LMFDB - Embedded newform 539.2.q.h.324.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(214,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 12]))

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

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

chi := DirichletCharacter("539.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.q (of order $15$, degree $8$, 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:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			324.1
Character	$\chi$	$=$	539.324
Dual form			539.2.q.h.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.57407 - 0.547134i) q^{2} +(-0.231369 + 2.20133i) q^{3} +(4.49937 + 2.00325i) q^{4} +(0.787136 + 0.874203i) q^{5} +(1.79998 - 5.53977i) q^{6} +(-6.22764 - 4.52465i) q^{8} +(-1.85787 - 0.394902i) q^{9} +O(q^{10})$	\(q+(-2.57407 - 0.547134i) q^{2} +(-0.231369 + 2.20133i) q^{3} +(4.49937 + 2.00325i) q^{4} +(0.787136 + 0.874203i) q^{5} +(1.79998 - 5.53977i) q^{6} +(-6.22764 - 4.52465i) q^{8} +(-1.85787 - 0.394902i) q^{9} +(-1.54783 - 2.68093i) q^{10} +(-3.26165 - 0.601380i) q^{11} +(-5.45081 + 9.44109i) q^{12} +(-0.0112624 - 0.0346622i) q^{13} +(-2.10653 + 1.53048i) q^{15} +(6.96361 + 7.73387i) q^{16} +(-5.95559 + 1.26590i) q^{17} +(4.56621 + 2.03301i) q^{18} +(-1.75961 + 0.783430i) q^{19} +(1.79037 + 5.51019i) q^{20} +(8.06666 + 3.33255i) q^{22} +(-1.02155 + 1.76938i) q^{23} +(11.4011 - 12.6622i) q^{24} +(0.377994 - 3.59637i) q^{25} +(0.0100254 + 0.0953849i) q^{26} +(-0.752823 + 2.31695i) q^{27} +(4.02767 - 2.92628i) q^{29} +(6.25972 - 2.78701i) q^{30} +(-1.89509 + 2.10472i) q^{31} +(-5.99553 - 10.3846i) q^{32} +(2.07848 - 7.04081i) q^{33} +16.0227 q^{34} +(-7.56813 - 5.49857i) q^{36} +(0.278295 + 2.64780i) q^{37} +(4.95800 - 1.05386i) q^{38} +(0.0789086 - 0.0167725i) q^{39} +(-0.946542 - 9.00574i) q^{40} +(-6.61499 - 4.80607i) q^{41} -2.96835 q^{43} +(-13.4706 - 9.23971i) q^{44} +(-1.11717 - 1.93499i) q^{45} +(3.59762 - 3.99557i) q^{46} +(-2.91785 + 1.29911i) q^{47} +(-18.6359 + 13.5398i) q^{48} +(-2.94068 + 9.05049i) q^{50} +(-1.40872 - 13.4031i) q^{51} +(0.0187631 - 0.178519i) q^{52} +(-6.63364 + 7.36740i) q^{53} +(3.20550 - 5.55209i) q^{54} +(-2.04163 - 3.32471i) q^{55} +(-1.31747 - 4.05475i) q^{57} +(-11.9686 + 5.32875i) q^{58} +(-3.70874 - 1.65124i) q^{59} +(-12.5440 + 2.66630i) q^{60} +(5.80710 + 6.44943i) q^{61} +(6.02966 - 4.38080i) q^{62} +(3.31928 + 10.2157i) q^{64} +(0.0214368 - 0.0371295i) q^{65} +(-9.20241 + 16.9863i) q^{66} +(-1.12669 - 1.95148i) q^{67} +(-29.3323 - 6.23477i) q^{68} +(-3.65862 - 2.65815i) q^{69} +(1.31384 - 4.04359i) q^{71} +(9.78334 + 10.8655i) q^{72} +(-3.92144 - 1.74594i) q^{73} +(0.732354 - 6.96788i) q^{74} +(7.82934 + 1.66418i) q^{75} -9.48655 q^{76} -0.212293 q^{78} +(3.03638 + 0.645402i) q^{79} +(-1.27967 + 12.1752i) q^{80} +(-10.1317 - 4.51091i) q^{81} +(14.3979 + 15.9904i) q^{82} +(-1.87581 + 5.77314i) q^{83} +(-5.79451 - 4.20996i) q^{85} +(7.64073 + 1.62409i) q^{86} +(5.50981 + 9.54328i) q^{87} +(17.5913 + 18.5030i) q^{88} +(2.16161 - 3.74402i) q^{89} +(1.81697 + 5.59204i) q^{90} +(-8.14083 + 5.91466i) q^{92} +(-4.19470 - 4.65869i) q^{93} +(8.22152 - 1.74754i) q^{94} +(-2.06993 - 0.921593i) q^{95} +(24.2470 - 10.7955i) q^{96} +(-1.43258 - 4.40904i) q^{97} +(5.82222 + 2.40531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} + 4 q^{3} - 3 q^{4} - 4 q^{5} + 16 q^{6} - 38 q^{8} + 7 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 - 4 * q^5 + 16 * q^6 - 38 * q^8 + 7 * q^9	$ 40 q - 3 q^{2} + 4 q^{3} - 3 q^{4} - 4 q^{5} + 16 q^{6} - 38 q^{8} + 7 q^{9} - 14 q^{10} - 9 q^{11} + 18 q^{12} - 6 q^{13} - 14 q^{15} - 5 q^{16} + 7 q^{17} + 24 q^{18} + 4 q^{19} + 30 q^{20} + 44 q^{22} - 14 q^{23} + 12 q^{24} + 21 q^{25} + 16 q^{27} + 16 q^{30} + 17 q^{31} - 30 q^{32} + 15 q^{33} - 48 q^{34} + 14 q^{36} + 24 q^{37} - 12 q^{38} + 28 q^{39} - 10 q^{40} - 60 q^{41} - 72 q^{43} + 18 q^{44} + 16 q^{45} + 8 q^{46} - 13 q^{47} - 128 q^{48} + 6 q^{50} - 7 q^{51} - 2 q^{52} + 33 q^{53} - 34 q^{54} + 6 q^{55} + 44 q^{57} - 17 q^{58} - 21 q^{59} - 48 q^{60} + 52 q^{62} + 94 q^{64} - 40 q^{65} + 49 q^{66} - 38 q^{67} + 23 q^{68} + 124 q^{69} + 20 q^{71} - 38 q^{72} - 11 q^{73} - 41 q^{74} + 11 q^{75} + 96 q^{76} - 100 q^{78} + 21 q^{79} - 12 q^{80} - 58 q^{81} - 6 q^{82} + 46 q^{83} - 78 q^{85} + 7 q^{86} - 48 q^{87} + 32 q^{88} + 10 q^{89} + 18 q^{90} - 110 q^{92} + 12 q^{93} - 37 q^{94} + 7 q^{95} + 53 q^{96} + 54 q^{97} - 36 q^{99}+O(q^{100}) $ 40 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 - 4 * q^5 + 16 * q^6 - 38 * q^8 + 7 * q^9 - 14 * q^10 - 9 * q^11 + 18 * q^12 - 6 * q^13 - 14 * q^15 - 5 * q^16 + 7 * q^17 + 24 * q^18 + 4 * q^19 + 30 * q^20 + 44 * q^22 - 14 * q^23 + 12 * q^24 + 21 * q^25 + 16 * q^27 + 16 * q^30 + 17 * q^31 - 30 * q^32 + 15 * q^33 - 48 * q^34 + 14 * q^36 + 24 * q^37 - 12 * q^38 + 28 * q^39 - 10 * q^40 - 60 * q^41 - 72 * q^43 + 18 * q^44 + 16 * q^45 + 8 * q^46 - 13 * q^47 - 128 * q^48 + 6 * q^50 - 7 * q^51 - 2 * q^52 + 33 * q^53 - 34 * q^54 + 6 * q^55 + 44 * q^57 - 17 * q^58 - 21 * q^59 - 48 * q^60 + 52 * q^62 + 94 * q^64 - 40 * q^65 + 49 * q^66 - 38 * q^67 + 23 * q^68 + 124 * q^69 + 20 * q^71 - 38 * q^72 - 11 * q^73 - 41 * q^74 + 11 * q^75 + 96 * q^76 - 100 * q^78 + 21 * q^79 - 12 * q^80 - 58 * q^81 - 6 * q^82 + 46 * q^83 - 78 * q^85 + 7 * q^86 - 48 * q^87 + 32 * q^88 + 10 * q^89 + 18 * q^90 - 110 * q^92 + 12 * q^93 - 37 * q^94 + 7 * q^95 + 53 * q^96 + 54 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−2.57407	−	0.547134i	−1.82014	−	0.386883i	−0.833861	−	0.551975i	$-0.813875\pi$
$2$	−2.57407	−	0.547134i	−1.82014	−	0.386883i	−0.986278	+	0.165092i	$0.947208\pi$
$3$	−0.231369	+	2.20133i	−0.133581	+	1.27094i	0.698228	+	0.715875i	$0.253972\pi$
$3$	−0.231369	+	2.20133i	−0.133581	+	1.27094i	−0.831809	+	0.555062i	$0.812695\pi$
$4$	4.49937	+	2.00325i	2.24968	+	1.00162i
$5$	0.787136	+	0.874203i	0.352018	+	0.390956i	0.892984	−	0.450089i	$-0.148608\pi$
$5$	0.787136	+	0.874203i	0.352018	+	0.390956i	−0.540966	+	0.841045i	$0.681941\pi$
$6$	1.79998	−	5.53977i	0.734839	−	2.26160i
$7$		0			0
$7$		0			0
$8$	−6.22764	−	4.52465i	−2.20180	−	1.59970i
$9$	−1.85787	−	0.394902i	−0.619289	−	0.131634i
$10$	−1.54783	−	2.68093i	−0.489468	−	0.847783i
$11$	−3.26165	−	0.601380i	−0.983424	−	0.181323i
$11$	−3.26165	−	0.601380i	−0.983424	−	0.181323i
$12$	−5.45081	+	9.44109i	−1.57351	+	2.72541i
$13$	−0.0112624	−	0.0346622i	−0.00312364	−	0.00961357i	0.949483	−	0.313820i	$-0.101609\pi$
$13$	−0.0112624	−	0.0346622i	−0.00312364	−	0.00961357i	−0.952606	+	0.304206i	$0.901609\pi$
$14$		0			0
$15$	−2.10653	+	1.53048i	−0.543903	+	0.395169i
$16$	6.96361	+	7.73387i	1.74090	+	1.93347i
$17$	−5.95559	+	1.26590i	−1.44444	+	0.307026i	−0.862439	−	0.506161i	$-0.831064\pi$
$17$	−5.95559	+	1.26590i	−1.44444	+	0.307026i	−0.582003	+	0.813187i	$0.697731\pi$
$18$	4.56621	+	2.03301i	1.07626	+	0.479184i
$19$	−1.75961	+	0.783430i	−0.403683	+	0.179731i	−0.598526	−	0.801103i	$-0.704247\pi$
$19$	−1.75961	+	0.783430i	−0.403683	+	0.179731i	0.194843	+	0.980834i	$0.437580\pi$
$20$	1.79037	+	5.51019i	0.400339	+	1.23212i
$21$		0			0
$22$	8.06666	+	3.33255i	1.71982	+	0.710502i
$23$	−1.02155	+	1.76938i	−0.213008	+	0.368941i	−0.952655	−	0.304055i	$-0.901659\pi$
$23$	−1.02155	+	1.76938i	−0.213008	+	0.368941i	0.739647	+	0.672996i	$0.234993\pi$
$24$	11.4011	−	12.6622i	2.32724	−	2.58466i
$25$	0.377994	−	3.59637i	0.0755988	−	0.719275i
$26$	0.0100254	+	0.0953849i	0.00196613	+	0.0187065i
$27$	−0.752823	+	2.31695i	−0.144881	+	0.445898i
$28$		0			0
$29$	4.02767	−	2.92628i	0.747920	−	0.543396i	−0.147261	−	0.989098i	$-0.547046\pi$
$29$	4.02767	−	2.92628i	0.747920	−	0.543396i	0.895182	+	0.445702i	$0.147046\pi$
$30$	6.25972	−	2.78701i	1.14286	−	0.508835i
$31$	−1.89509	+	2.10472i	−0.340369	+	0.378018i	−0.888892	−	0.458118i	$-0.848524\pi$
$31$	−1.89509	+	2.10472i	−0.340369	+	0.378018i	0.548523	+	0.836136i	$0.315190\pi$
$32$	−5.99553	−	10.3846i	−1.05987	−	1.83575i
$33$	2.07848	−	7.04081i	0.361816	−	1.22565i
$34$	16.0227			2.74787
$35$		0			0
$36$	−7.56813	−	5.49857i	−1.26136	−	0.916429i
$37$	0.278295	+	2.64780i	0.0457515	+	0.435296i	0.993290	+	0.115653i	$0.0368962\pi$
$37$	0.278295	+	2.64780i	0.0457515	+	0.435296i	−0.947538	+	0.319643i	$0.896437\pi$
$38$	4.95800	−	1.05386i	0.804294	−	0.170958i
$39$	0.0789086	−	0.0167725i	0.0126355	−	0.00268576i
$40$	−0.946542	−	9.00574i	−0.149661	−	1.42393i
$41$	−6.61499	−	4.80607i	−1.03309	−	0.750583i	−0.0641641	−	0.997939i	$-0.520438\pi$
$41$	−6.61499	−	4.80607i	−1.03309	−	0.750583i	−0.968925	+	0.247357i	$0.920438\pi$
$42$		0			0
$43$	−2.96835			−0.452669			−0.226335	−	0.974050i	$-0.572674\pi$
$43$	−2.96835			−0.452669			−0.226335	+	0.974050i	$0.572674\pi$
$44$	−13.4706	−	9.23971i	−2.03077	−	1.39294i
$45$	−1.11717	−	1.93499i	−0.166538	−	0.288452i
$46$	3.59762	−	3.99557i	0.530441	−	0.589114i
$47$	−2.91785	+	1.29911i	−0.425612	+	0.189495i	−0.608353	−	0.793666i	$-0.708170\pi$
$47$	−2.91785	+	1.29911i	−0.425612	+	0.189495i	0.182741	+	0.983161i	$0.441503\pi$
$48$	−18.6359	+	13.5398i	−2.68987	+	1.95430i
$49$		0			0
$50$	−2.94068	+	9.05049i	−0.415875	+	1.27993i
$51$	−1.40872	−	13.4031i	−0.197260	−	1.87681i
$52$	0.0187631	−	0.178519i	0.00260198	−	0.0247562i
$53$	−6.63364	+	7.36740i	−0.911200	+	1.01199i	0.0886731	+	0.996061i	$0.471737\pi$
