LMFDB - Embedded newform 471.2.e.c.169.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(169,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("471.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			169.13
Character	$\chi$	$=$	471.169
Dual form			471.2.e.c.301.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.49732 q^{2} +(-0.500000 - 0.866025i) q^{3} +4.23662 q^{4} +(1.51688 + 2.62731i) q^{5} +(-1.24866 - 2.16274i) q^{6} -1.77348 q^{7} +5.58556 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+2.49732 q^{2} +(-0.500000 - 0.866025i) q^{3} +4.23662 q^{4} +(1.51688 + 2.62731i) q^{5} +(-1.24866 - 2.16274i) q^{6} -1.77348 q^{7} +5.58556 q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.78813 + 6.56123i) q^{10} +(0.957157 + 1.65784i) q^{11} +(-2.11831 - 3.66902i) q^{12} +(1.94451 - 3.36798i) q^{13} -4.42896 q^{14} +(1.51688 - 2.62731i) q^{15} +5.47570 q^{16} +(-2.89691 - 5.01759i) q^{17} +(-1.24866 + 2.16274i) q^{18} +(1.60987 + 2.78837i) q^{19} +(6.42642 + 11.1309i) q^{20} +(0.886742 + 1.53588i) q^{21} +(2.39033 + 4.14017i) q^{22} -8.14909 q^{23} +(-2.79278 - 4.83724i) q^{24} +(-2.10182 + 3.64046i) q^{25} +(4.85606 - 8.41094i) q^{26} +1.00000 q^{27} -7.51358 q^{28} -1.03859 q^{29} +(3.78813 - 6.56123i) q^{30} +(2.29925 - 3.98243i) q^{31} +2.50348 q^{32} +(0.957157 - 1.65784i) q^{33} +(-7.23452 - 12.5306i) q^{34} +(-2.69016 - 4.65949i) q^{35} +(-2.11831 + 3.66902i) q^{36} +(4.66526 - 8.08046i) q^{37} +(4.02035 + 6.96345i) q^{38} -3.88901 q^{39} +(8.47260 + 14.6750i) q^{40} -0.436255 q^{41} +(2.21448 + 3.83559i) q^{42} +(-0.232170 + 0.402130i) q^{43} +(4.05511 + 7.02365i) q^{44} -3.03375 q^{45} -20.3509 q^{46} +(-5.04515 + 8.73846i) q^{47} +(-2.73785 - 4.74210i) q^{48} -3.85475 q^{49} +(-5.24893 + 9.09141i) q^{50} +(-2.89691 + 5.01759i) q^{51} +(8.23813 - 14.2689i) q^{52} +(0.137809 - 0.238693i) q^{53} +2.49732 q^{54} +(-2.90378 + 5.02949i) q^{55} -9.90590 q^{56} +(1.60987 - 2.78837i) q^{57} -2.59370 q^{58} +6.74876 q^{59} +(6.42642 - 11.1309i) q^{60} +(5.13322 + 8.89099i) q^{61} +(5.74198 - 9.94540i) q^{62} +(0.886742 - 1.53588i) q^{63} -4.69942 q^{64} +11.7983 q^{65} +(2.39033 - 4.14017i) q^{66} -6.32238 q^{67} +(-12.2731 - 21.2576i) q^{68} +(4.07454 + 7.05732i) q^{69} +(-6.71819 - 11.6362i) q^{70} +(-7.15074 + 12.3854i) q^{71} +(-2.79278 + 4.83724i) q^{72} +(1.85628 + 3.21518i) q^{73} +(11.6507 - 20.1795i) q^{74} +4.20364 q^{75} +(6.82039 + 11.8133i) q^{76} +(-1.69750 - 2.94016i) q^{77} -9.71212 q^{78} +0.892391 q^{79} +(8.30596 + 14.3863i) q^{80} +(-0.500000 - 0.866025i) q^{81} -1.08947 q^{82} +(7.66274 - 13.2722i) q^{83} +(3.75679 + 6.50695i) q^{84} +(8.78850 - 15.2221i) q^{85} +(-0.579803 + 1.00425i) q^{86} +(0.519295 + 0.899446i) q^{87} +(5.34625 + 9.25999i) q^{88} +(3.61146 + 6.25524i) q^{89} -7.57625 q^{90} +(-3.44855 + 5.97307i) q^{91} -34.5246 q^{92} -4.59851 q^{93} +(-12.5994 + 21.8227i) q^{94} +(-4.88393 + 8.45921i) q^{95} +(-1.25174 - 2.16807i) q^{96} +(-3.18057 + 5.50891i) q^{97} -9.62656 q^{98} -1.91431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.49732			1.76587			0.882937	−	0.469492i	$-0.155563\pi$
$2$	2.49732			1.76587			0.882937	+	0.469492i	$0.155563\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	4.23662			2.11831
$5$	1.51688	+	2.62731i	0.678367	+	1.17497i	0.975472	+	0.220122i	$0.0706455\pi$
$5$	1.51688	+	2.62731i	0.678367	+	1.17497i	−0.297105	+	0.954845i	$0.596021\pi$
$6$	−1.24866	−	2.16274i	−0.509764	−	0.882937i
$7$	−1.77348			−0.670314			−0.335157	−	0.942162i	$-0.608789\pi$
$7$	−1.77348			−0.670314			−0.335157	+	0.942162i	$0.608789\pi$
$8$	5.58556			1.97479
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	3.78813	+	6.56123i	1.19791	+	2.07484i
$11$	0.957157	+	1.65784i	0.288594	+	0.499859i	0.973474	−	0.228796i	$-0.0734790\pi$
$11$	0.957157	+	1.65784i	0.288594	+	0.499859i	−0.684881	+	0.728655i	$0.740146\pi$
$12$	−2.11831	−	3.66902i	−0.611503	−	1.05915i
$13$	1.94451	−	3.36798i	0.539309	−	0.934110i	−0.459632	−	0.888109i	$-0.652019\pi$
$13$	1.94451	−	3.36798i	0.539309	−	0.934110i	0.998941	−	0.0460012i	$-0.0146478\pi$
$14$	−4.42896			−1.18369
$15$	1.51688	−	2.62731i	0.391656	−	0.678367i
$16$	5.47570			1.36893
$17$	−2.89691	−	5.01759i	−0.702604	−	1.21695i	−0.967549	−	0.252682i	$-0.918687\pi$
$17$	−2.89691	−	5.01759i	−0.702604	−	1.21695i	0.264946	−	0.964263i	$-0.414646\pi$
$18$	−1.24866	+	2.16274i	−0.294312	+	0.509764i
$19$	1.60987	+	2.78837i	0.369328	+	0.639696i	0.989461	−	0.144802i	$-0.0462544\pi$
$19$	1.60987	+	2.78837i	0.369328	+	0.639696i	−0.620132	+	0.784497i	$0.712921\pi$
$20$	6.42642	+	11.1309i	1.43699	+	2.48894i
$21$	0.886742	+	1.53588i	0.193503	+	0.335157i
$22$	2.39033	+	4.14017i	0.509620	+	0.882687i
$23$	−8.14909			−1.69920			−0.849601	−	0.527425i	$-0.823157\pi$
$23$	−8.14909			−1.69920			−0.849601	+	0.527425i	$0.823157\pi$
$24$	−2.79278	−	4.83724i	−0.570074	−	0.987397i
$25$	−2.10182	+	3.64046i	−0.420364	+	0.728092i
$26$	4.85606	−	8.41094i	0.952351	−	1.64952i
$27$	1.00000			0.192450
$28$	−7.51358			−1.41993
$29$	−1.03859			−0.192861			−0.0964307	−	0.995340i	$-0.530743\pi$
$29$	−1.03859			−0.192861			−0.0964307	+	0.995340i	$0.530743\pi$
$30$	3.78813	−	6.56123i	0.691614	−	1.19791i
$31$	2.29925	−	3.98243i	0.412958	−	0.715265i	−0.582253	−	0.813007i	$-0.697829\pi$
$31$	2.29925	−	3.98243i	0.412958	−	0.715265i	0.995212	+	0.0977425i	$0.0311622\pi$
$32$	2.50348			0.442556
$33$	0.957157	−	1.65784i	0.166620	−	0.288594i
$34$	−7.23452	−	12.5306i	−1.24071	−	2.14897i
$35$	−2.69016	−	4.65949i	−0.454719	−	0.787597i
$36$	−2.11831	+	3.66902i	−0.353052	+	0.611503i
$37$	4.66526	−	8.08046i	0.766964	−	1.32842i	−0.172239	−	0.985055i	$-0.555100\pi$
$37$	4.66526	−	8.08046i	0.766964	−	1.32842i	0.939202	−	0.343365i	$-0.111567\pi$
$38$	4.02035	+	6.96345i	0.652187	+	1.12962i
$39$	−3.88901			−0.622740
$40$	8.47260	+	14.6750i	1.33964	+	2.32032i
$41$	−0.436255			−0.0681316			−0.0340658	−	0.999420i	$-0.510846\pi$
$41$	−0.436255			−0.0681316			−0.0340658	+	0.999420i	$0.510846\pi$
$42$	2.21448	+	3.83559i	0.341702	+	0.591845i
$43$	−0.232170	+	0.402130i	−0.0354056	+	0.0613243i	−0.883185	−	0.469024i	$-0.844606\pi$
$43$	−0.232170	+	0.402130i	−0.0354056	+	0.0613243i	0.847780	+	0.530349i	$0.177939\pi$
$44$	4.05511	+	7.02365i	0.611331	+	1.05886i
$45$	−3.03375			−0.452245
$46$	−20.3509			−3.00058
$47$	−5.04515	+	8.73846i	−0.735911	+	1.27464i	0.218412	+	0.975857i	$0.429912\pi$
$47$	−5.04515	+	8.73846i	−0.735911	+	1.27464i	−0.954323	+	0.298778i	$0.903421\pi$
$48$	−2.73785	−	4.74210i	−0.395175	−	0.684463i
$49$	−3.85475			−0.550679
$50$	−5.24893	+	9.09141i	−0.742310	+	1.28572i
$51$	−2.89691	+	5.01759i	−0.405648	+	0.702604i
$52$	8.23813	−	14.2689i	1.14242	−	1.97874i
$53$	0.137809	−	0.238693i	0.0189296	−	0.0327870i	−0.856405	−	0.516304i	$-0.827308\pi$
$53$	0.137809	−	0.238693i	0.0189296	−	0.0327870i	0.875335	+	0.483517i	$0.160641\pi$
$54$	2.49732			0.339843
$55$	−2.90378	+	5.02949i	−0.391545	+	0.678176i
$56$	−9.90590			−1.32373
$57$	1.60987	−	2.78837i	0.213232	−	0.369328i
$58$	−2.59370			−0.340569
$59$	6.74876			0.878613			0.439307	−	0.898337i	$-0.355224\pi$
$59$	6.74876			0.878613			0.439307	+	0.898337i	$0.355224\pi$
$60$	6.42642	−	11.1309i	0.829648	−	1.43699i
$61$	5.13322	+	8.89099i	0.657241	+	1.13838i	0.981327	+	0.192347i	$0.0616100\pi$
$61$	5.13322	+	8.89099i	0.657241	+	1.13838i	−0.324086	+	0.946028i	$0.605057\pi$
$62$	5.74198	−	9.94540i	0.729232	−	1.26307i
$63$	0.886742	−	1.53588i	0.111719	−	0.193503i
$64$	−4.69942			−0.587427
$65$	11.7983			1.46340
$66$	2.39033	−	4.14017i	0.294229	−	0.509620i
$67$	−6.32238			−0.772401			−0.386201	−	0.922415i	$-0.626213\pi$
$67$	−6.32238			−0.772401			−0.386201	+	0.922415i	$0.626213\pi$
$68$	−12.2731	−	21.2576i	−1.48833	−	2.57787i
$69$	4.07454	+	7.05732i	0.490518	+	0.849601i
$70$	−6.71819	−	11.6362i	−0.802977	−	1.39080i
$71$	−7.15074	+	12.3854i	−0.848637	+	1.46988i	0.0337888	+	0.999429i	$0.489243\pi$
$71$	−7.15074	+	12.3854i	−0.848637	+	1.46988i	−0.882425	+	0.470453i	$0.844091\pi$
$72$	−2.79278	+	4.83724i	−0.329132	+	0.570074i
$73$	1.85628	+	3.21518i	0.217261	+	0.376308i	0.953970	−	0.299903i	$-0.0969543\pi$
$73$	1.85628	+	3.21518i	0.217261	+	0.376308i	−0.736708	+	0.676211i	$0.763621\pi$
$74$	11.6507	−	20.1795i	1.35436	−	2.34582i
$75$	4.20364			0.485395
$76$	6.82039	+	11.8133i	0.782352	+	1.35507i
$77$	−1.69750	−	2.94016i	−0.193448	−	0.335062i
$78$	−9.71212			−1.09968
$79$	0.892391			0.100402			0.0502009	−	0.998739i	$-0.484014\pi$
$79$	0.892391			0.100402			0.0502009	+	0.998739i	$0.484014\pi$
