LMFDB - Embedded newform 54.2.e.b.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,2,Mod(7,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("54.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	54.e (of order $9$, degree $6$, minimal)

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:	no
Analytic conductor:	$0.431192170915$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			13.1
Root			$0.500000 + 2.42499i$ of defining polynomial
Character	$\chi$	$=$	54.13
Dual form			54.2.e.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(0.140451 - 1.72635i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.42692 + 2.03643i) q^{5} +(1.72451 - 0.161460i) q^{6} +(-3.46344 - 1.26059i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.96055 - 0.484935i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(0.140451 - 1.72635i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.42692 + 2.03643i) q^{5} +(1.72451 - 0.161460i) q^{6} +(-3.46344 - 1.26059i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.96055 - 0.484935i) q^{9} +(-1.58406 + 2.74367i) q^{10} +(-1.75046 + 1.46881i) q^{11} +(0.458464 + 1.67027i) q^{12} +(0.538357 - 3.05317i) q^{13} +(0.640018 - 3.62972i) q^{14} +(3.85644 - 3.90368i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.862878 + 1.49455i) q^{17} +(-0.0365258 - 2.99978i) q^{18} +(1.69740 + 2.93998i) q^{19} +(-2.97705 - 1.08356i) q^{20} +(-2.66266 + 5.80205i) q^{21} +(-1.75046 - 1.46881i) q^{22} +(3.15087 - 1.14682i) q^{23} +(-1.56529 + 0.741539i) q^{24} +(0.874658 + 4.96043i) q^{25} +3.10027 q^{26} +(-1.25298 + 5.04282i) q^{27} +3.68572 q^{28} +(-0.101661 - 0.576550i) q^{29} +(4.51404 + 3.11998i) q^{30} +(4.35827 - 1.58628i) q^{31} +(0.766044 + 0.642788i) q^{32} +(2.28983 + 3.22820i) q^{33} +(-1.62168 - 0.590243i) q^{34} +(-5.83839 - 10.1124i) q^{35} +(2.94786 - 0.556877i) q^{36} +(3.65360 - 6.32822i) q^{37} +(-2.60057 + 2.18213i) q^{38} +(-5.19523 - 1.35821i) q^{39} +(0.550137 - 3.11998i) q^{40} +(-1.22952 + 6.97295i) q^{41} +(-6.17627 - 1.61469i) q^{42} +(1.27004 - 1.06569i) q^{43} +(1.14253 - 1.97893i) q^{44} +(-6.19747 - 7.20583i) q^{45} +(1.67654 + 2.90386i) q^{46} +(3.61968 + 1.31746i) q^{47} +(-1.00208 - 1.41274i) q^{48} +(5.04404 + 4.23245i) q^{49} +(-4.73319 + 1.72274i) q^{50} +(2.45892 + 1.69954i) q^{51} +(0.538357 + 3.05317i) q^{52} -2.58267 q^{53} +(-5.18379 - 0.358266i) q^{54} -7.23936 q^{55} +(0.640018 + 3.62972i) q^{56} +(5.31383 - 2.51737i) q^{57} +(0.550137 - 0.200234i) q^{58} +(-7.40243 - 6.21138i) q^{59} +(-2.28873 + 4.98724i) q^{60} +(-12.3018 - 4.47750i) q^{61} +(2.31899 + 4.01660i) q^{62} +(9.64238 + 5.41158i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(7.52411 - 6.31348i) q^{65} +(-2.78154 + 2.81561i) q^{66} +(-1.49490 + 8.47798i) q^{67} +(0.299674 - 1.69954i) q^{68} +(-1.53727 - 5.60057i) q^{69} +(8.94493 - 7.50569i) q^{70} +(-0.993732 + 1.72119i) q^{71} +(1.06031 + 2.80638i) q^{72} +(-5.32371 - 9.22094i) q^{73} +(6.86652 + 2.49921i) q^{74} +(8.68627 - 0.813264i) q^{75} +(-2.60057 - 2.18213i) q^{76} +(7.91420 - 2.88053i) q^{77} +(0.435437 - 5.35215i) q^{78} +(2.44726 + 13.8791i) q^{79} +3.16812 q^{80} +(8.52968 + 2.87135i) q^{81} -7.08052 q^{82} +(-0.538035 - 3.05135i) q^{83} +(0.517664 - 6.36283i) q^{84} +(-5.13767 + 1.86996i) q^{85} +(1.27004 + 1.06569i) q^{86} +(-1.00960 + 0.0945255i) q^{87} +(2.14726 + 0.781539i) q^{88} +(8.67300 + 15.0221i) q^{89} +(6.02018 - 7.35459i) q^{90} +(-5.71337 + 9.89585i) q^{91} +(-2.56861 + 2.15532i) q^{92} +(-2.12635 - 7.74668i) q^{93} +(-0.668890 + 3.79346i) q^{94} +(-1.86760 + 10.5917i) q^{95} +(1.21727 - 1.23218i) q^{96} +(7.04084 - 5.90797i) q^{97} +(-3.29226 + 5.70237i) q^{98} +(5.89461 - 3.49963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9}+O(q^{10}) $ 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9} - 3 q^{10} - 12 q^{11} - 3 q^{12} + 12 q^{13} - 3 q^{14} - 18 q^{15} - 6 q^{17} + 6 q^{18} - 9 q^{19} + 6 q^{20} + 24 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{25} + 18 q^{26} + 12 q^{28} + 15 q^{29} + 27 q^{30} + 36 q^{33} - 15 q^{34} + 3 q^{35} - 3 q^{36} - 15 q^{37} + 3 q^{38} - 42 q^{39} - 3 q^{40} - 12 q^{41} - 15 q^{42} + 9 q^{43} - 3 q^{44} + 18 q^{45} + 3 q^{46} - 9 q^{47} + 3 q^{48} - 39 q^{49} - 27 q^{50} - 27 q^{51} + 12 q^{52} - 12 q^{53} - 36 q^{54} + 18 q^{55} - 3 q^{56} + 18 q^{57} - 3 q^{58} + 12 q^{59} - 18 q^{60} - 36 q^{61} - 12 q^{62} + 3 q^{63} - 6 q^{64} - 15 q^{65} - 18 q^{66} + 36 q^{67} + 3 q^{68} + 18 q^{69} + 39 q^{70} + 12 q^{71} + 24 q^{72} - 21 q^{73} + 33 q^{74} + 30 q^{75} + 3 q^{76} + 3 q^{77} + 18 q^{78} + 39 q^{79} + 6 q^{80} + 6 q^{82} + 18 q^{83} - 9 q^{84} + 45 q^{85} + 9 q^{86} + 27 q^{87} + 6 q^{88} + 12 q^{89} + 27 q^{90} - 6 q^{91} - 6 q^{92} - 33 q^{93} + 36 q^{94} - 15 q^{95} + 6 q^{96} + 39 q^{97} - 12 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9 - 3 * q^10 - 12 * q^11 - 3 * q^12 + 12 * q^13 - 3 * q^14 - 18 * q^15 - 6 * q^17 + 6 * q^18 - 9 * q^19 + 6 * q^20 + 24 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^25 + 18 * q^26 + 12 * q^28 + 15 * q^29 + 27 * q^30 + 36 * q^33 - 15 * q^34 + 3 * q^35 - 3 * q^36 - 15 * q^37 + 3 * q^38 - 42 * q^39 - 3 * q^40 - 12 * q^41 - 15 * q^42 + 9 * q^43 - 3 * q^44 + 18 * q^45 + 3 * q^46 - 9 * q^47 + 3 * q^48 - 39 * q^49 - 27 * q^50 - 27 * q^51 + 12 * q^52 - 12 * q^53 - 36 * q^54 + 18 * q^55 - 3 * q^56 + 18 * q^57 - 3 * q^58 + 12 * q^59 - 18 * q^60 - 36 * q^61 - 12 * q^62 + 3 * q^63 - 6 * q^64 - 15 * q^65 - 18 * q^66 + 36 * q^67 + 3 * q^68 + 18 * q^69 + 39 * q^70 + 12 * q^71 + 24 * q^72 - 21 * q^73 + 33 * q^74 + 30 * q^75 + 3 * q^76 + 3 * q^77 + 18 * q^78 + 39 * q^79 + 6 * q^80 + 6 * q^82 + 18 * q^83 - 9 * q^84 + 45 * q^85 + 9 * q^86 + 27 * q^87 + 6 * q^88 + 12 * q^89 + 27 * q^90 - 6 * q^91 - 6 * q^92 - 33 * q^93 + 36 * q^94 - 15 * q^95 + 6 * q^96 + 39 * q^97 - 12 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	0.140451	−	1.72635i	0.0810896	−	0.996707i
$3$	0.140451	−	1.72635i	0.0810896	−	0.996707i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	2.42692	+	2.03643i	1.08535	+	0.910717i	0.996354	−	0.0853149i	$-0.0271896\pi$
$5$	2.42692	+	2.03643i	1.08535	+	0.910717i	0.0889963	+	0.996032i	$0.471634\pi$
$6$	1.72451	−	0.161460i	0.704028	−	0.0659156i
$7$	−3.46344	−	1.26059i	−1.30906	−	0.476458i	−0.409122	−	0.912480i	$-0.634165\pi$
$7$	−3.46344	−	1.26059i	−1.30906	−	0.476458i	−0.899936	+	0.436021i	$0.856387\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−2.96055	−	0.484935i	−0.986849	−	0.161645i
$10$	−1.58406	+	2.74367i	−0.500923	+	0.867624i
$11$	−1.75046	+	1.46881i	−0.527785	+	0.442864i	−0.867336	−	0.497724i	$-0.834169\pi$
$11$	−1.75046	+	1.46881i	−0.527785	+	0.442864i	0.339551	+	0.940588i	$0.389725\pi$
$12$	0.458464	+	1.67027i	0.132347	+	0.482166i
$13$	0.538357	−	3.05317i	0.149313	−	0.846798i	−0.814489	−	0.580179i	$-0.802982\pi$
$13$	0.538357	−	3.05317i	0.149313	−	0.846798i	0.963802	−	0.266619i	$-0.0859065\pi$
$14$	0.640018	−	3.62972i	0.171052	−	0.970085i
$15$	3.85644	−	3.90368i	0.995728	−	1.00793i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.862878	+	1.49455i	−0.209279	+	0.362481i	−0.951487	−	0.307687i	$-0.900445\pi$
$17$	−0.862878	+	1.49455i	−0.209279	+	0.362481i	0.742209	+	0.670169i	$0.233778\pi$
$18$	−0.0365258	−	2.99978i	−0.00860921	−	0.707054i
$19$	1.69740	+	2.93998i	0.389410	+	0.674478i	0.992370	−	0.123293i	$-0.0393456\pi$
$19$	1.69740	+	2.93998i	0.389410	+	0.674478i	−0.602960	+	0.797771i	$0.706012\pi$
$20$	−2.97705	−	1.08356i	−0.665690	−	0.242291i
$21$	−2.66266	+	5.80205i	−0.581040	+	1.26611i
$22$	−1.75046	−	1.46881i	−0.373200	−	0.313152i
$23$	3.15087	−	1.14682i	0.657002	−	0.239129i	0.00806071	−	0.999968i	$-0.497434\pi$
$23$	3.15087	−	1.14682i	0.657002	−	0.239129i	0.648942	+	0.760838i	$0.275212\pi$
$24$	−1.56529	+	0.741539i	−0.319513	+	0.151366i
