LMFDB - Embedded newform 585.2.i.h.196.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.14
Character	$\chi$	$=$	585.196
Dual form			585.2.i.h.391.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26258 - 2.18685i) q^{2} +(-0.259881 + 1.71244i) q^{3} +(-2.18820 - 3.79007i) q^{4} +(0.500000 + 0.866025i) q^{5} +(3.41673 + 2.73041i) q^{6} +(0.799357 - 1.38453i) q^{7} -6.00077 q^{8} +(-2.86492 - 0.890062i) q^{9} +O(q^{10})$	\(q+(1.26258 - 2.18685i) q^{2} +(-0.259881 + 1.71244i) q^{3} +(-2.18820 - 3.79007i) q^{4} +(0.500000 + 0.866025i) q^{5} +(3.41673 + 2.73041i) q^{6} +(0.799357 - 1.38453i) q^{7} -6.00077 q^{8} +(-2.86492 - 0.890062i) q^{9} +2.52515 q^{10} +(2.68984 - 4.65893i) q^{11} +(7.05895 - 2.76220i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-2.01850 - 3.49614i) q^{14} +(-1.61296 + 0.631158i) q^{15} +(-3.20003 + 5.54262i) q^{16} +3.08624 q^{17} +(-5.56361 + 5.14138i) q^{18} +3.72202 q^{19} +(2.18820 - 3.79007i) q^{20} +(2.16319 + 1.72867i) q^{21} +(-6.79225 - 11.7645i) q^{22} +(-0.847988 - 1.46876i) q^{23} +(1.55948 - 10.2760i) q^{24} +(-0.500000 + 0.866025i) q^{25} -2.52515 q^{26} +(2.26872 - 4.67471i) q^{27} -6.99661 q^{28} +(-0.320437 + 0.555014i) q^{29} +(-0.656238 + 4.32418i) q^{30} +(-2.79393 - 4.83923i) q^{31} +(2.07980 + 3.60232i) q^{32} +(7.27912 + 5.81696i) q^{33} +(3.89662 - 6.74914i) q^{34} +1.59871 q^{35} +(2.89563 + 12.8059i) q^{36} +0.445044 q^{37} +(4.69933 - 8.13948i) q^{38} +(1.61296 - 0.631158i) q^{39} +(-3.00038 - 5.19682i) q^{40} +(3.19674 + 5.53691i) q^{41} +(6.51151 - 2.54798i) q^{42} +(-2.82920 + 4.90031i) q^{43} -23.5436 q^{44} +(-0.661646 - 2.92613i) q^{45} -4.28260 q^{46} +(-5.70445 + 9.88040i) q^{47} +(-8.65979 - 6.92029i) q^{48} +(2.22206 + 3.84872i) q^{49} +(1.26258 + 2.18685i) q^{50} +(-0.802054 + 5.28501i) q^{51} +(-2.18820 + 3.79007i) q^{52} -10.3086 q^{53} +(-7.35844 - 10.8635i) q^{54} +5.37967 q^{55} +(-4.79676 + 8.30823i) q^{56} +(-0.967280 + 6.37374i) q^{57} +(0.809153 + 1.40149i) q^{58} +(4.67420 + 8.09595i) q^{59} +(5.92161 + 4.73213i) q^{60} +(3.23867 - 5.60954i) q^{61} -14.1102 q^{62} +(-3.52241 + 3.25509i) q^{63} -2.29649 q^{64} +(0.500000 - 0.866025i) q^{65} +(21.9112 - 8.57397i) q^{66} +(7.64188 + 13.2361i) q^{67} +(-6.75331 - 11.6971i) q^{68} +(2.73554 - 1.07043i) q^{69} +(2.01850 - 3.49614i) q^{70} -5.56344 q^{71} +(17.1917 + 5.34105i) q^{72} +11.7669 q^{73} +(0.561902 - 0.973242i) q^{74} +(-1.35308 - 1.08128i) q^{75} +(-8.14451 - 14.1067i) q^{76} +(-4.30028 - 7.44830i) q^{77} +(0.656238 - 4.32418i) q^{78} +(2.66045 - 4.60803i) q^{79} -6.40006 q^{80} +(7.41558 + 5.09992i) q^{81} +16.1445 q^{82} +(4.87457 - 8.44301i) q^{83} +(1.81828 - 11.9813i) q^{84} +(1.54312 + 2.67276i) q^{85} +(7.14415 + 12.3740i) q^{86} +(-0.867154 - 0.692968i) q^{87} +(-16.1411 + 27.9572i) q^{88} -15.7300 q^{89} +(-7.23437 - 2.24754i) q^{90} -1.59871 q^{91} +(-3.71114 + 6.42787i) q^{92} +(9.01300 - 3.52683i) q^{93} +(14.4046 + 24.9495i) q^{94} +(1.86101 + 3.22336i) q^{95} +(-6.70927 + 2.62537i) q^{96} +(0.456931 - 0.791428i) q^{97} +11.2221 q^{98} +(-11.8529 + 10.9534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) $ 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	1.26258	−	2.18685i	0.892776	−	1.54633i	0.0562438	−	0.998417i	$-0.482088\pi$
$2$	1.26258	−	2.18685i	0.892776	−	1.54633i	0.836533	−	0.547917i	$-0.184579\pi$
$3$	−0.259881	+	1.71244i	−0.150042	+	0.988680i
$3$	−0.259881	+	1.71244i	−0.150042	+	0.988680i
$4$	−2.18820	−	3.79007i	−1.09410	−	1.89504i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	3.41673	+	2.73041i	1.39487	+	1.11469i
$7$	0.799357	−	1.38453i	0.302129	−	0.523302i	−0.674489	−	0.738285i	$-0.735636\pi$
$7$	0.799357	−	1.38453i	0.302129	−	0.523302i	0.976618	+	0.214983i	$0.0689695\pi$
$8$	−6.00077			−2.12159
$9$	−2.86492	−	0.890062i	−0.954975	−	0.296687i
$10$	2.52515			0.798524
$11$	2.68984	−	4.65893i	0.811016	−	1.40472i	−0.101137	−	0.994872i	$-0.532248\pi$
$11$	2.68984	−	4.65893i	0.811016	−	1.40472i	0.912153	−	0.409849i	$-0.134419\pi$
$12$	7.05895	−	2.76220i	2.03774	−	0.797379i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	−2.01850	−	3.49614i	−0.539466	−	0.934383i
$15$	−1.61296	+	0.631158i	−0.416464	+	0.162964i
$16$	−3.20003	+	5.54262i	−0.800008	+	1.38565i
$17$	3.08624			0.748524			0.374262	−	0.927323i	$-0.377896\pi$
$17$	3.08624			0.748524			0.374262	+	0.927323i	$0.377896\pi$
$18$	−5.56361	+	5.14138i	−1.31136	+	1.21183i
$19$	3.72202			0.853889			0.426944	−	0.904278i	$-0.359590\pi$
$19$	3.72202			0.853889			0.426944	+	0.904278i	$0.359590\pi$
$20$	2.18820	−	3.79007i	0.489296	−	0.847486i
$21$	2.16319	+	1.72867i	0.472046	+	0.377226i
$22$	−6.79225	−	11.7645i	−1.44811	−	2.50820i
$23$	−0.847988	−	1.46876i	−0.176818	−	0.306257i	0.763971	−	0.645251i	$-0.223247\pi$
$23$	−0.847988	−	1.46876i	−0.176818	−	0.306257i	−0.940789	+	0.338993i	$0.889914\pi$
$24$	1.55948	−	10.2760i	0.318328	−	2.09757i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.52515			−0.495223
$27$	2.26872	−	4.67471i	0.436615	−	0.899648i
$28$	−6.99661			−1.32223
$29$	−0.320437	+	0.555014i	−0.0595037	+	0.103063i	−0.894243	−	0.447582i	$-0.852285\pi$
$29$	−0.320437	+	0.555014i	−0.0595037	+	0.103063i	0.834739	+	0.550646i	$0.185618\pi$
$30$	−0.656238	+	4.32418i	−0.119812	+	0.789484i
$31$	−2.79393	−	4.83923i	−0.501805	−	0.869152i	−0.999998	−	0.00208580i	$-0.999336\pi$
$31$	−2.79393	−	4.83923i	−0.501805	−	0.869152i	0.498193	−	0.867066i	$-0.333997\pi$
$32$	2.07980	+	3.60232i	0.367660	+	0.636807i
$33$	7.27912	+	5.81696i	1.26713	+	1.01260i
$34$	3.89662	−	6.74914i	0.668264	−	1.15747i
$35$	1.59871			0.270232
$36$	2.89563	+	12.8059i	0.482604	+	2.13432i
$37$	0.445044			0.0731647			0.0365824	−	0.999331i	$-0.488353\pi$
$37$	0.445044			0.0731647			0.0365824	+	0.999331i	$0.488353\pi$
$38$	4.69933	−	8.13948i	0.762332	−	1.32040i
$39$	1.61296	−	0.631158i	0.258280	−	0.101066i
$40$	−3.00038	−	5.19682i	−0.474402	−	0.821689i
$41$	3.19674	+	5.53691i	0.499246	+	0.864720i	1.00000		0.000870040i	$-0.000276942\pi$
$41$	3.19674	+	5.53691i	0.499246	+	0.864720i	−0.500753	+	0.865590i	$0.666944\pi$
$42$	6.51151	−	2.54798i	1.00475	−	0.393163i
$43$	−2.82920	+	4.90031i	−0.431448	+	0.747290i	−0.996998	−	0.0774237i	$-0.975331\pi$
$43$	−2.82920	+	4.90031i	−0.431448	+	0.747290i	0.565550	+	0.824714i	$0.308664\pi$
$44$	−23.5436			−3.54933
$45$	−0.661646	−	2.92613i	−0.0986324	−	0.436201i
$46$	−4.28260			−0.631435
$47$	−5.70445	+	9.88040i	−0.832080	+	1.44120i	0.0643062	+	0.997930i	$0.479517\pi$
$47$	−5.70445	+	9.88040i	−0.832080	+	1.44120i	−0.896386	+	0.443274i	$0.853817\pi$
$48$	−8.65979	−	6.92029i	−1.24993	−	0.998858i
$49$	2.22206	+	3.84872i	0.317437	+	0.549817i
$50$	1.26258	+	2.18685i	0.178555	+	0.309267i
$51$	−0.802054	+	5.28501i	−0.112310	+	0.740050i
$52$	−2.18820	+	3.79007i	−0.303449	+	0.525588i
$53$	−10.3086			−1.41600			−0.708000	−	0.706212i	$-0.750402\pi$
$53$	−10.3086			−1.41600			−0.708000	+	0.706212i	$0.750402\pi$
$54$	−7.35844	−	10.8635i	−1.00136	−	1.47834i
$55$	5.37967			0.725395
$56$	−4.79676	+	8.30823i	−0.640993	+	1.11023i
$57$	−0.967280	+	6.37374i	−0.128119	+	0.844222i
$58$	0.809153	+	1.40149i	0.106247	+	0.184025i
$59$	4.67420	+	8.09595i	0.608529	+	1.05400i	0.991483	+	0.130236i	$0.0415734\pi$
$59$	4.67420	+	8.09595i	0.608529	+	1.05400i	−0.382954	+	0.923767i	$0.625093\pi$
$60$	5.92161	+	4.73213i	0.764477	+	0.610916i
$61$	3.23867	−	5.60954i	0.414669	−	0.718228i	−0.580724	−	0.814100i	$-0.697231\pi$
$61$	3.23867	−	5.60954i	0.414669	−	0.718228i	0.995394	+	0.0958721i	$0.0305640\pi$
$62$	−14.1102			−1.79200
$63$	−3.52241	+	3.25509i	−0.443782	+	0.410102i
$64$	−2.29649			−0.287062
$65$	0.500000	−	0.866025i	0.0620174	−	0.107417i
$66$	21.9112	−	8.57397i	2.69709	−	1.05538i
$67$	7.64188	+	13.2361i	0.933604	+	1.61705i	0.777105	+	0.629371i	$0.216687\pi$
$67$	7.64188	+	13.2361i	0.933604	+	1.61705i	0.156498	+	0.987678i	$0.449979\pi$
$68$	−6.75331	−	11.6971i	−0.818959	−	1.41848i
$69$	2.73554	−	1.07043i	0.329321	−	0.128865i
$70$	2.01850	−	3.49614i	0.241257	−	0.417869i
$71$	−5.56344			−0.660258			−0.330129	−	0.943936i	$-0.607092\pi$
$71$	−5.56344			−0.660258			−0.330129	+	0.943936i	$0.607092\pi$
$72$	17.1917	+	5.34105i	2.02607	+	0.629449i
$73$	11.7669			1.37721			0.688604	−	0.725138i	$-0.258224\pi$
$73$	11.7669			1.37721			0.688604	+	0.725138i	$0.258224\pi$
$74$	0.561902	−	0.973242i	0.0653197	−	0.113137i
$75$	−1.35308	−	1.08128i	−0.156240	−	0.124856i
$76$	−8.14451	−	14.1067i	−0.934239	−	1.61815i
$77$	−4.30028	−	7.44830i	−0.490062	−	0.848813i
$78$	0.656238	−	4.32418i	0.0743044	−	0.489617i
$79$	2.66045	−	4.60803i	0.299324	−	0.518444i	−0.676658	−	0.736298i	$-0.736572\pi$
$79$	2.66045	−	4.60803i	0.299324	−	0.518444i	0.975981	+	0.217854i	$0.0699056\pi$
$80$	−6.40006			−0.715549
$81$	7.41558	+	5.09992i	0.823953	+	0.566658i
$82$	16.1445			1.78286
