LMFDB - Embedded newform 441.2.f.g.148.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			148.4
Root			$1.29589 - 0.748185i$ of defining polynomial
Character	$\chi$	$=$	441.148
Dual form			441.2.f.g.295.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.119562 - 0.207087i) q^{2} +(1.12441 - 1.31746i) q^{3} +(0.971410 - 1.68253i) q^{4} +(-1.29589 + 2.24456i) q^{5} +(-0.407265 - 0.0753324i) q^{6} -0.942820 q^{8} +(-0.471410 - 2.96273i) q^{9} +O(q^{10})$	\(q+(-0.119562 - 0.207087i) q^{2} +(1.12441 - 1.31746i) q^{3} +(0.971410 - 1.68253i) q^{4} +(-1.29589 + 2.24456i) q^{5} +(-0.407265 - 0.0753324i) q^{6} -0.942820 q^{8} +(-0.471410 - 2.96273i) q^{9} +0.619757 q^{10} +(-2.09097 - 3.62167i) q^{11} +(-1.12441 - 3.17165i) q^{12} +(1.84155 - 3.18966i) q^{13} +(1.50000 + 4.23109i) q^{15} +(-1.83009 - 3.16982i) q^{16} -1.71107 q^{17} +(-0.557180 + 0.451852i) q^{18} +7.15561 q^{19} +(2.51769 + 4.36077i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(2.56238 - 4.43818i) q^{23} +(-1.06012 + 1.24213i) q^{24} +(-0.858685 - 1.48729i) q^{25} -0.880716 q^{26} +(-4.43334 - 2.71026i) q^{27} +(1.06238 + 1.84010i) q^{29} +(0.696860 - 0.816506i) q^{30} +(-3.26793 + 5.66021i) q^{31} +(-1.38044 + 2.39099i) q^{32} +(-7.12252 - 1.31746i) q^{33} +(0.204579 + 0.354341i) q^{34} +(-5.44282 - 2.08486i) q^{36} +1.66019 q^{37} +(-0.855536 - 1.48183i) q^{38} +(-2.13160 - 6.01266i) q^{39} +(1.22180 - 2.11621i) q^{40} +(-5.10948 + 8.84988i) q^{41} +(0.830095 + 1.43777i) q^{43} -8.12476 q^{44} +(7.26091 + 2.78128i) q^{45} -1.22545 q^{46} +(4.66912 + 8.08715i) q^{47} +(-6.23389 - 1.15309i) q^{48} +(-0.205332 + 0.355645i) q^{50} +(-1.92395 + 2.25427i) q^{51} +(-3.57780 - 6.19694i) q^{52} +10.6465 q^{53} +(-0.0312007 + 1.24213i) q^{54} +10.8387 q^{55} +(8.04583 - 9.42724i) q^{57} +(0.254040 - 0.440011i) q^{58} +(3.03215 - 5.25183i) q^{59} +(8.57605 + 1.58632i) q^{60} +(-3.99298 - 6.91605i) q^{61} +1.56287 q^{62} -6.66019 q^{64} +(4.77292 + 8.26693i) q^{65} +(0.578751 + 1.63250i) q^{66} +(-4.13160 + 7.15614i) q^{67} +(-1.66215 + 2.87893i) q^{68} +(-2.96596 - 8.36616i) q^{69} +6.23912 q^{71} +(0.444455 + 2.79332i) q^{72} -7.15561 q^{73} +(-0.198495 - 0.343803i) q^{74} +(-2.92495 - 0.541033i) q^{75} +(6.95103 - 12.0395i) q^{76} +(-0.990285 + 1.16031i) q^{78} +(4.91423 + 8.51170i) q^{79} +9.48644 q^{80} +(-8.55555 + 2.79332i) q^{81} +2.44359 q^{82} +(3.44733 + 5.97094i) q^{83} +(2.21737 - 3.84060i) q^{85} +(0.198495 - 0.343803i) q^{86} +(3.61881 + 0.669376i) q^{87} +(1.97141 + 3.41458i) q^{88} +5.03538 q^{89} +(-0.292160 - 1.83617i) q^{90} +(-4.97825 - 8.62258i) q^{92} +(3.78263 + 10.6698i) q^{93} +(1.11650 - 1.93383i) q^{94} +(-9.27292 + 16.0612i) q^{95} +(1.59786 + 4.50712i) q^{96} +(1.53167 + 2.65294i) q^{97} +(-9.74433 + 7.90228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 12 * q^9	$ 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9} - 8 q^{11} + 18 q^{15} - 6 q^{16} - 42 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} - 48 q^{30} - 16 q^{32} - 30 q^{36} - 12 q^{37} + 24 q^{39} - 6 q^{43} - 28 q^{44} + 24 q^{46} - 56 q^{50} - 18 q^{51} + 56 q^{53} - 6 q^{57} - 18 q^{58} + 108 q^{60} - 48 q^{64} + 6 q^{65} + 76 q^{71} + 60 q^{72} - 36 q^{74} + 36 q^{78} + 6 q^{79} - 48 q^{81} + 30 q^{85} + 36 q^{86} + 6 q^{88} - 62 q^{92} + 42 q^{93} - 60 q^{95} - 48 q^{99}+O(q^{100}) $ 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 12 * q^9 - 8 * q^11 + 18 * q^15 - 6 * q^16 - 42 * q^18 - 6 * q^22 - 4 * q^23 - 12 * q^25 - 22 * q^29 - 48 * q^30 - 16 * q^32 - 30 * q^36 - 12 * q^37 + 24 * q^39 - 6 * q^43 - 28 * q^44 + 24 * q^46 - 56 * q^50 - 18 * q^51 + 56 * q^53 - 6 * q^57 - 18 * q^58 + 108 * q^60 - 48 * q^64 + 6 * q^65 + 76 * q^71 + 60 * q^72 - 36 * q^74 + 36 * q^78 + 6 * q^79 - 48 * q^81 + 30 * q^85 + 36 * q^86 + 6 * q^88 - 62 * q^92 + 42 * q^93 - 60 * q^95 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.119562	−	0.207087i	−0.0845428	−	0.146433i	0.820653	−	0.571426i	$-0.193610\pi$
$2$	−0.119562	−	0.207087i	−0.0845428	−	0.146433i	−0.905196	+	0.424994i	$0.860276\pi$
$3$	1.12441	−	1.31746i	0.649178	−	0.760637i
$3$	1.12441	−	1.31746i	0.649178	−	0.760637i
$4$	0.971410	−	1.68253i	0.485705	−	0.841266i
$5$	−1.29589	+	2.24456i	−0.579542	+	1.00380i	0.415990	+	0.909369i	$0.363435\pi$
$5$	−1.29589	+	2.24456i	−0.579542	+	1.00380i	−0.995532	+	0.0944264i	$0.969898\pi$
$6$	−0.407265	−	0.0753324i	−0.166265	−	0.0307543i
$7$		0			0
$7$		0			0
$8$	−0.942820			−0.333337
$9$	−0.471410	−	2.96273i	−0.157137	−	0.987577i
$10$	0.619757			0.195984
$11$	−2.09097	−	3.62167i	−0.630452	−	1.09197i	−0.987459	−	0.157873i	$-0.949536\pi$
$11$	−2.09097	−	3.62167i	−0.630452	−	1.09197i	0.357008	−	0.934101i	$-0.383797\pi$
$12$	−1.12441	−	3.17165i	−0.324589	−	0.915576i
$13$	1.84155	−	3.18966i	0.510755	−	0.884653i	−0.489168	−	0.872190i	$-0.662699\pi$
$13$	1.84155	−	3.18966i	0.510755	−	0.884653i	0.999922	−	0.0124633i	$-0.00396730\pi$
$14$		0			0
$15$	1.50000	+	4.23109i	0.387298	+	1.09246i
$16$	−1.83009	−	3.16982i	−0.457524	−	0.792454i
$17$	−1.71107			−0.414996			−0.207498	−	0.978235i	$-0.566532\pi$
$17$	−1.71107			−0.414996			−0.207498	+	0.978235i	$0.566532\pi$
$18$	−0.557180	+	0.451852i	−0.131329	+	0.106502i
$19$	7.15561			1.64161			0.820805	−	0.571209i	$-0.193525\pi$
$19$	7.15561			1.64161			0.820805	+	0.571209i	$0.193525\pi$
$20$	2.51769	+	4.36077i	0.562973	+	0.975097i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	2.56238	−	4.43818i	0.534294	−	0.925424i	−0.464904	−	0.885361i	$-0.653911\pi$
$23$	2.56238	−	4.43818i	0.534294	−	0.925424i	0.999197	−	0.0400622i	$-0.0127556\pi$
$24$	−1.06012	+	1.24213i	−0.216395	+	0.253549i
$25$	−0.858685	−	1.48729i	−0.171737	−	0.297457i
$26$	−0.880716			−0.172723
$27$	−4.43334	−	2.71026i	−0.853197	−	0.521589i
$28$		0			0
$29$	1.06238	+	1.84010i	0.197279	+	0.341698i	0.947645	−	0.319325i	$-0.103456\pi$
$29$	1.06238	+	1.84010i	0.197279	+	0.341698i	−0.750366	+	0.661023i	$0.770123\pi$
$30$	0.696860	−	0.816506i	0.127229	−	0.149073i
$31$	−3.26793	+	5.66021i	−0.586937	+	1.01660i	0.407694	+	0.913119i	$0.366333\pi$
$31$	−3.26793	+	5.66021i	−0.586937	+	1.01660i	−0.994631	+	0.103486i	$0.967000\pi$
$32$	−1.38044	+	2.39099i	−0.244029	+	0.422671i
$33$	−7.12252	−	1.31746i	−1.23987	−	0.229341i
$34$	0.204579	+	0.354341i	0.0350850	+	0.0607689i
$35$		0			0
$36$	−5.44282	−	2.08486i	−0.907137	−	0.347477i
$37$	1.66019			0.272934			0.136467	−	0.990645i	$-0.456425\pi$
$37$	1.66019			0.272934			0.136467	+	0.990645i	$0.456425\pi$
$38$	−0.855536	−	1.48183i	−0.138786	−	0.240385i
$39$	−2.13160	−	6.01266i	−0.341329	−	0.962796i
$40$	1.22180	−	2.11621i	0.193183	−	0.334602i
$41$	−5.10948	+	8.84988i	−0.797967	+	1.38212i	0.122972	+	0.992410i	$0.460758\pi$
$41$	−5.10948	+	8.84988i	−0.797967	+	1.38212i	−0.920938	+	0.389708i	$0.872576\pi$
$42$		0			0
$43$	0.830095	+	1.43777i	0.126588	+	0.219257i	0.922353	−	0.386349i	$-0.126264\pi$
$43$	0.830095	+	1.43777i	0.126588	+	0.219257i	−0.795764	+	0.605606i	$0.792931\pi$
$44$	−8.12476			−1.22485
$45$	7.26091	+	2.78128i	1.08239	+	0.414609i
$46$	−1.22545			−0.180683
$47$	4.66912	+	8.08715i	0.681061	+	1.17963i	0.974657	+	0.223703i	$0.0718146\pi$
$47$	4.66912	+	8.08715i	0.681061	+	1.17963i	−0.293596	+	0.955930i	$0.594852\pi$
$48$	−6.23389	−	1.15309i	−0.899784	−	0.166434i
$49$		0			0
$50$	−0.205332	+	0.355645i	−0.0290383	+	0.0502958i
$51$	−1.92395	+	2.25427i	−0.269406	+	0.315661i
$52$	−3.57780	−	6.19694i	−0.496152	−	0.859361i
$53$	10.6465			1.46241			0.731206	−	0.682157i	$-0.238958\pi$
$53$	10.6465			1.46241			0.731206	+	0.682157i	$0.238958\pi$
$54$	−0.0312007	+	1.24213i	−0.00424588	+	0.169032i
$55$	10.8387			1.46149
$56$		0			0
$57$	8.04583	−	9.42724i	1.06570	−	1.24867i
$58$	0.254040	−	0.440011i	0.0333571	−	0.0577762i
$59$	3.03215	−	5.25183i	0.394752	−	0.683730i	−0.598318	−	0.801259i	$-0.704164\pi$
$59$	3.03215	−	5.25183i	0.394752	−	0.683730i	0.993069	+	0.117529i	$0.0374972\pi$
$60$	8.57605	+	1.58632i	1.10716	+	0.204794i
$61$	−3.99298	−	6.91605i	−0.511249	−	0.885509i	−0.999915	−	0.0130384i	$-0.995850\pi$
$61$	−3.99298	−	6.91605i	−0.511249	−	0.885509i	0.488666	−	0.872471i	$-0.337484\pi$
$62$	1.56287			0.198485
$63$		0			0
$64$	−6.66019			−0.832524
$65$	4.77292	+	8.26693i	0.592007	+	1.02539i
$66$	0.578751	+	1.63250i	0.0712393	+	0.200947i
$67$	−4.13160	+	7.15614i	−0.504755	+	0.874262i	0.495230	+	0.868762i	$0.335084\pi$
$67$	−4.13160	+	7.15614i	−0.504755	+	0.874262i	−0.999985	+	0.00549964i	$0.998249\pi$
