LMFDB - Embedded newform 585.2.j.f.406.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(406,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("585.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.j (of order $3$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1714608.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 30x^2 - 21*x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.1
Root			$0.500000 - 2.23871i$ of defining polynomial
Character	$\chi$	$=$	585.406
Dual form			585.2.j.f.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13090 - 1.95878i) q^{2} +(-1.55787 + 2.69832i) q^{4} -1.00000 q^{5} +(0.630901 - 1.09275i) q^{7} +2.52360 q^{8} +O(q^{10})$	\(q+(-1.13090 - 1.95878i) q^{2} +(-1.55787 + 2.69832i) q^{4} -1.00000 q^{5} +(0.630901 - 1.09275i) q^{7} +2.52360 q^{8} +(1.13090 + 1.95878i) q^{10} +(2.26180 + 3.91756i) q^{11} +(-3.45058 - 1.04571i) q^{13} -2.85395 q^{14} +(0.261802 + 0.453455i) q^{16} +(-2.24665 + 3.89131i) q^{17} +(-2.55787 + 4.43037i) q^{19} +(1.55787 - 2.69832i) q^{20} +(5.11575 - 8.86074i) q^{22} +(1.11575 + 1.93253i) q^{23} +1.00000 q^{25} +(1.85395 + 7.94151i) q^{26} +(1.96573 + 3.40474i) q^{28} +(-0.688776 - 1.19299i) q^{29} +8.87085 q^{31} +(3.11575 - 5.39664i) q^{32} +10.1630 q^{34} +(-0.630901 + 1.09275i) q^{35} +(0.115749 + 0.200484i) q^{37} +11.5708 q^{38} -2.52360 q^{40} +(0.573026 + 0.992511i) q^{41} +(-3.18878 + 5.52312i) q^{43} -14.0944 q^{44} +(2.52360 - 4.37101i) q^{46} +10.7854 q^{47} +(2.70393 + 4.68334i) q^{49} +(-1.13090 - 1.95878i) q^{50} +(8.19723 - 7.68167i) q^{52} -4.52360 q^{53} +(-2.26180 - 3.91756i) q^{55} +(1.59214 - 2.75768i) q^{56} +(-1.55787 + 2.69832i) q^{58} +(-0.426974 + 0.739540i) q^{59} +(-2.31968 + 4.01780i) q^{61} +(-10.0321 - 17.3760i) q^{62} -13.0472 q^{64} +(3.45058 + 1.04571i) q^{65} +(-6.56633 - 11.3732i) q^{67} +(-7.00000 - 12.1244i) q^{68} +2.85395 q^{70} +(-4.80453 + 8.32168i) q^{71} +13.7854 q^{73} +(0.261802 - 0.453455i) q^{74} +(-7.96970 - 13.8039i) q^{76} +5.70789 q^{77} -8.87085 q^{79} +(-0.261802 - 0.453455i) q^{80} +(1.29607 - 2.24486i) q^{82} +8.23150 q^{83} +(2.24665 - 3.89131i) q^{85} +14.4248 q^{86} +(5.70789 + 9.88636i) q^{88} +(3.31122 + 5.73521i) q^{89} +(-3.31968 + 3.11089i) q^{91} -6.95279 q^{92} +(-12.1972 - 21.1262i) q^{94} +(2.55787 - 4.43037i) q^{95} +(-5.33483 + 9.24019i) q^{97} +(6.11575 - 10.5928i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{5} - 3 q^{7} - 12 q^{8}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^5 - 3 * q^7 - 12 * q^8	$ 6 q - 6 q^{4} - 6 q^{5} - 3 q^{7} - 12 q^{8} + 3 q^{13} - 24 q^{14} - 12 q^{16} - 12 q^{19} + 6 q^{20} + 24 q^{22} + 6 q^{25} + 18 q^{26} - 12 q^{28} + 6 q^{29} + 6 q^{31} + 12 q^{32} + 3 q^{35} - 6 q^{37} - 12 q^{38} + 12 q^{40} - 9 q^{43} + 24 q^{44} - 12 q^{46} + 24 q^{47} + 6 q^{49} + 12 q^{52} + 30 q^{56} - 6 q^{58} - 6 q^{59} + 3 q^{61} - 6 q^{62} - 24 q^{64} - 3 q^{65} - 9 q^{67} - 42 q^{68} + 24 q^{70} - 12 q^{71} + 42 q^{73} - 12 q^{74} - 48 q^{76} + 48 q^{77} - 6 q^{79} + 12 q^{80} + 18 q^{82} + 36 q^{83} + 12 q^{86} + 48 q^{88} + 30 q^{89} - 3 q^{91} - 96 q^{92} - 36 q^{94} + 12 q^{95} - 15 q^{97} + 30 q^{98}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^5 - 3 * q^7 - 12 * q^8 + 3 * q^13 - 24 * q^14 - 12 * q^16 - 12 * q^19 + 6 * q^20 + 24 * q^22 + 6 * q^25 + 18 * q^26 - 12 * q^28 + 6 * q^29 + 6 * q^31 + 12 * q^32 + 3 * q^35 - 6 * q^37 - 12 * q^38 + 12 * q^40 - 9 * q^43 + 24 * q^44 - 12 * q^46 + 24 * q^47 + 6 * q^49 + 12 * q^52 + 30 * q^56 - 6 * q^58 - 6 * q^59 + 3 * q^61 - 6 * q^62 - 24 * q^64 - 3 * q^65 - 9 * q^67 - 42 * q^68 + 24 * q^70 - 12 * q^71 + 42 * q^73 - 12 * q^74 - 48 * q^76 + 48 * q^77 - 6 * q^79 + 12 * q^80 + 18 * q^82 + 36 * q^83 + 12 * q^86 + 48 * q^88 + 30 * q^89 - 3 * q^91 - 96 * q^92 - 36 * q^94 + 12 * q^95 - 15 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.13090	−	1.95878i	−0.799668	−	1.38507i	−0.919832	−	0.392311i	$-0.871676\pi$
$2$	−1.13090	−	1.95878i	−0.799668	−	1.38507i	0.120165	−	0.992754i	$-0.461658\pi$
$3$		0			0
$3$		0			0
$4$	−1.55787	+	2.69832i	−0.778937	+	1.34916i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	0.630901	−	1.09275i	0.238458	−	0.413022i	−0.721814	−	0.692087i	$-0.756691\pi$
$7$	0.630901	−	1.09275i	0.238458	−	0.413022i	0.960272	+	0.279066i	$0.0900247\pi$
$8$	2.52360			0.892229
$9$		0			0
$10$	1.13090	+	1.95878i	0.357622	+	0.619420i
$11$	2.26180	+	3.91756i	0.681959	+	1.18119i	0.974382	+	0.224899i	$0.0722051\pi$
$11$	2.26180	+	3.91756i	0.681959	+	1.18119i	−0.292423	+	0.956289i	$0.594462\pi$
$12$		0			0
$13$	−3.45058	−	1.04571i	−0.957018	−	0.290028i
$13$	−3.45058	−	1.04571i	−0.957018	−	0.290028i
$14$	−2.85395			−0.762749
$15$		0			0
$16$	0.261802	+	0.453455i	0.0654506	+	0.113364i
$17$	−2.24665	+	3.89131i	−0.544893	+	0.943782i	0.453721	+	0.891144i	$0.350096\pi$
$17$	−2.24665	+	3.89131i	−0.544893	+	0.943782i	−0.998614	+	0.0526381i	$0.983237\pi$
$18$		0			0
$19$	−2.55787	+	4.43037i	−0.586817	+	1.01640i	0.407830	+	0.913058i	$0.366286\pi$
$19$	−2.55787	+	4.43037i	−0.586817	+	1.01640i	−0.994646	+	0.103338i	$0.967048\pi$
$20$	1.55787	−	2.69832i	0.348351	−	0.603362i
$21$		0			0
$22$	5.11575	−	8.86074i	1.09068	−	1.88912i
$23$	1.11575	+	1.93253i	0.232650	+	0.402961i	0.958587	−	0.284800i	$-0.0919271\pi$
$23$	1.11575	+	1.93253i	0.232650	+	0.402961i	−0.725937	+	0.687761i	$0.758594\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	1.85395	+	7.94151i	0.363589	+	1.55746i
$27$		0			0
$28$	1.96573	+	3.40474i	0.371488	+	0.643436i
$29$	−0.688776	−	1.19299i	−0.127902	−	0.221534i	0.794961	−	0.606660i	$-0.207491\pi$
$29$	−0.688776	−	1.19299i	−0.127902	−	0.221534i	−0.922864	+	0.385127i	$0.874158\pi$
$30$		0			0
$31$	8.87085			1.59325			0.796626	−	0.604472i	$-0.206616\pi$
$31$	8.87085			1.59325			0.796626	+	0.604472i	$0.206616\pi$
$32$	3.11575	−	5.39664i	0.550792	−	0.954000i
$33$		0			0
$34$	10.1630			1.74293
$35$	−0.630901	+	1.09275i	−0.106642	+	0.184709i
$36$		0			0
$37$	0.115749	+	0.200484i	0.0190291	+	0.0329593i	0.875383	−	0.483430i	$-0.160609\pi$
$37$	0.115749	+	0.200484i	0.0190291	+	0.0329593i	−0.856354	+	0.516389i	$0.827276\pi$
$38$	11.5708			1.87703
$39$		0			0
$40$	−2.52360			−0.399017
$41$	0.573026	+	0.992511i	0.0894917	+	0.155004i	0.907296	−	0.420492i	$-0.138142\pi$
$41$	0.573026	+	0.992511i	0.0894917	+	0.155004i	−0.817805	+	0.575496i	$0.804809\pi$
$42$		0			0
$43$	−3.18878	+	5.52312i	−0.486284	+	0.842268i	−0.999876	−	0.0157664i	$-0.994981\pi$
$43$	−3.18878	+	5.52312i	−0.486284	+	0.842268i	0.513592	+	0.858035i	$0.328315\pi$
$44$	−14.0944			−2.12481
$45$		0			0
$46$	2.52360	−	4.37101i	0.372085	−	0.644470i
$47$	10.7854			1.57321			0.786607	−	0.617454i	$-0.211836\pi$
$47$	10.7854			1.57321			0.786607	+	0.617454i	$0.211836\pi$
$48$		0			0
$49$	2.70393	+	4.68334i	0.386275	+	0.669049i
$50$	−1.13090	−	1.95878i	−0.159934	−	0.277013i
$51$		0			0
$52$	8.19723	−	7.68167i	1.13675	−	1.06526i
$53$	−4.52360			−0.621365			−0.310682	−	0.950514i	$-0.600558\pi$
$53$	−4.52360			−0.621365			−0.310682	+	0.950514i	$0.600558\pi$
$54$		0			0
$55$	−2.26180	−	3.91756i	−0.304981	−	0.528243i
$56$	1.59214	−	2.75768i	0.212759	−	0.368510i
$57$		0			0
$58$	−1.55787	+	2.69832i	−0.204559	+	0.354307i
$59$	−0.426974	+	0.739540i	−0.0555872	+	0.0962799i	−0.892480	−	0.451087i	$-0.851036\pi$
$59$	−0.426974	+	0.739540i	−0.0555872	+	0.0962799i	0.836893	+	0.547367i	$0.184370\pi$
