LMFDB - Embedded newform 378.2.w.b.25.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,2,Mod(25,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([10, 12])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$378 = 2 \cdot 3^{3} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	378.w (of order $9$ , degree $6$ , minimal)

Newform invariants

comment:select newform

sage:traces = [72,0,0,0,0,3,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.11
Character	$\chi$	$=$	378.25
Dual form			378.2.w.b.121.11

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(1.56589 + 0.740254i) q^{3} +(0.766044 - 0.642788i) q^{4} +(1.77013 + 0.644273i) q^{5} +(1.72464 + 0.160044i) q^{6} +(-2.34950 - 1.21648i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.90405 + 2.31832i) q^{9} +1.88373 q^{10} +(0.319796 - 0.116396i) q^{11} +(1.67537 - 0.439470i) q^{12} +(-0.168029 - 0.952940i) q^{13} +(-2.62387 - 0.339542i) q^{14} +(2.29490 + 2.31921i) q^{15} +(0.173648 - 0.984808i) q^{16} -4.46285 q^{17} +(2.58213 + 1.52728i) q^{18} +1.18573 q^{19} +(1.77013 - 0.644273i) q^{20} +(-2.77857 - 3.64411i) q^{21} +(0.260700 - 0.218754i) q^{22} +(0.769854 + 4.36606i) q^{23} +(1.42403 - 0.985977i) q^{24} +(-1.11197 - 0.933050i) q^{25} +(-0.483820 - 0.838001i) q^{26} +(1.26539 + 5.03972i) q^{27} +(-2.58176 + 0.578353i) q^{28} +(1.20762 - 6.84877i) q^{29} +(2.94972 + 1.39444i) q^{30} +(-7.22451 + 6.06208i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.586930 + 0.0544663i) q^{33} +(-4.19371 + 1.52638i) q^{34} +(-3.37517 - 3.66705i) q^{35} +(2.94877 + 0.552038i) q^{36} +(-0.905954 + 1.56916i) q^{37} +(1.11423 - 0.405545i) q^{38} +(0.442302 - 1.61659i) q^{39} +(1.44302 - 1.21084i) q^{40} +(-1.05102 - 5.96062i) q^{41} +(-3.85736 - 2.47402i) q^{42} +(1.95189 + 1.63783i) q^{43} +(0.170160 - 0.294726i) q^{44} +(1.87677 + 5.33044i) q^{45} +(2.21671 + 3.83945i) q^{46} +(0.0254607 + 0.0213641i) q^{47} +(1.00092 - 1.41356i) q^{48} +(4.04034 + 5.71626i) q^{49} +(-1.36403 - 0.496466i) q^{50} +(-6.98835 - 3.30364i) q^{51} +(-0.741256 - 0.621987i) q^{52} +(5.22772 - 9.05468i) q^{53} +(2.91276 + 4.30300i) q^{54} +0.641071 q^{55} +(-2.22826 + 1.42649i) q^{56} +(1.85673 + 0.877745i) q^{57} +(-1.20762 - 6.84877i) q^{58} +(0.160747 + 0.911640i) q^{59} +(3.24875 + 0.301480i) q^{60} +(-4.38118 - 3.67625i) q^{61} +(-4.71546 + 8.16742i) q^{62} +(-1.65337 - 7.76314i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.316521 - 1.79508i) q^{65} +(0.570162 - 0.149560i) q^{66} +(2.00249 + 0.728847i) q^{67} +(-3.41874 + 2.86867i) q^{68} +(-2.02648 + 7.40667i) q^{69} +(-4.42583 - 2.29152i) q^{70} +(-6.38672 - 11.0621i) q^{71} +(2.95975 - 0.489794i) q^{72} +(5.21200 + 9.02746i) q^{73} +(-0.314634 + 1.78438i) q^{74} +(-1.05053 - 2.28420i) q^{75} +(0.908325 - 0.762175i) q^{76} +(-0.892957 - 0.115553i) q^{77} +(-0.137277 - 1.67037i) q^{78} +(-16.6635 + 6.06502i) q^{79} +(0.941864 - 1.63136i) q^{80} +(-1.74921 + 8.82838i) q^{81} +(-3.02629 - 5.24169i) q^{82} +(-0.527591 + 2.99212i) q^{83} +(-4.47090 - 1.00552i) q^{84} +(-7.89981 - 2.87529i) q^{85} +(2.39434 + 0.871470i) q^{86} +(6.96084 - 9.83050i) q^{87} +(0.0590960 - 0.335150i) q^{88} +1.04441 q^{89} +(3.58671 + 4.36708i) q^{90} +(-0.764449 + 2.44334i) q^{91} +(3.39619 + 2.84974i) q^{92} +(-15.8003 + 4.14461i) q^{93} +(0.0312322 + 0.0113676i) q^{94} +(2.09890 + 0.763936i) q^{95} +(0.457094 - 1.67065i) q^{96} +(10.1353 + 8.50450i) q^{97} +(5.75176 + 3.98965i) q^{98} +(0.878751 + 0.519766i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30}+ \cdots + 90 q^{99}+O(q^{100})$ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$ .

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	1.56589	+	0.740254i	0.904069	+	0.427386i
$3$	1.56589	+	0.740254i	0.904069	+	0.427386i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	1.77013	+	0.644273i	0.791624	+	0.288128i	0.706011	−	0.708201i	$-0.250493\pi$
$5$	1.77013	+	0.644273i	0.791624	+	0.288128i	0.0856131	+	0.996328i	$0.472715\pi$
$6$	1.72464	+	0.160044i	0.704082	+	0.0653378i
$7$	−2.34950	−	1.21648i	−0.888029	−	0.459787i
$7$	−2.34950	−	1.21648i	−0.888029	−	0.459787i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	1.90405	+	2.31832i	0.634682	+	0.772773i
$10$	1.88373			0.595687
$11$	0.319796	−	0.116396i	0.0964222	−	0.0350948i	−0.293359	−	0.956002i	$-0.594773\pi$
$11$	0.319796	−	0.116396i	0.0964222	−	0.0350948i	0.389781	+	0.920908i	$0.372551\pi$
$12$	1.67537	−	0.439470i	0.483638	−	0.126864i
$13$	−0.168029	−	0.952940i	−0.0466029	−	0.264298i	0.952600	−	0.304227i	$-0.0983980\pi$
$13$	−0.168029	−	0.952940i	−0.0466029	−	0.264298i	−0.999203	+	0.0399287i	$0.987287\pi$
$14$	−2.62387	−	0.339542i	−0.701260	−	0.0907463i
$15$	2.29490	+	2.31921i	0.592541	+	0.598816i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−4.46285			−1.08240			−0.541200	−	0.840894i	$-0.682030\pi$
$17$	−4.46285			−1.08240			−0.541200	+	0.840894i	$0.682030\pi$
$18$	2.58213	+	1.52728i	0.608614	+	0.359985i
$19$	1.18573			0.272026			0.136013	−	0.990707i	$-0.456571\pi$
$19$	1.18573			0.272026			0.136013	+	0.990707i	$0.456571\pi$
$20$	1.77013	−	0.644273i	0.395812	−	0.144064i
$21$	−2.77857	−	3.64411i	−0.606333	−	0.795211i
$22$	0.260700	−	0.218754i	0.0555815	−	0.0466384i
$23$	0.769854	+	4.36606i	0.160526	+	0.910386i	0.953559	+	0.301208i	$0.0973897\pi$
$23$	0.769854	+	4.36606i	0.160526	+	0.910386i	−0.793033	+	0.609179i	$0.791499\pi$
$24$	1.42403	−	0.985977i	0.290678	−	0.201262i
$25$	−1.11197	−	0.933050i	−0.222393	−	0.186610i
$26$	−0.483820	−	0.838001i	−0.0948849	−	0.164346i
$27$	1.26539	+	5.03972i	0.243524	+	0.969895i
$28$	−2.58176	+	0.578353i	−0.487908	+	0.109298i
$29$	1.20762	−	6.84877i	0.224250	−	1.27178i	−0.639864	−	0.768488i	$-0.721009\pi$
$29$	1.20762	−	6.84877i	0.224250	−	1.27178i	0.864114	−	0.503296i	$-0.167880\pi$
$30$	2.94972	+	1.39444i	0.538542	+	0.254588i
$31$	−7.22451	+	6.06208i	−1.29756	+	1.08878i	−0.307000	+	0.951710i	$0.599325\pi$
$31$	−7.22451	+	6.06208i	−1.29756	+	1.08878i	−0.990561	+	0.137073i	$0.956231\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	0.586930	+	0.0544663i	0.102171	+	0.00948136i
$34$	−4.19371	+	1.52638i	−0.719215	+	0.261773i
$35$	−3.37517	−	3.66705i	−0.570508	−	0.619844i
$36$	2.94877	+	0.552038i	0.491462	+	0.0920063i
$37$	−0.905954	+	1.56916i	−0.148938	+	0.257968i	−0.930835	−	0.365439i	$-0.880919\pi$
$37$	−0.905954	+	1.56916i	−0.148938	+	0.257968i	0.781897	+	0.623407i	$0.214252\pi$
$38$	1.11423	−	0.405545i	0.180751	−	0.0657881i
$39$	0.442302	−	1.61659i	0.0708250	−	0.258861i
$40$	1.44302	−	1.21084i	0.228161	−	0.191450i
$41$	−1.05102	−	5.96062i	−0.164142	−	0.930893i	−0.949945	−	0.312417i	$-0.898861\pi$
$41$	−1.05102	−	5.96062i	−0.164142	−	0.930893i	0.785804	−	0.618476i	$-0.212250\pi$
$42$	−3.85736	−	2.47402i	−0.595204	−	0.381750i
$43$	1.95189	+	1.63783i	0.297660	+	0.249766i	0.779370	−	0.626565i	$-0.215540\pi$
$43$	1.95189	+	1.63783i	0.297660	+	0.249766i	−0.481710	+	0.876331i	$0.659984\pi$
$44$	0.170160	−	0.294726i	0.0256526	−	0.0444316i
$45$	1.87677	+	5.33044i	0.279773	+	0.794615i
$46$	2.21671	+	3.83945i	0.326836	+	0.566096i
$47$	0.0254607	+	0.0213641i	0.00371383	+	0.00311627i	0.644643	−	0.764484i	$-0.277006\pi$
$47$	0.0254607	+	0.0213641i	0.00371383	+	0.00311627i	−0.640929	+	0.767600i	$0.721451\pi$
$48$	1.00092	−	1.41356i	0.144471	−	0.204030i
$49$	4.04034	+	5.71626i	0.577192	+	0.816609i
$50$	−1.36403	−	0.496466i	−0.192903	−	0.0702108i
$51$	−6.98835	−	3.30364i	−0.978565	−	0.462603i
$52$	−0.741256	−	0.621987i	−0.102794	−	0.0862541i
$53$	5.22772	−	9.05468i	0.718082	−	1.24376i	−0.243676	−	0.969857i	$-0.578353\pi$
$53$	5.22772	−	9.05468i	0.718082	−	1.24376i	0.961759	−	0.273899i	$-0.0883133\pi$
$54$	2.91276	+	4.30300i	0.396377	+	0.585564i
$55$	0.641071			0.0864419
$56$	−2.22826	+	1.42649i	−0.297763	+	0.190623i
$57$	1.85673	+	0.877745i	0.245930	+	0.116260i
$58$	−1.20762	−	6.84877i	−0.158569	−	0.899288i
$59$	0.160747	+	0.911640i	0.0209274	+	0.118685i	0.993482	−	0.113990i	$-0.0363632\pi$
$59$	0.160747	+	0.911640i	0.0209274	+	0.118685i	−0.972554	+	0.232675i	$0.925252\pi$
$60$	3.24875	+	0.301480i	0.419412	+	0.0389209i
$61$	−4.38118	−	3.67625i	−0.560953	−	0.470695i	0.317677	−	0.948199i	$-0.397097\pi$
$61$	−4.38118	−	3.67625i	−0.560953	−	0.470695i	−0.878630	+	0.477504i	$0.841542\pi$
$62$	−4.71546	+	8.16742i	−0.598865	+	1.03726i
$63$	−1.65337	−	7.76314i	−0.208305	−	0.978064i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.316521	−	1.79508i	0.0392596	−	0.222652i
$66$	0.570162	−	0.149560i	0.0701821	−	0.0184096i
$67$	2.00249	+	0.728847i	0.244643	+	0.0890429i	0.461432	−	0.887176i	$-0.347336\pi$
$67$	2.00249	+	0.728847i	0.244643	+	0.0890429i	−0.216788	+	0.976219i	$0.569558\pi$
$68$	−3.41874	+	2.86867i	−0.414583	+	0.347877i
$69$	−2.02648	+	7.40667i	−0.243960	+	0.891659i
$70$	−4.42583	−	2.29152i	−0.528988	−	0.273889i
