LMFDB - Embedded newform 539.2.q.c.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.c.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	−0.969639	−	0.244540i	$-0.921363\pi$
$3$	−1.08268	+	1.20243i	−0.625083	+	0.694225i	0.344556	+	0.938766i	$0.388030\pi$
$4$	−3.99550	+	0.849271i	−1.99775	+	0.424635i
$5$	−3.16702	+	1.41005i	−1.41633	+	0.630592i	−0.965116	−	0.261822i	$-0.915677\pi$
$5$	−3.16702	+	1.41005i	−1.41633	+	0.630592i	−0.451217	+	0.892414i	$0.649010\pi$
$6$	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	−0.512020	−	0.858973i	$-0.671103\pi$
$13$	0.528896	−	0.384266i	0.146689	−	0.106576i	0.658709	+	0.752397i	$0.271103\pi$
$14$		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	$-0.922631\pi$
$17$	0.118865	−	1.13092i	0.0288290	−	0.274289i	0.999435	−	0.0336149i	$-0.0107020\pi$
$18$	0.921618	−	0.195896i	0.217227	−	0.0461731i
$19$	5.94325	+	1.26328i	1.36347	+	0.289815i	0.830831	−	0.556525i	$-0.187866\pi$
$19$	5.94325	+	1.26328i	1.36347	+	0.289815i	0.532643	+	0.846340i	$0.321199\pi$
$20$	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	0.623109	−	0.782135i	$-0.285869\pi$
$31$	2.55456	+	1.13736i	0.458812	+	0.204276i	−0.164298	+	0.986411i	$0.552536\pi$
$32$	−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	$-0.947506\pi$
$41$	−1.82417	−	5.61423i	−0.284888	−	0.876795i	0.701544	−	0.712626i	$-0.252494\pi$
$42$		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	0.250848	−	0.968026i	$-0.419291\pi$
$47$	0.591489	+	0.125725i	0.0862776	+	0.0183389i	−0.164571	+	0.986365i	$0.552624\pi$
$48$	−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	−0.314508	−	0.949255i	$-0.601839\pi$
$59$	−1.65704	+	0.352214i	−0.215728	+	0.0458544i	0.0987798	+	0.995109i	$0.468506\pi$
$60$	−2.39502	+	22.7871i	−0.309196	+	2.94180i
$61$	6.26526	−	2.78947i	0.802185	−	0.357156i	0.0356547	−	0.999364i	$-0.488648\pi$
$61$	6.26526	−	2.78947i	0.802185	−	0.357156i	0.766530	+	0.642209i	$0.221982\pi$
$62$	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	−0.574887	−	0.818233i	$-0.694954\pi$
$73$	−6.55553	+	1.39342i	−0.767266	+	0.163088i	−0.192380	+	0.981321i	$0.561621\pi$
$74$	−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	0.249317	−	0.968422i	$-0.419794\pi$
$83$	−5.41765	−	3.93615i	−0.594664	−	0.432049i	−0.843981	+	0.536373i	$0.819794\pi$
$84$		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	−0.846930	−	0.531705i	$-0.821552\pi$
$89$	0.349107	−	0.604670i	0.0370052	−	0.0640949i	0.883935	+	0.467610i	$0.154885\pi$
$90$	−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	0.224396	−	0.974498i	$-0.427959\pi$
$97$	12.0209	−	8.73372i	1.22054	−	0.886775i	0.996145	+	0.0877234i	$0.0279592\pi$
$98$		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	0.759203	−	0.650854i	$-0.225589\pi$
$101$	7.87439	+	3.50590i	0.783531	+	0.348851i	0.0243278	+	0.999704i	$0.492255\pi$
$102$	3.03696	−	3.37289i	0.300704	−	0.333966i
$103$	−0.624271	−	0.693323i	−0.0615112	−	0.0683152i	0.711604	−	0.702581i	$-0.247969\pi$
$103$	−0.624271	−	0.693323i	−0.0615112	−	0.0683152i	−0.773115	+	0.634266i	$0.781302\pi$
$104$	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	−0.741776	−	0.670648i	$-0.766016\pi$
$131$	2.40253	−	4.16130i	0.209910	−	0.363574i	0.951686	+	0.307073i	$0.0993496\pi$
$132$	−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	$0.417615\pi$
$139$	−6.12278	+	18.8440i	−0.519327	+	1.59832i	−0.775268	+	0.631632i	$0.782385\pi$
