LMFDB - Embedded newform 539.2.e.j.177.2

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			177.2
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	539.177
Dual form			539.2.e.j.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11803 - 1.93649i) q^{2} +(1.61803 + 2.80252i) q^{3} +(-1.50000 - 2.59808i) q^{4} +(-1.00000 + 1.73205i) q^{5} +7.23607 q^{6} -2.23607 q^{8} +(-3.73607 + 6.47106i) q^{9} +O(q^{10})$	\(q+(1.11803 - 1.93649i) q^{2} +(1.61803 + 2.80252i) q^{3} +(-1.50000 - 2.59808i) q^{4} +(-1.00000 + 1.73205i) q^{5} +7.23607 q^{6} -2.23607 q^{8} +(-3.73607 + 6.47106i) q^{9} +(2.23607 + 3.87298i) q^{10} +(0.500000 + 0.866025i) q^{11} +(4.85410 - 8.40755i) q^{12} +1.23607 q^{13} -6.47214 q^{15} +(0.500000 - 0.866025i) q^{16} +(0.618034 + 1.07047i) q^{17} +(8.35410 + 14.4697i) q^{18} +(-1.23607 + 2.14093i) q^{19} +6.00000 q^{20} +2.23607 q^{22} +(3.23607 - 5.60503i) q^{23} +(-3.61803 - 6.26662i) q^{24} +(0.500000 + 0.866025i) q^{25} +(1.38197 - 2.39364i) q^{26} -14.4721 q^{27} -0.472136 q^{29} +(-7.23607 + 12.5332i) q^{30} +(-3.61803 - 6.26662i) q^{31} +(-3.35410 - 5.80948i) q^{32} +(-1.61803 + 2.80252i) q^{33} +2.76393 q^{34} +22.4164 q^{36} +(-0.236068 + 0.408882i) q^{37} +(2.76393 + 4.78727i) q^{38} +(2.00000 + 3.46410i) q^{39} +(2.23607 - 3.87298i) q^{40} +6.76393 q^{41} +8.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(-7.47214 - 12.9421i) q^{45} +(-7.23607 - 12.5332i) q^{46} +(3.61803 - 6.26662i) q^{47} +3.23607 q^{48} +2.23607 q^{50} +(-2.00000 + 3.46410i) q^{51} +(-1.85410 - 3.21140i) q^{52} +(-4.23607 - 7.33708i) q^{53} +(-16.1803 + 28.0252i) q^{54} -2.00000 q^{55} -8.00000 q^{57} +(-0.527864 + 0.914287i) q^{58} +(1.61803 + 2.80252i) q^{59} +(9.70820 + 16.8151i) q^{60} +(-1.38197 + 2.39364i) q^{61} -16.1803 q^{62} -13.0000 q^{64} +(-1.23607 + 2.14093i) q^{65} +(3.61803 + 6.26662i) q^{66} +(-2.76393 - 4.78727i) q^{67} +(1.85410 - 3.21140i) q^{68} +20.9443 q^{69} -1.52786 q^{71} +(8.35410 - 14.4697i) q^{72} +(-2.61803 - 4.53457i) q^{73} +(0.527864 + 0.914287i) q^{74} +(-1.61803 + 2.80252i) q^{75} +7.41641 q^{76} +8.94427 q^{78} +(-4.47214 + 7.74597i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-12.2082 - 21.1452i) q^{81} +(7.56231 - 13.0983i) q^{82} -15.4164 q^{83} -2.47214 q^{85} +(8.94427 - 15.4919i) q^{86} +(-0.763932 - 1.32317i) q^{87} +(-1.11803 - 1.93649i) q^{88} +(1.00000 - 1.73205i) q^{89} -33.4164 q^{90} -19.4164 q^{92} +(11.7082 - 20.2792i) q^{93} +(-8.09017 - 14.0126i) q^{94} +(-2.47214 - 4.28187i) q^{95} +(10.8541 - 18.7999i) q^{96} +9.41641 q^{97} -7.47214 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	$-0.543118\pi$
$2$	1.11803	−	1.93649i	0.790569	−	1.36931i	0.925615	−	0.378467i	$-0.123549\pi$
$3$	1.61803	+	2.80252i	0.934172	+	1.61803i	0.776103	+	0.630606i	$0.217194\pi$
$3$	1.61803	+	2.80252i	0.934172	+	1.61803i	0.158069	+	0.987428i	$0.449473\pi$
$4$	−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	$0.314250\pi$
$6$	7.23607			2.95411
$7$		0			0
$7$		0			0
$8$	−2.23607			−0.790569
$9$	−3.73607	+	6.47106i	−1.24536	+	2.15702i
$10$	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
$12$	4.85410	−	8.40755i	1.40126	−	2.42705i
$13$	1.23607			0.342824			0.171412	−	0.985199i	$-0.445167\pi$
$13$	1.23607			0.342824			0.171412	+	0.985199i	$0.445167\pi$
$14$		0			0
$15$	−6.47214			−1.67110
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.618034	+	1.07047i	0.149895	+	0.259626i	0.931189	−	0.364538i	$-0.118773\pi$
$17$	0.618034	+	1.07047i	0.149895	+	0.259626i	−0.781293	+	0.624164i	$0.785440\pi$
$18$	8.35410	+	14.4697i	1.96908	+	3.41055i
$19$	−1.23607	+	2.14093i	−0.283573	+	0.491164i	−0.972262	−	0.233893i	$-0.924853\pi$
$19$	−1.23607	+	2.14093i	−0.283573	+	0.491164i	0.688689	+	0.725057i	$0.258187\pi$
$20$	6.00000			1.34164
$21$		0			0
$22$	2.23607			0.476731
$23$	3.23607	−	5.60503i	0.674767	−	1.16873i	−0.301770	−	0.953381i	$-0.597578\pi$
$23$	3.23607	−	5.60503i	0.674767	−	1.16873i	0.976537	−	0.215350i	$-0.0690891\pi$
$24$	−3.61803	−	6.26662i	−0.738528	−	1.27917i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	1.38197	−	2.39364i	0.271026	−	0.469431i
$27$	−14.4721			−2.78516
$28$		0			0
$29$	−0.472136			−0.0876734			−0.0438367	−	0.999039i	$-0.513958\pi$
$29$	−0.472136			−0.0876734			−0.0438367	+	0.999039i	$0.513958\pi$
$30$	−7.23607	+	12.5332i	−1.32112	+	2.28825i
$31$	−3.61803	−	6.26662i	−0.649818	−	1.12552i	−0.983166	−	0.182714i	$-0.941512\pi$
$31$	−3.61803	−	6.26662i	−0.649818	−	1.12552i	0.333348	−	0.942804i	$-0.391822\pi$
$32$	−3.35410	−	5.80948i	−0.592927	−	1.02698i
$33$	−1.61803	+	2.80252i	−0.281664	+	0.487856i
$34$	2.76393			0.474010
$35$		0			0
$36$	22.4164			3.73607
$37$	−0.236068	+	0.408882i	−0.0388093	+	0.0672197i	−0.884778	−	0.466013i	$-0.845690\pi$
$37$	−0.236068	+	0.408882i	−0.0388093	+	0.0672197i	0.845968	+	0.533233i	$0.179023\pi$
$38$	2.76393	+	4.78727i	0.448369	+	0.776598i
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$	2.23607	−	3.87298i	0.353553	−	0.612372i
$41$	6.76393			1.05635			0.528174	−	0.849136i	$-0.322877\pi$
$41$	6.76393			1.05635			0.528174	+	0.849136i	$0.322877\pi$
$42$		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
$45$	−7.47214	−	12.9421i	−1.11388	−	1.92930i
$46$	−7.23607	−	12.5332i	−1.06690	−	1.84793i
$47$	3.61803	−	6.26662i	0.527744	−	0.914080i	−0.471732	−	0.881742i	$-0.656371\pi$
$47$	3.61803	−	6.26662i	0.527744	−	0.914080i	0.999477	−	0.0323386i	$-0.0102955\pi$
$48$	3.23607			0.467086
$49$		0			0
$50$	2.23607			0.316228
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$	−1.85410	−	3.21140i	−0.257118	−	0.445341i
$53$	−4.23607	−	7.33708i	−0.581869	−	1.00783i	−0.995258	−	0.0972717i	$-0.968988\pi$
$53$	−4.23607	−	7.33708i	−0.581869	−	1.00783i	0.413389	−	0.910554i	$-0.364345\pi$
$54$	−16.1803	+	28.0252i	−2.20187	+	3.81374i
$55$	−2.00000			−0.269680
$56$		0			0