$53$	−6.63364	+	7.36740i	−0.911200	+	1.01199i	−0.999873	+	0.0159294i	$0.994929\pi$
$54$	3.20550	−	5.55209i	0.436213	−	0.755544i
$55$	−2.04163	−	3.32471i	−0.275294	−	0.448304i
$56$		0			0
$57$	−1.31747	−	4.05475i	−0.174503	−	0.537064i
$58$	−11.9686	+	5.32875i	−1.57155	+	0.699699i
$59$	−3.70874	−	1.65124i	−0.482837	−	0.214973i	0.150858	−	0.988555i	$-0.451796\pi$
$59$	−3.70874	−	1.65124i	−0.482837	−	0.214973i	−0.633696	+	0.773582i	$0.718463\pi$
$60$	−12.5440	+	2.66630i	−1.61942	+	0.344218i
$61$	5.80710	+	6.44943i	0.743522	+	0.825765i	0.989655	−	0.143471i	$-0.0458264\pi$
$61$	5.80710	+	6.44943i	0.743522	+	0.825765i	−0.246132	+	0.969236i	$0.579160\pi$
$62$	6.02966	−	4.38080i	0.765767	−	0.556363i
$63$		0			0
$64$	3.31928	+	10.2157i	0.414910	+	1.27696i
$65$	0.0214368	−	0.0371295i	0.00265890	−	0.00460535i
$66$	−9.20241	+	16.9863i	−1.13274	+	2.09087i
$67$	−1.12669	−	1.95148i	−0.137647	−	0.238411i	0.788959	−	0.614446i	$-0.210621\pi$
$67$	−1.12669	−	1.95148i	−0.137647	−	0.238411i	−0.926605	+	0.376035i	$0.877287\pi$
$68$	−29.3323	−	6.23477i	−3.55706	−	0.756076i
$69$	−3.65862	−	2.65815i	−0.440446	−	0.320003i
$70$		0			0
$71$	1.31384	−	4.04359i	0.155924	−	0.479885i	−0.842329	−	0.538963i	$-0.818816\pi$
$71$	1.31384	−	4.04359i	0.155924	−	0.479885i	0.998253	+	0.0590780i	$0.0188161\pi$
$72$	9.78334	+	10.8655i	1.15298	+	1.28051i
$73$	−3.92144	−	1.74594i	−0.458970	−	0.204347i	0.164209	−	0.986426i	$-0.447493\pi$
$73$	−3.92144	−	1.74594i	−0.458970	−	0.204347i	−0.623180	+	0.782079i	$0.714159\pi$
$74$	0.732354	−	6.96788i	0.0851344	−	0.810000i
$75$	7.82934	+	1.66418i	0.904054	+	0.192163i
$76$	−9.48655			−1.08818
$77$		0			0
$78$	−0.212293			−0.0240374
$79$	3.03638	+	0.645402i	0.341619	+	0.0726133i	0.375527	−	0.926812i	$-0.377462\pi$
$79$	3.03638	+	0.645402i	0.341619	+	0.0726133i	−0.0339076	+	0.999425i	$0.510795\pi$
$80$	−1.27967	+	12.1752i	−0.143071	+	1.36123i
$81$	−10.1317	−	4.51091i	−1.12574	−	0.501213i
$82$	14.3979	+	15.9904i	1.58998	+	1.76585i
$83$	−1.87581	+	5.77314i	−0.205896	+	0.633684i	0.793779	+	0.608206i	$0.208111\pi$
$83$	−1.87581	+	5.77314i	−0.205896	+	0.633684i	−0.999675	+	0.0254778i	$0.991889\pi$
$84$		0			0
$85$	−5.79451	−	4.20996i	−0.628503	−	0.456634i
$86$	7.64073	+	1.62409i	0.823921	+	0.175130i
$87$	5.50981	+	9.54328i	0.590714	+	1.02315i
$88$	17.5913	+	18.5030i	1.87524	+	1.97242i
$89$	2.16161	−	3.74402i	0.229130	−	0.396866i	−0.728420	−	0.685131i	$-0.759745\pi$
$89$	2.16161	−	3.74402i	0.229130	−	0.396866i	0.957551	+	0.288265i	$0.0930784\pi$
$90$	1.81697	+	5.59204i	0.191525	+	0.589453i
$91$		0			0
$92$	−8.14083	+	5.91466i	−0.848740	+	0.616646i
$93$	−4.19470	−	4.65869i	−0.434970	−	0.483083i
$94$	8.22152	−	1.74754i	0.847985	−	0.180245i
$95$	−2.06993	−	0.921593i	−0.212371	−	0.0945535i
$96$	24.2470	−	10.7955i	2.47470	−	1.10181i
$97$	−1.43258	−	4.40904i	−0.145457	−	0.447670i	0.851613	−	0.524172i	$-0.175625\pi$
$97$	−1.43258	−	4.40904i	−0.145457	−	0.447670i	−0.997069	+	0.0765015i	$0.975625\pi$
$98$		0			0
$99$	5.82222	+	2.40531i	0.585155	+	0.241743i
$100$	8.90516	−	15.4242i	0.890516	−	1.54242i
$101$	11.3829	−	12.6420i	1.13264	−	1.25792i	0.170502	−	0.985357i	$-0.445461\pi$
$101$	11.3829	−	12.6420i	1.13264	−	1.25792i	0.962137	−	0.272566i	$-0.0878722\pi$
$102$	−3.70715	+	35.2712i	−0.367062	+	3.49237i
$103$	−1.76150	−	16.7595i	−0.173566	−	1.65137i	−0.641149	−	0.767417i	$-0.721542\pi$
$103$	−1.76150	−	16.7595i	−0.173566	−	1.65137i	0.467583	−	0.883949i	$-0.345125\pi$
$104$	−0.0866959	+	0.266822i	−0.00850123	+	0.0261641i
$105$		0			0
$106$	21.1064	−	15.3347i	2.05003	−	1.48944i
$107$	−0.852002	+	0.379336i	−0.0823661	+	0.0366718i	−0.447506	−	0.894281i	$-0.647688\pi$
$107$	−0.852002	+	0.379336i	−0.0823661	+	0.0366718i	0.365140	+	0.930953i	$0.381021\pi$
$108$	−8.02865	+	8.91672i	−0.772558	+	0.858012i
$109$	−0.811795	−	1.40607i	−0.0777558	−	0.134677i	0.824526	−	0.565825i	$-0.191442\pi$
$109$	−0.811795	−	1.40607i	−0.0777558	−	0.134677i	−0.902281	+	0.431148i	$0.858109\pi$
$110$	3.43623	+	9.67507i	0.327632	+	0.922482i
$111$	−5.89307			−0.559345
$112$		0			0
$113$	−2.86311	−	2.08017i	−0.269338	−	0.195686i	0.444915	−	0.895573i	$-0.353234\pi$
$113$	−2.86311	−	2.08017i	−0.269338	−	0.195686i	−0.714254	+	0.699887i	$0.753234\pi$
$114$	1.17275	+	11.1580i	0.109838	+	1.04504i
$115$	−2.35090	+	0.499698i	−0.219222	+	0.0465971i
$116$	23.9840	−	5.09796i	2.22686	−	0.473334i
$117$	0.00723593	+	0.0688453i	0.000668962	+	0.00636475i
$118$	8.64310	+	6.27958i	0.795662	+	0.578082i
$119$		0			0
$120$	20.0436			1.82972
$121$	10.2767	+	3.92298i	0.934244	+	0.356634i
$122$	−11.4191	−	19.7785i	−1.03384	−	1.79066i
$123$	12.1102	−	13.4498i	1.09194	−	1.21273i
$124$	−12.7430	+	5.67354i	−1.14435	+	0.509499i
$125$	8.19996	−	5.95762i	0.733427	−	0.532866i
$126$		0			0
$127$	−6.09131	+	18.7471i	−0.540516	+	1.66354i	0.190903	+	0.981609i	$0.438858\pi$
$127$	−6.09131	+	18.7471i	−0.540516	+	1.66354i	−0.731419	+	0.681928i	$0.761142\pi$
$128$	−0.447872	−	4.26121i	−0.0395866	−	0.376642i
$129$	0.686784	−	6.53431i	0.0604680	−	0.575314i
$130$	−0.0754945	+	0.0838451i	−0.00662130	+	0.00735370i
$131$	−8.09187	+	14.0155i	−0.706990	+	1.22454i	0.258979	+	0.965883i	$0.416614\pi$
$131$	−8.09187	+	14.0155i	−0.706990	+	1.22454i	−0.965969	+	0.258659i	$0.916719\pi$
$132$	23.4563	−	27.5155i	2.04161	−	2.39492i
$133$		0			0
$134$	1.83244	+	5.63968i	0.158299	+	0.487194i
$135$	−2.61806	+	1.16564i	−0.225327	+	0.100322i
$136$	42.8170	+	19.0634i	3.67153	+	1.63467i
$137$	16.6054	−	3.52958i	1.41869	−	0.301553i	0.566191	−	0.824274i	$-0.308417\pi$
$137$	16.6054	−	3.52958i	1.41869	−	0.301553i	0.852504	+	0.522721i	$0.175083\pi$
$138$	7.96317	+	8.84400i	0.677870	+	0.752851i
$139$	−5.94380	+	4.31842i	−0.504146	+	0.366284i	−0.810598	−	0.585602i	$-0.800858\pi$
$139$	−5.94380	+	4.31842i	−0.504146	+	0.366284i	0.306452	+	0.951886i	$0.400858\pi$
$140$		0			0
$141$	−2.18467	−	6.72371i	−0.183982	−	0.566239i
$142$	−5.59430	+	9.68961i	−0.469463	+	0.813134i
$143$	0.0158889	+	0.119829i	0.00132870	+	0.0100206i
$144$	−9.88334	−	17.1184i	−0.823611	−	1.42654i
$145$	5.72849	+	1.21763i	0.475725	+	0.101119i
$146$	9.13879	+	6.63972i	0.756332	+	0.549507i
$147$		0			0
$148$	−4.05205	+	12.4709i	−0.333076	+	1.02510i
$149$	−3.35966	−	3.73128i	−0.275234	−	0.305679i	0.589641	−	0.807665i	$-0.299269\pi$
$149$	−3.35966	−	3.73128i	−0.275234	−	0.305679i	−0.864875	+	0.501987i	$0.832603\pi$
$150$	−19.2427	−	8.56740i	−1.57116	−	0.699526i
$151$	−0.877823	+	8.35192i	−0.0714362	+	0.679670i	0.898940	+	0.438072i	$0.144338\pi$
$151$	−0.877823	+	8.35192i	−0.0714362	+	0.679670i	−0.970376	+	0.241598i	$0.922328\pi$
$152$	14.5030	+	3.08271i	1.17635	+	0.250040i
$153$	11.5646			0.934942
$154$		0			0
$155$	−3.33165			−0.267604
$156$	0.388638	+	0.0826076i	0.0311160	+	0.00661390i
$157$	−1.56236	+	14.8648i	−0.124690	+	1.18634i	0.735917	+	0.677072i	$0.236752\pi$
$157$	−1.56236	+	14.8648i	−0.124690	+	1.18634i	−0.860606	+	0.509271i	$0.829915\pi$
$158$	−7.46271	−	3.32261i	−0.593701	−	0.264333i
$159$	−14.6832	−	16.3074i	−1.16446	−	1.29326i
$160$	4.35892	−	13.4154i	0.344603	−	1.06058i
$161$		0			0
$162$	23.6115	+	17.1548i	1.85510	+	1.34781i
$163$	−2.43424	−	0.517414i	−0.190665	−	0.0405270i	0.111590	−	0.993754i	$-0.464406\pi$
$163$	−2.43424	−	0.517414i	−0.190665	−	0.0405270i	−0.302254	+	0.953227i	$0.597739\pi$
$164$	−20.1355	−	34.8758i	−1.57232	−	2.72334i
$165$	7.79115	−	3.72507i	0.606540	−	0.289996i
$166$	7.98713	−	13.8341i	0.619921	−	1.07374i
$167$	3.80261	+	11.7032i	0.294255	+	0.905624i	0.983471	+	0.181068i	$0.0579553\pi$
$167$	3.80261	+	11.7032i	0.294255	+	0.905624i	−0.689216	+	0.724556i	$0.742045\pi$
$168$		0			0
$169$	10.5161	−	7.64043i	0.808934	−	0.587725i
$170$	12.6120	+	14.0071i	0.967299	+	1.07429i
$171$	3.57850	−	0.760634i	0.273655	−	0.0581672i
$172$	−13.3557	−	5.94634i	−1.01836	−	0.453404i
$173$	−11.1499	+	4.96423i	−0.847708	+	0.377424i	−0.784163	−	0.620555i	$-0.786907\pi$
$173$	−11.1499	+	4.96423i	−0.847708	+	0.377424i	−0.0635449	+	0.997979i	$0.520241\pi$
$174$	−8.96116	−	27.5796i	−0.679344	−	2.09081i
$175$		0			0
$176$	−18.0618	−	29.4129i	−1.36146	−	2.21708i
$177$	4.49301	−	7.78211i	0.337715	−	0.584940i
$178$	−7.61261	+	8.45466i	−0.570590	+	0.633704i
$179$	−0.398664	+	3.79303i	−0.0297975	+	0.283504i	0.969469	+	0.245213i	$0.0788580\pi$
$179$	−0.398664	+	3.79303i	−0.0297975	+	0.283504i	−0.999267	+	0.0382910i	$0.987809\pi$
$180$	−1.15028	−	10.9442i	−0.0857371	−	0.815734i
$181$	−2.17667	+	6.69911i	−0.161791	+	0.497941i	−0.998785	−	0.0492703i	$-0.984310\pi$
$181$	−2.17667	+	6.69911i	−0.161791	+	0.497941i	0.836995	+	0.547211i	$0.184310\pi$
$182$		0			0
$183$	−15.5409	+	11.2911i	−1.14882	+	0.834664i
$184$	14.3677	−	6.39689i	1.05920	−	0.471585i
$185$	−2.09566	+	2.32747i	−0.154076	+	0.171119i
$186$	8.24851	+	14.2868i	0.604810	+	1.04756i
$187$	20.1863	−	0.547348i	1.47617	−	0.0400261i
$188$	−15.7309			−1.14729
$189$		0			0
$190$	4.82391	+	3.50477i	0.349963	+	0.254263i
$191$	1.66472	+	15.8388i	0.120455	+	1.14605i	0.873071	+	0.487593i	$0.162125\pi$
$191$	1.66472	+	15.8388i	0.120455	+	1.14605i	−0.752616	+	0.658460i	$0.771208\pi$
$192$	−23.2560	+	4.94323i	−1.67836	+	0.356747i
$193$	−14.4744	+	3.07662i	−1.04189	+	0.221460i	−0.696916	−	0.717153i	$-0.745445\pi$
$193$	−14.4744	+	3.07662i	−1.04189	+	0.221460i	−0.344972	+	0.938613i	$0.612112\pi$
$194$	1.27523	+	12.1330i	0.0915560	+	0.871097i
$195$	0.0767745	+	0.0557799i	0.00549793	+	0.00399448i
