LMFDB - Embedded newform 425.2.k.b.86.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(86,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.86"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [76] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			86.4
Character	$\chi$	$=$	425.86
Dual form			425.2.k.b.341.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.59626 + 1.15975i) q^{2} +(0.848137 - 2.61030i) q^{3} +(0.584991 - 1.80042i) q^{4} +(-0.617518 - 2.14911i) q^{5} +(1.67345 + 5.15034i) q^{6} -2.32069 q^{7} +(-0.0651963 - 0.200653i) q^{8} +(-3.66726 - 2.66442i) q^{9} +(3.47815 + 2.71437i) q^{10} +(-1.45463 + 1.05685i) q^{11} +(-4.20347 - 3.05400i) q^{12} +(-1.38238 - 1.00436i) q^{13} +(3.70442 - 2.69142i) q^{14} +(-6.13355 - 0.210834i) q^{15} +(3.39983 + 2.47012i) q^{16} +(0.309017 + 0.951057i) q^{17} +8.94397 q^{18} +(0.678772 + 2.08904i) q^{19} +(-4.23054 - 0.145420i) q^{20} +(-1.96826 + 6.05768i) q^{21} +(1.09629 - 3.37402i) q^{22} +(-1.45530 + 1.05734i) q^{23} -0.579060 q^{24} +(-4.23734 + 2.65423i) q^{25} +3.37144 q^{26} +(-3.40392 + 2.47309i) q^{27} +(-1.35758 + 4.17821i) q^{28} +(0.0601347 - 0.185075i) q^{29} +(10.0353 - 6.77685i) q^{30} +(2.54857 + 7.84368i) q^{31} -7.86979 q^{32} +(1.52497 + 4.69338i) q^{33} +(-1.59626 - 1.15975i) q^{34} +(1.43307 + 4.98741i) q^{35} +(-6.94239 + 5.04394i) q^{36} +(-1.70322 - 1.23746i) q^{37} +(-3.50627 - 2.54745i) q^{38} +(-3.79412 + 2.75659i) q^{39} +(-0.390966 + 0.264021i) q^{40} +(-7.70360 - 5.59699i) q^{41} +(-3.88355 - 11.9523i) q^{42} -2.01897 q^{43} +(1.05183 + 3.23720i) q^{44} +(-3.46153 + 9.52668i) q^{45} +(1.09679 - 3.37558i) q^{46} +(2.83884 - 8.73706i) q^{47} +(9.33128 - 6.77957i) q^{48} -1.61441 q^{49} +(3.68566 - 9.15110i) q^{50} +2.74463 q^{51} +(-2.61694 + 1.90132i) q^{52} +(2.11022 - 6.49460i) q^{53} +(2.56537 - 7.89540i) q^{54} +(3.16955 + 2.47354i) q^{55} +(0.151300 + 0.465654i) q^{56} +6.02872 q^{57} +(0.118651 + 0.365170i) q^{58} +(-8.31453 - 6.04086i) q^{59} +(-3.96766 + 10.9196i) q^{60} +(5.95712 - 4.32810i) q^{61} +(-13.1649 - 9.56485i) q^{62} +(8.51057 + 6.18329i) q^{63} +(5.76257 - 4.18675i) q^{64} +(-1.30483 + 3.59110i) q^{65} +(-7.87740 - 5.72327i) q^{66} +(-4.17661 - 12.8543i) q^{67} +1.89307 q^{68} +(1.52568 + 4.69555i) q^{69} +(-8.07171 - 6.29921i) q^{70} +(2.89556 - 8.91163i) q^{71} +(-0.295534 + 0.909559i) q^{72} +(-9.75365 + 7.08644i) q^{73} +4.15394 q^{74} +(3.33448 + 13.3119i) q^{75} +4.15823 q^{76} +(3.37575 - 2.45263i) q^{77} +(2.85945 - 8.80047i) q^{78} +(-4.57132 + 14.0691i) q^{79} +(3.20911 - 8.83196i) q^{80} +(-0.633795 - 1.95062i) q^{81} +18.7881 q^{82} +(0.428347 + 1.31832i) q^{83} +(9.75495 + 7.08738i) q^{84} +(1.85310 - 1.25141i) q^{85} +(3.22281 - 2.34151i) q^{86} +(-0.432099 - 0.313939i) q^{87} +(0.306898 + 0.222974i) q^{88} +(-2.88179 + 2.09374i) q^{89} +(-5.52306 - 19.2216i) q^{90} +(3.20807 + 2.33080i) q^{91} +(1.05231 + 3.23869i) q^{92} +22.6359 q^{93} +(5.60128 + 17.2390i) q^{94} +(4.07043 - 2.74878i) q^{95} +(-6.67466 + 20.5425i) q^{96} +(-4.33727 + 13.3487i) q^{97} +(2.57701 - 1.87231i) q^{98} +8.15042 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.59626	+	1.15975i	−1.12873	+	0.820068i	−0.985509	−	0.169623i	$-0.945745\pi$
$2$	−1.59626	+	1.15975i	−1.12873	+	0.820068i	−0.143218	+	0.989691i	$0.545745\pi$
$3$	0.848137	−	2.61030i	0.489672	−	1.50706i	−0.335426	−	0.942066i	$-0.608880\pi$
$3$	0.848137	−	2.61030i	0.489672	−	1.50706i	0.825098	−	0.564989i	$-0.191120\pi$
$4$	0.584991	−	1.80042i	0.292496	−	0.900209i
$5$	−0.617518	−	2.14911i	−0.276162	−	0.961111i
$5$	−0.617518	−	2.14911i	−0.276162	−	0.961111i
$6$	1.67345	+	5.15034i	0.683182	+	2.10262i
$7$	−2.32069			−0.877138			−0.438569	−	0.898698i	$-0.644514\pi$
$7$	−2.32069			−0.877138			−0.438569	+	0.898698i	$0.644514\pi$
$8$	−0.0651963	−	0.200653i	−0.0230504	−	0.0709417i
$9$	−3.66726	−	2.66442i	−1.22242	−	0.888141i
$10$	3.47815	+	2.71437i	1.09989	+	0.858360i
$11$	−1.45463	+	1.05685i	−0.438588	+	0.318653i	−0.785074	−	0.619402i	$-0.787375\pi$
$11$	−1.45463	+	1.05685i	−0.438588	+	0.318653i	0.346485	+	0.938055i	$0.387375\pi$
$12$	−4.20347	−	3.05400i	−1.21344	−	0.881614i
$13$	−1.38238	−	1.00436i	−0.383403	−	0.278559i	0.379344	−	0.925256i	$-0.376150\pi$
$13$	−1.38238	−	1.00436i	−0.383403	−	0.278559i	−0.762747	+	0.646697i	$0.776150\pi$
$14$	3.70442	−	2.69142i	0.990049	−	0.719312i
$15$	−6.13355	−	0.210834i	−1.58368	−	0.0544370i
$16$	3.39983	+	2.47012i	0.849958	+	0.617531i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$17$	0.309017	+	0.951057i	0.0749476	+	0.230665i
$18$	8.94397			2.10811
$19$	0.678772	+	2.08904i	0.155721	+	0.479260i	0.998233	−	0.0594174i	$-0.0189243\pi$
$19$	0.678772	+	2.08904i	0.155721	+	0.479260i	−0.842512	+	0.538677i	$0.818924\pi$
$20$	−4.23054	−	0.145420i	−0.945977	−	0.0325168i
$21$	−1.96826	+	6.05768i	−0.429510	+	1.32190i
$22$	1.09629	−	3.37402i	0.233729	−	0.719344i
$23$	−1.45530	+	1.05734i	−0.303452	+	0.220471i	−0.729082	−	0.684427i	$-0.760053\pi$
$23$	−1.45530	+	1.05734i	−0.303452	+	0.220471i	0.425630	+	0.904897i	$0.360053\pi$
$24$	−0.579060			−0.118200
$25$	−4.23734	+	2.65423i	−0.847469	+	0.530846i
$26$	3.37144			0.661195
$27$	−3.40392	+	2.47309i	−0.655084	+	0.475947i
$28$	−1.35758	+	4.17821i	−0.256559	+	0.789607i
$29$	0.0601347	−	0.185075i	0.0111667	−	0.0343676i	−0.945318	−	0.326150i	$-0.894248\pi$
$29$	0.0601347	−	0.185075i	0.0111667	−	0.0343676i	0.956485	+	0.291783i	$0.0942484\pi$
$30$	10.0353	−	6.77685i	1.83218	−	1.23728i
$31$	2.54857	+	7.84368i	0.457736	+	1.40877i	0.867893	+	0.496751i	$0.165474\pi$
$31$	2.54857	+	7.84368i	0.457736	+	1.40877i	−0.410157	+	0.912015i	$0.634526\pi$
$32$	−7.86979			−1.39119
$33$	1.52497	+	4.69338i	0.265463	+	0.817012i
$34$	−1.59626	−	1.15975i	−0.273756	−	0.198896i
$35$	1.43307	+	4.98741i	0.242232	+	0.843027i
$36$	−6.94239	+	5.04394i	−1.15706	+	0.840657i
$37$	−1.70322	−	1.23746i	−0.280008	−	0.203438i	0.438913	−	0.898530i	$-0.355364\pi$
$37$	−1.70322	−	1.23746i	−0.280008	−	0.203438i	−0.718921	+	0.695092i	$0.755364\pi$
$38$	−3.50627	−	2.54745i	−0.568792	−	0.413251i
$39$	−3.79412	+	2.75659i	−0.607545	+	0.441408i
$40$	−0.390966	+	0.264021i	−0.0618172	+	0.0417454i
$41$	−7.70360	−	5.59699i	−1.20310	−	0.874103i	−0.208514	−	0.978019i	$-0.566863\pi$
$41$	−7.70360	−	5.59699i	−1.20310	−	0.874103i	−0.994586	+	0.103916i	$0.966863\pi$
$42$	−3.88355	−	11.9523i	−0.599245	−	1.84429i
$43$	−2.01897			−0.307890			−0.153945	−	0.988079i	$-0.549198\pi$
$43$	−2.01897			−0.307890			−0.153945	+	0.988079i	$0.549198\pi$
$44$	1.05183	+	3.23720i	0.158569	+	0.488026i
$45$	−3.46153	+	9.52668i	−0.516015	+	1.42015i
$46$	1.09679	−	3.37558i	0.161713	−	0.497702i
$47$	2.83884	−	8.73706i	0.414088	−	1.27443i	−0.498977	−	0.866615i	$-0.666291\pi$
$47$	2.83884	−	8.73706i	0.414088	−	1.27443i	0.913064	−	0.407815i	$-0.133709\pi$
$48$	9.33128	−	6.77957i	1.34685	−	0.978546i
$49$	−1.61441			−0.230630
$50$	3.68566	−	9.15110i	0.521231	−	1.29416i
$51$	2.74463			0.384325
$52$	−2.61694	+	1.90132i	−0.362905	+	0.263666i
$53$	2.11022	−	6.49460i	0.289861	−	0.892102i	−0.695038	−	0.718973i	$-0.744612\pi$
$53$	2.11022	−	6.49460i	0.289861	−	0.892102i	0.984899	−	0.173128i	$-0.0553876\pi$
$54$	2.56537	−	7.89540i	0.349103	−	1.07443i
$55$	3.16955	+	2.47354i	0.427383	+	0.333532i
$56$	0.151300	+	0.465654i	0.0202183	+	0.0622257i
$57$	6.02872			0.798523
$58$	0.118651	+	0.365170i	0.0155796	+	0.0479492i
$59$	−8.31453	−	6.04086i	−1.08246	−	0.786453i	−0.104350	−	0.994541i	$-0.533276\pi$
$59$	−8.31453	−	6.04086i	−1.08246	−	0.786453i	−0.978110	+	0.208087i	$0.933276\pi$
$60$	−3.96766	+	10.9196i	−0.512223	+	1.40972i
$61$	5.95712	−	4.32810i	0.762730	−	0.554156i	−0.137016	−	0.990569i	$-0.543751\pi$
$61$	5.95712	−	4.32810i	0.762730	−	0.554156i	0.899747	+	0.436413i	$0.143751\pi$
$62$	−13.1649	−	9.56485i	−1.67194	−	1.21474i
$63$	8.51057	+	6.18329i	1.07223	+	0.779021i
$64$	5.76257	−	4.18675i	0.720321	−	0.523344i
$65$	−1.30483	+	3.59110i	−0.161844	+	0.445421i
$66$	−7.87740	−	5.72327i	−0.969641	−	0.704486i
$67$	−4.17661	−	12.8543i	−0.510254	−	1.57040i	−0.791754	−	0.610840i	$-0.790832\pi$
$67$	−4.17661	−	12.8543i	−0.510254	−	1.57040i	0.281500	−	0.959561i	$-0.409168\pi$
$68$	1.89307			0.229569
$69$	1.52568	+	4.69555i	0.183670	+	0.565277i
$70$	−8.07171	−	6.29921i	−0.964753	−	0.752900i
$71$	2.89556	−	8.91163i	0.343640	−	1.05762i	−0.618667	−	0.785653i	$-0.712327\pi$
$71$	2.89556	−	8.91163i	0.343640	−	1.05762i	0.962308	−	0.271963i	$-0.0876729\pi$
$72$	−0.295534	+	0.909559i	−0.0348290	+	0.107193i
$73$	−9.75365	+	7.08644i	−1.14158	+	0.829405i	−0.987338	−	0.158628i	$-0.949293\pi$
$73$	−9.75365	+	7.08644i	−1.14158	+	0.829405i	−0.154240	+	0.988033i	$0.549293\pi$
$74$	4.15394			0.482885
$75$	3.33448	+	13.3119i	0.385032	+	1.53712i
$76$	4.15823			0.476981
$77$	3.37575	−	2.45263i	0.384702	−	0.279503i
$78$	2.85945	−	8.80047i	0.323769	−	0.996457i
$79$	−4.57132	+	14.0691i	−0.514314	+	1.58290i	0.270212	+	0.962801i	$0.412906\pi$
