LMFDB - Embedded newform 80.2.l.a.61.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(21,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.2
Root			$-0.530822 - 1.31081i$ of defining polynomial
Character	$\chi$	$=$	80.61
Dual form			80.2.l.a.21.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17275 - 0.790349i) q^{2} +(1.37027 + 1.37027i) q^{3} +(0.750696 + 1.85377i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.523995 - 2.68998i) q^{6} +2.73482i q^{7} +(0.584744 - 2.76732i) q^{8} +0.755274i q^{9} +O(q^{10})$	\(q+(-1.17275 - 0.790349i) q^{2} +(1.37027 + 1.37027i) q^{3} +(0.750696 + 1.85377i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.523995 - 2.68998i) q^{6} +2.73482i q^{7} +(0.584744 - 2.76732i) q^{8} +0.755274i q^{9} +(1.38812 - 0.270400i) q^{10} +(4.12175 - 4.12175i) q^{11} +(-1.51151 + 3.56882i) q^{12} +(-1.37919 - 1.37919i) q^{13} +(2.16146 - 3.20726i) q^{14} -1.93785 q^{15} +(-2.87291 + 2.78323i) q^{16} -4.94921 q^{17} +(0.596931 - 0.885750i) q^{18} +(-0.292715 - 0.292715i) q^{19} +(-1.84163 - 0.779990i) q^{20} +(-3.74744 + 3.74744i) q^{21} +(-8.09141 + 1.57617i) q^{22} +1.64818i q^{23} +(4.59323 - 2.99072i) q^{24} -1.00000i q^{25} +(0.527407 + 2.70749i) q^{26} +(3.07588 - 3.07588i) q^{27} +(-5.06972 + 2.05302i) q^{28} +(-5.67267 - 5.67267i) q^{29} +(2.27262 + 1.53158i) q^{30} +3.95550 q^{31} +(5.56894 - 0.993438i) q^{32} +11.2958 q^{33} +(5.80420 + 3.91161i) q^{34} +(-1.93381 - 1.93381i) q^{35} +(-1.40010 + 0.566981i) q^{36} +(2.48772 - 2.48772i) q^{37} +(0.111935 + 0.574630i) q^{38} -3.77973i q^{39} +(1.54332 + 2.37027i) q^{40} +8.40843i q^{41} +(7.35660 - 1.43303i) q^{42} +(-3.22713 + 3.22713i) q^{43} +(10.7349 + 4.54659i) q^{44} +(-0.534060 - 0.534060i) q^{45} +(1.30264 - 1.93291i) q^{46} -5.19809 q^{47} +(-7.75044 - 0.122885i) q^{48} -0.479225 q^{49} +(-0.790349 + 1.17275i) q^{50} +(-6.78176 - 6.78176i) q^{51} +(1.52135 - 3.59205i) q^{52} +(7.20537 - 7.20537i) q^{53} +(-6.03826 + 1.17622i) q^{54} +5.82903i q^{55} +(7.56812 + 1.59917i) q^{56} -0.802198i q^{57} +(2.16925 + 11.1360i) q^{58} +(-6.41142 + 6.41142i) q^{59} +(-1.45474 - 3.59233i) q^{60} +(-3.82618 - 3.82618i) q^{61} +(-4.63883 - 3.12623i) q^{62} -2.06554 q^{63} +(-7.31615 - 3.23635i) q^{64} +1.95047 q^{65} +(-13.2472 - 8.92764i) q^{66} +(5.76044 + 5.76044i) q^{67} +(-3.71535 - 9.17470i) q^{68} +(-2.25846 + 2.25846i) q^{69} +(0.739494 + 3.79626i) q^{70} +7.92245i q^{71} +(2.09009 + 0.441642i) q^{72} -4.36276i q^{73} +(-4.88365 + 0.951312i) q^{74} +(1.37027 - 1.37027i) q^{75} +(0.322886 - 0.762367i) q^{76} +(11.2722 + 11.2722i) q^{77} +(-2.98730 + 4.43268i) q^{78} -5.56087 q^{79} +(0.0634130 - 3.99950i) q^{80} +10.6954 q^{81} +(6.64559 - 9.86100i) q^{82} +(-0.516191 - 0.516191i) q^{83} +(-9.76006 - 4.13369i) q^{84} +(3.49962 - 3.49962i) q^{85} +(6.33518 - 1.23406i) q^{86} -15.5462i q^{87} +(-8.99604 - 13.8164i) q^{88} +6.42236i q^{89} +(0.204226 + 1.04841i) q^{90} +(3.77184 - 3.77184i) q^{91} +(-3.05535 + 1.23729i) q^{92} +(5.42011 + 5.42011i) q^{93} +(6.09607 + 4.10830i) q^{94} +0.413962 q^{95} +(8.99222 + 6.26967i) q^{96} -9.44534 q^{97} +(0.562012 + 0.378755i) q^{98} +(3.11305 + 3.11305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) $ 16 * q - 4 * q^4 - 12 * q^6	$ 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} - 16 q^{37} + 20 q^{38} + 60 q^{42} + 8 q^{43} + 40 q^{44} - 4 q^{46} - 40 q^{47} - 40 q^{48} - 16 q^{49} - 4 q^{50} - 32 q^{51} + 56 q^{52} + 16 q^{53} + 32 q^{54} + 16 q^{56} - 12 q^{58} - 8 q^{59} - 28 q^{60} + 16 q^{61} - 8 q^{62} + 40 q^{63} - 16 q^{64} + 40 q^{67} - 48 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{72} - 72 q^{74} + 16 q^{77} - 16 q^{78} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 76 q^{82} + 40 q^{83} - 64 q^{84} - 16 q^{85} + 28 q^{86} + 36 q^{90} + 32 q^{91} - 52 q^{92} - 48 q^{93} - 36 q^{94} + 32 q^{95} + 8 q^{96} + 60 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 12 * q^6 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 4 * q^14 - 8 * q^15 + 16 * q^16 - 8 * q^19 + 8 * q^20 - 20 * q^22 + 8 * q^24 - 16 * q^26 + 24 * q^27 - 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 - 16 * q^37 + 20 * q^38 + 60 * q^42 + 8 * q^43 + 40 * q^44 - 4 * q^46 - 40 * q^47 - 40 * q^48 - 16 * q^49 - 4 * q^50 - 32 * q^51 + 56 * q^52 + 16 * q^53 + 32 * q^54 + 16 * q^56 - 12 * q^58 - 8 * q^59 - 28 * q^60 + 16 * q^61 - 8 * q^62 + 40 * q^63 - 16 * q^64 + 40 * q^67 - 48 * q^68 + 16 * q^69 - 8 * q^70 - 40 * q^72 - 72 * q^74 + 16 * q^77 - 16 * q^78 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 76 * q^82 + 40 * q^83 - 64 * q^84 - 16 * q^85 + 28 * q^86 + 36 * q^90 + 32 * q^91 - 52 * q^92 - 48 * q^93 - 36 * q^94 + 32 * q^95 + 8 * q^96 + 60 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.17275	−	0.790349i	−0.829261	−	0.558861i
$2$	−1.17275	−	0.790349i	−0.829261	−	0.558861i
$3$	1.37027	+	1.37027i	0.791125	+	0.791125i	0.981677	−	0.190552i	$-0.0610278\pi$
$3$	1.37027	+	1.37027i	0.791125	+	0.791125i	−0.190552	+	0.981677i	$0.561028\pi$
$4$	0.750696	+	1.85377i	0.375348	+	0.926884i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−0.523995	−	2.68998i	−0.213920	−	1.09818i
$7$			2.73482i			1.03366i	0.856087	+	0.516832i	$0.172889\pi$
$7$			2.73482i			1.03366i	−0.856087	+	0.516832i	$0.827111\pi$
$8$	0.584744	−	2.76732i	0.206738	−	0.978396i
$9$			0.755274i			0.251758i
$10$	1.38812	−	0.270400i	0.438963	−	0.0855079i
$11$	4.12175	−	4.12175i	1.24275	−	1.24275i	0.283900	−	0.958854i	$-0.408371\pi$
$11$	4.12175	−	4.12175i	1.24275	−	1.24275i	0.958854	−	0.283900i	$-0.0916285\pi$
$12$	−1.51151	+	3.56882i	−0.436334	+	1.03023i
$13$	−1.37919	−	1.37919i	−0.382519	−	0.382519i	0.489490	−	0.872009i	$-0.337183\pi$
$13$	−1.37919	−	1.37919i	−0.382519	−	0.382519i	−0.872009	+	0.489490i	$0.837183\pi$
$14$	2.16146	−	3.20726i	0.577675	−	0.857177i
$15$	−1.93785			−0.500352
$16$	−2.87291	+	2.78323i	−0.718228	+	0.695808i
$17$	−4.94921			−1.20036			−0.600180	−	0.799865i	$-0.704905\pi$
$17$	−4.94921			−1.20036			−0.600180	+	0.799865i	$0.704905\pi$
$18$	0.596931	−	0.885750i	0.140698	−	0.208773i
$19$	−0.292715	−	0.292715i	−0.0671535	−	0.0671535i	0.672732	−	0.739886i	$-0.265121\pi$
$19$	−0.292715	−	0.292715i	−0.0671535	−	0.0671535i	−0.739886	+	0.672732i	$0.765121\pi$
$20$	−1.84163	−	0.779990i	−0.411802	−	0.174411i
$21$	−3.74744	+	3.74744i	−0.817757	+	0.817757i
$22$	−8.09141	+	1.57617i	−1.72510	+	0.336040i
$23$			1.64818i			0.343670i	0.985126	+	0.171835i	$0.0549696\pi$
$23$			1.64818i			0.343670i	−0.985126	+	0.171835i	$0.945030\pi$
$24$	4.59323	−	2.99072i	0.937590	−	0.610478i
$25$		−	1.00000i		−	0.200000i
$26$	0.527407	+	2.70749i	0.103433	+	0.530983i
$27$	3.07588	−	3.07588i	0.591953	−	0.591953i
$28$	−5.06972	+	2.05302i	−0.958086	+	0.387984i
$29$	−5.67267	−	5.67267i	−1.05339	−	1.05339i	−0.998492	−	0.0548963i	$-0.982517\pi$
$29$	−5.67267	−	5.67267i	−1.05339	−	1.05339i	−0.0548963	−	0.998492i	$-0.517483\pi$
$30$	2.27262	+	1.53158i	0.414922	+	0.279627i
$31$	3.95550			0.710430			0.355215	−	0.934785i	$-0.384408\pi$
$31$	3.95550			0.710430			0.355215	+	0.934785i	$0.384408\pi$
$32$	5.56894	−	0.993438i	0.984459	−	0.175617i
$33$	11.2958			1.96635
$34$	5.80420	+	3.91161i	0.995413	+	0.670835i
$35$	−1.93381	−	1.93381i	−0.326873	−	0.326873i
$36$	−1.40010	+	0.566981i	−0.233351	+	0.0944969i
$37$	2.48772	−	2.48772i	0.408979	−	0.408979i	−0.472403	−	0.881382i	$-0.656613\pi$
$37$	2.48772	−	2.48772i	0.408979	−	0.408979i	0.881382	+	0.472403i	$0.156613\pi$
$38$	0.111935	+	0.574630i	0.0181583	+	0.0932173i
$39$		−	3.77973i		−	0.605241i
$40$	1.54332	+	2.37027i	0.244020	+	0.374772i
$41$			8.40843i			1.31318i	0.754250	+	0.656588i	$0.228001\pi$
$41$			8.40843i			1.31318i	−0.754250	+	0.656588i	$0.771999\pi$
$42$	7.35660	−	1.43303i	1.13515	−	0.221121i
$43$	−3.22713	+	3.22713i	−0.492133	+	0.492133i	−0.908978	−	0.416845i	$-0.863136\pi$
$43$	−3.22713	+	3.22713i	−0.492133	+	0.492133i	0.416845	+	0.908978i	$0.363136\pi$
$44$	10.7349	+	4.54659i	1.61835	+	0.685424i
$45$	−0.534060	−	0.534060i	−0.0796129	−	0.0796129i
$46$	1.30264	−	1.93291i	0.192064	−	0.284992i
$47$	−5.19809			−0.758219			−0.379109	−	0.925352i	$-0.623770\pi$
$47$	−5.19809			−0.758219			−0.379109	+	0.925352i	$0.623770\pi$
$48$	−7.75044	−	0.122885i	−1.11868	−	0.0177369i
$49$	−0.479225			−0.0684607
$50$	−0.790349	+	1.17275i	−0.111772	+	0.165852i
$51$	−6.78176	−	6.78176i	−0.949636	−	0.949636i
$52$	1.52135	−	3.59205i	0.210973	−	0.498128i
$53$	7.20537	−	7.20537i	0.989733	−	0.989733i	−0.0102143	−	0.999948i	$-0.503251\pi$
$53$	7.20537	−	7.20537i	0.989733	−	0.989733i	0.999948	+	0.0102143i	$0.00325138\pi$
$54$	−6.03826	+	1.17622i	−0.821703	+	0.160064i
$55$			5.82903i			0.785987i
$56$	7.56812	+	1.59917i	1.01133	+	0.213698i
$57$		−	0.802198i		−	0.106254i
$58$	2.16925	+	11.1360i	0.284836	+	1.46223i
$59$	−6.41142	+	6.41142i	−0.834695	+	0.834695i	−0.988155	−	0.153459i	$-0.950959\pi$
$59$	−6.41142	+	6.41142i	−0.834695	+	0.834695i	0.153459	+	0.988155i	$0.450959\pi$
$60$	−1.45474	−	3.59233i	−0.187806	−	0.463768i
$61$	−3.82618	−	3.82618i	−0.489892	−	0.489892i	0.418380	−	0.908272i	$-0.362598\pi$