$25$	0.874658	+	4.96043i	0.174932	+	0.992086i
$26$	3.10027			0.608014
$27$	−1.25298	+	5.04282i	−0.241136	+	0.970491i
$28$	3.68572			0.696535
$29$	−0.101661	−	0.576550i	−0.0188780	−	0.107063i	0.973913	−	0.226923i	$-0.0728665\pi$
$29$	−0.101661	−	0.576550i	−0.0188780	−	0.107063i	−0.992791	+	0.119860i	$0.961755\pi$
$30$	4.51404	+	3.11998i	0.824147	+	0.569629i
$31$	4.35827	−	1.58628i	0.782769	−	0.284904i	0.0804420	−	0.996759i	$-0.474367\pi$
$31$	4.35827	−	1.58628i	0.782769	−	0.284904i	0.702327	+	0.711855i	$0.252145\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	2.28983	+	3.22820i	0.398608	+	0.561958i
$34$	−1.62168	−	0.590243i	−0.278116	−	0.101226i
$35$	−5.83839	−	10.1124i	−0.986868	−	1.70931i
$36$	2.94786	−	0.556877i	0.491310	−	0.0928128i
$37$	3.65360	−	6.32822i	0.600648	−	1.04035i	−0.392075	−	0.919933i	$-0.628243\pi$
$37$	3.65360	−	6.32822i	0.600648	−	1.04035i	0.992723	−	0.120420i	$-0.0384240\pi$
$38$	−2.60057	+	2.18213i	−0.421867	+	0.353989i
$39$	−5.19523	−	1.35821i	−0.831902	−	0.217488i
$40$	0.550137	−	3.11998i	0.0869844	−	0.493313i
$41$	−1.22952	+	6.97295i	−0.192019	+	1.08899i	0.724582	+	0.689188i	$0.242033\pi$
$41$	−1.22952	+	6.97295i	−0.192019	+	1.08899i	−0.916601	+	0.399803i	$0.869078\pi$
$42$	−6.17627	−	1.61469i	−0.953019	−	0.249153i
$43$	1.27004	−	1.06569i	0.193679	−	0.162516i	−0.540791	−	0.841157i	$-0.681875\pi$
$43$	1.27004	−	1.06569i	0.193679	−	0.162516i	0.734470	+	0.678641i	$0.237431\pi$
$44$	1.14253	−	1.97893i	0.172243	−	0.298334i
$45$	−6.19747	−	7.20583i	−0.923864	−	1.07418i
$46$	1.67654	+	2.90386i	0.247193	+	0.428151i
$47$	3.61968	+	1.31746i	0.527984	+	0.192171i	0.592238	−	0.805763i	$-0.298244\pi$
$47$	3.61968	+	1.31746i	0.527984	+	0.192171i	−0.0642537	+	0.997934i	$0.520467\pi$
$48$	−1.00208	−	1.41274i	−0.144638	−	0.203911i
$49$	5.04404	+	4.23245i	0.720577	+	0.604636i
$50$	−4.73319	+	1.72274i	−0.669374	+	0.243632i
$51$	2.45892	+	1.69954i	0.344317	+	0.237983i
$52$	0.538357	+	3.05317i	0.0746567	+	0.423399i
$53$	−2.58267			−0.354757			−0.177379	−	0.984143i	$-0.556762\pi$
$53$	−2.58267			−0.354757			−0.177379	+	0.984143i	$0.556762\pi$
$54$	−5.18379	−	0.358266i	−0.705424	−	0.0487539i
$55$	−7.23936			−0.976155
$56$	0.640018	+	3.62972i	0.0855261	+	0.485042i
$57$	5.31383	−	2.51737i	0.703834	−	0.333434i
$58$	0.550137	−	0.200234i	0.0722366	−	0.0262920i
$59$	−7.40243	−	6.21138i	−0.963714	−	0.808652i	0.0178389	−	0.999841i	$-0.494321\pi$
$59$	−7.40243	−	6.21138i	−0.963714	−	0.808652i	−0.981553	+	0.191188i	$0.938766\pi$
$60$	−2.28873	+	4.98724i	−0.295474	+	0.643850i
$61$	−12.3018	−	4.47750i	−1.57509	−	0.573285i	−0.600960	−	0.799279i	$-0.705215\pi$
$61$	−12.3018	−	4.47750i	−1.57509	−	0.573285i	−0.974129	+	0.225994i	$0.927437\pi$
$62$	2.31899	+	4.01660i	0.294512	+	0.510109i
$63$	9.64238	+	5.41158i	1.21483	+	0.681795i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	7.52411	−	6.31348i	0.933251	−	0.783091i
$66$	−2.78154	+	2.81561i	−0.342383	+	0.346578i
$67$	−1.49490	+	8.47798i	−0.182631	+	1.03575i	0.746331	+	0.665574i	$0.231813\pi$
$67$	−1.49490	+	8.47798i	−0.182631	+	1.03575i	−0.928962	+	0.370175i	$0.879298\pi$
$68$	0.299674	−	1.69954i	0.0363408	−	0.206099i
$69$	−1.53727	−	5.60057i	−0.185066	−	0.674230i
$70$	8.94493	−	7.50569i	1.06912	−	0.897102i
$71$	−0.993732	+	1.72119i	−0.117934	+	0.204268i	−0.918949	−	0.394377i	$-0.870961\pi$
$71$	−0.993732	+	1.72119i	−0.117934	+	0.204268i	0.801015	+	0.598645i	$0.204294\pi$
$72$	1.06031	+	2.80638i	0.124958	+	0.330735i
$73$	−5.32371	−	9.22094i	−0.623094	−	1.07923i	−0.988906	−	0.148541i	$-0.952542\pi$
$73$	−5.32371	−	9.22094i	−0.623094	−	1.07923i	0.365812	−	0.930689i	$-0.380791\pi$
$74$	6.86652	+	2.49921i	0.798217	+	0.290527i
$75$	8.68627	−	0.813264i	1.00300	−	0.0939077i
$76$	−2.60057	−	2.18213i	−0.298305	−	0.250308i
$77$	7.91420	−	2.88053i	0.901907	−	0.328267i
$78$	0.435437	−	5.35215i	0.0493036	−	0.606012i
$79$	2.44726	+	13.8791i	0.275338	+	1.56152i	0.737886	+	0.674925i	$0.235824\pi$
$79$	2.44726	+	13.8791i	0.275338	+	1.56152i	−0.462548	+	0.886594i	$0.653065\pi$
$80$	3.16812			0.354206
$81$	8.52968	+	2.87135i	0.947742	+	0.319038i
$82$	−7.08052			−0.781912
$83$	−0.538035	−	3.05135i	−0.0590571	−	0.334929i	0.940936	−	0.338584i	$-0.109948\pi$
$83$	−0.538035	−	3.05135i	−0.0590571	−	0.334929i	−0.999993	+	0.00365453i	$0.998837\pi$
$84$	0.517664	−	6.36283i	0.0564817	−	0.694242i
$85$	−5.13767	+	1.86996i	−0.557258	+	0.202825i
$86$	1.27004	+	1.06569i	0.136952	+	0.114916i
$87$	−1.00960	+	0.0945255i	−0.108241	+	0.0101342i
$88$	2.14726	+	0.781539i	0.228899	+	0.0833123i
$89$	8.67300	+	15.0221i	0.919336	+	1.59234i	0.800425	+	0.599432i	$0.204607\pi$
$89$	8.67300	+	15.0221i	0.919336	+	1.59234i	0.118911	+	0.992905i	$0.462060\pi$
$90$	6.02018	−	7.35459i	0.634582	−	0.775242i
$91$	−5.71337	+	9.89585i	−0.598924	+	1.03737i
$92$	−2.56861	+	2.15532i	−0.267797	+	0.224708i
$93$	−2.12635	−	7.74668i	−0.220492	−	0.803294i
$94$	−0.668890	+	3.79346i	−0.0689907	+	0.391266i
$95$	−1.86760	+	10.5917i	−0.191612	+	1.08669i
$96$	1.21727	−	1.23218i	0.124237	−	0.125759i
$97$	7.04084	−	5.90797i	0.714889	−	0.599863i	−0.211077	−	0.977469i	$-0.567697\pi$
$97$	7.04084	−	5.90797i	0.714889	−	0.599863i	0.925966	+	0.377606i	$0.123253\pi$
$98$	−3.29226	+	5.70237i	−0.332569	+	0.576026i
$99$	5.89461	−	3.49963i	0.592430	−	0.351726i
$100$	−2.51848	−	4.36213i	−0.251848	−	0.436213i
$101$	−11.2389	−	4.09062i	−1.11831	−	0.407032i	−0.284276	−	0.958743i	$-0.591753\pi$
$101$	−11.2389	−	4.09062i	−1.11831	−	0.407032i	−0.834036	+	0.551710i	$0.813975\pi$
$102$	−1.24673	+	2.71668i	−0.123445	+	0.268991i
$103$	−9.76437	−	8.19328i	−0.962112	−	0.807308i	0.0191837	−	0.999816i	$-0.493893\pi$
$103$	−9.76437	−	8.19328i	−0.962112	−	0.807308i	−0.981295	+	0.192508i	$0.938338\pi$
$104$	−2.91331	+	1.06036i	−0.285673	+	0.103977i
$105$	−18.2775	+	8.65879i	−1.78370	+	0.845011i
$106$	−0.448476	−	2.54343i	−0.0435599	−	0.247040i
$107$	6.09894			0.589607			0.294803	−	0.955558i	$-0.404746\pi$
$107$	6.09894			0.589607			0.294803	+	0.955558i	$0.404746\pi$
$108$	−0.547332	−	5.16725i	−0.0526670	−	0.497218i
$109$	11.2390			1.07650			0.538250	−	0.842785i	$-0.319086\pi$
$109$	11.2390			1.07650			0.538250	+	0.842785i	$0.319086\pi$
$110$	−1.25710	−	7.12937i	−0.119860	−	0.679759i
$111$	−10.4115	−	7.19618i	−0.988220	−	0.683032i
$112$	−3.46344	+	1.26059i	−0.327265	+	0.119115i
$113$	−5.39062	−	4.52327i	−0.507107	−	0.425513i	0.353003	−	0.935622i	$-0.385161\pi$
$113$	−5.39062	−	4.52327i	−0.507107	−	0.425513i	−0.860110	+	0.510109i	$0.829605\pi$
$114$	3.40187	+	4.79596i	0.318614	+	0.449183i
$115$	9.98233	+	3.63327i	0.930857	+	0.338804i
$116$	0.292722	+	0.507009i	0.0271786	+	0.0470746i
$117$	−3.07442	+	8.77800i	−0.284230	+	0.811526i
$118$	4.83159	−	8.36857i	0.444784	−	0.770389i
$119$	4.87254	−	4.08855i	0.446665	−	0.374796i
$120$	−5.30891	−	1.38793i	−0.484635	−	0.126700i
$121$	−1.00342	+	5.69068i	−0.0912200	+	0.517334i
$122$	2.27329	−	12.8925i	0.205814	−	1.16723i
$123$	11.8650	+	3.10193i	1.06983	+	0.279692i
$124$	−3.55290	+	2.98123i	−0.319059	+	0.267723i
$125$	−0.0585380	+	0.101391i	−0.00523579	+	0.00906866i
$126$	−3.65499	+	10.4356i	−0.325612	+	0.929677i
$127$	−2.99250	−	5.18316i	−0.265541	−	0.459931i	0.702164	−	0.712015i	$-0.252217\pi$
$127$	−2.99250	−	5.18316i	−0.265541	−	0.459931i	−0.967705	+	0.252084i	$0.918884\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	−1.66137	−	2.34220i	−0.146275	−	0.206219i
$130$	7.52411	+	6.31348i	0.659908	+	0.553729i
$131$	−15.4251	+	5.61427i	−1.34770	+	0.490521i	−0.912228	−	0.409683i	$-0.865639\pi$
$131$	−15.4251	+	5.61427i	−1.34770	+	0.490521i	−0.435468	+	0.900204i	$0.643417\pi$
$132$	−3.25584	−	2.25035i	−0.283385	−	0.195868i
$133$	−2.17273	−	12.3222i	−0.188400	−	1.06847i
$134$	−8.60876			−0.743684
$135$	−13.3102	+	9.68691i	−1.14556	+	0.833717i
$136$	1.72576			0.147982
