LMFDB - Embedded newform 114.2.i.a.61.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(25,114)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			61.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	114.61
Dual form			114.2.i.a.43.1

$q$-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 $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

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

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	−0.822766	−	0.568380i	$-0.807570\pi$
$5$	−0.907604	+	0.761570i	−0.405893	+	0.340584i	0.416873	+	0.908965i	$0.363126\pi$
$6$	−0.173648	+	0.984808i	−0.0708916	+	0.402046i
$7$	0.733956	−	1.27125i	0.277409	−	0.480487i	−0.693331	−	0.720619i	$-0.743858\pi$
$7$	0.733956	−	1.27125i	0.277409	−	0.480487i	0.970740	+	0.240133i	$0.0771909\pi$
$8$	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	0.762792	−	0.646644i	$-0.223828\pi$
$11$	−0.592396	−	1.02606i	−0.178614	−	0.309369i	−0.941406	+	0.337275i	$0.890495\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.446967	−	2.53487i	0.123966	−	0.703047i	−0.857950	−	0.513733i	$-0.828262\pi$
$13$	0.446967	−	2.53487i	0.123966	−	0.703047i	0.981916	−	0.189315i	$-0.0606266\pi$
$14$	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	0.0755749	−	0.997140i	$-0.475921\pi$
$17$	−2.09240	−	0.761570i	−0.507481	−	0.184708i	−0.583056	+	0.812432i	$0.698143\pi$
$18$	−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	0.732489	−	0.680779i	$-0.238358\pi$
$23$	0.907604	+	0.761570i	0.189248	+	0.158798i	−0.543241	+	0.839577i	$0.682803\pi$
$24$	−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	−0.987434	−	0.158034i	$-0.949485\pi$
$29$	−8.84389	+	3.21891i	−1.64227	+	0.597737i	−0.654836	+	0.755771i	$0.727262\pi$
$30$	−0.592396	−	1.02606i	−0.108156	−	0.187332i
$31$	3.96451	−	6.86673i	0.712047	−	1.23330i	−0.252041	−	0.967717i	$-0.581102\pi$
$31$	3.96451	−	6.86673i	0.712047	−	1.23330i	0.964088	−	0.265584i	$-0.0855649\pi$
$32$	−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	0.776017	+	0.630713i	$0.217237\pi$
$41$	1.68092	+	9.53298i	0.262516	+	1.48880i	−0.513501	+	0.858089i	$0.671652\pi$
$42$	1.12449	+	0.943555i	0.173512	+	0.145594i
$43$	−5.55303	+	4.65955i	−0.846830	+	0.710574i	−0.959089	−	0.283104i	$-0.908636\pi$
$43$	−5.55303	+	4.65955i	−0.846830	+	0.710574i	0.112259	+	0.993679i	$0.464191\pi$
$44$	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	0.0136389	−	0.999907i	$-0.495658\pi$
$47$	4.57145	−	1.66387i	0.666815	−	0.242701i	0.653176	+	0.757206i	$0.273436\pi$
$48$	−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	0.563113	−	0.826380i	$-0.309604\pi$
$53$	−1.11334	−	0.934204i	−0.152929	−	0.128323i	−0.716042	+	0.698057i	$0.754048\pi$
$54$	−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	0.254725	−	0.967014i	$-0.418015\pi$
$59$	−1.31908	−	0.480105i	−0.171729	−	0.0625044i	−0.426454	+	0.904509i	$0.640237\pi$
$60$	−0.205737	−	1.16679i	−0.0265605	−	0.150632i
$61$	5.97565	+	5.01417i	0.765104	+	0.641998i	0.939450	−	0.342686i	$-0.111337\pi$
$61$	5.97565	+	5.01417i	0.765104	+	0.641998i	−0.174346	+	0.984684i	$0.555781\pi$
$62$	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	−0.789859	−	0.613288i	$-0.789847\pi$
$67$	−8.19119	+	2.98135i	−1.00071	+	0.364230i	−0.210854	+	0.977518i	$0.567624\pi$
$68$	−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	0.346904	−	0.937901i	$-0.387233\pi$
$71$	11.2135	−	9.40923i	1.33079	−	1.11667i	0.983891	−	0.178769i	$-0.0572114\pi$
$72$	−0.766044	−	0.642788i	−0.0902792	−	0.0757532i
$73$	1.13563	+	6.44047i	0.132915	+	0.753801i	0.976289	+	0.216473i	$0.0694552\pi$
$73$	1.13563	+	6.44047i	0.132915	+	0.753801i	−0.843373	+	0.537328i	$0.819434\pi$