$60$		0			0
$61$	−2.31968	+	4.01780i	−0.297004	+	0.514426i	−0.975449	−	0.220225i	$-0.929321\pi$
$61$	−2.31968	+	4.01780i	−0.297004	+	0.514426i	0.678445	+	0.734651i	$0.262654\pi$
$62$	−10.0321	−	17.3760i	−1.27407	−	2.20676i
$63$		0			0
$64$	−13.0472			−1.63090
$65$	3.45058	+	1.04571i	0.427992	+	0.129704i
$66$		0			0
$67$	−6.56633	−	11.3732i	−0.802205	−	1.38946i	−0.918162	−	0.396205i	$-0.870327\pi$
$67$	−6.56633	−	11.3732i	−0.802205	−	1.38946i	0.115958	−	0.993254i	$-0.463006\pi$
$68$	−7.00000	−	12.1244i	−0.848875	−	1.47029i
$69$		0			0
$70$	2.85395			0.341112
$71$	−4.80453	+	8.32168i	−0.570192	+	0.987602i	0.426354	+	0.904557i	$0.359798\pi$
$71$	−4.80453	+	8.32168i	−0.570192	+	0.987602i	−0.996546	+	0.0830453i	$0.973535\pi$
$72$		0			0
$73$	13.7854			1.61346			0.806730	−	0.590920i	$-0.201235\pi$
$73$	13.7854			1.61346			0.806730	+	0.590920i	$0.201235\pi$
$74$	0.261802	−	0.453455i	0.0304339	−	0.0527130i
$75$		0			0
$76$	−7.96970	−	13.8039i	−0.914187	−	1.58342i
$77$	5.70789			0.650475
$78$		0			0
$79$	−8.87085			−0.998049			−0.499024	−	0.866588i	$-0.666308\pi$
$79$	−8.87085			−0.998049			−0.499024	+	0.866588i	$0.666308\pi$
$80$	−0.261802	−	0.453455i	−0.0292704	−	0.0506978i
$81$		0			0
$82$	1.29607	−	2.24486i	0.143127	−	0.247904i
$83$	8.23150			0.903524			0.451762	−	0.892138i	$-0.350796\pi$
$83$	8.23150			0.903524			0.451762	+	0.892138i	$0.350796\pi$
$84$		0			0
$85$	2.24665	−	3.89131i	0.243683	−	0.422072i
$86$	14.4248			1.55546
$87$		0			0
$88$	5.70789	+	9.88636i	0.608464	+	1.05389i
$89$	3.31122	+	5.73521i	0.350989	+	0.607931i	0.986423	−	0.164224i	$-0.0525121\pi$
$89$	3.31122	+	5.73521i	0.350989	+	0.607931i	−0.635434	+	0.772155i	$0.719179\pi$
$90$		0			0
$91$	−3.31968	+	3.11089i	−0.347997	+	0.326110i
$92$	−6.95279			−0.724879
$93$		0			0
$94$	−12.1972	−	21.1262i	−1.25805	−	2.17900i
$95$	2.55787	−	4.43037i	0.262432	−	0.454546i
$96$		0			0
$97$	−5.33483	+	9.24019i	−0.541670	+	0.938200i	0.457139	+	0.889395i	$0.348874\pi$
$97$	−5.33483	+	9.24019i	−0.541670	+	0.938200i	−0.998808	+	0.0488041i	$0.984459\pi$
$98$	6.11575	−	10.5928i	0.617784	−	1.07003i
$99$		0			0
$100$	−1.55787	+	2.69832i	−0.155787	+	0.269832i
$101$	−8.52360	−	14.7633i	−0.848130	−	1.46900i	−0.882875	−	0.469609i	$-0.844395\pi$
$101$	−8.52360	−	14.7633i	−0.848130	−	1.46900i	0.0347444	−	0.999396i	$-0.488938\pi$
$102$		0			0
$103$	−13.9484			−1.37437			−0.687187	−	0.726481i	$-0.741155\pi$
$103$	−13.9484			−1.37437			−0.687187	+	0.726481i	$0.741155\pi$
$104$	−8.70789	−	2.63896i	−0.853879	−	0.258771i
$105$		0			0
$106$	5.11575	+	8.86074i	0.496886	+	0.860631i
$107$	6.24665	+	10.8195i	0.603886	+	1.04596i	0.992226	+	0.124446i	$0.0397153\pi$
$107$	6.24665	+	10.8195i	0.603886	+	1.04596i	−0.388340	+	0.921516i	$0.626951\pi$
$108$		0			0
$109$	−2.27871			−0.218261			−0.109130	−	0.994027i	$-0.534807\pi$
$109$	−2.27871			−0.218261			−0.109130	+	0.994027i	$0.534807\pi$
$110$	−5.11575	+	8.86074i	−0.487768	+	0.844838i
$111$		0			0
$112$	0.660685			0.0624289
$113$	−0.738198	+	1.27860i	−0.0694438	+	0.120280i	−0.898657	−	0.438653i	$-0.855456\pi$
$113$	−0.738198	+	1.27860i	−0.0694438	+	0.120280i	0.829213	+	0.558933i	$0.188789\pi$
$114$		0			0
$115$	−1.11575	−	1.93253i	−0.104044	−	0.180210i
$116$	4.29211			0.398512
$117$		0			0
$118$	1.93146			0.177805
$119$	2.83483	+	4.91007i	0.259868	+	0.450105i
$120$		0			0
$121$	−4.73150	+	8.19520i	−0.430136	+	0.745018i
$122$	10.4933			0.950019
$123$		0			0
$124$	−13.8197	+	23.9364i	−1.24104	+	2.14955i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	8.89270	+	15.4026i	0.789100	+	1.36676i	0.926519	+	0.376248i	$0.122786\pi$
$127$	8.89270	+	15.4026i	0.789100	+	1.36676i	−0.137419	+	0.990513i	$0.543881\pi$
$128$	8.52360	+	14.7633i	0.753387	+	1.30491i
$129$		0			0
$130$	−1.85395	−	7.94151i	−0.162602	−	0.696517i
$131$	−11.6697			−1.01958			−0.509791	−	0.860298i	$-0.670277\pi$
$131$	−11.6697			−1.01958			−0.509791	+	0.860298i	$0.670277\pi$
$132$		0			0
$133$	3.22753	+	5.59025i	0.279863	+	0.484736i
$134$	−14.8517	+	25.7240i	−1.28299	+	2.22221i
$135$		0			0
$136$	−5.66966	+	9.82013i	−0.486169	+	0.842070i
$137$	−10.0321	+	17.3760i	−0.857096	+	1.48453i	0.0175898	+	0.999845i	$0.494401\pi$
$137$	−10.0321	+	17.3760i	−0.857096	+	1.48453i	−0.874686	+	0.484689i	$0.838933\pi$
$138$		0			0
$139$	−8.16966	+	14.1503i	−0.692941	+	1.20021i	0.277928	+	0.960602i	$0.410352\pi$
$139$	−8.16966	+	14.1503i	−0.692941	+	1.20021i	−0.970870	+	0.239608i	$0.922981\pi$
$140$	−1.96573	−	3.40474i	−0.166134	−	0.287753i
$141$		0			0
$142$	21.7338			1.82386
$143$	−3.70789	−	15.8830i	−0.310070	−	1.32821i
$144$		0			0
$145$	0.688776	+	1.19299i	0.0571997	+	0.0990728i
$146$	−15.5899	−	27.0026i	−1.29023	−	2.23475i
$147$		0			0
$148$	−0.721292			−0.0592899
$149$	−1.62245	+	2.81016i	−0.132916	+	0.230218i	−0.924799	−	0.380455i	$-0.875767\pi$
$149$	−1.62245	+	2.81016i	−0.132916	+	0.230218i	0.791883	+	0.610672i	$0.209101\pi$
$150$		0			0
$151$	5.69996			0.463856			0.231928	−	0.972733i	$-0.425497\pi$
$151$	5.69996			0.463856			0.231928	+	0.972733i	$0.425497\pi$
$152$	−6.45506	+	11.1805i	−0.523575	+	0.906858i
$153$		0			0
$154$	−6.45506	−	11.1805i	−0.520164	−	0.900950i
$155$	−8.87085			−0.712524
$156$		0			0
$157$	−3.85395			−0.307578			−0.153789	−	0.988104i	$-0.549148\pi$
$157$	−3.85395			−0.307578			−0.153789	+	0.988104i	$0.549148\pi$
$158$	10.0321	+	17.3760i	0.798108	+	1.38236i
$159$		0			0
$160$	−3.11575	+	5.39664i	−0.246322	+	0.426642i
$161$	2.81571			0.221909
$162$		0			0
$163$	4.86240	−	8.42192i	0.380853	−	0.659656i	−0.610332	−	0.792146i	$-0.708964\pi$
$163$	4.86240	−	8.42192i	0.380853	−	0.659656i	0.991184	+	0.132490i	$0.0422972\pi$
$164$	−3.57081			−0.278834
$165$		0			0
$166$	−9.30901	−	16.1237i	−0.722519	−	1.25144i
$167$	−9.63935	−	16.6959i	−0.745916	−	1.29196i	−0.949766	−	0.312962i	$-0.898679\pi$
$167$	−9.63935	−	16.6959i	−0.745916	−	1.29196i	0.203850	−	0.979002i	$-0.434654\pi$
$168$		0			0
$169$	10.8130	+	7.21661i	0.831768	+	0.555124i
$170$	−10.1630			−0.779463
$171$		0			0
$172$	−9.93543	−	17.2087i	−0.757569	−	1.31215i
$173$	−1.50845	+	2.61272i	−0.114686	+	0.198641i	−0.917654	−	0.397380i	$-0.869919\pi$
$173$	−1.50845	+	2.61272i	−0.114686	+	0.198641i	0.802968	+	0.596022i	$0.203253\pi$
$174$		0			0
$175$	0.630901	−	1.09275i	0.0476916	−	0.0826043i
$176$	−1.18429	+	2.05125i	−0.0892692	+	0.154619i
$177$		0			0
$178$	7.48933	−	12.9719i	0.561349	−	0.972286i
$179$	−2.65847	−	4.60461i	−0.198704	−	0.344165i	0.749405	−	0.662112i	$-0.230340\pi$
$179$	−2.65847	−	4.60461i	−0.198704	−	0.344165i	−0.948108	+	0.317947i	$0.897006\pi$
$180$		0			0
$181$	25.8709			1.92297			0.961483	−	0.274866i	$-0.0886333\pi$
$181$	25.8709			1.92297			0.961483	+	0.274866i	$0.0886333\pi$
$182$	9.84777	+	2.98440i	0.729965	+	0.221219i
$183$		0			0
$184$	2.81571	+	4.87695i	0.207577	+	0.359534i
$185$	−0.115749	−	0.200484i	−0.00851006	−	0.0147399i
$186$		0			0
$187$	−20.3259			−1.48638
$188$	−16.8023	+	29.1025i	−1.22543	+	2.12251i
$189$		0			0
$190$	−11.5708			−0.839435
$191$	5.32813	−	9.22859i	0.385530	−	0.667757i	−0.606313	−	0.795226i	$-0.707352\pi$
$191$	5.32813	−	9.22859i	0.385530	−	0.667757i	0.991843	+	0.127469i	$0.0406853\pi$
$192$		0			0
$193$	−3.99155	−	6.91356i	−0.287318	−	0.497649i	0.685851	−	0.727742i	$-0.259430\pi$
$193$	−3.99155	−	6.91356i	−0.287318	−	0.497649i	−0.973169	+	0.230093i	$0.926097\pi$
$194$	24.1327			1.73262
$195$		0			0
