LMFDB - Embedded newform 3229.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3229,2,Mod(1,3229)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3229, 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("3229.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3229.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:	$25.7836948127$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - 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			$1.61803$ of defining polynomial
Character	$\chi$	$=$	3229.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.61803 q^{2} -2.00000 q^{3} +0.618034 q^{4} -0.618034 q^{5} +3.23607 q^{6} -1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.61803 q^{2} -2.00000 q^{3} +0.618034 q^{4} -0.618034 q^{5} +3.23607 q^{6} -1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +1.00000 q^{10} +5.23607 q^{11} -1.23607 q^{12} -4.61803 q^{13} +1.61803 q^{14} +1.23607 q^{15} -4.85410 q^{16} +0.763932 q^{17} -1.61803 q^{18} -3.85410 q^{19} -0.381966 q^{20} +2.00000 q^{21} -8.47214 q^{22} +4.47214 q^{23} -4.47214 q^{24} -4.61803 q^{25} +7.47214 q^{26} +4.00000 q^{27} -0.618034 q^{28} +5.38197 q^{29} -2.00000 q^{30} -7.38197 q^{31} +3.38197 q^{32} -10.4721 q^{33} -1.23607 q^{34} +0.618034 q^{35} +0.618034 q^{36} -3.09017 q^{37} +6.23607 q^{38} +9.23607 q^{39} -1.38197 q^{40} -1.09017 q^{41} -3.23607 q^{42} +5.09017 q^{43} +3.23607 q^{44} -0.618034 q^{45} -7.23607 q^{46} +2.23607 q^{47} +9.70820 q^{48} -6.00000 q^{49} +7.47214 q^{50} -1.52786 q^{51} -2.85410 q^{52} +1.47214 q^{53} -6.47214 q^{54} -3.23607 q^{55} -2.23607 q^{56} +7.70820 q^{57} -8.70820 q^{58} -2.23607 q^{59} +0.763932 q^{60} +2.00000 q^{61} +11.9443 q^{62} -1.00000 q^{63} +4.23607 q^{64} +2.85410 q^{65} +16.9443 q^{66} -0.708204 q^{67} +0.472136 q^{68} -8.94427 q^{69} -1.00000 q^{70} +12.7082 q^{71} +2.23607 q^{72} +14.4164 q^{73} +5.00000 q^{74} +9.23607 q^{75} -2.38197 q^{76} -5.23607 q^{77} -14.9443 q^{78} -2.29180 q^{79} +3.00000 q^{80} -11.0000 q^{81} +1.76393 q^{82} +6.38197 q^{83} +1.23607 q^{84} -0.472136 q^{85} -8.23607 q^{86} -10.7639 q^{87} +11.7082 q^{88} +7.79837 q^{89} +1.00000 q^{90} +4.61803 q^{91} +2.76393 q^{92} +14.7639 q^{93} -3.61803 q^{94} +2.38197 q^{95} -6.76393 q^{96} -3.85410 q^{97} +9.70820 q^{98} +5.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 4 q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 - 4 * q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^7 + 2 * q^9	$ 2 q - q^{2} - 4 q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{12} - 7 q^{13} + q^{14} - 2 q^{15} - 3 q^{16} + 6 q^{17} - q^{18} - q^{19} - 3 q^{20} + 4 q^{21} - 8 q^{22} - 7 q^{25} + 6 q^{26} + 8 q^{27} + q^{28} + 13 q^{29} - 4 q^{30} - 17 q^{31} + 9 q^{32} - 12 q^{33} + 2 q^{34} - q^{35} - q^{36} + 5 q^{37} + 8 q^{38} + 14 q^{39} - 5 q^{40} + 9 q^{41} - 2 q^{42} - q^{43} + 2 q^{44} + q^{45} - 10 q^{46} + 6 q^{48} - 12 q^{49} + 6 q^{50} - 12 q^{51} + q^{52} - 6 q^{53} - 4 q^{54} - 2 q^{55} + 2 q^{57} - 4 q^{58} + 6 q^{60} + 4 q^{61} + 6 q^{62} - 2 q^{63} + 4 q^{64} - q^{65} + 16 q^{66} + 12 q^{67} - 8 q^{68} - 2 q^{70} + 12 q^{71} + 2 q^{73} + 10 q^{74} + 14 q^{75} - 7 q^{76} - 6 q^{77} - 12 q^{78} - 18 q^{79} + 6 q^{80} - 22 q^{81} + 8 q^{82} + 15 q^{83} - 2 q^{84} + 8 q^{85} - 12 q^{86} - 26 q^{87} + 10 q^{88} - 9 q^{89} + 2 q^{90} + 7 q^{91} + 10 q^{92} + 34 q^{93} - 5 q^{94} + 7 q^{95} - 18 q^{96} - q^{97} + 6 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q - q^2 - 4 * q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^7 + 2 * q^9 + 2 * q^10 + 6 * q^11 + 2 * q^12 - 7 * q^13 + q^14 - 2 * q^15 - 3 * q^16 + 6 * q^17 - q^18 - q^19 - 3 * q^20 + 4 * q^21 - 8 * q^22 - 7 * q^25 + 6 * q^26 + 8 * q^27 + q^28 + 13 * q^29 - 4 * q^30 - 17 * q^31 + 9 * q^32 - 12 * q^33 + 2 * q^34 - q^35 - q^36 + 5 * q^37 + 8 * q^38 + 14 * q^39 - 5 * q^40 + 9 * q^41 - 2 * q^42 - q^43 + 2 * q^44 + q^45 - 10 * q^46 + 6 * q^48 - 12 * q^49 + 6 * q^50 - 12 * q^51 + q^52 - 6 * q^53 - 4 * q^54 - 2 * q^55 + 2 * q^57 - 4 * q^58 + 6 * q^60 + 4 * q^61 + 6 * q^62 - 2 * q^63 + 4 * q^64 - q^65 + 16 * q^66 + 12 * q^67 - 8 * q^68 - 2 * q^70 + 12 * q^71 + 2 * q^73 + 10 * q^74 + 14 * q^75 - 7 * q^76 - 6 * q^77 - 12 * q^78 - 18 * q^79 + 6 * q^80 - 22 * q^81 + 8 * q^82 + 15 * q^83 - 2 * q^84 + 8 * q^85 - 12 * q^86 - 26 * q^87 + 10 * q^88 - 9 * q^89 + 2 * q^90 + 7 * q^91 + 10 * q^92 + 34 * q^93 - 5 * q^94 + 7 * q^95 - 18 * q^96 - 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 $

$2$	−1.61803	−1.14412	−0.572061	−	0.820211i	$-0.693856\pi$
$2$	−1.61803	−1.14412	−0.572061	+	0.820211i	$0.693856\pi$
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	0.618034	0.309017
$5$	−0.618034	−0.276393	−0.138197	−	0.990405i	$-0.544131\pi$
$5$	−0.618034	−0.276393	−0.138197	+	0.990405i	$0.544131\pi$
$6$	3.23607	1.32112
$7$	−1.00000	−0.377964	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000	−0.377964	−0.188982	+	0.981981i	$0.560519\pi$
$8$	2.23607	0.790569
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	5.23607	1.57873	0.789367	−	0.613922i	$-0.210409\pi$
$11$	5.23607	1.57873	0.789367	+	0.613922i	$0.210409\pi$
$12$	−1.23607	−0.356822
$13$	−4.61803	−1.28081	−0.640406	−	0.768036i	$-0.721234\pi$
$13$	−4.61803	−1.28081	−0.640406	+	0.768036i	$0.721234\pi$
$14$	1.61803	0.432438
$15$	1.23607	0.319151
$16$	−4.85410	−1.21353
$17$	0.763932	0.185281	0.0926404	−	0.995700i	$-0.470469\pi$
$17$	0.763932	0.185281	0.0926404	+	0.995700i	$0.470469\pi$
$18$	−1.61803	−0.381374
$19$	−3.85410	−0.884192	−0.442096	−	0.896968i	$-0.645765\pi$
$19$	−3.85410	−0.884192	−0.442096	+	0.896968i	$0.645765\pi$
$20$	−0.381966	−0.0854102
$21$	2.00000	0.436436
$22$	−8.47214	−1.80627
$23$	4.47214	0.932505	0.466252	−	0.884652i	$-0.345604\pi$
$23$	4.47214	0.932505	0.466252	+	0.884652i	$0.345604\pi$
$24$	−4.47214	−0.912871
$25$	−4.61803	−0.923607
$26$	7.47214	1.46541
$27$	4.00000	0.769800
$28$	−0.618034	−0.116797
$29$	5.38197	0.999406	0.499703	−	0.866197i	$-0.333442\pi$
$29$	5.38197	0.999406	0.499703	+	0.866197i	$0.333442\pi$
$30$	−2.00000	−0.365148
$31$	−7.38197	−1.32584	−0.662920	−	0.748690i	$-0.730683\pi$
