LMFDB - Embedded newform 441.2.g.g.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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, 4]))

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
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			67.4
Root			$-1.29589 - 0.748185i$ of defining polynomial
Character	$\chi$	$=$	441.67
Dual form			441.2.g.g.79.4

$q$-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} +(0.578751 + 1.63250i) q^{3} +(0.971410 + 1.68253i) q^{4} +2.59179 q^{5} +(-0.407265 - 0.0753324i) q^{6} -0.942820 q^{8} +(-2.33009 + 1.88962i) q^{9} +(-0.309879 + 0.536725i) q^{10} +4.18194 q^{11} +(-2.18452 + 2.55959i) q^{12} +(1.84155 - 3.18966i) q^{13} +(1.50000 + 4.23109i) q^{15} +(-1.83009 + 3.16982i) q^{16} +(0.855536 - 1.48183i) q^{17} +(-0.112725 - 0.708458i) q^{18} +(-3.57780 - 6.19694i) q^{19} +(2.51769 + 4.36077i) q^{20} +(-0.500000 + 0.866025i) q^{22} -5.12476 q^{23} +(-0.545658 - 1.53915i) q^{24} +1.71737 q^{25} +(0.440358 + 0.762722i) q^{26} +(-4.43334 - 2.71026i) q^{27} +(1.06238 + 1.84010i) q^{29} +(-1.05555 - 0.195246i) q^{30} +(-3.26793 - 5.66021i) q^{31} +(-1.38044 - 2.39099i) q^{32} +(2.42030 + 6.82701i) q^{33} +(0.204579 + 0.354341i) q^{34} +(-5.44282 - 2.08486i) q^{36} +(-0.830095 - 1.43777i) q^{37} +1.71107 q^{38} +(6.27292 + 1.16031i) q^{39} -2.44359 q^{40} +(-5.10948 + 8.84988i) q^{41} +(0.830095 + 1.43777i) q^{43} +(4.06238 + 7.03625i) q^{44} +(-6.03911 + 4.89749i) q^{45} +(0.612725 - 1.06127i) q^{46} +(4.66912 - 8.08715i) q^{47} +(-6.23389 - 1.15309i) q^{48} +(-0.205332 + 0.355645i) q^{50} +(2.91423 + 0.539049i) q^{51} +7.15561 q^{52} +(-5.32326 + 9.22015i) q^{53} +(1.09132 - 0.594044i) q^{54} +10.8387 q^{55} +(8.04583 - 9.42724i) q^{57} -0.508080 q^{58} +(3.03215 + 5.25183i) q^{59} +(-5.66182 + 6.63392i) q^{60} +(-3.99298 + 6.91605i) q^{61} +1.56287 q^{62} -6.66019 q^{64} +(4.77292 - 8.26693i) q^{65} +(-1.70316 - 0.315036i) q^{66} +(-4.13160 - 7.15614i) q^{67} +3.32431 q^{68} +(-2.96596 - 8.36616i) q^{69} +6.23912 q^{71} +(2.19686 - 1.78157i) q^{72} +(3.57780 - 6.19694i) q^{73} +0.396990 q^{74} +(0.993929 + 2.80360i) q^{75} +(6.95103 - 12.0395i) q^{76} +(-0.990285 + 1.16031i) q^{78} +(4.91423 - 8.51170i) q^{79} +(-4.74322 + 8.21550i) q^{80} +(1.85868 - 8.80598i) q^{81} +(-1.22180 - 2.11621i) q^{82} +(3.44733 + 5.97094i) q^{83} +(2.21737 - 3.84060i) q^{85} -0.396990 q^{86} +(-2.38910 + 2.79929i) q^{87} -3.94282 q^{88} +(-2.51769 - 4.36077i) q^{89} +(-0.292160 - 1.83617i) q^{90} +(-4.97825 - 8.62258i) q^{92} +(7.34897 - 8.61073i) q^{93} +(1.11650 + 1.93383i) q^{94} +(-9.27292 - 16.0612i) q^{95} +(3.10435 - 3.63735i) 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} + 16 q^{11} + 18 q^{15} - 6 q^{16} + 18 q^{18} - 6 q^{22} + 8 q^{23} + 24 q^{25} - 22 q^{29} + 42 q^{30} - 16 q^{32} - 30 q^{36} + 6 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 + 16 * q^11 + 18 * q^15 - 6 * q^16 + 18 * q^18 - 6 * q^22 + 8 * q^23 + 24 * q^25 - 22 * q^29 + 42 * q^30 - 16 * q^32 - 30 * q^36 + 6 * q^37 + 24 * q^39 - 6 * q^43 + 14 * q^44 - 12 * q^46 - 56 * q^50 - 18 * q^51 - 28 * q^53 - 6 * q^57 + 36 * q^58 - 126 * q^60 - 48 * q^64 + 6 * q^65 + 76 * q^71 - 30 * q^72 + 72 * q^74 + 36 * q^78 + 6 * q^79 + 24 * q^81 + 30 * q^85 - 72 * q^86 - 12 * 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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	−0.905196	−	0.424994i	$-0.860276\pi$
$2$	−0.119562	+	0.207087i	−0.0845428	+	0.146433i	0.820653	+	0.571426i	$0.193610\pi$
$3$	0.578751	+	1.63250i	0.334142	+	0.942523i
$3$	0.578751	+	1.63250i	0.334142	+	0.942523i
$4$	0.971410	+	1.68253i	0.485705	+	0.841266i
$5$	2.59179			1.15908			0.579542	−	0.814943i	$-0.303232\pi$
$5$	2.59179			1.15908			0.579542	+	0.814943i	$0.303232\pi$
$6$	−0.407265	−	0.0753324i	−0.166265	−	0.0307543i
$7$		0			0
$7$		0			0
$8$	−0.942820			−0.333337
$9$	−2.33009	+	1.88962i	−0.776698	+	0.629873i
$10$	−0.309879	+	0.536725i	−0.0979922	+	0.169727i
$11$	4.18194			1.26090			0.630452	−	0.776228i	$-0.282870\pi$
$11$	4.18194			1.26090			0.630452	+	0.776228i	$0.282870\pi$
$12$	−2.18452	+	2.55959i	−0.630618	+	0.738890i
$13$	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
$17$	0.855536	−	1.48183i	0.207498	−	0.359397i	−0.743428	−	0.668816i	$-0.766801\pi$
$17$	0.855536	−	1.48183i	0.207498	−	0.359397i	0.950926	+	0.309419i	$0.100135\pi$
$18$	−0.112725	−	0.708458i	−0.0265696	−	0.166985i
$19$	−3.57780	−	6.19694i	−0.820805	−	1.42168i	−0.905084	−	0.425233i	$-0.860192\pi$
$19$	−3.57780	−	6.19694i	−0.820805	−	1.42168i	0.0842790	−	0.996442i	$-0.473141\pi$
$20$	2.51769	+	4.36077i	0.562973	+	0.975097i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.106600	+	0.184637i
$23$	−5.12476			−1.06859			−0.534294	−	0.845299i	$-0.679422\pi$
$23$	−5.12476			−1.06859			−0.534294	+	0.845299i	$0.679422\pi$
$24$	−0.545658	−	1.53915i	−0.111382	−	0.314178i
$25$	1.71737			0.343474
$26$	0.440358	+	0.762722i	0.0863613	+	0.149582i
$27$	−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	$0.770123\pi$
$30$	−1.05555	−	0.195246i	−0.192715	−	0.0356468i
$31$	−3.26793	−	5.66021i	−0.586937	−	1.01660i	−0.994631	−	0.103486i	$-0.967000\pi$
$31$	−3.26793	−	5.66021i	−0.586937	−	1.01660i	0.407694	−	0.913119i	$-0.366333\pi$
$32$	−1.38044	−	2.39099i	−0.244029	−	0.422671i
$33$	2.42030	+	6.82701i	0.421321	+	1.18843i
$34$	0.204579	+	0.354341i	0.0350850	+	0.0607689i
$35$		0			0
$36$	−5.44282	−	2.08486i	−0.907137	−	0.347477i
$37$	−0.830095	−	1.43777i	−0.136467	−	0.236367i	0.789690	−	0.613506i	$-0.210241\pi$
$37$	−0.830095	−	1.43777i	−0.136467	−	0.236367i	−0.926157	+	0.377139i	$0.876908\pi$
$38$	1.71107			0.277573
$39$	6.27292	+	1.16031i	1.00447	+	0.185798i
$40$	−2.44359			−0.386366
$41$	−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	$0.792931\pi$
$44$	4.06238	+	7.03625i	0.612427	+	1.06075i
$45$	−6.03911	+	4.89749i	−0.900258	+	0.730075i
$46$	0.612725	−	1.06127i	0.0903414	−	0.156476i
$47$	4.66912	−	8.08715i	0.681061	−	1.17963i	−0.293596	−	0.955930i	$-0.594852\pi$
$47$	4.66912	−	8.08715i	0.681061	−	1.17963i	0.974657	−	0.223703i	$-0.0718146\pi$
$48$	−6.23389	−	1.15309i	−0.899784	−	0.166434i
$49$		0			0
$50$	−0.205332	+	0.355645i	−0.0290383	+	0.0502958i
$51$	2.91423	+	0.539049i	0.408074	+	0.0754820i
$52$	7.15561			0.992305
$53$	−5.32326	+	9.22015i	−0.731206	+	1.26649i	0.225162	+	0.974321i	$0.427709\pi$
$53$	−5.32326	+	9.22015i	−0.731206	+	1.26649i	−0.956368	+	0.292164i	$0.905625\pi$
$54$	1.09132	−	0.594044i	0.148509	−	0.0808392i
$55$	10.8387			1.46149
$56$		0			0
$57$	8.04583	−	9.42724i	1.06570	−	1.24867i
$58$	−0.508080			−0.0667142
$59$	3.03215	+	5.25183i	0.394752	+	0.683730i	0.993069	−	0.117529i	$-0.0374972\pi$
$59$	3.03215	+	5.25183i	0.394752	+	0.683730i	−0.598318	+	0.801259i	$0.704164\pi$
$60$	−5.66182	+	6.63392i	−0.730938	+	0.856435i
