LMFDB - Embedded newform 114.2.i.a.43.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [114,2,Mod(25,114)] 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("114.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(114, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.i (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			43.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	114.43
Dual form			114.2.i.a.61.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.939693 - 0.342020i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.907604 - 0.761570i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(0.733956 + 1.27125i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-1.11334 - 0.405223i) q^{10} +(-0.592396 + 1.02606i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.446967 + 2.53487i) q^{13} +(1.12449 + 0.943555i) q^{14} +(-0.907604 + 0.761570i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-2.09240 + 0.761570i) q^{17} -1.00000 q^{18} +(0.819078 + 4.28125i) q^{19} -1.18479 q^{20} +(1.37939 - 0.502055i) q^{21} +(-0.205737 + 1.16679i) q^{22} +(0.907604 - 0.761570i) q^{23} +(-0.766044 - 0.642788i) q^{24} +(-0.624485 - 3.54163i) q^{25} +(1.28699 + 2.22913i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(1.37939 + 0.502055i) q^{28} +(-8.84389 - 3.21891i) q^{29} +(-0.592396 + 1.02606i) q^{30} +(3.96451 + 6.86673i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.907604 + 0.761570i) q^{33} +(-1.70574 + 1.43128i) q^{34} +(0.302004 - 1.71275i) q^{35} +(-0.939693 + 0.342020i) q^{36} -0.0641778 q^{37} +(2.23396 + 3.74292i) q^{38} +2.57398 q^{39} +(-1.11334 + 0.405223i) q^{40} +(1.68092 - 9.53298i) q^{41} +(1.12449 - 0.943555i) q^{42} +(-5.55303 - 4.65955i) q^{43} +(0.205737 + 1.16679i) q^{44} +(0.592396 + 1.02606i) q^{45} +(0.592396 - 1.02606i) q^{46} +(4.57145 + 1.66387i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(2.42262 - 4.19610i) q^{49} +(-1.79813 - 3.11446i) q^{50} +(0.386659 + 2.19285i) q^{51} +(1.97178 + 1.65452i) q^{52} +(-1.11334 + 0.934204i) q^{53} +(-0.173648 + 0.984808i) q^{54} +(1.31908 - 0.480105i) q^{55} +1.46791 q^{56} +(4.35844 - 0.0632028i) q^{57} -9.41147 q^{58} +(-1.31908 + 0.480105i) q^{59} +(-0.205737 + 1.16679i) q^{60} +(5.97565 - 5.01417i) q^{61} +(6.07398 + 5.09667i) q^{62} +(-0.254900 - 1.44561i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.52481 - 2.64106i) q^{65} +(1.11334 + 0.405223i) q^{66} +(-8.19119 - 2.98135i) q^{67} +(-1.11334 + 1.92836i) q^{68} +(-0.592396 - 1.02606i) q^{69} +(-0.302004 - 1.71275i) q^{70} +(11.2135 + 9.40923i) q^{71} +(-0.766044 + 0.642788i) q^{72} +(1.13563 - 6.44047i) q^{73} +(-0.0603074 + 0.0219501i) q^{74} -3.59627 q^{75} +(3.37939 + 2.75314i) q^{76} -1.73917 q^{77} +(2.41875 - 0.880352i) q^{78} +(2.24035 - 12.7057i) q^{79} +(-0.907604 + 0.761570i) q^{80} +(0.766044 + 0.642788i) q^{81} +(-1.68092 - 9.53298i) q^{82} +(-1.94949 - 3.37662i) q^{83} +(0.733956 - 1.27125i) q^{84} +(2.47906 + 0.902302i) q^{85} +(-6.81180 - 2.47929i) q^{86} +(-4.70574 + 8.15058i) q^{87} +(0.592396 + 1.02606i) q^{88} +(2.15523 + 12.2229i) q^{89} +(0.907604 + 0.761570i) q^{90} +(-2.89440 + 2.42869i) q^{91} +(0.205737 - 1.16679i) q^{92} +(7.45084 - 2.71188i) q^{93} +4.86484 q^{94} +(2.51707 - 4.50946i) q^{95} -1.00000 q^{96} +(-12.1356 + 4.41701i) q^{97} +(0.841367 - 4.77163i) q^{98} +(0.907604 - 0.761570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 9 q^{5} + 9 q^{7} + 3 q^{8} - 3 q^{12} + 15 q^{13} - 6 q^{14} - 9 q^{15} - 9 q^{17} - 6 q^{18} - 12 q^{19} - 3 q^{21} + 9 q^{22} + 9 q^{23} + 9 q^{25} - 3 q^{27} - 3 q^{28} - 9 q^{29} - 9 q^{31} + 9 q^{33}+ \cdots + 9 q^{99}+O(q^{100}) $ 6 * q - 9 * q^5 + 9 * q^7 + 3 * q^8 - 3 * q^12 + 15 * q^13 - 6 * q^14 - 9 * q^15 - 9 * q^17 - 6 * q^18 - 12 * q^19 - 3 * q^21 + 9 * q^22 + 9 * q^23 + 9 * q^25 - 3 * q^27 - 3 * q^28 - 9 * q^29 - 9 * q^31 + 9 * q^33 - 36 * q^35 + 18 * q^37 + 18 * q^38 + 27 * q^41 - 6 * q^42 - 21 * q^43 - 9 * q^44 + 27 * q^47 - 12 * q^49 + 3 * q^50 + 9 * q^51 - 3 * q^52 - 9 * q^55 + 18 * q^56 + 18 * q^57 - 36 * q^58 + 9 * q^59 + 9 * q^60 - 3 * q^61 + 21 * q^62 - 3 * q^63 - 3 * q^64 - 18 * q^65 - 3 * q^67 + 36 * q^70 + 9 * q^71 - 12 * q^73 - 6 * q^74 + 6 * q^75 + 9 * q^76 + 18 * q^77 + 12 * q^78 - 21 * q^79 - 9 * q^80 - 27 * q^82 - 9 * q^83 + 9 * q^84 + 18 * q^85 - 6 * q^86 - 18 * q^87 + 9 * q^90 + 24 * q^91 - 9 * q^92 + 33 * q^93 - 18 * q^94 + 36 * q^95 - 6 * q^96 - 54 * q^97 - 24 * q^98 + 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.907604	−	0.761570i	−0.405893	−	0.340584i	0.416873	−	0.908965i	$-0.363126\pi$
$5$	−0.907604	−	0.761570i	−0.405893	−	0.340584i	−0.822766	+	0.568380i	$0.807570\pi$
$6$	−0.173648	−	0.984808i	−0.0708916	−	0.402046i
$7$	0.733956	+	1.27125i	0.277409	+	0.480487i	0.970740	−	0.240133i	$-0.0771909\pi$
$7$	0.733956	+	1.27125i	0.277409	+	0.480487i	−0.693331	+	0.720619i	$0.743858\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	−1.11334	−	0.405223i	−0.352069	−	0.128143i
$11$	−0.592396	+	1.02606i	−0.178614	+	0.309369i	−0.941406	−	0.337275i	$-0.890495\pi$
$11$	−0.592396	+	1.02606i	−0.178614	+	0.309369i	0.762792	+	0.646644i	$0.223828\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.446967	+	2.53487i	0.123966	+	0.703047i	0.981916	+	0.189315i	$0.0606266\pi$
$13$	0.446967	+	2.53487i	0.123966	+	0.703047i	−0.857950	+	0.513733i	$0.828262\pi$
$14$	1.12449	+	0.943555i	0.300531	+	0.252176i
$15$	−0.907604	+	0.761570i	−0.234342	+	0.196637i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.09240	+	0.761570i	−0.507481	+	0.184708i	−0.583056	−	0.812432i	$-0.698143\pi$
$17$	−2.09240	+	0.761570i	−0.507481	+	0.184708i	0.0755749	+	0.997140i	$0.475921\pi$
$18$	−1.00000			−0.235702
$19$	0.819078	+	4.28125i	0.187909	+	0.982186i
$19$	0.819078	+	4.28125i	0.187909	+	0.982186i
$20$	−1.18479			−0.264928
$21$	1.37939	−	0.502055i	0.301007	−	0.109557i
$22$	−0.205737	+	1.16679i	−0.0438633	+	0.248761i
$23$	0.907604	−	0.761570i	0.189248	−	0.158798i	−0.543241	−	0.839577i	$-0.682803\pi$
$23$	0.907604	−	0.761570i	0.189248	−	0.158798i	0.732489	+	0.680779i	$0.238358\pi$
$24$	−0.766044	−	0.642788i	−0.156368	−	0.131208i
$25$	−0.624485	−	3.54163i	−0.124897	−	0.708326i
$26$	1.28699	+	2.22913i	0.252399	+	0.437168i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	1.37939	+	0.502055i	0.260679	+	0.0948795i
$29$	−8.84389	−	3.21891i	−1.64227	−	0.597737i	−0.654836	−	0.755771i	$-0.727262\pi$
$29$	−8.84389	−	3.21891i	−1.64227	−	0.597737i	−0.987434	+	0.158034i	$0.949485\pi$
$30$	−0.592396	+	1.02606i	−0.108156	+	0.187332i
$31$	3.96451	+	6.86673i	0.712047	+	1.23330i	0.964088	+	0.265584i	$0.0855649\pi$
$31$	3.96451	+	6.86673i	0.712047	+	1.23330i	−0.252041	+	0.967717i	$0.581102\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	0.907604	+	0.761570i	0.157994	+	0.132572i
$34$	−1.70574	+	1.43128i	−0.292531	+	0.245463i
$35$	0.302004	−	1.71275i	0.0510479	−	0.289507i
$36$	−0.939693	+	0.342020i	−0.156615	+	0.0570034i
$37$	−0.0641778			−0.0105508			−0.00527538	−	0.999986i	$-0.501679\pi$
$37$	−0.0641778			−0.0105508			−0.00527538	+	0.999986i	$0.501679\pi$
$38$	2.23396	+	3.74292i	0.362395	+	0.607182i
$39$	2.57398			0.412166
$40$	−1.11334	+	0.405223i	−0.176035	+	0.0640714i
$41$	1.68092	−	9.53298i	0.262516	−	1.48880i	−0.513501	−	0.858089i	$-0.671652\pi$
$41$	1.68092	−	9.53298i	0.262516	−	1.48880i	0.776017	−	0.630713i	$-0.217237\pi$
$42$	1.12449	−	0.943555i	0.173512	−	0.145594i
$43$	−5.55303	−	4.65955i	−0.846830	−	0.710574i	0.112259	−	0.993679i	$-0.464191\pi$
$43$	−5.55303	−	4.65955i	−0.846830	−	0.710574i	−0.959089	+	0.283104i	$0.908636\pi$
$44$	0.205737	+	1.16679i	0.0310160	+	0.175901i
$45$	0.592396	+	1.02606i	0.0883092	+	0.152956i
$46$	0.592396	−	1.02606i	0.0873441	−	0.151284i
$47$	4.57145	+	1.66387i	0.666815	+	0.242701i	0.653176	−	0.757206i	$-0.273436\pi$
$47$	4.57145	+	1.66387i	0.666815	+	0.242701i	0.0136389	+	0.999907i	$0.495658\pi$
$48$	−0.939693	−	0.342020i	−0.135633	−	0.0493664i
$49$	2.42262	−	4.19610i	0.346088	−	0.599443i
$50$	−1.79813	−	3.11446i	−0.254294	−	0.440451i
$51$	0.386659	+	2.19285i	0.0541431	+	0.307061i
$52$	1.97178	+	1.65452i	0.273437	+	0.229441i
$53$	−1.11334	+	0.934204i	−0.152929	+	0.128323i	−0.716042	−	0.698057i	$-0.754048\pi$
$53$	−1.11334	+	0.934204i	−0.152929	+	0.128323i	0.563113	+	0.826380i	$0.309604\pi$
$54$	−0.173648	+	0.984808i	−0.0236305	+	0.134015i
$55$	1.31908	−	0.480105i	0.177864	−	0.0647374i
$56$	1.46791			0.196158
$57$	4.35844	−	0.0632028i	0.577290	−	0.00837141i
$58$	−9.41147			−1.23579
$59$	−1.31908	+	0.480105i	−0.171729	+	0.0625044i	−0.426454	−	0.904509i	$-0.640237\pi$
$59$	−1.31908	+	0.480105i	−0.171729	+	0.0625044i	0.254725	+	0.967014i	$0.418015\pi$
$60$	−0.205737	+	1.16679i	−0.0265605	+	0.150632i
$61$	5.97565	−	5.01417i	0.765104	−	0.641998i	−0.174346	−	0.984684i	$-0.555781\pi$
$61$	5.97565	−	5.01417i	0.765104	−	0.641998i	0.939450	+	0.342686i	$0.111337\pi$
$62$	6.07398	+	5.09667i	0.771396	+	0.647278i
$63$	−0.254900	−	1.44561i	−0.0321144	−	0.182130i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	1.52481	−	2.64106i	0.189130	−	0.327583i
$66$	1.11334	+	0.405223i	0.137043	+	0.0498795i
$67$	−8.19119	−	2.98135i	−1.00071	−	0.364230i	−0.210854	−	0.977518i	$-0.567624\pi$
$67$	−8.19119	−	2.98135i	−1.00071	−	0.364230i	−0.789859	+	0.613288i	$0.789847\pi$
$68$	−1.11334	+	1.92836i	−0.135012	+	0.233848i
$69$	−0.592396	−	1.02606i	−0.0713161	−	0.123523i
