LMFDB - Embedded newform 720.2.cf.a.11.73

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.73
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.73

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.991317 - 1.00861i) q^{2} +(0.343013 + 1.69775i) q^{3} +(-0.0345817 - 1.99970i) q^{4} +(0.965926 + 0.258819i) q^{5} +(2.05240 + 1.33704i) q^{6} +(-2.10315 + 3.64276i) q^{7} +(-2.05120 - 1.94746i) q^{8} +(-2.76468 + 1.16470i) q^{9} +O(q^{10})$	\(q+(0.991317 - 1.00861i) q^{2} +(0.343013 + 1.69775i) q^{3} +(-0.0345817 - 1.99970i) q^{4} +(0.965926 + 0.258819i) q^{5} +(2.05240 + 1.33704i) q^{6} +(-2.10315 + 3.64276i) q^{7} +(-2.05120 - 1.94746i) q^{8} +(-2.76468 + 1.16470i) q^{9} +(1.21859 - 0.717669i) q^{10} +(1.83327 - 0.491224i) q^{11} +(3.38312 - 0.744634i) q^{12} +(4.09018 + 1.09596i) q^{13} +(1.58923 + 5.73239i) q^{14} +(-0.108084 + 1.72868i) q^{15} +(-3.99761 + 0.138306i) q^{16} +2.75737i q^{17} +(-1.56595 + 3.94307i) q^{18} +(4.95776 + 4.95776i) q^{19} +(0.484157 - 1.94051i) q^{20} +(-6.90590 - 2.32110i) q^{21} +(1.32190 - 2.33601i) q^{22} +(-0.879310 + 0.507670i) q^{23} +(2.60270 - 4.15041i) q^{24} +(0.866025 + 0.500000i) q^{25} +(5.16006 - 3.03895i) q^{26} +(-2.92568 - 4.29423i) q^{27} +(7.35717 + 4.07970i) q^{28} +(7.33255 - 1.96475i) q^{29} +(1.63641 + 1.82268i) q^{30} +(-1.97182 + 1.13843i) q^{31} +(-3.82340 + 4.16913i) q^{32} +(1.46281 + 2.94393i) q^{33} +(2.78110 + 2.73343i) q^{34} +(-2.97430 + 2.97430i) q^{35} +(2.42465 + 5.48826i) q^{36} +(-4.65691 - 4.65691i) q^{37} +(9.91514 - 0.0857270i) q^{38} +(-0.457679 + 7.32002i) q^{39} +(-1.47726 - 2.41199i) q^{40} +(-4.59061 - 7.95117i) q^{41} +(-9.18701 + 4.66440i) q^{42} +(2.53392 + 9.45670i) q^{43} +(-1.04570 - 3.64901i) q^{44} +(-2.97193 + 0.409459i) q^{45} +(-0.359635 + 1.39014i) q^{46} +(-2.57512 + 4.46023i) q^{47} +(-1.60604 - 6.73948i) q^{48} +(-5.34648 - 9.26038i) q^{49} +(1.36281 - 0.377822i) q^{50} +(-4.68131 + 0.945813i) q^{51} +(2.05015 - 8.21704i) q^{52} +(-2.51158 + 2.51158i) q^{53} +(-7.23147 - 1.30607i) q^{54} +1.89794 q^{55} +(11.4081 - 3.37623i) q^{56} +(-6.71644 + 10.1176i) q^{57} +(5.28722 - 9.34337i) q^{58} +(2.45650 - 9.16777i) q^{59} +(3.46057 + 0.156355i) q^{60} +(-3.37674 - 12.6021i) q^{61} +(-0.806467 + 3.11734i) q^{62} +(1.57183 - 12.5206i) q^{63} +(0.414815 + 7.98924i) q^{64} +(3.66716 + 2.11723i) q^{65} +(4.41938 + 1.44297i) q^{66} +(2.06274 - 7.69826i) q^{67} +(5.51391 - 0.0953544i) q^{68} +(-1.16351 - 1.31871i) q^{69} +(0.0514301 + 5.94839i) q^{70} -5.83879i q^{71} +(7.93911 + 2.99508i) q^{72} +5.77551i q^{73} +(-9.31348 + 0.0805250i) q^{74} +(-0.551815 + 1.64180i) q^{75} +(9.74258 - 10.0855i) q^{76} +(-2.06624 + 7.71130i) q^{77} +(6.92933 + 7.71808i) q^{78} +(2.00202 + 1.15587i) q^{79} +(-3.89719 - 0.901064i) q^{80} +(6.28696 - 6.44004i) q^{81} +(-12.5704 - 3.25200i) q^{82} +(-0.302176 - 1.12774i) q^{83} +(-4.40269 + 13.8900i) q^{84} +(-0.713659 + 2.66341i) q^{85} +(12.0500 + 6.81886i) q^{86} +(5.85081 + 11.7749i) q^{87} +(-4.71704 - 2.56262i) q^{88} +14.2044 q^{89} +(-2.53314 + 3.40341i) q^{90} +(-12.5946 + 12.5946i) q^{91} +(1.04560 + 1.74080i) q^{92} +(-2.60913 - 2.95715i) q^{93} +(1.94587 + 7.01878i) q^{94} +(3.50566 + 6.07199i) q^{95} +(-8.38959 - 5.06110i) q^{96} +(5.69888 - 9.87075i) q^{97} +(-14.6402 - 3.78747i) q^{98} +(-4.49629 + 3.49329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6}+O(q^{10}) $ 384 * q - 12 * q^6	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.991317	−	1.00861i	0.700967	−	0.713194i
$2$	0.991317	−	1.00861i	0.700967	−	0.713194i
$3$	0.343013	+	1.69775i	0.198039	+	0.980194i
$3$	0.343013	+	1.69775i	0.198039	+	0.980194i
$4$	−0.0345817	−	1.99970i	−0.0172908	−	0.999851i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	2.05240	+	1.33704i	0.837887	+	0.545844i
$7$	−2.10315	+	3.64276i	−0.794916	+	1.37684i	0.127976	+	0.991777i	$0.459152\pi$
$7$	−2.10315	+	3.64276i	−0.794916	+	1.37684i	−0.922892	+	0.385058i	$0.874181\pi$
$8$	−2.05120	−	1.94746i	−0.725208	−	0.688530i
$9$	−2.76468	+	1.16470i	−0.921561	+	0.388233i
$10$	1.21859	−	0.717669i	0.385351	−	0.226947i
$11$	1.83327	−	0.491224i	0.552752	−	0.148110i	0.0283778	−	0.999597i	$-0.490966\pi$
$11$	1.83327	−	0.491224i	0.552752	−	0.148110i	0.524375	+	0.851488i	$0.324299\pi$
$12$	3.38312	−	0.744634i	0.976623	−	0.214957i
$13$	4.09018	+	1.09596i	1.13441	+	0.303965i	0.776702	−	0.629868i	$-0.216891\pi$
$13$	4.09018	+	1.09596i	1.13441	+	0.303965i	0.357710	+	0.933833i	$0.383558\pi$
$14$	1.58923	+	5.73239i	0.424740	+	1.53205i
$15$	−0.108084	+	1.72868i	−0.0279072	+	0.446342i
$16$	−3.99761	+	0.138306i	−0.999402	+	0.0345765i
$17$			2.75737i			0.668760i	0.942438	+	0.334380i	$0.108527\pi$
$17$			2.75737i			0.668760i	−0.942438	+	0.334380i	$0.891473\pi$
$18$	−1.56595	+	3.94307i	−0.369099	+	0.929390i
$19$	4.95776	+	4.95776i	1.13739	+	1.13739i	0.988917	+	0.148471i	$0.0474351\pi$
$19$	4.95776	+	4.95776i	1.13739	+	1.13739i	0.148471	+	0.988917i	$0.452565\pi$
$20$	0.484157	−	1.94051i	0.108261	−	0.433912i
$21$	−6.90590	−	2.32110i	−1.50699	−	0.506506i
$22$	1.32190	−	2.33601i	0.281830	−	0.498039i
$23$	−0.879310	+	0.507670i	−0.183349	+	0.105857i	−0.588865	−	0.808231i	$-0.700425\pi$
$23$	−0.879310	+	0.507670i	−0.183349	+	0.105857i	0.405516	+	0.914088i	$0.367092\pi$
$24$	2.60270	−	4.15041i	0.531274	−	0.847200i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	5.16006	−	3.03895i	1.01197	−	0.595987i
$27$	−2.92568	−	4.29423i	−0.563048	−	0.826424i
$28$	7.35717	+	4.07970i	1.39037	+	0.770991i
$29$	7.33255	−	1.96475i	1.36162	−	0.364845i	0.497210	−	0.867630i	$-0.334358\pi$
$29$	7.33255	−	1.96475i	1.36162	−	0.364845i	0.864411	+	0.502785i	$0.167691\pi$
$30$	1.63641	+	1.82268i	0.298766	+	0.332774i
$31$	−1.97182	+	1.13843i	−0.354149	+	0.204468i	−0.666511	−	0.745495i	$-0.732213\pi$
$31$	−1.97182	+	1.13843i	−0.354149	+	0.204468i	0.312362	+	0.949963i	$0.398880\pi$
$32$	−3.82340	+	4.16913i	−0.675888	+	0.737004i
$33$	1.46281	+	2.94393i	0.254642	+	0.512473i
$34$	2.78110	+	2.73343i	0.476955	+	0.468779i
$35$	−2.97430	+	2.97430i	−0.502749	+	0.502749i
$36$	2.42465	+	5.48826i	0.404109	+	0.914711i
$37$	−4.65691	−	4.65691i	−0.765592	−	0.765592i	0.211735	−	0.977327i	$-0.432089\pi$
$37$	−4.65691	−	4.65691i	−0.765592	−	0.765592i	−0.977327	+	0.211735i	$0.932089\pi$
$38$	9.91514	−	0.0857270i	1.60845	−	0.0139068i
$39$	−0.457679	+	7.32002i	−0.0732872	+	1.17214i
$40$	−1.47726	−	2.41199i	−0.233576	−	0.381369i
$41$	−4.59061	−	7.95117i	−0.716933	−	1.24176i	−0.962209	−	0.272311i	$-0.912212\pi$
$41$	−4.59061	−	7.95117i	−0.716933	−	1.24176i	0.245276	−	0.969453i	$-0.421121\pi$
$42$	−9.18701	+	4.66440i	−1.41759	+	0.719732i
$43$	2.53392	+	9.45670i	0.386418	+	1.44213i	0.835919	+	0.548853i	$0.184935\pi$
$43$	2.53392	+	9.45670i	0.386418	+	1.44213i	−0.449500	+	0.893280i	$0.648398\pi$
$44$	−1.04570	−	3.64901i	−0.157645	−	0.550109i
$45$	−2.97193	+	0.409459i	−0.443029	+	0.0610385i
$46$	−0.359635	+	1.39014i	−0.0530253	+	0.204965i
$47$	−2.57512	+	4.46023i	−0.375619	+	0.650591i	−0.990419	−	0.138091i	$-0.955903\pi$
$47$	−2.57512	+	4.46023i	−0.375619	+	0.650591i	0.614800	+	0.788683i	$0.289237\pi$
$48$	−1.60604	−	6.73948i	−0.231812	−	0.972761i
$49$	−5.34648	−	9.26038i	−0.763784	−	1.32291i
$50$	1.36281	−	0.377822i	0.192730	−	0.0534321i
$51$	−4.68131	+	0.945813i	−0.655515	+	0.132440i
$52$	2.05015	−	8.21704i	0.284305	−	1.13950i
$53$	−2.51158	+	2.51158i	−0.344992	+	0.344992i	−0.858240	−	0.513249i	$-0.828442\pi$
$53$	−2.51158	+	2.51158i	−0.344992	+	0.344992i	0.513249	+	0.858240i	$0.328442\pi$
$54$	−7.23147	−	1.30607i	−0.984079	−	0.177734i
$55$	1.89794			0.255919
$56$	11.4081	−	3.37623i	1.52447	−	0.451167i
$57$	−6.71644	+	10.1176i	−0.889614	+	1.34011i
$58$	5.28722	−	9.34337i	0.694246	−	1.22684i
$59$	2.45650	−	9.16777i	0.319808	−	1.19354i	−0.599620	−	0.800285i	$-0.704682\pi$
$59$	2.45650	−	9.16777i	0.319808	−	1.19354i	0.919429	−	0.393257i	$-0.128652\pi$
$60$	3.46057	+	0.156355i	0.446758	+	0.0201854i
$61$	−3.37674	−	12.6021i	−0.432347	−	1.61354i	−0.747337	−	0.664445i	$-0.768668\pi$
$61$	−3.37674	−	12.6021i	−0.432347	−	1.61354i	0.314990	−	0.949095i	$-0.397999\pi$
$62$	−0.806467	+	3.11734i	−0.102421	+	0.395902i
$63$	1.57183	−	12.5206i	0.198032	−	1.57745i
$64$	0.414815	+	7.98924i	0.0518518	+	0.998655i
$65$	3.66716	+	2.11723i	0.454855	+	0.262611i
$66$	4.41938	+	1.44297i	0.543989	+	0.177617i
$67$	2.06274	−	7.69826i	0.252004	−	0.940492i	−0.717729	−	0.696323i	$-0.754818\pi$
$67$	2.06274	−	7.69826i	0.252004	−	0.940492i	0.969733	−	0.244169i	$-0.0785151\pi$
$68$	5.51391	−	0.0953544i	0.668660	−	0.0115634i
$69$	−1.16351	−	1.31871i	−0.140070	−	0.158754i
$70$	0.0514301	+	5.94839i	0.00614708	+	0.710968i
$71$		−	5.83879i		−	0.692937i	−0.938062	−	0.346468i	$-0.887381\pi$
$71$		−	5.83879i		−	0.692937i	0.938062	−	0.346468i	$-0.112619\pi$
$72$	7.93911	+	2.99508i	0.935633	+	0.352974i
$73$			5.77551i			0.675972i	0.941151	+	0.337986i	$0.109746\pi$
$73$			5.77551i			0.675972i	−0.941151	+	0.337986i	$0.890254\pi$
$74$	−9.31348	+	0.0805250i	−1.08267	+	0.00936084i
$75$	−0.551815	+	1.64180i	−0.0637181	+	0.189578i
$76$	9.74258	−	10.0855i	1.11755	−	1.15688i
$77$	−2.06624	+	7.71130i	−0.235469	+	0.878784i
$78$	6.92933	+	7.71808i	0.784592	+	0.873900i
