LMFDB - Embedded newform 54.2.e.b.25.1

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			25.1
Root			$0.500000 - 2.42499i$ of defining polynomial
Character	$\chi$	$=$	54.25
Dual form			54.2.e.b.13.1

$q$-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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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	0.0889963	−	0.996032i	$-0.471634\pi$
$5$	2.42692	−	2.03643i	1.08535	−	0.910717i	0.996354	+	0.0853149i	$0.0271896\pi$
$6$	1.72451	+	0.161460i	0.704028	+	0.0659156i
$7$	−3.46344	+	1.26059i	−1.30906	+	0.476458i	−0.899936	−	0.436021i	$-0.856387\pi$
$7$	−3.46344	+	1.26059i	−1.30906	+	0.476458i	−0.409122	+	0.912480i	$0.634165\pi$
$8$	−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	0.339551	−	0.940588i	$-0.389725\pi$
$11$	−1.75046	−	1.46881i	−0.527785	−	0.442864i	−0.867336	+	0.497724i	$0.834169\pi$
$12$	0.458464	−	1.67027i	0.132347	−	0.482166i
$13$	0.538357	+	3.05317i	0.149313	+	0.846798i	0.963802	+	0.266619i	$0.0859065\pi$
$13$	0.538357	+	3.05317i	0.149313	+	0.846798i	−0.814489	+	0.580179i	$0.802982\pi$
$14$	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	0.742209	−	0.670169i	$-0.233778\pi$
$17$	−0.862878	−	1.49455i	−0.209279	−	0.362481i	−0.951487	+	0.307687i	$0.900445\pi$
$18$	−0.0365258	+	2.99978i	−0.00860921	+	0.707054i
$19$	1.69740	−	2.93998i	0.389410	−	0.674478i	−0.602960	−	0.797771i	$-0.706012\pi$
$19$	1.69740	−	2.93998i	0.389410	−	0.674478i	0.992370	+	0.123293i	$0.0393456\pi$
$20$	−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	0.648942	−	0.760838i	$-0.275212\pi$
$23$	3.15087	+	1.14682i	0.657002	+	0.239129i	0.00806071	+	0.999968i	$0.497434\pi$
$24$	−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	−0.992791	−	0.119860i	$-0.961755\pi$
$29$	−0.101661	+	0.576550i	−0.0188780	+	0.107063i	0.973913	+	0.226923i	$0.0728665\pi$
$30$	4.51404	−	3.11998i	0.824147	−	0.569629i
$31$	4.35827	+	1.58628i	0.782769	+	0.284904i	0.702327	−	0.711855i	$-0.252145\pi$
$31$	4.35827	+	1.58628i	0.782769	+	0.284904i	0.0804420	+	0.996759i	$0.474367\pi$
$32$	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	0.992723	+	0.120420i	$0.0384240\pi$
$37$	3.65360	+	6.32822i	0.600648	+	1.04035i	−0.392075	+	0.919933i	$0.628243\pi$
$38$	−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	−0.916601	−	0.399803i	$-0.869078\pi$
$41$	−1.22952	−	6.97295i	−0.192019	−	1.08899i	0.724582	−	0.689188i	$-0.242033\pi$
$42$	−6.17627	+	1.61469i	−0.953019	+	0.249153i
$43$	1.27004	+	1.06569i	0.193679	+	0.162516i	0.734470	−	0.678641i	$-0.237431\pi$
$43$	1.27004	+	1.06569i	0.193679	+	0.162516i	−0.540791	+	0.841157i	$0.681875\pi$
$44$	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	−0.0642537	−	0.997934i	$-0.520467\pi$
$47$	3.61968	−	1.31746i	0.527984	−	0.192171i	0.592238	+	0.805763i	$0.298244\pi$
$48$	−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	−0.981553	−	0.191188i	$-0.938766\pi$
$59$	−7.40243	+	6.21138i	−0.963714	+	0.808652i	0.0178389	+	0.999841i	$0.494321\pi$
$60$	−2.28873	−	4.98724i	−0.295474	−	0.643850i
$61$	−12.3018	+	4.47750i	−1.57509	+	0.573285i	−0.974129	−	0.225994i	$-0.927437\pi$
$61$	−12.3018	+	4.47750i	−1.57509	+	0.573285i	−0.600960	+	0.799279i	$0.705215\pi$
