LMFDB - Embedded newform 54.2.e.a.7.1

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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	54.7
Dual form			54.2.e.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-1.11334 - 1.32683i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.439693 + 2.49362i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-1.79813 - 1.50881i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-1.11334 - 1.32683i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.439693 + 2.49362i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-1.79813 - 1.50881i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.520945 + 2.95442i) q^{9} +(1.26604 + 2.19285i) q^{10} +(-0.745100 + 4.22567i) q^{11} +(-1.70574 - 0.300767i) q^{12} +(-0.713011 - 0.259515i) q^{13} +(-2.20574 - 0.802823i) q^{14} +(2.81908 - 3.35965i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-2.46064 - 4.26195i) q^{17} +(0.520945 + 2.95442i) q^{18} +(3.62449 - 6.27779i) q^{19} +(1.93969 + 1.62760i) q^{20} +4.06564i q^{21} +(0.745100 + 4.22567i) q^{22} +(-0.233956 + 0.196312i) q^{23} +(-1.70574 + 0.300767i) q^{24} +(-1.32635 + 0.482753i) q^{25} -0.758770 q^{26} +(4.50000 - 2.59808i) q^{27} -2.34730 q^{28} +(2.91875 - 1.06234i) q^{29} +(1.50000 - 4.12122i) q^{30} +(-6.58512 + 5.52557i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(6.43629 - 3.71599i) q^{33} +(-3.76991 - 3.16333i) q^{34} +(2.97178 - 5.14728i) q^{35} +(1.50000 + 2.59808i) q^{36} +(3.78699 + 6.55926i) q^{37} +(1.25877 - 7.13884i) q^{38} +(0.449493 + 1.23497i) q^{39} +(2.37939 + 0.866025i) q^{40} +(-4.60607 - 1.67647i) q^{41} +(1.39053 + 3.82045i) q^{42} +(-0.283119 + 1.60565i) q^{43} +(2.14543 + 3.71599i) q^{44} -7.59627 q^{45} +(-0.152704 + 0.264490i) q^{46} +(-1.39053 - 1.16679i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(-0.258770 - 1.46756i) q^{49} +(-1.08125 + 0.907278i) q^{50} +(-2.91534 + 8.00984i) q^{51} +(-0.713011 + 0.259515i) q^{52} +0.573978 q^{53} +(3.34002 - 3.98048i) q^{54} -10.8648 q^{55} +(-2.20574 + 0.802823i) q^{56} +(-12.3648 + 2.18025i) q^{57} +(2.37939 - 1.99654i) q^{58} +(0.950837 + 5.39246i) q^{59} -4.38571i q^{60} +(8.46451 + 7.10257i) q^{61} +(-4.29813 + 7.44459i) q^{62} +(5.39440 - 4.52644i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.333626 - 1.89209i) q^{65} +(4.77719 - 5.69323i) q^{66} +(-0.0393628 - 0.0143269i) q^{67} +(-4.62449 - 1.68317i) q^{68} +(0.520945 + 0.0918566i) q^{69} +(1.03209 - 5.85327i) q^{70} +(2.10220 + 3.64111i) q^{71} +(2.29813 + 1.92836i) q^{72} +(5.54576 - 9.60554i) q^{73} +(5.80200 + 4.86846i) q^{74} +(2.11721 + 1.22237i) q^{75} +(-1.25877 - 7.13884i) q^{76} +(7.71554 - 6.47410i) q^{77} +(0.844770 + 1.00676i) q^{78} +(6.92989 - 2.52227i) q^{79} +2.53209 q^{80} +(-8.45723 - 3.07818i) q^{81} -4.90167 q^{82} +(-6.41147 + 2.33359i) q^{83} +(2.61334 + 3.11446i) q^{84} +(9.54576 - 8.00984i) q^{85} +(0.283119 + 1.60565i) q^{86} +(-4.65910 - 2.68993i) q^{87} +(3.28699 + 2.75811i) q^{88} +(-3.96064 + 6.86002i) q^{89} +(-7.13816 + 2.59808i) q^{90} +(0.890530 + 1.54244i) q^{91} +(-0.0530334 + 0.300767i) q^{92} +(14.6630 + 2.58548i) q^{93} +(-1.70574 - 0.620838i) q^{94} +(17.2481 + 6.27779i) q^{95} +(-1.11334 + 1.32683i) q^{96} +(-0.570108 + 3.23324i) q^{97} +(-0.745100 - 1.29055i) q^{98} +(-12.0963 - 4.40268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8	$ 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{10} - 3 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{17} + 9 q^{19} + 6 q^{20} + 3 q^{22} - 6 q^{23} - 9 q^{25} + 18 q^{26} + 27 q^{27} - 12 q^{28} + 15 q^{29} + 9 q^{30} - 18 q^{31} - 9 q^{33} + 6 q^{34} + 3 q^{35} + 9 q^{36} + 15 q^{37} - 15 q^{38} + 3 q^{40} - 3 q^{41} - 9 q^{42} - 18 q^{43} - 3 q^{44} - 18 q^{45} - 3 q^{46} + 9 q^{47} - 9 q^{48} + 21 q^{49} - 9 q^{50} + 27 q^{51} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 3 q^{56} - 27 q^{57} + 3 q^{58} - 6 q^{59} + 18 q^{61} - 12 q^{62} - 9 q^{63} - 3 q^{64} + 21 q^{65} + 18 q^{66} - 9 q^{67} - 15 q^{68} - 3 q^{70} + 12 q^{71} + 3 q^{73} - 3 q^{74} - 18 q^{75} + 15 q^{76} + 39 q^{77} + 18 q^{78} + 33 q^{79} + 6 q^{80} - 6 q^{82} - 18 q^{83} + 9 q^{84} + 27 q^{85} + 18 q^{86} + 9 q^{87} + 12 q^{88} - 15 q^{89} - 9 q^{90} - 12 q^{91} + 12 q^{92} + 27 q^{93} + 21 q^{95} - 12 q^{97} - 3 q^{98} - 45 q^{99}+O(q^{100}) $ 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^10 - 3 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^17 + 9 * q^19 + 6 * q^20 + 3 * q^22 - 6 * q^23 - 9 * q^25 + 18 * q^26 + 27 * q^27 - 12 * q^28 + 15 * q^29 + 9 * q^30 - 18 * q^31 - 9 * q^33 + 6 * q^34 + 3 * q^35 + 9 * q^36 + 15 * q^37 - 15 * q^38 + 3 * q^40 - 3 * q^41 - 9 * q^42 - 18 * q^43 - 3 * q^44 - 18 * q^45 - 3 * q^46 + 9 * q^47 - 9 * q^48 + 21 * q^49 - 9 * q^50 + 27 * q^51 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 3 * q^56 - 27 * q^57 + 3 * q^58 - 6 * q^59 + 18 * q^61 - 12 * q^62 - 9 * q^63 - 3 * q^64 + 21 * q^65 + 18 * q^66 - 9 * q^67 - 15 * q^68 - 3 * q^70 + 12 * q^71 + 3 * q^73 - 3 * q^74 - 18 * q^75 + 15 * q^76 + 39 * q^77 + 18 * q^78 + 33 * q^79 + 6 * q^80 - 6 * q^82 - 18 * q^83 + 9 * q^84 + 27 * q^85 + 18 * q^86 + 9 * q^87 + 12 * q^88 - 15 * q^89 - 9 * q^90 - 12 * q^91 + 12 * q^92 + 27 * q^93 + 21 * q^95 - 12 * q^97 - 3 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−1.11334	−	1.32683i	−0.642788	−	0.766044i
$3$	−1.11334	−	1.32683i	−0.642788	−	0.766044i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	0.439693	+	2.49362i	0.196637	+	1.11518i	0.910069	+	0.414457i	$0.136028\pi$
$5$	0.439693	+	2.49362i	0.196637	+	1.11518i	−0.713432	+	0.700724i	$0.752860\pi$
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	−1.79813	−	1.50881i	−0.679631	−	0.570278i	0.236268	−	0.971688i	$-0.424076\pi$
$7$	−1.79813	−	1.50881i	−0.679631	−	0.570278i	−0.915898	+	0.401410i	$0.868520\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.520945	+	2.95442i	−0.173648	+	0.984808i
$10$	1.26604	+	2.19285i	0.400358	+	0.693441i
$11$	−0.745100	+	4.22567i	−0.224656	+	1.27409i	0.638685	+	0.769468i	$0.279479\pi$
$11$	−0.745100	+	4.22567i	−0.224656	+	1.27409i	−0.863342	+	0.504620i	$0.831633\pi$
$12$	−1.70574	−	0.300767i	−0.492404	−	0.0868241i
$13$	−0.713011	−	0.259515i	−0.197754	−	0.0719765i	0.241245	−	0.970464i	$-0.422444\pi$
$13$	−0.713011	−	0.259515i	−0.197754	−	0.0719765i	−0.438998	+	0.898488i	$0.644667\pi$
$14$	−2.20574	−	0.802823i	−0.589508	−	0.214563i
$15$	2.81908	−	3.35965i	0.727883	−	0.867457i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.46064	−	4.26195i	−0.596792	−	1.03367i	−0.993291	−	0.115639i	$-0.963108\pi$
$17$	−2.46064	−	4.26195i	−0.596792	−	1.03367i	0.396499	−	0.918035i	$-0.370225\pi$
$18$	0.520945	+	2.95442i	0.122788	+	0.696364i
$19$	3.62449	−	6.27779i	0.831514	−	1.44022i	−0.0653235	−	0.997864i	$-0.520808\pi$
$19$	3.62449	−	6.27779i	0.831514	−	1.44022i	0.896837	−	0.442360i	$-0.145859\pi$
$20$	1.93969	+	1.62760i	0.433728	+	0.363941i
$21$			4.06564i			0.887195i
$22$	0.745100	+	4.22567i	0.158856	+	0.900916i
$23$	−0.233956	+	0.196312i	−0.0487831	+	0.0409339i	−0.666853	−	0.745189i	$-0.732359\pi$
$23$	−0.233956	+	0.196312i	−0.0487831	+	0.0409339i	0.618070	+	0.786123i	$0.287915\pi$
$24$	−1.70574	+	0.300767i	−0.348182	+	0.0613939i
$25$	−1.32635	+	0.482753i	−0.265270	+	0.0965505i
$26$	−0.758770			−0.148807
$27$	4.50000	−	2.59808i	0.866025	−	0.500000i
$28$	−2.34730			−0.443597
$29$	2.91875	−	1.06234i	0.541998	−	0.197271i	−0.0564897	−	0.998403i	$-0.517991\pi$
$29$	2.91875	−	1.06234i	0.541998	−	0.197271i	0.598488	+	0.801132i	$0.295769\pi$
$30$	1.50000	−	4.12122i	0.273861	−	0.752428i
$31$	−6.58512	+	5.52557i	−1.18272	+	0.992422i	−0.182766	+	0.983156i	$0.558505\pi$