$31$	−7.38197	−1.32584	−0.662920	+	0.748690i	$0.730683\pi$
$32$	3.38197	0.597853
$33$	−10.4721	−1.82296
$34$	−1.23607	−0.211984
$35$	0.618034	0.104467
$36$	0.618034	0.103006
$37$	−3.09017	−0.508021	−0.254010	−	0.967201i	$-0.581750\pi$
$37$	−3.09017	−0.508021	−0.254010	+	0.967201i	$0.581750\pi$
$38$	6.23607	1.01162
$39$	9.23607	1.47895
$40$	−1.38197	−0.218508
$41$	−1.09017	−0.170256	−0.0851280	−	0.996370i	$-0.527130\pi$
$41$	−1.09017	−0.170256	−0.0851280	+	0.996370i	$0.527130\pi$
$42$	−3.23607	−0.499336
$43$	5.09017	0.776244	0.388122	−	0.921608i	$-0.373124\pi$
$43$	5.09017	0.776244	0.388122	+	0.921608i	$0.373124\pi$
$44$	3.23607	0.487856
$45$	−0.618034	−0.0921311
$46$	−7.23607	−1.06690
$47$	2.23607	0.326164	0.163082	−	0.986613i	$-0.447856\pi$
$47$	2.23607	0.326164	0.163082	+	0.986613i	$0.447856\pi$
$48$	9.70820	1.40126
$49$	−6.00000	−0.857143
$50$	7.47214	1.05672
$51$	−1.52786	−0.213944
$52$	−2.85410	−0.395793
$53$	1.47214	0.202213	0.101107	−	0.994876i	$-0.467762\pi$
$53$	1.47214	0.202213	0.101107	+	0.994876i	$0.467762\pi$
$54$	−6.47214	−0.880746
$55$	−3.23607	−0.436351
$56$	−2.23607	−0.298807
$57$	7.70820	1.02098
$58$	−8.70820	−1.14344
$59$	−2.23607	−0.291111	−0.145556	−	0.989350i	$-0.546497\pi$
$59$	−2.23607	−0.291111	−0.145556	+	0.989350i	$0.546497\pi$
$60$	0.763932	0.0986232
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	11.9443	1.51692
$63$	−1.00000	−0.125988
$64$	4.23607	0.529508
$65$	2.85410	0.354008
$66$	16.9443	2.08570
$67$	−0.708204	−0.0865209	−0.0432604	−	0.999064i	$-0.513775\pi$
$67$	−0.708204	−0.0865209	−0.0432604	+	0.999064i	$0.513775\pi$
$68$	0.472136	0.0572549
$69$	−8.94427	−1.07676
$70$	−1.00000	−0.119523
$71$	12.7082	1.50819	0.754093	−	0.656767i	$-0.228077\pi$
$71$	12.7082	1.50819	0.754093	+	0.656767i	$0.228077\pi$
$72$	2.23607	0.263523
$73$	14.4164	1.68731	0.843656	−	0.536883i	$-0.180398\pi$
$73$	14.4164	1.68731	0.843656	+	0.536883i	$0.180398\pi$
$74$	5.00000	0.581238
$75$	9.23607	1.06649
$76$	−2.38197	−0.273230
$77$	−5.23607	−0.596705
$78$	−14.9443	−1.69211
$79$	−2.29180	−0.257847	−0.128924	−	0.991655i	$-0.541152\pi$
$79$	−2.29180	−0.257847	−0.128924	+	0.991655i	$0.541152\pi$
$80$	3.00000	0.335410
$81$	−11.0000	−1.22222
$82$	1.76393	0.194794
$83$	6.38197	0.700512	0.350256	−	0.936654i	$-0.386095\pi$
$83$	6.38197	0.700512	0.350256	+	0.936654i	$0.386095\pi$
$84$	1.23607	0.134866
$85$	−0.472136	−0.0512103
$86$	−8.23607	−0.888118
$87$	−10.7639	−1.15401
$88$	11.7082	1.24810
$89$	7.79837	0.826626	0.413313	−	0.910589i	$-0.364372\pi$
$89$	7.79837	0.826626	0.413313	+	0.910589i	$0.364372\pi$
$90$	1.00000	0.105409
$91$	4.61803	0.484102
$92$	2.76393	0.288160
$93$	14.7639	1.53095
$94$	−3.61803	−0.373172
$95$	2.38197	0.244385
$96$	−6.76393	−0.690341
$97$	−3.85410	−0.391325	−0.195662	−	0.980671i	$-0.562686\pi$
$97$	−3.85410	−0.391325	−0.195662	+	0.980671i	$0.562686\pi$
$98$	9.70820	0.980677
$99$	5.23607	0.526245
$100$	−2.85410	−0.285410
$101$	−7.79837	−0.775967	−0.387984	−	0.921666i	$-0.626828\pi$
$101$	−7.79837	−0.775967	−0.387984	+	0.921666i	$0.626828\pi$
$102$	2.47214	0.244778
$103$	9.09017	0.895681	0.447841	−	0.894113i	$-0.352193\pi$
$103$	9.09017	0.895681	0.447841	+	0.894113i	$0.352193\pi$
$104$	−10.3262	−1.01257
$105$	−1.23607	−0.120628
$106$	−2.38197	−0.231357
$107$	7.47214	0.722359	0.361179	−	0.932496i	$-0.382374\pi$
$107$	7.47214	0.722359	0.361179	+	0.932496i	$0.382374\pi$
$108$	2.47214	0.237881
$109$	6.70820	0.642529	0.321265	−	0.946989i	$-0.395892\pi$
$109$	6.70820	0.642529	0.321265	+	0.946989i	$0.395892\pi$
$110$	5.23607	0.499239
$111$	6.18034	0.586612
$112$	4.85410	0.458670
$113$	−3.47214	−0.326631	−0.163316	−	0.986574i	$-0.552219\pi$
$113$	−3.47214	−0.326631	−0.163316	+	0.986574i	$0.552219\pi$
$114$	−12.4721	−1.16812
$115$	−2.76393	−0.257738
$116$	3.32624	0.308833
$117$	−4.61803	−0.426937
$118$	3.61803	0.333067
$119$	−0.763932	−0.0700295
$120$	2.76393	0.252311
$121$	16.4164	1.49240
$122$	−3.23607	−0.292980
$123$	2.18034	0.196595
$124$	−4.56231	−0.409707
$125$	5.94427	0.531672
$126$	1.61803	0.144146
$127$	15.1803	1.34704	0.673519	−	0.739170i	$-0.264782\pi$
$127$	15.1803	1.34704	0.673519	+	0.739170i	$0.264782\pi$
$128$	−13.6180	−1.20368
$129$	−10.1803	−0.896329
$130$	−4.61803	−0.405028
$131$	−3.70820	−0.323987	−0.161994	−	0.986792i	$-0.551792\pi$
$131$	−3.70820	−0.323987	−0.161994	+	0.986792i	$0.551792\pi$
$132$	−6.47214	−0.563327
$133$	3.85410	0.334193
$134$	1.14590	0.0989905
$135$	−2.47214	−0.212768
$136$	1.70820	0.146477
$137$	−13.0902	−1.11837	−0.559184	−	0.829043i	$-0.688886\pi$
$137$	−13.0902	−1.11837	−0.559184	+	0.829043i	$0.688886\pi$
$138$	14.4721	1.23195
$139$	−18.0000	−1.52674	−0.763370	−	0.645961i	$-0.776457\pi$
$139$	−18.0000	−1.52674	−0.763370	+	0.645961i	$0.776457\pi$
$140$	0.381966	0.0322820
$141$	−4.47214	−0.376622
$142$	−20.5623	−1.72555
$143$	−24.1803	−2.02206
$144$	−4.85410	−0.404508
$145$	−3.32624	−0.276229
$146$	−23.3262	−1.93049
$147$	12.0000	0.989743
$148$	−1.90983	−0.156987
$149$	10.8541	0.889203	0.444601	−	0.895729i	$-0.353345\pi$
$149$	10.8541	0.889203	0.444601	+	0.895729i	$0.353345\pi$
$150$	−14.9443	−1.22019
$151$	−19.3820	−1.57728	−0.788641	−	0.614854i	$-0.789215\pi$
$151$	−19.3820	−1.57728	−0.788641	+	0.614854i	$0.789215\pi$
$152$	−8.61803	−0.699015
$153$	0.763932	0.0617602
$154$	8.47214	0.682704
$155$	4.56231	0.366453
$156$	5.70820	0.457022
$157$	5.00000	0.399043	0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000	0.399043	0.199522	+	0.979893i	$0.436061\pi$
$158$	3.70820	0.295009
$159$	−2.94427	−0.233496
$160$	−2.09017	−0.165242
$161$	−4.47214	−0.352454
$162$	17.7984	1.39837
$163$	6.56231	0.513999	0.257000	−	0.966411i	$-0.417266\pi$
$163$	6.56231	0.513999	0.257000	+	0.966411i	$0.417266\pi$
$164$	−0.673762	−0.0526120
$165$	6.47214	0.503855
$166$	−10.3262	−0.801471
$167$	−7.90983	−0.612081	−0.306041	−	0.952018i	$-0.599004\pi$
$167$	−7.90983	−0.612081	−0.306041	+	0.952018i	$0.599004\pi$
$168$	4.47214	0.345033
$169$	8.32624	0.640480
$170$	0.763932	0.0585909
$171$	−3.85410	−0.294731
$172$	3.14590	0.239872
$173$	0.708204	0.0538437	0.0269219	−	0.999638i	$-0.491429\pi$
