LMFDB - Embedded newform 539.2.q.b.520.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("539.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.q (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
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} - x^{15} - 5 x^{14} + 16 x^{13} + 4 x^{12} - 29 x^{11} + 10 x^{10} - 156 x^{9} + 251 x^{8} + \cdots + 625 $ x^16 - x^15 - 5x^14 + 16x^13 + 4x^12 - 29x^11 + 10x^10 - 156x^9 + 251x^8 + 240x^7 + 390x^6 - 1375x^5 - 300x^4 + 500x^3 + 375x^2 + 625x + 625
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			520.1
Root			$-0.981435 - 1.08999i$ of defining polynomial
Character	$\chi$	$=$	539.520
Dual form			539.2.q.b.312.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.257844 - 2.45322i) q^{2} +(1.08268 - 1.20243i) q^{3} +(-3.99550 + 0.849271i) q^{4} +(3.16702 - 1.41005i) q^{5} +(-3.22899 - 2.34600i) q^{6} +(1.58914 + 4.89086i) q^{8} +(0.0399263 + 0.379874i) q^{9} +O(q^{10})$	\(q+(-0.257844 - 2.45322i) q^{2} +(1.08268 - 1.20243i) q^{3} +(-3.99550 + 0.849271i) q^{4} +(3.16702 - 1.41005i) q^{5} +(-3.22899 - 2.34600i) q^{6} +(1.58914 + 4.89086i) q^{8} +(0.0399263 + 0.379874i) q^{9} +(-4.27575 - 7.40581i) q^{10} +(-0.0978940 - 3.31518i) q^{11} +(-3.30464 + 5.72381i) q^{12} +(-0.528896 + 0.384266i) q^{13} +(1.73337 - 5.33475i) q^{15} +(4.12537 - 1.83673i) q^{16} +(-0.118865 + 1.13092i) q^{17} +(0.921618 - 0.195896i) q^{18} +(-5.94325 - 1.26328i) q^{19} +(-11.4563 + 8.32350i) q^{20} +(-8.10762 + 1.09495i) q^{22} +(3.33354 - 5.77386i) q^{23} +(7.60146 + 3.38439i) q^{24} +(4.69611 - 5.21556i) q^{25} +(1.07906 + 1.19842i) q^{26} +(4.42705 + 3.21644i) q^{27} +(-1.41331 + 4.34973i) q^{29} +(-13.5343 - 2.87679i) q^{30} +(-2.55456 - 1.13736i) q^{31} +(-0.427051 - 0.739674i) q^{32} +(-4.09227 - 3.47155i) q^{33} +2.80505 q^{34} +(-0.482141 - 1.48388i) q^{36} +(-0.294256 - 0.326804i) q^{37} +(-1.56666 + 14.9058i) q^{38} +(-0.110569 + 1.05200i) q^{39} +(11.9292 + 13.2487i) q^{40} +(1.82417 + 5.61423i) q^{41} +8.70820 q^{43} +(3.20662 + 13.1627i) q^{44} +(0.662087 + 1.14677i) q^{45} +(-15.0241 - 6.68915i) q^{46} +(-0.591489 - 0.125725i) q^{47} +(2.25789 - 6.94907i) q^{48} +(-14.0058 - 10.1758i) q^{50} +(1.23117 + 1.36735i) q^{51} +(1.78686 - 1.98451i) q^{52} +(8.97327 + 3.99516i) q^{53} +(6.74915 - 11.6899i) q^{54} +(-4.98459 - 10.3612i) q^{55} +(-7.95362 + 5.77864i) q^{57} +(11.0352 + 2.34561i) q^{58} +(1.65704 - 0.352214i) q^{59} +(-2.39502 + 22.7871i) q^{60} +(-6.26526 + 2.78947i) q^{61} +(-2.13152 + 6.56015i) q^{62} +(5.60222 - 4.07025i) q^{64} +(-1.13319 + 1.96274i) q^{65} +(-7.46132 + 10.9344i) q^{66} +(3.08914 + 5.35054i) q^{67} +(-0.485535 - 4.61956i) q^{68} +(-3.33354 - 10.2596i) q^{69} +(4.38234 + 3.18395i) q^{71} +(-1.79446 + 0.798946i) q^{72} +(6.55553 - 1.39342i) q^{73} +(-0.725850 + 0.806138i) q^{74} +(-1.18700 - 11.2935i) q^{75} +24.8191 q^{76} +2.60929 q^{78} +(-0.277393 - 2.63921i) q^{79} +(10.4752 - 11.6339i) q^{80} +(7.53976 - 1.60263i) q^{81} +(13.3026 - 5.92269i) q^{82} +(5.41765 + 3.93615i) q^{83} +(1.21821 + 3.74926i) q^{85} +(-2.24536 - 21.3631i) q^{86} +(3.70010 + 6.40876i) q^{87} +(16.0585 - 5.74706i) q^{88} +(-0.349107 + 0.604670i) q^{89} +(2.64256 - 1.91993i) q^{90} +(-8.41560 + 25.9006i) q^{92} +(-4.13336 + 1.84029i) q^{93} +(-0.155919 + 1.48347i) q^{94} +(-20.6036 + 4.37944i) q^{95} +(-1.35177 - 0.287327i) q^{96} +(-12.0209 + 8.73372i) q^{97} +(1.25544 - 0.169550i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9	$ 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9} - 28 q^{10} - 5 q^{11} - 14 q^{12} - 10 q^{13} + 12 q^{15} + 3 q^{16} - 11 q^{17} - 4 q^{18} - 9 q^{19} - 42 q^{20} - 2 q^{22} + 16 q^{23} + 21 q^{24} - 5 q^{25} + 21 q^{26} + 44 q^{27} - 18 q^{29} - 14 q^{30} - 11 q^{31} + 20 q^{32} + 10 q^{33} + 48 q^{34} - 4 q^{36} - 6 q^{37} + 35 q^{38} + 5 q^{39} - 16 q^{40} + 44 q^{41} + 32 q^{43} - 29 q^{44} + 18 q^{45} - 29 q^{46} + 7 q^{47} - 8 q^{48} - 68 q^{50} - 3 q^{51} + 21 q^{52} - 2 q^{53} + 4 q^{54} - 52 q^{55} - 6 q^{57} + 39 q^{58} + 25 q^{59} + 38 q^{60} + 7 q^{61} + 10 q^{62} + 2 q^{64} - 24 q^{65} + 18 q^{66} + 30 q^{67} + 8 q^{68} - 16 q^{69} - 28 q^{71} - 3 q^{72} + 3 q^{73} + 9 q^{74} + 5 q^{75} + 104 q^{76} - 36 q^{78} + 9 q^{79} - 33 q^{80} + 28 q^{81} + 31 q^{82} - 46 q^{83} - 20 q^{85} + 17 q^{86} + 12 q^{87} + 7 q^{88} - 34 q^{89} - 4 q^{90} - 68 q^{92} - 8 q^{93} - 30 q^{94} - 24 q^{95} + 10 q^{96} - 60 q^{97}+O(q^{100}) $ 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9 - 28 * q^10 - 5 * q^11 - 14 * q^12 - 10 * q^13 + 12 * q^15 + 3 * q^16 - 11 * q^17 - 4 * q^18 - 9 * q^19 - 42 * q^20 - 2 * q^22 + 16 * q^23 + 21 * q^24 - 5 * q^25 + 21 * q^26 + 44 * q^27 - 18 * q^29 - 14 * q^30 - 11 * q^31 + 20 * q^32 + 10 * q^33 + 48 * q^34 - 4 * q^36 - 6 * q^37 + 35 * q^38 + 5 * q^39 - 16 * q^40 + 44 * q^41 + 32 * q^43 - 29 * q^44 + 18 * q^45 - 29 * q^46 + 7 * q^47 - 8 * q^48 - 68 * q^50 - 3 * q^51 + 21 * q^52 - 2 * q^53 + 4 * q^54 - 52 * q^55 - 6 * q^57 + 39 * q^58 + 25 * q^59 + 38 * q^60 + 7 * q^61 + 10 * q^62 + 2 * q^64 - 24 * q^65 + 18 * q^66 + 30 * q^67 + 8 * q^68 - 16 * q^69 - 28 * q^71 - 3 * q^72 + 3 * q^73 + 9 * q^74 + 5 * q^75 + 104 * q^76 - 36 * q^78 + 9 * q^79 - 33 * q^80 + 28 * q^81 + 31 * q^82 - 46 * q^83 - 20 * q^85 + 17 * q^86 + 12 * q^87 + 7 * q^88 - 34 * q^89 - 4 * q^90 - 68 * q^92 - 8 * q^93 - 30 * q^94 - 24 * q^95 + 10 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.257844	−	2.45322i	−0.182323	−	1.73469i	−0.577771	−	0.816199i	$-0.696077\pi$
$2$	−0.257844	−	2.45322i	−0.182323	−	1.73469i	0.395448	−	0.918489i	$-0.370589\pi$
$3$	1.08268	−	1.20243i	0.625083	−	0.694225i	−0.344556	−	0.938766i	$-0.611970\pi$
$3$	1.08268	−	1.20243i	0.625083	−	0.694225i	0.969639	+	0.244540i	$0.0786371\pi$
$4$	−3.99550	+	0.849271i	−1.99775	+	0.424635i
$5$	3.16702	−	1.41005i	1.41633	−	0.630592i	0.451217	−	0.892414i	$-0.350990\pi$
$5$	3.16702	−	1.41005i	1.41633	−	0.630592i	0.965116	+	0.261822i	$0.0843234\pi$
$6$	−3.22899	−	2.34600i	−1.31823	−	0.957751i
$7$		0			0
$7$		0			0
$8$	1.58914	+	4.89086i	0.561845	+	1.72918i
$9$	0.0399263	+	0.379874i	0.0133088	+	0.126625i
$10$	−4.27575	−	7.40581i	−1.35211	−	2.34192i
$11$	−0.0978940	−	3.31518i	−0.0295161	−	0.999564i
$11$	−0.0978940	−	3.31518i	−0.0295161	−	0.999564i
$12$	−3.30464	+	5.72381i	−0.953969	+	1.65232i
$13$	−0.528896	+	0.384266i	−0.146689	+	0.106576i	−0.658709	−	0.752397i	$-0.728897\pi$
$13$	−0.528896	+	0.384266i	−0.146689	+	0.106576i	0.512020	+	0.858973i	$0.328897\pi$
$14$		0			0
$15$	1.73337	−	5.33475i	0.447553	−	1.37743i
$16$	4.12537	−	1.83673i	1.03134	−	0.459183i
$17$	−0.118865	+	1.13092i	−0.0288290	+	0.274289i	0.970606	+	0.240675i	$0.0773686\pi$
$17$	−0.118865	+	1.13092i	−0.0288290	+	0.274289i	−0.999435	+	0.0336149i	$0.989298\pi$
$18$	0.921618	−	0.195896i	0.217227	−	0.0461731i
$19$	−5.94325	−	1.26328i	−1.36347	−	0.289815i	−0.532643	−	0.846340i	$-0.678801\pi$
$19$	−5.94325	−	1.26328i	−1.36347	−	0.289815i	−0.830831	+	0.556525i	$0.812134\pi$
$20$	−11.4563	+	8.32350i	−2.56171	+	1.86119i
$21$		0			0
$22$	−8.10762	+	1.09495i	−1.72855	+	0.233445i
$23$	3.33354	−	5.77386i	0.695091	−	1.20393i	−0.275059	−	0.961427i	$-0.588697\pi$
$23$	3.33354	−	5.77386i	0.695091	−	1.20393i	0.970150	−	0.242506i	$-0.0779694\pi$
$24$	7.60146	+	3.38439i	1.55164	+	0.690835i
$25$	4.69611	−	5.21556i	0.939222	−	1.04311i
$26$	1.07906	+	1.19842i	0.211621	+	0.235029i
$27$	4.42705	+	3.21644i	0.851986	+	0.619004i
$28$		0			0
$29$	−1.41331	+	4.34973i	−0.262445	+	0.807724i	0.729826	+	0.683633i	$0.239601\pi$
$29$	−1.41331	+	4.34973i	−0.262445	+	0.807724i	−0.992271	+	0.124090i	$0.960399\pi$
$30$	−13.5343	−	2.87679i	−2.47100	−	0.525228i
$31$	−2.55456	−	1.13736i	−0.458812	−	0.204276i	0.164298	−	0.986411i	$-0.447464\pi$
$31$	−2.55456	−	1.13736i	−0.458812	−	0.204276i	−0.623109	+	0.782135i	$0.714131\pi$
$32$	−0.427051	−	0.739674i	−0.0754927	−	0.130757i
$33$	−4.09227	−	3.47155i	−0.712373	−	0.604320i
$34$	2.80505			0.481063
$35$		0			0
$36$	−0.482141	−	1.48388i	−0.0803569	−	0.247313i
$37$	−0.294256	−	0.326804i	−0.0483753	−	0.0537263i	0.718471	−	0.695556i	$-0.244842\pi$
$37$	−0.294256	−	0.326804i	−0.0483753	−	0.0537263i	−0.766847	+	0.641830i	$0.778175\pi$
$38$	−1.56666	+	14.9058i	−0.254146	+	2.41804i
$39$	−0.110569	+	1.05200i	−0.0177053	+	0.168454i
$40$	11.9292	+	13.2487i	1.88617	+	2.09480i
$41$	1.82417	+	5.61423i	0.284888	+	0.876795i	0.986432	+	0.164169i	$0.0524943\pi$
$41$	1.82417	+	5.61423i	0.284888	+	0.876795i	−0.701544	+	0.712626i	$0.747506\pi$
$42$		0			0
$43$	8.70820			1.32799			0.663994	−	0.747738i	$-0.268860\pi$
$43$	8.70820			1.32799			0.663994	+	0.747738i	$0.268860\pi$
$44$	3.20662	+	13.1627i	0.483416	+	1.98435i
$45$	0.662087	+	1.14677i	0.0986981	+	0.170950i
$46$	−15.0241	−	6.68915i	−2.21518	−	0.986262i
$47$	−0.591489	−	0.125725i	−0.0862776	−	0.0183389i	0.164571	−	0.986365i	$-0.447376\pi$
$47$	−0.591489	−	0.125725i	−0.0862776	−	0.0183389i	−0.250848	+	0.968026i	$0.580709\pi$
$48$	2.25789	−	6.94907i	0.325898	−	1.00301i
$49$		0			0
$50$	−14.0058	−	10.1758i	−1.98072	−	1.43907i
$51$	1.23117	+	1.36735i	0.172398	+	0.191468i
$52$	1.78686	−	1.98451i	0.247793	−	0.275202i
$53$	8.97327	+	3.99516i	1.23257	+	0.548777i	0.916529	−	0.399968i	$-0.130979\pi$