$140$		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	−0.711945	−	0.702235i	$-0.752186\pi$
$157$	0.762592	−	0.846944i	0.0608615	−	0.0675935i	0.772807	+	0.634642i	$0.218852\pi$
$158$	−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	0.236558	−	0.971617i	$-0.423981\pi$
$167$	15.9432	−	11.5834i	1.23372	−	0.896351i	0.997164	+	0.0752658i	$0.0239805\pi$
$168$		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	0.709271	−	0.704935i	$-0.249024\pi$
$173$	14.0802	+	2.99285i	1.07050	+	0.227542i	0.361229	+	0.932477i	$0.382357\pi$
$174$	−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	0.248580	−	0.968611i	$-0.420036\pi$
$181$	−8.01578	−	5.82381i	−0.595808	−	0.432880i	−0.844389	+	0.535731i	$0.820036\pi$
$182$		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	0.587510	−	0.809217i	$-0.300108\pi$
$199$	−5.74211	−	9.94563i	−0.407047	−	0.705027i	−0.994557	+	0.104190i	$0.966775\pi$
$200$	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	$0.0124498\pi$
$223$	3.19302	+	9.82712i	0.213821	+	0.658072i	−0.785415	+	0.618970i	$0.787550\pi$
$224$		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	0.244054	−	0.969762i	$-0.421523\pi$
$227$	12.9790	−	2.75877i	0.861446	−	0.183106i	0.617392	+	0.786656i	$0.288189\pi$
$228$	26.8711	−	29.8434i	1.77958	−	1.97642i
$229$	0.260927	+	2.48255i	0.0172425	+	0.164052i	0.999755	−	0.0221465i	$-0.00705002\pi$
$229$	0.260927	+	2.48255i	0.0172425	+	0.164052i	−0.982512	+	0.186198i	$0.940383\pi$
$230$	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	0.516041	−	0.856564i	$-0.327405\pi$
$241$	−7.51038	−	13.0084i	−0.483786	−	0.837942i	−0.999827	+	0.0186224i	$0.994072\pi$
$242$	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	$0.636827\pi$
$251$	−22.3394	+	16.2305i	−1.41005	+	1.02446i	−0.993315	+	0.115436i	$0.963173\pi$
$252$		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	$-0.885503\pi$
$257$	−19.0488	−	21.1558i	−1.18823	−	1.31966i	−0.252230	−	0.967667i	$-0.581164\pi$
$258$	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	$-0.702646\pi$
$269$	2.52893	−	24.0611i	0.154191	−	1.46703i	0.748681	−	0.662930i	$-0.230687\pi$
$270$	4.89140	−	46.5386i	0.297681	−	2.83225i
$271$	4.98486	+	5.53624i	0.302808	+	0.336303i	0.875275	−	0.483625i	$-0.160680\pi$
$271$	4.98486	+	5.53624i	0.302808	+	0.336303i	−0.572467	+	0.819928i	$0.694013\pi$
$272$	−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	−0.581456	−	0.813578i	$-0.697517\pi$
$283$	4.85238	−	5.38912i	0.288444	−	0.320350i	0.869900	+	0.493228i	$0.164183\pi$
$284$	−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	−0.976231	−	0.216734i	$-0.930460\pi$
$293$	−1.01078	+	3.11088i	−0.0590507	+	0.181739i	0.917180	+	0.398473i	$0.130460\pi$
$294$		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	$-0.142026\pi$
$307$	31.6121			1.80420			0.902099	+	0.431530i	$0.142026\pi$
$308$		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	−0.889800	−	0.456351i	$-0.849156\pi$
$311$	−6.04779	+	6.71676i	−0.342939	+	0.380872i	0.546861	+	0.837224i	$0.315823\pi$
$312$	−5.32089	+	1.13099i	−0.301236	+	0.0640297i
$313$	13.2455	−	5.89729i	0.748681	−	0.333334i	0.00331948	−	0.999994i	$-0.498943\pi$
$313$	13.2455	−	5.89729i	0.748681	−	0.333334i	0.745362	+	0.666660i	$0.232277\pi$
$314$	−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	$0.192394\pi$
$349$	9.17597	+	28.2407i	0.491178	+	1.51169i	−0.331651	+	0.943402i	$0.607606\pi$
$350$		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	0.942436	−	0.334387i	$-0.108529\pi$