$79$	2.00202	+	1.15587i	0.225245	+	0.130045i	0.608377	−	0.793649i	$-0.291821\pi$
$79$	2.00202	+	1.15587i	0.225245	+	0.130045i	−0.383132	+	0.923694i	$0.625154\pi$
$80$	−3.89719	−	0.901064i	−0.435719	−	0.100742i
$81$	6.28696	−	6.44004i	0.698551	−	0.715560i
$82$	−12.5704	−	3.25200i	−1.38817	−	0.359124i
$83$	−0.302176	−	1.12774i	−0.0331681	−	0.123785i	0.947357	−	0.320180i	$-0.103743\pi$
$83$	−0.302176	−	1.12774i	−0.0331681	−	0.123785i	−0.980525	+	0.196395i	$0.937077\pi$
$84$	−4.40269	+	13.8900i	−0.480373	+	1.51552i
$85$	−0.713659	+	2.66341i	−0.0774072	+	0.288888i
$86$	12.0500	+	6.81886i	1.29939	+	0.735296i
$87$	5.85081	+	11.7749i	0.627273	+	1.26240i
$88$	−4.71704	−	2.56262i	−0.502838	−	0.273177i
$89$	14.2044			1.50566			0.752829	−	0.658216i	$-0.228689\pi$
$89$	14.2044			1.50566			0.752829	+	0.658216i	$0.228689\pi$
$90$	−2.53314	+	3.40341i	−0.267016	+	0.358751i
$91$	−12.5946	+	12.5946i	−1.32027	+	1.32027i
$92$	1.04560	+	1.74080i	0.109011	+	0.181491i
$93$	−2.60913	−	2.95715i	−0.270554	−	0.306642i
$94$	1.94587	+	7.01878i	0.200701	+	0.723932i
$95$	3.50566	+	6.07199i	0.359674	+	0.622973i
$96$	−8.38959	−	5.06110i	−0.856259	−	0.516546i
$97$	5.69888	−	9.87075i	0.578633	−	1.00222i	−0.417003	−	0.908905i	$-0.636920\pi$
$97$	5.69888	−	9.87075i	0.578633	−	1.00222i	0.995636	−	0.0933172i	$-0.0297471\pi$
$98$	−14.6402	−	3.78747i	−1.47888	−	0.382592i
$99$	−4.49629	+	3.49329i	−0.451894	+	0.351089i
$100$	0.969902	−	1.74908i	0.0969902	−	0.174908i
$101$	−0.544224	−	2.03107i	−0.0541524	−	0.202099i	0.933549	−	0.358449i	$-0.116694\pi$
$101$	−0.544224	−	2.03107i	−0.0541524	−	0.202099i	−0.987702	+	0.156349i	$0.950027\pi$
$102$	−3.68671	+	5.65921i	−0.365038	+	0.560345i
$103$	−7.24545	−	12.5495i	−0.713915	−	1.23654i	−0.963376	−	0.268153i	$-0.913587\pi$
$103$	−7.24545	−	12.5495i	−0.713915	−	1.23654i	0.249461	−	0.968385i	$-0.419747\pi$
$104$	−6.25543	−	10.2135i	−0.613395	−	1.00152i
$105$	−6.06984	−	4.02939i	−0.592356	−	0.393228i
$106$	0.0434289	+	5.02296i	0.00421819	+	0.487873i
$107$	7.46691	+	7.46691i	0.721853	+	0.721853i	0.968982	−	0.247129i	$-0.0794873\pi$
$107$	7.46691	+	7.46691i	0.721853	+	0.721853i	−0.247129	+	0.968982i	$0.579487\pi$
$108$	−8.48599	+	5.99899i	−0.816565	+	0.577253i
$109$	−7.54815	+	7.54815i	−0.722982	+	0.722982i	−0.969212	−	0.246230i	$-0.920808\pi$
$109$	−7.54815	+	7.54815i	−0.722982	+	0.722982i	0.246230	+	0.969212i	$0.420808\pi$
$110$	1.88146	−	1.91428i	0.179390	−	0.182520i
$111$	6.30888	−	9.50364i	0.598812	−	0.902046i
$112$	7.90376	−	14.8532i	0.746835	−	1.40350i
$113$	12.0540	−	6.95939i	1.13395	−	0.654684i	0.189022	−	0.981973i	$-0.439468\pi$
$113$	12.0540	−	6.95939i	1.13395	−	0.654684i	0.944924	+	0.327289i	$0.106135\pi$
$114$	3.54656	+	16.8040i	0.332166	+	1.57384i
$115$	−0.980743	+	0.262789i	−0.0914548	+	0.0245052i
$116$	−4.18249	−	14.5950i	−0.388334	−	1.35511i
$117$	−12.5845	+	1.73384i	−1.16344	+	0.160294i
$118$	−6.81152	−	11.5658i	−0.627051	−	1.06472i
$119$	−10.0444	−	5.79916i	−0.920772	−	0.531608i
$120$	3.58822	−	3.33536i	0.327559	−	0.304476i
$121$	−6.40669	+	3.69891i	−0.582427	+	0.336264i
$122$	−16.0580	−	9.08692i	−1.45383	−	0.822691i
$123$	11.9244	−	10.5210i	1.07519	−	0.948651i
$124$	2.34471	+	3.90368i	0.210561	+	0.350561i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−11.0702	−	13.9973i	−0.986214	−	1.24698i
$127$			2.09647i			0.186032i	0.995665	+	0.0930159i	$0.0296507\pi$
$127$			2.09647i			0.186032i	−0.995665	+	0.0930159i	$0.970349\pi$
$128$	8.46923	+	7.50148i	0.748581	+	0.663044i
$129$	−15.1859	+	7.54571i	−1.33704	+	0.664363i
$130$	5.77078	−	1.59988i	0.506130	−	0.140318i
$131$	17.5855	+	4.71202i	1.53645	+	0.411691i	0.925118	−	0.379681i	$-0.123966\pi$
$131$	17.5855	+	4.71202i	1.53645	+	0.411691i	0.611335	+	0.791372i	$0.290633\pi$
$132$	5.83640	−	3.02699i	0.507994	−	0.263465i
$133$	−28.4868	+	7.63303i	−2.47012	+	0.661867i
$134$	−5.71970	−	9.71191i	−0.494106	−	0.838981i
$135$	−1.71457	−	4.90513i	−0.147566	−	0.422166i
$136$	5.36986	−	5.65590i	0.460462	−	0.484990i
$137$	7.21222	−	12.4919i	0.616181	−	1.06726i	−0.373995	−	0.927431i	$-0.622012\pi$
$137$	7.21222	−	12.4919i	0.616181	−	1.06726i	0.990176	−	0.139826i	$-0.0446544\pi$
$138$	−2.48347	−	0.133732i	−0.211407	−	0.0113840i
$139$	−13.0914	−	3.50782i	−1.11039	−	0.297529i	−0.343404	−	0.939188i	$-0.611580\pi$
$139$	−13.0914	−	3.50782i	−1.11039	−	0.297529i	−0.766991	+	0.641658i	$0.778247\pi$
$140$	6.05058	+	5.84486i	0.511367	+	0.493981i
$141$	−8.45564	−	2.84198i	−0.712093	−	0.239338i
$142$	−5.88905	−	5.78809i	−0.494198	−	0.485726i
$143$	8.03678			0.672069
$144$	10.8910	−	5.03838i	0.907587	−	0.419865i
$145$	7.59122			0.630416
$146$	5.82522	+	5.72536i	0.482099	+	0.473834i
$147$	13.8879	−	12.2534i	1.14545	−	1.01064i
$148$	−9.15139	+	9.47348i	−0.752240	+	0.778715i
$149$	−5.89495	−	1.57955i	−0.482933	−	0.129402i	0.00913475	−	0.999958i	$-0.497092\pi$
$149$	−5.89495	−	1.57955i	−0.482933	−	0.129402i	−0.492068	+	0.870557i	$0.663759\pi$
$150$	1.10891	+	2.18411i	0.0905419	+	0.178332i
$151$	−5.28326	+	9.15088i	−0.429946	+	0.744688i	−0.996868	−	0.0790832i	$-0.974801\pi$
$151$	−5.28326	+	9.15088i	−0.429946	+	0.744688i	0.566922	+	0.823771i	$0.308134\pi$
$152$	−0.514311	−	19.8244i	−0.0417161	−	1.60797i
$153$	−3.21150	−	7.62325i	−0.259634	−	0.616303i
$154$	5.72938	+	9.72836i	0.461687	+	0.783934i
$155$	−2.19928	+	0.589295i	−0.176650	+	0.0473333i
$156$	14.6537	+	0.662082i	1.17323	+	0.0530090i
$157$	−22.0204	−	5.90034i	−1.75742	−	0.470898i	−0.771232	−	0.636554i	$-0.780359\pi$
$157$	−22.0204	−	5.90034i	−1.75742	−	0.470898i	−0.986184	+	0.165656i	$0.947026\pi$
$158$	3.15046	−	0.873425i	0.250637	−	0.0694859i
$159$	−5.12552	−	3.40252i	−0.406480	−	0.269837i
$160$	−4.77217	+	3.03750i	−0.377273	+	0.240135i
$161$		−	4.27083i		−	0.336588i
$162$	−0.263112	−	12.7252i	−0.0206721	−	0.999786i
$163$	5.24409	+	5.24409i	0.410749	+	0.410749i	0.882000	−	0.471250i	$-0.156197\pi$
$163$	5.24409	+	5.24409i	0.410749	+	0.410749i	−0.471250	+	0.882000i	$0.656197\pi$
$164$	−15.7412	+	9.45482i	−1.22918	+	0.738297i
$165$	0.651019	+	3.22223i	0.0506818	+	0.250850i
$166$	−1.43700	−	0.813166i	−0.111533	−	0.0631140i
$167$	13.6974	−	7.90822i	1.05994	−	0.611957i	0.134524	−	0.990910i	$-0.457049\pi$
$167$	13.6974	−	7.90822i	1.05994	−	0.611957i	0.925416	+	0.378954i	$0.123716\pi$
$168$	9.64510	+	18.2100i	0.744136	+	1.40493i
$169$	4.27013	+	2.46536i	0.328472	+	0.189643i
$170$	1.97888	+	3.36009i	0.151773	+	0.257707i
$171$	−19.4809	−	7.93235i	−1.48974	−	0.606602i
$172$	18.8229	−	5.39410i	1.43524	−	0.411296i
$173$	−1.53515	+	0.411343i	−0.116715	+	0.0312738i	−0.316704	−	0.948524i	$-0.602576\pi$
$173$	−1.53515	+	0.411343i	−0.116715	+	0.0312738i	0.199989	+	0.979798i	$0.435910\pi$
$174$	17.6763	+	5.77146i	1.34003	+	0.437533i
$175$	−3.64276	+	2.10315i	−0.275367	+	0.158983i
$176$	−7.26076	+	2.21727i	−0.547301	+	0.167133i
$177$	16.4072	+	1.02584i	1.23324	+	0.0771072i
$178$	14.0810	−	14.3266i	1.05542	−	1.07383i
$179$	−0.138298	+	0.138298i	−0.0103369	+	0.0103369i	−0.712256	−	0.701919i	$-0.752327\pi$
$179$	−0.138298	+	0.138298i	−0.0103369	+	0.0103369i	0.701919	+	0.712256i	$0.252327\pi$
$180$	0.921569	+	5.92880i	0.0686897	+	0.441907i
$181$	−6.71657	−	6.71657i	−0.499239	−	0.499239i	0.411962	−	0.911201i	$-0.364844\pi$
$181$	−6.71657	−	6.71657i	−0.499239	−	0.499239i	−0.911201	+	0.411962i	$0.864844\pi$
$182$	0.217779	+	25.1883i	0.0161429	+	1.86708i
$183$	20.2370	−	10.0555i	1.49596	−	0.743327i
$184$	2.79230	+	0.671089i	0.205851	+	0.0494733i
$185$	−3.29294	−	5.70353i	−0.242101	−	0.419332i
$186$	−5.56908	−	0.299889i	−0.408345	−	0.0219890i
$187$	1.35448	+	5.05501i	0.0990497	+	0.369659i
$188$	9.00818	+	4.99522i	0.656989	+	0.364314i
$189$	21.7960	−	1.62617i	1.58543	−	0.118286i
$190$	9.59948	+	2.48342i	0.696420	+	0.180166i
$191$	−5.01491	+	8.68607i	−0.362866	+	0.628502i	−0.988431	−	0.151670i	$-0.951535\pi$
$191$	−5.01491	+	8.68607i	−0.362866	+	0.628502i	0.625565	+	0.780172i	$0.284868\pi$
$192$	−13.4214	+	3.44466i	−0.968607	+	0.248597i
$193$	11.0436	+	19.1281i	0.794937	+	1.37687i	0.922879	+	0.385089i	$0.125829\pi$
$193$	11.0436	+	19.1281i	0.794937	+	1.37687i	−0.127943	+	0.991782i	$0.540837\pi$
$194$	−4.30632	−	15.5330i	−0.309176	−	1.11520i
$195$	−2.33664	+	6.95214i	−0.167331	+	0.497853i
$196$	−18.3331	+	11.0116i	−1.30951	+	0.786544i
$197$	−10.2322	+	10.2322i	−0.729014	+	0.729014i	−0.970423	−	0.241409i	$-0.922390\pi$
$197$	−10.2322	+	10.2322i	−0.729014	+	0.729014i	0.241409	+	0.970423i	$0.422390\pi$
$198$	−0.933892	+	7.99795i	−0.0663688	+	0.568390i
$199$	−2.01487			−0.142831			−0.0714153	−	0.997447i	$-0.522752\pi$
$199$	−2.01487			−0.142831			−0.0714153	+	0.997447i	$0.522752\pi$
$200$	−0.802659	−	2.71215i	−0.0567566	−	0.191778i
$201$	13.7772	+	0.861411i	0.971771	+	0.0607592i
$202$	−2.58806	−	1.46453i	−0.182095	−	0.103044i
$203$	−8.26434	+	30.8429i	−0.580043	+	2.16475i
$204$	2.05323	+	9.32851i	0.143755	+	0.653127i
$205$	−2.37628	−	8.86838i	−0.165966	−	0.619395i
$206$	−19.8401	−	5.13270i	−1.38232	−	0.357612i
$207$	1.83973	−	2.42768i	0.127870	−	0.168735i
$208$	−16.5025	−	3.81553i	−1.14424	−	0.264559i
$209$	11.5243	+	6.65355i	0.797152	+	0.460236i
$210$	−10.0812	+	2.12769i	−0.695669	+	0.146824i
$211$	3.15444	−	11.7725i	0.217161	−	0.810455i	−0.768234	−	0.640169i	$-0.778864\pi$
