LMFDB - Embedded newform 289.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.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:	$2.30767661842$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.87939 q^{2} -2.53209 q^{3} +1.53209 q^{4} -0.120615 q^{5} +4.75877 q^{6} +1.53209 q^{7} +0.879385 q^{8} +3.41147 q^{9} +O(q^{10})$	\(q-1.87939 q^{2} -2.53209 q^{3} +1.53209 q^{4} -0.120615 q^{5} +4.75877 q^{6} +1.53209 q^{7} +0.879385 q^{8} +3.41147 q^{9} +0.226682 q^{10} -2.69459 q^{11} -3.87939 q^{12} +4.57398 q^{13} -2.87939 q^{14} +0.305407 q^{15} -4.71688 q^{16} -6.41147 q^{18} -1.87939 q^{19} -0.184793 q^{20} -3.87939 q^{21} +5.06418 q^{22} -7.41147 q^{23} -2.22668 q^{24} -4.98545 q^{25} -8.59627 q^{26} -1.04189 q^{27} +2.34730 q^{28} -3.41147 q^{29} -0.573978 q^{30} -3.83750 q^{31} +7.10607 q^{32} +6.82295 q^{33} -0.184793 q^{35} +5.22668 q^{36} +5.24897 q^{37} +3.53209 q^{38} -11.5817 q^{39} -0.106067 q^{40} -6.24897 q^{41} +7.29086 q^{42} +5.49020 q^{43} -4.12836 q^{44} -0.411474 q^{45} +13.9290 q^{46} -7.34730 q^{47} +11.9436 q^{48} -4.65270 q^{49} +9.36959 q^{50} +7.00774 q^{52} +0.822948 q^{53} +1.95811 q^{54} +0.325008 q^{55} +1.34730 q^{56} +4.75877 q^{57} +6.41147 q^{58} -3.14290 q^{59} +0.467911 q^{60} -1.22668 q^{61} +7.21213 q^{62} +5.22668 q^{63} -3.92127 q^{64} -0.551689 q^{65} -12.8229 q^{66} -14.6236 q^{67} +18.7665 q^{69} +0.347296 q^{70} +0.170245 q^{71} +3.00000 q^{72} +11.8007 q^{73} -9.86484 q^{74} +12.6236 q^{75} -2.87939 q^{76} -4.12836 q^{77} +21.7665 q^{78} +4.14796 q^{79} +0.568926 q^{80} -7.59627 q^{81} +11.7442 q^{82} -2.43376 q^{83} -5.94356 q^{84} -10.3182 q^{86} +8.63816 q^{87} -2.36959 q^{88} -15.0915 q^{89} +0.773318 q^{90} +7.00774 q^{91} -11.3550 q^{92} +9.71688 q^{93} +13.8084 q^{94} +0.226682 q^{95} -17.9932 q^{96} -11.1925 q^{97} +8.74422 q^{98} -9.19253 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} - 6 q^{5} + 3 q^{6} - 3 q^{8}+O(q^{10}) $ 3 * q - 3 * q^3 - 6 * q^5 + 3 * q^6 - 3 * q^8	$ 3 q - 3 q^{3} - 6 q^{5} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 3 q^{14} + 3 q^{15} - 6 q^{16} - 9 q^{18} + 3 q^{20} - 6 q^{21} + 6 q^{22} - 12 q^{23} + 3 q^{25} - 12 q^{26} + 6 q^{28} + 6 q^{30} - 9 q^{31} + 9 q^{32} + 3 q^{35} + 9 q^{36} + 3 q^{37} + 6 q^{38} - 3 q^{39} + 12 q^{40} - 6 q^{41} + 6 q^{42} + 15 q^{43} + 6 q^{44} + 9 q^{45} + 9 q^{46} - 21 q^{47} + 21 q^{48} - 15 q^{49} + 21 q^{50} - 3 q^{52} - 18 q^{53} + 9 q^{54} + 6 q^{55} + 3 q^{56} + 3 q^{57} + 9 q^{58} - 9 q^{59} + 6 q^{60} + 3 q^{61} - 3 q^{62} + 9 q^{63} - 3 q^{64} - 18 q^{66} - 9 q^{67} + 21 q^{69} - 21 q^{71} + 9 q^{72} + 21 q^{73} - 6 q^{74} + 3 q^{75} - 3 q^{76} + 6 q^{77} + 30 q^{78} - 3 q^{79} + 9 q^{80} - 9 q^{81} + 6 q^{82} + 9 q^{83} - 3 q^{84} + 6 q^{86} + 9 q^{87} - 15 q^{89} + 9 q^{90} - 3 q^{91} - 9 q^{92} + 21 q^{93} + 3 q^{94} - 6 q^{95} - 12 q^{96} - 6 q^{97} - 3 q^{98}+O(q^{100}) $ 3 * q - 3 * q^3 - 6 * q^5 + 3 * q^6 - 3 * q^8 - 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 3 * q^14 + 3 * q^15 - 6 * q^16 - 9 * q^18 + 3 * q^20 - 6 * q^21 + 6 * q^22 - 12 * q^23 + 3 * q^25 - 12 * q^26 + 6 * q^28 + 6 * q^30 - 9 * q^31 + 9 * q^32 + 3 * q^35 + 9 * q^36 + 3 * q^37 + 6 * q^38 - 3 * q^39 + 12 * q^40 - 6 * q^41 + 6 * q^42 + 15 * q^43 + 6 * q^44 + 9 * q^45 + 9 * q^46 - 21 * q^47 + 21 * q^48 - 15 * q^49 + 21 * q^50 - 3 * q^52 - 18 * q^53 + 9 * q^54 + 6 * q^55 + 3 * q^56 + 3 * q^57 + 9 * q^58 - 9 * q^59 + 6 * q^60 + 3 * q^61 - 3 * q^62 + 9 * q^63 - 3 * q^64 - 18 * q^66 - 9 * q^67 + 21 * q^69 - 21 * q^71 + 9 * q^72 + 21 * q^73 - 6 * q^74 + 3 * q^75 - 3 * q^76 + 6 * q^77 + 30 * q^78 - 3 * q^79 + 9 * q^80 - 9 * q^81 + 6 * q^82 + 9 * q^83 - 3 * q^84 + 6 * q^86 + 9 * q^87 - 15 * q^89 + 9 * q^90 - 3 * q^91 - 9 * q^92 + 21 * q^93 + 3 * q^94 - 6 * q^95 - 12 * q^96 - 6 * q^97 - 3 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.87939	−1.32893	−0.664463	−	0.747321i	$-0.731340\pi$
$2$	−1.87939	−1.32893	−0.664463	+	0.747321i	$0.731340\pi$
$3$	−2.53209	−1.46190	−0.730951	−	0.682430i	$-0.760923\pi$
$3$	−2.53209	−1.46190	−0.730951	+	0.682430i	$0.760923\pi$
$4$	1.53209	0.766044
$5$	−0.120615	−0.0539406	−0.0269703	−	0.999636i	$-0.508586\pi$
$5$	−0.120615	−0.0539406	−0.0269703	+	0.999636i	$0.508586\pi$
$6$	4.75877	1.94276
$7$	1.53209	0.579075	0.289538	−	0.957167i	$-0.406498\pi$
$7$	1.53209	0.579075	0.289538	+	0.957167i	$0.406498\pi$
$8$	0.879385	0.310910
$9$	3.41147	1.13716
$10$	0.226682	0.0716830
$11$	−2.69459	−0.812450	−0.406225	−	0.913773i	$-0.633155\pi$
$11$	−2.69459	−0.812450	−0.406225	+	0.913773i	$0.633155\pi$
$12$	−3.87939	−1.11988
$13$	4.57398	1.26859	0.634297	−	0.773090i	$-0.281290\pi$
$13$	4.57398	1.26859	0.634297	+	0.773090i	$0.281290\pi$
$14$	−2.87939	−0.769548
$15$	0.305407	0.0788558
$16$	−4.71688	−1.17922
$17$	0	0
$17$	0	0
$18$	−6.41147	−1.51120
$19$	−1.87939	−0.431161	−0.215580	−	0.976486i	$-0.569164\pi$
$19$	−1.87939	−0.431161	−0.215580	+	0.976486i	$0.569164\pi$
$20$	−0.184793	−0.0413209
$21$	−3.87939	−0.846551
$22$	5.06418	1.07969
$23$	−7.41147	−1.54540	−0.772700	−	0.634772i	$-0.781094\pi$
$23$	−7.41147	−1.54540	−0.772700	+	0.634772i	$0.781094\pi$
$24$	−2.22668	−0.454519
$25$	−4.98545	−0.997090
$26$	−8.59627	−1.68587
$27$	−1.04189	−0.200512
$28$	2.34730	0.443597
$29$	−3.41147	−0.633495	−0.316747	−	0.948510i	$-0.602591\pi$
$29$	−3.41147	−0.633495	−0.316747	+	0.948510i	$0.602591\pi$
$30$	−0.573978	−0.104794
$31$	−3.83750	−0.689235	−0.344617	−	0.938743i	$-0.611991\pi$
$31$	−3.83750	−0.689235	−0.344617	+	0.938743i	$0.611991\pi$
$32$	7.10607	1.25619
$33$	6.82295	1.18772
$34$	0	0
$35$	−0.184793	−0.0312356
$36$	5.22668	0.871114
$37$	5.24897	0.862925	0.431463	−	0.902131i	$-0.357998\pi$
$37$	5.24897	0.862925	0.431463	+	0.902131i	$0.357998\pi$
$38$	3.53209	0.572980
$39$	−11.5817	−1.85456
$40$	−0.106067	−0.0167706
$41$	−6.24897	−0.975925	−0.487963	−	0.872865i	$-0.662260\pi$
$41$	−6.24897	−0.975925	−0.487963	+	0.872865i	$0.662260\pi$
$42$	7.29086	1.12500
$43$	5.49020	0.837248	0.418624	−	0.908160i	$-0.362513\pi$
$43$	5.49020	0.837248	0.418624	+	0.908160i	$0.362513\pi$
