LMFDB - Embedded newform 539.2.e.j.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(67,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("539.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.e (of order $3$, degree $2$, not 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.1
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	539.177
Dual form			539.2.e.j.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11803 + 1.93649i) q^{2} +(-0.618034 - 1.07047i) q^{3} +(-1.50000 - 2.59808i) q^{4} +(-1.00000 + 1.73205i) q^{5} +2.76393 q^{6} +2.23607 q^{8} +(0.736068 - 1.27491i) q^{9} +O(q^{10})$	\(q+(-1.11803 + 1.93649i) q^{2} +(-0.618034 - 1.07047i) q^{3} +(-1.50000 - 2.59808i) q^{4} +(-1.00000 + 1.73205i) q^{5} +2.76393 q^{6} +2.23607 q^{8} +(0.736068 - 1.27491i) q^{9} +(-2.23607 - 3.87298i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.85410 + 3.21140i) q^{12} -3.23607 q^{13} +2.47214 q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.61803 - 2.80252i) q^{17} +(1.64590 + 2.85078i) q^{18} +(3.23607 - 5.60503i) q^{19} +6.00000 q^{20} -2.23607 q^{22} +(-1.23607 + 2.14093i) q^{23} +(-1.38197 - 2.39364i) q^{24} +(0.500000 + 0.866025i) q^{25} +(3.61803 - 6.26662i) q^{26} -5.52786 q^{27} +8.47214 q^{29} +(-2.76393 + 4.78727i) q^{30} +(-1.38197 - 2.39364i) q^{31} +(3.35410 + 5.80948i) q^{32} +(0.618034 - 1.07047i) q^{33} +7.23607 q^{34} -4.41641 q^{36} +(4.23607 - 7.33708i) q^{37} +(7.23607 + 12.5332i) q^{38} +(2.00000 + 3.46410i) q^{39} +(-2.23607 + 3.87298i) q^{40} +11.2361 q^{41} +8.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(1.47214 + 2.54981i) q^{45} +(-2.76393 - 4.78727i) q^{46} +(1.38197 - 2.39364i) q^{47} -1.23607 q^{48} -2.23607 q^{50} +(-2.00000 + 3.46410i) q^{51} +(4.85410 + 8.40755i) q^{52} +(0.236068 + 0.408882i) q^{53} +(6.18034 - 10.7047i) q^{54} -2.00000 q^{55} -8.00000 q^{57} +(-9.47214 + 16.4062i) q^{58} +(-0.618034 - 1.07047i) q^{59} +(-3.70820 - 6.42280i) q^{60} +(-3.61803 + 6.26662i) q^{61} +6.18034 q^{62} -13.0000 q^{64} +(3.23607 - 5.60503i) q^{65} +(1.38197 + 2.39364i) q^{66} +(-7.23607 - 12.5332i) q^{67} +(-4.85410 + 8.40755i) q^{68} +3.05573 q^{69} -10.4721 q^{71} +(1.64590 - 2.85078i) q^{72} +(-0.381966 - 0.661585i) q^{73} +(9.47214 + 16.4062i) q^{74} +(0.618034 - 1.07047i) q^{75} -19.4164 q^{76} -8.94427 q^{78} +(4.47214 - 7.74597i) q^{79} +(1.00000 + 1.73205i) q^{80} +(1.20820 + 2.09267i) q^{81} +(-12.5623 + 21.7586i) q^{82} +11.4164 q^{83} +6.47214 q^{85} +(-8.94427 + 15.4919i) q^{86} +(-5.23607 - 9.06914i) q^{87} +(1.11803 + 1.93649i) q^{88} +(1.00000 - 1.73205i) q^{89} -6.58359 q^{90} +7.41641 q^{92} +(-1.70820 + 2.95870i) q^{93} +(3.09017 + 5.35233i) q^{94} +(6.47214 + 11.2101i) q^{95} +(4.14590 - 7.18091i) q^{96} -17.4164 q^{97} +1.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 6 q^{4} - 4 q^{5} + 20 q^{6} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 6 * q^4 - 4 * q^5 + 20 * q^6 - 6 * q^9	$ 4 q + 2 q^{3} - 6 q^{4} - 4 q^{5} + 20 q^{6} - 6 q^{9} + 2 q^{11} + 6 q^{12} - 4 q^{13} - 8 q^{15} + 2 q^{16} - 2 q^{17} + 20 q^{18} + 4 q^{19} + 24 q^{20} + 4 q^{23} - 10 q^{24} + 2 q^{25} + 10 q^{26} - 40 q^{27} + 16 q^{29} - 20 q^{30} - 10 q^{31} - 2 q^{33} + 20 q^{34} + 36 q^{36} + 8 q^{37} + 20 q^{38} + 8 q^{39} + 36 q^{41} + 32 q^{43} + 6 q^{44} - 12 q^{45} - 20 q^{46} + 10 q^{47} + 4 q^{48} - 8 q^{51} + 6 q^{52} - 8 q^{53} - 20 q^{54} - 8 q^{55} - 32 q^{57} - 20 q^{58} + 2 q^{59} + 12 q^{60} - 10 q^{61} - 20 q^{62} - 52 q^{64} + 4 q^{65} + 10 q^{66} - 20 q^{67} - 6 q^{68} + 48 q^{69} - 24 q^{71} + 20 q^{72} - 6 q^{73} + 20 q^{74} - 2 q^{75} - 24 q^{76} + 4 q^{80} - 22 q^{81} - 10 q^{82} - 8 q^{83} + 8 q^{85} - 12 q^{87} + 4 q^{89} - 80 q^{90} - 24 q^{92} + 20 q^{93} - 10 q^{94} + 8 q^{95} + 30 q^{96} - 16 q^{97} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 6 * q^4 - 4 * q^5 + 20 * q^6 - 6 * q^9 + 2 * q^11 + 6 * q^12 - 4 * q^13 - 8 * q^15 + 2 * q^16 - 2 * q^17 + 20 * q^18 + 4 * q^19 + 24 * q^20 + 4 * q^23 - 10 * q^24 + 2 * q^25 + 10 * q^26 - 40 * q^27 + 16 * q^29 - 20 * q^30 - 10 * q^31 - 2 * q^33 + 20 * q^34 + 36 * q^36 + 8 * q^37 + 20 * q^38 + 8 * q^39 + 36 * q^41 + 32 * q^43 + 6 * q^44 - 12 * q^45 - 20 * q^46 + 10 * q^47 + 4 * q^48 - 8 * q^51 + 6 * q^52 - 8 * q^53 - 20 * q^54 - 8 * q^55 - 32 * q^57 - 20 * q^58 + 2 * q^59 + 12 * q^60 - 10 * q^61 - 20 * q^62 - 52 * q^64 + 4 * q^65 + 10 * q^66 - 20 * q^67 - 6 * q^68 + 48 * q^69 - 24 * q^71 + 20 * q^72 - 6 * q^73 + 20 * q^74 - 2 * q^75 - 24 * q^76 + 4 * q^80 - 22 * q^81 - 10 * q^82 - 8 * q^83 + 8 * q^85 - 12 * q^87 + 4 * q^89 - 80 * q^90 - 24 * q^92 + 20 * q^93 - 10 * q^94 + 8 * q^95 + 30 * q^96 - 16 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.11803	+	1.93649i	−0.790569	+	1.36931i	0.135045	+	0.990839i	$0.456882\pi$
$2$	−1.11803	+	1.93649i	−0.790569	+	1.36931i	−0.925615	+	0.378467i	$0.876451\pi$
$3$	−0.618034	−	1.07047i	−0.356822	−	0.618034i	0.630606	−	0.776103i	$-0.282806\pi$
$3$	−0.618034	−	1.07047i	−0.356822	−	0.618034i	−0.987428	+	0.158069i	$0.949473\pi$
$4$	−1.50000	−	2.59808i	−0.750000	−	1.29904i
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$	2.76393			1.12837
$7$		0			0
$7$		0			0
$8$	2.23607			0.790569
$9$	0.736068	−	1.27491i	0.245356	−	0.424969i
$10$	−2.23607	−	3.87298i	−0.707107	−	1.22474i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−1.85410	+	3.21140i	−0.535233	+	0.927051i
$13$	−3.23607			−0.897524			−0.448762	−	0.893651i	$-0.648135\pi$
$13$	−3.23607			−0.897524			−0.448762	+	0.893651i	$0.648135\pi$
$14$		0			0
$15$	2.47214			0.638303
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.61803	−	2.80252i	−0.392431	−	0.679710i	0.600339	−	0.799746i	$-0.295032\pi$
$17$	−1.61803	−	2.80252i	−0.392431	−	0.679710i	−0.992770	+	0.120036i	$0.961699\pi$
$18$	1.64590	+	2.85078i	0.387942	+	0.671935i
$19$	3.23607	−	5.60503i	0.742405	−	1.28588i	−0.208993	−	0.977917i	$-0.567018\pi$
$19$	3.23607	−	5.60503i	0.742405	−	1.28588i	0.951397	−	0.307966i	$-0.0996482\pi$
$20$	6.00000			1.34164
$21$		0			0
$22$	−2.23607			−0.476731
$23$	−1.23607	+	2.14093i	−0.257738	+	0.446415i	−0.965636	−	0.259900i	$-0.916310\pi$
$23$	−1.23607	+	2.14093i	−0.257738	+	0.446415i	0.707898	+	0.706315i	$0.249644\pi$
$24$	−1.38197	−	2.39364i	−0.282093	−	0.488599i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	3.61803	−	6.26662i	0.709555	−	1.22899i
$27$	−5.52786			−1.06384
$28$		0			0
$29$	8.47214			1.57324			0.786618	−	0.617440i	$-0.211830\pi$
