LMFDB - Embedded newform 504.2.cc.b.293.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(293,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5, 3]))

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

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

chi := DirichletCharacter("504.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cc (of order $6$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.1
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.b.461.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41305 + 0.0572344i) q^{2} +(-1.67485 - 0.441454i) q^{3} +(1.99345 - 0.161751i) q^{4} +(-2.14271 - 1.23709i) q^{5} +(2.39192 + 0.527939i) q^{6} +(-0.933167 + 2.47572i) q^{7} +(-2.80759 + 0.342656i) q^{8} +(2.61024 + 1.47874i) q^{9} +O(q^{10})$	\(q+(-1.41305 + 0.0572344i) q^{2} +(-1.67485 - 0.441454i) q^{3} +(1.99345 - 0.161751i) q^{4} +(-2.14271 - 1.23709i) q^{5} +(2.39192 + 0.527939i) q^{6} +(-0.933167 + 2.47572i) q^{7} +(-2.80759 + 0.342656i) q^{8} +(2.61024 + 1.47874i) q^{9} +(3.09857 + 1.62545i) q^{10} +(0.478464 + 0.828724i) q^{11} +(-3.41013 - 0.609107i) q^{12} +(-0.381479 + 0.660741i) q^{13} +(1.17692 - 3.55174i) q^{14} +(3.04260 + 3.01785i) q^{15} +(3.94767 - 0.644883i) q^{16} +3.03743 q^{17} +(-3.77304 - 1.94014i) q^{18} +1.12344 q^{19} +(-4.47149 - 2.11950i) q^{20} +(2.65583 - 3.73451i) q^{21} +(-0.723527 - 1.14365i) q^{22} +(-6.36320 - 3.67380i) q^{23} +(4.85356 + 0.665525i) q^{24} +(0.560807 + 0.971347i) q^{25} +(0.501233 - 0.955496i) q^{26} +(-3.71896 - 3.62896i) q^{27} +(-1.45977 + 5.08616i) q^{28} +(-0.693080 - 1.20045i) q^{29} +(-4.47208 - 4.09025i) q^{30} +(5.99538 + 3.46144i) q^{31} +(-5.54137 + 1.13720i) q^{32} +(-0.435512 - 1.59921i) q^{33} +(-4.29205 + 0.173845i) q^{34} +(5.06221 - 4.15034i) q^{35} +(5.44256 + 2.52558i) q^{36} -10.4715i q^{37} +(-1.58749 + 0.0642997i) q^{38} +(0.930605 - 0.938235i) q^{39} +(6.43976 + 2.73905i) q^{40} +(5.90521 - 10.2281i) q^{41} +(-3.53909 + 5.42907i) q^{42} +(0.998446 - 0.576453i) q^{43} +(1.08784 + 1.57463i) q^{44} +(-3.76365 - 6.39762i) q^{45} +(9.20182 + 4.82708i) q^{46} +(0.645481 + 1.11801i) q^{47} +(-6.89644 - 0.662632i) q^{48} +(-5.25840 - 4.62052i) q^{49} +(-0.848046 - 1.34047i) q^{50} +(-5.08723 - 1.34088i) q^{51} +(-0.653583 + 1.37886i) q^{52} +10.7516 q^{53} +(5.46280 + 4.91506i) q^{54} -2.36762i q^{55} +(1.77163 - 7.27058i) q^{56} +(-1.88160 - 0.495949i) q^{57} +(1.04807 + 1.65663i) q^{58} +(4.44494 + 2.56629i) q^{59} +(6.55340 + 5.52379i) q^{60} +(-3.63481 - 6.29568i) q^{61} +(-8.66992 - 4.54806i) q^{62} +(-6.09673 + 5.08231i) q^{63} +(7.76517 - 1.92408i) q^{64} +(1.63480 - 0.943851i) q^{65} +(0.706932 + 2.23484i) q^{66} +(8.60083 + 4.96569i) q^{67} +(6.05495 - 0.491306i) q^{68} +(9.03559 + 8.96211i) q^{69} +(-6.91564 + 6.15439i) q^{70} -5.35590i q^{71} +(-7.83519 - 3.25728i) q^{72} -8.05526i q^{73} +(0.599327 + 14.7967i) q^{74} +(-0.510463 - 1.87443i) q^{75} +(2.23953 - 0.181718i) q^{76} +(-2.49818 + 0.411206i) q^{77} +(-1.26130 + 1.37904i) q^{78} +(-2.18757 - 3.78898i) q^{79} +(-9.25651 - 3.50185i) q^{80} +(4.62668 + 7.71970i) q^{81} +(-7.75898 + 14.7909i) q^{82} +(-4.73789 + 2.73542i) q^{83} +(4.69020 - 7.87414i) q^{84} +(-6.50833 - 3.75758i) q^{85} +(-1.37787 + 0.871706i) q^{86} +(0.630862 + 2.31654i) q^{87} +(-1.62730 - 2.16277i) q^{88} +2.16137 q^{89} +(5.68441 + 8.82477i) q^{90} +(-1.27983 - 1.56102i) q^{91} +(-13.2790 - 6.29427i) q^{92} +(-8.51330 - 8.44407i) q^{93} +(-0.976089 - 1.54286i) q^{94} +(-2.40722 - 1.38981i) q^{95} +(9.78298 + 0.541622i) q^{96} +(5.12352 - 2.95807i) q^{97} +(7.69486 + 6.22809i) q^{98} +(0.0234407 + 2.87069i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.41305	+	0.0572344i	−0.999181	+	0.0404708i
$2$	−1.41305	+	0.0572344i	−0.999181	+	0.0404708i
$3$	−1.67485	−	0.441454i	−0.966974	−	0.254873i
$3$	−1.67485	−	0.441454i	−0.966974	−	0.254873i
$4$	1.99345	−	0.161751i	0.996724	−	0.0808754i
$5$	−2.14271	−	1.23709i	−0.958250	−	0.553246i	−0.0626157	−	0.998038i	$-0.519944\pi$
$5$	−2.14271	−	1.23709i	−0.958250	−	0.553246i	−0.895634	+	0.444792i	$0.853278\pi$
$6$	2.39192	+	0.527939i	0.976497	+	0.215530i
$7$	−0.933167	+	2.47572i	−0.352704	+	0.935735i
$7$	−0.933167	+	2.47572i	−0.352704	+	0.935735i
$8$	−2.80759	+	0.342656i	−0.992635	+	0.121147i
$9$	2.61024	+	1.47874i	0.870079	+	0.492912i
$10$	3.09857	+	1.62545i	0.979855	+	0.514011i
$11$	0.478464	+	0.828724i	0.144262	+	0.249870i	0.929097	−	0.369835i	$-0.120586\pi$
$11$	0.478464	+	0.828724i	0.144262	+	0.249870i	−0.784835	+	0.619705i	$0.787252\pi$
$12$	−3.41013	−	0.609107i	−0.984420	−	0.175834i
$13$	−0.381479	+	0.660741i	−0.105803	+	0.183256i	−0.914066	−	0.405565i	$-0.867075\pi$
$13$	−0.381479	+	0.660741i	−0.105803	+	0.183256i	0.808263	+	0.588822i	$0.200408\pi$
$14$	1.17692	−	3.55174i	0.314545	−	0.949243i
$15$	3.04260	+	3.01785i	0.785595	+	0.779207i
$16$	3.94767	−	0.644883i	0.986918	−	0.161221i
$17$	3.03743			0.736684			0.368342	−	0.929690i	$-0.379926\pi$
$17$	3.03743			0.736684			0.368342	+	0.929690i	$0.379926\pi$
$18$	−3.77304	−	1.94014i	−0.889315	−	0.457295i
$19$	1.12344			0.257736			0.128868	−	0.991662i	$-0.458866\pi$
$19$	1.12344			0.257736			0.128868	+	0.991662i	$0.458866\pi$
$20$	−4.47149	−	2.11950i	−0.999854	−	0.473935i
$21$	2.65583	−	3.73451i	0.579550	−	0.814937i
$22$	−0.723527	−	1.14365i	−0.154257	−	0.243827i
$23$	−6.36320	−	3.67380i	−1.32682	−	0.766039i	−0.342013	−	0.939695i	$-0.611109\pi$
$23$	−6.36320	−	3.67380i	−1.32682	−	0.766039i	−0.984806	+	0.173656i	$0.944442\pi$
$24$	4.85356	+	0.665525i	0.990729	+	0.135850i
$25$	0.560807	+	0.971347i	0.112161	+	0.194269i
$26$	0.501233	−	0.955496i	0.0982999	−	0.187388i
$27$	−3.71896	−	3.62896i	−0.715714	−	0.698393i
$28$	−1.45977	+	5.08616i	−0.275871	+	0.961195i
$29$	−0.693080	−	1.20045i	−0.128702	−	0.222918i	0.794472	−	0.607301i	$-0.207748\pi$
$29$	−0.693080	−	1.20045i	−0.128702	−	0.222918i	−0.923174	+	0.384383i	$0.874414\pi$
$30$	−4.47208	−	4.09025i	−0.816487	−	0.746775i
$31$	5.99538	+	3.46144i	1.07680	+	0.621692i	0.930032	−	0.367478i	$-0.119779\pi$
$31$	5.99538	+	3.46144i	1.07680	+	0.621692i	0.146771	+	0.989171i	$0.453112\pi$
$32$	−5.54137	+	1.13720i	−0.979585	+	0.201030i
$33$	−0.435512	−	1.59921i	−0.0758129	−	0.278386i
$34$	−4.29205	+	0.173845i	−0.736080	+	0.0298142i
$35$	5.06221	−	4.15034i	0.855670	−	0.701536i
$36$	5.44256	+	2.52558i	0.907093	+	0.420929i
$37$		−	10.4715i		−	1.72150i	−0.509031	−	0.860748i	$-0.669996\pi$
$37$		−	10.4715i		−	1.72150i	0.509031	−	0.860748i	$-0.330004\pi$
$38$	−1.58749	+	0.0642997i	−0.257525	+	0.0104308i
$39$	0.930605	−	0.938235i	0.149016	−	0.150238i
$40$	6.43976	+	2.73905i	1.01822	+	0.433081i
$41$	5.90521	−	10.2281i	0.922238	−	1.59736i	0.126295	−	0.991993i	$-0.459692\pi$
$41$	5.90521	−	10.2281i	0.922238	−	1.59736i	0.795944	−	0.605371i	$-0.206975\pi$
$42$	−3.53909	+	5.42907i	−0.546094	+	0.837724i
$43$	0.998446	−	0.576453i	0.152262	−	0.0879083i	−0.421933	−	0.906627i	$-0.638648\pi$
$43$	0.998446	−	0.576453i	0.152262	−	0.0879083i	0.574195	+	0.818718i	$0.305315\pi$
$44$	1.08784	+	1.57463i	0.163998	+	0.237384i
$45$	−3.76365	−	6.39762i	−0.561052	−	0.953700i
$46$	9.20182	+	4.82708i	1.35673	+	0.711714i
$47$	0.645481	+	1.11801i	0.0941531	+	0.163078i	0.909255	−	0.416240i	$-0.136652\pi$
$47$	0.645481	+	1.11801i	0.0941531	+	0.163078i	−0.815102	+	0.579318i	$0.803319\pi$
$48$	−6.89644	−	0.662632i	−0.995416	−	0.0956427i
$49$	−5.25840	−	4.62052i	−0.751200	−	0.660075i
$50$	−0.848046	−	1.34047i	−0.119932	−	0.189571i
$51$	−5.08723	−	1.34088i	−0.712355	−	0.187761i
$52$	−0.653583	+	1.37886i	−0.0906356	+	0.191213i
$53$	10.7516			1.47684			0.738420	−	0.674341i	$-0.235572\pi$
$53$	10.7516			1.47684			0.738420	+	0.674341i	$0.235572\pi$
$54$	5.46280	+	4.91506i	0.743392	+	0.668856i
$55$		−	2.36762i		−	0.319250i
$56$	1.77163	−	7.27058i	0.236744	−	0.971572i
$57$	−1.88160	−	0.495949i	−0.249224	−	0.0656900i
$58$	1.04807	+	1.65663i	0.137618	+	0.217527i
$59$	4.44494	+	2.56629i	0.578682	+	0.334102i	0.760609	−	0.649210i	$-0.224900\pi$
$59$	4.44494	+	2.56629i	0.578682	+	0.334102i	−0.181928	+	0.983312i	$0.558234\pi$
$60$	6.55340	+	5.52379i	0.846040	+	0.713119i
$61$	−3.63481	−	6.29568i	−0.465390	−	0.806079i	0.533829	−	0.845592i	$-0.320753\pi$
$61$	−3.63481	−	6.29568i	−0.465390	−	0.806079i	−0.999219	+	0.0395134i	$0.987419\pi$
$62$	−8.66992	−	4.54806i	−1.10108	−	0.577604i
$63$	−6.09673	+	5.08231i	−0.768115	+	0.640311i
$64$	7.76517	−	1.92408i	0.970647	−	0.240510i
$65$	1.63480	−	0.943851i	0.202772	−	0.117070i
$66$	0.706932	+	2.23484i	0.0870173	+	0.275090i
$67$	8.60083	+	4.96569i	1.05076	+	0.606656i	0.922862	−	0.385131i	$-0.125844\pi$
$67$	8.60083	+	4.96569i	1.05076	+	0.606656i	0.127897	+	0.991787i	$0.459177\pi$
$68$	6.05495	−	0.491306i	0.734271	−	0.0595796i
$69$	9.03559	+	8.96211i	1.08776	+	1.07891i
$70$	−6.91564	+	6.15439i	−0.826577	+	0.735591i
$71$		−	5.35590i		−	0.635628i	−0.948153	−	0.317814i	$-0.897051\pi$
$71$		−	5.35590i		−	0.635628i	0.948153	−	0.317814i	$-0.102949\pi$
$72$	−7.83519	−	3.25728i	−0.923386	−	0.383874i
$73$		−	8.05526i		−	0.942797i	−0.881920	−	0.471398i	$-0.843749\pi$