$61$	−3.82618	−	3.82618i	−0.489892	−	0.489892i	−0.908272	+	0.418380i	$0.862598\pi$
$62$	−4.63883	−	3.12623i	−0.589132	−	0.397032i
$63$	−2.06554			−0.260233
$64$	−7.31615	−	3.23635i	−0.914519	−	0.404544i
$65$	1.95047			0.241926
$66$	−13.2472	−	8.92764i	−1.63062	−	1.09892i
$67$	5.76044	+	5.76044i	0.703750	+	0.703750i	0.965213	−	0.261463i	$-0.0842050\pi$
$67$	5.76044	+	5.76044i	0.703750	+	0.703750i	−0.261463	+	0.965213i	$0.584205\pi$
$68$	−3.71535	−	9.17470i	−0.450553	−	1.11260i
$69$	−2.25846	+	2.25846i	−0.271886	+	0.271886i
$70$	0.739494	+	3.79626i	0.0883864	+	0.453740i
$71$			7.92245i			0.940222i	0.882607	+	0.470111i	$0.155786\pi$
$71$			7.92245i			0.940222i	−0.882607	+	0.470111i	$0.844214\pi$
$72$	2.09009	+	0.441642i	0.246319	+	0.0520480i
$73$		−	4.36276i		−	0.510622i	−0.966859	−	0.255311i	$-0.917822\pi$
$73$		−	4.36276i		−	0.510622i	0.966859	−	0.255311i	$-0.0821779\pi$
$74$	−4.88365	+	0.951312i	−0.567713	+	0.110588i
$75$	1.37027	−	1.37027i	0.158225	−	0.158225i
$76$	0.322886	−	0.762367i	0.0370376	−	0.0874495i
$77$	11.2722	+	11.2722i	1.28459	+	1.28459i
$78$	−2.98730	+	4.43268i	−0.338246	+	0.501902i
$79$	−5.56087			−0.625647			−0.312824	−	0.949811i	$-0.601275\pi$
$79$	−5.56087			−0.625647			−0.312824	+	0.949811i	$0.601275\pi$
$80$	0.0634130	−	3.99950i	0.00708979	−	0.447157i
$81$	10.6954			1.18838
$82$	6.64559	−	9.86100i	0.733883	−	1.08897i
$83$	−0.516191	−	0.516191i	−0.0566594	−	0.0566594i	0.678209	−	0.734869i	$-0.262756\pi$
$83$	−0.516191	−	0.516191i	−0.0566594	−	0.0566594i	−0.734869	+	0.678209i	$0.762756\pi$
$84$	−9.76006	−	4.13369i	−1.06491	−	0.451023i
$85$	3.49962	−	3.49962i	0.379587	−	0.379587i
$86$	6.33518	−	1.23406i	0.683140	−	0.133073i
$87$		−	15.5462i		−	1.66672i
$88$	−8.99604	−	13.8164i	−0.958981	−	1.47283i
$89$			6.42236i			0.680768i	0.940286	+	0.340384i	$0.110557\pi$
$89$			6.42236i			0.680768i	−0.940286	+	0.340384i	$0.889443\pi$
$90$	0.204226	+	1.04841i	0.0215273	+	0.110512i
$91$	3.77184	−	3.77184i	0.395396	−	0.395396i
$92$	−3.05535	+	1.23729i	−0.318542	+	0.128996i
$93$	5.42011	+	5.42011i	0.562039	+	0.562039i
$94$	6.09607	+	4.10830i	0.628761	+	0.423739i
$95$	0.413962			0.0424716
$96$	8.99222	+	6.26967i	0.917765	+	0.639895i
$97$	−9.44534			−0.959029			−0.479515	−	0.877534i	$-0.659187\pi$
$97$	−9.44534			−0.959029			−0.479515	+	0.877534i	$0.659187\pi$
$98$	0.562012	+	0.378755i	0.0567718	+	0.0382600i
$99$	3.11305	+	3.11305i	0.312873	+	0.312873i
$100$	1.85377	−	0.750696i	0.185377	−	0.0750696i
$101$	−11.0542	+	11.0542i	−1.09993	+	1.09993i	−0.105515	+	0.994418i	$0.533649\pi$
$101$	−11.0542	+	11.0542i	−1.09993	+	1.09993i	−0.994418	+	0.105515i	$0.966351\pi$
$102$	2.59336	+	13.3133i	0.256781	+	1.31821i
$103$			5.46824i			0.538801i	0.963028	+	0.269401i	$0.0868256\pi$
$103$			5.46824i			0.538801i	−0.963028	+	0.269401i	$0.913174\pi$
$104$	−4.62314	+	3.01019i	−0.453336	+	0.295174i
$105$		−	5.29967i		−	0.517195i
$106$	−14.1449	+	2.75535i	−1.37387	+	0.267624i
$107$	0.293704	−	0.293704i	0.0283934	−	0.0283934i	−0.692768	−	0.721161i	$-0.743609\pi$
$107$	0.293704	−	0.293704i	0.0283934	−	0.0283934i	0.721161	+	0.692768i	$0.243609\pi$
$108$	8.01101	+	3.39292i	0.770860	+	0.326483i
$109$	10.4135	+	10.4135i	0.997429	+	0.997429i	0.999997	−	0.00256817i	$-0.000817475\pi$
$109$	10.4135	+	10.4135i	0.997429	+	0.997429i	−0.00256817	+	0.999997i	$0.500817\pi$
$110$	4.60697	−	6.83601i	0.439258	−	0.651788i
$111$	6.81770			0.647107
$112$	−7.61163	−	7.85689i	−0.719231	−	0.742406i
$113$	−17.4145			−1.63822			−0.819108	−	0.573639i	$-0.805531\pi$
$113$	−17.4145			−1.63822			−0.819108	+	0.573639i	$0.805531\pi$
$114$	−0.634017	+	0.940779i	−0.0593811	+	0.0881121i
$115$	−1.16544	−	1.16544i	−0.108678	−	0.108678i
$116$	6.25736	−	14.7743i	0.580982	−	1.37176i
$117$	1.04167	−	1.04167i	0.0963022	−	0.0963022i
$118$	12.5863	−	2.45175i	1.15866	−	0.225701i
$119$		−	13.5352i		−	1.24077i
$120$	−1.13315	+	5.36266i	−0.103442	+	0.489542i
$121$		−	22.9776i		−	2.08888i
$122$	1.46314	+	7.51117i	0.132467	+	0.680030i
$123$	−11.5218	+	11.5218i	−1.03889	+	1.03889i
$124$	2.96938	+	7.33259i	0.266658	+	0.658486i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	2.42236	+	1.63250i	0.215801	+	0.145434i
$127$	10.9793			0.974254			0.487127	−	0.873331i	$-0.338045\pi$
$127$	10.9793			0.974254			0.487127	+	0.873331i	$0.338045\pi$
$128$	6.02218	+	9.57775i	0.532291	+	0.846562i
$129$	−8.84407			−0.778677
$130$	−2.28742	−	1.54155i	−0.200620	−	0.135203i
$131$	5.77044	+	5.77044i	0.504166	+	0.504166i	0.912730	−	0.408564i	$-0.133970\pi$
$131$	5.77044	+	5.77044i	0.504166	+	0.504166i	−0.408564	+	0.912730i	$0.633970\pi$
$132$	8.47972	+	20.9398i	0.738065	+	1.82258i
$133$	0.800523	−	0.800523i	0.0694142	−	0.0694142i
$134$	−2.20281	−	11.3083i	−0.190294	−	0.976892i
$135$			4.34995i			0.374384i
$136$	−2.89402	+	13.6961i	−0.248160	+	1.17443i
$137$			7.18832i			0.614139i	0.951687	+	0.307070i	$0.0993484\pi$
$137$			7.18832i			0.614139i	−0.951687	+	0.307070i	$0.900652\pi$
$138$	4.43358	−	0.863640i	0.377411	−	0.0735180i
$139$	4.91327	−	4.91327i	0.416738	−	0.416738i	−0.467340	−	0.884078i	$-0.654788\pi$
$139$	4.91327	−	4.91327i	0.416738	−	0.416738i	0.884078	+	0.467340i	$0.154788\pi$
$140$	2.13313	−	5.03653i	0.180282	−	0.425665i
$141$	−7.12278	−	7.12278i	−0.599846	−	0.599846i
$142$	6.26150	−	9.29107i	0.525454	−	0.779689i
$143$	−11.3694			−0.950754
$144$	−2.10210	−	2.16984i	−0.175175	−	0.180820i
$145$	8.02237			0.666221
$146$	−3.44810	+	5.11644i	−0.285367	+	0.423439i
$147$	−0.656667	−	0.656667i	−0.0541609	−	0.0541609i
$148$	6.47918	+	2.74414i	0.532585	+	0.225567i
$149$	9.76620	−	9.76620i	0.800078	−	0.800078i	−0.183029	−	0.983107i	$-0.558590\pi$
$149$	9.76620	−	9.76620i	0.800078	−	0.800078i	0.983107	+	0.183029i	$0.0585903\pi$
$150$	−2.68998	+	0.523995i	−0.219636	+	0.0427840i
$151$		−	1.90755i		−	0.155234i	−0.996983	−	0.0776169i	$-0.975269\pi$
$151$		−	1.90755i		−	0.155234i	0.996983	−	0.0776169i	$-0.0247311\pi$
$152$	−0.981202	+	0.638874i	−0.0795860	+	0.0518196i
$153$		−	3.73801i		−	0.302201i
$154$	−4.31053	−	22.1285i	−0.347353	−	1.78317i
$155$	−2.79696	+	2.79696i	−0.224658	+	0.224658i
$156$	7.00674	−	2.83742i	0.560988	−	0.227176i
$157$	−4.41296	−	4.41296i	−0.352192	−	0.352192i	0.508732	−	0.860925i	$-0.330114\pi$
$157$	−4.41296	−	4.41296i	−0.352192	−	0.352192i	−0.860925	+	0.508732i	$0.830114\pi$
$158$	6.52153	+	4.39503i	0.518825	+	0.349650i
$159$	19.7466			1.56601
$160$	−3.23537	+	4.64030i	−0.255778	+	0.366848i
$161$	−4.50748			−0.355240
$162$	−12.5430	−	8.45309i	−0.985474	−	0.664137i
$163$	−3.58912	−	3.58912i	−0.281122	−	0.281122i	0.552435	−	0.833556i	$-0.313699\pi$
$163$	−3.58912	−	3.58912i	−0.281122	−	0.281122i	−0.833556	+	0.552435i	$0.813699\pi$
$164$	−15.5873	+	6.31217i	−1.21716	+	0.492898i
$165$	−7.98734	+	7.98734i	−0.621814	+	0.621814i
$166$	0.197393	+	1.01334i	0.0153207	+	0.0786501i
$167$		−	17.5993i		−	1.36188i	−0.732341	−	0.680938i	$-0.761572\pi$
$167$		−	17.5993i		−	1.36188i	0.732341	−	0.680938i	$-0.238428\pi$
$168$	8.17907	+	12.5617i	0.631029	+	0.969153i
$169$		−	9.19566i		−	0.707359i
$170$	−6.87012	+	1.33827i	−0.526914	+	0.102640i
$171$	0.221080	−	0.221080i	0.0169064	−	0.0169064i
$172$	−8.40494	−	3.55976i	−0.640871	−	0.271429i
$173$	−7.32377	−	7.32377i	−0.556816	−	0.556816i	0.371584	−	0.928400i	$-0.378815\pi$
$173$	−7.32377	−	7.32377i	−0.556816	−	0.556816i	−0.928400	+	0.371584i	$0.878815\pi$
$174$	−12.2869	+	18.2318i	−0.931468	+	1.38215i
$175$	2.73482			0.206733
$176$	−0.369636	+	23.3132i	−0.0278624	+	1.75730i
$177$	−17.5707			−1.32070
$178$	5.07590	−	7.53183i	0.380455	−	0.564535i
$179$	6.42849	+	6.42849i	0.480488	+	0.480488i	0.905287	−	0.424800i	$-0.139655\pi$
$179$	6.42849	+	6.42849i	0.480488	+	0.480488i	−0.424800	+	0.905287i	$0.639655\pi$
$180$	0.589106	−	1.39094i	0.0439094	−	0.103674i
$181$	−3.67884	+	3.67884i	−0.273446	+	0.273446i	−0.830486	−	0.557040i	$-0.811937\pi$
$181$	−3.67884	+	3.67884i	−0.273446	+	0.273446i	0.557040	+	0.830486i	$0.311937\pi$
$182$	−7.40450	+	1.44236i	−0.548858	+	0.106915i
$183$		−	10.4858i		−	0.775131i
$184$	4.56106	+	0.963766i	0.336246	+	0.0710498i
$185$			3.51817i			0.258661i
$186$	−2.07266	−	10.6402i	−0.151975	−	0.780179i
$187$	−20.3994	+	20.3994i	−1.49175	+	1.49175i
$188$	−3.90218	−	9.63605i	−0.284596	−	0.702781i
$189$	8.41196	+	8.41196i	0.611880	+	0.611880i
$190$	−0.485475	−	0.327175i	−0.0352201	−	0.0237357i
$191$	−5.39093			−0.390074			−0.195037	−	0.980796i	$-0.562483\pi$
$191$	−5.39093			−0.390074			−0.195037	+	0.980796i	$0.562483\pi$
$192$	−5.59042	−	14.4598i	−0.403454	−	1.04354i
$193$	−3.53818			−0.254684			−0.127342	−	0.991859i	$-0.540645\pi$
$193$	−3.53818			−0.254684			−0.127342	+	0.991859i	$0.540645\pi$
$194$	11.0770	+	7.46512i	0.795286	+	0.535964i
$195$	2.67267	+	2.67267i	0.191394	+	0.191394i
$196$	−0.359752	−	0.888371i	−0.0256966	−	0.0634551i
$197$	10.6900	−	10.6900i	0.761627	−	0.761627i	−0.214989	−	0.976616i	$-0.568972\pi$
$197$	10.6900	−	10.6900i	0.761627	−	0.761627i	0.976616	+	0.214989i	$0.0689716\pi$
$198$	−1.19044	−	6.11124i	−0.0846009	−	0.434307i
$199$			15.6543i			1.10971i	0.831948	+	0.554853i	$0.187226\pi$