$61$	−3.99298	+	6.91605i	−0.511249	+	0.885509i	0.488666	+	0.872471i	$0.337484\pi$
$61$	−3.99298	+	6.91605i	−0.511249	+	0.885509i	−0.999915	+	0.0130384i	$0.995850\pi$
$62$	1.56287			0.198485
$63$		0			0
$64$	−6.66019			−0.832524
$65$	4.77292	−	8.26693i	0.592007	−	1.02539i
$66$	−1.70316	−	0.315036i	−0.209644	−	0.0387782i
$67$	−4.13160	−	7.15614i	−0.504755	−	0.874262i	−0.999985	−	0.00549964i	$-0.998249\pi$
$67$	−4.13160	−	7.15614i	−0.504755	−	0.874262i	0.495230	−	0.868762i	$-0.335084\pi$
$68$	3.32431			0.403131
$69$	−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	$0.379281\pi$
$72$	2.19686	−	1.78157i	0.258902	−	0.209960i
$73$	3.57780	−	6.19694i	0.418750	−	0.725297i	−0.577064	−	0.816699i	$-0.695802\pi$
$73$	3.57780	−	6.19694i	0.418750	−	0.725297i	0.995814	+	0.0914022i	$0.0291349\pi$
$74$	0.396990			0.0461492
$75$	0.993929	+	2.80360i	0.114769	+	0.323732i
$76$	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	−0.445170	−	0.895446i	$-0.646857\pi$
$79$	4.91423	−	8.51170i	0.552894	−	0.957641i	0.998064	−	0.0621945i	$-0.0198099\pi$
$80$	−4.74322	+	8.21550i	−0.530308	+	0.918521i
$81$	1.85868	−	8.80598i	0.206521	−	0.978442i
$82$	−1.22180	−	2.11621i	−0.134925	−	0.233696i
$83$	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
$86$	−0.396990			−0.0428085
$87$	−2.38910	+	2.79929i	−0.256139	+	0.300116i
$88$	−3.94282			−0.420306
$89$	−2.51769	−	4.36077i	−0.266875	−	0.462240i	0.701178	−	0.712986i	$-0.252658\pi$
$89$	−2.51769	−	4.36077i	−0.266875	−	0.462240i	−0.968053	+	0.250745i	$0.919324\pi$
$90$	−0.292160	−	1.83617i	−0.0307963	−	0.193550i
$91$		0			0
$92$	−4.97825	−	8.62258i	−0.519018	−	0.898966i
$93$	7.34897	−	8.61073i	0.762053	−	0.892892i
$94$	1.11650	+	1.93383i	0.115158	+	0.199459i
$95$	−9.27292	−	16.0612i	−0.951381	−	1.64784i
$96$	3.10435	−	3.63735i	0.316837	−	0.371235i
$97$	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
$100$	1.66827	+	2.88953i	0.166827	+	0.288953i
$101$	11.0997			1.10446			0.552229	−	0.833692i	$-0.313777\pi$
$101$	11.0997			1.10446			0.552229	+	0.833692i	$0.313777\pi$
$102$	−0.460060	+	0.539049i	−0.0455527	+	0.0533738i
$103$	−7.98597			−0.786881			−0.393440	−	0.919350i	$-0.628715\pi$
$103$	−7.98597			−0.786881			−0.393440	+	0.919350i	$0.628715\pi$
$104$	−1.73625	+	3.00728i	−0.170254	+	0.294888i
$105$		0			0
$106$	−1.27292	−	2.20475i	−0.123636	−	0.214145i
$107$	−1.97825	−	3.42642i	−0.191244	−	0.331245i	0.754419	−	0.656394i	$-0.227919\pi$
$107$	−1.97825	−	3.42642i	−0.191244	−	0.331245i	−0.945663	+	0.325149i	$0.894586\pi$
$108$	0.253498	−	10.0920i	0.0243929	−	0.971104i
$109$	−3.63160	+	6.29012i	−0.347844	+	0.602484i	−0.985866	−	0.167534i	$-0.946420\pi$
$109$	−3.63160	+	6.29012i	−0.347844	+	0.602484i	0.638022	+	0.770018i	$0.279753\pi$
$110$	−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	$0.272341\pi$
$114$	0.990285	+	2.79332i	0.0927487	+	0.261619i
$115$	−13.2823			−1.23858
$116$	−2.06402	+	3.57498i	−0.191639	+	0.331929i
$117$	1.73625	+	10.9120i	0.160517	+	1.00882i
$118$	−1.45011			−0.133494
$119$		0			0
$120$	−1.41423	−	3.98916i	−0.129101	−	0.364158i
$121$	6.48865			0.589877
$122$	−0.954815	−	1.65379i	−0.0864449	−	0.149727i
$123$	−17.4045	−	3.21934i	−1.56931	−	0.290278i
$124$	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
$129$	−1.86673	+	2.18724i	−0.164357	+	0.192575i
$130$	1.14132	+	1.97682i	0.100100	+	0.173378i
$131$	4.30286			0.375943			0.187971	−	0.982175i	$-0.439809\pi$
$131$	4.30286			0.375943			0.187971	+	0.982175i	$0.439809\pi$
$132$	−9.13555	+	10.7041i	−0.795148	+	0.931669i
$133$		0			0
$134$	1.97592			0.170694
$135$	−11.4903	−	7.02441i	−0.988926	−	0.604565i
$136$	−0.806617	+	1.39710i	−0.0691668	+	0.119800i
$137$	20.5893			1.75907			0.879533	−	0.475838i	$-0.157855\pi$
$137$	20.5893			1.75907			0.879533	+	0.475838i	$0.157855\pi$
$138$	2.08714	+	0.386061i	0.177669	+	0.0328637i
$139$	−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
$143$	7.70127	−	13.3390i	0.644012	−	1.11546i
$144$	−1.72545	−	10.8442i	−0.143788	−	0.903680i
$145$	2.75347	+	4.76915i	0.228663	+	0.396056i
$146$	0.855536	+	1.48183i	0.0708047	+	0.122637i
$147$		0			0
$148$	1.61273	−	2.79332i	0.132565	−	0.229610i
$149$	6.06758			0.497076			0.248538	−	0.968622i	$-0.420050\pi$
$149$	6.06758			0.497076			0.248538	+	0.968622i	$0.420050\pi$
$150$	−0.699425	−	0.129374i	−0.0571078	−	0.0105633i
$151$	4.48865			0.365281			0.182641	−	0.983180i	$-0.441536\pi$
$151$	4.48865			0.365281			0.182641	+	0.983180i	$0.441536\pi$
$152$	3.37323	+	5.84260i	0.273605	+	0.473897i
$153$	0.806617	+	5.06945i	0.0652111	+	0.409841i
$154$		0			0
$155$	−8.46978	−	14.6701i	−0.680309	−	1.17833i
$156$	4.14132	+	11.6815i	0.331571	+	0.935270i
$157$	0.514457	+	0.891066i	0.0410582	+	0.0711148i	0.885824	−	0.464021i	$-0.153594\pi$
$157$	0.514457	+	0.891066i	0.0410582	+	0.0711148i	−0.844766	+	0.535136i	$0.820260\pi$
$158$	1.17511	+	2.03534i	0.0934865	+	0.161923i
$159$	−18.1327	−	3.35403i	−1.43802	−	0.265992i
$160$	−3.57780	−	6.19694i	−0.282850	−	0.489911i
$161$		0			0
$162$	1.60138	+	1.43777i	0.125816	+	0.112962i
$163$	−3.41423	−	5.91362i	−0.267423	−	0.463190i	0.700772	−	0.713385i	$-0.252839\pi$
$163$	−3.41423	−	5.91362i	−0.267423	−	0.463190i	−0.968196	+	0.250194i	$0.919505\pi$
$164$	−19.8536			−1.55031
$165$	6.27292	+	17.6942i	0.488346	+	1.37749i
$166$	−1.64867			−0.127962
$167$	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
$170$	0.530225	+	0.918376i	0.0406664	+	0.0704362i
$171$	20.0465	+	7.67877i	1.53299	+	0.587210i
$172$	−1.61273	+	2.79332i	−0.122969	+	0.212989i
$173$	−0.415178	+	0.719110i	−0.0315654	+	0.0546729i	−0.881377	−	0.472414i	$-0.843383\pi$
$173$	−0.415178	+	0.719110i	−0.0315654	+	0.0546729i	0.849811	+	0.527087i	$0.176716\pi$
$174$	−0.294052	−	0.829440i	−0.0222920	−	0.0628797i
$175$		0			0
$176$	−7.65335	+	13.2560i	−0.576893	+	0.999208i
$177$	−6.81875	+	7.98947i	−0.512528	+	0.600526i
$178$	1.20408			0.0902493
$179$	−3.78947	+	6.56355i	−0.283238	+	0.490583i	−0.972180	−	0.234233i	$-0.924742\pi$
$179$	−3.78947	+	6.56355i	−0.283238	+	0.490583i	0.688942	+	0.724816i	$0.258075\pi$
$180$	−14.1066	−	5.40353i	−1.05145	−	0.402755i
$181$	−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
$184$	4.83173			0.356200
$185$	−2.15143	−	3.72639i	−0.158176	−	0.273969i
$186$	0.904515	+	2.55139i	0.0663223	+	0.187077i
$187$	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	0.415779	+	0.909466i	$0.363509\pi$
$191$	−8.01204	+	13.8773i	−0.579731	+	1.00412i	−0.995510	+	0.0946575i	$0.969824\pi$
$192$	−3.85459	−	10.8727i	−0.278181	−	0.784673i
$193$	6.18715	+	10.7164i	0.445360	+	0.771387i	0.998077	−	0.0619822i	$-0.0197422\pi$
$193$	6.18715	+	10.7164i	0.445360	+	0.771387i	−0.552717	+	0.833369i	$0.686409\pi$
$194$	−0.732518			−0.0525917
$195$	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	$0.192312\pi$
