LMFDB - Embedded newform 546.2.bu.b.197.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.2
Character	$\chi$	$=$	546.197
Dual form			546.2.bu.b.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-1.34996 - 1.08518i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.429580 + 0.429580i) q^{5} +(1.39760 - 1.02310i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.644780 + 2.92989i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.34996 - 1.08518i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.429580 + 0.429580i) q^{5} +(1.39760 - 1.02310i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.644780 + 2.92989i) q^{9} +(-0.526126 + 0.303759i) q^{10} +(1.44890 + 0.388232i) q^{11} +(0.626510 + 1.61477i) q^{12} +(-1.82271 - 3.11091i) q^{13} -1.00000i q^{14} +(-0.113745 - 1.04609i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.50234 - 4.33419i) q^{17} +(-2.99694 - 0.135502i) q^{18} +(0.744411 + 2.77818i) q^{19} +(-0.157237 - 0.586817i) q^{20} +(1.58483 + 0.698806i) q^{21} +(-0.750007 + 1.29905i) q^{22} +(2.87235 + 4.97505i) q^{23} +(-1.72190 + 0.187229i) q^{24} -4.63092i q^{25} +(3.47666 - 0.955436i) q^{26} +(2.30902 - 4.65493i) q^{27} +(0.965926 + 0.258819i) q^{28} +(5.53687 - 3.19672i) q^{29} +(1.03988 + 0.160878i) q^{30} +(2.86572 - 2.86572i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.53466 - 2.09641i) q^{33} +(3.53885 + 3.53885i) q^{34} +(-0.526126 - 0.303759i) q^{35} +(0.906550 - 2.85975i) q^{36} +(2.29499 - 8.56502i) q^{37} -2.87618 q^{38} +(-0.915309 + 6.17756i) q^{39} +0.607518 q^{40} +(0.973141 - 3.63181i) q^{41} +(-1.08518 + 1.34996i) q^{42} +(9.35271 + 5.39979i) q^{43} +(-1.06067 - 1.06067i) q^{44} +(-0.981638 + 1.53561i) q^{45} +(-5.54895 + 1.48684i) q^{46} +(7.10501 - 7.10501i) q^{47} +(0.264812 - 1.71169i) q^{48} +(0.866025 - 0.500000i) q^{49} +(4.47313 + 1.19857i) q^{50} +(-8.08143 + 3.13549i) q^{51} +(0.0230552 + 3.60548i) q^{52} +7.88465i q^{53} +(3.89870 + 3.43513i) q^{54} +(0.455643 + 0.789196i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(2.00989 - 4.55825i) q^{57} +(1.65474 + 6.17558i) q^{58} +(3.35057 + 12.5045i) q^{59} +(-0.424537 + 0.962810i) q^{60} +(-0.879168 + 1.52276i) q^{61} +(2.02637 + 3.50978i) q^{62} +(-1.38112 - 2.66318i) q^{63} -1.00000i q^{64} +(0.553386 - 2.11938i) q^{65} +(2.42218 - 0.939774i) q^{66} +(-10.7168 - 2.87155i) q^{67} +(-4.33419 + 2.50234i) q^{68} +(1.52126 - 9.83312i) q^{69} +(0.429580 - 0.429580i) q^{70} +(-5.54815 + 1.48662i) q^{71} +(2.52767 + 1.61582i) q^{72} +(-10.8592 - 10.8592i) q^{73} +(7.67919 + 4.43358i) q^{74} +(-5.02537 + 6.25156i) q^{75} +(0.744411 - 2.77818i) q^{76} -1.50001 q^{77} +(-5.73016 - 2.48299i) q^{78} +3.68438 q^{79} +(-0.157237 + 0.586817i) q^{80} +(-8.16852 + 3.77827i) q^{81} +(3.25619 + 1.87996i) q^{82} +(-5.15594 - 5.15594i) q^{83} +(-1.02310 - 1.39760i) q^{84} +(2.93684 - 0.786923i) q^{85} +(-7.63646 + 7.63646i) q^{86} +(-10.9436 - 1.69306i) q^{87} +(1.29905 - 0.750007i) q^{88} +(6.57035 + 1.76052i) q^{89} +(-1.22922 - 1.34563i) q^{90} +(2.56576 + 2.53316i) q^{91} -5.74469i q^{92} +(-6.97843 + 0.758792i) q^{93} +(5.02400 + 8.70183i) q^{94} +(-0.873667 + 1.51324i) q^{95} +(1.58483 + 0.698806i) q^{96} +(-0.785006 - 2.92968i) q^{97} +(0.258819 + 0.965926i) q^{98} +(-0.203255 + 4.49545i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 56 * q + 8 * q^6 - 24 * q^9	$ 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) $ 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{12}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−1.34996	−	1.08518i	−0.779399	−	0.626527i
$3$	−1.34996	−	1.08518i	−0.779399	−	0.626527i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.429580	+	0.429580i	0.192114	+	0.192114i	0.796609	−	0.604495i	$-0.206625\pi$
$5$	0.429580	+	0.429580i	0.192114	+	0.192114i	−0.604495	+	0.796609i	$0.706625\pi$
$6$	1.39760	−	1.02310i	0.570566	−	0.417677i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.644780	+	2.92989i	0.214927	+	0.976630i
$10$	−0.526126	+	0.303759i	−0.166376	+	0.0960570i
$11$	1.44890	+	0.388232i	0.436860	+	0.117056i	0.470545	−	0.882376i	$-0.344057\pi$
$11$	1.44890	+	0.388232i	0.436860	+	0.117056i	−0.0336843	+	0.999433i	$0.510724\pi$
$12$	0.626510	+	1.61477i	0.180858	+	0.466144i
$13$	−1.82271	−	3.11091i	−0.505527	−	0.862811i
$13$	−1.82271	−	3.11091i	−0.505527	−	0.862811i
$14$		−	1.00000i		−	0.267261i
$15$	−0.113745	−	1.04609i	−0.0293688	−	0.270098i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.50234	−	4.33419i	0.606908	−	1.05119i	−0.384839	−	0.922984i	$-0.625743\pi$
$17$	2.50234	−	4.33419i	0.606908	−	1.05119i	0.991747	−	0.128211i	$-0.0409236\pi$
$18$	−2.99694	−	0.135502i	−0.706385	−	0.0319381i
$19$	0.744411	+	2.77818i	0.170780	+	0.637358i	0.997232	+	0.0743518i	$0.0236888\pi$
$19$	0.744411	+	2.77818i	0.170780	+	0.637358i	−0.826452	+	0.563007i	$0.809645\pi$
$20$	−0.157237	−	0.586817i	−0.0351593	−	0.131216i
$21$	1.58483	+	0.698806i	0.345837	+	0.152492i
$22$	−0.750007	+	1.29905i	−0.159902	+	0.276958i
$23$	2.87235	+	4.97505i	0.598925	+	1.03737i	0.992980	+	0.118282i	$0.0377387\pi$
$23$	2.87235	+	4.97505i	0.598925	+	1.03737i	−0.394055	+	0.919087i	$0.628928\pi$
$24$	−1.72190	+	0.187229i	−0.351482	+	0.0382180i
$25$		−	4.63092i		−	0.926184i
$26$	3.47666	−	0.955436i	0.681828	−	0.187376i
$27$	2.30902	−	4.65493i	0.444372	−	0.895842i
$28$	0.965926	+	0.258819i	0.182543	+	0.0489122i
$29$	5.53687	−	3.19672i	1.02817	−	0.593615i	0.111711	−	0.993741i	$-0.464367\pi$
$29$	5.53687	−	3.19672i	1.02817	−	0.593615i	0.916460	+	0.400125i	$0.131033\pi$
$30$	1.03988	+	0.160878i	0.189855	+	0.0293721i
$31$	2.86572	−	2.86572i	0.514699	−	0.514699i	−0.401263	−	0.915963i	$-0.631429\pi$
$31$	2.86572	−	2.86572i	0.514699	−	0.514699i	0.915963	+	0.401263i	$0.131429\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−1.53466	−	2.09641i	−0.267150	−	0.364939i
$34$	3.53885	+	3.53885i	0.606908	+	0.606908i
$35$	−0.526126	−	0.303759i	−0.0889315	−	0.0513446i
$36$	0.906550	−	2.85975i	0.151092	−	0.476625i
$37$	2.29499	−	8.56502i	0.377294	−	1.40808i	−0.472670	−	0.881240i	$-0.656710\pi$