$137$	−0.0366673	−	0.207951i	−0.00313270	−	0.0177664i	0.983201	−	0.182524i	$-0.0584268\pi$
$137$	−0.0366673	−	0.207951i	−0.00313270	−	0.0177664i	−0.986334	+	0.164758i	$0.947316\pi$
$138$	5.24854	−	2.48645i	0.446786	−	0.211660i
$139$	−3.45009	+	1.25573i	−0.292633	+	0.106510i	−0.484165	−	0.874977i	$-0.660877\pi$
$139$	−3.45009	+	1.25573i	−0.292633	+	0.106510i	0.191532	+	0.981486i	$0.438654\pi$
$140$	8.94493	+	7.50569i	0.755985	+	0.634347i
$141$	2.78277	−	6.06378i	0.234352	−	0.510663i
$142$	−1.86760	−	0.679753i	−0.156726	−	0.0570436i
$143$	3.54217	+	6.13522i	0.296211	+	0.513053i
$144$	−2.57962	+	1.53152i	−0.214968	+	0.127627i
$145$	0.927377	−	1.60626i	0.0770145	−	0.133393i
$146$	8.15640	−	6.84404i	0.675029	−	0.566416i
$147$	8.01512	−	8.11331i	0.661076	−	0.669174i
$148$	−1.26888	+	7.19618i	−0.104301	+	0.591523i
$149$	2.68710	−	15.2393i	0.220136	−	1.24845i	−0.651633	−	0.758535i	$-0.725916\pi$
$149$	2.68710	−	15.2393i	0.220136	−	1.24845i	0.871769	−	0.489918i	$-0.162973\pi$
$150$	2.30926	+	8.41309i	0.188551	+	0.686926i
$151$	15.4325	−	12.9494i	1.25588	−	1.05381i	0.259772	−	0.965670i	$-0.416352\pi$
$151$	15.4325	−	12.9494i	1.25588	−	1.05381i	0.996108	−	0.0881390i	$-0.0280920\pi$
$152$	1.69740	−	2.93998i	0.137677	−	0.238464i
$153$	3.27935	−	4.00624i	0.265120	−	0.323885i
$154$	4.21106	+	7.29377i	0.339337	+	0.587748i
$155$	13.8075	+	5.02552i	1.10905	+	0.403660i
$156$	5.34645	−	0.500569i	0.428059	−	0.0400776i
$157$	13.7868	+	11.5685i	1.10031	+	0.923269i	0.997446	−	0.0714264i	$-0.0227551\pi$
$157$	13.7868	+	11.5685i	1.10031	+	0.923269i	0.102863	+	0.994695i	$0.467200\pi$
$158$	−13.2433	+	4.82016i	−1.05358	+	0.383471i
$159$	−0.362739	+	4.45859i	−0.0287671	+	0.353589i
$160$	0.550137	+	3.11998i	0.0434922	+	0.246656i
$161$	−12.3585			−0.973989
$162$	−1.34656	+	8.89870i	−0.105796	+	0.699148i
$163$	3.05289			0.239121			0.119560	−	0.992827i	$-0.461851\pi$
$163$	3.05289			0.239121			0.119560	+	0.992827i	$0.461851\pi$
$164$	−1.22952	−	6.97295i	−0.0960093	−	0.544496i
$165$	−1.01678	+	12.4976i	−0.0791559	+	0.972940i
$166$	2.91156	−	1.05972i	0.225981	−	0.0822504i
$167$	−3.14170	−	2.63620i	−0.243112	−	0.203995i	0.513088	−	0.858336i	$-0.328502\pi$
$167$	−3.14170	−	2.63620i	−0.243112	−	0.203995i	−0.756199	+	0.654341i	$0.772946\pi$
$168$	6.35605	−	0.595094i	0.490380	−	0.0459125i
$169$	3.18396	+	1.15887i	0.244920	+	0.0891435i
$170$	−2.73370	−	4.73490i	−0.209665	−	0.363150i
$171$	−3.59953	−	9.52708i	−0.275263	−	0.728554i
$172$	−0.828957	+	1.43580i	−0.0632074	+	0.109478i
$173$	−13.0435	+	10.9448i	−0.991680	+	0.832118i	−0.985810	−	0.167864i	$-0.946313\pi$
$173$	−13.0435	+	10.9448i	−0.991680	+	0.832118i	−0.00586990	+	0.999983i	$0.501868\pi$
$174$	−0.268405	−	0.977851i	−0.0203478	−	0.0741307i
$175$	3.22374	−	18.2828i	0.243692	−	1.38205i
$176$	−0.396798	+	2.25035i	−0.0299098	+	0.169627i
$177$	−11.7627	+	11.9068i	−0.884137	+	0.894967i
$178$	−13.2878	+	11.1498i	−0.995964	+	0.835713i
$179$	7.27802	−	12.6059i	0.543985	−	0.942210i	−0.454685	−	0.890652i	$-0.650248\pi$
$179$	7.27802	−	12.6059i	0.543985	−	0.942210i	0.998670	−	0.0515575i	$-0.0164185\pi$
$180$	8.28825	+	4.65161i	0.617770	+	0.346710i
$181$	6.51190	+	11.2789i	0.484026	+	0.838357i	0.999832	−	0.0183482i	$-0.00584075\pi$
$181$	6.51190	+	11.2789i	0.484026	+	0.838357i	−0.515806	+	0.856706i	$0.672507\pi$
$182$	−10.7376	−	3.90818i	−0.795926	−	0.289693i
$183$	−9.45753	+	20.6084i	−0.699121	+	1.52341i
$184$	−2.56861	−	2.15532i	−0.189361	−	0.158893i
$185$	21.7539	−	7.91778i	1.59938	−	0.582127i
$186$	7.25976	−	3.43924i	0.532311	−	0.252177i
$187$	−0.684776	−	3.88356i	−0.0500758	−	0.283994i
$188$	−3.85198			−0.280935
$189$	10.6966	−	15.8860i	0.778060	−	1.15554i
$190$	−10.7551			−0.780258
$191$	0.625632	+	3.54814i	0.0452692	+	0.256734i	0.999040	−	0.0437996i	$-0.0139463\pi$
$191$	0.625632	+	3.54814i	0.0452692	+	0.256734i	−0.953771	+	0.300534i	$0.902835\pi$
$192$	1.42483	+	0.984808i	0.102829	+	0.0710724i
$193$	−1.38592	+	0.504435i	−0.0997610	+	0.0363100i	−0.391418	−	0.920213i	$-0.628015\pi$
$193$	−1.38592	+	0.504435i	−0.0997610	+	0.0363100i	0.291657	+	0.956523i	$0.405793\pi$
$194$	7.04084	+	5.90797i	0.505503	+	0.424167i
$195$	−9.84248	−	13.8760i	−0.704835	−	0.993678i
$196$	−6.18743	−	2.25204i	−0.441959	−	0.160860i
$197$	−1.26931	−	2.19851i	−0.0904346	−	0.156637i	0.817259	−	0.576270i	$-0.195492\pi$
$197$	−1.26931	−	2.19851i	−0.0904346	−	0.156637i	−0.907694	+	0.419633i	$0.862159\pi$
$198$	4.47005	+	5.19735i	0.317673	+	0.369360i
$199$	0.925891	−	1.60369i	0.0656347	−	0.113683i	−0.831341	−	0.555763i	$-0.812426\pi$
$199$	0.925891	−	1.60369i	0.0656347	−	0.113683i	0.896975	+	0.442081i	$0.145759\pi$
$200$	3.85853	−	3.23769i	0.272839	−	0.228939i
$201$	14.4260	+	3.77145i	1.01753	+	0.266018i
$202$	2.07686	−	11.7785i	0.146128	−	0.828731i
$203$	−0.374695	+	2.12500i	−0.0262984	+	0.149146i
$204$	−2.89190	−	0.756044i	−0.202474	−	0.0529337i
$205$	−17.1838	+	14.4189i	−1.20017	+	1.00706i
$206$	6.37324	−	11.0388i	0.444045	−	0.769108i
$207$	−9.88444	+	1.86726i	−0.687016	+	0.129783i
$208$	−1.55014	−	2.68492i	−0.107483	−	0.186165i
$209$	−7.28951	−	2.65317i	−0.504226	−	0.183523i
$210$	−11.7011	−	16.4962i	−0.807453	−	1.13835i
$211$	−14.5459	−	12.2054i	−1.00138	−	0.840257i	−0.0142043	−	0.999899i	$-0.504522\pi$
$211$	−14.5459	−	12.2054i	−1.00138	−	0.840257i	−0.987175	+	0.159642i	$0.948966\pi$
$212$	2.42692	−	0.883326i	0.166681	−	0.0606671i
$213$	2.83181	+	1.95727i	0.194032	+	0.134110i
$214$	1.05907	+	6.00628i	0.0723965	+	0.410581i
$215$	5.25247			0.358215
$216$	4.99370	−	1.43630i	0.339778	−	0.0977278i
$217$	−17.0943			−1.16043
$218$	1.95163	+	11.0683i	0.132181	+	0.749637i
$219$	−16.6663	+	7.89549i	−1.12620	+	0.533527i
$220$	6.80277	−	2.47601i	0.458643	−	0.166932i
$221$	4.09858	+	3.43912i	0.275700	+	0.231340i
$222$	5.27891	−	11.5030i	0.354297	−	0.772029i
$223$	6.81687	+	2.48114i	0.456491	+	0.166149i	0.560023	−	0.828477i	$-0.310792\pi$
$223$	6.81687	+	2.48114i	0.456491	+	0.166149i	−0.103532	+	0.994626i	$0.533014\pi$
$224$	−1.84286	−	3.19193i	−0.123131	−	0.213270i
$225$	−0.183979	−	15.1097i	−0.0122652	−	1.00732i
$226$	3.51848	−	6.09418i	0.234046	−	0.405379i
$227$	−21.8531	+	18.3369i	−1.45044	+	1.21706i	−0.518182	+	0.855271i	$0.673391\pi$
$227$	−21.8531	+	18.3369i	−1.45044	+	1.21706i	−0.932258	+	0.361793i	$0.882165\pi$
$228$	−4.13237	+	4.18299i	−0.273673	+	0.277026i
$229$	0.322184	−	1.82720i	0.0212905	−	0.120744i	−0.972310	−	0.233694i	$-0.924919\pi$
$229$	0.322184	−	1.82720i	0.0212905	−	0.120744i	0.993601	+	0.112949i	$0.0360298\pi$
$230$	−1.84466	+	10.4616i	−0.121633	+	0.689816i
$231$	−3.86124	−	14.0672i	−0.254051	−	0.925556i
$232$	−0.448476	+	0.376316i	−0.0294439	+	0.0247064i
$233$	−4.26735	+	7.39126i	−0.279563	+	0.484218i	−0.971276	−	0.237955i	$-0.923523\pi$
$233$	−4.26735	+	7.39126i	−0.279563	+	0.484218i	0.691713	+	0.722172i	$0.256856\pi$
$234$	−9.17851	−	1.50343i	−0.600018	−	0.0982824i
$235$	6.10176	+	10.5686i	0.398035	+	0.689417i
$236$	9.08043	+	3.30500i	0.591085	+	0.215137i
$237$	24.3038	−	2.27548i	1.57870	−	0.147808i
$238$	4.87254	+	4.08855i	0.315840	+	0.265021i
$239$	6.84845	−	2.49263i	0.442989	−	0.161235i	−0.110889	−	0.993833i	$-0.535370\pi$
$239$	6.84845	−	2.49263i	0.442989	−	0.161235i	0.553878	+	0.832598i	$0.313147\pi$
$240$	0.444966	−	5.46927i	0.0287224	−	0.353040i
$241$	−0.231806	−	1.31464i	−0.0149319	−	0.0846833i	0.976431	−	0.215829i	$-0.0692455\pi$
$241$	−0.231806	−	1.31464i	−0.0149319	−	0.0846833i	−0.991363	+	0.131146i	$0.958134\pi$
$242$	−5.77847			−0.371454
$243$	6.15494	−	14.3219i	0.394840	−	0.918750i
$244$	13.0913			0.838087
$245$	3.62239	+	20.5436i	0.231426	+	1.31248i
$246$	−0.994467	+	12.2234i	−0.0634049	+	0.779337i
$247$	9.89008	−	3.59969i	0.629291	−	0.229043i
$248$	−3.55290	−	2.98123i	−0.225609	−	0.189308i
$249$	−5.34326	+	0.500270i	−0.338615	+	0.0317033i
$250$	−0.110015	−	0.0400423i	−0.00695798	−	0.00253250i