$196$	−16.8495			−1.20354
$197$	8.66966	+	15.0163i	0.617688	+	1.06987i	0.989907	+	0.141721i	$0.0452637\pi$
$197$	8.66966	+	15.0163i	0.617688	+	1.06987i	−0.372219	+	0.928145i	$0.621403\pi$
$198$		0			0
$199$	0.615749	−	1.06651i	0.0436493	−	0.0756028i	−0.843375	−	0.537325i	$-0.819435\pi$
$199$	0.615749	−	1.06651i	0.0436493	−	0.0756028i	0.887025	+	0.461722i	$0.152768\pi$
$200$	2.52360			0.178446
$201$		0			0
$202$	−19.2787	+	33.3917i	−1.35645	+	2.34943i
$203$	−1.73820			−0.121998
$204$		0			0
$205$	−0.573026	−	0.992511i	−0.0400219	−	0.0693200i
$206$	15.7742	+	27.3218i	1.09904	+	1.90360i
$207$		0			0
$208$	−0.429187	−	1.83845i	−0.0297587	−	0.127474i
$209$	−23.1416			−1.60074
$210$		0			0
$211$	−5.16966	−	8.95411i	−0.355894	−	0.616426i	0.631377	−	0.775476i	$-0.282490\pi$
$211$	−5.16966	−	8.95411i	−0.355894	−	0.616426i	−0.987271	+	0.159050i	$0.949157\pi$
$212$	7.04721	−	12.2061i	0.484004	−	0.838320i
$213$		0			0
$214$	14.1287	−	24.4716i	0.965817	−	1.67284i
$215$	3.18878	−	5.52312i	0.217473	−	0.376674i
$216$		0			0
$217$	5.59663	−	9.69365i	0.379924	−	0.658048i
$218$	2.57699	+	4.46348i	0.174536	+	0.302305i
$219$		0			0
$220$	14.0944			0.950245
$221$	11.8214	−	11.0779i	0.795195	−	0.745182i
$222$		0			0
$223$	−10.7854	−	18.6809i	−0.722244	−	1.25096i	−0.960098	−	0.279663i	$-0.909777\pi$
$223$	−10.7854	−	18.6809i	−0.722244	−	1.25096i	0.237854	−	0.971301i	$-0.423556\pi$
$224$	−3.93146	−	6.80949i	−0.262682	−	0.454978i
$225$		0			0
$226$	3.33931			0.222128
$227$	2.72305	−	4.71645i	0.180735	−	0.313042i	−0.761396	−	0.648287i	$-0.775486\pi$
$227$	2.72305	−	4.71645i	0.180735	−	0.313042i	0.942131	+	0.335245i	$0.108819\pi$
$228$		0			0
$229$	21.9315			1.44927			0.724636	−	0.689132i	$-0.242008\pi$
$229$	21.9315			1.44927			0.724636	+	0.689132i	$0.242008\pi$
$230$	−2.52360	+	4.37101i	−0.166402	+	0.288216i
$231$		0			0
$232$	−1.73820	−	3.01065i	−0.114118	−	0.197659i
$233$	−25.3125			−1.65828			−0.829139	−	0.559042i	$-0.811169\pi$
$233$	−25.3125			−1.65828			−0.829139	+	0.559042i	$0.811169\pi$
$234$		0			0
$235$	−10.7854			−0.703562
$236$	−1.33034	−	2.30422i	−0.0865979	−	0.149992i
$237$		0			0
$238$	6.41182	−	11.1056i	0.415617	−	0.719869i
$239$	−22.5236			−1.45693			−0.728465	−	0.685083i	$-0.759766\pi$
$239$	−22.5236			−1.45693			−0.728465	+	0.685083i	$0.759766\pi$
$240$		0			0
$241$	−5.55787	+	9.62652i	−0.358014	+	0.620099i	−0.987629	−	0.156809i	$-0.949879\pi$
$241$	−5.55787	+	9.62652i	−0.358014	+	0.620099i	0.629615	+	0.776907i	$0.283213\pi$
$242$	21.4034			1.37586
$243$		0			0
$244$	−7.22753	−	12.5185i	−0.462695	−	0.801412i
$245$	−2.70393	−	4.68334i	−0.172748	−	0.299208i
$246$		0			0
$247$	13.4590	−	12.6125i	0.856378	−	0.802516i
$248$	22.3865			1.42155
$249$		0			0
$250$	1.13090	+	1.95878i	0.0715245	+	0.123884i
$251$	5.52360	−	9.56716i	0.348647	−	0.603874i	−0.637363	−	0.770564i	$-0.719975\pi$
$251$	5.52360	−	9.56716i	0.348647	−	0.603874i	0.986009	+	0.166690i	$0.0533079\pi$
$252$		0			0
$253$	−5.04721	+	8.74202i	−0.317315	+	0.549606i
$254$	20.1135	−	34.8377i	1.26204	−	2.18591i
$255$		0			0
$256$	6.23150	−	10.7933i	0.389469	−	0.674580i
$257$	−1.01515	−	1.75829i	−0.0633234	−	0.109679i	0.832626	−	0.553836i	$-0.186837\pi$
$257$	−1.01515	−	1.75829i	−0.0633234	−	0.109679i	−0.895949	+	0.444157i	$0.853503\pi$
$258$		0			0
$259$	0.292106			0.0181506
$260$	−8.19723	+	7.68167i	−0.508371	+	0.476397i
$261$		0			0
$262$	13.1972	+	22.8583i	0.815328	+	1.41219i
$263$	1.62420	+	2.81320i	0.100153	+	0.173469i	0.911747	−	0.410751i	$-0.134734\pi$
$263$	1.62420	+	2.81320i	0.100153	+	0.173469i	−0.811595	+	0.584221i	$0.801400\pi$
$264$		0			0
$265$	4.52360			0.277883
$266$	7.30004	−	12.6440i	0.447594	−	0.775256i
$267$		0			0
$268$	40.9181			2.49947
$269$	13.4742	−	23.3380i	0.821535	−	1.42294i	−0.0830032	−	0.996549i	$-0.526451\pi$
$269$	13.4742	−	23.3380i	0.821535	−	1.42294i	0.904539	−	0.426392i	$-0.140216\pi$
$270$		0			0
$271$	9.92476	+	17.1902i	0.602886	+	1.04423i	0.992382	+	0.123201i	$0.0393161\pi$
$271$	9.92476	+	17.1902i	0.602886	+	1.04423i	−0.389495	+	0.921028i	$0.627351\pi$
$272$	−2.35271			−0.142654
$273$		0			0
$274$	45.3811			2.74157
$275$	2.26180	+	3.91756i	0.136392	+	0.236238i
$276$		0			0
$277$	−8.04721	+	13.9382i	−0.483510	+	0.837464i	−0.999821	−	0.0189376i	$-0.993972\pi$
$277$	−8.04721	+	13.9382i	−0.483510	+	0.837464i	0.516311	+	0.856401i	$0.327305\pi$
$278$	36.9563			2.21649
$279$		0			0
$280$	−1.59214	+	2.75768i	−0.0951489	+	0.164803i
$281$	5.37755			0.320798			0.160399	−	0.987052i	$-0.448722\pi$
$281$	5.37755			0.320798			0.160399	+	0.987052i	$0.448722\pi$
$282$		0			0
$283$	−13.4332	−	23.2670i	−0.798522	−	1.38308i	−0.920579	−	0.390557i	$-0.872282\pi$
$283$	−13.4332	−	23.2670i	−0.798522	−	1.38308i	0.122057	−	0.992523i	$-0.461051\pi$
$284$	−14.9697	−	25.9283i	−0.888288	−	1.53856i
$285$		0			0
$286$	−26.9181	+	25.2251i	−1.59170	+	1.49159i
$287$	1.44609			0.0853601
$288$		0			0
$289$	−1.59488	−	2.76241i	−0.0938163	−	0.162495i
$290$	1.55787	−	2.69832i	0.0914816	−	0.158451i
$291$		0			0
$292$	−21.4759	+	37.1974i	−1.25678	+	2.17681i
$293$	10.7096	−	18.5497i	0.625664	−	1.08368i	−0.362748	−	0.931887i	$-0.618161\pi$
$293$	10.7096	−	18.5497i	0.625664	−	1.08368i	0.988412	−	0.151795i	$-0.0485054\pi$
$294$		0			0
$295$	0.426974	−	0.739540i	0.0248594	−	0.0430577i
$296$	0.292106	+	0.505942i	0.0169783	+	0.0294073i
$297$		0			0
$298$	7.33931			0.425155
$299$	−1.82911	−	7.83511i	−0.105780	−	0.453116i
$300$		0			0
$301$	4.02360	+	6.96909i	0.231917	+	0.401692i
$302$	−6.44609	−	11.1650i	−0.370931	−	0.642471i
$303$		0			0
$304$	−2.67863			−0.153630
$305$	2.31968	−	4.01780i	0.132824	−	0.230058i
$306$		0			0
$307$	−7.85395			−0.448248			−0.224124	−	0.974561i	$-0.571952\pi$
$307$	−7.85395			−0.448248			−0.224124	+	0.974561i	$0.571952\pi$
$308$	−8.89218	+	15.4017i	−0.506679	+	0.877594i
$309$		0			0
$310$	10.0321	+	17.3760i	0.569783	+	0.986892i
$311$	27.8744			1.58061			0.790305	−	0.612714i	$-0.209922\pi$
$311$	27.8744			1.58061			0.790305	+	0.612714i	$0.209922\pi$
$312$		0			0
$313$	7.88776			0.445842			0.222921	−	0.974836i	$-0.428441\pi$
$313$	7.88776			0.445842			0.222921	+	0.974836i	$0.428441\pi$
$314$	4.35843	+	7.54903i	0.245961	+	0.426016i
$315$		0			0
$316$	13.8197	−	23.9364i	0.777418	−	1.34653i
$317$	−13.2181			−0.742403			−0.371201	−	0.928552i	$-0.621054\pi$
$317$	−13.2181			−0.742403			−0.371201	+	0.928552i	$0.621054\pi$
$318$		0			0
$319$	3.11575	−	5.39664i	0.174448	−	0.302154i
$320$	13.0472			0.729361
$321$		0			0
$322$	−3.18429	−	5.51535i	−0.177454	−	0.307359i
$323$	−11.4933	−	19.9070i	−0.639504	−	1.10765i
$324$		0			0
$325$	−3.45058	−	1.04571i	−0.191404	−	0.0580056i
$326$	−21.9956			−1.21822
$327$		0			0
$328$	1.44609	+	2.50470i	0.0798471	+	0.138299i
$329$	6.80453	−	11.7858i	0.375146	−	0.649771i
$330$		0			0
$331$	11.9248	−	20.6543i	0.655444	−	1.13526i	−0.326338	−	0.945253i	$-0.605815\pi$
$331$	11.9248	−	20.6543i	0.655444	−	1.13526i	0.981782	−	0.190009i	$-0.0608519\pi$
$332$	−12.8236	+	22.2112i	−0.703789	+	1.21900i
$333$		0			0
$334$	−21.8023	+	37.7627i	−1.19297	+	2.06628i
$335$	6.56633	+	11.3732i	0.358757	+	0.621385i
$336$		0			0
$337$	5.68306			0.309576			0.154788	−	0.987948i	$-0.450531\pi$
$337$	5.68306			0.309576			0.154788	+	0.987948i	$0.450531\pi$
$338$	1.90734	−	29.3415i	0.103745	−	1.59597i
$339$		0			0
$340$	7.00000	+	12.1244i	0.379628	+	0.657536i
$341$	20.0641	+	34.7521i	1.08653	+	1.88193i