$37$	2.29499	−	8.56502i	0.377294	−	1.40808i	0.849964	−	0.526841i	$-0.176624\pi$
$38$	−2.87618			−0.466579
$39$	−0.915309	+	6.17756i	−0.146567	+	0.989201i
$40$	0.607518			0.0960570
$41$	0.973141	−	3.63181i	0.151979	−	0.567194i	−0.847366	−	0.531009i	$-0.821813\pi$
$41$	0.973141	−	3.63181i	0.151979	−	0.567194i	0.999345	−	0.0361844i	$-0.0115204\pi$
$42$	−1.08518	+	1.34996i	−0.167447	+	0.208303i
$43$	9.35271	+	5.39979i	1.42628	+	0.823460i	0.996824	−	0.0796301i	$-0.0253739\pi$
$43$	9.35271	+	5.39979i	1.42628	+	0.823460i	0.429451	+	0.903090i	$0.358707\pi$
$44$	−1.06067	−	1.06067i	−0.159902	−	0.159902i
$45$	−0.981638	+	1.53561i	−0.146334	+	0.228915i
$46$	−5.54895	+	1.48684i	−0.818147	+	0.219222i
$47$	7.10501	−	7.10501i	1.03637	−	1.03637i	0.0370599	−	0.999313i	$-0.488201\pi$
$47$	7.10501	−	7.10501i	1.03637	−	1.03637i	0.999313	−	0.0370599i	$-0.0117992\pi$
$48$	0.264812	−	1.71169i	0.0382223	−	0.247061i
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$	4.47313	+	1.19857i	0.632596	+	0.169504i
$51$	−8.08143	+	3.13549i	−1.13163	+	0.439056i
$52$	0.0230552	+	3.60548i	0.00319718	+	0.499990i
$53$			7.88465i			1.08304i	0.840688	+	0.541520i	$0.182151\pi$
$53$			7.88465i			1.08304i	−0.840688	+	0.541520i	$0.817849\pi$
$54$	3.89870	+	3.43513i	0.530546	+	0.467462i
$55$	0.455643	+	0.789196i	0.0614389	+	0.106415i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	2.00989	−	4.55825i	0.266217	−	0.603755i
$58$	1.65474	+	6.17558i	0.217278	+	0.810894i
$59$	3.35057	+	12.5045i	0.436207	+	1.62795i	0.738161	+	0.674625i	$0.235695\pi$
$59$	3.35057	+	12.5045i	0.436207	+	1.62795i	−0.301954	+	0.953323i	$0.597639\pi$
$60$	−0.424537	+	0.962810i	−0.0548075	+	0.124298i
$61$	−0.879168	+	1.52276i	−0.112566	+	0.194970i	−0.916804	−	0.399337i	$-0.869240\pi$
$61$	−0.879168	+	1.52276i	−0.112566	+	0.194970i	0.804238	+	0.594307i	$0.202574\pi$
$62$	2.02637	+	3.50978i	0.257350	+	0.445743i
$63$	−1.38112	−	2.66318i	−0.174005	−	0.335529i
$64$		−	1.00000i		−	0.125000i
$65$	0.553386	−	2.11938i	0.0686391	−	0.262877i
$66$	2.42218	−	0.939774i	0.298150	−	0.115678i
$67$	−10.7168	−	2.87155i	−1.30926	−	0.350815i	−0.464316	−	0.885670i	$-0.653700\pi$
$67$	−10.7168	−	2.87155i	−1.30926	−	0.350815i	−0.844944	+	0.534855i	$0.820366\pi$
$68$	−4.33419	+	2.50234i	−0.525597	+	0.303454i
$69$	1.52126	−	9.83312i	0.183138	−	1.18377i
$70$	0.429580	−	0.429580i	0.0513446	−	0.0513446i
$71$	−5.54815	+	1.48662i	−0.658444	+	0.176430i	−0.572544	−	0.819874i	$-0.694043\pi$
$71$	−5.54815	+	1.48662i	−0.658444	+	0.176430i	−0.0859005	+	0.996304i	$0.527377\pi$
$72$	2.52767	+	1.61582i	0.297889	+	0.190426i
$73$	−10.8592	−	10.8592i	−1.27097	−	1.27097i	−0.945580	−	0.325388i	$-0.894505\pi$
$73$	−10.8592	−	10.8592i	−1.27097	−	1.27097i	−0.325388	−	0.945580i	$-0.605495\pi$
$74$	7.67919	+	4.43358i	0.892687	+	0.515393i
$75$	−5.02537	+	6.25156i	−0.580280	+	0.721867i
$76$	0.744411	−	2.77818i	0.0853898	−	0.318679i
$77$	−1.50001			−0.170942
$78$	−5.73016	−	2.48299i	−0.648813	−	0.281143i
$79$	3.68438			0.414525			0.207262	−	0.978285i	$-0.433545\pi$
$79$	3.68438			0.414525			0.207262	+	0.978285i	$0.433545\pi$
$80$	−0.157237	+	0.586817i	−0.0175797	+	0.0656082i
$81$	−8.16852	+	3.77827i	−0.907613	+	0.419808i
$82$	3.25619	+	1.87996i	0.359586	+	0.207607i
$83$	−5.15594	−	5.15594i	−0.565938	−	0.565938i	0.365050	−	0.930988i	$-0.381052\pi$
$83$	−5.15594	−	5.15594i	−0.565938	−	0.565938i	−0.930988	+	0.365050i	$0.881052\pi$
$84$	−1.02310	−	1.39760i	−0.111629	−	0.152490i
$85$	2.93684	−	0.786923i	0.318545	−	0.0853538i
$86$	−7.63646	+	7.63646i	−0.823460	+	0.823460i
$87$	−10.9436	−	1.69306i	−1.17327	−	0.181515i
$88$	1.29905	−	0.750007i	0.138479	−	0.0799510i
$89$	6.57035	+	1.76052i	0.696455	+	0.186615i	0.589642	−	0.807664i	$-0.299269\pi$
$89$	6.57035	+	1.76052i	0.696455	+	0.186615i	0.106813	+	0.994279i	$0.465935\pi$
$90$	−1.22922	−	1.34563i	−0.129571	−	0.141842i
$91$	2.56576	+	2.53316i	0.268965	+	0.265547i
$92$		−	5.74469i		−	0.598925i
$93$	−6.97843	+	0.758792i	−0.723630	+	0.0786830i
$94$	5.02400	+	8.70183i	0.518186	+	0.897525i
$95$	−0.873667	+	1.51324i	−0.0896363	+	0.155255i
$96$	1.58483	+	0.698806i	0.161751	+	0.0713216i
$97$	−0.785006	−	2.92968i	−0.0797053	−	0.297464i	0.914554	−	0.404464i	$-0.132542\pi$
$97$	−0.785006	−	2.92968i	−0.0797053	−	0.297464i	−0.994259	+	0.107000i	$0.965875\pi$
$98$	0.258819	+	0.965926i	0.0261447	+	0.0975732i
$99$	−0.203255	+	4.49545i	−0.0204279	+	0.451810i
$100$	−2.31546	+	4.01050i	−0.231546	+	0.401050i
$101$	2.55267	+	4.42136i	0.254001	+	0.439942i	0.964624	−	0.263631i	$-0.0849202\pi$
$101$	2.55267	+	4.42136i	0.254001	+	0.439942i	−0.710623	+	0.703573i	$0.751587\pi$
$102$	−0.937023	−	8.61758i	−0.0927791	−	0.853268i
$103$		−	5.89303i		−	0.580658i	−0.956927	−	0.290329i	$-0.906235\pi$
$103$		−	5.89303i		−	0.580658i	0.956927	−	0.290329i	$-0.0937647\pi$
$104$	−3.48859	−	0.910897i	−0.342084	−	0.0893208i
$105$	0.380616	+	0.981002i	0.0371443	+	0.0957360i
$106$	−7.61599	−	2.04070i	−0.739730	−	0.198210i
$107$	−9.22495	+	5.32603i	−0.891810	+	0.514886i	−0.874534	−	0.484964i	$-0.838833\pi$
$107$	−9.22495	+	5.32603i	−0.891810	+	0.514886i	−0.0172756	+	0.999851i	$0.505499\pi$
$108$	−4.32714	+	2.87678i	−0.416379	+	0.276818i
$109$	−0.363108	+	0.363108i	−0.0347794	+	0.0347794i	−0.724283	−	0.689503i	$-0.757829\pi$
$109$	−0.363108	+	0.363108i	−0.0347794	+	0.0347794i	0.689503	+	0.724283i	$0.257829\pi$
$110$	−0.880234	+	0.235858i	−0.0839270	+	0.0224882i
$111$	−12.3927	+	9.07195i	−1.17626	+	0.861072i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	13.3023	+	7.68008i	1.25137	+	0.722481i	0.971382	−	0.237521i	$-0.0763350\pi$
$113$	13.3023	+	7.68008i	1.25137	+	0.722481i	0.279992	+	0.960002i	$0.409668\pi$
$114$	3.88273	+	3.12117i	0.363651	+	0.292324i
$115$	−0.903279	+	3.37108i	−0.0842312	+	0.314355i
$116$	−6.39343			−0.593615
$117$	7.93938	−	7.34618i	0.733996	−	0.679154i
$118$	−12.9456			−1.19174
$119$	−1.29531	+	4.83416i	−0.118741	+	0.443147i
$120$	−0.820125	−	0.659265i	−0.0748668	−	0.0601824i
$121$	−7.57769	−	4.37498i	−0.688881	−	0.397725i
$122$	−1.24333	−	1.24333i	−0.112566	−	0.112566i
$123$	−5.25486	+	3.84677i	−0.473815	+	0.346851i
