LMFDB - Embedded newform 2166.2.a.p.1.3

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			1.3
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.120615 q^{5} -1.00000 q^{6} -4.29086 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.120615 q^{5} -1.00000 q^{6} -4.29086 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.120615 q^{10} +2.57398 q^{11} +1.00000 q^{12} -0.815207 q^{13} +4.29086 q^{14} -0.120615 q^{15} +1.00000 q^{16} -0.467911 q^{17} -1.00000 q^{18} -0.120615 q^{20} -4.29086 q^{21} -2.57398 q^{22} +5.55438 q^{23} -1.00000 q^{24} -4.98545 q^{25} +0.815207 q^{26} +1.00000 q^{27} -4.29086 q^{28} -2.34730 q^{29} +0.120615 q^{30} -5.34730 q^{31} -1.00000 q^{32} +2.57398 q^{33} +0.467911 q^{34} +0.517541 q^{35} +1.00000 q^{36} +8.51754 q^{37} -0.815207 q^{39} +0.120615 q^{40} -3.83750 q^{41} +4.29086 q^{42} +9.33275 q^{43} +2.57398 q^{44} -0.120615 q^{45} -5.55438 q^{46} -9.47565 q^{47} +1.00000 q^{48} +11.4115 q^{49} +4.98545 q^{50} -0.467911 q^{51} -0.815207 q^{52} -12.7588 q^{53} -1.00000 q^{54} -0.310460 q^{55} +4.29086 q^{56} +2.34730 q^{58} -15.0496 q^{59} -0.120615 q^{60} -1.71688 q^{61} +5.34730 q^{62} -4.29086 q^{63} +1.00000 q^{64} +0.0983261 q^{65} -2.57398 q^{66} -11.4561 q^{67} -0.467911 q^{68} +5.55438 q^{69} -0.517541 q^{70} -13.3327 q^{71} -1.00000 q^{72} +2.28312 q^{73} -8.51754 q^{74} -4.98545 q^{75} -11.0446 q^{77} +0.815207 q^{78} -4.85710 q^{79} -0.120615 q^{80} +1.00000 q^{81} +3.83750 q^{82} +3.24897 q^{83} -4.29086 q^{84} +0.0564370 q^{85} -9.33275 q^{86} -2.34730 q^{87} -2.57398 q^{88} -3.43107 q^{89} +0.120615 q^{90} +3.49794 q^{91} +5.55438 q^{92} -5.34730 q^{93} +9.47565 q^{94} -1.00000 q^{96} -3.10101 q^{97} -11.4115 q^{98} +2.57398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.120615	−0.0539406	−0.0269703	−	0.999636i	$-0.508586\pi$
$5$	−0.120615	−0.0539406	−0.0269703	+	0.999636i	$0.508586\pi$
$6$	−1.00000	−0.408248
$7$	−4.29086	−1.62179	−0.810896	−	0.585190i	$-0.801020\pi$
$7$	−4.29086	−1.62179	−0.810896	+	0.585190i	$0.801020\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.120615	0.0381417
$11$	2.57398	0.776084	0.388042	−	0.921642i	$-0.373152\pi$
$11$	2.57398	0.776084	0.388042	+	0.921642i	$0.373152\pi$
$12$	1.00000	0.288675
$13$	−0.815207	−0.226098	−0.113049	−	0.993589i	$-0.536062\pi$
$13$	−0.815207	−0.226098	−0.113049	+	0.993589i	$0.536062\pi$
$14$	4.29086	1.14678
$15$	−0.120615	−0.0311426
$16$	1.00000	0.250000
$17$	−0.467911	−0.113485	−0.0567426	−	0.998389i	$-0.518071\pi$
$17$	−0.467911	−0.113485	−0.0567426	+	0.998389i	$0.518071\pi$
$18$	−1.00000	−0.235702
$19$	0	0
$19$	0	0
$20$	−0.120615	−0.0269703
$21$	−4.29086	−0.936342
$22$	−2.57398	−0.548774
$23$	5.55438	1.15817	0.579084	−	0.815268i	$-0.303410\pi$
$23$	5.55438	1.15817	0.579084	+	0.815268i	$0.303410\pi$
$24$	−1.00000	−0.204124
$25$	−4.98545	−0.997090
$26$	0.815207	0.159875
$27$	1.00000	0.192450
$28$	−4.29086	−0.810896
$29$	−2.34730	−0.435882	−0.217941	−	0.975962i	$-0.569934\pi$
$29$	−2.34730	−0.435882	−0.217941	+	0.975962i	$0.569934\pi$
$30$	0.120615	0.0220211
$31$	−5.34730	−0.960403	−0.480201	−	0.877158i	$-0.659436\pi$
$31$	−5.34730	−0.960403	−0.480201	+	0.877158i	$0.659436\pi$
$32$	−1.00000	−0.176777
$33$	2.57398	0.448072
$34$	0.467911	0.0802461
$35$	0.517541	0.0874804
$36$	1.00000	0.166667
$37$	8.51754	1.40028	0.700138	−	0.714008i	$-0.253122\pi$
$37$	8.51754	1.40028	0.700138	+	0.714008i	$0.253122\pi$
$38$	0	0
$39$	−0.815207	−0.130538
$40$	0.120615	0.0190709
$41$	−3.83750	−0.599316	−0.299658	−	0.954047i	$-0.596873\pi$
$41$	−3.83750	−0.599316	−0.299658	+	0.954047i	$0.596873\pi$
$42$	4.29086	0.662094
$43$	9.33275	1.42323	0.711615	−	0.702569i	$-0.247964\pi$
$43$	9.33275	1.42323	0.711615	+	0.702569i	$0.247964\pi$
$44$	2.57398	0.388042
$45$	−0.120615	−0.0179802
$46$	−5.55438	−0.818948
$47$	−9.47565	−1.38217	−0.691083	−	0.722775i	$-0.742866\pi$
$47$	−9.47565	−1.38217	−0.691083	+	0.722775i	$0.742866\pi$
$48$	1.00000	0.144338
$49$	11.4115	1.63021
$50$	4.98545	0.705049
$51$	−0.467911	−0.0655207
$52$	−0.815207	−0.113049
$53$	−12.7588	−1.75255	−0.876276	−	0.481810i	$-0.839980\pi$
$53$	−12.7588	−1.75255	−0.876276	+	0.481810i	$0.839980\pi$
$54$	−1.00000	−0.136083
$55$	−0.310460	−0.0418624
$56$	4.29086	0.573390
$57$	0	0
$58$	2.34730	0.308215
$59$	−15.0496	−1.95929	−0.979647	−	0.200726i	$-0.935670\pi$
$59$	−15.0496	−1.95929	−0.979647	+	0.200726i	$0.935670\pi$
$60$	−0.120615	−0.0155713
$61$	−1.71688	−0.219824	−0.109912	−	0.993941i	$-0.535057\pi$
$61$	−1.71688	−0.219824	−0.109912	+	0.993941i	$0.535057\pi$
$62$	5.34730	0.679107
$63$	−4.29086	−0.540597
$64$	1.00000	0.125000
$65$	0.0983261	0.0121958
$66$	−2.57398	−0.316835
$67$	−11.4561	−1.39958	−0.699790	−	0.714349i	$-0.746723\pi$
$67$	−11.4561	−1.39958	−0.699790	+	0.714349i	$0.746723\pi$
$68$	−0.467911	−0.0567426
$69$	5.55438	0.668668
$70$	−0.517541	−0.0618580
$71$	−13.3327	−1.58231	−0.791153	−	0.611618i	$-0.790519\pi$
$71$	−13.3327	−1.58231	−0.791153	+	0.611618i	$0.790519\pi$
$72$	−1.00000	−0.117851
$73$	2.28312	0.267219	0.133609	−	0.991034i	$-0.457343\pi$
$73$	2.28312	0.267219	0.133609	+	0.991034i	$0.457343\pi$
$74$	−8.51754	−0.990144
$75$	−4.98545	−0.575670
$76$	0	0
$77$	−11.0446	−1.25865
$78$	0.815207	0.0923041
$79$	−4.85710	−0.546466	−0.273233	−	0.961948i	$-0.588093\pi$
$79$	−4.85710	−0.546466	−0.273233	+	0.961948i	$0.588093\pi$
$80$	−0.120615	−0.0134851
$81$	1.00000	0.111111