$342$		0			0
$343$	15.6563			0.845359
$344$	−8.04721	+	13.9382i	−0.433876	+	0.751496i
$345$		0			0
$346$	6.82364			0.366841
$347$	−10.7248	+	18.5759i	−0.575737	+	0.997206i	0.420224	+	0.907421i	$0.361952\pi$
$347$	−10.7248	+	18.5759i	−0.575737	+	0.997206i	−0.995961	+	0.0897859i	$0.971382\pi$
$348$		0			0
$349$	−3.43543	−	5.95033i	−0.183894	−	0.318514i	0.759309	−	0.650730i	$-0.225537\pi$
$349$	−3.43543	−	5.95033i	−0.183894	−	0.318514i	−0.943203	+	0.332216i	$0.892204\pi$
$350$	−2.85395			−0.152550
$351$		0			0
$352$	28.1888			1.50247
$353$	17.2484	+	29.8751i	0.918040	+	1.59009i	0.802389	+	0.596802i	$0.203562\pi$
$353$	17.2484	+	29.8751i	0.918040	+	1.59009i	0.115651	+	0.993290i	$0.463104\pi$
$354$		0			0
$355$	4.80453	−	8.32168i	0.254998	−	0.441669i
$356$	−20.6339			−1.09359
$357$		0			0
$358$	−6.01294	+	10.4147i	−0.317794	+	0.550435i
$359$	8.15945			0.430639			0.215320	−	0.976544i	$-0.430921\pi$
$359$	8.15945			0.430639			0.215320	+	0.976544i	$0.430921\pi$
$360$		0			0
$361$	−3.58545	−	6.21017i	−0.188708	−	0.326851i
$362$	−29.2574	−	50.6753i	−1.53773	−	2.66343i
$363$		0			0
$364$	−3.22253	−	13.8039i	−0.168906	−	0.723522i
$365$	−13.7854			−0.721561
$366$		0			0
$367$	3.42027	+	5.92409i	0.178537	+	0.309235i	0.941380	−	0.337349i	$-0.109530\pi$
$367$	3.42027	+	5.92409i	0.178537	+	0.309235i	−0.762843	+	0.646584i	$0.776197\pi$
$368$	−0.584211	+	1.01188i	−0.0304541	+	0.0527481i
$369$		0			0
$370$	−0.261802	+	0.453455i	−0.0136105	+	0.0235740i
$371$	−2.85395	+	4.94318i	−0.148170	+	0.256637i
$372$		0			0
$373$	−6.90961	+	11.9678i	−0.357766	+	0.619669i	−0.987587	−	0.157071i	$-0.949795\pi$
$373$	−6.90961	+	11.9678i	−0.357766	+	0.619669i	0.629821	+	0.776740i	$0.283128\pi$
$374$	22.9866	+	39.8140i	1.18861	+	2.05873i
$375$		0			0
$376$	27.2181			1.40367
$377$	1.12915	+	4.83678i	0.0581540	+	0.249107i
$378$		0			0
$379$	−5.75784	−	9.97286i	−0.295760	−	0.512272i	0.679401	−	0.733767i	$-0.262240\pi$
$379$	−5.75784	−	9.97286i	−0.295760	−	0.512272i	−0.975161	+	0.221495i	$0.928906\pi$
$380$	7.96970	+	13.8039i	0.408837	+	0.708126i
$381$		0			0
$382$	−24.1024			−1.23318
$383$	11.4399	−	19.8145i	0.584552	−	1.01247i	−0.410379	−	0.911915i	$-0.634604\pi$
$383$	11.4399	−	19.8145i	0.584552	−	1.01247i	0.994931	−	0.100559i	$-0.0320631\pi$
$384$		0			0
$385$	−5.70789			−0.290901
$386$	−9.02809	+	15.6371i	−0.459518	+	0.795908i
$387$		0			0
$388$	−16.6220	−	28.7901i	−0.843854	−	1.46160i
$389$	4.35271			0.220691			0.110346	−	0.993893i	$-0.464804\pi$
$389$	4.35271			0.220691			0.110346	+	0.993893i	$0.464804\pi$
$390$		0			0
$391$	−10.0268			−0.507077
$392$	6.82364	+	11.8189i	0.344646	+	0.596944i
$393$		0			0
$394$	19.6091	−	33.9639i	0.987890	−	1.71108i
$395$	8.87085			0.446341
$396$		0			0
$397$	−3.81122	+	6.60123i	−0.191280	+	0.331306i	−0.945675	−	0.325115i	$-0.894597\pi$
$397$	−3.81122	+	6.60123i	−0.191280	+	0.331306i	0.754395	+	0.656421i	$0.227930\pi$
$398$	−2.78541			−0.139620
$399$		0			0
$400$	0.261802	+	0.453455i	0.0130901	+	0.0226727i
$401$	10.4248	+	18.0562i	0.520588	+	0.901684i	0.999713	+	0.0239381i	$0.00762045\pi$
$401$	10.4248	+	18.0562i	0.520588	+	0.901684i	−0.479126	+	0.877746i	$0.659046\pi$
$402$		0			0
$403$	−30.6096	−	9.27635i	−1.52477	−	0.462088i
$404$	53.1148			2.64256
$405$		0			0
$406$	1.96573	+	3.40474i	0.0975575	+	0.168975i
$407$	−0.523604	+	0.906910i	−0.0259541	+	0.0449538i
$408$		0			0
$409$	8.48264	−	14.6924i	0.419439	−	0.726490i	−0.576444	−	0.817137i	$-0.695560\pi$
$409$	8.48264	−	14.6924i	0.419439	−	0.726490i	0.995883	+	0.0906466i	$0.0288934\pi$
$410$	−1.29607	+	2.24486i	−0.0640085	+	0.110866i
$411$		0			0
$412$	21.7298	−	37.6371i	1.07055	−	1.85425i
$413$	0.538756	+	0.933153i	0.0265105	+	0.0459175i
$414$		0			0
$415$	−8.23150			−0.404068
$416$	−16.3945	+	15.3633i	−0.803804	+	0.753250i
$417$		0			0
$418$	26.1709	+	45.3293i	1.28006	+	2.21713i
$419$	1.04942	+	1.81765i	0.0512676	+	0.0887981i	0.890520	−	0.454943i	$-0.150341\pi$
$419$	1.04942	+	1.81765i	0.0512676	+	0.0887981i	−0.839253	+	0.543742i	$0.817007\pi$
$420$		0			0
$421$	−39.6598			−1.93290			−0.966449	−	0.256857i	$-0.917313\pi$
$421$	−39.6598			−1.93290			−0.966449	+	0.256857i	$0.917313\pi$
$422$	−11.6927	+	20.2524i	−0.569194	+	0.985873i
$423$		0			0
$424$	−11.4158			−0.554400
$425$	−2.24665	+	3.89131i	−0.108979	+	0.188756i
$426$		0			0
$427$	2.92697	+	5.06967i	0.141646	+	0.245338i
$428$	−38.9260			−1.88156
$429$		0			0
$430$	−14.4248			−0.695624
$431$	−11.0641	−	19.1636i	−0.532940	−	0.923079i	−0.999260	−	0.0384626i	$-0.987754\pi$
$431$	−11.0641	−	19.1636i	−0.532940	−	0.923079i	0.466320	−	0.884616i	$-0.345579\pi$
$432$		0			0
$433$	15.6781	−	27.1553i	0.753442	−	1.30500i	−0.192703	−	0.981257i	$-0.561725\pi$
$433$	15.6781	−	27.1553i	0.753442	−	1.30500i	0.946145	−	0.323743i	$-0.104941\pi$
$434$	−25.3169			−1.21525
$435$		0			0
$436$	3.54994	−	6.14868i	0.170011	−	0.294468i
$437$	−11.4158			−0.546091
$438$		0			0
$439$	−2.15672	−	3.73555i	−0.102935	−	0.178288i	0.809958	−	0.586488i	$-0.199490\pi$
$439$	−2.15672	−	3.73555i	−0.102935	−	0.178288i	−0.912892	+	0.408200i	$0.866157\pi$
$440$	−5.70789	−	9.88636i	−0.272113	−	0.471314i
$441$		0			0
$442$	−35.0681	−	10.6275i	−1.66802	−	0.505499i
$443$	−0.493301			−0.0234374			−0.0117187	−	0.999931i	$-0.503730\pi$
$443$	−0.493301			−0.0234374			−0.0117187	+	0.999931i	$0.503730\pi$
$444$		0			0
$445$	−3.31122	−	5.73521i	−0.156967	−	0.271875i
$446$	−24.3945	+	42.2524i	−1.15511	+	2.00071i
$447$		0			0
$448$	−8.23150	+	14.2574i	−0.388902	+	0.673598i
$449$	−11.6563	+	20.1892i	−0.550093	+	0.952789i	0.448174	+	0.893946i	$0.352074\pi$
$449$	−11.6563	+	20.1892i	−0.550093	+	0.952789i	−0.998267	+	0.0588427i	$0.981259\pi$
$450$		0			0
$451$	−2.59214	+	4.48973i	−0.122059	+	0.211413i
$452$	−2.30004	−	3.98378i	−0.108185	−	0.187381i
$453$		0			0
$454$	−12.3180			−0.578112
$455$	3.31968	−	3.11089i	0.155629	−	0.145841i
$456$		0			0
$457$	−3.33483	−	5.77609i	−0.155997	−	0.270194i	0.777425	−	0.628976i	$-0.216526\pi$
$457$	−3.33483	−	5.77609i	−0.155997	−	0.270194i	−0.933422	+	0.358782i	$0.883192\pi$
$458$	−24.8023	−	42.9589i	−1.15894	−	2.00734i
$459$		0			0
$460$	6.95279			0.324176
$461$	14.5596	−	25.2180i	0.678110	−	1.17452i	−0.297440	−	0.954740i	$-0.596133\pi$
$461$	14.5596	−	25.2180i	0.678110	−	1.17452i	0.975550	−	0.219780i	$-0.0705338\pi$
$462$		0			0
$463$	−1.79334			−0.0833436			−0.0416718	−	0.999131i	$-0.513268\pi$
$463$	−1.79334			−0.0833436			−0.0416718	+	0.999131i	$0.513268\pi$
$464$	0.360646	−	0.624657i	0.0167426	−	0.0289990i
$465$		0			0
$466$	28.6260	+	49.5816i	1.32607	+	2.29682i
$467$	−16.8192			−0.778301			−0.389150	−	0.921174i	$-0.627231\pi$
$467$	−16.8192			−0.778301			−0.389150	+	0.921174i	$0.627231\pi$
$468$		0			0
$469$	−16.5708			−0.765169
$470$	12.1972	+	21.1262i	0.562616	+	0.974480i
$471$		0			0
$472$	−1.07751	+	1.86631i	−0.0495965	+	0.0859037i
$473$	−28.8495			−1.32650
$474$		0			0
$475$	−2.55787	+	4.43037i	−0.117363	+	0.203279i
$476$	−17.6652			−0.809685
$477$		0			0
$478$	25.4720	+	44.1187i	1.16506	+	2.01794i
$479$	17.5765	+	30.4434i	0.803092	+	1.39100i	0.917571	+	0.397571i	$0.130147\pi$
$479$	17.5765	+	30.4434i	0.803092	+	1.39100i	−0.114479	+	0.993426i	$0.536520\pi$
$480$		0			0
$481$	−0.189754	−	0.812826i	−0.00865205	−	0.0370617i
$482$	25.1416			1.14517
$483$		0			0
$484$	−14.7422	−	25.5342i	−0.670098	−	1.16064i
$485$	5.33483	−	9.24019i	0.242242	−	0.419576i