$173$	0.708204	0.0538437	0.0269219	+	0.999638i	$0.491429\pi$
$174$	17.4164	1.32033
$175$	4.61803	0.349091
$176$	−25.4164	−1.91583
$177$	4.47214	0.336146
$178$	−12.6180	−0.945762
$179$	−3.32624	−0.248615	−0.124307	−	0.992244i	$-0.539671\pi$
$179$	−3.32624	−0.248615	−0.124307	+	0.992244i	$0.539671\pi$
$180$	−0.381966	−0.0284701
$181$	0.708204	0.0526404	0.0263202	−	0.999654i	$-0.491621\pi$
$181$	0.708204	0.0526404	0.0263202	+	0.999654i	$0.491621\pi$
$182$	−7.47214	−0.553872
$183$	−4.00000	−0.295689
$184$	10.0000	0.737210
$185$	1.90983	0.140413
$186$	−23.8885	−1.75159
$187$	4.00000	0.292509
$188$	1.38197	0.100790
$189$	−4.00000	−0.290957
$190$	−3.85410	−0.279606
$191$	3.70820	0.268316	0.134158	−	0.990960i	$-0.457167\pi$
$191$	3.70820	0.268316	0.134158	+	0.990960i	$0.457167\pi$
$192$	−8.47214	−0.611424
$193$	−14.5623	−1.04822	−0.524109	−	0.851651i	$-0.675602\pi$
$193$	−14.5623	−1.04822	−0.524109	+	0.851651i	$0.675602\pi$
$194$	6.23607	0.447724
$195$	−5.70820	−0.408773
$196$	−3.70820	−0.264872
$197$	−9.65248	−0.687710	−0.343855	−	0.939023i	$-0.611733\pi$
$197$	−9.65248	−0.687710	−0.343855	+	0.939023i	$0.611733\pi$
$198$	−8.47214	−0.602088
$199$	−1.18034	−0.0836721	−0.0418360	−	0.999124i	$-0.513321\pi$
$199$	−1.18034	−0.0836721	−0.0418360	+	0.999124i	$0.513321\pi$
$200$	−10.3262	−0.730175
$201$	1.41641	0.0999057
$202$	12.6180	0.887802
$203$	−5.38197	−0.377740
$204$	−0.944272	−0.0661123
$205$	0.673762	0.0470576
$206$	−14.7082	−1.02477
$207$	4.47214	0.310835
$208$	22.4164	1.55430
$209$	−20.1803	−1.39590
$210$	2.00000	0.138013
$211$	−2.43769	−0.167818	−0.0839089	−	0.996473i	$-0.526740\pi$
$211$	−2.43769	−0.167818	−0.0839089	+	0.996473i	$0.526740\pi$
$212$	0.909830	0.0624874
$213$	−25.4164	−1.74150
$214$	−12.0902	−0.826467
$215$	−3.14590	−0.214548
$216$	8.94427	0.608581
$217$	7.38197	0.501121
$218$	−10.8541	−0.735133
$219$	−28.8328	−1.94834
$220$	−2.00000	−0.134840
$221$	−3.52786	−0.237310
$222$	−10.0000	−0.671156
$223$	3.70820	0.248320	0.124160	−	0.992262i	$-0.460376\pi$
$223$	3.70820	0.248320	0.124160	+	0.992262i	$0.460376\pi$
$224$	−3.38197	−0.225967
$225$	−4.61803	−0.307869
$226$	5.61803	0.373706
$227$	−5.90983	−0.392249	−0.196125	−	0.980579i	$-0.562836\pi$
$227$	−5.90983	−0.392249	−0.196125	+	0.980579i	$0.562836\pi$
$228$	4.76393	0.315499
$229$	−16.0000	−1.05731	−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000	−1.05731	−0.528655	+	0.848837i	$0.677303\pi$
$230$	4.47214	0.294884
$231$	10.4721	0.689016
$232$	12.0344	0.790100
$233$	28.8885	1.89255	0.946276	−	0.323361i	$-0.104813\pi$
$233$	28.8885	1.89255	0.946276	+	0.323361i	$0.104813\pi$
$234$	7.47214	0.488469
$235$	−1.38197	−0.0901495
$236$	−1.38197	−0.0899583
$237$	4.58359	0.297736
$238$	1.23607	0.0801224
$239$	−12.5279	−0.810360	−0.405180	−	0.914237i	$-0.632791\pi$
$239$	−12.5279	−0.810360	−0.405180	+	0.914237i	$0.632791\pi$
$240$	−6.00000	−0.387298
$241$	−27.4164	−1.76605	−0.883023	−	0.469330i	$-0.844496\pi$
$241$	−27.4164	−1.76605	−0.883023	+	0.469330i	$0.844496\pi$
$242$	−26.5623	−1.70749
$243$	10.0000	0.641500
$244$	1.23607	0.0791311
$245$	3.70820	0.236908
$246$	−3.52786	−0.224928
$247$	17.7984	1.13248
$248$	−16.5066	−1.04817
$249$	−12.7639	−0.808881
$250$	−9.61803	−0.608298
$251$	−9.52786	−0.601393	−0.300697	−	0.953720i	$-0.597219\pi$
$251$	−9.52786	−0.601393	−0.300697	+	0.953720i	$0.597219\pi$
$252$	−0.618034	−0.0389325
$253$	23.4164	1.47218
$254$	−24.5623	−1.54118
$255$	0.944272	0.0591326
$256$	13.5623	0.847644
$257$	2.52786	0.157684	0.0788419	−	0.996887i	$-0.474878\pi$
$257$	2.52786	0.157684	0.0788419	+	0.996887i	$0.474878\pi$
$258$	16.4721	1.02551
$259$	3.09017	0.192014
$260$	1.76393	0.109394
$261$	5.38197	0.333135
$262$	6.00000	0.370681
$263$	−15.4721	−0.954053	−0.477026	−	0.878889i	$-0.658285\pi$
$263$	−15.4721	−0.954053	−0.477026	+	0.878889i	$0.658285\pi$
$264$	−23.4164	−1.44118
$265$	−0.909830	−0.0558904
$266$	−6.23607	−0.382358
$267$	−15.5967	−0.954505
$268$	−0.437694	−0.0267364
$269$	27.2705	1.66271	0.831356	−	0.555740i	$-0.187565\pi$
$269$	27.2705	1.66271	0.831356	+	0.555740i	$0.187565\pi$
$270$	4.00000	0.243432
$271$	−22.2705	−1.35284	−0.676419	−	0.736517i	$-0.736469\pi$
$271$	−22.2705	−1.35284	−0.676419	+	0.736517i	$0.736469\pi$
$272$	−3.70820	−0.224843
$273$	−9.23607	−0.558992
$274$	21.1803	1.27955
$275$	−24.1803	−1.45813
$276$	−5.52786	−0.332738
$277$	−22.6525	−1.36106	−0.680528	−	0.732722i	$-0.738249\pi$
$277$	−22.6525	−1.36106	−0.680528	+	0.732722i	$0.738249\pi$
$278$	29.1246	1.74678
$279$	−7.38197	−0.441947
$280$	1.38197	0.0825883
$281$	13.8541	0.826466	0.413233	−	0.910625i	$-0.364399\pi$
$281$	13.8541	0.826466	0.413233	+	0.910625i	$0.364399\pi$
$282$	7.23607	0.430902
$283$	8.43769	0.501569	0.250784	−	0.968043i	$-0.419311\pi$
$283$	8.43769	0.501569	0.250784	+	0.968043i	$0.419311\pi$
$284$	7.85410	0.466055
$285$	−4.76393	−0.282191
$286$	39.1246	2.31349
$287$	1.09017	0.0643507
$288$	3.38197	0.199284
$289$	−16.4164	−0.965671
$290$	5.38197	0.316040
$291$	7.70820	0.451863
$292$	8.90983	0.521408
$293$	14.5279	0.848727	0.424363	−	0.905492i	$-0.360498\pi$
$293$	14.5279	0.848727	0.424363	+	0.905492i	$0.360498\pi$
$294$	−19.4164	−1.13239
$295$	1.38197	0.0804612
$296$	−6.90983	−0.401626
$297$	20.9443	1.21531
$298$	−17.5623	−1.01736
$299$	−20.6525	−1.19436
$300$	5.70820	0.329563
$301$	−5.09017	−0.293393
$302$	31.3607	1.80460
$303$	15.5967	0.896010
$304$	18.7082	1.07299
$305$	−1.23607	−0.0707770
$306$	−1.23607	−0.0706613
$307$	−7.14590	−0.407838	−0.203919	−	0.978988i	$-0.565368\pi$
$307$	−7.14590	−0.407838	−0.203919	+	0.978988i	$0.565368\pi$
$308$	−3.23607	−0.184392
$309$	−18.1803	−1.03424
$310$	−7.38197	−0.419267
$311$	−11.7426	−0.665864	−0.332932	−	0.942951i	$-0.608038\pi$
$311$	−11.7426	−0.665864	−0.332932	+	0.942951i	$0.608038\pi$
$312$	20.6525	1.16922
$313$	19.1803	1.08414	0.542068	−	0.840334i	$-0.317641\pi$
$313$	19.1803	1.08414	0.542068	+	0.840334i	$0.317641\pi$
$314$	−8.09017	−0.456555
$315$	0.618034	0.0348223
$316$	−1.41641	−0.0796792
$317$	11.2361	0.631080	0.315540	−	0.948912i	$-0.397814\pi$
$317$	11.2361	0.631080	0.315540	+	0.948912i	$0.397814\pi$
$318$	4.76393	0.267148
$319$	28.1803	1.57780