$70$	−0.302004	−	1.71275i	−0.0360963	−	0.204713i
$71$	11.2135	+	9.40923i	1.33079	+	1.11667i	0.983891	+	0.178769i	$0.0572114\pi$
$71$	11.2135	+	9.40923i	1.33079	+	1.11667i	0.346904	+	0.937901i	$0.387233\pi$
$72$	−0.766044	+	0.642788i	−0.0902792	+	0.0757532i
$73$	1.13563	−	6.44047i	0.132915	−	0.753801i	−0.843373	−	0.537328i	$-0.819434\pi$
$73$	1.13563	−	6.44047i	0.132915	−	0.753801i	0.976289	−	0.216473i	$-0.0694552\pi$
$74$	−0.0603074	+	0.0219501i	−0.00701059	+	0.00255165i
$75$	−3.59627			−0.415261
$76$	3.37939	+	2.75314i	0.387642	+	0.315806i
$77$	−1.73917			−0.198197
$78$	2.41875	−	0.880352i	0.273869	−	0.0996803i
$79$	2.24035	−	12.7057i	0.252059	−	1.42950i	−0.551450	−	0.834208i	$-0.685925\pi$
$79$	2.24035	−	12.7057i	0.252059	−	1.42950i	0.803510	−	0.595292i	$-0.202963\pi$
$80$	−0.907604	+	0.761570i	−0.101473	+	0.0851461i
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	−1.68092	−	9.53298i	−0.185627	−	1.05274i
$83$	−1.94949	−	3.37662i	−0.213985	−	0.370632i	0.738973	−	0.673735i	$-0.235311\pi$
$83$	−1.94949	−	3.37662i	−0.213985	−	0.370632i	−0.952958	+	0.303102i	$0.901978\pi$
$84$	0.733956	−	1.27125i	0.0800811	−	0.138705i
$85$	2.47906	+	0.902302i	0.268891	+	0.0978684i
$86$	−6.81180	−	2.47929i	−0.734536	−	0.267349i
$87$	−4.70574	+	8.15058i	−0.504508	+	0.873833i
$88$	0.592396	+	1.02606i	0.0631497	+	0.109378i
$89$	2.15523	+	12.2229i	0.228454	+	1.29563i	0.855971	+	0.517024i	$0.172960\pi$
$89$	2.15523	+	12.2229i	0.228454	+	1.29563i	−0.627517	+	0.778603i	$0.715929\pi$
$90$	0.907604	+	0.761570i	0.0956698	+	0.0802765i
$91$	−2.89440	+	2.42869i	−0.303416	+	0.254596i
$92$	0.205737	−	1.16679i	0.0214496	−	0.121647i
$93$	7.45084	−	2.71188i	0.772616	−	0.281209i
$94$	4.86484			0.501770
$95$	2.51707	−	4.50946i	0.258246	−	0.462661i
$96$	−1.00000			−0.102062
$97$	−12.1356	+	4.41701i	−1.23219	+	0.448479i	−0.874346	−	0.485303i	$-0.838709\pi$
$97$	−12.1356	+	4.41701i	−1.23219	+	0.448479i	−0.357841	+	0.933783i	$0.616487\pi$
$98$	0.841367	−	4.77163i	0.0849909	−	0.482007i
$99$	0.907604	−	0.761570i	0.0912176	−	0.0765407i
$100$	−2.75490	−	2.31164i	−0.275490	−	0.231164i
$101$	2.38578	+	13.5304i	0.237394	+	1.34633i	0.837513	+	0.546418i	$0.184009\pi$
$101$	2.38578	+	13.5304i	0.237394	+	1.34633i	−0.600118	+	0.799911i	$0.704880\pi$
$102$	1.11334	+	1.92836i	0.110237	+	0.190936i
$103$	−8.56805	+	14.8403i	−0.844235	+	1.46226i	0.0420491	+	0.999116i	$0.486611\pi$
$103$	−8.56805	+	14.8403i	−0.844235	+	1.46226i	−0.886284	+	0.463142i	$0.846722\pi$
$104$	2.41875	+	0.880352i	0.237178	+	0.0863256i
$105$	−1.63429	−	0.594831i	−0.159490	−	0.0580496i
$106$	−0.726682	+	1.25865i	−0.0705816	+	0.122251i
$107$	5.25150	+	9.09586i	0.507681	+	0.879330i	0.999960	+	0.00889246i	$0.00283060\pi$
$107$	5.25150	+	9.09586i	0.507681	+	0.879330i	−0.492279	+	0.870437i	$0.663836\pi$
$108$	0.173648	+	0.984808i	0.0167093	+	0.0947632i
$109$	−6.16044	−	5.16923i	−0.590064	−	0.495122i	0.298171	−	0.954512i	$-0.403623\pi$
$109$	−6.16044	−	5.16923i	−0.590064	−	0.495122i	−0.888234	+	0.459390i	$0.848068\pi$
$110$	1.07532	−	0.902302i	0.102528	−	0.0860312i
$111$	−0.0111444	+	0.0632028i	−0.00105778	+	0.00599894i
$112$	1.37939	−	0.502055i	0.130340	−	0.0474398i
$113$	−19.1411			−1.80065			−0.900324	−	0.435220i	$-0.856670\pi$
$113$	−19.1411			−1.80065			−0.900324	+	0.435220i	$0.856670\pi$
$114$	4.07398	−	1.55007i	0.381563	−	0.145177i
$115$	−1.40373			−0.130899
$116$	−8.84389	+	3.21891i	−0.821135	+	0.298869i
$117$	0.446967	−	2.53487i	0.0413221	−	0.234349i
$118$	−1.07532	+	0.902302i	−0.0989914	+	0.0830637i
$119$	−2.50387	−	2.10100i	−0.229529	−	0.192598i
$120$	0.205737	+	1.16679i	0.0187811	+	0.106513i
$121$	4.79813	+	8.31061i	0.436194	+	0.755510i
$122$	3.90033	−	6.75557i	0.353119	−	0.611621i
$123$	−9.09627	−	3.31077i	−0.820183	−	0.298522i
$124$	7.45084	+	2.71188i	0.669105	+	0.243534i
$125$	−5.09240	+	8.82029i	−0.455478	+	0.788911i
$126$	−0.733956	−	1.27125i	−0.0653860	−	0.113252i
$127$	1.26352	+	7.16577i	0.112119	+	0.635859i	0.988136	+	0.153579i	$0.0490800\pi$
$127$	1.26352	+	7.16577i	0.112119	+	0.635859i	−0.876017	+	0.482280i	$0.839809\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−5.55303	+	4.65955i	−0.488917	+	0.410250i
$130$	0.529563	−	3.00330i	0.0464457	−	0.263407i
$131$	6.48293	−	2.35959i	0.566416	−	0.206159i	−0.0429093	−	0.999079i	$-0.513663\pi$
$131$	6.48293	−	2.35959i	0.566416	−	0.206159i	0.609325	+	0.792920i	$0.291440\pi$
$132$	1.18479			0.103123
$133$	−4.84137	+	4.18350i	−0.419800	+	0.362755i
$134$	−8.71688			−0.753024
$135$	1.11334	−	0.405223i	0.0958211	−	0.0348760i
$136$	−0.386659	+	2.19285i	−0.0331558	+	0.188036i
$137$	12.1211	−	10.1708i	1.03557	−	0.868950i	0.0440702	−	0.999028i	$-0.485967\pi$
$137$	12.1211	−	10.1708i	1.03557	−	0.868950i	0.991504	+	0.130079i	$0.0415230\pi$
$138$	−0.907604	−	0.761570i	−0.0772604	−	0.0648291i
$139$	−2.68732	−	15.2405i	−0.227935	−	1.29269i	−0.856993	−	0.515327i	$-0.827670\pi$
$139$	−2.68732	−	15.2405i	−0.227935	−	1.29269i	0.629058	−	0.777358i	$-0.283441\pi$
$140$	−0.869585	−	1.50617i	−0.0734934	−	0.127294i
$141$	2.43242	−	4.21307i	0.204847	−	0.354805i
$142$	13.7554	+	5.00654i	1.15432	+	0.420140i
$143$	−2.86571	−	1.04303i	−0.239643	−	0.0872230i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	5.57532	+	9.65674i	0.463005	+	0.801949i
$146$	−1.13563	−	6.44047i	−0.0939854	−	0.533018i
$147$	−3.71167	−	3.11446i	−0.306133	−	0.256876i
$148$	−0.0491630	+	0.0412527i	−0.00404118	+	0.00339095i
$149$	0.386659	−	2.19285i	0.0316764	−	0.179646i	−0.964865	−	0.262747i	$-0.915371\pi$
$149$	0.386659	−	2.19285i	0.0316764	−	0.179646i	0.996541	+	0.0831016i	$0.0264826\pi$
$150$	−3.37939	+	1.23000i	−0.275926	+	0.100429i
$151$	6.59627			0.536797			0.268398	−	0.963308i	$-0.413506\pi$
$151$	6.59627			0.536797			0.268398	+	0.963308i	$0.413506\pi$
$152$	4.11721	+	1.43128i	0.333950	+	0.116092i
$153$	2.22668			0.180017
$154$	−1.63429	+	0.594831i	−0.131694	+	0.0479329i
$155$	1.63129	−	9.25152i	0.131029	−	0.743100i
$156$	1.97178	−	1.65452i	0.157869	−	0.132468i
$157$	7.08899	+	5.94837i	0.565763	+	0.474732i	0.880237	−	0.474534i	$-0.157384\pi$
$157$	7.08899	+	5.94837i	0.565763	+	0.474732i	−0.314474	+	0.949266i	$0.601828\pi$
$158$	−2.24035	−	12.7057i	−0.178233	−	1.01081i
$159$	0.726682	+	1.25865i	0.0576296	+	0.0998174i
$160$	−0.592396	+	1.02606i	−0.0468330	+	0.0811172i
$161$	1.63429	+	0.594831i	0.128800	+	0.0468793i
$162$	0.939693	+	0.342020i	0.0738292	+	0.0268716i
$163$	1.57011	−	2.71951i	0.122980	−	0.213008i	−0.797961	−	0.602709i	$-0.794088\pi$
$163$	1.57011	−	2.71951i	0.122980	−	0.213008i	0.920942	+	0.389700i	$0.127421\pi$
$164$	−4.84002	−	8.38316i	−0.377942	−	0.654615i
$165$	−0.243756	−	1.38241i	−0.0189764	−	0.107620i
$166$	−2.98680	−	2.50622i	−0.231820	−	0.194520i
$167$	12.1591	−	10.2027i	0.940899	−	0.789508i	−0.0368422	−	0.999321i	$-0.511730\pi$
$167$	12.1591	−	10.2027i	0.940899	−	0.789508i	0.977742	+	0.209813i	$0.0672854\pi$
$168$	0.254900	−	1.44561i	0.0196660	−	0.111531i
$169$	5.99020	−	2.18025i	0.460785	−	0.167712i
$170$	2.63816			0.202337
$171$	0.694593	−	4.30320i	0.0531168	−	0.329074i
$172$	−7.24897			−0.552729
$173$	−3.25237	+	1.18377i	−0.247273	+	0.0900002i	−0.462684	−	0.886524i	$-0.653113\pi$
$173$	−3.25237	+	1.18377i	−0.247273	+	0.0900002i	0.215410	+	0.976524i	$0.430891\pi$
$174$	−1.63429	+	9.26849i	−0.123895	+	0.702643i
$175$	4.04395	−	3.39328i	0.305694	−	0.256508i
$176$	0.907604	+	0.761570i	0.0684132	+	0.0574055i
$177$	0.243756	+	1.38241i	0.0183218	+	0.103908i
$178$	6.20574	+	10.7487i	0.465140	+	0.805646i
$179$	0.315207	−	0.545955i	0.0235597	−	0.0408066i	−0.854005	−	0.520265i	$-0.825833\pi$
$179$	0.315207	−	0.545955i	0.0235597	−	0.0408066i	0.877565	+	0.479458i	$0.159167\pi$
$180$	1.11334	+	0.405223i	0.0829835	+	0.0302035i
$181$	11.0778	+	4.03201i	0.823410	+	0.299697i	0.719151	−	0.694853i	$-0.244531\pi$
$181$	11.0778	+	4.03201i	0.823410	+	0.299697i	0.104259	+	0.994550i	$0.466753\pi$
$182$	−1.88919	+	3.27217i	−0.140036	+	0.242549i
$183$	−3.90033	−	6.75557i	−0.288321	−	0.499386i
$184$	−0.205737	−	1.16679i	−0.0151671	−	0.0860171i
$185$	0.0582480	+	0.0488759i	0.00428248	+	0.00359342i
$186$	6.07398	−	5.09667i	0.445366	−	0.373706i
$187$	0.458111	−	2.59808i	0.0335004	−	0.189990i
$188$	4.57145	−	1.66387i	0.333407	−	0.121350i
$189$	−1.46791			−0.106775
$190$	0.822948	−	5.09840i	0.0597029	−	0.369877i
$191$	11.4192			0.826265			0.413133	−	0.910671i	$-0.364435\pi$
$191$	11.4192			0.826265			0.413133	+	0.910671i	$0.364435\pi$
$192$	−0.939693	+	0.342020i	−0.0678165	+	0.0246832i
$193$	1.64796	−	9.34602i	0.118622	−	0.672741i	−0.866270	−	0.499576i	$-0.833489\pi$
$193$	1.64796	−	9.34602i	0.118622	−	0.672741i	0.984893	−	0.173166i	$-0.0553996\pi$
$194$	−9.89306	+	8.30126i	−0.710280	+	0.595996i
$195$	−2.33615	−	1.96026i	−0.167295	−	0.140377i
$196$	−0.841367	−	4.77163i	−0.0600976	−	0.340830i
$197$	−3.56758	−	6.17923i	−0.254180	−	0.440252i	0.710493	−	0.703705i	$-0.248472\pi$
$197$	−3.56758	−	6.17923i	−0.254180	−	0.440252i	−0.964672	+	0.263452i	$0.915139\pi$
$198$	0.592396	−	1.02606i	0.0420998	−	0.0729189i
$199$	16.6814	+	6.07153i	1.18251	+	0.430399i	0.857089	−	0.515169i	$-0.172271\pi$
$199$	16.6814	+	6.07153i	1.18251	+	0.430399i	0.325424	+	0.945568i	$0.394493\pi$
$200$	−3.37939	−	1.23000i	−0.238959	−	0.0869738i
$201$	−4.35844	+	7.54904i	−0.307421	+	0.532468i
$202$	6.86959	+	11.8985i	0.483342	+	0.837173i
$203$	−2.39899	−	13.6053i	−0.168376	−	0.954907i