$353$	3.41253	+	5.91068i	0.181631	+	0.314594i	−0.760805	+	0.648980i	$0.775196\pi$
$354$	−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	0.861716	−	0.507391i	$-0.169390\pi$
$367$	35.5426	−	7.55481i	1.85531	−	0.394358i	0.993591	+	0.113034i	$0.0360568\pi$
$368$	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	$0.167979\pi$
$383$	2.41844	+	23.0100i	0.123577	+	1.17575i	−0.740380	+	0.672188i	$0.765355\pi$
$384$	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	$-0.640668\pi$
$397$	11.3370	−	19.6363i	0.568989	−	0.985518i	0.996666	−	0.0815862i	$-0.0259986\pi$
$398$	−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	−0.589101	−	0.808060i	$-0.700518\pi$
$409$	−32.0302	−	14.2608i	−1.58379	−	0.705149i	−0.994691	+	0.102910i	$0.967185\pi$
$410$	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	$-0.257445\pi$
$419$	28.2633			1.38075			0.690376	+	0.723451i	$0.257445\pi$
$420$		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	$-0.789333\pi$
$433$	4.38165	−	13.4853i	0.210569	−	0.648064i	0.999439	−	0.0335038i	$-0.0106666\pi$
$434$		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	$0.399784\pi$
$439$	−14.0093	+	24.2647i	−0.668625	+	1.15809i	−0.978289	+	0.207247i	$0.933550\pi$
$440$	−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	$-0.647728\pi$
$461$	−19.2216			−0.895240			−0.447620	+	0.894224i	$0.647728\pi$
$462$		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	0.456710	−	0.889616i	$-0.349028\pi$
$467$	30.7604	−	13.6954i	1.42342	−	0.633748i	0.966712	+	0.255868i	$0.0823612\pi$
$468$	−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	$0.138274\pi$
$479$	−1.48125	+	14.0931i	−0.0676800	+	0.643932i	−0.974803	+	0.223067i	$0.928393\pi$
$480$	−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	$-0.929427\pi$
$503$	−7.07731	−	21.7817i	−0.315561	−	0.971198i	0.659961	−	0.751300i	$-0.270573\pi$
$504$		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	0.698180	−	0.715923i	$-0.253994\pi$
$509$	23.5719	+	5.01037i	1.04481	+	0.222081i	0.346627	+	0.938003i	$0.387327\pi$
$510$	−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	0.576704	−	0.816953i	$-0.304338\pi$
$521$	32.7735	−	6.96623i	1.43583	−	0.305196i	0.859130	+	0.511757i	$0.171005\pi$
$522$	−0.450440	+	4.28565i	−0.0197152	+	0.187578i
$523$	−28.4637	+	12.6728i	−1.24463	+	0.554145i	−0.920082	−	0.391725i	$-0.871879\pi$
$523$	−28.4637	+	12.6728i	−1.24463	+	0.554145i	−0.324547	+	0.945870i	$0.605212\pi$
$524$	−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	0.545331	−	0.838221i	$-0.316404\pi$
$563$	6.81719	+	3.03521i	0.287310	+	0.127919i	−0.258021	+	0.966139i	$0.583070\pi$
$564$	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	$0.0876882\pi$
$577$	−0.853351	+	8.11909i	−0.0355255	+	0.338002i	−0.997820	+	0.0659930i	$0.978979\pi$
$578$	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	−0.998541	−	0.0539994i	$-0.982803\pi$
$587$	−3.85140	+	11.8534i	−0.158964	+	0.489242i	0.839577	+	0.543241i	$0.182803\pi$
$588$		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	−0.513852	−	0.857879i	$-0.671782\pi$
$593$	11.8353	−	20.4994i	0.486019	−	0.841809i	0.999871	+	0.0160697i	$0.00511535\pi$
$594$	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	$-0.685873\pi$
$601$	9.44078	−	29.0557i	0.385097	−	1.18521i	0.936410	−	0.350909i	$-0.114127\pi$
$602$		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	$-0.756852\pi$