$73$		−	8.05526i		−	0.942797i	0.881920	−	0.471398i	$-0.156251\pi$
$74$	0.599327	+	14.7967i	0.0696704	+	1.72009i
$75$	−0.510463	−	1.87443i	−0.0589432	−	0.216440i
$76$	2.23953	−	0.181718i	0.256892	−	0.0208445i
$77$	−2.49818	+	0.411206i	−0.284694	+	0.0468613i
$78$	−1.26130	+	1.37904i	−0.142814	+	0.156146i
$79$	−2.18757	−	3.78898i	−0.246121	−	0.426293i	0.716326	−	0.697766i	$-0.245823\pi$
$79$	−2.18757	−	3.78898i	−0.246121	−	0.426293i	−0.962446	+	0.271473i	$0.912489\pi$
$80$	−9.25651	−	3.50185i	−1.03491	−	0.391518i
$81$	4.62668	+	7.71970i	0.514075	+	0.857745i
$82$	−7.75898	+	14.7909i	−0.856836	+	1.63338i
$83$	−4.73789	+	2.73542i	−0.520051	+	0.300252i	−0.736956	−	0.675941i	$-0.763737\pi$
$83$	−4.73789	+	2.73542i	−0.520051	+	0.300252i	0.216905	+	0.976193i	$0.430404\pi$
$84$	4.69020	−	7.87414i	0.511743	−	0.859139i
$85$	−6.50833	−	3.75758i	−0.705927	−	0.407567i
$86$	−1.37787	+	0.871706i	−0.148579	+	0.0939984i
$87$	0.630862	+	2.31654i	0.0676355	+	0.248359i
$88$	−1.62730	−	2.16277i	−0.173471	−	0.230552i
$89$	2.16137			0.229104			0.114552	−	0.993417i	$-0.463457\pi$
$89$	2.16137			0.229104			0.114552	+	0.993417i	$0.463457\pi$
$90$	5.68441	+	8.82477i	0.599189	+	0.930213i
$91$	−1.27983	−	1.56102i	−0.134162	−	0.163639i
$92$	−13.2790	−	6.29427i	−1.38443	−	0.656223i
$93$	−8.51330	−	8.44407i	−0.882788	−	0.875609i
$94$	−0.976089	−	1.54286i	−0.100676	−	0.159134i
$95$	−2.40722	−	1.38981i	−0.246975	−	0.142591i
$96$	9.78298	+	0.541622i	0.998471	+	0.0552791i
$97$	5.12352	−	2.95807i	0.520215	−	0.300346i	−0.216808	−	0.976214i	$-0.569564\pi$
$97$	5.12352	−	2.95807i	0.520215	−	0.300346i	0.737023	+	0.675868i	$0.236231\pi$
$98$	7.69486	+	6.22809i	0.777298	+	0.629132i
$99$	0.0234407	+	2.87069i	0.00235587	+	0.288515i
$100$	1.27506	+	1.84562i	0.127506	+	0.184562i
$101$	−10.3427	+	5.97137i	−1.02914	+	0.594173i	−0.916738	−	0.399490i	$-0.869187\pi$
$101$	−10.3427	+	5.97137i	−1.02914	+	0.594173i	−0.112400	+	0.993663i	$0.535854\pi$
$102$	7.26528	+	1.60358i	0.719370	+	0.158778i
$103$	8.19904	+	4.73372i	0.807875	+	0.466427i	0.846217	−	0.532838i	$-0.178874\pi$
$103$	8.19904	+	4.73372i	0.807875	+	0.466427i	−0.0383422	+	0.999265i	$0.512208\pi$
$104$	0.844631	−	1.98581i	0.0828228	−	0.194724i
$105$	−10.3106	+	4.71646i	−1.00621	+	0.460280i
$106$	−15.1925	+	0.615359i	−1.47563	+	0.0597689i
$107$	−7.84797			−0.758692			−0.379346	−	0.925255i	$-0.623851\pi$
$107$	−7.84797			−0.758692			−0.379346	+	0.925255i	$0.623851\pi$
$108$	−8.00054	−	6.63260i	−0.769852	−	0.638222i
$109$			7.87525i			0.754312i	0.926150	+	0.377156i	$0.123098\pi$
$109$			7.87525i			0.754312i	−0.926150	+	0.377156i	$0.876902\pi$
$110$	0.135509	+	3.34558i	0.0129203	+	0.318988i
$111$	−4.62266	+	17.5381i	−0.438763	+	1.66464i
$112$	−2.08729	+	10.3751i	−0.197230	+	0.980357i
$113$	5.01121	+	2.89322i	0.471415	+	0.272171i	0.716832	−	0.697246i	$-0.245592\pi$
$113$	5.01121	+	2.89322i	0.471415	+	0.272171i	−0.245417	+	0.969418i	$0.578925\pi$
$114$	2.68719	+	0.593111i	0.251678	+	0.0555499i
$115$	9.08967	+	15.7438i	0.847616	+	1.46811i
$116$	−1.57579	−	2.28093i	−0.146309	−	0.211779i
$117$	−1.97281	+	1.16058i	−0.182386	+	0.107296i
$118$	−6.42782	−	3.37190i	−0.591729	−	0.310409i
$119$	−2.83443	+	7.51982i	−0.259831	+	0.689341i
$120$	−9.57647	−	7.43035i	−0.874208	−	0.678295i
$121$	5.04214	−	8.73325i	0.458377	−	0.793932i
$122$	5.49652	+	8.68810i	0.497631	+	0.786584i
$123$	−14.4056	+	14.5237i	−1.29891	+	1.30956i
$124$	12.5114	+	5.93044i	1.12356	+	0.532569i
$125$			9.59586i			0.858280i
$126$	8.32413	−	7.53053i	0.741572	−	0.670873i
$127$	−14.0191			−1.24399			−0.621996	−	0.783020i	$-0.713678\pi$
$127$	−14.0191			−1.24399			−0.621996	+	0.783020i	$0.713678\pi$
$128$	−10.8625	+	3.16327i	−0.960118	+	0.279596i
$129$	−1.92672	+	0.524704i	−0.169639	+	0.0461976i
$130$	−2.25604	+	1.42728i	−0.197868	+	0.125181i
$131$	14.7558	+	8.51928i	1.28922	+	0.744333i	0.978516	−	0.206172i	$-0.0661007\pi$
$131$	14.7558	+	8.51928i	1.28922	+	0.744333i	0.310707	+	0.950506i	$0.399434\pi$
$132$	−1.12684	−	3.11749i	−0.0980791	−	0.271343i
$133$	−1.04836	+	2.78134i	−0.0909045	+	0.241173i
$134$	−12.4377	−	6.52453i	−1.07445	−	0.563634i
$135$	3.47929	+	12.3765i	0.299450	+	1.06520i
$136$	−8.52786	+	1.04079i	−0.731258	+	0.0892473i
$137$	16.2043	−	9.35556i	1.38443	−	0.799300i	0.391748	−	0.920073i	$-0.371871\pi$
$137$	16.2043	−	9.35556i	1.38443	−	0.799300i	0.992680	+	0.120773i	$0.0385373\pi$
$138$	−13.2807	−	12.1468i	−1.13053	−	1.03400i
$139$	5.84488	−	10.1236i	0.495756	−	0.858675i	−0.504232	−	0.863568i	$-0.668224\pi$
$139$	5.84488	−	10.1236i	0.495756	−	0.858675i	0.999988	+	0.00489369i	$0.00155772\pi$
$140$	9.41993	−	9.09231i	0.796130	−	0.768440i
$141$	−0.587536	−	2.15744i	−0.0494794	−	0.181689i
$142$	0.306541	+	7.56817i	0.0257244	+	0.635107i
$143$	−0.730095			−0.0610536
$144$	11.2580	+	4.15427i	0.938165	+	0.346189i
$145$			3.42962i			0.284815i
$146$	0.461038	+	11.3825i	0.0381558	+	0.942024i
$147$	6.76728	+	10.0600i	0.558156	+	0.829736i
$148$	−1.69376	−	20.8743i	−0.139227	−	1.71586i
$149$	−8.00461	+	13.8644i	−0.655763	+	1.13581i	0.325939	+	0.945391i	$0.394320\pi$
$149$	−8.00461	+	13.8644i	−0.655763	+	1.13581i	−0.981702	+	0.190424i	$0.939014\pi$
$150$	0.828594	+	2.61946i	0.0676544	+	0.213878i
$151$	−7.95965	−	13.7865i	−0.647747	−	1.12193i	−0.983660	−	0.180038i	$-0.942378\pi$
$151$	−7.95965	−	13.7865i	−0.647747	−	1.12193i	0.335913	−	0.941893i	$-0.390955\pi$
$152$	−3.15418	+	0.384956i	−0.255838	+	0.0312240i
$153$	7.92840	+	4.49155i	0.640973	+	0.363120i
$154$	3.50653	−	0.724038i	0.282564	−	0.0583447i
$155$	−8.56425	−	14.8337i	−0.687897	−	1.19147i
$156$	1.70335	−	2.02085i	0.136377	−	0.161797i
$157$	4.47971	−	7.75909i	0.357520	−	0.619243i	−0.630026	−	0.776574i	$-0.716956\pi$
$157$	4.47971	−	7.75909i	0.357520	−	0.619243i	0.987546	+	0.157331i	$0.0502890\pi$
$158$	3.30801	+	5.22883i	0.263171	+	0.415983i
$159$	−18.0072	−	4.74631i	−1.42807	−	0.376407i
$160$	13.2804	+	4.41851i	1.04991	+	0.349314i
$161$	15.0332	−	12.3252i	1.18478	−	0.971366i
$162$	−6.97958	−	10.6436i	−0.548368	−	0.836237i
$163$		−	18.6472i		−	1.46056i	−0.683149	−	0.730279i	$-0.739390\pi$
$163$		−	18.6472i		−	1.46056i	0.683149	−	0.730279i	$-0.260610\pi$
$164$	10.1173	−	21.3444i	0.790030	−	1.66672i
$165$	−1.04519	+	3.96541i	−0.0813683	+	0.308707i
$166$	6.53834	−	4.13647i	0.507474	−	0.321052i
$167$	1.71845	−	2.97644i	0.132977	−	0.230324i	−0.791846	−	0.610721i	$-0.790880\pi$
$167$	1.71845	−	2.97644i	0.132977	−	0.230324i	0.924823	+	0.380398i	$0.124213\pi$
$168$	−6.17684	+	11.3950i	−0.476554	+	0.879145i
$169$	6.20895	+	10.7542i	0.477611	+	0.827247i
$170$	9.41168	+	4.93717i	0.721843	+	0.378664i
$171$	2.93246	+	1.66128i	0.224251	+	0.127041i
$172$	1.89711	−	1.31063i	0.144653	−	0.0999346i
$173$	−10.4852	+	6.05362i	−0.797173	+	0.460248i	−0.842482	−	0.538725i	$-0.818906\pi$
$173$	−10.4852	+	6.05362i	−0.797173	+	0.460248i	0.0453088	+	0.998973i	$0.485573\pi$
$174$	−1.02403	−	3.23728i	−0.0776313	−	0.245418i
$175$	−2.92811	+	0.481974i	−0.221344	+	0.0364338i
$176$	2.42325	+	2.96298i	0.182659	+	0.223343i
$177$	−6.31170	−	6.26038i	−0.474417	−	0.470559i
$178$	−3.05413	+	0.123704i	−0.228917	+	0.00927204i
$179$	−3.17955			−0.237651			−0.118825	−	0.992915i	$-0.537913\pi$
$179$	−3.17955			−0.237651			−0.118825	+	0.992915i	$0.537913\pi$
$180$	−8.53746	−	12.1445i	−0.636344	−	0.905201i
$181$	−0.509799			−0.0378931			−0.0189465	−	0.999820i	$-0.506031\pi$
$181$	−0.509799			−0.0378931			−0.0189465	+	0.999820i	$0.506031\pi$
$182$	1.89781	+	2.13255i	0.140675	+	0.158075i
$183$	3.30851	+	12.1489i	0.244572	+	0.898073i
$184$	19.1241	+	8.13414i	1.40985	+	0.599656i
$185$	−12.9542	+	22.4373i	−0.952410	+	1.64962i
$186$	12.5131	+	11.4447i	0.917501	+	0.839164i
$187$	1.45330	+	2.51719i	0.106276	+	0.184075i
$188$	1.46757	+	2.12428i	0.107034	+	0.154929i
$189$	12.4547	−	5.82069i	0.905946	−	0.423393i
$190$	3.48108	+	1.82610i	0.252544	+	0.132479i
$191$	10.4526	−	6.03481i	0.756324	−	0.436664i	−0.0716506	−	0.997430i	$-0.522827\pi$
$191$	10.4526	−	6.03481i	0.756324	−	0.436664i	0.827974	+	0.560766i	$0.189493\pi$
$192$	−13.8549	−	0.205419i	−0.999890	−	0.0148248i
$193$	−11.3351	+	19.6330i	−0.815919	+	1.41321i	0.0927479	+	0.995690i	$0.470435\pi$
$193$	−11.3351	+	19.6330i	−0.815919	+	1.41321i	−0.908666	+	0.417523i	$0.862898\pi$
$194$	−7.07052	+	4.47315i	−0.507634	+	0.321154i
$195$	−3.15470	+	0.859120i	−0.225913	+	0.0615229i
$196$	−11.2297	−	8.36023i	−0.802123	−	0.597159i
$197$	26.5564			1.89207			0.946033	−	0.324069i	$-0.105051\pi$
$197$	26.5564			1.89207			0.946033	+	0.324069i	$0.105051\pi$
$198$	−0.197425	−	4.05510i	−0.0140304	−	0.288183i
$199$		−	25.5041i		−	1.80794i	−0.427596	−	0.903970i	$-0.640639\pi$
$199$		−	25.5041i		−	1.80794i	0.427596	−	0.903970i	$-0.359361\pi$
$200$	−1.90736	−	2.53498i	−0.134871	−	0.179250i
$201$	−12.2130	−	12.1137i	−0.861437	−	0.854431i
$202$	14.2730	−	9.02983i	1.00425	−	0.635336i
$203$	3.61874	−	0.595653i	0.253986	−	0.0418067i
$204$	−10.3580	−	1.85012i	−0.725206	−	0.129534i
$205$	−25.3063	+	14.6106i	−1.76747	+	1.02045i
$206$	−11.8566	−	6.21973i	−0.826090	−	0.433349i
$207$	−11.1769	−	18.9990i	−0.776848	−	1.32052i