$204$	1.70574	+	1.43128i	0.119425	+	0.100210i
$205$	−8.78564	+	7.37203i	−0.613616	+	0.514885i
$206$	−2.97565	+	16.8758i	−0.207323	+	1.17579i
$207$	−1.11334	+	0.405223i	−0.0773825	+	0.0281649i
$208$	2.57398			0.178473
$209$	−4.87804	−	1.69577i	−0.337421	−	0.117299i
$210$	−1.73917			−0.120014
$211$	−2.03209	+	0.739620i	−0.139895	+	0.0509175i	−0.411019	−	0.911627i	$-0.634827\pi$
$211$	−2.03209	+	0.739620i	−0.139895	+	0.0509175i	0.271124	+	0.962544i	$0.412605\pi$
$212$	−0.252374	+	1.43128i	−0.0173331	+	0.0983009i
$213$	11.2135	−	9.40923i	0.768335	−	0.644709i
$214$	8.04576	+	6.75119i	0.549997	+	0.461502i
$215$	1.49138	+	8.45805i	0.101711	+	0.576834i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	−5.81954	+	10.0797i	−0.395056	+	0.684258i
$218$	−7.55690	−	2.75049i	−0.511818	−	0.186287i
$219$	−6.14543	−	2.23675i	−0.415270	−	0.151146i
$220$	0.701867	−	1.21567i	0.0473198	−	0.0819604i
$221$	−2.86571	−	4.96356i	−0.192769	−	0.333885i
$222$	0.0111444	+	0.0632028i	0.000747960	+	0.00424189i
$223$	−21.6446	−	18.1619i	−1.44943	−	1.21621i	−0.932997	−	0.359883i	$-0.882817\pi$
$223$	−21.6446	−	18.1619i	−1.44943	−	1.21621i	−0.516429	−	0.856330i	$-0.672739\pi$
$224$	1.12449	−	0.943555i	0.0751328	−	0.0630439i
$225$	−0.624485	+	3.54163i	−0.0416323	+	0.236109i
$226$	−17.9868	+	6.54666i	−1.19646	+	0.435477i
$227$	−21.0232			−1.39536			−0.697680	−	0.716409i	$-0.745784\pi$
$227$	−21.0232			−1.39536			−0.697680	+	0.716409i	$0.745784\pi$
$228$	3.29813	−	2.84997i	0.218424	−	0.188744i
$229$	7.96080			0.526064			0.263032	−	0.964787i	$-0.415277\pi$
$229$	7.96080			0.526064			0.263032	+	0.964787i	$0.415277\pi$
$230$	−1.31908	+	0.480105i	−0.0869774	+	0.0316572i
$231$	−0.302004	+	1.71275i	−0.0198704	+	0.112691i
$232$	−7.20961	+	6.04958i	−0.473334	+	0.397174i
$233$	11.2515	+	9.44113i	0.737110	+	0.618509i	0.932060	−	0.362304i	$-0.118010\pi$
$233$	11.2515	+	9.44113i	0.737110	+	0.618509i	−0.194950	+	0.980813i	$0.562454\pi$
$234$	−0.446967	−	2.53487i	−0.0292191	−	0.165710i
$235$	−2.88191	−	4.99162i	−0.187995	−	0.325617i
$236$	−0.701867	+	1.21567i	−0.0456876	+	0.0791333i
$237$	−12.1236	−	4.41263i	−0.787513	−	0.286631i
$238$	−3.07145	−	1.11792i	−0.199093	−	0.0724638i
$239$	−7.86484	+	13.6223i	−0.508734	+	0.881153i	0.491215	+	0.871038i	$0.336553\pi$
$239$	−7.86484	+	13.6223i	−0.508734	+	0.881153i	−0.999949	+	0.0101147i	$0.996780\pi$
$240$	0.592396	+	1.02606i	0.0382390	+	0.0662319i
$241$	1.71079	+	9.70237i	0.110202	+	0.624985i	0.989015	+	0.147818i	$0.0472250\pi$
$241$	1.71079	+	9.70237i	0.110202	+	0.624985i	−0.878813	+	0.477166i	$0.841664\pi$
$242$	7.35117	+	6.16836i	0.472551	+	0.396517i
$243$	0.766044	−	0.642788i	0.0491418	−	0.0412348i
$244$	1.35457	−	7.68215i	0.0867175	−	0.491799i
$245$	−5.39440	+	1.96340i	−0.344636	+	0.125437i
$246$	−9.68004			−0.617177
$247$	−10.4863	+	3.98983i	−0.667229	+	0.253867i
$248$	7.92902			0.503493
$249$	−3.66385	+	1.33353i	−0.232187	+	0.0845091i
$250$	−1.76857	+	10.0301i	−0.111854	+	0.634357i
$251$	3.54117	−	2.97140i	0.223517	−	0.187553i	−0.524152	−	0.851625i	$-0.675618\pi$
$251$	3.54117	−	2.97140i	0.223517	−	0.187553i	0.747669	+	0.664072i	$0.231173\pi$
$252$	−1.12449	−	0.943555i	−0.0708359	−	0.0594384i
$253$	0.243756	+	1.38241i	0.0153248	+	0.0869112i
$254$	3.63816	+	6.30147i	0.228278	+	0.395389i
$255$	1.31908	−	2.28471i	0.0826039	−	0.143074i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	2.83527	+	1.03196i	0.176860	+	0.0643716i	0.428932	−	0.903337i	$-0.358890\pi$
$257$	2.83527	+	1.03196i	0.176860	+	0.0643716i	−0.252073	+	0.967708i	$0.581112\pi$
$258$	−3.62449	+	6.27779i	−0.225651	+	0.390838i
$259$	−0.0471036	−	0.0815859i	−0.00292688	−	0.00506950i
$260$	−0.529563	−	3.00330i	−0.0328421	−	0.186257i
$261$	7.20961	+	6.04958i	0.446263	+	0.374460i
$262$	5.28493	−	4.43458i	0.326504	−	0.273969i
$263$	−0.869585	+	4.93166i	−0.0536209	+	0.304099i	−0.999810	−	0.0195163i	$-0.993787\pi$
$263$	−0.869585	+	4.93166i	−0.0536209	+	0.304099i	0.946189	+	0.323616i	$0.104898\pi$
$264$	1.11334	−	0.405223i	0.0685214	−	0.0249397i
$265$	1.72193			0.105778
$266$	−3.11856	+	5.58705i	−0.191211	+	0.342564i
$267$	12.4115			0.759570
$268$	−8.19119	+	2.98135i	−0.500357	+	0.182115i
$269$	−4.26945	+	24.2132i	−0.260313	+	1.47631i	0.521745	+	0.853102i	$0.325281\pi$
$269$	−4.26945	+	24.2132i	−0.260313	+	1.47631i	−0.782058	+	0.623206i	$0.785830\pi$
$270$	0.907604	−	0.761570i	0.0552350	−	0.0463477i
$271$	−1.28699	−	1.07991i	−0.0781790	−	0.0656000i	0.602861	−	0.797846i	$-0.294027\pi$
$271$	−1.28699	−	1.07991i	−0.0781790	−	0.0656000i	−0.681040	+	0.732246i	$0.738472\pi$
$272$	0.386659	+	2.19285i	0.0234447	+	0.132961i
$273$	1.88919	+	3.27217i	0.114339	+	0.198040i
$274$	7.91147	−	13.7031i	0.477950	−	0.827833i
$275$	4.00387	+	1.45729i	0.241442	+	0.0878779i
$276$	−1.11334	−	0.405223i	−0.0670152	−	0.0243916i
$277$	14.9907	−	25.9646i	0.900702	−	1.56006i	0.0741168	−	0.997250i	$-0.476386\pi$
$277$	14.9907	−	25.9646i	0.900702	−	1.56006i	0.826585	−	0.562812i	$-0.190280\pi$
$278$	−7.73783	−	13.4023i	−0.464084	−	0.803817i
$279$	−1.37686	−	7.80856i	−0.0824304	−	0.467486i
$280$	−1.33228	−	1.11792i	−0.0796191	−	0.0668083i
$281$	13.4914	−	11.3206i	0.804828	−	0.675331i	−0.144539	−	0.989499i	$-0.546170\pi$
$281$	13.4914	−	11.3206i	0.804828	−	0.675331i	0.949367	+	0.314168i	$0.101725\pi$
$282$	0.844770	−	4.79093i	0.0503053	−	0.285296i
$283$	−14.9547	+	5.44307i	−0.888965	+	0.323557i	−0.745822	−	0.666145i	$-0.767943\pi$
$283$	−14.9547	+	5.44307i	−0.888965	+	0.323557i	−0.143143	+	0.989702i	$0.545721\pi$
$284$	14.6382			0.868615
$285$	−4.00387	−	3.26189i	−0.237169	−	0.193218i
$286$	−3.04963			−0.180328
$287$	13.3525	−	4.85992i	0.788174	−	0.286872i
$288$	−0.173648	+	0.984808i	−0.0102323	+	0.0580304i
$289$	−9.22462	+	7.74038i	−0.542625	+	0.455316i
$290$	8.54189	+	7.16750i	0.501597	+	0.420890i
$291$	2.24257	+	12.7183i	0.131462	+	0.745558i
$292$	−3.26991	−	5.66366i	−0.191357	−	0.331441i
$293$	−0.134285	+	0.232589i	−0.00784503	+	0.0135880i	−0.869921	−	0.493191i	$-0.835831\pi$
$293$	−0.134285	+	0.232589i	−0.00784503	+	0.0135880i	0.862076	+	0.506779i	$0.169164\pi$
$294$	−4.55303	−	1.65717i	−0.265538	−	0.0966480i
$295$	1.56283	+	0.568825i	0.0909917	+	0.0331183i
$296$	−0.0320889	+	0.0555796i	−0.00186513	+	0.00323050i
$297$	−0.592396	−	1.02606i	−0.0343743	−	0.0595381i
$298$	−0.386659	−	2.19285i	−0.0223986	−	0.127029i
$299$	2.33615	+	1.96026i	0.135103	+	0.113365i
$300$	−2.75490	+	2.31164i	−0.159054	+	0.133462i
$301$	1.84776	−	10.4792i	0.106503	−	0.604010i
$302$	6.19846	−	2.25606i	0.356681	−	0.129821i
$303$	13.7392			0.789295
$304$	4.35844	−	0.0632028i	0.249974	−	0.00362493i
$305$	−9.24216			−0.529205
$306$	2.09240	−	0.761570i	0.119614	−	0.0435361i
$307$	−0.0992034	+	0.562610i	−0.00566184	+	0.0321099i	−0.987508	−	0.157570i	$-0.949634\pi$
$307$	−0.0992034	+	0.562610i	−0.00566184	+	0.0321099i	0.981846	+	0.189680i	$0.0607451\pi$
$308$	−1.33228	+	1.11792i	−0.0759138	+	0.0636992i
$309$	13.1270	+	11.0149i	0.746770	+	0.626614i
$310$	−1.63129	−	9.25152i	−0.0926512	−	0.525451i
$311$	−7.17617	−	12.4295i	−0.406924	−	0.704812i	0.587620	−	0.809137i	$-0.300065\pi$
$311$	−7.17617	−	12.4295i	−0.406924	−	0.704812i	−0.994543	+	0.104325i	$0.966732\pi$
$312$	1.28699	−	2.22913i	0.0728614	−	0.126200i
$313$	2.25877	+	0.822125i	0.127673	+	0.0464693i	0.405067	−	0.914287i	$-0.367248\pi$
$313$	2.25877	+	0.822125i	0.127673	+	0.0464693i	−0.277393	+	0.960756i	$0.589471\pi$
$314$	8.69594	+	3.16506i	0.490740	+	0.178615i
$315$	−0.869585	+	1.50617i	−0.0489956	+	0.0848628i
$316$	−6.45084	−	11.1732i	−0.362888	−	0.628540i
$317$	2.44104	+	13.8438i	0.137102	+	0.777546i	0.973373	+	0.229228i	$0.0736203\pi$
$317$	2.44104	+	13.8438i	0.137102	+	0.777546i	−0.836270	+	0.548317i	$0.815269\pi$
$318$	1.11334	+	0.934204i	0.0624331	+	0.0523876i
$319$	8.54189	−	7.16750i	0.478254	−	0.401303i
$320$	−0.205737	+	1.16679i	−0.0115011	+	0.0652257i
$321$	9.86959	−	3.59224i	0.550867	−	0.200499i
$322$	1.73917			0.0969202
$323$	−4.97431	−	8.33429i	−0.276778	−	0.463732i
$324$	1.00000			0.0555556
$325$	8.69846	−	3.16598i	0.482504	−	0.175617i
$326$	0.545293	−	3.09251i	0.0302010	−	0.171278i
$327$	−6.16044	+	5.16923i	−0.340673	+	0.285859i
$328$	−7.41534	−	6.22221i	−0.409444	−	0.343564i
$329$	1.24005	+	7.03266i	0.0683660	+	0.387723i
$330$	−0.701867	−	1.21567i	−0.0386365	−	0.0669204i
$331$	−13.4213	+	23.2463i	−0.737700	+	1.27773i	0.215829	+	0.976431i	$0.430755\pi$
$331$	−13.4213	+	23.2463i	−0.737700	+	1.27773i	−0.953529	+	0.301303i	$0.902579\pi$
$332$	−3.66385	−	1.33353i	−0.201080	−	0.0731871i
$333$	0.0603074	+	0.0219501i	0.00330482	+	0.00120286i
$334$	7.93629	−	13.7461i	0.434254	−	0.752151i
$335$	5.16385	+	8.94405i	0.282131	+	0.488665i
$336$	−0.254900	−	1.44561i	−0.0139059	−	0.0788645i
$337$	−16.0266	−	13.4479i	−0.873026	−	0.732556i	0.0917071	−	0.995786i	$-0.470768\pi$
$337$	−16.0266	−	13.4479i	−0.873026	−	0.732556i	−0.964733	+	0.263230i	$0.915212\pi$
$338$	4.88326	−	4.09754i	0.265614	−	0.222877i
$339$	−3.32383	+	18.8504i	−0.180525	+	1.02381i
$340$	2.47906	−	0.902302i	0.134446	−	0.0489342i
$341$	−9.39424			−0.508727
$342$	−0.819078	−	4.28125i	−0.0442907	−	0.231504i
$343$	17.3878			0.938851
$344$	−6.81180	+	2.47929i	−0.367268	+	0.133675i
$345$	−0.243756	+	1.38241i	−0.0131234	+	0.0744263i
$346$	−2.65136	+	2.22475i	−0.142538	+	0.119604i
$347$	−25.7670	−	21.6211i	−1.38324	−	1.16068i	−0.967994	−	0.250972i	$-0.919250\pi$