$71$	−6.38672	−	11.0621i	−0.757964	−	1.31283i	−0.943887	−	0.330268i	$-0.892861\pi$
$71$	−6.38672	−	11.0621i	−0.757964	−	1.31283i	0.185923	−	0.982564i	$-0.440473\pi$
$72$	2.95975	−	0.489794i	0.348810	−	0.0577227i
$73$	5.21200	+	9.02746i	0.610019	+	1.05658i	0.991237	+	0.132099i	$0.0421716\pi$
$73$	5.21200	+	9.02746i	0.610019	+	1.05658i	−0.381218	+	0.924485i	$0.624495\pi$
$74$	−0.314634	+	1.78438i	−0.0365755	+	0.207430i
$75$	−1.05053	−	2.28420i	−0.121304	−	0.263756i
$76$	0.908325	−	0.762175i	0.104192	−	0.0874275i
$77$	−0.892957	−	0.115553i	−0.101762	−	0.0131685i
$78$	−0.137277	−	1.67037i	−0.0155436	−	0.189132i
$79$	−16.6635	+	6.06502i	−1.87479	+	0.682368i	−0.913490	+	0.406861i	$0.866623\pi$
$79$	−16.6635	+	6.06502i	−1.87479	+	0.682368i	−0.961299	+	0.275507i	$0.911154\pi$
$80$	0.941864	−	1.63136i	0.105304	−	0.182391i
$81$	−1.74921	+	8.82838i	−0.194356	+	0.980931i
$82$	−3.02629	−	5.24169i	−0.334198	−	0.578847i
$83$	−0.527591	+	2.99212i	−0.0579107	+	0.328428i	−0.999975	−	0.00700320i	$-0.997771\pi$
$83$	−0.527591	+	2.99212i	−0.0579107	+	0.328428i	0.942065	+	0.335431i	$0.108882\pi$
$84$	−4.47090	−	1.00552i	−0.487815	−	0.109712i
$85$	−7.89981	−	2.87529i	−0.856854	−	0.311869i
$86$	2.39434	+	0.871470i	0.258189	+	0.0939730i
$87$	6.96084	−	9.83050i	0.746280	−	1.05394i
$88$	0.0590960	−	0.335150i	0.00629965	−	0.0357271i
$89$	1.04441			0.110707			0.0553535	−	0.998467i	$-0.482371\pi$
$89$	1.04441			0.110707			0.0553535	+	0.998467i	$0.482371\pi$
$90$	3.58671	+	4.36708i	0.378072	+	0.460331i
$91$	−0.764449	+	2.44334i	−0.0801361	+	0.256132i
$92$	3.39619	+	2.84974i	0.354077	+	0.297106i
$93$	−15.8003	+	4.14461i	−1.63841	+	0.429776i
$94$	0.0312322	+	0.0113676i	0.00322136	+	0.00117248i
$95$	2.09890	+	0.763936i	0.215342	+	0.0783782i
$96$	0.457094	−	1.67065i	0.0466519	−	0.170510i
$97$	10.1353	+	8.50450i	1.02908	+	0.863501i	0.990741	−	0.135763i	$-0.0433487\pi$
$97$	10.1353	+	8.50450i	1.02908	+	0.863501i	0.0383396	+	0.999265i	$0.487793\pi$
$98$	5.75176	+	3.98965i	0.581015	+	0.403016i
$99$	0.878751	+	0.519766i	0.0883178	+	0.0522384i
$100$	−1.45157			−0.145157
$101$	−1.48469	+	8.42010i	−0.147732	+	0.837831i	0.817400	+	0.576070i	$0.195414\pi$
$101$	−1.48469	+	8.42010i	−0.147732	+	0.837831i	−0.965133	+	0.261761i	$0.915697\pi$
$102$	−7.69681	−	0.714253i	−0.762098	−	0.0707216i
$103$	8.96895	+	3.26443i	0.883736	+	0.321654i	0.743717	−	0.668495i	$-0.233061\pi$
$103$	8.96895	+	3.26443i	0.883736	+	0.321654i	0.140020	+	0.990149i	$0.455283\pi$
$104$	−0.909284	−	0.330952i	−0.0891627	−	0.0324526i
$105$	−2.57061	−	8.24069i	−0.250866	−	0.804209i
$106$	1.81557	−	10.2966i	0.176344	−	1.00009i
$107$	−4.23818	−	7.34075i	−0.409721	−	0.709657i	0.585138	−	0.810934i	$-0.301040\pi$
$107$	−4.23818	−	7.34075i	−0.409721	−	0.709657i	−0.994858	+	0.101277i	$0.967707\pi$
$108$	4.20882	+	3.04727i	0.404993	+	0.293224i
$109$	6.41995	−	11.1197i	0.614920	−	1.06507i	−0.375478	−	0.926831i	$-0.622522\pi$
$109$	6.41995	−	11.1197i	0.614920	−	1.06507i	0.990399	−	0.138242i	$-0.0441451\pi$
$110$	0.602409	−	0.219259i	0.0574375	−	0.0209055i
$111$	−2.58020	+	1.78650i	−0.244902	+	0.169567i
$112$	−1.60599	+	2.10257i	−0.151752	+	0.198674i
$113$	6.87430	−	5.76822i	0.646679	−	0.542628i	−0.259382	−	0.965775i	$-0.583519\pi$
$113$	6.87430	−	5.76822i	0.646679	−	0.542628i	0.906061	+	0.423146i	$0.139074\pi$
$114$	2.04497	+	0.189770i	0.191529	+	0.0177736i
$115$	−1.45020	+	8.22447i	−0.135231	+	0.766936i
$116$	−3.47721	−	6.02271i	−0.322851	−	0.559194i
$117$	1.88928	−	2.20399i	0.174664	−	0.203759i
$118$	0.462852	+	0.801683i	0.0426090	+	0.0738009i
$119$	10.4855	+	5.42898i	0.961203	+	0.497674i
$120$	3.15594	−	0.827841i	0.288097	−	0.0755712i
$121$	−8.33777	+	6.99622i	−0.757979	+	0.636020i
$122$	−5.37431	−	1.95609i	−0.486567	−	0.177096i
$123$	2.76659	−	10.1117i	0.249455	−	0.911744i
$124$	−1.63766	+	9.28765i	−0.147067	+	0.834056i
$125$	−6.07650	−	10.5248i	−0.543499	−	0.941367i
$126$	−4.20881	−	6.72948i	−0.374951	−	0.599510i
$127$	1.52799	−	2.64656i	0.135587	−	0.234844i	−0.790234	−	0.612805i	$-0.790041\pi$
$127$	1.52799	−	2.64656i	0.135587	−	0.234844i	0.925822	+	0.377961i	$0.123375\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	1.84404	+	4.00956i	0.162359	+	0.353022i
$130$	−0.316521	−	1.79508i	−0.0277607	−	0.157439i
$131$	2.71064	+	15.3728i	0.236830	+	1.34313i	0.838726	+	0.544554i	$0.183301\pi$
$131$	2.71064	+	15.3728i	0.236830	+	1.34313i	−0.601896	+	0.798575i	$0.705588\pi$
$132$	0.484625	−	0.335548i	0.0421812	−	0.0292057i
$133$	−2.78589	−	1.44242i	−0.241567	−	0.125074i
$134$	2.13101			0.184091
$135$	−1.00706	+	9.73619i	−0.0866736	+	0.837958i
$136$	−2.23143	+	3.86494i	−0.191343	+	0.331416i
$137$	11.2689	+	9.45570i	0.962764	+	0.807855i	0.981400	−	0.191972i	$-0.0614882\pi$
$137$	11.2689	+	9.45570i	0.962764	+	0.807855i	−0.0186367	+	0.999826i	$0.505933\pi$
$138$	0.628959	+	7.65310i	0.0535406	+	0.651475i
$139$	−9.24908	−	3.36639i	−0.784497	−	0.285533i	−0.0814503	−	0.996677i	$-0.525955\pi$
$139$	−9.24908	−	3.36639i	−0.784497	−	0.285533i	−0.703046	+	0.711144i	$0.748177\pi$
$140$	−4.94266	−	0.639604i	−0.417731	−	0.0540564i
$141$	0.0240540	+	0.0523013i	0.00202571	+	0.00440457i
$142$	−9.78503	−	8.21061i	−0.821141	−	0.689019i
$143$	−0.164654	−	0.285189i	−0.0137690	−	0.0238487i
$144$	2.61373	−	1.47255i	0.217811	−	0.122712i
$145$	6.55012	−	11.3451i	0.543958	−	0.942163i
$146$	7.98525	+	6.70042i	0.660864	+	0.554531i
$147$	2.09526	+	11.9419i	0.172814	+	0.984954i
$148$	0.314634	+	1.78438i	0.0258628	+	0.146675i
$149$	15.2601	−	12.8048i	1.25016	−	1.04901i	0.253498	−	0.967336i	$-0.418419\pi$
$149$	15.2601	−	12.8048i	1.25016	−	1.04901i	0.996659	−	0.0816710i	$-0.0260257\pi$
$150$	−1.76841	−	1.78714i	−0.144390	−	0.145919i
$151$	−13.8473	+	5.03999i	−1.12687	+	0.410149i	−0.837157	−	0.546963i	$-0.815784\pi$
$151$	−13.8473	+	5.03999i	−1.12687	+	0.410149i	−0.289718	+	0.957112i	$0.593561\pi$
$152$	0.592867	−	1.02688i	0.0480879	−	0.0832906i
$153$	−8.49748	−	10.3463i	−0.686980	−	0.836450i
$154$	−0.878626	+	0.196825i	−0.0708017	+	0.0158606i
$155$	−16.6939	+	6.07609i	−1.34089	+	0.488044i
$156$	−0.700299	−	1.52268i	−0.0560688	−	0.121912i
$157$	3.41653	+	19.3761i	0.272669	+	1.54638i	0.746271	+	0.665642i	$0.231842\pi$
$157$	3.41653	+	19.3761i	0.272669	+	1.54638i	−0.473603	+	0.880739i	$0.657047\pi$
$158$	−13.5842	+	11.3985i	−1.08070	+	0.906816i
$159$	14.8888	−	10.3088i	1.18076	−	0.817543i
$160$	0.327106	−	1.85511i	0.0258600	−	0.146659i
$161$	3.50246	−	11.1946i	0.276032	−	0.882257i
$162$	1.37577	+	8.89423i	0.108090	+	0.698796i
$163$	2.27942	+	3.94807i	0.178538	+	0.309237i	0.941380	−	0.337348i	$-0.109530\pi$
$163$	2.27942	+	3.94807i	0.178538	+	0.309237i	−0.762842	+	0.646585i	$0.776197\pi$
$164$	−4.63654	−	3.89052i	−0.362053	−	0.303799i
$165$	1.00385	+	0.474555i	0.0781495	+	0.0369441i
$166$	0.527591	+	2.99212i	0.0409490	+	0.232233i
$167$	−4.44377	+	3.72877i	−0.343870	+	0.288541i	−0.798323	−	0.602230i	$-0.794279\pi$
$167$	−4.44377	+	3.72877i	−0.343870	+	0.288541i	0.454453	+	0.890771i	$0.349835\pi$
$168$	−4.54518	+	0.584254i	−0.350668	+	0.0450762i
$169$	11.3361	−	4.12602i	0.872011	−	0.317386i
$170$	−8.40680			−0.644772
$171$	2.25769	+	2.74891i	0.172650	+	0.210214i
$172$	2.54801			0.194284
$173$	1.18735	−	6.73378i	0.0902723	−	0.511960i	−0.905822	−	0.423659i	$-0.860745\pi$
$173$	1.18735	−	6.73378i	0.0902723	−	0.511960i	0.996094	−	0.0883004i	$-0.0281435\pi$
$174$	3.17882	−	11.6184i	0.240986	−	0.880788i
$175$	1.47753	+	3.54489i	0.111691	+	0.267969i
$176$	−0.0590960	−	0.335150i	−0.00445453	−	0.0252629i
$177$	−0.423133	+	1.54652i	−0.0318046	+	0.116244i
$178$	0.981422	−	0.357208i	0.0735607	−	0.0267739i
$179$	16.8343			1.25825			0.629126	−	0.777304i	$-0.283413\pi$
$179$	16.8343			1.25825			0.629126	+	0.777304i	$0.283413\pi$
$180$	4.86403	+	2.87699i	0.362544	+	0.214438i
$181$	10.4465	−	18.0939i	0.776484	−	1.34491i	−0.157472	−	0.987523i	$-0.550335\pi$
$181$	10.4465	−	18.0939i	0.776484	−	1.34491i	0.933957	−	0.357387i	$-0.116332\pi$
$182$	0.117324	+	2.55745i	0.00869664	+	0.189571i
$183$	−4.13911	−	8.99980i	−0.305972	−	0.665284i
$184$	4.16605	+	1.51632i	0.307125	+	0.111784i
$185$	−2.61462	+	2.19392i	−0.192231	+	0.161301i
$186$	−13.4299	+	9.29868i	−0.984727	+	0.681812i
$187$	−1.42720	+	0.519460i	−0.104367	+	0.0379866i
$188$	0.0332366			0.00242403
$189$	3.15769	−	13.3802i	0.229688	−	0.973264i
$190$	2.23360			0.162042
$191$	12.1595	−	4.42568i	0.879828	−	0.320231i	0.137687	−	0.990476i	$-0.456033\pi$
$191$	12.1595	−	4.42568i	0.879828	−	0.320231i	0.742140	+	0.670245i	$0.233811\pi$
$192$	−0.141868	−	1.72623i	−0.0102384	−	0.124580i
$193$	5.35351	−	4.49212i	0.385354	−	0.323350i	−0.429446	−	0.903092i	$-0.641291\pi$
$193$	5.35351	−	4.49212i	0.385354	−	0.323350i	0.814800	+	0.579742i	$0.196847\pi$
$194$	12.4328	+	4.52515i	0.892619	+	0.324887i
$195$	1.82445	−	2.57660i	0.130652	−	0.184514i
$196$	6.76942	+	1.78183i	0.483530	+	0.127273i
