LMFDB - Embedded newform 2166.2.a.t.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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.65270 q^{5} +1.00000 q^{6} +0.184793 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.65270 q^{5} +1.00000 q^{6} +0.184793 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.65270 q^{10} -4.34730 q^{11} +1.00000 q^{12} -6.47565 q^{13} +0.184793 q^{14} -1.65270 q^{15} +1.00000 q^{16} -2.12061 q^{17} +1.00000 q^{18} -1.65270 q^{20} +0.184793 q^{21} -4.34730 q^{22} +0.106067 q^{23} +1.00000 q^{24} -2.26857 q^{25} -6.47565 q^{26} +1.00000 q^{27} +0.184793 q^{28} +3.98545 q^{29} -1.65270 q^{30} -3.22668 q^{31} +1.00000 q^{32} -4.34730 q^{33} -2.12061 q^{34} -0.305407 q^{35} +1.00000 q^{36} +4.06418 q^{37} -6.47565 q^{39} -1.65270 q^{40} -8.63816 q^{41} +0.184793 q^{42} +0.0418891 q^{43} -4.34730 q^{44} -1.65270 q^{45} +0.106067 q^{46} -7.92127 q^{47} +1.00000 q^{48} -6.96585 q^{49} -2.26857 q^{50} -2.12061 q^{51} -6.47565 q^{52} -9.21213 q^{53} +1.00000 q^{54} +7.18479 q^{55} +0.184793 q^{56} +3.98545 q^{58} +10.0915 q^{59} -1.65270 q^{60} +3.59627 q^{61} -3.22668 q^{62} +0.184793 q^{63} +1.00000 q^{64} +10.7023 q^{65} -4.34730 q^{66} -7.98545 q^{67} -2.12061 q^{68} +0.106067 q^{69} -0.305407 q^{70} -4.04189 q^{71} +1.00000 q^{72} +15.1976 q^{73} +4.06418 q^{74} -2.26857 q^{75} -0.803348 q^{77} -6.47565 q^{78} +12.3969 q^{79} -1.65270 q^{80} +1.00000 q^{81} -8.63816 q^{82} +8.45605 q^{83} +0.184793 q^{84} +3.50475 q^{85} +0.0418891 q^{86} +3.98545 q^{87} -4.34730 q^{88} -17.9368 q^{89} -1.65270 q^{90} -1.19665 q^{91} +0.106067 q^{92} -3.22668 q^{93} -7.92127 q^{94} +1.00000 q^{96} +10.6878 q^{97} -6.96585 q^{98} -4.34730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 6 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 6 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 6 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 6 q^{10} - 12 q^{11} + 3 q^{12} - 3 q^{14} - 6 q^{15} + 3 q^{16} - 12 q^{17} + 3 q^{18} - 6 q^{20} - 3 q^{21} - 12 q^{22} - 12 q^{23} + 3 q^{24} + 3 q^{25} + 3 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{30} - 3 q^{31} + 3 q^{32} - 12 q^{33} - 12 q^{34} - 3 q^{35} + 3 q^{36} + 3 q^{37} - 6 q^{40} - 9 q^{41} - 3 q^{42} - 3 q^{43} - 12 q^{44} - 6 q^{45} - 12 q^{46} - 15 q^{47} + 3 q^{48} + 3 q^{50} - 12 q^{51} - 3 q^{53} + 3 q^{54} + 18 q^{55} - 3 q^{56} - 6 q^{58} - 6 q^{60} - 3 q^{61} - 3 q^{62} - 3 q^{63} + 3 q^{64} + 6 q^{65} - 12 q^{66} - 6 q^{67} - 12 q^{68} - 12 q^{69} - 3 q^{70} - 9 q^{71} + 3 q^{72} + 3 q^{73} + 3 q^{74} + 3 q^{75} + 21 q^{77} + 9 q^{79} - 6 q^{80} + 3 q^{81} - 9 q^{82} + 3 q^{83} - 3 q^{84} + 27 q^{85} - 3 q^{86} - 6 q^{87} - 12 q^{88} + 3 q^{89} - 6 q^{90} - 27 q^{91} - 12 q^{92} - 3 q^{93} - 15 q^{94} + 3 q^{96} - 12 q^{97} - 12 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 6 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 6 * q^10 - 12 * q^11 + 3 * q^12 - 3 * q^14 - 6 * q^15 + 3 * q^16 - 12 * q^17 + 3 * q^18 - 6 * q^20 - 3 * q^21 - 12 * q^22 - 12 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 - 3 * q^28 - 6 * q^29 - 6 * q^30 - 3 * q^31 + 3 * q^32 - 12 * q^33 - 12 * q^34 - 3 * q^35 + 3 * q^36 + 3 * q^37 - 6 * q^40 - 9 * q^41 - 3 * q^42 - 3 * q^43 - 12 * q^44 - 6 * q^45 - 12 * q^46 - 15 * q^47 + 3 * q^48 + 3 * q^50 - 12 * q^51 - 3 * q^53 + 3 * q^54 + 18 * q^55 - 3 * q^56 - 6 * q^58 - 6 * q^60 - 3 * q^61 - 3 * q^62 - 3 * q^63 + 3 * q^64 + 6 * q^65 - 12 * q^66 - 6 * q^67 - 12 * q^68 - 12 * q^69 - 3 * q^70 - 9 * q^71 + 3 * q^72 + 3 * q^73 + 3 * q^74 + 3 * q^75 + 21 * q^77 + 9 * q^79 - 6 * q^80 + 3 * q^81 - 9 * q^82 + 3 * q^83 - 3 * q^84 + 27 * q^85 - 3 * q^86 - 6 * q^87 - 12 * q^88 + 3 * q^89 - 6 * q^90 - 27 * q^91 - 12 * q^92 - 3 * q^93 - 15 * q^94 + 3 * q^96 - 12 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.65270	−0.739112	−0.369556	−	0.929209i	$-0.620490\pi$
$5$	−1.65270	−0.739112	−0.369556	+	0.929209i	$0.620490\pi$
$6$	1.00000	0.408248
$7$	0.184793	0.0698450	0.0349225	−	0.999390i	$-0.488882\pi$
$7$	0.184793	0.0698450	0.0349225	+	0.999390i	$0.488882\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.65270	−0.522631
$11$	−4.34730	−1.31076	−0.655380	−	0.755300i	$-0.727491\pi$
$11$	−4.34730	−1.31076	−0.655380	+	0.755300i	$0.727491\pi$
$12$	1.00000	0.288675
$13$	−6.47565	−1.79602	−0.898011	−	0.439972i	$-0.854988\pi$
$13$	−6.47565	−1.79602	−0.898011	+	0.439972i	$0.854988\pi$
$14$	0.184793	0.0493879
$15$	−1.65270	−0.426726
$16$	1.00000	0.250000
$17$	−2.12061	−0.514325	−0.257162	−	0.966368i	$-0.582788\pi$
$17$	−2.12061	−0.514325	−0.257162	+	0.966368i	$0.582788\pi$
$18$	1.00000	0.235702
$19$	0	0
$19$	0	0
$20$	−1.65270	−0.369556
$21$	0.184793	0.0403250
$22$	−4.34730	−0.926847
$23$	0.106067	0.0221165	0.0110582	−	0.999939i	$-0.496480\pi$
$23$	0.106067	0.0221165	0.0110582	+	0.999939i	$0.496480\pi$
$24$	1.00000	0.204124
$25$	−2.26857	−0.453714
$26$	−6.47565	−1.26998
$27$	1.00000	0.192450
$28$	0.184793	0.0349225
$29$	3.98545	0.740080	0.370040	−	0.929016i	$-0.379344\pi$
$29$	3.98545	0.740080	0.370040	+	0.929016i	$0.379344\pi$
$30$	−1.65270	−0.301741
$31$	−3.22668	−0.579529	−0.289765	−	0.957098i	$-0.593577\pi$
$31$	−3.22668	−0.579529	−0.289765	+	0.957098i	$0.593577\pi$
$32$	1.00000	0.176777
$33$	−4.34730	−0.756767
$34$	−2.12061	−0.363682
$35$	−0.305407	−0.0516233
$36$	1.00000	0.166667
$37$	4.06418	0.668147	0.334073	−	0.942547i	$-0.391577\pi$
$37$	4.06418	0.668147	0.334073	+	0.942547i	$0.391577\pi$
$38$	0	0
$39$	−6.47565	−1.03693
$40$	−1.65270	−0.261315
$41$	−8.63816	−1.34905	−0.674527	−	0.738251i	$-0.735652\pi$
$41$	−8.63816	−1.34905	−0.674527	+	0.738251i	$0.735652\pi$
$42$	0.184793	0.0285141
$43$	0.0418891	0.00638802	0.00319401	−	0.999995i	$-0.498983\pi$
$43$	0.0418891	0.00638802	0.00319401	+	0.999995i	$0.498983\pi$
$44$	−4.34730	−0.655380
$45$	−1.65270	−0.246371
$46$	0.106067	0.0156387
$47$	−7.92127	−1.15544	−0.577718	−	0.816236i	$-0.696057\pi$
$47$	−7.92127	−1.15544	−0.577718	+	0.816236i	$0.696057\pi$
