LMFDB - Embedded newform 187.2.g.e.69.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [187,2,Mod(69,187)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(187, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("187.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.g (of order $5$, degree $4$, 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:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			69.1
Root			$0.418926 - 1.28932i$ of defining polynomial
Character	$\chi$	$=$	187.69
Dual form			187.2.g.e.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.77460 + 1.28932i) q^{2} +(-0.227943 - 0.701538i) q^{3} +(0.868820 - 2.67395i) q^{4} +(-1.17784 - 0.855749i) q^{5} +(1.30902 + 0.951057i) q^{6} +(-0.986854 + 3.03722i) q^{7} +(0.550106 + 1.69305i) q^{8} +(1.98685 - 1.44353i) q^{9} +O(q^{10})$	\(q+(-1.77460 + 1.28932i) q^{2} +(-0.227943 - 0.701538i) q^{3} +(0.868820 - 2.67395i) q^{4} +(-1.17784 - 0.855749i) q^{5} +(1.30902 + 0.951057i) q^{6} +(-0.986854 + 3.03722i) q^{7} +(0.550106 + 1.69305i) q^{8} +(1.98685 - 1.44353i) q^{9} +3.19353 q^{10} +(3.04508 - 1.31433i) q^{11} -2.07392 q^{12} +(4.56489 - 3.31659i) q^{13} +(-2.16469 - 6.66223i) q^{14} +(-0.331860 + 1.02136i) q^{15} +(1.39009 + 1.00996i) q^{16} +(0.809017 + 0.587785i) q^{17} +(-1.66469 + 5.12339i) q^{18} +(2.23049 + 6.86473i) q^{19} +(-3.31156 + 2.40599i) q^{20} +2.35567 q^{21} +(-3.70922 + 6.25850i) q^{22} -1.04944 q^{23} +(1.06235 - 0.771840i) q^{24} +(-0.890091 - 2.73942i) q^{25} +(-3.82471 + 11.7712i) q^{26} +(-3.25587 - 2.36553i) q^{27} +(7.26400 + 5.27760i) q^{28} +(1.16215 - 3.57672i) q^{29} +(-0.727943 - 2.24038i) q^{30} +(8.75085 - 6.35787i) q^{31} -7.32938 q^{32} +(-1.61616 - 1.83665i) q^{33} -2.19353 q^{34} +(3.76145 - 2.73286i) q^{35} +(-2.13372 - 6.56693i) q^{36} +(-2.55635 + 7.86765i) q^{37} +(-12.8091 - 9.30634i) q^{38} +(-3.36725 - 2.44645i) q^{39} +(0.800892 - 2.46489i) q^{40} +(-0.426079 - 1.31134i) q^{41} +(-4.18038 + 3.03722i) q^{42} +4.75389 q^{43} +(-0.868820 - 9.28433i) q^{44} -3.57549 q^{45} +(1.86233 - 1.35307i) q^{46} +(-2.17094 - 6.68146i) q^{47} +(0.391663 - 1.20541i) q^{48} +(-2.58773 - 1.88010i) q^{49} +(5.11155 + 3.71376i) q^{50} +(0.227943 - 0.701538i) q^{51} +(-4.90233 - 15.0878i) q^{52} +(-2.99030 + 2.17258i) q^{53} +8.82781 q^{54} +(-4.71135 - 1.05776i) q^{55} -5.68506 q^{56} +(4.30744 - 3.12954i) q^{57} +(2.54920 + 7.84564i) q^{58} +(-1.85445 + 5.70740i) q^{59} +(2.44274 + 1.77476i) q^{60} +(-8.15409 - 5.92429i) q^{61} +(-7.33193 + 22.5653i) q^{62} +(2.42360 + 7.45908i) q^{63} +(10.2265 - 7.43002i) q^{64} -8.21486 q^{65} +(5.23607 + 1.17557i) q^{66} -0.586654 q^{67} +(2.27460 - 1.65259i) q^{68} +(0.239213 + 0.736221i) q^{69} +(-3.15155 + 9.69946i) q^{70} +(-1.66068 - 1.20656i) q^{71} +(3.53696 + 2.56975i) q^{72} +(0.917955 - 2.82517i) q^{73} +(-5.60743 - 17.2579i) q^{74} +(-1.71891 + 1.24886i) q^{75} +20.2939 q^{76} +(0.986854 + 10.5457i) q^{77} +9.12978 q^{78} +(-7.73558 + 5.62022i) q^{79} +(-0.773028 - 2.37914i) q^{80} +(1.35938 - 4.18374i) q^{81} +(2.44686 + 1.77775i) q^{82} +(13.2458 + 9.62366i) q^{83} +(2.04666 - 6.29896i) q^{84} +(-0.449894 - 1.38463i) q^{85} +(-8.43626 + 6.12930i) q^{86} -2.77411 q^{87} +(3.90035 + 4.43247i) q^{88} +10.9131 q^{89} +(6.34507 - 4.60997i) q^{90} +(5.56834 + 17.1376i) q^{91} +(-0.911774 + 2.80615i) q^{92} +(-6.45498 - 4.68982i) q^{93} +(12.4671 + 9.05789i) q^{94} +(3.24734 - 9.99428i) q^{95} +(1.67068 + 5.14184i) q^{96} +(-5.51890 + 4.00972i) q^{97} +7.01625 q^{98} +(4.15286 - 7.00706i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q - q^2 + 3 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9	\( 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 2 q^{12} + 3 q^{13} - 10 q^{15} + 7 q^{16} + 2 q^{17} + 4 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{21} - 9 q^{22} - 24 q^{23} - 7 q^{24} - 3 q^{25} - 19 q^{26} + 3 q^{27} + 16 q^{28} + 10 q^{29} - q^{30} + 17 q^{31} - 24 q^{32} - 8 q^{33} - 4 q^{34} + 6 q^{35} - q^{36} - 13 q^{37} - 38 q^{38} - 11 q^{39} + 15 q^{40} - 22 q^{41} - 9 q^{42} + 8 q^{43} - 5 q^{44} - 24 q^{45} - 20 q^{46} + 9 q^{47} + 13 q^{48} + q^{49} - q^{50} - 3 q^{51} - 18 q^{52} - 23 q^{53} + 22 q^{54} - 12 q^{55} + 2 q^{56} + 16 q^{57} - 6 q^{58} - 35 q^{59} - q^{60} - 19 q^{61} - 6 q^{62} - 4 q^{63} + 8 q^{64} + 10 q^{65} + 24 q^{66} - 10 q^{67} + 5 q^{68} + 12 q^{69} + 3 q^{70} - 5 q^{71} + 19 q^{72} + 39 q^{73} - 7 q^{74} + 6 q^{75} + 32 q^{76} - 3 q^{77} + 6 q^{78} - 3 q^{79} + 21 q^{80} + 7 q^{81} - 5 q^{82} + 29 q^{83} + 8 q^{84} - 2 q^{85} - 14 q^{86} + 32 q^{87} + 9 q^{88} + 40 q^{89} + 9 q^{90} + 21 q^{91} + 12 q^{92} - 14 q^{93} + 40 q^{94} + 23 q^{95} - 12 q^{96} - 5 q^{97} + 30 q^{98} + 20 q^{99}+O(q^{100}) \) 8 * q - q^2 + 3 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 2 * q^12 + 3 * q^13 - 10 * q^15 + 7 * q^16 + 2 * q^17 + 4 * q^18 - 5 * q^19 - 4 * q^20 + 6 * q^21 - 9 * q^22 - 24 * q^23 - 7 * q^24 - 3 * q^25 - 19 * q^26 + 3 * q^27 + 16 * q^28 + 10 * q^29 - q^30 + 17 * q^31 - 24 * q^32 - 8 * q^33 - 4 * q^34 + 6 * q^35 - q^36 - 13 * q^37 - 38 * q^38 - 11 * q^39 + 15 * q^40 - 22 * q^41 - 9 * q^42 + 8 * q^43 - 5 * q^44 - 24 * q^45 - 20 * q^46 + 9 * q^47 + 13 * q^48 + q^49 - q^50 - 3 * q^51 - 18 * q^52 - 23 * q^53 + 22 * q^54 - 12 * q^55 + 2 * q^56 + 16 * q^57 - 6 * q^58 - 35 * q^59 - q^60 - 19 * q^61 - 6 * q^62 - 4 * q^63 + 8 * q^64 + 10 * q^65 + 24 * q^66 - 10 * q^67 + 5 * q^68 + 12 * q^69 + 3 * q^70 - 5 * q^71 + 19 * q^72 + 39 * q^73 - 7 * q^74 + 6 * q^75 + 32 * q^76 - 3 * q^77 + 6 * q^78 - 3 * q^79 + 21 * q^80 + 7 * q^81 - 5 * q^82 + 29 * q^83 + 8 * q^84 - 2 * q^85 - 14 * q^86 + 32 * q^87 + 9 * q^88 + 40 * q^89 + 9 * q^90 + 21 * q^91 + 12 * q^92 - 14 * q^93 + 40 * q^94 + 23 * q^95 - 12 * q^96 - 5 * q^97 + 30 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.77460	+	1.28932i	−1.25483	+	0.911689i	−0.998492	−	0.0548977i	$-0.982517\pi$
$2$	−1.77460	+	1.28932i	−1.25483	+	0.911689i	−0.256340	+	0.966587i	$0.582517\pi$
$3$	−0.227943	−	0.701538i	−0.131603	−	0.405033i	0.863443	−	0.504446i	$-0.168303\pi$
$3$	−0.227943	−	0.701538i	−0.131603	−	0.405033i	−0.995046	+	0.0994134i	$0.968303\pi$
$4$	0.868820	−	2.67395i	0.434410	−	1.33698i
$5$	−1.17784	−	0.855749i	−0.526745	−	0.382702i	0.292394	−	0.956298i	$-0.405548\pi$
$5$	−1.17784	−	0.855749i	−0.526745	−	0.382702i	−0.819139	+	0.573595i	$0.805548\pi$
$6$	1.30902	+	0.951057i	0.534404	+	0.388267i
$7$	−0.986854	+	3.03722i	−0.372996	+	1.14796i	0.571825	+	0.820376i	$0.306236\pi$
$7$	−0.986854	+	3.03722i	−0.372996	+	1.14796i	−0.944821	+	0.327587i	$0.893764\pi$
$8$	0.550106	+	1.69305i	0.194492	+	0.598585i
$9$	1.98685	−	1.44353i	0.662285	−	0.481178i
$10$	3.19353			1.00988
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$11$	3.04508	−	1.31433i	0.918128	−	0.396285i
$12$	−2.07392			−0.598689
$13$	4.56489	−	3.31659i	1.26607	−	0.919856i	0.267034	−	0.963687i	$-0.413956\pi$
$13$	4.56489	−	3.31659i	1.26607	−	0.919856i	0.999039	+	0.0438312i	$0.0139564\pi$
$14$	−2.16469	−	6.66223i	−0.578538	−	1.78056i
$15$	−0.331860	+	1.02136i	−0.0856858	+	0.263714i
$16$	1.39009	+	1.00996i	0.347523	+	0.252490i
$17$	0.809017	+	0.587785i	0.196215	+	0.142559i
$17$	0.809017	+	0.587785i	0.196215	+	0.142559i
$18$	−1.66469	+	5.12339i	−0.392371	+	1.20760i
$19$	2.23049	+	6.86473i	0.511709	+	1.57488i	0.789191	+	0.614147i	$0.210500\pi$
$19$	2.23049	+	6.86473i	0.511709	+	1.57488i	−0.277482	+	0.960731i	$0.589500\pi$
$20$	−3.31156	+	2.40599i	−0.740488	+	0.537996i
$21$	2.35567			0.514050
$22$	−3.70922	+	6.25850i	−0.790808	+	1.33432i
$23$	−1.04944			−0.218823			−0.109412	−	0.993997i	$-0.534897\pi$
$23$	−1.04944			−0.218823			−0.109412	+	0.993997i	$0.534897\pi$
$24$	1.06235	−	0.771840i	0.216851	−	0.157551i
$25$	−0.890091	−	2.73942i	−0.178018	−	0.547883i
$26$	−3.82471	+	11.7712i	−0.750087	+	2.30853i
$27$	−3.25587	−	2.36553i	−0.626593	−	0.455247i
$28$	7.26400	+	5.27760i	1.37277	+	0.997373i
$29$	1.16215	−	3.57672i	0.215805	−	0.664180i	−0.783290	−	0.621656i	$-0.786460\pi$
$29$	1.16215	−	3.57672i	0.215805	−	0.664180i	0.999095	−	0.0425242i	$-0.0135399\pi$
$30$	−0.727943	−	2.24038i	−0.132904	−	0.409035i
$31$	8.75085	−	6.35787i	1.57170	−	1.14191i	0.646194	−	0.763173i	$-0.276360\pi$
$31$	8.75085	−	6.35787i	1.57170	−	1.14191i	0.925506	−	0.378733i	$-0.123640\pi$
$32$	−7.32938			−1.29566
$33$	−1.61616	−	1.83665i	−0.281337	−	0.319720i
$34$	−2.19353			−0.376187
$35$	3.76145	−	2.73286i	0.635802	−	0.461937i
$36$	−2.13372	−	6.56693i	−0.355621	−	1.09449i
$37$	−2.55635	+	7.86765i	−0.420262	+	1.29343i	0.487197	+	0.873292i	$0.338019\pi$
$37$	−2.55635	+	7.86765i	−0.420262	+	1.29343i	−0.907459	+	0.420141i	$0.861981\pi$
$38$	−12.8091	−	9.30634i	−2.07791	−	1.50969i
$39$	−3.36725	−	2.44645i	−0.539191	−	0.391745i
$40$	0.800892	−	2.46489i	0.126632	−	0.389734i
$41$	−0.426079	−	1.31134i	−0.0665424	−	0.204796i	0.912257	−	0.409619i	$-0.134338\pi$
$41$	−0.426079	−	1.31134i	−0.0665424	−	0.204796i	−0.978799	+	0.204822i	$0.934338\pi$
$42$	−4.18038	+	3.03722i	−0.645047	+	0.468654i
$43$	4.75389			0.724961			0.362481	−	0.931991i	$-0.381930\pi$
$43$	4.75389			0.724961			0.362481	+	0.931991i	$0.381930\pi$
$44$	−0.868820	−	9.28433i	−0.130980	−	1.39967i
$45$	−3.57549			−0.533003
$46$	1.86233	−	1.35307i	0.274586	−	0.199499i
$47$	−2.17094	−	6.68146i	−0.316664	−	0.974592i	−0.975064	−	0.221924i	$-0.928766\pi$