$196$		0			0
$197$	8.28808			0.590501			0.295251	−	0.955420i	$-0.404597\pi$
$197$	8.28808			0.590501			0.295251	+	0.955420i	$0.404597\pi$
$198$	−13.6707	−	9.37697i	−0.971537	−	0.666392i
$199$	9.14220	+	15.8348i	0.648073	+	1.12250i	0.983582	+	0.180459i	$0.0577583\pi$
$199$	9.14220	+	15.8348i	0.648073	+	1.12250i	−0.335509	+	0.942037i	$0.608908\pi$
$200$	−18.6263	+	20.6866i	−1.31708	+	1.46277i
$201$	4.55652	−	2.02869i	0.321392	−	0.143093i
$202$	−36.2171	+	26.3133i	−2.54823	+	1.85140i
$203$		0			0
$204$	20.5113	−	63.1274i	1.43608	−	4.41980i
$205$	−1.00542	−	9.56589i	−0.0702212	−	0.668111i
$206$	−4.63551	+	44.1039i	−0.322971	+	3.07286i
$207$	2.59663	−	2.88385i	0.180479	−	0.200442i
$208$	0.189646	−	0.328476i	0.0131496	−	0.0227757i
$209$	6.21038	−	1.49708i	0.429581	−	0.103555i
$210$		0			0
$211$	7.29409	+	22.4489i	0.502146	+	1.54545i	0.805516	+	0.592573i	$0.201888\pi$
$211$	7.29409	+	22.4489i	0.502146	+	1.54545i	−0.303370	+	0.952873i	$0.598112\pi$
$212$	−44.6059	+	19.8598i	−3.06354	+	1.36398i
$213$	8.59728	+	3.82775i	0.589076	+	0.262273i
$214$	2.40066	−	0.510275i	0.164105	−	0.0348817i
$215$	−2.33650	−	2.59494i	−0.159348	−	0.176974i
$216$	15.1717	−	11.0229i	1.03230	−	0.750013i
$217$		0			0
$218$	1.32030	+	4.06348i	0.0894222	+	0.275213i
$219$	4.75068	−	8.22842i	0.321021	−	0.556025i
$220$	−2.52584	−	19.0490i	−0.170292	−	1.28428i
$221$	0.110953	+	0.192177i	0.00746352	+	0.0129272i
$222$	15.1691	+	3.22430i	1.01809	+	0.216401i
$223$	−9.76962	−	7.09804i	−0.654222	−	0.475320i	0.210485	−	0.977597i	$-0.432496\pi$
$223$	−9.76962	−	7.09804i	−0.654222	−	0.475320i	−0.864707	+	0.502277i	$0.832496\pi$
$224$		0			0
$225$	−2.12248	+	6.53231i	−0.141498	+	0.435488i
$226$	6.23169	+	6.92100i	0.414526	+	0.460378i
$227$	9.43447	+	4.20050i	0.626188	+	0.278797i	0.695197	−	0.718819i	$-0.255317\pi$
$227$	9.43447	+	4.20050i	0.626188	+	0.278797i	−0.0690091	+	0.997616i	$0.521984\pi$
$228$	2.19489	−	20.8830i	0.145360	−	1.38301i
$229$	−26.9582	−	5.73015i	−1.78145	−	0.378659i	−0.804809	−	0.593534i	$-0.797732\pi$
$229$	−26.9582	−	5.73015i	−1.78145	−	0.378659i	−0.976641	+	0.214875i	$0.931065\pi$
$230$	6.32476			0.417042
$231$		0			0
$232$	−38.3233			−2.51605
$233$	−3.91278	−	0.831687i	−0.256335	−	0.0544856i	0.0779518	−	0.996957i	$-0.475162\pi$
$233$	−3.91278	−	0.831687i	−0.256335	−	0.0544856i	−0.334286	+	0.942472i	$0.608495\pi$
$234$	0.0190419	−	0.181171i	0.00124481	−	0.0118435i
$235$	−3.43243	−	1.52822i	−0.223907	−	0.0996899i
$236$	−13.3792	−	14.8591i	−0.870909	−	0.967242i
$237$	−2.12326	+	6.53473i	−0.137921	+	0.424476i
$238$		0			0
$239$	−17.1705	−	12.4751i	−1.11067	−	0.806946i	−0.127897	−	0.991787i	$-0.540823\pi$
$239$	−17.1705	−	12.4751i	−1.11067	−	0.806946i	−0.982768	+	0.184842i	$0.940823\pi$
$240$	−26.5056	−	5.63393i	−1.71093	−	0.363669i
$241$	−6.80326	−	11.7836i	−0.438237	−	0.759048i	0.559317	−	0.828954i	$-0.311064\pi$
$241$	−6.80326	−	11.7836i	−0.438237	−	0.759048i	−0.997554	+	0.0699056i	$0.977730\pi$
$242$	−24.3065	−	15.7207i	−1.56248	−	1.01057i
$243$	8.61987	−	14.9301i	0.552965	−	0.957763i
$244$	13.2084	+	40.6514i	0.845584	+	2.60244i
$245$		0			0
$246$	−38.5314	+	27.9947i	−2.45667	+	1.78488i
$247$	0.0469730	+	0.0521687i	0.00298882	+	0.00331942i
$248$	21.3251	−	4.53278i	1.35414	−	0.287832i
$249$	−12.2746	−	5.46499i	−0.777869	−	0.346329i
$250$	−24.3669	+	10.8488i	−1.54109	+	0.686140i
$251$	5.10309	+	15.7057i	0.322104	+	0.991334i	0.972731	+	0.231937i	$0.0745062\pi$
$251$	5.10309	+	15.7057i	0.322104	+	0.991334i	−0.650627	+	0.759398i	$0.725494\pi$
$252$		0			0
$253$	4.39600	−	5.15674i	0.276374	−	0.324202i
$254$	25.9366	−	44.9235i	1.62741	−	2.81875i
$255$	10.6082	−	11.7816i	0.664309	−	0.737790i
$256$	1.06696	−	10.1514i	0.0666850	−	0.634465i
$257$	3.05781	+	29.0931i	0.190741	+	1.81478i	0.502454	+	0.864604i	$0.332430\pi$
$257$	3.05781	+	29.0931i	0.190741	+	1.81478i	−0.311713	+	0.950176i	$0.600903\pi$
$258$	−5.34298	+	16.4440i	−0.332639	+	1.02376i
$259$		0			0
$260$	0.170831	−	0.124116i	0.0105945	−	0.00769737i
$261$	−8.63847	+	3.84610i	−0.534708	+	0.238067i
$262$	28.4974	−	31.6495i	1.76057	−	1.95531i
$263$	9.96601	+	17.2616i	0.614530	+	1.06440i	0.990467	+	0.137752i	$0.0439878\pi$
$263$	9.96601	+	17.2616i	0.614530	+	1.06440i	−0.375936	+	0.926646i	$0.622679\pi$
$264$	−44.8012	+	34.4433i	−2.75732	+	2.11984i
$265$	−11.6622			−0.716402
$266$		0			0
$267$	7.74169	+	5.62466i	0.473784	+	0.344224i
$268$	−1.16008	−	11.0374i	−0.0708633	−	0.674219i
$269$	0.605177	−	0.128634i	0.0368983	−	0.00784298i	−0.189426	−	0.981895i	$-0.560663\pi$
$269$	0.605177	−	0.128634i	0.0368983	−	0.00784298i	0.226324	+	0.974052i	$0.427329\pi$
$270$	7.37682	−	1.56799i	0.448939	−	0.0954250i
$271$	−0.0121050	−	0.115172i	−0.000735328	−	0.00699618i	0.994148	−	0.108026i	$-0.0344529\pi$
$271$	−0.0121050	−	0.115172i	−0.000735328	−	0.00699618i	−0.994883	+	0.101030i	$0.967786\pi$
$272$	−51.2627	−	37.2445i	−3.10826	−	2.25828i
$273$		0			0
$274$	−44.6745			−2.69889
$275$	−3.39567	+	11.5028i	−0.204767	+	0.693644i
$276$	−11.1366	−	19.2891i	−0.670342	−	1.16107i
$277$	6.46626	−	7.18151i	0.388520	−	0.431495i	−0.516878	−	0.856059i	$-0.672906\pi$
$277$	6.46626	−	7.18151i	0.388520	−	0.431495i	0.905398	+	0.424564i	$0.139573\pi$
$278$	17.6625	−	7.86384i	1.05932	−	0.471642i
$279$	4.35199	−	3.16190i	0.260547	−	0.189298i
$280$		0			0
$281$	−1.07026	+	3.29393i	−0.0638466	+	0.196500i	−0.977891	−	0.209114i	$-0.932942\pi$
$281$	−1.07026	+	3.29393i	−0.0638466	+	0.196500i	0.914045	+	0.405613i	$0.132942\pi$
$282$	1.94470	+	18.5026i	0.115805	+	1.10181i
$283$	2.75322	−	26.1952i	0.163662	−	1.55714i	−0.536959	−	0.843608i	$-0.680427\pi$
$283$	2.75322	−	26.1952i	0.163662	−	1.55714i	0.700621	−	0.713533i	$-0.252906\pi$
$284$	14.0118	−	15.5616i	0.831445	−	0.923413i
$285$	2.50765	−	4.34337i	0.148540	−	0.257279i
$286$	0.0246633	−	0.317141i	0.00145837	−	0.0187529i
$287$		0			0
$288$	7.03801	+	21.6608i	0.414719	+	1.27637i
$289$	18.3362	−	8.16382i	1.07860	−	0.480225i
$290$	−14.0793	−	6.26851i	−0.826765	−	0.368100i
$291$	10.0372	−	2.13347i	0.588391	−	0.125066i
$292$	−14.1465	−	15.7112i	−0.827859	−	0.919431i
$293$	12.3700	−	8.98734i	0.722664	−	0.525046i	−0.164570	−	0.986365i	$-0.552624\pi$
$293$	12.3700	−	8.98734i	0.722664	−	0.525046i	0.887234	+	0.461319i	$0.152624\pi$
$294$		0			0
$295$	−1.47577	−	4.54195i	−0.0859226	−	0.264442i
$296$	10.2473	−	17.7488i	0.595609	−	1.03163i
$297$	3.84881	−	7.10435i	0.223331	−	0.412236i
$298$	6.60648	+	11.4428i	0.382703	+	0.662861i
$299$	0.0728357	+	0.0154817i	0.00421220	+	0.000895330i
$300$	31.8933	+	23.1718i	1.84136	+	1.33783i
$301$		0			0
$302$	6.82920	−	21.0181i	0.392976	−	1.20946i
$303$	25.1955	+	27.9824i	1.44744	+	1.60755i
$304$	−18.3122	−	8.15312i	−1.05028	−	0.467613i
$305$	−1.06714	+	10.1532i	−0.0611043	+	0.581369i
$306$	−29.7680	−	6.32739i	−1.70172	−	0.361713i
$307$	−32.1611			−1.83553			−0.917766	−	0.397123i	$-0.870009\pi$
$307$	−32.1611			−1.83553			−0.917766	+	0.397123i	$0.870009\pi$
$308$		0			0
$309$	37.3008			2.12197
$310$	8.57588	+	1.82286i	0.487077	+	0.103531i
$311$	0.221418	−	2.10666i	0.0125555	−	0.119458i	−0.986449	−	0.164069i	$-0.947538\pi$
$311$	0.221418	−	2.10666i	0.0125555	−	0.119458i	0.999004	+	0.0446110i	$0.0142048\pi$
$312$	−0.567305	−	0.252580i	−0.0321173	−	0.0142995i
$313$	4.10743	+	4.56176i	0.232166	+	0.257846i	0.847959	−	0.530062i	$-0.177831\pi$
$313$	4.10743	+	4.56176i	0.232166	+	0.257846i	−0.615794	+	0.787907i	$0.711165\pi$
$314$	12.1547	−	37.4082i	0.685928	−	2.11107i
$315$		0			0
$316$	12.3689	+	8.98651i	0.695803	+	0.505530i
$317$	17.3855	+	3.69540i	0.976468	+	0.207555i	0.668394	−	0.743808i	$-0.266982\pi$
$317$	17.3855	+	3.69540i	0.976468	+	0.207555i	0.308074	+	0.951362i	$0.400316\pi$
$318$	28.8733	+	50.0100i	1.61913	+	2.80442i
$319$	−14.8967	+	7.12232i	−0.834053	+	0.398773i
$320$	−6.31787	+	10.9429i	−0.353179	+	0.611725i
$321$	−0.637915	−	1.96330i	−0.0356050	−	0.109581i
$322$		0			0
$323$	9.48778	−	6.89328i	0.527914	−	0.383552i
$324$	−36.5496	−	40.5925i	−2.03054	−	2.25514i
$325$	−0.128915	+	0.0274018i	−0.00715094	+	0.00151998i
$326$	5.98280	+	2.66372i	0.331357	+	0.147530i
$327$	3.28304	−	1.46170i	0.181553	−	0.0808325i
$328$	19.4500	+	59.8610i	1.07395	+	3.30527i
$329$		0			0
$330$	−22.0930	+	5.32576i	−1.21618	+	0.293174i
$331$	−9.78286	+	16.9444i	−0.537714	+	0.931349i	0.461312	+	0.887238i	$0.347379\pi$
$331$	−9.78286	+	16.9444i	−0.537714	+	0.931349i	−0.999027	+	0.0441108i	$0.985955\pi$
$332$	−20.0050	+	22.2178i	−1.09791	+	1.21936i
$333$	0.528586	−	5.02916i	0.0289663	−	0.275596i
$334$	−3.38493	−	32.2054i	−0.185215	−	1.76220i
$335$	0.819133	−	2.52103i	0.0447540	−	0.137739i
$336$		0			0
$337$	−18.6594	+	13.5569i	−1.01644	+	0.738489i	−0.965551	−	0.260215i	$-0.916207\pi$
$337$	−18.6594	+	13.5569i	−1.01644	+	0.738489i	−0.0508925	+	0.998704i	$0.516207\pi$
$338$	−31.2496	+	13.9132i	−1.69975	+	0.756779i
$339$	5.24157	−	5.82135i	0.284683	−	0.316172i
$340$	−17.6380	−	30.5500i	−0.956557	−	1.65681i
$341$	7.44686	−	5.72517i	0.403270	−	0.310035i
$342$	−9.62747			−0.520594
$343$		0			0
$344$	18.4858	+	13.4307i	0.996690	+	0.724137i
$345$	−0.556075	−	5.29070i	−0.0299381	−	0.284842i
$346$	31.4166	−	6.67780i	1.68896	−	0.359001i
$347$	24.4941	−	5.20638i	1.31491	−	0.279493i	0.503514	−	0.863987i	$-0.332040\pi$
$347$	24.4941	−	5.20638i	1.31491	−	0.279493i	0.811398	+	0.584494i	$0.198707\pi$
