LMFDB - Embedded newform 322.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(1,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("322.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.470683$ of defining polynomial
Character	$\chi$	$=$	322.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.24914 q^{3} +1.00000 q^{4} +4.24914 q^{5} -2.24914 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.05863 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.24914 q^{3} +1.00000 q^{4} +4.24914 q^{5} -2.24914 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.05863 q^{9} +4.24914 q^{10} -1.05863 q^{11} -2.24914 q^{12} +0.941367 q^{13} -1.00000 q^{14} -9.55691 q^{15} +1.00000 q^{16} +5.30777 q^{17} +2.05863 q^{18} +5.55691 q^{19} +4.24914 q^{20} +2.24914 q^{21} -1.05863 q^{22} -1.00000 q^{23} -2.24914 q^{24} +13.0552 q^{25} +0.941367 q^{26} +2.11727 q^{27} -1.00000 q^{28} -9.43965 q^{29} -9.55691 q^{30} -3.30777 q^{31} +1.00000 q^{32} +2.38101 q^{33} +5.30777 q^{34} -4.24914 q^{35} +2.05863 q^{36} -8.61555 q^{37} +5.55691 q^{38} -2.11727 q^{39} +4.24914 q^{40} -9.11383 q^{41} +2.24914 q^{42} -1.88273 q^{43} -1.05863 q^{44} +8.74742 q^{45} -1.00000 q^{46} +3.30777 q^{47} -2.24914 q^{48} +1.00000 q^{49} +13.0552 q^{50} -11.9379 q^{51} +0.941367 q^{52} +4.61555 q^{53} +2.11727 q^{54} -4.49828 q^{55} -1.00000 q^{56} -12.4983 q^{57} -9.43965 q^{58} -6.74742 q^{59} -9.55691 q^{60} -6.13187 q^{61} -3.30777 q^{62} -2.05863 q^{63} +1.00000 q^{64} +4.00000 q^{65} +2.38101 q^{66} +1.05863 q^{67} +5.30777 q^{68} +2.24914 q^{69} -4.24914 q^{70} -14.6155 q^{71} +2.05863 q^{72} -6.73281 q^{73} -8.61555 q^{74} -29.3630 q^{75} +5.55691 q^{76} +1.05863 q^{77} -2.11727 q^{78} +10.5535 q^{79} +4.24914 q^{80} -10.9379 q^{81} -9.11383 q^{82} +9.05863 q^{83} +2.24914 q^{84} +22.5535 q^{85} -1.88273 q^{86} +21.2311 q^{87} -1.05863 q^{88} +3.19051 q^{89} +8.74742 q^{90} -0.941367 q^{91} -1.00000 q^{92} +7.43965 q^{93} +3.30777 q^{94} +23.6121 q^{95} -2.24914 q^{96} -3.68879 q^{97} +1.00000 q^{98} -2.17934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} + 4 q^{10} - 4 q^{11} + 2 q^{12} + 2 q^{13} - 3 q^{14} - 12 q^{15} + 3 q^{16} + 8 q^{17} + 7 q^{18} + 4 q^{20} - 2 q^{21} - 4 q^{22} - 3 q^{23} + 2 q^{24} + 5 q^{25} + 2 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 12 q^{30} - 2 q^{31} + 3 q^{32} - 12 q^{33} + 8 q^{34} - 4 q^{35} + 7 q^{36} - 10 q^{37} - 8 q^{39} + 4 q^{40} + 6 q^{41} - 2 q^{42} - 4 q^{43} - 4 q^{44} - 3 q^{46} + 2 q^{47} + 2 q^{48} + 3 q^{49} + 5 q^{50} + 2 q^{52} - 2 q^{53} + 8 q^{54} + 4 q^{55} - 3 q^{56} - 20 q^{57} - 10 q^{58} + 6 q^{59} - 12 q^{60} - 8 q^{61} - 2 q^{62} - 7 q^{63} + 3 q^{64} + 12 q^{65} - 12 q^{66} + 4 q^{67} + 8 q^{68} - 2 q^{69} - 4 q^{70} - 28 q^{71} + 7 q^{72} - 6 q^{73} - 10 q^{74} - 46 q^{75} + 4 q^{77} - 8 q^{78} - 20 q^{79} + 4 q^{80} + 3 q^{81} + 6 q^{82} + 28 q^{83} - 2 q^{84} + 16 q^{85} - 4 q^{86} + 32 q^{87} - 4 q^{88} - 2 q^{91} - 3 q^{92} + 4 q^{93} + 2 q^{94} + 20 q^{95} + 2 q^{96} + 16 q^{97} + 3 q^{98} - 44 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 + 4 * q^10 - 4 * q^11 + 2 * q^12 + 2 * q^13 - 3 * q^14 - 12 * q^15 + 3 * q^16 + 8 * q^17 + 7 * q^18 + 4 * q^20 - 2 * q^21 - 4 * q^22 - 3 * q^23 + 2 * q^24 + 5 * q^25 + 2 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 12 * q^30 - 2 * q^31 + 3 * q^32 - 12 * q^33 + 8 * q^34 - 4 * q^35 + 7 * q^36 - 10 * q^37 - 8 * q^39 + 4 * q^40 + 6 * q^41 - 2 * q^42 - 4 * q^43 - 4 * q^44 - 3 * q^46 + 2 * q^47 + 2 * q^48 + 3 * q^49 + 5 * q^50 + 2 * q^52 - 2 * q^53 + 8 * q^54 + 4 * q^55 - 3 * q^56 - 20 * q^57 - 10 * q^58 + 6 * q^59 - 12 * q^60 - 8 * q^61 - 2 * q^62 - 7 * q^63 + 3 * q^64 + 12 * q^65 - 12 * q^66 + 4 * q^67 + 8 * q^68 - 2 * q^69 - 4 * q^70 - 28 * q^71 + 7 * q^72 - 6 * q^73 - 10 * q^74 - 46 * q^75 + 4 * q^77 - 8 * q^78 - 20 * q^79 + 4 * q^80 + 3 * q^81 + 6 * q^82 + 28 * q^83 - 2 * q^84 + 16 * q^85 - 4 * q^86 + 32 * q^87 - 4 * q^88 - 2 * q^91 - 3 * q^92 + 4 * q^93 + 2 * q^94 + 20 * q^95 + 2 * q^96 + 16 * q^97 + 3 * q^98 - 44 * 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
$3$	−2.24914	−1.29854	−0.649271	−	0.760557i	$-0.724926\pi$
$3$	−2.24914	−1.29854	−0.649271	+	0.760557i	$0.724926\pi$
$4$	1.00000	0.500000
$5$	4.24914	1.90027	0.950137	−	0.311834i	$-0.100943\pi$
$5$	4.24914	1.90027	0.950137	+	0.311834i	$0.100943\pi$
$6$	−2.24914	−0.918208
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	2.05863	0.686211
$10$	4.24914	1.34370
$11$	−1.05863	−0.319190	−0.159595	−	0.987183i	$-0.551019\pi$
$11$	−1.05863	−0.319190	−0.159595	+	0.987183i	$0.551019\pi$
$12$	−2.24914	−0.649271
$13$	0.941367	0.261088	0.130544	−	0.991443i	$-0.458328\pi$
$13$	0.941367	0.261088	0.130544	+	0.991443i	$0.458328\pi$
$14$	−1.00000	−0.267261
$15$	−9.55691	−2.46758
$16$	1.00000	0.250000
$17$	5.30777	1.28732	0.643662	−	0.765310i	$-0.277414\pi$
$17$	5.30777	1.28732	0.643662	+	0.765310i	$0.277414\pi$
$18$	2.05863	0.485224
$19$	5.55691	1.27484	0.637422	−	0.770515i	$-0.280001\pi$
$19$	5.55691	1.27484	0.637422	+	0.770515i	$0.280001\pi$
$20$	4.24914	0.950137
$21$	2.24914	0.490803
$22$	−1.05863	−0.225701
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.24914	−0.459104
$25$	13.0552	2.61104
$26$	0.941367	0.184617
$27$	2.11727	0.407468
$28$	−1.00000	−0.188982
$29$	−9.43965	−1.75290	−0.876449	−	0.481494i	$-0.840094\pi$
$29$	−9.43965	−1.75290	−0.876449	+	0.481494i	$0.840094\pi$
$30$	−9.55691	−1.74485
$31$	−3.30777	−0.594094	−0.297047	−	0.954863i	$-0.596002\pi$
$31$	−3.30777	−0.594094	−0.297047	+	0.954863i	$0.596002\pi$
$32$	1.00000	0.176777
$33$	2.38101	0.414481
$34$	5.30777	0.910276
$35$	−4.24914	−0.718236
$36$	2.05863	0.343106
$37$	−8.61555	−1.41639	−0.708194	−	0.706018i	$-0.750490\pi$
$37$	−8.61555	−1.41639	−0.708194	+	0.706018i	$0.750490\pi$
$38$	5.55691	0.901451
$39$	−2.11727	−0.339034
$40$	4.24914	0.671848
$41$	−9.11383	−1.42334	−0.711670	−	0.702513i	$-0.752061\pi$
$41$	−9.11383	−1.42334	−0.711670	+	0.702513i	$0.752061\pi$
$42$	2.24914	0.347050
$43$	−1.88273	−0.287114	−0.143557	−	0.989642i	$-0.545854\pi$