$211$	3.15444	−	11.7725i	0.217161	−	0.810455i	0.985395	−	0.170286i	$-0.0544692\pi$
$212$	5.10926	+	4.93555i	0.350905	+	0.338975i
$213$	9.91278	−	2.00278i	0.679213	−	0.137228i
$214$	14.9333	−	0.129114i	1.02082	−	0.00882604i
$215$			9.79030i			0.667693i
$216$	−2.36167	+	14.5059i	−0.160692	+	0.987005i
$217$		−	9.57716i		−	0.650140i
$218$	0.130519	+	15.0957i	0.00883985	+	1.02241i
$219$	−9.80535	+	1.98107i	−0.662584	+	0.133869i
$220$	−0.0656341	−	3.79532i	−0.00442505	−	0.255880i
$221$	−3.02197	+	11.2781i	−0.203280	+	0.758650i
$222$	−3.33135	−	15.7843i	−0.223586	−	1.05937i
$223$	−7.21436	−	4.16521i	−0.483109	−	0.278923i	0.238602	−	0.971117i	$-0.423311\pi$
$223$	−7.21436	−	4.16521i	−0.483109	−	0.278923i	−0.721711	+	0.692194i	$0.756644\pi$
$224$	−7.14596	−	22.6960i	−0.477459	−	1.51644i
$225$	−2.97664	−	0.373684i	−0.198442	−	0.0249123i
$226$	4.93005	−	19.0567i	0.327942	−	1.26764i
$227$	−1.36032	−	5.07680i	−0.0902879	−	0.336959i	0.905975	−	0.423331i	$-0.139139\pi$
$227$	−1.36032	−	5.07680i	−0.0902879	−	0.336959i	−0.996263	+	0.0863720i	$0.972473\pi$
$228$	20.4644	+	13.0810i	1.35529	+	0.866310i
$229$	1.95726	−	7.30458i	0.129339	−	0.482700i	−0.870618	−	0.491960i	$-0.836281\pi$
$229$	1.95726	−	7.30458i	0.129339	−	0.482700i	0.999957	+	0.00925960i	$0.00294746\pi$
$230$	−0.707176	+	1.24969i	−0.0466298	+	0.0824023i
$231$	−13.8006	−	0.862870i	−0.908011	−	0.0567726i
$232$	−18.8668	−	10.2497i	−1.23867	−	0.672929i
$233$	−16.6831			−1.09295			−0.546475	−	0.837476i	$-0.684031\pi$
$233$	−16.6831			−1.09295			−0.546475	+	0.837476i	$0.684031\pi$
$234$	−10.7265	+	14.4116i	−0.701213	+	0.942119i
$235$	−3.64176	+	3.64176i	−0.237562	+	0.237562i
$236$	−18.4177	−	4.59522i	−1.19889	−	0.299123i
$237$	−1.27565	+	3.79540i	−0.0828624	+	0.246538i
$238$	−15.8063	+	4.38210i	−1.02457	+	0.284049i
$239$	−3.83961	−	6.65040i	−0.248364	−	0.430178i	0.714708	−	0.699423i	$-0.246559\pi$
$239$	−3.83961	−	6.65040i	−0.248364	−	0.430178i	−0.963072	+	0.269244i	$0.913226\pi$
$240$	0.192991	−	6.92551i	0.0124575	−	0.447040i
$241$	−3.10583	+	5.37945i	−0.200064	+	0.346521i	−0.948549	−	0.316631i	$-0.897448\pi$
$241$	−3.10583	+	5.37945i	−0.200064	+	0.346521i	0.748485	+	0.663152i	$0.230782\pi$
$242$	−2.62032	+	10.1286i	−0.168440	+	0.651093i
$243$	13.0901	+	8.46464i	0.839728	+	0.543007i
$244$	−25.0838	+	7.18827i	−1.60582	+	0.460182i
$245$	−2.76754	−	10.3286i	−0.176812	−	0.659871i
$246$	1.20928	−	22.4568i	0.0771006	−	1.43179i
$247$	14.8446	+	25.7116i	0.944541	+	1.63599i
$248$	6.26163	+	1.50489i	0.397614	+	0.0955607i
$249$	1.81096	−	0.899846i	0.114765	−	0.0570254i
$250$	1.41416	−	0.0122269i	0.0894394	−	0.000773299i
$251$	−8.64452	−	8.64452i	−0.545637	−	0.545637i	0.379539	−	0.925176i	$-0.376083\pi$
$251$	−8.64452	−	8.64452i	−0.545637	−	0.545637i	−0.925176	+	0.379539i	$0.876083\pi$
$252$	−25.0919	−	2.71020i	−1.58064	−	0.170727i
$253$	−1.36264	+	1.36264i	−0.0856682	+	0.0856682i
$254$	2.11452	+	2.07827i	0.132677	+	0.130402i
$255$	−4.76659	−	0.298027i	−0.298496	−	0.0186632i
$256$	15.9617	−	1.10579i	0.997609	−	0.0691117i
$257$	4.35695	−	2.51549i	0.271779	−	0.156912i	−0.357917	−	0.933753i	$-0.616513\pi$
$257$	4.35695	−	2.51549i	0.271779	−	0.156912i	0.629696	+	0.776842i	$0.283180\pi$
$258$	−7.44338	+	22.7968i	−0.463405	+	1.41927i
$259$	26.7582	−	7.16985i	1.66268	−	0.445513i
$260$	4.10702	−	7.40644i	0.254707	−	0.459328i
$261$	−17.9839	+	13.9721i	−1.11317	+	0.864853i
$262$	22.1854	−	13.0658i	1.37062	−	0.807207i
$263$	4.78625	+	2.76334i	0.295133	+	0.170395i	0.640254	−	0.768163i	$-0.278829\pi$
$263$	4.78625	+	2.76334i	0.295133	+	0.170395i	−0.345122	+	0.938558i	$0.612162\pi$
$264$	2.73268	−	8.88735i	0.168185	−	0.546979i
$265$	−3.07604	+	1.77595i	−0.188960	+	0.109096i
$266$	−20.5408	+	36.2988i	−1.25943	+	2.22562i
$267$	4.87228	+	24.1154i	0.298178	+	1.47584i
$268$	−15.4655	−	3.85865i	−0.944708	−	0.235704i
$269$	20.9916	+	20.9916i	1.27988	+	1.27988i	0.940734	+	0.339146i	$0.110138\pi$
$269$	20.9916	+	20.9916i	1.27988	+	1.27988i	0.339146	+	0.940734i	$0.389862\pi$
$270$	−6.64703	−	3.13321i	−0.404525	−	0.190681i
$271$			0.504804i			0.0306647i	0.999882	+	0.0153323i	$0.00488062\pi$
$271$			0.504804i			0.0306647i	−0.999882	+	0.0153323i	$0.995119\pi$
$272$	−0.381361	−	11.0229i	−0.0231234	−	0.668360i
$273$	−25.7025	−	17.0623i	−1.55559	−	1.03266i
$274$	−5.44987	−	19.6578i	−0.329239	−	1.18757i
$275$	1.83327	+	0.491224i	0.110550	+	0.0296219i
$276$	−2.59679	+	2.37227i	−0.156308	+	0.142794i
$277$	19.7120	−	5.28182i	1.18438	−	0.317354i	0.387718	−	0.921778i	$-0.373263\pi$
$277$	19.7120	−	5.28182i	1.18438	−	0.317354i	0.796663	+	0.604424i	$0.206597\pi$
$278$	−16.5157	+	9.72670i	−0.990546	+	0.583368i
$279$	4.12553	−	5.44397i	0.246989	−	0.325922i
$280$	11.8932	−	0.308550i	0.710756	−	0.0184394i
$281$	−3.60865	+	6.25036i	−0.215274	+	0.372865i	−0.953357	−	0.301844i	$-0.902398\pi$
$281$	−3.60865	+	6.25036i	−0.215274	+	0.372865i	0.738083	+	0.674710i	$0.235731\pi$
$282$	−11.2487	+	5.71113i	−0.669848	+	0.340093i
$283$	28.9980	+	7.76998i	1.72375	+	0.461878i	0.978728	−	0.205162i	$-0.0657721\pi$
$283$	28.9980	+	7.76998i	1.72375	+	0.461878i	0.745022	+	0.667040i	$0.232439\pi$
$284$	−11.6758	+	0.201915i	−0.692833	+	0.0119815i
$285$	−9.10621	+	8.03450i	−0.539405	+	0.475923i
$286$	7.96700	−	8.10596i	0.471098	−	0.479316i
$287$	38.6190			2.27961
$288$	5.71472	−	15.9794i	0.336743	−	0.941597i
$289$	9.39692			0.552760
$290$	7.52530	−	7.65657i	0.441901	−	0.449609i
$291$	18.7128	+	6.28945i	1.09696	+	0.368694i
$292$	11.5493	−	0.199727i	0.675871	−	0.0116881i
$293$	19.6084	+	5.25405i	1.14553	+	0.306945i	0.781174	−	0.624313i	$-0.214621\pi$
$293$	19.6084	+	5.25405i	1.14553	+	0.306945i	0.364360	+	0.931258i	$0.381288\pi$
$294$	1.40839	−	26.1544i	0.0821390	−	1.52536i
$295$	4.74559	−	8.21959i	0.276299	−	0.478563i
$296$	0.483102	+	18.6214i	0.0280797	+	1.08235i
$297$	−7.47300	−	6.43532i	−0.433627	−	0.373415i
$298$	−7.43691	+	4.37987i	−0.430809	+	0.253719i
$299$	−4.15293	+	1.11277i	−0.240170	+	0.0643533i
$300$	3.30219	+	1.04669i	0.190652	+	0.0604306i
$301$	−39.7777	−	10.6584i	−2.29275	−	0.614341i
$302$	3.99227	+	14.4002i	0.229729	+	0.828637i
$303$	3.26157	−	1.62064i	0.187372	−	0.0931033i
$304$	−20.5049	−	19.1335i	−1.17603	−	1.09738i
$305$		−	13.0467i		−	0.747052i
$306$	−10.8725	−	4.31791i	−0.621539	−	0.246839i
$307$	4.07236	+	4.07236i	0.232422	+	0.232422i	0.813703	−	0.581281i	$-0.197448\pi$
$307$	4.07236	+	4.07236i	0.232422	+	0.232422i	−0.581281	+	0.813703i	$0.697448\pi$
$308$	15.4917	+	3.86518i	0.882724	+	0.220239i
$309$	18.8206	−	16.6056i	1.07066	−	0.944658i
$310$	−1.58581	+	2.80239i	−0.0900682	+	0.159165i
$311$	1.61571	−	0.932831i	0.0916185	−	0.0528960i	−0.453491	−	0.891261i	$-0.649821\pi$
$311$	1.61571	−	0.932831i	0.0916185	−	0.0528960i	0.545109	+	0.838365i	$0.316488\pi$
$312$	15.1942	−	14.1235i	0.860203	−	0.799585i
$313$	−3.71256	−	2.14345i	−0.209846	−	0.121155i	0.391394	−	0.920223i	$-0.371993\pi$
$313$	−3.71256	−	2.14345i	−0.209846	−	0.121155i	−0.601240	+	0.799069i	$0.705326\pi$
$314$	−27.7803	+	16.3608i	−1.56773	+	0.923294i
$315$	4.75885	−	11.6872i	0.268131	−	0.658498i
$316$	2.24216	−	4.04342i	0.126131	−	0.227460i
$317$	17.4370	−	4.67223i	0.979359	−	0.262419i	0.266585	−	0.963812i	$-0.414105\pi$
$317$	17.4370	−	4.67223i	0.979359	−	0.262419i	0.712775	+	0.701393i	$0.247438\pi$
$318$	−8.51282	+	1.79667i	−0.477375	+	0.100752i
$319$	12.4774	−	7.20385i	0.698602	−	0.403338i
$320$	−1.66709	+	7.82437i	−0.0931930	+	0.437396i
$321$	−10.1157	+	15.2382i	−0.564601	+	0.850511i
$322$	−4.30759	−	4.23374i	−0.240053	−	0.235937i
$323$	−13.6704	+	13.6704i	−0.760639	+	0.760639i
$324$	−13.0956	−	12.3493i	−0.727532	−	0.686074i
$325$	2.99422	+	2.99422i	0.166090	+	0.166090i
$326$	10.4878	−	0.0906782i	0.580865	−	0.00502220i
$327$	−15.4040	−	10.2257i	−0.851841	−	0.565484i
$328$	−6.06833	+	25.2494i	−0.335067	+	1.39417i
$329$	−10.8317	−	18.7611i	−0.597171	−	1.03433i
$330$	3.89533	+	2.53762i	0.214431	+	0.139692i
$331$	2.69866	+	10.0716i	0.148332	+	0.553583i	0.999584	+	0.0288261i	$0.00917692\pi$
$331$	2.69866	+	10.0716i	0.148332	+	0.553583i	−0.851252	+	0.524756i	$0.824156\pi$
$332$	−2.24468	+	0.643260i	−0.123193	+	0.0353035i
$333$	18.2988	+	7.45100i	1.00277	+	0.408312i
$334$	5.60221	−	21.6549i	0.306539	−	1.18490i
$335$	3.98491	−	6.90207i	0.217719	−	0.377100i
$336$	27.9281	+	8.32373i	1.52360	+	0.454096i
$337$	0.327747	+	0.567675i	0.0178535	+	0.0309232i	0.874814	−	0.484459i	$-0.160983\pi$
$337$	0.327747	+	0.567675i	0.0178535	+	0.0309232i	−0.856961	+	0.515382i	$0.827650\pi$
$338$	6.71964	−	1.86294i	0.365500	−	0.101330i
$339$	15.9500	+	18.0775i	0.866283	+	0.981835i
$340$	5.35071	+	1.33500i	0.290183	+	0.0724005i
$341$	−3.05566	+	3.05566i	−0.165473	+	0.165473i
$342$	−27.3124	+	11.7852i	−1.47689	+	0.637268i
$343$	15.5337			0.838743
$344$	13.2190	−	24.3322i	0.712719	−	1.31191i
$345$	−0.782557	−	1.57491i	−0.0421315	−	0.0847905i
$346$	−1.10694	+	1.95614i	−0.0595094	+	0.105163i
$347$	−4.53119	+	16.9106i	−0.243247	+	0.907810i	0.731010	+	0.682367i	$0.239049\pi$
$347$	−4.53119	+	16.9106i	−0.243247	+	0.907810i	−0.974256	+	0.225443i	$0.927617\pi$
$348$	23.3439	−	12.1071i	1.25137	−	0.649007i
$349$	1.71036	+	6.38315i	0.0915535	+	0.341682i	0.996474	−	0.0838975i	$-0.0267368\pi$
