615778
$621$	−8.23442	−0.330436
$622$	10.9932	0.440787
$623$	−41.9035	−1.67883
$624$	−5.41147	−0.216632
$625$	−27.2891	−1.09156
$626$	30.4516	1.21709
$627$	0	0
$628$	−14.3550	−0.572828
$629$	1.50980	0.0601997
$630$	8.38919	0.334233
$631$	−29.8753	−1.18932	−0.594658	−	0.803979i	$-0.702712\pi$
$631$	−29.8753	−1.18932	−0.594658	+	0.803979i	$0.702712\pi$
$632$	13.0077	0.517420
$633$	−2.31315	−0.0919394
$634$	11.3396	0.450351
$635$	20.4088	0.809898
$636$	−8.30541	−0.329331
$637$	−31.2422	−1.23786
$638$	9.59627	0.379920
$639$	−9.02229	−0.356916
$640$	2.34730	0.0927850
$641$	−7.18479	−0.283782	−0.141891	−	0.989882i	$-0.545318\pi$
$641$	−7.18479	−0.283782	−0.141891	+	0.989882i	$0.545318\pi$
$642$	10.0273	0.395748
$643$	9.08378	0.358229	0.179115	−	0.983828i	$-0.442677\pi$
$643$	9.08378	0.358229	0.179115	+	0.983828i	$0.442677\pi$
$644$	−29.4296	−1.15969
$645$	−11.7888	−0.464184
$646$	0	0
$647$	37.5749	1.47722	0.738611	−	0.674132i	$-0.235482\pi$
$647$	37.5749	1.47722	0.738611	+	0.674132i	$0.235482\pi$
$648$	−1.00000	−0.0392837
$649$	−7.42097	−0.291299
$650$	2.75877	0.108208
$651$	−23.3455	−0.914984
$652$	−17.1411	−0.671299
$653$	1.74153	0.0681515	0.0340758	−	0.999419i	$-0.489151\pi$
$653$	1.74153	0.0681515	0.0340758	+	0.999419i	$0.489151\pi$
$654$	13.9213	0.544365
$655$	29.6774	1.15959
$656$	1.94356	0.0758834
$657$	10.2909	0.401485
$658$	−10.6699	−0.415958
$659$	5.20439	0.202734	0.101367	−	0.994849i	$-0.467678\pi$
$659$	5.20439	0.202734	0.101367	+	0.994849i	$0.467678\pi$
$660$	−6.37733	−0.248237
$661$	24.8408	0.966195	0.483097	−	0.875567i	$-0.339512\pi$
$661$	24.8408	0.966195	0.483097	+	0.875567i	$0.339512\pi$
$662$	12.9317	0.502605
$663$	20.9932	0.815308
$664$	8.17024	0.317067
$665$	0	0
$666$	0.389185	0.0150806
$667$	29.0847	1.12616
$668$	14.6186	0.565609
$669$	−4.07098	−0.157393
$670$	35.0610	1.35452
$671$	17.0915	0.659811
$672$	−3.57398	−0.137869
$673$	−8.99226	−0.346626	−0.173313	−	0.984867i	$-0.555447\pi$
$673$	−8.99226	−0.346626	−0.173313	+	0.984867i	$0.555447\pi$
$674$	10.7469	0.413956
$675$	0.509800	0.0196222
$676$	16.2841	0.626310
$677$	−6.41559	−0.246571	−0.123286	−	0.992371i	$-0.539343\pi$
$677$	−6.41559	−0.246571	−0.123286	+	0.992371i	$0.539343\pi$
$678$	−0.226682	−0.00870565
$679$	30.7505	1.18010
$680$	−9.10607	−0.349202
$681$	0.440570	0.0168827
$682$	17.7469	0.679564
$683$	26.0000	0.994862	0.497431	−	0.867503i	$-0.334277\pi$
$683$	26.0000	0.994862	0.497431	+	0.867503i	$0.334277\pi$
$684$	0	0
$685$	−51.1566	−1.95459
$686$	4.38413	0.167387
$687$	−3.38919	−0.129305
$688$	5.02229	0.191473
$689$	44.9445	1.71225
$690$	−19.3286	−0.735828
$691$	−44.3019	−1.68532	−0.842662	−	0.538443i	$-0.819013\pi$