$53$	8.97327	+	3.99516i	1.23257	+	0.548777i	0.316044	+	0.948745i	$0.397645\pi$
$54$	6.74915	−	11.6899i	0.918442	−	1.59079i
$55$	−4.98459	−	10.3612i	−0.672122	−	1.39710i
$56$		0			0
$57$	−7.95362	+	5.77864i	−1.05348	+	0.765400i
$58$	11.0352	+	2.34561i	1.44900	+	0.307994i
$59$	1.65704	−	0.352214i	0.215728	−	0.0458544i	−0.0987798	−	0.995109i	$-0.531494\pi$
$59$	1.65704	−	0.352214i	0.215728	−	0.0458544i	0.314508	+	0.949255i	$0.398161\pi$
$60$	−2.39502	+	22.7871i	−0.309196	+	2.94180i
$61$	−6.26526	+	2.78947i	−0.802185	+	0.357156i	−0.766530	−	0.642209i	$-0.778018\pi$
$61$	−6.26526	+	2.78947i	−0.802185	+	0.357156i	−0.0356547	+	0.999364i	$0.511352\pi$
$62$	−2.13152	+	6.56015i	−0.270703	+	0.833139i
$63$		0			0
$64$	5.60222	−	4.07025i	0.700277	−	0.508781i
$65$	−1.13319	+	1.96274i	−0.140555	+	0.243448i
$66$	−7.46132	+	10.9344i	−0.918425	+	1.34593i
$67$	3.08914	+	5.35054i	0.377398	+	0.653673i	0.990683	−	0.136189i	$-0.0434855\pi$
$67$	3.08914	+	5.35054i	0.377398	+	0.653673i	−0.613285	+	0.789862i	$0.710152\pi$
$68$	−0.485535	−	4.61956i	−0.0588798	−	0.560204i
$69$	−3.33354	−	10.2596i	−0.401311	−	1.23511i
$70$		0			0
$71$	4.38234	+	3.18395i	0.520088	+	0.377866i	0.816637	−	0.577152i	$-0.195836\pi$
$71$	4.38234	+	3.18395i	0.520088	+	0.377866i	−0.296549	+	0.955018i	$0.595836\pi$
$72$	−1.79446	+	0.798946i	−0.211479	+	0.0941566i
$73$	6.55553	−	1.39342i	0.767266	−	0.163088i	0.192380	−	0.981321i	$-0.438379\pi$
$73$	6.55553	−	1.39342i	0.767266	−	0.163088i	0.574887	+	0.818233i	$0.305046\pi$
$74$	−0.725850	+	0.806138i	−0.0843783	+	0.0937116i
$75$	−1.18700	−	11.2935i	−0.137063	−	1.30406i
$76$	24.8191			2.84695
$77$		0			0
$78$	2.60929			0.295444
$79$	−0.277393	−	2.63921i	−0.0312091	−	0.296935i	−0.998982	−	0.0451103i	$-0.985636\pi$
$79$	−0.277393	−	2.63921i	−0.0312091	−	0.296935i	0.967773	−	0.251825i	$-0.0810306\pi$
$80$	10.4752	−	11.6339i	1.17117	−	1.30071i
$81$	7.53976	−	1.60263i	0.837751	−	0.178070i
$82$	13.3026	−	5.92269i	1.46902	−	0.654052i
$83$	5.41765	+	3.93615i	0.594664	+	0.432049i	0.843981	−	0.536373i	$-0.180206\pi$
$83$	5.41765	+	3.93615i	0.594664	+	0.432049i	−0.249317	+	0.968422i	$0.580206\pi$
$84$		0			0
$85$	1.21821	+	3.74926i	0.132133	+	0.406665i
$86$	−2.24536	−	21.3631i	−0.242123	−	2.30365i
$87$	3.70010	+	6.40876i	0.396692	+	0.687091i
$88$	16.0585	−	5.74706i	1.71184	−	0.612639i
$89$	−0.349107	+	0.604670i	−0.0370052	+	0.0640949i	−0.883935	−	0.467610i	$-0.845115\pi$
$89$	−0.349107	+	0.604670i	−0.0370052	+	0.0640949i	0.846930	+	0.531705i	$0.178448\pi$
$90$	2.64256	−	1.91993i	0.278550	−	0.202378i
$91$		0			0
$92$	−8.41560	+	25.9006i	−0.877387	+	2.70032i
$93$	−4.13336	+	1.84029i	−0.428609	+	0.190829i
$94$	−0.155919	+	1.48347i	−0.0160818	+	0.153008i
$95$	−20.6036	+	4.37944i	−2.11389	+	0.449321i
$96$	−1.35177	−	0.287327i	−0.137964	−	0.0293252i
$97$	−12.0209	+	8.73372i	−1.22054	+	0.886775i	−0.996145	−	0.0877234i	$-0.972041\pi$
$97$	−12.0209	+	8.73372i	−1.22054	+	0.886775i	−0.224396	+	0.974498i	$0.572041\pi$
$98$		0			0
$99$	1.25544	−	0.169550i	0.126177	−	0.0170404i
$100$	−14.3339	+	24.8271i	−1.43339	+	2.48271i
$101$	−7.87439	−	3.50590i	−0.783531	−	0.348851i	−0.0243278	−	0.999704i	$-0.507745\pi$
$101$	−7.87439	−	3.50590i	−0.783531	−	0.348851i	−0.759203	+	0.650854i	$0.774411\pi$
$102$	3.03696	−	3.37289i	0.300704	−	0.333966i
$103$	0.624271	+	0.693323i	0.0615112	+	0.0683152i	0.773115	−	0.634266i	$-0.218698\pi$
$103$	0.624271	+	0.693323i	0.0615112	+	0.0683152i	−0.711604	+	0.702581i	$0.752031\pi$
$104$	−2.71988	−	1.97611i	−0.266706	−	0.193773i
$105$		0			0
$106$	7.48729	−	23.0435i	0.727230	−	2.23818i
$107$	−6.47741	−	1.37682i	−0.626194	−	0.133102i	−0.116125	−	0.993235i	$-0.537047\pi$
$107$	−6.47741	−	1.37682i	−0.626194	−	0.133102i	−0.510070	+	0.860133i	$0.670380\pi$
$108$	−20.4199	−	9.09154i	−1.96491	−	0.874834i
$109$	2.06253	+	3.57242i	0.197555	+	0.342175i	0.947735	−	0.319058i	$-0.103367\pi$
$109$	2.06253	+	3.57242i	0.197555	+	0.342175i	−0.750180	+	0.661234i	$0.770033\pi$
$110$	−24.1330	+	14.8999i	−2.30099	+	1.42065i
$111$	−0.711544			−0.0675368
$112$		0			0
$113$	−5.81749	−	17.9044i	−0.547264	−	1.68430i	−0.715546	−	0.698566i	$-0.753822\pi$
$113$	−5.81749	−	17.9044i	−0.547264	−	1.68430i	0.168282	−	0.985739i	$-0.446178\pi$
$114$	16.2271	+	18.0220i	1.51980	+	1.68791i
$115$	2.41596	−	22.9864i	0.225290	−	2.14349i
$116$	1.95280	−	18.5796i	0.181313	−	1.72508i
$117$	−0.167089	−	0.185571i	−0.0154474	−	0.0171561i
$118$	−1.29131	−	3.97426i	−0.118875	−	0.365860i
$119$		0			0
$120$	28.8461			2.63328
$121$	−10.9808	+	0.649072i	−0.998258	+	0.0590066i
$122$	8.45865	+	14.6508i	0.765810	+	1.32642i
$123$	8.72573	+	3.88494i	0.786772	+	0.350294i
$124$	11.1727	+	2.37482i	1.00334	+	0.213265i
$125$	2.16209	−	6.65422i	0.193383	−	0.595171i
$126$		0			0
$127$	6.44491	+	4.68250i	0.571893	+	0.415505i	0.835792	−	0.549045i	$-0.185009\pi$
$127$	6.44491	+	4.68250i	0.571893	+	0.415505i	−0.263899	+	0.964550i	$0.585009\pi$
$128$	−12.5727	−	13.9634i	−1.11128	−	1.23420i
$129$	9.42816	−	10.4710i	0.830104	−	0.921923i
$130$	5.10723	+	2.27388i	0.447933	+	0.199433i
$131$	−2.40253	+	4.16130i	−0.209910	+	0.363574i	−0.951686	−	0.307073i	$-0.900650\pi$
$131$	−2.40253	+	4.16130i	−0.209910	+	0.363574i	0.741776	+	0.670648i	$0.233984\pi$
$132$	19.2990	+	10.3952i	1.67976	+	0.904783i
$133$		0			0
$134$	12.3295	−	8.95793i	1.06511	−	0.773848i
$135$	18.5559	+	3.94417i	1.59704	+	0.339460i
$136$	−5.72009	+	1.21584i	−0.490494	+	0.104258i
$137$	2.28685	−	21.7579i	0.195378	−	1.85890i	−0.256140	−	0.966640i	$-0.582451\pi$
$137$	2.28685	−	21.7579i	0.195378	−	1.85890i	0.451518	−	0.892262i	$-0.350883\pi$
$138$	−24.3095	+	10.8233i	−2.06936	+	0.921338i
$139$	6.12278	−	18.8440i	0.519327	−	1.59832i	−0.255941	−	0.966692i	$-0.582385\pi$
$139$	6.12278	−	18.8440i	0.519327	−	1.59832i	0.775268	−	0.631632i	$-0.217615\pi$
$140$		0			0
$141$	−0.791567	+	0.575107i	−0.0666620	+	0.0484328i
$142$	6.68098	−	11.5718i	0.560655	−	0.971083i
$143$	1.32569	+	1.71577i	0.110859	+	0.143480i
$144$	0.862437	+	1.49379i	0.0718698	+	0.124482i
$145$	1.65734	+	15.7685i	0.137634	+	1.30950i
$146$	−5.10867	−	15.7229i	−0.422796	−	1.30123i
$147$		0			0
$148$	1.45325	+	1.05584i	0.119456	+	0.0867899i
$149$	2.88873	−	1.28615i	0.236654	−	0.105365i	−0.284983	−	0.958532i	$-0.591988\pi$
$149$	2.88873	−	1.28615i	0.236654	−	0.105365i	0.521637	+	0.853167i	$0.325321\pi$
$150$	−27.3994	+	5.82393i	−2.23715	+	0.475522i
$151$	5.97404	−	6.63484i	0.486160	−	0.539936i	−0.449294	−	0.893384i	$-0.648324\pi$
$151$	5.97404	−	6.63484i	0.486160	−	0.539936i	0.935454	+	0.353448i	$0.114991\pi$
$152$	−3.26613	−	31.0751i	−0.264918	−	2.52053i
$153$	−0.434354			−0.0351155
$154$		0			0
$155$	−9.69406			−0.778645
$156$	−0.451650	−	4.29716i	−0.0361609	−	0.344048i
$157$	−0.762592	+	0.846944i	−0.0608615	+	0.0675935i	−0.772807	−	0.634642i	$-0.781148\pi$
$157$	−0.762592	+	0.846944i	−0.0608615	+	0.0675935i	0.711945	+	0.702235i	$0.247814\pi$
$158$	−6.40305	+	1.36101i	−0.509399	+	0.108276i
$159$	14.5191	−	6.46430i	1.15144	−	0.512652i
$160$	−2.39545	−	1.74040i	−0.189377	−	0.137591i
$161$		0			0
$162$	−5.87567	−	18.0835i	−0.461636	−	1.42077i
$163$	0.529675	+	5.03952i	0.0414873	+	0.394726i	0.995486	+	0.0949133i	$0.0302574\pi$
$163$	0.529675	+	5.03952i	0.0414873	+	0.394726i	−0.953998	+	0.299812i	$0.903076\pi$
$164$	−12.0565	−	20.8825i	−0.941454	−	1.63065i
$165$	−17.8553	−	5.22418i	−1.39004	−	0.406702i
$166$	8.25933	−	14.3056i	0.641048	−	1.11033i
$167$	−15.9432	+	11.5834i	−1.23372	+	0.896351i	−0.997164	−	0.0752658i	$-0.976019\pi$
$167$	−15.9432	+	11.5834i	−1.23372	+	0.896351i	−0.236558	+	0.971617i	$0.576019\pi$
$168$		0			0
$169$	−3.88515	+	11.9573i	−0.298858	+	0.919789i
$170$	8.88365	−	3.95526i	0.681345	−	0.303354i
$171$	0.242593	−	2.30812i	0.0185516	−	0.176506i
$172$	−34.7937	+	7.39562i	−2.65299	+	0.563911i
$173$	−14.0802	−	2.99285i	−1.07050	−	0.227542i	−0.361229	−	0.932477i	$-0.617643\pi$
$173$	−14.0802	−	2.99285i	−1.07050	−	0.227542i	−0.709271	+	0.704935i	$0.750976\pi$
$174$	14.7680	−	10.7296i	1.11956	−	0.813409i
$175$		0			0
$176$	−6.49295	−	13.4965i	−0.489424	−	1.01734i
$177$	1.37052	−	2.37381i	0.103015	−	0.178426i
$178$	1.57340	+	0.700525i	0.117932	+	0.0525065i
$179$	−3.12096	+	3.46618i	−0.233271	+	0.259074i	−0.848404	−	0.529350i	$-0.822436\pi$
$179$	−3.12096	+	3.46618i	−0.233271	+	0.259074i	0.615132	+	0.788424i	$0.289103\pi$
$180$	−3.61929	−	4.01963i	−0.269766	−	0.299605i
$181$	8.01578	+	5.82381i	0.595808	+	0.432880i	0.844389	−	0.535731i	$-0.179964\pi$
$181$	8.01578	+	5.82381i	0.595808	+	0.432880i	−0.248580	+	0.968611i	$0.579964\pi$
$182$		0			0
$183$	−3.42909	+	10.5537i	−0.253486	+	0.780149i
$184$	33.5366	+	7.12843i	2.47235	+	0.525515i
$185$	−1.39272	−	0.620080i	−0.102395	−	0.0455892i
$186$	5.58039	+	9.66553i	0.409174	+	0.708711i
$187$	3.76085	+	0.283348i	0.275021	+	0.0207205i
$188$	2.47007			0.180148
$189$		0			0
$190$	16.0562	+	49.4160i	1.16484	+	3.58502i
$191$	6.65313	+	7.38905i	0.481404	+	0.534653i	0.934100	−	0.357012i	$-0.116204\pi$
$191$	6.65313	+	7.38905i	0.481404	+	0.534653i	−0.452696	+	0.891665i	$0.649538\pi$
$192$	1.17118	−	11.1431i	0.0845228	−	0.804181i
$193$	−0.387450	+	3.68634i	−0.0278893	+	0.265349i	0.971688	+	0.236268i	$0.0759245\pi$