$31$	−6.58512	+	5.52557i	−1.18272	+	0.992422i	−0.999957	+	0.00926586i	$0.997051\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	6.43629	−	3.71599i	1.12041	−	0.646871i
$34$	−3.76991	−	3.16333i	−0.646535	−	0.542507i
$35$	2.97178	−	5.14728i	0.502323	−	0.870049i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	3.78699	+	6.55926i	0.622577	+	1.07834i	0.989004	+	0.147888i	$0.0472477\pi$
$37$	3.78699	+	6.55926i	0.622577	+	1.07834i	−0.366427	+	0.930447i	$0.619419\pi$
$38$	1.25877	−	7.13884i	0.204200	−	1.15807i
$39$	0.449493	+	1.23497i	0.0719765	+	0.197754i
$40$	2.37939	+	0.866025i	0.376214	+	0.136931i
$41$	−4.60607	−	1.67647i	−0.719347	−	0.261821i	−0.0436983	−	0.999045i	$-0.513914\pi$
$41$	−4.60607	−	1.67647i	−0.719347	−	0.261821i	−0.675648	+	0.737224i	$0.736136\pi$
$42$	1.39053	+	3.82045i	0.214563	+	0.589508i
$43$	−0.283119	+	1.60565i	−0.0431752	+	0.244859i	−0.998756	−	0.0498718i	$-0.984119\pi$
$43$	−0.283119	+	1.60565i	−0.0431752	+	0.244859i	0.955580	+	0.294730i	$0.0952298\pi$
$44$	2.14543	+	3.71599i	0.323436	+	0.560207i
$45$	−7.59627			−1.13238
$46$	−0.152704	+	0.264490i	−0.0225149	+	0.0389970i
$47$	−1.39053	−	1.16679i	−0.202830	−	0.170194i	0.535715	−	0.844399i	$-0.320042\pi$
$47$	−1.39053	−	1.16679i	−0.202830	−	0.170194i	−0.738545	+	0.674205i	$0.764487\pi$
$48$	−1.50000	+	0.866025i	−0.216506	+	0.125000i
$49$	−0.258770	−	1.46756i	−0.0369672	−	0.209651i
$50$	−1.08125	+	0.907278i	−0.152912	+	0.128308i
$51$	−2.91534	+	8.00984i	−0.408230	+	1.12160i
$52$	−0.713011	+	0.259515i	−0.0988768	+	0.0359882i
$53$	0.573978			0.0788419			0.0394210	−	0.999223i	$-0.487449\pi$
$53$	0.573978			0.0788419			0.0394210	+	0.999223i	$0.487449\pi$
$54$	3.34002	−	3.98048i	0.454519	−	0.541675i
$55$	−10.8648			−1.46501
$56$	−2.20574	+	0.802823i	−0.294754	+	0.107282i
$57$	−12.3648	+	2.18025i	−1.63776	+	0.288782i
$58$	2.37939	−	1.99654i	0.312429	−	0.262159i
$59$	0.950837	+	5.39246i	0.123788	+	0.702039i	0.982020	+	0.188777i	$0.0604522\pi$
$59$	0.950837	+	5.39246i	0.123788	+	0.702039i	−0.858232	+	0.513263i	$0.828437\pi$
$60$		−	4.38571i		−	0.566192i
$61$	8.46451	+	7.10257i	1.08377	+	0.909390i	0.996228	−	0.0867707i	$-0.0276547\pi$
$61$	8.46451	+	7.10257i	1.08377	+	0.909390i	0.0875408	+	0.996161i	$0.472099\pi$
$62$	−4.29813	+	7.44459i	−0.545863	+	0.945463i
$63$	5.39440	−	4.52644i	0.679631	−	0.570278i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.333626	−	1.89209i	0.0413812	−	0.234684i
$66$	4.77719	−	5.69323i	0.588031	−	0.700788i
$67$	−0.0393628	−	0.0143269i	−0.00480894	−	0.00175031i	0.339615	−	0.940565i	$-0.389703\pi$
$67$	−0.0393628	−	0.0143269i	−0.00480894	−	0.00175031i	−0.344423	+	0.938814i	$0.611926\pi$
$68$	−4.62449	−	1.68317i	−0.560801	−	0.204115i
$69$	0.520945	+	0.0918566i	0.0627144	+	0.0110582i
$70$	1.03209	−	5.85327i	0.123358	−	0.699599i
$71$	2.10220	+	3.64111i	0.249485	+	0.432120i	0.963383	−	0.268129i	$-0.0864054\pi$
$71$	2.10220	+	3.64111i	0.249485	+	0.432120i	−0.713898	+	0.700250i	$0.753072\pi$
$72$	2.29813	+	1.92836i	0.270838	+	0.227260i
$73$	5.54576	−	9.60554i	0.649082	−	1.12424i	−0.334260	−	0.942481i	$-0.608487\pi$
$73$	5.54576	−	9.60554i	0.649082	−	1.12424i	0.983342	−	0.181762i	$-0.0581802\pi$
$74$	5.80200	+	4.86846i	0.674469	+	0.565947i
$75$	2.11721	+	1.22237i	0.244474	+	0.141147i
$76$	−1.25877	−	7.13884i	−0.144391	−	0.818881i
$77$	7.71554	−	6.47410i	0.879267	−	0.737793i
$78$	0.844770	+	1.00676i	0.0956514	+	0.113993i
$79$	6.92989	−	2.52227i	0.779674	−	0.283778i	0.0786372	−	0.996903i	$-0.474943\pi$
$79$	6.92989	−	2.52227i	0.779674	−	0.283778i	0.701037	+	0.713125i	$0.252721\pi$
$80$	2.53209			0.283096
$81$	−8.45723	−	3.07818i	−0.939693	−	0.342020i
$82$	−4.90167			−0.541299
$83$	−6.41147	+	2.33359i	−0.703751	+	0.256144i	−0.669011	−	0.743252i	$-0.733282\pi$
$83$	−6.41147	+	2.33359i	−0.703751	+	0.256144i	−0.0347393	+	0.999396i	$0.511060\pi$
$84$	2.61334	+	3.11446i	0.285139	+	0.339815i
$85$	9.54576	−	8.00984i	1.03538	−	0.868789i
$86$	0.283119	+	1.60565i	0.0305295	+	0.173141i
$87$	−4.65910	−	2.68993i	−0.499508	−	0.288391i
$88$	3.28699	+	2.75811i	0.350394	+	0.294016i
$89$	−3.96064	+	6.86002i	−0.419827	+	0.727161i	−0.995922	−	0.0902216i	$-0.971242\pi$
$89$	−3.96064	+	6.86002i	−0.419827	+	0.727161i	0.576095	+	0.817383i	$0.304576\pi$
$90$	−7.13816	+	2.59808i	−0.752428	+	0.273861i
$91$	0.890530	+	1.54244i	0.0933529	+	0.161692i
$92$	−0.0530334	+	0.300767i	−0.00552912	+	0.0313572i
$93$	14.6630	+	2.58548i	1.52048	+	0.268102i
$94$	−1.70574	−	0.620838i	−0.175933	−	0.0640345i
$95$	17.2481	+	6.27779i	1.76962	+	0.644088i
$96$	−1.11334	+	1.32683i	−0.113630	+	0.135419i
$97$	−0.570108	+	3.23324i	−0.0578857	+	0.328286i	−0.999975	−	0.00707624i	$-0.997748\pi$
$97$	−0.570108	+	3.23324i	−0.0578857	+	0.328286i	0.942089	+	0.335362i	$0.108859\pi$
$98$	−0.745100	−	1.29055i	−0.0752665	−	0.130365i
$99$	−12.0963	−	4.40268i	−1.21572	−	0.442486i
$100$	−0.705737	+	1.22237i	−0.0705737	+	0.122237i
$101$	−9.18732	−	7.70908i	−0.914172	−	0.767082i	0.0587358	−	0.998274i	$-0.481293\pi$
$101$	−9.18732	−	7.70908i	−0.914172	−	0.767082i	−0.972908	+	0.231192i	$0.925737\pi$
$102$			8.52390i			0.843992i
$103$	0.418748	+	2.37484i	0.0412605	+	0.234000i	0.998463	−	0.0554184i	$-0.0176493\pi$
$103$	0.418748	+	2.37484i	0.0412605	+	0.234000i	−0.957203	+	0.289418i	$0.906538\pi$
$104$	−0.581252	+	0.487728i	−0.0569964	+	0.0478257i
$105$	−10.1382	+	1.78763i	−0.989383	+	0.174455i
$106$	0.539363	−	0.196312i	0.0523876	−	0.0190675i
$107$	−2.42602			−0.234532			−0.117266	−	0.993101i	$-0.537413\pi$
$107$	−2.42602			−0.234532			−0.117266	+	0.993101i	$0.537413\pi$
$108$	1.77719	−	4.88279i	0.171010	−	0.469846i
$109$	−2.32770			−0.222953			−0.111476	−	0.993767i	$-0.535558\pi$
$109$	−2.32770			−0.222953			−0.111476	+	0.993767i	$0.535558\pi$
$110$	−10.2096	+	3.71599i	−0.973448	+	0.354306i
$111$	4.48680	−	12.3274i	0.425868	−	1.17006i
$112$	−1.79813	+	1.50881i	−0.169908	+	0.142569i
$113$	−2.96198	−	16.7982i	−0.278640	−	1.58024i	−0.727157	−	0.686471i	$-0.759159\pi$
$113$	−2.96198	−	16.7982i	−0.278640	−	1.58024i	0.448518	−	0.893774i	$-0.351952\pi$
$114$	−10.8735	+	6.27779i	−1.01839	+	0.587969i
$115$	−0.592396	−	0.497079i	−0.0552412	−	0.0463529i
$116$	1.55303	−	2.68993i	0.144196	−	0.249754i
$117$	1.13816	−	1.97134i	0.105223	−	0.182251i
$118$	2.73783	+	4.74205i	0.252037	+	0.436541i
$119$	−2.00593	+	11.3762i	−0.183883	+	1.04285i
$120$	−1.50000	−	4.12122i	−0.136931	−	0.376214i
$121$	−6.96451	−	2.53487i	−0.633137	−	0.230443i
$122$	10.3833	+	3.77920i	0.940056	+	0.342152i
$123$	2.90373	+	7.97794i	0.261821	+	0.719347i
$124$	−1.49273	+	8.46567i	−0.134051	+	0.760240i
$125$	4.54323	+	7.86911i	0.406359	+	0.703835i
$126$	3.52094	−	6.09845i	0.313671	−	0.543294i
$127$	−6.32295	+	10.9517i	−0.561071	+	0.971803i	0.436332	+	0.899786i	$0.356277\pi$
$127$	−6.32295	+	10.9517i	−0.561071	+	0.971803i	−0.997403	+	0.0720178i	$0.977056\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	2.44562	−	1.41198i	0.215325	−	0.124318i
$130$	−0.333626	−	1.89209i	−0.0292609	−	0.165947i
$131$	−3.97565	+	3.33597i	−0.347354	+	0.291465i	−0.799727	−	0.600364i	$-0.795022\pi$
$131$	−3.97565	+	3.33597i	−0.347354	+	0.291465i	0.452372	+	0.891829i	$0.350578\pi$
$132$	2.54189	−	6.98378i	0.221243	−	0.607860i
$133$	−15.9893	+	5.81964i	−1.38645	+	0.504627i
$134$	−0.0418891			−0.00361866
$135$	8.45723	+	10.0789i	0.727883	+	0.867457i
$136$	−4.92127			−0.421996
$137$	16.0817	−	5.85327i	1.37395	−	0.500078i	0.453614	−	0.891198i	$-0.350134\pi$
$137$	16.0817	−	5.85327i	1.37395	−	0.500078i	0.920340	+	0.391120i	$0.127912\pi$
$138$	0.520945	−	0.0918566i	0.0443457	−	0.00781935i
$139$	9.34389	−	7.84046i	0.792539	−	0.665019i	−0.153834	−	0.988097i	$-0.549162\pi$