$48$	1.00000	0.144338
$49$	−6.96585	−0.995122
$50$	−2.26857	−0.320824
$51$	−2.12061	−0.296945
$52$	−6.47565	−0.898011
$53$	−9.21213	−1.26538	−0.632692	−	0.774404i	$-0.718050\pi$
$53$	−9.21213	−1.26538	−0.632692	+	0.774404i	$0.718050\pi$
$54$	1.00000	0.136083
$55$	7.18479	0.968797
$56$	0.184793	0.0246939
$57$	0	0
$58$	3.98545	0.523315
$59$	10.0915	1.31380	0.656902	−	0.753976i	$-0.271867\pi$
$59$	10.0915	1.31380	0.656902	+	0.753976i	$0.271867\pi$
$60$	−1.65270	−0.213363
$61$	3.59627	0.460455	0.230227	−	0.973137i	$-0.426053\pi$
$61$	3.59627	0.460455	0.230227	+	0.973137i	$0.426053\pi$
$62$	−3.22668	−0.409789
$63$	0.184793	0.0232817
$64$	1.00000	0.125000
$65$	10.7023	1.32746
$66$	−4.34730	−0.535115
$67$	−7.98545	−0.975578	−0.487789	−	0.872961i	$-0.662197\pi$
$67$	−7.98545	−0.975578	−0.487789	+	0.872961i	$0.662197\pi$
$68$	−2.12061	−0.257162
$69$	0.106067	0.0127689
$70$	−0.305407	−0.0365032
$71$	−4.04189	−0.479684	−0.239842	−	0.970812i	$-0.577096\pi$
$71$	−4.04189	−0.479684	−0.239842	+	0.970812i	$0.577096\pi$
$72$	1.00000	0.117851
$73$	15.1976	1.77874	0.889371	−	0.457185i	$-0.151142\pi$
$73$	15.1976	1.77874	0.889371	+	0.457185i	$0.151142\pi$
$74$	4.06418	0.472451
$75$	−2.26857	−0.261952
$76$	0	0
$77$	−0.803348	−0.0915500
$78$	−6.47565	−0.733223
$79$	12.3969	1.39476	0.697382	−	0.716700i	$-0.254348\pi$
$79$	12.3969	1.39476	0.697382	+	0.716700i	$0.254348\pi$
$80$	−1.65270	−0.184778
$81$	1.00000	0.111111
$82$	−8.63816	−0.953925
$83$	8.45605	0.928172	0.464086	−	0.885790i	$-0.346383\pi$
$83$	8.45605	0.928172	0.464086	+	0.885790i	$0.346383\pi$
$84$	0.184793	0.0201625
$85$	3.50475	0.380143
$86$	0.0418891	0.00451701
$87$	3.98545	0.427285
$88$	−4.34730	−0.463423
$89$	−17.9368	−1.90129	−0.950646	−	0.310277i	$-0.899578\pi$
$89$	−17.9368	−1.90129	−0.950646	+	0.310277i	$0.899578\pi$
$90$	−1.65270	−0.174210
$91$	−1.19665	−0.125443
$92$	0.106067	0.0110582
$93$	−3.22668	−0.334591
$94$	−7.92127	−0.817017
$95$	0	0
$96$	1.00000	0.102062
$97$	10.6878	1.08518	0.542590	−	0.839998i	$-0.317444\pi$
$97$	10.6878	1.08518	0.542590	+	0.839998i	$0.317444\pi$
$98$	−6.96585	−0.703657
$99$	−4.34730	−0.436920
$100$	−2.26857	−0.226857
$101$	8.06418	0.802416	0.401208	−	0.915987i	$-0.368591\pi$
$101$	8.06418	0.802416	0.401208	+	0.915987i	$0.368591\pi$
$102$	−2.12061	−0.209972
$103$	17.9290	1.76660	0.883299	−	0.468810i	$-0.155317\pi$
$103$	17.9290	1.76660	0.883299	+	0.468810i	$0.155317\pi$
$104$	−6.47565	−0.634990
$105$	−0.305407	−0.0298047
$106$	−9.21213	−0.894762
$107$	−13.9881	−1.35228	−0.676142	−	0.736771i	$-0.736350\pi$
$107$	−13.9881	−1.35228	−0.676142	+	0.736771i	$0.736350\pi$
$108$	1.00000	0.0962250
$109$	−4.77332	−0.457201	−0.228600	−	0.973520i	$-0.573415\pi$
$109$	−4.77332	−0.457201	−0.228600	+	0.973520i	$0.573415\pi$
$110$	7.18479	0.685043
$111$	4.06418	0.385755
$112$	0.184793	0.0174613
$113$	−0.753718	−0.0709038	−0.0354519	−	0.999371i	$-0.511287\pi$
$113$	−0.753718	−0.0709038	−0.0354519	+	0.999371i	$0.511287\pi$
$114$	0	0
$115$	−0.175297	−0.0163465
$116$	3.98545	0.370040
$117$	−6.47565	−0.598674
$118$	10.0915	0.929000
$119$	−0.391874	−0.0359230
$120$	−1.65270	−0.150871
$121$	7.89899	0.718090
$122$	3.59627	0.325591
$123$	−8.63816	−0.778876
$124$	−3.22668	−0.289765
$125$	12.0128	1.07446
$126$	0.184793	0.0164626
$127$	−10.8229	−0.960381	−0.480191	−	0.877164i	$-0.659433\pi$
$127$	−10.8229	−0.960381	−0.480191	+	0.877164i	$0.659433\pi$
$128$	1.00000	0.0883883
$129$	0.0418891	0.00368813
$130$	10.7023	0.938657
$131$	10.8452	0.947553	0.473776	−	0.880645i	$-0.342891\pi$
$131$	10.8452	0.947553	0.473776	+	0.880645i	$0.342891\pi$
$132$	−4.34730	−0.378384
$133$	0	0
$134$	−7.98545	−0.689838
$135$	−1.65270	−0.142242
$136$	−2.12061	−0.181841
$137$	−13.9513	−1.19194	−0.595970	−	0.803007i	$-0.703232\pi$
$137$	−13.9513	−1.19194	−0.595970	+	0.803007i	$0.703232\pi$
$138$	0.106067	0.00902901
$139$	5.96585	0.506017	0.253008	−	0.967464i	$-0.418580\pi$
$139$	5.96585	0.506017	0.253008	+	0.967464i	$0.418580\pi$
$140$	−0.305407	−0.0258116
$141$	−7.92127	−0.667092
$142$	−4.04189	−0.339188
$143$	28.1516	2.35415
$144$	1.00000	0.0833333
$145$	−6.58677	−0.547002
$146$	15.1976	1.25776
$147$	−6.96585	−0.574534
$148$	4.06418	0.334073
$149$	−14.2199	−1.16494	−0.582469	−	0.812853i	$-0.697913\pi$
$149$	−14.2199	−1.16494	−0.582469	+	0.812853i	$0.697913\pi$
$150$	−2.26857	−0.185228
$151$	−15.2003	−1.23698	−0.618490	−	0.785792i	$-0.712255\pi$
$151$	−15.2003	−1.23698	−0.618490	+	0.785792i	$0.712255\pi$
$152$	0	0
$153$	−2.12061	−0.171442
$154$	−0.803348	−0.0647356
$155$	5.33275	0.428337
$156$	−6.47565	−0.518467
$157$	9.40373	0.750500	0.375250	−	0.926924i	$-0.377557\pi$
$157$	9.40373	0.750500	0.375250	+	0.926924i	$0.377557\pi$
$158$	12.3969	0.986246
$159$	−9.21213	−0.730570
$160$	−1.65270	−0.130658
$161$	0.0196004	0.00154472
$162$	1.00000	0.0785674
$163$	−7.62361	−0.597127	−0.298564	−	0.954390i	$-0.596507\pi$
$163$	−7.62361	−0.597127	−0.298564	+	0.954390i	$0.596507\pi$
$164$	−8.63816	−0.674527
$165$	7.18479	0.559335
$166$	8.45605	0.656317
$167$	−17.2003	−1.33100	−0.665499	−	0.746399i	$-0.731781\pi$
$167$	−17.2003	−1.33100	−0.665499	+	0.746399i	$0.731781\pi$
$168$	0.184793	0.0142571
$169$	28.9341	2.22570
$170$	3.50475	0.268802
$171$	0	0
$172$	0.0418891	0.00319401
$173$	−6.62361	−0.503584	−0.251792	−	0.967781i	$-0.581020\pi$
$173$	−6.62361	−0.503584	−0.251792	+	0.967781i	$0.581020\pi$
$174$	3.98545	0.302136
$175$	−0.419215	−0.0316897
$176$	−4.34730	−0.327690
$177$	10.0915	0.758525
$178$	−17.9368	−1.34442
$179$	−21.4243	−1.60132	−0.800662	−	0.599116i	$-0.795519\pi$
$179$	−21.4243	−1.60132	−0.800662	+	0.599116i	$0.795519\pi$
$180$	−1.65270	−0.123185
$181$	−17.1848	−1.27734	−0.638668	−	0.769483i	$-0.720514\pi$
$181$	−17.1848	−1.27734	−0.638668	+	0.769483i	$0.720514\pi$
$182$	−1.19665	−0.0887018
$183$	3.59627	0.265844
$184$	0.106067	0.00781935
$185$	−6.71688	−0.493835
$186$	−3.22668	−0.236592
$187$	9.21894	0.674156
$188$	−7.92127	−0.577718
$189$	0.184793	0.0134417
$190$	0	0
$191$	−6.57398	−0.475676	−0.237838	−	0.971305i	$-0.576439\pi$
