LMFDB - Embedded newform 462.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(1,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("462.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ of defining polynomial
Character	$\chi$	$=$	462.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.46410 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.46410 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.46410 q^{10} +1.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} -3.46410 q^{15} +1.00000 q^{16} +3.46410 q^{17} -1.00000 q^{18} +5.46410 q^{19} -3.46410 q^{20} +1.00000 q^{21} -1.00000 q^{22} +6.92820 q^{23} -1.00000 q^{24} +7.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} -6.00000 q^{29} +3.46410 q^{30} +5.46410 q^{31} -1.00000 q^{32} +1.00000 q^{33} -3.46410 q^{34} -3.46410 q^{35} +1.00000 q^{36} -4.92820 q^{37} -5.46410 q^{38} +2.00000 q^{39} +3.46410 q^{40} +3.46410 q^{41} -1.00000 q^{42} -10.9282 q^{43} +1.00000 q^{44} -3.46410 q^{45} -6.92820 q^{46} +9.46410 q^{47} +1.00000 q^{48} +1.00000 q^{49} -7.00000 q^{50} +3.46410 q^{51} +2.00000 q^{52} -0.928203 q^{53} -1.00000 q^{54} -3.46410 q^{55} -1.00000 q^{56} +5.46410 q^{57} +6.00000 q^{58} +6.92820 q^{59} -3.46410 q^{60} +2.00000 q^{61} -5.46410 q^{62} +1.00000 q^{63} +1.00000 q^{64} -6.92820 q^{65} -1.00000 q^{66} +14.9282 q^{67} +3.46410 q^{68} +6.92820 q^{69} +3.46410 q^{70} -12.0000 q^{71} -1.00000 q^{72} -0.535898 q^{73} +4.92820 q^{74} +7.00000 q^{75} +5.46410 q^{76} +1.00000 q^{77} -2.00000 q^{78} -10.9282 q^{79} -3.46410 q^{80} +1.00000 q^{81} -3.46410 q^{82} +4.39230 q^{83} +1.00000 q^{84} -12.0000 q^{85} +10.9282 q^{86} -6.00000 q^{87} -1.00000 q^{88} -0.928203 q^{89} +3.46410 q^{90} +2.00000 q^{91} +6.92820 q^{92} +5.46410 q^{93} -9.46410 q^{94} -18.9282 q^{95} -1.00000 q^{96} +2.00000 q^{97} -1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{11} + 2 q^{12} + 4 q^{13} - 2 q^{14} + 2 q^{16} - 2 q^{18} + 4 q^{19} + 2 q^{21} - 2 q^{22} - 2 q^{24} + 14 q^{25} - 4 q^{26} + 2 q^{27} + 2 q^{28} - 12 q^{29} + 4 q^{31} - 2 q^{32} + 2 q^{33} + 2 q^{36} + 4 q^{37} - 4 q^{38} + 4 q^{39} - 2 q^{42} - 8 q^{43} + 2 q^{44} + 12 q^{47} + 2 q^{48} + 2 q^{49} - 14 q^{50} + 4 q^{52} + 12 q^{53} - 2 q^{54} - 2 q^{56} + 4 q^{57} + 12 q^{58} + 4 q^{61} - 4 q^{62} + 2 q^{63} + 2 q^{64} - 2 q^{66} + 16 q^{67} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 4 q^{74} + 14 q^{75} + 4 q^{76} + 2 q^{77} - 4 q^{78} - 8 q^{79} + 2 q^{81} - 12 q^{83} + 2 q^{84} - 24 q^{85} + 8 q^{86} - 12 q^{87} - 2 q^{88} + 12 q^{89} + 4 q^{91} + 4 q^{93} - 12 q^{94} - 24 q^{95} - 2 q^{96} + 4 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^11 + 2 * q^12 + 4 * q^13 - 2 * q^14 + 2 * q^16 - 2 * q^18 + 4 * q^19 + 2 * q^21 - 2 * q^22 - 2 * q^24 + 14 * q^25 - 4 * q^26 + 2 * q^27 + 2 * q^28 - 12 * q^29 + 4 * q^31 - 2 * q^32 + 2 * q^33 + 2 * q^36 + 4 * q^37 - 4 * q^38 + 4 * q^39 - 2 * q^42 - 8 * q^43 + 2 * q^44 + 12 * q^47 + 2 * q^48 + 2 * q^49 - 14 * q^50 + 4 * q^52 + 12 * q^53 - 2 * q^54 - 2 * q^56 + 4 * q^57 + 12 * q^58 + 4 * q^61 - 4 * q^62 + 2 * q^63 + 2 * q^64 - 2 * q^66 + 16 * q^67 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 4 * q^74 + 14 * q^75 + 4 * q^76 + 2 * q^77 - 4 * q^78 - 8 * q^79 + 2 * q^81 - 12 * q^83 + 2 * q^84 - 24 * q^85 + 8 * q^86 - 12 * q^87 - 2 * q^88 + 12 * q^89 + 4 * q^91 + 4 * q^93 - 12 * q^94 - 24 * q^95 - 2 * q^96 + 4 * q^97 - 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.46410	−1.54919	−0.774597	−	0.632456i	$-0.782047\pi$
$5$	−3.46410	−1.54919	−0.774597	+	0.632456i	$0.782047\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.46410	1.09545
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−1.00000	−0.267261
$15$	−3.46410	−0.894427
$16$	1.00000	0.250000
$17$	3.46410	0.840168	0.420084	−	0.907485i	$-0.362001\pi$
$17$	3.46410	0.840168	0.420084	+	0.907485i	$0.362001\pi$
$18$	−1.00000	−0.235702
$19$	5.46410	1.25355	0.626775	−	0.779200i	$-0.284374\pi$
$19$	5.46410	1.25355	0.626775	+	0.779200i	$0.284374\pi$
$20$	−3.46410	−0.774597
$21$	1.00000	0.218218
$22$	−1.00000	−0.213201
$23$	6.92820	1.44463	0.722315	−	0.691564i	$-0.243078\pi$
$23$	6.92820	1.44463	0.722315	+	0.691564i	$0.243078\pi$
$24$	−1.00000	−0.204124
$25$	7.00000	1.40000
$26$	−2.00000	−0.392232
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	3.46410	0.632456
$31$	5.46410	0.981382	0.490691	−	0.871334i	$-0.336744\pi$
$31$	5.46410	0.981382	0.490691	+	0.871334i	$0.336744\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−3.46410	−0.594089
$35$	−3.46410	−0.585540
$36$	1.00000	0.166667
$37$	−4.92820	−0.810192	−0.405096	−	0.914274i	$-0.632762\pi$
$37$	−4.92820	−0.810192	−0.405096	+	0.914274i	$0.632762\pi$
$38$	−5.46410	−0.886394
$39$	2.00000	0.320256
$40$	3.46410	0.547723
$41$	3.46410	0.541002	0.270501	−	0.962720i	$-0.412811\pi$
$41$	3.46410	0.541002	0.270501	+	0.962720i	$0.412811\pi$
$42$	−1.00000	−0.154303
$43$	−10.9282	−1.66654	−0.833268	−	0.552870i	$-0.813533\pi$
$43$	−10.9282	−1.66654	−0.833268	+	0.552870i	$0.813533\pi$
$44$	1.00000	0.150756
$45$	−3.46410	−0.516398
$46$	−6.92820	−1.02151
$47$	9.46410	1.38048	0.690241	−	0.723580i	$-0.257505\pi$
$47$	9.46410	1.38048	0.690241	+	0.723580i	$0.257505\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−7.00000	−0.989949
$51$	3.46410	0.485071
$52$	2.00000	0.277350
$53$	−0.928203	−0.127499	−0.0637493	−	0.997966i	$-0.520306\pi$
$53$	−0.928203	−0.127499	−0.0637493	+	0.997966i	$0.520306\pi$
$54$	−1.00000	−0.136083
$55$	−3.46410	−0.467099
$56$	−1.00000	−0.133631
$57$	5.46410	0.723738
$58$	6.00000	0.787839
$59$	6.92820	0.901975	0.450988	−	0.892530i	$-0.351072\pi$
$59$	6.92820	0.901975	0.450988	+	0.892530i	$0.351072\pi$
$60$	−3.46410	−0.447214