$79$	−4.57132	+	14.0691i	−0.514314	+	1.58290i	−0.784526	+	0.620095i	$0.787094\pi$
$80$	3.20911	−	8.83196i	0.358789	−	0.987443i
$81$	−0.633795	−	1.95062i	−0.0704217	−	0.216736i
$82$	18.7881			2.07479
$83$	0.428347	+	1.31832i	0.0470172	+	0.144704i	0.971809	−	0.235769i	$-0.0757610\pi$
$83$	0.428347	+	1.31832i	0.0470172	+	0.144704i	−0.924792	+	0.380473i	$0.875761\pi$
$84$	9.75495	+	7.08738i	1.06435	+	0.773297i
$85$	1.85310	−	1.25141i	0.200997	−	0.135734i
$86$	3.22281	−	2.34151i	0.347524	−	0.252491i
$87$	−0.432099	−	0.313939i	−0.0463259	−	0.0336577i
$88$	0.306898	+	0.222974i	0.0327154	+	0.0237691i
$89$	−2.88179	+	2.09374i	−0.305469	+	0.221936i	−0.729950	−	0.683501i	$-0.760457\pi$
$89$	−2.88179	+	2.09374i	−0.305469	+	0.221936i	0.424481	+	0.905437i	$0.360457\pi$
$90$	−5.52306	−	19.2216i	−0.582182	−	2.02613i
$91$	3.20807	+	2.33080i	0.336297	+	0.244334i
$92$	1.05231	+	3.23869i	0.109711	+	0.337657i
$93$	22.6359			2.34723
$94$	5.60128	+	17.2390i	0.577728	+	1.77806i
$95$	4.07043	−	2.74878i	0.417617	−	0.282019i
$96$	−6.67466	+	20.5425i	−0.681229	+	2.09661i
$97$	−4.33727	+	13.3487i	−0.440383	+	1.35536i	0.447085	+	0.894491i	$0.352462\pi$
$97$	−4.33727	+	13.3487i	−0.440383	+	1.35536i	−0.887469	+	0.460868i	$0.847538\pi$
$98$	2.57701	−	1.87231i	0.260318	−	0.189132i
$99$	8.15042			0.819148
$100$	2.29991	+	9.18169i	0.229991	+	0.918169i
$101$	−8.69283			−0.864968			−0.432484	−	0.901642i	$-0.642363\pi$
$101$	−8.69283			−0.864968			−0.432484	+	0.901642i	$0.642363\pi$
$102$	−4.38114	+	3.18309i	−0.433798	+	0.315173i
$103$	4.19910	−	12.9235i	0.413750	−	1.27339i	−0.499615	−	0.866248i	$-0.666525\pi$
$103$	4.19910	−	12.9235i	0.413750	−	1.27339i	0.913364	−	0.407143i	$-0.133475\pi$
$104$	−0.111402	+	0.342860i	−0.0109239	+	0.0336202i
$105$	14.2341	+	0.489279i	1.38910	+	0.0477487i
$106$	4.16365	+	12.8144i	0.404410	+	1.24465i
$107$	12.9553			1.25243			0.626217	−	0.779649i	$-0.284602\pi$
$107$	12.9553			1.25243			0.626217	+	0.779649i	$0.284602\pi$
$108$	2.46133	+	7.57521i	0.236842	+	0.728925i
$109$	1.73078	+	1.25749i	0.165779	+	0.120445i	0.667581	−	0.744537i	$-0.267330\pi$
$109$	1.73078	+	1.25749i	0.165779	+	0.120445i	−0.501803	+	0.864982i	$0.667330\pi$
$110$	−7.92813	−	0.272520i	−0.755917	−	0.0259837i
$111$	−4.67471	+	3.39638i	−0.443704	+	0.322370i
$112$	−7.88995	−	5.73238i	−0.745530	−	0.541659i
$113$	−5.45493	−	3.96324i	−0.513157	−	0.372830i	0.300863	−	0.953667i	$-0.402725\pi$
$113$	−5.45493	−	3.96324i	−0.513157	−	0.372830i	−0.814020	+	0.580837i	$0.802725\pi$
$114$	−9.62340	+	6.99181i	−0.901314	+	0.654843i
$115$	3.17102	+	2.47468i	0.295699	+	0.230765i
$116$	−0.298035	−	0.216535i	−0.0276718	−	0.0201048i
$117$	2.39352	+	7.36649i	0.221281	+	0.681032i
$118$	20.2781			1.86675
$119$	−0.717132	−	2.20711i	−0.0657394	−	0.202325i
$120$	0.357580	+	1.24446i	0.0326425	+	0.113604i
$121$	−2.40017	+	7.38696i	−0.218197	+	0.671541i
$122$	−4.48959	+	13.8175i	−0.406469	+	1.25098i
$123$	−21.1435	+	15.3617i	−1.90645	+	1.38511i
$124$	15.6128			1.40207
$125$	8.32086	+	7.46748i	0.744240	+	0.667912i
$126$	−20.7562			−1.84911
$127$	6.28990	−	4.56988i	0.558138	−	0.405511i	−0.272639	−	0.962116i	$-0.587896\pi$
$127$	6.28990	−	4.56988i	0.558138	−	0.405511i	0.830777	+	0.556605i	$0.187896\pi$
$128$	0.520825	−	1.60293i	0.0460348	−	0.141681i
$129$	−1.71237	+	5.27012i	−0.150765	+	0.464008i
$130$	−2.08193	−	7.24560i	−0.182597	−	0.635481i
$131$	−1.30390	−	4.01298i	−0.113922	−	0.350616i	0.877799	−	0.479030i	$-0.159011\pi$
$131$	−1.30390	−	4.01298i	−0.113922	−	0.350616i	−0.991721	+	0.128414i	$0.959011\pi$
$132$	9.34214			0.813129
$133$	−1.57522	−	4.84802i	−0.136589	−	0.420377i
$134$	21.5747	+	15.6750i	1.86377	+	1.35411i
$135$	7.41692	+	5.78821i	0.638347	+	0.498170i
$136$	0.170686	−	0.124011i	0.0146362	−	0.0106338i
$137$	−14.7888	−	10.7447i	−1.26349	−	0.917980i	−0.264567	−	0.964367i	$-0.585229\pi$
$137$	−14.7888	−	10.7447i	−1.26349	−	0.917980i	−0.998924	+	0.0463878i	$0.985229\pi$
$138$	−7.88104	−	5.72591i	−0.670879	−	0.487422i
$139$	13.8707	−	10.0777i	1.17650	−	0.854777i	0.184728	−	0.982790i	$-0.440860\pi$
$139$	13.8707	−	10.0777i	1.17650	−	0.854777i	0.991773	+	0.128012i	$0.0408597\pi$
$140$	9.81776	+	0.337474i	0.829752	+	0.0285217i
$141$	−20.3986	−	14.8204i	−1.71787	−	1.24811i
$142$	5.71320	+	17.5834i	0.479441	+	1.47557i
$143$	3.07231			0.256920
$144$	−5.88663	−	18.1172i	−0.490552	−	1.50976i
$145$	−0.434882	−	0.0149485i	−0.0361150	−	0.00124141i
$146$	7.35086	−	22.6236i	0.608361	−	1.87234i
$147$	−1.36924	+	4.21408i	−0.112933	+	0.347572i
$148$	−3.22432	+	2.34261i	−0.265038	+	0.192561i
$149$	17.6689			1.44749			0.723745	−	0.690067i	$-0.242419\pi$
$149$	17.6689			1.44749			0.723745	+	0.690067i	$0.242419\pi$
$150$	−20.7612	−	17.3821i	−1.69514	−	1.41924i
$151$	11.5249			0.937879			0.468940	−	0.883230i	$-0.344636\pi$
$151$	11.5249			0.937879			0.468940	+	0.883230i	$0.344636\pi$
$152$	0.374921	−	0.272396i	0.0304101	−	0.0220942i
$153$	1.40077	−	4.31112i	0.113245	−	0.348534i
$154$	−2.54414	+	7.83006i	−0.205013	+	0.630964i
$155$	15.2831	−	10.3208i	1.22757	−	0.828983i
$156$	2.74349	+	8.44358i	0.219655	+	0.676028i
$157$	−0.241207			−0.0192504			−0.00962521	−	0.999954i	$-0.503064\pi$
$157$	−0.241207			−0.0192504			−0.00962521	+	0.999954i	$0.503064\pi$
$158$	−9.01962	−	27.7595i	−0.717562	−	2.20843i
$159$	−15.1631	−	11.0166i	−1.20251	−	0.873674i
$160$	4.85974	+	16.9130i	0.384196	+	1.33709i
$161$	3.37731	−	2.45376i	0.266169	−	0.193383i
$162$	3.27394	+	2.37865i	0.257225	+	0.186885i
$163$	1.29372	+	0.939942i	0.101332	+	0.0736219i	0.637297	−	0.770618i	$-0.280052\pi$
$163$	1.29372	+	0.939942i	0.101332	+	0.0736219i	−0.535965	+	0.844240i	$0.680052\pi$
$164$	−14.5835	+	10.5955i	−1.13878	+	0.827370i
$165$	9.14489	−	6.17558i	0.711929	−	0.480768i
$166$	−2.21267	−	1.60760i	−0.171737	−	0.124774i
$167$	0.0719524	+	0.221447i	0.00556785	+	0.0171361i	0.953802	−	0.300436i	$-0.0971323\pi$
$167$	0.0719524	+	0.221447i	0.00556785	+	0.0171361i	−0.948234	+	0.317572i	$0.897132\pi$
$168$	1.34382			0.103678
$169$	−3.11498	−	9.58693i	−0.239614	−	0.737456i
$170$	−1.50671	+	4.14671i	−0.115560	+	0.318038i
$171$	3.07686	−	9.46961i	0.235293	−	0.724159i
$172$	−1.18108	+	3.63499i	−0.0900566	+	0.277166i
$173$	−17.8488	+	12.9679i	−1.35702	+	0.985929i	−0.358387	+	0.933573i	$0.616673\pi$
$173$	−17.8488	+	12.9679i	−1.35702	+	0.985929i	−0.998628	+	0.0523564i	$0.983327\pi$
$174$	1.05383			0.0798909
$175$	9.83355	−	6.15963i	0.743347	−	0.465625i
$176$	−7.55606			−0.569560
$177$	−22.8203	+	16.5799i	−1.71528	+	1.24622i
$178$	2.17186	−	6.68431i	0.162788	−	0.501010i
$179$	4.70396	−	14.4773i	0.351591	−	1.08209i	−0.606369	−	0.795183i	$-0.707375\pi$
$179$	4.70396	−	14.4773i	0.351591	−	1.08209i	0.957960	−	0.286902i	$-0.0926254\pi$
$180$	15.1270	+	11.8052i	1.12750	+	0.879910i
$181$	−5.19936	−	16.0020i	−0.386465	−	1.18942i	−0.935412	−	0.353560i	$-0.884971\pi$
$181$	−5.19936	−	16.0020i	−0.386465	−	1.18942i	0.548947	−	0.835857i	$-0.315029\pi$
$182$	−7.82407			−0.579959
$183$	−6.24517	−	19.2207i	−0.461656	−	1.42083i
$184$	0.307040	+	0.223077i	0.0226353	+	0.0164455i
$185$	−1.60767	+	4.42457i	−0.118199	+	0.325301i
$186$	−36.1327	+	26.2520i	−2.64938	+	1.92489i
$187$	−1.45463	−	1.05685i	−0.106373	−	0.0772847i
$188$	−14.0697	−	10.2222i	−1.02613	−	0.745531i
$189$	7.89943	−	5.73927i	0.574599	−	0.417471i
$190$	−3.30957	+	9.10845i	−0.240102	+	0.660797i
$191$	12.4879	+	9.07302i	0.903595	+	0.656500i	0.939387	−	0.342859i	$-0.111395\pi$
$191$	12.4879	+	9.07302i	0.903595	+	0.656500i	−0.0357917	+	0.999359i	$0.511395\pi$
$192$	−6.04122	−	18.5929i	−0.435987	−	1.34183i
$193$	6.38396			0.459527			0.229764	−	0.973246i	$-0.426205\pi$
$193$	6.38396			0.459527			0.229764	+	0.973246i	$0.426205\pi$
$194$	−8.55781	−	26.3382i	−0.614415	−	1.89097i
$195$	8.26715	+	6.45173i	0.592023	+	0.462018i
$196$	−0.944414	+	2.90661i	−0.0674581	+	0.207615i
$197$	−7.34078	+	22.5926i	−0.523009	+	1.60966i	0.245211	+	0.969470i	$0.421143\pi$
$197$	−7.34078	+	22.5926i	−0.523009	+	1.60966i	−0.768220	+	0.640186i	$0.778857\pi$
$198$	−13.0102	+	9.45246i	−0.924594	+	0.671757i
$199$	−13.4520			−0.953588			−0.476794	−	0.879015i	$-0.658201\pi$
$199$	−13.4520			−0.953588			−0.476794	+	0.879015i	$0.658201\pi$
$200$	0.808839	+	0.677192i	0.0571936	+	0.0478847i
$201$	−37.0958			−2.61654
$202$	13.8760	−	10.0815i	0.976313	−	0.709333i
$203$	−0.139554	+	0.429502i	−0.00979475	+	0.0301452i
$204$	1.60558	−	4.94148i	0.112413	−	0.345973i
$205$	−7.27144	+	20.0121i	−0.507859	+	1.39771i
$206$	8.28519	+	25.4992i	0.577257	+	1.77661i
$207$	8.15418			0.566755
$208$	−2.21897	−	6.82930i	−0.153858	−	0.473527i
$209$	−3.19518	−	2.32143i	−0.221015	−	0.160577i
$210$	−23.2887	+	15.7270i	−1.60707	+	1.08526i
$211$	20.4106	−	14.8292i	1.40512	−	1.02088i	0.411114	−	0.911584i	$-0.365140\pi$
$211$	20.4106	−	14.8292i	1.40512	−	1.02088i	0.994009	−	0.109298i	$-0.0348602\pi$
$212$	−10.4585	−	7.59857i	−0.718295	−	0.521872i
$213$	−20.8062	−	15.1166i	−1.42562	−	1.03577i
$214$	−20.6800	+	15.0249i	−1.41366	+	1.02708i