$83$	4.87457	−	8.44301i	0.535054	−	0.926741i	−0.464107	−	0.885779i	$-0.653625\pi$
$83$	4.87457	−	8.44301i	0.535054	−	0.926741i	0.999161	−	0.0409616i	$-0.0130421\pi$
$84$	1.81828	−	11.9813i	0.198391	−	1.30727i
$85$	1.54312	+	2.67276i	0.167375	+	0.289902i
$86$	7.14415	+	12.3740i	0.770374	+	1.33433i
$87$	−0.867154	−	0.692968i	−0.0929687	−	0.0742940i
$88$	−16.1411	+	27.9572i	−1.72065	+	2.98025i
$89$	−15.7300			−1.66737			−0.833687	−	0.552237i	$-0.813774\pi$
$89$	−15.7300			−1.66737			−0.833687	+	0.552237i	$0.813774\pi$
$90$	−7.23437	−	2.24754i	−0.762570	−	0.236912i
$91$	−1.59871			−0.167591
$92$	−3.71114	+	6.42787i	−0.386913	+	0.670152i
$93$	9.01300	−	3.52683i	0.934605	−	0.365715i
$94$	14.4046	+	24.9495i	1.48572	+	2.57335i
$95$	1.86101	+	3.22336i	0.190935	+	0.330710i
$96$	−6.70927	+	2.62537i	−0.684762	+	0.267951i
$97$	0.456931	−	0.791428i	0.0463943	−	0.0803573i	−0.841896	−	0.539640i	$-0.818560\pi$
$97$	0.456931	−	0.791428i	0.0463943	−	0.0803573i	0.888290	+	0.459283i	$0.151894\pi$
$98$	11.2221			1.13360
$99$	−11.8529	+	10.9534i	−1.19126	+	1.10086i
$100$	4.37640			0.437640
$101$	−2.91268	+	5.04491i	−0.289823	+	0.501988i	−0.973767	−	0.227546i	$-0.926930\pi$
$101$	−2.91268	+	5.04491i	−0.289823	+	0.501988i	0.683945	+	0.729534i	$0.260263\pi$
$102$	10.5449	+	8.42670i	1.04410	+	0.834368i
$103$	8.54446	+	14.7994i	0.841911	+	1.45823i	0.888277	+	0.459308i	$0.151902\pi$
$103$	8.54446	+	14.7994i	0.841911	+	1.45823i	−0.0463665	+	0.998924i	$0.514764\pi$
$104$	3.00038	+	5.19682i	0.294212	+	0.509590i
$105$	−0.415475	+	2.73771i	−0.0405462	+	0.267173i
$106$	−13.0154	+	22.5434i	−1.26417	+	2.18961i
$107$	6.04979			0.584855			0.292428	−	0.956288i	$-0.405537\pi$
$107$	6.04979			0.584855			0.292428	+	0.956288i	$0.405537\pi$
$108$	−22.6819	+	1.63059i	−2.18257	+	0.156904i
$109$	−3.64767			−0.349383			−0.174692	−	0.984623i	$-0.555893\pi$
$109$	−3.64767			−0.349383			−0.174692	+	0.984623i	$0.555893\pi$
$110$	6.79225	−	11.7645i	0.647616	−	1.12170i
$111$	−0.115658	+	0.762112i	−0.0109778	+	0.0723365i
$112$	5.11594	+	8.86106i	0.483410	+	0.837291i
$113$	−6.16716	−	10.6818i	−0.580158	−	1.00486i	−0.995460	−	0.0951792i	$-0.969658\pi$
$113$	−6.16716	−	10.6818i	−0.580158	−	1.00486i	0.415302	−	0.909683i	$-0.363676\pi$
$114$	12.7171	+	10.1626i	1.19107	+	0.951817i
$115$	0.847988	−	1.46876i	0.0790753	−	0.136962i
$116$	2.80472			0.260412
$117$	0.661646	+	2.92613i	0.0611692	+	0.270521i
$118$	23.6061			2.17312
$119$	2.46701	−	4.27298i	0.226150	−	0.391704i
$120$	9.67900	−	3.78744i	0.883568	−	0.345744i
$121$	−8.97044	−	15.5373i	−0.815495	−	1.41248i
$122$	−8.17814	−	14.1649i	−0.740414	−	1.28243i
$123$	−10.3124	+	4.03529i	−0.929839	+	0.363850i
$124$	−12.2274	+	21.1784i	−1.09805	+	1.90188i
$125$	−1.00000			−0.0894427
$126$	2.67106	+	11.8128i	0.237957	+	1.05237i
$127$	14.2039			1.26039			0.630197	−	0.776435i	$-0.282974\pi$
$127$	14.2039			1.26039			0.630197	+	0.776435i	$0.282974\pi$
$128$	−7.05910	+	12.2267i	−0.623942	+	1.08070i
$129$	−7.65625	−	6.11833i	−0.674095	−	0.538689i
$130$	−1.26258	−	2.18685i	−0.110735	−	0.191799i
$131$	−9.34730	−	16.1900i	−0.816678	−	1.41453i	−0.908117	−	0.418717i	$-0.862480\pi$
$131$	−9.34730	−	16.1900i	−0.816678	−	1.41453i	0.0914393	−	0.995811i	$-0.470853\pi$
$132$	6.11852	−	40.3171i	0.532549	−	3.50915i
$133$	2.97522	−	5.15323i	0.257984	−	0.446842i
$134$	38.5938			3.33400
$135$	5.18278	−	0.372587i	0.446062	−	0.0320672i
$136$	−18.5198			−1.58806
$137$	−6.92932	+	12.0019i	−0.592012	+	1.02539i	0.401950	+	0.915662i	$0.368333\pi$
$137$	−6.92932	+	12.0019i	−0.592012	+	1.02539i	−0.993961	+	0.109732i	$0.965001\pi$
$138$	1.11297	−	7.33371i	0.0947419	−	0.624287i
$139$	−3.26336	−	5.65230i	−0.276794	−	0.479422i	0.693792	−	0.720175i	$-0.255939\pi$
$139$	−3.26336	−	5.65230i	−0.276794	−	0.479422i	−0.970586	+	0.240754i	$0.922605\pi$
$140$	−3.49830	−	6.05924i	−0.295661	−	0.512099i
$141$	−15.4371	−	12.3363i	−1.30004	−	1.03890i
$142$	−7.02426	+	12.1664i	−0.589463	+	1.02098i
$143$	−5.37967			−0.449871
$144$	14.1011	−	13.0310i	1.17509	−	1.08591i
$145$	−0.640875			−0.0532217
$146$	14.8566	−	25.7323i	1.22954	−	2.12962i
$147$	−7.16818	+	2.80494i	−0.591221	+	0.231348i
$148$	−0.973844	−	1.68675i	−0.0800495	−	0.138650i
$149$	5.88878	+	10.1997i	0.482427	+	0.835589i	0.999796	−	0.0201737i	$-0.00642192\pi$
$149$	5.88878	+	10.1997i	0.482427	+	0.835589i	−0.517369	+	0.855762i	$0.673089\pi$
$150$	−4.07297	+	1.59377i	−0.332557	+	0.130131i
$151$	4.79569	−	8.30638i	0.390268	−	0.675964i	−0.602217	−	0.798332i	$-0.705716\pi$
$151$	4.79569	−	8.30638i	0.390268	−	0.675964i	0.992485	+	0.122369i	$0.0390491\pi$
$152$	−22.3350			−1.81160
$153$	−8.84185	−	2.74695i	−0.714821	−	0.222077i
$154$	−21.7177			−1.75006
$155$	2.79393	−	4.83923i	0.224414	−	0.388697i
$156$	−5.92161	−	4.73213i	−0.474108	−	0.378874i
$157$	−3.96466	−	6.86698i	−0.316414	−	0.548045i	0.663323	−	0.748333i	$-0.269146\pi$
$157$	−3.96466	−	6.86698i	−0.316414	−	0.548045i	−0.979737	+	0.200288i	$0.935812\pi$
$158$	−6.71804	−	11.6360i	−0.534458	−	0.925709i
$159$	2.67902	−	17.6530i	0.212460	−	1.39997i
$160$	−2.07980	+	3.60232i	−0.164423	+	0.284789i
$161$	−2.71138			−0.213687
$162$	20.5155	−	9.77770i	1.61185	−	0.768209i
$163$	−2.74092			−0.214685			−0.107343	−	0.994222i	$-0.534234\pi$
$163$	−2.74092			−0.214685			−0.107343	+	0.994222i	$0.534234\pi$
$164$	13.9902	−	24.2317i	1.09245	−	1.89218i
$165$	−1.39807	+	9.21239i	−0.108840	+	0.717183i
$166$	−12.3090	−	21.3199i	−0.955367	−	1.65474i
$167$	8.88551	+	15.3902i	0.687582	+	1.19093i	0.972618	+	0.232410i	$0.0746610\pi$
$167$	8.88551	+	15.3902i	0.687582	+	1.19093i	−0.285036	+	0.958517i	$0.592006\pi$
$168$	−12.9808	−	10.3733i	−1.00149	−	0.800319i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	7.79323			0.597714
$171$	−10.6633	−	3.31282i	−0.815442	−	0.253338i
$172$	24.7634			1.88819
$173$	−5.28655	+	9.15657i	−0.401929	+	0.696161i	−0.993959	−	0.109755i	$-0.964993\pi$
$173$	−5.28655	+	9.15657i	−0.401929	+	0.696161i	0.592030	+	0.805916i	$0.298327\pi$
$174$	−2.61026	+	1.02141i	−0.197884	+	0.0774327i
$175$	0.799357	+	1.38453i	0.0604257	+	0.104660i
$176$	17.2151	+	29.8175i	1.29764	+	2.24758i
$177$	−15.0786	+	5.90032i	−1.13338	+	0.443495i
$178$	−19.8603	+	34.3990i	−1.48859	+	2.57832i
$179$	5.47435			0.409172			0.204586	−	0.978849i	$-0.434415\pi$
$179$	5.47435			0.409172			0.204586	+	0.978849i	$0.434415\pi$
$180$	−9.64242	+	8.91064i	−0.718704	+	0.664160i
$181$	−1.35324			−0.100585			−0.0502927	−	0.998735i	$-0.516015\pi$
$181$	−1.35324			−0.100585			−0.0502927	+	0.998735i	$0.516015\pi$
$182$	−2.01850	+	3.49614i	−0.149621	+	0.259151i
$183$	8.76435	+	7.00385i	0.647880	+	0.517739i
$184$	5.08858	+	8.81368i	0.375135	+	0.649753i
$185$	0.222522	+	0.385419i	0.0163601	+	0.0283366i
$186$	3.66697	−	24.1630i	0.268876	−	1.77171i
$187$	8.30149	−	14.3786i	0.607065	−	1.05147i
$188$	49.9299			3.64151
$189$	−4.65875	−	6.87786i	−0.338874	−	0.500291i
$190$	9.39866			0.681850
$191$	−1.83277	+	3.17445i	−0.132615	+	0.229695i	−0.924684	−	0.380736i	$-0.875671\pi$
$191$	−1.83277	+	3.17445i	−0.132615	+	0.229695i	0.792069	+	0.610431i	$0.209004\pi$
$192$	0.596814	−	3.93262i	0.0430714	−	0.283812i
$193$	4.37529	+	7.57823i	0.314940	+	0.545493i	0.979425	−	0.201809i	$-0.0646821\pi$
$193$	4.37529	+	7.57823i	0.314940	+	0.545493i	−0.664484	+	0.747302i	$0.731349\pi$
$194$	−1.15382	−	1.99848i	−0.0828395	−	0.143482i
$195$	1.35308	+	1.08128i	0.0968960	+	0.0774324i
$196$	9.72461	−	16.8435i	0.694615	−	1.20311i
$197$	−9.50585			−0.677264			−0.338632	−	0.940919i	$-0.609964\pi$
$197$	−9.50585			−0.677264			−0.338632	+	0.940919i	$0.609964\pi$
$198$	8.98813	+	39.7500i	0.638758	+	2.82491i
$199$	25.5829			1.81353			0.906763	−	0.421640i	$-0.138545\pi$
$199$	25.5829			1.81353			0.906763	+	0.421640i	$0.138545\pi$
$200$	3.00038	−	5.19682i	0.212159	−	0.367471i
$201$	−24.6521	+	9.64647i	−1.73882	+	0.680409i
$202$	7.35497	+	12.7392i	0.517494	+	0.896326i
$203$	0.512288	+	0.887308i	0.0359555	+	0.0622768i
$204$	21.7856	−	8.52482i	1.52530	−	0.596857i
$205$	−3.19674	+	5.53691i	−0.223270	+	0.386715i
$206$	43.1521			3.00655
$207$	1.12214	+	4.96265i	0.0779939	+	0.344928i
$208$	6.40006			0.443765
$209$	10.0116	−	17.3406i	0.692518	−	1.19948i
$210$	5.46238	+	4.36514i	0.376940	+	0.301224i
$211$	2.59044	+	4.48678i	0.178333	+	0.308882i	0.941310	−	0.337544i	$-0.109596\pi$
$211$	2.59044	+	4.48678i	0.178333	+	0.308882i	−0.762976	+	0.646426i	$0.776263\pi$
$212$	22.5574	+	39.0705i	1.54925	+	2.68337i
$213$	1.44583	−	9.52707i	0.0990666	−	0.652784i
$214$	7.63832	−	13.2300i	0.522145	−	0.904381i
$215$	−5.65839			−0.385899
$216$	−13.6141	+	28.0519i	−0.926319	+	1.90869i
$217$	−8.93340			−0.606439
$218$	−4.60546	+	7.97689i	−0.311921	+	0.540263i
$219$	−3.05798	+	20.1501i	−0.206639	+	1.36162i
$220$	−11.7718	−	20.3893i	−0.793654	−	1.37465i
$221$	−1.54312	−	2.67276i	−0.103802	−	0.179790i
$222$	1.52059	+	1.21515i	0.102056	+	0.0815556i