$62$	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	−0.928962	−	0.370175i	$-0.879298\pi$
$67$	−1.49490	−	8.47798i	−0.182631	−	1.03575i	0.746331	−	0.665574i	$-0.231813\pi$
$68$	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	0.801015	−	0.598645i	$-0.204294\pi$
$71$	−0.993732	−	1.72119i	−0.117934	−	0.204268i	−0.918949	+	0.394377i	$0.870961\pi$
$72$	1.06031	−	2.80638i	0.124958	−	0.330735i
$73$	−5.32371	+	9.22094i	−0.623094	+	1.07923i	0.365812	+	0.930689i	$0.380791\pi$
$73$	−5.32371	+	9.22094i	−0.623094	+	1.07923i	−0.988906	+	0.148541i	$0.952542\pi$
$74$	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	−0.462548	−	0.886594i	$-0.653065\pi$
$79$	2.44726	−	13.8791i	0.275338	−	1.56152i	0.737886	−	0.674925i	$-0.235824\pi$
$80$	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	−0.999993	−	0.00365453i	$-0.998837\pi$
$83$	−0.538035	+	3.05135i	−0.0590571	+	0.334929i	0.940936	+	0.338584i	$0.109948\pi$
$84$	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	0.118911	−	0.992905i	$-0.462060\pi$
$89$	8.67300	−	15.0221i	0.919336	−	1.59234i	0.800425	−	0.599432i	$-0.204607\pi$
$90$	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	0.925966	−	0.377606i	$-0.123253\pi$
$97$	7.04084	+	5.90797i	0.714889	+	0.599863i	−0.211077	+	0.977469i	$0.567697\pi$
$98$	−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	−0.834036	−	0.551710i	$-0.813975\pi$
$101$	−11.2389	+	4.09062i	−1.11831	+	0.407032i	−0.284276	+	0.958743i	$0.591753\pi$
$102$	−1.24673	−	2.71668i	−0.123445	−	0.268991i
$103$	−9.76437	+	8.19328i	−0.962112	+	0.807308i	−0.981295	−	0.192508i	$-0.938338\pi$
$103$	−9.76437	+	8.19328i	−0.962112	+	0.807308i	0.0191837	+	0.999816i	$0.493893\pi$
$104$	−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	−0.860110	−	0.510109i	$-0.829605\pi$
$113$	−5.39062	+	4.52327i	−0.507107	+	0.425513i	0.353003	+	0.935622i	$0.385161\pi$
$114$	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	−0.967705	−	0.252084i	$-0.918884\pi$
$127$	−2.99250	+	5.18316i	−0.265541	+	0.459931i	0.702164	+	0.712015i	$0.252217\pi$
$128$	−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	−0.435468	−	0.900204i	$-0.643417\pi$
$131$	−15.4251	−	5.61427i	−1.34770	−	0.490521i	−0.912228	+	0.409683i	$0.865639\pi$
$132$	−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	−0.986334	−	0.164758i	$-0.947316\pi$
$137$	−0.0366673	+	0.207951i	−0.00313270	+	0.0177664i	0.983201	+	0.182524i	$0.0584268\pi$
$138$	5.24854	+	2.48645i	0.446786	+	0.211660i
$139$	−3.45009	−	1.25573i	−0.292633	−	0.106510i	0.191532	−	0.981486i	$-0.438654\pi$
$139$	−3.45009	−	1.25573i	−0.292633	−	0.106510i	−0.484165	+	0.874977i	$0.660877\pi$
$140$	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	0.871769	+	0.489918i	$0.162973\pi$
$149$	2.68710	+	15.2393i	0.220136	+	1.24845i	−0.651633	+	0.758535i	$0.725916\pi$
$150$	2.30926	−	8.41309i	0.188551	−	0.686926i
$151$	15.4325	+	12.9494i	1.25588	+	1.05381i	0.996108	+	0.0881390i	$0.0280920\pi$
$151$	15.4325	+	12.9494i	1.25588	+	1.05381i	0.259772	+	0.965670i	$0.416352\pi$
$152$	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	0.102863	−	0.994695i	$-0.467200\pi$
$157$	13.7868	−	11.5685i	1.10031	−	0.923269i	0.997446	+	0.0714264i	$0.0227551\pi$
$158$	−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	−0.756199	−	0.654341i	$-0.772946\pi$