$29$	8.47214			1.57324			0.786618	+	0.617440i	$0.211830\pi$
$30$	−2.76393	+	4.78727i	−0.504623	+	0.874032i
$31$	−1.38197	−	2.39364i	−0.248208	−	0.429910i	0.714820	−	0.699308i	$-0.246508\pi$
$31$	−1.38197	−	2.39364i	−0.248208	−	0.429910i	−0.963029	+	0.269399i	$0.913175\pi$
$32$	3.35410	+	5.80948i	0.592927	+	1.02698i
$33$	0.618034	−	1.07047i	0.107586	−	0.186344i
$34$	7.23607			1.24098
$35$		0			0
$36$	−4.41641			−0.736068
$37$	4.23607	−	7.33708i	0.696405	−	1.20621i	−0.273299	−	0.961929i	$-0.588115\pi$
$37$	4.23607	−	7.33708i	0.696405	−	1.20621i	0.969705	−	0.244280i	$-0.0785517\pi$
$38$	7.23607	+	12.5332i	1.17385	+	2.03316i
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$	−2.23607	+	3.87298i	−0.353553	+	0.612372i
$41$	11.2361			1.75478			0.877390	−	0.479779i	$-0.159283\pi$
$41$	11.2361			1.75478			0.877390	+	0.479779i	$0.159283\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$	1.47214	+	2.54981i	0.219453	+	0.380104i
$46$	−2.76393	−	4.78727i	−0.407520	−	0.705845i
$47$	1.38197	−	2.39364i	0.201580	−	0.349148i	−0.747457	−	0.664310i	$-0.768726\pi$
$47$	1.38197	−	2.39364i	0.201580	−	0.349148i	0.949038	+	0.315162i	$0.102059\pi$
$48$	−1.23607			−0.178411
$49$		0			0
$50$	−2.23607			−0.316228
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$	4.85410	+	8.40755i	0.673143	+	1.16592i
$53$	0.236068	+	0.408882i	0.0324264	+	0.0561642i	0.881783	−	0.471655i	$-0.156343\pi$
$53$	0.236068	+	0.408882i	0.0324264	+	0.0561642i	−0.849357	+	0.527819i	$0.823010\pi$
$54$	6.18034	−	10.7047i	0.841038	−	1.45672i
$55$	−2.00000			−0.269680
$56$		0			0
$57$	−8.00000			−1.05963
$58$	−9.47214	+	16.4062i	−1.24375	+	2.15424i
$59$	−0.618034	−	1.07047i	−0.0804612	−	0.139363i	0.822987	−	0.568060i	$-0.192306\pi$
$59$	−0.618034	−	1.07047i	−0.0804612	−	0.139363i	−0.903448	+	0.428697i	$0.858973\pi$
$60$	−3.70820	−	6.42280i	−0.478727	−	0.829180i
$61$	−3.61803	+	6.26662i	−0.463242	+	0.802358i	−0.999120	−	0.0419368i	$-0.986647\pi$
$61$	−3.61803	+	6.26662i	−0.463242	+	0.802358i	0.535878	+	0.844295i	$0.319981\pi$
$62$	6.18034			0.784904
$63$		0			0
$64$	−13.0000			−1.62500
$65$	3.23607	−	5.60503i	0.401385	−	0.695219i
$66$	1.38197	+	2.39364i	0.170108	+	0.294636i
$67$	−7.23607	−	12.5332i	−0.884026	−	1.53118i	−0.846825	−	0.531871i	$-0.821489\pi$
$67$	−7.23607	−	12.5332i	−0.884026	−	1.53118i	−0.0372009	−	0.999308i	$-0.511844\pi$
$68$	−4.85410	+	8.40755i	−0.588646	+	1.01957i
$69$	3.05573			0.367866
$70$		0			0
$71$	−10.4721			−1.24281			−0.621407	−	0.783488i	$-0.713439\pi$
$71$	−10.4721			−1.24281			−0.621407	+	0.783488i	$0.713439\pi$
$72$	1.64590	−	2.85078i	0.193971	−	0.335968i
$73$	−0.381966	−	0.661585i	−0.0447057	−	0.0774326i	0.842807	−	0.538216i	$-0.180902\pi$
$73$	−0.381966	−	0.661585i	−0.0447057	−	0.0774326i	−0.887512	+	0.460784i	$0.847568\pi$
$74$	9.47214	+	16.4062i	1.10111	+	1.90718i
$75$	0.618034	−	1.07047i	0.0713644	−	0.123607i
$76$	−19.4164			−2.22721
$77$		0			0
$78$	−8.94427			−1.01274
$79$	4.47214	−	7.74597i	0.503155	−	0.871489i	−0.496839	−	0.867843i	$-0.665506\pi$
$79$	4.47214	−	7.74597i	0.503155	−	0.871489i	0.999993	−	0.00364646i	$-0.00116071\pi$
$80$	1.00000	+	1.73205i	0.111803	+	0.193649i
$81$	1.20820	+	2.09267i	0.134245	+	0.232519i
$82$	−12.5623	+	21.7586i	−1.38727	+	2.40283i
$83$	11.4164			1.25311			0.626557	−	0.779376i	$-0.284464\pi$
$83$	11.4164			1.25311			0.626557	+	0.779376i	$0.284464\pi$
$84$		0			0
$85$	6.47214			0.702002
$86$	−8.94427	+	15.4919i	−0.964486	+	1.67054i
$87$	−5.23607	−	9.06914i	−0.561365	−	0.972313i
$88$	1.11803	+	1.93649i	0.119183	+	0.206431i
$89$	1.00000	−	1.73205i	0.106000	−	0.183597i	−0.808146	−	0.588982i	$-0.799529\pi$
$89$	1.00000	−	1.73205i	0.106000	−	0.183597i	0.914146	+	0.405385i	$0.132862\pi$
$90$	−6.58359			−0.693972
$91$		0			0
$92$	7.41641			0.773214
$93$	−1.70820	+	2.95870i	−0.177132	+	0.306802i
$94$	3.09017	+	5.35233i	0.318727	+	0.552051i
$95$	6.47214	+	11.2101i	0.664027	+	1.15013i
$96$	4.14590	−	7.18091i	0.423139	−	0.732898i
$97$	−17.4164			−1.76837			−0.884184	−	0.467139i	$-0.845285\pi$
$97$	−17.4164			−1.76837			−0.884184	+	0.467139i	$0.845285\pi$
$98$		0			0
$99$	1.47214			0.147955
$100$	1.50000	−	2.59808i	0.150000	−	0.259808i
$101$	−2.38197	−	4.12569i	−0.237014	−	0.410521i	0.722842	−	0.691014i	$-0.242836\pi$
$101$	−2.38197	−	4.12569i	−0.237014	−	0.410521i	−0.959856	+	0.280493i	$0.909502\pi$
$102$	−4.47214	−	7.74597i	−0.442807	−	0.766965i
$103$	3.85410	−	6.67550i	0.379756	−	0.657757i	−0.611271	−	0.791422i	$-0.709341\pi$
$103$	3.85410	−	6.67550i	0.379756	−	0.657757i	0.991027	+	0.133665i	$0.0426746\pi$
$104$	−7.23607			−0.709555
$105$		0			0
$106$	−1.05573			−0.102541
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	−0.753010	−	0.658009i	$-0.771399\pi$
$107$	2.00000	−	3.46410i	0.193347	−	0.334887i	0.946357	+	0.323122i	$0.104732\pi$
$108$	8.29180	+	14.3618i	0.797878	+	1.38197i
$109$	2.23607	+	3.87298i	0.214176	+	0.370965i	0.953018	−	0.302915i	$-0.0979599\pi$
$109$	2.23607	+	3.87298i	0.214176	+	0.370965i	−0.738841	+	0.673880i	$0.764627\pi$
$110$	2.23607	−	3.87298i	0.213201	−	0.369274i
$111$	−10.4721			−0.993971
$112$		0			0
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$	8.94427	−	15.4919i	0.837708	−	1.45095i
$115$	−2.47214	−	4.28187i	−0.230528	−	0.399286i
$116$	−12.7082	−	22.0113i	−1.17993	−	2.04369i
$117$	−2.38197	+	4.12569i	−0.220213	+	0.381420i
$118$	2.76393			0.254441
$119$		0			0
$120$	5.52786			0.504623
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−8.09017	−	14.0126i	−0.732450	−	1.26864i
$123$	−6.94427	−	12.0278i	−0.626144	−	1.08451i
$124$	−4.14590	+	7.18091i	−0.372313	+	0.644864i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	3.05573			0.271152			0.135576	−	0.990767i	$-0.456712\pi$
$127$	3.05573			0.271152			0.135576	+	0.990767i	$0.456712\pi$
$128$	7.82624	−	13.5554i	0.691748	−	1.19814i
$129$	−4.94427	−	8.56373i	−0.435319	−	0.753994i
$130$	7.23607	+	12.5332i	0.634645	+	1.09924i
$131$	10.9443	−	18.9560i	0.956205	−	1.65620i	0.224620	−	0.974446i	$-0.427886\pi$
$131$	10.9443	−	18.9560i	0.956205	−	1.65620i	0.731585	−	0.681750i	$-0.238781\pi$
$132$	−3.70820			−0.322758
$133$		0			0
$134$	32.3607			2.79554
$135$	5.52786	−	9.57454i	0.475763	−	0.824045i
$136$	−3.61803	−	6.26662i	−0.310244	−	0.537358i
$137$	−8.23607	−	14.2653i	−0.703655	−	1.21877i	−0.967175	−	0.254112i	$-0.918217\pi$
$137$	−8.23607	−	14.2653i	−0.703655	−	1.21877i	0.263520	−	0.964654i	$-0.415116\pi$
$138$	−3.41641	+	5.91739i	−0.290824	+	0.503722i
$139$	1.52786			0.129592			0.0647959	−	0.997899i	$-0.479360\pi$