$80$	8.30596	+	14.3863i	0.928634	+	1.60844i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.08947			−0.120312
$83$	7.66274	−	13.2722i	0.841095	−	1.45682i	−0.0478756	−	0.998853i	$-0.515245\pi$
$83$	7.66274	−	13.2722i	0.841095	−	1.45682i	0.888970	−	0.457965i	$-0.151422\pi$
$84$	3.75679	+	6.50695i	0.409899	+	0.709966i
$85$	8.78850	−	15.2221i	0.953247	−	1.65107i
$86$	−0.579803	+	1.00425i	−0.0625218	+	0.108291i
$87$	0.519295	+	0.899446i	0.0556743	+	0.0964307i
$88$	5.34625	+	9.25999i	0.569913	+	0.987118i
$89$	3.61146	+	6.25524i	0.382814	+	0.663054i	0.991463	−	0.130386i	$-0.0416216\pi$
$89$	3.61146	+	6.25524i	0.382814	+	0.663054i	−0.608649	+	0.793440i	$0.708288\pi$
$90$	−7.57625			−0.798607
$91$	−3.44855	+	5.97307i	−0.361506	+	0.626148i
$92$	−34.5246			−3.59944
$93$	−4.59851			−0.476843
$94$	−12.5994	+	21.8227i	−1.29953	+	2.25084i
$95$	−4.88393	+	8.45921i	−0.501081	+	0.867897i
$96$	−1.25174	−	2.16807i	−0.127755	−	0.221278i
$97$	−3.18057	+	5.50891i	−0.322938	+	0.559345i	−0.981093	−	0.193538i	$-0.938004\pi$
$97$	−3.18057	+	5.50891i	−0.322938	+	0.559345i	0.658155	+	0.752882i	$0.271337\pi$
$98$	−9.62656			−0.972429
$99$	−1.91431			−0.192396
$100$	−8.90462	+	15.4233i	−0.890462	+	1.54233i
$101$	19.1054			1.90106			0.950531	−	0.310631i	$-0.100540\pi$
$101$	19.1054			1.90106			0.950531	+	0.310631i	$0.100540\pi$
$102$	−7.23452	+	12.5306i	−0.716324	+	1.24071i
$103$	1.25696			0.123852			0.0619261	−	0.998081i	$-0.480276\pi$
$103$	1.25696			0.123852			0.0619261	+	0.998081i	$0.480276\pi$
$104$	10.8612	−	18.8121i	1.06502	−	1.84467i
$105$	−2.69016	+	4.65949i	−0.262532	+	0.454719i
$106$	0.344154	−	0.596093i	0.0334272	−	0.0578977i
$107$	−7.11976	+	12.3318i	−0.688293	+	1.19216i	0.284096	+	0.958796i	$0.408306\pi$
$107$	−7.11976	+	12.3318i	−0.688293	+	1.19216i	−0.972390	+	0.233363i	$0.925027\pi$
$108$	4.23662			0.407669
$109$	−6.17747	−	10.6997i	−0.591695	−	1.02485i	−0.994004	−	0.109342i	$-0.965126\pi$
$109$	−6.17747	−	10.6997i	−0.591695	−	1.02485i	0.402310	−	0.915504i	$-0.368208\pi$
$110$	−7.25166	+	12.5602i	−0.691419	+	1.19757i
$111$	−9.33051			−0.885613
$112$	−9.71107			−0.917610
$113$	−9.33519	−	16.1690i	−0.878181	−	1.52105i	−0.853335	−	0.521363i	$-0.825424\pi$
$113$	−9.33519	−	16.1690i	−0.878181	−	1.52105i	−0.0248462	−	0.999691i	$-0.507910\pi$
$114$	4.02035	−	6.96345i	0.376541	−	0.652187i
$115$	−12.3612	−	21.4101i	−1.15268	−	1.99651i
$116$	−4.40011			−0.408540
$117$	1.94451	+	3.36798i	0.179770	+	0.311370i
$118$	16.8538			1.55152
$119$	5.13762	+	8.89863i	0.470965	+	0.815736i
$120$	8.47260	−	14.6750i	0.773439	−	1.33964i
$121$	3.66770	−	6.35265i	0.333427	−	0.577513i
$122$	12.8193	+	22.2037i	1.16060	+	2.01023i
$123$	0.218127	+	0.377808i	0.0196679	+	0.0340658i
$124$	9.74107	−	16.8720i	0.874774	−	1.51515i
$125$	2.41595			0.216089
$126$	2.21448	−	3.83559i	0.197282	−	0.341702i
$127$	1.30367	−	2.25802i	0.115682	−	0.200367i	−0.802370	−	0.596827i	$-0.796428\pi$
$127$	1.30367	−	2.25802i	0.115682	−	0.200367i	0.918052	+	0.396460i	$0.129761\pi$
$128$	−16.7429			−1.47988
$129$	0.464340			0.0408828
$130$	29.4641			2.58418
$131$	−4.18835	+	7.25444i	−0.365938	+	0.633823i	−0.988926	−	0.148408i	$-0.952585\pi$
$131$	−4.18835	+	7.25444i	−0.365938	+	0.633823i	0.622988	+	0.782231i	$0.285918\pi$
$132$	4.05511	−	7.02365i	0.352952	−	0.611331i
$133$	−2.85507	−	4.94513i	−0.247566	−	0.428797i
$134$	−15.7890			−1.36396
$135$	1.51688	+	2.62731i	0.130552	+	0.226122i
$136$	−16.1809	−	28.0261i	−1.38750	−	2.40322i
$137$	−0.509339	−	0.882201i	−0.0435157	−	0.0753715i	0.843447	−	0.537212i	$-0.180523\pi$
$137$	−0.509339	−	0.882201i	−0.0435157	−	0.0753715i	−0.886963	+	0.461841i	$0.847189\pi$
$138$	10.1755	+	17.6244i	0.866192	+	1.50029i
$139$	−1.52322	+	2.63829i	−0.129198	+	0.223777i	−0.923366	−	0.383921i	$-0.874573\pi$
$139$	−1.52322	+	2.63829i	−0.129198	+	0.223777i	0.794168	+	0.607698i	$0.207907\pi$
$140$	−11.3972	−	19.7405i	−0.963236	−	1.66837i
$141$	10.0903			0.849757
$142$	−17.8577	+	30.9304i	−1.49858	+	2.59562i
$143$	7.44479			0.622564
$144$	−2.73785	+	4.74210i	−0.228154	+	0.395175i
$145$	−1.57541	−	2.72869i	−0.130831	−	0.226606i
$146$	4.63574	+	8.02933i	0.383656	+	0.664512i
$147$	1.92738	+	3.33831i	0.158967	+	0.275339i
$148$	19.7649	−	34.2338i	1.62467	−	2.81400i
$149$	20.2560			1.65943			0.829717	−	0.558185i	$-0.188502\pi$
$149$	20.2560			1.65943			0.829717	+	0.558185i	$0.188502\pi$
$150$	10.4979			0.857146
$151$	−4.13407	−	7.16042i	−0.336426	−	0.582707i	0.647332	−	0.762208i	$-0.275885\pi$
$151$	−4.13407	−	7.16042i	−0.336426	−	0.582707i	−0.983758	+	0.179502i	$0.942552\pi$
$152$	8.99200	+	15.5746i	0.729347	+	1.26327i
$153$	5.79382			0.468402
$154$	−4.23921	−	7.34253i	−0.341605	−	0.591678i
$155$	13.9507			1.12055
$156$	−16.4763			−1.31916
$157$	8.67616	−	9.04015i	0.692433	−	0.721482i
$157$	8.67616	−	9.04015i	0.692433	−	0.721482i
$158$	2.22859			0.177297
$159$	−0.275619			−0.0218580
$160$	3.79746	+	6.57739i	0.300216	+	0.519989i
$161$	14.4523			1.13900
$162$	−1.24866	−	2.16274i	−0.0981041	−	0.169921i
$163$	1.19058	+	2.06214i	0.0932532	+	0.161519i	0.908878	−	0.417062i	$-0.136940\pi$
$163$	1.19058	+	2.06214i	0.0932532	+	0.161519i	−0.815625	+	0.578581i	$0.803607\pi$
$164$	−1.84825			−0.144324
$165$	5.80755			0.452117
$166$	19.1363	−	33.1451i	1.48527	−	2.57256i
$167$	6.64180	+	11.5039i	0.513958	+	0.890201i	0.999869	+	0.0161928i	$0.00515455\pi$
$167$	6.64180	+	11.5039i	0.513958	+	0.890201i	−0.485911	+	0.874008i	$0.661512\pi$
$168$	4.95295	+	8.57876i	0.382128	+	0.661866i
$169$	−1.06221	−	1.83980i	−0.0817083	−	0.141523i
$170$	21.9477	−	38.0146i	1.68331	−	2.91558i
$171$	−3.21973			−0.246219
$172$	−0.983615	+	1.70367i	−0.0750000	+	0.129904i
$173$	−5.52778			−0.420269			−0.210135	−	0.977672i	$-0.567390\pi$
$173$	−5.52778			−0.420269			−0.210135	+	0.977672i	$0.567390\pi$
$174$	1.29685	+	2.24621i	0.0983138	+	0.170284i
$175$	3.72755	−	6.45630i	0.281776	−	0.488051i
$176$	5.24110	+	9.07786i	0.395063	+	0.684269i
$177$	−3.37438	−	5.84459i	−0.253634	−	0.439307i
$178$	9.01899	+	15.6213i	0.676002	+	1.17087i
$179$	13.2174	+	22.8932i	0.987914	+	1.71112i	0.628195	+	0.778056i	$0.283794\pi$
$179$	13.2174	+	22.8932i	0.987914	+	1.71112i	0.359719	+	0.933061i	$0.382873\pi$
$180$	−12.8528			−0.957995
$181$	0.363338	+	0.629320i	0.0270067	+	0.0467770i	0.879213	−	0.476429i	$-0.158069\pi$
$181$	0.363338	+	0.629320i	0.0270067	+	0.0467770i	−0.852206	+	0.523206i	$0.824736\pi$
$182$	−8.61215	+	14.9167i	−0.638375	+	1.10570i
$183$	5.13322	−	8.89099i	0.379458	−	0.657241i
$184$	−45.5172			−3.35557
$185$	28.3065			2.08113
$186$	−11.4840			−0.842045
$187$	5.54559	−	9.60525i	0.405534	−	0.702405i
$188$	−21.3744	+	37.0215i	−1.55889	+	2.70007i
$189$	−1.77348			−0.129002
$190$	−12.1967	+	21.1254i	−0.884845	+	1.53260i
$191$	−2.04310	−	3.53875i	−0.147833	−	0.256055i	0.782593	−	0.622534i	$-0.213897\pi$
$191$	−2.04310	−	3.53875i	−0.147833	−	0.256055i	−0.930426	+	0.366479i	$0.880563\pi$
$192$	2.34971	+	4.06982i	0.169576	+	0.293714i
$193$	1.87030	−	3.23945i	0.134627	−	0.233180i	−0.790828	−	0.612038i	$-0.790350\pi$
$193$	1.87030	−	3.23945i	0.134627	−	0.233180i	0.925455	+	0.378858i	$0.123683\pi$
$194$	−7.94290	+	13.7575i	−0.570267	+	0.987732i
$195$	−5.89915	−	10.2176i	−0.422447	−	0.731699i
$196$	−16.3311			−1.16651
$197$	−0.563137	−	0.975382i	−0.0401219	−	0.0694931i	0.845267	−	0.534344i	$-0.179441\pi$
$197$	−0.563137	−	0.975382i	−0.0401219	−	0.0694931i	−0.885389	+	0.464851i	$0.846108\pi$
$198$	−4.78066			−0.339747
$199$	−8.29349	−	14.3647i	−0.587910	−	1.01829i	−0.994506	−	0.104682i	$-0.966618\pi$
$199$	−8.29349	−	14.3647i	−0.587910	−	1.01829i	0.406596	−	0.913608i	$-0.366716\pi$
$200$	−11.7398	+	20.3340i	−0.830133	+	1.43783i
$201$	3.16119	+	5.47534i	0.222973	+	0.386201i
$202$	47.7124			3.35703
$203$	1.84192			0.129278
$204$	−12.2731	+	21.2576i	−0.859289	+	1.48833i
$205$	−0.661744	−	1.14617i	−0.0462182	−	0.0800523i
$206$	3.13904			0.218707
$207$	4.07454	−	7.05732i	0.283200	−	0.490518i
$208$	10.6475	−	18.4421i	0.738274	−	1.27873i
$209$	−3.08179	+	5.33781i	−0.213172	+	0.369224i
$210$	−6.71819	+	11.6362i	−0.463599	+	0.802977i
$211$	9.35240			0.643845			0.321923	−	0.946766i	$-0.395671\pi$
$211$	9.35240			0.643845			0.321923	+	0.946766i	$0.395671\pi$
$212$	0.583846	−	1.01125i	0.0400987	−	0.0694530i
$213$	14.3015			0.979921
$214$	−17.7803	+	30.7965i	−1.21544	+	2.10520i
$215$	−1.40869			−0.0960719
$216$	5.58556			0.380049
$217$	−4.07769	+	7.06277i	−0.276812	+	0.479452i
$218$	−15.4271	−	26.7206i	−1.04486	−	1.80975i
