LMFDB - Embedded newform 507.2.m.b.79.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(40,507)] 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("507.40"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [204] 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			79.3
Character	$\chi$	$=$	507.79
Dual form			507.2.m.b.430.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.80313 - 0.946355i) q^{2} +(-0.970942 - 0.239316i) q^{3} +(1.21956 + 1.76683i) q^{4} +(-0.526754 - 1.38893i) q^{5} +(1.52426 + 1.35037i) q^{6} +(-0.593546 - 4.88829i) q^{7} +(-0.0360490 - 0.296891i) q^{8} +(0.885456 + 0.464723i) q^{9} +(-0.364621 + 3.00293i) q^{10} +(2.35918 - 1.23819i) q^{11} +(-0.761288 - 2.00735i) q^{12} +(0.154800 - 3.60223i) q^{13} +(-3.55582 + 9.37593i) q^{14} +(0.179053 + 1.47464i) q^{15} +(1.30661 - 3.44526i) q^{16} +(-0.00730277 - 0.0601437i) q^{17} +(-1.15680 - 1.67591i) q^{18} +5.70075 q^{19} +(1.81161 - 2.62457i) q^{20} +(-0.593546 + 4.88829i) q^{21} -5.42568 q^{22} -4.11426 q^{23} +(-0.0360490 + 0.296891i) q^{24} +(2.09088 - 1.85236i) q^{25} +(-3.68811 + 6.34878i) q^{26} +(-0.748511 - 0.663123i) q^{27} +(7.91294 - 7.01025i) q^{28} +(-5.98063 - 3.13887i) q^{29} +(1.07267 - 2.82841i) q^{30} +(2.47487 + 2.19254i) q^{31} +(-6.06415 + 5.37237i) q^{32} +(-2.58695 + 0.637625i) q^{33} +(-0.0437495 + 0.115358i) q^{34} +(-6.47687 + 3.39932i) q^{35} +(0.258776 + 2.13121i) q^{36} +(-3.93666 - 3.48758i) q^{37} +(-10.2792 - 5.39494i) q^{38} +(-1.01237 + 3.46051i) q^{39} +(-0.393373 + 0.206458i) q^{40} +(4.12823 + 1.01752i) q^{41} +(5.69630 - 8.25252i) q^{42} +(-4.52647 + 4.01010i) q^{43} +(5.06484 + 2.65823i) q^{44} +(0.179053 - 1.47464i) q^{45} +(7.41855 + 3.89355i) q^{46} +(-0.466917 + 0.676446i) q^{47} +(-2.09315 + 3.03245i) q^{48} +(-16.7465 + 4.12764i) q^{49} +(-5.52312 + 1.36133i) q^{50} +(-0.00730277 + 0.0601437i) q^{51} +(6.55332 - 4.11962i) q^{52} +(0.375244 + 3.09041i) q^{53} +(0.722112 + 1.90405i) q^{54} +(-2.96248 - 2.62453i) q^{55} +(-1.42989 + 0.352436i) q^{56} +(-5.53510 - 1.36428i) q^{57} +(7.81335 + 11.3196i) q^{58} +(2.64411 + 6.97194i) q^{59} +(-2.38707 + 2.11476i) q^{60} +(-0.522904 + 4.30650i) q^{61} +(-2.38758 - 6.29554i) q^{62} +(1.74614 - 4.60420i) q^{63} +(8.86334 - 2.18462i) q^{64} +(-5.08480 + 1.68248i) q^{65} +(5.26802 + 1.29845i) q^{66} +(-3.54428 + 5.13478i) q^{67} +(0.0973578 - 0.0862515i) q^{68} +(3.99471 + 0.984607i) q^{69} +14.8956 q^{70} +(-0.237474 - 0.0585321i) q^{71} +(0.106052 - 0.279636i) q^{72} +(-6.39416 + 3.35592i) q^{73} +(3.79782 + 10.0140i) q^{74} +(-2.47342 + 1.29815i) q^{75} +(6.95240 + 10.0723i) q^{76} +(-7.45294 - 10.7974i) q^{77} +(5.10030 - 5.28168i) q^{78} +(2.58585 - 3.74625i) q^{79} -5.47350 q^{80} +(0.568065 + 0.822984i) q^{81} +(-6.48080 - 5.74149i) q^{82} +(7.19320 - 1.77297i) q^{83} +(-9.36066 + 4.91285i) q^{84} +(-0.0796889 + 0.0418240i) q^{85} +(11.9568 - 2.94708i) q^{86} +(5.05566 + 4.47892i) q^{87} +(-0.452654 - 0.655783i) q^{88} -11.6785 q^{89} +(-1.71839 + 2.48951i) q^{90} +(-17.7006 + 1.38138i) q^{91} +(-5.01758 - 7.26922i) q^{92} +(-1.87824 - 2.72110i) q^{93} +(1.48207 - 0.777851i) q^{94} +(-3.00289 - 7.91798i) q^{95} +(7.17363 - 3.76501i) q^{96} +(6.23992 - 16.4533i) q^{97} +(34.1023 + 8.40547i) q^{98} +2.66437 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{2}{13}\right)$

Coefficient data

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

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

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

$2$	−1.80313	−	0.946355i	−1.27500	−	0.669174i	−0.314983	−	0.949097i	$-0.601999\pi$
$2$	−1.80313	−	0.946355i	−1.27500	−	0.669174i	−0.960022	+	0.279923i	$0.909691\pi$
$3$	−0.970942	−	0.239316i	−0.560574	−	0.138169i
$3$	−0.970942	−	0.239316i	−0.560574	−	0.138169i
$4$	1.21956	+	1.76683i	0.609779	+	0.883417i
$5$	−0.526754	−	1.38893i	−0.235571	−	0.621151i	0.764143	−	0.645047i	$-0.223162\pi$
$5$	−0.526754	−	1.38893i	−0.235571	−	0.621151i	−0.999714	+	0.0238962i	$0.992393\pi$
$6$	1.52426	+	1.35037i	0.622275	+	0.551287i
$7$	−0.593546	−	4.88829i	−0.224339	−	1.84760i	−0.475576	−	0.879675i	$-0.657760\pi$
$7$	−0.593546	−	4.88829i	−0.224339	−	1.84760i	0.251237	−	0.967926i	$-0.419163\pi$
$8$	−0.0360490	−	0.296891i	−0.0127453	−	0.104967i
$9$	0.885456	+	0.464723i	0.295152	+	0.154908i
$10$	−0.364621	+	3.00293i	−0.115303	+	0.949608i
$11$	2.35918	−	1.23819i	0.711320	−	0.373330i	−0.0699265	−	0.997552i	$-0.522276\pi$
$11$	2.35918	−	1.23819i	0.711320	−	0.373330i	0.781247	+	0.624223i	$0.214584\pi$
$12$	−0.761288	−	2.00735i	−0.219765	−	0.579473i
$13$	0.154800	−	3.60223i	0.0429338	−	0.999078i
$13$	0.154800	−	3.60223i	0.0429338	−	0.999078i
$14$	−3.55582	+	9.37593i	−0.950333	+	2.50582i
$15$	0.179053	+	1.47464i	0.0462313	+	0.380749i
$16$	1.30661	−	3.44526i	0.326653	−	0.861314i
$17$	−0.00730277	−	0.0601437i	−0.00177118	−	0.0145870i	0.991796	−	0.127827i	$-0.0408002\pi$
$17$	−0.00730277	−	0.0601437i	−0.00177118	−	0.0145870i	−0.993568	+	0.113240i	$0.963877\pi$
$18$	−1.15680	−	1.67591i	−0.272660	−	0.395016i
$19$	5.70075			1.30784			0.653921	−	0.756563i	$-0.273123\pi$
$19$	5.70075			1.30784			0.653921	+	0.756563i	$0.273123\pi$
$20$	1.81161	−	2.62457i	0.405089	−	0.586872i
$21$	−0.593546	+	4.88829i	−0.129522	+	1.06671i
$22$	−5.42568			−1.15676
$23$	−4.11426			−0.857883			−0.428941	−	0.903332i	$-0.641113\pi$
$23$	−4.11426			−0.857883			−0.428941	+	0.903332i	$0.641113\pi$
$24$	−0.0360490	+	0.296891i	−0.00735848	+	0.0606025i
$25$	2.09088	−	1.85236i	0.418177	−	0.370472i
$26$	−3.68811	+	6.34878i	−0.723298	+	1.24510i
$27$	−0.748511	−	0.663123i	−0.144051	−	0.127618i
$28$	7.91294	−	7.01025i	1.49540	−	1.32481i
$29$	−5.98063	−	3.13887i	−1.11057	−	0.582874i	−0.193304	−	0.981139i	$-0.561920\pi$
$29$	−5.98063	−	3.13887i	−1.11057	−	0.582874i	−0.917271	+	0.398265i	$0.869613\pi$
$30$	1.07267	−	2.82841i	0.195842	−	0.516394i
$31$	2.47487	+	2.19254i	0.444499	+	0.393792i	0.855466	−	0.517858i	$-0.173271\pi$
$31$	2.47487	+	2.19254i	0.444499	+	0.393792i	−0.410967	+	0.911650i	$0.634809\pi$
$32$	−6.06415	+	5.37237i	−1.07200	+	0.949709i
$33$	−2.58695	+	0.637625i	−0.450330	+	0.110996i
$34$	−0.0437495	+	0.115358i	−0.00750297	+	0.0197837i
$35$	−6.47687	+	3.39932i	−1.09479	+	0.574590i
$36$	0.258776	+	2.13121i	0.0431293	+	0.355202i
$37$	−3.93666	−	3.48758i	−0.647183	−	0.573354i	0.274362	−	0.961627i	$-0.411533\pi$
$37$	−3.93666	−	3.48758i	−0.647183	−	0.573354i	−0.921545	+	0.388273i	$0.873072\pi$
$38$	−10.2792	−	5.39494i	−1.66751	−	0.875174i
$39$	−1.01237	+	3.46051i	−0.162109	+	0.554125i
$40$	−0.393373	+	0.206458i	−0.0621977	+	0.0326439i
$41$	4.12823	+	1.01752i	0.644722	+	0.158910i	0.548102	−	0.836412i	$-0.315351\pi$
$41$	4.12823	+	1.01752i	0.644722	+	0.158910i	0.0966200	+	0.995321i	$0.469197\pi$
$42$	5.69630	−	8.25252i	0.878958	−	1.27339i
$43$	−4.52647	+	4.01010i	−0.690280	+	0.611534i	−0.933560	−	0.358422i	$-0.883315\pi$
$43$	−4.52647	+	4.01010i	−0.690280	+	0.611534i	0.243280	+	0.969956i	$0.421777\pi$
$44$	5.06484	+	2.65823i	0.763554	+	0.400744i
$45$	0.179053	−	1.47464i	0.0266917	−	0.219826i
$46$	7.41855	+	3.89355i	1.09381	+	0.574073i
$47$	−0.466917	+	0.676446i	−0.0681069	+	0.0986699i	−0.855557	−	0.517708i	$-0.826785\pi$
$47$	−0.466917	+	0.676446i	−0.0681069	+	0.0986699i	0.787450	+	0.616378i	$0.211401\pi$
$48$	−2.09315	+	3.03245i	−0.302120	+	0.437697i
$49$	−16.7465	+	4.12764i	−2.39236	+	0.589663i
$50$	−5.52312	+	1.36133i	−0.781088	+	0.192521i
$51$	−0.00730277	+	0.0601437i	−0.00102259	+	0.00842180i
$52$	6.55332	−	4.11962i	0.908783	−	0.571288i
$53$	0.375244	+	3.09041i	0.0515437	+	0.424500i	0.995525	+	0.0945008i	$0.0301255\pi$
$53$	0.375244	+	3.09041i	0.0515437	+	0.424500i	−0.943981	+	0.329999i	$0.892951\pi$
$54$	0.722112	+	1.90405i	0.0982670	+	0.259109i
$55$	−2.96248	−	2.62453i	−0.399460	−	0.353891i
$56$	−1.42989	+	0.352436i	−0.191077	+	0.0470963i
$57$	−5.53510	−	1.36428i	−0.733142	−	0.180703i
$58$	7.81335	+	11.3196i	1.02594	+	1.48634i
$59$	2.64411	+	6.97194i	0.344233	+	0.907669i	0.989607	+	0.143801i	$0.0459327\pi$
$59$	2.64411	+	6.97194i	0.344233	+	0.907669i	−0.645373	+	0.763867i	$0.723298\pi$
$60$	−2.38707	+	2.11476i	−0.308169	+	0.273014i
$61$	−0.522904	+	4.30650i	−0.0669510	+	0.551391i	0.920182	+	0.391491i	$0.128040\pi$
$61$	−0.522904	+	4.30650i	−0.0669510	+	0.551391i	−0.987133	+	0.159901i	$0.948883\pi$
$62$	−2.38758	−	6.29554i	−0.303223	−	0.799534i
$63$	1.74614	−	4.60420i	0.219993	−	0.580075i
$64$	8.86334	−	2.18462i	1.10792	−	0.273077i
$65$	−5.08480	+	1.68248i	−0.630692	+	0.208686i
$66$	5.26802	+	1.29845i	0.648449	+	0.159828i
$67$	−3.54428	+	5.13478i	−0.433003	+	0.627314i	−0.977371	−	0.211533i	$-0.932154\pi$
$67$	−3.54428	+	5.13478i	−0.433003	+	0.627314i	0.544368	+	0.838847i	$0.316770\pi$
$68$	0.0973578	−	0.0862515i	0.0118064	−	0.0104595i
$69$	3.99471	+	0.984607i	0.480906	+	0.118533i
$70$	14.8956			1.78036
$71$	−0.237474	−	0.0585321i	−0.0281830	−	0.00694648i	0.225199	−	0.974313i	$-0.427697\pi$
$71$	−0.237474	−	0.0585321i	−0.0281830	−	0.00694648i	−0.253382	+	0.967366i	$0.581543\pi$
$72$	0.106052	−	0.279636i	0.0124984	−	0.0329555i
$73$	−6.39416	+	3.35592i	−0.748380	+	0.392780i	−0.795377	−	0.606115i	$-0.792727\pi$