$74$	−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	0.803510	+	0.595292i	$0.202963\pi$
$79$	2.24035	+	12.7057i	0.252059	+	1.42950i	−0.551450	+	0.834208i	$0.685925\pi$
$80$	−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	−0.952958	−	0.303102i	$-0.901978\pi$
$83$	−1.94949	+	3.37662i	−0.213985	+	0.370632i	0.738973	+	0.673735i	$0.235311\pi$
$84$	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	−0.627517	−	0.778603i	$-0.715929\pi$
$89$	2.15523	−	12.2229i	0.228454	−	1.29563i	0.855971	−	0.517024i	$-0.172960\pi$
$90$	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	−0.357841	−	0.933783i	$-0.616487\pi$
$97$	−12.1356	−	4.41701i	−1.23219	−	0.448479i	−0.874346	+	0.485303i	$0.838709\pi$
$98$	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	−0.600118	−	0.799911i	$-0.704880\pi$
$101$	2.38578	−	13.5304i	0.237394	−	1.34633i	0.837513	−	0.546418i	$-0.184009\pi$
$102$	1.11334	−	1.92836i	0.110237	−	0.190936i
$103$	−8.56805	−	14.8403i	−0.844235	−	1.46226i	−0.886284	−	0.463142i	$-0.846722\pi$
$103$	−8.56805	−	14.8403i	−0.844235	−	1.46226i	0.0420491	−	0.999116i	$-0.486611\pi$
$104$	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	−0.492279	−	0.870437i	$-0.663836\pi$
$107$	5.25150	−	9.09586i	0.507681	−	0.879330i	0.999960	−	0.00889246i	$-0.00283060\pi$
$108$	0.173648	−	0.984808i	0.0167093	−	0.0947632i
$109$	−6.16044	+	5.16923i	−0.590064	+	0.495122i	−0.888234	−	0.459390i	$-0.848068\pi$
$109$	−6.16044	+	5.16923i	−0.590064	+	0.495122i	0.298171	+	0.954512i	$0.403623\pi$
$110$	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	−0.876017	−	0.482280i	$-0.839809\pi$
$127$	1.26352	−	7.16577i	0.112119	−	0.635859i	0.988136	−	0.153579i	$-0.0490800\pi$
$128$	−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	0.609325	−	0.792920i	$-0.291440\pi$
$131$	6.48293	+	2.35959i	0.566416	+	0.206159i	−0.0429093	+	0.999079i	$0.513663\pi$
$132$	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	0.991504	−	0.130079i	$-0.0415230\pi$
$137$	12.1211	+	10.1708i	1.03557	+	0.868950i	0.0440702	+	0.999028i	$0.485967\pi$
$138$	−0.907604	+	0.761570i	−0.0772604	+	0.0648291i
$139$	−2.68732	+	15.2405i	−0.227935	+	1.29269i	0.629058	+	0.777358i	$0.283441\pi$
$139$	−2.68732	+	15.2405i	−0.227935	+	1.29269i	−0.856993	+	0.515327i	$0.827670\pi$
$140$	−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	0.996541	−	0.0831016i	$-0.0264826\pi$
$149$	0.386659	+	2.19285i	0.0316764	+	0.179646i	−0.964865	+	0.262747i	$0.915371\pi$
$150$	−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	−0.314474	−	0.949266i	$-0.601828\pi$
$157$	7.08899	−	5.94837i	0.565763	−	0.474732i	0.880237	+	0.474534i	$0.157384\pi$
$158$	−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	0.920942	−	0.389700i	$-0.127421\pi$
$163$	1.57011	+	2.71951i	0.122980	+	0.213008i	−0.797961	+	0.602709i	$0.794088\pi$
$164$	−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	0.977742	−	0.209813i	$-0.0672854\pi$
$167$	12.1591	+	10.2027i	0.940899	+	0.789508i	−0.0368422	+	0.999321i	$0.511730\pi$
$168$	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	0.215410	−	0.976524i	$-0.430891\pi$
$173$	−3.25237	−	1.18377i	−0.247273	−	0.0900002i	−0.462684	+	0.886524i	$0.653113\pi$
$174$	−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	0.877565	−	0.479458i	$-0.159167\pi$
$179$	0.315207	+	0.545955i	0.0235597	+	0.0408066i	−0.854005	+	0.520265i	$0.825833\pi$
$180$	1.11334	−	0.405223i	0.0829835	−	0.0302035i
$181$	11.0778	−	4.03201i	0.823410	−	0.299697i	0.104259	−	0.994550i	$-0.466753\pi$
$181$	11.0778	−	4.03201i	0.823410	−	0.299697i	0.719151	+	0.694853i	$0.244531\pi$
$182$	−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	0.984893	+	0.173166i	$0.0553996\pi$