$47$	−2.17094	−	6.68146i	−0.316664	−	0.974592i	0.658400	−	0.752668i	$-0.271234\pi$
$48$	0.391663	−	1.20541i	0.0565317	−	0.173987i
$49$	−2.58773	−	1.88010i	−0.369676	−	0.268586i
$50$	5.11155	+	3.71376i	0.722882	+	0.525205i
$51$	0.227943	−	0.701538i	0.0319185	−	0.0982349i
$52$	−4.90233	−	15.0878i	−0.679831	−	2.09230i
$53$	−2.99030	+	2.17258i	−0.410750	+	0.298427i	−0.773905	−	0.633301i	$-0.781699\pi$
$53$	−2.99030	+	2.17258i	−0.410750	+	0.298427i	0.363156	+	0.931729i	$0.381699\pi$
$54$	8.82781			1.20131
$55$	−4.71135	−	1.05776i	−0.635278	−	0.142629i
$56$	−5.68506			−0.759698
$57$	4.30744	−	3.12954i	0.570535	−	0.414518i
$58$	2.54920	+	7.84564i	0.334727	+	1.03018i
$59$	−1.85445	+	5.70740i	−0.241429	+	0.743041i	0.754775	+	0.655984i	$0.227746\pi$
$59$	−1.85445	+	5.70740i	−0.241429	+	0.743041i	−0.996203	+	0.0870566i	$0.972254\pi$
$60$	2.44274	+	1.77476i	0.315356	+	0.229120i
$61$	−8.15409	−	5.92429i	−1.04402	−	0.758528i	−0.0729572	−	0.997335i	$-0.523244\pi$
$61$	−8.15409	−	5.92429i	−1.04402	−	0.758528i	−0.971067	+	0.238807i	$0.923244\pi$
$62$	−7.33193	+	22.5653i	−0.931156	+	2.86580i
$63$	2.42360	+	7.45908i	0.305345	+	0.939756i
$64$	10.2265	−	7.43002i	1.27832	−	0.928753i
$65$	−8.21486			−1.01893
$66$	5.23607	+	1.17557i	0.644515	+	0.144703i
$67$	−0.586654			−0.0716712			−0.0358356	−	0.999358i	$-0.511409\pi$
$67$	−0.586654			−0.0716712			−0.0358356	+	0.999358i	$0.511409\pi$
$68$	2.27460	−	1.65259i	0.275836	−	0.200406i
$69$	0.239213	+	0.736221i	0.0287978	+	0.0886306i
$70$	−3.15155	+	9.69946i	−0.376682	+	1.15931i
$71$	−1.66068	−	1.20656i	−0.197087	−	0.143192i	0.484865	−	0.874589i	$-0.338869\pi$
$71$	−1.66068	−	1.20656i	−0.197087	−	0.143192i	−0.681952	+	0.731397i	$0.738869\pi$
$72$	3.53696	+	2.56975i	0.416835	+	0.302848i
$73$	0.917955	−	2.82517i	0.107438	−	0.330662i	−0.882857	−	0.469643i	$-0.844383\pi$
$73$	0.917955	−	2.82517i	0.107438	−	0.330662i	0.990295	+	0.138981i	$0.0443827\pi$
$74$	−5.60743	−	17.2579i	−0.651851	−	2.00619i
$75$	−1.71891	+	1.24886i	−0.198483	+	0.144206i
$76$	20.2939			2.32787
$77$	0.986854	+	10.5457i	0.112462	+	1.20179i
$78$	9.12978			1.03374
$79$	−7.73558	+	5.62022i	−0.870320	+	0.632325i	−0.930673	−	0.365852i	$-0.880777\pi$
$79$	−7.73558	+	5.62022i	−0.870320	+	0.632325i	0.0603526	+	0.998177i	$0.480777\pi$
$80$	−0.773028	−	2.37914i	−0.0864272	−	0.265996i
$81$	1.35938	−	4.18374i	0.151042	−	0.464860i
$82$	2.44686	+	1.77775i	0.270210	+	0.196319i
$83$	13.2458	+	9.62366i	1.45392	+	1.05633i	0.984896	+	0.173148i	$0.0553939\pi$
$83$	13.2458	+	9.62366i	1.45392	+	1.05633i	0.469023	+	0.883186i	$0.344606\pi$
$84$	2.04666	−	6.29896i	0.223309	−	0.687273i
$85$	−0.449894	−	1.38463i	−0.0487978	−	0.150184i
$86$	−8.43626	+	6.12930i	−0.909705	+	0.660939i
$87$	−2.77411			−0.297416
$88$	3.90035	+	4.43247i	0.415778	+	0.472503i
$89$	10.9131			1.15679			0.578394	−	0.815758i	$-0.303680\pi$
$89$	10.9131			1.15679			0.578394	+	0.815758i	$0.303680\pi$
$90$	6.34507	−	4.60997i	0.668829	−	0.485933i
$91$	5.56834	+	17.1376i	0.583721	+	1.79651i
$92$	−0.911774	+	2.80615i	−0.0950590	+	0.292561i
$93$	−6.45498	−	4.68982i	−0.669350	−	0.486312i
$94$	12.4671	+	9.05789i	1.28588	+	0.934250i
$95$	3.24734	−	9.99428i	0.333170	−	1.02539i
$96$	1.67068	+	5.14184i	0.170514	+	0.524787i
$97$	−5.51890	+	4.00972i	−0.560360	+	0.407125i	−0.831591	−	0.555389i	$-0.812569\pi$
$97$	−5.51890	+	4.00972i	−0.560360	+	0.407125i	0.271231	+	0.962514i	$0.412569\pi$
$98$	7.01625			0.708748
$99$	4.15286	−	7.00706i	0.417378	−	0.704236i
$100$	−8.09840			−0.809840
$101$	−5.27861	+	3.83513i	−0.525241	+	0.381610i	−0.818575	−	0.574400i	$-0.805235\pi$
$101$	−5.27861	+	3.83513i	−0.525241	+	0.381610i	0.293333	+	0.956010i	$0.405235\pi$
$102$	0.500000	+	1.53884i	0.0495074	+	0.152368i
$103$	0.360696	−	1.11011i	0.0355404	−	0.109382i	−0.931712	−	0.363197i	$-0.881685\pi$
$103$	0.360696	−	1.11011i	0.0355404	−	0.109382i	0.967253	+	0.253815i	$0.0816853\pi$
$104$	8.12633	+	5.90413i	0.796853	+	0.578947i
$105$	−2.77460	−	2.01587i	−0.270773	−	0.196728i
$106$	2.50543	−	7.71093i	0.243349	−	0.748952i
$107$	1.63784	+	5.04075i	0.158336	+	0.487308i	0.998484	−	0.0550497i	$-0.0175317\pi$
$107$	1.63784	+	5.04075i	0.158336	+	0.487308i	−0.840148	+	0.542358i	$0.817532\pi$
$108$	−9.15409	+	6.65084i	−0.880853	+	0.639977i
$109$	−11.0233			−1.05584			−0.527919	−	0.849294i	$-0.677028\pi$
$109$	−11.0233			−1.05584			−0.527919	+	0.849294i	$0.677028\pi$
$110$	9.72456	−	4.19734i	0.927201	−	0.400201i
$111$	6.10216			0.579191
$112$	−4.43929	+	3.22533i	−0.419474	+	0.304765i
$113$	1.84582	+	5.68085i	0.173640	+	0.534409i	0.999569	−	0.0293654i	$-0.00934863\pi$
$113$	1.84582	+	5.68085i	0.173640	+	0.534409i	−0.825929	+	0.563775i	$0.809349\pi$
$114$	−3.60900	+	11.1074i	−0.338014	+	1.04030i
$115$	1.23607	+	0.898056i	0.115264	+	0.0837441i
$116$	−8.55429	−	6.21506i	−0.794246	−	0.577053i
$117$	4.28217	−	13.1792i	0.395886	−	1.21841i
$118$	−4.06778	−	12.5193i	−0.374470	−	1.15250i
$119$	−2.58362	+	1.87711i	−0.236840	+	0.172074i
$120$	−1.91177			−0.174520
$121$	7.54508	−	8.00448i	0.685917	−	0.727680i
$122$	22.1086			2.00162
$123$	−0.822830	+	0.597821i	−0.0741921	+	0.0539037i
$124$	−9.39772	−	28.9232i	−0.843940	−	2.59738i
$125$	−3.54534	+	10.9114i	−0.317105	+	0.975948i
$126$	−13.9181	−	10.1121i	−1.23992	−	0.900856i
$127$	0.186199	+	0.135282i	0.0165225	+	0.0120043i	0.596016	−	0.802973i	$-0.296750\pi$
$127$	0.186199	+	0.135282i	0.0165225	+	0.0120043i	−0.579493	+	0.814977i	$0.696750\pi$
$128$	−4.03853	+	12.4293i	−0.356959	+	1.09861i
$129$	−1.08362	−	3.33503i	−0.0954072	−	0.293633i
$130$	14.5781	−	10.5916i	1.27858	−	0.928946i
$131$	−3.77246			−0.329601			−0.164801	−	0.986327i	$-0.552698\pi$
$131$	−3.77246			−0.329601			−0.164801	+	0.986327i	$0.552698\pi$
$132$	−6.31526	+	2.72581i	−0.549673	+	0.237251i
$133$	−23.0509			−1.99877
$134$	1.04108	−	0.756387i	0.0899353	−	0.0653418i
$135$	1.81059	+	5.57242i	0.155831	+	0.479598i
$136$	−0.550106	+	1.69305i	−0.0471712	+	0.145178i
$137$	8.03459	+	5.83747i	0.686441	+	0.498729i	0.875488	−	0.483239i	$-0.160540\pi$
$137$	8.03459	+	5.83747i	0.686441	+	0.498729i	−0.189047	+	0.981968i	$0.560540\pi$
$138$	−1.37373	−	0.998076i	−0.116940	−	0.0849618i
$139$	−3.19600	+	9.83629i	−0.271082	+	0.834303i	0.719148	+	0.694857i	$0.244532\pi$
$139$	−3.19600	+	9.83629i	−0.271082	+	0.834303i	−0.990230	+	0.139446i	$0.955468\pi$
$140$	−4.03950	−	12.4323i	−0.341400	−	1.05072i
$141$	−4.19245	+	3.04599i	−0.353068	+	0.256519i
$142$	4.50269			0.377857
$143$	9.54140	−	16.0991i	0.797892	−	1.34627i
$144$	4.21982			0.351652
$145$	−4.42960	+	3.21829i	−0.367858	+	0.267264i
$146$	2.01356	+	6.19710i	0.166643	+	0.512875i
$147$	−0.729103	+	2.24395i	−0.0601354	+	0.185078i
$148$	18.8167	+	13.6711i	1.54672	+	1.12376i
$149$	3.79217	+	2.75517i	0.310666	+	0.225712i	0.732182	−	0.681109i	$-0.238502\pi$
$149$	3.79217	+	2.75517i	0.310666	+	0.225712i	−0.421516	+	0.906821i	$0.638502\pi$
$150$	1.44020	−	4.43247i	0.117592	−	0.361910i
$151$	−0.287492	−	0.884808i	−0.0233957	−	0.0720047i	0.938677	−	0.344798i	$-0.112053\pi$
$151$	−0.287492	−	0.884808i	−0.0233957	−	0.0720047i	−0.962073	+	0.272793i	$0.912053\pi$
$152$	−10.3954	+	7.55267i	−0.843175	+	0.612602i
$153$	2.45589			0.198547
$154$	−15.3480	−	17.4420i	−1.23678	−	1.40551i
$155$	−15.7478			−1.26490
$156$	−9.46722	+	6.87834i	−0.757984	+	0.550708i
$157$	−6.58205	−	20.2575i	−0.525304	−	1.61672i	−0.763713	−	0.645556i	$-0.776626\pi$
$157$	−6.58205	−	20.2575i	−0.525304	−	1.61672i	0.238409	−	0.971165i	$-0.423374\pi$
$158$	6.48127	−	19.9473i	0.515622	−	1.58692i
$159$	2.20577	+	1.60258i	0.174929	+	0.127093i
$160$	8.63282	+	6.27211i	0.682484	+	0.495854i
$161$	1.03564	−	3.18738i	0.0816201	−	0.251201i
$162$	2.98183	+	9.17714i	0.234275	+	0.721024i
$163$	0.964011	−	0.700395i	0.0755072	−	0.0548592i	−0.549391	−	0.835565i	$-0.685140\pi$
$163$	0.964011	−	0.700395i	0.0755072	−	0.0548592i	0.624898	+	0.780706i	$0.285140\pi$
$164$	−3.87664			−0.302715
$165$	0.331860	+	3.54630i	0.0258352	+	0.276079i
$166$	−35.9141			−2.78747
$167$	−10.2689	+	7.46080i	−0.794632	+	0.577334i	−0.909335	−	0.416066i	$-0.863409\pi$
$167$	−10.2689	+	7.46080i	−0.794632	+	0.577334i	0.114702	+	0.993400i	$0.463409\pi$
$168$	1.29587	+	3.98828i	0.0999786	+	0.307703i
$169$	5.82126	−	17.9160i	0.447789	−	1.37815i
$170$	2.58362	+	1.87711i	0.198154	+	0.143968i
$171$	14.3411	+	10.4194i	1.09669	+	0.796795i
$172$	4.13027	−	12.7117i	0.314931	−	0.969256i
$173$	1.81943	+	5.59963i	0.138329	+	0.425732i	0.996093	−	0.0883113i	$-0.0281470\pi$
$173$	1.81943	+	5.59963i	0.138329	+	0.425732i	−0.857764	+	0.514043i	$0.828147\pi$
$174$	4.92293	−	3.57672i	0.373207	−	0.271151i
$175$	9.19862			0.695350
$176$	5.56036	+	1.24838i	0.419128	+	0.0941001i
$177$	4.42667			0.332729
$178$	−19.3664	+	14.0705i	−1.45157	+	1.05463i
$179$	−5.02037	−	15.4511i	−0.375240	−	1.15487i	−0.943317	−	0.331894i	$-0.892312\pi$
$179$	−5.02037	−	15.4511i	−0.375240	−	1.15487i	0.568077	−	0.822975i	$-0.307688\pi$
$180$	−3.10646	+	9.56070i	−0.231542	+	0.712613i
$181$	−6.71109	−	4.87589i	−0.498832	−	0.362422i	0.309739	−	0.950822i	$-0.399758\pi$
$181$	−6.71109	−	4.87589i	−0.498832	−	0.362422i	−0.808571	+	0.588399i	$0.799758\pi$
$182$	−31.9775	−	23.2330i	−2.37033	−	1.72214i
$183$	−2.29744	+	7.07080i	−0.169832	+	0.522689i
$184$	−0.577303	−	1.77676i	−0.0425593	−	0.130984i
$185$	9.74370	−	7.07921i	0.716371	−	0.520474i
$186$	17.5017			1.28329
$187$	3.23607	+	0.726543i	0.236645	+	0.0531301i