$193$	−0.387450	+	3.68634i	−0.0278893	+	0.265349i	−0.999577	+	0.0290801i	$0.990742\pi$
$194$	24.5252	+	27.2380i	1.76081	+	1.95558i
$195$	1.13319	+	3.48760i	0.0811495	+	0.249752i
$196$		0			0
$197$	5.91982			0.421770			0.210885	−	0.977511i	$-0.432365\pi$
$197$	5.91982			0.421770			0.210885	+	0.977511i	$0.432365\pi$
$198$	−0.739651	−	3.03615i	−0.0525647	−	0.215770i
$199$	5.74211	+	9.94563i	0.407047	+	0.705027i	0.994557	−	0.104190i	$-0.0332251\pi$
$199$	5.74211	+	9.94563i	0.407047	+	0.705027i	−0.587510	+	0.809217i	$0.699892\pi$
$200$	32.9714	+	14.6798i	2.33143	+	1.03802i
$201$	9.77821	+	2.07842i	0.689702	+	0.146601i
$202$	−6.57039	+	20.2216i	−0.462291	+	1.42279i
$203$		0			0
$204$	−6.08039	−	4.41766i	−0.425713	−	0.309298i
$205$	13.6935	+	15.2082i	0.956397	+	1.06219i
$206$	1.53991	−	1.71024i	0.107291	−	0.119158i
$207$	2.32643	+	1.03580i	0.161698	+	0.0719927i
$208$	−1.47610	+	2.55668i	−0.102349	+	0.177274i
$209$	−3.60618	+	19.8266i	−0.249445	+	1.37143i
$210$		0			0
$211$	−7.05857	+	5.12835i	−0.485932	+	0.353050i	−0.803618	−	0.595146i	$-0.797094\pi$
$211$	−7.05857	+	5.12835i	−0.485932	+	0.353050i	0.317686	+	0.948196i	$0.397094\pi$
$212$	−39.2457	−	8.34193i	−2.69541	−	0.572926i
$213$	8.57314	−	1.82228i	0.587422	−	0.124860i
$214$	−1.70747	+	16.2455i	−0.116720	+	1.11052i
$215$	27.5790	−	12.2790i	1.88087	−	0.837419i
$216$	−8.69598	+	26.7635i	−0.591686	+	1.82102i
$217$		0			0
$218$	8.23210	−	5.98097i	0.557548	−	0.405083i
$219$	5.42202	−	9.39121i	0.366386	−	0.634599i
$220$	28.7154	+	37.1649i	1.93599	+	2.50566i
$221$	−0.371708	−	0.643817i	−0.0250038	−	0.0433078i
$222$	0.183467	+	1.74557i	0.0123135	+	0.117155i
$223$	−3.19302	−	9.82712i	−0.213821	−	0.658072i	−0.999235	−	0.0391023i	$-0.987550\pi$
$223$	−3.19302	−	9.82712i	−0.213821	−	0.658072i	0.785415	−	0.618970i	$-0.212450\pi$
$224$		0			0
$225$	2.16875	+	1.57569i	0.144583	+	0.105046i
$226$	−42.4234	+	18.8881i	−2.82196	+	1.25642i
$227$	−12.9790	+	2.75877i	−0.861446	+	0.183106i	−0.617392	−	0.786656i	$-0.711811\pi$
$227$	−12.9790	+	2.75877i	−0.861446	+	0.183106i	−0.244054	+	0.969762i	$0.578477\pi$
$228$	26.8711	−	29.8434i	1.77958	−	1.97642i
$229$	−0.260927	−	2.48255i	−0.0172425	−	0.164052i	0.982512	−	0.186198i	$-0.0596167\pi$
$229$	−0.260927	−	2.48255i	−0.0172425	−	0.164052i	−0.999755	+	0.0221465i	$0.992950\pi$
$230$	−57.0135			−3.75936
$231$		0			0
$232$	−23.5199			−1.54415
$233$	1.00388	+	9.55127i	0.0657663	+	0.625725i	0.976912	+	0.213641i	$0.0685323\pi$
$233$	1.00388	+	9.55127i	0.0657663	+	0.625725i	−0.911146	+	0.412084i	$0.864801\pi$
$234$	−0.412164	+	0.457755i	−0.0269440	+	0.0299244i
$235$	−2.05053	+	0.435855i	−0.133762	+	0.0284320i
$236$	−6.32157	+	2.81454i	−0.411499	+	0.183211i
$237$	−3.47381	−	2.52387i	−0.225648	−	0.163943i
$238$		0			0
$239$	1.71914	+	5.29098i	0.111202	+	0.342245i	0.991136	−	0.132851i	$-0.0424132\pi$
$239$	1.71914	+	5.29098i	0.111202	+	0.342245i	−0.879934	+	0.475096i	$0.842413\pi$
$240$	−2.64774	−	25.1916i	−0.170911	−	1.62611i
$241$	7.51038	+	13.0084i	0.483786	+	0.837942i	0.999827	−	0.0186224i	$-0.00592803\pi$
$241$	7.51038	+	13.0084i	0.483786	+	0.837942i	−0.516041	+	0.856564i	$0.672595\pi$
$242$	4.42365	+	26.7710i	0.284363	+	1.72091i
$243$	−1.97214	+	3.41584i	−0.126513	+	0.219126i
$244$	22.6639	−	16.4663i	1.45090	−	1.05414i
$245$		0			0
$246$	7.28074	−	22.4078i	0.464203	−	1.42867i
$247$	3.62879	−	1.61564i	0.230895	−	0.102801i
$248$	1.50314	−	14.3014i	0.0954494	−	0.908140i
$249$	10.5985	−	2.25278i	0.671654	−	0.142764i
$250$	−16.8817	−	3.58832i	−1.06769	−	0.226946i
$251$	22.3394	−	16.2305i	1.41005	−	1.02446i	0.416738	−	0.909027i	$-0.363173\pi$
$251$	22.3394	−	16.2305i	1.41005	−	1.02446i	0.993315	−	0.115436i	$-0.0368266\pi$
$252$		0			0
$253$	−19.4677	−	10.4861i	−1.22393	−	0.659253i
$254$	9.82542	−	17.0181i	0.616502	−	1.06781i
$255$	5.82716	+	2.59442i	0.364911	+	0.162469i
$256$	−21.7464	+	24.1519i	−1.35915	+	1.50949i
$257$	19.0488	+	21.1558i	1.18823	+	1.31966i	0.936001	+	0.351997i	$0.114497\pi$
$257$	19.0488	+	21.1558i	1.18823	+	1.31966i	0.252230	+	0.967667i	$0.418836\pi$
$258$	−28.1187	−	20.4295i	−1.75060	−	1.27188i
$259$		0			0
$260$	2.86077	−	8.80454i	0.177417	−	0.546034i
$261$	−1.70877	−	0.363211i	−0.105770	−	0.0224822i
$262$	10.8281	+	4.82096i	0.668959	+	0.297840i
$263$	−7.09017	−	12.2805i	−0.437199	−	0.757250i	0.560274	−	0.828308i	$-0.310696\pi$
$263$	−7.09017	−	12.2805i	−0.437199	−	0.757250i	−0.997472	+	0.0710574i	$0.977363\pi$
$264$	10.4757	−	25.5315i	0.644736	−	1.57136i
$265$	34.0519			2.09179
$266$		0			0
$267$	0.349107	+	1.07444i	0.0213650	+	0.0657546i
$268$	−16.8867	−	18.7546i	−1.03152	−	1.14562i
$269$	−2.52893	+	24.0611i	−0.154191	+	1.46703i	0.594490	+	0.804103i	$0.297354\pi$
$269$	−2.52893	+	24.0611i	−0.154191	+	1.46703i	−0.748681	+	0.662930i	$0.769313\pi$
$270$	4.89140	−	46.5386i	0.297681	−	2.83225i
$271$	−4.98486	−	5.53624i	−0.302808	−	0.336303i	0.572467	−	0.819928i	$-0.305987\pi$
$271$	−4.98486	−	5.53624i	−0.302808	−	0.336303i	−0.875275	+	0.483625i	$0.839320\pi$
$272$	1.58684	+	4.88381i	0.0962166	+	0.296124i
$273$		0			0
$274$	−53.9665			−3.26024
$275$	−17.7502	−	15.0579i	−1.07038	−	0.908025i
$276$	22.0323	+	38.1611i	1.32619	+	2.29703i
$277$	−17.5300	−	7.80487i	−1.05328	−	0.468949i	−0.194289	−	0.980944i	$-0.562240\pi$
$277$	−17.5300	−	7.80487i	−1.05328	−	0.468949i	−0.858988	+	0.511995i	$0.828907\pi$
$278$	−47.8071	−	10.1617i	−2.86728	−	0.609459i
$279$	0.330060	−	1.01582i	0.0197602	−	0.0608155i
$280$		0			0
$281$	1.53764	+	1.11716i	0.0917279	+	0.0666442i	0.632704	−	0.774394i	$-0.281945\pi$
$281$	1.53764	+	1.11716i	0.0917279	+	0.0666442i	−0.540976	+	0.841038i	$0.681945\pi$
$282$	1.61496	+	1.79360i	0.0961697	+	0.106807i
$283$	−4.85238	+	5.38912i	−0.288444	+	0.320350i	−0.869900	−	0.493228i	$-0.835817\pi$
$283$	−4.85238	+	5.38912i	−0.288444	+	0.320350i	0.581456	+	0.813578i	$0.302483\pi$
$284$	−20.2137	−	8.99971i	−1.19946	−	0.534035i
$285$	−17.0411	+	29.5160i	−1.00943	+	1.74838i
$286$	3.86734	−	3.69460i	0.228680	−	0.218466i
$287$		0			0
$288$	0.263932	−	0.191758i	0.0155523	−	0.0112994i
$289$	15.3636	+	3.26564i	0.903744	+	0.192097i
$290$	38.2562	−	8.13161i	2.24648	−	0.477505i
$291$	−2.51306	+	23.9102i	−0.147318	+	1.40164i
$292$	−25.0092	+	11.1348i	−1.46356	+	0.651617i
$293$	1.01078	−	3.11088i	0.0590507	−	0.181739i	−0.917180	−	0.398473i	$-0.869540\pi$
$293$	1.01078	−	3.11088i	0.0590507	−	0.181739i	0.976231	+	0.216734i	$0.0695403\pi$
$294$		0			0
$295$	4.75122	−	3.45197i	0.276627	−	0.200981i
$296$	1.13074	−	1.95850i	0.0657230	−	0.113836i
$297$	10.2297	−	14.9913i	0.593587	−	0.869886i
$298$	−3.90004	−	6.75507i	−0.225923	−	0.391310i
$299$	0.455599	+	4.33474i	0.0263480	+	0.250684i
$300$	14.3339	+	44.1152i	0.827569	+	2.54699i
$301$		0			0
$302$	−17.8171	−	12.9449i	−1.02526	−	0.744894i
$303$	−12.7410	+	5.67267i	−0.731953	+	0.325887i
$304$	−26.8384	+	5.70468i	−1.53929	+	0.327186i
$305$	−15.9089	+	17.6686i	−0.910941	+	1.01170i
$306$	0.111995	+	1.06557i	0.00640236	+	0.0609143i
$307$	−31.6121			−1.80420			−0.902099	−	0.431530i	$-0.857974\pi$
$307$	−31.6121			−1.80420			−0.902099	+	0.431530i	$0.857974\pi$
$308$		0			0
$309$	1.50956			0.0858758
$310$	2.49955	+	23.7816i	0.141965	+	1.35071i
$311$	6.04779	−	6.71676i	0.342939	−	0.380872i	−0.546861	−	0.837224i	$-0.684177\pi$
$311$	6.04779	−	6.71676i	0.342939	−	0.380872i	0.889800	+	0.456351i	$0.150844\pi$
$312$	−5.32089	+	1.13099i	−0.301236	+	0.0640297i
$313$	−13.2455	+	5.89729i	−0.748681	+	0.333334i	−0.745362	−	0.666660i	$-0.767723\pi$
$313$	−13.2455	+	5.89729i	−0.748681	+	0.333334i	−0.00331948	+	0.999994i	$0.501057\pi$
$314$	2.27437	+	1.65243i	0.128350	+	0.0932518i
$315$		0			0
$316$	3.34973	+	10.3094i	0.188437	+	0.579950i
$317$	1.92514	+	18.3165i	0.108127	+	1.02876i	0.905233	+	0.424916i	$0.139697\pi$
$317$	1.92514	+	18.3165i	0.108127	+	1.02876i	−0.797106	+	0.603839i	$0.793637\pi$
$318$	−19.6020	−	33.9516i	−1.09922	−	1.90391i
$319$	14.5585	+	4.25957i	0.815118	+	0.238490i
$320$	12.0031	−	20.7899i	0.670992	−	1.16219i
$321$	−8.66846	+	6.29801i	−0.483826	+	0.351520i
$322$		0			0
$323$	2.13511	−	6.57120i	0.118801	−	0.365632i
$324$	−28.7641	+	12.8066i	−1.59800	+	0.711477i
$325$	−0.479595	+	4.56304i	−0.0266032	+	0.253112i
$326$	12.2265	−	2.59882i	0.677161	−	0.143935i
$327$	6.52865	+	1.38771i	0.361035	+	0.0767404i
$328$	−24.5596	+	17.8436i	−1.35608	+	0.985246i
$329$		0			0
$330$	−8.21217	+	45.1501i	−0.452065	+	2.48543i
$331$	3.23826	−	5.60884i	0.177991	−	0.308290i	−0.763201	−	0.646161i	$-0.776373\pi$
$331$	3.23826	−	5.60884i	0.177991	−	0.308290i	0.941192	+	0.337871i	$0.109707\pi$
$332$	−24.9891	−	11.1259i	−1.37145	−	0.610611i
$333$	0.112396	−	0.124828i	0.00615925	−	0.00684054i
$334$	32.5275	+	36.1255i	1.77983	+	1.97670i
$335$	17.3279	+	12.5894i	0.946723	+	0.687834i
$336$		0			0
$337$	1.93346	−	5.95059i	0.105322	−	0.324149i	−0.884484	−	0.466571i	$-0.845489\pi$
$337$	1.93346	−	5.95059i	0.105322	−	0.324149i	0.989806	+	0.142422i	$0.0454891\pi$
$338$	30.3355	+	6.44802i	1.65004	+	0.350726i
$339$	−27.8273	−	12.3895i	−1.51137	−	0.672906i
$340$	−8.05150	−	13.9456i	−0.436654	−	0.756307i
$341$	−3.52048	+	8.58015i	−0.190645	+	0.464641i
$342$	−5.72487			−0.309566
$343$		0			0
$344$	13.8385	+	42.5906i	0.746124	+	2.29633i