$73$	−6.39416	+	3.35592i	−0.748380	+	0.392780i	0.0469969	+	0.998895i	$0.485035\pi$
$74$	3.79782	+	10.0140i	0.441488	+	1.16411i
$75$	−2.47342	+	1.29815i	−0.285606	+	0.149898i
$76$	6.95240	+	10.0723i	0.797495	+	1.15537i
$77$	−7.45294	−	10.7974i	−0.849341	−	1.23048i
$78$	5.10030	−	5.28168i	0.577496	−	0.598032i
$79$	2.58585	−	3.74625i	0.290931	−	0.421486i	−0.650078	−	0.759867i	$-0.725264\pi$
$79$	2.58585	−	3.74625i	0.290931	−	0.421486i	0.941009	+	0.338381i	$0.109879\pi$
$80$	−5.47350			−0.611956
$81$	0.568065	+	0.822984i	0.0631183	+	0.0914427i
$82$	−6.48080	−	5.74149i	−0.715685	−	0.634042i
$83$	7.19320	−	1.77297i	0.789557	−	0.194608i	0.176137	−	0.984366i	$-0.443640\pi$
$83$	7.19320	−	1.77297i	0.789557	−	0.194608i	0.613419	+	0.789757i	$0.289794\pi$
$84$	−9.36066	+	4.91285i	−1.02133	+	0.536036i
$85$	−0.0796889	+	0.0418240i	−0.00864348	+	0.00453645i
$86$	11.9568	−	2.94708i	1.28933	−	0.317792i
$87$	5.05566	+	4.47892i	0.542023	+	0.480191i
$88$	−0.452654	−	0.655783i	−0.0482531	−	0.0699067i
$89$	−11.6785			−1.23792			−0.618959	−	0.785424i	$-0.712445\pi$
$89$	−11.6785			−1.23792			−0.618959	+	0.785424i	$0.712445\pi$
$90$	−1.71839	+	2.48951i	−0.181134	+	0.262417i
$91$	−17.7006	+	1.38138i	−1.85553	+	0.144808i
$92$	−5.01758	−	7.26922i	−0.523119	−	0.757869i
$93$	−1.87824	−	2.72110i	−0.194765	−	0.282165i
$94$	1.48207	−	0.777851i	0.152864	−	0.0802292i
$95$	−3.00289	−	7.91798i	−0.308090	−	0.812367i
$96$	7.17363	−	3.76501i	0.732155	−	0.384265i
$97$	6.23992	−	16.4533i	0.633568	−	1.67058i	−0.103389	−	0.994641i	$-0.532969\pi$
$97$	6.23992	−	16.4533i	0.633568	−	1.67058i	0.736957	−	0.675940i	$-0.236262\pi$
$98$	34.1023	+	8.40547i	3.44485	+	0.849080i
$99$	2.66437			0.267779
$100$	5.82277	+	1.43518i	0.582277	+	0.143518i
$101$	12.0089	−	10.6390i	1.19493	−	1.05862i	0.198013	−	0.980199i	$-0.436551\pi$
$101$	12.0089	−	10.6390i	1.19493	−	1.05862i	0.996920	−	0.0784198i	$-0.0249874\pi$
$102$	0.0700851	−	0.101536i	0.00693946	−	0.0100535i
$103$	8.31438	+	2.04931i	0.819240	+	0.201925i	0.626596	−	0.779344i	$-0.284448\pi$
$103$	8.31438	+	2.04931i	0.819240	+	0.201925i	0.192644	+	0.981269i	$0.438294\pi$
$104$	−1.07505	+	0.0838981i	−0.105417	+	0.00822689i
$105$	7.10217	−	1.75053i	0.693101	−	0.170834i
$106$	2.24801	−	5.92752i	0.218346	−	0.575732i
$107$	−1.02154	−	2.69357i	−0.0987556	−	0.260397i	0.876529	−	0.481349i	$-0.159853\pi$
$107$	−1.02154	−	2.69357i	−0.0987556	−	0.260397i	−0.975285	+	0.220952i	$0.929084\pi$
$108$	0.258776	−	2.13121i	0.0249007	−	0.205076i
$109$	11.0610	−	9.79921i	1.05945	−	0.938594i	0.0612271	−	0.998124i	$-0.480499\pi$
$109$	11.0610	−	9.79921i	1.05945	−	0.938594i	0.998227	+	0.0595298i	$0.0189601\pi$
$110$	2.85800	+	7.53592i	0.272499	+	0.718522i
$111$	2.98763	+	4.32834i	0.283574	+	0.410828i
$112$	−17.6170	−	4.34219i	−1.66465	−	0.410298i
$113$	13.1547	−	3.24234i	1.23749	−	0.305014i	0.434318	−	0.900760i	$-0.356990\pi$
$113$	13.1547	−	3.24234i	1.23749	−	0.305014i	0.803173	+	0.595746i	$0.203143\pi$
$114$	8.68941	+	7.69814i	0.813838	+	0.720997i
$115$	2.16720	+	5.71444i	0.202093	+	0.532875i
$116$	−1.74785	−	14.3948i	−0.162284	−	1.33652i
$117$	1.81111	−	3.11767i	0.167437	−	0.288229i
$118$	1.83026	−	15.0736i	0.168489	−	1.38763i
$119$	−0.289665	+	0.0713961i	−0.0265536	+	0.00654487i
$120$	0.431351	−	0.106318i	0.0393767	−	0.00970549i
$121$	−2.21610	+	3.21057i	−0.201464	+	0.291870i
$122$	5.01834	−	7.27033i	0.454340	−	0.658224i
$123$	−3.76477	−	1.97590i	−0.339458	−	0.178161i
$124$	−0.855613	+	7.04661i	−0.0768363	+	0.632804i
$125$	−10.2508	−	5.38002i	−0.916856	−	0.481203i
$126$	−7.50573	+	6.64950i	−0.668664	+	0.592384i
$127$	−1.90248	+	2.75622i	−0.168818	+	0.244575i	−0.898257	−	0.439471i	$-0.855166\pi$
$127$	−1.90248	+	2.75622i	−0.168818	+	0.244575i	0.729439	+	0.684046i	$0.239781\pi$
$128$	−2.31678	−	0.571035i	−0.204777	−	0.0504729i
$129$	5.35462	−	2.81032i	0.471448	−	0.247435i
$130$	10.7608	+	1.77830i	0.943782	+	0.155967i
$131$	−16.5512	−	8.68675i	−1.44609	−	0.758965i	−0.454789	−	0.890599i	$-0.650285\pi$
$131$	−16.5512	−	8.68675i	−1.44609	−	0.758965i	−0.991298	+	0.131634i	$0.957978\pi$
$132$	−4.28151	−	3.79309i	−0.372658	−	0.330146i
$133$	−3.38366	−	27.8669i	−0.293400	−	2.41637i
$134$	11.2501	−	5.90452i	0.971863	−	0.510073i
$135$	−0.526754	+	1.38893i	−0.0453357	+	0.119540i
$136$	−0.0175928	+	0.00433624i	−0.00150857	+	0.000371830i
$137$	−4.50400	+	3.99020i	−0.384803	+	0.340906i	−0.833243	−	0.552907i	$-0.813518\pi$
$137$	−4.50400	+	3.99020i	−0.384803	+	0.340906i	0.448440	+	0.893813i	$0.351980\pi$
$138$	−6.27119	−	5.55579i	−0.533839	−	0.472940i
$139$	−4.24884	+	11.2033i	−0.360382	+	0.950249i	0.625112	+	0.780535i	$0.285053\pi$
$139$	−4.24884	+	11.2033i	−0.360382	+	0.950249i	−0.985493	+	0.169713i	$0.945716\pi$
$140$	−13.9049	−	7.29788i	−1.17518	−	0.616783i
$141$	0.615234	−	0.545050i	0.0518120	−	0.0459014i
$142$	0.372804	+	0.330276i	0.0312851	+	0.0277161i
$143$	−4.09505	−	8.68998i	−0.342446	−	0.726693i
$144$	2.75804	−	2.44341i	0.229837	−	0.203618i
$145$	−1.20938	+	9.96011i	−0.100433	+	0.827143i
$146$	14.7054			1.21703
$147$	17.2477			1.42256
$148$	1.36099	−	11.2087i	0.111872	−	0.921351i
$149$	2.31963	−	3.36057i	0.190032	−	0.275308i	−0.716374	−	0.697716i	$-0.754200\pi$
$149$	2.31963	−	3.36057i	0.190032	−	0.275308i	0.906406	+	0.422408i	$0.138815\pi$
$150$	5.68842			0.464457
$151$	13.5329	+	19.6057i	1.10129	+	1.59549i	0.752889	+	0.658147i	$0.228660\pi$
$151$	13.5329	+	19.6057i	1.10129	+	1.59549i	0.348400	+	0.937346i	$0.386725\pi$
$152$	−0.205507	−	1.69250i	−0.0166688	−	0.137280i
$153$	0.0214839	−	0.0566484i	0.00173687	−	0.00457975i
$154$	3.22039	+	26.5223i	0.259507	+	2.13723i
$155$	1.74165	−	4.59236i	0.139893	−	0.368867i
$156$	−7.34879	+	2.43160i	−0.588374	+	0.194683i
$157$	2.06450	+	5.44365i	0.164765	+	0.434451i	0.991816	−	0.127677i	$-0.0407522\pi$
$157$	2.06450	+	5.44365i	0.164765	+	0.434451i	−0.827050	+	0.562128i	$0.809983\pi$
$158$	−8.20790	+	4.30784i	−0.652986	+	0.342713i
$159$	0.375244	−	3.09041i	0.0297587	−	0.245085i
$160$	10.6562	+	5.59279i	0.842445	+	0.442149i
$161$	2.44200	+	20.1117i	0.192457	+	1.58502i
$162$	−0.245459	−	2.02154i	−0.0192851	−	0.158827i
$163$	15.4539	+	13.6909i	1.21044	+	1.07236i	0.995405	+	0.0957510i	$0.0305253\pi$
$163$	15.4539	+	13.6909i	1.21044	+	1.07236i	0.215036	+	0.976606i	$0.431013\pi$
$164$	3.23683	+	8.53482i	0.252754	+	0.666458i
$165$	2.24830	+	3.25723i	0.175030	+	0.253575i
$166$	−14.6481	−	3.61044i	−1.13692	−	0.280225i
$167$	−9.91409	−	5.20332i	−0.767176	−	0.402645i	0.0352641	−	0.999378i	$-0.488773\pi$
$167$	−9.91409	−	5.20332i	−0.767176	−	0.402645i	−0.802440	+	0.596733i	$0.796465\pi$
$168$	1.47268			0.113620
$169$	−12.9521	−	1.11525i	−0.996313	−	0.0857884i
$170$	0.183270			0.0140562
$171$	5.04777	+	2.64927i	0.386012	+	0.202595i
$172$	−12.6055	−	3.10697i	−0.961158	−	0.236904i
$173$	10.5746	+	15.3200i	0.803973	+	1.16476i	0.983483	+	0.181000i	$0.0579333\pi$
$173$	10.5746	+	15.3200i	0.803973	+	1.16476i	−0.179510	+	0.983756i	$0.557451\pi$
$174$	−4.87735	−	12.8605i	−0.369751	−	0.974954i
$175$	−10.2959	−	9.12138i	−0.778298	−	0.689512i
$176$	−1.18336	−	9.74583i	−0.0891990	−	0.734620i
$177$	−0.898780	−	7.40212i	−0.0675565	−	0.556378i
$178$	21.0578	+	11.0520i	1.57835	+	0.828382i
$179$	1.16315	−	9.57938i	0.0869377	−	0.715997i	−0.882441	−	0.470424i	$-0.844101\pi$
$179$	1.16315	−	9.57938i	0.0869377	−	0.715997i	0.969378	−	0.245573i	$-0.0789759\pi$
$180$	2.82380	−	1.48205i	0.210474	−	0.110465i
$181$	−3.13800	−	8.27424i	−0.233246	−	0.615019i	0.766379	−	0.642388i	$-0.222056\pi$
$181$	−3.13800	−	8.27424i	−0.233246	−	0.615019i	−0.999625	+	0.0273690i	$0.991287\pi$
$182$	33.2238	+	14.2603i	2.46271	+	1.05704i
$183$	1.53832	−	4.05622i	0.113716	−	0.299845i
$184$	0.148315	+	1.22149i	0.0109339	+	0.0900491i
$185$	−2.77037	+	7.30486i	−0.203681	+	0.537064i
$186$	0.811583	+	6.68399i	0.0595081	+	0.490094i
$187$	−0.0916981	−	0.132848i	−0.00670563	−	0.00971478i
$188$	−1.76460			−0.128697
$189$	−2.79726	+	4.05253i	−0.203471	+	0.294778i
$190$	−2.07862	+	17.1189i	−0.150799	+	1.24194i
$191$	−0.146937			−0.0106320			−0.00531599	−	0.999986i	$-0.501692\pi$
$191$	−0.146937			−0.0106320			−0.00531599	+	0.999986i	$0.501692\pi$
$192$	−9.12860			−0.658800
$193$	1.57451	−	12.9673i	0.113336	−	0.933404i	−0.819494	−	0.573087i	$-0.805746\pi$
$193$	1.57451	−	12.9673i	0.113336	−	0.933404i	0.932830	−	0.360317i	$-0.117331\pi$
$194$	−26.8221	+	23.7623i	−1.92571	+	1.70603i
$195$	5.33969	−	0.416716i	0.382383	−	0.0298417i
$196$	−27.7162	−	24.5544i	−1.97973	−	1.75388i
$197$	19.9338	−	17.6598i	1.42023	−	1.25821i	0.500451	−	0.865765i	$-0.333168\pi$
$197$	19.9338	−	17.6598i	1.42023	−	1.25821i	0.919775	−	0.392445i	$-0.128371\pi$
$198$	−4.80420	−	2.52144i	−0.341420	−	0.179191i
$199$	−6.70788	+	17.6872i	−0.475509	+	1.25381i	0.455962	+	0.889999i	$0.349295\pi$
$199$	−6.70788	+	17.6872i	−0.475509	+	1.25381i	−0.931471	+	0.363815i	$0.881474\pi$
$200$	−0.625323	−	0.553987i	−0.0442170	−	0.0391728i
$201$	4.67013	−	4.13737i	0.329405	−	0.291828i
$202$	−31.7219	+	7.81875i	−2.23195	+	0.550126i
$203$	−11.7940	+	31.0981i	−0.827773	+	2.18266i
$204$	−0.115170	+	0.0604459i	−0.00806352	+	0.00423206i
$205$	−0.761295	−	6.26983i	−0.0531711	−	0.437904i
$206$	−13.0525	−	11.5635i	−0.909413	−	0.805669i