$139$	9.34389	−	7.84046i	0.792539	−	0.665019i	0.946372	+	0.323078i	$0.104718\pi$
$140$	−1.03209	−	5.85327i	−0.0872274	−	0.494691i
$141$			3.14403i			0.264775i
$142$	3.22075	+	2.70253i	0.270279	+	0.226791i
$143$	1.62789	−	2.81959i	0.136131	−	0.235786i
$144$	2.81908	+	1.02606i	0.234923	+	0.0855050i
$145$	3.93242	+	6.81115i	0.326570	+	0.565635i
$146$	1.92602	−	10.9230i	0.159399	−	0.903995i
$147$	−1.65910	+	1.97724i	−0.136840	+	0.163080i
$148$	7.11721	+	2.59045i	0.585031	+	0.212934i
$149$	−7.23783	−	2.63435i	−0.592946	−	0.215815i	0.0280788	−	0.999606i	$-0.491061\pi$
$149$	−7.23783	−	2.63435i	−0.592946	−	0.215815i	−0.621025	+	0.783791i	$0.713283\pi$
$150$	2.40760	+	0.424525i	0.196580	+	0.0346624i
$151$	−0.135630	+	0.769193i	−0.0110374	+	0.0625961i	−0.989829	−	0.142262i	$-0.954562\pi$
$151$	−0.135630	+	0.769193i	−0.0110374	+	0.0625961i	0.978792	+	0.204858i	$0.0656734\pi$
$152$	−3.62449	−	6.27779i	−0.293985	−	0.509196i
$153$	13.8735	−	5.04952i	1.12160	−	0.408230i
$154$	5.03596	−	8.72254i	0.405809	−	0.702882i
$155$	−16.6741	−	13.9912i	−1.33930	−	1.12380i
$156$	1.13816	+	0.657115i	0.0911254	+	0.0526113i
$157$	−1.80793	−	10.2533i	−0.144289	−	0.818302i	−0.967935	−	0.251199i	$-0.919175\pi$
$157$	−1.80793	−	10.2533i	−0.144289	−	0.818302i	0.823647	−	0.567103i	$-0.191936\pi$
$158$	5.64930	−	4.74033i	0.449434	−	0.377120i
$159$	−0.639033	−	0.761570i	−0.0506786	−	0.0603964i
$160$	2.37939	−	0.866025i	0.188107	−	0.0684653i
$161$	0.716881			0.0564982
$162$	−9.00000			−0.707107
$163$	−10.5740			−0.828218			−0.414109	−	0.910227i	$-0.635907\pi$
$163$	−10.5740			−0.828218			−0.414109	+	0.910227i	$0.635907\pi$
$164$	−4.60607	+	1.67647i	−0.359673	+	0.130910i
$165$	12.0963	+	14.4158i	0.941693	+	1.12227i
$166$	−5.22668	+	4.38571i	−0.405669	+	0.340397i
$167$	0.260992	+	1.48016i	0.0201962	+	0.114538i	0.993239	−	0.116085i	$-0.0370346\pi$
$167$	0.260992	+	1.48016i	0.0201962	+	0.114538i	−0.973043	+	0.230623i	$0.925923\pi$
$168$	3.52094	+	2.03282i	0.271647	+	0.156835i
$169$	−9.51754	−	7.98617i	−0.732119	−	0.614320i
$170$	6.23055	−	10.7916i	0.477862	−	0.827680i
$171$	16.6591	+	13.9786i	1.27395	+	1.06897i
$172$	0.815207	+	1.41198i	0.0621590	+	0.107663i
$173$	−1.93629	+	10.9812i	−0.147213	+	0.834888i	0.818350	+	0.574720i	$0.194889\pi$
$173$	−1.93629	+	10.9812i	−0.147213	+	0.834888i	−0.965563	+	0.260168i	$0.916222\pi$
$174$	−5.29813	−	0.934204i	−0.401650	−	0.0708218i
$175$	3.11334	+	1.13316i	0.235346	+	0.0856591i
$176$	4.03209	+	1.46756i	0.303930	+	0.110622i
$177$	6.09627	−	7.26525i	0.458223	−	0.546089i
$178$	−1.37551	+	7.80093i	−0.103099	+	0.584705i
$179$	−3.90420	−	6.76227i	−0.291814	−	0.505436i	0.682425	−	0.730956i	$-0.260925\pi$
$179$	−3.90420	−	6.76227i	−0.291814	−	0.505436i	−0.974239	+	0.225520i	$0.927592\pi$
$180$	−5.81908	+	4.88279i	−0.433728	+	0.363941i
$181$	−5.23783	+	9.07218i	−0.389325	+	0.674330i	−0.992359	−	0.123385i	$-0.960625\pi$
$181$	−5.23783	+	9.07218i	−0.389325	+	0.674330i	0.603034	+	0.797715i	$0.293958\pi$
$182$	1.36437	+	1.14484i	0.101134	+	0.0848614i
$183$		−	19.1385i		−	1.41476i
$184$	0.0530334	+	0.300767i	0.00390968	+	0.0221729i
$185$	−14.6912	+	12.3274i	−1.08012	+	0.906326i
$186$	14.6630	−	2.58548i	1.07514	−	0.189576i
$187$	19.8430	−	7.22227i	1.45107	−	0.528144i
$188$	−1.81521			−0.132388
$189$	−12.0116	−	2.11797i	−0.873716	−	0.154060i
$190$	18.3550			1.33161
$191$	11.4918	−	4.18269i	0.831521	−	0.302649i	0.109038	−	0.994038i	$-0.465223\pi$
$191$	11.4918	−	4.18269i	0.831521	−	0.302649i	0.722483	+	0.691389i	$0.243001\pi$
$192$	−0.592396	+	1.62760i	−0.0427525	+	0.117462i
$193$	−12.5385	+	10.5210i	−0.902540	+	0.757321i	−0.970685	−	0.240354i	$-0.922736\pi$
$193$	−12.5385	+	10.5210i	−0.902540	+	0.757321i	0.0681452	+	0.997675i	$0.478292\pi$
$194$	0.570108	+	3.23324i	0.0409313	+	0.232133i
$195$	−2.88191	+	1.66387i	−0.206378	+	0.119152i
$196$	−1.14156	−	0.957882i	−0.0815399	−	0.0684201i
$197$	−9.49794	+	16.4509i	−0.676700	+	1.17208i	0.299269	+	0.954169i	$0.403257\pi$
$197$	−9.49794	+	16.4509i	−0.676700	+	1.17208i	−0.975969	+	0.217910i	$0.930076\pi$
$198$	−12.8726			−0.914814
$199$	−11.5214	−	19.9557i	−0.816731	−	1.41462i	−0.908078	−	0.418801i	$-0.862451\pi$
$199$	−11.5214	−	19.9557i	−0.816731	−	1.41462i	0.0913469	−	0.995819i	$-0.470883\pi$
$200$	−0.245100	+	1.39003i	−0.0173312	+	0.0982900i
$201$	0.0248149	+	0.0681784i	0.00175031	+	0.00480894i
$202$	−11.2699	−	4.10191i	−0.792948	−	0.288610i
$203$	−6.85117	−	2.49362i	−0.480858	−	0.175018i
$204$	2.91534	+	8.00984i	0.204115	+	0.560801i
$205$	2.15523	−	12.2229i	0.150528	−	0.853685i
$206$	1.20574	+	2.08840i	0.0840077	+	0.145506i
$207$	−0.458111	−	0.793471i	−0.0318409	−	0.0551501i
$208$	−0.379385	+	0.657115i	−0.0263056	+	0.0455627i
$209$	23.8273	+	19.9935i	1.64817	+	1.38298i
$210$	−8.91534	+	5.14728i	−0.615217	+	0.355196i
$211$	3.03849	+	17.2321i	0.209178	+	1.18631i	0.890728	+	0.454536i	$0.150195\pi$
$211$	3.03849	+	17.2321i	0.209178	+	1.18631i	−0.681550	+	0.731771i	$0.738694\pi$
$212$	0.439693	−	0.368946i	0.0301982	−	0.0253393i
$213$	2.49067	−	6.84305i	0.170658	−	0.468878i
$214$	−2.27972	+	0.829748i	−0.155838	+	0.0567204i
$215$	−4.12836			−0.281552
$216$		−	5.19615i		−	0.353553i
$217$	20.1780			1.36977
$218$	−2.18732	+	0.796119i	−0.148144	+	0.0539200i
$219$	−18.9192	+	3.33597i	−1.27844	+	0.225424i
$220$	−8.32295	+	6.98378i	−0.561133	+	0.470847i
$221$	0.648423	+	3.67739i	0.0436176	+	0.247368i
$222$		−	13.1185i		−	0.880457i
$223$	−3.23190	−	2.71188i	−0.216424	−	0.181601i	0.528130	−	0.849163i	$-0.322893\pi$
$223$	−3.23190	−	2.71188i	−0.216424	−	0.181601i	−0.744554	+	0.667562i	$0.767338\pi$
$224$	−1.17365	+	2.03282i	−0.0784177	+	0.135823i
$225$	−0.735300	−	4.17009i	−0.0490200	−	0.278006i
$226$	−8.52869	−	14.7721i	−0.567320	−	0.982627i
$227$	2.77244	−	15.7233i	0.184013	−	1.04359i	−0.743203	−	0.669066i	$-0.766694\pi$
$227$	2.77244	−	15.7233i	0.184013	−	1.04359i	0.927216	−	0.374526i	$-0.122194\pi$
$228$	−8.07057	+	9.61814i	−0.534487	+	0.636977i
$229$	16.7713	+	6.10424i	1.10828	+	0.403379i	0.830361	−	0.557226i	$-0.188134\pi$
$229$	16.7713	+	6.10424i	1.10828	+	0.403379i	0.277915	+	0.960606i	$0.410357\pi$
$230$	−0.726682	−	0.264490i	−0.0479160	−	0.0174400i
$231$	−17.1800	−	3.02931i	−1.13036	−	0.199314i
$232$	0.539363	−	3.05888i	0.0354109	−	0.200825i
$233$	0.368241	+	0.637812i	0.0241243	+	0.0417844i	0.877835	−	0.478962i	$-0.158987\pi$
$233$	0.368241	+	0.637812i	0.0241243	+	0.0417844i	−0.853711	+	0.520747i	$0.825654\pi$
$234$	0.395277	−	2.24173i	0.0258401	−	0.146546i
$235$	2.29813	−	3.98048i	0.149914	−	0.259658i
$236$	4.19459	+	3.51968i	0.273045	+	0.229112i
$237$	−11.0620	−	6.38662i	−0.718551	−	0.414856i
$238$	2.00593	+	11.3762i	0.130025	+	0.737409i
$239$	−2.20187	+	1.84759i	−0.142427	+	0.119510i	−0.711218	−	0.702972i	$-0.751856\pi$
$239$	−2.20187	+	1.84759i	−0.142427	+	0.119510i	0.568791	+	0.822482i	$0.307411\pi$
$240$	−2.81908	−	3.35965i	−0.181971	−	0.216864i
$241$	−2.05051	+	0.746324i	−0.132085	+	0.0480749i	−0.407217	−	0.913332i	$-0.633501\pi$
$241$	−2.05051	+	0.746324i	−0.132085	+	0.0480749i	0.275132	+	0.961406i	$0.411278\pi$
$242$	−7.41147			−0.476428
$243$	5.33157	+	14.6484i	0.342020	+	0.939693i
$244$	11.0496			0.707380
$245$	3.54576	−	1.29055i	0.226530	−	0.0824503i
$246$	5.45723	+	6.50368i	0.347941	+	0.414659i
$247$	−4.21348	+	3.53553i	−0.268097	+	0.224960i
$248$	1.49273	+	8.46567i	0.0947882	+	0.537571i
$249$	10.2344	+	5.90885i	0.648580	+	0.374458i
$250$	6.96064	+	5.84067i	0.440229	+	0.369396i
$251$	13.0189	−	22.5494i	0.821745	−	1.42330i	−0.0826372	−	0.996580i	$-0.526334\pi$
$251$	13.0189	−	22.5494i	0.821745	−	1.42330i	0.904382	−	0.426724i	$-0.140332\pi$
$252$	1.22281	−	6.93491i	0.0770299	−	0.436858i