$223$	−7.52975	+	13.0419i	−0.504230	+	0.873351i	0.495759	+	0.868460i	$0.334890\pi$
$223$	−7.52975	+	13.0419i	−0.504230	+	0.873351i	−0.999988	+	0.00489073i	$0.998443\pi$
$224$	6.65001			0.444323
$225$	2.20328	−	2.03607i	0.146885	−	0.135738i
$226$	−31.1461			−2.07180
$227$	−10.8699	+	18.8272i	−0.721459	+	1.24960i	0.238956	+	0.971030i	$0.423195\pi$
$227$	−10.8699	+	18.8272i	−0.721459	+	1.24960i	−0.960415	+	0.278573i	$0.910139\pi$
$228$	26.2735	−	10.2810i	1.74001	−	0.680873i
$229$	−13.5876	−	23.5344i	−0.897892	−	1.55520i	−0.830183	−	0.557490i	$-0.811764\pi$
$229$	−13.5876	−	23.5344i	−0.897892	−	1.55520i	−0.0677090	−	0.997705i	$-0.521569\pi$
$230$	−2.14130	−	3.70884i	−0.141193	−	0.244554i
$231$	13.8724	−	5.42831i	0.912734	−	0.357157i
$232$	1.92287	−	3.33051i	0.126243	−	0.218659i
$233$	24.1372			1.58128			0.790641	−	0.612280i	$-0.209747\pi$
$233$	24.1372			1.58128			0.790641	+	0.612280i	$0.209747\pi$
$234$	7.23437	+	2.24754i	0.472926	+	0.146926i
$235$	−11.4089			−0.744235
$236$	20.4562	−	35.4311i	1.33158	−	2.30637i
$237$	7.19959	+	5.75340i	0.467664	+	0.373724i
$238$	−6.22957	−	10.7899i	−0.403803	−	0.699408i
$239$	−8.64007	−	14.9650i	−0.558879	−	0.968008i	−0.997590	−	0.0693793i	$-0.977898\pi$
$239$	−8.64007	−	14.9650i	−0.558879	−	0.968008i	0.438711	−	0.898628i	$-0.355435\pi$
$240$	1.66325	−	10.9597i	0.107363	−	0.707449i
$241$	8.28251	−	14.3457i	0.533523	−	0.924090i	−0.465710	−	0.884938i	$-0.654201\pi$
$241$	8.28251	−	14.3457i	0.533523	−	0.924090i	0.999233	−	0.0391522i	$-0.0124657\pi$
$242$	−45.3035			−2.91222
$243$	−10.6605	+	11.3734i	−0.683871	+	0.729603i
$244$	−28.3474			−1.81476
$245$	−2.22206	+	3.84872i	−0.141962	+	0.245885i
$246$	−4.19564	+	27.6465i	−0.267504	+	1.76268i
$247$	−1.86101	−	3.22336i	−0.118413	−	0.205097i
$248$	16.7657	+	29.0391i	1.06463	+	1.84399i
$249$	13.1914	+	10.5416i	0.835969	+	0.668047i
$250$	−1.26258	+	2.18685i	−0.0798524	+	0.138308i
$251$	10.2182			0.644965			0.322482	−	0.946575i	$-0.395483\pi$
$251$	10.2182			0.644965			0.322482	+	0.946575i	$0.395483\pi$
$252$	20.0448	+	6.22741i	1.26270	+	0.392290i
$253$	−9.12380			−0.573608
$254$	17.9335	−	31.0618i	1.12525	−	1.94899i
$255$	−4.97798	+	1.94791i	−0.311733	+	0.121983i
$256$	15.5288	+	26.8967i	0.970551	+	1.68104i
$257$	−14.2157	−	24.6224i	−0.886754	−	1.53590i	−0.843690	−	0.536831i	$-0.819621\pi$
$257$	−14.2157	−	24.6224i	−0.886754	−	1.53590i	−0.0430639	−	0.999072i	$-0.513712\pi$
$258$	−23.0465	+	9.01818i	−1.43481	+	0.561448i
$259$	0.355749	−	0.616175i	0.0221051	−	0.0382872i
$260$	−4.37640			−0.271413
$261$	1.41203	−	1.30486i	0.0874022	−	0.0807690i
$262$	−47.2067			−2.91644
$263$	−6.62365	+	11.4725i	−0.408432	+	0.707425i	−0.994714	−	0.102682i	$-0.967258\pi$
$263$	−6.62365	+	11.4725i	−0.408432	+	0.707425i	0.586282	+	0.810107i	$0.300591\pi$
$264$	−43.6803	−	34.9062i	−2.68834	−	2.14833i
$265$	−5.15432	−	8.92754i	−0.316627	−	0.548415i
$266$	−7.51288	−	13.0127i	−0.460644	−	0.797859i
$267$	4.08792	−	26.9367i	0.250176	−	1.64850i
$268$	33.4439	−	57.9265i	2.04291	−	3.53842i
$269$	−20.2913			−1.23718			−0.618590	−	0.785714i	$-0.712296\pi$
$269$	−20.2913			−1.23718			−0.618590	+	0.785714i	$0.712296\pi$
$270$	5.72886	−	11.8044i	0.348647	−	0.718390i
$271$	−7.28275			−0.442396			−0.221198	−	0.975229i	$-0.570997\pi$
$271$	−7.28275			−0.442396			−0.221198	+	0.975229i	$0.570997\pi$
$272$	−9.87607	+	17.1059i	−0.598825	+	1.03719i
$273$	0.415475	−	2.73771i	0.0251457	−	0.165694i
$274$	17.4976	+	30.3067i	1.05707	+	1.83090i
$275$	2.68984	+	4.65893i	0.162203	+	0.280944i
$276$	−10.0429	−	8.02559i	−0.604513	−	0.483084i
$277$	−6.87279	+	11.9040i	−0.412946	+	0.715244i	−0.995210	−	0.0977558i	$-0.968834\pi$
$277$	−6.87279	+	11.9040i	−0.412946	+	0.715244i	0.582264	+	0.813000i	$0.302167\pi$
$278$	−16.4809			−0.988461
$279$	3.69719	+	16.3508i	0.221345	+	0.978898i
$280$	−9.59351			−0.573322
$281$	0.451460	−	0.781952i	0.0269318	−	0.0466473i	−0.852245	−	0.523142i	$-0.824760\pi$
$281$	0.451460	−	0.781952i	0.0269318	−	0.0466473i	0.879177	+	0.476495i	$0.158093\pi$
$282$	−46.4681	+	18.1832i	−2.76714	+	1.08279i
$283$	13.9264	+	24.1212i	0.827836	+	1.43385i	0.899732	+	0.436442i	$0.143762\pi$
$283$	13.9264	+	24.1212i	0.827836	+	1.43385i	−0.0718962	+	0.997412i	$0.522905\pi$
$284$	12.1739	+	21.0858i	0.722388	+	1.25121i
$285$	−6.00346	+	2.34918i	−0.355614	+	0.139153i
$286$	−6.79225	+	11.7645i	−0.401634	+	0.695651i
$287$	10.2213			0.603346
$288$	−2.75218	−	12.1715i	−0.162174	−	0.717214i
$289$	−7.47511			−0.439713
$290$	−0.809153	+	1.40149i	−0.0475151	+	0.0822986i
$291$	1.23653	+	0.988146i	0.0724866	+	0.0579261i
$292$	−25.7482	−	44.5973i	−1.50680	−	2.60986i
$293$	1.62563	+	2.81568i	0.0949706	+	0.164494i	0.909596	−	0.415493i	$-0.136391\pi$
$293$	1.62563	+	2.81568i	0.0949706	+	0.164494i	−0.814626	+	0.579987i	$0.803058\pi$
$294$	−2.91640	+	19.2172i	−0.170088	+	1.12077i
$295$	−4.67420	+	8.09595i	−0.272142	+	0.471364i
$296$	−2.67060			−0.155226
$297$	−15.6767	−	23.1440i	−0.909653	−	1.34295i
$298$	29.7401			1.72280
$299$	−0.847988	+	1.46876i	−0.0490404	+	0.0849405i
$300$	−1.13734	+	7.49433i	−0.0656644	+	0.432686i
$301$	4.52307	+	7.83419i	0.260706	+	0.451555i
$302$	−12.1099	−	20.9749i	−0.696844	−	1.20697i
$303$	−7.88218	−	6.29888i	−0.452819	−	0.361861i
$304$	−11.9106	+	20.6297i	−0.683118	+	1.18319i
$305$	6.47734			0.370891
$306$	−17.1707	+	15.8675i	−0.981581	+	0.907087i
$307$	23.0790			1.31719			0.658593	−	0.752499i	$-0.271152\pi$
$307$	23.0790			1.31719			0.658593	+	0.752499i	$0.271152\pi$
$308$	−18.8197	+	32.5967i	−1.07235	+	1.85737i
$309$	−27.5637	+	10.7858i	−1.56805	+	0.613584i
$310$	−7.05511	−	12.2198i	−0.400703	−	0.694038i
$311$	−3.23713	−	5.60687i	−0.183561	−	0.317936i	0.759530	−	0.650472i	$-0.225429\pi$
$311$	−3.23713	−	5.60687i	−0.183561	−	0.317936i	−0.943091	+	0.332536i	$0.892096\pi$
$312$	−9.67900	+	3.78744i	−0.547965	+	0.214421i
$313$	−3.92191	+	6.79296i	−0.221680	+	0.383961i	−0.955318	−	0.295580i	$-0.904487\pi$
$313$	−3.92191	+	6.79296i	−0.221680	+	0.383961i	0.733638	+	0.679540i	$0.237821\pi$
$314$	−20.0227			−1.12995
$315$	−4.58019	−	1.42295i	−0.258065	−	0.0801744i
$316$	−23.2864			−1.30996
$317$	15.8696	−	27.4870i	0.891326	−	1.54382i	0.0530394	−	0.998592i	$-0.483109\pi$
$317$	15.8696	−	27.4870i	0.891326	−	1.54382i	0.838287	−	0.545230i	$-0.183558\pi$
$318$	−35.2219	−	28.1468i	−1.97514	−	1.57839i
$319$	1.72385	+	2.98579i	0.0965170	+	0.167172i
$320$	−1.14825	−	1.98882i	−0.0641889	−	0.111179i
$321$	−1.57222	+	10.3599i	−0.0877529	+	0.578234i
$322$	−3.42333	+	5.92938i	−0.190775	+	0.330431i
$323$	11.4870			0.639156
$324$	3.10229	−	39.2652i	0.172350	−	2.18140i
$325$	1.00000			0.0554700
$326$	−3.46062	+	5.99396i	−0.191666	+	0.331975i
$327$	0.947958	−	6.24642i	0.0524222	−	0.345428i
$328$	−19.1829	−	33.2257i	−1.05920	−	1.83458i
$329$	9.11979	+	15.7959i	0.502790	+	0.870858i
$330$	18.3809	+	14.6887i	1.01184	+	0.808587i
$331$	−9.05397	+	15.6819i	−0.497651	+	0.861958i	−0.999996	−	0.00270979i	$-0.999137\pi$
$331$	−9.05397	+	15.6819i	−0.497651	+	0.861958i	0.502345	+	0.864667i	$0.332471\pi$
$332$	−42.6662			−2.34161
$333$	−1.27502	−	0.396116i	−0.0698704	−	0.0217070i
$334$	44.8746			2.45543
$335$	−7.64188	+	13.2361i	−0.417520	+	0.723166i
$336$	−16.5036	+	6.45793i	−0.900345	+	0.352309i
$337$	7.48318	+	12.9613i	0.407635	+	0.706044i	0.994624	−	0.103550i	$-0.0330203\pi$
$337$	7.48318	+	12.9613i	0.407635	+	0.706044i	−0.586989	+	0.809595i	$0.699687\pi$
$338$	1.26258	+	2.18685i	0.0686751	+	0.118949i
$339$	19.8948	−	7.78491i	1.08054	−	0.422818i
$340$	6.75331	−	11.6971i	0.366250	−	0.634363i
$341$	−30.0609			−1.62789
$342$	−20.7079	+	19.1363i	−1.11975	+	1.03477i
$343$	18.2959			0.987884
$344$	16.9773	−	29.4056i	0.915357	−	1.58545i
$345$	2.29479	+	1.83383i	0.123547	+	0.0987303i
$346$	13.3493	+	23.1217i	0.717665	+	1.24303i
$347$	−5.90574	−	10.2290i	−0.317037	−	0.549124i	0.662831	−	0.748769i	$-0.269355\pi$
$347$	−5.90574	−	10.2290i	−0.317037	−	0.549124i	−0.979868	+	0.199645i	$0.936021\pi$
$348$	−0.728893	+	4.80293i	−0.0390728	+	0.257464i
$349$	11.6750	−	20.2217i	0.624949	−	1.08244i	−0.363602	−	0.931555i	$-0.618453\pi$
$349$	11.6750	−	20.2217i	0.624949	−	1.08244i	0.988551	−	0.150889i	$-0.0482137\pi$
$350$	4.03700			0.215787
$351$	−5.18278	+	0.372587i	−0.276636	+	0.0198872i
$352$	22.3773			1.19271
$353$	−6.78898	+	11.7589i	−0.361341	+	0.625861i	−0.988182	−	0.153286i	$-0.951014\pi$
$353$	−6.78898	+	11.7589i	−0.361341	+	0.625861i	0.626841	+	0.779147i	$0.284348\pi$
$354$	−6.13478	+	40.4242i	−0.326060	+	2.14852i
$355$	−2.78172	−	4.81808i	−0.147638	−	0.255717i
$356$	34.4203	+	59.6177i	1.82427	+	3.15973i
$357$	6.67612	+	5.33508i	0.353337	+	0.282362i
$358$	6.91178	−	11.9716i	0.365299	−	0.632716i
$359$	−5.90809			−0.311817			−0.155908	−	0.987772i	$-0.549830\pi$
$359$	−5.90809			−0.311817			−0.155908	+	0.987772i	$0.549830\pi$
$360$	3.97038	+	17.5590i	0.209258	+	0.925441i
$361$	−5.14660			−0.270874