$124$	−3.91465	+	1.04893i	−0.351546	+	0.0941965i
$125$	4.13725	−	4.13725i	0.370047	−	0.370047i
$126$	2.92989	−	0.644780i	0.261015	−	0.0574416i
$127$	9.14243	−	5.27839i	0.811260	−	0.468381i	−0.0361335	−	0.999347i	$-0.511504\pi$
$127$	9.14243	−	5.27839i	0.811260	−	0.468381i	0.847393	+	0.530966i	$0.178171\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−6.76605	−	17.4388i	−0.595717	−	1.53540i
$130$	1.90394	+	1.08307i	0.166986	+	0.0949912i
$131$		−	12.2294i		−	1.06848i	−0.845331	−	0.534242i	$-0.820597\pi$
$131$		−	12.2294i		−	1.06848i	0.845331	−	0.534242i	$-0.179403\pi$
$132$	0.280846	+	2.58288i	0.0244445	+	0.224811i
$133$	−1.43809	−	2.49085i	−0.124698	−	0.215984i
$134$	5.54740	−	9.60838i	0.479222	−	0.830037i
$135$	2.99158	−	1.00776i	0.257474	−	0.0867338i
$136$	−1.29531	−	4.83416i	−0.111072	−	0.414526i
$137$	4.39879	+	16.4165i	0.375814	+	1.40256i	0.852151	+	0.523295i	$0.175297\pi$
$137$	4.39879	+	16.4165i	0.375814	+	1.40256i	−0.476337	+	0.879263i	$0.658036\pi$
$138$	9.10433	+	4.01442i	0.775012	+	0.341730i
$139$	−3.35001	+	5.80239i	−0.284144	+	0.492152i	−0.972401	−	0.233315i	$-0.925043\pi$
$139$	−3.35001	+	5.80239i	−0.284144	+	0.492152i	0.688257	+	0.725467i	$0.258376\pi$
$140$	0.303759	+	0.526126i	0.0256723	+	0.0444658i
$141$	−17.3017	+	1.88128i	−1.45706	+	0.158432i
$142$		−	5.74387i		−	0.482015i
$143$	−1.43317	−	5.21503i	−0.119847	−	0.436103i
$144$	−2.21497	+	2.02334i	−0.184581	+	0.168612i
$145$	3.75178	+	1.00529i	0.311568	+	0.0834844i
$146$	13.2997	−	7.67859i	1.10069	−	0.635484i
$147$	−1.71169	−	0.264812i	−0.141178	−	0.0218413i
$148$	−6.27003	+	6.27003i	−0.515393	+	0.515393i
$149$	−20.1156	+	5.38997i	−1.64794	+	0.441564i	−0.959034	−	0.283289i	$-0.908574\pi$
$149$	−20.1156	+	5.38997i	−1.64794	+	0.441564i	−0.688904	+	0.724853i	$0.741908\pi$
$150$	−4.73788	−	6.47216i	−0.386846	−	0.528450i
$151$	1.83850	+	1.83850i	0.149615	+	0.149615i	0.777946	−	0.628331i	$-0.216262\pi$
$151$	1.83850	+	1.83850i	0.149615	+	0.149615i	−0.628331	+	0.777946i	$0.716262\pi$
$152$	2.49085	+	1.43809i	0.202034	+	0.116645i
$153$	14.3122	+	4.53700i	1.15707	+	0.366795i
$154$	0.388232	−	1.44890i	0.0312846	−	0.116756i
$155$	2.46212			0.197762
$156$	3.88146	−	4.89227i	0.310765	−	0.391695i
$157$	20.5606			1.64092			0.820459	−	0.571706i	$-0.193718\pi$
$157$	20.5606			1.64092			0.820459	+	0.571706i	$0.193718\pi$
$158$	−0.953587	+	3.55883i	−0.0758633	+	0.283126i
$159$	8.55625	−	10.6440i	0.678555	−	0.844121i
$160$	−0.526126	−	0.303759i	−0.0415939	−	0.0240143i
$161$	−4.06211	−	4.06211i	−0.320139	−	0.320139i
$162$	−1.53536	−	8.86807i	−0.120629	−	0.696741i
$163$	−6.48922	+	1.73878i	−0.508275	+	0.136192i	−0.503838	−	0.863798i	$-0.668079\pi$
$163$	−6.48922	+	1.73878i	−0.508275	+	0.136192i	−0.00443696	+	0.999990i	$0.501412\pi$
$164$	−2.65867	+	2.65867i	−0.207607	+	0.207607i
$165$	0.241319	−	1.55984i	0.0187867	−	0.121433i
$166$	6.31471	−	3.64580i	0.490116	−	0.282969i
$167$	−6.75418	−	1.80978i	−0.522654	−	0.140045i	−0.0121601	−	0.999926i	$-0.503871\pi$
$167$	−6.75418	−	1.80978i	−0.522654	−	0.140045i	−0.510494	+	0.859881i	$0.670537\pi$
$168$	1.61477	−	0.626510i	0.124582	−	0.0483363i
$169$	−6.35549	+	11.3405i	−0.488884	+	0.872349i
$170$			3.04044i			0.233191i
$171$	−7.65978	+	3.97236i	−0.585758	+	0.303774i
$172$	−5.39979	−	9.35271i	−0.411730	−	0.713138i
$173$	4.19368	−	7.26366i	0.318839	−	0.552246i	−0.661407	−	0.750027i	$-0.730040\pi$
$173$	4.19368	−	7.26366i	0.318839	−	0.552246i	0.980246	+	0.197781i	$0.0633736\pi$
$174$	4.46777	−	10.1325i	0.338701	−	0.768141i
$175$	1.19857	+	4.47313i	0.0906034	+	0.338137i
$176$	0.388232	+	1.44890i	0.0292641	+	0.109215i
$177$	9.04647	−	20.5165i	0.679974	−	1.54212i
$178$	−3.40106	+	5.89081i	−0.254920	+	0.441535i
$179$	−8.32290	−	14.4157i	−0.622083	−	1.07748i	−0.989097	−	0.147264i	$-0.952953\pi$
$179$	−8.32290	−	14.4157i	−0.622083	−	1.07748i	0.367015	−	0.930215i	$-0.380380\pi$
$180$	1.61793	−	0.839056i	0.120593	−	0.0625395i
$181$			4.99273i			0.371106i	0.982634	+	0.185553i	$0.0594077\pi$
$181$			4.99273i			0.371106i	−0.982634	+	0.185553i	$0.940592\pi$
$182$	−3.11091	+	1.82271i	−0.230596	+	0.135108i
$183$	2.83931	−	1.10162i	0.209888	−	0.0814338i
$184$	5.54895	+	1.48684i	0.409074	+	0.109611i
$185$	4.66524	−	2.69348i	0.342996	−	0.198029i
$186$	1.07321	−	6.93704i	0.0786919	−	0.508648i
$187$	5.30832	−	5.30832i	0.388183	−	0.388183i
$188$	−9.70563	+	2.60062i	−0.707856	+	0.189669i
$189$	−1.02556	+	5.09394i	−0.0745986	+	0.370530i
$190$	−1.23555	−	1.23555i	−0.0896363	−	0.0896363i
$191$	0.216953	+	0.125258i	0.0156981	+	0.00906332i	0.507829	−	0.861458i	$-0.330448\pi$
$191$	0.216953	+	0.125258i	0.0156981	+	0.00906332i	−0.492130	+	0.870521i	$0.663782\pi$
$192$	−1.08518	+	1.34996i	−0.0783159	+	0.0974249i
$193$	2.68125	−	10.0066i	0.193001	−	0.720288i	−0.799775	−	0.600300i	$-0.795048\pi$
$193$	2.68125	−	10.0066i	0.193001	−	0.720288i	0.992775	−	0.119988i	$-0.0382856\pi$
$194$	3.03303			0.217759
$195$	−3.04695	+	2.26056i	−0.218197	+	0.161882i
$196$	−1.00000			−0.0714286
$197$	−2.69377	+	10.0533i	−0.191923	+	0.716267i	0.801119	+	0.598505i	$0.204238\pi$
$197$	−2.69377	+	10.0533i	−0.191923	+	0.716267i	−0.993042	+	0.117761i	$0.962428\pi$
$198$	−4.28966	−	1.35984i	−0.304853	−	0.0966394i
$199$	−2.17443	−	1.25541i	−0.154141	−	0.0889936i	0.420945	−	0.907086i	$-0.361698\pi$
$199$	−2.17443	−	1.25541i	−0.154141	−	0.0889936i	−0.575087	+	0.818092i	$0.695032\pi$
$200$	−3.27456	−	3.27456i	−0.231546	−	0.231546i
$201$	11.3510	+	15.5060i	0.800641	+	1.09371i
$202$	−4.93139	+	1.32136i	−0.346971	+	0.0929706i
$203$	−4.52084	+	4.52084i	−0.317301	+	0.317301i
$204$	8.56646	+	1.32530i	0.599772	+	0.0927895i
$205$	1.97820	−	1.14211i	0.138163	−	0.0797685i
$206$	5.69223	+	1.52523i	0.396597	+	0.106268i
$207$	−12.7243	+	11.6235i	−0.884401	+	0.807887i
$208$	1.78277	−	3.13396i	0.123613	−	0.217301i
$209$			4.31432i			0.298428i
$210$	−1.04609	+	0.113745i	−0.0721868	+	0.00784915i
$211$	11.0701	+	19.1740i	0.762097	+	1.31999i	0.941768	+	0.336263i	$0.109163\pi$
$211$	11.0701	+	19.1740i	0.762097	+	1.31999i	−0.179671	+	0.983727i	$0.557503\pi$
$212$	3.94233	−	6.82831i	0.270760	−	0.468970i
