LMFDB - Embedded newform 462.2.a.h.1.2

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			1.2
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.46410 q^{10} +1.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} +3.46410 q^{15} +1.00000 q^{16} -3.46410 q^{17} -1.00000 q^{18} -1.46410 q^{19} +3.46410 q^{20} +1.00000 q^{21} -1.00000 q^{22} -6.92820 q^{23} -1.00000 q^{24} +7.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} -6.00000 q^{29} -3.46410 q^{30} -1.46410 q^{31} -1.00000 q^{32} +1.00000 q^{33} +3.46410 q^{34} +3.46410 q^{35} +1.00000 q^{36} +8.92820 q^{37} +1.46410 q^{38} +2.00000 q^{39} -3.46410 q^{40} -3.46410 q^{41} -1.00000 q^{42} +2.92820 q^{43} +1.00000 q^{44} +3.46410 q^{45} +6.92820 q^{46} +2.53590 q^{47} +1.00000 q^{48} +1.00000 q^{49} -7.00000 q^{50} -3.46410 q^{51} +2.00000 q^{52} +12.9282 q^{53} -1.00000 q^{54} +3.46410 q^{55} -1.00000 q^{56} -1.46410 q^{57} +6.00000 q^{58} -6.92820 q^{59} +3.46410 q^{60} +2.00000 q^{61} +1.46410 q^{62} +1.00000 q^{63} +1.00000 q^{64} +6.92820 q^{65} -1.00000 q^{66} +1.07180 q^{67} -3.46410 q^{68} -6.92820 q^{69} -3.46410 q^{70} -12.0000 q^{71} -1.00000 q^{72} -7.46410 q^{73} -8.92820 q^{74} +7.00000 q^{75} -1.46410 q^{76} +1.00000 q^{77} -2.00000 q^{78} +2.92820 q^{79} +3.46410 q^{80} +1.00000 q^{81} +3.46410 q^{82} -16.3923 q^{83} +1.00000 q^{84} -12.0000 q^{85} -2.92820 q^{86} -6.00000 q^{87} -1.00000 q^{88} +12.9282 q^{89} -3.46410 q^{90} +2.00000 q^{91} -6.92820 q^{92} -1.46410 q^{93} -2.53590 q^{94} -5.07180 q^{95} -1.00000 q^{96} +2.00000 q^{97} -1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.217953\pi$
$5$	3.46410	1.54919	0.774597	+	0.632456i	$0.217953\pi$
$6$	−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	$-0.637999\pi$
$17$	−3.46410	−0.840168	−0.420084	+	0.907485i	$0.637999\pi$
$18$	−1.00000	−0.235702
$19$	−1.46410	−0.335888	−0.167944	−	0.985797i	$-0.553713\pi$
$19$	−1.46410	−0.335888	−0.167944	+	0.985797i	$0.553713\pi$
$20$	3.46410	0.774597
$21$	1.00000	0.218218
$22$	−1.00000	−0.213201
$23$	−6.92820	−1.44463	−0.722315	−	0.691564i	$-0.756922\pi$
$23$	−6.92820	−1.44463	−0.722315	+	0.691564i	$0.756922\pi$
$24$	−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
$31$	−1.46410	−0.262960	−0.131480	−	0.991319i	$-0.541973\pi$
$31$	−1.46410	−0.262960	−0.131480	+	0.991319i	$0.541973\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	3.46410	0.594089
$35$	3.46410	0.585540
$36$	1.00000	0.166667
$37$	8.92820	1.46779	0.733894	−	0.679264i	$-0.237701\pi$
$37$	8.92820	1.46779	0.733894	+	0.679264i	$0.237701\pi$
$38$	1.46410	0.237509
$39$	2.00000	0.320256
$40$	−3.46410	−0.547723
$41$	−3.46410	−0.541002	−0.270501	−	0.962720i	$-0.587189\pi$
$41$	−3.46410	−0.541002	−0.270501	+	0.962720i	$0.587189\pi$
$42$	−1.00000	−0.154303
$43$	2.92820	0.446547	0.223273	−	0.974756i	$-0.428326\pi$
$43$	2.92820	0.446547	0.223273	+	0.974756i	$0.428326\pi$
$44$	1.00000	0.150756
$45$	3.46410	0.516398
$46$	6.92820	1.02151
$47$	2.53590	0.369899	0.184949	−	0.982748i	$-0.440788\pi$
$47$	2.53590	0.369899	0.184949	+	0.982748i	$0.440788\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−7.00000	−0.989949
$51$	−3.46410	−0.485071
$52$	2.00000	0.277350
$53$	12.9282	1.77583	0.887913	−	0.460012i	$-0.152155\pi$
$53$	12.9282	1.77583	0.887913	+	0.460012i	$0.152155\pi$
$54$	−1.00000	−0.136083
$55$	3.46410	0.467099
$56$	−1.00000	−0.133631
$57$	−1.46410	−0.193925
$58$	6.00000	0.787839
$59$	−6.92820	−0.901975	−0.450988	−	0.892530i	$-0.648928\pi$
$59$	−6.92820	−0.901975	−0.450988	+	0.892530i	$0.648928\pi$
$60$	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	$0.459132\pi$
$62$	1.46410	0.185941
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	6.92820	0.859338
$66$	−1.00000	−0.123091
$67$	1.07180	0.130941	0.0654704	−	0.997855i	$-0.479145\pi$
$67$	1.07180	0.130941	0.0654704	+	0.997855i	$0.479145\pi$
$68$	−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
$73$	−7.46410	−0.873607	−0.436804	−	0.899557i	$-0.643889\pi$
$73$	−7.46410	−0.873607	−0.436804	+	0.899557i	$0.643889\pi$
$74$	−8.92820	−1.03788
$75$	7.00000	0.808290
$76$	−1.46410	−0.167944
$77$	1.00000	0.113961
$78$	−2.00000	−0.226455
$79$	2.92820	0.329449	0.164724	−	0.986340i	$-0.447327\pi$
$79$	2.92820	0.329449	0.164724	+	0.986340i	$0.447327\pi$
$80$	3.46410	0.387298
$81$	1.00000	0.111111
$82$	3.46410	0.382546
$83$	−16.3923	−1.79929	−0.899645	−	0.436623i	$-0.856174\pi$
$83$	−16.3923	−1.79929	−0.899645	+	0.436623i	$0.856174\pi$
$84$	1.00000	0.109109
$85$	−12.0000	−1.30158
$86$	−2.92820	−0.315756
$87$	−6.00000	−0.643268
$88$	−1.00000	−0.106600
$89$	12.9282	1.37039	0.685193	−	0.728361i	$-0.259718\pi$
$89$	12.9282	1.37039	0.685193	+	0.728361i	$0.259718\pi$
$90$	−3.46410	−0.365148
$91$	2.00000	0.209657
$92$	−6.92820	−0.722315
$93$	−1.46410	−0.151820
$94$	−2.53590	−0.261558
$95$	−5.07180	−0.520355
$96$	−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
$101$	7.85641	0.781742	0.390871	−	0.920446i	$-0.372174\pi$