$57$	−8.00000			−1.05963
$58$	−0.527864	+	0.914287i	−0.0693119	+	0.120052i
$59$	1.61803	+	2.80252i	0.210650	+	0.364857i	0.951918	−	0.306352i	$-0.0991086\pi$
$59$	1.61803	+	2.80252i	0.210650	+	0.364857i	−0.741268	+	0.671209i	$0.765775\pi$
$60$	9.70820	+	16.8151i	1.25332	+	2.17082i
$61$	−1.38197	+	2.39364i	−0.176943	+	0.306474i	−0.940832	−	0.338874i	$-0.889954\pi$
$61$	−1.38197	+	2.39364i	−0.176943	+	0.306474i	0.763889	+	0.645347i	$0.223287\pi$
$62$	−16.1803			−2.05491
$63$		0			0
$64$	−13.0000			−1.62500
$65$	−1.23607	+	2.14093i	−0.153315	+	0.265550i
$66$	3.61803	+	6.26662i	0.445349	+	0.771367i
$67$	−2.76393	−	4.78727i	−0.337668	−	0.584858i	0.646326	−	0.763062i	$-0.276305\pi$
$67$	−2.76393	−	4.78727i	−0.337668	−	0.584858i	−0.983994	+	0.178204i	$0.942971\pi$
$68$	1.85410	−	3.21140i	0.224843	−	0.389439i
$69$	20.9443			2.52139
$70$		0			0
$71$	−1.52786			−0.181324			−0.0906621	−	0.995882i	$-0.528898\pi$
$71$	−1.52786			−0.181324			−0.0906621	+	0.995882i	$0.528898\pi$
$72$	8.35410	−	14.4697i	0.984540	−	1.70527i
$73$	−2.61803	−	4.53457i	−0.306418	−	0.530731i	0.671158	−	0.741314i	$-0.265797\pi$
$73$	−2.61803	−	4.53457i	−0.306418	−	0.530731i	−0.977576	+	0.210583i	$0.932464\pi$
$74$	0.527864	+	0.914287i	0.0613629	+	0.106284i
$75$	−1.61803	+	2.80252i	−0.186834	+	0.323607i
$76$	7.41641			0.850720
$77$		0			0
$78$	8.94427			1.01274
$79$	−4.47214	+	7.74597i	−0.503155	+	0.871489i	0.496839	+	0.867843i	$0.334494\pi$
$79$	−4.47214	+	7.74597i	−0.503155	+	0.871489i	−0.999993	+	0.00364646i	$0.998839\pi$
$80$	1.00000	+	1.73205i	0.111803	+	0.193649i
$81$	−12.2082	−	21.1452i	−1.35647	−	2.34947i
$82$	7.56231	−	13.0983i	0.835117	−	1.44647i
$83$	−15.4164			−1.69217			−0.846085	−	0.533048i	$-0.821047\pi$
$83$	−15.4164			−1.69217			−0.846085	+	0.533048i	$0.821047\pi$
$84$		0			0
$85$	−2.47214			−0.268141
$86$	8.94427	−	15.4919i	0.964486	−	1.67054i
$87$	−0.763932	−	1.32317i	−0.0819021	−	0.141859i
$88$	−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	$0.132862\pi$
$90$	−33.4164			−3.52240
$91$		0			0
$92$	−19.4164			−2.02430
$93$	11.7082	−	20.2792i	1.21408	−	2.10286i
$94$	−8.09017	−	14.0126i	−0.834437	−	1.44529i
$95$	−2.47214	−	4.28187i	−0.253636	−	0.439310i
$96$	10.8541	−	18.7999i	1.10779	−	1.91875i
$97$	9.41641			0.956091			0.478046	−	0.878335i	$-0.341345\pi$
$97$	9.41641			0.956091			0.478046	+	0.878335i	$0.341345\pi$
$98$		0			0
$99$	−7.47214			−0.750978
$100$	1.50000	−	2.59808i	0.150000	−	0.259808i
$101$	−4.61803	−	7.99867i	−0.459512	−	0.795897i	0.539424	−	0.842035i	$-0.318642\pi$
$101$	−4.61803	−	7.99867i	−0.459512	−	0.795897i	−0.998935	+	0.0461372i	$0.985309\pi$
$102$	4.47214	+	7.74597i	0.442807	+	0.766965i
$103$	−2.85410	+	4.94345i	−0.281223	+	0.487093i	−0.971686	−	0.236275i	$-0.924073\pi$
$103$	−2.85410	+	4.94345i	−0.281223	+	0.487093i	0.690463	+	0.723368i	$0.257407\pi$
$104$	−2.76393			−0.271026
$105$		0			0
$106$	−18.9443			−1.84003
$107$	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	$0.104732\pi$
$108$	21.7082	+	37.5997i	2.08887	+	3.61803i
$109$	−2.23607	−	3.87298i	−0.214176	−	0.370965i	0.738841	−	0.673880i	$-0.235373\pi$
$109$	−2.23607	−	3.87298i	−0.214176	−	0.370965i	−0.953018	+	0.302915i	$0.902040\pi$
$110$	−2.23607	+	3.87298i	−0.213201	+	0.369274i
$111$	−1.52786			−0.145018
$112$		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
$115$	6.47214	+	11.2101i	0.603530	+	1.04534i
$116$	0.708204	+	1.22665i	0.0657551	+	0.113891i
$117$	−4.61803	+	7.99867i	−0.426937	+	0.739477i
$118$	7.23607			0.666134
$119$		0			0
$120$	14.4721			1.32112
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	3.09017	+	5.35233i	0.279771	+	0.484577i
$123$	10.9443	+	18.9560i	0.986812	+	1.70921i
$124$	−10.8541	+	18.7999i	−0.974727	+	1.68828i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	20.9443			1.85850			0.929252	−	0.369447i	$-0.120453\pi$
$127$	20.9443			1.85850			0.929252	+	0.369447i	$0.120453\pi$
$128$	−7.82624	+	13.5554i	−0.691748	+	1.19814i
$129$	12.9443	+	22.4201i	1.13968	+	1.97398i
$130$	2.76393	+	4.78727i	0.242413	+	0.419871i
$131$	−6.94427	+	12.0278i	−0.606724	+	1.05088i	0.385053	+	0.922895i	$0.374183\pi$
$131$	−6.94427	+	12.0278i	−0.606724	+	1.05088i	−0.991776	+	0.127982i	$0.959150\pi$
$132$	9.70820			0.844991
$133$		0			0
$134$	−12.3607			−1.06780
$135$	14.4721	−	25.0665i	1.24556	−	2.15738i
$136$	−1.38197	−	2.39364i	−0.118503	−	0.205253i
$137$	−3.76393	−	6.51932i	−0.321574	−	0.556983i	0.659239	−	0.751934i	$-0.270879\pi$
$137$	−3.76393	−	6.51932i	−0.321574	−	0.556983i	−0.980813	+	0.194951i	$0.937545\pi$
$138$	23.4164	−	40.5584i	1.99334	−	3.45256i
$139$	10.4721			0.888235			0.444117	−	0.895969i	$-0.353517\pi$
$139$	10.4721			0.888235			0.444117	+	0.895969i	$0.353517\pi$
$140$		0			0
$141$	23.4164			1.97202
$142$	−1.70820	+	2.95870i	−0.143349	+	0.248288i
$143$	0.618034	+	1.07047i	0.0516826	+	0.0895169i
$144$	3.73607	+	6.47106i	0.311339	+	0.539255i
$145$	0.472136	−	0.817763i	0.0392088	−	0.0679116i
$146$	−11.7082			−0.968978
$147$		0			0
$148$	1.41641			0.116428
$149$	−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	$0.972267\pi$
$150$	3.61803	+	6.26662i	0.295411	+	0.511667i
$151$	4.47214	+	7.74597i	0.363937	+	0.630358i	0.988605	−	0.150533i	$-0.0480989\pi$
$151$	4.47214	+	7.74597i	0.363937	+	0.630358i	−0.624668	+	0.780891i	$0.714766\pi$
$152$	2.76393	−	4.78727i	0.224184	−	0.388299i
$153$	−9.23607			−0.746692
$154$		0			0
$155$	14.4721			1.16243
$156$	6.00000	−	10.3923i	0.480384	−	0.832050i
$157$	−3.47214	−	6.01392i	−0.277107	−	0.479963i	0.693558	−	0.720401i	$-0.256042\pi$
$157$	−3.47214	−	6.01392i	−0.277107	−	0.479963i	−0.970664	+	0.240438i	$0.922709\pi$
$158$	10.0000	+	17.3205i	0.795557	+	1.37795i
$159$	13.7082	−	23.7433i	1.08713	−	1.88297i
$160$	13.4164			1.06066
$161$		0			0
$162$	−54.5967			−4.28953
$163$	−11.7082	+	20.2792i	−0.917057	+	1.58839i	−0.113196	+	0.993573i	$0.536109\pi$