$345$	−25.0239	−	27.7918i	−1.34724	−	1.49626i
$346$	−3.71161	+	35.3136i	−0.199537	+	1.89847i
$347$	−2.37443	+	22.5912i	−0.127466	+	1.21276i	0.724542	+	0.689230i	$0.242051\pi$
$347$	−2.37443	+	22.5912i	−0.127466	+	1.21276i	−0.852008	+	0.523528i	$0.824615\pi$
$348$	−20.2265	−	22.4638i	−1.08426	−	1.20419i
$349$	−9.17597	−	28.2407i	−0.491178	−	1.51169i	−0.822829	−	0.568289i	$-0.807606\pi$
$349$	−9.17597	−	28.2407i	−0.491178	−	1.51169i	0.331651	−	0.943402i	$-0.392394\pi$
$350$		0			0
$351$	−3.57742			−0.190948
$352$	−2.41035	+	1.48816i	−0.128472	+	0.0793192i
$353$	−3.41253	−	5.91068i	−0.181631	−	0.314594i	0.760805	−	0.648980i	$-0.224804\pi$
$353$	−3.41253	−	5.91068i	−0.181631	−	0.314594i	−0.942436	+	0.334387i	$0.891471\pi$
$354$	−6.17686	−	2.75011i	−0.328296	−	0.146167i
$355$	18.3685	+	3.90434i	0.974897	+	0.207221i
$356$	0.881328	−	2.71245i	0.0467103	−	0.143760i
$357$		0			0
$358$	9.30801	+	6.76266i	0.491944	+	0.357418i
$359$	−4.85769	−	5.39501i	−0.256379	−	0.284738i	0.601191	−	0.799106i	$-0.294693\pi$
$359$	−4.85769	−	5.39501i	−0.256379	−	0.284738i	−0.857570	+	0.514368i	$0.828027\pi$
$360$	−4.55654	+	5.06055i	−0.240151	+	0.266714i
$361$	16.3689	+	7.28792i	0.861523	+	0.383575i
$362$	12.2202	−	21.1661i	0.642282	−	1.11247i
$363$	−11.1082	+	13.9065i	−0.583030	+	0.729900i
$364$		0			0
$365$	18.7967	−	13.6566i	0.983863	−	0.714818i
$366$	26.7746	+	5.69112i	1.39953	+	0.297479i
$367$	−35.5426	+	7.55481i	−1.85531	+	0.394358i	−0.993591	−	0.113034i	$-0.963943\pi$
$367$	−35.5426	+	7.55481i	−1.85531	+	0.394358i	−0.861716	+	0.507391i	$0.830610\pi$
$368$	3.14705	−	29.9421i	0.164051	−	1.56084i
$369$	−2.05986	+	0.917111i	−0.107232	+	0.0477429i
$370$	−1.16209	+	3.57654i	−0.0604140	+	0.185935i
$371$		0			0
$372$	14.9519	−	10.8632i	0.775222	−	0.563232i
$373$	7.14567	−	12.3767i	0.369989	−	0.640839i	−0.619575	−	0.784938i	$-0.712695\pi$
$373$	7.14567	−	12.3767i	0.369989	−	0.640839i	0.989563	+	0.144098i	$0.0460282\pi$
$374$	−0.274598	−	9.29926i	−0.0141991	−	0.480853i
$375$	−5.66042	−	9.80413i	−0.292303	−	0.506283i
$376$	−0.325054	−	3.09269i	−0.0167634	−	0.159493i
$377$	−0.923955	−	2.84364i	−0.0475861	−	0.146455i
$378$		0			0
$379$	2.05917	+	1.49608i	0.105773	+	0.0768482i	0.639414	−	0.768862i	$-0.279177\pi$
$379$	2.05917	+	1.49608i	0.105773	+	0.0768482i	−0.533642	+	0.845711i	$0.679177\pi$
$380$	78.6026	−	34.9961i	4.03223	−	1.79526i
$381$	12.6081	−	2.67994i	0.645935	−	0.137298i
$382$	16.4115	−	18.2268i	0.839685	−	0.932565i
$383$	−2.41844	−	23.0100i	−0.123577	−	1.17575i	−0.863957	−	0.503565i	$-0.832021\pi$
$383$	−2.41844	−	23.0100i	−0.123577	−	1.17575i	0.740380	−	0.672188i	$-0.234645\pi$
$384$	−30.4023			−1.55146
$385$		0			0
$386$	9.14330			0.465382
$387$	0.347687	+	3.30802i	0.0176739	+	0.168156i
$388$	40.6124	−	45.1046i	2.06178	−	2.28984i
$389$	−29.6002	+	6.29171i	−1.50079	+	0.319002i	−0.883761	−	0.467939i	$-0.844997\pi$
$389$	−29.6002	+	6.29171i	−1.50079	+	0.319002i	−0.617027	+	0.786942i	$0.711663\pi$
$390$	8.26367	−	3.67922i	0.418447	−	0.186305i
$391$	6.13356	+	4.45629i	0.310188	+	0.225364i
$392$		0			0
$393$	2.40253	+	7.39422i	0.121191	+	0.372989i
$394$	−1.52639	−	14.5226i	−0.0768983	−	0.731639i
$395$	−4.59992	−	7.96730i	−0.231447	−	0.400878i
$396$	−4.87212	+	1.74365i	−0.244833	+	0.0876216i
$397$	−11.3370	+	19.6363i	−0.568989	+	0.985518i	0.427677	+	0.903931i	$0.359332\pi$
$397$	−11.3370	+	19.6363i	−0.568989	+	0.985518i	−0.996666	+	0.0815862i	$0.974001\pi$
$398$	22.9182	−	16.6511i	1.14879	−	0.834643i
$399$		0			0
$400$	9.79361	−	30.1416i	0.489680	−	1.50708i
$401$	−14.8164	+	6.59669i	−0.739896	+	0.329423i	−0.741842	−	0.670575i	$-0.766047\pi$
$401$	−14.8164	+	6.59669i	−0.739896	+	0.329423i	0.00194545	+	0.999998i	$0.499381\pi$
$402$	2.57758	−	24.5240i	0.128558	−	1.22315i
$403$	1.78814	−	0.380082i	0.0890738	−	0.0189332i
$404$	34.4396	+	7.32037i	1.71343	+	0.364202i
$405$	21.6188	−	15.7070i	1.07425	−	0.780485i
$406$		0			0
$407$	−1.05461	+	1.00750i	−0.0522750	+	0.0499401i
$408$	−4.73103	+	8.19439i	−0.234221	+	0.405683i
$409$	32.0302	+	14.2608i	1.58379	+	0.705149i	0.994691	−	0.102910i	$-0.0328155\pi$
$409$	32.0302	+	14.2608i	1.58379	+	0.705149i	0.589101	+	0.808060i	$0.299482\pi$
$410$	33.7782	−	37.5145i	1.66819	−	1.85271i
$411$	−23.6865	−	26.3065i	−1.16837	−	1.29761i
$412$	−3.08310	−	2.24000i	−0.151893	−	0.110357i
$413$		0			0
$414$	1.94118	−	5.97432i	0.0954036	−	0.293622i
$415$	22.7079	+	4.82672i	1.11469	+	0.236934i
$416$	0.510097	+	0.227110i	0.0250096	+	0.0111350i
$417$	−16.0296	−	27.7641i	−0.784975	−	1.35962i
$418$	49.5688	+	3.73458i	2.42449	+	0.182664i
$419$	−28.2633			−1.38075			−0.690376	−	0.723451i	$-0.742555\pi$
$419$	−28.2633			−1.38075			−0.690376	+	0.723451i	$0.742555\pi$
$420$		0			0
$421$	−4.26279	−	13.1195i	−0.207756	−	0.639406i	−0.999589	−	0.0286688i	$-0.990873\pi$
$421$	−4.26279	−	13.1195i	−0.207756	−	0.639406i	0.791833	−	0.610737i	$-0.209127\pi$
$422$	14.4010	+	15.9939i	0.701029	+	0.778571i
$423$	0.0241436	−	0.229711i	0.00117390	−	0.0111689i
$424$	−5.28000	+	50.2359i	−0.256420	+	2.43967i
$425$	5.34020	+	5.93090i	0.259038	+	0.287691i
$426$	−6.68098	−	20.5619i	−0.323694	−	0.996229i
$427$		0			0
$428$	27.0498			1.30750
$429$	3.49839	+	0.263573i	0.168904	+	0.0127254i
$430$	−37.2341	−	64.4913i	−1.79559	−	3.11005i
$431$	25.7346	+	11.4578i	1.23959	+	0.551902i	0.918603	−	0.395181i	$-0.129318\pi$
$431$	25.7346	+	11.4578i	1.23959	+	0.551902i	0.320989	+	0.947083i	$0.395985\pi$
$432$	24.1710	+	5.13770i	1.16293	+	0.247188i
$433$	−4.38165	+	13.4853i	−0.210569	+	0.648064i	0.788870	+	0.614560i	$0.210667\pi$
$433$	−4.38165	+	13.4853i	−0.210569	+	0.648064i	−0.999439	+	0.0335038i	$0.989333\pi$
$434$		0			0
$435$	20.7549	+	15.0793i	0.995122	+	0.722999i
$436$	−11.2748	−	12.5219i	−0.539966	−	0.599693i
$437$	−27.1060	+	30.1043i	−1.29666	+	1.44008i
$438$	−24.4367	−	10.8799i	−1.16763	−	0.519863i
$439$	14.0093	−	24.2647i	0.668625	−	1.15809i	−0.309663	−	0.950846i	$-0.600216\pi$
$439$	14.0093	−	24.2647i	0.668625	−	1.15809i	0.978289	−	0.207247i	$-0.0664503\pi$
$440$	42.7540	−	40.8443i	2.03822	−	1.94718i
$441$		0			0
$442$	−1.48358	+	1.07789i	−0.0705668	+	0.0512698i
$443$	−16.9581	−	3.60456i	−0.805706	−	0.171258i	−0.213393	−	0.976966i	$-0.568452\pi$
$443$	−16.9581	−	3.60456i	−0.805706	−	0.171258i	−0.592312	+	0.805708i	$0.701785\pi$
$444$	2.84298	−	0.604293i	0.134922	−	0.0286785i
$445$	−0.253013	+	2.40726i	−0.0119940	+	0.114115i
$446$	−23.2848	+	10.3670i	−1.10257	+	0.490894i
$447$	1.58106	−	4.86599i	0.0747813	−	0.230153i
$448$		0			0
$449$	23.8834	−	17.3523i	1.12713	−	0.818906i	0.141853	−	0.989888i	$-0.454694\pi$
$449$	23.8834	−	17.3523i	1.12713	−	0.818906i	0.985274	+	0.170982i	$0.0546940\pi$
$450$	3.30631	−	5.72671i	0.155861	−	0.269959i
$451$	18.4336	−	6.59706i	0.868005	−	0.310644i
$452$	38.4495	+	66.5965i	1.80851	+	3.13244i
$453$	−1.51001	−	14.3668i	−0.0709464	−	0.675010i
$454$	10.1144	+	31.1290i	0.474693	+	1.46096i
$455$		0			0
$456$	−40.9019	−	29.7170i	−1.91541	−	1.39163i
$457$	8.85888	−	3.94423i	0.414401	−	0.184503i	−0.188936	−	0.981989i	$-0.560504\pi$
$457$	8.85888	−	3.94423i	0.414401	−	0.184503i	0.603337	+	0.797486i	$0.293837\pi$
$458$	−6.02297	+	1.28022i	−0.281435	+	0.0598208i
$459$	−4.16377	+	4.62434i	−0.194348	+	0.215846i
$460$	9.86865	+	93.8939i	0.460128	+	4.37783i
$461$	19.2216			0.895240			0.447620	−	0.894224i	$-0.352272\pi$
$461$	19.2216			0.895240			0.447620	+	0.894224i	$0.352272\pi$
$462$		0			0
$463$	20.5327			0.954235			0.477117	−	0.878840i	$-0.341682\pi$
$463$	20.5327			0.954235			0.477117	+	0.878840i	$0.341682\pi$
$464$	2.15885	+	20.5401i	0.100222	+	0.953550i
$465$	−10.4955	+	11.6565i	−0.486718	+	0.540555i
$466$	23.1725	−	4.92547i	1.07345	−	0.228168i
$467$	−30.7604	+	13.6954i	−1.42342	+	0.633748i	−0.966712	−	0.255868i	$-0.917639\pi$
$467$	−30.7604	+	13.6954i	−1.42342	+	0.633748i	−0.456710	+	0.889616i	$0.650972\pi$
$468$	0.825206	+	0.599547i	0.0381452	+	0.0277141i
$469$		0			0
$470$	1.59796	+	4.91803i	0.0737086	+	0.226852i
$471$	0.192754	+	1.83393i	0.00888164	+	0.0845032i
$472$	4.35589	+	7.54462i	0.200496	+	0.347269i
$473$	−0.852480	−	28.8693i	−0.0391971	−	1.32741i
$474$	−5.29590	+	9.17277i	−0.243249	+	0.421319i
$475$	−34.4988	+	25.0649i	−1.58292	+	1.15006i
$476$		0			0
$477$	−1.15938	+	3.56822i	−0.0530846	+	0.163378i
$478$	12.5367	−	5.58168i	0.573414	−	0.255300i
$479$	1.48125	−	14.0931i	0.0676800	−	0.643932i	−0.907123	−	0.420865i	$-0.861726\pi$
$479$	1.48125	−	14.0931i	0.0676800	−	0.643932i	0.974803	−	0.223067i	$-0.0716069\pi$
$480$	−4.68621	+	0.996085i	−0.213895	+	0.0454649i
$481$	0.281210	+	0.0597731i	0.0128221	+	0.00272542i
$482$	29.9758	−	21.7787i	1.36536	−	0.991993i
$483$		0			0
$484$	43.3227	−	11.9191i	1.96921	−	0.541776i
$485$	−25.7555	+	44.6099i	−1.16950	+	2.02563i
$486$	8.88830	+	3.95733i	0.403182	+	0.179508i
$487$	18.5627	−	20.6159i	0.841155	−	0.934197i	−0.157422	−	0.987531i	$-0.550318\pi$
$487$	18.5627	−	20.6159i	0.841155	−	0.934197i	0.998577	+	0.0533345i	$0.0169850\pi$
$488$	−23.5993	−	26.2097i	−1.06829	−	1.18646i
$489$	6.63315	+	4.81927i	0.299962	+	0.217935i
$490$		0			0
$491$	−1.06393	+	3.27444i	−0.0480145	+	0.147774i	−0.972189	−	0.234196i	$-0.924754\pi$
$491$	−1.06393	+	3.27444i	−0.0480145	+	0.147774i	0.924175	+	0.381970i	$0.124754\pi$