$44$	−4.12836	−0.622373
$45$	−0.411474	−0.0613389
$46$	13.9290	2.05372
$47$	−7.34730	−1.07171	−0.535857	−	0.844309i	$-0.680011\pi$
$47$	−7.34730	−1.07171	−0.535857	+	0.844309i	$0.680011\pi$
$48$	11.9436	1.72390
$49$	−4.65270	−0.664672
$50$	9.36959	1.32506
$51$	0	0
$52$	7.00774	0.971799
$53$	0.822948	0.113041	0.0565203	−	0.998401i	$-0.481999\pi$
$53$	0.822948	0.113041	0.0565203	+	0.998401i	$0.481999\pi$
$54$	1.95811	0.266465
$55$	0.325008	0.0438240
$56$	1.34730	0.180040
$57$	4.75877	0.630315
$58$	6.41147	0.841868
$59$	−3.14290	−0.409171	−0.204586	−	0.978849i	$-0.565585\pi$
$59$	−3.14290	−0.409171	−0.204586	+	0.978849i	$0.565585\pi$
$60$	0.467911	0.0604071
$61$	−1.22668	−0.157060	−0.0785302	−	0.996912i	$-0.525023\pi$
$61$	−1.22668	−0.157060	−0.0785302	+	0.996912i	$0.525023\pi$
$62$	7.21213	0.915942
$63$	5.22668	0.658500
$64$	−3.92127	−0.490159
$65$	−0.551689	−0.0684286
$66$	−12.8229	−1.57840
$67$	−14.6236	−1.78656	−0.893279	−	0.449503i	$-0.851601\pi$
$67$	−14.6236	−1.78656	−0.893279	+	0.449503i	$0.851601\pi$
$68$	0	0
$69$	18.7665	2.25922
$70$	0.347296	0.0415099
$71$	0.170245	0.0202043	0.0101022	−	0.999949i	$-0.496784\pi$
$71$	0.170245	0.0202043	0.0101022	+	0.999949i	$0.496784\pi$
$72$	3.00000	0.353553
$73$	11.8007	1.38116	0.690581	−	0.723255i	$-0.257355\pi$
$73$	11.8007	1.38116	0.690581	+	0.723255i	$0.257355\pi$
$74$	−9.86484	−1.14676
$75$	12.6236	1.45765
$76$	−2.87939	−0.330288
$77$	−4.12836	−0.470470
$78$	21.7665	2.46457
$79$	4.14796	0.466682	0.233341	−	0.972395i	$-0.425034\pi$
$79$	4.14796	0.466682	0.233341	+	0.972395i	$0.425034\pi$
$80$	0.568926	0.0636078
$81$	−7.59627	−0.844030
$82$	11.7442	1.29693
$83$	−2.43376	−0.267140	−0.133570	−	0.991039i	$-0.542644\pi$
$83$	−2.43376	−0.267140	−0.133570	+	0.991039i	$0.542644\pi$
$84$	−5.94356	−0.648496
$85$	0	0
$86$	−10.3182	−1.11264
$87$	8.63816	0.926108
$88$	−2.36959	−0.252599
$89$	−15.0915	−1.59970	−0.799849	−	0.600201i	$-0.795087\pi$
$89$	−15.0915	−1.59970	−0.799849	+	0.600201i	$0.795087\pi$
$90$	0.773318	0.0815149
$91$	7.00774	0.734611
$92$	−11.3550	−1.18384
$93$	9.71688	1.00759
$94$	13.8084	1.42423
$95$	0.226682	0.0232570
$96$	−17.9932	−1.83642
$97$	−11.1925	−1.13643	−0.568215	−	0.822880i	$-0.692366\pi$
$97$	−11.1925	−1.13643	−0.568215	+	0.822880i	$0.692366\pi$
$98$	8.74422	0.883300
$99$	−9.19253	−0.923884
$100$	−7.63816	−0.763816
$101$	7.78106	0.774244	0.387122	−	0.922028i	$-0.373469\pi$
$101$	7.78106	0.774244	0.387122	+	0.922028i	$0.373469\pi$
$102$	0	0
$103$	−10.8598	−1.07005	−0.535023	−	0.844837i	$-0.679697\pi$
$103$	−10.8598	−1.07005	−0.535023	+	0.844837i	$0.679697\pi$
$104$	4.02229	0.394418
$105$	0.467911	0.0456634
$106$	−1.54664	−0.150223
$107$	−12.0419	−1.16413	−0.582067	−	0.813141i	$-0.697756\pi$
$107$	−12.0419	−1.16413	−0.582067	+	0.813141i	$0.697756\pi$
$108$	−1.59627	−0.153601
$109$	6.61081	0.633201	0.316601	−	0.948559i	$-0.397459\pi$
$109$	6.61081	0.633201	0.316601	+	0.948559i	$0.397459\pi$
$110$	−0.610815	−0.0582389
$111$	−13.2909	−1.26151
$112$	−7.22668	−0.682857
$113$	5.08647	0.478495	0.239247	−	0.970959i	$-0.423099\pi$
$113$	5.08647	0.478495	0.239247	+	0.970959i	$0.423099\pi$
$114$	−8.94356	−0.837641
$115$	0.893933	0.0833597
$116$	−5.22668	−0.485285
$117$	15.6040	1.44259
$118$	5.90673	0.543758
$119$	0	0
$120$	0.268571	0.0245170
$121$	−3.73917	−0.339925
$122$	2.30541	0.208722
$123$	15.8229	1.42671
$124$	−5.87939	−0.527984
$125$	1.20439	0.107724
$126$	−9.82295	−0.875098
$127$	−2.20439	−0.195608	−0.0978041	−	0.995206i	$-0.531182\pi$
$127$	−2.20439	−0.195608	−0.0978041	+	0.995206i	$0.531182\pi$
$128$	−6.84255	−0.604802
$129$	−13.9017	−1.22397
$130$	1.03684	0.0909366
$131$	1.99319	0.174146	0.0870730	−	0.996202i	$-0.472249\pi$
$131$	1.99319	0.174146	0.0870730	+	0.996202i	$0.472249\pi$
$132$	10.4534	0.909848
$133$	−2.87939	−0.249674
$134$	27.4834	2.37420
$135$	0.125667	0.0108157
$136$	0	0
$137$	−12.6236	−1.07851	−0.539254	−	0.842143i	$-0.681294\pi$
$137$	−12.6236	−1.07851	−0.539254	+	0.842143i	$0.681294\pi$
$138$	−35.2695	−3.00234
$139$	−5.23442	−0.443978	−0.221989	−	0.975049i	$-0.571255\pi$
$139$	−5.23442	−0.443978	−0.221989	+	0.975049i	$0.571255\pi$
$140$	−0.283119	−0.0239279
$141$	18.6040	1.56674
$142$	−0.319955	−0.0268500
$143$	−12.3250	−1.03067
$144$	−16.0915	−1.34096
$145$	0.411474	0.0341711
$146$	−22.1780	−1.83546
$147$	11.7811	0.971685
$148$	8.04189	0.661039
$149$	9.65270	0.790780	0.395390	−	0.918513i	$-0.370609\pi$
$149$	9.65270	0.790780	0.395390	+	0.918513i	$0.370609\pi$
$150$	−23.7246	−1.93711
$151$	1.20708	0.0982309	0.0491154	−	0.998793i	$-0.484360\pi$
$151$	1.20708	0.0982309	0.0491154	+	0.998793i	$0.484360\pi$
$152$	−1.65270	−0.134052
$153$	0	0
$154$	7.75877	0.625220
$155$	0.462859	0.0371777
$156$	−17.7442	−1.42067
$157$	15.0942	1.20465	0.602324	−	0.798251i	$-0.294241\pi$
$157$	15.0942	1.20465	0.602324	+	0.798251i	$0.294241\pi$
$158$	−7.79561	−0.620185
$159$	−2.08378	−0.165254
$160$	−0.857097	−0.0677594
$161$	−11.3550	−0.894902
$162$	14.2763	1.12165
$163$	6.55438	0.513378	0.256689	−	0.966494i	$-0.417368\pi$
$163$	6.55438	0.513378	0.256689	+	0.966494i	$0.417368\pi$
$164$	−9.57398	−0.747602
$165$	−0.822948	−0.0640664
$166$	4.57398	0.355010
$167$	3.94356	0.305162	0.152581	−	0.988291i	$-0.451241\pi$
$167$	3.94356	0.305162	0.152581	+	0.988291i	$0.451241\pi$
$168$	−3.41147	−0.263201
$169$	7.92127	0.609329
$170$	0	0
$171$	−6.41147	−0.490298
$172$	8.41147	0.641369
$173$	18.9341	1.43953	0.719765	−	0.694218i	$-0.244249\pi$
$173$	18.9341	1.43953	0.719765	+	0.694218i	$0.244249\pi$
$174$	−16.2344	−1.23073
$175$	−7.63816	−0.577390
$176$	12.7101	0.958058
$177$	7.95811	0.598168
$178$	28.3628	2.12588
$179$	7.25402	0.542191	0.271096	−	0.962552i	$-0.412614\pi$
$179$	7.25402	0.542191	0.271096	+	0.962552i	$0.412614\pi$
$180$	−0.630415	−0.0469884
$181$	−25.0993	−1.86561	−0.932807	−	0.360377i	$-0.882648\pi$
$181$	−25.0993	−1.86561	−0.932807	+	0.360377i	$0.882648\pi$
$182$	−13.1702	−0.976243
$183$	3.10607	0.229607
$184$	−6.51754	−0.480479
$185$	−0.633103	−0.0465467
$186$	−18.2618	−1.33902
$187$	0	0
$188$	−11.2567	−0.820980
$189$	−1.59627	−0.116111