$215$	1.24675	+	4.33899i	0.0850278	+	0.295917i
$216$	0.718157	+	0.521772i	0.0488644	+	0.0355021i
$217$	−5.91442	−	18.2027i	−0.401497	−	1.23568i
$218$	−4.22115			−0.285892
$219$	10.2253	+	31.4702i	0.690961	+	2.12656i
$220$	6.30757	−	4.25952i	0.425256	−	0.287177i
$221$	0.528022	−	1.62509i	0.0355186	−	0.109315i
$222$	3.52311	−	10.8430i	0.236455	−	0.727735i
$223$	−7.16198	+	5.20349i	−0.479602	+	0.348451i	−0.801172	−	0.598435i	$-0.795790\pi$
$223$	−7.16198	+	5.20349i	−0.479602	+	0.348451i	0.321570	+	0.946886i	$0.395790\pi$
$224$	18.2633			1.22027
$225$	22.6114	+	1.55632i	1.50743	+	0.103755i
$226$	13.3039			0.884960
$227$	−16.3435	+	11.8742i	−1.08476	+	0.788121i	−0.978506	−	0.206218i	$-0.933884\pi$
$227$	−16.3435	+	11.8742i	−1.08476	+	0.788121i	−0.106250	+	0.994339i	$0.533884\pi$
$228$	3.52675	−	10.8542i	0.233564	−	0.718838i
$229$	1.24955	−	3.84572i	0.0825727	−	0.254133i	−0.901244	−	0.433313i	$-0.857345\pi$
$229$	1.24955	−	3.84572i	0.0825727	−	0.254133i	0.983816	+	0.179180i	$0.0573445\pi$
$230$	−7.93179	−	0.272646i	−0.523006	−	0.0179777i
$231$	−3.53898	−	10.8919i	−0.232848	−	0.716632i
$232$	−0.0410566			−0.00269550
$233$	−7.93748	−	24.4290i	−0.520001	−	1.60040i	−0.773994	−	0.633193i	$-0.781744\pi$
$233$	−7.93748	−	24.4290i	−0.520001	−	1.60040i	0.253993	−	0.967206i	$-0.418256\pi$
$234$	−12.3640	−	8.98295i	−0.808258	−	0.587234i
$235$	−20.5299	−	0.705692i	−1.33922	−	0.0460343i
$236$	−15.7400	+	11.4358i	−1.02459	+	0.744406i
$237$	32.8474	+	23.8650i	2.13367	+	1.55020i
$238$	3.70442	+	2.69142i	0.240122	+	0.174459i
$239$	−0.656374	+	0.476884i	−0.0424573	+	0.0308470i	−0.608812	−	0.793315i	$-0.708353\pi$
$239$	−0.656374	+	0.476884i	−0.0424573	+	0.0308470i	0.566354	+	0.824162i	$0.308353\pi$
$240$	−20.3323	−	15.8674i	−1.31244	−	1.02424i
$241$	−8.25527	−	5.99780i	−0.531768	−	0.386352i	0.289250	−	0.957253i	$-0.406594\pi$
$241$	−8.25527	−	5.99780i	−0.531768	−	0.386352i	−0.821019	+	0.570901i	$0.806594\pi$
$242$	−4.73574	−	14.5751i	−0.304425	−	0.936923i
$243$	−18.2517			−1.17084
$244$	−4.30752	−	13.2572i	−0.275761	−	0.848705i
$245$	0.996926	+	3.46954i	0.0636912	+	0.221661i
$246$	15.9349	−	49.0424i	1.01597	−	3.12683i
$247$	1.15983	−	3.56958i	0.0737981	−	0.227127i
$248$	1.40770	−	1.02276i	0.0893893	−	0.0649451i
$249$	3.80449			0.241100
$250$	−21.9427	−	2.26992i	−1.38778	−	0.143562i
$251$	5.84535			0.368955			0.184478	−	0.982837i	$-0.440941\pi$
$251$	5.84535			0.368955			0.184478	+	0.982837i	$0.440941\pi$
$252$	16.1111	−	11.7054i	1.01490	−	0.737372i
$253$	0.999481	−	3.07608i	0.0628368	−	0.193392i
$254$	−4.74040	+	14.5894i	−0.297439	+	0.915423i
$255$	−1.69486	−	5.89851i	−0.106136	−	0.369379i
$256$	5.42984	+	16.7113i	0.339365	+	1.04446i
$257$	9.31778			0.581227			0.290614	−	0.956840i	$-0.406141\pi$
$257$	9.31778			0.581227			0.290614	+	0.956840i	$0.406141\pi$
$258$	−3.37865	−	10.3984i	−0.210345	−	0.647376i
$259$	3.95265	+	2.87177i	0.245606	+	0.178443i
$260$	5.70216	+	4.45000i	0.353633	+	0.275977i
$261$	−0.713649	+	0.518496i	−0.0441737	+	0.0320941i
$262$	6.73542	+	4.89357i	0.416116	+	0.302326i
$263$	16.6376	+	12.0879i	1.02592	+	0.745371i	0.967487	−	0.252920i	$-0.0813911\pi$
$263$	16.6376	+	12.0879i	1.02592	+	0.745371i	0.0584284	+	0.998292i	$0.481391\pi$
$264$	0.842320	−	0.611982i	0.0518412	−	0.0376649i
$265$	−15.2607	−	0.524568i	−0.937457	−	0.0322240i
$266$	8.13695	+	5.91184i	0.498909	+	0.362478i
$267$	3.02113	+	9.29809i	0.184890	+	0.569034i
$268$	−25.5864			−1.56294
$269$	6.97937	+	21.4803i	0.425540	+	1.30968i	0.902477	+	0.430739i	$0.141747\pi$
$269$	6.97937	+	21.4803i	0.425540	+	1.30968i	−0.476937	+	0.878937i	$0.658253\pi$
$270$	−18.5522	−	0.637711i	−1.12905	−	0.0388098i
$271$	3.55761	−	10.9492i	0.216109	−	0.665116i	−0.782964	−	0.622067i	$-0.786293\pi$
$271$	3.55761	−	10.9492i	0.216109	−	0.665116i	0.999073	−	0.0430486i	$-0.0137070\pi$
$272$	−1.29862	+	3.99674i	−0.0787404	+	0.242338i
$273$	8.80497	−	6.39718i	0.532901	−	0.387175i
$274$	36.0679			2.17894
$275$	3.35865	−	8.33917i	0.202534	−	0.502871i
$276$	9.34645			0.562590
$277$	12.6667	−	9.20288i	0.761067	−	0.552948i	−0.138170	−	0.990408i	$-0.544122\pi$
$277$	12.6667	−	9.20288i	0.761067	−	0.552948i	0.899237	+	0.437461i	$0.144122\pi$
$278$	−10.4537	+	32.1732i	−0.626972	+	1.92962i
$279$	11.5526	−	35.5553i	0.691637	−	2.12864i
$280$	0.907311	−	0.612711i	0.0542222	−	0.0366165i
$281$	−7.60173	−	23.3957i	−0.453481	−	1.39567i	−0.872909	−	0.487883i	$-0.837769\pi$
$281$	−7.60173	−	23.3957i	−0.453481	−	1.39567i	0.419428	−	0.907789i	$-0.362231\pi$
$282$	49.7495			2.96254
$283$	2.91324	+	8.96603i	0.173174	+	0.532975i	0.999545	−	0.0301504i	$-0.00959862\pi$
$283$	2.91324	+	8.96603i	0.173174	+	0.532975i	−0.826371	+	0.563126i	$0.809599\pi$
$284$	−14.3508	−	10.4265i	−0.851562	−	0.618696i
$285$	−3.72284	−	12.9564i	−0.220522	−	0.767469i
$286$	−4.90421	+	3.56312i	−0.289992	+	0.210692i
$287$	17.8776	+	12.9889i	1.05528	+	0.766709i
$288$	28.8606	+	20.9684i	1.70063	+	1.23558i
$289$	−0.809017	+	0.587785i	−0.0475892	+	0.0345756i
$290$	0.711521	−	0.480493i	0.0417820	−	0.0282155i
$291$	31.1656	+	22.6431i	1.82696	+	1.32736i
$292$	7.05276	+	21.7061i	0.412731	+	1.27026i
$293$	−10.4996			−0.613395			−0.306697	−	0.951807i	$-0.599224\pi$
$293$	−10.4996			−0.613395			−0.306697	+	0.951807i	$0.599224\pi$
$294$	−2.70163	−	8.31475i	−0.157562	−	0.484926i
$295$	−7.84810	+	21.5992i	−0.456934	+	1.25755i
$296$	−0.137258	+	0.422436i	−0.00797794	+	0.0245536i
$297$	2.33776	−	7.19488i	0.135650	−	0.417489i
$298$	−28.2041	+	20.4915i	−1.63382	+	1.18704i
$299$	3.07373			0.177759
$300$	25.9176	+	1.78388i	1.49635	+	0.102992i
$301$	4.68541			0.270062
$302$	−18.3967	+	13.3660i	−1.05861	+	0.769125i
$303$	−7.37270	+	22.6909i	−0.423551	+	1.30356i
$304$	−2.85249	+	8.77905i	−0.163601	+	0.503513i
$305$	−12.9802	−	10.1298i	−0.743243	−	0.580032i
$306$	2.76384	+	8.50622i	0.157998	+	0.486268i
$307$	−31.3476			−1.78910			−0.894552	−	0.446964i	$-0.852505\pi$
$307$	−31.3476			−1.78910			−0.894552	+	0.446964i	$0.852505\pi$
$308$	−2.44097	−	7.51252i	−0.139087	−	0.428066i
$309$	−30.1728	−	21.9218i	−1.71647	−	1.24709i
$310$	−12.4264	+	34.1993i	−0.705770	+	1.94239i
$311$	−0.998875	+	0.725725i	−0.0566410	+	0.0411521i	−0.615745	−	0.787945i	$-0.711145\pi$
$311$	−0.998875	+	0.725725i	−0.0566410	+	0.0411521i	0.559105	+	0.829097i	$0.311145\pi$
$312$	0.800482	+	0.581584i	0.0453184	+	0.0329257i
$313$	20.6727	+	15.0196i	1.16849	+	0.848957i	0.990827	−	0.135134i	$-0.0431466\pi$
$313$	20.6727	+	15.0196i	1.16849	+	0.848957i	0.177662	+	0.984092i	$0.443147\pi$
$314$	0.385029	−	0.279740i	0.0217285	−	0.0157867i
$315$	8.03314	−	22.1084i	0.452616	−	1.24567i
$316$	22.6561	+	16.4606i	1.27450	+	0.925980i
$317$	2.74130	+	8.43687i	0.153967	+	0.473862i	0.998055	−	0.0623434i	$-0.0198574\pi$
$317$	2.74130	+	8.43687i	0.153967	+	0.473862i	−0.844088	+	0.536205i	$0.819857\pi$
$318$	36.9807			2.07378
$319$	0.108124	+	0.332770i	0.00605376	+	0.0186316i
$320$	−12.5563	−	9.79900i	−0.701917	−	0.547780i
$321$	10.9879	−	33.8171i	0.613282	−	1.88749i
$322$	−2.54531	+	7.83367i	−0.141845	+	0.436554i
$323$	−1.77705	+	1.29110i	−0.0988776	+	0.0718387i
$324$	−3.88270			−0.215705
$325$	8.52341	+	0.586657i	0.472794	+	0.0325419i
$326$	−3.15521			−0.174751
$327$	4.75035	−	3.45133i	0.262695	−	0.190859i
$328$	−0.620810	+	1.91066i	−0.0342785	+	0.105498i
$329$	−6.58807	+	20.2760i	−0.363212	+	1.11785i
$330$	−7.43549	+	20.4636i	−0.409310	+	1.12649i
$331$	−7.27401	−	22.3871i	−0.399816	−	1.23051i	−0.925147	−	0.379609i	$-0.876059\pi$
$331$	−7.27401	−	22.3871i	−0.399816	−	1.23051i	0.525331	−	0.850898i	$-0.323941\pi$
$332$	2.62410			0.144016
$333$	2.94904	+	9.07620i	0.161606	+	0.497373i
$334$	−0.371678	−	0.270040i	−0.0203373	−	0.0147759i
$335$	−25.0461	+	16.9137i	−1.36842	+	0.924097i
$336$	−21.6550	+	15.7333i	−1.18138	+	0.858320i
$337$	−10.6705	−	7.75255i	−0.581258	−	0.422308i	0.257920	−	0.966166i	$-0.416963\pi$
$337$	−10.6705	−	7.75255i	−0.581258	−	0.422308i	−0.839177	+	0.543858i	$0.816963\pi$
$338$	16.0908	+	11.6906i	0.875223	+	0.635886i
$339$	−14.9718	+	10.8776i	−0.813154	+	0.590791i
$340$	−1.16901	−	4.06842i	−0.0633982	−	0.220641i
$341$	−11.9968	−	8.71621i	−0.649665	−	0.472009i
$342$	6.07091	+	18.6844i	0.328277	+	1.01033i
$343$	19.9914			1.07943
$344$	0.131630	+	0.405114i	0.00709699	+	0.0218423i
$345$	9.14911	−	6.17843i	0.492572	−	0.332635i
$346$	13.4517	−	41.4002i	0.723171	−	2.22569i
$347$	−9.57402	+	29.4658i	−0.513960	+	1.58181i	0.271206	+	0.962521i	$0.412578\pi$
$347$	−9.57402	+	29.4658i	−0.513960	+	1.58181i	−0.785166	+	0.619285i	$0.787422\pi$
$348$	−0.817995	+	0.594308i	−0.0438491	+	0.0318583i
$349$	−0.742398			−0.0397396			−0.0198698	−	0.999803i	$-0.506325\pi$
$349$	−0.742398			−0.0397396			−0.0198698	+	0.999803i	$0.506325\pi$
$350$	−8.55327	+	21.2369i	−0.457191	+	1.13516i
$351$	7.18938			0.383741
$352$	11.4477	−	8.31721i	0.610162	−	0.443309i
$353$	1.46091	−	4.49623i	0.0777566	−	0.239310i	−0.904621	−	0.426217i	$-0.859846\pi$
$353$	1.46091	−	4.49623i	0.0777566	−	0.239310i	0.982378	+	0.186906i	$0.0598461\pi$