$68$	−1.66215	+	2.87893i	−0.201566	+	0.349122i
$69$	−2.96596	−	8.36616i	−0.357060	−	1.00717i
$70$		0			0
$71$	6.23912			0.740448			0.370224	−	0.928943i	$-0.379281\pi$
$71$	6.23912			0.740448			0.370224	+	0.928943i	$0.379281\pi$
$72$	0.444455	+	2.79332i	0.0523795	+	0.329196i
$73$	−7.15561			−0.837501			−0.418750	−	0.908101i	$-0.637532\pi$
$73$	−7.15561			−0.837501			−0.418750	+	0.908101i	$0.637532\pi$
$74$	−0.198495	−	0.343803i	−0.0230746	−	0.0399663i
$75$	−2.92495	−	0.541033i	−0.337745	−	0.0624731i
$76$	6.95103	−	12.0395i	0.797338	−	1.38103i
$77$		0			0
$78$	−0.990285	+	1.16031i	−0.112128	+	0.131379i
$79$	4.91423	+	8.51170i	0.552894	+	0.957641i	0.998064	+	0.0621945i	$0.0198099\pi$
$79$	4.91423	+	8.51170i	0.552894	+	0.957641i	−0.445170	+	0.895446i	$0.646857\pi$
$80$	9.48644			1.06062
$81$	−8.55555	+	2.79332i	−0.950616	+	0.310369i
$82$	2.44359			0.269849
$83$	3.44733	+	5.97094i	0.378393	+	0.655396i	0.990829	−	0.135124i	$-0.0431434\pi$
$83$	3.44733	+	5.97094i	0.378393	+	0.655396i	−0.612436	+	0.790521i	$0.709810\pi$
$84$		0			0
$85$	2.21737	−	3.84060i	0.240508	−	0.416571i
$86$	0.198495	−	0.343803i	0.0214043	−	0.0370733i
$87$	3.61881	+	0.669376i	0.387977	+	0.0717647i
$88$	1.97141	+	3.41458i	0.210153	+	0.363996i
$89$	5.03538			0.533749			0.266875	−	0.963731i	$-0.414009\pi$
$89$	5.03538			0.533749			0.266875	+	0.963731i	$0.414009\pi$
$90$	−0.292160	−	1.83617i	−0.0307963	−	0.193550i
$91$		0			0
$92$	−4.97825	−	8.62258i	−0.519018	−	0.898966i
$93$	3.78263	+	10.6698i	0.392240	+	1.10640i
$94$	1.11650	−	1.93383i	0.115158	−	0.199459i
$95$	−9.27292	+	16.0612i	−0.951381	+	1.64784i
$96$	1.59786	+	4.50712i	0.163081	+	0.460006i
$97$	1.53167	+	2.65294i	0.155518	+	0.269365i	0.933247	−	0.359234i	$-0.116962\pi$
$97$	1.53167	+	2.65294i	0.155518	+	0.269365i	−0.777730	+	0.628599i	$0.783629\pi$
$98$		0			0
$99$	−9.74433	+	7.90228i	−0.979342	+	0.794209i
$100$	−3.33654			−0.333654
$101$	−5.54984	−	9.61260i	−0.552229	−	0.956489i	−0.998113	−	0.0613986i	$-0.980444\pi$
$101$	−5.54984	−	9.61260i	−0.552229	−	0.956489i	0.445884	−	0.895091i	$-0.352889\pi$
$102$	0.696860	+	0.128899i	0.0689994	+	0.0127629i
$103$	3.99298	−	6.91605i	0.393440	−	0.681459i	−0.599460	−	0.800404i	$-0.704618\pi$
$103$	3.99298	−	6.91605i	0.393440	−	0.681459i	0.992901	+	0.118946i	$0.0379515\pi$
$104$	−1.73625	+	3.00728i	−0.170254	+	0.294888i
$105$		0			0
$106$	−1.27292	−	2.20475i	−0.123636	−	0.214145i
$107$	3.95649			0.382489			0.191244	−	0.981542i	$-0.438748\pi$
$107$	3.95649			0.382489			0.191244	+	0.981542i	$0.438748\pi$
$108$	−8.86668	+	4.82647i	−0.853197	+	0.464427i
$109$	7.26320			0.695688			0.347844	−	0.937552i	$-0.386914\pi$
$109$	7.26320			0.695688			0.347844	+	0.937552i	$0.386914\pi$
$110$	−1.29589	−	2.24456i	−0.123559	−	0.214010i
$111$	1.86673	−	2.18724i	0.177182	−	0.207603i
$112$		0			0
$113$	−3.46457	+	6.00082i	−0.325920	+	0.564509i	−0.981698	−	0.190444i	$-0.939007\pi$
$113$	−3.46457	+	6.00082i	−0.325920	+	0.564509i	0.655778	+	0.754953i	$0.272341\pi$
$114$	−2.91423	−	0.539049i	−0.272943	−	0.0504866i
$115$	6.64115	+	11.5028i	0.619291	+	1.07264i
$116$	4.12803			0.383278
$117$	−10.3182	−	3.95238i	−0.953921	−	0.365398i
$118$	−1.45011			−0.133494
$119$		0			0
$120$	−1.41423	−	3.98916i	−0.129101	−	0.364158i
$121$	−3.24433	+	5.61934i	−0.294939	+	0.510849i
$122$	−0.954815	+	1.65379i	−0.0864449	+	0.149727i
$123$	5.91423	+	16.6824i	0.533268	+	1.50420i
$124$	6.34899	+	10.9968i	0.570156	+	0.987540i
$125$	−8.50788			−0.760968
$126$		0			0
$127$	9.11109			0.808479			0.404239	−	0.914653i	$-0.367536\pi$
$127$	9.11109			0.808479			0.404239	+	0.914653i	$0.367536\pi$
$128$	3.55718	+	6.16122i	0.314413	+	0.544580i
$129$	2.82757	+	0.523019i	0.248954	+	0.0460493i
$130$	1.14132	−	1.97682i	0.100100	−	0.173378i
$131$	−2.15143	+	3.72639i	−0.187971	+	0.325576i	−0.944574	−	0.328299i	$-0.893525\pi$
$131$	−2.15143	+	3.72639i	−0.187971	+	0.325576i	0.756602	+	0.653875i	$0.226858\pi$
$132$	−9.13555	+	10.7041i	−0.795148	+	0.931669i
$133$		0			0
$134$	1.97592			0.170694
$135$	11.8285	−	6.43867i	1.01803	−	0.554153i
$136$	1.61323			0.138334
$137$	−10.2947	−	17.8309i	−0.879533	−	1.52340i	−0.851854	−	0.523779i	$-0.824522\pi$
$137$	−10.2947	−	17.8309i	−0.879533	−	1.52340i	−0.0276785	−	0.999617i	$-0.508811\pi$
$138$	−1.37791	+	1.61448i	−0.117295	+	0.137434i
$139$	−7.88067	+	13.6497i	−0.668429	+	1.15775i	0.309914	+	0.950765i	$0.399700\pi$
$139$	−7.88067	+	13.6497i	−0.668429	+	1.15775i	−0.978343	+	0.206989i	$0.933634\pi$
$140$		0			0
$141$	15.9045	+	2.94188i	1.33940	+	0.247751i
$142$	−0.745960	−	1.29204i	−0.0625996	−	0.108426i
$143$	−15.4025			−1.28802
$144$	−8.52859	+	6.91636i	−0.710716	+	0.576364i
$145$	−5.50694			−0.457326
$146$	0.855536	+	1.48183i	0.0708047	+	0.122637i
$147$		0			0
$148$	1.61273	−	2.79332i	0.132565	−	0.229610i
$149$	−3.03379	+	5.25468i	−0.248538	+	0.430480i	−0.963120	−	0.269071i	$-0.913283\pi$
$149$	−3.03379	+	5.25468i	−0.248538	+	0.430480i	0.714582	+	0.699551i	$0.246617\pi$
$150$	0.237672	+	0.670406i	0.0194058	+	0.0547385i
$151$	−2.24433	−	3.88728i	−0.182641	−	0.316343i	0.760138	−	0.649761i	$-0.225131\pi$
$151$	−2.24433	−	3.88728i	−0.182641	−	0.316343i	−0.942779	+	0.333418i	$0.891798\pi$
$152$	−6.74645			−0.547210
$153$	0.806617	+	5.06945i	0.0652111	+	0.409841i
$154$		0			0
$155$	−8.46978	−	14.6701i	−0.680309	−	1.17833i
$156$	−12.1871	−	2.25427i	−0.975753	−	0.180486i
$157$	0.514457	−	0.891066i	0.0410582	−	0.0711148i	−0.844766	−	0.535136i	$-0.820260\pi$
$157$	0.514457	−	0.891066i	0.0410582	−	0.0711148i	0.885824	+	0.464021i	$0.153594\pi$
$158$	1.17511	−	2.03534i	0.0934865	−	0.161923i
$159$	11.9710	−	14.0264i	0.949365	−	1.11236i
$160$	−3.57780	−	6.19694i	−0.282850	−	0.489911i
$161$		0			0
$162$	1.60138	+	1.43777i	0.125816	+	0.112962i
$163$	6.82846			0.534846			0.267423	−	0.963579i	$-0.413828\pi$
$163$	6.82846			0.534846			0.267423	+	0.963579i	$0.413828\pi$
$164$	9.92680	+	17.1937i	0.775153	+	1.34260i
$165$	12.1871	−	14.2796i	0.948768	−	1.11166i
$166$	0.824336	−	1.42779i	0.0639809	−	0.110818i
$167$	8.99716	−	15.5835i	0.696221	−	1.20589i	−0.273546	−	0.961859i	$-0.588197\pi$
$167$	8.99716	−	15.5835i	0.696221	−	1.20589i	0.969767	−	0.244032i	$-0.0784701\pi$
$168$		0			0
$169$	−0.282630	−	0.489530i	−0.0217408	−	0.0376561i
$170$	−1.06045			−0.0813328
$171$	−3.37323	−	21.2001i	−0.257957	−	1.62122i
$172$	3.22545			0.245938
$173$	−0.415178	−	0.719110i	−0.0315654	−	0.0546729i	0.849811	−	0.527087i	$-0.176716\pi$
$173$	−0.415178	−	0.719110i	−0.0315654	−	0.0546729i	−0.881377	+	0.472414i	$0.843383\pi$
$174$	−0.294052	−	0.829440i	−0.0222920	−	0.0628797i
$175$		0			0
$176$	−7.65335	+	13.2560i	−0.576893	+	0.999208i
$177$	−3.50972	−	9.89994i	−0.263806	−	0.744125i
$178$	−0.602038	−	1.04276i	−0.0451247	−	0.0781582i
$179$	7.57893			0.566476			0.283238	−	0.959050i	$-0.408591\pi$
$179$	7.57893			0.566476			0.283238	+	0.959050i	$0.408591\pi$
$180$	11.7329	−	9.51495i	0.874520	−	0.709202i
$181$	−0.409157			−0.0304124			−0.0152062	−	0.999884i	$-0.504840\pi$
$181$	−0.409157			−0.0304124			−0.0152062	+	0.999884i	$0.504840\pi$
$182$		0			0
$183$	−13.6014	−	2.51586i	−1.00544	−	0.185978i
$184$	−2.41586	+	4.18440i	−0.178100	+	0.308478i
$185$	−2.15143	+	3.72639i	−0.158176	+	0.273969i
$186$	1.75731	−	2.05903i	0.128852	−	0.150975i
$187$	3.57780	+	6.19694i	0.261635	+	0.453165i
$188$	18.1425			1.32318
$189$		0			0
$190$	4.43474			0.321730
$191$	−8.01204	−	13.8773i	−0.579731	−	1.00412i	−0.995510	−	0.0946575i	$-0.969824\pi$
$191$	−8.01204	−	13.8773i	−0.579731	−	1.00412i	0.415779	−	0.909466i	$-0.363509\pi$
$192$	−7.48878	+	8.77454i	−0.540456	+	0.633248i
$193$	6.18715	−	10.7164i	0.445360	−	0.771387i	−0.552717	−	0.833369i	$-0.686409\pi$
$193$	6.18715	−	10.7164i	0.445360	−	0.771387i	0.998077	+	0.0619822i	$0.0197422\pi$
$194$	0.366259	−	0.634379i	0.0262959	−	0.0455458i
$195$	16.2581	+	3.00728i	1.16426	+	0.215356i
$196$		0			0
$197$	23.1021			1.64595			0.822977	−	0.568075i	$-0.192312\pi$
$197$	23.1021			1.64595			0.822977	+	0.568075i	$0.192312\pi$
$198$	2.80150	+	1.07311i	0.199094	+	0.0762628i
$199$	6.74645			0.478243			0.239122	−	0.970990i	$-0.423141\pi$
$199$	6.74645			0.478243			0.239122	+	0.970990i	$0.423141\pi$
$200$	0.809585	+	1.40224i	0.0572463	+	0.0991536i
$201$	4.78233	+	13.4897i	0.337320	+	0.951487i
$202$	−1.32710	+	2.29860i	−0.0933741	+	0.161729i
$203$		0			0
$204$	1.92395	+	5.42692i	0.134703	+	0.379961i
$205$	−13.2427	−	22.9370i	−0.924910	−	1.60199i
$206$	−1.90963			−0.133050