$191$	−6.57398	−0.475676	−0.237838	+	0.971305i	$0.576439\pi$
$192$	1.00000	0.0721688
$193$	−11.3473	−0.816796	−0.408398	−	0.912804i	$-0.633912\pi$
$193$	−11.3473	−0.816796	−0.408398	+	0.912804i	$0.633912\pi$
$194$	10.6878	0.767338
$195$	10.7023	0.766410
$196$	−6.96585	−0.497561
$197$	6.44831	0.459423	0.229712	−	0.973259i	$-0.426222\pi$
$197$	6.44831	0.459423	0.229712	+	0.973259i	$0.426222\pi$
$198$	−4.34730	−0.308949
$199$	16.7246	1.18558	0.592789	−	0.805358i	$-0.298027\pi$
$199$	16.7246	1.18558	0.592789	+	0.805358i	$0.298027\pi$
$200$	−2.26857	−0.160412
$201$	−7.98545	−0.563250
$202$	8.06418	0.567394
$203$	0.736482	0.0516909
$204$	−2.12061	−0.148473
$205$	14.2763	0.997101
$206$	17.9290	1.24917
$207$	0.106067	0.00737215
$208$	−6.47565	−0.449006
$209$	0	0
$210$	−0.305407	−0.0210751
$211$	−4.87939	−0.335911	−0.167955	−	0.985795i	$-0.553716\pi$
$211$	−4.87939	−0.335911	−0.167955	+	0.985795i	$0.553716\pi$
$212$	−9.21213	−0.632692
$213$	−4.04189	−0.276946
$214$	−13.9881	−0.956210
$215$	−0.0692302	−0.00472146
$216$	1.00000	0.0680414
$217$	−0.596267	−0.0404772
$218$	−4.77332	−0.323290
$219$	15.1976	1.02696
$220$	7.18479	0.484399
$221$	13.7324	0.923739
$222$	4.06418	0.272770
$223$	28.7811	1.92732	0.963661	−	0.267128i	$-0.0860746\pi$
$223$	28.7811	1.92732	0.963661	+	0.267128i	$0.0860746\pi$
$224$	0.184793	0.0123470
$225$	−2.26857	−0.151238
$226$	−0.753718	−0.0501366
$227$	−3.75608	−0.249300	−0.124650	−	0.992201i	$-0.539781\pi$
$227$	−3.75608	−0.249300	−0.124650	+	0.992201i	$0.539781\pi$
$228$	0	0
$229$	17.5175	1.15759	0.578796	−	0.815472i	$-0.303523\pi$
$229$	17.5175	1.15759	0.578796	+	0.815472i	$0.303523\pi$
$230$	−0.175297	−0.0115587
$231$	−0.803348	−0.0528564
$232$	3.98545	0.261658
$233$	−7.00505	−0.458916	−0.229458	−	0.973319i	$-0.573695\pi$
$233$	−7.00505	−0.458916	−0.229458	+	0.973319i	$0.573695\pi$
$234$	−6.47565	−0.423327
$235$	13.0915	0.853997
$236$	10.0915	0.656902
$237$	12.3969	0.805267
$238$	−0.391874	−0.0254014
$239$	0.935822	0.0605333	0.0302667	−	0.999542i	$-0.490364\pi$
$239$	0.935822	0.0605333	0.0302667	+	0.999542i	$0.490364\pi$
$240$	−1.65270	−0.106682
$241$	−28.7297	−1.85064	−0.925321	−	0.379186i	$-0.876204\pi$
$241$	−28.7297	−1.85064	−0.925321	+	0.379186i	$0.876204\pi$
$242$	7.89899	0.507766
$243$	1.00000	0.0641500
$244$	3.59627	0.230227
$245$	11.5125	0.735506
$246$	−8.63816	−0.550749
$247$	0	0
$248$	−3.22668	−0.204894
$249$	8.45605	0.535880
$250$	12.0128	0.759756
$251$	24.1857	1.52659	0.763295	−	0.646050i	$-0.223580\pi$
$251$	24.1857	1.52659	0.763295	+	0.646050i	$0.223580\pi$
$252$	0.184793	0.0116408
$253$	−0.461104	−0.0289894
$254$	−10.8229	−0.679092
$255$	3.50475	0.219476
$256$	1.00000	0.0625000
$257$	8.80066	0.548970	0.274485	−	0.961591i	$-0.411493\pi$
$257$	8.80066	0.548970	0.274485	+	0.961591i	$0.411493\pi$
$258$	0.0418891	0.00260790
$259$	0.751030	0.0466667
$260$	10.7023	0.663731
$261$	3.98545	0.246693
$262$	10.8452	0.670021
$263$	1.30810	0.0806606	0.0403303	−	0.999186i	$-0.487159\pi$
$263$	1.30810	0.0806606	0.0403303	+	0.999186i	$0.487159\pi$
$264$	−4.34730	−0.267558
$265$	15.2249	0.935260
$266$	0	0
$267$	−17.9368	−1.09771
$268$	−7.98545	−0.487789
$269$	8.75103	0.533560	0.266780	−	0.963757i	$-0.414040\pi$
$269$	8.75103	0.533560	0.266780	+	0.963757i	$0.414040\pi$
$270$	−1.65270	−0.100580
$271$	−13.7469	−0.835065	−0.417533	−	0.908662i	$-0.637105\pi$
$271$	−13.7469	−0.835065	−0.417533	+	0.908662i	$0.637105\pi$
$272$	−2.12061	−0.128581
$273$	−1.19665	−0.0724247
$274$	−13.9513	−0.842829
$275$	9.86215	0.594710
$276$	0.106067	0.00638447
$277$	25.0077	1.50257	0.751285	−	0.659978i	$-0.229434\pi$
$277$	25.0077	1.50257	0.751285	+	0.659978i	$0.229434\pi$
$278$	5.96585	0.357808
$279$	−3.22668	−0.193176
$280$	−0.305407	−0.0182516
$281$	12.1557	0.725148	0.362574	−	0.931955i	$-0.381898\pi$
$281$	12.1557	0.725148	0.362574	+	0.931955i	$0.381898\pi$
$282$	−7.92127	−0.471705
$283$	−10.6973	−0.635887	−0.317944	−	0.948110i	$-0.602992\pi$
$283$	−10.6973	−0.635887	−0.317944	+	0.948110i	$0.602992\pi$
$284$	−4.04189	−0.239842
$285$	0	0
$286$	28.1516	1.66464
$287$	−1.59627	−0.0942246
$288$	1.00000	0.0589256
$289$	−12.5030	−0.735470
$290$	−6.58677	−0.386789
$291$	10.6878	0.626529
$292$	15.1976	0.889371
$293$	−13.3473	−0.779757	−0.389879	−	0.920866i	$-0.627483\pi$
$293$	−13.3473	−0.779757	−0.389879	+	0.920866i	$0.627483\pi$
$294$	−6.96585	−0.406257
$295$	−16.6783	−0.971048
$296$	4.06418	0.236226
$297$	−4.34730	−0.252256
$298$	−14.2199	−0.823735
$299$	−0.686852	−0.0397217
$300$	−2.26857	−0.130976
$301$	0.00774079	0.000446172 0
$302$	−15.2003	−0.874677
$303$	8.06418	0.463275
$304$	0	0
$305$	−5.94356	−0.340327
$306$	−2.12061	−0.121227
$307$	15.6631	0.893942	0.446971	−	0.894548i	$-0.352503\pi$
$307$	15.6631	0.893942	0.446971	+	0.894548i	$0.352503\pi$
$308$	−0.803348	−0.0457750
$309$	17.9290	1.01995
$310$	5.33275	0.302880
$311$	9.10607	0.516358	0.258179	−	0.966097i	$-0.416878\pi$
$311$	9.10607	0.516358	0.258179	+	0.966097i	$0.416878\pi$
$312$	−6.47565	−0.366612
$313$	17.7469	1.00311	0.501557	−	0.865124i	$-0.332761\pi$
$313$	17.7469	1.00311	0.501557	+	0.865124i	$0.332761\pi$
$314$	9.40373	0.530683
$315$	−0.305407	−0.0172078
$316$	12.3969	0.697382
$317$	31.0455	1.74369	0.871845	−	0.489782i	$-0.162924\pi$
$317$	31.0455	1.74369	0.871845	+	0.489782i	$0.162924\pi$
$318$	−9.21213	−0.516591
$319$	−17.3259	−0.970066
$320$	−1.65270	−0.0923889
$321$	−13.9881	−0.780742
$322$	0.0196004	0.00109229
$323$	0	0
$324$	1.00000	0.0555556
$325$	14.6905	0.814881
$326$	−7.62361	−0.422233
$327$	−4.77332	−0.263965
$328$	−8.63816	−0.476962
$329$	−1.46379	−0.0807015
$330$	7.18479	0.395510
$331$	−10.0797	−0.554028	−0.277014	−	0.960866i	$-0.589345\pi$
$331$	−10.0797	−0.554028	−0.277014	+	0.960866i	$0.589345\pi$
$332$	8.45605	0.464086
$333$	4.06418	0.222716
$334$	−17.2003	−0.941157
$335$	13.1976	0.721061
$336$	0.184793	0.0100813
$337$	−8.37733	−0.456342	−0.228171	−	0.973621i	$-0.573275\pi$
$337$	−8.37733	−0.456342	−0.228171	+	0.973621i	$0.573275\pi$
$338$	28.9341	1.57381