$101$	7.85641	0.781742	0.390871	+	0.920446i	$0.372174\pi$
$102$	3.46410	0.342997
$103$	−6.53590	−0.644001	−0.322001	−	0.946739i	$-0.604355\pi$
$103$	−6.53590	−0.644001	−0.322001	+	0.946739i	$0.604355\pi$
$104$	−2.00000	−0.196116
$105$	3.46410	0.338062
$106$	−12.9282	−1.25570
$107$	6.92820	0.669775	0.334887	−	0.942258i	$-0.391302\pi$
$107$	6.92820	0.669775	0.334887	+	0.942258i	$0.391302\pi$
$108$	1.00000	0.0962250
$109$	−11.8564	−1.13564	−0.567819	−	0.823154i	$-0.692213\pi$
$109$	−11.8564	−1.13564	−0.567819	+	0.823154i	$0.692213\pi$
$110$	−3.46410	−0.330289
$111$	8.92820	0.847428
$112$	1.00000	0.0944911
$113$	−19.8564	−1.86793	−0.933967	−	0.357360i	$-0.883677\pi$
$113$	−19.8564	−1.86793	−0.933967	+	0.357360i	$0.883677\pi$
$114$	1.46410	0.137126
$115$	−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
$124$	−1.46410	−0.131480
$125$	6.92820	0.619677
$126$	−1.00000	−0.0890871
$127$	2.92820	0.259836	0.129918	−	0.991525i	$-0.458529\pi$
$127$	2.92820	0.259836	0.129918	+	0.991525i	$0.458529\pi$
$128$	−1.00000	−0.0883883
$129$	2.92820	0.257814
$130$	−6.92820	−0.607644
$131$	16.3923	1.43220	0.716101	−	0.697997i	$-0.245925\pi$
$131$	16.3923	1.43220	0.716101	+	0.697997i	$0.245925\pi$
$132$	1.00000	0.0870388
$133$	−1.46410	−0.126954
$134$	−1.07180	−0.0925891
$135$	3.46410	0.298142
$136$	3.46410	0.297044
$137$	−19.8564	−1.69645	−0.848224	−	0.529638i	$-0.822328\pi$
$137$	−19.8564	−1.69645	−0.848224	+	0.529638i	$0.822328\pi$
$138$	6.92820	0.589768
$139$	−6.53590	−0.554368	−0.277184	−	0.960817i	$-0.589401\pi$
$139$	−6.53590	−0.554368	−0.277184	+	0.960817i	$0.589401\pi$
$140$	3.46410	0.292770
$141$	2.53590	0.213561
$142$	12.0000	1.00702
$143$	2.00000	0.167248
$144$	1.00000	0.0833333
$145$	−20.7846	−1.72607
$146$	7.46410	0.617733
$147$	1.00000	0.0824786
$148$	8.92820	0.733894
$149$	−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	$0.725663\pi$
$152$	1.46410	0.118754
$153$	−3.46410	−0.280056
$154$	−1.00000	−0.0805823
$155$	−5.07180	−0.407377
$156$	2.00000	0.160128
$157$	18.3923	1.46787	0.733933	−	0.679222i	$-0.237683\pi$
$157$	18.3923	1.46787	0.733933	+	0.679222i	$0.237683\pi$
$158$	−2.92820	−0.232955
$159$	12.9282	1.02527
$160$	−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
$166$	16.3923	1.27229
$167$	5.07180	0.392467	0.196234	−	0.980557i	$-0.437129\pi$
$167$	5.07180	0.392467	0.196234	+	0.980557i	$0.437129\pi$
$168$	−1.00000	−0.0771517
$169$	−9.00000	−0.692308
$170$	12.0000	0.920358
$171$	−1.46410	−0.111963
$172$	2.92820	0.223273
$173$	12.9282	0.982913	0.491457	−	0.870902i	$-0.336465\pi$
$173$	12.9282	0.982913	0.491457	+	0.870902i	$0.336465\pi$
$174$	6.00000	0.454859
$175$	7.00000	0.529150
$176$	1.00000	0.0753778
$177$	−6.92820	−0.520756
$178$	−12.9282	−0.969010
$179$	20.7846	1.55351	0.776757	−	0.629800i	$-0.216863\pi$
$179$	20.7846	1.55351	0.776757	+	0.629800i	$0.216863\pi$
$180$	3.46410	0.258199
$181$	−14.3923	−1.06977	−0.534886	−	0.844924i	$-0.679645\pi$
$181$	−14.3923	−1.06977	−0.534886	+	0.844924i	$0.679645\pi$
$182$	−2.00000	−0.148250
$183$	2.00000	0.147844
$184$	6.92820	0.510754
$185$	30.9282	2.27389
$186$	1.46410	0.107353
$187$	−3.46410	−0.253320
$188$	2.53590	0.184949
$189$	1.00000	0.0727393
$190$	5.07180	0.367947
$191$	−20.7846	−1.50392	−0.751961	−	0.659208i	$-0.770892\pi$
$191$	−20.7846	−1.50392	−0.751961	+	0.659208i	$0.770892\pi$
$192$	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
$199$	−20.3923	−1.44557	−0.722786	−	0.691072i	$-0.757139\pi$
$199$	−20.3923	−1.44557	−0.722786	+	0.691072i	$0.757139\pi$
$200$	−7.00000	−0.494975
$201$	1.07180	0.0755987
$202$	−7.85641	−0.552775
$203$	−6.00000	−0.421117
$204$	−3.46410	−0.242536
$205$	−12.0000	−0.838116
$206$	6.53590	0.455378
$207$	−6.92820	−0.481543
$208$	2.00000	0.138675
$209$	−1.46410	−0.101274
$210$	−3.46410	−0.239046
$211$	−24.7846	−1.70624	−0.853121	−	0.521712i	$-0.825293\pi$
$211$	−24.7846	−1.70624	−0.853121	+	0.521712i	$0.825293\pi$
$212$	12.9282	0.887913
$213$	−12.0000	−0.822226
$214$	−6.92820	−0.473602
$215$	10.1436	0.691787
$216$	−1.00000	−0.0680414
$217$	−1.46410	−0.0993897
$218$	11.8564	0.803017
$219$	−7.46410	−0.504377
$220$	3.46410	0.233550
$221$	−6.92820	−0.466041
$222$	−8.92820	−0.599222
$223$	12.3923	0.829850	0.414925	−	0.909856i	$-0.363808\pi$
$223$	12.3923	0.829850	0.414925	+	0.909856i	$0.363808\pi$
$224$	−1.00000	−0.0668153
$225$	7.00000	0.466667
$226$	19.8564	1.32083
$227$	16.3923	1.08800	0.543998	−	0.839087i	$-0.316910\pi$
$227$	16.3923	1.08800	0.543998	+	0.839087i	$0.316910\pi$
$228$	−1.46410	−0.0969625
$229$	13.3205	0.880244	0.440122	−	0.897938i	$-0.354935\pi$
$229$	13.3205	0.880244	0.440122	+	0.897938i	$0.354935\pi$
$230$	24.0000	1.58251
$231$	1.00000	0.0657952
$232$	6.00000	0.393919
$233$	19.8564	1.30084	0.650418	−	0.759576i	$-0.274594\pi$
$233$	19.8564	1.30084	0.650418	+	0.759576i	$0.274594\pi$
$234$	−2.00000	−0.130744
$235$	8.78461	0.573045
$236$	−6.92820	−0.450988
$237$	2.92820	0.190207
$238$	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