$43$	−1.88273	−0.287114	−0.143557	+	0.989642i	$0.545854\pi$
$44$	−1.05863	−0.159595
$45$	8.74742	1.30399
$46$	−1.00000	−0.147442
$47$	3.30777	0.482488	0.241244	−	0.970464i	$-0.422445\pi$
$47$	3.30777	0.482488	0.241244	+	0.970464i	$0.422445\pi$
$48$	−2.24914	−0.324635
$49$	1.00000	0.142857
$50$	13.0552	1.84628
$51$	−11.9379	−1.67164
$52$	0.941367	0.130544
$53$	4.61555	0.633994	0.316997	−	0.948427i	$-0.397325\pi$
$53$	4.61555	0.633994	0.316997	+	0.948427i	$0.397325\pi$
$54$	2.11727	0.288123
$55$	−4.49828	−0.606548
$56$	−1.00000	−0.133631
$57$	−12.4983	−1.65544
$58$	−9.43965	−1.23949
$59$	−6.74742	−0.878439	−0.439220	−	0.898380i	$-0.644745\pi$
$59$	−6.74742	−0.878439	−0.439220	+	0.898380i	$0.644745\pi$
$60$	−9.55691	−1.23379
$61$	−6.13187	−0.785106	−0.392553	−	0.919729i	$-0.628408\pi$
$61$	−6.13187	−0.785106	−0.392553	+	0.919729i	$0.628408\pi$
$62$	−3.30777	−0.420088
$63$	−2.05863	−0.259363
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	2.38101	0.293083
$67$	1.05863	0.129333	0.0646663	−	0.997907i	$-0.479402\pi$
$67$	1.05863	0.129333	0.0646663	+	0.997907i	$0.479402\pi$
$68$	5.30777	0.643662
$69$	2.24914	0.270765
$70$	−4.24914	−0.507869
$71$	−14.6155	−1.73455	−0.867273	−	0.497833i	$-0.834129\pi$
$71$	−14.6155	−1.73455	−0.867273	+	0.497833i	$0.834129\pi$
$72$	2.05863	0.242612
$73$	−6.73281	−0.788016	−0.394008	−	0.919107i	$-0.628912\pi$
$73$	−6.73281	−0.788016	−0.394008	+	0.919107i	$0.628912\pi$
$74$	−8.61555	−1.00154
$75$	−29.3630	−3.39054
$76$	5.55691	0.637422
$77$	1.05863	0.120642
$78$	−2.11727	−0.239733
$79$	10.5535	1.18736	0.593679	−	0.804702i	$-0.297675\pi$
$79$	10.5535	1.18736	0.593679	+	0.804702i	$0.297675\pi$
$80$	4.24914	0.475068
$81$	−10.9379	−1.21533
$82$	−9.11383	−1.00645
$83$	9.05863	0.994314	0.497157	−	0.867661i	$-0.334377\pi$
$83$	9.05863	0.994314	0.497157	+	0.867661i	$0.334377\pi$
$84$	2.24914	0.245401
$85$	22.5535	2.44627
$86$	−1.88273	−0.203020
$87$	21.2311	2.27621
$88$	−1.05863	−0.112851
$89$	3.19051	0.338193	0.169097	−	0.985599i	$-0.445915\pi$
$89$	3.19051	0.338193	0.169097	+	0.985599i	$0.445915\pi$
$90$	8.74742	0.922059
$91$	−0.941367	−0.0986821
$92$	−1.00000	−0.104257
$93$	7.43965	0.771456
$94$	3.30777	0.341171
$95$	23.6121	2.42255
$96$	−2.24914	−0.229552
$97$	−3.68879	−0.374540	−0.187270	−	0.982309i	$-0.559964\pi$
$97$	−3.68879	−0.374540	−0.187270	+	0.982309i	$0.559964\pi$
$98$	1.00000	0.101015
$99$	−2.17934	−0.219032
$100$	13.0552	1.30552
$101$	8.94137	0.889699	0.444850	−	0.895605i	$-0.353257\pi$
$101$	8.94137	0.889699	0.444850	+	0.895605i	$0.353257\pi$
$102$	−11.9379	−1.18203
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	0.941367	0.0923086
$105$	9.55691	0.932659
$106$	4.61555	0.448302
$107$	−0.234533	−0.0226731	−0.0113366	−	0.999936i	$-0.503609\pi$
$107$	−0.234533	−0.0226731	−0.0113366	+	0.999936i	$0.503609\pi$
$108$	2.11727	0.203734
$109$	−13.1138	−1.25608	−0.628038	−	0.778182i	$-0.716142\pi$
$109$	−13.1138	−1.25608	−0.628038	+	0.778182i	$0.716142\pi$
$110$	−4.49828	−0.428894
$111$	19.3776	1.83924
$112$	−1.00000	−0.0944911
$113$	14.4983	1.36388	0.681942	−	0.731406i	$-0.261136\pi$
$113$	14.4983	1.36388	0.681942	+	0.731406i	$0.261136\pi$
$114$	−12.4983	−1.17057
$115$	−4.24914	−0.396234
$116$	−9.43965	−0.876449
$117$	1.93793	0.179162
$118$	−6.74742	−0.621151
$119$	−5.30777	−0.486563
$120$	−9.55691	−0.872423
$121$	−9.87930	−0.898118
$122$	−6.13187	−0.555154
$123$	20.4983	1.84827
$124$	−3.30777	−0.297047
$125$	34.2277	3.06141
$126$	−2.05863	−0.183398
$127$	−3.50172	−0.310727	−0.155364	−	0.987857i	$-0.549655\pi$
$127$	−3.50172	−0.310727	−0.155364	+	0.987857i	$0.549655\pi$
$128$	1.00000	0.0883883
$129$	4.23453	0.372830
$130$	4.00000	0.350823
$131$	7.86813	0.687441	0.343721	−	0.939072i	$-0.388313\pi$
$131$	7.86813	0.687441	0.343721	+	0.939072i	$0.388313\pi$
$132$	2.38101	0.207241
$133$	−5.55691	−0.481846
$134$	1.05863	0.0914520
$135$	8.99656	0.774301
$136$	5.30777	0.455138
$137$	−15.7294	−1.34385	−0.671926	−	0.740619i	$-0.734533\pi$
$137$	−15.7294	−1.34385	−0.671926	+	0.740619i	$0.734533\pi$
$138$	2.24914	0.191460
$139$	8.13187	0.689737	0.344868	−	0.938651i	$-0.387924\pi$
$139$	8.13187	0.689737	0.344868	+	0.938651i	$0.387924\pi$
$140$	−4.24914	−0.359118
$141$	−7.43965	−0.626531
$142$	−14.6155	−1.22651
$143$	−0.996562	−0.0833367
$144$	2.05863	0.171553
$145$	−40.1104	−3.33099
$146$	−6.73281	−0.557212
$147$	−2.24914	−0.185506
$148$	−8.61555	−0.708194
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	−29.3630	−2.39748
$151$	−13.4948	−1.09819	−0.549097	−	0.835758i	$-0.685028\pi$
$151$	−13.4948	−1.09819	−0.549097	+	0.835758i	$0.685028\pi$
$152$	5.55691	0.450725
$153$	10.9268	0.883376
$154$	1.05863	0.0853071
$155$	−14.0552	−1.12894
$156$	−2.11727	−0.169517
$157$	12.2491	0.977588	0.488794	−	0.872399i	$-0.337437\pi$
$157$	12.2491	0.977588	0.488794	+	0.872399i	$0.337437\pi$
$158$	10.5535	0.839590
$159$	−10.3810	−0.823268
$160$	4.24914	0.335924
$161$	1.00000	0.0788110
$162$	−10.9379	−0.859365
$163$	3.61211	0.282922	0.141461	−	0.989944i	$-0.454820\pi$
$163$	3.61211	0.282922	0.141461	+	0.989944i	$0.454820\pi$
$164$	−9.11383	−0.711670
$165$	10.1173	0.787628
$166$	9.05863	0.703086
$167$	−11.3078	−0.875022	−0.437511	−	0.899213i	$-0.644140\pi$
$167$	−11.3078	−0.875022	−0.437511	+	0.899213i	$0.644140\pi$
$168$	2.24914	0.173525
$169$	−12.1138	−0.931833
$170$	22.5535	1.72977
$171$	11.4396	0.874812
$172$	−1.88273	−0.143557
$173$	23.5569	1.79100	0.895500	−	0.445062i	$-0.146819\pi$
$173$	23.5569	1.79100	0.895500	+	0.445062i	$0.146819\pi$
$174$	21.2311	1.60953
$175$	−13.0552	−0.986880
$176$	−1.05863	−0.0797975
$177$	15.1759	1.14069
$178$	3.19051	0.239139
$179$	18.8793	1.41110	0.705552	−	0.708658i	$-0.250699\pi$
$179$	18.8793	1.41110	0.705552	+	0.708658i	$0.250699\pi$
$180$	8.74742	0.651994
$181$	−11.3630	−0.844603	−0.422301	−	0.906455i	$-0.638778\pi$
$181$	−11.3630	−0.844603	−0.422301	+	0.906455i	$0.638778\pi$
$182$	−0.941367	−0.0697788
$183$	13.7914	1.01949
$184$	−1.00000	−0.0737210
$185$	−36.6087	−2.69152
$186$	7.43965	0.545501