$198$	−0.471410	−	2.96273i	−0.0335017	−	0.210552i
$199$	−3.37323	+	5.84260i	−0.239122	+	0.414171i	−0.960463	−	0.278409i	$-0.910193\pi$
$199$	−3.37323	+	5.84260i	−0.239122	+	0.414171i	0.721341	+	0.692580i	$0.243526\pi$
$200$	−1.61917			−0.114493
$201$	9.29121	−	10.8864i	0.655352	−	0.767871i
$202$	−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
$206$	0.954815	−	1.65379i	0.0665251	−	0.115225i
$207$	11.9412	−	9.68385i	0.829970	−	0.673074i
$208$	6.74043	+	11.6748i	0.467365	+	0.809500i
$209$	−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	$0.969239\pi$
$212$	−20.6843			−1.42060
$213$	3.61090	+	10.1854i	0.247415	+	0.697889i
$214$	0.946090			0.0646734
$215$	2.15143	+	3.72639i	0.146726	+	0.254138i
$216$	4.17984	+	2.55528i	0.284402	+	0.173865i
$217$		0			0
$218$	−0.868400	−	1.50411i	−0.0588155	−	0.101871i
$219$	12.1871	+	2.25427i	0.823531	+	0.152330i
$220$	10.5288	+	18.2365i	0.709854	+	1.22950i
$221$	−3.15103	−	5.45774i	−0.211961	−	0.367128i
$222$	0.229758	+	0.648085i	0.0154204	+	0.0434966i
$223$	−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
$226$	−0.828460	−	1.43494i	−0.0551084	−	0.0954505i
$227$	6.06429			0.402501			0.201251	−	0.979540i	$-0.435499\pi$
$227$	6.06429			0.402501			0.201251	+	0.979540i	$0.435499\pi$
$228$	23.6774	+	4.37965i	1.56808	+	0.290049i
$229$	11.0493			0.730159			0.365080	−	0.930976i	$-0.381042\pi$
$229$	11.0493			0.730159			0.365080	+	0.930976i	$0.381042\pi$
$230$	1.58805	−	2.75059i	0.104713	−	0.181369i
$231$		0			0
$232$	−1.00163	−	1.73488i	−0.0657605	−	0.113901i
$233$	4.06922	+	7.04809i	0.266583	+	0.461736i	0.967977	−	0.251038i	$-0.0807719\pi$
$233$	4.06922	+	7.04809i	0.266583	+	0.461736i	−0.701394	+	0.712774i	$0.747439\pi$
$234$	−2.46733	−	0.945107i	−0.161294	−	0.0617836i
$235$	12.1014	−	20.9602i	0.789407	−	1.36729i
$236$	−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	$0.926711\pi$
$240$	−16.1569	−	2.98857i	−1.04292	−	0.192911i
$241$	−13.6915			−0.881945			−0.440972	−	0.897521i	$-0.645366\pi$
$241$	−13.6915			−0.881945			−0.440972	+	0.897521i	$0.645366\pi$
$242$	−0.775794	+	1.34371i	−0.0498699	+	0.0863772i
$243$	15.4515	−	2.06217i	0.991211	−	0.132288i
$244$	−15.5153			−0.993265
$245$		0			0
$246$	2.74759	−	3.21934i	0.175180	−	0.205257i
$247$	−26.3549			−1.67692
$248$	3.08107	+	5.33656i	0.195648	+	0.338872i
$249$	−7.75241	+	9.08344i	−0.491289	+	0.575639i
$250$	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
$255$	7.55307	+	1.39710i	0.472992	+	0.0874899i
$256$	−5.80959	−	10.0625i	−0.363099	−	0.628906i
$257$	−25.6215			−1.59822			−0.799112	−	0.601182i	$-0.794697\pi$
$257$	−25.6215			−1.59822			−0.799112	+	0.601182i	$0.794697\pi$
$258$	−0.229758	−	0.648085i	−0.0143041	−	0.0403480i
$259$		0			0
$260$	18.5458			1.15016
$261$	−5.95254	−	2.28011i	−0.368453	−	0.141135i
$262$	−0.514457	+	0.891066i	−0.0317833	+	0.0550502i
$263$	7.10069			0.437847			0.218924	−	0.975742i	$-0.429745\pi$
$263$	7.10069			0.437847			0.218924	+	0.975742i	$0.429745\pi$
$264$	−2.28191	−	6.43664i	−0.140442	−	0.396148i
$265$	−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
$269$	−8.21572	+	14.2301i	−0.500922	+	0.867622i	0.499078	+	0.866557i	$0.333672\pi$
$269$	−8.21572	+	14.2301i	−0.500922	+	0.867622i	−0.999999	+	0.00106448i	$0.999661\pi$
$270$	2.82846	−	1.53964i	0.172135	−	0.0936993i
$271$	6.34899	+	10.9968i	0.385674	+	0.668007i	0.991862	−	0.127314i	$-0.0406357\pi$
$271$	6.34899	+	10.9968i	0.385674	+	0.668007i	−0.606189	+	0.795321i	$0.707302\pi$
$272$	3.13143	+	5.42379i	0.189871	+	0.328865i
$273$		0			0
$274$	−2.46169	+	4.26378i	−0.148716	+	0.257584i
$275$	7.18194			0.433087
$276$	11.1952	−	13.1173i	0.673870	−	0.789569i
$277$	−0.828460			−0.0497773			−0.0248887	−	0.999690i	$-0.507923\pi$
$277$	−0.828460			−0.0497773			−0.0248887	+	0.999690i	$0.507923\pi$
$278$	−1.88445	−	3.26396i	−0.113022	−	0.195760i
$279$	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	$0.883094\pi$
$282$	−2.51079	+	2.94188i	−0.149516	+	0.175186i
$283$	−3.67708	−	6.36890i	−0.218580	−	0.378592i	0.735794	−	0.677205i	$-0.236809\pi$
$283$	−3.67708	−	6.36890i	−0.218580	−	0.378592i	−0.954374	+	0.298614i	$0.903476\pi$
$284$	6.06075	+	10.4975i	0.359639	+	0.622913i
$285$	20.8531	−	24.4334i	1.23523	−	1.44731i
$286$	1.84155	+	3.18966i	0.108893	+	0.188609i
$287$		0			0
$288$	7.73461	+	2.96273i	0.455766	+	0.174581i
$289$	7.03611	+	12.1869i	0.413889	+	0.716877i
$290$	−1.31684			−0.0773273
$291$	−3.44445	+	4.03584i	−0.201918	+	0.236585i
$292$	13.9021			0.813557
$293$	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
$296$	0.782630	+	1.35556i	0.0454895	+	0.0787900i
$297$	−18.5400	−	11.3341i	−1.07580	−	0.657673i
$298$	−0.725450	+	1.25652i	−0.0420242	+	0.0727881i
$299$	−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
$303$	6.42395	+	18.1202i	0.369046	+	1.04098i
$304$	26.1909			1.50215
$305$	−10.3490	+	17.9249i	−0.592580	+	1.02638i
$306$	−1.14626	−	0.439072i	−0.0655271	−	0.0251001i
$307$	−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
$310$	4.05064			0.230061
$311$	−16.1588	−	27.9879i	−0.916281	−	1.58705i	−0.805015	−	0.593255i	$-0.797843\pi$
$311$	−16.1588	−	27.9879i	−0.916281	−	1.58705i	−0.111266	−	0.993791i	$-0.535491\pi$
$312$	−5.91423	−	1.09396i	−0.334827	−	0.0619335i
$313$	−12.1598	+	21.0614i	−0.687312	+	1.19046i	0.285392	+	0.958411i	$0.407876\pi$
$313$	−12.1598	+	21.0614i	−0.687312	+	1.19046i	−0.972704	+	0.232048i	$0.925457\pi$
$314$	−0.246037			−0.0138847
$315$		0			0
$316$	19.0949			1.07417
$317$	−2.56922	+	4.45002i	−0.144302	+	0.249938i	−0.929112	−	0.369798i	$-0.879427\pi$
$317$	−2.56922	+	4.45002i	−0.144302	+	0.249938i	0.784811	+	0.619736i	$0.212760\pi$
$318$	2.86255	−	3.35403i	0.160524	−	0.188085i
$319$	4.44282	+	7.69519i	0.248750	+	0.430848i
$320$	−17.2618			−0.964964
$321$	4.44872	−	5.21253i	0.248303	−	0.290935i
$322$		0			0
$323$	−12.2438			−0.681262
$324$	16.6219	−	5.42692i	0.923438	−	0.301496i
$325$	3.16263	−	5.47783i	0.175431	−	0.303855i
$326$	1.63284			0.0904349
$327$	−12.3704	−	2.28817i	−0.684084	−	0.126536i
$328$	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	−0.659307	−	0.751874i	$-0.729150\pi$
$331$	5.84897	−	10.1307i	0.321488	−	0.556834i	0.980795	+	0.195040i	$0.0624835\pi$
$332$	−6.69753	+	11.6005i	−0.367575	+	0.636658i
$333$	4.65103	+	1.78157i	0.254875	+	0.0976294i
$334$	2.15143	+	3.72639i	0.117721	+	0.203899i
$335$	−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	$-0.203316\pi$
$338$	0.135167			0.00735211
$339$	−11.8014	−	2.18293i	−0.640966	−	0.118560i
$340$	8.61590			0.467263
$341$	−13.6663	−	23.6707i	−0.740071	−	1.28184i
$342$	−3.98696	+	3.23327i	−0.215590	+	0.174835i
$343$		0			0
$344$	−0.782630	−	1.35556i	−0.0421966	−	0.0730866i
$345$	−7.68715	−	21.6833i	−0.413862	−	1.16739i
$346$	−0.0992788	−	0.171956i	−0.00533726	−	0.00924441i