$349$	1.71036	+	6.38315i	0.0915535	+	0.341682i	−0.904921	+	0.425580i	$0.860070\pi$
$350$	−1.48988	+	5.75901i	−0.0796373	+	0.307832i
$351$	−7.26027	−	20.7706i	−0.387525	−	1.10865i
$352$	−4.96136	+	9.52129i	−0.264441	+	0.507486i
$353$	2.01594	+	1.16390i	0.107298	+	0.0619484i	0.552689	−	0.833388i	$-0.313602\pi$
$353$	2.01594	+	1.16390i	0.107298	+	0.0619484i	−0.445391	+	0.895336i	$0.646935\pi$
$354$	17.2994	−	15.5315i	0.919451	−	0.825487i
$355$	1.51119	−	5.63984i	0.0802056	−	0.299331i
$356$	−0.491210	−	28.4045i	−0.0260341	−	1.50543i
$357$	6.40013	−	19.0421i	0.338731	−	1.00781i
$358$	0.00239138	+	0.276586i	0.000126388	+	0.0146180i
$359$		−	9.35966i		−	0.493984i	−0.969018	−	0.246992i	$-0.920558\pi$
$359$		−	9.35966i		−	0.493984i	0.969018	−	0.246992i	$-0.0794421\pi$
$360$	6.89341	+	4.94782i	0.363314	+	0.260773i
$361$			30.1587i			1.58730i
$362$	−13.4326	+	0.116139i	−0.706004	+	0.00610415i
$363$	−8.47738	−	9.60817i	−0.444947	−	0.504298i
$364$	25.6210	+	24.7499i	1.34290	+	1.29725i
$365$	−1.49481	+	5.57871i	−0.0782420	+	0.292003i
$366$	9.91917	−	30.3794i	0.518483	−	1.58796i
$367$	3.49748	+	2.01927i	0.182567	+	0.105405i	0.588498	−	0.808499i	$-0.299719\pi$
$367$	3.49748	+	2.01927i	0.182567	+	0.105405i	−0.405931	+	0.913904i	$0.633053\pi$
$368$	3.44492	−	2.15108i	0.179579	−	0.112133i
$369$	21.9523	+	16.6358i	1.14279	+	0.866026i
$370$	−9.01697	−	2.33273i	−0.468770	−	0.121273i
$371$	−3.86686	−	14.4313i	−0.200757	−	0.749236i
$372$	−5.82319	+	5.31973i	−0.301918	+	0.275815i
$373$	5.39710	−	20.1423i	0.279451	−	1.04293i	−0.673348	−	0.739326i	$-0.735144\pi$
$373$	5.39710	−	20.1423i	0.279451	−	1.04293i	0.952799	−	0.303601i	$-0.0981890\pi$
$374$	6.44124	+	3.64497i	0.333069	+	0.188477i
$375$	−0.957941	+	1.44303i	−0.0494679	+	0.0745180i
$376$	13.9682	−	4.13388i	0.720354	−	0.213189i
$377$	32.1448			1.65554
$378$	19.9666	−	23.5957i	1.02697	−	1.21363i
$379$	0.319749	−	0.319749i	0.0164244	−	0.0164244i	−0.698847	−	0.715271i	$-0.746303\pi$
$379$	0.319749	−	0.319749i	0.0164244	−	0.0164244i	0.715271	+	0.698847i	$0.246303\pi$
$380$	12.0209	−	7.22026i	0.616661	−	0.370391i
$381$	−3.55928	+	0.719117i	−0.182347	+	0.0368415i
$382$	3.78948	+	13.6687i	0.193887	+	0.699353i
$383$	−8.85928	−	15.3447i	−0.452688	−	0.784079i	0.545864	−	0.837874i	$-0.316202\pi$
$383$	−8.85928	−	15.3447i	−0.452688	−	0.784079i	−0.998552	+	0.0537949i	$0.982868\pi$
$384$	−9.83056	+	16.9517i	−0.501664	+	0.865063i
$385$	−3.99166	+	6.91376i	−0.203434	+	0.352358i
$386$	30.2405	+	7.82333i	1.53920	+	0.398197i
$387$	−18.0197	−	23.1935i	−0.915991	−	1.17899i
$388$	−19.9356	−	11.0547i	−1.01208	−	0.561218i
$389$	−6.93326	−	25.8753i	−0.351530	−	1.31193i	−0.884795	−	0.465981i	$-0.845702\pi$
$389$	−6.93326	−	25.8753i	−0.351530	−	1.31193i	0.533265	−	0.845948i	$-0.320965\pi$
$390$	4.69563	+	9.24853i	0.237773	+	0.468318i
$391$	−1.39983	−	2.42458i	−0.0707926	−	0.122616i
$392$	−7.06752	+	29.4069i	−0.356963	+	1.48527i
$393$	−1.96776	+	31.4720i	−0.0992605	+	1.58755i
$394$	0.176930	+	20.4636i	0.00891360	+	1.03094i
$395$	1.63464	+	1.63464i	0.0822479	+	0.0822479i
$396$	7.14102	+	8.87044i	0.358850	+	0.445756i
$397$	−5.44832	+	5.44832i	−0.273443	+	0.273443i	−0.830485	−	0.557041i	$-0.811937\pi$
$397$	−5.44832	+	5.44832i	−0.273443	+	0.273443i	0.557041	+	0.830485i	$0.311937\pi$
$398$	−1.99738	+	2.03222i	−0.100120	+	0.101866i
$399$	−22.7303	−	45.7452i	−1.13794	−	2.29013i
$400$	−3.53118	−	1.87903i	−0.176559	−	0.0939514i
$401$	21.8322	−	12.6048i	1.09025	−	0.629454i	0.156604	−	0.987661i	$-0.449945\pi$
$401$	21.8322	−	12.6048i	1.09025	−	0.629454i	0.933642	+	0.358208i	$0.116612\pi$
$402$	14.5264	−	13.0419i	0.724512	−	0.650471i
$403$	−9.31278	+	2.49535i	−0.463902	+	0.124302i
$404$	−4.04272	+	1.15852i	−0.201133	+	0.0576387i
$405$	7.73954	−	4.59342i	0.384581	−	0.228249i
$406$	22.9159	+	38.9106i	1.13730	+	1.93110i
$407$	−10.8250	−	6.24980i	−0.536574	−	0.309791i
$408$	11.4442	+	7.17661i	0.566573	+	0.355295i
$409$	22.9927	−	13.2748i	1.13691	−	0.656398i	0.191250	−	0.981541i	$-0.438746\pi$
$409$	22.9927	−	13.2748i	1.13691	−	0.656398i	0.945665	+	0.325143i	$0.105413\pi$
$410$	−11.3004	−	6.39464i	−0.558085	−	0.315809i
$411$	23.6820	+	7.95962i	1.16815	+	0.392619i
$412$	−24.8447	+	14.9227i	−1.22401	+	0.735190i
$413$	28.2296	+	28.2296i	1.38909	+	1.38909i
$414$	−0.624818	−	4.26217i	−0.0307081	−	0.209474i
$415$		−	1.16752i		−	0.0573112i
$416$	−20.2076	+	12.8622i	−0.990759	+	0.630621i
$417$	1.46488	−	23.4290i	0.0717356	−	1.14732i
$418$	18.1350	−	5.02772i	0.887014	−	0.245914i
$419$	−13.3045	−	3.56493i	−0.649967	−	0.174158i	−0.0812528	−	0.996694i	$-0.525892\pi$
$419$	−13.3045	−	3.56493i	−0.649967	−	0.174158i	−0.568714	+	0.822536i	$0.692559\pi$
$420$	−7.84767	+	12.2772i	−0.382927	+	0.599066i
$421$	−13.5649	+	3.63471i	−0.661114	+	0.177145i	−0.573749	−	0.819031i	$-0.694511\pi$
$421$	−13.5649	+	3.63471i	−0.661114	+	0.177145i	−0.0873652	+	0.996176i	$0.527845\pi$
$422$	−8.74683	−	14.8519i	−0.425789	−	0.722980i
$423$	1.92456	−	15.3304i	0.0935753	−	0.745388i
$424$	10.0429	−	0.260547i	0.487728	−	0.0126533i
$425$	−1.37868	+	2.38795i	−0.0668760	+	0.115833i
$426$	7.80669	−	11.9835i	0.378235	−	0.580603i
$427$	53.0084	+	14.2036i	2.56526	+	0.687359i
$428$	14.6734	−	15.1898i	0.709264	−	0.734227i
$429$	2.75672	+	13.6444i	0.133096	+	0.658759i
$430$	9.87457	+	9.70529i	0.476194	+	0.468030i
$431$	−15.3658			−0.740147			−0.370073	−	0.929003i	$-0.620667\pi$
$431$	−15.3658			−0.740147			−0.370073	+	0.929003i	$0.620667\pi$
$432$	12.2897	+	16.7620i	0.591286	+	0.806462i
$433$	19.2101			0.923179			0.461589	−	0.887094i	$-0.347279\pi$
$433$	19.2101			0.923179			0.461589	+	0.887094i	$0.347279\pi$
$434$	−9.65961	−	9.49400i	−0.463676	−	0.455727i
$435$	2.60389	+	12.8880i	0.124847	+	0.617931i
$436$	15.3551	+	14.8330i	0.735375	+	0.710373i
$437$	−6.87631	−	1.84250i	−0.328939	−	0.0881388i
$438$	−7.72208	+	11.8536i	−0.368975	+	0.566388i
$439$	−12.6002	+	21.8242i	−0.601374	+	1.04161i	0.391239	+	0.920289i	$0.372047\pi$
$439$	−12.6002	+	21.8242i	−0.601374	+	1.04161i	−0.992613	+	0.121322i	$0.961287\pi$
$440$	−3.89305	−	3.69616i	−0.185594	−	0.176208i
$441$	25.5669	+	19.3750i	1.21747	+	0.922619i
$442$	8.37950	+	14.2282i	0.398572	+	0.676766i
$443$	−34.3842	+	9.21322i	−1.63364	+	0.437733i	−0.954969	−	0.296707i	$-0.904112\pi$
$443$	−34.3842	+	9.21322i	−1.63364	+	0.437733i	−0.678674	+	0.734440i	$0.737445\pi$
$444$	−19.2226	−	12.2872i	−0.912265	−	0.583125i
$445$	13.7204	+	3.67636i	0.650407	+	0.174276i
$446$	−11.3528	+	3.14742i	−0.537570	+	0.149035i
$447$	0.659627	−	10.5499i	0.0311993	−	0.498995i
$448$	−29.9753	−	15.2915i	−1.41620	−	0.722455i
$449$			0.713073i			0.0336520i	0.999858	+	0.0168260i	$0.00535614\pi$
$449$			0.713073i			0.0336520i	−0.999858	+	0.0168260i	$0.994644\pi$
$450$	−3.32769	+	2.63182i	−0.156869	+	0.124065i
$451$	−12.3216	−	12.3216i	−0.580204	−	0.580204i
$452$	−14.3335	−	23.8638i	−0.674193	−	1.12246i
$453$	−17.3481	−	5.83077i	−0.815085	−	0.273954i
$454$	−6.46902	−	3.66068i	−0.303606	−	0.171804i
$455$	−15.4252	+	8.90573i	−0.723143	+	0.417507i
$456$	33.4803	−	7.67318i	1.56786	−	0.359330i
$457$	−30.2390	−	17.4585i	−1.41452	−	0.816673i	−0.418709	−	0.908121i	$-0.637517\pi$
$457$	−30.2390	−	17.4585i	−1.41452	−	0.816673i	−0.995810	+	0.0914479i	$0.970850\pi$
$458$	−5.42720	−	9.21525i	−0.253596	−	0.430600i
$459$	11.8408	−	8.06719i	0.552679	−	0.376544i
$460$	0.559416	+	1.95211i	0.0260829	+	0.0910174i
$461$	−12.2932	+	3.29396i	−0.572552	+	0.153415i	−0.533467	−	0.845821i	$-0.679111\pi$
$461$	−12.2932	+	3.29396i	−0.572552	+	0.153415i	−0.0390853	+	0.999236i	$0.512444\pi$
$462$	−14.5510	+	13.0640i	−0.676975	+	0.607792i
$463$	−9.47765	+	5.47192i	−0.440464	+	0.254302i	−0.703794	−	0.710404i	$-0.748512\pi$
$463$	−9.47765	+	5.47192i	−0.440464	+	0.254302i	0.263331	+	0.964706i	$0.415179\pi$
$464$	−29.0409	+	8.86845i	−1.34819	+	0.411707i
$465$	−1.75485	−	3.53168i	−0.0813794	−	0.163778i
$466$	−16.5383	+	16.8268i	−0.766121	+	0.779485i
$467$	−21.4998	+	21.4998i	−0.994893	+	0.994893i	−0.999987	−	0.00509444i	$-0.998378\pi$
$467$	−21.4998	+	21.4998i	−0.994893	+	0.994893i	0.00509444	+	0.999987i	$0.498378\pi$
$468$	3.90235	+	25.1053i	0.180386	+	1.16049i
$469$	23.7047	+	23.7047i	1.09458	+	1.09458i
$470$	0.0629715	+	7.28325i	0.00290466	+	0.335951i
$471$	2.46401	−	39.4089i	0.113535	−	1.81586i
$472$	−22.8926	+	14.0210i	−1.05372	+	0.645367i
$473$	9.29071	+	16.0920i	0.427187	+	0.739910i
$474$	2.56350	+	5.04908i	0.117745	+	0.231912i
$475$	1.81467	+	6.77242i	0.0832625	+	0.310740i
$476$	−11.2492	+	20.2864i	−0.515608	+	0.929827i
$477$	4.01849	−	9.86894i	0.183994	−	0.451868i
$478$	−10.5139	−	2.71999i	−0.480895	−	0.124409i
$479$	−10.2628	+	17.7756i	−0.468918	+	0.812190i	−0.999369	−	0.0355260i	$-0.988689\pi$
$479$	−10.2628	+	17.7756i	−0.468918	+	0.812190i	0.530451	+	0.847716i	$0.322023\pi$
$480$	−6.79382	−	7.06003i	−0.310094	−	0.322245i
$481$	−13.9438	−	24.1514i	−0.635784	−	1.10121i
$482$	2.34690	+	8.46531i	0.106898	+	0.385584i
$483$	7.25078	−	1.46495i	0.329922	−	0.0666575i
$484$	7.61826	+	12.6836i	0.346285	+	0.576525i
$485$	8.05943	−	8.05943i	0.365960	−	0.365960i
$486$	21.5139	−	4.81161i	0.975891	−	0.218259i
$487$	−28.7442			−1.30252			−0.651261	−	0.758854i	$-0.725760\pi$
$487$	−28.7442			−1.30252			−0.651261	+	0.758854i	$0.725760\pi$