$82$	3.83750	0.423781
$83$	3.24897	0.356621	0.178310	−	0.983974i	$-0.442937\pi$
$83$	3.24897	0.356621	0.178310	+	0.983974i	$0.442937\pi$
$84$	−4.29086	−0.468171
$85$	0.0564370	0.00612145
$86$	−9.33275	−1.00638
$87$	−2.34730	−0.251657
$88$	−2.57398	−0.274387
$89$	−3.43107	−0.363693	−0.181847	−	0.983327i	$-0.558207\pi$
$89$	−3.43107	−0.363693	−0.181847	+	0.983327i	$0.558207\pi$
$90$	0.120615	0.0127139
$91$	3.49794	0.366684
$92$	5.55438	0.579084
$93$	−5.34730	−0.554489
$94$	9.47565	0.977339
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−3.10101	−0.314860	−0.157430	−	0.987530i	$-0.550321\pi$
$97$	−3.10101	−0.314860	−0.157430	+	0.987530i	$0.550321\pi$
$98$	−11.4115	−1.15273
$99$	2.57398	0.258695
$100$	−4.98545	−0.498545
$101$	−16.7297	−1.66466	−0.832332	−	0.554277i	$-0.812995\pi$
$101$	−16.7297	−1.66466	−0.832332	+	0.554277i	$0.812995\pi$
$102$	0.467911	0.0463301
$103$	10.3969	1.02444	0.512220	−	0.858854i	$-0.328823\pi$
$103$	10.3969	1.02444	0.512220	+	0.858854i	$0.328823\pi$
$104$	0.815207	0.0799377
$105$	0.517541	0.0505068
$106$	12.7588	1.23924
$107$	9.11381	0.881065	0.440533	−	0.897737i	$-0.354790\pi$
$107$	9.11381	0.881065	0.440533	+	0.897737i	$0.354790\pi$
$108$	1.00000	0.0962250
$109$	−3.82976	−0.366824	−0.183412	−	0.983036i	$-0.558714\pi$
$109$	−3.82976	−0.366824	−0.183412	+	0.983036i	$0.558714\pi$
$110$	0.310460	0.0296012
$111$	8.51754	0.808449
$112$	−4.29086	−0.405448
$113$	−5.41147	−0.509069	−0.254534	−	0.967064i	$-0.581922\pi$
$113$	−5.41147	−0.509069	−0.254534	+	0.967064i	$0.581922\pi$
$114$	0	0
$115$	−0.669940	−0.0624722
$116$	−2.34730	−0.217941
$117$	−0.815207	−0.0753660
$118$	15.0496	1.38543
$119$	2.00774	0.184049
$120$	0.120615	0.0110106
$121$	−4.37464	−0.397694
$122$	1.71688	0.155439
$123$	−3.83750	−0.346015
$124$	−5.34730	−0.480201
$125$	1.20439	0.107724
$126$	4.29086	0.382260
$127$	−4.24123	−0.376348	−0.188174	−	0.982136i	$-0.560257\pi$
$127$	−4.24123	−0.376348	−0.188174	+	0.982136i	$0.560257\pi$
$128$	−1.00000	−0.0883883
$129$	9.33275	0.821703
$130$	−0.0983261	−0.00862377
$131$	21.0428	1.83852	0.919260	−	0.393651i	$-0.128788\pi$
$131$	21.0428	1.83852	0.919260	+	0.393651i	$0.128788\pi$
$132$	2.57398	0.224036
$133$	0	0
$134$	11.4561	0.989652
$135$	−0.120615	−0.0103809
$136$	0.467911	0.0401230
$137$	−12.3209	−1.05264	−0.526322	−	0.850285i	$-0.676429\pi$
$137$	−12.3209	−1.05264	−0.526322	+	0.850285i	$0.676429\pi$
$138$	−5.55438	−0.472820
$139$	−5.58853	−0.474013	−0.237006	−	0.971508i	$-0.576166\pi$
$139$	−5.58853	−0.474013	−0.237006	+	0.971508i	$0.576166\pi$
$140$	0.517541	0.0437402
$141$	−9.47565	−0.797994
$142$	13.3327	1.11886
$143$	−2.09833	−0.175471
$144$	1.00000	0.0833333
$145$	0.283119	0.0235117
$146$	−2.28312	−0.188952
$147$	11.4115	0.941203
$148$	8.51754	0.700138
$149$	11.0942	0.908873	0.454436	−	0.890779i	$-0.349841\pi$
$149$	11.0942	0.908873	0.454436	+	0.890779i	$0.349841\pi$
$150$	4.98545	0.407060
$151$	−12.5963	−1.02507	−0.512535	−	0.858666i	$-0.671293\pi$
$151$	−12.5963	−1.02507	−0.512535	+	0.858666i	$0.671293\pi$
$152$	0	0
$153$	−0.467911	−0.0378284
$154$	11.0446	0.889997
$155$	0.644963	0.0518047
$156$	−0.815207	−0.0652688
$157$	−3.97771	−0.317456	−0.158728	−	0.987322i	$-0.550739\pi$
$157$	−3.97771	−0.317456	−0.158728	+	0.987322i	$0.550739\pi$
$158$	4.85710	0.386410
$159$	−12.7588	−1.01184
$160$	0.120615	0.00953543
$161$	−23.8331	−1.87831
$162$	−1.00000	−0.0785674
$163$	19.2003	1.50388	0.751941	−	0.659231i	$-0.229118\pi$
$163$	19.2003	1.50388	0.751941	+	0.659231i	$0.229118\pi$
$164$	−3.83750	−0.299658
$165$	−0.310460	−0.0241693
$166$	−3.24897	−0.252169
$167$	15.3746	1.18973	0.594863	−	0.803827i	$-0.297206\pi$
$167$	15.3746	1.18973	0.594863	+	0.803827i	$0.297206\pi$
$168$	4.29086	0.331047
$169$	−12.3354	−0.948880
$170$	−0.0564370	−0.00432852
$171$	0	0
$172$	9.33275	0.711615
$173$	6.59358	0.501300	0.250650	−	0.968078i	$-0.419356\pi$
$173$	6.59358	0.501300	0.250650	+	0.968078i	$0.419356\pi$
$174$	2.34730	0.177948
$175$	21.3919	1.61707
$176$	2.57398	0.194021
$177$	−15.0496	−1.13120
$178$	3.43107	0.257170
$179$	−1.24123	−0.0927738	−0.0463869	−	0.998924i	$-0.514771\pi$
$179$	−1.24123	−0.0927738	−0.0463869	+	0.998924i	$0.514771\pi$
$180$	−0.120615	−0.00899009
$181$	−4.03003	−0.299550	−0.149775	−	0.988720i	$-0.547855\pi$
$181$	−4.03003	−0.299550	−0.149775	+	0.988720i	$0.547855\pi$
$182$	−3.49794	−0.259285
$183$	−1.71688	−0.126916
$184$	−5.55438	−0.409474
$185$	−1.02734	−0.0755316
$186$	5.34730	0.392083
$187$	−1.20439	−0.0880739
$188$	−9.47565	−0.691083
$189$	−4.29086	−0.312114
$190$	0	0
$191$	−24.0847	−1.74271	−0.871354	−	0.490654i	$-0.836758\pi$
$191$	−24.0847	−1.74271	−0.871354	+	0.490654i	$0.836758\pi$
$192$	1.00000	0.0721688
$193$	9.85978	0.709723	0.354861	−	0.934919i	$-0.384528\pi$
$193$	9.85978	0.709723	0.354861	+	0.934919i	$0.384528\pi$
$194$	3.10101	0.222640
$195$	0.0983261	0.00704127
$196$	11.4115	0.815105
$197$	−6.45605	−0.459975	−0.229987	−	0.973194i	$-0.573868\pi$
$197$	−6.45605	−0.459975	−0.229987	+	0.973194i	$0.573868\pi$
$198$	−2.57398	−0.182925
$199$	24.7716	1.75601	0.878005	−	0.478652i	$-0.158874\pi$
$199$	24.7716	1.75601	0.878005	+	0.478652i	$0.158874\pi$
$200$	4.98545	0.352525
$201$	−11.4561	−0.808048
$202$	16.7297	1.17710
$203$	10.0719	0.706910
$204$	−0.467911	−0.0327603
$205$	0.462859	0.0323275
$206$	−10.3969	−0.724388
$207$	5.55438	0.386056
$208$	−0.815207	−0.0565245
$209$	0	0