$213$	9.10303	+	4.01385i	0.623729	+	0.275024i
$214$	−2.75695	−	10.2891i	−0.188462	−	0.703348i
$215$	1.69810	+	6.33738i	0.115809	+	0.432206i
$216$	−1.65881	−	4.92426i	−0.112868	−	0.335054i
$217$	−2.02637	+	3.50978i	−0.137559	+	0.238259i
$218$	−0.256756	−	0.444715i	−0.0173897	−	0.0301199i
$219$	2.87531	+	26.4435i	0.194295	+	1.78689i
$220$		−	0.911286i		−	0.0614389i
$221$	−18.0443	+	0.115384i	−1.21379	+	0.00776156i
$222$	−5.55537	−	14.3184i	−0.372852	−	0.960990i
$223$	9.49542	+	2.54429i	0.635860	+	0.170378i	0.562328	−	0.826914i	$-0.309906\pi$
$223$	9.49542	+	2.54429i	0.635860	+	0.170378i	0.0735328	+	0.997293i	$0.476573\pi$
$224$	0.866025	−	0.500000i	0.0578638	−	0.0334077i
$225$	13.5681	−	2.98593i	0.904540	−	0.199062i
$226$	−10.8613	+	10.8613i	−0.722481	+	0.722481i
$227$	5.59370	−	1.49883i	0.371267	−	0.0994807i	−0.0683609	−	0.997661i	$-0.521777\pi$
$227$	5.59370	−	1.49883i	0.371267	−	0.0994807i	0.439628	+	0.898180i	$0.355110\pi$
$228$	−4.01974	+	2.94261i	−0.266214	+	0.194879i
$229$	1.44073	+	1.44073i	0.0952059	+	0.0952059i	0.753106	−	0.657900i	$-0.228555\pi$
$229$	1.44073	+	1.44073i	0.0952059	+	0.0952059i	−0.657900	+	0.753106i	$0.728555\pi$
$230$	−3.02243	−	1.74500i	−0.199293	−	0.115062i
$231$	2.02496	+	1.62778i	0.133232	+	0.107100i
$232$	1.65474	−	6.17558i	0.108639	−	0.405447i
$233$	−12.7341			−0.834241			−0.417120	−	0.908851i	$-0.636961\pi$
$233$	−12.7341			−0.834241			−0.417120	+	0.908851i	$0.636961\pi$
$234$	5.04100	+	9.57018i	0.329541	+	0.625622i
$235$	6.10435			0.398204
$236$	3.35057	−	12.5045i	0.218104	−	0.813974i
$237$	−4.97376	−	3.99820i	−0.323080	−	0.259711i
$238$	−4.33419	−	2.50234i	−0.280944	−	0.162203i
$239$	13.2419	+	13.2419i	0.856548	+	0.856548i	0.990930	−	0.134382i	$-0.0429049\pi$
$239$	13.2419	+	13.2419i	0.856548	+	0.856548i	−0.134382	+	0.990930i	$0.542905\pi$
$240$	0.849065	−	0.621549i	0.0548069	−	0.0401208i
$241$	−15.6813	+	4.20178i	−1.01012	+	0.270661i	−0.725679	−	0.688033i	$-0.758474\pi$
$241$	−15.6813	+	4.20178i	−1.01012	+	0.270661i	−0.284440	+	0.958694i	$0.591808\pi$
$242$	6.18715	−	6.18715i	0.397725	−	0.397725i
$243$	15.1273	+	3.76378i	0.970414	+	0.241447i
$244$	1.52276	−	0.879168i	0.0974850	−	0.0562830i
$245$	0.586817	+	0.157237i	0.0374904	+	0.0100455i
$246$	−2.35563	−	6.07142i	−0.150190	−	0.387100i
$247$	7.28582	−	7.37960i	0.463586	−	0.469553i
$248$		−	4.05275i		−	0.257350i
$249$	1.36520	+	12.5554i	0.0865159	+	0.795667i
$250$	2.92548	+	5.06708i	0.185024	+	0.320470i
$251$	0.537453	−	0.930896i	0.0339237	−	0.0587576i	−0.848565	−	0.529091i	$-0.822533\pi$
$251$	0.537453	−	0.930896i	0.0339237	−	0.0587576i	0.882489	+	0.470333i	$0.155866\pi$
$252$	−0.135502	+	2.99694i	−0.00853582	+	0.188789i
$253$	2.23027	+	8.32350i	0.140216	+	0.523294i
$254$	2.73229	+	10.1971i	0.171439	+	0.639820i
$255$	−4.81856	−	2.12468i	−0.301750	−	0.133052i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.8936	−	18.8683i	−0.679524	−	1.17697i	−0.975125	−	0.221658i	$-0.928853\pi$
$257$	−10.8936	−	18.8683i	−0.679524	−	1.17697i	0.295601	−	0.955312i	$-0.404480\pi$
$258$	18.5958	−	2.02199i	1.15772	−	0.125884i
$259$			8.86716i			0.550978i
$260$	−1.53894	+	1.55875i	−0.0954408	+	0.0966693i
$261$	12.9361	+	14.1613i	0.800724	+	0.876560i
$262$	11.8127	+	3.16519i	0.729789	+	0.195546i
$263$	7.39268	−	4.26816i	0.455852	−	0.263186i	−0.254447	−	0.967087i	$-0.581893\pi$
$263$	7.39268	−	4.26816i	0.455852	−	0.263186i	0.710298	+	0.703901i	$0.248560\pi$
$264$	−2.56756	−	0.397221i	−0.158022	−	0.0244473i
$265$	−3.38709	+	3.38709i	−0.208067	+	0.208067i
$266$	2.77818	−	0.744411i	0.170341	−	0.0456428i
$267$	−6.95922	−	9.50662i	−0.425898	−	0.581796i
$268$	7.84521	+	7.84521i	0.479222	+	0.479222i
$269$	13.8882	+	8.01838i	0.846782	+	0.488890i	0.859564	−	0.511029i	$-0.170735\pi$
$269$	13.8882	+	8.01838i	0.846782	+	0.488890i	−0.0127821	+	0.999918i	$0.504069\pi$
$270$	0.199140	+	3.15047i	0.0121193	+	0.191731i
$271$	−2.03506	+	7.59496i	−0.123621	+	0.461361i	−0.999787	−	0.0206495i	$-0.993427\pi$
$271$	−2.03506	+	7.59496i	−0.123621	+	0.461361i	0.876165	+	0.482010i	$0.160093\pi$
$272$	5.00469			0.303454
$273$	−0.714749	−	6.20396i	−0.0432586	−	0.375481i
$274$	−16.9956			−1.02674
$275$	1.79787	−	6.70975i	0.108416	−	0.404613i
$276$	−6.23401	+	7.75510i	−0.375243	+	0.466802i
$277$	16.7024	+	9.64316i	1.00355	+	0.579401i	0.909297	−	0.416147i	$-0.136620\pi$
$277$	16.7024	+	9.64316i	1.00355	+	0.579401i	0.0942548	+	0.995548i	$0.469953\pi$
$278$	−4.73763	−	4.73763i	−0.284144	−	0.284144i
$279$	10.2440	+	6.54850i	0.613293	+	0.392048i
$280$	−0.586817	+	0.157237i	−0.0350690	+	0.00939672i
$281$	16.0700	−	16.0700i	0.958654	−	0.958654i	−0.0405247	−	0.999179i	$-0.512903\pi$
$281$	16.0700	−	16.0700i	0.958654	−	0.958654i	0.999179	+	0.0405247i	$0.0129029\pi$
$282$	2.66083	−	17.1991i	0.158450	−	1.02419i
$283$	−12.6510	+	7.30408i	−0.752026	+	0.434182i	−0.826426	−	0.563046i	$-0.809629\pi$
$283$	−12.6510	+	7.30408i	−0.752026	+	0.434182i	0.0743994	+	0.997229i	$0.476296\pi$
$284$	5.54815	+	1.48662i	0.329222	+	0.0882148i
$285$	2.82154	−	1.09472i	0.167134	−	0.0648458i
$286$	5.40827	−	0.0345831i	0.319798	−	0.00204494i
$287$			3.75993i			0.221941i
$288$	−1.38112	−	2.66318i	−0.0813833	−	0.156929i
$289$	−4.02345	−	6.96883i	−0.236674	−	0.409931i
$290$	−1.94206	+	3.36375i	−0.114042	+	0.197526i
$291$	−2.11950	+	4.80682i	−0.124247	+	0.281781i
$292$	3.97473	+	14.8339i	0.232603	+	0.868088i
$293$	2.19074	+	8.17594i	0.127984	+	0.477643i	0.999928	−	0.0119617i	$-0.00380762\pi$
$293$	2.19074	+	8.17594i	0.127984	+	0.477643i	−0.871944	+	0.489605i	$0.837141\pi$
$294$	0.698806	−	1.58483i	0.0407552	−	0.0924289i
$295$	−3.93235	+	6.81102i	−0.228950	+	0.396553i
$296$	−4.43358	−	7.67919i	−0.257697	−	0.446344i
$297$	5.15275	−	5.84811i	0.298993	−	0.339342i
$298$		−	20.8253i		−	1.20637i
$299$	10.2415	−	18.0036i	0.592280	−	1.04118i
$300$	7.47788	−	2.90132i	0.431735	−	0.167508i
$301$	−10.4316	−	2.79514i	−0.601267	−	0.161109i
$302$	−2.25169	+	1.30001i	−0.129570	+	0.0748073i
$303$	1.35196	−	8.73876i	0.0776678	−	0.502029i
$304$	−2.03377	+	2.03377i	−0.116645	+	0.116645i
$305$	−1.03182	+	0.276476i	−0.0590820	+	0.0158310i