$488$	−17.6158	+	32.4255i	−0.797430	+	1.46784i
$489$	−7.10435	+	10.7019i	−0.321270	+	0.483958i
$490$	−13.1610	−	7.44756i	−0.594555	−	0.336447i
$491$	7.47527	−	27.8981i	0.337354	−	1.25902i	−0.563940	−	0.825816i	$-0.690715\pi$
$491$	7.47527	−	27.8981i	0.337354	−	1.25902i	0.901294	−	0.433208i	$-0.142618\pi$
$492$	−21.4513	−	23.4815i	−0.967100	−	1.05863i
$493$	5.41754	+	20.2186i	0.243994	+	0.910598i
$494$	40.6487	+	10.5160i	1.82887	+	0.473136i
$495$	−5.24721	+	2.21053i	−0.235845	+	0.0993559i
$496$	7.72511	−	4.82371i	0.346868	−	0.216591i
$497$	21.2693	+	12.2799i	0.954060	+	0.550827i
$498$	0.887642	−	2.71858i	0.0397762	−	0.121823i
$499$	−5.68327	+	21.2103i	−0.254418	+	0.949502i	0.713995	+	0.700151i	$0.246884\pi$
$499$	−5.68327	+	21.2103i	−0.254418	+	0.949502i	−0.968413	+	0.249351i	$0.919783\pi$
$500$	1.38955	−	1.43846i	0.0621425	−	0.0643297i
$501$	18.1246	+	20.5422i	0.809745	+	0.917756i
$502$	−17.2884	+	0.149477i	−0.771619	+	0.00667146i
$503$		−	38.9793i		−	1.73800i	−0.494810	−	0.869001i	$-0.664762\pi$
$503$		−	38.9793i		−	1.73800i	0.494810	−	0.869001i	$-0.335238\pi$
$504$	−27.6075	+	22.6212i	−1.22974	+	1.00763i
$505$		−	2.10272i		−	0.0935699i
$506$	0.0235620	+	2.72517i	0.00104746	+	0.121149i
$507$	−2.72085	+	8.09525i	−0.120837	+	0.359523i
$508$	4.19232	−	0.0724995i	0.186004	−	0.00321665i
$509$	−0.00437675	+	0.0163342i	−0.000193996	+	0.000724002i	−0.966023	−	0.258457i	$-0.916786\pi$
$509$	−0.00437675	+	0.0163342i	−0.000193996	+	0.000724002i	0.965829	+	0.259181i	$0.0834526\pi$
$510$	−5.02580	+	4.51219i	−0.222546	+	0.199803i
$511$	−21.0388	−	12.1468i	−0.930702	−	0.537341i
$512$	14.7078	−	17.1953i	0.650001	−	0.759934i
$513$	6.78490	−	35.7946i	0.299561	−	1.58037i
$514$	1.78198	−	6.88810i	0.0785996	−	0.303821i
$515$	−3.75052	−	13.9971i	−0.165268	−	0.616788i
$516$	15.6143	+	30.1063i	0.687382	+	1.32536i
$517$	−2.52992	+	9.44177i	−0.111266	+	0.415249i
$518$	19.2943	−	34.0962i	0.847744	−	1.49810i
$519$	−1.22493	−	2.46520i	−0.0537686	−	0.108210i
$520$	−3.39884	−	11.4845i	−0.149049	−	0.503629i
$521$	3.42960			0.150254			0.0751268	−	0.997174i	$-0.476064\pi$
$521$	3.42960			0.150254			0.0751268	+	0.997174i	$0.476064\pi$
$522$	−3.73530	+	31.9895i	−0.163489	+	1.40014i
$523$	−18.3365	+	18.3365i	−0.801801	+	0.801801i	−0.983377	−	0.181576i	$-0.941880\pi$
$523$	−18.3365	+	18.3365i	−0.801801	+	0.801801i	0.181576	+	0.983377i	$0.441880\pi$
$524$	8.81450	−	35.3287i	0.385063	−	1.54334i
$525$	−4.82013	−	5.46308i	−0.210368	−	0.238428i
$526$	7.53182	−	2.08810i	0.328403	−	0.0910456i
$527$	−3.13907	−	5.43703i	−0.136740	−	0.236841i
$528$	−6.25490	−	11.5664i	−0.272210	−	0.503362i
$529$	−10.9845	+	19.0258i	−0.477589	+	0.827208i
$530$	−1.25809	+	4.86305i	−0.0546479	+	0.211237i
$531$	3.88624	+	28.2071i	0.168649	+	1.22408i
$532$	16.2489	+	56.7012i	0.704479	+	2.45831i
$533$	−10.0623	−	37.5529i	−0.435845	−	1.62660i
$534$	29.1529	+	18.9918i	1.26157	+	0.821854i
$535$	5.27990	+	9.14505i	0.228270	+	0.395375i
$536$	−19.2231	+	11.7735i	−0.830312	+	0.508539i
$537$	−0.282233	−	0.187357i	−0.0121792	−	0.00808504i
$538$	41.9816	−	0.362976i	1.80996	−	0.0156490i
$539$	−14.3505	−	14.3505i	−0.618119	−	0.618119i
$540$	−9.74949	+	3.59825i	−0.419551	+	0.154844i
$541$	25.0807	−	25.0807i	1.07830	−	1.07830i	0.0816419	−	0.996662i	$-0.473984\pi$
$541$	25.0807	−	25.0807i	1.07830	−	1.07830i	0.996662	−	0.0816419i	$-0.0260164\pi$
$542$	0.509150	+	0.500421i	0.0218698	+	0.0214949i
$543$	9.09916	−	13.7069i	0.390482	−	0.588219i
$544$	−11.4958	−	10.5425i	−0.492879	−	0.452007i
$545$	−9.24456	+	5.33735i	−0.395994	+	0.228627i
$546$	−42.6886	+	9.00963i	−1.82690	+	0.385577i
$547$	44.5703	−	11.9426i	1.90569	−	0.510628i	0.910393	−	0.413744i	$-0.135779\pi$
$547$	44.5703	−	11.9426i	1.90569	−	0.510628i	0.995296	−	0.0968841i	$-0.0308876\pi$
$548$	−25.2295	−	13.9903i	−1.07775	−	0.597635i
$549$	24.0133	+	30.9081i	1.02486	+	1.31913i
$550$	2.31281	−	1.36210i	0.0986184	−	0.0580799i
$551$	46.0938	+	26.6123i	1.96366	+	1.13372i
$552$	−0.181542	+	4.97082i	−0.00772695	+	0.211572i
$553$	−8.42111	+	4.86193i	−0.358102	+	0.206750i
$554$	14.2136	−	25.1177i	0.603877	−	1.06715i
$555$	8.55363	−	7.54695i	0.363081	−	0.320350i
$556$	−6.56187	+	26.3001i	−0.278285	+	1.11537i
$557$	−9.63503	−	9.63503i	−0.408249	−	0.408249i	0.472879	−	0.881128i	$-0.343215\pi$
$557$	−9.63503	−	9.63503i	−0.408249	−	0.408249i	−0.881128	+	0.472879i	$0.843215\pi$
$558$	−1.40113	−	9.55775i	−0.0593145	−	0.404612i
$559$			41.4567i			1.75343i
$560$	11.4787	−	12.3015i	0.485065	−	0.519832i
$561$	−8.11751	+	4.03350i	−0.342722	+	0.170295i
$562$	2.72685	+	9.83580i	0.115025	+	0.414898i
$563$	−35.3625	−	9.47535i	−1.49035	−	0.399339i	−0.580496	−	0.814263i	$-0.697141\pi$
$563$	−35.3625	−	9.47535i	−1.49035	−	0.399339i	−0.909856	+	0.414925i	$0.863808\pi$
$564$	−5.39069	+	17.0070i	−0.226989	+	0.716125i
$565$	13.4445	−	3.60244i	0.565615	−	0.151556i
$566$	36.5830	−	21.5451i	1.53770	−	0.905607i
$567$	10.2371	+	36.4463i	0.429919	+	1.53060i
$568$	−11.3708	+	11.9765i	−0.477108	+	0.502523i
$569$	−1.64625	+	2.85139i	−0.0690144	+	0.119536i	−0.898468	−	0.439040i	$-0.855319\pi$
$569$	−1.64625	+	2.85139i	−0.0690144	+	0.119536i	0.829453	+	0.558576i	$0.188652\pi$
$570$	−0.923475	+	17.1493i	−0.0386801	+	0.718306i
$571$	−31.9411	−	8.55858i	−1.33669	−	0.358166i	−0.481486	−	0.876454i	$-0.659903\pi$
$571$	−31.9411	−	8.55858i	−1.33669	−	0.358166i	−0.855206	+	0.518288i	$0.826569\pi$
$572$	−0.277925	−	16.0712i	−0.0116206	−	0.671969i
$573$	−16.4669	−	5.53460i	−0.687916	−	0.231211i
$574$	38.2837	−	38.9514i	1.59793	−	1.62580i
$575$	−1.01534			−0.0423426
$576$	−10.4519	−	21.6046i	−0.435495	−	0.900191i
$577$	−9.27040			−0.385932			−0.192966	−	0.981205i	$-0.561811\pi$
$577$	−9.27040			−0.385932			−0.192966	+	0.981205i	$0.561811\pi$
$578$	9.31533	−	9.47781i	0.387467	−	0.394225i
$579$	−28.6866	+	25.3104i	−1.19217	+	1.05187i
$580$	−0.262517	−	15.1802i	−0.0109004	−	0.630322i
$581$	4.74360	+	1.27104i	0.196798	+	0.0527317i
$582$	24.8939	−	12.6391i	1.03189	−	0.523906i
$583$	−3.37066	+	5.83815i	−0.139598	+	0.241791i
$584$	11.2476	−	11.8467i	0.465427	−	0.490220i
$585$	−12.6045	−	1.58235i	−0.521131	−	0.0654223i
$586$	24.7374	−	14.5688i	1.02189	−	0.601830i
$587$	−18.5456	+	4.96929i	−0.765460	+	0.205104i	−0.620365	−	0.784313i	$-0.713015\pi$
$587$	−18.5456	+	4.96929i	−0.765460	+	0.205104i	−0.145095	+	0.989418i	$0.546349\pi$
$588$	−24.9834	−	27.3478i	−1.03030	−	1.12781i
$589$	−15.4199	−	4.13174i	−0.635364	−	0.170245i
$590$	−3.58597	−	12.9347i	−0.147632	−	0.532512i
$591$	−20.8815	−	13.8619i	−0.858948	−	0.570202i
$592$	19.2606	+	17.9724i	0.791606	+	0.738663i
$593$			27.8224i			1.14253i	0.820766	+	0.571264i	$0.193547\pi$
$593$			27.8224i			1.14253i	−0.820766	+	0.571264i	$0.806453\pi$
$594$	−13.8988	+	1.15789i	−0.570276	+	0.0475088i
$595$	−8.20125	−	8.20125i	−0.336218	−	0.336218i
$596$	−2.95477	+	11.8428i	−0.121032	+	0.485099i
$597$	−0.691128	−	3.42075i	−0.0282860	−	0.140002i
$598$	−2.99451	+	5.29179i	−0.122455	+	0.216397i
$599$	7.37573	−	4.25838i	0.301364	−	0.173993i	−0.341691	−	0.939812i	$-0.611000\pi$
$599$	7.37573	−	4.25838i	0.301364	−	0.173993i	0.643056	+	0.765819i	$0.277666\pi$
$600$	4.32921	−	2.29301i	0.176739	−	0.0936119i
$601$	7.13746	+	4.12082i	0.291143	+	0.168092i	0.638457	−	0.769657i	$-0.279573\pi$
$601$	7.13746	+	4.12082i	0.291143	+	0.168092i	−0.347314	+	0.937749i	$0.612906\pi$
$602$	−50.1825	+	29.5543i	−2.04529	+	1.20454i
$603$	3.26331	+	23.6857i	0.132892	+	0.964557i
$604$	18.4817	+	10.2485i	0.752011	+	0.417005i
$605$	−7.14574	+	1.91469i	−0.290516	+	0.0778434i
$606$	1.59866	−	4.89622i	0.0649411	−	0.198895i
$607$	−8.90944	+	5.14387i	−0.361623	+	0.208783i	−0.669793	−	0.742548i	$-0.733617\pi$
$607$	−8.90944	+	5.14387i	−0.361623	+	0.208783i	0.308169	+	0.951331i	$0.400284\pi$
$608$	−39.6250	+	1.71403i	−1.60701	+	0.0695130i
$609$	−55.1983	−	3.45123i	−2.23675	−	0.139851i
$610$	−13.1590	−	12.9334i	−0.532793	−	0.523659i
$611$	−15.4209	+	15.4209i	−0.623864	+	0.623864i
$612$	−15.1332	+	6.68566i	−0.611722	+	0.270252i
$613$	30.5036	+	30.5036i	1.23203	+	1.23203i	0.963184	+	0.268844i	$0.0866417\pi$
$613$	30.5036	+	30.5036i	1.23203	+	1.23203i	0.268844	+	0.963184i	$0.413358\pi$
$614$	8.14442	−	0.0704172i	0.328682	−	0.00284181i
$615$	14.2412	−	7.07628i	0.574259	−	0.285343i
$616$	19.2557	−	11.7935i	0.775833	−	0.475173i
$617$	2.02649	+	3.50999i	0.0815836	+	0.141307i	0.903930	−	0.427680i	$-0.140669\pi$
$617$	2.02649	+	3.50999i	0.0815836	+	0.141307i	−0.822347	+	0.568987i	$0.807336\pi$
$618$	1.90862	−	35.4440i	0.0767761	−	1.42577i
$619$	−8.26476	−	30.8445i	−0.332189	−	1.23975i	−0.906885	−	0.421379i	$-0.861546\pi$
$619$	−8.26476	−	30.8445i	−0.332189	−	1.23975i	0.574696	−	0.818367i	$-0.305120\pi$
$620$	1.25447	+	4.37752i	0.0503807	+	0.175805i
$621$	4.75263	+	2.29068i	0.190717	+	0.0919216i
$622$	0.660820	−	2.55435i	0.0264965	−	0.102420i
$623$	−29.8739	+	51.7431i	−1.19687	+	2.07304i
$624$	0.817216	−	29.3259i	0.0327148	−	1.17397i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−5.84222	+	1.61968i	−0.233502	+	0.0647355i
$627$	−7.34306	+	21.8476i	−0.293254	+	0.872508i
$628$	−11.0374	+	44.2382i	−0.440440	+	1.76530i
$629$	12.8408	−	12.8408i	0.511997	−	0.511997i
$630$	−7.07026	−	16.3855i	−0.281686	−	0.652814i