$486$		0			0
$487$	4.31298	−	7.47030i	0.195440	−	0.338511i	−0.751605	−	0.659614i	$-0.770720\pi$
$487$	4.31298	−	7.47030i	0.195440	−	0.338511i	0.947045	+	0.321102i	$0.104053\pi$
$488$	−5.85395	+	10.1393i	−0.264996	+	0.458986i
$489$		0			0
$490$	−6.11575	+	10.5928i	−0.276281	+	0.478533i
$491$	−11.6068	−	20.1036i	−0.523809	−	0.907264i	−0.999616	−	0.0277143i	$-0.991177\pi$
$491$	−11.6068	−	20.1036i	−0.523809	−	0.907264i	0.475807	−	0.879550i	$-0.342156\pi$
$492$		0			0
$493$	6.18975			0.278773
$494$	−39.9260	−	12.0997i	−1.79636	−	0.544392i
$495$		0			0
$496$	2.32241	+	4.02253i	0.104279	+	0.180617i
$497$	6.06236	+	10.5003i	0.271934	+	0.471004i
$498$		0			0
$499$	29.0393			1.29998			0.649988	−	0.759944i	$-0.274774\pi$
$499$	29.0393			1.29998			0.649988	+	0.759944i	$0.274774\pi$
$500$	1.55787	−	2.69832i	0.0696703	−	0.120672i
$501$		0			0
$502$	−24.9866			−1.11521
$503$	−8.69996	+	15.0688i	−0.387912	+	0.671883i	−0.992169	−	0.124906i	$-0.960137\pi$
$503$	−8.69996	+	15.0688i	−0.387912	+	0.671883i	0.604256	+	0.796790i	$0.293470\pi$
$504$		0			0
$505$	8.52360	+	14.7633i	0.379295	+	0.656959i
$506$	22.8316			1.01499
$507$		0			0
$508$	−55.4149			−2.45864
$509$	−11.4382	−	19.8115i	−0.506987	−	0.878128i	−0.999967	−	0.00808731i	$-0.997426\pi$
$509$	−11.4382	−	19.8115i	−0.506987	−	0.878128i	0.492980	−	0.870041i	$-0.335908\pi$
$510$		0			0
$511$	8.69723	−	15.0640i	0.384743	−	0.666394i
$512$	5.90558			0.260992
$513$		0			0
$514$	−2.29607	+	3.97691i	−0.101275	+	0.175414i
$515$	13.9484			0.614638
$516$		0			0
$517$	24.3945	+	42.2524i	1.07287	+	1.85826i
$518$	−0.330343	−	0.572170i	−0.0145144	−	0.0251397i
$519$		0			0
$520$	8.70789	+	2.63896i	0.381866	+	0.115726i
$521$	26.3642			1.15503			0.577517	−	0.816378i	$-0.304022\pi$
$521$	26.3642			1.15503			0.577517	+	0.816378i	$0.304022\pi$
$522$		0			0
$523$	13.1461	+	22.7696i	0.574837	+	0.995646i	0.996059	+	0.0886892i	$0.0282678\pi$
$523$	13.1461	+	22.7696i	0.574837	+	0.995646i	−0.421223	+	0.906957i	$0.638399\pi$
$524$	18.1799	−	31.4884i	0.794191	−	1.37558i
$525$		0			0
$526$	3.67362	−	6.36290i	0.160178	−	0.277436i
$527$	−19.9297	+	34.5193i	−0.868152	+	1.50368i
$528$		0			0
$529$	9.01021	−	15.6061i	0.391748	−	0.678528i
$530$	−5.11575	−	8.86074i	−0.222214	−	0.384886i
$531$		0			0
$532$	−20.1124			−0.871981
$533$	−0.939393	−	4.02396i	−0.0406896	−	0.174297i
$534$		0			0
$535$	−6.24665	−	10.8195i	−0.270066	−	0.467768i
$536$	−16.5708	−	28.7015i	−0.715750	−	1.23972i
$537$		0			0
$538$	−60.9519			−2.62782
$539$	−12.2315	+	21.1856i	−0.526848	+	0.912527i
$540$		0			0
$541$	−0.107816			−0.00463537			−0.00231768	−	0.999997i	$-0.500738\pi$
$541$	−0.107816			−0.00463537			−0.00231768	+	0.999997i	$0.500738\pi$
$542$	22.4478	−	38.8808i	0.964218	−	1.67007i
$543$		0			0
$544$	14.0000	+	24.2487i	0.600245	+	1.03965i
$545$	2.27871			0.0976091
$546$		0			0
$547$	12.1193			0.518182			0.259091	−	0.965853i	$-0.416577\pi$
$547$	12.1193			0.518182			0.259091	+	0.965853i	$0.416577\pi$
$548$	−31.2574	−	54.1394i	−1.33525	−	2.31272i
$549$		0			0
$550$	5.11575	−	8.86074i	0.218136	−	0.377823i
$551$	7.04721			0.300221
$552$		0			0
$553$	−5.59663	+	9.69365i	−0.237993	+	0.412216i
$554$	36.4024			1.54659
$555$		0			0
$556$	−25.4546	−	44.0887i	−1.07952	−	1.86978i
$557$	19.0035	+	32.9150i	0.805204	+	1.39466i	0.916153	+	0.400829i	$0.131278\pi$
$557$	19.0035	+	32.9150i	0.805204	+	1.39466i	−0.110948	+	0.993826i	$0.535389\pi$
$558$		0			0
$559$	16.7787	−	15.7234i	0.709664	−	0.665030i
$560$	−0.660685			−0.0279191
$561$		0			0
$562$	−6.08148	−	10.5334i	−0.256532	−	0.444326i
$563$	7.75510	−	13.4322i	0.326839	−	0.566101i	−0.655044	−	0.755591i	$-0.727350\pi$
$563$	7.75510	−	13.4322i	0.326839	−	0.566101i	0.981883	+	0.189490i	$0.0606833\pi$
$564$		0			0
$565$	0.738198	−	1.27860i	0.0310562	−	0.0537909i
$566$	−30.3833	+	52.6254i	−1.27710	+	2.21201i
$567$		0			0
$568$	−12.1247	+	21.0006i	−0.508742	+	0.881167i
$569$	9.62024	+	16.6627i	0.403301	+	0.698538i	0.994122	−	0.108265i	$-0.0345293\pi$
$569$	9.62024	+	16.6627i	0.403301	+	0.698538i	−0.590821	+	0.806803i	$0.701196\pi$
$570$		0			0
$571$	27.7338			1.16062			0.580311	−	0.814395i	$-0.302931\pi$
$571$	27.7338			1.16062			0.580311	+	0.814395i	$0.302931\pi$
$572$	48.6339	+	14.7387i	2.03349	+	0.616255i
$573$		0			0
$574$	−1.63539	−	2.83257i	−0.0682597	−	0.118229i
$575$	1.11575	+	1.93253i	0.0465300	+	0.0805923i
$576$		0			0
$577$	26.9866			1.12347			0.561733	−	0.827318i	$-0.310135\pi$
$577$	26.9866			1.12347			0.561733	+	0.827318i	$0.310135\pi$
$578$	−3.60730	+	6.24802i	−0.150044	+	0.259883i
$579$		0			0
$580$	−4.29211			−0.178220
$581$	5.19326	−	8.99499i	0.215453	−	0.373175i
$582$		0			0
$583$	−10.2315	−	17.7215i	−0.423745	−	0.733949i
$584$	34.7889			1.43958
$585$		0			0
$586$	−48.4462			−2.00129
$587$	−15.4265	−	26.7195i	−0.636720	−	1.10283i	−0.986148	−	0.165869i	$-0.946957\pi$
$587$	−15.4265	−	26.7195i	−0.636720	−	1.10283i	0.349427	−	0.936963i	$-0.386376\pi$
$588$		0			0
$589$	−22.6905	+	39.3012i	−0.934947	+	1.61938i
$590$	−1.93146			−0.0795169
$591$		0			0
$592$	−0.0606069	+	0.104974i	−0.00249093	+	0.00431441i
$593$	−4.29211			−0.176256			−0.0881278	−	0.996109i	$-0.528088\pi$
$593$	−4.29211			−0.176256			−0.0881278	+	0.996109i	$0.528088\pi$
$594$		0			0
$595$	−2.83483	−	4.91007i	−0.116217	−	0.201293i
$596$	−5.05514	−	8.75576i	−0.207067	−	0.358650i
$597$		0			0
$598$	−13.2787	+	12.4436i	−0.543007	+	0.508855i
$599$	24.0224			0.981527			0.490764	−	0.871293i	$-0.336718\pi$
$599$	24.0224			0.981527			0.490764	+	0.871293i	$0.336718\pi$
$600$		0			0
$601$	−1.26577	−	2.19238i	−0.0516318	−	0.0894289i	0.839054	−	0.544048i	$-0.183109\pi$
$601$	−1.26577	−	2.19238i	−0.0516318	−	0.0894289i	−0.890686	+	0.454619i	$0.849776\pi$
$602$	9.10060	−	15.7627i	0.370913	−	0.642440i
$603$		0			0
$604$	−8.87982	+	15.3803i	−0.361315	+	0.625816i
$605$	4.73150	−	8.19520i	0.192363	−	0.333182i
$606$		0			0
$607$	−5.72083	+	9.90877i	−0.232201	+	0.402185i	−0.958456	−	0.285242i	$-0.907926\pi$
$607$	−5.72083	+	9.90877i	−0.232201	+	0.402185i	0.726254	+	0.687426i	$0.241260\pi$
$608$	15.9394	+	27.6078i	0.646428	+	1.11965i
$609$		0			0
$610$	−10.4933			−0.424861
$611$	−37.2159	−	11.2784i	−1.50559	−	0.456276i
$612$		0			0
$613$	3.59663	+	6.22955i	0.145267	+	0.251609i	0.929472	−	0.368892i	$-0.120263\pi$
$613$	3.59663	+	6.22955i	0.145267	+	0.251609i	−0.784206	+	0.620501i	$0.786929\pi$
$614$	8.88204	+	15.3841i	0.358450	+	0.620853i
$615$		0			0
$616$	14.4045			0.580373
$617$	12.7854	−	22.1450i	0.514721	−	0.891523i	−0.485133	−	0.874440i	$-0.661229\pi$
$617$	12.7854	−	22.1450i	0.514721	−	0.891523i	0.999854	−	0.0170827i	$-0.00543786\pi$
$618$		0			0
$619$	5.98660			0.240622			0.120311	−	0.992736i	$-0.461611\pi$
$619$	5.98660			0.240622			0.120311	+	0.992736i	$0.461611\pi$
$620$	13.8197	−	23.9364i	0.555012	−	0.961308i
$621$		0			0
$622$	−31.5231	−	54.5997i	−1.26396	−	2.18925i
$623$	8.35622			0.334785
$624$		0			0
$625$	1.00000			0.0400000
$626$	−8.92027	−	15.4504i	−0.356526	−	0.617521i
$627$		0			0
$628$	6.00397	−	10.3992i	0.239584	−	0.414972i
$629$	−1.04019			−0.0414752
$630$		0			0
$631$	21.5129	−	37.2615i	0.856417	−	1.48336i	−0.0189080	−	0.999821i	$-0.506019\pi$
$631$	21.5129	−	37.2615i	0.856417	−	1.48336i	0.875325	−	0.483536i	$-0.160648\pi$
$632$	−22.3865			−0.890488
$633$		0			0
$634$	14.9484	+	25.8913i	0.593675	+	1.02828i
$635$	−8.89270	−	15.4026i	−0.352896	−	0.611234i