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−5.46410	−0.693942
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−6.92820	−0.859338
$66$	−1.00000	−0.123091
$67$	14.9282	1.82377	0.911885	−	0.410445i	$-0.134627\pi$
$67$	14.9282	1.82377	0.911885	+	0.410445i	$0.134627\pi$
$68$	3.46410	0.420084
$69$	6.92820	0.834058
$70$	3.46410	0.414039
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	−1.00000	−0.117851
$73$	−0.535898	−0.0627222	−0.0313611	−	0.999508i	$-0.509984\pi$
$73$	−0.535898	−0.0627222	−0.0313611	+	0.999508i	$0.509984\pi$
$74$	4.92820	0.572892
$75$	7.00000	0.808290
$76$	5.46410	0.626775
$77$	1.00000	0.113961
$78$	−2.00000	−0.226455
$79$	−10.9282	−1.22952	−0.614759	−	0.788715i	$-0.710747\pi$
$79$	−10.9282	−1.22952	−0.614759	+	0.788715i	$0.710747\pi$
$80$	−3.46410	−0.387298
$81$	1.00000	0.111111
$82$	−3.46410	−0.382546
$83$	4.39230	0.482118	0.241059	−	0.970510i	$-0.422505\pi$
$83$	4.39230	0.482118	0.241059	+	0.970510i	$0.422505\pi$
$84$	1.00000	0.109109
$85$	−12.0000	−1.30158
$86$	10.9282	1.17842
$87$	−6.00000	−0.643268
$88$	−1.00000	−0.106600
$89$	−0.928203	−0.0983893	−0.0491947	−	0.998789i	$-0.515665\pi$
$89$	−0.928203	−0.0983893	−0.0491947	+	0.998789i	$0.515665\pi$
$90$	3.46410	0.365148
$91$	2.00000	0.209657
$92$	6.92820	0.722315
$93$	5.46410	0.566601
$94$	−9.46410	−0.976148
$95$	−18.9282	−1.94199
$96$	−1.00000	−0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−1.00000	−0.101015
$99$	1.00000	0.100504
$100$	7.00000	0.700000
$101$	−19.8564	−1.97579	−0.987893	−	0.155136i	$-0.950418\pi$
$101$	−19.8564	−1.97579	−0.987893	+	0.155136i	$0.950418\pi$
$102$	−3.46410	−0.342997
$103$	−13.4641	−1.32666	−0.663329	−	0.748328i	$-0.730857\pi$
$103$	−13.4641	−1.32666	−0.663329	+	0.748328i	$0.730857\pi$
$104$	−2.00000	−0.196116
$105$	−3.46410	−0.338062
$106$	0.928203	0.0901551
$107$	−6.92820	−0.669775	−0.334887	−	0.942258i	$-0.608698\pi$
$107$	−6.92820	−0.669775	−0.334887	+	0.942258i	$0.608698\pi$
$108$	1.00000	0.0962250
$109$	15.8564	1.51877	0.759384	−	0.650643i	$-0.225500\pi$
$109$	15.8564	1.51877	0.759384	+	0.650643i	$0.225500\pi$
$110$	3.46410	0.330289
$111$	−4.92820	−0.467764
$112$	1.00000	0.0944911
$113$	7.85641	0.739069	0.369534	−	0.929217i	$-0.379517\pi$
$113$	7.85641	0.739069	0.369534	+	0.929217i	$0.379517\pi$
$114$	−5.46410	−0.511760
$115$	−24.0000	−2.23801
$116$	−6.00000	−0.557086
$117$	2.00000	0.184900
$118$	−6.92820	−0.637793
$119$	3.46410	0.317554
$120$	3.46410	0.316228
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	3.46410	0.312348
$124$	5.46410	0.490691
$125$	−6.92820	−0.619677
$126$	−1.00000	−0.0890871
$127$	−10.9282	−0.969721	−0.484861	−	0.874591i	$-0.661130\pi$
$127$	−10.9282	−0.969721	−0.484861	+	0.874591i	$0.661130\pi$
$128$	−1.00000	−0.0883883
$129$	−10.9282	−0.962175
$130$	6.92820	0.607644
$131$	−4.39230	−0.383757	−0.191879	−	0.981419i	$-0.561458\pi$
$131$	−4.39230	−0.383757	−0.191879	+	0.981419i	$0.561458\pi$
$132$	1.00000	0.0870388
$133$	5.46410	0.473798
$134$	−14.9282	−1.28960
$135$	−3.46410	−0.298142
$136$	−3.46410	−0.297044
$137$	7.85641	0.671218	0.335609	−	0.942001i	$-0.391058\pi$
$137$	7.85641	0.671218	0.335609	+	0.942001i	$0.391058\pi$
$138$	−6.92820	−0.589768
$139$	−13.4641	−1.14201	−0.571005	−	0.820947i	$-0.693446\pi$
$139$	−13.4641	−1.14201	−0.571005	+	0.820947i	$0.693446\pi$
$140$	−3.46410	−0.292770
$141$	9.46410	0.797021
$142$	12.0000	1.00702
$143$	2.00000	0.167248
$144$	1.00000	0.0833333
$145$	20.7846	1.72607
$146$	0.535898	0.0443513
$147$	1.00000	0.0824786
$148$	−4.92820	−0.405096
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	−7.00000	−0.571548
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	−5.46410	−0.443197
$153$	3.46410	0.280056
$154$	−1.00000	−0.0805823
$155$	−18.9282	−1.52035
$156$	2.00000	0.160128
$157$	−2.39230	−0.190927	−0.0954634	−	0.995433i	$-0.530433\pi$
$157$	−2.39230	−0.190927	−0.0954634	+	0.995433i	$0.530433\pi$
$158$	10.9282	0.869401
$159$	−0.928203	−0.0736113
$160$	3.46410	0.273861
$161$	6.92820	0.546019
$162$	−1.00000	−0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	3.46410	0.270501
$165$	−3.46410	−0.269680
$166$	−4.39230	−0.340909
$167$	18.9282	1.46471	0.732354	−	0.680924i	$-0.238422\pi$
$167$	18.9282	1.46471	0.732354	+	0.680924i	$0.238422\pi$
$168$	−1.00000	−0.0771517
$169$	−9.00000	−0.692308
$170$	12.0000	0.920358
$171$	5.46410	0.417850
$172$	−10.9282	−0.833268
$173$	−0.928203	−0.0705700	−0.0352850	−	0.999377i	$-0.511234\pi$
$173$	−0.928203	−0.0705700	−0.0352850	+	0.999377i	$0.511234\pi$
$174$	6.00000	0.454859
$175$	7.00000	0.529150
$176$	1.00000	0.0753778
$177$	6.92820	0.520756
$178$	0.928203	0.0695718
$179$	−20.7846	−1.55351	−0.776757	−	0.629800i	$-0.783137\pi$
$179$	−20.7846	−1.55351	−0.776757	+	0.629800i	$0.783137\pi$
$180$	−3.46410	−0.258199
$181$	6.39230	0.475136	0.237568	−	0.971371i	$-0.423650\pi$
$181$	6.39230	0.475136	0.237568	+	0.971371i	$0.423650\pi$
$182$	−2.00000	−0.148250
$183$	2.00000	0.147844
$184$	−6.92820	−0.510754
$185$	17.0718	1.25514
$186$	−5.46410	−0.400647
$187$	3.46410	0.253320
$188$	9.46410	0.690241
$189$	1.00000	0.0727393
$190$	18.9282	1.37320
$191$	20.7846	1.50392	0.751961	−	0.659208i	$-0.229108\pi$
$191$	20.7846	1.50392	0.751961	+	0.659208i	$0.229108\pi$
$192$	1.00000	0.0721688
$193$	26.0000	1.87152	0.935760	−	0.352636i	$-0.114715\pi$
$193$	26.0000	1.87152	0.935760	+	0.352636i	$0.114715\pi$
$194$	−2.00000	−0.143592
$195$	−6.92820	−0.496139
$196$	1.00000	0.0714286
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	−1.00000	−0.0710669
$199$	0.392305	0.0278098	0.0139049	−	0.999903i	$-0.495574\pi$
$199$	0.392305	0.0278098	0.0139049	+	0.999903i	$0.495574\pi$
$200$	−7.00000	−0.494975
$201$	14.9282	1.05295
$202$	19.8564	1.39709
$203$	−6.00000	−0.421117
$204$	3.46410	0.242536
$205$	−12.0000	−0.838116