$320$	−2.61803	−0.146353
$321$	−14.9443	−0.834108
$322$	7.23607	0.403250
$323$	−2.94427	−0.163824
$324$	−6.79837	−0.377687
$325$	21.3262	1.18297
$326$	−10.6180	−0.588079
$327$	−13.4164	−0.741929
$328$	−2.43769	−0.134599
$329$	−2.23607	−0.123278
$330$	−10.4721	−0.576472
$331$	−0.909830	−0.0500088	−0.0250044	−	0.999687i	$-0.507960\pi$
$331$	−0.909830	−0.0500088	−0.0250044	+	0.999687i	$0.507960\pi$
$332$	3.94427	0.216470
$333$	−3.09017	−0.169340
$334$	12.7984	0.700296
$335$	0.437694	0.0239138
$336$	−9.70820	−0.529626
$337$	−12.4721	−0.679401	−0.339700	−	0.940534i	$-0.610326\pi$
$337$	−12.4721	−0.679401	−0.339700	+	0.940534i	$0.610326\pi$
$338$	−13.4721	−0.732788
$339$	6.94427	0.377161
$340$	−0.291796	−0.0158249
$341$	−38.6525	−2.09315
$342$	6.23607	0.337208
$343$	13.0000	0.701934
$344$	11.3820	0.613674
$345$	5.52786	0.297610
$346$	−1.14590	−0.0616039
$347$	−16.8541	−0.904776	−0.452388	−	0.891821i	$-0.649428\pi$
$347$	−16.8541	−0.904776	−0.452388	+	0.891821i	$0.649428\pi$
$348$	−6.65248	−0.356610
$349$	−34.0000	−1.81998	−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000	−1.81998	−0.909989	+	0.414632i	$0.863910\pi$
$350$	−7.47214	−0.399402
$351$	−18.4721	−0.985970
$352$	17.7082	0.943850
$353$	−4.52786	−0.240994	−0.120497	−	0.992714i	$-0.538449\pi$
$353$	−4.52786	−0.240994	−0.120497	+	0.992714i	$0.538449\pi$
$354$	−7.23607	−0.384593
$355$	−7.85410	−0.416852
$356$	4.81966	0.255441
$357$	1.52786	0.0808631
$358$	5.38197	0.284446
$359$	−28.6869	−1.51404	−0.757019	−	0.653393i	$-0.773345\pi$
$359$	−28.6869	−1.51404	−0.757019	+	0.653393i	$0.773345\pi$
$360$	−1.38197	−0.0728360
$361$	−4.14590	−0.218205
$362$	−1.14590	−0.0602271
$363$	−32.8328	−1.72328
$364$	2.85410	0.149596
$365$	−8.90983	−0.466362
$366$	6.47214	0.338304
$367$	−9.52786	−0.497350	−0.248675	−	0.968587i	$-0.579995\pi$
$367$	−9.52786	−0.497350	−0.248675	+	0.968587i	$0.579995\pi$
$368$	−21.7082	−1.13162
$369$	−1.09017	−0.0567520
$370$	−3.09017	−0.160650
$371$	−1.47214	−0.0764295
$372$	9.12461	0.473089
$373$	7.76393	0.402001	0.201001	−	0.979591i	$-0.435581\pi$
$373$	7.76393	0.402001	0.201001	+	0.979591i	$0.435581\pi$
$374$	−6.47214	−0.334666
$375$	−11.8885	−0.613922
$376$	5.00000	0.257855
$377$	−24.8541	−1.28005
$378$	6.47214	0.332891
$379$	−4.81966	−0.247569	−0.123785	−	0.992309i	$-0.539503\pi$
$379$	−4.81966	−0.247569	−0.123785	+	0.992309i	$0.539503\pi$
$380$	1.47214	0.0755190
$381$	−30.3607	−1.55542
$382$	−6.00000	−0.306987
$383$	7.58359	0.387503	0.193752	−	0.981051i	$-0.437934\pi$
$383$	7.58359	0.387503	0.193752	+	0.981051i	$0.437934\pi$
$384$	27.2361	1.38988
$385$	3.23607	0.164925
$386$	23.5623	1.19929
$387$	5.09017	0.258748
$388$	−2.38197	−0.120926
$389$	8.47214	0.429554	0.214777	−	0.976663i	$-0.431097\pi$
$389$	8.47214	0.429554	0.214777	+	0.976663i	$0.431097\pi$
$390$	9.23607	0.467686
$391$	3.41641	0.172775
$392$	−13.4164	−0.677631
$393$	7.41641	0.374108
$394$	15.6180	0.786825
$395$	1.41641	0.0712672
$396$	3.23607	0.162619
$397$	−33.2705	−1.66980	−0.834900	−	0.550402i	$-0.814474\pi$
$397$	−33.2705	−1.66980	−0.834900	+	0.550402i	$0.814474\pi$
$398$	1.90983	0.0957311
$399$	−7.70820	−0.385893
$400$	22.4164	1.12082
$401$	10.2361	0.511165	0.255582	−	0.966787i	$-0.417733\pi$
$401$	10.2361	0.511165	0.255582	+	0.966787i	$0.417733\pi$
$402$	−2.29180	−0.114304
$403$	34.0902	1.69815
$404$	−4.81966	−0.239787
$405$	6.79837	0.337814
$406$	8.70820	0.432181
$407$	−16.1803	−0.802030
$408$	−3.41641	−0.169137
$409$	14.7639	0.730029	0.365015	−	0.931002i	$-0.381064\pi$
$409$	14.7639	0.730029	0.365015	+	0.931002i	$0.381064\pi$
$410$	−1.09017	−0.0538397
$411$	26.1803	1.29138
$412$	5.61803	0.276781
$413$	2.23607	0.110030
$414$	−7.23607	−0.355633
$415$	−3.94427	−0.193617
$416$	−15.6180	−0.765737
$417$	36.0000	1.76293
$418$	32.6525	1.59708
$419$	−24.2705	−1.18569	−0.592846	−	0.805316i	$-0.701996\pi$
$419$	−24.2705	−1.18569	−0.592846	+	0.805316i	$0.701996\pi$
$420$	−0.763932	−0.0372761
$421$	−32.7082	−1.59410	−0.797050	−	0.603913i	$-0.793607\pi$
$421$	−32.7082	−1.59410	−0.797050	+	0.603913i	$0.793607\pi$
$422$	3.94427	0.192004
$423$	2.23607	0.108721
$424$	3.29180	0.159864
$425$	−3.52786	−0.171127
$426$	41.1246	1.99249
$427$	−2.00000	−0.0967868
$428$	4.61803	0.223221
$429$	48.3607	2.33488
$430$	5.09017	0.245470
$431$	−24.4508	−1.17776	−0.588878	−	0.808222i	$-0.700430\pi$
$431$	−24.4508	−1.17776	−0.588878	+	0.808222i	$0.700430\pi$
$432$	−19.4164	−0.934172
$433$	0.888544	0.0427007	0.0213503	−	0.999772i	$-0.493203\pi$
$433$	0.888544	0.0427007	0.0213503	+	0.999772i	$0.493203\pi$
$434$	−11.9443	−0.573343
$435$	6.65248	0.318962
$436$	4.14590	0.198553
$437$	−17.2361	−0.824513
$438$	46.6525	2.22914
$439$	−16.1459	−0.770602	−0.385301	−	0.922791i	$-0.625902\pi$
$439$	−16.1459	−0.770602	−0.385301	+	0.922791i	$0.625902\pi$
$440$	−7.23607	−0.344966
$441$	−6.00000	−0.285714
$442$	5.70820	0.271512
$443$	−21.2705	−1.01059	−0.505296	−	0.862946i	$-0.668617\pi$
$443$	−21.2705	−1.01059	−0.505296	+	0.862946i	$0.668617\pi$
$444$	3.81966	0.181273
$445$	−4.81966	−0.228474
$446$	−6.00000	−0.284108
$447$	−21.7082	−1.02676
$448$	−4.23607	−0.200135
$449$	17.8885	0.844213	0.422106	−	0.906546i	$-0.361291\pi$
$449$	17.8885	0.844213	0.422106	+	0.906546i	$0.361291\pi$
$450$	7.47214	0.352240
$451$	−5.70820	−0.268789
$452$	−2.14590	−0.100935
$453$	38.7639	1.82129
$454$	9.56231	0.448781
$455$	−2.85410	−0.133802
$456$	17.2361	0.807153
$457$	−4.81966	−0.225454	−0.112727	−	0.993626i	$-0.535959\pi$
$457$	−4.81966	−0.225454	−0.112727	+	0.993626i	$0.535959\pi$
$458$	25.8885	1.20969
$459$	3.05573	0.142629
$460$	−1.70820	−0.0796454
$461$	−6.50658	−0.303042	−0.151521	−	0.988454i	$-0.548417\pi$
$461$	−6.50658	−0.303042	−0.151521	+	0.988454i	$0.548417\pi$
$462$	−16.9443	−0.788319
$463$	17.4164	0.809409	0.404705	−	0.914447i	$-0.367374\pi$
$463$	17.4164	0.809409	0.404705	+	0.914447i	$0.367374\pi$
$464$	−26.1246	−1.21280
$465$	−9.12461	−0.423144
$466$	−46.7426	−2.16531
$467$	−21.8885	−1.01288	−0.506441	−	0.862275i	$-0.669039\pi$
$467$	−21.8885	−1.01288	−0.506441	+	0.862275i	$0.669039\pi$
$468$	−2.85410	−0.131931
$469$	0.708204	0.0327018
$470$	2.23607	0.103142