$190$	−0.426022	−0.0309069
$191$	14.1557	1.02427	0.512135	−	0.858905i	$-0.328855\pi$
$191$	14.1557	1.02427	0.512135	+	0.858905i	$0.328855\pi$
$192$	9.92902	0.716565
$193$	16.4311	1.18273	0.591367	−	0.806402i	$-0.298588\pi$
$193$	16.4311	1.18273	0.591367	+	0.806402i	$0.298588\pi$
$194$	21.0351	1.51023
$195$	1.39693	0.100036
$196$	−7.12836	−0.509168
$197$	20.2395	1.44200	0.721001	−	0.692934i	$-0.243682\pi$
$197$	20.2395	1.44200	0.721001	+	0.692934i	$0.243682\pi$
$198$	17.2763	1.22777
$199$	−22.1753	−1.57197	−0.785983	−	0.618249i	$-0.787842\pi$
$199$	−22.1753	−1.57197	−0.785983	+	0.618249i	$0.787842\pi$
$200$	−4.38413	−0.310005
$201$	37.0283	2.61177
$202$	−14.6236	−1.02891
$203$	−5.22668	−0.366841
$204$	0	0
$205$	0.753718	0.0526420
$206$	20.4097	1.42201
$207$	−25.2841	−1.75736
$208$	−21.5749	−1.49595
$209$	5.06418	0.350297
$210$	−0.879385	−0.0606833
$211$	−7.18748	−0.494807	−0.247403	−	0.968913i	$-0.579577\pi$
$211$	−7.18748	−0.494807	−0.247403	+	0.968913i	$0.579577\pi$
$212$	1.26083	0.0865942
$213$	−0.431074	−0.0295367
$214$	22.6313	1.54705
$215$	−0.662199	−0.0451616
$216$	−0.916222	−0.0623410
$217$	−5.87939	−0.399119
$218$	−12.4243	−0.841478
$219$	−29.8803	−2.01912
$220$	0.497941	0.0335711
$221$	0	0
$222$	24.9786	1.67646
$223$	−6.01960	−0.403102	−0.201551	−	0.979478i	$-0.564598\pi$
$223$	−6.01960	−0.403102	−0.201551	+	0.979478i	$0.564598\pi$
$224$	10.8871	0.727427
$225$	−17.0077	−1.13385
$226$	−9.55943	−0.635884
$227$	−22.0351	−1.46252	−0.731260	−	0.682099i	$-0.761067\pi$
$227$	−22.0351	−1.46252	−0.731260	+	0.682099i	$0.761067\pi$
$228$	7.29086	0.482849
$229$	3.69965	0.244479	0.122240	−	0.992501i	$-0.460992\pi$
$229$	3.69965	0.244479	0.122240	+	0.992501i	$0.460992\pi$
$230$	−1.68004	−0.110779
$231$	10.4534	0.687781
$232$	−3.00000	−0.196960
$233$	29.1506	1.90972	0.954861	−	0.297053i	$-0.0960037\pi$
$233$	29.1506	1.90972	0.954861	+	0.297053i	$0.0960037\pi$
$234$	−29.3259	−1.91710
$235$	0.886192	0.0578088
$236$	−4.81521	−0.313443
$237$	−10.5030	−0.682243
$238$	0	0
$239$	12.4834	0.807484	0.403742	−	0.914873i	$-0.367709\pi$
$239$	12.4834	0.807484	0.403742	+	0.914873i	$0.367709\pi$
$240$	−1.44057	−0.0929884
$241$	−16.2172	−1.04464	−0.522320	−	0.852749i	$-0.674933\pi$
$241$	−16.2172	−1.04464	−0.522320	+	0.852749i	$0.674933\pi$
$242$	7.02734	0.451735
$243$	22.3601	1.43440
$244$	−1.87939	−0.120315
$245$	0.561185	0.0358528
$246$	−29.7374	−1.89599
$247$	−8.59627	−0.546967
$248$	−3.37464	−0.214290
$249$	6.16250	0.390533
$250$	−2.26352	−0.143157
$251$	15.9959	1.00965	0.504826	−	0.863221i	$-0.331557\pi$
$251$	15.9959	1.00965	0.504826	+	0.863221i	$0.331557\pi$
$252$	8.00774	0.504440
$253$	19.9709	1.25556
$254$	4.14290	0.259949
$255$	0	0
$256$	20.7023	1.29390
$257$	−9.66044	−0.602602	−0.301301	−	0.953529i	$-0.597421\pi$
$257$	−9.66044	−0.602602	−0.301301	+	0.953529i	$0.597421\pi$
$258$	26.1266	1.62657
$259$	8.04189	0.499699
$260$	−0.845237	−0.0524194
$261$	−11.6382	−0.720384
$262$	−3.74598	−0.231427
$263$	27.9813	1.72540	0.862701	−	0.505714i	$-0.168771\pi$
$263$	27.9813	1.72540	0.862701	+	0.505714i	$0.168771\pi$
$264$	6.00000	0.369274
$265$	−0.0992597	−0.00609748
$266$	5.41147	0.331799
$267$	38.2131	2.33860
$268$	−22.4047	−1.36858
$269$	6.64590	0.405207	0.202604	−	0.979261i	$-0.435060\pi$
$269$	6.64590	0.405207	0.202604	+	0.979261i	$0.435060\pi$
$270$	−0.236177	−0.0143733
$271$	17.0000	1.03268	0.516338	−	0.856385i	$-0.327295\pi$
$271$	17.0000	1.03268	0.516338	+	0.856385i	$0.327295\pi$
$272$	0	0
$273$	−17.7442	−1.07393
$274$	23.7246	1.43326
$275$	13.4338	0.810086
$276$	28.7520	1.73066
$277$	−20.1489	−1.21063	−0.605315	−	0.795986i	$-0.706953\pi$
$277$	−20.1489	−1.21063	−0.605315	+	0.795986i	$0.706953\pi$
$278$	9.83750	0.590014
$279$	−13.0915	−0.783769
$280$	−0.162504	−0.00971146
$281$	16.4730	0.982695	0.491347	−	0.870964i	$-0.336505\pi$
$281$	16.4730	0.982695	0.491347	+	0.870964i	$0.336505\pi$
$282$	−34.9641	−2.08208
$283$	18.4456	1.09648	0.548239	−	0.836322i	$-0.315298\pi$
$283$	18.4456	1.09648	0.548239	+	0.836322i	$0.315298\pi$
$284$	0.260830	0.0154774
$285$	−0.573978	−0.0339995
$286$	23.1634	1.36968
$287$	−9.57398	−0.565134
$288$	24.2422	1.42848
$289$	0	0
$290$	−0.773318	−0.0454108
$291$	28.3405	1.66135
$292$	18.0797	1.05803
$293$	−10.9513	−0.639782	−0.319891	−	0.947454i	$-0.603646\pi$
$293$	−10.9513	−0.639782	−0.319891	+	0.947454i	$0.603646\pi$
$294$	−22.1411	−1.29130
$295$	0.379081	0.0220709
$296$	4.61587	0.268292
$297$	2.80747	0.162906
$298$	−18.1411	−1.05089
$299$	−33.8999	−1.96048
$300$	19.3405	1.11662
$301$	8.41147	0.484829
$302$	−2.26857	−0.130542
$303$	−19.7023	−1.13187
$304$	8.86484	0.508433
$305$	0.147956	0.00847193
$306$	0	0
$307$	−5.78106	−0.329942	−0.164971	−	0.986298i	$-0.552753\pi$
$307$	−5.78106	−0.329942	−0.164971	+	0.986298i	$0.552753\pi$
$308$	−6.32501	−0.360401
$309$	27.4979	1.56430
$310$	−0.869890	−0.0494064
$311$	−0.120615	−0.00683944	−0.00341972	−	0.999994i	$-0.501089\pi$
$311$	−0.120615	−0.00683944	−0.00341972	+	0.999994i	$0.501089\pi$
$312$	−10.1848	−0.576600
$313$	−10.3892	−0.587231	−0.293616	−	0.955924i	$-0.594859\pi$
$313$	−10.3892	−0.587231	−0.293616	+	0.955924i	$0.594859\pi$
$314$	−28.3678	−1.60089
$315$	−0.630415	−0.0355199
$316$	6.35504	0.357499
$317$	−27.8016	−1.56149	−0.780747	−	0.624848i	$-0.785161\pi$
$317$	−27.8016	−1.56149	−0.780747	+	0.624848i	$0.785161\pi$
$318$	3.91622	0.219611
$319$	9.19253	0.514683
$320$	0.472964	0.0264395
$321$	30.4911	1.70185
$322$	21.3405	1.18926
$323$	0	0
$324$	−11.6382	−0.646564
$325$	−22.8033	−1.26490
$326$	−12.3182	−0.682242
$327$	−16.7392	−0.925678
$328$	−5.49525	−0.303425
$329$	−11.2567	−0.620603
$330$	1.54664	0.0851396
$331$	8.77837	0.482503	0.241251	−	0.970463i	$-0.422442\pi$
$331$	8.77837	0.482503	0.241251	+	0.970463i	$0.422442\pi$
$332$	−3.72874	−0.204641
$333$	17.9067	0.981283
$334$	−7.41147	−0.405538
$335$	1.76382	0.0963679
$336$	18.2986	0.998270
$337$	−1.46110	−0.0795914	−0.0397957	−	0.999208i	$-0.512671\pi$
$337$	−1.46110	−0.0795914	−0.0397957	+	0.999208i	$0.512671\pi$
$338$	−14.8871	−0.809753
$339$	−12.8794	−0.699512
$340$	0	0