$347$	−13.6557	−	23.6523i	−0.733075	−	1.26972i	−0.955563	−	0.294788i	$-0.904751\pi$
$347$	−13.6557	−	23.6523i	−0.733075	−	1.26972i	0.222488	−	0.974936i	$-0.428582\pi$
$348$	−7.03070	−	1.30048i	−0.376885	−	0.0697129i
$349$	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
$352$	−5.77292	−	9.99898i	−0.307697	−	0.532948i
$353$	−10.2693			−0.546581			−0.273290	−	0.961932i	$-0.588112\pi$
$353$	−10.2693			−0.546581			−0.273290	+	0.961932i	$0.588112\pi$
$354$	−0.839255	−	2.36731i	−0.0446059	−	0.125821i
$355$	16.1705			0.858241
$356$	4.89142	−	8.47218i	0.259245	−	0.449025i
$357$		0			0
$358$	−0.906150	−	1.56950i	−0.0478915	−	0.0829505i
$359$	−5.05034	−	8.74745i	−0.266547	−	0.461673i	0.701421	−	0.712747i	$-0.252549\pi$
$359$	−5.05034	−	8.74745i	−0.266547	−	0.461673i	−0.967968	+	0.251075i	$0.919216\pi$
$360$	5.69380	−	4.61745i	0.300090	−	0.243361i
$361$	−16.1014	+	27.8884i	−0.847441	+	1.46781i
$362$	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
$366$	2.14721	−	2.51586i	0.112236	−	0.131506i
$367$	7.77537			0.405871			0.202935	−	0.979192i	$-0.434952\pi$
$367$	7.77537			0.405871			0.202935	+	0.979192i	$0.434952\pi$
$368$	9.37880	−	16.2446i	0.488904	−	0.846806i
$369$	−4.81732	−	30.2760i	−0.250780	−	1.57611i
$370$	1.02891			0.0534907
$371$		0			0
$372$	21.6267	+	4.00032i	1.12129	+	0.207407i
$373$	24.1111			1.24842			0.624212	−	0.781255i	$-0.285420\pi$
$373$	24.1111			1.24842			0.624212	+	0.781255i	$0.285420\pi$
$374$	0.855536	+	1.48183i	0.0442387	+	0.0766237i
$375$	−4.92395	−	13.8891i	−0.254271	−	0.717230i
$376$	−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
$381$	5.27305	+	14.8738i	0.270147	+	0.762009i
$382$	−1.91586	−	3.31838i	−0.0980242	−	0.169783i
$383$	9.24040			0.472162			0.236081	−	0.971733i	$-0.424137\pi$
$383$	9.24040			0.472162			0.236081	+	0.971733i	$0.424137\pi$
$384$	12.1169	+	2.24128i	0.618337	+	0.114375i
$385$		0			0
$386$	−2.95898			−0.150608
$387$	−4.65103	−	1.78157i	−0.236425	−	0.0905623i
$388$	−2.97577	+	5.15418i	−0.151072	+	0.261664i
$389$	10.4484			0.529756			0.264878	−	0.964282i	$-0.414668\pi$
$389$	10.4484			0.529756			0.264878	+	0.964282i	$0.414668\pi$
$390$	−2.56661	+	3.00728i	−0.129965	+	0.152279i
$391$	−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
$395$	12.7366	−	22.0605i	0.640850	−	1.10999i
$396$	−22.7616	−	8.71878i	−1.14381	−	0.438135i
$397$	−0.204579	−	0.354341i	−0.0102675	−	0.0177838i	0.860846	−	0.508866i	$-0.169935\pi$
$397$	−0.204579	−	0.354341i	−0.0102675	−	0.0177838i	−0.871114	+	0.491082i	$0.836602\pi$
$398$	−0.806617	−	1.39710i	−0.0404321	−	0.0700304i
$399$		0			0
$400$	−3.14295	+	5.44375i	−0.157147	+	0.272187i
$401$	15.2528			0.761688			0.380844	−	0.924639i	$-0.375633\pi$
$401$	15.2528			0.761688			0.380844	+	0.924639i	$0.375633\pi$
$402$	1.14357	+	3.22569i	0.0570360	+	0.160883i
$403$	−24.0722			−1.19912
$404$	10.7823	+	18.6756i	0.536441	+	0.929143i
$405$	4.81732	−	22.8232i	0.239375	−	1.13410i
$406$		0			0
$407$	−3.47141	−	6.01266i	−0.172071	−	0.298036i
$408$	−2.74759	−	0.508226i	−0.136026	−	0.0251610i
$409$	−3.06335	−	5.30587i	−0.151473	−	0.262359i	0.780296	−	0.625410i	$-0.215068\pi$
$409$	−3.06335	−	5.30587i	−0.151473	−	0.262359i	−0.931769	+	0.363051i	$0.881735\pi$
$410$	−3.16664	−	5.48477i	−0.156389	−	0.270874i
$411$	11.9161	+	33.6120i	0.587778	+	1.65796i
$412$	−7.75765	−	13.4366i	−0.382192	−	0.661976i
$413$		0			0
$414$	0.577690	+	3.63068i	0.0283919	+	0.178438i
$415$	8.93474	+	15.4754i	0.438589	+	0.759659i
$416$	−10.1686			−0.498557
$417$	−26.8441	−	4.96538i	−1.31456	−	0.243156i
$418$	7.15561			0.349992
$419$	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	$-0.358520\pi$
$422$	−2.01887	−	3.49679i	−0.0982773	−	0.170221i
$423$	4.40214	+	27.6667i	0.214039	+	1.34520i
$424$	5.01887	−	8.69295i	0.243738	−	0.422167i
$425$	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
$429$	26.2330	+	4.85235i	1.26654	+	0.234274i
$430$	−1.02891			−0.0496187
$431$	−0.502879	+	0.871011i	−0.0242228	+	0.0419551i	−0.877883	−	0.478876i	$-0.841044\pi$
$431$	−0.502879	+	0.871011i	−0.0242228	+	0.0419551i	0.853660	+	0.520831i	$0.174378\pi$
$432$	16.7045	−	9.09286i	0.803693	−	0.437480i
$433$	−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
$436$	−14.1111			−0.675799
$437$	18.3354	+	31.7579i	0.877101	+	1.51918i
$438$	−1.92395	+	2.25427i	−0.0919297	+	0.107713i
$439$	9.30704	−	16.1203i	0.444201	−	0.769378i	−0.553795	−	0.832653i	$-0.686821\pi$
$439$	9.30704	−	16.1203i	0.444201	−	0.769378i	0.997996	+	0.0632744i	$0.0201543\pi$
$440$	−10.2190			−0.487170
$441$		0			0
$442$	1.50697			0.0716792
$443$	0.559503	−	0.969088i	0.0265828	−	0.0460427i	−0.852428	−	0.522845i	$-0.824871\pi$
$443$	0.559503	−	0.969088i	0.0265828	−	0.0460427i	0.879011	+	0.476802i	$0.158204\pi$
$444$	5.49346	+	1.01613i	0.260708	+	0.0482235i
$445$	−6.52532	−	11.3022i	−0.309330	−	0.535775i
$446$	1.07639			0.0509687
$447$	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	$0.880791\pi$
$450$	−0.193591	−	1.21668i	−0.00912595	−	0.0573550i
$451$	−21.3676	+	37.0097i	−1.00616	+	1.74272i
$452$	−13.4621			−0.633203
$453$	2.59781	+	7.32771i	0.122056	+	0.344286i
$454$	−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	−0.118205	−	0.992989i	$-0.537714\pi$
$457$	17.1202	−	29.6531i	0.800852	−	1.38712i	0.919056	−	0.394126i	$-0.128953\pi$
$458$	−1.32107	+	2.28817i	−0.0617297	+	0.106919i
$459$	−7.80903	+	4.25075i	−0.364494	+	0.198408i
$460$	−12.9026	−	22.3479i	−0.601585	−	1.04198i
$461$	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	$0.217243\pi$
$464$	−7.77704			−0.361040
$465$	19.0470	−	22.3172i	0.883282	−	1.03494i
$466$	−1.94609			−0.0901509
$467$	12.3956	+	21.4698i	0.573598	+	0.993502i	0.996192	+	0.0871825i	$0.0277863\pi$
$467$	12.3956	+	21.4698i	0.573598	+	0.993502i	−0.422594	+	0.906319i	$0.638880\pi$
$468$	−16.6733	+	13.5214i	−0.770721	+	0.625026i
$469$		0			0
$470$	2.89372	+	5.01207i	0.133477	+	0.231190i
$471$	−1.15692	+	1.35556i	−0.0533081	+	0.0624607i
$472$	−2.85877	−	4.95153i	−0.131586	−	0.227913i
$473$	3.47141	+	6.01266i	0.159616	+	0.276462i
$474$	−2.64260	+	3.09632i	−0.121379	+	0.142219i
$475$	−6.14441	−	10.6424i	−0.281925	−	0.488309i
$476$		0			0
$477$	−5.01887	−	31.5428i	−0.229798	−	1.44424i
$478$	−2.53022	−	4.38248i	−0.115730	−	0.200450i
$479$	11.0997			0.507157			0.253579	−	0.967315i	$-0.418392\pi$
$479$	11.0997			0.507157			0.253579	+	0.967315i	$0.418392\pi$
$480$	8.04583	−	9.42724i	0.367240	−	0.430293i
$481$	−6.11465			−0.278804
$482$	1.63697	−	2.83532i	0.0745621	−	0.129145i
$483$		0			0
$484$	6.30314	+	10.9174i	0.286506	+	0.496244i
$485$	3.96978	+	6.87585i	0.180258	+	0.312216i
$486$	−1.42035	+	3.44635i	−0.0644285	+	0.156330i
$487$	5.01887	−	8.69295i	0.227427	−	0.393915i	−0.729618	−	0.683855i	$-0.760302\pi$
$487$	5.01887	−	8.69295i	0.227427	−	0.393915i	0.957045	+	0.289940i	$0.0936354\pi$