$187$	−5.61899	−0.410901
$188$	3.30777	0.241244
$189$	−2.11727	−0.154008
$190$	23.6121	1.71300
$191$	22.2277	1.60834	0.804168	−	0.594402i	$-0.202611\pi$
$191$	22.2277	1.60834	0.804168	+	0.594402i	$0.202611\pi$
$192$	−2.24914	−0.162318
$193$	26.9966	1.94326	0.971628	−	0.236516i	$-0.0760057\pi$
$193$	26.9966	1.94326	0.971628	+	0.236516i	$0.0760057\pi$
$194$	−3.68879	−0.264840
$195$	−8.99656	−0.644257
$196$	1.00000	0.0714286
$197$	−2.99656	−0.213496	−0.106748	−	0.994286i	$-0.534044\pi$
$197$	−2.99656	−0.213496	−0.106748	+	0.994286i	$0.534044\pi$
$198$	−2.17934	−0.154879
$199$	−16.9966	−1.20485	−0.602427	−	0.798174i	$-0.705800\pi$
$199$	−16.9966	−1.20485	−0.602427	+	0.798174i	$0.705800\pi$
$200$	13.0552	0.923142
$201$	−2.38101	−0.167944
$202$	8.94137	0.629112
$203$	9.43965	0.662533
$204$	−11.9379	−0.835822
$205$	−38.7259	−2.70474
$206$	−8.00000	−0.557386
$207$	−2.05863	−0.143085
$208$	0.941367	0.0652720
$209$	−5.88273	−0.406917
$210$	9.55691	0.659490
$211$	23.1138	1.59122	0.795611	−	0.605808i	$-0.207150\pi$
$211$	23.1138	1.59122	0.795611	+	0.605808i	$0.207150\pi$
$212$	4.61555	0.316997
$213$	32.8724	2.25238
$214$	−0.234533	−0.0160323
$215$	−8.00000	−0.545595
$216$	2.11727	0.144062
$217$	3.30777	0.224546
$218$	−13.1138	−0.888181
$219$	15.1430	1.02327
$220$	−4.49828	−0.303274
$221$	4.99656	0.336105
$222$	19.3776	1.30054
$223$	−0.926759	−0.0620604	−0.0310302	−	0.999518i	$-0.509879\pi$
$223$	−0.926759	−0.0620604	−0.0310302	+	0.999518i	$0.509879\pi$
$224$	−1.00000	−0.0668153
$225$	26.8759	1.79172
$226$	14.4983	0.964411
$227$	−22.5535	−1.49693	−0.748463	−	0.663176i	$-0.769208\pi$
$227$	−22.5535	−1.49693	−0.748463	+	0.663176i	$0.769208\pi$
$228$	−12.4983	−0.827719
$229$	10.8647	0.717959	0.358979	−	0.933345i	$-0.383125\pi$
$229$	10.8647	0.717959	0.358979	+	0.933345i	$0.383125\pi$
$230$	−4.24914	−0.280180
$231$	−2.38101	−0.156659
$232$	−9.43965	−0.619743
$233$	10.8241	0.709110	0.354555	−	0.935035i	$-0.384632\pi$
$233$	10.8241	0.709110	0.354555	+	0.935035i	$0.384632\pi$
$234$	1.93793	0.126686
$235$	14.0552	0.916860
$236$	−6.74742	−0.439220
$237$	−23.7363	−1.54184
$238$	−5.30777	−0.344052
$239$	−8.26375	−0.534537	−0.267269	−	0.963622i	$-0.586121\pi$
$239$	−8.26375	−0.534537	−0.267269	+	0.963622i	$0.586121\pi$
$240$	−9.55691	−0.616896
$241$	−6.45769	−0.415977	−0.207988	−	0.978131i	$-0.566692\pi$
$241$	−6.45769	−0.415977	−0.207988	+	0.978131i	$0.566692\pi$
$242$	−9.87930	−0.635065
$243$	18.2491	1.17068
$244$	−6.13187	−0.392553
$245$	4.24914	0.271468
$246$	20.4983	1.30692
$247$	5.23109	0.332847
$248$	−3.30777	−0.210044
$249$	−20.3741	−1.29116
$250$	34.2277	2.16475
$251$	−20.4362	−1.28992	−0.644961	−	0.764215i	$-0.723126\pi$
$251$	−20.4362	−1.28992	−0.644961	+	0.764215i	$0.723126\pi$
$252$	−2.05863	−0.129682
$253$	1.05863	0.0665557
$254$	−3.50172	−0.219717
$255$	−50.7259	−3.17658
$256$	1.00000	0.0625000
$257$	16.8793	1.05290	0.526451	−	0.850206i	$-0.323522\pi$
$257$	16.8793	1.05290	0.526451	+	0.850206i	$0.323522\pi$
$258$	4.23453	0.263630
$259$	8.61555	0.535344
$260$	4.00000	0.248069
$261$	−19.4328	−1.20286
$262$	7.86813	0.486094
$263$	−2.55348	−0.157454	−0.0787270	−	0.996896i	$-0.525086\pi$
$263$	−2.55348	−0.157454	−0.0787270	+	0.996896i	$0.525086\pi$
$264$	2.38101	0.146541
$265$	19.6121	1.20476
$266$	−5.55691	−0.340716
$267$	−7.17590	−0.439158
$268$	1.05863	0.0646663
$269$	28.3189	1.72664	0.863318	−	0.504660i	$-0.168382\pi$
$269$	28.3189	1.72664	0.863318	+	0.504660i	$0.168382\pi$
$270$	8.99656	0.547513
$271$	−19.3078	−1.17286	−0.586432	−	0.809999i	$-0.699468\pi$
$271$	−19.3078	−1.17286	−0.586432	+	0.809999i	$0.699468\pi$
$272$	5.30777	0.321831
$273$	2.11727	0.128143
$274$	−15.7294	−0.950246
$275$	−13.8207	−0.833417
$276$	2.24914	0.135382
$277$	16.5535	0.994602	0.497301	−	0.867578i	$-0.334324\pi$
$277$	16.5535	0.994602	0.497301	+	0.867578i	$0.334324\pi$
$278$	8.13187	0.487717
$279$	−6.80949	−0.407674
$280$	−4.24914	−0.253935
$281$	12.3810	0.738589	0.369295	−	0.929312i	$-0.379599\pi$
$281$	12.3810	0.738589	0.369295	+	0.929312i	$0.379599\pi$
$282$	−7.43965	−0.443025
$283$	10.7880	0.641281	0.320640	−	0.947201i	$-0.396102\pi$
$283$	10.7880	0.641281	0.320640	+	0.947201i	$0.396102\pi$
$284$	−14.6155	−0.867273
$285$	−53.1070	−3.14578
$286$	−0.996562	−0.0589280
$287$	9.11383	0.537972
$288$	2.05863	0.121306
$289$	11.1725	0.657204
$290$	−40.1104	−2.35536
$291$	8.29660	0.486356
$292$	−6.73281	−0.394008
$293$	4.24914	0.248237	0.124119	−	0.992267i	$-0.460390\pi$
$293$	4.24914	0.248237	0.124119	+	0.992267i	$0.460390\pi$
$294$	−2.24914	−0.131173
$295$	−28.6707	−1.66928
$296$	−8.61555	−0.500769
$297$	−2.24141	−0.130060
$298$	−2.00000	−0.115857
$299$	−0.941367	−0.0544406
$300$	−29.3630	−1.69527
$301$	1.88273	0.108519
$302$	−13.4948	−0.776541
$303$	−20.1104	−1.15531
$304$	5.55691	0.318711
$305$	−26.0552	−1.49192
$306$	10.9268	0.624641
$307$	−5.75086	−0.328219	−0.164109	−	0.986442i	$-0.552475\pi$
$307$	−5.75086	−0.328219	−0.164109	+	0.986442i	$0.552475\pi$
$308$	1.05863	0.0603212
$309$	17.9931	1.02359
$310$	−14.0552	−0.798281
$311$	29.3009	1.66150	0.830751	−	0.556645i	$-0.187911\pi$
$311$	29.3009	1.66150	0.830751	+	0.556645i	$0.187911\pi$
$312$	−2.11727	−0.119867
$313$	−18.6922	−1.05655	−0.528274	−	0.849074i	$-0.677160\pi$
$313$	−18.6922	−1.05655	−0.528274	+	0.849074i	$0.677160\pi$
$314$	12.2491	0.691259
$315$	−8.74742	−0.492861
$316$	10.5535	0.593679
$317$	−5.20512	−0.292348	−0.146174	−	0.989259i	$-0.546696\pi$
$317$	−5.20512	−0.292348	−0.146174	+	0.989259i	$0.546696\pi$
$318$	−10.3810	−0.582138
$319$	9.99312	0.559508
$320$	4.24914	0.237534
$321$	0.527497	0.0294420
$322$	1.00000	0.0557278
$323$	29.4948	1.64114
$324$	−10.9379	−0.607663
$325$	12.2897	0.681711
$326$	3.61211	0.200056
$327$	29.4948	1.63107
$328$	−9.11383	−0.503227
$329$	−3.30777	−0.182363
$330$	10.1173	0.556937
$331$	−8.96735	−0.492890	−0.246445	−	0.969157i	$-0.579262\pi$
$331$	−8.96735	−0.492890	−0.246445	+	0.969157i	$0.579262\pi$
$332$	9.05863	0.497157
$333$	−17.7363	−0.971941
$334$	−11.3078	−0.618734
$335$	4.49828	0.245767