$193$	1.64796	+	9.34602i	0.118622	+	0.672741i	−0.866270	+	0.499576i	$0.833489\pi$
$194$	−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	−0.964672	−	0.263452i	$-0.915139\pi$
$197$	−3.56758	+	6.17923i	−0.254180	+	0.440252i	0.710493	+	0.703705i	$0.248472\pi$
$198$	0.592396	+	1.02606i	0.0420998	+	0.0729189i
$199$	16.6814	−	6.07153i	1.18251	−	0.430399i	0.325424	−	0.945568i	$-0.394493\pi$
$199$	16.6814	−	6.07153i	1.18251	−	0.430399i	0.857089	+	0.515169i	$0.172271\pi$
$200$	−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	0.271124	−	0.962544i	$-0.412605\pi$
$211$	−2.03209	−	0.739620i	−0.139895	−	0.0509175i	−0.411019	+	0.911627i	$0.634827\pi$
$212$	−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	−0.516429	+	0.856330i	$0.672739\pi$
$223$	−21.6446	+	18.1619i	−1.44943	+	1.21621i	−0.932997	+	0.359883i	$0.882817\pi$
$224$	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	−0.194950	−	0.980813i	$-0.562454\pi$
$233$	11.2515	−	9.44113i	0.737110	−	0.618509i	0.932060	+	0.362304i	$0.118010\pi$
$234$	−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	−0.999949	−	0.0101147i	$-0.996780\pi$
$239$	−7.86484	−	13.6223i	−0.508734	−	0.881153i	0.491215	−	0.871038i	$-0.336553\pi$
$240$	0.592396	−	1.02606i	0.0382390	−	0.0662319i
$241$	1.71079	−	9.70237i	0.110202	−	0.624985i	−0.878813	−	0.477166i	$-0.841664\pi$
$241$	1.71079	−	9.70237i	0.110202	−	0.624985i	0.989015	−	0.147818i	$-0.0472250\pi$
$242$	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	0.747669	−	0.664072i	$-0.231173\pi$
$251$	3.54117	+	2.97140i	0.223517	+	0.187553i	−0.524152	+	0.851625i	$0.675618\pi$
$252$	−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	−0.252073	−	0.967708i	$-0.581112\pi$
$257$	2.83527	−	1.03196i	0.176860	−	0.0643716i	0.428932	+	0.903337i	$0.358890\pi$
$258$	−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	0.946189	−	0.323616i	$-0.104898\pi$
$263$	−0.869585	−	4.93166i	−0.0536209	−	0.304099i	−0.999810	+	0.0195163i	$0.993787\pi$
$264$	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	−0.782058	−	0.623206i	$-0.785830\pi$
$269$	−4.26945	−	24.2132i	−0.260313	−	1.47631i	0.521745	−	0.853102i	$-0.325281\pi$
$270$	0.907604	+	0.761570i	0.0552350	+	0.0463477i
$271$	−1.28699	+	1.07991i	−0.0781790	+	0.0656000i	−0.681040	−	0.732246i	$-0.738472\pi$
$271$	−1.28699	+	1.07991i	−0.0781790	+	0.0656000i	0.602861	+	0.797846i	$0.294027\pi$
$272$	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	0.826585	+	0.562812i	$0.190280\pi$
$277$	14.9907	+	25.9646i	0.900702	+	1.56006i	0.0741168	+	0.997250i	$0.476386\pi$
$278$	−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	0.949367	−	0.314168i	$-0.101725\pi$
$281$	13.4914	+	11.3206i	0.804828	+	0.675331i	−0.144539	+	0.989499i	$0.546170\pi$
$282$	0.844770	+	4.79093i	0.0503053	+	0.285296i
$283$	−14.9547	−	5.44307i	−0.888965	−	0.323557i	−0.143143	−	0.989702i	$-0.545721\pi$
$283$	−14.9547	−	5.44307i	−0.888965	−	0.323557i	−0.745822	+	0.666145i	$0.767943\pi$
$284$	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	0.862076	−	0.506779i	$-0.169164\pi$
$293$	−0.134285	−	0.232589i	−0.00784503	−	0.0135880i	−0.869921	+	0.493191i	$0.835831\pi$
$294$	−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	0.981846	−	0.189680i	$-0.0607451\pi$
$307$	−0.0992034	−	0.562610i	−0.00566184	−	0.0321099i	−0.987508	+	0.157570i	$0.949634\pi$
$308$	−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	−0.994543	−	0.104325i	$-0.966732\pi$
$311$	−7.17617	+	12.4295i	−0.406924	+	0.704812i	0.587620	+	0.809137i	$0.300065\pi$
$312$	1.28699	+	2.22913i	0.0728614	+	0.126200i
$313$	2.25877	−	0.822125i	0.127673	−	0.0464693i	−0.277393	−	0.960756i	$-0.589471\pi$