$631$	6.13581			0.244263			0.122131	−	0.992514i	$-0.461027\pi$
$631$	6.13581			0.244263			0.122131	+	0.992514i	$0.461027\pi$
$632$	−1.85554	−	6.26977i	−0.0738093	−	0.249398i
$633$	21.0688	+	1.31731i	0.837410	+	0.0523584i
$634$	12.5731	−	22.2188i	0.499343	−	0.882420i
$635$	−0.542607	+	2.02504i	−0.0215327	+	0.0803611i
$636$	−6.62676	+	10.3672i	−0.262768	+	0.411085i
$637$	−11.7191	−	43.7362i	−0.464327	−	1.73289i
$638$	5.10323	−	19.7261i	0.202039	−	0.780966i
$639$	6.80042	+	16.1424i	0.269021	+	0.638584i
$640$	6.23912	+	9.43787i	0.246623	+	0.373065i
$641$	9.62873	+	5.55915i	0.380312	+	0.219573i	0.677954	−	0.735104i	$-0.262867\pi$
$641$	9.62873	+	5.55915i	0.380312	+	0.219573i	−0.297642	+	0.954678i	$0.596200\pi$
$642$	5.34150	+	25.3086i	0.210812	+	0.998850i
$643$	2.14451	−	8.00343i	0.0845713	−	0.315624i	−0.910661	−	0.413154i	$-0.864427\pi$
$643$	2.14451	−	8.00343i	0.0845713	−	0.315624i	0.995233	+	0.0975292i	$0.0310939\pi$
$644$	−8.54037	+	0.147692i	−0.336538	+	0.00581989i
$645$	−16.6214	+	3.35820i	−0.654468	+	0.132229i
$646$	0.236381	+	27.3397i	0.00930028	+	1.07567i
$647$		−	26.9071i		−	1.05783i	−0.848675	−	0.528915i	$-0.822599\pi$
$647$		−	26.9071i		−	1.05783i	0.848675	−	0.528915i	$-0.177401\pi$
$648$	−25.4375	+	0.966205i	−0.999279	+	0.0379561i
$649$		−	18.0137i		−	0.707100i
$650$	5.98822	−	0.0517745i	0.234877	−	0.00203076i
$651$	16.2596	−	3.28509i	0.637264	−	0.128753i
$652$	10.3053	−	10.6680i	0.403586	−	0.417790i
$653$	−8.28987	+	30.9382i	−0.324408	+	1.21071i	0.590498	+	0.807039i	$0.298931\pi$
$653$	−8.28987	+	30.9382i	−0.324408	+	1.21071i	−0.914906	+	0.403667i	$0.867735\pi$
$654$	−25.5840	+	5.39962i	−1.00041	+	0.211142i
$655$	15.7667	+	9.10293i	0.616057	+	0.355681i
$656$	19.4512	+	31.1508i	0.759440	+	1.21623i
$657$	−6.72672	−	15.9675i	−0.262434	−	0.622950i
$658$	−29.6602	−	7.67321i	−1.15628	−	0.299133i
$659$	−10.6609	−	39.7870i	−0.415289	−	1.54988i	−0.784256	−	0.620437i	$-0.786955\pi$
$659$	−10.6609	−	39.7870i	−0.415289	−	1.54988i	0.368967	−	0.929443i	$-0.379712\pi$
$660$	6.42097	−	1.41327i	0.249936	−	0.0550116i
$661$	1.81787	−	6.78437i	0.0707068	−	0.263881i	−0.921519	−	0.388334i	$-0.873051\pi$
$661$	1.81787	−	6.78437i	0.0707068	−	0.263881i	0.992226	+	0.124452i	$0.0397174\pi$
$662$	12.8335	+	7.26220i	0.498787	+	0.282254i
$663$	−20.1840	−	1.26199i	−0.783881	−	0.0490116i
$664$	−1.57640	+	2.90168i	−0.0611760	+	0.112607i
$665$	−29.4918			−1.14364
$666$	25.6550	−	11.0700i	0.994113	−	0.428954i
$667$	−5.45014	+	5.45014i	−0.211030	+	0.211030i
$668$	−16.2878	−	27.1173i	−0.630192	−	1.04920i
$669$	4.59685	−	13.6769i	0.177725	−	0.528778i
$670$	−3.01117	−	10.8614i	−0.116332	−	0.419611i
$671$	−12.3810	−	21.4444i	−0.477961	−	0.827853i
$672$	36.0810	−	19.9171i	1.39185	−	0.768317i
$673$	0.938707	−	1.62589i	0.0361845	−	0.0626734i	−0.847366	−	0.531009i	$-0.821813\pi$
$673$	0.938707	−	1.62589i	0.0361845	−	0.0626734i	0.883551	+	0.468336i	$0.155146\pi$
$674$	0.897463	+	0.232177i	0.0345690	+	0.00894313i
$675$	−0.386603	−	5.18175i	−0.0148804	−	0.199446i
$676$	4.78232	−	8.62425i	0.183935	−	0.331702i
$677$	2.78791	+	10.4046i	0.107148	+	0.399883i	0.998580	−	0.0532723i	$-0.0169651\pi$
$677$	2.78791	+	10.4046i	0.107148	+	0.399883i	−0.891432	+	0.453155i	$0.850298\pi$
$678$	34.0446	+	1.83327i	1.30747	+	0.0704062i
$679$	23.9712	+	41.5193i	0.919930	+	1.59337i
$680$	6.65074	−	4.07336i	0.255044	−	0.156206i
$681$	8.15251	−	4.05089i	0.312405	−	0.155231i
$682$	0.0528369	+	6.11109i	0.00202323	+	0.234006i
$683$	20.4458	+	20.4458i	0.782335	+	0.782335i	0.980224	−	0.197889i	$-0.0634086\pi$
$683$	20.4458	+	20.4458i	0.782335	+	0.782335i	−0.197889	+	0.980224i	$0.563409\pi$
$684$	−15.1886	+	39.2303i	−0.580752	+	1.50001i
$685$	10.1996	−	10.1996i	0.389707	−	0.389707i
$686$	15.3989	−	15.6675i	0.587931	−	0.598187i
$687$	13.0727	+	0.817359i	0.498754	+	0.0311842i
$688$	−11.4375	−	37.4537i	−0.436051	−	1.42791i
$689$	−13.0254	+	7.52022i	−0.496228	+	0.286497i
$690$	−2.36423	−	0.771944i	−0.0900048	−	0.0293874i
$691$	−27.4013	+	7.34215i	−1.04239	+	0.279309i	−0.739105	−	0.673590i	$-0.764751\pi$
$691$	−27.4013	+	7.34215i	−1.04239	+	0.279309i	−0.303289	+	0.952899i	$0.598085\pi$
$692$	0.875651	+	3.05562i	0.0332873	+	0.116157i
$693$	−3.26884	−	23.7258i	−0.124173	−	0.901270i
$694$	12.5644	+	21.3340i	0.476936	+	0.809827i
$695$	−11.7374	−	6.77659i	−0.445225	−	0.257051i
$696$	10.9299	−	35.5468i	0.414298	−	1.34740i
$697$	21.9243	−	12.6580i	0.830442	−	0.479456i
$698$	8.13361	+	4.60264i	0.307862	+	0.174213i
$699$	−5.72254	−	28.3238i	−0.216446	−	1.07130i
$700$	4.33165	+	7.21171i	0.163721	+	0.272577i
$701$	22.1609	+	22.1609i	0.837005	+	0.837005i	0.988464	−	0.151458i	$-0.0483969\pi$
$701$	22.1609	+	22.1609i	0.837005	+	0.837005i	−0.151458	+	0.988464i	$0.548397\pi$
$702$	−28.1466	−	13.2675i	−1.06233	−	0.500749i
$703$		−	46.1757i		−	1.74155i
$704$	4.68497	+	14.4427i	0.176572	+	0.544329i
$705$	−7.43196	−	4.93362i	−0.279904	−	0.185811i
$706$	3.17236	−	0.879498i	0.119393	−	0.0331003i
$707$	8.54331	+	2.28917i	0.321304	+	0.0860932i
$708$	1.48399	−	32.8449i	0.0557719	−	1.23439i
$709$	37.0425	−	9.92550i	1.39116	−	0.372760i	0.515997	−	0.856590i	$-0.327422\pi$
$709$	37.0425	−	9.92550i	1.39116	−	0.372760i	0.875162	+	0.483830i	$0.160755\pi$
$710$	−4.19032	−	7.11506i	−0.157260	−	0.267024i
$711$	−6.88119	−	0.863860i	−0.258065	−	0.0323973i
$712$	−29.1359	−	27.6624i	−1.09191	−	1.03669i
$713$	1.15589	−	2.00207i	0.0432886	−	0.0749780i
$714$	−12.8615	−	25.3320i	−0.481328	−	0.948025i
$715$	7.76293	+	2.08007i	0.290317	+	0.0777903i
$716$	0.281337	+	0.271772i	0.0105141	+	0.0101566i
$717$	9.97365	−	8.79985i	0.372473	−	0.328637i
$718$	−9.44023	−	9.27839i	−0.352306	−	0.346266i
$719$	−6.68902			−0.249459			−0.124729	−	0.992191i	$-0.539806\pi$
$719$	−6.68902			−0.249459			−0.124729	+	0.992191i	$0.539806\pi$
$720$	11.8240	−	2.04789i	0.440653	−	0.0763204i
$721$	60.9531			2.27001
$722$	30.4183	+	29.8968i	1.13205	+	1.11265i
$723$	−10.1983	−	3.42769i	−0.379278	−	0.127477i
$724$	−13.1989	+	13.6634i	−0.490532	+	0.507796i
$725$	7.33255	+	1.96475i	0.272324	+	0.0729691i
$726$	−18.0946	−	0.974379i	−0.671555	−	0.0361626i
$727$	−4.24268	+	7.34853i	−0.157352	+	0.272542i	−0.933913	−	0.357500i	$-0.883629\pi$
$727$	−4.24268	+	7.34853i	−0.157352	+	0.272542i	0.776561	+	0.630042i	$0.216962\pi$
$728$	50.3614	−	1.30655i	1.86652	−	0.0484238i
$729$	−9.88075	+	25.1271i	−0.365954	+	0.930633i
$730$	4.14490	+	7.03795i	0.153410	+	0.260486i
$731$	−26.0756	+	6.98694i	−0.964441	+	0.258421i
$732$	−20.8079	−	40.1202i	−0.769082	−	1.48288i
$733$	−14.3340	−	3.84079i	−0.529439	−	0.141863i	−0.0158099	−	0.999875i	$-0.505033\pi$
$733$	−14.3340	−	3.84079i	−0.529439	−	0.141863i	−0.513629	+	0.858012i	$0.671699\pi$
$734$	5.50376	−	1.52585i	0.203148	−	0.0563202i
$735$	16.5861	−	8.24144i	0.611786	−	0.303990i
$736$	1.24541	−	5.60698i	0.0459066	−	0.206676i
$737$		−	15.1263i		−	0.557183i
$738$	38.5407	−	5.64992i	1.41870	−	0.207976i
$739$	−18.5065	−	18.5065i	−0.680773	−	0.680773i	0.279401	−	0.960174i	$-0.409864\pi$
$739$	−18.5065	−	18.5065i	−0.680773	−	0.680773i	−0.960174	+	0.279401i	$0.909864\pi$
$740$	−11.2915	+	6.78212i	−0.415083	+	0.249316i
$741$	−38.5599	+	34.0218i	−1.41654	+	1.24982i
$742$	−18.3888	−	10.4058i	−0.675074	−	0.382011i
$743$	18.8062	−	10.8578i	0.689933	−	0.398333i	−0.113654	−	0.993520i	$-0.536256\pi$
$743$	18.8062	−	10.8578i	0.689933	−	0.398333i	0.803587	+	0.595187i	$0.202922\pi$
$744$	−0.407101	+	11.1469i	−0.0149251	+	0.408664i
$745$	−5.28527	−	3.05145i	−0.193637	−	0.111797i
$746$	−14.9654	−	25.4109i	−0.547923	−	0.930360i
$747$	2.14889	+	2.76589i	0.0786239	+	0.101199i
$748$	10.0617	−	2.88338i	0.367891	−	0.105427i
$749$	−42.9042	+	11.4961i	−1.56769	+	0.420060i
$750$	0.505834	+	2.39669i	0.0184704	+	0.0875148i
$751$	−22.0426	+	12.7263i	−0.804344	+	0.464388i	−0.844988	−	0.534785i	$-0.820392\pi$
$751$	−22.0426	+	12.7263i	−0.804344	+	0.464388i	0.0406437	+	0.999174i	$0.487059\pi$
$752$	9.67742	−	18.1864i	0.352899	−	0.663190i
$753$	11.7110	−	17.6414i	0.426773	−	0.642887i
$754$	31.8657	−	32.4215i	1.16048	−	1.18072i
$755$	−7.47166	+	7.47166i	−0.271922	+	0.271922i
$756$	−4.00559	−	43.5293i	−0.145682	−	1.58314i
$757$	−23.7595	−	23.7595i	−0.863554	−	0.863554i	0.128195	−	0.991749i	$-0.459082\pi$
$757$	−23.7595	−	23.7595i	−0.863554	−	0.863554i	−0.991749	+	0.128195i	$0.959082\pi$
$758$	−0.00552894	−	0.639474i	−0.000200820	−	0.0232267i
$759$	−2.78081	−	1.84601i	−0.100937	−	0.0670058i
$760$	4.63414	−	19.2820i	0.168098	−	0.699431i
$761$	−20.4603	−	35.4382i	−0.741684	−	1.28463i	−0.951728	−	0.306942i	$-0.900694\pi$
$761$	−20.4603	−	35.4382i	−0.741684	−	1.28463i	0.210045	−	0.977692i	$-0.432639\pi$
$762$	−2.80306	+	4.30279i	−0.101544	+	0.155874i
$763$	−11.6212	−	43.3710i	−0.420717	−	1.57014i
$764$	17.5430	+	9.72793i	0.634682	+	0.351944i
$765$	−1.12903	−	8.19469i	−0.0408201	−	0.296280i
$766$	−24.2592	−	6.27594i	−0.876520	−	0.226759i
$767$	20.0950	−	34.8056i	0.725590	−	1.25676i
$768$	7.35243	+	26.7197i	0.265308	+	0.964164i
$769$	11.3556	+	19.6685i	0.409494	+	0.709264i	0.994833	−	0.101524i	$-0.0323719\pi$
$769$	11.3556	+	19.6685i	0.409494	+	0.709264i	−0.585339	+	0.810789i	$0.699039\pi$
$770$	3.01627	+	10.8797i	0.108699	+	0.392079i
$771$	5.76515	+	6.53415i	0.207627	+	0.235322i