$207$	−14.3571	−	5.49945i	−0.997884	−	0.382238i
$208$	−13.4809			−0.934730
$209$	−14.9622	−	25.9153i	−1.03496	−	1.79260i
$210$		0			0
$211$	−8.44282	+	14.6234i	−0.581228	+	1.00672i	0.414106	+	0.910228i	$0.364094\pi$
$211$	−8.44282	+	14.6234i	−0.581228	+	1.00672i	−0.995334	+	0.0964875i	$0.969239\pi$
$212$	10.3421	−	17.9131i	0.710301	−	1.23028i
$213$	7.01532	−	8.21981i	0.480682	−	0.563212i
$214$	−0.473045	−	0.819338i	−0.0323367	−	0.0560088i
$215$	−4.30286			−0.293453
$216$	4.17984	+	2.55528i	0.284402	+	0.173865i
$217$		0			0
$218$	−0.868400	−	1.50411i	−0.0588155	−	0.101871i
$219$	−8.04583	+	9.42724i	−0.543687	+	0.637034i
$220$	10.5288	−	18.2365i	0.709854	−	1.22950i
$221$	−3.15103	+	5.45774i	−0.211961	+	0.367128i
$222$	−0.676137	−	0.125066i	−0.0453794	−	0.00839388i
$223$	−2.25071	−	3.89834i	−0.150719	−	0.261052i	0.780773	−	0.624815i	$-0.214825\pi$
$223$	−2.25071	−	3.89834i	−0.150719	−	0.261052i	−0.931492	+	0.363762i	$0.881492\pi$
$224$		0			0
$225$	−4.00163	+	3.24517i	−0.266776	+	0.216345i
$226$	1.65692			0.110217
$227$	−3.03215	−	5.25183i	−0.201251	−	0.348576i	0.747681	−	0.664058i	$-0.231167\pi$
$227$	−3.03215	−	5.25183i	−0.201251	−	0.348576i	−0.948932	+	0.315482i	$0.897834\pi$
$228$	−8.04583	−	22.6951i	−0.532848	−	1.50302i
$229$	−5.52466	+	9.56899i	−0.365080	+	0.632336i	−0.988789	−	0.149320i	$-0.952292\pi$
$229$	−5.52466	+	9.56899i	−0.365080	+	0.632336i	0.623709	+	0.781656i	$0.285625\pi$
$230$	1.58805	−	2.75059i	0.104713	−	0.181369i
$231$		0			0
$232$	−1.00163	−	1.73488i	−0.0657605	−	0.113901i
$233$	−8.13844			−0.533167			−0.266583	−	0.963812i	$-0.585895\pi$
$233$	−8.13844			−0.533167			−0.266583	+	0.963812i	$0.585895\pi$
$234$	0.415178	+	2.60932i	0.0271411	+	0.170577i
$235$	−24.2028			−1.57881
$236$	−5.89092	−	10.2034i	−0.383466	−	0.664183i
$237$	16.7394	+	3.09632i	1.08734	+	0.201127i
$238$		0			0
$239$	−10.5813	+	18.3273i	−0.684445	+	1.18549i	0.289166	+	0.957279i	$0.406622\pi$
$239$	−10.5813	+	18.3273i	−0.684445	+	1.18549i	−0.973611	+	0.228214i	$0.926711\pi$
$240$	10.6666	−	12.4980i	0.688528	−	0.806744i
$241$	6.84573	+	11.8572i	0.440972	+	0.763786i	0.997762	−	0.0668671i	$-0.0213004\pi$
$241$	6.84573	+	11.8572i	0.440972	+	0.763786i	−0.556790	+	0.830654i	$0.687967\pi$
$242$	1.55159			0.0997398
$243$	−5.93984	+	14.4124i	−0.381041	+	0.924558i
$244$	−15.5153			−0.993265
$245$		0			0
$246$	2.74759	−	3.21934i	0.175180	−	0.205257i
$247$	13.1774	−	22.8240i	0.838460	−	1.45225i
$248$	3.08107	−	5.33656i	0.195648	−	0.338872i
$249$	11.7427	+	2.17206i	0.744163	+	0.137649i
$250$	1.01722	+	1.76187i	0.0643344	+	0.111430i
$251$	−15.2040			−0.959667			−0.479833	−	0.877360i	$-0.659303\pi$
$251$	−15.2040			−0.959667			−0.479833	+	0.877360i	$0.659303\pi$
$252$		0			0
$253$	−21.4315			−1.34738
$254$	−1.08934	−	1.88679i	−0.0683511	−	0.118388i
$255$	−2.56661	−	7.23970i	−0.160727	−	0.453368i
$256$	−5.80959	+	10.0625i	−0.363099	+	0.628906i
$257$	12.8107	−	22.1889i	0.799112	−	1.38410i	−0.121082	−	0.992642i	$-0.538637\pi$
$257$	12.8107	−	22.1889i	0.799112	−	1.38410i	0.920195	−	0.391461i	$-0.128030\pi$
$258$	−0.229758	−	0.648085i	−0.0143041	−	0.0403480i
$259$		0			0
$260$	18.5458			1.15016
$261$	4.95090	−	4.01499i	0.306453	−	0.248522i
$262$	1.02891			0.0635665
$263$	−3.55034	−	6.14938i	−0.218924	−	0.379187i	0.735556	−	0.677464i	$-0.236921\pi$
$263$	−3.55034	−	6.14938i	−0.218924	−	0.379187i	−0.954479	+	0.298278i	$0.903588\pi$
$264$	6.71525	+	1.24213i	0.413295	+	0.0764478i
$265$	−13.7968	+	23.8967i	−0.847528	+	1.46796i
$266$		0			0
$267$	5.66182	−	6.63392i	0.346498	−	0.405989i
$268$	8.02696	+	13.9031i	0.490324	+	0.849267i
$269$	16.4314			1.00184			0.500922	−	0.865493i	$-0.332994\pi$
$269$	16.4314			1.00184			0.500922	+	0.865493i	$0.332994\pi$
$270$	−2.74759	−	1.67970i	−0.167213	−	0.102223i
$271$	−12.6980			−0.771348			−0.385674	−	0.922635i	$-0.626031\pi$
$271$	−12.6980			−0.771348			−0.385674	+	0.922635i	$0.626031\pi$
$272$	3.13143	+	5.42379i	0.189871	+	0.328865i
$273$		0			0
$274$	−2.46169	+	4.26378i	−0.148716	+	0.257584i
$275$	−3.59097	+	6.21975i	−0.216544	+	0.375065i
$276$	−16.9575	−	3.13665i	−1.02072	−	0.188804i
$277$	0.414230	+	0.717468i	0.0248887	+	0.0431084i	0.878201	−	0.478291i	$-0.158744\pi$
$277$	0.414230	+	0.717468i	0.0248887	+	0.0431084i	−0.853313	+	0.521399i	$0.825410\pi$
$278$	3.76890			0.226044
$279$	18.3102	+	7.01370i	1.09620	+	0.419899i
$280$		0			0
$281$	−2.60985	−	4.52039i	−0.155690	−	0.269664i	0.777620	−	0.628735i	$-0.216427\pi$
$281$	−2.60985	−	4.52039i	−0.155690	−	0.269664i	−0.933310	+	0.359071i	$0.883094\pi$
$282$	−1.29235	−	3.64535i	−0.0769580	−	0.217078i
$283$	−3.67708	+	6.36890i	−0.218580	+	0.378592i	−0.954374	−	0.298614i	$-0.903476\pi$
$283$	−3.67708	+	6.36890i	−0.218580	+	0.378592i	0.735794	+	0.677205i	$0.236809\pi$
$284$	6.06075	−	10.4975i	0.359639	−	0.622913i
$285$	10.7334	+	30.2760i	0.635793	+	1.79340i
$286$	1.84155	+	3.18966i	0.108893	+	0.188609i
$287$		0			0
$288$	7.73461	+	2.96273i	0.455766	+	0.174581i
$289$	−14.0722			−0.827778
$290$	0.658419	+	1.14041i	0.0386637	+	0.0669674i
$291$	5.21737	+	0.965064i	0.305848	+	0.0565731i
$292$	−6.95103	+	12.0395i	−0.406778	+	0.704561i
$293$	3.91286	−	6.77728i	0.228592	−	0.395933i	−0.728799	−	0.684728i	$-0.759921\pi$
$293$	3.91286	−	6.77728i	0.228592	−	0.395933i	0.957391	+	0.288795i	$0.0932545\pi$
$294$		0			0
$295$	7.85868	+	13.6116i	0.457550	+	0.792500i
$296$	−1.56526			−0.0909789
$297$	−0.545658	+	21.7232i	−0.0316623	+	1.26051i
$298$	1.45090			0.0840484
$299$	−9.43752	−	16.3463i	−0.545786	−	0.945329i
$300$	−3.75164	+	4.39576i	−0.216601	+	0.253790i
$301$		0			0
$302$	−0.536670	+	0.929540i	−0.0308819	+	0.0534890i
$303$	−18.9045	−	3.49679i	−1.08604	−	0.200886i
$304$	−13.0954	−	22.6820i	−0.751075	−	1.30090i
$305$	20.6979			1.18516
$306$	0.953375	−	0.773151i	0.0545008	−	0.0441981i
$307$	−22.6709			−1.29390			−0.646948	−	0.762534i	$-0.723955\pi$
$307$	−22.6709			−1.29390			−0.646948	+	0.762534i	$0.723955\pi$
$308$		0			0
$309$	−4.62188	−	13.0371i	−0.262930	−	0.741653i
$310$	−2.02532	+	3.50796i	−0.115030	+	0.199239i
$311$	−16.1588	+	27.9879i	−0.916281	+	1.58705i	−0.111266	+	0.993791i	$0.535491\pi$
$311$	−16.1588	+	27.9879i	−0.916281	+	1.58705i	−0.805015	+	0.593255i	$0.797843\pi$
$312$	2.00972	+	5.66886i	0.113778	+	0.320936i
$313$	−12.1598	−	21.0614i	−0.687312	−	1.19046i	−0.972704	−	0.232048i	$-0.925457\pi$
$313$	−12.1598	−	21.0614i	−0.687312	−	1.19046i	0.285392	−	0.958411i	$-0.407876\pi$
$314$	−0.246037			−0.0138847
$315$		0			0
$316$	19.0949			1.07417
$317$	−2.56922	−	4.45002i	−0.144302	−	0.249938i	0.784811	−	0.619736i	$-0.212760\pi$
$317$	−2.56922	−	4.45002i	−0.144302	−	0.249938i	−0.929112	+	0.369798i	$0.879427\pi$
$318$	−4.33595	−	0.802027i	−0.243148	−	0.0449755i
$319$	4.44282	−	7.69519i	0.248750	−	0.430848i
$320$	8.63090	−	14.9492i	0.482482	−	0.835684i
$321$	4.44872	−	5.21253i	0.248303	−	0.290935i
$322$		0			0
$323$	−12.2438			−0.681262
$324$	−3.61109	+	17.1084i	−0.200616	+	0.950469i
$325$	−6.32525			−0.350862
$326$	−0.816422	−	1.41408i	−0.0452174	−	0.0783189i
$327$	8.16681	−	9.56899i	0.451625	−	0.529166i
$328$	4.81732	−	8.34384i	0.265992	−	0.460712i
$329$		0			0
$330$	−4.41423	−	0.816506i	−0.242995	−	0.0449472i
$331$	5.84897	+	10.1307i	0.321488	+	0.556834i	0.980795	−	0.195040i	$-0.0624835\pi$
$331$	5.84897	+	10.1307i	0.321488	+	0.556834i	−0.659307	+	0.751874i	$0.729150\pi$
$332$	13.3951			0.735150
$333$	−0.782630	−	4.91870i	−0.0428879	−	0.269543i
$334$	−4.30286			−0.235442
$335$	−10.7082	−	18.5472i	−0.585053	−	1.01334i
$336$		0			0
$337$	16.8473	−	29.1804i	0.917733	−	1.58956i	0.114883	−	0.993379i	$-0.463351\pi$
$337$	16.8473	−	29.1804i	0.917733	−	1.58956i	0.802850	−	0.596181i	$-0.203316\pi$
$338$	−0.0675835	+	0.117058i	−0.00367606	+	0.00636711i
$339$	4.01025	+	11.3118i	0.217807	+	0.614373i
$340$	−4.30795	−	7.46159i	−0.233631	−	0.404661i
$341$	27.3326			1.48014
$342$	−3.98696	+	3.23327i	−0.215590	+	0.174835i
$343$		0			0
$344$	−0.782630	−	1.35556i	−0.0421966	−	0.0730866i
$345$	22.6219	+	4.18440i	1.21792	+	0.225281i
$346$	−0.0992788	+	0.171956i	−0.00533726	+	0.00924441i
$347$	−13.6557	+	23.6523i	−0.733075	+	1.26972i	0.222488	+	0.974936i	$0.428582\pi$
$347$	−13.6557	+	23.6523i	−0.733075	+	1.26972i	−0.955563	+	0.294788i	$0.904751\pi$
$348$	4.64160	−	5.43852i	0.248816	−	0.291536i
$349$	11.4585	+	19.8467i	0.613358	+	1.06237i	0.990670	+	0.136281i	$0.0435150\pi$
$349$	11.4585	+	19.8467i	0.613358	+	1.06237i	−0.377312	+	0.926086i	$0.623152\pi$