$251$	1.43928	+	2.49291i	0.0908466	+	0.157351i	0.907868	−	0.419257i	$-0.137709\pi$
$251$	1.43928	+	2.49291i	0.0908466	+	0.157351i	−0.817021	+	0.576608i	$0.804376\pi$
$252$	−10.9117	−	1.78733i	−0.687375	−	0.112591i
$253$	−3.83102	+	6.63552i	−0.240854	+	0.417171i
$254$	4.58477	−	3.84708i	0.287674	−	0.241387i
$255$	2.50660	+	9.13203i	0.156970	+	0.571870i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−4.47629	+	25.3863i	−0.279223	+	1.58355i	0.445996	+	0.895035i	$0.352850\pi$
$257$	−4.47629	+	25.3863i	−0.279223	+	1.58355i	−0.725219	+	0.688518i	$0.758262\pi$
$258$	2.01812	−	2.04285i	0.125643	−	0.127182i
$259$	−20.6313	+	17.3117i	−1.28197	+	1.07570i
$260$	−4.91101	+	8.50613i	−0.304568	+	0.527528i
$261$	0.0213838	+	1.75620i	0.00132362	+	0.108706i
$262$	−8.20752	−	14.2158i	−0.507062	−	0.878257i
$263$	14.1609	+	5.15414i	0.873197	+	0.317818i	0.739461	−	0.673199i	$-0.235080\pi$
$263$	14.1609	+	5.15414i	0.873197	+	0.317818i	0.133736	+	0.991017i	$0.457303\pi$
$264$	1.65079	−	3.59715i	0.101599	−	0.221389i
$265$	−6.26793	−	5.25942i	−0.385036	−	0.323083i
$266$	11.7577	−	4.27945i	0.720910	−	0.262390i
$267$	27.1515	−	12.8627i	1.66164	−	0.787187i
$268$	−1.49490	−	8.47798i	−0.0913153	−	0.517875i
$269$	16.0615			0.979286			0.489643	−	0.871923i	$-0.337127\pi$
$269$	16.0615			0.979286			0.489643	+	0.871923i	$0.337127\pi$
$270$	−11.8510	−	11.4259i	−0.721231	−	0.695357i
$271$	9.41446			0.571888			0.285944	−	0.958246i	$-0.407693\pi$
$271$	9.41446			0.571888			0.285944	+	0.958246i	$0.407693\pi$
$272$	0.299674	+	1.69954i	0.0181704	+	0.103050i
$273$	16.2812	+	11.2531i	0.985384	+	0.681071i
$274$	0.198424	−	0.0722205i	0.0119872	−	0.00436300i
$275$	−8.81700	−	7.39834i	−0.531685	−	0.446137i
$276$	3.36007	+	4.73704i	0.202253	+	0.285136i
$277$	−5.23856	−	1.90668i	−0.314755	−	0.114561i	0.179812	−	0.983701i	$-0.442451\pi$
$277$	−5.23856	−	1.90668i	−0.314755	−	0.114561i	−0.494567	+	0.869140i	$0.664673\pi$
$278$	−1.83576	−	3.17962i	−0.110101	−	0.190701i
$279$	−13.6721	+	2.58278i	−0.818528	+	0.154627i
$280$	−5.83839	+	10.1124i	−0.348911	+	0.604331i
$281$	21.4529	−	18.0011i	1.27977	−	1.07386i	0.286499	−	0.958081i	$-0.407509\pi$
$281$	21.4529	−	18.0011i	1.27977	−	1.07386i	0.993275	−	0.115777i	$-0.0369359\pi$
$282$	6.45488	+	1.68753i	0.384383	+	0.100491i
$283$	1.06884	−	6.06171i	0.0635361	−	0.360331i	−0.936419	−	0.350883i	$-0.885881\pi$
$283$	1.06884	−	6.06171i	0.0635361	−	0.360331i	0.999955	−	0.00944797i	$-0.00300743\pi$
$284$	0.345119	−	1.95727i	0.0204791	−	0.116143i
$285$	18.0227	+	4.71175i	1.06757	+	0.279100i
$286$	−5.42692	+	4.55372i	−0.320900	+	0.269267i
$287$	13.0484	−	22.6005i	0.770222	−	1.33406i
$288$	−1.95620	−	2.27448i	−0.115270	−	0.134025i
$289$	7.01088	+	12.1432i	0.412405	+	0.714306i
$290$	1.74290	+	0.634363i	0.102347	+	0.0372511i
$291$	−9.21031	−	12.9847i	−0.539918	−	0.761177i
$292$	8.15640	+	6.84404i	0.477317	+	0.400517i
$293$	−2.19428	+	0.798651i	−0.128191	+	0.0466577i	−0.405319	−	0.914175i	$-0.632840\pi$
$293$	−2.19428	+	0.798651i	−0.128191	+	0.0466577i	0.277128	+	0.960833i	$0.410617\pi$
$294$	9.38186	+	6.48449i	0.547161	+	0.378183i
$295$	−5.31608	−	30.1490i	−0.309514	−	1.75534i
$296$	−7.30720			−0.424722
$297$	−5.21367	−	10.6677i	−0.302528	−	0.619001i
$298$	15.4744			0.896408
$299$	−1.80516	−	10.2376i	−0.104395	−	0.592054i
$300$	−7.88427	+	3.73510i	−0.455199	+	0.215646i
$301$	−5.74209	+	2.08995i	−0.330969	+	0.120463i
$302$	15.4325	+	12.9494i	0.888042	+	0.745155i
$303$	−8.64035	+	18.8277i	−0.496375	+	1.08162i
$304$	3.19007	+	1.16109i	0.182963	+	0.0665930i
$305$	−20.7374	−	35.9183i	−1.18742	−	2.05668i
$306$	4.51483	+	2.53385i	0.258096	+	0.144851i
$307$	−3.41265	+	5.91088i	−0.194770	+	0.337351i	−0.946825	−	0.321749i	$-0.895729\pi$
$307$	−3.41265	+	5.91088i	−0.194770	+	0.337351i	0.752055	+	0.659100i	$0.229063\pi$
$308$	−6.45172	+	5.41363i	−0.367621	+	0.308470i
$309$	−15.5159	+	15.7059i	−0.882666	+	0.893479i
$310$	−2.55152	+	14.4704i	−0.144917	+	0.821864i
$311$	1.49254	−	8.46464i	0.0846344	−	0.479986i	−0.912800	−	0.408406i	$-0.866085\pi$
$311$	1.49254	−	8.46464i	0.0846344	−	0.479986i	0.997435	−	0.0715798i	$-0.0228040\pi$
$312$	1.42137	+	5.17830i	0.0804690	+	0.293164i
$313$	−16.5993	+	13.9285i	−0.938250	+	0.787285i	−0.977280	−	0.211953i	$-0.932018\pi$
$313$	−16.5993	+	13.9285i	−0.938250	+	0.787285i	0.0390299	+	0.999238i	$0.487573\pi$
$314$	−8.99872	+	15.5862i	−0.507827	+	0.879582i
$315$	12.3810	+	32.7694i	0.697589	+	1.84635i
$316$	−7.04660	−	12.2051i	−0.396402	−	0.686588i
$317$	−33.1899	−	12.0801i	−1.86413	−	0.678488i	−0.975554	−	0.219760i	$-0.929473\pi$
$317$	−33.1899	−	12.0801i	−1.86413	−	0.678488i	−0.888577	−	0.458728i	$-0.848305\pi$
$318$	−4.45384	+	0.416997i	−0.249759	+	0.0233840i
$319$	1.02480	+	0.859908i	0.0573777	+	0.0481456i
$320$	−2.97705	+	1.08356i	−0.166422	+	0.0605728i
$321$	0.856604	−	10.5289i	0.0478110	−	0.587665i
$322$	−2.14604	−	12.1708i	−0.119594	−	0.678251i
$323$	−5.85859			−0.325981
$324$	−8.99733	+	0.219138i	−0.499852	+	0.0121744i
$325$	15.6159			0.866217
$326$	0.530129	+	3.00651i	0.0293611	+	0.166515i
$327$	1.57853	−	19.4024i	0.0872929	−	1.07296i
$328$	6.65351	−	2.42168i	0.367379	−	0.133715i
$329$	−10.8758	−	9.12586i	−0.599601	−	0.503125i
$330$	−12.4843	+	1.16886i	−0.687240	+	0.0643438i
$331$	24.2569	+	8.82879i	1.33328	+	0.485274i	0.907690	−	0.419642i	$-0.137844\pi$
$331$	24.2569	+	8.82879i	1.33328	+	0.485274i	0.425590	+	0.904916i	$0.360067\pi$
$332$	1.54921	+	2.68331i	0.0850240	+	0.147266i
$333$	−13.8854	+	16.9632i	−0.760917	+	0.929579i
$334$	2.05060	−	3.55174i	0.112204	−	0.194343i
$335$	−20.8928	+	17.5311i	−1.14149	+	0.957826i
$336$	1.68977	+	6.15616i	0.0921846	+	0.335846i
$337$	−0.587727	+	3.33317i	−0.0320156	+	0.181569i	−0.996622	−	0.0821241i	$-0.973830\pi$
$337$	−0.587727	+	3.33317i	−0.0320156	+	0.181569i	0.964607	+	0.263693i	$0.0849407\pi$
$338$	−0.588371	+	3.33682i	−0.0320032	+	0.181499i
$339$	−8.56585	+	8.67078i	−0.465233	+	0.470932i
$340$	4.18826	−	3.51437i	0.227141	−	0.190594i
$341$	−5.29904	+	9.17821i	−0.286959	+	0.497028i
$342$	8.75729	−	5.19920i	0.473540	−	0.281141i
$343$	0.765664	+	1.32617i	0.0413420	+	0.0716064i
$344$	−1.55793	−	0.567040i	−0.0839980	−	0.0305728i
$345$	7.67431	−	16.7227i	0.413171	−	0.900318i
$346$	−13.0435	−	10.9448i	−0.701224	−	0.588397i
$347$	15.2230	−	5.54073i	0.817216	−	0.297442i	0.100615	−	0.994925i	$-0.467919\pi$
$347$	15.2230	−	5.54073i	0.817216	−	0.297442i	0.716601	+	0.697483i	$0.245697\pi$
$348$	0.916387	−	0.434130i	0.0491235	−	0.0232718i
$349$	0.780120	+	4.42428i	0.0417589	+	0.236826i	0.998542	−	0.0539752i	$-0.0171892\pi$
$349$	0.780120	+	4.42428i	0.0417589	+	0.236826i	−0.956783	+	0.290801i	$0.906078\pi$
$350$	18.5648			0.992330
$351$	14.7221	+	6.54040i	0.785806	+	0.349101i
$352$	−2.28507			−0.121795
$353$	−4.03327	−	22.8738i	−0.214669	−	1.21745i	−0.881479	−	0.472222i	$-0.843452\pi$
$353$	−4.03327	−	22.8738i	−0.214669	−	1.21745i	0.666810	−	0.745228i	$-0.267659\pi$
$354$	−13.7684	−	9.51638i	−0.731785	−	0.505790i
$355$	−5.91679	+	2.15353i	−0.314030	+	0.114298i
$356$	−13.2878	−	11.1498i	−0.704253	−	0.590938i
$357$	−6.37389	−	8.98593i	−0.337342	−	0.475586i
$358$	13.6782	+	4.97846i	0.722916	+	0.263120i
$359$	5.77697	+	10.0060i	0.304897	+	0.528097i	0.977238	−	0.212144i	$-0.0680447\pi$
$359$	5.77697	+	10.0060i	0.304897	+	0.528097i	−0.672341	+	0.740241i	$0.734711\pi$
$360$	−3.14170	+	8.97008i	−0.165582	+	0.472765i
$361$	3.73768	−	6.47385i	0.196720	−	0.340729i
$362$	−9.97681	+	8.37154i	−0.524370	+	0.439998i
$363$	9.68315	+	2.53151i	0.508234	+	0.132870i
$364$	1.98423	−	11.2531i	0.104002	−	0.589825i
$365$	5.85755	−	33.2198i	0.306598	−	1.73880i
$366$	−21.9376	−	5.73524i	−1.14669	−	0.299786i
$367$	11.9271	−	10.0080i	0.622589	−	0.522414i	−0.276027	−	0.961150i	$-0.589018\pi$
$367$	11.9271	−	10.0080i	0.622589	−	0.522414i	0.898616	+	0.438735i	$0.144573\pi$