$691$	−44.3019	−1.68532	−0.842662	+	0.538443i	$0.819013\pi$
$692$	20.6682	0.785687
$693$	9.71007	0.368855
$694$	−22.8033	−0.865603
$695$	26.3523	0.999602
$696$	3.53209	0.133883
$697$	−7.53983	−0.285591
$698$	25.3628	0.959995
$699$	2.11381	0.0799515
$700$	1.82201	0.0688657
$701$	−46.7229	−1.76470	−0.882349	−	0.470595i	$-0.844039\pi$
$701$	−46.7229	−1.76470	−0.882349	+	0.470595i	$0.844039\pi$
$702$	5.41147	0.204243
$703$	0	0
$704$	2.71688	0.102396
$705$	−7.00774	−0.263927
$706$	12.1925	0.458872
$707$	−4.59545	−0.172830
$708$	−2.73143	−0.102653
$709$	−15.1949	−0.570656	−0.285328	−	0.958430i	$-0.592103\pi$
$709$	−15.1949	−0.570656	−0.285328	+	0.958430i	$0.592103\pi$
$710$	−21.1780	−0.794796
$711$	−13.0077	−0.487828
$712$	11.7246	0.439399
$713$	53.7880	2.01438
$714$	13.8648	0.518878
$715$	34.5107	1.29063
$716$	−5.69459	−0.212817
$717$	−4.02910	−0.150469
$718$	−29.1634	−1.08837
$719$	23.3969	0.872558	0.436279	−	0.899811i	$-0.356296\pi$
$719$	23.3969	0.872558	0.436279	+	0.899811i	$0.356296\pi$
$720$	−2.34730	−0.0874786
$721$	−2.63217	−0.0980271
$722$	0	0
$723$	10.1771	0.378489
$724$	22.2199	0.825795
$725$	−1.80066	−0.0668748
$726$	3.61856	0.134297
$727$	34.0820	1.26403	0.632016	−	0.774955i	$-0.282228\pi$
$727$	34.0820	1.26403	0.632016	+	0.774955i	$0.282228\pi$
$728$	19.3405	0.716806
$729$	1.00000	0.0370370
$730$	24.1557	0.894042
$731$	−19.4834	−0.720619
$732$	6.29086	0.232517
$733$	−30.0128	−1.10855	−0.554274	−	0.832334i	$-0.687004\pi$
$733$	−30.0128	−1.10855	−0.554274	+	0.832334i	$0.687004\pi$
$734$	−13.9923	−0.516464
$735$	−13.5517	−0.499862
$736$	8.23442	0.303525
$737$	40.5814	1.49483
$738$	−1.94356	−0.0715435
$739$	23.8425	0.877062	0.438531	−	0.898716i	$-0.355499\pi$
$739$	23.8425	0.877062	0.438531	+	0.898716i	$0.355499\pi$
$740$	0.913534	0.0335822
$741$	0	0
$742$	29.6833	1.08971
$743$	−30.9941	−1.13706	−0.568532	−	0.822661i	$-0.692488\pi$
$743$	−30.9941	−1.13706	−0.568532	+	0.822661i	$0.692488\pi$
$744$	6.53209	0.239478
$745$	51.5904	1.89013
$746$	−6.82026	−0.249707
$747$	−8.17024	−0.298934
$748$	−10.5398	−0.385374
$749$	−35.8375	−1.30947
$750$	−10.5398	−0.384860
$751$	−22.0446	−0.804418	−0.402209	−	0.915548i	$-0.631757\pi$
$751$	−22.0446	−0.804418	−0.402209	+	0.915548i	$0.631757\pi$
$752$	2.98545	0.108868
$753$	2.90941	0.106025
$754$	−19.1138	−0.696084
$755$	5.54395	0.201765
$756$	3.57398	0.129984
$757$	−14.3250	−0.520651	−0.260326	−	0.965521i	$-0.583830\pi$
$757$	−14.3250	−0.520651	−0.260326	+	0.965521i	$0.583830\pi$
$758$	31.9341	1.15990
$759$	−22.3719	−0.812050
$760$	0	0
$761$	17.2635	0.625802	0.312901	−	0.949786i	$-0.398699\pi$