$488$	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	$0.0764879\pi$
$492$	−11.4903	−	32.4109i	−0.518022	−	1.46120i
$493$	3.63562			0.163740
$494$	3.15103	−	5.45774i	0.141772	−	0.245556i
$495$	−25.2552	+	20.4810i	−1.13514	+	0.920554i
$496$	23.9225			1.07415
$497$		0			0
$498$	−0.954170	−	2.69145i	−0.0427574	−	0.120607i
$499$	10.2222			0.457608			0.228804	−	0.973473i	$-0.426519\pi$
$499$	10.2222			0.457608			0.228804	+	0.973473i	$0.426519\pi$
$500$	−8.26464	−	14.3148i	−0.369606	−	0.640177i
$501$	30.6472	+	5.66886i	1.36922	+	0.253266i
$502$	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
$507$	0.635584	−	0.744709i	0.0282273	−	0.0330737i
$508$	8.85060	+	15.3297i	0.392682	+	0.680145i
$509$	10.5657			0.468317			0.234159	−	0.972198i	$-0.424767\pi$
$509$	10.5657			0.468317			0.234159	+	0.972198i	$0.424767\pi$
$510$	−1.19238	+	1.39710i	−0.0527994	+	0.0618647i
$511$		0			0
$512$	17.0071			0.751616
$513$	−0.933660	+	37.1699i	−0.0412221	+	1.64109i
$514$	3.06335	−	5.30587i	0.135118	−	0.234032i
$515$	−20.6979			−0.912060
$516$	−5.49346	−	1.01613i	−0.241836	−	0.0447327i
$517$	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
$521$	9.87788	−	17.1090i	0.432758	−	0.749558i	−0.564352	−	0.825534i	$-0.690874\pi$
$521$	9.87788	−	17.1090i	0.432758	−	0.749558i	0.997110	+	0.0759760i	$0.0242072\pi$
$522$	1.18388	−	0.960078i	0.0518168	−	0.0420215i
$523$	−16.2641	−	28.1702i	−0.711179	−	1.23180i	−0.964415	−	0.264394i	$-0.914828\pi$
$523$	−16.2641	−	28.1702i	−0.711179	−	1.23180i	0.253236	−	0.967405i	$-0.418505\pi$
$524$	4.17984	+	7.23970i	0.182597	+	0.316268i
$525$		0			0
$526$	−0.848970	+	1.47046i	−0.0370168	+	0.0641150i
$527$	−11.1833			−0.487153
$528$	−26.0698	−	4.82216i	−1.13454	−	0.209858i
$529$	3.26320			0.141878
$530$	−3.29913	−	5.71426i	−0.143305	−	0.248211i
$531$	−16.9891	−	6.50767i	−0.737266	−	0.282409i
$532$		0			0
$533$	18.8187	+	32.5950i	0.815130	+	1.41185i
$534$	0.696860	+	1.96565i	0.0301561	+	0.0850621i
$535$	−5.12720	−	8.88057i	−0.221668	−	0.383940i
$536$	3.89536	+	6.74695i	0.168254	+	0.291424i
$537$	−12.9081	−	2.38763i	−0.557027	−	0.103034i
$538$	−1.96457	−	3.40274i	−0.0846987	−	0.146702i
$539$		0			0
$540$	0.657014	−	26.1563i	0.0282734	−	1.12559i
$541$	−7.61109	−	13.1828i	−0.327226	−	0.566773i	0.654734	−	0.755859i	$-0.272781\pi$
$541$	−7.61109	−	13.1828i	−0.327226	−	0.566773i	−0.981960	+	0.189087i	$0.939447\pi$
$542$	−3.03638			−0.130424
$543$	−0.236800	−	0.667948i	−0.0101621	−	0.0286644i
$544$	−4.72406			−0.202542
$545$	−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	$0.999892\pi$
$548$	20.0007	+	34.6422i	0.854387	+	1.47984i
$549$	−3.76466	−	23.6603i	−0.160672	−	1.00980i
$550$	−0.858685	+	1.48729i	−0.0366144	+	0.0634181i
$551$	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
$555$	4.83818	−	5.66886i	0.205369	−	0.240629i
$556$	−30.6214			−1.29864
$557$	−13.8337	+	23.9606i	−0.586151	+	1.01524i	0.408580	+	0.912723i	$0.366024\pi$
$557$	−13.8337	+	23.9606i	−0.586151	+	1.01524i	−0.994731	+	0.102521i	$0.967309\pi$
$558$	−3.64165	+	2.95324i	−0.154163	+	0.125020i
$559$	6.11465			0.258622
$560$		0			0
$561$	12.1871	+	2.25427i	0.514542	+	0.0951755i
$562$	1.24815			0.0526500
$563$	−4.27912	−	7.41166i	−0.180343	−	0.312364i	0.761654	−	0.647984i	$-0.224388\pi$
$563$	−4.27912	−	7.41166i	−0.180343	−	0.312364i	−0.941998	+	0.335620i	$0.891054\pi$
$564$	10.5000	+	29.6176i	0.442130	+	1.24713i
$565$	−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	−0.973272	−	0.229655i	$-0.926240\pi$
$569$	−6.86389	+	11.8886i	−0.287749	+	0.498396i	0.685523	+	0.728051i	$0.259574\pi$
$570$	2.56661	+	7.23970i	0.107503	+	0.303238i
$571$	−5.35868	−	9.28151i	−0.224254	−	0.388419i	0.731841	−	0.681475i	$-0.238661\pi$
$571$	−5.35868	−	9.28151i	−0.224254	−	0.388419i	−0.956095	+	0.293056i	$0.905328\pi$
$572$	29.9244			1.25120
$573$	−27.2916	−	5.04816i	−1.14012	−	0.210890i
$574$		0			0
$575$	−8.80111			−0.367032
$576$	15.5189	−	12.5852i	0.646620	−	0.524384i
$577$	22.8177	−	39.5214i	0.949912	−	1.64530i	0.204307	−	0.978907i	$-0.434506\pi$
$577$	22.8177	−	39.5214i	0.949912	−	1.64530i	0.745605	−	0.666389i	$-0.232161\pi$
$578$	−3.36500			−0.139965
$579$	−13.9138	+	16.3027i	−0.578236	+	0.677515i
$580$	−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
$584$	−3.37323	+	5.84260i	−0.139585	+	0.241768i
$585$	4.50000	+	28.2817i	0.186052	+	1.16931i
$586$	0.935657	+	1.62060i	0.0386516	+	0.0669466i
$587$	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
$590$	−3.75839			−0.154730
$591$	13.3703	+	37.7141i	0.549982	+	1.55135i
$592$	6.07661			0.249747
$593$	−5.69804	−	9.86929i	−0.233990	−	0.405283i	0.724988	−	0.688761i	$-0.241845\pi$
$593$	−5.69804	−	9.86929i	−0.233990	−	0.405283i	−0.958979	+	0.283478i	$0.908512\pi$
$594$	4.56382	−	2.48426i	0.187256	−	0.101930i
$595$		0			0
$596$	5.89411	+	10.2089i	0.241432	+	0.418173i
$597$	−11.4903	−	2.12537i	−0.470266	−	0.0869857i
$598$	−2.25673	−	3.90877i	−0.0922846	−	0.159842i
$599$	17.2873	+	29.9424i	0.706339	+	1.22341i	0.966206	+	0.257771i	$0.0829879\pi$
$599$	17.2873	+	29.9424i	0.706339	+	1.22341i	−0.259867	+	0.965644i	$0.583679\pi$
$600$	−0.937096	−	2.64329i	−0.0382568	−	0.107912i
$601$	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
$604$	4.36032	+	7.55230i	0.177419	+	0.307299i
$605$	16.8172			0.683717
$606$	−4.52051	−	0.836165i	−0.183633	−	0.0339669i
$607$	−41.3325			−1.67763			−0.838817	−	0.544414i	$-0.816752\pi$
$607$	−41.3325			−1.67763			−0.838817	+	0.544414i	$0.816752\pi$
$608$	−9.87788	+	17.1090i	−0.400601	+	0.693861i
$609$		0			0
$610$	−2.47468	−	4.28627i	−0.100197	−	0.173546i
$611$	−17.1969	−	29.7858i	−0.695710	−	1.20501i
$612$	−7.74595	+	6.28167i	−0.313111	+	0.253921i
$613$	14.3285	−	24.8176i	0.578721	−	1.00237i	−0.416905	−	0.908950i	$-0.636885\pi$
$613$	14.3285	−	24.8176i	0.578721	−	1.00237i	0.995626	−	0.0934244i	$-0.0297813\pi$
$614$	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	$-0.0706726\pi$
$618$	3.25241	+	0.601602i	0.130831	+	0.0242000i
$619$	1.43807			0.0578010			0.0289005	−	0.999582i	$-0.490799\pi$
$619$	1.43807			0.0578010			0.0289005	+	0.999582i	$0.490799\pi$
$620$	16.4552	−	28.5013i	0.660859	−	1.14464i
$621$	22.7198	+	13.8894i	0.911715	+	0.557363i
$622$	7.72789			0.309860
$623$		0			0
$624$	−15.1580	+	17.7605i	−0.606806	+	0.710990i
$625$	−30.6375			−1.22550
$626$	−2.90769	−	5.03626i	−0.116215	−	0.201290i
$627$	33.6472	−	39.4242i	1.34374	−	1.57445i
$628$	−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
$633$	−28.7589	−	5.31958i	−1.14307	−	0.211434i
$634$	−0.614360	−	1.06410i	−0.0243993	−	0.0422609i
$635$	23.6140			0.937094
$636$	−11.9710	−	33.7670i	−0.474682	−	1.33895i
$637$		0			0
$638$	−2.12476			−0.0841202
$639$	−14.5377	+	11.7896i	−0.575104	+	0.466388i
$640$	9.21946	−	15.9686i	0.364431	−	0.631213i