$336$	2.24914	0.122701
$337$	−17.1138	−0.932250	−0.466125	−	0.884719i	$-0.654350\pi$
$337$	−17.1138	−0.932250	−0.466125	+	0.884719i	$0.654350\pi$
$338$	−12.1138	−0.658905
$339$	−32.6087	−1.77106
$340$	22.5535	1.22313
$341$	3.50172	0.189629
$342$	11.4396	0.618585
$343$	−1.00000	−0.0539949
$344$	−1.88273	−0.101510
$345$	9.55691	0.514527
$346$	23.5569	1.26643
$347$	20.6087	1.10633	0.553166	−	0.833071i	$-0.313420\pi$
$347$	20.6087	1.10633	0.553166	+	0.833071i	$0.313420\pi$
$348$	21.2311	1.13811
$349$	−22.2017	−1.18843	−0.594214	−	0.804307i	$-0.702537\pi$
$349$	−22.2017	−1.18843	−0.594214	+	0.804307i	$0.702537\pi$
$350$	−13.0552	−0.697830
$351$	1.99312	0.106385
$352$	−1.05863	−0.0564253
$353$	−3.14992	−0.167653	−0.0838267	−	0.996480i	$-0.526714\pi$
$353$	−3.14992	−0.167653	−0.0838267	+	0.996480i	$0.526714\pi$
$354$	15.1759	0.806590
$355$	−62.1035	−3.29611
$356$	3.19051	0.169097
$357$	11.9379	0.631822
$358$	18.8793	0.997802
$359$	3.67418	0.193916	0.0969579	−	0.995288i	$-0.469089\pi$
$359$	3.67418	0.193916	0.0969579	+	0.995288i	$0.469089\pi$
$360$	8.74742	0.461030
$361$	11.8793	0.625226
$362$	−11.3630	−0.597224
$363$	22.2199	1.16624
$364$	−0.941367	−0.0493410
$365$	−28.6087	−1.49745
$366$	13.7914	0.720890
$367$	−16.7328	−0.873446	−0.436723	−	0.899596i	$-0.643861\pi$
$367$	−16.7328	−0.873446	−0.436723	+	0.899596i	$0.643861\pi$
$368$	−1.00000	−0.0521286
$369$	−18.7620	−0.976712
$370$	−36.6087	−1.90319
$371$	−4.61555	−0.239627
$372$	7.43965	0.385728
$373$	9.76547	0.505637	0.252818	−	0.967514i	$-0.418642\pi$
$373$	9.76547	0.505637	0.252818	+	0.967514i	$0.418642\pi$
$374$	−5.61899	−0.290551
$375$	−76.9828	−3.97538
$376$	3.30777	0.170585
$377$	−8.88617	−0.457661
$378$	−2.11727	−0.108900
$379$	−26.0552	−1.33837	−0.669183	−	0.743098i	$-0.733356\pi$
$379$	−26.0552	−1.33837	−0.669183	+	0.743098i	$0.733356\pi$
$380$	23.6121	1.21128
$381$	7.87586	0.403492
$382$	22.2277	1.13727
$383$	14.1465	0.722851	0.361426	−	0.932401i	$-0.382290\pi$
$383$	14.1465	0.722851	0.361426	+	0.932401i	$0.382290\pi$
$384$	−2.24914	−0.114776
$385$	4.49828	0.229254
$386$	26.9966	1.37409
$387$	−3.87586	−0.197021
$388$	−3.68879	−0.187270
$389$	−32.8793	−1.66705	−0.833523	−	0.552484i	$-0.813680\pi$
$389$	−32.8793	−1.66705	−0.833523	+	0.552484i	$0.813680\pi$
$390$	−8.99656	−0.455559
$391$	−5.30777	−0.268426
$392$	1.00000	0.0505076
$393$	−17.6965	−0.892671
$394$	−2.99656	−0.150965
$395$	44.8432	2.25631
$396$	−2.17934	−0.109516
$397$	7.16902	0.359803	0.179901	−	0.983685i	$-0.442422\pi$
$397$	7.16902	0.359803	0.179901	+	0.983685i	$0.442422\pi$
$398$	−16.9966	−0.851961
$399$	12.4983	0.625697
$400$	13.0552	0.652760
$401$	−21.3484	−1.06609	−0.533043	−	0.846088i	$-0.678952\pi$
$401$	−21.3484	−1.06609	−0.533043	+	0.846088i	$0.678952\pi$
$402$	−2.38101	−0.118754
$403$	−3.11383	−0.155111
$404$	8.94137	0.444850
$405$	−46.4768	−2.30945
$406$	9.43965	0.468482
$407$	9.12070	0.452097
$408$	−11.9379	−0.591016
$409$	3.38445	0.167350	0.0836752	−	0.996493i	$-0.473334\pi$
$409$	3.38445	0.167350	0.0836752	+	0.996493i	$0.473334\pi$
$410$	−38.7259	−1.91254
$411$	35.3776	1.74505
$412$	−8.00000	−0.394132
$413$	6.74742	0.332019
$414$	−2.05863	−0.101176
$415$	38.4914	1.88947
$416$	0.941367	0.0461543
$417$	−18.2897	−0.895652
$418$	−5.88273	−0.287734
$419$	7.20512	0.351993	0.175996	−	0.984391i	$-0.443685\pi$
$419$	7.20512	0.351993	0.175996	+	0.984391i	$0.443685\pi$
$420$	9.55691	0.466330
$421$	13.6121	0.663414	0.331707	−	0.943383i	$-0.392376\pi$
$421$	13.6121	0.663414	0.331707	+	0.943383i	$0.392376\pi$
$422$	23.1138	1.12516
$423$	6.80949	0.331089
$424$	4.61555	0.224151
$425$	69.2940	3.36125
$426$	32.8724	1.59267
$427$	6.13187	0.296742
$428$	−0.234533	−0.0113366
$429$	2.24141	0.108216
$430$	−8.00000	−0.385794
$431$	−33.9931	−1.63739	−0.818696	−	0.574228i	$-0.805302\pi$
$431$	−33.9931	−1.63739	−0.818696	+	0.574228i	$0.805302\pi$
$432$	2.11727	0.101867
$433$	18.5389	0.890921	0.445461	−	0.895302i	$-0.353040\pi$
$433$	18.5389	0.890921	0.445461	+	0.895302i	$0.353040\pi$
$434$	3.30777	0.158778
$435$	90.2139	4.32543
$436$	−13.1138	−0.628038
$437$	−5.55691	−0.265823
$438$	15.1430	0.723563
$439$	13.3009	0.634817	0.317409	−	0.948289i	$-0.397187\pi$
$439$	13.3009	0.634817	0.317409	+	0.948289i	$0.397187\pi$
$440$	−4.49828	−0.214447
$441$	2.05863	0.0980302
$442$	4.99656	0.237662
$443$	−16.1104	−0.765428	−0.382714	−	0.923867i	$-0.625010\pi$
$443$	−16.1104	−0.765428	−0.382714	+	0.923867i	$0.625010\pi$
$444$	19.3776	0.919619
$445$	13.5569	0.642659
$446$	−0.926759	−0.0438833
$447$	4.49828	0.212761
$448$	−1.00000	−0.0472456
$449$	−23.8207	−1.12417	−0.562083	−	0.827081i	$-0.690000\pi$
$449$	−23.8207	−1.12417	−0.562083	+	0.827081i	$0.690000\pi$
$450$	26.8759	1.26694
$451$	9.64820	0.454316
$452$	14.4983	0.681942
$453$	30.3518	1.42605
$454$	−22.5535	−1.05849
$455$	−4.00000	−0.187523
$456$	−12.4983	−0.585286
$457$	7.61899	0.356401	0.178201	−	0.983994i	$-0.442972\pi$
$457$	7.61899	0.356401	0.178201	+	0.983994i	$0.442972\pi$
$458$	10.8647	0.507674
$459$	11.2380	0.524544
$460$	−4.24914	−0.198117
$461$	−16.3189	−0.760049	−0.380024	−	0.924976i	$-0.624084\pi$
$461$	−16.3189	−0.760049	−0.380024	+	0.924976i	$0.624084\pi$
$462$	−2.38101	−0.110775
$463$	−31.2242	−1.45111	−0.725556	−	0.688163i	$-0.758417\pi$
$463$	−31.2242	−1.45111	−0.725556	+	0.688163i	$0.758417\pi$
$464$	−9.43965	−0.438225
$465$	31.6121	1.46598
$466$	10.8241	0.501417
$467$	2.44309	0.113053	0.0565263	−	0.998401i	$-0.481998\pi$
$467$	2.44309	0.113053	0.0565263	+	0.998401i	$0.481998\pi$
$468$	1.93793	0.0895808
$469$	−1.05863	−0.0488831
$470$	14.0552	0.648318
$471$	−27.5500	−1.26944
$472$	−6.74742	−0.310575
$473$	1.99312	0.0916440
$474$	−23.7363	−1.09024
$475$	72.5466	3.32867
$476$	−5.30777	−0.243281
$477$	9.50172	0.435054
$478$	−8.26375	−0.377975
$479$	23.8759	1.09092	0.545458	−	0.838138i	$-0.316356\pi$
$479$	23.8759	1.09092	0.545458	+	0.838138i	$0.316356\pi$
$480$	−9.55691	−0.436211
$481$	−8.11039	−0.369802
$482$	−6.45769	−0.294140
$483$	−2.24914	−0.102339
$484$	−9.87930	−0.449059
$485$	−15.6742	−0.711728