$188$	−19.7521			−1.44057
$189$	10.3977	−	7.55439i	0.756323	−	0.549501i
$190$	7.12312	+	21.9227i	0.516766	+	1.59044i
$191$	−7.28872	+	22.4324i	−0.527393	+	1.62315i	0.232141	+	0.972682i	$0.425427\pi$
$191$	−7.28872	+	22.4324i	−0.527393	+	1.62315i	−0.759534	+	0.650467i	$0.774573\pi$
$192$	−7.54351	−	5.48068i	−0.544406	−	0.395534i
$193$	−12.1738	−	8.84477i	−0.876288	−	0.636661i	0.0559785	−	0.998432i	$-0.482172\pi$
$193$	−12.1738	−	8.84477i	−0.876288	−	0.636661i	−0.932267	+	0.361771i	$0.882172\pi$
$194$	4.62403	−	14.2313i	0.331986	−	1.02175i
$195$	1.87252	+	5.76304i	0.134094	+	0.412700i
$196$	−7.27557	+	5.28601i	−0.519684	+	0.377572i
$197$	−13.3202			−0.949022			−0.474511	−	0.880249i	$-0.657375\pi$
$197$	−13.3202			−0.949022			−0.474511	+	0.880249i	$0.657375\pi$
$198$	1.66469	+	17.7891i	0.118304	+	1.26422i
$199$	21.1886			1.50202			0.751009	−	0.660292i	$-0.229567\pi$
$199$	21.1886			1.50202			0.751009	+	0.660292i	$0.229567\pi$
$200$	4.14833	−	3.01394i	0.293332	−	0.213118i
$201$	0.133724	+	0.411560i	0.00943216	+	0.0290292i
$202$	4.42270	−	13.6117i	0.311180	−	0.957713i
$203$	9.71644	+	7.05940i	0.681960	+	0.495473i
$204$	−1.67784	−	1.21902i	−0.117472	−	0.0853485i
$205$	−0.620323	+	1.90916i	−0.0433252	+	0.133341i
$206$	0.791195	+	2.43505i	0.0551252	+	0.169658i
$207$	−2.08508	+	1.51490i	−0.144923	+	0.105293i
$208$	9.69523			0.672243
$209$	15.8145	+	17.9721i	1.09391	+	1.24316i
$210$	7.52291			0.519130
$211$	−19.6000	+	14.2402i	−1.34932	+	0.980336i	−0.350272	+	0.936648i	$0.613911\pi$
$211$	−19.6000	+	14.2402i	−1.34932	+	0.980336i	−0.999045	+	0.0436881i	$0.986089\pi$
$212$	3.21135	+	9.88351i	0.220556	+	0.678803i
$213$	−0.467903	+	1.44006i	−0.0320602	+	0.0986712i
$214$	−9.40567	−	6.83362i	−0.642959	−	0.467137i
$215$	−5.59931	−	4.06814i	−0.381870	−	0.277445i
$216$	2.21389	−	6.81366i	0.150636	−	0.463611i
$217$	10.6745	+	32.8526i	0.724629	+	2.23018i
$218$	19.5619	−	14.2126i	1.32490	−	0.962597i
$219$	−2.19121			−0.148068
$220$	−6.92173	+	11.6789i	−0.466663	+	0.787393i
$221$	5.64252			0.379557
$222$	−10.8289	+	7.86765i	−0.726788	+	0.528042i
$223$	−1.71521	−	5.27887i	−0.114859	−	0.353500i	0.877059	−	0.480383i	$-0.159502\pi$
$223$	−1.71521	−	5.27887i	−0.114859	−	0.353500i	−0.991918	+	0.126884i	$0.959502\pi$
$224$	7.23303	−	22.2610i	0.483277	−	1.48737i
$225$	−5.72292	−	4.15795i	−0.381528	−	0.277196i
$226$	−10.6000	−	7.70138i	−0.705104	−	0.512288i
$227$	1.22678	−	3.77565i	0.0814245	−	0.250599i	−0.902054	−	0.431623i	$-0.857941\pi$
$227$	1.22678	−	3.77565i	0.0814245	−	0.250599i	0.983479	+	0.181024i	$0.0579412\pi$
$228$	−4.62585	−	14.2369i	−0.306355	−	0.942863i
$229$	10.5977	−	7.69971i	0.700318	−	0.508811i	−0.179718	−	0.983718i	$-0.557518\pi$
$229$	10.5977	−	7.69971i	0.700318	−	0.508811i	0.880036	+	0.474907i	$0.157518\pi$
$230$	−3.35141			−0.220986
$231$	7.17323	−	3.09613i	0.471964	−	0.203710i
$232$	6.69488			0.439541
$233$	3.43106	−	2.49281i	0.224776	−	0.163309i	−0.469698	−	0.882827i	$-0.655637\pi$
$233$	3.43106	−	2.49281i	0.224776	−	0.163309i	0.694474	+	0.719518i	$0.255637\pi$
$234$	9.39305	+	28.9088i	0.614043	+	1.88983i
$235$	−3.16064	+	9.72746i	−0.206178	+	0.634549i
$236$	13.6501	+	9.91741i	0.888549	+	0.645569i
$237$	5.70607	+	4.14570i	0.370649	+	0.269292i
$238$	2.16469	−	6.66223i	0.140316	−	0.431849i
$239$	−1.78897	−	5.50589i	−0.115719	−	0.356147i	0.876377	−	0.481625i	$-0.159953\pi$
$239$	−1.78897	−	5.50589i	−0.115719	−	0.356147i	−0.992096	+	0.125479i	$0.959953\pi$
$240$	−1.49285	+	1.08462i	−0.0963629	+	0.0700117i
$241$	−1.09198			−0.0703406			−0.0351703	−	0.999381i	$-0.511197\pi$
$241$	−1.09198			−0.0703406			−0.0351703	+	0.999381i	$0.511197\pi$
$242$	−3.06915	+	23.9328i	−0.197293	+	1.53846i
$243$	−15.3184			−0.982673
$244$	−22.9257	+	16.6565i	−1.46767	+	1.06632i
$245$	1.43904	+	4.42890i	0.0919367	+	0.282952i
$246$	0.689411	−	2.12179i	0.0439552	−	0.135280i
$247$	32.9494	+	23.9392i	2.09652	+	1.52321i
$248$	15.5781	+	11.3182i	0.989211	+	0.718704i
$249$	3.73206	−	11.4861i	0.236510	−	0.727902i
$250$	−7.77680	−	23.9345i	−0.491848	−	1.51375i
$251$	0.255462	−	0.185604i	0.0161246	−	0.0117152i	−0.579694	−	0.814834i	$-0.696828\pi$
$251$	0.255462	−	0.185604i	0.0161246	−	0.0117152i	0.595818	+	0.803119i	$0.296828\pi$
$252$	22.0509			1.38908
$253$	−3.19563	+	1.37931i	−0.200908	+	0.0867163i
$254$	−0.504851			−0.0316772
$255$	−0.868820	+	0.631235i	−0.0544076	+	0.0395295i
$256$	−1.04624	−	3.22001i	−0.0653903	−	0.201251i
$257$	7.49016	−	23.0523i	0.467223	−	1.43796i	−0.388942	−	0.921262i	$-0.627159\pi$
$257$	7.49016	−	23.0523i	0.467223	−	1.43796i	0.856165	−	0.516703i	$-0.172841\pi$
$258$	6.22292	+	4.52122i	0.387422	+	0.281479i
$259$	−21.3731	−	15.5284i	−1.32806	−	0.964891i
$260$	−7.13724	+	21.9662i	−0.442633	+	1.36228i
$261$	−2.85410	−	8.78402i	−0.176664	−	0.543717i
$262$	6.69461	−	4.86392i	0.413594	−	0.300494i
$263$	−25.1456			−1.55054			−0.775271	−	0.631629i	$-0.782387\pi$
$263$	−25.1456			−1.55054			−0.775271	+	0.631629i	$0.782387\pi$
$264$	2.22049	−	3.74659i	0.136661	−	0.230587i
$265$	5.38127			0.330569
$266$	40.9062	−	29.7201i	2.50812	−	1.82225i
$267$	−2.48757	−	7.65596i	−0.152237	−	0.468537i
$268$	−0.509697	+	1.56869i	−0.0311347	+	0.0958227i
$269$	−2.62577	−	1.90774i	−0.160096	−	0.116317i	0.504853	−	0.863205i	$-0.331547\pi$
$269$	−2.62577	−	1.90774i	−0.160096	−	0.116317i	−0.664949	+	0.746889i	$0.731547\pi$
$270$	−10.3977	−	7.55439i	−0.632785	−	0.459745i
$271$	−1.30943	+	4.03001i	−0.0795422	+	0.244806i	−0.982918	−	0.184044i	$-0.941081\pi$
$271$	−1.30943	+	4.03001i	−0.0795422	+	0.244806i	0.903376	+	0.428850i	$0.141081\pi$
$272$	0.530967	+	1.63415i	0.0321946	+	0.0990849i
$273$	10.7534	−	7.81280i	0.650825	−	0.472852i
$274$	−21.7846			−1.31605
$275$	−6.31089	−	7.17189i	−0.380561	−	0.432481i
$276$	2.17645			0.131007
$277$	8.91540	−	6.47742i	0.535674	−	0.389190i	−0.286802	−	0.957990i	$-0.592592\pi$
$277$	8.91540	−	6.47742i	0.535674	−	0.389190i	0.822476	+	0.568800i	$0.192592\pi$
$278$	−7.01052	−	21.5762i	−0.420463	−	1.29405i
$279$	8.20887	−	25.2643i	0.491452	−	1.51253i
$280$	6.69607	+	4.86498i	0.400167	+	0.290738i
$281$	−22.9870	−	16.7010i	−1.37129	−	0.996301i	−0.997635	−	0.0687332i	$-0.978104\pi$
$281$	−22.9870	−	16.7010i	−1.37129	−	0.996301i	−0.373655	−	0.927568i	$-0.621896\pi$
$282$	3.51265	−	10.8108i	0.209175	−	0.643776i
$283$	−3.44677	−	10.6081i	−0.204889	−	0.630584i	−0.999718	−	0.0237500i	$-0.992439\pi$
$283$	−3.44677	−	10.6081i	−0.204889	−	0.630584i	0.794829	−	0.606834i	$-0.207561\pi$
$284$	−4.66911	+	3.39231i	−0.277061	+	0.201296i
$285$	−7.75157			−0.459163
$286$	3.82471	+	40.8713i	0.226160	+	2.41677i
$287$	4.40330			0.259919
$288$	−14.5624	+	10.5802i	−0.858098	+	0.623445i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	3.71135	−	11.4224i	0.217938	−	0.670744i
$291$	4.07096	+	2.95773i	0.238644	+	0.173385i
$292$	−6.75685	−	4.90914i	−0.395415	−	0.287285i
$293$	−2.39305	+	7.36504i	−0.139803	+	0.430270i	−0.996306	−	0.0858719i	$-0.972632\pi$
$293$	−2.39305	+	7.36504i	−0.139803	+	0.430270i	0.856503	+	0.516142i	$0.172632\pi$
$294$	−1.59931	−	4.92216i	−0.0932735	−	0.287066i
$295$	7.06834	−	5.13545i	0.411535	−	0.298997i
$296$	−14.7266			−0.855967
$297$	−13.0235	−	2.92396i	−0.755700	−	0.169665i
$298$	−10.2819			−0.595614
$299$	−4.79057	+	3.48056i	−0.277046	+	0.201286i
$300$	1.84598	+	5.68133i	0.106578	+	0.328012i
$301$	−4.69140	+	14.4386i	−0.270408	+	0.832229i
$302$	1.65099	+	1.19951i	0.0950036	+	0.0690241i
$303$	3.89371	+	2.82895i	0.223688	+	0.162519i
$304$	−3.83253	+	11.7953i	−0.219811	+	0.676507i
$305$	4.53448	+	13.9557i	0.259644	+	0.799101i
$306$	−4.35822	+	3.16643i	−0.249143	+	0.181013i
$307$	10.3573			0.591124			0.295562	−	0.955324i	$-0.404493\pi$
$307$	10.3573			0.591124			0.295562	+	0.955324i	$0.404493\pi$
$308$	29.0560	+	6.52348i	1.65562	+	0.371710i
$309$	−0.861000			−0.0489806
$310$	27.9461	−	20.3040i	1.58723	−	1.15319i
$311$	−0.242662	−	0.746836i	−0.0137601	−	0.0423492i	0.943941	−	0.330115i	$-0.107088\pi$
$311$	−0.242662	−	0.746836i	−0.0137601	−	0.0423492i	−0.957701	+	0.287766i	$0.907088\pi$
$312$	2.28962	−	7.04674i	0.129624	−	0.398943i
$313$	4.97795	+	3.61670i	0.281371	+	0.204428i	0.719515	−	0.694477i	$-0.244364\pi$
$313$	4.97795	+	3.61670i	0.281371	+	0.204428i	−0.438144	+	0.898905i	$0.644364\pi$
$314$	37.7989	+	27.4625i	2.13312	+	1.54980i
$315$	3.52849	−	10.8596i	0.198808	−	0.611868i
$316$	8.30740	+	25.5675i	0.467327	+	1.43829i
$317$	−8.69450	+	6.31692i	−0.488332	+	0.354794i	−0.804542	−	0.593895i	$-0.797589\pi$
$317$	−8.69450	+	6.31692i	−0.488332	+	0.354794i	0.316211	+	0.948689i	$0.397589\pi$
$318$	−5.98061			−0.335376
$319$	−1.16215	−	12.4189i	−0.0650678	−	0.695323i
$320$	−18.4034			−1.02878
$321$	3.16294	−	2.29801i	0.176538	−	0.128263i
$322$	2.27171	+	6.99161i	0.126598	+	0.389627i
$323$	−2.23049	+	6.86473i	−0.124108	+	0.381964i
$324$	−10.0061	−	7.26983i	−0.555892	−	0.403879i
$325$	−13.1487	−	9.55308i	−0.729358	−	0.529909i
$326$	−0.807700	+	2.48584i	−0.0447343	+	0.137678i
$327$	2.51268	+	7.73325i	0.138952	+	0.427649i
$328$	1.98577	−	1.44275i	0.109646	−	0.0796625i
$329$	22.4355			1.23691
$330$	−5.16124	−	5.86539i	−0.284117	−	0.322879i
$331$	−4.11550			−0.226208			−0.113104	−	0.993583i	$-0.536079\pi$
$331$	−4.11550			−0.226208			−0.113104	+	0.993583i	$0.536079\pi$
$332$	37.2415	−	27.0575i	2.04389	−	1.48497i
$333$	6.27812	+	19.3221i	0.344039	+	1.05884i
$334$	8.60384	−	26.4799i	0.470781	−	1.44891i