$197$	8.26055	−	14.3077i	0.588540	−	1.01938i	−0.405884	−	0.913925i	$-0.633036\pi$
$197$	8.26055	−	14.3077i	0.588540	−	1.01938i	0.994424	−	0.105456i	$-0.0336303\pi$
$198$	1.00353	+	0.187869i	0.0713175	+	0.0133513i
$199$	13.4101			0.950618			0.475309	−	0.879819i	$-0.342336\pi$
$199$	13.4101			0.950618			0.475309	+	0.879819i	$0.342336\pi$
$200$	−1.36403	+	0.496466i	−0.0964514	+	0.0351054i
$201$	2.59616	+	2.62365i	0.183119	+	0.185058i
$202$	1.48469	+	8.42010i	0.104463	+	0.592436i
$203$	−11.1687	+	14.6222i	−0.783891	+	1.02627i
$204$	−7.47693	+	1.96129i	−0.523490	+	0.137318i
$205$	1.97983	−	11.2282i	0.138278	−	0.784211i
$206$	9.54455			0.665000
$207$	−8.65608	+	10.0980i	−0.601639	+	0.701856i
$208$	−0.967640			−0.0670938
$209$	0.379193	−	0.138015i	0.0262294	−	0.00954671i
$210$	−5.23407	−	6.86452i	−0.361185	−	0.473697i
$211$	8.51283	−	7.14311i	0.586047	−	0.491752i	−0.300880	−	0.953662i	$-0.597280\pi$
$211$	8.51283	−	7.14311i	0.586047	−	0.491752i	0.886927	+	0.461910i	$0.152836\pi$
$212$	−1.81557	−	10.2966i	−0.124694	−	0.707173i
$213$	−1.81214	−	22.0499i	−0.124166	−	1.51084i
$214$	−6.49327	−	5.44850i	−0.443871	−	0.372452i
$215$	2.39988	+	4.15671i	0.163670	+	0.283485i
$216$	4.99722	+	1.42400i	0.340018	+	0.0968910i
$217$	24.3484	−	5.45440i	1.65288	−	0.370269i
$218$	2.22963	−	12.6448i	0.151009	−	0.856417i
$219$	1.47883	+	17.9942i	0.0999303	+	1.21594i
$220$	0.491089	−	0.412072i	0.0331092	−	0.0277819i
$221$	0.749888	+	4.25283i	0.0504429	+	0.286076i
$222$	−1.81358	+	2.56124i	−0.121719	+	0.171899i
$223$	19.3545	−	7.04446i	1.29607	−	0.471732i	0.400357	−	0.916359i	$-0.368886\pi$
$223$	19.3545	−	7.04446i	1.29607	−	0.471732i	0.895715	+	0.444628i	$0.146664\pi$
$224$	−0.790014	+	2.52505i	−0.0527850	+	0.168712i
$225$	0.0458725	−	4.35446i	0.00305817	−	0.290298i
$226$	4.48688	−	7.77150i	0.298463	−	0.516953i
$227$	20.6181	−	7.50437i	1.36847	−	0.498082i	0.449807	−	0.893126i	$-0.351493\pi$
$227$	20.6181	−	7.50437i	1.36847	−	0.498082i	0.918662	+	0.395043i	$0.129270\pi$
$228$	1.98654	−	0.521094i	0.131562	−	0.0345103i
$229$	−16.3779	+	13.7427i	−1.08228	+	0.908143i	−0.996108	−	0.0881369i	$-0.971909\pi$
$229$	−16.3779	+	13.7427i	−1.08228	+	0.908143i	−0.0861745	+	0.996280i	$0.527464\pi$
$230$	1.45020	+	8.22447i	0.0956231	+	0.542305i
$231$	−1.31274	−	0.841959i	−0.0863718	−	0.0553968i
$232$	−5.32740	−	4.47022i	−0.349761	−	0.293484i
$233$	−9.42783	+	16.3295i	−0.617638	+	1.06978i	0.372278	+	0.928121i	$0.378577\pi$
$233$	−9.42783	+	16.3295i	−0.617638	+	1.06978i	−0.989916	+	0.141658i	$0.954757\pi$
$234$	1.02154	−	2.71724i	0.0667800	−	0.177632i
$235$	0.0313044	+	0.0542208i	0.00204207	+	0.00353697i
$236$	0.709130	+	0.595031i	0.0461604	+	0.0387332i
$237$	−30.5829	−	2.83805i	−1.98657	−	0.184351i
$238$	11.7100	+	1.51532i	0.759044	+	0.0982239i
$239$	8.87313	+	3.22955i	0.573955	+	0.208902i	0.612658	−	0.790348i	$-0.290100\pi$
$239$	8.87313	+	3.22955i	0.573955	+	0.208902i	−0.0387029	+	0.999251i	$0.512323\pi$
$240$	2.68248	−	1.85731i	0.173153	−	0.119889i
$241$	3.29189	+	2.76222i	0.212049	+	0.177930i	0.742626	−	0.669707i	$-0.233580\pi$
$241$	3.29189	+	2.76222i	0.212049	+	0.177930i	−0.530577	+	0.847637i	$0.678025\pi$
$242$	−5.44209	+	9.42598i	−0.349831	+	0.605925i
$243$	−9.27432	+	12.5294i	−0.594948	+	0.803764i
$244$	−5.71922			−0.366136
$245$	3.46908	+	12.7216i	0.221631	+	0.812752i
$246$	−0.858667	−	10.4481i	−0.0547466	−	0.666149i
$247$	−0.199238	−	1.12993i	−0.0126772	−	0.0718959i
$248$	1.63766	+	9.28765i	0.103992	+	0.589767i
$249$	−3.04108	+	4.29479i	−0.192721	+	0.272171i
$250$	−9.30974	−	7.81180i	−0.588800	−	0.494062i
$251$	−11.0022	+	19.0563i	−0.694451	+	1.20282i	0.275914	+	0.961182i	$0.411019\pi$
$251$	−11.0022	+	19.0563i	−0.694451	+	1.20282i	−0.970365	+	0.241642i	$0.922314\pi$
$252$	−6.25661	−	4.88414i	−0.394129	−	0.307672i
$253$	0.754390	+	1.30664i	0.0474281	+	0.0821479i
$254$	0.530666	−	3.00956i	0.0332970	−	0.188836i
$255$	−10.2418	−	10.3503i	−0.641367	−	0.648159i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−13.6146	+	11.4240i	−0.849255	+	0.712610i	−0.959626	−	0.281281i	$-0.909241\pi$
$257$	−13.6146	+	11.4240i	−0.849255	+	0.712610i	0.110370	+	0.993891i	$0.464796\pi$
$258$	3.10418	+	3.13705i	0.193258	+	0.195304i
$259$	4.03740	−	2.58467i	0.250872	−	0.160603i
$260$	−0.911386	−	1.57857i	−0.0565217	−	0.0978985i
$261$	18.1770	−	10.2407i	1.12513	−	0.633885i
$262$	7.80498	+	13.5186i	0.482193	+	0.835183i
$263$	−4.50756	+	25.5636i	−0.277948	+	1.57632i	0.451491	+	0.892276i	$0.350892\pi$
$263$	−4.50756	+	25.5636i	−0.277948	+	1.57632i	−0.729439	+	0.684046i	$0.760219\pi$
$264$	0.340634	−	0.481063i	0.0209646	−	0.0296074i
$265$	15.0874	−	12.6598i	0.926812	−	0.777687i
$266$	−3.11122	−	0.402606i	−0.190761	−	0.0246854i
$267$	1.63543	+	0.773127i	0.100087	+	0.0473146i
$268$	2.00249	−	0.728847i	0.122322	−	0.0445214i
$269$	2.38738	−	4.13506i	0.145561	−	0.252119i	−0.784021	−	0.620734i	$-0.786835\pi$
$269$	2.38738	−	4.13506i	0.145561	−	0.252119i	0.929582	+	0.368615i	$0.120168\pi$
$270$	2.38365	+	9.49346i	0.145064	+	0.577754i
$271$	−8.28533	−	14.3506i	−0.503298	−	0.871738i	−0.999993	−	0.00381253i	$-0.998786\pi$
$271$	−8.28533	−	14.3506i	−0.503298	−	0.871738i	0.496695	−	0.867925i	$-0.334547\pi$
$272$	−0.774966	+	4.39505i	−0.0469892	+	0.266489i
$273$	−3.00574	+	3.26012i	−0.181916	+	0.197312i
$274$	13.8233	+	5.03127i	0.835096	+	0.303950i
$275$	−0.464206	−	0.168957i	−0.0279927	−	0.0101885i
$276$	3.20854	+	6.97644i	0.193131	+	0.419932i
$277$	1.68368	−	9.54864i	0.101163	−	0.573722i	−0.891521	−	0.452979i	$-0.850361\pi$
$277$	1.68368	−	9.54864i	0.101163	−	0.573722i	0.992684	−	0.120743i	$-0.0385277\pi$
$278$	−9.84267			−0.590324
$279$	−27.8097	−	5.20623i	−1.66492	−	0.311689i
$280$	−4.86334	+	1.08946i	−0.290640	+	0.0651076i
$281$	−5.64454	−	4.73633i	−0.336725	−	0.282546i	0.458708	−	0.888587i	$-0.348312\pi$
$281$	−5.64454	−	4.73633i	−0.336725	−	0.282546i	−0.795433	+	0.606041i	$0.792757\pi$
$282$	0.0404914	+	0.0409202i	0.00241123	+	0.00243676i
$283$	−9.49765	−	3.45686i	−0.564576	−	0.205489i	0.0439346	−	0.999034i	$-0.486011\pi$
$283$	−9.49765	−	3.45686i	−0.564576	−	0.205489i	−0.608511	+	0.793545i	$0.708233\pi$
$284$	−12.0031	−	4.36877i	−0.712254	−	0.259239i
$285$	2.72114	+	2.74996i	0.161187	+	0.162894i
$286$	−0.252264	−	0.211675i	−0.0149167	−	0.0125166i
$287$	−4.78162	+	15.2831i	−0.282250	+	0.902130i
$288$	1.95246	−	2.27769i	0.115050	−	0.134214i
$289$	2.91704			0.171591
$290$	2.27483	−	12.9012i	0.133583	−	0.757586i
$291$	9.57527	+	20.8198i	0.561312	+	1.22048i
$292$	9.79537	+	3.56522i	0.573230	+	0.208639i
$293$	−2.03220	−	0.739659i	−0.118722	−	0.0432113i	0.281976	−	0.959421i	$-0.409010\pi$
$293$	−2.03220	−	0.739659i	−0.118722	−	0.0432113i	−0.400698	+	0.916210i	$0.631232\pi$
$294$	6.05328	+	10.5051i	0.353035	+	0.612672i
$295$	−0.302803	+	1.71728i	−0.0176299	+	0.0999840i
$296$	0.905954	+	1.56916i	0.0526575	+	0.0912055i
$297$	0.991272	+	1.46440i	0.0575194	+	0.0849730i
$298$	9.96033	−	17.2518i	0.576987	−	0.999370i
$299$	4.03123	−	1.46725i	0.233132	−	0.0848532i
$300$	−2.27300	−	1.07453i	−0.131232	−	0.0620380i
$301$	−2.59358	−	6.22252i	−0.149491	−	0.358660i
$302$	−11.2884	+	9.47209i	−0.649574	+	0.545057i
$303$	−8.55788	+	12.0859i	−0.491638	+	0.694319i
$304$	0.205901	−	1.16772i	0.0118092	−	0.0669733i
$305$	−5.38673	−	9.33009i	−0.308443	−	0.534240i
$306$	−11.5237	−	6.81605i	−0.658764	−	0.389647i
$307$	2.78755	+	4.82818i	0.159094	+	0.275559i	0.934542	−	0.355852i	$-0.115809\pi$
$307$	2.78755	+	4.82818i	0.159094	+	0.275559i	−0.775448	+	0.631411i	$0.782476\pi$
$308$	−0.758321	+	0.485463i	−0.0432093	+	0.0276618i
$309$	11.6279	+	11.7510i	0.661489	+	0.668494i
$310$	−13.6090	+	11.4193i	−0.772940	+	0.648574i
$311$	−16.5884	−	6.03767i	−0.940640	−	0.342365i	−0.174222	−	0.984706i	$-0.555741\pi$
$311$	−16.5884	−	6.03767i	−0.940640	−	0.342365i	−0.766419	+	0.642341i	$0.777963\pi$
$312$	−1.17885	−	1.19134i	−0.0667395	−	0.0674462i
$313$	3.02380	−	17.1488i	0.170915	−	0.969307i	−0.771839	−	0.635818i	$-0.780663\pi$
$313$	3.02380	−	17.1488i	0.170915	−	0.969307i	0.942754	−	0.333489i	$-0.108226\pi$
$314$	9.83750	+	17.0390i	0.555162	+	0.961569i
$315$	2.07490	−	14.8070i	0.116908	−	0.834277i
$316$	−8.86646	+	15.3572i	−0.498777	+	0.863908i
$317$	−0.189499	−	0.159009i	−0.0106433	−	0.00893083i	0.637450	−	0.770491i	$-0.279989\pi$
$317$	−0.189499	−	0.159009i	−0.0106433	−	0.00893083i	−0.648094	+	0.761561i	$0.724434\pi$
$318$	10.4651	−	14.7794i	0.586853	−	0.828787i
$319$	−0.410978	−	2.33077i	−0.0230104	−	0.130498i
$320$	−0.327106	−	1.85511i	−0.0182858	−	0.103704i
$321$	−1.20252	−	14.6322i	−0.0671184	−	0.816688i
$322$	−0.537541	−	11.7174i	−0.0299560	−	0.652984i
$323$	−5.29176			−0.294441
$324$	4.33480	+	7.88730i	0.240822	+	0.438183i
$325$	−0.702298	+	1.21642i	−0.0389565	+	0.0674746i
$326$	3.49227	+	2.93036i	0.193419	+	0.162298i
$327$	18.2844	−	12.6599i	1.01113	−	0.700091i
$328$	−5.68756	−	2.07010i	−0.314043	−	0.114302i