$341$	10.3405	0.559969
$342$	12.0496	0.651569
$343$	−17.8530	−0.963970
$344$	4.82800	0.260308
$345$	−2.26352	−0.121864
$346$	−35.5844	−1.91303
$347$	−31.3560	−1.68328	−0.841638	−	0.540042i	$-0.818409\pi$
$347$	−31.3560	−1.68328	−0.841638	+	0.540042i	$0.818409\pi$
$348$	13.2344	0.709440
$349$	−29.7743	−1.59378	−0.796890	−	0.604125i	$-0.793523\pi$
$349$	−29.7743	−1.59378	−0.796890	+	0.604125i	$0.793523\pi$
$350$	14.3550	0.767309
$351$	−4.76558	−0.254368
$352$	−19.1480	−1.02059
$353$	−28.3141	−1.50701	−0.753503	−	0.657444i	$-0.771638\pi$
$353$	−28.3141	−1.50701	−0.753503	+	0.657444i	$0.771638\pi$
$354$	−14.9564	−0.794921
$355$	−0.0205340	−0.00108983
$356$	−23.1215	−1.22544
$357$	0	0
$358$	−13.6331	−0.720532
$359$	−2.81790	−0.148723	−0.0743614	−	0.997231i	$-0.523692\pi$
$359$	−2.81790	−0.148723	−0.0743614	+	0.997231i	$0.523692\pi$
$360$	−0.361844	−0.0190709
$361$	−15.4679	−0.814101
$362$	47.1712	2.47926
$363$	9.46791	0.496936
$364$	10.7365	0.562745
$365$	−1.42333	−0.0745007
$366$	−5.83750	−0.305131
$367$	8.31820	0.434207	0.217103	−	0.976149i	$-0.430339\pi$
$367$	8.31820	0.434207	0.217103	+	0.976149i	$0.430339\pi$
$368$	34.9590	1.82237
$369$	−21.3182	−1.10978
$370$	1.18984	0.0618571
$371$	1.26083	0.0654590
$372$	14.8871	0.771862
$373$	−9.21894	−0.477339	−0.238669	−	0.971101i	$-0.576711\pi$
$373$	−9.21894	−0.477339	−0.238669	+	0.971101i	$0.576711\pi$
$374$	0	0
$375$	−3.04963	−0.157482
$376$	−6.46110	−0.333206
$377$	−15.6040	−0.803647
$378$	3.00000	0.154303
$379$	10.3628	0.532300	0.266150	−	0.963932i	$-0.414248\pi$
$379$	10.3628	0.532300	0.266150	+	0.963932i	$0.414248\pi$
$380$	0.347296	0.0178159
$381$	5.58172	0.285960
$382$	−26.6040	−1.36118
$383$	13.2713	0.678130	0.339065	−	0.940763i	$-0.389889\pi$
$383$	13.2713	0.678130	0.339065	+	0.940763i	$0.389889\pi$
$384$	17.3259	0.884161
$385$	0.497941	0.0253774
$386$	−30.8803	−1.57177
$387$	18.7297	0.952083
$388$	−17.1480	−0.870556
$389$	−26.2763	−1.33226	−0.666131	−	0.745835i	$-0.732051\pi$
$389$	−26.2763	−1.33226	−0.666131	+	0.745835i	$0.732051\pi$
$390$	−2.62536	−0.132940
$391$	0	0
$392$	−4.09152	−0.206653
$393$	−5.04694	−0.254585
$394$	−38.0378	−1.91632
$395$	−0.500305	−0.0251731
$396$	−14.0838	−0.707736
$397$	25.4766	1.27863	0.639317	−	0.768944i	$-0.279217\pi$
$397$	25.4766	1.27863	0.639317	+	0.768944i	$0.279217\pi$
$398$	41.6759	2.08903
$399$	7.29086	0.365000
$400$	23.5158	1.17579
$401$	−0.900740	−0.0449808	−0.0224904	−	0.999747i	$-0.507160\pi$
$401$	−0.900740	−0.0449808	−0.0224904	+	0.999747i	$0.507160\pi$
$402$	−69.5904	−3.47085
$403$	−17.5526	−0.874358
$404$	11.9213	0.593106
$405$	0.916222	0.0455274
$406$	9.82295	0.487505
$407$	−14.1438	−0.701084
$408$	0	0
$409$	−15.3259	−0.757819	−0.378910	−	0.925434i	$-0.623701\pi$
$409$	−15.3259	−0.757819	−0.378910	+	0.925434i	$0.623701\pi$
$410$	−1.41653	−0.0699573
$411$	31.9641	1.57667
$412$	−16.6382	−0.819703
$413$	−4.81521	−0.236941
$414$	47.5185	2.33541
$415$	0.293548	0.0144097
$416$	32.5030	1.59359
$417$	13.2540	0.649052
$418$	−9.51754	−0.465518
$419$	2.38413	0.116473	0.0582363	−	0.998303i	$-0.481452\pi$
$419$	2.38413	0.116473	0.0582363	+	0.998303i	$0.481452\pi$
$420$	0.716881	0.0349802
$421$	−8.28581	−0.403826	−0.201913	−	0.979404i	$-0.564716\pi$
$421$	−8.28581	−0.403826	−0.201913	+	0.979404i	$0.564716\pi$
$422$	13.5080	0.657561
$423$	−25.0651	−1.21871
$424$	0.723689	0.0351454
$425$	0	0
$426$	0.810155	0.0392521
$427$	−1.87939	−0.0909498
$428$	−18.4492	−0.891778
$429$	31.2080	1.50674
$430$	1.24453	0.0600164
$431$	32.3191	1.55676	0.778379	−	0.627795i	$-0.216042\pi$
$431$	32.3191	1.55676	0.778379	+	0.627795i	$0.216042\pi$
$432$	4.91447	0.236447
$433$	−15.0642	−0.723938	−0.361969	−	0.932190i	$-0.617895\pi$
$433$	−15.0642	−0.723938	−0.361969	+	0.932190i	$0.617895\pi$
$434$	11.0496	0.530399
$435$	−1.04189	−0.0499548
$436$	10.1284	0.485060
$437$	13.9290	0.666315
$438$	56.1566	2.68327
$439$	−2.57304	−0.122805	−0.0614024	−	0.998113i	$-0.519557\pi$
$439$	−2.57304	−0.122805	−0.0614024	+	0.998113i	$0.519557\pi$
$440$	0.285807	0.0136253
$441$	−15.8726	−0.755837
$442$	0	0
$443$	23.4662	1.11491	0.557455	−	0.830207i	$-0.311778\pi$
$443$	23.4662	1.11491	0.557455	+	0.830207i	$0.311778\pi$
$444$	−20.3628	−0.966375
$445$	1.82026	0.0862886
$446$	11.3131	0.535693
$447$	−24.4415	−1.15604
$448$	−6.00774	−0.283839
$449$	18.8580	0.889965	0.444983	−	0.895539i	$-0.353210\pi$
$449$	18.8580	0.889965	0.444983	+	0.895539i	$0.353210\pi$
$450$	31.9641	1.50680
$451$	16.8384	0.792891
$452$	7.79292	0.366548
$453$	−3.05644	−0.143604
$454$	41.4124	1.94358
$455$	−0.845237	−0.0396253
$456$	4.18479	0.195971
$457$	−2.10782	−0.0985997	−0.0492999	−	0.998784i	$-0.515699\pi$
$457$	−2.10782	−0.0985997	−0.0492999	+	0.998784i	$0.515699\pi$
$458$	−6.95306	−0.324895
$459$	0	0
$460$	1.36959	0.0638572
$461$	−21.9077	−1.02034	−0.510171	−	0.860073i	$-0.670418\pi$
$461$	−21.9077	−1.02034	−0.510171	+	0.860073i	$0.670418\pi$
$462$	−19.6459	−0.914010
$463$	14.1557	0.657871	0.328936	−	0.944352i	$-0.393310\pi$
$463$	14.1557	0.657871	0.328936	+	0.944352i	$0.393310\pi$
$464$	16.0915	0.747030
$465$	−1.17200	−0.0543502
$466$	−54.7853	−2.53788
$467$	−29.6878	−1.37379	−0.686893	−	0.726758i	$-0.741026\pi$
$467$	−29.6878	−1.37379	−0.686893	+	0.726758i	$0.741026\pi$
$468$	23.9067	1.10509
$469$	−22.4047	−1.03455
$470$	−1.66550	−0.0768236
$471$	−38.2199	−1.76108
$472$	−2.76382	−0.127215
$473$	−14.7939	−0.680222
$474$	19.7392	0.906650
$475$	9.36959	0.429906
$476$	0	0
$477$	2.80747	0.128545
$478$	−23.4611	−1.07309
$479$	−38.2959	−1.74978	−0.874892	−	0.484317i	$-0.839068\pi$
$479$	−38.2959	−1.74978	−0.874892	+	0.484317i	$0.839068\pi$
$480$	2.17024	0.0990577
$481$	24.0087	1.09470
$482$	30.4783	1.38825
$483$	28.7520	1.30826
$484$	−5.72874	−0.260397
$485$	1.34998	0.0612996
$486$	−42.0232	−1.90621
$487$	23.3509	1.05813	0.529066	−	0.848581i	$-0.322543\pi$
$487$	23.3509	1.05813	0.529066	+	0.848581i	$0.322543\pi$
$488$	−1.07873	−0.0488316
$489$	−16.5963	−0.750509
$490$	−1.05468	−0.0476457
$491$	31.3928	1.41674	0.708369	−	0.705843i	$-0.249431\pi$
$491$	31.3928	1.41674	0.708369	+	0.705843i	$0.249431\pi$