$607$	−3.93208	−	37.4112i	−0.159598	−	1.51848i	0.562565	−	0.826753i	$-0.309814\pi$
$608$	−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	−0.820776	−	0.571250i	$-0.806459\pi$
$619$	−4.15145	+	4.61065i	−0.166861	+	0.185318i	0.653915	+	0.756568i	$0.273125\pi$
$620$	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	0.818355	−	0.574713i	$-0.194886\pi$
$643$	13.3039	+	9.66588i	0.524656	+	0.381185i	−0.293699	+	0.955898i	$0.594886\pi$
$644$		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	−0.139412	−	0.990235i	$-0.544521\pi$
$647$	−24.6371	−	10.9691i	−0.968584	−	0.431241i	−0.829172	+	0.558993i	$0.811188\pi$
$648$	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	$0.0617846\pi$
$661$	16.9082	+	29.2859i	0.657654	+	1.13909i	−0.323567	+	0.946205i	$0.604882\pi$
$662$	−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	−0.996591	−	0.0825038i	$-0.973708\pi$
$677$	−41.6861	+	18.5599i	−1.60213	+	0.713313i	−0.605537	+	0.795817i	$0.707042\pi$
$678$	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	$0.138790\pi$
$691$	2.82890	+	26.9152i	0.107617	+	1.02390i	−0.798823	+	0.601567i	$0.794543\pi$
$692$	−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	0.897047	−	0.441936i	$-0.145708\pi$
$719$	9.75407	+	10.8330i	0.363765	+	0.404002i	−0.533281	+	0.845938i	$0.679041\pi$
$720$	−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	$-0.476084\pi$
$727$	4.04780			0.150125			0.0750623	+	0.997179i	$0.476084\pi$
$728$		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	0.379088	−	0.925361i	$-0.376238\pi$
$733$	−15.7254	−	17.4648i	−0.580829	−	0.645076i	−0.959917	+	0.280285i	$0.909571\pi$
$734$	−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	0.986045	−	0.166482i	$-0.0532407\pi$
$761$	−0.360443	−	3.42939i	−0.0130661	−	0.124315i	−0.999111	+	0.0421665i	$0.986574\pi$
$762$	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	$-0.282775\pi$
$769$	34.9787			1.26137			0.630683	+	0.776041i	$0.282775\pi$
$770$		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	−0.355823	−	0.934553i	$-0.615799\pi$
$773$	16.9821	−	18.8605i	0.610804	−	0.678367i	0.966627	+	0.256187i	$0.0824662\pi$
$774$	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	$0.211265\pi$
$787$	−3.11026	+	29.5922i	−0.110869	+	1.05485i	−0.898582	+	0.438805i	$0.855402\pi$
$788$	−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	0.673638	−	0.739062i	$-0.264731\pi$
$797$	5.05094	+	3.66972i	0.178913	+	0.129988i	−0.494724	+	0.869050i	$0.664731\pi$
$798$		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	0.861142	−	0.508365i	$-0.169750\pi$
$811$	−3.82591	−	11.7749i	−0.134346	−	0.413474i	−0.995488	+	0.0948906i	$0.969750\pi$
$812$		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	−0.209369	−	0.977837i	$-0.567141\pi$
$829$	−0.0839306	+	0.0178400i	−0.00291503	+	0.000619609i	0.206454	+	0.978456i	$0.433808\pi$
$830$	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	0.991748	−	0.128203i	$-0.0409208\pi$
$839$	3.30355	+	10.1673i	0.114051	+	0.351014i	−0.877697	+	0.479217i	$0.840921\pi$
$840$		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	0.254079	−	0.967183i	$-0.418228\pi$
$853$	−17.1514	−	12.4612i	−0.587252	−	0.426664i	−0.841331	+	0.540520i	$0.818228\pi$
$854$		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	0.935394	−	0.353607i	$-0.115045\pi$
$857$	4.72680	+	8.18705i	0.161464	+	0.279664i	−0.773930	+	0.633271i	$0.781712\pi$
$858$	−0.255434	−	8.65027i	−0.00872036	−	0.295315i