$329$	−0.0338311	−	0.0811676i	−0.00186517	−	0.00447491i
$330$	1.10562	+	0.102600i	0.0608622	+	0.00564792i
$331$	−6.32432	−	5.30674i	−0.347616	−	0.291685i	0.452216	−	0.891909i	$-0.350634\pi$
$331$	−6.32432	−	5.30674i	−0.347616	−	0.291685i	−0.799832	+	0.600224i	$0.795078\pi$
$332$	1.51914	+	2.63123i	0.0833736	+	0.144407i
$333$	−5.36279	+	0.887461i	−0.293879	+	0.0486326i
$334$	−2.90047	+	5.02376i	−0.158707	+	0.274888i
$335$	3.07508	+	2.58030i	0.168010	+	0.140977i
$336$	−4.07124	+	2.10356i	−0.222105	+	0.114759i
$337$	4.74727	+	26.9231i	0.258600	+	1.46660i	0.786659	+	0.617388i	$0.211809\pi$
$337$	4.74727	+	26.9231i	0.258600	+	1.46660i	−0.528059	+	0.849208i	$0.677080\pi$
$338$	9.24131	−	7.75438i	0.502661	−	0.421783i
$339$	15.0344	−	3.94369i	0.816555	−	0.214192i
$340$	−7.89981	+	2.87529i	−0.428427	+	0.155935i
$341$	−1.60477	+	2.77954i	−0.0869030	+	0.150520i
$342$	3.06172	+	1.81095i	0.165559	+	0.0979252i
$343$	−2.53907	−	18.3454i	−0.137097	−	0.990558i
$344$	2.39434	−	0.871470i	0.129094	−	0.0469865i
$345$	−8.35905	+	11.8051i	−0.450036	+	0.635567i
$346$	−1.18735	−	6.73378i	−0.0638322	−	0.362010i
$347$	7.77138	−	6.52097i	0.417190	−	0.350064i	−0.409903	−	0.912129i	$-0.634437\pi$
$347$	7.77138	−	6.52097i	0.417190	−	0.350064i	0.827093	+	0.562065i	$0.189993\pi$
$348$	−0.986610	−	12.0049i	−0.0528878	−	0.643532i
$349$	−4.83658	+	27.4296i	−0.258896	+	1.46827i	0.526974	+	0.849881i	$0.323326\pi$
$349$	−4.83658	+	27.4296i	−0.258896	+	1.46827i	−0.785870	+	0.618391i	$0.787785\pi$
$350$	2.60085	+	2.82576i	0.139021	+	0.151043i
$351$	4.58993	−	2.05266i	0.244992	−	0.109563i
$352$	−0.170160	−	0.294726i	−0.00906956	−	0.0157089i
$353$	−24.5054	−	20.5625i	−1.30429	−	1.09443i	−0.989387	−	0.145307i	$-0.953583\pi$
$353$	−24.5054	−	20.5625i	−1.30429	−	1.09443i	−0.314905	−	0.949123i	$-0.601973\pi$
$354$	0.131328	+	1.59798i	0.00697999	+	0.0849316i
$355$	−4.17827	−	23.6961i	−0.221760	−	1.25766i
$356$	0.800062	−	0.671332i	0.0424032	−	0.0355805i
$357$	12.4003	+	16.2631i	0.656295	+	0.860736i
$358$	15.8190	−	5.75765i	0.836062	−	0.304302i
$359$	18.7206			0.988037			0.494018	−	0.869451i	$-0.335528\pi$
$359$	18.7206			0.988037			0.494018	+	0.869451i	$0.335528\pi$
$360$	5.55468	+	1.03989i	0.292758	+	0.0548069i
$361$	−17.5940			−0.926002
$362$	3.62804	−	20.5756i	0.190686	−	1.08143i
$363$	−18.2350	+	4.78327i	−0.957091	+	0.251056i
$364$	0.984947	+	2.36309i	0.0516252	+	0.123859i
$365$	3.40976	+	19.3377i	0.178475	+	1.01218i
$366$	−6.96760	−	7.04139i	−0.364202	−	0.368059i
$367$	−6.64895	+	2.42002i	−0.347073	+	0.126324i	−0.509674	−	0.860368i	$-0.670234\pi$
$367$	−6.64895	+	2.42002i	−0.347073	+	0.126324i	0.162601	+	0.986692i	$0.448012\pi$
$368$	4.43341			0.231108
$369$	11.8174	−	13.7859i	0.615191	−	0.717666i
$370$	−1.70657	+	2.95587i	−0.0887204	+	0.153668i
$371$	−23.2974	+	14.9146i	−1.20954	+	0.774326i
$372$	−9.43963	+	13.3312i	−0.489422	+	0.691190i
$373$	10.5552	+	3.84180i	0.546530	+	0.198921i	0.600504	−	0.799622i	$-0.294967\pi$
$373$	10.5552	+	3.84180i	0.546530	+	0.198921i	−0.0539741	+	0.998542i	$0.517189\pi$
$374$	−1.16347	+	0.976265i	−0.0601614	+	0.0504814i
$375$	−1.72412	−	20.9789i	−0.0890332	−	1.08335i
$376$	0.0312322	−	0.0113676i	0.00161068	−	0.000586239i
$377$	−6.72938			−0.346581
$378$	−1.60903	−	13.6532i	−0.0827595	−	0.702247i
$379$	−29.7564			−1.52848			−0.764242	−	0.644929i	$-0.776887\pi$
$379$	−29.7564			−1.52848			−0.764242	+	0.644929i	$0.776887\pi$
$380$	2.09890	−	0.763936i	0.107671	−	0.0391891i
$381$	4.35180	−	3.01313i	0.222950	−	0.154367i
$382$	9.91248	−	8.31756i	0.507167	−	0.425563i
$383$	−27.5479	−	10.0266i	−1.40763	−	0.512336i	−0.477199	−	0.878795i	$-0.658348\pi$
$383$	−27.5479	−	10.0266i	−1.40763	−	0.512336i	−0.930434	+	0.366459i	$0.880570\pi$
$384$	−0.723718	−	1.57360i	−0.0369321	−	0.0803027i
$385$	−1.50620	−	0.779851i	−0.0767630	−	0.0397449i
$386$	3.49425	−	6.05222i	0.177853	−	0.308050i
$387$	−0.0805222	+	7.64360i	−0.00409318	+	0.388546i
$388$	13.2307			0.671685
$389$	−19.6552	+	7.15392i	−0.996560	+	0.362718i	−0.788257	−	0.615346i	$-0.789016\pi$
$389$	−19.6552	+	7.15392i	−0.996560	+	0.362718i	−0.208303	+	0.978064i	$0.566794\pi$
$390$	0.833177	−	3.04521i	0.0421896	−	0.154200i
$391$	−3.43574	−	19.4851i	−0.173753	−	0.985403i
$392$	6.97060	−	0.640908i	0.352068	−	0.0323707i
$393$	−7.13521	+	26.0788i	−0.359924	+	1.31550i
$394$	2.86886	−	16.2701i	0.144531	−	0.819676i
$395$	−33.4040			−1.68074
$396$	1.00726	−	0.166687i	0.0506168	−	0.00837632i
$397$	−35.7775			−1.79562			−0.897812	−	0.440380i	$-0.854844\pi$
$397$	−35.7775			−1.79562			−0.897812	+	0.440380i	$0.854844\pi$
$398$	12.6014	−	4.58653i	0.631650	−	0.229902i
$399$	−3.29464	−	4.32095i	−0.164938	−	0.216318i
$400$	−1.11197	+	0.933050i	−0.0555983	+	0.0466525i
$401$	−4.22360	−	23.9532i	−0.210917	−	1.19617i	−0.887853	−	0.460127i	$-0.847804\pi$
$401$	−4.22360	−	23.9532i	−0.210917	−	1.19617i	0.676937	−	0.736041i	$-0.263307\pi$
$402$	3.33693	+	1.57749i	0.166431	+	0.0786779i
$403$	6.99073	+	5.86592i	0.348233	+	0.292202i
$404$	4.27500	+	7.40451i	0.212689	+	0.368388i
$405$	−8.78420	+	14.5004i	−0.436491	+	0.720529i
$406$	−5.49409	+	17.5603i	−0.272667	+	0.871501i
$407$	−0.107076	+	0.607261i	−0.00530758	+	0.0301008i
$408$	−6.35522	+	4.40027i	−0.314630	+	0.217846i
$409$	−13.5435	+	11.3644i	−0.669684	+	0.561932i	−0.912972	−	0.408023i	$-0.866218\pi$
$409$	−13.5435	+	11.3644i	−0.669684	+	0.561932i	0.243288	+	0.969954i	$0.421774\pi$
$410$	−1.97983	−	11.2282i	−0.0977770	−	0.554521i
$411$	10.6462	+	23.1484i	0.525139	+	1.14183i
$412$	8.96895	−	3.26443i	0.441868	−	0.160827i
$413$	0.731319	−	2.33745i	0.0359858	−	0.115018i
$414$	−4.68035	+	12.4495i	−0.230027	+	0.611861i
$415$	−2.86164	+	4.95651i	−0.140473	+	0.243306i
$416$	−0.909284	+	0.330952i	−0.0445813	+	0.0162263i
$417$	−11.9911	−	12.1181i	−0.587206	−	0.593425i
$418$	0.309121	−	0.259384i	0.0151196	−	0.0126869i
$419$	5.75680	+	32.6484i	0.281238	+	1.59498i	0.718422	+	0.695608i	$0.244865\pi$
$419$	5.75680	+	32.6484i	0.281238	+	1.59498i	−0.437184	+	0.899372i	$0.644024\pi$
$420$	−7.26622	−	4.66038i	−0.354555	−	0.227403i
$421$	9.80351	+	8.22613i	0.477794	+	0.400917i	0.849628	−	0.527382i	$-0.176826\pi$
$421$	9.80351	+	8.22613i	0.477794	+	0.400917i	−0.371834	+	0.928299i	$0.621271\pi$
$422$	5.55635	−	9.62388i	0.270479	−	0.468483i
$423$	−0.00105035	+	0.0997044i	−5.10695e−5	+	0.00484779i
$424$	−5.22772	−	9.05468i	−0.253881	−	0.439734i
$425$	4.96254	+	4.16406i	0.240718	+	0.201987i
$426$	−9.24437	−	20.1004i	−0.447891	−	0.973865i
$427$	5.82151	+	13.9670i	0.281723	+	0.675910i
$428$	−7.96518	−	2.89909i	−0.385011	−	0.140133i
$429$	−0.0467182	−	0.568461i	−0.00225557	−	0.0274455i
$430$	3.67682	+	3.08522i	0.177312	+	0.148783i
$431$	7.93212	−	13.7388i	0.382077	−	0.661776i	−0.609282	−	0.792953i	$-0.708542\pi$
$431$	7.93212	−	13.7388i	0.382077	−	0.661776i	0.991359	+	0.131177i	$0.0418757\pi$
$432$	5.18289	−	0.371028i	0.249362	−	0.0178511i
$433$	−12.8512			−0.617588			−0.308794	−	0.951129i	$-0.599925\pi$
$433$	−12.8512			−0.617588			−0.308794	+	0.951129i	$0.599925\pi$
$434$	21.0145	−	13.4531i	1.00873	−	0.645770i
$435$	18.6551	−	12.9165i	0.894443	−	0.619300i
$436$	−2.22963	−	12.6448i	−0.106780	−	0.605578i
$437$	0.912842	+	5.17699i	0.0436672	+	0.247649i
$438$	7.54404	+	16.4033i	0.360468	+	0.783779i
$439$	3.80193	+	3.19020i	0.181456	+	0.152260i	0.728992	−	0.684523i	$-0.239989\pi$
$439$	3.80193	+	3.19020i	0.181456	+	0.152260i	−0.547535	+	0.836783i	$0.684434\pi$
$440$	0.320535	−	0.555183i	0.0152809	−	0.0264673i
$441$	−5.55912	+	20.2508i	−0.264720	+	0.964325i
$442$	2.15922	+	3.73987i	0.102703	+	0.177888i
$443$	1.04525	−	5.92791i	0.0496613	−	0.281643i	−0.949857	−	0.312685i	$-0.898771\pi$
$443$	1.04525	−	5.92791i	0.0496613	−	0.281643i	0.999518	+	0.0310421i	$0.00988258\pi$
$444$	−0.828211	+	3.02706i	−0.0393052	+	0.143658i
$445$	1.84873	+	0.672883i	0.0876383	+	0.0318977i
$446$	15.7779	−	13.2392i	0.747106	−	0.626897i
$447$	33.3745	−	8.75453i	1.57856	−	0.414075i
$448$	0.121248	+	2.64297i	0.00572841	+	0.124869i
$449$	−0.599759	−	1.03881i	−0.0283044	−	0.0490246i	0.851526	−	0.524312i	$-0.175677\pi$
$449$	−0.599759	−	1.03881i	−0.0283044	−	0.0490246i	−0.879831	+	0.475287i	$0.842344\pi$
$450$	−1.44621	−	4.10755i	−0.0681749	−	0.193632i
$451$	−1.02991	−	1.78385i	−0.0484964	−	0.0839983i
$452$	1.55828	−	8.83743i	0.0732952	−	0.415678i
$453$	−25.4142	−	2.35840i	−1.19406	−	0.110807i
$454$	16.8080	−	14.1036i	0.788839	−	0.661914i
$455$	−2.92735	+	3.83250i	−0.137236	+	0.179671i
$456$	1.68852	−	1.16911i	0.0790720	−	0.0547484i
$457$	21.5458	−	7.84204i	1.00787	−	0.366835i	0.215256	−	0.976558i	$-0.430941\pi$
$457$	21.5458	−	7.84204i	1.00787	−	0.366835i	0.792615	+	0.609723i	$0.208719\pi$
$458$	−10.6899	+	18.5155i	−0.499507	+	0.865172i
$459$	−5.64725	−	22.4915i	−0.263591	−	1.04981i
$460$	4.17567	+	7.23248i	0.194692	+	0.337216i
$461$	4.79983	−	27.2212i	0.223551	−	1.26782i	−0.641886	−	0.766800i	$-0.721848\pi$