$761$	17.2635	0.625802	0.312901	+	0.949786i	$0.398699\pi$
$762$	8.69459	0.314972
$763$	−49.7543	−1.80123
$764$	6.04694	0.218771
$765$	9.10607	0.329231
$766$	−36.8188	−1.33032
$767$	14.7811	0.533713
$768$	1.00000	0.0360844
$769$	18.3200	0.660634	0.330317	−	0.943870i	$-0.392844\pi$
$769$	18.3200	0.660634	0.330317	+	0.943870i	$0.392844\pi$
$770$	22.7924	0.821382
$771$	2.55943	0.0921756
$772$	−6.29860	−0.226692
$773$	41.1438	1.47984	0.739920	−	0.672694i	$-0.234863\pi$
$773$	41.1438	1.47984	0.739920	+	0.672694i	$0.234863\pi$
$774$	−5.02229	−0.180522
$775$	−3.33006	−0.119619
$776$	−8.60401	−0.308866
$777$	−1.39094	−0.0498997
$778$	3.35504	0.120284
$779$	0	0
$780$	12.7023	0.454816
$781$	−24.5125	−0.877126
$782$	−31.9445	−1.14233
$783$	−3.53209	−0.126227
$784$	5.77332	0.206190
$785$	33.6955	1.20264
$786$	12.6432	0.450968
$787$	−13.6732	−0.487398	−0.243699	−	0.969851i	$-0.578361\pi$
$787$	−13.6732	−0.487398	−0.243699	+	0.969851i	$0.578361\pi$
$788$	19.9368	0.710218
$789$	15.9290	0.567088
$790$	−30.5330	−1.08632
$791$	0.810155	0.0288058
$792$	−2.71688	−0.0965402
$793$	−34.0428	−1.20890
$794$	−6.88444	−0.244320
$795$	19.4953	0.691425
$796$	12.8821	0.456593
$797$	−33.4935	−1.18640	−0.593200	−	0.805055i	$-0.702136\pi$
$797$	−33.4935	−1.18640	−0.593200	+	0.805055i	$0.702136\pi$
$798$	0	0
$799$	−11.5817	−0.409732
$800$	−0.509800	−0.0180242
$801$	−11.7246	−0.414269
$802$	−5.03003	−0.177617
$803$	27.9590	0.986653
$804$	14.9368	0.526779
$805$	69.0801	2.43475
$806$	−35.3482	−1.24509
$807$	−16.8949	−0.594727
$808$	1.28581	0.0452345
$809$	10.3841	0.365087	0.182543	−	0.983198i	$-0.441567\pi$
$809$	10.3841	0.365087	0.182543	+	0.983198i	$0.441567\pi$
$810$	2.34730	0.0824756
$811$	−30.9855	−1.08805	−0.544023	−	0.839070i	$-0.683100\pi$
$811$	−30.9855	−1.08805	−0.544023	+	0.839070i	$0.683100\pi$
$812$	−12.6236	−0.443002
$813$	−0.622674	−0.0218381
$814$	1.05737	0.0370608
$815$	40.2354	1.40938
$816$	−3.87939	−0.135806
$817$	0	0
$818$	−10.4088	−0.363935
$819$	−19.3405	−0.675811
$820$	−4.56212	−0.159316
$821$	−44.2719	−1.54510	−0.772549	−	0.634955i	$-0.781019\pi$
$821$	−44.2719	−1.54510	−0.772549	+	0.634955i	$0.781019\pi$
$822$	−21.7939	−0.760148
$823$	−19.9659	−0.695966	−0.347983	−	0.937501i	$-0.613133\pi$
$823$	−19.9659	−0.695966	−0.347983	+	0.937501i	$0.613133\pi$
$824$	0.736482	0.0256566
$825$	1.38507	0.0482218
$826$	9.76207	0.339666
$827$	−8.42871	−0.293095	−0.146547	−	0.989204i	$-0.546816\pi$
$827$	−8.42871	−0.293095	−0.146547	+	0.989204i	$0.546816\pi$
$828$	−8.23442	−0.286166
$829$	−4.24722	−0.147512	−0.0737559	−	0.997276i	$-0.523499\pi$
$829$	−4.24722	−0.147512	−0.0737559	+	0.997276i	$0.523499\pi$