$163$	−11.7082	+	20.2792i	−0.917057	+	1.58839i	−0.803861	+	0.594817i	$0.797224\pi$
$164$	−10.1459	−	17.5732i	−0.792262	−	1.37224i
$165$	−3.23607	−	5.60503i	−0.251928	−	0.436351i
$166$	−17.2361	+	29.8537i	−1.33778	+	2.31710i
$167$	12.9443			1.00166			0.500829	−	0.865546i	$-0.333029\pi$
$167$	12.9443			1.00166			0.500829	+	0.865546i	$0.333029\pi$
$168$		0			0
$169$	−11.4721			−0.882472
$170$	−2.76393	+	4.78727i	−0.211984	+	0.367167i
$171$	−9.23607	−	15.9973i	−0.706300	−	1.22335i
$172$	−12.0000	−	20.7846i	−0.914991	−	1.58481i
$173$	−8.61803	+	14.9269i	−0.655217	+	1.13487i	0.326622	+	0.945155i	$0.394089\pi$
$173$	−8.61803	+	14.9269i	−0.655217	+	1.13487i	−0.981839	+	0.189714i	$0.939244\pi$
$174$	−3.41641			−0.258997
$175$		0			0
$176$	1.00000			0.0753778
$177$	−5.23607	+	9.06914i	−0.393567	+	0.681678i
$178$	−2.23607	−	3.87298i	−0.167600	−	0.290292i
$179$	−4.47214	−	7.74597i	−0.334263	−	0.578961i	0.649080	−	0.760720i	$-0.275154\pi$
$179$	−4.47214	−	7.74597i	−0.334263	−	0.578961i	−0.983343	+	0.181760i	$0.941821\pi$
$180$	−22.4164	+	38.8264i	−1.67082	+	2.89395i
$181$	−1.41641			−0.105281			−0.0526404	−	0.998614i	$-0.516764\pi$
$181$	−1.41641			−0.105281			−0.0526404	+	0.998614i	$0.516764\pi$
$182$		0			0
$183$	−8.94427			−0.661180
$184$	−7.23607	+	12.5332i	−0.533450	+	0.923963i
$185$	−0.472136	−	0.817763i	−0.0347121	−	0.0601232i
$186$	−26.1803	−	45.3457i	−1.91964	−	3.32491i
$187$	−0.618034	+	1.07047i	−0.0451951	+	0.0782802i
$188$	−21.7082			−1.58323
$189$		0			0
$190$	−11.0557			−0.802067
$191$	10.4721	−	18.1383i	0.757737	−	1.31244i	−0.186265	−	0.982500i	$-0.559638\pi$
$191$	10.4721	−	18.1383i	0.757737	−	1.31244i	0.944002	−	0.329940i	$-0.107028\pi$
$192$	−21.0344	−	36.4327i	−1.51803	−	2.62931i
$193$	11.9443	+	20.6881i	0.859768	+	1.48916i	0.872151	+	0.489238i	$0.162725\pi$
$193$	11.9443	+	20.6881i	0.859768	+	1.48916i	−0.0123830	+	0.999923i	$0.503942\pi$
$194$	10.5279	−	18.2348i	0.755857	−	1.30918i
$195$	−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	$0.522698\pi$
$198$	−8.35410	+	14.4697i	−0.593700	+	1.02832i
$199$	10.0902	+	17.4767i	0.715273	+	1.23889i	0.962854	+	0.270022i	$0.0870311\pi$
$199$	10.0902	+	17.4767i	0.715273	+	1.23889i	−0.247581	+	0.968867i	$0.579636\pi$
$200$	−1.11803	−	1.93649i	−0.0790569	−	0.136931i
$201$	8.94427	−	15.4919i	0.630880	−	1.09272i
$202$	−20.6525			−1.45310
$203$		0			0
$204$	12.0000			0.840168
$205$	−6.76393	+	11.7155i	−0.472414	+	0.818244i
$206$	6.38197	+	11.0539i	0.444653	+	0.770161i
$207$	24.1803	+	41.8816i	1.68065	+	2.91097i
$208$	0.618034	−	1.07047i	0.0428529	−	0.0742235i
$209$	−2.47214			−0.171001
$210$		0			0
$211$	21.8885			1.50687			0.753435	−	0.657523i	$-0.228396\pi$
$211$	21.8885			1.50687			0.753435	+	0.657523i	$0.228396\pi$
$212$	−12.7082	+	22.0113i	−0.872803	+	1.51174i
$213$	−2.47214	−	4.28187i	−0.169388	−	0.293389i
$214$	−4.47214	−	7.74597i	−0.305709	−	0.529503i
$215$	−8.00000	+	13.8564i	−0.545595	+	0.944999i
$216$	32.3607			2.20187
$217$		0			0
$218$	−10.0000			−0.677285
$219$	8.47214	−	14.6742i	0.572494	−	0.991589i
$220$	3.00000	+	5.19615i	0.202260	+	0.350325i
$221$	0.763932	+	1.32317i	0.0513876	+	0.0890060i
$222$	−1.70820	+	2.95870i	−0.114647	+	0.198575i
$223$	−12.1803			−0.815656			−0.407828	−	0.913059i	$-0.633714\pi$
$223$	−12.1803			−0.815656			−0.407828	+	0.913059i	$0.633714\pi$
$224$		0			0
$225$	−7.47214			−0.498142
$226$	2.23607	−	3.87298i	0.148741	−	0.257627i
$227$	−14.9443	−	25.8842i	−0.991886	−	1.71800i	−0.606040	−	0.795434i	$-0.707243\pi$
$227$	−14.9443	−	25.8842i	−0.991886	−	1.71800i	−0.385846	−	0.922563i	$-0.626090\pi$
$228$	12.0000	+	20.7846i	0.794719	+	1.37649i
$229$	2.23607	−	3.87298i	0.147764	−	0.255934i	−0.782637	−	0.622478i	$-0.786126\pi$
$229$	2.23607	−	3.87298i	0.147764	−	0.255934i	0.930401	+	0.366544i	$0.119459\pi$
$230$	28.9443			1.90853
$231$		0			0
$232$	1.05573			0.0693119
$233$	8.70820	−	15.0831i	0.570493	−	0.988124i	−0.426022	−	0.904713i	$-0.640085\pi$
$233$	8.70820	−	15.0831i	0.570493	−	0.988124i	0.996515	−	0.0834107i	$-0.0265813\pi$
$234$	10.3262	+	17.8856i	0.675047	+	1.16922i
$235$	7.23607	+	12.5332i	0.472029	+	0.817578i
$236$	4.85410	−	8.40755i	0.315975	−	0.547285i
$237$	−28.9443			−1.88013
$238$		0			0
$239$	25.8885			1.67459			0.837295	−	0.546751i	$-0.184136\pi$
$239$	25.8885			1.67459			0.837295	+	0.546751i	$0.184136\pi$
$240$	−3.23607	+	5.60503i	−0.208887	+	0.361803i
$241$	13.5623	+	23.4906i	0.873625	+	1.51316i	0.858220	+	0.513281i	$0.171570\pi$
$241$	13.5623	+	23.4906i	0.873625	+	1.51316i	0.0154046	+	0.999881i	$0.495096\pi$
$242$	1.11803	+	1.93649i	0.0718699	+	0.124482i
$243$	17.7984	−	30.8277i	1.14177	−	1.97760i
$244$	8.29180			0.530828
$245$		0			0
$246$	48.9443			3.12057
$247$	−1.52786	+	2.64634i	−0.0972157	+	0.168382i
$248$	8.09017	+	14.0126i	0.513726	+	0.889800i
$249$	−24.9443	−	43.2047i	−1.58078	−	2.73799i
$250$	−13.4164	+	23.2379i	−0.848528	+	1.46969i
$251$	−17.7082			−1.11773			−0.558866	−	0.829258i	$-0.688763\pi$
$251$	−17.7082			−1.11773			−0.558866	+	0.829258i	$0.688763\pi$
$252$		0			0
$253$	6.47214			0.406900
$254$	23.4164	−	40.5584i	1.46928	−	2.54486i
$255$	−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	$0.226587\pi$
$258$	57.8885			3.60398
$259$		0			0
$260$	7.41641			0.459946
$261$	1.76393	−	3.05522i	0.109185	−	0.189113i
$262$	15.5279	+	26.8950i	0.959315	+	1.66158i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$	3.61803	−	6.26662i	0.222675	−	0.385684i
$265$	16.9443			1.04088
$266$		0			0
$267$	6.47214			0.396088
$268$	−8.29180	+	14.3618i	−0.506502	+	0.877287i
$269$	−6.70820	−	11.6190i	−0.409006	−	0.708420i	0.585772	−	0.810476i	$-0.300791\pi$
$269$	−6.70820	−	11.6190i	−0.409006	−	0.708420i	−0.994779	+	0.102056i	$0.967458\pi$
$270$	−32.3607	−	56.0503i	−1.96941	−	3.41112i
$271$	−0.763932	+	1.32317i	−0.0464056	+	0.0803768i	−0.888295	−	0.459273i	$-0.848110\pi$
