LMFDB - Embedded newform 209.2.f.b.58.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [209,2,Mod(20,209)] 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("209.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(209, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [28] 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:	$1.66887340224$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			58.6
Character	$\chi$	$=$	209.58
Dual form			209.2.f.b.191.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50708 - 1.09496i) q^{2} +(0.282042 + 0.868036i) q^{3} +(0.454323 - 1.39826i) q^{4} +(0.593812 + 0.431430i) q^{5} +(1.37552 + 0.999375i) q^{6} +(0.0915185 - 0.281665i) q^{7} +(0.304970 + 0.938602i) q^{8} +(1.75311 - 1.27371i) q^{9} +1.36732 q^{10} +(-1.65611 - 2.87355i) q^{11} +1.34188 q^{12} +(-2.96634 + 2.15518i) q^{13} +(-0.170485 - 0.524700i) q^{14} +(-0.207017 + 0.637132i) q^{15} +(3.86621 + 2.80896i) q^{16} +(-1.81772 - 1.32065i) q^{17} +(1.24742 - 3.83917i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(0.873034 - 0.634296i) q^{20} +0.270307 q^{21} +(-5.64231 - 2.51729i) q^{22} -5.83266 q^{23} +(-0.728726 + 0.529450i) q^{24} +(-1.37860 - 4.24291i) q^{25} +(-2.11069 + 6.49604i) q^{26} +(3.81526 + 2.77195i) q^{27} +(-0.352262 - 0.255933i) q^{28} +(-1.76976 + 5.44677i) q^{29} +(0.385641 + 1.18688i) q^{30} +(-5.47079 + 3.97476i) q^{31} +6.92857 q^{32} +(2.02725 - 2.24803i) q^{33} -4.18550 q^{34} +(0.175863 - 0.127772i) q^{35} +(-0.984502 - 3.02998i) q^{36} +(2.21666 - 6.82217i) q^{37} +(-1.50708 - 1.09496i) q^{38} +(-2.70740 - 1.96704i) q^{39} +(-0.223846 + 0.688926i) q^{40} +(2.39926 + 7.38417i) q^{41} +(0.407374 - 0.295975i) q^{42} +0.607360 q^{43} +(-4.77038 + 1.01016i) q^{44} +1.59054 q^{45} +(-8.79029 + 6.38652i) q^{46} +(-3.42710 - 10.5475i) q^{47} +(-1.34785 + 4.14825i) q^{48} +(5.59216 + 4.06294i) q^{49} +(-6.72346 - 4.88488i) q^{50} +(0.633698 - 1.95032i) q^{51} +(1.66582 + 5.12687i) q^{52} +(2.66534 - 1.93648i) q^{53} +8.78507 q^{54} +(0.256315 - 2.42085i) q^{55} +0.292282 q^{56} +(0.738395 - 0.536476i) q^{57} +(3.29680 + 10.1465i) q^{58} +(1.75566 - 5.40337i) q^{59} +(0.796824 + 0.578927i) q^{60} +(3.67616 + 2.67088i) q^{61} +(-3.89272 + 11.9806i) q^{62} +(-0.198317 - 0.610358i) q^{63} +(2.70948 - 1.96856i) q^{64} -2.69126 q^{65} +(0.593734 - 5.60771i) q^{66} +8.01514 q^{67} +(-2.67244 + 1.94164i) q^{68} +(-1.64506 - 5.06296i) q^{69} +(0.125135 - 0.385126i) q^{70} +(2.66426 + 1.93570i) q^{71} +(1.73015 + 1.25703i) q^{72} +(-4.26185 + 13.1166i) q^{73} +(-4.12931 - 12.7087i) q^{74} +(3.29417 - 2.39335i) q^{75} -1.47022 q^{76} +(-0.960943 + 0.203486i) q^{77} -6.23410 q^{78} +(-1.96725 + 1.42929i) q^{79} +(1.08393 + 3.33599i) q^{80} +(0.678799 - 2.08913i) q^{81} +(11.7012 + 8.50144i) q^{82} +(-3.22570 - 2.34361i) q^{83} +(0.122807 - 0.377960i) q^{84} +(-0.509615 - 1.56844i) q^{85} +(0.915339 - 0.665033i) q^{86} -5.22713 q^{87} +(2.19205 - 2.43078i) q^{88} +3.00216 q^{89} +(2.39706 - 1.74157i) q^{90} +(0.335562 + 1.03275i) q^{91} +(-2.64991 + 8.15559i) q^{92} +(-4.99323 - 3.62779i) q^{93} +(-16.7140 - 12.1434i) q^{94} +(0.226816 - 0.698068i) q^{95} +(1.95415 + 6.01424i) q^{96} +(8.00955 - 5.81928i) q^{97} +12.8766 q^{98} +(-6.56342 - 2.92825i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + q^{3} - 6 q^{4} + 7 q^{5} - 14 q^{6} - 12 q^{7} + 4 q^{8} + 6 q^{9} - 12 q^{10} + 2 q^{11} - 16 q^{12} + 5 q^{13} + 23 q^{14} + 15 q^{15} + 30 q^{16} - 15 q^{17} - 38 q^{18} + 7 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + q^3 - 6 * q^4 + 7 * q^5 - 14 * q^6 - 12 * q^7 + 4 * q^8 + 6 * q^9 - 12 * q^10 + 2 * q^11 - 16 * q^12 + 5 * q^13 + 23 * q^14 + 15 * q^15 + 30 * q^16 - 15 * q^17 - 38 * q^18 + 7 * q^19 + 8 * q^20 - 18 * q^21 + 18 * q^22 - 42 * q^23 - 4 * q^24 + 2 * q^25 + 14 * q^26 + 28 * q^27 - 15 * q^28 - 21 * q^29 + 10 * q^30 + 19 * q^31 - 4 * q^32 - 28 * q^33 - 20 * q^34 - 16 * q^35 + 46 * q^36 + 23 * q^37 + 2 * q^38 - 4 * q^39 - 84 * q^40 + 5 * q^41 + 34 * q^42 - 12 * q^43 - 11 * q^44 - 22 * q^45 + 19 * q^46 + 43 * q^47 + 28 * q^48 - q^49 - 43 * q^50 - 6 * q^51 - 21 * q^52 + 46 * q^53 + 60 * q^54 - 92 * q^55 - 60 * q^56 - q^57 + 63 * q^58 + 3 * q^59 + 40 * q^60 - 12 * q^61 - 25 * q^62 + 9 * q^63 + 44 * q^64 + 26 * q^65 + 13 * q^66 + 24 * q^67 - 19 * q^68 - q^69 - 14 * q^70 + 14 * q^71 - 7 * q^72 + 7 * q^73 - 58 * q^74 + 50 * q^75 - 14 * q^76 - 60 * q^77 + 6 * q^78 - 62 * q^79 + 85 * q^80 + 31 * q^81 + 36 * q^82 + 5 * q^83 - 59 * q^84 - 9 * q^85 + 34 * q^86 - 34 * q^87 - 16 * q^88 - 108 * q^89 - 28 * q^90 + 45 * q^91 + 62 * q^92 + 13 * q^93 - 80 * q^94 - 7 * q^95 - 40 * q^96 + 38 * q^97 + 84 * q^98 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.50708	−	1.09496i	1.06567	−	0.774252i	0.0905377	−	0.995893i	$-0.471141\pi$
$2$	1.50708	−	1.09496i	1.06567	−	0.774252i	0.975128	+	0.221641i	$0.0711414\pi$
$3$	0.282042	+	0.868036i	0.162837	+	0.501161i	0.998870	−	0.0475178i	$-0.0151311\pi$
$3$	0.282042	+	0.868036i	0.162837	+	0.501161i	−0.836033	+	0.548679i	$0.815131\pi$
$4$	0.454323	−	1.39826i	0.227161	−	0.699131i
$5$	0.593812	+	0.431430i	0.265561	+	0.192941i	0.712595	−	0.701576i	$-0.247520\pi$
$5$	0.593812	+	0.431430i	0.265561	+	0.192941i	−0.447034	+	0.894517i	$0.647520\pi$
$6$	1.37552	+	0.999375i	0.561554	+	0.407993i
$7$	0.0915185	−	0.281665i	0.0345907	−	0.106459i	−0.932270	−	0.361762i	$-0.882175\pi$
$7$	0.0915185	−	0.281665i	0.0345907	−	0.106459i	0.966861	+	0.255303i	$0.0821752\pi$
$8$	0.304970	+	0.938602i	0.107823	+	0.331846i
$9$	1.75311	−	1.27371i	0.584371	−	0.424570i
$10$	1.36732			0.432384
$11$	−1.65611	−	2.87355i	−0.499337	−	0.866408i
$11$	−1.65611	−	2.87355i	−0.499337	−	0.866408i
$12$	1.34188			0.387367
$13$	−2.96634	+	2.15518i	−0.822716	+	0.597738i	−0.917489	−	0.397761i	$-0.869787\pi$
$13$	−2.96634	+	2.15518i	−0.822716	+	0.597738i	0.0947733	+	0.995499i	$0.469787\pi$
$14$	−0.170485	−	0.524700i	−0.0455641	−	0.140232i
$15$	−0.207017	+	0.637132i	−0.0534515	+	0.164507i
$16$	3.86621	+	2.80896i	0.966552	+	0.702241i
$17$	−1.81772	−	1.32065i	−0.440861	−	0.320304i	0.345116	−	0.938560i	$-0.387840\pi$
$17$	−1.81772	−	1.32065i	−0.440861	−	0.320304i	−0.785977	+	0.618256i	$0.787840\pi$
$18$	1.24742	−	3.83917i	0.294020	−	0.904900i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	0.873034	−	0.634296i	0.195216	−	0.141833i
$21$	0.270307			0.0589859
$22$	−5.64231	−	2.51729i	−1.20294	−	0.536689i
$23$	−5.83266			−1.21619			−0.608097	−	0.793863i	$-0.708067\pi$
$23$	−5.83266			−1.21619			−0.608097	+	0.793863i	$0.708067\pi$
$24$	−0.728726	+	0.529450i	−0.148750	+	0.108074i
$25$	−1.37860	−	4.24291i	−0.275721	−	0.848581i
$26$	−2.11069	+	6.49604i	−0.413941	+	1.27398i
$27$	3.81526	+	2.77195i	0.734248	+	0.533462i
$28$	−0.352262	−	0.255933i	−0.0665713	−	0.0483669i
$29$	−1.76976	+	5.44677i	−0.328636	+	1.01144i	0.641136	+	0.767427i	$0.278464\pi$
$29$	−1.76976	+	5.44677i	−0.328636	+	1.01144i	−0.969772	+	0.244012i	$0.921536\pi$
$30$	0.385641	+	1.18688i	0.0704082	+	0.216694i
$31$	−5.47079	+	3.97476i	−0.982583	+	0.713888i	−0.958284	−	0.285816i	$-0.907735\pi$
$31$	−5.47079	+	3.97476i	−0.982583	+	0.713888i	−0.0242986	+	0.999705i	$0.507735\pi$
$32$	6.92857			1.22481
$33$	2.02725	−	2.24803i	0.352899	−	0.391331i
$34$	−4.18550			−0.717807
$35$	0.175863	−	0.127772i	0.0297263	−	0.0215975i
$36$	−0.984502	−	3.02998i	−0.164084	−	0.504997i
$37$	2.21666	−	6.82217i	0.364416	−	1.12156i	−0.585930	−	0.810362i	$-0.699270\pi$
$37$	2.21666	−	6.82217i	0.364416	−	1.12156i	0.950346	−	0.311196i	$-0.100730\pi$
$38$	−1.50708	−	1.09496i	−0.244481	−	0.177625i
$39$	−2.70740	−	1.96704i	−0.433531	−	0.314979i
$40$	−0.223846	+	0.688926i	−0.0353931	+	0.108929i
$41$	2.39926	+	7.38417i	0.374702	+	1.15321i	0.943680	+	0.330861i	$0.107339\pi$
$41$	2.39926	+	7.38417i	0.374702	+	1.15321i	−0.568978	+	0.822353i	$0.692661\pi$
$42$	0.407374	−	0.295975i	0.0628592	−	0.0456699i
$43$	0.607360			0.0926215			0.0463107	−	0.998927i	$-0.485254\pi$
$43$	0.607360			0.0926215			0.0463107	+	0.998927i	$0.485254\pi$
$44$	−4.77038	+	1.01016i	−0.719162	+	0.152287i
$45$	1.59054			0.237103
$46$	−8.79029	+	6.38652i	−1.29606	+	0.941640i
$47$	−3.42710	−	10.5475i	−0.499893	−	1.53851i	−0.809190	−	0.587547i	$-0.800094\pi$
$47$	−3.42710	−	10.5475i	−0.499893	−	1.53851i	0.309296	−	0.950966i	$-0.399906\pi$
$48$	−1.34785	+	4.14825i	−0.194545	+	0.598749i
$49$	5.59216	+	4.06294i	0.798880	+	0.580420i
$50$	−6.72346	−	4.88488i	−0.950842	−	0.690827i
$51$	0.633698	−	1.95032i	0.0887355	−	0.273100i
$52$	1.66582	+	5.12687i	0.231008	+	0.710969i
$53$	2.66534	−	1.93648i	0.366113	−	0.265997i	−0.389484	−	0.921033i	$-0.627347\pi$
$53$	2.66534	−	1.93648i	0.366113	−	0.265997i	0.755597	+	0.655037i	$0.227347\pi$
$54$	8.78507			1.19550
$55$	0.256315	−	2.42085i	0.0345615	−	0.326427i
$56$	0.292282			0.0390578
$57$	0.738395	−	0.536476i	0.0978029	−	0.0710579i
$58$	3.29680	+	10.1465i	0.432892	+	1.33230i
$59$	1.75566	−	5.40337i	0.228568	−	0.703459i	−0.769342	−	0.638837i	$-0.779416\pi$
$59$	1.75566	−	5.40337i	0.228568	−	0.703459i	0.997910	−	0.0646222i	$-0.0205842\pi$
$60$	0.796824	+	0.578927i	0.102870	+	0.0747391i