$199$			15.6543i			1.10971i	−0.831948	+	0.554853i	$0.812774\pi$
$200$	−2.76732	−	0.584744i	−0.195679	−	0.0413476i
$201$			15.7867i			1.11351i
$202$	21.7005	−	4.22715i	1.52684	−	0.297421i
$203$	15.5137	−	15.5137i	1.08885	−	1.08885i
$204$	7.48076	−	17.6628i	0.523758	−	1.23665i
$205$	−5.94566	−	5.94566i	−0.415263	−	0.415263i
$206$	4.32182	−	6.41289i	0.301115	−	0.446807i
$207$	−1.24483			−0.0865218
$208$	7.80090	+	0.123685i	0.540895	+	0.00857603i
$209$	−2.41300			−0.166911
$210$	−4.18859	+	6.21520i	−0.289040	+	0.428890i
$211$	−19.9359	−	19.9359i	−1.37244	−	1.37244i	−0.856809	−	0.515634i	$-0.827556\pi$
$211$	−19.9359	−	19.9359i	−1.37244	−	1.37244i	−0.515634	−	0.856809i	$-0.672444\pi$
$212$	18.7661	+	7.94804i	1.28886	+	0.545874i
$213$	−10.8559	+	10.8559i	−0.743833	+	0.743833i
$214$	−0.576570	+	0.112313i	−0.0394135	+	0.00767757i
$215$		−	4.56385i		−	0.311252i
$216$	−6.71335	−	10.3105i	−0.456785	−	0.701544i
$217$			10.8176i			0.734345i
$218$	−3.98214	−	20.4427i	−0.269704	−	1.38455i
$219$	5.97815	−	5.97815i	0.403966	−	0.403966i
$220$	−10.8057	+	4.37583i	−0.728519	+	0.295019i
$221$	6.82591	+	6.82591i	0.459161	+	0.459161i
$222$	−7.99547	−	5.38836i	−0.536621	−	0.361643i
$223$	21.2173			1.42081			0.710406	−	0.703792i	$-0.248511\pi$
$223$	21.2173			1.42081			0.710406	+	0.703792i	$0.248511\pi$
$224$	2.71687	+	15.2300i	0.181529	+	1.01760i
$225$	0.755274			0.0503516
$226$	20.4229	+	13.7635i	1.35851	+	0.915536i
$227$	12.0356	+	12.0356i	0.798832	+	0.798832i	0.982911	−	0.184079i	$-0.0589303\pi$
$227$	12.0356	+	12.0356i	0.798832	+	0.798832i	−0.184079	+	0.982911i	$0.558930\pi$
$228$	1.48709	−	0.602207i	0.0984849	−	0.0398821i
$229$	6.70809	−	6.70809i	0.443283	−	0.443283i	−0.449831	−	0.893114i	$-0.648516\pi$
$229$	6.70809	−	6.70809i	0.443283	−	0.443283i	0.893114	+	0.449831i	$0.148516\pi$
$230$	0.445669	+	2.28788i	0.0293865	+	0.150858i
$231$			30.8920i			2.03254i
$232$	−19.0152	+	12.3810i	−1.24841	+	0.812856i
$233$			5.40431i			0.354048i	0.984207	+	0.177024i	$0.0566470\pi$
$233$			5.40431i			0.354048i	−0.984207	+	0.177024i	$0.943353\pi$
$234$	−2.04490	+	0.398337i	−0.133679	+	0.0260401i
$235$	3.67560	−	3.67560i	0.239770	−	0.239770i
$236$	−16.6983	−	7.07226i	−1.08697	−	0.460365i
$237$	−7.61989	−	7.61989i	−0.494965	−	0.494965i
$238$	−10.6975	+	15.8734i	−0.693418	+	1.02892i
$239$	−1.86569			−0.120681			−0.0603406	−	0.998178i	$-0.519219\pi$
$239$	−1.86569			−0.120681			−0.0603406	+	0.998178i	$0.519219\pi$
$240$	5.56728	−	5.39349i	0.359366	−	0.348149i
$241$	16.3740			1.05474			0.527369	−	0.849636i	$-0.323178\pi$
$241$	16.3740			1.05474			0.527369	+	0.849636i	$0.323178\pi$
$242$	−18.1604	+	26.9471i	−1.16739	+	1.73222i
$243$	5.42792	+	5.42792i	0.348201	+	0.348201i
$244$	4.22055	−	9.96514i	0.270193	−	0.637953i
$245$	0.338863	−	0.338863i	0.0216492	−	0.0216492i
$246$	22.6185	−	4.40597i	1.44210	−	0.280915i
$247$			0.807421i			0.0513750i
$248$	2.31296	−	10.9462i	0.146873	−	0.695082i
$249$		−	1.41464i		−	0.0896493i
$250$	−0.270400	−	1.38812i	−0.0171016	−	0.0877926i
$251$	3.01154	−	3.01154i	0.190087	−	0.190087i	−0.605647	−	0.795734i	$-0.707086\pi$
$251$	3.01154	−	3.01154i	0.190087	−	0.190087i	0.795734	+	0.605647i	$0.207086\pi$
$252$	−1.55059	−	3.82903i	−0.0976780	−	0.241206i
$253$	6.79340	+	6.79340i	0.427098	+	0.427098i
$254$	−12.8760	−	8.67747i	−0.807911	−	0.544473i
$255$	9.59085			0.600602
$256$	0.507240	−	15.9920i	0.0317025	−	0.999497i
$257$	22.7407			1.41853			0.709263	−	0.704944i	$-0.249028\pi$
$257$	22.7407			1.41853			0.709263	+	0.704944i	$0.249028\pi$
$258$	10.3719	+	6.98991i	0.645727	+	0.435173i
$259$	6.80346	+	6.80346i	0.422747	+	0.422747i
$260$	1.46421	+	3.61572i	0.0908065	+	0.224237i
$261$	4.28442	−	4.28442i	0.265199	−	0.265199i
$262$	−2.20663	−	11.3280i	−0.136326	−	0.699844i
$263$		−	12.0300i		−	0.741805i	−0.928672	−	0.370902i	$-0.879048\pi$
$263$		−	12.0300i		−	0.741805i	0.928672	−	0.370902i	$-0.120952\pi$
$264$	6.60516	−	31.2592i	0.406519	−	1.92387i
$265$			10.1899i			0.625962i
$266$	−1.57151	+	0.306122i	−0.0963554	+	0.0187696i
$267$	−8.80035	+	8.80035i	−0.538573	+	0.538573i
$268$	−6.35419	+	15.0029i	−0.388144	+	0.916446i
$269$	4.90068	+	4.90068i	0.298800	+	0.298800i	0.840544	−	0.541744i	$-0.182236\pi$
$269$	4.90068	+	4.90068i	0.298800	+	0.298800i	−0.541744	+	0.840544i	$0.682236\pi$
$270$	3.43798	−	5.10141i	0.209229	−	0.310462i
$271$	−4.14616			−0.251862			−0.125931	−	0.992039i	$-0.540192\pi$
$271$	−4.14616			−0.251862			−0.125931	+	0.992039i	$0.540192\pi$
$272$	14.2187	−	13.7748i	0.862133	−	0.835221i
$273$	10.3369			0.625615
$274$	5.68128	−	8.43011i	0.343219	−	0.509282i
$275$	−4.12175	−	4.12175i	−0.248551	−	0.248551i
$276$	−5.88207	−	2.49124i	−0.354059	−	0.149955i
$277$	−10.4815	+	10.4815i	−0.629775	+	0.629775i	−0.948011	−	0.318236i	$-0.896909\pi$
$277$	−10.4815	+	10.4815i	−0.629775	+	0.629775i	0.318236	+	0.948011i	$0.396909\pi$
$278$	−9.64525	+	1.87885i	−0.578483	+	0.112686i
$279$			2.98749i			0.178856i
$280$	−6.48225	+	4.22069i	−0.387389	+	0.252234i
$281$			3.51927i			0.209942i	0.994475	+	0.104971i	$0.0334750\pi$
$281$			3.51927i			0.209942i	−0.994475	+	0.104971i	$0.966525\pi$
$282$	2.72377	+	13.9827i	0.162198	+	0.832660i
$283$	−2.88462	+	2.88462i	−0.171473	+	0.171473i	−0.787626	−	0.616153i	$-0.788690\pi$
$283$	−2.88462	+	2.88462i	−0.171473	+	0.171473i	0.616153	+	0.787626i	$0.288690\pi$
$284$	−14.6864	+	5.94735i	−0.871477	+	0.352910i
$285$	0.567240	+	0.567240i	0.0336004	+	0.0336004i
$286$	13.3334	+	8.98577i	0.788423	+	0.531340i
$287$	−22.9955			−1.35738
$288$	0.750318	+	4.20608i	0.0442129	+	0.247845i
$289$	7.49472			0.440866
$290$	−9.40825	−	6.34047i	−0.552471	−	0.372325i
$291$	−12.9427	−	12.9427i	−0.758712	−	0.758712i
$292$	8.08754	−	3.27511i	0.473288	−	0.191661i
$293$	3.92351	−	3.92351i	0.229214	−	0.229214i	−0.583150	−	0.812364i	$-0.698180\pi$
$293$	3.92351	−	3.92351i	0.229214	−	0.229214i	0.812364	+	0.583150i	$0.198180\pi$
$294$	0.251111	+	1.28910i	0.0146451	+	0.0751820i
$295$		−	9.06711i		−	0.527908i
$296$	−5.42965	−	8.33901i	−0.315592	−	0.484695i
$297$		−	25.3560i		−	1.47130i
$298$	−19.1720	+	3.73462i	−1.11061	+	0.216341i
$299$	2.27316	−	2.27316i	0.131460	−	0.131460i
$300$	3.56882	+	1.51151i	0.206046	+	0.0872668i
$301$	−8.82561	−	8.82561i	−0.508700	−	0.508700i
$302$	−1.50763	+	2.23708i	−0.0867542	+	0.128729i
$303$	−30.2944			−1.74037
$304$	1.65564	+	0.0262506i	0.0949575	+	0.00150557i
$305$	5.41103			0.309835
$306$	−2.95434	+	4.38377i	−0.168888	+	0.250603i
$307$	−0.196482	−	0.196482i	−0.0112138	−	0.0112138i	0.701478	−	0.712691i	$-0.252524\pi$
$307$	−0.196482	−	0.196482i	−0.0112138	−	0.0112138i	−0.712691	+	0.701478i	$0.752524\pi$
$308$	−12.4341	+	29.3581i	−0.708498	+	1.67283i
$309$	−7.49296	+	7.49296i	−0.426259	+	0.426259i
$310$	5.49072	−	1.06957i	0.311852	−	0.0607473i
$311$		−	2.52927i		−	0.143422i	−0.997425	−	0.0717110i	$-0.977154\pi$
$311$		−	2.52927i		−	0.143422i	0.997425	−	0.0717110i	$-0.0228459\pi$
$312$	−10.4597	−	2.21017i	−0.592165	−	0.125126i
$313$			3.84874i			0.217543i	0.994067	+	0.108772i	$0.0346917\pi$
$313$			3.84874i			0.217543i	−0.994067	+	0.108772i	$0.965308\pi$
$314$	1.68753	+	8.66308i	0.0952327	+	0.488886i
$315$	1.46056	−	1.46056i	0.0822930	−	0.0822930i
$316$	−4.17453	−	10.3086i	−0.234835	−	0.579902i
$317$	−6.78901	−	6.78901i	−0.381309	−	0.381309i	0.490265	−	0.871574i	$-0.336900\pi$
$317$	−6.78901	−	6.78901i	−0.381309	−	0.381309i	−0.871574	+	0.490265i	$0.836900\pi$
$318$	−23.1579	−	15.6067i	−1.29863	−	0.875180i
$319$	−46.7627			−2.61821
$320$	7.46174	−	2.88485i	0.417124	−	0.161268i
$321$	0.804906			0.0449255
$322$	5.28616	+	3.56249i	0.294586	+	0.198530i
$323$	1.44871	+	1.44871i	0.0806085	+	0.0806085i
$324$	8.02898	+	19.8268i	0.446054	+	1.10149i
$325$	−1.37919	+	1.37919i	−0.0765038	+	0.0765038i
$326$	1.37249	+	7.04581i	0.0760152	+	0.390231i
$327$			28.5385i			1.57818i
$328$	23.2688	+	4.91678i	1.28481	+	0.271484i
$329$		−	14.2158i		−	0.783743i
$330$	15.6800	−	3.05438i	0.863154	−	0.168138i
$331$	1.79195	−	1.79195i	0.0984944	−	0.0984944i	−0.656143	−	0.754637i	$-0.727813\pi$
$331$	1.79195	−	1.79195i	0.0984944	−	0.0984944i	0.754637	+	0.656143i	$0.227813\pi$
$332$	0.569396	−	1.34440i	0.0312497	−	0.0737836i
$333$	1.87891	+	1.87891i	0.102964	+	0.102964i
$334$	−13.9096	+	20.6396i	−0.761100	+	1.12935i
$335$	−8.14650			−0.445091
$336$	0.336068	−	21.1960i	0.0183340	−	1.15634i
$337$	16.1071			0.877411			0.438706	−	0.898631i	$-0.355437\pi$
$337$	16.1071			0.877411			0.438706	+	0.898631i	$0.355437\pi$
$338$	−7.26779	+	10.7842i	−0.395315	+	0.586585i
$339$	−23.8625	−	23.8625i	−1.29603	−	1.29603i
$340$	9.11464	+	3.86034i	0.494311	+	0.209356i
$341$	16.3036	−	16.3036i	0.882889	−	0.882889i
$342$	−0.434003	+	0.0845418i	−0.0234682	+	0.00457150i
$343$			17.8331i			0.962898i
$344$	7.04347	+	10.8176i	0.379758	+	0.583243i
$345$		−	3.19394i		−	0.171956i
$346$	2.80063	+	14.3773i	0.150563	+	0.772929i
$347$	12.6577	−	12.6577i	0.679502	−	0.679502i	−0.280385	−	0.959888i	$-0.590462\pi$
$347$	12.6577	−	12.6577i	0.679502	−	0.679502i	0.959888	+	0.280385i	$0.0904622\pi$
$348$	28.8190	−	11.6704i	1.54486	−	0.625601i
$349$	−16.3020	−	16.3020i	−0.872627	−	0.872627i	0.120131	−	0.992758i	$-0.461669\pi$