$348$	5.67313	+	53.9762i	0.304112	+	2.89343i
$349$	15.8320	+	11.5026i	0.847467	+	0.615721i	0.924446	−	0.381312i	$-0.124528\pi$
$349$	15.8320	+	11.5026i	0.847467	+	0.615721i	−0.0769797	+	0.997033i	$0.524528\pi$
$350$		0			0
$351$	0.0887893			0.00473922
$352$	13.3102	+	37.4763i	0.709438	+	1.99750i
$353$	10.1136	+	17.5172i	0.538292	+	0.932349i	0.998996	+	0.0447952i	$0.0142635\pi$
$353$	10.1136	+	17.5172i	0.538292	+	0.932349i	−0.460704	+	0.887554i	$0.652403\pi$
$354$	−15.8232	+	17.5734i	−0.840991	+	0.934015i
$355$	4.56909	−	2.03429i	0.242502	−	0.107969i
$356$	17.2261	−	12.5155i	0.912981	−	0.663319i
$357$		0			0
$358$	3.10148	−	9.54539i	0.163919	−	0.504489i
$359$	2.60519	+	24.7867i	0.137497	+	1.30819i	0.817902	+	0.575357i	$0.195137\pi$
$359$	2.60519	+	24.7867i	0.137497	+	1.30819i	−0.680405	+	0.732836i	$0.738196\pi$
$360$	−1.79783	+	17.1053i	−0.0947542	+	0.901526i
$361$	−10.2310	+	11.3627i	−0.538474	+	0.598036i
$362$	9.26821	−	16.0530i	0.487126	−	0.843727i
$363$	−11.0135	+	21.7147i	−0.578057	+	1.13973i
$364$		0			0
$365$	−1.56040	−	4.80243i	−0.0816753	−	0.251371i
$366$	46.1810	−	20.5611i	2.41392	−	1.07475i
$367$	−6.84200	−	3.04625i	−0.357149	−	0.159013i	0.220316	−	0.975429i	$-0.429291\pi$
$367$	−6.84200	−	3.04625i	−0.357149	−	0.159013i	−0.577465	+	0.816416i	$0.695958\pi$
$368$	−20.7978	+	4.42071i	−1.08416	+	0.230446i
$369$	10.3918	+	11.5413i	0.540978	+	0.600817i
$370$	6.66781	−	4.84445i	0.346643	−	0.251851i
$371$		0			0
$372$	−9.54099	−	29.3642i	−0.494678	−	1.52246i
$373$	0.802488	−	1.38995i	0.0415513	−	0.0719689i	−0.844502	−	0.535553i	$-0.820103\pi$
$373$	0.802488	−	1.38995i	0.0415513	−	0.0719689i	0.886053	+	0.463584i	$0.153437\pi$
$374$	−52.2603	−	9.63572i	−2.70232	−	0.498251i
$375$	11.2175	+	19.4292i	0.579267	+	1.00332i
$376$	24.0493	+	5.11184i	1.24025	+	0.263623i
$377$	−0.146793	−	0.106651i	−0.00756021	−	0.00549281i
$378$		0			0
$379$	5.26757	−	16.2119i	0.270577	−	0.832751i	−0.719779	−	0.694204i	$-0.755757\pi$
$379$	5.26757	−	16.2119i	0.270577	−	0.832751i	0.990356	−	0.138547i	$-0.0442433\pi$
$380$	−7.46721	−	8.29317i	−0.383060	−	0.425431i
$381$	−39.8592	−	17.7465i	−2.04205	−	0.909178i
$382$	4.38084	−	41.6809i	0.224143	−	2.13258i
$383$	−17.0414	−	3.62225i	−0.870773	−	0.185089i	−0.249207	−	0.968450i	$-0.580170\pi$
$383$	−17.0414	−	3.62225i	−0.870773	−	0.185089i	−0.621566	+	0.783362i	$0.713503\pi$
$384$	9.48395			0.483976
$385$		0			0
$386$	38.9413			1.98206
$387$	5.51480	+	1.17221i	0.280333	+	0.0595866i
$388$	2.38668	−	22.7077i	0.121165	−	1.15281i
$389$	−10.2642	−	4.56993i	−0.520417	−	0.231705i	0.129680	−	0.991556i	$-0.458605\pi$
$389$	−10.2642	−	4.56993i	−0.520417	−	0.231705i	−0.650097	+	0.759851i	$0.725272\pi$
$390$	−0.167103	−	0.185587i	−0.00846161	−	0.00939757i
$391$	3.84408	−	11.8309i	0.194403	−	0.598312i
$392$		0			0
$393$	−28.9805	−	21.0556i	−1.46188	−	1.06211i
$394$	−21.3341	−	4.53470i	−1.07479	−	0.228455i
$395$	1.82583	+	3.16243i	0.0918674	+	0.159119i
$396$	21.3779	+	22.4857i	1.07428	+	1.12995i
$397$	9.85421	−	17.0680i	0.494568	−	0.856618i	−0.505412	−	0.862878i	$-0.668659\pi$
$397$	9.85421	−	17.0680i	0.494568	−	0.856618i	0.999980	+	0.00626047i	$0.00199278\pi$
$398$	−14.8689	−	45.7617i	−0.745310	−	2.29383i
$399$		0			0
$400$	30.4461	−	22.1204i	1.52231	−	1.10602i
$401$	−8.38973	−	9.31774i	−0.418963	−	0.465306i	0.496306	−	0.868147i	$-0.334689\pi$
$401$	−8.38973	−	9.31774i	−0.418963	−	0.465306i	−0.915270	+	0.402842i	$0.868023\pi$
$402$	−12.8388	+	2.72896i	−0.640339	+	0.136108i
$403$	0.0942975	+	0.0419839i	0.00469729	+	0.00209137i
$404$	76.5407	−	34.0781i	3.80804	−	1.69545i
$405$	−4.03156	−	12.4079i	−0.200330	−	0.616551i
$406$		0			0
$407$	0.684633	−	8.80356i	0.0339360	−	0.436376i
$408$	−51.8712	+	89.8436i	−2.56801	+	4.44792i
$409$	−10.4423	+	11.5973i	−0.516337	+	0.573450i	−0.943773	−	0.330596i	$-0.892750\pi$
$409$	−10.4423	+	11.5973i	−0.516337	+	0.573450i	0.427436	+	0.904046i	$0.359417\pi$
$410$	−2.64582	+	25.1733i	−0.130668	+	1.24322i
$411$	3.92780	+	37.3705i	0.193744	+	1.84335i
$412$	25.6479	−	78.9360i	1.26358	−	3.88890i
$413$		0			0
$414$	−8.26176	+	6.00252i	−0.406043	+	0.295008i
$415$	−6.52341	+	2.90441i	−0.320222	+	0.142572i
$416$	−0.292427	+	0.324774i	−0.0143374	+	0.0159233i
$417$	−8.13105	−	14.0834i	−0.398179	−	0.689666i
$418$	−16.8050	+	0.455665i	−0.821960	+	0.0222873i
$419$	31.8183			1.55443			0.777213	−	0.629238i	$-0.216633\pi$
$419$	31.8183			1.55443			0.777213	+	0.629238i	$0.216633\pi$
$420$		0			0
$421$	−19.3204	−	14.0371i	−0.941617	−	0.684125i	0.00719220	−	0.999974i	$-0.497711\pi$
$421$	−19.3204	−	14.0371i	−0.941617	−	0.684125i	−0.948809	+	0.315849i	$0.897711\pi$
$422$	−6.49290	−	61.7758i	−0.316069	−	3.00720i
$423$	5.93399	−	1.26131i	0.288521	−	0.0613270i
$424$	74.6468	−	15.8667i	3.62517	−	0.770554i
$425$	2.30147	+	21.8970i	0.111638	+	1.06216i
$426$	−20.0357	−	14.5568i	−0.970731	−	0.705277i
$427$		0			0
$428$	−4.59337			−0.222029
$429$	−0.267459	+	0.00725210i	−0.0129130	+	0.000350135i
$430$	4.59452	+	7.95793i	0.221567	+	0.383766i
$431$	−5.58314	+	6.20070i	−0.268930	+	0.298677i	−0.862450	−	0.506142i	$-0.831071\pi$
$431$	−5.58314	+	6.20070i	−0.268930	+	0.298677i	0.593520	+	0.804819i	$0.297738\pi$
$432$	−23.1614	+	10.3121i	−1.11435	+	0.496142i
$433$	10.3850	−	7.54511i	0.499069	−	0.362595i	−0.309592	−	0.950869i	$-0.600193\pi$
$433$	10.3850	−	7.54511i	0.499069	−	0.362595i	0.808661	+	0.588275i	$0.200193\pi$
$434$		0			0
$435$	−4.00579	+	12.3286i	−0.192063	+	0.591109i
$436$	−0.835857	−	7.95265i	−0.0400303	−	0.380863i
$437$	0.411350	−	3.91373i	0.0196775	−	0.187219i
$438$	−16.7306	+	18.5812i	−0.799420	+	0.887846i
$439$	−12.2991	+	21.3026i	−0.587002	+	1.01672i	0.407620	+	0.913151i	$0.366359\pi$
$439$	−12.2991	+	21.3026i	−0.587002	+	1.01672i	−0.994623	+	0.103566i	$0.966975\pi$
$440$	−2.32858	+	29.9428i	−0.111011	+	1.42747i
$441$		0			0
$442$	−0.180454	−	0.555382i	−0.00858334	−	0.0264168i
$443$	−14.7328	+	6.55945i	−0.699975	+	0.311649i	−0.725691	−	0.688020i	$-0.758480\pi$
$443$	−14.7328	+	6.55945i	−0.699975	+	0.311649i	0.0257164	+	0.999669i	$0.491813\pi$
$444$	−26.5151	−	11.8053i	−1.25835	−	0.560253i
$445$	4.97452	−	1.05737i	0.235815	−	0.0501240i
$446$	21.2641	+	23.6161i	1.00688	+	1.11826i
$447$	8.99109	−	6.53241i	0.425264	−	0.308972i
$448$		0			0
$449$	10.6496	+	32.7763i	0.502588	+	1.54681i	0.804788	+	0.593562i	$0.202279\pi$
$449$	10.6496	+	32.7763i	0.502588	+	1.54681i	−0.302200	+	0.953245i	$0.597721\pi$
$450$	9.03745	−	15.6533i	0.426029	−	0.737905i
$451$	18.6855	+	19.6538i	0.879866	+	0.925463i
$452$	−8.71507	−	15.0950i	−0.409923	−	0.710007i
$453$	−18.1822	−	3.86475i	−0.854275	−	0.181582i
$454$	−21.9867	−	15.9743i	−1.03189	−	0.749710i
$455$		0			0
$456$	−10.1416	+	31.2126i	−0.474923	+	1.46166i
$457$	−21.7120	−	24.1137i	−1.01565	−	1.12799i	−0.991739	−	0.128275i	$-0.959056\pi$
$457$	−21.7120	−	24.1137i	−1.01565	−	1.12799i	−0.0239074	−	0.999714i	$-0.507611\pi$
$458$	66.2571	+	29.4996i	3.09599	+	1.37842i
$459$	1.55048	−	14.7518i	0.0723701	−	0.688555i
$460$	−11.5786	−	2.46110i	−0.539853	−	0.114749i
$461$	29.4973			1.37383			0.686914	−	0.726739i	$-0.258965\pi$
$461$	29.4973			1.37383			0.686914	+	0.726739i	$0.258965\pi$
$462$		0			0
$463$	22.2588			1.03445			0.517227	−	0.855848i	$-0.326964\pi$
$463$	22.2588			1.03445			0.517227	+	0.855848i	$0.326964\pi$
$464$	50.6786	+	10.7721i	2.35269	+	0.500081i
$465$	0.770839	−	7.33405i	0.0357468	−	0.340108i
$466$	9.61670	+	4.28163i	0.445485	+	0.198343i
$467$	−15.8303	−	17.5813i	−0.732539	−	0.813567i	0.255656	−	0.966768i	$-0.417708\pi$
$467$	−15.8303	−	17.5813i	−0.732539	−	0.813567i	−0.988195	+	0.153201i	$0.951042\pi$
$468$	−0.105357	+	0.324256i	−0.00487013	+	0.0149887i
$469$		0			0
$470$	7.99916	+	5.81173i	0.368974	+	0.268075i
$471$	−32.3609	−	6.87852i	−1.49111	−	0.316945i
$472$	15.6255	+	27.0641i	0.719220	+	1.24573i
$473$	9.68172	+	1.78511i	0.445166	+	0.0820793i
$474$	9.04079	−	15.6591i	0.415257	−	0.719247i
$475$	2.15239	+	6.62436i	0.0987582	+	0.303946i
$476$		0			0
$477$	15.2338	−	11.0680i	0.697508	−	0.506769i
$478$	37.3724	+	41.5062i	1.70937	+	1.89845i
$479$	−11.3019	+	2.40230i	−0.516399	+	0.109764i	−0.458737	−	0.888572i	$-0.651698\pi$
$479$	−11.3019	+	2.40230i	−0.516399	+	0.109764i	−0.0576623	+	0.998336i	$0.518365\pi$
$480$	28.5231	+	12.6993i	1.30190	+	0.579641i
$481$	0.0886444	−	0.0394670i	0.00404184	−	0.00179954i
$482$	11.0648	+	34.0541i	0.503989	+	1.55112i
$483$		0			0
$484$	38.3799	+	38.2376i	1.74454	+	1.73807i
$485$	2.72676	−	4.72289i	0.123816	−	0.214455i
$486$	−30.3569	+	33.7147i	−1.37701	+	1.52933i
$487$	−0.0137727	+	0.131038i	−0.000624101	+	0.00593792i	−0.994830	−	0.101559i	$-0.967617\pi$
$487$	−0.0137727	+	0.131038i	−0.000624101	+	0.00593792i	0.994205	+	0.107497i	$0.0342836\pi$
$488$	−6.98311	−	66.4398i	−0.316110	−	3.00759i
$489$	1.70221	−	5.23885i	0.0769764	−	0.236909i
$490$		0			0
$491$	0.0180456	−	0.0131109i	0.000814388	−	0.000591687i	−0.587378	−	0.809313i	$-0.699840\pi$
$491$	0.0180456	−	0.0131109i	0.000814388	−	0.000591687i	0.588192	+	0.808721i	$0.299840\pi$
$492$	81.4317	−	36.2557i	3.67122	−	1.63453i
$493$	−20.2828	+	22.5263i	−0.913491	+	1.01453i
$494$	−0.0923681	−	0.159986i	−0.00415584	−	0.00719812i
$495$	2.48015	+	6.98311i	0.111474	+	0.313868i
$496$	−29.4743			−1.32343
$497$		0			0
$498$	28.6054	+	20.7831i	1.28184	+	0.931312i
$499$	0.724289	+	6.89115i	0.0324236	+	0.308490i	0.998700	+	0.0509816i	$0.0162350\pi$