$339$	−0.753718	−0.0409363
$340$	3.50475	0.190072
$341$	14.0273	0.759623
$342$	0	0
$343$	−2.58079	−0.139349
$344$	0.0418891	0.00225851
$345$	−0.175297	−0.00943768
$346$	−6.62361	−0.356087
$347$	13.0155	0.698708	0.349354	−	0.936991i	$-0.386401\pi$
$347$	13.0155	0.698708	0.349354	+	0.936991i	$0.386401\pi$
$348$	3.98545	0.213643
$349$	−6.70739	−0.359038	−0.179519	−	0.983754i	$-0.557454\pi$
$349$	−6.70739	−0.359038	−0.179519	+	0.983754i	$0.557454\pi$
$350$	−0.419215	−0.0224080
$351$	−6.47565	−0.345645
$352$	−4.34730	−0.231712
$353$	10.6459	0.566624	0.283312	−	0.959028i	$-0.408567\pi$
$353$	10.6459	0.566624	0.283312	+	0.959028i	$0.408567\pi$
$354$	10.0915	0.536358
$355$	6.68004	0.354540
$356$	−17.9368	−0.950646
$357$	−0.391874	−0.0207402
$358$	−21.4243	−1.13231
$359$	−29.1634	−1.53919	−0.769594	−	0.638534i	$-0.779541\pi$
$359$	−29.1634	−1.53919	−0.769594	+	0.638534i	$0.779541\pi$
$360$	−1.65270	−0.0871051
$361$	0	0
$362$	−17.1848	−0.903213
$363$	7.89899	0.414589
$364$	−1.19665	−0.0627216
$365$	−25.1171	−1.31469
$366$	3.59627	0.187980
$367$	−3.53890	−0.184729	−0.0923644	−	0.995725i	$-0.529442\pi$
$367$	−3.53890	−0.184729	−0.0923644	+	0.995725i	$0.529442\pi$
$368$	0.106067	0.00552912
$369$	−8.63816	−0.449684
$370$	−6.71688	−0.349194
$371$	−1.70233	−0.0883808
$372$	−3.22668	−0.167296
$373$	10.2094	0.528625	0.264313	−	0.964437i	$-0.414855\pi$
$373$	10.2094	0.528625	0.264313	+	0.964437i	$0.414855\pi$
$374$	9.21894	0.476700
$375$	12.0128	0.620338
$376$	−7.92127	−0.408509
$377$	−25.8084	−1.32920
$378$	0.184793	0.00950470
$379$	12.6287	0.648691	0.324345	−	0.945939i	$-0.394856\pi$
$379$	12.6287	0.648691	0.324345	+	0.945939i	$0.394856\pi$
$380$	0	0
$381$	−10.8229	−0.554476
$382$	−6.57398	−0.336354
$383$	−8.71419	−0.445274	−0.222637	−	0.974901i	$-0.571467\pi$
$383$	−8.71419	−0.445274	−0.222637	+	0.974901i	$0.571467\pi$
$384$	1.00000	0.0510310
$385$	1.32770	0.0676657
$386$	−11.3473	−0.577562
$387$	0.0418891	0.00212934
$388$	10.6878	0.542590
$389$	−8.64496	−0.438317	−0.219159	−	0.975689i	$-0.570331\pi$
$389$	−8.64496	−0.438317	−0.219159	+	0.975689i	$0.570331\pi$
$390$	10.7023	0.541934
$391$	−0.224927	−0.0113750
$392$	−6.96585	−0.351829
$393$	10.8452	0.547070
$394$	6.44831	0.324861
$395$	−20.4884	−1.03089
$396$	−4.34730	−0.218460
$397$	−6.87433	−0.345013	−0.172506	−	0.985008i	$-0.555187\pi$
$397$	−6.87433	−0.345013	−0.172506	+	0.985008i	$0.555187\pi$
$398$	16.7246	0.838330
$399$	0	0
$400$	−2.26857	−0.113429
$401$	−29.4388	−1.47010	−0.735052	−	0.678011i	$-0.762842\pi$
$401$	−29.4388	−1.47010	−0.735052	+	0.678011i	$0.762842\pi$
$402$	−7.98545	−0.398278
$403$	20.8949	1.04085
$404$	8.06418	0.401208
$405$	−1.65270	−0.0821235
$406$	0.736482	0.0365510
$407$	−17.6682	−0.875779
$408$	−2.12061	−0.104986
$409$	−21.2763	−1.05205	−0.526023	−	0.850470i	$-0.676317\pi$
$409$	−21.2763	−1.05205	−0.526023	+	0.850470i	$0.676317\pi$
$410$	14.2763	0.705057
$411$	−13.9513	−0.688167
$412$	17.9290	0.883299
$413$	1.86484	0.0917626
$414$	0.106067	0.00521290
$415$	−13.9753	−0.686023
$416$	−6.47565	−0.317495
$417$	5.96585	0.292149
$418$	0	0
$419$	15.8922	0.776384	0.388192	−	0.921579i	$-0.373100\pi$
$419$	15.8922	0.776384	0.388192	+	0.921579i	$0.373100\pi$
$420$	−0.305407	−0.0149023
$421$	19.5945	0.954978	0.477489	−	0.878638i	$-0.341547\pi$
$421$	19.5945	0.954978	0.477489	+	0.878638i	$0.341547\pi$
$422$	−4.87939	−0.237525
$423$	−7.92127	−0.385146
$424$	−9.21213	−0.447381
$425$	4.81076	0.233356
$426$	−4.04189	−0.195830
$427$	0.664563	0.0321605
$428$	−13.9881	−0.676142
$429$	28.1516	1.35917
$430$	−0.0692302	−0.00333858
$431$	−4.15476	−0.200128	−0.100064	−	0.994981i	$-0.531905\pi$
$431$	−4.15476	−0.200128	−0.100064	+	0.994981i	$0.531905\pi$
$432$	1.00000	0.0481125
$433$	−3.56212	−0.171184	−0.0855922	−	0.996330i	$-0.527278\pi$
$433$	−3.56212	−0.171184	−0.0855922	+	0.996330i	$0.527278\pi$
$434$	−0.596267	−0.0286217
$435$	−6.58677	−0.315812
$436$	−4.77332	−0.228600
$437$	0	0
$438$	15.1976	0.726169
$439$	−8.21482	−0.392072	−0.196036	−	0.980597i	$-0.562807\pi$
$439$	−8.21482	−0.392072	−0.196036	+	0.980597i	$0.562807\pi$
$440$	7.18479	0.342522
$441$	−6.96585	−0.331707
$442$	13.7324	0.653182
$443$	−18.9463	−0.900164	−0.450082	−	0.892987i	$-0.648605\pi$
$443$	−18.9463	−0.900164	−0.450082	+	0.892987i	$0.648605\pi$
$444$	4.06418	0.192877
$445$	29.6441	1.40527
$446$	28.7811	1.36282
$447$	−14.2199	−0.672577
$448$	0.184793	0.00873063
$449$	10.4926	0.495175	0.247587	−	0.968866i	$-0.420362\pi$
$449$	10.4926	0.495175	0.247587	+	0.968866i	$0.420362\pi$
$450$	−2.26857	−0.106941
$451$	37.5526	1.76828
$452$	−0.753718	−0.0354519
$453$	−15.2003	−0.714171
$454$	−3.75608	−0.176282
$455$	1.97771	0.0927165
$456$	0	0
$457$	−0.415593	−0.0194406	−0.00972031	−	0.999953i	$-0.503094\pi$
$457$	−0.415593	−0.0194406	−0.00972031	+	0.999953i	$0.503094\pi$
$458$	17.5175	0.818541
$459$	−2.12061	−0.0989818
$460$	−0.175297	−0.00817327
$461$	25.2576	1.17637	0.588183	−	0.808728i	$-0.299844\pi$
$461$	25.2576	1.17637	0.588183	+	0.808728i	$0.299844\pi$
$462$	−0.803348	−0.0373751
$463$	18.7912	0.873299	0.436650	−	0.899632i	$-0.356165\pi$
$463$	18.7912	0.873299	0.436650	+	0.899632i	$0.356165\pi$
$464$	3.98545	0.185020
$465$	5.33275	0.247300
$466$	−7.00505	−0.324503
$467$	−17.1334	−0.792840	−0.396420	−	0.918069i	$-0.629748\pi$
$467$	−17.1334	−0.792840	−0.396420	+	0.918069i	$0.629748\pi$
$468$	−6.47565	−0.299337
$469$	−1.47565	−0.0681393
$470$	13.0915	0.603867
$471$	9.40373	0.433301
$472$	10.0915	0.464500
$473$	−0.182104	−0.00837316
$474$	12.3969	0.569410
$475$	0	0
$476$	−0.391874	−0.0179615
$477$	−9.21213	−0.421795
$478$	0.935822	0.0428035
$479$	−10.9581	−0.500689	−0.250344	−	0.968157i	$-0.580544\pi$
$479$	−10.9581	−0.500689	−0.250344	+	0.968157i	$0.580544\pi$
$480$	−1.65270	−0.0754353
$481$	−26.3182	−1.20001
$482$	−28.7297	−1.30860
$483$	0.0196004	0.000891847 0
$484$	7.89899	0.359045
$485$	−17.6637	−0.802069
$486$	1.00000	0.0453609
$487$	16.8803	0.764920	0.382460	−	0.923972i	$-0.375077\pi$
$487$	16.8803	0.764920	0.382460	+	0.923972i	$0.375077\pi$
