LMFDB - Embedded newform 720.2.t.c.541.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(181,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("720.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.t (of order $4$, degree $2$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			541.3
Root			$-0.966675 + 1.03225i$ of defining polynomial
Character	$\chi$	$=$	720.541
Dual form			720.2.t.c.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.562546 - 1.29751i) q^{2} +(-1.36708 + 1.45982i) q^{4} +(-0.707107 + 0.707107i) q^{5} +1.73696i q^{7} +(2.66319 + 0.952595i) q^{8} +O(q^{10})$	\(q+(-0.562546 - 1.29751i) q^{2} +(-1.36708 + 1.45982i) q^{4} +(-0.707107 + 0.707107i) q^{5} +1.73696i q^{7} +(2.66319 + 0.952595i) q^{8} +(1.31526 + 0.519701i) q^{10} +(-0.505430 + 0.505430i) q^{11} +(-1.88750 - 1.88750i) q^{13} +(2.25374 - 0.977122i) q^{14} +(-0.262159 - 3.99140i) q^{16} -4.53524 q^{17} +(-3.22022 - 3.22022i) q^{19} +(-0.0655751 - 1.99892i) q^{20} +(0.940130 + 0.371475i) q^{22} -8.85045i q^{23} -1.00000i q^{25} +(-1.38725 + 3.51086i) q^{26} +(-2.53566 - 2.37458i) q^{28} +(2.44059 + 2.44059i) q^{29} -5.70401 q^{31} +(-5.03142 + 2.58550i) q^{32} +(2.55128 + 5.88454i) q^{34} +(-1.22822 - 1.22822i) q^{35} +(-5.35670 + 5.35670i) q^{37} +(-2.36676 + 5.98979i) q^{38} +(-2.55674 + 1.20957i) q^{40} -10.0343i q^{41} +(-2.10564 + 2.10564i) q^{43} +(-0.0468722 - 1.42880i) q^{44} +(-11.4836 + 4.97878i) q^{46} -4.32303 q^{47} +3.98295 q^{49} +(-1.29751 + 0.562546i) q^{50} +(5.33578 - 0.175041i) q^{52} +(1.37458 - 1.37458i) q^{53} -0.714786i q^{55} +(-1.65462 + 4.62586i) q^{56} +(1.79375 - 4.53964i) q^{58} +(-6.64140 + 6.64140i) q^{59} +(5.26208 + 5.26208i) q^{61} +(3.20877 + 7.40103i) q^{62} +(6.18513 + 5.07388i) q^{64} +2.66933 q^{65} +(-10.5578 - 10.5578i) q^{67} +(6.20006 - 6.62065i) q^{68} +(-0.902702 + 2.28456i) q^{70} +14.0437i q^{71} -6.63830i q^{73} +(9.96378 + 3.93700i) q^{74} +(9.10325 - 0.298634i) q^{76} +(-0.877914 - 0.877914i) q^{77} +4.27297 q^{79} +(3.00772 + 2.63697i) q^{80} +(-13.0196 + 5.64474i) q^{82} +(-9.15483 - 9.15483i) q^{83} +(3.20690 - 3.20690i) q^{85} +(3.91661 + 1.54758i) q^{86} +(-1.82752 + 0.864585i) q^{88} -3.23826i q^{89} +(3.27852 - 3.27852i) q^{91} +(12.9201 + 12.0993i) q^{92} +(2.43190 + 5.60919i) q^{94} +4.55407 q^{95} +1.94129 q^{97} +(-2.24059 - 5.16794i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4}+O(q^{10}) $ 16 * q - 4 * q^4	$ 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47} - 16 q^{49} + 4 q^{50} + 56 q^{52} - 16 q^{53} - 16 q^{56} - 12 q^{58} + 8 q^{59} + 16 q^{61} + 8 q^{62} - 16 q^{64} + 40 q^{67} + 48 q^{68} - 8 q^{70} + 72 q^{74} - 16 q^{77} + 16 q^{79} - 16 q^{80} - 76 q^{82} - 40 q^{83} - 16 q^{85} - 28 q^{86} + 32 q^{91} + 52 q^{92} - 36 q^{94} - 32 q^{95} - 60 q^{98}+O(q^{100}) $ 16 * q - 4 * q^4 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 8 * q^20 - 20 * q^22 + 16 * q^26 - 4 * q^28 + 16 * q^29 + 16 * q^34 - 16 * q^37 - 20 * q^38 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 40 * q^47 - 16 * q^49 + 4 * q^50 + 56 * q^52 - 16 * q^53 - 16 * q^56 - 12 * q^58 + 8 * q^59 + 16 * q^61 + 8 * q^62 - 16 * q^64 + 40 * q^67 + 48 * q^68 - 8 * q^70 + 72 * q^74 - 16 * q^77 + 16 * q^79 - 16 * q^80 - 76 * q^82 - 40 * q^83 - 16 * q^85 - 28 * q^86 + 32 * q^91 + 52 * q^92 - 36 * q^94 - 32 * q^95 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

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 $

$2$	−0.562546	−	1.29751i	−0.397780	−	0.917481i
$2$	−0.562546	−	1.29751i	−0.397780	−	0.917481i
$3$		0			0
$3$		0			0
$4$	−1.36708	+	1.45982i	−0.683542	+	0.729911i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$		0			0
$7$			1.73696i			0.656511i	0.944589	+	0.328255i	$0.106461\pi$
$7$			1.73696i			0.656511i	−0.944589	+	0.328255i	$0.893539\pi$
$8$	2.66319	+	0.952595i	0.941579	+	0.336793i
$9$		0			0
$10$	1.31526	+	0.519701i	0.415922	+	0.164344i
$11$	−0.505430	+	0.505430i	−0.152393	+	0.152393i	−0.779186	−	0.626793i	$-0.784367\pi$
$11$	−0.505430	+	0.505430i	−0.152393	+	0.152393i	0.626793	+	0.779186i	$0.284367\pi$
$12$		0			0
$13$	−1.88750	−	1.88750i	−0.523498	−	0.523498i	0.395128	−	0.918626i	$-0.370700\pi$
$13$	−1.88750	−	1.88750i	−0.523498	−	0.523498i	−0.918626	+	0.395128i	$0.870700\pi$
$14$	2.25374	−	0.977122i	0.602336	−	0.261147i
$15$		0			0
$16$	−0.262159	−	3.99140i	−0.0655399	−	0.997850i
$17$	−4.53524			−1.09996			−0.549979	−	0.835178i	$-0.685364\pi$
$17$	−4.53524			−1.09996			−0.549979	+	0.835178i	$0.685364\pi$
$18$		0			0
$19$	−3.22022	−	3.22022i	−0.738768	−	0.738768i	0.233571	−	0.972340i	$-0.424959\pi$
$19$	−3.22022	−	3.22022i	−0.738768	−	0.738768i	−0.972340	+	0.233571i	$0.924959\pi$
$20$	−0.0655751	−	1.99892i	−0.0146630	−	0.446973i
$21$		0			0
$22$	0.940130	+	0.371475i	0.200436	+	0.0791987i
$23$		−	8.85045i		−	1.84545i	−0.385463	−	0.922723i	$-0.625958\pi$
$23$		−	8.85045i		−	1.84545i	0.385463	−	0.922723i	$-0.374042\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	−1.38725	+	3.51086i	−0.272062	+	0.688536i
$27$		0			0
$28$	−2.53566	−	2.37458i	−0.479195	−	0.448753i
$29$	2.44059	+	2.44059i	0.453205	+	0.453205i	0.896417	−	0.443212i	$-0.146161\pi$
$29$	2.44059	+	2.44059i	0.453205	+	0.453205i	−0.443212	+	0.896417i	$0.646161\pi$
$30$		0			0
$31$	−5.70401			−1.02447			−0.512235	−	0.858845i	$-0.671182\pi$
$31$	−5.70401			−1.02447			−0.512235	+	0.858845i	$0.671182\pi$
$32$	−5.03142	+	2.58550i	−0.889438	+	0.457056i
$33$		0			0
$34$	2.55128	+	5.88454i	0.437541	+	1.00919i
$35$	−1.22822	−	1.22822i	−0.207607	−	0.207607i
$36$		0			0
$37$	−5.35670	+	5.35670i	−0.880636	+	0.880636i	−0.993599	−	0.112963i	$-0.963966\pi$
$37$	−5.35670	+	5.35670i	−0.880636	+	0.880636i	0.112963	+	0.993599i	$0.463966\pi$
$38$	−2.36676	+	5.98979i	−0.383939	+	0.971673i
$39$		0			0
$40$	−2.55674	+	1.20957i	−0.404257	+	0.191250i
$41$		−	10.0343i		−	1.56709i	−0.621335	−	0.783545i	$-0.713409\pi$
$41$		−	10.0343i		−	1.56709i	0.621335	−	0.783545i	$-0.286591\pi$
$42$		0			0
$43$	−2.10564	+	2.10564i	−0.321107	+	0.321107i	−0.849192	−	0.528085i	$-0.822910\pi$
$43$	−2.10564	+	2.10564i	−0.321107	+	0.321107i	0.528085	+	0.849192i	$0.322910\pi$
$44$	−0.0468722	−	1.42880i	−0.00706625	−	0.215400i
$45$		0			0
$46$	−11.4836	+	4.97878i	−1.69316	+	0.734082i
$47$	−4.32303			−0.630578			−0.315289	−	0.948996i	$-0.602101\pi$
$47$	−4.32303			−0.630578			−0.315289	+	0.948996i	$0.602101\pi$
$48$		0			0
$49$	3.98295			0.568993
$50$	−1.29751	+	0.562546i	−0.183496	+	0.0795560i
$51$		0			0
$52$	5.33578	−	0.175041i	0.739940	−	0.0242739i
$53$	1.37458	−	1.37458i	0.188814	−	0.188814i	−0.606369	−	0.795183i	$-0.707375\pi$
$53$	1.37458	−	1.37458i	0.188814	−	0.188814i	0.795183	+	0.606369i	$0.207375\pi$
$54$		0			0
$55$		−	0.714786i		−	0.0963817i
$56$	−1.65462	+	4.62586i	−0.221108	+	0.618157i
$57$		0			0
$58$	1.79375	−	4.53964i	0.235531	−	0.596083i
$59$	−6.64140	+	6.64140i	−0.864637	+	0.864637i	−0.991872	−	0.127236i	$-0.959389\pi$
$59$	−6.64140	+	6.64140i	−0.864637	+	0.864637i	0.127236	+	0.991872i	$0.459389\pi$
$60$		0			0
$61$	5.26208	+	5.26208i	0.673741	+	0.673741i	0.958576	−	0.284836i	$-0.0919391\pi$
$61$	5.26208	+	5.26208i	0.673741	+	0.673741i	−0.284836	+	0.958576i	$0.591939\pi$
$62$	3.20877	+	7.40103i	0.407514	+	0.939932i
$63$		0			0
$64$	6.18513	+	5.07388i	0.773141	+	0.634234i
$65$	2.66933			0.331089
$66$		0			0
$67$	−10.5578	−	10.5578i	−1.28984	−	1.28984i	−0.934884	−	0.354954i	$-0.884497\pi$
$67$	−10.5578	−	10.5578i	−1.28984	−	1.28984i	−0.354954	−	0.934884i	$-0.615503\pi$