$830$	−19.1780	−0.665678
$831$	−27.4766	−0.953152
$832$	−5.41147	−0.187609
$833$	−22.3969	−0.776007
$834$	11.2267	0.388748
$835$	−34.3141	−1.18749
$836$	0	0
$837$	−6.53209	−0.225782
$838$	6.22256	0.214955
$839$	−6.04870	−0.208824	−0.104412	−	0.994534i	$-0.533296\pi$
$839$	−6.04870	−0.208824	−0.104412	+	0.994534i	$0.533296\pi$
$840$	8.38919	0.289454
$841$	−16.5243	−0.569805
$842$	−26.6195	−0.917368
$843$	2.48070	0.0854400
$844$	−2.31315	−0.0796218
$845$	−38.2235	−1.31493
$846$	−2.98545	−0.102642
$847$	−12.9326	−0.444371
$848$	−8.30541	−0.285209
$849$	2.28312	0.0783564
$850$	1.97771	0.0678349
$851$	3.20472	0.109856
$852$	−9.02229	−0.309099
$853$	−25.7588	−0.881964	−0.440982	−	0.897516i	$-0.645370\pi$
$853$	−25.7588	−0.881964	−0.440982	+	0.897516i	$0.645370\pi$
$854$	−22.4834	−0.769366
$855$	0	0
$856$	10.0273	0.342727
$857$	58.2116	1.98847	0.994236	−	0.107215i	$-0.0341934\pi$
$857$	58.2116	1.98847	0.994236	+	0.107215i	$0.0341934\pi$
$858$	14.7023	0.501929
$859$	−10.1162	−0.345159	−0.172580	−	0.984996i	$-0.555210\pi$
$859$	−10.1162	−0.345159	−0.172580	+	0.984996i	$0.555210\pi$
$860$	−11.7888	−0.401995
$861$	6.94625	0.236728
$862$	−13.7324	−0.467726
$863$	36.3414	1.23708	0.618538	−	0.785755i	$-0.287725\pi$
$863$	36.3414	1.23708	0.618538	+	0.785755i	$0.287725\pi$
$864$	−1.00000	−0.0340207
$865$	−48.5144	−1.64954
$866$	−24.6946	−0.839156
$867$	−1.95037	−0.0662380
$868$	−23.3455	−0.792399
$869$	−35.3405	−1.19884
$870$	−8.29086	−0.281086
$871$	−80.8299	−2.73882
$872$	13.9213	0.471434
$873$	8.60401	0.291202
$874$	0	0
$875$	37.6691	1.27345
$876$	10.2909	0.347696
$877$	7.17942	0.242432	0.121216	−	0.992626i	$-0.461321\pi$
$877$	7.17942	0.242432	0.121216	+	0.992626i	$0.461321\pi$
$878$	18.1411	0.612234
$879$	2.39599	0.0808148
$880$	−6.37733	−0.214980
$881$	13.1712	0.443748	0.221874	−	0.975075i	$-0.428783\pi$
$881$	13.1712	0.443748	0.221874	+	0.975075i	$0.428783\pi$
$882$	−5.77332	−0.194398
$883$	−12.5330	−0.421770	−0.210885	−	0.977511i	$-0.567635\pi$
$883$	−12.5330	−0.421770	−0.210885	+	0.977511i	$0.567635\pi$
$884$	20.9932	0.706077
$885$	6.41147	0.215519
$886$	12.8625	0.432123
$887$	53.0015	1.77962	0.889809	−	0.456333i	$-0.150838\pi$
$887$	53.0015	1.77962	0.889809	+	0.456333i	$0.150838\pi$
$888$	0.389185	0.0130602
$889$	−31.0743	−1.04220
$890$	−27.5212	−0.922511
$891$	2.71688	0.0910190
$892$	−4.07098	−0.136307
$893$	0	0
$894$	21.9786	0.735076
$895$	13.3669	0.446806
$896$	−3.57398	−0.119398
$897$	44.5604	1.48783
$898$	−21.9317	−0.731870
$899$	23.0719	0.769492
$900$	0.509800	0.0169933
$901$	32.2199	1.07340
$902$	−5.28043	−0.175819
$903$	17.9495	0.597324
$904$	−0.226682	−0.00753932