$641$	9.23912			0.364923			0.182462	−	0.983213i	$-0.441593\pi$
$641$	9.23912			0.364923			0.182462	+	0.983213i	$0.441593\pi$
$642$	0.547550	+	1.54449i	0.0216101	+	0.0609561i
$643$	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
$647$	−14.1556	+	24.5181i	−0.556512	+	0.963908i	0.441272	+	0.897374i	$0.354528\pi$
$647$	−14.1556	+	24.5181i	−0.556512	+	0.963908i	−0.997784	+	0.0665343i	$0.978806\pi$
$648$	−1.75241	+	8.30245i	−0.0688410	+	0.326151i
$649$	12.6803	+	21.9629i	0.497744	+	0.862118i
$650$	0.756258	+	1.30988i	0.0296629	+	0.0513776i
$651$		0			0
$652$	6.63323	−	11.4891i	0.259778	−	0.449948i
$653$	−8.35021			−0.326769			−0.163385	−	0.986562i	$-0.552241\pi$
$653$	−8.35021			−0.326769			−0.163385	+	0.986562i	$0.552241\pi$
$654$	1.95287	−	2.28817i	0.0763634	−	0.0894744i
$655$	11.1521			0.435749
$656$	−18.7017	−	32.3922i	−0.730177	−	1.26470i
$657$	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	$0.606466\pi$
$660$	−23.6774	+	27.7427i	−0.921643	+	1.07988i
$661$	8.47668	+	14.6820i	0.329705	+	0.571065i	0.982453	−	0.186509i	$-0.0597175\pi$
$661$	8.47668	+	14.6820i	0.329705	+	0.571065i	−0.652748	+	0.757575i	$0.726384\pi$
$662$	1.39862	+	2.42249i	0.0543591	+	0.0941527i
$663$	7.08609	−	8.30272i	0.275201	−	0.322451i
$664$	−3.25021	−	5.62952i	−0.126133	−	0.218468i
$665$		0			0
$666$	−0.925025	+	0.750160i	−0.0358440	+	0.0290681i
$667$	−5.44445	−	9.43007i	−0.210810	−	0.365134i
$668$	34.9597			1.35263
$669$	5.06144	−	5.93045i	0.195686	−	0.229284i
$670$	5.12118			0.197848
$671$	−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	$0.506058\pi$
$674$	4.02859	+	6.97772i	0.155175	+	0.268772i
$675$	−7.61369	−	4.65451i	−0.293051	−	0.179152i
$676$	0.549100	−	0.951068i	0.0211192	−	0.0365796i
$677$	7.18681	−	12.4479i	0.276212	−	0.478412i	−0.694229	−	0.719755i	$-0.744254\pi$
$677$	7.18681	−	12.4479i	0.276212	−	0.478412i	0.970440	+	0.241342i	$0.0775876\pi$
$678$	1.86306	−	2.18293i	0.0715502	−	0.0838349i
$679$		0			0
$680$	−2.09058	+	3.62099i	−0.0801701	+	0.138859i
$681$	3.50972	+	9.89994i	0.134493	+	0.379367i
$682$	6.53585			0.250271
$683$	16.1546	−	27.9806i	0.618138	−	1.07065i	−0.371687	−	0.928358i	$-0.621220\pi$
$683$	16.1546	−	27.9806i	0.618138	−	1.07065i	0.989825	−	0.142289i	$-0.0454462\pi$
$684$	6.55357	+	41.1881i	0.250582	+	1.57487i
$685$	53.3632			2.03890
$686$		0			0
$687$	6.39480	+	18.0380i	0.243977	+	0.688192i
$688$	−6.07661			−0.231669
$689$	19.6061	+	33.9588i	0.746934	+	1.29373i
$690$	5.40942	+	1.00059i	0.205933	+	0.0380917i
$691$	14.4981	−	25.1114i	0.551533	−	0.955283i	−0.446631	−	0.894718i	$-0.647376\pi$
$691$	14.4981	−	25.1114i	0.551533	−	0.955283i	0.998164	−	0.0605650i	$-0.0192902\pi$
$692$	−1.61323			−0.0613259
$693$		0			0
$694$	6.53078			0.247905
$695$	−20.4250	+	35.3772i	−0.774765	+	1.34193i
$696$	2.25249	−	2.63923i	0.0853806	−	0.100040i
$697$	8.74269	+	15.1428i	0.331153	+	0.573574i
$698$	−5.47997			−0.207420
$699$	−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	$0.666076\pi$
$702$	0.114915	−	4.57489i	0.00433720	−	0.172668i
$703$	−5.93984	+	10.2881i	−0.224025	+	0.388023i
$704$	−27.8525			−1.04973
$705$	41.2211	+	7.62473i	1.55248	+	0.287164i
$706$	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	−0.782441	−	0.622725i	$-0.786025\pi$
$709$	3.94282	−	6.82916i	0.148076	−	0.256475i	0.930516	+	0.366251i	$0.119359\pi$
$710$	−1.93337	+	3.34870i	−0.0725581	+	0.125674i
$711$	4.63323	+	29.1191i	0.173760	+	1.09205i
$712$	2.37373	+	4.11142i	0.0889592	+	0.154082i
$713$	16.7473	+	29.0073i	0.627193	+	1.08633i
$714$		0			0
$715$	19.9601	−	34.5718i	0.746464	−	1.29291i
$716$	−14.7245			−0.550281
$717$	−36.0431	−	6.66695i	−1.34606	−	0.248982i
$718$	2.41531			0.0901385
$719$	16.5754	+	28.7095i	0.618159	+	1.07068i	0.989822	+	0.142314i	$0.0454544\pi$
$719$	16.5754	+	28.7095i	0.618159	+	1.07068i	−0.371663	+	0.928368i	$0.621212\pi$
$720$	−4.47200	−	28.1058i	−0.166662	−	1.04744i
$721$		0			0
$722$	−3.85021	−	6.66877i	−0.143290	−	0.248186i
$723$	−7.92395	−	22.3513i	−0.294695	−	0.831253i
$724$	−0.397460	−	0.688420i	−0.0147715	−	0.0255849i
$725$	1.82450	+	3.16013i	0.0677603	+	0.117364i
$726$	−2.64260	−	0.488805i	−0.0980761	−	0.0181413i
$727$	−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
$730$	2.21737	+	3.84060i	0.0820685	+	0.142147i
$731$	2.84071			0.105067
$732$	−8.97949	−	25.3287i	−0.331892	−	0.936175i
$733$	−44.5589			−1.64582			−0.822911	−	0.568170i	$-0.807651\pi$
$733$	−44.5589			−1.64582			−0.822911	+	0.568170i	$0.807651\pi$
$734$	−0.929636	+	1.61018i	−0.0343135	+	0.0594327i
$735$		0			0
$736$	7.07442	+	12.2533i	0.260767	+	0.451661i
$737$	−17.2781	−	29.9266i	−0.636448	−	1.10236i
$738$	6.84573	+	2.62225i	0.251995	+	0.0965262i
$739$	−19.9045	+	34.4756i	−0.732199	+	1.26821i	0.223742	+	0.974648i	$0.428173\pi$
$739$	−19.9045	+	34.4756i	−0.732199	+	1.26821i	−0.955941	+	0.293558i	$0.905161\pi$
$740$	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	$0.229797\pi$
$744$	−6.92876	+	8.11837i	−0.254021	+	0.297634i
$745$	15.7259			0.576152
$746$	−2.88276	+	4.99309i	−0.105545	+	0.182810i
$747$	−19.3154	−	7.39873i	−0.706713	−	0.270706i
$748$	13.9021			0.508310
$749$		0			0
$750$	3.46496	+	0.640919i	0.126523	+	0.0234031i
$751$	19.7141			0.719378			0.359689	−	0.933072i	$-0.382883\pi$
$751$	19.7141			0.719378			0.359689	+	0.933072i	$0.382883\pi$
$752$	17.0899	+	29.6005i	0.623203	+	1.07942i
$753$	−8.79931	−	24.8205i	−0.320665	−	0.904508i
$754$	−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
$759$	−12.4035	−	34.9868i	−0.450218	−	1.26994i
$760$	8.74269	+	15.1428i	0.317131	+	0.549286i
$761$	−39.1144			−1.41790			−0.708948	−	0.705261i	$-0.750830\pi$
$761$	−39.1144			−1.41790			−0.708948	+	0.705261i	$0.750830\pi$
$762$	−3.71063	−	0.686360i	−0.134422	−	0.0248642i
$763$		0			0
$764$	−31.1319			−1.12631
$765$	2.09058	+	13.1389i	0.0755851	+	0.475039i
$766$	−1.10480	+	1.91357i	−0.0399180	+	0.0691399i
$767$	22.3354			0.806486
$768$	13.0647	−	15.3078i	0.471432	−	0.552373i
$769$	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
$773$	−14.9133	+	25.8305i	−0.536393	+	0.929059i	0.462702	+	0.886514i	$0.346880\pi$
$773$	−14.9133	+	25.8305i	−0.536393	+	0.929059i	−0.999095	+	0.0425453i	$0.986453\pi$
$774$	0.925025	−	0.750160i	0.0332493	−	0.0269639i
$775$	−5.61224	−	9.72068i	−0.201598	−	0.349177i
$776$	−1.44409	−	2.50124i	−0.0518399	−	0.0897894i
$777$		0			0
$778$	−1.24923	+	2.16373i	−0.0447870	+	0.0775734i
$779$	73.1229			2.61990
$780$	10.7334	+	30.2760i	0.384318	+	1.08406i
$781$	26.0917			0.933633
$782$	−1.04842	−	1.81591i	−0.0374913	−	0.0649369i
$783$	0.277238	−	11.0371i	0.00990768	−	0.394434i
$784$		0			0
$785$	1.33336	+	2.30946i	0.0475898	+	0.0824280i
$786$	−1.75241	−	0.324145i	−0.0625062	−	0.0115619i
$787$	−8.81030	−	15.2599i	−0.314053	−	0.543956i	0.665182	−	0.746681i	$-0.268354\pi$