$368$	1.67654	−	2.90386i	0.0873959	−	0.151374i
$369$	7.02147	−	20.0475i	0.365523	−	1.04363i
$370$	11.5750	+	20.0485i	0.601757	+	1.04227i
$371$	8.94493	+	3.25569i	0.464398	+	0.169027i
$372$	4.64763	+	6.55225i	0.240969	+	0.339718i
$373$	−7.47450	−	6.27185i	−0.387015	−	0.324744i	0.428434	−	0.903573i	$-0.359065\pi$
$373$	−7.47450	−	6.27185i	−0.387015	−	0.324744i	−0.815449	+	0.578829i	$0.803510\pi$
$374$	3.70565	−	1.34875i	0.191614	−	0.0697420i
$375$	0.166814	+	0.115297i	0.00861423	+	0.00595392i
$376$	−0.668890	−	3.79346i	−0.0344953	−	0.195633i
$377$	−1.81504			−0.0934792
$378$	17.5021	+	7.77547i	0.900212	+	0.399927i
$379$	−18.7904			−0.965197			−0.482599	−	0.875842i	$-0.660307\pi$
$379$	−18.7904			−0.965197			−0.482599	+	0.875842i	$0.660307\pi$
$380$	−1.86760	−	10.5917i	−0.0958061	−	0.543343i
$381$	−9.36823	+	4.43811i	−0.479949	+	0.227371i
$382$	−3.38559	+	1.23226i	−0.173222	+	0.0630477i
$383$	23.5697	+	19.7773i	1.20435	+	1.01057i	0.999495	+	0.0317817i	$0.0101181\pi$
$383$	23.5697	+	19.7773i	1.20435	+	1.01057i	0.204859	+	0.978791i	$0.434326\pi$
$384$	−0.722426	+	1.57420i	−0.0368662	+	0.0803330i
$385$	25.0731	+	9.12586i	1.27784	+	0.465097i
$386$	−0.737435	−	1.27727i	−0.0375344	−	0.0650116i
$387$	−4.27679	+	2.53913i	−0.217402	+	0.129071i
$388$	−4.59558	+	7.95978i	−0.233305	+	0.404097i
$389$	22.6754	−	19.0269i	1.14969	−	0.964704i	0.149978	−	0.988689i	$-0.452080\pi$
$389$	22.6754	−	19.0269i	1.14969	−	0.964704i	0.999712	+	0.0239850i	$0.00763540\pi$
$390$	11.9560	−	12.1025i	0.605417	−	0.612833i
$391$	−1.00483	+	5.69870i	−0.0508167	+	0.288196i
$392$	1.14339	−	6.48449i	0.0577499	−	0.327516i
$393$	7.52571	+	27.4176i	0.379622	+	1.38303i
$394$	1.94470	−	1.63179i	0.0979724	−	0.0822086i
$395$	−22.3244	+	38.6670i	−1.12326	+	1.94555i
$396$	−4.34218	+	5.30465i	−0.218203	+	0.266569i
$397$	−8.07134	−	13.9800i	−0.405089	−	0.701635i	0.589243	−	0.807956i	$-0.299426\pi$
$397$	−8.07134	−	13.9800i	−0.405089	−	0.701635i	−0.994332	+	0.106321i	$0.966093\pi$
$398$	1.74011	+	0.633347i	0.0872237	+	0.0317468i
$399$	−21.5775	+	2.02022i	−1.08023	+	0.101138i
$400$	3.85853	+	3.23769i	0.192927	+	0.161885i
$401$	−23.8328	+	8.67444i	−1.19016	+	0.433181i	−0.859778	−	0.510668i	$-0.829398\pi$
$401$	−23.8328	+	8.67444i	−1.19016	+	0.433181i	−0.330377	+	0.943849i	$0.607176\pi$
$402$	−1.20911	+	14.8617i	−0.0603050	+	0.741235i
$403$	−2.49689	−	14.1605i	−0.124379	−	0.705387i
$404$	11.9602			0.595041
$405$	14.8535	+	24.3386i	0.738078	+	1.20939i
$406$	−2.15778			−0.107089
$407$	2.89948	+	16.4438i	0.143722	+	0.815087i
$408$	0.242384	−	2.97925i	0.0119998	−	0.147495i
$409$	21.3980	−	7.78825i	1.05806	−	0.385104i	0.246364	−	0.969177i	$-0.420764\pi$
$409$	21.3980	−	7.78825i	1.05806	−	0.385104i	0.811701	+	0.584073i	$0.198542\pi$
$410$	−17.1838	−	14.4189i	−0.848649	−	0.712101i
$411$	−0.364145	+	0.0340936i	−0.0179619	+	0.00168171i
$412$	11.9778	+	4.35955i	0.590102	+	0.214780i
$413$	17.8079	+	30.8442i	0.876269	+	1.51774i
$414$	−3.55530	−	9.41003i	−0.174734	−	0.462478i
$415$	4.90808	−	8.50104i	0.240928	−	0.417300i
$416$	2.37495	−	1.99282i	0.116441	−	0.0977060i
$417$	1.68326	+	6.13242i	0.0824294	+	0.300306i
$418$	1.34705	−	7.63949i	0.0658863	−	0.373660i
$419$	−0.854828	+	4.84797i	−0.0417611	+	0.236839i	−0.998543	−	0.0539688i	$-0.982813\pi$
$419$	−0.854828	+	4.84797i	−0.0417611	+	0.236839i	0.956782	+	0.290808i	$0.0939240\pi$
$420$	14.2138	−	14.3879i	0.693560	−	0.702056i
$421$	15.1046	−	12.6742i	0.736151	−	0.617704i	−0.195650	−	0.980674i	$-0.562682\pi$
$421$	15.1046	−	12.6742i	0.736151	−	0.617704i	0.931801	+	0.362970i	$0.118237\pi$
$422$	9.49415	−	16.4443i	0.462168	−	0.800498i
$423$	−10.0773	−	5.65570i	−0.489977	−	0.274989i
$424$	1.29134	+	2.23666i	0.0627128	+	0.108622i
$425$	−8.16833	−	2.97303i	−0.396222	−	0.144213i
$426$	−1.43580	+	3.12866i	−0.0695645	+	0.151584i
$427$	36.9624	+	31.0151i	1.78874	+	1.50093i
$428$	−5.73113	+	2.08596i	−0.277025	+	0.100829i
$429$	11.0890	−	5.25331i	0.535383	−	0.253632i
$430$	0.912081	+	5.17267i	0.0439845	+	0.249448i
$431$	−6.16323			−0.296873			−0.148436	−	0.988922i	$-0.547424\pi$
$431$	−6.16323			−0.296873			−0.148436	+	0.988922i	$0.547424\pi$
$432$	2.28163	+	4.66842i	0.109775	+	0.224610i
$433$	−14.7838			−0.710466			−0.355233	−	0.934778i	$-0.615599\pi$
$433$	−14.7838			−0.710466			−0.355233	+	0.934778i	$0.615599\pi$
$434$	−2.96839	−	16.8346i	−0.142487	−	0.808085i
$435$	−2.64272	−	1.82658i	−0.126709	−	0.0875776i
$436$	−10.5612	+	3.84396i	−0.505790	+	0.184092i
$437$	8.71993	+	7.31689i	0.417131	+	0.350014i
$438$	−10.6696	−	15.0420i	−0.509813	−	0.718736i
$439$	−27.9719	−	10.1809i	−1.33502	−	0.485909i	−0.426782	−	0.904354i	$-0.640353\pi$
$439$	−27.9719	−	10.1809i	−1.33502	−	0.485909i	−0.908242	+	0.418445i	$0.862575\pi$
$440$	3.61968	+	6.26947i	0.172561	+	0.298885i
$441$	−12.8806	−	14.9764i	−0.613364	−	0.713162i
$442$	−2.67516	+	4.63351i	−0.127244	+	0.220394i
$443$	23.3447	−	19.5885i	1.10914	−	0.930680i	0.111136	−	0.993805i	$-0.464551\pi$
$443$	23.3447	−	19.5885i	1.10914	−	0.930680i	0.998006	+	0.0631253i	$0.0201068\pi$
$444$	12.2449	+	3.20124i	0.581117	+	0.151924i
$445$	−9.54269	+	54.1193i	−0.452367	+	2.56550i
$446$	−1.25971	+	7.14415i	−0.0596488	+	0.338285i
$447$	−25.9309	−	6.77925i	−1.22649	−	0.320647i
$448$	2.82342	−	2.36913i	0.133394	−	0.111931i
$449$	−5.92055	+	10.2547i	−0.279408	+	0.483949i	−0.971238	−	0.238112i	$-0.923472\pi$
$449$	−5.92055	+	10.2547i	−0.279408	+	0.483949i	0.691830	+	0.722061i	$0.256805\pi$
$450$	14.8482	−	2.80496i	0.699953	−	0.132227i
$451$	−8.08973	−	14.0118i	−0.380930	−	0.659791i
$452$	6.61257	+	2.40678i	0.311029	+	0.113205i
$453$	−20.1877	−	28.4606i	−0.948500	−	1.33720i
$454$	−21.8531	−	18.3369i	−1.02562	−	0.860594i
$455$	−34.0180	+	12.3816i	−1.59479	+	0.580456i
$456$	−4.83702	−	3.34322i	−0.226514	−	0.156561i
$457$	−0.0323668	−	0.183561i	−0.00151406	−	0.00858664i	0.984041	−	0.177940i	$-0.0569432\pi$
$457$	−0.0323668	−	0.183561i	−0.00151406	−	0.00858664i	−0.985555	+	0.169353i	$0.945832\pi$
$458$	1.85538			0.0866963
$459$	−6.45557	−	6.22397i	−0.301320	−	0.290510i
$460$	−10.6230			−0.495299
$461$	1.80687	+	10.2473i	0.0841543	+	0.477263i	0.997536	+	0.0701583i	$0.0223505\pi$
$461$	1.80687	+	10.2473i	0.0841543	+	0.477263i	−0.913382	+	0.407105i	$0.866538\pi$
$462$	13.1830	−	6.24533i	0.613330	−	0.290559i
$463$	−24.2332	+	8.82016i	−1.12621	+	0.409907i	−0.836915	−	0.547332i	$-0.815643\pi$
$463$	−24.2332	+	8.82016i	−1.12621	+	0.409907i	−0.289296	+	0.957240i	$0.593421\pi$
$464$	−0.448476	−	0.376316i	−0.0208200	−	0.0174700i
$465$	10.6151	−	23.1307i	0.492262	−	1.07266i
$466$	−8.01999	−	2.91904i	−0.371519	−	0.135222i
$467$	−10.8506	−	18.7937i	−0.502104	−	0.869670i	−0.999997	−	0.00243153i	$-0.999226\pi$
$467$	−10.8506	−	18.7937i	−0.502104	−	0.869670i	0.497893	−	0.867239i	$-0.334107\pi$
$468$	−0.113240	−	9.30014i	−0.00523452	−	0.429899i
$469$	15.8647	−	27.4785i	0.732566	−	1.26884i
$470$	−9.34844	+	7.84427i	−0.431211	+	0.361829i
$471$	21.9077	−	22.1760i	1.00945	−	1.02182i
$472$	−1.67799	+	9.51638i	−0.0772360	+	0.438027i
$473$	−0.657857	+	3.73089i	−0.0302483	+	0.171547i
$474$	6.46123	+	23.5395i	0.296774	+	1.08120i
$475$	−13.0989	+	10.9913i	−0.601020	+	0.504316i
$476$	−3.18032	+	5.50848i	−0.145770	+	0.252481i
$477$	7.64612	+	1.25243i	0.350092	+	0.0573447i
$478$	3.64398	+	6.31156i	0.166672	+	0.288684i
$479$	36.7619	+	13.3802i	1.67970	+	0.611359i	0.993268	−	0.115839i	$-0.0369558\pi$
$479$	36.7619	+	13.3802i	1.67970	+	0.611359i	0.686427	+	0.727199i	$0.259178\pi$
$480$	5.46344	−	0.511522i	0.249371	−	0.0233477i
$481$	−17.3542	−	14.5619i	−0.791284	−	0.663966i
$482$	1.25441	−	0.456569i	0.0571370	−	0.0207962i
$483$	−1.73577	+	21.3351i	−0.0789804	+	0.970782i
$484$	−1.00342	−	5.69068i	−0.0456100	−	0.258667i
$485$	29.1187			1.32221
$486$	15.1731	+	3.57446i	0.688266	+	0.162141i
$487$	−10.4833			−0.475043			−0.237522	−	0.971382i	$-0.576335\pi$