$219$	1.85628	−	3.21518i	0.125436	−	0.217261i
$220$	−12.3022	+	21.3080i	−0.829413	+	1.43659i
$221$	−22.5322			−1.51568
$222$	−23.3013			−1.56388
$223$	9.40510	−	16.2901i	0.629812	−	1.09087i	−0.357777	−	0.933807i	$-0.616465\pi$
$223$	9.40510	−	16.2901i	0.629812	−	1.09087i	0.987589	−	0.157059i	$-0.0502013\pi$
$224$	−4.43988			−0.296652
$225$	−2.10182	−	3.64046i	−0.140121	−	0.242697i
$226$	−23.3130	−	40.3793i	−1.55076	−	2.68599i
$227$	0.241660	+	0.418567i	0.0160395	+	0.0277812i	0.873934	−	0.486045i	$-0.161561\pi$
$227$	0.241660	+	0.418567i	0.0160395	+	0.0277812i	−0.857894	+	0.513826i	$0.828228\pi$
$228$	6.82039	−	11.8133i	0.451691	−	0.782352i
$229$	−10.7976	+	18.7020i	−0.713524	+	1.23586i	0.250002	+	0.968245i	$0.419569\pi$
$229$	−10.7976	+	18.7020i	−0.713524	+	1.23586i	−0.963526	+	0.267614i	$0.913765\pi$
$230$	−30.8698	−	53.4680i	−2.03549	−	3.52558i
$231$	−1.69750	+	2.94016i	−0.111687	+	0.193448i
$232$	−5.80111			−0.380861
$233$	11.2389	+	19.4663i	0.736284	+	1.27528i	0.954158	+	0.299304i	$0.0967546\pi$
$233$	11.2389	+	19.4663i	0.736284	+	1.27528i	−0.217874	+	0.975977i	$0.569912\pi$
$234$	4.85606	+	8.41094i	0.317450	+	0.549840i
$235$	−30.6115			−1.99687
$236$	28.5919			1.86117
$237$	−0.446196	−	0.772833i	−0.0289835	−	0.0502009i
$238$	12.8303	+	22.2227i	0.831665	+	1.44049i
$239$	−9.80800			−0.634427			−0.317213	−	0.948354i	$-0.602747\pi$
$239$	−9.80800			−0.634427			−0.317213	+	0.948354i	$0.602747\pi$
$240$	8.30596	−	14.3863i	0.536147	−	0.928634i
$241$	7.68313	+	13.3076i	0.494914	+	0.857216i	0.999983	−	0.00586272i	$-0.00186617\pi$
$241$	7.68313	+	13.3076i	0.494914	+	0.857216i	−0.505069	+	0.863079i	$0.668533\pi$
$242$	9.15943	−	15.8646i	0.588791	−	1.01982i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	21.7475	+	37.6678i	1.39224	+	2.41143i
$245$	−5.84718	−	10.1276i	−0.373563	−	0.647029i
$246$	0.544734	+	0.943508i	0.0347310	+	0.0601559i
$247$	12.5216			0.796728
$248$	12.8426	−	22.2441i	0.815507	−	1.41250i
$249$	−15.3255			−0.971212
$250$	6.03340			0.381585
$251$	14.1134	−	24.4451i	0.890829	−	1.54296i	0.0519461	−	0.998650i	$-0.483458\pi$
$251$	14.1134	−	24.4451i	0.890829	−	1.54296i	0.838883	−	0.544312i	$-0.183209\pi$
$252$	3.75679	−	6.50695i	0.236655	−	0.409899i
$253$	−7.79996	−	13.5099i	−0.490379	−	0.849361i
$254$	3.25568	−	5.63900i	0.204280	−	0.353823i
$255$	−17.5770			−1.10071
$256$	−32.4136			−2.02585
$257$	−12.4402	+	21.5470i	−0.775997	+	1.34407i	0.158235	+	0.987402i	$0.449420\pi$
$257$	−12.4402	+	21.5470i	−0.775997	+	1.34407i	−0.934232	+	0.356665i	$0.883914\pi$
$258$	1.15961			0.0721939
$259$	−8.27376	+	14.3306i	−0.514107	+	0.890459i
$260$	49.9849			3.09993
$261$	0.519295	−	0.899446i	0.0321436	−	0.0556743i
$262$	−10.4597	+	18.1167i	−0.646200	+	1.11925i
$263$	−5.05804	+	8.76078i	−0.311892	+	0.540213i	−0.978772	−	0.204952i	$-0.934296\pi$
$263$	−5.05804	+	8.76078i	−0.311892	+	0.540213i	0.666880	+	0.745165i	$0.267629\pi$
$264$	5.34625	−	9.25999i	0.329039	−	0.569913i
$265$	0.836158			0.0513648
$266$	−7.13003	−	12.3496i	−0.437170	−	0.757201i
$267$	3.61146	−	6.25524i	0.221018	−	0.382814i
$268$	−26.7855			−1.63618
$269$	−3.15836			−0.192569			−0.0962843	−	0.995354i	$-0.530696\pi$
$269$	−3.15836			−0.192569			−0.0962843	+	0.995354i	$0.530696\pi$
$270$	3.78813	+	6.56123i	0.230538	+	0.399304i
$271$	7.39003	−	12.7999i	0.448913	−	0.777539i	−0.549403	−	0.835557i	$-0.685145\pi$
$271$	7.39003	−	12.7999i	0.448913	−	0.777539i	0.998316	+	0.0580182i	$0.0184782\pi$
$272$	−15.8626	−	27.4748i	−0.961812	−	1.66591i
$273$	6.89710			0.417432
$274$	−1.27198	−	2.20314i	−0.0768433	−	0.133097i
$275$	−8.04709			−0.485258
$276$	17.2623	+	29.8992i	1.03907	+	1.79972i
$277$	−15.0365	+	26.0440i	−0.903458	+	1.56483i	−0.0804835	+	0.996756i	$0.525646\pi$
$277$	−15.0365	+	26.0440i	−0.903458	+	1.56483i	−0.822974	+	0.568079i	$0.807687\pi$
$278$	−3.80396	+	6.58866i	−0.228147	+	0.395161i
$279$	2.29925	+	3.98243i	0.137653	+	0.238422i
$280$	−15.0260	−	26.0258i	−0.897976	−	1.55534i
$281$	3.73830	−	6.47493i	0.223009	−	0.386262i	−0.732712	−	0.680539i	$-0.761746\pi$
$281$	3.73830	−	6.47493i	0.223009	−	0.386262i	0.955720	+	0.294277i	$0.0950789\pi$
$282$	25.1987			1.50056
$283$	5.40821	−	9.36729i	0.321484	−	0.556827i	−0.659310	−	0.751871i	$-0.729152\pi$
$283$	5.40821	−	9.36729i	0.321484	−	0.556827i	0.980795	+	0.195044i	$0.0624849\pi$
$284$	−30.2950	+	52.4724i	−1.79767	+	3.11366i
$285$	9.76786			0.578598
$286$	18.5920			1.09937
$287$	0.773691			0.0456696
$288$	−1.25174	+	2.16807i	−0.0737593	+	0.127755i
$289$	−8.28417	+	14.3486i	−0.487304	+	0.844035i
$290$	−3.93431	−	6.81443i	−0.231031	−	0.400157i
$291$	6.36114			0.372896
$292$	7.86436	+	13.6215i	0.460227	+	0.797136i
$293$	−4.11171	−	7.12168i	−0.240208	−	0.416053i	0.720565	−	0.693387i	$-0.243882\pi$
$293$	−4.11171	−	7.12168i	−0.240208	−	0.416053i	−0.960774	+	0.277334i	$0.910549\pi$
$294$	4.81328	+	8.33684i	0.280716	+	0.486215i
$295$	10.2370	+	17.7310i	0.596022	+	1.03234i
$296$	26.0581	−	45.1339i	1.51459	−	2.62335i
$297$	0.957157	+	1.65784i	0.0555399	+	0.0961979i
$298$	50.5857			2.93035
$299$	−15.8460	+	27.4460i	−0.916395	+	1.58724i
$300$	17.8092			1.02822
$301$	0.411750	−	0.713171i	0.0237329	−	0.0411065i
$302$	−10.3241	−	17.8819i	−0.594086	−	1.02899i
$303$	−9.55271	−	16.5458i	−0.548789	−	0.950531i
$304$	8.81514	+	15.2683i	0.505583	+	0.875696i
$305$	−15.5729	+	26.9731i	−0.891702	+	1.54447i
$306$	14.4690			0.827140
$307$	13.8075			0.788034			0.394017	−	0.919103i	$-0.371085\pi$
$307$	13.8075			0.788034			0.394017	+	0.919103i	$0.371085\pi$
$308$	−7.19167	−	12.4563i	−0.409784	−	0.709766i
$309$	−0.628481	−	1.08856i	−0.0357530	−	0.0619261i
$310$	34.8395			1.97875
$311$	−12.8266	−	22.2162i	−0.727327	−	1.25977i	−0.958009	−	0.286738i	$-0.907429\pi$
$311$	−12.8266	−	22.2162i	−0.727327	−	1.25977i	0.230682	−	0.973029i	$-0.425904\pi$
$312$	−21.7223			−1.22978
$313$	22.9243			1.29576			0.647880	−	0.761742i	$-0.275656\pi$
$313$	22.9243			1.29576			0.647880	+	0.761742i	$0.275656\pi$
$314$	21.6672	−	22.5762i	1.22275	−	1.27405i
$315$	5.38031			0.303146
$316$	3.78072			0.212682
$317$	−5.85737	−	10.1453i	−0.328983	−	0.569815i	0.653327	−	0.757075i	$-0.273372\pi$
$317$	−5.85737	−	10.1453i	−0.328983	−	0.569815i	−0.982310	+	0.187260i	$0.940039\pi$
$318$	−0.688309			−0.0385984
$319$	−0.994094	−	1.72182i	−0.0556586	−	0.0964035i
$320$	−7.12843	−	12.3468i	−0.398491	−	0.690207i
$321$	14.2395			0.794773
$322$	36.0920			2.01133
$323$	9.32727	−	16.1553i	0.518983	−	0.898905i
$324$	−2.11831	−	3.66902i	−0.117684	−	0.203834i
$325$	8.17401	+	14.1578i	0.453413	+	0.785334i
$326$	2.97325	+	5.14983i	0.164673	+	0.285222i
$327$	−6.17747	+	10.6997i	−0.341615	+	0.591695i
$328$	−2.43673			−0.134546
$329$	8.94750	−	15.4975i	0.493292	−	0.854406i
$330$	14.5033			0.798382
$331$	5.21029	+	9.02449i	0.286383	+	0.496031i	0.972944	−	0.231042i	$-0.0742136\pi$
$331$	5.21029	+	9.02449i	0.286383	+	0.496031i	−0.686560	+	0.727073i	$0.740880\pi$
$332$	32.4641	−	56.2295i	1.78170	−	3.08599i
$333$	4.66526	+	8.08046i	0.255655	+	0.442807i
$334$	16.5867	+	28.7290i	0.907584	+	1.57198i
$335$	−9.59026	−	16.6108i	−0.523972	−	0.907545i
$336$	4.85554	+	8.41004i	0.264891	+	0.458805i
$337$	−0.00753719			−0.000410577			−0.000205288	−	1.00000i	$-0.500065\pi$
$337$	−0.00753719			−0.000410577			−0.000205288		1.00000i	$0.500065\pi$
$338$	−2.65267	−	4.59457i	−0.144286	−	0.249911i
$339$	−9.33519	+	16.1690i	−0.507018	+	0.878181i
$340$	37.2335	−	64.4904i	2.01927	−	3.49748i
$341$	8.80299			0.476709
$342$	−8.04070			−0.434792
$343$	19.2507			1.03944
$344$	−1.29680	+	2.24612i	−0.0699187	+	0.121103i
$345$	−12.3612	+	21.4101i	−0.665502	+	1.15268i
$346$	−13.8046			−0.742142
$347$	−13.5412	+	23.4540i	−0.726928	+	1.25908i	0.231247	+	0.972895i	$0.425719\pi$
$347$	−13.5412	+	23.4540i	−0.726928	+	1.25908i	−0.958175	+	0.286182i	$0.907614\pi$
$348$	2.20006	+	3.81061i	0.117935	+	0.204270i
$349$	−12.2993	−	21.3029i	−0.658364	−	1.14032i	−0.981039	−	0.193810i	$-0.937916\pi$
$349$	−12.2993	−	21.3029i	−0.658364	−	1.14032i	0.322675	−	0.946510i	$-0.395418\pi$
$350$	9.30889	−	16.1235i	0.497581	−	0.861836i
$351$	1.94451	−	3.36798i	0.103790	−	0.179770i
$352$	2.39622	+	4.15037i	0.127719	+	0.221216i
$353$	−28.0706			−1.49405			−0.747024	−	0.664797i	$-0.768518\pi$
$353$	−28.0706			−1.49405			−0.747024	+	0.664797i	$0.768518\pi$
$354$	−8.42691	−	14.5958i	−0.447885	−	0.775760i
$355$	−43.3871			−2.30275
$356$	15.3004	+	26.5011i	0.810919	+	1.40455i
$357$	5.13762	−	8.89863i	0.271912	−	0.470965i
$358$	33.0081	+	57.1717i	1.74453	+	3.02162i