$362$	−1.70857	+	2.95932i	−0.0898003	+	0.155539i
$363$	28.9379	−	11.3235i	1.51885	−	0.594332i
$364$	3.49830	+	6.05924i	0.183361	+	0.317590i
$365$	5.88343	+	10.1904i	0.307953	+	0.533390i
$366$	26.3820	−	10.3234i	1.37901	−	0.539613i
$367$	1.22318	−	2.11861i	0.0638494	−	0.110590i	−0.832334	−	0.554275i	$-0.812996\pi$
$367$	1.22318	−	2.11861i	0.0638494	−	0.110590i	0.896183	+	0.443685i	$0.146329\pi$
$368$	10.8544			0.565823
$369$	−4.23022	−	18.7081i	−0.220216	−	0.973906i
$370$	1.12380			0.0584237
$371$	−8.24028	+	14.2726i	−0.427814	+	0.740996i
$372$	−33.0892	−	26.4425i	−1.71559	−	1.37098i
$373$	4.09993	+	7.10128i	0.212286	+	0.367690i	0.952430	−	0.304759i	$-0.0985758\pi$
$373$	4.09993	+	7.10128i	0.212286	+	0.367690i	−0.740143	+	0.672449i	$0.765242\pi$
$374$	−20.9625	−	36.3082i	−1.08395	−	1.87745i
$375$	0.259881	−	1.71244i	0.0134202	−	0.0884302i
$376$	34.2311	−	59.2900i	1.76533	−	3.05765i
$377$	0.640875			0.0330067
$378$	−20.9229	+	1.50413i	−1.07616	+	0.0773643i
$379$	−0.155663			−0.00799586			−0.00399793	−	0.999992i	$-0.501273\pi$
$379$	−0.155663			−0.00799586			−0.00399793	+	0.999992i	$0.501273\pi$
$380$	8.14451	−	14.1067i	0.417805	−	0.723659i
$381$	−3.69133	+	24.3234i	−0.189112	+	1.24613i
$382$	4.62802	+	8.01597i	0.236790	+	0.410133i
$383$	−8.30317	−	14.3815i	−0.424272	−	0.734861i	0.572080	−	0.820198i	$-0.306137\pi$
$383$	−8.30317	−	14.3815i	−0.424272	−	0.734861i	−0.996352	+	0.0853368i	$0.972803\pi$
$384$	−19.1030	−	15.2658i	−0.974848	−	0.779030i
$385$	4.30028	−	7.44830i	0.219163	−	0.379601i
$386$	22.0966			1.12469
$387$	12.4670	−	11.5209i	0.633734	−	0.585638i
$388$	−3.99943			−0.203040
$389$	−10.4497	+	18.0994i	−0.529819	+	0.917674i	0.469576	+	0.882892i	$0.344407\pi$
$389$	−10.4497	+	18.0994i	−0.529819	+	0.917674i	−0.999395	+	0.0347817i	$0.988926\pi$
$390$	4.07297	−	1.59377i	0.206243	−	0.0807038i
$391$	−2.61710	−	4.53295i	−0.132352	−	0.229241i
$392$	−13.3341	−	23.0953i	−0.673471	−	1.16649i
$393$	30.1536	−	11.7993i	1.52105	−	0.595194i
$394$	−12.0019	+	20.7878i	−0.604645	+	1.04728i
$395$	5.32090			0.267723
$396$	67.4506	+	20.9553i	3.38952	+	1.05304i
$397$	−15.5139			−0.778618			−0.389309	−	0.921107i	$-0.627286\pi$
$397$	−15.5139			−0.778618			−0.389309	+	0.921107i	$0.627286\pi$
$398$	32.3004	−	55.9460i	1.61907	−	2.80432i
$399$	8.05141	+	6.43412i	0.403075	+	0.322109i
$400$	−3.20003	−	5.54262i	−0.160002	−	0.277131i
$401$	−16.8282	−	29.1473i	−0.840360	−	1.45555i	−0.889590	−	0.456759i	$-0.849010\pi$
$401$	−16.8282	−	29.1473i	−0.840360	−	1.45555i	0.0492298	−	0.998787i	$-0.484323\pi$
$402$	−10.0298	+	66.0897i	−0.500240	+	3.29626i
$403$	−2.79393	+	4.83923i	−0.139176	+	0.241059i
$404$	25.4941			1.26838
$405$	−0.708869	+	8.97204i	−0.0352240	+	0.445824i
$406$	2.58721			0.128401
$407$	1.19709	−	2.07343i	0.0593378	−	0.102776i
$408$	4.81294	−	31.7141i	0.238276	−	1.57008i
$409$	−10.0723	−	17.4458i	−0.498044	−	0.862638i	0.501953	−	0.864895i	$-0.332615\pi$
$409$	−10.0723	−	17.4458i	−0.498044	−	0.862638i	−0.999997	+	0.00225691i	$0.999282\pi$
$410$	8.07225	+	13.9815i	0.398660	+	0.690499i
$411$	−18.7518	−	14.9851i	−0.924960	−	0.739162i
$412$	37.3940	−	64.7682i	1.84227	−	3.19090i
$413$	14.9454			0.735416
$414$	12.2693	+	3.81178i	0.603005	+	0.187339i
$415$	9.74915			0.478567
$416$	2.07980	−	3.60232i	0.101971	−	0.176618i
$417$	10.5273	−	4.11939i	0.515525	−	0.201727i
$418$	−25.2809	−	43.7877i	−1.23653	−	2.14173i
$419$	16.7215	+	28.9625i	0.816898	+	1.41491i	0.907957	+	0.419064i	$0.137642\pi$
$419$	16.7215	+	28.9625i	0.816898	+	1.41491i	−0.0910582	+	0.995846i	$0.529025\pi$
$420$	11.2852	−	4.41597i	0.550664	−	0.215477i
$421$	−13.1682	+	22.8081i	−0.641781	+	1.11160i	0.343254	+	0.939243i	$0.388471\pi$
$421$	−13.1682	+	22.8081i	−0.641781	+	1.11160i	−0.985035	+	0.172355i	$0.944862\pi$
$422$	13.0825			0.636847
$423$	25.1370	−	23.2293i	1.22220	−	1.12945i
$424$	61.8598			3.00418
$425$	−1.54312	+	2.67276i	−0.0748524	+	0.129648i
$426$	−19.0088	−	15.1905i	−0.920978	−	0.735980i
$427$	−5.17771	−	8.96805i	−0.250567	−	0.433994i
$428$	−13.2381	−	22.9291i	−0.639890	−	1.10832i
$429$	1.39807	−	9.21239i	0.0674996	−	0.444778i
$430$	−7.14415	+	12.3740i	−0.344522	+	0.596729i
$431$	10.7108			0.515922			0.257961	−	0.966155i	$-0.416949\pi$
$431$	10.7108			0.515922			0.257961	+	0.966155i	$0.416949\pi$
$432$	18.6502	+	27.5339i	0.897306	+	1.32472i
$433$	−10.5665			−0.507795			−0.253898	−	0.967231i	$-0.581713\pi$
$433$	−10.5665			−0.507795			−0.253898	+	0.967231i	$0.581713\pi$
$434$	−11.2791	+	19.5360i	−0.541414	+	0.937757i
$435$	0.166551	−	1.09746i	0.00798551	−	0.0526193i
$436$	7.98182	+	13.8249i	0.382260	+	0.662094i
$437$	−3.15623	−	5.46674i	−0.150983	−	0.261510i
$438$	40.2042	+	32.1284i	1.92103	+	1.53515i
$439$	16.9499	−	29.3581i	0.808975	−	1.40119i	−0.104599	−	0.994514i	$-0.533356\pi$
$439$	16.9499	−	29.3581i	0.808975	−	1.40119i	0.913574	−	0.406672i	$-0.133311\pi$
$440$	−32.2822			−1.53899
$441$	−2.94043	−	13.0040i	−0.140020	−	0.619240i
$442$	−7.79323			−0.370686
$443$	−14.7155	+	25.4881i	−0.699157	+	1.21097i	0.269603	+	0.962972i	$0.413108\pi$
$443$	−14.7155	+	25.4881i	−0.699157	+	1.21097i	−0.968759	+	0.248003i	$0.920226\pi$
$444$	3.14154	−	1.22930i	0.149091	−	0.0583400i
$445$	−7.86499	−	13.6226i	−0.372836	−	0.645771i
$446$	19.0138	+	32.9328i	0.900328	+	1.55941i
$447$	−18.9967	+	7.43350i	−0.898514	+	0.351593i
$448$	−1.83572	+	3.17956i	−0.0867295	+	0.150220i
$449$	37.6658			1.77756			0.888780	−	0.458335i	$-0.151554\pi$
$449$	37.6658			1.77756			0.888780	+	0.458335i	$0.151554\pi$
$450$	−1.67076	−	7.38892i	−0.0787603	−	0.348317i
$451$	34.3948			1.61959
$452$	−26.9900	+	46.7480i	−1.26950	+	2.19884i
$453$	12.9779	+	10.3710i	0.609755	+	0.487273i
$454$	27.4481	+	47.5415i	1.28820	+	2.23123i
$455$	−0.799357	−	1.38453i	−0.0374744	−	0.0649076i
$456$	5.80442	−	38.2473i	0.271817	−	1.79110i
$457$	15.9738	−	27.6674i	0.747223	−	1.29423i	−0.201926	−	0.979401i	$-0.564720\pi$
$457$	15.9738	−	27.6674i	0.747223	−	1.29423i	0.949149	−	0.314827i	$-0.101947\pi$
$458$	−68.6214			−3.20647
$459$	7.00181	−	14.4273i	0.326817	−	0.673408i
$460$	−7.42227			−0.346065
$461$	7.01569	−	12.1515i	0.326753	−	0.565953i	−0.655112	−	0.755531i	$-0.727379\pi$
$461$	7.01569	−	12.1515i	0.326753	−	0.565953i	0.981866	+	0.189578i	$0.0607121\pi$
$462$	5.64402	−	37.1904i	0.262583	−	1.73025i
$463$	−20.4647	−	35.4460i	−0.951077	−	1.64731i	−0.743101	−	0.669180i	$-0.766646\pi$
$463$	−20.4647	−	35.4460i	−0.951077	−	1.64731i	−0.207976	−	0.978134i	$-0.566688\pi$
$464$	−2.05082	−	3.55212i	−0.0952069	−	0.164903i
$465$	7.56083	+	6.04208i	0.350625	+	0.280195i
$466$	30.4751	−	52.7844i	1.41173	−	2.44519i
$467$	−4.20484			−0.194577			−0.0972884	−	0.995256i	$-0.531017\pi$
$467$	−4.20484			−0.194577			−0.0972884	+	0.995256i	$0.531017\pi$
$468$	9.64242	−	8.91064i	0.445721	−	0.411894i
$469$	24.4343			1.12827
$470$	−14.4046	+	24.9495i	−0.664435	+	1.15084i
$471$	12.7897	−	5.00465i	0.589316	−	0.230602i
$472$	−28.0488	−	48.5819i	−1.29105	−	2.23616i
$473$	15.2201	+	26.3621i	0.699823	+	1.21213i
$474$	21.6718	−	8.48029i	0.995421	−	0.389513i
$475$	−1.86101	+	3.22336i	−0.0853889	+	0.147898i
$476$	−21.5932			−0.989724
$477$	29.5335	+	9.17533i	1.35224	+	0.420109i
$478$	−43.6350			−1.99582
$479$	−13.2705	+	22.9851i	−0.606344	+	1.05022i	0.385494	+	0.922710i	$0.374031\pi$
$479$	−13.2705	+	22.9851i	−0.606344	+	1.05022i	−0.991838	+	0.127507i	$0.959302\pi$
$480$	−5.62827	−	4.49772i	−0.256894	−	0.205292i
$481$	−0.222522	−	0.385419i	−0.0101461	−	0.0175736i
$482$	−20.9146	−	36.2252i	−0.952634	−	1.65001i
$483$	0.704636	−	4.64309i	0.0320620	−	0.211268i
$484$	−39.2582	+	67.9972i	−1.78446	+	3.09078i
$485$	0.913862			0.0414963
$486$	11.4122	+	37.6726i	0.517667	+	1.70887i
$487$	29.2682			1.32627			0.663135	−	0.748500i	$-0.269225\pi$
$487$	29.2682			1.32627			0.663135	+	0.748500i	$0.269225\pi$
$488$	−19.4345	+	33.6616i	−0.879759	+	1.52379i
$489$	0.712311	−	4.69366i	0.0322118	−	0.212255i
$490$	5.61103	+	9.71860i	0.253481	+	0.439041i
$491$	−11.4610	−	19.8511i	−0.517229	−	0.895867i	−0.999800	−	0.0200103i	$-0.993630\pi$
$491$	−11.4610	−	19.8511i	−0.517229	−	0.895867i	0.482570	−	0.875857i	$-0.339703\pi$
$492$	37.8597	+	30.2548i	1.70685	+	1.36399i
$493$	−0.988947	+	1.71291i	−0.0445399	+	0.0771454i
$494$	−9.39866			−0.422866
$495$	−15.4124	−	4.78824i	−0.692734	−	0.215215i
$496$	35.7627			1.60579
$497$	−4.44717	+	7.70273i	−0.199483	+	0.345514i
$498$	39.7080	−	15.5379i	1.77936	−	0.696271i
$499$	−2.93038	−	5.07556i	−0.131182	−	0.227213i	0.792951	−	0.609286i	$-0.208544\pi$
$499$	−2.93038	−	5.07556i	−0.131182	−	0.227213i	−0.924132	+	0.382072i	$0.875210\pi$
$500$	2.18820	+	3.79007i	0.0978592	+	0.169497i
$501$	−28.6640	+	11.2163i	−1.28061	+	0.501109i
$502$	12.9012	−	22.3456i	0.575809	−	0.997331i
$503$	0.171544			0.00764877			0.00382439	−	0.999993i	$-0.498783\pi$
$503$	0.171544			0.00764877			0.00382439	+	0.999993i	$0.498783\pi$