$492$	−38.1630	−	8.11181i	−1.72052	−	0.365708i
$493$	−4.75122	−	2.11538i	−0.213984	−	0.0952719i
$494$	−4.89919	−	8.48564i	−0.220425	−	0.381787i
$495$	3.73693	−	2.30720i	0.167962	−	0.103701i
$496$	−12.6275			−0.566992
$497$		0			0
$498$	−8.25933	−	25.4196i	−0.370109	−	1.13908i
$499$	−1.73253	−	1.92417i	−0.0775589	−	0.0861379i	0.703116	−	0.711075i	$-0.251791\pi$
$499$	−1.73253	−	1.92417i	−0.0775589	−	0.0861379i	−0.780675	+	0.624937i	$0.785125\pi$
$500$	−2.98739	+	28.4232i	−0.133600	+	1.27112i
$501$	−3.33304	+	31.7117i	−0.148909	+	1.41678i
$502$	−45.5772	−	50.6186i	−2.03421	−	2.25922i
$503$	7.07731	+	21.7817i	0.315561	+	0.971198i	0.975523	+	0.219899i	$0.0705727\pi$
$503$	7.07731	+	21.7817i	0.315561	+	0.971198i	−0.659961	+	0.751300i	$0.729427\pi$
$504$		0			0
$505$	−29.8818			−1.32972
$506$	−20.7050	+	50.4624i	−0.920448	+	2.24333i
$507$	10.1715	+	17.6175i	0.451730	+	0.782420i
$508$	−29.7274	−	13.2355i	−1.31894	−	0.587229i
$509$	−23.5719	−	5.01037i	−1.04481	−	0.222081i	−0.346627	−	0.938003i	$-0.612673\pi$
$509$	−23.5719	−	5.01037i	−1.04481	−	0.222081i	−0.698180	+	0.715923i	$0.746006\pi$
$510$	4.86218	−	14.9643i	0.215301	−	0.662629i
$511$		0			0
$512$	34.4547	+	25.0328i	1.52270	+	1.10631i
$513$	−22.2478	−	24.7087i	−0.982264	−	1.09092i
$514$	46.9883	−	52.1858i	2.07256	−	2.30182i
$515$	2.95469	+	1.31551i	0.130199	+	0.0579685i
$516$	−28.7775	+	49.8441i	−1.26686	+	2.19427i
$517$	−0.358897	+	1.97320i	−0.0157843	+	0.0867813i
$518$		0			0
$519$	−18.8430	+	13.6903i	−0.827117	+	0.600936i
$520$	−11.4003	−	2.42321i	−0.499937	−	0.106265i
$521$	−32.7735	+	6.96623i	−1.43583	+	0.305196i	−0.859130	−	0.511757i	$-0.828995\pi$
$521$	−32.7735	+	6.96623i	−1.43583	+	0.305196i	−0.576704	+	0.816953i	$0.695662\pi$
$522$	−0.450440	+	4.28565i	−0.0197152	+	0.187578i
$523$	28.4637	−	12.6728i	1.24463	−	0.554145i	0.324547	−	0.945870i	$-0.394788\pi$
$523$	28.4637	−	12.6728i	1.24463	−	0.554145i	0.920082	+	0.391725i	$0.128121\pi$
$524$	6.06524	−	18.6669i	0.264961	−	0.815466i
$525$		0			0
$526$	−28.2987	+	20.5602i	−1.23388	+	0.896467i
$527$	1.58992	−	2.75382i	0.0692579	−	0.119958i
$528$	−23.2585	−	6.80504i	−1.01219	−	0.296151i
$529$	−10.7250	−	18.5762i	−0.466304	−	0.807662i
$530$	−8.78006	−	83.5366i	−0.381381	−	3.62860i
$531$	0.199956	+	0.615402i	0.00867736	+	0.0267062i
$532$		0			0
$533$	−3.12215	−	2.26838i	−0.135235	−	0.0982543i
$534$	2.54582	−	1.13347i	0.110168	−	0.0490502i
$535$	−22.4554	+	4.77305i	−0.970833	+	0.206357i
$536$	−21.2597	+	23.6113i	−0.918280	+	1.01985i
$537$	0.788859	+	7.50549i	0.0340418	+	0.323886i
$538$	59.6793			2.57296
$539$		0			0
$540$	−77.4898			−3.33463
$541$	−2.36309	−	22.4833i	−0.101597	−	0.966633i	−0.919982	−	0.391962i	$-0.871797\pi$
$541$	−2.36309	−	22.4833i	−0.101597	−	0.966633i	0.818384	−	0.574671i	$-0.194870\pi$
$542$	−12.2963	+	13.6564i	−0.528171	+	0.586594i
$543$	15.6812	−	3.33315i	0.672946	−	0.143039i
$544$	0.887277	−	0.395041i	0.0380417	−	0.0169372i
$545$	11.5694	+	8.40563i	0.495577	+	0.360058i
$546$		0			0
$547$	−8.48072	−	26.1010i	−0.362610	−	1.11600i	−0.951464	−	0.307759i	$-0.900421\pi$
$547$	−8.48072	−	26.1010i	−0.362610	−	1.11600i	0.588855	−	0.808239i	$-0.299579\pi$
$548$	9.34123	+	88.8759i	0.399038	+	3.79659i
$549$	−1.30980	−	2.26863i	−0.0559007	−	0.0968229i
$550$	−32.3635	+	47.4278i	−1.37998	+	2.02233i
$551$	13.8946	−	24.0661i	0.591928	−	1.02525i
$552$	44.8808	−	32.6078i	1.91025	−	1.38788i
$553$		0			0
$554$	−14.6271	+	45.0174i	−0.621444	+	1.91261i
$555$	−2.25347	+	1.00331i	−0.0956545	+	0.0425881i
$556$	−8.45995	+	80.4910i	−0.358782	+	3.41358i
$557$	29.5893	−	6.28941i	1.25374	−	0.266491i	0.467268	−	0.884116i	$-0.345238\pi$
$557$	29.5893	−	6.28941i	1.25374	−	0.266491i	0.786473	+	0.617625i	$0.211905\pi$
$558$	−2.57713	−	0.547786i	−0.109099	−	0.0231896i
$559$	−4.60574	+	3.34626i	−0.194802	+	0.141532i
$560$		0			0
$561$	4.41249	−	4.21540i	0.186296	−	0.177974i
$562$	2.34417	−	4.06022i	0.0988828	−	0.171270i
$563$	−6.81719	−	3.03521i	−0.287310	−	0.127919i	0.258021	−	0.966139i	$-0.416930\pi$
$563$	−6.81719	−	3.03521i	−0.287310	−	0.127919i	−0.545331	+	0.838221i	$0.683596\pi$
$564$	2.67429	−	2.97010i	0.112608	−	0.125064i
$565$	−43.6702	−	48.5006i	−1.83722	−	2.04044i
$566$	14.4718	+	10.5144i	0.608297	+	0.441954i
$567$		0			0
$568$	−8.60815	+	26.4932i	−0.361190	+	1.11163i
$569$	−34.8693	−	7.41170i	−1.46180	−	0.310715i	−0.592727	−	0.805403i	$-0.701949\pi$
$569$	−34.8693	−	7.41170i	−1.46180	−	0.310715i	−0.869070	+	0.494688i	$0.835282\pi$
$570$	76.8032	+	34.1950i	3.21693	+	1.43227i
$571$	−12.9451	−	22.4216i	−0.541737	−	0.938315i	−0.998804	−	0.0488835i	$-0.984434\pi$
$571$	−12.9451	−	22.4216i	−0.541737	−	0.938315i	0.457068	−	0.889432i	$-0.348900\pi$
$572$	−6.75393	−	5.72949i	−0.282396	−	0.239562i
$573$	16.0880			0.672087
$574$		0			0
$575$	−14.4592	−	44.5010i	−0.602992	−	1.85582i
$576$	1.76986	+	1.96562i	0.0737440	+	0.0819010i
$577$	0.853351	−	8.11909i	0.0355255	−	0.338002i	−0.962295	−	0.272009i	$-0.912312\pi$
$577$	0.853351	−	8.11909i	0.0355255	−	0.338002i	0.997820	−	0.0659930i	$-0.0210215\pi$
$578$	4.04992	−	38.5324i	0.168454	−	1.60274i
$579$	4.01310	+	4.45699i	0.166779	+	0.185226i
$580$	−20.0136	−	61.5955i	−0.831020	−	2.55762i
$581$		0			0
$582$	59.3048			2.45826
$583$	12.3662	−	30.1391i	0.512157	−	1.24823i
$584$	17.2327	+	29.8479i	0.713093	+	1.23511i
$585$	−0.790839	−	0.352104i	−0.0326972	−	0.0145577i
$586$	−7.89228	−	1.67756i	−0.326027	−	0.0692992i
$587$	3.85140	−	11.8534i	0.158964	−	0.489242i	−0.839577	−	0.543241i	$-0.817197\pi$
$587$	3.85140	−	11.8534i	0.158964	−	0.489242i	0.998541	+	0.0539994i	$0.0171969\pi$
$588$		0			0
$589$	13.7456	+	9.98673i	0.566376	+	0.411496i
$590$	−9.69350	−	10.7657i	−0.399075	−	0.443218i
$591$	6.40925	−	7.11819i	0.263641	−	0.292803i
$592$	−1.81417	−	0.807719i	−0.0745618	−	0.0331970i
$593$	−11.8353	+	20.4994i	−0.486019	+	0.841809i	−0.999871	−	0.0160697i	$-0.994885\pi$
$593$	−11.8353	+	20.4994i	−0.486019	+	0.841809i	0.513852	+	0.857879i	$0.328218\pi$
$594$	−39.4147	−	21.2303i	−1.61720	−	0.871088i
$595$		0			0
$596$	−10.4497	+	7.59212i	−0.428034	+	0.310985i
$597$	18.1758	+	3.86339i	0.743886	+	0.158118i
$598$	10.5166	−	2.23537i	0.430055	−	0.0914111i
$599$	−4.07461	+	38.7673i	−0.166484	+	1.58399i	0.518271	+	0.855217i	$0.326576\pi$
$599$	−4.07461	+	38.7673i	−0.166484	+	1.58399i	−0.684755	+	0.728774i	$0.740091\pi$
$600$	53.3488	−	23.7524i	2.17796	−	0.969688i
$601$	−9.44078	+	29.0557i	−0.385097	+	1.18521i	0.551312	+	0.834299i	$0.314127\pi$
$601$	−9.44078	+	29.0557i	−0.385097	+	1.18521i	−0.936410	+	0.350909i	$0.885873\pi$
$602$		0			0
$603$	−1.90919	+	1.38711i	−0.0777483	+	0.0564875i
$604$	−18.2345	+	31.5831i	−0.741952	+	1.28510i
$605$	−33.8613	+	17.5391i	−1.37666	+	0.713066i
$606$	17.2015	+	29.7939i	0.698763	+	1.21029i
$607$	3.93208	+	37.4112i	0.159598	+	1.51848i	0.722164	+	0.691722i	$0.243148\pi$
$607$	3.93208	+	37.4112i	0.159598	+	1.51848i	−0.562565	+	0.826753i	$0.690186\pi$
$608$	1.60366	+	4.93555i	0.0650369	+	0.200163i
$609$		0			0
$610$	47.4470	+	34.4723i	1.92107	+	1.39574i
$611$	0.361148	−	0.160793i	0.0146105	−	0.00650501i
$612$	1.73546	−	0.368884i	0.0701520	−	0.0149113i
$613$	11.7949	−	13.0996i	0.476392	−	0.529087i	−0.456269	−	0.889842i	$-0.650814\pi$
$613$	11.7949	−	13.0996i	0.476392	−	0.529087i	0.932660	+	0.360755i	$0.117481\pi$
$614$	8.15098	+	77.5514i	0.328947	+	3.12972i
$615$	33.1125			1.33522
$616$		0			0
$617$	−44.4849			−1.79089			−0.895447	−	0.445168i	$-0.853144\pi$
$617$	−44.4849			−1.79089			−0.895447	+	0.445168i	$0.853144\pi$
$618$	−0.389230	−	3.70328i	−0.0156571	−	0.148968i
$619$	4.15145	−	4.61065i	0.166861	−	0.185318i	−0.653915	−	0.756568i	$-0.726875\pi$
$619$	4.15145	−	4.61065i	0.166861	−	0.185318i	0.820776	+	0.571250i	$0.193541\pi$
$620$	38.7326	−	8.23288i	1.55554	−	0.330640i
$621$	33.3290	−	14.8390i	1.33745	−	0.595470i
$622$	−18.0371	−	13.1047i	−0.723220	−	0.525450i
$623$		0			0
$624$	1.47610	+	4.54297i	0.0590913	+	0.181864i
$625$	1.13263	+	10.7762i	0.0453052	+	0.431050i
$626$	17.8826	+	30.9736i	0.714733	+	1.23795i
$627$	19.9358	+	25.8020i	0.796161	+	1.03043i
$628$	2.32766	−	4.03162i	0.0928836	−	0.160879i
$629$	0.404567	−	0.293935i	0.0161312	−	0.0117200i
$630$		0			0
$631$	13.8457	−	42.6128i	0.551190	−	1.69639i	−0.154609	−	0.987976i	$-0.549412\pi$
$631$	13.8457	−	42.6128i	0.551190	−	1.69639i	0.705799	−	0.708412i	$-0.250588\pi$
$632$	12.4672	−	5.55076i	0.495919	−	0.220798i
$633$	−1.47564	+	14.0398i	−0.0586516	+	0.558032i
$634$	44.4379	−	9.44558i	1.76486	−	0.375132i
$635$	27.0137	+	5.74194i	1.07201	+	0.227862i
$636$	−52.5210	+	38.1587i	−2.08259	+	1.51309i
$637$		0			0
$638$	6.69585	−	36.8134i	0.265091	−	1.45746i
$639$	−1.03453	+	1.79186i	−0.0409253	+	0.0708848i
$640$	−59.5071	−	26.4943i	−2.35222	−	1.04728i
$641$	−6.87574	+	7.63628i	−0.271575	+	0.301615i	−0.863470	−	0.504400i	$-0.831714\pi$
$641$	−6.87574	+	7.63628i	−0.271575	+	0.301615i	0.591894	+	0.806015i	$0.298380\pi$
$642$	17.6855	+	19.6417i	0.697991	+	0.775197i
$643$	−13.3039	−	9.66588i	−0.524656	−	0.381185i	0.293699	−	0.955898i	$-0.405114\pi$
$643$	−13.3039	−	9.66588i	−0.524656	−	0.381185i	−0.818355	+	0.574713i	$0.805114\pi$
$644$		0			0
$645$	15.0945	−	46.4561i	0.594346	−	1.82921i
