LMFDB - Embedded newform 1734.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1734,2,Mod(1,1734)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1734, 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("1734.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1734 = 2 \cdot 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1734.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:	$13.8460597105$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.347296$ of defining polynomial
Character	$\chi$	$=$	1734.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.34730 q^{5} -1.00000 q^{6} +4.06418 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.34730 q^{5} -1.00000 q^{6} +4.06418 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.34730 q^{10} +2.83750 q^{11} +1.00000 q^{12} +2.69459 q^{13} -4.06418 q^{14} +2.34730 q^{15} +1.00000 q^{16} -1.00000 q^{18} -6.45336 q^{19} +2.34730 q^{20} +4.06418 q^{21} -2.83750 q^{22} +6.00000 q^{23} -1.00000 q^{24} +0.509800 q^{25} -2.69459 q^{26} +1.00000 q^{27} +4.06418 q^{28} +8.70233 q^{29} -2.34730 q^{30} +0.573978 q^{31} -1.00000 q^{32} +2.83750 q^{33} +9.53983 q^{35} +1.00000 q^{36} -7.88713 q^{37} +6.45336 q^{38} +2.69459 q^{39} -2.34730 q^{40} -3.43376 q^{41} -4.06418 q^{42} -11.6459 q^{43} +2.83750 q^{44} +2.34730 q^{45} -6.00000 q^{46} -10.5817 q^{47} +1.00000 q^{48} +9.51754 q^{49} -0.509800 q^{50} +2.69459 q^{52} -3.29086 q^{53} -1.00000 q^{54} +6.66044 q^{55} -4.06418 q^{56} -6.45336 q^{57} -8.70233 q^{58} +4.34730 q^{59} +2.34730 q^{60} -13.0642 q^{61} -0.573978 q^{62} +4.06418 q^{63} +1.00000 q^{64} +6.32501 q^{65} -2.83750 q^{66} +12.2121 q^{67} +6.00000 q^{69} -9.53983 q^{70} -11.6013 q^{71} -1.00000 q^{72} -2.36184 q^{73} +7.88713 q^{74} +0.509800 q^{75} -6.45336 q^{76} +11.5321 q^{77} -2.69459 q^{78} -7.37464 q^{79} +2.34730 q^{80} +1.00000 q^{81} +3.43376 q^{82} +3.21213 q^{83} +4.06418 q^{84} +11.6459 q^{86} +8.70233 q^{87} -2.83750 q^{88} -6.34049 q^{89} -2.34730 q^{90} +10.9513 q^{91} +6.00000 q^{92} +0.573978 q^{93} +10.5817 q^{94} -15.1480 q^{95} -1.00000 q^{96} +8.11381 q^{97} -9.51754 q^{98} +2.83750 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 6 q^{11} + 3 q^{12} + 6 q^{13} - 3 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{21} - 6 q^{22} + 18 q^{23} - 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} + 3 q^{28} - 6 q^{30} - 6 q^{31} - 3 q^{32} + 6 q^{33} + 3 q^{36} + 6 q^{37} + 6 q^{38} + 6 q^{39} - 6 q^{40} + 6 q^{41} - 3 q^{42} + 6 q^{43} + 6 q^{44} + 6 q^{45} - 18 q^{46} + 3 q^{48} + 6 q^{49} - 3 q^{50} + 6 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{55} - 3 q^{56} - 6 q^{57} + 12 q^{59} + 6 q^{60} - 30 q^{61} + 6 q^{62} + 3 q^{63} + 3 q^{64} + 24 q^{65} - 6 q^{66} + 12 q^{67} + 18 q^{69} - 6 q^{71} - 3 q^{72} - 24 q^{73} - 6 q^{74} + 3 q^{75} - 6 q^{76} + 30 q^{77} - 6 q^{78} + 6 q^{80} + 3 q^{81} - 6 q^{82} - 15 q^{83} + 3 q^{84} - 6 q^{86} - 6 q^{88} + 24 q^{89} - 6 q^{90} - 6 q^{91} + 18 q^{92} - 6 q^{93} - 30 q^{95} - 3 q^{96} - 12 q^{97} - 6 q^{98} + 6 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 + 6 * q^11 + 3 * q^12 + 6 * q^13 - 3 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^18 - 6 * q^19 + 6 * q^20 + 3 * q^21 - 6 * q^22 + 18 * q^23 - 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 + 3 * q^28 - 6 * q^30 - 6 * q^31 - 3 * q^32 + 6 * q^33 + 3 * q^36 + 6 * q^37 + 6 * q^38 + 6 * q^39 - 6 * q^40 + 6 * q^41 - 3 * q^42 + 6 * q^43 + 6 * q^44 + 6 * q^45 - 18 * q^46 + 3 * q^48 + 6 * q^49 - 3 * q^50 + 6 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^55 - 3 * q^56 - 6 * q^57 + 12 * q^59 + 6 * q^60 - 30 * q^61 + 6 * q^62 + 3 * q^63 + 3 * q^64 + 24 * q^65 - 6 * q^66 + 12 * q^67 + 18 * q^69 - 6 * q^71 - 3 * q^72 - 24 * q^73 - 6 * q^74 + 3 * q^75 - 6 * q^76 + 30 * q^77 - 6 * q^78 + 6 * q^80 + 3 * q^81 - 6 * q^82 - 15 * q^83 + 3 * q^84 - 6 * q^86 - 6 * q^88 + 24 * q^89 - 6 * q^90 - 6 * q^91 + 18 * q^92 - 6 * q^93 - 30 * q^95 - 3 * q^96 - 12 * q^97 - 6 * q^98 + 6 * 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
$5$	2.34730	1.04974	0.524871	−	0.851182i	$-0.324113\pi$
$5$	2.34730	1.04974	0.524871	+	0.851182i	$0.324113\pi$
$6$	−1.00000	−0.408248
$7$	4.06418	1.53611	0.768057	−	0.640381i	$-0.221224\pi$
$7$	4.06418	1.53611	0.768057	+	0.640381i	$0.221224\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.34730	−0.742280
$11$	2.83750	0.855537	0.427769	−	0.903888i	$-0.359300\pi$
$11$	2.83750	0.855537	0.427769	+	0.903888i	$0.359300\pi$
$12$	1.00000	0.288675
$13$	2.69459	0.747346	0.373673	−	0.927561i	$-0.378098\pi$
$13$	2.69459	0.747346	0.373673	+	0.927561i	$0.378098\pi$
$14$	−4.06418	−1.08620
$15$	2.34730	0.606069
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	−1.00000	−0.235702
$19$	−6.45336	−1.48050	−0.740252	−	0.672330i	$-0.765294\pi$
$19$	−6.45336	−1.48050	−0.740252	+	0.672330i	$0.765294\pi$
$20$	2.34730	0.524871
$21$	4.06418	0.886876
$22$	−2.83750	−0.604956
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	−1.00000	−0.204124
$25$	0.509800	0.101960
$26$	−2.69459	−0.528453
$27$	1.00000	0.192450
$28$	4.06418	0.768057
$29$	8.70233	1.61598	0.807991	−	0.589194i	$-0.200555\pi$
$29$	8.70233	1.61598	0.807991	+	0.589194i	$0.200555\pi$
$30$	−2.34730	−0.428556
$31$	0.573978	0.103089	0.0515447	−	0.998671i	$-0.483586\pi$
$31$	0.573978	0.103089	0.0515447	+	0.998671i	$0.483586\pi$
$32$	−1.00000	−0.176777
$33$	2.83750	0.493945
$34$	0	0
$35$	9.53983	1.61253
$36$	1.00000	0.166667
$37$	−7.88713	−1.29664	−0.648318	−	0.761370i	$-0.724527\pi$
$37$	−7.88713	−1.29664	−0.648318	+	0.761370i	$0.724527\pi$
$38$	6.45336	1.04687
$39$	2.69459	0.431480
$40$	−2.34730	−0.371140
$41$	−3.43376	−0.536264	−0.268132	−	0.963382i	$-0.586406\pi$
$41$	−3.43376	−0.536264	−0.268132	+	0.963382i	$0.586406\pi$
$42$	−4.06418	−0.627116
$43$	−11.6459	−1.77598	−0.887991	−	0.459860i	$-0.847899\pi$
$43$	−11.6459	−1.77598	−0.887991	+	0.459860i	$0.847899\pi$
$44$	2.83750	0.427769