$471$	−10.0000	−0.460776
$472$	−5.00000	−0.230144
$473$	26.6525	1.22548
$474$	−7.41641	−0.340647
$475$	17.7984	0.816645
$476$	−0.472136	−0.0216403
$477$	1.47214	0.0674045
$478$	20.2705	0.927152
$479$	23.5623	1.07659	0.538295	−	0.842757i	$-0.319069\pi$
$479$	23.5623	1.07659	0.538295	+	0.842757i	$0.319069\pi$
$480$	4.18034	0.190806
$481$	14.2705	0.650679
$482$	44.3607	2.02057
$483$	8.94427	0.406978
$484$	10.1459	0.461177
$485$	2.38197	0.108160
$486$	−16.1803	−0.733955
$487$	−9.97871	−0.452179	−0.226089	−	0.974107i	$-0.572594\pi$
$487$	−9.97871	−0.452179	−0.226089	+	0.974107i	$0.572594\pi$
$488$	4.47214	0.202444
$489$	−13.1246	−0.593515
$490$	−6.00000	−0.271052
$491$	37.5967	1.69672	0.848359	−	0.529422i	$-0.177591\pi$
$491$	37.5967	1.69672	0.848359	+	0.529422i	$0.177591\pi$
$492$	1.34752	0.0607511
$493$	4.11146	0.185171
$494$	−28.7984	−1.29570
$495$	−3.23607	−0.145450
$496$	35.8328	1.60894
$497$	−12.7082	−0.570041
$498$	20.6525	0.925460
$499$	−14.5279	−0.650357	−0.325178	−	0.945653i	$-0.605424\pi$
$499$	−14.5279	−0.650357	−0.325178	+	0.945653i	$0.605424\pi$
$500$	3.67376	0.164296
$501$	15.8197	0.706770
$502$	15.4164	0.688068
$503$	8.03444	0.358238	0.179119	−	0.983827i	$-0.442675\pi$
$503$	8.03444	0.358238	0.179119	+	0.983827i	$0.442675\pi$
$504$	−2.23607	−0.0996024
$505$	4.81966	0.214472
$506$	−37.8885	−1.68435
$507$	−16.6525	−0.739562
$508$	9.38197	0.416257
$509$	−14.7426	−0.653456	−0.326728	−	0.945118i	$-0.605946\pi$
$509$	−14.7426	−0.653456	−0.326728	+	0.945118i	$0.605946\pi$
$510$	−1.52786	−0.0676550
$511$	−14.4164	−0.637744
$512$	5.29180	0.233867
$513$	−15.4164	−0.680651
$514$	−4.09017	−0.180410
$515$	−5.61803	−0.247560
$516$	−6.29180	−0.276981
$517$	11.7082	0.514926
$518$	−5.00000	−0.219687
$519$	−1.41641	−0.0621734
$520$	6.38197	0.279868
$521$	33.6180	1.47283	0.736416	−	0.676529i	$-0.236516\pi$
$521$	33.6180	1.47283	0.736416	+	0.676529i	$0.236516\pi$
$522$	−8.70820	−0.381148
$523$	−19.4164	−0.849020	−0.424510	−	0.905423i	$-0.639554\pi$
$523$	−19.4164	−0.849020	−0.424510	+	0.905423i	$0.639554\pi$
$524$	−2.29180	−0.100118
$525$	−9.23607	−0.403095
$526$	25.0344	1.09155
$527$	−5.63932	−0.245653
$528$	50.8328	2.21221
$529$	−3.00000	−0.130435
$530$	1.47214	0.0639455
$531$	−2.23607	−0.0970371
$532$	2.38197	0.103271
$533$	5.03444	0.218066
$534$	25.2361	1.09207
$535$	−4.61803	−0.199655
$536$	−1.58359	−0.0684008
$537$	6.65248	0.287076
$538$	−44.1246	−1.90235
$539$	−31.4164	−1.35320
$540$	−1.52786	−0.0657488
$541$	27.1803	1.16857	0.584287	−	0.811547i	$-0.301374\pi$
$541$	27.1803	1.16857	0.584287	+	0.811547i	$0.301374\pi$
$542$	36.0344	1.54781
$543$	−1.41641	−0.0607839
$544$	2.58359	0.110771
$545$	−4.14590	−0.177591
$546$	14.9443	0.639556
$547$	23.5410	1.00654	0.503271	−	0.864129i	$-0.332130\pi$
$547$	23.5410	1.00654	0.503271	+	0.864129i	$0.332130\pi$
$548$	−8.09017	−0.345595
$549$	2.00000	0.0853579
$550$	39.1246	1.66828
$551$	−20.7426	−0.883666
$552$	−20.0000	−0.851257
$553$	2.29180	0.0974571
$554$	36.6525	1.55721
$555$	−3.81966	−0.162136
$556$	−11.1246	−0.471789
$557$	−12.9787	−0.549926	−0.274963	−	0.961455i	$-0.588666\pi$
$557$	−12.9787	−0.549926	−0.274963	+	0.961455i	$0.588666\pi$
$558$	11.9443	0.505641
$559$	−23.5066	−0.994222
$560$	−3.00000	−0.126773
$561$	−8.00000	−0.337760
$562$	−22.4164	−0.945579
$563$	−22.7984	−0.960837	−0.480418	−	0.877039i	$-0.659515\pi$
$563$	−22.7984	−0.960837	−0.480418	+	0.877039i	$0.659515\pi$
$564$	−2.76393	−0.116383
$565$	2.14590	0.0902786
$566$	−13.6525	−0.573856
$567$	11.0000	0.461957
$568$	28.4164	1.19233
$569$	11.1803	0.468704	0.234352	−	0.972152i	$-0.424703\pi$
$569$	11.1803	0.468704	0.234352	+	0.972152i	$0.424703\pi$
$570$	7.70820	0.322861
$571$	0.708204	0.0296374	0.0148187	−	0.999890i	$-0.495283\pi$
$571$	0.708204	0.0296374	0.0148187	+	0.999890i	$0.495283\pi$
$572$	−14.9443	−0.624851
$573$	−7.41641	−0.309825
$574$	−1.76393	−0.0736251
$575$	−20.6525	−0.861268
$576$	4.23607	0.176503
$577$	5.81966	0.242276	0.121138	−	0.992636i	$-0.461346\pi$
$577$	5.81966	0.242276	0.121138	+	0.992636i	$0.461346\pi$
$578$	26.5623	1.10485
$579$	29.1246	1.21038
$580$	−2.05573	−0.0853595
$581$	−6.38197	−0.264769
$582$	−12.4721	−0.516987
$583$	7.70820	0.319241
$584$	32.2361	1.33394
$585$	2.85410	0.118003
$586$	−23.5066	−0.971048
$587$	0.180340	0.00744342	0.00372171	−	0.999993i	$-0.498815\pi$
$587$	0.180340	0.00744342	0.00372171	+	0.999993i	$0.498815\pi$
$588$	7.41641	0.305848
$589$	28.4508	1.17230
$590$	−2.23607	−0.0920575
$591$	19.3050	0.794100
$592$	15.0000	0.616496
$593$	2.52786	0.103807	0.0519035	−	0.998652i	$-0.483471\pi$
$593$	2.52786	0.103807	0.0519035	+	0.998652i	$0.483471\pi$
$594$	−33.8885	−1.39046
$595$	0.472136	0.0193557
$596$	6.70820	0.274779
$597$	2.36068	0.0966162
$598$	33.4164	1.36650
$599$	41.7984	1.70784	0.853918	−	0.520408i	$-0.174220\pi$
$599$	41.7984	1.70784	0.853918	+	0.520408i	$0.174220\pi$
$600$	20.6525	0.843134
$601$	0.437694	0.0178539	0.00892696	−	0.999960i	$-0.497158\pi$
$601$	0.437694	0.0178539	0.00892696	+	0.999960i	$0.497158\pi$
$602$	8.23607	0.335677
$603$	−0.708204	−0.0288403
$604$	−11.9787	−0.487407
$605$	−10.1459	−0.412489
$606$	−25.2361	−1.02515
$607$	−45.8328	−1.86030	−0.930148	−	0.367184i	$-0.880322\pi$
$607$	−45.8328	−1.86030	−0.930148	+	0.367184i	$0.880322\pi$
$608$	−13.0344	−0.528616
$609$	10.7639	0.436177
$610$	2.00000	0.0809776
$611$	−10.3262	−0.417755
$612$	0.472136	0.0190850
$613$	38.1459	1.54070	0.770349	−	0.637622i	$-0.220082\pi$
$613$	38.1459	1.54070	0.770349	+	0.637622i	$0.220082\pi$
$614$	11.5623	0.466617
$615$	−1.34752	−0.0543374
$616$	−11.7082	−0.471737
$617$	−20.2361	−0.814673	−0.407337	−	0.913278i	$-0.633542\pi$
$617$	−20.2361	−0.814673	−0.407337	+	0.913278i	$0.633542\pi$
$618$	29.4164	1.18330
$619$	−43.7639	−1.75902	−0.879510	−	0.475880i	$-0.842130\pi$
$619$	−43.7639	−1.75902	−0.879510	+	0.475880i	$0.842130\pi$
$620$	2.81966	0.113240
$621$	17.8885	0.717843
$622$	19.0000	0.761831
$623$	−7.79837	−0.312435
$624$	−44.8328	−1.79475
$625$	19.4164	0.776656
$626$	−31.0344	−1.24039
$627$	40.3607	1.61185
$628$	3.09017	0.123311
$629$	−2.36068	−0.0941265
$630$	−1.00000	−0.0398410