$206$	13.4641	0.938088
$207$	6.92820	0.481543
$208$	2.00000	0.138675
$209$	5.46410	0.377960
$210$	3.46410	0.239046
$211$	16.7846	1.15550	0.577750	−	0.816214i	$-0.303931\pi$
$211$	16.7846	1.15550	0.577750	+	0.816214i	$0.303931\pi$
$212$	−0.928203	−0.0637493
$213$	−12.0000	−0.822226
$214$	6.92820	0.473602
$215$	37.8564	2.58179
$216$	−1.00000	−0.0680414
$217$	5.46410	0.370927
$218$	−15.8564	−1.07393
$219$	−0.535898	−0.0362127
$220$	−3.46410	−0.233550
$221$	6.92820	0.466041
$222$	4.92820	0.330759
$223$	−8.39230	−0.561990	−0.280995	−	0.959709i	$-0.590664\pi$
$223$	−8.39230	−0.561990	−0.280995	+	0.959709i	$0.590664\pi$
$224$	−1.00000	−0.0668153
$225$	7.00000	0.466667
$226$	−7.85641	−0.522600
$227$	−4.39230	−0.291528	−0.145764	−	0.989319i	$-0.546564\pi$
$227$	−4.39230	−0.291528	−0.145764	+	0.989319i	$0.546564\pi$
$228$	5.46410	0.361869
$229$	−21.3205	−1.40890	−0.704449	−	0.709754i	$-0.748806\pi$
$229$	−21.3205	−1.40890	−0.704449	+	0.709754i	$0.748806\pi$
$230$	24.0000	1.58251
$231$	1.00000	0.0657952
$232$	6.00000	0.393919
$233$	−7.85641	−0.514690	−0.257345	−	0.966320i	$-0.582848\pi$
$233$	−7.85641	−0.514690	−0.257345	+	0.966320i	$0.582848\pi$
$234$	−2.00000	−0.130744
$235$	−32.7846	−2.13863
$236$	6.92820	0.450988
$237$	−10.9282	−0.709863
$238$	−3.46410	−0.224544
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	−3.46410	−0.223607
$241$	9.60770	0.618886	0.309443	−	0.950918i	$-0.399857\pi$
$241$	9.60770	0.618886	0.309443	+	0.950918i	$0.399857\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	−3.46410	−0.221313
$246$	−3.46410	−0.220863
$247$	10.9282	0.695345
$248$	−5.46410	−0.346971
$249$	4.39230	0.278351
$250$	6.92820	0.438178
$251$	30.9282	1.95217	0.976085	−	0.217387i	$-0.0697534\pi$
$251$	30.9282	1.95217	0.976085	+	0.217387i	$0.0697534\pi$
$252$	1.00000	0.0629941
$253$	6.92820	0.435572
$254$	10.9282	0.685696
$255$	−12.0000	−0.751469
$256$	1.00000	0.0625000
$257$	12.9282	0.806439	0.403220	−	0.915103i	$-0.367891\pi$
$257$	12.9282	0.806439	0.403220	+	0.915103i	$0.367891\pi$
$258$	10.9282	0.680360
$259$	−4.92820	−0.306224
$260$	−6.92820	−0.429669
$261$	−6.00000	−0.371391
$262$	4.39230	0.271357
$263$	−5.07180	−0.312740	−0.156370	−	0.987699i	$-0.549979\pi$
$263$	−5.07180	−0.312740	−0.156370	+	0.987699i	$0.549979\pi$
$264$	−1.00000	−0.0615457
$265$	3.21539	0.197520
$266$	−5.46410	−0.335026
$267$	−0.928203	−0.0568051
$268$	14.9282	0.911885
$269$	24.2487	1.47847	0.739235	−	0.673448i	$-0.235187\pi$
$269$	24.2487	1.47847	0.739235	+	0.673448i	$0.235187\pi$
$270$	3.46410	0.210819
$271$	−24.7846	−1.50556	−0.752779	−	0.658273i	$-0.771287\pi$
$271$	−24.7846	−1.50556	−0.752779	+	0.658273i	$0.771287\pi$
$272$	3.46410	0.210042
$273$	2.00000	0.121046
$274$	−7.85641	−0.474623
$275$	7.00000	0.422116
$276$	6.92820	0.417029
$277$	−11.8564	−0.712382	−0.356191	−	0.934413i	$-0.615925\pi$
$277$	−11.8564	−0.712382	−0.356191	+	0.934413i	$0.615925\pi$
$278$	13.4641	0.807523
$279$	5.46410	0.327127
$280$	3.46410	0.207020
$281$	−7.85641	−0.468674	−0.234337	−	0.972155i	$-0.575292\pi$
$281$	−7.85641	−0.468674	−0.234337	+	0.972155i	$0.575292\pi$
$282$	−9.46410	−0.563579
$283$	−13.4641	−0.800358	−0.400179	−	0.916437i	$-0.631052\pi$
$283$	−13.4641	−0.800358	−0.400179	+	0.916437i	$0.631052\pi$
$284$	−12.0000	−0.712069
$285$	−18.9282	−1.12121
$286$	−2.00000	−0.118262
$287$	3.46410	0.204479
$288$	−1.00000	−0.0589256
$289$	−5.00000	−0.294118
$290$	−20.7846	−1.22051
$291$	2.00000	0.117242
$292$	−0.535898	−0.0313611
$293$	−24.9282	−1.45632	−0.728161	−	0.685407i	$-0.759625\pi$
$293$	−24.9282	−1.45632	−0.728161	+	0.685407i	$0.759625\pi$
$294$	−1.00000	−0.0583212
$295$	−24.0000	−1.39733
$296$	4.92820	0.286446
$297$	1.00000	0.0580259
$298$	6.00000	0.347571
$299$	13.8564	0.801337
$300$	7.00000	0.404145
$301$	−10.9282	−0.629891
$302$	16.0000	0.920697
$303$	−19.8564	−1.14072
$304$	5.46410	0.313388
$305$	−6.92820	−0.396708
$306$	−3.46410	−0.198030
$307$	10.5359	0.601315	0.300658	−	0.953732i	$-0.402794\pi$
$307$	10.5359	0.601315	0.300658	+	0.953732i	$0.402794\pi$
$308$	1.00000	0.0569803
$309$	−13.4641	−0.765946
$310$	18.9282	1.07505
$311$	28.3923	1.60998	0.804990	−	0.593288i	$-0.202171\pi$
$311$	28.3923	1.60998	0.804990	+	0.593288i	$0.202171\pi$
$312$	−2.00000	−0.113228
$313$	−16.9282	−0.956839	−0.478419	−	0.878132i	$-0.658790\pi$
$313$	−16.9282	−0.956839	−0.478419	+	0.878132i	$0.658790\pi$
$314$	2.39230	0.135006
$315$	−3.46410	−0.195180
$316$	−10.9282	−0.614759
$317$	12.9282	0.726120	0.363060	−	0.931766i	$-0.381732\pi$
$317$	12.9282	0.726120	0.363060	+	0.931766i	$0.381732\pi$
$318$	0.928203	0.0520511
$319$	−6.00000	−0.335936
$320$	−3.46410	−0.193649
$321$	−6.92820	−0.386695
$322$	−6.92820	−0.386094
$323$	18.9282	1.05319
$324$	1.00000	0.0555556
$325$	14.0000	0.776580
$326$	4.00000	0.221540
$327$	15.8564	0.876861
$328$	−3.46410	−0.191273
$329$	9.46410	0.521773
$330$	3.46410	0.190693
$331$	−9.07180	−0.498631	−0.249316	−	0.968422i	$-0.580206\pi$
$331$	−9.07180	−0.498631	−0.249316	+	0.968422i	$0.580206\pi$
$332$	4.39230	0.241059
$333$	−4.92820	−0.270064
$334$	−18.9282	−1.03571
$335$	−51.7128	−2.82537
$336$	1.00000	0.0545545
$337$	20.9282	1.14003	0.570016	−	0.821634i	$-0.306937\pi$
$337$	20.9282	1.14003	0.570016	+	0.821634i	$0.306937\pi$
$338$	9.00000	0.489535
$339$	7.85641	0.426701
$340$	−12.0000	−0.650791
$341$	5.46410	0.295898
$342$	−5.46410	−0.295465
$343$	1.00000	0.0539949
$344$	10.9282	0.589209
$345$	−24.0000	−1.29212
$346$	0.928203	0.0499005
$347$	−20.7846	−1.11578	−0.557888	−	0.829916i	$-0.688388\pi$
$347$	−20.7846	−1.11578	−0.557888	+	0.829916i	$0.688388\pi$
$348$	−6.00000	−0.321634
$349$	10.7846	0.577287	0.288643	−	0.957437i	$-0.406796\pi$
$349$	10.7846	0.577287	0.288643	+	0.957437i	$0.406796\pi$
$350$	−7.00000	−0.374166