$45$	2.34730	0.349914
$46$	−6.00000	−0.884652
$47$	−10.5817	−1.54350	−0.771751	−	0.635925i	$-0.780619\pi$
$47$	−10.5817	−1.54350	−0.771751	+	0.635925i	$0.780619\pi$
$48$	1.00000	0.144338
$49$	9.51754	1.35965
$50$	−0.509800	−0.0720966
$51$	0	0
$52$	2.69459	0.373673
$53$	−3.29086	−0.452034	−0.226017	−	0.974123i	$-0.572571\pi$
$53$	−3.29086	−0.452034	−0.226017	+	0.974123i	$0.572571\pi$
$54$	−1.00000	−0.136083
$55$	6.66044	0.898094
$56$	−4.06418	−0.543099
$57$	−6.45336	−0.854769
$58$	−8.70233	−1.14267
$59$	4.34730	0.565970	0.282985	−	0.959124i	$-0.408675\pi$
$59$	4.34730	0.565970	0.282985	+	0.959124i	$0.408675\pi$
$60$	2.34730	0.303035
$61$	−13.0642	−1.67270	−0.836348	−	0.548198i	$-0.815314\pi$
$61$	−13.0642	−1.67270	−0.836348	+	0.548198i	$0.815314\pi$
$62$	−0.573978	−0.0728953
$63$	4.06418	0.512038
$64$	1.00000	0.125000
$65$	6.32501	0.784521
$66$	−2.83750	−0.349272
$67$	12.2121	1.49195	0.745975	−	0.665974i	$-0.231984\pi$
$67$	12.2121	1.49195	0.745975	+	0.665974i	$0.231984\pi$
$68$	0	0
$69$	6.00000	0.722315
$70$	−9.53983	−1.14023
$71$	−11.6013	−1.37682	−0.688412	−	0.725320i	$-0.741692\pi$
$71$	−11.6013	−1.37682	−0.688412	+	0.725320i	$0.741692\pi$
$72$	−1.00000	−0.117851
$73$	−2.36184	−0.276433	−0.138216	−	0.990402i	$-0.544137\pi$
$73$	−2.36184	−0.276433	−0.138216	+	0.990402i	$0.544137\pi$
$74$	7.88713	0.916860
$75$	0.509800	0.0588667
$76$	−6.45336	−0.740252
$77$	11.5321	1.31420
$78$	−2.69459	−0.305103
$79$	−7.37464	−0.829712	−0.414856	−	0.909887i	$-0.636168\pi$
$79$	−7.37464	−0.829712	−0.414856	+	0.909887i	$0.636168\pi$
$80$	2.34730	0.262436
$81$	1.00000	0.111111
$82$	3.43376	0.379196
$83$	3.21213	0.352577	0.176289	−	0.984338i	$-0.443591\pi$
$83$	3.21213	0.352577	0.176289	+	0.984338i	$0.443591\pi$
$84$	4.06418	0.443438
$85$	0	0
$86$	11.6459	1.25581
$87$	8.70233	0.932988
$88$	−2.83750	−0.302478
$89$	−6.34049	−0.672091	−0.336045	−	0.941846i	$-0.609090\pi$
$89$	−6.34049	−0.672091	−0.336045	+	0.941846i	$0.609090\pi$
$90$	−2.34730	−0.247427
$91$	10.9513	1.14801
$92$	6.00000	0.625543
$93$	0.573978	0.0595187
$94$	10.5817	1.09142
$95$	−15.1480	−1.55415
$96$	−1.00000	−0.102062
$97$	8.11381	0.823832	0.411916	−	0.911222i	$-0.364860\pi$
$97$	8.11381	0.823832	0.411916	+	0.911222i	$0.364860\pi$
$98$	−9.51754	−0.961417
$99$	2.83750	0.285179
$100$	0.509800	0.0509800
$101$	−9.17024	−0.912473	−0.456237	−	0.889858i	$-0.650803\pi$
$101$	−9.17024	−0.912473	−0.456237	+	0.889858i	$0.650803\pi$
$102$	0	0
$103$	−7.35235	−0.724448	−0.362224	−	0.932091i	$-0.617983\pi$
$103$	−7.35235	−0.724448	−0.362224	+	0.932091i	$0.617983\pi$
$104$	−2.69459	−0.264227
$105$	9.53983	0.930992
$106$	3.29086	0.319637
$107$	−5.02734	−0.486011	−0.243006	−	0.970025i	$-0.578133\pi$
$107$	−5.02734	−0.486011	−0.243006	+	0.970025i	$0.578133\pi$
$108$	1.00000	0.0962250
$109$	−9.06418	−0.868191	−0.434095	−	0.900867i	$-0.642932\pi$
$109$	−9.06418	−0.868191	−0.434095	+	0.900867i	$0.642932\pi$
$110$	−6.66044	−0.635048
$111$	−7.88713	−0.748613
$112$	4.06418	0.384029
$113$	11.1480	1.04871	0.524356	−	0.851499i	$-0.324306\pi$
$113$	11.1480	1.04871	0.524356	+	0.851499i	$0.324306\pi$
$114$	6.45336	0.604413
$115$	14.0838	1.31332
$116$	8.70233	0.807991
$117$	2.69459	0.249115
$118$	−4.34730	−0.400201
$119$	0	0
$120$	−2.34730	−0.214278
$121$	−2.94862	−0.268056
$122$	13.0642	1.18278
$123$	−3.43376	−0.309612
$124$	0.573978	0.0515447
$125$	−10.5398	−0.942711
$126$	−4.06418	−0.362066
$127$	−1.93582	−0.171776	−0.0858882	−	0.996305i	$-0.527373\pi$
$127$	−1.93582	−0.171776	−0.0858882	+	0.996305i	$0.527373\pi$
$128$	−1.00000	−0.0883883
$129$	−11.6459	−1.02536
$130$	−6.32501	−0.554740
$131$	16.7297	1.46168	0.730839	−	0.682550i	$-0.239129\pi$
$131$	16.7297	1.46168	0.730839	+	0.682550i	$0.239129\pi$
$132$	2.83750	0.246972
$133$	−26.2276	−2.27422
$134$	−12.2121	−1.05497
$135$	2.34730	0.202023
$136$	0	0
$137$	4.45336	0.380476	0.190238	−	0.981738i	$-0.439074\pi$
$137$	4.45336	0.380476	0.190238	+	0.981738i	$0.439074\pi$
$138$	−6.00000	−0.510754
$139$	−12.7392	−1.08052	−0.540261	−	0.841497i	$-0.681675\pi$
$139$	−12.7392	−1.08052	−0.540261	+	0.841497i	$0.681675\pi$
$140$	9.53983	0.806263
$141$	−10.5817	−0.891141
$142$	11.6013	0.973561
$143$	7.64590	0.639382
$144$	1.00000	0.0833333
$145$	20.4270	1.69637
$146$	2.36184	0.195468
$147$	9.51754	0.784994
$148$	−7.88713	−0.648318
$149$	19.2909	1.58037	0.790184	−	0.612869i	$-0.209985\pi$
$149$	19.2909	1.58037	0.790184	+	0.612869i	$0.209985\pi$
$150$	−0.509800	−0.0416250
$151$	13.0787	1.06433	0.532166	−	0.846640i	$-0.321378\pi$
$151$	13.0787	1.06433	0.532166	+	0.846640i	$0.321378\pi$
$152$	6.45336	0.523437
$153$	0	0
$154$	−11.5321	−0.929282
$155$	1.34730	0.108217
$156$	2.69459	0.215740
$157$	10.1284	0.808331	0.404165	−	0.914686i	$-0.367562\pi$
$157$	10.1284	0.808331	0.404165	+	0.914686i	$0.367562\pi$
$158$	7.37464	0.586695
$159$	−3.29086	−0.260982
$160$	−2.34730	−0.185570
$161$	24.3851	1.92181
$162$	−1.00000	−0.0785674
$163$	0.212134	0.0166156	0.00830780	−	0.999965i	$-0.497356\pi$
$163$	0.212134	0.0166156	0.00830780	+	0.999965i	$0.497356\pi$
$164$	−3.43376	−0.268132
$165$	6.66044	0.518515
$166$	−3.21213	−0.249310
$167$	8.49794	0.657590	0.328795	−	0.944401i	$-0.393357\pi$
$167$	8.49794	0.657590	0.328795	+	0.944401i	$0.393357\pi$
$168$	−4.06418	−0.313558
$169$	−5.73917	−0.441475
$170$	0	0
$171$	−6.45336	−0.493501
$172$	−11.6459	−0.887991
$173$	0.226682	0.0172343	0.00861714	−	0.999963i	$-0.497257\pi$
$173$	0.226682	0.0172343	0.00861714	+	0.999963i	$0.497257\pi$
$174$	−8.70233	−0.659722
$175$	2.07192	0.156622
$176$	2.83750	0.213884
$177$	4.34730	0.326763
$178$	6.34049	0.475240
$179$	11.6946	0.874095	0.437047	−	0.899438i	$-0.356024\pi$
$179$	11.6946	0.874095	0.437047	+	0.899438i	$0.356024\pi$
$180$	2.34730	0.174957
$181$	2.49794	0.185670	0.0928352	−	0.995681i	$-0.470407\pi$
$181$	2.49794	0.185670	0.0928352	+	0.995681i	$0.470407\pi$
$182$	−10.9513	−0.811765
$183$	−13.0642	−0.965732
$184$	−6.00000	−0.442326
$185$	−18.5134	−1.36113