$207$	−3.64300	−	1.91199i	−0.253206	−	0.132893i
$208$	−12.2083	−	5.24005i	−0.846496	−	0.363332i
$209$	13.4491	−	7.05864i	0.930295	−	0.488256i
$210$	−14.4628	−	3.56475i	−0.998025	−	0.245991i
$211$	7.28238	−	10.5503i	0.501340	−	0.726316i	−0.487855	−	0.872925i	$-0.662220\pi$
$211$	7.28238	−	10.5503i	0.501340	−	0.726316i	0.989195	+	0.146609i	$0.0468359\pi$
$212$	−5.00261	+	4.43192i	−0.343581	+	0.304386i
$213$	0.216566	+	0.113663i	0.0148389	+	0.00778803i
$214$	−0.707111	+	5.82359i	−0.0483371	+	0.398092i
$215$	7.95410	+	4.17463i	0.542465	+	0.284708i
$216$	−0.169892	+	0.246131i	−0.0115597	+	0.0167471i
$217$	9.24883	−	13.3992i	0.627851	−	0.909600i
$218$	−29.2180	+	7.20159i	−1.97889	+	0.487753i
$219$	7.01148	−	1.72818i	0.473792	−	0.116779i
$220$	1.02419	−	8.43497i	0.0690509	−	0.568686i
$221$	−0.217782	+	0.0169960i	−0.0146496	+	0.00114327i
$222$	−1.29095	−	10.6319i	−0.0866428	−	0.713567i
$223$	−6.71211	−	17.6984i	−0.449476	−	1.18517i	−0.947993	−	0.318291i	$-0.896891\pi$
$223$	−6.71211	−	17.6984i	−0.449476	−	1.18517i	0.498517	−	0.866880i	$-0.333878\pi$
$224$	29.8610	+	26.4546i	1.99517	+	1.76757i
$225$	2.71222	−	0.668502i	0.180815	−	0.0445668i
$226$	−26.7880	−	6.60266i	−1.78191	−	0.439202i
$227$	10.7023	+	15.5049i	0.710336	+	1.02910i	0.997462	+	0.0712061i	$0.0226848\pi$
$227$	10.7023	+	15.5049i	0.710336	+	1.02910i	−0.287126	+	0.957893i	$0.592700\pi$
$228$	−4.33992	−	11.4434i	−0.287418	−	0.757859i
$229$	−15.1205	+	13.3956i	−0.999191	+	0.885206i	−0.993391	−	0.114777i	$-0.963385\pi$
$229$	−15.1205	+	13.3956i	−0.999191	+	0.885206i	−0.00580007	+	0.999983i	$0.501846\pi$
$230$	1.50015	−	12.3548i	0.0989168	−	0.814653i
$231$	4.65237	+	12.2673i	0.306103	+	0.807128i
$232$	−0.716306	+	1.88874i	−0.0470278	+	0.124002i
$233$	−19.2805	+	4.75222i	−1.26311	+	0.311328i	−0.813325	−	0.581810i	$-0.802345\pi$
$233$	−19.2805	+	4.75222i	−1.26311	+	0.311328i	−0.449783	+	0.893138i	$0.648499\pi$
$234$	−6.21609	+	3.90762i	−0.406358	+	0.255449i
$235$	1.18549	+	0.292197i	0.0773329	+	0.0190608i
$236$	−9.09362	+	13.1744i	−0.591944	+	0.857579i
$237$	−3.40724	+	3.01855i	−0.221324	+	0.196076i
$238$	0.589870	+	0.145390i	0.0382356	+	0.00942423i
$239$	10.9134			0.705927			0.352964	−	0.935637i	$-0.385174\pi$
$239$	10.9134			0.705927			0.352964	+	0.935637i	$0.385174\pi$
$240$	5.31445	+	1.30989i	0.343046	+	0.0845534i
$241$	2.58216	−	6.80859i	0.166331	−	0.438580i	−0.825772	−	0.564004i	$-0.809260\pi$
$241$	2.58216	−	6.80859i	0.166331	−	0.438580i	0.992103	+	0.125425i	$0.0400293\pi$
$242$	7.03426	−	3.69186i	0.452179	−	0.237322i
$243$	−0.354605	−	0.935016i	−0.0227479	−	0.0599813i
$244$	−8.24659	+	4.32814i	−0.527934	+	0.277081i
$245$	14.5543	+	21.0855i	0.929840	+	1.34711i
$246$	4.91845	+	7.12561i	0.313589	+	0.454312i
$247$	0.882477	−	20.5354i	0.0561506	−	1.30664i
$248$	0.561728	−	0.813803i	0.0356698	−	0.0516766i
$249$	−7.40848			−0.469493
$250$	13.3920	+	19.4017i	0.846987	+	1.22707i
$251$	−10.9727	−	9.72100i	−0.692593	−	0.613584i	0.241590	−	0.970378i	$-0.422331\pi$
$251$	−10.9727	−	9.72100i	−0.692593	−	0.613584i	−0.934183	+	0.356795i	$0.883870\pi$
$252$	10.2644	−	2.52994i	0.646595	−	0.159371i
$253$	−9.70629	+	5.09426i	−0.610229	+	0.320273i
$254$	6.03878	−	3.16940i	0.378907	−	0.198866i
$255$	0.0873825	−	0.0215378i	0.00547210	−	0.00134875i
$256$	−10.0287	−	8.88462i	−0.626791	−	0.555289i
$257$	6.38286	+	9.24717i	0.398152	+	0.576823i	0.969869	−	0.243628i	$-0.0783377\pi$
$257$	6.38286	+	9.24717i	0.398152	+	0.576823i	−0.571717	+	0.820451i	$0.693722\pi$
$258$	−12.3146			−0.766675
$259$	−14.7117	+	21.3136i	−0.914140	+	1.32436i
$260$	−9.17387	−	6.93212i	−0.568939	−	0.429912i
$261$	−3.83687	−	5.55867i	−0.237497	−	0.344073i
$262$	21.6232	+	31.3267i	1.33589	+	1.93537i
$263$	−21.6433	+	11.3593i	−1.33458	+	0.700443i	−0.972762	−	0.231804i	$-0.925537\pi$
$263$	−21.6433	+	11.3593i	−1.33458	+	0.700443i	−0.361821	+	0.932248i	$0.617845\pi$
$264$	0.282562	+	0.745054i	0.0173905	+	0.0458549i
$265$	4.09472	−	2.14907i	0.251536	−	0.132016i
$266$	−20.2708	+	53.4498i	−1.24289	+	3.27722i
$267$	11.3391	+	2.79484i	0.693944	+	0.171042i
$268$	−13.3948			−0.818216
$269$	−22.2511	−	5.48440i	−1.35667	−	0.334390i	−0.507111	−	0.861881i	$-0.669287\pi$
$269$	−22.2511	−	5.48440i	−1.35667	−	0.334390i	−0.849561	+	0.527491i	$0.823133\pi$
$270$	2.26423	−	2.00593i	0.137797	−	0.122077i
$271$	−10.0473	+	14.5560i	−0.610328	+	0.884212i	−0.999314	−	0.0370313i	$-0.988210\pi$
$271$	−10.0473	+	14.5560i	−0.610328	+	0.884212i	0.388987	+	0.921243i	$0.372825\pi$
$272$	−0.216752	−	0.0534247i	−0.0131425	−	0.00323935i
$273$	17.5169	+	2.89479i	1.06017	+	0.175201i
$274$	11.8974	−	2.93246i	0.718751	−	0.177156i
$275$	2.63919	−	6.95897i	0.159149	−	0.419642i
$276$	3.13214	+	8.25877i	0.188533	+	0.497120i
$277$	0.102255	−	0.842150i	0.00614394	−	0.0505999i	−0.989314	−	0.145797i	$-0.953425\pi$
$277$	0.102255	−	0.842150i	0.00614394	−	0.0505999i	0.995458	+	0.0951976i	$0.0303483\pi$
$278$	18.2635	−	16.1800i	1.09537	−	0.970413i
$279$	1.17246	+	3.09153i	0.0701934	+	0.185085i
$280$	1.24271	+	1.80038i	0.0742662	+	0.107593i
$281$	21.0491	+	5.18815i	1.25569	+	0.309499i	0.810393	−	0.585886i	$-0.199253\pi$
$281$	21.0491	+	5.18815i	1.25569	+	0.309499i	0.445293	+	0.895385i	$0.353100\pi$
$282$	−1.62516	+	0.400565i	−0.0967767	+	0.0238533i
$283$	3.69511	+	3.27358i	0.219652	+	0.194594i	0.765772	−	0.643113i	$-0.222357\pi$
$283$	3.69511	+	3.27358i	0.219652	+	0.194594i	−0.546120	+	0.837707i	$0.683896\pi$
$284$	−0.186197	−	0.490961i	−0.0110488	−	0.0291332i
$285$	1.02074	+	8.40653i	0.0604633	+	0.497960i
$286$	−0.839896	+	19.5445i	−0.0496641	+	1.15569i
$287$	2.52363	−	20.7839i	0.148965	−	1.22684i
$288$	−7.86620	+	1.93884i	−0.463520	+	0.114247i
$289$	16.5024	−	4.06749i	0.970732	−	0.239264i
$290$	11.6065	−	16.8149i	0.681555	−	0.987403i
$291$	−9.99613	+	14.4819i	−0.585984	+	0.848944i
$292$	−13.7274	−	7.20469i	−0.803335	−	0.421623i
$293$	4.05822	−	33.4225i	0.237084	−	1.95256i	−0.0613108	−	0.998119i	$-0.519528\pi$
$293$	4.05822	−	33.4225i	0.237084	−	1.95256i	0.298395	−	0.954443i	$-0.403549\pi$
$294$	−31.0998	−	16.3224i	−1.81378	−	0.951944i
$295$	8.29078	−	7.34499i	0.482708	−	0.427642i
$296$	−0.893515	+	1.29448i	−0.0519345	+	0.0752401i
$297$	−2.58695	−	0.637625i	−0.150110	−	0.0369988i
$298$	−7.36289	+	3.86434i	−0.426521	+	0.223855i
$299$	−0.636888	+	14.8205i	−0.0368322	+	0.857092i
$300$	−5.31010	−	2.78696i	−0.306579	−	0.160905i
$301$	22.2892	+	19.7465i	1.28473	+	1.13817i
$302$	−5.84751	−	48.1586i	−0.336487	−	2.77122i
$303$	−14.2061	+	7.45591i	−0.816117	+	0.428331i
$304$	7.44868	−	19.6406i	0.427211	−	1.12646i
$305$	6.25689	−	1.54219i	0.358269	−	0.0883053i
$306$	−0.0923477	+	0.0818129i	−0.00527917	+	0.00467693i
$307$	15.9461	+	14.1270i	0.910094	+	0.806273i	0.981557	−	0.191170i	$-0.0612282\pi$
$307$	15.9461	+	14.1270i	0.910094	+	0.806273i	−0.0714626	+	0.997443i	$0.522767\pi$
$308$	9.98800	−	26.3362i	0.569119	−	1.50064i
$309$	−7.58235	−	3.97952i	−0.431345	−	0.226387i
$310$	−7.48642	+	6.63239i	−0.425200	+	0.376695i
$311$	−24.3978	−	21.6146i	−1.38347	−	1.22565i	−0.945069	−	0.326872i	$-0.894005\pi$
$311$	−24.3978	−	21.6146i	−1.38347	−	1.22565i	−0.438404	−	0.898778i	$-0.644456\pi$
$312$	1.06389	+	0.175815i	0.0602307	+	0.00995359i
$313$	−14.9654	+	13.2582i	−0.845892	+	0.749395i	−0.970060	−	0.242866i	$-0.921912\pi$
$313$	−14.9654	+	13.2582i	−0.845892	+	0.749395i	0.124167	+	0.992261i	$0.460374\pi$
$314$	1.42906	−	11.7694i	0.0806465	−	0.664183i
$315$	−7.31472			−0.412138
$316$	9.77259			0.549751
$317$	1.98150	−	16.3191i	0.111292	−	0.916573i	−0.824947	−	0.565210i	$-0.808795\pi$
$317$	1.98150	−	16.3191i	0.111292	−	0.916573i	0.936239	−	0.351363i	$-0.114282\pi$
$318$	−3.60124	+	5.21729i	−0.201947	+	0.292571i
$319$	−17.9959			−1.00758
$320$	−7.70309	−	11.1599i	−0.430616	−	0.623855i
$321$	0.347239	+	2.85977i	0.0193810	+	0.159617i
$322$	14.6296	−	38.5750i	0.815274	−	2.14970i
$323$	−0.0416313	−	0.342864i	−0.00231643	−	0.0190775i
$324$	−0.761288	+	2.00735i	−0.0422938	+	0.111520i
$325$	−6.34895	−	7.81858i	−0.352177	−	0.433697i
$326$	−14.9088	−	39.3114i	−0.825725	−	2.17726i
$327$	−13.0847	+	6.86739i	−0.723586	+	0.379767i
$328$	0.153273	−	1.26231i	0.00846307	−	0.0696996i
$329$	3.58380	+	1.88093i	0.197581	+	0.103699i
$330$	−0.971485	−	8.00090i	−0.0534785	−	0.440435i
$331$	−1.78115	−	14.6691i	−0.0979008	−	0.806286i	−0.956115	−	0.292993i	$-0.905349\pi$
$331$	−1.78115	−	14.6691i	−0.0979008	−	0.806286i	0.858214	−	0.513293i	$-0.171574\pi$
$332$	11.9051	+	10.5470i	0.653375	+	0.578840i
$333$	−1.86498	−	4.91755i	−0.102200	−	0.269480i
$334$	12.9522	+	18.7645i	0.708713	+	1.02675i
$335$	8.99884	+	2.21802i	0.491659	+	0.121183i
$336$	16.0659	+	8.43203i	0.876466	+	0.460005i
$337$	−2.27902			−0.124146			−0.0620731	−	0.998072i	$-0.519771\pi$
$337$	−2.27902			−0.124146			−0.0620731	+	0.998072i	$0.519771\pi$
$338$	22.2988	+	14.2682i	1.21290	+	0.776088i
$339$	−13.5484			−0.735848
$340$	−0.171081	−	0.0897904i	−0.00927819	−	0.00486957i
$341$	8.55345	+	2.10824i	0.463195	+	0.114167i
$342$	−6.59462	−	9.55396i	−0.356596	−	0.516619i
$343$	17.8939	+	47.1824i	0.966181	+	2.54761i
$344$	1.35374	+	1.19930i	0.0729885	+	0.0646622i
$345$	−0.736672	−	6.06704i	−0.0396611	−	0.326638i
$346$	−4.56926	−	37.6312i	−0.245645	−	2.02307i
