LMFDB - Embedded newform 441.2.f.g.148.3

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			148.3
Root			$-1.29589 + 0.748185i$ of defining polynomial
Character	$\chi$	$=$	441.148
Dual form			441.2.f.g.295.3

$q$-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} -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} - 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}+ \cdots - 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

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	$-0.636565\pi$
$5$	1.29589	−	2.24456i	0.579542	−	1.00380i	0.995532	−	0.0944264i	$-0.0301017\pi$
$6$	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	$0.337301\pi$
$13$	−1.84155	+	3.18966i	−0.510755	+	0.884653i	−0.999922	+	0.0124633i	$0.996033\pi$
$14$		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	$-0.433468\pi$
$17$	1.71107			0.414996			0.207498	+	0.978235i	$0.433468\pi$
$18$	−0.557180	+	0.451852i	−0.131329	+	0.106502i
$19$	−7.15561			−1.64161			−0.820805	−	0.571209i	$-0.806475\pi$
$19$	−7.15561			−1.64161			−0.820805	+	0.571209i	$0.806475\pi$
$20$	−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	$-0.633667\pi$
$31$	3.26793	−	5.66021i	0.586937	−	1.01660i	0.994631	−	0.103486i	$-0.0329997\pi$
$32$	−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	$-0.539242\pi$
$41$	5.10948	−	8.84988i	0.797967	−	1.38212i	0.920938	−	0.389708i	$-0.127424\pi$
$42$		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	$-0.928185\pi$
$47$	−4.66912	−	8.08715i	−0.681061	−	1.17963i	0.293596	−	0.955930i	$-0.405148\pi$
$48$	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	−0.993069	−	0.117529i	$-0.962503\pi$
$59$	−3.03215	+	5.25183i	−0.394752	+	0.683730i	0.598318	+	0.801259i	$0.295836\pi$
$60$	8.57605	+	1.58632i	1.10716	+	0.204794i
$61$	3.99298	+	6.91605i	0.511249	+	0.885509i	0.999915	+	0.0130384i	$0.00415038\pi$
$61$	3.99298	+	6.91605i	0.511249	+	0.885509i	−0.488666	+	0.872471i	$0.662516\pi$
$62$	−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	$-0.362468\pi$
$73$	7.15561			0.837501			0.418750	+	0.908101i	$0.362468\pi$
$74$	−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	0.612436	−	0.790521i	$-0.290190\pi$
$83$	−3.44733	−	5.97094i	−0.378393	−	0.655396i	−0.990829	+	0.135124i	$0.956857\pi$
$84$		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	$-0.585991\pi$
$89$	−5.03538			−0.533749			−0.266875	+	0.963731i	$0.585991\pi$
$90$	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	0.777730	−	0.628599i	$-0.216371\pi$
$97$	−1.53167	−	2.65294i	−0.155518	−	0.269365i	−0.933247	+	0.359234i	$0.883038\pi$
$98$		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	$0.0195561\pi$
$101$	5.54984	+	9.61260i	0.552229	+	0.956489i	−0.445884	+	0.895091i	$0.647111\pi$
$102$	0.696860	+	0.128899i	0.0689994	+	0.0127629i
$103$	−3.99298	+	6.91605i	−0.393440	+	0.681459i	−0.992901	−	0.118946i	$-0.962049\pi$
$103$	−3.99298	+	6.91605i	−0.393440	+	0.681459i	0.599460	+	0.800404i	$0.295382\pi$
$104$	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	−0.756602	−	0.653875i	$-0.773142\pi$
$131$	2.15143	−	3.72639i	0.187971	−	0.325576i	0.944574	+	0.328299i	$0.106475\pi$
$132$	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	$-0.600300\pi$
$139$	7.88067	−	13.6497i	0.668429	−	1.15775i	0.978343	−	0.206989i	$-0.0663665\pi$
$140$		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	−0.885824	−	0.464021i	$-0.846406\pi$
$157$	−0.514457	+	0.891066i	−0.0410582	+	0.0711148i	0.844766	+	0.535136i	$0.179740\pi$
$158$	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	$0.411803\pi$
$167$	−8.99716	+	15.5835i	−0.696221	+	1.20589i	−0.969767	+	0.244032i	$0.921530\pi$
$168$		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	0.881377	−	0.472414i	$-0.156617\pi$
$173$	0.415178	+	0.719110i	0.0315654	+	0.0546729i	−0.849811	+	0.527087i	$0.823284\pi$
$174$	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	$-0.495160\pi$
$181$	0.409157			0.0304124			0.0152062	+	0.999884i	$0.495160\pi$
$182$		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	$-0.576859\pi$