$186$	−0.573978	−0.0420861
$187$	0	0
$188$	−10.5817	−0.771751
$189$	4.06418	0.295625
$190$	15.1480	1.09895
$191$	−2.73917	−0.198199	−0.0990997	−	0.995078i	$-0.531596\pi$
$191$	−2.73917	−0.198199	−0.0990997	+	0.995078i	$0.531596\pi$
$192$	1.00000	0.0721688
$193$	13.2540	0.954045	0.477023	−	0.878891i	$-0.341716\pi$
$193$	13.2540	0.954045	0.477023	+	0.878891i	$0.341716\pi$
$194$	−8.11381	−0.582537
$195$	6.32501	0.452943
$196$	9.51754	0.679824
$197$	23.0155	1.63979	0.819893	−	0.572517i	$-0.194033\pi$
$197$	23.0155	1.63979	0.819893	+	0.572517i	$0.194033\pi$
$198$	−2.83750	−0.201652
$199$	−18.1215	−1.28460	−0.642301	−	0.766452i	$-0.722020\pi$
$199$	−18.1215	−1.28460	−0.642301	+	0.766452i	$0.722020\pi$
$200$	−0.509800	−0.0360483
$201$	12.2121	0.861377
$202$	9.17024	0.645216
$203$	35.3678	2.48234
$204$	0	0
$205$	−8.06006	−0.562939
$206$	7.35235	0.512262
$207$	6.00000	0.417029
$208$	2.69459	0.186836
$209$	−18.3114	−1.26663
$210$	−9.53983	−0.658311
$211$	15.5621	1.07134	0.535670	−	0.844427i	$-0.320059\pi$
$211$	15.5621	1.07134	0.535670	+	0.844427i	$0.320059\pi$
$212$	−3.29086	−0.226017
$213$	−11.6013	−0.794909
$214$	5.02734	0.343662
$215$	−27.3364	−1.86432
$216$	−1.00000	−0.0680414
$217$	2.33275	0.158357
$218$	9.06418	0.613904
$219$	−2.36184	−0.159599
$220$	6.66044	0.449047
$221$	0	0
$222$	7.88713	0.529349
$223$	13.3063	0.891058	0.445529	−	0.895267i	$-0.353016\pi$
$223$	13.3063	0.891058	0.445529	+	0.895267i	$0.353016\pi$
$224$	−4.06418	−0.271549
$225$	0.509800	0.0339867
$226$	−11.1480	−0.741551
$227$	−3.69459	−0.245219	−0.122609	−	0.992455i	$-0.539126\pi$
$227$	−3.69459	−0.245219	−0.122609	+	0.992455i	$0.539126\pi$
$228$	−6.45336	−0.427384
$229$	8.85204	0.584960	0.292480	−	0.956272i	$-0.405520\pi$
$229$	8.85204	0.584960	0.292480	+	0.956272i	$0.405520\pi$
$230$	−14.0838	−0.928657
$231$	11.5321	0.758756
$232$	−8.70233	−0.571336
$233$	−5.88713	−0.385678	−0.192839	−	0.981230i	$-0.561770\pi$
$233$	−5.88713	−0.385678	−0.192839	+	0.981230i	$0.561770\pi$
$234$	−2.69459	−0.176151
$235$	−24.8384	−1.62028
$236$	4.34730	0.282985
$237$	−7.37464	−0.479034
$238$	0	0
$239$	16.6108	1.07446	0.537232	−	0.843434i	$-0.319470\pi$
$239$	16.6108	1.07446	0.537232	+	0.843434i	$0.319470\pi$
$240$	2.34730	0.151517
$241$	−8.51485	−0.548490	−0.274245	−	0.961660i	$-0.588428\pi$
$241$	−8.51485	−0.548490	−0.274245	+	0.961660i	$0.588428\pi$
$242$	2.94862	0.189544
$243$	1.00000	0.0641500
$244$	−13.0642	−0.836348
$245$	22.3405	1.42728
$246$	3.43376	0.218929
$247$	−17.3892	−1.10645
$248$	−0.573978	−0.0364476
$249$	3.21213	0.203561
$250$	10.5398	0.666597
$251$	−6.89899	−0.435460	−0.217730	−	0.976009i	$-0.569865\pi$
$251$	−6.89899	−0.435460	−0.217730	+	0.976009i	$0.569865\pi$
$252$	4.06418	0.256019
$253$	17.0250	1.07035
$254$	1.93582	0.121464
$255$	0	0
$256$	1.00000	0.0625000
$257$	22.5526	1.40679	0.703397	−	0.710797i	$-0.251666\pi$
$257$	22.5526	1.40679	0.703397	+	0.710797i	$0.251666\pi$
$258$	11.6459	0.725042
$259$	−32.0547	−1.99178
$260$	6.32501	0.392260
$261$	8.70233	0.538661
$262$	−16.7297	−1.03356
$263$	−16.9513	−1.04526	−0.522631	−	0.852559i	$-0.675049\pi$
$263$	−16.9513	−1.04526	−0.522631	+	0.852559i	$0.675049\pi$
$264$	−2.83750	−0.174636
$265$	−7.72462	−0.474520
$266$	26.2276	1.60812
$267$	−6.34049	−0.388032
$268$	12.2121	0.745975
$269$	10.8084	0.659000	0.329500	−	0.944156i	$-0.393120\pi$
$269$	10.8084	0.659000	0.329500	+	0.944156i	$0.393120\pi$
$270$	−2.34730	−0.142852
$271$	−21.3131	−1.29468	−0.647341	−	0.762201i	$-0.724119\pi$
$271$	−21.3131	−1.29468	−0.647341	+	0.762201i	$0.724119\pi$
$272$	0	0
$273$	10.9513	0.662803
$274$	−4.45336	−0.269038
$275$	1.44656	0.0872306
$276$	6.00000	0.361158
$277$	22.1438	1.33049	0.665247	−	0.746623i	$-0.268326\pi$
$277$	22.1438	1.33049	0.665247	+	0.746623i	$0.268326\pi$
$278$	12.7392	0.764045
$279$	0.573978	0.0343632
$280$	−9.53983	−0.570114
$281$	−10.0155	−0.597474	−0.298737	−	0.954336i	$-0.596565\pi$
$281$	−10.0155	−0.597474	−0.298737	+	0.954336i	$0.596565\pi$
$282$	10.5817	0.630132
$283$	−10.0838	−0.599418	−0.299709	−	0.954031i	$-0.596890\pi$
$283$	−10.0838	−0.599418	−0.299709	+	0.954031i	$0.596890\pi$
$284$	−11.6013	−0.688412
$285$	−15.1480	−0.897287
$286$	−7.64590	−0.452111
$287$	−13.9554	−0.823763
$288$	−1.00000	−0.0589256
$289$	0	0
$290$	−20.4270	−1.19951
$291$	8.11381	0.475640
$292$	−2.36184	−0.138216
$293$	−14.5594	−0.850571	−0.425285	−	0.905059i	$-0.639826\pi$
$293$	−14.5594	−0.850571	−0.425285	+	0.905059i	$0.639826\pi$
$294$	−9.51754	−0.555074
$295$	10.2044	0.594123
$296$	7.88713	0.458430
$297$	2.83750	0.164648
$298$	−19.2909	−1.11749
$299$	16.1676	0.934994
$300$	0.509800	0.0294333
$301$	−47.3310	−2.72811
$302$	−13.0787	−0.752596
$303$	−9.17024	−0.526817
$304$	−6.45336	−0.370126
$305$	−30.6655	−1.75590
$306$	0	0
$307$	−19.6459	−1.12125	−0.560625	−	0.828070i	$-0.689439\pi$
$307$	−19.6459	−1.12125	−0.560625	+	0.828070i	$0.689439\pi$
$308$	11.5321	0.657102
$309$	−7.35235	−0.418261
$310$	−1.34730	−0.0765213
$311$	14.2567	0.808424	0.404212	−	0.914665i	$-0.367546\pi$
$311$	14.2567	0.808424	0.404212	+	0.914665i	$0.367546\pi$
$312$	−2.69459	−0.152551
$313$	21.0351	1.18897	0.594487	−	0.804106i	$-0.297355\pi$
$313$	21.0351	1.18897	0.594487	+	0.804106i	$0.297355\pi$
$314$	−10.1284	−0.571576
$315$	9.53983	0.537509
$316$	−7.37464	−0.414856
$317$	−5.72369	−0.321474	−0.160737	−	0.986997i	$-0.551387\pi$
$317$	−5.72369	−0.321474	−0.160737	+	0.986997i	$0.551387\pi$
$318$	3.29086	0.184542
$319$	24.6928	1.38253
$320$	2.34730	0.131218
$321$	−5.02734	−0.280599
$322$	−24.3851	−1.35893
$323$	0	0
$324$	1.00000	0.0555556
$325$	1.37370	0.0761994
$326$	−0.212134	−0.0117490
$327$	−9.06418	−0.501250
$328$	3.43376	0.189598
$329$	−43.0060	−2.37100
$330$	−6.66044	−0.366645
$331$	3.14796	0.173027	0.0865137	−	0.996251i	$-0.472427\pi$
$331$	3.14796	0.173027	0.0865137	+	0.996251i	$0.472427\pi$
$332$	3.21213	0.176289
$333$	−7.88713	−0.432212
$334$	−8.49794	−0.464987
$335$	28.6655	1.56616
$336$	4.06418	0.221719