$335$	0.690983	+	0.502029i	0.0377524	+	0.0274287i
$336$	3.27460	+	2.37914i	0.178644	+	0.129793i
$337$	−1.36927	+	4.21419i	−0.0745891	+	0.229562i	−0.981399	−	0.191977i	$-0.938510\pi$
$337$	−1.36927	+	4.21419i	−0.0745891	+	0.229562i	0.906810	+	0.421539i	$0.138510\pi$
$338$	12.7691	+	39.2992i	0.694547	+	2.13760i
$339$	3.56459	−	2.58982i	0.193602	−	0.140660i
$340$	−4.09331			−0.221991
$341$	18.2908	−	30.8617i	0.990501	−	1.67126i
$342$	−38.8838			−2.10260
$343$	−9.82132	+	7.13561i	−0.530302	+	0.385287i
$344$	2.61514	+	8.04859i	0.140999	+	0.433951i
$345$	0.348267	−	1.07185i	0.0187500	−	0.0577067i
$346$	−10.4485	−	7.59128i	−0.561715	−	0.408110i
$347$	9.73650	+	7.07398i	0.522683	+	0.379751i	0.817614	−	0.575767i	$-0.195297\pi$
$347$	9.73650	+	7.07398i	0.522683	+	0.379751i	−0.294931	+	0.955519i	$0.595297\pi$
$348$	−2.41020	+	7.41784i	−0.129200	+	0.397638i
$349$	7.59032	+	23.3606i	0.406300	+	1.25046i	0.919804	+	0.392377i	$0.128347\pi$
$349$	7.59032	+	23.3606i	0.406300	+	1.25046i	−0.513504	+	0.858087i	$0.671653\pi$
$350$	−16.3239	+	11.8600i	−0.872547	+	0.633943i
$351$	−22.7082			−1.21207
$352$	−22.3186	+	9.63321i	−1.18958	+	0.513452i
$353$	0.191367			0.0101854			0.00509272	−	0.999987i	$-0.498379\pi$
$353$	0.191367			0.0101854			0.00509272	+	0.999987i	$0.498379\pi$
$354$	−7.85557	+	5.70740i	−0.417519	+	0.303345i
$355$	0.923505	+	2.84226i	0.0490145	+	0.150851i
$356$	9.48153	−	29.1811i	0.502520	−	1.54660i
$357$	1.90578	+	1.38463i	0.100865	+	0.0732824i
$358$	28.8306	+	20.9467i	1.52374	+	1.10707i
$359$	−9.61855	+	29.6029i	−0.507648	+	1.56238i	0.288625	+	0.957442i	$0.406802\pi$
$359$	−9.61855	+	29.6029i	−0.507648	+	1.56238i	−0.796273	+	0.604937i	$0.793198\pi$
$360$	−1.96690	−	6.05350i	−0.103665	−	0.319047i
$361$	−26.7782	+	19.4555i	−1.40938	+	1.02397i
$362$	18.1961			0.956367
$363$	−7.33530	−	3.46859i	−0.385003	−	0.182054i
$364$	50.6630			2.65546
$365$	−3.49884	+	2.54206i	−0.183138	+	0.133057i
$366$	−5.03950	−	15.5100i	−0.263419	−	0.810721i
$367$	−5.20882	+	16.0311i	−0.271898	+	0.836816i	0.718126	+	0.695914i	$0.245000\pi$
$367$	−5.20882	+	16.0311i	−0.271898	+	0.836816i	−0.990024	+	0.140902i	$0.955000\pi$
$368$	−1.45881	−	1.05989i	−0.0760460	−	0.0552506i
$369$	−2.73952	−	1.99038i	−0.142614	−	0.103615i
$370$	−8.16379	+	25.1256i	−0.424415	+	1.30622i
$371$	−3.64763	−	11.2262i	−0.189375	−	0.582838i
$372$	−18.1486	+	13.1857i	−0.940960	+	0.683647i
$373$	−34.4940			−1.78603			−0.893015	−	0.450026i	$-0.851415\pi$
$373$	−34.4940			−1.78603			−0.893015	+	0.450026i	$0.851415\pi$
$374$	−6.67948	+	2.88301i	−0.345388	+	0.149077i
$375$	8.46292			0.437023
$376$	10.1178	−	7.35103i	0.521787	−	0.379100i
$377$	−6.55743	−	20.1817i	−0.337725	−	1.03941i
$378$	−8.71176	+	26.8120i	−0.448085	+	1.37906i
$379$	−13.5696	−	9.85887i	−0.697022	−	0.506416i	0.181939	−	0.983310i	$-0.441763\pi$
$379$	−13.5696	−	9.85887i	−0.697022	−	0.506416i	−0.878961	+	0.476894i	$0.841763\pi$
$380$	−23.9029	−	17.3665i	−1.22619	−	0.890880i
$381$	0.0524623	−	0.161462i	0.00268772	−	0.00827196i
$382$	−15.9880	−	49.2060i	−0.818017	−	2.51760i
$383$	12.4601	−	9.05282i	0.636683	−	0.462577i	−0.222026	−	0.975041i	$-0.571267\pi$
$383$	12.4601	−	9.05282i	0.636683	−	0.462577i	0.858709	+	0.512463i	$0.171267\pi$
$384$	9.64020			0.491949
$385$	7.86208	−	13.2656i	0.400689	−	0.676076i
$386$	33.0074			1.68003
$387$	9.44529	−	6.86240i	0.480131	−	0.348835i
$388$	5.92686	+	18.2410i	0.300891	+	0.926047i
$389$	−9.49647	+	29.2271i	−0.481490	+	1.48187i	0.355510	+	0.934672i	$0.384307\pi$
$389$	−9.49647	+	29.2271i	−0.481490	+	1.48187i	−0.837001	+	0.547202i	$0.815693\pi$
$390$	−10.7534	−	7.81280i	−0.544519	−	0.395617i
$391$	−0.849014	−	0.616845i	−0.0429365	−	0.0311952i
$392$	1.75958	−	5.41542i	0.0888721	−	0.273520i
$393$	0.859907	+	2.64652i	0.0433766	+	0.133499i
$394$	23.6380	−	17.1740i	1.19086	−	0.865213i
$395$	13.9207			0.700429
$396$	−15.1285	−	17.1924i	−0.760234	−	0.863953i
$397$	35.3949			1.77642			0.888211	−	0.459436i	$-0.151949\pi$
$397$	35.3949			1.77642			0.888211	+	0.459436i	$0.151949\pi$
$398$	−37.6013	+	27.3189i	−1.88478	+	1.36937i
$399$	5.25430	+	16.1711i	0.263044	+	0.809567i
$400$	1.52940	−	4.70699i	0.0764698	−	0.235350i
$401$	20.5744	+	14.9482i	1.02744	+	0.746476i	0.967794	−	0.251743i	$-0.0810039\pi$
$401$	20.5744	+	14.9482i	1.02744	+	0.746476i	0.0596425	+	0.998220i	$0.481004\pi$
$402$	−0.767940	−	0.557941i	−0.0383014	−	0.0278276i
$403$	18.8603	−	58.0459i	0.939497	−	2.89147i
$404$	5.66881	+	17.4468i	0.282034	+	0.868011i
$405$	−5.18135	+	3.76447i	−0.257463	+	0.187058i
$406$	−26.3446			−1.30746
$407$	2.55635	+	27.3175i	0.126714	+	1.35408i
$408$	1.31313			0.0650098
$409$	−2.15607	+	1.56648i	−0.106611	+	0.0774574i	−0.639813	−	0.768530i	$-0.720988\pi$
$409$	−2.15607	+	1.56648i	−0.106611	+	0.0774574i	0.533202	+	0.845988i	$0.320988\pi$
$410$	−1.36070	−	4.18779i	−0.0672000	−	0.206820i
$411$	2.26377	−	6.96718i	0.111664	−	0.343666i
$412$	−2.65499	−	1.92897i	−0.130802	−	0.0950333i
$413$	−15.5046	−	11.2647i	−0.762931	−	0.554302i
$414$	1.74699	−	5.37669i	0.0858600	−	0.264250i
$415$	−7.36600	−	22.6702i	−0.361583	−	1.11284i
$416$	−33.4578	+	24.3085i	−1.64041	+	1.19182i
$417$	7.62904			0.373595
$418$	−51.2363	−	11.5033i	−2.50605	−	0.562644i
$419$	−9.85168			−0.481286			−0.240643	−	0.970614i	$-0.577358\pi$
$419$	−9.85168			−0.481286			−0.240643	+	0.970614i	$0.577358\pi$
$420$	−7.80096	+	5.66773i	−0.380648	+	0.276557i
$421$	3.15858	+	9.72110i	0.153940	+	0.473777i	0.998052	−	0.0623890i	$-0.0198719\pi$
$421$	3.15858	+	9.72110i	0.153940	+	0.473777i	−0.844112	+	0.536166i	$0.819872\pi$
$422$	16.4219	−	50.5414i	0.799405	−	2.46031i
$423$	−13.9583	−	10.1413i	−0.678674	−	0.493085i
$424$	−5.32328	−	3.86759i	−0.258521	−	0.187827i
$425$	0.890091	−	2.73942i	0.0431757	−	0.132881i
$426$	−1.02636	−	3.15881i	−0.0497272	−	0.153045i
$427$	26.0403	−	18.9194i	1.26018	−	0.915573i
$428$	14.9017			0.720302
$429$	−13.4690	−	3.02398i	−0.650289	−	0.145999i
$430$	15.1817			0.732125
$431$	7.85320	−	5.70568i	0.378275	−	0.274833i	−0.382359	−	0.924014i	$-0.624888\pi$
$431$	7.85320	−	5.70568i	0.378275	−	0.274833i	0.760634	+	0.649181i	$0.224888\pi$
$432$	−2.13687	−	6.57661i	−0.102810	−	0.316417i
$433$	2.71621	−	8.35964i	0.130533	−	0.401739i	−0.864336	−	0.502915i	$-0.832261\pi$
$433$	2.71621	−	8.35964i	0.130533	−	0.401739i	0.994868	+	0.101177i	$0.0322607\pi$
$434$	−61.3005	−	44.5374i	−2.94252	−	2.13786i
$435$	3.26745	+	2.37394i	0.156662	+	0.113822i
$436$	−9.57725	+	29.4757i	−0.458667	+	1.41163i
$437$	−2.34076	−	7.20412i	−0.111974	−	0.344620i
$438$	3.88852	−	2.82517i	0.185801	−	0.134992i
$439$	12.3475			0.589313			0.294656	−	0.955603i	$-0.404795\pi$
$439$	12.3475			0.589313			0.294656	+	0.955603i	$0.404795\pi$
$440$	−0.800892	−	8.55844i	−0.0381810	−	0.408008i
$441$	−7.85544			−0.374068
$442$	−10.0132	+	7.27502i	−0.476280	+	0.346038i
$443$	2.75505	+	8.47917i	0.130896	+	0.402858i	0.994929	−	0.100578i	$-0.0320692\pi$
$443$	2.75505	+	8.47917i	0.130896	+	0.402858i	−0.864033	+	0.503435i	$0.832069\pi$
$444$	5.30168	−	16.3169i	0.251606	−	0.774365i
$445$	−12.8539	−	9.33888i	−0.609332	−	0.442705i
$446$	9.84999	+	7.15643i	0.466410	+	0.338867i
$447$	1.06846	−	3.28837i	0.0505363	−	0.155535i
$448$	12.4745	+	38.3927i	0.589366	+	1.81388i
$449$	−24.7055	+	17.9496i	−1.16592	+	0.847093i	−0.990515	−	0.137402i	$-0.956125\pi$
$449$	−24.7055	+	17.9496i	−1.16592	+	0.847093i	−0.175409	+	0.984496i	$0.556125\pi$
$450$	15.5168			0.731471
$451$	−3.02097	−	3.43312i	−0.142252	−	0.161660i
$452$	16.7940			0.789924
$453$	−0.555194	+	0.403372i	−0.0260853	+	0.0189521i
$454$	2.69098	+	8.28199i	0.126294	+	0.388693i
$455$	8.10687	−	24.9504i	0.380056	−	1.16969i
$456$	7.66803	+	5.57115i	0.359088	+	0.260893i
$457$	17.5774	+	12.7708i	0.822238	+	0.597391i	0.917353	−	0.398076i	$-0.130322\pi$
$457$	17.5774	+	12.7708i	0.822238	+	0.597391i	−0.0951148	+	0.995466i	$0.530322\pi$
$458$	−8.87934	+	27.3278i	−0.414904	+	1.27694i
$459$	−1.24363	−	3.82751i	−0.0580478	−	0.178653i
$460$	3.47528	−	2.52494i	0.162036	−	0.117726i
$461$	27.4465			1.27831			0.639155	−	0.769078i	$-0.279284\pi$
$461$	27.4465			1.27831			0.639155	+	0.769078i	$0.279284\pi$
$462$	−8.73771	+	14.7430i	−0.406515	+	0.685906i
$463$	−19.9753			−0.928329			−0.464165	−	0.885749i	$-0.653645\pi$
$463$	−19.9753			−0.928329			−0.464165	+	0.885749i	$0.653645\pi$
$464$	5.22784	−	3.79824i	0.242696	−	0.176329i
$465$	3.58961	+	11.0477i	0.166464	+	0.512324i
$466$	−2.87472	+	8.84749i	−0.133169	+	0.409852i
$467$	0.544221	+	0.395400i	0.0251836	+	0.0182969i	0.600306	−	0.799771i	$-0.295046\pi$
$467$	0.544221	+	0.395400i	0.0251836	+	0.0182969i	−0.575122	+	0.818067i	$0.695046\pi$
$468$	−31.5200	−	22.9006i	−1.45701	−	1.05858i
$469$	0.578942	−	1.78180i	0.0267331	−	0.0822759i
$470$	−6.93295	−	21.3374i	−0.319793	−	0.984223i
$471$	−12.7110	+	9.23510i	−0.585693	+	0.425531i
$472$	−10.6831			−0.491729
$473$	14.4760	−	6.24817i	0.665607	−	0.287291i
$474$	−15.4712			−0.710614
$475$	16.8200	−	12.2205i	0.771756	−	0.560714i
$476$	2.77460	+	8.53934i	0.127174	+	0.391400i
$477$	−2.80510	+	8.63321i	−0.128437	+	0.395287i
$478$	10.2736	+	7.46420i	0.469903	+	0.341404i
$479$	−7.41192	−	5.38508i	−0.338659	−	0.246050i	0.405437	−	0.914123i	$-0.367119\pi$
$479$	−7.41192	−	5.38508i	−0.338659	−	0.246050i	−0.744096	+	0.668073i	$0.767119\pi$
$480$	2.43233	−	7.48593i	0.111020	−	0.341685i
$481$	14.4243	+	44.3933i	0.657690	+	2.02416i