$646$	−16.6711	−	3.54356i	−0.655917	−	0.139419i
$647$	24.6371	+	10.9691i	0.968584	+	0.431241i	0.829172	−	0.558993i	$-0.188812\pi$
$647$	24.6371	+	10.9691i	0.968584	+	0.431241i	0.139412	+	0.990235i	$0.455479\pi$
$648$	19.8199	+	34.3291i	0.778601	+	1.34858i
$649$	−1.32987	−	5.45889i	−0.0522018	−	0.214280i
$650$	11.3178			0.443921
$651$		0			0
$652$	−6.39623	−	19.6856i	−0.250496	−	0.770947i
$653$	4.75486	+	5.28080i	0.186072	+	0.206654i	0.828962	−	0.559304i	$-0.188932\pi$
$653$	4.75486	+	5.28080i	0.186072	+	0.206654i	−0.642891	+	0.765958i	$0.722265\pi$
$654$	1.72098	−	16.3740i	0.0672956	−	0.640275i
$655$	−1.74122	+	16.5666i	−0.0680350	+	0.647310i
$656$	17.8372	+	19.8103i	0.696427	+	0.773461i
$657$	0.791062	+	2.43464i	0.0308623	+	0.0949843i
$658$		0			0
$659$	−32.6279			−1.27100			−0.635502	−	0.772099i	$-0.719207\pi$
$659$	−32.6279			−1.27100			−0.635502	+	0.772099i	$0.719207\pi$
$660$	75.7778	+	5.70921i	2.94965	+	0.222231i
$661$	−16.9082	−	29.2859i	−0.657654	−	1.13909i	−0.981221	−	0.192885i	$-0.938215\pi$
$661$	−16.9082	−	29.2859i	−0.657654	−	1.13909i	0.323567	−	0.946205i	$-0.395118\pi$
$662$	−14.5947	−	6.49797i	−0.567238	−	0.252551i
$663$	−1.17659	−	0.250091i	−0.0456949	−	0.00971274i
$664$	−10.6418	+	32.7520i	−0.412981	+	1.27103i
$665$		0			0
$666$	−0.335211	−	0.243545i	−0.0129892	−	0.00943718i
$667$	20.4034	+	22.6603i	0.790022	+	0.877409i
$668$	53.8637	−	59.8217i	2.08405	−	2.31457i
$669$	−15.2735	−	6.80018i	−0.590506	−	0.262910i
$670$	26.4168	−	45.7552i	1.02057	−	1.76768i
$671$	9.86094	+	20.4974i	0.380677	+	0.791293i
$672$		0			0
$673$	−19.2138	+	13.9596i	−0.740638	+	0.538105i	−0.892911	−	0.450234i	$-0.851341\pi$
$673$	−19.2138	+	13.9596i	−0.740638	+	0.538105i	0.152273	+	0.988338i	$0.451341\pi$
$674$	−15.0966	−	3.20889i	−0.581500	−	0.123602i
$675$	37.5655	−	7.98479i	1.44590	−	0.307335i
$676$	5.36818	−	51.0748i	0.206468	−	1.96442i
$677$	41.6861	−	18.5599i	1.60213	−	0.713313i	0.605537	−	0.795817i	$-0.292958\pi$
$677$	41.6861	−	18.5599i	1.60213	−	0.713313i	0.996591	+	0.0825038i	$0.0262917\pi$
$678$	−23.2191	+	71.4611i	−0.891724	+	2.74445i
$679$		0			0
$680$	−16.4012	+	11.9162i	−0.628958	+	0.456965i
$681$	−10.7348	+	18.5932i	−0.411359	+	0.712494i
$682$	21.9567	+	6.42418i	0.840767	+	0.245994i
$683$	14.4364	+	25.0045i	0.552392	+	0.956771i	0.998101	+	0.0615931i	$0.0196181\pi$
$683$	14.4364	+	25.0045i	0.552392	+	0.956771i	−0.445710	+	0.895178i	$0.647049\pi$
$684$	0.990936	+	9.42813i	0.0378894	+	0.360494i
$685$	−23.4372	−	72.1322i	−0.895488	−	2.75603i
$686$		0			0
$687$	−3.26760	−	2.37405i	−0.124667	−	0.0905758i
$688$	35.9246	−	15.9946i	1.36961	−	0.609790i
$689$	−6.28113	+	1.33510i	−0.239292	+	0.0508631i
$690$	−61.7272	+	68.5550i	−2.34991	+	2.60984i
$691$	−2.82890	−	26.9152i	−0.107617	−	1.02390i	−0.906439	−	0.422337i	$-0.861210\pi$
$691$	−2.82890	−	26.9152i	−0.107617	−	1.02390i	0.798823	−	0.601567i	$-0.205457\pi$
$692$	58.7994			2.23522
$693$		0			0
$694$	56.0334			2.12700
$695$	−7.17994	−	68.3126i	−0.272351	−	2.59124i
$696$	−25.4644	+	28.2811i	−0.965225	+	1.07199i
$697$	−6.56610	+	1.39567i	−0.248709	+	0.0528647i
$698$	−66.9147	+	29.7923i	−2.53276	+	1.12766i
$699$	12.5716	+	9.13384i	0.475503	+	0.345473i
$700$		0			0
$701$	11.9020	+	36.6305i	0.449531	+	1.38352i	0.877437	+	0.479692i	$0.159252\pi$
$701$	11.9020	+	36.6305i	0.449531	+	1.38352i	−0.427905	+	0.903823i	$0.640748\pi$
$702$	0.922415	+	8.77619i	0.0348143	+	0.331236i
$703$	1.33599	+	2.31400i	0.0503878	+	0.0872743i
$704$	−14.0420	−	18.1739i	−0.529229	−	0.684955i
$705$	−1.69598	+	2.93752i	−0.0638742	+	0.110633i
$706$	−13.6203	+	9.89572i	−0.512606	+	0.372430i
$707$		0			0
$708$	−3.45991	+	10.6485i	−0.130031	+	0.400195i
$709$	−1.73084	+	0.770620i	−0.0650031	+	0.0289413i	−0.438981	−	0.898496i	$-0.644660\pi$
$709$	−1.73084	+	0.770620i	−0.0650031	+	0.0289413i	0.373978	+	0.927438i	$0.377994\pi$
$710$	4.84200	−	46.0686i	0.181717	−	1.72892i
$711$	0.991492	−	0.210748i	0.0371839	−	0.00790368i
$712$	−3.51214	−	0.746528i	−0.131623	−	0.0279773i
$713$	−15.0827	+	10.9582i	−0.564851	+	0.410388i
$714$		0			0
$715$	6.61778	+	3.56459i	0.247491	+	0.133308i
$716$	9.52608	−	16.4997i	0.356006	−	0.616621i
$717$	8.22333	+	3.66126i	0.307106	+	0.136732i
$718$	−11.9826	+	13.3080i	−0.447187	+	0.496652i
$719$	−9.75407	−	10.8330i	−0.363765	−	0.404002i	0.533281	−	0.845938i	$-0.320959\pi$
$719$	−9.75407	−	10.8330i	−0.363765	−	0.404002i	−0.897047	+	0.441936i	$0.854292\pi$
$720$	4.83766	+	3.51477i	0.180289	+	0.130988i
$721$		0			0
$722$	13.6582	−	42.0357i	0.508307	−	1.56441i
$723$	23.7730	+	5.05310i	0.884127	+	0.187927i
$724$	−36.9731	−	16.4615i	−1.37409	−	0.611786i
$725$	16.0492	+	27.7980i	0.596052	+	1.03239i
$726$	36.9798	+	23.6652i	1.37245	+	0.878298i
$727$	−4.04780			−0.150125			−0.0750623	−	0.997179i	$-0.523916\pi$
$727$	−4.04780			−0.150125			−0.0750623	+	0.997179i	$0.523916\pi$
$728$		0			0
$729$	9.11803	+	28.0624i	0.337705	+	1.03935i
$730$	−38.3492	−	42.5911i	−1.41937	−	1.57637i
$731$	−1.03510	+	9.84832i	−0.0382846	+	0.364253i
$732$	4.73804	−	45.0794i	0.175123	−	1.66618i
$733$	15.7254	+	17.4648i	0.580829	+	0.645076i	0.959917	−	0.280285i	$-0.0904288\pi$
$733$	15.7254	+	17.4648i	0.580829	+	0.645076i	−0.379088	+	0.925361i	$0.623762\pi$
$734$	27.6980	+	85.2457i	1.02235	+	3.14648i
$735$		0			0
$736$	−5.69437			−0.209897
$737$	17.4356	−	10.7648i	0.642249	−	0.396528i
$738$	2.78100	+	4.81683i	0.102370	+	0.177310i
$739$	−29.8534	−	13.2916i	−1.09818	−	0.488939i	−0.224020	−	0.974585i	$-0.571918\pi$
$739$	−29.8534	−	13.2916i	−1.09818	−	0.488939i	−0.874156	+	0.485645i	$0.838585\pi$
$740$	6.09124	+	1.29473i	0.223919	+	0.0475953i
$741$	1.98610	−	6.11260i	0.0729614	−	0.224552i
$742$		0			0
$743$	14.6479	+	10.6423i	0.537379	+	0.390429i	0.823111	−	0.567881i	$-0.192237\pi$
$743$	14.6479	+	10.6423i	0.537379	+	0.390429i	−0.285731	+	0.958310i	$0.592237\pi$
$744$	−15.5691	−	17.2912i	−0.570790	−	0.633927i
$745$	7.33514	−	8.14649i	0.268739	−	0.298464i
$746$	−32.2051	−	14.3386i	−1.17911	−	0.524975i
$747$	−1.27893	+	2.21518i	−0.0467937	+	0.0810491i
$748$	−15.2671	+	2.06186i	−0.558222	+	0.0753892i
$749$		0			0
$750$	−22.5922	+	16.4142i	−0.824949	+	0.599361i
$751$	−8.94376	−	1.90105i	−0.326362	−	0.0693705i	0.0418168	−	0.999125i	$-0.486685\pi$
$751$	−8.94376	−	1.90105i	−0.326362	−	0.0693705i	−0.368179	+	0.929755i	$0.620019\pi$
$752$	−2.67103	+	0.567746i	−0.0974026	+	0.0207036i
$753$	4.67021	−	44.4341i	0.170192	−	1.61927i
$754$	−6.73784	+	2.99988i	−0.245377	+	0.109249i
$755$	9.56444	−	29.4363i	0.348086	−	1.07130i
$756$		0			0
$757$	−38.3077	+	27.8322i	−1.39232	+	1.01158i	−0.396710	+	0.917944i	$0.629848\pi$
$757$	−38.3077	+	27.8322i	−1.39232	+	1.01158i	−0.995607	+	0.0936338i	$0.970152\pi$
$758$	3.13926	−	5.43735i	0.114023	−	0.197494i
$759$	−33.6860	+	12.0556i	−1.22273	+	0.437592i
$760$	−54.1613	−	93.8101i	−1.96464	−	3.40285i
$761$	0.360443	+	3.42939i	0.0130661	+	0.124315i	0.999111	−	0.0421665i	$-0.0134260\pi$
$761$	0.360443	+	3.42939i	0.0130661	+	0.124315i	−0.986045	+	0.166482i	$0.946759\pi$
$762$	−9.82542	−	30.2395i	−0.355937	−	1.09546i
$763$		0			0
$764$	−32.8579	−	23.8727i	−1.18876	−	0.863683i
$765$	−1.37561	+	0.612460i	−0.0497352	+	0.0221435i
$766$	−55.8249	+	11.8659i	−2.01703	+	0.428734i
$767$	−0.741057	+	0.823027i	−0.0267580	+	0.0297178i
$768$	5.49667	+	52.2973i	0.198344	+	1.88712i
$769$	−34.9787			−1.26137			−0.630683	−	0.776041i	$-0.717225\pi$
$769$	−34.9787			−1.26137			−0.630683	+	0.776041i	$0.717225\pi$
$770$		0			0
$771$	46.0622			1.65889
$772$	−1.58264	−	15.0578i	−0.0569605	−	0.541943i
$773$	−16.9821	+	18.8605i	−0.610804	+	0.678367i	−0.966627	−	0.256187i	$-0.917534\pi$
$773$	−16.9821	+	18.8605i	−0.610804	+	0.678367i	0.355823	+	0.934553i	$0.384201\pi$
$774$	8.02564	−	1.70590i	0.288476	−	0.0613174i
$775$	−17.9285	+	7.98226i	−0.644009	+	0.286731i
$776$	−61.8183	−	44.9137i	−2.21915	−	1.61231i
$777$		0			0
$778$	23.0672	+	70.9934i	0.826998	+	2.54524i
$779$	−3.74919	−	35.6712i	−0.134329	−	1.27805i
$780$	−7.48959	−	12.9723i	−0.268170	−	0.464484i
$781$	10.1264	−	14.8399i	0.362350	−	0.531014i
$782$	9.35076	−	16.1960i	0.334383	−	0.579168i
$783$	−20.2474	+	14.7106i	−0.723584	+	0.525715i
$784$		0			0
$785$	−1.22091	+	3.75758i	−0.0435762	+	0.134114i
$786$	17.5202	−	7.80048i	0.624923	−	0.278234i
$787$	3.11026	−	29.5922i	0.110869	−	1.05485i	−0.787713	−	0.616042i	$-0.788735\pi$
$787$	3.11026	−	29.5922i	0.110869	−	1.05485i	0.898582	−	0.438805i	$-0.144598\pi$
$788$	−23.6527	+	5.02753i	−0.842591	+	0.179098i
$789$	−22.4429	−	4.77038i	−0.798988	−	0.169830i
$790$	−18.3595	+	13.3389i	−0.653201	+	0.474578i
$791$		0			0
$792$	2.82432	+	5.87075i	0.100358	+	0.208608i
$793$	2.24177	−	3.88287i	0.0796077	−	0.137885i
$794$	51.0953	+	22.7491i	1.81330	+	0.807335i
$795$	36.8671	−	40.9451i	1.30754	−	1.45217i
$796$	−31.3892	−	34.8612i	−1.11256	−	1.23562i
$797$	−5.05094	−	3.66972i	−0.178913	−	0.129988i	0.494724	−	0.869050i	$-0.335269\pi$
$797$	−5.05094	−	3.66972i	−0.178913	−	0.129988i	−0.673638	+	0.739062i	$0.735269\pi$
$798$		0			0
$799$	0.212493	−	0.653985i	0.00751745	−	0.0231363i
$800$	−5.86329	−	1.24628i	−0.207299	−	0.0440627i
$801$	−0.243637	−	0.108474i	−0.00860849	−	0.00383274i
$802$	20.0034	+	34.6470i	0.706346	+	1.22343i