$306$	−8.08666	+	12.6502i	−0.462284	+	0.723165i
$307$	5.74908	+	5.74908i	0.328117	+	0.328117i	0.851870	−	0.523753i	$-0.175469\pi$
$307$	5.74908	+	5.74908i	0.328117	+	0.328117i	−0.523753	+	0.851870i	$0.675469\pi$
$308$	1.29905	+	0.750007i	0.0740203	+	0.0427356i
$309$	−6.39499	+	7.95535i	−0.363798	+	0.452564i
$310$	−0.637243	+	2.37822i	−0.0361929	+	0.135074i
$311$	−26.7307			−1.51576			−0.757879	−	0.652395i	$-0.773764\pi$
$311$	−26.7307			−1.51576			−0.757879	+	0.652395i	$0.773764\pi$
$312$	3.72097	+	5.01541i	0.210659	+	0.283942i
$313$	16.9273			0.956789			0.478395	−	0.878145i	$-0.341219\pi$
$313$	16.9273			0.956789			0.478395	+	0.878145i	$0.341219\pi$
$314$	−5.32148	+	19.8601i	−0.300309	+	1.12077i
$315$	0.550745	−	1.73735i	0.0310310	−	0.0978885i
$316$	−3.19076	−	1.84219i	−0.179494	−	0.103631i
$317$	−5.59592	−	5.59592i	−0.314298	−	0.314298i	0.532274	−	0.846572i	$-0.321338\pi$
$317$	−5.59592	−	5.59592i	−0.314298	−	0.314298i	−0.846572	+	0.532274i	$0.821338\pi$
$318$	8.06676	+	11.0196i	0.452361	+	0.617946i
$319$	9.26346	−	2.48214i	0.518654	−	0.138973i
$320$	0.429580	−	0.429580i	0.0240143	−	0.0240143i
$321$	18.2330	+	2.82079i	1.01767	+	0.157441i
$322$	4.97505	−	2.87235i	0.277249	−	0.160070i
$323$	13.9039	+	3.72555i	0.773635	+	0.207295i
$324$	8.96328	+	0.812182i	0.497960	+	0.0451212i
$325$	−14.4064	+	8.44081i	−0.799122	+	0.468212i
$326$		−	6.71813i		−	0.372083i
$327$	0.884218	−	0.0961444i	0.0488973	−	0.00531680i
$328$	−1.87996	−	3.25619i	−0.103804	−	0.179793i
$329$	−5.02400	+	8.70183i	−0.276982	+	0.479747i
$330$	1.44423	+	0.636812i	0.0795021	+	0.0350553i
$331$	−5.58301	−	20.8361i	−0.306870	−	1.14525i	−0.931324	−	0.364193i	$-0.881345\pi$
$331$	−5.58301	−	20.8361i	−0.306870	−	1.14525i	0.624454	−	0.781062i	$-0.285322\pi$
$332$	1.88720	+	7.04314i	0.103574	+	0.386543i
$333$	26.5743	+	1.20152i	1.45626	+	0.0658428i
$334$	3.49622	−	6.05563i	0.191305	−	0.331349i
$335$	−3.37015	−	5.83726i	−0.184131	−	0.318924i
$336$	0.187229	+	1.72190i	0.0102142	+	0.0939374i
$337$		−	26.6748i		−	1.45307i	−0.687129	−	0.726535i	$-0.741129\pi$
$337$		−	26.6748i		−	1.45307i	0.687129	−	0.726535i	$-0.258871\pi$
$338$	−9.30919	−	9.07408i	−0.506353	−	0.493565i
$339$	−9.62330	−	24.8031i	−0.522666	−	1.34712i
$340$	−2.93684	−	0.786923i	−0.159272	−	0.0426769i
$341$	5.26472	−	3.03959i	0.285101	−	0.164603i
$342$	−1.85451	−	8.42690i	−0.100280	−	0.455675i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	10.4316	−	2.79514i	0.562434	−	0.150704i
$345$	4.87761	−	3.57061i	0.262602	−	0.192235i
$346$	5.93075	+	5.93075i	0.318839	+	0.318839i
$347$	−11.0636	−	6.38760i	−0.593928	−	0.342904i	0.172721	−	0.984971i	$-0.444744\pi$
$347$	−11.0636	−	6.38760i	−0.593928	−	0.342904i	−0.766649	+	0.642066i	$0.778077\pi$
$348$	8.63087	+	6.93801i	0.462663	+	0.371916i
$349$	−7.64398	+	28.5277i	−0.409173	+	1.52705i	0.387054	+	0.922057i	$0.373493\pi$
$349$	−7.64398	+	28.5277i	−0.409173	+	1.52705i	−0.796227	+	0.604997i	$0.793174\pi$
$350$	−4.63092			−0.247533
$351$	−18.6897	+	1.30141i	−0.997584	+	0.0694641i
$352$	−1.50001			−0.0799510
$353$	5.52047	−	20.6027i	0.293825	−	1.09657i	−0.648321	−	0.761367i	$-0.724528\pi$
$353$	5.52047	−	20.6027i	0.293825	−	1.09657i	0.942146	−	0.335203i	$-0.108805\pi$
$354$	17.4760	+	14.0483i	0.928842	+	0.746658i
$355$	−3.02200	−	1.74475i	−0.160391	−	0.0926018i
$356$	−4.80983	−	4.80983i	−0.254920	−	0.254920i
$357$	6.99453	−	5.12028i	0.370190	−	0.270994i
$358$	16.0786	−	4.30825i	0.849781	−	0.227698i
$359$	6.63087	−	6.63087i	0.349964	−	0.349964i	−0.510132	−	0.860096i	$-0.670403\pi$
$359$	6.63087	−	6.63087i	0.349964	−	0.349964i	0.860096	+	0.510132i	$0.170403\pi$
$360$	0.391715	+	1.77996i	0.0206452	+	0.0938122i
$361$	9.29034	−	5.36378i	0.488965	−	0.282304i
$362$	−4.82260	−	1.29221i	−0.253470	−	0.0679172i
$363$	5.48194	+	14.1292i	0.287727	+	0.741589i
$364$	−0.955436	−	3.47666i	−0.0500784	−	0.182226i
$365$		−	9.32976i		−	0.488342i
$366$	0.329212	+	3.02768i	0.0172082	+	0.158260i
$367$	2.21303	+	3.83308i	0.115519	+	0.200085i	0.917987	−	0.396610i	$-0.129814\pi$
$367$	2.21303	+	3.83308i	0.115519	+	0.200085i	−0.802468	+	0.596695i	$0.796480\pi$
$368$	−2.87235	+	4.97505i	−0.149731	+	0.259342i
$369$	11.2683	+	0.509477i	0.586603	+	0.0265223i
$370$	1.39425	+	5.20340i	0.0724835	+	0.270512i
$371$	−2.04070	−	7.61599i	−0.105948	−	0.395403i
$372$	6.42289	+	2.83208i	0.333012	+	0.146837i
$373$	9.33873	−	16.1752i	0.483541	−	0.837518i	−0.516280	−	0.856420i	$-0.672684\pi$
$373$	9.33873	−	16.1752i	0.483541	−	0.837518i	0.999821	+	0.0189019i	$0.00601701\pi$
$374$	3.75355	+	6.50134i	0.194092	+	0.336176i
$375$	−10.0748	+	1.09547i	−0.520259	+	0.0565698i
$376$		−	10.0480i		−	0.518186i
$377$	−20.0368	−	11.3980i	−1.03195	−	0.587029i
$378$	−4.65493	−	2.30902i	−0.239424	−	0.118763i
$379$	−28.2454	−	7.56834i	−1.45087	−	0.388759i	−0.554544	−	0.832154i	$-0.687107\pi$
$379$	−28.2454	−	7.56834i	−1.45087	−	0.388759i	−0.896326	+	0.443395i	$0.853774\pi$
$380$	1.51324	−	0.873667i	0.0776273	−	0.0448182i
$381$	−18.0699	−	2.79556i	−0.925749	−	0.143221i
$382$	−0.177141	+	0.177141i	−0.00906332	+	0.00906332i
$383$	−22.1048	+	5.92296i	−1.12950	+	0.302649i	−0.774723	−	0.632301i	$-0.782111\pi$
$383$	−22.1048	+	5.92296i	−1.12950	+	0.302649i	−0.354779	+	0.934950i	$0.615444\pi$
$384$	−1.02310	−	1.39760i	−0.0522096	−	0.0713208i
$385$	−0.644376	−	0.644376i	−0.0328405	−	0.0328405i
$386$	8.97164	+	5.17978i	0.456645	+	0.263644i
$387$	−9.79035	+	30.8841i	−0.497672	+	1.56993i
$388$	−0.785006	+	2.92968i	−0.0398526	+	0.148732i
$389$	6.65640			0.337493			0.168746	−	0.985659i	$-0.446028\pi$
$389$	6.65640			0.337493			0.168746	+	0.985659i	$0.446028\pi$
$390$	−1.39492	−	3.52821i	−0.0706345	−	0.178658i
$391$	28.7504			1.45397
$392$	0.258819	−	0.965926i	0.0130723	−	0.0487866i
$393$	−13.2710	+	16.5091i	−0.669435	+	0.832776i
$394$	−9.01352	−	5.20396i	−0.454095	−	0.262172i
$395$	1.58273	+	1.58273i	0.0796360	+	0.0796360i
$396$	2.42375	−	3.79155i	0.121798	−	0.190532i
$397$	−20.0004	+	5.35909i	−1.00379	+	0.268965i	−0.723033	−	0.690814i	$-0.757253\pi$
$397$	−20.0004	+	5.35909i	−1.00379	+	0.268965i	−0.280758	+	0.959779i	$0.590586\pi$