$347$	−25.7670	−	21.6211i	−1.38324	−	1.16068i	−0.415249	−	0.909708i	$-0.636306\pi$
$348$	1.63429	+	9.26849i	0.0876069	+	0.496843i
$349$	−13.5758	−	23.5140i	−0.726695	−	1.25867i	−0.958272	−	0.285857i	$-0.907722\pi$
$349$	−13.5758	−	23.5140i	−0.726695	−	1.25867i	0.231577	−	0.972817i	$-0.425611\pi$
$350$	2.63950	−	4.57175i	0.141087	−	0.244370i
$351$	−2.41875	−	0.880352i	−0.129103	−	0.0469897i
$352$	1.11334	+	0.405223i	0.0593413	+	0.0215985i
$353$	8.37258	−	14.5017i	0.445627	−	0.771849i	−0.552468	−	0.833534i	$-0.686314\pi$
$353$	8.37258	−	14.5017i	0.445627	−	0.771849i	0.998096	+	0.0616847i	$0.0196473\pi$
$354$	0.701867	+	1.21567i	0.0373038	+	0.0646121i
$355$	−3.01161	−	17.0797i	−0.159840	−	0.906496i
$356$	9.50774	+	7.97794i	0.503909	+	0.422830i
$357$	−2.50387	+	2.10100i	−0.132519	+	0.111197i
$358$	0.109470	−	0.620838i	0.00578569	−	0.0328123i
$359$	4.45336	−	1.62089i	0.235040	−	0.0855474i	−0.221815	−	0.975089i	$-0.571198\pi$
$359$	4.45336	−	1.62089i	0.235040	−	0.0855474i	0.456855	+	0.889541i	$0.348976\pi$
$360$	1.18479			0.0624440
$361$	−17.6582	+	7.01336i	−0.929380	+	0.369124i
$362$	11.7888			0.619606
$363$	9.01754	−	3.28212i	0.473298	−	0.172266i
$364$	−0.656107	+	3.72097i	−0.0343894	+	0.195032i
$365$	−5.93557	+	4.98054i	−0.310682	+	0.260693i
$366$	−5.97565	−	5.01417i	−0.312352	−	0.262095i
$367$	1.52687	+	8.65933i	0.0797022	+	0.452014i	0.998375	+	0.0569932i	$0.0181513\pi$
$367$	1.52687	+	8.65933i	0.0797022	+	0.452014i	−0.918672	+	0.395020i	$0.870738\pi$
$368$	−0.592396	−	1.02606i	−0.0308808	−	0.0534871i
$369$	−4.84002	+	8.38316i	−0.251962	+	0.436410i
$370$	0.0714517	+	0.0260063i	0.00371460	+	0.00135200i
$371$	−2.00475	−	0.729669i	−0.104081	−	0.0378825i
$372$	3.96451	−	6.86673i	0.205550	−	0.356023i
$373$	4.72281	+	8.18015i	0.244538	+	0.423552i	0.962002	−	0.273044i	$-0.0880304\pi$
$373$	4.72281	+	8.18015i	0.244538	+	0.423552i	−0.717464	+	0.696596i	$0.754697\pi$
$374$	−0.458111	−	2.59808i	−0.0236884	−	0.134343i
$375$	7.80200	+	6.54666i	0.402894	+	0.338068i
$376$	3.72668	−	3.12706i	0.192189	−	0.161266i
$377$	4.20661	−	23.8569i	0.216652	−	1.22869i
$378$	−1.37939	+	0.502055i	−0.0709479	+	0.0258229i
$379$	36.9077			1.89582			0.947910	−	0.318540i	$-0.103192\pi$
$379$	36.9077			1.89582			0.947910	+	0.318540i	$0.103192\pi$
$380$	−0.970437	−	5.07239i	−0.0497824	−	0.260208i
$381$	7.27631			0.372777
$382$	10.7306	−	3.90560i	0.549023	−	0.199828i
$383$	−5.11721	+	29.0211i	−0.261477	+	1.48291i	0.517405	+	0.855741i	$0.326898\pi$
$383$	−5.11721	+	29.0211i	−0.261477	+	1.48291i	−0.778882	+	0.627171i	$0.784213\pi$
$384$	−0.766044	+	0.642788i	−0.0390920	+	0.0328021i
$385$	1.57848	+	1.32450i	0.0804467	+	0.0675028i
$386$	−1.64796	−	9.34602i	−0.0838787	−	0.475700i
$387$	3.62449	+	6.27779i	0.184243	+	0.319118i
$388$	−6.45723	+	11.1843i	−0.327816	+	0.567795i
$389$	−16.6211	−	6.04958i	−0.842722	−	0.306726i	−0.115653	−	0.993290i	$-0.536896\pi$
$389$	−16.6211	−	6.04958i	−0.842722	−	0.306726i	−0.727069	+	0.686564i	$0.759118\pi$
$390$	−2.86571	−	1.04303i	−0.145111	−	0.0528161i
$391$	−1.31908	+	2.28471i	−0.0667086	+	0.115543i
$392$	−2.42262	−	4.19610i	−0.122361	−	0.211935i
$393$	−1.19800	−	6.79417i	−0.0604309	−	0.342721i
$394$	−5.46585	−	4.58639i	−0.275366	−	0.231059i
$395$	−11.7096	+	9.82553i	−0.589174	+	0.494376i
$396$	0.205737	−	1.16679i	0.0103387	−	0.0586335i
$397$	−11.8302	+	4.30585i	−0.593742	+	0.216104i	−0.621374	−	0.783514i	$-0.713425\pi$
$397$	−11.8302	+	4.30585i	−0.593742	+	0.216104i	0.0276326	+	0.999618i	$0.491203\pi$
$398$	17.7520			0.889826
$399$	3.27925	+	5.49427i	0.164168	+	0.275058i
$400$	−3.59627			−0.179813
$401$	22.6211	−	8.23340i	1.12964	−	0.411156i	0.291480	−	0.956577i	$-0.405852\pi$
$401$	22.6211	−	8.23340i	1.12964	−	0.411156i	0.838163	+	0.545420i	$0.183630\pi$
$402$	−1.51367	+	8.58445i	−0.0754950	+	0.428154i
$403$	−15.6343	+	13.1187i	−0.778799	+	0.653490i
$404$	10.5248	+	8.83137i	0.523629	+	0.439377i
$405$	−0.205737	−	1.16679i	−0.0102232	−	0.0579784i
$406$	−6.90760	−	11.9643i	−0.342819	−	0.593779i
$407$	0.0380187	−	0.0658503i	0.00188452	−	0.00326408i
$408$	2.09240	+	0.761570i	0.103589	+	0.0377033i
$409$	33.2276	+	12.0939i	1.64300	+	0.598003i	0.987560	−	0.157244i	$-0.0502610\pi$
$409$	33.2276	+	12.0939i	1.64300	+	0.598003i	0.655440	+	0.755247i	$0.272483\pi$
$410$	−5.73442	+	9.93231i	−0.283203	+	0.490522i
$411$	−7.91147	−	13.7031i	−0.390244	−	0.675923i
$412$	2.97565	+	16.8758i	0.146600	+	0.831409i
$413$	−1.57848	−	1.32450i	−0.0776718	−	0.0651744i
$414$	−0.907604	+	0.761570i	−0.0446063	+	0.0374291i
$415$	−0.802166	+	4.54931i	−0.0393768	+	0.223317i
$416$	2.41875	−	0.880352i	0.118589	−	0.0431628i
$417$	−15.4757			−0.757846
$418$	−5.16385	+	0.0748822i	−0.252572	+	0.00366261i
$419$	4.57903			0.223700			0.111850	−	0.993725i	$-0.464322\pi$
$419$	4.57903			0.223700			0.111850	+	0.993725i	$0.464322\pi$
$420$	−1.63429	+	0.594831i	−0.0797450	+	0.0290248i
$421$	0.0482857	−	0.273842i	0.00235330	−	0.0133462i	−0.983608	−	0.180317i	$-0.942288\pi$
$421$	0.0482857	−	0.273842i	0.00235330	−	0.0133462i	0.985962	+	0.166971i	$0.0533987\pi$
$422$	−1.65657	+	1.39003i	−0.0806408	+	0.0676656i
$423$	−3.72668	−	3.12706i	−0.181197	−	0.152043i
$424$	0.252374	+	1.43128i	0.0122564	+	0.0695093i
$425$	4.00387	+	6.93491i	0.194216	+	0.336392i
$426$	7.31908	−	12.6770i	0.354610	−	0.614203i
$427$	10.7601	+	3.91636i	0.520718	+	0.189526i
$428$	9.86959	+	3.59224i	0.477064	+	0.173637i
$429$	−1.52481	+	2.64106i	−0.0736188	+	0.127511i
$430$	4.29426	+	7.43788i	0.207088	+	0.358687i
$431$	−2.08079	−	11.8007i	−0.100228	−	0.568421i	−0.993019	−	0.117951i	$-0.962368\pi$
$431$	−2.08079	−	11.8007i	−0.100228	−	0.568421i	0.892792	−	0.450470i	$-0.148744\pi$
$432$	0.766044	+	0.642788i	0.0368563	+	0.0309261i
$433$	−22.3286	+	18.7359i	−1.07305	+	0.900392i	−0.995325	−	0.0965831i	$-0.969209\pi$
$433$	−22.3286	+	18.7359i	−1.07305	+	0.900392i	−0.0777205	+	0.996975i	$0.524764\pi$
$434$	−2.02111	+	11.4623i	−0.0970162	+	0.550206i
$435$	10.4782	−	3.81374i	0.502390	−	0.182855i
$436$	−8.04189			−0.385137
$437$	4.00387	+	3.26189i	0.191531	+	0.156038i
$438$	−6.53983			−0.312485
$439$	−5.91787	+	2.15393i	−0.282445	+	0.102801i	−0.479358	−	0.877619i	$-0.659130\pi$
$439$	−5.91787	+	2.15393i	−0.282445	+	0.102801i	0.196913	+	0.980421i	$0.436908\pi$
$440$	0.243756	−	1.38241i	0.0116206	−	0.0659037i
$441$	−3.71167	+	3.11446i	−0.176746	+	0.148308i
$442$	−4.39053	−	3.68409i	−0.208836	−	0.175234i
$443$	3.62583	+	20.5631i	0.172268	+	0.976982i	0.941250	+	0.337711i	$0.109653\pi$
$443$	3.62583	+	20.5631i	0.172268	+	0.976982i	−0.768981	+	0.639271i	$0.779236\pi$
$444$	0.0320889	+	0.0555796i	0.00152287	+	0.00263769i
$445$	7.35251	−	12.7349i	0.348542	−	0.603693i
$446$	−26.5510	−	9.66376i	−1.25723	−	0.457592i
$447$	−2.09240	−	0.761570i	−0.0989669	−	0.0360210i
$448$	0.733956	−	1.27125i	0.0346761	−	0.0600608i
$449$	−20.6878	−	35.8323i	−0.976317	−	1.69103i	−0.675519	−	0.737343i	$-0.736080\pi$
$449$	−20.6878	−	35.8323i	−0.976317	−	1.69103i	−0.300798	−	0.953688i	$-0.597253\pi$
$450$	0.624485	+	3.54163i	0.0294385	+	0.166954i
$451$	8.78564	+	7.37203i	0.413700	+	0.347135i
$452$	−14.6630	+	12.3037i	−0.689688	+	0.578717i
$453$	1.14543	−	6.49605i	0.0538170	−	0.305211i
$454$	−19.7554	+	7.19037i	−0.927165	+	0.337461i
$455$	4.47659			0.209866
$456$	2.12449	−	3.80612i	0.0994881	−	0.178238i
$457$	−27.6245			−1.29222			−0.646111	−	0.763244i	$-0.723606\pi$
$457$	−27.6245			−1.29222			−0.646111	+	0.763244i	$0.723606\pi$
$458$	7.48070	−	2.72275i	0.349550	−	0.127226i
$459$	0.386659	−	2.19285i	0.0180477	−	0.102354i
$460$	−1.07532	+	0.902302i	−0.0501372	+	0.0420701i
$461$	−14.1800	−	11.8985i	−0.660431	−	0.554167i	0.249785	−	0.968301i	$-0.419640\pi$
$461$	−14.1800	−	11.8985i	−0.660431	−	0.554167i	−0.910216	+	0.414134i	$0.864084\pi$
$462$	0.302004	+	1.71275i	0.0140505	+	0.0796843i
$463$	1.80928	+	3.13376i	0.0840843	+	0.145638i	0.905001	−	0.425410i	$-0.139870\pi$
$463$	1.80928	+	3.13376i	0.0840843	+	0.145638i	−0.820916	+	0.571048i	$0.806537\pi$
$464$	−4.70574	+	8.15058i	−0.218458	+	0.378381i
$465$	−8.82770	−	3.21302i	−0.409375	−	0.149000i
$466$	13.8020	+	5.02352i	0.639365	+	0.232710i
$467$	7.20099	−	12.4725i	0.333222	−	0.577158i	−0.649920	−	0.760003i	$-0.725197\pi$
$467$	7.20099	−	12.4725i	0.333222	−	0.577158i	0.983142	+	0.182845i	$0.0585308\pi$
$468$	−1.28699	−	2.22913i	−0.0594911	−	0.103042i
$469$	−2.22193	−	12.6012i	−0.102599	−	0.581870i
$470$	−4.41534	−	3.70491i	−0.203665	−	0.170895i
$471$	7.08899	−	5.94837i	0.326644	−	0.274086i
$472$	−0.243756	+	1.38241i	−0.0112198	+	0.0636305i
$473$	8.07057	−	2.93745i	0.371085	−	0.135064i
$474$	−12.9017			−0.592594
$475$	14.6511	−	5.57445i	0.672239	−	0.255773i
$476$	−3.26857			−0.149815
$477$	1.36571	−	0.497079i	0.0625318	−	0.0227597i
$478$	−2.73143	+	15.4907i	−0.124933	+	0.708528i
$479$	−24.4029	+	20.4764i	−1.11499	+	0.935592i	−0.998341	−	0.0575808i	$-0.981661\pi$
$479$	−24.4029	+	20.4764i	−1.11499	+	0.935592i	−0.116654	+	0.993173i	$0.537217\pi$
$480$	0.907604	+	0.761570i	0.0414263	+	0.0347608i
$481$	−0.0286853	−	0.162683i	−0.00130794	−	0.00741768i
$482$	4.92602	+	8.53212i	0.224374	+	0.388627i
$483$	0.869585	−	1.50617i	0.0395675	−	0.0685329i
$484$	9.01754	+	3.28212i	0.409888	+	0.149187i
$485$	14.3782	+	5.23324i	0.652881	+	0.237629i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	9.87346	+	17.1013i	0.447409	+	0.774935i	0.998217	−	0.0596972i	$-0.0190135\pi$
$487$	9.87346	+	17.1013i	0.447409	+	0.774935i	−0.550808	+	0.834632i	$0.685680\pi$