$313$	2.25877	−	0.822125i	0.127673	−	0.0464693i	0.405067	+	0.914287i	$0.367248\pi$
$314$	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	−0.836270	−	0.548317i	$-0.815269\pi$
$317$	2.44104	−	13.8438i	0.137102	−	0.777546i	0.973373	−	0.229228i	$-0.0736203\pi$
$318$	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	−0.953529	−	0.301303i	$-0.902579\pi$
$331$	−13.4213	−	23.2463i	−0.737700	−	1.27773i	0.215829	−	0.976431i	$-0.430755\pi$
$332$	−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	−0.964733	−	0.263230i	$-0.915212\pi$
$337$	−16.0266	+	13.4479i	−0.873026	+	0.732556i	0.0917071	+	0.995786i	$0.470768\pi$
$338$	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	−0.415249	+	0.909708i	$0.636306\pi$
$347$	−25.7670	+	21.6211i	−1.38324	+	1.16068i	−0.967994	+	0.250972i	$0.919250\pi$
$348$	1.63429	−	9.26849i	0.0876069	−	0.496843i
$349$	−13.5758	+	23.5140i	−0.726695	+	1.25867i	0.231577	+	0.972817i	$0.425611\pi$
$349$	−13.5758	+	23.5140i	−0.726695	+	1.25867i	−0.958272	+	0.285857i	$0.907722\pi$
$350$	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	0.998096	−	0.0616847i	$-0.0196473\pi$
$353$	8.37258	+	14.5017i	0.445627	+	0.771849i	−0.552468	+	0.833534i	$0.686314\pi$
$354$	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	0.456855	−	0.889541i	$-0.348976\pi$
$359$	4.45336	+	1.62089i	0.235040	+	0.0855474i	−0.221815	+	0.975089i	$0.571198\pi$
$360$	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	−0.918672	−	0.395020i	$-0.870738\pi$
$367$	1.52687	−	8.65933i	0.0797022	−	0.452014i	0.998375	−	0.0569932i	$-0.0181513\pi$
$368$	−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	−0.717464	−	0.696596i	$-0.754697\pi$
$373$	4.72281	−	8.18015i	0.244538	−	0.423552i	0.962002	+	0.273044i	$0.0880304\pi$
$374$	−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	−0.778882	−	0.627171i	$-0.784213\pi$
$383$	−5.11721	−	29.0211i	−0.261477	−	1.48291i	0.517405	−	0.855741i	$-0.326898\pi$
$384$	−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	−0.727069	−	0.686564i	$-0.759118\pi$
$389$	−16.6211	+	6.04958i	−0.842722	+	0.306726i	−0.115653	+	0.993290i	$0.536896\pi$
$390$	−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	0.0276326	−	0.999618i	$-0.491203\pi$
$397$	−11.8302	−	4.30585i	−0.593742	−	0.216104i	−0.621374	+	0.783514i	$0.713425\pi$
$398$	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	0.838163	−	0.545420i	$-0.183630\pi$
$401$	22.6211	+	8.23340i	1.12964	+	0.411156i	0.291480	+	0.956577i	$0.405852\pi$
$402$	−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	0.655440	−	0.755247i	$-0.272483\pi$
$409$	33.2276	−	12.0939i	1.64300	−	0.598003i	0.987560	+	0.157244i	$0.0502610\pi$
$410$	−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	0.985962	−	0.166971i	$-0.0533987\pi$
$421$	0.0482857	+	0.273842i	0.00235330	+	0.0133462i	−0.983608	+	0.180317i	$0.942288\pi$
$422$	−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	0.892792	+	0.450470i	$0.148744\pi$
$431$	−2.08079	+	11.8007i	−0.100228	+	0.568421i	−0.993019	+	0.117951i	$0.962368\pi$
$432$	0.766044	−	0.642788i	0.0368563	−	0.0309261i
$433$	−22.3286	−	18.7359i	−1.07305	−	0.900392i	−0.0777205	−	0.996975i	$-0.524764\pi$
$433$	−22.3286	−	18.7359i	−1.07305	−	0.900392i	−0.995325	+	0.0965831i	$0.969209\pi$
$434$	−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	0.196913	−	0.980421i	$-0.436908\pi$
$439$	−5.91787	−	2.15393i	−0.282445	−	0.102801i	−0.479358	+	0.877619i	$0.659130\pi$
$440$	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	−0.768981	−	0.639271i	$-0.779236\pi$
$443$	3.62583	−	20.5631i	0.172268	−	0.976982i	0.941250	−	0.337711i	$-0.109653\pi$