$350$		0			0
$351$	−16.8090	+	9.14978i	−0.897200	+	0.488379i
$352$	11.5458			0.615395
$353$	5.13466	+	8.89349i	0.273290	+	0.473353i	0.969702	−	0.244289i	$-0.0785547\pi$
$353$	5.13466	+	8.89349i	0.273290	+	0.473353i	−0.696412	+	0.717642i	$0.745221\pi$
$354$	−1.63052	+	1.91047i	−0.0866612	+	0.101540i
$355$	−8.08525	+	14.0041i	−0.429120	+	0.743258i
$356$	4.89142	−	8.47218i	0.259245	−	0.449025i
$357$		0			0
$358$	−0.906150	−	1.56950i	−0.0478915	−	0.0829505i
$359$	10.1007			0.533094			0.266547	−	0.963822i	$-0.414117\pi$
$359$	10.1007			0.533094			0.266547	+	0.963822i	$0.414117\pi$
$360$	−6.84573	−	2.62225i	−0.360802	−	0.138205i
$361$	32.2028			1.69488
$362$	0.0489195	+	0.0847311i	0.00257115	+	0.00445337i
$363$	3.75531	+	10.5927i	0.197103	+	0.555973i
$364$		0			0
$365$	9.27292	−	16.0612i	0.485367	−	0.840680i
$366$	1.10520	+	3.11747i	0.0577697	+	0.162953i
$367$	−3.88768	−	6.73367i	−0.202935	−	0.351494i	0.746538	−	0.665343i	$-0.231715\pi$
$367$	−3.88768	−	6.73367i	−0.202935	−	0.351494i	−0.949473	+	0.313849i	$0.898381\pi$
$368$	−18.7576			−0.977808
$369$	28.6285	+	10.9661i	1.49034	+	0.570872i
$370$	1.02891			0.0534907
$371$		0			0
$372$	21.6267	+	4.00032i	1.12129	+	0.207407i
$373$	−12.0555	+	20.8808i	−0.624212	+	1.08117i	0.364480	+	0.931211i	$0.381247\pi$
$373$	−12.0555	+	20.8808i	−0.624212	+	1.08117i	−0.988693	+	0.149957i	$0.952087\pi$
$374$	0.855536	−	1.48183i	0.0442387	−	0.0766237i
$375$	−9.56634	+	11.2088i	−0.494004	+	0.578821i
$376$	−4.40214	−	7.62473i	−0.227023	−	0.393215i
$377$	7.82573			0.403045
$378$		0			0
$379$	−13.3581			−0.686161			−0.343081	−	0.939306i	$-0.611470\pi$
$379$	−13.3581			−0.686161			−0.343081	+	0.939306i	$0.611470\pi$
$380$	18.0156	+	31.2039i	0.924181	+	1.60073i
$381$	10.2446	−	12.0035i	0.524846	−	0.614959i
$382$	−1.91586	+	3.31838i	−0.0980242	+	0.169783i
$383$	−4.62020	+	8.00242i	−0.236081	+	0.408905i	−0.959586	−	0.281414i	$-0.909196\pi$
$383$	−4.62020	+	8.00242i	−0.236081	+	0.408905i	0.723505	+	0.690319i	$0.242530\pi$
$384$	12.1169	+	2.24128i	0.618337	+	0.114375i
$385$		0			0
$386$	−2.95898			−0.150608
$387$	3.86840	−	3.13713i	0.196642	−	0.159469i
$388$	5.95153			0.302143
$389$	−5.22421	−	9.04859i	−0.264878	−	0.458782i	0.702654	−	0.711532i	$-0.251998\pi$
$389$	−5.22421	−	9.04859i	−0.264878	−	0.458782i	−0.967532	+	0.252750i	$0.918665\pi$
$390$	−1.32107	−	3.72639i	−0.0668952	−	0.188693i
$391$	−4.38442	+	7.59404i	−0.221730	+	0.384047i
$392$		0			0
$393$	2.49028	+	7.02441i	0.125618	+	0.354335i
$394$	−2.76212	−	4.78413i	−0.139154	−	0.241021i
$395$	−25.4733			−1.28170
$396$	3.83009	+	24.0715i	0.192470	+	1.20964i
$397$	0.409157			0.0205350			0.0102675	−	0.999947i	$-0.496732\pi$
$397$	0.409157			0.0205350			0.0102675	+	0.999947i	$0.496732\pi$
$398$	−0.806617	−	1.39710i	−0.0404321	−	0.0700304i
$399$		0			0
$400$	−3.14295	+	5.44375i	−0.157147	+	0.272187i
$401$	−7.62640	+	13.2093i	−0.380844	+	0.659641i	−0.991183	−	0.132499i	$-0.957700\pi$
$401$	−7.62640	+	13.2093i	−0.380844	+	0.659641i	0.610339	+	0.792140i	$0.291033\pi$
$402$	2.22175	−	2.60320i	0.110811	−	0.129836i
$403$	12.0361	+	20.8472i	0.599562	+	1.03847i
$404$	−21.5647			−1.07288
$405$	4.81732	−	22.8232i	0.239375	−	1.13410i
$406$		0			0
$407$	−3.47141	−	6.01266i	−0.172071	−	0.298036i
$408$	1.81393	−	2.12537i	0.0898031	−	0.105222i
$409$	−3.06335	+	5.30587i	−0.151473	+	0.262359i	−0.931769	−	0.363051i	$-0.881735\pi$
$409$	−3.06335	+	5.30587i	−0.151473	+	0.262359i	0.780296	+	0.625410i	$0.215068\pi$
$410$	−3.16664	+	5.48477i	−0.156389	+	0.270874i
$411$	−35.0669	−	6.48638i	−1.72972	−	0.319949i
$412$	−7.75765	−	13.4366i	−0.382192	−	0.661976i
$413$		0			0
$414$	0.577690	+	3.63068i	0.0283919	+	0.178438i
$415$	−17.8695			−0.877178
$416$	5.08430	+	8.80626i	0.249278	+	0.431763i
$417$	9.12188	+	25.7303i	0.446701	+	1.26002i
$418$	−3.57780	+	6.19694i	−0.174996	+	0.303102i
$419$	0.781437	−	1.35349i	0.0381757	−	0.0661223i	−0.846306	−	0.532697i	$-0.821179\pi$
$419$	0.781437	−	1.35349i	0.0381757	−	0.0661223i	0.884482	+	0.466574i	$0.154512\pi$
$420$		0			0
$421$	−11.6316	−	20.1465i	−0.566889	−	0.981881i	−0.996871	−	0.0790438i	$-0.974813\pi$
$421$	−11.6316	−	20.1465i	−0.566889	−	0.981881i	0.429982	−	0.902838i	$-0.358520\pi$
$422$	4.03775			0.196555
$423$	21.7590	−	17.6457i	1.05796	−	0.857964i
$424$	−10.0377			−0.487476
$425$	1.46927	+	2.54485i	0.0712702	+	0.123444i
$426$	−2.54098	−	0.470008i	−0.123111	−	0.0227720i
$427$		0			0
$428$	3.84338	−	6.65692i	0.185777	−	0.321775i
$429$	−17.3187	+	20.2922i	−0.836157	+	0.979719i
$430$	0.514457	+	0.891066i	0.0248093	+	0.0429710i
$431$	1.00576			0.0484456			0.0242228	−	0.999707i	$-0.492289\pi$
$431$	1.00576			0.0484456			0.0242228	+	0.999707i	$0.492289\pi$
$432$	−0.477580	+	19.0129i	−0.0229776	+	0.914759i
$433$	−13.1071			−0.629889			−0.314945	−	0.949110i	$-0.601986\pi$
$433$	−13.1071			−0.629889			−0.314945	+	0.949110i	$0.601986\pi$
$434$		0			0
$435$	−6.19205	+	7.25518i	−0.296886	+	0.347859i
$436$	7.05555	−	12.2206i	0.337899	−	0.585259i
$437$	18.3354	−	31.7579i	0.877101	−	1.51918i
$438$	2.91423	+	0.539049i	0.139247	+	0.0257568i
$439$	9.30704	+	16.1203i	0.444201	+	0.769378i	0.997996	−	0.0632744i	$-0.0201543\pi$
$439$	9.30704	+	16.1203i	0.444201	+	0.769378i	−0.553795	+	0.832653i	$0.686821\pi$
$440$	−10.2190			−0.487170
$441$		0			0
$442$	1.50697			0.0716792
$443$	0.559503	+	0.969088i	0.0265828	+	0.0460427i	0.879011	−	0.476802i	$-0.158204\pi$
$443$	0.559503	+	0.969088i	0.0265828	+	0.0460427i	−0.852428	+	0.522845i	$0.824871\pi$
$444$	−1.86673	−	5.26554i	−0.0885912	−	0.249891i
$445$	−6.52532	+	11.3022i	−0.309330	+	0.535775i
$446$	−0.538197	+	0.932185i	−0.0254844	+	0.0441402i
$447$	3.51162	+	9.90531i	0.166094	+	0.468505i
$448$		0			0
$449$	−39.4419			−1.86138			−0.930689	−	0.365813i	$-0.880791\pi$
$449$	−39.4419			−1.86138			−0.930689	+	0.365813i	$0.880791\pi$
$450$	1.15047	+	0.440688i	0.0542339	+	0.0207742i
$451$	42.7351			2.01232
$452$	6.73104	+	11.6585i	0.316602	+	0.548370i
$453$	−7.64489	−	1.41409i	−0.359188	−	0.0664395i
$454$	−0.725057	+	1.25584i	−0.0340286	+	0.0589393i
$455$		0			0
$456$	−7.58577	+	8.88819i	−0.355236	+	0.416228i
$457$	17.1202	+	29.6531i	0.800852	+	1.38712i	0.919056	+	0.394126i	$0.128953\pi$
$457$	17.1202	+	29.6531i	0.800852	+	1.38712i	−0.118205	+	0.992989i	$0.537714\pi$
$458$	2.64215			0.123459
$459$	7.58577	+	4.63744i	0.354073	+	0.216457i
$460$	25.8051			1.20317
$461$	10.1938	+	17.6561i	0.474772	+	0.822328i	0.999583	−	0.0288903i	$-0.00919735\pi$
$461$	10.1938	+	17.6561i	0.474772	+	0.822328i	−0.524811	+	0.851219i	$0.675864\pi$
$462$		0			0
$463$	−3.40451	+	5.89679i	−0.158221	+	0.274047i	−0.934227	−	0.356678i	$-0.883909\pi$
$463$	−3.40451	+	5.89679i	−0.158221	+	0.274047i	0.776006	+	0.630725i	$0.217243\pi$
$464$	3.88852	−	6.73511i	0.180520	−	0.312670i
$465$	−28.8508	−	5.33656i	−1.33792	−	0.247477i
$466$	0.973045	+	1.68536i	0.0450754	+	0.0780729i
$467$	−24.7911			−1.14720			−0.573598	−	0.819137i	$-0.694453\pi$
$467$	−24.7911			−1.14720			−0.573598	+	0.819137i	$0.694453\pi$
$468$	−16.6733	+	13.5214i	−0.770721	+	0.625026i
$469$		0			0
$470$	2.89372	+	5.01207i	0.133477	+	0.231190i
$471$	−0.595485	−	1.67970i	−0.0274385	−	0.0773965i
$472$	−2.85877	+	4.95153i	−0.131586	+	0.227913i
$473$	3.47141	−	6.01266i	0.159616	−	0.276462i
$474$	−1.36019	−	3.83672i	−0.0624755	−	0.176226i
$475$	−6.14441	−	10.6424i	−0.281925	−	0.488309i
$476$		0			0
$477$	−5.01887	−	31.5428i	−0.229798	−	1.44424i
$478$	5.06045			0.231460
$479$	−5.54984	−	9.61260i	−0.253579	−	0.439211i	0.710930	−	0.703263i	$-0.248274\pi$
$479$	−5.54984	−	9.61260i	−0.253579	−	0.439211i	−0.964508	+	0.264052i	$0.914941\pi$
$480$	−12.1871	−	2.25427i	−0.556265	−	0.102893i
$481$	3.05733	−	5.29545i	0.139402	−	0.241452i
$482$	1.63697	−	2.83532i	0.0745621	−	0.129145i
$483$		0			0
$484$	6.30314	+	10.9174i	0.286506	+	0.496244i
$485$	−7.93955			−0.360516
$486$	3.69480	−	0.493113i	0.167600	−	0.0223681i
$487$	−10.0377			−0.454854			−0.227427	−	0.973795i	$-0.573031\pi$
$487$	−10.0377			−0.454854			−0.227427	+	0.973795i	$0.573031\pi$
$488$	3.76466	+	6.52059i	0.170418	+	0.295173i
$489$	7.67798	−	8.99623i	0.347210	−	0.406824i
$490$		0			0
$491$	6.19398	−	10.7283i	0.279530	−	0.484161i	−0.691738	−	0.722149i	$-0.743155\pi$
$491$	6.19398	−	10.7283i	0.279530	−	0.484161i	0.971268	+	0.237988i	$0.0764879\pi$
$492$	33.8138	+	6.25459i	1.52445	+	0.281979i
$493$	−1.81781	−	3.14854i	−0.0818702	−	0.141803i
$494$	−6.30206			−0.283543
$495$	−5.10948	−	32.1122i	−0.229654	−	1.44334i