$631$	−4.59675	−0.182994	−0.0914968	−	0.995805i	$-0.529165\pi$
$631$	−4.59675	−0.182994	−0.0914968	+	0.995805i	$0.529165\pi$
$632$	−5.12461	−0.203846
$633$	4.87539	0.193779
$634$	−18.1803	−0.722034
$635$	−9.38197	−0.372312
$636$	−1.81966	−0.0721542
$637$	27.7082	1.09784
$638$	−45.5967	−1.80519
$639$	12.7082	0.502729
$640$	8.41641	0.332688
$641$	28.0902	1.10950	0.554748	−	0.832019i	$-0.312815\pi$
$641$	28.0902	1.10950	0.554748	+	0.832019i	$0.312815\pi$
$642$	24.1803	0.954322
$643$	8.52786	0.336306	0.168153	−	0.985761i	$-0.446220\pi$
$643$	8.52786	0.336306	0.168153	+	0.985761i	$0.446220\pi$
$644$	−2.76393	−0.108914
$645$	6.29180	0.247739
$646$	4.76393	0.187434
$647$	5.79837	0.227958	0.113979	−	0.993483i	$-0.463640\pi$
$647$	5.79837	0.227958	0.113979	+	0.993483i	$0.463640\pi$
$648$	−24.5967	−0.966252
$649$	−11.7082	−0.459587
$650$	−34.5066	−1.35346
$651$	−14.7639	−0.578644
$652$	4.05573	0.158835
$653$	−14.0557	−0.550043	−0.275022	−	0.961438i	$-0.588685\pi$
$653$	−14.0557	−0.550043	−0.275022	+	0.961438i	$0.588685\pi$
$654$	21.7082	0.848858
$655$	2.29180	0.0895479
$656$	5.29180	0.206610
$657$	14.4164	0.562438
$658$	3.61803	0.141046
$659$	36.3607	1.41641	0.708205	−	0.706006i	$-0.249505\pi$
$659$	36.3607	1.41641	0.708205	+	0.706006i	$0.249505\pi$
$660$	4.00000	0.155700
$661$	−12.2361	−0.475928	−0.237964	−	0.971274i	$-0.576480\pi$
$661$	−12.2361	−0.475928	−0.237964	+	0.971274i	$0.576480\pi$
$662$	1.47214	0.0572162
$663$	7.05573	0.274022
$664$	14.2705	0.553803
$665$	−2.38197	−0.0923687
$666$	5.00000	0.193746
$667$	24.0689	0.931951
$668$	−4.88854	−0.189143
$669$	−7.41641	−0.286735
$670$	−0.708204	−0.0273603
$671$	10.4721	0.404272
$672$	6.76393	0.260924
$673$	−25.8541	−0.996602	−0.498301	−	0.867004i	$-0.666043\pi$
$673$	−25.8541	−0.996602	−0.498301	+	0.867004i	$0.666043\pi$
$674$	20.1803	0.777318
$675$	−18.4721	−0.710993
$676$	5.14590	0.197919
$677$	27.0000	1.03769	0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000	1.03769	0.518847	+	0.854867i	$0.326361\pi$
$678$	−11.2361	−0.431519
$679$	3.85410	0.147907
$680$	−1.05573	−0.0404853
$681$	11.8197	0.452930
$682$	62.5410	2.39482
$683$	3.81966	0.146155	0.0730776	−	0.997326i	$-0.476718\pi$
$683$	3.81966	0.146155	0.0730776	+	0.997326i	$0.476718\pi$
$684$	−2.38197	−0.0910767
$685$	8.09017	0.309110
$686$	−21.0344	−0.803099
$687$	32.0000	1.22088
$688$	−24.7082	−0.941991
$689$	−6.79837	−0.258997
$690$	−8.94427	−0.340503
$691$	−17.8328	−0.678392	−0.339196	−	0.940716i	$-0.610155\pi$
$691$	−17.8328	−0.678392	−0.339196	+	0.940716i	$0.610155\pi$
$692$	0.437694	0.0166386
$693$	−5.23607	−0.198902
$694$	27.2705	1.03517
$695$	11.1246	0.421981
$696$	−24.0689	−0.912329
$697$	−0.832816	−0.0315451
$698$	55.0132	2.08228
$699$	−57.7771	−2.18533
$700$	2.85410	0.107875
$701$	8.65248	0.326800	0.163400	−	0.986560i	$-0.447754\pi$
$701$	8.65248	0.326800	0.163400	+	0.986560i	$0.447754\pi$
$702$	29.8885	1.12807
$703$	11.9098	0.449188
$704$	22.1803	0.835953
$705$	2.76393	0.104096
$706$	7.32624	0.275727
$707$	7.79837	0.293288
$708$	2.76393	0.103875
$709$	−4.58359	−0.172140	−0.0860702	−	0.996289i	$-0.527431\pi$
$709$	−4.58359	−0.172140	−0.0860702	+	0.996289i	$0.527431\pi$
$710$	12.7082	0.476930
$711$	−2.29180	−0.0859491
$712$	17.4377	0.653505
$713$	−33.0132	−1.23635
$714$	−2.47214	−0.0925174
$715$	14.9443	0.558884
$716$	−2.05573	−0.0768262
$717$	25.0557	0.935723
$718$	46.4164	1.73224
$719$	−2.11146	−0.0787440	−0.0393720	−	0.999225i	$-0.512536\pi$
$719$	−2.11146	−0.0787440	−0.0393720	+	0.999225i	$0.512536\pi$
$720$	3.00000	0.111803
$721$	−9.09017	−0.338536
$722$	6.70820	0.249653
$723$	54.8328	2.03925
$724$	0.437694	0.0162668
$725$	−24.8541	−0.923058
$726$	53.1246	1.97164
$727$	30.8885	1.14559	0.572796	−	0.819698i	$-0.305859\pi$
$727$	30.8885	1.14559	0.572796	+	0.819698i	$0.305859\pi$
$728$	10.3262	0.382716
$729$	13.0000	0.481481
$730$	14.4164	0.533575
$731$	3.88854	0.143823
$732$	−2.47214	−0.0913728
$733$	−40.9574	−1.51280	−0.756399	−	0.654111i	$-0.773043\pi$
$733$	−40.9574	−1.51280	−0.756399	+	0.654111i	$0.773043\pi$
$734$	15.4164	0.569030
$735$	−7.41641	−0.273558
$736$	15.1246	0.557501
$737$	−3.70820	−0.136593
$738$	1.76393	0.0649312
$739$	−11.3607	−0.417909	−0.208955	−	0.977925i	$-0.567006\pi$
$739$	−11.3607	−0.417909	−0.208955	+	0.977925i	$0.567006\pi$
$740$	1.18034	0.0433902
$741$	−35.5967	−1.30768
$742$	2.38197	0.0874447
$743$	32.0132	1.17445	0.587224	−	0.809424i	$-0.300221\pi$
$743$	32.0132	1.17445	0.587224	+	0.809424i	$0.300221\pi$
$744$	33.0132	1.21032
$745$	−6.70820	−0.245770
$746$	−12.5623	−0.459939
$747$	6.38197	0.233504
$748$	2.47214	0.0903902
$749$	−7.47214	−0.273026
$750$	19.2361	0.702402
$751$	−10.1459	−0.370229	−0.185115	−	0.982717i	$-0.559266\pi$
$751$	−10.1459	−0.370229	−0.185115	+	0.982717i	$0.559266\pi$
$752$	−10.8541	−0.395808
$753$	19.0557	0.694429
$754$	40.2148	1.46454
$755$	11.9787	0.435950
$756$	−2.47214	−0.0899107
$757$	8.43769	0.306673	0.153337	−	0.988174i	$-0.450998\pi$
$757$	8.43769	0.306673	0.153337	+	0.988174i	$0.450998\pi$
$758$	7.79837	0.283250
$759$	−46.8328	−1.69992
$760$	5.32624	0.193203
$761$	−20.9656	−0.760001	−0.380000	−	0.924986i	$-0.624076\pi$
$761$	−20.9656	−0.760001	−0.380000	+	0.924986i	$0.624076\pi$
$762$	49.1246	1.77960
$763$	−6.70820	−0.242853
$764$	2.29180	0.0829143
$765$	−0.472136	−0.0170701
$766$	−12.2705	−0.443352
$767$	10.3262	0.372859
$768$	−27.1246	−0.978775
$769$	−16.1246	−0.581468	−0.290734	−	0.956804i	$-0.593900\pi$
$769$	−16.1246	−0.581468	−0.290734	+	0.956804i	$0.593900\pi$
$770$	−5.23607	−0.188695
$771$	−5.05573	−0.182078
$772$	−9.00000	−0.323917
$773$	−7.61803	−0.274002	−0.137001	−	0.990571i	$-0.543746\pi$
$773$	−7.61803	−0.274002	−0.137001	+	0.990571i	$0.543746\pi$
$774$	−8.23607	−0.296039
$775$	34.0902	1.22456
$776$	−8.61803	−0.309369
$777$	−6.18034	−0.221718
$778$	−13.7082	−0.491463
$779$	4.20163	0.150539
$780$	−3.52786	−0.126318
$781$	66.5410	2.38102
$782$	−5.52786	−0.197676
$783$	21.5279	0.769343
$784$	29.1246	1.04016
$785$	−3.09017	−0.110293
$786$	−12.0000	−0.428026
$787$	−39.9098	−1.42263	−0.711316	−	0.702872i	$-0.751900\pi$
$787$	−39.9098	−1.42263	−0.711316	+	0.702872i	$0.751900\pi$