$461$	4.79983	−	27.2212i	0.223551	−	1.26782i	0.865437	−	0.501018i	$-0.167041\pi$
$462$	−1.52154	−	0.342200i	−0.0707883	−	0.0159206i
$463$	−39.7405	−	14.4644i	−1.84690	−	0.672216i	−0.986767	−	0.162146i	$-0.948158\pi$
$463$	−39.7405	−	14.4644i	−1.84690	−	0.672216i	−0.860133	−	0.510070i	$-0.829619\pi$
$464$	−6.53502	−	2.37855i	−0.303381	−	0.110422i
$465$	−30.6388	−	2.84323i	−1.42084	−	0.131852i
$466$	−3.27425	+	18.5692i	−0.151677	+	0.860201i
$467$	29.7274			1.37562			0.687809	−	0.725892i	$-0.258573\pi$
$467$	29.7274			1.37562			0.687809	+	0.725892i	$0.258573\pi$
$468$	0.0305794	−	2.90276i	0.00141353	−	0.134180i
$469$	−3.81823	−	4.14843i	−0.176310	−	0.191557i
$470$	0.0479611	+	0.0402441i	0.00221228	+	0.00185632i
$471$	−8.99331	+	32.8700i	−0.414390	+	1.51457i
$472$	0.869877	+	0.316609i	0.0400393	+	0.0145731i
$473$	0.814843	+	0.296579i	0.0374665	+	0.0136367i
$474$	−29.7092	+	7.79308i	−1.36459	+	0.357948i
$475$	−1.31850	−	1.10635i	−0.0604968	−	0.0507628i
$476$	11.5220	−	2.58110i	0.528111	−	0.118305i
$477$	30.9455	−	5.12101i	1.41689	−	0.234475i
$478$	9.44258			0.431894
$479$	4.52764	−	25.6776i	0.206873	−	1.17324i	−0.687591	−	0.726098i	$-0.741332\pi$
$479$	4.52764	−	25.6776i	0.206873	−	1.17324i	0.894464	−	0.447139i	$-0.147557\pi$
$480$	1.88547	−	2.66276i	0.0860594	−	0.121538i
$481$	1.64754	+	0.599655i	0.0751213	+	0.0273419i
$482$	4.03810	+	1.46975i	0.183930	+	0.0669452i
$483$	13.7713	−	14.9368i	0.626617	−	0.679649i
$484$	−1.89002	+	10.7188i	−0.0859099	+	0.487219i
$485$	12.4615	+	21.5839i	0.565847	+	0.980075i
$486$	−4.42969	+	14.9458i	−0.200935	+	0.677957i
$487$	−3.43250	+	5.94527i	−0.155541	+	0.269406i	−0.933256	−	0.359212i	$-0.883046\pi$
$487$	−3.43250	+	5.94527i	−0.155541	+	0.269406i	0.777715	+	0.628618i	$0.216379\pi$
$488$	−5.37431	+	1.95609i	−0.243284	+	0.0885480i
$489$	0.646753	+	7.86960i	0.0292472	+	0.355876i
$490$	7.61090	+	10.7679i	0.343826	+	0.486443i
$491$	−7.45052	+	6.25173i	−0.336237	+	0.282137i	−0.795236	−	0.606301i	$-0.792653\pi$
$491$	−7.45052	+	6.25173i	−0.336237	+	0.282137i	0.458998	+	0.888437i	$0.348208\pi$
$492$	−4.38036	−	9.52436i	−0.197482	−	0.429391i
$493$	−5.38944	+	30.5650i	−0.242728	+	1.37658i
$494$	−0.573682	−	0.993647i	−0.0258112	−	0.0447063i
$495$	1.22063	+	1.48621i	0.0548632	+	0.0668000i
$496$	4.71546	+	8.16742i	0.211731	+	0.366728i
$497$	1.54875	+	33.7598i	0.0694709	+	1.51434i
$498$	−1.38878	+	5.07589i	−0.0622326	+	0.227456i
$499$	−19.5888	+	16.4370i	−0.876916	+	0.735820i	−0.965543	−	0.260245i	$-0.916197\pi$
$499$	−19.5888	+	16.4370i	−0.876916	+	0.735820i	0.0886268	+	0.996065i	$0.471752\pi$
$500$	−11.4201	−	4.15657i	−0.510722	−	0.185888i
$501$	−9.71872	+	2.54933i	−0.434200	+	0.113896i
$502$	−3.82102	+	21.6701i	−0.170540	+	0.967182i
$503$	1.14213	+	1.97823i	0.0509252	+	0.0882051i	0.890364	−	0.455249i	$-0.150450\pi$
$503$	1.14213	+	1.97823i	0.0509252	+	0.0882051i	−0.839439	+	0.543454i	$0.817116\pi$
$504$	−7.54976	−	2.44971i	−0.336293	−	0.109119i
$505$	−8.05293	+	13.9481i	−0.358351	+	0.620682i
$506$	1.15579	+	0.969825i	0.0513812	+	0.0431140i
$507$	20.8055	+	1.93072i	0.924005	+	0.0857463i
$508$	−0.530666	−	3.00956i	−0.0235445	−	0.133528i
$509$	−0.438128	−	2.48475i	−0.0194197	−	0.110135i	0.973557	−	0.228444i	$-0.0733637\pi$
$509$	−0.438128	−	2.48475i	−0.0194197	−	0.110135i	−0.992977	+	0.118309i	$0.962253\pi$
$510$	−13.1642	−	6.22317i	−0.582918	−	0.275567i
$511$	−1.26389	−	27.5504i	−0.0559110	−	1.21876i
$512$	−1.00000			−0.0441942
$513$	1.50042	+	5.97577i	0.0662450	+	0.263837i
$514$	−8.88630	+	15.3915i	−0.391958	+	0.678891i
$515$	13.7730	+	11.5569i	0.606910	+	0.509258i
$516$	3.98991	+	1.88617i	0.175646	+	0.0830342i
$517$	0.0106290	+	0.00386862i	0.000467461	+	0.000170142i
$518$	2.90990	−	3.80966i	0.127854	−	0.167387i
$519$	6.84397	−	9.66544i	0.300417	−	0.424266i
$520$	−1.39632	−	1.17165i	−0.0612329	−	0.0513805i
$521$	−6.13331	−	10.6232i	−0.268705	−	0.465411i	0.699823	−	0.714317i	$-0.253262\pi$
$521$	−6.13331	−	10.6232i	−0.268705	−	0.465411i	−0.968528	+	0.248906i	$0.919929\pi$
$522$	13.5783	−	15.8400i	0.594304	−	0.693300i
$523$	11.0554	−	19.1485i	0.483418	−	0.837305i	−0.516401	−	0.856347i	$-0.672728\pi$
$523$	11.0554	−	19.1485i	0.483418	−	0.837305i	0.999819	+	0.0190425i	$0.00606178\pi$
$524$	11.9579	+	10.0339i	0.522384	+	0.438332i
$525$	−0.310467	+	6.64467i	−0.0135499	+	0.289997i
$526$	4.50756	+	25.5636i	0.196539	+	1.11463i
$527$	32.2419	−	27.0542i	1.40448	−	1.17850i
$528$	0.155558	−	0.568555i	0.00676980	−	0.0247432i
$529$	3.14313	−	1.14401i	0.136658	−	0.0497394i
$530$	9.84760	−	17.0565i	0.427752	−	0.740889i
$531$	−1.80740	+	2.10847i	−0.0784346	+	0.0914997i
$532$	−3.06129	+	0.685773i	−0.132724	+	0.0297320i
$533$	−5.50351	+	2.00312i	−0.238384	+	0.0867646i
$534$	1.80123	+	0.167151i	0.0779467	+	0.00723335i
$535$	−2.77267	−	15.7246i	−0.119873	−	0.679833i
$536$	1.63245	−	1.36979i	0.0705109	−	0.0591657i
$537$	26.3607	+	12.4616i	1.13755	+	0.537759i
$538$	0.829127	−	4.70221i	0.0357462	−	0.202727i
$539$	1.95744	+	1.35776i	0.0843128	+	0.0584828i
$540$	5.48686	+	8.10568i	0.236117	+	0.348813i
$541$	11.1968	+	19.3935i	0.481389	+	0.833791i	0.999772	−	0.0213582i	$-0.00679903\pi$
$541$	11.1968	+	19.3935i	0.481389	+	0.833791i	−0.518383	+	0.855149i	$0.673466\pi$
$542$	−12.6939	−	10.6514i	−0.545248	−	0.457518i
$543$	29.7522	−	20.6001i	1.27679	−	0.884033i
$544$	0.774966	+	4.39505i	0.0332264	+	0.188436i
$545$	18.5282	−	15.5470i	0.793662	−	0.665962i
$546$	−1.70944	+	4.09154i	−0.0731574	+	0.175102i
$547$	−15.8728	+	5.77722i	−0.678671	+	0.247016i	−0.658277	−	0.752776i	$-0.728714\pi$
$547$	−15.8728	+	5.77722i	−0.678671	+	0.247016i	−0.0203944	+	0.999792i	$0.506492\pi$
$548$	14.7105			0.628399
$549$	0.180739	−	17.1567i	0.00771376	−	0.732231i
$550$	−0.493998			−0.0210641
$551$	1.43192	−	8.12082i	0.0610018	−	0.345959i
$552$	5.40113	+	5.45832i	0.229887	+	0.232322i
$553$	46.5289	+	6.02106i	1.97861	+	0.256042i
$554$	−1.68368	−	9.54864i	−0.0715329	−	0.405683i
$555$	−5.71828	+	1.49997i	−0.242727	+	0.0636702i
$556$	−9.24908	+	3.36639i	−0.392248	+	0.142767i
$557$	8.02547			0.340050			0.170025	−	0.985440i	$-0.445615\pi$
$557$	8.02547			0.340050			0.170025	+	0.985440i	$0.445615\pi$
$558$	−27.9132	+	4.61921i	−1.18166	+	0.195547i
$559$	1.23278	−	2.13523i	0.0521409	−	0.0903107i
$560$	−4.19743	+	2.68712i	−0.177374	+	0.113551i
$561$	−2.61938	−	0.243075i	−0.110590	−	0.0102626i
$562$	−6.92406	−	2.52015i	−0.292074	−	0.106306i
$563$	15.4361	−	12.9524i	0.650553	−	0.545879i	−0.256686	−	0.966495i	$-0.582631\pi$
$563$	15.4361	−	12.9524i	0.650553	−	0.545879i	0.907239	+	0.420616i	$0.138186\pi$
$564$	0.0520450	+	0.0246036i	0.00219149	+	0.00103600i
$565$	15.8847	−	5.78155i	0.668273	−	0.243232i
$566$	−10.1072			−0.424837
$567$	14.8493	−	18.6144i	0.623614	−	0.781733i
$568$	−12.7734			−0.535962
$569$	−38.3207	+	13.9476i	−1.60649	+	0.584714i	−0.980741	−	0.195313i	$-0.937428\pi$
$569$	−38.3207	+	13.9476i	−1.60649	+	0.584714i	−0.625747	+	0.780026i	$0.715206\pi$
$570$	3.49758	+	1.65343i	0.146498	+	0.0692547i
$571$	3.69292	−	3.09873i	0.154544	−	0.129678i	−0.562237	−	0.826976i	$-0.690059\pi$
$571$	3.69292	−	3.09873i	0.154544	−	0.129678i	0.716781	+	0.697298i	$0.245615\pi$
$572$	−0.309448	−	0.112630i	−0.0129387	−	0.00470929i
$573$	22.3166	+	2.07094i	0.932287	+	0.0865149i
$574$	0.733860	+	15.9968i	0.0306307	+	0.667693i
$575$	3.21770	−	5.57322i	0.134187	−	0.232419i
$576$	1.05570	−	2.80811i	0.0439875	−	0.117005i
$577$	−19.7557			−0.822439			−0.411220	−	0.911536i	$-0.634897\pi$
$577$	−19.7557			−0.822439			−0.411220	+	0.911536i	$0.634897\pi$
$578$	2.74112	−	0.997686i	0.114016	−	0.0414983i
$579$	11.7083	−	3.07124i	0.486582	−	0.127636i
$580$	−2.27483	−	12.9012i	−0.0944573	−	0.535694i
$581$	4.87944	−	6.38819i	0.202433	−	0.265027i
$582$	16.1186	+	16.2893i	0.668138	+	0.675213i
$583$	0.617874	−	3.50414i	0.0255897	−	0.145127i
$584$	10.4240			0.431349
$585$	4.76424	−	2.68412i	0.196977	−	0.110975i
$586$	−2.16262			−0.0893369
$587$	20.4162	−	7.43090i	0.842669	−	0.306706i	0.115621	−	0.993293i	$-0.463114\pi$
$587$	20.4162	−	7.43090i	0.842669	−	0.306706i	0.727048	+	0.686587i	$0.240892\pi$
$588$	9.28119	+	7.80125i	0.382750	+	0.321718i
$589$	−8.56635	+	7.18802i	−0.352970	+	0.296177i
$590$	0.302803	+	1.71728i	0.0124662	+	0.0706994i
$591$	23.5265	−	16.2894i	0.967750	−	0.670057i
$592$	1.38800	+	1.16467i	0.0570465	+	0.0478677i
$593$	−12.8927	−	22.3308i	−0.529439	−	0.917016i	−0.999410	−	0.0343341i	$-0.989069\pi$
$593$	−12.8927	−	22.3308i	−0.529439	−	0.917016i	0.469971	−	0.882682i	$-0.344264\pi$
$594$	1.43234	+	1.03705i	0.0587698	+	0.0425506i
$595$	15.0629	+	16.3655i	0.617518	+	0.670920i
$596$	3.45919	−	19.6180i	0.141694	−	0.803586i
$597$	20.9988	+	9.92689i	0.859424	+	0.406281i
$598$	3.28629	−	2.75753i	0.134386	−	0.112764i
$599$	−1.71563	−	9.72984i	−0.0700989	−	0.397550i	−0.999588	−	0.0287011i	$-0.990863\pi$