$496$	23.9225			1.07415
$497$		0			0
$498$	−0.954170	−	2.69145i	−0.0427574	−	0.120607i
$499$	−5.11109	+	8.85267i	−0.228804	+	0.396300i	−0.957454	−	0.288586i	$-0.906815\pi$
$499$	−5.11109	+	8.85267i	−0.228804	+	0.396300i	0.728650	+	0.684886i	$0.240148\pi$
$500$	−8.26464	+	14.3148i	−0.369606	+	0.640177i
$501$	−10.4142	−	29.3757i	−0.465273	−	1.31241i
$502$	1.81781	+	3.14854i	0.0811329	+	0.140526i
$503$	8.45753			0.377102			0.188551	−	0.982063i	$-0.439621\pi$
$503$	8.45753			0.377102			0.188551	+	0.982063i	$0.439621\pi$
$504$		0			0
$505$	28.7680			1.28016
$506$	2.56238	+	4.43818i	0.113912	+	0.197301i
$507$	−0.962729	−	0.178077i	−0.0427563	−	0.00790869i
$508$	8.85060	−	15.3297i	0.392682	−	0.680145i
$509$	−5.28286	+	9.15018i	−0.234159	+	0.405574i	−0.959028	−	0.283312i	$-0.908567\pi$
$509$	−5.28286	+	9.15018i	−0.234159	+	0.405574i	0.724869	+	0.688886i	$0.241900\pi$
$510$	−1.19238	+	1.39710i	−0.0527994	+	0.0618647i
$511$		0			0
$512$	17.0071			0.751616
$513$	−31.7233	−	19.3935i	−1.40062	−	0.856245i
$514$	−6.12670			−0.270237
$515$	10.3490	+	17.9249i	0.456030	+	0.789867i
$516$	3.62672	−	4.24941i	0.159658	−	0.187070i
$517$	19.5260	−	33.8200i	0.858752	−	1.48740i
$518$		0			0
$519$	−1.41423	−	0.261592i	−0.0620778	−	0.0114826i
$520$	−4.50000	−	7.79423i	−0.197338	−	0.341800i
$521$	−19.7558			−0.865515			−0.432758	−	0.901510i	$-0.642459\pi$
$521$	−19.7558			−0.865515			−0.432758	+	0.901510i	$0.642459\pi$
$522$	−1.42339	−	0.545227i	−0.0623001	−	0.0238639i
$523$	32.5282			1.42236			0.711179	−	0.703011i	$-0.248161\pi$
$523$	32.5282			1.42236			0.711179	+	0.703011i	$0.248161\pi$
$524$	4.17984	+	7.23970i	0.182597	+	0.316268i
$525$		0			0
$526$	−0.848970	+	1.47046i	−0.0370168	+	0.0641150i
$527$	5.59166	−	9.68504i	0.243577	−	0.421887i
$528$	8.85877	+	24.9882i	0.385528	+	1.08747i
$529$	−1.63160	−	2.82601i	−0.0709391	−	0.122870i
$530$	6.59825			0.286610
$531$	−16.9891	−	6.50767i	−0.737266	−	0.282409i
$532$		0			0
$533$	18.8187	+	32.5950i	0.815130	+	1.41185i
$534$	−2.05073	−	0.379327i	−0.0887440	−	0.0164151i
$535$	−5.12720	+	8.88057i	−0.221668	+	0.383940i
$536$	3.89536	−	6.74695i	0.168254	−	0.291424i
$537$	8.52182	−	9.98495i	0.367744	−	0.430883i
$538$	−1.96457	−	3.40274i	−0.0846987	−	0.146702i
$539$		0			0
$540$	0.657014	−	26.1563i	0.0282734	−	1.12559i
$541$	15.2222			0.654453			0.327226	−	0.944946i	$-0.393886\pi$
$541$	15.2222			0.654453			0.327226	+	0.944946i	$0.393886\pi$
$542$	1.51819	+	2.62959i	0.0652119	+	0.112950i
$543$	−0.460060	+	0.539049i	−0.0197431	+	0.0231328i
$544$	2.36203	−	4.09116i	0.101271	−	0.175407i
$545$	−9.41234	+	16.3027i	−0.403180	+	0.698329i
$546$		0			0
$547$	−11.6871	−	20.2427i	−0.499706	−	0.865517i	0.500294	−	0.865856i	$-0.333225\pi$
$547$	−11.6871	−	20.2427i	−0.499706	−	0.865517i	−1.00000		0.000339172i	$0.999892\pi$
$548$	−40.0014			−1.70877
$549$	−18.6081	+	15.0904i	−0.794173	+	0.644044i
$550$	1.71737			0.0732289
$551$	7.60199	+	13.1670i	0.323856	+	0.560934i
$552$	2.79637	+	7.88779i	0.119021	+	0.335726i
$553$		0			0
$554$	0.0990521	−	0.171563i	0.00420832	−	0.00728902i
$555$	2.49028	+	7.02441i	0.105707	+	0.298170i
$556$	15.3107	+	26.5189i	0.649319	+	1.12465i
$557$	27.6673			1.17230			0.586151	−	0.810202i	$-0.300643\pi$
$557$	27.6673			1.17230			0.586151	+	0.810202i	$0.300643\pi$
$558$	−0.736755	−	4.63038i	−0.0311893	−	0.196019i
$559$	6.11465			0.258622
$560$		0			0
$561$	12.1871	+	2.25427i	0.514542	+	0.0951755i
$562$	−0.624075	+	1.08093i	−0.0263250	+	0.0455963i
$563$	−4.27912	+	7.41166i	−0.180343	+	0.312364i	−0.941998	−	0.335620i	$-0.891054\pi$
$563$	−4.27912	+	7.41166i	−0.180343	+	0.312364i	0.761654	+	0.647984i	$0.224388\pi$
$564$	20.3996	−	23.9021i	0.858979	−	1.00646i
$565$	−8.97944	−	15.5529i	−0.377768	−	0.654313i
$566$	1.75855			0.0739175
$567$		0			0
$568$	−5.88237			−0.246819
$569$	−6.86389	−	11.8886i	−0.287749	−	0.498396i	0.685523	−	0.728051i	$-0.259574\pi$
$569$	−6.86389	−	11.8886i	−0.287749	−	0.498396i	−0.973272	+	0.229655i	$0.926240\pi$
$570$	4.98646	−	5.84260i	0.208860	−	0.244720i
$571$	−5.35868	+	9.28151i	−0.224254	+	0.388419i	−0.956095	−	0.293056i	$-0.905328\pi$
$571$	−5.35868	+	9.28151i	−0.224254	+	0.388419i	0.731841	+	0.681475i	$0.238661\pi$
$572$	−14.9622	+	25.9153i	−0.625600	+	1.08357i
$573$	−27.2916	−	5.04816i	−1.14012	−	0.210890i
$574$		0			0
$575$	−8.80111			−0.367032
$576$	3.13968	+	19.7323i	0.130820	+	0.822181i
$577$	−45.6353			−1.89982			−0.949912	−	0.312518i	$-0.898827\pi$
$577$	−45.6353			−1.89982			−0.949912	+	0.312518i	$0.898827\pi$
$578$	1.68250	+	2.91417i	0.0699827	+	0.121214i
$579$	−7.16163	−	20.2010i	−0.297627	−	0.839525i
$580$	−5.34950	+	9.26560i	−0.222126	+	0.384733i
$581$		0			0
$582$	−0.423945	−	1.19583i	−0.0175731	−	0.0495689i
$583$	−22.2616	−	38.5582i	−0.921980	−	1.59692i
$584$	6.74645			0.279170
$585$	22.2427	−	18.0380i	0.919622	−	0.745779i
$586$	−1.87131			−0.0773032
$587$	5.10948	+	8.84988i	0.210891	+	0.365274i	0.951994	−	0.306118i	$-0.0990302\pi$
$587$	5.10948	+	8.84988i	0.210891	+	0.365274i	−0.741103	+	0.671392i	$0.765697\pi$
$588$		0			0
$589$	−23.3840	+	40.5023i	−0.963521	+	1.66887i
$590$	1.87919	−	3.25486i	0.0773652	−	0.134000i
$591$	25.9762	−	30.4361i	1.06852	−	1.25197i
$592$	−3.03831	−	5.26250i	−0.124874	−	0.216287i
$593$	11.3961			0.467981			0.233990	−	0.972239i	$-0.424822\pi$
$593$	11.3961			0.467981			0.233990	+	0.972239i	$0.424822\pi$
$594$	4.56382	−	2.48426i	0.187256	−	0.101930i
$595$		0			0
$596$	5.89411	+	10.2089i	0.241432	+	0.418173i
$597$	7.58577	−	8.88819i	0.310465	−	0.363769i
$598$	−2.25673	+	3.90877i	−0.0922846	+	0.159842i
$599$	17.2873	−	29.9424i	0.706339	−	1.22341i	−0.259867	−	0.965644i	$-0.583679\pi$
$599$	17.2873	−	29.9424i	0.706339	−	1.22341i	0.966206	−	0.257771i	$-0.0829879\pi$
$600$	2.75771	+	0.510097i	0.112583	+	0.0208246i
$601$	19.4207	+	33.6376i	0.792187	+	1.37211i	0.924610	+	0.380915i	$0.124391\pi$
$601$	19.4207	+	33.6376i	0.792187	+	1.37211i	−0.132423	+	0.991193i	$0.542276\pi$
$602$		0			0
$603$	23.1494	+	8.86734i	0.942716	+	0.361106i
$604$	−8.72064			−0.354838
$605$	−8.40861	−	14.5641i	−0.341858	−	0.592116i
$606$	1.53611	+	4.33296i	0.0624004	+	0.176014i
$607$	20.6662	−	35.7950i	0.838817	−	1.45287i	−0.0520683	−	0.998644i	$-0.516581\pi$
$607$	20.6662	−	35.7950i	0.838817	−	1.45287i	0.890885	−	0.454229i	$-0.150085\pi$
$608$	−9.87788	+	17.1090i	−0.400601	+	0.693861i
$609$		0			0
$610$	−2.47468	−	4.28627i	−0.100197	−	0.173546i
$611$	34.3937			1.39142
$612$	9.31306	+	3.56735i	0.376458	+	0.144202i
$613$	−28.6569			−1.15744			−0.578721	−	0.815526i	$-0.696448\pi$
$613$	−28.6569			−1.15744			−0.578721	+	0.815526i	$0.696448\pi$
$614$	2.71057	+	4.69485i	0.109390	+	0.189469i
$615$	−45.1088	−	8.34384i	−1.81896	−	0.336456i
$616$		0			0
$617$	16.8518	−	29.1883i	0.678430	−	1.17508i	−0.297024	−	0.954870i	$-0.595994\pi$
$617$	16.8518	−	29.1883i	0.678430	−	1.17508i	0.975454	−	0.220205i	$-0.0706726\pi$
$618$	−2.14721	+	2.51586i	−0.0863733	+	0.101203i
$619$	−0.719036	−	1.24541i	−0.0289005	−	0.0500571i	0.851213	−	0.524820i	$-0.175867\pi$
$619$	−0.719036	−	1.24541i	−0.0289005	−	0.0500571i	−0.880114	+	0.474763i	$0.842534\pi$
$620$	−32.9105			−1.32172
$621$	−23.3885	+	12.7312i	−0.938548	+	0.510887i
$622$	7.72789			0.309860
$623$		0			0
$624$	−15.1580	+	17.7605i	−0.606806	+	0.710990i
$625$	15.3187	−	26.5328i	0.612750	−	1.06131i
$626$	−2.90769	+	5.03626i	−0.116215	+	0.201290i
$627$	−50.9660	−	9.42724i	−2.03538	−	0.376488i
$628$	−0.999498	−	1.73118i	−0.0398843	−	0.0690816i
$629$	−2.84071			−0.113266
$630$		0			0
$631$	−30.7680			−1.22486			−0.612428	−	0.790527i	$-0.709807\pi$
$631$	−30.7680			−1.22486			−0.612428	+	0.790527i	$0.709807\pi$
$632$	−4.63323	−	8.02500i	−0.184300	−	0.319217i
$633$	9.77258	+	27.5658i	0.388425	+	1.09564i
$634$	−0.614360	+	1.06410i	−0.0243993	+	0.0422609i
$635$	−11.8070	+	20.4503i	−0.468547	+	0.811547i
$636$	−11.9710	−	33.7670i	−0.474682	−	1.33895i
$637$		0			0
$638$	−2.12476			−0.0841202
$639$	−2.94119	−	18.4848i	−0.116351	−	0.731249i
$640$	−18.4389			−0.728862
$641$	−4.61956	−	8.00132i	−0.182462	−	0.316033i	0.760257	−	0.649623i	$-0.225073\pi$
$641$	−4.61956	−	8.00132i	−0.182462	−	0.316033i	−0.942718	+	0.333590i	$0.891740\pi$
$642$	−1.61134	−	0.298052i	−0.0635946	−	0.0117632i
$643$	12.7795	−	22.1348i	0.503976	−	0.872912i	−0.496013	−	0.868315i	$-0.665203\pi$
$643$	12.7795	−	22.1348i	0.503976	−	0.872912i	0.999989	−	0.00459728i	$-0.00146337\pi$
$644$		0			0
$645$	−4.83818	+	5.66886i	−0.190503	+	0.223211i