$337$	31.9377	1.73976	0.869878	−	0.493266i	$-0.164197\pi$
$337$	31.9377	1.73976	0.869878	+	0.493266i	$0.164197\pi$
$338$	5.73917	0.312170
$339$	11.1480	0.605474
$340$	0	0
$341$	1.62866	0.0881969
$342$	6.45336	0.348958
$343$	10.2317	0.552462
$344$	11.6459	0.627905
$345$	14.0838	0.758245
$346$	−0.226682	−0.0121865
$347$	−36.1215	−1.93911	−0.969553	−	0.244881i	$-0.921251\pi$
$347$	−36.1215	−1.93911	−0.969553	+	0.244881i	$0.921251\pi$
$348$	8.70233	0.466494
$349$	12.7493	0.682453	0.341227	−	0.939981i	$-0.389158\pi$
$349$	12.7493	0.682453	0.341227	+	0.939981i	$0.389158\pi$
$350$	−2.07192	−0.110749
$351$	2.69459	0.143827
$352$	−2.83750	−0.151239
$353$	−7.09327	−0.377537	−0.188768	−	0.982022i	$-0.560450\pi$
$353$	−7.09327	−0.377537	−0.188768	+	0.982022i	$0.560450\pi$
$354$	−4.34730	−0.231056
$355$	−27.2317	−1.44531
$356$	−6.34049	−0.336045
$357$	0	0
$358$	−11.6946	−0.618078
$359$	10.6655	0.562903	0.281452	−	0.959575i	$-0.409184\pi$
$359$	10.6655	0.562903	0.281452	+	0.959575i	$0.409184\pi$
$360$	−2.34730	−0.123713
$361$	22.6459	1.19189
$362$	−2.49794	−0.131289
$363$	−2.94862	−0.154762
$364$	10.9513	0.574004
$365$	−5.54395	−0.290184
$366$	13.0642	0.682876
$367$	−24.2499	−1.26583	−0.632917	−	0.774219i	$-0.718143\pi$
$367$	−24.2499	−1.26583	−0.632917	+	0.774219i	$0.718143\pi$
$368$	6.00000	0.312772
$369$	−3.43376	−0.178755
$370$	18.5134	0.962467
$371$	−13.3746	−0.694377
$372$	0.573978	0.0297594
$373$	−22.7547	−1.17819	−0.589096	−	0.808063i	$-0.700516\pi$
$373$	−22.7547	−1.17819	−0.589096	+	0.808063i	$0.700516\pi$
$374$	0	0
$375$	−10.5398	−0.544274
$376$	10.5817	0.545710
$377$	23.4492	1.20770
$378$	−4.06418	−0.209039
$379$	19.8425	1.01924	0.509622	−	0.860399i	$-0.329785\pi$
$379$	19.8425	1.01924	0.509622	+	0.860399i	$0.329785\pi$
$380$	−15.1480	−0.777074
$381$	−1.93582	−0.0991752
$382$	2.73917	0.140148
$383$	−15.7196	−0.803232	−0.401616	−	0.915808i	$-0.631551\pi$
$383$	−15.7196	−0.803232	−0.401616	+	0.915808i	$0.631551\pi$
$384$	−1.00000	−0.0510310
$385$	27.0692	1.37958
$386$	−13.2540	−0.674612
$387$	−11.6459	−0.591994
$388$	8.11381	0.411916
$389$	32.4766	1.64663	0.823314	−	0.567586i	$-0.192123\pi$
$389$	32.4766	1.64663	0.823314	+	0.567586i	$0.192123\pi$
$390$	−6.32501	−0.320279
$391$	0	0
$392$	−9.51754	−0.480708
$393$	16.7297	0.843900
$394$	−23.0155	−1.15950
$395$	−17.3105	−0.870984
$396$	2.83750	0.142590
$397$	1.84255	0.0924749	0.0462374	−	0.998930i	$-0.485277\pi$
$397$	1.84255	0.0924749	0.0462374	+	0.998930i	$0.485277\pi$
$398$	18.1215	0.908351
$399$	−26.2276	−1.31302
$400$	0.509800	0.0254900
$401$	10.6655	0.532609	0.266305	−	0.963889i	$-0.414197\pi$
$401$	10.6655	0.532609	0.266305	+	0.963889i	$0.414197\pi$
$402$	−12.2121	−0.609086
$403$	1.54664	0.0770435
$404$	−9.17024	−0.456237
$405$	2.34730	0.116638
$406$	−35.3678	−1.75528
$407$	−22.3797	−1.10932
$408$	0	0
$409$	−5.33544	−0.263820	−0.131910	−	0.991262i	$-0.542111\pi$
$409$	−5.33544	−0.263820	−0.131910	+	0.991262i	$0.542111\pi$
$410$	8.06006	0.398058
$411$	4.45336	0.219668
$412$	−7.35235	−0.362224
$413$	17.6682	0.869395
$414$	−6.00000	−0.294884
$415$	7.53983	0.370116
$416$	−2.69459	−0.132113
$417$	−12.7392	−0.623840
$418$	18.3114	0.895640
$419$	−24.6040	−1.20198	−0.600992	−	0.799255i	$-0.705228\pi$
$419$	−24.6040	−1.20198	−0.600992	+	0.799255i	$0.705228\pi$
$420$	9.53983	0.465496
$421$	−2.89662	−0.141173	−0.0705863	−	0.997506i	$-0.522487\pi$
$421$	−2.89662	−0.141173	−0.0705863	+	0.997506i	$0.522487\pi$
$422$	−15.5621	−0.757552
$423$	−10.5817	−0.514501
$424$	3.29086	0.159818
$425$	0	0
$426$	11.6013	0.562086
$427$	−53.0951	−2.56945
$428$	−5.02734	−0.243006
$429$	7.64590	0.369147
$430$	27.3364	1.31828
$431$	−8.17293	−0.393676	−0.196838	−	0.980436i	$-0.563067\pi$
$431$	−8.17293	−0.393676	−0.196838	+	0.980436i	$0.563067\pi$
$432$	1.00000	0.0481125
$433$	−21.7365	−1.04459	−0.522294	−	0.852765i	$-0.674924\pi$
$433$	−21.7365	−1.04459	−0.522294	+	0.852765i	$0.674924\pi$
$434$	−2.33275	−0.111976
$435$	20.4270	0.979398
$436$	−9.06418	−0.434095
$437$	−38.7202	−1.85224
$438$	2.36184	0.112853
$439$	11.2608	0.537450	0.268725	−	0.963217i	$-0.413398\pi$
$439$	11.2608	0.537450	0.268725	+	0.963217i	$0.413398\pi$
$440$	−6.66044	−0.317524
$441$	9.51754	0.453216
$442$	0	0
$443$	−22.4730	−1.06772	−0.533861	−	0.845572i	$-0.679260\pi$
$443$	−22.4730	−1.06772	−0.533861	+	0.845572i	$0.679260\pi$
$444$	−7.88713	−0.374306
$445$	−14.8830	−0.705522
$446$	−13.3063	−0.630074
$447$	19.2909	0.912426
$448$	4.06418	0.192014
$449$	−9.31551	−0.439626	−0.219813	−	0.975542i	$-0.570545\pi$
$449$	−9.31551	−0.439626	−0.219813	+	0.975542i	$0.570545\pi$
$450$	−0.509800	−0.0240322
$451$	−9.74329	−0.458794
$452$	11.1480	0.524356
$453$	13.0787	0.614492
$454$	3.69459	0.173396
$455$	25.7060	1.20511
$456$	6.45336	0.302206
$457$	21.4124	1.00163	0.500815	−	0.865554i	$-0.333034\pi$
$457$	21.4124	1.00163	0.500815	+	0.865554i	$0.333034\pi$
$458$	−8.85204	−0.413629
$459$	0	0
$460$	14.0838	0.656660
$461$	−20.6287	−0.960772	−0.480386	−	0.877057i	$-0.659504\pi$
$461$	−20.6287	−0.960772	−0.480386	+	0.877057i	$0.659504\pi$
$462$	−11.5321	−0.536521
$463$	−25.6973	−1.19425	−0.597127	−	0.802147i	$-0.703691\pi$
$463$	−25.6973	−1.19425	−0.597127	+	0.802147i	$0.703691\pi$
$464$	8.70233	0.403996
$465$	1.34730	0.0624794
$466$	5.88713	0.272716
$467$	−3.15570	−0.146028	−0.0730141	−	0.997331i	$-0.523262\pi$
$467$	−3.15570	−0.146028	−0.0730141	+	0.997331i	$0.523262\pi$
$468$	2.69459	0.124558
$469$	49.6323	2.29181
$470$	24.8384	1.14571
$471$	10.1284	0.466690
$472$	−4.34730	−0.200101
$473$	−33.0452	−1.51942
$474$	7.37464	0.338728
$475$	−3.28993	−0.150952
$476$	0	0
$477$	−3.29086	−0.150678
$478$	−16.6108	−0.759761
$479$	1.92633	0.0880161	0.0440081	−	0.999031i	$-0.485987\pi$
$479$	1.92633	0.0880161	0.0440081	+	0.999031i	$0.485987\pi$
$480$	−2.34730	−0.107139
$481$	−21.2526	−0.969035
$482$	8.51485	0.387841
$483$	24.3851	1.10956
$484$	−2.94862	−0.134028
$485$	19.0455	0.864812
$486$	−1.00000	−0.0453609