$351$	2.00000	0.106752
$352$	−1.00000	−0.0533002
$353$	12.9282	0.688099	0.344049	−	0.938952i	$-0.388201\pi$
$353$	12.9282	0.688099	0.344049	+	0.938952i	$0.388201\pi$
$354$	−6.92820	−0.368230
$355$	41.5692	2.20627
$356$	−0.928203	−0.0491947
$357$	3.46410	0.183340
$358$	20.7846	1.09850
$359$	−5.07180	−0.267679	−0.133840	−	0.991003i	$-0.542731\pi$
$359$	−5.07180	−0.267679	−0.133840	+	0.991003i	$0.542731\pi$
$360$	3.46410	0.182574
$361$	10.8564	0.571390
$362$	−6.39230	−0.335972
$363$	1.00000	0.0524864
$364$	2.00000	0.104828
$365$	1.85641	0.0971688
$366$	−2.00000	−0.104542
$367$	19.3205	1.00852	0.504261	−	0.863551i	$-0.331765\pi$
$367$	19.3205	1.00852	0.504261	+	0.863551i	$0.331765\pi$
$368$	6.92820	0.361158
$369$	3.46410	0.180334
$370$	−17.0718	−0.887520
$371$	−0.928203	−0.0481899
$372$	5.46410	0.283300
$373$	29.7128	1.53847	0.769236	−	0.638965i	$-0.220637\pi$
$373$	29.7128	1.53847	0.769236	+	0.638965i	$0.220637\pi$
$374$	−3.46410	−0.179124
$375$	−6.92820	−0.357771
$376$	−9.46410	−0.488074
$377$	−12.0000	−0.618031
$378$	−1.00000	−0.0514344
$379$	−17.8564	−0.917222	−0.458611	−	0.888637i	$-0.651653\pi$
$379$	−17.8564	−0.917222	−0.458611	+	0.888637i	$0.651653\pi$
$380$	−18.9282	−0.970996
$381$	−10.9282	−0.559869
$382$	−20.7846	−1.06343
$383$	14.5359	0.742750	0.371375	−	0.928483i	$-0.378886\pi$
$383$	14.5359	0.742750	0.371375	+	0.928483i	$0.378886\pi$
$384$	−1.00000	−0.0510310
$385$	−3.46410	−0.176547
$386$	−26.0000	−1.32337
$387$	−10.9282	−0.555512
$388$	2.00000	0.101535
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	6.92820	0.350823
$391$	24.0000	1.21373
$392$	−1.00000	−0.0505076
$393$	−4.39230	−0.221562
$394$	−18.0000	−0.906827
$395$	37.8564	1.90476
$396$	1.00000	0.0502519
$397$	−2.39230	−0.120066	−0.0600332	−	0.998196i	$-0.519121\pi$
$397$	−2.39230	−0.120066	−0.0600332	+	0.998196i	$0.519121\pi$
$398$	−0.392305	−0.0196645
$399$	5.46410	0.273547
$400$	7.00000	0.350000
$401$	4.14359	0.206921	0.103461	−	0.994634i	$-0.467008\pi$
$401$	4.14359	0.206921	0.103461	+	0.994634i	$0.467008\pi$
$402$	−14.9282	−0.744551
$403$	10.9282	0.544373
$404$	−19.8564	−0.987893
$405$	−3.46410	−0.172133
$406$	6.00000	0.297775
$407$	−4.92820	−0.244282
$408$	−3.46410	−0.171499
$409$	−9.32051	−0.460869	−0.230435	−	0.973088i	$-0.574015\pi$
$409$	−9.32051	−0.460869	−0.230435	+	0.973088i	$0.574015\pi$
$410$	12.0000	0.592638
$411$	7.85641	0.387528
$412$	−13.4641	−0.663329
$413$	6.92820	0.340915
$414$	−6.92820	−0.340503
$415$	−15.2154	−0.746894
$416$	−2.00000	−0.0980581
$417$	−13.4641	−0.659340
$418$	−5.46410	−0.267258
$419$	−36.0000	−1.75872	−0.879358	−	0.476162i	$-0.842028\pi$
$419$	−36.0000	−1.75872	−0.879358	+	0.476162i	$0.842028\pi$
$420$	−3.46410	−0.169031
$421$	−37.7128	−1.83801	−0.919005	−	0.394246i	$-0.871006\pi$
$421$	−37.7128	−1.83801	−0.919005	+	0.394246i	$0.871006\pi$
$422$	−16.7846	−0.817062
$423$	9.46410	0.460160
$424$	0.928203	0.0450775
$425$	24.2487	1.17624
$426$	12.0000	0.581402
$427$	2.00000	0.0967868
$428$	−6.92820	−0.334887
$429$	2.00000	0.0965609
$430$	−37.8564	−1.82560
$431$	−18.9282	−0.911739	−0.455870	−	0.890047i	$-0.650672\pi$
$431$	−18.9282	−0.911739	−0.455870	+	0.890047i	$0.650672\pi$
$432$	1.00000	0.0481125
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	−5.46410	−0.262285
$435$	20.7846	0.996546
$436$	15.8564	0.759384
$437$	37.8564	1.81092
$438$	0.535898	0.0256062
$439$	−24.7846	−1.18290	−0.591452	−	0.806340i	$-0.701445\pi$
$439$	−24.7846	−1.18290	−0.591452	+	0.806340i	$0.701445\pi$
$440$	3.46410	0.165145
$441$	1.00000	0.0476190
$442$	−6.92820	−0.329541
$443$	−20.7846	−0.987507	−0.493753	−	0.869602i	$-0.664375\pi$
$443$	−20.7846	−0.987507	−0.493753	+	0.869602i	$0.664375\pi$
$444$	−4.92820	−0.233882
$445$	3.21539	0.152424
$446$	8.39230	0.397387
$447$	−6.00000	−0.283790
$448$	1.00000	0.0472456
$449$	−19.8564	−0.937082	−0.468541	−	0.883442i	$-0.655220\pi$
$449$	−19.8564	−0.937082	−0.468541	+	0.883442i	$0.655220\pi$
$450$	−7.00000	−0.329983
$451$	3.46410	0.163118
$452$	7.85641	0.369534
$453$	−16.0000	−0.751746
$454$	4.39230	0.206141
$455$	−6.92820	−0.324799
$456$	−5.46410	−0.255880
$457$	15.8564	0.741731	0.370866	−	0.928687i	$-0.379061\pi$
$457$	15.8564	0.741731	0.370866	+	0.928687i	$0.379061\pi$
$458$	21.3205	0.996242
$459$	3.46410	0.161690
$460$	−24.0000	−1.11901
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	−1.00000	−0.0465242
$463$	8.00000	0.371792	0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000	0.371792	0.185896	+	0.982569i	$0.440481\pi$
$464$	−6.00000	−0.278543
$465$	−18.9282	−0.877774
$466$	7.85641	0.363941
$467$	−15.7128	−0.727102	−0.363551	−	0.931574i	$-0.618436\pi$
$467$	−15.7128	−0.727102	−0.363551	+	0.931574i	$0.618436\pi$
$468$	2.00000	0.0924500
$469$	14.9282	0.689320
$470$	32.7846	1.51224
$471$	−2.39230	−0.110232
$472$	−6.92820	−0.318896
$473$	−10.9282	−0.502479
$474$	10.9282	0.501949
$475$	38.2487	1.75497
$476$	3.46410	0.158777
$477$	−0.928203	−0.0424995
$478$	24.0000	1.09773
$479$	−13.8564	−0.633115	−0.316558	−	0.948573i	$-0.602527\pi$
$479$	−13.8564	−0.633115	−0.316558	+	0.948573i	$0.602527\pi$
$480$	3.46410	0.158114
$481$	−9.85641	−0.449413
$482$	−9.60770	−0.437619
$483$	6.92820	0.315244
$484$	1.00000	0.0454545
$485$	−6.92820	−0.314594
$486$	−1.00000	−0.0453609
$487$	40.7846	1.84813	0.924064	−	0.382239i	$-0.124847\pi$
$487$	40.7846	1.84813	0.924064	+	0.382239i	$0.124847\pi$
$488$	−2.00000	−0.0905357
$489$	−4.00000	−0.180886
$490$	3.46410	0.156492
$491$	−1.85641	−0.0837785	−0.0418892	−	0.999122i	$-0.513338\pi$
$491$	−1.85641	−0.0837785	−0.0418892	+	0.999122i	$0.513338\pi$
$492$	3.46410	0.156174
$493$	−20.7846	−0.936092
$494$	−10.9282	−0.491683
$495$	−3.46410	−0.155700
$496$	5.46410	0.245345
$497$	−12.0000	−0.538274
$498$	−4.39230	−0.196824