$646$	1.46389	+	2.53552i	0.0575958	+	0.0997588i
$647$	28.3111			1.11302			0.556512	−	0.830839i	$-0.312139\pi$
$647$	28.3111			1.11302			0.556512	+	0.830839i	$0.312139\pi$
$648$	8.06634	−	2.63360i	0.316876	−	0.103458i
$649$	−25.3605			−0.995488
$650$	0.756258	+	1.30988i	0.0296629	+	0.0513776i
$651$		0			0
$652$	6.63323	−	11.4891i	0.259778	−	0.449948i
$653$	4.17511	−	7.23150i	0.163385	−	0.282990i	−0.772696	−	0.634776i	$-0.781092\pi$
$653$	4.17511	−	7.23150i	0.163385	−	0.282990i	0.936080	+	0.351786i	$0.114426\pi$
$654$	−2.95805	−	0.547154i	−0.115669	−	0.0213954i
$655$	−5.57605	−	9.65801i	−0.217874	−	0.377370i
$656$	37.4033			1.46035
$657$	3.37323	+	21.2001i	0.131602	+	0.827096i
$658$		0			0
$659$	16.7862	+	29.0745i	0.653897	+	1.13258i	0.982169	+	0.188000i	$0.0602005\pi$
$659$	16.7862	+	29.0745i	0.653897	+	1.13258i	−0.328272	+	0.944583i	$0.606466\pi$
$660$	−12.1871	−	34.3766i	−0.474384	−	1.33811i
$661$	8.47668	−	14.6820i	0.329705	−	0.571065i	−0.652748	−	0.757575i	$-0.726384\pi$
$661$	8.47668	−	14.6820i	0.329705	−	0.571065i	0.982453	+	0.186509i	$0.0597175\pi$
$662$	1.39862	−	2.42249i	0.0543591	−	0.0941527i
$663$	3.64732	+	10.2881i	0.141650	+	0.399557i
$664$	−3.25021	−	5.62952i	−0.126133	−	0.218468i
$665$		0			0
$666$	−0.925025	+	0.750160i	−0.0358440	+	0.0290681i
$667$	10.8889			0.421620
$668$	−17.4799	−	30.2760i	−0.676316	−	1.17141i
$669$	−7.66664	−	1.41811i	−0.296409	−	0.0548272i
$670$	−2.56059	+	4.43507i	−0.0989242	+	0.171342i
$671$	−16.6984	+	28.9225i	−0.644636	+	1.11654i
$672$		0			0
$673$	22.2157	+	38.4788i	0.856354	+	1.48325i	0.875384	+	0.483429i	$0.160609\pi$
$673$	22.2157	+	38.4788i	0.856354	+	1.48325i	−0.0190299	+	0.999819i	$0.506058\pi$
$674$	−8.05718			−0.310351
$675$	−0.224082	+	8.92090i	−0.00862490	+	0.343366i
$676$	−1.09820			−0.0422384
$677$	7.18681	+	12.4479i	0.276212	+	0.478412i	0.970440	−	0.241342i	$-0.0775876\pi$
$677$	7.18681	+	12.4479i	0.276212	+	0.478412i	−0.694229	+	0.719755i	$0.744254\pi$
$678$	1.86306	−	2.18293i	0.0715502	−	0.0838349i
$679$		0			0
$680$	−2.09058	+	3.62099i	−0.0801701	+	0.138859i
$681$	−10.3285	−	1.91047i	−0.395787	−	0.0732093i
$682$	−3.26793	−	5.66021i	−0.125135	−	0.216741i
$683$	−32.3092			−1.23628			−0.618138	−	0.786069i	$-0.712113\pi$
$683$	−32.3092			−1.23628			−0.618138	+	0.786069i	$0.712113\pi$
$684$	−38.9467	−	14.9185i	−1.48916	−	0.570422i
$685$	53.3632			2.03890
$686$		0			0
$687$	6.39480	+	18.0380i	0.243977	+	0.688192i
$688$	3.03831	−	5.26250i	0.115834	−	0.200631i
$689$	19.6061	−	33.9588i	0.746934	−	1.29373i
$690$	−1.83818	−	5.18499i	−0.0699781	−	0.197389i
$691$	14.4981	+	25.1114i	0.551533	+	0.955283i	0.998164	+	0.0605650i	$0.0192902\pi$
$691$	14.4981	+	25.1114i	0.551533	+	0.955283i	−0.446631	+	0.894718i	$0.647376\pi$
$692$	−1.61323			−0.0613259
$693$		0			0
$694$	6.53078			0.247905
$695$	−20.4250	−	35.3772i	−0.774765	−	1.34193i
$696$	−3.41189	−	0.631101i	−0.129327	−	0.0239218i
$697$	8.74269	−	15.1428i	0.331153	−	0.573574i
$698$	2.73999	−	4.74580i	0.103710	−	0.179631i
$699$	−9.15093	+	10.7221i	−0.346120	+	0.405546i
$700$		0			0
$701$	−26.3912			−0.996783			−0.498392	−	0.866952i	$-0.666076\pi$
$701$	−26.3912			−0.996783			−0.498392	+	0.866952i	$0.666076\pi$
$702$	3.90451	+	2.38697i	0.147366	+	0.0900902i
$703$	11.8797			0.448050
$704$	13.9263	+	24.1210i	0.524866	+	0.909095i
$705$	−27.2138	+	31.8862i	−1.02493	+	1.20090i
$706$	1.22782	−	2.12664i	0.0462095	−	0.0800372i
$707$		0			0
$708$	−20.0663	−	3.71170i	−0.754139	−	0.139494i
$709$	3.94282	+	6.82916i	0.148076	+	0.256475i	0.930516	−	0.366251i	$-0.119359\pi$
$709$	3.94282	+	6.82916i	0.148076	+	0.256475i	−0.782441	+	0.622725i	$0.786025\pi$
$710$	3.86674			0.145116
$711$	22.9012	−	18.5720i	0.858864	−	0.696506i
$712$	−4.74746			−0.177918
$713$	16.7473	+	29.0073i	0.627193	+	1.08633i
$714$		0			0
$715$	19.9601	−	34.5718i	0.746464	−	1.29291i
$716$	7.36225	−	12.7518i	0.275140	−	0.476557i
$717$	12.2478	+	34.5477i	0.457403	+	1.29021i
$718$	−1.20765	−	2.09172i	−0.0450693	−	0.0780623i
$719$	−33.1508			−1.23632			−0.618159	−	0.786053i	$-0.712121\pi$
$719$	−33.1508			−1.23632			−0.618159	+	0.786053i	$0.712121\pi$
$720$	−4.47200	−	28.1058i	−0.166662	−	1.04744i
$721$		0			0
$722$	−3.85021	−	6.66877i	−0.143290	−	0.248186i
$723$	23.3187	+	4.31330i	0.867233	+	0.160413i
$724$	−0.397460	+	0.688420i	−0.0147715	+	0.0255849i
$725$	1.82450	−	3.16013i	0.0677603	−	0.117364i
$726$	1.74462	−	2.04416i	0.0647489	−	0.0758658i
$727$	−16.5502	−	28.6658i	−0.613814	−	1.06316i	−0.990591	−	0.136853i	$-0.956301\pi$
$727$	−16.5502	−	28.6658i	−0.613814	−	1.06316i	0.376777	−	0.926304i	$-0.377032\pi$
$728$		0			0
$729$	12.3090	+	24.0310i	0.455890	+	0.890036i
$730$	−4.43474			−0.164137
$731$	−1.42035	−	2.46012i	−0.0525337	−	0.0909910i
$732$	−17.4455	+	20.4408i	−0.644805	+	0.755514i
$733$	22.2795	−	38.5892i	0.822911	−	1.42532i	−0.0805946	−	0.996747i	$-0.525682\pi$
$733$	22.2795	−	38.5892i	0.822911	−	1.42532i	0.903505	−	0.428577i	$-0.140985\pi$
$734$	−0.929636	+	1.61018i	−0.0343135	+	0.0594327i
$735$		0			0
$736$	7.07442	+	12.2533i	0.260767	+	0.451661i
$737$	34.5562			1.27290
$738$	−1.15193	−	7.23970i	−0.0424032	−	0.266497i
$739$	39.8090			1.46440			0.732199	−	0.681090i	$-0.238494\pi$
$739$	39.8090			1.46440			0.732199	+	0.681090i	$0.238494\pi$
$740$	4.17984	+	7.23970i	0.153654	+	0.266137i
$741$	−15.2529	−	43.0242i	−0.560329	−	1.58053i
$742$		0			0
$743$	−5.37072	+	9.30237i	−0.197033	+	0.341271i	−0.947565	−	0.319563i	$-0.896464\pi$
$743$	−5.37072	+	9.30237i	−0.197033	+	0.341271i	0.750532	+	0.660834i	$0.229797\pi$
$744$	−3.56634	−	10.0597i	−0.130748	−	0.368805i
$745$	−7.86295	−	13.6190i	−0.288076	−	0.498962i
$746$	5.76552			0.211091
$747$	16.0652	−	13.0283i	0.587795	−	0.476679i
$748$	13.9021			0.508310
$749$		0			0
$750$	3.46496	+	0.640919i	0.126523	+	0.0234031i
$751$	−9.85705	+	17.0729i	−0.359689	+	0.622999i	−0.987909	−	0.155036i	$-0.950450\pi$
$751$	−9.85705	+	17.0729i	−0.359689	+	0.622999i	0.628220	+	0.778036i	$0.283784\pi$
$752$	17.0899	−	29.6005i	0.623203	−	1.07942i
$753$	−17.0955	+	20.0307i	−0.622994	+	0.729958i
$754$	−0.935657	−	1.62060i	−0.0340746	−	0.0590189i
$755$	11.6336			0.423391
$756$		0			0
$757$	35.3549			1.28499			0.642497	−	0.766288i	$-0.277898\pi$
$757$	35.3549			1.28499			0.642497	+	0.766288i	$0.277898\pi$
$758$	1.59712	+	2.76629i	0.0580100	+	0.100476i
$759$	−24.0977	+	28.2351i	−0.874692	+	1.02487i
$760$	8.74269	−	15.1428i	0.317131	−	0.549286i
$761$	19.5572	−	33.8741i	0.708948	−	1.22793i	−0.256300	−	0.966597i	$-0.582503\pi$
$761$	19.5572	−	33.8741i	0.708948	−	1.22793i	0.965248	−	0.261336i	$-0.0841632\pi$
$762$	−3.71063	−	0.686360i	−0.134422	−	0.0248642i
$763$		0			0
$764$	−31.1319			−1.12631
$765$	−12.4239	−	4.75897i	−0.449189	−	0.172061i
$766$	2.20960			0.0798359
$767$	−11.1677	−	19.3430i	−0.403243	−	0.698437i
$768$	6.72460	+	18.9683i	0.242653	+	0.684458i
$769$	18.9240	−	32.7773i	0.682415	−	1.18198i	−0.291826	−	0.956471i	$-0.594263\pi$
$769$	18.9240	−	32.7773i	0.682415	−	1.18198i	0.974242	−	0.225507i	$-0.0724038\pi$
$770$		0			0
$771$	−14.8285	−	41.8270i	−0.534034	−	1.50636i
$772$	−12.0205	−	20.8201i	−0.432628	−	0.749333i
$773$	29.8265			1.07279			0.536393	−	0.843969i	$-0.319787\pi$
$773$	29.8265			1.07279			0.536393	+	0.843969i	$0.319787\pi$
$774$	−1.11217	−	0.426015i	−0.0399761	−	0.0153128i
$775$	11.2245			0.403195
$776$	−1.44409	−	2.50124i	−0.0518399	−	0.0897894i
$777$		0			0
$778$	−1.24923	+	2.16373i	−0.0447870	+	0.0775734i
$779$	−36.5614	+	63.3263i	−1.30995	+	2.26890i
$780$	20.8531	−	24.4334i	0.746661	−	0.874857i
$781$	−13.0458	−	22.5960i	−0.466817	−	0.808550i
$782$	2.09683			0.0749827
$783$	0.277238	−	11.0371i	0.00990768	−	0.394434i
$784$		0			0
$785$	1.33336	+	2.30946i	0.0475898	+	0.0824280i
$786$	1.15692	−	1.35556i	0.0412660	−	0.0483511i
$787$	−8.81030	+	15.2599i	−0.314053	+	0.543956i	−0.979236	−	0.202724i	$-0.935020\pi$
$787$	−8.81030	+	15.2599i	−0.314053	+	0.543956i	0.665182	+	0.746681i	$0.268354\pi$
$788$	22.4416	−	38.8700i	0.799448	−	1.38468i
$789$	−12.0936	−	2.23697i	−0.430544	−	0.0796382i
$790$	3.04563	+	5.27518i	0.108359	+	0.187683i
$791$		0			0
$792$	9.18715	−	7.45043i	0.326451	−	0.264739i
$793$	−29.4132			−1.04449
$794$	−0.0489195	−	0.0847311i	−0.00173609	−	0.00300699i
$795$	15.9698	+	45.0464i	0.566390	+	1.59763i
$796$	6.55357	−	11.3511i	0.232285	−	0.402330i
$797$	−5.06056	+	8.76515i	−0.179254	+	0.310477i	−0.941625	−	0.336663i	$-0.890702\pi$