$210$	−0.517541	−0.0357137
$211$	1.38413	0.0952876	0.0476438	−	0.998864i	$-0.484829\pi$
$211$	1.38413	0.0952876	0.0476438	+	0.998864i	$0.484829\pi$
$212$	−12.7588	−0.876276
$213$	−13.3327	−0.913545
$214$	−9.11381	−0.623007
$215$	−1.12567	−0.0767699
$216$	−1.00000	−0.0680414
$217$	22.9445	1.55757
$218$	3.82976	0.259384
$219$	2.28312	0.154279
$220$	−0.310460	−0.0209312
$221$	0.381445	0.0256587
$222$	−8.51754	−0.571660
$223$	−22.3131	−1.49420	−0.747099	−	0.664712i	$-0.768554\pi$
$223$	−22.3131	−1.49420	−0.747099	+	0.664712i	$0.768554\pi$
$224$	4.29086	0.286695
$225$	−4.98545	−0.332363
$226$	5.41147	0.359966
$227$	20.7665	1.37832	0.689161	−	0.724608i	$-0.257979\pi$
$227$	20.7665	1.37832	0.689161	+	0.724608i	$0.257979\pi$
$228$	0	0
$229$	5.51754	0.364609	0.182305	−	0.983242i	$-0.441644\pi$
$229$	5.51754	0.364609	0.182305	+	0.983242i	$0.441644\pi$
$230$	0.669940	0.0441745
$231$	−11.0446	−0.726680
$232$	2.34730	0.154108
$233$	−15.0865	−0.988347	−0.494174	−	0.869363i	$-0.664529\pi$
$233$	−15.0865	−0.988347	−0.494174	+	0.869363i	$0.664529\pi$
$234$	0.815207	0.0532918
$235$	1.14290	0.0745548
$236$	−15.0496	−0.979647
$237$	−4.85710	−0.315502
$238$	−2.00774	−0.130143
$239$	−28.9513	−1.87270	−0.936352	−	0.351062i	$-0.885821\pi$
$239$	−28.9513	−1.87270	−0.936352	+	0.351062i	$0.885821\pi$
$240$	−0.120615	−0.00778565
$241$	19.3696	1.24770	0.623852	−	0.781542i	$-0.285567\pi$
$241$	19.3696	1.24770	0.623852	+	0.781542i	$0.285567\pi$
$242$	4.37464	0.281212
$243$	1.00000	0.0641500
$244$	−1.71688	−0.109912
$245$	−1.37639	−0.0879345
$246$	3.83750	0.244670
$247$	0	0
$248$	5.34730	0.339554
$249$	3.24897	0.205895
$250$	−1.20439	−0.0761725
$251$	−4.34224	−0.274080	−0.137040	−	0.990566i	$-0.543759\pi$
$251$	−4.34224	−0.274080	−0.137040	+	0.990566i	$0.543759\pi$
$252$	−4.29086	−0.270299
$253$	14.2968	0.898835
$254$	4.24123	0.266118
$255$	0.0564370	0.00353422
$256$	1.00000	0.0625000
$257$	−17.7665	−1.10824	−0.554122	−	0.832435i	$-0.686946\pi$
$257$	−17.7665	−1.10824	−0.554122	+	0.832435i	$0.686946\pi$
$258$	−9.33275	−0.581032
$259$	−36.5476	−2.27096
$260$	0.0983261	0.00609792
$261$	−2.34730	−0.145294
$262$	−21.0428	−1.30003
$263$	−2.31315	−0.142635	−0.0713174	−	0.997454i	$-0.522720\pi$
$263$	−2.31315	−0.142635	−0.0713174	+	0.997454i	$0.522720\pi$
$264$	−2.57398	−0.158417
$265$	1.53890	0.0945336
$266$	0	0
$267$	−3.43107	−0.209978
$268$	−11.4561	−0.699790
$269$	2.81790	0.171810	0.0859051	−	0.996303i	$-0.472622\pi$
$269$	2.81790	0.171810	0.0859051	+	0.996303i	$0.472622\pi$
$270$	0.120615	0.00734038
$271$	−6.68954	−0.406361	−0.203180	−	0.979141i	$-0.565128\pi$
$271$	−6.68954	−0.406361	−0.203180	+	0.979141i	$0.565128\pi$
$272$	−0.467911	−0.0283713
$273$	3.49794	0.211705
$274$	12.3209	0.744332
$275$	−12.8324	−0.773825
$276$	5.55438	0.334334
$277$	8.25166	0.495794	0.247897	−	0.968786i	$-0.420261\pi$
$277$	8.25166	0.495794	0.247897	+	0.968786i	$0.420261\pi$
$278$	5.58853	0.335178
$279$	−5.34730	−0.320134
$280$	−0.517541	−0.0309290
$281$	−27.9368	−1.66657	−0.833284	−	0.552846i	$-0.813542\pi$
$281$	−27.9368	−1.66657	−0.833284	+	0.552846i	$0.813542\pi$
$282$	9.47565	0.564267
$283$	2.42602	0.144212	0.0721060	−	0.997397i	$-0.477028\pi$
$283$	2.42602	0.144212	0.0721060	+	0.997397i	$0.477028\pi$
$284$	−13.3327	−0.791153
$285$	0	0
$286$	2.09833	0.124077
$287$	16.4662	0.971966
$288$	−1.00000	−0.0589256
$289$	−16.7811	−0.987121
$290$	−0.283119	−0.0166253
$291$	−3.10101	−0.181785
$292$	2.28312	0.133609
$293$	14.1010	0.823790	0.411895	−	0.911231i	$-0.364867\pi$
$293$	14.1010	0.823790	0.411895	+	0.911231i	$0.364867\pi$
$294$	−11.4115	−0.665531
$295$	1.81521	0.105685
$296$	−8.51754	−0.495072
$297$	2.57398	0.149357
$298$	−11.0942	−0.642670
$299$	−4.52797	−0.261859
$300$	−4.98545	−0.287835
$301$	−40.0455	−2.30818
$302$	12.5963	0.724834
$303$	−16.7297	−0.961095
$304$	0	0
$305$	0.207081	0.0118574
$306$	0.467911	0.0267487
$307$	20.2071	1.15328	0.576640	−	0.816999i	$-0.304364\pi$
$307$	20.2071	1.15328	0.576640	+	0.816999i	$0.304364\pi$
$308$	−11.0446	−0.629323
$309$	10.3969	0.591460
$310$	−0.644963	−0.0366314
$311$	9.61856	0.545418	0.272709	−	0.962097i	$-0.412080\pi$
$311$	9.61856	0.545418	0.272709	+	0.962097i	$0.412080\pi$
$312$	0.815207	0.0461520
$313$	24.8881	1.40676	0.703378	−	0.710816i	$-0.251674\pi$
$313$	24.8881	1.40676	0.703378	+	0.710816i	$0.251674\pi$
$314$	3.97771	0.224475
$315$	0.517541	0.0291601
$316$	−4.85710	−0.273233
$317$	−17.2635	−0.969616	−0.484808	−	0.874621i	$-0.661110\pi$
$317$	−17.2635	−0.969616	−0.484808	+	0.874621i	$0.661110\pi$
$318$	12.7588	0.715476
$319$	−6.04189	−0.338281
$320$	−0.120615	−0.00674257
$321$	9.11381	0.508683
$322$	23.8331	1.32816
$323$	0	0
$324$	1.00000	0.0555556
$325$	4.06418	0.225440
$326$	−19.2003	−1.06340
$327$	−3.82976	−0.211786
$328$	3.83750	0.211890
$329$	40.6587	2.24159
$330$	0.310460	0.0170902
$331$	−9.99050	−0.549128	−0.274564	−	0.961569i	$-0.588533\pi$
$331$	−9.99050	−0.549128	−0.274564	+	0.961569i	$0.588533\pi$
$332$	3.24897	0.178310
$333$	8.51754	0.466758
$334$	−15.3746	−0.841263
$335$	1.38177	0.0754941
$336$	−4.29086	−0.234086
$337$	−6.76382	−0.368449	−0.184224	−	0.982884i	$-0.558977\pi$
$337$	−6.76382	−0.368449	−0.184224	+	0.982884i	$0.558977\pi$
$338$	12.3354	0.670959
$339$	−5.41147	−0.293911
$340$	0.0564370	0.00306073
$341$	−13.7638	−0.745353
$342$	0	0
$343$	−18.9290	−1.02207
$344$	−9.33275	−0.503188
$345$	−0.669940	−0.0360684