$599$	−1.71563	−	9.72984i	−0.0700989	−	0.397550i	0.929489	−	0.368849i	$-0.120248\pi$
$600$	−2.50343	−	0.232315i	−0.102202	−	0.00948423i
$601$	18.6462	−	6.78666i	0.760594	−	0.276834i	0.0675376	−	0.997717i	$-0.478486\pi$
$601$	18.6462	−	6.78666i	0.760594	−	0.276834i	0.693057	+	0.720883i	$0.256264\pi$
$602$	−4.56539	−	4.96020i	−0.186072	−	0.202163i
$603$	2.12314	+	6.03018i	0.0864609	+	0.245568i
$604$	−7.36797	+	12.7617i	−0.299799	+	0.519266i
$605$	−19.2664	+	7.01238i	−0.783289	+	0.285094i
$606$	−3.90815	+	14.2840i	−0.158758	+	0.580249i
$607$	−25.4060	+	21.3181i	−1.03120	+	0.865277i	−0.990993	−	0.133915i	$-0.957245\pi$
$607$	−25.4060	+	21.3181i	−1.03120	+	0.865277i	−0.0402039	+	0.999191i	$0.512801\pi$
$608$	−0.205901	−	1.16772i	−0.00835037	−	0.0473573i
$609$	−28.3132	+	14.6291i	−1.14731	+	0.592799i
$610$	−8.25295	−	6.92505i	−0.334152	−	0.280387i
$611$	0.0160806	−	0.0278523i	0.000650550	−	0.00112678i
$612$	−13.1599	−	2.46366i	−0.531959	−	0.0995876i
$613$	5.35498	+	9.27509i	0.216285	+	0.374617i	0.953669	−	0.300856i	$-0.0972725\pi$
$613$	5.35498	+	9.27509i	0.216285	+	0.374617i	−0.737384	+	0.675474i	$0.763939\pi$
$614$	4.27077	+	3.58360i	0.172354	+	0.144622i
$615$	11.4119	−	16.1166i	0.460173	−	0.649883i
$616$	−0.546550	+	0.715547i	−0.0220211	+	0.0288302i
$617$	32.8209	+	11.9458i	1.32132	+	0.480920i	0.903880	−	0.427785i	$-0.140706\pi$
$617$	32.8209	+	11.9458i	1.32132	+	0.480920i	0.417437	+	0.908706i	$0.362928\pi$
$618$	14.9458	+	7.06540i	0.601206	+	0.284212i
$619$	25.4224	+	21.3319i	1.02181	+	0.857402i	0.989854	−	0.142087i	$-0.0453814\pi$
$619$	25.4224	+	21.3319i	1.02181	+	0.857402i	0.0319576	+	0.999489i	$0.489826\pi$
$620$	−8.88265	+	15.3852i	−0.356736	+	0.617885i
$621$	−21.0296	+	9.40462i	−0.843887	+	0.377394i
$622$	−17.6530			−0.707820
$623$	−2.45384	−	1.27050i	−0.0983110	−	0.0509016i
$624$	−1.51522	−	0.716300i	−0.0606574	−	0.0286749i
$625$	−2.71501	−	15.3976i	−0.108600	−	0.615903i
$626$	−3.02380	−	17.1488i	−0.120855	−	0.685404i
$627$	0.695943	+	0.0645825i	0.0277933	+	0.00257918i
$628$	15.0719	+	12.6468i	0.601435	+	0.504664i
$629$	4.04314	−	7.00292i	0.161210	−	0.279225i
$630$	−3.11451	−	14.6236i	−0.124085	−	0.582620i
$631$	−19.9253	−	34.5117i	−0.793214	−	1.37389i	−0.923967	−	0.382472i	$-0.875073\pi$
$631$	−19.9253	−	34.5117i	−0.793214	−	1.37389i	0.130753	−	0.991415i	$-0.458261\pi$
$632$	−3.07929	+	17.4635i	−0.122488	+	0.694661i
$633$	18.6179	−	4.88369i	0.739995	−	0.194109i
$634$	−0.232455	−	0.0846069i	−0.00923199	−	0.00336017i
$635$	4.40984	−	3.70030i	0.174999	−	0.146842i
$636$	4.77911	−	17.4674i	0.189504	−	0.692626i
$637$	4.76836	−	4.81070i	0.188929	−	0.190607i
$638$	−1.18337	−	2.04965i	−0.0468499	−	0.0811464i
$639$	13.4849	−	35.8693i	0.533455	−	1.41897i
$640$	−0.941864	−	1.63136i	−0.0372304	−	0.0644850i
$641$	6.43144	−	36.4745i	0.254027	−	1.44066i	−0.544532	−	0.838740i	$-0.683293\pi$
$641$	6.43144	−	36.4745i	0.254027	−	1.44066i	0.798559	−	0.601917i	$-0.205596\pi$
$642$	−6.13450	−	13.3384i	−0.242109	−	0.526427i
$643$	18.1285	−	15.2116i	0.714919	−	0.599888i	−0.211056	−	0.977474i	$-0.567690\pi$
$643$	18.1285	−	15.2116i	0.714919	−	0.599888i	0.925975	+	0.377586i	$0.123246\pi$
$644$	−4.51270	−	10.8269i	−0.177825	−	0.426639i
$645$	0.680931	+	8.28548i	0.0268116	+	0.326241i
$646$	−4.97262	+	1.80989i	−0.195645	+	0.0712090i
$647$	−13.5369	+	23.4465i	−0.532189	+	0.921778i	0.467105	+	0.884202i	$0.345297\pi$
$647$	−13.5369	+	23.4465i	−0.532189	+	0.921778i	−0.999294	+	0.0375761i	$0.988036\pi$
$648$	6.77100	+	5.92905i	0.265990	+	0.232915i
$649$	0.157518	+	0.272829i	0.00618311	+	0.0107095i
$650$	−0.243906	+	1.38326i	−0.00956676	+	0.0542558i
$651$	42.1647	+	9.48302i	1.65257	+	0.371669i
$652$	4.28390	+	1.55921i	0.167771	+	0.0610635i
$653$	33.0035	+	12.0123i	1.29153	+	0.470078i	0.894228	−	0.447611i	$-0.147725\pi$
$653$	33.0035	+	12.0123i	1.29153	+	0.470078i	0.397300	+	0.917689i	$0.369947\pi$
$654$	12.8518	−	18.1500i	0.502543	−	0.709721i
$655$	−5.10611	+	28.9582i	−0.199512	+	1.13149i
$656$	−6.05258			−0.236313
$657$	−11.0046	+	29.2718i	−0.429331	+	1.14200i
$658$	−0.0595518	−	0.0647017i	−0.00232157	−	0.00252233i
$659$	2.10686	+	1.76786i	0.0820715	+	0.0688661i	0.682900	−	0.730511i	$-0.260718\pi$
$659$	2.10686	+	1.76786i	0.0820715	+	0.0688661i	−0.600829	+	0.799378i	$0.705163\pi$
$660$	1.07403	−	0.281731i	0.0418066	−	0.0109664i
$661$	−37.4880	−	13.6445i	−1.45811	−	0.530710i	−0.513269	−	0.858228i	$-0.671566\pi$
$661$	−37.4880	−	13.6445i	−1.45811	−	0.530710i	−0.944845	+	0.327517i	$0.893788\pi$
$662$	−7.75793	−	2.82366i	−0.301520	−	0.109744i
$663$	−1.97393	+	7.21459i	−0.0766610	+	0.280191i
$664$	2.32746	+	1.95297i	0.0903228	+	0.0757898i
$665$	−4.00206	−	4.34814i	−0.155193	−	0.168614i
$666$	−4.73584	+	2.66812i	−0.183510	+	0.103388i
$667$	30.8318			1.19381
$668$	−1.00732	+	5.71281i	−0.0389745	+	0.221035i
$669$	35.5218	+	3.29637i	1.37335	+	0.127445i
$670$	3.77215	+	1.37295i	0.145731	+	0.0530417i
$671$	−1.82899	−	0.665697i	−0.0706073	−	0.0256989i
$672$	−3.10626	+	3.36915i	−0.119826	+	0.129968i
$673$	−5.25751	+	29.8168i	−0.202662	+	1.14936i	0.698414	+	0.715694i	$0.253890\pi$
$673$	−5.25751	+	29.8168i	−0.202662	+	1.14936i	−0.901076	+	0.433661i	$0.857222\pi$
$674$	13.6692	+	23.6758i	0.526519	+	0.911957i
$675$	3.29524	−	6.78467i	0.126834	−	0.261142i
$676$	6.03184	−	10.4474i	0.231994	−	0.401825i
$677$	−22.4589	+	8.17437i	−0.863166	+	0.314167i	−0.735396	−	0.677637i	$-0.763004\pi$
$677$	−22.4589	+	8.17437i	−0.863166	+	0.314167i	−0.127770	+	0.991804i	$0.540782\pi$
$678$	12.7789	−	8.84792i	0.490769	−	0.339802i
$679$	−13.4673	−	32.3107i	−0.516827	−	1.23997i
$680$	−6.43998	+	5.40379i	−0.246962	+	0.207226i
$681$	37.8409	+	3.51158i	1.45006	+	0.134564i
$682$	−0.557330	+	3.16078i	−0.0213413	+	0.121032i
$683$	18.7102	+	32.4069i	0.715924	+	1.24002i	0.962602	+	0.270920i	$0.0873278\pi$
$683$	18.7102	+	32.4069i	0.715924	+	1.24002i	−0.246678	+	0.969098i	$0.579339\pi$
$684$	3.49646	+	0.654570i	0.133690	+	0.0250281i
$685$	13.8552	+	23.9980i	0.529382	+	0.916916i
$686$	−8.66044	−	16.3706i	−0.330657	−	0.625033i
$687$	−35.8192	+	9.39579i	−1.36659	+	0.358472i
$688$	1.95189	−	1.63783i	0.0744150	−	0.0624416i
$689$	−9.50697	−	3.46025i	−0.362187	−	0.131825i
$690$	−3.81735	+	13.9522i	−0.145324	+	0.531150i
$691$	−3.93113	+	22.2946i	−0.149547	+	0.848125i	0.814056	+	0.580787i	$0.197255\pi$
$691$	−3.93113	+	22.2946i	−0.149547	+	0.848125i	−0.963603	+	0.267338i	$0.913856\pi$
$692$	−3.41883	−	5.92159i	−0.129964	−	0.225105i
$693$	−1.43234	−	2.29018i	−0.0544102	−	0.0869966i
$694$	5.07241	−	8.78567i	0.192546	−	0.333500i
$695$	−14.2032	−	11.9179i	−0.538757	−	0.452070i
$696$	−5.03304	−	10.9435i	−0.190777	−	0.414813i
$697$	4.69054	+	26.6014i	0.177667	+	1.00760i
$698$	4.83658	+	27.4296i	0.183067	+	1.03823i
$699$	−26.8509	+	18.5912i	−1.01560	+	0.703185i
$700$	3.41047	+	1.76581i	0.128904	+	0.0667412i
$701$	−6.12643			−0.231392			−0.115696	−	0.993285i	$-0.536910\pi$
$701$	−6.12643			−0.231392			−0.115696	+	0.993285i	$0.536910\pi$
$702$	3.61107	−	3.49872i	0.136291	−	0.132051i
$703$	−1.07422	+	1.86060i	−0.0405150	+	0.0701740i
$704$	−0.260700	−	0.218754i	−0.00982551	−	0.00824459i
$705$	0.00888218	+	0.108077i	0.000334522	+	0.00407042i
$706$	−30.0603	−	10.9411i	−1.13134	−	0.411773i
$707$	13.7312	−	17.9770i	0.516415	−	0.676093i
$708$	0.669948	+	1.45669i	0.0251782	+	0.0547458i
$709$	−38.9947	−	32.7204i	−1.46448	−	1.22884i	−0.921084	−	0.389364i	$-0.872695\pi$
$709$	−38.9947	−	32.7204i	−1.46448	−	1.22884i	−0.543393	−	0.839478i	$-0.682861\pi$
$710$	−12.0308	−	20.8380i	−0.451510	−	0.782038i
$711$	−45.7887	−	27.0832i	−1.71721	−	1.01570i
$712$	0.522204	−	0.904483i	0.0195704	−	0.0338969i
$713$	−32.0292	−	26.8757i	−1.19950	−	1.00650i
$714$	17.2148	+	11.0412i	0.644249	+	0.413206i
$715$	−0.107718	−	0.610902i	−0.00402844	−	0.0228464i
$716$	12.8958	−	10.8209i	0.481938	−	0.404394i
$717$	11.5037	+	11.6255i	0.429613	+	0.434163i
$718$	17.5916	−	6.40283i	0.656514	−	0.238951i
$719$	−12.3580	+	21.4047i	−0.460877	+	0.798262i	−0.999005	−	0.0446012i	$-0.985798\pi$
$719$	−12.3580	+	21.4047i	−0.460877	+	0.798262i	0.538128	+	0.842863i	$0.319132\pi$
$720$	5.57536	−	0.922638i	0.207781	−	0.0343847i
$721$	−17.1015	−	18.5804i	−0.636892	−	0.691969i
$722$	−16.5330	+	6.01751i	−0.615294	+	0.223949i
$723$	3.11000	+	6.76218i	0.115662	+	0.251488i
$724$	−3.62804	−	20.5756i	−0.134835	−	0.764688i
$725$	−7.73308	+	6.48883i	−0.287199	+	0.240989i
$726$	−15.4994	+	10.7316i	−0.575235	+	0.398285i
$727$	6.12263	−	34.7231i	0.227076	−	1.28781i	−0.631601	−	0.775293i	$-0.717602\pi$
$727$	6.12263	−	34.7231i	0.227076	−	1.28781i	0.858677	−	0.512517i	$-0.171287\pi$
$728$	1.73377	+	1.88370i	0.0642578	+	0.0698147i
$729$	−23.7976	+	12.7544i	−0.881392	+	0.472386i
$730$	9.81800	+	17.0053i	0.363380	+	0.629393i
$731$	−8.71098	−	7.30938i	−0.322187	−	0.270347i
$732$	−8.95570	−	4.23368i	−0.331012	−	0.156481i