$349$	−16.3020	−	16.3020i	−0.872627	−	0.872627i	−0.992758	+	0.120131i	$0.961669\pi$
$350$	−3.20726	−	2.16146i	−0.171435	−	0.115535i
$351$	−8.48445			−0.452866
$352$	18.8591	−	27.0485i	1.00519	−	1.44169i
$353$	−13.2637			−0.705954			−0.352977	−	0.935632i	$-0.614831\pi$
$353$	−13.2637			−0.705954			−0.352977	+	0.935632i	$0.614831\pi$
$354$	20.6061	+	13.8870i	1.09520	+	0.738087i
$355$	−5.60202	−	5.60202i	−0.297324	−	0.297324i
$356$	−11.9056	+	4.82124i	−0.630993	+	0.255525i
$357$	18.5469	−	18.5469i	0.981604	−	0.981604i
$358$	−2.45827	−	12.6198i	−0.129924	−	0.666976i
$359$			13.3561i			0.704906i	0.935830	+	0.352453i	$0.114652\pi$
$359$			13.3561i			0.704906i	−0.935830	+	0.352453i	$0.885348\pi$
$360$	−1.79020	+	1.16563i	−0.0943520	+	0.0614339i
$361$		−	18.8286i		−	0.990981i
$362$	7.22194	−	1.40680i	0.379577	−	0.0739398i
$363$	31.4855	−	31.4855i	1.65256	−	1.65256i
$364$	9.82361	+	4.16061i	0.514897	+	0.218075i
$365$	3.08494	+	3.08494i	0.161473	+	0.161473i
$366$	−8.28743	+	12.2972i	−0.433191	+	0.642786i
$367$	11.8938			0.620852			0.310426	−	0.950598i	$-0.399528\pi$
$367$	11.8938			0.620852			0.310426	+	0.950598i	$0.399528\pi$
$368$	−4.58728	−	4.73509i	−0.239129	−	0.246834i
$369$	−6.35067			−0.330603
$370$	2.78058	−	4.12594i	0.144556	−	0.214498i
$371$	19.7054	+	19.7054i	1.02305	+	1.02305i
$372$	−5.97877	+	14.1165i	−0.309985	+	0.731905i
$373$	−19.0494	+	19.0494i	−0.986342	+	0.986342i	−0.999908	−	0.0135655i	$-0.995682\pi$
$373$	−19.0494	+	19.0494i	−0.986342	+	0.986342i	0.0135655	+	0.999908i	$0.495682\pi$
$374$	40.0461	−	7.80080i	2.07074	−	0.403370i
$375$			1.93785i			0.100070i
$376$	−3.03955	+	14.3848i	−0.156753	+	0.741839i
$377$			15.6474i			0.805882i
$378$	−3.21676	−	16.5135i	−0.165452	−	0.849365i
$379$	−4.64554	+	4.64554i	−0.238625	+	0.238625i	−0.816281	−	0.577655i	$-0.803968\pi$
$379$	−4.64554	+	4.64554i	−0.238625	+	0.238625i	0.577655	+	0.816281i	$0.303968\pi$
$380$	0.310760	+	0.767390i	0.0159416	+	0.0393663i
$381$	15.0446	+	15.0446i	0.770757	+	0.770757i
$382$	6.32222	+	4.26072i	0.323473	+	0.217997i
$383$	38.5131			1.96793			0.983964	−	0.178366i	$-0.0570811\pi$
$383$	38.5131			1.96793			0.983964	+	0.178366i	$0.0570811\pi$
$384$	−4.87208	+	21.3761i	−0.248628	+	1.09084i
$385$	−15.9413			−0.812446
$386$	4.14941	+	2.79640i	0.211200	+	0.142333i
$387$	−2.43737	−	2.43737i	−0.123898	−	0.123898i
$388$	−7.09058	−	17.5095i	−0.359970	−	0.888909i
$389$	−0.903192	+	0.903192i	−0.0457937	+	0.0457937i	−0.729633	−	0.683839i	$-0.760309\pi$
$389$	−0.903192	+	0.903192i	−0.0457937	+	0.0457937i	0.683839	+	0.729633i	$0.260309\pi$
$390$	−1.02204	−	5.24672i	−0.0517529	−	0.265678i
$391$		−	8.15722i		−	0.412528i
$392$	−0.280224	+	1.32617i	−0.0141534	+	0.0669817i
$393$			15.8141i			0.797716i
$394$	−20.9855	+	4.08787i	−1.05723	+	0.205944i
$395$	3.93213	−	3.93213i	0.197847	−	0.197847i
$396$	−3.43392	+	8.10783i	−0.172561	+	0.407434i
$397$	4.44748	+	4.44748i	0.223212	+	0.223212i	0.809850	−	0.586637i	$-0.199549\pi$
$397$	4.44748	+	4.44748i	0.223212	+	0.223212i	−0.586637	+	0.809850i	$0.699549\pi$
$398$	12.3724	−	18.3587i	0.620172	−	0.920237i
$399$	2.19386			0.109831
$400$	2.78323	+	2.87291i	0.139162	+	0.143646i
$401$	27.3379			1.36519			0.682596	−	0.730796i	$-0.260851\pi$
$401$	27.3379			1.36519			0.682596	+	0.730796i	$0.260851\pi$
$402$	12.4770	−	18.5139i	0.622297	−	0.923390i
$403$	−5.45540	−	5.45540i	−0.271753	−	0.271753i
$404$	−28.7902	−	12.1936i	−1.43237	−	0.606652i
$405$	−7.56278	+	7.56278i	−0.375797	+	0.375797i
$406$	−30.4550	+	5.93249i	−1.51146	+	0.294425i
$407$		−	20.5075i		−	1.01652i
$408$	−22.7329	+	14.8017i	−1.12545	+	0.732794i
$409$			38.6889i			1.91304i	0.291661	+	0.956522i	$0.405792\pi$
$409$			38.6889i			1.91304i	−0.291661	+	0.956522i	$0.594208\pi$
$410$	2.27364	+	11.6719i	0.112287	+	0.576435i
$411$	−9.84993	+	9.84993i	−0.485861	+	0.485861i
$412$	−10.1368	+	4.10498i	−0.499406	+	0.202238i
$413$	−17.5341	−	17.5341i	−0.862794	−	0.862794i
$414$	1.45988	+	0.983852i	0.0717492	+	0.0483537i
$415$	0.730005			0.0358345
$416$	−9.05077	−	6.31049i	−0.443751	−	0.309397i
$417$	13.4650			0.659384
$418$	2.82985	+	1.90711i	0.138413	+	0.0932799i
$419$	7.41439	+	7.41439i	0.362217	+	0.362217i	0.864628	−	0.502412i	$-0.167554\pi$
$419$	7.41439	+	7.41439i	0.362217	+	0.362217i	−0.502412	+	0.864628i	$0.667554\pi$
$420$	9.82437	−	3.97844i	0.479380	−	0.194128i
$421$	−10.3279	+	10.3279i	−0.503351	+	0.503351i	−0.912478	−	0.409127i	$-0.865833\pi$
$421$	−10.3279	+	10.3279i	−0.503351	+	0.503351i	0.409127	+	0.912478i	$0.365833\pi$
$422$	7.62354	+	39.1362i	0.371108	+	1.90512i
$423$		−	3.92598i		−	0.190888i
$424$	−15.7263	−	24.1529i	−0.763736	−	1.17297i
$425$			4.94921i			0.240072i
$426$	21.3112	−	4.15132i	1.03253	−	0.201132i
$427$	10.4639	−	10.4639i	0.506383	−	0.506383i
$428$	0.764940	+	0.323976i	0.0369748	+	0.0156600i
$429$	−15.5791	−	15.5791i	−0.752165	−	0.752165i
$430$	−3.60704	+	5.35227i	−0.173947	+	0.258109i
$431$	−14.8644			−0.715991			−0.357995	−	0.933723i	$-0.616540\pi$
$431$	−14.8644			−0.715991			−0.357995	+	0.933723i	$0.616540\pi$
$432$	−0.275843	+	17.3976i	−0.0132715	+	0.837043i
$433$	−4.96284			−0.238499			−0.119249	−	0.992864i	$-0.538049\pi$
$433$	−4.96284			−0.238499			−0.119249	+	0.992864i	$0.538049\pi$
$434$	8.54967	−	12.6863i	0.410397	−	0.608964i
$435$	10.9928	+	10.9928i	0.527064	+	0.527064i
$436$	−11.4868	+	27.1215i	−0.550118	+	1.29888i
$437$	0.482449	−	0.482449i	0.0230787	−	0.0230787i
$438$	−11.7357	+	2.28606i	−0.560755	+	0.109232i
$439$		−	13.7348i		−	0.655527i	−0.944760	−	0.327763i	$-0.893705\pi$
$439$		−	13.7348i		−	0.655527i	0.944760	−	0.327763i	$-0.106295\pi$
$440$	16.1308	+	3.40849i	0.769007	+	0.162494i
$441$		−	0.361946i		−	0.0172355i
$442$	−2.61025	−	13.4000i	−0.124157	−	0.637371i
$443$	−7.62584	+	7.62584i	−0.362315	+	0.362315i	−0.864664	−	0.502350i	$-0.832469\pi$
$443$	−7.62584	+	7.62584i	−0.362315	+	0.362315i	0.502350	+	0.864664i	$0.332469\pi$
$444$	5.11802	+	12.6384i	0.242890	+	0.599793i
$445$	−4.54129	−	4.54129i	−0.215278	−	0.215278i
$446$	−24.8826	−	16.7690i	−1.17822	−	0.794037i
$447$	26.7646			1.26592
$448$	8.85083	−	20.0083i	0.418162	−	0.945305i
$449$	−15.8544			−0.748215			−0.374108	−	0.927385i	$-0.622051\pi$
$449$	−15.8544			−0.748215			−0.374108	+	0.927385i	$0.622051\pi$
$450$	−0.885750	−	0.596931i	−0.0417546	−	0.0281396i
$451$	34.6574	+	34.6574i	1.63195	+	1.63195i
$452$	−13.0730	−	32.2824i	−0.614901	−	1.51844i
$453$	2.61385	−	2.61385i	0.122809	−	0.122809i
$454$	−4.60246	−	23.6271i	−0.216004	−	1.10888i
$455$			5.33418i			0.250070i
$456$	−2.21994	−	0.469080i	−0.103958	−	0.0219667i
$457$		−	14.1978i		−	0.664144i	−0.943254	−	0.332072i	$-0.892252\pi$
$457$		−	14.1978i		−	0.664144i	0.943254	−	0.332072i	$-0.107748\pi$
$458$	−13.1687	+	2.56519i	−0.615331	+	0.119864i
$459$	−15.2232	+	15.2232i	−0.710557	+	0.710557i
$460$	1.28557	−	3.03535i	0.0599399	−	0.141524i
$461$	−22.8952	−	22.8952i	−1.06634	−	1.06634i	−0.997638	−	0.0686980i	$-0.978116\pi$
$461$	−22.8952	−	22.8952i	−1.06634	−	1.06634i	−0.0686980	−	0.997638i	$-0.521884\pi$
$462$	24.4155	−	36.2286i	1.13591	−	1.68551i
$463$	25.0175			1.16266			0.581330	−	0.813668i	$-0.302533\pi$
$463$	25.0175			1.16266			0.581330	+	0.813668i	$0.302533\pi$
$464$	32.0854	+	0.508722i	1.48953	+	0.0236168i
$465$	−7.66519			−0.355465
$466$	4.27129	−	6.33792i	0.197864	−	0.293598i
$467$	−23.5446	−	23.5446i	−1.08951	−	1.08951i	−0.995578	−	0.0939334i	$-0.970056\pi$
$467$	−23.5446	−	23.5446i	−1.08951	−	1.08951i	−0.0939334	−	0.995578i	$-0.529944\pi$
$468$	2.71299	+	1.14903i	0.125408	+	0.0531142i
$469$	−15.7538	+	15.7538i	−0.727441	+	0.727441i
$470$	−7.21558	+	1.40556i	−0.332830	+	0.0648337i
$471$		−	12.0939i		−	0.557256i
$472$	13.9934	+	21.4915i	0.644100	+	0.989226i
$473$			26.6028i			1.22320i
$474$	2.91387	+	14.9586i	0.133838	+	0.687072i
$475$	−0.292715	+	0.292715i	−0.0134307	+	0.0134307i
$476$	25.0911	−	10.1608i	1.15005	−	0.465720i
$477$	5.44203	+	5.44203i	0.249173	+	0.249173i
$478$	2.18799	+	1.47454i	0.100076	+	0.0674441i
$479$	39.3416			1.79756			0.898781	−	0.438398i	$-0.144454\pi$
$479$	39.3416			1.79756			0.898781	+	0.438398i	$0.144454\pi$
$480$	−10.7918	+	1.92514i	−0.492575	+	0.0878701i
$481$	−6.86209			−0.312884
$482$	−19.2026	−	12.9411i	−0.874654	−	0.589453i
$483$	−6.17647	−	6.17647i	−0.281039	−	0.281039i
$484$	42.5952	−	17.2492i	1.93615	−	0.784055i
$485$	6.67886	−	6.67886i	0.303272	−	0.303272i
$486$	−2.07565	−	10.6556i	−0.0941535	−	0.483346i
$487$			25.6970i			1.16444i	0.813030	+	0.582222i	$0.197816\pi$
$487$			25.6970i			1.16444i	−0.813030	+	0.582222i	$0.802184\pi$
$488$	−12.8256	+	8.35093i	−0.580588	+	0.378029i
$489$		−	9.83612i		−	0.444805i
$490$	−0.665222	+	0.129582i	−0.0300517	+	0.00585393i
$491$	−29.0344	+	29.0344i	−1.31030	+	1.31030i	−0.389113	+	0.921190i	$0.627219\pi$
$491$	−29.0344	+	29.0344i	−1.31030	+	1.31030i	−0.921190	+	0.389113i	$0.872781\pi$
$492$	−30.0081	−	12.7094i	−1.35287	−	0.572983i
$493$	28.0753	+	28.0753i	1.26445	+	1.26445i
$494$	0.638145	−	0.946905i	0.0287115	−	0.0426033i
$495$	−4.40252			−0.197879
$496$	−11.3638	+	11.0091i	−0.510250	+	0.494323i
$497$	−21.6665			−0.971873