$487$	−10.4833			−0.475043			−0.237522	+	0.971382i	$0.576335\pi$
$488$	2.27329	+	12.8925i	0.102907	+	0.583614i
$489$	0.428782	−	5.27035i	0.0193902	−	0.238334i
$490$	−19.6025	+	7.13472i	−0.885550	+	0.322314i
$491$	5.25278	+	4.40761i	0.237055	+	0.198913i	0.753574	−	0.657363i	$-0.228328\pi$
$491$	5.25278	+	4.40761i	0.237055	+	0.198913i	−0.516519	+	0.856276i	$0.672773\pi$
$492$	−12.2104	+	1.14322i	−0.550488	+	0.0515402i
$493$	0.949403	+	0.345554i	0.0427589	+	0.0155630i
$494$	5.26240	+	9.11475i	0.236767	+	0.410092i
$495$	21.4325	+	3.51062i	0.963317	+	0.157791i
$496$	2.31899	−	4.01660i	0.104126	−	0.180351i
$497$	5.61145	−	4.70857i	0.251708	−	0.211208i
$498$	−1.42052	−	5.17521i	−0.0636549	−	0.231907i
$499$	3.26002	−	18.4885i	0.145939	−	0.827659i	−0.820670	−	0.571402i	$-0.806400\pi$
$499$	3.26002	−	18.4885i	0.145939	−	0.827659i	0.966609	−	0.256257i	$-0.0824892\pi$
$500$	0.0203300	−	0.115297i	0.000909186	−	0.00515625i
$501$	−4.99225	+	5.05340i	−0.223037	+	0.225769i
$502$	−2.20511	+	1.85030i	−0.0984187	+	0.0825831i
$503$	6.21350	−	10.7621i	0.277046	−	0.479858i	−0.693603	−	0.720357i	$-0.743978\pi$
$503$	6.21350	−	10.7621i	0.277046	−	0.479858i	0.970649	+	0.240499i	$0.0773112\pi$
$504$	−0.134624	−	11.0563i	−0.00599662	−	0.492488i
$505$	−18.9456	−	32.8148i	−0.843069	−	1.46024i
$506$	−7.19996	−	2.62057i	−0.320077	−	0.116499i
$507$	2.44779	−	5.33385i	0.108710	−	0.236885i
$508$	4.58477	+	3.84708i	0.203416	+	0.170687i
$509$	−30.9889	+	11.2790i	−1.37356	+	0.499935i	−0.920219	−	0.391403i	$-0.871990\pi$
$509$	−30.9889	+	11.2790i	−1.37356	+	0.499935i	−0.453340	+	0.891338i	$0.649768\pi$
$510$	−8.55803	+	4.05428i	−0.378956	+	0.179527i
$511$	6.81455	+	38.6472i	0.301458	+	1.70965i
$512$	1.00000			0.0441942
$513$	−16.9526	+	4.87594i	−0.748476	+	0.215278i
$514$	−25.7779			−1.13702
$515$	−7.01231	−	39.7688i	−0.308999	−	1.75242i
$516$	2.36225	+	1.63273i	0.103992	+	0.0718768i
$517$	−8.27121	+	3.01047i	−0.363767	+	0.132400i
$518$	−20.6313	−	17.3117i	−0.906488	−	0.760634i
$519$	17.0626	+	24.0548i	0.748963	+	1.05589i
$520$	−9.22969	−	3.35933i	−0.404749	−	0.147316i
$521$	−7.16598	−	12.4118i	−0.313947	−	0.543773i	0.665266	−	0.746607i	$-0.268318\pi$
$521$	−7.16598	−	12.4118i	−0.313947	−	0.543773i	−0.979213	+	0.202834i	$0.934985\pi$
$522$	−1.72581	+	0.326020i	−0.0755366	+	0.0142695i
$523$	2.85442	−	4.94400i	0.124815	−	0.216186i	−0.796846	−	0.604183i	$-0.793500\pi$
$523$	2.85442	−	4.94400i	0.124815	−	0.216186i	0.921661	+	0.387997i	$0.126833\pi$
$524$	12.5746	−	10.5514i	0.549326	−	0.460939i
$525$	−31.1096	−	8.13313i	−1.35773	−	0.354959i
$526$	−2.61682	+	14.8408i	−0.114099	+	0.647087i
$527$	−1.38988	+	7.88241i	−0.0605442	+	0.343363i
$528$	3.82916	+	1.00108i	0.166643	+	0.0435662i
$529$	−9.00623	+	7.55712i	−0.391575	+	0.328571i
$530$	4.09110	−	7.08599i	0.177706	−	0.307796i
$531$	18.9031	+	21.9788i	0.820326	+	0.953797i
$532$	6.25613	+	10.8359i	0.271238	+	0.469798i
$533$	20.6277	+	7.50787i	0.893485	+	0.325202i
$534$	17.3821	+	24.5054i	0.752198	+	1.06045i
$535$	14.8016	+	12.4200i	0.639930	+	0.536965i
$536$	8.08959	−	2.94437i	0.349417	−	0.127177i
$537$	−20.7400	−	14.3349i	−0.894995	−	0.618597i
$538$	2.78905	+	15.8175i	0.120244	+	0.681939i
$539$	−15.0461			−0.648081
$540$	9.19438	−	13.6551i	0.395663	−	0.587621i
$541$	18.0099			0.774305			0.387153	−	0.922016i	$-0.373459\pi$
$541$	18.0099			0.774305			0.387153	+	0.922016i	$0.373459\pi$
$542$	1.63480	+	9.27143i	0.0702208	+	0.398242i
$543$	20.3860	−	9.65766i	0.874846	−	0.414450i
$544$	−1.62168	+	0.590243i	−0.0695289	+	0.0253065i
$545$	27.2761	+	22.8874i	1.16838	+	0.980387i
$546$	−8.25498	+	17.9880i	−0.353281	+	0.769813i
$547$	19.3837	+	7.05509i	0.828788	+	0.301654i	0.721361	−	0.692559i	$-0.243517\pi$
$547$	19.3837	+	7.05509i	0.828788	+	0.301654i	0.107426	+	0.994213i	$0.465739\pi$
$548$	0.105579	+	0.182869i	0.00451012	+	0.00781176i
$549$	34.2489	+	19.2214i	1.46171	+	0.820351i
$550$	5.75489	−	9.96776i	0.245389	−	0.425027i
$551$	1.52249	−	1.27752i	0.0648601	−	0.0544241i
$552$	−4.08160	+	4.13160i	−0.173724	+	0.175853i
$553$	9.01990	−	51.1544i	0.383565	−	2.17531i
$554$	0.968047	−	5.49007i	0.0411284	−	0.233251i
$555$	−10.6135	−	38.6669i	−0.450517	−	1.64132i
$556$	2.81254	−	2.36000i	0.119278	−	0.100086i
$557$	1.90209	−	3.29452i	0.0805942	−	0.139593i	−0.822911	−	0.568170i	$-0.807652\pi$
$557$	1.90209	−	3.29452i	0.0805942	−	0.139593i	0.903505	+	0.428577i	$0.140985\pi$
$558$	−4.91768	−	13.0159i	−0.208182	−	0.551007i
$559$	−2.57000	−	4.45136i	−0.108699	−	0.188273i
$560$	−10.9726	−	3.99369i	−0.463676	−	0.168764i
$561$	−6.80054	+	0.636710i	−0.287119	+	0.0268819i
$562$	21.4529	+	18.0011i	0.904937	+	0.759332i
$563$	10.4037	−	3.78663i	0.438463	−	0.159587i	−0.113351	−	0.993555i	$-0.536158\pi$
$563$	10.4037	−	3.78663i	0.438463	−	0.159587i	0.551813	+	0.833968i	$0.313936\pi$
$564$	−0.541015	+	6.64986i	−0.0227809	+	0.280009i
$565$	−3.87129	−	21.9552i	−0.162866	−	0.923662i
$566$	6.15522			0.258723
$567$	−25.9225	−	20.6972i	−1.08864	−	0.869199i
$568$	1.98746			0.0833921
$569$	8.11202	+	46.0056i	0.340074	+	1.92865i	0.369836	+	0.929097i	$0.379414\pi$
$569$	8.11202	+	46.0056i	0.340074	+	1.92865i	−0.0297623	+	0.999557i	$0.509475\pi$
$570$	−1.51057	+	18.5670i	−0.0632707	+	0.777688i
$571$	29.7753	−	10.8373i	1.24606	−	0.453528i	0.366990	−	0.930225i	$-0.380388\pi$
$571$	29.7753	−	10.8373i	1.24606	−	0.453528i	0.879068	+	0.476697i	$0.158166\pi$
$572$	−5.42692	−	4.55372i	−0.226911	−	0.190401i
$573$	6.21319	−	0.581718i	0.259560	−	0.0243016i
$574$	24.5230	+	8.92563i	1.02357	+	0.372549i
$575$	8.44468	+	14.6266i	0.352167	+	0.609972i
$576$	1.90024	−	2.32144i	0.0791766	−	0.0967267i
$577$	−22.1642	+	38.3895i	−0.922707	+	1.59818i	−0.127499	+	0.991839i	$0.540695\pi$
$577$	−22.1642	+	38.3895i	−0.922707	+	1.59818i	−0.795208	+	0.606336i	$0.792639\pi$
$578$	−10.7413	+	9.01302i	−0.446779	+	0.374892i
$579$	0.676175	+	2.46343i	0.0281009	+	0.102377i
$580$	−0.322075	+	1.82658i	−0.0133734	+	0.0758445i
$581$	−1.98305	+	11.2464i	−0.0822707	+	0.466580i
$582$	11.1881	−	11.3252i	0.463761	−	0.469443i
$583$	4.52087	−	3.79346i	0.187235	−	0.157109i
$584$	−5.32371	+	9.22094i	−0.220297	+	0.381565i
$585$	−25.3371	+	15.0426i	−1.04756	+	0.621937i
$586$	−1.16755	−	2.02226i	−0.0482310	−	0.0835386i
$587$	−38.5694	−	14.0381i	−1.59193	−	0.579414i	−0.614174	−	0.789170i	$-0.710511\pi$
$587$	−38.5694	−	14.0381i	−1.59193	−	0.579414i	−0.977754	+	0.209756i	$0.932733\pi$
$588$	−4.75683	+	10.3653i	−0.196169	+	0.427460i
$589$	12.0614	+	10.1207i	0.496980	+	0.417015i
$590$	28.7678	−	10.4706i	1.18435	−	0.431069i
$591$	−3.97367	+	1.88249i	−0.163455	+	0.0774351i
$592$	−1.26888	−	7.19618i	−0.0521507	−	0.295761i
$593$	−9.69265			−0.398029			−0.199015	−	0.979996i	$-0.563774\pi$
$593$	−9.69265			−0.398029			−0.199015	+	0.979996i	$0.563774\pi$
$594$	9.60025	−	6.98688i	0.393903	−	0.286675i
$595$	20.1513			0.826121
$596$	2.68710	+	15.2393i	0.110068	+	0.624226i
$597$	−2.63848	−	1.82365i	−0.107986	−	0.0746370i
$598$	9.76857	−	3.55547i	0.399467	−	0.145394i
$599$	−22.8572	−	19.1794i	−0.933918	−	0.783651i	0.0425983	−	0.999092i	$-0.486436\pi$
$599$	−22.8572	−	19.1794i	−0.933918	−	0.783651i	−0.976517	+	0.215442i	$0.930881\pi$
$600$	−5.04744	−	7.11590i	−0.206061	−	0.290505i
$601$	−11.7938	−	4.29259i	−0.481079	−	0.175098i	0.0900856	−	0.995934i	$-0.471286\pi$
$601$	−11.7938	−	4.29259i	−0.481079	−	0.175098i	−0.571165	+	0.820836i	$0.693508\pi$
$602$	−3.05530	−	5.29194i	−0.124525	−	0.215683i
$603$	8.53698	−	24.3745i	0.347653	−	0.992607i
$604$	−10.0729	+	17.4467i	−0.409859	+	0.709896i
$605$	−14.0239	+	11.7674i	−0.570151	+	0.478413i
$606$	−20.0420	−	5.23969i	−0.814152	−	0.212848i
$607$	−0.482765	+	2.73790i	−0.0195948	+	0.111128i	−0.993036	−	0.117808i	$-0.962413\pi$
$607$	−0.482765	+	2.73790i	−0.0195948	+	0.111128i	0.973442	+	0.228935i	$0.0735245\pi$