$271$	−0.763932	+	1.32317i	−0.0464056	+	0.0803768i	0.841890	+	0.539650i	$0.181443\pi$
$272$	1.23607			0.0749476
$273$		0			0
$274$	−16.8328			−1.01691
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	−31.4164	−	54.4148i	−1.89105	−	3.27539i
$277$	−7.94427	−	13.7599i	−0.477325	−	0.826751i	0.522337	−	0.852739i	$-0.325060\pi$
$277$	−7.94427	−	13.7599i	−0.477325	−	0.826751i	−0.999662	+	0.0259878i	$0.991727\pi$
$278$	11.7082	−	20.2792i	0.702211	−	1.21627i
$279$	54.0689			3.23702
$280$		0			0
$281$	−12.4721			−0.744025			−0.372013	−	0.928228i	$-0.621332\pi$
$281$	−12.4721			−0.744025			−0.372013	+	0.928228i	$0.621332\pi$
$282$	26.1803	−	45.3457i	1.55902	−	2.70030i
$283$	−2.94427	−	5.09963i	−0.175019	−	0.303141i	0.765149	−	0.643853i	$-0.222665\pi$
$283$	−2.94427	−	5.09963i	−0.175019	−	0.303141i	−0.940168	+	0.340712i	$0.889332\pi$
$284$	2.29180	+	3.96951i	0.135993	+	0.235547i
$285$	8.00000	−	13.8564i	0.473879	−	0.820783i
$286$	2.76393			0.163435
$287$		0			0
$288$	50.1246			2.95362
$289$	7.73607	−	13.3993i	0.455063	−	0.788192i
$290$	−1.05573	−	1.82857i	−0.0619945	−	0.107378i
$291$	15.2361	+	26.3896i	0.893154	+	1.54699i
$292$	−7.85410	+	13.6037i	−0.459627	+	0.796097i
$293$	−15.1246			−0.883589			−0.441795	−	0.897116i	$-0.645658\pi$
$293$	−15.1246			−0.883589			−0.441795	+	0.897116i	$0.645658\pi$
$294$		0			0
$295$	−6.47214			−0.376822
$296$	0.527864	−	0.914287i	0.0306815	−	0.0531419i
$297$	−7.23607	−	12.5332i	−0.419879	−	0.727252i
$298$	15.6525	+	27.1109i	0.906724	+	1.57049i
$299$	4.00000	−	6.92820i	0.231326	−	0.400668i
$300$	9.70820			0.560503
$301$		0			0
$302$	20.0000			1.15087
$303$	14.9443	−	25.8842i	0.858526	−	1.48701i
$304$	1.23607	+	2.14093i	0.0708934	+	0.122791i
$305$	−2.76393	−	4.78727i	−0.158262	−	0.274118i
$306$	−10.3262	+	17.8856i	−0.590312	+	1.02245i
$307$	−8.94427			−0.510477			−0.255238	−	0.966878i	$-0.582154\pi$
$307$	−8.94427			−0.510477			−0.255238	+	0.966878i	$0.582154\pi$
$308$		0			0
$309$	−18.4721			−1.05084
$310$	16.1803	−	28.0252i	0.918982	−	1.59172i
$311$	−10.8541	−	18.7999i	−0.615480	−	1.06604i	−0.990300	−	0.138945i	$-0.955629\pi$
$311$	−10.8541	−	18.7999i	−0.615480	−	1.06604i	0.374820	−	0.927097i	$-0.377704\pi$
$312$	−4.47214	−	7.74597i	−0.253185	−	0.438529i
$313$	−1.47214	+	2.54981i	−0.0832100	+	0.144124i	−0.904627	−	0.426204i	$-0.859851\pi$
$313$	−1.47214	+	2.54981i	−0.0832100	+	0.144124i	0.821417	+	0.570328i	$0.193184\pi$
$314$	−15.5279			−0.876288
$315$		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	$0.295285\pi$
$318$	−30.6525	−	53.0916i	−1.71891	−	2.97723i
$319$	−0.236068	−	0.408882i	−0.0132173	−	0.0228930i
$320$	13.0000	−	22.5167i	0.726722	−	1.25872i
$321$	12.9443			0.722479
$322$		0			0
$323$	−3.05573			−0.170025
$324$	−36.6246	+	63.4357i	−2.03470	+	3.52420i
$325$	0.618034	+	1.07047i	0.0342824	+	0.0593788i
$326$	26.1803	+	45.3457i	1.44999	+	2.51146i
$327$	7.23607	−	12.5332i	0.400155	−	0.693090i
$328$	−15.1246			−0.835117
$329$		0			0
$330$	−14.4721			−0.796665
$331$	−10.9443	+	18.9560i	−0.601552	+	1.04192i	0.391035	+	0.920376i	$0.372117\pi$
$331$	−10.9443	+	18.9560i	−0.601552	+	1.04192i	−0.992586	+	0.121542i	$0.961216\pi$
$332$	23.1246	+	40.0530i	1.26913	+	2.19819i
$333$	−1.76393	−	3.05522i	−0.0966629	−	0.167425i
$334$	14.4721	−	25.0665i	0.791880	−	1.37158i
$335$	11.0557			0.604039
$336$		0			0
$337$	−20.4721			−1.11519			−0.557594	−	0.830114i	$-0.688275\pi$
$337$	−20.4721			−1.11519			−0.557594	+	0.830114i	$0.688275\pi$
$338$	−12.8262	+	22.2157i	−0.697655	+	1.20837i
$339$	3.23607	+	5.60503i	0.175759	+	0.304424i
$340$	3.70820	+	6.42280i	0.201106	+	0.348325i
$341$	3.61803	−	6.26662i	0.195928	−	0.339356i
$342$	−41.3050			−2.23352
$343$		0			0
$344$	−17.8885			−0.964486
$345$	−20.9443	+	36.2765i	−1.12760	+	1.95306i
$346$	19.2705	+	33.3775i	1.03599	+	1.79439i
$347$	−1.52786	−	2.64634i	−0.0820200	−	0.142063i	0.822097	−	0.569347i	$-0.192804\pi$
$347$	−1.52786	−	2.64634i	−0.0820200	−	0.142063i	−0.904118	+	0.427284i	$0.859470\pi$
$348$	−2.29180	+	3.96951i	−0.122853	+	0.212788i
$349$	2.76393			0.147950			0.0739749	−	0.997260i	$-0.476432\pi$
$349$	2.76393			0.147950			0.0739749	+	0.997260i	$0.476432\pi$
$350$		0			0
$351$	−17.8885			−0.954820
$352$	3.35410	−	5.80948i	0.178774	−	0.309646i
$353$	−7.94427	−	13.7599i	−0.422831	−	0.732365i	0.573384	−	0.819287i	$-0.305630\pi$
$353$	−7.94427	−	13.7599i	−0.422831	−	0.732365i	−0.996215	+	0.0869220i	$0.972297\pi$
$354$	11.7082	+	20.2792i	0.622284	+	1.07783i
$355$	1.52786	−	2.64634i	0.0810906	−	0.140453i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−20.0000			−1.05703
$359$	3.52786	−	6.11044i	0.186194	−	0.322497i	−0.757785	−	0.652505i	$-0.773718\pi$
$359$	3.52786	−	6.11044i	0.186194	−	0.322497i	0.943978	+	0.330008i	$0.107052\pi$
$360$	16.7082	+	28.9395i	0.880600	+	1.52524i
$361$	6.44427	+	11.1618i	0.339172	+	0.587463i
$362$	−1.58359	+	2.74286i	−0.0832318	+	0.144162i
$363$	−3.23607			−0.169850
$364$		0			0
$365$	10.4721			0.548137
$366$	−10.0000	+	17.3205i	−0.522708	+	0.905357i
$367$	8.56231	+	14.8303i	0.446949	+	0.774138i	0.998186	−	0.0602108i	$-0.0191773\pi$
$367$	8.56231	+	14.8303i	0.446949	+	0.774138i	−0.551237	+	0.834349i	$0.685844\pi$
$368$	−3.23607	−	5.60503i	−0.168692	−	0.292183i
$369$	−25.2705	+	43.7698i	−1.31553	+	2.27857i
$370$	−2.11146			−0.109769
$371$		0			0
$372$	−70.2492			−3.64225
$373$	−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	$0.216312\pi$
$374$	1.38197	+	2.39364i	0.0714598	+	0.123772i
$375$	−19.4164	−	33.6302i	−1.00266	−	1.73666i
$376$	−8.09017	+	14.0126i	−0.417219	+	0.722644i
$377$	−0.583592			−0.0300565
$378$		0			0
$379$	−25.3050			−1.29983			−0.649914	−	0.760008i	$-0.725195\pi$
$379$	−25.3050			−1.29983			−0.649914	+	0.760008i	$0.725195\pi$
$380$	−7.41641	+	12.8456i	−0.380454	+	0.658965i
$381$	33.8885	+	58.6967i	1.73616	+	3.00712i