$444$	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	−0.300798	+	0.953688i	$0.597253\pi$
$449$	−20.6878	+	35.8323i	−0.976317	+	1.69103i	−0.675519	+	0.737343i	$0.736080\pi$
$450$	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	−0.910216	−	0.414134i	$-0.864084\pi$
$461$	−14.1800	+	11.8985i	−0.660431	+	0.554167i	0.249785	+	0.968301i	$0.419640\pi$
$462$	0.302004	−	1.71275i	0.0140505	−	0.0796843i
$463$	1.80928	−	3.13376i	0.0840843	−	0.145638i	−0.820916	−	0.571048i	$-0.806537\pi$
$463$	1.80928	−	3.13376i	0.0840843	−	0.145638i	0.905001	+	0.425410i	$0.139870\pi$
$464$	−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	0.983142	−	0.182845i	$-0.0585308\pi$
$467$	7.20099	+	12.4725i	0.333222	+	0.577158i	−0.649920	+	0.760003i	$0.725197\pi$
$468$	−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	−0.116654	−	0.993173i	$-0.537217\pi$
$479$	−24.4029	−	20.4764i	−1.11499	−	0.935592i	−0.998341	+	0.0575808i	$0.981661\pi$
$480$	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	−0.550808	−	0.834632i	$-0.685680\pi$
$487$	9.87346	−	17.1013i	0.447409	−	0.774935i	0.998217	+	0.0596972i	$0.0190135\pi$
$488$	−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	−0.855491	−	0.517818i	$-0.826744\pi$
$491$	−5.06758	−	28.7397i	−0.228697	−	1.29700i	0.626794	−	0.779185i	$-0.284367\pi$
$492$	−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	−0.730421	−	0.682997i	$-0.760676\pi$
$499$	−4.12449	+	3.46085i	−0.184637	+	0.154929i	0.545784	+	0.837926i	$0.316232\pi$
$500$	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	−0.801141	−	0.598476i	$-0.795773\pi$
$503$	−23.1040	+	8.40917i	−1.03016	+	0.374946i	−0.229016	+	0.973423i	$0.573551\pi$
$504$	−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	0.558456	−	0.829534i	$-0.311394\pi$
$509$	−3.64362	−	3.05736i	−0.161501	−	0.135515i	−0.719957	+	0.694019i	$0.755838\pi$
$510$	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	0.983354	+	0.181701i	$0.0581603\pi$
$521$	14.8145	+	25.6595i	0.649035	+	1.12416i	−0.334319	+	0.942460i	$0.608506\pi$
$522$	8.84389	−	3.21891i	0.387087	−	0.140888i
$523$	10.0890	−	3.67209i	0.441161	−	0.160569i	−0.111883	−	0.993721i	$-0.535688\pi$
$523$	10.0890	−	3.67209i	0.441161	−	0.160569i	0.553044	+	0.833152i	$0.313466\pi$
$524$	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	−0.861866	−	0.507136i	$-0.830704\pi$
$541$	−27.8209	+	10.1260i	−1.19611	+	0.435350i	−0.334247	+	0.942485i	$0.608482\pi$
$542$	−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	0.834841	−	0.550492i	$-0.185560\pi$
$547$	10.2365	+	8.58943i	0.437680	+	0.367257i	−0.397160	+	0.917749i	$0.630004\pi$
$548$	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	−0.994745	−	0.102382i	$-0.967354\pi$
$557$	−0.589403	+	3.34267i	−0.0249738	+	0.141634i	0.969771	+	0.244015i	$0.0784647\pi$
$558$	−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	0.0191757	−	0.999816i	$-0.493896\pi$
$563$	20.7724	−	35.9789i	0.875454	−	1.51633i	0.856278	−	0.516515i	$-0.172771\pi$
$564$	−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	−0.960599	−	0.277937i	$-0.910349\pi$
$577$	−5.75537	+	9.96859i	−0.239599	+	0.414998i	0.721000	+	0.692935i	$0.243683\pi$
$578$	−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	−0.00269254	−	0.999996i	$-0.500857\pi$
$587$	−15.6887	−	5.71021i	−0.647540	−	0.235685i	−0.644848	+	0.764311i	$0.723079\pi$
$588$	−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	0.959953	+	0.280160i	$0.0903875\pi$
$593$	34.1544	+	28.6589i	1.40255	+	1.17688i	0.442598	+	0.896720i	$0.354057\pi$
$594$	−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	−0.173391	−	0.984853i	$-0.555472\pi$
$599$	7.99912	−	2.91144i	0.326835	−	0.118958i	0.500226	+	0.865895i	$0.333250\pi$