$241$	30.3923	1.95774	0.978870	−	0.204482i	$-0.0655511\pi$
$241$	30.3923	1.95774	0.978870	+	0.204482i	$0.0655511\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	2.00000	0.128037
$245$	3.46410	0.221313
$246$	3.46410	0.220863
$247$	−2.92820	−0.186317
$248$	1.46410	0.0929705
$249$	−16.3923	−1.03882
$250$	−6.92820	−0.438178
$251$	17.0718	1.07756	0.538781	−	0.842446i	$-0.318885\pi$
$251$	17.0718	1.07756	0.538781	+	0.842446i	$0.318885\pi$
$252$	1.00000	0.0629941
$253$	−6.92820	−0.435572
$254$	−2.92820	−0.183732
$255$	−12.0000	−0.751469
$256$	1.00000	0.0625000
$257$	−0.928203	−0.0578997	−0.0289499	−	0.999581i	$-0.509216\pi$
$257$	−0.928203	−0.0578997	−0.0289499	+	0.999581i	$0.509216\pi$
$258$	−2.92820	−0.182302
$259$	8.92820	0.554772
$260$	6.92820	0.429669
$261$	−6.00000	−0.371391
$262$	−16.3923	−1.01272
$263$	−18.9282	−1.16716	−0.583582	−	0.812055i	$-0.698349\pi$
$263$	−18.9282	−1.16716	−0.583582	+	0.812055i	$0.698349\pi$
$264$	−1.00000	−0.0615457
$265$	44.7846	2.75110
$266$	1.46410	0.0897698
$267$	12.9282	0.791193
$268$	1.07180	0.0654704
$269$	−24.2487	−1.47847	−0.739235	−	0.673448i	$-0.764813\pi$
$269$	−24.2487	−1.47847	−0.739235	+	0.673448i	$0.764813\pi$
$270$	−3.46410	−0.210819
$271$	16.7846	1.01959	0.509796	−	0.860295i	$-0.329721\pi$
$271$	16.7846	1.01959	0.509796	+	0.860295i	$0.329721\pi$
$272$	−3.46410	−0.210042
$273$	2.00000	0.121046
$274$	19.8564	1.19957
$275$	7.00000	0.422116
$276$	−6.92820	−0.417029
$277$	15.8564	0.952719	0.476360	−	0.879251i	$-0.341956\pi$
$277$	15.8564	0.952719	0.476360	+	0.879251i	$0.341956\pi$
$278$	6.53590	0.391997
$279$	−1.46410	−0.0876535
$280$	−3.46410	−0.207020
$281$	19.8564	1.18453	0.592267	−	0.805742i	$-0.298233\pi$
$281$	19.8564	1.18453	0.592267	+	0.805742i	$0.298233\pi$
$282$	−2.53590	−0.151011
$283$	−6.53590	−0.388519	−0.194259	−	0.980950i	$-0.562230\pi$
$283$	−6.53590	−0.388519	−0.194259	+	0.980950i	$0.562230\pi$
$284$	−12.0000	−0.712069
$285$	−5.07180	−0.300427
$286$	−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
$292$	−7.46410	−0.436804
$293$	−11.0718	−0.646821	−0.323411	−	0.946259i	$-0.604830\pi$
$293$	−11.0718	−0.646821	−0.323411	+	0.946259i	$0.604830\pi$
$294$	−1.00000	−0.0583212
$295$	−24.0000	−1.39733
$296$	−8.92820	−0.518941
$297$	1.00000	0.0580259
$298$	6.00000	0.347571
$299$	−13.8564	−0.801337
$300$	7.00000	0.404145
$301$	2.92820	0.168779
$302$	16.0000	0.920697
$303$	7.85641	0.451339
$304$	−1.46410	−0.0839720
$305$	6.92820	0.396708
$306$	3.46410	0.198030
$307$	17.4641	0.996729	0.498364	−	0.866968i	$-0.333934\pi$
$307$	17.4641	0.996729	0.498364	+	0.866968i	$0.333934\pi$
$308$	1.00000	0.0569803
$309$	−6.53590	−0.371814
$310$	5.07180	0.288059
$311$	7.60770	0.431393	0.215696	−	0.976460i	$-0.430798\pi$
$311$	7.60770	0.431393	0.215696	+	0.976460i	$0.430798\pi$
$312$	−2.00000	−0.113228
$313$	−3.07180	−0.173628	−0.0868141	−	0.996225i	$-0.527669\pi$
$313$	−3.07180	−0.173628	−0.0868141	+	0.996225i	$0.527669\pi$
$314$	−18.3923	−1.03794
$315$	3.46410	0.195180
$316$	2.92820	0.164724
$317$	−0.928203	−0.0521331	−0.0260665	−	0.999660i	$-0.508298\pi$
$317$	−0.928203	−0.0521331	−0.0260665	+	0.999660i	$0.508298\pi$
$318$	−12.9282	−0.724978
$319$	−6.00000	−0.335936
$320$	3.46410	0.193649
$321$	6.92820	0.386695
$322$	6.92820	0.386094
$323$	5.07180	0.282202
$324$	1.00000	0.0555556
$325$	14.0000	0.776580
$326$	4.00000	0.221540
$327$	−11.8564	−0.655661
$328$	3.46410	0.191273
$329$	2.53590	0.139809
$330$	−3.46410	−0.190693
$331$	−22.9282	−1.26025	−0.630124	−	0.776495i	$-0.716996\pi$
$331$	−22.9282	−1.26025	−0.630124	+	0.776495i	$0.716996\pi$
$332$	−16.3923	−0.899645
$333$	8.92820	0.489263
$334$	−5.07180	−0.277516
$335$	3.71281	0.202853
$336$	1.00000	0.0545545
$337$	7.07180	0.385225	0.192613	−	0.981275i	$-0.438304\pi$
$337$	7.07180	0.385225	0.192613	+	0.981275i	$0.438304\pi$
$338$	9.00000	0.489535
$339$	−19.8564	−1.07845
$340$	−12.0000	−0.650791
$341$	−1.46410	−0.0792855
$342$	1.46410	0.0791695
$343$	1.00000	0.0539949
$344$	−2.92820	−0.157878
$345$	−24.0000	−1.29212
$346$	−12.9282	−0.695025
$347$	20.7846	1.11578	0.557888	−	0.829916i	$-0.311612\pi$
$347$	20.7846	1.11578	0.557888	+	0.829916i	$0.311612\pi$
$348$	−6.00000	−0.321634
$349$	−30.7846	−1.64786	−0.823931	−	0.566690i	$-0.808224\pi$
$349$	−30.7846	−1.64786	−0.823931	+	0.566690i	$0.808224\pi$
$350$	−7.00000	−0.374166
$351$	2.00000	0.106752
$352$	−1.00000	−0.0533002
$353$	−0.928203	−0.0494033	−0.0247016	−	0.999695i	$-0.507864\pi$
$353$	−0.928203	−0.0494033	−0.0247016	+	0.999695i	$0.507864\pi$
$354$	6.92820	0.368230
$355$	−41.5692	−2.20627
$356$	12.9282	0.685193
$357$	−3.46410	−0.183340
$358$	−20.7846	−1.09850
$359$	−18.9282	−0.998992	−0.499496	−	0.866316i	$-0.666482\pi$
$359$	−18.9282	−0.998992	−0.499496	+	0.866316i	$0.666482\pi$
$360$	−3.46410	−0.182574
$361$	−16.8564	−0.887179
$362$	14.3923	0.756443
$363$	1.00000	0.0524864
$364$	2.00000	0.104828
$365$	−25.8564	−1.35339
$366$	−2.00000	−0.104542
$367$	−15.3205	−0.799724	−0.399862	−	0.916575i	$-0.630942\pi$