$382$	−23.4164	−	40.5584i	−1.19809	−	2.07515i
$383$	13.3262	−	23.0817i	0.680939	−	1.17942i	−0.293756	−	0.955881i	$-0.594905\pi$
$383$	13.3262	−	23.0817i	0.680939	−	1.17942i	0.974695	−	0.223540i	$-0.0717614\pi$
$384$	−50.6525			−2.58485
$385$		0			0
$386$	53.4164			2.71882
$387$	−29.8885	+	51.7685i	−1.51932	+	2.63154i
$388$	−14.1246	−	24.4645i	−0.717069	−	1.24200i
$389$	9.94427	+	17.2240i	0.504195	+	0.873291i	0.999988	+	0.00485030i	$0.00154390\pi$
$389$	9.94427	+	17.2240i	0.504195	+	0.873291i	−0.495794	+	0.868440i	$0.665123\pi$
$390$	−8.94427	+	15.4919i	−0.452911	+	0.784465i
$391$	8.00000			0.404577
$392$		0			0
$393$	−44.9443			−2.26714
$394$	−2.23607	+	3.87298i	−0.112651	+	0.195118i
$395$	−8.94427	−	15.4919i	−0.450035	−	0.779484i
$396$	11.2082	+	19.4132i	0.563233	+	0.975549i
$397$	−0.0557281	+	0.0965239i	−0.00279691	+	0.00484439i	−0.867420	−	0.497576i	$-0.834224\pi$
$397$	−0.0557281	+	0.0965239i	−0.00279691	+	0.00484439i	0.864624	+	0.502420i	$0.167557\pi$
$398$	45.1246			2.26189
$399$		0			0
$400$	1.00000			0.0500000
$401$	−2.52786	+	4.37839i	−0.126236	+	0.218646i	−0.922215	−	0.386677i	$-0.873623\pi$
$401$	−2.52786	+	4.37839i	−0.126236	+	0.218646i	0.795980	+	0.605323i	$0.206956\pi$
$402$	−20.0000	−	34.6410i	−0.997509	−	1.72774i
$403$	−4.47214	−	7.74597i	−0.222773	−	0.385854i
$404$	−13.8541	+	23.9960i	−0.689267	+	1.19385i
$405$	48.8328			2.42652
$406$		0			0
$407$	−0.472136			−0.0234029
$408$	4.47214	−	7.74597i	0.221404	−	0.383482i
$409$	−15.5623	−	26.9547i	−0.769507	−	1.33282i	−0.937831	−	0.347093i	$-0.887169\pi$
$409$	−15.5623	−	26.9547i	−0.769507	−	1.33282i	0.168324	−	0.985732i	$-0.446164\pi$
$410$	15.1246	+	26.1966i	0.746951	+	1.29376i
$411$	12.1803	−	21.0970i	0.600812	−	1.04064i
$412$	17.1246			0.843669
$413$		0			0
$414$	108.138			5.31468
$415$	15.4164	−	26.7020i	0.756762	−	1.31075i
$416$	−4.14590	−	7.18091i	−0.203269	−	0.352073i
$417$	16.9443	+	29.3483i	0.829765	+	1.43719i
$418$	−2.76393	+	4.78727i	−0.135188	+	0.234153i
$419$	6.65248			0.324995			0.162497	−	0.986709i	$-0.448045\pi$
$419$	6.65248			0.324995			0.162497	+	0.986709i	$0.448045\pi$
$420$		0			0
$421$	−22.3607			−1.08979			−0.544896	−	0.838503i	$-0.683431\pi$
$421$	−22.3607			−1.08979			−0.544896	+	0.838503i	$0.683431\pi$
$422$	24.4721	−	42.3870i	1.19128	−	2.06337i
$423$	27.0344	+	46.8250i	1.31446	+	2.27671i
$424$	9.47214	+	16.4062i	0.460008	+	0.796757i
$425$	−0.618034	+	1.07047i	−0.0299791	+	0.0519252i
$426$	−11.0557			−0.535652
$427$		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	$0.926659\pi$
$432$	−7.23607	+	12.5332i	−0.348145	+	0.603006i
$433$	−0.472136			−0.0226894			−0.0113447	−	0.999936i	$-0.503611\pi$
$433$	−0.472136			−0.0226894			−0.0113447	+	0.999936i	$0.503611\pi$
$434$		0			0
$435$	3.05573			0.146511
$436$	−6.70820	+	11.6190i	−0.321265	+	0.556447i
$437$	8.00000	+	13.8564i	0.382692	+	0.662842i
$438$	−18.9443	−	32.8124i	−0.905192	−	1.56784i
$439$	0.763932	−	1.32317i	0.0364605	−	0.0631514i	−0.847219	−	0.531243i	$-0.821725\pi$
$439$	0.763932	−	1.32317i	0.0364605	−	0.0631514i	0.883680	+	0.468092i	$0.155058\pi$
$440$	4.47214			0.213201
$441$		0			0
$442$	3.41641			0.162502
$443$	3.52786	−	6.11044i	0.167614	−	0.290316i	−0.769967	−	0.638084i	$-0.779727\pi$
$443$	3.52786	−	6.11044i	0.167614	−	0.290316i	0.937580	+	0.347768i	$0.113060\pi$
$444$	2.29180	+	3.96951i	0.108764	+	0.188384i
$445$	2.00000	+	3.46410i	0.0948091	+	0.164214i
$446$	−13.6180	+	23.5871i	−0.644833	+	1.11688i
$447$	−45.3050			−2.14285
$448$		0			0
$449$	−19.5279			−0.921577			−0.460788	−	0.887510i	$-0.652433\pi$
$449$	−19.5279			−0.921577			−0.460788	+	0.887510i	$0.652433\pi$
$450$	−8.35410	+	14.4697i	−0.393816	+	0.682110i
$451$	3.38197	+	5.85774i	0.159251	+	0.275830i
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	−14.4721	+	25.0665i	−0.679960	+	1.17773i
$454$	−66.8328			−3.13662
$455$		0			0
$456$	17.8885			0.837708
$457$	−12.4164	+	21.5058i	−0.580815	+	1.00600i	0.414568	+	0.910018i	$0.363933\pi$
$457$	−12.4164	+	21.5058i	−0.580815	+	1.00600i	−0.995383	+	0.0959828i	$0.969401\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$	−8.94427	−	15.4919i	−0.417483	−	0.723102i
$460$	19.4164	−	33.6302i	0.905295	−	1.56802i
$461$	−10.1803			−0.474146			−0.237073	−	0.971492i	$-0.576188\pi$
$461$	−10.1803			−0.474146			−0.237073	+	0.971492i	$0.576188\pi$
$462$		0			0
$463$	−14.4721			−0.672577			−0.336289	−	0.941759i	$-0.609172\pi$
$463$	−14.4721			−0.672577			−0.336289	+	0.941759i	$0.609172\pi$
$464$	−0.236068	+	0.408882i	−0.0109592	+	0.0189819i
$465$	23.4164	+	40.5584i	1.08591	+	1.88085i
$466$	−19.4721	−	33.7267i	−0.902029	−	1.56236i
$467$	−17.0344	+	29.5045i	−0.788260	+	1.36531i	0.138772	+	0.990324i	$0.455684\pi$
$467$	−17.0344	+	29.5045i	−0.788260	+	1.36531i	−0.927032	+	0.374982i	$0.877649\pi$
$468$	27.7082			1.28081
$469$		0			0
$470$	32.3607			1.49269
$471$	11.2361	−	19.4614i	0.517731	−	0.896736i
$472$	−3.61803	−	6.26662i	−0.166534	−	0.288445i
$473$	4.00000	+	6.92820i	0.183920	+	0.318559i
$474$	−32.3607	+	56.0503i	−1.48638	+	2.57448i
$475$	−2.47214			−0.113429
$476$		0			0
$477$	63.3050			2.89853
$478$	28.9443	−	50.1329i	1.32388	−	2.29303i
$479$	11.2361	+	19.4614i	0.513389	+	0.889216i	0.999879	+	0.0155300i	$0.00494354\pi$
$479$	11.2361	+	19.4614i	0.513389	+	0.889216i	−0.486490	+	0.873686i	$0.661723\pi$
$480$	21.7082	+	37.5997i	0.990839	+	1.71618i
$481$	−0.291796	+	0.505406i	−0.0133048	+	0.0230445i
$482$	60.6525			2.76264
$483$		0			0
$484$	3.00000			0.136364
$485$	−9.41641	+	16.3097i	−0.427577	+	0.740585i
$486$	−39.7984	−	68.9328i	−1.80529	−	3.12686i
$487$	−4.18034	−	7.24056i	−0.189429	−	0.328101i	0.755631	−	0.654998i	$-0.227330\pi$
$487$	−4.18034	−	7.24056i	−0.189429	−	0.328101i	−0.945060	+	0.326897i	$0.893997\pi$
$488$	3.09017	−	5.35233i	0.139885	−	0.242289i
$489$	−75.7771			−3.42676
$490$		0			0