$139$	1.52786			0.129592			0.0647959	+	0.997899i	$0.479360\pi$
$140$		0			0
$141$	−3.41641			−0.287713
$142$	11.7082	−	20.2792i	0.982531	−	1.70179i
$143$	−1.61803	−	2.80252i	−0.135307	−	0.234358i
$144$	−0.736068	−	1.27491i	−0.0613390	−	0.106242i
$145$	−8.47214	+	14.6742i	−0.703573	+	1.21862i
$146$	1.70820			0.141372
$147$		0			0
$148$	−25.4164			−2.08922
$149$	−7.00000	+	12.1244i	−0.573462	+	0.993266i	0.422744	+	0.906249i	$0.361067\pi$
$149$	−7.00000	+	12.1244i	−0.573462	+	0.993266i	−0.996207	+	0.0870170i	$0.972267\pi$
$150$	1.38197	+	2.39364i	0.112837	+	0.195440i
$151$	−4.47214	−	7.74597i	−0.363937	−	0.630358i	0.624668	−	0.780891i	$-0.285234\pi$
$151$	−4.47214	−	7.74597i	−0.363937	−	0.630358i	−0.988605	+	0.150533i	$0.951901\pi$
$152$	7.23607	−	12.5332i	0.586923	−	1.01658i
$153$	−4.76393			−0.385141
$154$		0			0
$155$	5.52786			0.444009
$156$	6.00000	−	10.3923i	0.480384	−	0.832050i
$157$	5.47214	+	9.47802i	0.436724	+	0.756428i	0.997435	−	0.0715837i	$-0.0228053\pi$
$157$	5.47214	+	9.47802i	0.436724	+	0.756428i	−0.560711	+	0.828012i	$0.689472\pi$
$158$	10.0000	+	17.3205i	0.795557	+	1.37795i
$159$	0.291796	−	0.505406i	0.0231409	−	0.0400813i
$160$	−13.4164			−1.06066
$161$		0			0
$162$	−5.40325			−0.424520
$163$	1.70820	−	2.95870i	0.133797	−	0.231743i	−0.791340	−	0.611376i	$-0.790616\pi$
$163$	1.70820	−	2.95870i	0.133797	−	0.231743i	0.925137	+	0.379633i	$0.123950\pi$
$164$	−16.8541	−	29.1922i	−1.31608	−	2.27952i
$165$	1.23607	+	2.14093i	0.0962278	+	0.166671i
$166$	−12.7639	+	22.1078i	−0.990673	+	1.71590i
$167$	−4.94427			−0.382599			−0.191300	−	0.981532i	$-0.561270\pi$
$167$	−4.94427			−0.382599			−0.191300	+	0.981532i	$0.561270\pi$
$168$		0			0
$169$	−2.52786			−0.194451
$170$	−7.23607	+	12.5332i	−0.554981	+	0.961255i
$171$	−4.76393	−	8.25137i	−0.364307	−	0.630998i
$172$	−12.0000	−	20.7846i	−0.914991	−	1.58481i
$173$	−6.38197	+	11.0539i	−0.485212	+	0.840412i	−0.999856	−	0.0169925i	$-0.994591\pi$
$173$	−6.38197	+	11.0539i	−0.485212	+	0.840412i	0.514644	+	0.857404i	$0.327924\pi$
$174$	23.4164			1.77519
$175$		0			0
$176$	1.00000			0.0753778
$177$	−0.763932	+	1.32317i	−0.0574206	+	0.0994555i
$178$	2.23607	+	3.87298i	0.167600	+	0.290292i
$179$	4.47214	+	7.74597i	0.334263	+	0.578961i	0.983343	−	0.181760i	$-0.0581792\pi$
$179$	4.47214	+	7.74597i	0.334263	+	0.578961i	−0.649080	+	0.760720i	$0.724846\pi$
$180$	4.41641	−	7.64944i	0.329180	−	0.570156i
$181$	25.4164			1.88919			0.944593	−	0.328243i	$-0.106456\pi$
$181$	25.4164			1.88919			0.944593	+	0.328243i	$0.106456\pi$
$182$		0			0
$183$	8.94427			0.661180
$184$	−2.76393	+	4.78727i	−0.203760	+	0.352922i
$185$	8.47214	+	14.6742i	0.622884	+	1.07887i
$186$	−3.81966	−	6.61585i	−0.280071	−	0.485097i
$187$	1.61803	−	2.80252i	0.118322	−	0.204940i
$188$	−8.29180			−0.604741
$189$		0			0
$190$	−28.9443			−2.09984
$191$	1.52786	−	2.64634i	0.110552	−	0.191482i	−0.805441	−	0.592676i	$-0.798071\pi$
$191$	1.52786	−	2.64634i	0.110552	−	0.191482i	0.915993	+	0.401194i	$0.131405\pi$
$192$	8.03444	+	13.9161i	0.579836	+	1.00431i
$193$	−5.94427	−	10.2958i	−0.427878	−	0.741107i	0.568806	−	0.822472i	$-0.307405\pi$
$193$	−5.94427	−	10.2958i	−0.427878	−	0.741107i	−0.996684	+	0.0813650i	$0.974072\pi$
$194$	19.4721	−	33.7267i	1.39802	−	2.42144i
$195$	−8.00000			−0.572892
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$	−1.64590	+	2.85078i	−0.116969	+	0.202596i
$199$	−1.09017	−	1.88823i	−0.0772801	−	0.133853i	0.824795	−	0.565431i	$-0.191290\pi$
$199$	−1.09017	−	1.88823i	−0.0772801	−	0.133853i	−0.902076	+	0.431578i	$0.857957\pi$
$200$	1.11803	+	1.93649i	0.0790569	+	0.136931i
$201$	−8.94427	+	15.4919i	−0.630880	+	1.09272i
$202$	10.6525			0.749506
$203$		0			0
$204$	12.0000			0.840168
$205$	−11.2361	+	19.4614i	−0.784761	+	1.35925i
$206$	8.61803	+	14.9269i	0.600447	+	1.04000i
$207$	1.81966	+	3.15174i	0.126475	+	0.219061i
$208$	−1.61803	+	2.80252i	−0.112190	+	0.194320i
$209$	6.47214			0.447687
$210$		0			0
$211$	−13.8885			−0.956127			−0.478063	−	0.878325i	$-0.658661\pi$
$211$	−13.8885			−0.956127			−0.478063	+	0.878325i	$0.658661\pi$
$212$	0.708204	−	1.22665i	0.0486396	−	0.0842463i
$213$	6.47214	+	11.2101i	0.443463	+	0.768101i
$214$	4.47214	+	7.74597i	0.305709	+	0.529503i
$215$	−8.00000	+	13.8564i	−0.545595	+	0.944999i
$216$	−12.3607			−0.841038
$217$		0			0
$218$	−10.0000			−0.677285
$219$	−0.472136	+	0.817763i	−0.0319040	+	0.0552593i
$220$	3.00000	+	5.19615i	0.202260	+	0.350325i
$221$	5.23607	+	9.06914i	0.352216	+	0.610056i
$222$	11.7082	−	20.2792i	0.785803	−	1.36105i
$223$	10.1803			0.681726			0.340863	−	0.940113i	$-0.389281\pi$
$223$	10.1803			0.681726			0.340863	+	0.940113i	$0.389281\pi$
$224$		0			0
$225$	1.47214			0.0981424
$226$	−2.23607	+	3.87298i	−0.148741	+	0.257627i
$227$	2.94427	+	5.09963i	0.195418	+	0.338474i	0.947038	−	0.321123i	$-0.104060\pi$
$227$	2.94427	+	5.09963i	0.195418	+	0.338474i	−0.751619	+	0.659597i	$0.770727\pi$
$228$	12.0000	+	20.7846i	0.794719	+	1.37649i
$229$	−2.23607	+	3.87298i	−0.147764	+	0.255934i	−0.930401	−	0.366544i	$-0.880541\pi$
$229$	−2.23607	+	3.87298i	−0.147764	+	0.255934i	0.782637	+	0.622478i	$0.213874\pi$
$230$	11.0557			0.728993
$231$		0			0
$232$	18.9443			1.24375
$233$	−4.70820	+	8.15485i	−0.308445	+	0.534242i	−0.978022	−	0.208500i	$-0.933142\pi$
$233$	−4.70820	+	8.15485i	−0.308445	+	0.534242i	0.669578	+	0.742742i	$0.266475\pi$
$234$	−5.32624	−	9.22531i	−0.348187	−	0.603078i
$235$	2.76393	+	4.78727i	0.180299	+	0.312287i
$236$	−1.85410	+	3.21140i	−0.120692	+	0.209044i
$237$	−11.0557			−0.718147
$238$		0			0
$239$	−9.88854			−0.639637			−0.319818	−	0.947479i	$-0.603622\pi$
$239$	−9.88854			−0.639637			−0.319818	+	0.947479i	$0.603622\pi$
$240$	1.23607	−	2.14093i	0.0797878	−	0.138197i
$241$	−6.56231	−	11.3662i	−0.422715	−	0.732164i	0.573489	−	0.819213i	$-0.305590\pi$
$241$	−6.56231	−	11.3662i	−0.422715	−	0.732164i	−0.996204	+	0.0870491i	$0.972256\pi$
$242$	−1.11803	−	1.93649i	−0.0718699	−	0.124482i
$243$	−6.79837	+	11.7751i	−0.436116	+	0.755375i
$244$	21.7082			1.38973
$245$		0			0
$246$	31.0557			1.98004
$247$	−10.4721	+	18.1383i	−0.666326	+	1.15411i
$248$	−3.09017	−	5.35233i	−0.196226	−	0.339873i
$249$	−7.05573	−	12.2209i	−0.447139	−	0.774467i
$250$	13.4164	−	23.2379i	0.848528	−	1.46969i
$251$	−4.29180			−0.270896			−0.135448	−	0.990784i	$-0.543247\pi$
$251$	−4.29180			−0.270896			−0.135448	+	0.990784i	$0.543247\pi$
$252$		0			0
$253$	−2.47214			−0.155422
$254$	−3.41641	+	5.91739i	−0.214364	+	0.371290i
$255$	−4.00000	−	6.92820i	−0.250490	−	0.433861i