$486$	18.2491	0.827798
$487$	−23.2242	−1.05239	−0.526195	−	0.850364i	$-0.676382\pi$
$487$	−23.2242	−1.05239	−0.526195	+	0.850364i	$0.676382\pi$
$488$	−6.13187	−0.277577
$489$	−8.12414	−0.367386
$490$	4.24914	0.191957
$491$	27.2242	1.22861	0.614306	−	0.789068i	$-0.289436\pi$
$491$	27.2242	1.22861	0.614306	+	0.789068i	$0.289436\pi$
$492$	20.4983	0.924134
$493$	−50.1035	−2.25655
$494$	5.23109	0.235358
$495$	−9.26031	−0.416220
$496$	−3.30777	−0.148523
$497$	14.6155	0.655597
$498$	−20.3741	−0.912987
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	34.2277	1.53071
$501$	25.4328	1.13625
$502$	−20.4362	−0.912113
$503$	−20.1104	−0.896678	−0.448339	−	0.893864i	$-0.647984\pi$
$503$	−20.1104	−0.896678	−0.448339	+	0.893864i	$0.647984\pi$
$504$	−2.05863	−0.0916988
$505$	37.9931	1.69067
$506$	1.05863	0.0470620
$507$	27.2457	1.21002
$508$	−3.50172	−0.155364
$509$	35.6673	1.58093	0.790463	−	0.612510i	$-0.209840\pi$
$509$	35.6673	1.58093	0.790463	+	0.612510i	$0.209840\pi$
$510$	−50.7259	−2.24618
$511$	6.73281	0.297842
$512$	1.00000	0.0441942
$513$	11.7655	0.519458
$514$	16.8793	0.744514
$515$	−33.9931	−1.49792
$516$	4.23453	0.186415
$517$	−3.50172	−0.154005
$518$	8.61555	0.378545
$519$	−52.9828	−2.32569
$520$	4.00000	0.175412
$521$	15.3009	0.670345	0.335172	−	0.942157i	$-0.391205\pi$
$521$	15.3009	0.670345	0.335172	+	0.942157i	$0.391205\pi$
$522$	−19.4328	−0.850549
$523$	22.5535	0.986195	0.493097	−	0.869974i	$-0.335865\pi$
$523$	22.5535	0.986195	0.493097	+	0.869974i	$0.335865\pi$
$524$	7.86813	0.343721
$525$	29.3630	1.28151
$526$	−2.55348	−0.111337
$527$	−17.5569	−0.764791
$528$	2.38101	0.103620
$529$	1.00000	0.0434783
$530$	19.6121	0.851896
$531$	−13.8905	−0.602795
$532$	−5.55691	−0.240923
$533$	−8.57946	−0.371617
$534$	−7.17590	−0.310532
$535$	−0.996562	−0.0430851
$536$	1.05863	0.0457260
$537$	−42.4622	−1.83238
$538$	28.3189	1.22092
$539$	−1.05863	−0.0455986
$540$	8.99656	0.387150
$541$	−5.20512	−0.223785	−0.111893	−	0.993720i	$-0.535691\pi$
$541$	−5.20512	−0.223785	−0.111893	+	0.993720i	$0.535691\pi$
$542$	−19.3078	−0.829340
$543$	25.5569	1.09675
$544$	5.30777	0.227569
$545$	−55.7225	−2.38689
$546$	2.11727	0.0906106
$547$	−24.8432	−1.06222	−0.531109	−	0.847303i	$-0.678225\pi$
$547$	−24.8432	−1.06222	−0.531109	+	0.847303i	$0.678225\pi$
$548$	−15.7294	−0.671926
$549$	−12.6233	−0.538748
$550$	−13.8207	−0.589315
$551$	−52.4553	−2.23467
$552$	2.24914	0.0957298
$553$	−10.5535	−0.448779
$554$	16.5535	0.703290
$555$	82.3380	3.49506
$556$	8.13187	0.344868
$557$	25.4588	1.07872	0.539361	−	0.842075i	$-0.318666\pi$
$557$	25.4588	1.07872	0.539361	+	0.842075i	$0.318666\pi$
$558$	−6.80949	−0.288269
$559$	−1.77234	−0.0749621
$560$	−4.24914	−0.179559
$561$	12.6379	0.533572
$562$	12.3810	0.522262
$563$	−20.9053	−0.881052	−0.440526	−	0.897740i	$-0.645208\pi$
$563$	−20.9053	−0.881052	−0.440526	+	0.897740i	$0.645208\pi$
$564$	−7.43965	−0.313266
$565$	61.6052	2.59175
$566$	10.7880	0.453454
$567$	10.9379	0.459350
$568$	−14.6155	−0.613255
$569$	1.53093	0.0641801	0.0320901	−	0.999485i	$-0.489784\pi$
$569$	1.53093	0.0641801	0.0320901	+	0.999485i	$0.489784\pi$
$570$	−53.1070	−2.22441
$571$	5.12070	0.214295	0.107147	−	0.994243i	$-0.465828\pi$
$571$	5.12070	0.214295	0.107147	+	0.994243i	$0.465828\pi$
$572$	−0.996562	−0.0416684
$573$	−49.9931	−2.08849
$574$	9.11383	0.380404
$575$	−13.0552	−0.544439
$576$	2.05863	0.0857764
$577$	−19.4948	−0.811581	−0.405790	−	0.913966i	$-0.633004\pi$
$577$	−19.4948	−0.811581	−0.405790	+	0.913966i	$0.633004\pi$
$578$	11.1725	0.464713
$579$	−60.7191	−2.52340
$580$	−40.1104	−1.66549
$581$	−9.05863	−0.375815
$582$	8.29660	0.343905
$583$	−4.88617	−0.202365
$584$	−6.73281	−0.278606
$585$	8.23453	0.340456
$586$	4.24914	0.175530
$587$	39.3561	1.62440	0.812200	−	0.583379i	$-0.198270\pi$
$587$	39.3561	1.62440	0.812200	+	0.583379i	$0.198270\pi$
$588$	−2.24914	−0.0927530
$589$	−18.3810	−0.757377
$590$	−28.6707	−1.18036
$591$	6.73969	0.277234
$592$	−8.61555	−0.354097
$593$	7.88273	0.323705	0.161853	−	0.986815i	$-0.448253\pi$
$593$	7.88273	0.323705	0.161853	+	0.986815i	$0.448253\pi$
$594$	−2.24141	−0.0919661
$595$	−22.5535	−0.924602
$596$	−2.00000	−0.0819232
$597$	38.2277	1.56455
$598$	−0.941367	−0.0384954
$599$	38.1035	1.55687	0.778434	−	0.627727i	$-0.216015\pi$
$599$	38.1035	1.55687	0.778434	+	0.627727i	$0.216015\pi$
$600$	−29.3630	−1.19874
$601$	−14.2637	−0.581830	−0.290915	−	0.956749i	$-0.593960\pi$
$601$	−14.2637	−0.581830	−0.290915	+	0.956749i	$0.593960\pi$
$602$	1.88273	0.0767345
$603$	2.17934	0.0887495
$604$	−13.4948	−0.549097
$605$	−41.9785	−1.70667
$606$	−20.1104	−0.816929
$607$	48.8838	1.98413	0.992066	−	0.125719i	$-0.0401236\pi$
$607$	48.8838	1.98413	0.992066	+	0.125719i	$0.0401236\pi$
$608$	5.55691	0.225363
$609$	−21.2311	−0.860327
$610$	−26.0552	−1.05494
$611$	3.11383	0.125972
$612$	10.9268	0.441688
$613$	−9.34836	−0.377577	−0.188788	−	0.982018i	$-0.560456\pi$
$613$	−9.34836	−0.377577	−0.188788	+	0.982018i	$0.560456\pi$
$614$	−5.75086	−0.232086
$615$	87.1001	3.51221
$616$	1.05863	0.0426535
$617$	−19.7586	−0.795451	−0.397725	−	0.917504i	$-0.630200\pi$
$617$	−19.7586	−0.795451	−0.397725	+	0.917504i	$0.630200\pi$
$618$	17.9931	0.723790
$619$	26.4001	1.06111	0.530555	−	0.847650i	$-0.321983\pi$
$619$	26.4001	1.06111	0.530555	+	0.847650i	$0.321983\pi$
$620$	−14.0552	−0.564470
$621$	−2.11727	−0.0849630
$622$	29.3009	1.17486
$623$	−3.19051	−0.127825
$624$	−2.11727	−0.0847585
$625$	80.1621	3.20649
$626$	−18.6922	−0.747092
$627$	13.2311	0.528399
$628$	12.2491	0.488794
$629$	−45.7294	−1.82335
$630$	−8.74742	−0.348506
$631$	−27.2051	−1.08302	−0.541509	−	0.840695i	$-0.682147\pi$
$631$	−27.2051	−1.08302	−0.541509	+	0.840695i	$0.682147\pi$
$632$	10.5535	0.419795
$633$	−51.9862	−2.06627
$634$	−5.20512	−0.206722
$635$	−14.8793	−0.590467
$636$	−10.3810	−0.411634
$637$	0.941367	0.0372983
$638$	9.99312	0.395632
$639$	−30.0881	−1.19026
$640$	4.24914	0.167962
$641$	−7.77234	−0.306989	−0.153495	−	0.988149i	$-0.549053\pi$
$641$	−7.77234	−0.306989	−0.153495	+	0.988149i	$0.549053\pi$