$68$	6.20006	−	6.62065i	0.751868	−	0.802871i
$69$		0			0
$70$	−0.902702	+	2.28456i	−0.107894	+	0.273057i
$71$			14.0437i			1.66668i	0.552764	+	0.833338i	$0.313573\pi$
$71$			14.0437i			1.66668i	−0.552764	+	0.833338i	$0.686427\pi$
$72$		0			0
$73$		−	6.63830i		−	0.776954i	−0.921458	−	0.388477i	$-0.873001\pi$
$73$		−	6.63830i		−	0.776954i	0.921458	−	0.388477i	$-0.126999\pi$
$74$	9.96378	+	3.93700i	1.15827	+	0.457667i
$75$		0			0
$76$	9.10325	−	0.298634i	1.04421	−	0.0342557i
$77$	−0.877914	−	0.877914i	−0.100048	−	0.100048i
$78$		0			0
$79$	4.27297			0.480746			0.240373	−	0.970681i	$-0.422730\pi$
$79$	4.27297			0.480746			0.240373	+	0.970681i	$0.422730\pi$
$80$	3.00772	+	2.63697i	0.336273	+	0.294822i
$81$		0			0
$82$	−13.0196	+	5.64474i	−1.43778	+	0.623357i
$83$	−9.15483	−	9.15483i	−1.00487	−	1.00487i	−0.999988	−	0.00488547i	$-0.998445\pi$
$83$	−9.15483	−	9.15483i	−1.00487	−	1.00487i	−0.00488547	−	0.999988i	$-0.501555\pi$
$84$		0			0
$85$	3.20690	−	3.20690i	0.347837	−	0.347837i
$86$	3.91661	+	1.54758i	0.422339	+	0.166879i
$87$		0			0
$88$	−1.82752	+	0.864585i	−0.194815	+	0.0921650i
$89$		−	3.23826i		−	0.343255i	−0.985162	−	0.171627i	$-0.945097\pi$
$89$		−	3.23826i		−	0.343255i	0.985162	−	0.171627i	$-0.0549025\pi$
$90$		0			0
$91$	3.27852	−	3.27852i	0.343682	−	0.343682i
$92$	12.9201	+	12.0993i	1.34701	+	1.26144i
$93$		0			0
$94$	2.43190	+	5.60919i	0.250831	+	0.578543i
$95$	4.55407			0.467238
$96$		0			0
$97$	1.94129			0.197108			0.0985541	−	0.995132i	$-0.468578\pi$
$97$	1.94129			0.197108			0.0985541	+	0.995132i	$0.468578\pi$
$98$	−2.24059	−	5.16794i	−0.226334	−	0.522041i
$99$		0			0
$100$	1.45982	+	1.36708i	0.145982	+	0.136708i
$101$	−10.3395	+	10.3395i	−1.02882	+	1.02882i	−0.0292464	+	0.999572i	$0.509311\pi$
$101$	−10.3395	+	10.3395i	−1.02882	+	1.02882i	−0.999572	+	0.0292464i	$0.990689\pi$
$102$		0			0
$103$		−	4.96401i		−	0.489118i	−0.969634	−	0.244559i	$-0.921357\pi$
$103$		−	4.96401i		−	0.489118i	0.969634	−	0.244559i	$-0.0786433\pi$
$104$	−3.22874	−	6.82478i	−0.316604	−	0.669225i
$105$		0			0
$106$	−2.55681	−	1.01028i	−0.248339	−	0.0981266i
$107$	2.74631	−	2.74631i	0.265496	−	0.265496i	−0.561787	−	0.827282i	$-0.689886\pi$
$107$	2.74631	−	2.74631i	0.265496	−	0.265496i	0.827282	+	0.561787i	$0.189886\pi$
$108$		0			0
$109$	6.99959	+	6.99959i	0.670439	+	0.670439i	0.957817	−	0.287378i	$-0.0927837\pi$
$109$	6.99959	+	6.99959i	0.670439	+	0.670439i	−0.287378	+	0.957817i	$0.592784\pi$
$110$	−0.927445	+	0.402100i	−0.0884284	+	0.0383387i
$111$		0			0
$112$	6.93292	−	0.455362i	0.655099	−	0.0430276i
$113$	6.53194			0.614474			0.307237	−	0.951633i	$-0.400596\pi$
$113$	6.53194			0.614474			0.307237	+	0.951633i	$0.400596\pi$
$114$		0			0
$115$	6.25821	+	6.25821i	0.583582	+	0.583582i
$116$	−6.89931	+	0.226333i	−0.640585	+	0.0210145i
$117$		0			0
$118$	12.3534	+	4.88122i	1.13722	+	0.449353i
$119$		−	7.87756i		−	0.722134i
$120$		0			0
$121$			10.4891i			0.953553i
$122$	3.86746	−	9.78779i	0.350144	−	0.886145i
$123$		0			0
$124$	7.79786	−	8.32684i	0.700269	−	0.747772i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$		0			0
$127$	−2.50861			−0.222603			−0.111302	−	0.993787i	$-0.535502\pi$
$127$	−2.50861			−0.222603			−0.111302	+	0.993787i	$0.535502\pi$
$128$	3.10401	−	10.8796i	0.274358	−	0.961628i
$129$		0			0
$130$	−1.50162	−	3.46349i	−0.131701	−	0.303768i
$131$	−8.55783	−	8.55783i	−0.747701	−	0.747701i	0.226346	−	0.974047i	$-0.427322\pi$
$131$	−8.55783	−	8.55783i	−0.747701	−	0.747701i	−0.974047	+	0.226346i	$0.927322\pi$
$132$		0			0
$133$	5.59340	−	5.59340i	0.485009	−	0.485009i
$134$	−7.75963	+	19.6381i	−0.670330	+	1.69647i
$135$		0			0
$136$	−12.0782	−	4.32025i	−1.03570	−	0.370458i
$137$			6.47131i			0.552881i	0.961031	+	0.276440i	$0.0891549\pi$
$137$			6.47131i			0.552881i	−0.961031	+	0.276440i	$0.910845\pi$
$138$		0			0
$139$	−16.4430	+	16.4430i	−1.39468	+	1.39468i	−0.580223	+	0.814458i	$0.697035\pi$
$139$	−16.4430	+	16.4430i	−1.39468	+	1.39468i	−0.814458	+	0.580223i	$0.802965\pi$
$140$	3.47206	−	0.113902i	0.293443	−	0.00962645i
$141$		0			0
$142$	18.2218	−	7.90020i	1.52914	−	0.662970i
$143$	1.90800			0.159555
$144$		0			0
$145$	−3.45151			−0.286632
$146$	−8.61329	+	3.73435i	−0.712841	+	0.309057i
$147$		0			0
$148$	−0.496766	−	15.1429i	−0.0408339	−	1.24474i
$149$	2.72803	−	2.72803i	0.223489	−	0.223489i	−0.586477	−	0.809966i	$-0.699486\pi$
$149$	2.72803	−	2.72803i	0.223489	−	0.223489i	0.809966	+	0.586477i	$0.199486\pi$
$150$		0			0
$151$		−	11.5196i		−	0.937453i	−0.883343	−	0.468726i	$-0.844713\pi$
$151$		−	11.5196i		−	0.937453i	0.883343	−	0.468726i	$-0.155287\pi$
$152$	−5.50848	−	11.6436i	−0.446796	−	0.944420i
$153$		0			0
$154$	−0.645239	+	1.63297i	−0.0519948	+	0.131589i
$155$	4.03334	−	4.03334i	0.323966	−	0.323966i
$156$		0			0
$157$	3.28013	+	3.28013i	0.261783	+	0.261783i	0.825778	−	0.563995i	$-0.190736\pi$
$157$	3.28013	+	3.28013i	0.261783	+	0.261783i	−0.563995	+	0.825778i	$0.690736\pi$
$158$	−2.40374	−	5.54423i	−0.191231	−	0.441076i
$159$		0			0
$160$	1.72953	−	5.38598i	0.136731	−	0.425799i
$161$	15.3729			1.21156
$162$		0			0
$163$	−9.27367	−	9.27367i	−0.726370	−	0.726370i	0.243525	−	0.969895i	$-0.421696\pi$
$163$	−9.27367	−	9.27367i	−0.726370	−	0.726370i	−0.969895	+	0.243525i	$0.921696\pi$
$164$	14.6482	+	13.7177i	1.14384	+	1.07117i
$165$		0			0
$166$	−6.72851	+	17.0285i	−0.522234	+	1.32167i
$167$		−	7.08065i		−	0.547917i	−0.961742	−	0.273958i	$-0.911667\pi$
$167$		−	7.08065i		−	0.547917i	0.961742	−	0.273958i	$-0.0883331\pi$
$168$		0			0
$169$		−	5.87470i		−	0.451900i
$170$	−5.96503	−	2.35697i	−0.457497	−	0.180771i
$171$		0			0
$172$	−0.195271	−	5.95244i	−0.0148893	−	0.453869i
$173$	5.21471	+	5.21471i	0.396467	+	0.396467i	0.876985	−	0.480518i	$-0.159551\pi$
$173$	5.21471	+	5.21471i	0.396467	+	0.396467i	−0.480518	+	0.876985i	$0.659551\pi$
$174$		0			0
$175$	1.73696			0.131302
$176$	2.14988	+	1.88487i	0.162053	+	0.142077i
$177$		0			0
$178$	−4.20169	+	1.82167i	−0.314930	+	0.136540i
$179$	−6.32196	−	6.32196i	−0.472525	−	0.472525i	0.430206	−	0.902731i	$-0.358441\pi$
$179$	−6.32196	−	6.32196i	−0.472525	−	0.472525i	−0.902731	+	0.430206i	$0.858441\pi$
$180$		0			0
$181$	13.0695	−	13.0695i	0.971448	−	0.971448i	−0.0281553	−	0.999604i	$-0.508963\pi$
$181$	13.0695	−	13.0695i	0.971448	−	0.971448i	0.999604	+	0.0281553i	$0.00896329\pi$
$182$	−6.09824	−	2.40961i	−0.452031	−	0.178612i
$183$		0			0
$184$	8.43089	−	23.5704i	0.621534	−	1.73763i
$185$		−	7.57552i		−	0.556963i
$186$		0			0
$187$	2.29225	−	2.29225i	0.167626	−	0.167626i
$188$	5.90994	−	6.31085i	0.431027	−	0.460266i
$189$		0			0
$190$	−2.56187	−	5.90897i	−0.185858	−	0.428682i
$191$	22.1722			1.60433			0.802164	−	0.597104i	$-0.203682\pi$
$191$	22.1722			1.60433			0.802164	+	0.597104i	$0.203682\pi$
$192$		0			0
$193$	7.97695			0.574193			0.287097	−	0.957902i	$-0.407310\pi$
$193$	7.97695			0.574193			0.287097	+	0.957902i	$0.407310\pi$
$194$	−1.09206	−	2.51885i	−0.0784056	−	0.180843i
$195$		0			0
$196$	−5.44503	+	5.81440i	−0.388931	+	0.415314i
$197$	−5.76327	+	5.76327i	−0.410616	+	0.410616i	−0.881953	−	0.471337i	$-0.843772\pi$
$197$	−5.76327	+	5.76327i	−0.410616	+	0.410616i	0.471337	+	0.881953i	$0.343772\pi$
$198$		0			0
$199$		−	5.38869i		−	0.381994i	−0.981591	−	0.190997i	$-0.938828\pi$
$199$		−	5.38869i		−	0.381994i	0.981591	−	0.190997i	$-0.0611721\pi$
$200$	0.952595	−	2.66319i	0.0673586	−	0.188316i
$201$		0			0
$202$	19.2321	+	7.59920i	1.35316	+	0.534678i
$203$	−4.23921	+	4.23921i	−0.297534	+	0.297534i
$204$		0			0