$498$	−1.11806	+	1.65902i	−0.0501015	+	0.0743427i
$499$	−7.89904	−	7.89904i	−0.353610	−	0.353610i	0.507841	−	0.861451i	$-0.330444\pi$
$499$	−7.89904	−	7.89904i	−0.353610	−	0.353610i	−0.861451	+	0.507841i	$0.830444\pi$
$500$	−0.779990	+	1.84163i	−0.0348822	+	0.0823604i
$501$	24.1158	−	24.1158i	1.07741	−	1.07741i
$502$	−5.91197	+	1.15162i	−0.263864	+	0.0513995i
$503$			9.53668i			0.425220i	0.977137	+	0.212610i	$0.0681963\pi$
$503$			9.53668i			0.425220i	−0.977137	+	0.212610i	$0.931804\pi$
$504$	−1.20781	+	5.71601i	−0.0538002	+	0.254611i
$505$		−	15.6330i		−	0.695658i
$506$	−2.59782	−	13.3361i	−0.115487	−	0.592864i
$507$	12.6005	−	12.6005i	0.559609	−	0.559609i
$508$	8.24211	+	20.3531i	0.365684	+	0.903021i
$509$	−4.24956	−	4.24956i	−0.188358	−	0.188358i	0.606628	−	0.794986i	$-0.292522\pi$
$509$	−4.24956	−	4.24956i	−0.188358	−	0.188358i	−0.794986	+	0.606628i	$0.792522\pi$
$510$	−11.2477	−	7.58012i	−0.498056	−	0.335653i
$511$	11.9313			0.527812
$512$	−13.2341	+	18.3537i	−0.584870	+	0.811127i
$513$	−1.80071			−0.0795035
$514$	−26.6692	−	17.9731i	−1.17633	−	0.792759i
$515$	−3.86663	−	3.86663i	−0.170384	−	0.170384i
$516$	−6.63921	−	16.3949i	−0.292275	−	0.721743i
$517$	−21.4252	+	21.4252i	−0.942280	+	0.942280i
$518$	−2.60166	−	13.3559i	−0.114311	−	0.586824i
$519$		−	20.0711i		−	0.881022i
$520$	1.14053	−	5.39758i	0.0500154	−	0.236700i
$521$		−	9.71766i		−	0.425739i	−0.977081	−	0.212869i	$-0.931719\pi$
$521$		−	9.71766i		−	0.425739i	0.977081	−	0.212869i	$-0.0682809\pi$
$522$	−8.41076	+	1.63838i	−0.368129	+	0.0717098i
$523$	−4.62580	+	4.62580i	−0.202272	+	0.202272i	−0.800973	−	0.598701i	$-0.795684\pi$
$523$	−4.62580	+	4.62580i	−0.202272	+	0.202272i	0.598701	+	0.800973i	$0.295684\pi$
$524$	−6.36521	+	15.0289i	−0.278066	+	0.656541i
$525$	3.74744	+	3.74744i	0.163551	+	0.163551i
$526$	−9.50794	+	14.1083i	−0.414566	+	0.615150i
$527$	−19.5766			−0.852772
$528$	−32.4519	+	31.4389i	−1.41229	+	1.36820i
$529$	20.2835			0.881891
$530$	8.05360	−	11.9503i	0.349826	−	0.519086i
$531$	−4.84238	−	4.84238i	−0.210141	−	0.210141i
$532$	2.08493	+	0.883035i	0.0903933	+	0.0382844i
$533$	11.5968	−	11.5968i	0.502314	−	0.502314i
$534$	17.2760	−	3.36528i	0.747605	−	0.145630i
$535$			0.415360i			0.0179576i
$536$	19.3094	−	12.5726i	0.834039	−	0.543055i
$537$			17.6175i			0.760252i
$538$	−1.87403	−	9.62053i	−0.0807953	−	0.414771i
$539$	−1.97524	+	1.97524i	−0.0850798	+	0.0850798i
$540$	−8.06379	+	3.26549i	−0.347010	+	0.140524i
$541$	24.0206	+	24.0206i	1.03272	+	1.03272i	0.999446	+	0.0332788i	$0.0105949\pi$
$541$	24.0206	+	24.0206i	1.03272	+	1.03272i	0.0332788	+	0.999446i	$0.489405\pi$
$542$	4.86242	+	3.27692i	0.208859	+	0.140756i
$543$	−10.0820			−0.432660
$544$	−27.5619	+	4.91674i	−1.18171	+	0.210803i
$545$	−14.7269			−0.630829
$546$	−12.1226	−	8.16973i	−0.518798	−	0.349632i
$547$	4.63900	+	4.63900i	0.198349	+	0.198349i	0.799292	−	0.600943i	$-0.205208\pi$
$547$	4.63900	+	4.63900i	0.198349	+	0.198349i	−0.600943	+	0.799292i	$0.705208\pi$
$548$	−13.3255	+	5.39624i	−0.569236	+	0.230516i
$549$	2.88981	−	2.88981i	0.123334	−	0.123334i
$550$	1.57617	+	8.09141i	0.0672081	+	0.345019i
$551$			3.32096i			0.141477i
$552$	4.92926	+	7.57050i	0.209803	+	0.322222i
$553$		−	15.2080i		−	0.646709i
$554$	20.5763	−	4.00818i	0.874205	−	0.170291i
$555$	−4.82084	+	4.82084i	−0.204633	+	0.204633i
$556$	12.7964	+	5.41969i	0.542690	+	0.229846i
$557$	13.6258	+	13.6258i	0.577345	+	0.577345i	0.934171	−	0.356826i	$-0.116141\pi$
$557$	13.6258	+	13.6258i	0.577345	+	0.577345i	−0.356826	+	0.934171i	$0.616141\pi$
$558$	2.36116	−	3.50359i	0.0999559	−	0.148319i
$559$	8.90166			0.376500
$560$	10.9379	+	0.173423i	0.462210	+	0.00732846i
$561$	−55.9054			−2.36033
$562$	2.78145	−	4.12723i	0.117328	−	0.174097i
$563$	28.0885	+	28.0885i	1.18379	+	1.18379i	0.978755	+	0.205035i	$0.0657308\pi$
$563$	28.0885	+	28.0885i	1.18379	+	1.18379i	0.205035	+	0.978755i	$0.434269\pi$
$564$	7.85694	−	18.5510i	0.330837	−	0.781139i
$565$	12.3139	−	12.3139i	0.518050	−	0.518050i
$566$	5.66280	−	1.10309i	0.238025	−	0.0463662i
$567$			29.2499i			1.22838i
$568$	21.9240	+	4.63261i	0.919910	+	0.194380i
$569$		−	42.3770i		−	1.77654i	−0.459326	−	0.888268i	$-0.651909\pi$
$569$		−	42.3770i		−	1.77654i	0.459326	−	0.888268i	$-0.348091\pi$
$570$	−0.216914	−	1.11355i	−0.00908553	−	0.0466414i
$571$	7.99217	−	7.99217i	0.334462	−	0.334462i	−0.519816	−	0.854278i	$-0.674000\pi$
$571$	7.99217	−	7.99217i	0.334462	−	0.334462i	0.854278	+	0.519816i	$0.174000\pi$
$572$	−8.53493	−	21.0762i	−0.356863	−	0.881239i
$573$	−7.38702	−	7.38702i	−0.308597	−	0.308597i
$574$	26.9680	+	18.1745i	1.12562	+	0.758588i
$575$	1.64818			0.0687341
$576$	2.44433	−	5.52570i	0.101847	−	0.230238i
$577$	−20.4651			−0.851972			−0.425986	−	0.904730i	$-0.640073\pi$
$577$	−20.4651			−0.851972			−0.425986	+	0.904730i	$0.640073\pi$
$578$	−8.78945	−	5.92345i	−0.365593	−	0.246383i
$579$	−4.84826	−	4.84826i	−0.201487	−	0.201487i
$580$	6.02236	+	14.8716i	0.250065	+	0.617510i
$581$	1.41169	−	1.41169i	0.0585667	−	0.0585667i
$582$	4.94931	+	25.4078i	0.205156	+	1.05319i
$583$		−	59.3974i		−	2.45999i
$584$	−12.0732	−	2.55110i	−0.499591	−	0.105565i
$585$			1.47314i			0.0609069i
$586$	−7.70224	+	1.50036i	−0.318177	+	0.0619793i
$587$	0.429976	−	0.429976i	0.0177470	−	0.0177470i	−0.698178	−	0.715925i	$-0.746005\pi$
$587$	0.429976	−	0.429976i	0.0177470	−	0.0177470i	0.715925	+	0.698178i	$0.246005\pi$
$588$	0.724351	−	1.71026i	0.0298717	−	0.0705301i
$589$	−1.15784	−	1.15784i	−0.0477079	−	0.0477079i
$590$	−7.16619	+	10.6335i	−0.295027	+	0.437773i
$591$	29.2962			1.20509
$592$	−0.223098	+	14.0709i	−0.00916926	+	0.578311i
$593$	37.9620			1.55891			0.779455	−	0.626458i	$-0.215496\pi$
$593$	37.9620			1.55891			0.779455	+	0.626458i	$0.215496\pi$
$594$	−20.0401	+	29.7363i	−0.822255	+	1.22010i
$595$	9.57083	+	9.57083i	0.392366	+	0.392366i
$596$	25.4357	+	10.7728i	1.04189	+	0.441272i
$597$	−21.4507	+	21.4507i	−0.877917	+	0.877917i
$598$	−4.46245	+	0.869264i	−0.182483	+	0.0355468i
$599$			13.7108i			0.560207i	0.959970	+	0.280104i	$0.0903688\pi$
$599$			13.7108i			0.560207i	−0.959970	+	0.280104i	$0.909631\pi$
$600$	−2.99072	−	4.59323i	−0.122096	−	0.187518i
$601$			2.84070i			0.115875i	0.998320	+	0.0579373i	$0.0184523\pi$
$601$			2.84070i			0.115875i	−0.998320	+	0.0579373i	$0.981548\pi$
$602$	3.37494	+	17.3256i	0.137552	+	0.706138i
$603$	−4.35072	+	4.35072i	−0.177175	+	0.177175i
$604$	3.53615	−	1.43199i	0.143884	−	0.0582667i
$605$	16.2476	+	16.2476i	0.660561	+	0.660561i
$606$	35.5278	+	23.9432i	1.44322	+	0.972625i
$607$	−42.8562			−1.73948			−0.869740	−	0.493510i	$-0.835713\pi$
$607$	−42.8562			−1.73948			−0.869740	+	0.493510i	$0.835713\pi$
$608$	−1.92091	−	1.33932i	−0.0779032	−	0.0543166i
$609$	42.5159			1.72283
$610$	−6.34580	−	4.27661i	−0.256934	−	0.173155i
$611$	7.16916	+	7.16916i	0.290033	+	0.290033i
$612$	6.92941	−	2.80611i	0.280105	−	0.113430i
$613$	5.48393	−	5.48393i	0.221494	−	0.221494i	−0.587633	−	0.809127i	$-0.699940\pi$
$613$	5.48393	−	5.48393i	0.221494	−	0.221494i	0.809127	+	0.587633i	$0.199940\pi$
$614$	0.0751353	+	0.385714i	0.00303221	+	0.0155661i
$615$		−	16.2943i		−	0.657049i
$616$	37.7853	−	24.6025i	1.52241	−	0.991264i
$617$		−	22.2539i		−	0.895908i	−0.894057	−	0.447954i	$-0.852153\pi$
$617$		−	22.2539i		−	0.895908i	0.894057	−	0.447954i	$-0.147847\pi$
$618$	14.7094	−	2.86533i	0.591700	−	0.115260i
$619$	10.0974	−	10.0974i	0.405849	−	0.405849i	−0.474439	−	0.880288i	$-0.657349\pi$
$619$	10.0974	−	10.0974i	0.405849	−	0.405849i	0.880288	+	0.474439i	$0.157349\pi$
$620$	−7.28459	−	3.08525i	−0.292556	−	0.123907i
$621$	5.06962	+	5.06962i	0.203437	+	0.203437i
$622$	−1.99901	+	2.96621i	−0.0801530	+	0.118934i
$623$	−17.5640			−0.703685
$624$	10.5199	+	10.8588i	0.421131	+	0.434701i
$625$	−1.00000			−0.0400000
$626$	3.04185	−	4.51361i	0.121577	−	0.180400i
$627$	−3.30646	−	3.30646i	−0.132047	−	0.132047i
$628$	4.86781	−	11.4934i	0.194247	−	0.458636i
$629$	−12.3123	+	12.3123i	−0.490922	+	0.490922i
$630$	−2.86722	+	0.558521i	−0.114233	+	0.0222520i
$631$		−	49.5996i		−	1.97453i	−0.159086	−	0.987265i	$-0.550855\pi$
$631$		−	49.5996i		−	1.97453i	0.159086	−	0.987265i	$-0.449145\pi$
$632$	−3.25169	+	15.3887i	−0.129345	+	0.612131i
$633$		−	54.6351i		−	2.17155i
$634$	2.59614	+	13.3275i	0.103106	+	0.529303i
$635$	−7.76353	+	7.76353i	−0.308086	+	0.308086i
$636$	14.8237	+	36.6056i	0.587797	+	1.45151i
$637$	0.660942	+	0.660942i	0.0261875	+	0.0261875i
$638$	54.8410	+	36.9588i	2.17118	+	1.46321i
$639$	−5.98362			−0.236709
$640$	−11.0308	−	2.51417i	−0.436031	−	0.0993811i
$641$	−42.5379			−1.68015			−0.840074	−	0.542472i	$-0.817488\pi$
$641$	−42.5379			−1.68015			−0.840074	+	0.542472i	$0.817488\pi$
$642$	−0.943955	−	0.636157i	−0.0372549	−	0.0251071i
$643$	−29.3128	−	29.3128i	−1.15598	−	1.15598i	−0.985331	−	0.170653i	$-0.945412\pi$
$643$	−29.3128	−	29.3128i	−1.15598	−	1.15598i	−0.170653	−	0.985331i	$-0.554588\pi$
$644$	−3.38375	−	8.35583i	−0.133338	−	0.329266i
$645$	6.25370	−	6.25370i	0.246239	−	0.246239i
$646$	−0.553992	−	2.84397i	−0.0217965	−	0.111894i
$647$		−	4.35345i		−	0.171152i	−0.996332	−	0.0855759i	$-0.972727\pi$