$167$	−3.14170	+	2.63620i	−0.243112	+	0.203995i	0.513088	+	0.858336i	$0.328502\pi$
$168$	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	−0.00586990	−	0.999983i	$-0.501868\pi$
$173$	−13.0435	−	10.9448i	−0.991680	−	0.832118i	−0.985810	+	0.167864i	$0.946313\pi$
$174$	−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	0.998670	+	0.0515575i	$0.0164185\pi$
$179$	7.27802	+	12.6059i	0.543985	+	0.942210i	−0.454685	+	0.890652i	$0.650248\pi$
$180$	8.28825	−	4.65161i	0.617770	−	0.346710i
$181$	6.51190	−	11.2789i	0.484026	−	0.838357i	−0.515806	−	0.856706i	$-0.672507\pi$
$181$	6.51190	−	11.2789i	0.484026	−	0.838357i	0.999832	+	0.0183482i	$0.00584075\pi$
$182$	−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	−0.953771	−	0.300534i	$-0.902835\pi$
$191$	0.625632	−	3.54814i	0.0452692	−	0.256734i	0.999040	+	0.0437996i	$0.0139463\pi$
$192$	1.42483	−	0.984808i	0.102829	−	0.0710724i
$193$	−1.38592	−	0.504435i	−0.0997610	−	0.0363100i	0.291657	−	0.956523i	$-0.405793\pi$
$193$	−1.38592	−	0.504435i	−0.0997610	−	0.0363100i	−0.391418	+	0.920213i	$0.628015\pi$
$194$	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	−0.907694	−	0.419633i	$-0.862159\pi$
$197$	−1.26931	+	2.19851i	−0.0904346	+	0.156637i	0.817259	+	0.576270i	$0.195492\pi$
$198$	4.47005	−	5.19735i	0.317673	−	0.369360i
$199$	0.925891	+	1.60369i	0.0656347	+	0.113683i	0.896975	−	0.442081i	$-0.145759\pi$
$199$	0.925891	+	1.60369i	0.0656347	+	0.113683i	−0.831341	+	0.555763i	$0.812426\pi$
$200$	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	−0.987175	−	0.159642i	$-0.948966\pi$
$211$	−14.5459	+	12.2054i	−1.00138	+	0.840257i	−0.0142043	+	0.999899i	$0.504522\pi$
$212$	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	−0.103532	−	0.994626i	$-0.533014\pi$
$223$	6.81687	−	2.48114i	0.456491	−	0.166149i	0.560023	+	0.828477i	$0.310792\pi$
$224$	−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	−0.932258	−	0.361793i	$-0.882165\pi$
$227$	−21.8531	−	18.3369i	−1.45044	−	1.21706i	−0.518182	−	0.855271i	$-0.673391\pi$
$228$	−4.13237	−	4.18299i	−0.273673	−	0.277026i
$229$	0.322184	+	1.82720i	0.0212905	+	0.120744i	0.993601	−	0.112949i	$-0.0360298\pi$
$229$	0.322184	+	1.82720i	0.0212905	+	0.120744i	−0.972310	+	0.233694i	$0.924919\pi$
$230$	−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	0.691713	−	0.722172i	$-0.256856\pi$
$233$	−4.26735	−	7.39126i	−0.279563	−	0.484218i	−0.971276	+	0.237955i	$0.923523\pi$
$234$	−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	0.553878	−	0.832598i	$-0.313147\pi$
$239$	6.84845	+	2.49263i	0.442989	+	0.161235i	−0.110889	+	0.993833i	$0.535370\pi$
$240$	0.444966	+	5.46927i	0.0287224	+	0.353040i
$241$	−0.231806	+	1.31464i	−0.0149319	+	0.0846833i	−0.991363	−	0.131146i	$-0.958134\pi$
$241$	−0.231806	+	1.31464i	−0.0149319	+	0.0846833i	0.976431	+	0.215829i	$0.0692455\pi$
$242$	−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	−0.817021	−	0.576608i	$-0.804376\pi$
$251$	1.43928	−	2.49291i	0.0908466	−	0.157351i	0.907868	+	0.419257i	$0.137709\pi$
$252$	−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	−0.725219	−	0.688518i	$-0.758262\pi$
$257$	−4.47629	−	25.3863i	−0.279223	−	1.58355i	0.445996	−	0.895035i	$-0.352850\pi$