$205$	7.09530	+	7.09530i	0.495557	+	0.495557i
$206$	−6.44087	+	2.79248i	−0.448757	+	0.194561i
$207$		0			0
$208$	−7.03893	+	8.02858i	−0.488062	+	0.556682i
$209$	3.25519			0.225166
$210$		0			0
$211$	10.7547	+	10.7547i	0.740384	+	0.740384i	0.972652	−	0.232268i	$-0.0746147\pi$
$211$	10.7547	+	10.7547i	0.740384	+	0.740384i	−0.232268	+	0.972652i	$0.574615\pi$
$212$	0.127475	+	3.88582i	0.00875503	+	0.266879i
$213$		0			0
$214$	−5.10830	−	2.01845i	−0.349196	−	0.137978i
$215$		−	2.97782i		−	0.203086i
$216$		0			0
$217$		−	9.90766i		−	0.672576i
$218$	5.14447	−	13.0197i	0.348428	−	0.881802i
$219$		0			0
$220$	1.04346	+	0.977173i	0.0703501	+	0.0658810i
$221$	8.56026	+	8.56026i	0.575826	+	0.575826i
$222$		0			0
$223$	−3.98714			−0.266998			−0.133499	−	0.991049i	$-0.542621\pi$
$223$	−3.98714			−0.266998			−0.133499	+	0.991049i	$0.542621\pi$
$224$	−4.49092	−	8.73940i	−0.300062	−	0.583926i
$225$		0			0
$226$	−3.67452	−	8.47529i	−0.244425	−	0.563768i
$227$	3.82103	+	3.82103i	0.253611	+	0.253611i	0.822449	−	0.568839i	$-0.192607\pi$
$227$	3.82103	+	3.82103i	0.253611	+	0.253611i	−0.568839	+	0.822449i	$0.692607\pi$
$228$		0			0
$229$	−8.80687	+	8.80687i	−0.581974	+	0.581974i	−0.935445	−	0.353471i	$-0.885001\pi$
$229$	−8.80687	+	8.80687i	−0.581974	+	0.581974i	0.353471	+	0.935445i	$0.385001\pi$
$230$	4.59959	−	11.6407i	0.303288	−	0.767562i
$231$		0			0
$232$	4.17485	+	8.82463i	0.274092	+	0.579365i
$233$		−	16.6042i		−	1.08778i	−0.839157	−	0.543889i	$-0.816951\pi$
$233$		−	16.6042i		−	1.08778i	0.839157	−	0.543889i	$-0.183049\pi$
$234$		0			0
$235$	3.05684	−	3.05684i	0.199406	−	0.199406i
$236$	−0.615905	−	18.7746i	−0.0400920	−	1.22212i
$237$		0			0
$238$	−10.2212	+	4.43149i	−0.662545	+	0.287251i
$239$	−3.81234			−0.246600			−0.123300	−	0.992369i	$-0.539348\pi$
$239$	−3.81234			−0.246600			−0.123300	+	0.992369i	$0.539348\pi$
$240$		0			0
$241$	9.54985			0.615160			0.307580	−	0.951522i	$-0.400481\pi$
$241$	9.54985			0.615160			0.307580	+	0.951522i	$0.400481\pi$
$242$	13.6097	−	5.90059i	0.874866	−	0.379304i
$243$		0			0
$244$	−14.8754	+	0.487991i	−0.952301	+	0.0312404i
$245$	−2.81637	+	2.81637i	−0.179932	+	0.179932i
$246$		0			0
$247$			12.1563i			0.773487i
$248$	−15.1908	−	5.43361i	−0.964619	−	0.345034i
$249$		0			0
$250$	0.519701	−	1.31526i	0.0328688	−	0.0831844i
$251$	−11.9933	+	11.9933i	−0.757010	+	0.757010i	−0.975777	−	0.218767i	$-0.929797\pi$
$251$	−11.9933	+	11.9933i	−0.757010	+	0.757010i	0.218767	+	0.975777i	$0.429797\pi$
$252$		0			0
$253$	4.47328	+	4.47328i	0.281233	+	0.281233i
$254$	1.41121	+	3.25496i	0.0885471	+	0.204234i
$255$		0			0
$256$	−15.8625	+	2.09277i	−0.991409	+	0.130798i
$257$	−18.8752			−1.17740			−0.588702	−	0.808350i	$-0.700361\pi$
$257$	−18.8752			−1.17740			−0.588702	+	0.808350i	$0.700361\pi$
$258$		0			0
$259$	−9.30440	−	9.30440i	−0.578147	−	0.578147i
$260$	−3.64919	+	3.89674i	−0.226313	+	0.241666i
$261$		0			0
$262$	−6.28973	+	15.9181i	−0.388581	+	0.983422i
$263$			23.1398i			1.42686i	0.700727	+	0.713429i	$0.252859\pi$
$263$			23.1398i			1.42686i	−0.700727	+	0.713429i	$0.747141\pi$
$264$		0			0
$265$			1.94396i			0.119416i
$266$	−10.4041	−	4.11097i	−0.637914	−	0.252060i
$267$		0			0
$268$	29.8458	−	0.979099i	1.82313	−	0.0598080i
$269$	10.6368	+	10.6368i	0.648539	+	0.648539i	0.952640	−	0.304101i	$-0.0983560\pi$
$269$	10.6368	+	10.6368i	0.648539	+	0.648539i	−0.304101	+	0.952640i	$0.598356\pi$
$270$		0			0
$271$	19.9763			1.21348			0.606738	−	0.794902i	$-0.292478\pi$
$271$	19.9763			1.21348			0.606738	+	0.794902i	$0.292478\pi$
$272$	1.18896	+	18.1020i	0.0720911	+	1.09759i
$273$		0			0
$274$	8.39661	−	3.64041i	0.507258	−	0.219925i
$275$	0.505430	+	0.505430i	0.0304786	+	0.0304786i
$276$		0			0
$277$	−16.1534	+	16.1534i	−0.970563	+	0.970563i	−0.999579	−	0.0290160i	$-0.990763\pi$
$277$	−16.1534	+	16.1534i	−0.970563	+	0.970563i	0.0290160	+	0.999579i	$0.490763\pi$
$278$	30.5850	+	12.0851i	1.83437	+	0.724817i
$279$		0			0
$280$	−2.10098	−	4.44097i	−0.125558	−	0.265399i
$281$			9.43520i			0.562857i	0.959582	+	0.281429i	$0.0908082\pi$
$281$			9.43520i			0.562857i	−0.959582	+	0.281429i	$0.909192\pi$
$282$		0			0
$283$	8.71287	−	8.71287i	0.517926	−	0.517926i	−0.399017	−	0.916943i	$-0.630649\pi$
$283$	8.71287	−	8.71287i	0.517926	−	0.517926i	0.916943	+	0.399017i	$0.130649\pi$
$284$	−20.5012	−	19.1989i	−1.21653	−	1.13924i
$285$		0			0
$286$	−1.07334	−	2.47565i	−0.0634676	−	0.146388i
$287$	17.4292			1.02881
$288$		0			0
$289$	3.56843			0.209908
$290$	1.94163	+	4.47838i	0.114017	+	0.262980i
$291$		0			0
$292$	9.69074	+	9.07512i	0.567107	+	0.531081i
$293$	11.1045	−	11.1045i	0.648729	−	0.648729i	−0.303957	−	0.952686i	$-0.598308\pi$
$293$	11.1045	−	11.1045i	0.648729	−	0.648729i	0.952686	+	0.303957i	$0.0983079\pi$
$294$		0			0
$295$		−	9.39236i		−	0.546844i
$296$	−19.3687	+	9.16313i	−1.12578	+	0.532596i
$297$		0			0
$298$	−5.07429	−	2.00501i	−0.293946	−	0.116147i
$299$	−16.7052	+	16.7052i	−0.966087	+	0.966087i
$300$		0			0
$301$	−3.65742	−	3.65742i	−0.210810	−	0.210810i
$302$	−14.9469	+	6.48031i	−0.860095	+	0.372900i
$303$		0			0
$304$	−12.0090	+	13.6974i	−0.688761	+	0.785599i
$305$	−7.44171			−0.426111
$306$		0			0
$307$	−2.99854	−	2.99854i	−0.171136	−	0.171136i	0.616343	−	0.787478i	$-0.288614\pi$
$307$	−2.99854	−	2.99854i	−0.171136	−	0.171136i	−0.787478	+	0.616343i	$0.788614\pi$
$308$	2.48178	−	0.0814153i	0.141413	−	0.00463907i
$309$		0			0
$310$	−7.50226	−	2.96438i	−0.426100	−	0.168365i
$311$		−	9.06099i		−	0.513802i	−0.966438	−	0.256901i	$-0.917299\pi$
$311$		−	9.06099i		−	0.513802i	0.966438	−	0.256901i	$-0.0827014\pi$
$312$		0			0
$313$			19.5699i			1.10616i	0.833129	+	0.553078i	$0.186547\pi$
$313$			19.5699i			1.10616i	−0.833129	+	0.553078i	$0.813453\pi$
$314$	2.41079	−	6.10124i	0.136049	−	0.344313i
$315$		0			0
$316$	−5.84151	+	6.23777i	−0.328610	+	0.350902i
$317$	11.1019	+	11.1019i	0.623546	+	0.623546i	0.946436	−	0.322890i	$-0.104654\pi$
$317$	11.1019	+	11.1019i	0.623546	+	0.623546i	−0.322890	+	0.946436i	$0.604654\pi$
$318$		0			0
$319$	−2.46709			−0.138131
$320$	−7.96132	+	0.785774i	−0.445051	+	0.0439261i
$321$		0			0
$322$	−8.64797	−	19.9466i	−0.481933	−	1.11158i
$323$	14.6045	+	14.6045i	0.812614	+	0.812614i
$324$		0			0
$325$	−1.88750	+	1.88750i	−0.104700	+	0.104700i
$326$	−6.81585	+	17.2496i	−0.377495	+	0.955366i
$327$		0			0
$328$	9.55859	−	26.7231i	0.527785	−	1.47554i
$329$		−	7.50894i		−	0.413981i
$330$		0			0
$331$	−8.14718	+	8.14718i	−0.447810	+	0.447810i	−0.894626	−	0.446816i	$-0.852558\pi$
$331$	−8.14718	+	8.14718i	−0.447810	+	0.447810i	0.446816	+	0.894626i	$0.352558\pi$
$332$	25.8799	−	0.848994i	1.42034	−	0.0465946i
$333$		0			0
$334$	−9.18724	+	3.98319i	−0.502703	+	0.217950i
$335$	14.9309			0.815765
$336$		0			0
$337$	−25.1380			−1.36935			−0.684677	−	0.728847i	$-0.740057\pi$
$337$	−25.1380			−1.36935			−0.684677	+	0.728847i	$0.740057\pi$
$338$	−7.62251	+	3.30479i	−0.414610	+	0.179757i
$339$		0			0
$340$	0.297399	+	9.06561i	0.0161287	+	0.491652i
$341$	2.88298	−	2.88298i	0.156122	−	0.156122i
$342$		0			0
$343$			19.0770i			1.03006i
$344$	−7.61353	+	3.60189i	−0.410494	+	0.194201i
$345$		0			0
$346$	3.83265	−	9.69967i	0.206044	−	0.521458i
$347$	−7.36719	+	7.36719i	−0.395491	+	0.395491i	−0.876639	−	0.481148i	$-0.840220\pi$
$347$	−7.36719	+	7.36719i	−0.395491	+	0.395491i	0.481148	+	0.876639i	$0.340220\pi$
$348$		0			0
$349$	−3.25982	−	3.25982i	−0.174494	−	0.174494i	0.614457	−	0.788951i	$-0.289375\pi$
$349$	−3.25982	−	3.25982i	−0.174494	−	0.174494i	−0.788951	+	0.614457i	$0.789375\pi$