$647$		−	4.35345i		−	0.171152i	0.996332	−	0.0855759i	$-0.0272730\pi$
$648$	6.25406	−	29.5976i	0.245683	−	1.16270i
$649$			52.8525i			2.07464i
$650$	2.70749	−	0.527407i	0.106197	−	0.0206866i
$651$	−14.8230	+	14.8230i	−0.580959	+	0.580959i
$652$	3.95906	−	9.34774i	0.155049	−	0.366086i
$653$	−12.3460	−	12.3460i	−0.483137	−	0.483137i	0.422995	−	0.906132i	$-0.360979\pi$
$653$	−12.3460	−	12.3460i	−0.483137	−	0.483137i	−0.906132	+	0.422995i	$0.860979\pi$
$654$	22.5554	−	33.4686i	0.881985	−	1.30872i
$655$	−8.16063			−0.318862
$656$	−23.4026	−	24.1567i	−0.913718	−	0.943159i
$657$	3.29508			0.128553
$658$	−11.2355	+	16.6716i	−0.438004	+	0.649928i
$659$	19.5367	+	19.5367i	0.761040	+	0.761040i	0.976510	−	0.215470i	$-0.0691284\pi$
$659$	19.5367	+	19.5367i	0.761040	+	0.761040i	−0.215470	+	0.976510i	$0.569128\pi$
$660$	−20.8028	−	8.81062i	−0.809746	−	0.342953i
$661$	26.4901	−	26.4901i	1.03035	−	1.03035i	0.0308210	−	0.999525i	$-0.490188\pi$
$661$	26.4901	−	26.4901i	1.03035	−	1.03035i	0.999525	−	0.0308210i	$-0.00981219\pi$
$662$	−3.51778	+	0.685247i	−0.136722	+	0.0266329i
$663$			18.7067i			0.726507i
$664$	−1.73031	+	1.12663i	−0.0671490	+	0.0437217i
$665$			1.13211i			0.0439014i
$666$	−0.718502	−	3.68850i	−0.0278414	−	0.142926i
$667$	9.34961	−	9.34961i	0.362018	−	0.362018i
$668$	32.6250	−	13.2117i	1.26230	−	0.511177i
$669$	29.0734	+	29.0734i	1.12404	+	1.12404i
$670$	9.55382	+	6.43858i	0.369096	+	0.248744i
$671$	−31.5411			−1.21763
$672$	−17.1464	+	24.5921i	−0.661436	+	0.948660i
$673$	−11.5260			−0.444295			−0.222148	−	0.975013i	$-0.571307\pi$
$673$	−11.5260			−0.444295			−0.222148	+	0.975013i	$0.571307\pi$
$674$	−18.8897	−	12.7303i	−0.727603	−	0.490351i
$675$	−3.07588	−	3.07588i	−0.118391	−	0.118391i
$676$	17.0466	−	6.90315i	0.655639	−	0.265506i
$677$	−15.8009	+	15.8009i	−0.607278	+	0.607278i	−0.942234	−	0.334956i	$-0.891279\pi$
$677$	−15.8009	+	15.8009i	−0.607278	+	0.607278i	0.334956	+	0.942234i	$0.391279\pi$
$678$	9.12510	+	46.8446i	0.350447	+	1.79905i
$679$		−	25.8313i		−	0.991314i
$680$	−7.63820	−	11.7310i	−0.292912	−	0.449862i
$681$			32.9841i			1.26395i
$682$	−32.0056	+	6.23454i	−1.22556	+	0.238733i
$683$	−25.1439	+	25.1439i	−0.962105	+	0.962105i	−0.999308	−	0.0372032i	$-0.988155\pi$
$683$	−25.1439	+	25.1439i	−0.962105	+	0.962105i	0.0372032	+	0.999308i	$0.488155\pi$
$684$	0.575796	+	0.243868i	0.0220161	+	0.00932452i
$685$	−5.08291	−	5.08291i	−0.194208	−	0.194208i
$686$	14.0944	−	20.9138i	0.538127	−	0.798494i
$687$	18.3838			0.701385
$688$	0.289407	−	18.2531i	0.0110336	−	0.695893i
$689$	−19.8752			−0.757183
$690$	−2.52433	+	3.74570i	−0.0960995	+	0.142596i
$691$	−27.2647	−	27.2647i	−1.03720	−	1.03720i	−0.999281	−	0.0379162i	$-0.987928\pi$
$691$	−27.2647	−	27.2647i	−1.03720	−	1.03720i	−0.0379162	−	0.999281i	$-0.512072\pi$
$692$	8.07865	−	19.0745i	0.307104	−	0.725103i
$693$	−8.51363	+	8.51363i	−0.323406	+	0.323406i
$694$	−24.8484	+	4.84035i	−0.943232	+	0.183737i
$695$			6.94841i			0.263568i
$696$	−43.0213	−	9.09053i	−1.63072	−	0.344576i
$697$		−	41.6151i		−	1.57628i
$698$	6.23394	+	32.0025i	0.235958	+	1.21131i
$699$	−7.40536	+	7.40536i	−0.280096	+	0.280096i
$700$	2.05302	+	5.06972i	0.0775967	+	0.191617i
$701$	12.5566	+	12.5566i	0.474257	+	0.474257i	0.903289	−	0.429032i	$-0.141145\pi$
$701$	12.5566	+	12.5566i	0.474257	+	0.474257i	−0.429032	+	0.903289i	$0.641145\pi$
$702$	9.95016	+	6.70568i	0.375544	+	0.253090i
$703$	−1.45639			−0.0549288
$704$	−43.4948	+	16.8159i	−1.63927	+	0.633773i
$705$	10.0731			0.379376
$706$	15.5550	+	10.4829i	0.585420	+	0.394531i
$707$	−30.2312	−	30.2312i	−1.13696	−	1.13696i
$708$	−13.1903	−	32.5721i	−0.495721	−	1.22413i
$709$	18.0518	−	18.0518i	0.677950	−	0.677950i	−0.281586	−	0.959536i	$-0.590860\pi$
$709$	18.0518	−	18.0518i	0.677950	−	0.677950i	0.959536	+	0.281586i	$0.0908604\pi$
$710$	2.14223	+	10.9973i	0.0803964	+	0.412723i
$711$		−	4.19999i		−	0.157512i
$712$	17.7727	+	3.75543i	0.666061	+	0.140741i
$713$			6.51940i			0.244154i
$714$	−36.4094	+	7.09237i	−1.36259	+	0.265425i
$715$	8.03935	−	8.03935i	0.300655	−	0.300655i
$716$	−7.09109	+	16.7428i	−0.265006	+	0.625707i
$717$	−2.55649	−	2.55649i	−0.0954739	−	0.0954739i
$718$	10.5560	−	15.6633i	0.393945	−	0.584551i
$719$	−1.68053			−0.0626731			−0.0313366	−	0.999509i	$-0.509976\pi$
$719$	−1.68053			−0.0626731			−0.0313366	+	0.999509i	$0.509976\pi$
$720$	3.02072	+	0.0478942i	0.112576	+	0.00178491i
$721$	−14.9546			−0.556939
$722$	−14.8812	+	22.0813i	−0.553821	+	0.821782i
$723$	22.4367	+	22.4367i	0.834431	+	0.834431i
$724$	−9.58141	−	4.05803i	−0.356090	−	0.150815i
$725$	−5.67267	+	5.67267i	−0.210678	+	0.210678i
$726$	−61.8093	+	12.0402i	−2.29396	+	0.446852i
$727$			15.5235i			0.575735i	0.957670	+	0.287867i	$0.0929462\pi$
$727$			15.5235i			0.575735i	−0.957670	+	0.287867i	$0.907054\pi$
$728$	−8.23233	−	12.6434i	−0.305110	−	0.468597i
$729$		−	17.2107i		−	0.637435i
$730$	−1.17969	−	6.05604i	−0.0436622	−	0.224144i
$731$	15.9718	−	15.9718i	0.590737	−	0.590737i
$732$	19.4382	−	7.87163i	0.718457	−	0.290944i
$733$	−8.79758	−	8.79758i	−0.324946	−	0.324946i	0.525715	−	0.850661i	$-0.323798\pi$
$733$	−8.79758	−	8.79758i	−0.324946	−	0.324946i	−0.850661	+	0.525715i	$0.823798\pi$
$734$	−13.9485	−	9.40027i	−0.514849	−	0.346970i
$735$	0.928667			0.0342544
$736$	1.63737	+	9.17864i	0.0603542	+	0.338329i
$737$	47.4862			1.74918
$738$	7.44776	+	5.01925i	0.274156	+	0.184761i
$739$	−6.44190	−	6.44190i	−0.236969	−	0.236969i	0.578625	−	0.815594i	$-0.303590\pi$
$739$	−6.44190	−	6.44190i	−0.236969	−	0.236969i	−0.815594	+	0.578625i	$0.803590\pi$
$740$	−6.52187	+	2.64108i	−0.239749	+	0.0970879i
$741$	−1.10638	+	1.10638i	−0.0406440	+	0.0406440i
$742$	−7.53539	−	38.6836i	−0.276633	−	1.42012i
$743$			34.8920i			1.28006i	0.768348	+	0.640032i	$0.221079\pi$
$743$			34.8920i			1.28006i	−0.768348	+	0.640032i	$0.778921\pi$
$744$	18.1686	−	11.8298i	0.666092	−	0.433702i
$745$			13.8115i			0.506014i
$746$	37.3960	−	7.28456i	1.36916	−	0.266707i
$747$	0.389866	−	0.389866i	0.0142645	−	0.0142645i
$748$	−53.1296	−	22.5020i	−1.94261	−	0.822756i
$749$	0.803225	+	0.803225i	0.0293492	+	0.0293492i
$750$	1.53158	−	2.27262i	0.0559254	−	0.0829844i
$751$	17.4058			0.635148			0.317574	−	0.948234i	$-0.397132\pi$
$751$	17.4058			0.635148			0.317574	+	0.948234i	$0.397132\pi$
$752$	14.9336	−	14.4675i	0.544574	−	0.527575i
$753$	8.25325			0.300765
$754$	12.3669	−	18.3505i	0.450376	−	0.668286i
$755$	1.34884	+	1.34884i	0.0490893	+	0.0490893i
$756$	−9.27900	+	21.9087i	−0.337474	+	0.796810i
$757$	20.6521	−	20.6521i	0.750614	−	0.750614i	−0.223980	−	0.974594i	$-0.571905\pi$
$757$	20.6521	−	20.6521i	0.750614	−	0.750614i	0.974594	+	0.223980i	$0.0719050\pi$
$758$	9.11967	−	1.77647i	0.331241	−	0.0645242i
$759$			18.6176i			0.675776i
$760$	0.242062	−	1.14557i	0.00878051	−	0.0415541i
$761$			8.36636i			0.303280i	0.988436	+	0.151640i	$0.0484555\pi$
$761$			8.36636i			0.303280i	−0.988436	+	0.151640i	$0.951545\pi$
$762$	−5.75309	−	29.5340i	−0.208413	−	1.06991i
$763$	−28.4789	+	28.4789i	−1.03101	+	1.03101i
$764$	−4.04695	−	9.99353i	−0.146413	−	0.361553i
$765$	2.64318	+	2.64318i	0.0955642	+	0.0955642i
$766$	−45.1663	−	30.4388i	−1.63193	−	1.09980i
$767$	17.6851			0.638574
$768$	22.6083	−	21.2182i	0.815808	−	0.765647i
$769$	45.1264			1.62730			0.813650	−	0.581356i	$-0.197477\pi$
$769$	45.1264			1.62730			0.813650	+	0.581356i	$0.197477\pi$
$770$	18.6952	+	12.5992i	0.673730	+	0.454045i
$771$	31.1609	+	31.1609i	1.12223	+	1.12223i
$772$	−2.65610	−	6.55897i	−0.0955951	−	0.236062i
$773$	−11.1233	+	11.1233i	−0.400076	+	0.400076i	−0.878260	−	0.478184i	$-0.841295\pi$
$773$	−11.1233	+	11.1233i	−0.400076	+	0.400076i	0.478184	+	0.878260i	$0.341295\pi$
$774$	0.932057	+	4.78480i	0.0335021	+	0.171986i
$775$		−	3.95550i		−	0.142086i
$776$	−5.52311	+	26.1383i	−0.198268	+	0.938311i
$777$			18.6452i			0.668891i
$778$	1.77306	−	0.345383i	0.0635672	−	0.0123826i
$779$	2.46128	−	2.46128i	0.0881844	−	0.0881844i
$780$	−2.94815	+	6.96087i	−0.105561	+	0.249239i
$781$	32.6544	+	32.6544i	1.16846	+	1.16846i
$782$	−6.44705	+	9.56640i	−0.230546	+	0.342094i
$783$	−34.8969			−1.24711
$784$	1.37677	−	1.33379i	0.0491704	−	0.0476355i
$785$	6.24086			0.222746
$786$	12.4987	−	18.5460i	0.445813	−	0.661515i
$787$	7.41779	+	7.41779i	0.264416	+	0.264416i	0.826845	−	0.562430i	$-0.190133\pi$
$787$	7.41779	+	7.41779i	0.264416	+	0.264416i	−0.562430	+	0.826845i	$0.690133\pi$
$788$	27.8416	+	11.7918i	0.991816	+	0.420065i
$789$	16.4844	−	16.4844i	0.586860	−	0.586860i
$790$	−7.71917	+	1.50366i	−0.274636	+	0.0534978i
$791$		−	47.6254i		−	1.69337i
$792$	10.4352	−	6.79448i	0.370797	−	0.241431i
$793$			10.5541i			0.374786i
$794$	−1.70073	−	8.73085i	−0.0603566	−	0.309846i
$795$	−13.9629	+	13.9629i	−0.495215	+	0.495215i
$796$	−29.0195	+	11.7516i	−1.02857	+	0.416526i
$797$	−8.05803	−	8.05803i	−0.285430	−	0.285430i	0.549840	−	0.835270i	$-0.314689\pi$
$797$	−8.05803	−	8.05803i	−0.285430	−	0.285430i	−0.835270	+	0.549840i	$0.814689\pi$
$798$	−2.57286	−	1.73392i	−0.0910782	−	0.0613801i
$799$	25.7264			0.910136
$800$	−0.993438	−	5.56894i	−0.0351233	−	0.196892i
$801$	−4.85064			−0.171389