$359$	−15.0970			−0.796789			−0.398395	−	0.917214i	$-0.630433\pi$
$359$	−15.0970			−0.796789			−0.398395	+	0.917214i	$0.630433\pi$
$360$	−16.9452			−0.893090
$361$	4.31667	−	7.47669i	0.227193	−	0.393510i
$362$	0.907372	+	1.57161i	0.0476904	+	0.0826022i
$363$	−7.33540			−0.385009
$364$	−14.6102	+	25.3056i	−0.765783	+	1.32637i
$365$	−5.63150	+	9.75404i	−0.294766	+	0.510550i
$366$	12.8193	−	22.2037i	0.670075	−	1.16060i
$367$	8.77920	−	15.2060i	0.458271	−	0.793748i	−0.540599	−	0.841280i	$-0.681802\pi$
$367$	8.77920	−	15.2060i	0.458271	−	0.793748i	0.998870	+	0.0475324i	$0.0151357\pi$
$368$	−44.6220			−2.32608
$369$	0.218127	−	0.377808i	0.0113553	−	0.0196679i
$370$	70.6903			3.67502
$371$	−0.244403	+	0.423318i	−0.0126888	+	0.0219776i
$372$	−19.4821			−1.01010
$373$	−27.5225			−1.42506			−0.712530	−	0.701641i	$-0.752451\pi$
$373$	−27.5225			−1.42506			−0.712530	+	0.701641i	$0.752451\pi$
$374$	13.8491	−	23.9874i	0.716122	−	1.24036i
$375$	−1.20797	−	2.09227i	−0.0623795	−	0.108044i
$376$	−28.1800	+	48.8092i	−1.45327	+	2.51714i
$377$	−2.01955	+	3.49796i	−0.104012	+	0.180154i
$378$	−4.42896			−0.227801
$379$	−28.0142			−1.43899			−0.719495	−	0.694497i	$-0.755627\pi$
$379$	−28.0142			−1.43899			−0.719495	+	0.694497i	$0.755627\pi$
$380$	−20.6913	+	35.8385i	−1.06144	+	1.83847i
$381$	−2.60734			−0.133578
$382$	−5.10227	−	8.83740i	−0.261055	−	0.452161i
$383$	−7.09134	−	12.2826i	−0.362350	−	0.627609i	0.625997	−	0.779826i	$-0.284692\pi$
$383$	−7.09134	−	12.2826i	−0.362350	−	0.627609i	−0.988347	+	0.152216i	$0.951359\pi$
$384$	8.37146	+	14.4998i	0.427204	+	0.739939i
$385$	5.14980	−	8.91972i	0.262458	−	0.454591i
$386$	4.67073	−	8.08994i	0.237734	−	0.411767i
$387$	−0.232170	−	0.402130i	−0.0118019	−	0.0204414i
$388$	−13.4749	+	23.3391i	−0.684082	+	1.18487i
$389$	34.1601			1.73199			0.865993	−	0.500056i	$-0.166687\pi$
$389$	34.1601			1.73199			0.865993	+	0.500056i	$0.166687\pi$
$390$	−14.7321	−	25.5167i	−0.745987	−	1.29209i
$391$	23.6072	+	40.8888i	1.19387	+	2.06784i
$392$	−21.5309			−1.08748
$393$	8.37670			0.422549
$394$	−1.40634	−	2.43584i	−0.0708501	−	0.122716i
$395$	1.35365	+	2.34458i	0.0681093	+	0.117969i
$396$	−8.11022			−0.407554
$397$	−8.97616	+	15.5472i	−0.450500	+	0.780290i	−0.998417	−	0.0562433i	$-0.982088\pi$
$397$	−8.97616	+	15.5472i	−0.450500	+	0.780290i	0.547917	+	0.836533i	$0.315421\pi$
$398$	−20.7115	−	35.8734i	−1.03817	−	1.79817i
$399$	−2.85507	+	4.94513i	−0.142932	+	0.247566i
$400$	−11.5089	+	19.9341i	−0.575447	+	0.996704i
$401$	1.79098	+	3.10206i	0.0894371	+	0.154910i	0.907273	−	0.420541i	$-0.138160\pi$
$401$	1.79098	+	3.10206i	0.0894371	+	0.154910i	−0.817836	+	0.575451i	$0.804827\pi$
$402$	7.89450	+	13.6737i	0.393742	+	0.681981i
$403$	−8.94183	−	15.4877i	−0.445424	−	0.771497i
$404$	80.9424			4.02704
$405$	1.51688	−	2.62731i	0.0753741	−	0.130552i
$406$	4.59988			0.228288
$407$	17.8615			0.885363
$408$	−16.1809	+	28.0261i	−0.801072	+	1.38750i
$409$	4.90063	−	8.48814i	0.242321	−	0.419712i	−0.719054	−	0.694954i	$-0.755425\pi$
$409$	4.90063	−	8.48814i	0.242321	−	0.419712i	0.961375	+	0.275242i	$0.0887581\pi$
$410$	−1.65259	−	2.86237i	−0.0816155	−	0.141362i
$411$	−0.509339	+	0.882201i	−0.0251238	+	0.0435157i
$412$	5.32527			0.262357
$413$	−11.9688			−0.588947
$414$	10.1755	−	17.6244i	0.500096	−	0.866192i
$415$	46.4937			2.28228
$416$	4.86802	−	8.43166i	0.238674	−	0.413396i
$417$	3.04643			0.149185
$418$	−7.69622	+	13.3302i	−0.376434	+	0.652003i
$419$	−16.1285	+	27.9353i	−0.787927	+	1.36473i	0.139307	+	0.990249i	$0.455512\pi$
$419$	−16.1285	+	27.9353i	−0.787927	+	1.36473i	−0.927235	+	0.374481i	$0.877821\pi$
$420$	−11.3972	+	19.7405i	−0.556125	+	0.963236i
$421$	−6.76570	+	11.7185i	−0.329740	+	0.571127i	−0.982460	−	0.186472i	$-0.940295\pi$
$421$	−6.76570	+	11.7185i	−0.329740	+	0.571127i	0.652720	+	0.757599i	$0.273628\pi$
$422$	23.3559			1.13695
$423$	−5.04515	−	8.73846i	−0.245304	−	0.424878i
$424$	0.769742	−	1.33323i	0.0373820	−	0.0647475i
$425$	24.3552			1.18140
$426$	35.7154			1.73042
$427$	−9.10368	−	15.7680i	−0.440558	−	0.763069i
$428$	−30.1637	+	52.2451i	−1.45802	+	2.52536i
$429$	−3.72239	−	6.44738i	−0.179719	−	0.311282i
$430$	−3.51796			−0.169651
$431$	−13.8578	−	24.0024i	−0.667506	−	1.15615i	−0.978599	−	0.205775i	$-0.934028\pi$
$431$	−13.8578	−	24.0024i	−0.667506	−	1.15615i	0.311093	−	0.950379i	$-0.399305\pi$
$432$	5.47570			0.263450
$433$	−2.77074	−	4.79907i	−0.133153	−	0.230629i	0.791737	−	0.610862i	$-0.209177\pi$
$433$	−2.77074	−	4.79907i	−0.133153	−	0.230629i	−0.924891	+	0.380233i	$0.875844\pi$
$434$	−10.1833	+	17.6380i	−0.488815	+	0.846652i
$435$	−1.57541	+	2.72869i	−0.0755353	+	0.130831i
$436$	−26.1716	−	45.3305i	−1.25339	−	2.17094i
$437$	−13.1189	−	22.7227i	−0.627564	−	1.08697i
$438$	4.63574	−	8.02933i	0.221504	−	0.383656i
$439$	−26.5585			−1.26757			−0.633784	−	0.773510i	$-0.718499\pi$
$439$	−26.5585			−1.26757			−0.633784	+	0.773510i	$0.718499\pi$
$440$	−16.2192	+	28.0925i	−0.773220	+	1.33926i
$441$	1.92738	−	3.33831i	0.0917798	−	0.158967i
$442$	−56.2702			−2.67650
$443$	38.4364			1.82617			0.913084	−	0.407772i	$-0.133694\pi$
$443$	38.4364			1.82617			0.913084	+	0.407772i	$0.133694\pi$
$444$	−39.5298			−1.87600
$445$	−10.9563	+	18.9768i	−0.519377	+	0.899588i
$446$	23.4876	−	40.6816i	1.11217	−	1.92633i
$447$	−10.1280	−	17.5422i	−0.479037	−	0.829717i
$448$	8.33435			0.393761
$449$	0.896184	+	1.55224i	0.0422936	+	0.0732546i	0.886397	−	0.462925i	$-0.153200\pi$
$449$	0.896184	+	1.55224i	0.0422936	+	0.0732546i	−0.844104	+	0.536180i	$0.819867\pi$
$450$	−5.24893	−	9.09141i	−0.247437	−	0.428573i
$451$	−0.417564	−	0.723243i	−0.0196623	−	0.0340562i
$452$	−39.5497	−	68.5020i	−1.86026	−	3.22206i
$453$	−4.13407	+	7.16042i	−0.194236	+	0.336426i
$454$	0.603502	+	1.04530i	0.0283237	+	0.0490582i
$455$	−20.9241			−0.980937
$456$	8.99200	−	15.5746i	0.421089	−	0.729347i
$457$	−37.6648			−1.76189			−0.880943	−	0.473222i	$-0.843091\pi$
$457$	−37.6648			−1.76189			−0.880943	+	0.473222i	$0.843091\pi$
$458$	−26.9650	+	46.7048i	−1.25999	+	2.18237i
$459$	−2.89691	−	5.01759i	−0.135216	−	0.234201i
$460$	−52.3695	−	90.7066i	−2.44174	−	4.22922i
$461$	0.843477	+	1.46095i	0.0392846	+	0.0680430i	0.884999	−	0.465593i	$-0.154159\pi$
$461$	0.843477	+	1.46095i	0.0392846	+	0.0680430i	−0.845715	+	0.533636i	$0.820825\pi$
$462$	−4.23921	+	7.34253i	−0.197226	+	0.341605i
$463$	20.1910			0.938355			0.469177	−	0.883104i	$-0.344550\pi$
$463$	20.1910			0.938355			0.469177	+	0.883104i	$0.344550\pi$
$464$	−5.68701			−0.264013
$465$	−6.97537	−	12.0817i	−0.323475	−	0.560275i
$466$	28.0671	+	48.6137i	1.30018	+	2.25199i
$467$	30.1135			1.39349			0.696744	−	0.717320i	$-0.254632\pi$
$467$	30.1135			1.39349			0.696744	+	0.717320i	$0.254632\pi$
$468$	8.23813	+	14.2689i	0.380808	+	0.659578i
$469$	11.2126			0.517751
$470$	−76.4467			−3.52622
$471$	−12.1671	−	2.99370i	−0.560629	−	0.137942i
$472$	37.6956			1.73508
$473$	−0.888892			−0.0408713
$474$	−1.11429	−	1.93001i	−0.0511812	−	0.0886485i
$475$	−13.5346			−0.621010
$476$	21.7662	+	37.7001i	0.997650	+	1.72798i
$477$	0.137809	+	0.238693i	0.00630986	+	0.0109290i
$478$	−24.4937			−1.12032
$479$	−18.8023			−0.859100			−0.429550	−	0.903043i	$-0.641328\pi$
$479$	−18.8023			−0.859100			−0.429550	+	0.903043i	$0.641328\pi$
$480$	3.79746	−	6.57739i	0.173330	−	0.300216i
$481$	−18.1432	−	31.4250i	−0.827261	−	1.43286i
$482$	19.1873	+	33.2333i	0.873956	+	1.51374i
$483$	−7.22614	−	12.5160i	−0.328801	−	0.569500i
$484$	15.5387	−	26.9137i	0.706302	−	1.22335i
$485$	−19.2981			−0.876282
$486$	−1.24866	+	2.16274i	−0.0566404	+	0.0981041i
$487$	−36.6535			−1.66093			−0.830464	−	0.557073i	$-0.811925\pi$
$487$	−36.6535			−1.66093			−0.830464	+	0.557073i	$0.811925\pi$
$488$	28.6719	+	49.6612i	1.29792	+	2.24806i
$489$	1.19058	−	2.06214i	0.0538397	−	0.0932532i
$490$	−14.6023	−	25.2919i	−0.659664	−	1.14257i
$491$	−11.1337	−	19.2842i	−0.502458	−	0.870282i	−0.999996	−	0.00284039i	$-0.999096\pi$
$491$	−11.1337	−	19.2842i	−0.502458	−	0.870282i	0.497538	−	0.867442i	$-0.334237\pi$
$492$	0.924123	+	1.60063i	0.0416627	+	0.0721619i
$493$	3.00870	+	5.21123i	0.135505	+	0.234702i
$494$	31.2704			1.40692
$495$	−2.90378	−	5.02949i	−0.130515	−	0.226059i
$496$	12.5900	−	21.8066i	0.565309	−	0.979144i
$497$	12.6817	−	21.9654i	0.568853	−	0.985283i
$498$	−38.2726			−1.71504
$499$	−15.1347			−0.677524			−0.338762	−	0.940872i	$-0.610008\pi$
$499$	−15.1347			−0.677524			−0.338762	+	0.940872i	$0.610008\pi$
$500$	10.2354			0.457743
$501$	6.64180	−	11.5039i	0.296734	−	0.513958i
$502$	35.2457	−	61.0473i	1.57309	−	2.72467i