$487$	−7.94862	−0.360186	−0.180093	−	0.983650i	$-0.557640\pi$
$487$	−7.94862	−0.360186	−0.180093	+	0.983650i	$0.557640\pi$
$488$	13.0642	0.591388
$489$	0.212134	0.00959302
$490$	−22.3405	−1.00924
$491$	5.25402	0.237111	0.118555	−	0.992947i	$-0.462174\pi$
$491$	5.25402	0.237111	0.118555	+	0.992947i	$0.462174\pi$
$492$	−3.43376	−0.154806
$493$	0	0
$494$	17.3892	0.782376
$495$	6.66044	0.299365
$496$	0.573978	0.0257724
$497$	−47.1498	−2.11496
$498$	−3.21213	−0.143939
$499$	−24.8776	−1.11368	−0.556838	−	0.830621i	$-0.687986\pi$
$499$	−24.8776	−1.11368	−0.556838	+	0.830621i	$0.687986\pi$
$500$	−10.5398	−0.471356
$501$	8.49794	0.379660
$502$	6.89899	0.307917
$503$	−10.9358	−0.487604	−0.243802	−	0.969825i	$-0.578395\pi$
$503$	−10.9358	−0.487604	−0.243802	+	0.969825i	$0.578395\pi$
$504$	−4.06418	−0.181033
$505$	−21.5253	−0.957862
$506$	−17.0250	−0.756853
$507$	−5.73917	−0.254885
$508$	−1.93582	−0.0858882
$509$	38.4219	1.70302	0.851510	−	0.524338i	$-0.175687\pi$
$509$	38.4219	1.70302	0.851510	+	0.524338i	$0.175687\pi$
$510$	0	0
$511$	−9.59896	−0.424633
$512$	−1.00000	−0.0441942
$513$	−6.45336	−0.284923
$514$	−22.5526	−0.994754
$515$	−17.2581	−0.760485
$516$	−11.6459	−0.512682
$517$	−30.0256	−1.32052
$518$	32.0547	1.40840
$519$	0.226682	0.00995022
$520$	−6.32501	−0.277370
$521$	31.2181	1.36769	0.683845	−	0.729627i	$-0.260306\pi$
$521$	31.2181	1.36769	0.683845	+	0.729627i	$0.260306\pi$
$522$	−8.70233	−0.380891
$523$	−17.5567	−0.767703	−0.383851	−	0.923395i	$-0.625402\pi$
$523$	−17.5567	−0.767703	−0.383851	+	0.923395i	$0.625402\pi$
$524$	16.7297	0.730839
$525$	2.07192	0.0904259
$526$	16.9513	0.739112
$527$	0	0
$528$	2.83750	0.123486
$529$	13.0000	0.565217
$530$	7.72462	0.335536
$531$	4.34730	0.188657
$532$	−26.2276	−1.13711
$533$	−9.25259	−0.400774
$534$	6.34049	0.274380
$535$	−11.8007	−0.510187
$536$	−12.2121	−0.527484
$537$	11.6946	0.504659
$538$	−10.8084	−0.465983
$539$	27.0060	1.16323
$540$	2.34730	0.101012
$541$	−10.6791	−0.459131	−0.229565	−	0.973293i	$-0.573730\pi$
$541$	−10.6791	−0.459131	−0.229565	+	0.973293i	$0.573730\pi$
$542$	21.3131	0.915478
$543$	2.49794	0.107197
$544$	0	0
$545$	−21.2763	−0.911377
$546$	−10.9513	−0.468673
$547$	7.56212	0.323333	0.161666	−	0.986845i	$-0.448313\pi$
$547$	7.56212	0.323333	0.161666	+	0.986845i	$0.448313\pi$
$548$	4.45336	0.190238
$549$	−13.0642	−0.557566
$550$	−1.44656	−0.0616814
$551$	−56.1593	−2.39247
$552$	−6.00000	−0.255377
$553$	−29.9718	−1.27453
$554$	−22.1438	−0.940801
$555$	−18.5134	−0.785851
$556$	−12.7392	−0.540261
$557$	−13.9222	−0.589903	−0.294951	−	0.955512i	$-0.595303\pi$
$557$	−13.9222	−0.589903	−0.294951	+	0.955512i	$0.595303\pi$
$558$	−0.573978	−0.0242984
$559$	−31.3809	−1.32727
$560$	9.53983	0.403131
$561$	0	0
$562$	10.0155	0.422478
$563$	−2.71595	−0.114464	−0.0572318	−	0.998361i	$-0.518227\pi$
$563$	−2.71595	−0.114464	−0.0572318	+	0.998361i	$0.518227\pi$
$564$	−10.5817	−0.445571
$565$	26.1676	1.10088
$566$	10.0838	0.423853
$567$	4.06418	0.170679
$568$	11.6013	0.486781
$569$	29.8735	1.25236	0.626181	−	0.779677i	$-0.284617\pi$
$569$	29.8735	1.25236	0.626181	+	0.779677i	$0.284617\pi$
$570$	15.1480	0.634478
$571$	33.0506	1.38312	0.691562	−	0.722318i	$-0.256923\pi$
$571$	33.0506	1.38312	0.691562	+	0.722318i	$0.256923\pi$
$572$	7.64590	0.319691
$573$	−2.73917	−0.114430
$574$	13.9554	0.582488
$575$	3.05880	0.127561
$576$	1.00000	0.0416667
$577$	8.96080	0.373043	0.186521	−	0.982451i	$-0.440279\pi$
$577$	8.96080	0.373043	0.186521	+	0.982451i	$0.440279\pi$
$578$	0	0
$579$	13.2540	0.550818
$580$	20.4270	0.848183
$581$	13.0547	0.541599
$582$	−8.11381	−0.336328
$583$	−9.33780	−0.386732
$584$	2.36184	0.0977338
$585$	6.32501	0.261507
$586$	14.5594	0.601445
$587$	−12.3919	−0.511467	−0.255734	−	0.966747i	$-0.582317\pi$
$587$	−12.3919	−0.511467	−0.255734	+	0.966747i	$0.582317\pi$
$588$	9.51754	0.392497
$589$	−3.70409	−0.152624
$590$	−10.2044	−0.420108
$591$	23.0155	0.946730
$592$	−7.88713	−0.324159
$593$	−46.4005	−1.90544	−0.952721	−	0.303846i	$-0.901729\pi$
$593$	−46.4005	−1.90544	−0.952721	+	0.303846i	$0.901729\pi$
$594$	−2.83750	−0.116424
$595$	0	0
$596$	19.2909	0.790184
$597$	−18.1215	−0.741666
$598$	−16.1676	−0.661141
$599$	19.4492	0.794675	0.397337	−	0.917673i	$-0.369934\pi$
$599$	19.4492	0.794675	0.397337	+	0.917673i	$0.369934\pi$
$600$	−0.509800	−0.0208125
$601$	−31.7665	−1.29578	−0.647892	−	0.761733i	$-0.724349\pi$
$601$	−31.7665	−1.29578	−0.647892	+	0.761733i	$0.724349\pi$
$602$	47.3310	1.92907
$603$	12.2121	0.497317
$604$	13.0787	0.532166
$605$	−6.92127	−0.281390
$606$	9.17024	0.372516
$607$	9.22399	0.374390	0.187195	−	0.982323i	$-0.440060\pi$
$607$	9.22399	0.374390	0.187195	+	0.982323i	$0.440060\pi$
$608$	6.45336	0.261718
$609$	35.3678	1.43318
$610$	30.6655	1.24161
$611$	−28.5134	−1.15353
$612$	0	0
$613$	17.1634	0.693225	0.346612	−	0.938008i	$-0.387332\pi$
$613$	17.1634	0.693225	0.346612	+	0.938008i	$0.387332\pi$
$614$	19.6459	0.792844
$615$	−8.06006	−0.325013
$616$	−11.5321	−0.464641
$617$	−16.3750	−0.659231	−0.329616	−	0.944115i	$-0.606919\pi$
$617$	−16.3750	−0.659231	−0.329616	+	0.944115i	$0.606919\pi$
$618$	7.35235	0.295755
$619$	30.2276	1.21495	0.607475	−	0.794339i	$-0.292182\pi$
$619$	30.2276	1.21495	0.607475	+	0.794339i	$0.292182\pi$
$620$	1.34730	0.0541087
$621$	6.00000	0.240772
$622$	−14.2567	−0.571642
$623$	−25.7689	−1.03241
$624$	2.69459	0.107870
$625$	−27.2891	−1.09156
$626$	−21.0351	−0.840731
$627$	−18.3114	−0.731287
$628$	10.1284	0.404165
$629$	0	0
$630$	−9.53983	−0.380076
$631$	15.1848	0.604497	0.302249	−	0.953229i	$-0.402263\pi$
$631$	15.1848	0.604497	0.302249	+	0.953229i	$0.402263\pi$
$632$	7.37464	0.293347
$633$	15.5621	0.618539
$634$	5.72369	0.227317
$635$	−4.54395	−0.180321
$636$	−3.29086	−0.130491
$637$	25.6459	1.01613
$638$	−24.6928	−0.977599
$639$	−11.6013	−0.458941
$640$	−2.34730	−0.0927850
$641$	8.38507	0.331190	0.165595	−	0.986194i	$-0.447046\pi$
$641$	8.38507	0.331190	0.165595	+	0.986194i	$0.447046\pi$
$642$	5.02734	0.198413