$256$	4.50000	+	7.79423i	0.281250	+	0.487139i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	22.1115			1.37660
$259$		0			0
$260$	−19.4164			−1.20415
$261$	6.23607	−	10.8012i	0.386003	−	0.668577i
$262$	24.4721	+	42.3870i	1.51189	+	2.61868i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$	1.38197	−	2.39364i	0.0850541	−	0.147318i
$265$	−0.944272			−0.0580062
$266$		0			0
$267$	−2.47214			−0.151292
$268$	−21.7082	+	37.5997i	−1.32604	+	2.29677i
$269$	6.70820	+	11.6190i	0.409006	+	0.708420i	0.994779	−	0.102056i	$-0.0325420\pi$
$269$	6.70820	+	11.6190i	0.409006	+	0.708420i	−0.585772	+	0.810476i	$0.699209\pi$
$270$	12.3607	+	21.4093i	0.752247	+	1.30293i
$271$	−5.23607	+	9.06914i	−0.318068	+	0.550911i	−0.980085	−	0.198578i	$-0.936368\pi$
$271$	−5.23607	+	9.06914i	−0.318068	+	0.550911i	0.662017	+	0.749489i	$0.269701\pi$
$272$	−3.23607			−0.196215
$273$		0			0
$274$	36.8328			2.22515
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	−4.58359	−	7.93901i	−0.275900	−	0.477873i
$277$	9.94427	+	17.2240i	0.597493	+	1.03489i	0.993190	+	0.116508i	$0.0371699\pi$
$277$	9.94427	+	17.2240i	0.597493	+	1.03489i	−0.395696	+	0.918381i	$0.629497\pi$
$278$	−1.70820	+	2.95870i	−0.102451	+	0.177451i
$279$	−4.06888			−0.243598
$280$		0			0
$281$	−3.52786			−0.210455			−0.105227	−	0.994448i	$-0.533557\pi$
$281$	−3.52786			−0.210455			−0.105227	+	0.994448i	$0.533557\pi$
$282$	3.81966	−	6.61585i	0.227457	−	0.393968i
$283$	14.9443	+	25.8842i	0.888345	+	1.53866i	0.841831	+	0.539741i	$0.181478\pi$
$283$	14.9443	+	25.8842i	0.888345	+	1.53866i	0.0465134	+	0.998918i	$0.485189\pi$
$284$	15.7082	+	27.2074i	0.932110	+	1.61446i
$285$	8.00000	−	13.8564i	0.473879	−	0.820783i
$286$	7.23607			0.427878
$287$		0			0
$288$	9.87539			0.581913
$289$	3.26393	−	5.65330i	0.191996	−	0.332547i
$290$	−18.9443	−	32.8124i	−1.11245	−	1.92681i
$291$	10.7639	+	18.6437i	0.630993	+	1.09291i
$292$	−1.14590	+	1.98475i	−0.0670586	+	0.116149i
$293$	25.1246			1.46780			0.733898	−	0.679260i	$-0.237699\pi$
$293$	25.1246			1.46780			0.733898	+	0.679260i	$0.237699\pi$
$294$		0			0
$295$	2.47214			0.143933
$296$	9.47214	−	16.4062i	0.550557	−	0.953592i
$297$	−2.76393	−	4.78727i	−0.160380	−	0.277786i
$298$	−15.6525	−	27.1109i	−0.906724	−	1.57049i
$299$	4.00000	−	6.92820i	0.231326	−	0.400668i
$300$	−3.70820			−0.214093
$301$		0			0
$302$	20.0000			1.15087
$303$	−2.94427	+	5.09963i	−0.169144	+	0.292966i
$304$	−3.23607	−	5.60503i	−0.185601	−	0.321471i
$305$	−7.23607	−	12.5332i	−0.414336	−	0.717651i
$306$	5.32624	−	9.22531i	0.304481	−	0.527376i
$307$	8.94427			0.510477			0.255238	−	0.966878i	$-0.417846\pi$
$307$	8.94427			0.510477			0.255238	+	0.966878i	$0.417846\pi$
$308$		0			0
$309$	−9.52786			−0.542021
$310$	−6.18034	+	10.7047i	−0.351020	+	0.607984i
$311$	−4.14590	−	7.18091i	−0.235092	−	0.407192i	0.724207	−	0.689582i	$-0.242206\pi$
$311$	−4.14590	−	7.18091i	−0.235092	−	0.407192i	−0.959300	+	0.282391i	$0.908873\pi$
$312$	4.47214	+	7.74597i	0.253185	+	0.438529i
$313$	7.47214	−	12.9421i	0.422350	−	0.731532i	−0.573819	−	0.818982i	$-0.694539\pi$
$313$	7.47214	−	12.9421i	0.422350	−	0.731532i	0.996169	+	0.0874505i	$0.0278720\pi$
$314$	−24.4721			−1.38104
$315$		0			0
$316$	−26.8328			−1.50946
$317$	−7.00000	+	12.1244i	−0.393159	+	0.680972i	−0.992864	−	0.119249i	$-0.961951\pi$
$317$	−7.00000	+	12.1244i	−0.393159	+	0.680972i	0.599705	+	0.800221i	$0.295285\pi$
$318$	0.652476	+	1.13012i	0.0365890	+	0.0633741i
$319$	4.23607	+	7.33708i	0.237174	+	0.410798i
$320$	13.0000	−	22.5167i	0.726722	−	1.25872i
$321$	−4.94427			−0.275962
$322$		0			0
$323$	−20.9443			−1.16537
$324$	3.62461	−	6.27801i	0.201367	−	0.348778i
$325$	−1.61803	−	2.80252i	−0.0897524	−	0.155456i
$326$	3.81966	+	6.61585i	0.211551	+	0.366418i
$327$	2.76393	−	4.78727i	0.152846	−	0.264737i
$328$	25.1246			1.38727
$329$		0			0
$330$	−5.52786			−0.304299
$331$	6.94427	−	12.0278i	0.381692	−	0.661109i	−0.609613	−	0.792700i	$-0.708675\pi$
$331$	6.94427	−	12.0278i	0.381692	−	0.661109i	0.991304	+	0.131590i	$0.0420083\pi$
$332$	−17.1246	−	29.6607i	−0.939835	−	1.62784i
$333$	−6.23607	−	10.8012i	−0.341734	−	0.591901i
$334$	5.52786	−	9.57454i	0.302471	−	0.523896i
$335$	28.9443			1.58139
$336$		0			0
$337$	−11.5279			−0.627963			−0.313981	−	0.949429i	$-0.601663\pi$
$337$	−11.5279			−0.627963			−0.313981	+	0.949429i	$0.601663\pi$
$338$	2.82624	−	4.89519i	0.153727	−	0.266263i
$339$	−1.23607	−	2.14093i	−0.0671340	−	0.116279i
$340$	−9.70820	−	16.8151i	−0.526501	−	0.911927i
$341$	1.38197	−	2.39364i	0.0748377	−	0.129623i
$342$	21.3050			1.15204
$343$		0			0
$344$	17.8885			0.964486
$345$	−3.05573	+	5.29268i	−0.164515	+	0.284948i
$346$	−14.2705	−	24.7172i	−0.767187	−	1.32881i
$347$	−10.4721	−	18.1383i	−0.562174	−	0.973713i	−0.997306	−	0.0733471i	$-0.976632\pi$
$347$	−10.4721	−	18.1383i	−0.562174	−	0.973713i	0.435133	−	0.900366i	$-0.356701\pi$
$348$	−15.7082	+	27.2074i	−0.842048	+	1.45847i
$349$	7.23607			0.387338			0.193669	−	0.981067i	$-0.437961\pi$
$349$	7.23607			0.387338			0.193669	+	0.981067i	$0.437961\pi$
$350$		0			0
$351$	17.8885			0.954820
$352$	−3.35410	+	5.80948i	−0.178774	+	0.309646i
$353$	9.94427	+	17.2240i	0.529280	+	0.916740i	0.999417	+	0.0341465i	$0.0108713\pi$
$353$	9.94427	+	17.2240i	0.529280	+	0.916740i	−0.470137	+	0.882594i	$0.655795\pi$
$354$	−1.70820	−	2.95870i	−0.0907900	−	0.157253i
$355$	10.4721	−	18.1383i	0.555803	−	0.962679i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−20.0000			−1.05703
$359$	12.4721	−	21.6024i	0.658254	−	1.14013i	−0.322813	−	0.946463i	$-0.604629\pi$
$359$	12.4721	−	21.6024i	0.658254	−	1.14013i	0.981067	−	0.193667i	$-0.0620381\pi$
$360$	3.29180	+	5.70156i	0.173493	+	0.300498i
$361$	−11.4443	−	19.8221i	−0.602330	−	1.04327i
$362$	−28.4164	+	49.2187i	−1.49353	+	2.58688i
$363$	1.23607			0.0648767
$364$		0			0
$365$	1.52786			0.0799721
$366$	−10.0000	+	17.3205i	−0.522708	+	0.905357i
$367$	−11.5623	−	20.0265i	−0.603547	−	1.04537i	−0.992279	−	0.124024i	$-0.960420\pi$
$367$	−11.5623	−	20.0265i	−0.603547	−	1.04537i	0.388732	−	0.921351i	$-0.372913\pi$
$368$	1.23607	+	2.14093i	0.0644345	+	0.111604i
$369$	8.27051	−	14.3249i	0.430546	−	0.745727i
$370$	−37.8885			−1.96973
$371$		0			0
$372$	10.2492			0.531397
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	−0.933181	−	0.359408i	$-0.882979\pi$
$373$	−3.00000	+	5.19615i	−0.155334	+	0.269047i	0.777847	+	0.628454i	$0.216312\pi$
$374$	3.61803	+	6.26662i	0.187084	+	0.324039i
$375$	7.41641	+	12.8456i	0.382982	+	0.663344i