$636$		0			0
$637$	−4.43269	−	18.9878i	−0.175630	−	0.752322i
$638$	−14.0944			−0.558003
$639$		0			0
$640$	−8.52360	−	14.7633i	−0.336925	−	0.583571i
$641$	−3.34725	+	5.79760i	−0.132208	+	0.228992i	−0.924528	−	0.381115i	$-0.875540\pi$
$641$	−3.34725	+	5.79760i	−0.132208	+	0.228992i	0.792319	+	0.610107i	$0.208873\pi$
$642$		0			0
$643$	−4.09039	+	7.08477i	−0.161309	+	0.279396i	−0.935338	−	0.353754i	$-0.884905\pi$
$643$	−4.09039	+	7.08477i	−0.161309	+	0.279396i	0.774029	+	0.633150i	$0.218238\pi$
$644$	−4.38652	+	7.59768i	−0.172853	+	0.299391i
$645$		0			0
$646$	−25.9956	+	45.0257i	−1.02278	+	1.77151i
$647$	−5.63935	−	9.76765i	−0.221706	−	0.384006i	0.733620	−	0.679560i	$-0.237829\pi$
$647$	−5.63935	−	9.76765i	−0.221706	−	0.384006i	−0.955326	+	0.295554i	$0.904496\pi$
$648$		0			0
$649$	−3.86292			−0.151633
$650$	1.85395	+	7.94151i	0.0727178	+	0.311492i
$651$		0			0
$652$	15.1500	+	26.2406i	0.593321	+	1.02766i
$653$	13.6242	+	23.5978i	0.533156	+	0.923454i	0.999250	+	0.0387184i	$0.0123275\pi$
$653$	13.6242	+	23.5978i	0.533156	+	0.923454i	−0.466094	+	0.884735i	$0.654339\pi$
$654$		0			0
$655$	11.6697			0.455971
$656$	−0.300039	+	0.519683i	−0.0117146	+	0.0202902i
$657$		0			0
$658$	−30.7810			−1.19997
$659$	3.37755	−	5.85009i	0.131571	−	0.227887i	−0.792711	−	0.609597i	$-0.791331\pi$
$659$	3.37755	−	5.85009i	0.131571	−	0.227887i	0.924282	+	0.381710i	$0.124665\pi$
$660$		0			0
$661$	13.2551	+	22.9585i	0.515564	+	0.892983i	0.999837	+	0.0180657i	$0.00575081\pi$
$661$	13.2551	+	22.9585i	0.515564	+	0.892983i	−0.484273	+	0.874917i	$0.660916\pi$
$662$	−53.9429			−2.09655
$663$		0			0
$664$	20.7730			0.806151
$665$	−3.22753	−	5.59025i	−0.125158	−	0.216781i
$666$		0			0
$667$	1.53700	−	2.66217i	0.0595130	−	0.103079i
$668$	60.0676			2.32409
$669$		0			0
$670$	14.8517	−	25.7240i	0.573773	−	0.993803i
$671$	−20.9866			−0.810179
$672$		0			0
$673$	0.338795	+	0.586811i	0.0130596	+	0.0226199i	0.872481	−	0.488647i	$-0.162510\pi$
$673$	0.338795	+	0.586811i	0.0130596	+	0.0226199i	−0.859422	+	0.511267i	$0.829176\pi$
$674$	−6.42697	−	11.1318i	−0.247558	−	0.428783i
$675$		0			0
$676$	−36.3180	+	17.9343i	−1.39685	+	0.689780i
$677$	10.4630			0.402126			0.201063	−	0.979578i	$-0.435560\pi$
$677$	10.4630			0.402126			0.201063	+	0.979578i	$0.435560\pi$
$678$		0			0
$679$	6.73150	+	11.6593i	0.258331	+	0.447443i
$680$	5.66966	−	9.82013i	0.217421	−	0.376585i
$681$		0			0
$682$	45.3811	−	78.6023i	1.73773	−	3.00984i
$683$	−9.37580	+	16.2394i	−0.358755	+	0.621382i	−0.987753	−	0.156025i	$-0.950132\pi$
$683$	−9.37580	+	16.2394i	−0.358755	+	0.621382i	0.628998	+	0.777407i	$0.283465\pi$
$684$		0			0
$685$	10.0321	−	17.3760i	0.383305	−	0.663904i
$686$	−17.7057	−	30.6671i	−0.676006	−	1.17088i
$687$		0			0
$688$	−3.33931			−0.127310
$689$	15.6091	+	4.73038i	0.594657	+	0.180213i
$690$		0			0
$691$	−21.7827	−	37.7287i	−0.828652	−	1.43527i	−0.899096	−	0.437752i	$-0.855775\pi$
$691$	−21.7827	−	37.7287i	−0.828652	−	1.43527i	0.0704440	−	0.997516i	$-0.477558\pi$
$692$	−4.69996	−	8.14057i	−0.178666	−	0.309458i
$693$		0			0
$694$	48.5148			1.84159
$695$	8.16966	−	14.1503i	0.309893	−	0.536750i
$696$		0			0
$697$	−5.14956			−0.195054
$698$	−7.77026	+	13.4585i	−0.294108	+	0.509411i
$699$		0			0
$700$	1.96573	+	3.40474i	0.0742976	+	0.128687i
$701$	19.0810			0.720680			0.360340	−	0.932821i	$-0.382661\pi$
$701$	19.0810			0.720680			0.360340	+	0.932821i	$0.382661\pi$
$702$		0			0
$703$	−1.18429			−0.0446663
$704$	−29.5102	−	51.1132i	−1.11221	−	1.92640i
$705$		0			0
$706$	39.0125	−	67.5716i	1.46825	−	2.54309i
$707$	−21.5102			−0.808975
$708$		0			0
$709$	−22.3023	+	38.6287i	−0.837581	+	1.45073i	0.0543307	+	0.998523i	$0.482697\pi$
$709$	−22.3023	+	38.6287i	−0.837581	+	1.45073i	−0.891912	+	0.452210i	$0.850636\pi$
$710$	−21.7338			−0.815654
$711$		0			0
$712$	8.35622	+	14.4734i	0.313163	+	0.542414i
$713$	9.89765	+	17.1432i	0.370670	+	0.642019i
$714$		0			0
$715$	3.70789	+	15.8830i	0.138667	+	0.593991i
$716$	16.5663			0.619110
$717$		0			0
$718$	−9.22753	−	15.9826i	−0.344368	−	0.596464i
$719$	−6.49109	+	11.2429i	−0.242077	+	0.419289i	−0.961306	−	0.275484i	$-0.911162\pi$
$719$	−6.49109	+	11.2429i	−0.242077	+	0.419289i	0.719229	+	0.694773i	$0.244495\pi$
$720$		0			0
$721$	−8.80004	+	15.2421i	−0.327731	+	0.567646i
$722$	−8.10957	+	14.0462i	−0.301807	+	0.522745i
$723$		0			0
$724$	−40.3035	+	69.8078i	−1.49787	+	2.59439i
$725$	−0.688776	−	1.19299i	−0.0255805	−	0.0443067i
$726$		0			0
$727$	17.3980			0.645255			0.322627	−	0.946526i	$-0.395434\pi$
$727$	17.3980			0.645255			0.322627	+	0.946526i	$0.395434\pi$
$728$	−8.37755	+	7.85065i	−0.310493	+	0.290965i
$729$		0			0
$730$	15.5899	+	27.0026i	0.577009	+	0.999409i
$731$	−14.3281	−	24.8170i	−0.529945	−	0.917892i
$732$		0			0
$733$	45.8272			1.69266			0.846332	−	0.532655i	$-0.178806\pi$
$733$	45.8272			1.69266			0.846332	+	0.532655i	$0.178806\pi$
$734$	7.73598	−	13.3991i	0.285540	−	0.494570i
$735$		0			0
$736$	13.9056			0.512567
$737$	29.7035	−	51.4479i	1.09414	−	1.89511i
$738$		0			0
$739$	−8.78541	−	15.2168i	−0.323176	−	0.559758i	0.657965	−	0.753048i	$-0.271417\pi$
$739$	−8.78541	−	15.2168i	−0.323176	−	0.559758i	−0.981142	+	0.193290i	$0.938084\pi$
$740$	0.721292			0.0265152
$741$		0			0
$742$	12.9101			0.473946
$743$	−15.1781	−	26.2893i	−0.556831	−	0.964459i	−0.997759	−	0.0669167i	$-0.978684\pi$
$743$	−15.1781	−	26.2893i	−0.556831	−	0.964459i	0.440928	−	0.897543i	$-0.354650\pi$
$744$		0			0
$745$	1.62245	−	2.81016i	0.0594419	−	0.102956i
$746$	31.2563			1.14438
$747$		0			0
$748$	31.6652	−	54.8458i	1.15780	−	2.00536i
$749$	15.7641			0.576007
$750$		0			0
$751$	−1.90162	−	3.29369i	−0.0693909	−	0.120189i	0.829242	−	0.558889i	$-0.188772\pi$
$751$	−1.90162	−	3.29369i	−0.0693909	−	0.120189i	−0.898633	+	0.438700i	$0.855439\pi$
$752$	2.82364	+	4.89069i	0.102968	+	0.178345i
$753$		0			0
$754$	8.19723	−	7.68167i	0.298525	−	0.279750i
$755$	−5.69996			−0.207443
$756$		0			0
$757$	1.70393	+	2.95129i	0.0619303	+	0.107266i	0.895328	−	0.445407i	$-0.146941\pi$
$757$	1.70393	+	2.95129i	0.0619303	+	0.107266i	−0.833398	+	0.552673i	$0.813608\pi$
$758$	−13.0231	+	22.5566i	−0.473020	+	0.819294i
$759$		0			0
$760$	6.45506	−	11.1805i	0.234150	−	0.405559i
$761$	3.62245	−	6.27426i	0.131314	−	0.227442i	−0.792870	−	0.609391i	$-0.791414\pi$
$761$	3.62245	−	6.27426i	0.131314	−	0.227442i	0.924183	+	0.381949i	$0.124747\pi$
$762$		0			0
$763$	−1.43764	+	2.49006i	−0.0520460	+	0.0901464i
$764$	16.6011	+	28.7540i	0.600607	+	1.04028i
$765$		0			0
$766$	−51.7496			−1.86979
$767$	2.24665	−	2.10535i	0.0811218	−	0.0760198i
$768$		0			0
$769$	−15.5882	−	26.9995i	−0.562124	−	0.973627i	−0.997311	−	0.0732873i	$-0.976651\pi$
$769$	−15.5882	−	26.9995i	−0.562124	−	0.973627i	0.435187	−	0.900340i	$-0.356682\pi$
$770$	6.45506	+	11.1805i	0.232624	+	0.402917i
$771$		0			0
$772$	24.8733			0.895210
$773$	9.73026	−	16.8533i	0.349973	−	0.606172i	−0.636271	−	0.771466i	$-0.719524\pi$
$773$	9.73026	−	16.8533i	0.349973	−	0.606172i	0.986244	+	0.165294i	$0.0528573\pi$
$774$		0			0
$775$	8.87085			0.318650
$776$	−13.4630	+	23.3186i	−0.483293	+	0.837089i
$777$		0			0
$778$	−4.92249	−	8.52600i	−0.176480	−	0.305672i
$779$	−5.86292			−0.210061
$780$		0			0
$781$	−43.4675			−1.55539
$782$	11.3393	+	19.6403i	0.405493	+	0.702335i
$783$		0			0
$784$	−1.41579	+	2.45222i	−0.0505639	+	0.0875792i
$785$	3.85395			0.137553
$786$		0			0