$346$	−6.59358	−0.354473
$347$	24.6013	1.32067	0.660334	−	0.750972i	$-0.270415\pi$
$347$	24.6013	1.32067	0.660334	+	0.750972i	$0.270415\pi$
$348$	−2.34730	−0.125828
$349$	−6.83481	−0.365859	−0.182929	−	0.983126i	$-0.558558\pi$
$349$	−6.83481	−0.365859	−0.182929	+	0.983126i	$0.558558\pi$
$350$	−21.3919	−1.14344
$351$	−0.815207	−0.0435126
$352$	−2.57398	−0.137193
$353$	−5.08378	−0.270582	−0.135291	−	0.990806i	$-0.543197\pi$
$353$	−5.08378	−0.270582	−0.135291	+	0.990806i	$0.543197\pi$
$354$	15.0496	0.799879
$355$	1.60813	0.0853505
$356$	−3.43107	−0.181847
$357$	2.00774	0.106261
$358$	1.24123	0.0656010
$359$	−2.86753	−0.151342	−0.0756711	−	0.997133i	$-0.524110\pi$
$359$	−2.86753	−0.151342	−0.0756711	+	0.997133i	$0.524110\pi$
$360$	0.120615	0.00635696
$361$	0	0
$362$	4.03003	0.211814
$363$	−4.37464	−0.229609
$364$	3.49794	0.183342
$365$	−0.275378	−0.0144139
$366$	1.71688	0.0897428
$367$	22.1429	1.15585	0.577925	−	0.816090i	$-0.303863\pi$
$367$	22.1429	1.15585	0.577925	+	0.816090i	$0.303863\pi$
$368$	5.55438	0.289542
$369$	−3.83750	−0.199772
$370$	1.02734	0.0534089
$371$	54.7461	2.84228
$372$	−5.34730	−0.277244
$373$	−17.6732	−0.915086	−0.457543	−	0.889188i	$-0.651270\pi$
$373$	−17.6732	−0.915086	−0.457543	+	0.889188i	$0.651270\pi$
$374$	1.20439	0.0622777
$375$	1.20439	0.0621946
$376$	9.47565	0.488669
$377$	1.91353	0.0985520
$378$	4.29086	0.220698
$379$	9.75970	0.501322	0.250661	−	0.968075i	$-0.419352\pi$
$379$	9.75970	0.501322	0.250661	+	0.968075i	$0.419352\pi$
$380$	0	0
$381$	−4.24123	−0.217285
$382$	24.0847	1.23228
$383$	22.3155	1.14027	0.570135	−	0.821551i	$-0.306891\pi$
$383$	22.3155	1.14027	0.570135	+	0.821551i	$0.306891\pi$
$384$	−1.00000	−0.0510310
$385$	1.33214	0.0678921
$386$	−9.85978	−0.501850
$387$	9.33275	0.474410
$388$	−3.10101	−0.157430
$389$	7.02229	0.356044	0.178022	−	0.984026i	$-0.443030\pi$
$389$	7.02229	0.356044	0.178022	+	0.984026i	$0.443030\pi$
$390$	−0.0983261	−0.00497893
$391$	−2.59896	−0.131435
$392$	−11.4115	−0.576366
$393$	21.0428	1.06147
$394$	6.45605	0.325251
$395$	0.585838	0.0294767
$396$	2.57398	0.129347
$397$	−19.9786	−1.00270	−0.501350	−	0.865245i	$-0.667163\pi$
$397$	−19.9786	−1.00270	−0.501350	+	0.865245i	$0.667163\pi$
$398$	−24.7716	−1.24169
$399$	0	0
$400$	−4.98545	−0.249273
$401$	1.18984	0.0594180	0.0297090	−	0.999559i	$-0.490542\pi$
$401$	1.18984	0.0594180	0.0297090	+	0.999559i	$0.490542\pi$
$402$	11.4561	0.571376
$403$	4.35916	0.217145
$404$	−16.7297	−0.832332
$405$	−0.120615	−0.00599340
$406$	−10.0719	−0.499861
$407$	21.9240	1.08673
$408$	0.467911	0.0231651
$409$	−9.48845	−0.469173	−0.234587	−	0.972095i	$-0.575374\pi$
$409$	−9.48845	−0.469173	−0.234587	+	0.972095i	$0.575374\pi$
$410$	−0.462859	−0.0228590
$411$	−12.3209	−0.607745
$412$	10.3969	0.512220
$413$	64.5758	3.17757
$414$	−5.55438	−0.272983
$415$	−0.391874	−0.0192363
$416$	0.815207	0.0399688
$417$	−5.58853	−0.273671
$418$	0	0
$419$	4.72638	0.230899	0.115449	−	0.993313i	$-0.463169\pi$
$419$	4.72638	0.230899	0.115449	+	0.993313i	$0.463169\pi$
$420$	0.517541	0.0252534
$421$	−1.38682	−0.0675895	−0.0337948	−	0.999429i	$-0.510759\pi$
$421$	−1.38682	−0.0675895	−0.0337948	+	0.999429i	$0.510759\pi$
$422$	−1.38413	−0.0673785
$423$	−9.47565	−0.460722
$424$	12.7588	0.619621
$425$	2.33275	0.113155
$426$	13.3327	0.645974
$427$	7.36690	0.356509
$428$	9.11381	0.440533
$429$	−2.09833	−0.101308
$430$	1.12567	0.0542845
$431$	−2.71183	−0.130624	−0.0653121	−	0.997865i	$-0.520804\pi$
$431$	−2.71183	−0.130624	−0.0653121	+	0.997865i	$0.520804\pi$
$432$	1.00000	0.0481125
$433$	20.2412	0.972731	0.486366	−	0.873755i	$-0.338322\pi$
$433$	20.2412	0.972731	0.486366	+	0.873755i	$0.338322\pi$
$434$	−22.9445	−1.10137
$435$	0.283119	0.0135745
$436$	−3.82976	−0.183412
$437$	0	0
$438$	−2.28312	−0.109092
$439$	18.2003	0.868652	0.434326	−	0.900756i	$-0.356987\pi$
$439$	18.2003	0.868652	0.434326	+	0.900756i	$0.356987\pi$
$440$	0.310460	0.0148006
$441$	11.4115	0.543404
$442$	−0.381445	−0.0181435
$443$	−35.7425	−1.69818	−0.849088	−	0.528252i	$-0.822848\pi$
$443$	−35.7425	−1.69818	−0.849088	+	0.528252i	$0.822848\pi$
$444$	8.51754	0.404225
$445$	0.413838	0.0196178
$446$	22.3131	1.05656
$447$	11.0942	0.524738
$448$	−4.29086	−0.202724
$449$	18.9905	0.896217	0.448109	−	0.893979i	$-0.352098\pi$
$449$	18.9905	0.896217	0.448109	+	0.893979i	$0.352098\pi$
$450$	4.98545	0.235016
$451$	−9.87763	−0.465119
$452$	−5.41147	−0.254534
$453$	−12.5963	−0.591824
$454$	−20.7665	−0.974621
$455$	−0.421903	−0.0197791
$456$	0	0
$457$	25.9632	1.21451	0.607253	−	0.794509i	$-0.292272\pi$
$457$	25.9632	1.21451	0.607253	+	0.794509i	$0.292272\pi$
$458$	−5.51754	−0.257818
$459$	−0.467911	−0.0218402
$460$	−0.669940	−0.0312361
$461$	−29.2344	−1.36158	−0.680791	−	0.732477i	$-0.738364\pi$
$461$	−29.2344	−1.36158	−0.680791	+	0.732477i	$0.738364\pi$
$462$	11.0446	0.513840
$463$	−21.1908	−0.984819	−0.492410	−	0.870364i	$-0.663884\pi$
$463$	−21.1908	−0.984819	−0.492410	+	0.870364i	$0.663884\pi$
$464$	−2.34730	−0.108970
$465$	0.644963	0.0299094
$466$	15.0865	0.698867
$467$	−2.14527	−0.0992711	−0.0496356	−	0.998767i	$-0.515806\pi$
$467$	−2.14527	−0.0992711	−0.0496356	+	0.998767i	$0.515806\pi$
$468$	−0.815207	−0.0376830
$469$	49.1563	2.26983
$470$	−1.14290	−0.0527182
$471$	−3.97771	−0.183283
$472$	15.0496	0.692715
$473$	24.0223	1.10455
$474$	4.85710	0.223094
$475$	0	0
$476$	2.00774	0.0920246
$477$	−12.7588	−0.584184
$478$	28.9513	1.32420