$642$	0.527497	0.0208186
$643$	43.4396	1.71309	0.856546	−	0.516070i	$-0.172606\pi$
$643$	43.4396	1.71309	0.856546	+	0.516070i	$0.172606\pi$
$644$	1.00000	0.0394055
$645$	17.9931	0.708479
$646$	29.4948	1.16046
$647$	−13.3009	−0.522912	−0.261456	−	0.965215i	$-0.584203\pi$
$647$	−13.3009	−0.522912	−0.261456	+	0.965215i	$0.584203\pi$
$648$	−10.9379	−0.429682
$649$	7.14304	0.280389
$650$	12.2897	0.482043
$651$	−7.43965	−0.291583
$652$	3.61211	0.141461
$653$	−10.6516	−0.416831	−0.208415	−	0.978040i	$-0.566831\pi$
$653$	−10.6516	−0.416831	−0.208415	+	0.978040i	$0.566831\pi$
$654$	29.4948	1.15334
$655$	33.4328	1.30633
$656$	−9.11383	−0.355835
$657$	−13.8604	−0.540745
$658$	−3.30777	−0.128950
$659$	46.3380	1.80507	0.902537	−	0.430612i	$-0.141702\pi$
$659$	46.3380	1.80507	0.902537	+	0.430612i	$0.141702\pi$
$660$	10.1173	0.393814
$661$	10.8647	0.422587	0.211294	−	0.977423i	$-0.432232\pi$
$661$	10.8647	0.422587	0.211294	+	0.977423i	$0.432232\pi$
$662$	−8.96735	−0.348526
$663$	−11.2380	−0.436447
$664$	9.05863	0.351543
$665$	−23.6121	−0.915638
$666$	−17.7363	−0.687266
$667$	9.43965	0.365505
$668$	−11.3078	−0.437511
$669$	2.08441	0.0805880
$670$	4.49828	0.173784
$671$	6.49141	0.250598
$672$	2.24914	0.0867625
$673$	−1.93793	−0.0747017	−0.0373508	−	0.999302i	$-0.511892\pi$
$673$	−1.93793	−0.0747017	−0.0373508	+	0.999302i	$0.511892\pi$
$674$	−17.1138	−0.659200
$675$	27.6413	1.06392
$676$	−12.1138	−0.465916
$677$	36.9820	1.42133	0.710666	−	0.703530i	$-0.248394\pi$
$677$	36.9820	1.42133	0.710666	+	0.703530i	$0.248394\pi$
$678$	−32.6087	−1.25233
$679$	3.68879	0.141563
$680$	22.5535	0.864886
$681$	50.7259	1.94382
$682$	3.50172	0.134088
$683$	−9.88273	−0.378152	−0.189076	−	0.981962i	$-0.560549\pi$
$683$	−9.88273	−0.378152	−0.189076	+	0.981962i	$0.560549\pi$
$684$	11.4396	0.437406
$685$	−66.8363	−2.55368
$686$	−1.00000	−0.0381802
$687$	−24.4362	−0.932300
$688$	−1.88273	−0.0717785
$689$	4.34492	0.165528
$690$	9.55691	0.363826
$691$	8.78351	0.334141	0.167070	−	0.985945i	$-0.446569\pi$
$691$	8.78351	0.334141	0.167070	+	0.985945i	$0.446569\pi$
$692$	23.5569	0.895500
$693$	2.17934	0.0827862
$694$	20.6087	0.782294
$695$	34.5535	1.31069
$696$	21.2311	0.804763
$697$	−48.3741	−1.83230
$698$	−22.2017	−0.840346
$699$	−24.3449	−0.920810
$700$	−13.0552	−0.493440
$701$	−12.3810	−0.467624	−0.233812	−	0.972282i	$-0.575120\pi$
$701$	−12.3810	−0.467624	−0.233812	+	0.972282i	$0.575120\pi$
$702$	1.99312	0.0752256
$703$	−47.8759	−1.80567
$704$	−1.05863	−0.0398987
$705$	−31.6121	−1.19058
$706$	−3.14992	−0.118549
$707$	−8.94137	−0.336275
$708$	15.1759	0.570345
$709$	13.2672	0.498260	0.249130	−	0.968470i	$-0.419855\pi$
$709$	13.2672	0.498260	0.249130	+	0.968470i	$0.419855\pi$
$710$	−62.1035	−2.33070
$711$	21.7257	0.814779
$712$	3.19051	0.119569
$713$	3.30777	0.123877
$714$	11.9379	0.446766
$715$	−4.23453	−0.158363
$716$	18.8793	0.705552
$717$	18.5863	0.694119
$718$	3.67418	0.137119
$719$	7.15442	0.266815	0.133407	−	0.991061i	$-0.457408\pi$
$719$	7.15442	0.266815	0.133407	+	0.991061i	$0.457408\pi$
$720$	8.74742	0.325997
$721$	8.00000	0.297936
$722$	11.8793	0.442102
$723$	14.5243	0.540163
$724$	−11.3630	−0.422301
$725$	−123.236	−4.57689
$726$	22.2199	0.824659
$727$	−15.8759	−0.588803	−0.294401	−	0.955682i	$-0.595120\pi$
$727$	−15.8759	−0.588803	−0.294401	+	0.955682i	$0.595120\pi$
$728$	−0.941367	−0.0348894
$729$	−8.23109	−0.304855
$730$	−28.6087	−1.05885
$731$	−9.99312	−0.369609
$732$	13.7914	0.509747
$733$	33.0112	1.21930	0.609648	−	0.792672i	$-0.291311\pi$
$733$	33.0112	1.21930	0.609648	+	0.792672i	$0.291311\pi$
$734$	−16.7328	−0.617619
$735$	−9.55691	−0.352512
$736$	−1.00000	−0.0368605
$737$	−1.12070	−0.0412817
$738$	−18.7620	−0.690640
$739$	30.2569	1.11302	0.556509	−	0.830842i	$-0.312141\pi$
$739$	30.2569	1.11302	0.556509	+	0.830842i	$0.312141\pi$
$740$	−36.6087	−1.34576
$741$	−11.7655	−0.432215
$742$	−4.61555	−0.169442
$743$	8.09129	0.296841	0.148420	−	0.988924i	$-0.452581\pi$
$743$	8.09129	0.296841	0.148420	+	0.988924i	$0.452581\pi$
$744$	7.43965	0.272751
$745$	−8.49828	−0.311353
$746$	9.76547	0.357539
$747$	18.6484	0.682309
$748$	−5.61899	−0.205450
$749$	0.234533	0.00856964
$750$	−76.9828	−2.81101
$751$	7.43965	0.271477	0.135738	−	0.990745i	$-0.456659\pi$
$751$	7.43965	0.271477	0.135738	+	0.990745i	$0.456659\pi$
$752$	3.30777	0.120622
$753$	45.9639	1.67502
$754$	−8.88617	−0.323615
$755$	−57.3415	−2.08687
$756$	−2.11727	−0.0770042
$757$	18.2345	0.662745	0.331373	−	0.943500i	$-0.392488\pi$
$757$	18.2345	0.662745	0.331373	+	0.943500i	$0.392488\pi$
$758$	−26.0552	−0.946367
$759$	−2.38101	−0.0864254
$760$	23.6121	0.856501
$761$	43.0777	1.56157	0.780783	−	0.624802i	$-0.214820\pi$
$761$	43.0777	1.56157	0.780783	+	0.624802i	$0.214820\pi$
$762$	7.87586	0.285312
$763$	13.1138	0.474752
$764$	22.2277	0.804168
$765$	46.4293	1.67866
$766$	14.1465	0.511133
$767$	−6.35180	−0.229350
$768$	−2.24914	−0.0811589
$769$	12.8387	0.462976	0.231488	−	0.972838i	$-0.425641\pi$
$769$	12.8387	0.462976	0.231488	+	0.972838i	$0.425641\pi$
$770$	4.49828	0.162107
$771$	−37.9639	−1.36724
$772$	26.9966	0.971628
$773$	−14.8647	−0.534646	−0.267323	−	0.963607i	$-0.586139\pi$
$773$	−14.8647	−0.534646	−0.267323	+	0.963607i	$0.586139\pi$
$774$	−3.87586	−0.139315
$775$	−43.1836	−1.55120
$776$	−3.68879	−0.132420
$777$	−19.3776	−0.695167
$778$	−32.8793	−1.17878
$779$	−50.6448	−1.81454
$780$	−8.99656	−0.322129
$781$	15.4725	0.553650
$782$	−5.30777	−0.189806
$783$	−19.9862	−0.714250
$784$	1.00000	0.0357143
$785$	52.0483	1.85768
$786$	−17.6965	−0.631214
$787$	11.8275	0.421606	0.210803	−	0.977529i	$-0.432392\pi$
$787$	11.8275	0.421606	0.210803	+	0.977529i	$0.432392\pi$
$788$	−2.99656	−0.106748
$789$	5.74313	0.204461
$790$	44.8432	1.59545
$791$	−14.4983	−0.515500
$792$	−2.17934	−0.0774394
$793$	−5.77234	−0.204982
$794$	7.16902	0.254419
$795$	−44.1104	−1.56443
$796$	−16.9966	−0.602427
$797$	−35.3630	−1.25262	−0.626310	−	0.779574i	$-0.715436\pi$
$797$	−35.3630	−1.25262	−0.626310	+	0.779574i	$0.715436\pi$
$798$	12.4983	0.442434
$799$	17.5569	0.621119