$600$	−1.79813	−	3.11446i	−0.0734085	−	0.127147i
$601$	−16.7613	+	29.0314i	−0.683708	+	1.18422i	0.290134	+	0.956986i	$0.406300\pi$
$601$	−16.7613	+	29.0314i	−0.683708	+	1.18422i	−0.973841	+	0.227230i	$0.927033\pi$
$602$	−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	−0.501829	−	0.864967i	$-0.667339\pi$
$613$	6.50799	−	5.46085i	0.262855	−	0.220562i	0.764684	+	0.644405i	$0.222895\pi$
$614$	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	0.251068	−	0.967970i	$-0.419218\pi$
$617$	26.4688	−	9.63387i	1.06560	−	0.387845i	0.814528	+	0.580124i	$0.196996\pi$
$618$	16.1027	−	5.86089i	0.647744	−	0.235760i
$619$	11.4483	+	19.8291i	0.460146	+	0.796997i	0.998968	−	0.0454230i	$-0.0144636\pi$
$619$	11.4483	+	19.8291i	0.460146	+	0.796997i	−0.538821	+	0.842420i	$0.681130\pi$
$620$	−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	−0.00510629	−	0.999987i	$-0.501625\pi$
$631$	−24.8883	−	20.8838i	−0.990788	−	0.831370i	−0.985682	+	0.168617i	$0.946070\pi$
$632$	−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	−0.523872	−	0.851797i	$-0.675513\pi$
$641$	5.67159	−	4.75903i	0.224014	−	0.187970i	0.747887	+	0.663826i	$0.231069\pi$
$642$	8.04576	+	6.75119i	0.317541	+	0.266448i
$643$	−7.38847	−	41.9021i	−0.291373	−	1.65246i	−0.681590	−	0.731734i	$-0.738711\pi$
$643$	−7.38847	−	41.9021i	−0.291373	−	1.65246i	0.390217	−	0.920723i	$-0.372400\pi$
$644$	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	−0.477827	−	0.878454i	$-0.658576\pi$
$653$	13.3353	−	23.0974i	0.521850	−	0.903870i	0.999677	−	0.0254163i	$-0.00809113\pi$
$654$	−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	0.912184	+	0.409780i	$0.134395\pi$
$659$	−2.18567	+	12.3955i	−0.0851416	+	0.482862i	−0.997326	+	0.0730819i	$0.976717\pi$
$660$	−1.07532	+	0.902302i	−0.0418569	+	0.0351221i
$661$	6.35432	+	5.33191i	0.247154	+	0.207387i	0.757946	−	0.652317i	$-0.226203\pi$
$661$	6.35432	+	5.33191i	0.247154	+	0.207387i	−0.510791	+	0.859705i	$0.670648\pi$
$662$	−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	0.849937	−	0.526884i	$-0.176640\pi$
$673$	−0.812681	−	1.40761i	−0.0313266	−	0.0542592i	−0.881264	+	0.472625i	$0.843307\pi$
$674$	−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	−0.709696	−	0.704508i	$-0.751168\pi$
$677$	6.64203	−	11.5043i	0.255274	−	0.442147i	0.964970	+	0.262361i	$0.0845011\pi$
$678$	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	−0.696523	−	0.717535i	$-0.745271\pi$
$691$	7.18004	−	12.4362i	0.273142	−	0.473095i	0.969665	+	0.244439i	$0.0786039\pi$
$692$	−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	−0.728406	−	0.685146i	$-0.759738\pi$
$701$	−45.7195	−	16.6405i	−1.72680	−	0.628504i	−0.998395	+	0.0566421i	$0.981961\pi$
$702$	−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	0.936408	+	0.350913i	$0.114129\pi$
$709$	−1.69207	+	9.59619i	−0.0635469	+	0.360392i	−0.999955	+	0.00947962i	$0.996982\pi$
$710$	−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	0.996473	−	0.0839181i	$-0.0267434\pi$
$719$	0.841777	+	4.77396i	0.0313930	+	0.178038i	−0.965080	+	0.261957i	$0.915632\pi$
$720$	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	−0.821728	−	0.569880i	$-0.806990\pi$
$727$	−10.8714	+	9.12218i	−0.403198	+	0.338323i	0.418530	+	0.908203i	$0.362545\pi$
$728$	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	0.750915	−	0.660399i	$-0.229613\pi$
$733$	−5.31908	−	9.21291i	−0.196465	−	0.340287i	−0.947380	+	0.320112i	$0.896279\pi$
$734$	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	0.771718	−	0.635964i	$-0.219397\pi$
$739$	25.9368	+	9.44021i	0.954099	+	0.347264i	0.182381	+	0.983228i	$0.441620\pi$