$787$	−8.81030	−	15.2599i	−0.314053	−	0.543956i	−0.979236	+	0.202724i	$0.935020\pi$
$788$	22.4416	+	38.8700i	0.799448	+	1.38468i
$789$	4.10953	+	11.5919i	0.146303	+	0.412681i
$790$	3.04563	+	5.27518i	0.108359	+	0.187683i
$791$		0			0
$792$	9.18715	−	7.45043i	0.326451	−	0.264739i
$793$	14.7066	+	25.4725i	0.522246	+	0.904556i
$794$	0.0978390			0.00347218
$795$	−46.9962	−	8.69295i	−1.66678	−	0.308307i
$796$	−13.1071			−0.464570
$797$	−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
$800$	−2.37072	−	4.10621i	−0.0838177	−	0.145177i
$801$	14.1066	+	5.40353i	0.498434	+	0.190924i
$802$	−1.82365	+	3.15865i	−0.0643953	+	0.111536i
$803$	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
$807$	−27.9854	−	5.17649i	−0.985132	−	0.182221i
$808$	−10.4650			−0.368157
$809$	23.5735	−	40.8305i	0.828799	−	1.43552i	−0.0701816	−	0.997534i	$-0.522358\pi$
$809$	23.5735	−	40.8305i	0.828799	−	1.43552i	0.898981	−	0.437988i	$-0.144309\pi$
$810$	4.15043	+	3.72639i	0.145831	+	0.130932i
$811$	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
$814$	1.66019			0.0581896
$815$	−8.84896	−	15.3269i	−0.309966	−	0.536876i
$816$	−7.04200	+	8.25107i	−0.246519	+	0.288845i
$817$	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	−0.946818	−	0.321768i	$-0.895723\pi$
$821$	−5.58018	+	9.66515i	−0.194750	+	0.337316i	0.752069	+	0.659085i	$0.229056\pi$
$822$	−8.38532	−	1.55104i	−0.292472	−	0.0540989i
$823$	−4.71737	−	8.17072i	−0.164437	−	0.284814i	0.772018	−	0.635601i	$-0.219247\pi$
$823$	−4.71737	−	8.17072i	−0.164437	−	0.284814i	−0.936455	+	0.350787i	$0.885914\pi$
$824$	7.52933			0.262297
$825$	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	$0.402955\pi$
$828$	27.8932	+	10.6844i	0.969354	+	0.371310i
$829$	24.2263	−	41.9612i	0.841415	−	1.45737i	−0.0472838	−	0.998881i	$-0.515057\pi$
$829$	24.2263	−	41.9612i	0.841415	−	1.45737i	0.888699	−	0.458492i	$-0.151610\pi$
$830$	−4.27301			−0.148318
$831$	−0.479472	−	1.35246i	−0.0166327	−	0.0469163i
$832$	−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
$836$	29.0688	−	50.3487i	1.00537	−	1.74135i
$837$	−0.852795	+	33.9506i	−0.0294769	+	1.17350i
$838$	0.186860	+	0.323651i	0.00645497	+	0.0111803i
$839$	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
$842$	5.56277			0.191706
$843$	5.86907	−	6.87674i	0.202141	−	0.236848i
$844$	−32.8058			−1.12922
$845$	−0.732518	−	1.26876i	−0.0251994	−	0.0436466i
$846$	−6.25574	−	2.39625i	−0.215077	−	0.0823848i
$847$		0			0
$848$	−19.4841	−	33.7475i	−0.669088	−	1.15889i
$849$	8.26909	−	9.68883i	0.283794	−	0.332520i
$850$	0.351337	+	0.608534i	0.0120508	+	0.0208725i
$851$	4.25404	+	7.36821i	0.145827	+	0.252579i
$852$	−13.6295	+	15.9696i	−0.466939	+	0.547110i
$853$	−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
$856$	1.86513	+	3.23050i	0.0637488	+	0.110416i
$857$	−43.1322			−1.47337			−0.736684	−	0.676237i	$-0.763610\pi$
$857$	−43.1322			−1.47337			−0.736684	+	0.676237i	$0.763610\pi$
$858$	−4.14132	+	4.85235i	−0.141382	+	0.165656i
$859$	−2.44359			−0.0833742			−0.0416871	−	0.999131i	$-0.513273\pi$
$859$	−2.44359			−0.0833742			−0.0416871	+	0.999131i	$0.513273\pi$
$860$	−4.17984	+	7.23970i	−0.142531	+	0.246872i
$861$		0			0
$862$	−0.120250	−	0.208279i	−0.00409573	−	0.00709401i
$863$	−12.8594	−	22.2731i	−0.437738	−	0.758185i	0.559777	−	0.828644i	$-0.310887\pi$
$863$	−12.8594	−	22.2731i	−0.437738	−	0.758185i	−0.997515	+	0.0704589i	$0.977554\pi$
$864$	−0.360238	+	14.3414i	−0.0122555	+	0.487905i
$865$	−1.07605	+	1.86378i	−0.0365870	+	0.0633705i
$866$	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
$870$	−0.762121	−	2.14973i	−0.0258383	−	0.0728828i
$871$	−30.4342			−1.03122
$872$	3.42395	−	5.93045i	0.115949	−	0.200830i
$873$	−8.58198	−	3.28732i	−0.290456	−	0.111259i
$874$	−8.76884			−0.296611
$875$		0			0
$876$	8.04583	+	22.6951i	0.271843	+	0.766796i
$877$	−21.9590			−0.741502			−0.370751	−	0.928732i	$-0.620900\pi$
$877$	−21.9590			−0.741502			−0.370751	+	0.928732i	$0.620900\pi$
$878$	2.22553	+	3.85473i	0.0751080	+	0.130091i
$879$	13.3285	+	2.46538i	0.449558	+	0.0831553i
$880$	−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
$885$	−17.6727	+	20.7070i	−0.594063	+	0.696059i
$886$	0.133790	+	0.231731i	0.00449477	+	0.00778517i
$887$	47.8180			1.60557			0.802785	−	0.596269i	$-0.203351\pi$
$887$	47.8180			1.60557			0.802785	+	0.596269i	$0.203351\pi$
$888$	−1.75999	+	2.06217i	−0.0590615	+	0.0692019i
$889$		0			0
$890$	3.12071			0.104607
$891$	7.77292	−	36.8261i	0.260402	−	1.23372i
$892$	4.37272	−	7.57378i	0.146410	−	0.253589i
$893$	−66.8208			−2.23607
$894$	−2.47111	−	0.457085i	−0.0826464	−	0.0152872i
$895$	−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
$899$	6.94357	−	12.0266i	0.231581	−	0.401110i
$900$	−9.34733	−	3.58048i	−0.311578	−	0.119349i
$901$	9.10848	+	15.7764i	0.303448	+	0.525587i
$902$	−5.10948	−	8.84988i	−0.170127	−	0.294669i
$903$		0			0
$904$	3.26647	−	5.65769i	0.108641	−	0.188172i
$905$	−1.06045			−0.0352505
$906$	−1.82807	−	0.338141i	−0.0607336	−	0.0112340i
$907$	−19.1144			−0.634682			−0.317341	−	0.948312i	$-0.602790\pi$
$907$	−19.1144			−0.634682			−0.317341	+	0.948312i	$0.602790\pi$
$908$	5.89092	+	10.2034i	0.195497	+	0.338611i
$909$	−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	$0.736629\pi$
$912$	15.1580	+	42.7566i	0.501932	+	1.41581i
$913$	14.4165	+	24.9701i	0.477117	+	0.826391i
$914$	4.09385	+	7.09076i	0.135413	+	0.234541i
$915$	−35.2519	−	6.52059i	−1.16539	−	0.215564i
$916$	10.7334	+	18.5908i	0.354642	+	0.614258i
$917$		0			0
$918$	0.0533866	−	2.12537i	0.00176202	−	0.0701478i
$919$	−8.10464	−	14.0377i	−0.267348	−	0.463060i	0.700828	−	0.713330i	$-0.252814\pi$
$919$	−8.10464	−	14.0377i	−0.267348	−	0.463060i	−0.968176	+	0.250270i	$0.919481\pi$
$920$	12.5228			0.412865
$921$	−13.1208	−	37.0102i	−0.432345	−	1.21953i
$922$	−4.87514			−0.160554
$923$	11.4897	−	19.9007i	0.378187	−	0.655039i
$924$		0			0
$925$	−1.42558	−	2.46918i	−0.0468728	−	0.0811860i
$926$	−0.814099	−	1.41006i	−0.0267529	−	0.0463375i
$927$	18.6081	−	15.0904i	0.611169	−	0.495635i
$928$	2.93310	−	5.08029i	0.0962839	−	0.166769i
$929$	−11.3415	+	19.6440i	−0.372102	+	0.644499i	−0.989889	−	0.141846i	$-0.954696\pi$
$929$	−11.3415	+	19.6440i	−0.372102	+	0.644499i	0.617787	+	0.786345i	$0.288029\pi$
$930$	2.34431	+	6.61266i	0.0768730	+	0.216838i
$931$		0			0
$932$	−7.90576	+	13.6932i	−0.258962	+	0.448535i
$933$	36.3382	−	42.5772i	1.18966	−	1.39391i
$934$	−5.92814			−0.193975
$935$	9.27292	−	16.0612i	0.303257	−	0.525256i
$936$	−1.63697	−	10.2881i	−0.0535062	−	0.336277i
$937$	−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
$940$	47.0216			1.53368
$941$	−15.9659	−	27.6538i	−0.520474	−	0.901487i	−0.999717	−	0.0238048i	$-0.992422\pi$
$941$	−15.9659	−	27.6538i	−0.520474	−	0.901487i	0.479243	−	0.877682i	$-0.340911\pi$