$643$	−5.43376	−0.214287	−0.107143	−	0.994244i	$-0.534170\pi$
$643$	−5.43376	−0.214287	−0.107143	+	0.994244i	$0.534170\pi$
$644$	24.3851	0.960906
$645$	−27.3364	−1.07637
$646$	0	0
$647$	13.0797	0.514214	0.257107	−	0.966383i	$-0.417231\pi$
$647$	13.0797	0.514214	0.257107	+	0.966383i	$0.417231\pi$
$648$	−1.00000	−0.0392837
$649$	12.3354	0.484208
$650$	−1.37370	−0.0538811
$651$	2.33275	0.0914276
$652$	0.212134	0.00830780
$653$	−29.5175	−1.15511	−0.577555	−	0.816352i	$-0.695993\pi$
$653$	−29.5175	−1.15511	−0.577555	+	0.816352i	$0.695993\pi$
$654$	9.06418	0.354437
$655$	39.2695	1.53439
$656$	−3.43376	−0.134066
$657$	−2.36184	−0.0921443
$658$	43.0060	1.67655
$659$	21.5084	0.837847	0.418924	−	0.908022i	$-0.362408\pi$
$659$	21.5084	0.837847	0.418924	+	0.908022i	$0.362408\pi$
$660$	6.66044	0.259257
$661$	35.2080	1.36943	0.684717	−	0.728809i	$-0.259926\pi$
$661$	35.2080	1.36943	0.684717	+	0.728809i	$0.259926\pi$
$662$	−3.14796	−0.122349
$663$	0	0
$664$	−3.21213	−0.124655
$665$	−61.5640	−2.38735
$666$	7.88713	0.305620
$667$	52.2140	2.02173
$668$	8.49794	0.328795
$669$	13.3063	0.514453
$670$	−28.6655	−1.10744
$671$	−37.0696	−1.43105
$672$	−4.06418	−0.156779
$673$	−1.94181	−0.0748512	−0.0374256	−	0.999299i	$-0.511916\pi$
$673$	−1.94181	−0.0748512	−0.0374256	+	0.999299i	$0.511916\pi$
$674$	−31.9377	−1.23019
$675$	0.509800	0.0196222
$676$	−5.73917	−0.220737
$677$	−1.44799	−0.0556506	−0.0278253	−	0.999613i	$-0.508858\pi$
$677$	−1.44799	−0.0556506	−0.0278253	+	0.999613i	$0.508858\pi$
$678$	−11.1480	−0.428135
$679$	32.9760	1.26550
$680$	0	0
$681$	−3.69459	−0.141577
$682$	−1.62866	−0.0623646
$683$	−17.5553	−0.671735	−0.335868	−	0.941909i	$-0.609029\pi$
$683$	−17.5553	−0.671735	−0.335868	+	0.941909i	$0.609029\pi$
$684$	−6.45336	−0.246751
$685$	10.4534	0.399402
$686$	−10.2317	−0.390649
$687$	8.85204	0.337727
$688$	−11.6459	−0.443996
$689$	−8.86753	−0.337826
$690$	−14.0838	−0.536160
$691$	17.8425	0.678763	0.339381	−	0.940649i	$-0.389782\pi$
$691$	17.8425	0.678763	0.339381	+	0.940649i	$0.389782\pi$
$692$	0.226682	0.00861714
$693$	11.5321	0.438068
$694$	36.1215	1.37116
$695$	−29.9026	−1.13427
$696$	−8.70233	−0.329861
$697$	0	0
$698$	−12.7493	−0.482567
$699$	−5.88713	−0.222672
$700$	2.07192	0.0783112
$701$	43.0051	1.62428	0.812139	−	0.583464i	$-0.198303\pi$
$701$	43.0051	1.62428	0.812139	+	0.583464i	$0.198303\pi$
$702$	−2.69459	−0.101701
$703$	50.8985	1.91967
$704$	2.83750	0.106942
$705$	−24.8384	−0.935469
$706$	7.09327	0.266959
$707$	−37.2695	−1.40166
$708$	4.34730	0.163381
$709$	10.8966	0.409231	0.204616	−	0.978842i	$-0.434406\pi$
$709$	10.8966	0.409231	0.204616	+	0.978842i	$0.434406\pi$
$710$	27.2317	1.02199
$711$	−7.37464	−0.276571
$712$	6.34049	0.237620
$713$	3.44387	0.128974
$714$	0	0
$715$	17.9472	0.671187
$716$	11.6946	0.437047
$717$	16.6108	0.620342
$718$	−10.6655	−0.398033
$719$	9.80335	0.365603	0.182802	−	0.983150i	$-0.441483\pi$
$719$	9.80335	0.365603	0.182802	+	0.983150i	$0.441483\pi$
$720$	2.34730	0.0874786
$721$	−29.8813	−1.11284
$722$	−22.6459	−0.842793
$723$	−8.51485	−0.316671
$724$	2.49794	0.0928352
$725$	4.43645	0.164766
$726$	2.94862	0.109433
$727$	−0.598631	−0.0222020	−0.0111010	−	0.999938i	$-0.503534\pi$
$727$	−0.598631	−0.0222020	−0.0111010	+	0.999938i	$0.503534\pi$
$728$	−10.9513	−0.405882
$729$	1.00000	0.0370370
$730$	5.54395	0.205191
$731$	0	0
$732$	−13.0642	−0.482866
$733$	44.4944	1.64344	0.821720	−	0.569892i	$-0.193015\pi$
$733$	44.4944	1.64344	0.821720	+	0.569892i	$0.193015\pi$
$734$	24.2499	0.895080
$735$	22.3405	0.824041
$736$	−6.00000	−0.221163
$737$	34.6519	1.27642
$738$	3.43376	0.126399
$739$	−21.0060	−0.772718	−0.386359	−	0.922349i	$-0.626267\pi$
$739$	−21.0060	−0.772718	−0.386359	+	0.922349i	$0.626267\pi$
$740$	−18.5134	−0.680567
$741$	−17.3892	−0.638808
$742$	13.3746	0.490998
$743$	24.0702	0.883049	0.441524	−	0.897249i	$-0.354438\pi$
$743$	24.0702	0.883049	0.441524	+	0.897249i	$0.354438\pi$
$744$	−0.573978	−0.0210431
$745$	45.2814	1.65898
$746$	22.7547	0.833107
$747$	3.21213	0.117526
$748$	0	0
$749$	−20.4320	−0.746569
$750$	10.5398	0.384860
$751$	1.48515	0.0541938	0.0270969	−	0.999633i	$-0.491374\pi$
$751$	1.48515	0.0541938	0.0270969	+	0.999633i	$0.491374\pi$
$752$	−10.5817	−0.385876
$753$	−6.89899	−0.251413
$754$	−23.4492	−0.853971
$755$	30.6996	1.11727
$756$	4.06418	0.147813
$757$	36.5134	1.32710	0.663551	−	0.748131i	$-0.269048\pi$
$757$	36.5134	1.32710	0.663551	+	0.748131i	$0.269048\pi$
$758$	−19.8425	−0.720714
$759$	17.0250	0.617968
$760$	15.1480	0.549474
$761$	−7.06418	−0.256076	−0.128038	−	0.991769i	$-0.540868\pi$
$761$	−7.06418	−0.256076	−0.128038	+	0.991769i	$0.540868\pi$
$762$	1.93582	0.0701274
$763$	−36.8384	−1.33364
$764$	−2.73917	−0.0990997
$765$	0	0
$766$	15.7196	0.567971
$767$	11.7142	0.422975
$768$	1.00000	0.0360844
$769$	9.04189	0.326059	0.163029	−	0.986621i	$-0.447873\pi$
$769$	9.04189	0.326059	0.163029	+	0.986621i	$0.447873\pi$
$770$	−27.0692	−0.975507
$771$	22.5526	0.812213
$772$	13.2540	0.477023
$773$	3.06324	0.110177	0.0550886	−	0.998481i	$-0.482456\pi$
$773$	3.06324	0.110177	0.0550886	+	0.998481i	$0.482456\pi$
$774$	11.6459	0.418603
$775$	0.292614	0.0105110
$776$	−8.11381	−0.291269
$777$	−32.0547	−1.14996
$778$	−32.4766	−1.16434
$779$	22.1593	0.793940
$780$	6.32501	0.226472
$781$	−32.9187	−1.17792
$782$	0	0
$783$	8.70233	0.310996
$784$	9.51754	0.339912
$785$	23.7743	0.848539
$786$	−16.7297	−0.596728
$787$	−18.2466	−0.650421	−0.325211	−	0.945642i	$-0.605435\pi$
$787$	−18.2466	−0.650421	−0.325211	+	0.945642i	$0.605435\pi$
$788$	23.0155	0.819893
$789$	−16.9513	−0.603482
$790$	17.3105	0.615879
$791$	45.3073	1.61094
$792$	−2.83750	−0.100826
$793$	−35.2026	−1.25008
$794$	−1.84255	−0.0653896
$795$	−7.72462	−0.273964
$796$	−18.1215	−0.642301
$797$	45.2222	1.60185	0.800927	−	0.598762i	$-0.204341\pi$
$797$	45.2222	1.60185	0.800927	+	0.598762i	$0.204341\pi$
$798$	26.2276	0.928448
$799$	0	0
$800$	−0.509800	−0.0180242
$801$	−6.34049	−0.224030