$61$	3.67616	+	2.67088i	0.470683	+	0.341972i	0.797708	−	0.603044i	$-0.206046\pi$
$61$	3.67616	+	2.67088i	0.470683	+	0.341972i	−0.327024	+	0.945016i	$0.606046\pi$
$62$	−3.89272	+	11.9806i	−0.494376	+	1.52153i
$63$	−0.198317	−	0.610358i	−0.0249856	−	0.0768979i
$64$	2.70948	−	1.96856i	0.338685	−	0.246069i
$65$	−2.69126			−0.333810
$66$	0.593734	−	5.60771i	0.0730835	−	0.690261i
$67$	8.01514			0.979206			0.489603	−	0.871946i	$-0.337142\pi$
$67$	8.01514			0.979206			0.489603	+	0.871946i	$0.337142\pi$
$68$	−2.67244	+	1.94164i	−0.324081	+	0.235459i
$69$	−1.64506	−	5.06296i	−0.198041	−	0.609509i
$70$	0.125135	−	0.385126i	0.0149565	−	0.0460313i
$71$	2.66426	+	1.93570i	0.316190	+	0.229725i	0.734548	−	0.678557i	$-0.237394\pi$
$71$	2.66426	+	1.93570i	0.316190	+	0.229725i	−0.418358	+	0.908282i	$0.637394\pi$
$72$	1.73015	+	1.25703i	0.203901	+	0.148142i
$73$	−4.26185	+	13.1166i	−0.498812	+	1.53519i	0.312118	+	0.950043i	$0.398962\pi$
$73$	−4.26185	+	13.1166i	−0.498812	+	1.53519i	−0.810930	+	0.585143i	$0.801038\pi$
$74$	−4.12931	−	12.7087i	−0.480022	−	1.47736i
$75$	3.29417	−	2.39335i	0.380378	−	0.276361i
$76$	−1.47022			−0.168646
$77$	−0.960943	+	0.203486i	−0.109510	+	0.0231894i
$78$	−6.23410			−0.705873
$79$	−1.96725	+	1.42929i	−0.221333	+	0.160808i	−0.692926	−	0.721008i	$-0.743679\pi$
$79$	−1.96725	+	1.42929i	−0.221333	+	0.160808i	0.471594	+	0.881816i	$0.343679\pi$
$80$	1.08393	+	3.33599i	0.121187	+	0.372975i
$81$	0.678799	−	2.08913i	0.0754221	−	0.232125i
$82$	11.7012	+	8.50144i	1.29218	+	0.938827i
$83$	−3.22570	−	2.34361i	−0.354067	−	0.257245i	0.396506	−	0.918032i	$-0.370223\pi$
$83$	−3.22570	−	2.34361i	−0.354067	−	0.257245i	−0.750573	+	0.660787i	$0.770223\pi$
$84$	0.122807	−	0.377960i	0.0133993	−	0.0412388i
$85$	−0.509615	−	1.56844i	−0.0552756	−	0.170121i
$86$	0.915339	−	0.665033i	0.0987036	−	0.0717123i
$87$	−5.22713			−0.560408
$88$	2.19205	−	2.43078i	0.233674	−	0.259122i
$89$	3.00216			0.318228			0.159114	−	0.987260i	$-0.449136\pi$
$89$	3.00216			0.318228			0.159114	+	0.987260i	$0.449136\pi$
$90$	2.39706	−	1.74157i	0.252673	−	0.183578i
$91$	0.335562	+	1.03275i	0.0351764	+	0.108262i
$92$	−2.64991	+	8.15559i	−0.276272	+	0.850279i
$93$	−4.99323	−	3.62779i	−0.517774	−	0.376185i
$94$	−16.7140	−	12.1434i	−1.72392	−	1.25250i
$95$	0.226816	−	0.698068i	0.0232708	−	0.0716203i
$96$	1.95415	+	6.01424i	0.199444	+	0.613826i
$97$	8.00955	−	5.81928i	0.813247	−	0.590858i	−0.101523	−	0.994833i	$-0.532372\pi$
$97$	8.00955	−	5.81928i	0.813247	−	0.590858i	0.914770	+	0.403975i	$0.132372\pi$
$98$	12.8766			1.30073
$99$	−6.56342	−	2.92825i	−0.659649	−	0.294300i
$100$	−6.55902			−0.655902
$101$	5.47532	−	3.97806i	0.544815	−	0.395831i	−0.281055	−	0.959692i	$-0.590684\pi$
$101$	5.47532	−	3.97806i	0.544815	−	0.395831i	0.825870	+	0.563860i	$0.190684\pi$
$102$	−1.18049	−	3.63316i	−0.116886	−	0.359737i
$103$	−3.41390	+	10.5069i	−0.336381	+	1.03527i	0.629656	+	0.776874i	$0.283196\pi$
$103$	−3.41390	+	10.5069i	−0.336381	+	1.03527i	−0.966038	+	0.258401i	$0.916804\pi$
$104$	−2.92750	−	2.12695i	−0.287065	−	0.208565i
$105$	0.160512	+	0.116619i	0.0156643	+	0.0113808i
$106$	1.89651	−	5.83687i	0.184206	−	0.566927i
$107$	−4.08695	−	12.5783i	−0.395100	−	1.21599i	−0.928884	−	0.370372i	$-0.879230\pi$
$107$	−4.08695	−	12.5783i	−0.395100	−	1.21599i	0.533784	−	0.845621i	$-0.320770\pi$
$108$	5.60927	−	4.07538i	0.539753	−	0.392153i
$109$	12.9485			1.24024			0.620119	−	0.784507i	$-0.287084\pi$
$109$	12.9485			1.24024			0.620119	+	0.784507i	$0.287084\pi$
$110$	−2.26444	−	3.92906i	−0.215906	−	0.374621i
$111$	6.54708			0.621421
$112$	1.14502	−	0.831903i	0.108194	−	0.0786074i
$113$	−5.14792	−	15.8437i	−0.484276	−	1.49045i	−0.833027	−	0.553233i	$-0.813394\pi$
$113$	−5.14792	−	15.8437i	−0.484276	−	1.49045i	0.348751	−	0.937215i	$-0.386606\pi$
$114$	0.525402	−	1.61702i	0.0492085	−	0.151448i
$115$	−3.46351	−	2.51639i	−0.322974	−	0.234654i
$116$	6.81196	+	4.94918i	0.632474	+	0.459520i
$117$	−2.45527	+	7.55653i	−0.226989	+	0.698601i
$118$	−3.27054	−	10.0657i	−0.301078	−	0.926622i
$119$	−0.538335	+	0.391123i	−0.0493491	+	0.0358542i
$120$	−0.661147			−0.0603542
$121$	−5.51458	+	9.51785i	−0.501325	+	0.865259i
$122$	8.46476			0.766363
$123$	−5.73303	+	4.16529i	−0.516930	+	0.375572i
$124$	3.07225	+	9.45542i	0.275896	+	0.849122i
$125$	2.14597	−	6.60460i	0.191941	−	0.590733i
$126$	−0.967196	−	0.702709i	−0.0861647	−	0.0626023i
$127$	−2.06781	−	1.50235i	−0.183489	−	0.133312i	0.492249	−	0.870454i	$-0.336175\pi$
$127$	−2.06781	−	1.50235i	−0.183489	−	0.133312i	−0.675738	+	0.737142i	$0.736175\pi$
$128$	−2.35417	+	7.24538i	−0.208081	+	0.640407i
$129$	0.171301	+	0.527210i	0.0150822	+	0.0464183i
$130$	−4.05594	+	2.94681i	−0.355729	+	0.258453i
$131$	7.47735			0.653299			0.326650	−	0.945145i	$-0.394080\pi$
$131$	7.47735			0.653299			0.326650	+	0.945145i	$0.394080\pi$
$132$	−2.22230	−	3.85596i	−0.193427	−	0.335618i
$133$	−0.296160			−0.0256803
$134$	12.0795	−	8.77624i	1.04351	−	0.758152i
$135$	1.06965	+	3.29204i	0.0920606	+	0.283333i
$136$	0.685214	−	2.10887i	0.0587566	−	0.180834i
$137$	1.02217	+	0.742649i	0.0873297	+	0.0634487i	0.630593	−	0.776113i	$-0.282812\pi$
$137$	1.02217	+	0.742649i	0.0873297	+	0.0634487i	−0.543264	+	0.839562i	$0.682812\pi$
$138$	−8.02295	−	5.82902i	−0.682959	−	0.496199i
$139$	−2.17264	+	6.68670i	−0.184281	+	0.567158i	−0.999935	−	0.0113812i	$-0.996377\pi$
$139$	−2.17264	+	6.68670i	−0.184281	+	0.567158i	0.815654	+	0.578540i	$0.196377\pi$
$140$	−0.0987603	−	0.303953i	−0.00834677	−	0.0256887i
$141$	8.18904	−	5.94968i	0.689641	−	0.501054i
$142$	6.13476			0.514818
$143$	11.1056	+	4.95472i	0.928697	+	0.414335i
$144$	10.3557			0.862975
$145$	−3.40080	+	2.47083i	−0.282421	+	0.205191i
$146$	7.93920	+	24.4344i	0.657053	+	2.02220i
$147$	−1.94956	+	6.00011i	−0.160797	+	0.494881i
$148$	−8.53210	−	6.19893i	−0.701334	−	0.509549i
$149$	9.73714	+	7.07444i	0.797697	+	0.579561i	0.910238	−	0.414086i	$-0.135899\pi$
$149$	9.73714	+	7.07444i	0.797697	+	0.579561i	−0.112540	+	0.993647i	$0.535899\pi$
$150$	2.34395	−	7.21395i	0.191383	−	0.589017i
$151$	−0.671339	−	2.06617i	−0.0546328	−	0.168143i	0.920017	−	0.391879i	$-0.128175\pi$
$151$	−0.671339	−	2.06617i	−0.0546328	−	0.168143i	−0.974650	+	0.223736i	$0.928175\pi$
$152$	0.798422	−	0.580088i	0.0647606	−	0.0470513i
$153$	−4.86879			−0.393618
$154$	−1.22541	+	1.35886i	−0.0987462	+	0.109500i
$155$	−4.96345			−0.398674
$156$	−3.98047	+	2.89198i	−0.318693	+	0.231544i
$157$	7.01031	+	21.5755i	0.559484	+	1.72191i	0.683799	+	0.729670i	$0.260327\pi$
$157$	7.01031	+	21.5755i	0.559484	+	1.72191i	−0.124315	+	0.992243i	$0.539673\pi$
$158$	−1.39979	+	4.30811i	−0.111361	+	0.342735i
$159$	2.43268	+	1.76744i	0.192924	+	0.140167i
$160$	4.11427	+	2.98919i	0.325261	+	0.236316i
$161$	−0.533796	+	1.64286i	−0.0420691	+	0.129475i
$162$	−1.26450	−	3.89174i	−0.0993487	−	0.305764i
$163$	1.40989	−	1.02435i	0.110431	−	0.0802330i	−0.531199	−	0.847247i	$-0.678258\pi$
$163$	1.40989	−	1.02435i	0.110431	−	0.0802330i	0.641630	+	0.767014i	$0.278258\pi$
$164$	11.4150			0.891365
$165$	2.17367	−	0.460290i	0.169220	−	0.0358335i
$166$	−7.42755			−0.576489
$167$	−6.60210	+	4.79671i	−0.510886	+	0.371181i	−0.813160	−	0.582041i	$-0.802254\pi$
$167$	−6.60210	+	4.79671i	−0.510886	+	0.371181i	0.302273	+	0.953221i	$0.402254\pi$
$168$	0.0824357	+	0.253711i	0.00636005	+	0.0195742i
$169$	0.137197	−	0.422250i	0.0105536	−	0.0324807i
$170$	−2.48540	−	1.80575i	−0.190621	−	0.138495i
$171$	−1.75311	−	1.27371i	−0.134064	−	0.0974031i
$172$	0.275937	−	0.849248i	0.0210400	−	0.0647545i
$173$	−0.715606	−	2.20241i	−0.0544065	−	0.167446i	0.920161	−	0.391540i	$-0.128058\pi$
$173$	−0.715606	−	2.20241i	−0.0544065	−	0.167446i	−0.974567	+	0.224094i	$0.928058\pi$
$174$	−7.87771	+	5.72349i	−0.597207	+	0.433897i
$175$	−1.32125			−0.0998768
$176$	1.66882	−	15.7617i	0.125792	−	1.18808i
$177$	5.18549			0.389766
$178$	4.52449	−	3.28723i	0.339125	−	0.246389i
$179$	−5.62198	−	17.3027i	−0.420207	−	1.29326i	−0.907510	−	0.420030i	$-0.862020\pi$
$179$	−5.62198	−	17.3027i	−0.420207	−	1.29326i	0.487304	−	0.873233i	$-0.337980\pi$
$180$	0.722617	−	2.22399i	0.0538607	−	0.165766i
$181$	13.4213	+	9.75113i	0.997596	+	0.724796i	0.961571	−	0.274555i	$-0.0885306\pi$
$181$	13.4213	+	9.75113i	0.997596	+	0.724796i	0.0360244	+	0.999351i	$0.488531\pi$
$182$	1.63654	+	1.18902i	0.121308	+	0.0881357i
$183$	−1.28159	+	3.94434i	−0.0947380	+	0.291574i
$184$	−1.77879	−	5.47455i	−0.131134	−	0.403589i
$185$	4.25957	−	3.09476i	0.313170	−	0.227531i
$186$	−11.4975			−0.843035
$187$	−0.784604	+	7.41045i	−0.0573759	+	0.541905i
$188$	−16.3052			−1.18918
$189$	1.12993	−	0.820941i	0.0821902	−	0.0597147i
$190$	−0.422525	−	1.30040i	−0.0306532	−	0.0943408i
$191$	−5.82219	+	17.9189i	−0.421279	+	1.29656i	0.485234	+	0.874384i	$0.338734\pi$
$191$	−5.82219	+	17.9189i	−0.421279	+	1.29656i	−0.906513	+	0.422178i	$0.861266\pi$
$192$	2.47296	+	1.79671i	0.178471	+	0.129667i
$193$	−2.25267	−	1.63666i	−0.162151	−	0.117809i	0.503751	−	0.863849i	$-0.331953\pi$
$193$	−2.25267	−	1.63666i	−0.162151	−	0.117809i	−0.665902	+	0.746040i	$0.731953\pi$
$194$	5.69917	−	17.5402i	0.409176	−	1.25932i
$195$	−0.759048	−	2.33611i	−0.0543565	−	0.167292i