$488$	3.59627	0.162795
$489$	−7.62361	−0.344751
$490$	11.5125	0.520081
$491$	−11.2567	−0.508008	−0.254004	−	0.967203i	$-0.581748\pi$
$491$	−11.2567	−0.508008	−0.254004	+	0.967203i	$0.581748\pi$
$492$	−8.63816	−0.389438
$493$	−8.45161	−0.380641
$494$	0	0
$495$	7.18479	0.322932
$496$	−3.22668	−0.144882
$497$	−0.746911	−0.0335035
$498$	8.45605	0.378925
$499$	−9.77063	−0.437393	−0.218697	−	0.975793i	$-0.570181\pi$
$499$	−9.77063	−0.437393	−0.218697	+	0.975793i	$0.570181\pi$
$500$	12.0128	0.537228
$501$	−17.2003	−0.768452
$502$	24.1857	1.07946
$503$	−37.4374	−1.66925	−0.834625	−	0.550818i	$-0.814316\pi$
$503$	−37.4374	−1.66925	−0.834625	+	0.550818i	$0.814316\pi$
$504$	0.184793	0.00823131
$505$	−13.3277	−0.593075
$506$	−0.461104	−0.0204986
$507$	28.9341	1.28501
$508$	−10.8229	−0.480191
$509$	−3.71688	−0.164748	−0.0823739	−	0.996601i	$-0.526250\pi$
$509$	−3.71688	−0.164748	−0.0823739	+	0.996601i	$0.526250\pi$
$510$	3.50475	0.155193
$511$	2.80840	0.124236
$512$	1.00000	0.0441942
$513$	0	0
$514$	8.80066	0.388180
$515$	−29.6313	−1.30571
$516$	0.0418891	0.00184406
$517$	34.4361	1.51450
$518$	0.751030	0.0329984
$519$	−6.62361	−0.290744
$520$	10.7023	0.469328
$521$	−0.892178	−0.0390870	−0.0195435	−	0.999809i	$-0.506221\pi$
$521$	−0.892178	−0.0390870	−0.0195435	+	0.999809i	$0.506221\pi$
$522$	3.98545	0.174438
$523$	−14.0651	−0.615024	−0.307512	−	0.951544i	$-0.599496\pi$
$523$	−14.0651	−0.615024	−0.307512	+	0.951544i	$0.599496\pi$
$524$	10.8452	0.473776
$525$	−0.419215	−0.0182960
$526$	1.30810	0.0570357
$527$	6.84255	0.298066
$528$	−4.34730	−0.189192
$529$	−22.9887	−0.999511
$530$	15.2249	0.661329
$531$	10.0915	0.437935
$532$	0	0
$533$	55.9377	2.42293
$534$	−17.9368	−0.776199
$535$	23.1183	0.999489
$536$	−7.98545	−0.344919
$537$	−21.4243	−0.924525
$538$	8.75103	0.377284
$539$	30.2826	1.30436
$540$	−1.65270	−0.0711210
$541$	25.6186	1.10143	0.550714	−	0.834694i	$-0.314356\pi$
$541$	25.6186	1.10143	0.550714	+	0.834694i	$0.314356\pi$
$542$	−13.7469	−0.590480
$543$	−17.1848	−0.737470
$544$	−2.12061	−0.0909206
$545$	7.88888	0.337923
$546$	−1.19665	−0.0512120
$547$	36.3164	1.55278	0.776390	−	0.630253i	$-0.217049\pi$
$547$	36.3164	1.55278	0.776390	+	0.630253i	$0.217049\pi$
$548$	−13.9513	−0.595970
$549$	3.59627	0.153485
$550$	9.86215	0.420523
$551$	0	0
$552$	0.106067	0.00451450
$553$	2.29086	0.0974172
$554$	25.0077	1.06248
$555$	−6.71688	−0.285116
$556$	5.96585	0.253008
$557$	23.3191	0.988063	0.494032	−	0.869444i	$-0.335523\pi$
$557$	23.3191	0.988063	0.494032	+	0.869444i	$0.335523\pi$
$558$	−3.22668	−0.136596
$559$	−0.271259	−0.0114730
$560$	−0.305407	−0.0129058
$561$	9.21894	0.389224
$562$	12.1557	0.512757
$563$	4.53983	0.191331	0.0956655	−	0.995414i	$-0.469502\pi$
$563$	4.53983	0.191331	0.0956655	+	0.995414i	$0.469502\pi$
$564$	−7.92127	−0.333546
$565$	1.24567	0.0524058
$566$	−10.6973	−0.449640
$567$	0.184793	0.00776056
$568$	−4.04189	−0.169594
$569$	−6.26621	−0.262693	−0.131347	−	0.991337i	$-0.541930\pi$
$569$	−6.26621	−0.262693	−0.131347	+	0.991337i	$0.541930\pi$
$570$	0	0
$571$	1.03777	0.0434293	0.0217147	−	0.999764i	$-0.493087\pi$
$571$	1.03777	0.0434293	0.0217147	+	0.999764i	$0.493087\pi$
$572$	28.1516	1.17708
$573$	−6.57398	−0.274632
$574$	−1.59627	−0.0666269
$575$	−0.240620	−0.0100346
$576$	1.00000	0.0416667
$577$	−40.2422	−1.67530	−0.837652	−	0.546205i	$-0.816072\pi$
$577$	−40.2422	−1.67530	−0.837652	+	0.546205i	$0.816072\pi$
$578$	−12.5030	−0.520056
$579$	−11.3473	−0.471578
$580$	−6.58677	−0.273501
$581$	1.56262	0.0648282
$582$	10.6878	0.443023
$583$	40.0479	1.65861
$584$	15.1976	0.628881
$585$	10.7023	0.442487
$586$	−13.3473	−0.551372
$587$	−48.2354	−1.99089	−0.995443	−	0.0953574i	$-0.969601\pi$
$587$	−48.2354	−1.99089	−0.995443	+	0.0953574i	$0.969601\pi$
$588$	−6.96585	−0.287267
$589$	0	0
$590$	−16.6783	−0.686634
$591$	6.44831	0.265248
$592$	4.06418	0.167037
$593$	−17.4757	−0.717639	−0.358820	−	0.933407i	$-0.616821\pi$
$593$	−17.4757	−0.717639	−0.358820	+	0.933407i	$0.616821\pi$
$594$	−4.34730	−0.178372
$595$	0.647651	0.0265511
$596$	−14.2199	−0.582469
$597$	16.7246	0.684493
$598$	−0.686852	−0.0280875
$599$	21.9050	0.895013	0.447506	−	0.894281i	$-0.352312\pi$
$599$	21.9050	0.895013	0.447506	+	0.894281i	$0.352312\pi$
$600$	−2.26857	−0.0926140
$601$	9.27807	0.378460	0.189230	−	0.981933i	$-0.439401\pi$
$601$	9.27807	0.378460	0.189230	+	0.981933i	$0.439401\pi$
$602$	0.00774079	0.000315491 0
$603$	−7.98545	−0.325193
$604$	−15.2003	−0.618490
$605$	−13.0547	−0.530748
$606$	8.06418	0.327585
$607$	29.3354	1.19069	0.595344	−	0.803471i	$-0.297016\pi$
$607$	29.3354	1.19069	0.595344	+	0.803471i	$0.297016\pi$
$608$	0	0
$609$	0.736482	0.0298437
$610$	−5.94356	−0.240648
$611$	51.2954	2.07519
$612$	−2.12061	−0.0857208
$613$	−24.2499	−0.979444	−0.489722	−	0.871879i	$-0.662902\pi$
$613$	−24.2499	−0.979444	−0.489722	+	0.871879i	$0.662902\pi$
$614$	15.6631	0.632113
$615$	14.2763	0.575676
$616$	−0.803348	−0.0323678
$617$	20.0310	0.806416	0.403208	−	0.915108i	$-0.367895\pi$
$617$	20.0310	0.806416	0.403208	+	0.915108i	$0.367895\pi$
$618$	17.9290	0.721211
$619$	−8.01548	−0.322169	−0.161085	−	0.986941i	$-0.551499\pi$
$619$	−8.01548	−0.322169	−0.161085	+	0.986941i	$0.551499\pi$
$620$	5.33275	0.214168
$621$	0.106067	0.00425632
$622$	9.10607	0.365120
$623$	−3.31458	−0.132796
$624$	−6.47565	−0.259234
$625$	−8.51073	−0.340429
$626$	17.7469	0.709309
$627$	0	0
$628$	9.40373	0.375250
$629$	−8.61856	−0.343644
$630$	−0.305407	−0.0121677
$631$	3.98814	0.158765	0.0793827	−	0.996844i	$-0.474705\pi$
$631$	3.98814	0.158765	0.0793827	+	0.996844i	$0.474705\pi$
$632$	12.3969	0.493123
$633$	−4.87939	−0.193938
$634$	31.0455	1.23297
$635$	17.8871	0.709829
$636$	−9.21213	−0.365285
$637$	45.1084	1.78726
$638$	−17.3259	−0.685941
$639$	−4.04189	−0.159895
$640$	−1.65270	−0.0653288
$641$	−27.9050	−1.10218	−0.551090	−	0.834446i	$-0.685788\pi$
$641$	−27.9050	−1.10218	−0.551090	+	0.834446i	$0.685788\pi$
$642$	−13.9881	−0.552068
$643$	−10.8033	−0.426042	−0.213021	−	0.977048i	$-0.568330\pi$