$479$	−3.39693	−0.155210	−0.0776048	−	0.996984i	$-0.524727\pi$
$479$	−3.39693	−0.155210	−0.0776048	+	0.996984i	$0.524727\pi$
$480$	0.120615	0.00550529
$481$	−6.94356	−0.316599
$482$	−19.3696	−0.882260
$483$	−23.8331	−1.08444
$484$	−4.37464	−0.198847
$485$	0.374028	0.0169837
$486$	−1.00000	−0.0453609
$487$	−19.7861	−0.896594	−0.448297	−	0.893885i	$-0.647969\pi$
$487$	−19.7861	−0.896594	−0.448297	+	0.893885i	$0.647969\pi$
$488$	1.71688	0.0777196
$489$	19.2003	0.868266
$490$	1.37639	0.0621791
$491$	25.1438	1.13473	0.567363	−	0.823468i	$-0.307964\pi$
$491$	25.1438	1.13473	0.567363	+	0.823468i	$0.307964\pi$
$492$	−3.83750	−0.173008
$493$	1.09833	0.0494661
$494$	0	0
$495$	−0.310460	−0.0139541
$496$	−5.34730	−0.240101
$497$	57.2089	2.56617
$498$	−3.24897	−0.145590
$499$	35.1584	1.57391	0.786953	−	0.617013i	$-0.211658\pi$
$499$	35.1584	1.57391	0.786953	+	0.617013i	$0.211658\pi$
$500$	1.20439	0.0538621
$501$	15.3746	0.686888
$502$	4.34224	0.193804
$503$	20.3455	0.907163	0.453581	−	0.891215i	$-0.350146\pi$
$503$	20.3455	0.907163	0.453581	+	0.891215i	$0.350146\pi$
$504$	4.29086	0.191130
$505$	2.01785	0.0897930
$506$	−14.2968	−0.635572
$507$	−12.3354	−0.547836
$508$	−4.24123	−0.188174
$509$	13.1652	0.583537	0.291768	−	0.956489i	$-0.405756\pi$
$509$	13.1652	0.583537	0.291768	+	0.956489i	$0.405756\pi$
$510$	−0.0564370	−0.00249907
$511$	−9.79654	−0.433373
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	17.7665	0.783647
$515$	−1.25402	−0.0552588
$516$	9.33275	0.410851
$517$	−24.3901	−1.07268
$518$	36.5476	1.60581
$519$	6.59358	0.289426
$520$	−0.0983261	−0.00431188
$521$	−20.4911	−0.897733	−0.448866	−	0.893599i	$-0.648172\pi$
$521$	−20.4911	−0.897733	−0.448866	+	0.893599i	$0.648172\pi$
$522$	2.34730	0.102738
$523$	42.9195	1.87674	0.938370	−	0.345633i	$-0.112336\pi$
$523$	42.9195	1.87674	0.938370	+	0.345633i	$0.112336\pi$
$524$	21.0428	0.919260
$525$	21.3919	0.933618
$526$	2.31315	0.100858
$527$	2.50206	0.108991
$528$	2.57398	0.112018
$529$	7.85111	0.341353
$530$	−1.53890	−0.0668454
$531$	−15.0496	−0.653098
$532$	0	0
$533$	3.12836	0.135504
$534$	3.43107	0.148477
$535$	−1.09926	−0.0475251
$536$	11.4561	0.494826
$537$	−1.24123	−0.0535630
$538$	−2.81790	−0.121488
$539$	29.3729	1.26518
$540$	−0.120615	−0.00519043
$541$	−14.5767	−0.626700	−0.313350	−	0.949638i	$-0.601451\pi$
$541$	−14.5767	−0.626700	−0.313350	+	0.949638i	$0.601451\pi$
$542$	6.68954	0.287340
$543$	−4.03003	−0.172945
$544$	0.467911	0.0200615
$545$	0.461925	0.0197867
$546$	−3.49794	−0.149698
$547$	−18.5689	−0.793950	−0.396975	−	0.917829i	$-0.629940\pi$
$547$	−18.5689	−0.793950	−0.396975	+	0.917829i	$0.629940\pi$
$548$	−12.3209	−0.526322
$549$	−1.71688	−0.0732747
$550$	12.8324	0.547177
$551$	0	0
$552$	−5.55438	−0.236410
$553$	20.8411	0.886254
$554$	−8.25166	−0.350579
$555$	−1.02734	−0.0436082
$556$	−5.58853	−0.237006
$557$	15.5381	0.658369	0.329185	−	0.944266i	$-0.393226\pi$
$557$	15.5381	0.658369	0.329185	+	0.944266i	$0.393226\pi$
$558$	5.34730	0.226369
$559$	−7.60813	−0.321789
$560$	0.517541	0.0218701
$561$	−1.20439	−0.0508495
$562$	27.9368	1.17844
$563$	12.1557	0.512302	0.256151	−	0.966637i	$-0.417546\pi$
$563$	12.1557	0.512302	0.256151	+	0.966637i	$0.417546\pi$
$564$	−9.47565	−0.398997
$565$	0.652704	0.0274594
$566$	−2.42602	−0.101973
$567$	−4.29086	−0.180199
$568$	13.3327	0.559430
$569$	−13.6709	−0.573113	−0.286556	−	0.958063i	$-0.592511\pi$
$569$	−13.6709	−0.573113	−0.286556	+	0.958063i	$0.592511\pi$
$570$	0	0
$571$	28.2003	1.18014	0.590072	−	0.807350i	$-0.299099\pi$
$571$	28.2003	1.18014	0.590072	+	0.807350i	$0.299099\pi$
$572$	−2.09833	−0.0877354
$573$	−24.0847	−1.00615
$574$	−16.4662	−0.687284
$575$	−27.6911	−1.15480
$576$	1.00000	0.0416667
$577$	20.2189	0.841726	0.420863	−	0.907124i	$-0.361727\pi$
$577$	20.2189	0.841726	0.420863	+	0.907124i	$0.361727\pi$
$578$	16.7811	0.698000
$579$	9.85978	0.409759
$580$	0.283119	0.0117559
$581$	−13.9409	−0.578365
$582$	3.10101	0.128541
$583$	−32.8408	−1.36013
$584$	−2.28312	−0.0944761
$585$	0.0983261	0.00406528
$586$	−14.1010	−0.582508
$587$	−5.20708	−0.214919	−0.107460	−	0.994209i	$-0.534272\pi$
$587$	−5.20708	−0.214919	−0.107460	+	0.994209i	$0.534272\pi$
$588$	11.4115	0.470601
$589$	0	0
$590$	−1.81521	−0.0747309
$591$	−6.45605	−0.265566
$592$	8.51754	0.350069
$593$	−43.5449	−1.78817	−0.894087	−	0.447893i	$-0.852174\pi$
$593$	−43.5449	−1.78817	−0.894087	+	0.447893i	$0.852174\pi$
$594$	−2.57398	−0.105612
$595$	−0.242163	−0.00992772
$596$	11.0942	0.454436
$597$	24.7716	1.01383
$598$	4.52797	0.185162
$599$	32.7246	1.33709	0.668546	−	0.743671i	$-0.266917\pi$
$599$	32.7246	1.33709	0.668546	+	0.743671i	$0.266917\pi$
$600$	4.98545	0.203530
$601$	20.7733	0.847361	0.423681	−	0.905812i	$-0.360738\pi$
$601$	20.7733	0.847361	0.423681	+	0.905812i	$0.360738\pi$
$602$	40.0455	1.63213
$603$	−11.4561	−0.466526
$604$	−12.5963	−0.512535
$605$	0.527646	0.0214519
$606$	16.7297	0.679597
$607$	23.0419	0.935241	0.467621	−	0.883929i	$-0.345111\pi$
$607$	23.0419	0.935241	0.467621	+	0.883929i	$0.345111\pi$
$608$	0	0
$609$	10.0719	0.408135
$610$	−0.207081	−0.00838447
$611$	7.72462	0.312505
$612$	−0.467911	−0.0189142
$613$	21.2003	0.856271	0.428136	−	0.903715i	$-0.359171\pi$
$613$	21.2003	0.856271	0.428136	+	0.903715i	$0.359171\pi$
$614$	−20.2071	−0.815491
$615$	0.462859	0.0186643
$616$	11.0446	0.444999
$617$	−20.4825	−0.824593	−0.412296	−	0.911050i	$-0.635273\pi$