$787$	−7.20171	+	12.4737i	−0.256713	+	0.444641i	−0.965359	−	0.260923i	$-0.915973\pi$
$787$	−7.20171	+	12.4737i	−0.256713	+	0.444641i	0.708646	+	0.705564i	$0.249306\pi$
$788$	−54.0250			−1.92456
$789$		0			0
$790$	−10.0321	−	17.3760i	−0.356925	−	0.618212i
$791$	0.931460	+	1.61334i	0.0331189	+	0.0573636i
$792$		0			0
$793$	12.2057	−	11.4380i	0.433436	−	0.406176i
$794$	17.2405			0.611841
$795$		0			0
$796$	1.91852	+	3.32298i	0.0680002	+	0.117780i
$797$	−11.8006	+	20.4392i	−0.417997	+	0.723992i	−0.995738	−	0.0922279i	$-0.970601\pi$
$797$	−11.8006	+	20.4392i	−0.417997	+	0.723992i	0.577741	+	0.816220i	$0.303934\pi$
$798$		0			0
$799$	−24.2310	+	41.9694i	−0.857233	+	1.48477i
$800$	3.11575	−	5.39664i	0.110158	−	0.190800i
$801$		0			0
$802$	23.5787	−	40.8396i	0.832595	−	1.44210i
$803$	31.1799	+	54.0051i	1.10031	+	1.90580i
$804$		0			0
$805$	−2.81571			−0.0992407
$806$	16.4461	+	70.4480i	0.579289	+	2.48142i
$807$		0			0
$808$	−21.5102	−	37.2568i	−0.756726	−	1.31069i
$809$	13.3776	+	23.1706i	0.470330	+	0.814635i	0.999424	−	0.0339280i	$-0.0108017\pi$
$809$	13.3776	+	23.1706i	0.470330	+	0.814635i	−0.529095	+	0.848563i	$0.677468\pi$
$810$		0			0
$811$	−3.58421			−0.125859			−0.0629293	−	0.998018i	$-0.520044\pi$
$811$	−3.58421			−0.125859			−0.0629293	+	0.998018i	$0.520044\pi$
$812$	2.70789	−	4.69021i	0.0950285	−	0.164594i
$813$		0			0
$814$	2.36858			0.0830187
$815$	−4.86240	+	8.42192i	−0.170322	+	0.295007i
$816$		0			0
$817$	−16.3130	−	28.2549i	−0.570719	−	0.988514i
$818$	−38.3721			−1.34165
$819$		0			0
$820$	3.57081			0.124698
$821$	7.91806	+	13.7145i	0.276342	+	0.478639i	0.970473	−	0.241210i	$-0.0775443\pi$
$821$	7.91806	+	13.7145i	0.276342	+	0.478639i	−0.694131	+	0.719849i	$0.744211\pi$
$822$		0			0
$823$	−3.70789	+	6.42226i	−0.129249	+	0.223866i	−0.923386	−	0.383873i	$-0.874590\pi$
$823$	−3.70789	+	6.42226i	−0.129249	+	0.223866i	0.794137	+	0.607739i	$0.207923\pi$
$824$	−35.2002			−1.22626
$825$		0			0
$826$	1.21856	−	2.11061i	0.0423991	−	0.0734374i
$827$	16.6036			0.577363			0.288682	−	0.957425i	$-0.406783\pi$
$827$	16.6036			0.577363			0.288682	+	0.957425i	$0.406783\pi$
$828$		0			0
$829$	14.6421	+	25.3608i	0.508541	+	0.880818i	0.999951	+	0.00989015i	$0.00314819\pi$
$829$	14.6421	+	25.3608i	0.508541	+	0.880818i	−0.491410	+	0.870928i	$0.663518\pi$
$830$	9.30901	+	16.1237i	0.323120	+	0.559661i
$831$		0			0
$832$	45.0204	+	13.6436i	1.56080	+	0.473007i
$833$	−24.2991			−0.841915
$834$		0			0
$835$	9.63935	+	16.6959i	0.333584	+	0.577784i
$836$	36.0518	−	62.4435i	1.24688	−	2.15965i
$837$		0			0
$838$	2.37358	−	4.11117i	0.0819941	−	0.142018i
$839$	−15.0810	+	26.1211i	−0.520655	+	0.901800i	0.479057	+	0.877784i	$0.340979\pi$
$839$	−15.0810	+	26.1211i	−0.520655	+	0.901800i	−0.999712	+	0.0240164i	$0.992355\pi$
$840$		0			0
$841$	13.5512	−	23.4713i	0.467282	−	0.809356i
$842$	44.8513	+	77.6847i	1.54568	+	2.67719i
$843$		0			0
$844$	32.2147			1.10888
$845$	−10.8130	−	7.21661i	−0.371978	−	0.248259i
$846$		0			0
$847$	5.97022	+	10.3407i	0.205139	+	0.355311i
$848$	−1.18429	−	2.05125i	−0.0406687	−	0.0704402i
$849$		0			0
$850$	10.1630			0.348587
$851$	−0.258295	+	0.447379i	−0.00885423	+	0.0153360i
$852$		0			0
$853$	−2.50670			−0.0858277			−0.0429139	−	0.999079i	$-0.513664\pi$
$853$	−2.50670			−0.0858277			−0.0429139	+	0.999079i	$0.513664\pi$
$854$	6.62024	−	11.4666i	0.226540	−	0.392378i
$855$		0			0
$856$	15.7641	+	27.3042i	0.538805	+	0.933238i
$857$	24.4327			0.834605			0.417302	−	0.908768i	$-0.362976\pi$
$857$	24.4327			0.834605			0.417302	+	0.908768i	$0.362976\pi$
$858$		0			0
$859$	−7.10235			−0.242329			−0.121165	−	0.992632i	$-0.538663\pi$
$859$	−7.10235			−0.242329			−0.121165	+	0.992632i	$0.538663\pi$
$860$	9.93543	+	17.2087i	0.338795	+	0.586811i
$861$		0			0
$862$	−25.0248	+	43.3443i	−0.852349	+	1.47631i
$863$	3.24490			0.110458			0.0552288	−	0.998474i	$-0.482411\pi$
$863$	3.24490			0.110458			0.0552288	+	0.998474i	$0.482411\pi$
$864$		0			0
$865$	1.50845	−	2.61272i	0.0512889	−	0.0888350i
$866$	−70.9216			−2.41001
$867$		0			0
$868$	17.4377	+	30.2030i	0.591874	+	1.02516i
$869$	−20.0641	−	34.7521i	−0.680628	−	1.17888i
$870$		0			0
$871$	10.7645	+	46.1106i	0.364742	+	1.56240i
$872$	−5.75056			−0.194738
$873$		0			0
$874$	12.9101	+	22.3610i	0.436692	+	0.756372i
$875$	−0.630901	+	1.09275i	−0.0213284	+	0.0369418i
$876$		0			0
$877$	−9.49330	+	16.4429i	−0.320566	+	0.555237i	−0.980605	−	0.195995i	$-0.937206\pi$
$877$	−9.49330	+	16.4429i	−0.320566	+	0.555237i	0.660039	+	0.751231i	$0.270540\pi$
$878$	−4.87807	+	8.44907i	−0.164627	+	0.285142i
$879$		0			0
$880$	1.18429	−	2.05125i	0.0399224	−	0.0691476i
$881$	−9.73820	−	16.8671i	−0.328088	−	0.568265i	0.654044	−	0.756456i	$-0.273071\pi$
$881$	−9.73820	−	16.8671i	−0.328088	−	0.568265i	−0.982132	+	0.188191i	$0.939738\pi$
$882$		0			0
$883$	−50.5664			−1.70169			−0.850847	−	0.525413i	$-0.823911\pi$
$883$	−50.5664			−1.70169			−0.850847	+	0.525413i	$0.823911\pi$
$884$	11.4755	+	49.1560i	0.385962	+	1.65330i
$885$		0			0
$886$	0.557875	+	0.966267i	0.0187422	+	0.0324624i
$887$	−6.26356	−	10.8488i	−0.210310	−	0.364267i	0.741502	−	0.670951i	$-0.234114\pi$
$887$	−6.26356	−	10.8488i	−0.210310	−	0.364267i	−0.951811	+	0.306684i	$0.900781\pi$
$888$		0			0
$889$	22.4417			0.752669
$890$	−7.48933	+	12.9719i	−0.251043	+	0.434819i
$891$		0			0
$892$	67.2092			2.25033
$893$	−27.5877	+	47.7833i	−0.923188	+	1.59901i
$894$		0			0
$895$	2.65847	+	4.60461i	0.0888629	+	0.153915i
$896$	21.5102			0.718606
$897$		0			0
$898$	52.7283			1.75957
$899$	−6.11003	−	10.5829i	−0.203781	−	0.352959i
$900$		0			0
$901$	10.1630	−	17.6028i	0.338577	−	0.586433i
$902$	11.7258			0.390428
$903$		0			0
$904$	−1.86292	+	3.22667i	−0.0619598	+	0.107317i
$905$	−25.8709			−0.859976
$906$		0			0
$907$	−14.0209	−	24.2849i	−0.465555	−	0.806366i	0.533671	−	0.845692i	$-0.320812\pi$
$907$	−14.0209	−	24.2849i	−0.465555	−	0.806366i	−0.999226	+	0.0393265i	$0.987479\pi$
$908$	8.48433	+	14.6953i	0.281562	+	0.487680i
$909$		0			0
$910$	−9.84777	−	2.98440i	−0.326450	−	0.0989320i
$911$	−16.1977			−0.536653			−0.268327	−	0.963328i	$-0.586471\pi$
$911$	−16.1977			−0.536653			−0.268327	+	0.963328i	$0.586471\pi$
$912$		0			0
$913$	18.6180	+	32.2474i	0.616167	+	1.06723i
$914$	−7.54272	+	13.0644i	−0.249491	+	0.432131i
$915$		0			0
$916$	−34.1665	+	59.1781i	−1.12889	+	1.95530i
$917$	−7.36240	+	12.7521i	−0.243128	+	0.421110i
$918$		0			0
$919$	21.6389	−	37.4797i	0.713801	−	1.23634i	−0.249619	−	0.968344i	$-0.580305\pi$
$919$	21.6389	−	37.4797i	0.713801	−	1.23634i	0.963420	−	0.267996i	$-0.0863614\pi$
$920$	−2.81571	−	4.87695i	−0.0928312	−	0.160788i
$921$		0			0
$922$	−65.8620			−2.16905
$923$	25.2805	−	23.6905i	0.832117	−	0.779781i
$924$		0			0
$925$	0.115749	+	0.200484i	0.00380582	+	0.00659187i
$926$	2.02809	+	3.51276i	0.0666472	+	0.115436i
$927$		0			0
$928$	−8.58421			−0.281791
$929$	6.88425	−	11.9239i	0.225865	−	0.391210i	−0.730714	−	0.682684i	$-0.760813\pi$
$929$	6.88425	−	11.9239i	0.225865	−	0.391210i	0.956579	+	0.291475i	$0.0941459\pi$
$930$		0			0
$931$	−27.6652			−0.906691
$932$	39.4337	−	68.3012i	1.29169	−	2.23728i
$933$		0			0
$934$	19.0209	+	32.9451i	0.622382	+	1.07800i
$935$	20.3259			0.664729
$936$		0			0
$937$	−38.1888			−1.24757			−0.623787	−	0.781594i	$-0.714407\pi$
$937$	−38.1888			−1.24757			−0.623787	+	0.781594i	$0.714407\pi$
$938$	18.7400	+	32.4585i	0.611881	+	1.05981i