$367$	−15.3205	−0.799724	−0.399862	+	0.916575i	$0.630942\pi$
$368$	−6.92820	−0.361158
$369$	−3.46410	−0.180334
$370$	−30.9282	−1.60788
$371$	12.9282	0.671199
$372$	−1.46410	−0.0759101
$373$	−25.7128	−1.33136	−0.665679	−	0.746238i	$-0.731858\pi$
$373$	−25.7128	−1.33136	−0.665679	+	0.746238i	$0.731858\pi$
$374$	3.46410	0.179124
$375$	6.92820	0.357771
$376$	−2.53590	−0.130779
$377$	−12.0000	−0.618031
$378$	−1.00000	−0.0514344
$379$	9.85641	0.506290	0.253145	−	0.967428i	$-0.418535\pi$
$379$	9.85641	0.506290	0.253145	+	0.967428i	$0.418535\pi$
$380$	−5.07180	−0.260178
$381$	2.92820	0.150016
$382$	20.7846	1.06343
$383$	21.4641	1.09676	0.548382	−	0.836228i	$-0.315244\pi$
$383$	21.4641	1.09676	0.548382	+	0.836228i	$0.315244\pi$
$384$	−1.00000	−0.0510310
$385$	3.46410	0.176547
$386$	−26.0000	−1.32337
$387$	2.92820	0.148849
$388$	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
$393$	16.3923	0.826882
$394$	−18.0000	−0.906827
$395$	10.1436	0.510380
$396$	1.00000	0.0502519
$397$	18.3923	0.923083	0.461542	−	0.887119i	$-0.347296\pi$
$397$	18.3923	0.923083	0.461542	+	0.887119i	$0.347296\pi$
$398$	20.3923	1.02217
$399$	−1.46410	−0.0732968
$400$	7.00000	0.350000
$401$	31.8564	1.59083	0.795417	−	0.606063i	$-0.207252\pi$
$401$	31.8564	1.59083	0.795417	+	0.606063i	$0.207252\pi$
$402$	−1.07180	−0.0534564
$403$	−2.92820	−0.145864
$404$	7.85641	0.390871
$405$	3.46410	0.172133
$406$	6.00000	0.297775
$407$	8.92820	0.442555
$408$	3.46410	0.171499
$409$	25.3205	1.25202	0.626009	−	0.779816i	$-0.284687\pi$
$409$	25.3205	1.25202	0.626009	+	0.779816i	$0.284687\pi$
$410$	12.0000	0.592638
$411$	−19.8564	−0.979444
$412$	−6.53590	−0.322001
$413$	−6.92820	−0.340915
$414$	6.92820	0.340503
$415$	−56.7846	−2.78745
$416$	−2.00000	−0.0980581
$417$	−6.53590	−0.320064
$418$	1.46410	0.0716116
$419$	−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
$421$	17.7128	0.863270	0.431635	−	0.902048i	$-0.357937\pi$
$421$	17.7128	0.863270	0.431635	+	0.902048i	$0.357937\pi$
$422$	24.7846	1.20650
$423$	2.53590	0.123300
$424$	−12.9282	−0.627849
$425$	−24.2487	−1.17624
$426$	12.0000	0.581402
$427$	2.00000	0.0967868
$428$	6.92820	0.334887
$429$	2.00000	0.0965609
$430$	−10.1436	−0.489168
$431$	−5.07180	−0.244300	−0.122150	−	0.992512i	$-0.538979\pi$
$431$	−5.07180	−0.244300	−0.122150	+	0.992512i	$0.538979\pi$
$432$	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	$0.484697\pi$
$434$	1.46410	0.0702791
$435$	−20.7846	−0.996546
$436$	−11.8564	−0.567819
$437$	10.1436	0.485234
$438$	7.46410	0.356649
$439$	16.7846	0.801086	0.400543	−	0.916278i	$-0.368822\pi$
$439$	16.7846	0.801086	0.400543	+	0.916278i	$0.368822\pi$
$440$	−3.46410	−0.165145
$441$	1.00000	0.0476190
$442$	6.92820	0.329541
$443$	20.7846	0.987507	0.493753	−	0.869602i	$-0.335625\pi$
$443$	20.7846	0.987507	0.493753	+	0.869602i	$0.335625\pi$
$444$	8.92820	0.423714
$445$	44.7846	2.12299
$446$	−12.3923	−0.586793
$447$	−6.00000	−0.283790
$448$	1.00000	0.0472456
$449$	7.85641	0.370767	0.185383	−	0.982666i	$-0.440647\pi$
$449$	7.85641	0.370767	0.185383	+	0.982666i	$0.440647\pi$
$450$	−7.00000	−0.329983
$451$	−3.46410	−0.163118
$452$	−19.8564	−0.933967
$453$	−16.0000	−0.751746
$454$	−16.3923	−0.769329
$455$	6.92820	0.324799
$456$	1.46410	0.0685628
$457$	−11.8564	−0.554619	−0.277310	−	0.960781i	$-0.589443\pi$
$457$	−11.8564	−0.554619	−0.277310	+	0.960781i	$0.589443\pi$
$458$	−13.3205	−0.622426
$459$	−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
$465$	−5.07180	−0.235199
$466$	−19.8564	−0.919830
$467$	39.7128	1.83769	0.918845	−	0.394619i	$-0.129123\pi$
$467$	39.7128	1.83769	0.918845	+	0.394619i	$0.129123\pi$
$468$	2.00000	0.0924500
$469$	1.07180	0.0494910
$470$	−8.78461	−0.405204
$471$	18.3923	0.847473
$472$	6.92820	0.318896
$473$	2.92820	0.134639
$474$	−2.92820	−0.134497
$475$	−10.2487	−0.470243
$476$	−3.46410	−0.158777
$477$	12.9282	0.591942
$478$	24.0000	1.09773
$479$	13.8564	0.633115	0.316558	−	0.948573i	$-0.397473\pi$
$479$	13.8564	0.633115	0.316558	+	0.948573i	$0.397473\pi$
$480$	−3.46410	−0.158114
$481$	17.8564	0.814182
$482$	−30.3923	−1.38433
$483$	−6.92820	−0.315244
$484$	1.00000	0.0454545
$485$	6.92820	0.314594
$486$	−1.00000	−0.0453609
$487$	−0.784610	−0.0355541	−0.0177770	−	0.999842i	$-0.505659\pi$
$487$	−0.784610	−0.0355541	−0.0177770	+	0.999842i	$0.505659\pi$
$488$	−2.00000	−0.0905357
$489$	−4.00000	−0.180886
$490$	−3.46410	−0.156492
$491$	25.8564	1.16688	0.583442	−	0.812155i	$-0.301706\pi$
$491$	25.8564	1.16688	0.583442	+	0.812155i	$0.301706\pi$
$492$	−3.46410	−0.156174
$493$	20.7846	0.936092
$494$	2.92820	0.131746
$495$	3.46410	0.155700
$496$	−1.46410	−0.0657401
$497$	−12.0000	−0.538274
$498$	16.3923	0.734557
$499$	−22.9282	−1.02641	−0.513204	−	0.858267i	$-0.671541\pi$
$499$	−22.9282	−1.02641	−0.513204	+	0.858267i	$0.671541\pi$
$500$	6.92820	0.309839
$501$	5.07180	0.226591
$502$	−17.0718	−0.761952
$503$	5.07180	0.226140	0.113070	−	0.993587i	$-0.463932\pi$
$503$	5.07180	0.226140	0.113070	+	0.993587i	$0.463932\pi$