$643$	−10.8033	−0.426042	−0.213021	+	0.977048i	$0.568330\pi$
$644$	0.0196004	0.000772362 0
$645$	−0.0692302	−0.00272594
$646$	0	0
$647$	−34.4662	−1.35500	−0.677502	−	0.735521i	$-0.736938\pi$
$647$	−34.4662	−1.35500	−0.677502	+	0.735521i	$0.736938\pi$
$648$	1.00000	0.0392837
$649$	−43.8708	−1.72208
$650$	14.6905	0.576208
$651$	−0.596267	−0.0233695
$652$	−7.62361	−0.298564
$653$	−22.9941	−0.899830	−0.449915	−	0.893071i	$-0.648546\pi$
$653$	−22.9941	−0.899830	−0.449915	+	0.893071i	$0.648546\pi$
$654$	−4.77332	−0.186652
$655$	−17.9240	−0.700347
$656$	−8.63816	−0.337263
$657$	15.1976	0.592914
$658$	−1.46379	−0.0570646
$659$	−34.0374	−1.32591	−0.662955	−	0.748659i	$-0.730698\pi$
$659$	−34.0374	−1.32591	−0.662955	+	0.748659i	$0.730698\pi$
$660$	7.18479	0.279668
$661$	8.56036	0.332960	0.166480	−	0.986045i	$-0.446760\pi$
$661$	8.56036	0.332960	0.166480	+	0.986045i	$0.446760\pi$
$662$	−10.0797	−0.391757
$663$	13.7324	0.533321
$664$	8.45605	0.328158
$665$	0	0
$666$	4.06418	0.157484
$667$	0.422724	0.0163680
$668$	−17.2003	−0.665499
$669$	28.7811	1.11274
$670$	13.1976	0.509867
$671$	−15.6340	−0.603545
$672$	0.184793	0.00712853
$673$	−12.1402	−0.467971	−0.233985	−	0.972240i	$-0.575177\pi$
$673$	−12.1402	−0.467971	−0.233985	+	0.972240i	$0.575177\pi$
$674$	−8.37733	−0.322683
$675$	−2.26857	−0.0873173
$676$	28.9341	1.11285
$677$	1.55344	0.0597037	0.0298519	−	0.999554i	$-0.490496\pi$
$677$	1.55344	0.0597037	0.0298519	+	0.999554i	$0.490496\pi$
$678$	−0.753718	−0.0289464
$679$	1.97502	0.0757944
$680$	3.50475	0.134401
$681$	−3.75608	−0.143933
$682$	14.0273	0.537135
$683$	−35.3892	−1.35413	−0.677065	−	0.735923i	$-0.736748\pi$
$683$	−35.3892	−1.35413	−0.677065	+	0.735923i	$0.736748\pi$
$684$	0	0
$685$	23.0574	0.880977
$686$	−2.58079	−0.0985348
$687$	17.5175	0.668336
$688$	0.0418891	0.00159701
$689$	59.6546	2.27266
$690$	−0.175297	−0.00667344
$691$	−39.2823	−1.49437	−0.747185	−	0.664617i	$-0.768595\pi$
$691$	−39.2823	−1.49437	−0.747185	+	0.664617i	$0.768595\pi$
$692$	−6.62361	−0.251792
$693$	−0.803348	−0.0305167
$694$	13.0155	0.494061
$695$	−9.85978	−0.374003
$696$	3.98545	0.151068
$697$	18.3182	0.693851
$698$	−6.70739	−0.253878
$699$	−7.00505	−0.264955
$700$	−0.419215	−0.0158448
$701$	16.6527	0.628964	0.314482	−	0.949263i	$-0.398169\pi$
$701$	16.6527	0.628964	0.314482	+	0.949263i	$0.398169\pi$
$702$	−6.47565	−0.244408
$703$	0	0
$704$	−4.34730	−0.163845
$705$	13.0915	0.493055
$706$	10.6459	0.400664
$707$	1.49020	0.0560447
$708$	10.0915	0.379263
$709$	43.5645	1.63610	0.818049	−	0.575148i	$-0.195056\pi$
$709$	43.5645	1.63610	0.818049	+	0.575148i	$0.195056\pi$
$710$	6.68004	0.250698
$711$	12.3969	0.464921
$712$	−17.9368	−0.672208
$713$	−0.342244	−0.0128171
$714$	−0.391874	−0.0146655
$715$	−46.5262	−1.73998
$716$	−21.4243	−0.800662
$717$	0.935822	0.0349489
$718$	−29.1634	−1.08837
$719$	6.46110	0.240959	0.120479	−	0.992716i	$-0.461557\pi$
$719$	6.46110	0.240959	0.120479	+	0.992716i	$0.461557\pi$
$720$	−1.65270	−0.0615926
$721$	3.31315	0.123388
$722$	0	0
$723$	−28.7297	−1.06847
$724$	−17.1848	−0.638668
$725$	−9.04128	−0.335785
$726$	7.89899	0.293159
$727$	1.84430	0.0684014	0.0342007	−	0.999415i	$-0.489111\pi$
$727$	1.84430	0.0684014	0.0342007	+	0.999415i	$0.489111\pi$
$728$	−1.19665	−0.0443509
$729$	1.00000	0.0370370
$730$	−25.1171	−0.929626
$731$	−0.0888306	−0.00328552
$732$	3.59627	0.132922
$733$	32.3587	1.19519	0.597597	−	0.801796i	$-0.296122\pi$
$733$	32.3587	1.19519	0.597597	+	0.801796i	$0.296122\pi$
$734$	−3.53890	−0.130623
$735$	11.5125	0.424645
$736$	0.106067	0.00390968
$737$	34.7151	1.27875
$738$	−8.63816	−0.317975
$739$	−10.9358	−0.402281	−0.201140	−	0.979562i	$-0.564465\pi$
$739$	−10.9358	−0.402281	−0.201140	+	0.979562i	$0.564465\pi$
$740$	−6.71688	−0.246917
$741$	0	0
$742$	−1.70233	−0.0624946
$743$	−10.4706	−0.384129	−0.192065	−	0.981382i	$-0.561518\pi$
$743$	−10.4706	−0.384129	−0.192065	+	0.981382i	$0.561518\pi$
$744$	−3.22668	−0.118296
$745$	23.5012	0.861019
$746$	10.2094	0.373794
$747$	8.45605	0.309391
$748$	9.21894	0.337078
$749$	−2.58490	−0.0944503
$750$	12.0128	0.438645
$751$	−26.3797	−0.962609	−0.481304	−	0.876554i	$-0.659837\pi$
$751$	−26.3797	−0.962609	−0.481304	+	0.876554i	$0.659837\pi$
$752$	−7.92127	−0.288859
$753$	24.1857	0.881377
$754$	−25.8084	−0.939887
$755$	25.1215	0.914267
$756$	0.184793	0.00672084
$757$	22.8075	0.828951	0.414476	−	0.910060i	$-0.363965\pi$
$757$	22.8075	0.828951	0.414476	+	0.910060i	$0.363965\pi$
$758$	12.6287	0.458694
$759$	−0.461104	−0.0167370
$760$	0	0
$761$	41.5012	1.50442	0.752209	−	0.658924i	$-0.228988\pi$
$761$	41.5012	1.50442	0.752209	+	0.658924i	$0.228988\pi$
$762$	−10.8229	−0.392074
$763$	−0.882074	−0.0319332
$764$	−6.57398	−0.237838
$765$	3.50475	0.126714
$766$	−8.71419	−0.314857
$767$	−65.3492	−2.35962
$768$	1.00000	0.0360844
$769$	19.0009	0.685191	0.342596	−	0.939483i	$-0.388694\pi$
$769$	19.0009	0.685191	0.342596	+	0.939483i	$0.388694\pi$
$770$	1.32770	0.0478468
$771$	8.80066	0.316948
$772$	−11.3473	−0.408398
$773$	17.1438	0.616621	0.308310	−	0.951286i	$-0.400236\pi$
$773$	17.1438	0.616621	0.308310	+	0.951286i	$0.400236\pi$
$774$	0.0418891	0.00150567
$775$	7.31996	0.262941
$776$	10.6878	0.383669
$777$	0.751030	0.0269430
$778$	−8.64496	−0.309937
$779$	0	0
$780$	10.7023	0.383205
$781$	17.5713	0.628750
$782$	−0.224927	−0.00804337
$783$	3.98545	0.142428
$784$	−6.96585	−0.248780
$785$	−15.5416	−0.554703
$786$	10.8452	0.386837
$787$	−18.2003	−0.648770	−0.324385	−	0.945925i	$-0.605157\pi$
$787$	−18.2003	−0.648770	−0.324385	+	0.945925i	$0.605157\pi$
$788$	6.44831	0.229712
$789$	1.30810	0.0465694
$790$	−20.4884	−0.728946
$791$	−0.139281	−0.00495228
$792$	−4.34730	−0.154474
$793$	−23.2882	−0.826987
$794$	−6.87433	−0.243961
$795$	15.2249	0.539973
$796$	16.7246	0.592789
$797$	−26.4584	−0.937205	−0.468603	−	0.883409i	$-0.655242\pi$
$797$	−26.4584	−0.937205	−0.468603	+	0.883409i	$0.655242\pi$
$798$	0	0
$799$	16.7980	0.594270
$800$	−2.26857	−0.0802061
$801$	−17.9368	−0.633764
$802$	−29.4388	−1.03952
$803$	−66.0684	−2.33150
$804$	−7.98545	−0.281625