$354$	17.1986	−	52.9317i	0.914094	−	2.81329i
$355$	−20.9401	−	0.719792i	−1.11139	−	0.0382026i
$356$	2.08379	+	6.41324i	0.110441	+	0.339901i
$357$	−6.36943			−0.337106
$358$	9.28133	+	28.5650i	0.490533	+	1.50971i
$359$	9.74742	+	7.08191i	0.514449	+	0.373769i	0.814509	−	0.580151i	$-0.197007\pi$
$359$	9.74742	+	7.08191i	0.514449	+	0.373769i	−0.300060	+	0.953920i	$0.597007\pi$
$360$	2.13724	+	0.0734651i	0.112642	+	0.00387195i
$361$	11.4679	−	8.33195i	0.603576	−	0.438524i
$362$	26.8578	+	19.5134i	1.41162	+	1.02560i
$363$	17.2465	+	12.5303i	0.905205	+	0.657670i
$364$	6.07311	−	4.41237i	0.318317	−	0.231271i
$365$	21.2526	+	16.5857i	1.11241	+	0.868133i
$366$	32.2601	+	23.4383i	1.68626	+	1.22514i
$367$	−5.28149	−	16.2547i	−0.275691	−	0.848491i	−0.989036	−	0.147677i	$-0.952820\pi$
$367$	−5.28149	−	16.2547i	−0.275691	−	0.848491i	0.713344	−	0.700814i	$-0.247180\pi$
$368$	−7.55955			−0.394069
$369$	13.3384	+	41.0513i	0.694367	+	2.13704i
$370$	−2.56513	−	8.92726i	−0.133355	−	0.464106i
$371$	−4.89717	+	15.0719i	−0.254248	+	0.782496i
$372$	13.2418	−	40.7540i	0.686554	−	2.11300i
$373$	9.18212	−	6.67120i	0.475432	−	0.345422i	−0.324122	−	0.946015i	$-0.605069\pi$
$373$	9.18212	−	6.67120i	0.475432	−	0.345422i	0.799555	+	0.600593i	$0.205069\pi$
$374$	3.54766			0.183445
$375$	26.5496	−	15.3865i	1.37101	−	0.794554i
$376$	−1.93820			−0.0999552
$377$	−0.269011	+	0.195448i	−0.0138548	+	0.0100661i
$378$	−5.95342	+	18.3227i	−0.306211	+	0.942420i
$379$	−0.753452	+	2.31889i	−0.0387022	+	0.119113i	−0.968541	−	0.248854i	$-0.919946\pi$
$379$	−0.753452	+	2.31889i	−0.0387022	+	0.119113i	0.929839	+	0.367967i	$0.119946\pi$
$380$	−2.56778	−	8.93649i	−0.131724	−	0.458432i
$381$	−6.59405	−	20.2944i	−0.337823	−	1.03971i
$382$	−30.4564			−1.55829
$383$	5.10530	+	15.7125i	0.260869	+	0.802871i	0.992616	+	0.121295i	$0.0387049\pi$
$383$	5.10530	+	15.7125i	0.260869	+	0.802871i	−0.731748	+	0.681575i	$0.761295\pi$
$384$	−3.74240	−	2.71901i	−0.190979	−	0.138754i
$385$	−7.35555	−	5.74031i	−0.374873	−	0.292553i
$386$	−10.1905	+	7.40380i	−0.518681	+	0.376844i
$387$	7.40410	+	5.37940i	0.376372	+	0.273450i
$388$	21.4961	+	15.6178i	1.09130	+	0.792873i
$389$	7.60439	−	5.52491i	0.385558	−	0.280124i	−0.378075	−	0.925775i	$-0.623414\pi$
$389$	7.60439	−	5.52491i	0.385558	−	0.280124i	0.763633	+	0.645651i	$0.223414\pi$
$390$	−20.6789	−	0.710814i	−1.04712	−	0.0359934i
$391$	−1.45530	−	1.05734i	−0.0735979	−	0.0534720i
$392$	0.105253	+	0.323936i	0.00531610	+	0.0163613i
$393$	−11.5810			−0.584182
$394$	−14.4840	−	44.5772i	−0.729693	−	2.24576i
$395$	33.0589	+	1.13636i	1.66337	+	0.0571765i
$396$	4.76792	−	14.6742i	0.239597	−	0.737404i
$397$	5.69295	−	17.5211i	0.285721	−	0.879358i	−0.700461	−	0.713691i	$-0.747022\pi$
$397$	5.69295	−	17.5211i	0.285721	−	0.879358i	0.986182	−	0.165667i	$-0.0529778\pi$
$398$	21.4729	−	15.6010i	1.07634	−	0.782007i
$399$	−13.9908			−0.700415
$400$	−20.9625	−	1.44283i	−1.04813	−	0.0721414i
$401$	−6.39157			−0.319180			−0.159590	−	0.987183i	$-0.551017\pi$
$401$	−6.39157			−0.319180			−0.159590	+	0.987183i	$0.551017\pi$
$402$	59.2146	−	43.0219i	2.95336	−	2.14574i
$403$	4.35477	−	13.4026i	0.216927	−	0.667632i
$404$	−5.08523	+	15.6507i	−0.252999	+	0.778652i
$405$	−3.80072	+	2.56664i	−0.188859	+	0.127537i
$406$	−0.275352	−	0.847445i	−0.0136655	−	0.0420580i
$407$	3.78538			0.187634
$408$	−0.178940	−	0.550719i	−0.00885883	−	0.0272647i
$409$	−23.5521	−	17.1116i	−1.16458	−	0.846115i	−0.174227	−	0.984706i	$-0.555743\pi$
$409$	−23.5521	−	17.1116i	−1.16458	−	0.846115i	−0.990350	+	0.138591i	$0.955743\pi$
$410$	−11.6020	−	40.3776i	−0.572980	−	1.99411i
$411$	−40.5897	+	29.4901i	−2.00214	+	1.45464i
$412$	−20.8113	−	15.1203i	−1.02530	−	0.744922i
$413$	19.2954	+	14.0190i	0.949466	+	0.689828i
$414$	−13.0162	+	9.45682i	−0.639711	+	0.464778i
$415$	2.56869	−	1.73465i	0.126092	−	0.0851506i
$416$	10.8790	+	7.90408i	0.533389	+	0.387530i
$417$	−14.5414	−	44.7540i	−0.712098	−	2.19161i
$418$	7.79262			0.381149
$419$	−2.30994	−	7.10927i	−0.112848	−	0.347311i	0.878644	−	0.477477i	$-0.158449\pi$
$419$	−2.30994	−	7.10927i	−0.112848	−	0.347311i	−0.991492	+	0.130167i	$0.958449\pi$
$420$	9.20771	−	25.3410i	0.449290	−	1.23652i
$421$	−0.926646	+	2.85192i	−0.0451620	+	0.138994i	−0.971095	−	0.238694i	$-0.923281\pi$
$421$	−0.926646	+	2.85192i	−0.0451620	+	0.138994i	0.925933	+	0.377688i	$0.123281\pi$
$422$	−15.3825	+	47.3424i	−0.748808	+	2.30459i
$423$	−33.6900	+	24.4772i	−1.63806	+	1.19012i
$424$	−1.44074			−0.0699686
$425$	−3.83373	−	3.20975i	−0.185963	−	0.155696i
$426$	50.7435			2.45853
$427$	−13.8246	+	10.0442i	−0.669020	+	0.486071i
$428$	7.57873	−	23.3249i	0.366332	−	1.12745i
$429$	2.60574	−	8.01965i	0.125806	−	0.387192i
$430$	−7.02230	−	5.48024i	−0.338645	−	0.264281i
$431$	−5.15236	−	15.8573i	−0.248180	−	0.763820i	−0.995097	−	0.0989028i	$-0.968467\pi$
$431$	−5.15236	−	15.8573i	−0.248180	−	0.763820i	0.746917	−	0.664917i	$-0.231533\pi$
$432$	−17.6816			−0.850706
$433$	10.2748	+	31.6226i	0.493776	+	1.51969i	0.818855	+	0.574000i	$0.194609\pi$
$433$	10.2748	+	31.6226i	0.493776	+	1.51969i	−0.325079	+	0.945687i	$0.605391\pi$
$434$	30.5516	+	22.1970i	1.46652	+	1.06549i
$435$	−0.407859	+	1.12249i	−0.0195554	+	0.0538194i
$436$	3.27649	−	2.38051i	0.156916	−	0.114006i
$437$	−3.19665	−	2.32250i	−0.152917	−	0.111100i
$438$	−52.8198	−	38.3758i	−2.52383	−	1.83367i
$439$	7.37045	−	5.35495i	0.351773	−	0.255578i	−0.397840	−	0.917455i	$-0.630240\pi$
$439$	7.37045	−	5.35495i	0.351773	−	0.255578i	0.749612	+	0.661877i	$0.230240\pi$
$440$	0.289681	−	0.797248i	0.0138100	−	0.0380073i
$441$	5.92045	+	4.30146i	0.281926	+	0.204832i
$442$	1.04183	+	3.20643i	0.0495550	+	0.152515i
$443$	−18.4088			−0.874626			−0.437313	−	0.899309i	$-0.644070\pi$
$443$	−18.4088			−0.874626			−0.437313	+	0.899309i	$0.644070\pi$
$444$	3.38023	+	10.4033i	0.160419	+	0.493718i
$445$	6.27923	+	4.90035i	0.297664	+	0.232299i
$446$	5.39764	−	16.6122i	0.255586	−	0.786612i
$447$	14.9856	−	46.1210i	0.708795	−	2.18145i
$448$	−13.3731	+	9.71614i	−0.631821	+	0.459045i
$449$	−22.0701			−1.04155			−0.520776	−	0.853694i	$-0.674357\pi$
$449$	−22.0701			−1.04155			−0.520776	+	0.853694i	$0.674357\pi$
$450$	−37.8987	+	23.7393i	−1.78656	+	1.11908i
$451$	17.1211			0.806201
$452$	−10.3266	+	7.50269i	−0.485721	+	0.352897i
$453$	9.77465	−	30.0833i	0.459253	−	1.41344i
$454$	12.3173	−	37.9088i	0.578080	−	1.77915i
$455$	3.02810	−	8.33381i	0.141960	−	0.390695i
$456$	−0.393050	−	1.20968i	−0.0184062	−	0.0566486i
$457$	−4.98599			−0.233235			−0.116617	−	0.993177i	$-0.537205\pi$
$457$	−4.98599			−0.233235			−0.116617	+	0.993177i	$0.537205\pi$
$458$	2.46547	+	7.58795i	0.115204	+	0.354562i
$459$	−3.40392	−	2.47309i	−0.158881	−	0.115434i
$460$	6.31048	−	4.26149i	0.294228	−	0.198693i
$461$	−4.10957	+	2.98578i	−0.191402	+	0.139062i	−0.679359	−	0.733806i	$-0.737742\pi$
$461$	−4.10957	+	2.98578i	−0.191402	+	0.139062i	0.487957	+	0.872867i	$0.337742\pi$
$462$	18.2810	+	13.2819i	0.850509	+	0.617931i
$463$	−7.06359	−	5.13200i	−0.328273	−	0.238504i	0.411425	−	0.911444i	$-0.365031\pi$
$463$	−7.06359	−	5.13200i	−0.328273	−	0.238504i	−0.739697	+	0.672940i	$0.765031\pi$
$464$	0.661607	−	0.480685i	0.0307143	−	0.0223153i
$465$	−13.9781	−	48.6469i	−0.648217	−	2.25595i
$466$	41.0019	+	29.7896i	1.89938	+	1.37998i
$467$	−8.67241	−	26.6909i	−0.401311	−	1.23511i	−0.923936	−	0.382547i	$-0.875047\pi$
$467$	−8.67241	−	26.6909i	−0.401311	−	1.23511i	0.522625	−	0.852563i	$-0.324953\pi$
$468$	14.6629			0.677795
$469$	9.69261	+	29.8308i	0.447563	+	1.37746i
$470$	33.5895	−	22.6831i	1.54937	−	1.04630i
$471$	−0.204577	+	0.629622i	−0.00942639	+	0.0290115i
$472$	−0.670043	+	2.06218i	−0.0308412	+	0.0949196i
$473$	2.93686	−	2.13376i	0.135037	−	0.0981102i
$474$	−80.1105			−3.67960
$475$	−8.42099	−	7.05038i	−0.386381	−	0.323494i
$476$	−4.39323			−0.201363
$477$	−25.0431	+	18.1949i	−1.14664	+	0.833086i
$478$	0.494678	−	1.52246i	0.0226260	−	0.0696358i
$479$	−1.55088	+	4.77313i	−0.0708617	+	0.218090i	−0.980215	−	0.197934i	$-0.936577\pi$
$479$	−1.55088	+	4.77313i	−0.0708617	+	0.218090i	0.909354	+	0.416024i	$0.136577\pi$
$480$	48.2698	+	1.65922i	2.20320	+	0.0757325i
$481$	1.11164	+	3.42129i	0.0506866	+	0.155997i
$482$	20.1335			0.917056
$483$	−3.54062	−	10.8969i	−0.161104	−	0.495826i
$484$	11.8955	+	8.64261i	0.540706	+	0.392846i
$485$	31.3663	+	1.07818i	1.42427	+	0.0489575i
$486$	29.1344	−	21.1674i	1.32156	−	0.960172i
$487$	−26.5091	−	19.2600i	−1.20124	−	0.872755i	−0.206837	−	0.978375i	$-0.566317\pi$
$487$	−26.5091	−	19.2600i	−1.20124	−	0.872755i	−0.994407	+	0.105620i	$0.966317\pi$
$488$	−1.25683	−	0.913140i	−0.0568940	−	0.0413359i
$489$	3.55078	−	2.57979i	0.160572	−	0.116662i
$490$	−5.61515	−	4.38210i	−0.253667	−	0.197963i
$491$	22.2748	+	16.1836i	1.00525	+	0.730355i	0.963207	−	0.268761i	$-0.0866141\pi$
$491$	22.2748	+	16.1836i	1.00525	+	0.730355i	0.0420406	+	0.999116i	$0.486614\pi$
$492$	15.2886	+	47.0536i	0.689265	+	2.12134i
$493$	0.194600			0.00876434