$617$	−20.4825	−0.824593	−0.412296	+	0.911050i	$0.635273\pi$
$618$	−10.3969	−0.418226
$619$	−15.7452	−0.632851	−0.316426	−	0.948617i	$-0.602483\pi$
$619$	−15.7452	−0.632851	−0.316426	+	0.948617i	$0.602483\pi$
$620$	0.644963	0.0259023
$621$	5.55438	0.222889
$622$	−9.61856	−0.385669
$623$	14.7223	0.589835
$624$	−0.815207	−0.0326344
$625$	24.7820	0.991280
$626$	−24.8881	−0.994727
$627$	0	0
$628$	−3.97771	−0.158728
$629$	−3.98545	−0.158910
$630$	−0.517541	−0.0206193
$631$	−21.1530	−0.842088	−0.421044	−	0.907040i	$-0.638336\pi$
$631$	−21.1530	−0.842088	−0.421044	+	0.907040i	$0.638336\pi$
$632$	4.85710	0.193205
$633$	1.38413	0.0550143
$634$	17.2635	0.685622
$635$	0.511555	0.0203004
$636$	−12.7588	−0.505918
$637$	−9.30272	−0.368587
$638$	6.04189	0.239201
$639$	−13.3327	−0.527435
$640$	0.120615	0.00476772
$641$	−8.22668	−0.324934	−0.162467	−	0.986714i	$-0.551945\pi$
$641$	−8.22668	−0.324934	−0.162467	+	0.986714i	$0.551945\pi$
$642$	−9.11381	−0.359693
$643$	−4.27631	−0.168641	−0.0843206	−	0.996439i	$-0.526872\pi$
$643$	−4.27631	−0.168641	−0.0843206	+	0.996439i	$0.526872\pi$
$644$	−23.8331	−0.939154
$645$	−1.12567	−0.0443231
$646$	0	0
$647$	0.947682	0.0372572	0.0186286	−	0.999826i	$-0.494070\pi$
$647$	0.947682	0.0372572	0.0186286	+	0.999826i	$0.494070\pi$
$648$	−1.00000	−0.0392837
$649$	−38.7374	−1.52058
$650$	−4.06418	−0.159410
$651$	22.9445	0.899266
$652$	19.2003	0.751941
$653$	−32.8435	−1.28526	−0.642632	−	0.766175i	$-0.722158\pi$
$653$	−32.8435	−1.28526	−0.642632	+	0.766175i	$0.722158\pi$
$654$	3.82976	0.149755
$655$	−2.53807	−0.0991708
$656$	−3.83750	−0.149829
$657$	2.28312	0.0890729
$658$	−40.6587	−1.58504
$659$	−4.74422	−0.184809	−0.0924043	−	0.995722i	$-0.529455\pi$
$659$	−4.74422	−0.184809	−0.0924043	+	0.995722i	$0.529455\pi$
$660$	−0.310460	−0.0120846
$661$	−39.4056	−1.53270	−0.766350	−	0.642423i	$-0.777929\pi$
$661$	−39.4056	−1.53270	−0.766350	+	0.642423i	$0.777929\pi$
$662$	9.99050	0.388292
$663$	0.381445	0.0148141
$664$	−3.24897	−0.126085
$665$	0	0
$666$	−8.51754	−0.330048
$667$	−13.0378	−0.504824
$668$	15.3746	0.594863
$669$	−22.3131	−0.862676
$670$	−1.38177	−0.0533824
$671$	−4.41921	−0.170602
$672$	4.29086	0.165523
$673$	−17.1429	−0.660810	−0.330405	−	0.943839i	$-0.607185\pi$
$673$	−17.1429	−0.660810	−0.330405	+	0.943839i	$0.607185\pi$
$674$	6.76382	0.260533
$675$	−4.98545	−0.191890
$676$	−12.3354	−0.474440
$677$	−7.13011	−0.274032	−0.137016	−	0.990569i	$-0.543751\pi$
$677$	−7.13011	−0.274032	−0.137016	+	0.990569i	$0.543751\pi$
$678$	5.41147	0.207826
$679$	13.3060	0.510638
$680$	−0.0564370	−0.00216426
$681$	20.7665	0.795774
$682$	13.7638	0.527044
$683$	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
$685$	1.48608	0.0567802
$686$	18.9290	0.722713
$687$	5.51754	0.210507
$688$	9.33275	0.355808
$689$	10.4010	0.396248
$690$	0.669940	0.0255042
$691$	39.3715	1.49776	0.748880	−	0.662705i	$-0.230592\pi$
$691$	39.3715	1.49776	0.748880	+	0.662705i	$0.230592\pi$
$692$	6.59358	0.250650
$693$	−11.0446	−0.419549
$694$	−24.6013	−0.933853
$695$	0.674059	0.0255685
$696$	2.34730	0.0889740
$697$	1.79561	0.0680135
$698$	6.83481	0.258701
$699$	−15.0865	−0.570623
$700$	21.3919	0.808537
$701$	5.63404	0.212795	0.106397	−	0.994324i	$-0.466068\pi$
$701$	5.63404	0.212795	0.106397	+	0.994324i	$0.466068\pi$
$702$	0.815207	0.0307680
$703$	0	0
$704$	2.57398	0.0970104
$705$	1.14290	0.0430442
$706$	5.08378	0.191331
$707$	71.7847	2.69974
$708$	−15.0496	−0.565600
$709$	30.6664	1.15170	0.575851	−	0.817555i	$-0.304671\pi$
$709$	30.6664	1.15170	0.575851	+	0.817555i	$0.304671\pi$
$710$	−1.60813	−0.0603519
$711$	−4.85710	−0.182155
$712$	3.43107	0.128585
$713$	−29.7009	−1.11231
$714$	−2.00774	−0.0751378
$715$	0.253089	0.00946500
$716$	−1.24123	−0.0463869
$717$	−28.9513	−1.08121
$718$	2.86753	0.107015
$719$	6.33956	0.236426	0.118213	−	0.992988i	$-0.462284\pi$
$719$	6.33956	0.236426	0.118213	+	0.992988i	$0.462284\pi$
$720$	−0.120615	−0.00449505
$721$	−44.6117	−1.66143
$722$	0	0
$723$	19.3696	0.720363
$724$	−4.03003	−0.149775
$725$	11.7023	0.434614
$726$	4.37464	0.162358
$727$	−23.3414	−0.865685	−0.432843	−	0.901469i	$-0.642489\pi$
$727$	−23.3414	−0.865685	−0.432843	+	0.901469i	$0.642489\pi$
$728$	−3.49794	−0.129642
$729$	1.00000	0.0370370
$730$	0.275378	0.0101922
$731$	−4.36690	−0.161516
$732$	−1.71688	−0.0634578
$733$	1.58946	0.0587080	0.0293540	−	0.999569i	$-0.490655\pi$
$733$	1.58946	0.0587080	0.0293540	+	0.999569i	$0.490655\pi$
$734$	−22.1429	−0.817309
$735$	−1.37639	−0.0507690
$736$	−5.55438	−0.204737
$737$	−29.4876	−1.08619
$738$	3.83750	0.141260
$739$	3.65951	0.134617	0.0673086	−	0.997732i	$-0.478559\pi$
$739$	3.65951	0.134617	0.0673086	+	0.997732i	$0.478559\pi$
$740$	−1.02734	−0.0377658
$741$	0	0
$742$	−54.7461	−2.00979
$743$	18.3800	0.674297	0.337149	−	0.941451i	$-0.390537\pi$
$743$	18.3800	0.674297	0.337149	+	0.941451i	$0.390537\pi$
$744$	5.34730	0.196041
$745$	−1.33813	−0.0490251
$746$	17.6732	0.647063
$747$	3.24897	0.118874
$748$	−1.20439	−0.0440370
$749$	−39.1061	−1.42890
$750$	−1.20439	−0.0439782
$751$	−30.6655	−1.11900	−0.559500	−	0.828830i	$-0.689007\pi$
$751$	−30.6655	−1.11900	−0.559500	+	0.828830i	$0.689007\pi$
$752$	−9.47565	−0.345541
$753$	−4.34224	−0.158240
$754$	−1.91353	−0.0696868
$755$	1.51930	0.0552928
$756$	−4.29086	−0.156057
$757$	−7.78787	−0.283055	−0.141527	−	0.989934i	$-0.545201\pi$
$757$	−7.78787	−0.283055	−0.141527	+	0.989934i	$0.545201\pi$