$488$	−1.35457	−	7.68215i	−0.0613185	−	0.347755i
$489$	−2.40554	−	2.01849i	−0.108782	−	0.0912793i
$490$	−4.39756	+	3.68999i	−0.198661	+	0.166697i
$491$	−5.06758	+	28.7397i	−0.228697	+	1.29700i	0.626794	+	0.779185i	$0.284367\pi$
$491$	−5.06758	+	28.7397i	−0.228697	+	1.29700i	−0.855491	+	0.517818i	$0.826744\pi$
$492$	−9.09627	+	3.31077i	−0.410091	+	0.149261i
$493$	20.9564			0.943827
$494$	−8.48932	+	7.33575i	−0.381953	+	0.330051i
$495$	−1.40373			−0.0630931
$496$	7.45084	−	2.71188i	0.334552	−	0.121767i
$497$	−3.73127	+	21.1611i	−0.167370	+	0.949204i
$498$	−2.98680	+	2.50622i	−0.133842	+	0.112306i
$499$	−4.12449	−	3.46085i	−0.184637	−	0.154929i	0.545784	−	0.837926i	$-0.316232\pi$
$499$	−4.12449	−	3.46085i	−0.184637	−	0.154929i	−0.730421	+	0.682997i	$0.760676\pi$
$500$	1.76857	+	10.0301i	0.0790929	+	0.448558i
$501$	−7.93629	−	13.7461i	−0.354567	−	0.614128i
$502$	2.31134	−	4.00335i	0.103160	−	0.178678i
$503$	−23.1040	−	8.40917i	−1.03016	−	0.374946i	−0.229016	−	0.973423i	$-0.573551\pi$
$503$	−23.1040	−	8.40917i	−1.03016	−	0.374946i	−0.801141	+	0.598476i	$0.795773\pi$
$504$	−1.37939	−	0.502055i	−0.0614427	−	0.0223633i
$505$	8.13903	−	14.0972i	0.362182	−	0.627318i
$506$	0.701867	+	1.21567i	0.0312018	+	0.0540431i
$507$	−1.10694	−	6.27779i	−0.0491611	−	0.278807i
$508$	5.57398	+	4.67712i	0.247305	+	0.207514i
$509$	−3.64362	+	3.05736i	−0.161501	+	0.135515i	−0.719957	−	0.694019i	$-0.755838\pi$
$509$	−3.64362	+	3.05736i	−0.161501	+	0.135515i	0.558456	+	0.829534i	$0.311394\pi$
$510$	0.458111	−	2.59808i	0.0202855	−	0.115045i
$511$	9.02094	−	3.28336i	0.399063	−	0.145247i
$512$	−1.00000			−0.0441942
$513$	−4.11721	−	1.43128i	−0.181779	−	0.0631927i
$514$	3.01724			0.133085
$515$	19.0783	−	6.94394i	0.840691	−	0.305987i
$516$	−1.25877	+	7.13884i	−0.0554143	+	0.314270i
$517$	−4.41534	+	3.70491i	−0.194187	+	0.162942i
$518$	−0.0721670	−	0.0605553i	−0.00317083	−	0.00266065i
$519$	0.601014	+	3.40852i	0.0263816	+	0.149618i
$520$	−1.52481	−	2.64106i	−0.0668676	−	0.115818i
$521$	14.8145	−	25.6595i	0.649035	−	1.12416i	−0.334319	−	0.942460i	$-0.608506\pi$
$521$	14.8145	−	25.6595i	0.649035	−	1.12416i	0.983354	−	0.181701i	$-0.0581603\pi$
$522$	8.84389	+	3.21891i	0.387087	+	0.140888i
$523$	10.0890	+	3.67209i	0.441161	+	0.160569i	0.553044	−	0.833152i	$-0.313466\pi$
$523$	10.0890	+	3.67209i	0.441161	+	0.160569i	−0.111883	+	0.993721i	$0.535688\pi$
$524$	3.44949	−	5.97470i	0.150692	−	0.261006i
$525$	−2.63950	−	4.57175i	−0.115197	−	0.199527i
$526$	0.869585	+	4.93166i	0.0379157	+	0.215031i
$527$	−13.5248	−	11.3487i	−0.589150	−	0.494356i
$528$	0.907604	−	0.761570i	0.0394984	−	0.0331431i
$529$	−3.75015	+	21.2682i	−0.163050	+	0.924703i
$530$	1.61809	−	0.588936i	0.0702853	−	0.0255817i
$531$	1.40373			0.0609168
$532$	−1.01960	+	6.31672i	−0.0442053	+	0.273864i
$533$	24.9162			1.07924
$534$	11.6630	−	4.24497i	0.504706	−	0.183698i
$535$	2.16085	−	12.2548i	0.0934219	−	0.529822i
$536$	−6.67752	+	5.60310i	−0.288425	+	0.242017i
$537$	−0.482926	−	0.405223i	−0.0208398	−	0.0174867i
$538$	4.26945	+	24.2132i	0.184069	+	1.04391i
$539$	2.87030	+	4.97151i	0.123633	+	0.214138i
$540$	0.592396	−	1.02606i	0.0254927	−	0.0441546i
$541$	−27.8209	−	10.1260i	−1.19611	−	0.435350i	−0.334247	−	0.942485i	$-0.608482\pi$
$541$	−27.8209	−	10.1260i	−1.19611	−	0.435350i	−0.861866	+	0.507136i	$0.830704\pi$
$542$	−1.57873	−	0.574609i	−0.0678121	−	0.0246816i
$543$	5.89440	−	10.2094i	0.252953	−	0.438127i
$544$	1.11334	+	1.92836i	0.0477341	+	0.0826779i
$545$	1.65451	+	9.38322i	0.0708716	+	0.401933i
$546$	2.89440	+	2.42869i	0.123869	+	0.103938i
$547$	10.2365	−	8.58943i	0.437680	−	0.367257i	−0.397160	−	0.917749i	$-0.630004\pi$
$547$	10.2365	−	8.58943i	0.437680	−	0.367257i	0.834841	+	0.550492i	$0.185560\pi$
$548$	2.74763	−	15.5826i	0.117373	−	0.665654i
$549$	−7.33022	+	2.66798i	−0.312846	+	0.113867i
$550$	4.26083			0.181682
$551$	6.53714	−	40.4995i	0.278492	−	1.72534i
$552$	−1.18479			−0.0504281
$553$	17.7964	−	6.47735i	0.756779	−	0.275445i
$554$	5.20620	−	29.5258i	0.221190	−	1.25443i
$555$	0.0582480	−	0.0488759i	0.00247249	−	0.00207466i
$556$	−11.8550	−	9.94756i	−0.502766	−	0.421870i
$557$	−0.589403	−	3.34267i	−0.0249738	−	0.141634i	0.969771	−	0.244015i	$-0.0784647\pi$
$557$	−0.589403	−	3.34267i	−0.0249738	−	0.141634i	−0.994745	+	0.102382i	$0.967354\pi$
$558$	−3.96451	−	6.86673i	−0.167831	−	0.290692i
$559$	9.32934	−	16.1589i	0.394589	−	0.683449i
$560$	−1.63429	−	0.594831i	−0.0690612	−	0.0251362i
$561$	−2.47906	−	0.902302i	−0.104666	−	0.0380952i
$562$	8.80587	−	15.2522i	0.371453	−	0.643376i
$563$	20.7724	+	35.9789i	0.875454	+	1.51633i	0.856278	+	0.516515i	$0.172771\pi$
$563$	20.7724	+	35.9789i	0.875454	+	1.51633i	0.0191757	+	0.999816i	$0.493896\pi$
$564$	−0.844770	−	4.79093i	−0.0355712	−	0.201735i
$565$	17.3726	+	14.5773i	0.730870	+	0.613273i
$566$	−12.1912	+	10.2296i	−0.512434	+	0.429983i
$567$	−0.254900	+	1.44561i	−0.0107048	+	0.0607099i
$568$	13.7554	−	5.00654i	0.577162	−	0.210070i
$569$	2.17705			0.0912668			0.0456334	−	0.998958i	$-0.485469\pi$
$569$	2.17705			0.0912668			0.0456334	+	0.998958i	$0.485469\pi$
$570$	−4.87804	−	1.69577i	−0.204319	−	0.0710281i
$571$	−2.50980			−0.105032			−0.0525159	−	0.998620i	$-0.516724\pi$
$571$	−2.50980			−0.105032			−0.0525159	+	0.998620i	$0.516724\pi$
$572$	−2.86571	+	1.04303i	−0.119822	+	0.0436115i
$573$	1.98293	−	11.2457i	0.0828379	−	0.469797i
$574$	10.8851	−	9.13366i	0.454334	−	0.381231i
$575$	−3.26399	−	2.73881i	−0.136118	−	0.114216i
$576$	0.173648	+	0.984808i	0.00723534	+	0.0410337i
$577$	−5.75537	−	9.96859i	−0.239599	−	0.414998i	0.721000	−	0.692935i	$-0.243683\pi$
$577$	−5.75537	−	9.96859i	−0.239599	−	0.414998i	−0.960599	+	0.277937i	$0.910349\pi$
$578$	−6.02094	+	10.4286i	−0.250438	+	0.433772i
$579$	−8.91787	−	3.24584i	−0.370614	−	0.134892i
$580$	10.4782	+	3.81374i	0.435083	+	0.158357i
$581$	2.86168	−	4.95658i	0.118723	−	0.205634i
$582$	6.45723	+	11.1843i	0.267661	+	0.463602i
$583$	−0.299011	−	1.69577i	−0.0123838	−	0.0702318i
$584$	−5.00980	−	4.20372i	−0.207307	−	0.173951i
$585$	−2.33615	+	1.96026i	−0.0965880	+	0.0810470i
$586$	−0.0466368	+	0.264490i	−0.00192655	+	0.0109260i
$587$	−15.6887	+	5.71021i	−0.647540	+	0.235685i	−0.644848	−	0.764311i	$-0.723079\pi$
$587$	−15.6887	+	5.71021i	−0.647540	+	0.235685i	−0.00269254	+	0.999996i	$0.500857\pi$
$588$	−4.84524			−0.199814
$589$	−26.1509	+	22.5974i	−1.07753	+	0.931111i
$590$	1.66313			0.0684701
$591$	−6.70486	+	2.44037i	−0.275801	+	0.100383i
$592$	−0.0111444	+	0.0632028i	−0.000458030	+	0.00259762i
$593$	34.1544	−	28.6589i	1.40255	−	1.17688i	0.442598	−	0.896720i	$-0.354057\pi$
$593$	34.1544	−	28.6589i	1.40255	−	1.17688i	0.959953	−	0.280160i	$-0.0903875\pi$
$594$	−0.907604	−	0.761570i	−0.0372394	−	0.0312476i
$595$	0.672466	+	3.81374i	0.0275684	+	0.156348i
$596$	−1.11334	−	1.92836i	−0.0456042	−	0.0789888i
$597$	8.87598	−	15.3737i	0.363270	−	0.629202i
$598$	2.86571	+	1.04303i	0.117188	+	0.0426529i
$599$	7.99912	+	2.91144i	0.326835	+	0.118958i	0.500226	−	0.865895i	$-0.333250\pi$
$599$	7.99912	+	2.91144i	0.326835	+	0.118958i	−0.173391	+	0.984853i	$0.555472\pi$
$600$	−1.79813	+	3.11446i	−0.0734085	+	0.127147i
$601$	−16.7613	−	29.0314i	−0.683708	−	1.18422i	−0.973841	−	0.227230i	$-0.927033\pi$
$601$	−16.7613	−	29.0314i	−0.683708	−	1.18422i	0.290134	−	0.956986i	$-0.406300\pi$
$602$	−1.84776	−	10.4792i	−0.0753092	−	0.427100i
$603$	6.67752	+	5.60310i	0.271930	+	0.228176i
$604$	5.05303	−	4.24000i	0.205605	−	0.172523i
$605$	1.97431	−	11.1969i	0.0802670	−	0.455217i
$606$	12.9106	−	4.69907i	0.524457	−	0.190887i
$607$	1.89393			0.0768724			0.0384362	−	0.999261i	$-0.487762\pi$
$607$	1.89393			0.0768724			0.0384362	+	0.999261i	$0.487762\pi$
$608$	4.07398	−	1.55007i	0.165222	−	0.0628635i
$609$	−13.8152			−0.559820
$610$	−8.68479	+	3.16101i	−0.351637	+	0.127985i
$611$	−2.17442	+	12.3317i	−0.0879676	+	0.498889i
$612$	1.70574	−	1.43128i	0.0689503	−	0.0578562i
$613$	6.50799	+	5.46085i	0.262855	+	0.220562i	0.764684	−	0.644405i	$-0.222895\pi$
$613$	6.50799	+	5.46085i	0.262855	+	0.220562i	−0.501829	+	0.864967i	$0.667339\pi$
$614$	0.0992034	+	0.562610i	0.00400352	+	0.0227051i
$615$	5.73442	+	9.93231i	0.231234	+	0.400509i
$616$	−0.869585	+	1.50617i	−0.0350366	+	0.0606851i
$617$	26.4688	+	9.63387i	1.06560	+	0.387845i	0.814528	−	0.580124i	$-0.196996\pi$
$617$	26.4688	+	9.63387i	1.06560	+	0.387845i	0.251068	+	0.967970i	$0.419218\pi$
$618$	16.1027	+	5.86089i	0.647744	+	0.235760i
$619$	11.4483	−	19.8291i	0.460146	−	0.796997i	−0.538821	−	0.842420i	$-0.681130\pi$
$619$	11.4483	−	19.8291i	0.460146	−	0.796997i	0.998968	+	0.0454230i	$0.0144636\pi$
$620$	−4.69712	−	8.13565i	−0.188641	−	0.326736i
$621$	0.205737	+	1.16679i	0.00825594	+	0.0468218i
$622$	−10.9945	−	9.22551i	−0.440841	−	0.369909i
$623$	−13.9565	+	11.7109i	−0.559156	+	0.469188i
$624$	0.446967	−	2.53487i	0.0178930	−	0.101476i
$625$	−5.55778	+	2.02287i	−0.222311	+	0.0809147i
$626$	2.40373			0.0960725
$627$	−2.51707	+	4.50946i	−0.100522	+	0.180091i
$628$	9.25402			0.369276
$629$	0.134285	−	0.0488759i	0.00535431	−	0.00194881i
$630$	−0.302004	+	1.71275i	−0.0120321	+	0.0682375i
$631$	−24.8883	+	20.8838i	−0.990788	+	0.831370i	−0.985682	−	0.168617i	$-0.946070\pi$
$631$	−24.8883	+	20.8838i	−0.990788	+	0.831370i	−0.00510629	+	0.999987i	$0.501625\pi$
$632$	−9.88326	−	8.29304i	−0.393135	−	0.329879i
$633$	0.375515	+	2.12965i	0.0149254	+	0.0846460i