$504$	−1.00000	−0.0445435
$505$	27.2154	1.21107
$506$	6.92820	0.307996
$507$	−9.00000	−0.399704
$508$	2.92820	0.129918
$509$	−6.67949	−0.296063	−0.148032	−	0.988983i	$-0.547294\pi$
$509$	−6.67949	−0.296063	−0.148032	+	0.988983i	$0.547294\pi$
$510$	12.0000	0.531369
$511$	−7.46410	−0.330192
$512$	−1.00000	−0.0441942
$513$	−1.46410	−0.0646417
$514$	0.928203	0.0409413
$515$	−22.6410	−0.997682
$516$	2.92820	0.128907
$517$	2.53590	0.111529
$518$	−8.92820	−0.392283
$519$	12.9282	0.567485
$520$	−6.92820	−0.303822
$521$	23.0718	1.01079	0.505397	−	0.862887i	$-0.331346\pi$
$521$	23.0718	1.01079	0.505397	+	0.862887i	$0.331346\pi$
$522$	6.00000	0.262613
$523$	3.60770	0.157753	0.0788767	−	0.996884i	$-0.474867\pi$
$523$	3.60770	0.157753	0.0788767	+	0.996884i	$0.474867\pi$
$524$	16.3923	0.716101
$525$	7.00000	0.305505
$526$	18.9282	0.825309
$527$	5.07180	0.220931
$528$	1.00000	0.0435194
$529$	25.0000	1.08696
$530$	−44.7846	−1.94532
$531$	−6.92820	−0.300658
$532$	−1.46410	−0.0634769
$533$	−6.92820	−0.300094
$534$	−12.9282	−0.559458
$535$	24.0000	1.03761
$536$	−1.07180	−0.0462946
$537$	20.7846	0.896922
$538$	24.2487	1.04544
$539$	1.00000	0.0430730
$540$	3.46410	0.149071
$541$	29.7128	1.27745	0.638727	−	0.769434i	$-0.279461\pi$
$541$	29.7128	1.27745	0.638727	+	0.769434i	$0.279461\pi$
$542$	−16.7846	−0.720961
$543$	−14.3923	−0.617633
$544$	3.46410	0.148522
$545$	−41.0718	−1.75932
$546$	−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	$0.611123\pi$
$548$	−19.8564	−0.848224
$549$	2.00000	0.0853579
$550$	−7.00000	−0.298481
$551$	8.78461	0.374237
$552$	6.92820	0.294884
$553$	2.92820	0.124520
$554$	−15.8564	−0.673674
$555$	30.9282	1.31283
$556$	−6.53590	−0.277184
$557$	−33.7128	−1.42846	−0.714229	−	0.699912i	$-0.753222\pi$
$557$	−33.7128	−1.42846	−0.714229	+	0.699912i	$0.753222\pi$
$558$	1.46410	0.0619804
$559$	5.85641	0.247700
$560$	3.46410	0.146385
$561$	−3.46410	−0.146254
$562$	−19.8564	−0.837592
$563$	30.2487	1.27483	0.637416	−	0.770520i	$-0.280003\pi$
$563$	30.2487	1.27483	0.637416	+	0.770520i	$0.280003\pi$
$564$	2.53590	0.106781
$565$	−68.7846	−2.89379
$566$	6.53590	0.274724
$567$	1.00000	0.0419961
$568$	12.0000	0.503509
$569$	−4.14359	−0.173708	−0.0868542	−	0.996221i	$-0.527681\pi$
$569$	−4.14359	−0.173708	−0.0868542	+	0.996221i	$0.527681\pi$
$570$	5.07180	0.212434
$571$	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
$577$	10.7846	0.448969	0.224485	−	0.974478i	$-0.427930\pi$
$577$	10.7846	0.448969	0.224485	+	0.974478i	$0.427930\pi$
$578$	5.00000	0.207973
$579$	26.0000	1.08052
$580$	−20.7846	−0.863034
$581$	−16.3923	−0.680067
$582$	−2.00000	−0.0829027
$583$	12.9282	0.535431
$584$	7.46410	0.308867
$585$	6.92820	0.286446
$586$	11.0718	0.457372
$587$	20.7846	0.857873	0.428936	−	0.903335i	$-0.358888\pi$
$587$	20.7846	0.857873	0.428936	+	0.903335i	$0.358888\pi$
$588$	1.00000	0.0412393
$589$	2.14359	0.0883252
$590$	24.0000	0.988064
$591$	18.0000	0.740421
$592$	8.92820	0.366947
$593$	−27.4641	−1.12782	−0.563908	−	0.825838i	$-0.690703\pi$
$593$	−27.4641	−1.12782	−0.563908	+	0.825838i	$0.690703\pi$
$594$	−1.00000	−0.0410305
$595$	−12.0000	−0.491952
$596$	−6.00000	−0.245770
$597$	−20.3923	−0.834601
$598$	13.8564	0.566631
$599$	−25.8564	−1.05646	−0.528232	−	0.849100i	$-0.677145\pi$
$599$	−25.8564	−1.05646	−0.528232	+	0.849100i	$0.677145\pi$
$600$	−7.00000	−0.285774
$601$	−2.39230	−0.0975842	−0.0487921	−	0.998809i	$-0.515537\pi$
$601$	−2.39230	−0.0975842	−0.0487921	+	0.998809i	$0.515537\pi$
$602$	−2.92820	−0.119345
$603$	1.07180	0.0436469
$604$	−16.0000	−0.651031
$605$	3.46410	0.140836
$606$	−7.85641	−0.319145
$607$	35.7128	1.44954	0.724769	−	0.688992i	$-0.241946\pi$
$607$	35.7128	1.44954	0.724769	+	0.688992i	$0.241946\pi$
$608$	1.46410	0.0593772
$609$	−6.00000	−0.243132
$610$	−6.92820	−0.280515
$611$	5.07180	0.205183
$612$	−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	$0.646543\pi$
$614$	−17.4641	−0.704794
$615$	−12.0000	−0.483887
$616$	−1.00000	−0.0402911
$617$	7.85641	0.316287	0.158144	−	0.987416i	$-0.449449\pi$
$617$	7.85641	0.316287	0.158144	+	0.987416i	$0.449449\pi$
$618$	6.53590	0.262912
$619$	23.7128	0.953098	0.476549	−	0.879148i	$-0.341887\pi$
$619$	23.7128	0.953098	0.476549	+	0.879148i	$0.341887\pi$
$620$	−5.07180	−0.203688
$621$	−6.92820	−0.278019
$622$	−7.60770	−0.305041
$623$	12.9282	0.517958
$624$	2.00000	0.0800641
$625$	−11.0000	−0.440000
$626$	3.07180	0.122774
$627$	−1.46410	−0.0584706
$628$	18.3923	0.733933
$629$	−30.9282	−1.23319
$630$	−3.46410	−0.138013
$631$	40.7846	1.62361	0.811805	−	0.583929i	$-0.198485\pi$
$631$	40.7846	1.62361	0.811805	+	0.583929i	$0.198485\pi$
$632$	−2.92820	−0.116478
$633$	−24.7846	−0.985100
$634$	0.928203	0.0368637
$635$	10.1436	0.402536
$636$	12.9282	0.512637
$637$	2.00000	0.0792429
$638$	6.00000	0.237542
$639$	−12.0000	−0.474713
$640$	−3.46410	−0.136931
$641$	4.14359	0.163662	0.0818311	−	0.996646i	$-0.473923\pi$
$641$	4.14359	0.163662	0.0818311	+	0.996646i	$0.473923\pi$