$758$	−9.75970	−0.354488
$759$	14.2968	0.518943
$760$	0	0
$761$	28.3969	1.02939	0.514694	−	0.857374i	$-0.327906\pi$
$761$	28.3969	1.02939	0.514694	+	0.857374i	$0.327906\pi$
$762$	4.24123	0.153644
$763$	16.4329	0.594912
$764$	−24.0847	−0.871354
$765$	0.0564370	0.00204048
$766$	−22.3155	−0.806292
$767$	12.2686	0.442992
$768$	1.00000	0.0360844
$769$	35.2344	1.27059	0.635293	−	0.772271i	$-0.280879\pi$
$769$	35.2344	1.27059	0.635293	+	0.772271i	$0.280879\pi$
$770$	−1.33214	−0.0480070
$771$	−17.7665	−0.639845
$772$	9.85978	0.354861
$773$	20.1034	0.723068	0.361534	−	0.932359i	$-0.382253\pi$
$773$	20.1034	0.723068	0.361534	+	0.932359i	$0.382253\pi$
$774$	−9.33275	−0.335459
$775$	26.6587	0.957608
$776$	3.10101	0.111320
$777$	−36.5476	−1.31114
$778$	−7.02229	−0.251761
$779$	0	0
$780$	0.0983261	0.00352064
$781$	−34.3182	−1.22800
$782$	2.59896	0.0929384
$783$	−2.34730	−0.0838855
$784$	11.4115	0.407553
$785$	0.479771	0.0171238
$786$	−21.0428	−0.750573
$787$	23.8530	0.850267	0.425133	−	0.905131i	$-0.360227\pi$
$787$	23.8530	0.850267	0.425133	+	0.905131i	$0.360227\pi$
$788$	−6.45605	−0.229987
$789$	−2.31315	−0.0823503
$790$	−0.585838	−0.0208432
$791$	23.2199	0.825604
$792$	−2.57398	−0.0914623
$793$	1.39961	0.0497018
$794$	19.9786	0.709016
$795$	1.53890	0.0545790
$796$	24.7716	0.878005
$797$	28.5262	1.01045	0.505225	−	0.862988i	$-0.331409\pi$
$797$	28.5262	1.01045	0.505225	+	0.862988i	$0.331409\pi$
$798$	0	0
$799$	4.43376	0.156855
$800$	4.98545	0.176262
$801$	−3.43107	−0.121231
$802$	−1.18984	−0.0420149
$803$	5.87670	0.207384
$804$	−11.4561	−0.404024
$805$	2.87462	0.101317
$806$	−4.35916	−0.153545
$807$	2.81790	0.0991946
$808$	16.7297	0.588548
$809$	24.9290	0.876457	0.438229	−	0.898863i	$-0.355606\pi$
$809$	24.9290	0.876457	0.438229	+	0.898863i	$0.355606\pi$
$810$	0.120615	0.00423797
$811$	−18.5243	−0.650478	−0.325239	−	0.945632i	$-0.605445\pi$
$811$	−18.5243	−0.650478	−0.325239	+	0.945632i	$0.605445\pi$
$812$	10.0719	0.353455
$813$	−6.68954	−0.234612
$814$	−21.9240	−0.768434
$815$	−2.31584	−0.0811202
$816$	−0.467911	−0.0163802
$817$	0	0
$818$	9.48845	0.331756
$819$	3.49794	0.122228
$820$	0.462859	0.0161637
$821$	35.5613	1.24110	0.620549	−	0.784168i	$-0.286910\pi$
$821$	35.5613	1.24110	0.620549	+	0.784168i	$0.286910\pi$
$822$	12.3209	0.429740
$823$	−18.4953	−0.644704	−0.322352	−	0.946620i	$-0.604473\pi$
$823$	−18.4953	−0.644704	−0.322352	+	0.946620i	$0.604473\pi$
$824$	−10.3969	−0.362194
$825$	−12.8324	−0.446768
$826$	−64.5758	−2.24688
$827$	−31.5945	−1.09865	−0.549324	−	0.835609i	$-0.685115\pi$
$827$	−31.5945	−1.09865	−0.549324	+	0.835609i	$0.685115\pi$
$828$	5.55438	0.193028
$829$	41.1438	1.42898	0.714492	−	0.699643i	$-0.246658\pi$
$829$	41.1438	1.42898	0.714492	+	0.699643i	$0.246658\pi$
$830$	0.391874	0.0136021
$831$	8.25166	0.286247
$832$	−0.815207	−0.0282622
$833$	−5.33956	−0.185005
$834$	5.58853	0.193515
$835$	−1.85441	−0.0641744
$836$	0	0
$837$	−5.34730	−0.184830
$838$	−4.72638	−0.163270
$839$	−19.9804	−0.689800	−0.344900	−	0.938639i	$-0.612087\pi$
$839$	−19.9804	−0.689800	−0.344900	+	0.938639i	$0.612087\pi$
$840$	−0.517541	−0.0178569
$841$	−23.4902	−0.810007
$842$	1.38682	0.0477930
$843$	−27.9368	−0.962193
$844$	1.38413	0.0476438
$845$	1.48784	0.0511831
$846$	9.47565	0.325780
$847$	18.7710	0.644978
$848$	−12.7588	−0.438138
$849$	2.42602	0.0832609
$850$	−2.33275	−0.0800126
$851$	47.3096	1.62175
$852$	−13.3327	−0.456772
$853$	−18.9358	−0.648350	−0.324175	−	0.945997i	$-0.605087\pi$
$853$	−18.9358	−0.648350	−0.324175	+	0.945997i	$0.605087\pi$
$854$	−7.36690	−0.252090
$855$	0	0
$856$	−9.11381	−0.311504
$857$	21.3402	0.728966	0.364483	−	0.931210i	$-0.381246\pi$
$857$	21.3402	0.728966	0.364483	+	0.931210i	$0.381246\pi$
$858$	2.09833	0.0716357
$859$	45.8367	1.56393	0.781964	−	0.623324i	$-0.214218\pi$
$859$	45.8367	1.56393	0.781964	+	0.623324i	$0.214218\pi$
$860$	−1.12567	−0.0383849
$861$	16.4662	0.561165
$862$	2.71183	0.0923653
$863$	−15.2594	−0.519436	−0.259718	−	0.965685i	$-0.583630\pi$
$863$	−15.2594	−0.519436	−0.259718	+	0.965685i	$0.583630\pi$
$864$	−1.00000	−0.0340207
$865$	−0.795283	−0.0270404
$866$	−20.2412	−0.687825
$867$	−16.7811	−0.569915
$868$	22.9445	0.778787
$869$	−12.5021	−0.424103
$870$	−0.283119	−0.00959862
$871$	9.33906	0.316442
$872$	3.82976	0.129692
$873$	−3.10101	−0.104953
$874$	0	0
$875$	−5.16788	−0.174706
$876$	2.28312	0.0771394
$877$	−22.3806	−0.755740	−0.377870	−	0.925859i	$-0.623343\pi$
$877$	−22.3806	−0.755740	−0.377870	+	0.925859i	$0.623343\pi$
$878$	−18.2003	−0.614229
$879$	14.1010	0.475615
$880$	−0.310460	−0.0104656
$881$	−27.0104	−0.910004	−0.455002	−	0.890490i	$-0.650362\pi$
$881$	−27.0104	−0.910004	−0.455002	+	0.890490i	$0.650362\pi$
$882$	−11.4115	−0.384244
$883$	17.4142	0.586033	0.293017	−	0.956107i	$-0.405341\pi$
$883$	17.4142	0.586033	0.293017	+	0.956107i	$0.405341\pi$
$884$	0.381445	0.0128294
$885$	1.81521	0.0610175
$886$	35.7425	1.20079
$887$	−58.5768	−1.96682	−0.983408	−	0.181408i	$-0.941934\pi$
$887$	−58.5768	−1.96682	−0.983408	+	0.181408i	$0.941934\pi$
$888$	−8.51754	−0.285830
$889$	18.1985	0.610359
$890$	−0.413838	−0.0138719
$891$	2.57398	0.0862315
$892$	−22.3131	−0.747099
$893$	0	0
$894$	−11.0942	−0.371046
$895$	0.149711	0.00500427
$896$	4.29086	0.143348
$897$	−4.52797	−0.151185
$898$	−18.9905	−0.633721
$899$	12.5517	0.418622
$900$	−4.98545	−0.166182
$901$	5.96997	0.198889
$902$	9.87763	0.328889