$376$	3.09017	−	5.35233i	0.159363	−	0.276025i
$377$	−27.4164			−1.41202
$378$		0			0
$379$	37.3050			1.91623			0.958113	−	0.286389i	$-0.0924551\pi$
$379$	37.3050			1.91623			0.958113	+	0.286389i	$0.0924551\pi$
$380$	19.4164	−	33.6302i	0.996041	−	1.72519i
$381$	−1.88854	−	3.27105i	−0.0967530	−	0.167581i
$382$	3.41641	+	5.91739i	0.174799	+	0.302760i
$383$	−2.32624	+	4.02916i	−0.118865	+	0.205881i	−0.919318	−	0.393515i	$-0.871259\pi$
$383$	−2.32624	+	4.02916i	−0.118865	+	0.205881i	0.800453	+	0.599395i	$0.204592\pi$
$384$	−19.3475			−0.987324
$385$		0			0
$386$	26.5836			1.35307
$387$	5.88854	−	10.1993i	0.299332	−	0.518457i
$388$	26.1246	+	45.2492i	1.32628	+	2.29718i
$389$	−7.94427	−	13.7599i	−0.402791	−	0.697654i	0.591271	−	0.806473i	$-0.298626\pi$
$389$	−7.94427	−	13.7599i	−0.402791	−	0.697654i	−0.994062	+	0.108819i	$0.965293\pi$
$390$	8.94427	−	15.4919i	0.452911	−	0.784465i
$391$	8.00000			0.404577
$392$		0			0
$393$	−27.0557			−1.36478
$394$	2.23607	−	3.87298i	0.112651	−	0.195118i
$395$	8.94427	+	15.4919i	0.450035	+	0.779484i
$396$	−2.20820	−	3.82472i	−0.110966	−	0.192199i
$397$	−17.9443	+	31.0804i	−0.900597	+	1.55988i	−0.0738766	+	0.997267i	$0.523537\pi$
$397$	−17.9443	+	31.0804i	−0.900597	+	1.55988i	−0.826721	+	0.562613i	$0.809796\pi$
$398$	4.87539			0.244381
$399$		0			0
$400$	1.00000			0.0500000
$401$	−11.4721	+	19.8703i	−0.572891	+	0.992277i	0.423376	+	0.905954i	$0.360845\pi$
$401$	−11.4721	+	19.8703i	−0.572891	+	0.992277i	−0.996267	+	0.0863225i	$0.972488\pi$
$402$	−20.0000	−	34.6410i	−0.997509	−	1.72774i
$403$	4.47214	+	7.74597i	0.222773	+	0.385854i
$404$	−7.14590	+	12.3771i	−0.355522	+	0.615782i
$405$	−4.83282			−0.240145
$406$		0			0
$407$	8.47214			0.419948
$408$	−4.47214	+	7.74597i	−0.221404	+	0.383482i
$409$	4.56231	+	7.90215i	0.225592	+	0.390736i	0.956497	−	0.291743i	$-0.0942352\pi$
$409$	4.56231	+	7.90215i	0.225592	+	0.390736i	−0.730905	+	0.682479i	$0.760902\pi$
$410$	−25.1246	−	43.5171i	−1.24082	−	2.14916i
$411$	−10.1803	+	17.6329i	−0.502159	+	0.869765i
$412$	−23.1246			−1.13927
$413$		0			0
$414$	−8.13777			−0.399949
$415$	−11.4164	+	19.7738i	−0.560409	+	0.970658i
$416$	−10.8541	−	18.7999i	−0.532166	−	0.921739i
$417$	−0.944272	−	1.63553i	−0.0462412	−	0.0800921i
$418$	−7.23607	+	12.5332i	−0.353928	+	0.613021i
$419$	−24.6525			−1.20435			−0.602176	−	0.798363i	$-0.705700\pi$
$419$	−24.6525			−1.20435			−0.602176	+	0.798363i	$0.705700\pi$
$420$		0			0
$421$	22.3607			1.08979			0.544896	−	0.838503i	$-0.316569\pi$
$421$	22.3607			1.08979			0.544896	+	0.838503i	$0.316569\pi$
$422$	15.5279	−	26.8950i	0.755885	−	1.30923i
$423$	−2.03444	−	3.52376i	−0.0989179	−	0.171331i
$424$	0.527864	+	0.914287i	0.0256353	+	0.0444017i
$425$	1.61803	−	2.80252i	0.0784862	−	0.135942i
$426$	−28.9443			−1.40235
$427$		0			0
$428$	−12.0000			−0.580042
$429$	−2.00000	+	3.46410i	−0.0965609	+	0.167248i
$430$	−17.8885	−	30.9839i	−0.862662	−	1.49417i
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	−2.76393	+	4.78727i	−0.132980	+	0.230328i
$433$	8.47214			0.407145			0.203572	−	0.979060i	$-0.434745\pi$
$433$	8.47214			0.407145			0.203572	+	0.979060i	$0.434745\pi$
$434$		0			0
$435$	20.9443			1.00420
$436$	6.70820	−	11.6190i	0.321265	−	0.556447i
$437$	8.00000	+	13.8564i	0.382692	+	0.662842i
$438$	−1.05573	−	1.82857i	−0.0504446	−	0.0873727i
$439$	5.23607	−	9.06914i	0.249904	−	0.432846i	−0.713595	−	0.700558i	$-0.752934\pi$
$439$	5.23607	−	9.06914i	0.249904	−	0.432846i	0.963499	+	0.267712i	$0.0862676\pi$
$440$	−4.47214			−0.213201
$441$		0			0
$442$	−23.4164			−1.11380
$443$	12.4721	−	21.6024i	0.592569	−	1.02636i	−0.401316	−	0.915940i	$-0.631447\pi$
$443$	12.4721	−	21.6024i	0.592569	−	1.02636i	0.993885	−	0.110420i	$-0.0352196\pi$
$444$	15.7082	+	27.2074i	0.745478	+	1.29121i
$445$	2.00000	+	3.46410i	0.0948091	+	0.164214i
$446$	−11.3820	+	19.7141i	−0.538952	+	0.933492i
$447$	17.3050			0.818496
$448$		0			0
$449$	−28.4721			−1.34368			−0.671842	−	0.740695i	$-0.734496\pi$
$449$	−28.4721			−1.34368			−0.671842	+	0.740695i	$0.734496\pi$
$450$	−1.64590	+	2.85078i	−0.0775884	+	0.134387i
$451$	5.61803	+	9.73072i	0.264543	+	0.458202i
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	−5.52786	+	9.57454i	−0.259722	+	0.449851i
$454$	−13.1672			−0.617967
$455$		0			0
$456$	−17.8885			−0.837708
$457$	14.4164	−	24.9700i	0.674371	−	1.16805i	−0.302281	−	0.953219i	$-0.597748\pi$
$457$	14.4164	−	24.9700i	0.674371	−	1.16805i	0.976652	−	0.214826i	$-0.0689185\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$	8.94427	+	15.4919i	0.417483	+	0.723102i
$460$	−7.41641	+	12.8456i	−0.345792	+	0.598929i
$461$	12.1803			0.567295			0.283647	−	0.958929i	$-0.408455\pi$
$461$	12.1803			0.567295			0.283647	+	0.958929i	$0.408455\pi$
$462$		0			0
$463$	−5.52786			−0.256902			−0.128451	−	0.991716i	$-0.541000\pi$
$463$	−5.52786			−0.256902			−0.128451	+	0.991716i	$0.541000\pi$
$464$	4.23607	−	7.33708i	0.196655	−	0.340616i
$465$	−3.41641	−	5.91739i	−0.158432	−	0.274412i
$466$	−10.5279	−	18.2348i	−0.487694	−	0.844711i
$467$	12.0344	−	20.8443i	0.556888	−	0.964558i	−0.440866	−	0.897573i	$-0.645329\pi$
$467$	12.0344	−	20.8443i	0.556888	−	0.964558i	0.997754	−	0.0669848i	$-0.0213379\pi$
$468$	14.2918			0.660639
$469$		0			0
$470$	−12.3607			−0.570156
$471$	6.76393	−	11.7155i	0.311666	−	0.539821i
$472$	−1.38197	−	2.39364i	−0.0636101	−	0.110176i
$473$	4.00000	+	6.92820i	0.183920	+	0.318559i
$474$	12.3607	−	21.4093i	0.567745	−	0.983363i
$475$	6.47214			0.296962
$476$		0			0
$477$	0.695048			0.0318241
$478$	11.0557	−	19.1491i	0.505677	−	0.875859i
$479$	6.76393	+	11.7155i	0.309052	+	0.535294i	0.978155	−	0.207876i	$-0.0666550\pi$
$479$	6.76393	+	11.7155i	0.309052	+	0.535294i	−0.669103	+	0.743169i	$0.733322\pi$
$480$	8.29180	+	14.3618i	0.378467	+	0.655524i
$481$	−13.7082	+	23.7433i	−0.625040	+	1.08260i
$482$	29.3475			1.33674
$483$		0			0
$484$	3.00000			0.136364
$485$	17.4164	−	30.1661i	0.790838	−	1.36977i
$486$	−15.2016	−	26.3300i	−0.689560	−	1.19435i
$487$	18.1803	+	31.4893i	0.823830	+	1.42692i	0.902810	+	0.430039i	$0.141500\pi$
$487$	18.1803	+	31.4893i	0.823830	+	1.42692i	−0.0789805	+	0.996876i	$0.525166\pi$
$488$	−8.09017	+	14.0126i	−0.366225	+	0.634320i
$489$	−4.22291			−0.190967
$490$		0			0
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	−20.8328	+	36.0835i	−0.939216	+	1.62677i
$493$	−13.7082	−	23.7433i	−0.617386	−	1.06934i
$494$	−23.4164	−	40.5584i	−1.05355	−	1.82481i
$495$	−1.47214	+	2.54981i	−0.0661676	+	0.114606i