$499$	0.724289	+	6.89115i	0.0324236	+	0.308490i	−0.966276	+	0.257509i	$0.917098\pi$
$500$	48.8292	−	10.3790i	2.18371	−	0.464161i
$501$	−26.6425	+	5.66303i	−1.19030	+	0.253006i
$502$	−4.54256	−	43.2195i	−0.202744	−	1.92898i
$503$	−6.79200	−	4.93468i	−0.302840	−	0.220026i	0.425978	−	0.904734i	$-0.359930\pi$
$503$	−6.79200	−	4.93468i	−0.302840	−	0.220026i	−0.728818	+	0.684707i	$0.759930\pi$
$504$		0			0
$505$	20.0115			0.890502
$506$	−14.1370	+	10.8686i	−0.628468	+	0.483168i
$507$	14.3860	+	24.9172i	0.638903	+	1.10661i
$508$	−64.9621	+	72.1477i	−2.88223	+	3.20104i
$509$	1.13266	−	0.504291i	0.0502041	−	0.0223523i	−0.381481	−	0.924377i	$-0.624586\pi$
$509$	1.13266	−	0.504291i	0.0502041	−	0.0223523i	0.431685	+	0.902024i	$0.357919\pi$
$510$	−33.7522	+	24.5224i	−1.49457	+	1.08587i
$511$		0			0
$512$	−10.9487	+	33.6967i	−0.483869	+	1.48920i
$513$	−0.490492	−	4.66672i	−0.0216558	−	0.206041i
$514$	8.04685	−	76.5607i	0.354931	−	3.37695i
$515$	13.2647	−	14.7319i	0.584513	−	0.649167i
$516$	16.1799	−	28.0245i	0.712282	−	1.23371i
$517$	10.2983	−	2.48250i	0.452917	−	0.109180i
$518$		0			0
$519$	−8.34818	−	25.6930i	−0.366444	−	1.12780i
$520$	−0.301499	+	0.134236i	−0.0132216	+	0.00588663i
$521$	−39.9641	−	17.7932i	−1.75086	−	0.779532i	−0.991692	−	0.128635i	$-0.958940\pi$
$521$	−39.9641	−	17.7932i	−1.75086	−	0.779532i	−0.759166	−	0.650897i	$-0.774393\pi$
$522$	24.3403	−	5.17370i	1.06535	−	0.226447i
$523$	20.4158	+	22.6740i	0.892721	+	0.991467i	0.999996	−	0.00276239i	$-0.000879296\pi$
$523$	20.4158	+	22.6740i	0.892721	+	0.991467i	−0.107275	+	0.994229i	$0.534213\pi$
$524$	−64.4848	+	46.8510i	−2.81703	+	2.04669i
$525$		0			0
$526$	−16.2087	−	49.8853i	−0.706734	−	2.17510i
$527$	8.62204	−	14.9338i	0.375582	−	0.650527i
$528$	68.9264	−	32.9548i	2.99964	−	1.43417i
$529$	9.41287	+	16.3036i	0.409255	+	0.708851i
$530$	30.0192	+	6.38078i	1.30395	+	0.277163i
$531$	6.23827	+	4.53237i	0.270718	+	0.196688i
$532$		0			0
$533$	−0.0920882	+	0.283418i	−0.00398878	+	0.0122762i
$534$	−16.8502	−	18.7140i	−0.729178	−	0.809834i
$535$	−1.00226	−	0.446234i	−0.0433314	−	0.0192924i
$536$	−1.81315	+	17.2510i	−0.0783161	+	0.745128i
$537$	−8.25746	−	1.75518i	−0.356336	−	0.0757415i
$538$	−1.62815			−0.0701944
$539$		0			0
$540$	−14.1147			−0.607399
$541$	−0.277681	−	0.0590230i	−0.0119384	−	0.00253760i	0.201939	−	0.979398i	$-0.435276\pi$
$541$	−0.277681	−	0.0590230i	−0.0119384	−	0.00253760i	−0.213877	+	0.976861i	$0.568609\pi$
$542$	−0.0318553	+	0.303083i	−0.00136830	+	0.0130185i
$543$	−14.2433	−	6.34153i	−0.611239	−	0.272141i
$544$	48.8527	+	54.2564i	2.09454	+	2.32622i
$545$	0.590198	−	1.81644i	0.0252813	−	0.0778078i
$546$		0			0
$547$	−8.71258	−	6.33006i	−0.372523	−	0.270654i	0.385733	−	0.922610i	$-0.373948\pi$
$547$	−8.71258	−	6.33006i	−0.372523	−	0.270654i	−0.758256	+	0.651957i	$0.773948\pi$
$548$	81.7844	+	17.3838i	3.49365	+	0.742599i
$549$	−8.24192	−	14.2754i	−0.351756	−	0.609260i
$550$	15.0342	−	27.7510i	0.641063	−	1.18331i
$551$	−4.79461	+	8.30452i	−0.204257	+	0.353784i
$552$	10.7574	+	33.1080i	0.457867	+	1.40917i
$553$		0			0
$554$	−20.5738	+	14.9478i	−0.874098	+	0.635070i
$555$	−4.63865	−	5.15174i	−0.196900	−	0.218679i
$556$	−35.3942	+	7.52326i	−1.50105	+	0.319057i
$557$	36.4980	+	16.2499i	1.54647	+	0.688532i	0.989834	−	0.142225i	$-0.0454258\pi$
$557$	36.4980	+	16.2499i	1.54647	+	0.688532i	0.556634	+	0.830758i	$0.312092\pi$
$558$	−12.9323	+	5.75783i	−0.547467	+	0.243748i
$559$	0.0334309	+	0.102890i	0.00141398	+	0.00435177i
$560$		0			0
$561$	−3.46559	+	44.5633i	−0.146317	+	1.88146i
$562$	4.55716	−	7.89323i	0.192232	−	0.332956i
$563$	7.99139	−	8.87534i	0.336797	−	0.374051i	−0.550827	−	0.834619i	$-0.685688\pi$
$563$	7.99139	−	8.87534i	0.336797	−	0.374051i	0.887624	+	0.460568i	$0.152354\pi$
$564$	3.63964	−	34.6289i	0.153257	−	1.45814i
$565$	−0.435165	−	4.14031i	−0.0183075	−	0.174184i
$566$	−21.4193	+	65.9217i	−0.900319	+	2.77090i
$567$		0			0
$568$	−26.4779	+	19.2374i	−1.11099	+	0.807181i
$569$	−10.0266	+	4.46414i	−0.420337	+	0.187146i	−0.605995	−	0.795468i	$-0.707225\pi$
$569$	−10.0266	+	4.46414i	−0.420337	+	0.187146i	0.185658	+	0.982614i	$0.440558\pi$
$570$	−8.83125	+	9.80810i	−0.369901	+	0.410816i
$571$	−3.74628	−	6.48874i	−0.156777	−	0.271545i	0.776928	−	0.629590i	$-0.216777\pi$
$571$	−3.74628	−	6.48874i	−0.156777	−	0.271545i	−0.933705	+	0.358044i	$0.883444\pi$
$572$	−0.168557	+	0.570984i	−0.00704771	+	0.0238740i
$573$	−35.2515			−1.47265
$574$		0			0
$575$	5.97720	+	4.34269i	0.249267	+	0.181103i
$576$	−2.13258	−	20.2902i	−0.0888576	−	0.845424i
$577$	−35.0599	+	7.45221i	−1.45956	+	0.310240i	−0.868220	−	0.496180i	$-0.834736\pi$
$577$	−35.0599	+	7.45221i	−1.45956	+	0.310240i	−0.591343	+	0.806420i	$0.701402\pi$
$578$	−51.6654	+	10.9818i	−2.14900	+	0.456783i
$579$	−3.42374	−	32.5747i	−0.142286	−	1.35376i
$580$	23.3354	+	16.9541i	0.968948	+	0.703982i
$581$		0			0
$582$	−27.0037			−1.11934
$583$	26.0672	−	20.0405i	1.07959	−	0.829994i
$584$	16.5216	+	28.6162i	0.683668	+	1.18415i
$585$	−0.0544891	+	0.0605163i	−0.00225285	+	0.00250204i
$586$	−36.7585	+	16.3659i	−1.51848	+	0.676071i
$587$	8.11634	−	5.89686i	0.334997	−	0.243390i	−0.407551	−	0.913182i	$-0.633617\pi$
$587$	8.11634	−	5.89686i	0.334997	−	0.243390i	0.742548	+	0.669793i	$0.233617\pi$
$588$		0			0
$589$	1.68574	−	5.18816i	0.0694595	−	0.213774i
$590$	1.31367	+	12.4987i	0.0540828	+	0.514564i
$591$	−1.91760	+	18.2448i	−0.0788797	+	0.750490i
$592$	−18.5398	+	20.5906i	−0.761982	+	0.846267i
$593$	14.1715	−	24.5458i	0.581954	−	1.00797i	−0.413293	−	0.910598i	$-0.635622\pi$
$593$	14.1715	−	24.5458i	0.581954	−	1.00797i	0.995248	−	0.0973765i	$-0.0310451\pi$
$594$	−13.7941	+	16.1812i	−0.565980	+	0.663924i
$595$		0			0
$596$	−7.64167	−	23.5186i	−0.313015	−	0.963361i
$597$	−36.9727	+	16.4613i	−1.51319	+	0.673716i
$598$	−0.179013	−	0.0797018i	−0.00732039	−	0.00325925i
$599$	−32.6564	+	6.94133i	−1.33430	+	0.283615i	−0.819197	−	0.573512i	$-0.805581\pi$
$599$	−32.6564	+	6.94133i	−1.33430	+	0.283615i	−0.515106	+	0.857127i	$0.672247\pi$
$600$	−41.2285	−	45.7889i	−1.68315	−	1.86932i
$601$	−1.42697	+	1.03676i	−0.0582074	+	0.0422901i	−0.616508	−	0.787348i	$-0.711453\pi$
$601$	−1.42697	+	1.03676i	−0.0582074	+	0.0422901i	0.558301	+	0.829638i	$0.311453\pi$
$602$		0			0
$603$	1.32259	+	4.07052i	0.0538601	+	0.165764i
$604$	−20.6806	+	35.8199i	−0.841482	+	1.45749i
$605$	4.65967	+	12.0718i	0.189443	+	0.490790i
$606$	−49.5446	−	85.8138i	−2.01261	−	3.48595i
$607$	−13.9937	−	2.97445i	−0.567985	−	0.120729i	−0.0850370	−	0.996378i	$-0.527101\pi$
$607$	−13.9937	−	2.97445i	−0.567985	−	0.120729i	−0.482948	+	0.875649i	$0.660434\pi$
$608$	18.6854	+	13.5757i	0.757792	+	0.550568i
$609$		0			0
$610$	8.30204	−	25.5510i	0.336140	−	1.03453i
$611$	0.0778921	+	0.0865080i	0.00315118	+	0.00349974i
$612$	52.0333	+	23.1667i	2.10332	+	0.936459i
$613$	0.595783	−	5.66850i	0.0240634	−	0.228948i	−0.975880	−	0.218308i	$-0.929946\pi$
$613$	0.595783	−	5.66850i	0.0240634	−	0.228948i	0.999943	−	0.0106405i	$-0.00338703\pi$
$614$	82.7848	+	17.5964i	3.34092	+	0.710135i
$615$	21.2903			0.858506
$616$		0			0
$617$	17.9653			0.723257			0.361628	−	0.932322i	$-0.382221\pi$
$617$	17.9653			0.723257			0.361628	+	0.932322i	$0.382221\pi$
$618$	−96.0146	−	20.4085i	−3.86227	−	0.820952i
$619$	0.636885	−	6.05956i	0.0255986	−	0.243554i	−0.974239	−	0.225519i	$-0.927592\pi$
$619$	0.636885	−	6.05956i	0.0255986	−	0.243554i	0.999837	−	0.0180353i	$-0.00574111\pi$
$620$	−14.9903	−	6.67411i	−0.602025	−	0.268039i
$621$	−3.33051	−	3.69891i	−0.133649	−	0.148432i
$622$	−1.72257	+	5.30152i	−0.0690688	+	0.212572i
$623$		0			0
$624$	0.679206	+	0.493472i	0.0271900	+	0.0197547i
$625$	−6.02315	−	1.28026i	−0.240926	−	0.0512104i
$626$	−8.07689	−	13.9896i	−0.322817	−	0.559136i
$627$	1.85867	+	14.0174i	0.0742281	+	0.559803i
$628$	−36.8076	+	63.7526i	−1.46878	+	2.54400i
$629$	−5.00926	−	15.4169i	−0.199732	−	0.614713i
$630$		0			0
$631$	−35.8264	+	26.0294i	−1.42623	+	1.03621i	−0.435522	+	0.900178i	$0.643436\pi$
$631$	−35.8264	+	26.0294i	−1.42623	+	1.03621i	−0.990704	+	0.136036i	$0.956564\pi$
$632$	−15.9893	−	17.7579i	−0.636018	−	0.706370i
$633$	−51.1050	+	10.8627i	−2.03124	+	0.431754i
$634$	−42.7296	−	19.0244i	−1.69701	−	0.755556i
$635$	−21.1835	+	9.43149i	−0.840641	+	0.374277i
$636$	−33.3975	−	102.787i	−1.32430	−	4.07577i
$637$		0			0
$638$	42.2418	−	10.1828i	1.67237	−	0.403143i
$639$	−4.03776	+	6.99361i	−0.159731	+	0.276663i
$640$	3.37263	−	3.74569i	0.133315	−	0.148061i
$641$	−4.00363	+	38.0920i	−0.158134	+	1.50454i	0.571441	+	0.820643i	$0.306385\pi$
$641$	−4.00363	+	38.0920i	−0.158134	+	1.50454i	−0.729575	+	0.683901i	$0.760282\pi$
$642$	0.567846	+	5.40269i	0.0224111	+	0.213227i
$643$	8.87538	−	27.3156i	0.350011	−	1.07722i	−0.608835	−	0.793297i	$-0.708363\pi$
$643$	8.87538	−	27.3156i	0.350011	−	1.07722i	0.958846	−	0.283926i	$-0.0916371\pi$
$644$		0			0
$645$	6.25291	−	4.54301i	0.246208	−	0.178881i
$646$	−28.1937	+	12.5527i	−1.10927	+	0.493878i
$647$	13.6948	−	15.2096i	0.538399	−	0.597953i	−0.411152	−	0.911567i	$-0.634873\pi$
$647$	13.6948	−	15.2096i	0.538399	−	0.597953i	0.949550	+	0.313614i	$0.101540\pi$
$648$	42.6862	+	73.9346i	1.67687	+	2.90443i
$649$	11.1036	+	7.61612i	0.435854	+	0.298959i
$650$	0.346829			0.0136038
$651$		0			0
$652$	−9.91604	−	7.20442i	−0.388342	−	0.282147i
$653$	−2.95381	−	28.1036i	−0.115591	−	1.09978i	−0.886467	−	0.462793i	$-0.846847\pi$