$903$	−40.0455	−1.33263
$904$	5.41147	0.179983
$905$	0.486081	0.0161579
$906$	12.5963	0.418483
$907$	9.86753	0.327646	0.163823	−	0.986490i	$-0.447617\pi$
$907$	9.86753	0.327646	0.163823	+	0.986490i	$0.447617\pi$
$908$	20.7665	0.689161
$909$	−16.7297	−0.554888
$910$	0.421903	0.0139860
$911$	13.9813	0.463222	0.231611	−	0.972808i	$-0.425600\pi$
$911$	13.9813	0.463222	0.231611	+	0.972808i	$0.425600\pi$
$912$	0	0
$913$	8.36278	0.276768
$914$	−25.9632	−0.858785
$915$	0.207081	0.00684589
$916$	5.51754	0.182305
$917$	−90.2918	−2.98170
$918$	0.467911	0.0154434
$919$	−12.7246	−0.419747	−0.209873	−	0.977729i	$-0.567305\pi$
$919$	−12.7246	−0.419747	−0.209873	+	0.977729i	$0.567305\pi$
$920$	0.669940	0.0220873
$921$	20.2071	0.665846
$922$	29.2344	0.962784
$923$	10.8690	0.357756
$924$	−11.0446	−0.363340
$925$	−42.4638	−1.39620
$926$	21.1908	0.696372
$927$	10.3969	0.341480
$928$	2.34730	0.0770538
$929$	20.9463	0.687224	0.343612	−	0.939112i	$-0.388349\pi$
$929$	20.9463	0.687224	0.343612	+	0.939112i	$0.388349\pi$
$930$	−0.644963	−0.0211492
$931$	0	0
$932$	−15.0865	−0.494174
$933$	9.61856	0.314897
$934$	2.14527	0.0701953
$935$	0.145268	0.00475076
$936$	0.815207	0.0266459
$937$	−9.72462	−0.317690	−0.158845	−	0.987304i	$-0.550777\pi$
$937$	−9.72462	−0.317690	−0.158845	+	0.987304i	$0.550777\pi$
$938$	−49.1563	−1.60501
$939$	24.8881	0.812191
$940$	1.14290	0.0372774
$941$	23.1857	0.755833	0.377917	−	0.925840i	$-0.376641\pi$
$941$	23.1857	0.755833	0.377917	+	0.925840i	$0.376641\pi$
$942$	3.97771	0.129601
$943$	−21.3149	−0.694109
$944$	−15.0496	−0.489824
$945$	0.517541	0.0168356
$946$	−24.0223	−0.781032
$947$	27.5212	0.894318	0.447159	−	0.894455i	$-0.352436\pi$
$947$	27.5212	0.894318	0.447159	+	0.894455i	$0.352436\pi$
$948$	−4.85710	−0.157751
$949$	−1.86122	−0.0604176
$950$	0	0
$951$	−17.2635	−0.559808
$952$	−2.00774	−0.0650713
$953$	−50.4243	−1.63340	−0.816701	−	0.577061i	$-0.804200\pi$
$953$	−50.4243	−1.63340	−0.816701	+	0.577061i	$0.804200\pi$
$954$	12.7588	0.413080
$955$	2.90497	0.0940027
$956$	−28.9513	−0.936352
$957$	−6.04189	−0.195307
$958$	3.39693	0.109750
$959$	52.8672	1.70717
$960$	−0.120615	−0.00389282
$961$	−2.40642	−0.0776265
$962$	6.94356	0.223869
$963$	9.11381	0.293688
$964$	19.3696	0.623852
$965$	−1.18924	−0.0382828
$966$	23.8331	0.766816
$967$	31.8640	1.02468	0.512339	−	0.858783i	$-0.328779\pi$
$967$	31.8640	1.02468	0.512339	+	0.858783i	$0.328779\pi$
$968$	4.37464	0.140606
$969$	0	0
$970$	−0.374028	−0.0120093
$971$	2.24123	0.0719245	0.0359622	−	0.999353i	$-0.488550\pi$
$971$	2.24123	0.0719245	0.0359622	+	0.999353i	$0.488550\pi$
$972$	1.00000	0.0320750
$973$	23.9796	0.768750
$974$	19.7861	0.633988
$975$	4.06418	0.130158
$976$	−1.71688	−0.0549560
$977$	1.46791	0.0469626	0.0234813	−	0.999724i	$-0.492525\pi$
$977$	1.46791	0.0469626	0.0234813	+	0.999724i	$0.492525\pi$
$978$	−19.2003	−0.613957
$979$	−8.83151	−0.282256
$980$	−1.37639	−0.0439672
$981$	−3.82976	−0.122275
$982$	−25.1438	−0.802372
$983$	−30.0188	−0.957450	−0.478725	−	0.877965i	$-0.658901\pi$
$983$	−30.0188	−0.957450	−0.478725	+	0.877965i	$0.658901\pi$
$984$	3.83750	0.122335
$985$	0.778695	0.0248113
$986$	−1.09833	−0.0349778
$987$	40.6587	1.29418
$988$	0	0
$989$	51.8376	1.64834
$990$	0.310460	0.00986706
$991$	−54.7351	−1.73872	−0.869358	−	0.494183i	$-0.835467\pi$
$991$	−54.7351	−1.73872	−0.869358	+	0.494183i	$0.835467\pi$
$992$	5.34730	0.169777
$993$	−9.99050	−0.317039
$994$	−57.2089	−1.81456
$995$	−2.98782	−0.0947201
$996$	3.24897	0.102948
$997$	−48.6219	−1.53987	−0.769935	−	0.638123i	$-0.779711\pi$
$997$	−48.6219	−1.53987	−0.769935	+	0.638123i	$0.779711\pi$
$998$	−35.1584	−1.11292
$999$	8.51754	0.269483

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.120615 q^{5} -1.00000 q^{6} -4.29086 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.120615 q^{5} -1.00000 q^{6} -4.29086 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.120615 q^{10} +2.57398 q^{11} +1.00000 q^{12} -0.815207 q^{13} +4.29086 q^{14} -0.120615 q^{15} +1.00000 q^{16} -0.467911 q^{17} -1.00000 q^{18} -0.120615 q^{20} -4.29086 q^{21} -2.57398 q^{22} +5.55438 q^{23} -1.00000 q^{24} -4.98545 q^{25} +0.815207 q^{26} +1.00000 q^{27} -4.29086 q^{28} -2.34730 q^{29} +0.120615 q^{30} -5.34730 q^{31} -1.00000 q^{32} +2.57398 q^{33} +0.467911 q^{34} +0.517541 q^{35} +1.00000 q^{36} +8.51754 q^{37} -0.815207 q^{39} +0.120615 q^{40} -3.83750 q^{41} +4.29086 q^{42} +9.33275 q^{43} +2.57398 q^{44} -0.120615 q^{45} -5.55438 q^{46} -9.47565 q^{47} +1.00000 q^{48} +11.4115 q^{49} +4.98545 q^{50} -0.467911 q^{51} -0.815207 q^{52} -12.7588 q^{53} -1.00000 q^{54} -0.310460 q^{55} +4.29086 q^{56} +2.34730 q^{58} -15.0496 q^{59} -0.120615 q^{60} -1.71688 q^{61} +5.34730 q^{62} -4.29086 q^{63} +1.00000 q^{64} +0.0983261 q^{65} -2.57398 q^{66} -11.4561 q^{67} -0.467911 q^{68} +5.55438 q^{69} -0.517541 q^{70} -13.3327 q^{71} -1.00000 q^{72} +2.28312 q^{73} -8.51754 q^{74} -4.98545 q^{75} -11.0446 q^{77} +0.815207 q^{78} -4.85710 q^{79} -0.120615 q^{80} +1.00000 q^{81} +3.83750 q^{82} +3.24897 q^{83} -4.29086 q^{84} +0.0564370 q^{85} -9.33275 q^{86} -2.34730 q^{87} -2.57398 q^{88} -3.43107 q^{89} +0.120615 q^{90} +3.49794 q^{91} +5.55438 q^{92} -5.34730 q^{93} +9.47565 q^{94} -1.00000 q^{96} -3.10101 q^{97} -11.4115 q^{98} +2.57398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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