$347$	17.6769	+	9.27753i	0.948944	+	0.498044i	0.866844	−	0.498580i	$-0.166145\pi$
$347$	17.6769	+	9.27753i	0.948944	+	0.498044i	0.0821000	+	0.996624i	$0.473837\pi$
$348$	−1.74785	+	14.3948i	−0.0936944	+	0.771643i
$349$	−14.9390	+	7.84058i	−0.799665	+	0.419696i	−0.814478	−	0.580194i	$-0.802977\pi$
$349$	−14.9390	+	7.84058i	−0.799665	+	0.419696i	0.0148137	+	0.999890i	$0.495284\pi$
$350$	9.93279	+	26.1906i	0.530930	+	1.39995i
$351$	−2.50459	+	2.59365i	−0.133685	+	0.138439i
$352$	−7.65439	+	20.1830i	−0.407981	+	1.07576i
$353$	−1.45652	−	11.9955i	−0.0775225	−	0.638455i	−0.978742	−	0.205093i	$-0.934250\pi$
$353$	−1.45652	−	11.9955i	−0.0775225	−	0.638455i	0.901220	−	0.433362i	$-0.142673\pi$
$354$	−5.38442	+	14.1975i	−0.286179	+	0.754591i
$355$	0.0437930	+	0.360668i	0.00232429	+	0.0191423i
$356$	−14.2426	−	20.6339i	−0.754856	−	1.09360i
$357$	0.298334			0.0157895
$358$	−11.1628	+	16.1721i	−0.589972	+	0.854723i
$359$	3.24210	−	26.7011i	0.171111	−	1.40923i	−0.613722	−	0.789522i	$-0.710328\pi$
$359$	3.24210	−	26.7011i	0.171111	−	1.40923i	0.784833	−	0.619707i	$-0.212749\pi$
$360$	−0.444260			−0.0234146
$361$	13.4986			0.710452
$362$	−2.17214	+	17.8892i	−0.114165	+	0.940235i
$363$	2.92004	−	2.58693i	0.153263	−	0.135779i
$364$	−24.0276	−	29.5894i	−1.25939	−	1.55090i
$365$	8.02930	+	7.11334i	0.420273	+	0.372329i
$366$	−6.61242	+	5.85810i	−0.345637	+	0.306208i
$367$	−3.56964	−	1.87349i	−0.186334	−	0.0977956i	0.368977	−	0.929439i	$-0.379708\pi$
$367$	−3.56964	−	1.87349i	−0.186334	−	0.0977956i	−0.555310	+	0.831643i	$0.687401\pi$
$368$	−5.37575	+	14.1747i	−0.280230	+	0.738907i
$369$	3.18250	+	2.81945i	0.165675	+	0.146775i
$370$	11.9083	−	10.5498i	0.619084	−	0.548460i
$371$	14.8841	−	3.66860i	0.772743	−	0.190464i
$372$	2.51711	−	6.63709i	0.130506	−	0.344117i
$373$	20.4598	−	10.7381i	1.05937	−	0.555998i	0.157280	−	0.987554i	$-0.449728\pi$
$373$	20.4598	−	10.7381i	1.05937	−	0.555998i	0.902086	+	0.431556i	$0.142035\pi$
$374$	0.0396225	+	0.326321i	0.00204883	+	0.0168736i
$375$	8.66537	+	7.67685i	0.447478	+	0.396431i
$376$	0.217662	+	0.114238i	0.0112251	+	0.00589138i
$377$	−12.2327	+	21.0577i	−0.630018	+	1.08453i
$378$	8.87896	−	4.66004i	0.456684	−	0.239686i
$379$	23.2153	+	5.72205i	1.19249	+	0.293922i	0.785121	−	0.619343i	$-0.212601\pi$
$379$	23.2153	+	5.72205i	1.19249	+	0.293922i	0.407367	+	0.913265i	$0.366447\pi$
$380$	10.3275	−	14.9620i	0.529792	−	0.767536i
$381$	2.50681	−	2.22084i	0.128428	−	0.113777i
$382$	0.264946	+	0.139055i	0.0135558	+	0.00711465i
$383$	−1.52826	+	12.5863i	−0.0780902	+	0.643131i	0.900139	+	0.435603i	$0.143465\pi$
$383$	−1.52826	+	12.5863i	−0.0780902	+	0.643131i	−0.978229	+	0.207528i	$0.933458\pi$
$384$	2.11280	+	1.10888i	0.107818	+	0.0565875i
$385$	−11.0711	+	16.0392i	−0.564235	+	0.817435i
$386$	−15.1107	+	21.8916i	−0.769113	+	1.11425i
$387$	−5.87157	+	1.44721i	−0.298469	+	0.0735660i
$388$	36.6802	−	9.04086i	1.86216	−	0.458980i
$389$	0.845419	−	6.96265i	0.0428644	−	0.353020i	−0.955458	−	0.295126i	$-0.904638\pi$
$389$	0.845419	−	6.96265i	0.0428644	−	0.353020i	0.998323	−	0.0578943i	$-0.0184386\pi$
$390$	−10.0225	−	4.30185i	−0.507510	−	0.217833i
$391$	0.0300455	+	0.247447i	0.00151947	+	0.0125139i
$392$	1.82915	+	4.82308i	0.0923861	+	0.243602i
$393$	13.9914	+	12.3953i	0.705773	+	0.625260i
$394$	−52.6557	+	12.9785i	−2.65276	+	0.653846i
$395$	−6.56540	−	1.61823i	−0.330341	−	0.0814218i
$396$	3.24935	+	4.70750i	0.163286	+	0.236561i
$397$	−11.1657	−	29.4415i	−0.560389	−	1.47762i	−0.853267	−	0.521475i	$-0.825382\pi$
$397$	−11.1657	−	29.4415i	−0.560389	−	1.47762i	0.292878	−	0.956150i	$-0.405387\pi$
$398$	28.8336	−	25.5443i	1.44530	−	1.28042i
$399$	−3.38366	+	27.8669i	−0.169395	+	1.39509i
$400$	−3.64988	−	9.62395i	−0.182494	−	0.481197i
$401$	−4.52654	+	11.9355i	−0.226045	+	0.596031i	−0.999274	−	0.0380956i	$-0.987871\pi$
$401$	−4.52654	+	11.9355i	−0.226045	+	0.596031i	0.773229	+	0.634126i	$0.218640\pi$
$402$	−12.3363	+	3.04062i	−0.615277	+	0.151652i
$403$	8.28114	−	8.57563i	0.412513	−	0.427182i
$404$	33.4429	+	8.24294i	1.66385	+	0.410102i
$405$	0.843841	−	1.22251i	0.0419308	−	0.0607472i
$406$	50.6959	−	44.9126i	2.51599	−	2.22898i
$407$	−13.6056	−	3.35348i	−0.674404	−	0.166226i
$408$	0.0181194			0.000897042
$409$	8.72908	+	2.15153i	0.431625	+	0.106386i	0.449142	−	0.893460i	$-0.351730\pi$
$409$	8.72908	+	2.15153i	0.431625	+	0.106386i	−0.0175164	+	0.999847i	$0.505576\pi$
$410$	−4.56077	+	12.0258i	−0.225240	+	0.593910i
$411$	5.32804	−	2.79637i	0.262813	−	0.137935i
$412$	6.51907	+	17.1894i	0.321172	+	0.846860i
$413$	32.5115	−	17.0633i	1.59978	−	0.839632i
$414$	4.75937	+	6.89514i	0.233910	+	0.338878i
$415$	−6.25158	−	9.05698i	−0.306878	−	0.444589i
$416$	18.4137	+	22.6761i	0.902808	+	1.11179i
$417$	6.80649	−	9.86091i	0.333315	−	0.482891i
$418$	−30.9305			−1.51286
$419$	−12.2156	−	17.6973i	−0.596770	−	0.864570i	0.401924	−	0.915673i	$-0.368342\pi$
$419$	−12.2156	−	17.6973i	−0.596770	−	0.864570i	−0.998693	+	0.0511032i	$0.983726\pi$
$420$	11.7544	+	10.4135i	0.573556	+	0.508126i
$421$	29.9196	−	7.37453i	1.45819	−	0.359413i	0.571054	−	0.820913i	$-0.306535\pi$
$421$	29.9196	−	7.37453i	1.45819	−	0.359413i	0.887140	+	0.461500i	$0.152689\pi$
$422$	−23.1154	+	12.1319i	−1.12524	+	0.590573i
$423$	−0.727795	+	0.381976i	−0.0353866	+	0.0185723i
$424$	0.903986	−	0.222812i	0.0439014	−	0.0108207i
$425$	−0.126677	−	0.112226i	−0.00614474	−	0.00544376i
$426$	−0.282931	−	0.409897i	−0.0137081	−	0.0198596i
$427$	21.3618			1.03377
$428$	3.51327	−	5.08984i	0.169820	−	0.246027i
$429$	1.89641	+	9.41748i	0.0915596	+	0.454680i
$430$	−10.3916	−	15.0548i	−0.501127	−	0.726007i
$431$	2.86420	+	4.14951i	0.137964	+	0.199875i	0.885875	−	0.463923i	$-0.153559\pi$
$431$	2.86420	+	4.14951i	0.137964	+	0.199875i	−0.747912	+	0.663798i	$0.768943\pi$
$432$	−3.26264	+	1.71237i	−0.156974	+	0.0823863i
$433$	−10.6481	−	28.0768i	−0.511717	−	1.34929i	−0.903247	−	0.429122i	$-0.858823\pi$
$433$	−10.6481	−	28.0768i	−0.511717	−	1.34929i	0.391530	−	0.920166i	$-0.371946\pi$
$434$	−29.3573	+	15.4079i	−1.40919	+	0.739602i
$435$	3.55785	−	9.38127i	0.170586	−	0.449797i
$436$	30.8031	+	7.59229i	1.47520	+	0.363605i
$437$	−23.4544			−1.12198
$438$	−14.2781	−	3.51923i	−0.682233	−	0.168155i
$439$	−16.9597	+	15.0250i	−0.809444	+	0.717105i	−0.962550	−	0.271105i	$-0.912611\pi$
$439$	−16.9597	+	15.0250i	−0.809444	+	0.717105i	0.153106	+	0.988210i	$0.451073\pi$
$440$	−0.672403	+	0.974143i	−0.0320555	+	0.0464405i
$441$	−16.7465	−	4.12764i	−0.797452	−	0.196554i
$442$	0.408773	+	0.175453i	0.0194433	+	0.00834545i
$443$	22.5300	−	5.55314i	1.07043	−	0.263838i	0.335542	−	0.942025i	$-0.391080\pi$
$443$	22.5300	−	5.55314i	1.07043	−	0.263838i	0.734889	+	0.678188i	$0.237234\pi$
$444$	−4.00386	+	10.5573i	−0.190015	+	0.501028i
$445$	6.15168	+	16.2207i	0.291618	+	0.768933i
$446$	−4.64615	+	38.2645i	−0.220002	+	1.81188i
$447$	−3.05646	+	2.70779i	−0.144566	+	0.128074i
$448$	−15.9398	−	42.0299i	−0.753087	−	1.98573i
$449$	−1.02874	−	1.49038i	−0.0485491	−	0.0703355i	0.797958	−	0.602714i	$-0.205914\pi$
$449$	−1.02874	−	1.49038i	−0.0485491	−	0.0703355i	−0.846507	+	0.532378i	$0.821298\pi$
$450$	−5.52312	−	1.36133i	−0.260363	−	0.0641736i
$451$	10.9991	−	2.71104i	0.517929	−	0.127658i
$452$	21.7716	+	19.2880i	1.02405	+	0.907229i
$453$	−8.44767	−	22.2747i	−0.396906	−	1.04656i
$454$	−4.62443	−	38.0856i	−0.217035	−	1.78744i
$455$	11.2425	+	23.8574i	0.527057	+	1.11845i
$456$	−0.205507	+	1.69250i	−0.00962373	+	0.0792585i
$457$	−13.0889	+	3.22612i	−0.612272	+	0.150912i	−0.533245	−	0.845961i	$-0.679028\pi$
$457$	−13.0889	+	3.22612i	−0.612272	+	0.150912i	−0.0790273	+	0.996872i	$0.525181\pi$
$458$	39.9412	−	9.84463i	1.86633	−	0.460009i
$459$	−0.0344165	+	0.0498608i	−0.00160642	+	0.00232730i
$460$	−7.45344	+	10.7982i	−0.347519	+	0.503468i
$461$	−24.0736	−	12.6348i	−1.12122	−	0.588461i	−0.200892	−	0.979613i	$-0.564384\pi$
$461$	−24.0736	−	12.6348i	−1.12122	−	0.588461i	−0.920326	+	0.391153i	$0.872076\pi$
$462$	3.22039	−	26.5223i	0.149826	−	1.23393i
$463$	−7.04984	−	3.70004i	−0.327634	−	0.171955i	0.292884	−	0.956148i	$-0.405385\pi$
$463$	−7.04984	−	3.70004i	−0.327634	−	0.171955i	−0.620517	+	0.784193i	$0.713077\pi$
$464$	−18.6286	+	16.5035i	−0.864811	+	0.766156i
$465$	−2.79007	+	4.04211i	−0.129386	+	0.187448i
$466$	39.2625	+	9.67735i	1.81880	+	0.448294i
$467$	26.0074	−	13.6498i	1.20348	−	0.631635i	0.260820	−	0.965387i	$-0.416007\pi$
$467$	26.0074	−	13.6498i	1.20348	−	0.631635i	0.942661	+	0.333752i	$0.108315\pi$
$468$	7.71716	−	0.602258i	0.356726	−	0.0278394i
$469$	27.2040	+	14.2778i	1.25616	+	0.659286i
$470$	−1.86107	−	1.64876i	−0.0858448	−	0.0760518i
$471$	−0.701763	−	5.77954i	−0.0323355	−	0.266307i
$472$	1.97458	−	1.03634i	0.0908876	−	0.0477015i
$473$	−5.71348	+	15.0652i	−0.262706	+	0.692699i
$474$	9.00033	−	2.21838i	0.413399	−	0.101894i
$475$	11.9196	−	10.5598i	0.546909	−	0.484519i
$476$	−0.479409	−	0.424719i	−0.0219737	−	0.0194670i
$477$	−1.10392	+	2.91081i	−0.0505452	+	0.133277i
$478$	−19.6782	−	10.3279i	−0.900061	−	0.472388i
$479$	22.8666	−	20.2580i	1.04480	−	0.925612i	0.0474870	−	0.998872i	$-0.484879\pi$
$479$	22.8666	−	20.2580i	1.04480	−	0.925612i	0.997313	+	0.0732600i	$0.0233403\pi$
$480$	−9.00809	−	7.98047i	−0.411161	−	0.364257i