$504$	21.1372	−	19.5330i	0.941525	−	0.870070i
$505$	−5.82536			−0.259225
$506$	−11.5195	+	19.9524i	−0.512104	+	0.886990i
$507$	−1.35308	−	1.08128i	−0.0600924	−	0.0480215i
$508$	−31.0810	−	53.8339i	−1.37900	−	2.38849i
$509$	18.2170	+	31.5528i	0.807454	+	1.39855i	0.914622	+	0.404311i	$0.132489\pi$
$509$	18.2170	+	31.5528i	0.807454	+	1.39855i	−0.107167	+	0.994241i	$0.534178\pi$
$510$	−2.02531	+	13.3455i	−0.0896823	+	0.590947i
$511$	9.40593	−	16.2915i	0.416094	−	0.720696i
$512$	50.1889			2.21806
$513$	8.44421	−	17.3993i	0.372821	−	0.768200i
$514$	−71.7939			−3.16669
$515$	−8.54446	+	14.7994i	−0.376514	+	0.652141i
$516$	−6.43552	+	42.4059i	−0.283308	+	1.86681i
$517$	30.6881	+	53.1533i	1.34966	+	2.33768i
$518$	−0.898320	−	1.55594i	−0.0394699	−	0.0683639i
$519$	−14.3062	−	11.4325i	−0.627974	−	0.501832i
$520$	−3.00038	+	5.19682i	−0.131576	+	0.227896i
$521$	6.99027			0.306249			0.153125	−	0.988207i	$-0.451066\pi$
$521$	6.99027			0.306249			0.153125	+	0.988207i	$0.451066\pi$
$522$	−1.07075	−	4.73537i	−0.0468653	−	0.207262i
$523$	10.2358			0.447579			0.223790	−	0.974637i	$-0.428157\pi$
$523$	10.2358			0.447579			0.223790	+	0.974637i	$0.428157\pi$
$524$	−40.9075	+	70.8539i	−1.78705	+	3.09527i
$525$	−2.57866	+	1.00904i	−0.112542	+	0.0440382i
$526$	16.7257	+	28.9698i	0.729277	+	1.26314i
$527$	−8.62275	−	14.9350i	−0.375613	−	0.650581i
$528$	−55.5346	+	21.7309i	−2.41683	+	0.945718i
$529$	10.0618	−	17.4276i	0.437471	−	0.757722i
$530$	−26.0309			−1.13071
$531$	−6.18533	−	27.3546i	−0.268420	−	1.18709i
$532$	−26.0415			−1.12904
$533$	3.19674	−	5.53691i	0.138466	−	0.239830i
$534$	−53.7451	−	42.9493i	−2.32578	−	1.85860i
$535$	3.02489	+	5.23927i	0.130778	+	0.226513i
$536$	−45.8571	−	79.4269i	−1.98073	−	3.43072i
$537$	−1.42268	+	9.37451i	−0.0613930	+	0.404540i
$538$	−25.6193	+	44.3739i	−1.10453	+	1.91309i
$539$	23.9079			1.02979
$540$	−12.7531	−	18.8278i	−0.548805	−	0.810220i
$541$	−14.1128			−0.606755			−0.303378	−	0.952870i	$-0.598114\pi$
$541$	−14.1128			−0.606755			−0.303378	+	0.952870i	$0.598114\pi$
$542$	−9.19503	+	15.9263i	−0.394960	+	0.684092i
$543$	0.351680	−	2.31734i	0.0150920	−	0.0994467i
$544$	6.41877	+	11.1176i	0.275202	+	0.476665i
$545$	−1.82383	−	3.15897i	−0.0781244	−	0.135316i
$546$	−5.46238	−	4.36514i	−0.233768	−	0.186811i
$547$	3.24835	−	5.62631i	0.138890	−	0.240564i	−0.788187	−	0.615436i	$-0.788980\pi$
$547$	3.24835	−	5.62631i	0.138890	−	0.240564i	0.927077	+	0.374872i	$0.122313\pi$
$548$	60.6509			2.59088
$549$	−14.2714	+	13.1883i	−0.609088	+	0.562863i
$550$	13.5845			0.579245
$551$	−1.19267	+	2.06577i	−0.0508096	+	0.0880047i
$552$	−16.4154	+	6.42340i	−0.698684	+	0.273398i
$553$	−4.25329	−	7.36692i	−0.180868	−	0.313273i
$554$	17.3549	+	30.0595i	0.737337	+	1.27711i
$555$	−0.717837	+	0.280893i	−0.0304705	+	0.0119232i
$556$	−14.2817	+	24.7367i	−0.605681	+	1.04907i
$557$	13.7471			0.582483			0.291242	−	0.956650i	$-0.405932\pi$
$557$	13.7471			0.582483			0.291242	+	0.956650i	$0.405932\pi$
$558$	40.4247	+	12.5590i	1.71131	+	0.531663i
$559$	5.65839			0.239324
$560$	−5.11594	+	8.86106i	−0.216188	+	0.374448i
$561$	22.4651	+	17.9525i	0.948479	+	0.757957i
$562$	−1.14001	−	1.97455i	−0.0480882	−	0.0832913i
$563$	−0.645415	−	1.11789i	−0.0272010	−	0.0471135i	0.852104	−	0.523372i	$-0.175326\pi$
$563$	−0.645415	−	1.11789i	−0.0272010	−	0.0471135i	−0.879305	+	0.476258i	$0.841993\pi$
$564$	−12.9758	+	85.5021i	−0.546380	+	3.60029i
$565$	6.16716	−	10.6818i	0.259454	−	0.449388i
$566$	70.3324			2.95629
$567$	12.9887	−	6.19041i	0.545473	−	0.259973i
$568$	33.3849			1.40080
$569$	−5.81243	+	10.0674i	−0.243670	+	0.422048i	−0.961757	−	0.273905i	$-0.911685\pi$
$569$	−5.81243	+	10.0674i	−0.243670	+	0.422048i	0.718087	+	0.695953i	$0.245018\pi$
$570$	−2.44253	+	16.0947i	−0.102306	+	0.674132i
$571$	8.88874	+	15.3958i	0.371982	+	0.644292i	0.989870	−	0.141974i	$-0.0453449\pi$
$571$	8.88874	+	15.3958i	0.371982	+	0.644292i	−0.617888	+	0.786266i	$0.712012\pi$
$572$	11.7718	+	20.3893i	0.492203	+	0.852521i
$573$	−4.95976	−	3.96349i	−0.207197	−	0.165577i
$574$	12.9052	−	22.3525i	0.538653	−	0.932975i
$575$	1.69598			0.0707271
$576$	6.57928	+	2.04402i	0.274137	+	0.0851675i
$577$	−30.0210			−1.24979			−0.624896	−	0.780708i	$-0.714859\pi$
$577$	−30.0210			−1.24979			−0.624896	+	0.780708i	$0.714859\pi$
$578$	−9.43790	+	16.3469i	−0.392565	+	0.679942i
$579$	−14.1143	+	5.52300i	−0.586572	+	0.229528i
$580$	1.40236	+	2.42896i	0.0582299	+	0.100857i
$581$	−7.79305	−	13.4980i	−0.323310	−	0.559990i
$582$	3.72213	−	1.45649i	0.154287	−	0.0603734i
$583$	−27.7286	+	48.0273i	−1.14840	+	1.98909i
$584$	−70.6103			−2.92187
$585$	−2.20328	+	2.03607i	−0.0910943	+	0.0841810i
$586$	8.20995			0.339150
$587$	1.10857	−	1.92010i	0.0457556	−	0.0792510i	−0.842241	−	0.539102i	$-0.818764\pi$
$587$	1.10857	−	1.92010i	0.0457556	−	0.0792510i	0.887996	+	0.459851i	$0.152097\pi$
$588$	26.3163	+	21.0301i	1.08527	+	0.867268i
$589$	−10.3991	−	18.0117i	−0.428486	−	0.742159i
$590$	11.8031	+	20.4435i	0.485925	+	0.841646i
$591$	2.47039	−	16.2782i	0.101618	−	0.669597i
$592$	−1.42415	+	2.46671i	−0.0585323	+	0.101381i
$593$	15.6211			0.641483			0.320742	−	0.947167i	$-0.396068\pi$
$593$	15.6211			0.641483			0.320742	+	0.947167i	$0.396068\pi$
$594$	−70.4054	+	5.06141i	−2.88877	+	0.207672i
$595$	4.93402			0.202275
$596$	25.7716	−	44.6378i	1.05565	−	1.82843i
$597$	−6.64851	+	43.8093i	−0.272105	+	1.79300i
$598$	2.14130	+	3.70884i	0.0875643	+	0.151666i
$599$	−11.5585	−	20.0200i	−0.472269	−	0.817994i	0.527227	−	0.849724i	$-0.323232\pi$
$599$	−11.5585	−	20.0200i	−0.472269	−	0.817994i	−0.999496	+	0.0317303i	$0.989898\pi$
$600$	8.11951	+	6.48854i	0.331478	+	0.264894i
$601$	1.70480	−	2.95280i	0.0695402	−	0.120447i	−0.829159	−	0.559013i	$-0.811180\pi$
$601$	1.70480	−	2.95280i	0.0695402	−	0.120447i	0.898699	+	0.438566i	$0.144513\pi$
$602$	22.8429			0.931007
$603$	−10.1124	−	44.7222i	−0.411810	−	1.82123i
$604$	−41.9757			−1.70797
$605$	8.97044	−	15.5373i	0.364700	−	0.631679i
$606$	−23.7265	+	9.28430i	−0.963825	+	0.377149i
$607$	−10.5060	−	18.1970i	−0.426427	−	0.738593i	0.570126	−	0.821558i	$-0.306895\pi$
$607$	−10.5060	−	18.1970i	−0.426427	−	0.738593i	−0.996553	+	0.0829645i	$0.973561\pi$
$608$	7.74105	+	13.4079i	0.313941	+	0.543762i
$609$	−1.65260	+	0.646669i	−0.0669667	+	0.0262044i
$610$	8.17814	−	14.1649i	0.331123	−	0.573522i
$611$	11.4089			0.461555
$612$	8.93660	+	39.5221i	0.361241	+	1.59759i
$613$	4.34045			0.175309			0.0876546	−	0.996151i	$-0.472063\pi$
$613$	4.34045			0.175309			0.0876546	+	0.996151i	$0.472063\pi$
$614$	29.1390	−	50.4702i	1.17595	−	2.03681i
$615$	−8.65087	−	6.91317i	−0.348837	−	0.278766i
$616$	25.8050	+	44.6955i	1.03971	+	1.80083i
$617$	−12.3921	−	21.4637i	−0.498887	−	0.864098i	0.501112	−	0.865382i	$-0.332924\pi$
$617$	−12.3921	−	21.4637i	−0.498887	−	0.864098i	−0.999999	+	0.00128460i	$0.999591\pi$
$618$	−11.2144	+	73.8956i	−0.451110	+	2.97252i
$619$	−17.4471	+	30.2193i	−0.701258	+	1.21461i	0.266767	+	0.963761i	$0.414045\pi$
$619$	−17.4471	+	30.2193i	−0.701258	+	1.21461i	−0.968025	+	0.250853i	$0.919289\pi$
$620$	−24.4547			−0.982126
$621$	−8.78987	+	0.631899i	−0.352725	+	0.0253572i
$622$	−16.3485			−0.655514
$623$	−12.5739	+	21.7786i	−0.503761	+	0.872540i
$624$	−1.66325	+	10.9597i	−0.0665834	+	0.438741i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	9.90343	+	17.1533i	0.395821	+	0.685582i
$627$	27.0930	+	21.6508i	1.08199	+	0.864650i
$628$	−17.3509	+	30.0527i	−0.692377	+	1.19923i
$629$	1.37351			0.0547655
$630$	−8.89463	+	8.21959i	−0.354370	+	0.327476i
$631$	−27.9002			−1.11069			−0.555344	−	0.831620i	$-0.687414\pi$
$631$	−27.9002			−1.11069			−0.555344	+	0.831620i	$0.687414\pi$
$632$	−15.9647	+	27.6517i	−0.635043	+	1.09993i
$633$	−8.35656	+	3.26996i	−0.332143	+	0.129969i
$634$	−40.0732	−	69.4088i	−1.59151	−	2.75658i
$635$	7.10196	+	12.3010i	0.281833	+	0.488149i
$636$	−72.7682	+	28.4745i	−2.88545	+	1.12909i
$637$	2.22206	−	3.84872i	0.0880411	−	0.152492i
$638$	8.70596			0.344672
$639$	15.9388	+	4.95180i	0.630530	+	0.195890i
$640$	−14.1182			−0.558071
$641$	−1.63649	+	2.83448i	−0.0646374	+	0.111955i	−0.896533	−	0.442977i	$-0.853922\pi$
$641$	−1.63649	+	2.83448i	−0.0646374	+	0.111955i	0.831896	+	0.554932i	$0.187256\pi$
$642$	20.6705	+	16.5184i	0.815800	+	0.651929i
$643$	−17.2981	−	29.9612i	−0.682170	−	1.18155i	−0.974317	−	0.225179i	$-0.927703\pi$
$643$	−17.2981	−	29.9612i	−0.682170	−	1.18155i	0.292148	−	0.956373i	$-0.405630\pi$
$644$	5.93304	+	10.2763i	0.233795	+	0.404944i
$645$	1.47051	−	9.68967i	0.0579011	−	0.381531i
$646$	14.5033	−	25.1204i	0.570623	−	0.988349i
$647$	32.2974			1.26974			0.634871	−	0.772618i	$-0.281053\pi$
$647$	32.2974			1.26974			0.634871	+	0.772618i	$0.281053\pi$
$648$	−44.4992	−	30.6034i	−1.74809	−	1.20222i
$649$	50.2913			1.97411
$650$	1.26258	−	2.18685i	0.0495223	−	0.0857752i
$651$	2.32162	−	15.2979i	0.0909914	−	0.599574i