$496$	−2.76393			−0.124104
$497$		0			0
$498$	31.5542			1.41398
$499$	−0.763932	+	1.32317i	−0.0341983	+	0.0592332i	−0.882618	−	0.470091i	$-0.844221\pi$
$499$	−0.763932	+	1.32317i	−0.0341983	+	0.0592332i	0.848420	+	0.529324i	$0.177554\pi$
$500$	18.0000	+	31.1769i	0.804984	+	1.39427i
$501$	3.05573	+	5.29268i	0.136520	+	0.236459i
$502$	4.79837	−	8.31103i	0.214162	−	0.370939i
$503$	−23.4164			−1.04409			−0.522043	−	0.852919i	$-0.674830\pi$
$503$	−23.4164			−1.04409			−0.522043	+	0.852919i	$0.674830\pi$
$504$		0			0
$505$	9.52786			0.423984
$506$	2.76393	−	4.78727i	0.122872	−	0.212820i
$507$	1.56231	+	2.70599i	0.0693844	+	0.120177i
$508$	−4.58359	−	7.93901i	−0.203364	−	0.352237i
$509$	20.2361	−	35.0499i	0.896948	−	1.55356i	0.0655728	−	0.997848i	$-0.479113\pi$
$509$	20.2361	−	35.0499i	0.896948	−	1.55356i	0.831375	−	0.555712i	$-0.187554\pi$
$510$	17.8885			0.792118
$511$		0			0
$512$	11.1803			0.494106
$513$	−17.8885	+	30.9839i	−0.789799	+	1.36797i
$514$	−6.70820	−	11.6190i	−0.295886	−	0.512490i
$515$	7.70820	+	13.3510i	0.339664	+	0.588315i
$516$	−14.8328	+	25.6912i	−0.652978	+	1.13099i
$517$	2.76393			0.121558
$518$		0			0
$519$	15.7771			0.692537
$520$	7.23607	−	12.5332i	0.317323	−	0.549619i
$521$	15.1803	+	26.2931i	0.665063	+	1.15192i	0.979268	+	0.202568i	$0.0649286\pi$
$521$	15.1803	+	26.2931i	0.665063	+	1.15192i	−0.314206	+	0.949355i	$0.601738\pi$
$522$	13.9443	+	24.1522i	0.610324	+	1.05711i
$523$	22.0000	−	38.1051i	0.961993	−	1.66622i	0.244507	−	0.969648i	$-0.421374\pi$
$523$	22.0000	−	38.1051i	0.961993	−	1.66622i	0.717486	−	0.696573i	$-0.245293\pi$
$524$	−65.6656			−2.86862
$525$		0			0
$526$		0			0
$527$	−4.47214	+	7.74597i	−0.194809	+	0.337420i
$528$	−0.618034	−	1.07047i	−0.0268965	−	0.0465861i
$529$	8.44427	+	14.6259i	0.367142	+	0.635909i
$530$	1.05573	−	1.82857i	0.0458579	−	0.0794282i
$531$	−1.81966			−0.0789665
$532$		0			0
$533$	−36.3607			−1.57496
$534$	2.76393	−	4.78727i	0.119607	−	0.207165i
$535$	4.00000	+	6.92820i	0.172935	+	0.299532i
$536$	−16.1803	−	28.0252i	−0.698884	−	1.21050i
$537$	5.52786	−	9.57454i	0.238545	−	0.413172i
$538$	−30.0000			−1.29339
$539$		0			0
$540$	−33.1672			−1.42729
$541$	−10.4164	+	18.0417i	−0.447836	+	0.775675i	−0.998245	−	0.0592201i	$-0.981139\pi$
$541$	−10.4164	+	18.0417i	−0.447836	+	0.775675i	0.550409	+	0.834895i	$0.314472\pi$
$542$	−11.7082	−	20.2792i	−0.502910	−	0.871066i
$543$	−15.7082	−	27.2074i	−0.674104	−	1.16758i
$544$	10.8541	−	18.7999i	0.465366	−	0.806037i
$545$	−8.94427			−0.383131
$546$		0			0
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	−24.7082	+	42.7959i	−1.05548	+	1.82815i
$549$	5.32624	+	9.22531i	0.227318	+	0.393727i
$550$	−1.11803	−	1.93649i	−0.0476731	−	0.0825723i
$551$	27.4164	−	47.4866i	1.16798	−	2.02300i
$552$	6.83282			0.290824
$553$		0			0
$554$	−44.4721			−1.88944
$555$	10.4721	−	18.1383i	0.444517	−	0.769927i
$556$	−2.29180	−	3.96951i	−0.0971938	−	0.168345i
$557$	19.4721	+	33.7267i	0.825061	+	1.42905i	0.901873	+	0.432002i	$0.142193\pi$
$557$	19.4721	+	33.7267i	0.825061	+	1.42905i	−0.0768119	+	0.997046i	$0.524474\pi$
$558$	4.54915	−	7.87936i	0.192581	−	0.333560i
$559$	−25.8885			−1.09497
$560$		0			0
$561$	−4.00000			−0.168880
$562$	3.94427	−	6.83168i	0.166379	−	0.288177i
$563$	6.29180	+	10.8977i	0.265168	+	0.459284i	0.967608	−	0.252459i	$-0.0812394\pi$
$563$	6.29180	+	10.8977i	0.265168	+	0.459284i	−0.702440	+	0.711743i	$0.747906\pi$
$564$	5.12461	+	8.87609i	0.215785	+	0.373751i
$565$	−2.00000	+	3.46410i	−0.0841406	+	0.145736i
$566$	−66.8328			−2.80919
$567$		0			0
$568$	−23.4164			−0.982531
$569$	−3.76393	+	6.51932i	−0.157792	+	0.273304i	−0.934072	−	0.357084i	$-0.883771\pi$
$569$	−3.76393	+	6.51932i	−0.157792	+	0.273304i	0.776280	+	0.630388i	$0.217104\pi$
$570$	17.8885	+	30.9839i	0.749269	+	1.29777i
$571$	7.52786	+	13.0386i	0.315031	+	0.545650i	0.979444	−	0.201716i	$-0.0646516\pi$
$571$	7.52786	+	13.0386i	0.315031	+	0.545650i	−0.664413	+	0.747366i	$0.731318\pi$
$572$	−4.85410	+	8.40755i	−0.202960	+	0.351537i
$573$	−3.77709			−0.157790
$574$		0			0
$575$	−2.47214			−0.103095
$576$	−9.56888	+	16.5738i	−0.398703	+	0.690575i
$577$	−9.76393	−	16.9116i	−0.406478	−	0.704040i	0.588014	−	0.808850i	$-0.299910\pi$
$577$	−9.76393	−	16.9116i	−0.406478	−	0.704040i	−0.994492	+	0.104810i	$0.966576\pi$
$578$	7.29837	+	12.6412i	0.303572	+	0.525803i
$579$	−7.34752	+	12.7263i	−0.305353	+	0.528886i
$580$	50.8328			2.11072
$581$		0			0
$582$	−48.1378			−1.99537
$583$	−0.236068	+	0.408882i	−0.00977694	+	0.0169342i
$584$	−0.854102	−	1.47935i	−0.0353430	−	0.0612159i
$585$	−4.76393	−	8.25137i	−0.196964	−	0.341152i
$586$	−28.0902	+	48.6536i	−1.16039	+	2.00986i
$587$	−27.1246			−1.11955			−0.559776	−	0.828644i	$-0.689113\pi$
$587$	−27.1246			−1.11955			−0.559776	+	0.828644i	$0.689113\pi$
$588$		0			0
$589$	−17.8885			−0.737085
$590$	−2.76393	+	4.78727i	−0.113789	+	0.197089i
$591$	1.23607	+	2.14093i	0.0508450	+	0.0880662i
$592$	−4.23607	−	7.33708i	−0.174101	−	0.301552i
$593$	−22.8541	+	39.5845i	−0.938505	+	1.62554i	−0.170245	+	0.985402i	$0.554456\pi$
$593$	−22.8541	+	39.5845i	−0.938505	+	1.62554i	−0.768260	+	0.640137i	$0.778877\pi$
$594$	12.3607			0.507165
$595$		0			0
$596$	42.0000			1.72039
$597$	−1.34752	+	2.33398i	−0.0551505	+	0.0955235i
$598$	8.94427	+	15.4919i	0.365758	+	0.633512i
$599$	11.7082	+	20.2792i	0.478384	+	0.828586i	0.999693	−	0.0247824i	$-0.00788929\pi$
$599$	11.7082	+	20.2792i	0.478384	+	0.828586i	−0.521309	+	0.853368i	$0.674556\pi$
$600$	1.38197	−	2.39364i	0.0564185	−	0.0977198i
$601$	37.1246			1.51434			0.757172	−	0.653215i	$-0.226580\pi$
$601$	37.1246			1.51434			0.757172	+	0.653215i	$0.226580\pi$
$602$		0			0
$603$	−21.3050			−0.867605
$604$	−13.4164	+	23.2379i	−0.545906	+	0.945537i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$	−6.58359	−	11.4031i	−0.267440	−	0.463220i
$607$	6.47214	−	11.2101i	0.262696	−	0.455003i	−0.704262	−	0.709941i	$-0.748722\pi$
$607$	6.47214	−	11.2101i	0.262696	−	0.455003i	0.966957	+	0.254938i	$0.0820551\pi$
$608$	43.4164			1.76077
$609$		0			0
$610$	32.3607			1.31025
$611$	−4.47214	+	7.74597i	−0.180923	+	0.313368i
$612$	7.14590	+	12.3771i	0.288856	+	0.500313i
$613$	−7.65248	−	13.2545i	−0.309081	−	0.535343i	0.669081	−	0.743190i	$-0.266688\pi$
$613$	−7.65248	−	13.2545i	−0.309081	−	0.535343i	−0.978162	+	0.207846i	$0.933355\pi$
$614$	−10.0000	+	17.3205i	−0.403567	+	0.698999i
$615$	27.7771			1.12008
$616$		0			0
$617$	6.58359			0.265045			0.132523	−	0.991180i	$-0.457692\pi$
$617$	6.58359			0.265045			0.132523	+	0.991180i	$0.457692\pi$