$499$	−9.07180	−0.406109	−0.203055	−	0.979167i	$-0.565087\pi$
$499$	−9.07180	−0.406109	−0.203055	+	0.979167i	$0.565087\pi$
$500$	−6.92820	−0.309839
$501$	18.9282	0.845650
$502$	−30.9282	−1.38039
$503$	18.9282	0.843967	0.421983	−	0.906604i	$-0.361334\pi$
$503$	18.9282	0.843967	0.421983	+	0.906604i	$0.361334\pi$
$504$	−1.00000	−0.0445435
$505$	68.7846	3.06087
$506$	−6.92820	−0.307996
$507$	−9.00000	−0.399704
$508$	−10.9282	−0.484861
$509$	−41.3205	−1.83150	−0.915750	−	0.401749i	$-0.868402\pi$
$509$	−41.3205	−1.83150	−0.915750	+	0.401749i	$0.868402\pi$
$510$	12.0000	0.531369
$511$	−0.535898	−0.0237067
$512$	−1.00000	−0.0441942
$513$	5.46410	0.241246
$514$	−12.9282	−0.570239
$515$	46.6410	2.05525
$516$	−10.9282	−0.481087
$517$	9.46410	0.416231
$518$	4.92820	0.216533
$519$	−0.928203	−0.0407436
$520$	6.92820	0.303822
$521$	36.9282	1.61785	0.808927	−	0.587909i	$-0.200049\pi$
$521$	36.9282	1.61785	0.808927	+	0.587909i	$0.200049\pi$
$522$	6.00000	0.262613
$523$	24.3923	1.06660	0.533301	−	0.845926i	$-0.320952\pi$
$523$	24.3923	1.06660	0.533301	+	0.845926i	$0.320952\pi$
$524$	−4.39230	−0.191879
$525$	7.00000	0.305505
$526$	5.07180	0.221141
$527$	18.9282	0.824525
$528$	1.00000	0.0435194
$529$	25.0000	1.08696
$530$	−3.21539	−0.139668
$531$	6.92820	0.300658
$532$	5.46410	0.236899
$533$	6.92820	0.300094
$534$	0.928203	0.0401673
$535$	24.0000	1.03761
$536$	−14.9282	−0.644800
$537$	−20.7846	−0.896922
$538$	−24.2487	−1.04544
$539$	1.00000	0.0430730
$540$	−3.46410	−0.149071
$541$	−25.7128	−1.10548	−0.552740	−	0.833354i	$-0.686418\pi$
$541$	−25.7128	−1.10548	−0.552740	+	0.833354i	$0.686418\pi$
$542$	24.7846	1.06459
$543$	6.39230	0.274320
$544$	−3.46410	−0.148522
$545$	−54.9282	−2.35287
$546$	−2.00000	−0.0855921
$547$	−16.0000	−0.684111	−0.342055	−	0.939680i	$-0.611123\pi$
$547$	−16.0000	−0.684111	−0.342055	+	0.939680i	$0.611123\pi$
$548$	7.85641	0.335609
$549$	2.00000	0.0853579
$550$	−7.00000	−0.298481
$551$	−32.7846	−1.39667
$552$	−6.92820	−0.294884
$553$	−10.9282	−0.464714
$554$	11.8564	0.503730
$555$	17.0718	0.724657
$556$	−13.4641	−0.571005
$557$	21.7128	0.920001	0.460001	−	0.887919i	$-0.347849\pi$
$557$	21.7128	0.920001	0.460001	+	0.887919i	$0.347849\pi$
$558$	−5.46410	−0.231314
$559$	−21.8564	−0.924427
$560$	−3.46410	−0.146385
$561$	3.46410	0.146254
$562$	7.85641	0.331403
$563$	−18.2487	−0.769091	−0.384546	−	0.923106i	$-0.625642\pi$
$563$	−18.2487	−0.769091	−0.384546	+	0.923106i	$0.625642\pi$
$564$	9.46410	0.398511
$565$	−27.2154	−1.14496
$566$	13.4641	0.565938
$567$	1.00000	0.0419961
$568$	12.0000	0.503509
$569$	−31.8564	−1.33549	−0.667745	−	0.744390i	$-0.732740\pi$
$569$	−31.8564	−1.33549	−0.667745	+	0.744390i	$0.732740\pi$
$570$	18.9282	0.792815
$571$	8.00000	0.334790	0.167395	−	0.985890i	$-0.446465\pi$
$571$	8.00000	0.334790	0.167395	+	0.985890i	$0.446465\pi$
$572$	2.00000	0.0836242
$573$	20.7846	0.868290
$574$	−3.46410	−0.144589
$575$	48.4974	2.02248
$576$	1.00000	0.0416667
$577$	−30.7846	−1.28158	−0.640790	−	0.767716i	$-0.721393\pi$
$577$	−30.7846	−1.28158	−0.640790	+	0.767716i	$0.721393\pi$
$578$	5.00000	0.207973
$579$	26.0000	1.08052
$580$	20.7846	0.863034
$581$	4.39230	0.182224
$582$	−2.00000	−0.0829027
$583$	−0.928203	−0.0384422
$584$	0.535898	0.0221756
$585$	−6.92820	−0.286446
$586$	24.9282	1.02977
$587$	−20.7846	−0.857873	−0.428936	−	0.903335i	$-0.641112\pi$
$587$	−20.7846	−0.857873	−0.428936	+	0.903335i	$0.641112\pi$
$588$	1.00000	0.0412393
$589$	29.8564	1.23021
$590$	24.0000	0.988064
$591$	18.0000	0.740421
$592$	−4.92820	−0.202548
$593$	−20.5359	−0.843308	−0.421654	−	0.906757i	$-0.638550\pi$
$593$	−20.5359	−0.843308	−0.421654	+	0.906757i	$0.638550\pi$
$594$	−1.00000	−0.0410305
$595$	−12.0000	−0.491952
$596$	−6.00000	−0.245770
$597$	0.392305	0.0160560
$598$	−13.8564	−0.566631
$599$	1.85641	0.0758507	0.0379254	−	0.999281i	$-0.487925\pi$
$599$	1.85641	0.0758507	0.0379254	+	0.999281i	$0.487925\pi$
$600$	−7.00000	−0.285774
$601$	18.3923	0.750238	0.375119	−	0.926977i	$-0.377602\pi$
$601$	18.3923	0.750238	0.375119	+	0.926977i	$0.377602\pi$
$602$	10.9282	0.445400
$603$	14.9282	0.607923
$604$	−16.0000	−0.651031
$605$	−3.46410	−0.140836
$606$	19.8564	0.806611
$607$	−19.7128	−0.800118	−0.400059	−	0.916489i	$-0.631010\pi$
$607$	−19.7128	−0.800118	−0.400059	+	0.916489i	$0.631010\pi$
$608$	−5.46410	−0.221599
$609$	−6.00000	−0.243132
$610$	6.92820	0.280515
$611$	18.9282	0.765753
$612$	3.46410	0.140028
$613$	−22.0000	−0.888572	−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000	−0.888572	−0.444286	+	0.895885i	$0.646543\pi$
$614$	−10.5359	−0.425194
$615$	−12.0000	−0.483887
$616$	−1.00000	−0.0402911
$617$	−19.8564	−0.799389	−0.399694	−	0.916648i	$-0.630884\pi$
$617$	−19.8564	−0.799389	−0.399694	+	0.916648i	$0.630884\pi$
$618$	13.4641	0.541606
$619$	−31.7128	−1.27465	−0.637323	−	0.770597i	$-0.719958\pi$
$619$	−31.7128	−1.27465	−0.637323	+	0.770597i	$0.719958\pi$
$620$	−18.9282	−0.760175
$621$	6.92820	0.278019
$622$	−28.3923	−1.13843
$623$	−0.928203	−0.0371877
$624$	2.00000	0.0800641
$625$	−11.0000	−0.440000
$626$	16.9282	0.676587
$627$	5.46410	0.218215
$628$	−2.39230	−0.0954634
$629$	−17.0718	−0.680697
$630$	3.46410	0.138013
$631$	−0.784610	−0.0312348	−0.0156174	−	0.999878i	$-0.504971\pi$
$631$	−0.784610	−0.0312348	−0.0156174	+	0.999878i	$0.504971\pi$
$632$	10.9282	0.434701
$633$	16.7846	0.667128
$634$	−12.9282	−0.513445
$635$	37.8564	1.50229
$636$	−0.928203	−0.0368057
$637$	2.00000	0.0792429
$638$	6.00000	0.237542
$639$	−12.0000	−0.474713
$640$	3.46410	0.136931
$641$	31.8564	1.25825	0.629126	−	0.777303i	$-0.283413\pi$
$641$	31.8564	1.25825	0.629126	+	0.777303i	$0.283413\pi$
$642$	6.92820	0.273434
$643$	14.9282	0.588711	0.294355	−	0.955696i	$-0.404895\pi$