$805$	−0.0323936	−0.00114172
$806$	20.8949	0.735990
$807$	8.75103	0.308051
$808$	8.06418	0.283697
$809$	−30.5672	−1.07468	−0.537342	−	0.843364i	$-0.680572\pi$
$809$	−30.5672	−1.07468	−0.537342	+	0.843364i	$0.680572\pi$
$810$	−1.65270	−0.0580701
$811$	−6.85710	−0.240785	−0.120393	−	0.992726i	$-0.538415\pi$
$811$	−6.85710	−0.240785	−0.120393	+	0.992726i	$0.538415\pi$
$812$	0.736482	0.0258454
$813$	−13.7469	−0.482125
$814$	−17.6682	−0.619270
$815$	12.5996	0.441343
$816$	−2.12061	−0.0742364
$817$	0	0
$818$	−21.2763	−0.743909
$819$	−1.19665	−0.0418144
$820$	14.2763	0.498550
$821$	39.6800	1.38484	0.692422	−	0.721493i	$-0.256544\pi$
$821$	39.6800	1.38484	0.692422	+	0.721493i	$0.256544\pi$
$822$	−13.9513	−0.486608
$823$	−46.7205	−1.62857	−0.814287	−	0.580462i	$-0.802872\pi$
$823$	−46.7205	−1.62857	−0.814287	+	0.580462i	$0.802872\pi$
$824$	17.9290	0.624587
$825$	9.86215	0.343356
$826$	1.86484	0.0648860
$827$	−41.9172	−1.45760	−0.728801	−	0.684725i	$-0.759922\pi$
$827$	−41.9172	−1.45760	−0.728801	+	0.684725i	$0.759922\pi$
$828$	0.106067	0.00368608
$829$	−0.502059	−0.0174372	−0.00871862	−	0.999962i	$-0.502775\pi$
$829$	−0.502059	−0.0174372	−0.00871862	+	0.999962i	$0.502775\pi$
$830$	−13.9753	−0.485091
$831$	25.0077	0.867509
$832$	−6.47565	−0.224503
$833$	14.7719	0.511816
$834$	5.96585	0.206581
$835$	28.4270	0.983755
$836$	0	0
$837$	−3.22668	−0.111530
$838$	15.8922	0.548986
$839$	−31.4142	−1.08454	−0.542269	−	0.840205i	$-0.682435\pi$
$839$	−31.4142	−1.08454	−0.542269	+	0.840205i	$0.682435\pi$
$840$	−0.305407	−0.0105376
$841$	−13.1162	−0.452282
$842$	19.5945	0.675271
$843$	12.1557	0.418664
$844$	−4.87939	−0.167955
$845$	−47.8194	−1.64504
$846$	−7.92127	−0.272339
$847$	1.45967	0.0501550
$848$	−9.21213	−0.316346
$849$	−10.6973	−0.367130
$850$	4.81076	0.165008
$851$	0.431074	0.0147770
$852$	−4.04189	−0.138473
$853$	18.8128	0.644139	0.322070	−	0.946716i	$-0.395621\pi$
$853$	18.8128	0.644139	0.322070	+	0.946716i	$0.395621\pi$
$854$	0.664563	0.0227409
$855$	0	0
$856$	−13.9881	−0.478105
$857$	29.9632	1.02352	0.511761	−	0.859128i	$-0.328993\pi$
$857$	29.9632	1.02352	0.511761	+	0.859128i	$0.328993\pi$
$858$	28.1516	0.961079
$859$	−33.1702	−1.13175	−0.565877	−	0.824490i	$-0.691462\pi$
$859$	−33.1702	−1.13175	−0.565877	+	0.824490i	$0.691462\pi$
$860$	−0.0692302	−0.00236073
$861$	−1.59627	−0.0544006
$862$	−4.15476	−0.141512
$863$	−38.2475	−1.30196	−0.650981	−	0.759094i	$-0.725642\pi$
$863$	−38.2475	−1.30196	−0.650981	+	0.759094i	$0.725642\pi$
$864$	1.00000	0.0340207
$865$	10.9469	0.372204
$866$	−3.56212	−0.121046
$867$	−12.5030	−0.424624
$868$	−0.596267	−0.0202386
$869$	−53.8931	−1.82820
$870$	−6.58677	−0.223312
$871$	51.7110	1.75216
$872$	−4.77332	−0.161645
$873$	10.6878	0.361727
$874$	0	0
$875$	2.21987	0.0750455
$876$	15.1976	0.513479
$877$	−48.1671	−1.62649	−0.813243	−	0.581924i	$-0.802300\pi$
$877$	−48.1671	−1.62649	−0.813243	+	0.581924i	$0.802300\pi$
$878$	−8.21482	−0.277237
$879$	−13.3473	−0.450193
$880$	7.18479	0.242199
$881$	37.7083	1.27043	0.635213	−	0.772337i	$-0.280912\pi$
$881$	37.7083	1.27043	0.635213	+	0.772337i	$0.280912\pi$
$882$	−6.96585	−0.234552
$883$	−30.3500	−1.02136	−0.510679	−	0.859771i	$-0.670606\pi$
$883$	−30.3500	−1.02136	−0.510679	+	0.859771i	$0.670606\pi$
$884$	13.7324	0.461869
$885$	−16.6783	−0.560635
$886$	−18.9463	−0.636512
$887$	−0.926651	−0.0311139	−0.0155569	−	0.999879i	$-0.504952\pi$
$887$	−0.926651	−0.0311139	−0.0155569	+	0.999879i	$0.504952\pi$
$888$	4.06418	0.136385
$889$	−2.00000	−0.0670778
$890$	29.6441	0.993674
$891$	−4.34730	−0.145640
$892$	28.7811	0.963661
$893$	0	0
$894$	−14.2199	−0.475584
$895$	35.4080	1.18356
$896$	0.184793	0.00617349
$897$	−0.686852	−0.0229333
$898$	10.4926	0.350141
$899$	−12.8598	−0.428898
$900$	−2.26857	−0.0756190
$901$	19.5354	0.650818
$902$	37.5526	1.25037
$903$	0.00774079	0.000257597 0
$904$	−0.753718	−0.0250683
$905$	28.4014	0.944093
$906$	−15.2003	−0.504995
$907$	−4.24535	−0.140964	−0.0704822	−	0.997513i	$-0.522454\pi$
$907$	−4.24535	−0.140964	−0.0704822	+	0.997513i	$0.522454\pi$
$908$	−3.75608	−0.124650
$909$	8.06418	0.267472
$910$	1.97771	0.0655605
$911$	−56.5509	−1.87361	−0.936807	−	0.349847i	$-0.886234\pi$
$911$	−56.5509	−1.87361	−0.936807	+	0.349847i	$0.886234\pi$
$912$	0	0
$913$	−36.7610	−1.21661
$914$	−0.415593	−0.0137466
$915$	−5.94356	−0.196488
$916$	17.5175	0.578796
$917$	2.00412	0.0661818
$918$	−2.12061	−0.0699907
$919$	58.9555	1.94476	0.972382	−	0.233396i	$-0.0749838\pi$
$919$	58.9555	1.94476	0.972382	+	0.233396i	$0.0749838\pi$
$920$	−0.175297	−0.00577937
$921$	15.6631	0.516118
$922$	25.2576	0.831816
$923$	26.1739	0.861523
$924$	−0.803348	−0.0264282
$925$	−9.21987	−0.303148
$926$	18.7912	0.617516
$927$	17.9290	0.588866
$928$	3.98545	0.130829
$929$	−12.4070	−0.407061	−0.203531	−	0.979069i	$-0.565242\pi$
$929$	−12.4070	−0.407061	−0.203531	+	0.979069i	$0.565242\pi$
$930$	5.33275	0.174868
$931$	0	0
$932$	−7.00505	−0.229458
$933$	9.10607	0.298119
$934$	−17.1334	−0.560622
$935$	−15.2362	−0.498276
$936$	−6.47565	−0.211663
$937$	27.8016	0.908238	0.454119	−	0.890941i	$-0.349954\pi$
$937$	27.8016	0.908238	0.454119	+	0.890941i	$0.349954\pi$
$938$	−1.47565	−0.0481817
$939$	17.7469	0.579149
$940$	13.0915	0.426998
$941$	−19.9617	−0.650734	−0.325367	−	0.945588i	$-0.605488\pi$
$941$	−19.9617	−0.650734	−0.325367	+	0.945588i	$0.605488\pi$
$942$	9.40373	0.306390
$943$	−0.916222	−0.0298363
$944$	10.0915	0.328451
$945$	−0.305407	−0.00993490
$946$	−0.182104	−0.00592072
$947$	29.9992	0.974842	0.487421	−	0.873167i	$-0.337938\pi$
$947$	29.9992	0.974842	0.487421	+	0.873167i	$0.337938\pi$
$948$	12.3969	0.402633
$949$	−98.4143	−3.19466
$950$	0	0
$951$	31.0455	1.00672
$952$	−0.391874	−0.0127007
$953$	22.9377	0.743025	0.371512	−	0.928428i	$-0.378839\pi$
$953$	22.9377	0.743025	0.371512	+	0.928428i	$0.378839\pi$
$954$	−9.21213	−0.298254
$955$	10.8648	0.351578
$956$	0.935822	0.0302667
$957$	−17.3259	−0.560068
$958$	−10.9581	−0.354040
$959$	−2.57810	−0.0832511
$960$	−1.65270	−0.0533408
$961$	−20.5885	−0.664146