$253$	−0.655230	−	1.13489i	−0.0411939	−	0.0713500i
$254$	−2.19594	+	12.4538i	−0.137785	+	0.781419i
$255$	−21.2554	−	3.74789i	−1.33106	−	0.234702i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−9.38965	−	3.41755i	−0.585710	−	0.213181i	0.0321313	−	0.999484i	$-0.489771\pi$
$257$	−9.38965	−	3.41755i	−0.585710	−	0.213181i	−0.617842	+	0.786302i	$0.711993\pi$
$258$	1.81521	−	2.16328i	0.113010	−	0.134680i
$259$	3.08718	−	17.5083i	0.191828	−	1.08791i
$260$	−0.960637	−	1.66387i	−0.0595762	−	0.103189i
$261$	1.61809	+	9.17664i	0.100157	+	0.568020i
$262$	−2.59492	+	4.49454i	−0.160315	+	0.277673i
$263$	11.6612	+	9.78487i	0.719058	+	0.603361i	0.927125	−	0.374753i	$-0.122273\pi$
$263$	11.6612	+	9.78487i	0.719058	+	0.603361i	−0.208067	+	0.978115i	$0.566717\pi$
$264$		−	7.43199i		−	0.457407i
$265$	0.252374	+	1.43128i	0.0155032	+	0.0879230i
$266$	−13.0346	+	10.9373i	−0.799204	+	0.670611i
$267$	13.5116	−	2.38246i	0.826897	−	0.145804i
$268$	−0.0393628	+	0.0143269i	−0.00240447	+	0.000875155i
$269$	30.5476			1.86252			0.931259	−	0.364358i	$-0.118711\pi$
$269$	30.5476			1.86252			0.931259	+	0.364358i	$0.118711\pi$
$270$	11.3944	+	6.57856i	0.693441	+	0.400358i
$271$	25.8307			1.56910			0.784551	−	0.620064i	$-0.212893\pi$
$271$	25.8307			1.56910			0.784551	+	0.620064i	$0.212893\pi$
$272$	−4.62449	+	1.68317i	−0.280401	+	0.102057i
$273$	1.05509	−	2.89884i	0.0638571	−	0.175446i
$274$	13.1099	−	11.0005i	0.792000	−	0.664567i
$275$	−1.05169	−	5.96443i	−0.0634192	−	0.359668i
$276$	0.458111	−	0.264490i	0.0275750	−	0.0159205i
$277$	−17.1860	−	14.4207i	−1.03261	−	0.866459i	−0.0414465	−	0.999141i	$-0.513197\pi$
$277$	−17.1860	−	14.4207i	−1.03261	−	0.866459i	−0.991159	+	0.132682i	$0.957641\pi$
$278$	6.09879	−	10.5634i	0.365781	−	0.633552i
$279$	−12.8944	−	22.3338i	−0.771968	−	1.33709i
$280$	−2.97178	−	5.14728i	−0.177598	−	0.307609i
$281$	1.01485	−	5.75552i	0.0605410	−	0.343345i	−0.939459	−	0.342662i	$-0.888671\pi$
$281$	1.01485	−	5.75552i	0.0605410	−	0.343345i	1.00000		0.000683195i	$-0.000217468\pi$
$282$	1.07532	+	2.95442i	0.0640345	+	0.175933i
$283$	6.96451	+	2.53487i	0.413997	+	0.150683i	0.540617	−	0.841269i	$-0.318191\pi$
$283$	6.96451	+	2.53487i	0.413997	+	0.150683i	−0.126620	+	0.991951i	$0.540413\pi$
$284$	3.95084	+	1.43799i	0.234439	+	0.0853288i
$285$	−10.8735	−	29.8746i	−0.644088	−	1.76962i
$286$	0.565360	−	3.20631i	0.0334304	−	0.189593i
$287$	5.75284	+	9.96421i	0.339579	+	0.588169i
$288$	3.00000			0.176777
$289$	−3.60947	+	6.25179i	−0.212322	+	0.367752i
$290$	6.02481	+	5.05542i	0.353789	+	0.296864i
$291$	4.92468	−	2.84326i	0.288690	−	0.166675i
$292$	−1.92602	−	10.9230i	−0.112712	−	0.639221i
$293$	−6.79994	+	5.70583i	−0.397257	+	0.333338i	−0.819432	−	0.573176i	$-0.805711\pi$
$293$	−6.79994	+	5.70583i	−0.397257	+	0.333338i	0.422175	+	0.906514i	$0.361267\pi$
$294$	−0.882789	+	2.42544i	−0.0514853	+	0.141455i
$295$	−13.0287	+	4.74205i	−0.758559	+	0.276093i
$296$	7.57398			0.440229
$297$	7.62567	+	20.9513i	0.442486	+	1.21572i
$298$	−7.70233			−0.446184
$299$	0.217759	−	0.0792577i	0.0125933	−	0.00458359i
$300$	2.40760	−	0.424525i	0.139003	−	0.0245100i
$301$	2.93170	−	2.45999i	0.168981	−	0.141792i
$302$	0.135630	+	0.769193i	0.00780460	+	0.0442621i
$303$			20.7728i			1.19337i
$304$	−5.55303	−	4.65955i	−0.318488	−	0.267243i
$305$	−13.9893	+	24.2302i	−0.801026	+	1.38742i
$306$	11.3097	−	9.49000i	0.646535	−	0.542507i
$307$	8.04963	+	13.9424i	0.459417	+	0.795733i	0.998930	−	0.0462440i	$-0.0147252\pi$
$307$	8.04963	+	13.9424i	0.459417	+	0.795733i	−0.539514	+	0.841977i	$0.681392\pi$
$308$	1.74897	−	9.91890i	0.0996568	−	0.565182i
$309$	2.68479	−	3.19961i	0.152733	−	0.182020i
$310$	−20.4538	−	7.44459i	−1.16170	−	0.422824i
$311$	−12.7699	−	4.64787i	−0.724115	−	0.263556i	−0.0464436	−	0.998921i	$-0.514789\pi$
$311$	−12.7699	−	4.64787i	−0.724115	−	0.263556i	−0.677672	+	0.735364i	$0.737011\pi$
$312$	1.29426	+	0.228213i	0.0732732	+	0.0129200i
$313$	−3.73442	+	21.1790i	−0.211082	+	1.19711i	0.676495	+	0.736447i	$0.263498\pi$
$313$	−3.73442	+	21.1790i	−0.211082	+	1.19711i	−0.887577	+	0.460659i	$0.847613\pi$
$314$	−5.20574	−	9.01660i	−0.293777	−	0.508836i
$315$	13.6591	+	11.4613i	0.769603	+	0.645774i
$316$	3.68732	−	6.38662i	0.207428	−	0.359276i
$317$	−16.1578	−	13.5580i	−0.907510	−	0.761491i	0.0641337	−	0.997941i	$-0.479572\pi$
$317$	−16.1578	−	13.5580i	−0.907510	−	0.761491i	−0.971644	+	0.236450i	$0.924016\pi$
$318$	−0.860967	−	0.497079i	−0.0482806	−	0.0278748i
$319$	2.31433	+	13.1252i	0.129578	+	0.734871i
$320$	1.93969	−	1.62760i	0.108432	−	0.0909853i
$321$	2.70099	+	3.21891i	0.150755	+	0.179662i
$322$	0.673648	−	0.245188i	0.0375409	−	0.0136638i
$323$	−35.6742			−1.98496
$324$	−8.45723	+	3.07818i	−0.469846	+	0.171010i
$325$	1.07098			0.0594076
$326$	−9.93629	+	3.61651i	−0.550320	+	0.200300i
$327$	2.59152	+	3.08845i	0.143311	+	0.170792i
$328$	−3.75490	+	3.15074i	−0.207330	+	0.173970i
$329$	0.739885	+	4.19610i	0.0407912	+	0.231338i
$330$	16.2973	+	9.40923i	0.897134	+	0.517961i
$331$	12.5929	+	10.5667i	0.692166	+	0.580797i	0.919533	−	0.393013i	$-0.128567\pi$
$331$	12.5929	+	10.5667i	0.692166	+	0.580797i	−0.227367	+	0.973809i	$0.573012\pi$
$332$	−3.41147	+	5.90885i	−0.187229	+	0.324290i
$333$	−21.3516	+	7.77136i	−1.17006	+	0.425868i
$334$	0.751497	+	1.30163i	0.0411201	+	0.0712220i
$335$	0.0184183	−	0.104455i	0.00100630	−	0.00570701i
$336$	4.00387	+	0.705990i	0.218429	+	0.0385149i
$337$	−9.91534	−	3.60889i	−0.540123	−	0.196589i	0.0575296	−	0.998344i	$-0.481678\pi$
$337$	−9.91534	−	3.60889i	−0.540123	−	0.196589i	−0.597653	+	0.801755i	$0.703900\pi$
$338$	−11.6750	−	4.24935i	−0.635036	−	0.231134i
$339$	−18.9907	+	22.6322i	−1.03143	+	1.22921i
$340$	2.16385	−	12.2718i	0.117351	−	0.665531i
$341$	−18.4427	−	31.9437i	−0.998727	−	1.72985i
$342$	20.4354	+	7.43788i	1.10502	+	0.402195i
$343$	−9.96451	+	17.2590i	−0.538033	+	0.931900i
$344$	1.24897	+	1.04801i	0.0673400	+	0.0565049i
$345$			1.33943i			0.0721123i
$346$	1.93629	+	10.9812i	0.104096	+	0.590355i
$347$	21.7251	−	18.2295i	1.16626	−	0.978612i	0.166292	−	0.986077i	$-0.446821\pi$
$347$	21.7251	−	18.2295i	1.16626	−	0.978612i	0.999972	+	0.00746500i	$0.00237621\pi$
$348$	−5.29813	+	0.934204i	−0.284010	+	0.0500786i
$349$	−14.7554	+	5.37051i	−0.789837	+	0.287477i	−0.705268	−	0.708941i	$-0.749173\pi$
$349$	−14.7554	+	5.37051i	−0.789837	+	0.287477i	−0.0845685	+	0.996418i	$0.526951\pi$
$350$	3.31315			0.177095
$351$	−3.88279	+	0.684640i	−0.207248	+	0.0365434i
$352$	4.29086			0.228704
$353$	1.93969	−	0.705990i	0.103239	−	0.0375761i	−0.289884	−	0.957062i	$-0.593617\pi$
$353$	1.93969	−	0.705990i	0.103239	−	0.0375761i	0.393123	+	0.919486i	$0.371395\pi$
$354$	3.24376	−	8.91215i	0.172404	−	0.473675i
$355$	−8.15523	+	6.84305i	−0.432835	+	0.363191i
$356$	1.37551	+	7.80093i	0.0729021	+	0.413449i
$357$	17.3275	−	10.0041i	0.917070	−	0.529471i
$358$	−5.98158	−	5.01914i	−0.316136	−	0.265270i
$359$	17.4820	−	30.2798i	0.922667	−	1.59811i	0.127397	−	0.991852i	$-0.459338\pi$
$359$	17.4820	−	30.2798i	0.922667	−	1.59811i	0.795271	−	0.606255i	$-0.207329\pi$
$360$	−3.79813	+	6.57856i	−0.200179	+	0.346721i
$361$	−16.7738	−	29.0530i	−0.882831	−	1.52911i
$362$	−1.81908	+	10.3165i	−0.0956086	+	0.542223i
$363$	4.39053	+	12.0629i	0.230443	+	0.633137i
$364$	1.67365	+	0.609158i	0.0877230	+	0.0319286i
$365$	26.3910	+	9.60554i	1.38137	+	0.502777i
$366$	−6.54576	−	17.9843i	−0.342152	−	0.940056i
$367$	−0.0773815	+	0.438852i	−0.00403928	+	0.0229079i	−0.986761	−	0.162182i	$-0.948147\pi$
$367$	−0.0773815	+	0.438852i	−0.00403928	+	0.0229079i	0.982722	+	0.185090i	$0.0592578\pi$
$368$	0.152704	+	0.264490i	0.00796023	+	0.0137875i
$369$	7.35251	−	12.7349i	0.382756	−	0.662954i
$370$	−9.58899	+	16.6086i	−0.498508	+	0.863441i