$803$	−5.26119	−	21.5963i	−0.185663	−	0.762118i
$804$	−40.8340			−1.44010
$805$		0			0
$806$	−1.39349	−	4.28871i	−0.0490834	−	0.151063i
$807$	26.1939	+	29.0913i	0.922069	+	1.02406i
$808$	4.63341	−	44.0839i	0.163003	−	1.55087i
$809$	−4.09606	+	38.9714i	−0.144010	+	1.37016i	0.648925	+	0.760853i	$0.275219\pi$
$809$	−4.09606	+	38.9714i	−0.144010	+	1.37016i	−0.792934	+	0.609307i	$0.791448\pi$
$810$	−44.1069	−	48.9856i	−1.54976	−	1.72118i
$811$	3.82591	+	11.7749i	0.134346	+	0.413474i	0.995488	−	0.0948906i	$-0.0302501\pi$
$811$	3.82591	+	11.7749i	0.134346	+	0.413474i	−0.861142	+	0.508365i	$0.830250\pi$
$812$		0			0
$813$	−12.0539			−0.422750
$814$	2.74355	+	2.32741i	0.0961613	+	0.0815756i
$815$	8.78345	+	15.2134i	0.307671	+	0.532901i
$816$	7.59049	+	3.37950i	0.265720	+	0.118306i
$817$	−51.7550	−	11.0009i	−1.81068	−	0.384872i
$818$	26.7260	−	82.2541i	0.934452	−	2.87595i
$819$		0			0
$820$	−67.6284	−	49.1349i	−2.36168	−	1.71586i
$821$	31.9167	+	35.4471i	1.11390	+	1.23711i	0.968840	+	0.247688i	$0.0796709\pi$
$821$	31.9167	+	35.4471i	1.11390	+	1.23711i	0.145060	+	0.989423i	$0.453662\pi$
$822$	−58.4282	+	64.8911i	−2.03792	+	2.26334i
$823$	−13.2653	−	5.90611i	−0.462401	−	0.205874i	0.162295	−	0.986742i	$-0.448110\pi$
$823$	−13.2653	−	5.90611i	−0.462401	−	0.205874i	−0.624696	+	0.780868i	$0.714777\pi$
$824$	−2.39890	+	4.15501i	−0.0835695	+	0.144747i
$825$	−37.3239	+	5.04068i	−1.29945	+	0.175494i
$826$		0			0
$827$	25.0287	−	18.1844i	0.870335	−	0.632335i	−0.0603420	−	0.998178i	$-0.519219\pi$
$827$	25.0287	−	18.1844i	0.870335	−	0.632335i	0.930677	+	0.365843i	$0.119219\pi$
$828$	−10.1749	−	2.16275i	−0.353604	−	0.0751608i
$829$	0.0839306	−	0.0178400i	0.00291503	−	0.000619609i	−0.206454	−	0.978456i	$-0.566192\pi$
$829$	0.0839306	−	0.0178400i	0.00291503	−	0.000619609i	0.209369	+	0.977837i	$0.432859\pi$
$830$	5.98590	−	56.9521i	0.207774	−	1.97683i
$831$	−28.3642	+	12.6285i	−0.983943	+	0.438080i
$832$	−1.39893	+	4.30548i	−0.0484993	+	0.149266i
$833$		0			0
$834$	−63.9784	+	46.4830i	−2.21539	+	1.60958i
$835$	−34.1592	+	59.1655i	−1.18213	+	2.04751i
$836$	−2.42964	−	82.2799i	−0.0840309	−	2.84571i
$837$	−7.65089	−	13.2517i	−0.264454	−	0.458047i
$838$	7.28751	+	69.3360i	0.251743	+	2.39517i
$839$	−3.30355	−	10.1673i	−0.114051	−	0.351014i	0.877697	−	0.479217i	$-0.159079\pi$
$839$	−3.30355	−	10.1673i	−0.114051	−	0.351014i	−0.991748	+	0.128203i	$0.959079\pi$
$840$		0			0
$841$	6.53883	+	4.75074i	0.225477	+	0.163819i
$842$	−31.0859	+	13.8403i	−1.07129	+	0.476970i
$843$	3.00808	−	0.639387i	0.103604	−	0.0220217i
$844$	23.8472	−	26.4850i	0.820854	−	0.911651i
$845$	4.55596	+	43.3471i	0.156730	+	1.49119i
$846$	−0.569756			−0.0195886
$847$		0			0
$848$	44.3561			1.52319
$849$	1.22650	+	11.6693i	0.0420933	+	0.400491i
$850$	13.1728	−	14.6299i	0.451825	−	0.501802i
$851$	−2.86784	+	0.609577i	−0.0983081	+	0.0208960i
$852$	−32.7064	+	14.5618i	−1.12050	+	0.498880i
$853$	17.1514	+	12.4612i	0.587252	+	0.426664i	0.841331	−	0.540520i	$-0.181772\pi$
$853$	17.1514	+	12.4612i	0.587252	+	0.426664i	−0.254079	+	0.967183i	$0.581772\pi$
$854$		0			0
$855$	−2.48626	−	7.65192i	−0.0850283	−	0.261690i
$856$	−3.55968	−	33.8681i	−0.121667	−	1.15759i
$857$	−4.72680	−	8.18705i	−0.161464	−	0.279664i	0.773930	−	0.633271i	$-0.218288\pi$
$857$	−4.72680	−	8.18705i	−0.161464	−	0.279664i	−0.935394	+	0.353607i	$0.884955\pi$
$858$	−0.255434	−	8.65027i	−0.00872036	−	0.295315i
$859$	−19.4131	+	33.6244i	−0.662365	+	1.14725i	0.317627	+	0.948216i	$0.397114\pi$
$859$	−19.4131	+	33.6244i	−0.662365	+	1.14725i	−0.979992	+	0.199035i	$0.936219\pi$
$860$	−99.7640	+	72.4828i	−3.40192	+	2.47164i
$861$		0			0
$862$	21.4730	−	66.0869i	0.731372	−	2.25093i
$863$	−34.3535	+	15.2952i	−1.16941	+	0.520654i	−0.897217	−	0.441589i	$-0.854415\pi$
$863$	−34.3535	+	15.2952i	−1.16941	+	0.520654i	−0.272191	+	0.962243i	$0.587748\pi$
$864$	0.488541	−	4.64816i	0.0166205	−	0.158134i
$865$	−48.8124	+	10.3754i	−1.65967	+	0.352774i
$866$	34.2123	+	7.27204i	1.16258	+	0.247114i
$867$	20.5606	−	14.9381i	0.698274	−	0.507326i
$868$		0			0
$869$	−8.72231	+	1.17797i	−0.295884	+	0.0399599i
$870$	31.6414	−	54.8045i	1.07274	−	1.85805i
$871$	−3.68986	−	1.64283i	−0.125026	−	0.0556653i
$872$	−14.1945	+	15.7646i	−0.480688	+	0.533858i
$873$	−3.79766	−	4.21773i	−0.128531	−	0.142748i
$874$	80.8416	+	58.7348i	2.73451	+	1.98674i
$875$		0			0
$876$	−13.6880	+	42.1274i	−0.462475	+	1.42335i
$877$	−21.5277	−	4.57584i	−0.726937	−	0.154515i	−0.170444	−	0.985367i	$-0.554520\pi$
$877$	−21.5277	−	4.57584i	−0.726937	−	0.154515i	−0.556493	+	0.830852i	$0.687854\pi$
$878$	−63.1389	−	28.1113i	−2.13084	−	0.948709i
$879$	−2.64627	−	4.58347i	−0.0892564	−	0.154597i
$880$	−39.5940	−	33.5884i	−1.33471	−	1.13226i
$881$	6.92969			0.233467			0.116734	−	0.993163i	$-0.462758\pi$
$881$	6.92969			0.233467			0.116734	+	0.993163i	$0.462758\pi$
$882$		0			0
$883$	13.0834	+	40.2666i	0.440292	+	1.35508i	0.887566	+	0.460681i	$0.152395\pi$
$883$	13.0834	+	40.2666i	0.440292	+	1.35508i	−0.447274	+	0.894397i	$0.647605\pi$
$884$	2.03194	+	2.25669i	0.0683414	+	0.0759008i
$885$	0.993276	−	9.45039i	0.0333886	−	0.317672i
$886$	−4.47024	+	42.5315i	−0.150181	+	1.42887i
$887$	−5.39083	−	5.98712i	−0.181006	−	0.201028i	0.645813	−	0.763496i	$-0.276519\pi$
$887$	−5.39083	−	5.98712i	−0.181006	−	0.201028i	−0.826819	+	0.562468i	$0.809852\pi$
$888$	−1.13074	−	3.48006i	−0.0379452	−	0.116783i
$889$		0			0
$890$	5.97077			0.200141
$891$	−6.05109	−	24.8388i	−0.202719	−	0.832130i
$892$	21.1036	+	36.5525i	0.706601	+	1.22387i
$893$	3.35654	+	1.49443i	0.112322	+	0.0500091i
$894$	−12.3450	−	2.62401i	−0.412878	−	0.0877600i
$895$	−4.99666	+	15.3781i	−0.167020	+	0.514034i
$896$		0			0
$897$	5.70550	+	4.14529i	0.190501	+	0.138407i
$898$	−48.7272	−	54.1170i	−1.62605	−	1.80591i
$899$	8.55759	−	9.50417i	0.285412	−	0.316982i
$900$	−10.0034	−	4.45382i	−0.333448	−	0.148461i
$901$	−5.58483	+	9.67321i	−0.186058	+	0.322261i
$902$	−20.9370	−	43.5207i	−0.697127	−	1.44908i
$903$		0			0
$904$	78.3232	−	56.9051i	2.60499	−	1.89264i
$905$	33.5980	+	7.14146i	1.11683	+	0.237390i
$906$	−34.8555	+	7.40876i	−1.15800	+	0.246140i
$907$	−0.302536	+	2.87843i	−0.0100455	+	0.0955768i	−0.998396	−	0.0566193i	$-0.981968\pi$
$907$	−0.302536	+	2.87843i	−0.0100455	+	0.0955768i	0.988350	+	0.152196i	$0.0486345\pi$
$908$	49.5147	−	22.0454i	1.64320	−	0.731601i
$909$	1.01740	−	3.13125i	0.0337452	−	0.103857i
$910$		0			0
$911$	16.3826	−	11.9026i	0.542779	−	0.394352i	−0.282337	−	0.959315i	$-0.591110\pi$
$911$	16.3826	−	11.9026i	0.542779	−	0.394352i	0.825116	+	0.564963i	$0.191110\pi$
$912$	−22.1978	+	38.4477i	−0.735042	+	1.27313i
$913$	12.5187	−	18.3458i	0.414308	−	0.607157i
$914$	−11.9603	−	20.7158i	−0.395610	−	0.685217i
$915$	4.02116	+	38.2588i	0.132936	+	1.26480i
$916$	3.15089	+	9.69745i	0.104108	+	0.320413i
$917$		0			0
$918$	12.4181	+	9.02229i	0.409859	+	0.297780i
$919$	17.1072	−	7.61660i	0.564313	−	0.251248i	−0.104694	−	0.994505i	$-0.533386\pi$
$919$	17.1072	−	7.61660i	0.564313	−	0.251248i	0.669007	+	0.743256i	$0.266720\pi$
$920$	116.262	−	24.7124i	3.83306	−	0.814742i
$921$	−34.2257	+	38.0114i	−1.12777	+	1.25252i
$922$	−4.95617	−	47.1548i	−0.163223	−	1.55296i
$923$	−3.54128			−0.116563
$924$		0			0
$925$	−3.08632			−0.101478
$926$	−5.29422	−	50.3712i	−0.173979	−	1.65530i
$927$	−0.238450	+	0.264826i	−0.00783173	+	0.00869802i
$928$	3.82094	−	0.812165i	0.125428	−	0.0266606i
$929$	41.3563	−	18.4130i	1.35686	−	0.604111i	0.406036	−	0.913857i	$-0.366911\pi$
$929$	41.3563	−	18.4130i	1.35686	−	0.604111i	0.950819	+	0.309746i	$0.100244\pi$
$930$	31.3020	+	22.7423i	1.02643	+	0.745748i
$931$		0			0
$932$	−12.1226	−	37.3096i	−0.397090	−	1.22212i
$933$	−1.52865	−	14.5441i	−0.0500458	−	0.476154i
$934$	41.5292	+	71.9307i	1.35888	+	2.35364i
$935$	12.3102	−	4.40561i	0.402587	−	0.144079i
$936$	0.642076	−	1.11211i	0.0209869	−	0.0363504i
$937$	23.8336	−	17.3161i	0.778609	−	0.565692i	−0.125952	−	0.992036i	$-0.540199\pi$
$937$	23.8336	−	17.3161i	0.778609	−	0.565692i	0.904561	+	0.426344i	$0.140199\pi$
$938$		0			0
$939$	−7.24952	+	22.3117i	−0.236579	+	0.728115i
$940$	7.82276	−	3.48292i	0.255150	−	0.113600i
$941$	6.08717	−	57.9156i	0.198436	−	1.88799i	−0.213741	−	0.976890i	$-0.568565\pi$
$941$	6.08717	−	57.9156i	0.198436	−	1.88799i	0.412178	−	0.911104i	$-0.364768\pi$
$942$	4.44934	−	0.945736i	0.144967	−	0.0308137i
$943$	38.4967	+	8.18274i	1.25363	+	0.266467i
$944$	6.18897	−	4.49655i	0.201434	−	0.146350i
$945$		0			0
$946$	−70.6028	+	9.53508i	−2.29550	+	0.310012i
$947$	−22.6821	+	39.2865i	−0.737069	+	1.27664i	0.216741	+	0.976229i	$0.430457\pi$
$947$	−22.6821	+	39.2865i	−0.737069	+	1.27664i	−0.953810	+	0.300412i	$0.902876\pi$
$948$	16.0231	+	7.13392i	0.520405	+	0.231699i
$949$	−2.93175	+	3.25604i	−0.0951686	+	0.105695i
$950$	70.3849	+	78.1704i	2.28359	+	2.53618i
$951$	24.1087	+	17.5160i	0.781777	+	0.567994i
$952$		0			0
$953$	−12.7740	+	39.3143i	−0.413790	+	1.27352i	0.499538	+	0.866292i	$0.333503\pi$
$953$	−12.7740	+	39.3143i	−0.413790	+	1.27352i	−0.913328	+	0.407224i	$0.866497\pi$
$954$	9.05256	+	1.92418i	0.293088	+	0.0622977i
$955$	31.4895	+	14.0200i	1.01898	+	0.453677i
$956$	−11.3623	−	19.6801i	−0.367484	−	0.636501i
$957$	20.8840	−	12.8939i	0.675083	−	0.416800i