$642$	−6.92820	−0.273434
$643$	1.07180	0.0422675	0.0211338	−	0.999777i	$-0.493272\pi$
$643$	1.07180	0.0422675	0.0211338	+	0.999777i	$0.493272\pi$
$644$	−6.92820	−0.273009
$645$	10.1436	0.399404
$646$	−5.07180	−0.199547
$647$	35.3205	1.38859	0.694296	−	0.719689i	$-0.255716\pi$
$647$	35.3205	1.38859	0.694296	+	0.719689i	$0.255716\pi$
$648$	−1.00000	−0.0392837
$649$	−6.92820	−0.271956
$650$	−14.0000	−0.549125
$651$	−1.46410	−0.0573827
$652$	−4.00000	−0.156652
$653$	21.7128	0.849688	0.424844	−	0.905267i	$-0.360329\pi$
$653$	21.7128	0.849688	0.424844	+	0.905267i	$0.360329\pi$
$654$	11.8564	0.463622
$655$	56.7846	2.21876
$656$	−3.46410	−0.135250
$657$	−7.46410	−0.291202
$658$	−2.53590	−0.0988596
$659$	−30.9282	−1.20479	−0.602396	−	0.798197i	$-0.705787\pi$
$659$	−30.9282	−1.20479	−0.602396	+	0.798197i	$0.705787\pi$
$660$	3.46410	0.134840
$661$	−4.24871	−0.165256	−0.0826279	−	0.996580i	$-0.526331\pi$
$661$	−4.24871	−0.165256	−0.0826279	+	0.996580i	$0.526331\pi$
$662$	22.9282	0.891130
$663$	−6.92820	−0.269069
$664$	16.3923	0.636145
$665$	−5.07180	−0.196676
$666$	−8.92820	−0.345961
$667$	41.5692	1.60957
$668$	5.07180	0.196234
$669$	12.3923	0.479114
$670$	−3.71281	−0.143438
$671$	2.00000	0.0772091
$672$	−1.00000	−0.0385758
$673$	7.07180	0.272598	0.136299	−	0.990668i	$-0.456479\pi$
$673$	7.07180	0.272598	0.136299	+	0.990668i	$0.456479\pi$
$674$	−7.07180	−0.272395
$675$	7.00000	0.269430
$676$	−9.00000	−0.346154
$677$	−38.7846	−1.49061	−0.745307	−	0.666722i	$-0.767697\pi$
$677$	−38.7846	−1.49061	−0.745307	+	0.666722i	$0.767697\pi$
$678$	19.8564	0.762581
$679$	2.00000	0.0767530
$680$	12.0000	0.460179
$681$	16.3923	0.628154
$682$	1.46410	0.0560633
$683$	44.7846	1.71364	0.856818	−	0.515619i	$-0.172438\pi$
$683$	44.7846	1.71364	0.856818	+	0.515619i	$0.172438\pi$
$684$	−1.46410	−0.0559813
$685$	−68.7846	−2.62812
$686$	−1.00000	−0.0381802
$687$	13.3205	0.508209
$688$	2.92820	0.111637
$689$	25.8564	0.985051
$690$	24.0000	0.913664
$691$	−46.9282	−1.78523	−0.892616	−	0.450817i	$-0.851133\pi$
$691$	−46.9282	−1.78523	−0.892616	+	0.450817i	$0.851133\pi$
$692$	12.9282	0.491457
$693$	1.00000	0.0379869
$694$	−20.7846	−0.788973
$695$	−22.6410	−0.858823
$696$	6.00000	0.227429
$697$	12.0000	0.454532
$698$	30.7846	1.16521
$699$	19.8564	0.751038
$700$	7.00000	0.264575
$701$	−9.71281	−0.366848	−0.183424	−	0.983034i	$-0.558718\pi$
$701$	−9.71281	−0.366848	−0.183424	+	0.983034i	$0.558718\pi$
$702$	−2.00000	−0.0754851
$703$	−13.0718	−0.493012
$704$	1.00000	0.0376889
$705$	8.78461	0.330848
$706$	0.928203	0.0349334
$707$	7.85641	0.295471
$708$	−6.92820	−0.260378
$709$	5.21539	0.195868	0.0979340	−	0.995193i	$-0.468777\pi$
$709$	5.21539	0.195868	0.0979340	+	0.995193i	$0.468777\pi$
$710$	41.5692	1.56007
$711$	2.92820	0.109816
$712$	−12.9282	−0.484505
$713$	10.1436	0.379881
$714$	3.46410	0.129641
$715$	6.92820	0.259100
$716$	20.7846	0.776757
$717$	−24.0000	−0.896296
$718$	18.9282	0.706394
$719$	25.1769	0.938940	0.469470	−	0.882948i	$-0.344445\pi$
$719$	25.1769	0.938940	0.469470	+	0.882948i	$0.344445\pi$
$720$	3.46410	0.129099
$721$	−6.53590	−0.243410
$722$	16.8564	0.627330
$723$	30.3923	1.13030
$724$	−14.3923	−0.534886
$725$	−42.0000	−1.55984
$726$	−1.00000	−0.0371135
$727$	−29.1769	−1.08211	−0.541056	−	0.840987i	$-0.681975\pi$
$727$	−29.1769	−1.08211	−0.541056	+	0.840987i	$0.681975\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	25.8564	0.956989
$731$	−10.1436	−0.375174
$732$	2.00000	0.0739221
$733$	39.8564	1.47213	0.736065	−	0.676911i	$-0.236682\pi$
$733$	39.8564	1.47213	0.736065	+	0.676911i	$0.236682\pi$
$734$	15.3205	0.565490
$735$	3.46410	0.127775
$736$	6.92820	0.255377
$737$	1.07180	0.0394801
$738$	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	$0.452992\pi$
$740$	30.9282	1.13694
$741$	−2.92820	−0.107570
$742$	−12.9282	−0.474609
$743$	41.5692	1.52503	0.762513	−	0.646972i	$-0.223965\pi$
$743$	41.5692	1.52503	0.762513	+	0.646972i	$0.223965\pi$
$744$	1.46410	0.0536766
$745$	−20.7846	−0.761489
$746$	25.7128	0.941413
$747$	−16.3923	−0.599763
$748$	−3.46410	−0.126660
$749$	6.92820	0.253151
$750$	−6.92820	−0.252982
$751$	16.7846	0.612479	0.306240	−	0.951954i	$-0.400929\pi$
$751$	16.7846	0.612479	0.306240	+	0.951954i	$0.400929\pi$
$752$	2.53590	0.0924747
$753$	17.0718	0.622131
$754$	12.0000	0.437014
$755$	−55.4256	−2.01715
$756$	1.00000	0.0363696
$757$	−18.7846	−0.682738	−0.341369	−	0.939929i	$-0.610891\pi$
$757$	−18.7846	−0.682738	−0.341369	+	0.939929i	$0.610891\pi$
$758$	−9.85641	−0.358001
$759$	−6.92820	−0.251478
$760$	5.07180	0.183973
$761$	−46.3923	−1.68172	−0.840860	−	0.541253i	$-0.817950\pi$
$761$	−46.3923	−1.68172	−0.840860	+	0.541253i	$0.817950\pi$
$762$	−2.92820	−0.106078
$763$	−11.8564	−0.429231
$764$	−20.7846	−0.751961
$765$	−12.0000	−0.433861
$766$	−21.4641	−0.775530
$767$	−13.8564	−0.500326
$768$	1.00000	0.0360844
$769$	35.4641	1.27887	0.639434	−	0.768846i	$-0.279169\pi$
$769$	35.4641	1.27887	0.639434	+	0.768846i	$0.279169\pi$