$802$	−32.0606	−	21.6065i	−1.13210	−	0.762953i
$803$	−17.9822	−	17.9822i	−0.634578	−	0.634578i
$804$	−29.2649	+	11.8510i	−1.03209	+	0.417953i
$805$	3.18727	−	3.18727i	0.112337	−	0.112337i
$806$	2.08616	+	10.7095i	0.0734819	+	0.377226i
$807$			13.4305i			0.472776i
$808$	24.1266	+	37.0544i	0.848772	+	1.30357i
$809$		−	20.1500i		−	0.708436i	−0.935163	−	0.354218i	$-0.884747\pi$
$809$		−	20.1500i		−	0.708436i	0.935163	−	0.354218i	$-0.115253\pi$
$810$	14.8465	−	2.89203i	0.521653	−	0.101616i
$811$	−10.5575	+	10.5575i	−0.370723	+	0.370723i	−0.867741	−	0.497018i	$-0.834428\pi$
$811$	−10.5575	+	10.5575i	−0.370723	+	0.370723i	0.497018	+	0.867741i	$0.334428\pi$
$812$	40.4049	+	17.1127i	1.41793	+	0.600540i
$813$	−5.68136	−	5.68136i	−0.199254	−	0.199254i
$814$	−16.2081	+	24.0503i	−0.568094	+	0.842961i
$815$	5.07578			0.177797
$816$	38.3586	+	0.608184i	1.34282	+	0.0212907i
$817$	1.88926			0.0660969
$818$	30.5778	−	45.3725i	1.06913	−	1.58641i
$819$	2.84877	+	2.84877i	0.0995441	+	0.0995441i
$820$	6.55849	−	15.4852i	0.229032	−	0.540768i
$821$	−24.3826	+	24.3826i	−0.850957	+	0.850957i	−0.990251	−	0.139294i	$-0.955517\pi$
$821$	−24.3826	+	24.3826i	−0.850957	+	0.850957i	0.139294	+	0.990251i	$0.455517\pi$
$822$	19.3364	−	3.76664i	0.674435	−	0.131377i
$823$			32.5617i			1.13503i	0.823363	+	0.567515i	$0.192095\pi$
$823$			32.5617i			1.13503i	−0.823363	+	0.567515i	$0.807905\pi$
$824$	15.1324	+	3.19752i	0.527161	+	0.111391i
$825$		−	11.2958i		−	0.393270i
$826$	6.70507	+	34.4211i	0.233299	+	1.19766i
$827$	−1.31121	+	1.31121i	−0.0455952	+	0.0455952i	−0.729537	−	0.683942i	$-0.760264\pi$
$827$	−1.31121	+	1.31121i	−0.0455952	+	0.0455952i	0.683942	+	0.729537i	$0.260264\pi$
$828$	−0.934490	−	2.30763i	−0.0324758	−	0.0801957i
$829$	−20.8346	−	20.8346i	−0.723617	−	0.723617i	0.245723	−	0.969340i	$-0.420975\pi$
$829$	−20.8346	−	20.8346i	−0.723617	−	0.723617i	−0.969340	+	0.245723i	$0.920975\pi$
$830$	−0.856115	−	0.576959i	−0.0297162	−	0.0200265i
$831$	−28.7251			−0.996462
$832$	5.62682	+	14.5539i	0.195075	+	0.504566i
$833$	2.37179			0.0821775
$834$	−15.7911	−	10.6421i	−0.546801	−	0.368504i
$835$	12.4446	+	12.4446i	0.430663	+	0.430663i
$836$	−1.81143	−	4.47314i	−0.0626496	−	0.154707i
$837$	12.1666	−	12.1666i	0.420541	−	0.420541i
$838$	−2.83528	−	14.5552i	−0.0979432	−	0.502801i
$839$			54.2029i			1.87129i	0.352939	+	0.935646i	$0.385182\pi$
$839$			54.2029i			1.87129i	−0.352939	+	0.935646i	$0.614818\pi$
$840$	−14.6659	−	3.09895i	−0.506022	−	0.106924i
$841$			35.3584i			1.21925i
$842$	20.2747	−	3.94942i	0.698712	−	0.136106i
$843$	−4.82234	+	4.82234i	−0.166090	+	0.166090i
$844$	21.9907	−	51.9223i	0.756952	−	1.78724i
$845$	6.50232	+	6.50232i	0.223686	+	0.223686i
$846$	−3.10290	+	4.60420i	−0.106680	+	0.158296i
$847$	62.8396			2.15920
$848$	−0.646174	+	40.7546i	−0.0221897	+	1.39952i
$849$	−7.90541			−0.271313
$850$	3.91161	−	5.80420i	0.134167	−	0.199083i
$851$	4.10023	+	4.10023i	0.140554	+	0.140554i
$852$	−28.2738	−	11.9748i	−0.968643	−	0.410251i
$853$	28.4548	−	28.4548i	0.974274	−	0.974274i	−0.0254034	−	0.999677i	$-0.508087\pi$
$853$	28.4548	−	28.4548i	0.974274	−	0.974274i	0.999677	+	0.0254034i	$0.00808702\pi$
$854$	−20.5417	+	4.00142i	−0.702922	+	0.136926i
$855$			0.312655i			0.0106926i
$856$	−0.641031	−	0.984514i	−0.0219100	−	0.0336500i
$857$			28.9592i			0.989228i	0.869113	+	0.494614i	$0.164691\pi$
$857$			28.9592i			0.989228i	−0.869113	+	0.494614i	$0.835309\pi$
$858$	5.95749	+	30.5833i	0.203385	+	1.04410i
$859$	35.6101	−	35.6101i	1.21500	−	1.21500i	0.245640	−	0.969361i	$-0.421002\pi$
$859$	35.6101	−	35.6101i	1.21500	−	1.21500i	0.969361	−	0.245640i	$-0.0789982\pi$
$860$	8.46032	−	3.42606i	0.288495	−	0.116828i
$861$	−31.5100	−	31.5100i	−1.07386	−	1.07386i
$862$	17.4322	+	11.7480i	0.593743	+	0.400140i
$863$	−31.8081			−1.08276			−0.541380	−	0.840778i	$-0.682098\pi$
$863$	−31.8081			−1.08276			−0.541380	+	0.840778i	$0.682098\pi$
$864$	14.0737	−	20.1851i	0.478796	−	0.686710i
$865$	10.3574			0.352161
$866$	5.82018	+	3.92237i	0.197778	+	0.133288i
$867$	10.2698	+	10.2698i	0.348780	+	0.348780i
$868$	−20.0533	+	8.12071i	−0.680653	+	0.275635i
$869$	−22.9205	+	22.9205i	−0.777526	+	0.777526i
$870$	−4.20368	−	21.5800i	−0.142518	−	0.731630i
$871$		−	15.8895i		−	0.538396i
$872$	34.9066	−	22.7282i	1.18209	−	0.769674i
$873$		−	7.13382i		−	0.241443i
$874$	−0.947097	+	0.184490i	−0.0320360	+	0.00624047i
$875$	−1.93381	+	1.93381i	−0.0653746	+	0.0653746i
$876$	15.5699	+	6.59434i	0.526058	+	0.222802i
$877$	−29.2864	−	29.2864i	−0.988932	−	0.988932i	0.0110076	−	0.999939i	$-0.496496\pi$
$877$	−29.2864	−	29.2864i	−0.988932	−	0.988932i	−0.999939	+	0.0110076i	$0.996496\pi$
$878$	−10.8553	+	16.1075i	−0.366349	+	0.543603i
$879$	10.7525			0.362673
$880$	−16.2236	−	16.7463i	−0.546896	−	0.564518i
$881$	−6.72061			−0.226423			−0.113212	−	0.993571i	$-0.536114\pi$
$881$	−6.72061			−0.226423			−0.113212	+	0.993571i	$0.536114\pi$
$882$	−0.286064	+	0.424473i	−0.00963227	+	0.0142928i
$883$	−26.2186	−	26.2186i	−0.882327	−	0.882327i	0.111444	−	0.993771i	$-0.464453\pi$
$883$	−26.2186	−	26.2186i	−0.882327	−	0.882327i	−0.993771	+	0.111444i	$0.964453\pi$
$884$	−7.52947	+	17.7778i	−0.253244	+	0.597934i
$885$	12.4244	−	12.4244i	0.417641	−	0.417641i
$886$	14.9703	−	2.91614i	0.502937	−	0.0979697i
$887$			10.4628i			0.351307i	0.984452	+	0.175654i	$0.0562039\pi$
$887$			10.4628i			0.351307i	−0.984452	+	0.175654i	$0.943796\pi$
$888$	3.98661	−	18.8668i	0.133782	−	0.633127i
$889$			30.0263i			1.00705i
$890$	1.73660	+	8.91502i	0.0582111	+	0.298832i
$891$	44.0837	−	44.0837i	1.47686	−	1.47686i
$892$	15.9277	+	39.3319i	0.533299	+	1.31693i
$893$	1.52156	+	1.52156i	0.0509171	+	0.0509171i
$894$	−31.3883	−	21.1534i	−1.04978	−	0.707476i
$895$	−9.09126			−0.303887
$896$	−26.1934	+	16.4696i	−0.875060	+	0.550210i
$897$	6.22969			0.208003
$898$	18.5933	+	12.5305i	0.620466	+	0.418148i
$899$	−22.4383	−	22.4383i	−0.748358	−	0.748358i
$900$	0.566981	+	1.40010i	0.0188994	+	0.0466701i
$901$	−35.6609	+	35.6609i	−1.18804	+	1.18804i
$902$	−13.2531	−	68.0361i	−0.441280	−	2.26535i
$903$		−	24.1869i		−	0.804890i
$904$	−10.1830	+	48.1915i	−0.338682	+	1.60283i
$905$		−	5.20267i		−	0.172943i
$906$	−5.13125	+	0.999544i	−0.170475	+	0.0332076i
$907$	12.4762	−	12.4762i	0.414267	−	0.414267i	−0.468955	−	0.883222i	$-0.655369\pi$
$907$	12.4762	−	12.4762i	0.414267	−	0.414267i	0.883222	+	0.468955i	$0.155369\pi$
$908$	−13.2762	+	31.3463i	−0.440585	+	1.04026i
$909$	−8.34894	−	8.34894i	−0.276917	−	0.276917i
$910$	4.21587	−	6.25567i	0.139755	−	0.207374i
$911$	49.3786			1.63599			0.817994	−	0.575227i	$-0.195086\pi$
$911$	49.3786			1.63599			0.817994	+	0.575227i	$0.195086\pi$
$912$	2.23270	+	2.30464i	0.0739322	+	0.0763144i
$913$	−4.25522			−0.140827
$914$	−11.2212	+	16.6505i	−0.371164	+	0.550749i
$915$	7.41457	+	7.41457i	0.245118	+	0.245118i
$916$	17.4710	+	7.39951i	0.577257	+	0.244487i
$917$	−15.7811	+	15.7811i	−0.521138	+	0.521138i
$918$	29.8846	−	5.82139i	0.986340	−	0.192134i
$919$			26.6465i			0.878988i	0.898246	+	0.439494i	$0.144842\pi$
$919$			26.6465i			0.878988i	−0.898246	+	0.439494i	$0.855158\pi$
$920$	−3.90664	+	2.54367i	−0.128798	+	0.0838623i
$921$		−	0.538466i		−	0.0177431i
$922$	8.75519	+	44.9456i	0.288337	+	1.48020i
$923$	10.9266	−	10.9266i	0.359653	−	0.359653i
$924$	−57.2666	+	23.1905i	−1.88393	+	0.762911i
$925$	−2.48772	−	2.48772i	−0.0817958	−	0.0817958i
$926$	−29.3393	−	19.7725i	−0.964149	−	0.649766i
$927$	−4.13002			−0.135648
$928$	−37.2262	−	25.9553i	−1.22201	−	0.852025i
$929$	−29.5531			−0.969606			−0.484803	−	0.874623i	$-0.661109\pi$
$929$	−29.5531			−0.969606			−0.484803	+	0.874623i	$0.661109\pi$
$930$	8.98936	+	6.05817i	0.294773	+	0.198655i
$931$	0.140276	+	0.140276i	0.00459737	+	0.00459737i
$932$	−10.0183	+	4.05699i	−0.328162	+	0.132891i
$933$	3.46579	−	3.46579i	0.113465	−	0.113465i
$934$	9.00351	+	46.2203i	0.294604	+	1.51238i
$935$		−	28.8491i		−	0.943468i
$936$	−2.27352	−	3.49174i	−0.0743124	−	0.114131i
$937$			30.5505i			0.998042i	0.866590	+	0.499021i	$0.166307\pi$
$937$			30.5505i			0.998042i	−0.866590	+	0.499021i	$0.833693\pi$
$938$	30.9262	−	6.02429i	1.00978	−	0.196700i
$939$	−5.27380	+	5.27380i	−0.172104	+	0.172104i
$940$	9.57297	+	4.05445i	0.312236	+	0.132242i
$941$	0.808622	+	0.808622i	0.0263603	+	0.0263603i	0.720164	−	0.693804i	$-0.244067\pi$
$941$	0.808622	+	0.808622i	0.0263603	+	0.0263603i	−0.693804	+	0.720164i	$0.744067\pi$
$942$	−9.55839	+	14.1831i	−0.311429	+	0.462111i
$943$	−13.8586			−0.451299
$944$	0.574973	−	36.2639i	0.0187138	−	1.18029i
$945$	−11.8963			−0.386987
$946$	21.0255	−	31.1985i	0.683599	−	1.01435i
$947$	−16.7181	−	16.7181i	−0.543265	−	0.543265i	0.381220	−	0.924484i	$-0.375504\pi$
$947$	−16.7181	−	16.7181i	−0.543265	−	0.543265i	−0.924484	+	0.381220i	$0.875504\pi$
$948$	8.40529	−	19.8457i	0.272991	−	0.644560i
$949$	−6.01708	+	6.01708i	−0.195323	+	0.195323i
$950$	0.574630	−	0.111935i	0.0186435	−	0.00363166i
$951$		−	18.6055i		−	0.603326i
$952$	−37.4563	−	7.91462i	−1.21396	−	0.256514i
$953$			5.39705i			0.174828i	0.996172	+	0.0874138i	$0.0278603\pi$
$953$			5.39705i			0.174828i	−0.996172	+	0.0874138i	$0.972140\pi$