$958$	−34.9555			−1.12936
$959$		0			0
$960$	−12.0031	−	36.9417i	−0.387398	−	1.19229i
$961$	−15.5109	−	17.2266i	−0.500351	−	0.555696i
$962$	0.0741282	−	0.705282i	0.00238999	−	0.0227392i
$963$	0.264397	−	2.51557i	0.00852006	−	0.0810630i
$964$	−41.0553	−	45.5966i	−1.32230	−	1.46857i
$965$	3.97085	+	12.2210i	0.127826	+	0.393409i
$966$		0			0
$967$	−6.52818			−0.209932			−0.104966	−	0.994476i	$-0.533473\pi$
$967$	−6.52818			−0.209932			−0.104966	+	0.994476i	$0.533473\pi$
$968$	−20.6246	−	52.6743i	−0.662899	−	1.69302i
$969$	−5.58980	−	9.68182i	−0.179570	−	0.311025i
$970$	116.079	+	51.6816i	3.72706	+	1.65940i
$971$	28.2281	+	6.00006i	0.905881	+	0.192551i	0.637218	−	0.770683i	$-0.280085\pi$
$971$	28.2281	+	6.00006i	0.905881	+	0.192551i	0.268663	+	0.963234i	$0.413418\pi$
$972$	4.97870	−	15.3229i	0.159692	−	0.491482i
$973$		0			0
$974$	−55.3617	−	40.2226i	−1.77390	−	1.28882i
$975$	4.96751	+	5.51698i	0.159088	+	0.176685i
$976$	−20.7230	+	23.0152i	−0.663327	+	0.736700i
$977$	−8.20778	−	3.65434i	−0.262590	−	0.116913i	0.271219	−	0.962518i	$-0.412573\pi$
$977$	−8.20778	−	3.65434i	−0.262590	−	0.116913i	−0.533809	+	0.845605i	$0.679240\pi$
$978$	10.1124	−	17.5152i	0.323359	−	0.560074i
$979$	2.03877	+	1.09816i	0.0651593	+	0.0350973i
$980$		0			0
$981$	−1.27472	+	0.926136i	−0.0406986	+	0.0295692i
$982$	8.30725	+	1.76576i	0.265095	+	0.0563477i
$983$	36.0759	−	7.66818i	1.15064	−	0.244577i	0.407176	−	0.913350i	$-0.366513\pi$
$983$	36.0759	−	7.66818i	1.15064	−	0.244577i	0.743467	+	0.668773i	$0.233180\pi$
$984$	−5.13435	+	48.8501i	−0.163677	+	1.55728i
$985$	18.7482	−	8.34722i	0.597366	−	0.265965i
$986$	−3.96441	+	12.2012i	−0.126253	+	0.388566i
$987$		0			0
$988$	−13.1267	+	9.53713i	−0.417617	+	0.303417i
$989$	29.0292	−	50.2800i	0.923073	−	1.59881i
$990$	−6.62361	−	8.57261i	−0.210512	−	0.272455i
$991$	1.49176	+	2.58380i	0.0473873	+	0.0820772i	0.888746	−	0.458400i	$-0.151577\pi$
$991$	1.49176	+	2.58380i	0.0473873	+	0.0820772i	−0.841359	+	0.540477i	$0.818244\pi$
$992$	0.249649	+	2.37525i	0.00792636	+	0.0754143i
$993$	−3.23826	−	9.96635i	−0.102763	−	0.316273i
$994$		0			0
$995$	32.2092	+	23.4013i	1.02110	+	0.741872i
$996$	−40.4332	+	18.0020i	−1.28117	+	0.570416i
$997$	61.4818	−	13.0684i	1.94715	−	0.413879i	0.953491	−	0.301422i	$-0.0974612\pi$
$997$	61.4818	−	13.0684i	1.94715	−	0.413879i	0.993657	−	0.112457i	$-0.0358722\pi$
$998$	−4.27370	+	4.74642i	−0.135282	+	0.150245i
$999$	−0.251539	−	2.39323i	−0.00795834	−	0.0757186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.q.b.520.1		16
7.2	even	3		539.2.f.d.344.1		8
7.3	odd	6		539.2.q.c.410.2		16
7.4	even	3	inner	539.2.q.b.410.2		16
7.5	odd	6		77.2.f.a.36.1	yes	8
7.6	odd	2		539.2.q.c.520.1		16
11.4	even	5	inner	539.2.q.b.422.2		16
21.5	even	6		693.2.m.g.190.2		8
77.2	odd	30		5929.2.a.bb.1.1		4
77.4	even	15	inner	539.2.q.b.312.1		16
77.5	odd	30		847.2.f.p.372.2		8
77.9	even	15		5929.2.a.bi.1.4		4
77.19	even	30		847.2.f.s.148.1		8
77.26	odd	30		77.2.f.a.15.1	✓	8
77.37	even	15		539.2.f.d.246.1		8
77.40	even	30		847.2.f.q.323.2		8
77.47	odd	30		847.2.f.p.148.2		8
77.48	odd	10		539.2.q.c.422.2		16
77.54	even	6		847.2.f.q.729.2		8
77.59	odd	30		539.2.q.c.312.1		16
77.61	even	30		847.2.f.s.372.1		8
77.68	even	30		847.2.a.k.1.1		4
77.75	odd	30		847.2.a.l.1.4		4
231.26	even	30		693.2.m.g.631.2		8
231.68	odd	30		7623.2.a.co.1.4		4
231.152	even	30		7623.2.a.ch.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.1	✓	8	77.26	odd	30
77.2.f.a.36.1	yes	8	7.5	odd	6
539.2.f.d.246.1		8	77.37	even	15
539.2.f.d.344.1		8	7.2	even	3
539.2.q.b.312.1		16	77.4	even	15	inner
539.2.q.b.410.2		16	7.4	even	3	inner
539.2.q.b.422.2		16	11.4	even	5	inner
539.2.q.b.520.1		16	1.1	even	1	trivial
539.2.q.c.312.1		16	77.59	odd	30
539.2.q.c.410.2		16	7.3	odd	6
539.2.q.c.422.2		16	77.48	odd	10
539.2.q.c.520.1		16	7.6	odd	2
693.2.m.g.190.2		8	21.5	even	6
693.2.m.g.631.2		8	231.26	even	30
847.2.a.k.1.1		4	77.68	even	30
847.2.a.l.1.4		4	77.75	odd	30
847.2.f.p.148.2		8	77.47	odd	30
847.2.f.p.372.2		8	77.5	odd	30
847.2.f.q.323.2		8	77.40	even	30
847.2.f.q.729.2		8	77.54	even	6
847.2.f.s.148.1		8	77.19	even	30
847.2.f.s.372.1		8	77.61	even	30
5929.2.a.bb.1.1		4	77.2	odd	30
5929.2.a.bi.1.4		4	77.9	even	15
7623.2.a.ch.1.1		4	231.152	even	30
7623.2.a.co.1.4		4	231.68	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.q (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.257844 - 2.45322i) q^{2} +(1.08268 - 1.20243i) q^{3} +(-3.99550 + 0.849271i) q^{4} +(3.16702 - 1.41005i) q^{5} +(-3.22899 - 2.34600i) q^{6} +(1.58914 + 4.89086i) q^{8} +(0.0399263 + 0.379874i) q^{9} +O(q^{10})\)	\(q+(-0.257844 - 2.45322i) q^{2} +(1.08268 - 1.20243i) q^{3} +(-3.99550 + 0.849271i) q^{4} +(3.16702 - 1.41005i) q^{5} +(-3.22899 - 2.34600i) q^{6} +(1.58914 + 4.89086i) q^{8} +(0.0399263 + 0.379874i) q^{9} +(-4.27575 - 7.40581i) q^{10} +(-0.0978940 - 3.31518i) q^{11} +(-3.30464 + 5.72381i) q^{12} +(-0.528896 + 0.384266i) q^{13} +(1.73337 - 5.33475i) q^{15} +(4.12537 - 1.83673i) q^{16} +(-0.118865 + 1.13092i) q^{17} +(0.921618 - 0.195896i) q^{18} +(-5.94325 - 1.26328i) q^{19} +(-11.4563 + 8.32350i) q^{20} +(-8.10762 + 1.09495i) q^{22} +(3.33354 - 5.77386i) q^{23} +(7.60146 + 3.38439i) q^{24} +(4.69611 - 5.21556i) q^{25} +(1.07906 + 1.19842i) q^{26} +(4.42705 + 3.21644i) q^{27} +(-1.41331 + 4.34973i) q^{29} +(-13.5343 - 2.87679i) q^{30} +(-2.55456 - 1.13736i) q^{31} +(-0.427051 - 0.739674i) q^{32} +(-4.09227 - 3.47155i) q^{33} +2.80505 q^{34} +(-0.482141 - 1.48388i) q^{36} +(-0.294256 - 0.326804i) q^{37} +(-1.56666 + 14.9058i) q^{38} +(-0.110569 + 1.05200i) q^{39} +(11.9292 + 13.2487i) q^{40} +(1.82417 + 5.61423i) q^{41} +8.70820 q^{43} +(3.20662 + 13.1627i) q^{44} +(0.662087 + 1.14677i) q^{45} +(-15.0241 - 6.68915i) q^{46} +(-0.591489 - 0.125725i) q^{47} +(2.25789 - 6.94907i) q^{48} +(-14.0058 - 10.1758i) q^{50} +(1.23117 + 1.36735i) q^{51} +(1.78686 - 1.98451i) q^{52} +(8.97327 + 3.99516i) q^{53} +(6.74915 - 11.6899i) q^{54} +(-4.98459 - 10.3612i) q^{55} +(-7.95362 + 5.77864i) q^{57} +(11.0352 + 2.34561i) q^{58} +(1.65704 - 0.352214i) q^{59} +(-2.39502 + 22.7871i) q^{60} +(-6.26526 + 2.78947i) q^{61} +(-2.13152 + 6.56015i) q^{62} +(5.60222 - 4.07025i) q^{64} +(-1.13319 + 1.96274i) q^{65} +(-7.46132 + 10.9344i) q^{66} +(3.08914 + 5.35054i) q^{67} +(-0.485535 - 4.61956i) q^{68} +(-3.33354 - 10.2596i) q^{69} +(4.38234 + 3.18395i) q^{71} +(-1.79446 + 0.798946i) q^{72} +(6.55553 - 1.39342i) q^{73} +(-0.725850 + 0.806138i) q^{74} +(-1.18700 - 11.2935i) q^{75} +24.8191 q^{76} +2.60929 q^{78} +(-0.277393 - 2.63921i) q^{79} +(10.4752 - 11.6339i) q^{80} +(7.53976 - 1.60263i) q^{81} +(13.3026 - 5.92269i) q^{82} +(5.41765 + 3.93615i) q^{83} +(1.21821 + 3.74926i) q^{85} +(-2.24536 - 21.3631i) q^{86} +(3.70010 + 6.40876i) q^{87} +(16.0585 - 5.74706i) q^{88} +(-0.349107 + 0.604670i) q^{89} +(2.64256 - 1.91993i) q^{90} +(-8.41560 + 25.9006i) q^{92} +(-4.13336 + 1.84029i) q^{93} +(-0.155919 + 1.48347i) q^{94} +(-20.6036 + 4.37944i) q^{95} +(-1.35177 - 0.287327i) q^{96} +(-12.0209 + 8.73372i) q^{97} +(1.25544 - 0.169550i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9	\( 16 q + q^{2} - 4 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} + 6 q^{8} + 2 q^{9} - 28 q^{10} - 5 q^{11} - 14 q^{12} - 10 q^{13} + 12 q^{15} + 3 q^{16} - 11 q^{17} - 4 q^{18} - 9 q^{19} - 42 q^{20} - 2 q^{22} + 16 q^{23} + 21 q^{24} - 5 q^{25} + 21 q^{26} + 44 q^{27} - 18 q^{29} - 14 q^{30} - 11 q^{31} + 20 q^{32} + 10 q^{33} + 48 q^{34} - 4 q^{36} - 6 q^{37} + 35 q^{38} + 5 q^{39} - 16 q^{40} + 44 q^{41} + 32 q^{43} - 29 q^{44} + 18 q^{45} - 29 q^{46} + 7 q^{47} - 8 q^{48} - 68 q^{50} - 3 q^{51} + 21 q^{52} - 2 q^{53} + 4 q^{54} - 52 q^{55} - 6 q^{57} + 39 q^{58} + 25 q^{59} + 38 q^{60} + 7 q^{61} + 10 q^{62} + 2 q^{64} - 24 q^{65} + 18 q^{66} + 30 q^{67} + 8 q^{68} - 16 q^{69} - 28 q^{71} - 3 q^{72} + 3 q^{73} + 9 q^{74} + 5 q^{75} + 104 q^{76} - 36 q^{78} + 9 q^{79} - 33 q^{80} + 28 q^{81} + 31 q^{82} - 46 q^{83} - 20 q^{85} + 17 q^{86} + 12 q^{87} + 7 q^{88} - 34 q^{89} - 4 q^{90} - 68 q^{92} - 8 q^{93} - 30 q^{94} - 24 q^{95} + 10 q^{96} - 60 q^{97}+O(q^{100}) \) 16 * q + q^2 - 4 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 + 6 * q^8 + 2 * q^9 - 28 * q^10 - 5 * q^11 - 14 * q^12 - 10 * q^13 + 12 * q^15 + 3 * q^16 - 11 * q^17 - 4 * q^18 - 9 * q^19 - 42 * q^20 - 2 * q^22 + 16 * q^23 + 21 * q^24 - 5 * q^25 + 21 * q^26 + 44 * q^27 - 18 * q^29 - 14 * q^30 - 11 * q^31 + 20 * q^32 + 10 * q^33 + 48 * q^34 - 4 * q^36 - 6 * q^37 + 35 * q^38 + 5 * q^39 - 16 * q^40 + 44 * q^41 + 32 * q^43 - 29 * q^44 + 18 * q^45 - 29 * q^46 + 7 * q^47 - 8 * q^48 - 68 * q^50 - 3 * q^51 + 21 * q^52 - 2 * q^53 + 4 * q^54 - 52 * q^55 - 6 * q^57 + 39 * q^58 + 25 * q^59 + 38 * q^60 + 7 * q^61 + 10 * q^62 + 2 * q^64 - 24 * q^65 + 18 * q^66 + 30 * q^67 + 8 * q^68 - 16 * q^69 - 28 * q^71 - 3 * q^72 + 3 * q^73 + 9 * q^74 + 5 * q^75 + 104 * q^76 - 36 * q^78 + 9 * q^79 - 33 * q^80 + 28 * q^81 + 31 * q^82 - 46 * q^83 - 20 * q^85 + 17 * q^86 + 12 * q^87 + 7 * q^88 - 34 * q^89 - 4 * q^90 - 68 * q^92 - 8 * q^93 - 30 * q^94 - 24 * q^95 + 10 * q^96 - 60 * q^97

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