$208$	−1.07985	+	2.85440i	−0.0748743	+	0.197917i
$209$	0.537528	+	0.931026i	0.0371816	+	0.0644004i
$210$	14.2995	−	7.25474i	0.986761	−	0.500625i
$211$	7.82929	+	4.52024i	0.538990	+	0.311186i	0.744670	−	0.667433i	$-0.232607\pi$
$211$	7.82929	+	4.52024i	0.538990	+	0.311186i	−0.205679	+	0.978619i	$0.565940\pi$
$212$	21.4327	−	1.73907i	1.47200	−	0.119440i
$213$	−2.36438	+	8.97031i	−0.162005	+	0.614636i
$214$	11.0896	−	0.449174i	0.758071	−	0.0307049i
$215$	−2.85251			−0.194540
$216$	11.6848	+	8.91432i	0.795051	+	0.606542i
$217$	−14.1643	+	11.6128i	−0.961532	+	0.788329i
$218$	−0.450735	−	11.1282i	−0.0305276	−	0.753694i
$219$	−3.55602	+	13.4913i	−0.240294	+	0.911660i
$220$	−0.382964	−	4.71973i	−0.0258195	−	0.318204i
$221$	−1.15871	+	2.00695i	−0.0779435	+	0.135002i
$222$	5.52829	−	25.0469i	0.371035	−	1.68104i
$223$	−12.9553	+	7.47976i	−0.867553	+	0.500882i	−0.866534	−	0.499118i	$-0.833658\pi$
$223$	−12.9553	+	7.47976i	−0.867553	+	0.500882i	−0.00101850	+	0.999999i	$0.500324\pi$
$224$	2.35564	−	14.7801i	0.157393	−	0.987536i
$225$	0.0274748	+	3.36473i	0.00183165	+	0.224315i
$226$	−7.24670	−	3.80147i	−0.482043	−	0.252870i
$227$	5.07367	−	2.92929i	0.336752	−	0.194424i	−0.322083	−	0.946711i	$-0.604383\pi$
$227$	5.07367	−	2.92929i	0.336752	−	0.194424i	0.658835	+	0.752288i	$0.271050\pi$
$228$	−3.83109	−	0.684298i	−0.253720	−	0.0453187i
$229$	8.47830	−	14.6848i	0.560262	−	0.970402i	−0.437211	−	0.899359i	$-0.644034\pi$
$229$	8.47830	−	14.6848i	0.560262	−	0.970402i	0.997473	−	0.0710433i	$-0.0226328\pi$
$230$	−13.7453	−	21.7266i	−0.906337	−	1.43261i
$231$	4.36560	+	0.414121i	0.287235	+	0.0272472i
$232$	2.35723	+	3.13289i	0.154760	+	0.205684i
$233$		−	23.1459i		−	1.51634i	−0.652057	−	0.758170i	$-0.726094\pi$
$233$		−	23.1459i		−	1.51634i	0.652057	−	0.758170i	$-0.273906\pi$
$234$	2.72126	−	1.75288i	0.177895	−	0.114589i
$235$		−	3.19409i		−	0.208359i
$236$	9.27585	+	4.39679i	0.603807	+	0.286207i
$237$	1.99119	+	7.31167i	0.129341	+	0.474944i
$238$	3.57481	−	10.7881i	0.231720	−	0.699292i
$239$	0.356755	+	0.205973i	0.0230766	+	0.0133233i	0.511494	−	0.859287i	$-0.329092\pi$
$239$	0.356755	+	0.205973i	0.0230766	+	0.0133233i	−0.488417	+	0.872610i	$0.662426\pi$
$240$	13.9573	+	9.95138i	0.900943	+	0.642359i
$241$	15.5353	−	8.96929i	1.00071	−	0.577763i	0.0922548	−	0.995735i	$-0.470593\pi$
$241$	15.5353	−	8.96929i	1.00071	−	0.577763i	0.908460	+	0.417973i	$0.137259\pi$
$242$	−6.62498	+	12.6291i	−0.425870	+	0.811832i
$243$	−4.34110	−	14.9718i	−0.278482	−	0.960442i
$244$	−8.26414	−	11.9622i	−0.529057	−	0.765800i
$245$	5.55120	+	16.4056i	0.354653	+	1.04811i
$246$	19.5246	−	21.3472i	1.24484	−	1.36105i
$247$	−0.428570	+	0.742306i	−0.0272693	+	0.0472318i
$248$	−18.0187	−	7.66395i	−1.14419	−	0.486662i
$249$	9.14281	−	2.48986i	0.579402	−	0.157788i
$250$	−0.549213	−	13.5595i	−0.0347353	−	0.857577i
$251$		−	29.0664i		−	1.83465i	−0.398136	−	0.917326i	$-0.630343\pi$
$251$		−	29.0664i		−	1.83465i	0.398136	−	0.917326i	$-0.369657\pi$
$252$	−11.3314	+	11.1175i	−0.713814	+	0.700336i
$253$		−	7.03112i		−	0.442042i
$254$	19.8097	−	0.802374i	1.24297	−	0.0503454i
$255$	9.24166	+	9.16651i	0.578735	+	0.574029i
$256$	15.1683	−	5.09158i	0.948016	−	0.318224i
$257$	−8.68523	+	15.0433i	−0.541770	+	0.938373i	0.457033	+	0.889450i	$0.348912\pi$
$257$	−8.68523	+	15.0433i	−0.541770	+	0.938373i	−0.998803	+	0.0489228i	$0.984421\pi$
$258$	2.69254	−	0.851711i	0.167630	−	0.0530252i
$259$	25.9244	+	9.77161i	1.61086	+	0.607179i
$260$	3.10622	−	2.14595i	0.192639	−	0.133086i
$261$	−0.0339550	−	4.15834i	−0.00210176	−	0.257395i
$262$	−21.3384	−	11.1937i	−1.31829	−	0.691548i
$263$	−0.608479	+	0.351305i	−0.0375204	+	0.0216624i	−0.518643	−	0.854991i	$-0.673563\pi$
$263$	−0.608479	+	0.351305i	−0.0375204	+	0.0216624i	0.481122	+	0.876653i	$0.340229\pi$
$264$	1.77072	+	4.34069i	0.108980	+	0.267151i
$265$	−23.0375	−	13.3007i	−1.41518	−	0.817055i
$266$	1.32220	−	3.99018i	0.0810696	−	0.244654i
$267$	−3.61996	−	0.954143i	−0.221538	−	0.0583926i
$268$	17.9485	+	8.50766i	1.09638	+	0.519688i
$269$		−	13.8101i		−	0.842019i	−0.907056	−	0.421010i	$-0.861676\pi$
$269$		−	13.8101i		−	0.842019i	0.907056	−	0.421010i	$-0.138324\pi$
$270$	−5.62479	−	17.2896i	−0.342314	−	1.05221i
$271$			8.90979i			0.541231i	0.962687	+	0.270616i	$0.0872272\pi$
$271$			8.90979i			0.541231i	−0.962687	+	0.270616i	$0.912773\pi$
$272$	11.9908	−	1.95879i	0.727047	−	0.118769i
$273$	1.45440	+	3.17945i	0.0880243	+	0.192429i
$274$	−22.3621	+	14.1474i	−1.35095	+	0.854674i
$275$	−0.536652	+	0.929509i	−0.0323613	+	0.0560515i
$276$	19.4616	+	16.4040i	1.17145	+	0.987404i
$277$	4.70931	−	2.71892i	0.282955	−	0.163364i	−0.351805	−	0.936073i	$-0.614432\pi$
$277$	4.70931	−	2.71892i	0.282955	−	0.163364i	0.634761	+	0.772709i	$0.281099\pi$
$278$	−7.67971	+	14.6398i	−0.460599	+	0.878035i
$279$	10.5308	+	17.9008i	0.630464	+	1.07169i
$280$	−12.7905	+	13.3871i	−0.764378	+	0.800031i
$281$	−6.08260	+	3.51179i	−0.362858	+	0.209496i	−0.670334	−	0.742060i	$-0.733849\pi$
$281$	−6.08260	+	3.51179i	−0.362858	+	0.209496i	0.307476	+	0.951556i	$0.400516\pi$
$282$	0.953700	+	3.01496i	0.0567920	+	0.179538i
$283$	−4.91115	+	8.50636i	−0.291938	+	0.505651i	−0.974268	−	0.225393i	$-0.927633\pi$
$283$	−4.91115	+	8.50636i	−0.291938	+	0.505651i	0.682330	+	0.731044i	$0.260967\pi$
$284$	−0.866320	−	10.6767i	−0.0514066	−	0.633546i
$285$	3.41819	+	3.39039i	0.202476	+	0.200830i
$286$	1.03166	−	0.0417866i	0.0610036	−	0.00247089i
$287$	19.8114	+	24.1642i	1.16943	+	1.42637i
$288$	−16.1459	−	5.22587i	−0.951407	−	0.307937i
$289$	−7.77405			−0.457297
$290$	−0.196292	−	4.84625i	−0.0115267	−	0.284581i
$291$	−9.88698	+	2.69252i	−0.579585	+	0.157838i
$292$	−1.30294	−	16.0577i	−0.0762490	−	0.939708i
$293$	20.2939	+	11.7167i	1.18558	+	0.684495i	0.957299	−	0.289100i	$-0.0933561\pi$
$293$	20.2939	+	11.7167i	1.18558	+	0.684495i	0.228281	+	0.973595i	$0.426689\pi$
$294$	−10.1383	−	13.8280i	−0.591278	−	0.806468i
$295$	−6.34948	−	10.9976i	−0.369681	−	0.640306i
$296$	3.58811	+	29.3996i	0.208555	+	1.70882i
$297$	1.22802	−	4.81832i	0.0712567	−	0.279587i
$298$	10.5174	−	20.0493i	0.609258	−	1.16142i
$299$	4.85485	−	2.80295i	0.280763	−	0.162099i
$300$	−1.32077	−	3.65401i	−0.0762548	−	0.210964i
$301$	0.495421	+	3.00980i	0.0285556	+	0.173482i
$302$	12.0365	+	19.0255i	0.692622	+	1.09480i
$303$	19.9586	−	5.43531i	1.14659	−	0.312250i
$304$	4.43499	−	0.724491i	0.254364	−	0.0415524i
$305$			17.9864i			1.02990i
$306$	−11.4603	−	5.89303i	−0.655144	−	0.336882i
$307$	−20.6427			−1.17814			−0.589072	−	0.808081i	$-0.700506\pi$
$307$	−20.6427			−1.17814			−0.589072	+	0.808081i	$0.700506\pi$
$308$	−4.91347	+	1.22380i	−0.279971	+	0.0697325i
$309$	−11.6424	−	11.5478i	−0.662315	−	0.656929i
$310$	12.9508	+	20.4707i	0.735554	+	1.16266i
$311$	−11.5944	+	20.0821i	−0.657458	+	1.13875i	0.323814	+	0.946121i	$0.395035\pi$
$311$	−11.5944	+	20.0821i	−0.657458	+	1.13875i	−0.981272	+	0.192630i	$0.938298\pi$
$312$	−2.29127	+	2.95306i	−0.129718	+	0.167184i
$313$	−17.2838	+	9.97878i	−0.976936	+	0.564034i	−0.901344	−	0.433105i	$-0.857418\pi$
$313$	−17.2838	+	9.97878i	−0.976936	+	0.564034i	−0.0755920	+	0.997139i	$0.524085\pi$
$314$	−5.88599	+	11.2204i	−0.332166	+	0.633205i
$315$	19.3508	−	3.34770i	1.09030	−	0.188622i
$316$	−4.97367	−	7.19929i	−0.279791	−	0.404992i
$317$	0.906674	+	1.57041i	0.0509239	+	0.0882028i	0.890364	−	0.455250i	$-0.150450\pi$
$317$	0.906674	+	1.57041i	0.0509239	+	0.0882028i	−0.839440	+	0.543453i	$0.817117\pi$
$318$	25.7169	+	5.67617i	1.44213	+	0.318304i
$319$	0.663228	−	1.14874i	0.0371336	−	0.0643173i
$320$	−19.0188	−	5.48351i	−1.06318	−	0.306537i
$321$	13.1442	+	3.46452i	0.733636	+	0.193370i
$322$	−20.5373	+	18.2767i	−1.14450	+	1.01852i
$323$	3.41238			0.189870
$324$	10.4717	+	14.6405i	0.581762	+	0.813359i
$325$	−0.855744			−0.0474681
$326$	1.06726	+	26.3495i	0.0591100	+	1.45936i
$327$	3.47656	−	13.1899i	0.192254	−	0.729400i
$328$	−13.0747	+	30.7399i	−0.721929	+	1.69732i
$329$	−3.37022	+	0.554746i	−0.185806	+	0.0305841i
$330$	1.24996	−	5.66316i	0.0688080	−	0.311747i
$331$	−12.7331	+	7.35146i	−0.699874	+	0.404073i	−0.807301	−	0.590140i	$-0.799072\pi$
$331$	−12.7331	+	7.35146i	−0.699874	+	0.404073i	0.107426	+	0.994213i	$0.465739\pi$
$332$	−9.00228	+	6.21928i	−0.494064	+	0.341327i
$333$	15.4845	−	27.3330i	0.848546	−	1.49784i
$334$	−2.25790	+	4.30422i	−0.123547	+	0.235517i
$335$	−12.2861	−	21.2801i	−0.671260	−	1.16266i
$336$	8.07603	−	16.4553i	0.440583	−	0.897712i
$337$	−3.74944	+	6.49423i	−0.204245	+	0.353763i	−0.949892	−	0.312578i	$-0.898807\pi$
$337$	−3.74944	+	6.49423i	−0.204245	+	0.353763i	0.745647	+	0.666341i	$0.232141\pi$
$338$	−9.38910	−	14.8409i	−0.510699	−	0.807240i
$339$	−7.11579	−	7.05792i	−0.386477	−	0.383334i
$340$	−13.5818	−	6.43782i	−0.736577	−	0.349140i
$341$			6.62469i			0.358747i
$342$	−4.23881	−	2.17964i	−0.229208	−	0.117861i
$343$	16.3461	−	8.70661i	0.882606	−	0.470113i
$344$	−2.60571	+	1.96057i	−0.140490	+	0.105707i
$345$	−8.27368	−	30.3811i	−0.445440	−	1.63566i
$346$	14.4696	−	9.15421i	0.777893	−	0.492133i
$347$	5.94818	−	10.3026i	0.319315	−	0.553070i	−0.661030	−	0.750359i	$-0.729880\pi$