$196$	8.22170	−	5.97341i	0.587264	−	0.426672i
$197$	−22.3866			−1.59498			−0.797488	−	0.603334i	$-0.793838\pi$
$197$	−22.3866			−1.59498			−0.797488	+	0.603334i	$0.793838\pi$
$198$	−13.0979	+	2.77357i	−0.930827	+	0.197109i
$199$	−22.5321			−1.59726			−0.798628	−	0.601825i	$-0.794440\pi$
$199$	−22.5321			−1.59726			−0.798628	+	0.601825i	$0.794440\pi$
$200$	3.56197	−	2.58792i	0.251869	−	0.182994i
$201$	2.26061	+	6.95743i	0.159451	+	0.490739i
$202$	3.89595	−	11.9905i	0.274118	−	0.843648i
$203$	1.37220	+	0.996959i	0.0963093	+	0.0699728i
$204$	−2.43916	−	1.77215i	−0.170775	−	0.124075i
$205$	−1.76104	+	5.41993i	−0.122996	+	0.378544i
$206$	6.35958	+	19.5728i	0.443093	+	1.36370i
$207$	−10.2253	+	7.42913i	−0.710709	+	0.516360i
$208$	−17.5223			−1.21495
$209$	−2.22114	+	2.46303i	−0.153640	+	0.170372i
$210$	0.369596			0.0255046
$211$	−13.3379	+	9.69052i	−0.918216	+	0.667123i	−0.943079	−	0.332568i	$-0.892085\pi$
$211$	−13.3379	+	9.69052i	−0.918216	+	0.667123i	0.0248634	+	0.999691i	$0.492085\pi$
$212$	−1.49679	−	4.60663i	−0.102800	−	0.316385i
$213$	−0.928823	+	2.85862i	−0.0636419	+	0.195870i
$214$	−19.9321	−	14.4815i	−1.36253	−	0.989935i
$215$	0.360658	+	0.262033i	0.0245966	+	0.0178705i
$216$	−1.43822	+	4.42638i	−0.0978583	+	0.301177i
$217$	0.618873	+	1.90469i	0.0420118	+	0.129299i
$218$	19.5144	−	14.1780i	1.32168	−	0.960257i
$219$	−12.5877			−0.850600
$220$	−3.26853	−	1.45824i	−0.220364	−	0.0983145i
$221$	8.23821			0.554162
$222$	9.86697	−	7.16877i	0.662227	−	0.481136i
$223$	3.01063	+	9.26576i	0.201606	+	0.620481i	0.999836	+	0.0181271i	$0.00577036\pi$
$223$	3.01063	+	9.26576i	0.201606	+	0.620481i	−0.798229	+	0.602354i	$0.794230\pi$
$224$	0.634092	−	1.95153i	0.0423670	−	0.130392i
$225$	−7.82108	−	5.68235i	−0.521405	−	0.378823i
$226$	−25.1065	−	18.2409i	−1.67006	−	1.21337i
$227$	−3.42655	+	10.5458i	−0.227428	+	0.699951i	0.770608	+	0.637309i	$0.219953\pi$
$227$	−3.42655	+	10.5458i	−0.227428	+	0.699951i	−0.998036	+	0.0626421i	$0.980047\pi$
$228$	−0.414663	−	1.27620i	−0.0274618	−	0.0845186i
$229$	−4.91880	+	3.57372i	−0.325043	+	0.236158i	−0.738325	−	0.674446i	$-0.764383\pi$
$229$	−4.91880	+	3.57372i	−0.325043	+	0.236158i	0.413281	+	0.910604i	$0.364383\pi$
$230$	−7.97511			−0.525863
$231$	−0.447660	−	0.776741i	−0.0294538	−	0.0511058i
$232$	−5.65207			−0.371076
$233$	20.9127	−	15.1940i	1.37004	−	0.995390i	0.372303	−	0.928111i	$-0.378568\pi$
$233$	20.9127	−	15.1940i	1.37004	−	0.995390i	0.997734	−	0.0672787i	$-0.0214317\pi$
$234$	4.57380	+	14.0767i	0.298998	+	0.920223i
$235$	2.51546	−	7.74179i	0.164091	−	0.505019i
$236$	−6.75769	−	4.90975i	−0.439888	−	0.319597i
$237$	−1.79552	−	1.30452i	−0.116632	−	0.0847379i
$238$	−0.383050	+	1.17891i	−0.0248295	+	0.0764173i
$239$	−3.44432	−	10.6005i	−0.222795	−	0.685691i	−0.998508	−	0.0546060i	$-0.982610\pi$
$239$	−3.44432	−	10.6005i	−0.222795	−	0.685691i	0.775713	−	0.631085i	$-0.217390\pi$
$240$	−2.59005	+	1.88178i	−0.167187	+	0.121468i
$241$	3.42982			0.220934			0.110467	−	0.993880i	$-0.464765\pi$
$241$	3.42982			0.220934			0.110467	+	0.993880i	$0.464765\pi$
$242$	2.11073	+	20.3824i	0.135683	+	1.31023i
$243$	16.1527			1.03619
$244$	5.40475	−	3.92678i	0.346004	−	0.251386i
$245$	1.56782	+	4.82525i	0.100164	+	0.308274i
$246$	−4.07932	+	12.5549i	−0.260088	+	0.800468i
$247$	2.96634	+	2.15518i	0.188744	+	0.137131i
$248$	−5.39915	−	3.92271i	−0.342846	−	0.249092i
$249$	1.12455	−	3.46102i	0.0712658	−	0.219333i
$250$	−3.99762	−	12.3034i	−0.252831	−	0.778135i
$251$	9.27983	−	6.74219i	0.585738	−	0.425563i	−0.255050	−	0.966928i	$-0.582092\pi$
$251$	9.27983	−	6.74219i	0.585738	−	0.425563i	0.840788	+	0.541364i	$0.182092\pi$
$252$	−0.943540			−0.0594375
$253$	9.65955	+	16.7604i	0.607291	+	1.05372i
$254$	−4.76137			−0.298755
$255$	1.21773	−	0.884729i	0.0762569	−	0.0554039i
$256$	6.45533	+	19.8674i	0.403458	+	1.24172i
$257$	−2.71685	+	8.36160i	−0.169472	+	0.521583i	−0.999338	−	0.0363808i	$-0.988417\pi$
$257$	−2.71685	+	8.36160i	−0.169472	+	0.521583i	0.829866	+	0.557963i	$0.188417\pi$
$258$	0.835436	+	0.606980i	0.0520120	+	0.0377889i
$259$	−1.71870	−	1.24871i	−0.106795	−	0.0775910i
$260$	−1.22270	+	3.76308i	−0.0758286	+	0.233376i
$261$	3.83501	+	11.8030i	0.237381	+	0.730585i
$262$	11.2690	−	8.18738i	0.696199	−	0.505818i
$263$	−10.4488			−0.644302			−0.322151	−	0.946688i	$-0.604406\pi$
$263$	−10.4488			−0.644302			−0.322151	+	0.946688i	$0.604406\pi$
$264$	2.72825	+	1.21720i	0.167912	+	0.0749135i
$265$	2.41817			0.148547
$266$	−0.446337	+	0.324283i	−0.0273667	+	0.0198830i
$267$	0.846734	+	2.60598i	0.0518193	+	0.159483i
$268$	3.64146	−	11.2073i	0.222438	−	0.684593i
$269$	10.4964	+	7.62608i	0.639977	+	0.464971i	0.859842	−	0.510560i	$-0.170562\pi$
$269$	10.4964	+	7.62608i	0.639977	+	0.464971i	−0.219865	+	0.975530i	$0.570562\pi$
$270$	5.21668	+	3.79014i	0.317477	+	0.230661i
$271$	5.71168	−	17.5788i	0.346960	−	1.06783i	−0.613566	−	0.789643i	$-0.710266\pi$
$271$	5.71168	−	17.5788i	0.346960	−	1.06783i	0.960526	−	0.278190i	$-0.0897344\pi$
$272$	−3.31802	−	10.2118i	−0.201184	−	0.619182i
$273$	−0.801824	+	0.582560i	−0.0485286	+	0.0352581i
$274$	2.35366			0.142190
$275$	−9.90908	+	10.9882i	−0.597540	+	0.662615i
$276$	−7.82673			−0.471114
$277$	−9.95920	+	7.23578i	−0.598390	+	0.434756i	−0.845307	−	0.534281i	$-0.820583\pi$
$277$	−9.95920	+	7.23578i	−0.598390	+	0.434756i	0.246917	+	0.969037i	$0.420583\pi$
$278$	4.04731	+	12.4563i	0.242741	+	0.747081i
$279$	−4.52821	+	13.9364i	−0.271097	+	0.834351i
$280$	0.173560	+	0.126099i	0.0103722	+	0.00753586i
$281$	−2.62072	−	1.90406i	−0.156339	−	0.113587i	0.506866	−	0.862025i	$-0.330804\pi$
$281$	−2.62072	−	1.90406i	−0.156339	−	0.113587i	−0.663205	+	0.748438i	$0.730804\pi$
$282$	5.82688	−	17.9333i	0.346986	−	1.06791i
$283$	−2.44807	−	7.53439i	−0.145523	−	0.447873i	0.851555	−	0.524265i	$-0.175660\pi$
$283$	−2.44807	−	7.53439i	−0.145523	−	0.447873i	−0.997078	+	0.0763922i	$0.975660\pi$
$284$	3.91705	−	2.84590i	0.232434	−	0.168873i
$285$	0.669920			0.0396826
$286$	22.1622	−	4.69300i	1.31048	−	0.277503i
$287$	2.29944			0.135732
$288$	12.1466	−	8.82499i	0.715743	−	0.520017i
$289$	−3.69331	−	11.3668i	−0.217253	−	0.668637i
$290$	−2.41983	+	7.44747i	−0.142097	+	0.437330i
$291$	7.31037	+	5.31130i	0.428542	+	0.311354i
$292$	16.4042	+	11.9184i	0.959985	+	0.697470i
$293$	7.87599	−	24.2398i	0.460120	−	1.41610i	−0.404897	−	0.914362i	$-0.632693\pi$
$293$	7.87599	−	24.2398i	0.460120	−	1.41610i	0.865017	−	0.501742i	$-0.167307\pi$
$294$	3.63173	+	11.1773i	0.211807	+	0.651875i
$295$	3.37371	−	2.45114i	0.196425	−	0.142711i
$296$	7.07932			0.411477
$297$	1.64683	−	15.5540i	0.0955588	−	0.902536i
$298$	22.4208			1.29880
$299$	17.3017	−	12.5704i	1.00058	−	0.726966i
$300$	−1.84992	−	5.69347i	−0.106805	−	0.328712i
$301$	0.0555846	−	0.171072i	0.00320385	−	0.00986042i
$302$	−3.27413	−	2.37879i	−0.188405	−	0.136884i
$303$	4.99737	+	3.63080i	0.287091	+	0.208584i
$304$	1.47676	−	4.54500i	0.0846980	−	0.260674i
$305$	1.03065	+	3.17201i	0.0590147	+	0.181629i
$306$	−7.33765	+	5.33111i	−0.419465	+	0.304759i
$307$	−25.3685			−1.44786			−0.723928	−	0.689876i	$-0.757665\pi$
$307$	−25.3685			−1.44786			−0.723928	+	0.689876i	$0.757665\pi$
$308$	−0.152051	+	1.43610i	−0.00866393	+	0.0818293i
$309$	−10.0832			−0.573614
$310$	−7.48032	+	5.43477i	−0.424853	+	0.308674i
$311$	−8.54587	−	26.3015i	−0.484592	−	1.49142i	−0.832571	−	0.553918i	$-0.813132\pi$
$311$	−8.54587	−	26.3015i	−0.484592	−	1.49142i	0.347980	−	0.937502i	$-0.386868\pi$
$312$	1.02059	−	3.14106i	0.0577797	−	0.177828i
$313$	3.21164	+	2.33339i	0.181533	+	0.131891i	0.674841	−	0.737964i	$-0.264212\pi$
$313$	3.21164	+	2.33339i	0.181533	+	0.131891i	−0.493308	+	0.869855i	$0.664212\pi$
$314$	34.1893	+	24.8400i	1.92942	+	1.40180i
$315$	0.145563	−	0.447998i	0.00820157	−	0.0252418i
$316$	1.10476	+	3.40009i	0.0621473	+	0.191270i
$317$	−6.03020	+	4.38119i	−0.338690	+	0.246072i	−0.744109	−	0.668059i	$-0.767126\pi$
$317$	−6.03020	+	4.38119i	−0.338690	+	0.246072i	0.405419	+	0.914131i	$0.367126\pi$
$318$	5.60151			0.314117
$319$	18.5825	−	3.93497i	1.04042	−	0.220316i
$320$	2.45822			0.137419
$321$	9.76575	−	7.09523i	0.545071	−	0.396017i
$322$	0.994384	+	3.06040i	0.0554149	+	0.170549i
$323$	−0.694306	+	2.13686i	−0.0386322	+	0.118898i
$324$	−2.61275	−	1.89828i	−0.145153	−	0.105460i
$325$	13.2336	+	9.61479i	0.734069	+	0.533332i
$326$	1.00320	−	3.08754i	0.0555623	−	0.171003i
$327$	3.65201	+	11.2397i	0.201957	+	0.621559i
$328$	−6.19909	+	4.50390i	−0.342288	+	0.248687i
$329$	−3.28451			−0.181081
$330$	2.77190	−	3.07377i	0.152588	−	0.169206i
$331$	30.0258			1.65037			0.825184	−	0.564864i	$-0.191071\pi$
$331$	30.0258			1.65037			0.825184	+	0.564864i	$0.191071\pi$
$332$	−4.74249	+	3.44562i	−0.260278	+	0.189103i
$333$	−4.80342	−	14.7834i	−0.263226	−	0.810126i
$334$	−4.69770	+	14.4580i	−0.257047	+	0.791109i
$335$	4.75949	+	3.45797i	0.260039	+	0.188929i
$336$	1.04506	+	0.759283i	0.0570129	+	0.0414223i
$337$	3.71047	−	11.4197i	0.202122	−	0.622068i	−0.797697	−	0.603058i	$-0.793949\pi$
$337$	3.71047	−	11.4197i	0.202122	−	0.622068i	0.999819	−	0.0190099i	$-0.00605140\pi$
$338$	−0.255578	−	0.786589i	−0.0139016	−	0.0427848i