$371$	−1.03209	−	0.866025i	−0.0535834	−	0.0449618i
$372$	12.8944	−	7.44459i	0.668543	−	0.385984i
$373$	−3.83110	−	21.7272i	−0.198367	−	1.12499i	−0.907542	−	0.419962i	$-0.862044\pi$
$373$	−3.83110	−	21.7272i	−0.198367	−	1.12499i	0.709175	−	0.705032i	$-0.249068\pi$
$374$	16.1762	−	13.5734i	0.836450	−	0.701865i
$375$	5.38279	−	14.7891i	0.277966	−	0.763705i
$376$	−1.70574	+	0.620838i	−0.0879667	+	0.0320173i
$377$	−2.35679			−0.121381
$378$	−12.0116	+	2.11797i	−0.617811	+	0.108937i
$379$	13.1138			0.673611			0.336806	−	0.941574i	$-0.390654\pi$
$379$	13.1138			0.673611			0.336806	+	0.941574i	$0.390654\pi$
$380$	17.2481	−	6.27779i	0.884808	−	0.322044i
$381$	21.5706	−	3.80347i	1.10509	−	0.194858i
$382$	9.36824	−	7.86089i	0.479321	−	0.402198i
$383$	2.79767	+	15.8664i	0.142954	+	0.810733i	0.968987	+	0.247111i	$0.0794813\pi$
$383$	2.79767	+	15.8664i	0.142954	+	0.810733i	−0.826033	+	0.563622i	$0.809408\pi$
$384$			1.73205i			0.0883883i
$385$	19.5364	+	16.3930i	0.995668	+	0.835465i
$386$	−8.18392	+	14.1750i	−0.416550	+	0.721486i
$387$	−4.59627	−	1.67290i	−0.233641	−	0.0850385i
$388$	1.64156	+	2.84326i	0.0833375	+	0.144345i
$389$	0.0984882	−	0.558554i	0.00499355	−	0.0283198i	−0.982209	−	0.187790i	$-0.939868\pi$
$389$	0.0984882	−	0.558554i	0.00499355	−	0.0283198i	0.987203	+	0.159470i	$0.0509786\pi$
$390$	−2.13903	+	2.54920i	−0.108314	+	0.129084i
$391$	1.41235	+	0.514054i	0.0714257	+	0.0259968i
$392$	−1.40033	−	0.509678i	−0.0707273	−	0.0257426i
$393$	8.85251	+	1.56094i	0.446550	+	0.0787388i
$394$	−3.29860	+	18.7073i	−0.166181	+	0.942460i
$395$	9.33662	+	16.1715i	0.469776	+	0.813676i
$396$	−12.0963	+	4.40268i	−0.607860	+	0.221243i
$397$	−18.0107	+	31.1955i	−0.903933	+	1.56566i	−0.0815894	+	0.996666i	$0.526000\pi$
$397$	−18.0107	+	31.1955i	−0.903933	+	1.56566i	−0.822343	+	0.568992i	$0.807334\pi$
$398$	−17.6518	−	14.8116i	−0.884806	−	0.742440i
$399$	25.5232	+	14.7358i	1.27776	+	0.737715i
$400$	0.245100	+	1.39003i	0.0122550	+	0.0695015i
$401$	27.5724	−	23.1360i	1.37690	−	1.15536i	0.406556	−	0.913626i	$-0.366730\pi$
$401$	27.5724	−	23.1360i	1.37690	−	1.15536i	0.970344	−	0.241730i	$-0.0777147\pi$
$402$	0.0466368	+	0.0555796i	0.00232603	+	0.00277206i
$403$	6.12923	−	2.23086i	0.305319	−	0.111127i
$404$	−11.9932			−0.596684
$405$	3.95723	−	22.4426i	0.196637	−	1.11518i
$406$	−7.29086			−0.361839
$407$	−30.5390	+	11.1153i	−1.51376	+	0.550963i
$408$	5.47906	+	6.52968i	0.271254	+	0.323268i
$409$	9.71032	−	8.14793i	0.480145	−	0.402889i	−0.370334	−	0.928899i	$-0.620757\pi$
$409$	9.71032	−	8.14793i	0.480145	−	0.402889i	0.850479	+	0.526009i	$0.176312\pi$
$410$	−2.15523	−	12.2229i	−0.106439	−	0.603647i
$411$	−25.6707	−	14.8210i	−1.26624	−	0.731066i
$412$	1.84730	+	1.55007i	0.0910098	+	0.0763663i
$413$	6.42649	−	11.1310i	0.316227	−	0.547721i
$414$	−0.701867	−	0.588936i	−0.0344949	−	0.0289446i
$415$	−8.63816	−	14.9617i	−0.424030	−	0.734442i
$416$	−0.131759	+	0.747243i	−0.00646002	+	0.0366366i
$417$	−20.8059	−	3.66864i	−1.01887	−	0.179654i
$418$	29.2285	+	10.6383i	1.42961	+	0.520336i
$419$	−13.3991	−	4.87689i	−0.654591	−	0.238252i	−0.00669178	−	0.999978i	$-0.502130\pi$
$419$	−13.3991	−	4.87689i	−0.654591	−	0.238252i	−0.647899	+	0.761726i	$0.724352\pi$
$420$	−6.61721	+	7.88609i	−0.322887	+	0.384802i
$421$	0.546637	−	3.10013i	0.0266414	−	0.151091i	−0.968585	−	0.248682i	$-0.920003\pi$
$421$	0.546637	−	3.10013i	0.0266414	−	0.151091i	0.995227	+	0.0975909i	$0.0311137\pi$
$422$	8.74897	+	15.1537i	0.425893	+	0.737669i
$423$	4.17159	−	3.50038i	0.202830	−	0.170194i
$424$	0.286989	−	0.497079i	0.0139374	−	0.0241403i
$425$	5.32114	+	4.46496i	0.258113	+	0.216583i
$426$		−	7.28222i		−	0.352825i
$427$	−4.50387	−	25.5427i	−0.217958	−	1.23610i
$428$	−1.85844	+	1.55942i	−0.0898311	+	0.0753773i
$429$	−5.55350	+	0.979232i	−0.268126	+	0.0472778i
$430$	−3.87939	+	1.41198i	−0.187081	+	0.0680918i
$431$	15.4911			0.746182			0.373091	−	0.927795i	$-0.378298\pi$
$431$	15.4911			0.746182			0.373091	+	0.927795i	$0.378298\pi$
$432$	−1.77719	−	4.88279i	−0.0855050	−	0.234923i
$433$	−2.22844			−0.107092			−0.0535459	−	0.998565i	$-0.517052\pi$
$433$	−2.22844			−0.107092			−0.0535459	+	0.998565i	$0.517052\pi$
$434$	18.9611	−	6.90128i	0.910162	−	0.331272i
$435$	4.65910	−	12.8008i	0.223387	−	0.613750i
$436$	−1.78312	+	1.49621i	−0.0853959	+	0.0716557i
$437$	0.384438	+	2.18025i	0.0183901	+	0.104296i
$438$	−16.6373	+	9.60554i	−0.794960	+	0.458970i
$439$	13.1570	+	11.0401i	0.627951	+	0.526914i	0.900292	−	0.435287i	$-0.143353\pi$
$439$	13.1570	+	11.0401i	0.627951	+	0.526914i	−0.272340	+	0.962201i	$0.587798\pi$
$440$	−5.43242	+	9.40923i	−0.258980	+	0.448567i
$441$	4.47060			0.212886
$442$	1.86706	+	3.23384i	0.0888069	+	0.153818i
$443$	−4.10173	+	23.2621i	−0.194879	+	1.10521i	0.717712	+	0.696340i	$0.245190\pi$
$443$	−4.10173	+	23.2621i	−0.194879	+	1.10521i	−0.912591	+	0.408874i	$0.865922\pi$
$444$	−4.48680	−	12.3274i	−0.212934	−	0.585031i
$445$	−18.8478	−	6.86002i	−0.893470	−	0.325196i
$446$	−3.96451	−	1.44296i	−0.187725	−	0.0683263i
$447$	4.56283	+	12.5363i	0.215815	+	0.592946i
$448$	−0.407604	+	2.31164i	−0.0192575	+	0.109215i
$449$	10.1295	+	17.5449i	0.478042	+	0.827994i	0.999683	−	0.0251715i	$-0.00801318\pi$
$449$	10.1295	+	17.5449i	0.478042	+	0.827994i	−0.521641	+	0.853165i	$0.674680\pi$
$450$	−2.11721	−	3.66712i	−0.0998063	−	0.172870i
$451$	10.5162	−	18.2146i	0.495188	−	0.857691i
$452$	−13.0667	−	10.9643i	−0.614606	−	0.515716i
$453$	1.17159	−	0.676417i	0.0550460	−	0.0317808i
$454$	−2.77244	−	15.7233i	−0.130117	−	0.737931i
$455$	−3.45471	+	2.89884i	−0.161959	+	0.135900i
$456$	−4.29426	+	11.7984i	−0.201097	+	0.552510i
$457$	38.1143	−	13.8725i	1.78291	−	0.648926i	0.783282	−	0.621666i	$-0.213544\pi$
$457$	38.1143	−	13.8725i	1.78291	−	0.648926i	0.999628	−	0.0272600i	$-0.00867822\pi$
$458$	17.8476			0.833964
$459$	−22.1457	−	12.7858i	−1.03367	−	0.596792i
$460$	−0.773318			−0.0360562
$461$	−12.8824	+	4.68880i	−0.599992	+	0.218379i	−0.624119	−	0.781330i	$-0.714542\pi$
$461$	−12.8824	+	4.68880i	−0.599992	+	0.218379i	0.0241264	+	0.999709i	$0.492320\pi$
$462$	−17.1800	+	3.02931i	−0.799288	+	0.140936i
$463$	4.14022	−	3.47405i	0.192412	−	0.161453i	−0.541492	−	0.840706i	$-0.682140\pi$
$463$	4.14022	−	3.47405i	0.192412	−	0.161453i	0.733904	+	0.679253i	$0.237696\pi$
$464$	−0.539363	−	3.05888i	−0.0250393	−	0.142005i
$465$			37.7007i			1.74833i
$466$	0.564178	+	0.473401i	0.0261350	+	0.0219299i
$467$	−15.7451	+	27.2713i	−0.728596	+	1.26197i	0.228880	+	0.973455i	$0.426494\pi$
$467$	−15.7451	+	27.2713i	−0.728596	+	1.26197i	−0.957477	+	0.288511i	$0.906840\pi$
$468$	−0.395277	−	2.24173i	−0.0182717	−	0.103624i
$469$	0.0491630	+	0.0851529i	0.00227014	+	0.00393199i
$470$	0.798133	−	4.52644i	0.0368151	−	0.208789i
$471$	−11.5915	+	13.8142i	−0.534109	+	0.636526i
$472$	5.14543	+	1.87278i	0.236838	+	0.0862018i
$473$	−6.57398	−	2.39273i	−0.302272	−	0.110018i
$474$	−12.5792	−	2.21805i	−0.577781	−	0.101878i
$475$	−1.77672	+	10.0763i	−0.0815216	+	0.462332i
$476$	5.77584	+	10.0041i	0.264735	+	0.458535i
$477$	−0.299011	+	1.69577i	−0.0136908	+	0.0776441i
$478$	−1.43717	+	2.48925i	−0.0657345	+	0.113855i
$479$	−16.0667	−	13.4816i	−0.734106	−	0.615988i	0.197141	−	0.980375i	$-0.436834\pi$
$479$	−16.0667	−	13.4816i	−0.734106	−	0.615988i	−0.931248	+	0.364387i	$0.881279\pi$
$480$	−3.79813	−	2.19285i	−0.173360	−	0.100090i
$481$	−0.997941	−	5.65960i	−0.0455022	−	0.258056i
$482$	−1.67159	+	1.40263i	−0.0761388	+	0.0638880i
$483$	−0.798133	−	0.951178i	−0.0363163	−	0.0432801i
$484$	−6.96451	+	2.53487i	−0.316569	+	0.115222i
$485$	−8.31315			−0.377481
$486$	10.0201	+	11.9415i	0.454519	+	0.541675i
$487$	−15.4492			−0.700072			−0.350036	−	0.936736i	$-0.613831\pi$