$347$	5.94818	−	10.3026i	0.319315	−	0.553070i	0.980345	+	0.197289i	$0.0632138\pi$
$348$	1.63229	+	4.51585i	0.0875000	+	0.242075i
$349$	−3.51702	−	6.09165i	−0.188262	−	0.326079i	0.756409	−	0.654099i	$-0.226952\pi$
$349$	−3.51702	−	6.09165i	−0.188262	−	0.326079i	−0.944671	+	0.328020i	$0.893619\pi$
$350$	4.11000	−	0.848645i	0.219689	−	0.0453620i
$351$	3.81650	−	1.07290i	0.203710	−	0.0572670i
$352$	−3.59377	−	4.04816i	−0.191549	−	0.215768i
$353$	0.725539	+	1.25667i	0.0386165	+	0.0668858i	0.884688	−	0.466184i	$-0.154372\pi$
$353$	0.725539	+	1.25667i	0.0386165	+	0.0668858i	−0.846071	+	0.533070i	$0.821038\pi$
$354$	9.27709	+	8.48501i	0.493072	+	0.450973i
$355$	−6.62575	+	11.4761i	−0.351658	+	0.609090i
$356$	4.30857	−	0.349602i	0.228354	−	0.0185289i
$357$	8.06689	−	11.3433i	0.426945	−	0.600351i
$358$	4.49288	−	0.181980i	0.237456	−	0.00961792i
$359$			12.7877i			0.674908i	0.941342	+	0.337454i	$0.109566\pi$
$359$			12.7877i			0.674908i	−0.941342	+	0.337454i	$0.890434\pi$
$360$	12.7590	+	16.6723i	0.672457	+	0.878706i
$361$	−17.7379			−0.933572
$362$	0.720374	−	0.0291781i	0.0378620	−	0.00153356i
$363$	−12.3002	+	12.4010i	−0.645591	+	0.650884i
$364$	−2.80376	−	2.90479i	−0.146957	−	0.152253i
$365$	−9.96512	+	17.2601i	−0.521598	+	0.903434i
$366$	−5.37044	−	16.9777i	−0.280718	−	0.887439i
$367$	24.2534	−	14.0027i	1.26602	−	0.730937i	0.291787	−	0.956483i	$-0.405750\pi$
$367$	24.2534	−	14.0027i	1.26602	−	0.730937i	0.974232	+	0.225546i	$0.0724168\pi$
$368$	−27.4890	−	10.3994i	−1.43296	−	0.542107i
$369$	30.5387	−	17.9656i	1.58978	−	0.935250i
$370$	17.0208	−	32.4466i	0.884868	−	1.68682i
$371$	−10.0330	+	26.6179i	−0.520887	+	1.38193i
$372$	−18.3367	−	15.4558i	−0.950711	−	0.801345i
$373$	−19.8517	−	11.4614i	−1.02788	−	0.593447i	−0.111504	−	0.993764i	$-0.535567\pi$
$373$	−19.8517	−	11.4614i	−1.02788	−	0.593447i	−0.916377	+	0.400317i	$0.868900\pi$
$374$	−2.19766	−	3.47375i	−0.113638	−	0.179623i
$375$	4.23613	−	16.0716i	0.218753	−	0.829935i
$376$	−2.19534	−	2.91773i	−0.113216	−	0.150470i
$377$	1.05758			0.0544682
$378$	−17.2660	+	8.93779i	−0.888069	+	0.459710i
$379$			11.9438i			0.613513i	0.951788	+	0.306757i	$0.0992438\pi$
$379$			11.9438i			0.613513i	−0.951788	+	0.306757i	$0.900756\pi$
$380$	−5.02347	−	2.38114i	−0.257698	−	0.122150i
$381$	23.4798	+	6.18877i	1.20291	+	0.317060i
$382$	−14.4247	+	9.12577i	−0.738032	+	0.466915i
$383$	10.3901	−	17.9961i	0.530908	−	0.919559i	−0.468442	−	0.883494i	$-0.655184\pi$
$383$	10.3901	−	17.9961i	0.530908	−	0.919559i	0.999349	−	0.0360650i	$-0.0114823\pi$
$384$	19.5895	−	0.502708i	0.999671	−	0.0256537i
$385$	5.86157	+	2.20939i	0.298733	+	0.112601i
$386$	14.8934	−	28.3912i	0.758056	−	1.44508i
$387$	3.45860	−	0.0282413i	0.175811	−	0.00143559i
$388$	9.73501	−	6.72549i	0.494220	−	0.341435i
$389$	−4.73358	−	8.19880i	−0.240002	−	0.415696i	0.720713	−	0.693234i	$-0.243815\pi$
$389$	−4.73358	−	8.19880i	−0.240002	−	0.415696i	−0.960715	+	0.277538i	$0.910481\pi$
$390$	4.40860	−	1.39454i	0.223238	−	0.0706154i
$391$	−19.3277	−	11.1589i	−0.977446	−	0.564329i
$392$	16.3467	+	11.1707i	0.825633	+	0.564207i
$393$	−20.9529	−	20.7825i	−1.05694	−	1.04834i
$394$	−37.5257	+	1.51994i	−1.89052	+	0.0765735i
$395$			10.8249i			0.544660i
$396$	0.511064	+	5.71878i	0.0256819	+	0.287379i
$397$	25.7984			1.29479			0.647393	−	0.762156i	$-0.275859\pi$
$397$	25.7984			1.29479			0.647393	+	0.762156i	$0.275859\pi$
$398$	1.45971	+	36.0387i	0.0731688	+	1.80646i
$399$	2.98368	−	4.19552i	0.149371	−	0.210039i
$400$	2.84029	+	3.47290i	0.142014	+	0.173645i
$401$	−8.71125	−	5.02944i	−0.435019	−	0.251158i	0.266463	−	0.963845i	$-0.414145\pi$
$401$	−8.71125	−	5.02944i	−0.435019	−	0.251158i	−0.701483	+	0.712687i	$0.747478\pi$
$402$	17.9509	+	16.4183i	0.895311	+	0.818868i
$403$	−4.57422	+	2.64093i	−0.227858	+	0.131554i
$404$	−19.6518	+	13.5765i	−0.977713	+	0.675459i
$405$	−0.363630	−	22.2647i	−0.0180689	−	1.10634i
$406$	−5.07939	+	1.04881i	−0.252086	+	0.0520514i
$407$	8.67794	−	5.01021i	0.430150	−	0.248347i
$408$	14.7423	+	2.02148i	0.729854	+	0.100078i
$409$	−6.37499	−	3.68060i	−0.315223	−	0.181994i	0.334038	−	0.942559i	$-0.391588\pi$
$409$	−6.37499	−	3.68060i	−0.315223	−	0.181994i	−0.649261	+	0.760565i	$0.724922\pi$
$410$	34.9230	−	22.0940i	1.72472	−	1.09114i
$411$	−31.2698	+	8.51570i	−1.54243	+	0.420049i
$412$	17.1100	+	8.11022i	0.842951	+	0.399562i
$413$	−10.5013	+	8.60966i	−0.516734	+	0.423654i
$414$	16.8810	+	26.2069i	0.829654	+	1.28800i
$415$	13.5359			0.664452
$416$	1.36252	−	4.09522i	0.0668031	−	0.200785i
$417$	−14.2584	+	14.3753i	−0.698237	+	0.703961i
$418$	−0.812843	−	1.28483i	−0.0397575	−	0.0628429i
$419$	0.137413	+	0.0793353i	0.00671306	+	0.00387579i	0.503353	−	0.864081i	$-0.332100\pi$
$419$	0.137413	+	0.0793353i	0.00671306	+	0.00387579i	−0.496640	+	0.867957i	$0.665433\pi$
$420$	−19.7908	+	11.0698i	−0.965692	+	0.540150i
$421$	11.9396	−	6.89331i	0.581898	−	0.335959i	−0.179989	−	0.983669i	$-0.557606\pi$
$421$	11.9396	−	6.89331i	0.581898	−	0.335959i	0.761887	+	0.647709i	$0.224273\pi$
$422$	−11.3219	−	5.93925i	−0.551143	−	0.289118i
$423$	0.0316231	+	3.87276i	0.00153757	+	0.188300i
$424$	−30.1860	+	3.68409i	−1.46596	+	0.178915i
$425$	1.70341	+	2.95039i	0.0826275	+	0.143115i
$426$	2.82759	−	12.8109i	0.136997	−	0.620689i
$427$	18.9782	−	3.12386i	0.918421	−	0.151174i
$428$	−15.6445	+	1.26942i	−0.756207	+	0.0613595i
$429$	1.22280	+	0.322303i	0.0590373	+	0.0155609i
$430$	4.03075	−	0.163262i	0.194380	−	0.00787318i
$431$			0.549132i			0.0264508i	0.999913	+	0.0132254i	$0.00420989\pi$
$431$			0.549132i			0.0264508i	−0.999913	+	0.0132254i	$0.995790\pi$
$432$	−17.0215	−	11.9276i	−0.818947	−	0.573869i
$433$			30.6426i			1.47259i	0.676660	+	0.736295i	$0.263427\pi$
$433$			30.6426i			1.47259i	−0.676660	+	0.736295i	$0.736573\pi$
$434$	19.3502	−	17.2202i	0.928840	−	0.826597i
$435$	1.51402	−	5.74410i	0.0725917	−	0.275409i
$436$	1.27383	+	15.6989i	0.0610053	+	0.751841i
$437$	−7.14870	−	4.12731i	−0.341969	−	0.197436i
$438$	4.25269	−	19.2675i	0.203201	−	0.920638i
$439$	−17.0141	+	9.82308i	−0.812037	+	0.468830i	−0.847663	−	0.530535i	$-0.821991\pi$
$439$	−17.0141	+	9.82308i	−0.812037	+	0.468830i	0.0356257	+	0.999365i	$0.488658\pi$
$440$	0.811281	+	6.64732i	0.0386763	+	0.316899i
$441$	−6.89313	−	19.8364i	−0.328244	−	0.944593i
$442$	1.52246	−	2.90225i	0.0724160	−	0.138046i
$443$	−16.5072	−	28.5914i	−0.784282	−	1.35842i	−0.929427	−	0.369006i	$-0.879698\pi$
$443$	−16.5072	−	28.5914i	−0.784282	−	1.35842i	0.145145	−	0.989410i	$-0.453635\pi$
$444$	−6.37823	+	35.7090i	−0.302698	+	1.69467i
$445$	−4.63118	−	2.67381i	−0.219539	−	0.126751i
$446$	17.8785	−	11.3108i	0.846571	−	0.535582i
$447$	19.5270	−	19.6871i	0.923595	−	0.931167i
$448$	−2.48271	+	21.0199i	−0.117297	+	0.993097i
$449$			40.5402i			1.91321i	0.291391	+	0.956604i	$0.405882\pi$
$449$			40.5402i			1.91321i	−0.291391	+	0.956604i	$0.594118\pi$
$450$	−0.231402	−	4.75298i	−0.0109084	−	0.224058i
$451$	11.3017			0.532177
$452$	10.4576	+	4.95692i	0.491882	+	0.233154i
$453$	7.24510	+	26.6042i	0.340405	+	1.24997i
$454$	−7.00172	+	4.42963i	−0.328607	+	0.207893i
$455$	0.811173	+	4.92807i	0.0380284	+	0.231032i
$456$	5.45271	+	0.747680i	0.255347	+	0.0350133i
$457$	−5.21970	−	9.04079i	−0.244167	−	0.422910i	0.717730	−	0.696322i	$-0.245181\pi$
$457$	−5.21970	−	9.04079i	−0.244167	−	0.422910i	−0.961897	+	0.273411i	$0.911848\pi$
$458$	−11.1398	+	21.2357i	−0.520530	+	0.992281i
$459$	−11.2961	−	11.0227i	−0.527255	−	0.514495i
$460$	20.6663	+	29.9141i	0.963573	+	1.39475i
$461$	1.13799	−	0.657021i	0.0530017	−	0.0306005i	−0.473265	−	0.880920i	$-0.656925\pi$
$461$	1.13799	−	0.657021i	0.0530017	−	0.0306005i	0.526267	+	0.850320i	$0.323591\pi$
$462$	−6.19253	−	0.335314i	−0.288103	−	0.0156002i
$463$	−9.84358	+	17.0496i	−0.457470	+	0.792361i	−0.998826	−	0.0484320i	$-0.984578\pi$
$463$	−9.84358	+	17.0496i	−0.457470	+	0.792361i	0.541357	+	0.840793i	$0.317911\pi$
$464$	−3.51020	−	4.29203i	−0.162957	−	0.199252i
$465$	7.79543	+	28.6250i	0.361504	+	1.32745i
$466$	1.32474	+	32.7065i	0.0613675	+	1.51510i
$467$		−	13.4673i		−	0.623192i	−0.950215	−	0.311596i	$-0.899136\pi$
$467$		−	13.4673i		−	0.623192i	0.950215	−	0.311596i	$-0.100864\pi$
$468$	−3.74497	+	2.63267i	−0.173111	+	0.121695i
$469$	−20.3197	+	16.6595i	−0.938276	+	0.769262i
$470$	0.182812	+	4.51342i	0.00843247	+	0.208189i
$471$	−10.9281	+	11.0177i	−0.503541	+	0.507670i
$472$	−13.3589	−	5.68200i	−0.614895	−	0.261535i
$473$	0.955441	+	0.551624i	0.0439312	+	0.0253637i
$474$	−3.23214	−	10.2178i	−0.148457	−	0.469321i
$475$	0.630036	+	1.09125i	0.0289080	+	0.0500702i
$476$	−4.43394	+	15.4488i	−0.203230	+	0.708097i
$477$	28.0641	+	15.8987i	1.28497	+	0.727952i
$478$	−0.515903	−	0.270632i	−0.0235969	−	0.0123784i
$479$	−15.1722	−	26.2790i	−0.693234	−	1.20072i	−0.970772	−	0.240002i	$-0.922852\pi$
$479$	−15.1722	−	26.2790i	−0.693234	−	1.20072i	0.277539	−	0.960714i	$-0.410481\pi$
$480$	−20.2921	−	13.2630i	−0.926201	−	0.605371i
$481$	6.91891	+	3.99464i	0.315475	+	0.182140i
$482$	−21.4388	+	13.5633i	−0.976512	+	0.617789i
$483$	−30.6194	+	14.0065i	−1.39323	+	0.637316i
$484$	8.63865	−	18.2249i	0.392666	−	0.828402i
$485$	−14.6376			−0.664661