$339$	12.3010	−	8.93716i	0.668096	−	0.485400i
$340$	−2.42461			−0.131493
$341$	20.4819	+	9.13793i	1.10916	+	0.494847i
$342$	−4.03674			−0.218282
$343$	3.33336	−	2.42183i	0.179985	−	0.130767i
$344$	0.185227	+	0.570069i	0.00998675	+	0.0307361i
$345$	1.20746	−	3.71617i	0.0650074	−	0.200072i
$346$	−3.49002	−	2.53565i	−0.187624	−	0.136317i
$347$	−2.80807	−	2.04018i	−0.150745	−	0.109523i	0.509856	−	0.860260i	$-0.329699\pi$
$347$	−2.80807	−	2.04018i	−0.150745	−	0.109523i	−0.660601	+	0.750737i	$0.729699\pi$
$348$	−2.37481	+	7.30890i	−0.127303	+	0.391798i
$349$	−11.1246	−	34.2380i	−0.595487	−	1.83272i	−0.552288	−	0.833653i	$-0.686245\pi$
$349$	−11.1246	−	34.2380i	−0.595487	−	1.83272i	−0.0431983	−	0.999067i	$-0.513755\pi$
$350$	−1.99122	+	1.44671i	−0.106435	+	0.0773297i
$351$	−17.2914			−0.922948
$352$	−11.4745	−	19.9096i	−0.611592	−	1.06118i
$353$	−19.5047			−1.03813			−0.519064	−	0.854735i	$-0.673719\pi$
$353$	−19.5047			−1.03813			−0.519064	+	0.854735i	$0.673719\pi$
$354$	7.81495	−	5.67789i	0.415360	−	0.301777i
$355$	0.746953	+	2.29888i	0.0396441	+	0.122012i
$356$	1.36395	−	4.19780i	0.0722891	−	0.222483i
$357$	−0.491342	−	0.356981i	−0.0260046	−	0.0188934i
$358$	−27.4185	−	19.9207i	−1.44911	−	1.05284i
$359$	−6.31131	+	19.4242i	−0.333098	+	1.02517i	0.634553	+	0.772879i	$0.281184\pi$
$359$	−6.31131	+	19.4242i	−0.333098	+	1.02517i	−0.967651	+	0.252291i	$0.918816\pi$
$360$	0.485066	+	1.49288i	0.0255652	+	0.0786817i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	30.9040			1.62428
$363$	−9.81718	−	2.10242i	−0.515268	−	0.110348i
$364$	1.59651			0.0836800
$365$	−8.18965	+	5.95013i	−0.428666	+	0.311444i
$366$	2.38742	+	7.34772i	0.124792	+	0.384071i
$367$	1.55610	−	4.78918i	0.0812276	−	0.249993i	−0.902193	−	0.431333i	$-0.858043\pi$
$367$	1.55610	−	4.78918i	0.0812276	−	0.249993i	0.983420	+	0.181340i	$0.0580434\pi$
$368$	−22.5503	−	16.3837i	−1.17551	−	0.854061i
$369$	13.6115	+	9.88932i	0.708585	+	0.514817i
$370$	3.03088	−	9.32808i	0.157568	−	0.484944i
$371$	−0.301512	−	0.927957i	−0.0156537	−	0.0481771i
$372$	−7.34114	+	5.33365i	−0.380620	+	0.276537i
$373$	−29.6254			−1.53395			−0.766973	−	0.641679i	$-0.778238\pi$
$373$	−29.6254			−1.53395			−0.766973	+	0.641679i	$0.778238\pi$
$374$	6.93166	+	12.0272i	0.358428	+	0.621914i
$375$	6.33828			0.327308
$376$	8.85475	−	6.43335i	0.456649	−	0.331775i
$377$	−6.48901	−	19.9711i	−0.334201	−	1.02857i
$378$	0.803996	−	2.47445i	0.0413531	−	0.127272i
$379$	25.8973	+	18.8155i	1.33025	+	0.966486i	0.999743	+	0.0226836i	$0.00722105\pi$
$379$	25.8973	+	18.8155i	1.33025	+	0.966486i	0.330511	+	0.943802i	$0.392779\pi$
$380$	−0.873034	−	0.634296i	−0.0447857	−	0.0325387i
$381$	0.720887	−	2.21866i	0.0369322	−	0.113665i
$382$	10.8459	+	33.3802i	0.554923	+	1.70788i
$383$	8.57520	−	6.23025i	0.438173	−	0.318351i	−0.346736	−	0.937963i	$-0.612710\pi$
$383$	8.57520	−	6.23025i	0.438173	−	0.318351i	0.784908	+	0.619612i	$0.212710\pi$
$384$	−6.95322			−0.354830
$385$	−0.658410	−	0.293747i	−0.0335557	−	0.0149707i
$386$	−5.18702			−0.264012
$387$	1.06477	−	0.773601i	0.0541253	−	0.0393243i
$388$	−4.49795	−	13.8433i	−0.228349	−	0.702786i
$389$	3.05945	−	9.41601i	0.155120	−	0.477411i	−0.843053	−	0.537831i	$-0.819244\pi$
$389$	3.05945	−	9.41601i	0.155120	−	0.477411i	0.998173	+	0.0604199i	$0.0192440\pi$
$390$	−3.70188	−	2.68958i	−0.187452	−	0.136192i
$391$	10.6021	+	7.70290i	0.536173	+	0.389552i
$392$	−2.10804	+	6.48789i	−0.106472	+	0.327688i
$393$	2.10893	+	6.49061i	0.106381	+	0.327408i
$394$	−33.7383	+	24.5123i	−1.69971	+	1.23491i
$395$	−1.78482			−0.0898038
$396$	−7.07636	+	7.84701i	−0.355601	+	0.394327i
$397$	22.2668			1.11754			0.558770	−	0.829322i	$-0.311273\pi$
$397$	22.2668			1.11754			0.558770	+	0.829322i	$0.311273\pi$
$398$	−33.9576	+	24.6716i	−1.70214	+	1.23668i
$399$	−0.0835295	−	0.257078i	−0.00418171	−	0.0128700i
$400$	6.58820	−	20.2764i	0.329410	−	1.01382i
$401$	−4.05496	−	2.94610i	−0.202495	−	0.147121i	0.481917	−	0.876217i	$-0.339941\pi$
$401$	−4.05496	−	2.94610i	−0.202495	−	0.147121i	−0.684412	+	0.729096i	$0.739941\pi$
$402$	11.0250	+	8.01013i	0.549877	+	0.399509i
$403$	7.66194	−	23.5810i	0.381668	−	1.17465i
$404$	−3.07480	−	9.46325i	−0.152977	−	0.470814i
$405$	1.30439	−	0.947696i	0.0648158	−	0.0470914i
$406$	3.15964			0.156810
$407$	−23.2749	+	4.92861i	−1.15369	+	0.244302i
$408$	2.02383			0.100195
$409$	−12.7449	+	9.25972i	−0.630195	+	0.457863i	−0.856468	−	0.516201i	$-0.827346\pi$
$409$	−12.7449	+	9.25972i	−0.630195	+	0.457863i	0.226273	+	0.974064i	$0.427346\pi$
$410$	3.28056	+	10.0965i	0.162015	+	0.498632i
$411$	−0.356351	+	1.09674i	−0.0175775	+	0.0540980i
$412$	13.1404	+	9.54704i	0.647380	+	0.470349i
$413$	−1.36127	−	0.989017i	−0.0669835	−	0.0486663i
$414$	−7.27578	+	22.3926i	−0.357585	+	1.10053i
$415$	−0.904359	−	2.78333i	−0.0443932	−	0.136628i
$416$	−20.5525	+	14.9323i	−1.00767	+	0.732115i
$417$	−6.41707			−0.314245
$418$	−0.650519	+	6.14404i	−0.0318179	+	0.300515i
$419$	−21.7421			−1.06217			−0.531084	−	0.847319i	$-0.678215\pi$
$419$	−21.7421			−1.06217			−0.531084	+	0.847319i	$0.678215\pi$
$420$	0.235987	−	0.171455i	0.0115150	−	0.00836614i
$421$	−11.9469	−	36.7687i	−0.582255	−	1.79200i	−0.610024	−	0.792383i	$-0.708840\pi$
$421$	−11.9469	−	36.7687i	−0.582255	−	1.79200i	0.0277686	−	0.999614i	$-0.491160\pi$
$422$	−9.49050	+	29.2088i	−0.461990	+	1.42186i
$423$	−19.4426	−	14.1259i	−0.945330	−	0.686822i
$424$	2.63044	+	1.91112i	0.127745	+	0.0928124i
$425$	−3.09748	+	9.53306i	−0.150250	+	0.462421i
$426$	1.73026	+	5.32519i	0.0838314	+	0.258006i
$427$	1.08873	−	0.791009i	0.0526873	−	0.0382796i
$428$	−19.4446			−0.939889
$429$	−1.16863	+	11.0375i	−0.0564220	+	0.532896i
$430$	0.830455			0.0400481
$431$	−24.9980	+	18.1621i	−1.20411	+	0.874838i	−0.994683	−	0.102986i	$-0.967160\pi$
$431$	−24.9980	+	18.1621i	−1.20411	+	0.874838i	−0.209428	+	0.977824i	$0.567160\pi$
$432$	6.96429	+	21.4339i	0.335069	+	1.03124i
$433$	6.44978	−	19.8504i	0.309957	−	0.953949i	−0.667824	−	0.744319i	$-0.732774\pi$
$433$	6.44978	−	19.8504i	0.309957	−	0.953949i	0.977781	−	0.209630i	$-0.0672258\pi$
$434$	3.01825	+	2.19289i	0.144881	+	0.105262i
$435$	−3.10394	−	2.25514i	−0.148822	−	0.108126i
$436$	5.88278	−	18.1053i	0.281734	−	0.867089i
$437$	1.80239	+	5.54719i	0.0862201	+	0.265358i
$438$	−18.9707	+	13.7830i	−0.906455	+	0.658578i
$439$	25.4602			1.21515			0.607574	−	0.794263i	$-0.292143\pi$
$439$	25.4602			1.21515			0.607574	+	0.794263i	$0.292143\pi$
$440$	2.35038	−	0.497709i	0.112050	−	0.0237273i
$441$	14.9787			0.713271
$442$	12.4156	−	9.02048i	0.590551	−	0.429061i
$443$	−10.7264	−	33.0125i	−0.509628	−	1.56847i	−0.792849	−	0.609418i	$-0.791403\pi$
$443$	−10.7264	−	33.0125i	−0.509628	−	1.56847i	0.283221	−	0.959055i	$-0.408597\pi$
$444$	2.97449	−	9.15453i	0.141163	−	0.434455i
$445$	1.78272	+	1.29522i	0.0845089	+	0.0613993i
$446$	14.6829	+	10.6677i	0.695254	+	0.505131i
$447$	−3.39459	+	10.4475i	−0.160559	+	0.494149i
$448$	−0.306505	−	0.943326i	−0.0144810	−	0.0445679i
$449$	−25.6017	+	18.6008i	−1.20822	+	0.877824i	−0.995068	−	0.0991947i	$-0.968373\pi$
$449$	−25.6017	+	18.6008i	−1.20822	+	0.877824i	−0.213153	+	0.977019i	$0.568373\pi$
$450$	−18.0089			−0.848949
$451$	17.2453	−	19.1234i	0.812051	−	0.900487i
$452$	−24.4924			−1.15203
$453$	1.60416	−	1.16549i	0.0753702	−	0.0547597i
$454$	6.38315	+	19.6453i	0.299576	+	0.922001i
$455$	−0.246300	+	0.758033i	−0.0115467	+	0.0355371i
$456$	0.728726	+	0.529450i	0.0341257	+	0.0247938i
$457$	−27.8464	−	20.2316i	−1.30260	−	0.946394i	−0.302623	−	0.953110i	$-0.597862\pi$
$457$	−27.8464	−	20.2316i	−1.30260	−	0.946394i	−0.999977	+	0.00671615i	$0.997862\pi$
$458$	−3.49995	+	10.7718i	−0.163542	+	0.503331i
$459$	−3.27430	−	10.0772i	−0.152831	−	0.470366i
$460$	−5.09211	+	3.69964i	−0.237421	+	0.172496i
$461$	18.0496			0.840655			0.420328	−	0.907372i	$-0.361915\pi$
$461$	18.0496			0.840655			0.420328	+	0.907372i	$0.361915\pi$
$462$	−1.52516	−	0.680443i	−0.0709567	−	0.0316571i
$463$	19.7430			0.917534			0.458767	−	0.888557i	$-0.348291\pi$
$463$	19.7430			0.917534			0.458767	+	0.888557i	$0.348291\pi$
$464$	−22.1420	+	16.0871i	−1.02792	+	0.746826i
$465$	−1.39990	−	4.30846i	−0.0649189	−	0.199800i
$466$	14.8804	−	45.7970i	0.689319	−	2.12151i
$467$	−25.4857	−	18.5164i	−1.17934	−	0.856838i	−0.187239	−	0.982314i	$-0.559954\pi$
$467$	−25.4857	−	18.5164i	−1.17934	−	0.856838i	−0.992097	+	0.125477i	$0.959954\pi$
$468$	9.45052	+	6.86620i	0.436850	+	0.317390i
$469$	0.733534	−	2.25758i	0.0338714	−	0.104246i
$470$	−4.68593	−	14.4218i	−0.216146	−	0.665229i
$471$	−16.7511	+	12.1704i	−0.771851	+	0.560782i
$472$	5.60704			0.258085
$473$	−1.00586	−	1.74528i	−0.0462493	−	0.0802480i
$474$	−4.13439			−0.189899
$475$	−3.60923	+	2.62226i	−0.165603	+	0.120318i
$476$	0.302315	+	0.930429i	0.0138566	+	0.0426462i
$477$	2.20612	−	6.78975i	0.101011	−	0.310881i
$478$	−16.7980	−	12.2045i	−0.768322	−	0.558219i
$479$	6.19181	+	4.49861i	0.282911	+	0.205547i	0.720186	−	0.693781i	$-0.244056\pi$
$479$	6.19181	+	4.49861i	0.282911	+	0.205547i	−0.437275	+	0.899328i	$0.644056\pi$
$480$	−1.43433	+	4.41441i	−0.0654678	+	0.201489i
$481$	8.12760	+	25.0142i	0.370587	+	1.14055i
$482$	5.16901	−	3.75550i	0.235442	−	0.171059i