$942$	−0.142394	−	0.401655i	−0.00463946	−	0.0130866i
$943$	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	−0.827211	−	0.561891i	$-0.810074\pi$
$947$	2.24665	−	3.89131i	0.0730063	−	0.126451i	0.900218	+	0.435440i	$0.143407\pi$
$948$	11.0512	+	31.1724i	0.358926	+	1.01243i
$949$	−13.1774	−	22.8240i	−0.427757	−	0.740898i
$950$	2.93854			0.0953390
$951$	−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	$0.494090\pi$
$954$	7.13216	+	2.73196i	0.230912	+	0.0884505i
$955$	−20.7655	+	35.9669i	−0.671956	+	1.16386i
$956$	−41.1150			−1.32975
$957$	−9.99109	+	11.7065i	−0.322966	+	0.378417i
$958$	−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
$962$	0.731078	−	1.26626i	0.0235709	−	0.0408260i
$963$	11.0841	+	4.24576i	0.357181	+	0.136818i
$964$	−13.3000	−	23.0363i	−0.428365	−	0.741950i
$965$	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	$0.872680\pi$
$968$	−6.11763			−0.196628
$969$	−7.08609	−	19.9879i	−0.227638	−	0.642105i
$970$	−1.89853			−0.0609582
$971$	−2.56661	−	4.44550i	−0.0823664	−	0.142663i	0.821900	−	0.569632i	$-0.192914\pi$
$971$	−2.56661	−	4.44550i	−0.0823664	−	0.142663i	−0.904266	+	0.426970i	$0.859581\pi$
$972$	18.4794	+	23.9943i	0.592726	+	0.769619i
$973$		0			0
$974$	1.20013	+	2.07869i	0.0384546	+	0.0666054i
$975$	10.7729	+	1.99268i	0.345009	+	0.0638169i
$976$	−14.6151	−	25.3141i	−0.467817	−	0.810283i
$977$	−15.5974	−	27.0155i	−0.499006	−	0.864303i	0.500994	−	0.865451i	$-0.332968\pi$
$977$	−15.5974	−	27.0155i	−0.499006	−	0.864303i	−0.999999	+	0.00114787i	$0.999635\pi$
$978$	0.945010	+	2.66561i	0.0302181	+	0.0852369i
$979$	−10.5288	−	18.2365i	−0.336503	−	0.582840i
$980$		0			0
$981$	−3.42395	−	21.5189i	−0.109318	−	0.687046i
$982$	1.48113	+	2.56538i	0.0472646	+	0.0818647i
$983$	−20.3401			−0.648748			−0.324374	−	0.945929i	$-0.605154\pi$
$983$	−20.3401			−0.648748			−0.324374	+	0.945929i	$0.605154\pi$
$984$	16.4093	+	3.03526i	0.523110	+	0.0967604i
$985$	59.8757			1.90780
$986$	−0.434681	+	0.752890i	−0.0138431	+	0.0239769i
$987$		0			0
$988$	−25.6014	−	44.3429i	−0.814488	−	1.41074i
$989$	−4.25404	−	7.36821i	−0.135271	−	0.234296i
$990$	−1.22180	−	7.67877i	−0.0388312	−	0.244047i
$991$	6.48276	−	11.2285i	0.205932	−	0.356684i	−0.744498	−	0.667625i	$-0.767311\pi$
$991$	6.48276	−	11.2285i	0.205932	−	0.356684i	0.950429	+	0.310941i	$0.100644\pi$
$992$	−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
$996$	−22.8139	−	4.21992i	−0.722887	−	0.133713i
$997$	49.4816			1.56710			0.783548	−	0.621331i	$-0.213408\pi$
$997$	49.4816			1.56710			0.783548	+	0.621331i	$0.213408\pi$
$998$	−1.22218	+	2.11688i	−0.0386875	+	0.0670086i
$999$	−0.216621	+	8.62388i	−0.00685358	+	0.272847i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.g.148.3	✓	12	7.3	odd	6
441.2.f.g.148.4	yes	12	7.4	even	3
441.2.f.g.295.3	yes	12	63.52	odd	6
441.2.f.g.295.4	yes	12	63.25	even	3
441.2.g.g.67.3		12	7.6	odd	2	inner
441.2.g.g.67.4		12	1.1	even	1	trivial
441.2.g.g.79.3		12	63.61	odd	6	inner
441.2.g.g.79.4		12	63.16	even	3	inner
441.2.h.g.214.3		12	9.7	even	3
441.2.h.g.214.4		12	63.34	odd	6
441.2.h.g.373.3		12	7.2	even	3
441.2.h.g.373.4		12	7.5	odd	6
1323.2.f.g.442.3		12	21.17	even	6
1323.2.f.g.442.4		12	21.11	odd	6
1323.2.f.g.883.3		12	63.38	even	6
1323.2.f.g.883.4		12	63.11	odd	6
1323.2.g.g.361.3		12	3.2	odd	2
1323.2.g.g.361.4		12	21.20	even	2
1323.2.g.g.667.3		12	63.2	odd	6
1323.2.g.g.667.4		12	63.47	even	6
1323.2.h.g.226.3		12	21.5	even	6
1323.2.h.g.226.4		12	21.2	odd	6
1323.2.h.g.802.3		12	63.20	even	6
1323.2.h.g.802.4		12	9.2	odd	6
3969.2.a.bd.1.3		6	63.32	odd	6
3969.2.a.bd.1.4		6	63.59	even	6
3969.2.a.be.1.3		6	63.31	odd	6
3969.2.a.be.1.4		6	63.4	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.119562 + 0.207087i) q^{2} +(0.578751 + 1.63250i) q^{3} +(0.971410 + 1.68253i) q^{4} +2.59179 q^{5} +(-0.407265 - 0.0753324i) q^{6} -0.942820 q^{8} +(-2.33009 + 1.88962i) q^{9} +(-0.309879 + 0.536725i) q^{10} +4.18194 q^{11} +(-2.18452 + 2.55959i) q^{12} +(1.84155 - 3.18966i) q^{13} +(1.50000 + 4.23109i) q^{15} +(-1.83009 + 3.16982i) q^{16} +(0.855536 - 1.48183i) q^{17} +(-0.112725 - 0.708458i) q^{18} +(-3.57780 - 6.19694i) q^{19} +(2.51769 + 4.36077i) q^{20} +(-0.500000 + 0.866025i) q^{22} -5.12476 q^{23} +(-0.545658 - 1.53915i) q^{24} +1.71737 q^{25} +(0.440358 + 0.762722i) q^{26} +(-4.43334 - 2.71026i) q^{27} +(1.06238 + 1.84010i) q^{29} +(-1.05555 - 0.195246i) q^{30} +(-3.26793 - 5.66021i) q^{31} +(-1.38044 - 2.39099i) q^{32} +(2.42030 + 6.82701i) q^{33} +(0.204579 + 0.354341i) q^{34} +(-5.44282 - 2.08486i) q^{36} +(-0.830095 - 1.43777i) q^{37} +1.71107 q^{38} +(6.27292 + 1.16031i) q^{39} -2.44359 q^{40} +(-5.10948 + 8.84988i) q^{41} +(0.830095 + 1.43777i) q^{43} +(4.06238 + 7.03625i) q^{44} +(-6.03911 + 4.89749i) q^{45} +(0.612725 - 1.06127i) q^{46} +(4.66912 - 8.08715i) q^{47} +(-6.23389 - 1.15309i) q^{48} +(-0.205332 + 0.355645i) q^{50} +(2.91423 + 0.539049i) q^{51} +7.15561 q^{52} +(-5.32326 + 9.22015i) q^{53} +(1.09132 - 0.594044i) q^{54} +10.8387 q^{55} +(8.04583 - 9.42724i) q^{57} -0.508080 q^{58} +(3.03215 + 5.25183i) q^{59} +(-5.66182 + 6.63392i) q^{60} +(-3.99298 + 6.91605i) q^{61} +1.56287 q^{62} -6.66019 q^{64} +(4.77292 - 8.26693i) q^{65} +(-1.70316 - 0.315036i) q^{66} +(-4.13160 - 7.15614i) q^{67} +3.32431 q^{68} +(-2.96596 - 8.36616i) q^{69} +6.23912 q^{71} +(2.19686 - 1.78157i) q^{72} +(3.57780 - 6.19694i) q^{73} +0.396990 q^{74} +(0.993929 + 2.80360i) q^{75} +(6.95103 - 12.0395i) q^{76} +(-0.990285 + 1.16031i) q^{78} +(4.91423 - 8.51170i) q^{79} +(-4.74322 + 8.21550i) q^{80} +(1.85868 - 8.80598i) q^{81} +(-1.22180 - 2.11621i) q^{82} +(3.44733 + 5.97094i) q^{83} +(2.21737 - 3.84060i) q^{85} -0.396990 q^{86} +(-2.38910 + 2.79929i) q^{87} -3.94282 q^{88} +(-2.51769 - 4.36077i) q^{89} +(-0.292160 - 1.83617i) q^{90} +(-4.97825 - 8.62258i) q^{92} +(7.34897 - 8.61073i) q^{93} +(1.11650 + 1.93383i) q^{94} +(-9.27292 - 16.0612i) q^{95} +(3.10435 - 3.63735i) q^{96} +(1.53167 + 2.65294i) q^{97} +(-9.74433 + 7.90228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 12 q^{9} + 16 q^{11} + 18 q^{15} - 6 q^{16} + 18 q^{18} - 6 q^{22} + 8 q^{23} + 24 q^{25} - 22 q^{29} + 42 q^{30} - 16 q^{32} - 30 q^{36} + 6 q^{37} + 24 q^{39} - 6 q^{43}+ \cdots - 48 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 - 12 * q^9 + 16 * q^11 + 18 * q^15 - 6 * q^16 + 18 * q^18 - 6 * q^22 + 8 * q^23 + 24 * q^25 - 22 * q^29 + 42 * q^30 - 16 * q^32 - 30 * q^36 + 6 * q^37 + 24 * q^39 - 6 * q^43 + 14 * q^44 - 12 * q^46 - 56 * q^50 - 18 * q^51 - 28 * q^53 - 6 * q^57 + 36 * q^58 - 126 * q^60 - 48 * q^64 + 6 * q^65 + 76 * q^71 - 30 * q^72 + 72 * q^74 + 36 * q^78 + 6 * q^79 + 24 * q^81 + 30 * q^85 - 72 * q^86 - 12 * q^88 - 62 * q^92 + 42 * q^93 - 60 * q^95 - 48 * q^99

Introduction

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