$634$	7.02869	+	12.1740i	0.279145	+	0.483493i
$635$	4.31046	−	7.46594i	0.171055	−	0.296277i
$636$	1.36571	+	0.497079i	0.0541541	+	0.0197105i
$637$	11.7194	+	4.26552i	0.464340	+	0.169006i
$638$	5.57532	−	9.65674i	0.220729	−	0.382314i
$639$	−7.31908	−	12.6770i	−0.289538	−	0.501495i
$640$	0.205737	+	1.16679i	0.00813247	+	0.0461215i
$641$	5.67159	+	4.75903i	0.224014	+	0.187970i	0.747887	−	0.663826i	$-0.231069\pi$
$641$	5.67159	+	4.75903i	0.224014	+	0.187970i	−0.523872	+	0.851797i	$0.675513\pi$
$642$	8.04576	−	6.75119i	0.317541	−	0.266448i
$643$	−7.38847	+	41.9021i	−0.291373	+	1.65246i	0.390217	+	0.920723i	$0.372400\pi$
$643$	−7.38847	+	41.9021i	−0.291373	+	1.65246i	−0.681590	+	0.731734i	$0.738711\pi$
$644$	1.63429	−	0.594831i	0.0643999	−	0.0234396i
$645$	8.58853			0.338173
$646$	−7.52481	−	6.13036i	−0.296060	−	0.241196i
$647$	−41.2063			−1.61999			−0.809993	−	0.586440i	$-0.800529\pi$
$647$	−41.2063			−1.61999			−0.809993	+	0.586440i	$0.800529\pi$
$648$	0.939693	−	0.342020i	0.0369146	−	0.0134358i
$649$	0.288800	−	1.63787i	0.0113364	−	0.0642919i
$650$	7.09105	−	5.95010i	0.278134	−	0.233382i
$651$	8.91606	+	7.48146i	0.349448	+	0.293222i
$652$	−0.545293	−	3.09251i	−0.0213553	−	0.121112i
$653$	13.3353	+	23.0974i	0.521850	+	0.903870i	0.999677	+	0.0254163i	$0.00809113\pi$
$653$	13.3353	+	23.0974i	0.521850	+	0.903870i	−0.477827	+	0.878454i	$0.658576\pi$
$654$	−4.02094	+	6.96448i	−0.157231	+	0.272333i
$655$	−7.68092	−	2.79563i	−0.300118	−	0.109234i
$656$	−9.09627	−	3.31077i	−0.355150	−	0.129264i
$657$	−3.26991	+	5.66366i	−0.127572	+	0.220960i
$658$	3.57057	+	6.18442i	0.139195	+	0.241094i
$659$	−2.18567	−	12.3955i	−0.0851416	−	0.482862i	−0.997326	−	0.0730819i	$-0.976717\pi$
$659$	−2.18567	−	12.3955i	−0.0851416	−	0.482862i	0.912184	−	0.409780i	$-0.134395\pi$
$660$	−1.07532	−	0.902302i	−0.0418569	−	0.0351221i
$661$	6.35432	−	5.33191i	0.247154	−	0.207387i	−0.510791	−	0.859705i	$-0.670648\pi$
$661$	6.35432	−	5.33191i	0.247154	−	0.207387i	0.757946	+	0.652317i	$0.226203\pi$
$662$	−4.66116	+	26.4347i	−0.181161	+	1.02742i
$663$	−5.38578	+	1.96026i	−0.209166	+	0.0761304i
$664$	−3.89899			−0.151310
$665$	7.58007	−	0.109920i	0.293943	−	0.00426253i
$666$	0.0641778			0.00248684
$667$	−10.4782	+	3.81374i	−0.405717	+	0.147669i
$668$	2.75624	−	15.6314i	0.106642	−	0.604798i
$669$	−21.6446	+	18.1619i	−0.836827	+	0.702181i
$670$	7.91147	+	6.63852i	0.305647	+	0.256468i
$671$	1.60488	+	9.10175i	0.0619559	+	0.351369i
$672$	−0.733956	−	1.27125i	−0.0283130	−	0.0490395i
$673$	−0.812681	+	1.40761i	−0.0313266	+	0.0542592i	−0.881264	−	0.472625i	$-0.843307\pi$
$673$	−0.812681	+	1.40761i	−0.0313266	+	0.0542592i	0.849937	+	0.526884i	$0.176640\pi$
$674$	−19.6596	−	7.15550i	−0.757258	−	0.275619i
$675$	3.37939	+	1.23000i	0.130073	+	0.0473426i
$676$	3.18732	−	5.52060i	0.122589	−	0.212331i
$677$	6.64203	+	11.5043i	0.255274	+	0.442147i	0.964970	−	0.262361i	$-0.0845011\pi$
$677$	6.64203	+	11.5043i	0.255274	+	0.442147i	−0.709696	+	0.704508i	$0.751168\pi$
$678$	3.32383	+	18.8504i	0.127651	+	0.723943i
$679$	−14.5221	−	12.1855i	−0.557308	−	0.467637i
$680$	2.02094	−	1.69577i	0.0774997	−	0.0650300i
$681$	−3.65064	+	20.7038i	−0.139893	+	0.793373i
$682$	−8.82770	+	3.21302i	−0.338030	+	0.123033i
$683$	2.90673			0.111223			0.0556114	−	0.998452i	$-0.482289\pi$
$683$	2.90673			0.111223			0.0556114	+	0.998452i	$0.482289\pi$
$684$	−2.23396	−	3.74292i	−0.0854174	−	0.143114i
$685$	−18.7469			−0.716283
$686$	16.3391	−	5.94696i	0.623831	−	0.227056i
$687$	1.38238	−	7.83986i	0.0527410	−	0.299109i
$688$	−5.55303	+	4.65955i	−0.211707	+	0.177644i
$689$	−2.86571	−	2.40462i	−0.109175	−	0.0916087i
$690$	0.243756	+	1.38241i	0.00927962	+	0.0526274i
$691$	7.18004	+	12.4362i	0.273142	+	0.473095i	0.969665	−	0.244439i	$-0.0786039\pi$
$691$	7.18004	+	12.4362i	0.273142	+	0.473095i	−0.696523	+	0.717535i	$0.745271\pi$
$692$	−1.73055	+	2.99740i	−0.0657857	+	0.113944i
$693$	1.63429	+	0.594831i	0.0620814	+	0.0225958i
$694$	−31.6079	−	11.5043i	−1.19982	−	0.436698i
$695$	−9.16772	+	15.8790i	−0.347751	+	0.602323i
$696$	4.70574	+	8.15058i	0.178371	+	0.308947i
$697$	3.74288	+	21.2269i	0.141772	+	0.804027i
$698$	−20.7993	−	17.4527i	−0.787266	−	0.660594i
$699$	11.2515	−	9.44113i	0.425571	−	0.357096i
$700$	0.916689	−	5.19880i	0.0346476	−	0.196496i
$701$	−45.7195	+	16.6405i	−1.72680	+	0.628504i	−0.998395	−	0.0566421i	$-0.981961\pi$
$701$	−45.7195	+	16.6405i	−1.72680	+	0.628504i	−0.728406	+	0.685146i	$0.759738\pi$
$702$	−2.57398			−0.0971485
$703$	−0.0525666	−	0.274761i	−0.00198259	−	0.0103628i
$704$	1.18479			0.0446535
$705$	−5.41622	+	1.97134i	−0.203987	+	0.0742451i
$706$	2.90777	−	16.4908i	0.109435	−	0.620638i
$707$	−15.4495	+	12.9637i	−0.581038	+	0.487549i
$708$	1.07532	+	0.902302i	0.0404131	+	0.0339106i
$709$	−1.69207	−	9.59619i	−0.0635469	−	0.360392i	−0.999955	−	0.00947962i	$-0.996982\pi$
$709$	−1.69207	−	9.59619i	−0.0635469	−	0.360392i	0.936408	−	0.350913i	$-0.114129\pi$
$710$	−8.67159	−	15.0196i	−0.325439	−	0.563677i
$711$	−6.45084	+	11.1732i	−0.241925	+	0.419027i
$712$	11.6630	+	4.24497i	0.437088	+	0.159087i
$713$	8.82770	+	3.21302i	0.330600	+	0.120328i
$714$	−1.63429	+	2.83067i	−0.0611616	+	0.105935i
$715$	1.80659	+	3.12910i	0.0675626	+	0.117022i
$716$	−0.109470	−	0.620838i	−0.00409110	−	0.0232018i
$717$	12.0496	+	10.1108i	0.450002	+	0.377596i
$718$	3.63041	−	3.04628i	0.135486	−	0.113686i
$719$	0.841777	−	4.77396i	0.0313930	−	0.178038i	−0.965080	−	0.261957i	$-0.915632\pi$
$719$	0.841777	−	4.77396i	0.0313930	−	0.178038i	0.996473	+	0.0839181i	$0.0267434\pi$
$720$	1.11334	−	0.405223i	0.0414918	−	0.0151018i
$721$	−25.1543			−0.936794
$722$	−14.1946	+	12.6299i	−0.528268	+	0.470035i
$723$	9.85204			0.366401
$724$	11.0778	−	4.03201i	0.411705	−	0.149848i
$725$	−5.87733	+	33.3320i	−0.218278	+	1.23792i
$726$	7.35117	−	6.16836i	0.272827	−	0.228929i
$727$	−10.8714	−	9.12218i	−0.403198	−	0.338323i	0.418530	−	0.908203i	$-0.362545\pi$
$727$	−10.8714	−	9.12218i	−0.403198	−	0.338323i	−0.821728	+	0.569880i	$0.806990\pi$
$728$	0.656107	+	3.72097i	0.0243170	+	0.137908i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−3.87417	+	6.71026i	−0.143389	+	0.248358i
$731$	15.1677	+	5.52060i	0.560998	+	0.204187i
$732$	−7.33022	−	2.66798i	−0.270933	−	0.0986115i
$733$	−5.31908	+	9.21291i	−0.196465	+	0.340287i	−0.947380	−	0.320112i	$-0.896279\pi$
$733$	−5.31908	+	9.21291i	−0.196465	+	0.340287i	0.750915	+	0.660399i	$0.229613\pi$
$734$	4.39646	+	7.61489i	0.162276	+	0.281071i
$735$	0.996845	+	5.65339i	0.0367692	+	0.208528i
$736$	−0.907604	−	0.761570i	−0.0334547	−	0.0280718i
$737$	7.91147	−	6.63852i	0.291423	−	0.244533i
$738$	−1.68092	+	9.53298i	−0.0618756	+	0.350914i
$739$	25.9368	−	9.44021i	0.954099	−	0.347264i	0.182381	−	0.983228i	$-0.441620\pi$
$739$	25.9368	−	9.44021i	0.954099	−	0.347264i	0.771718	+	0.635964i	$0.219397\pi$
$740$	0.0760373			0.00279519
$741$	2.10829	+	11.0198i	0.0774499	+	0.404824i
$742$	−2.13341			−0.0783199
$743$	−1.13816	+	0.414255i	−0.0417549	+	0.0151975i	−0.362813	−	0.931862i	$-0.618184\pi$
$743$	−1.13816	+	0.414255i	−0.0417549	+	0.0151975i	0.321058	+	0.947059i	$0.395961\pi$
$744$	1.37686	−	7.80856i	0.0504781	−	0.286276i
$745$	−2.02094	+	1.69577i	−0.0740417	+	0.0621283i
$746$	7.23577	+	6.07153i	0.264920	+	0.222294i
$747$	0.677052	+	3.83975i	0.0247720	+	0.140489i
$748$	−1.31908	−	2.28471i	−0.0482303	−	0.0835373i
$749$	−7.70873	+	13.3519i	−0.281671	+	0.487868i
$750$	9.57057	+	3.48340i	0.349468	+	0.127196i
$751$	−46.0925	−	16.7763i	−1.68194	−	0.612175i	−0.688364	−	0.725365i	$-0.741671\pi$
$751$	−46.0925	−	16.7763i	−1.68194	−	0.612175i	−0.993573	+	0.113190i	$0.963893\pi$
$752$	2.43242	−	4.21307i	0.0887012	−	0.153635i
$753$	−2.31134	−	4.00335i	−0.0842298	−	0.145890i
$754$	−4.20661	−	23.8569i	−0.153196	−	0.868817i
$755$	−5.98680	−	5.02352i	−0.217882	−	0.182825i
$756$	−1.12449	+	0.943555i	−0.0408971	+	0.0343168i
$757$	6.26445	−	35.5275i	0.227685	−	1.29127i	−0.629799	−	0.776758i	$-0.716863\pi$
$757$	6.26445	−	35.5275i	0.227685	−	1.29127i	0.857484	−	0.514510i	$-0.172026\pi$
$758$	34.6819	−	12.6232i	1.25970	−	0.458494i
$759$	1.40373			0.0509523
$760$	−2.64677	−	4.43458i	−0.0960086	−	0.160859i
$761$	4.72193			0.171170			0.0855850	−	0.996331i	$-0.472724\pi$
$761$	4.72193			0.171170			0.0855850	+	0.996331i	$0.472724\pi$
$762$	6.83750	−	2.48865i	0.247696	−	0.0901541i
$763$	2.04988	−	11.6254i	0.0742106	−	0.420869i
$764$	8.74763	−	7.34013i	0.316478	−	0.265557i
$765$	−2.02094	−	1.69577i	−0.0730674	−	0.0613108i
$766$	5.11721	+	29.0211i	0.184892	+	1.04858i
$767$	−1.80659	−	3.12910i	−0.0652322	−	0.112985i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−20.3893	−	7.42112i	−0.735259	−	0.267612i	−0.0528696	−	0.998601i	$-0.516837\pi$
$769$	−20.3893	−	7.42112i	−0.735259	−	0.267612i	−0.682389	+	0.730989i	$0.739059\pi$
$770$	1.93629	+	0.704752i	0.0697790	+	0.0253975i
$771$	1.50862	−	2.61300i	0.0543316	−	0.0941050i
$772$	−4.74510	−	8.21875i	−0.170780	−	0.295799i
$773$	7.65611	+	43.4199i	0.275371	+	1.56171i	0.737781	+	0.675040i	$0.235874\pi$
$773$	7.65611	+	43.4199i	0.275371	+	1.56171i	−0.462410	+	0.886666i	$0.653015\pi$
$774$	5.55303	+	4.65955i	0.199600	+	0.167484i
$775$	21.8436	−	18.3290i	0.784647	−	0.658397i
$776$	−2.24257	+	12.7183i	−0.0805037	+	0.456559i
$777$	−0.0885259	+	0.0322208i	−0.00317585	+	0.00115591i
$778$	−17.6878			−0.634138
$779$	42.1899	−	0.611806i	1.51161	−	0.0219202i