$788$	−5.96556	−0.212514
$789$	30.9443	1.10165
$790$	−2.29180	−0.0815384
$791$	3.47214	0.123455
$792$	11.7082	0.416033
$793$	−9.23607	−0.327982
$794$	53.8328	1.91046
$795$	1.81966	0.0645367
$796$	−0.729490	−0.0258561
$797$	−6.18034	−0.218919	−0.109459	−	0.993991i	$-0.534912\pi$
$797$	−6.18034	−0.218919	−0.109459	+	0.993991i	$0.534912\pi$
$798$	12.4721	0.441509
$799$	1.70820	0.0604319
$800$	−15.6180	−0.552181
$801$	7.79837	0.275542
$802$	−16.5623	−0.584835
$803$	75.4853	2.66382
$804$	0.875388	0.0308726
$805$	2.76393	0.0974158
$806$	−55.1591	−1.94289
$807$	−54.5410	−1.91993
$808$	−17.4377	−0.613456
$809$	−38.8328	−1.36529	−0.682645	−	0.730751i	$-0.739170\pi$
$809$	−38.8328	−1.36529	−0.682645	+	0.730751i	$0.739170\pi$
$810$	−11.0000	−0.386501
$811$	−11.8754	−0.417001	−0.208501	−	0.978022i	$-0.566858\pi$
$811$	−11.8754	−0.417001	−0.208501	+	0.978022i	$0.566858\pi$
$812$	−3.32624	−0.116728
$813$	44.5410	1.56212
$814$	26.1803	0.917620
$815$	−4.05573	−0.142066
$816$	7.41641	0.259626
$817$	−19.6180	−0.686348
$818$	−23.8885	−0.835243
$819$	4.61803	0.161367
$820$	0.416408	0.0145416
$821$	39.3050	1.37175	0.685876	−	0.727718i	$-0.259419\pi$
$821$	39.3050	1.37175	0.685876	+	0.727718i	$0.259419\pi$
$822$	−42.3607	−1.47750
$823$	−56.4296	−1.96701	−0.983505	−	0.180878i	$-0.942106\pi$
$823$	−56.4296	−1.96701	−0.983505	+	0.180878i	$0.942106\pi$
$824$	20.3262	0.708098
$825$	48.3607	1.68370
$826$	−3.61803	−0.125888
$827$	−16.6525	−0.579063	−0.289532	−	0.957168i	$-0.593500\pi$
$827$	−16.6525	−0.579063	−0.289532	+	0.957168i	$0.593500\pi$
$828$	2.76393	0.0960533
$829$	−17.9230	−0.622491	−0.311246	−	0.950330i	$-0.600746\pi$
$829$	−17.9230	−0.622491	−0.311246	+	0.950330i	$0.600746\pi$
$830$	6.38197	0.221521
$831$	45.3050	1.57161
$832$	−19.5623	−0.678201
$833$	−4.58359	−0.158812
$834$	−58.2492	−2.01701
$835$	4.88854	0.169175
$836$	−12.4721	−0.431358
$837$	−29.5279	−1.02063
$838$	39.2705	1.35658
$839$	−21.0000	−0.725001	−0.362500	−	0.931984i	$-0.618077\pi$
$839$	−21.0000	−0.725001	−0.362500	+	0.931984i	$0.618077\pi$
$840$	−2.76393	−0.0953647
$841$	−0.0344419	−0.00118765
$842$	52.9230	1.82385
$843$	−27.7082	−0.954321
$844$	−1.50658	−0.0518585
$845$	−5.14590	−0.177024
$846$	−3.61803	−0.124391
$847$	−16.4164	−0.564074
$848$	−7.14590	−0.245391
$849$	−16.8754	−0.579162
$850$	5.70820	0.195790
$851$	−13.8197	−0.473732
$852$	−15.7082	−0.538154
$853$	33.8328	1.15841	0.579207	−	0.815181i	$-0.303362\pi$
$853$	33.8328	1.15841	0.579207	+	0.815181i	$0.303362\pi$
$854$	3.23607	0.110736
$855$	2.38197	0.0814615
$856$	16.7082	0.571075
$857$	−33.0000	−1.12726	−0.563629	−	0.826028i	$-0.690595\pi$
$857$	−33.0000	−1.12726	−0.563629	+	0.826028i	$0.690595\pi$
$858$	−78.2492	−2.67138
$859$	−11.5836	−0.395227	−0.197614	−	0.980280i	$-0.563319\pi$
$859$	−11.5836	−0.395227	−0.197614	+	0.980280i	$0.563319\pi$
$860$	−1.94427	−0.0662991
$861$	−2.18034	−0.0743058
$862$	39.5623	1.34750
$863$	7.58359	0.258148	0.129074	−	0.991635i	$-0.458799\pi$
$863$	7.58359	0.258148	0.129074	+	0.991635i	$0.458799\pi$
$864$	13.5279	0.460227
$865$	−0.437694	−0.0148820
$866$	−1.43769	−0.0488548
$867$	32.8328	1.11506
$868$	4.56231	0.154855
$869$	−12.0000	−0.407072
$870$	−10.7639	−0.364931
$871$	3.27051	0.110817
$872$	15.0000	0.507964
$873$	−3.85410	−0.130442
$874$	27.8885	0.943344
$875$	−5.94427	−0.200953
$876$	−17.8197	−0.602071
$877$	8.47214	0.286084	0.143042	−	0.989717i	$-0.454312\pi$
$877$	8.47214	0.286084	0.143042	+	0.989717i	$0.454312\pi$
$878$	26.1246	0.881663
$879$	−29.0557	−0.980025
$880$	15.7082	0.529523
$881$	33.9787	1.14477	0.572386	−	0.819984i	$-0.306018\pi$
$881$	33.9787	1.14477	0.572386	+	0.819984i	$0.306018\pi$
$882$	9.70820	0.326892
$883$	−19.1803	−0.645470	−0.322735	−	0.946489i	$-0.604602\pi$
$883$	−19.1803	−0.645470	−0.322735	+	0.946489i	$0.604602\pi$
$884$	−2.18034	−0.0733328
$885$	−2.76393	−0.0929086
$886$	34.4164	1.15624
$887$	−8.88854	−0.298448	−0.149224	−	0.988803i	$-0.547678\pi$
$887$	−8.88854	−0.298448	−0.149224	+	0.988803i	$0.547678\pi$
$888$	13.8197	0.463757
$889$	−15.1803	−0.509132
$890$	7.79837	0.261402
$891$	−57.5967	−1.92956
$892$	2.29180	0.0767350
$893$	−8.61803	−0.288392
$894$	35.1246	1.17474
$895$	2.05573	0.0687154
$896$	13.6180	0.454947
$897$	41.3050	1.37913
$898$	−28.9443	−0.965883
$899$	−39.7295	−1.32505
$900$	−2.85410	−0.0951367
$901$	1.12461	0.0374663
$902$	9.23607	0.307527
$903$	10.1803	0.338780
$904$	−7.76393	−0.258225
$905$	−0.437694	−0.0145494
$906$	−62.7214	−2.08378
$907$	−34.0000	−1.12895	−0.564476	−	0.825450i	$-0.690922\pi$
$907$	−34.0000	−1.12895	−0.564476	+	0.825450i	$0.690922\pi$
$908$	−3.65248	−0.121212
$909$	−7.79837	−0.258656
$910$	4.61803	0.153086
$911$	1.76393	0.0584417	0.0292208	−	0.999573i	$-0.490697\pi$
$911$	1.76393	0.0584417	0.0292208	+	0.999573i	$0.490697\pi$
$912$	−37.4164	−1.23898
$913$	33.4164	1.10592
$914$	7.79837	0.257947
$915$	2.47214	0.0817263
$916$	−9.88854	−0.326727
$917$	3.70820	0.122456
$918$	−4.94427	−0.163185
$919$	−2.49342	−0.0822504	−0.0411252	−	0.999154i	$-0.513094\pi$
$919$	−2.49342	−0.0822504	−0.0411252	+	0.999154i	$0.513094\pi$
$920$	−6.18034	−0.203760
$921$	14.2918	0.470931
$922$	10.5279	0.346717
$923$	−58.6869	−1.93170
$924$	6.47214	0.212918
$925$	14.2705	0.469211
$926$	−28.1803	−0.926063
$927$	9.09017	0.298560
$928$	18.2016	0.597498
$929$	−30.5967	−1.00385	−0.501923	−	0.864912i	$-0.667374\pi$
$929$	−30.5967	−1.00385	−0.501923	+	0.864912i	$0.667374\pi$
$930$	14.7639	0.484128
$931$	23.1246	0.757879
$932$	17.8541	0.584831
$933$	23.4853	0.768874
$934$	35.4164	1.15886
$935$	−2.47214	−0.0808475
$936$	−10.3262	−0.337524
$937$	8.12461	0.265419	0.132710	−	0.991155i	$-0.457632\pi$
$937$	8.12461	0.265419	0.132710	+	0.991155i	$0.457632\pi$
$938$	−1.14590	−0.0374149
$939$	−38.3607	−1.25185
$940$	−0.854102	−0.0278577
$941$	23.8328	0.776928	0.388464	−	0.921464i	$-0.373006\pi$
$941$	23.8328	0.776928	0.388464	+	0.921464i	$0.373006\pi$
$942$	16.1803	0.527184
$943$	−4.87539	−0.158764
$944$	10.8541	0.353271
$945$	2.47214	0.0804186
$946$	−43.1246	−1.40210
$947$	−11.0902	−0.360382	−0.180191	−	0.983632i	$-0.557672\pi$
$947$	−11.0902	−0.360382	−0.180191	+	0.983632i	$0.557672\pi$