$797$	−5.06056	+	8.76515i	−0.179254	+	0.310477i	0.762371	+	0.647140i	$0.224035\pi$
$798$		0			0
$799$	−7.98921	−	13.8377i	−0.282638	−	0.489543i
$800$	4.74145			0.167635
$801$	−2.37373	−	14.9185i	−0.0838716	−	0.527118i
$802$	3.64730			0.128791
$803$	14.9622	+	25.9153i	0.528004	+	0.914529i
$804$	27.3424	+	5.05756i	0.964291	+	0.178366i
$805$		0			0
$806$	2.87812	−	4.98504i	0.101377	−	0.175591i
$807$	18.4757	−	21.6478i	0.650374	−	0.762039i
$808$	5.23250	+	9.06295i	0.184079	+	0.318834i
$809$	−47.1469			−1.65760			−0.828799	−	0.559546i	$-0.810975\pi$
$809$	−47.1469			−1.65760			−0.828799	+	0.559546i	$0.810975\pi$
$810$	−5.30236	+	1.73118i	−0.186306	+	0.0608275i
$811$	21.0577			0.739435			0.369717	−	0.929144i	$-0.379454\pi$
$811$	21.0577			0.739435			0.369717	+	0.929144i	$0.379454\pi$
$812$		0			0
$813$	−14.2777	+	16.7291i	−0.500742	+	0.586715i
$814$	−0.830095	+	1.43777i	−0.0290948	+	0.0503937i
$815$	−8.84896	+	15.3269i	−0.309966	+	0.536876i
$816$	10.6666	+	1.97302i	0.373407	+	0.0690696i
$817$	5.93984	+	10.2881i	0.207809	+	0.359935i
$818$	1.46504			0.0512238
$819$		0			0
$820$	−51.4563			−1.79693
$821$	−5.58018	−	9.66515i	−0.194750	−	0.337316i	0.752069	−	0.659085i	$-0.229056\pi$
$821$	−5.58018	−	9.66515i	−0.194750	−	0.337316i	−0.946818	+	0.321768i	$0.895723\pi$
$822$	2.84942	+	8.03742i	0.0993848	+	0.280337i
$823$	−4.71737	+	8.17072i	−0.164437	+	0.284814i	−0.936455	−	0.350787i	$-0.885914\pi$
$823$	−4.71737	+	8.17072i	−0.164437	+	0.284814i	0.772018	+	0.635601i	$0.219247\pi$
$824$	−3.76466	+	6.52059i	−0.131148	+	0.227156i
$825$	4.15656	+	11.7245i	0.144713	+	0.408195i
$826$		0			0
$827$	17.2646			0.600348			0.300174	−	0.953884i	$-0.402955\pi$
$827$	17.2646			0.600348			0.300174	+	0.953884i	$0.402955\pi$
$828$	−23.1996	+	18.8140i	−0.806241	+	0.653831i
$829$	−48.4526			−1.68283			−0.841415	−	0.540390i	$-0.818277\pi$
$829$	−48.4526			−1.68283			−0.841415	+	0.540390i	$0.818277\pi$
$830$	2.13650	+	3.70053i	0.0741591	+	0.128447i
$831$	1.41100	+	0.260995i	0.0489470	+	0.00905380i
$832$	−12.2651	+	21.2438i	−0.425215	+	0.736495i
$833$		0			0
$834$	4.23779	−	4.96538i	0.146743	−	0.171937i
$835$	23.3187	+	40.3893i	0.806978	+	1.39773i
$836$	−58.1376			−2.01073
$837$	29.8285	−	16.2367i	1.03102	−	0.561224i
$838$	−0.373720			−0.0129099
$839$	7.43429	+	12.8766i	0.256660	+	0.444548i	0.965345	−	0.260977i	$-0.0840446\pi$
$839$	7.43429	+	12.8766i	0.256660	+	0.444548i	−0.708685	+	0.705525i	$0.750711\pi$
$840$		0			0
$841$	12.2427	−	21.2050i	0.422162	−	0.731206i
$842$	−2.78139	+	4.81750i	−0.0958529	+	0.166022i
$843$	−8.88997	−	1.64439i	−0.306187	−	0.0566358i
$844$	16.4029	+	28.4106i	0.564610	+	0.977934i
$845$	1.46504			0.0503988
$846$	−6.25574	−	2.39625i	−0.215077	−	0.0823848i
$847$		0			0
$848$	−19.4841	−	33.7475i	−0.669088	−	1.15889i
$849$	4.25623	+	12.0057i	0.146073	+	0.412033i
$850$	0.351337	−	0.608534i	0.0120508	−	0.0208725i
$851$	4.25404	−	7.36821i	0.145827	−	0.252579i
$852$	−7.01532	−	19.7883i	−0.240341	−	0.677936i
$853$	−3.99900	−	6.92648i	−0.136923	−	0.237158i	0.789407	−	0.613870i	$-0.210388\pi$
$853$	−3.99900	−	6.92648i	−0.136923	−	0.237158i	−0.926331	+	0.376712i	$0.877055\pi$
$854$		0			0
$855$	51.9562	+	19.9018i	1.77687	+	0.680626i
$856$	−3.73026			−0.127498
$857$	21.5661	+	37.3536i	0.736684	+	1.27597i	0.953980	+	0.299869i	$0.0969429\pi$
$857$	21.5661	+	37.3536i	0.736684	+	1.27597i	−0.217296	+	0.976106i	$0.569724\pi$
$858$	6.27292	+	1.16031i	0.214154	+	0.0396123i
$859$	1.22180	−	2.11621i	0.0416871	−	0.0722042i	−0.844429	−	0.535667i	$-0.820060\pi$
$859$	1.22180	−	2.11621i	0.0416871	−	0.0722042i	0.886116	+	0.463463i	$0.153393\pi$
$860$	−4.17984	+	7.23970i	−0.142531	+	0.246872i
$861$		0			0
$862$	−0.120250	−	0.208279i	−0.00409573	−	0.00709401i
$863$	25.7187			0.875476			0.437738	−	0.899103i	$-0.355780\pi$
$863$	25.7187			0.875476			0.437738	+	0.899103i	$0.355780\pi$
$864$	12.6001	−	6.85873i	0.428666	−	0.233339i
$865$	2.15211			0.0731739
$866$	1.56711	+	2.71432i	0.0532526	+	0.0922362i
$867$	−15.8229	+	18.5396i	−0.537375	+	0.629639i
$868$		0			0
$869$	20.5510	−	35.5954i	0.697146	−	1.20749i
$870$	2.24278	+	0.414851i	0.0760375	+	0.0140648i
$871$	15.2171	+	26.3568i	0.515612	+	0.893067i
$872$	−6.84789			−0.231899
$873$	7.13789	−	5.78856i	0.241581	−	0.195913i
$874$	−8.76884			−0.296611
$875$		0			0
$876$	8.04583	+	22.6951i	0.271843	+	0.766796i
$877$	10.9795	−	19.0170i	0.370751	−	0.642160i	−0.618930	−	0.785446i	$-0.712434\pi$
$877$	10.9795	−	19.0170i	0.370751	−	0.642160i	0.989681	+	0.143286i	$0.0457670\pi$
$878$	2.22553	−	3.85473i	0.0751080	−	0.130091i
$879$	−4.52915	−	12.7755i	−0.152764	−	0.430906i
$880$	−19.8359	−	34.3567i	−0.668667	−	1.15817i
$881$	−35.0576			−1.18112			−0.590560	−	0.806994i	$-0.701093\pi$
$881$	−35.0576			−1.18112			−0.590560	+	0.806994i	$0.701093\pi$
$882$		0			0
$883$	26.3009			0.885097			0.442549	−	0.896744i	$-0.354074\pi$
$883$	26.3009			0.885097			0.442549	+	0.896744i	$0.354074\pi$
$884$	6.12188	+	10.6034i	0.205901	+	0.356631i
$885$	26.7692	+	4.95153i	0.899836	+	0.166444i
$886$	0.133790	−	0.231731i	0.00449477	−	0.00778517i
$887$	−23.9090	+	41.4116i	−0.802785	+	1.39046i	0.114991	+	0.993366i	$0.463316\pi$
$887$	−23.9090	+	41.4116i	−0.802785	+	1.39046i	−0.917776	+	0.397098i	$0.870017\pi$
$888$	−1.75999	+	2.06217i	−0.0590615	+	0.0692019i
$889$		0			0
$890$	3.12071			0.104607
$891$	28.0059	+	25.1446i	0.938233	+	0.842376i
$892$	−8.74545			−0.292819
$893$	33.4104	+	57.8685i	1.11804	+	1.93650i
$894$	1.63141	−	1.91151i	0.0545623	−	0.0639303i
$895$	−9.82150	+	17.0113i	−0.328296	+	0.568626i
$896$		0			0
$897$	−32.1472	−	5.94631i	−1.07336	−	0.198542i
$898$	4.71574	+	8.16789i	0.157366	+	0.272566i
$899$	−13.8871			−0.463162
$900$	1.57288	+	9.88527i	0.0524293	+	0.329509i
$901$	−18.2170			−0.606895
$902$	−5.10948	−	8.84988i	−0.170127	−	0.294669i
$903$		0			0
$904$	3.26647	−	5.65769i	0.108641	−	0.188172i
$905$	0.530225	−	0.918376i	0.0176253	−	0.0305279i
$906$	0.621197	+	1.75223i	0.0206379	+	0.0582138i
$907$	9.55718	+	16.5535i	0.317341	+	0.549651i	0.979932	−	0.199330i	$-0.0638767\pi$
$907$	9.55718	+	16.5535i	0.317341	+	0.549651i	−0.662591	+	0.748981i	$0.730543\pi$
$908$	−11.7818			−0.390994
$909$	−25.8633	+	20.9741i	−0.857831	+	0.695669i
$910$		0			0
$911$	9.02928	+	15.6392i	0.299153	+	0.518149i	0.975942	−	0.218028i	$-0.0699625\pi$
$911$	9.02928	+	15.6392i	0.299153	+	0.518149i	−0.676789	+	0.736177i	$0.736629\pi$
$912$	−44.6073	−	8.25107i	−1.47709	−	0.273220i
$913$	14.4165	−	24.9701i	0.477117	−	0.826391i
$914$	4.09385	−	7.09076i	0.135413	−	0.234541i
$915$	23.2729	−	27.2687i	0.769380	−	0.901477i
$916$	10.7334	+	18.5908i	0.354642	+	0.614258i
$917$		0			0
$918$	0.0533866	−	2.12537i	0.00176202	−	0.0701478i
$919$	16.2093			0.534695			0.267348	−	0.963600i	$-0.413853\pi$
$919$	16.2093			0.534695			0.267348	+	0.963600i	$0.413853\pi$
$920$	−6.26141	−	10.8451i	−0.206433	−	0.357552i
$921$	−25.4914	+	29.8680i	−0.839969	+	0.984186i
$922$	2.43757	−	4.22199i	0.0802771	−	0.139044i
$923$	11.4897	−	19.9007i	0.378187	−	0.655039i
$924$		0			0
$925$	−1.42558	−	2.46918i	−0.0468728	−	0.0811860i
$926$	1.62820			0.0535059
$927$	−22.3727	−	8.56984i	−0.734817	−	0.281470i
$928$	−5.86621			−0.192568
$929$	−11.3415	−	19.6440i	−0.372102	−	0.644499i	0.617787	−	0.786345i	$-0.288029\pi$
$929$	−11.3415	−	19.6440i	−0.372102	−	0.644499i	−0.989889	+	0.141846i	$0.954696\pi$
$930$	2.34431	+	6.61266i	0.0768730	+	0.216838i
$931$		0			0
$932$	−7.90576	+	13.6932i	−0.258962	+	0.448535i
$933$	18.7038	+	52.7584i	0.612336	+	1.72723i
$934$	2.96407	+	5.13392i	0.0969873	+	0.167987i
$935$	−18.5458			−0.606513
$936$	9.72824	+	3.72639i	0.317977	+	0.121801i
$937$	−51.2933			−1.67568			−0.837840	−	0.545915i	$-0.816182\pi$
$937$	−51.2933			−1.67568			−0.837840	+	0.545915i	$0.816182\pi$
$938$		0			0
$939$	−41.4201	−	7.66154i	−1.35169	−	0.250025i
$940$	−23.5108	+	40.7219i	−0.766838	+	1.32820i
$941$	−15.9659	+	27.6538i	−0.520474	+	0.901487i	0.479243	+	0.877682i	$0.340911\pi$
$941$	−15.9659	+	27.6538i	−0.520474	+	0.901487i	−0.999717	+	0.0238048i	$0.992422\pi$
$942$	−0.276647	+	0.324145i	−0.00901363	+	0.0105612i
$943$	26.1849	+	45.3535i	0.852697	+	1.47691i
$944$	−22.1965			−0.722433
$945$		0			0
$946$	−1.66019			−0.0539774
$947$	2.24665	+	3.89131i	0.0730063	+	0.126451i	0.900218	−	0.435440i	$-0.143407\pi$
$947$	2.24665	+	3.89131i	0.0730063	+	0.126451i	−0.827211	+	0.561891i	$0.810074\pi$
$948$	21.4705	−	25.1568i	0.697330	−	0.817056i
$949$	−13.1774	+	22.8240i	−0.427757	+	0.740898i