$608$	−0.589500	+	3.34322i	−0.0239074	+	0.135586i
$609$	3.61586	+	0.945312i	0.146522	+	0.0383060i
$610$	31.7716	−	26.6595i	1.28639	−	1.07941i
$611$	5.97110	−	10.3422i	0.241565	−	0.418403i
$612$	−1.71136	+	4.88624i	−0.0691778	+	0.197514i
$613$	4.29646	+	7.44168i	0.173532	+	0.300567i	0.939652	−	0.342131i	$-0.111149\pi$
$613$	4.29646	+	7.44168i	0.173532	+	0.300567i	−0.766120	+	0.642697i	$0.777815\pi$
$614$	−6.41368	−	2.33439i	−0.258835	−	0.0942082i
$615$	22.4786	+	31.6904i	0.906425	+	1.27788i
$616$	−6.45172	−	5.41363i	−0.259947	−	0.218121i
$617$	18.8681	−	6.86743i	0.759602	−	0.276472i	0.0669615	−	0.997756i	$-0.478670\pi$
$617$	18.8681	−	6.86743i	0.759602	−	0.276472i	0.692640	+	0.721283i	$0.256447\pi$
$618$	−18.1616	−	12.5528i	−0.730567	−	0.504949i
$619$	1.45723	+	8.26436i	0.0585710	+	0.332173i	0.999987	−	0.00507458i	$-0.00161530\pi$
$619$	1.45723	+	8.26436i	0.0585710	+	0.332173i	−0.941416	+	0.337247i	$0.890504\pi$
$620$	−14.6936			−0.590111
$621$	1.83525	+	17.3262i	0.0736461	+	0.695278i
$622$	8.59522			0.344637
$623$	−11.1018	−	62.9612i	−0.444783	−	2.52249i
$624$	−4.85282	+	2.29898i	−0.194268	+	0.0920327i
$625$	23.3174	−	8.48684i	0.932696	−	0.339474i
$626$	−16.5993	−	13.9285i	−0.663443	−	0.556695i
$627$	−5.60411	+	12.2116i	−0.223806	+	0.487684i
$628$	−16.9121	−	6.15549i	−0.674865	−	0.245631i
$629$	6.30522	+	10.9210i	0.251405	+	0.435447i
$630$	−30.1217	+	17.8832i	−1.20008	+	0.712485i
$631$	−8.78157	+	15.2101i	−0.349589	+	0.605506i	−0.986176	−	0.165699i	$-0.947012\pi$
$631$	−8.78157	+	15.2101i	−0.349589	+	0.605506i	0.636588	+	0.771204i	$0.280345\pi$
$632$	10.7960	−	9.05893i	0.429442	−	0.360345i
$633$	−23.1138	+	23.3970i	−0.918691	+	0.929946i
$634$	6.13325	−	34.7834i	0.243582	−	1.38142i
$635$	3.29257	−	18.6731i	0.130662	−	0.741019i
$636$	−1.18406	−	4.31376i	−0.0469511	−	0.171052i
$637$	15.6379	−	13.1218i	0.619596	−	0.519903i
$638$	−0.668890	+	1.15855i	−0.0264816	+	0.0458675i
$639$	3.77666	−	4.61378i	0.149402	−	0.182518i
$640$	−1.58406	−	2.74367i	−0.0626154	−	0.108453i
$641$	12.6056	+	4.58808i	0.497893	+	0.181218i	0.578746	−	0.815508i	$-0.303542\pi$
$641$	12.6056	+	4.58808i	0.497893	+	0.181218i	−0.0808532	+	0.996726i	$0.525765\pi$
$642$	10.5177	−	0.984732i	0.415100	−	0.0388643i
$643$	−7.99375	−	6.70755i	−0.315243	−	0.264520i	0.471412	−	0.881913i	$-0.343744\pi$
$643$	−7.99375	−	6.70755i	−0.315243	−	0.264520i	−0.786655	+	0.617393i	$0.788189\pi$
$644$	11.6132	−	4.22687i	0.457625	−	0.166562i
$645$	0.737715	−	9.06758i	0.0290475	−	0.357035i
$646$	−1.01733	−	5.76958i	−0.0400264	−	0.227001i
$647$	−37.9585			−1.49230			−0.746152	−	0.665775i	$-0.768101\pi$
$647$	−37.9585			−1.49230			−0.746152	+	0.665775i	$0.768101\pi$
$648$	−1.77818	−	8.82259i	−0.0698535	−	0.346584i
$649$	22.0810			0.866756
$650$	2.71168	+	15.3787i	0.106361	+	0.603202i
$651$	−2.40091	+	29.5106i	−0.0940991	+	1.15661i
$652$	−2.86878	+	1.04415i	−0.112350	+	0.0408921i
$653$	−20.9178	−	17.5521i	−0.818578	−	0.686868i	0.134061	−	0.990973i	$-0.457198\pi$
$653$	−20.9178	−	17.5521i	−0.818578	−	0.686868i	−0.952639	+	0.304105i	$0.901643\pi$
$654$	19.3817	−	1.81464i	0.757886	−	0.0709582i
$655$	−48.8684	−	17.7867i	−1.90945	−	0.694982i
$656$	3.54026	+	6.13191i	0.138224	+	0.239411i
$657$	11.2895	+	29.8807i	0.440447	+	1.16576i
$658$	7.09866	−	12.2952i	0.276735	−	0.479318i
$659$	−26.3174	+	22.0829i	−1.02518	+	0.860228i	−0.990270	−	0.139162i	$-0.955559\pi$
$659$	−26.3174	+	22.0829i	−1.02518	+	0.860228i	−0.0349104	+	0.999390i	$0.511115\pi$
$660$	−3.31899	−	12.0917i	−0.129191	−	0.470669i
$661$	−4.26787	+	24.2043i	−0.166001	+	0.941439i	0.782025	+	0.623247i	$0.214187\pi$
$661$	−4.26787	+	24.2043i	−0.166001	+	0.941439i	−0.948026	+	0.318192i	$0.896924\pi$
$662$	−4.48249	+	25.4215i	−0.174217	+	0.988034i
$663$	6.51276	−	6.59254i	0.252935	−	0.256033i
$664$	−2.37353	+	1.99163i	−0.0921108	+	0.0772901i
$665$	19.8202	−	34.3295i	0.768593	−	1.33124i
$666$	−19.1167	−	10.7288i	−0.740757	−	0.415734i
$667$	−0.981523	−	1.70005i	−0.0380047	−	0.0658261i
$668$	3.85386	+	1.40269i	0.149110	+	0.0542718i
$669$	5.24074	−	11.4198i	0.202619	−	0.441515i
$670$	−20.8928	−	17.5311i	−0.807157	−	0.677285i
$671$	28.1105	−	10.2314i	1.08519	−	0.394979i
$672$	−5.76920	+	2.73310i	−0.222552	+	0.105432i
$673$	7.44524	+	42.2241i	0.286993	+	1.62762i	0.698078	+	0.716021i	$0.254039\pi$
$673$	7.44524	+	42.2241i	0.286993	+	1.62762i	−0.411085	+	0.911597i	$0.634850\pi$
$674$	−3.38459			−0.130369
$675$	−26.1105	−	1.80457i	−1.00499	−	0.0694580i
$676$	−3.38830			−0.130319
$677$	1.30018	+	7.37368i	0.0499699	+	0.283393i	0.999546	−	0.0301446i	$-0.00959678\pi$
$677$	1.30018	+	7.37368i	0.0499699	+	0.283393i	−0.949576	+	0.313538i	$0.898486\pi$
$678$	−10.0265	−	6.93005i	−0.385065	−	0.266147i
$679$	−31.8331	+	11.5863i	−1.22164	+	0.444641i
$680$	4.18826	+	3.51437i	0.160613	+	0.134770i
$681$	28.5866	+	40.3014i	1.09544	+	1.54435i
$682$	−9.95894	−	3.62476i	−0.381348	−	0.138799i
$683$	−8.37724	−	14.5098i	−0.320546	−	0.555202i	0.660055	−	0.751218i	$-0.270533\pi$
$683$	−8.37724	−	14.5098i	−0.320546	−	0.555202i	−0.980601	+	0.196015i	$0.937200\pi$
$684$	6.64090	+	7.72141i	0.253921	+	0.295236i
$685$	0.334487	−	0.579349i	0.0127801	−	0.0221358i
$686$	−1.17307	+	0.984318i	−0.0447878	+	0.0375815i
$687$	−3.10912	−	0.812833i	−0.118620	−	0.0310115i
$688$	0.287894	−	1.63273i	0.0109759	−	0.0622471i
$689$	−1.39040	+	7.88535i	−0.0529700	+	0.300408i
$690$	17.8012	+	4.65386i	0.677682	+	0.177170i
$691$	−11.4550	+	9.61189i	−0.435769	+	0.365653i	−0.834123	−	0.551578i	$-0.814026\pi$
$691$	−11.4550	+	9.61189i	−0.435769	+	0.365653i	0.398354	+	0.917232i	$0.369581\pi$
$692$	8.51355	−	14.7459i	0.323637	−	0.560555i
$693$	−24.8272	+	4.69008i	−0.943109	+	0.178161i
$694$	8.10001	+	14.0296i	0.307472	+	0.532558i
$695$	−10.9303	−	3.97830i	−0.414609	−	0.150905i
$696$	0.586663	+	0.827079i	0.0222374	+	0.0313504i
$697$	−9.36048	−	7.85437i	−0.354553	−	0.297506i
$698$	−4.22160	+	1.53654i	−0.159790	+	0.0581587i
$699$	12.1605	+	8.40503i	0.459953	+	0.317908i
$700$	3.22374	+	18.2828i	0.121846	+	0.691023i
$701$	−42.1025			−1.59019			−0.795094	−	0.606486i	$-0.792579\pi$
$701$	−42.1025			−1.59019			−0.795094	+	0.606486i	$0.792579\pi$
$702$	−3.88458	+	15.6341i	−0.146614	+	0.590072i
$703$	24.8065			0.935593
$704$	−0.396798	−	2.25035i	−0.0149549	−	0.0848133i
$705$	19.1020	−	9.04939i	0.719423	−	0.340820i
$706$	21.8259	−	7.94399i	0.821430	−	0.298976i
$707$	33.7687	+	28.3353i	1.27000	+	1.06566i
$708$	6.98094	−	15.2118i	0.262360	−	0.571693i
$709$	−26.7677	−	9.74265i	−1.00528	−	0.365893i	−0.213663	−	0.976907i	$-0.568539\pi$
$709$	−26.7677	−	9.74265i	−1.00528	−	0.365893i	−0.791619	+	0.611015i	$0.790762\pi$
$710$	−3.14826	−	5.45294i	−0.118152	−	0.204645i
$711$	−0.514765	−	42.2764i	−0.0193052	−	1.58549i
$712$	8.67300	−	15.0221i	0.325035	−	0.562976i
$713$	11.9132	−	9.99634i	0.446152	−	0.374366i
$714$	7.74260	−	7.83745i	0.289760	−	0.293309i
$715$	−3.89736	+	22.1030i	−0.145753	+	0.826606i
$716$	−2.52763	+	14.3349i	−0.0944620	+	0.535721i
$717$	−3.34127	−	12.1729i	−0.124782	−	0.454605i
$718$	−8.85083	+	7.42673i	−0.330310	+	0.277163i
$719$	−1.26744	+	2.19526i	−0.0472674	+	0.0818695i	−0.888691	−	0.458506i	$-0.848385\pi$
$719$	−1.26744	+	2.19526i	−0.0472674	+	0.0818695i	0.841424	+	0.540376i	$0.181718\pi$
$720$	−9.37935	−	1.53633i	−0.349548	−	0.0572556i
$721$	23.4900	+	40.6858i	0.874812	+	1.51522i
$722$	7.02454	+	2.55672i	0.261426	+	0.0951513i
$723$	−2.30208	+	0.215535i	−0.0856152	+	0.00801585i
$724$	−9.97681	−	8.37154i	−0.370785	−	0.311126i
$725$	2.77102	−	1.00857i	0.102913	−	0.0374573i
$726$	−0.811593	+	9.97564i	−0.0301210	+	0.370231i
$727$	3.45271	+	19.5813i	0.128054	+	0.726231i	0.979447	+	0.201702i	$0.0646473\pi$
$727$	3.45271	+	19.5813i	0.128054	+	0.726231i	−0.851393	+	0.524529i	$0.824242\pi$
$728$	11.4267			0.423503
$729$	−23.8601	−	12.6371i	−0.883707	−	0.468040i
$730$	33.7323			1.24849