$491$		0			0			−	1.00000i	$-0.5\pi$
$491$		0			0				1.00000i	$0.5\pi$
$492$	32.8328	−	56.8681i	1.48022	−	2.56381i
$493$	−0.291796	−	0.505406i	−0.0131418	−	0.0227623i
$494$	3.41641	+	5.91739i	0.153711	+	0.266236i
$495$	7.47214	−	12.9421i	0.335848	−	0.581705i
$496$	−7.23607			−0.324909
$497$		0			0
$498$	−111.554			−4.99886
$499$	−5.23607	+	9.06914i	−0.234399	+	0.405990i	−0.959098	−	0.283075i	$-0.908645\pi$
$499$	−5.23607	+	9.06914i	−0.234399	+	0.405990i	0.724699	+	0.689065i	$0.241979\pi$
$500$	18.0000	+	31.1769i	0.804984	+	1.39427i
$501$	20.9443	+	36.2765i	0.935721	+	1.62072i
$502$	−19.7984	+	34.2918i	−0.883645	+	1.53052i
$503$	3.41641			0.152330			0.0761650	−	0.997095i	$-0.475732\pi$
$503$	3.41641			0.152330			0.0761650	+	0.997095i	$0.475732\pi$
$504$		0			0
$505$	18.4721			0.821999
$506$	7.23607	−	12.5332i	0.321682	−	0.557170i
$507$	−18.5623	−	32.1509i	−0.824381	−	1.42787i
$508$	−31.4164	−	54.4148i	−1.39388	−	2.41427i
$509$	15.7639	−	27.3039i	0.698724	−	1.21023i	−0.270185	−	0.962808i	$-0.587085\pi$
$509$	15.7639	−	27.3039i	0.698724	−	1.21023i	0.968909	−	0.247417i	$-0.0795818\pi$
$510$	−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
$515$	−5.70820	−	9.88690i	−0.251534	−	0.435669i
$516$	38.8328	−	67.2604i	1.70952	−	2.96097i
$517$	7.23607			0.318242
$518$		0			0
$519$	−55.7771			−2.44834
$520$	2.76393	−	4.78727i	0.121206	−	0.209936i
$521$	−7.18034	−	12.4367i	−0.314576	−	0.544862i	0.664771	−	0.747047i	$-0.268529\pi$
$521$	−7.18034	−	12.4367i	−0.314576	−	0.544862i	−0.979347	+	0.202185i	$0.935196\pi$
$522$	−3.94427	−	6.83168i	−0.172636	−	0.299014i
$523$	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	$-0.245293\pi$
$524$	41.6656			1.82017
$525$		0			0
$526$		0			0
$527$	4.47214	−	7.74597i	0.194809	−	0.337420i
$528$	1.61803	+	2.80252i	0.0704159	+	0.121964i
$529$	−9.44427	−	16.3580i	−0.410621	−	0.711216i
$530$	18.9443	−	32.8124i	0.822887	−	1.42528i
$531$	−24.1803			−1.04934
$532$		0			0
$533$	8.36068			0.362141
$534$	7.23607	−	12.5332i	0.313135	−	0.542366i
$535$	4.00000	+	6.92820i	0.172935	+	0.299532i
$536$	6.18034	+	10.7047i	0.266950	+	0.462371i
$537$	14.4721	−	25.0665i	0.624519	−	1.08170i
$538$	−30.0000			−1.29339
$539$		0			0
$540$	−86.8328			−3.73669
$541$	16.4164	−	28.4341i	0.705797	−	1.22248i	−0.260607	−	0.965445i	$-0.583923\pi$
$541$	16.4164	−	28.4341i	0.705797	−	1.22248i	0.966403	−	0.257030i	$-0.0827440\pi$
$542$	1.70820	+	2.95870i	0.0733736	+	0.127087i
$543$	−2.29180	−	3.96951i	−0.0983504	−	0.170348i
$544$	4.14590	−	7.18091i	0.177754	−	0.307879i
$545$	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	$0.295725\pi$
$548$	−11.2918	+	19.5580i	−0.482362	+	0.835475i
$549$	−10.3262	−	17.8856i	−0.440713	−	0.763337i
$550$	1.11803	+	1.93649i	0.0476731	+	0.0825723i
$551$	0.583592	−	1.01081i	0.0248619	−	0.0430620i
$552$	−46.8328			−1.99334
$553$		0			0
$554$	−35.5279			−1.50943
$555$	1.52786	−	2.64634i	0.0648542	−	0.112331i
$556$	−15.7082	−	27.2074i	−0.666176	−	1.15385i
$557$	10.5279	+	18.2348i	0.446080	+	0.772633i	0.998127	−	0.0611800i	$-0.0194864\pi$
$557$	10.5279	+	18.2348i	0.446080	+	0.772633i	−0.552047	+	0.833813i	$0.686153\pi$
$558$	60.4508	−	104.704i	2.55909	−	4.43247i
$559$	9.88854			0.418241
$560$		0			0
$561$	−4.00000			−0.168880
$562$	−13.9443	+	24.1522i	−0.588204	+	1.01880i
$563$	19.7082	+	34.1356i	0.830602	+	1.43864i	0.897562	+	0.440889i	$0.145337\pi$
$563$	19.7082	+	34.1356i	0.830602	+	1.43864i	−0.0669600	+	0.997756i	$0.521330\pi$
$564$	−35.1246	−	60.8376i	−1.47901	−	2.56173i
$565$	−2.00000	+	3.46410i	−0.0841406	+	0.145736i
$566$	−13.1672			−0.553458
$567$		0			0
$568$	3.41641			0.143349
$569$	−8.23607	+	14.2653i	−0.345274	+	0.598032i	−0.985403	−	0.170235i	$-0.945547\pi$
$569$	−8.23607	+	14.2653i	−0.345274	+	0.598032i	0.640130	+	0.768267i	$0.278881\pi$
$570$	−17.8885	−	30.9839i	−0.749269	−	1.29777i
$571$	16.4721	+	28.5306i	0.689337	+	1.19397i	0.972053	+	0.234764i	$0.0754316\pi$
$571$	16.4721	+	28.5306i	0.689337	+	1.19397i	−0.282715	+	0.959204i	$0.591235\pi$
$572$	1.85410	−	3.21140i	0.0775239	−	0.134275i
$573$	67.7771			2.83143
$574$		0			0
$575$	6.47214			0.269907
$576$	48.5689	−	84.1238i	2.02370	−	3.50516i
$577$	−14.2361	−	24.6576i	−0.592655	−	1.02651i	−0.993873	−	0.110526i	$-0.964746\pi$
$577$	−14.2361	−	24.6576i	−0.592655	−	1.02651i	0.401218	−	0.915983i	$-0.368587\pi$
$578$	−17.2984	−	29.9617i	−0.719517	−	1.24624i
$579$	−38.6525	+	66.9481i	−1.60634	+	2.78227i
$580$	−2.83282			−0.117626
$581$		0			0
$582$	68.1378			2.82440
$583$	4.23607	−	7.33708i	0.175440	−	0.303871i
$584$	5.85410	+	10.1396i	0.242244	+	0.419580i
$585$	−9.23607	−	15.9973i	−0.381864	−	0.661409i
$586$	−16.9098	+	29.2887i	−0.698539	+	1.20990i
$587$	13.1246			0.541711			0.270855	−	0.962620i	$-0.412693\pi$
$587$	13.1246			0.541711			0.270855	+	0.962620i	$0.412693\pi$
$588$		0			0
$589$	17.8885			0.737085
$590$	−7.23607	+	12.5332i	−0.297904	+	0.515985i
$591$	−3.23607	−	5.60503i	−0.133114	−	0.230560i
$592$	0.236068	+	0.408882i	0.00970233	+	0.0168049i
$593$	−16.1459	+	27.9655i	−0.663033	+	1.14841i	0.316782	+	0.948498i	$0.397398\pi$
$593$	−16.1459	+	27.9655i	−0.663033	+	1.14841i	−0.979815	+	0.199908i	$0.935936\pi$
$594$	−32.3607			−1.32777
$595$		0			0
$596$	42.0000			1.72039
$597$	−32.6525	+	56.5557i	−1.33638	+	2.31467i
$598$	−8.94427	−	15.4919i	−0.365758	−	0.633512i
$599$	−1.70820	−	2.95870i	−0.0697953	−	0.120889i	0.829016	−	0.559225i	$-0.188901\pi$
$599$	−1.70820	−	2.95870i	−0.0697953	−	0.120889i	−0.898811	+	0.438336i	$0.855568\pi$
$600$	3.61803	−	6.26662i	0.147706	−	0.255834i
$601$	−3.12461			−0.127456			−0.0637278	−	0.997967i	$-0.520299\pi$
$601$	−3.12461			−0.127456			−0.0637278	+	0.997967i	$0.520299\pi$
$602$		0			0
$603$	41.3050			1.68207
$604$	13.4164	−	23.2379i	0.545906	−	0.945537i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$	−33.4164	−	57.8789i	−1.35745	−	2.35117i