$483$	−1.57661			−0.0717383
$484$	10.8030	+	12.0350i	0.491047	+	0.547045i
$485$	7.26678			0.329968
$486$	24.3433	−	17.6865i	1.10424	−	0.802275i
$487$	7.81838	+	24.0625i	0.354285	+	1.09038i	0.956423	+	0.291984i	$0.0943155\pi$
$487$	7.81838	+	24.0625i	0.354285	+	1.09038i	−0.602139	+	0.798392i	$0.705685\pi$
$488$	−1.38578	+	4.26499i	−0.0627312	+	0.193067i
$489$	1.28682	+	0.934928i	0.0581919	+	0.0422789i
$490$	7.64627	+	5.55534i	0.345423	+	0.250965i
$491$	5.60480	−	17.2498i	0.252941	−	0.778473i	−0.741287	−	0.671188i	$-0.765784\pi$
$491$	5.60480	−	17.2498i	0.252941	−	0.778473i	0.994228	−	0.107285i	$-0.0342157\pi$
$492$	3.21952	+	9.90866i	0.145147	+	0.446717i
$493$	10.4102	−	7.56345i	0.468851	−	0.340641i
$494$	6.83034			0.307312
$495$	−2.63411	−	4.57049i	−0.118394	−	0.205428i
$496$	−32.3162			−1.45104
$497$	0.789048	−	0.573277i	0.0353936	−	0.0257150i
$498$	−2.09488	−	6.44738i	−0.0938738	−	0.288914i
$499$	3.95661	−	12.1772i	0.177122	−	0.545126i	−0.822602	−	0.568618i	$-0.807478\pi$
$499$	3.95661	−	12.1772i	0.177122	−	0.545126i	0.999724	+	0.0234918i	$0.00747835\pi$
$500$	−8.26000	−	6.00124i	−0.369398	−	0.268384i
$501$	−6.02579	−	4.37799i	−0.269212	−	0.195594i
$502$	6.60303	−	20.3220i	0.294708	−	0.907017i
$503$	6.03265	+	18.5666i	0.268982	+	0.827843i	0.990749	+	0.135706i	$0.0433304\pi$
$503$	6.03265	+	18.5666i	0.268982	+	0.827843i	−0.721767	+	0.692136i	$0.756670\pi$
$504$	0.512402	−	0.372282i	0.0228242	−	0.0165828i
$505$	4.96757			0.221054
$506$	32.9097	+	14.6825i	1.46301	+	0.652718i
$507$	0.405223			0.0179966
$508$	−3.04014	+	2.20879i	−0.134884	+	0.0979991i
$509$	1.31595	+	4.05009i	0.0583286	+	0.179517i	0.975976	−	0.217879i	$-0.0699139\pi$
$509$	1.31595	+	4.05009i	0.0583286	+	0.179517i	−0.917647	+	0.397396i	$0.869914\pi$
$510$	0.866468	−	2.66671i	0.0383678	−	0.118084i
$511$	3.30446	+	2.40083i	0.146181	+	0.106206i
$512$	19.1561	+	13.9177i	0.846589	+	0.615083i
$513$	1.45730	−	4.48511i	0.0643414	−	0.198023i
$514$	5.06109	+	15.5764i	0.223235	+	0.687047i
$515$	−6.56020	+	4.76627i	−0.289077	+	0.210027i
$516$	0.815003			0.0358785
$517$	−24.6331	+	27.3158i	−1.08336	+	1.20135i
$518$	−3.95750			−0.173883
$519$	1.70994	−	1.24234i	0.0750580	−	0.0545328i
$520$	−0.820754	−	2.52602i	−0.0359924	−	0.110773i
$521$	−4.54841	+	13.9986i	−0.199269	+	0.613288i	0.800631	+	0.599158i	$0.204498\pi$
$521$	−4.54841	+	13.9986i	−0.199269	+	0.613288i	−0.999900	+	0.0141301i	$0.995502\pi$
$522$	18.7034	+	13.5888i	0.818626	+	0.594766i
$523$	14.5457	+	10.5681i	0.636040	+	0.462110i	0.858487	−	0.512835i	$-0.171405\pi$
$523$	14.5457	+	10.5681i	0.636040	+	0.462110i	−0.222447	+	0.974945i	$0.571405\pi$
$524$	3.39713	−	10.4553i	0.148404	−	0.456742i
$525$	−0.372647	−	1.14689i	−0.0162636	−	0.0500543i
$526$	−15.7472	+	11.4410i	−0.686611	+	0.498852i
$527$	15.1936			0.661844
$528$	14.1524	−	2.99687i	0.615904	−	0.130422i
$529$	11.0200			0.479129
$530$	3.64437	−	2.64779i	0.158301	−	0.115013i
$531$	−3.80446	−	11.7089i	−0.165100	−	0.508124i
$532$	−0.134552	+	0.414109i	−0.00583358	+	0.0179539i
$533$	−23.0312	−	16.7332i	−0.997593	−	0.724794i
$534$	4.12953	+	3.00028i	0.178702	+	0.129835i
$535$	2.99979	−	9.23240i	0.129692	−	0.399151i
$536$	2.44438	+	7.52303i	0.105581	+	0.324945i
$537$	13.4337	−	9.76016i	0.579707	−	0.421182i
$538$	24.1691			1.04201
$539$	2.41381	−	22.7980i	0.103970	−	0.981981i
$540$	5.08909			0.219000
$541$	−13.2144	+	9.60085i	−0.568133	+	0.412773i	−0.834426	−	0.551119i	$-0.814201\pi$
$541$	−13.2144	+	9.60085i	−0.568133	+	0.412773i	0.266294	+	0.963892i	$0.414201\pi$
$542$	−10.6400	−	32.7466i	−0.457028	−	1.40659i
$543$	−4.67897	+	14.4004i	−0.200794	+	0.617979i
$544$	−12.5942	−	9.15020i	−0.539971	−	0.392312i
$545$	7.68896	+	5.58636i	0.329359	+	0.239293i
$546$	−0.570535	+	1.75593i	−0.0244167	+	0.0751467i
$547$	0.0715631	+	0.220249i	0.00305982	+	0.00941715i	0.952575	−	0.304305i	$-0.0984241\pi$
$547$	0.0715631	+	0.220249i	0.00305982	+	0.00941715i	−0.949515	+	0.313722i	$0.898424\pi$
$548$	1.50281	−	1.09186i	0.0641969	−	0.0466418i
$549$	9.84665			0.420245
$550$	−2.90213	+	27.4101i	−0.123747	+	1.16877i
$551$	5.72707			0.243981
$552$	4.25041	−	3.08810i	0.180910	−	0.131438i
$553$	0.222541	+	0.684912i	0.00946342	+	0.0291254i
$554$	−7.08643	+	21.8098i	−0.301074	+	0.926609i
$555$	3.88774	+	2.82461i	0.165025	+	0.119898i
$556$	8.36267	+	6.07584i	0.354656	+	0.257673i
$557$	2.30369	−	7.09002i	0.0976104	−	0.300414i	−0.890315	−	0.455345i	$-0.849516\pi$
$557$	2.30369	−	7.09002i	0.0976104	−	0.300414i	0.987925	+	0.154932i	$0.0495157\pi$
$558$	8.43539	+	25.9615i	0.357099	+	1.09904i
$559$	−1.80164	+	1.30897i	−0.0762012	+	0.0553634i
$560$	1.03883			0.0438987
$561$	−6.65382	+	1.40899i	−0.280925	+	0.0594877i
$562$	−6.03450			−0.254550
$563$	−0.817337	+	0.593830i	−0.0344467	+	0.0250270i	−0.604875	−	0.796320i	$-0.706777\pi$
$563$	−0.817337	+	0.593830i	−0.0344467	+	0.0250270i	0.570429	+	0.821347i	$0.306777\pi$
$564$	−4.59875	−	14.1535i	−0.193642	−	0.595969i
$565$	3.77854	−	11.6291i	0.158964	−	0.489242i
$566$	−11.9393	−	8.67439i	−0.501845	−	0.364612i
$567$	−0.526312	−	0.382388i	−0.0221030	−	0.0160588i
$568$	−1.00433	+	3.09101i	−0.0421408	+	0.129696i
$569$	2.21142	+	6.80606i	0.0927076	+	0.285325i	0.986649	−	0.162858i	$-0.0520713\pi$
$569$	2.21142	+	6.80606i	0.0927076	+	0.285325i	−0.893942	+	0.448183i	$0.852071\pi$
$570$	1.00962	−	0.733534i	0.0422884	−	0.0307243i
$571$	41.5870			1.74036			0.870181	−	0.492733i	$-0.164002\pi$
$571$	41.5870			1.74036			0.870181	+	0.492733i	$0.164002\pi$
$572$	11.9735	−	13.2775i	0.500638	−	0.555160i
$573$	−17.1963			−0.718386
$574$	3.46544	−	2.51779i	0.144645	−	0.105090i
$575$	8.04093	+	24.7474i	0.335330	+	1.03204i
$576$	2.24266	−	6.90220i	0.0934442	−	0.287592i
$577$	22.7940	+	16.5608i	0.948925	+	0.689435i	0.950552	−	0.310564i	$-0.100518\pi$
$577$	22.7940	+	16.5608i	0.948925	+	0.689435i	−0.00162704	+	0.999999i	$0.500518\pi$
$578$	−18.0123	−	13.0867i	−0.749213	−	0.544335i
$579$	0.785332	−	2.41700i	0.0326373	−	0.100447i
$580$	1.90980	+	5.87776i	0.0793002	+	0.244061i
$581$	−0.955325	+	0.694084i	−0.0396335	+	0.0287955i
$582$	16.8330			0.697749
$583$	−9.97869	−	4.45195i	−0.413275	−	0.184381i
$584$	−13.6110			−0.563229
$585$	−4.71808	+	3.42789i	−0.195069	+	0.141726i
$586$	−14.6718	−	45.1552i	−0.606087	−	1.86534i
$587$	4.67777	−	14.3967i	0.193072	−	0.594215i	−0.806921	−	0.590659i	$-0.798868\pi$
$587$	4.67777	−	14.3967i	0.193072	−	0.594215i	0.999994	−	0.00355646i	$-0.00113206\pi$
$588$	7.50400	+	5.45198i	0.309460	+	0.224836i
$589$	5.47079	+	3.97476i	0.225420	+	0.163777i
$590$	2.40055	−	7.38814i	0.0988291	−	0.304165i
$591$	−6.31395	−	19.4323i	−0.259721	−	0.799340i
$592$	27.7333	−	20.1494i	1.13983	−	0.828136i
$593$	5.59804			0.229884			0.114942	−	0.993372i	$-0.463332\pi$
$593$	5.59804			0.229884			0.114942	+	0.993372i	$0.463332\pi$
$594$	−14.5491	−	25.2443i	−0.596956	−	1.03579i
$595$	−0.488412			−0.0200230
$596$	14.3157	−	10.4010i	0.586395	−	0.426041i
$597$	−6.35499	−	19.5586i	−0.260092	−	0.800482i
$598$	12.3110	−	37.8892i	0.503432	−	1.54941i
$599$	12.1837	+	8.85198i	0.497813	+	0.361682i	0.808181	−	0.588934i	$-0.200452\pi$
$599$	12.1837	+	8.85198i	0.497813	+	0.361682i	−0.310368	+	0.950616i	$0.600452\pi$
$600$	3.25103	+	2.36201i	0.132723	+	0.0964287i
$601$	−7.90935	+	24.3425i	−0.322629	+	0.992951i	0.649870	+	0.760045i	$0.274823\pi$
$601$	−7.90935	+	24.3425i	−0.322629	+	0.992951i	−0.972499	+	0.232905i	$0.925177\pi$
$602$	−0.103546	−	0.318682i	−0.00422022	−	0.0129885i
$603$	14.0514	−	10.2090i	0.572219	−	0.415742i
$604$	−3.19405			−0.129964
$605$	−7.38091	+	3.27266i	−0.300077	+	0.133053i
$606$	11.5070			0.467440
$607$	−14.1254	+	10.2627i	−0.573331	+	0.416549i	−0.836314	−	0.548251i	$-0.815294\pi$
$607$	−14.1254	+	10.2627i	−0.573331	+	0.416549i	0.262983	+	0.964801i	$0.415294\pi$
$608$	−2.14104	−	6.58946i	−0.0868308	−	0.267238i
$609$	−0.478379	+	1.47230i	−0.0193849	+	0.0596606i
$610$	5.02648	+	3.65195i	0.203516	+	0.147863i
$611$	32.8977	+	23.9016i	1.33090	+	0.966954i
$612$	−2.21200	+	6.80784i	−0.0894148	+	0.275190i
$613$	4.63631	+	14.2691i	0.187259	+	0.576323i	0.999980	−	0.00632948i	$-0.00201475\pi$
$613$	4.63631	+	14.2691i	0.187259	+	0.576323i	−0.812721	+	0.582653i	$0.802015\pi$
$614$	−38.2323	+	27.7774i	−1.54293	+	1.12100i
$615$	−5.20138			−0.209740
$616$	−0.484051	−	0.839886i	−0.0195030	−	0.0338400i
$617$	−21.4377			−0.863049			−0.431525	−	0.902101i	$-0.642024\pi$
$617$	−21.4377			−0.863049			−0.431525	+	0.902101i	$0.642024\pi$
$618$	−15.1962	+	11.0407i	−0.611281	+	0.444122i
$619$	9.52881	+	29.3267i	0.382995	+	1.17874i	0.937924	+	0.346841i	$0.112746\pi$
$619$	9.52881	+	29.3267i	0.382995	+	1.17874i	−0.554929	+	0.831898i	$0.687254\pi$
$620$	−2.25501	+	6.94020i	−0.0905633	+	0.278725i
$621$	−22.2532	−	16.1679i	−0.892988	−	0.648794i
$622$	−41.6783	−	30.2810i	−1.67115	−	1.21416i
$623$	0.274753	−	0.845602i	0.0110077	−	0.0338783i
$624$	−4.94203	−	15.2100i	−0.197839	−	0.608887i
$625$	−13.9224	+	10.1152i	−0.556897	+	0.404610i
$626$	7.39516			0.295570
$627$	−2.76446	−	1.23335i	−0.110402	−	0.0492553i
$628$	33.3531			1.33094
$629$	−13.0389	+	9.47335i	−0.519897	+	0.377727i
$630$	−0.271163	−	0.834555i	−0.0108034	−	0.0332495i