$486$	6.99111	+	20.9075i	0.317123	+	0.948384i
$487$	34.8943			1.58121			0.790605	−	0.612326i	$-0.209766\pi$
$487$	34.8943			1.58121			0.790605	+	0.612326i	$0.209766\pi$
$488$	12.3623	+	16.4302i	0.559616	+	0.743761i
$489$	−8.23186	+	31.2312i	−0.372257	+	1.41232i
$490$	−8.78312	−	22.8643i	−0.396781	−	1.03290i
$491$	−6.21946	+	10.7724i	−0.280680	+	0.486153i	−0.971552	−	0.236824i	$-0.923893\pi$
$491$	−6.21946	+	10.7724i	−0.280680	+	0.486153i	0.690872	+	0.722977i	$0.257227\pi$
$492$	−26.3675	+	31.2823i	−1.18874	+	1.41032i
$493$	−2.10518	−	3.64628i	−0.0948125	−	0.164220i
$494$	0.563108	−	1.07345i	0.0253354	−	0.0482967i
$495$	3.50109	−	6.18005i	0.157362	−	0.277773i
$496$	25.9000	+	9.79830i	1.16295	+	0.439957i
$497$	13.2597	+	4.99794i	0.594779	+	0.224188i
$498$	−12.7768	+	4.04159i	−0.572542	+	0.181108i
$499$	26.7819	+	15.4625i	1.19892	+	0.692197i	0.960314	−	0.278920i	$-0.0899763\pi$
$499$	26.7819	+	15.4625i	1.19892	+	0.692197i	0.238606	+	0.971117i	$0.423310\pi$
$500$	1.55214	+	19.1289i	0.0694137	+	0.855468i
$501$	−4.19210	+	4.22647i	−0.187289	+	0.188825i
$502$	1.66360	+	41.0724i	0.0742499	+	1.83315i
$503$	−12.8465			−0.572795			−0.286398	−	0.958111i	$-0.592458\pi$
$503$	−12.8465			−0.572795			−0.286398	+	0.958111i	$0.592458\pi$
$504$	15.3756	−	16.3582i	0.684886	−	0.728650i
$505$	29.5486			1.31489
$506$	0.402422	+	9.93535i	0.0178898	+	0.441680i
$507$	−5.65156	−	20.7526i	−0.250995	−	0.921657i
$508$	−27.9463	+	2.26760i	−1.23992	+	0.100608i
$509$	−10.0227	−	5.78663i	−0.444250	−	0.256488i	0.261149	−	0.965299i	$-0.415899\pi$
$509$	−10.0227	−	5.78663i	−0.444250	−	0.256488i	−0.705399	+	0.708811i	$0.749232\pi$
$510$	−13.5836	−	12.4238i	−0.601493	−	0.550137i
$511$	19.9426	+	7.51690i	0.882208	+	0.332528i
$512$	−21.1422	+	8.06283i	−0.934360	+	0.356330i
$513$	−4.17805	−	4.07693i	−0.184465	−	0.180001i
$514$	11.4117	−	21.7540i	0.503349	−	0.959530i
$515$	−11.7121	−	20.2860i	−0.516097	−	0.893907i
$516$	−3.75595	+	1.35762i	−0.165347	+	0.0597659i
$517$	−0.617679	+	1.06985i	−0.0271655	+	0.0470520i
$518$	−37.1919	−	12.3241i	−1.63412	−	0.541488i
$519$	20.2335	−	5.51018i	0.888151	−	0.241870i
$520$	−4.26643	+	3.21012i	−0.187095	+	0.140773i
$521$	−43.7766			−1.91789			−0.958943	−	0.283599i	$-0.908471\pi$
$521$	−43.7766			−1.91789			−0.958943	+	0.283599i	$0.908471\pi$
$522$	0.285981	+	5.87402i	0.0125170	+	0.257099i
$523$	−40.2810			−1.76136			−0.880682	−	0.473709i	$-0.842915\pi$
$523$	−40.2810			−1.76136			−0.880682	+	0.473709i	$0.842915\pi$
$524$	30.7930	+	14.5960i	1.34520	+	0.637629i
$525$	5.11691	+	0.485391i	0.223320	+	0.0211842i
$526$	0.839707	−	0.531240i	0.0366130	−	0.0231631i
$527$	18.2105	+	10.5139i	0.793263	+	0.457991i
$528$	−2.75056	−	6.03229i	−0.119703	−	0.262522i
$529$	15.4935	+	26.8356i	0.673632	+	1.16677i
$530$	33.3145	+	17.4761i	1.44709	+	0.759112i
$531$	7.80749	+	13.2715i	0.338816	+	0.575934i
$532$	−1.63997	+	5.71403i	−0.0711018	+	0.247734i
$533$	4.50542	+	7.80362i	0.195151	+	0.338012i
$534$	5.16981	+	1.14107i	0.223720	+	0.0493789i
$535$	16.8159	+	9.70869i	0.727016	+	0.419743i
$536$	−25.8492	−	10.9945i	−1.11651	−	0.474891i
$537$	5.32527	+	1.40362i	0.229802	+	0.0605708i
$538$	0.790415	+	19.5145i	0.0340772	+	0.841329i
$539$	1.31318	−	6.56852i	0.0565629	−	0.282926i
$540$	8.93770	+	24.1092i	0.384617	+	1.03749i
$541$			6.34930i			0.272978i	0.990642	+	0.136489i	$0.0435818\pi$
$541$			6.34930i			0.272978i	−0.990642	+	0.136489i	$0.956418\pi$
$542$	−0.509947	−	12.5900i	−0.0219041	−	0.540788i
$543$	0.853837	+	0.225053i	0.0366416	+	0.00965794i
$544$	−16.8315	+	3.45416i	−0.721645	+	0.148096i
$545$	9.74243	−	16.8744i	0.417320	−	0.722819i
$546$	−2.23712	−	4.40950i	−0.0957399	−	0.188709i
$547$	23.7804	−	13.7296i	1.01678	−	0.587037i	0.103609	−	0.994618i	$-0.466961\pi$
$547$	23.7804	−	13.7296i	1.01678	−	0.587037i	0.913169	+	0.407581i	$0.133628\pi$
$548$	30.7892	−	21.2709i	1.31525	−	0.908648i
$549$	−0.178075	−	21.8081i	−0.00760005	−	0.930749i
$550$	0.705119	−	1.34416i	0.0300664	−	0.0573153i
$551$	−0.778637	−	1.34864i	−0.0331711	−	0.0574540i
$552$	−28.4392	−	22.0659i	−1.21045	−	0.939186i
$553$	11.4218	−	1.88006i	0.485705	−	0.0799483i
$554$	−6.49890	+	4.11152i	−0.276112	+	0.174682i
$555$	31.6013	−	31.8604i	1.34140	−	1.35240i
$556$	10.0140	−	21.1263i	0.424686	−	0.895956i
$557$	−2.15844			−0.0914560			−0.0457280	−	0.998954i	$-0.514561\pi$
$557$	−2.15844			−0.0914560			−0.0457280	+	0.998954i	$0.514561\pi$
$558$	−15.9052	−	24.6920i	−0.673320	−	1.04530i
$559$			0.879619i			0.0372039i
$560$	17.3075	−	19.6487i	0.731374	−	0.830310i
$561$	−1.32283	−	4.85747i	−0.0558501	−	0.205083i
$562$	8.39406	−	5.31049i	0.354082	−	0.224010i
$563$	−27.9068	−	16.1120i	−1.17613	−	0.679039i	−0.221014	−	0.975271i	$-0.570936\pi$
$563$	−27.9068	−	16.1120i	−1.17613	−	0.679039i	−0.955116	+	0.296232i	$0.904270\pi$
$564$	−1.52019	−	4.20571i	−0.0640115	−	0.177093i
$565$	−7.15838	−	12.3987i	−0.301155	−	0.521616i
$566$	6.45287	−	12.3010i	0.271234	−	0.517052i
$567$	−23.4293	+	4.25060i	−0.983938	+	0.178508i
$568$	1.83523	+	15.0372i	0.0770046	+	0.630946i
$569$	−1.62581	+	0.938661i	−0.0681574	+	0.0393507i	−0.533691	−	0.845679i	$-0.679196\pi$
$569$	−1.62581	+	0.938661i	−0.0681574	+	0.0393507i	0.465534	+	0.885030i	$0.345862\pi$
$570$	−5.02414	−	4.59517i	−0.210438	−	0.192471i
$571$	−26.0661	−	15.0493i	−1.09083	−	0.629793i	−0.157035	−	0.987593i	$-0.550194\pi$
$571$	−26.0661	−	15.0493i	−1.09083	−	0.629793i	−0.933798	+	0.357800i	$0.883527\pi$
$572$	−1.45541	+	0.118093i	−0.0608536	+	0.00493773i
$573$	−20.1706	+	5.49306i	−0.842640	+	0.229476i
$574$	−29.3777	−	33.0114i	−1.22620	−	1.37787i
$575$		−	8.24116i		−	0.343680i
$576$	23.1142	+	6.46033i	0.963090	+	0.269181i
$577$		−	9.79839i		−	0.407912i	−0.978980	−	0.203956i	$-0.934620\pi$
$577$		−	9.79839i		−	0.407912i	0.978980	−	0.203956i	$-0.0653800\pi$
$578$	10.9852	−	0.444943i	0.456922	−	0.0185072i
$579$	27.6516	−	27.8783i	1.14916	−	1.15858i
$580$	0.554744	+	6.83678i	0.0230345	+	0.283882i
$581$	−2.35090	−	14.2823i	−0.0975318	−	0.592530i
$582$	13.8167	−	4.37055i	0.572722	−	0.181165i
$583$	5.14423	+	8.91007i	0.213052	+	0.369017i
$584$	2.76019	+	22.6159i	0.114217	+	0.935852i
$585$	5.66292	−	0.0462406i	0.234133	−	0.00191181i
$586$	−29.3469	−	15.3948i	−1.21231	−	0.635953i
$587$	33.1610	−	19.1455i	1.36870	−	0.790220i	0.377939	−	0.925830i	$-0.376633\pi$
$587$	33.1610	−	19.1455i	1.36870	−	0.790220i	0.990762	+	0.135610i	$0.0432994\pi$
$588$	15.1174	+	18.9595i	0.623432	+	0.781877i
$589$	6.73548	+	3.88873i	0.277531	+	0.160232i
$590$	9.60161	+	15.1768i	0.395292	+	0.624820i
$591$	−44.4780	−	11.7234i	−1.82958	−	0.482237i
$592$	−6.75287	−	41.3379i	−0.277541	−	1.69898i
$593$	40.1855			1.65022			0.825111	−	0.564970i	$-0.191112\pi$
$593$	40.1855			1.65022			0.825111	+	0.564970i	$0.191112\pi$
$594$	−1.45948	+	6.87883i	−0.0598832	+	0.282242i
$595$	15.3761	−	12.6064i	0.630358	−	0.516810i
$596$	−13.7142	+	28.9327i	−0.561755	+	1.18513i
$597$	−11.2589	+	42.7156i	−0.460796	+	1.74823i
$598$	−6.69975	+	4.23859i	−0.273973	+	0.173329i
$599$	−29.1630	−	16.8373i	−1.19157	−	0.687952i	−0.232905	−	0.972499i	$-0.574823\pi$
$599$	−29.1630	−	16.8373i	−1.19157	−	0.687952i	−0.958662	+	0.284548i	$0.908157\pi$
$600$	2.07546	+	5.08772i	0.0847302	+	0.207705i
$601$	−25.3603	+	14.6418i	−1.03447	+	0.597251i	−0.918262	−	0.395974i	$-0.870407\pi$
$601$	−25.3603	+	14.6418i	−1.03447	+	0.597251i	−0.116207	+	0.993225i	$0.537074\pi$
$602$	−0.872321	−	4.22466i	−0.0355532	−	0.172184i
$603$	15.1073	+	25.6800i	0.615216	+	1.04577i
$604$	−18.0971	−	26.1952i	−0.736362	−	1.06587i
$605$	−21.6077	+	12.4752i	−0.878479	+	0.507190i
$606$	−27.8914	+	8.82271i	−1.13301	+	0.358398i
$607$	40.9876	+	23.6642i	1.66363	+	0.960500i	0.970957	+	0.239253i	$0.0769024\pi$
$607$	40.9876	+	23.6642i	1.66363	+	0.960500i	0.692678	+	0.721247i	$0.256431\pi$
$608$	−6.22542	+	1.27758i	−0.252474	+	0.0518127i
$609$	−6.32380	−	0.599876i	−0.256253	−	0.0243082i
$610$	−1.02944	−	25.4158i	−0.0416809	−	1.02906i
$611$	−0.984950			−0.0398468
$612$	16.5314	+	7.67125i	0.668241	+	0.310092i
$613$			13.5597i			0.547673i	0.961776	+	0.273836i	$0.0882927\pi$
$613$			13.5597i			0.547673i	−0.961776	+	0.273836i	$0.911707\pi$
$614$	29.1693	−	1.18148i	1.17718	−	0.0476805i
$615$	48.8341	−	13.2990i	1.96918	−	0.536267i
$616$	6.87297	−	2.01052i	0.276920	−	0.0810060i
$617$	−4.83875	−	2.79365i	−0.194801	−	0.112468i	0.399427	−	0.916765i	$-0.369209\pi$
$617$	−4.83875	−	2.79365i	−0.194801	−	0.112468i	−0.594228	+	0.804297i	$0.702542\pi$
$618$	17.1123	+	15.6513i	0.688359	+	0.629586i
$619$	−8.96221	−	15.5230i	−0.360222	−	0.623922i	0.627776	−	0.778394i	$-0.283966\pi$
$619$	−8.96221	−	15.5230i	−0.360222	−	0.623922i	−0.987997	+	0.154472i	$0.950632\pi$
$620$	−19.4718	−	28.1850i	−0.782005	−	1.13194i
$621$	10.3324	+	36.7545i	0.414626	+	1.47491i
$622$	15.2341	−	29.0407i	0.610833	−	1.16443i
$623$	−2.01691	+	5.35094i	−0.0808060	+	0.214381i
$624$	3.06867	−	4.30398i	0.122845	−	0.172297i
$625$	14.6750	−	25.4179i	0.587001	−	1.01672i
$626$	23.8518	−	15.0898i	0.953308	−	0.603109i
$627$	−0.489273	−	1.79662i	−0.0195397	−	0.0717501i
$628$	7.67504	−	16.1919i	0.306267	−	0.646129i