$652$	5.99767	+	10.3883i	0.234887	+	0.406836i
$653$	−17.7871	−	30.8081i	−0.696062	−	1.20561i	−0.969821	−	0.243816i	$-0.921601\pi$
$653$	−17.7871	−	30.8081i	−0.696062	−	1.20561i	0.273760	−	0.961798i	$-0.411733\pi$
$654$	−12.4631	−	9.95963i	−0.487346	−	0.389452i
$655$	9.34730	−	16.1900i	0.365229	−	0.632596i
$656$	−40.9186			−1.59760
$657$	−33.7112	−	10.4732i	−1.31520	−	0.408600i
$658$	46.0577			1.79552
$659$	15.0300	−	26.0327i	0.585484	−	1.01409i	−0.409330	−	0.912386i	$-0.634238\pi$
$659$	15.0300	−	26.0327i	0.585484	−	1.01409i	0.994815	−	0.101703i	$-0.0324290\pi$
$660$	37.9749	−	14.8597i	1.47817	−	0.578414i
$661$	−2.58617	−	4.47938i	−0.100590	−	0.174228i	0.811338	−	0.584578i	$-0.198740\pi$
$661$	−2.58617	−	4.47938i	−0.100590	−	0.174228i	−0.911928	+	0.410350i	$0.865407\pi$
$662$	22.8627	+	39.5993i	0.888583	+	1.53907i
$663$	4.97798	−	1.94791i	0.193329	−	0.0756505i
$664$	−29.2512	+	50.6646i	−1.13517	+	1.96617i
$665$	5.95044			0.230748
$666$	−2.47605	+	2.28814i	−0.0959450	+	0.0886635i
$667$	1.08691			0.0420853
$668$	38.8865	−	67.3535i	1.50457	−	2.60598i
$669$	−20.3767	−	16.2836i	−0.787809	−	0.629561i
$670$	19.2969	+	33.4232i	0.745504	+	1.29125i
$671$	−17.4230	−	30.1775i	−0.672607	−	1.16499i
$672$	−1.72821	+	11.3878i	−0.0666672	+	0.439293i
$673$	−5.71413	+	9.89716i	−0.220263	+	0.381507i	−0.954888	−	0.296967i	$-0.904025\pi$
$673$	−5.71413	+	9.89716i	−0.220263	+	0.381507i	0.734624	+	0.678474i	$0.237358\pi$
$674$	37.7924			1.45571
$675$	2.91406	+	4.30212i	0.112162	+	0.165589i
$676$	4.37640			0.168323
$677$	4.25402	−	7.36818i	0.163495	−	0.283182i	−0.772625	−	0.634863i	$-0.781056\pi$
$677$	4.25402	−	7.36818i	0.163495	−	0.283182i	0.936120	+	0.351681i	$0.114390\pi$
$678$	8.09426	−	53.3358i	0.310858	−	2.04835i
$679$	−0.730502	−	1.26527i	−0.0280341	−	0.0485565i
$680$	−9.25991	−	16.0386i	−0.355101	−	0.615054i
$681$	−29.4156	−	23.5069i	−1.12721	−	0.900785i
$682$	−37.9542	+	65.7386i	−1.45334	+	2.51726i
$683$	−17.6393			−0.674947			−0.337474	−	0.941335i	$-0.609572\pi$
$683$	−17.6393			−0.674947			−0.337474	+	0.941335i	$0.609572\pi$
$684$	10.7776	+	47.6638i	0.412090	+	1.82247i
$685$	−13.8586			−0.529511
$686$	23.0999	−	40.0102i	0.881959	−	1.52760i
$687$	43.8324	−	17.1518i	1.67231	−	0.654383i
$688$	−18.1070	−	31.3623i	−0.690324	−	1.19568i
$689$	5.15432	+	8.92754i	0.196364	+	0.340112i
$690$	6.90766	−	2.70300i	0.262970	−	0.102901i
$691$	−17.4651	+	30.2505i	−0.664404	+	1.15078i	0.315042	+	0.949078i	$0.397981\pi$
$691$	−17.4651	+	30.2505i	−0.664404	+	1.15078i	−0.979447	+	0.201704i	$0.935352\pi$
$692$	46.2721			1.75900
$693$	5.69052	+	25.1663i	0.216165	+	0.955990i
$694$	−29.8258			−1.13217
$695$	3.26336	−	5.65230i	0.123786	−	0.214404i
$696$	5.20359	+	4.15834i	0.197242	+	0.157622i
$697$	9.86590	+	17.0882i	0.373698	+	0.647263i
$698$	−29.4812	−	51.0629i	−1.11588	−	1.93276i
$699$	−6.27280	+	41.3336i	−0.237259	+	1.56338i
$700$	3.49830	−	6.05924i	0.132223	−	0.229018i
$701$	−49.5629			−1.87197			−0.935983	−	0.352045i	$-0.885486\pi$
$701$	−49.5629			−1.87197			−0.935983	+	0.352045i	$0.885486\pi$
$702$	−5.72886	+	11.8044i	−0.216222	+	0.445527i
$703$	1.65646			0.0624745
$704$	−6.17719	+	10.6992i	−0.232812	+	0.403242i
$705$	2.96495	−	19.5371i	0.111667	−	0.735810i
$706$	17.1432	+	29.6929i	0.645194	+	1.11751i
$707$	4.65655	+	8.06537i	0.175127	+	0.303330i
$708$	55.3576	+	44.2379i	2.08047	+	1.66256i
$709$	−18.0806	+	31.3165i	−0.679031	+	1.17612i	0.296243	+	0.955113i	$0.404266\pi$
$709$	−18.0806	+	31.3165i	−0.679031	+	1.17612i	−0.975273	+	0.221003i	$0.929067\pi$
$710$	−14.0485			−0.527232
$711$	−11.7234	+	10.8337i	−0.439662	+	0.406295i
$712$	94.3919			3.53749
$713$	−4.73845	+	8.20723i	−0.177456	+	0.307363i
$714$	20.0961	−	7.86370i	0.752078	−	0.294291i
$715$	−2.68984	−	4.65893i	−0.100594	−	0.174234i
$716$	−11.9790	−	20.7482i	−0.447675	−	0.775395i
$717$	27.8722	−	10.9065i	1.04090	−	0.407311i
$718$	−7.45941	+	12.9201i	−0.278383	+	0.482173i
$719$	21.1195			0.787624			0.393812	−	0.919191i	$-0.371156\pi$
$719$	21.1195			0.787624			0.393812	+	0.919191i	$0.371156\pi$
$720$	18.3357	+	5.69645i	0.683331	+	0.212294i
$721$	27.3203			1.01746
$722$	−6.49798	+	11.2548i	−0.241830	+	0.418861i
$723$	22.4138	+	17.9115i	0.833578	+	0.666136i
$724$	2.96115	+	5.12887i	0.110050	+	0.190613i
$725$	−0.320437	−	0.555014i	−0.0119007	−	0.0206127i
$726$	11.7735	−	77.5796i	0.436955	−	2.87925i
$727$	13.6302	−	23.6081i	0.505515	−	0.875577i	−0.494465	−	0.869198i	$-0.664636\pi$
$727$	13.6302	−	23.6081i	0.505515	−	0.875577i	0.999980	−	0.00637961i	$-0.00203071\pi$
$728$	9.59351			0.355559
$729$	−16.7058	−	21.2112i	−0.618734	−	0.785600i
$730$	29.7131			1.09973
$731$	−8.73158	+	15.1235i	−0.322949	+	0.559364i
$732$	7.36695	−	48.5433i	0.272290	−	1.79421i
$733$	5.80668	+	10.0575i	0.214474	+	0.371481i	0.953110	−	0.302624i	$-0.0978628\pi$
$733$	5.80668	+	10.0575i	0.214474	+	0.371481i	−0.738635	+	0.674105i	$0.764529\pi$
$734$	−3.08871	−	5.34981i	−0.114006	−	0.197465i
$735$	−6.01324	−	4.80535i	−0.221802	−	0.177248i
$736$	3.52730	−	6.10945i	0.130018	−	0.225197i
$737$	82.2216			3.02867
$738$	−46.2528	−	14.3696i	−1.70259	−	0.528952i
$739$	42.9401			1.57958			0.789788	−	0.613380i	$-0.210191\pi$
$739$	42.9401			1.57958			0.789788	+	0.613380i	$0.210191\pi$
$740$	0.973844	−	1.68675i	0.0357992	−	0.0620061i
$741$	6.00346	−	2.34918i	0.220543	−	0.0862993i
$742$	20.8080	+	36.0405i	0.763885	+	1.32309i
$743$	17.3555	+	30.0606i	0.636711	+	1.10282i	0.986150	+	0.165856i	$0.0530388\pi$
$743$	17.3555	+	30.0606i	0.636711	+	1.10282i	−0.349439	+	0.936959i	$0.613628\pi$
$744$	−54.0850	+	21.1637i	−1.98285	+	0.775898i
$745$	−5.88878	+	10.1997i	−0.215748	+	0.373687i
$746$	20.7059			0.758096
$747$	−21.4801	+	19.8499i	−0.785915	+	0.726270i
$748$	−72.6612			−2.65676
$749$	4.83594	−	8.37609i	0.176701	−	0.306056i
$750$	−3.41673	−	2.73041i	−0.124761	−	0.0997005i
$751$	−0.655127	−	1.13471i	−0.0239059	−	0.0414062i	0.853825	−	0.520560i	$-0.174277\pi$
$751$	−0.655127	−	1.13471i	−0.0239059	−	0.0414062i	−0.877731	+	0.479154i	$0.840944\pi$
$752$	−36.5089	−	63.2352i	−1.33134	−	2.30595i
$753$	−2.65550	+	17.4980i	−0.0967719	+	0.637663i
$754$	0.809153	−	1.40149i	0.0294676	−	0.0510394i
$755$	9.59138			0.349066
$756$	−15.8733	+	32.7071i	−0.577308	+	1.18955i
$757$	1.73705			0.0631343			0.0315671	−	0.999502i	$-0.489950\pi$
$757$	1.73705			0.0631343			0.0315671	+	0.999502i	$0.489950\pi$
$758$	−0.196536	+	0.340411i	−0.00713852	+	0.0123643i
$759$	2.37110	−	15.6240i	0.0860655	−	0.567115i
$760$	−11.1675	−	19.3426i	−0.405087	−	0.701631i
$761$	9.10484	+	15.7700i	0.330050	+	0.571663i	0.982521	−	0.186150i	$-0.0596010\pi$
$761$	9.10484	+	15.7700i	0.330050	+	0.571663i	−0.652471	+	0.757813i	$0.726268\pi$
$762$	48.5310	+	38.7825i	1.75809	+	1.40494i
$763$	−2.91579	+	5.05029i	−0.105559	+	0.182833i
$764$	16.0419			0.580374
$765$	−2.04200	−	9.03074i	−0.0738286	−	0.326507i
$766$	−41.9336			−1.51512
$767$	4.67420	−	8.09595i	0.168776	−	0.292328i
$768$	−50.0947	+	19.6023i	−1.80764	+	0.707337i
$769$	−20.5593	−	35.6098i	−0.741388	−	1.28412i	−0.951863	−	0.306523i	$-0.900834\pi$
$769$	−20.5593	−	35.6098i	−0.741388	−	1.28412i	0.210475	−	0.977599i	$-0.432499\pi$
$770$	−10.8589	−	18.8081i	−0.391326	−	0.677797i
$771$	45.8589	−	17.9448i	1.65157	−	0.646265i
$772$	19.1480	−	33.1653i	0.689152	−	1.19365i
$773$	21.2243			0.763384			0.381692	−	0.924290i	$-0.375342\pi$
$773$	21.2243			0.763384			0.381692	+	0.924290i	$0.375342\pi$
$774$	−9.45380	−	41.8094i	−0.339810	−	1.50281i
$775$	5.58787			0.200722
$776$	−2.74194	+	4.74918i	−0.0984298	+	0.170485i
$777$	0.962712	+	0.769331i	0.0345371	+	0.0275996i
$778$	26.3870	+	45.7037i	0.946020	+	1.63856i
$779$	11.8983	+	20.6085i	0.426301	+	0.738375i
$780$	1.13734	−	7.49433i	0.0407233	−	0.268340i
$781$	−14.9647	+	25.9197i	−0.535480	+	0.927479i
$782$	−13.2171			−0.472644
$783$	1.86755	+	2.75712i	0.0667407	+	0.0985315i
$784$	−28.4426			−1.01581
$785$	3.96466	−	6.86698i	0.141505	−	0.245093i
$786$	12.2681	−	80.8389i	0.437589	−	2.88343i
$787$	4.82991	+	8.36565i	0.172168	+	0.298203i	0.939177	−	0.343432i	$-0.111590\pi$
$787$	4.82991	+	8.36565i	0.172168	+	0.298203i	−0.767010	+	0.641636i	$0.778256\pi$
$788$	20.8007	+	36.0279i	0.740994	+	1.28344i
$789$	−17.9247	−	14.3241i	−0.638135	−	0.509952i
$790$	6.71804	−	11.6360i	0.239017	−	0.413990i
$791$	−19.7191			−0.701129
$792$	71.1266	−	65.7286i	2.52737	−	2.33557i
$793$	−6.47734			−0.230017
$794$	−19.5874	+	33.9264i	−0.695132	+	1.20400i
$795$	16.6274	−	6.50638i	0.589714	−	0.230758i
$796$	−55.9806	−	96.9612i	−1.98418	−	3.43670i
$797$	17.9391	+	31.0714i	0.635435	+	1.10061i	0.986423	+	0.164225i	$0.0525124\pi$
$797$	17.9391	+	31.0714i	0.635435	+	1.10061i	−0.350988	+	0.936380i	$0.614154\pi$
$798$	24.2360	−	9.48364i	0.857943	−	0.335717i
$799$	−17.6053	+	30.4933i	−0.622831	+	1.07878i
$800$	−4.15960			−0.147064
$801$	45.0652	+	14.0006i	1.59230	+	0.494689i