$492$	24.2422	1.09292
$493$	0	0
$494$	16.1557	0.726879
$495$	1.10876	0.0498348
$496$	18.1010	0.812760
$497$	0.260830	0.0116998
$498$	−11.5817	−0.518989
$499$	−16.1310	−0.722125	−0.361062	−	0.932542i	$-0.617586\pi$
$499$	−16.1310	−0.722125	−0.361062	+	0.932542i	$0.617586\pi$
$500$	1.84524	0.0825215
$501$	−9.98545	−0.446117
$502$	−30.0624	−1.34175
$503$	34.3637	1.53220	0.766101	−	0.642720i	$-0.222194\pi$
$503$	34.3637	1.53220	0.766101	+	0.642720i	$0.222194\pi$
$504$	4.59627	0.204734
$505$	−0.938511	−0.0417632
$506$	−37.5330	−1.66855
$507$	−20.0574	−0.890779
$508$	−3.37733	−0.149845
$509$	20.0283	0.887738	0.443869	−	0.896092i	$-0.353606\pi$
$509$	20.0283	0.887738	0.443869	+	0.896092i	$0.353606\pi$
$510$	0	0
$511$	18.0797	0.799797
$512$	−25.2226	−1.11469
$513$	1.95811	0.0864527
$514$	18.1557	0.800813
$515$	1.30985	0.0577189
$516$	−21.2986	−0.937619
$517$	19.7980	0.870714
$518$	−15.1138	−0.664063
$519$	−47.9427	−2.10445
$520$	−0.485147	−0.0212751
$521$	5.58584	0.244720	0.122360	−	0.992486i	$-0.460954\pi$
$521$	5.58584	0.244720	0.122360	+	0.992486i	$0.460954\pi$
$522$	21.8726	0.957337
$523$	5.51249	0.241044	0.120522	−	0.992711i	$-0.461543\pi$
$523$	5.51249	0.241044	0.120522	+	0.992711i	$0.461543\pi$
$524$	3.05375	0.133404
$525$	19.3405	0.844088
$526$	−52.5877	−2.29293
$527$	0	0
$528$	−32.1830	−1.40059
$529$	31.9299	1.38826
$530$	0.186547	0.00810309
$531$	−10.7219	−0.465292
$532$	−4.41147	−0.191262
$533$	−28.5827	−1.23805
$534$	−71.8171	−3.10783
$535$	1.45243	0.0627940
$536$	−12.8598	−0.555458
$537$	−18.3678	−0.792630
$538$	−12.4902	−0.538491
$539$	12.5371	0.540013
$540$	0.192533	0.00828531
$541$	−13.9949	−0.601690	−0.300845	−	0.953673i	$-0.597269\pi$
$541$	−13.9949	−0.601690	−0.300845	+	0.953673i	$0.597269\pi$
$542$	−31.9495	−1.37235
$543$	63.5536	2.72734
$544$	0	0
$545$	−0.797362	−0.0341552
$546$	33.3482	1.42717
$547$	29.4175	1.25780	0.628900	−	0.777486i	$-0.283506\pi$
$547$	29.4175	1.25780	0.628900	+	0.777486i	$0.283506\pi$
$548$	−19.3405	−0.826185
$549$	−4.18479	−0.178603
$550$	−25.2472	−1.07654
$551$	6.41147	0.273138
$552$	16.5030	0.702414
$553$	6.35504	0.270244
$554$	37.8675	1.60884
$555$	1.60307	0.0680467
$556$	−8.01960	−0.340107
$557$	32.0574	1.35831	0.679157	−	0.733993i	$-0.262345\pi$
$557$	32.0574	1.35831	0.679157	+	0.733993i	$0.262345\pi$
$558$	24.6040	1.04157
$559$	25.1121	1.06213
$560$	0.871644	0.0368337
$561$	0	0
$562$	−30.9590	−1.30593
$563$	18.6483	0.785930	0.392965	−	0.919553i	$-0.371449\pi$
$563$	18.6483	0.785930	0.392965	+	0.919553i	$0.371449\pi$
$564$	28.5030	1.20019
$565$	−0.613503	−0.0258103
$566$	−34.6664	−1.45714
$567$	−11.6382	−0.488757
$568$	0.149711	0.00628172
$569$	27.6554	1.15937	0.579687	−	0.814839i	$-0.303175\pi$
$569$	27.6554	1.15937	0.579687	+	0.814839i	$0.303175\pi$
$570$	1.07873	0.0451828
$571$	−33.1762	−1.38838	−0.694191	−	0.719791i	$-0.744238\pi$
$571$	−33.1762	−1.38838	−0.694191	+	0.719791i	$0.744238\pi$
$572$	−18.8830	−0.789538
$573$	−35.8435	−1.49738
$574$	17.9932	0.751021
$575$	36.9495	1.54090
$576$	−13.3773	−0.557389
$577$	2.70233	0.112500	0.0562498	−	0.998417i	$-0.482086\pi$
$577$	2.70233	0.112500	0.0562498	+	0.998417i	$0.482086\pi$
$578$	0	0
$579$	−41.6049	−1.72904
$580$	0.630415	0.0261766
$581$	−3.72874	−0.154694
$582$	−53.2627	−2.20781
$583$	−2.21751	−0.0918399
$584$	10.3773	0.429417
$585$	−1.88207	−0.0778142
$586$	20.5817	0.850223
$587$	6.31551	0.260669	0.130335	−	0.991470i	$-0.458395\pi$
$587$	6.31551	0.260669	0.130335	+	0.991470i	$0.458395\pi$
$588$	18.0496	0.744354
$589$	7.21213	0.297171
$590$	−0.712438	−0.0293306
$591$	−51.2481	−2.10807
$592$	−24.7588	−1.01758
$593$	−10.2148	−0.419472	−0.209736	−	0.977758i	$-0.567261\pi$
$593$	−10.2148	−0.419472	−0.209736	+	0.977758i	$0.567261\pi$
$594$	−5.27631	−0.216490
$595$	0	0
$596$	14.7888	0.605773
$597$	56.1498	2.29806
$598$	63.7110	2.60534
$599$	−21.4347	−0.875798	−0.437899	−	0.899024i	$-0.644277\pi$
$599$	−21.4347	−0.875798	−0.437899	+	0.899024i	$0.644277\pi$
$600$	11.1010	0.453197
$601$	−17.4557	−0.712034	−0.356017	−	0.934479i	$-0.615865\pi$
$601$	−17.4557	−0.712034	−0.356017	+	0.934479i	$0.615865\pi$
$602$	−15.8084	−0.644302
$603$	−49.8881	−2.03160
$604$	1.84936	0.0752492
$605$	0.450999	0.0183357
$606$	37.0283	1.50417
$607$	8.50980	0.345402	0.172701	−	0.984974i	$-0.444751\pi$
$607$	8.50980	0.345402	0.172701	+	0.984974i	$0.444751\pi$
$608$	−13.3550	−0.541618
$609$	13.2344	0.536286
$610$	−0.278066	−0.0112586
$611$	−33.6064	−1.35957
$612$	0	0
$613$	9.78106	0.395053	0.197527	−	0.980298i	$-0.436709\pi$
$613$	9.78106	0.395053	0.197527	+	0.980298i	$0.436709\pi$
$614$	10.8648	0.438469
$615$	−1.90848	−0.0769574
$616$	−3.63041	−0.146274
$617$	−22.8512	−0.919956	−0.459978	−	0.887930i	$-0.652143\pi$
$617$	−22.8512	−0.919956	−0.459978	+	0.887930i	$0.652143\pi$
$618$	−51.6792	−2.07884
$619$	41.2627	1.65849	0.829244	−	0.558887i	$-0.188771\pi$
$619$	41.2627	1.65849	0.829244	+	0.558887i	$0.188771\pi$
$620$	0.709141	0.0284798
$621$	7.72193	0.309871
$622$	0.226682	0.00908910
$623$	−23.1215	−0.926345
$624$	54.6296	2.18693
$625$	24.7820	0.991280
$626$	19.5253	0.780387
$627$	−12.8229	−0.512099
$628$	23.1257	0.922815
$629$	0	0
$630$	1.18479	0.0472033
$631$	9.54252	0.379882	0.189941	−	0.981796i	$-0.439170\pi$
$631$	9.54252	0.379882	0.189941	+	0.981796i	$0.439170\pi$
$632$	3.64765	0.145096
$633$	18.1993	0.723359
$634$	52.2499	2.07511
$635$	0.265882	0.0105512
$636$	−3.19253	−0.126592
$637$	−21.2814	−0.843198
$638$	−17.2763	−0.683976
$639$	0.580785	0.0229755
$640$	0.825312	0.0326233
$641$	−9.42871	−0.372412	−0.186206	−	0.982511i	$-0.559619\pi$
$641$	−9.42871	−0.372412	−0.186206	+	0.982511i	$0.559619\pi$
$642$	−57.3046	−2.26163
$643$	−11.0060	−0.434034	−0.217017	−	0.976168i	$-0.569633\pi$
$643$	−11.0060	−0.434034	−0.217017	+	0.976168i	$0.569633\pi$
$644$	−17.3969	−0.685535
$645$	1.67675	0.0660219
$646$	0	0
$647$	28.9840	1.13948	0.569740	−	0.821825i	$-0.307044\pi$
$647$	28.9840	1.13948	0.569740	+	0.821825i	$0.307044\pi$
$648$	−6.68004	−0.262417
$649$	8.46884	0.332431
$650$	42.8563	1.68096
$651$	14.8871	0.583472
$652$	10.0419	0.393271