$350$	−0.977122	−	2.25374i	−0.0522294	−	0.120467i
$351$		0			0
$352$	1.23624	−	3.84982i	0.0658919	−	0.205196i
$353$	−0.502832			−0.0267630			−0.0133815	−	0.999910i	$-0.504260\pi$
$353$	−0.502832			−0.0267630			−0.0133815	+	0.999910i	$0.504260\pi$
$354$		0			0
$355$	−9.93037	−	9.93037i	−0.527049	−	0.527049i
$356$	4.72728	+	4.42697i	0.250545	+	0.234629i
$357$		0			0
$358$	−4.64644	+	11.7592i	−0.245572	+	0.621494i
$359$			5.95161i			0.314114i	0.987590	+	0.157057i	$0.0502007\pi$
$359$			5.95161i			0.314114i	−0.987590	+	0.157057i	$0.949799\pi$
$360$		0			0
$361$			1.73958i			0.0915571i
$362$	−24.3100	−	9.60567i	−1.27771	−	0.504863i
$363$		0			0
$364$	0.304041	+	9.26806i	0.0159361	+	0.485778i
$365$	4.69399	+	4.69399i	0.245695	+	0.245695i
$366$		0			0
$367$	1.95365			0.101980			0.0509898	−	0.998699i	$-0.483762\pi$
$367$	1.95365			0.101980			0.0509898	+	0.998699i	$0.483762\pi$
$368$	−35.3257	+	2.32023i	−1.84148	+	0.120950i
$369$		0			0
$370$	−9.82934	+	4.26157i	−0.511003	+	0.221549i
$371$	2.38760	+	2.38760i	0.123958	+	0.123958i
$372$		0			0
$373$	−18.6509	+	18.6509i	−0.965708	+	0.965708i	−0.999431	−	0.0337233i	$-0.989264\pi$
$373$	−18.6509	+	18.6509i	−0.965708	+	0.965708i	0.0337233	+	0.999431i	$0.489264\pi$
$374$	−4.26372	−	1.68473i	−0.220472	−	0.0871153i
$375$		0			0
$376$	−11.5130	−	4.11809i	−0.593739	−	0.212374i
$377$		−	9.21320i		−	0.474504i
$378$		0			0
$379$	−3.85143	+	3.85143i	−0.197835	+	0.197835i	−0.799071	−	0.601236i	$-0.794675\pi$
$379$	−3.85143	+	3.85143i	−0.197835	+	0.197835i	0.601236	+	0.799071i	$0.294675\pi$
$380$	−6.22580	+	6.64814i	−0.319377	+	0.341042i
$381$		0			0
$382$	−12.4729	−	28.7688i	−0.638169	−	1.47194i
$383$	−2.29258			−0.117145			−0.0585726	−	0.998283i	$-0.518655\pi$
$383$	−2.29258			−0.117145			−0.0585726	+	0.998283i	$0.518655\pi$
$384$		0			0
$385$	1.24156			0.0632757
$386$	−4.48740	−	10.3502i	−0.228403	−	0.526812i
$387$		0			0
$388$	−2.65391	+	2.83394i	−0.134732	+	0.143871i
$389$	−4.90500	+	4.90500i	−0.248693	+	0.248693i	−0.820434	−	0.571741i	$-0.806268\pi$
$389$	−4.90500	+	4.90500i	−0.248693	+	0.248693i	0.571741	+	0.820434i	$0.306268\pi$
$390$		0			0
$391$			40.1389i			2.02991i
$392$	10.6073	+	3.79414i	0.535752	+	0.191633i
$393$		0			0
$394$	10.7200	+	4.23582i	0.540067	+	0.213398i
$395$	−3.02144	+	3.02144i	−0.152025	+	0.152025i
$396$		0			0
$397$	−10.8616	−	10.8616i	−0.545126	−	0.545126i	0.379901	−	0.925027i	$-0.375958\pi$
$397$	−10.8616	−	10.8616i	−0.545126	−	0.545126i	−0.925027	+	0.379901i	$0.875958\pi$
$398$	−6.99190	+	3.03138i	−0.350472	+	0.151950i
$399$		0			0
$400$	−3.99140	+	0.262159i	−0.199570	+	0.0131080i
$401$	7.10783			0.354948			0.177474	−	0.984125i	$-0.443207\pi$
$401$	7.10783			0.354948			0.177474	+	0.984125i	$0.443207\pi$
$402$		0			0
$403$	10.7663	+	10.7663i	0.536308	+	0.536308i
$404$	−0.958857	−	29.2288i	−0.0477049	−	1.45419i
$405$		0			0
$406$	7.88519	+	3.11569i	0.391335	+	0.154629i
$407$		−	5.41487i		−	0.268405i
$408$		0			0
$409$		−	29.1697i		−	1.44235i	−0.692752	−	0.721176i	$-0.743602\pi$
$409$		−	29.1697i		−	1.44235i	0.692752	−	0.721176i	$-0.256398\pi$
$410$	5.21482	−	13.1977i	0.257542	−	0.651787i
$411$		0			0
$412$	7.24657	+	6.78622i	0.357013	+	0.334333i
$413$	−11.5359	−	11.5359i	−0.567643	−	0.567643i
$414$		0			0
$415$	12.9469			0.635538
$416$	14.3769	+	4.61667i	0.704887	+	0.226351i
$417$		0			0
$418$	−1.83119	−	4.22365i	−0.0895665	−	0.206586i
$419$	−3.06616	−	3.06616i	−0.149792	−	0.149792i	0.628233	−	0.778025i	$-0.283778\pi$
$419$	−3.06616	−	3.06616i	−0.149792	−	0.149792i	−0.778025	+	0.628233i	$0.783778\pi$
$420$		0			0
$421$	−0.532242	+	0.532242i	−0.0259399	+	0.0259399i	−0.719958	−	0.694018i	$-0.755839\pi$
$421$	−0.532242	+	0.532242i	−0.0259399	+	0.0259399i	0.694018	+	0.719958i	$0.255839\pi$
$422$	7.90436	−	20.0044i	0.384778	−	0.973798i
$423$		0			0
$424$	4.97020	−	2.35135i	0.241374	−	0.114192i
$425$			4.53524i			0.219992i
$426$		0			0
$427$	−9.14005	+	9.14005i	−0.442318	+	0.442318i
$428$	0.254685	+	7.76356i	0.0123107	+	0.375266i
$429$		0			0
$430$	−3.86376	+	1.67516i	−0.186327	+	0.0807834i
$431$	−16.7237			−0.805555			−0.402777	−	0.915298i	$-0.631955\pi$
$431$	−16.7237			−0.805555			−0.402777	+	0.915298i	$0.631955\pi$
$432$		0			0
$433$	28.3675			1.36326			0.681628	−	0.731699i	$-0.261272\pi$
$433$	28.3675			1.36326			0.681628	+	0.731699i	$0.261272\pi$
$434$	−12.8553	+	5.57351i	−0.617076	+	0.267537i
$435$		0			0
$436$	−19.7872	+	0.649122i	−0.947634	+	0.0310873i
$437$	−28.5004	+	28.5004i	−1.36336	+	1.36336i
$438$		0			0
$439$		−	13.5018i		−	0.644405i	−0.946671	−	0.322203i	$-0.895577\pi$
$439$		−	13.5018i		−	0.644405i	0.946671	−	0.322203i	$-0.104423\pi$
$440$	0.680901	−	1.90361i	0.0324607	−	0.0907510i
$441$		0			0
$442$	6.29152	−	15.9226i	0.299257	−	0.757361i
$443$	9.55246	−	9.55246i	0.453851	−	0.453851i	−0.442780	−	0.896630i	$-0.646008\pi$
$443$	9.55246	−	9.55246i	0.453851	−	0.453851i	0.896630	+	0.442780i	$0.146008\pi$
$444$		0			0
$445$	2.28980	+	2.28980i	0.108547	+	0.108547i
$446$	2.24295	+	5.17337i	0.106207	+	0.244966i
$447$		0			0
$448$	−8.81314	+	10.7433i	−0.416382	+	0.507575i
$449$	9.35573			0.441524			0.220762	−	0.975328i	$-0.429146\pi$
$449$	9.35573			0.441524			0.220762	+	0.975328i	$0.429146\pi$
$450$		0			0
$451$	5.07162	+	5.07162i	0.238813	+	0.238813i
$452$	−8.92972	+	9.53547i	−0.420019	+	0.448511i
$453$		0			0
$454$	2.80833	−	7.10734i	0.131802	−	0.333564i
$455$			4.63652i			0.217364i
$456$		0			0
$457$		−	6.84779i		−	0.320326i	−0.987091	−	0.160163i	$-0.948798\pi$
$457$		−	6.84779i		−	0.320326i	0.987091	−	0.160163i	$-0.0512020\pi$
$458$	16.3813	+	6.47277i	0.765448	+	0.302453i
$459$		0			0
$460$	−17.6914	+	0.580370i	−0.824865	+	0.0270599i
$461$	11.7403	+	11.7403i	0.546801	+	0.546801i	0.925514	−	0.378713i	$-0.123633\pi$
$461$	11.7403	+	11.7403i	0.546801	+	0.546801i	−0.378713	+	0.925514i	$0.623633\pi$
$462$		0			0
$463$	−26.6096			−1.23665			−0.618326	−	0.785922i	$-0.712189\pi$
$463$	−26.6096			−1.23665			−0.618326	+	0.785922i	$0.712189\pi$
$464$	9.10153	−	10.3812i	0.422528	−	0.481934i
$465$		0			0
$466$	−21.5442	+	9.34063i	−0.998015	+	0.432696i
$467$	−1.47583	−	1.47583i	−0.0682933	−	0.0682933i	0.672135	−	0.740428i	$-0.265377\pi$
$467$	−1.47583	−	1.47583i	−0.0682933	−	0.0682933i	−0.740428	+	0.672135i	$0.765377\pi$
$468$		0			0
$469$	18.3385	−	18.3385i	0.846792	−	0.846792i
$470$	−5.68591	−	2.24668i	−0.262271	−	0.103632i
$471$		0			0
$472$	−24.0139	+	11.3607i	−1.10533	+	0.522920i
$473$		−	2.12851i		−	0.0978688i
$474$		0			0
$475$	−3.22022	+	3.22022i	−0.147754	+	0.147754i
$476$	11.4998	+	10.7693i	0.527094	+	0.493609i
$477$		0			0
$478$	2.14462	+	4.94656i	0.0980924	+	0.226251i
$479$	2.78600			0.127296			0.0636479	−	0.997972i	$-0.479727\pi$
$479$	2.78600			0.127296			0.0636479	+	0.997972i	$0.479727\pi$
$480$		0			0
$481$	20.2215			0.922022
$482$	−5.37223	−	12.3911i	−0.244698	−	0.564397i
$483$		0			0
$484$	−15.3122	−	14.3395i	−0.696009	−	0.651794i
$485$	−1.37270	+	1.37270i	−0.0623311	+	0.0623311i
$486$		0			0
$487$		−	16.9499i		−	0.768073i	−0.923318	−	0.384036i	$-0.874534\pi$
$487$		−	16.9499i		−	0.768073i	0.923318	−	0.384036i	$-0.125466\pi$
$488$	9.00128	+	19.0265i	0.407469	+	0.861291i
$489$		0			0
$490$	5.23862	+	2.06994i	0.236657	+	0.0935106i
$491$	22.8390	−	22.8390i	1.03071	−	1.03071i	0.0311972	−	0.999513i	$-0.490068\pi$
$491$	22.8390	−	22.8390i	1.03071	−	1.03071i	0.999513	−	0.0311972i	$-0.00993197\pi$
$492$		0			0
$493$	−11.0687	−	11.0687i	−0.498507	−	0.498507i