$802$	−10.6655	−0.376612
$803$	−6.70172	−0.236499
$804$	12.2121	0.430689
$805$	57.2390	2.01741
$806$	−1.54664	−0.0544780
$807$	10.8084	0.380474
$808$	9.17024	0.322608
$809$	−14.9905	−0.527038	−0.263519	−	0.964654i	$-0.584883\pi$
$809$	−14.9905	−0.527038	−0.263519	+	0.964654i	$0.584883\pi$
$810$	−2.34730	−0.0824756
$811$	20.1438	0.707346	0.353673	−	0.935369i	$-0.384933\pi$
$811$	20.1438	0.707346	0.353673	+	0.935369i	$0.384933\pi$
$812$	35.3678	1.24117
$813$	−21.3131	−0.747485
$814$	22.3797	0.784408
$815$	0.497941	0.0174421
$816$	0	0
$817$	75.1552	2.62935
$818$	5.33544	0.186549
$819$	10.9513	0.382670
$820$	−8.06006	−0.281469
$821$	−42.9959	−1.50057	−0.750283	−	0.661116i	$-0.770083\pi$
$821$	−42.9959	−1.50057	−0.750283	+	0.661116i	$0.770083\pi$
$822$	−4.45336	−0.155329
$823$	−15.0104	−0.523231	−0.261615	−	0.965172i	$-0.584255\pi$
$823$	−15.0104	−0.523231	−0.261615	+	0.965172i	$0.584255\pi$
$824$	7.35235	0.256131
$825$	1.44656	0.0503626
$826$	−17.6682	−0.614755
$827$	−7.33780	−0.255160	−0.127580	−	0.991828i	$-0.540721\pi$
$827$	−7.33780	−0.255160	−0.127580	+	0.991828i	$0.540721\pi$
$828$	6.00000	0.208514
$829$	−14.0310	−0.487315	−0.243658	−	0.969861i	$-0.578347\pi$
$829$	−14.0310	−0.487315	−0.243658	+	0.969861i	$0.578347\pi$
$830$	−7.53983	−0.261711
$831$	22.1438	0.768161
$832$	2.69459	0.0934182
$833$	0	0
$834$	12.7392	0.441121
$835$	19.9472	0.690301
$836$	−18.3114	−0.633313
$837$	0.573978	0.0198396
$838$	24.6040	0.849931
$839$	31.6323	1.09207	0.546034	−	0.837763i	$-0.316137\pi$
$839$	31.6323	1.09207	0.546034	+	0.837763i	$0.316137\pi$
$840$	−9.53983	−0.329155
$841$	46.7306	1.61140
$842$	2.89662	0.0998242
$843$	−10.0155	−0.344952
$844$	15.5621	0.535670
$845$	−13.4715	−0.463435
$846$	10.5817	0.363807
$847$	−11.9837	−0.411765
$848$	−3.29086	−0.113009
$849$	−10.0838	−0.346074
$850$	0	0
$851$	−47.3228	−1.62220
$852$	−11.6013	−0.397455
$853$	33.7743	1.15641	0.578204	−	0.815892i	$-0.303754\pi$
$853$	33.7743	1.15641	0.578204	+	0.815892i	$0.303754\pi$
$854$	53.0951	1.81688
$855$	−15.1480	−0.518049
$856$	5.02734	0.171831
$857$	−9.57222	−0.326981	−0.163490	−	0.986545i	$-0.552275\pi$
$857$	−9.57222	−0.326981	−0.163490	+	0.986545i	$0.552275\pi$
$858$	−7.64590	−0.261027
$859$	−45.6870	−1.55882	−0.779410	−	0.626515i	$-0.784481\pi$
$859$	−45.6870	−1.55882	−0.779410	+	0.626515i	$0.784481\pi$
$860$	−27.3364	−0.932162
$861$	−13.9554	−0.475600
$862$	8.17293	0.278371
$863$	−38.6674	−1.31625	−0.658126	−	0.752908i	$-0.728651\pi$
$863$	−38.6674	−1.31625	−0.658126	+	0.752908i	$0.728651\pi$
$864$	−1.00000	−0.0340207
$865$	0.532089	0.0180916
$866$	21.7365	0.738636
$867$	0	0
$868$	2.33275	0.0791786
$869$	−20.9255	−0.709849
$870$	−20.4270	−0.692539
$871$	32.9067	1.11500
$872$	9.06418	0.306952
$873$	8.11381	0.274611
$874$	38.7202	1.30973
$875$	−42.8357	−1.44811
$876$	−2.36184	−0.0797993
$877$	−9.59121	−0.323872	−0.161936	−	0.986801i	$-0.551774\pi$
$877$	−9.59121	−0.323872	−0.161936	+	0.986801i	$0.551774\pi$
$878$	−11.2608	−0.380035
$879$	−14.5594	−0.491077
$880$	6.66044	0.224524
$881$	45.4884	1.53254	0.766272	−	0.642516i	$-0.222109\pi$
$881$	45.4884	1.53254	0.766272	+	0.642516i	$0.222109\pi$
$882$	−9.51754	−0.320472
$883$	47.3911	1.59484	0.797418	−	0.603427i	$-0.206199\pi$
$883$	47.3911	1.59484	0.797418	+	0.603427i	$0.206199\pi$
$884$	0	0
$885$	10.2044	0.343017
$886$	22.4730	0.754994
$887$	−1.10876	−0.0372284	−0.0186142	−	0.999827i	$-0.505925\pi$
$887$	−1.10876	−0.0372284	−0.0186142	+	0.999827i	$0.505925\pi$
$888$	7.88713	0.264675
$889$	−7.86753	−0.263868
$890$	14.8830	0.498880
$891$	2.83750	0.0950597
$892$	13.3063	0.445529
$893$	68.2877	2.28516
$894$	−19.2909	−0.645183
$895$	27.4507	0.917575
$896$	−4.06418	−0.135775
$897$	16.1676	0.539819
$898$	9.31551	0.310863
$899$	4.99495	0.166591
$900$	0.509800	0.0169933
$901$	0	0
$902$	9.74329	0.324416
$903$	−47.3310	−1.57508
$904$	−11.1480	−0.370775
$905$	5.86341	0.194906
$906$	−13.0787	−0.434512
$907$	3.64403	0.120998	0.0604990	−	0.998168i	$-0.480731\pi$
$907$	3.64403	0.120998	0.0604990	+	0.998168i	$0.480731\pi$
$908$	−3.69459	−0.122609
$909$	−9.17024	−0.304158
$910$	−25.7060	−0.852144
$911$	−5.45748	−0.180814	−0.0904072	−	0.995905i	$-0.528817\pi$
$911$	−5.45748	−0.180814	−0.0904072	+	0.995905i	$0.528817\pi$
$912$	−6.45336	−0.213692
$913$	9.11442	0.301643
$914$	−21.4124	−0.708259
$915$	−30.6655	−1.01377
$916$	8.85204	0.292480
$917$	67.9924	2.24531
$918$	0	0
$919$	−44.0060	−1.45162	−0.725812	−	0.687893i	$-0.758536\pi$
$919$	−44.0060	−1.45162	−0.725812	+	0.687893i	$0.758536\pi$
$920$	−14.0838	−0.464328
$921$	−19.6459	−0.647354
$922$	20.6287	0.679369
$923$	−31.2608	−1.02896
$924$	11.5321	0.379378
$925$	−4.02086	−0.132205
$926$	25.6973	0.844465
$927$	−7.35235	−0.241483
$928$	−8.70233	−0.285668
$929$	47.2472	1.55013	0.775065	−	0.631881i	$-0.217717\pi$
$929$	47.2472	1.55013	0.775065	+	0.631881i	$0.217717\pi$
$930$	−1.34730	−0.0441796
$931$	−61.4201	−2.01296
$932$	−5.88713	−0.192839
$933$	14.2567	0.466744
$934$	3.15570	0.103258
$935$	0	0
$936$	−2.69459	−0.0880755
$937$	−42.9445	−1.40294	−0.701468	−	0.712701i	$-0.747472\pi$
$937$	−42.9445	−1.40294	−0.701468	+	0.712701i	$0.747472\pi$
$938$	−49.6323	−1.62055
$939$	21.0351	0.686454
$940$	−24.8384	−0.810140
$941$	−56.6418	−1.84647	−0.923235	−	0.384237i	$-0.874465\pi$
$941$	−56.6418	−1.84647	−0.923235	+	0.384237i	$0.874465\pi$
$942$	−10.1284	−0.330000
$943$	−20.6026	−0.670912
$944$	4.34730	0.141492
$945$	9.53983	0.310331
$946$	33.0452	1.07439
$947$	−56.0610	−1.82174	−0.910869	−	0.412696i	$-0.864587\pi$
$947$	−56.0610	−1.82174	−0.910869	+	0.412696i	$0.864587\pi$
$948$	−7.37464	−0.239517
$949$	−6.36421	−0.206591
$950$	3.28993	0.106739
$951$	−5.72369	−0.185603
$952$	0	0
$953$	41.5586	1.34622	0.673108	−	0.739544i	$-0.264959\pi$
$953$	41.5586	1.34622	0.673108	+	0.739544i	$0.264959\pi$
$954$	3.29086	0.106546
$955$	−6.42964	−0.208058
$956$	16.6108	0.537232
$957$	24.6928	0.798206
$958$	−1.92633	−0.0622368
$959$	18.0993	0.584456
$960$	2.34730	0.0757587