$482$	1.93783	−	1.40791i	0.0882656	−	0.0641287i
$483$	−2.47214			−0.112486
$484$	−14.8483	−	27.1297i	−0.674922	−	1.23317i
$485$	9.93168			0.450974
$486$	27.1840	−	19.7503i	1.23309	−	0.895892i
$487$	−11.7725	−	36.2320i	−0.533463	−	1.64183i	−0.746948	−	0.664883i	$-0.768481\pi$
$487$	−11.7725	−	36.2320i	−0.533463	−	1.64183i	0.213485	−	0.976946i	$-0.431519\pi$
$488$	5.54453	−	17.0643i	0.250989	−	0.772464i
$489$	−0.711094	−	0.516640i	−0.0321568	−	0.0233633i
$490$	−8.26400	−	6.00415i	−0.373329	−	0.271240i
$491$	−5.38477	+	16.5726i	−0.243011	+	0.747911i	0.752946	+	0.658082i	$0.228632\pi$
$491$	−5.38477	+	16.5726i	−0.243011	+	0.747911i	−0.995957	+	0.0898290i	$0.971368\pi$
$492$	0.883655	+	2.71961i	0.0398382	+	0.122609i
$493$	3.04254	−	2.21054i	0.137029	−	0.0995575i
$494$	−89.3374			−4.01948
$495$	−10.8877	+	4.69937i	−0.489365	+	0.211221i
$496$	18.5857			0.834521
$497$	5.30344	−	3.85317i	0.237892	−	0.172838i
$498$	8.18637	+	25.1951i	0.366840	+	1.12902i
$499$	−9.85335	+	30.3255i	−0.441097	+	1.35756i	0.445611	+	0.895227i	$0.352986\pi$
$499$	−9.85335	+	30.3255i	−0.441097	+	1.35756i	−0.886708	+	0.462330i	$0.847014\pi$
$500$	26.0964	+	18.9601i	1.16707	+	0.847924i
$501$	7.57476	+	5.50339i	0.338415	+	0.245873i
$502$	−0.214039	+	0.658746i	−0.00955305	+	0.0294013i
$503$	−8.87921	−	27.3274i	−0.395904	−	1.21847i	−0.928255	−	0.371944i	$-0.878691\pi$
$503$	−8.87921	−	27.3274i	−0.395904	−	1.21847i	0.532351	−	0.846524i	$-0.321309\pi$
$504$	−11.2954	+	8.20657i	−0.503136	+	0.365550i
$505$	9.49925			0.422711
$506$	3.89260	−	6.56792i	0.173047	−	0.291980i
$507$	−13.8957			−0.617128
$508$	0.523510	−	0.380352i	0.0232270	−	0.0168754i
$509$	4.19337	+	12.9059i	0.185868	+	0.572042i	0.999962	−	0.00869018i	$-0.00276620\pi$
$509$	4.19337	+	12.9059i	0.185868	+	0.572042i	−0.814094	+	0.580733i	$0.802766\pi$
$510$	0.727943	−	2.24038i	0.0322339	−	0.0992057i
$511$	7.67480	+	5.57607i	0.339513	+	0.246671i
$512$	−15.1377	−	10.9982i	−0.669000	−	0.486057i
$513$	8.97656	−	27.6270i	0.396325	−	1.21976i
$514$	16.4299	+	50.5659i	0.724690	+	2.23037i
$515$	−1.37481	+	0.998860i	−0.0605815	+	0.0440150i
$516$	−9.85919			−0.434027
$517$	−15.3923	−	17.4923i	−0.676954	−	0.769310i
$518$	57.9498			2.54617
$519$	3.51363	−	2.55280i	0.154231	−	0.112055i
$520$	−4.51905	−	13.9082i	−0.198173	−	0.609915i
$521$	−1.08051	+	3.32548i	−0.0473382	+	0.145692i	−0.971932	−	0.235263i	$-0.924405\pi$
$521$	−1.08051	+	3.32548i	−0.0473382	+	0.145692i	0.924594	+	0.380955i	$0.124405\pi$
$522$	16.3903	+	11.9083i	0.717385	+	0.521211i
$523$	5.60409	+	4.07161i	0.245050	+	0.178039i	0.703530	−	0.710665i	$-0.251606\pi$
$523$	5.60409	+	4.07161i	0.245050	+	0.178039i	−0.458480	+	0.888705i	$0.651606\pi$
$524$	−3.27759	+	10.0874i	−0.143182	+	0.440669i
$525$	−2.09676	−	6.45317i	−0.0915103	−	0.281640i
$526$	44.6233	−	32.4207i	1.94567	−	1.41361i
$527$	10.8166			0.471181
$528$	−0.391663	−	4.18536i	−0.0170449	−	0.182145i
$529$	−21.8987			−0.952116
$530$	−9.54961	+	6.93820i	−0.414809	+	0.301376i
$531$	4.55431	+	14.0167i	0.197640	+	0.608274i
$532$	−20.0271	+	61.6371i	−0.868285	+	2.67231i
$533$	−6.29417	−	4.57298i	−0.272631	−	0.198078i
$534$	14.2854	+	10.3790i	0.618192	+	0.449143i
$535$	2.38451	−	7.33877i	0.103091	−	0.317283i
$536$	−0.322722	−	0.993236i	−0.0139395	−	0.0429013i
$537$	−9.69517	+	7.04395i	−0.418377	+	0.303969i
$538$	7.11939			0.306939
$539$	−10.3509	−	2.32393i	−0.445846	−	0.100099i
$540$	16.4735			0.708905
$541$	10.3451	−	7.51616i	0.444771	−	0.323145i	−0.342757	−	0.939424i	$-0.611361\pi$
$541$	10.3451	−	7.51616i	0.444771	−	0.323145i	0.787528	+	0.616279i	$0.211361\pi$
$542$	−2.87227	−	8.83994i	−0.123375	−	0.379708i
$543$	−1.89087	+	5.81951i	−0.0811452	+	0.249739i
$544$	−5.92960	−	4.30810i	−0.254229	−	0.184708i
$545$	12.9836	+	9.43316i	0.556158	+	0.404072i
$546$	−9.00976	+	27.7292i	−0.385582	+	1.18670i
$547$	0.363840	+	1.11979i	0.0155567	+	0.0478786i	0.958534	−	0.284980i	$-0.0919869\pi$
$547$	0.363840	+	1.11979i	0.0155567	+	0.0478786i	−0.942977	+	0.332858i	$0.891987\pi$
$548$	22.5897	−	16.4124i	0.964986	−	0.701103i
$549$	−24.7529			−1.05643
$550$	20.4462	+	4.59046i	0.871829	+	0.195738i
$551$	27.1454			1.15643
$552$	−1.11487	+	0.809999i	−0.0474519	+	0.0344759i
$553$	−9.43600	−	29.0410i	−0.401260	−	1.23495i
$554$	−7.46979	+	22.9897i	−0.317361	+	0.976737i
$555$	−7.18735	−	5.22191i	−0.305086	−	0.221658i
$556$	23.5250	+	17.0919i	0.997683	+	0.724859i
$557$	5.75180	−	17.7022i	0.243712	−	0.750067i	−0.752134	−	0.659010i	$-0.770975\pi$
$557$	5.75180	−	17.7022i	0.243712	−	0.750067i	0.995846	−	0.0910570i	$-0.0290245\pi$
$558$	18.0064	+	55.4179i	0.762271	+	2.34603i
$559$	21.7010	−	15.7667i	0.917854	−	0.666860i
$560$	7.98884			0.337590
$561$	−0.227943	−	2.43583i	−0.00962378	−	0.102841i
$562$	62.3258			2.62906
$563$	31.0093	−	22.5296i	1.30689	−	0.949508i	0.306888	−	0.951746i	$-0.400712\pi$
$563$	31.0093	−	22.5296i	1.30689	−	0.949508i	0.999997	+	0.00223809i	$0.000712405\pi$
$564$	4.50236	+	13.8568i	0.189583	+	0.583478i
$565$	2.68730	−	8.27067i	0.113056	−	0.347950i
$566$	19.7938	+	14.3811i	0.831997	+	0.604481i
$567$	11.3654	+	8.25747i	0.477304	+	0.346781i
$568$	1.12921	−	3.47536i	0.0473807	−	0.145823i
$569$	−8.19309	−	25.2157i	−0.343472	−	1.05710i	−0.962397	−	0.271648i	$-0.912431\pi$
$569$	−8.19309	−	25.2157i	−0.343472	−	1.05710i	0.618924	−	0.785451i	$-0.287569\pi$
$570$	13.7559	−	9.99428i	0.576173	−	0.418614i
$571$	−7.67510			−0.321193			−0.160596	−	0.987020i	$-0.551342\pi$
$571$	−7.67510			−0.321193			−0.160596	+	0.987020i	$0.551342\pi$
$572$	−34.7584	−	39.5004i	−1.45332	−	1.65160i
$573$	17.3986			0.726835
$574$	−7.81411	+	5.67728i	−0.326154	+	0.236965i
$575$	0.934096	+	2.87485i	0.0389545	+	0.119890i
$576$	9.59317	−	29.5247i	0.399715	−	1.23020i
$577$	−2.62856	−	1.90976i	−0.109428	−	0.0795043i	0.531725	−	0.846917i	$-0.321544\pi$
$577$	−2.62856	−	1.90976i	−0.109428	−	0.0795043i	−0.641154	+	0.767413i	$0.721544\pi$
$578$	−1.77460	−	1.28932i	−0.0738137	−	0.0536288i
$579$	−3.43001	+	10.5565i	−0.142546	+	0.438712i
$580$	4.75703	+	14.6406i	0.197525	+	0.607920i
$581$	−42.3009	+	30.7334i	−1.75494	+	1.27504i
$582$	−11.0378			−0.457532
$583$	−6.25024	+	10.5459i	−0.258859	+	0.436768i
$584$	5.28814			0.218825
$585$	−16.3217	+	11.8584i	−0.674821	+	0.490286i
$586$	−5.24921	−	16.1554i	−0.216843	−	0.667374i
$587$	−12.1238	+	37.3134i	−0.500405	+	1.54009i	0.307957	+	0.951400i	$0.400355\pi$
$587$	−12.1238	+	37.3134i	−0.500405	+	1.54009i	−0.808361	+	0.588687i	$0.799645\pi$
$588$	5.36676	+	3.89918i	0.221321	+	0.160799i
$589$	63.1637	+	45.8911i	2.60262	+	1.89091i
$590$	−5.92223	+	18.2267i	−0.243814	+	0.750383i
$591$	3.03624	+	9.34460i	0.124894	+	0.384385i
$592$	−11.4996	+	8.35493i	−0.472630	+	0.343386i
$593$	11.6776			0.479540			0.239770	−	0.970830i	$-0.422928\pi$
$593$	11.6776			0.479540			0.239770	+	0.970830i	$0.422928\pi$
$594$	26.8814	−	11.6026i	1.10296	−	0.476062i
$595$	4.64941			0.190607
$596$	10.6619	−	7.74633i	0.436729	−	0.317302i
$597$	−4.82980	−	14.8646i	−0.197670	−	0.608367i
$598$	4.01380	−	12.3532i	0.164136	−	0.505160i
$599$	19.7487	+	14.3482i	0.806908	+	0.586253i	0.912933	−	0.408110i	$-0.133812\pi$
$599$	19.7487	+	14.3482i	0.806908	+	0.586253i	−0.106024	+	0.994364i	$0.533812\pi$
$600$	−3.05998	−	2.22320i	−0.124923	−	0.0907619i
$601$	8.42001	−	25.9141i	0.343460	−	1.05706i	−0.618944	−	0.785435i	$-0.712439\pi$
$601$	8.42001	−	25.9141i	0.343460	−	1.05706i	0.962403	−	0.271624i	$-0.0875609\pi$
$602$	−10.2907	−	31.6715i	−0.419418	−	1.29084i
$603$	−1.16560	+	0.846855i	−0.0474667	+	0.0344866i
$604$	−2.61571			−0.106432
$605$	−15.7367	+	2.97128i	−0.639788	+	0.120800i
$606$	−10.5572			−0.428858
$607$	17.2661	−	12.5445i	0.700807	−	0.509166i	−0.179388	−	0.983778i	$-0.557412\pi$
$607$	17.2661	−	12.5445i	0.700807	−	0.509166i	0.880195	+	0.474612i	$0.157412\pi$
$608$	−16.3481	−	50.3143i	−0.663003	−	2.04051i
$609$	2.73764	−	8.42559i	0.110935	−	0.341422i
$610$	−26.0403	−	18.9194i	−1.05434	−	0.766024i
$611$	−32.0698	−	23.3000i	−1.29740	−	0.942619i
$612$	2.13372	−	6.56693i	0.0862507	−	0.265452i
$613$	5.54446	+	17.0641i	0.223939	+	0.689212i	0.998398	+	0.0565880i	$0.0180222\pi$
$613$	5.54446	+	17.0641i	0.223939	+	0.689212i	−0.774459	+	0.632624i	$0.781978\pi$
$614$	−18.3801	+	13.3539i	−0.741761	+	0.538921i
$615$	1.48074			0.0597094
$616$	−17.3115	+	7.47203i	−0.697499	+	0.301057i
$617$	34.2506			1.37888			0.689439	−	0.724343i	$-0.257857\pi$
$617$	34.2506			1.37888			0.689439	+	0.724343i	$0.257857\pi$
$618$	1.52793	−	1.11011i	0.0614624	−	0.0446550i
$619$	11.9845	+	36.8845i	0.481697	+	1.48251i	0.836708	+	0.547649i	$0.184477\pi$
$619$	11.9845	+	36.8845i	0.481697	+	1.48251i	−0.355011	+	0.934862i	$0.615523\pi$
$620$	−13.6820	+	42.1089i	−0.549483	+	1.69114i
$621$	3.41684	+	2.48248i	0.137113	+	0.0996185i
$622$	1.39354	+	1.01247i	0.0558758	+	0.0405962i
$623$	−10.7696	+	33.1456i	−0.431477	+	1.32795i
$624$	−2.20996	−	6.80157i	−0.0884694	−	0.272281i
$625$	1.86184	−	1.35271i	0.0744737	−	0.0541083i
$626$	−13.4970			−0.539447
$627$	9.00329	−	15.1911i	0.359557	−	0.606675i
$628$	−59.8861			−2.38972
$629$	−6.69262	+	4.86247i	−0.266852	+	0.193880i
$630$	7.73984	+	23.8208i	0.308363	+	0.949042i
$631$	7.10340	−	21.8620i	0.282782	−	0.870313i	−0.704273	−	0.709929i	$-0.748727\pi$
$631$	7.10340	−	21.8620i	0.282782	−	0.870313i	0.987055	−	0.160384i	$-0.0512731\pi$
$632$	−13.7707	−	10.0050i	−0.547770	−	0.397978i
$633$	14.4577	+	10.5041i	0.574643	+	0.417502i