$653$	−2.95381	−	28.1036i	−0.115591	−	1.09978i	0.770875	−	0.636986i	$-0.219819\pi$
$654$	−9.25052	+	1.96626i	−0.361724	+	0.0768868i
$655$	−18.6218	+	3.95819i	−0.727615	+	0.154659i
$656$	−8.89467	−	84.6271i	−0.347279	−	3.30413i
$657$	6.59604	+	4.79231i	0.257336	+	0.186966i
$658$		0			0
$659$	25.1666			0.980350			0.490175	−	0.871624i	$-0.336933\pi$
$659$	25.1666			0.980350			0.490175	+	0.871624i	$0.336933\pi$
$660$	42.5174	−	1.15285i	1.65499	−	0.0448747i
$661$	10.3561	+	17.9373i	0.402805	+	0.697679i	0.994063	−	0.108803i	$-0.0347018\pi$
$661$	10.3561	+	17.9373i	0.402805	+	0.697679i	−0.591258	+	0.806483i	$0.701368\pi$
$662$	34.4526	−	38.2635i	1.33904	−	1.48715i
$663$	−0.448715	+	0.199781i	−0.0174266	+	0.00775884i
$664$	37.8033	−	27.4657i	1.46705	−	1.06588i
$665$		0			0
$666$	−4.11224	+	12.6562i	−0.159346	+	0.490417i
$667$	1.06321	+	10.1158i	0.0411678	+	0.391686i
$668$	−6.33513	+	60.2747i	−0.245114	+	2.33210i
$669$	17.8855	−	19.8639i	0.691493	−	0.767981i
$670$	−3.48785	+	6.04113i	−0.134747	+	0.233389i
$671$	−15.0621	−	24.5280i	−0.581467	−	0.946895i
$672$		0			0
$673$	−6.06417	−	18.6636i	−0.233757	−	0.719429i	−0.997284	−	0.0736535i	$-0.976534\pi$
$673$	−6.06417	−	18.6636i	−0.233757	−	0.719429i	0.763527	−	0.645776i	$-0.223466\pi$
$674$	55.4480	−	24.6870i	2.13578	−	0.950909i
$675$	8.04806	+	3.58323i	0.309770	+	0.137919i
$676$	62.6216	−	13.3106i	2.40852	−	0.511948i
$677$	−15.2531	−	16.9403i	−0.586226	−	0.651070i	0.374938	−	0.927050i	$-0.377664\pi$
$677$	−15.2531	−	16.9403i	−0.586226	−	0.651070i	−0.961163	+	0.275981i	$0.910997\pi$
$678$	−16.6772	+	12.1167i	−0.640484	+	0.465339i
$679$		0			0
$680$	17.0376	+	52.4363i	0.653361	+	2.01084i
$681$	−11.4295	+	19.7965i	−0.437980	+	0.758603i
$682$	−22.3011	+	10.6625i	−0.853955	+	0.408289i
$683$	11.9753	+	20.7418i	0.458222	+	0.793664i	0.998867	−	0.0475871i	$-0.0151532\pi$
$683$	11.9753	+	20.7418i	0.458222	+	0.793664i	−0.540645	+	0.841251i	$0.681820\pi$
$684$	17.6247	+	3.74625i	0.673899	+	0.143242i
$685$	16.1563	+	11.7382i	0.617300	+	0.448495i
$686$		0			0
$687$	18.8512	−	58.0181i	0.719219	−	2.21353i
$688$	−20.6704	−	22.9569i	−0.788053	−	0.875222i
$689$	0.330081	+	0.146962i	0.0125751	+	0.00559879i
$690$	−1.46335	+	13.9229i	−0.0557089	+	0.530034i
$691$	40.0438	+	8.51156i	1.52334	+	0.323795i	0.892115	−	0.451808i	$-0.149221\pi$
$691$	40.0438	+	8.51156i	1.52334	+	0.323795i	0.631221	+	0.775603i	$0.282554\pi$
$692$	−60.1119			−2.28511
$693$		0			0
$694$	−65.8980			−2.50145
$695$	−8.45376	−	1.79690i	−0.320669	−	0.0681603i
$696$	8.86681	−	84.3621i	0.336096	−	3.19774i
$697$	45.4802	+	20.2491i	1.72268	+	0.766989i
$698$	−34.4591	−	38.2707i	−1.30430	−	1.44857i
$699$	2.73611	−	8.42088i	0.103489	−	0.318507i
$700$		0			0
$701$	−8.05784	−	5.85436i	−0.304340	−	0.221116i	0.425124	−	0.905135i	$-0.360231\pi$
$701$	−8.05784	−	5.85436i	−0.304340	−	0.221116i	−0.729464	+	0.684019i	$0.760231\pi$
$702$	−0.228549	−	0.0485797i	−0.00862604	−	0.00183352i
$703$	−2.56406	−	4.44108i	−0.0967054	−	0.167499i
$704$	−4.68281	−	35.3161i	−0.176490	−	1.33103i
$705$	4.15826	−	7.20232i	0.156609	−	0.271255i
$706$	−16.4487	−	50.6240i	−0.619057	−	1.90526i
$707$		0			0
$708$	35.8052	−	26.0140i	1.34564	−	0.977665i
$709$	−31.7961	−	35.3132i	−1.19413	−	1.32621i	−0.932554	−	0.361031i	$-0.882425\pi$
$709$	−31.7961	−	35.3132i	−1.19413	−	1.32621i	−0.261574	−	0.965183i	$-0.584242\pi$
$710$	−12.8742	+	2.73649i	−0.483159	+	0.102699i
$711$	−5.38631	−	2.39814i	−0.202002	−	0.0899373i
$712$	−30.4021	+	13.5359i	−1.13937	+	0.507279i
$713$	−1.78810	−	5.50321i	−0.0669649	−	0.206097i
$714$		0			0
$715$	−0.0922481	+	0.108212i	−0.00344988	+	0.00404689i
$716$	−9.39211	+	16.2676i	−0.351000	+	0.607949i
$717$	31.4344	−	34.9115i	1.17394	−	1.30379i
$718$	6.85574	−	65.2280i	0.255854	−	2.43429i
$719$	2.06385	+	19.6362i	0.0769686	+	0.732307i	0.963149	+	0.268968i	$0.0866824\pi$
$719$	2.06385	+	19.6362i	0.0769686	+	0.732307i	−0.886181	+	0.463340i	$0.846651\pi$
$720$	7.18547	−	22.1146i	0.267787	−	0.824162i
$721$		0			0
$722$	32.5522	−	23.6506i	1.21147	−	0.880182i
$723$	27.5136	−	12.2499i	1.02324	−	0.455577i
$724$	−23.2136	+	25.7813i	−0.862727	+	0.958155i
$725$	−9.00155	−	15.5911i	−0.334309	−	0.579040i
$726$	40.2302	−	49.8692i	1.49308	−	1.85082i
$727$	−38.0241			−1.41024			−0.705118	−	0.709090i	$-0.749106\pi$
$727$	−38.0241			−1.41024			−0.705118	+	0.709090i	$0.749106\pi$
$728$		0			0
$729$	3.95434	+	2.87300i	0.146457	+	0.106407i
$730$	1.38901	+	13.2155i	0.0514095	+	0.489129i
$731$	17.6783	−	3.75763i	0.653855	−	0.138981i
$732$	−92.5431	+	19.6706i	−3.42049	+	0.727048i
$733$	2.99094	+	28.4569i	0.110473	+	1.05108i	0.899559	+	0.436798i	$0.143888\pi$
$733$	2.99094	+	28.4569i	0.110473	+	1.05108i	−0.789086	+	0.614282i	$0.789446\pi$
$734$	15.9450	+	11.5847i	0.588542	+	0.427601i
$735$		0			0
$736$	24.4989			0.903042
$737$	2.50127	+	7.04260i	0.0921356	+	0.259417i
$738$	−20.4346	−	35.3938i	−0.752210	−	1.30287i
$739$	6.06096	−	6.73137i	0.222956	−	0.247618i	−0.621281	−	0.783588i	$-0.713387\pi$
$739$	6.06096	−	6.73137i	0.222956	−	0.247618i	0.844237	+	0.535970i	$0.180054\pi$
$740$	−14.0916	+	6.27400i	−0.518019	+	0.230637i
$741$	−0.125709	+	0.0913326i	−0.00461802	+	0.00335519i
$742$		0			0
$743$	2.57977	−	7.93973i	0.0946427	−	0.291280i	−0.892518	−	0.451012i	$-0.851063\pi$
$743$	2.57977	−	7.93973i	0.0946427	−	0.291280i	0.987160	+	0.159732i	$0.0510630\pi$
$744$	5.04418	+	47.9922i	0.184929	+	1.75948i
$745$	0.617388	−	5.87406i	0.0226194	−	0.215209i
$746$	−2.82615	+	3.13875i	−0.103473	+	0.114918i
$747$	5.76482	−	9.98496i	0.210924	−	0.365331i
$748$	91.9221	+	37.9754i	3.36100	+	1.38852i
$749$		0			0
$750$	−18.2441	−	56.1495i	−0.666179	−	2.05029i
$751$	44.9611	−	20.0180i	1.64065	−	0.730466i	0.641330	−	0.767265i	$-0.278383\pi$
$751$	44.9611	−	20.0180i	1.64065	−	0.730466i	0.999323	+	0.0367995i	$0.0117163\pi$
$752$	−30.3659	−	13.5198i	−1.10733	−	0.493015i
$753$	−35.7541	+	7.59976i	−1.30295	+	0.276951i
$754$	0.319501	+	0.354842i	0.0116356	+	0.0129226i
$755$	−7.99225	+	5.80671i	−0.290868	+	0.211328i
$756$		0			0
$757$	6.92221	+	21.3044i	0.251592	+	0.774320i	0.994482	+	0.104907i	$0.0334545\pi$
$757$	6.92221	+	21.3044i	0.251592	+	0.774320i	−0.742890	+	0.669413i	$0.766546\pi$
$758$	−22.4292	+	38.8485i	−0.814665	+	1.41104i
$759$	10.3346	+	10.8702i	0.375122	+	0.394562i
$760$	8.72092	+	15.1051i	0.316341	+	0.547919i
$761$	−24.8315	−	5.27809i	−0.900140	−	0.191331i	−0.265474	−	0.964118i	$-0.585529\pi$
$761$	−24.8315	−	5.27809i	−0.900140	−	0.191331i	−0.634665	+	0.772787i	$0.718862\pi$
$762$	92.8905	+	67.4889i	3.36507	+	2.44486i
$763$		0			0
$764$	−24.2388	+	74.5993i	−0.876928	+	2.69891i
$765$	9.10291	+	10.1098i	0.329116	+	0.365521i
$766$	41.8837	+	18.6478i	1.51332	+	0.673774i
$767$	−0.0154661	+	0.147150i	−0.000558449	+	0.00531329i
$768$	22.0998	+	4.69746i	0.797458	+	0.169505i
$769$	44.5582			1.60681			0.803406	−	0.595432i	$-0.203019\pi$
$769$	44.5582			1.60681			0.803406	+	0.595432i	$0.203019\pi$
$770$		0			0
$771$	−64.7510			−2.33195
$772$	−71.2887	−	15.1529i	−2.56574	−	0.545364i
$773$	3.45360	−	32.8588i	0.124217	−	1.18185i	−0.737818	−	0.675000i	$-0.764144\pi$
$773$	3.45360	−	32.8588i	0.124217	−	1.18185i	0.862035	−	0.506848i	$-0.169190\pi$
$774$	−13.5541	−	6.03468i	−0.487192	−	0.216912i
$775$	6.85301	+	7.61104i	0.246167	+	0.273397i
$776$	−11.0277	+	33.9399i	−0.395873	+	1.21837i
$777$		0			0
$778$	23.9204	+	17.3792i	0.857589	+	0.623075i
$779$	15.4051	+	3.27445i	0.551943	+	0.117319i
$780$	0.233696	+	0.404772i	0.00836764	+	0.0144932i
$781$	−6.71702	+	12.3986i	−0.240354	+	0.443658i
$782$	−16.3680	+	28.3502i	−0.585318	+	1.01380i
$783$	3.74792	+	11.5349i	0.133940	+	0.412224i
$784$		0			0
$785$	−14.2247	+	10.3348i	−0.507701	+	0.368866i
$786$	63.0776	+	70.0547i	2.24990	+	2.49877i
$787$	42.2344	−	8.97720i	1.50549	−	0.320003i	0.619981	−	0.784617i	$-0.287140\pi$
$787$	42.2344	−	8.97720i	1.50549	−	0.320003i	0.885513	+	0.464615i	$0.153807\pi$
$788$	37.2911	+	16.6031i	1.32844	+	0.591460i
$789$	−40.3043	+	17.9446i	−1.43487	+	0.638846i
$790$	−2.96953	−	9.13927i	−0.105651	−	0.325161i
$791$		0			0
$792$	−25.3755	−	41.3229i	−0.901679	−	1.46835i
$793$	0.158150	−	0.273923i	0.00561606	−	0.00972729i
$794$	−34.7039	+	38.5425i	−1.23159	+	1.36782i
$795$	2.69827	−	25.6723i	0.0956976	−	0.910502i
$796$	9.41318	+	89.5604i	0.333641	+	3.17439i
$797$	3.31341	−	10.1976i	0.117367	−	0.361218i	−0.875066	−	0.484003i	$-0.839182\pi$
$797$	3.31341	−	10.1976i	0.117367	−	0.361218i	0.992433	+	0.122785i	$0.0391825\pi$
$798$		0			0
$799$	15.7330	−	11.4307i	0.556592	−	0.404388i
$800$	−39.6130	+	17.6369i	−1.40053	+	0.623557i
$801$	−5.49451	+	6.10227i	−0.194139	+	0.215613i
$802$	16.4977	+	28.5748i	0.582553	+	1.00901i
$803$	11.7404	+	8.05291i	0.414309	+	0.284181i
$804$	24.5654			0.866356
$805$		0			0
$806$	−0.219757	−	0.159663i	−0.00774061	−	0.00562388i
$807$	0.143147	+	1.36196i	0.00503902	+	0.0479431i
$808$	−128.089	+	27.2262i	−4.50616	+	0.957813i
$809$	1.12546	−	0.239224i	0.0395690	−	0.00841066i	−0.188085	−	0.982153i	$-0.560228\pi$
$809$	1.12546	−	0.239224i	0.0395690	−	0.00841066i	0.227654	+	0.973742i	$0.426895\pi$
$810$	3.58872	+	34.1444i	0.126095	+	1.19971i
$811$	−28.6938	−	20.8473i	−1.00758	−	0.732047i	−0.0438772	−	0.999037i	$-0.513971\pi$
$811$	−28.6938	−	20.8473i	−1.00758	−	0.732047i	−0.963699	+	0.266990i	$0.913971\pi$
$812$		0			0