$653$	14.7178	0.575953	0.287976	−	0.957638i	$-0.407018\pi$
$653$	14.7178	0.575953	0.287976	+	0.957638i	$0.407018\pi$
$654$	31.4593	1.23016
$655$	−0.240408	−0.00939354
$656$	29.4757	1.15083
$657$	40.2576	1.57060
$658$	21.1557	0.824735
$659$	2.19759	0.0856058	0.0428029	−	0.999084i	$-0.486371\pi$
$659$	2.19759	0.0856058	0.0428029	+	0.999084i	$0.486371\pi$
$660$	−1.26083	−0.0490777
$661$	−26.6023	−1.03471	−0.517354	−	0.855772i	$-0.673083\pi$
$661$	−26.6023	−1.03471	−0.517354	+	0.855772i	$0.673083\pi$
$662$	−16.4979	−0.641211
$663$	0	0
$664$	−2.14022	−0.0830565
$665$	0.347296	0.0134676
$666$	−33.6536	−1.30405
$667$	25.2841	0.979002
$668$	6.04189	0.233768
$669$	15.2422	0.589296
$670$	−3.31490	−0.128066
$671$	3.30541	0.127604
$672$	−27.5672	−1.06343
$673$	−7.24392	−0.279233	−0.139616	−	0.990206i	$-0.544587\pi$
$673$	−7.24392	−0.279233	−0.139616	+	0.990206i	$0.544587\pi$
$674$	2.74598	0.105771
$675$	5.19429	0.199928
$676$	12.1361	0.466773
$677$	−22.9273	−0.881166	−0.440583	−	0.897712i	$-0.645228\pi$
$677$	−22.9273	−0.881166	−0.440583	+	0.897712i	$0.645228\pi$
$678$	24.2053	0.929600
$679$	−17.1480	−0.658078
$680$	0	0
$681$	55.7948	2.13806
$682$	−19.4338	−0.744157
$683$	−4.29591	−0.164378	−0.0821892	−	0.996617i	$-0.526191\pi$
$683$	−4.29591	−0.164378	−0.0821892	+	0.996617i	$0.526191\pi$
$684$	−9.82295	−0.375590
$685$	1.52259	0.0581753
$686$	33.5526	1.28105
$687$	−9.36783	−0.357405
$688$	−25.8966	−0.987299
$689$	3.76415	0.143403
$690$	4.25402	0.161948
$691$	−20.6331	−0.784920	−0.392460	−	0.919769i	$-0.628376\pi$
$691$	−20.6331	−0.784920	−0.392460	+	0.919769i	$0.628376\pi$
$692$	29.0087	1.10274
$693$	−14.0838	−0.534998
$694$	58.9299	2.23695
$695$	0.631349	0.0239484
$696$	7.59627	0.287936
$697$	0	0
$698$	55.9573	2.11801
$699$	−73.8120	−2.79183
$700$	−11.7023	−0.442307
$701$	−28.2772	−1.06802	−0.534008	−	0.845479i	$-0.679315\pi$
$701$	−28.2772	−1.06802	−0.534008	+	0.845479i	$0.679315\pi$
$702$	8.95636	0.338036
$703$	−9.86484	−0.372059
$704$	10.5662	0.398230
$705$	−2.24392	−0.0845108
$706$	53.2131	2.00270
$707$	11.9213	0.448346
$708$	12.1925	0.458223
$709$	27.1002	1.01777	0.508885	−	0.860835i	$-0.330058\pi$
$709$	27.1002	1.01777	0.508885	+	0.860835i	$0.330058\pi$
$710$	0.0385913	0.00144831
$711$	14.1506	0.530691
$712$	−13.2713	−0.497361
$713$	28.4415	1.06514
$714$	0	0
$715$	1.48658	0.0555949
$716$	11.1138	0.415342
$717$	−31.6091	−1.18046
$718$	5.29591	0.197642
$719$	−25.8402	−0.963676	−0.481838	−	0.876260i	$-0.660031\pi$
$719$	−25.8402	−0.963676	−0.481838	+	0.876260i	$0.660031\pi$
$720$	1.94087	0.0723321
$721$	−16.6382	−0.619637
$722$	29.0702	1.08188
$723$	41.0634	1.52716
$724$	−38.4543	−1.42914
$725$	17.0077	0.631652
$726$	−17.7939	−0.660392
$727$	−31.6290	−1.17305	−0.586527	−	0.809930i	$-0.699505\pi$
$727$	−31.6290	−1.17305	−0.586527	+	0.809930i	$0.699505\pi$
$728$	6.16250	0.228398
$729$	−33.8289	−1.25292
$730$	2.67499	0.0990059
$731$	0	0
$732$	4.75877	0.175889
$733$	25.6040	0.945706	0.472853	−	0.881141i	$-0.343224\pi$
$733$	25.6040	0.945706	0.472853	+	0.881141i	$0.343224\pi$
$734$	−15.6331	−0.577028
$735$	−1.42097	−0.0524133
$736$	−52.6664	−1.94131
$737$	39.4047	1.45149
$738$	40.0651	1.47482
$739$	21.6382	0.795972	0.397986	−	0.917391i	$-0.369709\pi$
$739$	21.6382	0.795972	0.397986	+	0.917391i	$0.369709\pi$
$740$	−0.969971	−0.0356568
$741$	21.7665	0.799613
$742$	−2.36959	−0.0869902
$743$	−26.7547	−0.981533	−0.490766	−	0.871291i	$-0.663283\pi$
$743$	−26.7547	−0.981533	−0.490766	+	0.871291i	$0.663283\pi$
$744$	8.54488	0.313271
$745$	−1.16426	−0.0426551
$746$	17.3259	0.634348
$747$	−8.30272	−0.303781
$748$	0	0
$749$	−18.4492	−0.674121
$750$	5.73143	0.209282
$751$	41.9513	1.53082	0.765412	−	0.643540i	$-0.222535\pi$
$751$	41.9513	1.53082	0.765412	+	0.643540i	$0.222535\pi$
$752$	34.6563	1.26379
$753$	−40.5030	−1.47601
$754$	29.3259	1.06799
$755$	−0.145592	−0.00529863
$756$	−2.44562	−0.0889464
$757$	−4.99319	−0.181481	−0.0907403	−	0.995875i	$-0.528923\pi$
$757$	−4.99319	−0.181481	−0.0907403	+	0.995875i	$0.528923\pi$
$758$	−19.4757	−0.707388
$759$	−50.5681	−1.83551
$760$	0.199340	0.00723084
$761$	13.2935	0.481891	0.240945	−	0.970539i	$-0.422543\pi$
$761$	13.2935	0.481891	0.240945	+	0.970539i	$0.422543\pi$
$762$	−10.4902	−0.380020
$763$	10.1284	0.366671
$764$	21.6878	0.784637
$765$	0	0
$766$	−24.9418	−0.901184
$767$	−14.3756	−0.519072
$768$	−52.4201	−1.89155
$769$	8.25166	0.297562	0.148781	−	0.988870i	$-0.452465\pi$
$769$	8.25166	0.297562	0.148781	+	0.988870i	$0.452465\pi$
$770$	−0.935822	−0.0337247
$771$	24.4611	0.880945
$772$	25.1739	0.906027
$773$	26.1043	0.938907	0.469453	−	0.882957i	$-0.344451\pi$
$773$	26.1043	0.938907	0.469453	+	0.882957i	$0.344451\pi$
$774$	−35.2003	−1.26525
$775$	19.1317	0.687229
$776$	−9.84255	−0.353327
$777$	−20.3628	−0.730511
$778$	49.3833	1.77048
$779$	11.7442	0.420780
$780$	2.14022	0.0766320
$781$	−0.458740	−0.0164150
$782$	0	0
$783$	3.55438	0.127023
$784$	21.9463	0.783795
$785$	−1.82058	−0.0649794
$786$	9.48515	0.338324
$787$	26.8634	0.957577	0.478789	−	0.877930i	$-0.341076\pi$
$787$	26.8634	0.957577	0.478789	+	0.877930i	$0.341076\pi$
$788$	31.0087	1.10464
$789$	−70.8512	−2.52237
$790$	0.940265	0.0334531
$791$	7.79292	0.277084
$792$	−8.08378	−0.287245
$793$	−5.61081	−0.199246
$794$	−47.8803	−1.69921
$795$	0.251334	0.00891391
$796$	−33.9745	−1.20420
$797$	−18.8212	−0.666681	−0.333340	−	0.942807i	$-0.608176\pi$
$797$	−18.8212	−0.666681	−0.333340	+	0.942807i	$0.608176\pi$
$798$	−13.7023	−0.485057
$799$	0	0
$800$	−35.4270	−1.25253
$801$	−51.4843	−1.81911
$802$	1.69284	0.0597762
$803$	−31.7980	−1.12213
$804$	56.7306	2.00073
$805$	1.36959	0.0482715
$806$	32.9881	1.16196
$807$	−16.8280	−0.592374
$808$	6.84255	0.240720
$809$	25.7573	0.905580	0.452790	−	0.891617i	$-0.350429\pi$
$809$	25.7573	0.905580	0.452790	+	0.891617i	$0.350429\pi$
$810$	−1.72193	−0.0605026
$811$	26.4483	0.928726	0.464363	−	0.885645i	$-0.346283\pi$
$811$	26.4483	0.928726	0.464363	+	0.885645i	$0.346283\pi$
$812$	−8.00774	−0.281017
$813$	−43.0455	−1.50967
$814$	26.5817	0.931689
$815$	−0.790555	−0.0276919
$816$	0	0