$481$	−13.1724	+	13.6409i	−0.600611	+	0.621970i
$482$	−11.0993	+	9.83313i	−0.505560	+	0.447887i
$483$	2.44200	−	20.1117i	0.111115	−	0.915115i
$484$	−8.37521			−0.380691
$485$	−26.1395			−1.18693
$486$	−0.245459	+	2.02154i	−0.0111343	+	0.0916988i
$487$	5.95198	−	8.62293i	0.269710	−	0.390742i	−0.664603	−	0.747197i	$-0.731399\pi$
$487$	5.95198	−	8.62293i	0.269710	−	0.390742i	0.934313	+	0.356455i	$0.116015\pi$
$488$	1.29741			0.0587310
$489$	−11.7284	−	16.9915i	−0.530375	−	0.768380i
$490$	−6.28887	−	51.7935i	−0.284102	−	2.33979i
$491$	7.87876	−	20.7746i	0.355563	−	0.937543i	−0.631235	−	0.775591i	$-0.717452\pi$
$491$	7.87876	−	20.7746i	0.355563	−	0.937543i	0.986799	−	0.161952i	$-0.0517790\pi$
$492$	−1.10026	−	9.06144i	−0.0496035	−	0.408521i
$493$	−0.145108	+	0.382620i	−0.00653536	+	0.0172323i
$494$	−21.0250	+	36.1929i	−0.945960	+	1.62839i
$495$	−1.40347	−	3.70064i	−0.0630811	−	0.166331i
$496$	10.7876	−	5.66175i	0.484376	−	0.254220i
$497$	−0.145170	+	1.19558i	−0.00651177	+	0.0536293i
$498$	13.3584	+	7.01105i	0.598606	+	0.314173i
$499$	3.64999	+	30.0604i	0.163396	+	1.34569i	0.811596	+	0.584219i	$0.198599\pi$
$499$	3.64999	+	30.0604i	0.163396	+	1.34569i	−0.648200	+	0.761470i	$0.724478\pi$
$500$	−2.99580	−	24.6726i	−0.133976	−	1.10339i
$501$	8.38077	+	7.42472i	0.374425	+	0.331712i
$502$	10.5857	+	27.9123i	0.472465	+	1.24579i
$503$	14.5556	+	21.0874i	0.649003	+	0.940243i	0.999993	+	0.00386331i	$0.00122973\pi$
$503$	14.5556	+	21.0874i	0.649003	+	0.940243i	−0.350990	+	0.936379i	$0.614155\pi$
$504$	−1.42989	−	0.352436i	−0.0636924	−	0.0156988i
$505$	−21.1026	−	11.0755i	−0.939054	−	0.492854i
$506$	22.3227			0.992364
$507$	12.3088	+	4.18248i	0.546654	+	0.185750i
$508$	−7.18997			−0.319003
$509$	20.4023	+	10.7079i	0.904314	+	0.474621i	0.851721	−	0.523995i	$-0.175559\pi$
$509$	20.4023	+	10.7079i	0.904314	+	0.474621i	0.0525929	+	0.998616i	$0.483251\pi$
$510$	−0.177944	−	0.0438593i	−0.00787951	−	0.00194212i
$511$	20.1999	+	29.2646i	0.893592	+	1.29459i
$512$	11.3672	+	29.9729i	0.502365	+	1.32463i
$513$	−4.26707	−	3.78030i	−0.188396	−	0.166904i
$514$	−2.75802	−	22.7143i	−0.121651	−	1.00188i
$515$	−1.53327	−	12.6276i	−0.0675640	−	0.556439i
$516$	11.4956	+	6.03337i	0.506067	+	0.265604i
$517$	−0.263971	+	2.17399i	−0.0116094	+	0.0956122i
$518$	46.6973	−	24.5086i	2.05176	−	1.07685i
$519$	−6.60102	−	17.4055i	−0.289753	−	0.764015i
$520$	0.682814	+	1.44898i	0.0299434	+	0.0635419i
$521$	0.0161902	−	0.0426900i	0.000709305	−	0.00187028i	−0.934661	−	0.355540i	$-0.884297\pi$
$521$	0.0161902	−	0.0426900i	0.000709305	−	0.00187028i	0.935370	+	0.353670i	$0.115066\pi$
$522$	1.65790	+	13.6540i	0.0725644	+	0.597621i
$523$	−2.35016	+	6.19687i	−0.102765	+	0.270970i	−0.976531	−	0.215377i	$-0.930902\pi$
$523$	−2.35016	+	6.19687i	−0.102765	+	0.270970i	0.873765	+	0.486347i	$0.161671\pi$
$524$	−4.83712	−	39.8373i	−0.211311	−	1.74030i
$525$	7.81384	+	11.3203i	0.341024	+	0.494059i
$526$	49.7756			2.17032
$527$	0.113794	−	0.164859i	0.00495695	−	0.00718138i
$528$	−1.18336	+	9.74583i	−0.0514990	+	0.424133i
$529$	−6.07285			−0.264037
$530$	−9.41709			−0.409052
$531$	−0.898780	+	7.40212i	−0.0390037	+	0.321225i
$532$	45.1097	−	39.9637i	1.95575	−	1.73265i
$533$	4.30438	−	14.7133i	0.186443	−	0.637305i
$534$	−17.8010	−	15.7703i	−0.770325	−	0.682448i
$535$	−3.20309	+	2.83769i	−0.138482	+	0.122684i
$536$	1.65224	+	0.867160i	0.0713657	+	0.0374556i
$537$	−3.42184	+	9.02266i	−0.147663	+	0.389357i
$538$	34.9314	+	30.9465i	1.50600	+	1.33420i
$539$	−34.3972	+	30.4733i	−1.48159	+	1.31258i
$540$	−3.09642	+	0.763200i	−0.133249	+	0.0328429i
$541$	14.1747	−	37.3757i	0.609419	−	1.60691i	−0.173536	−	0.984828i	$-0.555519\pi$
$541$	14.1747	−	37.3757i	0.609419	−	1.60691i	0.782955	−	0.622078i	$-0.213711\pi$
$542$	31.8916	−	16.7380i	1.36986	−	0.718959i
$543$	1.06667	+	8.78478i	0.0457750	+	0.376991i
$544$	0.367399	+	0.325487i	0.0157521	+	0.0139551i
$545$	−19.4369	−	10.2013i	−0.832585	−	0.436974i
$546$	−28.8456	−	21.7969i	−1.23448	−	0.932819i
$547$	2.89872	−	1.52137i	0.123940	−	0.0650489i	−0.401613	−	0.915809i	$-0.631550\pi$
$547$	2.89872	−	1.52137i	0.123940	−	0.0650489i	0.525554	+	0.850760i	$0.323858\pi$
$548$	−12.5429	−	3.09155i	−0.535807	−	0.132064i
$549$	−2.46434	+	3.57021i	−0.105175	+	0.152373i
$550$	−11.3445	+	10.0503i	−0.483730	+	0.428547i
$551$	−34.0941	−	17.8940i	−1.45246	−	0.762308i
$552$	0.148315	−	1.22149i	0.00631271	−	0.0519899i
$553$	−19.8476	−	10.4168i	−0.844005	−	0.442968i
$554$	−0.981352	+	1.42173i	−0.0416937	+	0.0604037i
$555$	4.43803	−	6.42960i	0.188384	−	0.272921i
$556$	−24.9760	+	6.15603i	−1.05922	+	0.261074i
$557$	−44.7581	+	11.0319i	−1.89646	+	0.467436i	−0.896774	+	0.442489i	$0.854096\pi$
$557$	−44.7581	+	11.0319i	−1.89646	+	0.467436i	−0.999689	+	0.0249471i	$0.992058\pi$
$558$	0.811583	−	6.68399i	0.0343570	−	0.282956i
$559$	13.7446	+	16.9261i	0.581334	+	0.715899i
$560$	3.24878	+	26.7561i	0.137286	+	1.13065i
$561$	0.0572410	+	0.150932i	0.00241672	+	0.00637236i
$562$	−33.0445	−	29.2749i	−1.39390	−	1.23489i
$563$	−27.9020	+	6.87722i	−1.17593	+	0.289840i	−0.778411	−	0.627755i	$-0.783974\pi$
$563$	−27.9020	+	6.87722i	−1.17593	+	0.289840i	−0.397517	+	0.917595i	$0.630128\pi$
$564$	1.71333	+	0.422297i	0.0721440	+	0.0177819i
$565$	−11.4327	−	16.5631i	−0.480977	−	0.696816i
$566$	−3.56479	−	9.39959i	−0.149839	−	0.395094i
$567$	3.68581	−	3.26534i	0.154790	−	0.137132i
$568$	−0.00881692	+	0.0726138i	−0.000369950	+	0.00304681i
$569$	12.1552	+	32.0506i	0.509572	+	1.34363i	0.905108	+	0.425181i	$0.139790\pi$
$569$	12.1552	+	32.0506i	0.509572	+	1.34363i	−0.395536	+	0.918451i	$0.629441\pi$
$570$	6.11504	−	16.1240i	0.256131	−	0.675362i
$571$	19.7992	−	4.88007i	0.828571	−	0.204224i	0.197848	−	0.980233i	$-0.436605\pi$
$571$	19.7992	−	4.88007i	0.828571	−	0.204224i	0.630723	+	0.776008i	$0.282759\pi$
$572$	10.3596	−	17.8332i	0.433157	−	0.745644i
$573$	0.142667	+	0.0351643i	0.00596001	+	0.00146901i
$574$	−24.2194	+	35.0879i	−1.01090	+	1.46454i
$575$	−8.60244	+	7.62110i	−0.358747	+	0.317822i
$576$	8.86334	+	2.18462i	0.369306	+	0.0910257i
$577$	−8.61794			−0.358770			−0.179385	−	0.983779i	$-0.557411\pi$
$577$	−8.61794			−0.358770			−0.179385	+	0.983779i	$0.557411\pi$
$578$	−33.6053	−	8.28297i	−1.39780	−	0.344526i
$579$	−4.63203	+	12.2137i	−0.192500	+	0.507582i
$580$	−19.0728	+	10.0102i	−0.791954	+	0.415649i
$581$	−12.9363	−	34.1101i	−0.536687	−	1.41513i
$582$	31.7293	−	16.6528i	1.31522	−	0.690283i
$583$	4.71179	+	6.82621i	0.195143	+	0.282713i
$584$	1.22684	+	1.77739i	0.0507671	+	0.0735489i
$585$	−5.28425	−	0.873264i	−0.218477	−	0.0361050i
$586$	−38.9470	+	56.4245i	−1.60889	+	2.33087i
$587$	16.1111			0.664976			0.332488	−	0.943107i	$-0.392112\pi$
$587$	16.1111			0.664976			0.332488	+	0.943107i	$0.392112\pi$
$588$	21.0345	+	30.4738i	0.867450	+	1.25672i
$589$	14.1086	+	12.4991i	0.581335	+	0.515018i
$590$	−21.9003	+	5.39794i	−0.901621	+	0.222230i
$591$	−23.5809	+	12.3762i	−0.969987	+	0.509088i
$592$	−17.1593	+	9.00589i	−0.705242	+	0.370140i
$593$	−23.8742	+	5.88446i	−0.980395	+	0.241646i	−0.696774	−	0.717291i	$-0.745382\pi$
$593$	−23.8742	+	5.88446i	−0.980395	+	0.241646i	−0.283621	+	0.958936i	$0.591536\pi$
$594$	4.06118	+	3.59789i	0.166632	+	0.147623i
$595$	0.251747	+	0.364718i	0.0103206	+	0.0149520i
$596$	8.76649			0.359089
$597$	10.7458	−	15.5680i	0.439796	−	0.637155i
$598$	15.1739	−	26.1206i	0.620505	−	1.06815i
$599$	6.15296	+	8.91410i	0.251403	+	0.364220i	0.928284	−	0.371873i	$-0.121284\pi$
$599$	6.15296	+	8.91410i	0.251403	+	0.364220i	−0.676881	+	0.736093i	$0.736669\pi$
$600$	0.474574	+	0.687539i	0.0193744	+	0.0280687i
$601$	−11.9919	+	6.29386i	−0.489162	+	0.256732i	−0.691224	−	0.722641i	$-0.742928\pi$
$601$	−11.9919	+	6.29386i	−0.489162	+	0.256732i	0.202062	+	0.979373i	$0.435236\pi$
$602$	−21.5031	−	56.6990i	−0.876401	−	2.31088i
$603$	−5.52456	+	2.89951i	−0.224977	+	0.118077i
$604$	−18.1360	+	47.8207i	−0.737943	+	1.94580i
$605$	5.62662	+	1.38684i	0.228754	+	0.0563829i
$606$	32.6713			1.32718
$607$	11.2920	+	2.78324i	0.458330	+	0.112968i	0.461719	−	0.887026i	$-0.347233\pi$
$607$	11.2920	+	2.78324i	0.458330	+	0.112968i	−0.00338954	+	0.999994i	$0.501079\pi$
$608$	−34.5702	+	30.6265i	−1.40201	+	1.24207i
$609$	18.8935	−	27.3720i	0.765604	−	1.10917i
$610$	−12.7414	−	3.14048i	−0.515886	−	0.127154i
$611$	2.36443	+	1.78666i	0.0956548	+	0.0722804i
$612$	0.126289	−	0.0311275i	0.00510494	−	0.00125825i
$613$	1.43681	−	3.78855i	0.0580321	−	0.153018i	−0.902865	−	0.429925i	$-0.858540\pi$
$613$	1.43681	−	3.78855i	0.0580321	−	0.153018i	0.960897	+	0.276907i	$0.0893093\pi$
$614$	−15.3837	−	40.5636i	−0.620838	−	1.63701i
$615$	−0.761295	+	6.26983i	−0.0306984	+	0.252824i
$616$	−2.93699	+	2.60194i	−0.118335	+	0.104835i
$617$	3.95184	+	10.4201i	0.159095	+	0.419499i	0.990734	−	0.135818i	$-0.0433661\pi$
$617$	3.95184	+	10.4201i	0.159095	+	0.419499i	−0.831639	+	0.555317i	$0.812597\pi$
$618$	9.90591	+	14.3512i	0.398474	+	0.577289i
$619$	8.57117	+	2.11260i	0.344505	+	0.0849128i	0.407772	−	0.913084i	$-0.366306\pi$
$619$	8.57117	+	2.11260i	0.344505	+	0.0849128i	−0.0632672	+	0.997997i	$0.520152\pi$
$620$	10.2380	−	2.52343i	0.411167	−	0.101344i
$621$	3.07957	+	2.72826i	0.123579	+	0.109481i