$487$	−15.4492			−0.700072			−0.350036	+	0.936736i	$0.613831\pi$
$488$	10.3833	−	3.77920i	0.470028	−	0.171076i
$489$	11.7724	+	14.0298i	0.532368	+	0.634452i
$490$	2.89053	−	2.42544i	0.130581	−	0.109570i
$491$	2.75443	+	15.6212i	0.124306	+	0.704973i	0.981718	+	0.190343i	$0.0609599\pi$
$491$	2.75443	+	15.6212i	0.124306	+	0.704973i	−0.857412	+	0.514631i	$0.827929\pi$
$492$	7.35251	+	4.24497i	0.331477	+	0.191378i
$493$	−11.7096	−	9.82553i	−0.527374	−	0.442519i
$494$	−2.75015	+	4.76340i	−0.123735	+	0.214316i
$495$	5.65998	−	32.0993i	0.254397	−	1.44276i
$496$	4.29813	+	7.44459i	0.192992	+	0.334272i
$497$	1.71373	−	9.71902i	0.0768711	−	0.435958i
$498$	11.6382	+	2.05212i	0.521518	+	0.0919577i
$499$	7.03596	+	2.56088i	0.314973	+	0.114641i	0.494669	−	0.869081i	$-0.335289\pi$
$499$	7.03596	+	2.56088i	0.314973	+	0.114641i	−0.179696	+	0.983722i	$0.557511\pi$
$500$	8.53849	+	3.10775i	0.381853	+	0.138983i
$501$	1.67334	−	1.99421i	0.0747595	−	0.0890949i
$502$	4.52141	−	25.6422i	0.201800	−	1.14447i
$503$	10.0667	+	17.4360i	0.448852	+	0.777435i	0.998312	−	0.0580857i	$-0.0184997\pi$
$503$	10.0667	+	17.4360i	0.448852	+	0.777435i	−0.549459	+	0.835520i	$0.685166\pi$
$504$	−1.22281	−	6.93491i	−0.0544683	−	0.308905i
$505$	15.1839	−	26.2993i	0.675675	−	1.17030i
$506$	−1.00387	−	0.842347i	−0.0446275	−	0.0374469i
$507$			21.5195i			0.955713i
$508$	2.19594	+	12.4538i	0.0974289	+	0.552547i
$509$	−28.7900	+	24.1577i	−1.27609	+	1.07077i	−0.282324	+	0.959319i	$0.591105\pi$
$509$	−28.7900	+	24.1577i	−1.27609	+	1.07077i	−0.993770	+	0.111450i	$0.964450\pi$
$510$	−21.2554	+	3.74789i	−0.941203	+	0.165960i
$511$	−24.4650	+	8.90452i	−1.08227	+	0.393913i
$512$	−1.00000			−0.0441942
$513$		−	37.6668i		−	1.66303i
$514$	−9.99226			−0.440740
$515$	−5.73783	+	2.08840i	−0.252839	+	0.0920258i
$516$	0.965852	−	2.65366i	0.0425193	−	0.116821i
$517$	5.96657	−	5.00654i	0.262409	−	0.220188i
$518$	−3.08718	−	17.5083i	−0.135643	−	0.769270i
$519$	16.7260	−	9.65674i	0.734188	−	0.423884i
$520$	−1.47178	−	1.23497i	−0.0645419	−	0.0541571i
$521$	−13.9645	+	24.1872i	−0.611796	+	1.05966i	0.379141	+	0.925339i	$0.376219\pi$
$521$	−13.9645	+	24.1872i	−0.611796	+	1.05966i	−0.990938	+	0.134323i	$0.957114\pi$
$522$	4.65910	+	8.06980i	0.203923	+	0.353205i
$523$	−3.64677	−	6.31640i	−0.159462	−	0.276197i	0.775213	−	0.631700i	$-0.217643\pi$
$523$	−3.64677	−	6.31640i	−0.159462	−	0.276197i	−0.934675	+	0.355504i	$0.884309\pi$
$524$	−0.901207	+	5.11100i	−0.0393694	+	0.223275i
$525$	−1.96270	−	5.39246i	−0.0856591	−	0.235346i
$526$	14.3045	+	5.20642i	0.623707	+	0.227011i
$527$	39.7533	+	14.4690i	1.73168	+	0.630280i
$528$	−2.54189	−	6.98378i	−0.110622	−	0.303930i
$529$	−3.97771	+	22.5587i	−0.172944	+	0.980814i
$530$	0.726682	+	1.25865i	0.0315650	+	0.0546722i
$531$	−16.4270			−0.712869
$532$	−8.50774	+	14.7358i	−0.368857	+	0.638880i
$533$	2.84911	+	2.39068i	0.123409	+	0.103552i
$534$	11.8819	−	6.86002i	0.514181	−	0.296862i
$535$	−1.06670	−	6.04958i	−0.0461176	−	0.261546i
$536$	−0.0320889	+	0.0269258i	−0.00138603	+	0.00116302i
$537$	−4.62567	+	12.7089i	−0.199612	+	0.548430i
$538$	28.7053	−	10.4479i	1.23757	−	0.450440i
$539$	6.39424			0.275419
$540$	12.9572	+	2.28471i	0.557591	+	0.0983183i
$541$	−2.88444			−0.124012			−0.0620058	−	0.998076i	$-0.519750\pi$
$541$	−2.88444			−0.124012			−0.0620058	+	0.998076i	$0.519750\pi$
$542$	24.2729	−	8.83462i	1.04261	−	0.379479i
$543$	17.8687	−	3.15074i	0.766820	−	0.135211i
$544$	−3.76991	+	3.16333i	−0.161634	+	0.135627i
$545$	−1.02347	−	5.80439i	−0.0438407	−	0.248633i
$546$		−	3.08489i		−	0.132021i
$547$	−8.57263	−	7.19329i	−0.366539	−	0.307563i	0.440851	−	0.897580i	$-0.354677\pi$
$547$	−8.57263	−	7.19329i	−0.366539	−	0.307563i	−0.807391	+	0.590017i	$0.799121\pi$
$548$	8.55690	−	14.8210i	0.365533	−	0.633121i
$549$	−25.3935	+	21.3077i	−1.08377	+	0.909390i
$550$	−3.02822	−	5.24503i	−0.129124	−	0.223649i
$551$	3.90983	−	22.1737i	0.166564	−	0.944632i
$552$	0.340022	−	0.405223i	0.0144723	−	0.0172474i
$553$	−16.2665	−	5.92053i	−0.691722	−	0.251766i
$554$	−21.0817	−	7.67312i	−0.895676	−	0.326000i
$555$	32.7126	+	5.76811i	1.38857	+	0.244843i
$556$	2.11809	−	12.0123i	0.0898270	−	0.509434i
$557$	−16.6741	−	28.8804i	−0.706505	−	1.22370i	−0.966146	−	0.257997i	$-0.916937\pi$
$557$	−16.6741	−	28.8804i	−0.706505	−	1.22370i	0.259641	−	0.965705i	$-0.416396\pi$
$558$	−19.7554	−	16.5767i	−0.836311	−	0.701749i
$559$	0.618555	−	1.07137i	0.0261621	−	0.0453141i
$560$	−4.55303	−	3.82045i	−0.192401	−	0.161443i
$561$	−31.6747	−	18.2874i	−1.33731	−	0.772096i
$562$	−1.01485	−	5.75552i	−0.0428090	−	0.242782i
$563$	14.1668	−	11.8874i	0.597061	−	0.500994i	−0.293438	−	0.955978i	$-0.594800\pi$
$563$	14.1668	−	11.8874i	0.597061	−	0.500994i	0.890500	+	0.454984i	$0.150355\pi$
$564$	2.02094	+	2.40847i	0.0850971	+	0.101415i
$565$	40.5861	−	14.7721i	1.70747	−	0.621468i
$566$	7.41147			0.311527
$567$	10.5628	+	18.2954i	0.443597	+	0.768333i
$568$	4.20439			0.176412
$569$	−27.5638	+	10.0324i	−1.15553	+	0.420580i	−0.847500	−	0.530796i	$-0.821893\pi$
$569$	−27.5638	+	10.0324i	−1.15553	+	0.420580i	−0.308033	+	0.951376i	$0.599671\pi$
$570$	−20.4354	−	24.3540i	−0.855945	−	1.02008i
$571$	1.50387	−	1.26190i	0.0629350	−	0.0528087i	−0.610778	−	0.791802i	$-0.709143\pi$
$571$	1.50387	−	1.26190i	0.0629350	−	0.0528087i	0.673713	+	0.738993i	$0.264699\pi$
$572$	−0.565360	−	3.20631i	−0.0236389	−	0.134063i
$573$	−18.3441	−	10.5909i	−0.766334	−	0.442443i
$574$	8.81386	+	7.39571i	0.367884	+	0.308691i
$575$	0.215537	−	0.373321i	0.00898852	−	0.0155686i
$576$	2.81908	−	1.02606i	0.117462	−	0.0427525i
$577$	5.52956	+	9.57748i	0.230199	+	0.398716i	0.957866	−	0.287214i	$-0.0927291\pi$
$577$	5.52956	+	9.57748i	0.230199	+	0.398716i	−0.727668	+	0.685930i	$0.759396\pi$
$578$	−1.25356	+	7.10927i	−0.0521411	+	0.295707i
$579$	27.9192	+	4.92291i	1.16028	+	0.204589i
$580$	7.39053	+	2.68993i	0.306875	+	0.111693i
$581$	15.0496	+	5.47762i	0.624364	+	0.227250i
$582$	3.65523	−	4.35613i	0.151514	−	0.180568i
$583$	−0.427671	+	2.42544i	−0.0177123	+	0.100452i
$584$	−5.54576	−	9.60554i	−0.229485	−	0.397480i
$585$	5.41622	+	1.97134i	0.223933	+	0.0815050i
$586$	−4.43835	+	7.68745i	−0.183346	+	0.317565i
$587$	25.3917	+	21.3062i	1.04803	+	0.879400i	0.992885	−	0.119078i	$-0.0379940\pi$
$587$	25.3917	+	21.3062i	1.04803	+	0.879400i	0.0551433	+	0.998478i	$0.482438\pi$
$588$			2.58110i			0.106443i
$589$	10.8207	+	61.3674i	0.445860	+	2.52860i
$590$	−10.6211	+	8.91215i	−0.437263	+	0.366907i
$591$	32.4020	−	5.71334i	1.33284	−	0.235016i
$592$	7.11721	−	2.59045i	0.292516	−	0.106467i
$593$	14.8283			0.608926			0.304463	−	0.952524i	$-0.401523\pi$
$593$	14.8283			0.608926			0.304463	+	0.952524i	$0.401523\pi$
$594$	14.3316	+	17.0797i	0.588031	+	0.700788i
$595$	−29.2499			−1.19913
$596$	−7.23783	+	2.63435i	−0.296473	+	0.107907i
$597$	−13.6505	+	37.5044i	−0.558677	+	1.53495i
$598$	0.177519	−	0.148956i	0.00725927	−	0.00609125i
$599$	−8.20930	−	46.5573i	−0.335423	−	1.90228i	−0.423016	−	0.906122i	$-0.639029\pi$
$599$	−8.20930	−	46.5573i	−0.335423	−	1.90228i	0.0875932	−	0.996156i	$-0.472082\pi$
$600$	2.11721	−	1.22237i	0.0864348	−	0.0499031i
$601$	28.1996	+	23.6623i	1.15029	+	0.965206i	0.999726	−	0.0233949i	$-0.00744749\pi$
$601$	28.1996	+	23.6623i	1.15029	+	0.965206i	0.150561	+	0.988601i	$0.451892\pi$
$602$	1.91353	−	3.31434i	0.0779898	−	0.135082i
$603$	0.0628336	−	0.108831i	0.00255878	−	0.00443194i
$604$	0.390530	+	0.676417i	0.0158904	+	0.0275230i
$605$	3.25877	−	18.4814i	0.132488	−	0.751376i
$606$	7.10472	+	19.5201i	0.288610	+	0.792948i
$607$	−38.8764	−	14.1499i	−1.57795	−	0.574326i	−0.603190	−	0.797597i	$-0.706104\pi$
$607$	−38.8764	−	14.1499i	−1.57795	−	0.574326i	−0.974756	+	0.223272i	$0.928326\pi$