$905$	−52.1566	−1.73375
$906$	2.36184	0.0784670
$907$	−22.1634	−0.735925	−0.367962	−	0.929841i	$-0.619944\pi$
$907$	−22.1634	−0.735925	−0.367962	+	0.929841i	$0.619944\pi$
$908$	0.440570	0.0146208
$909$	−1.28581	−0.0426475
$910$	−45.3979	−1.50492
$911$	−37.1908	−1.23219	−0.616093	−	0.787674i	$-0.711285\pi$
$911$	−37.1908	−1.23219	−0.616093	+	0.787674i	$0.711285\pi$
$912$	0	0
$913$	−22.1976	−0.734633
$914$	−30.8452	−1.02027
$915$	−14.7665	−0.488166
$916$	−3.38919	−0.111982
$917$	−45.1865	−1.49219
$918$	3.87939	0.128039
$919$	11.1557	0.367992	0.183996	−	0.982927i	$-0.441097\pi$
$919$	11.1557	0.367992	0.183996	+	0.982927i	$0.441097\pi$
$920$	−19.3286	−0.637246
$921$	5.23349	0.172449
$922$	12.3200	0.405736
$923$	48.8239	1.60706
$924$	9.71007	0.319438
$925$	−0.198407	−0.00652358
$926$	−12.2094	−0.401227
$927$	−0.736482	−0.0241892
$928$	3.53209	0.115946
$929$	−12.4124	−0.407238	−0.203619	−	0.979050i	$-0.565270\pi$
$929$	−12.4124	−0.407238	−0.203619	+	0.979050i	$0.565270\pi$
$930$	−15.3327	−0.502781
$931$	0	0
$932$	2.11381	0.0692401
$933$	−10.9932	−0.359901
$934$	26.7401	0.874963
$935$	24.7401	0.809088
$936$	5.41147	0.176880
$937$	14.1557	0.462446	0.231223	−	0.972901i	$-0.425727\pi$
$937$	14.1557	0.462446	0.231223	+	0.972901i	$0.425727\pi$
$938$	−53.3836	−1.74304
$939$	−30.4516	−0.993751
$940$	−7.00774	−0.228567
$941$	−18.6509	−0.608004	−0.304002	−	0.952671i	$-0.598323\pi$
$941$	−18.6509	−0.608004	−0.304002	+	0.952671i	$0.598323\pi$
$942$	14.3550	0.467712
$943$	−16.0041	−0.521166
$944$	−2.73143	−0.0889005
$945$	−8.38919	−0.272900
$946$	−13.6450	−0.443636
$947$	−42.9350	−1.39520	−0.697600	−	0.716487i	$-0.745749\pi$
$947$	−42.9350	−1.39520	−0.697600	+	0.716487i	$0.745749\pi$
$948$	−13.0077	−0.422472
$949$	−55.6887	−1.80773
$950$	0	0
$951$	−11.3396	−0.367710
$952$	13.8648	0.449362
$953$	−37.3500	−1.20988	−0.604942	−	0.796269i	$-0.706804\pi$
$953$	−37.3500	−1.20988	−0.604942	+	0.796269i	$0.706804\pi$
$954$	8.30541	0.268897
$955$	−14.1940	−0.459306
$956$	−4.02910	−0.130310
$957$	−9.59627	−0.310203
$958$	−7.73648	−0.249954
$959$	77.8907	2.51522
$960$	−2.34730	−0.0757587
$961$	11.6682	0.376393
$962$	−2.10607	−0.0679023
$963$	−10.0273	−0.323127
$964$	10.1771	0.327781
$965$	14.7847	0.475936
$966$	29.4296	0.946883
$967$	−26.0297	−0.837059	−0.418529	−	0.908203i	$-0.637454\pi$
$967$	−26.0297	−0.837059	−0.418529	+	0.908203i	$0.637454\pi$
$968$	3.61856	0.116305
$969$	0	0
$970$	20.1962	0.648459
$971$	6.69459	0.214840	0.107420	−	0.994214i	$-0.465741\pi$
$971$	6.69459	0.214840	0.107420	+	0.994214i	$0.465741\pi$
$972$	1.00000	0.0320750
$973$	−40.1239	−1.28631
$974$	13.3919	0.429103
$975$	−2.75877	−0.0883514