$731$	0.496834	+	2.81769i	0.0183761	+	0.104216i
$732$	1.83869	−	22.6002i	0.0679601	−	0.835327i
$733$	9.40733	−	3.42399i	0.347468	−	0.126468i	−0.162390	−	0.986727i	$-0.551920\pi$
$733$	9.40733	−	3.42399i	0.347468	−	0.126468i	0.509858	+	0.860259i	$0.329698\pi$
$734$	11.9271	+	10.0080i	0.440237	+	0.369403i
$735$	35.9742	−	3.36813i	1.32693	−	0.124235i
$736$	3.15087	+	1.14682i	0.116143	+	0.0422725i
$737$	−9.83580	−	17.0361i	−0.362306	−	0.627533i
$738$	20.9622	+	3.43359i	0.771629	+	0.126392i
$739$	20.1957	−	34.9800i	0.742911	−	1.28676i	−0.208253	−	0.978075i	$-0.566778\pi$
$739$	20.1957	−	34.9800i	0.742911	−	1.28676i	0.951164	−	0.308685i	$-0.0998890\pi$
$740$	−17.7340	+	14.8806i	−0.651913	+	0.547020i
$741$	−4.82525	−	17.5793i	−0.177260	−	0.645791i
$742$	−1.65296	+	9.37439i	−0.0606820	+	0.344145i
$743$	6.19059	−	35.1086i	0.227111	−	1.28801i	−0.631498	−	0.775377i	$-0.717560\pi$
$743$	6.19059	−	35.1086i	0.227111	−	1.28801i	0.858609	−	0.512631i	$-0.171329\pi$
$744$	−5.64565	+	5.71481i	−0.206980	+	0.209515i
$745$	37.5551	−	31.5124i	1.37591	−	1.15453i
$746$	4.87863	−	8.45004i	0.178619	−	0.309378i
$747$	0.113172	+	9.29458i	0.00414076	+	0.340071i
$748$	1.97173	+	3.41514i	0.0720937	+	0.124870i
$749$	−21.1233	−	7.68826i	−0.771830	−	0.280923i
$750$	−0.0845787	+	0.184301i	−0.00308838	+	0.00672971i
$751$	−7.25347	−	6.08638i	−0.264683	−	0.222095i	0.500781	−	0.865574i	$-0.333046\pi$
$751$	−7.25347	−	6.08638i	−0.264683	−	0.222095i	−0.765464	+	0.643479i	$0.777491\pi$
$752$	3.61968	−	1.31746i	0.131996	−	0.0480426i
$753$	4.50577	−	2.13457i	0.164199	−	0.0777879i
$754$	−0.315178	−	1.78746i	−0.0114781	−	0.0650956i
$755$	63.8240			2.32279
$756$	−4.61813	+	18.5864i	−0.167960	+	0.675982i
$757$	−37.9651			−1.37987			−0.689933	−	0.723873i	$-0.742360\pi$
$757$	−37.9651			−1.37987			−0.689933	+	0.723873i	$0.742360\pi$
$758$	−3.26292	−	18.5049i	−0.118514	−	0.672129i
$759$	10.9171	+	7.54563i	0.396267	+	0.273889i
$760$	10.1065	−	3.67846i	0.366601	−	0.133432i
$761$	34.3845	+	28.8520i	1.24644	+	1.04588i	0.996993	+	0.0774952i	$0.0246922\pi$
$761$	34.3845	+	28.8520i	1.24644	+	1.04588i	0.249444	+	0.968389i	$0.419752\pi$
$762$	−5.99746	−	8.45523i	−0.217265	−	0.306301i
$763$	−38.9256	−	14.1678i	−1.40920	−	0.512908i

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	54.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.140451 - 1.72635i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.42692 + 2.03643i) q^{5} +(1.72451 - 0.161460i) q^{6} +(-3.46344 - 1.26059i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.96055 - 0.484935i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.140451 - 1.72635i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(2.42692 + 2.03643i) q^{5} +(1.72451 - 0.161460i) q^{6} +(-3.46344 - 1.26059i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.96055 - 0.484935i) q^{9} +(-1.58406 + 2.74367i) q^{10} +(-1.75046 + 1.46881i) q^{11} +(0.458464 + 1.67027i) q^{12} +(0.538357 - 3.05317i) q^{13} +(0.640018 - 3.62972i) q^{14} +(3.85644 - 3.90368i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-0.862878 + 1.49455i) q^{17} +(-0.0365258 - 2.99978i) q^{18} +(1.69740 + 2.93998i) q^{19} +(-2.97705 - 1.08356i) q^{20} +(-2.66266 + 5.80205i) q^{21} +(-1.75046 - 1.46881i) q^{22} +(3.15087 - 1.14682i) q^{23} +(-1.56529 + 0.741539i) q^{24} +(0.874658 + 4.96043i) q^{25} +3.10027 q^{26} +(-1.25298 + 5.04282i) q^{27} +3.68572 q^{28} +(-0.101661 - 0.576550i) q^{29} +(4.51404 + 3.11998i) q^{30} +(4.35827 - 1.58628i) q^{31} +(0.766044 + 0.642788i) q^{32} +(2.28983 + 3.22820i) q^{33} +(-1.62168 - 0.590243i) q^{34} +(-5.83839 - 10.1124i) q^{35} +(2.94786 - 0.556877i) q^{36} +(3.65360 - 6.32822i) q^{37} +(-2.60057 + 2.18213i) q^{38} +(-5.19523 - 1.35821i) q^{39} +(0.550137 - 3.11998i) q^{40} +(-1.22952 + 6.97295i) q^{41} +(-6.17627 - 1.61469i) q^{42} +(1.27004 - 1.06569i) q^{43} +(1.14253 - 1.97893i) q^{44} +(-6.19747 - 7.20583i) q^{45} +(1.67654 + 2.90386i) q^{46} +(3.61968 + 1.31746i) q^{47} +(-1.00208 - 1.41274i) q^{48} +(5.04404 + 4.23245i) q^{49} +(-4.73319 + 1.72274i) q^{50} +(2.45892 + 1.69954i) q^{51} +(0.538357 + 3.05317i) q^{52} -2.58267 q^{53} +(-5.18379 - 0.358266i) q^{54} -7.23936 q^{55} +(0.640018 + 3.62972i) q^{56} +(5.31383 - 2.51737i) q^{57} +(0.550137 - 0.200234i) q^{58} +(-7.40243 - 6.21138i) q^{59} +(-2.28873 + 4.98724i) q^{60} +(-12.3018 - 4.47750i) q^{61} +(2.31899 + 4.01660i) q^{62} +(9.64238 + 5.41158i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(7.52411 - 6.31348i) q^{65} +(-2.78154 + 2.81561i) q^{66} +(-1.49490 + 8.47798i) q^{67} +(0.299674 - 1.69954i) q^{68} +(-1.53727 - 5.60057i) q^{69} +(8.94493 - 7.50569i) q^{70} +(-0.993732 + 1.72119i) q^{71} +(1.06031 + 2.80638i) q^{72} +(-5.32371 - 9.22094i) q^{73} +(6.86652 + 2.49921i) q^{74} +(8.68627 - 0.813264i) q^{75} +(-2.60057 - 2.18213i) q^{76} +(7.91420 - 2.88053i) q^{77} +(0.435437 - 5.35215i) q^{78} +(2.44726 + 13.8791i) q^{79} +3.16812 q^{80} +(8.52968 + 2.87135i) q^{81} -7.08052 q^{82} +(-0.538035 - 3.05135i) q^{83} +(0.517664 - 6.36283i) q^{84} +(-5.13767 + 1.86996i) q^{85} +(1.27004 + 1.06569i) q^{86} +(-1.00960 + 0.0945255i) q^{87} +(2.14726 + 0.781539i) q^{88} +(8.67300 + 15.0221i) q^{89} +(6.02018 - 7.35459i) q^{90} +(-5.71337 + 9.89585i) q^{91} +(-2.56861 + 2.15532i) q^{92} +(-2.12635 - 7.74668i) q^{93} +(-0.668890 + 3.79346i) q^{94} +(-1.86760 + 10.5917i) q^{95} +(1.21727 - 1.23218i) q^{96} +(7.04084 - 5.90797i) q^{97} +(-3.29226 + 5.70237i) q^{98} +(5.89461 - 3.49963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9}+O(q^{10}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9	\( 12 q - 3 q^{5} + 3 q^{6} - 3 q^{7} - 6 q^{8} - 12 q^{9} - 3 q^{10} - 12 q^{11} - 3 q^{12} + 12 q^{13} - 3 q^{14} - 18 q^{15} - 6 q^{17} + 6 q^{18} - 9 q^{19} + 6 q^{20} + 24 q^{21} - 12 q^{22} + 30 q^{23} - 9 q^{25} + 18 q^{26} + 12 q^{28} + 15 q^{29} + 27 q^{30} + 36 q^{33} - 15 q^{34} + 3 q^{35} - 3 q^{36} - 15 q^{37} + 3 q^{38} - 42 q^{39} - 3 q^{40} - 12 q^{41} - 15 q^{42} + 9 q^{43} - 3 q^{44} + 18 q^{45} + 3 q^{46} - 9 q^{47} + 3 q^{48} - 39 q^{49} - 27 q^{50} - 27 q^{51} + 12 q^{52} - 12 q^{53} - 36 q^{54} + 18 q^{55} - 3 q^{56} + 18 q^{57} - 3 q^{58} + 12 q^{59} - 18 q^{60} - 36 q^{61} - 12 q^{62} + 3 q^{63} - 6 q^{64} - 15 q^{65} - 18 q^{66} + 36 q^{67} + 3 q^{68} + 18 q^{69} + 39 q^{70} + 12 q^{71} + 24 q^{72} - 21 q^{73} + 33 q^{74} + 30 q^{75} + 3 q^{76} + 3 q^{77} + 18 q^{78} + 39 q^{79} + 6 q^{80} + 6 q^{82} + 18 q^{83} - 9 q^{84} + 45 q^{85} + 9 q^{86} + 27 q^{87} + 6 q^{88} + 12 q^{89} + 27 q^{90} - 6 q^{91} - 6 q^{92} - 33 q^{93} + 36 q^{94} - 15 q^{95} + 6 q^{96} + 39 q^{97} - 12 q^{98} + 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^5 + 3 * q^6 - 3 * q^7 - 6 * q^8 - 12 * q^9 - 3 * q^10 - 12 * q^11 - 3 * q^12 + 12 * q^13 - 3 * q^14 - 18 * q^15 - 6 * q^17 + 6 * q^18 - 9 * q^19 + 6 * q^20 + 24 * q^21 - 12 * q^22 + 30 * q^23 - 9 * q^25 + 18 * q^26 + 12 * q^28 + 15 * q^29 + 27 * q^30 + 36 * q^33 - 15 * q^34 + 3 * q^35 - 3 * q^36 - 15 * q^37 + 3 * q^38 - 42 * q^39 - 3 * q^40 - 12 * q^41 - 15 * q^42 + 9 * q^43 - 3 * q^44 + 18 * q^45 + 3 * q^46 - 9 * q^47 + 3 * q^48 - 39 * q^49 - 27 * q^50 - 27 * q^51 + 12 * q^52 - 12 * q^53 - 36 * q^54 + 18 * q^55 - 3 * q^56 + 18 * q^57 - 3 * q^58 + 12 * q^59 - 18 * q^60 - 36 * q^61 - 12 * q^62 + 3 * q^63 - 6 * q^64 - 15 * q^65 - 18 * q^66 + 36 * q^67 + 3 * q^68 + 18 * q^69 + 39 * q^70 + 12 * q^71 + 24 * q^72 - 21 * q^73 + 33 * q^74 + 30 * q^75 + 3 * q^76 + 3 * q^77 + 18 * q^78 + 39 * q^79 + 6 * q^80 + 6 * q^82 + 18 * q^83 - 9 * q^84 + 45 * q^85 + 9 * q^86 + 27 * q^87 + 6 * q^88 + 12 * q^89 + 27 * q^90 - 6 * q^91 - 6 * q^92 - 33 * q^93 + 36 * q^94 - 15 * q^95 + 6 * q^96 + 39 * q^97 - 12 * q^98 + 9 * q^99

Introduction

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