$643$	14.9282	0.588711	0.294355	+	0.955696i	$0.404895\pi$
$644$	6.92820	0.273009
$645$	37.8564	1.49059
$646$	−18.9282	−0.744720
$647$	0.679492	0.0267136	0.0133568	−	0.999911i	$-0.495748\pi$
$647$	0.679492	0.0267136	0.0133568	+	0.999911i	$0.495748\pi$
$648$	−1.00000	−0.0392837
$649$	6.92820	0.271956
$650$	−14.0000	−0.549125
$651$	5.46410	0.214155
$652$	−4.00000	−0.156652
$653$	−33.7128	−1.31928	−0.659642	−	0.751580i	$-0.729292\pi$
$653$	−33.7128	−1.31928	−0.659642	+	0.751580i	$0.729292\pi$
$654$	−15.8564	−0.620035
$655$	15.2154	0.594514
$656$	3.46410	0.135250
$657$	−0.535898	−0.0209074
$658$	−9.46410	−0.368949
$659$	−17.0718	−0.665023	−0.332511	−	0.943099i	$-0.607896\pi$
$659$	−17.0718	−0.665023	−0.332511	+	0.943099i	$0.607896\pi$
$660$	−3.46410	−0.134840
$661$	44.2487	1.72108	0.860538	−	0.509387i	$-0.170128\pi$
$661$	44.2487	1.72108	0.860538	+	0.509387i	$0.170128\pi$
$662$	9.07180	0.352585
$663$	6.92820	0.269069
$664$	−4.39230	−0.170454
$665$	−18.9282	−0.734004
$666$	4.92820	0.190964
$667$	−41.5692	−1.60957
$668$	18.9282	0.732354
$669$	−8.39230	−0.324465
$670$	51.7128	1.99784
$671$	2.00000	0.0772091
$672$	−1.00000	−0.0385758
$673$	20.9282	0.806723	0.403361	−	0.915041i	$-0.367842\pi$
$673$	20.9282	0.806723	0.403361	+	0.915041i	$0.367842\pi$
$674$	−20.9282	−0.806124
$675$	7.00000	0.269430
$676$	−9.00000	−0.346154
$677$	2.78461	0.107021	0.0535106	−	0.998567i	$-0.482959\pi$
$677$	2.78461	0.107021	0.0535106	+	0.998567i	$0.482959\pi$
$678$	−7.85641	−0.301723
$679$	2.00000	0.0767530
$680$	12.0000	0.460179
$681$	−4.39230	−0.168313
$682$	−5.46410	−0.209231
$683$	3.21539	0.123033	0.0615167	−	0.998106i	$-0.480406\pi$
$683$	3.21539	0.123033	0.0615167	+	0.998106i	$0.480406\pi$
$684$	5.46410	0.208925
$685$	−27.2154	−1.03985
$686$	−1.00000	−0.0381802
$687$	−21.3205	−0.813428
$688$	−10.9282	−0.416634
$689$	−1.85641	−0.0707235
$690$	24.0000	0.913664
$691$	−33.0718	−1.25811	−0.629055	−	0.777361i	$-0.716558\pi$
$691$	−33.0718	−1.25811	−0.629055	+	0.777361i	$0.716558\pi$
$692$	−0.928203	−0.0352850
$693$	1.00000	0.0379869
$694$	20.7846	0.788973
$695$	46.6410	1.76919
$696$	6.00000	0.227429
$697$	12.0000	0.454532
$698$	−10.7846	−0.408203
$699$	−7.85641	−0.297157
$700$	7.00000	0.264575
$701$	45.7128	1.72655	0.863275	−	0.504735i	$-0.168410\pi$
$701$	45.7128	1.72655	0.863275	+	0.504735i	$0.168410\pi$
$702$	−2.00000	−0.0754851
$703$	−26.9282	−1.01562
$704$	1.00000	0.0376889
$705$	−32.7846	−1.23474
$706$	−12.9282	−0.486559
$707$	−19.8564	−0.746777
$708$	6.92820	0.260378
$709$	46.7846	1.75703	0.878516	−	0.477712i	$-0.158534\pi$
$709$	46.7846	1.75703	0.878516	+	0.477712i	$0.158534\pi$
$710$	−41.5692	−1.56007
$711$	−10.9282	−0.409840
$712$	0.928203	0.0347859
$713$	37.8564	1.41773
$714$	−3.46410	−0.129641
$715$	−6.92820	−0.259100
$716$	−20.7846	−0.776757
$717$	−24.0000	−0.896296
$718$	5.07180	0.189278
$719$	−37.1769	−1.38646	−0.693232	−	0.720714i	$-0.743814\pi$
$719$	−37.1769	−1.38646	−0.693232	+	0.720714i	$0.743814\pi$
$720$	−3.46410	−0.129099
$721$	−13.4641	−0.501429
$722$	−10.8564	−0.404034
$723$	9.60770	0.357314
$724$	6.39230	0.237568
$725$	−42.0000	−1.55984
$726$	−1.00000	−0.0371135
$727$	33.1769	1.23046	0.615232	−	0.788346i	$-0.289062\pi$
$727$	33.1769	1.23046	0.615232	+	0.788346i	$0.289062\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	−1.85641	−0.0687087
$731$	−37.8564	−1.40017
$732$	2.00000	0.0739221
$733$	12.1436	0.448534	0.224267	−	0.974528i	$-0.428001\pi$
$733$	12.1436	0.448534	0.224267	+	0.974528i	$0.428001\pi$
$734$	−19.3205	−0.713133
$735$	−3.46410	−0.127775
$736$	−6.92820	−0.255377
$737$	14.9282	0.549887
$738$	−3.46410	−0.127515
$739$	8.00000	0.294285	0.147142	−	0.989115i	$-0.452992\pi$
$739$	8.00000	0.294285	0.147142	+	0.989115i	$0.452992\pi$
$740$	17.0718	0.627572
$741$	10.9282	0.401458
$742$	0.928203	0.0340754
$743$	−41.5692	−1.52503	−0.762513	−	0.646972i	$-0.776035\pi$
$743$	−41.5692	−1.52503	−0.762513	+	0.646972i	$0.776035\pi$
$744$	−5.46410	−0.200324
$745$	20.7846	0.761489
$746$	−29.7128	−1.08786
$747$	4.39230	0.160706
$748$	3.46410	0.126660
$749$	−6.92820	−0.253151
$750$	6.92820	0.252982
$751$	−24.7846	−0.904403	−0.452202	−	0.891916i	$-0.649361\pi$
$751$	−24.7846	−0.904403	−0.452202	+	0.891916i	$0.649361\pi$
$752$	9.46410	0.345120
$753$	30.9282	1.12709
$754$	12.0000	0.437014
$755$	55.4256	2.01715
$756$	1.00000	0.0363696
$757$	22.7846	0.828121	0.414060	−	0.910249i	$-0.364110\pi$
$757$	22.7846	0.828121	0.414060	+	0.910249i	$0.364110\pi$
$758$	17.8564	0.648574
$759$	6.92820	0.251478
$760$	18.9282	0.686598
$761$	−25.6077	−0.928278	−0.464139	−	0.885762i	$-0.653636\pi$
$761$	−25.6077	−0.928278	−0.464139	+	0.885762i	$0.653636\pi$
$762$	10.9282	0.395887
$763$	15.8564	0.574040
$764$	20.7846	0.751961
$765$	−12.0000	−0.433861
$766$	−14.5359	−0.525203
$767$	13.8564	0.500326
$768$	1.00000	0.0360844
$769$	28.5359	1.02903	0.514515	−	0.857481i	$-0.327972\pi$
$769$	28.5359	1.02903	0.514515	+	0.857481i	$0.327972\pi$
$770$	3.46410	0.124838
$771$	12.9282	0.465598
$772$	26.0000	0.935760
$773$	−32.5359	−1.17023	−0.585117	−	0.810949i	$-0.698952\pi$
$773$	−32.5359	−1.17023	−0.585117	+	0.810949i	$0.698952\pi$
$774$	10.9282	0.392806
$775$	38.2487	1.37393
$776$	−2.00000	−0.0717958
$777$	−4.92820	−0.176798
$778$	30.0000	1.07555
$779$	18.9282	0.678173
$780$	−6.92820	−0.248069
$781$	−12.0000	−0.429394
$782$	−24.0000	−0.858238
$783$	−6.00000	−0.214423
$784$	1.00000	0.0357143
$785$	8.28719	0.295782
$786$	4.39230	0.156668
$787$	33.1769	1.18263	0.591315	−	0.806441i	$-0.298609\pi$
$787$	33.1769	1.18263	0.591315	+	0.806441i	$0.298609\pi$
$788$	18.0000	0.641223
$789$	−5.07180	−0.180561
$790$	−37.8564	−1.34687
$791$	7.85641	0.279342
$792$	−1.00000	−0.0355335
$793$	4.00000	0.142044
$794$	2.39230	0.0848997
$795$	3.21539	0.114038