$733$	−2.95882	−	16.7803i	−0.109287	−	0.619795i	−0.989421	−	0.145071i	$-0.953659\pi$
$733$	−2.95882	−	16.7803i	−0.109287	−	0.619795i	0.880135	−	0.474724i	$-0.157452\pi$
$734$	−5.42028	+	4.54815i	−0.200066	+	0.167875i
$735$	−3.98500	+	22.4886i	−0.146989	+	0.829506i
$736$	4.16605	−	1.51632i	0.153562	−	0.0558922i
$737$	0.725225			0.0267140
$738$	6.38970	−	16.9963i	0.235208	−	0.625643i
$739$	−16.3135			−0.600100			−0.300050	−	0.953923i	$-0.597003\pi$
$739$	−16.3135			−0.600100			−0.300050	+	0.953923i	$0.597003\pi$
$740$	−0.592686	+	3.36129i	−0.0217876	+	0.123563i
$741$	0.524453	−	1.91684i	0.0192663	−	0.0704170i
$742$	−16.7913	+	21.9833i	−0.616429	+	0.807032i
$743$	−1.99428	−	11.3101i	−0.0731630	−	0.414928i	−0.999289	−	0.0377126i	$-0.987993\pi$
$743$	−1.99428	−	11.3101i	−0.0731630	−	0.414928i	0.926126	−	0.377215i	$-0.123118\pi$
$744$	−4.31082	+	15.7558i	−0.158042	+	0.577634i
$745$	35.2621	−	12.8343i	1.29190	−	0.470214i
$746$	11.2327			0.411257
$747$	−7.94124	+	4.47401i	−0.290555	+	0.163695i
$748$	−0.759399	+	1.31532i	−0.0277664	+	0.0480928i
$749$	1.02774	+	22.4028i	0.0375528	+	0.818580i
$750$	−8.79535	−	19.1240i	−0.321161	−	0.698311i
$751$	−39.8738	−	14.5129i	−1.45502	−	0.529582i	−0.511028	−	0.859564i	$-0.670735\pi$
$751$	−39.8738	−	14.5129i	−1.45502	−	0.529582i	−0.943987	+	0.329982i	$0.892957\pi$
$752$	0.0254607	−	0.0213641i	0.000928458	−	0.000779068i
$753$	−31.3348	+	21.6958i	−1.14190	+	0.790638i
$754$	−6.32355	+	2.30158i	−0.230290	+	0.0838187i
$755$	−27.7585			−1.01024
$756$	−6.18168	−	12.2795i	−0.224825	−	0.446602i
$757$	10.4060			0.378211			0.189106	−	0.981957i	$-0.439441\pi$
$757$	10.4060			0.378211			0.189106	+	0.981957i	$0.439441\pi$
$758$	−27.9619	+	10.1773i	−1.01562	+	0.369656i
$759$	0.214047	+	2.60450i	0.00776943	+	0.0945374i
$760$	1.71104	−	1.43573i	0.0620659	−	0.0520794i
$761$	−1.16859	−	0.425333i	−0.0423615	−	0.0154183i	0.320753	−	0.947163i	$-0.396064\pi$
$761$	−1.16859	−	0.425333i	−0.0423615	−	0.0154183i	−0.363114	+	0.931745i	$0.618286\pi$
$762$	3.05880	−	4.31982i	0.110809	−	0.156491i
$763$	−28.6106	+	18.3160i	−1.03577	+	0.663083i
$764$	6.46991	−	11.2062i	0.234073	−	0.405427i
$765$	−8.37575	−	23.7890i	−0.302826	−	0.860092i
$766$	−29.3159			−1.05923
$767$	0.841728	−	0.306364i	0.0303930	−	0.0110622i
$768$	−1.21828	−	1.23118i	−0.0439608	−	0.0444263i
$769$	2.23762	+	12.6902i	0.0806907	+	0.457620i	0.998204	+	0.0599137i	$0.0190826\pi$
$769$	2.23762	+	12.6902i	0.0806907	+	0.457620i	−0.917513	+	0.397706i	$0.869806\pi$
$770$	−1.68209	−	0.217670i	−0.0606182	−	0.00784429i
$771$	−29.7757	+	7.81051i	−1.07235	+	0.281289i
$772$	1.21354	−	6.88233i	0.0436763	−	0.247701i
$773$	−7.52239			−0.270561			−0.135281	−	0.990807i	$-0.543194\pi$
$773$	−7.52239			−0.270561			−0.135281	+	0.990807i	$0.543194\pi$
$774$	2.53860	+	7.21017i	0.0912480	+	0.259164i
$775$	13.6896			0.491746
$776$	12.4328	−	4.52515i	0.446310	−	0.162443i
$777$	8.23544	−	1.05861i	0.295445	−	0.0379776i
$778$	−16.0231	+	13.4450i	−0.574456	+	0.482026i
$779$	−1.24623	−	7.06772i	−0.0446508	−	0.253227i
$780$	−0.258593	−	3.14652i	−0.00925911	−	0.112664i
$781$	−3.33004	−	2.79424i	−0.119158	−	0.0999856i
$782$	−9.89283	−	17.1349i	−0.353767	−	0.612742i
$783$	36.0440	−	2.58028i	1.28811	−	0.0922118i
$784$	6.33102	−	2.98634i	0.226108	−	0.106655i
$785$	−6.43581	+	36.4993i	−0.229704	+	1.30272i
$786$	2.21455	+	26.9464i	0.0789905	+	0.961146i
$787$	36.3698	−	30.5179i	1.29644	−	1.08785i	0.305696	−	0.952129i	$-0.401111\pi$
$787$	36.3698	−	30.5179i	1.29644	−	1.08785i	0.990748	−	0.135717i	$-0.0433337\pi$
$788$	−2.86886	−	16.2701i	−0.102199	−	0.579599i
$789$	−25.9819	+	36.6932i	−0.924982	+	1.30631i
$790$	−31.3895	+	11.4248i	−1.11679	+	0.406478i
$791$	−23.1681	+	5.19000i	−0.823764	+	0.184535i
$792$	0.889506	−	0.501138i	0.0316072	−	0.0178072i
$793$	−2.76708	+	4.79272i	−0.0982618	+	0.170194i
$794$	−33.6199	+	12.2366i	−1.19313	+	0.434262i
$795$	32.9968	−	8.65544i	1.17027	−	0.306977i
$796$	10.2727	−	8.61985i	0.364108	−	0.305523i
$797$	5.95165	+	33.7535i	0.210818	+	1.19561i	0.888018	+	0.459810i	$0.152082\pi$
$797$	5.95165	+	33.7535i	0.210818	+	1.19561i	−0.677199	+	0.735799i	$0.736807\pi$
$798$	−4.57380	−	2.93353i	−0.161911	−	0.103846i
$799$	−0.113627	−	0.0953448i	−0.00401985	−	0.00337306i
$800$	−0.725784	+	1.25710i	−0.0256603	+	0.0444450i
$801$	1.98860	+	2.42127i	0.0702638	+	0.0855513i
$802$	−12.1614	−	21.0641i	−0.429433	−	0.743800i
$803$	2.71754	+	2.28029i	0.0959000	+	0.0804697i
$804$	3.67522	+	0.341055i	0.129615	+	0.0120281i
$805$	13.4122	−	17.5593i	0.472717	−	0.618884i
$806$	8.57540	+	3.12119i	0.302056	+	0.109939i
$807$	6.79937	−	4.70779i	0.239349	−	0.165722i
$808$	6.54968	+	5.49583i	0.230417	+	0.193343i
$809$	19.3960	−	33.5948i	0.681927	−	1.18113i	−0.292466	−	0.956276i	$-0.594476\pi$
$809$	19.3960	−	33.5948i	0.681927	−	1.18113i	0.974392	−	0.224855i	$-0.0721910\pi$
$810$	−3.29503	+	16.6303i	−0.115776	+	0.584328i
$811$	−27.9334			−0.980875			−0.490437	−	0.871476i	$-0.663163\pi$
$811$	−27.9334			−0.980875			−0.490437	+	0.871476i	$0.663163\pi$
$812$	0.843207	+	18.3803i	0.0295908	+	0.645024i
$813$	−2.35085	−	28.6048i	−0.0824478	−	1.00321i
$814$	0.107076	+	0.607261i	0.00375303	+	0.0212845i
$815$	1.49122	+	8.45714i	0.0522352	+	0.296241i
$816$	−4.46697	+	6.30851i	−0.156375	+	0.220842i
$817$	2.31442	+	1.94203i	0.0809713	+	0.0679430i
$818$	−8.83990	+	15.3112i	−0.309080	+	0.535342i
$819$	−7.11999	+	2.88000i	−0.248793	+	0.100635i
$820$	−5.70070	−	9.87391i	−0.199077	−	0.344812i
$821$	2.90002	−	16.4468i	0.101211	−	0.573999i	−0.891455	−	0.453110i	$-0.850315\pi$
$821$	2.90002	−	16.4468i	0.101211	−	0.573999i	0.992666	−	0.120889i	$-0.0385744\pi$
$822$	17.9214	+	18.1112i	0.625081	+	0.631701i
$823$	21.9712	+	7.99687i	0.765869	+	0.278753i	0.695267	−	0.718751i	$-0.255286\pi$
$823$	21.9712	+	7.99687i	0.765869	+	0.278753i	0.0706014	+	0.997505i	$0.477508\pi$
$824$	7.31155	−	6.13512i	0.254710	−	0.213727i
$825$	−0.601826	−	0.608200i	−0.0209529	−	0.0211748i
$826$	−0.112239	−	2.44661i	−0.00390530	−	0.0851284i
$827$	−4.30436	−	7.45537i	−0.149677	−	0.259249i	0.781431	−	0.623992i	$-0.214490\pi$
$827$	−4.30436	−	7.45537i	−0.149677	−	0.259249i	−0.931108	+	0.364743i	$0.881157\pi$
$828$	−0.140105	+	13.2995i	−0.00486898	+	0.462190i
$829$	−9.30483	−	16.1164i	−0.323170	−	0.559747i	0.657970	−	0.753044i	$-0.271415\pi$
$829$	−9.30483	−	16.1164i	−0.323170	−	0.559747i	−0.981140	+	0.193297i	$0.938082\pi$
$830$	−0.993838	+	5.63634i	−0.0344966	+	0.195640i
$831$	9.70489	−	13.7058i	0.336659	−	0.475449i
$832$	−0.741256	+	0.621987i	−0.0256984	+	0.0215635i
$833$	−18.0314	−	25.5108i	−0.624752	−	0.883898i
$834$	−15.4126	−	7.28608i	−0.533694	−	0.252296i
$835$	−10.2684	+	3.73739i	−0.355352	+	0.129338i
$836$	0.201765	−	0.349467i	0.00697818	−	0.0120866i
$837$	−39.6930	−	28.7386i	−1.37199	−	0.993352i
$838$	16.5760	+	28.7105i	0.572610	+	0.991789i
$839$	1.13909	−	6.46010i	0.0393258	−	0.223028i	−0.958811	−	0.284045i	$-0.908323\pi$
$839$	1.13909	−	6.46010i	0.0393258	−	0.223028i	0.998137	+	0.0610176i	$0.0194346\pi$
$840$	−8.42195	−	1.89413i	−0.290585	−	0.0653538i
$841$	−18.1962	−	6.62288i	−0.627456	−	0.228375i
$842$	12.0258	+	4.37703i	0.414436	+	0.150842i
$843$	−5.33266	−	11.5950i	−0.183667	−	0.399353i
$844$	1.92970	−	10.9439i	0.0664230	−	0.376704i
$845$	22.7247			0.781753
$846$	0.0331139	+	0.0940507i	0.00113848	+	0.00323353i
$847$	28.1004	−	6.29490i	0.965541	−	0.216295i
$848$	−8.00933	−	6.72063i	−0.275042	−	0.230787i
$849$	−12.3134	−	12.4437i	−0.422593	−	0.427068i
$850$	6.08745	+	2.21565i	0.208798	+	0.0759962i
$851$	−7.54849	−	2.74743i	−0.258759	−	0.0941805i
$852$	−15.5616	−	15.7264i	−0.533131	−	0.538777i
$853$	23.7456	+	19.9249i	0.813034	+	0.682216i	0.951330	−	0.308175i	$-0.0997181\pi$
$853$	23.7456	+	19.9249i	0.813034	+	0.682216i	−0.138296	+	0.990391i	$0.544163\pi$
$854$	10.2474	+	11.1336i	0.350660	+	0.380984i
$855$	2.22535	+	6.32049i	0.0761055	+	0.216156i
$856$	−8.47636			−0.289716
$857$	3.71016	−	21.0414i	0.126737	−	0.718760i	−0.853524	−	0.521053i	$-0.825539\pi$
$857$	3.71016	−	21.0414i	0.126737	−	0.718760i	0.980261	−	0.197707i	$-0.0633495\pi$
$858$	−0.238326	−	0.518200i	−0.00813631	−	0.0176911i
$859$	2.31253	+	0.841691i	0.0789024	+	0.0287181i	0.381170	−	0.924505i	$-0.375521\pi$
$859$	2.31253	+	0.841691i	0.0789024	+	0.0287181i	−0.302267	+	0.953223i	$0.597744\pi$
$860$	4.51029	+	1.64161i	0.153800	+	0.0559785i
$861$	−18.8009	+	20.3920i	−0.640732	+	0.694959i
$862$	2.75480	−	15.6232i	0.0938287	−	0.532129i
$863$	21.1354	+	36.6076i	0.719459	+	1.24614i	0.961215	+	0.275802i	$0.0889433\pi$
$863$	21.1354	+	36.6076i	0.719459	+	1.24614i	−0.241756	+	0.970337i	$0.577723\pi$
$864$	4.74342	−	2.12130i	0.161375	−	0.0721682i
$865$	6.44014	−	11.1547i	0.218971	−	0.379270i
$866$	−12.0762	+	4.39536i	−0.410365	+	0.149360i
$867$	4.56777	+	2.15935i	0.155130	+	0.0733354i
$868$	15.1460	−	19.8292i	0.514087	−	0.673047i
$869$	−4.62298	+	3.87914i	−0.156824	+	0.131591i