$780$	−3.04963			−0.109194
$781$	−16.2973	+	5.93172i	−0.583162	+	0.212253i
$782$	−0.458111	+	2.59808i	−0.0163820	+	0.0929070i
$783$	7.20961	−	6.04958i	0.257650	−	0.216194i
$784$	−3.71167	−	3.11446i	−0.132560	−	0.111231i
$785$	−1.90390	−	10.7975i	−0.0679529	−	0.385380i
$786$	−3.44949	−	5.97470i	−0.123039	−	0.213110i
$787$	10.0694	−	17.4407i	0.358935	−	0.621694i	−0.628848	−	0.777528i	$-0.716473\pi$
$787$	10.0694	−	17.4407i	0.358935	−	0.621694i	0.987783	+	0.155834i	$0.0498066\pi$
$788$	−6.70486	−	2.44037i	−0.238851	−	0.0869346i
$789$	4.70574	+	1.71275i	0.167529	+	0.0609755i
$790$	−7.64290	+	13.2379i	−0.271922	+	0.470983i
$791$	−14.0488	−	24.3332i	−0.499516	−	0.865187i
$792$	−0.205737	−	1.16679i	−0.00731055	−	0.0414602i
$793$	15.3812	+	12.9064i	0.546202	+	0.458318i
$794$	−9.64409	+	8.09235i	−0.342256	+	0.287187i
$795$	0.299011	−	1.69577i	0.0106048	−	0.0601429i
$796$	16.6814	−	6.07153i	0.591256	−	0.215200i
$797$	12.0729			0.427642			0.213821	−	0.976873i	$-0.431409\pi$
$797$	12.0729			0.427642			0.213821	+	0.976873i	$0.431409\pi$
$798$	4.96064	+	4.04136i	0.175605	+	0.143063i
$799$	−10.8324			−0.383224
$800$	−3.37939	+	1.23000i	−0.119479	+	0.0434869i
$801$	2.15523	−	12.2229i	0.0761513	−	0.431875i
$802$	18.4409	−	15.4737i	0.651170	−	0.546396i
$803$	5.93557	+	4.98054i	0.209462	+	0.175759i
$804$	1.51367	+	8.58445i	0.0533830	+	0.302750i
$805$	−1.03028	−	1.78449i	−0.0363125	−	0.0628951i
$806$	−10.2046	+	17.6748i	−0.359440	+	0.622569i
$807$	23.1040	+	8.40917i	0.813300	+	0.296017i
$808$	12.9106	+	4.69907i	0.454193	+	0.165313i
$809$	19.4868	−	33.7521i	0.685119	−	1.18666i	−0.288280	−	0.957546i	$-0.593083\pi$
$809$	19.4868	−	33.7521i	0.685119	−	1.18666i	0.973399	−	0.229115i	$-0.0735833\pi$
$810$	−0.592396	−	1.02606i	−0.0208147	−	0.0360521i
$811$	−3.71641	−	21.0768i	−0.130501	−	0.740108i	−0.977888	−	0.209131i	$-0.932936\pi$
$811$	−3.71641	−	21.0768i	−0.130501	−	0.740108i	0.847387	−	0.530976i	$-0.178175\pi$
$812$	−10.5831	−	8.88024i	−0.371393	−	0.311635i
$813$	−1.28699	+	1.07991i	−0.0451367	+	0.0378742i
$814$	0.0132037	−	0.0748822i	0.000462791	−	0.00262462i
$815$	−3.49613	+	1.27249i	−0.122464	+	0.0445733i
$816$	2.22668			0.0779494
$817$	15.4003	−	27.5905i	0.538789	−	0.965268i
$818$	35.3601			1.23634
$819$	3.55051	−	1.29228i	0.124065	−	0.0451559i
$820$	−1.99154	+	11.2946i	−0.0695477	+	0.394425i
$821$	37.4564	−	31.4296i	1.30724	−	1.09690i	0.318390	−	0.947960i	$-0.396858\pi$
$821$	37.4564	−	31.4296i	1.30724	−	1.09690i	0.988846	−	0.148941i	$-0.0475865\pi$
$822$	−12.1211	−	10.1708i	−0.422771	−	0.354747i
$823$	−5.20217	−	29.5030i	−0.181336	−	1.02841i	−0.930573	−	0.366107i	$-0.880690\pi$
$823$	−5.20217	−	29.5030i	−0.181336	−	1.02841i	0.749237	−	0.662302i	$-0.230421\pi$
$824$	8.56805	+	14.8403i	0.298482	+	0.516986i
$825$	2.13041	−	3.68999i	0.0741715	−	0.128469i
$826$	−1.93629	−	0.704752i	−0.0673721	−	0.0245214i
$827$	21.7601	+	7.92003i	0.756673	+	0.275407i	0.691411	−	0.722462i	$-0.256989\pi$
$827$	21.7601	+	7.92003i	0.756673	+	0.275407i	0.0652623	+	0.997868i	$0.479212\pi$
$828$	−0.592396	+	1.02606i	−0.0205872	+	0.0356581i
$829$	−15.4290	−	26.7238i	−0.535872	−	0.928157i	−0.999121	−	0.0419290i	$-0.986650\pi$
$829$	−15.4290	−	26.7238i	−0.535872	−	0.928157i	0.463249	−	0.886228i	$-0.346684\pi$
$830$	0.802166	+	4.54931i	0.0278436	+	0.157909i
$831$	−22.9670	−	19.2716i	−0.796718	−	0.668525i
$832$	1.97178	−	1.65452i	0.0683592	−	0.0573602i
$833$	−1.87346	+	10.6249i	−0.0649114	+	0.368131i
$834$	−14.5424	+	5.29298i	−0.503561	+	0.183281i
$835$	−18.8057			−0.650798
$836$	−4.82682	+	1.83651i	−0.166939	+	0.0635169i
$837$	−7.92902			−0.274067
$838$	4.30288	−	1.56612i	0.148641	−	0.0541007i
$839$	1.95707	−	11.0991i	0.0675656	−	0.383184i	−0.932208	−	0.361922i	$-0.882121\pi$
$839$	1.95707	−	11.0991i	0.0675656	−	0.383184i	0.999774	−	0.0212615i	$-0.00676826\pi$
$840$	−1.33228	+	1.11792i	−0.0459681	+	0.0385718i
$841$	45.6377	+	38.2946i	1.57372	+	1.32050i
$842$	−0.0482857	−	0.273842i	−0.00166403	−	0.00943721i
$843$	−8.80587	−	15.2522i	−0.303290	−	0.525314i
$844$	−1.08125	+	1.87278i	−0.0372182	+	0.0644639i
$845$	−7.09714	−	2.58315i	−0.244149	−	0.0888630i
$846$	−4.57145	−	1.66387i	−0.157170	−	0.0572051i
$847$	−7.04323	+	12.1992i	−0.242008	+	0.419171i
$848$	0.726682	+	1.25865i	0.0249543	+	0.0432222i
$849$	2.76352	+	15.6727i	0.0948437	+	0.537885i
$850$	6.13429	+	5.14728i	0.210404	+	0.176550i
$851$	−0.0582480	+	0.0488759i	−0.00199672	+	0.00167544i
$852$	2.54189	−	14.4158i	0.0870837	−	0.493876i
$853$	18.4338	−	6.70934i	0.631160	−	0.229723i	−0.00657610	−	0.999978i	$-0.502093\pi$
$853$	18.4338	−	6.70934i	0.631160	−	0.229723i	0.637736	+	0.770255i	$0.279871\pi$
$854$	11.4507			0.391834
$855$	−3.90760	+	3.37662i	−0.133637	+	0.115478i
$856$	10.5030			0.358985
$857$	−21.7707	+	7.92388i	−0.743672	+	0.270675i	−0.685941	−	0.727657i	$-0.740609\pi$
$857$	−21.7707	+	7.92388i	−0.743672	+	0.270675i	−0.0577318	+	0.998332i	$0.518387\pi$
$858$	−0.529563	+	3.00330i	−0.0180790	+	0.102531i
$859$	1.85529	−	1.55677i	0.0633015	−	0.0531163i	−0.610588	−	0.791948i	$-0.709067\pi$
$859$	1.85529	−	1.55677i	0.0633015	−	0.0531163i	0.673889	+	0.738832i	$0.264622\pi$
$860$	6.57919	+	5.52060i	0.224349	+	0.188251i
$861$	−2.46744	−	13.9936i	−0.0840903	−	0.476900i
$862$	−5.99138	−	10.3774i	−0.204067	−	0.353455i
$863$	8.33615	−	14.4386i	0.283766	−	0.491497i	−0.688543	−	0.725195i	$-0.741749\pi$
$863$	8.33615	−	14.4386i	0.283766	−	0.491497i	0.972309	+	0.233698i	$0.0750828\pi$
$864$	0.939693	+	0.342020i	0.0319690	+	0.0116358i
$865$	3.85339	+	1.40252i	0.131019	+	0.0476871i
$866$	−14.5740	+	25.2429i	−0.495244	+	0.857788i
$867$	6.02094	+	10.4286i	0.204482	+	0.354173i
$868$	2.02111	+	11.4623i	0.0686008	+	0.389055i
$869$	11.7096	+	9.82553i	0.397221	+	0.333308i
$870$	8.54189	−	7.16750i	0.289597	−	0.243001i
$871$	3.89615	−	22.0962i	0.132016	−	0.748701i
$872$	−7.55690	+	2.75049i	−0.255909	+	0.0931433i
$873$	12.9145			0.437088
$874$	4.87804	+	1.69577i	0.165002	+	0.0573604i
$875$	−14.9504			−0.505415
$876$	−6.14543	+	2.23675i	−0.207635	+	0.0755729i
$877$	−6.63294	+	37.6173i	−0.223979	+	1.27025i	0.640650	+	0.767833i	$0.278665\pi$
$877$	−6.63294	+	37.6173i	−0.223979	+	1.27025i	−0.864628	+	0.502412i	$0.832446\pi$
$878$	−4.82429	+	4.04806i	−0.162812	+	0.136615i
$879$	0.205737	+	0.172634i	0.00693934	+	0.00582280i
$880$	−0.243756	−	1.38241i	−0.00821700	−	0.0466009i
$881$	11.7592	+	20.3676i	0.396179	+	0.686202i	0.993251	−	0.115986i	$-0.0370027\pi$
$881$	11.7592	+	20.3676i	0.396179	+	0.686202i	−0.597072	+	0.802188i	$0.703669\pi$
$882$	−2.42262	+	4.19610i	−0.0815738	+	0.141290i
$883$	17.3042	+	6.29822i	0.582334	+	0.211952i	0.616354	−	0.787469i	$-0.288609\pi$
$883$	17.3042	+	6.29822i	0.582334	+	0.211952i	−0.0340206	+	0.999421i	$0.510831\pi$
$884$	−5.38578	−	1.96026i	−0.181143	−	0.0659308i
$885$	0.831566	−	1.44032i	0.0279528	−	0.0484157i
$886$	10.4402	+	18.0829i	0.350744	+	0.607506i
$887$	−4.78317	−	27.1267i	−0.160603	−	0.910827i	−0.953483	−	0.301448i	$-0.902530\pi$
$887$	−4.78317	−	27.1267i	−0.160603	−	0.910827i	0.792879	−	0.609379i	$-0.208581\pi$
$888$	0.0491630	+	0.0412527i	0.00164980	+	0.00138435i
$889$	−8.18210	+	6.86560i	−0.274419	+	0.230265i
$890$	2.55350	−	14.4816i	0.0855935	−	0.485425i
$891$	−1.11334	+	0.405223i	−0.0372983	+	0.0135755i
$892$	−28.2550			−0.946046
$893$	−3.37908	+	20.9344i	−0.113077	+	0.700542i
$894$	−2.22668			−0.0744714
$895$	−0.701867	+	0.255459i	−0.0234608	+	0.00853904i
$896$	0.254900	−	1.44561i	0.00851561	−	0.0482944i
$897$	2.33615	−	1.96026i	0.0780018	−	0.0654513i
$898$	−31.6955	−	26.5957i	−1.05769	−	0.887510i
$899$	−12.9583	−	73.4900i	−0.432183	−	2.45103i
$900$	1.79813	+	3.11446i	0.0599378	+	0.103815i
$901$	1.61809	−	2.80261i	0.0539063	−	0.0933685i
$902$	10.7772	+	3.92258i	0.358841	+	0.130607i
$903$	−9.99912	−	3.63938i	−0.332750	−	0.121111i
$904$	−9.57057	+	16.5767i	−0.318313	+	0.551334i
$905$	−6.98364	−	12.0960i	−0.232144	−	0.402085i
$906$	−1.14543	−	6.49605i	−0.0380544	−	0.215817i
$907$	15.9559	+	13.3886i	0.529807	+	0.444561i	0.868035	−	0.496504i	$-0.165383\pi$
$907$	15.9559	+	13.3886i	0.529807	+	0.444561i	−0.338228	+	0.941064i	$0.609828\pi$
$908$	−16.1047	+	13.5135i	−0.534454	+	0.448460i
$909$	2.38578	−	13.5304i	0.0791314	−	0.448776i
$910$	4.20661	−	1.53108i	0.139448	−	0.0507549i
$911$	13.7300			0.454895			0.227448	−	0.973790i	$-0.426962\pi$
$911$	13.7300			0.454895			0.227448	+	0.973790i	$0.426962\pi$
$912$	0.694593	−	4.30320i	0.0230003	−	0.142493i
$913$	4.61949			0.152883
$914$	−25.9586	+	9.44815i	−0.858633	+	0.312517i
$915$	−1.60488	+	9.10175i	−0.0530559	+	0.300895i
$916$	6.09833	−	5.11710i	0.201494	−	0.169074i
$917$	7.75781	+	6.50957i	0.256185	+	0.214965i
$918$	−0.386659	−	2.19285i	−0.0127617	−	0.0723749i
$919$	22.2245	+	38.4939i	0.733117	+	1.26980i	0.955544	+	0.294847i	$0.0952687\pi$
$919$	22.2245	+	38.4939i	0.733117	+	1.26980i	−0.222427	+	0.974949i	$0.571398\pi$
$920$	−0.701867	+	1.21567i	−0.0231399	+	0.0400794i
$921$	0.536837	+	0.195393i	0.0176894	+	0.00643840i
$922$	−17.3944	−	6.33104i	−0.572854	−	0.208502i
$923$	−18.8391	+	32.6304i	−0.620098	+	1.07404i
$924$	0.869585	+	1.50617i	0.0286072	+	0.0495492i
$925$	0.0400781	+	0.227294i	0.00131776	+	0.00747338i
$926$	2.77197	+	2.32596i	0.0910927	+	0.0764359i
$927$	13.1270	−	11.0149i	0.431148	−	0.361776i
$928$	−1.63429	+	9.26849i	−0.0536480	+	0.304253i
$929$	−9.12866	+	3.32256i	−0.299502	+	0.109010i	−0.487400	−	0.873179i	$-0.662055\pi$