$199$	−6.74645			−0.478243			−0.239122	+	0.970990i	$0.576859\pi$
$200$	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	0.931492	−	0.363762i	$-0.118508\pi$
$223$	2.25071	+	3.89834i	0.150719	+	0.261052i	−0.780773	+	0.624815i	$0.785175\pi$
$224$		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	0.948932	−	0.315482i	$-0.102166\pi$
$227$	3.03215	+	5.25183i	0.201251	+	0.348576i	−0.747681	+	0.664058i	$0.768833\pi$
$228$	−8.04583	−	22.6951i	−0.532848	−	1.50302i
$229$	5.52466	−	9.56899i	0.365080	−	0.632336i	−0.623709	−	0.781656i	$-0.714375\pi$
$229$	5.52466	−	9.56899i	0.365080	−	0.632336i	0.988789	+	0.149320i	$0.0477084\pi$
$230$	−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	0.556790	−	0.830654i	$-0.312033\pi$
$241$	−6.84573	−	11.8572i	−0.440972	−	0.763786i	−0.997762	+	0.0668671i	$0.978700\pi$
$242$	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	$-0.340697\pi$
$251$	15.2040			0.959667			0.479833	+	0.877360i	$0.340697\pi$
$252$		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	$0.461363\pi$
$257$	−12.8107	+	22.1889i	−0.799112	+	1.38410i	−0.920195	+	0.391461i	$0.871970\pi$
$258$	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	$-0.667006\pi$
$269$	−16.4314			−1.00184			−0.500922	+	0.865493i	$0.667006\pi$
$270$	−2.74759	−	1.67970i	−0.167213	−	0.102223i
$271$	12.6980			0.771348			0.385674	−	0.922635i	$-0.373969\pi$
$271$	12.6980			0.771348			0.385674	+	0.922635i	$0.373969\pi$
$272$	−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	−0.735794	−	0.677205i	$-0.763191\pi$
$283$	3.67708	−	6.36890i	0.218580	−	0.378592i	0.954374	+	0.298614i	$0.0965242\pi$
$284$	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	−0.957391	−	0.288795i	$-0.906745\pi$
$293$	−3.91286	+	6.77728i	−0.228592	+	0.395933i	0.728799	+	0.684728i	$0.240079\pi$
$294$		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	$-0.276045\pi$
$307$	22.6709			1.29390			0.646948	+	0.762534i	$0.276045\pi$
$308$		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	$-0.464509\pi$
$311$	16.1588	−	27.9879i	0.916281	−	1.58705i	0.805015	−	0.593255i	$-0.202157\pi$
$312$	2.00972	+	5.66886i	0.113778	+	0.320936i
$313$	12.1598	+	21.0614i	0.687312	+	1.19046i	0.972704	+	0.232048i	$0.0745428\pi$
$313$	12.1598	+	21.0614i	0.687312	+	1.19046i	−0.285392	+	0.958411i	$0.592124\pi$
$314$	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	$-0.956485\pi$
$349$	−11.4585	−	19.8467i	−0.613358	−	1.06237i	0.377312	−	0.926086i	$-0.376848\pi$
$350$		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	0.696412	−	0.717642i	$-0.254779\pi$
$353$	−5.13466	−	8.89349i	−0.273290	−	0.473353i	−0.969702	+	0.244289i	$0.921445\pi$
$354$	−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	0.949473	−	0.313849i	$-0.101619\pi$
$367$	3.88768	+	6.73367i	0.202935	+	0.351494i	−0.746538	+	0.665343i	$0.768285\pi$
$368$	−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	−0.723505	−	0.690319i	$-0.757470\pi$
$383$	4.62020	−	8.00242i	0.236081	−	0.408905i	0.959586	+	0.281414i	$0.0908035\pi$
$384$	−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	$-0.503268\pi$
$397$	−0.409157			−0.0205350			−0.0102675	+	0.999947i	$0.503268\pi$
$398$	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	−0.780296	−	0.625410i	$-0.784932\pi$
$409$	3.06335	−	5.30587i	0.151473	−	0.262359i	0.931769	+	0.363051i	$0.118265\pi$
$410$	−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	−0.884482	−	0.466574i	$-0.845488\pi$
$419$	−0.781437	+	1.35349i	−0.0381757	+	0.0661223i	0.846306	+	0.532697i	$0.178821\pi$
$420$		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	$-0.398014\pi$
$433$	13.1071			0.629889			0.314945	+	0.949110i	$0.398014\pi$
$434$		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	0.553795	−	0.832653i	$-0.313179\pi$
$439$	−9.30704	−	16.1203i	−0.444201	−	0.769378i	−0.997996	+	0.0632744i	$0.979846\pi$
$440$	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	0.524811	−	0.851219i	$-0.324136\pi$
$461$	−10.1938	−	17.6561i	−0.474772	−	0.822328i	−0.999583	+	0.0288903i	$0.990803\pi$