$398$	1.77542	−	1.77542i	0.0889936	−	0.0889936i
$399$	−0.761647	+	4.92313i	−0.0381300	+	0.246465i
$400$	4.01050	−	2.31546i	0.200525	−	0.115773i
$401$	22.2943	+	5.97375i	1.11333	+	0.298315i	0.768180	−	0.640234i	$-0.221163\pi$
$401$	22.2943	+	5.97375i	1.11333	+	0.298315i	0.345146	+	0.938549i	$0.387829\pi$
$402$	−17.9156	+	6.95101i	−0.893547	+	0.346685i
$403$	−14.1384	−	3.69163i	−0.704283	−	0.183893i
$404$		−	5.10535i		−	0.254001i
$405$	−5.13210	−	1.88596i	−0.255016	−	0.0937143i
$406$	−3.19672	−	5.53687i	−0.158650	−	0.274790i
$407$	6.65043	−	11.5189i	0.329650	−	0.570970i
$408$	−3.49731	+	7.93156i	−0.173142	+	0.392671i
$409$	−6.78397	−	25.3181i	−0.335446	−	1.25190i	−0.903385	−	0.428830i	$-0.858926\pi$
$409$	−6.78397	−	25.3181i	−0.335446	−	1.25190i	0.567940	−	0.823070i	$-0.307741\pi$
$410$	0.591201	+	2.20639i	0.0291973	+	0.108966i
$411$	11.8766	−	26.9351i	0.585832	−	1.32861i
$412$	−2.94652	+	5.10352i	−0.145164	+	0.251432i
$413$	−6.47281	−	11.2112i	−0.318506	−	0.551669i
$414$	−7.93411	−	15.2991i	−0.389940	−	0.751911i
$415$		−	4.42978i		−	0.217449i
$416$	2.56576	+	2.53316i	0.125797	+	0.124198i
$417$	10.8190	−	4.19763i	0.529808	−	0.205559i
$418$	−4.16731	−	1.11663i	−0.203830	−	0.0546160i
$419$	−16.6593	+	9.61826i	−0.813860	+	0.469883i	−0.848295	−	0.529524i	$-0.822370\pi$
$419$	−16.6593	+	9.61826i	−0.813860	+	0.469883i	0.0344342	+	0.999407i	$0.489037\pi$
$420$	0.160878	−	1.03988i	0.00785003	−	0.0507410i
$421$	6.20540	−	6.20540i	0.302433	−	0.302433i	−0.539532	−	0.841965i	$-0.681399\pi$
$421$	6.20540	−	6.20540i	0.302433	−	0.302433i	0.841965	+	0.539532i	$0.181399\pi$
$422$	−21.3858	+	5.73030i	−1.04104	+	0.278947i
$423$	25.3981	+	16.2357i	1.23490	+	0.789409i
$424$	5.57529	+	5.57529i	0.270760	+	0.270760i
$425$	−20.0713	−	11.5882i	−0.973600	−	0.562108i
$426$	−6.23312	+	7.75399i	−0.301995	+	0.375682i
$427$	0.455091	−	1.69842i	0.0220234	−	0.0821924i
$428$	10.6521			0.514886
$429$	−3.72452	+	8.59532i	−0.179822	+	0.414986i
$430$	−6.56094			−0.316397
$431$	−1.96096	+	7.31839i	−0.0944559	+	0.352514i	−0.996936	−	0.0782165i	$-0.975077\pi$
$431$	−1.96096	+	7.31839i	−0.0944559	+	0.352514i	0.902480	+	0.430731i	$0.141744\pi$
$432$	5.18580	−	0.327793i	0.249502	−	0.0157709i
$433$	3.29167	+	1.90044i	0.158187	+	0.0913295i	0.577004	−	0.816741i	$-0.304222\pi$
$433$	3.29167	+	1.90044i	0.158187	+	0.0913295i	−0.418817	+	0.908071i	$0.637555\pi$
$434$	−2.86572	−	2.86572i	−0.137559	−	0.137559i
$435$	−3.97383	−	5.42844i	−0.190531	−	0.260274i
$436$	0.496015	−	0.132907i	0.0237548	−	0.00636508i
$437$	−11.6834	+	11.6834i	−0.558892	+	0.558892i
$438$	−26.2867	−	4.06676i	−1.25603	−	0.194317i
$439$	3.83310	−	2.21304i	0.182944	−	0.105623i	−0.405731	−	0.913992i	$-0.632983\pi$
$439$	3.83310	−	2.21304i	0.182944	−	0.105623i	0.588675	+	0.808370i	$0.299650\pi$
$440$	0.880234	+	0.235858i	0.0419635	+	0.0112441i
$441$	2.02334	+	2.21497i	0.0963496	+	0.105475i
$442$	4.55875	−	17.4593i	0.216838	−	0.830455i
$443$		−	0.744366i		−	0.0353659i	−0.999844	−	0.0176829i	$-0.994371\pi$
$443$		−	0.744366i		−	0.0353659i	0.999844	−	0.0176829i	$-0.00562895\pi$
$444$	15.2684	−	1.66019i	0.724605	−	0.0787891i
$445$	2.06621	+	3.57877i	0.0979476	+	0.169650i
$446$	−4.91519	+	8.51336i	−0.232741	+	0.403119i
$447$	33.0044	+	14.5528i	1.56105	+	0.688324i
$448$	0.258819	+	0.965926i	0.0122281	+	0.0456357i
$449$	3.55603	+	13.2713i	0.167819	+	0.626310i	0.997664	+	0.0683153i	$0.0217624\pi$
$449$	3.55603	+	13.2713i	0.167819	+	0.626310i	−0.829845	+	0.557995i	$0.811571\pi$
$450$	−0.627499	+	13.8786i	−0.0295806	+	0.654243i
$451$	2.81997	−	4.88433i	0.132787	−	0.229994i
$452$	−7.68008	−	13.3023i	−0.361241	−	0.625687i
$453$	−0.486800	−	4.47699i	−0.0228719	−	0.210347i
$454$			5.79103i			0.271786i
$455$	0.0140064	+	2.19039i	0.000656631	+	0.102687i
$456$	−1.80196	−	4.64438i	−0.0843845	−	0.217493i
$457$	13.1858	+	3.53312i	0.616805	+	0.165272i	0.553675	−	0.832733i	$-0.313225\pi$
$457$	13.1858	+	3.53312i	0.616805	+	0.165272i	0.0631300	+	0.998005i	$0.479892\pi$
$458$	−1.76452	+	1.01875i	−0.0824507	+	0.0476029i
$459$	−14.3974	−	21.6560i	−0.672012	−	1.01082i
$460$	2.46780	−	2.46780i	0.115062	−	0.115062i
$461$	−18.9023	+	5.06487i	−0.880370	+	0.235894i	−0.670567	−	0.741849i	$-0.733949\pi$
$461$	−18.9023	+	5.06487i	−0.880370	+	0.235894i	−0.209803	+	0.977744i	$0.567282\pi$
$462$	−2.09641	+	1.53466i	−0.0975340	+	0.0713988i
$463$	1.12387	+	1.12387i	0.0522307	+	0.0522307i	0.732740	−	0.680509i	$-0.238241\pi$
$463$	1.12387	+	1.12387i	0.0522307	+	0.0522307i	−0.680509	+	0.732740i	$0.738241\pi$
$464$	5.53687	+	3.19672i	0.257043	+	0.148404i
$465$	−3.32376	−	2.67183i	−0.154136	−	0.123903i
$466$	3.29584	−	12.3002i	0.152677	−	0.569797i
$467$	−27.6183			−1.27802			−0.639011	−	0.769198i	$-0.720656\pi$
$467$	−27.6183			−1.27802			−0.639011	+	0.769198i	$0.720656\pi$
$468$	−10.5488	+	2.39229i	−0.487618	+	0.110584i
$469$	11.0948			0.512310
$470$	−1.57992	+	5.89635i	−0.0728763	+	0.271978i
$471$	−27.7560	−	22.3119i	−1.27893	−	1.02808i
$472$	11.2112	+	6.47281i	0.516039	+	0.297935i
$473$	11.4548	+	11.4548i	0.526692	+	0.526692i
$474$	5.14927	−	3.76947i	0.236514	−	0.173138i
$475$	12.8655	−	3.44731i	0.590311	−	0.158173i
$476$	3.53885	−	3.53885i	0.162203	−	0.162203i
$477$	−23.1012	+	5.08387i	−1.05773	+	0.232774i
$478$	−16.2180	+	9.36344i	−0.741792	+	0.428274i
$479$	39.4326	+	10.5659i	1.80172	+	0.482770i	0.994245	−	0.107131i	$-0.0341665\pi$
$479$	39.4326	+	10.5659i	1.80172	+	0.482770i	0.807476	+	0.589901i	$0.200833\pi$
$480$	0.380616	+	0.981002i	0.0173727	+	0.0447764i
$481$	−30.8281	+	8.47200i	−1.40564	+	0.386290i
$482$		−	16.2344i		−	0.739459i
$483$	1.07557	+	9.89179i	0.0489403	+	0.450092i
$484$	4.37498	+	7.57769i	0.198863	+	0.344440i
$485$	0.921310	−	1.59576i	0.0418345	−	0.0724595i
$486$	−7.55076	+	13.6377i	−0.342509	+	0.618617i
$487$	−0.944238	−	3.52394i	−0.0427875	−	0.159685i	0.941227	−	0.337776i	$-0.109675\pi$
$487$	−0.944238	−	3.52394i	−0.0427875	−	0.159685i	−0.984014	+	0.178091i	$0.943008\pi$
$488$	0.455091	+	1.69842i	0.0206010	+	0.0768840i
$489$	10.6471	+	4.69467i	0.481477	+	0.212300i
$490$	−0.303759	+	0.526126i	−0.0137224	+	0.0237680i