$770$	−3.46410	−0.124838
$771$	−0.928203	−0.0334284
$772$	26.0000	0.935760
$773$	−39.4641	−1.41943	−0.709713	−	0.704491i	$-0.751175\pi$
$773$	−39.4641	−1.41943	−0.709713	+	0.704491i	$0.751175\pi$
$774$	−2.92820	−0.105252
$775$	−10.2487	−0.368145
$776$	−2.00000	−0.0717958
$777$	8.92820	0.320298
$778$	30.0000	1.07555
$779$	5.07180	0.181716
$780$	6.92820	0.248069
$781$	−12.0000	−0.429394
$782$	−24.0000	−0.858238
$783$	−6.00000	−0.214423
$784$	1.00000	0.0357143
$785$	63.7128	2.27401
$786$	−16.3923	−0.584694
$787$	−29.1769	−1.04004	−0.520022	−	0.854153i	$-0.674076\pi$
$787$	−29.1769	−1.04004	−0.520022	+	0.854153i	$0.674076\pi$
$788$	18.0000	0.641223
$789$	−18.9282	−0.673862
$790$	−10.1436	−0.360893
$791$	−19.8564	−0.706013
$792$	−1.00000	−0.0355335
$793$	4.00000	0.142044
$794$	−18.3923	−0.652718
$795$	44.7846	1.58835
$796$	−20.3923	−0.722786
$797$	−39.4641	−1.39789	−0.698945	−	0.715175i	$-0.746347\pi$
$797$	−39.4641	−1.39789	−0.698945	+	0.715175i	$0.746347\pi$
$798$	1.46410	0.0518286
$799$	−8.78461	−0.310777
$800$	−7.00000	−0.247487
$801$	12.9282	0.456796
$802$	−31.8564	−1.12489
$803$	−7.46410	−0.263402
$804$	1.07180	0.0377994
$805$	−24.0000	−0.845889
$806$	2.92820	0.103142
$807$	−24.2487	−0.853595
$808$	−7.85641	−0.276387
$809$	24.9282	0.876429	0.438214	−	0.898870i	$-0.355611\pi$
$809$	24.9282	0.876429	0.438214	+	0.898870i	$0.355611\pi$
$810$	−3.46410	−0.121716
$811$	45.1769	1.58638	0.793188	−	0.608977i	$-0.208420\pi$
$811$	45.1769	1.58638	0.793188	+	0.608977i	$0.208420\pi$
$812$	−6.00000	−0.210559
$813$	16.7846	0.588662
$814$	−8.92820	−0.312933
$815$	−13.8564	−0.485369
$816$	−3.46410	−0.121268
$817$	−4.28719	−0.149990
$818$	−25.3205	−0.885311
$819$	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	$0.533388\pi$
$822$	19.8564	0.692572
$823$	−0.784610	−0.0273498	−0.0136749	−	0.999906i	$-0.504353\pi$
$823$	−0.784610	−0.0273498	−0.0136749	+	0.999906i	$0.504353\pi$
$824$	6.53590	0.227689
$825$	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
$829$	−4.24871	−0.147564	−0.0737819	−	0.997274i	$-0.523507\pi$
$829$	−4.24871	−0.147564	−0.0737819	+	0.997274i	$0.523507\pi$
$830$	56.7846	1.97102
$831$	15.8564	0.550053
$832$	2.00000	0.0693375
$833$	−3.46410	−0.120024
$834$	6.53590	0.226320
$835$	17.5692	0.608008
$836$	−1.46410	−0.0506370
$837$	−1.46410	−0.0506068
$838$	36.0000	1.24360
$839$	−26.5359	−0.916121	−0.458060	−	0.888921i	$-0.651456\pi$
$839$	−26.5359	−0.916121	−0.458060	+	0.888921i	$0.651456\pi$
$840$	−3.46410	−0.119523
$841$	7.00000	0.241379
$842$	−17.7128	−0.610424
$843$	19.8564	0.683891
$844$	−24.7846	−0.853121
$845$	−31.1769	−1.07252
$846$	−2.53590	−0.0871860
$847$	1.00000	0.0343604
$848$	12.9282	0.443956
$849$	−6.53590	−0.224311
$850$	24.2487	0.831724
$851$	−61.8564	−2.12041
$852$	−12.0000	−0.411113
$853$	5.71281	0.195603	0.0978015	−	0.995206i	$-0.468819\pi$
$853$	5.71281	0.195603	0.0978015	+	0.995206i	$0.468819\pi$
$854$	−2.00000	−0.0684386
$855$	−5.07180	−0.173452
$856$	−6.92820	−0.236801
$857$	29.3205	1.00157	0.500785	−	0.865572i	$-0.333045\pi$
$857$	29.3205	1.00157	0.500785	+	0.865572i	$0.333045\pi$
$858$	−2.00000	−0.0682789
$859$	11.2154	0.382664	0.191332	−	0.981525i	$-0.438719\pi$
$859$	11.2154	0.382664	0.191332	+	0.981525i	$0.438719\pi$
$860$	10.1436	0.345894
$861$	−3.46410	−0.118056
$862$	5.07180	0.172746
$863$	3.21539	0.109453	0.0547266	−	0.998501i	$-0.482571\pi$
$863$	3.21539	0.109453	0.0547266	+	0.998501i	$0.482571\pi$
$864$	−1.00000	−0.0340207
$865$	44.7846	1.52272
$866$	−2.00000	−0.0679628
$867$	−5.00000	−0.169809
$868$	−1.46410	−0.0496948
$869$	2.92820	0.0993325
$870$	20.7846	0.704664
$871$	2.14359	0.0726329
$872$	11.8564	0.401509
$873$	2.00000	0.0676897
$874$	−10.1436	−0.343112
$875$	6.92820	0.234216
$876$	−7.46410	−0.252189
$877$	−46.0000	−1.55331	−0.776655	−	0.629926i	$-0.783085\pi$
$877$	−46.0000	−1.55331	−0.776655	+	0.629926i	$0.783085\pi$
$878$	−16.7846	−0.566453
$879$	−11.0718	−0.373442
$880$	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
$883$	−14.1436	−0.475970	−0.237985	−	0.971269i	$-0.576487\pi$
$883$	−14.1436	−0.475970	−0.237985	+	0.971269i	$0.576487\pi$
$884$	−6.92820	−0.233021
$885$	−24.0000	−0.806751
$886$	−20.7846	−0.698273
$887$	37.8564	1.27109	0.635547	−	0.772062i	$-0.280775\pi$
$887$	37.8564	1.27109	0.635547	+	0.772062i	$0.280775\pi$
$888$	−8.92820	−0.299611
$889$	2.92820	0.0982088
$890$	−44.7846	−1.50118
$891$	1.00000	0.0335013
$892$	12.3923	0.414925
$893$	−3.71281	−0.124245
$894$	6.00000	0.200670
$895$	72.0000	2.40669
$896$	−1.00000	−0.0334077
$897$	−13.8564	−0.462652
$898$	−7.85641	−0.262172
$899$	8.78461	0.292983
$900$	7.00000	0.233333
$901$	−44.7846	−1.49199
$902$	3.46410	0.115342
$903$	2.92820	0.0974445
$904$	19.8564	0.660414
$905$	−49.8564	−1.65728
$906$	16.0000	0.531564
$907$	1.07180	0.0355884	0.0177942	−	0.999842i	$-0.494336\pi$
$907$	1.07180	0.0355884	0.0177942	+	0.999842i	$0.494336\pi$
$908$	16.3923	0.543998
$909$	7.85641	0.260581
$910$	−6.92820	−0.229668