$629$		−	31.8063i		−	1.26820i
$630$	−27.1522	+	5.83802i	−1.08177	+	0.232592i
$631$	7.68661			0.305999			0.153000	−	0.988226i	$-0.451107\pi$
$631$	7.68661			0.305999			0.153000	+	0.988226i	$0.451107\pi$
$632$	7.44012	+	9.88833i	0.295952	+	0.393337i
$633$	−11.1174	−	11.0270i	−0.441877	−	0.438283i
$634$	−1.37106	−	2.16718i	−0.0544518	−	0.0860696i
$635$	30.0388	+	17.3429i	1.19205	+	0.688233i
$636$	−36.6642	−	6.54885i	−1.45383	−	0.259679i
$637$	5.05893	−	1.71181i	0.200442	−	0.0678242i
$638$	−0.871430	+	1.66120i	−0.0345002	+	0.0657675i
$639$	7.91996	−	13.9802i	0.313309	−	0.553047i
$640$	27.1884	+	6.65997i	1.07472	+	0.263258i
$641$	8.14981	−	4.70530i	0.321898	−	0.185848i	−0.330340	−	0.943862i	$-0.607163\pi$
$641$	8.14981	−	4.70530i	0.321898	−	0.185848i	0.652238	+	0.758014i	$0.273830\pi$
$642$	−18.7717	−	4.14325i	−0.740861	−	0.163521i
$643$	6.74414	−	11.6812i	0.265963	−	0.460661i	−0.701853	−	0.712322i	$-0.747643\pi$
$643$	6.74414	−	11.6812i	0.265963	−	0.460661i	0.967815	+	0.251661i	$0.0809768\pi$
$644$	27.9743	−	27.0014i	1.10234	−	1.06400i
$645$	4.77752	+	1.25925i	0.188115	+	0.0495829i
$646$	−4.82188	+	0.195306i	−0.189714	+	0.00768419i
$647$	−17.9993			−0.707624			−0.353812	−	0.935316i	$-0.615115\pi$
$647$	−17.9993			−0.707624			−0.353812	+	0.935316i	$0.615115\pi$
$648$	−15.6350	−	20.0884i	−0.614203	−	0.789148i
$649$			4.91150i			0.192793i
$650$	1.20921	−	0.0489780i	0.0474293	−	0.00192108i
$651$	28.8495	−	13.1968i	1.13070	−	0.517225i
$652$	−3.01619	−	37.1722i	−0.118123	−	1.45577i
$653$	9.03369	−	15.6468i	0.353516	−	0.612307i	−0.633347	−	0.773868i	$-0.718319\pi$
$653$	9.03369	−	15.6468i	0.353516	−	0.612307i	0.986863	+	0.161561i	$0.0516527\pi$
$654$	−4.15765	+	18.8370i	−0.162577	+	0.736584i
$655$	−21.0783	−	36.5087i	−0.823598	−	1.42651i
$656$	16.7159	−	44.1854i	0.652646	−	1.72515i
$657$	11.9116	−	21.0261i	0.464716	−	0.820308i
$658$	4.73055	−	0.976778i	0.184416	−	0.0380788i
$659$	−5.96184	−	10.3262i	−0.232240	−	0.402252i	0.726227	−	0.687455i	$-0.241272\pi$
$659$	−5.96184	−	10.3262i	−0.232240	−	0.402252i	−0.958467	+	0.285203i	$0.907939\pi$
$660$	−1.44213	+	8.07390i	−0.0561350	+	0.314276i
$661$	−3.58369	+	6.20713i	−0.139389	+	0.241429i	−0.927266	−	0.374404i	$-0.877847\pi$
$661$	−3.58369	+	6.20713i	−0.139389	+	0.241429i	0.787876	+	0.615834i	$0.211181\pi$
$662$	17.5718	−	11.1168i	0.682948	−	0.432066i
$663$	2.82664	−	2.84982i	0.109778	−	0.110678i
$664$	12.3648	−	9.30342i	0.479846	−	0.361043i
$665$	5.68711	−	4.66268i	0.220537	−	0.180811i
$666$	−20.3161	+	39.5092i	−0.787232	+	1.53095i
$667$			10.1849i			0.394362i
$668$	2.94419	−	6.21133i	0.113914	−	0.240324i
$669$	25.0002	−	6.80829i	0.966563	−	0.263224i
$670$	18.5788	+	29.3668i	0.717763	+	1.13454i
$671$	3.47825	−	6.02451i	0.134276	−	0.232574i
$672$	−10.4701	+	23.7145i	−0.403891	+	0.914807i
$673$	3.81915	+	6.61497i	0.147217	+	0.254988i	0.930198	−	0.367058i	$-0.119635\pi$
$673$	3.81915	+	6.61497i	0.147217	+	0.254988i	−0.782981	+	0.622046i	$0.786302\pi$
$674$	4.92648	−	9.39130i	0.189761	−	0.361739i
$675$	1.43936	−	5.64755i	0.0554009	−	0.217374i
$676$	14.1167	+	20.4337i	0.542951	+	0.785910i
$677$	5.55381	−	3.20650i	0.213450	−	0.123236i	−0.389464	−	0.921042i	$-0.627340\pi$
$677$	5.55381	−	3.20650i	0.213450	−	0.123236i	0.602914	+	0.797806i	$0.294006\pi$
$678$	10.4590	+	9.56597i	0.401674	+	0.367379i
$679$	2.54225	+	15.4448i	0.0975626	+	0.592717i
$680$	19.5603	+	8.31965i	0.750103	+	0.319044i
$681$	−9.79078	+	2.66632i	−0.375184	+	0.102174i
$682$	−0.379160	−	9.36105i	−0.0145188	−	0.358453i
$683$	−16.0691			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$683$	−16.0691			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$684$	6.11442	+	2.83735i	0.233791	+	0.108489i
$685$	−46.2949			−1.76884
$686$	−22.5996	+	13.2385i	−0.862857	+	0.505448i
$687$	−20.6826	+	20.8521i	−0.789089	+	0.795558i
$688$	3.56980	−	2.91953i	0.136097	−	0.111306i
$689$	−4.10149	+	7.10399i	−0.156254	+	0.270640i
$690$	13.4300	+	42.4566i	0.511271	+	1.61630i
$691$	−6.05515	−	10.4878i	−0.230349	−	0.398976i	0.727562	−	0.686042i	$-0.240653\pi$
$691$	−6.05515	−	10.4878i	−0.230349	−	0.398976i	−0.957911	+	0.287066i	$0.907320\pi$
$692$	−19.9225	+	13.7636i	−0.757339	+	0.523212i
$693$	−7.12890	−	2.62080i	−0.270805	−	0.0995559i
$694$	−7.81545	+	14.8985i	−0.296670	+	0.565540i
$695$	−25.0478	+	14.4613i	−0.950116	+	0.548550i
$696$	−2.56498	−	6.28772i	−0.0972253	−	0.238336i
$697$	17.9366	−	31.0671i	0.679398	−	1.17675i
$698$	5.31839	+	8.40655i	0.201304	+	0.318193i
$699$	−10.2178	+	38.7659i	−0.386475	+	1.46626i
$700$	−5.75908	+	1.43441i	−0.217673	+	0.0542158i
$701$	21.7890			0.822959			0.411480	−	0.911419i	$-0.365012\pi$
$701$	21.7890			0.822959			0.411480	+	0.911419i	$0.365012\pi$
$702$	−5.33152	+	1.73450i	−0.201225	+	0.0654644i
$703$		−	11.7641i		−	0.443691i
$704$	5.30989	+	5.51458i	0.200124	+	0.207839i
$705$	−1.41004	+	5.34961i	−0.0531052	+	0.201478i
$706$	−1.09715	−	1.73422i	−0.0412918	−	0.0652682i
$707$	−5.13197	−	31.1780i	−0.193007	−	1.17257i
$708$	−13.5947	−	11.4588i	−0.510919	−	0.430649i
$709$	−1.04092	+	0.600974i	−0.0390925	+	0.0225701i	−0.519419	−	0.854520i	$-0.673852\pi$
$709$	−1.04092	+	0.600974i	−0.0390925	+	0.0225701i	0.480326	+	0.877090i	$0.340518\pi$
$710$	8.70572	−	16.5956i	0.326720	−	0.622823i
$711$	−0.107172	−	13.1250i	−0.00401927	−	0.492225i
$712$	−6.06824	+	0.740606i	−0.227417	+	0.0277554i
$713$	−25.4332	−	44.0516i	−0.952482	−	1.64975i
$714$	−10.7497	+	16.4904i	−0.402298	+	0.617138i
$715$	1.56438	+	0.903197i	0.0585046	+	0.0337777i
$716$	−6.33827	+	0.514294i	−0.236872	+	0.0192201i
$717$	−0.506584	−	0.502464i	−0.0189187	−	0.0187649i
$718$	−0.731895	−	18.0697i	−0.0273141	−	0.674355i
$719$	20.8544			0.777736			0.388868	−	0.921293i	$-0.372866\pi$
$719$	20.8544			0.777736			0.388868	+	0.921293i	$0.372866\pi$
$720$	−18.9834	−	22.8286i	−0.707468	−	0.850771i
$721$	−19.3704	+	15.8812i	−0.721393	+	0.591446i
$722$	25.0646	−	1.01522i	0.932807	−	0.0377824i
$723$	−29.9787	+	8.16411i	−1.11492	+	0.303626i
$724$	−1.01626	+	0.0824604i	−0.0377690	+	0.00306462i
$725$	0.777369	−	1.34644i	0.0288708	−	0.0500056i
$726$	16.6710	−	18.2273i	0.618720	−	0.676478i
$727$	−7.96139	+	4.59651i	−0.295272	+	0.170475i	−0.640317	−	0.768111i	$-0.721197\pi$
$727$	−7.96139	+	4.59651i	−0.295272	+	0.170475i	0.345045	+	0.938586i	$0.387864\pi$
$728$	4.12813	+	3.94416i	0.152999	+	0.146180i
$729$	0.661326	+	26.9919i	0.0244936	+	0.999700i
$730$	13.0934	−	24.9598i	0.484608	−	0.923804i
$731$	3.03271	−	1.75093i	0.112169	−	0.0647606i
$732$	8.56044	+	23.6831i	0.316403	+	0.875352i
$733$	−10.3352	+	17.9011i	−0.381739	+	0.661191i	−0.991311	−	0.131539i	$-0.958008\pi$
$733$	−10.3352	+	17.9011i	−0.381739	+	0.661191i	0.609572	+	0.792731i	$0.291341\pi$
$734$	−33.4700	+	21.1748i	−1.23540	+	0.781575i
$735$	−2.05512	−	29.9275i	−0.0758043	−	1.10389i
$736$	39.4387	+	13.1216i	1.45373	+	0.483670i
$737$			9.50362i			0.350070i
$738$	−42.1246	+	27.1342i	−1.55063	+	0.998824i
$739$		−	12.0919i		−	0.444807i	−0.974955	−	0.222403i	$-0.928610\pi$
$739$		−	12.0919i		−	0.444807i	0.974955	−	0.222403i	$-0.0713902\pi$
$740$	−22.1942	+	46.8229i	−0.815876	+	1.72125i
$741$	1.04548	−	1.05406i	0.0384068	−	0.0387217i
$742$	12.6537	−	38.1867i	0.464533	−	1.40188i
$743$	−9.49317	−	5.48089i	−0.348271	−	0.201074i	0.315653	−	0.948875i	$-0.397777\pi$
$743$	−9.49317	−	5.48089i	−0.348271	−	0.201074i	−0.663923	+	0.747801i	$0.731110\pi$
$744$	26.7953	+	20.7904i	0.982364	+	0.762212i
$745$	34.3031	−	19.8049i	1.25677	−	0.725596i
$746$	28.7075	+	15.0593i	1.05106	+	0.551362i
$747$	−16.4120	+	0.134012i	−0.600483	+	0.00490326i
$748$	3.30423	+	4.78281i	0.120815	+	0.174877i
$749$	7.32347	−	19.4294i	0.267594	−	0.709935i
$750$	−5.06603	+	22.9525i	−0.184985	+	0.838108i
$751$	−1.03029	+	1.78452i	−0.0375959	+	0.0651179i	−0.884211	−	0.467088i	$-0.845303\pi$
$751$	−1.03029	+	1.78452i	−0.0375959	+	0.0651179i	0.846615	+	0.532205i	$0.178637\pi$
$752$	3.26913	+	3.99726i	0.119213	+	0.145765i
$753$	−12.8315	+	48.6818i	−0.467604	+	1.77406i
$754$	−1.49442	+	0.0605300i	−0.0544236	+	0.00220437i
$755$			39.3874i			1.43345i
$756$	23.8863	−	13.6178i	0.868737	−	0.495274i
$757$			28.5736i			1.03853i	0.854614	+	0.519263i	$0.173794\pi$
$757$			28.5736i			1.03853i	−0.854614	+	0.519263i	$0.826206\pi$
$758$	−0.683598	−	16.8773i	−0.0248294	−	0.613011i
$759$	−3.10391	+	11.7761i	−0.112665	+	0.427444i
$760$	7.23472	+	3.07717i	0.262431	+	0.111621i
$761$	5.12616	−	8.87878i	0.185823	−	0.321855i	−0.758030	−	0.652219i	$-0.773838\pi$
$761$	5.12616	−	8.87878i	0.185823	−	0.321855i	0.943854	+	0.330364i	$0.107171\pi$
$762$	−33.5325	−	7.40122i	−1.21475	−	0.268118i
$763$	−19.4969	−	7.34892i	−0.705836	−	0.266049i
$764$	19.8606	−	13.7208i	0.718531	−	0.496401i
$765$	−11.4318	−	19.4323i	−0.413318	−	0.702576i
$766$	−13.6517	+	26.0242i	−0.493258	+	0.940292i
$767$	−3.39130	+	1.95797i	−0.122453	+	0.0706981i
$768$	−27.6522	+	1.83155i	−0.997814	+	0.0660902i
$769$	10.9009	+	6.29364i	0.393096	+	0.226954i	0.683501	−	0.729950i	$-0.260457\pi$
$769$	10.9009	+	6.29364i	0.393096	+	0.226954i	−0.290404	+	0.956904i	$0.593790\pi$
$770$	−8.40918	−	2.78650i	−0.303046	−	0.100419i