$802$	−84.9876			−3.00102
$803$	31.6510	−	54.8211i	1.11694	−	1.93459i
$804$	90.5044	+	72.3247i	3.19185	+	2.55070i
$805$	−1.35569	−	2.34813i	−0.0477818	−	0.0827606i
$806$	7.05511	+	12.2198i	0.248506	+	0.430424i
$807$	5.27331	−	34.7476i	0.185629	−	1.22318i
$808$	17.4783	−	30.2734i	0.614886	−	1.06501i
$809$	35.0035			1.23066			0.615329	−	0.788270i	$-0.289023\pi$
$809$	35.0035			1.23066			0.615329	+	0.788270i	$0.289023\pi$
$810$	18.7255	+	12.8781i	0.657946	+	0.452489i
$811$	10.9673			0.385115			0.192558	−	0.981286i	$-0.438322\pi$
$811$	10.9673			0.385115			0.192558	+	0.981286i	$0.438322\pi$
$812$	2.24197	−	3.88321i	0.0786779	−	0.136274i
$813$	1.89265	−	12.4713i	0.0663780	−	0.437388i
$814$	−3.02285	−	5.23572i	−0.105951	−	0.183512i
$815$	−1.37046	−	2.37370i	−0.0480051	−	0.0831472i
$816$	−26.7262	−	21.3577i	−0.935605	−	0.747669i
$817$	−10.5303	+	18.2390i	−0.368409	+	0.638103i
$818$	−50.8683			−1.77857
$819$	4.58019	+	1.42295i	0.160045	+	0.0497220i
$820$	27.9804			0.977117
$821$	−12.6573	+	21.9230i	−0.441741	+	0.765118i	−0.997819	−	0.0660120i	$-0.978972\pi$
$821$	−12.6573	+	21.9230i	−0.441741	+	0.765118i	0.556077	+	0.831130i	$0.312306\pi$
$822$	−56.4458	+	22.0875i	−1.96877	+	0.770390i
$823$	−10.0481	−	17.4038i	−0.350254	−	0.606657i	0.636040	−	0.771656i	$-0.280571\pi$
$823$	−10.0481	−	17.4038i	−0.350254	−	0.606657i	−0.986294	+	0.164999i	$0.947238\pi$
$824$	−51.2733	−	88.8080i	−1.78619	−	3.09377i
$825$	−8.67720	+	3.39543i	−0.302101	+	0.118214i
$826$	18.8697	−	32.6833i	0.656562	−	1.13720i
$827$	−25.4134			−0.883710			−0.441855	−	0.897086i	$-0.645679\pi$
$827$	−25.4134			−0.883710			−0.441855	+	0.897086i	$0.645679\pi$
$828$	16.3533	−	15.1122i	0.568317	−	0.525186i
$829$	−9.17826			−0.318774			−0.159387	−	0.987216i	$-0.550952\pi$
$829$	−9.17826			−0.318774			−0.159387	+	0.987216i	$0.550952\pi$
$830$	12.3090	−	21.3199i	0.427253	−	0.740024i
$831$	−18.5989	−	14.8629i	−0.645188	−	0.515588i
$832$	1.14825	+	1.98882i	0.0398083	+	0.0689500i
$833$	6.85780	+	11.8781i	0.237609	+	0.411551i
$834$	4.28308	−	28.2227i	0.148311	−	0.977272i
$835$	−8.88551	+	15.3902i	−0.307496	+	0.532598i
$836$	−87.6296			−3.03073
$837$	−28.9607	+	2.08197i	−1.00103	+	0.0719633i
$838$	84.4487			2.91723
$839$	0.0468293	−	0.0811108i	0.00161673	−	0.00280025i	−0.865216	−	0.501399i	$-0.832819\pi$
$839$	0.0468293	−	0.0811108i	0.00161673	−	0.00280025i	0.866833	+	0.498599i	$0.166152\pi$
$840$	2.49317	−	16.4283i	0.0860225	−	0.566832i
$841$	14.2946	+	24.7590i	0.492919	+	0.853760i
$842$	33.2518	+	57.5939i	1.14593	+	1.98482i
$843$	1.22172	+	0.976314i	0.0420783	+	0.0336260i
$844$	11.3368	−	19.6359i	0.390229	−	0.675896i
$845$	−1.00000			−0.0344010
$846$	−19.0615	−	84.2995i	−0.655348	−	2.89828i
$847$	−28.6823			−0.985537
$848$	32.9880	−	57.1368i	1.13281	−	1.96209i
$849$	−44.9253	+	17.5795i	−1.54183	+	0.603326i
$850$	3.89662	+	6.74914i	0.133653	+	0.231493i
$851$	−0.377392	−	0.653662i	−0.0129368	−	0.0224072i
$852$	−39.2720	+	15.3673i	−1.34544	+	0.526476i
$853$	−11.8513	+	20.5270i	−0.405780	+	0.702832i	−0.994412	−	0.105570i	$-0.966333\pi$
$853$	−11.8513	+	20.5270i	−0.405780	+	0.702832i	0.588632	+	0.808401i	$0.299667\pi$
$854$	−26.1490			−0.894800
$855$	−2.46266	−	10.8911i	−0.0842211	−	0.372468i
$856$	−36.3034			−1.24082
$857$	6.30907	−	10.9276i	0.215514	−	0.373281i	−0.737918	−	0.674891i	$-0.764191\pi$
$857$	6.30907	−	10.9276i	0.215514	−	0.373281i	0.953431	+	0.301610i	$0.0975241\pi$
$858$	−18.3809	−	14.6887i	−0.627514	−	0.501464i
$859$	−0.261117	−	0.452268i	−0.00890921	−	0.0154312i	0.861536	−	0.507696i	$-0.169503\pi$
$859$	−0.261117	−	0.452268i	−0.00890921	−	0.0154312i	−0.870446	+	0.492265i	$0.836169\pi$
$860$	12.3817	+	21.4457i	0.422212	+	0.731293i
$861$	−2.65633	+	17.5035i	−0.0905274	+	0.596516i
$862$	13.5232	−	23.4229i	0.460603	−	0.797789i
$863$	−34.3229			−1.16837			−0.584183	−	0.811622i	$-0.698585\pi$
$863$	−34.3229			−1.16837			−0.584183	+	0.811622i	$0.698585\pi$
$864$	21.5583	−	1.54981i	0.733428	−	0.0527258i
$865$	−10.5731			−0.359496
$866$	−13.3411	+	23.1074i	−0.453348	+	0.785221i
$867$	1.94264	−	12.8007i	0.0659754	−	0.434735i
$868$	19.5481	+	33.8582i	0.663504	+	1.14922i
$869$	−14.3123	−	24.7897i	−0.485513	−	0.840933i
$870$	−2.18970	−	1.74985i	−0.0742377	−	0.0593255i
$871$	7.64188	−	13.2361i	0.258935	−	0.448489i
$872$	21.8888			0.741249
$873$	−2.01349	+	1.86068i	−0.0681464	+	0.0629746i
$874$	−15.9399			−0.539175
$875$	−0.799357	+	1.38453i	−0.0270232	+	0.0468055i
$876$	83.0618	−	32.5024i	2.80640	−	1.09816i
$877$	2.26797	+	3.92824i	0.0765839	+	0.132647i	0.901774	−	0.432208i	$-0.142265\pi$
$877$	2.26797	+	3.92824i	0.0765839	+	0.132647i	−0.825190	+	0.564855i	$0.808932\pi$
$878$	−42.8011	−	74.1337i	−1.44447	−	2.50189i
$879$	−5.24417	+	2.05207i	−0.176881	+	0.0692145i
$880$	−17.2151	+	29.8175i	−0.580322	+	1.00515i
$881$	36.4784			1.22899			0.614494	−	0.788922i	$-0.289360\pi$
$881$	36.4784			1.22899			0.614494	+	0.788922i	$0.289360\pi$
$882$	−32.1504	−	9.98833i	−1.08256	−	0.336325i
$883$	−15.3187			−0.515515			−0.257757	−	0.966210i	$-0.582983\pi$
$883$	−15.3187			−0.515515			−0.257757	+	0.966210i	$0.582983\pi$
$884$	−6.75331	+	11.6971i	−0.227138	+	0.393415i
$885$	−12.6491	−	10.1083i	−0.425196	−	0.339786i
$886$	37.1590	+	64.3613i	1.24838	+	2.16226i
$887$	10.4154	+	18.0400i	0.349715	+	0.605725i	0.986199	−	0.165566i	$-0.0529450\pi$
$887$	10.4154	+	18.0400i	0.349715	+	0.605725i	−0.636483	+	0.771290i	$0.719612\pi$
$888$	0.694038	−	4.57326i	0.0232904	−	0.153468i
$889$	11.3540	−	19.6657i	0.380801	−	0.659567i
$890$	−39.7206			−1.33144
$891$	43.7069	−	20.8307i	1.46424	−	0.697856i
$892$	65.9064			2.20671
$893$	−21.2321	+	36.7750i	−0.710504	+	1.23063i
$894$	−7.72888	+	50.9283i	−0.258492	+	1.70330i
$895$	2.73717	+	4.74092i	0.0914936	+	0.158472i
$896$	11.2855	+	19.5470i	0.377022	+	0.653020i
$897$	−2.29479	−	1.83383i	−0.0766208	−	0.0612299i
$898$	47.5560	−	82.3693i	1.58696	−	2.74870i
$899$	3.58112			0.119437
$900$	−12.5380	−	3.89526i	−0.417935	−	0.129842i
$901$	−31.8149			−1.05991
$902$	43.4261	−	75.2161i	1.44593	−	2.50442i
$903$	−14.5911	+	5.70955i	−0.485560	+	0.190002i
$904$	37.0077	+	64.0992i	1.23086	+	2.13191i
$905$	−0.676619	−	1.17194i	−0.0224916	−	0.0389566i
$906$	39.0654	−	15.2865i	1.29786	−	0.507859i
$907$	−5.91025	+	10.2369i	−0.196247	+	0.339909i	−0.947308	−	0.320323i	$-0.896209\pi$
$907$	−5.91025	+	10.2369i	−0.196247	+	0.339909i	0.751062	+	0.660232i	$0.229542\pi$
$908$	95.1418			3.15739
$909$	12.8349	−	11.8608i	0.425707	−	0.393399i
$910$	−4.03700			−0.133825
$911$	−2.86152	+	4.95631i	−0.0948065	+	0.164210i	−0.909528	−	0.415643i	$-0.863557\pi$
$911$	−2.86152	+	4.95631i	−0.0948065	+	0.164210i	0.814721	+	0.579853i	$0.196890\pi$
$912$	−32.2319	−	25.7574i	−1.06730	−	0.852914i
$913$	−26.2236	−	45.4206i	−0.867875	−	1.50320i
$914$	−40.3363	−	69.8645i	−1.33421	−	2.31091i
$915$	−1.68334	+	11.0921i	−0.0556494	+	0.366693i
$916$	−59.4647	+	102.996i	−1.96477	+	3.40308i
$917$	−29.8873			−0.986966
$918$	−22.7099	−	33.5274i	−0.749540	−	1.10657i
$919$	16.2414			0.535754			0.267877	−	0.963453i	$-0.413678\pi$
$919$	16.2414			0.535754			0.267877	+	0.963453i	$0.413678\pi$
$920$	−5.08858	+	8.81368i	−0.167766	+	0.290579i
$921$	−5.99778	+	39.5214i	−0.197634	+	1.30228i
$922$	−17.7157	−	30.6845i	−0.583435	−	1.01054i
$923$	2.78172	+	4.81808i	0.0915614	+	0.158589i
$924$	−50.9292	−	40.6990i	−1.67545	−	1.33890i
$925$	−0.222522	+	0.385419i	−0.00731647	+	0.0126725i
$926$	−103.353			−3.39640
$927$	−11.3068	−	50.0044i	−0.371365	−	1.64236i
$928$	−2.66578			−0.0875087
$929$	2.98637	−	5.17255i	0.0979797	−	0.169706i	−0.812869	−	0.582447i	$-0.802095\pi$
$929$	2.98637	−	5.17255i	0.0979797	−	0.169706i	0.910848	+	0.412741i	$0.135429\pi$
$930$	22.7592	−	8.90578i	0.746304	−	0.292032i
$931$	8.27053	+	14.3250i	0.271056	+	0.469482i
$932$	−52.8171	−	91.4818i	−1.73008	−	2.99659i
$933$	10.4427	−	4.08628i	0.341879	−	0.133779i
$934$	−5.30893	+	9.19534i	−0.173714	+	0.300881i
$935$	16.6030			0.542975
$936$	−3.97038	−	17.5590i	−0.129776	−	0.573934i
$937$	−36.1153			−1.17984			−0.589918	−	0.807463i	$-0.700840\pi$
$937$	−36.1153			−1.17984			−0.589918	+	0.807463i	$0.700840\pi$
$938$	30.8502	−	53.4342i	1.00730	−	1.74469i
$939$	−10.6133	−	8.48141i	−0.346353	−	0.276780i
$940$	24.9650	+	43.2406i	0.814267	+	1.41035i
$941$	−3.01318	−	5.21898i	−0.0982268	−	0.170134i	0.812724	−	0.582649i	$-0.197984\pi$
$941$	−3.01318	−	5.21898i	−0.0982268	−	0.170134i	−0.910951	+	0.412515i	$0.864650\pi$
$942$	5.20352	−	34.2878i	0.169540	−	1.11716i
$943$	5.42159	−	9.39047i	0.176551	−	0.305796i
$944$	−59.8303			−1.94731
$945$	3.62703	−	7.47352i	0.117987	−	0.243114i
$946$	76.8664			2.49914
$947$	−12.9752	+	22.4737i	−0.421638	+	0.730298i	−0.996100	−	0.0882332i	$-0.971878\pi$
$947$	−12.9752	+	22.4737i	−0.421638	+	0.730298i	0.574462	+	0.818531i	$0.305211\pi$
$948$	6.05167	−	39.8766i	0.196549	−	1.29513i