$258$	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	0.133736	−	0.991017i	$-0.457303\pi$
$263$	14.1609	−	5.15414i	0.873197	−	0.317818i	0.739461	+	0.673199i	$0.235080\pi$
$264$	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	−0.494567	−	0.869140i	$-0.664673\pi$
$277$	−5.23856	+	1.90668i	−0.314755	+	0.114561i	0.179812	+	0.983701i	$0.442451\pi$
$278$	−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	0.993275	+	0.115777i	$0.0369359\pi$
$281$	21.4529	+	18.0011i	1.27977	+	1.07386i	0.286499	+	0.958081i	$0.407509\pi$
$282$	6.45488	−	1.68753i	0.384383	−	0.100491i
$283$	1.06884	+	6.06171i	0.0635361	+	0.360331i	0.999955	+	0.00944797i	$0.00300743\pi$
$283$	1.06884	+	6.06171i	0.0635361	+	0.360331i	−0.936419	+	0.350883i	$0.885881\pi$
$284$	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	0.277128	−	0.960833i	$-0.410617\pi$
$293$	−2.19428	−	0.798651i	−0.128191	−	0.0466577i	−0.405319	+	0.914175i	$0.632840\pi$
$294$	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	0.752055	−	0.659100i	$-0.229063\pi$
$307$	−3.41265	−	5.91088i	−0.194770	−	0.337351i	−0.946825	+	0.321749i	$0.895729\pi$
$308$	−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	0.997435	+	0.0715798i	$0.0228040\pi$
$311$	1.49254	+	8.46464i	0.0846344	+	0.479986i	−0.912800	+	0.408406i	$0.866085\pi$
$312$	1.42137	−	5.17830i	0.0804690	−	0.293164i
$313$	−16.5993	−	13.9285i	−0.938250	−	0.787285i	0.0390299	−	0.999238i	$-0.487573\pi$
$313$	−16.5993	−	13.9285i	−0.938250	−	0.787285i	−0.977280	+	0.211953i	$0.932018\pi$
$314$	−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	−0.888577	+	0.458728i	$0.848305\pi$
$317$	−33.1899	+	12.0801i	−1.86413	+	0.678488i	−0.975554	+	0.219760i	$0.929473\pi$
$318$	−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	0.425590	−	0.904916i	$-0.360067\pi$
$331$	24.2569	−	8.82879i	1.33328	−	0.485274i	0.907690	+	0.419642i	$0.137844\pi$
$332$	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	0.964607	−	0.263693i	$-0.0849407\pi$
$337$	−0.587727	−	3.33317i	−0.0320156	−	0.181569i	−0.996622	+	0.0821241i	$0.973830\pi$
$338$	−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	0.716601	−	0.697483i	$-0.245697\pi$
$347$	15.2230	+	5.54073i	0.817216	+	0.297442i	0.100615	+	0.994925i	$0.467919\pi$
$348$	0.916387	+	0.434130i	0.0491235	+	0.0232718i
$349$	0.780120	−	4.42428i	0.0417589	−	0.236826i	−0.956783	−	0.290801i	$-0.906078\pi$
$349$	0.780120	−	4.42428i	0.0417589	−	0.236826i	0.998542	+	0.0539752i	$0.0171892\pi$
$350$	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	0.666810	+	0.745228i	$0.267659\pi$
$353$	−4.03327	+	22.8738i	−0.214669	+	1.21745i	−0.881479	+	0.472222i	$0.843452\pi$
$354$	−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	−0.672341	−	0.740241i	$-0.734711\pi$
$359$	5.77697	−	10.0060i	0.304897	−	0.528097i	0.977238	+	0.212144i	$0.0680447\pi$
$360$	−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	0.898616	−	0.438735i	$-0.144573\pi$
$367$	11.9271	+	10.0080i	0.622589	+	0.522414i	−0.276027	+	0.961150i	$0.589018\pi$
$368$	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	−0.815449	−	0.578829i	$-0.803510\pi$
$373$	−7.47450	+	6.27185i	−0.387015	+	0.324744i	0.428434	+	0.903573i	$0.359065\pi$
$374$	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	0.204859	−	0.978791i	$-0.434326\pi$