$740$	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	0.321058	−	0.947059i	$-0.395961\pi$
$743$	−1.13816	−	0.414255i	−0.0417549	−	0.0151975i	−0.362813	+	0.931862i	$0.618184\pi$
$744$	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	−0.993573	−	0.113190i	$-0.963893\pi$
$751$	−46.0925	+	16.7763i	−1.68194	+	0.612175i	−0.688364	+	0.725365i	$0.741671\pi$
$752$	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	0.857484	+	0.514510i	$0.172026\pi$
$757$	6.26445	+	35.5275i	0.227685	+	1.29127i	−0.629799	+	0.776758i	$0.716863\pi$
$758$	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	−0.682389	−	0.730989i	$-0.739059\pi$
$769$	−20.3893	+	7.42112i	−0.735259	+	0.267612i	−0.0528696	+	0.998601i	$0.516837\pi$
$770$	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	−0.462410	−	0.886666i	$-0.653015\pi$
$773$	7.65611	−	43.4199i	0.275371	−	1.56171i	0.737781	−	0.675040i	$-0.235874\pi$
$774$	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	0.987783	−	0.155834i	$-0.0498066\pi$
$787$	10.0694	+	17.4407i	0.358935	+	0.621694i	−0.628848	+	0.777528i	$0.716473\pi$
$788$	−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	0.973399	+	0.229115i	$0.0735833\pi$
$809$	19.4868	+	33.7521i	0.685119	+	1.18666i	−0.288280	+	0.957546i	$0.593083\pi$
$810$	−0.592396	+	1.02606i	−0.0208147	+	0.0360521i
$811$	−3.71641	+	21.0768i	−0.130501	+	0.740108i	0.847387	+	0.530976i	$0.178175\pi$
$811$	−3.71641	+	21.0768i	−0.130501	+	0.740108i	−0.977888	+	0.209131i	$0.932936\pi$
$812$	−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	0.988846	+	0.148941i	$0.0475865\pi$
$821$	37.4564	+	31.4296i	1.30724	+	1.09690i	0.318390	+	0.947960i	$0.396858\pi$
$822$	−12.1211	+	10.1708i	−0.422771	+	0.354747i
$823$	−5.20217	+	29.5030i	−0.181336	+	1.02841i	0.749237	+	0.662302i	$0.230421\pi$
$823$	−5.20217	+	29.5030i	−0.181336	+	1.02841i	−0.930573	+	0.366107i	$0.880690\pi$
$824$	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	0.0652623	−	0.997868i	$-0.479212\pi$
$827$	21.7601	−	7.92003i	0.756673	−	0.275407i	0.691411	+	0.722462i	$0.256989\pi$
$828$	−0.592396	−	1.02606i	−0.0205872	−	0.0356581i
$829$	−15.4290	+	26.7238i	−0.535872	+	0.928157i	0.463249	+	0.886228i	$0.346684\pi$
$829$	−15.4290	+	26.7238i	−0.535872	+	0.928157i	−0.999121	+	0.0419290i	$0.986650\pi$
$830$	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	0.999774	+	0.0212615i	$0.00676826\pi$
$839$	1.95707	+	11.0991i	0.0675656	+	0.383184i	−0.932208	+	0.361922i	$0.882121\pi$
$840$	−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	0.637736	−	0.770255i	$-0.279871\pi$
$853$	18.4338	+	6.70934i	0.631160	+	0.229723i	−0.00657610	+	0.999978i	$0.502093\pi$
$854$	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	−0.0577318	−	0.998332i	$-0.518387\pi$
$857$	−21.7707	−	7.92388i	−0.743672	−	0.270675i	−0.685941	+	0.727657i	$0.740609\pi$
$858$	−0.529563	−	3.00330i	−0.0180790	−	0.102531i
$859$	1.85529	+	1.55677i	0.0633015	+	0.0531163i	0.673889	−	0.738832i	$-0.264622\pi$
$859$	1.85529	+	1.55677i	0.0633015	+	0.0531163i	−0.610588	+	0.791948i	$0.709067\pi$
$860$	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	0.972309	−	0.233698i	$-0.0750828\pi$
$863$	8.33615	+	14.4386i	0.283766	+	0.491497i	−0.688543	+	0.725195i	$0.741749\pi$
$864$	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	−0.864628	−	0.502412i	$-0.832446\pi$
$877$	−6.63294	−	37.6173i	−0.223979	−	1.27025i	0.640650	−	0.767833i	$-0.278665\pi$
$878$	−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	−0.597072	−	0.802188i	$-0.703669\pi$
$881$	11.7592	−	20.3676i	0.396179	−	0.686202i	0.993251	+	0.115986i	$0.0370027\pi$
$882$	−2.42262	−	4.19610i	−0.0815738	−	0.141290i
$883$	17.3042	−	6.29822i	0.582334	−	0.211952i	−0.0340206	−	0.999421i	$-0.510831\pi$