$817$	−10.3182	−0.360988
$818$	28.8033	1.00709
$819$	23.9067	0.835369
$820$	1.15476	0.0403261
$821$	31.5030	1.09946	0.549731	−	0.835342i	$-0.314730\pi$
$821$	31.5030	1.09946	0.549731	+	0.835342i	$0.314730\pi$
$822$	−60.0729	−2.09528
$823$	11.6895	0.407472	0.203736	−	0.979026i	$-0.434692\pi$
$823$	11.6895	0.407472	0.203736	+	0.979026i	$0.434692\pi$
$824$	−9.54993	−0.332688
$825$	−34.0155	−1.18427
$826$	9.04963	0.314877
$827$	3.32264	0.115540	0.0577698	−	0.998330i	$-0.481601\pi$
$827$	3.32264	0.115540	0.0577698	+	0.998330i	$0.481601\pi$
$828$	−38.7374	−1.34622
$829$	6.01186	0.208801	0.104400	−	0.994535i	$-0.466708\pi$
$829$	6.01186	0.208801	0.104400	+	0.994535i	$0.466708\pi$
$830$	−0.551689	−0.0191494
$831$	51.0188	1.76982
$832$	−17.9358	−0.621813
$833$	0	0
$834$	−24.9094	−0.862542
$835$	−0.475652	−0.0164606
$836$	7.75877	0.268343
$837$	3.99825	0.138200
$838$	−4.48070	−0.154783
$839$	−41.4115	−1.42968	−0.714841	−	0.699287i	$-0.753501\pi$
$839$	−41.4115	−1.42968	−0.714841	+	0.699287i	$0.753501\pi$
$840$	0.411474	0.0141972
$841$	−17.3618	−0.598684
$842$	15.5722	0.536654
$843$	−41.7110	−1.43660
$844$	−11.0119	−0.379044
$845$	−0.955423	−0.0328675
$846$	47.1070	1.61957
$847$	−5.72874	−0.196842
$848$	−3.88175	−0.133300
$849$	−46.7060	−1.60294
$850$	0	0
$851$	−38.9026	−1.33356
$852$	−0.660444	−0.0226265
$853$	−23.9982	−0.821684	−0.410842	−	0.911706i	$-0.634765\pi$
$853$	−23.9982	−0.821684	−0.410842	+	0.911706i	$0.634765\pi$
$854$	3.53209	0.120866
$855$	0.773318	0.0264469
$856$	−10.5895	−0.361940
$857$	−31.8553	−1.08816	−0.544079	−	0.839034i	$-0.683121\pi$
$857$	−31.8553	−1.08816	−0.544079	+	0.839034i	$0.683121\pi$
$858$	−58.6519	−2.00234
$859$	24.0806	0.821619	0.410810	−	0.911721i	$-0.365246\pi$
$859$	24.0806	0.821619	0.410810	+	0.911721i	$0.365246\pi$
$860$	−1.01455	−0.0345958
$861$	24.2422	0.826171
$862$	−60.7401	−2.06882
$863$	−20.8590	−0.710047	−0.355024	−	0.934857i	$-0.615527\pi$
$863$	−20.8590	−0.710047	−0.355024	+	0.934857i	$0.615527\pi$
$864$	−7.40373	−0.251880
$865$	−2.28373	−0.0776491
$866$	28.3114	0.962060
$867$	0	0
$868$	−9.00774	−0.305743
$869$	−11.1771	−0.379156
$870$	1.95811	0.0663862
$871$	−66.8881	−2.26642
$872$	5.81345	0.196868
$873$	−38.1830	−1.29230
$874$	−26.1780	−0.885484
$875$	1.84524	0.0623804
$876$	−45.7793	−1.54674
$877$	−22.3669	−0.755276	−0.377638	−	0.925953i	$-0.623264\pi$
$877$	−22.3669	−0.755276	−0.377638	+	0.925953i	$0.623264\pi$
$878$	4.83574	0.163198
$879$	27.7297	0.935299
$880$	−1.53302	−0.0516782
$881$	−56.4279	−1.90110	−0.950552	−	0.310566i	$-0.899482\pi$
$881$	−56.4279	−1.90110	−0.950552	+	0.310566i	$0.899482\pi$
$882$	29.8307	1.00445
$883$	−45.4219	−1.52857	−0.764284	−	0.644879i	$-0.776908\pi$
$883$	−45.4219	−1.52857	−0.764284	+	0.644879i	$0.776908\pi$
$884$	0	0
$885$	−0.959866	−0.0322655
$886$	−44.1019	−1.48163
$887$	−17.4816	−0.586976	−0.293488	−	0.955963i	$-0.594816\pi$
$887$	−17.4816	−0.586976	−0.293488	+	0.955963i	$0.594816\pi$
$888$	−11.6878	−0.392216
$889$	−3.37733	−0.113272
$890$	−3.42097	−0.114671
$891$	20.4688	0.685732
$892$	−9.22256	−0.308794
$893$	13.8084	0.462080
$894$	45.9350	1.53630
$895$	−0.874942	−0.0292461
$896$	−10.4834	−0.350226
$897$	85.8376	2.86603
$898$	−35.4415	−1.18270
$899$	13.0915	0.436627
$900$	−26.0574	−0.868579
$901$	0	0
$902$	−31.6459	−1.05369
$903$	−21.2986	−0.708773
$904$	4.47296	0.148769
$905$	3.02734	0.100632
$906$	5.74422	0.190839
$907$	10.4138	0.345786	0.172893	−	0.984941i	$-0.444689\pi$
$907$	10.4138	0.345786	0.172893	+	0.984941i	$0.444689\pi$
$908$	−33.7597	−1.12036
$909$	26.5449	0.880438
$910$	1.58853	0.0526591
$911$	−44.2722	−1.46680	−0.733402	−	0.679796i	$-0.762068\pi$
$911$	−44.2722	−1.46680	−0.733402	+	0.679796i	$0.762068\pi$
$912$	−22.4466	−0.743280
$913$	6.55800	0.217038
$914$	3.96141	0.131032
$915$	−0.374638	−0.0123851
$916$	5.66819	0.187282
$917$	3.05375	0.100844
$918$	0	0
$919$	−31.0615	−1.02462	−0.512312	−	0.858799i	$-0.671211\pi$
$919$	−31.0615	−1.02462	−0.512312	+	0.858799i	$0.671211\pi$
$920$	0.786112	0.0259173
$921$	14.6382	0.482344
$922$	41.1729	1.35596
$923$	0.778695	0.0256311
$924$	16.0155	0.526871
$925$	−26.1685	−0.860415
$926$	−26.6040	−0.874262
$927$	−37.0479	−1.21681
$928$	−24.2422	−0.795788
$929$	−22.3969	−0.734819	−0.367410	−	0.930059i	$-0.619755\pi$
$929$	−22.3969	−0.734819	−0.367410	+	0.930059i	$0.619755\pi$
$930$	2.20264	0.0722274
$931$	8.74422	0.286580
$932$	44.6614	1.46293
$933$	0.305407	0.00999859
$934$	55.7948	1.82566
$935$	0	0
$936$	13.7219	0.448515
$937$	58.1661	1.90020	0.950102	−	0.311939i	$-0.100978\pi$
$937$	58.1661	1.90020	0.950102	+	0.311939i	$0.100978\pi$
$938$	42.1070	1.37484
$939$	26.3063	0.858475
$940$	1.35773	0.0442841
$941$	−10.4397	−0.340326	−0.170163	−	0.985416i	$-0.554429\pi$
$941$	−10.4397	−0.340326	−0.170163	+	0.985416i	$0.554429\pi$
$942$	71.8299	2.34034
$943$	46.3141	1.50819
$944$	14.8247	0.482503
$945$	0.192533	0.00626311
$946$	27.8033	0.903965
$947$	4.04364	0.131401	0.0657004	−	0.997839i	$-0.479072\pi$
$947$	4.04364	0.131401	0.0657004	+	0.997839i	$0.479072\pi$
$948$	−16.0915	−0.522628
$949$	53.9760	1.75213
$950$	−17.6091	−0.571313
$951$	70.3961	2.28275
$952$	0	0
$953$	4.37639	0.141765	0.0708826	−	0.997485i	$-0.477418\pi$
$953$	4.37639	0.141765	0.0708826	+	0.997485i	$0.477418\pi$
$954$	−5.27631	−0.170827
$955$	−1.70739	−0.0552497
$956$	19.1257	0.618568
$957$	−23.2763	−0.752416
$958$	71.9728	2.32533
$959$	−19.3405	−0.624537
$960$	−1.19759	−0.0386519
$961$	−16.2736	−0.524956
$962$	−45.1215	−1.45478
$963$	−41.0806	−1.32380
$964$	−24.8462	−0.800241
$965$	−1.98183	−0.0637974
$966$	−54.0360	−1.73858
$967$	24.4371	0.785843	0.392921	−	0.919572i	$-0.371464\pi$
$967$	24.4371	0.785843	0.392921	+	0.919572i	$0.371464\pi$
$968$	−3.28817	−0.105686
$969$	0	0
$970$	−2.53714	−0.0814627
$971$	20.5253	0.658688	0.329344	−	0.944210i	$-0.393172\pi$
$971$	20.5253	0.658688	0.329344	+	0.944210i	$0.393172\pi$
$972$	34.2576	1.09881
$973$	−8.01960	−0.257097
$974$	−43.8854	−1.40618
$975$	57.7401	1.84916
$976$	5.78611	0.185209
$977$	28.3073	0.905630	0.452815	−	0.891605i	$-0.350420\pi$