$962$	−26.3182	−0.848533
$963$	−13.9881	−0.450762
$964$	−28.7297	−0.925321
$965$	18.7537	0.603704
$966$	0.0196004	0.000630631 0
$967$	−37.8485	−1.21713	−0.608563	−	0.793505i	$-0.708254\pi$
$967$	−37.8485	−1.21713	−0.608563	+	0.793505i	$0.708254\pi$
$968$	7.89899	0.253883
$969$	0	0
$970$	−17.6637	−0.567149
$971$	−29.3364	−0.941449	−0.470724	−	0.882280i	$-0.656007\pi$
$971$	−29.3364	−0.941449	−0.470724	+	0.882280i	$0.656007\pi$
$972$	1.00000	0.0320750
$973$	1.10244	0.0353428
$974$	16.8803	0.540880
$975$	14.6905	0.470472
$976$	3.59627	0.115114
$977$	14.1611	0.453053	0.226526	−	0.974005i	$-0.427263\pi$
$977$	14.1611	0.453053	0.226526	+	0.974005i	$0.427263\pi$
$978$	−7.62361	−0.243776
$979$	77.9764	2.49214
$980$	11.5125	0.367753
$981$	−4.77332	−0.152400
$982$	−11.2567	−0.359216
$983$	−34.7692	−1.10897	−0.554483	−	0.832195i	$-0.687084\pi$
$983$	−34.7692	−1.10897	−0.554483	+	0.832195i	$0.687084\pi$
$984$	−8.63816	−0.275374
$985$	−10.6571	−0.339565
$986$	−8.45161	−0.269154
$987$	−1.46379	−0.0465930
$988$	0	0
$989$	0.00444304	0.000141280 0
$990$	7.18479	0.228348
$991$	−5.48784	−0.174327	−0.0871634	−	0.996194i	$-0.527780\pi$
$991$	−5.48784	−0.174327	−0.0871634	+	0.996194i	$0.527780\pi$
$992$	−3.22668	−0.102447
$993$	−10.0797	−0.319868
$994$	−0.746911	−0.0236906
$995$	−27.6408	−0.876274
$996$	8.45605	0.267940
$997$	−9.62454	−0.304812	−0.152406	−	0.988318i	$-0.548702\pi$
$997$	−9.62454	−0.304812	−0.152406	+	0.988318i	$0.548702\pi$
$998$	−9.77063	−0.309284
$999$	4.06418	0.128585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.2.a.t.1.2		3
3.2	odd	2		6498.2.a.bo.1.2		3
19.6	even	9		114.2.i.b.55.1	✓	6
19.16	even	9		114.2.i.b.85.1	yes	6
19.18	odd	2		2166.2.a.n.1.2		3
57.35	odd	18		342.2.u.d.199.1		6
57.44	odd	18		342.2.u.d.55.1		6
57.56	even	2		6498.2.a.bt.1.2		3
76.35	odd	18		912.2.bo.c.769.1		6
76.63	odd	18		912.2.bo.c.625.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.b.55.1	✓	6	19.6	even	9
114.2.i.b.85.1	yes	6	19.16	even	9
342.2.u.d.55.1		6	57.44	odd	18
342.2.u.d.199.1		6	57.35	odd	18
912.2.bo.c.625.1		6	76.63	odd	18
912.2.bo.c.769.1		6	76.35	odd	18
2166.2.a.n.1.2		3	19.18	odd	2
2166.2.a.t.1.2		3	1.1	even	1	trivial
6498.2.a.bo.1.2		3	3.2	odd	2
6498.2.a.bt.1.2		3	57.56	even	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.65270 q^{5} +1.00000 q^{6} +0.184793 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.65270 q^{5} +1.00000 q^{6} +0.184793 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.65270 q^{10} -4.34730 q^{11} +1.00000 q^{12} -6.47565 q^{13} +0.184793 q^{14} -1.65270 q^{15} +1.00000 q^{16} -2.12061 q^{17} +1.00000 q^{18} -1.65270 q^{20} +0.184793 q^{21} -4.34730 q^{22} +0.106067 q^{23} +1.00000 q^{24} -2.26857 q^{25} -6.47565 q^{26} +1.00000 q^{27} +0.184793 q^{28} +3.98545 q^{29} -1.65270 q^{30} -3.22668 q^{31} +1.00000 q^{32} -4.34730 q^{33} -2.12061 q^{34} -0.305407 q^{35} +1.00000 q^{36} +4.06418 q^{37} -6.47565 q^{39} -1.65270 q^{40} -8.63816 q^{41} +0.184793 q^{42} +0.0418891 q^{43} -4.34730 q^{44} -1.65270 q^{45} +0.106067 q^{46} -7.92127 q^{47} +1.00000 q^{48} -6.96585 q^{49} -2.26857 q^{50} -2.12061 q^{51} -6.47565 q^{52} -9.21213 q^{53} +1.00000 q^{54} +7.18479 q^{55} +0.184793 q^{56} +3.98545 q^{58} +10.0915 q^{59} -1.65270 q^{60} +3.59627 q^{61} -3.22668 q^{62} +0.184793 q^{63} +1.00000 q^{64} +10.7023 q^{65} -4.34730 q^{66} -7.98545 q^{67} -2.12061 q^{68} +0.106067 q^{69} -0.305407 q^{70} -4.04189 q^{71} +1.00000 q^{72} +15.1976 q^{73} +4.06418 q^{74} -2.26857 q^{75} -0.803348 q^{77} -6.47565 q^{78} +12.3969 q^{79} -1.65270 q^{80} +1.00000 q^{81} -8.63816 q^{82} +8.45605 q^{83} +0.184793 q^{84} +3.50475 q^{85} +0.0418891 q^{86} +3.98545 q^{87} -4.34730 q^{88} -17.9368 q^{89} -1.65270 q^{90} -1.19665 q^{91} +0.106067 q^{92} -3.22668 q^{93} -7.92127 q^{94} +1.00000 q^{96} +10.6878 q^{97} -6.96585 q^{98} -4.34730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 6 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 6 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 6 q^{5} + 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 6 q^{10} - 12 q^{11} + 3 q^{12} - 3 q^{14} - 6 q^{15} + 3 q^{16} - 12 q^{17} + 3 q^{18} - 6 q^{20} - 3 q^{21} - 12 q^{22} - 12 q^{23} + 3 q^{24} + 3 q^{25} + 3 q^{27} - 3 q^{28} - 6 q^{29} - 6 q^{30} - 3 q^{31} + 3 q^{32} - 12 q^{33} - 12 q^{34} - 3 q^{35} + 3 q^{36} + 3 q^{37} - 6 q^{40} - 9 q^{41} - 3 q^{42} - 3 q^{43} - 12 q^{44} - 6 q^{45} - 12 q^{46} - 15 q^{47} + 3 q^{48} + 3 q^{50} - 12 q^{51} - 3 q^{53} + 3 q^{54} + 18 q^{55} - 3 q^{56} - 6 q^{58} - 6 q^{60} - 3 q^{61} - 3 q^{62} - 3 q^{63} + 3 q^{64} + 6 q^{65} - 12 q^{66} - 6 q^{67} - 12 q^{68} - 12 q^{69} - 3 q^{70} - 9 q^{71} + 3 q^{72} + 3 q^{73} + 3 q^{74} + 3 q^{75} + 21 q^{77} + 9 q^{79} - 6 q^{80} + 3 q^{81} - 9 q^{82} + 3 q^{83} - 3 q^{84} + 27 q^{85} - 3 q^{86} - 6 q^{87} - 12 q^{88} + 3 q^{89} - 6 q^{90} - 27 q^{91} - 12 q^{92} - 3 q^{93} - 15 q^{94} + 3 q^{96} - 12 q^{97} - 12 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 6 * q^5 + 3 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 6 * q^10 - 12 * q^11 + 3 * q^12 - 3 * q^14 - 6 * q^15 + 3 * q^16 - 12 * q^17 + 3 * q^18 - 6 * q^20 - 3 * q^21 - 12 * q^22 - 12 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 - 3 * q^28 - 6 * q^29 - 6 * q^30 - 3 * q^31 + 3 * q^32 - 12 * q^33 - 12 * q^34 - 3 * q^35 + 3 * q^36 + 3 * q^37 - 6 * q^40 - 9 * q^41 - 3 * q^42 - 3 * q^43 - 12 * q^44 - 6 * q^45 - 12 * q^46 - 15 * q^47 + 3 * q^48 + 3 * q^50 - 12 * q^51 - 3 * q^53 + 3 * q^54 + 18 * q^55 - 3 * q^56 - 6 * q^58 - 6 * q^60 - 3 * q^61 - 3 * q^62 - 3 * q^63 + 3 * q^64 + 6 * q^65 - 12 * q^66 - 6 * q^67 - 12 * q^68 - 12 * q^69 - 3 * q^70 - 9 * q^71 + 3 * q^72 + 3 * q^73 + 3 * q^74 + 3 * q^75 + 21 * q^77 + 9 * q^79 - 6 * q^80 + 3 * q^81 - 9 * q^82 + 3 * q^83 - 3 * q^84 + 27 * q^85 - 3 * q^86 - 6 * q^87 - 12 * q^88 + 3 * q^89 - 6 * q^90 - 27 * q^91 - 12 * q^92 - 3 * q^93 - 15 * q^94 + 3 * q^96 - 12 * q^97 - 12 * q^99

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