$631$	9.95622	−	30.6421i	0.396351	−	1.21984i	−0.531554	−	0.847025i	$-0.678392\pi$
$631$	9.95622	−	30.6421i	0.396351	−	1.21984i	0.927905	−	0.372818i	$-0.121608\pi$
$632$	−1.94149	−	1.41057i	−0.0772282	−	0.0561096i
$633$	−12.1736	−	8.84460i	−0.483855	−	0.351541i
$634$	−4.29076	+	13.2056i	−0.170408	+	0.524462i
$635$	−0.579732	−	1.78423i	−0.0230060	−	0.0708051i
$636$	3.57657	−	2.59853i	0.141820	−	0.103038i
$637$	−25.3446			−1.00419
$638$	23.6966	−	26.2773i	0.938159	−	1.04033i
$639$	7.13627			0.282307
$640$	−4.52381	+	3.28674i	−0.178819	+	0.129920i
$641$	8.73507	+	26.8838i	0.345015	+	1.06185i	0.961576	+	0.274539i	$0.0885252\pi$
$641$	8.73507	+	26.8838i	0.345015	+	1.06185i	−0.616561	+	0.787307i	$0.711475\pi$
$642$	6.94878	−	21.3862i	0.274247	−	0.844044i
$643$	−17.1380	−	12.4515i	−0.675857	−	0.491039i	0.196124	−	0.980579i	$-0.437165\pi$
$643$	−17.1380	−	12.4515i	−0.675857	−	0.491039i	−0.871981	+	0.489540i	$0.837165\pi$
$644$	2.05463	+	1.49277i	0.0809636	+	0.0588235i
$645$	−0.125734	+	0.386968i	−0.00495075	+	0.0152369i
$646$	1.29339	+	3.98065i	0.0508878	+	0.156616i
$647$	−37.2726	+	27.0802i	−1.46534	+	1.06463i	−0.483407	+	0.875396i	$0.660601\pi$
$647$	−37.2726	+	27.0802i	−1.46534	+	1.06463i	−0.981932	+	0.189235i	$0.939399\pi$
$648$	2.16787			0.0851621
$649$	−18.4344	+	3.90362i	−0.723615	+	0.153230i
$650$	30.4719			1.19521
$651$	−1.47879	+	1.07441i	−0.0579585	+	0.0421093i
$652$	−0.791758	−	2.43678i	−0.0310076	−	0.0954317i
$653$	−0.0809850	+	0.249246i	−0.00316919	+	0.00975375i	−0.952629	−	0.304136i	$-0.901632\pi$
$653$	−0.0809850	+	0.249246i	−0.00316919	+	0.00975375i	0.949459	+	0.313890i	$0.101632\pi$
$654$	17.8109	+	12.9404i	0.696461	+	0.506009i
$655$	4.44014	+	3.22595i	0.173491	+	0.126048i
$656$	−11.4658	+	35.2882i	−0.447665	+	1.37777i
$657$	9.23529	+	28.4233i	0.360303	+	1.10890i
$658$	−4.95001	+	3.59639i	−0.192972	+	0.140202i
$659$	30.7500			1.19785			0.598924	−	0.800806i	$-0.295595\pi$
$659$	30.7500			1.19785			0.598924	+	0.800806i	$0.295595\pi$
$660$	0.343943	−	3.24848i	0.0133880	−	0.126447i
$661$	−38.5290			−1.49860			−0.749302	−	0.662228i	$-0.769611\pi$
$661$	−38.5290			−1.49860			−0.749302	+	0.662228i	$0.769611\pi$
$662$	45.2513	−	32.8770i	1.75874	−	1.27780i
$663$	2.32352	+	7.15106i	0.0902380	+	0.277724i
$664$	1.21597	−	3.74238i	0.0471889	−	0.145233i
$665$	−0.175863	−	0.127772i	−0.00681969	−	0.00495480i
$666$	−23.4263	−	17.0202i	−0.907752	−	0.659521i
$667$	10.3224	−	31.7692i	0.399686	−	1.23011i
$668$	3.70757	+	11.4107i	0.143450	+	0.441494i
$669$	−7.19389	+	5.22666i	−0.278132	+	0.202075i
$670$	10.9593			0.423393
$671$	1.58678	−	14.9869i	0.0612571	−	0.578563i
$672$	1.87284			0.0722464
$673$	−12.7799	+	9.28512i	−0.492628	+	0.357915i	−0.806194	−	0.591651i	$-0.798476\pi$
$673$	−12.7799	+	9.28512i	−0.492628	+	0.357915i	0.313566	+	0.949566i	$0.398476\pi$
$674$	−6.91206	−	21.2731i	−0.266243	−	0.819410i
$675$	6.50139	−	20.0092i	0.250239	−	0.770156i
$676$	−0.528084	−	0.383675i	−0.0203109	−	0.0147567i
$677$	−15.9382	−	11.5798i	−0.612556	−	0.445048i	0.237757	−	0.971325i	$-0.423588\pi$
$677$	−15.9382	−	11.5798i	−0.612556	−	0.445048i	−0.850314	+	0.526276i	$0.823588\pi$
$678$	8.75270	−	26.9380i	0.336145	−	1.03455i
$679$	−0.906065	−	2.78858i	−0.0347716	−	0.107016i
$680$	1.31672	−	0.956652i	0.0504938	−	0.0366859i
$681$	−10.1206			−0.387822
$682$	40.8735	−	8.65525i	1.56513	−	0.331426i
$683$	41.9347			1.60459			0.802293	−	0.596930i	$-0.203613\pi$
$683$	41.9347			1.60459			0.802293	+	0.596930i	$0.203613\pi$
$684$	−2.57746	+	1.87263i	−0.0985516	+	0.0716019i
$685$	0.286575	+	0.881988i	0.0109495	+	0.0336990i
$686$	2.37184	−	7.29978i	0.0905574	−	0.278707i
$687$	−4.48942	−	3.26176i	−0.171282	−	0.124444i
$688$	2.34818	+	1.70605i	0.0895235	+	0.0650426i
$689$	−3.73286	+	11.4886i	−0.142211	+	0.437679i
$690$	−2.24932	−	6.92268i	−0.0856300	−	0.263542i
$691$	−6.93507	+	5.03862i	−0.263823	+	0.191678i	−0.711831	−	0.702351i	$-0.752134\pi$
$691$	−6.93507	+	5.03862i	−0.263823	+	0.191678i	0.448008	+	0.894030i	$0.352134\pi$
$692$	−3.40466			−0.129426
$693$	−1.42546	+	1.58070i	−0.0541487	+	0.0600457i
$694$	−6.46590			−0.245442
$695$	−4.17498	+	3.03330i	−0.158366	+	0.115060i
$696$	−1.59412	−	4.90620i	−0.0604250	−	0.185969i
$697$	5.39072	−	16.5909i	0.204188	−	0.628426i
$698$	−54.2548	−	39.4184i	−2.05358	−	1.49201i
$699$	19.0872	+	13.8676i	0.721943	+	0.524522i
$700$	−0.600272	+	1.84745i	−0.0226881	+	0.0698269i
$701$	13.9668	+	42.9854i	0.527519	+	1.62354i	0.759280	+	0.650764i	$0.225551\pi$
$701$	13.9668	+	42.9854i	0.527519	+	1.62354i	−0.231761	+	0.972773i	$0.574449\pi$
$702$	−26.0596	+	18.9334i	−0.983554	+	0.714594i
$703$	−7.17325			−0.270544
$704$	−10.1440	−	4.52569i	−0.382315	−	0.170568i
$705$	7.42962			0.279816
$706$	−29.3951	+	21.3568i	−1.10630	+	0.803773i
$707$	−0.619385	−	1.90627i	−0.0232944	−	0.0716928i
$708$	2.35589	−	7.25067i	0.0885396	−	0.272497i
$709$	13.4653	+	9.78308i	0.505698	+	0.367411i	0.811189	−	0.584784i	$-0.198821\pi$
$709$	13.4653	+	9.78308i	0.505698	+	0.367411i	−0.305491	+	0.952195i	$0.598821\pi$
$710$	3.64290	+	2.64672i	0.136715	+	0.0993296i
$711$	−1.62831	+	5.01141i	−0.0610663	+	0.187943i
$712$	0.915569	+	2.81783i	0.0343124	+	0.105603i
$713$	31.9093	−	23.1834i	1.19501	−	0.868227i
$714$	−1.13137			−0.0423405
$715$	4.45703	+	7.73347i	0.166683	+	0.289215i
$716$	−26.7479			−0.999614
$717$	8.23020	−	5.97959i	0.307362	−	0.223312i
$718$	11.7570	+	36.1844i	0.438769	+	1.35039i
$719$	−15.8474	+	48.7733i	−0.591009	+	1.81894i	−0.0173429	+	0.999850i	$0.505521\pi$
$719$	−15.8474	+	48.7733i	−0.591009	+	1.81894i	−0.573666	+	0.819089i	$0.694479\pi$
$720$	6.14934	+	4.46776i	0.229172	+	0.166504i
$721$	2.64699	+	1.92315i	0.0985790	+	0.0716218i
$722$	−0.575653	+	1.77168i	−0.0214236	+	0.0659350i
$723$	0.967353	+	2.97721i	0.0359762	+	0.110723i
$724$	19.7322	−	14.3363i	0.733342	−	0.532804i
$725$	25.5499			0.948900
$726$	−17.0973	+	7.58088i	−0.634541	+	0.281353i
$727$	−12.6166			−0.467924			−0.233962	−	0.972246i	$-0.575169\pi$
$727$	−12.6166			−0.467924			−0.233962	+	0.972246i	$0.575169\pi$
$728$	−0.867008	+	0.629918i	−0.0321334	+	0.0233463i
$729$	2.51933	+	7.75371i	0.0933086	+	0.287174i
$730$	−5.82731	+	17.9346i	−0.215679	+	0.663790i
$731$	−1.10401	−	0.802109i	−0.0408332	−	0.0296671i
$732$	4.93296	+	3.58400i	0.182327	+	0.132469i
$733$	−0.823812	+	2.53543i	−0.0304282	+	0.0936483i	−0.965117	−	0.261818i	$-0.915678\pi$
$733$	−0.823812	+	2.53543i	−0.0304282	+	0.0936483i	0.934689	+	0.355466i	$0.115678\pi$
$734$	−2.89878	−	8.92153i	−0.106996	−	0.329300i
$735$	−3.74630	+	2.72185i	−0.138184	+	0.100397i
$736$	−40.4120			−1.48961
$737$	−13.2740	−	23.0319i	−0.488954	−	0.848391i
$738$	31.3419			1.15371
$739$	26.1403	−	18.9920i	0.961586	−	0.698633i	0.00806742	−	0.999967i	$-0.497432\pi$
$739$	26.1403	−	18.9920i	0.961586	−	0.698633i	0.953519	+	0.301334i	$0.0974320\pi$
$740$	−2.39206	−	7.36200i	−0.0879339	−	0.270633i
$741$	−1.03414	+	3.18274i	−0.0379899	+	0.116921i
$742$	−1.47048	−	1.06836i	−0.0539829	−	0.0392208i
$743$	37.0293	+	26.9034i	1.35847	+	0.986989i	0.998540	+	0.0540110i	$0.0172006\pi$
$743$	37.0293	+	26.9034i	1.35847	+	0.986989i	0.359933	+	0.932978i	$0.382799\pi$
$744$	1.88227	−	5.79302i	0.0690072	−	0.212382i
$745$	2.72990	+	8.40178i	0.100016	+	0.307818i
$746$	−44.6478	+	32.4386i	−1.63467	+	1.18766i
$747$	−8.64011			−0.316125
$748$	10.0053	+	4.46381i	0.365829	+	0.163213i
$749$	−3.91690			−0.143121
$750$	9.55229	−	6.94015i	0.348800	−	0.253418i
$751$	−14.1274	−	43.4796i	−0.515516	−	1.58659i	−0.782342	−	0.622850i	$-0.785975\pi$
$751$	−14.1274	−	43.4796i	−0.515516	−	1.58659i	0.266826	−	0.963745i	$-0.414025\pi$
$752$	16.3777	−	50.4055i	0.597234	−	1.83810i
$753$	8.46977	+	6.15365i	0.308655	+	0.224251i
$754$	−31.6470	−	22.9929i	−1.15252	−	0.837351i
$755$	0.492758	−	1.51655i	0.0179333	−	0.0551930i
$756$	−0.634538	−	1.95291i	−0.0230779	−	0.0710266i
$757$	−20.6314	+	14.9896i	−0.749861	+	0.544806i	−0.895784	−	0.444490i	$-0.853385\pi$
$757$	−20.6314	+	14.9896i	−0.749861	+	0.544806i	0.145923	+	0.989296i	$0.453385\pi$
$758$	59.6314			2.16591
$759$	−11.8243	+	13.1120i	−0.429194	+	0.475935i
$760$	0.724380			0.0262760
$761$	37.3354	−	27.1257i	1.35341	−	0.983307i	0.354573	−	0.935028i	$-0.384626\pi$
$761$	37.3354	−	27.1257i	1.35341	−	0.983307i	0.998834	−	0.0482789i	$-0.0153736\pi$
$762$	−1.34291	−	4.13304i	−0.0486483	−	0.149724i
$763$	1.18502	−	3.64713i	0.0429008	−	0.132035i
$764$	22.4101	+	16.2819i	0.810768	+	0.589058i
$765$	−2.89115	−	2.10054i	−0.104530	−	0.0759452i
$766$	6.10166	−	18.7790i	0.220462	−	0.678512i
$767$	6.43732	+	19.8120i	0.232438	+	0.715371i
$768$	−15.4250	+	11.2069i	−0.556601	+	0.404394i
$769$	−22.7536			−0.820514			−0.410257	−	0.911970i	$-0.634561\pi$
$769$	−22.7536			−0.820514			−0.410257	+	0.911970i	$0.634561\pi$
$770$	−1.31392	+	0.278231i	−0.0473502	+	0.0100267i
$771$	−8.02444			−0.288993
$772$	−3.31191	+	2.40625i	−0.119198	+	0.0866027i
$773$	−1.39066	−	4.28000i	−0.0500184	−	0.153941i	0.922928	−	0.384974i	$-0.125790\pi$
$773$	−1.39066	−	4.28000i	−0.0500184	−	0.153941i	−0.972946	+	0.231033i	$0.925790\pi$
$774$	0.757633	−	2.33175i	0.0272326	−	0.0838132i
$775$	24.4066	+	17.7324i	0.876711	+	0.636968i