$491$	−12.1442	−	21.0344i	−0.548061	−	0.949269i	−0.998407	−	0.0564153i	$-0.982033\pi$
$491$	−12.1442	−	21.0344i	−0.548061	−	0.949269i	0.450347	−	0.892854i	$-0.351300\pi$
$492$	6.47423	−	0.703967i	0.291881	−	0.0317373i
$493$		−	31.9971i		−	1.44108i
$494$	5.24244	+	8.94754i	0.235868	+	0.402569i
$495$	−2.01847	+	1.84384i	−0.0907235	+	0.0828745i
$496$	3.91465	+	1.04893i	0.175773	+	0.0470983i
$497$	4.97434	−	2.87193i	0.223129	−	0.128824i
$498$	−12.4809	−	1.93090i	−0.559284	−	0.0865257i
$499$	−6.04184	+	6.04184i	−0.270470	+	0.270470i	−0.829289	−	0.558819i	$-0.811254\pi$
$499$	−6.04184	+	6.04184i	−0.270470	+	0.270470i	0.558819	+	0.829289i	$0.311254\pi$
$500$	−5.65159	+	1.51434i	−0.252747	+	0.0677233i
$501$	7.15394	+	9.77261i	0.319614	+	0.436608i
$502$	0.760073	+	0.760073i	0.0339237	+	0.0339237i
$503$	16.7473	+	9.66904i	0.746724	+	0.431121i	0.824509	−	0.565849i	$-0.191452\pi$
$503$	16.7473	+	9.66904i	0.746724	+	0.431121i	−0.0777852	+	0.996970i	$0.524785\pi$
$504$	−2.85975	−	0.906550i	−0.127383	−	0.0403809i
$505$	−0.802751	+	2.99591i	−0.0357219	+	0.133316i
$506$	−8.61712			−0.383078
$507$	20.8861	−	8.41242i	0.927586	−	0.373609i
$508$	−10.5568			−0.468381
$509$	−9.82494	+	36.6672i	−0.435483	+	1.62524i	0.304426	+	0.952536i	$0.401535\pi$
$509$	−9.82494	+	36.6672i	−0.435483	+	1.62524i	−0.739908	+	0.672708i	$0.765131\pi$
$510$	3.29942	−	4.10447i	0.146101	−	0.181749i
$511$	13.2997	+	7.67859i	0.588344	+	0.339681i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	14.6511	+	2.94970i	0.646862	+	0.130233i
$514$	21.0448	−	5.63894i	0.928246	−	0.248723i
$515$	2.53153	−	2.53153i	0.111553	−	0.111553i
$516$	−2.85985	+	18.4855i	−0.125898	+	0.813779i
$517$	13.0529	−	7.53608i	0.574064	−	0.331436i
$518$	−8.56502	−	2.29499i	−0.376325	−	0.100836i
$519$	−13.5437	+	5.25476i	−0.594500	+	0.230658i
$520$	−1.10733	−	1.88993i	−0.0485595	−	0.0828790i
$521$		−	13.5471i		−	0.593507i	−0.954954	−	0.296754i	$-0.904096\pi$
$521$		−	13.5471i		−	0.593507i	0.954954	−	0.296754i	$-0.0959040\pi$
$522$	−17.0268	+	8.83010i	−0.745244	+	0.386483i
$523$	−21.9843	−	38.0779i	−0.961305	−	1.66503i	−0.719231	−	0.694771i	$-0.755506\pi$
$523$	−21.9843	−	38.0779i	−0.961305	−	1.66503i	−0.242074	−	0.970258i	$-0.577828\pi$
$524$	−6.11468	+	10.5909i	−0.267121	+	0.462667i
$525$	3.23611	−	7.33920i	0.141236	−	0.320309i
$526$	2.20936	+	8.24546i	0.0963328	+	0.359519i
$527$	−5.24956	−	19.5916i	−0.228674	−	0.853424i
$528$	1.04822	−	2.37726i	0.0456179	−	0.103457i
$529$	−5.00074	+	8.66153i	−0.217423	+	0.376588i
$530$	−2.39503	−	4.14832i	−0.104034	−	0.180192i
$531$	−34.4764	+	17.8795i	−1.49615	+	0.775902i
$532$			2.87618i			0.124698i
$533$	−13.0720	+	3.59237i	−0.566210	+	0.155603i
$534$	10.9839	−	4.26160i	0.475319	−	0.184417i
$535$	−6.25081	−	1.67490i	−0.270246	−	0.0724122i
$536$	−9.60838	+	5.54740i	−0.415019	+	0.239611i
$537$	−4.40800	+	28.4924i	−0.190219	+	1.22954i
$538$	−11.3397	+	11.3397i	−0.488890	+	0.488890i
$539$	1.44890	−	0.388232i	0.0624086	−	0.0167223i
$540$	−3.09466	−	0.623047i	−0.133173	−	0.0268117i
$541$	−20.4730	−	20.4730i	−0.880204	−	0.880204i	0.113351	−	0.993555i	$-0.463841\pi$
$541$	−20.4730	−	20.4730i	−0.880204	−	0.880204i	−0.993555	+	0.113351i	$0.963841\pi$
$542$	−6.80945	−	3.93144i	−0.292491	−	0.168870i
$543$	5.41799	−	6.73998i	0.232508	−	0.289240i
$544$	−1.29531	+	4.83416i	−0.0555359	+	0.207263i
$545$	−0.311968			−0.0133632
$546$	6.17756	+	0.915309i	0.264375	+	0.0391716i
$547$	−14.9014			−0.637139			−0.318569	−	0.947900i	$-0.603202\pi$
$547$	−14.9014			−0.637139			−0.318569	+	0.947900i	$0.603202\pi$
$548$	4.39879	−	16.4165i	0.187907	−	0.701279i
$549$	−5.02840	−	1.59402i	−0.214607	−	0.0680311i
$550$	6.01580	+	3.47322i	0.256515	+	0.148099i
$551$	13.0028	+	13.0028i	0.553936	+	0.553936i
$552$	−5.87737	−	8.02876i	−0.250157	−	0.341727i
$553$	−3.55883	+	0.953587i	−0.151337	+	0.0405506i
$554$	−13.6375	+	13.6375i	−0.579401	+	0.579401i
$555$	−9.22079	−	1.42653i	−0.391401	−	0.0605528i
$556$	5.80239	−	3.35001i	0.246076	−	0.142072i
$557$	−5.20313	−	1.39418i	−0.220464	−	0.0590731i	0.146896	−	0.989152i	$-0.453072\pi$
$557$	−5.20313	−	1.39418i	−0.220464	−	0.0590731i	−0.367360	+	0.930079i	$0.619738\pi$
$558$	−8.97671	+	8.20009i	−0.380014	+	0.347137i
$559$	−0.248986	−	38.9376i	−0.0105310	−	1.64689i
$560$		−	0.607518i		−	0.0256723i
$561$	−12.9265	+	1.40555i	−0.545757	+	0.0593423i
$562$	11.3632	+	19.6816i	0.479327	+	0.830219i
$563$	−20.4692	+	35.4536i	−0.862672	+	1.49419i	0.00666798	+	0.999978i	$0.497877\pi$
$563$	−20.4692	+	35.4536i	−0.862672	+	1.49419i	−0.869340	+	0.494214i	$0.835456\pi$
$564$	15.9243	+	7.02161i	0.670535	+	0.295663i
$565$	2.41519	+	9.01361i	0.101608	+	0.379205i
$566$	−3.78087	−	14.1104i	−0.158922	−	0.593104i
$567$	6.91229	−	5.76370i	0.290289	−	0.242052i
$568$	−2.87193	+	4.97434i	−0.120504	+	0.208718i
$569$	18.8139	+	32.5867i	0.788722	+	1.36611i	0.926750	+	0.375678i	$0.122590\pi$
$569$	18.8139	+	32.5867i	0.788722	+	1.36611i	−0.138029	+	0.990428i	$0.544077\pi$
$570$	0.327152	+	3.00874i	0.0137029	+	0.126022i
$571$			46.6107i			1.95060i	0.220892	+	0.975298i	$0.429103\pi$
$571$			46.6107i			1.95060i	−0.220892	+	0.975298i	$0.570897\pi$
$572$	−1.36636	+	5.23294i	−0.0571303	+	0.218800i
$573$	−0.156950	−	0.404525i	−0.00655670	−	0.0168993i
$574$	−3.63181	−	0.973141i	−0.151589	−	0.0406181i
$575$	23.0391	−	13.3016i	0.960795	−	0.554715i
$576$	2.92989	−	0.644780i	0.122079	−	0.0268658i
$577$	−19.7783	+	19.7783i	−0.823382	+	0.823382i	−0.986591	−	0.163210i	$-0.947815\pi$
$577$	−19.7783	+	19.7783i	−0.823382	+	0.823382i	0.163210	+	0.986591i	$0.447815\pi$
$578$	7.77272	−	2.08269i	0.323302	−	0.0866286i
$579$	−14.4785	+	10.5988i	−0.601705	+	0.440472i
$580$	−2.74649	−	2.74649i	−0.114042	−	0.114042i
$581$	6.31471	+	3.64580i	0.261978	+	0.151253i
$582$	−4.09447	−	3.29137i	−0.169721	−	0.136432i
$583$	−3.06108	+	11.4241i	−0.126777	+	0.473138i
$584$	−15.3572			−0.635484
$585$	6.56637	+	0.254826i	0.271486	+	0.0105358i
$586$	−8.46435			−0.349659
$587$	−4.80513	+	17.9330i	−0.198329	+	0.740174i	0.793051	+	0.609156i	$0.208491\pi$
$587$	−4.80513	+	17.9330i	−0.198329	+	0.740174i	−0.991380	+	0.131019i	$0.958175\pi$