$929$	−9.12866	+	3.32256i	−0.299502	+	0.109010i	0.187898	+	0.982188i	$0.439832\pi$
$930$	−9.39424			−0.308049
$931$	19.9489	+	6.93491i	0.653798	+	0.227282i
$932$	14.6878			0.481114
$933$	−13.4868	+	4.90879i	−0.441538	+	0.160707i
$934$	2.50088	−	14.1832i	0.0818312	−	0.464088i
$935$	−2.39440	+	2.00914i	−0.0783053	+	0.0657059i
$936$	−1.97178	−	1.65452i	−0.0644497	−	0.0540797i
$937$	−1.98808	−	11.2750i	−0.0649479	−	0.368338i	−0.999908	−	0.0135842i	$-0.995676\pi$
$937$	−1.98808	−	11.2750i	−0.0649479	−	0.368338i	0.934960	−	0.354754i	$-0.115435\pi$
$938$	−6.39780	−	11.0813i	−0.208896	−	0.361818i
$939$	1.20187	−	2.08169i	0.0392214	−	0.0679335i
$940$	−5.41622	−	1.97134i	−0.176658	−	0.0642981i
$941$	−42.3546	−	15.4158i	−1.38072	−	0.502541i	−0.458324	−	0.888785i	$-0.651550\pi$
$941$	−42.3546	−	15.4158i	−1.38072	−	0.502541i	−0.922397	+	0.386243i	$0.873772\pi$
$942$	4.62701	−	8.01422i	0.150756	−	0.261117i
$943$	−5.73442	−	9.93231i	−0.186738	−	0.323441i
$944$	0.243756	+	1.38241i	0.00793357	+	0.0449935i
$945$	1.33228	+	1.11792i	0.0433391	+	0.0363658i
$946$	6.57919	−	5.52060i	0.213908	−	0.179490i
$947$	7.66014	−	43.4428i	0.248921	−	1.41170i	−0.562286	−	0.826943i	$-0.690078\pi$
$947$	7.66014	−	43.4428i	0.248921	−	1.41170i	0.811207	−	0.584759i	$-0.198811\pi$
$948$	−12.1236	+	4.41263i	−0.393756	+	0.143316i
$949$	16.8334			0.546435
$950$	11.8610	−	10.2492i	0.384821	−	0.332529i
$951$	14.0574			0.455841
$952$	−3.07145	+	1.11792i	−0.0995463	+	0.0362319i
$953$	0.318201	−	1.80460i	0.0103075	−	0.0584569i	−0.979220	−	0.202800i	$-0.934996\pi$
$953$	0.318201	−	1.80460i	0.0103075	−	0.0584569i	0.989528	+	0.144343i	$0.0461069\pi$
$954$	1.11334	−	0.934204i	0.0360457	−	0.0302460i
$955$	−10.3641	−	8.69653i	−0.335375	−	0.281413i
$956$	2.73143	+	15.4907i	0.0883407	+	0.501005i
$957$	−5.57532	−	9.65674i	−0.180225	−	0.312158i
$958$	−15.9278	+	27.5878i	−0.514605	+	0.891322i
$959$	21.8259	+	7.94399i	0.704796	+	0.256525i
$960$	1.11334	+	0.405223i	0.0359329	+	0.0130785i
$961$	−15.9346	+	27.5996i	−0.514021	+	0.890310i
$962$	−0.0825961	−	0.143061i	−0.00266300	−	0.00461246i
$963$	−1.82383	−	10.3434i	−0.0587720	−	0.333312i
$964$	7.54710	+	6.33277i	0.243076	+	0.203965i
$965$	−8.61334	+	7.22745i	−0.277273	+	0.232660i
$966$	0.302004	−	1.71275i	0.00971681	−	0.0551068i
$967$	−15.4941	+	5.63938i	−0.498256	+	0.181350i	−0.578909	−	0.815392i	$-0.696521\pi$
$967$	−15.4941	+	5.63938i	−0.498256	+	0.181350i	0.0806536	+	0.996742i	$0.474299\pi$
$968$	9.59627			0.308436
$969$	−9.07145	+	3.45150i	−0.291417	+	0.110878i
$970$	15.3010			0.491284
$971$	−41.8803	+	15.2432i	−1.34400	+	0.489177i	−0.911071	−	0.412249i	$-0.864743\pi$
$971$	−41.8803	+	15.2432i	−1.34400	+	0.489177i	−0.432932	+	0.901426i	$0.642521\pi$
$972$	0.173648	−	0.984808i	0.00556977	−	0.0315877i
$973$	17.4021	−	14.6021i	0.557887	−	0.468123i
$974$	15.1270	+	12.6931i	0.484701	+	0.406712i
$975$	−1.60741	−	9.11608i	−0.0514784	−	0.291948i
$976$	−3.90033	−	6.75557i	−0.124847	−	0.216241i
$977$	−15.7049	+	27.2016i	−0.502443	+	0.870257i	0.497553	+	0.867434i	$0.334232\pi$
$977$	−15.7049	+	27.2016i	−0.502443	+	0.870257i	−0.999996	+	0.00282321i	$0.999101\pi$
$978$	−2.95084	−	1.07402i	−0.0943574	−	0.0343433i
$979$	−13.8182	−	5.02941i	−0.441632	−	0.160741i
$980$	−2.87030	+	4.97151i	−0.0916884	+	0.158809i
$981$	4.02094	+	6.96448i	0.128379	+	0.222359i
$982$	5.06758	+	28.7397i	0.161713	+	0.917120i
$983$	−22.2592	−	18.6777i	−0.709959	−	0.595727i	0.214628	−	0.976696i	$-0.431146\pi$
$983$	−22.2592	−	18.6777i	−0.709959	−	0.595727i	−0.924588	+	0.380969i	$0.875590\pi$
$984$	−7.41534	+	6.22221i	−0.236393	+	0.198357i
$985$	−1.46797	+	8.32526i	−0.0467733	+	0.265265i
$986$	19.6925	−	7.16750i	0.627138	−	0.228260i
$987$	7.14115			0.227305
$988$	−5.46838	+	9.79687i	−0.173972	+	0.311680i
$989$	−8.58853			−0.273099
$990$	−1.31908	+	0.480105i	−0.0419230	+	0.0152587i
$991$	0.686137	−	3.89127i	0.0217959	−	0.123610i	−0.971969	−	0.235111i	$-0.924455\pi$
$991$	0.686137	−	3.89127i	0.0217959	−	0.123610i	0.993764	+	0.111501i	$0.0355657\pi$
$992$	6.07398	−	5.09667i	0.192849	−	0.161820i
$993$	20.5626	+	17.2541i	0.652534	+	0.547541i
$994$	3.73127	+	21.1611i	0.118349	+	0.671188i
$995$	−10.5162	−	18.2146i	−0.333386	−	0.577441i
$996$	−1.94949	+	3.37662i	−0.0617720	+	0.106992i
$997$	44.2139	+	16.0926i	1.40027	+	0.509656i	0.928258	−	0.371936i	$-0.121306\pi$
$997$	44.2139	+	16.0926i	1.40027	+	0.509656i	0.472011	+	0.881592i	$0.343528\pi$
$998$	−5.05943	−	1.84148i	−0.160153	−	0.0582911i
$999$	0.0320889	−	0.0555796i	0.00101525	−	0.00175846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.i.a.43.1	✓	6
3.2	odd	2		342.2.u.e.271.1		6
4.3	odd	2		912.2.bo.a.385.1		6
19.2	odd	18		2166.2.a.s.1.2		3
19.4	even	9	inner	114.2.i.a.61.1	yes	6
19.17	even	9		2166.2.a.q.1.2		3
57.2	even	18		6498.2.a.bm.1.2		3
57.17	odd	18		6498.2.a.br.1.2		3
57.23	odd	18		342.2.u.e.289.1		6
76.23	odd	18		912.2.bo.a.289.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.a.43.1	✓	6	1.1	even	1	trivial
114.2.i.a.61.1	yes	6	19.4	even	9	inner
342.2.u.e.271.1		6	3.2	odd	2
342.2.u.e.289.1		6	57.23	odd	18
912.2.bo.a.289.1		6	76.23	odd	18
912.2.bo.a.385.1		6	4.3	odd	2
2166.2.a.q.1.2		3	19.17	even	9
2166.2.a.s.1.2		3	19.2	odd	18
6498.2.a.bm.1.2		3	57.2	even	18
6498.2.a.br.1.2		3	57.17	odd	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(0.173648 - 0.984808i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.907604 - 0.761570i) q^{5} +(-0.173648 - 0.984808i) q^{6} +(0.733956 + 1.27125i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-1.11334 - 0.405223i) q^{10} +(-0.592396 + 1.02606i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.446967 + 2.53487i) q^{13} +(1.12449 + 0.943555i) q^{14} +(-0.907604 + 0.761570i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-2.09240 + 0.761570i) q^{17} -1.00000 q^{18} +(0.819078 + 4.28125i) q^{19} -1.18479 q^{20} +(1.37939 - 0.502055i) q^{21} +(-0.205737 + 1.16679i) q^{22} +(0.907604 - 0.761570i) q^{23} +(-0.766044 - 0.642788i) q^{24} +(-0.624485 - 3.54163i) q^{25} +(1.28699 + 2.22913i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(1.37939 + 0.502055i) q^{28} +(-8.84389 - 3.21891i) q^{29} +(-0.592396 + 1.02606i) q^{30} +(3.96451 + 6.86673i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.907604 + 0.761570i) q^{33} +(-1.70574 + 1.43128i) q^{34} +(0.302004 - 1.71275i) q^{35} +(-0.939693 + 0.342020i) q^{36} -0.0641778 q^{37} +(2.23396 + 3.74292i) q^{38} +2.57398 q^{39} +(-1.11334 + 0.405223i) q^{40} +(1.68092 - 9.53298i) q^{41} +(1.12449 - 0.943555i) q^{42} +(-5.55303 - 4.65955i) q^{43} +(0.205737 + 1.16679i) q^{44} +(0.592396 + 1.02606i) q^{45} +(0.592396 - 1.02606i) q^{46} +(4.57145 + 1.66387i) q^{47} +(-0.939693 - 0.342020i) q^{48} +(2.42262 - 4.19610i) q^{49} +(-1.79813 - 3.11446i) q^{50} +(0.386659 + 2.19285i) q^{51} +(1.97178 + 1.65452i) q^{52} +(-1.11334 + 0.934204i) q^{53} +(-0.173648 + 0.984808i) q^{54} +(1.31908 - 0.480105i) q^{55} +1.46791 q^{56} +(4.35844 - 0.0632028i) q^{57} -9.41147 q^{58} +(-1.31908 + 0.480105i) q^{59} +(-0.205737 + 1.16679i) q^{60} +(5.97565 - 5.01417i) q^{61} +(6.07398 + 5.09667i) q^{62} +(-0.254900 - 1.44561i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(1.52481 - 2.64106i) q^{65} +(1.11334 + 0.405223i) q^{66} +(-8.19119 - 2.98135i) q^{67} +(-1.11334 + 1.92836i) q^{68} +(-0.592396 - 1.02606i) q^{69} +(-0.302004 - 1.71275i) q^{70} +(11.2135 + 9.40923i) q^{71} +(-0.766044 + 0.642788i) q^{72} +(1.13563 - 6.44047i) q^{73} +(-0.0603074 + 0.0219501i) q^{74} -3.59627 q^{75} +(3.37939 + 2.75314i) q^{76} -1.73917 q^{77} +(2.41875 - 0.880352i) q^{78} +(2.24035 - 12.7057i) q^{79} +(-0.907604 + 0.761570i) q^{80} +(0.766044 + 0.642788i) q^{81} +(-1.68092 - 9.53298i) q^{82} +(-1.94949 - 3.37662i) q^{83} +(0.733956 - 1.27125i) q^{84} +(2.47906 + 0.902302i) q^{85} +(-6.81180 - 2.47929i) q^{86} +(-4.70574 + 8.15058i) q^{87} +(0.592396 + 1.02606i) q^{88} +(2.15523 + 12.2229i) q^{89} +(0.907604 + 0.761570i) q^{90} +(-2.89440 + 2.42869i) q^{91} +(0.205737 - 1.16679i) q^{92} +(7.45084 - 2.71188i) q^{93} +4.86484 q^{94} +(2.51707 - 4.50946i) q^{95} -1.00000 q^{96} +(-12.1356 + 4.41701i) q^{97} +(0.841367 - 4.77163i) q^{98} +(0.907604 - 0.761570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 9 q^{5} + 9 q^{7} + 3 q^{8} - 3 q^{12} + 15 q^{13} - 6 q^{14} - 9 q^{15} - 9 q^{17} - 6 q^{18} - 12 q^{19} - 3 q^{21} + 9 q^{22} + 9 q^{23} + 9 q^{25} - 3 q^{27} - 3 q^{28} - 9 q^{29} - 9 q^{31} + 9 q^{33}+ \cdots + 9 q^{99}+O(q^{100}) \) 6 * q - 9 * q^5 + 9 * q^7 + 3 * q^8 - 3 * q^12 + 15 * q^13 - 6 * q^14 - 9 * q^15 - 9 * q^17 - 6 * q^18 - 12 * q^19 - 3 * q^21 + 9 * q^22 + 9 * q^23 + 9 * q^25 - 3 * q^27 - 3 * q^28 - 9 * q^29 - 9 * q^31 + 9 * q^33 - 36 * q^35 + 18 * q^37 + 18 * q^38 + 27 * q^41 - 6 * q^42 - 21 * q^43 - 9 * q^44 + 27 * q^47 - 12 * q^49 + 3 * q^50 + 9 * q^51 - 3 * q^52 - 9 * q^55 + 18 * q^56 + 18 * q^57 - 36 * q^58 + 9 * q^59 + 9 * q^60 - 3 * q^61 + 21 * q^62 - 3 * q^63 - 3 * q^64 - 18 * q^65 - 3 * q^67 + 36 * q^70 + 9 * q^71 - 12 * q^73 - 6 * q^74 + 6 * q^75 + 9 * q^76 + 18 * q^77 + 12 * q^78 - 21 * q^79 - 9 * q^80 - 27 * q^82 - 9 * q^83 + 9 * q^84 + 18 * q^85 - 6 * q^86 - 18 * q^87 + 9 * q^90 + 24 * q^91 - 9 * q^92 + 33 * q^93 - 18 * q^94 + 36 * q^95 - 6 * q^96 - 54 * q^97 - 24 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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