$494$	15.7730	−	6.83848i	0.709660	−	0.307678i
$495$		0			0
$496$	1.49536	+	22.7670i	0.0671436	+	1.02227i
$497$	−24.3933			−1.09419
$498$		0			0
$499$	2.33906	+	2.33906i	0.104711	+	0.104711i	0.757521	−	0.652811i	$-0.226410\pi$
$499$	2.33906	+	2.33906i	0.104711	+	0.104711i	−0.652811	+	0.757521i	$0.726410\pi$
$500$	−1.99892	+	0.0655751i	−0.0893946	+	0.00293261i
$501$		0			0
$502$	22.3083	+	8.81469i	0.995666	+	0.393419i
$503$		−	1.58801i		−	0.0708057i	−0.999373	−	0.0354029i	$-0.988729\pi$
$503$		−	1.58801i		−	0.0708057i	0.999373	−	0.0354029i	$-0.0112714\pi$
$504$		0			0
$505$		−	14.6223i		−	0.650682i
$506$	3.28772	−	8.32058i	0.146157	−	0.369895i
$507$		0			0
$508$	3.42948	−	3.66212i	0.152159	−	0.162480i
$509$	3.61613	+	3.61613i	0.160282	+	0.160282i	0.782692	−	0.622410i	$-0.213846\pi$
$509$	3.61613	+	3.61613i	0.160282	+	0.160282i	−0.622410	+	0.782692i	$0.713846\pi$
$510$		0			0
$511$	11.5305			0.510079
$512$	11.6388	+	19.4046i	0.514367	+	0.857570i
$513$		0			0
$514$	10.6182	+	24.4909i	0.468348	+	1.08025i
$515$	3.51009	+	3.51009i	0.154673	+	0.154673i
$516$		0			0
$517$	2.18499	−	2.18499i	0.0960956	−	0.0960956i
$518$	−6.83844	+	17.3067i	−0.300464	+	0.760414i
$519$		0			0
$520$	7.10891	+	2.54279i	0.311746	+	0.111509i
$521$			8.93031i			0.391244i	0.980679	+	0.195622i	$0.0626725\pi$
$521$			8.93031i			0.391244i	−0.980679	+	0.195622i	$0.937327\pi$
$522$		0			0
$523$	15.0355	−	15.0355i	0.657455	−	0.657455i	−0.297323	−	0.954777i	$-0.596094\pi$
$523$	15.0355	−	15.0355i	0.657455	−	0.657455i	0.954777	+	0.297323i	$0.0960937\pi$
$524$	24.1922	−	0.793629i	1.05684	−	0.0346699i
$525$		0			0
$526$	30.0242	−	13.0172i	1.30912	−	0.567576i
$527$	25.8691			1.12687
$528$		0			0
$529$	−55.3305			−2.40567
$530$	2.52231	−	1.09356i	0.109562	−	0.0475014i
$531$		0			0
$532$	0.518717	+	15.8120i	0.0224892	+	0.685538i
$533$	−18.9397	+	18.9397i	−0.820368	+	0.820368i
$534$		0			0
$535$			3.88387i			0.167914i
$536$	−18.0600	−	38.1746i	−0.780075	−	1.64889i
$537$		0			0
$538$	7.81773	−	19.7851i	0.337046	−	0.852998i
$539$	−2.01310	+	2.01310i	−0.0867106	+	0.0867106i
$540$		0			0
$541$	5.57591	+	5.57591i	0.239727	+	0.239727i	0.816737	−	0.577010i	$-0.195781\pi$
$541$	5.57591	+	5.57591i	0.239727	+	0.239727i	−0.577010	+	0.816737i	$0.695781\pi$
$542$	−11.2376	−	25.9196i	−0.482696	−	1.11334i
$543$		0			0
$544$	22.8187	−	11.7259i	0.978344	−	0.502743i
$545$	−9.89891			−0.424023
$546$		0			0
$547$	32.8366	+	32.8366i	1.40399	+	1.40399i	0.786856	+	0.617136i	$0.211707\pi$
$547$	32.8366	+	32.8366i	1.40399	+	1.40399i	0.617136	+	0.786856i	$0.288293\pi$
$548$	−9.44695	−	8.84682i	−0.403554	−	0.377918i
$549$		0			0
$550$	0.371475	−	0.940130i	0.0158397	−	0.0400873i
$551$		−	15.7184i		−	0.669628i
$552$		0			0
$553$			7.42199i			0.315615i
$554$	30.0463	+	11.8722i	1.27654	+	0.504402i
$555$		0			0
$556$	−1.52488	−	46.4829i	−0.0646694	−	1.97132i
$557$	−24.2077	−	24.2077i	−1.02571	−	1.02571i	−0.999661	−	0.0260537i	$-0.991706\pi$
$557$	−24.2077	−	24.2077i	−1.02571	−	1.02571i	−0.0260537	−	0.999661i	$-0.508294\pi$
$558$		0			0
$559$	7.94877			0.336197
$560$	−4.58033	+	5.22430i	−0.193554	+	0.220767i
$561$		0			0
$562$	12.2423	−	5.30773i	0.516411	−	0.223893i
$563$	−22.3407	−	22.3407i	−0.941547	−	0.941547i	0.0568365	−	0.998384i	$-0.481899\pi$
$563$	−22.3407	−	22.3407i	−0.941547	−	0.941547i	−0.998384	+	0.0568365i	$0.981899\pi$
$564$		0			0
$565$	−4.61878	+	4.61878i	−0.194314	+	0.194314i
$566$	−16.2065	−	6.40368i	−0.681208	−	0.269167i
$567$		0			0
$568$	−13.3779	+	37.4009i	−0.561325	+	1.56931i
$569$		−	29.3339i		−	1.22974i	−0.788629	−	0.614870i	$-0.789209\pi$
$569$		−	29.3339i		−	1.22974i	0.788629	−	0.614870i	$-0.210791\pi$
$570$		0			0
$571$	23.9934	−	23.9934i	1.00409	−	1.00409i	0.00410070	−	0.999992i	$-0.498695\pi$
$571$	23.9934	−	23.9934i	1.00409	−	1.00409i	0.999992	−	0.00410070i	$-0.00130530\pi$
$572$	−2.60839	+	2.78534i	−0.109062	+	0.116461i
$573$		0			0
$574$	−9.80471	−	22.6146i	−0.409241	−	0.943915i
$575$	−8.85045			−0.369089
$576$		0			0
$577$	−31.9232			−1.32898			−0.664490	−	0.747297i	$-0.731351\pi$
$577$	−31.9232			−1.32898			−0.664490	+	0.747297i	$0.731351\pi$
$578$	−2.00740	−	4.63009i	−0.0834970	−	0.192586i
$579$		0			0
$580$	4.71851	−	5.03859i	0.195925	−	0.209216i
$581$	15.9016	−	15.9016i	0.659710	−	0.659710i
$582$		0			0
$583$			1.38951i			0.0575477i
$584$	6.32361	−	17.6790i	0.261673	−	0.731564i
$585$		0			0
$586$	−20.6549	−	8.16142i	−0.853248	−	0.337145i
$587$	26.2847	−	26.2847i	1.08488	−	1.08488i	0.0888379	−	0.996046i	$-0.471685\pi$
$587$	26.2847	−	26.2847i	1.08488	−	1.08488i	0.996046	−	0.0888379i	$-0.0283153\pi$
$588$		0			0
$589$	18.3681	+	18.3681i	0.756846	+	0.756846i
$590$	−12.1867	+	5.28363i	−0.501719	+	0.217524i
$591$		0			0
$592$	22.7850	+	19.9764i	0.936459	+	0.821026i
$593$	38.2085			1.56904			0.784518	−	0.620106i	$-0.212910\pi$
$593$	38.2085			1.56904			0.784518	+	0.620106i	$0.212910\pi$
$594$		0			0
$595$	5.57027	+	5.57027i	0.228359	+	0.228359i
$596$	0.252990	+	7.71187i	0.0103629	+	0.315891i
$597$		0			0
$598$	31.0727	+	12.2778i	1.27066	+	0.502076i
$599$			25.1150i			1.02617i	0.858337	+	0.513086i	$0.171498\pi$
$599$			25.1150i			1.02617i	−0.858337	+	0.513086i	$0.828502\pi$
$600$		0			0
$601$		−	22.2022i		−	0.905647i	−0.891600	−	0.452823i	$-0.850417\pi$
$601$		−	22.2022i		−	0.905647i	0.891600	−	0.452823i	$-0.149583\pi$
$602$	−2.68809	+	6.80302i	−0.109558	+	0.277270i
$603$		0			0
$604$	16.8166	+	15.7483i	0.684257	+	0.640789i
$605$	−7.41690	−	7.41690i	−0.301540	−	0.301540i
$606$		0			0
$607$	12.9648			0.526226			0.263113	−	0.964765i	$-0.415251\pi$
$607$	12.9648			0.526226			0.263113	+	0.964765i	$0.415251\pi$
$608$	24.5281	+	7.87639i	0.994747	+	0.319430i
$609$		0			0
$610$	4.18630	+	9.65572i	0.169498	+	0.390949i
$611$	8.15970	+	8.15970i	0.330106	+	0.330106i
$612$		0			0
$613$	7.42804	−	7.42804i	0.300016	−	0.300016i	−0.541004	−	0.841020i	$-0.681956\pi$
$613$	7.42804	−	7.42804i	0.300016	−	0.300016i	0.841020	+	0.541004i	$0.181956\pi$
$614$	−2.20383	+	5.57746i	−0.0889394	+	0.225088i
$615$		0			0
$616$	−1.50175	−	3.17435i	−0.0605074	−	0.127898i
$617$		−	23.2743i		−	0.936989i	−0.883467	−	0.468494i	$-0.844797\pi$
$617$		−	23.2743i		−	0.936989i	0.883467	−	0.468494i	$-0.155203\pi$
$618$		0			0
$619$	−31.6213	+	31.6213i	−1.27097	+	1.27097i	−0.325386	+	0.945581i	$0.605494\pi$
$619$	−31.6213	+	31.6213i	−1.27097	+	1.27097i	−0.945581	+	0.325386i	$0.894506\pi$
$620$	0.374041	+	11.4019i	0.0150219	+	0.457911i
$621$		0			0
$622$	−11.7568	+	5.09722i	−0.471403	+	0.204380i
$623$	5.62474			0.225351
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	25.3922	−	11.0090i	1.01488	−	0.440007i
$627$		0			0
$628$	−9.27262	+	0.304190i	−0.370018	+	0.0121385i
$629$	24.2939	−	24.2939i	0.968663	−	0.968663i
$630$		0			0
$631$		−	29.9258i		−	1.19133i	−0.803234	−	0.595663i	$-0.796889\pi$
$631$		−	29.9258i		−	1.19133i	0.803234	−	0.595663i	$-0.203111\pi$
$632$	11.3797	+	4.07041i	0.452661	+	0.161912i
$633$		0			0
$634$	8.15956	−	20.6502i	0.324058	−	0.820126i
$635$	1.77386	−	1.77386i	0.0703933	−	0.0703933i
$636$		0			0
$637$	−7.51782	−	7.51782i	−0.297867	−	0.297867i
$638$	1.38785	+	3.20109i	0.0549456	+	0.126732i
$639$		0			0
$640$	5.49816	+	9.88789i	0.217334	+	0.390853i
$641$	−10.2240			−0.403825			−0.201912	−	0.979404i	$-0.564716\pi$
$641$	−10.2240			−0.403825			−0.201912	+	0.979404i	$0.564716\pi$
$642$		0			0
$643$	−13.7202	−	13.7202i	−0.541074	−	0.541074i	0.382770	−	0.923844i	$-0.374970\pi$
$643$	−13.7202	−	13.7202i	−0.541074	−	0.541074i	−0.923844	+	0.382770i	$0.874970\pi$