$961$	−30.6705	−0.989373
$962$	21.2526	0.685211
$963$	−5.02734	−0.162004
$964$	−8.51485	−0.274245
$965$	31.1111	1.00150
$966$	−24.3851	−0.784577
$967$	−25.3040	−0.813721	−0.406861	−	0.913490i	$-0.633376\pi$
$967$	−25.3040	−0.813721	−0.406861	+	0.913490i	$0.633376\pi$
$968$	2.94862	0.0947721
$969$	0	0
$970$	−19.0455	−0.611515
$971$	20.2558	0.650039	0.325019	−	0.945707i	$-0.394629\pi$
$971$	20.2558	0.650039	0.325019	+	0.945707i	$0.394629\pi$
$972$	1.00000	0.0320750
$973$	−51.7743	−1.65981
$974$	7.94862	0.254690
$975$	1.37370	0.0439937
$976$	−13.0642	−0.418174
$977$	1.17705	0.0376572	0.0188286	−	0.999823i	$-0.494006\pi$
$977$	1.17705	0.0376572	0.0188286	+	0.999823i	$0.494006\pi$
$978$	−0.212134	−0.00678329
$979$	−17.9911	−0.574998
$980$	22.3405	0.713641
$981$	−9.06418	−0.289397
$982$	−5.25402	−0.167663
$983$	−34.1593	−1.08951	−0.544757	−	0.838594i	$-0.683378\pi$
$983$	−34.1593	−1.08951	−0.544757	+	0.838594i	$0.683378\pi$
$984$	3.43376	0.109464
$985$	54.0242	1.72135
$986$	0	0
$987$	−43.0060	−1.36890
$988$	−17.3892	−0.553224
$989$	−69.8754	−2.22191
$990$	−6.66044	−0.211683
$991$	−16.0642	−0.510295	−0.255148	−	0.966902i	$-0.582124\pi$
$991$	−16.0642	−0.510295	−0.255148	+	0.966902i	$0.582124\pi$
$992$	−0.573978	−0.0182238
$993$	3.14796	0.0998974
$994$	47.1498	1.49550
$995$	−42.5366	−1.34850
$996$	3.21213	0.101780
$997$	18.7784	0.594717	0.297358	−	0.954766i	$-0.403894\pi$
$997$	18.7784	0.594717	0.297358	+	0.954766i	$0.403894\pi$
$998$	24.8776	0.787488
$999$	−7.88713	−0.249538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1734.2.a.q.1.2	yes	3
3.2	odd	2		5202.2.a.bm.1.2		3
17.2	even	8		1734.2.f.n.1483.5		12
17.4	even	4		1734.2.b.j.577.2		6
17.8	even	8		1734.2.f.n.829.2		12
17.9	even	8		1734.2.f.n.829.5		12
17.13	even	4		1734.2.b.j.577.5		6
17.15	even	8		1734.2.f.n.1483.2		12
17.16	even	2		1734.2.a.p.1.2	✓	3
51.50	odd	2		5202.2.a.bp.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1734.2.a.p.1.2	✓	3	17.16	even	2
1734.2.a.q.1.2	yes	3	1.1	even	1	trivial
1734.2.b.j.577.2		6	17.4	even	4
1734.2.b.j.577.5		6	17.13	even	4
1734.2.f.n.829.2		12	17.8	even	8
1734.2.f.n.829.5		12	17.9	even	8
1734.2.f.n.1483.2		12	17.15	even	8
1734.2.f.n.1483.5		12	17.2	even	8
5202.2.a.bm.1.2		3	3.2	odd	2
5202.2.a.bp.1.2		3	51.50	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:	\( N \)	\(=\)	\( 1734 = 2 \cdot 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1734.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.34730 q^{5} -1.00000 q^{6} +4.06418 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.34730 q^{5} -1.00000 q^{6} +4.06418 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.34730 q^{10} +2.83750 q^{11} +1.00000 q^{12} +2.69459 q^{13} -4.06418 q^{14} +2.34730 q^{15} +1.00000 q^{16} -1.00000 q^{18} -6.45336 q^{19} +2.34730 q^{20} +4.06418 q^{21} -2.83750 q^{22} +6.00000 q^{23} -1.00000 q^{24} +0.509800 q^{25} -2.69459 q^{26} +1.00000 q^{27} +4.06418 q^{28} +8.70233 q^{29} -2.34730 q^{30} +0.573978 q^{31} -1.00000 q^{32} +2.83750 q^{33} +9.53983 q^{35} +1.00000 q^{36} -7.88713 q^{37} +6.45336 q^{38} +2.69459 q^{39} -2.34730 q^{40} -3.43376 q^{41} -4.06418 q^{42} -11.6459 q^{43} +2.83750 q^{44} +2.34730 q^{45} -6.00000 q^{46} -10.5817 q^{47} +1.00000 q^{48} +9.51754 q^{49} -0.509800 q^{50} +2.69459 q^{52} -3.29086 q^{53} -1.00000 q^{54} +6.66044 q^{55} -4.06418 q^{56} -6.45336 q^{57} -8.70233 q^{58} +4.34730 q^{59} +2.34730 q^{60} -13.0642 q^{61} -0.573978 q^{62} +4.06418 q^{63} +1.00000 q^{64} +6.32501 q^{65} -2.83750 q^{66} +12.2121 q^{67} +6.00000 q^{69} -9.53983 q^{70} -11.6013 q^{71} -1.00000 q^{72} -2.36184 q^{73} +7.88713 q^{74} +0.509800 q^{75} -6.45336 q^{76} +11.5321 q^{77} -2.69459 q^{78} -7.37464 q^{79} +2.34730 q^{80} +1.00000 q^{81} +3.43376 q^{82} +3.21213 q^{83} +4.06418 q^{84} +11.6459 q^{86} +8.70233 q^{87} -2.83750 q^{88} -6.34049 q^{89} -2.34730 q^{90} +10.9513 q^{91} +6.00000 q^{92} +0.573978 q^{93} +10.5817 q^{94} -15.1480 q^{95} -1.00000 q^{96} +8.11381 q^{97} -9.51754 q^{98} +2.83750 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} - 6 q^{10} + 6 q^{11} + 3 q^{12} + 6 q^{13} - 3 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{21} - 6 q^{22} + 18 q^{23} - 3 q^{24} + 3 q^{25} - 6 q^{26} + 3 q^{27} + 3 q^{28} - 6 q^{30} - 6 q^{31} - 3 q^{32} + 6 q^{33} + 3 q^{36} + 6 q^{37} + 6 q^{38} + 6 q^{39} - 6 q^{40} + 6 q^{41} - 3 q^{42} + 6 q^{43} + 6 q^{44} + 6 q^{45} - 18 q^{46} + 3 q^{48} + 6 q^{49} - 3 q^{50} + 6 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{55} - 3 q^{56} - 6 q^{57} + 12 q^{59} + 6 q^{60} - 30 q^{61} + 6 q^{62} + 3 q^{63} + 3 q^{64} + 24 q^{65} - 6 q^{66} + 12 q^{67} + 18 q^{69} - 6 q^{71} - 3 q^{72} - 24 q^{73} - 6 q^{74} + 3 q^{75} - 6 q^{76} + 30 q^{77} - 6 q^{78} + 6 q^{80} + 3 q^{81} - 6 q^{82} - 15 q^{83} + 3 q^{84} - 6 q^{86} - 6 q^{88} + 24 q^{89} - 6 q^{90} - 6 q^{91} + 18 q^{92} - 6 q^{93} - 30 q^{95} - 3 q^{96} - 12 q^{97} - 6 q^{98} + 6 q^{99}+O(q^{100}) \) 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 + 6 * q^11 + 3 * q^12 + 6 * q^13 - 3 * q^14 + 6 * q^15 + 3 * q^16 - 3 * q^18 - 6 * q^19 + 6 * q^20 + 3 * q^21 - 6 * q^22 + 18 * q^23 - 3 * q^24 + 3 * q^25 - 6 * q^26 + 3 * q^27 + 3 * q^28 - 6 * q^30 - 6 * q^31 - 3 * q^32 + 6 * q^33 + 3 * q^36 + 6 * q^37 + 6 * q^38 + 6 * q^39 - 6 * q^40 + 6 * q^41 - 3 * q^42 + 6 * q^43 + 6 * q^44 + 6 * q^45 - 18 * q^46 + 3 * q^48 + 6 * q^49 - 3 * q^50 + 6 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^55 - 3 * q^56 - 6 * q^57 + 12 * q^59 + 6 * q^60 - 30 * q^61 + 6 * q^62 + 3 * q^63 + 3 * q^64 + 24 * q^65 - 6 * q^66 + 12 * q^67 + 18 * q^69 - 6 * q^71 - 3 * q^72 - 24 * q^73 - 6 * q^74 + 3 * q^75 - 6 * q^76 + 30 * q^77 - 6 * q^78 + 6 * q^80 + 3 * q^81 - 6 * q^82 - 15 * q^83 + 3 * q^84 - 6 * q^86 - 6 * q^88 + 24 * q^89 - 6 * q^90 - 6 * q^91 + 18 * q^92 - 6 * q^93 - 30 * q^95 - 3 * q^96 - 12 * q^97 - 6 * q^98 + 6 * q^99

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