$772$	37.8686	−	22.7454i	1.36292	−	0.818625i
$773$	−35.2109	+	35.2109i	−1.26645	+	1.26645i	−0.318536	+	0.947911i	$0.603191\pi$
$773$	−35.2109	+	35.2109i	−1.26645	+	1.26645i	−0.947911	+	0.318536i	$0.896809\pi$
$774$	−41.2564	−	4.81736i	−1.48293	−	0.173156i
$775$	−2.27686			−0.0817873
$776$	−30.9124	+	9.14851i	−1.10969	+	0.328413i
$777$	21.3510	+	42.9693i	0.765963	+	1.54152i
$778$	−32.9711	−	18.6577i	−1.18207	−	0.668910i
$779$	16.6608	−	62.1791i	0.596937	−	2.22780i
$780$	13.9830	+	4.43217i	0.500672	+	0.158697i
$781$	−2.86815	−	10.7041i	−0.102631	−	0.383022i
$782$	−3.83313	−	0.991646i	−0.137073	−	0.0354612i
$783$	−29.8898	−	25.7394i	−1.06818	−	0.919851i
$784$	22.6539	+	36.2799i	0.809069	+	1.29571i
$785$	−19.7429	−	11.3986i	−0.704655	−	0.406833i
$786$	29.7923	+	33.1834i	1.06265	+	1.18361i
$787$	−2.76715	+	10.3271i	−0.0986381	+	0.368122i	−0.997546	−	0.0700154i	$-0.977695\pi$
$787$	−2.76715	+	10.3271i	−0.0986381	+	0.368122i	0.898908	+	0.438138i	$0.144362\pi$
$788$	20.8152	+	20.1075i	0.741510	+	0.716300i
$789$	−3.04971	+	9.07369i	−0.108572	+	0.323032i
$790$	3.26917	−	0.0282654i	0.116312	−	0.00100564i
$791$			58.5466i			2.08168i
$792$	16.0258	+	1.59092i	0.569452	+	0.0565309i
$793$		−	55.2459i		−	1.96184i
$794$	0.0942096	+	10.8962i	0.00334337	+	0.386693i
$795$	−4.07024	−	4.61316i	−0.144356	−	0.163612i
$796$	0.0696777	+	4.02915i	0.00246966	+	0.142809i
$797$	6.85892	−	25.5979i	0.242956	−	0.906722i	−0.731444	−	0.681901i	$-0.761153\pi$
$797$	6.85892	−	25.5979i	0.242956	−	0.906722i	0.974400	−	0.224821i	$-0.0721799\pi$
$798$	−68.6719	−	22.4220i	−2.43096	−	0.793731i
$799$	−12.2985	−	7.10054i	−0.435089	−	0.251199i
$800$	−5.39572	+	1.69887i	−0.190768	+	0.0600641i
$801$	−39.2705	+	16.5438i	−1.38756	+	0.584546i
$802$	8.92928	−	34.5154i	0.315304	−	1.21878i
$803$	2.83707	+	10.5881i	0.100118	+	0.373645i
$804$	1.24612	−	27.5801i	0.0439474	−	0.972676i
$805$	1.10537	−	4.12530i	0.0389592	−	0.145398i
$806$	−6.71508	+	11.8666i	−0.236529	+	0.417984i
$807$	−28.4380	+	42.8388i	−1.00107	+	1.50800i
$808$	−2.83912	+	5.22599i	−0.0998798	+	0.183850i
$809$	26.5581			0.933732			0.466866	−	0.884328i	$-0.345383\pi$
$809$	26.5581			0.933732			0.466866	+	0.884328i	$0.345383\pi$
$810$	3.03938	−	12.3597i	0.106793	−	0.434276i
$811$	−0.216412	+	0.216412i	−0.00759926	+	0.00759926i	−0.710896	−	0.703297i	$-0.751710\pi$
$811$	−0.216412	+	0.216412i	−0.00759926	+	0.00759926i	0.703297	+	0.710896i	$0.251710\pi$
$812$	61.9624	+	15.4596i	2.17446	+	0.542526i
$813$	−0.857029	+	0.173154i	−0.0300573	+	0.00607279i
$814$	−17.0346	+	4.72263i	−0.597062	+	0.165528i
$815$	3.70814	+	6.42268i	0.129890	+	0.224977i
$816$	18.5832	−	4.42844i	0.650543	−	0.155026i
$817$	−34.3215	+	59.4466i	−1.20076	+	2.07977i
$818$	9.40393	−	36.3502i	0.328801	−	1.27095i
$819$	20.1512	−	49.4890i	0.704140	−	1.72929i
$820$	−17.6519	+	5.05852i	−0.616432	+	0.176651i
$821$	−0.0233547	−	0.0871610i	−0.000815085	−	0.00304194i	0.965517	−	0.260340i	$-0.0838346\pi$
$821$	−0.0233547	−	0.0871610i	−0.000815085	−	0.00304194i	−0.966332	+	0.257298i	$0.917168\pi$
$822$	31.5045	−	15.9954i	1.09885	−	0.557902i
$823$	16.9341	+	29.3308i	0.590286	+	1.02241i	0.994194	+	0.107606i	$0.0343185\pi$
$823$	16.9341	+	29.3308i	0.590286	+	1.02241i	−0.403907	+	0.914800i	$0.632348\pi$
$824$	−9.57776	+	39.8517i	−0.333657	+	1.38830i
$825$	−0.205137	+	3.28093i	−0.00714197	+	0.114227i
$826$	56.4571	−	0.488132i	1.96440	−	0.0169843i
$827$	−24.5846	−	24.5846i	−0.854891	−	0.854891i	0.135840	−	0.990731i	$-0.456627\pi$
$827$	−24.5846	−	24.5846i	−0.854891	−	0.854891i	−0.990731	+	0.135840i	$0.956627\pi$
$828$	−4.91825	−	3.59496i	−0.170921	−	0.124934i
$829$	−20.7958	+	20.7958i	−0.722270	+	0.722270i	−0.969067	−	0.246797i	$-0.920622\pi$
$829$	−20.7958	+	20.7958i	−0.722270	+	0.722270i	0.246797	+	0.969067i	$0.420622\pi$
$830$	−1.17757	−	1.15738i	−0.0408740	−	0.0401733i
$831$	15.7287	+	31.6543i	0.545622	+	1.09808i
$832$	−7.05923	+	33.1321i	−0.244735	+	1.14865i
$833$	25.5343	−	14.7422i	0.884710	−	0.510788i
$834$	−22.1786	−	24.7031i	−0.767981	−	0.855398i
$835$	15.2775	−	4.09360i	0.528700	−	0.141665i
$836$	12.9066	−	23.2752i	0.446383	−	0.804990i
$837$	10.6576	+	5.13675i	0.368380	+	0.177552i
$838$	−16.7846	+	9.88504i	−0.579813	+	0.341473i
$839$	−26.0385	−	15.0334i	−0.898950	−	0.519009i	−0.0220908	−	0.999756i	$-0.507032\pi$
$839$	−26.0385	−	15.0334i	−0.898950	−	0.519009i	−0.876859	+	0.480747i	$0.840366\pi$
$840$	4.60337	+	20.0858i	0.158831	+	0.693027i
$841$	24.7914	−	14.3133i	0.854875	−	0.493562i
$842$	−9.78114	+	17.2848i	−0.337080	+	0.595675i
$843$	−11.8493	−	3.98261i	−0.408113	−	0.137169i
$844$	−23.6507	−	5.90083i	−0.814089	−	0.203115i
$845$	3.48655	+	3.48655i	0.119941	+	0.119941i
$846$	−13.5545	−	17.1384i	−0.466013	−	0.589229i
$847$		−	31.1174i		−	1.06921i
$848$	9.69293	−	10.3877i	0.332857	−	0.356714i
$849$	−3.24478	+	51.8964i	−0.111361	+	1.78108i
$850$	1.04179	+	3.75777i	0.0357332	+	0.128890i
$851$	6.45905	+	1.73070i	0.221413	+	0.0593275i
$852$	−4.34776	−	19.7533i	−0.148952	−	0.676738i
$853$	−43.0681	+	11.5401i	−1.47462	+	0.395124i	−0.904514	−	0.426444i	$-0.859766\pi$
$853$	−43.0681	+	11.5401i	−1.47462	+	0.395124i	−0.570110	+	0.821568i	$0.693099\pi$
$854$	66.8740	−	39.3845i	2.28838	−	1.34771i
$855$	−16.7641	−	12.7041i	−0.573320	−	0.434471i
$856$	−0.774606	−	29.8576i	−0.0264755	−	1.02051i
$857$	−10.6517	+	18.4494i	−0.363857	+	0.630218i	−0.988592	−	0.150618i	$-0.951874\pi$
$857$	−10.6517	+	18.4494i	−0.363857	+	0.630218i	0.624735	+	0.780837i	$0.285207\pi$
$858$	16.4947	+	10.7455i	0.563118	+	0.366845i
$859$	8.41718	+	2.25538i	0.287190	+	0.0769524i	0.399538	−	0.916717i	$-0.369170\pi$
$859$	8.41718	+	2.25538i	0.287190	+	0.0769524i	−0.112348	+	0.993669i	$0.535837\pi$
$860$	19.5777	−	0.338565i	0.667593	−	0.0115450i
$861$	13.2468	+	65.5653i	0.451450	+	2.23446i
$862$	−15.2324	+	15.4981i	−0.518818	+	0.527868i
$863$	−11.7018			−0.398335			−0.199168	−	0.979965i	$-0.563824\pi$
$863$	−11.7018			−0.398335			−0.199168	+	0.979965i	$0.563824\pi$
$864$	29.0892	+	4.22100i	0.989636	+	0.143601i
$865$	−1.58931			−0.0540381
$866$	19.0433	−	19.3755i	0.647118	−	0.658405i
$867$	3.22327	+	15.9536i	0.109468	+	0.541812i
$868$	−19.1515	+	0.331194i	−0.650043	+	0.0112415i
$869$	4.23804	+	1.13558i	0.143766	+	0.0385219i
$870$	15.5802	+	10.1498i	0.528218	+	0.344109i
$871$	16.8740	−	29.2266i	0.571753	−	0.990305i
$872$	30.1825	−	0.783035i	1.02211	−	0.0265169i
$873$	−4.25916	+	33.9270i	−0.144151	+	1.14825i
$874$	−8.67497	+	5.10900i	−0.293435	+	0.172815i
$875$	−4.06297	+	1.08867i	−0.137354	+	0.0368038i
$876$	4.30064	+	19.5392i	0.145305	+	0.660170i
$877$	−40.3169	−	10.8029i	−1.36140	−	0.364787i	−0.497072	−	0.867709i	$-0.665592\pi$
$877$	−40.3169	−	10.8029i	−1.36140	−	0.364787i	−0.864332	+	0.502922i	$0.832258\pi$
$878$	9.52126	+	34.3433i	0.321327	+	1.15903i
$879$	−2.19412	+	35.0923i	−0.0740057	+	1.18363i
$880$	−7.58723	+	0.262497i	−0.255766	+	0.00884877i
$881$		−	37.5973i		−	1.26669i	−0.773871	−	0.633343i	$-0.781682\pi$
$881$		−	37.5973i		−	1.26669i	0.773871	−	0.633343i	$-0.218318\pi$
$882$	44.8867	−	6.58022i	1.51141	−	0.221567i
$883$	−20.9881	−	20.9881i	−0.706304	−	0.706304i	0.259452	−	0.965756i	$-0.416458\pi$
$883$	−20.9881	−	20.9881i	−0.706304	−	0.706304i	−0.965756	+	0.259452i	$0.916458\pi$
$884$	22.6574	+	5.65302i	0.762051	+	0.190131i
$885$	15.5826	+	5.23737i	0.523803	+	0.176052i
$886$	−24.7931	+	43.8134i	−0.832941	+	1.47194i
$887$	24.5296	−	14.1622i	0.823625	−	0.475520i	−0.0280400	−	0.999607i	$-0.508927\pi$
$887$	24.5296	−	14.1622i	0.823625	−	0.475520i	0.851665	+	0.524087i	$0.175593\pi$
$888$	−31.4487	+	7.20756i	−1.05535	+	0.241870i
$889$	−7.63695	−	4.40920i	−0.256135	−	0.147880i
$890$	17.3092	−	10.1940i	0.580206	−	0.341705i
$891$	8.36220	−	14.8947i	0.280144	−	0.498990i
$892$	−8.07969	+	14.5706i	−0.270528	+	0.487860i
$893$	−34.8795	+	9.34594i	−1.16720	+	0.312750i
$894$	−9.98686	−	11.1236i	−0.334011	−	0.372030i
$895$	−0.169380	+	0.0977914i	−0.00566174	+	0.00326881i
$896$	−45.1382	+	15.0746i	−1.50796	+	0.503608i
$897$	−3.31371	−	6.66892i	−0.110642	−	0.222669i
$898$	0.719212	+	0.706882i	0.0240004	+	0.0235889i
$899$	−12.2217	+	12.2217i	−0.407618	+	0.407618i
$900$	−0.644320	+	5.96530i	−0.0214773	+	0.198843i
$901$	−6.92534	−	6.92534i	−0.230716	−	0.230716i
$902$	−24.6424	+	0.213060i	−0.820501	+	0.00709411i
$903$	4.45100	−	71.1885i	0.148120	−	2.36900i
$904$	−38.2783	−	9.19961i	−1.27312	−	0.305975i
$905$	−4.74933	−	8.22608i	−0.157873	−	0.273444i
$906$	−23.0784	+	11.7173i	−0.766730	+	0.389281i
$907$	−3.85380	−	14.3826i	−0.127963	−	0.477566i	0.871965	−	0.489569i	$-0.162846\pi$
$907$	−3.85380	−	14.3826i	−0.127963	−	0.477566i	−0.999928	+	0.0120032i	$0.996179\pi$
$908$	−10.1050	+	2.89581i	−0.335348	+	0.0961007i
$909$	3.87020	+	4.98142i	0.128366	+	0.165223i
$910$	−6.30884	+	24.3864i	−0.209136	+	0.808400i
$911$	−10.6985	+	18.5304i	−0.354457	+	0.613938i	−0.987025	−	0.160567i	$-0.948668\pi$
$911$	−10.6985	+	18.5304i	−0.354457	+	0.613938i	0.632568	+	0.774505i	$0.282001\pi$
$912$	25.4504	−	41.3751i	0.842746	−	1.37007i
$913$	−1.10794	−	1.91901i	−0.0366675	−	0.0635100i
$914$	−47.5851	+	13.1924i	−1.57398	+	0.436365i
$915$	22.1500	−	4.47519i	0.732256	−	0.147945i
$916$	−14.6747	−	3.66132i	−0.484864	−	0.120973i