$796$	0.392305	0.0139049
$797$	−32.5359	−1.15248	−0.576240	−	0.817280i	$-0.695481\pi$
$797$	−32.5359	−1.15248	−0.576240	+	0.817280i	$0.695481\pi$
$798$	−5.46410	−0.193427
$799$	32.7846	1.15984
$800$	−7.00000	−0.247487
$801$	−0.928203	−0.0327964
$802$	−4.14359	−0.146315
$803$	−0.535898	−0.0189114
$804$	14.9282	0.526477
$805$	−24.0000	−0.845889
$806$	−10.9282	−0.384930
$807$	24.2487	0.853595
$808$	19.8564	0.698546
$809$	11.0718	0.389264	0.194632	−	0.980876i	$-0.437649\pi$
$809$	11.0718	0.389264	0.194632	+	0.980876i	$0.437649\pi$
$810$	3.46410	0.121716
$811$	−17.1769	−0.603163	−0.301582	−	0.953440i	$-0.597515\pi$
$811$	−17.1769	−0.603163	−0.301582	+	0.953440i	$0.597515\pi$
$812$	−6.00000	−0.210559
$813$	−24.7846	−0.869234
$814$	4.92820	0.172733
$815$	13.8564	0.485369
$816$	3.46410	0.121268
$817$	−59.7128	−2.08909
$818$	9.32051	0.325884
$819$	2.00000	0.0698857
$820$	−12.0000	−0.419058
$821$	−6.00000	−0.209401	−0.104701	−	0.994504i	$-0.533388\pi$
$821$	−6.00000	−0.209401	−0.104701	+	0.994504i	$0.533388\pi$
$822$	−7.85641	−0.274024
$823$	40.7846	1.42166	0.710831	−	0.703363i	$-0.248319\pi$
$823$	40.7846	1.42166	0.710831	+	0.703363i	$0.248319\pi$
$824$	13.4641	0.469044
$825$	7.00000	0.243709
$826$	−6.92820	−0.241063
$827$	12.0000	0.417281	0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000	0.417281	0.208640	+	0.977992i	$0.433096\pi$
$828$	6.92820	0.240772
$829$	44.2487	1.53682	0.768411	−	0.639957i	$-0.221048\pi$
$829$	44.2487	1.53682	0.768411	+	0.639957i	$0.221048\pi$
$830$	15.2154	0.528134
$831$	−11.8564	−0.411294
$832$	2.00000	0.0693375
$833$	3.46410	0.120024
$834$	13.4641	0.466224
$835$	−65.5692	−2.26912
$836$	5.46410	0.188980
$837$	5.46410	0.188867
$838$	36.0000	1.24360
$839$	−33.4641	−1.15531	−0.577655	−	0.816281i	$-0.696032\pi$
$839$	−33.4641	−1.15531	−0.577655	+	0.816281i	$0.696032\pi$
$840$	3.46410	0.119523
$841$	7.00000	0.241379
$842$	37.7128	1.29967
$843$	−7.85641	−0.270589
$844$	16.7846	0.577750
$845$	31.1769	1.07252
$846$	−9.46410	−0.325383
$847$	1.00000	0.0343604
$848$	−0.928203	−0.0318746
$849$	−13.4641	−0.462087
$850$	−24.2487	−0.831724
$851$	−34.1436	−1.17043
$852$	−12.0000	−0.411113
$853$	−49.7128	−1.70213	−0.851067	−	0.525057i	$-0.824044\pi$
$853$	−49.7128	−1.70213	−0.851067	+	0.525057i	$0.824044\pi$
$854$	−2.00000	−0.0684386
$855$	−18.9282	−0.647331
$856$	6.92820	0.236801
$857$	−5.32051	−0.181745	−0.0908725	−	0.995863i	$-0.528966\pi$
$857$	−5.32051	−0.181745	−0.0908725	+	0.995863i	$0.528966\pi$
$858$	−2.00000	−0.0682789
$859$	52.7846	1.80099	0.900494	−	0.434869i	$-0.143205\pi$
$859$	52.7846	1.80099	0.900494	+	0.434869i	$0.143205\pi$
$860$	37.8564	1.29089
$861$	3.46410	0.118056
$862$	18.9282	0.644697
$863$	44.7846	1.52449	0.762243	−	0.647291i	$-0.224098\pi$
$863$	44.7846	1.52449	0.762243	+	0.647291i	$0.224098\pi$
$864$	−1.00000	−0.0340207
$865$	3.21539	0.109327
$866$	−2.00000	−0.0679628
$867$	−5.00000	−0.169809
$868$	5.46410	0.185464
$869$	−10.9282	−0.370714
$870$	−20.7846	−0.704664
$871$	29.8564	1.01165
$872$	−15.8564	−0.536966
$873$	2.00000	0.0676897
$874$	−37.8564	−1.28051
$875$	−6.92820	−0.234216
$876$	−0.535898	−0.0181063
$877$	−46.0000	−1.55331	−0.776655	−	0.629926i	$-0.783085\pi$
$877$	−46.0000	−1.55331	−0.776655	+	0.629926i	$0.783085\pi$
$878$	24.7846	0.836440
$879$	−24.9282	−0.840807
$880$	−3.46410	−0.116775
$881$	−6.00000	−0.202145	−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000	−0.202145	−0.101073	+	0.994879i	$0.532227\pi$
$882$	−1.00000	−0.0336718
$883$	−41.8564	−1.40858	−0.704290	−	0.709912i	$-0.748735\pi$
$883$	−41.8564	−1.40858	−0.704290	+	0.709912i	$0.748735\pi$
$884$	6.92820	0.233021
$885$	−24.0000	−0.806751
$886$	20.7846	0.698273
$887$	10.1436	0.340589	0.170294	−	0.985393i	$-0.445528\pi$
$887$	10.1436	0.340589	0.170294	+	0.985393i	$0.445528\pi$
$888$	4.92820	0.165380
$889$	−10.9282	−0.366520
$890$	−3.21539	−0.107780
$891$	1.00000	0.0335013
$892$	−8.39230	−0.280995
$893$	51.7128	1.73050
$894$	6.00000	0.200670
$895$	72.0000	2.40669
$896$	−1.00000	−0.0334077
$897$	13.8564	0.462652
$898$	19.8564	0.662617
$899$	−32.7846	−1.09343
$900$	7.00000	0.233333
$901$	−3.21539	−0.107120
$902$	−3.46410	−0.115342
$903$	−10.9282	−0.363668
$904$	−7.85641	−0.261300
$905$	−22.1436	−0.736078
$906$	16.0000	0.531564
$907$	14.9282	0.495683	0.247841	−	0.968801i	$-0.420279\pi$
$907$	14.9282	0.495683	0.247841	+	0.968801i	$0.420279\pi$
$908$	−4.39230	−0.145764
$909$	−19.8564	−0.658595
$910$	6.92820	0.229668
$911$	−48.4974	−1.60679	−0.803396	−	0.595446i	$-0.796976\pi$
$911$	−48.4974	−1.60679	−0.803396	+	0.595446i	$0.796976\pi$
$912$	5.46410	0.180934
$913$	4.39230	0.145364
$914$	−15.8564	−0.524483
$915$	−6.92820	−0.229039
$916$	−21.3205	−0.704449
$917$	−4.39230	−0.145047
$918$	−3.46410	−0.114332
$919$	21.8564	0.720976	0.360488	−	0.932764i	$-0.382610\pi$
$919$	21.8564	0.720976	0.360488	+	0.932764i	$0.382610\pi$
$920$	24.0000	0.791257
$921$	10.5359	0.347170
$922$	6.00000	0.197599
$923$	−24.0000	−0.789970
$924$	1.00000	0.0328976
$925$	−34.4974	−1.13427
$926$	−8.00000	−0.262896
$927$	−13.4641	−0.442219
$928$	6.00000	0.196960
$929$	40.6410	1.33339	0.666694	−	0.745331i	$-0.267709\pi$
$929$	40.6410	1.33339	0.666694	+	0.745331i	$0.267709\pi$
$930$	18.9282	0.620680
$931$	5.46410	0.179079
$932$	−7.85641	−0.257345
$933$	28.3923	0.929522
$934$	15.7128	0.514139
$935$	−12.0000	−0.392442
$936$	−2.00000	−0.0653720
$937$	−14.3923	−0.470176	−0.235088	−	0.971974i	$-0.575538\pi$
$937$	−14.3923	−0.470176	−0.235088	+	0.971974i	$0.575538\pi$
$938$	−14.9282	−0.487423
$939$	−16.9282	−0.552431
$940$	−32.7846	−1.06932
$941$	−11.0718	−0.360930	−0.180465	−	0.983581i	$-0.557760\pi$
$941$	−11.0718	−0.360930	−0.180465	+	0.983581i	$0.557760\pi$
$942$	2.39230	0.0779455
$943$	24.0000	0.781548
$944$	6.92820	0.225494