$976$	6.29086	0.201366
$977$	4.87939	0.156105	0.0780527	−	0.996949i	$-0.475130\pi$
$977$	4.87939	0.156105	0.0780527	+	0.996949i	$0.475130\pi$
$978$	17.1411	0.548113
$979$	−31.8544	−1.01807
$980$	−13.5517	−0.432893
$981$	−13.9213	−0.444472
$982$	20.2472	0.646115
$983$	6.22130	0.198429	0.0992144	−	0.995066i	$-0.468367\pi$
$983$	6.22130	0.198429	0.0992144	+	0.995066i	$0.468367\pi$
$984$	−1.94356	−0.0619585
$985$	−46.7975	−1.49109
$986$	−13.7023	−0.436371
$987$	10.6699	0.339628
$988$	0	0
$989$	−41.3556	−1.31503
$990$	6.37733	0.202685
$991$	9.32687	0.296278	0.148139	−	0.988967i	$-0.452672\pi$
$991$	9.32687	0.296278	0.148139	+	0.988967i	$0.452672\pi$
$992$	6.53209	0.207394
$993$	−12.9317	−0.410375
$994$	32.2455	1.02276
$995$	−30.2380	−0.958610
$996$	−8.17024	−0.258884
$997$	−23.5152	−0.744733	−0.372367	−	0.928086i	$-0.621454\pi$
$997$	−23.5152	−0.744733	−0.372367	+	0.928086i	$0.621454\pi$
$998$	4.73742	0.149960
$999$	−0.389185	−0.0123133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.2.a.p.1.2		3
3.2	odd	2		6498.2.a.bu.1.2		3
19.3	odd	18		114.2.i.c.85.1	yes	6
19.13	odd	18		114.2.i.c.55.1	✓	6
19.18	odd	2		2166.2.a.r.1.2		3
57.32	even	18		342.2.u.b.55.1		6
57.41	even	18		342.2.u.b.199.1		6
57.56	even	2		6498.2.a.bp.1.2		3
76.3	even	18		912.2.bo.d.769.1		6
76.51	even	18		912.2.bo.d.625.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.c.55.1	✓	6	19.13	odd	18
114.2.i.c.85.1	yes	6	19.3	odd	18
342.2.u.b.55.1		6	57.32	even	18
342.2.u.b.199.1		6	57.41	even	18
912.2.bo.d.625.1		6	76.51	even	18
912.2.bo.d.769.1		6	76.3	even	18
2166.2.a.p.1.2		3	1.1	even	1	trivial
2166.2.a.r.1.2		3	19.18	odd	2
6498.2.a.bp.1.2		3	57.56	even	2
6498.2.a.bu.1.2		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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.34730 q^{5} -1.00000 q^{6} +3.57398 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.34730 q^{5} -1.00000 q^{6} +3.57398 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.34730 q^{10} +2.71688 q^{11} +1.00000 q^{12} -5.41147 q^{13} -3.57398 q^{14} -2.34730 q^{15} +1.00000 q^{16} -3.87939 q^{17} -1.00000 q^{18} -2.34730 q^{20} +3.57398 q^{21} -2.71688 q^{22} -8.23442 q^{23} -1.00000 q^{24} +0.509800 q^{25} +5.41147 q^{26} +1.00000 q^{27} +3.57398 q^{28} -3.53209 q^{29} +2.34730 q^{30} -6.53209 q^{31} -1.00000 q^{32} +2.71688 q^{33} +3.87939 q^{34} -8.38919 q^{35} +1.00000 q^{36} -0.389185 q^{37} -5.41147 q^{39} +2.34730 q^{40} +1.94356 q^{41} -3.57398 q^{42} +5.02229 q^{43} +2.71688 q^{44} -2.34730 q^{45} +8.23442 q^{46} +2.98545 q^{47} +1.00000 q^{48} +5.77332 q^{49} -0.509800 q^{50} -3.87939 q^{51} -5.41147 