$939$		0			0
$940$	16.8023	−	29.1025i	0.548031	−	0.949218i
$941$	13.9618			0.455140			0.227570	−	0.973762i	$-0.426922\pi$
$941$	13.9618			0.455140			0.227570	+	0.973762i	$0.426922\pi$
$942$		0			0
$943$	−1.27871	+	2.21479i	−0.0416405	+	0.0721234i
$944$	−0.447131			−0.0145529
$945$		0			0
$946$	32.6260	+	56.5098i	1.06076	+	1.83729i
$947$	3.68481	+	6.38228i	0.119740	+	0.207396i	0.919665	−	0.392705i	$-0.128461\pi$
$947$	3.68481	+	6.38228i	0.119740	+	0.207396i	−0.799924	+	0.600101i	$0.795127\pi$
$948$		0			0
$949$	−47.5676	−	14.4155i	−1.54411	−	0.467948i
$950$	11.5708			0.375407
$951$		0			0
$952$	7.15399	+	12.3911i	0.231862	+	0.401597i
$953$	11.6091	−	20.1075i	0.376054	−	0.651345i	−0.614430	−	0.788971i	$-0.710614\pi$
$953$	11.6091	−	20.1075i	0.376054	−	0.651345i	0.990484	+	0.137627i	$0.0439474\pi$
$954$		0			0
$955$	−5.32813	+	9.22859i	−0.172414	+	0.298630i
$956$	35.0890	−	60.7759i	1.13486	−	1.96563i
$957$		0			0
$958$	39.7546	−	68.8571i	1.28441	−	2.22467i
$959$	12.6585	+	21.9251i	0.408763	+	0.707999i
$960$		0			0
$961$	47.6920			1.53845
$962$	−1.37755	+	1.29091i	−0.0444140	+	0.0416207i
$963$		0			0
$964$	−17.3169	−	29.9938i	−0.557741	−	0.966036i
$965$	3.99155	+	6.91356i	0.128492	+	0.222555i
$966$		0			0
$967$	−7.54402			−0.242599			−0.121300	−	0.992616i	$-0.538706\pi$
$967$	−7.54402			−0.242599			−0.121300	+	0.992616i	$0.538706\pi$
$968$	−11.9404	+	20.6814i	−0.383780	+	0.664726i
$969$		0			0
$970$	−24.1327			−0.774853
$971$	−15.2921	+	26.4867i	−0.490747	+	0.849999i	−0.999943	−	0.0106517i	$-0.996609\pi$
$971$	−15.2921	+	26.4867i	−0.490747	+	0.849999i	0.509196	+	0.860650i	$0.329943\pi$
$972$		0			0
$973$	10.3085	+	17.8548i	0.330475	+	0.572400i
$974$	−19.5102			−0.625147
$975$		0			0
$976$	−2.42919			−0.0777564
$977$	−17.8405	−	30.9007i	−0.570770	−	0.988602i	−0.996487	−	0.0837460i	$-0.973312\pi$
$977$	−17.8405	−	30.9007i	−0.570770	−	0.988602i	0.425717	−	0.904856i	$-0.360022\pi$
$978$		0			0
$979$	−14.9787	+	25.9438i	−0.478720	+	0.829168i
$980$	16.8495			0.538238
$981$		0			0
$982$	−26.2524	+	45.4704i	−0.837747	+	1.45102i
$983$	−12.9866			−0.414208			−0.207104	−	0.978319i	$-0.566404\pi$
$983$	−12.9866			−0.414208			−0.207104	+	0.978319i	$0.566404\pi$
$984$		0			0
$985$	−8.66966	−	15.0163i	−0.276238	−	0.478459i
$986$	−7.00000	−	12.1244i	−0.222925	−	0.386118i
$987$		0			0
$988$	13.0652	+	55.9655i	0.415658	+	1.78050i
$989$	−14.2315			−0.452535
$990$		0			0
$991$	11.3736	+	19.6996i	0.361294	+	0.625779i	0.988174	−	0.153336i	$-0.0490018\pi$
$991$	11.3736	+	19.6996i	0.361294	+	0.625779i	−0.626880	+	0.779116i	$0.715668\pi$
$992$	27.6394	−	47.8728i	0.877550	−	1.51996i
$993$		0			0
$994$	13.7119	−	23.7496i	0.434914	−	0.753293i
$995$	−0.615749	+	1.06651i	−0.0195206	+	0.0338106i
$996$		0			0
$997$	6.92301	−	11.9910i	0.219254	−	0.379759i	−0.735326	−	0.677713i	$-0.762971\pi$
$997$	6.92301	−	11.9910i	0.219254	−	0.379759i	0.954580	+	0.297955i	$0.0963044\pi$
$998$	−32.8405	−	56.8815i	−1.03955	−	1.80055i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.f.406.1		6
3.2	odd	2		195.2.i.d.16.3	✓	6
13.3	even	3		7605.2.a.bv.1.3		3
13.9	even	3	inner	585.2.j.f.451.1		6
13.10	even	6		7605.2.a.bw.1.1		3
15.2	even	4		975.2.bb.k.874.2		12
15.8	even	4		975.2.bb.k.874.5		12
15.14	odd	2		975.2.i.l.601.1		6
39.23	odd	6		2535.2.a.ba.1.3		3
39.29	odd	6		2535.2.a.bb.1.1		3
39.35	odd	6		195.2.i.d.61.3	yes	6
195.74	odd	6		975.2.i.l.451.1		6
195.113	even	12		975.2.bb.k.724.2		12
195.152	even	12		975.2.bb.k.724.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.d.16.3	✓	6	3.2	odd	2
195.2.i.d.61.3	yes	6	39.35	odd	6
585.2.j.f.406.1		6	1.1	even	1	trivial
585.2.j.f.451.1		6	13.9	even	3	inner
975.2.i.l.451.1		6	195.74	odd	6
975.2.i.l.601.1		6	15.14	odd	2
975.2.bb.k.724.2		12	195.113	even	12
975.2.bb.k.724.5		12	195.152	even	12
975.2.bb.k.874.2		12	15.2	even	4
975.2.bb.k.874.5		12	15.8	even	4
2535.2.a.ba.1.3		3	39.23	odd	6
2535.2.a.bb.1.1		3	39.29	odd	6
7605.2.a.bv.1.3		3	13.3	even	3
7605.2.a.bw.1.1		3	13.10	even	6

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13090 - 1.95878i) q^{2} +(-1.55787 + 2.69832i) q^{4} -1.00000 q^{5} +(0.630901 - 1.09275i) q^{7} +2.52360 q^{8} +O(q^{10})\)	\(q+(-1.13090 - 1.95878i) q^{2} +(-1.55787 + 2.69832i) q^{4} -1.00000 q^{5} +(0.630901 - 1.09275i) q^{7} +2.52360 q^{8} +(1.13090 + 1.95878i) q^{10} +(2.26180 + 3.91756i) q^{11} +(-3.45058 - 1.04571i) q^{13} -2.85395 q^{14} +(0.261802 + 0.453455i) q^{16} +(-2.24665 + 3.89131i) q^{17} +(-2.55787 + 4.43037i) q^{19} +(1.55787 - 2.69832i) q^{20} +(5.11575 - 8.86074i) q^{22} +(1.11575 + 1.93253i) q^{23} +1.00000 q^{25} +(1.85395 + 7.94151i) q^{26} +(1.96573 + 3.40474i) q^{28} +(-0.688776 - 1.19299i) q^{29} +8.87085 q^{31} +(3.11575 - 5.39664i) q^{32} +10.1630 q^{34} +(-0.630901 + 1.09275i) q^{35} +(0.115749 + 0.200484i) q^{37} +11.5708 q^{38} -2.52360 q^{40} +(0.573026 + 0.992511i) q^{41} +(-3.18878 + 5.52312i) q^{43} -14.0944 q^{44} +(2.52360 - 4.37101i) q^{46} +10.7854 q^{47} +(2.70393 + 4.68334i) q^{49} +(-1.13090 - 1.95878i) q^{50} +(8.19723 - 7.68167i) q^{52} -4.52360 q^{53} +(-2.26180 - 3.91756i) q^{55} +(1.59214 - 2.75768i) q^{56} +(-1.55787 + 2.69832i) q^{58} +(-0.426974 + 0.739540i) q^{59} +(-2.31968 + 4.01780i) q^{61} +(-10.0321 - 17.3760i) q^{62} -13.0472 q^{64} +(3.45058 + 1.04571i) q^{65} +(-6.56633 - 11.3732i) q^{67} +(-7.00000 - 12.1244i) q^{68} +2.85395 q^{70} +(-4.80453 + 8.32168i) q^{71} +13.7854 q^{73} +(0.261802 - 0.453455i) q^{74} +(-7.96970 - 13.8039i) q^{76} +5.70789 q^{77} -8.87085 q^{79} +(-0.261802 - 0.453455i) q^{80} +(1.29607 - 2.24486i) q^{82} +8.23150 q^{83} +(2.24665 - 3.89131i) q^{85} +14.4248 q^{86} +(5.70789 + 9.88636i) q^{88} +(3.31122 + 5.73521i) q^{89} +(-3.31968 + 3.11089i) q^{91} -6.95279 q^{92} +(-12.1972 - 21.1262i) q^{94} +(2.55787 - 4.43037i) q^{95} +(-5.33483 + 9.24019i) q^{97} +(6.11575 - 10.5928i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{5} - 3 q^{7} - 12 q^{8}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^5 - 3 * q^7 - 12 * q^8	\( 6 q - 6 q^{4} - 6 q^{5} - 3 q^{7} - 12 q^{8} + 3 q^{13} - 24 q^{14} - 12 q^{16} - 12 q^{19} + 6 q^{20} + 24 q^{22} + 6 q^{25} + 18 q^{26} - 12 q^{28} + 6 q^{29} + 6 q^{31} + 12 q^{32} + 3 q^{35} - 6 q^{37} - 12 q^{38} + 12 q^{40} - 9 q^{43} + 24 q^{44} - 12 q^{46} + 24 q^{47} + 6 q^{49} + 12 q^{52} + 30 q^{56} - 6 q^{58} - 6 q^{59} + 3 q^{61} - 6 q^{62} - 24 q^{64} - 3 q^{65} - 9 q^{67} - 42 q^{68} + 24 q^{70} - 12 q^{71} + 42 q^{73} - 12 q^{74} - 48 q^{76} + 48 q^{77} - 6 q^{79} + 12 q^{80} + 18 q^{82} + 36 q^{83} + 12 q^{86} + 48 q^{88} + 30 q^{89} - 3 q^{91} - 96 q^{92} - 36 q^{94} + 12 q^{95} - 15 q^{97} + 30 q^{98}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^5 - 3 * q^7 - 12 * q^8 + 3 * q^13 - 24 * q^14 - 12 * q^16 - 12 * q^19 + 6 * q^20 + 24 * q^22 + 6 * q^25 + 18 * q^26 - 12 * q^28 + 6 * q^29 + 6 * q^31 + 12 * q^32 + 3 * q^35 - 6 * q^37 - 12 * q^38 + 12 * q^40 - 9 * q^43 + 24 * q^44 - 12 * q^46 + 24 * q^47 + 6 * q^49 + 12 * q^52 + 30 * q^56 - 6 * q^58 - 6 * q^59 + 3 * q^61 - 6 * q^62 - 24 * q^64 - 3 * q^65 - 9 * q^67 - 42 * q^68 + 24 * q^70 - 12 * q^71 + 42 * q^73 - 12 * q^74 - 48 * q^76 + 48 * q^77 - 6 * q^79 + 12 * q^80 + 18 * q^82 + 36 * q^83 + 12 * q^86 + 48 * q^88 + 30 * q^89 - 3 * q^91 - 96 * q^92 - 36 * q^94 + 12 * q^95 - 15 * q^97 + 30 * q^98

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