$503$	31.2048			1.39135			0.695676	−	0.718355i	$-0.255105\pi$
$503$	31.2048			1.39135			0.695676	+	0.718355i	$0.255105\pi$
$504$	4.95295	−	8.57876i	0.220622	−	0.382128i
$505$	28.9806	+	50.1958i	1.28962	+	2.23368i
$506$	−19.4790	−	33.7386i	−0.865947	−	1.49986i
$507$	−1.06221	+	1.83980i	−0.0471743	+	0.0817083i
$508$	5.52315	−	9.56637i	0.245050	−	0.424439i
$509$	−3.87083	−	6.70447i	−0.171571	−	0.297170i	0.767398	−	0.641171i	$-0.221551\pi$
$509$	−3.87083	−	6.70447i	−0.171571	−	0.297170i	−0.938969	+	0.344001i	$0.888218\pi$
$510$	−43.8954			−1.94372
$511$	−3.29209	−	5.70206i	−0.145633	−	0.252244i
$512$	−47.4614			−2.09752
$513$	1.60987	+	2.78837i	0.0710773	+	0.123109i
$514$	−31.0672	+	53.8099i	−1.37031	+	2.37345i
$515$	1.90665	+	3.30242i	0.0840172	+	0.145522i
$516$	1.96723			0.0866025
$517$	−19.3160			−0.849517
$518$	−20.6623	+	35.7881i	−0.907847	+	1.57244i
$519$	2.76389	+	4.78720i	0.121321	+	0.210135i
$520$	65.9001			2.88991
$521$	−14.6204	+	25.3232i	−0.640530	+	1.10943i	0.344785	+	0.938682i	$0.387952\pi$
$521$	−14.6204	+	25.3232i	−0.640530	+	1.10943i	−0.985315	+	0.170748i	$0.945382\pi$
$522$	1.29685	−	2.24621i	0.0567615	−	0.0983138i
$523$	−10.0603	+	17.4249i	−0.439905	+	0.761938i	−0.997682	−	0.0680532i	$-0.978321\pi$
$523$	−10.0603	+	17.4249i	−0.439905	+	0.761938i	0.557777	+	0.829991i	$0.311655\pi$
$524$	−17.7444	+	30.7343i	−0.775170	+	1.34263i
$525$	−7.45510			−0.325367
$526$	−12.6316	+	21.8785i	−0.550762	+	0.953948i
$527$	−26.6429			−1.16058
$528$	5.24110	−	9.07786i	0.228090	−	0.395063i
$529$	43.4077			1.88729
$530$	2.08816			0.0907037
$531$	−3.37438	+	5.84459i	−0.146436	+	0.253634i
$532$	−12.0958	−	20.9506i	−0.524422	−	0.908325i
$533$	−0.848300	+	1.46930i	−0.0367440	+	0.0636424i
$534$	9.01899	−	15.6213i	0.390290	−	0.676002i
$535$	−43.1992			−1.86766
$536$	−35.3140			−1.52533
$537$	13.2174	−	22.8932i	0.570372	−	0.987914i
$538$	−7.88744			−0.340052
$539$	−3.68960	−	6.39058i	−0.158922	−	0.275262i
$540$	6.42642	+	11.1309i	0.276549	+	0.478997i
$541$	12.0689	+	20.9039i	0.518882	+	0.898731i	0.999759	+	0.0219425i	$0.00698509\pi$
$541$	12.0689	+	20.9039i	0.518882	+	0.898731i	−0.480877	+	0.876788i	$0.659682\pi$
$542$	18.4553	−	31.9655i	0.792723	−	1.37304i
$543$	0.363338	−	0.629320i	0.0155923	−	0.0270067i
$544$	−7.25234	−	12.5614i	−0.310942	−	0.538567i
$545$	18.7409	−	32.4602i	0.802773	−	1.39044i
$546$	17.2243			0.737132
$547$	14.6583	+	25.3889i	0.626743	+	1.08555i	0.988201	+	0.153162i	$0.0489458\pi$
$547$	14.6583	+	25.3889i	0.626743	+	1.08555i	−0.361458	+	0.932388i	$0.617721\pi$
$548$	−2.15787	−	3.73755i	−0.0921798	−	0.159660i
$549$	−10.2664			−0.438161
$550$	−20.0962			−0.856904
$551$	−1.67199	−	2.89597i	−0.0712292	−	0.123373i
$552$	22.7586	+	39.4191i	0.968671	+	1.67779i
$553$	−1.58264			−0.0673008
$554$	−37.5511	+	65.0404i	−1.59539	+	2.76330i
$555$	−14.1532	−	24.5141i	−0.600771	−	1.04057i
$556$	−6.45329	+	11.1774i	−0.273680	+	0.474028i
$557$	−9.71343	+	16.8242i	−0.411571	+	0.712862i	−0.995062	−	0.0992576i	$-0.968353\pi$
$557$	−9.71343	+	16.8242i	−0.411571	+	0.712862i	0.583490	+	0.812120i	$0.301687\pi$
$558$	5.74198	+	9.94540i	0.243077	+	0.421022i
$559$	0.902911	+	1.56389i	0.0381891	+	0.0661454i
$560$	−14.7305	−	25.5140i	−0.622477	−	1.07816i
$561$	−11.0912			−0.468270
$562$	9.33575	−	16.1700i	0.393805	−	0.682090i
$563$	−44.2877			−1.86650			−0.933251	−	0.359225i	$-0.883041\pi$
$563$	−44.2877			−1.86650			−0.933251	+	0.359225i	$0.883041\pi$
$564$	42.7488			1.80005
$565$	28.3207	−	49.0528i	1.19146	−	2.06367i
$566$	13.5060	−	23.3931i	0.567701	−	0.983287i
$567$	0.886742	+	1.53588i	0.0372397	+	0.0645010i
$568$	−39.9409	+	69.1796i	−1.67588	+	2.90271i
$569$	−15.1003			−0.633037			−0.316518	−	0.948586i	$-0.602514\pi$
$569$	−15.1003			−0.633037			−0.316518	+	0.948586i	$0.602514\pi$
$570$	24.3935			1.02173
$571$	−0.199211	+	0.345044i	−0.00833672	+	0.0144396i	−0.870164	−	0.492763i	$-0.835987\pi$
$571$	−0.199211	+	0.345044i	−0.00833672	+	0.0144396i	0.861827	+	0.507202i	$0.169320\pi$
$572$	31.5407			1.31878
$573$	−2.04310	+	3.53875i	−0.0853516	+	0.147833i
$574$	1.93216			0.0806467
$575$	17.1279	−	29.6665i	0.714284	−	1.23718i
$576$	2.34971	−	4.06982i	0.0979045	−	0.169576i
$577$	9.00311	−	15.5938i	0.374804	−	0.649180i	−0.615494	−	0.788142i	$-0.711043\pi$
$577$	9.00311	−	15.5938i	0.374804	−	0.649180i	0.990298	+	0.138962i	$0.0443766\pi$
$578$	−20.6882	+	35.8331i	−0.860517	+	1.49046i
$579$	−3.74059			−0.155454
$580$	−6.67442	−	11.5604i	−0.277140	−	0.480021i
$581$	−13.5897	+	23.5381i	−0.563798	+	0.976526i
$582$	15.8858			0.658488
$583$	0.527621			0.0218518
$584$	10.3684	+	17.9585i	0.429046	+	0.743130i
$585$	−5.89915	+	10.2176i	−0.243900	+	0.422447i
$586$	−10.2683	−	17.7851i	−0.424178	−	0.734697i
$587$	3.67233			0.151573			0.0757866	−	0.997124i	$-0.475853\pi$
$587$	3.67233			0.151573			0.0757866	+	0.997124i	$0.475853\pi$
$588$	8.16556	+	14.1432i	0.336742	+	0.583254i
$589$	14.8060			0.610069
$590$	25.5651	+	44.2801i	1.05250	+	1.82298i
$591$	−0.563137	+	0.975382i	−0.0231644	+	0.0401219i
$592$	25.5456	−	44.2462i	1.04992	−	1.81851i
$593$	7.89356	+	13.6720i	0.324150	+	0.561444i	0.981340	−	0.192281i	$-0.0615885\pi$
$593$	7.89356	+	13.6720i	0.324150	+	0.561444i	−0.657190	+	0.753725i	$0.728255\pi$
$594$	2.39033	+	4.14017i	0.0980764	+	0.169873i
$595$	−15.5863	+	26.9962i	−0.638975	+	1.10674i
$596$	85.8168			3.51519
$597$	−8.29349	+	14.3647i	−0.339430	+	0.587910i
$598$	−39.5725	+	68.5415i	−1.61824	+	2.80287i
$599$	28.8421			1.17846			0.589228	−	0.807967i	$-0.299432\pi$
$599$	28.8421			1.17846			0.589228	+	0.807967i	$0.299432\pi$
$600$	23.4797			0.958555
$601$	16.9652			0.692025			0.346012	−	0.938230i	$-0.387536\pi$
$601$	16.9652			0.692025			0.346012	+	0.938230i	$0.387536\pi$
$602$	1.02827	−	1.78102i	0.0419092	−	0.0725889i
$603$	3.16119	−	5.47534i	0.128734	−	0.222973i
$604$	−17.5145	−	30.3360i	−0.712654	−	1.23435i
$605$	22.2538			0.904745
$606$	−23.8562	−	41.3202i	−0.969092	−	1.67852i
$607$	0.649908	+	1.12567i	0.0263789	+	0.0456897i	0.878914	−	0.476981i	$-0.158269\pi$
$607$	0.649908	+	1.12567i	0.0263789	+	0.0456897i	−0.852535	+	0.522671i	$0.824936\pi$
$608$	4.03026	+	6.98061i	0.163449	+	0.283101i
$609$	−0.920962	−	1.59515i	−0.0373193	−	0.0646389i
$610$	−38.8906	+	67.3604i	−1.57463	+	2.72734i
$611$	19.6207	+	33.9840i	0.793767	+	1.37484i
$612$	24.5462			0.992221
$613$	23.4635	−	40.6400i	0.947682	−	1.64143i	0.197393	−	0.980325i	$-0.436753\pi$
$613$	23.4635	−	40.6400i	0.947682	−	1.64143i	0.750290	−	0.661109i	$-0.229914\pi$
$614$	34.4817			1.39157
$615$	−0.661744	+	1.14617i	−0.0266841	+	0.0462182i
$616$	−9.48150	−	16.4224i	−0.382021	−	0.661679i
$617$	6.36134	+	11.0182i	0.256098	+	0.443574i	0.965193	−	0.261538i	$-0.0842297\pi$
$617$	6.36134	+	11.0182i	0.256098	+	0.443574i	−0.709095	+	0.705113i	$0.750896\pi$
$618$	−1.56952	−	2.71849i	−0.0631353	−	0.109354i
$619$	13.8304	−	23.9550i	0.555892	−	0.962834i	−0.441941	−	0.897044i	$-0.645710\pi$
$619$	13.8304	−	23.9550i	0.555892	−	0.962834i	0.997834	−	0.0657897i	$-0.0209566\pi$
$620$	59.1039			2.37367
$621$	−8.14909			−0.327012
$622$	−32.0320	−	55.4811i	−1.28437	−	2.22459i
$623$	−6.40487	−	11.0936i	−0.256606	−	0.444454i
$624$	−21.2951			−0.852485
$625$	14.1738	+	24.5497i	0.566952	+	0.981990i
$626$	57.2495			2.28815
$627$	6.16357			0.246149
$628$	36.7576	−	38.2997i	1.46679	−	1.52832i
$629$	−54.0593			−2.15549
$630$	13.4364			0.535318
$631$	3.38360	+	5.86057i	0.134699	+	0.233306i	0.925482	−	0.378790i	$-0.123660\pi$
$631$	3.38360	+	5.86057i	0.134699	+	0.233306i	−0.790783	+	0.612096i	$0.790327\pi$
$632$	4.98450			0.198273
$633$	−4.67620	−	8.09941i	−0.185862	−	0.321923i
$634$	−14.6277	−	25.3360i	−0.580942	−	1.00622i
$635$	7.91001			0.313899
$636$	−1.16769			−0.0463020
$637$	−7.49559	+	12.9827i	−0.296986	+	0.514395i
$638$	−2.48257	−	4.29994i	−0.0982860	−	0.170236i
$639$	−7.15074	−	12.3854i	−0.282879	−	0.489961i
$640$	−25.3969	−	43.9887i	−1.00390	−	1.73881i
$641$	−0.142580	+	0.246956i	−0.00563157	+	0.00975417i	−0.868827	−	0.495115i	$-0.835126\pi$
$641$	−0.142580	+	0.246956i	−0.00563157	+	0.00975417i	0.863196	+	0.504869i	$0.168459\pi$
$642$	35.5607			1.40347
$643$	−3.38024	+	5.85475i	−0.133304	+	0.230889i	−0.924948	−	0.380093i	$-0.875892\pi$
$643$	−3.38024	+	5.85475i	−0.133304	+	0.230889i	0.791644	+	0.610982i	$0.209225\pi$
$644$	61.2288			2.41275
$645$	0.704346	+	1.21996i	0.0277336	+	0.0480360i
$646$	23.2932	−	40.3450i	0.916458	−	1.58735i
$647$	9.77094	+	16.9238i	0.384135	+	0.665342i	0.991649	−	0.128967i	$-0.0411663\pi$