$948$	2.83282	0.0920056
$949$	−66.5755	−2.16113
$950$	−28.7984	−0.934343
$951$	−22.4721	−0.728709
$952$	−1.70820	−0.0553632
$953$	−13.0557	−0.422917	−0.211458	−	0.977387i	$-0.567821\pi$
$953$	−13.0557	−0.422917	−0.211458	+	0.977387i	$0.567821\pi$
$954$	−2.38197	−0.0771190
$955$	−2.29180	−0.0741608
$956$	−7.74265	−0.250415
$957$	−56.3607	−1.82188
$958$	−38.1246	−1.23175
$959$	13.0902	0.422704
$960$	5.23607	0.168993
$961$	23.4934	0.757852
$962$	−23.0902	−0.744457
$963$	7.47214	0.240786
$964$	−16.9443	−0.545738
$965$	9.00000	0.289720
$966$	−14.4721	−0.465633
$967$	13.1591	0.423167	0.211583	−	0.977360i	$-0.432138\pi$
$967$	13.1591	0.423167	0.211583	+	0.977360i	$0.432138\pi$
$968$	36.7082	1.17985
$969$	5.88854	0.189167
$970$	−3.85410	−0.123748
$971$	−37.4721	−1.20254	−0.601269	−	0.799047i	$-0.705338\pi$
$971$	−37.4721	−1.20254	−0.601269	+	0.799047i	$0.705338\pi$
$972$	6.18034	0.198234
$973$	18.0000	0.577054
$974$	16.1459	0.517348
$975$	−42.6525	−1.36597
$976$	−9.70820	−0.310752
$977$	−1.31308	−0.0420092	−0.0210046	−	0.999779i	$-0.506686\pi$
$977$	−1.31308	−0.0420092	−0.0210046	+	0.999779i	$0.506686\pi$
$978$	21.2361	0.679055
$979$	40.8328	1.30502
$980$	2.29180	0.0732087
$981$	6.70820	0.214176
$982$	−60.8328	−1.94125
$983$	31.8885	1.01709	0.508543	−	0.861036i	$-0.330184\pi$
$983$	31.8885	1.01709	0.508543	+	0.861036i	$0.330184\pi$
$984$	4.87539	0.155422
$985$	5.96556	0.190078
$986$	−6.65248	−0.211858
$987$	4.47214	0.142350
$988$	11.0000	0.349957
$989$	22.7639	0.723851
$990$	5.23607	0.166413
$991$	35.5410	1.12900	0.564499	−	0.825434i	$-0.309069\pi$
$991$	35.5410	1.12900	0.564499	+	0.825434i	$0.309069\pi$
$992$	−24.9656	−0.792657
$993$	1.81966	0.0577452
$994$	20.5623	0.652197
$995$	0.729490	0.0231264
$996$	−7.88854	−0.249958
$997$	1.58359	0.0501529	0.0250764	−	0.999686i	$-0.492017\pi$
$997$	1.58359	0.0501529	0.0250764	+	0.999686i	$0.492017\pi$
$998$	23.5066	0.744088
$999$	−12.3607	−0.391075

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3229.2.a.b.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3229.2.a.b.1.1	✓	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3229.a (trivial)

\(f(q)\)	\(=\)	\(q-1.61803 q^{2} -2.00000 q^{3} +0.618034 q^{4} -0.618034 q^{5} +3.23607 q^{6} -1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.61803 q^{2} -2.00000 q^{3} +0.618034 q^{4} -0.618034 q^{5} +3.23607 q^{6} -1.00000 q^{7} +2.23607 q^{8} +1.00000 q^{9} +1.00000 q^{10} +5.23607 q^{11} -1.23607 q^{12} -4.61803 q^{13} +1.61803 q^{14} +1.23607 q^{15} -4.85410 q^{16} +0.763932 q^{17} -1.61803 q^{18} -3.85410 q^{19} -0.381966 q^{20} +2.00000 q^{21} -8.47214 q^{22} +4.47214 q^{23} -4.47214 q^{24} -4.61803 q^{25} +7.47214 q^{26} +4.00000 q^{27} -0.618034 q^{28} +5.38197 q^{29} -2.00000 q^{30} -7.38197 q^{31} +3.38197 q^{32} -10.4721 q^{33} -1.23607 q^{34} +0.618034 q^{35} +0.618034 q^{36} -3.09017 q^{37} +6.23607 q^{38} +9.23607 q^{39} -1.38197 q^{40} -1.09017 q^{41} -3.23607 q^{42} +5.09017 q^{43} +3.23607 q^{44} -0.618034 q^{45} -7.23607 q^{46} +2.23607 q^{47} +9.70820 q^{48} -6.00000 q^{49} +7.47214 q^{50} -1.52786 q^{51} -2.85410 q^{52} +1.47214 q^{53} -6.47214 q^{54} -3.23607 q^{55} -2.23607 q^{56} +7.70820 q^{57} -8.70820 q^{58} -2.23607 q^{59} +0.763932 q^{60} +2.00000 q^{61} +11.9443 q^{62} -1.00000 q^{63} +4.23607 q^{64} +2.85410 q^{65} +16.9443 q^{66} -0.708204 q^{67} +0.472136 q^{68} -8.94427 q^{69} -1.00000 q^{70} +12.7082 q^{71} +2.23607 q^{72} +14.4164 q^{73} +5.00000 q^{74} +9.23607 q^{75} -2.38197 q^{76} -5.23607 q^{77} -14.9443 q^{78} -2.29180 q^{79} +3.00000 q^{80} -11.0000 q^{81} +1.76393 q^{82} +6.38197 q^{83} +1.23607 q^{84} -0.472136 q^{85} -8.23607 q^{86} -10.7639 q^{87} +11.7082 q^{88} +7.79837 q^{89} +1.00000 q^{90} +4.61803 q^{91} +2.76393 q^{92} +14.7639 q^{93} -3.61803 q^{94} +2.38197 q^{95} -6.76393 q^{96} -3.85410 q^{97} +9.70820 q^{98} +5.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 4 q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 - 4 * q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^7 + 2 * q^9	\( 2 q - q^{2} - 4 q^{3} - q^{4} + q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{9} + 2 q^{10} + 6 q^{11} + 2 q^{12} - 7 q^{13} + q^{14} - 2 q^{15} - 3 q^{16} + 6 q^{17} - q^{18} - q^{19} - 3 q^{20} + 4 q^{21} - 8 q^{22} - 7 q^{25} + 6 q^{26} + 8 q^{27} + q^{28} + 13 q^{29} - 4 q^{30} - 17 q^{31} + 9 q^{32} - 12 q^{33} + 2 q^{34} - q^{35} - q^{36} + 5 q^{37} + 8 q^{38} + 14 q^{39} - 5 q^{40} + 9 q^{41} - 2 q^{42} - q^{43} + 2 q^{44} + q^{45} - 10 q^{46} + 6 q^{48} - 12 q^{49} + 6 q^{50} - 12 q^{51} + q^{52} - 6 q^{53} - 4 q^{54} - 2 q^{55} + 2 q^{57} - 4 q^{58} + 6 q^{60} + 4 q^{61} + 6 q^{62} - 2 q^{63} + 4 q^{64} - q^{65} + 16 q^{66} + 12 q^{67} - 8 q^{68} - 2 q^{70} + 12 q^{71} + 2 q^{73} + 10 q^{74} + 14 q^{75} - 7 q^{76} - 6 q^{77} - 12 q^{78} - 18 q^{79} + 6 q^{80} - 22 q^{81} + 8 q^{82} + 15 q^{83} - 2 q^{84} + 8 q^{85} - 12 q^{86} - 26 q^{87} + 10 q^{88} - 9 q^{89} + 2 q^{90} + 7 q^{91} + 10 q^{92} + 34 q^{93} - 5 q^{94} + 7 q^{95} - 18 q^{96} - q^{97} + 6 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - q^2 - 4 * q^3 - q^4 + q^5 + 2 * q^6 - 2 * q^7 + 2 * q^9 + 2 * q^10 + 6 * q^11 + 2 * q^12 - 7 * q^13 + q^14 - 2 * q^15 - 3 * q^16 + 6 * q^17 - q^18 - q^19 - 3 * q^20 + 4 * q^21 - 8 * q^22 - 7 * q^25 + 6 * q^26 + 8 * q^27 + q^28 + 13 * q^29 - 4 * q^30 - 17 * q^31 + 9 * q^32 - 12 * q^33 + 2 * q^34 - q^35 - q^36 + 5 * q^37 + 8 * q^38 + 14 * q^39 - 5 * q^40 + 9 * q^41 - 2 * q^42 - q^43 + 2 * q^44 + q^45 - 10 * q^46 + 6 * q^48 - 12 * q^49 + 6 * q^50 - 12 * q^51 + q^52 - 6 * q^53 - 4 * q^54 - 2 * q^55 + 2 * q^57 - 4 * q^58 + 6 * q^60 + 4 * q^61 + 6 * q^62 - 2 * q^63 + 4 * q^64 - q^65 + 16 * q^66 + 12 * q^67 - 8 * q^68 - 2 * q^70 + 12 * q^71 + 2 * q^73 + 10 * q^74 + 14 * q^75 - 7 * q^76 - 6 * q^77 - 12 * q^78 - 18 * q^79 + 6 * q^80 - 22 * q^81 + 8 * q^82 + 15 * q^83 - 2 * q^84 + 8 * q^85 - 12 * q^86 - 26 * q^87 + 10 * q^88 - 9 * q^89 + 2 * q^90 + 7 * q^91 + 10 * q^92 + 34 * q^93 - 5 * q^94 + 7 * q^95 - 18 * q^96 - q^97 + 6 * q^98 + 6 * q^99

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