$622$	23.5373	+	62.0629i	0.943761	+	2.48849i
$623$	6.93172	+	57.0878i	0.277713	+	2.28718i
$624$	10.5996	+	8.00943i	0.424322	+	0.320634i
$625$	−0.389336	+	3.20647i	−0.0155734	+	0.128259i
$626$	39.5314	−	9.74362i	1.57999	−	0.389433i
$627$	−14.7475	+	3.63494i	−0.588960	+	0.145166i
$628$	−7.10024	+	10.2865i	−0.283331	+	0.410475i
$629$	−0.181007	+	0.262234i	−0.00721723	+	0.0104560i
$630$	13.1894	+	6.92233i	0.525478	+	0.275792i
$631$	5.14204	−	42.3485i	0.204701	−	1.68587i	−0.421990	−	0.906601i	$-0.638668\pi$
$631$	5.14204	−	42.3485i	0.204701	−	1.68587i	0.626691	−	0.779268i	$-0.284409\pi$
$632$	−1.20544	−	0.632665i	−0.0479499	−	0.0251661i
$633$	−9.59563	+	8.50099i	−0.381392	+	0.337884i
$634$	−19.0166	+	27.5503i	−0.755245	+	1.09416i
$635$	4.83035	+	1.19057i	0.191687	+	0.0472465i
$636$	5.91787	−	3.10594i	0.234659	−	0.123158i
$637$	12.2763	+	60.9636i	0.486406	+	2.41547i
$638$	32.4490	+	17.0305i	1.28467	+	0.674245i
$639$	−0.183072	−	0.162187i	−0.00724220	−	0.00641603i
$640$	0.427242	+	3.51865i	0.0168882	+	0.139087i
$641$	−24.6926	+	12.9597i	−0.975300	+	0.511877i	−0.875546	−	0.483135i	$-0.839498\pi$
$641$	−24.6926	+	12.9597i	−0.975300	+	0.511877i	−0.0997540	+	0.995012i	$0.531806\pi$
$642$	2.08024	−	5.48514i	0.0821005	−	0.216481i
$643$	2.49832	−	0.615781i	0.0985242	−	0.0242840i	−0.189745	−	0.981833i	$-0.560766\pi$
$643$	2.49832	−	0.615781i	0.0985242	−	0.0242840i	0.288270	+	0.957549i	$0.406920\pi$
$644$	−32.5559	+	28.8420i	−1.28288	+	1.13653i
$645$	−6.72391	−	5.95687i	−0.264754	−	0.234551i
$646$	−0.249405	+	0.657627i	−0.00981271	+	0.0258740i
$647$	25.0602	+	13.1526i	0.985216	+	0.517081i	0.878774	−	0.477238i	$-0.158362\pi$
$647$	25.0602	+	13.1526i	0.985216	+	0.517081i	0.106442	+	0.994319i	$0.466054\pi$
$648$	0.223858	−	0.198321i	0.00879397	−	0.00779078i
$649$	14.8705	+	13.1741i	0.583720	+	0.517131i
$650$	4.04883	+	20.1063i	0.158808	+	0.788633i
$651$	−12.1867	+	10.7965i	−0.477635	+	0.423148i
$652$	−5.34273	+	44.0013i	−0.209237	+	1.72323i
$653$	−19.4371			−0.760631			−0.380316	−	0.924857i	$-0.624185\pi$
$653$	−19.4371			−0.760631			−0.380316	+	0.924857i	$0.624185\pi$
$654$	30.0924			1.17671
$655$	−3.34692	+	27.5644i	−0.130775	+	1.07703i
$656$	8.89962	−	12.8933i	0.347472	−	0.503400i
$657$	−7.22132			−0.281731
$658$	−4.68204	−	6.78310i	−0.182525	−	0.264433i
$659$	−0.466969	−	3.84584i	−0.0181905	−	0.149812i	0.980783	−	0.195099i	$-0.0625029\pi$
$659$	−0.466969	−	3.84584i	−0.0181905	−	0.149812i	−0.998974	+	0.0452868i	$0.985580\pi$
$660$	−3.01305	+	7.94476i	−0.117283	+	0.309249i
$661$	−2.50613	−	20.6399i	−0.0974773	−	0.802798i	−0.956676	−	0.291155i	$-0.905960\pi$
$661$	−2.50613	−	20.6399i	−0.0974773	−	0.802798i	0.859199	−	0.511642i	$-0.170963\pi$
$662$	−10.6705	+	28.1359i	−0.414722	+	1.09353i
$663$	0.215521	+	0.0356165i	0.00837013	+	0.00138323i
$664$	−0.785685	−	2.07168i	−0.0304905	−	0.0803968i
$665$	−36.9230	+	19.3787i	−1.43181	+	0.751473i
$666$	−1.29095	+	10.6319i	−0.0500232	+	0.411978i
$667$	24.6059	+	12.9142i	0.952743	+	0.500038i
$668$	−2.89741	−	23.8623i	−0.112104	−	0.923260i
$669$	2.28157	+	18.7904i	0.0882105	+	0.726479i
$670$	−14.1270	−	12.5155i	−0.545775	−	0.483515i
$671$	4.09866	+	10.8073i	0.158227	+	0.417210i
$672$	−22.6623	−	32.8321i	−0.874219	−	1.26652i
$673$	−18.5350	−	4.56847i	−0.714473	−	0.176102i	−0.134708	−	0.990885i	$-0.543009\pi$
$673$	−18.5350	−	4.56847i	−0.714473	−	0.176102i	−0.579765	+	0.814784i	$0.696856\pi$
$674$	4.10937	+	2.15676i	0.158287	+	0.0830754i
$675$	−2.79339			−0.107518
$676$	−13.8253	−	24.2443i	−0.531744	−	0.932472i
$677$	25.5558			0.982188			0.491094	−	0.871107i	$-0.336597\pi$
$677$	25.5558			0.982188			0.491094	+	0.871107i	$0.336597\pi$
$678$	24.4295	+	12.8216i	0.938210	+	0.492411i
$679$	−84.1323	−	20.7367i	−3.22870	−	0.795803i
$680$	0.0152899	+	0.0221512i	0.000586339	+	0.000849459i
$681$	−6.68072	−	17.6156i	−0.256006	−	0.675032i
$682$	−13.4278	−	11.8960i	−0.514178	−	0.455522i
$683$	1.74261	+	14.3517i	0.0666793	+	0.549153i	0.987320	+	0.158743i	$0.0507440\pi$
$683$	1.74261	+	14.3517i	0.0666793	+	0.549153i	−0.920641	+	0.390411i	$0.872333\pi$
$684$	1.47522	+	12.1495i	0.0564063	+	0.464548i
$685$	7.91463	+	4.15392i	0.302402	+	0.158713i
$686$	12.3863	−	102.010i	0.472909	−	3.89476i
$687$	17.8869	−	9.38778i	0.682428	−	0.358166i
$688$	7.90148	+	20.8345i	0.301241	+	0.794308i
$689$	11.1904	−	0.873317i	0.426322	−	0.0332707i
$690$	−4.41326	+	11.6368i	−0.168010	+	0.443006i
$691$	−4.17102	−	34.3514i	−0.158673	−	1.30679i	−0.826696	−	0.562649i	$-0.809782\pi$
$691$	−4.17102	−	34.3514i	−0.158673	−	1.30679i	0.668023	−	0.744141i	$-0.267141\pi$
$692$	−14.1715	+	37.3672i	−0.538720	+	1.42049i
$693$	−1.58143	−	13.0242i	−0.0600734	−	0.494749i
$694$	−23.0938	−	33.4572i	−0.876630	−	1.27002i
$695$	17.7987			0.675143
$696$	1.14750	−	1.66244i	0.0434958	−	0.0630145i
$697$	0.0310498	−	0.255718i	0.00117609	−	0.00968601i
$698$	34.3569			1.30043
$699$	19.8575			0.751081
$700$	3.55951	−	29.3152i	0.134537	−	1.10801i
$701$	8.64036	−	7.65469i	0.326342	−	0.289114i	−0.484004	−	0.875066i	$-0.660818\pi$
$701$	8.64036	−	7.65469i	0.326342	−	0.289114i	0.810346	+	0.585952i	$0.199279\pi$
$702$	6.97061	−	2.30646i	0.263089	−	0.0870519i
$703$	−22.4419	−	19.8818i	−0.846413	−	0.749856i
$704$	18.2053	−	16.1284i	0.686136	−	0.607864i
$705$	−1.08111	−	0.567413i	−0.0407171	−	0.0213700i
$706$	−8.72570	+	23.0078i	−0.328396	+	0.865909i
$707$	−59.1343	−	52.3884i	−2.22398	−	1.97027i
$708$	11.9822	−	10.6153i	0.450319	−	0.398948i
$709$	22.9081	−	5.64634i	0.860331	−	0.212053i	0.215619	−	0.976478i	$-0.430823\pi$
$709$	22.9081	−	5.64634i	0.860331	−	0.212053i	0.644713	+	0.764425i	$0.276977\pi$
$710$	0.262356	−	0.691775i	0.00984603	−	0.0259619i
$711$	4.03062	−	2.11543i	0.151160	−	0.0793350i
$712$	0.420998	+	3.46723i	0.0157776	+	0.129940i
$713$	−10.1823	−	9.02069i	−0.381328	−	0.337827i
$714$	−0.537936	−	0.282330i	−0.0201317	−	0.0105659i
$715$	−9.91273	+	10.2652i	−0.370715	+	0.383898i
$716$	18.3437	−	9.62752i	0.685536	−	0.359797i
$717$	−10.5962	−	2.61174i	−0.395724	−	0.0975372i
$718$	−31.1146	+	45.0773i	−1.16119	+	1.68227i
$719$	33.8720	−	30.0079i	1.26321	−	1.11911i	0.275753	−	0.961229i	$-0.411073\pi$
$719$	33.8720	−	30.0079i	1.26321	−	1.11911i	0.987458	−	0.157879i	$-0.0504656\pi$
$720$	−4.84655	−	2.54366i	−0.180620	−	0.0947967i
$721$	5.08266	−	41.8595i	0.189288	−	1.55893i
$722$	−24.3397	−	12.7745i	−0.905830	−	0.475416i
$723$	−4.13653	+	5.99279i	−0.153839	+	0.222874i
$724$	10.7922	−	15.6352i	0.401090	−	0.581079i
$725$	−18.3191	+	4.51526i	−0.680355	+	0.167692i
$726$	−7.71337	+	1.90118i	−0.286270	+	0.0705593i
$727$	−1.65967	+	13.6686i	−0.0615537	+	0.506940i	0.929027	+	0.370011i	$0.120646\pi$
$727$	−1.65967	+	13.6686i	−0.0615537	+	0.506940i	−0.990581	+	0.136929i	$0.956277\pi$
$728$	1.04821	+	5.20535i	0.0388492	+	0.192923i
$729$	0.120537	+	0.992709i	0.00446432	+	0.0367670i
$730$	−7.74612	−	20.4248i	−0.286697	−	0.755957i
$731$	0.274238	+	0.242954i	0.0101431	+	0.00898597i
$732$	9.04275	−	2.22884i	0.334230	−	0.0823802i
$733$	6.26137	+	1.54329i	0.231269	+	0.0570026i	0.353247	−	0.935530i	$-0.385078\pi$
$733$	6.26137	+	1.54329i	0.231269	+	0.0570026i	−0.121978	+	0.992533i	$0.538924\pi$
$734$	4.66354	+	6.75630i	0.172134	+	0.249380i
$735$	−9.08528	−	23.9559i	−0.335116	−	0.883627i
$736$	24.9495	−	22.1033i	0.919651	−	0.814739i
$737$	−2.00375	+	16.5024i	−0.0738092	+	0.607874i
$738$	−3.07026	−	8.09562i	−0.113018	−	0.298004i
$739$	7.14111	−	18.8295i	0.262690	−	0.692656i	−0.737167	−	0.675711i	$-0.763837\pi$
$739$	7.14111	−	18.8295i	0.262690	−	0.692656i	0.999856	−	0.0169451i	$-0.00539404\pi$
$740$	−16.2851	+	4.01391i	−0.598652	+	0.147554i
$741$	−5.77128	+	19.7275i	−0.212013	+	0.724708i
$742$	−30.3097	−	7.47068i	−1.11271	−	0.274257i
$743$	−11.8693	+	17.1957i	−0.435444	+	0.630849i	−0.977860	−	0.209261i	$-0.932894\pi$
$743$	−11.8693	+	17.1957i	−0.435444	+	0.630849i	0.542416	+	0.840110i	$0.317510\pi$
$744$	−0.740161	+	0.655725i	−0.0271356	+	0.0240401i
$745$	−5.88948	−	1.45163i	−0.215774	−	0.0531835i
$746$	−47.0536			−1.72276
$747$	7.19320	+	1.77297i	0.263186	+	0.0648694i
$748$	0.122889	−	0.324031i	0.00449325	−	0.0118477i
$749$	−12.5606	+	6.59232i	−0.458955	+	0.240878i
$750$	−8.35976	−	22.0429i	−0.305255	−	0.804892i
$751$	21.0844	−	11.0659i	0.769380	−	0.403802i	−0.0338835	−	0.999426i	$-0.510788\pi$
$751$	21.0844	−	11.0659i	0.769380	−	0.403802i	0.803263	+	0.595624i	$0.203095\pi$
$752$	1.72045	+	2.49250i	0.0627384	+	0.0908923i
$753$	8.32750	+	12.0645i	0.303471	+	0.439654i
$754$	41.9853	−	26.3932i	1.52901	−	0.961183i
$755$	20.1026	−	29.1237i	0.731609	−	1.05992i
$756$	−10.5716			−0.384484
$757$	26.2691	+	38.0574i	0.954768	+	1.38322i	0.923453	+	0.383711i	$0.125354\pi$
$757$	26.2691	+	38.0574i	0.954768	+	1.38322i	0.0313153	+	0.999510i	$0.490030\pi$
$758$	−36.4450	−	32.2875i	−1.32374	−	1.17273i
$759$	10.6434	−	2.62336i	0.386330	−	0.0952218i
$760$	−2.24252	+	1.17697i	−0.0813448	+	0.0426930i
$761$	−12.0273	+	6.31240i	−0.435988	+	0.228824i	−0.668413	−	0.743790i	$-0.733026\pi$
$761$	−12.0273	+	6.31240i	−0.435988	+	0.228824i	0.232425	+	0.972614i	$0.425334\pi$
$762$	−6.62180	+	1.63213i	−0.239882	+	0.0591257i
$763$	−54.4666	−	48.2532i	−1.97182	−	1.74688i
$764$	−0.179198	−	0.259613i	−0.00648316	−	0.00939248i