$647$	9.77094	+	16.9238i	0.384135	+	0.665342i	−0.607513	+	0.794309i	$0.707833\pi$
$648$	−2.79278	−	4.83724i	−0.109711	−	0.190025i
$649$	6.45962	+	11.1884i	0.253562	+	0.439183i
$650$	20.4131	+	35.3566i	0.800669	+	1.38680i
$651$	8.15539			0.319635
$652$	5.04402	+	8.73650i	0.197539	+	0.342148i
$653$	16.3433	−	28.3073i	0.639561	−	1.10775i	−0.345968	−	0.938246i	$-0.612450\pi$
$653$	16.3433	−	28.3073i	0.639561	−	1.10775i	0.985529	−	0.169506i	$-0.0542172\pi$
$654$	−15.4271	+	26.7206i	−0.603249	+	1.04486i
$655$	−25.4128			−0.992961
$656$	−2.38880			−0.0932670
$657$	−3.71256			−0.144841
$658$	22.3448	−	38.7023i	0.871091	−	1.50877i
$659$	−0.981967	+	1.70082i	−0.0382520	+	0.0662544i	−0.884518	−	0.466507i	$-0.845512\pi$
$659$	−0.981967	+	1.70082i	−0.0382520	+	0.0662544i	0.846266	+	0.532761i	$0.178846\pi$
$660$	24.6044			0.957724
$661$	−6.22153	+	10.7760i	−0.241990	+	0.419138i	−0.961281	−	0.275570i	$-0.911133\pi$
$661$	−6.22153	+	10.7760i	−0.241990	+	0.419138i	0.719291	+	0.694709i	$0.244467\pi$
$662$	13.0118	+	22.5370i	0.505717	+	0.875927i
$663$	11.2661	+	19.5135i	0.437540	+	0.757841i
$664$	42.8007	−	74.1329i	1.66099	−	2.87691i
$665$	8.66158	−	15.0023i	0.335881	−	0.581764i
$666$	11.6507	+	20.1795i	0.451454	+	0.781940i
$667$	8.46357			0.327711
$668$	28.1388	+	48.7378i	1.08872	+	1.88572i
$669$	−18.8102			−0.727244
$670$	−23.9500	−	41.4825i	−0.925268	−	1.60261i
$671$	−9.82659	+	17.0202i	−0.379351	+	0.657056i
$672$	2.21994	+	3.84504i	0.0856360	+	0.148326i
$673$	13.6404			0.525799			0.262899	−	0.964823i	$-0.415321\pi$
$673$	13.6404			0.525799			0.262899	+	0.964823i	$0.415321\pi$
$674$	−0.0188228			−0.000725027
$675$	−2.10182	+	3.64046i	−0.0808992	+	0.140121i
$676$	−4.50017	−	7.79452i	−0.173083	−	0.299789i
$677$	27.0482			1.03955			0.519773	−	0.854305i	$-0.326017\pi$
$677$	27.0482			1.03955			0.519773	+	0.854305i	$0.326017\pi$
$678$	−23.3130	+	40.3793i	−0.895330	+	1.55076i
$679$	5.64069	−	9.76996i	0.216470	−	0.374937i
$680$	49.0887	−	85.0241i	1.88247	−	3.26053i
$681$	0.241660	−	0.418567i	0.00926042	−	0.0160395i
$682$	21.9839			0.841807
$683$	−3.11386	+	5.39336i	−0.119148	+	0.206371i	−0.919430	−	0.393253i	$-0.871350\pi$
$683$	−3.11386	+	5.39336i	−0.119148	+	0.206371i	0.800282	+	0.599624i	$0.204683\pi$
$684$	−13.6408			−0.521568
$685$	1.54521	−	2.67638i	0.0590393	−	0.102259i
$686$	48.0753			1.83552
$687$	21.5952			0.823906
$688$	−1.27129	+	2.20194i	−0.0484676	+	0.0839483i
$689$	−0.535942	−	0.928279i	−0.0204178	−	0.0353646i
$690$	−30.8698	+	53.4680i	−1.17519	+	2.03549i
$691$	20.2481	−	35.0707i	0.770274	−	1.33415i	−0.167138	−	0.985933i	$-0.553453\pi$
$691$	20.2481	−	35.0707i	0.770274	−	1.33415i	0.937413	−	0.348221i	$-0.113214\pi$
$692$	−23.4191			−0.890260
$693$	3.39501			0.128966
$694$	−33.8167	+	58.5722i	−1.28366	+	2.22337i
$695$	−9.24212			−0.350574
$696$	2.90055	+	5.02391i	0.109945	+	0.190431i
$697$	1.26379	+	2.18895i	0.0478695	+	0.0829124i
$698$	−30.7152	−	53.2003i	−1.16259	−	2.01366i
$699$	11.2389	−	19.4663i	0.425094	−	0.736284i
$700$	15.7922	−	27.3529i	0.596889	−	1.03384i
$701$	−14.4092	−	24.9575i	−0.544228	−	0.942630i	−0.998655	−	0.0518463i	$-0.983489\pi$
$701$	−14.4092	−	24.9575i	−0.544228	−	0.942630i	0.454427	−	0.890784i	$-0.349844\pi$
$702$	4.85606	−	8.41094i	0.183280	−	0.317450i
$703$	30.0417			1.13305
$704$	−4.49808	−	7.79090i	−0.169528	−	0.293631i
$705$	15.3057	+	26.5103i	0.576447	+	0.998436i
$706$	−70.1013			−2.63830
$707$	−33.8832			−1.27431
$708$	−14.2960	−	24.7613i	−0.537275	−	0.930587i
$709$	−15.7200	−	27.2279i	−0.590378	−	1.02257i	−0.994181	−	0.107719i	$-0.965645\pi$
$709$	−15.7200	−	27.2279i	−0.590378	−	1.02257i	0.403803	−	0.914846i	$-0.367688\pi$
$710$	−108.352			−4.06636
$711$	−0.446196	+	0.772833i	−0.0167336	+	0.0289835i
$712$	20.1720	+	34.9390i	0.755979	+	1.30939i
$713$	−18.7368	+	32.4531i	−0.701700	+	1.21538i
$714$	12.8303	−	22.2227i	0.480162	−	0.831665i
$715$	11.2928	+	19.5597i	0.422327	+	0.731493i
$716$	55.9970	+	96.9897i	2.09271	+	3.62467i
$717$	4.90400	+	8.49397i	0.183143	+	0.317213i
$718$	−37.7021			−1.40703
$719$	−7.30919	+	12.6599i	−0.272587	+	0.472134i	−0.969523	−	0.244998i	$-0.921213\pi$
$719$	−7.30919	+	12.6599i	−0.272587	+	0.472134i	0.696937	+	0.717133i	$0.254546\pi$
$720$	−16.6119			−0.619089
$721$	−2.22920			−0.0830198
$722$	10.7801	−	18.6717i	0.401194	−	0.694889i
$723$	7.68313	−	13.3076i	0.285739	−	0.494914i
$724$	1.53932	+	2.66619i	0.0572085	+	0.0990881i
$725$	2.18293	−	3.78095i	0.0810721	−	0.140421i
$726$	−18.3189			−0.679877
$727$	5.10752			0.189428			0.0947138	−	0.995505i	$-0.469806\pi$
$727$	5.10752			0.189428			0.0947138	+	0.995505i	$0.469806\pi$
$728$	−19.2621	+	33.3629i	−0.713900	+	1.23651i
$729$	1.00000			0.0370370
$730$	−14.0637	+	24.3590i	−0.520520	+	0.901566i
$731$	2.69030			0.0995044
$732$	21.7475	−	37.6678i	0.803810	−	1.39224i
$733$	1.15287	−	1.99683i	0.0425822	−	0.0737545i	−0.843949	−	0.536424i	$-0.819775\pi$
$733$	1.15287	−	1.99683i	0.0425822	−	0.0737545i	0.886531	+	0.462669i	$0.153108\pi$
$734$	21.9245	−	37.9743i	0.809248	−	1.40166i
$735$	−5.84718	+	10.1276i	−0.215676	+	0.373563i
$736$	−20.4010			−0.751992
$737$	−6.05150	−	10.4815i	−0.222910	−	0.386091i
$738$	0.544734	−	0.943508i	0.0200520	−	0.0347310i
$739$	19.0584			0.701076			0.350538	−	0.936548i	$-0.385999\pi$
$739$	19.0584			0.701076			0.350538	+	0.936548i	$0.385999\pi$
$740$	119.924			4.40848
$741$	−6.26079	−	10.8440i	−0.229996	−	0.398364i
$742$	−0.610352	+	1.05716i	−0.0224067	+	0.0388096i
$743$	0.232457	+	0.402628i	0.00852803	+	0.0147710i	0.870258	−	0.492596i	$-0.163952\pi$
$743$	0.232457	+	0.402628i	0.00852803	+	0.0147710i	−0.861730	+	0.507367i	$0.830619\pi$
$744$	−25.6852			−0.941667
$745$	30.7258	+	53.2186i	1.12571	+	1.94978i
$746$	−68.7325			−2.51648
$747$	7.66274	+	13.2722i	0.280365	+	0.485606i
$748$	23.4946	−	40.6938i	0.859046	−	1.48791i
$749$	12.6268	−	21.8702i	0.461373	−	0.799121i
$750$	−3.01670	−	5.22507i	−0.110154	−	0.190793i
$751$	−22.3962	−	38.7913i	−0.817247	−	1.41551i	−0.907703	−	0.419614i	$-0.862166\pi$
$751$	−22.3962	−	38.7913i	−0.817247	−	1.41551i	0.0904554	−	0.995901i	$-0.471168\pi$
$752$	−27.6257	+	47.8492i	−1.00741	+	1.74488i
$753$	−28.2268			−1.02864
$754$	−5.04346	+	8.73552i	−0.183672	+	0.318129i
$755$	12.5417	−	21.7229i	0.456441	−	0.790579i
$756$	−7.51358			−0.273266
$757$	−21.0045			−0.763423			−0.381712	−	0.924281i	$-0.624665\pi$
$757$	−21.0045			−0.763423			−0.381712	+	0.924281i	$0.624665\pi$
$758$	−69.9604			−2.54108
$759$	−7.79996	+	13.5099i	−0.283120	+	0.490379i
$760$	−27.2795	+	47.2494i	−0.989531	+	1.71392i
$761$	−7.64172	−	13.2359i	−0.277012	−	0.479799i	0.693629	−	0.720333i	$-0.256011\pi$
$761$	−7.64172	−	13.2359i	−0.277012	−	0.479799i	−0.970641	+	0.240533i	$0.922678\pi$
$762$	−6.51136			−0.235882
$763$	10.9557	+	18.9758i	0.396621	+	0.686968i
$764$	−8.65583	−	14.9923i	−0.313157	−	0.542404i
$765$	8.78850	+	15.2221i	0.317749	+	0.550357i
$766$	−17.7094	−	30.6735i	−0.639865	−	1.10828i
$767$	13.1230	−	22.7297i	0.473844	−	0.820722i
$768$	16.2068	+	28.0710i	0.584813	+	1.01293i
$769$	3.90604			0.140855			0.0704277	−	0.997517i	$-0.477564\pi$
$769$	3.90604			0.140855			0.0704277	+	0.997517i	$0.477564\pi$
$770$	12.8607	−	22.2754i	0.463468	−	0.802750i
$771$	24.8804			0.896045
$772$	7.92373	−	13.7243i	0.285181	−	0.493948i
$773$	−25.5847	−	44.3140i	−0.920217	−	1.59386i	−0.799078	−	0.601228i	$-0.794679\pi$
$773$	−25.5847	−	44.3140i	−0.920217	−	1.59386i	−0.121139	−	0.992636i	$-0.538655\pi$
$774$	−0.579803	−	1.00425i	−0.0208406	−	0.0360970i
$775$	9.66525	+	16.7407i	0.347186	+	0.601344i
$776$	−17.7653	+	30.7703i	−0.637735	+	1.10459i
$777$	16.5475			0.593639
$778$	85.3088			3.05847
$779$	−0.702312	−	1.21644i	−0.0251629	−	0.0435835i
$780$	−24.9924	−	43.2882i	−0.894873	−	1.54997i
$781$	−27.3775			−0.979644
$782$	58.9547	+	102.113i	2.10822	+	3.65154i
$783$	−1.03859			−0.0371162
$784$	−21.1075			−0.753838
$785$	36.9119	+	9.08213i	1.31744	+	0.324155i
$786$	20.9193			0.746168
$787$	−44.7639			−1.59566			−0.797830	−	0.602882i	$-0.794019\pi$
$787$	−44.7639			−1.59566			−0.797830	+	0.602882i	$0.794019\pi$
$788$	−2.38580	−	4.13232i	−0.0849905	−	0.147208i
$789$	10.1161			0.360142
$790$	3.38049	+	5.85518i	0.120272	+	0.208318i
$791$	16.5558	+	28.6755i	0.588657	+	1.01958i
$792$	−10.6925			−0.379942
$793$	39.9263			1.41782
$794$	−22.4164	+	38.8263i	−0.795527	+	1.37789i
$795$	−0.418079	−	0.724134i	−0.0148277	−	0.0256824i
$796$	−35.1364	−	60.8580i	−1.24538	−	2.15705i
$797$	−23.1244	−	40.0527i	−0.819110	−	1.41874i	−0.906339	−	0.422551i	$-0.861135\pi$