$618$	10.6525	−	18.4506i	0.428505	−	0.742193i
$619$	5.56231	+	9.63420i	0.223568	+	0.387231i	0.955889	−	0.293729i	$-0.0948962\pi$
$619$	5.56231	+	9.63420i	0.223568	+	0.387231i	−0.732321	+	0.680960i	$0.761563\pi$
$620$	−8.29180	−	14.3618i	−0.333007	−	0.576784i
$621$	6.83282	−	11.8348i	0.274191	−	0.474914i
$622$	18.5410			0.743427
$623$		0			0
$624$	4.00000			0.160128
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	16.7082	+	28.9395i	0.667794	+	1.15665i
$627$	−4.00000	−	6.92820i	−0.159745	−	0.276686i
$628$	16.4164	−	28.4341i	0.655086	−	1.13464i
$629$	−27.4164			−1.09316
$630$		0			0
$631$	−24.0000			−0.955425			−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000			−0.955425			−0.477712	+	0.878516i	$0.658534\pi$
$632$	10.0000	−	17.3205i	0.397779	−	0.688973i
$633$	8.58359	+	14.8672i	0.341167	+	0.590919i
$634$	−15.6525	−	27.1109i	−0.621639	−	1.07671i
$635$	−3.05573	+	5.29268i	−0.121263	+	0.210033i
$636$	−1.75078			−0.0694228
$637$		0			0
$638$	−18.9443			−0.750011
$639$	−7.70820	+	13.3510i	−0.304932	+	0.528157i
$640$	15.6525	+	27.1109i	0.618718	+	1.07165i
$641$	7.76393	+	13.4475i	0.306657	+	0.531145i	0.977629	−	0.210337i	$-0.0674563\pi$
$641$	7.76393	+	13.4475i	0.306657	+	0.531145i	−0.670972	+	0.741483i	$0.734123\pi$
$642$	5.52786	−	9.57454i	0.218167	−	0.377877i
$643$	−11.1246			−0.438712			−0.219356	−	0.975645i	$-0.570396\pi$
$643$	−11.1246			−0.438712			−0.219356	+	0.975645i	$0.570396\pi$
$644$		0			0
$645$	19.7771			0.778722
$646$	23.4164	−	40.5584i	0.921306	−	1.59575i
$647$	18.0344	+	31.2366i	0.709007	+	1.22804i	0.965226	+	0.261417i	$0.0841899\pi$
$647$	18.0344	+	31.2366i	0.709007	+	1.22804i	−0.256219	+	0.966619i	$0.582477\pi$
$648$	2.70163	+	4.67935i	0.106130	+	0.183822i
$649$	0.618034	−	1.07047i	0.0242600	−	0.0420195i
$650$	7.23607			0.283822
$651$		0			0
$652$	−10.2492			−0.401391
$653$	−12.5279	+	21.6989i	−0.490253	+	0.849143i	−0.999937	−	0.0112183i	$-0.996429\pi$
$653$	−12.5279	+	21.6989i	−0.490253	+	0.849143i	0.509684	+	0.860362i	$0.329762\pi$
$654$	6.18034	+	10.7047i	0.241670	+	0.418585i
$655$	21.8885	+	37.9121i	0.855256	+	1.48135i
$656$	5.61803	−	9.73072i	0.219347	−	0.379921i
$657$	−1.12461			−0.0438753
$658$		0			0
$659$	−17.8885			−0.696839			−0.348419	−	0.937339i	$-0.613281\pi$
$659$	−17.8885			−0.696839			−0.348419	+	0.937339i	$0.613281\pi$
$660$	3.70820	−	6.42280i	0.144342	−	0.250007i
$661$	−20.4164	−	35.3623i	−0.794106	−	1.37543i	−0.923405	−	0.383827i	$-0.874606\pi$
$661$	−20.4164	−	35.3623i	−0.794106	−	1.37543i	0.129299	−	0.991606i	$-0.458727\pi$
$662$	15.5279	+	26.8950i	0.603508	+	1.04531i
$663$	6.47214	−	11.2101i	0.251357	−	0.435363i
$664$	25.5279			0.990673
$665$		0			0
$666$	27.8885			1.08066
$667$	−10.4721	+	18.1383i	−0.405483	+	0.702317i
$668$	7.41641	+	12.8456i	0.286949	+	0.497011i
$669$	−6.29180	−	10.8977i	−0.243255	−	0.421330i
$670$	−32.3607	+	56.0503i	−1.25020	+	2.16541i
$671$	−7.23607			−0.279345
$672$		0			0
$673$	−21.4164			−0.825542			−0.412771	−	0.910835i	$-0.635439\pi$
$673$	−21.4164			−0.825542			−0.412771	+	0.910835i	$0.635439\pi$
$674$	12.8885	−	22.3236i	0.496448	−	0.859873i
$675$	−2.76393	−	4.78727i	−0.106384	−	0.184262i
$676$	3.79180	+	6.56758i	0.145838	+	0.252599i
$677$	−4.85410	+	8.40755i	−0.186558	+	0.323128i	−0.944101	−	0.329658i	$-0.893067\pi$
$677$	−4.85410	+	8.40755i	−0.186558	+	0.323128i	0.757542	+	0.652786i	$0.226400\pi$
$678$	5.52786			0.212296
$679$		0			0
$680$	14.4721			0.554981
$681$	3.63932	−	6.30349i	0.139459	−	0.241550i
$682$	3.09017	+	5.35233i	0.118329	+	0.204951i
$683$	2.94427	+	5.09963i	0.112659	+	0.195132i	0.916842	−	0.399251i	$-0.130730\pi$
$683$	2.94427	+	5.09963i	0.112659	+	0.195132i	−0.804182	+	0.594383i	$0.797396\pi$
$684$	−14.2918	+	24.7541i	−0.546460	+	0.946497i
$685$	32.9443			1.25874
$686$		0			0
$687$	5.52786			0.210901
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	−0.763932	−	1.32317i	−0.0291035	−	0.0504087i
$690$	−6.83282	−	11.8348i	−0.260121	−	0.450543i
$691$	9.27051	−	16.0570i	0.352667	−	0.610837i	−0.634049	−	0.773293i	$-0.718608\pi$
$691$	9.27051	−	16.0570i	0.352667	−	0.610837i	0.986716	+	0.162456i	$0.0519416\pi$
$692$	38.2918			1.45564
$693$		0			0
$694$	46.8328			1.77775
$695$	−1.52786	+	2.64634i	−0.0579552	+	0.100381i
$696$	−11.7082	−	20.2792i	−0.443798	−	0.768681i
$697$	−18.1803	−	31.4893i	−0.688629	−	1.19274i
$698$	−8.09017	+	14.0126i	−0.306217	+	0.530384i
$699$	11.6393			0.440240
$700$		0			0
$701$	−15.5279			−0.586479			−0.293240	−	0.956039i	$-0.594733\pi$
$701$	−15.5279			−0.586479			−0.293240	+	0.956039i	$0.594733\pi$
$702$	−20.0000	+	34.6410i	−0.754851	+	1.30744i
$703$	−27.4164	−	47.4866i	−1.03403	−	1.79099i
$704$	−6.50000	−	11.2583i	−0.244978	−	0.424314i
$705$	3.41641	−	5.91739i	0.128669	−	0.222862i
$706$	−44.4721			−1.67373
$707$		0			0
$708$	4.58359			0.172262
$709$	7.47214	−	12.9421i	0.280622	−	0.486051i	−0.690916	−	0.722935i	$-0.742793\pi$
$709$	7.47214	−	12.9421i	0.280622	−	0.486051i	0.971538	+	0.236883i	$0.0761260\pi$
$710$	23.4164	+	40.5584i	0.878802	+	1.52213i
$711$	−6.58359	−	11.4031i	−0.246904	−	0.427650i
$712$	2.23607	−	3.87298i	0.0838002	−	0.145146i
$713$	6.83282			0.255891
$714$		0			0
$715$	6.47214			0.242044
$716$	13.4164	−	23.2379i	0.501395	−	0.868441i
$717$	6.11146	+	10.5854i	0.228237	+	0.395317i
$718$	27.8885	+	48.3044i	1.04079	+	1.80270i
$719$	−25.7426	+	44.5876i	−0.960039	+	1.66284i	−0.237647	+	0.971352i	$0.576376\pi$
$719$	−25.7426	+	44.5876i	−0.960039	+	1.66284i	−0.722392	+	0.691484i	$0.756957\pi$
$720$	2.94427			0.109727
$721$		0			0
$722$	51.1803			1.90474
$723$	−8.11146	+	14.0495i	−0.301668	+	0.522505i
$724$	−38.1246	−	66.0338i	−1.41689	−	2.45413i
$725$	4.23607	+	7.33708i	0.157324	+	0.272492i
$726$	−1.38197	+	2.39364i	−0.0512896	+	0.0888361i
$727$	−25.0132			−0.927687			−0.463843	−	0.885917i	$-0.653530\pi$
$727$	−25.0132			−0.927687			−0.463843	+	0.885917i	$0.653530\pi$
$728$		0			0
$729$	24.0557			0.890953
$730$	−1.70820	+	2.95870i	−0.0632235	+	0.109506i
$731$	−12.9443	−	22.4201i	−0.478761	−	0.829239i
$732$	−13.4164	−	23.2379i	−0.495885	−	0.858898i
$733$	4.38197	−	7.58979i	0.161852	−	0.280335i	−0.773681	−	0.633575i	$-0.781587\pi$
$733$	4.38197	−	7.58979i	0.161852	−	0.280335i	0.935533	+	0.353240i	$0.114920\pi$
$734$	51.7082			1.90858
$735$		0			0
$736$	−16.5836			−0.611279
$737$	7.23607	−	12.5332i	0.266544	−	0.461668i
$738$	18.4934	+	32.0315i	0.680752	+	1.17910i
$739$	−12.4721	−	21.6024i	−0.458795	−	0.794656i	0.540103	−	0.841599i	$-0.318385\pi$