$800$	13.0552	0.461571
$801$	6.56808	0.232072
$802$	−21.3484	−0.753837
$803$	7.12758	0.251527
$804$	−2.38101	−0.0839719
$805$	4.24914	0.149763
$806$	−3.11383	−0.109680
$807$	−63.6933	−2.24211
$808$	8.94137	0.314556
$809$	2.99656	0.105354	0.0526768	−	0.998612i	$-0.483225\pi$
$809$	2.99656	0.105354	0.0526768	+	0.998612i	$0.483225\pi$
$810$	−46.4768	−1.63303
$811$	2.63703	0.0925987	0.0462993	−	0.998928i	$-0.485257\pi$
$811$	2.63703	0.0925987	0.0462993	+	0.998928i	$0.485257\pi$
$812$	9.43965	0.331267
$813$	43.4259	1.52301
$814$	9.12070	0.319681
$815$	15.3484	0.537630
$816$	−11.9379	−0.417911
$817$	−10.4622	−0.366026
$818$	3.38445	0.118335
$819$	−1.93793	−0.0677167
$820$	−38.7259	−1.35237
$821$	−38.5466	−1.34529	−0.672643	−	0.739967i	$-0.734841\pi$
$821$	−38.5466	−1.34529	−0.672643	+	0.739967i	$0.734841\pi$
$822$	35.3776	1.23393
$823$	10.1984	0.355495	0.177748	−	0.984076i	$-0.443119\pi$
$823$	10.1984	0.355495	0.177748	+	0.984076i	$0.443119\pi$
$824$	−8.00000	−0.278693
$825$	31.0846	1.08223
$826$	6.74742	0.234773
$827$	20.5275	0.713811	0.356906	−	0.934140i	$-0.383832\pi$
$827$	20.5275	0.713811	0.356906	+	0.934140i	$0.383832\pi$
$828$	−2.05863	−0.0715424
$829$	−32.6639	−1.13446	−0.567231	−	0.823558i	$-0.691986\pi$
$829$	−32.6639	−1.13446	−0.567231	+	0.823558i	$0.691986\pi$
$830$	38.4914	1.33606
$831$	−37.2311	−1.29153
$832$	0.941367	0.0326360
$833$	5.30777	0.183903
$834$	−18.2897	−0.633321
$835$	−48.0483	−1.66278
$836$	−5.88273	−0.203459
$837$	−7.00344	−0.242074
$838$	7.20512	0.248897
$839$	45.4948	1.57066	0.785328	−	0.619080i	$-0.212494\pi$
$839$	45.4948	1.57066	0.785328	+	0.619080i	$0.212494\pi$
$840$	9.55691	0.329745
$841$	60.1070	2.07265
$842$	13.6121	0.469104
$843$	−27.8466	−0.959089
$844$	23.1138	0.795611
$845$	−51.4734	−1.77074
$846$	6.80949	0.234115
$847$	9.87930	0.339457
$848$	4.61555	0.158499
$849$	−24.2637	−0.832730
$850$	69.2940	2.37677
$851$	8.61555	0.295337
$852$	32.8724	1.12619
$853$	−2.64153	−0.0904442	−0.0452221	−	0.998977i	$-0.514400\pi$
$853$	−2.64153	−0.0904442	−0.0452221	+	0.998977i	$0.514400\pi$
$854$	6.13187	0.209828
$855$	48.6087	1.66238
$856$	−0.234533	−0.00801616
$857$	−32.9897	−1.12691	−0.563453	−	0.826148i	$-0.690527\pi$
$857$	−32.9897	−1.12691	−0.563453	+	0.826148i	$0.690527\pi$
$858$	2.24141	0.0765204
$859$	7.35609	0.250987	0.125493	−	0.992094i	$-0.459949\pi$
$859$	7.35609	0.250987	0.125493	+	0.992094i	$0.459949\pi$
$860$	−8.00000	−0.272798
$861$	−20.4983	−0.698580
$862$	−33.9931	−1.15781
$863$	6.61555	0.225196	0.112598	−	0.993641i	$-0.464083\pi$
$863$	6.61555	0.225196	0.112598	+	0.993641i	$0.464083\pi$
$864$	2.11727	0.0720309
$865$	100.097	3.40339
$866$	18.5389	0.629976
$867$	−25.1284	−0.853406
$868$	3.30777	0.112273
$869$	−11.1723	−0.378993
$870$	90.2139	3.05854
$871$	0.996562	0.0337672
$872$	−13.1138	−0.444090
$873$	−7.59386	−0.257013
$874$	−5.55691	−0.187965
$875$	−34.2277	−1.15711
$876$	15.1430	0.511636
$877$	−6.67074	−0.225255	−0.112627	−	0.993637i	$-0.535927\pi$
$877$	−6.67074	−0.225255	−0.112627	+	0.993637i	$0.535927\pi$
$878$	13.3009	0.448884
$879$	−9.55691	−0.322347
$880$	−4.49828	−0.151637
$881$	35.2717	1.18833	0.594167	−	0.804342i	$-0.297482\pi$
$881$	35.2717	1.18833	0.594167	+	0.804342i	$0.297482\pi$
$882$	2.05863	0.0693178
$883$	11.3484	0.381903	0.190951	−	0.981599i	$-0.438843\pi$
$883$	11.3484	0.381903	0.190951	+	0.981599i	$0.438843\pi$
$884$	4.99656	0.168053
$885$	64.4845	2.16762
$886$	−16.1104	−0.541239
$887$	51.1836	1.71858	0.859289	−	0.511490i	$-0.170906\pi$
$887$	51.1836	1.71858	0.859289	+	0.511490i	$0.170906\pi$
$888$	19.3776	0.650269
$889$	3.50172	0.117444
$890$	13.5569	0.454429
$891$	11.5793	0.387920
$892$	−0.926759	−0.0310302
$893$	18.3810	0.615097
$894$	4.49828	0.150445
$895$	80.2208	2.68148
$896$	−1.00000	−0.0334077
$897$	2.11727	0.0706935
$898$	−23.8207	−0.794906
$899$	31.2242	1.04139
$900$	26.8759	0.895862
$901$	24.4983	0.816156
$902$	9.64820	0.321250
$903$	−4.23453	−0.140916
$904$	14.4983	0.482206
$905$	−48.2829	−1.60498
$906$	30.3518	1.00837
$907$	−45.2173	−1.50142	−0.750709	−	0.660633i	$-0.770288\pi$
$907$	−45.2173	−1.50142	−0.750709	+	0.660633i	$0.770288\pi$
$908$	−22.5535	−0.748463
$909$	18.4070	0.610521
$910$	−4.00000	−0.132599
$911$	44.5466	1.47589	0.737947	−	0.674858i	$-0.235795\pi$
$911$	44.5466	1.47589	0.737947	+	0.674858i	$0.235795\pi$
$912$	−12.4983	−0.413859
$913$	−9.58977	−0.317375
$914$	7.61899	0.252014
$915$	58.6018	1.93732
$916$	10.8647	0.358979
$917$	−7.86813	−0.259828
$918$	11.2380	0.370908
$919$	−47.7846	−1.57627	−0.788134	−	0.615504i	$-0.788953\pi$
$919$	−47.7846	−1.57627	−0.788134	+	0.615504i	$0.788953\pi$
$920$	−4.24914	−0.140090
$921$	12.9345	0.426206
$922$	−16.3189	−0.537436
$923$	−13.7586	−0.452870
$924$	−2.38101	−0.0783296
$925$	−112.478	−3.69824
$926$	−31.2242	−1.02609
$927$	−16.4691	−0.540915
$928$	−9.43965	−0.309872
$929$	−14.0000	−0.459325	−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000	−0.459325	−0.229663	+	0.973270i	$0.573762\pi$
$930$	31.6121	1.03660
$931$	5.55691	0.182121
$932$	10.8241	0.354555
$933$	−65.9018	−2.15753
$934$	2.44309	0.0799402
$935$	−23.8759	−0.780824
$936$	1.93793	0.0633432
$937$	7.81293	0.255237	0.127619	−	0.991823i	$-0.459267\pi$
$937$	7.81293	0.255237	0.127619	+	0.991823i	$0.459267\pi$
$938$	−1.05863	−0.0345656
$939$	42.0414	1.37197
$940$	14.0552	0.458430
$941$	−4.48367	−0.146164	−0.0730818	−	0.997326i	$-0.523283\pi$
$941$	−4.48367	−0.146164	−0.0730818	+	0.997326i	$0.523283\pi$
$942$	−27.5500	−0.897629
$943$	9.11383	0.296787
$944$	−6.74742	−0.219610
$945$	−8.99656	−0.292658
$946$	1.99312	0.0648021
$947$	−21.7294	−0.706110	−0.353055	−	0.935603i	$-0.614857\pi$
$947$	−21.7294	−0.706110	−0.353055	+	0.935603i	$0.614857\pi$
$948$	−23.7363	−0.770918
$949$	−6.33805	−0.205742
$950$	72.5466	2.35372
$951$	11.7070	0.379627
$952$	−5.30777	−0.172026
$953$	31.8827	1.03278	0.516392	−	0.856353i	$-0.327275\pi$
$953$	31.8827	1.03278	0.516392	+	0.856353i	$0.327275\pi$
$954$	9.50172	0.307630
$955$	94.4484	3.05628
$956$	−8.26375	−0.267269
$957$	−22.4759	−0.726544