$797$	−23.1244	−	40.0527i	−0.819110	−	1.41874i	0.0872293	−	0.996188i	$-0.472199\pi$
$798$	−7.13003	+	12.3496i	−0.252400	+	0.437170i
$799$	58.4614			2.06822
$800$	−5.26186	+	9.11381i	−0.186035	+	0.322222i
$801$	−7.22293			−0.255210
$802$	4.47264	+	7.74685i	0.157935	+	0.273551i
$803$	−3.55351	+	6.15485i	−0.125401	+	0.217200i
$804$	13.3927	+	23.1969i	0.472326	+	0.818092i
$805$	21.9223	+	37.9706i	0.772660	+	1.33829i
$806$	−22.3306	−	38.6778i	−0.786563	−	1.36237i
$807$	1.57918	+	2.73522i	0.0555898	+	0.0962843i
$808$	106.714			3.75420
$809$	9.00046	+	15.5893i	0.316439	+	0.548089i	0.979742	−	0.200262i	$-0.0641793\pi$
$809$	9.00046	+	15.5893i	0.316439	+	0.548089i	−0.663303	+	0.748351i	$0.730846\pi$
$810$	3.78813	−	6.56123i	0.133101	−	0.230538i
$811$	4.49862	−	7.79184i	0.157968	−	0.273609i	−0.776168	−	0.630526i	$-0.782839\pi$
$811$	4.49862	−	7.79184i	0.157968	−	0.273609i	0.934136	+	0.356918i	$0.116172\pi$
$812$	7.80353			0.273850
$813$	−14.7801			−0.518360
$814$	44.6060			1.56344
$815$	−3.61191	+	6.25602i	−0.126520	+	0.219139i
$816$	−15.8626	+	27.4748i	−0.555302	+	0.961812i
$817$	−1.49505			−0.0523051
$818$	12.2385	−	21.1976i	0.427908	−	0.741158i
$819$	−3.44855	−	5.97307i	−0.120502	−	0.208716i
$820$	−2.80356	−	4.85591i	−0.0979045	−	0.169576i
$821$	11.7107	−	20.2836i	0.408707	−	0.707902i	−0.586038	−	0.810284i	$-0.699313\pi$
$821$	11.7107	−	20.2836i	0.408707	−	0.707902i	0.994745	+	0.102382i	$0.0326463\pi$
$822$	−1.27198	+	2.20314i	−0.0443655	+	0.0768433i
$823$	−18.6458	−	32.2955i	−0.649953	−	1.12575i	−0.983134	−	0.182888i	$-0.941455\pi$
$823$	−18.6458	−	32.2955i	−0.649953	−	1.12575i	0.333181	−	0.942863i	$-0.391878\pi$
$824$	7.02083			0.244582
$825$	4.02355	+	6.96899i	0.140082	+	0.242629i
$826$	−29.8900			−1.04001
$827$	−4.18198	−	7.24340i	−0.145422	−	0.251878i	0.784108	−	0.620624i	$-0.213121\pi$
$827$	−4.18198	−	7.24340i	−0.145422	−	0.251878i	−0.929530	+	0.368746i	$0.879787\pi$
$828$	17.2623	−	29.8992i	0.599906	−	1.03907i
$829$	9.30430	+	16.1155i	0.323152	+	0.559715i	0.981137	−	0.193316i	$-0.0619242\pi$
$829$	9.30430	+	16.1155i	0.323152	+	0.559715i	−0.657985	+	0.753031i	$0.728591\pi$
$830$	116.110			4.03023
$831$	30.0731			1.04322
$832$	−9.13805	+	15.8276i	−0.316805	+	0.548722i
$833$	11.1669	+	19.3416i	0.386909	+	0.670146i
$834$	7.60793			0.263441
$835$	−20.1496	+	34.9001i	−0.697304	+	1.20777i
$836$	−13.0564	+	22.6143i	−0.451564	+	0.782131i
$837$	2.29925	−	3.98243i	0.0794739	−	0.137653i
$838$	−40.2780	+	69.7635i	−1.39138	+	2.40994i
$839$	8.06411			0.278404			0.139202	−	0.990264i	$-0.455546\pi$
$839$	8.06411			0.278404			0.139202	+	0.990264i	$0.455546\pi$
$840$	−15.0260	+	26.0258i	−0.518447	+	0.897976i
$841$	−27.9213			−0.962804
$842$	−16.8961	+	29.2650i	−0.582280	+	1.00854i
$843$	−7.47661			−0.257508
$844$	39.6225			1.36386
$845$	3.22247	−	5.58149i	0.110856	−	0.192009i
$846$	−12.5994	−	21.8227i	−0.433175	−	0.750281i
$847$	−6.50461	+	11.2663i	−0.223501	+	0.387115i
$848$	0.754603	−	1.30701i	0.0259132	−	0.0448829i
$849$	−10.8164			−0.371218
$850$	60.8227			2.08620
$851$	−38.0176	+	65.8484i	−1.30323	+	2.25725i
$852$	60.5899			2.07578
$853$	16.1162	+	27.9140i	0.551807	+	0.955758i	0.998144	+	0.0608931i	$0.0193949\pi$
$853$	16.1162	+	27.9140i	0.551807	+	0.955758i	−0.446337	+	0.894865i	$0.647272\pi$
$854$	−22.7348	−	39.3779i	−0.777970	−	1.34748i
$855$	−4.88393	−	8.45921i	−0.167027	−	0.289299i
$856$	−39.7678	+	68.8799i	−1.35924	+	2.35427i
$857$	17.2193	−	29.8248i	0.588201	−	1.01879i	−0.406267	−	0.913754i	$-0.633170\pi$
$857$	17.2193	−	29.8248i	0.588201	−	1.01879i	0.994468	−	0.105040i	$-0.0334970\pi$
$858$	−9.29602	−	16.1012i	−0.317361	−	0.549685i
$859$	20.1760	−	34.9458i	0.688395	−	1.19234i	−0.283962	−	0.958836i	$-0.591649\pi$
$859$	20.1760	−	34.9458i	0.688395	−	1.19234i	0.972357	−	0.233499i	$-0.0750177\pi$
$860$	−5.96809			−0.203510
$861$	−0.386846	−	0.670036i	−0.0131837	−	0.0228348i
$862$	−34.6074	−	59.9417i	−1.17873	−	2.04162i
$863$	−19.6144			−0.667682			−0.333841	−	0.942629i	$-0.608345\pi$
$863$	−19.6144			−0.667682			−0.333841	+	0.942629i	$0.608345\pi$
$864$	2.50348			0.0851700
$865$	−8.38495	−	14.5232i	−0.285097	−	0.493802i
$866$	−6.91944	−	11.9848i	−0.235132	−	0.407261i
$867$	16.5683			0.562690
$868$	−17.2756	+	29.9223i	−0.586373	+	1.01563i
$869$	0.854158	+	1.47945i	0.0289753	+	0.0501868i
$870$	−3.93431	+	6.81443i	−0.133386	+	0.231031i
$871$	−12.2939	+	21.2937i	−0.416563	+	0.721508i
$872$	−34.5046	−	59.7638i	−1.16847	−	2.02386i
$873$	−3.18057	−	5.50891i	−0.107646	−	0.186448i
$874$	−32.7622	−	56.7458i	−1.10820	−	1.91946i
$875$	−4.28464			−0.144847
$876$	7.86436	−	13.6215i	0.265712	−	0.460227i
$877$	43.2626			1.46088			0.730438	−	0.682979i	$-0.239316\pi$
$877$	43.2626			1.46088			0.730438	+	0.682979i	$0.239316\pi$
$878$	−66.3251			−2.23836
$879$	−4.11171	+	7.12168i	−0.138684	+	0.240208i
$880$	−15.9002	+	27.5400i	−0.535996	+	0.928372i
$881$	−3.82784	−	6.63001i	−0.128963	−	0.223371i	0.794312	−	0.607510i	$-0.207832\pi$
$881$	−3.82784	−	6.63001i	−0.128963	−	0.223371i	−0.923275	+	0.384139i	$0.874498\pi$
$882$	4.81328	−	8.33684i	0.162072	−	0.280716i
$883$	−2.87556			−0.0967704			−0.0483852	−	0.998829i	$-0.515407\pi$
$883$	−2.87556			−0.0967704			−0.0483852	+	0.998829i	$0.515407\pi$
$884$	−95.4605			−3.21068
$885$	10.2370	−	17.7310i	0.344114	−	0.596022i
$886$	95.9880			3.22478
$887$	−17.7571	+	30.7563i	−0.596227	+	1.03269i	0.397146	+	0.917755i	$0.370001\pi$
$887$	−17.7571	+	30.7563i	−0.596227	+	1.03269i	−0.993373	+	0.114939i	$0.963333\pi$
$888$	−52.1161			−1.74890
$889$	−2.31204	+	4.00456i	−0.0775432	+	0.134309i
$890$	−27.3614	+	47.3913i	−0.917155	+	1.58856i
$891$	0.957157	−	1.65784i	0.0320660	−	0.0555399i
$892$	39.8458	−	69.0150i	1.33414	−	2.31079i
$893$	−32.4881			−1.08717
$894$	−25.2928	−	43.8085i	−0.845919	−	1.46517i
$895$	−40.0983	+	69.4522i	−1.34034	+	2.32153i
$896$	29.6933			0.991984
$897$	31.6919			1.05816
$898$	2.23806	+	3.87644i	0.0746851	+	0.129358i
$899$	−2.38798	+	4.13611i	−0.0796437	+	0.137947i
$900$	−8.90462	−	15.4233i	−0.296821	−	0.514108i
$901$	−1.59688			−0.0531999
$902$	−1.04279	−	1.80617i	−0.0347212	−	0.0601389i
$903$	−0.823499			−0.0274043
$904$	−52.1423	−	90.3131i	−1.73423	−	3.00377i
$905$	−1.10228	+	1.90920i	−0.0366409	+	0.0634639i
$906$	−10.3241	+	17.8819i	−0.342996	+	0.594086i
$907$	−4.54022	−	7.86389i	−0.150756	−	0.261116i	0.780750	−	0.624844i	$-0.214837\pi$
$907$	−4.54022	−	7.86389i	−0.150756	−	0.261116i	−0.931505	+	0.363727i	$0.881504\pi$
$908$	1.02382	+	1.77331i	0.0339766	+	0.0588493i
$909$	−9.55271	+	16.5458i	−0.316844	+	0.548789i
$910$	−52.2542			−1.73221
$911$	9.65090	−	16.7159i	0.319749	−	0.553821i	−0.660687	−	0.750662i	$-0.729735\pi$
$911$	9.65090	−	16.7159i	0.319749	−	0.553821i	0.980435	+	0.196841i	$0.0630682\pi$
$912$	8.81514	−	15.2683i	0.291899	−	0.505583i
$913$	29.3378			0.970938
$914$	−94.0612			−3.11127
$915$	31.1458			1.02965
$916$	−45.7452	+	79.2330i	−1.51146	+	2.61793i
$917$	7.42798	−	12.8656i	0.245293	−	0.424861i
$918$	−7.23452	−	12.5306i	−0.238775	−	0.413570i
$919$	−4.17687			−0.137782			−0.0688911	−	0.997624i	$-0.521946\pi$
$919$	−4.17687			−0.137782			−0.0688911	+	0.997624i	$0.521946\pi$
$920$	−69.0439	−	119.588i	−2.27631	−	3.94269i
$921$	−6.90374	−	11.9576i	−0.227486	−	0.394017i
$922$	2.10643	+	3.64845i	0.0693717	+	0.120155i
$923$	27.8093	+	48.1671i	0.915355	+	1.58544i
$924$	−7.19167	+	12.4563i	−0.236589	+	0.409784i
$925$	19.6111	+	33.9674i	0.644808	+	1.11684i
$926$	50.4234			1.65702
$927$	−0.628481	+	1.08856i	−0.0206420	+	0.0357530i
$928$	−2.60009			−0.0853520
$929$	8.21999	−	14.2374i	0.269689	−	0.467115i	−0.699092	−	0.715031i	$-0.746412\pi$
$929$	8.21999	−	14.2374i	0.269689	−	0.467115i	0.968782	+	0.247916i	$0.0797457\pi$
$930$	−17.4197	−	30.1719i	−0.571216	−	0.989375i
$931$	−6.20563	−	10.7485i	−0.203381	−	0.352267i
$932$	47.6149	+	82.4714i	1.55968	+	2.70144i
$933$	−12.8266	+	22.2162i	−0.419923	+	0.727327i
$934$	75.2031			2.46072
$935$	33.6479			1.10040
$936$	10.8612	+	18.8121i	0.355008	+	0.614892i
$937$	−2.12065	−	3.67308i	−0.0692787	−	0.119994i	0.829305	−	0.558796i	$-0.188736\pi$
$937$	−2.12065	−	3.67308i	−0.0692787	−	0.119994i	−0.898584	+	0.438802i	$0.855403\pi$
$938$	28.0016			0.914284
$939$	−11.4622	−	19.8531i	−0.374054	−	0.647880i
$940$	−129.689			−4.22999
$941$	−2.37323			−0.0773650			−0.0386825	−	0.999252i	$-0.512316\pi$
$941$	−2.37323			−0.0773650			−0.0386825	+	0.999252i	$0.512316\pi$
$942$	−30.3851	−	7.47623i	−0.990001	−	0.243589i
$943$	3.55508			0.115769
$944$	36.9542			1.20276