$739$	−12.4721	−	21.6024i	−0.458795	−	0.794656i	−0.998898	+	0.0469430i	$0.985052\pi$
$740$	25.4164	−	44.0225i	0.934326	−	1.61830i
$741$	25.8885			0.951039
$742$		0			0
$743$	1.88854			0.0692840			0.0346420	−	0.999400i	$-0.488971\pi$
$743$	1.88854			0.0692840			0.0346420	+	0.999400i	$0.488971\pi$
$744$	−3.81966	+	6.61585i	−0.140036	+	0.242549i
$745$	−14.0000	−	24.2487i	−0.512920	−	0.888404i
$746$	−6.70820	−	11.6190i	−0.245605	−	0.425400i
$747$	8.40325	−	14.5549i	0.307459	−	0.532534i
$748$	−9.70820			−0.354967
$749$		0			0
$750$	−33.1672			−1.21109
$751$	−14.7639	+	25.5719i	−0.538744	+	0.933131i	0.460229	+	0.887800i	$0.347767\pi$
$751$	−14.7639	+	25.5719i	−0.538744	+	0.933131i	−0.998972	+	0.0453307i	$0.985566\pi$
$752$	−1.38197	−	2.39364i	−0.0503951	−	0.0872869i
$753$	2.65248	+	4.59422i	0.0966616	+	0.167423i
$754$	30.6525	−	53.0916i	1.11630	−	1.93348i
$755$	17.8885			0.651031
$756$		0			0
$757$	15.8885			0.577479			0.288739	−	0.957408i	$-0.406764\pi$
$757$	15.8885			0.577479			0.288739	+	0.957408i	$0.406764\pi$
$758$	−41.7082	+	72.2407i	−1.51491	+	2.62390i
$759$	1.52786	+	2.64634i	0.0554580	+	0.0960560i
$760$	14.4721	+	25.0665i	0.524960	+	0.909257i
$761$	−15.7984	+	27.3636i	−0.572691	+	0.991929i	0.423598	+	0.905850i	$0.360767\pi$
$761$	−15.7984	+	27.3636i	−0.572691	+	0.991929i	−0.996288	+	0.0860788i	$0.972566\pi$
$762$	8.44582			0.305960
$763$		0			0
$764$	−9.16718			−0.331657
$765$	4.76393	−	8.25137i	0.172240	−	0.298329i
$766$	−5.20163	−	9.00948i	−0.187942	−	0.325526i
$767$	2.00000	+	3.46410i	0.0722158	+	0.125081i
$768$	5.56231	−	9.63420i	0.200712	−	0.347644i
$769$	−18.2918			−0.659619			−0.329810	−	0.944047i	$-0.606985\pi$
$769$	−18.2918			−0.659619			−0.329810	+	0.944047i	$0.606985\pi$
$770$		0			0
$771$	7.41641			0.267095
$772$	−17.8328	+	30.8873i	−0.641817	+	1.11166i
$773$	−19.1803	−	33.2213i	−0.689869	−	1.19489i	−0.971880	−	0.235477i	$-0.924335\pi$
$773$	−19.1803	−	33.2213i	−0.689869	−	1.19489i	0.282011	−	0.959411i	$-0.408999\pi$
$774$	13.1672	+	22.8062i	0.473285	+	0.819753i
$775$	1.38197	−	2.39364i	0.0496417	−	0.0859819i
$776$	−38.9443			−1.39802

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.11803 + 1.93649i) q^{2} +(-0.618034 - 1.07047i) q^{3} +(-1.50000 - 2.59808i) q^{4} +(-1.00000 + 1.73205i) q^{5} +2.76393 q^{6} +2.23607 q^{8} +(0.736068 - 1.27491i) q^{9} +O(q^{10})\)	\(q+(-1.11803 + 1.93649i) q^{2} +(-0.618034 - 1.07047i) q^{3} +(-1.50000 - 2.59808i) q^{4} +(-1.00000 + 1.73205i) q^{5} +2.76393 q^{6} +2.23607 q^{8} +(0.736068 - 1.27491i) q^{9} +(-2.23607 - 3.87298i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.85410 + 3.21140i) q^{12} -3.23607 q^{13} +2.47214 q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.61803 - 2.80252i) q^{17} +(1.64590 + 2.85078i) q^{18} +(3.23607 - 5.60503i) q^{19} +6.00000 q^{20} -2.23607 q^{22} +(-1.23607 + 2.14093i) q^{23} +(-1.38197 - 2.39364i) q^{24} +(0.500000 + 0.866025i) q^{25} +(3.61803 - 6.26662i) q^{26} -5.52786 q^{27} +8.47214 q^{29} +(-2.76393 + 4.78727i) q^{30} +(-1.38197 - 2.39364i) q^{31} +(3.35410 + 5.80948i) q^{32} +(0.618034 - 1.07047i) q^{33} +7.23607 q^{34} -4.41641 q^{36} +(4.23607 - 7.33708i) q^{37} +(7.23607 + 12.5332i) q^{38} +(2.00000 + 3.46410i) q^{39} +(-2.23607 + 3.87298i) q^{40} +11.2361 q^{41} +8.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(1.47214 + 2.54981i) q^{45} +(-2.76393 - 4.78727i) q^{46} +(1.38197 - 2.39364i) q^{47} -1.23607 q^{48} -2.23607 q^{50} +(-2.00000 + 3.46410i) q^{51} +(4.85410 + 8.40755i) q^{52} +(0.236068 + 0.408882i) q^{53} +(6.18034 - 10.7047i) q^{54} -2.00000 q^{55} -8.00000 q^{57} +(-9.47214 + 16.4062i) q^{58} +(-0.618034 - 1.07047i) q^{59} +(-3.70820 - 6.42280i) q^{60} +(-3.61803 + 6.26662i) q^{61} +6.18034 q^{62} -13.0000 q^{64} +(3.23607 - 5.60503i) q^{65} +(1.38197 + 2.39364i) q^{66} +(-7.23607 - 12.5332i) q^{67} +(-4.85410 + 8.40755i) q^{68} +3.05573 q^{69} -10.4721 q^{71} +(1.64590 - 2.85078i) q^{72} +(-0.381966 - 0.661585i) q^{73} +(9.47214 + 16.4062i) q^{74} +(0.618034 - 1.07047i) q^{75} -19.4164 q^{76} -8.94427 q^{78} +(4.47214 - 7.74597i) q^{79} +(1.00000 + 1.73205i) q^{80} +(1.20820 + 2.09267i) q^{81} +(-12.5623 + 21.7586i) q^{82} +11.4164 q^{83} +6.47214 q^{85} +(-8.94427 + 15.4919i) q^{86} +(-5.23607 - 9.06914i) q^{87} +(1.11803 + 1.93649i) q^{88} +(1.00000 - 1.73205i) q^{89} -6.58359 q^{90} +7.41641 q^{92} +(-1.70820 + 2.95870i) q^{93} +(3.09017 + 5.35233i) q^{94} +(6.47214 + 11.2101i) q^{95} +(4.14590 - 7.18091i) q^{96} -17.4164 q^{97} +1.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 6 q^{4} - 4 q^{5} + 20 q^{6} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 6 * q^4 - 4 * q^5 + 20 * q^6 - 6 * q^9	\( 4 q + 2 q^{3} - 6 q^{4} - 4 q^{5} + 20 q^{6} - 6 q^{9} + 2 q^{11} + 6 q^{12} - 4 q^{13} - 8 q^{15} + 2 q^{16} - 2 q^{17} + 20 q^{18} + 4 q^{19} + 24 q^{20} + 4 q^{23} - 10 q^{24} + 2 q^{25} + 10 q^{26} - 40 q^{27} + 16 q^{29} - 20 q^{30} - 10 q^{31} - 2 q^{33} + 20 q^{34} + 36 q^{36} + 8 q^{37} + 20 q^{38} + 8 q^{39} + 36 q^{41} + 32 q^{43} + 6 q^{44} - 12 q^{45} - 20 q^{46} + 10 q^{47} + 4 q^{48} - 8 q^{51} + 6 q^{52} - 8 q^{53} - 20 q^{54} - 8 q^{55} - 32 q^{57} - 20 q^{58} + 2 q^{59} + 12 q^{60} - 10 q^{61} - 20 q^{62} - 52 q^{64} + 4 q^{65} + 10 q^{66} - 20 q^{67} - 6 q^{68} + 48 q^{69} - 24 q^{71} + 20 q^{72} - 6 q^{73} + 20 q^{74} - 2 q^{75} - 24 q^{76} + 4 q^{80} - 22 q^{81} - 10 q^{82} - 8 q^{83} + 8 q^{85} - 12 q^{87} + 4 q^{89} - 80 q^{90} - 24 q^{92} + 20 q^{93} - 10 q^{94} + 8 q^{95} + 30 q^{96} - 16 q^{97} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 6 * q^4 - 4 * q^5 + 20 * q^6 - 6 * q^9 + 2 * q^11 + 6 * q^12 - 4 * q^13 - 8 * q^15 + 2 * q^16 - 2 * q^17 + 20 * q^18 + 4 * q^19 + 24 * q^20 + 4 * q^23 - 10 * q^24 + 2 * q^25 + 10 * q^26 - 40 * q^27 + 16 * q^29 - 20 * q^30 - 10 * q^31 - 2 * q^33 + 20 * q^34 + 36 * q^36 + 8 * q^37 + 20 * q^38 + 8 * q^39 + 36 * q^41 + 32 * q^43 + 6 * q^44 - 12 * q^45 - 20 * q^46 + 10 * q^47 + 4 * q^48 - 8 * q^51 + 6 * q^52 - 8 * q^53 - 20 * q^54 - 8 * q^55 - 32 * q^57 - 20 * q^58 + 2 * q^59 + 12 * q^60 - 10 * q^61 - 20 * q^62 - 52 * q^64 + 4 * q^65 + 10 * q^66 - 20 * q^67 - 6 * q^68 + 48 * q^69 - 24 * q^71 + 20 * q^72 - 6 * q^73 + 20 * q^74 - 2 * q^75 - 24 * q^76 + 4 * q^80 - 22 * q^81 - 10 * q^82 - 8 * q^83 + 8 * q^85 - 12 * q^87 + 4 * q^89 - 80 * q^90 - 24 * q^92 + 20 * q^93 - 10 * q^94 + 8 * q^95 + 30 * q^96 - 16 * q^97 - 12 * q^99

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