$383$	23.5697	−	19.7773i	1.20435	−	1.01057i	0.999495	−	0.0317817i	$-0.0101181\pi$
$384$	−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	0.999712	−	0.0239850i	$-0.00763540\pi$
$389$	22.6754	+	19.0269i	1.14969	+	0.964704i	0.149978	+	0.988689i	$0.452080\pi$
$390$	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	−0.994332	−	0.106321i	$-0.966093\pi$
$397$	−8.07134	+	13.9800i	−0.405089	+	0.701635i	0.589243	+	0.807956i	$0.299426\pi$
$398$	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	−0.330377	−	0.943849i	$-0.607176\pi$
$401$	−23.8328	−	8.67444i	−1.19016	−	0.433181i	−0.859778	+	0.510668i	$0.829398\pi$
$402$	−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	0.811701	−	0.584073i	$-0.198542\pi$
$409$	21.3980	+	7.78825i	1.05806	+	0.385104i	0.246364	+	0.969177i	$0.420764\pi$
$410$	−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	0.956782	−	0.290808i	$-0.0939240\pi$
$419$	−0.854828	−	4.84797i	−0.0417611	−	0.236839i	−0.998543	+	0.0539688i	$0.982813\pi$
$420$	14.2138	+	14.3879i	0.693560	+	0.702056i
$421$	15.1046	+	12.6742i	0.736151	+	0.617704i	0.931801	−	0.362970i	$-0.118237\pi$
$421$	15.1046	+	12.6742i	0.736151	+	0.617704i	−0.195650	+	0.980674i	$0.562682\pi$
$422$	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	−0.908242	−	0.418445i	$-0.862575\pi$
$439$	−27.9719	+	10.1809i	−1.33502	+	0.485909i	−0.426782	+	0.904354i	$0.640353\pi$
$440$	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	0.998006	−	0.0631253i	$-0.0201068\pi$
$443$	23.3447	+	19.5885i	1.10914	+	0.930680i	0.111136	+	0.993805i	$0.464551\pi$
$444$	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	0.691830	−	0.722061i	$-0.256805\pi$
$449$	−5.92055	−	10.2547i	−0.279408	−	0.483949i	−0.971238	+	0.238112i	$0.923472\pi$
$450$	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	−0.985555	−	0.169353i	$-0.945832\pi$
$457$	−0.0323668	+	0.183561i	−0.00151406	+	0.00858664i	0.984041	+	0.177940i	$0.0569432\pi$
$458$	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	−0.913382	−	0.407105i	$-0.866538\pi$
$461$	1.80687	−	10.2473i	0.0841543	−	0.477263i	0.997536	−	0.0701583i	$-0.0223505\pi$
$462$	13.1830	+	6.24533i	0.613330	+	0.290559i
$463$	−24.2332	−	8.82016i	−1.12621	−	0.409907i	−0.289296	−	0.957240i	$-0.593421\pi$
$463$	−24.2332	−	8.82016i	−1.12621	−	0.409907i	−0.836915	+	0.547332i	$0.815643\pi$
$464$	−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	0.497893	+	0.867239i	$0.334107\pi$
$467$	−10.8506	+	18.7937i	−0.502104	+	0.869670i	−0.999997	+	0.00243153i	$0.999226\pi$
$468$	−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	0.686427	−	0.727199i	$-0.259178\pi$
$479$	36.7619	−	13.3802i	1.67970	−	0.611359i	0.993268	+	0.115839i	$0.0369558\pi$
$480$	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	−0.516519	−	0.856276i	$-0.672773\pi$
$491$	5.25278	−	4.40761i	0.237055	−	0.198913i	0.753574	+	0.657363i	$0.228328\pi$
$492$	−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	0.966609	+	0.256257i	$0.0824892\pi$
$499$	3.26002	+	18.4885i	0.145939	+	0.827659i	−0.820670	+	0.571402i	$0.806400\pi$
$500$	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	0.970649	−	0.240499i	$-0.0773112\pi$
$503$	6.21350	+	10.7621i	0.277046	+	0.479858i	−0.693603	+	0.720357i	$0.743978\pi$