$607$	−2.47214	+	4.28187i	−0.100341	+	0.173796i	−0.911825	−	0.410579i	$-0.865327\pi$
$607$	−2.47214	+	4.28187i	−0.100341	+	0.173796i	0.811484	+	0.584374i	$0.198660\pi$
$608$	16.5836			0.672553
$609$		0			0
$610$	−12.3607			−0.500469
$611$	4.47214	−	7.74597i	0.180923	−	0.313368i
$612$	13.8541	+	23.9960i	0.560019	+	0.969981i
$613$	23.6525	+	40.9673i	0.955315	+	1.65465i	0.733647	+	0.679531i	$0.237817\pi$
$613$	23.6525	+	40.9673i	0.955315	+	1.65465i	0.221668	+	0.975122i	$0.428850\pi$
$614$	−10.0000	+	17.3205i	−0.403567	+	0.698999i
$615$	−43.7771			−1.76526
$616$		0			0
$617$	33.4164			1.34529			0.672647	−	0.739964i	$-0.265157\pi$
$617$	33.4164			1.34529			0.672647	+	0.739964i	$0.265157\pi$
$618$	−20.6525	+	35.7711i	−0.830764	+	1.43893i
$619$	−14.5623	−	25.2227i	−0.585308	−	1.01378i	−0.994837	−	0.101487i	$-0.967640\pi$
$619$	−14.5623	−	25.2227i	−0.585308	−	1.01378i	0.409528	−	0.912297i	$-0.365693\pi$
$620$	−21.7082	−	37.5997i	−0.871822	−	1.51004i
$621$	−46.8328	+	81.1168i	−1.87934	+	3.25511i
$622$	−48.5410			−1.94632
$623$		0			0
$624$	4.00000			0.160128
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	3.29180	+	5.70156i	0.131567	+	0.227880i
$627$	−4.00000	−	6.92820i	−0.159745	−	0.276686i
$628$	−10.4164	+	18.0417i	−0.415660	+	0.719944i
$629$	−0.583592			−0.0232693
$630$		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
$633$	35.4164	+	61.3430i	1.40768	+	2.43817i
$634$	15.6525	+	27.1109i	0.621639	+	1.07671i
$635$	−20.9443	+	36.2765i	−0.831148	+	1.43959i
$636$	−82.2492			−3.26139
$637$		0			0
$638$	−1.05573			−0.0417967
$639$	5.70820	−	9.88690i	0.225813	−	0.391120i
$640$	−15.6525	−	27.1109i	−0.618718	−	1.07165i
$641$	12.2361	+	21.1935i	0.483296	+	0.837093i	0.999816	−	0.0191823i	$-0.00610630\pi$
$641$	12.2361	+	21.1935i	0.483296	+	0.837093i	−0.516520	+	0.856275i	$0.672773\pi$
$642$	14.4721	−	25.0665i	0.571170	−	0.989295i
$643$	29.1246			1.14856			0.574281	−	0.818658i	$-0.305282\pi$
$643$	29.1246			1.14856			0.574281	+	0.818658i	$0.305282\pi$
$644$		0			0
$645$	−51.7771			−2.03872
$646$	−3.41641	+	5.91739i	−0.134417	+	0.232817i
$647$	−11.0344	−	19.1122i	−0.433809	−	0.751379i	0.563389	−	0.826192i	$-0.309497\pi$
$647$	−11.0344	−	19.1122i	−0.433809	−	0.751379i	−0.997198	+	0.0748132i	$0.976164\pi$
$648$	27.2984	+	47.2822i	1.07238	+	1.85742i
$649$	−1.61803	+	2.80252i	−0.0635134	+	0.110008i
$650$	2.76393			0.108410
$651$		0			0
$652$	70.2492			2.75117
$653$	−21.4721	+	37.1908i	−0.840270	+	1.45539i	0.0493971	+	0.998779i	$0.484270\pi$
$653$	−21.4721	+	37.1908i	−0.840270	+	1.45539i	−0.889667	+	0.456610i	$0.849063\pi$
$654$	−16.1803	−	28.0252i	−0.632701	−	1.09587i
$655$	−13.8885	−	24.0557i	−0.542670	−	0.939933i
$656$	3.38197	−	5.85774i	0.132044	−	0.228706i
$657$	39.1246			1.52640
$658$		0			0
$659$	17.8885			0.696839			0.348419	−	0.937339i	$-0.386719\pi$
$659$	17.8885			0.696839			0.348419	+	0.937339i	$0.386719\pi$
$660$	−9.70820	+	16.8151i	−0.377891	+	0.654527i
$661$	6.41641	+	11.1135i	0.249569	+	0.432267i	0.963406	−	0.268045i	$-0.0863776\pi$
$661$	6.41641	+	11.1135i	0.249569	+	0.432267i	−0.713837	+	0.700312i	$0.753044\pi$
$662$	24.4721	+	42.3870i	0.951137	+	1.64742i
$663$	−2.47214	+	4.28187i	−0.0960098	+	0.166294i
$664$	34.4721			1.33778
$665$		0			0
$666$	−7.88854			−0.305675
$667$	−1.52786	+	2.64634i	−0.0591591	+	0.102467i
$668$	−19.4164	−	33.6302i	−0.751243	−	1.30119i
$669$	−19.7082	−	34.1356i	−0.761963	−	1.31976i
$670$	12.3607	−	21.4093i	0.477535	−	0.827114i
$671$	−2.76393			−0.106700
$672$		0			0
$673$	5.41641			0.208787			0.104394	−	0.994536i	$-0.466710\pi$
$673$	5.41641			0.208787			0.104394	+	0.994536i	$0.466710\pi$
$674$	−22.8885	+	39.6441i	−0.881634	+	1.52703i
$675$	−7.23607	−	12.5332i	−0.278516	−	0.482405i
$676$	17.2082	+	29.8055i	0.661854	+	1.14636i
$677$	1.85410	−	3.21140i	0.0712589	−	0.123424i	−0.828194	−	0.560441i	$-0.810632\pi$
$677$	1.85410	−	3.21140i	0.0712589	−	0.123424i	0.899453	+	0.437017i	$0.143965\pi$
$678$	14.4721			0.555799
$679$		0			0
$680$	5.52786			0.211984
$681$	48.3607	−	83.7632i	1.85319	−	3.20981i
$682$	−8.09017	−	14.0126i	−0.309789	−	0.536570i
$683$	−14.9443	−	25.8842i	−0.571827	−	0.990433i	−0.996378	−	0.0850292i	$-0.972902\pi$
$683$	−14.9443	−	25.8842i	−0.571827	−	0.990433i	0.424552	−	0.905404i	$-0.360432\pi$
$684$	−27.7082	+	47.9920i	−1.05945	+	1.83502i
$685$	15.0557			0.575250
$686$		0			0
$687$	14.4721			0.552146
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	−5.23607	−	9.06914i	−0.199478	−	0.345507i
$690$	46.8328	+	81.1168i	1.78289	+	3.08806i
$691$	−24.2705	+	42.0378i	−0.923294	+	1.59919i	−0.129011	+	0.991643i	$0.541180\pi$
$691$	−24.2705	+	42.0378i	−0.923294	+	1.59919i	−0.794283	+	0.607548i	$0.792153\pi$
$692$	51.7082			1.96565
$693$		0			0
$694$	−6.83282			−0.259370
$695$	−10.4721	+	18.1383i	−0.397231	+	0.688024i
$696$	1.70820	+	2.95870i	0.0647493	+	0.112149i
$697$	4.18034	+	7.24056i	0.158342	+	0.274256i
$698$	3.09017	−	5.35233i	0.116965	−	0.202589i
$699$	56.3607			2.13176
$700$		0			0
$701$	−24.4721			−0.924300			−0.462150	−	0.886802i	$-0.652922\pi$
$701$	−24.4721			−0.924300			−0.462150	+	0.886802i	$0.652922\pi$
$702$	−20.0000	+	34.6410i	−0.754851	+	1.30744i
$703$	−0.583592	−	1.01081i	−0.0220106	−	0.0381235i
$704$	−6.50000	−	11.2583i	−0.244978	−	0.424314i
$705$	−23.4164	+	40.5584i	−0.881913	+	1.52752i
$706$	−35.5279			−1.33711
$707$		0			0
$708$	31.4164			1.18070
$709$	−1.47214	+	2.54981i	−0.0552872	+	0.0957603i	−0.892344	−	0.451355i	$-0.850941\pi$
$709$	−1.47214	+	2.54981i	−0.0552872	+	0.0957603i	0.837057	+	0.547115i	$0.184274\pi$
$710$	−3.41641	−	5.91739i	−0.128216	−	0.222076i
$711$	−33.4164	−	57.8789i	−1.25321	−	2.17063i
$712$	−2.23607	+	3.87298i	−0.0838002	+	0.145146i
$713$	−46.8328			−1.75390
$714$		0			0
$715$	−2.47214			−0.0924526
$716$	−13.4164	+	23.2379i	−0.501395	+	0.868441i