$608$	−6.81180	−	2.47929i	−0.276255	−	0.100549i
$609$	4.31908	+	11.8666i	0.175018	+	0.480858i
$610$	−4.85844	+	27.5536i	−0.196713	+	1.11561i
$611$	0.688663	+	1.19280i	0.0278603	+	0.0482555i
$612$	7.38191	−	12.7858i	0.298396	−	0.516837i
$613$	20.6755	−	35.8109i	0.835074	−	1.44639i	−0.0588963	−	0.998264i	$-0.518758\pi$
$613$	20.6755	−	35.8109i	0.835074	−	1.44639i	0.893970	−	0.448126i	$-0.147909\pi$
$614$	12.3327	+	10.3484i	0.497709	+	0.417628i
$615$	−18.6172	+	10.7487i	−0.750718	+	0.433427i
$616$	−1.74897	−	9.91890i	−0.0704680	−	0.399644i
$617$	18.7867	−	15.7639i	0.756326	−	0.634633i	−0.180842	−	0.983512i	$-0.557882\pi$
$617$	18.7867	−	15.7639i	0.756326	−	0.634633i	0.937168	+	0.348880i	$0.113438\pi$
$618$	1.42855	−	3.92490i	0.0574646	−	0.157883i
$619$	−37.2768	+	13.5676i	−1.49828	+	0.545329i	−0.955615	−	0.294619i	$-0.904807\pi$
$619$	−37.2768	+	13.5676i	−1.49828	+	0.545329i	−0.542666	+	0.839949i	$0.682585\pi$
$620$	−21.7665			−0.874164
$621$	−0.542766	+	1.49124i	−0.0217805	+	0.0598413i
$622$	−13.5895			−0.544888
$623$	17.4722	−	6.35938i	0.700011	−	0.254783i
$624$	1.29426	−	0.228213i	0.0518120	−	0.00913585i
$625$	−23.0312	+	19.3255i	−0.921248	+	0.773019i
$626$	3.73442	+	21.1790i	0.149258	+	0.846482i
$627$		−	53.8742i		−	2.15153i
$628$	−7.97565	−	6.69237i	−0.318263	−	0.267054i
$629$	18.6368	−	32.2799i	0.743098	−	1.28708i
$630$	16.7554	+	6.09845i	0.667550	+	0.242968i
$631$	16.6596	+	28.8552i	0.663207	+	1.14871i	0.979768	+	0.200136i	$0.0641384\pi$
$631$	16.6596	+	28.8552i	0.663207	+	1.14871i	−0.316561	+	0.948572i	$0.602528\pi$
$632$	1.28059	−	7.26260i	0.0509392	−	0.288891i
$633$	19.4812	−	23.2168i	0.774307	−	0.922783i
$634$	−19.8204	−	7.21404i	−0.787170	−	0.286506i
$635$	−30.0895	−	10.9517i	−1.19406	−	0.434604i
$636$	−0.979055	−	0.172634i	−0.0388221	−	0.00684538i
$637$	−0.196347	+	1.11354i	−0.00777957	+	0.0441201i
$638$	6.66385	+	11.5421i	0.263824	+	0.456957i
$639$	−11.8525	+	4.31396i	−0.468878	+	0.170658i
$640$	1.26604	−	2.19285i	0.0500448	−	0.0866801i
$641$	5.55690	+	4.66280i	0.219485	+	0.184169i	0.745900	−	0.666058i	$-0.232020\pi$
$641$	5.55690	+	4.66280i	0.219485	+	0.184169i	−0.526415	+	0.850228i	$0.676464\pi$
$642$	3.63903	+	2.10100i	0.143621	+	0.0829197i
$643$	−1.34120	−	7.60635i	−0.0528919	−	0.299965i	0.946874	−	0.321605i	$-0.104222\pi$
$643$	−1.34120	−	7.60635i	−0.0528919	−	0.299965i	−0.999766	+	0.0216400i	$0.993111\pi$
$644$	0.549163	−	0.460802i	0.0216401	−	0.0181582i
$645$	4.59627	+	5.47762i	0.180978	+	0.215681i
$646$	−33.5228	+	12.2013i	−1.31894	+	0.480053i
$647$	−40.9469			−1.60979			−0.804894	−	0.593419i	$-0.797778\pi$
$647$	−40.9469			−1.60979			−0.804894	+	0.593419i	$0.797778\pi$
$648$	−6.89440	+	5.78509i	−0.270838	+	0.227260i
$649$	−23.4953			−0.922269
$650$	1.00640	−	0.366298i	0.0394741	−	0.0143674i
$651$	−22.4650	−	26.7727i	−0.880472	−	1.04931i
$652$	−8.10014	+	6.79682i	−0.317226	+	0.266184i
$653$	3.45171	+	19.5756i	0.135076	+	0.766054i	0.974807	+	0.223051i	$0.0716017\pi$
$653$	3.45171	+	19.5756i	0.135076	+	0.766054i	−0.839731	+	0.543003i	$0.817287\pi$
$654$	3.49154	+	2.01584i	0.136530	+	0.0788257i
$655$	−10.0667	−	8.44697i	−0.393339	−	0.330050i
$656$	−2.45084	+	4.24497i	−0.0956891	+	0.165738i
$657$	25.4898	+	21.3885i	0.994451	+	0.834444i
$658$	2.13041	+	3.68999i	0.0830522	+	0.143851i
$659$	2.98499	−	16.9287i	0.116279	−	0.659448i	−0.869831	−	0.493350i	$-0.835772\pi$
$659$	2.98499	−	16.9287i	0.116279	−	0.659448i	0.986109	−	0.166098i	$-0.0531168\pi$
$660$	18.5326	+	3.26779i	0.721379	+	0.127199i
$661$	32.3276	+	11.7663i	1.25740	+	0.457655i	0.882895	−	0.469571i	$-0.155591\pi$
$661$	32.3276	+	11.7663i	1.25740	+	0.457655i	0.374503	+	0.927226i	$0.377813\pi$
$662$	15.4474	+	5.62241i	0.600382	+	0.218521i
$663$	4.15735	−	4.95453i	0.161458	−	0.192418i
$664$	−1.18479	+	6.71929i	−0.0459789	+	0.260759i
$665$	−21.5424	−	37.3125i	−0.835377	−	1.44691i
$666$	−17.4060	+	14.6054i	−0.674469	+	0.565947i
$667$	−0.474308	+	0.821525i	−0.0183653	+	0.0318096i
$668$	1.15136	+	0.966105i	0.0445474	+	0.0373797i
$669$			7.30742i			0.282521i
$670$	−0.0184183	−	0.104455i	−0.000711562	−	0.00403547i
$671$	−36.3200	+	30.4761i	−1.40212	+	1.17652i
$672$	4.00387	−	0.705990i	0.154453	−	0.0272342i
$673$	−22.4513	+	8.17161i	−0.865434	+	0.314992i	−0.736317	−	0.676637i	$-0.763437\pi$
$673$	−22.4513	+	8.17161i	−0.865434	+	0.314992i	−0.129117	+	0.991629i	$0.541214\pi$
$674$	−10.5517			−0.406436
$675$	−4.71436	+	5.61835i	−0.181456	+	0.216250i
$676$	−12.4243			−0.477856
$677$	−32.6238	+	11.8741i	−1.25383	+	0.456358i	−0.881695	−	0.471819i	$-0.843597\pi$
$677$	−32.6238	+	11.8741i	−1.25383	+	0.456358i	−0.372138	+	0.928177i	$0.621375\pi$
$678$	−10.1047	+	27.7625i	−0.388070	+	1.06621i
$679$	5.90348	−	4.95361i	0.226555	−	0.190102i
$680$	−2.16385	−	12.2718i	−0.0829798	−	0.470602i
$681$	−23.9488	+	13.8268i	−0.917719	+	0.529845i
$682$	−28.2558	−	23.7095i	−1.08197	−	0.907882i
$683$	19.5030	−	33.7802i	0.746261	−	1.29256i	−0.203342	−	0.979108i	$-0.565180\pi$
$683$	19.5030	−	33.7802i	0.746261	−	1.29256i	0.949603	−	0.313455i	$-0.101486\pi$
$684$	21.7469			0.831514
$685$	21.6668	+	37.5281i	0.827847	+	1.43387i
$686$	−3.46064	+	19.6262i	−0.132128	+	0.749334i
$687$	−10.5729	−	29.0487i	−0.403379	−	1.10828i
$688$	1.53209	+	0.557635i	0.0584103	+	0.0212596i
$689$	−0.409253	−	0.148956i	−0.0155913	−	0.00567476i
$690$	0.458111	+	1.25865i	0.0174400	+	0.0479160i
$691$	4.39780	−	24.9412i	0.167300	−	0.948807i	−0.779361	−	0.626576i	$-0.784456\pi$
$691$	4.39780	−	24.9412i	0.167300	−	0.948807i	0.946661	−	0.322232i	$-0.104433\pi$
$692$	5.57532	+	9.65674i	0.211942	+	0.367094i
$693$	15.1079	+	26.1676i	0.573901	+	0.994025i
$694$	14.1800	−	24.5606i	0.538267	−	0.932306i
$695$	23.6596	+	19.8527i	0.897459	+	0.753057i
$696$	−4.65910	+	2.68993i	−0.176603	+	0.101962i
$697$	4.18883	+	23.7560i	0.158663	+	0.899823i
$698$	−12.0287	+	10.0933i	−0.455292	+	0.382036i
$699$	0.436289	−	1.19869i	0.0165020	−	0.0453388i
$700$	3.11334	−	1.13316i	0.117673	−	0.0428295i
$701$	42.3054			1.59785			0.798927	−	0.601429i	$-0.205402\pi$
$701$	42.3054			1.59785			0.798927	+	0.601429i	$0.205402\pi$
$702$	−3.41447	+	1.97134i	−0.128871	+	0.0744036i
$703$	54.9035			2.07073
$704$	4.03209	−	1.46756i	0.151965	−	0.0553108i
$705$	−7.84002	+	1.38241i	−0.295272	+	0.0520645i
$706$	1.58125	−	1.32683i	0.0595112	−	0.0499358i
$707$	4.88847	+	27.7239i	0.183850	+	1.04266i
$708$		−	9.48411i		−	0.356435i
$709$	−36.7098	−	30.8032i	−1.37867	−	1.15684i	−0.969703	−	0.244288i	$-0.921446\pi$
$709$	−36.7098	−	30.8032i	−1.37867	−	1.15684i	−0.408964	−	0.912551i	$-0.634110\pi$
$710$	−5.32295	+	9.21962i	−0.199767	+	0.346006i
$711$	3.84178	+	21.7878i	0.144078	+	0.817106i
$712$	3.96064	+	6.86002i	0.148431	+	0.257090i
$713$	0.455889	−	2.58548i	0.0170732	−	0.0968269i
$714$	12.8610	−	15.3271i	0.481310	−	0.573602i
$715$	7.74675	+	2.81959i	0.289712	+	0.105447i
$716$	−7.33750	−	2.67063i	−0.274215	−	0.0998061i
$717$	4.90286	+	0.864506i	0.183101	+	0.0322856i
$718$	6.07145	−	34.4329i	0.226585	−	1.28502i
$719$	−6.15451	−	10.6599i	−0.229525	−	0.397548i	0.728143	−	0.685426i	$-0.240384\pi$
$719$	−6.15451	−	10.6599i	−0.229525	−	0.397548i	−0.957667	+	0.287877i	$0.907050\pi$
$720$	−1.31908	+	7.48086i	−0.0491591	+	0.278795i
$721$	2.83022	−	4.90209i	0.105403	−	0.182563i
$722$	−25.6989	−	21.5640i	−0.956415	−	0.802528i
$723$	3.27316	+	1.88976i	0.121730	+	0.0702808i
$724$	1.81908	+	10.3165i	0.0676055	+	0.383410i
$725$	−3.35844	+	2.81807i	−0.124729	+	0.104660i
$726$	8.25150	+	9.83375i	0.306242	+	0.364965i
$727$	16.3542	−	5.95243i	0.606542	−	0.220763i	−0.0204474	−	0.999791i	$-0.506509\pi$
$727$	16.3542	−	5.95243i	0.606542	−	0.220763i	0.626990	+	0.779028i	$0.284287\pi$