$504$	−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	−0.453340	−	0.891338i	$-0.649768\pi$
$509$	−30.9889	−	11.2790i	−1.37356	−	0.499935i	−0.920219	+	0.391403i	$0.871990\pi$
$510$	−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	−0.979213	−	0.202834i	$-0.934985\pi$
$521$	−7.16598	+	12.4118i	−0.313947	+	0.543773i	0.665266	+	0.746607i	$0.268318\pi$
$522$	−1.72581	−	0.326020i	−0.0755366	−	0.0142695i
$523$	2.85442	+	4.94400i	0.124815	+	0.216186i	0.921661	−	0.387997i	$-0.126833\pi$
$523$	2.85442	+	4.94400i	0.124815	+	0.216186i	−0.796846	+	0.604183i	$0.793500\pi$
$524$	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	0.107426	−	0.994213i	$-0.465739\pi$
$547$	19.3837	−	7.05509i	0.828788	−	0.301654i	0.721361	+	0.692559i	$0.243517\pi$
$548$	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	0.903505	−	0.428577i	$-0.140985\pi$
$557$	1.90209	+	3.29452i	0.0805942	+	0.139593i	−0.822911	+	0.568170i	$0.807652\pi$
$558$	−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	0.551813	−	0.833968i	$-0.313936\pi$
$563$	10.4037	+	3.78663i	0.438463	+	0.159587i	−0.113351	+	0.993555i	$0.536158\pi$
$564$	−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	−0.0297623	−	0.999557i	$-0.509475\pi$
$569$	8.11202	−	46.0056i	0.340074	−	1.92865i	0.369836	−	0.929097i	$-0.379414\pi$
$570$	−1.51057	−	18.5670i	−0.0632707	−	0.777688i
$571$	29.7753	+	10.8373i	1.24606	+	0.453528i	0.879068	−	0.476697i	$-0.158166\pi$
$571$	29.7753	+	10.8373i	1.24606	+	0.453528i	0.366990	+	0.930225i	$0.380388\pi$
$572$	−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	−0.795208	−	0.606336i	$-0.792639\pi$
$577$	−22.1642	−	38.3895i	−0.922707	−	1.59818i	−0.127499	−	0.991839i	$-0.540695\pi$
$578$	−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	−0.977754	−	0.209756i	$-0.932733\pi$
$587$	−38.5694	+	14.0381i	−1.59193	+	0.579414i	−0.614174	+	0.789170i	$0.710511\pi$
$588$	−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	−0.976517	−	0.215442i	$-0.930881\pi$
$599$	−22.8572	+	19.1794i	−0.933918	+	0.783651i	0.0425983	+	0.999092i	$0.486436\pi$
$600$	−5.04744	+	7.11590i	−0.206061	+	0.290505i
$601$	−11.7938	+	4.29259i	−0.481079	+	0.175098i	−0.571165	−	0.820836i	$-0.693508\pi$
$601$	−11.7938	+	4.29259i	−0.481079	+	0.175098i	0.0900856	+	0.995934i	$0.471286\pi$
$602$	−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	0.973442	−	0.228935i	$-0.0735245\pi$
$607$	−0.482765	−	2.73790i	−0.0195948	−	0.111128i	−0.993036	+	0.117808i	$0.962413\pi$
$608$	−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	−0.766120	−	0.642697i	$-0.777815\pi$
$613$	4.29646	−	7.44168i	0.173532	−	0.300567i	0.939652	+	0.342131i	$0.111149\pi$
$614$	−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	0.692640	−	0.721283i	$-0.256447\pi$
$617$	18.8681	+	6.86743i	0.759602	+	0.276472i	0.0669615	+	0.997756i	$0.478670\pi$
$618$	−18.1616	+	12.5528i	−0.730567	+	0.504949i
$619$	1.45723	−	8.26436i	0.0585710	−	0.332173i	−0.941416	−	0.337247i	$-0.890504\pi$
$619$	1.45723	−	8.26436i	0.0585710	−	0.332173i	0.999987	+	0.00507458i	$0.00161530\pi$
$620$	−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	0.636588	−	0.771204i	$-0.280345\pi$
$631$	−8.78157	−	15.2101i	−0.349589	−	0.605506i	−0.986176	+	0.165699i	$0.947012\pi$