$883$	17.3042	−	6.29822i	0.582334	−	0.211952i	0.616354	+	0.787469i	$0.288609\pi$
$884$	−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	0.792879	+	0.609379i	$0.208581\pi$
$887$	−4.78317	+	27.1267i	−0.160603	+	0.910827i	−0.953483	+	0.301448i	$0.902530\pi$
$888$	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	−0.338228	−	0.941064i	$-0.609828\pi$
$907$	15.9559	−	13.3886i	0.529807	−	0.444561i	0.868035	+	0.496504i	$0.165383\pi$
$908$	−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	−0.222427	−	0.974949i	$-0.571398\pi$
$919$	22.2245	−	38.4939i	0.733117	−	1.26980i	0.955544	−	0.294847i	$-0.0952687\pi$
$920$	−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	0.187898	−	0.982188i	$-0.439832\pi$
$929$	−9.12866	−	3.32256i	−0.299502	−	0.109010i	−0.487400	+	0.873179i	$0.662055\pi$
$930$	−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	0.934960	+	0.354754i	$0.115435\pi$
$937$	−1.98808	+	11.2750i	−0.0649479	+	0.368338i	−0.999908	+	0.0135842i	$0.995676\pi$
$938$	−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	−0.922397	−	0.386243i	$-0.873772\pi$
$941$	−42.3546	+	15.4158i	−1.38072	+	0.502541i	−0.458324	+	0.888785i	$0.651550\pi$
$942$	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	0.811207	+	0.584759i	$0.198811\pi$
$947$	7.66014	+	43.4428i	0.248921	+	1.41170i	−0.562286	+	0.826943i	$0.690078\pi$
$948$	−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	0.989528	−	0.144343i	$-0.0461069\pi$
$953$	0.318201	+	1.80460i	0.0103075	+	0.0584569i	−0.979220	+	0.202800i	$0.934996\pi$
$954$	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	0.0806536	−	0.996742i	$-0.474299\pi$
$967$	−15.4941	−	5.63938i	−0.498256	−	0.181350i	−0.578909	+	0.815392i	$0.696521\pi$
$968$	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	−0.432932	−	0.901426i	$-0.642521\pi$
$971$	−41.8803	−	15.2432i	−1.34400	−	0.489177i	−0.911071	+	0.412249i	$0.864743\pi$
$972$	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	−0.999996	−	0.00282321i	$-0.999101\pi$
$977$	−15.7049	−	27.2016i	−0.502443	−	0.870257i	0.497553	−	0.867434i	$-0.334232\pi$
$978$	−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	−0.924588	−	0.380969i	$-0.875590\pi$
$983$	−22.2592	+	18.6777i	−0.709959	+	0.595727i	0.214628	+	0.976696i	$0.431146\pi$
$984$	−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	0.993764	−	0.111501i	$-0.0355657\pi$
$991$	0.686137	+	3.89127i	0.0217959	+	0.123610i	−0.971969	+	0.235111i	$0.924455\pi$
$992$	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	0.472011	−	0.881592i	$-0.343528\pi$
$997$	44.2139	−	16.0926i	1.40027	−	0.509656i	0.928258	+	0.371936i	$0.121306\pi$
$998$	−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.61.1	yes	6
3.2	odd	2		342.2.u.e.289.1		6
4.3	odd	2		912.2.bo.a.289.1		6
19.5	even	9	inner	114.2.i.a.43.1	✓	6
19.9	even	9		2166.2.a.q.1.2		3
19.10	odd	18		2166.2.a.s.1.2		3
57.5	odd	18		342.2.u.e.271.1		6
57.29	even	18		6498.2.a.bm.1.2		3
57.47	odd	18		6498.2.a.br.1.2		3
76.43	odd	18		912.2.bo.a.385.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.a.43.1	✓	6	19.5	even	9	inner
114.2.i.a.61.1	yes	6	1.1	even	1	trivial
342.2.u.e.271.1		6	57.5	odd	18
342.2.u.e.289.1		6	3.2	odd	2
912.2.bo.a.289.1		6	4.3	odd	2
912.2.bo.a.385.1		6	76.43	odd	18
2166.2.a.q.1.2		3	19.9	even	9
2166.2.a.s.1.2		3	19.10	odd	18
6498.2.a.bm.1.2		3	57.29	even	18
6498.2.a.br.1.2		3	57.47	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 $\F_{q}$

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

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Representations

Groups

Database

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