$771$	21.1873	−	21.3611i	0.763044	−	0.769300i
$772$	−19.4203	+	40.9708i	−0.698952	+	1.47457i
$773$		−	14.7573i		−	0.530784i	−0.964141	−	0.265392i	$-0.914499\pi$
$773$		−	14.7573i		−	0.530784i	0.964141	−	0.265392i	$-0.0855014\pi$
$774$	−4.88558	+	0.237858i	−0.175609	+	0.00854962i
$775$			7.76480i			0.278920i
$776$	−13.3712	+	10.0607i	−0.479997	+	0.361157i
$777$	−39.1057	−	27.8104i	−1.40291	−	0.997692i
$778$	7.15806	+	11.3144i	0.256629	+	0.405642i
$779$	6.63417	−	11.4907i	0.237694	−	0.411698i
$780$	−6.14978	+	2.22289i	−0.220197	+	0.0795921i
$781$	4.43856	−	2.56260i	0.158824	−	0.0916971i
$782$	27.9498	+	14.6619i	0.999484	+	0.524308i
$783$	−1.77885	+	6.97958i	−0.0635708	+	0.249430i
$784$	−23.7381	−	14.8493i	−0.847791	−	0.530331i
$785$	−19.1975	+	11.0837i	−0.685187	+	0.395593i
$786$	30.7971	+	28.1676i	1.09850	+	1.00471i
$787$	−1.24450	+	2.15554i	−0.0443617	+	0.0768367i	−0.887354	−	0.461089i	$-0.847459\pi$
$787$	−1.24450	+	2.15554i	−0.0443617	+	0.0768367i	0.842992	+	0.537926i	$0.180792\pi$
$788$	52.9389	−	4.29552i	1.88587	−	0.153022i
$789$	1.17419	−	0.319768i	0.0418024	−	0.0113840i
$790$	−0.619557	−	15.2962i	−0.0220429	−	0.544214i
$791$	−11.8391	+	9.70649i	−0.420950	+	0.345123i
$792$	−1.04947	−	8.05170i	−0.0372914	−	0.286105i
$793$	5.54641			0.196959
$794$	−36.4546	+	1.47656i	−1.29373	+	0.0524011i
$795$	32.7127	+	32.4466i	1.16020	+	1.15076i
$796$	−4.12531	−	50.8412i	−0.146218	−	1.80202i
$797$	31.8295	+	18.3768i	1.12746	+	0.650938i	0.943294	−	0.331957i	$-0.107709\pi$
$797$	31.8295	+	18.3768i	1.12746	+	0.650938i	0.184164	+	0.982896i	$0.441042\pi$
$798$	−3.97597	+	6.09926i	−0.140748	+	0.215912i
$799$	1.96060	+	3.39586i	0.0693611	+	0.120137i
$800$	−4.21225	−	4.74484i	−0.148926	−	0.167755i
$801$	5.64168	+	3.19609i	0.199339	+	0.112928i
$802$	12.5973	+	6.60830i	0.444827	+	0.233347i
$803$	6.67558	−	3.85415i	0.235576	−	0.136010i
$804$	−26.3053	−	22.1725i	−0.927717	−	0.781963i
$805$	−47.4594	+	7.81193i	−1.67272	+	0.275334i
$806$	6.31248	−	3.99358i	0.222348	−	0.140668i
$807$	−6.09654	+	23.1299i	−0.214608	+	0.814211i
$808$	26.9920	−	20.3092i	0.949575	−	0.714474i
$809$			28.3360i			0.996241i	0.867108	+	0.498121i	$0.165976\pi$
$809$			28.3360i			0.996241i	−0.867108	+	0.498121i	$0.834024\pi$
$810$	1.78814	+	31.4405i	0.0628288	+	1.10471i
$811$	38.2190			1.34205			0.671024	−	0.741435i	$-0.265855\pi$
$811$	38.2190			1.34205			0.671024	+	0.741435i	$0.265855\pi$
$812$	7.11742	−	1.77274i	0.249773	−	0.0622109i
$813$	3.93326	−	14.9226i	0.137945	−	0.523357i
$814$	−11.9757	+	7.57638i	−0.419746	+	0.265552i
$815$	−23.0683	+	39.9555i	−0.808048	+	1.39958i
$816$	−20.9474	−	2.01270i	−0.733307	−	0.0704585i
$817$	1.12170	−	0.647614i	0.0392433	−	0.0226571i
$818$	9.21887	+	4.83602i	0.322330	+	0.169088i
$819$	−1.03232	−	5.96715i	−0.0360722	−	0.208509i
$820$	−48.0835	+	33.2188i	−1.67915	+	1.16005i
$821$	−6.91469	−	11.9766i	−0.241324	−	0.417986i	0.719767	−	0.694215i	$-0.244248\pi$
$821$	−6.91469	−	11.9766i	−0.241324	−	0.417986i	−0.961092	+	0.276229i	$0.910915\pi$
$822$	43.6986	−	13.8229i	1.52416	−	0.482128i
$823$	7.03157	−	12.1790i	0.245105	−	0.424535i	−0.717056	−	0.697016i	$-0.754511\pi$
$823$	7.03157	−	12.1790i	0.245105	−	0.424535i	0.962161	+	0.272481i	$0.0878442\pi$
$824$	−24.6416	−	10.4809i	−0.858431	−	0.365120i
$825$	1.30915	−	1.31988i	0.0455786	−	0.0459523i
$826$	14.3461	−	12.7670i	0.499165	−	0.444219i
$827$	32.8815			1.14340			0.571701	−	0.820462i	$-0.306284\pi$
$827$	32.8815			1.14340			0.571701	+	0.820462i	$0.306284\pi$
$828$	−25.3537	−	36.0656i	−0.881100	−	1.25337i
$829$	55.3869			1.92367			0.961834	−	0.273634i	$-0.0882256\pi$
$829$	55.3869			1.92367			0.961834	+	0.273634i	$0.0882256\pi$
$830$	−19.1270	+	0.774720i	−0.663907	+	0.0268909i
$831$	−9.08767	+	2.47484i	−0.315248	+	0.0858514i
$832$	−1.69093	+	5.86476i	−0.0586225	+	0.203324i
$833$	−15.9720	−	14.0345i	−0.553397	−	0.486267i
$834$	19.3251	−	21.1292i	0.669175	−	0.731643i
$835$	−7.36427	+	4.25176i	−0.254851	+	0.147138i
$836$	1.22213	+	1.76901i	0.0422682	+	0.0611824i
$837$	−9.73519	−	34.6299i	−0.336497	−	1.19699i
$838$	−0.198713	−	0.104240i	−0.00686441	−	0.00360093i
$839$	−0.953627	−	1.65173i	−0.0329229	−	0.0570241i	0.849095	−	0.528241i	$-0.177148\pi$
$839$	−0.953627	−	1.65173i	−0.0329229	−	0.0570241i	−0.882017	+	0.471217i	$0.843815\pi$
$840$	27.3319	−	16.7749i	0.943041	−	0.578790i
$841$	13.5393	−	23.4507i	0.466872	−	0.808646i
$842$	−16.4767	+	10.4240i	−0.567825	+	0.359234i
$843$	11.7377	−	3.19654i	0.404269	−	0.110095i
$844$	16.3384	+	7.74448i	0.562392	+	0.266576i
$845$		−	30.7242i		−	1.05695i
$846$	−0.266340	−	5.47061i	−0.00915696	−	0.188083i
$847$	16.9159	+	20.6325i	0.581238	+	0.708942i
$848$	42.4436	−	6.93350i	1.45752	−	0.238097i
$849$	11.9806	−	12.0788i	0.411173	−	0.414544i
$850$	−2.57588	−	4.07157i	−0.0883518	−	0.139654i
$851$	−38.4700	+	66.6319i	−1.31873	+	2.28411i
$852$	−3.26231	+	18.2643i	−0.111765	+	0.625725i
$853$	−15.0846	−	26.1273i	−0.516487	−	0.894582i	−0.999817	−	0.0191438i	$-0.993906\pi$
$853$	−15.0846	−	26.1273i	−0.516487	−	0.894582i	0.483329	−	0.875439i	$-0.339427\pi$
$854$	−26.6385	+	5.50040i	−0.911551	+	0.188220i
$855$	−4.22825	−	7.18737i	−0.144603	−	0.245803i
$856$	22.0339	−	2.68916i	0.753104	−	0.0919136i
$857$	9.90140	+	17.1497i	0.338225	+	0.585823i	0.984099	−	0.177621i	$-0.0568401\pi$
$857$	9.90140	+	17.1497i	0.338225	+	0.585823i	−0.645874	+	0.763444i	$0.723507\pi$
$858$	−1.74633	−	0.385446i	−0.0596187	−	0.0131589i
$859$	−20.3948	+	35.3248i	−0.695862	+	1.20527i	0.274028	+	0.961722i	$0.411644\pi$
$859$	−20.3948	+	35.3248i	−0.695862	+	1.20527i	−0.969889	+	0.243546i	$0.921689\pi$
$860$	−5.68633	+	0.461395i	−0.193902	+	0.0157335i
$861$	−22.5138	−	49.2172i	−0.767268	−	1.67732i
$862$	−0.0314292	−	0.775953i	−0.00107048	−	0.0264291i
$863$		−	11.3171i		−	0.385240i	−0.981273	−	0.192620i	$-0.938302\pi$
$863$		−	11.3171i		−	0.385240i	0.981273	−	0.192620i	$-0.0616985\pi$
$864$	24.7350	+	15.8802i	0.841501	+	0.540255i
$865$	29.9556			1.01852
$866$	−1.75381	−	43.2997i	−0.0595970	−	1.47138i
$867$	13.0204	+	3.43188i	0.442194	+	0.116553i
$868$	−26.3573	+	25.4406i	−0.894626	+	0.863511i
$869$	2.09334	−	3.62578i	0.0710118	−	0.122996i
$870$	−1.81063	+	8.20338i	−0.0613862	+	0.278121i
$871$	−6.56207	+	3.78861i	−0.222347	+	0.128372i
$872$	−2.69851	−	22.1105i	−0.0913829	−	0.748756i
$873$	17.7478	−	0.144920i	0.600673	−	0.00490480i
$874$	10.3377	+	5.42296i	0.349679	+	0.183434i
$875$	−23.7567	−	8.95454i	−0.803123	−	0.302719i
$876$	−4.90651	+	27.4695i	−0.165776	+	0.928108i
$877$	36.7423	+	21.2132i	1.24070	+	0.716317i	0.969236	−	0.246132i	$-0.0791596\pi$
$877$	36.7423	+	21.2132i	1.24070	+	0.716317i	0.271462	+	0.962449i	$0.412493\pi$
$878$	23.4796	−	14.8543i	0.792398	−	0.501310i
$879$	−28.8168	−	28.5824i	−0.971966	−	0.964062i
$880$	−1.52684	−	9.34660i	−0.0514698	−	0.315074i
$881$	−12.9928			−0.437739			−0.218869	−	0.975754i	$-0.570237\pi$
$881$	−12.9928			−0.437739			−0.218869	+	0.975754i	$0.570237\pi$
$882$	10.8757	+	27.6355i	0.366204	+	0.930535i
$883$			39.5864i			1.33219i	0.745867	+	0.666094i	$0.232035\pi$
$883$			39.5864i			1.33219i	−0.745867	+	0.666094i	$0.767965\pi$
$884$	−1.98521	+	4.18817i	−0.0667698	+	0.140864i
$885$	5.77948	+	21.2224i	0.194275	+	0.713382i
$886$	24.9620	+	39.4564i	0.838616	+	1.32556i
$887$	20.9394	−	36.2682i	0.703078	−	1.21777i	−0.264303	−	0.964440i	$-0.585142\pi$
$887$	20.9394	−	36.2682i	0.703078	−	1.21777i	0.967381	−	0.253327i	$-0.0815248\pi$
$888$	6.96901	−	50.8239i	0.233865	−	1.70554i
$889$	13.0821	−	34.7073i	0.438761	−	1.16405i
$890$	6.69715	+	3.51318i	0.224489	+	0.117762i
$891$	−4.18380	+	7.52784i	−0.140163	+	0.252192i
$892$	−24.6159	+	17.0060i	−0.824202	+	0.569405i
$893$	0.725163	+	1.25602i	0.0242666	+	0.0420311i
$894$	−26.4659	+	28.9366i	−0.885153	+	0.967783i
$895$	6.81286	+	3.93340i	0.227729	+	0.131479i
$896$	2.30515	−	29.8444i	0.0770097	−	0.997030i
$897$	−9.36851	+	2.55133i	−0.312806	+	0.0851863i
$898$	−2.32029	−	57.2855i	−0.0774291	−	1.91164i
$899$		−	9.59621i		−	0.320052i
$900$	0.599017	+	6.70297i	0.0199672	+	0.223432i
$901$	32.6571			1.08796
$902$	−15.9699	+	0.646847i	−0.531741	+	0.0215376i
$903$	0.498933	−	5.25967i	0.0166035	−	0.175031i
$904$	−15.0608	−	6.40587i	−0.500915	−	0.213056i
$905$	1.09235	+	0.630670i	0.0363110	+	0.0209642i
$906$	−11.7604	−	37.1785i	−0.390713	−	1.23517i
$907$	−28.0457	+	16.1922i	−0.931241	+	0.537653i	−0.887204	−	0.461377i	$-0.847355\pi$
$907$	−28.0457	+	16.1922i	−0.931241	+	0.537653i	−0.0440375	+	0.999030i	$0.514022\pi$
$908$	9.64029	−	6.66005i	0.319924	−	0.221022i
$909$	−35.8270	+	0.292546i	−1.18831	+	0.00970314i
$910$	−1.42829	−	6.91721i	−0.0473473	−	0.229303i
$911$	−12.7121	+	7.33934i	−0.421171	+	0.243163i	−0.695578	−	0.718450i	$-0.744852\pi$
$911$	−12.7121	+	7.33934i	−0.421171	+	0.243163i	0.274407	+	0.961614i	$0.411518\pi$
$912$	−7.74777	−	0.744431i	−0.256554	−	0.0246506i
$913$	−4.53382	−	2.61760i	−0.150048	−	0.0866300i
$914$	7.89317	+	12.4764i	0.261083	+	0.412682i
$915$	7.94017	−	30.1245i	0.262494	−	0.995887i
$916$	14.5258	−	30.6449i	0.479945	−	1.01253i
$917$	−34.8610	+	28.5814i	−1.15121	+	0.943842i
$918$	16.5928	+	14.9291i	0.547645	+	0.492735i