$945$	−3.46410	−0.112687
$946$	10.9282	0.355307
$947$	49.8564	1.62012	0.810058	−	0.586350i	$-0.199436\pi$
$947$	49.8564	1.62012	0.810058	+	0.586350i	$0.199436\pi$
$948$	−10.9282	−0.354932
$949$	−1.07180	−0.0347920
$950$	−38.2487	−1.24095
$951$	12.9282	0.419226
$952$	−3.46410	−0.112272
$953$	−26.7846	−0.867639	−0.433819	−	0.901000i	$-0.642834\pi$
$953$	−26.7846	−0.867639	−0.433819	+	0.901000i	$0.642834\pi$
$954$	0.928203	0.0300517
$955$	−72.0000	−2.32987
$956$	−24.0000	−0.776215
$957$	−6.00000	−0.193952
$958$	13.8564	0.447680
$959$	7.85641	0.253697
$960$	−3.46410	−0.111803
$961$	−1.14359	−0.0368901
$962$	9.85641	0.317783
$963$	−6.92820	−0.223258
$964$	9.60770	0.309443
$965$	−90.0666	−2.89935
$966$	−6.92820	−0.222911
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	−1.00000	−0.0321412
$969$	18.9282	0.608061
$970$	6.92820	0.222451
$971$	−15.7128	−0.504248	−0.252124	−	0.967695i	$-0.581129\pi$
$971$	−15.7128	−0.504248	−0.252124	+	0.967695i	$0.581129\pi$
$972$	1.00000	0.0320750
$973$	−13.4641	−0.431639
$974$	−40.7846	−1.30682
$975$	14.0000	0.448359
$976$	2.00000	0.0640184
$977$	−47.5692	−1.52187	−0.760937	−	0.648826i	$-0.775260\pi$
$977$	−47.5692	−1.52187	−0.760937	+	0.648826i	$0.775260\pi$
$978$	4.00000	0.127906
$979$	−0.928203	−0.0296655
$980$	−3.46410	−0.110657
$981$	15.8564	0.506256
$982$	1.85641	0.0592403
$983$	23.3205	0.743809	0.371904	−	0.928271i	$-0.378705\pi$
$983$	23.3205	0.743809	0.371904	+	0.928271i	$0.378705\pi$
$984$	−3.46410	−0.110432
$985$	−62.3538	−1.98676
$986$	20.7846	0.661917
$987$	9.46410	0.301246
$988$	10.9282	0.347672
$989$	−75.7128	−2.40753
$990$	3.46410	0.110096
$991$	−2.14359	−0.0680935	−0.0340467	−	0.999420i	$-0.510840\pi$
$991$	−2.14359	−0.0680935	−0.0340467	+	0.999420i	$0.510840\pi$
$992$	−5.46410	−0.173485
$993$	−9.07180	−0.287885
$994$	12.0000	0.380617
$995$	−1.35898	−0.0430827
$996$	4.39230	0.139176
$997$	24.6410	0.780389	0.390194	−	0.920732i	$-0.372408\pi$
$997$	24.6410	0.780389	0.390194	+	0.920732i	$0.372408\pi$
$998$	9.07180	0.287163
$999$	−4.92820	−0.155921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.a.h.1.1	✓	2
3.2	odd	2		1386.2.a.p.1.2		2
4.3	odd	2		3696.2.a.bc.1.1		2
7.6	odd	2		3234.2.a.x.1.2		2
11.10	odd	2		5082.2.a.bu.1.1		2
21.20	even	2		9702.2.a.dd.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.a.h.1.1	✓	2	1.1	even	1	trivial
1386.2.a.p.1.2		2	3.2	odd	2
3234.2.a.x.1.2		2	7.6	odd	2
3696.2.a.bc.1.1		2	4.3	odd	2
5082.2.a.bu.1.1		2	11.10	odd	2
9702.2.a.dd.1.1		2	21.20	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.46410 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.46410 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.46410 q^{10} +1.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} -3.46410 q^{15} +1.00000 q^{16} +3.46410 q^{17} -1.00000 q^{18} +5.46410 q^{19} -3.46410 q^{20} +1.00000 q^{21} -1.00000 q^{22} +6.92820 q^{23} -1.00000 q^{24} +7.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} -6.00000 q^{29} +3.46410 q^{30} +5.46410 q^{31} -1.00000 q^{32} +1.00000 q^{33} -3.46410 q^{34} -3.46410 q^{35} +1.00000 q^{36} -4.92820 q^{37} -5.46410 q^{38} +2.00000 q^{39} +3.46410 q^{40} +3.46410 q^{41} -1.00000 q^{42} -10.9282 q^{43} +1.00000 q^{44} -3.46410 q^{45} -6.92820 q^{46} +9.46410 q^{47} +1.00000 q^{48} +1.00000 q^{49} -7.00000 q^{50} +3.46410 q^{51} +2.00000 q^{52} -0.928203 q^{53} -1.00000 q^{54} -3.46410 q^{55} -1.00000 q^{56} +5.46410 q^{57} +6.00000 q^{58} +6.92820 q^{59} -3.46410 q^{60} +2.00000 q^{61} -5.46410 q^{62} +1.00000 q^{63} +1.00000 q^{64} -6.92820 q^{65} -1.00000 q^{66} +14.9282 q^{67} +3.46410 q^{68} +6.92820 q^{69} +3.46410 q^{70} -12.0000 q^{71} -1.00000 q^{72} -0.535898 q^{73} +4.92820 q^{74} +7.00000 q^{75} +5.46410 q^{76} +1.00000 q^{77} -2.00000 q^{78} -10.9282 q^{79} -3.46410 q^{80} +1.00000 q^{81} -3.46410 q^{82} +4.39230 q^{83} +1.00000 q^{84} -12.0000 q^{85} +10.9282 q^{86} -6.00000 q^{87} -1.00000 q^{88} -0.928203 q^{89} +3.46410 q^{90} +2.00000 q^{91} +6.92820 q^{92} +5.46410 q^{93} -9.46410 q^{94} -18.9282 q^{95} -1.00000 q^{96} +2.00000 q^{97} -1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{11} + 2 q^{12} + 4 q^{13} - 2 q^{14} + 2 q^{16} - 2 q^{18} + 4 q^{19} + 2 q^{21} - 2 q^{22} - 2 q^{24} + 14 q^{25} - 4 q^{26} + 2 q^{27} + 2 q^{28} - 12 q^{29} + 4 q^{31} - 2 q^{32} + 2 q^{33} + 2 q^{36} + 4 q^{37} - 4 q^{38} + 4 q^{39} - 2 q^{42} - 8 q^{43} + 2 q^{44} + 12 q^{47} + 2 q^{48} + 2 q^{49} - 14 q^{50} + 4 q^{52} + 12 q^{53} - 2 q^{54} - 2 q^{56} + 4 q^{57} + 12 q^{58} + 4 q^{61} - 4 q^{62} + 2 q^{63} + 2 q^{64} - 2 q^{66} + 16 q^{67} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 4 q^{74} + 14 q^{75} + 4 q^{76} + 2 q^{77} - 4 q^{78} - 8 q^{79} + 2 q^{81} - 12 q^{83} + 2 q^{84} - 24 q^{85} + 8 q^{86} - 12 q^{87} - 2 q^{88} + 12 q^{89} + 4 q^{91} + 4 q^{93} - 12 q^{94} - 24 q^{95} - 2 q^{96} + 4 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^11 + 2 * q^12 + 4 * q^13 - 2 * q^14 + 2 * q^16 - 2 * q^18 + 4 * q^19 + 2 * q^21 - 2 * q^22 - 2 * q^24 + 14 * q^25 - 4 * q^26 + 2 * q^27 + 2 * q^28 - 12 * q^29 + 4 * q^31 - 2 * q^32 + 2 * q^33 + 2 * q^36 + 4 * q^37 - 4 * q^38 + 4 * q^39 - 2 * q^42 - 8 * q^43 + 2 * q^44 + 12 * q^47 + 2 * q^48 + 2 * q^49 - 14 * q^50 + 4 * q^52 + 12 * q^53 - 2 * q^54 - 2 * q^56 + 4 * q^57 + 12 * q^58 + 4 * q^61 - 4 * q^62 + 2 * q^63 + 2 * q^64 - 2 * q^66 + 16 * q^67 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 4 * q^74 + 14 * q^75 + 4 * q^76 + 2 * q^77 - 4 * q^78 - 8 * q^79 + 2 * q^81 - 12 * q^83 + 2 * q^84 - 24 * q^85 + 8 * q^86 - 12 * q^87 - 2 * q^88 + 12 * q^89 + 4 * q^91 + 4 * q^93 - 12 * q^94 - 24 * q^95 - 2 * q^96 + 4 * q^97 - 2 * q^98 + 2 * q^99

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