$494$	2.28844	+	7.04310i	0.102962	+	0.316884i
$495$	−5.03303	−	17.5161i	−0.226218	−	0.787292i
$496$	−10.7102	+	32.9625i	−0.480900	+	1.48006i
$497$	−6.71970	+	20.6811i	−0.301420	+	0.927675i
$498$	−6.07296	+	4.41227i	−0.272136	+	0.197718i
$499$	43.7371			1.95794			0.978970	−	0.204005i	$-0.0653958\pi$
$499$	43.7371			1.95794			0.978970	+	0.204005i	$0.0653958\pi$
$500$	18.3122	−	10.6126i	0.818947	−	0.474611i
$501$	0.639068			0.0285514
$502$	−9.33070	+	6.77915i	−0.416450	+	0.302568i
$503$	−2.44403	+	7.52194i	−0.108974	+	0.335387i	−0.990643	−	0.136482i	$-0.956420\pi$
$503$	−2.44403	+	7.52194i	−0.108974	+	0.335387i	0.881669	+	0.471869i	$0.156420\pi$
$504$	0.685842	−	2.11080i	0.0305498	−	0.0940226i
$505$	5.36798	+	18.6818i	0.238872	+	0.831331i
$506$	1.97206	+	6.06938i	0.0876688	+	0.269817i
$507$	−27.6667			−1.22872
$508$	−4.54816	−	13.9978i	−0.201792	−	0.621051i
$509$	−19.3618	−	14.0672i	−0.858196	−	0.623516i	0.0691974	−	0.997603i	$-0.477956\pi$
$509$	−19.3618	−	14.0672i	−0.858196	−	0.623516i	−0.927394	+	0.374087i	$0.877956\pi$
$510$	9.54624	+	7.44994i	0.422714	+	0.329889i
$511$	22.6352	−	16.4454i	1.00132	−	0.727502i
$512$	−25.3214	−	18.3970i	−1.11906	−	0.813042i
$513$	−7.47688	−	5.43227i	−0.330112	−	0.239841i
$514$	−14.8736	+	10.8063i	−0.656047	+	0.476646i
$515$	−30.3670	−	1.04383i	−1.33813	−	0.0459967i
$516$	8.48670	+	6.16595i	0.373606	+	0.271441i
$517$	5.10431	+	15.7094i	0.224487	+	0.690901i
$518$	−9.63999			−0.423557
$519$	18.7118	+	57.5891i	0.821358	+	2.52788i
$520$	0.805636	+	0.0276928i	0.0353295	+	0.00121441i
$521$	8.85252	−	27.2453i	0.387836	−	1.19364i	−0.546566	−	0.837416i	$-0.684065\pi$
$521$	8.85252	−	27.2453i	0.387836	−	1.19364i	0.934402	−	0.356221i	$-0.115935\pi$
$522$	0.537843	−	1.65531i	0.0235407	−	0.0724509i
$523$	7.52267	−	5.46554i	0.328943	−	0.238991i	−0.411039	−	0.911618i	$-0.634834\pi$
$523$	7.52267	−	5.46554i	0.328943	−	0.238991i	0.739982	+	0.672627i	$0.234834\pi$
$524$	−7.98782			−0.348949
$525$	−7.73828	−	30.8927i	−0.337726	−	1.34827i
$526$	−40.5768			−1.76923
$527$	−6.67223	+	4.84766i	−0.290647	+	0.211167i
$528$	−6.40858	+	19.7236i	−0.278897	+	0.858358i
$529$	−6.10745	+	18.7968i	−0.265541	+	0.817252i
$530$	24.9684	−	16.8613i	1.08456	−	0.732407i
$531$	14.3962	+	44.3068i	0.624740	+	1.92275i
$532$	−9.64995			−0.418378
$533$	5.02792	+	15.4743i	0.217783	+	0.670268i
$534$	−15.6060	−	11.3384i	−0.675337	−	0.490661i
$535$	−8.00012	−	27.8423i	−0.345875	−	1.20373i
$536$	−2.30696	+	1.67610i	−0.0996454	+	0.0723966i
$537$	−33.8005	−	24.5575i	−1.45860	−	1.05973i
$538$	−36.0527	−	26.1938i	−1.55434	−	1.12930i
$539$	2.34837	−	1.70619i	0.101151	−	0.0734908i
$540$	14.7600	−	9.96751i	0.635171	−	0.428933i
$541$	12.4961	+	9.07898i	0.537251	+	0.390336i	0.823063	−	0.567950i	$-0.192263\pi$
$541$	12.4961	+	9.07898i	0.537251	+	0.390336i	−0.285812	+	0.958286i	$0.592263\pi$
$542$	7.01947	+	21.6037i	0.301512	+	0.927958i
$543$	−46.1797			−1.98176
$544$	−2.43190	−	7.48461i	−0.104267	−	0.320900i
$545$	1.63369	−	4.49616i	0.0699795	−	0.192594i
$546$	−6.63588	+	20.4231i	−0.283990	+	0.874030i
$547$	−4.18586	+	12.8828i	−0.178975	+	0.550827i	−0.999793	−	0.0203625i	$-0.993518\pi$
$547$	−4.18586	+	12.8828i	−0.178975	+	0.550827i	0.820818	+	0.571190i	$0.193518\pi$
$548$	−27.9962	+	20.3404i	−1.19594	+	0.868900i
$549$	−33.3782			−1.42455
$550$	4.31009	+	17.2067i	0.183783	+	0.733696i
$551$	0.427448			0.0182099
$552$	0.842709	−	0.612264i	0.0358681	−	0.0260597i
$553$	10.6086	−	32.6500i	0.451124	−	1.38842i
$554$	−9.54627	+	29.3804i	−0.405582	+	1.24825i
$555$	10.1859	+	7.94914i	0.432368	+	0.337422i
$556$	−10.0298	−	30.8685i	−0.425357	−	1.30911i
$557$	−7.52130			−0.318688			−0.159344	−	0.987223i	$-0.550938\pi$
$557$	−7.52130			−0.318688			−0.159344	+	0.987223i	$0.550938\pi$
$558$	22.7943	+	70.1536i	0.964960	+	2.96984i
$559$	2.79099	+	2.02777i	0.118046	+	0.0857656i
$560$	−7.44733	+	20.4962i	−0.314707	+	0.866123i
$561$	−3.99243	+	2.90067i	−0.168560	+	0.122466i
$562$	39.2676	+	28.5295i	1.65640	+	1.20345i
$563$	15.7983	+	11.4781i	0.665817	+	0.483745i	0.868623	−	0.495474i	$-0.165006\pi$
$563$	15.7983	+	11.4781i	0.665817	+	0.483745i	−0.202805	+	0.979219i	$0.565006\pi$
$564$	−38.6160	+	28.0561i	−1.62603	+	1.18138i
$565$	−5.14892	+	14.1706i	−0.216617	+	0.596162i
$566$	−15.0487	−	10.9335i	−0.632542	−	0.459569i
$567$	1.47084	+	4.52678i	0.0617695	+	0.190107i
$568$	−1.97693			−0.0829501
$569$	0.160842	+	0.495020i	0.00674283	+	0.0207523i	0.954371	−	0.298622i	$-0.0965271\pi$
$569$	0.160842	+	0.495020i	0.00674283	+	0.0207523i	−0.947628	+	0.319375i	$0.896527\pi$
$570$	20.9688	+	16.3642i	0.878286	+	0.685420i
$571$	−12.2330	+	37.6494i	−0.511937	+	1.57558i	0.276851	+	0.960913i	$0.410709\pi$
$571$	−12.2330	+	37.6494i	−0.511937	+	1.57558i	−0.788787	+	0.614666i	$0.789291\pi$
$572$	1.79728	−	5.53145i	0.0751479	−	0.231281i
$573$	34.2747	−	24.9021i	1.43185	−	1.04030i
$574$	−43.6012			−1.81988
$575$	3.36020	−	8.34302i	0.140130	−	0.347928i
$576$	−32.2881			−1.34534
$577$	14.9375	−	10.8527i	0.621857	−	0.451805i	−0.231713	−	0.972784i	$-0.574433\pi$
$577$	14.9375	−	10.8527i	0.621857	−	0.451805i	0.853570	+	0.520979i	$0.174433\pi$
$578$	0.609717	−	1.87652i	0.0253609	−	0.0780528i
$579$	5.41447	−	16.6640i	0.225018	−	0.692533i
$580$	−0.281316	+	0.774224i	−0.0116810	+	0.0321479i
$581$	−0.994060	−	3.05940i	−0.0412405	−	0.126925i
$582$	−76.0088			−3.15067
$583$	3.79423	+	11.6774i	0.157141	+	0.483631i
$584$	2.05782	+	1.49509i	0.0851532	+	0.0618674i
$585$	14.3533	−	9.69287i	0.593438	−	0.400751i
$586$	16.7601	−	12.1770i	0.692355	−	0.503026i
$587$	16.4599	+	11.9588i	0.679373	+	0.493594i	0.873150	−	0.487452i	$-0.162074\pi$
$587$	16.4599	+	11.9588i	0.679373	+	0.493594i	−0.193776	+	0.981046i	$0.562074\pi$
$588$	6.78612	+	4.93040i	0.279855	+	0.203326i
$589$	−14.6559	+	10.6481i	−0.603886	+	0.438749i
$590$	−12.5221	−	43.5798i	−0.515525	−	1.79415i
$591$	52.7474	+	38.3232i	2.16974	+	1.57641i
$592$	−2.73398	−	8.41434i	−0.112366	−	0.345827i
$593$	18.9476			0.778083			0.389041	−	0.921220i	$-0.372806\pi$
$593$	18.9476			0.778083			0.389041	+	0.921220i	$0.372806\pi$
$594$	4.61260	+	14.1961i	0.189257	+	0.582474i
$595$	−4.30047	+	2.90412i	−0.176302	+	0.119057i
$596$	10.3361	−	31.8113i	0.423384	−	1.30304i
$597$	−11.4092	+	35.1138i	−0.466945	+	1.43711i
$598$	−4.90648	+	3.56477i	−0.200641	+	0.145774i
$599$	29.6852			1.21291			0.606453	−	0.795119i	$-0.292592\pi$
$599$	29.6852			1.21291			0.606453	+	0.795119i	$0.292592\pi$
$600$	2.45368	−	1.53696i	0.100171	−	0.0627461i
$601$	22.5986			0.921815			0.460907	−	0.887448i	$-0.347524\pi$
$601$	22.5986			0.921815			0.460907	+	0.887448i	$0.347524\pi$
$602$	−7.47913	+	5.43391i	−0.304827	+	0.221469i
$603$	−18.9325	+	58.2683i	−0.770992	+	2.37287i
$604$	6.74194	−	20.7496i	0.274326	−	0.844287i
$605$	17.3575	+	0.596644i	0.705684	+	0.0242570i
$606$	−14.5470	−	44.7710i	−0.590931	−	1.81870i
$607$	20.4527			0.830150			0.415075	−	0.909787i	$-0.363755\pi$
$607$	20.4527			0.830150			0.415075	+	0.909787i	$0.363755\pi$
$608$	−5.34179	−	16.4403i	−0.216638	−	0.666744i
$609$	1.00277	+	0.728553i	0.0406342	+	0.0295225i
$610$	32.4678	+	1.11604i	1.31458	+	0.0451872i
$611$	−12.6995	+	9.22672i	−0.513766	+	0.373273i
$612$	−6.94239	−	5.04394i	−0.280629	−	0.203889i
$613$	1.68187	+	1.22195i	0.0679302	+	0.0493542i	0.621232	−	0.783627i	$-0.286632\pi$
$613$	1.68187	+	1.22195i	0.0679302	+	0.0493542i	−0.553302	+	0.832981i	$0.686632\pi$
$614$	50.0390	−	36.3555i	2.01941	−	1.46719i
$615$	46.0704	+	35.9536i	1.85774	+	1.44979i
$616$	−0.712214	−	0.517454i	−0.0286959	−	0.0208488i
$617$	−13.9610	−	42.9675i	−0.562049	−	1.72981i	−0.676562	−	0.736386i	$-0.736531\pi$
$617$	−13.9610	−	42.9675i	−0.562049	−	1.72981i	0.114513	−	0.993422i	$-0.463469\pi$
$618$	73.5874			2.96012
$619$	−7.20167	−	22.1645i	−0.289460	−	0.890865i	−0.985026	−	0.172404i	$-0.944847\pi$
$619$	−7.20167	−	22.1645i	−0.289460	−	0.890865i	0.695567	−	0.718462i	$-0.255153\pi$
$620$	−9.64118	−	33.5536i	−0.387199	−	1.34754i
$621$	2.33884	−	7.19820i	0.0938543	−	0.288854i
$622$	0.752804	−	2.31689i	0.0301847	−	0.0928989i
$623$	6.68773	−	4.85892i	0.267938	−	0.194668i
$624$	−19.7085			−0.788971
$625$	10.9102	−	22.4937i	0.436406	−	0.899750i
$626$	−50.4180			−2.01511
$627$	−8.76957	+	6.37147i	−0.350223	+	0.254452i
$628$	−0.141104	+	0.434274i	−0.00563066	+	0.0173294i
$629$	0.650573	−	2.00226i	0.0259400	−	0.0798353i
$630$	12.8173	+	44.6073i	0.510654	+	1.77720i
$631$	4.85890	+	14.9542i	0.193430	+	0.595316i	0.999991	+	0.00416564i	$0.00132597\pi$
$631$	4.85890	+	14.9542i	0.193430	+	0.595316i	−0.806561	+	0.591150i	$0.798674\pi$
$632$	3.12105			0.124149
$633$	−21.3975	−	65.8549i	−0.850476	−	2.61750i
$634$	−14.1605	−	10.2882i	−0.562385	−	0.408597i
$635$	−13.7053	−	10.6957i	−0.543878	−	0.424446i
$636$	−28.7048	+	20.8552i	−1.13822	+	0.826964i
$637$	2.23172	+	1.62144i	0.0884241	+	0.0642439i
$638$	−0.558524	−	0.405792i	−0.0221122	−	0.0160654i
$639$	−34.3631	+	24.9663i	−1.35938	+	0.987651i