$911$	48.4974	1.60679	0.803396	−	0.595446i	$-0.203024\pi$
$911$	48.4974	1.60679	0.803396	+	0.595446i	$0.203024\pi$
$912$	−1.46410	−0.0484812
$913$	−16.3923	−0.542506
$914$	11.8564	0.392175
$915$	6.92820	0.229039
$916$	13.3205	0.440122
$917$	16.3923	0.541322
$918$	3.46410	0.114332
$919$	−5.85641	−0.193185	−0.0965925	−	0.995324i	$-0.530794\pi$
$919$	−5.85641	−0.193185	−0.0965925	+	0.995324i	$0.530794\pi$
$920$	24.0000	0.791257
$921$	17.4641	0.575462
$922$	6.00000	0.197599
$923$	−24.0000	−0.789970
$924$	1.00000	0.0328976
$925$	62.4974	2.05490
$926$	−8.00000	−0.262896
$927$	−6.53590	−0.214667
$928$	6.00000	0.196960
$929$	−28.6410	−0.939681	−0.469841	−	0.882751i	$-0.655689\pi$
$929$	−28.6410	−0.939681	−0.469841	+	0.882751i	$0.655689\pi$
$930$	5.07180	0.166311
$931$	−1.46410	−0.0479840
$932$	19.8564	0.650418
$933$	7.60770	0.249065
$934$	−39.7128	−1.29944
$935$	−12.0000	−0.392442
$936$	−2.00000	−0.0653720
$937$	6.39230	0.208827	0.104414	−	0.994534i	$-0.466703\pi$
$937$	6.39230	0.208827	0.104414	+	0.994534i	$0.466703\pi$
$938$	−1.07180	−0.0349954
$939$	−3.07180	−0.100244
$940$	8.78461	0.286522
$941$	−24.9282	−0.812636	−0.406318	−	0.913732i	$-0.633188\pi$
$941$	−24.9282	−0.812636	−0.406318	+	0.913732i	$0.633188\pi$
$942$	−18.3923	−0.599254
$943$	24.0000	0.781548
$944$	−6.92820	−0.225494
$945$	3.46410	0.112687
$946$	−2.92820	−0.0952041
$947$	22.1436	0.719570	0.359785	−	0.933035i	$-0.382850\pi$
$947$	22.1436	0.719570	0.359785	+	0.933035i	$0.382850\pi$
$948$	2.92820	0.0951036
$949$	−14.9282	−0.484590
$950$	10.2487	0.332512
$951$	−0.928203	−0.0300991
$952$	3.46410	0.112272
$953$	14.7846	0.478920	0.239460	−	0.970906i	$-0.423030\pi$
$953$	14.7846	0.478920	0.239460	+	0.970906i	$0.423030\pi$
$954$	−12.9282	−0.418566
$955$	−72.0000	−2.32987
$956$	−24.0000	−0.776215
$957$	−6.00000	−0.193952
$958$	−13.8564	−0.447680
$959$	−19.8564	−0.641197
$960$	3.46410	0.111803
$961$	−28.8564	−0.930852
$962$	−17.8564	−0.575714
$963$	6.92820	0.223258
$964$	30.3923	0.978870
$965$	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
$969$	5.07180	0.162930
$970$	−6.92820	−0.222451
$971$	39.7128	1.27444	0.637222	−	0.770680i	$-0.280083\pi$
$971$	39.7128	1.27444	0.637222	+	0.770680i	$0.280083\pi$
$972$	1.00000	0.0320750
$973$	−6.53590	−0.209531
$974$	0.784610	0.0251405
$975$	14.0000	0.448359
$976$	2.00000	0.0640184
$977$	35.5692	1.13796	0.568980	−	0.822351i	$-0.307338\pi$
$977$	35.5692	1.13796	0.568980	+	0.822351i	$0.307338\pi$
$978$	4.00000	0.127906
$979$	12.9282	0.413187
$980$	3.46410	0.110657
$981$	−11.8564	−0.378546
$982$	−25.8564	−0.825111
$983$	−11.3205	−0.361068	−0.180534	−	0.983569i	$-0.557783\pi$
$983$	−11.3205	−0.361068	−0.180534	+	0.983569i	$0.557783\pi$
$984$	3.46410	0.110432
$985$	62.3538	1.98676
$986$	−20.7846	−0.661917
$987$	2.53590	0.0807185
$988$	−2.92820	−0.0931586
$989$	−20.2872	−0.645095
$990$	−3.46410	−0.110096
$991$	−29.8564	−0.948420	−0.474210	−	0.880412i	$-0.657266\pi$
$991$	−29.8564	−0.948420	−0.474210	+	0.880412i	$0.657266\pi$
$992$	1.46410	0.0464853
$993$	−22.9282	−0.727605
$994$	12.0000	0.380617
$995$	−70.6410	−2.23947
$996$	−16.3923	−0.519410
$997$	−44.6410	−1.41380	−0.706898	−	0.707316i	$-0.749906\pi$
$997$	−44.6410	−1.41380	−0.706898	+	0.707316i	$0.749906\pi$
$998$	22.9282	0.725780
$999$	8.92820	0.282476

Twists

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

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

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.46410 q^{10} +1.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} +3.46410 q^{15} +1.00000 q^{16} -3.46410 q^{17} -1.00000 q^{18} -1.46410 q^{19} +3.46410 q^{20} +1.00000 q^{21} -1.00000 q^{22} -6.92820 q^{23} -1.00000 q^{24} +7.00000 q^{25} -2.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} -6.00000 q^{29} -3.46410 q^{30} -1.46410 q^{31} -1.00000 q^{32} +1.00000 q^{33} +3.46410 q^{34} +3.46410 q^{35} +1.00000 q^{36} +8.92820 q^{37} +1.46410 q^{38} +2.00000 q^{39} -3.46410 q^{40} -3.46410 q^{41} -1.00000 q^{42} +2.92820 q^{43} +1.00000 q^{44} +3.46410 q^{45} +6.92820 q^{46} +2.53590 q^{47} +1.00000 q^{48} +1.00000 q^{49} -7.00000 q^{50} -3.46410 q^{51} +2.00000 q^{52} +12.9282 q^{53} -1.00000 q^{54} +3.46410 q^{55} -1.00000 q^{56} -1.46410 q^{57} +6.00000 q^{58} -6.92820 q^{59} +3.46410 q^{60} +2.00000 q^{61} +1.46410 q^{62} +1.00000 q^{63} +1.00000 q^{64} +6.92820 q^{65} -1.00000 q^{66} +1.07180 q^{67} -3.46410 q^{68} -6.92820 q^{69} -3.46410 q^{70} -12.0000 q^{71} -1.00000 q^{72} -7.46410 q^{73} -8.92820 q^{74} +7.00000 q^{75} -1.46410 q^{76} +1.00000 q^{77} -2.00000 q^{78} +2.92820 q^{79} +3.46410 q^{80} +1.00000 q^{81} +3.46410 q^{82} -16.3923 q^{83} +1.00000 q^{84} -12.0000 q^{85} -2.92820 q^{86} -6.00000 q^{87} -1.00000 q^{88} +12.9282 q^{89} -3.46410 q^{90} +2.00000 q^{91} -6.92820 q^{92} -1.46410 q^{93} -2.53590 q^{94} -5.07180 q^{95} -1.00000 q^{96} +2.00000 q^{97} -1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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