$634$	7.28471	−	22.4200i	0.289313	−	0.890413i
$635$	−0.103545	−	0.318679i	−0.00410907	−	0.0126464i
$636$	6.20165	−	4.50576i	0.245911	−	0.178665i
$637$	−18.0482			−0.715097
$638$	18.0743	+	20.5401i	0.715567	+	0.813192i
$639$	−5.04124			−0.199428
$640$	15.3931	−	11.1838i	0.608466	−	0.442077i
$641$	9.45362	+	29.0953i	0.373396	+	1.14919i	0.944555	+	0.328354i	$0.106494\pi$
$641$	9.45362	+	29.0953i	0.373396	+	1.14919i	−0.571159	+	0.820839i	$0.693506\pi$
$642$	−2.65008	+	8.15611i	−0.104590	+	0.321896i
$643$	12.0648	+	8.76563i	0.475791	+	0.345683i	0.799694	−	0.600408i	$-0.204995\pi$
$643$	12.0648	+	8.76563i	0.475791	+	0.345683i	−0.323903	+	0.946090i	$0.604995\pi$
$644$	−7.62312	−	5.53852i	−0.300393	−	0.218248i
$645$	−1.57762	+	4.85543i	−0.0621189	+	0.191182i
$646$	−4.89263	−	15.0580i	−0.192498	−	0.592448i
$647$	−0.372807	+	0.270860i	−0.0146566	+	0.0106486i	−0.595089	−	0.803659i	$-0.702883\pi$
$647$	−0.372807	+	0.270860i	−0.0146566	+	0.0106486i	0.580433	+	0.814308i	$0.302883\pi$
$648$	7.83109			0.307634
$649$	1.85445	+	19.8169i	0.0727934	+	0.777881i
$650$	35.6507			1.39833
$651$	20.6142	−	14.9771i	0.807933	−	0.586997i
$652$	−1.03527	−	3.18624i	−0.0405444	−	0.124783i
$653$	0.986960	−	3.03755i	0.0386227	−	0.118868i	−0.929886	−	0.367847i	$-0.880095\pi$
$653$	0.986960	−	3.03755i	0.0386227	−	0.118868i	0.968509	+	0.248979i	$0.0800949\pi$
$654$	−14.4297	−	10.4838i	−0.564244	−	0.409948i
$655$	4.44334	+	3.22828i	0.173616	+	0.126139i
$656$	0.732109	−	2.25320i	0.0285841	−	0.0879727i
$657$	−2.25439	−	6.93831i	−0.0879522	−	0.270689i
$658$	−39.8141	+	28.9266i	−1.55211	+	1.12768i
$659$	−28.0269			−1.09177			−0.545887	−	0.837859i	$-0.683807\pi$
$659$	−28.0269			−1.09177			−0.545887	+	0.837859i	$0.683807\pi$
$660$	9.77096	+	2.19372i	0.380334	+	0.0853904i
$661$	−33.4451			−1.30086			−0.650431	−	0.759565i	$-0.725412\pi$
$661$	−33.4451			−1.30086			−0.650431	+	0.759565i	$0.725412\pi$
$662$	7.30337	−	5.30621i	0.283854	−	0.206232i
$663$	−1.28617	−	3.95844i	−0.0499509	−	0.153733i
$664$	−9.00675	+	27.7199i	−0.349530	+	1.07574i
$665$	27.1502	+	19.7258i	1.05284	+	0.764933i
$666$	−36.0535	−	26.1944i	−1.39705	−	1.01501i
$667$	−1.21960	+	3.75355i	−0.0472232	+	0.145338i
$668$	11.0280	+	33.9407i	0.426686	+	1.31320i
$669$	−3.31236	+	2.40657i	−0.128063	+	0.0930433i
$670$	−1.87350			−0.0723795
$671$	−32.6164	−	7.32283i	−1.25914	−	0.282695i
$672$	−17.2656			−0.666036
$673$	20.1133	−	14.6131i	0.775309	−	0.563295i	−0.128258	−	0.991741i	$-0.540939\pi$
$673$	20.1133	−	14.6131i	0.775309	−	0.563295i	0.903567	+	0.428446i	$0.140939\pi$
$674$	−3.00354	−	9.24394i	−0.115692	−	0.356063i
$675$	−3.58215	+	11.0247i	−0.137877	+	0.424342i
$676$	−42.8489	−	31.1315i	−1.64803	−	1.19737i
$677$	−20.0485	−	14.5661i	−0.770525	−	0.559819i	0.131595	−	0.991304i	$-0.457990\pi$
$677$	−20.0485	−	14.5661i	−0.770525	−	0.559819i	−0.902121	+	0.431484i	$0.857990\pi$
$678$	−2.98660	+	9.19181i	−0.114700	+	0.353009i
$679$	−6.73206	−	20.7191i	−0.258353	−	0.795128i
$680$	2.09676	−	1.52339i	0.0804072	−	0.0584193i
$681$	−2.92840			−0.112216
$682$	7.33193	+	78.3500i	0.280754	+	3.00018i
$683$	−29.0687			−1.11228			−0.556142	−	0.831087i	$-0.687719\pi$
$683$	−29.0687			−1.11228			−0.556142	+	0.831087i	$0.687719\pi$
$684$	40.3210	−	29.2949i	1.54171	−	1.12012i
$685$	−4.46803	−	13.7512i	−0.170715	−	0.525406i
$686$	8.22882	−	25.3257i	0.314178	−	0.966940i
$687$	−7.81732	−	5.67961i	−0.298249	−	0.216691i
$688$	6.60834	+	4.80124i	0.251940	+	0.183045i
$689$	−6.44485	+	19.8352i	−0.245529	+	0.755661i
$690$	0.763932	+	2.35114i	0.0290824	+	0.0895064i
$691$	9.40582	−	6.83373i	0.357814	−	0.259967i	−0.394326	−	0.918971i	$-0.629022\pi$
$691$	9.40582	−	6.83373i	0.357814	−	0.259967i	0.752140	+	0.659004i	$0.229022\pi$
$692$	16.5539			0.629285
$693$	17.1838	+	19.5281i	0.652757	+	0.741812i
$694$	−26.3990			−1.00209
$695$	12.1818	−	8.85057i	0.462081	−	0.335721i
$696$	−1.52605	−	4.69671i	−0.0578449	−	0.178028i
$697$	0.426079	−	1.31134i	0.0161389	−	0.0496704i
$698$	−43.5891	−	31.6694i	−1.64987	−	1.19870i
$699$	−2.53089	−	1.83880i	−0.0957270	−	0.0695497i
$700$	7.99194	−	24.5967i	0.302067	−	0.929667i
$701$	−5.38059	−	16.5598i	−0.203222	−	0.625454i	−0.999782	−	0.0208936i	$-0.993349\pi$
$701$	−5.38059	−	16.5598i	−0.203222	−	0.625454i	0.796559	−	0.604560i	$-0.206651\pi$
$702$	40.2980	−	29.2782i	1.52095	−	1.10503i
$703$	−59.7112			−2.25205
$704$	21.3752	−	36.0661i	0.805609	−	1.35929i
$705$	7.54462			0.284147
$706$	−0.339600	+	0.246734i	−0.0127810	+	0.00928596i
$707$	−6.43895	−	19.8170i	−0.242162	−	0.745296i
$708$	3.84598	−	11.8367i	0.144541	−	0.444850i
$709$	−7.21351	−	5.24092i	−0.270909	−	0.196827i	0.444033	−	0.896010i	$-0.353547\pi$
$709$	−7.21351	−	5.24092i	−0.270909	−	0.196827i	−0.714942	+	0.699183i	$0.753547\pi$
$710$	−5.30344	−	3.85317i	−0.199034	−	0.144607i
$711$	−7.25647	+	22.3331i	−0.272139	+	0.837558i
$712$	6.00337	+	18.4765i	0.224986	+	0.692435i
$713$	−9.18348	+	6.67219i	−0.343924	+	0.249876i
$714$	−5.16724			−0.193379
$715$	−25.0150	+	10.7970i	−0.935506	+	0.403786i
$716$	−45.6773			−1.70704
$717$	−3.45481	+	2.51006i	−0.129022	+	0.0937401i
$718$	−21.0986	−	64.9347i	−0.787391	−	2.42334i
$719$	−1.78021	+	5.47893i	−0.0663907	+	0.204330i	−0.978749	−	0.205064i	$-0.934260\pi$
$719$	−1.78021	+	5.47893i	−0.0663907	+	0.204330i	0.912358	+	0.409394i	$0.134260\pi$
$720$	−4.97026	−	3.61110i	−0.185231	−	0.134578i
$721$	3.01569	+	2.19103i	0.112310	+	0.0815981i
$722$	22.4362	−	69.0514i	0.834988	−	2.56983i
$723$	0.248910	+	0.766065i	0.00925705	+	0.0284903i
$724$	−18.8686	+	13.7089i	−0.701248	+	0.509486i
$725$	−10.8325			−0.402311
$726$	17.4894	−	3.30220i	0.649091	−	0.122556i
$727$	−23.6451			−0.876949			−0.438475	−	0.898744i	$-0.644481\pi$
$727$	−23.6451			−0.876949			−0.438475	+	0.898744i	$0.644481\pi$
$728$	−25.9517	+	18.8550i	−0.961833	+	0.698812i
$729$	−0.586417	−	1.80481i	−0.0217191	−	0.0668446i
$730$	2.93151	−	9.02227i	0.108500	−	0.333929i
$731$	3.84598	+	2.79427i	0.142249	+	0.103350i
$732$	16.9109	+	12.2865i	0.625046	+	0.454123i
$733$	0.294949	−	0.907759i	0.0108942	−	0.0335288i	−0.945462	−	0.325733i	$-0.894389\pi$
$733$	0.294949	−	0.907759i	0.0108942	−	0.0335288i	0.956356	+	0.292205i	$0.0943888\pi$
$734$	−11.4257	−	35.1646i	−0.421729	−	1.29795i
$735$	2.77902	−	2.01908i	0.102506	−	0.0744748i
$736$	7.69174			0.283521
$737$	−1.78641	+	0.771056i	−0.0658033	+	0.0284022i
$738$	7.42779			0.273421
$739$	−7.14649	+	5.19223i	−0.262888	+	0.190999i	−0.711419	−	0.702768i	$-0.751947\pi$
$739$	−7.14649	+	5.19223i	−0.262888	+	0.190999i	0.448531	+	0.893767i	$0.351947\pi$
$740$	−10.4640	−	32.2048i	−0.384663	−	1.18387i
$741$	9.28362	−	28.5720i	0.341042	−	1.04962i
$742$	20.9473	+	15.2191i	0.769001	+	0.558712i
$743$	−17.4206	−	12.6568i	−0.639100	−	0.464333i	0.220441	−	0.975400i	$-0.429250\pi$
$743$	−17.4206	−	12.6568i	−0.639100	−	0.464333i	−0.859541	+	0.511067i	$0.829250\pi$
$744$	4.38919	−	13.5085i	0.160915	−	0.495247i
$745$	−2.10882	−	6.49028i	−0.0772612	−	0.237786i
$746$	61.2130	−	44.4739i	2.24117	−	1.62830i
$747$	40.2096			1.47119
$748$	4.75430	−	8.02186i	0.173834	−	0.293308i
$749$	−16.9262			−0.618470
$750$	−15.0183	+	10.9114i	−0.548391	+	0.398429i
$751$	−1.64986	−	5.07776i	−0.0602044	−	0.185290i	0.916431	−	0.400192i	$-0.131057\pi$
$751$	−1.64986	−	5.07776i	−0.0602044	−	0.185290i	−0.976636	+	0.214902i	$0.931057\pi$
$752$	3.73021	−	11.4804i	0.136027	−	0.418647i
$753$	−0.188439	−	0.136909i	−0.00686710	−	0.00498924i
$754$	37.6576	+	27.3598i	1.37141	+	0.996386i
$755$	−0.418555	+	1.28818i	−0.0152328	+	0.0468817i
$756$	−11.1663	−	34.3664i	−0.406116	−	1.24990i
$757$	0.358218	−	0.260261i	0.0130197	−	0.00945934i	−0.581256	−	0.813720i	$-0.697439\pi$
$757$	0.358218	−	0.260261i	0.0130197	−	0.00945934i	0.594276	+	0.804261i	$0.297439\pi$
$758$	36.7918			1.33634
$759$	1.69606	+	1.92745i	0.0615630	+	0.0699620i
$760$	18.7072			0.678582
$761$	3.47307	−	2.52333i	0.125899	−	0.0914707i	−0.523054	−	0.852300i	$-0.675207\pi$
$761$	3.47307	−	2.52333i	0.125899	−	0.0914707i	0.648953	+	0.760829i	$0.275207\pi$
$762$	0.115077	+	0.354172i	0.00416881	+	0.0128303i
$763$	10.8784	−	33.4802i	0.393823	−	1.21206i
$764$	53.6505	+	38.9794i	1.94101	+	1.41022i
$765$	−2.89263	−	2.10162i	−0.104583	−	0.0759843i
$766$	−10.4398	+	32.1303i	−0.377204	+	1.16091i
$767$	10.4638	+	32.2041i	0.377824	+	1.16282i
$768$	−2.02047	+	1.46796i	−0.0729076	+	0.0529704i
$769$	34.8414			1.25641			0.628206	−	0.778047i	$-0.283789\pi$
$769$	34.8414			1.25641			0.628206	+	0.778047i	$0.283789\pi$
$770$	3.15155	+	33.6778i	0.113574	+	1.21367i
$771$	−17.8794			−0.643911
$772$	−34.2273	+	24.8676i	−1.23187	+	0.895005i
$773$	8.74943	+	26.9280i	0.314695	+	0.968532i	0.975880	+	0.218309i	$0.0700540\pi$
$773$	8.74943	+	26.9280i	0.314695	+	0.968532i	−0.661185	+	0.750223i	$0.729946\pi$
$774$	−7.91376	+	24.3560i	−0.284454	+	0.875460i
$775$	−25.2059	−	18.3132i	−0.905423	−	0.657828i
$776$	−9.82464	−	7.13802i	−0.352684	−	0.256240i
$777$	−6.02194	+	18.5336i	−0.216036	+	0.664890i
$778$	−20.8308	−	64.1105i	−0.746819	−	2.29847i
$779$	8.05162	−	5.84984i	0.288479	−	0.209592i
$780$	17.0370			0.610022
$781$	−6.64273	−	1.49139i	−0.237696	−	0.0533660i
$782$	2.30197			0.0823184
$783$	−12.2447	+	8.89626i	−0.437588	+	0.317926i
$784$	−1.69836	−	5.22702i	−0.0606557	−	0.186679i
$785$	−9.58271	+	29.4926i	−0.342022	+	1.05263i
$786$	−4.93821	−	3.58782i	−0.176140	−	0.127973i