$640$	−3.76650	−	0.129469i	−0.148884	−	0.00511771i
$641$	−15.6554	−	11.3743i	−0.618351	−	0.449258i	0.233994	−	0.972238i	$-0.424820\pi$
$641$	−15.6554	−	11.3743i	−0.618351	−	0.449258i	−0.852345	+	0.522980i	$0.824820\pi$
$642$	21.6800	+	66.7241i	0.855641	+	2.63339i
$643$	34.6816			1.36771			0.683855	−	0.729618i	$-0.260302\pi$
$643$	34.6816			1.36771			0.683855	+	0.729618i	$0.260302\pi$
$644$	−2.44209	−	7.51599i	−0.0962320	−	0.296172i
$645$	12.3835	+	0.425667i	0.487599	+	0.0167606i
$646$	1.33928	−	4.12187i	0.0526931	−	0.162173i
$647$	12.4957	−	38.4577i	0.491256	−	1.51193i	−0.331456	−	0.943471i	$-0.607540\pi$
$647$	12.4957	−	38.4577i	0.491256	−	1.51193i	0.822712	−	0.568459i	$-0.192460\pi$
$648$	−0.350078	+	0.254346i	−0.0137524	+	0.00999167i
$649$	18.4789			0.725360
$650$	−14.2860	+	8.94858i	−0.560342	+	0.350992i
$651$	−52.5308			−2.05884
$652$	2.44910	−	1.77938i	0.0959143	−	0.0696858i
$653$	3.24091	−	9.97451i	0.126827	−	0.390333i	−0.867403	−	0.497607i	$-0.834212\pi$
$653$	3.24091	−	9.97451i	0.126827	−	0.390333i	0.994229	+	0.107274i	$0.0342122\pi$
$654$	−3.58011	+	11.0185i	−0.139994	+	0.430856i
$655$	−7.81916	+	5.28031i	−0.305520	+	0.206319i
$656$	−12.3657	−	38.0577i	−0.482799	−	1.48590i
$657$	54.6505			2.13212
$658$	−12.9988	−	40.0063i	−0.506747	−	1.55961i
$659$	27.2384	+	19.7899i	1.06106	+	0.770904i	0.974284	−	0.225325i	$-0.0723442\pi$
$659$	27.2384	+	19.7899i	1.06106	+	0.770904i	0.0867739	+	0.996228i	$0.472344\pi$
$660$	−5.76894	−	20.0773i	−0.224556	−	0.781507i
$661$	14.8324	−	10.7764i	0.576915	−	0.419153i	−0.260696	−	0.965421i	$-0.583952\pi$
$661$	14.8324	−	10.7764i	0.576915	−	0.419153i	0.837611	+	0.546268i	$0.183952\pi$
$662$	37.5747	+	27.2996i	1.46038	+	1.06103i
$663$	−3.79412	−	2.75659i	−0.147351	−	0.107057i
$664$	0.236598	−	0.171899i	0.00918179	−	0.00667096i
$665$	−9.44620	+	6.37905i	−0.366308	+	0.247369i
$666$	−15.2336	−	11.0678i	−0.590289	−	0.428870i
$667$	0.108174	+	0.332924i	0.00418850	+	0.0128909i
$668$	0.440788			0.0170546
$669$	7.50830	+	23.1082i	0.290288	+	0.893414i
$670$	20.3644	−	56.0460i	0.786746	−	2.16525i
$671$	−4.09125	+	12.5916i	−0.157941	+	0.486093i
$672$	15.4898	−	47.6727i	0.597532	−	1.83901i
$673$	−8.69267	+	6.31559i	−0.335078	+	0.243448i	−0.742582	−	0.669755i	$-0.766399\pi$
$673$	−8.69267	+	6.31559i	−0.335078	+	0.243448i	0.407504	+	0.913203i	$0.366399\pi$
$674$	26.0239			1.00240
$675$	7.85942	−	19.5141i	0.302509	−	0.751098i
$676$	−19.0827			−0.733950
$677$	24.3120	−	17.6637i	0.934386	−	0.678871i	−0.0126764	−	0.999920i	$-0.504035\pi$
$677$	24.3120	−	17.6637i	0.934386	−	0.678871i	0.947063	+	0.321048i	$0.104035\pi$
$678$	11.2835	−	34.7270i	0.433340	−	1.33368i
$679$	10.0654	−	30.9783i	0.386277	−	1.18884i
$680$	−0.371914	−	0.290244i	−0.0142623	−	0.0111304i
$681$	17.1338	+	52.7324i	0.656568	+	2.02071i
$682$	29.2587			1.12037
$683$	11.5415	+	35.5211i	0.441624	+	1.35918i	0.886144	+	0.463410i	$0.153374\pi$
$683$	11.5415	+	35.5211i	0.441624	+	1.35918i	−0.444520	+	0.895769i	$0.646626\pi$
$684$	−15.2493	−	11.0793i	−0.583072	−	0.423627i
$685$	−13.9591	+	38.4177i	−0.533352	+	1.46787i
$686$	−31.9114	+	23.1850i	−1.21838	+	0.885207i
$687$	−8.97869	−	6.52340i	−0.342558	−	0.248883i
$688$	−6.86417	−	4.98711i	−0.261694	−	0.190132i
$689$	−9.44003	+	6.85858i	−0.359637	+	0.261291i
$690$	−7.43893	+	20.4731i	−0.283195	+	0.779397i
$691$	20.6142	+	14.9771i	0.784202	+	0.569756i	0.906237	−	0.422769i	$-0.138942\pi$
$691$	20.6142	+	14.9771i	0.784202	+	0.569756i	−0.122035	+	0.992526i	$0.538942\pi$
$692$	12.9062	+	39.7213i	0.490621	+	1.50998i
$693$	−18.9146			−0.718506
$694$	−18.8904	−	58.1386i	−0.717068	−	2.20691i
$695$	−30.2235	−	23.5866i	−1.14644	−	0.894690i
$696$	−0.0348216	+	0.107170i	−0.00131991	+	0.00406226i
$697$	2.94251	−	9.05612i	0.111456	−	0.343025i
$698$	1.18506	−	0.860997i	0.0448552	−	0.0325892i
$699$	−70.4991			−2.66652
$700$	−5.33737	−	21.3078i	−0.201734	−	0.805360i
$701$	−13.0490			−0.492853			−0.246426	−	0.969162i	$-0.579256\pi$
$701$	−13.0490			−0.492853			−0.246426	+	0.969162i	$0.579256\pi$
$702$	−11.4761	+	8.33789i	−0.433138	+	0.314693i
$703$	1.42902	−	4.39806i	0.0538964	−	0.165876i
$704$	−3.95764	+	12.1804i	−0.149159	+	0.459065i
$705$	−19.2543	+	52.9907i	−0.725157	+	1.99574i
$706$	2.88251	+	8.87146i	0.108485	+	0.333882i
$707$	20.1733			0.758696
$708$	16.5011	+	50.7852i	0.620150	+	1.90862i
$709$	36.7420	+	26.6946i	1.37987	+	1.00254i	0.996892	+	0.0787819i	$0.0251031\pi$
$709$	36.7420	+	26.6946i	1.37987	+	1.00254i	0.382983	+	0.923756i	$0.374897\pi$
$710$	34.2607	−	23.1364i	1.28578	−	0.868293i
$711$	54.2502	−	39.4151i	2.03454	−	1.47818i
$712$	0.607998	+	0.441736i	0.0227857	+	0.0165548i
$713$	−12.0024	−	8.72024i	−0.449493	−	0.326575i
$714$	10.1673	−	7.38695i	0.380500	−	0.276450i
$715$	−1.89721	−	6.60274i	−0.0709516	−	0.246928i
$716$	−23.3134	−	16.9382i	−0.871264	−	0.633010i
$717$	0.688113	+	2.11779i	0.0256980	+	0.0790905i
$718$	−23.7727			−0.887188
$719$	9.14936	+	28.1588i	0.341214	+	1.05015i	0.963580	+	0.267421i	$0.0861715\pi$
$719$	9.14936	+	28.1588i	0.341214	+	1.05015i	−0.622366	+	0.782726i	$0.713829\pi$
$720$	−35.3007	+	23.8387i	−1.31558	+	0.888415i
$721$	−9.74480	+	29.9914i	−0.362915	+	1.11694i
$722$	−8.64284	+	26.5999i	−0.321653	+	0.989947i
$723$	−22.6576	+	16.4617i	−0.842647	+	0.612219i
$724$	−31.8518			−1.18376
$725$	0.236421	+	0.943839i	0.00878046	+	0.0350533i
$726$	−42.0619			−1.56106
$727$	−7.45537	+	5.41664i	−0.276504	+	0.200892i	−0.717391	−	0.696670i	$-0.754664\pi$
$727$	−7.45537	+	5.41664i	−0.276504	+	0.200892i	0.440887	+	0.897563i	$0.354664\pi$
$728$	0.258529	−	0.795671i	0.00958172	−	0.0294895i
$729$	−13.5785	+	41.7904i	−0.502908	+	1.54779i
$730$	−53.1599	−	1.82731i	−1.96754	−	0.0676317i
$731$	−0.623897	−	1.92016i	−0.0230757	−	0.0710196i
$732$	−38.2586			−1.41408
$733$	−5.66472	−	17.4342i	−0.209231	−	0.643948i	−0.999513	−	0.0312040i	$-0.990066\pi$
$733$	−5.66472	−	17.4342i	−0.209231	−	0.643948i	0.790282	−	0.612744i	$-0.209934\pi$
$734$	27.2821	+	19.8216i	1.00700	+	0.731629i
$735$	9.90205	+	0.340371i	0.365243	+	0.0125548i
$736$	11.4529	−	8.32105i	0.422161	−	0.306718i
$737$	19.6605	+	14.2842i	0.724205	+	0.526166i
$738$	−68.9008	−	50.0593i	−2.53627	−	1.84271i
$739$	−23.1541	+	16.8224i	−0.851736	+	0.618822i	−0.925624	−	0.378444i	$-0.876459\pi$
$739$	−23.1541	+	16.8224i	−0.851736	+	0.618822i	0.0738882	+	0.997267i	$0.476459\pi$
$740$	7.02559	+	5.48282i	0.258266	+	0.201552i
$741$	−8.33398	−	6.05499i	−0.306156	−	0.222436i
$742$	−9.66254	−	29.7382i	−0.354723	−	1.09172i
$743$	31.3500			1.15012			0.575060	−	0.818111i	$-0.304979\pi$
$743$	31.3500			1.15012			0.575060	+	0.818111i	$0.304979\pi$
$744$	−1.47577	−	4.54196i	−0.0541045	−	0.166516i
$745$	−10.9108	−	37.9723i	−0.399742	−	1.39120i
$746$	−6.92012	+	21.2980i	−0.253364	+	0.779774i
$747$	1.94169	−	5.97591i	0.0710427	−	0.218647i
$748$	−2.75372	+	2.00070i	−0.100686	+	0.0731527i
$749$	−30.0652			−1.09856
$750$	−24.5356	+	55.3517i	−0.895912	+	2.02116i
$751$	−14.2004			−0.518180			−0.259090	−	0.965853i	$-0.583423\pi$
$751$	−14.2004			−0.518180			−0.259090	+	0.965853i	$0.583423\pi$
$752$	31.2332	−	22.6922i	1.13896	−	0.827501i
$753$	4.95766	−	15.2581i	0.180667	−	0.556036i
$754$	0.202741	−	0.623972i	0.00738338	−	0.0227237i
$755$	−7.11681	−	24.7682i	−0.259007	−	0.901406i
$756$	−5.71199	−	17.5797i	−0.207743	−	0.639367i
$757$	−40.3483			−1.46649			−0.733243	−	0.679967i	$-0.761994\pi$
$757$	−40.3483			−1.46649			−0.733243	+	0.679967i	$0.761994\pi$
$758$	−1.48663	−	4.57536i	−0.0539967	−	0.166185i
$759$	−7.18180	−	5.21788i	−0.260683	−	0.189397i
$760$	−0.816929	−	0.637536i	−0.0296331	−	0.0231259i
$761$	−37.9858	+	27.5983i	−1.37698	+	1.00044i	−0.379828	+	0.925057i	$0.624017\pi$
$761$	−37.9858	+	27.5983i	−1.37698	+	1.00044i	−0.997155	+	0.0753792i	$0.975983\pi$
$762$	34.0623	+	24.7477i	1.23395	+	0.896514i
$763$	−4.01660	−	2.91823i	−0.145411	−	0.105647i
$764$	23.6406	−	17.1759i	0.855285	−	0.621401i
$765$	−10.1301	−	0.348209i	−0.366254	−	0.0125895i
$766$	−26.3720	−	19.1604i	−0.952858	−	0.692292i
$767$	5.42666	+	16.7015i	0.195945	+	0.603057i
$768$	48.2268			1.74023
$769$	−8.87072	−	27.3013i	−0.319886	−	0.984509i	−0.973696	−	0.227850i	$-0.926830\pi$
$769$	−8.87072	−	27.3013i	−0.319886	−	0.984509i	0.653810	−	0.756659i	$-0.273170\pi$
$770$	18.3987	+	0.632434i	0.663043	+	0.0227913i
$771$	7.90275	−	24.3222i	0.284611	−	0.875942i
$772$	3.73456	−	11.4938i	0.134410	−	0.413671i
$773$	−16.2627	+	11.8155i	−0.584928	+	0.424975i	−0.840497	−	0.541816i	$-0.817737\pi$
$773$	−16.2627	+	11.8155i	−0.584928	+	0.424975i	0.255569	+	0.966791i	$0.417737\pi$
$774$	−18.0576			−0.649068
$775$	−31.6181	−	26.4719i	−1.13575	−	0.950898i
$776$	2.96125			0.106303
$777$	10.8485	−	7.88193i	0.389190	−	0.282763i
$778$	−5.73106	+	17.6384i	−0.205469	+	0.632367i
$779$	6.46338	−	19.8922i	0.231575	−	0.712713i
$780$	16.4520	−	11.1101i	0.589077	−	0.397806i
$781$	5.20630	+	16.0233i	0.186296	+	0.573360i
$782$	3.54930			0.126923
$783$	0.253015	+	0.778700i	0.00904202	+	0.0278285i