$776$	7.90466	+	5.74307i	0.283761	+	0.206164i
$777$	0.599179	−	1.84408i	0.0214954	−	0.0661561i
$778$	−5.69930	−	17.5406i	−0.204330	−	0.628863i
$779$	6.28135	−	4.56367i	0.225053	−	0.163510i
$780$	−3.61134			−0.129307
$781$	1.15001	−	10.8616i	0.0411505	−	0.388660i
$782$	24.4126			0.872993
$783$	−21.8503	+	15.8752i	−0.780865	+	0.567332i
$784$	10.2078	+	31.4163i	0.364564	+	1.12201i
$785$	−5.14551	+	15.8363i	−0.183651	+	0.565220i
$786$	10.2853	+	7.47268i	0.366863	+	0.266542i
$787$	34.6823	+	25.1982i	1.23629	+	0.898219i	0.997346	−	0.0728140i	$-0.0231979\pi$
$787$	34.6823	+	25.1982i	1.23629	+	0.898219i	0.238947	+	0.971033i	$0.423198\pi$
$788$	−10.1707	+	31.3023i	−0.362317	+	1.11510i
$789$	−2.94701	−	9.06995i	−0.104916	−	0.322899i
$790$	−2.68986	+	1.95430i	−0.0957009	+	0.0695307i
$791$	−4.93374			−0.175424
$792$	0.746808	−	7.05347i	0.0265367	−	0.250634i
$793$	−16.6610			−0.591648
$794$	33.5579	−	24.3812i	1.19093	−	0.865258i
$795$	0.682025	+	2.09906i	0.0241889	+	0.0744459i
$796$	−10.2368	+	31.5057i	−0.362835	+	1.11669i
$797$	7.54282	+	5.48018i	0.267180	+	0.194118i	0.713307	−	0.700852i	$-0.247197\pi$
$797$	7.54282	+	5.48018i	0.267180	+	0.194118i	−0.446126	+	0.894970i	$0.647197\pi$
$798$	−0.407374	−	0.295975i	−0.0144209	−	0.0104774i
$799$	−7.70007	+	23.6984i	−0.272409	+	0.838389i
$800$	−9.55175	−	29.3973i	−0.337705	−	1.03935i
$801$	5.26312	−	3.82388i	0.185963	−	0.135110i
$802$	−9.33699			−0.329701
$803$	44.7494	−	9.47599i	1.57917	−	0.334400i
$804$	10.7554			0.379312
$805$	−1.02575	+	0.745253i	−0.0361530	+	0.0262667i
$806$	−14.2731	−	43.9280i	−0.502747	−	1.54730i
$807$	−3.65929	+	11.2621i	−0.128813	+	0.396446i
$808$	5.40362	+	3.92596i	0.190099	+	0.138115i
$809$	−31.6575	−	23.0005i	−1.11302	−	0.808656i	−0.129883	−	0.991529i	$-0.541460\pi$
$809$	−31.6575	−	23.0005i	−1.11302	−	0.808656i	−0.983136	+	0.182874i	$0.941460\pi$
$810$	0.928135	−	2.85651i	0.0326113	−	0.100367i
$811$	−9.03545	−	27.8082i	−0.317277	−	0.976479i	−0.974807	−	0.223051i	$-0.928398\pi$
$811$	−9.03545	−	27.8082i	−0.317277	−	0.976479i	0.657529	−	0.753429i	$-0.271602\pi$
$812$	2.01743	−	1.46575i	0.0707979	−	0.0514377i
$813$	16.8699			0.591654
$814$	−29.6805	+	32.9128i	−1.04030	+	1.15359i
$815$	1.27914			0.0448065
$816$	7.92839	−	5.76031i	0.277549	−	0.201651i
$817$	−0.187684	−	0.577633i	−0.00656625	−	0.0202088i
$818$	−9.06859	+	27.9102i	−0.317076	+	0.975859i
$819$	1.90371	+	1.38312i	0.0665209	+	0.0483303i
$820$	6.77839	+	4.92479i	0.236712	+	0.171981i
$821$	14.7451	−	45.3809i	0.514609	−	1.58380i	−0.269383	−	0.963033i	$-0.586820\pi$
$821$	14.7451	−	45.3809i	0.514609	−	1.58380i	0.783992	−	0.620771i	$-0.213180\pi$
$822$	0.663830	+	2.04306i	0.0231537	+	0.0712598i
$823$	−3.80852	+	2.76705i	−0.132757	+	0.0964534i	−0.652182	−	0.758063i	$-0.726146\pi$
$823$	−3.80852	+	2.76705i	−0.132757	+	0.0964534i	0.519425	+	0.854516i	$0.326146\pi$
$824$	−10.9029			−0.379821
$825$	−12.3329	−	5.50229i	−0.429378	−	0.191565i
$826$	−3.13447			−0.109062
$827$	−41.0243	+	29.8059i	−1.42656	+	1.03645i	−0.435911	+	0.899990i	$0.643574\pi$
$827$	−41.0243	+	29.8059i	−1.42656	+	1.03645i	−0.990645	+	0.136464i	$0.956426\pi$
$828$	5.74227	+	17.6729i	0.199558	+	0.614175i
$829$	−0.971103	+	2.98875i	−0.0337278	+	0.103804i	−0.966503	−	0.256655i	$-0.917380\pi$
$829$	−0.971103	+	2.98875i	−0.0337278	+	0.103804i	0.932775	+	0.360458i	$0.117380\pi$
$830$	−4.41057	−	3.20447i	−0.153093	−	0.111229i
$831$	−9.08983	−	6.60415i	−0.315323	−	0.229095i
$832$	−3.79468	+	11.6788i	−0.131557	+	0.404890i
$833$	−4.79925	−	14.7706i	−0.166284	−	0.511770i
$834$	−9.67103	+	7.02642i	−0.334880	+	0.243305i
$835$	−5.98985			−0.207287
$836$	2.43485	+	4.22475i	0.0842110	+	0.146116i
$837$	−31.8904			−1.10229
$838$	−32.7670	+	23.8066i	−1.13192	+	0.822386i
$839$	4.25389	+	13.0921i	0.146861	+	0.451990i	0.997246	−	0.0741707i	$-0.0236310\pi$
$839$	4.25389	+	13.0921i	0.146861	+	0.451990i	−0.850385	+	0.526161i	$0.823631\pi$
$840$	−0.0605071	+	0.186222i	−0.00208769	+	0.00642526i
$841$	−3.07371	−	2.23318i	−0.105990	−	0.0770062i
$842$	−58.2651	−	42.3320i	−2.00795	−	1.45886i
$843$	0.913643	−	2.81190i	0.0314675	−	0.0968471i
$844$	7.49019	+	23.0524i	0.257823	+	0.793497i
$845$	0.263641	−	0.191546i	0.00906951	−	0.00658938i
$846$	−44.7687			−1.53918
$847$	2.17616	+	2.42432i	0.0747737	+	0.0833007i
$848$	15.7443			0.540661
$849$	5.84966	−	4.25003i	0.200760	−	0.145861i
$850$	5.77014	+	17.7587i	0.197914	+	0.609118i
$851$	−12.9290	+	39.7914i	−0.443201	+	1.36403i
$852$	3.57512	+	2.59747i	0.122481	+	0.0889880i
$853$	−33.1055	−	24.0525i	−1.13351	−	0.823543i	−0.147308	−	0.989091i	$-0.547061\pi$
$853$	−33.1055	−	24.0525i	−1.13351	−	0.823543i	−0.986202	+	0.165547i	$0.947061\pi$
$854$	0.774682	−	2.38423i	0.0265091	−	0.0815865i
$855$	−0.491503	−	1.51269i	−0.0168090	−	0.0517329i
$856$	10.5596	−	7.67203i	0.360921	−	0.262225i
$857$	−42.4726			−1.45084			−0.725418	−	0.688308i	$-0.758354\pi$
$857$	−42.4726			−1.45084			−0.725418	+	0.688308i	$0.758354\pi$
$858$	10.3244	+	17.9140i	0.352468	+	0.611574i
$859$	−13.8794			−0.473558			−0.236779	−	0.971564i	$-0.576092\pi$
$859$	−13.8794			−0.473558			−0.236779	+	0.971564i	$0.576092\pi$
$860$	0.530246	−	0.385246i	0.0180812	−	0.0131368i
$861$	0.648538	+	1.99600i	0.0221021	+	0.0680233i
$862$	−17.7872	+	54.7435i	−0.605835	+	1.86457i
$863$	10.8289	+	7.86762i	0.368618	+	0.267817i	0.756638	−	0.653834i	$-0.226841\pi$
$863$	10.8289	+	7.86762i	0.368618	+	0.267817i	−0.388019	+	0.921651i	$0.626841\pi$
$864$	26.4343	+	19.2056i	0.899313	+	0.653389i
$865$	0.525249	−	1.61655i	0.0178590	−	0.0549644i
$866$	−12.0150	−	36.9783i	−0.408286	−	1.25658i
$867$	8.82515	−	6.41184i	0.299718	−	0.217758i
$868$	2.94443			0.0999404
$869$	7.36513	+	3.28592i	0.249845	+	0.111467i
$870$	−7.14716			−0.242311
$871$	−23.7757	+	17.2740i	−0.805608	+	0.585309i
$872$	3.94890	+	12.1535i	0.133727	+	0.411568i
$873$	6.62957	−	20.4037i	0.224377	−	0.690561i
$874$	8.79029	+	6.38652i	0.297336	+	0.216027i
$875$	−1.66389	−	1.20889i	−0.0562497	−	0.0408678i
$876$	−5.71889	+	17.6009i	−0.193223	+	0.594680i
$877$	12.0097	+	36.9620i	0.405538	+	1.24812i	0.920445	+	0.390872i	$0.127826\pi$
$877$	12.0097	+	36.9620i	0.405538	+	1.24812i	−0.514907	+	0.857246i	$0.672174\pi$
$878$	38.3705	−	27.8778i	1.29494	−	0.940830i
$879$	23.2624			0.784620
$880$	7.79103	−	8.63951i	0.262636	−	0.291238i
$881$	2.13057			0.0717807			0.0358903	−	0.999356i	$-0.488573\pi$
$881$	2.13057			0.0717807			0.0358903	+	0.999356i	$0.488573\pi$
$882$	22.5741	−	16.4010i	0.760109	−	0.552251i
$883$	10.8851	+	33.5010i	0.366314	+	1.12740i	0.949154	+	0.314812i	$0.101942\pi$
$883$	10.8851	+	33.5010i	0.366314	+	1.12740i	−0.582840	+	0.812587i	$0.698058\pi$
$884$	3.74280	−	11.5192i	0.125884	−	0.387431i
$885$	3.07921	+	2.23718i	0.103506	+	0.0752019i
$886$	−52.3129	−	38.0075i	−1.75749	−	1.27689i
$887$	13.7096	−	42.1937i	0.460322	−	1.41673i	−0.404449	−	0.914561i	$-0.632537\pi$
$887$	13.7096	−	42.1937i	0.460322	−	1.41673i	0.864771	−	0.502166i	$-0.167463\pi$
$888$	1.99666	+	6.14510i	0.0670037	+	0.206216i
$889$	−0.612403	+	0.444937i	−0.0205393	+	0.0149227i
$890$	4.10491			0.137597
$891$	−7.12739	+	1.50927i	−0.238776	+	0.0505625i
$892$	14.3237			0.479594
$893$	−8.97225	+	6.51872i	−0.300245	+	0.218141i
$894$	6.32362	+	19.4621i	0.211493	+	0.650910i
$895$	4.12649	−	12.7000i	0.137933	−	0.424515i
$896$	1.82532	+	1.32617i	0.0609796	+	0.0443043i
$897$	15.7914	+	11.4731i	0.527259	+	0.383076i
$898$	−18.2168	+	56.0656i	−0.607903	+	1.87093i
$899$	−11.9676	−	36.8325i	−0.399142	−	1.22843i
$900$	−11.4987	+	8.35430i	−0.383290	+	0.278477i
$901$	−7.40225			−0.246605
$902$	5.05075	−	47.7034i	0.168172	−	1.58835i
$903$	0.164174			0.00546336
$904$	13.3009	−	9.66370i	0.442383	−	0.321410i
$905$	3.76279	+	11.5807i	0.125079	+	0.384955i
$906$	1.14144	−	3.51298i	0.0379217	−	0.116711i
$907$	−10.8239	−	7.86404i	−0.359402	−	0.261121i	0.393400	−	0.919367i	$-0.371299\pi$
$907$	−10.8239	−	7.86404i	−0.359402	−	0.261121i	−0.752803	+	0.658246i	$0.771299\pi$
$908$	13.1891	+	9.58242i	0.437695	+	0.318004i
$909$	4.53197	−	13.9480i	0.150316	−	0.462625i
$910$	0.458820	+	1.41210i	0.0152097	+	0.0468108i
$911$	24.8320	−	18.0415i	0.822722	−	0.597742i	−0.0947690	−	0.995499i	$-0.530211\pi$
$911$	24.8320	−	18.0415i	0.822722	−	0.597742i	0.917491	+	0.397757i	$0.130211\pi$
$912$	4.36173			0.144431
$913$	−1.39235	+	13.1505i	−0.0460801	+	0.435218i
$914$	−64.1195			−2.12088
$915$	−2.46273	+	1.78928i	−0.0814153	+	0.0591517i
$916$	2.76227	+	8.50139i	0.0912679	+	0.280894i
$917$	0.684316	−	2.10611i	0.0225981	−	0.0695498i
$918$	−15.9688	−	11.6020i	−0.527048	−	0.382923i
$919$	28.3647	+	20.6081i	0.935664	+	0.679800i	0.947373	−	0.320132i	$-0.103727\pi$
$919$	28.3647	+	20.6081i	0.935664	+	0.679800i	−0.0117088	+	0.999931i	$0.503727\pi$
$920$	1.30562	−	4.01828i	0.0430449	−	0.132479i
$921$	−7.15498	−	22.0207i	−0.235764	−	0.725608i
$922$	27.2022	−	19.7636i	0.895857	−	0.650879i
$923$	−12.0749			−0.397450
$924$	−1.28947	+	0.273054i	−0.0424204	+	0.00898281i
$925$	−32.0017			−1.05221
$926$	29.7542	−	21.6177i	0.977785	−	0.710402i
$927$	7.39780	+	22.7681i	0.242976	+	0.747802i
$928$	−12.2619	+	37.7383i	−0.402517	+	1.23882i