q^{52} -8.30541 q^{53} -1.00000 q^{54} -6.37733 q^{55} -3.57398 q^{56} +3.53209 q^{58} -2.73143 q^{59} -2.34730 q^{60} +6.29086 q^{61} +6.53209 q^{62} +3.57398 q^{63} +1.00000 q^{64} +12.7023 q^{65} -2.71688 q^{66} +14.9368 q^{67} -3.87939 q^{68} -8.23442 q^{69} +8.38919 q^{70} -9.02229 q^{71} -1.00000 q^{72} +10.2909 q^{73} +0.389185 q^{74} +0.509800 q^{75} +9.71007 q^{77} +5.41147 q^{78} -13.0077 q^{79} -2.34730 q^{80} +1.00000 q^{81} -1.94356 q^{82} -8.17024 q^{83} +3.57398 q^{84} +9.10607 q^{85} -5.02229 q^{86} -3.53209 q^{87} -2.71688 q^{88} -11.7246 q^{89} +2.34730 q^{90} -19.3405 q^{91} -8.23442 q^{92} -6.53209 q^{93} -2.98545 q^{94} -1.00000 q^{96} +8.60401 q^{97} -5.77332 q^{98} +2.71688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 6 q^{10} + 3 q^{12} - 6 q^{13} - 3 q^{14} - 6 q^{15} + 3 q^{16} - 6 q^{17} - 3 q^{18} - 6 q^{20} + 3 q^{21} + 6 q^{23} - 3 q^{24} + 3 q^{25} + 6 q^{26} + 3 q^{27} + 3 q^{28} - 6 q^{29} + 6 q^{30} - 15 q^{31} - 3 q^{32} + 6 q^{34} - 21 q^{35} + 3 q^{36} + 3 q^{37} - 6 q^{39} + 6 q^{40} - 9 q^{41} - 3 q^{42} + 9 q^{43} - 6 q^{45} - 6 q^{46} - 9 q^{47} + 3 q^{48} + 24 q^{49} - 3 q^{50} - 6 q^{51} - 6 q^{52} - 27 q^{53} - 3 q^{54} + 12 q^{55} - 3 q^{56} + 6 q^{58} - 18 q^{59} - 6 q^{60} + 3 q^{61} + 15 q^{62} + 3 q^{63} + 3 q^{64} + 12 q^{65} - 12 q^{67} - 6 q^{68} + 6 q^{69} + 21 q^{70} - 21 q^{71} - 3 q^{72} + 15 q^{73} - 3 q^{74} + 3 q^{75} - 21 q^{77} + 6 q^{78} - 15 q^{79} - 6 q^{80} + 3 q^{81} + 9 q^{82} - 3 q^{83} + 3 q^{84} + 15 q^{85} - 9 q^{86} - 6 q^{87} - 3 q^{89} + 6 q^{90} - 15 q^{91} + 6 q^{92} - 15 q^{93} + 9 q^{94} - 3 q^{96} - 12 q^{97} - 24 q^{98}+O(q^{100}) \) 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 + 3 * q^12 - 6 * q^13 - 3 * q^14 - 6 * q^15 + 3 * q^16 - 6 * q^17 - 3 * q^18 - 6 * q^20 + 3 * q^21 + 6 * q^23 - 3 * q^24 + 3 * q^25 + 6 * q^26 + 3 * q^27 + 3 * q^28 - 6 * q^29 + 6 * q^30 - 15 * q^31 - 3 * q^32 + 6 * q^34 - 21 * q^35 + 3 * q^36 + 3 * q^37 - 6 * q^39 + 6 * q^40 - 9 * q^41 - 3 * q^42 + 9 * q^43 - 6 * q^45 - 6 * q^46 - 9 * q^47 + 3 * q^48 + 24 * q^49 - 3 * q^50 - 6 * q^51 - 6 * q^52 - 27 * q^53 - 3 * q^54 + 12 * q^55 - 3 * q^56 + 6 * q^58 - 18 * q^59 - 6 * q^60 + 3 * q^61 + 15 * q^62 + 3 * q^63 + 3 * q^64 + 12 * q^65 - 12 * q^67 - 6 * q^68 + 6 * q^69 + 21 * q^70 - 21 * q^71 - 3 * q^72 + 15 * q^73 - 3 * q^74 + 3 * q^75 - 21 * q^77 + 6 * q^78 - 15 * q^79 - 6 * q^80 + 3 * q^81 + 9 * q^82 - 3 * q^83 + 3 * q^84 + 15 * q^85 - 9 * q^86 - 6 * q^87 - 3 * q^89 + 6 * q^90 - 15 * q^91 + 6 * q^92 - 15 * q^93 + 9 * q^94 - 3 * q^96 - 12 * q^97 - 24 * q^98

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