$784$	−5.48871	−	3.98778i	−0.196025	−	0.142421i
$785$	0.148950	+	0.518380i	0.00531624	+	0.0185018i
$786$	18.4862	−	13.4310i	0.659382	−	0.479069i
$787$	13.2698	+	9.64107i	0.473017	+	0.343667i	0.798616	−	0.601841i	$-0.205566\pi$
$787$	13.2698	+	9.64107i	0.473017	+	0.343667i	−0.325599	+	0.945508i	$0.605566\pi$
$788$	36.3818	+	26.4329i	1.29605	+	0.941635i
$789$	45.6639	−	33.1768i	1.62568	−	1.18112i
$790$	−54.0885	+	36.5262i	−1.92438	+	1.29954i
$791$	12.6592	+	9.19744i	0.450109	+	0.327023i
$792$	−0.531377	−	1.63541i	−0.0188817	−	0.0581118i
$793$	−12.5820			−0.446798
$794$	11.2327	+	34.5706i	0.398633	+	1.22687i
$795$	−14.3124	+	39.3901i	−0.507610	+	1.39702i
$796$	−7.86931	+	24.2193i	−0.278920	+	0.858429i
$797$	4.52109	−	13.9145i	0.160145	−	0.492876i	−0.838501	−	0.544901i	$-0.816567\pi$
$797$	4.52109	−	13.9145i	0.160145	−	0.492876i	0.998646	+	0.0520244i	$0.0165674\pi$
$798$	22.3329	−	16.2258i	0.790577	−	0.574388i
$799$	9.18668			0.325002
$800$	33.3470	−	20.8882i	1.17899	−	0.738510i
$801$	16.1469			0.570522
$802$	10.2026	−	7.41263i	0.360267	−	0.261749i
$803$	6.69866	−	20.6163i	0.236390	−	0.727535i
$804$	−21.7007	+	66.7880i	−0.765326	+	2.35543i
$805$	−7.35894	−	5.74296i	−0.259369	−	0.202413i
$806$	8.59235	+	26.4445i	0.302653	+	0.931469i
$807$	61.9894			2.18213
$808$	0.566740	+	1.74425i	0.0199378	+	0.0613623i
$809$	−21.1771	−	15.3860i	−0.744546	−	0.540944i	0.149586	−	0.988749i	$-0.452206\pi$
$809$	−21.1771	−	15.3860i	−0.744546	−	0.540944i	−0.894131	+	0.447805i	$0.852206\pi$
$810$	3.09027	−	8.50491i	0.108581	−	0.298832i
$811$	10.2698	−	7.46144i	0.360621	−	0.262007i	−0.392690	−	0.919671i	$-0.628455\pi$
$811$	10.2698	−	7.46144i	0.360621	−	0.262007i	0.753311	+	0.657664i	$0.228455\pi$
$812$	0.691646	+	0.502510i	0.0242720	+	0.0176347i
$813$	−25.5633	−	18.5728i	−0.896544	−	0.651377i
$814$	−6.04245	+	4.39010i	−0.211788	+	0.153873i
$815$	1.22114	−	3.36078i	0.0427748	−	0.117723i
$816$	9.33128	+	6.77957i	0.326660	+	0.237332i
$817$	−1.37042	−	4.21772i	−0.0479450	−	0.147559i
$818$	57.4405			2.00836
$819$	−5.55461	−	17.0953i	−0.194094	−	0.597359i
$820$	31.7764	+	24.7985i	1.10968	+	0.866002i
$821$	14.8501	−	45.7039i	0.518272	−	1.59508i	−0.258976	−	0.965884i	$-0.583385\pi$
$821$	14.8501	−	45.7039i	0.518272	−	1.59508i	0.777248	−	0.629194i	$-0.216615\pi$
$822$	30.5905	−	94.1479i	1.06697	−	3.28379i
$823$	7.56946	−	5.49954i	0.263855	−	0.191702i	−0.447990	−	0.894039i	$-0.647860\pi$
$823$	7.56946	−	5.49954i	0.263855	−	0.191702i	0.711845	+	0.702337i	$0.247860\pi$
$824$	−2.86691			−0.0998736
$825$	−18.9191	−	15.8398i	−0.658679	−	0.551472i
$826$	−47.0590			−1.63739
$827$	−25.5798	+	18.5848i	−0.889498	+	0.646258i	−0.935747	−	0.352672i	$-0.885273\pi$
$827$	−25.5798	+	18.5848i	−0.889498	+	0.646258i	0.0462488	+	0.998930i	$0.485273\pi$
$828$	4.77013	−	14.6809i	0.165773	−	0.510198i
$829$	−7.98905	+	24.5878i	−0.277471	+	0.853969i	0.711084	+	0.703107i	$0.248205\pi$
$829$	−7.98905	+	24.5878i	−0.277471	+	0.853969i	−0.988555	+	0.150861i	$0.951795\pi$
$830$	−2.08854	+	5.74800i	−0.0724944	+	0.199516i
$831$	−13.2792	−	40.8691i	−0.460650	−	1.41773i
$832$	−12.1711			−0.421955
$833$	−0.498879	−	1.53539i	−0.0172851	−	0.0531982i
$834$	75.1154	+	54.5745i	2.60103	+	1.88976i
$835$	0.431482	−	0.291381i	0.0149320	−	0.0100837i
$836$	−6.04870	+	4.39463i	−0.209198	+	0.151992i
$837$	−28.0732	−	20.3964i	−0.970353	−	0.705003i
$838$	11.9323	+	8.66930i	0.412193	+	0.299476i
$839$	−1.85242	+	1.34586i	−0.0639525	+	0.0464642i	−0.619302	−	0.785153i	$-0.712584\pi$
$839$	−1.85242	+	1.34586i	−0.0639525	+	0.0464642i	0.555350	+	0.831617i	$0.312584\pi$
$840$	−0.829832	−	2.88801i	−0.0286319	−	0.0996459i
$841$	23.4309	+	17.0235i	0.807961	+	0.587018i
$842$	−1.82835	−	5.62709i	−0.0630092	−	0.193922i
$843$	−67.5171			−2.32541
$844$	−14.7587	−	45.4225i	−0.508014	−	1.56351i
$845$	−18.6798	+	12.6145i	−0.642605	+	0.433953i
$846$	25.3905	−	78.1440i	0.872944	−	2.68665i
$847$	5.57004	−	17.1428i	0.191389	−	0.589034i
$848$	23.2169	−	16.8680i	0.797270	−	0.579251i
$849$	25.8748			0.888022
$850$	9.84215	+	0.677425i	0.337583	+	0.0232355i
$851$	3.78713			0.129821
$852$	−39.3876	+	28.6167i	−1.34940	+	0.980393i
$853$	−0.990070	+	3.04712i	−0.0338993	+	0.104331i	−0.966574	−	0.256386i	$-0.917468\pi$
$853$	−0.990070	+	3.04712i	−0.0338993	+	0.104331i	0.932675	+	0.360718i	$0.117468\pi$
$854$	10.4189	−	32.0662i	0.356529	−	1.09728i
$855$	−22.2512	−	0.764860i	−0.760976	−	0.0261577i
$856$	−0.844636	−	2.59952i	−0.0288691	−	0.0888499i
$857$	−9.78644			−0.334298			−0.167149	−	0.985932i	$-0.553456\pi$
$857$	−9.78644			−0.334298			−0.167149	+	0.985932i	$0.553456\pi$
$858$	5.14136	+	15.8235i	0.175523	+	0.540204i
$859$	−42.5673	−	30.9270i	−1.45238	−	1.05521i	−0.985268	−	0.171016i	$-0.945295\pi$
$859$	−42.5673	−	30.9270i	−1.45238	−	1.05521i	−0.467110	−	0.884199i	$-0.654705\pi$
$860$	8.54134	+	0.293598i	0.291257	+	0.0100116i
$861$	49.0675	−	35.6496i	1.67222	−	1.21494i
$862$	26.6151	+	19.3370i	0.906512	+	0.658620i
$863$	5.79788	+	4.21241i	0.197362	+	0.143392i	0.682077	−	0.731280i	$-0.261077\pi$
$863$	5.79788	+	4.21241i	0.197362	+	0.143392i	−0.484715	+	0.874672i	$0.661077\pi$
$864$	26.7881	−	19.4627i	0.911350	−	0.662134i
$865$	38.8913	+	30.3510i	1.32234	+	1.03197i
$866$	−53.0757	−	38.5618i	−1.80359	−	1.31038i
$867$	0.848137	+	2.61030i	0.0288042	+	0.0886503i
$868$	−36.2324			−1.22981
$869$	−8.21936	−	25.2966i	−0.278823	−	0.858128i
$870$	−0.650761	−	2.26480i	−0.0220629	−	0.0767841i
$871$	−7.13664	+	21.9643i	−0.241816	+	0.744233i
$872$	0.139479	−	0.429271i	0.00472334	−	0.0145369i
$873$	51.4726	−	37.3970i	1.74208	−	1.26570i
$874$	7.79621			0.263711
$875$	−19.3101	−	17.3297i	−0.652801	−	0.585851i
$876$	62.6412			2.11645
$877$	28.2784	−	20.5454i	0.954892	−	0.693770i	0.00293340	−	0.999996i	$-0.499066\pi$
$877$	28.2784	−	20.5454i	0.954892	−	0.693770i	0.951959	+	0.306226i	$0.0990663\pi$
$878$	−5.55476	+	17.0958i	−0.187464	+	0.576955i
$879$	−8.90512	+	27.4072i	−0.300362	+	0.924420i
$880$	4.66601	+	16.2388i	0.157291	+	0.547410i
$881$	4.38303	+	13.4896i	0.147668	+	0.454476i	0.997344	−	0.0728290i	$-0.0232027\pi$
$881$	4.38303	+	13.4896i	0.147668	+	0.454476i	−0.849676	+	0.527304i	$0.823203\pi$
$882$	−14.4392			−0.486194
$883$	0.0144184	+	0.0443753i	0.000485218	+	0.00149335i	0.951299	−	0.308270i	$-0.0997501\pi$
$883$	0.0144184	+	0.0443753i	0.000485218	+	0.00149335i	−0.950814	+	0.309764i	$0.899750\pi$
$884$	−2.61694	−	1.90132i	−0.0880174	−	0.0639484i
$885$	49.7240	+	38.8049i	1.67145	+	1.30441i
$886$	29.3852	−	21.3496i	0.987214	−	0.717253i
$887$	0.988452	+	0.718153i	0.0331890	+	0.0241132i	0.604256	−	0.796790i	$-0.293470\pi$
$887$	0.988452	+	0.718153i	0.0331890	+	0.0241132i	−0.571067	+	0.820903i	$0.693470\pi$
$888$	0.986269	+	0.716566i	0.0330970	+	0.0240464i
$889$	−14.5969	+	10.6053i	−0.489564	+	0.355689i
$890$	−15.7065	−	0.539892i	−0.526482	−	0.0180972i
$891$	2.98346	+	2.16761i	0.0999496	+	0.0726176i
$892$	5.17875	+	15.9386i	0.173397	+	0.533662i
$893$	20.1790			0.675265
$894$	29.5679	+	91.0007i	0.988899	+	3.04352i
$895$	−34.0181	−	1.16933i	−1.13710	−	0.0390865i
$896$	−1.20867	+	3.71991i	−0.0403789	+	0.124273i
$897$	2.60695	−	8.02335i	0.0870434	−	0.267892i
$898$	35.2296	−	25.5958i	1.17563	−	0.854143i
$899$	1.60493			0.0535274
$900$	16.0295	−	39.7996i	0.534317	−	1.32665i
$901$	6.82882			0.227501
$902$	−27.3297	+	19.8562i	−0.909981	+	0.661140i
$903$	3.97387	−	12.2303i	0.132242	−	0.406999i
$904$	−0.439597	+	1.35294i	−0.0146208	+	0.0449981i
$905$	−31.1793	+	21.0555i	−1.03643	+	0.699908i
$906$	19.2862	+	59.3569i	0.640742	+	1.97200i
$907$	−42.7865			−1.42070			−0.710351	−	0.703848i	$-0.751464\pi$
$907$	−42.7865			−1.42070			−0.710351	+	0.703848i	$0.751464\pi$
$908$	11.8178	+	36.3715i	0.392187	+	1.20703i
$909$	31.8789	+	23.1614i	1.05736	+	0.768214i
$910$	4.83150	+	16.8148i	0.160163	+	0.557405i
$911$	28.9580	−	21.0392i	0.959423	−	0.697061i	0.00640601	−	0.999979i	$-0.497961\pi$
$911$	28.9580	−	21.0392i	0.959423	−	0.697061i	0.953017	+	0.302918i	$0.0979609\pi$
$912$	20.4966	+	14.8917i	0.678711	+	0.493112i
$913$	−2.01635	−	1.46497i	−0.0667316	−	0.0484833i
$914$	7.95894	−	5.78250i	0.263258	−	0.191268i
$915$	−37.4508	+	25.2907i	−1.23809	+	0.836083i
$916$	−6.19293	−	4.49943i	−0.204620	−	0.148665i
$917$	3.02594	+	9.31288i	0.0999253	+	0.307538i
$918$	8.30171			0.273997
$919$	−10.8197	−	33.2997i	−0.356910	−	1.09846i	−0.954894	−	0.296947i	$-0.904031\pi$
$919$	−10.8197	−	33.2997i	−0.356910	−	1.09846i	0.597984	−	0.801508i	$-0.295969\pi$
$920$	0.289815	−	0.797616i	0.00955492	−	0.0262966i
$921$	−26.5871	+	81.8266i	−0.876074	+	2.69628i
$922$	3.09719	−	9.53216i	0.102000	−	0.313925i
$923$	−12.9532	+	9.41108i	−0.426361	+	0.309769i
$924$	−21.6802			−0.713226
$925$	10.5016	+	0.722817i	0.345292	+	0.0237661i
$926$	17.2272			0.566120
$927$	−49.8329	+	36.2057i	−1.63673	+	1.18915i
$928$	−0.473247	+	1.45650i	−0.0155351	+	0.0478121i
$929$	−15.5648	+	47.9035i	−0.510665	+	1.57166i	0.280369	+	0.959892i	$0.409543\pi$