$787$	−19.5514	−	14.2049i	−0.696933	−	0.506352i	0.181999	−	0.983299i	$-0.441743\pi$
$787$	−19.5514	−	14.2049i	−0.696933	−	0.506352i	−0.878932	+	0.476947i	$0.841743\pi$
$788$	−11.5728	+	35.6175i	−0.412265	+	1.26882i
$789$	5.73176	+	17.6406i	0.204056	+	0.628020i
$790$	−24.7038	+	17.9483i	−0.878921	+	0.638573i
$791$	−19.0756			−0.678249
$792$	14.1478	+	3.17639i	0.502722	+	0.112868i
$793$	−56.8710			−2.01955
$794$	−62.8119	+	45.6355i	−2.22911	+	1.61954i
$795$	−1.22663	−	3.77517i	−0.0435039	−	0.133891i
$796$	18.4091	−	56.6573i	0.652492	−	2.00816i
$797$	11.9508	+	8.68277i	0.423319	+	0.307559i	0.778972	−	0.627059i	$-0.215741\pi$
$797$	11.9508	+	8.68277i	0.423319	+	0.307559i	−0.355653	+	0.934618i	$0.615741\pi$
$798$	−30.1740	−	21.9227i	−1.06815	−	0.776056i
$799$	2.17094	−	6.68146i	0.0768023	−	0.236373i
$800$	6.52381	+	20.0782i	0.230652	+	0.709873i
$801$	21.6828	−	15.7534i	0.766122	−	0.556621i
$802$	−55.7844			−1.96981
$803$	−0.917955	−	9.80939i	−0.0323939	−	0.346166i
$804$	1.21667			0.0429088
$805$	−3.94742	+	2.86797i	−0.139128	+	0.101083i
$806$	41.3705	+	127.325i	1.45721	+	4.48484i
$807$	−0.739821	+	2.27694i	−0.0260429	+	0.0801519i
$808$	−9.39688	−	6.82723i	−0.330581	−	0.240181i
$809$	36.6314	+	26.6142i	1.28789	+	0.935707i	0.999760	−	0.0218848i	$-0.00696672\pi$
$809$	36.6314	+	26.6142i	1.28789	+	0.935707i	0.288129	+	0.957592i	$0.406967\pi$
$810$	4.34121	−	13.3609i	0.152535	−	0.469453i
$811$	6.45320	+	19.8609i	0.226603	+	0.697411i	0.998125	+	0.0612089i	$0.0194956\pi$
$811$	6.45320	+	19.8609i	0.226603	+	0.697411i	−0.771522	+	0.636202i	$0.780504\pi$
$812$	27.3184	−	19.8479i	0.958686	−	0.696526i
$813$	3.12568			0.109622
$814$	−39.7576	−	45.1818i	−1.39350	−	1.58362i
$815$	−1.73481			−0.0607678
$816$	1.02539	−	0.744987i	0.0358957	−	0.0260798i
$817$	10.6035	+	32.6342i	0.370969	+	1.14173i
$818$	1.80647	−	5.55975i	0.0631618	−	0.194392i
$819$	35.8022	+	26.0118i	1.25103	+	0.908926i
$820$	4.56605	+	3.31743i	0.159453	+	0.115850i
$821$	−13.8040	+	42.4844i	−0.481763	+	1.48271i	0.354852	+	0.934923i	$0.384531\pi$
$821$	−13.8040	+	42.4844i	−0.481763	+	1.48271i	−0.836615	+	0.547792i	$0.815469\pi$
$822$	4.96565	+	15.2827i	0.173197	+	0.533045i
$823$	3.96474	−	2.88055i	0.138202	−	0.100410i	−0.516536	−	0.856265i	$-0.672779\pi$
$823$	3.96474	−	2.88055i	0.138202	−	0.100410i	0.654738	+	0.755856i	$0.272779\pi$
$824$	2.07789			0.0723867
$825$	−3.59282	+	6.06211i	−0.125086	+	0.211056i
$826$	42.0384			1.46270
$827$	−28.4468	+	20.6678i	−0.989191	+	0.718689i	−0.959744	−	0.280877i	$-0.909375\pi$
$827$	−28.4468	+	20.6678i	−0.989191	+	0.718689i	−0.0294469	+	0.999566i	$0.509375\pi$
$828$	2.23921	+	6.89159i	0.0778180	+	0.239499i
$829$	3.77737	−	11.6255i	0.131193	−	0.403772i	−0.863785	−	0.503860i	$-0.831913\pi$
$829$	3.77737	−	11.6255i	0.131193	−	0.403772i	0.994979	+	0.100088i	$0.0319126\pi$
$830$	42.3009	+	30.7334i	1.46829	+	1.06677i
$831$	−6.57636	−	4.77800i	−0.228131	−	0.165747i
$832$	22.0408	−	67.8345i	0.764126	−	2.35174i
$833$	−0.988426	−	3.04206i	−0.0342469	−	0.105401i
$834$	−13.5385	+	9.83629i	−0.468800	+	0.340603i
$835$	18.4797			0.639516
$836$	61.7966	−	26.6728i	2.13728	−	0.922498i
$837$	−43.5314			−1.50467
$838$	17.4828	−	12.7020i	0.603933	−	0.438783i
$839$	−7.43229	−	22.8742i	−0.256591	−	0.789706i	−0.993512	−	0.113727i	$-0.963721\pi$
$839$	−7.43229	−	22.8742i	−0.256591	−	0.789706i	0.736921	−	0.675979i	$-0.236279\pi$
$840$	1.88664	−	5.80649i	0.0650953	−	0.200343i
$841$	12.0191	+	8.73242i	0.414453	+	0.301118i
$842$	−18.1389	−	13.1786i	−0.625106	−	0.454166i
$843$	−6.47667	+	19.9331i	−0.223068	+	0.686534i
$844$	21.0488	+	64.7816i	0.724530	+	2.22987i
$845$	−22.1881	+	16.1206i	−0.763293	+	0.554565i
$846$	37.8457			1.30116
$847$	16.8655	+	30.8154i	0.579506	+	1.05883i
$848$	−6.35101			−0.218095
$849$	−6.65628	+	4.83607i	−0.228443	+	0.165974i
$850$	1.95244	+	6.00899i	0.0669681	+	0.206107i
$851$	2.68274	−	8.25662i	0.0919630	−	0.283033i
$852$	3.44413	+	2.50230i	0.117994	+	0.0857275i
$853$	21.4855	+	15.6102i	0.735651	+	0.534482i	0.891346	−	0.453323i	$-0.149762\pi$
$853$	21.4855	+	15.6102i	0.735651	+	0.534482i	−0.155695	+	0.987805i	$0.549762\pi$
$854$	−21.8179	+	67.1487i	−0.746595	+	2.29778i
$855$	−7.97509	−	24.5448i	−0.272742	−	0.839415i
$856$	−7.63328	+	5.54590i	−0.260900	+	0.189555i
$857$	28.5076			0.973803			0.486901	−	0.873457i	$-0.338127\pi$
$857$	28.5076			0.973803			0.486901	+	0.873457i	$0.338127\pi$
$858$	27.8010	−	11.9995i	0.949109	−	0.409657i
$859$	−30.5730			−1.04314			−0.521569	−	0.853209i	$-0.674653\pi$
$859$	−30.5730			−1.04314			−0.521569	+	0.853209i	$0.674653\pi$
$860$	−15.7428	+	11.4378i	−0.536825	+	0.390026i
$861$	−1.00370	−	3.08908i	−0.0342061	−	0.105276i
$862$	−6.57982	+	20.2506i	−0.224110	+	0.689739i
$863$	−0.121179	−	0.0880414i	−0.00412497	−	0.00299697i	0.585721	−	0.810513i	$-0.300811\pi$
$863$	−0.121179	−	0.0880414i	−0.00412497	−	0.00299697i	−0.589846	+	0.807516i	$0.700811\pi$
$864$	23.8635	+	17.3379i	0.811854	+	0.589847i
$865$	2.64889	−	8.15243i	0.0900648	−	0.277191i
$866$	5.95809	+	18.3371i	0.202464	+	0.623120i
$867$	0.596764	−	0.433574i	0.0202672	−	0.0147249i
$868$	97.1205			3.29648
$869$	−16.1687	+	27.2811i	−0.548484	+	0.925449i
$870$	−8.85919			−0.300355
$871$	−2.67801	+	1.94569i	−0.0907410	+	0.0659272i
$872$	−6.06398	−	18.6630i	−0.205352	−	0.632009i
$873$	−5.17709	+	15.9334i	−0.175218	+	0.539265i
$874$	13.4423	+	9.76644i	0.454694	+	0.330355i
$875$	−29.6417	−	21.5360i	−1.00207	−	0.728049i
$876$	−1.90377	+	5.85919i	−0.0643223	+	0.197964i
$877$	−9.43239	−	29.0299i	−0.318509	−	0.980271i	−0.974286	−	0.225316i	$-0.927659\pi$
$877$	−9.43239	−	29.0299i	−0.318509	−	0.980271i	0.655776	−	0.754955i	$-0.272341\pi$
$878$	−21.9118	+	15.9199i	−0.739489	+	0.537270i
$879$	5.71233			0.192672
$880$	−5.48090	−	6.22866i	−0.184761	−	0.209968i
$881$	−31.8605			−1.07341			−0.536703	−	0.843771i	$-0.680331\pi$
$881$	−31.8605			−1.07341			−0.536703	+	0.843771i	$0.680331\pi$
$882$	13.9403	−	10.1282i	0.469393	−	0.341034i
$883$	−11.3691	−	34.9904i	−0.382600	−	1.17752i	−0.938207	−	0.346076i	$-0.887514\pi$
$883$	−11.3691	−	34.9904i	−0.382600	−	1.17752i	0.555607	−	0.831445i	$-0.312486\pi$
$884$	4.90233	−	15.0878i	0.164883	−	0.507458i
$885$	−5.21389	−	3.78811i	−0.175263	−	0.127336i
$886$	−15.8215	−	11.4950i	−0.531534	−	0.386182i
$887$	13.2335	−	40.7285i	0.444337	−	1.36753i	−0.438871	−	0.898550i	$-0.644622\pi$
$887$	13.2335	−	40.7285i	0.444337	−	1.36753i	0.883209	−	0.468980i	$-0.155378\pi$
$888$	3.35683	+	10.3313i	0.112648	+	0.346695i
$889$	−0.594632	+	0.432025i	−0.0199433	+	0.0144897i
$890$	34.8513			1.16822
$891$	−1.35938	−	14.5265i	−0.0455409	−	0.486656i
$892$	−15.6057			−0.522517
$893$	41.0242	−	29.8058i	1.37282	−	0.997415i
$894$	2.34369	+	7.21313i	0.0783847	+	0.241243i
$895$	−7.30908	+	22.4950i	−0.244316	+	0.751926i
$896$	−33.7652	−	24.5319i	−1.12802	−	0.819552i
$897$	3.53372	+	2.56740i	0.117987	+	0.0857229i
$898$	20.6996	−	63.7067i	0.690753	−	2.12592i
$899$	−12.5705	−	38.6881i	−0.419251	−	1.29032i
$900$	−16.0903	+	11.6903i	−0.536345	+	0.389677i
$901$	−3.69622			−0.123139
$902$	9.78743	+	2.19741i	0.325886	+	0.0731659i
$903$	11.1986			0.372667
$904$	−8.60258	+	6.25014i	−0.286118	+	0.207877i
$905$	3.73203	+	11.4860i	0.124057	+	0.381808i
$906$	0.465171	−	1.43165i	0.0154543	−	0.0475634i
$907$	46.9451	+	34.1076i	1.55879	+	1.13253i	0.936995	+	0.349343i	$0.113595\pi$
$907$	46.9451	+	34.1076i	1.55879	+	1.13253i	0.621792	+	0.783182i	$0.286405\pi$
$908$	−9.03006	−	6.56072i	−0.299673	−	0.217725i
$909$	−4.95168	+	15.2397i	−0.164237	+	0.505469i
$910$	17.7826	+	54.7294i	0.589489	+	1.81426i
$911$	10.9498	−	7.95551i	0.362784	−	0.263578i	−0.391429	−	0.920208i	$-0.628019\pi$
$911$	10.9498	−	7.95551i	0.362784	−	0.263578i	0.754212	+	0.656631i	$0.228019\pi$
$912$	9.14845			0.302935
$913$	52.9833	+	11.8955i	1.75349	+	0.393684i
$914$	−47.6586			−1.57640
$915$	8.75685	−	6.36222i	0.289492	−	0.210329i
$916$	−11.3811	−	35.0275i	−0.376043	−	1.15734i
$917$	3.72287	−	11.4578i	0.122940	−	0.378370i
$918$	7.14185	+	5.18886i	0.235716	+	0.171258i
$919$	−21.1207	−	15.3451i	−0.696709	−	0.506189i	0.182150	−	0.983271i	$-0.441694\pi$
$919$	−21.1207	−	15.3451i	−0.696709	−	0.506189i	−0.878859	+	0.477082i	$0.841694\pi$
$920$	−0.840488	+	2.58675i	−0.0277101	+	0.0852828i
$921$	−2.36088	−	7.26605i	−0.0777938	−	0.239425i
$922$	−48.7066	+	35.3874i	−1.60407	+	1.16542i
$923$	−11.5825			−0.381242
$924$	−2.04666	−	21.8709i	−0.0673301	−	0.719498i
$925$	23.8282			0.783465
$926$	35.4481	−	25.7546i	1.16490	−	0.846347i
$927$	−0.885827	−	2.72630i	−0.0290944	−	0.0895433i
$928$	−8.51782	+	26.2152i	−0.279611	+	0.860555i
$929$	13.7554	+	9.99390i	0.451301	+	0.327889i	0.790109	−	0.612966i	$-0.210024\pi$
$929$	13.7554	+	9.99390i	0.451301	+	0.327889i	−0.338808	+	0.940855i	$0.610024\pi$
$930$	−20.6142	−	14.9771i	−0.675965	−	0.491117i
$931$	7.13447	−	21.9576i	0.233823	−	0.719633i
$932$	−3.68469	−	11.3403i	−0.120696	−	0.371464i
$933$	−0.468620	+	0.340472i	−0.0153419	+	0.0111466i
$934$	−1.47557			−0.0482823
$935$	−3.18982	−	3.62501i	−0.104318	−	0.118551i
$936$	24.6686			0.806320
$937$	−14.8937	+	10.8209i	−0.486555	+	0.353503i	−0.803858	−	0.594821i	$-0.797223\pi$
$937$	−14.8937	+	10.8209i	−0.486555	+	0.353503i	0.317303	+	0.948324i	$0.397223\pi$
$938$	1.26993	+	3.90843i	0.0414645	+	0.127615i
$939$	1.40256	−	4.31662i	0.0457707	−	0.140868i
$940$	23.2647	+	16.9028i	0.758812	+	0.551309i