$644$	−21.0161	+	22.4417i	−0.828150	+	0.884328i
$645$		0			0
$646$	10.7338	−	27.1652i	0.422316	−	1.06880i
$647$			18.6767i			0.734255i	0.930171	+	0.367128i	$0.119659\pi$
$647$			18.6767i			0.734255i	−0.930171	+	0.367128i	$0.880341\pi$
$648$		0			0
$649$		−	6.71353i		−	0.263529i
$650$	3.51086	+	1.38725i	0.137707	+	0.0544125i
$651$		0			0
$652$	26.2158	−	0.860014i	1.02669	−	0.0336808i
$653$	−12.7935	−	12.7935i	−0.500647	−	0.500647i	0.410992	−	0.911639i	$-0.365183\pi$
$653$	−12.7935	−	12.7935i	−0.500647	−	0.500647i	−0.911639	+	0.410992i	$0.865183\pi$
$654$		0			0
$655$	12.1026			0.472888
$656$	−40.0508	+	2.63058i	−1.56372	+	0.102707i
$657$		0			0
$658$	−9.74296	+	4.22412i	−0.379820	+	0.164673i
$659$	−12.3193	−	12.3193i	−0.479893	−	0.479893i	0.425204	−	0.905097i	$-0.360202\pi$
$659$	−12.3193	−	12.3193i	−0.479893	−	0.479893i	−0.905097	+	0.425204i	$0.860202\pi$
$660$		0			0
$661$	−24.0352	+	24.0352i	−0.934862	+	0.934862i	−0.998005	−	0.0631421i	$-0.979888\pi$
$661$	−24.0352	+	24.0352i	−0.934862	+	0.934862i	0.0631421	+	0.998005i	$0.479888\pi$
$662$	15.1542	+	5.98792i	0.588987	+	0.232727i
$663$		0			0
$664$	−15.6602	−	33.1019i	−0.607733	−	1.28460i
$665$			7.91026i			0.306747i
$666$		0			0
$667$	21.6003	−	21.6003i	0.836367	−	0.836367i
$668$	10.3365	+	9.67984i	0.399931	+	0.374524i
$669$		0			0
$670$	−8.39934	−	19.3731i	−0.324495	−	0.748449i
$671$	−5.31923			−0.205347
$672$		0			0
$673$	−21.5360			−0.830150			−0.415075	−	0.909787i	$-0.636245\pi$
$673$	−21.5360			−0.830150			−0.415075	+	0.909787i	$0.636245\pi$
$674$	14.1413	+	32.6169i	0.544701	+	1.25636i
$675$		0			0
$676$	8.57602	+	8.03121i	0.329847	+	0.308893i
$677$	−13.1852	+	13.1852i	−0.506750	+	0.506750i	−0.913527	−	0.406778i	$-0.866652\pi$
$677$	−13.1852	+	13.1852i	−0.506750	+	0.506750i	0.406778	+	0.913527i	$0.366652\pi$
$678$		0			0
$679$			3.37195i			0.129404i
$680$	11.5955	−	5.48570i	0.444665	−	0.210367i
$681$		0			0
$682$	−5.36251	−	2.11890i	−0.205341	−	0.0811367i
$683$	−30.6011	+	30.6011i	−1.17092	+	1.17092i	−0.188926	+	0.981991i	$0.560501\pi$
$683$	−30.6011	+	30.6011i	−1.17092	+	1.17092i	−0.981991	+	0.188926i	$0.939499\pi$
$684$		0			0
$685$	−4.57590	−	4.57590i	−0.174836	−	0.174836i
$686$	24.7527	−	10.7317i	0.945062	−	0.409738i
$687$		0			0
$688$	8.95645	+	7.85243i	0.341462	+	0.299371i
$689$	−5.18905			−0.197687
$690$		0			0
$691$	−25.2675	−	25.2675i	−0.961220	−	0.961220i	0.0380558	−	0.999276i	$-0.487884\pi$
$691$	−25.2675	−	25.2675i	−0.961220	−	0.961220i	−0.999276	+	0.0380558i	$0.987884\pi$
$692$	−14.7415	+	0.483598i	−0.560388	+	0.0183836i
$693$		0			0
$694$	13.7034	+	5.41465i	0.520174	+	0.205537i
$695$		−	23.2540i		−	0.882074i
$696$		0			0
$697$			45.5079i			1.72373i
$698$	−2.39586	+	6.06345i	−0.0906847	+	0.229505i
$699$		0			0
$700$	−2.37458	+	2.53566i	−0.0897506	+	0.0958389i
$701$	−18.5583	−	18.5583i	−0.700937	−	0.700937i	0.263675	−	0.964612i	$-0.415065\pi$
$701$	−18.5583	−	18.5583i	−0.700937	−	0.700937i	−0.964612	+	0.263675i	$0.915065\pi$
$702$		0			0
$703$	34.4995			1.30117
$704$	−5.69064	+	0.561660i	−0.214474	+	0.0211684i
$705$		0			0
$706$	0.282866	+	0.652431i	0.0106458	+	0.0245546i
$707$	−17.9593	−	17.9593i	−0.675431	−	0.675431i
$708$		0			0
$709$	4.38093	−	4.38093i	0.164529	−	0.164529i	−0.620040	−	0.784570i	$-0.712884\pi$
$709$	4.38093	−	4.38093i	0.164529	−	0.164529i	0.784570	+	0.620040i	$0.212884\pi$
$710$	−7.29850	+	18.4711i	−0.273908	+	0.693207i
$711$		0			0
$712$	3.08475	−	8.62409i	0.115606	−	0.323201i
$713$			50.4831i			1.89061i
$714$		0			0
$715$	−1.34916	+	1.34916i	−0.0504556	+	0.0504556i
$716$	17.8716	−	0.586281i	0.667892	−	0.0219103i
$717$		0			0
$718$	7.72230	−	3.34806i	0.288194	−	0.124948i
$719$	−1.61691			−0.0603007			−0.0301503	−	0.999545i	$-0.509599\pi$
$719$	−1.61691			−0.0603007			−0.0301503	+	0.999545i	$0.509599\pi$
$720$		0			0
$721$	8.62231			0.321112
$722$	2.25713	−	0.978596i	0.0840018	−	0.0364196i
$723$		0			0
$724$	1.21203	+	36.9463i	0.0450447	+	1.37310i
$725$	2.44059	−	2.44059i	0.0906411	−	0.0906411i
$726$		0			0
$727$		−	39.3600i		−	1.45978i	−0.683563	−	0.729891i	$-0.739571\pi$
$727$		−	39.3600i		−	1.45978i	0.683563	−	0.729891i	$-0.260429\pi$
$728$	11.8544	−	5.60821i	0.439353	−	0.207854i
$729$		0			0
$730$	3.44993	−	8.73110i	0.127688	−	0.323152i
$731$	9.54958	−	9.54958i	0.353204	−	0.353204i
$732$		0			0
$733$	−34.0787	−	34.0787i	−1.25873	−	1.25873i	−0.951701	−	0.307026i	$-0.900666\pi$
$733$	−34.0787	−	34.0787i	−1.25873	−	1.25873i	−0.307026	−	0.951701i	$-0.599334\pi$
$734$	−1.09902	−	2.53488i	−0.0405654	−	0.0935643i
$735$		0			0
$736$	22.8828	+	44.5303i	0.843473	+	1.64141i
$737$	10.6724			0.393124
$738$		0			0
$739$	15.4278	+	15.4278i	0.567520	+	0.567520i	0.931433	−	0.363913i	$-0.118559\pi$
$739$	15.4278	+	15.4278i	0.567520	+	0.567520i	−0.363913	+	0.931433i	$0.618559\pi$
$740$	11.0589	+	10.3564i	0.406533	+	0.380708i
$741$		0			0
$742$	1.75481	−	4.44109i	0.0644212	−	0.163037i
$743$			23.5004i			0.862147i	0.902317	+	0.431074i	$0.141865\pi$
$743$			23.5004i			0.862147i	−0.902317	+	0.431074i	$0.858135\pi$
$744$		0			0
$745$			3.85801i			0.141347i
$746$	34.6918	+	13.7078i	1.27016	+	0.501879i
$747$		0			0
$748$	0.212577	+	6.47997i	0.00777258	+	0.236931i
$749$	4.77024	+	4.77024i	0.174301	+	0.174301i
$750$		0			0
$751$	10.8586			0.396236			0.198118	−	0.980178i	$-0.436517\pi$
$751$	10.8586			0.396236			0.198118	+	0.980178i	$0.436517\pi$
$752$	1.13332	+	17.2549i	0.0413280	+	0.629222i
$753$		0			0
$754$	−11.9543	+	5.18285i	−0.435348	+	0.188748i
$755$	8.14560	+	8.14560i	0.296449	+	0.296449i
$756$		0			0
$757$	18.8434	−	18.8434i	0.684874	−	0.684874i	−0.276220	−	0.961094i	$-0.589082\pi$
$757$	18.8434	−	18.8434i	0.684874	−	0.684874i	0.961094	+	0.276220i	$0.0890819\pi$
$758$	7.16389	+	2.83068i	0.260204	+	0.102815i
$759$		0			0
$760$	12.1283	+	4.33819i	0.439941	+	0.157363i
$761$		−	22.2837i		−	0.807783i	−0.914807	−	0.403891i	$-0.867657\pi$
$761$		−	22.2837i		−	0.807783i	0.914807	−	0.403891i	$-0.132343\pi$
$762$		0			0
$763$	−12.1580	+	12.1580i	−0.440151	+	0.440151i
$764$	−30.3113	+	32.3675i	−1.09663	+	1.17102i
$765$		0			0
$766$	1.28968	+	2.97465i	0.0465980	+	0.107478i
$767$	25.0713			0.905271
$768$		0			0
$769$	10.5399			0.380077			0.190039	−	0.981777i	$-0.439139\pi$
$769$	10.5399			0.380077			0.190039	+	0.981777i	$0.439139\pi$
$770$	−0.698433	−	1.61094i	−0.0251698	−	0.0580542i
$771$		0			0
$772$	−10.9052	+	11.6449i	−0.392486	+	0.419110i
$773$	−4.07768	+	4.07768i	−0.146664	+	0.146664i	−0.776626	−	0.629962i	$-0.783070\pi$
$773$	−4.07768	+	4.07768i	−0.146664	+	0.146664i	0.629962	+	0.776626i	$0.283070\pi$
$774$		0			0
$775$			5.70401i			0.204894i
$776$	5.17002	+	1.84926i	0.185593	+	0.0663846i
$777$		0			0
$778$	9.12358	+	3.60502i	0.327096	+	0.129246i
$779$	−32.3125	+	32.3125i	−1.15772	+	1.15772i
$780$		0			0
$781$	−7.09809	−	7.09809i	−0.253990	−	0.253990i
$782$	52.0808	−	22.5800i	1.86241	−	0.807459i
$783$		0			0
$784$	−1.04417	−	15.8976i	−0.0372918	−	0.567770i
$785$	−4.63881			−0.165566
$786$		0			0
$787$	−8.16669	−	8.16669i	−0.291111	−	0.291111i	0.546408	−	0.837519i	$-0.315995\pi$
$787$	−8.16669	−	8.16669i	−0.291111	−	0.291111i	−0.837519	+	0.546408i	$0.815995\pi$
$788$	−0.534470	−	16.2922i	−0.0190397	−	0.580387i
$789$		0			0
$790$	5.62007	+	2.22067i	0.199953	+	0.0790077i
$791$			11.3458i			0.403409i
$792$		0			0
$793$		−	19.8643i		−	0.705403i
$794$	−7.98290	+	20.2032i	−0.283303	+	0.716983i
$795$		0			0
$796$	7.86653	+	7.36679i	0.278822	+	0.261109i