$859$	19.4131	−	33.6244i	0.662365	−	1.14725i	−0.317627	−	0.948216i	$-0.602886\pi$
$859$	19.4131	−	33.6244i	0.662365	−	1.14725i	0.979992	−	0.199035i	$-0.0637806\pi$
$860$	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	$-0.537242\pi$
$881$	−6.92969			−0.233467			−0.116734	+	0.993163i	$0.537242\pi$
$882$		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	0.826819	−	0.562468i	$-0.190148\pi$
$887$	5.39083	+	5.98712i	0.181006	+	0.201028i	−0.645813	+	0.763496i	$0.723481\pi$
$888$	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	−0.950819	−	0.309746i	$-0.899756\pi$
$929$	−41.3563	+	18.4130i	−1.35686	+	0.604111i	−0.406036	+	0.913857i	$0.633089\pi$
$930$	−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	−0.904561	−	0.426344i	$-0.859801\pi$
$937$	−23.8336	+	17.3161i	−0.778609	+	0.565692i	0.125952	+	0.992036i	$0.459801\pi$
$938$		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	$0.431435\pi$
$941$	−6.08717	+	57.9156i	−0.198436	+	1.88799i	−0.412178	+	0.911104i	$0.635232\pi$
$942$	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	−0.268663	−	0.963234i	$-0.586582\pi$
$971$	−28.2281	−	6.00006i	−0.905881	−	0.192551i	−0.637218	+	0.770683i	$0.719915\pi$
$972$	−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	−0.743467	−	0.668773i	$-0.766820\pi$
$983$	−36.0759	+	7.66818i	−1.15064	+	0.244577i	−0.407176	+	0.913350i	$0.633487\pi$
$984$	−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	$0.902539\pi$
$997$	−61.4818	+	13.0684i	−1.94715	+	0.413879i	−0.993657	+	0.112457i	$0.964128\pi$
$998$	−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.c.520.1		16
7.2	even	3		77.2.f.a.36.1	yes	8
7.3	odd	6		539.2.q.b.410.2		16
7.4	even	3	inner	539.2.q.c.410.2		16
7.5	odd	6		539.2.f.d.344.1		8
7.6	odd	2		539.2.q.b.520.1		16
11.4	even	5	inner	539.2.q.c.422.2		16
21.2	odd	6		693.2.m.g.190.2		8
77.2	odd	30		847.2.a.k.1.1		4
77.4	even	15	inner	539.2.q.c.312.1		16
77.9	even	15		847.2.a.l.1.4		4
77.16	even	15		847.2.f.p.372.2		8
77.26	odd	30		539.2.f.d.246.1		8
77.30	odd	30		847.2.f.s.148.1		8
77.37	even	15		77.2.f.a.15.1	✓	8
77.48	odd	10		539.2.q.b.422.2		16
77.51	odd	30		847.2.f.q.323.2		8
77.58	even	15		847.2.f.p.148.2		8
77.59	odd	30		539.2.q.b.312.1		16
77.65	odd	6		847.2.f.q.729.2		8
77.68	even	30		5929.2.a.bb.1.1		4
77.72	odd	30		847.2.f.s.372.1		8
77.75	odd	30		5929.2.a.bi.1.4		4
231.2	even	30		7623.2.a.co.1.4		4
231.86	odd	30		7623.2.a.ch.1.1		4
231.191	odd	30		693.2.m.g.631.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.1	✓	8	77.37	even	15
77.2.f.a.36.1	yes	8	7.2	even	3
539.2.f.d.246.1		8	77.26	odd	30
539.2.f.d.344.1		8	7.5	odd	6
539.2.q.b.312.1		16	77.59	odd	30
539.2.q.b.410.2		16	7.3	odd	6
539.2.q.b.422.2		16	77.48	odd	10
539.2.q.b.520.1		16	7.6	odd	2
539.2.q.c.312.1		16	77.4	even	15	inner
539.2.q.c.410.2		16	7.4	even	3	inner
539.2.q.c.422.2		16	11.4	even	5	inner
539.2.q.c.520.1		16	1.1	even	1	trivial
693.2.m.g.190.2		8	21.2	odd	6
693.2.m.g.631.2		8	231.191	odd	30
847.2.a.k.1.1		4	77.2	odd	30
847.2.a.l.1.4		4	77.9	even	15
847.2.f.p.148.2		8	77.58	even	15
847.2.f.p.372.2		8	77.16	even	15
847.2.f.q.323.2		8	77.51	odd	30
847.2.f.q.729.2		8	77.65	odd	6
847.2.f.s.148.1		8	77.30	odd	30
847.2.f.s.372.1		8	77.72	odd	30
5929.2.a.bb.1.1		4	77.68	even	30
5929.2.a.bi.1.4		4	77.75	odd	30
7623.2.a.ch.1.1		4	231.86	odd	30
7623.2.a.co.1.4		4	231.2	even	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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