$870$	13.1123	−	18.5180i	0.444550	−	0.627819i
$871$	0.358071	−	2.03072i	0.0121328	−	0.0688084i
$872$	−6.41995	−	11.1197i	−0.217407	−	0.376560i
$873$	−0.418116	+	39.6898i	−0.0141511	+	1.34330i
$874$	2.62842	+	4.55257i	0.0889078	+	0.153993i
$875$	1.47352	+	32.1200i	0.0498141	+	1.08586i
$876$	12.6993	+	12.8338i	0.429071	+	0.433615i
$877$	−6.68364	+	5.60824i	−0.225690	+	0.189377i	−0.748620	−	0.662999i	$-0.769283\pi$
$877$	−6.68364	+	5.60824i	−0.225690	+	0.189377i	0.522930	+	0.852376i	$0.324839\pi$
$878$	4.66376	+	1.69747i	0.157394	+	0.0572869i
$879$	−2.63467	−	2.66257i	−0.0888651	−	0.0898062i
$880$	0.111321	−	0.631331i	0.00375262	−	0.0212822i
$881$	−13.4444	−	23.2864i	−0.452954	−	0.784539i	0.545614	−	0.838037i	$-0.316296\pi$
$881$	−13.4444	−	23.2864i	−0.452954	−	0.784539i	−0.998568	+	0.0534974i	$0.982963\pi$
$882$	1.70233	+	20.9309i	0.0573205	+	0.704780i
$883$	−9.70390	+	16.8077i	−0.326562	+	0.565622i	−0.981827	−	0.189777i	$-0.939224\pi$
$883$	−9.70390	+	16.8077i	−0.326562	+	0.565622i	0.655265	+	0.755399i	$0.272557\pi$
$884$	3.30811	+	2.77584i	0.111264	+	0.0933615i
$885$	−1.74538	+	2.46493i	−0.0586704	+	0.0828577i
$886$	−1.04525	−	5.92791i	−0.0351158	−	0.199152i
$887$	−6.17928	−	35.0445i	−0.207480	−	1.17668i	−0.893489	−	0.449085i	$-0.851750\pi$
$887$	−6.17928	−	35.0445i	−0.207480	−	1.17668i	0.686009	−	0.727593i	$-0.259361\pi$
$888$	0.257052	+	3.12777i	0.00862609	+	0.104961i
$889$	−6.80952	+	4.35933i	−0.228384	+	0.146207i
$890$	1.96738			0.0659467
$891$	0.468201	+	3.02688i	0.0156853	+	0.101404i
$892$	10.2983	−	17.8372i	0.344813	−	0.597233i
$893$	0.0301897	+	0.0253321i	0.00101026	+	0.000847708i
$894$	28.3676	−	19.6413i	0.948753	−	0.656904i
$895$	29.7987	+	10.8459i	0.996062	+	0.362537i
$896$	1.01788	+	2.44211i	0.0340052	+	0.0815852i
$897$	7.39862	+	0.686582i	0.247033	+	0.0229243i
$898$	−0.918884	−	0.771036i	−0.0306636	−	0.0257298i
$899$	32.7933	+	56.7997i	1.09372	+	1.89438i
$900$	−2.76386	−	3.36520i	−0.0921285	−	0.112173i
$901$	−23.3305	+	40.4097i	−0.777253	+	1.34624i
$902$	−1.57791	−	1.32402i	−0.0525386	−	0.0440851i
$903$	0.544978	−	11.6637i	0.0181357	−	0.388144i
$904$	−1.55828	−	8.83743i	−0.0518275	−	0.293928i
$905$	30.1491	−	25.2981i	1.00219	−	0.840937i
$906$	−24.6882	+	6.47600i	−0.820210	+	0.215151i
$907$	−46.6520	+	16.9800i	−1.54906	+	0.563810i	−0.968196	−	0.250193i	$-0.919506\pi$
$907$	−46.6520	+	16.9800i	−1.54906	+	0.563810i	−0.580860	+	0.814004i	$0.697284\pi$
$908$	10.9706	−	19.0017i	0.364074	−	0.630594i
$909$	−22.3474	+	12.5903i	−0.741217	+	0.417593i
$910$	−1.44001	+	4.60259i	−0.0477360	+	0.152574i
$911$	4.93752	−	1.79711i	0.163587	−	0.0595410i	−0.258928	−	0.965897i	$-0.583369\pi$
$911$	4.93752	−	1.79711i	0.163587	−	0.0595410i	0.422516	+	0.906356i	$0.361147\pi$
$912$	1.18683	−	1.67611i	0.0392998	−	0.0555015i
$913$	0.179550	+	1.01828i	0.00594224	+	0.0337001i
$914$	17.5643	−	14.7382i	0.580976	−	0.487497i
$915$	−1.52841	−	18.5975i	−0.0505276	−	0.614814i
$916$	−3.71257	+	21.0550i	−0.122667	+	0.695678i
$917$	12.3321	−	39.4159i	0.407241	−	1.30163i
$918$	−12.9992	−	19.2036i	−0.429039	−	0.633815i
$919$	9.29344	+	16.0967i	0.306562	+	0.530982i	0.977608	−	0.210434i	$-0.0674879\pi$
$919$	9.29344	+	16.0967i	0.306562	+	0.530982i	−0.671046	+	0.741416i	$0.734155\pi$
$920$	6.39750	+	5.36814i	0.210919	+	0.176982i
$921$	0.790928	+	9.62391i	0.0260619	+	0.317118i
$922$	−4.79983	−	27.2212i	−0.158074	−	0.896483i
$923$	−9.46839	+	7.94492i	−0.311656	+	0.261510i
$924$	−1.54682	+	0.198833i	−0.0508865	+	0.00654114i
$925$	2.47149	−	0.899550i	0.0812622	−	0.0295770i
$926$	−42.2910			−1.38977
$927$	9.50931	+	27.0085i	0.312327	+	0.887076i
$928$	−6.95442			−0.228290
$929$	−5.13524	+	29.1234i	−0.168482	+	0.955507i	0.776920	+	0.629600i	$0.216781\pi$
$929$	−5.13524	+	29.1234i	−0.168482	+	0.955507i	−0.945402	+	0.325908i	$0.894330\pi$
$930$	−29.7635	+	7.80731i	−0.975983	+	0.256012i
$931$	4.79077	+	6.77797i	0.157011	+	0.222139i
$932$	3.27425	+	18.5692i	0.107252	+	0.608254i
$933$	−21.5062	−	21.7340i	−0.704082	−	0.711538i
$934$	27.9346	−	10.1674i	0.914047	−	0.332686i
$935$	−2.86100			−0.0935648
$936$	−0.964067	−	2.73816i	−0.0315115	−	0.0894996i
$937$	−5.45899	+	9.45526i	−0.178338	+	0.308890i	−0.941311	−	0.337540i	$-0.890405\pi$
$937$	−5.45899	+	9.45526i	−0.178338	+	0.308890i	0.762974	+	0.646430i	$0.223739\pi$
$938$	−5.00681	−	2.59233i	−0.163478	−	0.0846427i
$939$	17.4294	−	24.6148i	0.568787	−	0.803274i
$940$	0.0588330	+	0.0214135i	0.00191892	+	0.000698430i
$941$	17.2751	−	14.4955i	0.563152	−	0.472540i	−0.316214	−	0.948688i	$-0.602412\pi$
$941$	17.2751	−	14.4955i	0.563152	−	0.472540i	0.879365	+	0.476148i	$0.157967\pi$
$942$	2.79125	+	33.9636i	0.0909439	+	1.10659i
$943$	25.2153	−	9.17762i	0.821123	−	0.298865i
$944$	0.925703			0.0301291
$945$	14.2100	−	21.6502i	0.462251	−	0.704280i
$946$	0.867138			0.0281931
$947$	−12.3848	+	4.50771i	−0.402453	+	0.146481i	−0.535313	−	0.844654i	$-0.679806\pi$
$947$	−12.3848	+	4.50771i	−0.402453	+	0.146481i	0.132860	+	0.991135i	$0.457584\pi$
$948$	−25.2521	+	17.4842i	−0.820151	+	0.567862i
$949$	7.72685	−	6.48360i	0.250824	−	0.210467i
$950$	−1.61737	−	0.588676i	−0.0524746	−	0.0190992i
$951$	−0.179029	−	0.389269i	−0.00580541	−	0.0126229i
$952$	9.94438	−	6.36621i	0.322299	−	0.206330i
$953$	−25.3941	+	43.9839i	−0.822597	+	1.42478i	0.0811451	+	0.996702i	$0.474142\pi$
$953$	−25.3941	+	43.9839i	−0.822597	+	1.42478i	−0.903742	+	0.428077i	$0.859191\pi$
$954$	27.3277	−	15.3961i	0.884768	−	0.498469i
$955$	24.3751			0.788760
$956$	8.87313	−	3.22955i	0.286977	−	0.104451i
$957$	1.08182	−	3.95397i	0.0349702	−	0.127814i
$958$	−4.52764	−	25.6776i	−0.146282	−	0.829604i
$959$	−14.9735	−	35.9246i	−0.483521	−	1.16006i
$960$	0.861040	−	3.14705i	0.0277899	−	0.101571i
$961$	10.0616	−	57.0622i	0.324568	−	1.84071i
$962$	1.75327			0.0565279
$963$	8.94850	−	23.8026i	0.288361	−	0.767028i
$964$	4.29725			0.138405
$965$	12.3705	−	4.50251i	0.398222	−	0.144941i
$966$	7.83211	−	18.7461i	0.251994	−	0.603146i
$967$	20.0567	−	16.8295i	0.644979	−	0.541202i	−0.260564	−	0.965457i	$-0.583908\pi$
$967$	20.0567	−	16.8295i	0.644979	−	0.541202i	0.905543	+	0.424255i	$0.139464\pi$
$968$	1.89002	+	10.7188i	0.0607475	+	0.344516i
$969$	−8.28633	−	3.91724i	−0.266195	−	0.125840i
$970$	19.0921	+	16.0202i	0.613010	+	0.514377i
$971$	5.68943	+	9.85438i	0.182583	+	0.316242i	0.942759	−	0.333474i	$-0.108221\pi$
$971$	5.68943	+	9.85438i	0.182583	+	0.316242i	−0.760177	+	0.649716i	$0.774888\pi$
$972$	0.949232	+	15.5595i	0.0304466	+	0.499072i
$973$	17.6356	+	19.1607i	0.565371	+	0.614264i
$974$	−1.19210	+	6.76071i	−0.0381972	+	0.216627i
$975$	−2.00018	+	1.38490i	−0.0640571	+	0.0443523i
$976$	−4.38118	+	3.67625i	−0.140238	+	0.117674i
$977$	1.86608	+	10.5831i	0.0597011	+	0.338582i	0.999998	−	0.00177234i	$-0.000564155\pi$
$977$	1.86608	+	10.5831i	0.0597011	+	0.338582i	−0.940297	+	0.340354i	$0.889453\pi$
$978$	3.29931	+	7.17381i	0.105500	+	0.229393i
$979$	0.333998	−	0.121565i	0.0106746	−	0.00388524i
$980$	10.8347	+	7.51542i	0.346103	+	0.240071i
$981$	38.0029	−	6.28891i	1.21334	−	0.200789i
$982$	−4.86298	+	8.42293i	−0.155184	+	0.268787i
$983$	15.5149	−	5.64698i	0.494850	−	0.180111i	−0.0825263	−	0.996589i	$-0.526299\pi$
$983$	15.5149	−	5.64698i	0.494850	−	0.180111i	0.577376	+	0.816478i	$0.304077\pi$
$984$	−7.37372	−	7.45180i	−0.235065	−	0.237555i
$985$	23.8403	−	20.0044i	0.759614	−	0.637392i
$986$	5.38944	+	30.5650i	0.171635	+	0.973389i
$987$	0.00710878	−	0.152143i	0.000226275	−	0.00484278i
$988$	−0.878932	−	0.737512i	−0.0279626	−	0.0234634i
$989$	−5.64819	+	9.78294i	−0.179602	+	0.311080i
$990$	1.65533	+	0.979097i	0.0526098	+	0.0311178i
$991$	1.46112	+	2.53074i	0.0464141	+	0.0803915i	0.888299	−	0.459265i	$-0.151887\pi$
$991$	1.46112	+	2.53074i	0.0464141	+	0.0803915i	−0.841885	+	0.539657i	$0.818554\pi$
$992$	7.22451	+	6.06208i	0.229378	+	0.192471i
$993$	−5.97488	−	12.9914i	−0.189607	−	0.412269i
$994$	13.0019	+	31.1942i	0.412395	+	0.989419i
$995$	23.7376	+	8.63977i	0.752532	+	0.273899i
$996$	0.431034	+	5.24477i	0.0136578	+	0.166187i
$997$	−24.3435	−	20.4266i	−0.770966	−	0.646917i	0.169990	−	0.985446i	$-0.445626\pi$
$997$	−24.3435	−	20.4266i	−0.770966	−	0.646917i	−0.940956	+	0.338529i	$0.890071\pi$
$998$	−12.7857	+	22.1455i	−0.404724	+	0.701002i
$999$	−9.05450	−	2.58016i	−0.286472	−	0.0816326i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.b.25.11	yes	72
7.2	even	3		378.2.v.a.79.2	yes	72
27.13	even	9		378.2.v.a.67.2	✓	72
189.121	even	9	inner	378.2.w.b.121.11	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.2	✓	72	27.13	even	9
378.2.v.a.79.2	yes	72	7.2	even	3
378.2.w.b.25.11	yes	72	1.1	even	1	trivial
378.2.w.b.121.11	yes	72	189.121	even	9	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	378.2.w.b.25.11

Level	$378$
Weight	$2$
Character	378.25
Analytic conductor	$3.018$
Analytic rank	$0$
Dimension	$72$
Inner twists	$2$