$797$	−17.9971	−	17.9971i	−0.637491	−	0.637491i	0.312445	−	0.949936i	$-0.398852\pi$
$797$	−17.9971	−	17.9971i	−0.637491	−	0.637491i	−0.949936	+	0.312445i	$0.898852\pi$
$798$		0			0
$799$	19.6060			0.693609
$800$	2.58550	+	5.03142i	0.0914112	+	0.177888i
$801$		0			0
$802$	−3.99848	−	9.22250i	−0.141191	−	0.325658i
$803$	3.35520	+	3.35520i	0.118402	+	0.118402i
$804$		0			0
$805$	−10.8703	+	10.8703i	−0.383128	+	0.383128i
$806$	7.91289	−	20.0260i	0.278720	−	0.705385i
$807$		0			0
$808$	−37.3854	+	17.6867i	−1.31521	+	0.622215i
$809$		−	42.0296i		−	1.47768i	−0.673879	−	0.738841i	$-0.735373\pi$
$809$		−	42.0296i		−	1.47768i	0.673879	−	0.738841i	$-0.264627\pi$
$810$		0			0
$811$	18.7601	−	18.7601i	0.658757	−	0.658757i	−0.296329	−	0.955086i	$-0.595762\pi$
$811$	18.7601	−	18.7601i	0.658757	−	0.658757i	0.955086	+	0.296329i	$0.0957624\pi$
$812$	−0.393133	−	11.9839i	−0.0137963	−	0.420551i
$813$		0			0
$814$	−7.02587	+	3.04611i	−0.246257	+	0.106766i
$815$	13.1149			0.459397
$816$		0			0
$817$	13.5612			0.474447
$818$	−37.8482	+	16.4093i	−1.32333	+	0.573738i
$819$		0			0
$820$	−20.0578	+	0.657999i	−0.700447	+	0.0229783i
$821$	21.4050	−	21.4050i	0.747038	−	0.747038i	−0.226884	−	0.973922i	$-0.572854\pi$
$821$	21.4050	−	21.4050i	0.747038	−	0.747038i	0.973922	+	0.226884i	$0.0728538\pi$
$822$		0			0
$823$			43.7323i			1.52441i	0.647334	+	0.762206i	$0.275884\pi$
$823$			43.7323i			1.52441i	−0.647334	+	0.762206i	$0.724116\pi$
$824$	4.72869	−	13.2201i	0.164732	−	0.460544i
$825$		0			0
$826$	−8.47850	+	21.4574i	−0.295005	+	0.746599i
$827$	19.9621	−	19.9621i	0.694149	−	0.694149i	−0.268993	−	0.963142i	$-0.586691\pi$
$827$	19.9621	−	19.9621i	0.694149	−	0.694149i	0.963142	+	0.268993i	$0.0866908\pi$
$828$		0			0
$829$	31.3869	+	31.3869i	1.09011	+	1.09011i	0.995516	+	0.0945964i	$0.0301561\pi$
$829$	31.3869	+	31.3869i	1.09011	+	1.09011i	0.0945964	+	0.995516i	$0.469844\pi$
$830$	−7.28322	−	16.7988i	−0.252804	−	0.583094i
$831$		0			0
$832$	−2.09749	−	21.2513i	−0.0727172	−	0.736758i
$833$	−18.0637			−0.625869
$834$		0			0
$835$	5.00677	+	5.00677i	0.173267	+	0.173267i
$836$	−4.45012	+	4.75199i	−0.153911	+	0.164351i
$837$		0			0
$838$	−2.25353	+	5.70324i	−0.0778469	+	0.197015i
$839$		−	54.5335i		−	1.88271i	−0.337423	−	0.941353i	$-0.609555\pi$
$839$		−	54.5335i		−	1.88271i	0.337423	−	0.941353i	$-0.390445\pi$
$840$		0			0
$841$		−	17.0871i		−	0.589210i
$842$	0.990001	+	0.391181i	0.0341177	+	0.0134810i
$843$		0			0
$844$	−30.4025	+	0.997361i	−1.04650	+	0.0343306i
$845$	4.15404	+	4.15404i	0.142903	+	0.142903i
$846$		0			0
$847$	−18.2192			−0.626018
$848$	−5.84688	−	5.12615i	−0.200783	−	0.176033i
$849$		0			0
$850$	5.88454	−	2.55128i	0.201838	−	0.0875082i
$851$	47.4092	+	47.4092i	1.62517	+	1.62517i
$852$		0			0
$853$	21.5932	−	21.5932i	0.739336	−	0.739336i	−0.233114	−	0.972449i	$-0.574891\pi$
$853$	21.5932	−	21.5932i	0.739336	−	0.739336i	0.972449	+	0.233114i	$0.0748914\pi$
$854$	17.0010	+	6.71765i	0.581764	+	0.229873i
$855$		0			0
$856$	9.93005	−	4.69781i	0.339402	−	0.160568i
$857$			41.3609i			1.41286i	0.707782	+	0.706431i	$0.249696\pi$
$857$			41.3609i			1.41286i	−0.707782	+	0.706431i	$0.750304\pi$
$858$		0			0
$859$	−0.700596	+	0.700596i	−0.0239040	+	0.0239040i	−0.718958	−	0.695054i	$-0.755381\pi$
$859$	−0.700596	+	0.700596i	−0.0239040	+	0.0239040i	0.695054	+	0.718958i	$0.255381\pi$
$860$	4.34709	+	4.07093i	0.148234	+	0.138818i
$861$		0			0
$862$	9.40787	+	21.6993i	0.320433	+	0.739081i
$863$	−55.0780			−1.87488			−0.937439	−	0.348150i	$-0.886810\pi$
$863$	−55.0780			−1.87488			−0.937439	+	0.348150i	$0.886810\pi$
$864$		0			0
$865$	−7.37471			−0.250748
$866$	−15.9580	−	36.8072i	−0.542276	−	1.25076i
$867$		0			0
$868$	14.4634	+	13.5446i	0.490920	+	0.459734i
$869$	−2.15969	+	2.15969i	−0.0732623	+	0.0732623i
$870$		0			0
$871$			39.8556i			1.35045i
$872$	11.9734	+	25.3090i	0.405472	+	0.857070i
$873$		0			0
$874$	53.0124	+	20.9469i	1.79317	+	0.708538i
$875$	−1.22822	+	1.22822i	−0.0415214	+	0.0415214i
$876$		0			0
$877$	−36.5100	−	36.5100i	−1.23285	−	1.23285i	−0.962863	−	0.269992i	$-0.912979\pi$
$877$	−36.5100	−	36.5100i	−1.23285	−	1.23285i	−0.269992	−	0.962863i	$-0.587021\pi$
$878$	−17.5188	+	7.59537i	−0.591229	+	0.256331i
$879$		0			0
$880$	−2.85300	+	0.187388i	−0.0961745	+	0.00631685i
$881$	−54.3503			−1.83111			−0.915554	−	0.402196i	$-0.868247\pi$
$881$	−54.3503			−1.83111			−0.915554	+	0.402196i	$0.868247\pi$
$882$		0			0
$883$	35.5476	+	35.5476i	1.19627	+	1.19627i	0.975274	+	0.220999i	$0.0709319\pi$
$883$	35.5476	+	35.5476i	1.19627	+	1.19627i	0.220999	+	0.975274i	$0.429068\pi$
$884$	−24.1991	+	0.793855i	−0.813902	+	0.0267002i
$885$		0			0
$886$	−17.7681	−	7.02075i	−0.596932	−	0.235867i
$887$			0.817003i			0.0274323i	0.999906	+	0.0137161i	$0.00436612\pi$
$887$			0.817003i			0.0274323i	−0.999906	+	0.0137161i	$0.995634\pi$
$888$		0			0
$889$		−	4.35737i		−	0.146141i
$890$	1.68293	−	4.25916i	0.0564118	−	0.142767i
$891$		0			0
$892$	5.45075	−	5.82051i	0.182505	−	0.194885i
$893$	13.9211	+	13.9211i	0.465851	+	0.465851i
$894$		0			0
$895$	8.94060			0.298851
$896$	18.8974	+	5.39155i	0.631319	+	0.180119i
$897$		0			0
$898$	−5.26302	−	12.1392i	−0.175629	−	0.405090i
$899$	−13.9211	−	13.9211i	−0.464296	−	0.464296i
$900$		0			0
$901$	−6.23407	+	6.23407i	−0.207687	+	0.207687i
$902$	3.72748	−	9.43352i	0.124112	−	0.314102i
$903$		0			0
$904$	17.3958	+	6.22230i	0.578575	+	0.206950i
$905$			18.4831i			0.614398i
$906$		0			0
$907$	−3.36159	+	3.36159i	−0.111620	+	0.111620i	−0.760711	−	0.649091i	$-0.775149\pi$
$907$	−3.36159	+	3.36159i	−0.111620	+	0.111620i	0.649091	+	0.760711i	$0.275149\pi$
$908$	−10.8017	+	0.354352i	−0.358467	+	0.0117596i
$909$		0			0
$910$	6.01595	−	2.60826i	0.199427	−	0.0864629i
$911$	−34.6568			−1.14823			−0.574116	−	0.818774i	$-0.694654\pi$
$911$	−34.6568			−1.14823			−0.574116	+	0.818774i	$0.694654\pi$
$912$		0			0
$913$	9.25426			0.306271
$914$	−8.88510	+	3.85219i	−0.293893	+	0.127419i
$915$		0			0
$916$	−0.816725	−	24.8962i	−0.0269853	−	0.822593i
$917$	14.8646	−	14.8646i	0.490874	−	0.490874i
$918$		0			0
$919$		−	24.3452i		−	0.803074i	−0.915843	−	0.401537i	$-0.868476\pi$
$919$		−	24.3452i		−	0.803074i	0.915843	−	0.401537i	$-0.131524\pi$
$920$	10.7053	+	22.6283i	0.352942	+	0.746034i
$921$		0			0
$922$	8.62875	−	21.8377i	0.284173	−	0.719185i
$923$	26.5074	−	26.5074i	0.872501	−	0.872501i
$924$		0			0
$925$	5.35670	+	5.35670i	0.176127	+	0.176127i
$926$	14.9691	+	34.5263i	0.491915	+	1.13460i
$927$		0			0
$928$	−18.5898	−	5.96948i	−0.610238	−	0.195958i
$929$	−3.16600			−0.103873			−0.0519366	−	0.998650i	$-0.516539\pi$
$929$	−3.16600			−0.103873			−0.0519366	+	0.998650i	$0.516539\pi$
$930$		0			0
$931$	−12.8260	−	12.8260i	−0.420354	−	0.420354i
$932$	24.2392	+	22.6994i	0.793981	+	0.743542i
$933$		0			0
$934$	−1.08469	+	2.74513i	−0.0354921	+	0.0898235i
$935$			3.24173i			0.106016i
$936$		0			0
$937$			23.4847i			0.767211i	0.923497	+	0.383606i	$0.125318\pi$
$937$			23.4847i			0.767211i	−0.923497	+	0.383606i	$0.874682\pi$
$938$	−34.1107	−	13.4782i	−1.11375	−	0.440079i
$939$		0			0
$940$	0.283483	+	8.64140i	0.00924619	+	0.281851i
$941$	−27.7583	−	27.7583i	−0.904896	−	0.904896i	0.0909585	−	0.995855i	$-0.471007\pi$
$941$	−27.7583	−	27.7583i	−0.904896	−	0.904896i	−0.995855	+	0.0909585i	$0.971007\pi$
$942$		0			0
$943$	−88.8078			−2.89198
$944$	28.2496	+	24.7674i	0.919446	+	0.806109i
$945$		0			0
$946$	−2.76177	+	1.19738i	−0.0897927	+	0.0389302i
$947$	27.2916	+	27.2916i	0.886857	+	0.886857i	0.994220	−	0.107363i	$-0.0342407\pi$