$632$	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	−0.0808532	−	0.996726i	$-0.525765\pi$
$641$	12.6056	−	4.58808i	0.497893	−	0.181218i	0.578746	+	0.815508i	$0.303542\pi$
$642$	10.5177	+	0.984732i	0.415100	+	0.0388643i
$643$	−7.99375	+	6.70755i	−0.315243	+	0.264520i	−0.786655	−	0.617393i	$-0.788189\pi$
$643$	−7.99375	+	6.70755i	−0.315243	+	0.264520i	0.471412	+	0.881913i	$0.343744\pi$
$644$	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	−0.952639	−	0.304105i	$-0.901643\pi$
$653$	−20.9178	+	17.5521i	−0.818578	+	0.686868i	0.134061	+	0.990973i	$0.457198\pi$
$654$	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	−0.0349104	−	0.999390i	$-0.511115\pi$
$659$	−26.3174	−	22.0829i	−1.02518	−	0.860228i	−0.990270	+	0.139162i	$0.955559\pi$
$660$	−3.31899	+	12.0917i	−0.129191	+	0.470669i
$661$	−4.26787	−	24.2043i	−0.166001	−	0.941439i	−0.948026	−	0.318192i	$-0.896924\pi$
$661$	−4.26787	−	24.2043i	−0.166001	−	0.941439i	0.782025	−	0.623247i	$-0.214187\pi$
$662$	−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	−0.411085	−	0.911597i	$-0.634850\pi$
$673$	7.44524	−	42.2241i	0.286993	−	1.62762i	0.698078	−	0.716021i	$-0.254039\pi$
$674$	−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	−0.949576	−	0.313538i	$-0.898486\pi$
$677$	1.30018	−	7.37368i	0.0499699	−	0.283393i	0.999546	+	0.0301446i	$0.00959678\pi$
$678$	−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	−0.980601	−	0.196015i	$-0.937200\pi$
$683$	−8.37724	+	14.5098i	−0.320546	+	0.555202i	0.660055	+	0.751218i	$0.270533\pi$
$684$	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	0.398354	−	0.917232i	$-0.369581\pi$
$691$	−11.4550	−	9.61189i	−0.435769	−	0.365653i	−0.834123	+	0.551578i	$0.814026\pi$
$692$	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	−0.791619	−	0.611015i	$-0.790762\pi$
$709$	−26.7677	+	9.74265i	−1.00528	+	0.365893i	−0.213663	+	0.976907i	$0.568539\pi$
$710$	−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	0.841424	−	0.540376i	$-0.181718\pi$
$719$	−1.26744	−	2.19526i	−0.0472674	−	0.0818695i	−0.888691	+	0.458506i	$0.848385\pi$
$720$	−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	−0.851393	−	0.524529i	$-0.824242\pi$
$727$	3.45271	−	19.5813i	0.128054	−	0.726231i	0.979447	−	0.201702i	$-0.0646473\pi$
$728$	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	0.509858	−	0.860259i	$-0.329698\pi$
$733$	9.40733	+	3.42399i	0.347468	+	0.126468i	−0.162390	+	0.986727i	$0.551920\pi$
$734$	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	0.951164	+	0.308685i	$0.0998890\pi$
$739$	20.1957	+	34.9800i	0.742911	+	1.28676i	−0.208253	+	0.978075i	$0.566778\pi$
$740$	−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	0.858609	+	0.512631i	$0.171329\pi$
$743$	6.19059	+	35.1086i	0.227111	+	1.28801i	−0.631498	+	0.775377i	$0.717560\pi$
$744$	−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	−0.765464	−	0.643479i	$-0.777491\pi$
$751$	−7.25347	+	6.08638i	−0.264683	+	0.222095i	0.500781	+	0.865574i	$0.333046\pi$
$752$	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	0.249444	−	0.968389i	$-0.419752\pi$
$761$	34.3845	−	28.8520i	1.24644	−	1.04588i	0.996993	−	0.0774952i	$-0.0246922\pi$
$762$	−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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