$929$	−15.5648	+	47.9035i	−0.510665	+	1.57166i	−0.791034	+	0.611772i	$0.790457\pi$
$930$	78.7310	+	61.4421i	2.58169	+	2.01477i
$931$	−1.09581	−	3.37257i	−0.0359138	−	0.110531i
$932$	−48.6258			−1.59279
$933$	1.04717	+	3.22287i	0.0342830	+	0.105512i
$934$	44.7983	+	32.5479i	1.46584	+	1.06500i
$935$	−1.37303	+	3.77879i	−0.0449029	+	0.123580i
$936$	1.32206	−	0.960535i	0.0432130	−	0.0313961i
$937$	−43.1757	−	31.3690i	−1.41049	−	1.02478i	−0.993251	−	0.115982i	$-0.962999\pi$
$937$	−43.1757	−	31.3690i	−1.41049	−	1.02478i	−0.417237	−	0.908798i	$-0.637001\pi$
$938$	−50.0682	−	36.3767i	−1.63479	−	1.18774i
$939$	56.7388	−	41.2232i	1.85160	−	1.34527i
$940$	−13.2804	+	36.5496i	−0.433158	+	1.19212i
$941$	−40.2167	−	29.2192i	−1.31103	−	0.952518i	−0.999998	−	0.00211747i	$-0.999326\pi$
$941$	−40.2167	−	29.2192i	−1.31103	−	0.952518i	−0.311030	−	0.950400i	$-0.600674\pi$
$942$	−0.403647	−	1.24230i	−0.0131515	−	0.0404763i
$943$	17.1290			0.557797
$944$	−13.3463	−	41.0758i	−0.434387	−	1.33690i
$945$	−17.2124	−	13.4326i	−0.559918	−	0.436964i
$946$	−2.21337	+	6.81206i	−0.0719630	+	0.221479i
$947$	−1.17715	+	3.62289i	−0.0382522	+	0.117728i	−0.968359	−	0.249561i	$-0.919714\pi$
$947$	−1.17715	+	3.62289i	−0.0382522	+	0.117728i	0.930107	+	0.367289i	$0.119714\pi$
$948$	62.1824	−	45.1782i	2.01959	−	1.46732i
$949$	20.6006			0.668723
$950$	21.6188	+	1.48800i	0.701406	+	0.0482770i
$951$	24.3477			0.789529
$952$	−0.396109	+	0.287790i	−0.0128380	+	0.00932733i
$953$	−8.08550	+	24.8846i	−0.261915	+	0.806091i	0.730473	+	0.682941i	$0.239300\pi$
$953$	−8.08550	+	24.8846i	−0.261915	+	0.806091i	−0.992388	+	0.123150i	$0.960700\pi$
$954$	18.8738	−	58.0875i	0.611061	−	1.88065i
$955$	11.7874	−	32.4407i	0.381431	−	1.04976i
$956$	0.474617	+	1.46072i	0.0153502	+	0.0472431i
$957$	0.960333			0.0310432
$958$	−3.06003	−	9.41780i	−0.0988651	−	0.304275i
$959$	34.3201	+	24.9350i	1.10825	+	0.805194i
$960$	−36.2277	+	24.4647i	−1.16924	+	0.789595i
$961$	−29.9486	+	21.7589i	−0.966083	+	0.701900i
$962$	−5.74232	−	4.17204i	−0.185140	−	0.134512i
$963$	−47.5104	−	34.5183i	−1.53100	−	1.11234i
$964$	−15.6278	+	11.3543i	−0.503338	+	0.365696i
$965$	−3.94221	−	13.7198i	−0.126904	−	0.441657i
$966$	18.2894	+	13.2881i	0.588453	+	0.427536i
$967$	1.51873	+	4.67418i	0.0488391	+	0.150311i	0.972502	−	0.232895i	$-0.0748198\pi$
$967$	1.51873	+	4.67418i	0.0488391	+	0.150311i	−0.923663	+	0.383206i	$0.874820\pi$
$968$	1.63870			0.0526698
$969$	1.86298	+	5.73365i	0.0598474	+	0.184191i
$970$	−51.3191	+	34.6560i	−1.64776	+	1.11274i
$971$	−4.64789	+	14.3047i	−0.149158	+	0.459061i	−0.997522	−	0.0703520i	$-0.977588\pi$
$971$	−4.64789	+	14.3047i	−0.149158	+	0.459061i	0.848364	+	0.529413i	$0.177588\pi$
$972$	−10.6771	+	32.8606i	−0.342467	+	1.05400i
$973$	−32.1896	+	23.3871i	−1.03195	+	0.749757i
$974$	64.6523			2.07159
$975$	8.76037	−	21.7511i	0.280556	−	0.696592i
$976$	30.9441			0.990497
$977$	45.7284	−	33.2237i	1.46298	−	1.06292i	0.480409	−	0.877044i	$-0.340488\pi$
$977$	45.7284	−	33.2237i	1.46298	−	1.06292i	0.982573	−	0.185875i	$-0.0595119\pi$
$978$	−2.67605	+	8.23604i	−0.0855707	+	0.263359i
$979$	1.97917	−	6.09125i	0.0632544	−	0.194677i
$980$	6.82981	+	0.234767i	0.218170	+	0.00749934i
$981$	−2.99676	−	9.22307i	−0.0956790	−	0.294470i
$982$	−54.3253			−1.73359
$983$	7.79744	+	23.9980i	0.248700	+	0.765419i	0.995006	+	0.0998160i	$0.0318254\pi$
$983$	7.79744	+	23.9980i	0.248700	+	0.765419i	−0.746306	+	0.665603i	$0.768175\pi$
$984$	4.46085	+	3.24100i	0.142207	+	0.103319i
$985$	53.0870	+	1.82480i	1.69149	+	0.0581431i
$986$	−0.310632	+	0.225687i	−0.00989254	+	0.00718735i
$987$	47.3387	+	34.3936i	1.50681	+	1.09476i
$988$	−5.74825	−	4.17635i	−0.182876	−	0.132867i
$989$	2.93822	−	2.13474i	0.0934300	−	0.0678808i
$990$	28.3484	+	22.1233i	0.900971	+	0.703124i
$991$	−26.5226	−	19.2698i	−0.842518	−	0.612125i	0.0805547	−	0.996750i	$-0.474331\pi$
$991$	−26.5226	−	19.2698i	−0.842518	−	0.612125i	−0.923073	+	0.384625i	$0.874331\pi$
$992$	−20.0567	−	61.7281i	−0.636800	−	1.95987i
$993$	−64.6063			−2.05022
$994$	−13.2586	−	40.8056i	−0.420536	−	1.29428i
$995$	8.30686	+	28.9099i	0.263345	+	0.916504i
$996$	2.22560	−	6.84968i	0.0705207	−	0.217040i
$997$	−9.16158	+	28.1965i	−0.290150	+	0.892991i	0.694657	+	0.719341i	$0.255556\pi$
$997$	−9.16158	+	28.1965i	−0.290150	+	0.892991i	−0.984807	+	0.173650i	$0.944444\pi$
$998$	−69.8158	+	50.7241i	−2.20998	+	1.60564i
$999$	8.85799			0.280254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.k.b.86.4	✓	76
25.16	even	5	inner	425.2.k.b.341.4	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.k.b.86.4	✓	76	1.1	even	1	trivial
425.2.k.b.341.4	yes	76	25.16	even	5	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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59626 + 1.15975i) q^{2} +(0.848137 - 2.61030i) q^{3} +(0.584991 - 1.80042i) q^{4} +(-0.617518 - 2.14911i) q^{5} +(1.67345 + 5.15034i) q^{6} -2.32069 q^{7} +(-0.0651963 - 0.200653i) q^{8} +(-3.66726 - 2.66442i) q^{9} +(3.47815 + 2.71437i) q^{10} +(-1.45463 + 1.05685i) q^{11} +(-4.20347 - 3.05400i) q^{12} +(-1.38238 - 1.00436i) q^{13} +(3.70442 - 2.69142i) q^{14} +(-6.13355 - 0.210834i) q^{15} +(3.39983 + 2.47012i) q^{16} +(0.309017 + 0.951057i) q^{17} +8.94397 q^{18} +(0.678772 + 2.08904i) q^{19} +(-4.23054 - 0.145420i) q^{20} +(-1.96826 + 6.05768i) q^{21} +(1.09629 - 3.37402i) q^{22} +(-1.45530 + 1.05734i) q^{23} -0.579060 q^{24} +(-4.23734 + 2.65423i) q^{25} +3.37144 q^{26} +(-3.40392 + 2.47309i) q^{27} +(-1.35758 + 4.17821i) q^{28} +(0.0601347 - 0.185075i) q^{29} +(10.0353 - 6.77685i) q^{30} +(2.54857 + 7.84368i) q^{31} -7.86979 q^{32} +(1.52497 + 4.69338i) q^{33} +(-1.59626 - 1.15975i) q^{34} +(1.43307 + 4.98741i) q^{35} +(-6.94239 + 5.04394i) q^{36} +(-1.70322 - 1.23746i) q^{37} +(-3.50627 - 2.54745i) q^{38} +(-3.79412 + 2.75659i) q^{39} +(-0.390966 + 0.264021i) q^{40} +(-7.70360 - 5.59699i) q^{41} +(-3.88355 - 11.9523i) q^{42} -2.01897 q^{43} +(1.05183 + 3.23720i) q^{44} +(-3.46153 + 9.52668i) q^{45} +(1.09679 - 3.37558i) q^{46} +(2.83884 - 8.73706i) q^{47} +(9.33128 - 6.77957i) q^{48} -1.61441 q^{49} +(3.68566 - 9.15110i) q^{50} +2.74463 q^{51} +(-2.61694 + 1.90132i) q^{52} +(2.11022 - 6.49460i) q^{53} +(2.56537 - 7.89540i) q^{54} +(3.16955 + 2.47354i) q^{55} +(0.151300 + 0.465654i) q^{56} +6.02872 q^{57} +(0.118651 + 0.365170i) q^{58} +(-8.31453 - 6.04086i) q^{59} +(-3.96766 + 10.9196i) q^{60} +(5.95712 - 4.32810i) q^{61} +(-13.1649 - 9.56485i) q^{62} +(8.51057 + 6.18329i) q^{63} +(5.76257 - 4.18675i) q^{64} +(-1.30483 + 3.59110i) q^{65} +(-7.87740 - 5.72327i) q^{66} +(-4.17661 - 12.8543i) q^{67} +1.89307 q^{68} +(1.52568 + 4.69555i) q^{69} +(-8.07171 - 6.29921i) q^{70} +(2.89556 - 8.91163i) q^{71} +(-0.295534 + 0.909559i) q^{72} +(-9.75365 + 7.08644i) q^{73} +4.15394 q^{74} +(3.33448 + 13.3119i) q^{75} +4.15823 q^{76} +(3.37575 - 2.45263i) q^{77} +(2.85945 - 8.80047i) q^{78} +(-4.57132 + 14.0691i) q^{79} +(3.20911 - 8.83196i) q^{80} +(-0.633795 - 1.95062i) q^{81} +18.7881 q^{82} +(0.428347 + 1.31832i) q^{83} +(9.75495 + 7.08738i) q^{84} +(1.85310 - 1.25141i) q^{85} +(3.22281 - 2.34151i) q^{86} +(-0.432099 - 0.313939i) q^{87} +(0.306898 + 0.222974i) q^{88} +(-2.88179 + 2.09374i) q^{89} +(-5.52306 - 19.2216i) q^{90} +(3.20807 + 2.33080i) q^{91} +(1.05231 + 3.23869i) q^{92} +22.6359 q^{93} +(5.60128 + 17.2390i) q^{94} +(4.07043 - 2.74878i) q^{95} +(-6.67466 + 20.5425i) q^{96} +(-4.33727 + 13.3487i) q^{97} +(2.57701 - 1.87231i) q^{98} +8.15042 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 6 q^{2} - 7 q^{3} - 26 q^{4} + 13 q^{5} + 12 q^{6} + 22 q^{7} + 10 q^{8} - 24 q^{9} - 6 q^{10} - 16 q^{11} - 15 q^{12} - q^{13} - 19 q^{14} - 3 q^{15} + 30 q^{16} - 19 q^{17} + 6 q^{18} + 18 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 76 * q - 6 * q^2 - 7 * q^3 - 26 * q^4 + 13 * q^5 + 12 * q^6 + 22 * q^7 + 10 * q^8 - 24 * q^9 - 6 * q^10 - 16 * q^11 - 15 * q^12 - q^13 - 19 * q^14 - 3 * q^15 + 30 * q^16 - 19 * q^17 + 6 * q^18 + 18 * q^19 - 23 * q^20 - 22 * q^21 - 15 * q^22 - 8 * q^23 - 22 * q^24 + 35 * q^25 - 14 * q^26 - 10 * q^27 - 29 * q^28 - 25 * q^29 + 57 * q^30 + 22 * q^31 + 54 * q^32 - 22 * q^33 - 6 * q^34 - 19 * q^35 - 91 * q^36 - 49 * q^37 + 15 * q^38 + 25 * q^39 - 2 * q^40 + 16 * q^41 - 28 * q^42 + 104 * q^43 + 18 * q^44 + 10 * q^45 - 55 * q^46 - 26 * q^47 - 86 * q^48 + 2 * q^49 - 17 * q^50 + 18 * q^51 + 53 * q^52 - 41 * q^53 - 6 * q^54 + 67 * q^55 + 115 * q^56 + 84 * q^57 - 12 * q^58 - 7 * q^59 - 32 * q^60 - 21 * q^61 - 23 * q^62 - 21 * q^63 + 6 * q^64 - 72 * q^65 + 102 * q^66 - 15 * q^67 + 74 * q^68 + 48 * q^69 - 60 * q^70 - 8 * q^71 + 9 * q^72 - 25 * q^73 - 60 * q^74 + 68 * q^75 - 76 * q^76 - 36 * q^77 - 51 * q^78 + 2 * q^79 + 217 * q^80 + 20 * q^81 - 12 * q^82 - 41 * q^83 - 48 * q^84 - 7 * q^85 - 87 * q^86 - 54 * q^87 - 4 * q^88 + 77 * q^89 - 93 * q^90 + 79 * q^91 - 19 * q^92 + 72 * q^93 + 15 * q^94 + 57 * q^95 + 28 * q^96 + 13 * q^97 - 62 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more