$945$	−2.69016	−	4.65949i	−0.0875108	−	0.151573i
$946$	−2.21985			−0.0721735
$947$	−4.25759	−	7.37436i	−0.138353	−	0.239635i	0.788520	−	0.615009i	$-0.210848\pi$
$947$	−4.25759	−	7.37436i	−0.138353	−	0.239635i	−0.926873	+	0.375374i	$0.877514\pi$
$948$	−1.89036	−	3.27420i	−0.0613961	−	0.106341i
$949$	14.4382			0.468684
$950$	−33.8003			−1.09663
$951$	−5.85737	+	10.1453i	−0.189938	+	0.328983i
$952$	28.6965	+	49.7038i	0.930059	+	1.61091i
$953$	−15.3641	−	26.6115i	−0.497693	−	0.862030i	0.502303	−	0.864692i	$-0.332486\pi$
$953$	−15.3641	−	26.6115i	−0.497693	−	0.862030i	−0.999996	+	0.00266134i	$0.999153\pi$
$954$	0.344154	+	0.596093i	0.0111424	+	0.0192992i
$955$	6.19825	−	10.7357i	0.200571	−	0.347399i
$956$	−41.5527			−1.34391
$957$	−0.994094	+	1.72182i	−0.0321345	+	0.0556586i
$958$	−46.9555			−1.51706
$959$	0.903305	+	1.56457i	0.0291692	+	0.0505226i
$960$	−7.12843	+	12.3468i	−0.230069	+	0.398491i
$961$	4.92686	+	8.53356i	0.158931	+	0.275276i
$962$	−45.3095	−	78.4784i	−1.46084	−	2.53024i
$963$	−7.11976	−	12.3318i	−0.229431	−	0.397386i
$964$	32.5505	+	56.3791i	1.04838	+	1.81585i
$965$	11.3480			0.365306
$966$	−18.0460	−	31.2566i	−0.580621	−	1.00566i
$967$	14.0947	−	24.4128i	0.453256	−	0.785063i	−0.545330	−	0.838221i	$-0.683596\pi$
$967$	14.0947	−	24.4128i	0.453256	−	0.785063i	0.998586	+	0.0531589i	$0.0169290\pi$
$968$	20.4862	−	35.4831i	0.658450	−	1.14047i
$969$	−18.6545			−0.599270
$970$	−48.1936			−1.54740
$971$	49.9238			1.60213			0.801066	−	0.598576i	$-0.204266\pi$
$971$	49.9238			1.60213			0.801066	+	0.598576i	$0.204266\pi$
$972$	−2.11831	+	3.66902i	−0.0679448	+	0.117684i
$973$	2.70140	−	4.67897i	0.0866030	−	0.150001i
$974$	−91.5355			−2.93299
$975$	8.17401	−	14.1578i	0.261778	−	0.453413i
$976$	28.1080	+	48.6844i	0.899714	+	1.55835i
$977$	−8.72812	−	15.1175i	−0.279237	−	0.483653i	0.691958	−	0.721938i	$-0.256748\pi$
$977$	−8.72812	−	15.1175i	−0.279237	−	0.483653i	−0.971195	+	0.238285i	$0.923415\pi$
$978$	2.97325	−	5.14983i	0.0950742	−	0.164673i
$979$	−6.91347	+	11.9745i	−0.220956	+	0.382706i
$980$	−24.7723	−	42.9068i	−0.791321	−	1.37061i
$981$	12.3549			0.394463
$982$	−27.8045	−	48.1588i	−0.887277	−	1.53681i
$983$	51.8598			1.65407			0.827035	−	0.562150i	$-0.190026\pi$
$983$	51.8598			1.65407			0.827035	+	0.562150i	$0.190026\pi$
$984$	1.21836	+	2.11027i	0.0388400	+	0.0672729i
$985$	1.70842	−	2.95907i	0.0544347	−	0.0942837i
$986$	7.51370	+	13.0141i	0.239285	+	0.414454i
$987$	−17.8950			−0.569604
$988$	53.0491			1.68772
$989$	1.89197	−	3.27699i	0.0601612	−	0.104202i
$990$	−7.25166	−	12.5602i	−0.230473	−	0.399191i
$991$	−9.04492			−0.287321			−0.143661	−	0.989627i	$-0.545887\pi$
$991$	−9.04492			−0.287321			−0.143661	+	0.989627i	$0.545887\pi$
$992$	5.75613	−	9.96991i	0.182757	−	0.316545i
$993$	5.21029	−	9.02449i	0.165344	−	0.286383i
$994$	31.6704	−	54.8547i	1.00452	−	1.73988i
$995$	25.1604	−	43.5791i	0.797638	−	1.38155i
$996$	−64.9282			−2.05733
$997$	−15.0841	+	26.1264i	−0.477718	+	0.827432i	−0.999674	−	0.0255404i	$-0.991869\pi$
$997$	−15.0841	+	26.1264i	−0.477718	+	0.827432i	0.521956	+	0.852973i	$0.325203\pi$
$998$	−37.7963			−1.19642
$999$	4.66526	−	8.08046i	0.147602	−	0.255655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.e.c.169.13	✓	28
157.144	even	3	inner	471.2.e.c.301.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.e.c.169.13	✓	28	1.1	even	1	trivial
471.2.e.c.301.13	yes	28	157.144	even	3	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:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.49732 q^{2} +(-0.500000 - 0.866025i) q^{3} +4.23662 q^{4} +(1.51688 + 2.62731i) q^{5} +(-1.24866 - 2.16274i) q^{6} -1.77348 q^{7} +5.58556 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+2.49732 q^{2} +(-0.500000 - 0.866025i) q^{3} +4.23662 q^{4} +(1.51688 + 2.62731i) q^{5} +(-1.24866 - 2.16274i) q^{6} -1.77348 q^{7} +5.58556 q^{8} +(-0.500000 + 0.866025i) q^{9} +(3.78813 + 6.56123i) q^{10} +(0.957157 + 1.65784i) q^{11} +(-2.11831 - 3.66902i) q^{12} +(1.94451 - 3.36798i) q^{13} -4.42896 q^{14} +(1.51688 - 2.62731i) q^{15} +5.47570 q^{16} +(-2.89691 - 5.01759i) q^{17} +(-1.24866 + 2.16274i) q^{18} +(1.60987 + 2.78837i) q^{19} +(6.42642 + 11.1309i) q^{20} +(0.886742 + 1.53588i) q^{21} +(2.39033 + 4.14017i) q^{22} -8.14909 q^{23} +(-2.79278 - 4.83724i) q^{24} +(-2.10182 + 3.64046i) q^{25} +(4.85606 - 8.41094i) q^{26} +1.00000 q^{27} -7.51358 q^{28} -1.03859 q^{29} +(3.78813 - 6.56123i) q^{30} +(2.29925 - 3.98243i) q^{31} +2.50348 q^{32} +(0.957157 - 1.65784i) q^{33} +(-7.23452 - 12.5306i) q^{34} +(-2.69016 - 4.65949i) q^{35} +(-2.11831 + 3.66902i) q^{36} +(4.66526 - 8.08046i) q^{37} +(4.02035 + 6.96345i) q^{38} -3.88901 q^{39} +(8.47260 + 14.6750i) q^{40} -0.436255 q^{41} +(2.21448 + 3.83559i) q^{42} +(-0.232170 + 0.402130i) q^{43} +(4.05511 + 7.02365i) q^{44} -3.03375 q^{45} -20.3509 q^{46} +(-5.04515 + 8.73846i) q^{47} +(-2.73785 - 4.74210i) q^{48} -3.85475 q^{49} +(-5.24893 + 9.09141i) q^{50} +(-2.89691 + 5.01759i) q^{51} +(8.23813 - 14.2689i) q^{52} +(0.137809 - 0.238693i) q^{53} +2.49732 q^{54} +(-2.90378 + 5.02949i) q^{55} -9.90590 q^{56} +(1.60987 - 2.78837i) q^{57} -2.59370 q^{58} +6.74876 q^{59} +(6.42642 - 11.1309i) q^{60} +(5.13322 + 8.89099i) q^{61} +(5.74198 - 9.94540i) q^{62} +(0.886742 - 1.53588i) q^{63} -4.69942 q^{64} +11.7983 q^{65} +(2.39033 - 4.14017i) q^{66} -6.32238 q^{67} +(-12.2731 - 21.2576i) q^{68} +(4.07454 + 7.05732i) q^{69} +(-6.71819 - 11.6362i) q^{70} +(-7.15074 + 12.3854i) q^{71} +(-2.79278 + 4.83724i) q^{72} +(1.85628 + 3.21518i) q^{73} +(11.6507 - 20.1795i) q^{74} +4.20364 q^{75} +(6.82039 + 11.8133i) q^{76} +(-1.69750 - 2.94016i) q^{77} -9.71212 q^{78} +0.892391 q^{79} +(8.30596 + 14.3863i) q^{80} +(-0.500000 - 0.866025i) q^{81} -1.08947 q^{82} +(7.66274 - 13.2722i) q^{83} +(3.75679 + 6.50695i) q^{84} +(8.78850 - 15.2221i) q^{85} +(-0.579803 + 1.00425i) q^{86} +(0.519295 + 0.899446i) q^{87} +(5.34625 + 9.25999i) q^{88} +(3.61146 + 6.25524i) q^{89} -7.57625 q^{90} +(-3.44855 + 5.97307i) q^{91} -34.5246 q^{92} -4.59851 q^{93} +(-12.5994 + 21.8227i) q^{94} +(-4.88393 + 8.45921i) q^{95} +(-1.25174 - 2.16807i) q^{96} +(-3.18057 + 5.50891i) q^{97} -9.62656 q^{98} -1.91431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9	\( 28 q + 2 q^{2} - 14 q^{3} + 26 q^{4} - 2 q^{5} - q^{6} + 4 q^{7} - 14 q^{9} - q^{10} + 2 q^{11} - 13 q^{12} - 14 q^{14} - 2 q^{15} + 14 q^{16} + 3 q^{17} - q^{18} - 11 q^{19} + q^{20} - 2 q^{21} - 2 q^{22} - 6 q^{23} - 20 q^{25} + 12 q^{26} + 28 q^{27} + 2 q^{28} - 10 q^{29} - q^{30} - 14 q^{31} + 12 q^{32} + 2 q^{33} - 15 q^{34} - 13 q^{35} - 13 q^{36} - q^{37} + 18 q^{38} - 8 q^{40} + 16 q^{41} + 7 q^{42} - 16 q^{43} + 12 q^{44} + 4 q^{45} + 16 q^{46} - 29 q^{47} - 7 q^{48} + 44 q^{49} - 29 q^{50} + 3 q^{51} + 27 q^{52} + 6 q^{53} + 2 q^{54} - 29 q^{55} - 26 q^{56} - 11 q^{57} + 62 q^{58} - 8 q^{59} + q^{60} + 14 q^{61} + 52 q^{62} - 2 q^{63} + 16 q^{64} - 52 q^{65} - 2 q^{66} + 36 q^{67} + 6 q^{68} + 3 q^{69} - 37 q^{70} - 27 q^{71} - 10 q^{73} - 5 q^{74} + 40 q^{75} - 43 q^{76} + 11 q^{77} - 24 q^{78} - 16 q^{79} - 26 q^{80} - 14 q^{81} - 24 q^{82} + 12 q^{83} - q^{84} + 12 q^{85} - 56 q^{86} + 5 q^{87} + 47 q^{88} - 13 q^{89} + 2 q^{90} + 13 q^{91} - 50 q^{92} + 28 q^{93} - 40 q^{94} - 7 q^{95} - 6 q^{96} + 6 q^{97} - 46 q^{98} - 4 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 14 * q^3 + 26 * q^4 - 2 * q^5 - q^6 + 4 * q^7 - 14 * q^9 - q^10 + 2 * q^11 - 13 * q^12 - 14 * q^14 - 2 * q^15 + 14 * q^16 + 3 * q^17 - q^18 - 11 * q^19 + q^20 - 2 * q^21 - 2 * q^22 - 6 * q^23 - 20 * q^25 + 12 * q^26 + 28 * q^27 + 2 * q^28 - 10 * q^29 - q^30 - 14 * q^31 + 12 * q^32 + 2 * q^33 - 15 * q^34 - 13 * q^35 - 13 * q^36 - q^37 + 18 * q^38 - 8 * q^40 + 16 * q^41 + 7 * q^42 - 16 * q^43 + 12 * q^44 + 4 * q^45 + 16 * q^46 - 29 * q^47 - 7 * q^48 + 44 * q^49 - 29 * q^50 + 3 * q^51 + 27 * q^52 + 6 * q^53 + 2 * q^54 - 29 * q^55 - 26 * q^56 - 11 * q^57 + 62 * q^58 - 8 * q^59 + q^60 + 14 * q^61 + 52 * q^62 - 2 * q^63 + 16 * q^64 - 52 * q^65 - 2 * q^66 + 36 * q^67 + 6 * q^68 + 3 * q^69 - 37 * q^70 - 27 * q^71 - 10 * q^73 - 5 * q^74 + 40 * q^75 - 43 * q^76 + 11 * q^77 - 24 * q^78 - 16 * q^79 - 26 * q^80 - 14 * q^81 - 24 * q^82 + 12 * q^83 - q^84 + 12 * q^85 - 56 * q^86 + 5 * q^87 + 47 * q^88 - 13 * q^89 + 2 * q^90 + 13 * q^91 - 50 * q^92 + 28 * q^93 - 40 * q^94 - 7 * q^95 - 6 * q^96 + 6 * q^97 - 46 * q^98 - 4 * q^99

Introduction

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