$947$	27.2916	+	27.2916i	0.886857	+	0.886857i	−0.107363	+	0.994220i	$0.534241\pi$
$948$		0			0
$949$	−12.5298	+	12.5298i	−0.406734	+	0.406734i
$950$	5.98979	+	2.36676i	0.194335	+	0.0767877i
$951$		0			0
$952$	7.50412	−	20.9794i	0.243210	−	0.679946i
$953$			12.1516i			0.393630i	0.980441	+	0.196815i	$0.0630598\pi$
$953$			12.1516i			0.393630i	−0.980441	+	0.196815i	$0.936940\pi$
$954$		0			0
$955$	−15.6781	+	15.6781i	−0.507333	+	0.507333i
$956$	5.21179	−	5.56534i	0.168561	−	0.179996i
$957$		0			0
$958$	−1.56725	−	3.61488i	−0.0506357	−	0.116791i
$959$	−11.2404			−0.362972
$960$		0			0
$961$	1.53571			0.0495392
$962$	−11.3755	−	26.2377i	−0.366762	−	0.845938i
$963$		0			0
$964$	−13.0554	+	13.9411i	−0.420488	+	0.449012i
$965$	−5.64056	+	5.64056i	−0.181576	+	0.181576i
$966$		0			0
$967$			48.2694i			1.55224i	0.630585	+	0.776120i	$0.282815\pi$
$967$			48.2694i			1.55224i	−0.630585	+	0.776120i	$0.717185\pi$
$968$	−9.99184	+	27.9344i	−0.321150	+	0.897845i
$969$		0			0
$970$	2.55330	+	1.00889i	0.0819816	+	0.0323935i
$971$	−5.92047	+	5.92047i	−0.189997	+	0.189997i	−0.795695	−	0.605698i	$-0.792894\pi$
$971$	−5.92047	+	5.92047i	−0.189997	+	0.189997i	0.605698	+	0.795695i	$0.292894\pi$
$972$		0			0
$973$	−28.5610	−	28.5610i	−0.915623	−	0.915623i
$974$	−21.9927	+	9.53509i	−0.704692	+	0.305524i
$975$		0			0
$976$	19.6236	−	22.3826i	0.628135	−	0.716449i
$977$	27.7522			0.887872			0.443936	−	0.896059i	$-0.353582\pi$
$977$	27.7522			0.887872			0.443936	+	0.896059i	$0.353582\pi$
$978$		0			0
$979$	1.63671	+	1.63671i	0.0523096	+	0.0523096i
$980$	−0.261183	−	7.96162i	−0.00834318	−	0.254325i
$981$		0			0
$982$	−42.4819	−	16.7859i	−1.35565	−	0.535661i
$983$		−	28.3604i		−	0.904556i	−0.891877	−	0.452278i	$-0.850611\pi$
$983$		−	28.3604i		−	0.904556i	0.891877	−	0.452278i	$-0.149389\pi$
$984$		0			0
$985$		−	8.15050i		−	0.259697i
$986$	−8.13511	+	20.5884i	−0.259075	+	0.655667i
$987$		0			0
$988$	−17.7460	−	16.6187i	−0.564577	−	0.528711i
$989$	18.6358	+	18.6358i	0.592585	+	0.592585i
$990$		0			0
$991$	−43.7506			−1.38979			−0.694893	−	0.719114i	$-0.744548\pi$
$991$	−43.7506			−1.38979			−0.694893	+	0.719114i	$0.744548\pi$
$992$	28.6993	−	14.7477i	0.911203	−	0.468240i
$993$		0			0
$994$	13.7224	+	31.6507i	0.435247	+	1.00390i
$995$	3.81038	+	3.81038i	0.120797	+	0.120797i
$996$		0			0
$997$	10.5572	−	10.5572i	0.334349	−	0.334349i	−0.519887	−	0.854235i	$-0.674026\pi$
$997$	10.5572	−	10.5572i	0.334349	−	0.334349i	0.854235	+	0.519887i	$0.174026\pi$
$998$	1.71913	−	4.35079i	0.0544183	−	0.137722i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.c.541.3		16
3.2	odd	2		80.2.l.a.61.6	yes	16
4.3	odd	2		2880.2.t.c.721.1		16
12.11	even	2		320.2.l.a.81.4		16
15.2	even	4		400.2.q.h.349.2		16
15.8	even	4		400.2.q.g.349.7		16
15.14	odd	2		400.2.l.h.301.3		16
16.5	even	4	inner	720.2.t.c.181.3		16
16.11	odd	4		2880.2.t.c.2161.4		16
24.5	odd	2		640.2.l.b.161.4		16
24.11	even	2		640.2.l.a.161.5		16
48.5	odd	4		80.2.l.a.21.6	✓	16
48.11	even	4		320.2.l.a.241.4		16
48.29	odd	4		640.2.l.b.481.4		16
48.35	even	4		640.2.l.a.481.5		16
60.23	odd	4		1600.2.q.h.849.5		16
60.47	odd	4		1600.2.q.g.849.4		16
60.59	even	2		1600.2.l.i.401.5		16
96.5	odd	8		5120.2.a.v.1.3		8
96.11	even	8		5120.2.a.u.1.3		8
96.53	odd	8		5120.2.a.s.1.6		8
96.59	even	8		5120.2.a.t.1.6		8
240.53	even	4		400.2.q.h.149.2		16
240.59	even	4		1600.2.l.i.1201.5		16
240.107	odd	4		1600.2.q.h.49.5		16
240.149	odd	4		400.2.l.h.101.3		16
240.197	even	4		400.2.q.g.149.7		16
240.203	odd	4		1600.2.q.g.49.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.6	✓	16	48.5	odd	4
80.2.l.a.61.6	yes	16	3.2	odd	2
320.2.l.a.81.4		16	12.11	even	2
320.2.l.a.241.4		16	48.11	even	4
400.2.l.h.101.3		16	240.149	odd	4
400.2.l.h.301.3		16	15.14	odd	2
400.2.q.g.149.7		16	240.197	even	4
400.2.q.g.349.7		16	15.8	even	4
400.2.q.h.149.2		16	240.53	even	4
400.2.q.h.349.2		16	15.2	even	4
640.2.l.a.161.5		16	24.11	even	2
640.2.l.a.481.5		16	48.35	even	4
640.2.l.b.161.4		16	24.5	odd	2
640.2.l.b.481.4		16	48.29	odd	4
720.2.t.c.181.3		16	16.5	even	4	inner
720.2.t.c.541.3		16	1.1	even	1	trivial
1600.2.l.i.401.5		16	60.59	even	2
1600.2.l.i.1201.5		16	240.59	even	4
1600.2.q.g.49.4		16	240.203	odd	4
1600.2.q.g.849.4		16	60.47	odd	4
1600.2.q.h.49.5		16	240.107	odd	4
1600.2.q.h.849.5		16	60.23	odd	4
2880.2.t.c.721.1		16	4.3	odd	2
2880.2.t.c.2161.4		16	16.11	odd	4
5120.2.a.s.1.6		8	96.53	odd	8
5120.2.a.t.1.6		8	96.59	even	8
5120.2.a.u.1.3		8	96.11	even	8
5120.2.a.v.1.3		8	96.5	odd	8

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.562546 - 1.29751i) q^{2} +(-1.36708 + 1.45982i) q^{4} +(-0.707107 + 0.707107i) q^{5} +1.73696i q^{7} +(2.66319 + 0.952595i) q^{8} +O(q^{10})\)	\(q+(-0.562546 - 1.29751i) q^{2} +(-1.36708 + 1.45982i) q^{4} +(-0.707107 + 0.707107i) q^{5} +1.73696i q^{7} +(2.66319 + 0.952595i) q^{8} +(1.31526 + 0.519701i) q^{10} +(-0.505430 + 0.505430i) q^{11} +(-1.88750 - 1.88750i) q^{13} +(2.25374 - 0.977122i) q^{14} +(-0.262159 - 3.99140i) q^{16} -4.53524 q^{17} +(-3.22022 - 3.22022i) q^{19} +(-0.0655751 - 1.99892i) q^{20} +(0.940130 + 0.371475i) q^{22} -8.85045i q^{23} -1.00000i q^{25} +(-1.38725 + 3.51086i) q^{26} +(-2.53566 - 2.37458i) q^{28} +(2.44059 + 2.44059i) q^{29} -5.70401 q^{31} +(-5.03142 + 2.58550i) q^{32} +(2.55128 + 5.88454i) q^{34} +(-1.22822 - 1.22822i) q^{35} +(-5.35670 + 5.35670i) q^{37} +(-2.36676 + 5.98979i) q^{38} +(-2.55674 + 1.20957i) q^{40} -10.0343i q^{41} +(-2.10564 + 2.10564i) q^{43} +(-0.0468722 - 1.42880i) q^{44} +(-11.4836 + 4.97878i) q^{46} -4.32303 q^{47} +3.98295 q^{49} +(-1.29751 + 0.562546i) q^{50} +(5.33578 - 0.175041i) q^{52} +(1.37458 - 1.37458i) q^{53} -0.714786i q^{55} +(-1.65462 + 4.62586i) q^{56} +(1.79375 - 4.53964i) q^{58} +(-6.64140 + 6.64140i) q^{59} +(5.26208 + 5.26208i) q^{61} +(3.20877 + 7.40103i) q^{62} +(6.18513 + 5.07388i) q^{64} +2.66933 q^{65} +(-10.5578 - 10.5578i) q^{67} +(6.20006 - 6.62065i) q^{68} +(-0.902702 + 2.28456i) q^{70} +14.0437i q^{71} -6.63830i q^{73} +(9.96378 + 3.93700i) q^{74} +(9.10325 - 0.298634i) q^{76} +(-0.877914 - 0.877914i) q^{77} +4.27297 q^{79} +(3.00772 + 2.63697i) q^{80} +(-13.0196 + 5.64474i) q^{82} +(-9.15483 - 9.15483i) q^{83} +(3.20690 - 3.20690i) q^{85} +(3.91661 + 1.54758i) q^{86} +(-1.82752 + 0.864585i) q^{88} -3.23826i q^{89} +(3.27852 - 3.27852i) q^{91} +(12.9201 + 12.0993i) q^{92} +(2.43190 + 5.60919i) q^{94} +4.55407 q^{95} +1.94129 q^{97} +(-2.24059 - 5.16794i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4}+O(q^{10}) \) 16 * q - 4 * q^4	\( 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47} - 16 q^{49} + 4 q^{50} + 56 q^{52} - 16 q^{53} - 16 q^{56} - 12 q^{58} + 8 q^{59} + 16 q^{61} + 8 q^{62} - 16 q^{64} + 40 q^{67} + 48 q^{68} - 8 q^{70} + 72 q^{74} - 16 q^{77} + 16 q^{79} - 16 q^{80} - 76 q^{82} - 40 q^{83} - 16 q^{85} - 28 q^{86} + 32 q^{91} + 52 q^{92} - 36 q^{94} - 32 q^{95} - 60 q^{98}+O(q^{100}) \) 16 * q - 4 * q^4 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 8 * q^20 - 20 * q^22 + 16 * q^26 - 4 * q^28 + 16 * q^29 + 16 * q^34 - 16 * q^37 - 20 * q^38 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 40 * q^47 - 16 * q^49 + 4 * q^50 + 56 * q^52 - 16 * q^53 - 16 * q^56 - 12 * q^58 + 8 * q^59 + 16 * q^61 + 8 * q^62 - 16 * q^64 + 40 * q^67 + 48 * q^68 - 8 * q^70 + 72 * q^74 - 16 * q^77 + 16 * q^79 - 16 * q^80 - 76 * q^82 - 40 * q^83 - 16 * q^85 - 28 * q^86 + 32 * q^91 + 52 * q^92 - 36 * q^94 - 32 * q^95 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more