$954$	−2.08105	−	10.6833i	−0.0673764	−	0.345883i
$955$	3.81196	−	3.81196i	0.123352	−	0.123352i
$956$	−1.40056	−	3.45855i	−0.0452974	−	0.111857i
$957$	−64.0774	−	64.0774i	−2.07133	−	2.07133i
$958$	−46.1379	−	31.0936i	−1.49065	−	1.00459i
$959$	−19.6587			−0.634813
$960$	14.1776	+	6.27157i	0.457581	+	0.202414i
$961$	−15.3540			−0.495290
$962$	8.04753	+	5.42345i	0.259463	+	0.174859i
$963$	0.221827	+	0.221827i	0.00714827	+	0.00714827i
$964$	12.2919	+	30.3535i	0.395894	+	0.977621i
$965$	2.50187	−	2.50187i	0.0805381	−	0.0805381i
$966$	2.36190	+	12.1250i	0.0759928	+	0.390116i
$967$		−	14.0430i		−	0.451593i	−0.974175	−	0.225796i	$-0.927502\pi$
$967$		−	14.0430i		−	0.451593i	0.974175	−	0.225796i	$-0.0724984\pi$
$968$	−63.5865	−	13.4360i	−2.04375	−	0.431851i
$969$			3.97025i			0.127543i
$970$	−13.1113	+	2.55402i	−0.420978	+	0.0820046i
$971$	13.5960	−	13.5960i	0.436316	−	0.436316i	−0.454454	−	0.890770i	$-0.650166\pi$
$971$	13.5960	−	13.5960i	0.436316	−	0.436316i	0.890770	+	0.454454i	$0.150166\pi$
$972$	−5.98739	+	14.1368i	−0.192046	+	0.453439i
$973$	13.4369	+	13.4369i	0.430767	+	0.430767i
$974$	20.3096	−	30.1363i	0.650763	−	0.965628i
$975$	−3.77973			−0.121048
$976$	21.6414	+	0.343130i	0.692725	+	0.0109833i
$977$	44.9303			1.43745			0.718724	−	0.695295i	$-0.244726\pi$
$977$	44.9303			1.43745			0.718724	+	0.695295i	$0.244726\pi$
$978$	−7.77397	+	11.5353i	−0.248584	+	0.368859i
$979$	26.4713	+	26.4713i	0.846028	+	0.846028i
$980$	0.882556	+	0.373790i	0.0281922	+	0.0119403i
$981$	−7.86502	+	7.86502i	−0.251111	+	0.251111i
$982$	56.9974	−	11.1028i	1.81886	−	0.354306i
$983$			55.7813i			1.77915i	0.456791	+	0.889574i	$0.348999\pi$
$983$			55.7813i			1.77915i	−0.456791	+	0.889574i	$0.651001\pi$
$984$	25.1472	+	38.6219i	0.801665	+	1.23122i
$985$			15.1179i			0.481696i
$986$	−10.7361	−	55.1146i	−0.341906	−	1.75521i
$987$	19.4795	−	19.4795i	0.620039	−	0.620039i
$988$	−1.49677	+	0.606128i	−0.0476186	+	0.0192835i
$989$	−5.31891	−	5.31891i	−0.169131	−	0.169131i
$990$	5.16307	+	3.47953i	0.164093	+	0.110587i
$991$	−46.1815			−1.46700			−0.733502	−	0.679688i	$-0.762115\pi$
$991$	−46.1815			−1.46700			−0.733502	+	0.679688i	$0.762115\pi$
$992$	22.0280	−	3.92955i	0.699389	−	0.124763i
$993$	4.91090			0.155843
$994$	25.4094	+	17.1241i	0.805937	+	0.543142i
$995$	−11.0693	−	11.0693i	−0.350920	−	0.350920i
$996$	2.62242	−	1.06197i	0.0830945	−	0.0336497i
$997$	−33.4837	+	33.4837i	−1.06044	+	1.06044i	−0.0623860	+	0.998052i	$0.519871\pi$
$997$	−33.4837	+	33.4837i	−1.06044	+	1.06044i	−0.998052	+	0.0623860i	$0.980129\pi$
$998$	3.02062	+	15.5066i	0.0956160	+	0.490854i
$999$		−	15.3039i		−	0.484193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.l.a.61.2	yes	16
3.2	odd	2		720.2.t.c.541.7		16
4.3	odd	2		320.2.l.a.81.3		16
5.2	odd	4		400.2.q.h.349.5		16
5.3	odd	4		400.2.q.g.349.4		16
5.4	even	2		400.2.l.h.301.7		16
8.3	odd	2		640.2.l.a.161.6		16
8.5	even	2		640.2.l.b.161.3		16
12.11	even	2		2880.2.t.c.721.5		16
16.3	odd	4		640.2.l.a.481.6		16
16.5	even	4	inner	80.2.l.a.21.2	✓	16
16.11	odd	4		320.2.l.a.241.3		16
16.13	even	4		640.2.l.b.481.3		16
20.3	even	4		1600.2.q.h.849.6		16
20.7	even	4		1600.2.q.g.849.3		16
20.19	odd	2		1600.2.l.i.401.6		16
32.5	even	8		5120.2.a.s.1.3		8
32.11	odd	8		5120.2.a.t.1.3		8
32.21	even	8		5120.2.a.v.1.6		8
32.27	odd	8		5120.2.a.u.1.6		8
48.5	odd	4		720.2.t.c.181.7		16
48.11	even	4		2880.2.t.c.2161.8		16
80.27	even	4		1600.2.q.h.49.6		16
80.37	odd	4		400.2.q.g.149.4		16
80.43	even	4		1600.2.q.g.49.3		16
80.53	odd	4		400.2.q.h.149.5		16
80.59	odd	4		1600.2.l.i.1201.6		16
80.69	even	4		400.2.l.h.101.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.2	✓	16	16.5	even	4	inner
80.2.l.a.61.2	yes	16	1.1	even	1	trivial
320.2.l.a.81.3		16	4.3	odd	2
320.2.l.a.241.3		16	16.11	odd	4
400.2.l.h.101.7		16	80.69	even	4
400.2.l.h.301.7		16	5.4	even	2
400.2.q.g.149.4		16	80.37	odd	4
400.2.q.g.349.4		16	5.3	odd	4
400.2.q.h.149.5		16	80.53	odd	4
400.2.q.h.349.5		16	5.2	odd	4
640.2.l.a.161.6		16	8.3	odd	2
640.2.l.a.481.6		16	16.3	odd	4
640.2.l.b.161.3		16	8.5	even	2
640.2.l.b.481.3		16	16.13	even	4
720.2.t.c.181.7		16	48.5	odd	4
720.2.t.c.541.7		16	3.2	odd	2
1600.2.l.i.401.6		16	20.19	odd	2
1600.2.l.i.1201.6		16	80.59	odd	4
1600.2.q.g.49.3		16	80.43	even	4
1600.2.q.g.849.3		16	20.7	even	4
1600.2.q.h.49.6		16	80.27	even	4
1600.2.q.h.849.6		16	20.3	even	4
2880.2.t.c.721.5		16	12.11	even	2
2880.2.t.c.2161.8		16	48.11	even	4
5120.2.a.s.1.3		8	32.5	even	8
5120.2.a.t.1.3		8	32.11	odd	8
5120.2.a.u.1.6		8	32.27	odd	8
5120.2.a.v.1.6		8	32.21	even	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17275 - 0.790349i) q^{2} +(1.37027 + 1.37027i) q^{3} +(0.750696 + 1.85377i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.523995 - 2.68998i) q^{6} +2.73482i q^{7} +(0.584744 - 2.76732i) q^{8} +0.755274i q^{9} +O(q^{10})\)	\(q+(-1.17275 - 0.790349i) q^{2} +(1.37027 + 1.37027i) q^{3} +(0.750696 + 1.85377i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-0.523995 - 2.68998i) q^{6} +2.73482i q^{7} +(0.584744 - 2.76732i) q^{8} +0.755274i q^{9} +(1.38812 - 0.270400i) q^{10} +(4.12175 - 4.12175i) q^{11} +(-1.51151 + 3.56882i) q^{12} +(-1.37919 - 1.37919i) q^{13} +(2.16146 - 3.20726i) q^{14} -1.93785 q^{15} +(-2.87291 + 2.78323i) q^{16} -4.94921 q^{17} +(0.596931 - 0.885750i) q^{18} +(-0.292715 - 0.292715i) q^{19} +(-1.84163 - 0.779990i) q^{20} +(-3.74744 + 3.74744i) q^{21} +(-8.09141 + 1.57617i) q^{22} +1.64818i q^{23} +(4.59323 - 2.99072i) q^{24} -1.00000i q^{25} +(0.527407 + 2.70749i) q^{26} +(3.07588 - 3.07588i) q^{27} +(-5.06972 + 2.05302i) q^{28} +(-5.67267 - 5.67267i) q^{29} +(2.27262 + 1.53158i) q^{30} +3.95550 q^{31} +(5.56894 - 0.993438i) q^{32} +11.2958 q^{33} +(5.80420 + 3.91161i) q^{34} +(-1.93381 - 1.93381i) q^{35} +(-1.40010 + 0.566981i) q^{36} +(2.48772 - 2.48772i) q^{37} +(0.111935 + 0.574630i) q^{38} -3.77973i q^{39} +(1.54332 + 2.37027i) q^{40} +8.40843i q^{41} +(7.35660 - 1.43303i) q^{42} +(-3.22713 + 3.22713i) q^{43} +(10.7349 + 4.54659i) q^{44} +(-0.534060 - 0.534060i) q^{45} +(1.30264 - 1.93291i) q^{46} -5.19809 q^{47} +(-7.75044 - 0.122885i) q^{48} -0.479225 q^{49} +(-0.790349 + 1.17275i) q^{50} +(-6.78176 - 6.78176i) q^{51} +(1.52135 - 3.59205i) q^{52} +(7.20537 - 7.20537i) q^{53} +(-6.03826 + 1.17622i) q^{54} +5.82903i q^{55} +(7.56812 + 1.59917i) q^{56} -0.802198i q^{57} +(2.16925 + 11.1360i) q^{58} +(-6.41142 + 6.41142i) q^{59} +(-1.45474 - 3.59233i) q^{60} +(-3.82618 - 3.82618i) q^{61} +(-4.63883 - 3.12623i) q^{62} -2.06554 q^{63} +(-7.31615 - 3.23635i) q^{64} +1.95047 q^{65} +(-13.2472 - 8.92764i) q^{66} +(5.76044 + 5.76044i) q^{67} +(-3.71535 - 9.17470i) q^{68} +(-2.25846 + 2.25846i) q^{69} +(0.739494 + 3.79626i) q^{70} +7.92245i q^{71} +(2.09009 + 0.441642i) q^{72} -4.36276i q^{73} +(-4.88365 + 0.951312i) q^{74} +(1.37027 - 1.37027i) q^{75} +(0.322886 - 0.762367i) q^{76} +(11.2722 + 11.2722i) q^{77} +(-2.98730 + 4.43268i) q^{78} -5.56087 q^{79} +(0.0634130 - 3.99950i) q^{80} +10.6954 q^{81} +(6.64559 - 9.86100i) q^{82} +(-0.516191 - 0.516191i) q^{83} +(-9.76006 - 4.13369i) q^{84} +(3.49962 - 3.49962i) q^{85} +(6.33518 - 1.23406i) q^{86} -15.5462i q^{87} +(-8.99604 - 13.8164i) q^{88} +6.42236i q^{89} +(0.204226 + 1.04841i) q^{90} +(3.77184 - 3.77184i) q^{91} +(-3.05535 + 1.23729i) q^{92} +(5.42011 + 5.42011i) q^{93} +(6.09607 + 4.10830i) q^{94} +0.413962 q^{95} +(8.99222 + 6.26967i) q^{96} -9.44534 q^{97} +(0.562012 + 0.378755i) q^{98} +(3.11305 + 3.11305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 12 q^{6}+O(q^{10}) \) 16 * q - 4 * q^4 - 12 * q^6	\( 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36} - 16 q^{37} + 20 q^{38} + 60 q^{42} + 8 q^{43} + 40 q^{44} - 4 q^{46} - 40 q^{47} - 40 q^{48} - 16 q^{49} - 4 q^{50} - 32 q^{51} + 56 q^{52} + 16 q^{53} + 32 q^{54} + 16 q^{56} - 12 q^{58} - 8 q^{59} - 28 q^{60} + 16 q^{61} - 8 q^{62} + 40 q^{63} - 16 q^{64} + 40 q^{67} - 48 q^{68} + 16 q^{69} - 8 q^{70} - 40 q^{72} - 72 q^{74} + 16 q^{77} - 16 q^{78} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 76 q^{82} + 40 q^{83} - 64 q^{84} - 16 q^{85} + 28 q^{86} + 36 q^{90} + 32 q^{91} - 52 q^{92} - 48 q^{93} - 36 q^{94} + 32 q^{95} + 8 q^{96} + 60 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 12 * q^6 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 4 * q^14 - 8 * q^15 + 16 * q^16 - 8 * q^19 + 8 * q^20 - 20 * q^22 + 8 * q^24 - 16 * q^26 + 24 * q^27 - 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 - 16 * q^37 + 20 * q^38 + 60 * q^42 + 8 * q^43 + 40 * q^44 - 4 * q^46 - 40 * q^47 - 40 * q^48 - 16 * q^49 - 4 * q^50 - 32 * q^51 + 56 * q^52 + 16 * q^53 + 32 * q^54 + 16 * q^56 - 12 * q^58 - 8 * q^59 - 28 * q^60 + 16 * q^61 - 8 * q^62 + 40 * q^63 - 16 * q^64 + 40 * q^67 - 48 * q^68 + 16 * q^69 - 8 * q^70 - 40 * q^72 - 72 * q^74 + 16 * q^77 - 16 * q^78 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 76 * q^82 + 40 * q^83 - 64 * q^84 - 16 * q^85 + 28 * q^86 + 36 * q^90 + 32 * q^91 - 52 * q^92 - 48 * q^93 - 36 * q^94 + 32 * q^95 + 8 * q^96 + 60 * q^98 - 8 * q^99

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