$929$	−12.7348	−	9.25236i	−0.417815	−	0.303560i	0.358943	−	0.933359i	$-0.383137\pi$
$929$	−12.7348	−	9.25236i	−0.417815	−	0.303560i	−0.776758	+	0.629799i	$0.783137\pi$
$930$	−6.82734	−	4.96035i	−0.223877	−	0.162656i
$931$	2.13601	−	6.57398i	0.0700051	−	0.215453i
$932$	−11.7440	−	36.1444i	−0.384688	−	1.18395i
$933$	20.4203	−	14.8362i	0.668532	−	0.485717i
$934$	−58.6836			−1.92019
$935$	−3.66300	+	4.06191i	−0.119793	+	0.132839i
$936$	−7.84135			−0.256303
$937$	7.37113	−	5.35544i	0.240804	−	0.174955i	−0.460837	−	0.887485i	$-0.652451\pi$
$937$	7.37113	−	5.35544i	0.240804	−	0.174955i	0.701642	+	0.712530i	$0.252451\pi$
$938$	−1.36647	−	4.20555i	−0.0446167	−	0.137316i
$939$	−1.11965	+	3.44593i	−0.0365385	+	0.112454i
$940$	−9.68222	−	7.03454i	−0.315799	−	0.229442i
$941$	25.8605	+	18.7887i	0.843027	+	0.612495i	0.923215	−	0.384285i	$-0.125552\pi$
$941$	25.8605	+	18.7887i	0.843027	+	0.612495i	−0.0801878	+	0.996780i	$0.525552\pi$
$942$	−11.9192	+	36.6835i	−0.388348	+	1.19521i
$943$	−13.9941	−	43.0694i	−0.455710	−	1.40253i
$944$	21.9656	−	15.9590i	0.714921	−	0.519420i
$945$	1.02514			0.0333479
$946$	−3.42691	−	1.52890i	−0.111418	−	0.0497089i
$947$	33.9127			1.10201			0.551007	−	0.834500i	$-0.314244\pi$
$947$	33.9127			1.10201			0.551007	+	0.834500i	$0.314244\pi$
$948$	−2.63981	+	1.91793i	−0.0857371	+	0.0622916i
$949$	−15.6265	−	48.0935i	−0.507258	−	1.56118i
$950$	−2.56814	+	7.90391i	−0.0833213	+	0.256437i
$951$	−5.50380	−	3.99875i	−0.178473	−	0.129668i
$952$	−0.531285	−	0.386001i	−0.0172191	−	0.0125104i
$953$	−12.3442	+	37.9914i	−0.399866	+	1.23066i	0.525240	+	0.850954i	$0.323976\pi$
$953$	−12.3442	+	37.9914i	−0.399866	+	1.23066i	−0.925106	+	0.379708i	$0.876024\pi$
$954$	−4.10968	−	12.6483i	−0.133056	−	0.409504i
$955$	−11.1880	+	8.12857i	−0.362036	+	0.263034i
$956$	−16.3871			−0.529998
$957$	8.65673	+	15.0204i	0.279832	+	0.485542i
$958$	14.2573			0.460633
$959$	0.302725	−	0.219943i	0.00977551	−	0.00710232i
$960$	0.693321	+	2.13382i	0.0223768	+	0.0688688i
$961$	4.55129	−	14.0074i	0.146816	−	0.451853i
$962$	39.6384	+	28.7990i	1.27799	+	0.928517i
$963$	−23.1860	−	16.8456i	−0.747159	−	0.542843i
$964$	1.55824	−	4.79578i	0.0501877	−	0.154462i
$965$	−0.631558	−	1.94374i	−0.0203306	−	0.0625711i
$966$	−2.37608	+	1.72632i	−0.0764491	+	0.0555435i
$967$	18.0066			0.579052			0.289526	−	0.957170i	$-0.406502\pi$
$967$	18.0066			0.579052			0.289526	+	0.957170i	$0.406502\pi$
$968$	−10.6153	−	2.27333i	−0.341187	−	0.0730676i
$969$	−2.05069			−0.0658777
$970$	10.9516	−	7.95682i	0.351635	−	0.255478i
$971$	2.33117	+	7.17462i	0.0748110	+	0.230244i	0.981469	−	0.191623i	$-0.0613749\pi$
$971$	2.33117	+	7.17462i	0.0748110	+	0.230244i	−0.906658	+	0.421867i	$0.861375\pi$
$972$	7.33852	−	22.5856i	0.235383	−	0.724435i
$973$	1.68457	+	1.22391i	0.0540049	+	0.0392368i
$974$	38.1303	+	27.7033i	1.22177	+	0.887671i
$975$	−4.61354	+	14.1990i	−0.147752	+	0.454733i
$976$	6.71036	+	20.6524i	0.214793	+	0.661066i
$977$	41.0732	−	29.8414i	1.31405	−	0.954712i	0.314063	−	0.949402i	$-0.398310\pi$
$977$	41.0732	−	29.8414i	1.31405	−	0.954712i	0.999986	−	0.00530992i	$-0.00169021\pi$
$978$	2.96304			0.0947476
$979$	−4.97191	−	8.62685i	−0.158903	−	0.275715i
$980$	7.45925			0.238277
$981$	22.7001	−	16.4926i	0.724759	−	0.526568i
$982$	−10.4409	−	32.1339i	−0.333183	−	1.02543i
$983$	−5.17569	+	15.9291i	−0.165079	+	0.508061i	−0.999042	−	0.0437593i	$-0.986067\pi$
$983$	−5.17569	+	15.9291i	−0.165079	+	0.508061i	0.833963	+	0.551820i	$0.186067\pi$
$984$	−5.65795	−	4.11074i	−0.180369	−	0.131046i
$985$	−13.2934	−	9.65823i	−0.423563	−	0.307737i
$986$	7.40733	−	22.7974i	0.235898	−	0.726018i
$987$	−0.926369	−	2.85107i	−0.0294866	−	0.0907506i
$988$	4.36118	−	3.16858i	0.138747	−	0.100806i
$989$	−3.54253			−0.112646
$990$	−8.97430	−	4.00385i	−0.285222	−	0.127251i
$991$	−4.56365			−0.144969			−0.0724846	−	0.997370i	$-0.523093\pi$
$991$	−4.56365			−0.144969			−0.0724846	+	0.997370i	$0.523093\pi$
$992$	−37.9047	+	27.5394i	−1.20348	+	0.874377i
$993$	8.46854	+	26.0635i	0.268741	+	0.827100i
$994$	0.561444	−	1.72795i	0.0178079	−	0.0548072i
$995$	−13.3798	−	9.72100i	−0.424169	−	0.308177i
$996$	−4.32850	−	3.14484i	−0.137154	−	0.0996482i
$997$	−1.16537	+	3.58665i	−0.0369077	+	0.113590i	−0.967813	−	0.251670i	$-0.919020\pi$
$997$	−1.16537	+	3.58665i	−0.0369077	+	0.113590i	0.930905	+	0.365261i	$0.119020\pi$
$998$	−7.37058	−	22.6843i	−0.233312	−	0.718059i
$999$	27.3679	−	19.8839i	0.865881	−	0.629099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.f.b.58.6	✓	28
11.2	odd	10		2299.2.a.u.1.11		14
11.4	even	5	inner	209.2.f.b.191.6	yes	28
11.9	even	5		2299.2.a.t.1.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.f.b.58.6	✓	28	1.1	even	1	trivial
209.2.f.b.191.6	yes	28	11.4	even	5	inner
2299.2.a.t.1.4		14	11.9	even	5
2299.2.a.u.1.11		14	11.2	odd	10

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:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50708 - 1.09496i) q^{2} +(0.282042 + 0.868036i) q^{3} +(0.454323 - 1.39826i) q^{4} +(0.593812 + 0.431430i) q^{5} +(1.37552 + 0.999375i) q^{6} +(0.0915185 - 0.281665i) q^{7} +(0.304970 + 0.938602i) q^{8} +(1.75311 - 1.27371i) q^{9} +1.36732 q^{10} +(-1.65611 - 2.87355i) q^{11} +1.34188 q^{12} +(-2.96634 + 2.15518i) q^{13} +(-0.170485 - 0.524700i) q^{14} +(-0.207017 + 0.637132i) q^{15} +(3.86621 + 2.80896i) q^{16} +(-1.81772 - 1.32065i) q^{17} +(1.24742 - 3.83917i) q^{18} +(-0.309017 - 0.951057i) q^{19} +(0.873034 - 0.634296i) q^{20} +0.270307 q^{21} +(-5.64231 - 2.51729i) q^{22} -5.83266 q^{23} +(-0.728726 + 0.529450i) q^{24} +(-1.37860 - 4.24291i) q^{25} +(-2.11069 + 6.49604i) q^{26} +(3.81526 + 2.77195i) q^{27} +(-0.352262 - 0.255933i) q^{28} +(-1.76976 + 5.44677i) q^{29} +(0.385641 + 1.18688i) q^{30} +(-5.47079 + 3.97476i) q^{31} +6.92857 q^{32} +(2.02725 - 2.24803i) q^{33} -4.18550 q^{34} +(0.175863 - 0.127772i) q^{35} +(-0.984502 - 3.02998i) q^{36} +(2.21666 - 6.82217i) q^{37} +(-1.50708 - 1.09496i) q^{38} +(-2.70740 - 1.96704i) q^{39} +(-0.223846 + 0.688926i) q^{40} +(2.39926 + 7.38417i) q^{41} +(0.407374 - 0.295975i) q^{42} +0.607360 q^{43} +(-4.77038 + 1.01016i) q^{44} +1.59054 q^{45} +(-8.79029 + 6.38652i) q^{46} +(-3.42710 - 10.5475i) q^{47} +(-1.34785 + 4.14825i) q^{48} +(5.59216 + 4.06294i) q^{49} +(-6.72346 - 4.88488i) q^{50} +(0.633698 - 1.95032i) q^{51} +(1.66582 + 5.12687i) q^{52} +(2.66534 - 1.93648i) q^{53} +8.78507 q^{54} +(0.256315 - 2.42085i) q^{55} +0.292282 q^{56} +(0.738395 - 0.536476i) q^{57} +(3.29680 + 10.1465i) q^{58} +(1.75566 - 5.40337i) q^{59} +(0.796824 + 0.578927i) q^{60} +(3.67616 + 2.67088i) q^{61} +(-3.89272 + 11.9806i) q^{62} +(-0.198317 - 0.610358i) q^{63} +(2.70948 - 1.96856i) q^{64} -2.69126 q^{65} +(0.593734 - 5.60771i) q^{66} +8.01514 q^{67} +(-2.67244 + 1.94164i) q^{68} +(-1.64506 - 5.06296i) q^{69} +(0.125135 - 0.385126i) q^{70} +(2.66426 + 1.93570i) q^{71} +(1.73015 + 1.25703i) q^{72} +(-4.26185 + 13.1166i) q^{73} +(-4.12931 - 12.7087i) q^{74} +(3.29417 - 2.39335i) q^{75} -1.47022 q^{76} +(-0.960943 + 0.203486i) q^{77} -6.23410 q^{78} +(-1.96725 + 1.42929i) q^{79} +(1.08393 + 3.33599i) q^{80} +(0.678799 - 2.08913i) q^{81} +(11.7012 + 8.50144i) q^{82} +(-3.22570 - 2.34361i) q^{83} +(0.122807 - 0.377960i) q^{84} +(-0.509615 - 1.56844i) q^{85} +(0.915339 - 0.665033i) q^{86} -5.22713 q^{87} +(2.19205 - 2.43078i) q^{88} +3.00216 q^{89} +(2.39706 - 1.74157i) q^{90} +(0.335562 + 1.03275i) q^{91} +(-2.64991 + 8.15559i) q^{92} +(-4.99323 - 3.62779i) q^{93} +(-16.7140 - 12.1434i) q^{94} +(0.226816 - 0.698068i) q^{95} +(1.95415 + 6.01424i) q^{96} +(8.00955 - 5.81928i) q^{97} +12.8766 q^{98} +(-6.56342 - 2.92825i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + q^{3} - 6 q^{4} + 7 q^{5} - 14 q^{6} - 12 q^{7} + 4 q^{8} + 6 q^{9} - 12 q^{10} + 2 q^{11} - 16 q^{12} + 5 q^{13} + 23 q^{14} + 15 q^{15} + 30 q^{16} - 15 q^{17} - 38 q^{18} + 7 q^{19}+ \cdots - 64 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + q^3 - 6 * q^4 + 7 * q^5 - 14 * q^6 - 12 * q^7 + 4 * q^8 + 6 * q^9 - 12 * q^10 + 2 * q^11 - 16 * q^12 + 5 * q^13 + 23 * q^14 + 15 * q^15 + 30 * q^16 - 15 * q^17 - 38 * q^18 + 7 * q^19 + 8 * q^20 - 18 * q^21 + 18 * q^22 - 42 * q^23 - 4 * q^24 + 2 * q^25 + 14 * q^26 + 28 * q^27 - 15 * q^28 - 21 * q^29 + 10 * q^30 + 19 * q^31 - 4 * q^32 - 28 * q^33 - 20 * q^34 - 16 * q^35 + 46 * q^36 + 23 * q^37 + 2 * q^38 - 4 * q^39 - 84 * q^40 + 5 * q^41 + 34 * q^42 - 12 * q^43 - 11 * q^44 - 22 * q^45 + 19 * q^46 + 43 * q^47 + 28 * q^48 - q^49 - 43 * q^50 - 6 * q^51 - 21 * q^52 + 46 * q^53 + 60 * q^54 - 92 * q^55 - 60 * q^56 - q^57 + 63 * q^58 + 3 * q^59 + 40 * q^60 - 12 * q^61 - 25 * q^62 + 9 * q^63 + 44 * q^64 + 26 * q^65 + 13 * q^66 + 24 * q^67 - 19 * q^68 - q^69 - 14 * q^70 + 14 * q^71 - 7 * q^72 + 7 * q^73 - 58 * q^74 + 50 * q^75 - 14 * q^76 - 60 * q^77 + 6 * q^78 - 62 * q^79 + 85 * q^80 + 31 * q^81 + 36 * q^82 + 5 * q^83 - 59 * q^84 - 9 * q^85 + 34 * q^86 - 34 * q^87 - 16 * q^88 - 108 * q^89 - 28 * q^90 + 45 * q^91 + 62 * q^92 + 13 * q^93 - 80 * q^94 - 7 * q^95 - 40 * q^96 + 38 * q^97 + 84 * q^98 - 64 * q^99

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