$950$	−1.46927	+	2.54485i	−0.0476695	+	0.0825660i
$951$	−8.75158	−	1.61879i	−0.283789	−	0.0524929i
$952$		0			0
$953$	1.14635			0.0371340			0.0185670	−	0.999828i	$-0.494090\pi$
$953$	1.14635			0.0371340			0.0185670	+	0.999828i	$0.494090\pi$
$954$	−5.93203	+	4.81065i	−0.192056	+	0.155750i
$955$	41.5310			1.34391
$956$	20.5575	+	35.6066i	0.664876	+	1.15160i
$957$	−5.14257	−	14.5058i	−0.166236	−	0.468905i
$958$	−1.32710	+	2.29860i	−0.0428765	+	0.0742643i
$959$		0			0
$960$	−9.99028	−	28.1799i	−0.322435	−	0.909501i
$961$	−5.85868	−	10.1475i	−0.188990	−	0.327340i
$962$	−1.46216			−0.0471418
$963$	−1.86513	−	11.7220i	−0.0601030	−	0.377737i
$964$	26.6000			0.856730
$965$	16.0358	+	27.7748i	0.516210	+	0.894102i
$966$		0			0
$967$	−24.8080	+	42.9686i	−0.797770	+	1.38178i	0.123295	+	0.992370i	$0.460654\pi$
$967$	−24.8080	+	42.9686i	−0.797770	+	1.38178i	−0.921065	+	0.389408i	$0.872680\pi$
$968$	3.05881	−	5.29802i	0.0983140	−	0.170285i
$969$	−13.7670	+	16.1307i	−0.442260	+	0.518193i
$970$	0.949266	+	1.64418i	0.0304791	+	0.0527913i
$971$	5.13322			0.164733			0.0823664	−	0.996602i	$-0.473752\pi$
$971$	5.13322			0.164733			0.0823664	+	0.996602i	$0.473752\pi$
$972$	18.4794	+	23.9943i	0.592726	+	0.769619i
$973$		0			0
$974$	1.20013	+	2.07869i	0.0384546	+	0.0666054i
$975$	−7.11217	+	8.33328i	−0.227772	+	0.266878i
$976$	−14.6151	+	25.3141i	−0.467817	+	0.810283i
$977$	−15.5974	+	27.0155i	−0.499006	+	0.864303i	−0.999999	−	0.00114787i	$-0.999635\pi$
$977$	−15.5974	+	27.0155i	−0.499006	+	0.864303i	0.500994	+	0.865451i	$0.332968\pi$
$978$	−2.78099	−	0.514404i	−0.0889264	−	0.0164488i
$979$	−10.5288	−	18.2365i	−0.336503	−	0.582840i
$980$		0			0
$981$	−3.42395	−	21.5189i	−0.109318	−	0.687046i
$982$	−2.96225			−0.0945292
$983$	10.1700	+	17.6150i	0.324374	+	0.561832i	0.981385	−	0.192049i	$-0.0615131\pi$
$983$	10.1700	+	17.6150i	0.324374	+	0.561832i	−0.657012	+	0.753880i	$0.728180\pi$
$984$	−5.57605	−	15.7285i	−0.177758	−	0.501407i
$985$	−29.9378	+	51.8539i	−0.953899	+	1.65220i
$986$	−0.434681	+	0.752890i	−0.0138431	+	0.0239769i
$987$		0			0
$988$	−25.6014	−	44.3429i	−0.814488	−	1.41074i
$989$	8.50808			0.270541
$990$	−6.03911	+	4.89749i	−0.191936	+	0.155653i
$991$	−12.9655			−0.411863			−0.205932	−	0.978566i	$-0.566022\pi$
$991$	−12.9655			−0.411863			−0.205932	+	0.978566i	$0.566022\pi$
$992$	−9.02234	−	15.6272i	−0.286460	−	0.496163i
$993$	19.9235	+	3.68527i	0.632252	+	0.116948i
$994$		0			0
$995$	−8.74269	+	15.1428i	−0.277162	+	0.480059i
$996$	15.0615	−	17.6475i	0.477243	−	0.559182i
$997$	−24.7408	−	42.8523i	−0.783548	−	1.35715i	−0.929863	−	0.367907i	$-0.880074\pi$
$997$	−24.7408	−	42.8523i	−0.783548	−	1.35715i	0.146314	−	0.989238i	$-0.453259\pi$
$998$	2.44436			0.0773749
$999$	−7.36019	−	4.49954i	−0.232866	−	0.142359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.f.g.148.4	yes	12
3.2	odd	2		1323.2.f.g.442.4		12
7.2	even	3		441.2.g.g.67.4		12
7.3	odd	6		441.2.h.g.373.4		12
7.4	even	3		441.2.h.g.373.3		12
7.5	odd	6		441.2.g.g.67.3		12
7.6	odd	2	inner	441.2.f.g.148.3	✓	12
9.2	odd	6		1323.2.f.g.883.4		12
9.4	even	3		3969.2.a.be.1.4		6
9.5	odd	6		3969.2.a.bd.1.3		6
9.7	even	3	inner	441.2.f.g.295.4	yes	12
21.2	odd	6		1323.2.g.g.361.3		12
21.5	even	6		1323.2.g.g.361.4		12
21.11	odd	6		1323.2.h.g.226.4		12
21.17	even	6		1323.2.h.g.226.3		12
21.20	even	2		1323.2.f.g.442.3		12
63.2	odd	6		1323.2.h.g.802.4		12
63.11	odd	6		1323.2.g.g.667.3		12
63.13	odd	6		3969.2.a.be.1.3		6
63.16	even	3		441.2.h.g.214.3		12
63.20	even	6		1323.2.f.g.883.3		12
63.25	even	3		441.2.g.g.79.4		12
63.34	odd	6	inner	441.2.f.g.295.3	yes	12
63.38	even	6		1323.2.g.g.667.4		12
63.41	even	6		3969.2.a.bd.1.4		6
63.47	even	6		1323.2.h.g.802.3		12
63.52	odd	6		441.2.g.g.79.3		12
63.61	odd	6		441.2.h.g.214.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.3	✓	12	7.6	odd	2	inner
441.2.f.g.148.4	yes	12	1.1	even	1	trivial
441.2.f.g.295.3	yes	12	63.34	odd	6	inner
441.2.f.g.295.4	yes	12	9.7	even	3	inner
441.2.g.g.67.3		12	7.5	odd	6
441.2.g.g.67.4		12	7.2	even	3
441.2.g.g.79.3		12	63.52	odd	6
441.2.g.g.79.4		12	63.25	even	3
441.2.h.g.214.3		12	63.16	even	3
441.2.h.g.214.4		12	63.61	odd	6
441.2.h.g.373.3		12	7.4	even	3
441.2.h.g.373.4		12	7.3	odd	6
1323.2.f.g.442.3		12	21.20	even	2
1323.2.f.g.442.4		12	3.2	odd	2
1323.2.f.g.883.3		12	63.20	even	6
1323.2.f.g.883.4		12	9.2	odd	6
1323.2.g.g.361.3		12	21.2	odd	6
1323.2.g.g.361.4		12	21.5	even	6
1323.2.g.g.667.3		12	63.11	odd	6
1323.2.g.g.667.4		12	63.38	even	6
1323.2.h.g.226.3		12	21.17	even	6
1323.2.h.g.226.4		12	21.11	odd	6
1323.2.h.g.802.3		12	63.47	even	6
1323.2.h.g.802.4		12	63.2	odd	6
3969.2.a.bd.1.3		6	9.5	odd	6
3969.2.a.bd.1.4		6	63.41	even	6
3969.2.a.be.1.3		6	63.13	odd	6
3969.2.a.be.1.4		6	9.4	even	3

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.119562 - 0.207087i) q^{2} +(1.12441 - 1.31746i) q^{3} +(0.971410 - 1.68253i) q^{4} +(-1.29589 + 2.24456i) q^{5} +(-0.407265 - 0.0753324i) q^{6} -0.942820 q^{8} +(-0.471410 - 2.96273i) q^{9} +O(q^{10})\)	\(q+(-0.119562 - 0.207087i) q^{2} +(1.12441 - 1.31746i) q^{3} +(0.971410 - 1.68253i) q^{4} +(-1.29589 + 2.24456i) q^{5} +(-0.407265 - 0.0753324i) q^{6} -0.942820 q^{8} +(-0.471410 - 2.96273i) q^{9} +0.619757 q^{10} +(-2.09097 - 3.62167i) q^{11} +(-1.12441 - 3.17165i) q^{12} +(1.84155 - 3.18966i) q^{13} +(1.50000 + 4.23109i) q^{15} +(-1.83009 - 3.16982i) q^{16} -1.71107 q^{17} +(-0.557180 + 0.451852i) q^{18} +7.15561 q^{19} +(2.51769 + 4.36077i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(2.56238 - 4.43818i) q^{23} +(-1.06012 + 1.24213i) q^{24} +(-0.858685 - 1.48729i) q^{25} -0.880716 q^{26} +(-4.43334 - 2.71026i) q^{27} +(1.06238 + 1.84010i) q^{29} +(0.696860 - 0.816506i) q^{30} +(-3.26793 + 5.66021i) q^{31} +(-1.38044 + 2.39099i) q^{32} +(-7.12252 - 1.31746i) q^{33} +(0.204579 + 0.354341i) q^{34} +(-5.44282 - 2.08486i) q^{36} +1.66019 q^{37} +(-0.855536 - 1.48183i) q^{38} +(-2.13160 - 6.01266i) q^{39} +(1.22180 - 2.11621i) q^{40} +(-5.10948 + 8.84988i) q^{41} +(0.830095 + 1.43777i) q^{43} -8.12476 q^{44} +(7.26091 + 2.78128i) q^{45} -1.22545 q^{46} +(4.66912 + 8.08715i) q^{47} +(-6.23389 - 1.15309i) q^{48} +(-0.205332 + 0.355645i) q^{50} +(-1.92395 + 2.25427i) q^{51} +(-3.57780 - 6.19694i) q^{52} +10.6465 q^{53} +(-0.0312007 + 1.24213i) q^{54} +10.8387 q^{55} +(8.04583 - 9.42724i) q^{57} +(0.254040 - 0.440011i) q^{58} +(3.03215 - 5.25183i) q^{59} +(8.57605 + 1.58632i) q^{60} +(-3.99298 - 6.91605i) q^{61} +1.56287 q^{62} -6.66019 q^{64} +(4.77292 + 8.26693i) q^{65} +(0.578751 + 1.63250i) q^{66} +(-4.13160 + 7.15614i) q^{67} +(-1.66215 + 2.87893i) q^{68} +(-2.96596 - 8.36616i) q^{69} +6.23912 q^{71} +(0.444455 + 2.79332i) q^{72} -7.15561 q^{73} +(-0.198495 - 0.343803i) q^{74} +(-2.92495 - 0.541033i) q^{75} +(6.95103 - 12.0395i) q^{76} +(-0.990285 + 1.16031i) q^{78} +(4.91423 + 8.51170i) q^{79} +9.48644 q^{80} +(-8.55555 + 2.79332i) q^{81} +2.44359 q^{82} +(3.44733 + 5.97094i) q^{83} +(2.21737 - 3.84060i) q^{85} +(0.198495 - 0.343803i) q^{86} +(3.61881 + 0.669376i) q^{87} +(1.97141 + 3.41458i) q^{88} +5.03538 q^{89} +(-0.292160 - 1.83617i) q^{90} +(-4.97825 - 8.62258i) q^{92} +(3.78263 + 10.6698i) q^{93} +(1.11650 - 1.93383i) q^{94} +(-9.27292 + 16.0612i) q^{95} +(1.59786 + 4.50712i) q^{96} +(1.53167 + 2.65294i) q^{97} +(-9.74433 + 7.90228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 12 * q^9	\( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9} - 8 q^{11} + 18 q^{15} - 6 q^{16} - 42 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} - 48 q^{30} - 16 q^{32} - 30 q^{36} - 12 q^{37} + 24 q^{39} - 6 q^{43} - 28 q^{44} + 24 q^{46} - 56 q^{50} - 18 q^{51} + 56 q^{53} - 6 q^{57} - 18 q^{58} + 108 q^{60} - 48 q^{64} + 6 q^{65} + 76 q^{71} + 60 q^{72} - 36 q^{74} + 36 q^{78} + 6 q^{79} - 48 q^{81} + 30 q^{85} + 36 q^{86} + 6 q^{88} - 62 q^{92} + 42 q^{93} - 60 q^{95} - 48 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 + 12 * q^9 - 8 * q^11 + 18 * q^15 - 6 * q^16 - 42 * q^18 - 6 * q^22 - 4 * q^23 - 12 * q^25 - 22 * q^29 - 48 * q^30 - 16 * q^32 - 30 * q^36 - 12 * q^37 + 24 * q^39 - 6 * q^43 - 28 * q^44 + 24 * q^46 - 56 * q^50 - 18 * q^51 + 56 * q^53 - 6 * q^57 - 18 * q^58 + 108 * q^60 - 48 * q^64 + 6 * q^65 + 76 * q^71 + 60 * q^72 - 36 * q^74 + 36 * q^78 + 6 * q^79 - 48 * q^81 + 30 * q^85 + 36 * q^86 + 6 * q^88 - 62 * q^92 + 42 * q^93 - 60 * q^95 - 48 * q^99

Introduction

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