$949$	−5.88343	−	10.1904i	−0.190984	−	0.330795i
$950$	4.69933	+	8.13948i	0.152466	+	0.264079i
$951$	42.9457	+	34.3191i	1.39261	+	1.11287i
$952$	−14.8039	+	25.6412i	−0.479799	+	0.831036i
$953$	−46.4390			−1.50431			−0.752153	−	0.658988i	$-0.770985\pi$
$953$	−46.4390			−1.50431			−0.752153	+	0.658988i	$0.770985\pi$
$954$	57.3533	−	53.0006i	1.85688	−	1.71596i
$955$	−3.66554			−0.118614
$956$	−37.8124	+	65.4929i	−1.22294	+	2.11819i
$957$	−5.56100	+	2.17604i	−0.179761	+	0.0703415i
$958$	33.5100	+	58.0410i	1.08266	+	1.87522i
$959$	11.0780	+	19.1877i	0.357727	+	0.619602i
$960$	3.70415	−	1.44945i	0.119551	−	0.0467808i
$961$	−0.112129	+	0.194212i	−0.00361705	+	0.00626492i
$962$	−1.12380			−0.0362329
$963$	−17.3322	−	5.38468i	−0.558522	−	0.173519i
$964$	−72.4951			−2.33491
$965$	−4.37529	+	7.57823i	−0.140846	+	0.243952i
$966$	−9.26406	−	7.40318i	−0.298066	−	0.238194i
$967$	−13.7469	−	23.8104i	−0.442072	−	0.765691i	0.555771	−	0.831335i	$-0.312423\pi$
$967$	−13.7469	−	23.8104i	−0.442072	−	0.765691i	−0.997843	+	0.0656445i	$0.979090\pi$
$968$	53.8295	+	93.2355i	1.73015	+	2.99670i
$969$	−2.98526	+	19.6709i	−0.0959003	+	0.631920i
$970$	1.15382	−	1.99848i	0.0370470	−	0.0641672i
$971$	−8.04171			−0.258071			−0.129035	−	0.991640i	$-0.541188\pi$
$971$	−8.04171			−0.258071			−0.129035	+	0.991640i	$0.541188\pi$
$972$	66.4332	+	15.5168i	2.13085	+	0.497701i
$973$	−10.4343			−0.334510
$974$	36.9534	−	64.0051i	1.18406	−	2.05086i
$975$	−0.259881	+	1.71244i	−0.00832284	+	0.0548421i
$976$	20.7277	+	35.9014i	0.663477	+	1.14918i
$977$	5.27839	+	9.14245i	0.168871	+	0.292493i	0.938023	−	0.346573i	$-0.112655\pi$
$977$	5.27839	+	9.14245i	0.168871	+	0.292493i	−0.769152	+	0.639065i	$0.779321\pi$
$978$	−9.36498	−	7.48383i	−0.299459	−	0.239306i
$979$	−42.3111	+	73.2849i	−1.35227	+	2.34220i
$980$	19.4492			0.621282
$981$	10.4503	+	3.24665i	0.333652	+	0.103658i
$982$	−57.8817			−1.84708
$983$	6.03646	−	10.4555i	0.192533	−	0.333477i	−0.753556	−	0.657384i	$-0.771663\pi$
$983$	6.03646	−	10.4555i	0.192533	−	0.333477i	0.946089	+	0.323906i	$0.104996\pi$
$984$	61.8824	−	24.2149i	1.97274	−	0.771942i
$985$	−4.75293	−	8.23231i	−0.151441	−	0.262303i
$986$	2.49724	+	4.32535i	0.0795284	+	0.137747i
$987$	−29.4197	+	11.5121i	−0.936439	+	0.366433i
$988$	−8.14451	+	14.1067i	−0.259111	+	0.448794i
$989$	9.59650			0.305151
$990$	−29.9304	+	27.6589i	−0.951251	+	0.879059i
$991$	15.6841			0.498222			0.249111	−	0.968475i	$-0.419862\pi$
$991$	15.6841			0.498222			0.249111	+	0.968475i	$0.419862\pi$
$992$	11.6217	−	20.1293i	0.368988	−	0.639106i
$993$	−24.5015	−	19.5799i	−0.777531	−	0.621348i
$994$	11.2298	+	19.4506i	0.356187	+	0.616934i
$995$	12.7915	+	22.1555i	0.405517	+	0.702376i
$996$	11.0881	−	73.0634i	0.351340	−	2.31510i
$997$	0.939391	−	1.62707i	0.0297508	−	0.0515299i	−0.850767	−	0.525544i	$-0.823862\pi$
$997$	0.939391	−	1.62707i	0.0297508	−	0.0515299i	0.880517	+	0.474014i	$0.157195\pi$
$998$	−14.7993			−0.468464
$999$	1.00968	−	2.08045i	0.0319448	−	0.0658225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.h.196.14	✓	30
3.2	odd	2		1755.2.i.h.586.2		30
9.2	odd	6		5265.2.a.bl.1.14		15
9.4	even	3	inner	585.2.i.h.391.14	yes	30
9.5	odd	6		1755.2.i.h.1171.2		30
9.7	even	3		5265.2.a.bk.1.2		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.h.196.14	✓	30	1.1	even	1	trivial
585.2.i.h.391.14	yes	30	9.4	even	3	inner
1755.2.i.h.586.2		30	3.2	odd	2
1755.2.i.h.1171.2		30	9.5	odd	6
5265.2.a.bk.1.2		15	9.7	even	3
5265.2.a.bl.1.14		15	9.2	odd	6

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26258 - 2.18685i) q^{2} +(-0.259881 + 1.71244i) q^{3} +(-2.18820 - 3.79007i) q^{4} +(0.500000 + 0.866025i) q^{5} +(3.41673 + 2.73041i) q^{6} +(0.799357 - 1.38453i) q^{7} -6.00077 q^{8} +(-2.86492 - 0.890062i) q^{9} +O(q^{10})\)	\(q+(1.26258 - 2.18685i) q^{2} +(-0.259881 + 1.71244i) q^{3} +(-2.18820 - 3.79007i) q^{4} +(0.500000 + 0.866025i) q^{5} +(3.41673 + 2.73041i) q^{6} +(0.799357 - 1.38453i) q^{7} -6.00077 q^{8} +(-2.86492 - 0.890062i) q^{9} +2.52515 q^{10} +(2.68984 - 4.65893i) q^{11} +(7.05895 - 2.76220i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-2.01850 - 3.49614i) q^{14} +(-1.61296 + 0.631158i) q^{15} +(-3.20003 + 5.54262i) q^{16} +3.08624 q^{17} +(-5.56361 + 5.14138i) q^{18} +3.72202 q^{19} +(2.18820 - 3.79007i) q^{20} +(2.16319 + 1.72867i) q^{21} +(-6.79225 - 11.7645i) q^{22} +(-0.847988 - 1.46876i) q^{23} +(1.55948 - 10.2760i) q^{24} +(-0.500000 + 0.866025i) q^{25} -2.52515 q^{26} +(2.26872 - 4.67471i) q^{27} -6.99661 q^{28} +(-0.320437 + 0.555014i) q^{29} +(-0.656238 + 4.32418i) q^{30} +(-2.79393 - 4.83923i) q^{31} +(2.07980 + 3.60232i) q^{32} +(7.27912 + 5.81696i) q^{33} +(3.89662 - 6.74914i) q^{34} +1.59871 q^{35} +(2.89563 + 12.8059i) q^{36} +0.445044 q^{37} +(4.69933 - 8.13948i) q^{38} +(1.61296 - 0.631158i) q^{39} +(-3.00038 - 5.19682i) q^{40} +(3.19674 + 5.53691i) q^{41} +(6.51151 - 2.54798i) q^{42} +(-2.82920 + 4.90031i) q^{43} -23.5436 q^{44} +(-0.661646 - 2.92613i) q^{45} -4.28260 q^{46} +(-5.70445 + 9.88040i) q^{47} +(-8.65979 - 6.92029i) q^{48} +(2.22206 + 3.84872i) q^{49} +(1.26258 + 2.18685i) q^{50} +(-0.802054 + 5.28501i) q^{51} +(-2.18820 + 3.79007i) q^{52} -10.3086 q^{53} +(-7.35844 - 10.8635i) q^{54} +5.37967 q^{55} +(-4.79676 + 8.30823i) q^{56} +(-0.967280 + 6.37374i) q^{57} +(0.809153 + 1.40149i) q^{58} +(4.67420 + 8.09595i) q^{59} +(5.92161 + 4.73213i) q^{60} +(3.23867 - 5.60954i) q^{61} -14.1102 q^{62} +(-3.52241 + 3.25509i) q^{63} -2.29649 q^{64} +(0.500000 - 0.866025i) q^{65} +(21.9112 - 8.57397i) q^{66} +(7.64188 + 13.2361i) q^{67} +(-6.75331 - 11.6971i) q^{68} +(2.73554 - 1.07043i) q^{69} +(2.01850 - 3.49614i) q^{70} -5.56344 q^{71} +(17.1917 + 5.34105i) q^{72} +11.7669 q^{73} +(0.561902 - 0.973242i) q^{74} +(-1.35308 - 1.08128i) q^{75} +(-8.14451 - 14.1067i) q^{76} +(-4.30028 - 7.44830i) q^{77} +(0.656238 - 4.32418i) q^{78} +(2.66045 - 4.60803i) q^{79} -6.40006 q^{80} +(7.41558 + 5.09992i) q^{81} +16.1445 q^{82} +(4.87457 - 8.44301i) q^{83} +(1.81828 - 11.9813i) q^{84} +(1.54312 + 2.67276i) q^{85} +(7.14415 + 12.3740i) q^{86} +(-0.867154 - 0.692968i) q^{87} +(-16.1411 + 27.9572i) q^{88} -15.7300 q^{89} +(-7.23437 - 2.24754i) q^{90} -1.59871 q^{91} +(-3.71114 + 6.42787i) q^{92} +(9.01300 - 3.52683i) q^{93} +(14.4046 + 24.9495i) q^{94} +(1.86101 + 3.22336i) q^{95} +(-6.70927 + 2.62537i) q^{96} +(0.456931 - 0.791428i) q^{97} +11.2221 q^{98} +(-11.8529 + 10.9534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9}+O(q^{10}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9	\( 30 q + q^{2} + q^{3} - 21 q^{4} + 15 q^{5} - 9 q^{6} - 10 q^{7} + q^{9} + 2 q^{10} + 9 q^{11} + 18 q^{12} - 15 q^{13} + 3 q^{14} + 2 q^{15} - 33 q^{16} + 6 q^{17} + 9 q^{18} + 30 q^{19} + 21 q^{20} + 9 q^{21} - 10 q^{22} - 6 q^{23} + 24 q^{24} - 15 q^{25} - 2 q^{26} - 2 q^{27} + 70 q^{28} + 8 q^{29} - 6 q^{30} - 22 q^{31} + 21 q^{32} - 20 q^{33} - 9 q^{34} - 20 q^{35} - 7 q^{36} + 8 q^{37} - 14 q^{38} - 2 q^{39} + 13 q^{41} + 21 q^{42} - 24 q^{43} + 10 q^{44} - 7 q^{45} - 6 q^{46} - q^{47} - 27 q^{48} - 37 q^{49} + q^{50} - q^{51} - 21 q^{52} + 14 q^{53} - 24 q^{54} + 18 q^{55} + 17 q^{56} - 55 q^{57} - 22 q^{58} + 19 q^{59} + 9 q^{60} - 16 q^{61} + 26 q^{62} + 4 q^{63} + 72 q^{64} + 15 q^{65} + 24 q^{66} - 11 q^{67} - 28 q^{68} + 44 q^{69} - 3 q^{70} - 56 q^{71} - 18 q^{72} + 52 q^{73} + 8 q^{74} + q^{75} - 18 q^{76} - 24 q^{77} + 6 q^{78} - 44 q^{79} - 66 q^{80} + 37 q^{81} + 70 q^{82} - 3 q^{83} - 139 q^{84} + 3 q^{85} + 40 q^{86} + 60 q^{87} - 37 q^{88} - 8 q^{89} - 12 q^{90} + 20 q^{91} - 74 q^{92} - 55 q^{93} - 2 q^{94} + 15 q^{95} + 55 q^{96} - 33 q^{97} + 6 q^{98} + 26 q^{99}+O(q^{100}) \) 30 * q + q^2 + q^3 - 21 * q^4 + 15 * q^5 - 9 * q^6 - 10 * q^7 + q^9 + 2 * q^10 + 9 * q^11 + 18 * q^12 - 15 * q^13 + 3 * q^14 + 2 * q^15 - 33 * q^16 + 6 * q^17 + 9 * q^18 + 30 * q^19 + 21 * q^20 + 9 * q^21 - 10 * q^22 - 6 * q^23 + 24 * q^24 - 15 * q^25 - 2 * q^26 - 2 * q^27 + 70 * q^28 + 8 * q^29 - 6 * q^30 - 22 * q^31 + 21 * q^32 - 20 * q^33 - 9 * q^34 - 20 * q^35 - 7 * q^36 + 8 * q^37 - 14 * q^38 - 2 * q^39 + 13 * q^41 + 21 * q^42 - 24 * q^43 + 10 * q^44 - 7 * q^45 - 6 * q^46 - q^47 - 27 * q^48 - 37 * q^49 + q^50 - q^51 - 21 * q^52 + 14 * q^53 - 24 * q^54 + 18 * q^55 + 17 * q^56 - 55 * q^57 - 22 * q^58 + 19 * q^59 + 9 * q^60 - 16 * q^61 + 26 * q^62 + 4 * q^63 + 72 * q^64 + 15 * q^65 + 24 * q^66 - 11 * q^67 - 28 * q^68 + 44 * q^69 - 3 * q^70 - 56 * q^71 - 18 * q^72 + 52 * q^73 + 8 * q^74 + q^75 - 18 * q^76 - 24 * q^77 + 6 * q^78 - 44 * q^79 - 66 * q^80 + 37 * q^81 + 70 * q^82 - 3 * q^83 - 139 * q^84 + 3 * q^85 + 40 * q^86 + 60 * q^87 - 37 * q^88 - 8 * q^89 - 12 * q^90 + 20 * q^91 - 74 * q^92 - 55 * q^93 - 2 * q^94 + 15 * q^95 + 55 * q^96 - 33 * q^97 + 6 * q^98 + 26 * q^99

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