$765$	−0.0899976			−0.00325387
$766$	14.6668	−	21.2485i	0.529932	−	0.767739i
$767$	25.5238	−	8.44542i	0.921611	−	0.304946i
$768$	7.61102	+	11.0265i	0.274639	+	0.397883i
$769$	22.0590	+	31.9580i	0.795467	+	1.15243i	0.985336	+	0.170624i	$0.0545783\pi$
$769$	22.0590	+	31.9580i	0.795467	+	1.15243i	−0.189869	+	0.981809i	$0.560806\pi$
$770$	35.1414	−	18.4436i	1.26641	−	0.664662i
$771$	−3.98439	−	10.5060i	−0.143494	−	0.378364i
$772$	24.8312	−	13.0324i	0.893695	−	0.469047i
$773$	18.1147	−	47.7646i	0.651542	−	1.71797i	−0.0435481	−	0.999051i	$-0.513866\pi$
$773$	18.1147	−	47.7646i	0.651542	−	1.71797i	0.695090	−	0.718923i	$-0.255365\pi$
$774$	11.9568	+	2.94708i	0.429778	+	0.105931i
$775$	9.23603			0.331768
$776$	−5.10978	−	1.25945i	−0.183430	−	0.0452115i
$777$	19.3849	−	17.1735i	0.695428	−	0.616096i
$778$	−8.11354	+	11.7545i	−0.290885	+	0.421419i
$779$	23.5340	+	5.80062i	0.843194	+	0.207829i
$780$	7.24833	+	8.92613i	0.259532	+	0.319607i
$781$	−0.632719	+	0.155951i	−0.0226405	+	0.00558037i
$782$	0.179997	−	0.474613i	0.00643667	−	0.0169721i
$783$	2.39510	+	6.31537i	0.0855940	+	0.225693i
$784$	−7.66042	+	63.0892i	−0.273586	+	2.25319i
$785$	6.47339	−	5.73492i	0.231045	−	0.204688i
$786$	−13.4980	−	35.5912i	−0.481456	−	1.26949i
$787$	1.88161	+	2.72599i	0.0670723	+	0.0971710i	0.855085	−	0.518488i	$-0.173505\pi$
$787$	1.88161	+	2.72599i	0.0670723	+	0.0971710i	−0.788012	+	0.615659i	$0.788890\pi$
$788$	55.5124	+	13.6826i	1.97755	+	0.487422i
$789$	23.7328	−	5.84962i	0.844912	−	0.208252i
$790$	10.3068	+	9.13107i	0.366701	+	0.324869i
$791$	−23.6574	−	62.3796i	−0.841162	−	2.21796i
$792$	−0.0960479	−	0.791026i	−0.00341291	−	0.0281079i
$793$	15.4320	+	2.55027i	0.548008	+	0.0905626i
$794$	−7.72893	+	63.6534i	−0.274289	+	2.25898i
$795$	−4.49004	+	1.10669i	−0.159245	+	0.0392504i
$796$	−39.4311	+	9.71888i	−1.39760	+	0.344477i
$797$	24.5866	−	35.6199i	0.870903	−	1.26172i	−0.0930541	−	0.995661i	$-0.529663\pi$
$797$	24.5866	−	35.6199i	0.870903	−	1.26172i	0.963957	−	0.266059i	$-0.0857217\pi$
$798$	32.4732	−	47.0456i	1.14954	−	1.66539i
$799$	0.0440938	+	0.0231422i	0.00155993	+	0.000818712i
$800$	−2.72786	+	22.4660i	−0.0964445	+	0.794292i
$801$	−10.3408	−	5.42726i	−0.365374	−	0.191763i
$802$	19.4572	−	17.2375i	0.687056	−	0.608679i
$803$	−10.9297	+	15.8344i	−0.385701	+	0.558785i
$804$	13.0055	+	3.20558i	0.458670	+	0.113052i
$805$	26.6475	−	13.9857i	0.939202	−	0.492931i
$806$	−23.0475	+	7.62606i	−0.811815	+	0.268617i
$807$	20.2920	+	10.6501i	0.714312	+	0.374900i
$808$	−3.59153	−	3.18181i	−0.126349	−	0.111936i
$809$	−5.19663	−	42.7981i	−0.182704	−	1.50470i	−0.738993	−	0.673713i	$-0.764698\pi$
$809$	−5.19663	−	42.7981i	−0.182704	−	1.50470i	0.556289	−	0.830989i	$-0.312225\pi$
$810$	−2.67849	+	1.40578i	−0.0941125	+	0.0493940i
$811$	−2.48298	+	6.54708i	−0.0871893	+	0.229899i	−0.971518	−	0.236965i	$-0.923847\pi$
$811$	−2.48298	+	6.54708i	−0.0871893	+	0.229899i	0.884329	+	0.466865i	$0.154616\pi$
$812$	−69.3286	+	17.0880i	−2.43296	+	0.599670i
$813$	13.2388	−	11.7285i	0.464304	−	0.411338i
$814$	21.3591	+	18.9225i	0.748634	+	0.663232i
$815$	10.8754	−	28.6762i	0.380950	−	1.00448i
$816$	0.197669	+	0.103745i	0.00691979	+	0.00363178i
$817$	−25.8043	+	22.8606i	−0.902777	+	0.799791i
$818$	−13.7036	−	12.1403i	−0.479134	−	0.424475i
$819$	−16.3151	−	7.00273i	−0.570095	−	0.244695i
$820$	10.1493	−	8.99150i	0.354429	−	0.313997i
$821$	−6.44527	+	53.0816i	−0.224941	+	1.85256i	0.244569	+	0.969632i	$0.421354\pi$
$821$	−6.44527	+	53.0816i	−0.224941	+	1.85256i	−0.469510	+	0.882927i	$0.655569\pi$
$822$	−12.2535			−0.427390
$823$	−33.3785			−1.16350			−0.581751	−	0.813367i	$-0.697632\pi$
$823$	−33.3785			−1.16350			−0.581751	+	0.813367i	$0.697632\pi$
$824$	0.308696	−	2.54234i	0.0107539	−	0.0885665i
$825$	−4.22789	+	6.12516i	−0.147196	+	0.213251i
$826$	−74.7703			−2.60159
$827$	−9.44825	−	13.6881i	−0.328548	−	0.475984i	0.623547	−	0.781786i	$-0.285691\pi$
$827$	−9.44825	−	13.6881i	−0.328548	−	0.475984i	−0.952095	+	0.305802i	$0.901075\pi$
$828$	−1.06467	−	8.76836i	−0.0369999	−	0.304722i
$829$	−12.8093	+	33.7753i	−0.444885	+	1.17307i	0.505730	+	0.862692i	$0.331223\pi$
$829$	−12.8093	+	33.7753i	−0.444885	+	1.17307i	−0.950615	+	0.310374i	$0.899546\pi$
$830$	2.70129	+	22.2471i	0.0937631	+	0.772209i
$831$	−0.300824	+	0.793207i	−0.0104355	+	0.0275160i
$832$	−6.49744	−	32.2660i	−0.225258	−	1.11862i
$833$	0.370547	+	0.977053i	0.0128387	+	0.0338529i
$834$	−21.6049	+	11.3391i	−0.748117	+	0.392642i
$835$	−2.00479	+	16.5109i	−0.0693785	+	0.571383i
$836$	28.8734	+	15.1539i	0.998608	+	0.524110i
$837$	−0.398541	−	3.28228i	−0.0137756	−	0.113452i
$838$	5.27831	+	43.4708i	0.182336	+	1.50167i
$839$	−9.37776	−	8.30797i	−0.323756	−	0.286823i	0.485551	−	0.874208i	$-0.338619\pi$
$839$	−9.37776	−	8.30797i	−0.323756	−	0.286823i	−0.809307	+	0.587385i	$0.800157\pi$
$840$	−0.775741	−	2.04546i	−0.0267656	−	0.0705751i
$841$	9.44148	+	13.6783i	0.325568	+	0.471667i
$842$	−60.9279	−	15.0174i	−2.09971	−	0.517533i
$843$	−19.1959	−	10.0748i	−0.661141	−	0.346994i
$844$	27.5220			0.947346
$845$	5.27354	+	18.5771i	0.181415	+	0.639070i
$846$	1.67379			0.0575462
$847$	17.0096	+	8.92731i	0.584456	+	0.306746i
$848$	11.1376	+	2.74516i	0.382465	+	0.0942692i
$849$	−2.80432	−	4.06276i	−0.0962440	−	0.139434i
$850$	0.122209	+	0.322240i	0.00419175	+	0.0110527i
$851$	16.1964	+	14.3488i	0.555207	+	0.491870i
$852$	0.0632917	+	0.521254i	0.00216834	+	0.0178579i
$853$	−3.59501	−	29.6076i	−0.123091	−	1.01374i	−0.915098	−	0.403232i	$-0.867887\pi$
$853$	−3.59501	−	29.6076i	−0.123091	−	1.01374i	0.792007	−	0.610512i	$-0.209036\pi$
$854$	−38.5181	−	20.2159i	−1.31806	−	0.691772i
$855$	1.02074	−	8.40653i	0.0349085	−	0.287497i
$856$	−0.762869	+	0.400385i	−0.0260743	+	0.0136849i
$857$	7.94559	+	20.9508i	0.271416	+	0.715666i	0.999543	+	0.0302234i	$0.00962187\pi$
$857$	7.94559	+	20.9508i	0.271416	+	0.715666i	−0.728127	+	0.685442i	$0.759609\pi$
$858$	5.49280	−	18.7756i	0.187521	−	0.640989i
$859$	−6.89862	+	18.1902i	−0.235378	+	0.620641i	−0.999707	−	0.0241851i	$-0.992301\pi$
$859$	−6.89862	+	18.1902i	−0.235378	+	0.620641i	0.764329	+	0.644826i	$0.223070\pi$
$860$	2.32460	+	19.1448i	0.0792681	+	0.652832i
$861$	−7.42422	+	19.5761i	−0.253017	+	0.667150i
$862$	−1.23761	−	10.1926i	−0.0421532	−	0.347163i
$863$	2.56579	+	3.71718i	0.0873404	+	0.126534i	0.864219	−	0.503116i	$-0.167813\pi$
$863$	2.56579	+	3.71718i	0.0873404	+	0.126534i	−0.776878	+	0.629651i	$0.783198\pi$
$864$	8.10162			0.275623
$865$	15.7082	−	22.7573i	0.534096	−	0.773771i
$866$	−7.37069	+	60.7031i	−0.250466	+	2.06278i
$867$	−16.9963			−0.577226
$868$	34.9537			1.18641
$869$	1.46190	−	12.0399i	0.0495917	−	0.408424i
$870$	−15.2933	+	13.5487i	−0.518490	+	0.459342i
$871$	17.9480	+	13.5622i	0.608145	+	0.459537i
$872$	−3.30803	−	2.93066i	−0.112024	−	0.0992447i
$873$	13.1714	−	11.6689i	0.445785	−	0.394931i
$874$	42.2913	+	22.1962i	1.43052	+	0.750797i
$875$	−20.2148	+	53.3020i	−0.683384	+	1.80194i
$876$	11.6043	+	10.2805i	0.392073	+	0.347347i
$877$	31.4762	−	27.8855i	1.06288	−	0.941626i	0.0644615	−	0.997920i	$-0.479467\pi$
$877$	31.4762	−	27.8855i	1.06288	−	0.941626i	0.998414	+	0.0562945i	$0.0179286\pi$
$878$	44.7996	−	11.0421i	1.51191	−	0.372653i
$879$	−11.9388	+	31.4801i	−0.402686	+	1.06180i
$880$	−12.9130	+	6.77726i	−0.435297	+	0.228461i
$881$	−4.01859	−	33.0961i	−0.135390	−	1.11504i	−0.889063	−	0.457785i	$-0.848643\pi$
$881$	−4.01859	−	33.0961i	−0.135390	−	1.11504i	0.753673	−	0.657250i	$-0.228280\pi$
$882$	26.2899	+	23.2908i	0.885226	+	0.784242i
$883$	17.8657	+	9.37662i	0.601227	+	0.315548i	0.737735	−	0.675091i	$-0.235895\pi$
$883$	17.8657	+	9.37662i	0.601227	+	0.315548i	−0.136507	+	0.990639i	$0.543588\pi$
$884$	−0.295626	−	0.364057i	−0.00994299	−	0.0122445i
$885$	−9.80763	+	5.14744i	−0.329680	+	0.173029i
$886$	−45.8797	−	11.3083i	−1.54136	−	0.379911i
$887$	−24.1753	+	35.0239i	−0.811726	+	1.17599i	0.169954	+	0.985452i	$0.445638\pi$
$887$	−24.1753	+	35.0239i	−0.811726	+	1.17599i	−0.981680	+	0.190537i	$0.938977\pi$
$888$	1.17734	−	1.04303i	0.0395090	−	0.0350019i
$889$	14.6024	+	7.66394i	0.489749	+	0.257040i
$890$	4.25822	−	35.0696i	0.142736	−	1.17554i
$891$	2.35918	+	1.23819i	0.0790356	+	0.0414811i
$892$	23.0843	−	33.4434i	0.772919	−	1.11977i
$893$	−2.66178	+	3.85625i	−0.0890731	+	0.129045i
$894$	8.07373	−	1.99000i	0.270026	−	0.0665554i
$895$	−13.9178	+	3.43044i	−0.465222	+	0.114667i
$896$	−1.41627	+	11.6640i	−0.0473143	+	0.389668i
$897$	4.16516	−	14.2374i	0.139071	−	0.475374i
$898$	0.444514	+	3.66090i	0.0148336	+	0.122166i
$899$	−7.91914	−	20.8811i	−0.264118	−	0.696422i
$900$	4.48884	+	3.97677i	0.149628	+	0.132559i
$901$	0.183128	−	0.0451371i	0.00610089	−	0.00150373i
$902$	−22.3985	−	5.52073i	−0.745788	−	0.183820i
$903$	−16.9159	−	24.5069i	−0.562925	−	0.815537i
$904$	−1.43684	−	3.78862i	−0.0477884	−	0.126008i
$905$	−9.83942	+	8.71697i	−0.327074	+	0.289762i
$906$	−5.84751	+	48.1586i	−0.194271	+	1.59996i
$907$	−4.88769	−	12.8878i	−0.162293	−	0.427932i	0.829059	−	0.559161i	$-0.188877\pi$
$907$	−4.88769	−	12.8878i	−0.162293	−	0.427932i	−0.991352	+	0.131229i	$0.958108\pi$
$908$	−14.3426	+	37.8183i	−0.475976	+	1.25505i
$909$	15.5776	−	3.83953i	0.516675	−	0.127349i