$977$	28.3073	0.905630	0.452815	+	0.891605i	$0.350420\pi$
$978$	31.1908	0.997371
$979$	40.6655	1.29967
$980$	0.859785	0.0274648
$981$	22.5526	0.720050
$982$	−58.9992	−1.88274
$983$	26.6742	0.850774	0.425387	−	0.905012i	$-0.360138\pi$
$983$	26.6742	0.850774	0.425387	+	0.905012i	$0.360138\pi$
$984$	13.9145	0.443577
$985$	−2.44118	−0.0777824
$986$	0	0
$987$	28.5030	0.907260
$988$	−13.1702	−0.419001
$989$	−40.6905	−1.29388
$990$	−2.08378	−0.0662268
$991$	−34.8857	−1.10818	−0.554090	−	0.832457i	$-0.686934\pi$
$991$	−34.8857	−1.10818	−0.554090	+	0.832457i	$0.686934\pi$
$992$	−27.2695	−0.865808
$993$	−22.2276	−0.705372
$994$	−0.490200	−0.0155482
$995$	2.67467	0.0847927
$996$	9.44150	0.299165
$997$	45.3164	1.43519	0.717593	−	0.696463i	$-0.245244\pi$
$997$	45.3164	1.43519	0.717593	+	0.696463i	$0.245244\pi$
$998$	30.3164	0.959650
$999$	−5.46884	−0.173027

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.a.d.1.1	✓	3
3.2	odd	2		2601.2.a.x.1.3		3
4.3	odd	2		4624.2.a.bg.1.3		3
5.4	even	2		7225.2.a.t.1.3		3
17.2	even	8		289.2.c.d.38.1		12
17.3	odd	16		289.2.d.f.179.1		24
17.4	even	4		289.2.b.d.288.6		6
17.5	odd	16		289.2.d.f.110.6		24
17.6	odd	16		289.2.d.f.155.1		24
17.7	odd	16		289.2.d.f.134.6		24
17.8	even	8		289.2.c.d.251.6		12
17.9	even	8		289.2.c.d.251.5		12
17.10	odd	16		289.2.d.f.134.5		24
17.11	odd	16		289.2.d.f.155.2		24
17.12	odd	16		289.2.d.f.110.5		24
17.13	even	4		289.2.b.d.288.5		6
17.14	odd	16		289.2.d.f.179.2		24
17.15	even	8		289.2.c.d.38.2		12
17.16	even	2		289.2.a.e.1.1	yes	3
51.50	odd	2		2601.2.a.w.1.3		3
68.67	odd	2		4624.2.a.bd.1.1		3
85.84	even	2		7225.2.a.s.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.d.1.1	✓	3	1.1	even	1	trivial
289.2.a.e.1.1	yes	3	17.16	even	2
289.2.b.d.288.5		6	17.13	even	4
289.2.b.d.288.6		6	17.4	even	4
289.2.c.d.38.1		12	17.2	even	8
289.2.c.d.38.2		12	17.15	even	8
289.2.c.d.251.5		12	17.9	even	8
289.2.c.d.251.6		12	17.8	even	8
289.2.d.f.110.5		24	17.12	odd	16
289.2.d.f.110.6		24	17.5	odd	16
289.2.d.f.134.5		24	17.10	odd	16
289.2.d.f.134.6		24	17.7	odd	16
289.2.d.f.155.1		24	17.6	odd	16
289.2.d.f.155.2		24	17.11	odd	16
289.2.d.f.179.1		24	17.3	odd	16
289.2.d.f.179.2		24	17.14	odd	16
2601.2.a.w.1.3		3	51.50	odd	2
2601.2.a.x.1.3		3	3.2	odd	2
4624.2.a.bd.1.1		3	68.67	odd	2
4624.2.a.bg.1.3		3	4.3	odd	2
7225.2.a.s.1.3		3	85.84	even	2
7225.2.a.t.1.3		3	5.4	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-1.87939 q^{2} -2.53209 q^{3} +1.53209 q^{4} -0.120615 q^{5} +4.75877 q^{6} +1.53209 q^{7} +0.879385 q^{8} +3.41147 q^{9} +O(q^{10})\)	\(q-1.87939 q^{2} -2.53209 q^{3} +1.53209 q^{4} -0.120615 q^{5} +4.75877 q^{6} +1.53209 q^{7} +0.879385 q^{8} +3.41147 q^{9} +0.226682 q^{10} -2.69459 q^{11} -3.87939 q^{12} +4.57398 q^{13} -2.87939 q^{14} +0.305407 q^{15} -4.71688 q^{16} -6.41147 q^{18} -1.87939 q^{19} -0.184793 q^{20} -3.87939 q^{21} +5.06418 q^{22} -7.41147 q^{23} -2.22668 q^{24} -4.98545 q^{25} -8.59627 q^{26} -1.04189 q^{27} +2.34730 q^{28} -3.41147 q^{29} -0.573978 q^{30} -3.83750 q^{31} +7.10607 q^{32} +6.82295 q^{33} -0.184793 q^{35} +5.22668 q^{36} +5.24897 q^{37} +3.53209 q^{38} -11.5817 q^{39} -0.106067 q^{40} -6.24897 q^{41} +7.29086 q^{42} +5.49020 q^{43} -4.12836 q^{44} -0.411474 q^{45} +13.9290 q^{46} -7.34730 q^{47} +11.9436 q^{48} -4.65270 q^{49} +9.36959 q^{50} +7.00774 q^{52} +0.822948 q^{53} +1.95811 q^{54} +0.325008 q^{55} +1.34730 q^{56} +4.75877 q^{57} +6.41147 q^{58} -3.14290 q^{59} +0.467911 q^{60} -1.22668 q^{61} +7.21213 q^{62} +5.22668 q^{63} -3.92127 q^{64} -0.551689 q^{65} -12.8229 q^{66} -14.6236 q^{67} +18.7665 q^{69} +0.347296 q^{70} +0.170245 q^{71} +3.00000 q^{72} +11.8007 q^{73} -9.86484 q^{74} +12.6236 q^{75} -2.87939 q^{76} -4.12836 q^{77} +21.7665 q^{78} +4.14796 q^{79} +0.568926 q^{80} -7.59627 q^{81} +11.7442 q^{82} -2.43376 q^{83} -5.94356 q^{84} -10.3182 q^{86} +8.63816 q^{87} -2.36959 q^{88} -15.0915 q^{89} +0.773318 q^{90} +7.00774 q^{91} -11.3550 q^{92} +9.71688 q^{93} +13.8084 q^{94} +0.226682 q^{95} -17.9932 q^{96} -11.1925 q^{97} +8.74422 q^{98} -9.19253 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} - 6 q^{5} + 3 q^{6} - 3 q^{8}+O(q^{10}) \) 3 * q - 3 * q^3 - 6 * q^5 + 3 * q^6 - 3 * q^8	\( 3 q - 3 q^{3} - 6 q^{5} + 3 q^{6} - 3 q^{8} - 6 q^{10} - 6 q^{11} - 6 q^{12} + 6 q^{13} - 3 q^{14} + 3 q^{15} - 6 q^{16} - 9 q^{18} + 3 q^{20} - 6 q^{21} + 6 q^{22} - 12 q^{23} + 3 q^{25} - 12 q^{26} + 6 q^{28} + 6 q^{30} - 9 q^{31} + 9 q^{32} + 3 q^{35} + 9 q^{36} + 3 q^{37} + 6 q^{38} - 3 q^{39} + 12 q^{40} - 6 q^{41} + 6 q^{42} + 15 q^{43} + 6 q^{44} + 9 q^{45} + 9 q^{46} - 21 q^{47} + 21 q^{48} - 15 q^{49} + 21 q^{50} - 3 q^{52} - 18 q^{53} + 9 q^{54} + 6 q^{55} + 3 q^{56} + 3 q^{57} + 9 q^{58} - 9 q^{59} + 6 q^{60} + 3 q^{61} - 3 q^{62} + 9 q^{63} - 3 q^{64} - 18 q^{66} - 9 q^{67} + 21 q^{69} - 21 q^{71} + 9 q^{72} + 21 q^{73} - 6 q^{74} + 3 q^{75} - 3 q^{76} + 6 q^{77} + 30 q^{78} - 3 q^{79} + 9 q^{80} - 9 q^{81} + 6 q^{82} + 9 q^{83} - 3 q^{84} + 6 q^{86} + 9 q^{87} - 15 q^{89} + 9 q^{90} - 3 q^{91} - 9 q^{92} + 21 q^{93} + 3 q^{94} - 6 q^{95} - 12 q^{96} - 6 q^{97} - 3 q^{98}+O(q^{100}) \) 3 * q - 3 * q^3 - 6 * q^5 + 3 * q^6 - 3 * q^8 - 6 * q^10 - 6 * q^11 - 6 * q^12 + 6 * q^13 - 3 * q^14 + 3 * q^15 - 6 * q^16 - 9 * q^18 + 3 * q^20 - 6 * q^21 + 6 * q^22 - 12 * q^23 + 3 * q^25 - 12 * q^26 + 6 * q^28 + 6 * q^30 - 9 * q^31 + 9 * q^32 + 3 * q^35 + 9 * q^36 + 3 * q^37 + 6 * q^38 - 3 * q^39 + 12 * q^40 - 6 * q^41 + 6 * q^42 + 15 * q^43 + 6 * q^44 + 9 * q^45 + 9 * q^46 - 21 * q^47 + 21 * q^48 - 15 * q^49 + 21 * q^50 - 3 * q^52 - 18 * q^53 + 9 * q^54 + 6 * q^55 + 3 * q^56 + 3 * q^57 + 9 * q^58 - 9 * q^59 + 6 * q^60 + 3 * q^61 - 3 * q^62 + 9 * q^63 - 3 * q^64 - 18 * q^66 - 9 * q^67 + 21 * q^69 - 21 * q^71 + 9 * q^72 + 21 * q^73 - 6 * q^74 + 3 * q^75 - 3 * q^76 + 6 * q^77 + 30 * q^78 - 3 * q^79 + 9 * q^80 - 9 * q^81 + 6 * q^82 + 9 * q^83 - 3 * q^84 + 6 * q^86 + 9 * q^87 - 15 * q^89 + 9 * q^90 - 3 * q^91 - 9 * q^92 + 21 * q^93 + 3 * q^94 - 6 * q^95 - 12 * q^96 - 6 * q^97 - 3 * q^98

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