$917$	−54.1497	+	54.1497i	−1.78818	+	1.78818i
$918$	3.60132	−	19.9398i	0.118861	−	0.658112i
$919$	−46.6435			−1.53863			−0.769314	−	0.638871i	$-0.779402\pi$
$919$	−46.6435			−1.53863			−0.769314	+	0.638871i	$0.779402\pi$
$920$	2.52347	+	1.37092i	0.0831963	+	0.0451980i
$921$	−5.51696	+	8.31071i	−0.181790	+	0.273847i
$922$	−8.86416	+	15.6644i	−0.291926	+	0.515879i
$923$	6.39909	−	23.8817i	0.210628	−	0.786076i
$924$	−1.24823	+	27.6268i	−0.0410639	+	0.908857i
$925$	−1.70455	−	6.36146i	−0.0560452	−	0.209164i
$926$	−3.87633	+	14.9836i	−0.127384	+	0.492393i
$927$	34.6477	+	26.2566i	1.13798	+	0.862380i
$928$	−19.8440	+	38.0824i	−0.651411	+	1.25012i
$929$	20.0054	+	11.5501i	0.656355	+	0.378947i	0.790887	−	0.611963i	$-0.209620\pi$
$929$	20.0054	+	11.5501i	0.656355	+	0.378947i	−0.134532	+	0.990909i	$0.542953\pi$
$930$	−5.30170	−	1.73105i	−0.173850	−	0.0567635i
$931$	19.4042	−	72.4173i	0.635946	−	2.37338i
$932$	0.576931	+	33.3613i	0.0188980	+	1.09279i
$933$	2.13792	+	2.42309i	0.0699923	+	0.0793285i
$934$	0.371764	+	42.9980i	0.0121645	+	1.40694i
$935$			5.23333i			0.171148i
$936$	29.1899	+	20.9514i	0.954102	+	0.684818i
$937$			18.3750i			0.600287i	0.953894	+	0.300143i	$0.0970345\pi$
$937$			18.3750i			0.600287i	−0.953894	+	0.300143i	$0.902966\pi$
$938$	47.4076	−	0.409889i	1.54791	−	0.0133834i
$939$	2.36557	−	7.03821i	0.0771976	−	0.229683i
$940$	7.40837	+	7.15650i	0.241635	+	0.233419i
$941$	11.0627	−	41.2864i	0.360632	−	1.34590i	−0.512614	−	0.858619i	$-0.671323\pi$
$941$	11.0627	−	41.2864i	0.360632	−	1.34590i	0.873246	−	0.487279i	$-0.162011\pi$
$942$	−37.3055	−	41.5519i	−1.21548	−	1.35383i
$943$	8.07314	+	4.66103i	0.262898	+	0.151784i
$944$	−8.55215	+	36.9889i	−0.278349	+	1.20389i
$945$	21.4742	+	4.07046i	0.698556	+	0.132412i
$946$	25.4406	+	6.58157i	0.827144	+	0.213985i
$947$	2.61788	+	9.77006i	0.0850697	+	0.317484i	0.995327	−	0.0965579i	$-0.0307833\pi$
$947$	2.61788	+	9.77006i	0.0850697	+	0.317484i	−0.910258	+	0.414042i	$0.864117\pi$
$948$	7.63378	+	2.41967i	0.247934	+	0.0785872i
$949$	−6.32973	+	23.6229i	−0.205472	+	0.766831i
$950$	8.62963	+	4.88333i	0.279982	+	0.158436i
$951$	13.9134	+	28.0010i	0.451172	+	0.907993i
$952$	9.30950	+	31.4563i	0.301723	+	1.01951i
$953$	47.9062			1.55183			0.775917	−	0.630835i	$-0.217288\pi$
$953$	47.9062			1.55183			0.775917	+	0.630835i	$0.217288\pi$
$954$	−5.97030	−	13.8363i	−0.193296	−	0.447968i
$955$	−7.09215	+	7.09215i	−0.229497	+	0.229497i
$956$	−13.1660	+	7.90805i	−0.425820	+	0.255765i
$957$	16.5102	+	18.7125i	0.533700	+	0.604889i
$958$	7.75500	+	27.9724i	0.250553	+	0.903747i
$959$	30.3367	+	52.5448i	0.979625	+	1.69676i
$960$	−13.8556	−	0.146429i	−0.447189	−	0.00472598i
$961$	−12.9080	+	22.3572i	−0.416386	+	0.721201i
$962$	−38.1821	−	9.87785i	−1.23104	−	0.318475i
$963$	−29.3403	−	11.9470i	−0.945479	−	0.384985i
$964$	10.8647	+	6.02470i	0.349929	+	0.194042i
$965$	5.71660	+	21.3346i	0.184024	+	0.686786i
$966$	5.71026	−	8.76542i	0.183725	−	0.282023i
$967$	6.08626	+	10.5417i	0.195721	+	0.338999i	0.947137	−	0.320830i	$-0.103962\pi$
$967$	6.08626	+	10.5417i	0.195721	+	0.338999i	−0.751416	+	0.659829i	$0.770629\pi$
$968$	20.3449	+	4.88958i	0.653908	+	0.157157i
$969$	−27.8979	−	18.5197i	−0.896210	−	0.594938i
$970$	−0.139360	−	16.1183i	−0.00447456	−	0.517526i
$971$	19.0394	+	19.0394i	0.611003	+	0.611003i	0.943207	−	0.332204i	$-0.107792\pi$
$971$	19.0394	+	19.0394i	0.611003	+	0.611003i	−0.332204	+	0.943207i	$0.607792\pi$
$972$	16.4741	−	26.4689i	0.528406	−	0.848992i
$973$	40.3113	−	40.3113i	1.29232	−	1.29232i
$974$	−28.4946	+	28.9916i	−0.913025	+	0.928951i
$975$	−4.05637	+	6.11048i	−0.129908	+	0.195692i
$976$	15.2418	+	49.9114i	0.487879	+	1.59763i
$977$	18.9502	−	10.9409i	0.606270	−	0.350030i	−0.165234	−	0.986254i	$-0.552838\pi$
$977$	18.9502	−	10.9409i	0.606270	−	0.350030i	0.771504	+	0.636224i	$0.219505\pi$
$978$	3.75140	+	17.7745i	0.119956	+	0.568366i
$979$	26.0404	−	6.97752i	0.832256	−	0.223002i
$980$	−20.5584	+	5.89144i	−0.656715	+	0.188195i
$981$	12.0769	−	29.6596i	0.385587	−	0.946958i
$982$	−20.7279	−	35.1955i	−0.661454	−	1.12313i
$983$	−27.9848	−	16.1570i	−0.892577	−	0.515330i	−0.0177926	−	0.999842i	$-0.505664\pi$
$983$	−27.9848	−	16.1570i	−0.892577	−	0.515330i	−0.874785	+	0.484512i	$0.838997\pi$
$984$	−44.9487	−	1.64160i	−1.43291	−	0.0523322i
$985$	−12.5318	+	7.23526i	−0.399297	+	0.230534i
$986$	25.7631	+	14.5788i	0.820464	+	0.464284i
$987$	28.1361	−	24.8248i	0.895583	−	0.790182i
$988$	50.9022	−	30.5740i	1.61942	−	0.972687i
$989$	−7.02898	−	7.02898i	−0.223509	−	0.223509i
$990$	−2.97209	+	7.48372i	−0.0944593	+	0.237848i
$991$			50.7573i			1.61236i	0.591671	+	0.806179i	$0.298468\pi$
$991$			50.7573i			1.61236i	−0.591671	+	0.806179i	$0.701532\pi$
$992$	2.79279	−	12.5734i	0.0886713	−	0.399207i
$993$	−16.1733	+	8.03632i	−0.513243	+	0.255025i
$994$	33.4702	−	9.27920i	1.06161	−	0.294318i
$995$	−1.94622	−	0.521488i	−0.0616993	−	0.0165323i
$996$	−1.86205	−	3.59026i	−0.0590013	−	0.113762i
$997$	22.3928	−	6.00013i	0.709187	−	0.190026i	0.113845	−	0.993499i	$-0.463683\pi$
$997$	22.3928	−	6.00013i	0.709187	−	0.190026i	0.595342	+	0.803472i	$0.297017\pi$
$998$	15.7589	+	26.7583i	0.498840	+	0.847019i
$999$	−6.37319	+	33.6225i	−0.201639	+	1.06377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.73	✓	384
9.5	odd	6	inner	720.2.cf.a.491.40	yes	384
16.3	odd	4	inner	720.2.cf.a.371.40	yes	384
144.131	even	12	inner	720.2.cf.a.131.73	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.73	✓	384	1.1	even	1	trivial
720.2.cf.a.131.73	yes	384	144.131	even	12	inner
720.2.cf.a.371.40	yes	384	16.3	odd	4	inner
720.2.cf.a.491.40	yes	384	9.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.991317 - 1.00861i) q^{2} +(0.343013 + 1.69775i) q^{3} +(-0.0345817 - 1.99970i) q^{4} +(0.965926 + 0.258819i) q^{5} +(2.05240 + 1.33704i) q^{6} +(-2.10315 + 3.64276i) q^{7} +(-2.05120 - 1.94746i) q^{8} +(-2.76468 + 1.16470i) q^{9} +O(q^{10})\)	\(q+(0.991317 - 1.00861i) q^{2} +(0.343013 + 1.69775i) q^{3} +(-0.0345817 - 1.99970i) q^{4} +(0.965926 + 0.258819i) q^{5} +(2.05240 + 1.33704i) q^{6} +(-2.10315 + 3.64276i) q^{7} +(-2.05120 - 1.94746i) q^{8} +(-2.76468 + 1.16470i) q^{9} +(1.21859 - 0.717669i) q^{10} +(1.83327 - 0.491224i) q^{11} +(3.38312 - 0.744634i) q^{12} +(4.09018 + 1.09596i) q^{13} +(1.58923 + 5.73239i) q^{14} +(-0.108084 + 1.72868i) q^{15} +(-3.99761 + 0.138306i) q^{16} +2.75737i q^{17} +(-1.56595 + 3.94307i) q^{18} +(4.95776 + 4.95776i) q^{19} +(0.484157 - 1.94051i) q^{20} +(-6.90590 - 2.32110i) q^{21} +(1.32190 - 2.33601i) q^{22} +(-0.879310 + 0.507670i) q^{23} +(2.60270 - 4.15041i) q^{24} +(0.866025 + 0.500000i) q^{25} +(5.16006 - 3.03895i) q^{26} +(-2.92568 - 4.29423i) q^{27} +(7.35717 + 4.07970i) q^{28} +(7.33255 - 1.96475i) q^{29} +(1.63641 + 1.82268i) q^{30} +(-1.97182 + 1.13843i) q^{31} +(-3.82340 + 4.16913i) q^{32} +(1.46281 + 2.94393i) q^{33} +(2.78110 + 2.73343i) q^{34} +(-2.97430 + 2.97430i) q^{35} +(2.42465 + 5.48826i) q^{36} +(-4.65691 - 4.65691i) q^{37} +(9.91514 - 0.0857270i) q^{38} +(-0.457679 + 7.32002i) q^{39} +(-1.47726 - 2.41199i) q^{40} +(-4.59061 - 7.95117i) q^{41} +(-9.18701 + 4.66440i) q^{42} +(2.53392 + 9.45670i) q^{43} +(-1.04570 - 3.64901i) q^{44} +(-2.97193 + 0.409459i) q^{45} +(-0.359635 + 1.39014i) q^{46} +(-2.57512 + 4.46023i) q^{47} +(-1.60604 - 6.73948i) q^{48} +(-5.34648 - 9.26038i) q^{49} +(1.36281 - 0.377822i) q^{50} +(-4.68131 + 0.945813i) q^{51} +(2.05015 - 8.21704i) q^{52} +(-2.51158 + 2.51158i) q^{53} +(-7.23147 - 1.30607i) q^{54} +1.89794 q^{55} +(11.4081 - 3.37623i) q^{56} +(-6.71644 + 10.1176i) q^{57} +(5.28722 - 9.34337i) q^{58} +(2.45650 - 9.16777i) q^{59} +(3.46057 + 0.156355i) q^{60} +(-3.37674 - 12.6021i) q^{61} +(-0.806467 + 3.11734i) q^{62} +(1.57183 - 12.5206i) q^{63} +(0.414815 + 7.98924i) q^{64} +(3.66716 + 2.11723i) q^{65} +(4.41938 + 1.44297i) q^{66} +(2.06274 - 7.69826i) q^{67} +(5.51391 - 0.0953544i) q^{68} +(-1.16351 - 1.31871i) q^{69} +(0.0514301 + 5.94839i) q^{70} -5.83879i q^{71} +(7.93911 + 2.99508i) q^{72} +5.77551i q^{73} +(-9.31348 + 0.0805250i) q^{74} +(-0.551815 + 1.64180i) q^{75} +(9.74258 - 10.0855i) q^{76} +(-2.06624 + 7.71130i) q^{77} +(6.92933 + 7.71808i) q^{78} +(2.00202 + 1.15587i) q^{79} +(-3.89719 - 0.901064i) q^{80} +(6.28696 - 6.44004i) q^{81} +(-12.5704 - 3.25200i) q^{82} +(-0.302176 - 1.12774i) q^{83} +(-4.40269 + 13.8900i) q^{84} +(-0.713659 + 2.66341i) q^{85} +(12.0500 + 6.81886i) q^{86} +(5.85081 + 11.7749i) q^{87} +(-4.71704 - 2.56262i) q^{88} +14.2044 q^{89} +(-2.53314 + 3.40341i) q^{90} +(-12.5946 + 12.5946i) q^{91} +(1.04560 + 1.74080i) q^{92} +(-2.60913 - 2.95715i) q^{93} +(1.94587 + 7.01878i) q^{94} +(3.50566 + 6.07199i) q^{95} +(-8.38959 - 5.06110i) q^{96} +(5.69888 - 9.87075i) q^{97} +(-14.6402 - 3.78747i) q^{98} +(-4.49629 + 3.49329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6}+O(q^{10}) \) 384 * q - 12 * q^6	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64} - 72 q^{66} - 156 q^{68} - 112 q^{72} - 168 q^{74} + 12 q^{76} - 116 q^{78} + 72 q^{82} - 120 q^{83} - 116 q^{84} - 36 q^{90} + 48 q^{93} + 20 q^{96} - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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