$462$		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	$-0.305547\pi$
$467$	24.7911			1.14720			0.573598	+	0.819137i	$0.305547\pi$
$468$	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	0.964508	−	0.264052i	$-0.0850590\pi$
$479$	5.54984	+	9.61260i	0.253579	+	0.439211i	−0.710930	+	0.703263i	$0.751726\pi$
$480$	−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	$-0.560379\pi$
$503$	−8.45753			−0.377102			−0.188551	+	0.982063i	$0.560379\pi$
$504$		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	−0.724869	−	0.688886i	$-0.758100\pi$
$509$	5.28286	−	9.15018i	0.234159	−	0.405574i	0.959028	+	0.283312i	$0.0914332\pi$
$510$	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	$-0.357541\pi$
$521$	19.7558			0.865515			0.432758	+	0.901510i	$0.357541\pi$
$522$	−1.42339	−	0.545227i	−0.0623001	−	0.0238639i
$523$	−32.5282			−1.42236			−0.711179	−	0.703011i	$-0.751839\pi$
$523$	−32.5282			−1.42236			−0.711179	+	0.703011i	$0.751839\pi$
$524$	−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	−0.761654	−	0.647984i	$-0.775612\pi$
$563$	4.27912	−	7.41166i	0.180343	−	0.312364i	0.941998	+	0.335620i	$0.108946\pi$
$564$	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	$-0.101173\pi$
$577$	45.6353			1.89982			0.949912	+	0.312518i	$0.101173\pi$
$578$	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	0.741103	−	0.671392i	$-0.234303\pi$
$587$	−5.10948	−	8.84988i	−0.210891	−	0.365274i	−0.951994	+	0.306118i	$0.900970\pi$
$588$		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	$-0.575178\pi$
$593$	−11.3961			−0.467981			−0.233990	+	0.972239i	$0.575178\pi$
$594$	−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	$-0.875609\pi$
$601$	−19.4207	−	33.6376i	−0.792187	−	1.37211i	0.132423	−	0.991193i	$-0.457724\pi$
$602$		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	$0.483419\pi$
$607$	−20.6662	+	35.7950i	−0.838817	+	1.45287i	−0.890885	+	0.454229i	$0.849915\pi$
$608$	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	0.880114	−	0.474763i	$-0.157466\pi$
$619$	0.719036	+	1.24541i	0.0289005	+	0.0500571i	−0.851213	+	0.524820i	$0.824133\pi$
$620$	−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	$0.334797\pi$
$643$	−12.7795	+	22.1348i	−0.503976	+	0.872912i	−0.999989	+	0.00459728i	$0.998537\pi$
$644$		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	$-0.687861\pi$
$647$	−28.3111			−1.11302			−0.556512	+	0.830839i	$0.687861\pi$
$648$	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	−0.982453	−	0.186509i	$-0.940283\pi$
$661$	−8.47668	+	14.6820i	−0.329705	+	0.571065i	0.652748	+	0.757575i	$0.273616\pi$
$662$	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	0.694229	−	0.719755i	$-0.255746\pi$
$677$	−7.18681	−	12.4479i	−0.276212	−	0.478412i	−0.970440	+	0.241342i	$0.922412\pi$
$678$	−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	$-0.980710\pi$
$691$	−14.4981	−	25.1114i	−0.551533	−	0.955283i	0.446631	−	0.894718i	$-0.352624\pi$
$692$	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	$-0.287879\pi$
$719$	33.1508			1.23632			0.618159	+	0.786053i	$0.287879\pi$
$720$	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	$0.0436989\pi$
$727$	16.5502	+	28.6658i	0.613814	+	1.06316i	−0.376777	+	0.926304i	$0.622968\pi$
$728$		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	$0.474318\pi$
$733$	−22.2795	+	38.5892i	−0.822911	+	1.42532i	−0.903505	+	0.428577i	$0.859015\pi$
$734$	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	$0.417497\pi$
$761$	−19.5572	+	33.8741i	−0.708948	+	1.22793i	−0.965248	+	0.261336i	$0.915837\pi$
$762$	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	$0.405737\pi$
$769$	−18.9240	+	32.7773i	−0.682415	+	1.18198i	−0.974242	+	0.225507i	$0.927596\pi$
$770$		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	$-0.680213\pi$
$773$	−29.8265			−1.07279			−0.536393	+	0.843969i	$0.680213\pi$
$774$	−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	−0.665182	−	0.746681i	$-0.731646\pi$
$787$	8.81030	−	15.2599i	0.314053	−	0.543956i	0.979236	+	0.202724i	$0.0649796\pi$