$958$	23.8759	0.771394
$959$	15.7294	0.507928
$960$	−9.55691	−0.308448
$961$	−20.0586	−0.647053
$962$	−8.11039	−0.261489
$963$	−0.482817	−0.0155585
$964$	−6.45769	−0.207988
$965$	114.712	3.69272
$966$	−2.24914	−0.0723649
$967$	9.12070	0.293302	0.146651	−	0.989188i	$-0.453151\pi$
$967$	9.12070	0.293302	0.146651	+	0.989188i	$0.453151\pi$
$968$	−9.87930	−0.317533
$969$	−66.3380	−2.13109
$970$	−15.6742	−0.503268
$971$	−39.1621	−1.25677	−0.628387	−	0.777901i	$-0.716284\pi$
$971$	−39.1621	−1.25677	−0.628387	+	0.777901i	$0.716284\pi$
$972$	18.2491	0.585341
$973$	−8.13187	−0.260696
$974$	−23.2242	−0.744152
$975$	−27.6413	−0.885231
$976$	−6.13187	−0.196277
$977$	−3.14992	−0.100775	−0.0503874	−	0.998730i	$-0.516046\pi$
$977$	−3.14992	−0.100775	−0.0503874	+	0.998730i	$0.516046\pi$
$978$	−8.12414	−0.259781
$979$	−3.37758	−0.107948
$980$	4.24914	0.135734
$981$	−26.9966	−0.861934
$982$	27.2242	0.868760
$983$	6.49141	0.207044	0.103522	−	0.994627i	$-0.466989\pi$
$983$	6.49141	0.207044	0.103522	+	0.994627i	$0.466989\pi$
$984$	20.4983	0.653461
$985$	−12.7328	−0.405701
$986$	−50.1035	−1.59562
$987$	7.43965	0.236807
$988$	5.23109	0.166423
$989$	1.88273	0.0598674
$990$	−9.26031	−0.294312
$991$	−34.9085	−1.10891	−0.554453	−	0.832215i	$-0.687072\pi$
$991$	−34.9085	−1.10891	−0.554453	+	0.832215i	$0.687072\pi$
$992$	−3.30777	−0.105022
$993$	20.1688	0.640038
$994$	14.6155	0.463577
$995$	−72.2208	−2.28955
$996$	−20.3741	−0.645579
$997$	37.7846	1.19665	0.598325	−	0.801254i	$-0.295833\pi$
$997$	37.7846	1.19665	0.598325	+	0.801254i	$0.295833\pi$
$998$	4.00000	0.126618
$999$	−18.2414	−0.577133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.a.g.1.1	✓	3
3.2	odd	2		2898.2.a.be.1.1		3
4.3	odd	2		2576.2.a.w.1.3		3
5.4	even	2		8050.2.a.bh.1.3		3
7.6	odd	2		2254.2.a.p.1.3		3
23.22	odd	2		7406.2.a.x.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.a.g.1.1	✓	3	1.1	even	1	trivial
2254.2.a.p.1.3		3	7.6	odd	2
2576.2.a.w.1.3		3	4.3	odd	2
2898.2.a.be.1.1		3	3.2	odd	2
7406.2.a.x.1.1		3	23.22	odd	2
8050.2.a.bh.1.3		3	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.24914 q^{3} +1.00000 q^{4} +4.24914 q^{5} -2.24914 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.05863 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.24914 q^{3} +1.00000 q^{4} +4.24914 q^{5} -2.24914 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.05863 q^{9} +4.24914 q^{10} -1.05863 q^{11} -2.24914 q^{12} +0.941367 q^{13} -1.00000 q^{14} -9.55691 q^{15} +1.00000 q^{16} +5.30777 q^{17} +2.05863 q^{18} +5.55691 q^{19} +4.24914 q^{20} +2.24914 q^{21} -1.05863 q^{22} -1.00000 q^{23} -2.24914 q^{24} +13.0552 q^{25} +0.941367 q^{26} +2.11727 q^{27} -1.00000 q^{28} -9.43965 q^{29} -9.55691 q^{30} -3.30777 q^{31} +1.00000 q^{32} +2.38101 q^{33} +5.30777 q^{34} -4.24914 q^{35} +2.05863 q^{36} -8.61555 q^{37} +5.55691 q^{38} -2.11727 q^{39} +4.24914 q^{40} -9.11383 q^{41} +2.24914 q^{42} -1.88273 q^{43} -1.05863 q^{44} +8.74742 q^{45} -1.00000 q^{46} +3.30777 q^{47} -2.24914 q^{48} +1.00000 q^{49} +13.0552 q^{50} -11.9379 q^{51} +0.941367 q^{52} +4.61555 q^{53} +2.11727 q^{54} -4.49828 q^{55} -1.00000 q^{56} -12.4983 q^{57} -9.43965 q^{58} -6.74742 q^{59} -9.55691 q^{60} -6.13187 q^{61} -3.30777 q^{62} -2.05863 q^{63} +1.00000 q^{64} +4.00000 q^{65} +2.38101 q^{66} +1.05863 q^{67} +5.30777 q^{68} +2.24914 q^{69} -4.24914 q^{70} -14.6155 q^{71} +2.05863 q^{72} -6.73281 q^{73} -8.61555 q^{74} -29.3630 q^{75} +5.55691 q^{76} +1.05863 q^{77} -2.11727 q^{78} +10.5535 q^{79} +4.24914 q^{80} -10.9379 q^{81} -9.11383 q^{82} +9.05863 q^{83} +2.24914 q^{84} +22.5535 q^{85} -1.88273 q^{86} +21.2311 q^{87} -1.05863 q^{88} +3.19051 q^{89} +8.74742 q^{90} -0.941367 q^{91} -1.00000 q^{92} +7.43965 q^{93} +3.30777 q^{94} +23.6121 q^{95} -2.24914 q^{96} -3.68879 q^{97} +1.00000 q^{98} -2.17934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 4 q^{5} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 7 q^{9} + 4 q^{10} - 4 q^{11} + 2 q^{12} + 2 q^{13} - 3 q^{14} - 12 q^{15} + 3 q^{16} + 8 q^{17} + 7 q^{18} + 4 q^{20} - 2 q^{21} - 4 q^{22} - 3 q^{23} + 2 q^{24} + 5 q^{25} + 2 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 12 q^{30} - 2 q^{31} + 3 q^{32} - 12 q^{33} + 8 q^{34} - 4 q^{35} + 7 q^{36} - 10 q^{37} - 8 q^{39} + 4 q^{40} + 6 q^{41} - 2 q^{42} - 4 q^{43} - 4 q^{44} - 3 q^{46} + 2 q^{47} + 2 q^{48} + 3 q^{49} + 5 q^{50} + 2 q^{52} - 2 q^{53} + 8 q^{54} + 4 q^{55} - 3 q^{56} - 20 q^{57} - 10 q^{58} + 6 q^{59} - 12 q^{60} - 8 q^{61} - 2 q^{62} - 7 q^{63} + 3 q^{64} + 12 q^{65} - 12 q^{66} + 4 q^{67} + 8 q^{68} - 2 q^{69} - 4 q^{70} - 28 q^{71} + 7 q^{72} - 6 q^{73} - 10 q^{74} - 46 q^{75} + 4 q^{77} - 8 q^{78} - 20 q^{79} + 4 q^{80} + 3 q^{81} + 6 q^{82} + 28 q^{83} - 2 q^{84} + 16 q^{85} - 4 q^{86} + 32 q^{87} - 4 q^{88} - 2 q^{91} - 3 q^{92} + 4 q^{93} + 2 q^{94} + 20 q^{95} + 2 q^{96} + 16 q^{97} + 3 q^{98} - 44 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 4 * q^5 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 7 * q^9 + 4 * q^10 - 4 * q^11 + 2 * q^12 + 2 * q^13 - 3 * q^14 - 12 * q^15 + 3 * q^16 + 8 * q^17 + 7 * q^18 + 4 * q^20 - 2 * q^21 - 4 * q^22 - 3 * q^23 + 2 * q^24 + 5 * q^25 + 2 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 12 * q^30 - 2 * q^31 + 3 * q^32 - 12 * q^33 + 8 * q^34 - 4 * q^35 + 7 * q^36 - 10 * q^37 - 8 * q^39 + 4 * q^40 + 6 * q^41 - 2 * q^42 - 4 * q^43 - 4 * q^44 - 3 * q^46 + 2 * q^47 + 2 * q^48 + 3 * q^49 + 5 * q^50 + 2 * q^52 - 2 * q^53 + 8 * q^54 + 4 * q^55 - 3 * q^56 - 20 * q^57 - 10 * q^58 + 6 * q^59 - 12 * q^60 - 8 * q^61 - 2 * q^62 - 7 * q^63 + 3 * q^64 + 12 * q^65 - 12 * q^66 + 4 * q^67 + 8 * q^68 - 2 * q^69 - 4 * q^70 - 28 * q^71 + 7 * q^72 - 6 * q^73 - 10 * q^74 - 46 * q^75 + 4 * q^77 - 8 * q^78 - 20 * q^79 + 4 * q^80 + 3 * q^81 + 6 * q^82 + 28 * q^83 - 2 * q^84 + 16 * q^85 - 4 * q^86 + 32 * q^87 - 4 * q^88 - 2 * q^91 - 3 * q^92 + 4 * q^93 + 2 * q^94 + 20 * q^95 + 2 * q^96 + 16 * q^97 + 3 * q^98 - 44 * q^99

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