$813$	0.256331			0.00898993
$814$	−6.57902	+	22.2864i	−0.230595	+	0.781136i
$815$	−1.46375	−	2.53530i	−0.0512731	−	0.0888076i
$816$	93.8479	−	104.229i	3.28533	−	3.64873i
$817$	5.22315	−	2.32550i	0.182735	−	0.0813588i
$818$	33.2244	−	24.1389i	1.16166	−	0.843997i
$819$		0			0
$820$	14.6391	−	45.0545i	0.511220	−	1.57337i
$821$	−2.06152	−	19.6140i	−0.0719475	−	0.684535i	−0.969744	−	0.244124i	$-0.921500\pi$
$821$	−2.06152	−	19.6140i	−0.0719475	−	0.684535i	0.897796	−	0.440411i	$-0.145167\pi$
$822$	10.3363	−	98.3432i	0.360519	−	3.43011i
$823$	27.3181	−	30.3398i	0.952248	−	1.05758i	−0.0460316	−	0.998940i	$-0.514658\pi$
$823$	27.3181	−	30.3398i	0.952248	−	1.05758i	0.998279	−	0.0586382i	$-0.0186758\pi$
$824$	−64.8610	+	112.343i	−2.25954	+	3.91364i
$825$	−24.5357	−	10.1364i	−0.854225	−	0.352903i
$826$		0			0
$827$	−0.289657	−	0.891474i	−0.0100724	−	0.0309996i	0.945894	−	0.324476i	$-0.105188\pi$
$827$	−0.289657	−	0.891474i	−0.0100724	−	0.0309996i	−0.955966	+	0.293476i	$0.905188\pi$
$828$	17.4603	−	7.77382i	0.606787	−	0.270159i
$829$	13.9732	+	6.22128i	0.485310	+	0.216074i	0.634781	−	0.772692i	$-0.281090\pi$
$829$	13.9732	+	6.22128i	0.485310	+	0.216074i	−0.149471	+	0.988766i	$0.547757\pi$
$830$	18.3808	−	3.90696i	0.638007	−	0.135612i
$831$	14.3128	+	15.8959i	0.496504	+	0.551424i
$832$	0.316715	−	0.230107i	0.0109801	−	0.00797753i
$833$		0			0
$834$	13.2243	+	40.7003i	0.457921	+	1.40934i
$835$	−7.23784	+	12.5363i	−0.250476	+	0.433837i
$836$	30.9418	+	5.70501i	1.07014	+	0.197312i
$837$	−3.44985	−	5.97532i	−0.119244	−	0.206537i
$838$	−81.9024	−	17.4089i	−2.82927	−	0.601380i
$839$	11.3598	+	8.25338i	0.392184	+	0.284938i	0.766350	−	0.642423i	$-0.222071\pi$
$839$	11.3598	+	8.25338i	0.392184	+	0.284938i	−0.374166	+	0.927362i	$0.622071\pi$
$840$		0			0
$841$	−1.30243	+	4.00846i	−0.0449113	+	0.138223i
$842$	42.0517	+	46.7032i	1.44920	+	1.60950i
$843$	−7.00340	−	3.11812i	−0.241210	−	0.107394i
$844$	−12.1519	+	115.618i	−0.418286	+	3.97972i
$845$	14.9569	+	3.17919i	0.514534	+	0.109368i
$846$	−15.9646			−0.548874
$847$		0			0
$848$	−103.173			−3.54296
$849$	57.0271	+	12.1215i	1.95717	+	0.416009i
$850$	6.05648	−	57.6236i	0.207736	−	1.97647i
$851$	−4.96925	−	2.21245i	−0.170344	−	0.0758420i
$852$	31.0144	+	34.4449i	1.06253	+	1.18006i
$853$	−1.13225	+	3.48472i	−0.0387677	+	0.119315i	−0.968567	−	0.248751i	$-0.919980\pi$
$853$	−1.13225	+	3.48472i	−0.0387677	+	0.119315i	0.929800	+	0.368066i	$0.119980\pi$
$854$		0			0
$855$	3.48172	+	2.52962i	0.119072	+	0.0865111i
$856$	7.02232	+	1.49264i	0.240018	+	0.0510174i
$857$	2.52090	+	4.36633i	0.0861124	+	0.149151i	0.905865	−	0.423567i	$-0.139222\pi$
$857$	2.52090	+	4.36633i	0.0861124	+	0.149151i	−0.819752	+	0.572718i	$0.805889\pi$
$858$	0.692424	+	0.127669i	0.0236390	+	0.00435853i
$859$	26.8888	−	46.5728i	0.917434	−	1.58904i	0.114137	−	0.993465i	$-0.463590\pi$
$859$	26.8888	−	46.5728i	0.917434	−	1.58904i	0.803298	−	0.595578i	$-0.203077\pi$
$860$	−5.31445	−	16.3562i	−0.181221	−	0.557741i
$861$		0			0
$862$	17.7640	−	12.9063i	0.605043	−	0.439590i
$863$	−22.2649	−	24.7276i	−0.757904	−	0.841738i	0.233529	−	0.972350i	$-0.424973\pi$
$863$	−22.2649	−	24.7276i	−0.757904	−	0.841738i	−0.991434	+	0.130612i	$0.958306\pi$
$864$	28.5741	−	6.07361i	0.972110	−	0.206628i
$865$	−13.1162	−	5.83971i	−0.445964	−	0.198556i
$866$	−30.8597	+	13.7396i	−1.04866	+	0.466892i
$867$	13.7288	+	42.2529i	0.466255	+	1.43498i
$868$		0			0
$869$	−9.51545	−	3.93109i	−0.322790	−	0.133353i
$870$	17.0565	−	29.5428i	0.578271	−	1.00160i
$871$	−0.0549533	+	0.0610318i	−0.00186202	+	0.00206798i
$872$	−1.30640	+	12.4296i	−0.0442404	+	0.420919i
$873$	0.920412	+	8.75714i	0.0311512	+	0.296384i
$874$	−3.20018	+	9.84914i	−0.108248	+	0.333152i
$875$		0			0
$876$	37.8586	−	27.5059i	1.27912	−	0.929338i
$877$	−12.0283	+	5.35537i	−0.406168	+	0.180838i	−0.599643	−	0.800267i	$-0.704691\pi$
$877$	−12.0283	+	5.35537i	−0.406168	+	0.180838i	0.193475	+	0.981105i	$0.438024\pi$
$878$	43.3140	−	48.1050i	1.46178	−	1.62347i
$879$	16.9220	+	29.3098i	0.570766	+	0.988596i
$880$	11.4958	−	38.9417i	0.387522	−	1.31272i
$881$	33.1960			1.11840			0.559201	−	0.829032i	$-0.311108\pi$
$881$	33.1960			1.11840			0.559201	+	0.829032i	$0.311108\pi$
$882$		0			0
$883$	25.2028	+	18.3109i	0.848143	+	0.616212i	0.924633	−	0.380859i	$-0.124372\pi$
$883$	25.2028	+	18.3109i	0.848143	+	0.616212i	−0.0764906	+	0.997070i	$0.524372\pi$
$884$	0.114242	+	1.08694i	0.00384237	+	0.0365577i
$885$	10.3398	−	2.19778i	0.347567	−	0.0738777i
$886$	41.5120	−	8.82365i	1.39462	−	0.296436i
$887$	−3.46334	−	32.9515i	−0.116288	−	1.10640i	−0.884608	−	0.466336i	$-0.845574\pi$
$887$	−3.46334	−	32.9515i	−0.116288	−	1.10640i	0.768320	−	0.640066i	$-0.221093\pi$
$888$	36.6999	+	26.6641i	1.23157	+	0.894787i
$889$		0			0
$890$	−13.3833			−0.448608
$891$	30.3332	+	20.8060i	1.01620	+	0.697027i
$892$	−29.7380	−	51.5076i	−0.995700	−	1.72460i
$893$	4.11652	−	4.57186i	0.137754	−	0.152992i
$894$	−26.7178	+	11.8955i	−0.893576	+	0.397846i
$895$	−3.62968	+	2.63712i	−0.121327	+	0.0881492i
$896$		0			0
$897$	−0.0509322	+	0.156753i	−0.00170058	+	0.00523384i
$898$	−9.47988	−	90.1950i	−0.316348	−	3.00985i
$899$	−1.47384	+	14.0227i	−0.0491554	+	0.467683i
$900$	−22.6356	+	25.1394i	−0.754521	+	0.837981i
$901$	30.1808	−	52.2747i	1.00547	−	1.74152i
$902$	−37.3444	−	60.8138i	−1.24343	−	2.02488i
$903$		0			0
$904$	8.41838	+	25.9091i	0.279991	+	0.861724i
$905$	−7.56972	+	3.37026i	−0.251626	+	0.112031i
$906$	44.6877	+	19.8962i	1.48465	+	0.661008i
$907$	−11.0937	+	2.35804i	−0.368360	+	0.0782973i	−0.388373	−	0.921502i	$-0.626963\pi$
$907$	−11.0937	+	2.35804i	−0.368360	+	0.0782973i	0.0200127	+	0.999800i	$0.493629\pi$
$908$	34.0345	+	37.7992i	1.12947	+	1.25441i
$909$	−26.1402	+	18.9920i	−0.867016	+	0.629924i
$910$		0			0
$911$	−9.02202	−	27.7669i	−0.298913	−	0.919959i	−0.981879	−	0.189509i	$-0.939310\pi$
$911$	−9.02202	−	27.7669i	−0.298913	−	0.919959i	0.682966	−	0.730450i	$-0.260690\pi$
$912$	22.1846	−	38.4248i	0.734604	−	1.27237i
$913$	9.59006	−	17.7019i	0.317385	−	0.585846i
$914$	42.6948	+	73.9495i	1.41222	+	2.44603i
$915$	−22.1035	−	4.69825i	−0.730720	−	0.155319i
$916$	−109.816	−	79.7860i	−3.62842	−	2.63620i
$917$		0			0
$918$	−12.0623	+	37.1238i	−0.398114	+	1.22527i
$919$	9.73920	+	10.8165i	0.321266	+	0.356803i	0.882047	−	0.471162i	$-0.156165\pi$
$919$	9.73920	+	10.8165i	0.321266	+	0.356803i	−0.560780	+	0.827965i	$0.689499\pi$
$920$	16.9015	+	7.52503i	0.557226	+	0.248093i
$921$	7.44108	−	70.7971i	0.245192	−	2.33284i
$922$	−75.9280	−	16.1390i	−2.50056	−	0.531510i
$923$	−0.154957			−0.00510046
$924$		0			0
$925$	9.62768			0.316556
$926$	−57.2956	−	12.1786i	−1.88285	−	0.400212i
$927$	−3.34574	+	31.8326i	−0.109889	+	1.04552i
$928$	−54.5361	−	24.2810i	−1.79024	−	0.797064i
$929$	4.40136	+	4.88821i	0.144404	+	0.160377i	0.811008	−	0.585035i	$-0.198919\pi$
$929$	4.40136	+	4.88821i	0.144404	+	0.160377i	−0.666604	+	0.745412i	$0.732253\pi$
$930$	−5.99690	+	18.4566i	−0.196646	+	0.605214i
$931$		0			0
$932$	−15.9389	−	11.5803i	−0.522098	−	0.379326i
$933$	4.58621	+	0.974829i	0.150146	+	0.0319145i
$934$	31.1289	+	53.9168i	1.01857	+	1.76421i
$935$	16.3679	+	17.2161i	0.535287	+	0.563027i
$936$	0.266438	−	0.461484i	0.00870880	−	0.0150841i
$937$	9.37722	+	28.8601i	0.306340	+	0.942818i	0.979174	+	0.203024i	$0.0650771\pi$
$937$	9.37722	+	28.8601i	0.306340	+	0.942818i	−0.672833	+	0.739794i	$0.734923\pi$
$938$		0			0
$939$	−10.9923	+	7.98634i	−0.358719	+	0.260624i
$940$	−12.3824	−	13.7520i	−0.403868	−	0.448541i
$941$	−14.9130	+	3.16985i	−0.486149	+	0.103334i	−0.444464	−	0.895797i	$-0.646606\pi$
$941$	−14.9130	+	3.16985i	−0.486149	+	0.103334i	−0.0416850	+	0.999131i	$0.513273\pi$
$942$	79.5356	+	35.4115i	2.59141	+	1.15377i
$943$	15.2613	−	6.79477i	0.496977	−	0.221268i
$944$	−13.0558	−	40.1815i	−0.424929	−	1.30780i
$945$		0			0
$946$	−23.9447	−	9.89218i	−0.778509	−	0.321623i
$947$	−15.6044	+	27.0276i	−0.507075	+	0.878280i	0.492891	+	0.870091i	$0.335940\pi$
$947$	−15.6044	+	27.0276i	−0.507075	+	0.878280i	−0.999966	+	0.00818941i	$0.997393\pi$
$948$	−22.6440	+	25.1487i	−0.735443	+	0.816792i
$949$	−0.0163531	+	0.155589i	−0.000530844	+	0.00505065i
$950$	−1.91596	−	18.2292i	−0.0621621	−	0.591433i
$951$	−12.1573	+	37.4162i	−0.394226	+	1.21330i
$952$		0			0
$953$	−17.4834	+	12.7024i	−0.566342	+	0.411471i	−0.833774	−	0.552105i	$-0.813825\pi$
$953$	−17.4834	+	12.7024i	−0.566342	+	0.411471i	0.267433	+	0.963577i	$0.413825\pi$
$954$	−45.2685	+	20.1548i	−1.46562	+	0.652537i
$955$	−12.5359	+	13.9226i	−0.405654	+	0.450524i
$956$	−52.2656	−	90.5266i	−1.69039	−	2.92784i
$957$	−12.2319	−	34.4403i	−0.395402	−	1.11330i
$958$	30.4063			0.982384
$959$		0			0
$960$	−22.6271	−	16.4395i	−0.730285	−	0.530583i
$961$	2.40194	+	22.8529i	0.0774819	+	0.737191i
$962$	−0.249770	+	0.0530903i	−0.00805292	+	0.00171170i
$963$	1.73271	−	0.368298i	0.0558357	−	0.0118682i
$964$	−7.00492	−	66.6473i	−0.225613	−	2.14657i
$965$	−14.0829	−	10.2318i	−0.453345	−	0.329374i
$966$		0			0
$967$	5.74025			0.184594			0.0922970	−	0.995732i	$-0.470579\pi$
$967$	5.74025			0.184594			0.0922970	+	0.995732i	$0.470579\pi$
$968$	−46.2494	−	70.9293i	−1.48651	−	2.27975i
$969$	12.9792	+	22.4806i	0.416951	+	0.722181i
$970$	−9.60291	+	10.6651i	−0.308331	+	0.342436i
$971$	6.26859	−	2.79096i	0.201169	−	0.0895660i	−0.303679	−	0.952774i	$-0.598215\pi$