$919$	−18.8799			−0.622789			−0.311395	−	0.950281i	$-0.600796\pi$
$919$	−18.8799			−0.622789			−0.311395	+	0.950281i	$0.600796\pi$
$920$	−30.9148	−	41.0875i	−1.01923	−	1.35461i
$921$	34.5735	+	9.11281i	1.13923	+	0.300277i
$922$	−1.57044	+	0.993540i	−0.0517198	+	0.0327205i
$923$	3.53886	+	2.04316i	0.116483	+	0.0672514i
$924$	8.76958	+	0.119391i	0.288498	+	0.00392768i
$925$	10.1714	−	5.87247i	0.334434	−	0.193085i
$926$	12.9337	−	24.6554i	0.425028	−	0.810226i
$927$	14.4015	+	24.4803i	0.473008	+	0.804040i
$928$	5.20576	+	5.86397i	0.170888	+	0.192494i
$929$	−13.0046	−	22.5247i	−0.426668	−	0.739011i	0.569906	−	0.821710i	$-0.306980\pi$
$929$	−13.0046	−	22.5247i	−0.426668	−	0.739011i	−0.996575	+	0.0826984i	$0.973646\pi$
$930$	−12.6537	−	40.0025i	−0.414931	−	1.31173i
$931$	−5.90752	−	5.19090i	−0.193611	−	0.170125i
$932$	−3.74387	−	46.1402i	−0.122634	−	1.51137i
$933$	28.2842	−	28.5161i	0.925982	−	0.933574i
$934$	0.770793	+	19.0300i	0.0252211	+	0.622682i
$935$		−	7.19147i		−	0.235186i
$936$	5.14117	−	3.93444i	0.168044	−	0.128601i
$937$			37.1170i			1.21256i	0.795252	+	0.606279i	$0.207339\pi$
$937$			37.1170i			1.21256i	−0.795252	+	0.606279i	$0.792661\pi$
$938$	27.7593	−	24.7037i	0.906375	−	0.806605i
$939$	33.3528	−	9.08297i	1.08843	−	0.296412i
$940$	−0.516646	−	6.36725i	−0.0168511	−	0.207677i
$941$	21.8518	+	12.6162i	0.712349	+	0.411275i	0.811930	−	0.583755i	$-0.198417\pi$
$941$	21.8518	+	12.6162i	0.712349	+	0.411275i	−0.0995812	+	0.995029i	$0.531750\pi$
$942$	14.8114	−	16.1941i	0.482583	−	0.527633i
$943$	−75.1520	+	43.3890i	−2.44729	+	1.41294i
$944$	19.2021	+	7.26439i	0.624976	+	0.236436i
$945$	−33.8876	−	2.93560i	−1.10236	−	0.0954950i
$946$	−1.38166	−	0.724791i	−0.0449217	−	0.0235650i
$947$	30.0858	+	52.1102i	0.977658	+	1.69335i	0.670868	+	0.741577i	$0.265922\pi$
$947$	30.0858	+	52.1102i	0.977658	+	1.69335i	0.306791	+	0.951777i	$0.400745\pi$
$948$	5.15200	+	14.2534i	0.167329	+	0.462928i
$949$	5.32244	+	3.07291i	0.172774	+	0.0997509i
$950$	−0.952733	−	1.50594i	−0.0309107	−	0.0488592i
$951$	−0.825281	−	3.03045i	−0.0267616	−	0.0982690i
$952$	5.38120	−	22.0838i	0.174406	−	0.715741i
$953$		−	32.8517i		−	1.06417i	−0.846691	−	0.532085i	$-0.821409\pi$
$953$		−	32.8517i		−	1.06417i	0.846691	−	0.532085i	$-0.178591\pi$
$954$	−40.5661	−	20.8595i	−1.31338	−	0.675352i
$955$	−29.8625			−0.966329
$956$	0.744489	+	0.352891i	0.0240785	+	0.0114133i
$957$	−1.61792	+	1.63119i	−0.0523000	+	0.0527288i
$958$	22.9432	+	36.2652i	0.741260	+	1.17168i
$959$	8.04045	+	48.8477i	0.259640	+	1.57737i
$960$	29.4329	+	17.5800i	0.949942	+	0.567391i
$961$	8.46309	+	14.6585i	0.273003	+	0.472855i
$962$	−10.0054	−	5.24864i	−0.322588	−	0.169223i
$963$	−20.4851	−	11.6051i	−0.660122	−	0.373969i
$964$	29.5180	−	20.3927i	0.950709	−	0.656803i
$965$	48.5757	−	28.0452i	1.56371	−	0.902807i
$966$	42.4652	−	21.5444i	1.36630	−	0.693179i
$967$	19.8245	−	34.3370i	0.637512	−	1.10420i	−0.348464	−	0.937322i	$-0.613297\pi$
$967$	19.8245	−	34.3370i	0.637512	−	1.10420i	0.985977	−	0.166882i	$-0.0533699\pi$
$968$	−11.1638	+	26.2471i	−0.358818	+	0.843615i
$969$	−5.71522	−	1.50641i	−0.183599	−	0.0483928i
$970$	20.6838	−	0.837777i	0.664117	−	0.0268994i
$971$			26.0169i			0.834923i	0.908695	+	0.417461i	$0.137080\pi$
$971$			26.0169i			0.834923i	−0.908695	+	0.417461i	$0.862920\pi$
$972$	−11.0755	−	29.1433i	−0.355245	−	0.934773i
$973$	19.6090	+	23.9173i	0.628637	+	0.766754i
$974$	−49.3075	+	1.99715i	−1.57992	+	0.0639929i
$975$	1.43324	+	0.377771i	0.0459005	+	0.0120984i
$976$	−18.4090	−	22.5093i	−0.589259	−	0.720504i
$977$	−5.15989	−	2.97906i	−0.165079	−	0.0953086i	0.415184	−	0.909737i	$-0.363717\pi$
$977$	−5.15989	−	2.97906i	−0.165079	−	0.0953086i	−0.580264	+	0.814429i	$0.697050\pi$
$978$	9.84457	−	44.6025i	0.314795	−	1.42623i
$979$	1.03414	+	1.79118i	0.0330511	+	0.0572462i
$980$	13.7197	+	31.8058i	0.438258	+	1.01600i
$981$	−11.6454	+	20.5563i	−0.371809	+	0.656311i
$982$	8.17189	−	15.5780i	0.260775	−	0.497114i
$983$	15.4665	+	26.7888i	0.493305	+	0.854429i	0.999970	−	0.00771366i	$-0.00245536\pi$
$983$	15.4665	+	26.7888i	0.493305	+	0.854429i	−0.506665	+	0.862143i	$0.669122\pi$
$984$	35.4684	−	45.7128i	1.13069	−	1.45727i
$985$	−56.9027	−	32.8528i	−1.81307	−	1.04678i
$986$	3.18343	+	5.03190i	0.101381	+	0.160248i
$987$	5.88950	+	0.558679i	0.187465	+	0.0177829i
$988$	−0.734264	+	1.54907i	−0.0233601	+	0.0492825i
$989$	−8.47109			−0.269365
$990$	−4.59352	+	8.93314i	−0.145992	+	0.283914i
$991$	1.73685			0.0551729			0.0275864	−	0.999619i	$-0.491218\pi$
$991$	1.73685			0.0551729			0.0275864	+	0.999619i	$0.491218\pi$
$992$	−37.1590	−	12.3632i	−1.17980	−	0.392531i
$993$	24.5713	−	6.69151i	0.779748	−	0.212349i
$994$	−19.0227	−	6.30346i	−0.603365	−	0.199934i
$995$	−31.5510	+	54.6480i	−1.00023	+	1.73246i
$996$	17.8230	−	6.44226i	0.564743	−	0.204131i
$997$	14.3421	+	24.8413i	0.454220	+	0.786733i	0.998643	−	0.0520783i	$-0.0165845\pi$
$997$	14.3421	+	24.8413i	0.454220	+	0.786733i	−0.544423	+	0.838811i	$0.683251\pi$
$998$	−38.7292	−	20.3165i	−1.22595	−	0.643109i
$999$	−38.0005	+	38.9429i	−1.20228	+	1.23210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cc.b.293.1	✓	168
7.6	odd	2	inner	504.2.cc.b.293.2	yes	168
8.5	even	2	inner	504.2.cc.b.293.28	yes	168
9.2	odd	6	inner	504.2.cc.b.461.27	yes	168
56.13	odd	2	inner	504.2.cc.b.293.27	yes	168
63.20	even	6	inner	504.2.cc.b.461.28	yes	168
72.29	odd	6	inner	504.2.cc.b.461.2	yes	168
504.461	even	6	inner	504.2.cc.b.461.1	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.b.293.1	✓	168	1.1	even	1	trivial
504.2.cc.b.293.2	yes	168	7.6	odd	2	inner
504.2.cc.b.293.27	yes	168	56.13	odd	2	inner
504.2.cc.b.293.28	yes	168	8.5	even	2	inner
504.2.cc.b.461.1	yes	168	504.461	even	6	inner
504.2.cc.b.461.2	yes	168	72.29	odd	6	inner
504.2.cc.b.461.27	yes	168	9.2	odd	6	inner
504.2.cc.b.461.28	yes	168	63.20	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41305 + 0.0572344i) q^{2} +(-1.67485 - 0.441454i) q^{3} +(1.99345 - 0.161751i) q^{4} +(-2.14271 - 1.23709i) q^{5} +(2.39192 + 0.527939i) q^{6} +(-0.933167 + 2.47572i) q^{7} +(-2.80759 + 0.342656i) q^{8} +(2.61024 + 1.47874i) q^{9} +O(q^{10})\)	\(q+(-1.41305 + 0.0572344i) q^{2} +(-1.67485 - 0.441454i) q^{3} +(1.99345 - 0.161751i) q^{4} +(-2.14271 - 1.23709i) q^{5} +(2.39192 + 0.527939i) q^{6} +(-0.933167 + 2.47572i) q^{7} +(-2.80759 + 0.342656i) q^{8} +(2.61024 + 1.47874i) q^{9} +(3.09857 + 1.62545i) q^{10} +(0.478464 + 0.828724i) q^{11} +(-3.41013 - 0.609107i) q^{12} +(-0.381479 + 0.660741i) q^{13} +(1.17692 - 3.55174i) q^{14} +(3.04260 + 3.01785i) q^{15} +(3.94767 - 0.644883i) q^{16} +3.03743 q^{17} +(-3.77304 - 1.94014i) q^{18} +1.12344 q^{19} +(-4.47149 - 2.11950i) q^{20} +(2.65583 - 3.73451i) q^{21} +(-0.723527 - 1.14365i) q^{22} +(-6.36320 - 3.67380i) q^{23} +(4.85356 + 0.665525i) q^{24} +(0.560807 + 0.971347i) q^{25} +(0.501233 - 0.955496i) q^{26} +(-3.71896 - 3.62896i) q^{27} +(-1.45977 + 5.08616i) q^{28} +(-0.693080 - 1.20045i) q^{29} +(-4.47208 - 4.09025i) q^{30} +(5.99538 + 3.46144i) q^{31} +(-5.54137 + 1.13720i) q^{32} +(-0.435512 - 1.59921i) q^{33} +(-4.29205 + 0.173845i) q^{34} +(5.06221 - 4.15034i) q^{35} +(5.44256 + 2.52558i) q^{36} -10.4715i q^{37} +(-1.58749 + 0.0642997i) q^{38} +(0.930605 - 0.938235i) q^{39} +(6.43976 + 2.73905i) q^{40} +(5.90521 - 10.2281i) q^{41} +(-3.53909 + 5.42907i) q^{42} +(0.998446 - 0.576453i) q^{43} +(1.08784 + 1.57463i) q^{44} +(-3.76365 - 6.39762i) q^{45} +(9.20182 + 4.82708i) q^{46} +(0.645481 + 1.11801i) q^{47} +(-6.89644 - 0.662632i) q^{48} +(-5.25840 - 4.62052i) q^{49} +(-0.848046 - 1.34047i) q^{50} +(-5.08723 - 1.34088i) q^{51} +(-0.653583 + 1.37886i) q^{52} +10.7516 q^{53} +(5.46280 + 4.91506i) q^{54} -2.36762i q^{55} +(1.77163 - 7.27058i) q^{56} +(-1.88160 - 0.495949i) q^{57} +(1.04807 + 1.65663i) q^{58} +(4.44494 + 2.56629i) q^{59} +(6.55340 + 5.52379i) q^{60} +(-3.63481 - 6.29568i) q^{61} +(-8.66992 - 4.54806i) q^{62} +(-6.09673 + 5.08231i) q^{63} +(7.76517 - 1.92408i) q^{64} +(1.63480 - 0.943851i) q^{65} +(0.706932 + 2.23484i) q^{66} +(8.60083 + 4.96569i) q^{67} +(6.05495 - 0.491306i) q^{68} +(9.03559 + 8.96211i) q^{69} +(-6.91564 + 6.15439i) q^{70} -5.35590i q^{71} +(-7.83519 - 3.25728i) q^{72} -8.05526i q^{73} +(0.599327 + 14.7967i) q^{74} +(-0.510463 - 1.87443i) q^{75} +(2.23953 - 0.181718i) q^{76} +(-2.49818 + 0.411206i) q^{77} +(-1.26130 + 1.37904i) q^{78} +(-2.18757 - 3.78898i) q^{79} +(-9.25651 - 3.50185i) q^{80} +(4.62668 + 7.71970i) q^{81} +(-7.75898 + 14.7909i) q^{82} +(-4.73789 + 2.73542i) q^{83} +(4.69020 - 7.87414i) q^{84} +(-6.50833 - 3.75758i) q^{85} +(-1.37787 + 0.871706i) q^{86} +(0.630862 + 2.31654i) q^{87} +(-1.62730 - 2.16277i) q^{88} +2.16137 q^{89} +(5.68441 + 8.82477i) q^{90} +(-1.27983 - 1.56102i) q^{91} +(-13.2790 - 6.29427i) q^{92} +(-8.51330 - 8.44407i) q^{93} +(-0.976089 - 1.54286i) q^{94} +(-2.40722 - 1.38981i) q^{95} +(9.78298 + 0.541622i) q^{96} +(5.12352 - 2.95807i) q^{97} +(7.69486 + 6.22809i) q^{98} +(0.0234407 + 2.87069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

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