$941$	−24.6276	−	17.8930i	−0.802836	−	0.583295i	0.108908	−	0.994052i	$-0.465264\pi$
$941$	−24.6276	−	17.8930i	−0.802836	−	0.583295i	−0.911745	+	0.410757i	$0.865264\pi$
$942$	10.6500	−	32.7772i	0.346995	−	1.06794i
$943$	0.447144	+	1.37617i	0.0145610	+	0.0448142i
$944$	−8.34210	+	6.06089i	−0.271512	+	0.197265i
$945$	−18.7115			−0.608685
$946$	−17.6332	+	29.7522i	−0.573305	+	0.967329i
$947$	17.5898			0.571593			0.285796	−	0.958290i	$-0.407742\pi$
$947$	17.5898			0.571593			0.285796	+	0.958290i	$0.407742\pi$
$948$	16.0430	−	11.6559i	0.521051	−	0.378566i
$949$	−5.17957	−	15.9411i	−0.168136	−	0.517470i
$950$	−14.0927	+	43.3729i	−0.457228	+	1.40720i
$951$	6.41341	+	4.65962i	0.207969	+	0.151098i
$952$	−4.59931	−	3.34159i	−0.149064	−	0.108302i
$953$	12.0400	−	37.0554i	0.390015	−	1.20034i	−0.542762	−	0.839887i	$-0.682621\pi$
$953$	12.0400	−	37.0554i	0.390015	−	1.20034i	0.932777	−	0.360455i	$-0.117379\pi$
$954$	−6.15306	−	18.9372i	−0.199213	−	0.613114i
$955$	27.7814	−	20.1844i	0.898985	−	0.653151i
$956$	−16.2768			−0.526429
$957$	−8.44740	+	3.64609i	−0.273066	+	0.117861i
$958$	20.0963			0.649282
$959$	−25.6587	+	18.6421i	−0.828562	+	0.601986i
$960$	4.19494	+	12.9107i	0.135391	+	0.416691i
$961$	26.5754	−	81.7908i	0.857272	−	2.63841i
$962$	−82.8347	−	60.1829i	−2.67070	−	1.94037i
$963$	10.5307	+	7.65097i	0.339345	+	0.246549i
$964$	−0.948734	+	2.91990i	−0.0305567	+	0.0940437i
$965$	6.76983	+	20.8354i	0.217929	+	0.670716i
$966$	4.38705	−	3.18738i	0.141151	−	0.102552i
$967$	40.8919			1.31500			0.657498	−	0.753456i	$-0.271615\pi$
$967$	40.8919			1.31500			0.657498	+	0.753456i	$0.271615\pi$
$968$	17.7026	+	8.37091i	0.568983	+	0.269051i
$969$	5.32429			0.171041
$970$	−17.6248	+	12.8051i	−0.565897	+	0.411148i
$971$	3.30060	+	10.1582i	0.105921	+	0.325992i	0.989946	−	0.141449i	$-0.0451761\pi$
$971$	3.30060	+	10.1582i	0.105921	+	0.325992i	−0.884024	+	0.467441i	$0.845176\pi$
$972$	−13.3089	+	40.9606i	−0.426883	+	1.31381i
$973$	−26.7210	−	19.4140i	−0.856637	−	0.622383i
$974$	67.6062	+	49.1188i	2.16624	+	1.57387i
$975$	−3.70469	+	11.4019i	−0.118645	+	0.365152i
$976$	−5.35162	−	16.4706i	−0.171301	−	0.527211i
$977$	6.47752	−	4.70620i	0.207234	−	0.150565i	−0.479327	−	0.877636i	$-0.659119\pi$
$977$	6.47752	−	4.70620i	0.207234	−	0.150565i	0.686561	+	0.727072i	$0.259119\pi$
$978$	1.92802			0.0616514
$979$	33.2313	−	14.3434i	1.06208	−	0.458417i
$980$	13.0929			0.418239
$981$	−21.9017	+	15.9125i	−0.699266	+	0.508046i
$982$	−11.8116	−	36.3525i	−0.376924	−	1.16005i
$983$	−12.1757	+	37.4730i	−0.388345	+	1.19520i	0.545680	+	0.837994i	$0.316271\pi$
$983$	−12.1757	+	37.4730i	−0.388345	+	1.19520i	−0.934025	+	0.357209i	$0.883729\pi$
$984$	−1.46479	−	1.06423i	−0.0466957	−	0.0339264i
$985$	15.6890	+	11.3987i	0.499893	+	0.363193i
$986$	−2.54920	+	7.84564i	−0.0811831	+	0.249856i
$987$	−5.11403	−	15.7394i	−0.162781	−	0.500989i
$988$	92.6393	−	67.3064i	2.94725	−	2.14130i
$989$	−4.98892			−0.158638
$990$	13.2623	−	22.3772i	0.421503	−	0.711195i
$991$	−18.4676			−0.586643			−0.293322	−	0.956014i	$-0.594761\pi$
$991$	−18.4676			−0.586643			−0.293322	+	0.956014i	$0.594761\pi$
$992$	−64.1383	+	46.5992i	−2.03639	+	1.47953i
$993$	0.938102	+	2.88718i	0.0297698	+	0.0916219i
$994$	−4.44350	+	13.6757i	−0.140939	+	0.433766i
$995$	−24.9567	−	18.1321i	−0.791180	−	0.574826i
$996$	−27.4708	−	19.9587i	−0.870446	−	0.632416i
$997$	−9.16168	+	28.1968i	−0.290153	+	0.893000i	0.694653	+	0.719345i	$0.255558\pi$
$997$	−9.16168	+	28.1968i	−0.290153	+	0.893000i	−0.984806	+	0.173655i	$0.944442\pi$
$998$	−21.6136	−	66.5198i	−0.684167	−	2.10565i
$999$	26.9343	−	19.5689i	0.852165	−	0.619134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.g.e.69.1	✓	8
11.2	odd	10		2057.2.a.r.1.1		4
11.4	even	5	inner	187.2.g.e.103.1	yes	8
11.9	even	5		2057.2.a.u.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.g.e.69.1	✓	8	1.1	even	1	trivial
187.2.g.e.103.1	yes	8	11.4	even	5	inner
2057.2.a.r.1.1		4	11.2	odd	10
2057.2.a.u.1.4		4	11.9	even	5

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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.77460 + 1.28932i) q^{2} +(-0.227943 - 0.701538i) q^{3} +(0.868820 - 2.67395i) q^{4} +(-1.17784 - 0.855749i) q^{5} +(1.30902 + 0.951057i) q^{6} +(-0.986854 + 3.03722i) q^{7} +(0.550106 + 1.69305i) q^{8} +(1.98685 - 1.44353i) q^{9} +O(q^{10})\)	\(q+(-1.77460 + 1.28932i) q^{2} +(-0.227943 - 0.701538i) q^{3} +(0.868820 - 2.67395i) q^{4} +(-1.17784 - 0.855749i) q^{5} +(1.30902 + 0.951057i) q^{6} +(-0.986854 + 3.03722i) q^{7} +(0.550106 + 1.69305i) q^{8} +(1.98685 - 1.44353i) q^{9} +3.19353 q^{10} +(3.04508 - 1.31433i) q^{11} -2.07392 q^{12} +(4.56489 - 3.31659i) q^{13} +(-2.16469 - 6.66223i) q^{14} +(-0.331860 + 1.02136i) q^{15} +(1.39009 + 1.00996i) q^{16} +(0.809017 + 0.587785i) q^{17} +(-1.66469 + 5.12339i) q^{18} +(2.23049 + 6.86473i) q^{19} +(-3.31156 + 2.40599i) q^{20} +2.35567 q^{21} +(-3.70922 + 6.25850i) q^{22} -1.04944 q^{23} +(1.06235 - 0.771840i) q^{24} +(-0.890091 - 2.73942i) q^{25} +(-3.82471 + 11.7712i) q^{26} +(-3.25587 - 2.36553i) q^{27} +(7.26400 + 5.27760i) q^{28} +(1.16215 - 3.57672i) q^{29} +(-0.727943 - 2.24038i) q^{30} +(8.75085 - 6.35787i) q^{31} -7.32938 q^{32} +(-1.61616 - 1.83665i) q^{33} -2.19353 q^{34} +(3.76145 - 2.73286i) q^{35} +(-2.13372 - 6.56693i) q^{36} +(-2.55635 + 7.86765i) q^{37} +(-12.8091 - 9.30634i) q^{38} +(-3.36725 - 2.44645i) q^{39} +(0.800892 - 2.46489i) q^{40} +(-0.426079 - 1.31134i) q^{41} +(-4.18038 + 3.03722i) q^{42} +4.75389 q^{43} +(-0.868820 - 9.28433i) q^{44} -3.57549 q^{45} +(1.86233 - 1.35307i) q^{46} +(-2.17094 - 6.68146i) q^{47} +(0.391663 - 1.20541i) q^{48} +(-2.58773 - 1.88010i) q^{49} +(5.11155 + 3.71376i) q^{50} +(0.227943 - 0.701538i) q^{51} +(-4.90233 - 15.0878i) q^{52} +(-2.99030 + 2.17258i) q^{53} +8.82781 q^{54} +(-4.71135 - 1.05776i) q^{55} -5.68506 q^{56} +(4.30744 - 3.12954i) q^{57} +(2.54920 + 7.84564i) q^{58} +(-1.85445 + 5.70740i) q^{59} +(2.44274 + 1.77476i) q^{60} +(-8.15409 - 5.92429i) q^{61} +(-7.33193 + 22.5653i) q^{62} +(2.42360 + 7.45908i) q^{63} +(10.2265 - 7.43002i) q^{64} -8.21486 q^{65} +(5.23607 + 1.17557i) q^{66} -0.586654 q^{67} +(2.27460 - 1.65259i) q^{68} +(0.239213 + 0.736221i) q^{69} +(-3.15155 + 9.69946i) q^{70} +(-1.66068 - 1.20656i) q^{71} +(3.53696 + 2.56975i) q^{72} +(0.917955 - 2.82517i) q^{73} +(-5.60743 - 17.2579i) q^{74} +(-1.71891 + 1.24886i) q^{75} +20.2939 q^{76} +(0.986854 + 10.5457i) q^{77} +9.12978 q^{78} +(-7.73558 + 5.62022i) q^{79} +(-0.773028 - 2.37914i) q^{80} +(1.35938 - 4.18374i) q^{81} +(2.44686 + 1.77775i) q^{82} +(13.2458 + 9.62366i) q^{83} +(2.04666 - 6.29896i) q^{84} +(-0.449894 - 1.38463i) q^{85} +(-8.43626 + 6.12930i) q^{86} -2.77411 q^{87} +(3.90035 + 4.43247i) q^{88} +10.9131 q^{89} +(6.34507 - 4.60997i) q^{90} +(5.56834 + 17.1376i) q^{91} +(-0.911774 + 2.80615i) q^{92} +(-6.45498 - 4.68982i) q^{93} +(12.4671 + 9.05789i) q^{94} +(3.24734 - 9.99428i) q^{95} +(1.67068 + 5.14184i) q^{96} +(-5.51890 + 4.00972i) q^{97} +7.01625 q^{98} +(4.15286 - 7.00706i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q - q^2 + 3 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9	\( 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 2 q^{12} + 3 q^{13} - 10 q^{15} + 7 q^{16} + 2 q^{17} + 4 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{21} - 9 q^{22} - 24 q^{23} - 7 q^{24} - 3 q^{25} - 19 q^{26} + 3 q^{27} + 16 q^{28} + 10 q^{29} - q^{30} + 17 q^{31} - 24 q^{32} - 8 q^{33} - 4 q^{34} + 6 q^{35} - q^{36} - 13 q^{37} - 38 q^{38} - 11 q^{39} + 15 q^{40} - 22 q^{41} - 9 q^{42} + 8 q^{43} - 5 q^{44} - 24 q^{45} - 20 q^{46} + 9 q^{47} + 13 q^{48} + q^{49} - q^{50} - 3 q^{51} - 18 q^{52} - 23 q^{53} + 22 q^{54} - 12 q^{55} + 2 q^{56} + 16 q^{57} - 6 q^{58} - 35 q^{59} - q^{60} - 19 q^{61} - 6 q^{62} - 4 q^{63} + 8 q^{64} + 10 q^{65} + 24 q^{66} - 10 q^{67} + 5 q^{68} + 12 q^{69} + 3 q^{70} - 5 q^{71} + 19 q^{72} + 39 q^{73} - 7 q^{74} + 6 q^{75} + 32 q^{76} - 3 q^{77} + 6 q^{78} - 3 q^{79} + 21 q^{80} + 7 q^{81} - 5 q^{82} + 29 q^{83} + 8 q^{84} - 2 q^{85} - 14 q^{86} + 32 q^{87} + 9 q^{88} + 40 q^{89} + 9 q^{90} + 21 q^{91} + 12 q^{92} - 14 q^{93} + 40 q^{94} + 23 q^{95} - 12 q^{96} - 5 q^{97} + 30 q^{98} + 20 q^{99}+O(q^{100}) \) 8 * q - q^2 + 3 * q^3 + 5 * q^4 - 3 * q^5 + 6 * q^6 + 3 * q^7 + 6 * q^8 + 5 * q^9 + 12 * q^10 + 2 * q^11 + 2 * q^12 + 3 * q^13 - 10 * q^15 + 7 * q^16 + 2 * q^17 + 4 * q^18 - 5 * q^19 - 4 * q^20 + 6 * q^21 - 9 * q^22 - 24 * q^23 - 7 * q^24 - 3 * q^25 - 19 * q^26 + 3 * q^27 + 16 * q^28 + 10 * q^29 - q^30 + 17 * q^31 - 24 * q^32 - 8 * q^33 - 4 * q^34 + 6 * q^35 - q^36 - 13 * q^37 - 38 * q^38 - 11 * q^39 + 15 * q^40 - 22 * q^41 - 9 * q^42 + 8 * q^43 - 5 * q^44 - 24 * q^45 - 20 * q^46 + 9 * q^47 + 13 * q^48 + q^49 - q^50 - 3 * q^51 - 18 * q^52 - 23 * q^53 + 22 * q^54 - 12 * q^55 + 2 * q^56 + 16 * q^57 - 6 * q^58 - 35 * q^59 - q^60 - 19 * q^61 - 6 * q^62 - 4 * q^63 + 8 * q^64 + 10 * q^65 + 24 * q^66 - 10 * q^67 + 5 * q^68 + 12 * q^69 + 3 * q^70 - 5 * q^71 + 19 * q^72 + 39 * q^73 - 7 * q^74 + 6 * q^75 + 32 * q^76 - 3 * q^77 + 6 * q^78 - 3 * q^79 + 21 * q^80 + 7 * q^81 - 5 * q^82 + 29 * q^83 + 8 * q^84 - 2 * q^85 - 14 * q^86 + 32 * q^87 + 9 * q^88 + 40 * q^89 + 9 * q^90 + 21 * q^91 + 12 * q^92 - 14 * q^93 + 40 * q^94 + 23 * q^95 - 12 * q^96 - 5 * q^97 + 30 * q^98 + 20 * q^99

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