$971$	6.26859	−	2.79096i	0.201169	−	0.0895660i	0.504848	+	0.863208i	$0.331549\pi$
$972$	68.6925	−	49.9080i	2.20331	−	1.60080i
$973$		0			0
$974$	0.107148	−	0.329766i	0.00343323	−	0.0105664i
$975$	−0.0304934	−	0.290125i	−0.000976569	−	0.00929144i
$976$	−9.44074	+	89.8227i	−0.302191	+	2.87515i
$977$	−6.96892	+	7.73977i	−0.222955	+	0.247617i	−0.844237	−	0.535971i	$-0.819946\pi$
$977$	−6.96892	+	7.73977i	−0.222955	+	0.247617i	0.621281	+	0.783588i	$0.286612\pi$
$978$	−7.24794	+	12.5538i	−0.231764	+	0.401426i
$979$	−9.30199	+	10.9117i	−0.297293	+	0.348740i
$980$		0			0
$981$	0.952947	+	2.93287i	0.0304252	+	0.0936393i
$982$	−0.0536241	+	0.0238750i	−0.00171121	+	0.000761881i
$983$	−14.3900	−	6.40682i	−0.458969	−	0.204346i	0.164210	−	0.986425i	$-0.447492\pi$
$983$	−14.3900	−	6.40682i	−0.458969	−	0.204346i	−0.623179	+	0.782079i	$0.714159\pi$
$984$	−136.274	+	28.9659i	−4.34425	+	0.923399i
$985$	6.52385	+	7.24547i	0.207867	+	0.230860i
$986$	64.5342	−	46.8868i	2.05519	−	1.49318i
$987$		0			0
$988$	0.106842	+	0.328825i	0.00339908	+	0.0104613i
$989$	3.03232	−	5.25213i	0.0964222	−	0.167008i
$990$	−2.56336	−	19.3320i	−0.0814689	−	0.614410i
$991$	−4.05884	−	7.03011i	−0.128933	−	0.223319i	0.794330	−	0.607486i	$-0.207822\pi$
$991$	−4.05884	−	7.03011i	−0.128933	−	0.223319i	−0.923264	+	0.384167i	$0.874489\pi$
$992$	33.2186	+	7.06084i	1.05469	+	0.224182i
$993$	−35.0367	−	25.4557i	−1.11186	−	0.807811i
$994$		0			0
$995$	−6.64664	+	20.4563i	−0.210713	+	0.648507i
$996$	−44.2800	−	49.1779i	−1.40307	−	1.55826i
$997$	37.6879	+	16.7797i	1.19359	+	0.531420i	0.904744	−	0.425956i	$-0.140062\pi$
$997$	37.6879	+	16.7797i	1.19359	+	0.531420i	0.288845	+	0.957376i	$0.406729\pi$
$998$	1.90602	−	18.1346i	0.0603340	−	0.574040i
$999$	−6.34434	−	1.34853i	−0.200726	−	0.0426656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.h.324.1		40
7.2	even	3		539.2.f.g.148.5		20
7.3	odd	6		77.2.m.b.60.5	yes	40
7.4	even	3	inner	539.2.q.h.214.5		40
7.5	odd	6		539.2.f.h.148.5		20
7.6	odd	2		77.2.m.b.16.1	yes	40
11.9	even	5	inner	539.2.q.h.471.5		40
21.17	even	6		693.2.by.b.676.1		40
21.20	even	2		693.2.by.b.478.5		40
77.3	odd	30		847.2.e.i.606.1		20
77.6	even	10		847.2.n.h.807.1		40
77.9	even	15		539.2.f.g.295.5		20
77.10	even	6		847.2.n.j.753.1		40
77.13	even	10		847.2.n.j.9.1		40
77.17	even	30		847.2.n.h.81.5		40
77.19	even	30		5929.2.a.by.1.1		10
77.20	odd	10		77.2.m.b.9.5	✓	40
77.24	even	30		847.2.n.j.130.5		40
77.27	odd	10		847.2.n.i.807.5		40
77.30	odd	30		5929.2.a.bz.1.1		10
77.31	odd	30		77.2.m.b.53.1	yes	40
77.38	odd	30		847.2.n.i.81.1		40
77.41	even	10		847.2.e.h.485.10		20
77.47	odd	30		5929.2.a.bw.1.10		10
77.48	odd	10		847.2.n.i.366.1		40
77.52	even	30		847.2.e.h.606.10		20
77.53	even	15	inner	539.2.q.h.361.1		40
77.58	even	15		5929.2.a.bx.1.10		10
77.59	odd	30		847.2.n.i.487.5		40
77.62	even	10		847.2.n.h.366.5		40
77.69	odd	10		847.2.e.i.485.1		20
77.73	even	30		847.2.n.h.487.1		40
77.75	odd	30		539.2.f.h.295.5		20
77.76	even	2		847.2.n.j.632.5		40
231.20	even	10		693.2.by.b.163.1		40
231.185	even	30		693.2.by.b.361.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.9.5	✓	40	77.20	odd	10
77.2.m.b.16.1	yes	40	7.6	odd	2
77.2.m.b.53.1	yes	40	77.31	odd	30
77.2.m.b.60.5	yes	40	7.3	odd	6
539.2.f.g.148.5		20	7.2	even	3
539.2.f.g.295.5		20	77.9	even	15
539.2.f.h.148.5		20	7.5	odd	6
539.2.f.h.295.5		20	77.75	odd	30
539.2.q.h.214.5		40	7.4	even	3	inner
539.2.q.h.324.1		40	1.1	even	1	trivial
539.2.q.h.361.1		40	77.53	even	15	inner
539.2.q.h.471.5		40	11.9	even	5	inner
693.2.by.b.163.1		40	231.20	even	10
693.2.by.b.361.5		40	231.185	even	30
693.2.by.b.478.5		40	21.20	even	2
693.2.by.b.676.1		40	21.17	even	6
847.2.e.h.485.10		20	77.41	even	10
847.2.e.h.606.10		20	77.52	even	30
847.2.e.i.485.1		20	77.69	odd	10
847.2.e.i.606.1		20	77.3	odd	30
847.2.n.h.81.5		40	77.17	even	30
847.2.n.h.366.5		40	77.62	even	10
847.2.n.h.487.1		40	77.73	even	30
847.2.n.h.807.1		40	77.6	even	10
847.2.n.i.81.1		40	77.38	odd	30
847.2.n.i.366.1		40	77.48	odd	10
847.2.n.i.487.5		40	77.59	odd	30
847.2.n.i.807.5		40	77.27	odd	10
847.2.n.j.9.1		40	77.13	even	10
847.2.n.j.130.5		40	77.24	even	30
847.2.n.j.632.5		40	77.76	even	2
847.2.n.j.753.1		40	77.10	even	6
5929.2.a.bw.1.10		10	77.47	odd	30
5929.2.a.bx.1.10		10	77.58	even	15
5929.2.a.by.1.1		10	77.19	even	30
5929.2.a.bz.1.1		10	77.30	odd	30

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.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.57407 - 0.547134i) q^{2} +(-0.231369 + 2.20133i) q^{3} +(4.49937 + 2.00325i) q^{4} +(0.787136 + 0.874203i) q^{5} +(1.79998 - 5.53977i) q^{6} +(-6.22764 - 4.52465i) q^{8} +(-1.85787 - 0.394902i) q^{9} +O(q^{10})\)	\(q+(-2.57407 - 0.547134i) q^{2} +(-0.231369 + 2.20133i) q^{3} +(4.49937 + 2.00325i) q^{4} +(0.787136 + 0.874203i) q^{5} +(1.79998 - 5.53977i) q^{6} +(-6.22764 - 4.52465i) q^{8} +(-1.85787 - 0.394902i) q^{9} +(-1.54783 - 2.68093i) q^{10} +(-3.26165 - 0.601380i) q^{11} +(-5.45081 + 9.44109i) q^{12} +(-0.0112624 - 0.0346622i) q^{13} +(-2.10653 + 1.53048i) q^{15} +(6.96361 + 7.73387i) q^{16} +(-5.95559 + 1.26590i) q^{17} +(4.56621 + 2.03301i) q^{18} +(-1.75961 + 0.783430i) q^{19} +(1.79037 + 5.51019i) q^{20} +(8.06666 + 3.33255i) q^{22} +(-1.02155 + 1.76938i) q^{23} +(11.4011 - 12.6622i) q^{24} +(0.377994 - 3.59637i) q^{25} +(0.0100254 + 0.0953849i) q^{26} +(-0.752823 + 2.31695i) q^{27} +(4.02767 - 2.92628i) q^{29} +(6.25972 - 2.78701i) q^{30} +(-1.89509 + 2.10472i) q^{31} +(-5.99553 - 10.3846i) q^{32} +(2.07848 - 7.04081i) q^{33} +16.0227 q^{34} +(-7.56813 - 5.49857i) q^{36} +(0.278295 + 2.64780i) q^{37} +(4.95800 - 1.05386i) q^{38} +(0.0789086 - 0.0167725i) q^{39} +(-0.946542 - 9.00574i) q^{40} +(-6.61499 - 4.80607i) q^{41} -2.96835 q^{43} +(-13.4706 - 9.23971i) q^{44} +(-1.11717 - 1.93499i) q^{45} +(3.59762 - 3.99557i) q^{46} +(-2.91785 + 1.29911i) q^{47} +(-18.6359 + 13.5398i) q^{48} +(-2.94068 + 9.05049i) q^{50} +(-1.40872 - 13.4031i) q^{51} +(0.0187631 - 0.178519i) q^{52} +(-6.63364 + 7.36740i) q^{53} +(3.20550 - 5.55209i) q^{54} +(-2.04163 - 3.32471i) q^{55} +(-1.31747 - 4.05475i) q^{57} +(-11.9686 + 5.32875i) q^{58} +(-3.70874 - 1.65124i) q^{59} +(-12.5440 + 2.66630i) q^{60} +(5.80710 + 6.44943i) q^{61} +(6.02966 - 4.38080i) q^{62} +(3.31928 + 10.2157i) q^{64} +(0.0214368 - 0.0371295i) q^{65} +(-9.20241 + 16.9863i) q^{66} +(-1.12669 - 1.95148i) q^{67} +(-29.3323 - 6.23477i) q^{68} +(-3.65862 - 2.65815i) q^{69} +(1.31384 - 4.04359i) q^{71} +(9.78334 + 10.8655i) q^{72} +(-3.92144 - 1.74594i) q^{73} +(0.732354 - 6.96788i) q^{74} +(7.82934 + 1.66418i) q^{75} -9.48655 q^{76} -0.212293 q^{78} +(3.03638 + 0.645402i) q^{79} +(-1.27967 + 12.1752i) q^{80} +(-10.1317 - 4.51091i) q^{81} +(14.3979 + 15.9904i) q^{82} +(-1.87581 + 5.77314i) q^{83} +(-5.79451 - 4.20996i) q^{85} +(7.64073 + 1.62409i) q^{86} +(5.50981 + 9.54328i) q^{87} +(17.5913 + 18.5030i) q^{88} +(2.16161 - 3.74402i) q^{89} +(1.81697 + 5.59204i) q^{90} +(-8.14083 + 5.91466i) q^{92} +(-4.19470 - 4.65869i) q^{93} +(8.22152 - 1.74754i) q^{94} +(-2.06993 - 0.921593i) q^{95} +(24.2470 - 10.7955i) q^{96} +(-1.43258 - 4.40904i) q^{97} +(5.82222 + 2.40531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} + 4 q^{3} - 3 q^{4} - 4 q^{5} + 16 q^{6} - 38 q^{8} + 7 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 - 4 * q^5 + 16 * q^6 - 38 * q^8 + 7 * q^9	\( 40 q - 3 q^{2} + 4 q^{3} - 3 q^{4} - 4 q^{5} + 16 q^{6} - 38 q^{8} + 7 q^{9} - 14 q^{10} - 9 q^{11} + 18 q^{12} - 6 q^{13} - 14 q^{15} - 5 q^{16} + 7 q^{17} + 24 q^{18} + 4 q^{19} + 30 q^{20} + 44 q^{22} - 14 q^{23} + 12 q^{24} + 21 q^{25} + 16 q^{27} + 16 q^{30} + 17 q^{31} - 30 q^{32} + 15 q^{33} - 48 q^{34} + 14 q^{36} + 24 q^{37} - 12 q^{38} + 28 q^{39} - 10 q^{40} - 60 q^{41} - 72 q^{43} + 18 q^{44} + 16 q^{45} + 8 q^{46} - 13 q^{47} - 128 q^{48} + 6 q^{50} - 7 q^{51} - 2 q^{52} + 33 q^{53} - 34 q^{54} + 6 q^{55} + 44 q^{57} - 17 q^{58} - 21 q^{59} - 48 q^{60} + 52 q^{62} + 94 q^{64} - 40 q^{65} + 49 q^{66} - 38 q^{67} + 23 q^{68} + 124 q^{69} + 20 q^{71} - 38 q^{72} - 11 q^{73} - 41 q^{74} + 11 q^{75} + 96 q^{76} - 100 q^{78} + 21 q^{79} - 12 q^{80} - 58 q^{81} - 6 q^{82} + 46 q^{83} - 78 q^{85} + 7 q^{86} - 48 q^{87} + 32 q^{88} + 10 q^{89} + 18 q^{90} - 110 q^{92} + 12 q^{93} - 37 q^{94} + 7 q^{95} + 53 q^{96} + 54 q^{97} - 36 q^{99}+O(q^{100}) \) 40 * q - 3 * q^2 + 4 * q^3 - 3 * q^4 - 4 * q^5 + 16 * q^6 - 38 * q^8 + 7 * q^9 - 14 * q^10 - 9 * q^11 + 18 * q^12 - 6 * q^13 - 14 * q^15 - 5 * q^16 + 7 * q^17 + 24 * q^18 + 4 * q^19 + 30 * q^20 + 44 * q^22 - 14 * q^23 + 12 * q^24 + 21 * q^25 + 16 * q^27 + 16 * q^30 + 17 * q^31 - 30 * q^32 + 15 * q^33 - 48 * q^34 + 14 * q^36 + 24 * q^37 - 12 * q^38 + 28 * q^39 - 10 * q^40 - 60 * q^41 - 72 * q^43 + 18 * q^44 + 16 * q^45 + 8 * q^46 - 13 * q^47 - 128 * q^48 + 6 * q^50 - 7 * q^51 - 2 * q^52 + 33 * q^53 - 34 * q^54 + 6 * q^55 + 44 * q^57 - 17 * q^58 - 21 * q^59 - 48 * q^60 + 52 * q^62 + 94 * q^64 - 40 * q^65 + 49 * q^66 - 38 * q^67 + 23 * q^68 + 124 * q^69 + 20 * q^71 - 38 * q^72 - 11 * q^73 - 41 * q^74 + 11 * q^75 + 96 * q^76 - 100 * q^78 + 21 * q^79 - 12 * q^80 - 58 * q^81 - 6 * q^82 + 46 * q^83 - 78 * q^85 + 7 * q^86 - 48 * q^87 + 32 * q^88 + 10 * q^89 + 18 * q^90 - 110 * q^92 + 12 * q^93 - 37 * q^94 + 7 * q^95 + 53 * q^96 + 54 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more