$910$	2.30584	−	53.6573i	0.0764378	−	1.77872i
$911$	24.9812	+	6.15731i	0.827663	+	0.204001i	0.630322	−	0.776334i	$-0.282923\pi$
$911$	24.9812	+	6.15731i	0.827663	+	0.204001i	0.197342	+	0.980335i	$0.436769\pi$
$912$	−11.9325	+	17.2873i	−0.395126	+	0.572438i
$913$	14.7748	−	13.0893i	0.488974	−	0.433194i
$914$	26.6540	+	6.56962i	0.881636	+	0.217304i
$915$	−6.44415			−0.213037
$916$	−42.1081	−	10.3787i	−1.39129	−	0.342923i
$917$	−32.6395	+	86.0632i	−1.07785	+	2.84206i
$918$	0.109243	−	0.0573354i	0.00360557	−	0.00189235i
$919$	10.4411	+	27.5310i	0.344421	+	0.908164i	0.989563	+	0.144101i	$0.0460291\pi$
$919$	10.4411	+	27.5310i	0.344421	+	0.908164i	−0.645142	+	0.764063i	$0.723202\pi$
$920$	1.61844	−	0.849422i	0.0533583	−	0.0280046i
$921$	−12.1020	−	17.5327i	−0.398773	−	0.577722i
$922$	31.4508	+	45.5643i	1.03578	+	1.50058i
$923$	−0.247607	+	0.846375i	−0.00815008	+	0.0278588i
$924$	−16.0004	+	23.1806i	−0.526376	+	0.762587i
$925$	−14.6913			−0.483048
$926$	9.21022	+	13.3433i	0.302667	+	0.438488i
$927$	6.40966	+	5.67846i	0.210521	+	0.186505i
$928$	53.1306	−	13.0955i	1.74410	−	0.429881i
$929$	8.03393	−	4.21653i	0.263585	−	0.138340i	−0.327754	−	0.944763i	$-0.606292\pi$
$929$	8.03393	−	4.21653i	0.263585	−	0.138340i	0.591339	+	0.806423i	$0.298600\pi$
$930$	8.85612	−	4.64805i	0.290404	−	0.152416i
$931$	−95.4676	+	23.5307i	−3.12883	+	0.771186i
$932$	−31.9101	−	28.2699i	−1.04525	−	0.926010i
$933$	18.5161	+	26.8253i	0.606191	+	0.878220i
$934$	−59.8123			−1.95712
$935$	−0.136214	+	0.197341i	−0.00445469	+	0.00645373i
$936$	−0.990896	−	0.425311i	−0.0323885	−	0.0139017i
$937$	13.9938	+	20.2735i	0.457157	+	0.662307i	0.981997	−	0.188894i	$-0.0604903\pi$
$937$	13.9938	+	20.2735i	0.457157	+	0.662307i	−0.524840	+	0.851201i	$0.675875\pi$
$938$	−35.5405	−	51.4893i	−1.16044	−	1.68119i
$939$	17.7034	−	9.29145i	0.577728	−	0.303215i
$940$	0.929510	+	2.45092i	0.0303173	+	0.0799401i
$941$	14.7186	−	7.72494i	0.479814	−	0.251826i	−0.207433	−	0.978249i	$-0.566511\pi$
$941$	14.7186	−	7.72494i	0.479814	−	0.251826i	0.687248	+	0.726423i	$0.258819\pi$
$942$	−4.20412	+	11.0854i	−0.136978	+	0.361181i
$943$	−16.9846	−	4.18634i	−0.553096	−	0.136326i
$944$	27.4749			0.894233
$945$	7.10217	+	1.75053i	0.231034	+	0.0569447i
$946$	24.5592	−	21.7575i	0.798487	−	0.707398i
$947$	27.9289	−	40.4620i	0.907567	−	1.31484i	−0.0412952	−	0.999147i	$-0.513148\pi$
$947$	27.9289	−	40.4620i	0.907567	−	1.31484i	0.948862	−	0.315691i	$-0.102236\pi$
$948$	−9.48862	−	2.33873i	−0.308176	−	0.0759585i
$949$	11.0990	+	23.5527i	0.360287	+	0.764554i
$950$	−31.4860	+	7.76059i	−1.02154	+	0.251787i
$951$	−5.82934	+	15.3707i	−0.189029	+	0.498430i
$952$	0.0316390	+	0.0834251i	0.00102543	+	0.00270382i
$953$	0.127415	−	1.04936i	0.00412738	−	0.0339920i	−0.990500	−	0.137515i	$-0.956088\pi$
$953$	0.127415	−	1.04936i	0.00412738	−	0.0339920i	0.994627	+	0.103523i	$0.0330115\pi$
$954$	4.74517	−	4.20385i	0.153631	−	0.136105i
$955$	0.0773996	+	0.204086i	0.00250459	+	0.00660406i
$956$	13.3095	+	19.2821i	0.430459	+	0.623628i
$957$	17.4730	+	4.30671i	0.564822	+	0.139216i
$958$	−60.4026	+	14.8879i	−1.95152	+	0.481007i
$959$	22.1786	+	19.6485i	0.716184	+	0.634484i
$960$	4.80852	+	12.6790i	0.155194	+	0.409214i
$961$	−2.41891	−	19.9215i	−0.0780292	−	0.642629i
$962$	36.6607	−	12.1304i	1.18199	−	0.391101i
$963$	0.347239	−	2.85977i	0.0111896	−	0.0921547i
$964$	15.1787	−	3.74122i	0.488874	−	0.120497i
$965$	−18.8401	+	4.64366i	−0.606483	+	0.149485i
$966$	−23.4361	+	33.9530i	−0.754043	+	1.09242i
$967$	17.9864	−	26.0579i	0.578405	−	0.837965i	−0.419145	−	0.907919i	$-0.637670\pi$
$967$	17.9864	−	26.0579i	0.578405	−	0.837965i	0.997550	+	0.0699548i	$0.0222855\pi$
$968$	1.03308	+	0.542201i	0.0332044	+	0.0174270i
$969$	−0.0416313	+	0.342864i	−0.00133739	+	0.0110144i
$970$	47.1329	+	24.7372i	1.51335	+	0.794265i
$971$	−9.44743	+	8.36969i	−0.303182	+	0.268596i	−0.800972	−	0.598701i	$-0.795684\pi$
$971$	−9.44743	+	8.36969i	−0.303182	+	0.268596i	0.497790	+	0.867298i	$0.334145\pi$
$972$	1.21956	−	1.76683i	0.0391173	−	0.0566712i
$973$	57.2867	+	14.1199i	1.83653	+	0.452663i
$974$	−18.8925	+	9.91557i	−0.605356	+	0.317715i
$975$	4.29336	+	9.11079i	0.137497	+	0.291779i
$976$	14.1538	+	7.42847i	0.453051	+	0.237780i
$977$	15.5980	+	13.8186i	0.499025	+	0.442097i	0.874708	−	0.484651i	$-0.161053\pi$
$977$	15.5980	+	13.8186i	0.499025	+	0.442097i	−0.375683	+	0.926748i	$0.622592\pi$
$978$	5.06779	+	41.7370i	0.162050	+	1.33460i
$979$	−27.5517	+	14.4602i	−0.880555	+	0.462151i
$980$	−19.5049	+	51.4301i	−0.623060	+	1.64287i
$981$	14.3480	−	3.53646i	0.458095	−	0.112910i
$982$	−33.8665	+	30.0031i	−1.08072	+	0.957439i
$983$	−9.93953	−	8.80566i	−0.317022	−	0.280857i	0.489572	−	0.871963i	$-0.337153\pi$
$983$	−9.93953	−	8.80566i	−0.317022	−	0.280857i	−0.806594	+	0.591106i	$0.798691\pi$
$984$	−0.450910	+	1.18895i	−0.0143745	+	0.0379024i
$985$	−35.0286	−	18.3844i	−1.11610	−	0.585776i
$986$	0.623743	−	0.552588i	0.0198640	−	0.0175980i
$987$	−3.02953	−	2.68393i	−0.0964310	−	0.0854304i
$988$	37.3589	−	23.4849i	1.18854	−	0.747155i
$989$	18.6231	−	16.4986i	0.592179	−	0.524625i
$990$	−0.971485	+	8.00090i	−0.0308758	+	0.254285i
$991$	14.1982			0.451021			0.225510	−	0.974241i	$-0.427595\pi$
$991$	14.1982			0.451021			0.225510	+	0.974241i	$0.427595\pi$
$992$	−26.7871			−0.850491
$993$	−1.78115	+	14.6691i	−0.0565231	+	0.465509i
$994$	1.39321	−	2.01841i	0.0441899	−	0.0640201i
$995$	28.0998			0.890824
$996$	−9.03507	−	13.0896i	−0.286287	−	0.414758i
$997$	0.947346	+	7.80210i	0.0300028	+	0.247095i	0.999992	+	0.00394793i	$0.00125667\pi$
$997$	0.947346	+	7.80210i	0.0300028	+	0.247095i	−0.969989	+	0.243147i	$0.921820\pi$
$998$	21.8664	−	57.6570i	0.692169	−	1.82510i
$999$	0.633941	+	5.22097i	0.0200570	+	0.165184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.79.3	✓	204
169.92	even	13	inner	507.2.m.b.430.3	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.79.3	✓	204	1.1	even	1	trivial
507.2.m.b.430.3	yes	204	169.92	even	13	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.m (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80313 - 0.946355i) q^{2} +(-0.970942 - 0.239316i) q^{3} +(1.21956 + 1.76683i) q^{4} +(-0.526754 - 1.38893i) q^{5} +(1.52426 + 1.35037i) q^{6} +(-0.593546 - 4.88829i) q^{7} +(-0.0360490 - 0.296891i) q^{8} +(0.885456 + 0.464723i) q^{9} +(-0.364621 + 3.00293i) q^{10} +(2.35918 - 1.23819i) q^{11} +(-0.761288 - 2.00735i) q^{12} +(0.154800 - 3.60223i) q^{13} +(-3.55582 + 9.37593i) q^{14} +(0.179053 + 1.47464i) q^{15} +(1.30661 - 3.44526i) q^{16} +(-0.00730277 - 0.0601437i) q^{17} +(-1.15680 - 1.67591i) q^{18} +5.70075 q^{19} +(1.81161 - 2.62457i) q^{20} +(-0.593546 + 4.88829i) q^{21} -5.42568 q^{22} -4.11426 q^{23} +(-0.0360490 + 0.296891i) q^{24} +(2.09088 - 1.85236i) q^{25} +(-3.68811 + 6.34878i) q^{26} +(-0.748511 - 0.663123i) q^{27} +(7.91294 - 7.01025i) q^{28} +(-5.98063 - 3.13887i) q^{29} +(1.07267 - 2.82841i) q^{30} +(2.47487 + 2.19254i) q^{31} +(-6.06415 + 5.37237i) q^{32} +(-2.58695 + 0.637625i) q^{33} +(-0.0437495 + 0.115358i) q^{34} +(-6.47687 + 3.39932i) q^{35} +(0.258776 + 2.13121i) q^{36} +(-3.93666 - 3.48758i) q^{37} +(-10.2792 - 5.39494i) q^{38} +(-1.01237 + 3.46051i) q^{39} +(-0.393373 + 0.206458i) q^{40} +(4.12823 + 1.01752i) q^{41} +(5.69630 - 8.25252i) q^{42} +(-4.52647 + 4.01010i) q^{43} +(5.06484 + 2.65823i) q^{44} +(0.179053 - 1.47464i) q^{45} +(7.41855 + 3.89355i) q^{46} +(-0.466917 + 0.676446i) q^{47} +(-2.09315 + 3.03245i) q^{48} +(-16.7465 + 4.12764i) q^{49} +(-5.52312 + 1.36133i) q^{50} +(-0.00730277 + 0.0601437i) q^{51} +(6.55332 - 4.11962i) q^{52} +(0.375244 + 3.09041i) q^{53} +(0.722112 + 1.90405i) q^{54} +(-2.96248 - 2.62453i) q^{55} +(-1.42989 + 0.352436i) q^{56} +(-5.53510 - 1.36428i) q^{57} +(7.81335 + 11.3196i) q^{58} +(2.64411 + 6.97194i) q^{59} +(-2.38707 + 2.11476i) q^{60} +(-0.522904 + 4.30650i) q^{61} +(-2.38758 - 6.29554i) q^{62} +(1.74614 - 4.60420i) q^{63} +(8.86334 - 2.18462i) q^{64} +(-5.08480 + 1.68248i) q^{65} +(5.26802 + 1.29845i) q^{66} +(-3.54428 + 5.13478i) q^{67} +(0.0973578 - 0.0862515i) q^{68} +(3.99471 + 0.984607i) q^{69} +14.8956 q^{70} +(-0.237474 - 0.0585321i) q^{71} +(0.106052 - 0.279636i) q^{72} +(-6.39416 + 3.35592i) q^{73} +(3.79782 + 10.0140i) q^{74} +(-2.47342 + 1.29815i) q^{75} +(6.95240 + 10.0723i) q^{76} +(-7.45294 - 10.7974i) q^{77} +(5.10030 - 5.28168i) q^{78} +(2.58585 - 3.74625i) q^{79} -5.47350 q^{80} +(0.568065 + 0.822984i) q^{81} +(-6.48080 - 5.74149i) q^{82} +(7.19320 - 1.77297i) q^{83} +(-9.36066 + 4.91285i) q^{84} +(-0.0796889 + 0.0418240i) q^{85} +(11.9568 - 2.94708i) q^{86} +(5.05566 + 4.47892i) q^{87} +(-0.452654 - 0.655783i) q^{88} -11.6785 q^{89} +(-1.71839 + 2.48951i) q^{90} +(-17.7006 + 1.38138i) q^{91} +(-5.01758 - 7.26922i) q^{92} +(-1.87824 - 2.72110i) q^{93} +(1.48207 - 0.777851i) q^{94} +(-3.00289 - 7.91798i) q^{95} +(7.17363 - 3.76501i) q^{96} +(6.23992 - 16.4533i) q^{97} +(34.1023 + 8.40547i) q^{98} +2.66437 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19}+ \cdots + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

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Database

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