$717$	41.8885	+	72.5531i	1.56436	+	2.70954i
$718$	−7.88854	−	13.6634i	−0.294398	−	0.509912i
$719$	16.7426	−	28.9991i	0.624395	−	1.08148i	−0.364262	−	0.931296i	$-0.618679\pi$
$719$	16.7426	−	28.9991i	0.624395	−	1.08148i	0.988657	−	0.150188i	$-0.0479879\pi$
$720$	−14.9443			−0.556940
$721$		0			0
$722$	28.8197			1.07256
$723$	−43.8885	+	76.0172i	−1.63223	+	2.82711i
$724$	2.12461	+	3.67994i	0.0789606	+	0.136764i
$725$	−0.236068	−	0.408882i	−0.00876734	−	0.0151855i
$726$	−3.61803	+	6.26662i	−0.134278	+	0.232576i
$727$	51.0132			1.89197			0.945987	−	0.324206i	$-0.105097\pi$
$727$	51.0132			1.89197			0.945987	+	0.324206i	$0.105097\pi$
$728$		0			0
$729$	41.9443			1.55349
$730$	11.7082	−	20.2792i	0.433340	−	0.750567i
$731$	4.94427	+	8.56373i	0.182871	+	0.316741i
$732$	13.4164	+	23.2379i	0.495885	+	0.858898i
$733$	6.61803	−	11.4628i	0.244443	−	0.423387i	−0.717532	−	0.696525i	$-0.754728\pi$
$733$	6.61803	−	11.4628i	0.244443	−	0.423387i	0.961975	+	0.273138i	$0.0880617\pi$
$734$	38.2918			1.41338
$735$		0			0
$736$	−43.4164			−1.60035
$737$	2.76393	−	4.78727i	0.101811	−	0.176341i
$738$	56.5066	+	97.8723i	2.08004	+	3.60273i
$739$	−3.52786	−	6.11044i	−0.129775	−	0.224776i	0.793815	−	0.608160i	$-0.208092\pi$
$739$	−3.52786	−	6.11044i	−0.129775	−	0.224776i	−0.923589	+	0.383384i	$0.874759\pi$
$740$	−1.41641	+	2.45329i	−0.0520682	+	0.0901847i
$741$	−9.88854			−0.363265
$742$		0			0
$743$	−33.8885			−1.24325			−0.621625	−	0.783315i	$-0.713527\pi$
$743$	−33.8885			−1.24325			−0.621625	+	0.783315i	$0.713527\pi$
$744$	−26.1803	+	45.3457i	−0.959818	+	1.66245i
$745$	−14.0000	−	24.2487i	−0.512920	−	0.888404i
$746$	6.70820	+	11.6190i	0.245605	+	0.425400i
$747$	57.5967	−	99.7605i	2.10735	−	3.65005i
$748$	3.70820			0.135585
$749$		0			0
$750$	−86.8328			−3.17069
$751$	−19.2361	+	33.3178i	−0.701934	+	1.21579i	0.265853	+	0.964014i	$0.414347\pi$
$751$	−19.2361	+	33.3178i	−0.701934	+	1.21579i	−0.967787	+	0.251772i	$0.918987\pi$
$752$	−3.61803	−	6.26662i	−0.131936	−	0.228520i
$753$	−28.6525	−	49.6275i	−1.04415	−	1.80853i
$754$	−0.652476	+	1.13012i	−0.0237618	+	0.0411566i
$755$	−17.8885			−0.651031
$756$		0			0
$757$	−19.8885			−0.722861			−0.361431	−	0.932399i	$-0.617712\pi$
$757$	−19.8885			−0.722861			−0.361431	+	0.932399i	$0.617712\pi$
$758$	−28.2918	+	49.0028i	−1.02760	+	1.77986i
$759$	10.4721	+	18.1383i	0.380114	+	0.658378i
$760$	5.52786	+	9.57454i	0.200517	+	0.347305i
$761$	8.79837	−	15.2392i	0.318941	−	0.552422i	−0.661327	−	0.750098i	$-0.730006\pi$
$761$	8.79837	−	15.2392i	0.318941	−	0.552422i	0.980267	+	0.197676i	$0.0633395\pi$
$762$	151.554			5.49023
$763$		0			0
$764$	−62.8328			−2.27321
$765$	9.23607	−	15.9973i	0.333931	−	0.578385i
$766$	−29.7984	−	51.6123i	−1.07666	−	1.86483i
$767$	2.00000	+	3.46410i	0.0722158	+	0.125081i
$768$	−14.5623	+	25.2227i	−0.525472	+	0.910144i
$769$	−31.7082			−1.14343			−0.571714	−	0.820453i	$-0.693721\pi$
$769$	−31.7082			−1.14343			−0.571714	+	0.820453i	$0.693721\pi$
$770$		0			0
$771$	−19.4164			−0.699265
$772$	35.8328	−	62.0643i	1.28965	−	2.23374i
$773$	3.18034	+	5.50851i	0.114389	+	0.198127i	0.917535	−	0.397654i	$-0.130176\pi$
$773$	3.18034	+	5.50851i	0.114389	+	0.198127i	−0.803146	+	0.595782i	$0.796842\pi$
$774$	66.8328	+	115.758i	2.40226	+	4.16083i
$775$	3.61803	−	6.26662i	0.129964	−	0.225104i
$776$	−21.0557			−0.755857

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)

\(f(q)\)	\(=\)	\(q+(1.11803 - 1.93649i) q^{2} +(1.61803 + 2.80252i) q^{3} +(-1.50000 - 2.59808i) q^{4} +(-1.00000 + 1.73205i) q^{5} +7.23607 q^{6} -2.23607 q^{8} +(-3.73607 + 6.47106i) q^{9} +O(q^{10})\)	\(q+(1.11803 - 1.93649i) q^{2} +(1.61803 + 2.80252i) q^{3} +(-1.50000 - 2.59808i) q^{4} +(-1.00000 + 1.73205i) q^{5} +7.23607 q^{6} -2.23607 q^{8} +(-3.73607 + 6.47106i) q^{9} +(2.23607 + 3.87298i) q^{10} +(0.500000 + 0.866025i) q^{11} +(4.85410 - 8.40755i) q^{12} +1.23607 q^{13} -6.47214 q^{15} +(0.500000 - 0.866025i) q^{16} +(0.618034 + 1.07047i) q^{17} +(8.35410 + 14.4697i) q^{18} +(-1.23607 + 2.14093i) q^{19} +6.00000 q^{20} +2.23607 q^{22} +(3.23607 - 5.60503i) q^{23} +(-3.61803 - 6.26662i) q^{24} +(0.500000 + 0.866025i) q^{25} +(1.38197 - 2.39364i) q^{26} -14.4721 q^{27} -0.472136 q^{29} +(-7.23607 + 12.5332i) q^{30} +(-3.61803 - 6.26662i) q^{31} +(-3.35410 - 5.80948i) q^{32} +(-1.61803 + 2.80252i) q^{33} +2.76393 q^{34} +22.4164 q^{36} +(-0.236068 + 0.408882i) q^{37} +(2.76393 + 4.78727i) q^{38} +(2.00000 + 3.46410i) q^{39} +(2.23607 - 3.87298i) q^{40} +6.76393 q^{41} +8.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(-7.47214 - 12.9421i) q^{45} +(-7.23607 - 12.5332i) q^{46} +(3.61803 - 6.26662i) q^{47} +3.23607 q^{48} +2.23607 q^{50} +(-2.00000 + 3.46410i) q^{51} +(-1.85410 - 3.21140i) q^{52} +(-4.23607 - 7.33708i) q^{53} +(-16.1803 + 28.0252i) q^{54} -2.00000 q^{55} -8.00000 q^{57} +(-0.527864 + 0.914287i) q^{58} +(1.61803 + 2.80252i) q^{59} +(9.70820 + 16.8151i) q^{60} +(-1.38197 + 2.39364i) q^{61} -16.1803 q^{62} -13.0000 q^{64} +(-1.23607 + 2.14093i) q^{65} +(3.61803 + 6.26662i) q^{66} +(-2.76393 - 4.78727i) q^{67} +(1.85410 - 3.21140i) q^{68} +20.9443 q^{69} -1.52786 q^{71} +(8.35410 - 14.4697i) q^{72} +(-2.61803 - 4.53457i) q^{73} +(0.527864 + 0.914287i) q^{74} +(-1.61803 + 2.80252i) q^{75} +7.41641 q^{76} +8.94427 q^{78} +(-4.47214 + 7.74597i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-12.2082 - 21.1452i) q^{81} +(7.56231 - 13.0983i) q^{82} -15.4164 q^{83} -2.47214 q^{85} +(8.94427 - 15.4919i) q^{86} +(-0.763932 - 1.32317i) q^{87} +(-1.11803 - 1.93649i) q^{88} +(1.00000 - 1.73205i) q^{89} -33.4164 q^{90} -19.4164 q^{92} +(11.7082 - 20.2792i) q^{93} +(-8.09017 - 14.0126i) q^{94} +(-2.47214 - 4.28187i) q^{95} +(10.8541 - 18.7999i) q^{96} +9.41641 q^{97} -7.47214 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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