$788$	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	−0.762371	−	0.647140i	$-0.775965\pi$
$797$	5.06056	−	8.76515i	0.179254	−	0.310477i	0.941625	+	0.336663i	$0.109298\pi$
$798$		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	$-0.620546\pi$
$811$	−21.0577			−0.739435			−0.369717	+	0.929144i	$0.620546\pi$
$812$		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	$-0.181723\pi$
$829$	48.4526			1.68283			0.841415	+	0.540390i	$0.181723\pi$
$830$	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	0.708685	−	0.705525i	$-0.249289\pi$
$839$	−7.43429	−	12.8766i	−0.256660	−	0.444548i	−0.965345	+	0.260977i	$0.915955\pi$
$840$		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	0.926331	−	0.376712i	$-0.122945\pi$
$853$	3.99900	+	6.92648i	0.136923	+	0.237158i	−0.789407	+	0.613870i	$0.789612\pi$
$854$		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	$-0.903057\pi$
$857$	−21.5661	−	37.3536i	−0.736684	−	1.27597i	0.217296	−	0.976106i	$-0.430276\pi$
$858$	6.27292	+	1.16031i	0.214154	+	0.0396123i
$859$	−1.22180	+	2.11621i	−0.0416871	+	0.0722042i	−0.886116	−	0.463463i	$-0.846607\pi$
$859$	−1.22180	+	2.11621i	−0.0416871	+	0.0722042i	0.844429	+	0.535667i	$0.179940\pi$
$860$	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	$-0.298907\pi$
$881$	35.0576			1.18112			0.590560	+	0.806994i	$0.298907\pi$
$882$		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	$-0.536684\pi$
$887$	23.9090	−	41.4116i	0.802785	−	1.39046i	0.917776	−	0.397098i	$-0.129983\pi$
$888$	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	0.989889	−	0.141846i	$-0.0453039\pi$
$929$	11.3415	+	19.6440i	0.372102	+	0.644499i	−0.617787	+	0.786345i	$0.711971\pi$
$930$	−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	$-0.183818\pi$
$937$	51.2933			1.67568			0.837840	+	0.545915i	$0.183818\pi$
$938$		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	$-0.659089\pi$
$941$	15.9659	−	27.6538i	0.520474	−	0.901487i	0.999717	−	0.0238048i	$-0.00757801\pi$
$942$	−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	$-0.526248\pi$
$971$	−5.13322			−0.164733			−0.0823664	+	0.996602i	$0.526248\pi$
$972$	−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	0.657012	−	0.753880i	$-0.271820\pi$
$983$	−10.1700	−	17.6150i	−0.324374	−	0.561832i	−0.981385	+	0.192049i	$0.938487\pi$
$984$	−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	$0.119926\pi$
$997$	24.7408	+	42.8523i	0.783548	+	1.35715i	−0.146314	+	0.989238i	$0.546741\pi$
$998$	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.148.3	✓	12
3.2	odd	2		1323.2.f.g.442.3		12
7.2	even	3		441.2.g.g.67.3		12
7.3	odd	6		441.2.h.g.373.3		12
7.4	even	3		441.2.h.g.373.4		12
7.5	odd	6		441.2.g.g.67.4		12
7.6	odd	2	inner	441.2.f.g.148.4	yes	12
9.2	odd	6		1323.2.f.g.883.3		12
9.4	even	3		3969.2.a.be.1.3		6
9.5	odd	6		3969.2.a.bd.1.4		6
9.7	even	3	inner	441.2.f.g.295.3	yes	12
21.2	odd	6		1323.2.g.g.361.4		12
21.5	even	6		1323.2.g.g.361.3		12
21.11	odd	6		1323.2.h.g.226.3		12
21.17	even	6		1323.2.h.g.226.4		12
21.20	even	2		1323.2.f.g.442.4		12
63.2	odd	6		1323.2.h.g.802.3		12
63.11	odd	6		1323.2.g.g.667.4		12
63.13	odd	6		3969.2.a.be.1.4		6
63.16	even	3		441.2.h.g.214.4		12
63.20	even	6		1323.2.f.g.883.4		12
63.25	even	3		441.2.g.g.79.3		12
63.34	odd	6	inner	441.2.f.g.295.4	yes	12
63.38	even	6		1323.2.g.g.667.3		12
63.41	even	6		3969.2.a.bd.1.3		6
63.47	even	6		1323.2.h.g.802.4		12
63.52	odd	6		441.2.g.g.79.4		12
63.61	odd	6		441.2.h.g.214.3		12

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

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} -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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 12 q^{9} - 8 q^{11} + 18 q^{15} - 6 q^{16} - 42 q^{18} - 6 q^{22} - 4 q^{23} - 12 q^{25} - 22 q^{29} - 48 q^{30} - 16 q^{32} - 30 q^{36} - 12 q^{37} + 24 q^{39} - 6 q^{43}+ \cdots - 48 q^{99}+O(q^{100}) \) 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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