$728$	1.78106			0.0660104
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	28.0847			1.03946
$731$	7.53983	−	2.74427i	0.278871	−	0.101501i
$732$	−12.3020	−	14.6610i	−0.454695	−	0.541885i
$733$	11.0266	−	9.25244i	0.407278	−	0.341747i	−0.416021	−	0.909355i	$-0.636576\pi$
$733$	11.0266	−	9.25244i	0.407278	−	0.341747i	0.823299	+	0.567608i	$0.192131\pi$
$734$	0.0773815	+	0.438852i	0.00285620	+	0.0161983i
$735$	−5.65998	−	3.26779i	−0.208771	−	0.120534i
$736$	0.233956	+	0.196312i	0.00862372	+	0.00723616i
$737$	0.0898700	−	0.155659i	0.00331041	−	0.00573379i
$738$	2.55350	−	14.4816i	0.0939956	−	0.533076i
$739$	6.82383	+	11.8192i	0.251018	+	0.434777i	0.963806	−	0.266603i	$-0.0859012\pi$
$739$	6.82383	+	11.8192i	0.251018	+	0.434777i	−0.712788	+	0.701380i	$0.752568\pi$
$740$	−3.33022	+	18.8866i	−0.122421	+	0.694286i
$741$	9.38207	+	1.65431i	0.344659	+	0.0607727i
$742$	−1.26604	−	0.460802i	−0.0464780	−	0.0169166i
$743$	17.2459	+	6.27698i	0.632690	+	0.230280i	0.638402	−	0.769703i	$-0.279596\pi$
$743$	17.2459	+	6.27698i	0.632690	+	0.230280i	−0.00571190	+	0.999984i	$0.501818\pi$
$744$	9.57057	−	11.4058i	0.350874	−	0.418156i
$745$	3.38666	−	19.2067i	0.124078	−	0.703679i
$746$	−11.0312	−	19.1066i	−0.403881	−	0.699543i
$747$	−3.55438	−	20.1579i	−0.130048	−	0.737538i
$748$	10.5582	−	18.2874i	0.386048	−	0.668654i
$749$	4.36231	+	3.66041i	0.159395	+	0.133749i
$750$		−	15.7382i		−	0.574679i
$751$	−7.01460	−	39.7818i	−0.255967	−	1.45166i	−0.793579	−	0.608467i	$-0.791785\pi$
$751$	−7.01460	−	39.7818i	−0.255967	−	1.45166i	0.537613	−	0.843192i	$-0.319326\pi$
$752$	−1.39053	+	1.16679i	−0.0507074	+	0.0425486i
$753$	−44.4136	+	7.83131i	−1.61852	+	0.285389i
$754$	−2.21466	+	0.806070i	−0.0806532	+	0.0293553i
$755$	−1.97771			−0.0719763
$756$	−10.5628	+	6.09845i	−0.384167	+	0.221799i
$757$	3.71595			0.135058			0.0675292	−	0.997717i	$-0.478488\pi$
$757$	3.71595			0.135058			0.0675292	+	0.997717i	$0.478488\pi$
$758$	12.3229	−	4.48519i	0.447590	−	0.162909i
$759$	−0.776311	+	2.13290i	−0.0281783	+	0.0774193i
$760$	14.0608	−	11.7984i	0.510038	−	0.427973i
$761$	−6.41147	−	36.3613i	−0.232416	−	1.31810i	−0.847988	−	0.530015i	$-0.822186\pi$
$761$	−6.41147	−	36.3613i	−0.232416	−	1.31810i	0.615573	−	0.788080i	$-0.288925\pi$
$762$	18.9688	−	10.9517i	0.687169	−	0.396737i
$763$	4.18551	+	3.51206i	0.151526	+	0.127145i
$764$	6.11468	−	10.5909i	0.221222	−	0.383167i
$765$	18.6917	+	32.3749i	0.675798	+	1.17052i

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)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.11334 - 1.32683i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.439693 + 2.49362i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-1.79813 - 1.50881i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.11334 - 1.32683i) q^{3} +(0.766044 - 0.642788i) q^{4} +(0.439693 + 2.49362i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-1.79813 - 1.50881i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.520945 + 2.95442i) q^{9} +(1.26604 + 2.19285i) q^{10} +(-0.745100 + 4.22567i) q^{11} +(-1.70574 - 0.300767i) q^{12} +(-0.713011 - 0.259515i) q^{13} +(-2.20574 - 0.802823i) q^{14} +(2.81908 - 3.35965i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-2.46064 - 4.26195i) q^{17} +(0.520945 + 2.95442i) q^{18} +(3.62449 - 6.27779i) q^{19} +(1.93969 + 1.62760i) q^{20} +4.06564i q^{21} +(0.745100 + 4.22567i) q^{22} +(-0.233956 + 0.196312i) q^{23} +(-1.70574 + 0.300767i) q^{24} +(-1.32635 + 0.482753i) q^{25} -0.758770 q^{26} +(4.50000 - 2.59808i) q^{27} -2.34730 q^{28} +(2.91875 - 1.06234i) q^{29} +(1.50000 - 4.12122i) q^{30} +(-6.58512 + 5.52557i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(6.43629 - 3.71599i) q^{33} +(-3.76991 - 3.16333i) q^{34} +(2.97178 - 5.14728i) q^{35} +(1.50000 + 2.59808i) q^{36} +(3.78699 + 6.55926i) q^{37} +(1.25877 - 7.13884i) q^{38} +(0.449493 + 1.23497i) q^{39} +(2.37939 + 0.866025i) q^{40} +(-4.60607 - 1.67647i) q^{41} +(1.39053 + 3.82045i) q^{42} +(-0.283119 + 1.60565i) q^{43} +(2.14543 + 3.71599i) q^{44} -7.59627 q^{45} +(-0.152704 + 0.264490i) q^{46} +(-1.39053 - 1.16679i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(-0.258770 - 1.46756i) q^{49} +(-1.08125 + 0.907278i) q^{50} +(-2.91534 + 8.00984i) q^{51} +(-0.713011 + 0.259515i) q^{52} +0.573978 q^{53} +(3.34002 - 3.98048i) q^{54} -10.8648 q^{55} +(-2.20574 + 0.802823i) q^{56} +(-12.3648 + 2.18025i) q^{57} +(2.37939 - 1.99654i) q^{58} +(0.950837 + 5.39246i) q^{59} -4.38571i q^{60} +(8.46451 + 7.10257i) q^{61} +(-4.29813 + 7.44459i) q^{62} +(5.39440 - 4.52644i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.333626 - 1.89209i) q^{65} +(4.77719 - 5.69323i) q^{66} +(-0.0393628 - 0.0143269i) q^{67} +(-4.62449 - 1.68317i) q^{68} +(0.520945 + 0.0918566i) q^{69} +(1.03209 - 5.85327i) q^{70} +(2.10220 + 3.64111i) q^{71} +(2.29813 + 1.92836i) q^{72} +(5.54576 - 9.60554i) q^{73} +(5.80200 + 4.86846i) q^{74} +(2.11721 + 1.22237i) q^{75} +(-1.25877 - 7.13884i) q^{76} +(7.71554 - 6.47410i) q^{77} +(0.844770 + 1.00676i) q^{78} +(6.92989 - 2.52227i) q^{79} +2.53209 q^{80} +(-8.45723 - 3.07818i) q^{81} -4.90167 q^{82} +(-6.41147 + 2.33359i) q^{83} +(2.61334 + 3.11446i) q^{84} +(9.54576 - 8.00984i) q^{85} +(0.283119 + 1.60565i) q^{86} +(-4.65910 - 2.68993i) q^{87} +(3.28699 + 2.75811i) q^{88} +(-3.96064 + 6.86002i) q^{89} +(-7.13816 + 2.59808i) q^{90} +(0.890530 + 1.54244i) q^{91} +(-0.0530334 + 0.300767i) q^{92} +(14.6630 + 2.58548i) q^{93} +(-1.70574 - 0.620838i) q^{94} +(17.2481 + 6.27779i) q^{95} +(-1.11334 + 1.32683i) q^{96} +(-0.570108 + 3.23324i) q^{97} +(-0.745100 - 1.29055i) q^{98} +(-12.0963 - 4.40268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8	\( 6 q - 3 q^{5} - 9 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{10} - 3 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{17} + 9 q^{19} + 6 q^{20} + 3 q^{22} - 6 q^{23} - 9 q^{25} + 18 q^{26} + 27 q^{27} - 12 q^{28} + 15 q^{29} + 9 q^{30} - 18 q^{31} - 9 q^{33} + 6 q^{34} + 3 q^{35} + 9 q^{36} + 15 q^{37} - 15 q^{38} + 3 q^{40} - 3 q^{41} - 9 q^{42} - 18 q^{43} - 3 q^{44} - 18 q^{45} - 3 q^{46} + 9 q^{47} - 9 q^{48} + 21 q^{49} - 9 q^{50} + 27 q^{51} - 12 q^{52} - 12 q^{53} - 18 q^{55} - 3 q^{56} - 27 q^{57} + 3 q^{58} - 6 q^{59} + 18 q^{61} - 12 q^{62} - 9 q^{63} - 3 q^{64} + 21 q^{65} + 18 q^{66} - 9 q^{67} - 15 q^{68} - 3 q^{70} + 12 q^{71} + 3 q^{73} - 3 q^{74} - 18 q^{75} + 15 q^{76} + 39 q^{77} + 18 q^{78} + 33 q^{79} + 6 q^{80} - 6 q^{82} - 18 q^{83} + 9 q^{84} + 27 q^{85} + 18 q^{86} + 9 q^{87} + 12 q^{88} - 15 q^{89} - 9 q^{90} - 12 q^{91} + 12 q^{92} + 27 q^{93} + 21 q^{95} - 12 q^{97} - 3 q^{98} - 45 q^{99}+O(q^{100}) \) 6 * q - 3 * q^5 - 9 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^10 - 3 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^17 + 9 * q^19 + 6 * q^20 + 3 * q^22 - 6 * q^23 - 9 * q^25 + 18 * q^26 + 27 * q^27 - 12 * q^28 + 15 * q^29 + 9 * q^30 - 18 * q^31 - 9 * q^33 + 6 * q^34 + 3 * q^35 + 9 * q^36 + 15 * q^37 - 15 * q^38 + 3 * q^40 - 3 * q^41 - 9 * q^42 - 18 * q^43 - 3 * q^44 - 18 * q^45 - 3 * q^46 + 9 * q^47 - 9 * q^48 + 21 * q^49 - 9 * q^50 + 27 * q^51 - 12 * q^52 - 12 * q^53 - 18 * q^55 - 3 * q^56 - 27 * q^57 + 3 * q^58 - 6 * q^59 + 18 * q^61 - 12 * q^62 - 9 * q^63 - 3 * q^64 + 21 * q^65 + 18 * q^66 - 9 * q^67 - 15 * q^68 - 3 * q^70 + 12 * q^71 + 3 * q^73 - 3 * q^74 - 18 * q^75 + 15 * q^76 + 39 * q^77 + 18 * q^78 + 33 * q^79 + 6 * q^80 - 6 * q^82 - 18 * q^83 + 9 * q^84 + 27 * q^85 + 18 * q^86 + 9 * q^87 + 12 * q^88 - 15 * q^89 - 9 * q^90 - 12 * q^91 + 12 * q^92 + 27 * q^93 + 21 * q^95 - 12 * q^97 - 3 * q^98 - 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more