$588$	1.34996	+	1.08518i	0.0556714	+	0.0447520i
$589$	10.0948	+	5.82822i	0.415948	+	0.240148i
$590$	−5.56118	−	5.56118i	−0.228950	−	0.228950i
$591$	14.5461	−	10.6483i	0.598345	−	0.438013i
$592$	8.56502	−	2.29499i	0.352020	−	0.0943235i
$593$	−23.0341	+	23.0341i	−0.945899	+	0.945899i	−0.998610	−	0.0527111i	$-0.983214\pi$
$593$	−23.0341	+	23.0341i	−0.945899	+	0.945899i	0.0527111	+	0.998610i	$0.483214\pi$
$594$	4.31521	+	6.49077i	0.177055	+	0.266320i
$595$	−2.63310	+	1.52022i	−0.107946	+	0.0623229i
$596$	20.1156	+	5.38997i	0.823969	+	0.220782i
$597$	1.57305	+	4.05439i	0.0643808	+	0.165935i
$598$	14.7395	+	14.5522i	0.602743	+	0.595083i
$599$			18.7978i			0.768058i	0.923321	+	0.384029i	$0.125464\pi$
$599$			18.7978i			0.768058i	−0.923321	+	0.384029i	$0.874536\pi$
$600$	0.867043	+	7.97399i	0.0353969	+	0.325537i
$601$	3.42337	+	5.92945i	0.139642	+	0.241867i	0.927361	−	0.374167i	$-0.122071\pi$
$601$	3.42337	+	5.92945i	0.139642	+	0.241867i	−0.787719	+	0.616035i	$0.788738\pi$
$602$	5.39979	−	9.35271i	0.220079	−	0.381188i
$603$	1.50337	−	33.2504i	0.0612218	−	1.35406i
$604$	−0.672936	−	2.51143i	−0.0273814	−	0.102189i
$605$	−1.37582	−	5.13463i	−0.0559350	−	0.208752i
$606$	8.09108	+	3.56765i	0.328678	+	0.144926i
$607$	22.9741	−	39.7924i	0.932491	−	1.61512i	0.153443	−	0.988157i	$-0.450964\pi$
$607$	22.9741	−	39.7924i	0.932491	−	1.61512i	0.779048	−	0.626964i	$-0.215703\pi$
$608$	−1.43809	−	2.49085i	−0.0583223	−	0.101017i
$609$	11.0089	−	1.19704i	0.446102	−	0.0485063i
$610$		−	1.06822i		−	0.0432510i
$611$	−35.0534	−	9.15270i	−1.41811	−	0.370279i
$612$	−10.1262	−	11.0852i	−0.409327	−	0.448094i
$613$	−16.8630	−	4.51842i	−0.681089	−	0.182497i	−0.0983444	−	0.995152i	$-0.531355\pi$
$613$	−16.8630	−	4.51842i	−0.681089	−	0.182497i	−0.582745	+	0.812655i	$0.698021\pi$
$614$	−7.04115	+	4.06521i	−0.284158	+	0.164059i
$615$	−3.90988	−	0.604889i	−0.157661	−	0.0243915i
$616$	−1.06067	+	1.06067i	−0.0427356	+	0.0427356i
$617$	−17.9619	+	4.81288i	−0.723119	+	0.193759i	−0.601563	−	0.798825i	$-0.705455\pi$
$617$	−17.9619	+	4.81288i	−0.723119	+	0.193759i	−0.121556	+	0.992585i	$0.538788\pi$
$618$	−6.02914	−	8.23608i	−0.242527	−	0.331304i
$619$	14.2267	+	14.2267i	0.571818	+	0.571818i	0.932636	−	0.360818i	$-0.117502\pi$
$619$	14.2267	+	14.2267i	0.571818	+	0.571818i	−0.360818	+	0.932636i	$0.617502\pi$
$620$	−2.13226	−	1.23106i	−0.0856334	−	0.0494405i
$621$	29.7908	−	1.88307i	1.19546	−	0.0755649i
$622$	6.91841	−	25.8199i	0.277403	−	1.03528i
$623$	−6.80212			−0.272521
$624$	−5.80758	+	2.29610i	−0.232489	+	0.0919175i
$625$	−19.6000			−0.784002
$626$	−4.38112	+	16.3505i	−0.175105	+	0.653499i
$627$	4.68180	−	5.82415i	0.186973	−	0.232594i
$628$	−17.8060	−	10.2803i	−0.710538	−	0.410229i
$629$	−31.3795	−	31.3795i	−1.25118	−	1.25118i
$630$	1.53561	+	0.981638i	0.0611801	+	0.0391094i
$631$	18.0970	−	4.84907i	0.720430	−	0.193039i	0.120066	−	0.992766i	$-0.461689\pi$
$631$	18.0970	−	4.84907i	0.720430	−	0.193039i	0.600363	+	0.799727i	$0.295023\pi$
$632$	2.60525	−	2.60525i	0.103631	−	0.103631i
$633$	5.86298	−	37.8971i	0.233032	−	1.50627i
$634$	6.85358	−	3.95692i	0.272190	−	0.157149i
$635$	6.19490	+	1.65992i	0.245837	+	0.0658718i
$636$	−12.7319	+	4.93982i	−0.504853	+	0.195876i
$637$	−3.13396	−	1.78277i	−0.124172	−	0.0706360i
$638$			9.59024i			0.379681i
$639$	−7.93298	−	15.2969i	−0.313824	−	0.605137i
$640$	0.303759	+	0.526126i	0.0120071	+	0.0207970i
$641$	12.0969	−	20.9525i	0.477799	−	0.827573i	−0.521877	−	0.853021i	$-0.674768\pi$
$641$	12.0969	−	20.9525i	0.477799	−	0.827573i	0.999676	+	0.0254482i	$0.00810130\pi$
$642$	−7.44372	+	16.8816i	−0.293780	+	0.666265i
$643$	−2.06922	−	7.72242i	−0.0816020	−	0.304543i	0.913047	−	0.407854i	$-0.133723\pi$
$643$	−2.06922	−	7.72242i	−0.0816020	−	0.304543i	−0.994649	+	0.103311i	$0.967056\pi$
$644$	1.48684	+	5.54895i	0.0585895	+	0.218659i
$645$	4.58482	−	10.3979i	0.180527	−	0.409419i
$646$	−7.19720	+	12.4659i	−0.283170	+	0.490465i
$647$	−12.4194	−	21.5110i	−0.488256	−	0.845684i	0.511653	−	0.859192i	$-0.329033\pi$
$647$	−12.4194	−	21.5110i	−0.488256	−	0.845684i	−0.999909	+	0.0135085i	$0.995700\pi$
$648$	−3.10437	+	8.44765i	−0.121951	+	0.331855i
$649$			19.4186i			0.762247i
$650$	−4.42455	−	16.1001i	−0.173545	−	0.631499i
$651$	6.54426	−	2.53909i	0.256490	−	0.0995147i
$652$	6.48922	+	1.73878i	0.254137	+	0.0680959i
$653$	31.1279	−	17.9717i	1.21813	−	0.703287i	0.253611	−	0.967306i	$-0.418382\pi$
$653$	31.1279	−	17.9717i	1.21813	−	0.703287i	0.964517	+	0.264019i	$0.0850483\pi$
$654$	−0.135984	+	0.878973i	−0.00531739	+	0.0343705i
$655$	5.25349	−	5.25349i	0.205271	−	0.205271i
$656$	3.63181	−	0.973141i	0.141798	−	0.0379948i
$657$	24.8144	−	38.8179i	0.968102	−	1.51443i
$658$	−7.10501	−	7.10501i	−0.276982	−	0.276982i
$659$	18.0111	+	10.3987i	0.701611	+	0.405075i	0.807947	−	0.589255i	$-0.200579\pi$
$659$	18.0111	+	10.3987i	0.701611	+	0.405075i	−0.106336	+	0.994330i	$0.533912\pi$
$660$	−0.988907	+	1.23020i	−0.0384931	+	0.0478854i
$661$	−8.51046	+	31.7615i	−0.331018	+	1.23538i	0.577103	+	0.816671i	$0.304183\pi$
$661$	−8.51046	+	31.7615i	−0.331018	+	1.23538i	−0.908122	+	0.418706i	$0.862484\pi$
$662$	21.5711			0.838384
$663$	24.4843	+	19.4255i	0.950890	+	0.754424i
$664$	−7.29160			−0.282969
$665$	0.452243	−	1.68779i	0.0175372	−	0.0654499i
$666$	−8.03852	+	25.3579i	−0.311486	+	0.982597i
$667$	31.8076	+	18.3641i	1.23160	+	0.711063i
$668$	4.94440	+	4.94440i	0.191305	+	0.191305i
$669$	−10.0574	−	13.7389i	−0.388843	−	0.531177i
$670$	6.51062	−	1.74452i	0.251527	−	0.0673965i
$671$	−1.86502	+	1.86502i	−0.0719981	+	0.0719981i
$672$	−1.71169	−	0.264812i	−0.0660298	−	0.0102153i
$673$	−27.0469	+	15.6155i	−1.04258	+	0.601934i	−0.920563	−	0.390594i	$-0.872270\pi$
$673$	−27.0469	+	15.6155i	−1.04258	+	0.601934i	−0.122017	+	0.992528i	$0.538936\pi$
$674$	25.7659	+	6.90396i	0.992466	+	0.265930i
$675$	−21.5566	−	10.6929i	−0.829715	−	0.411570i
$676$	11.1743	−	6.64344i	0.429780	−	0.255517i
$677$			2.63720i			0.101356i	0.998715	+	0.0506778i	$0.0161382\pi$
$677$			2.63720i			0.101356i	−0.998715	+	0.0506778i	$0.983862\pi$
$678$	26.4487	−	2.87587i	1.01576	−	0.110447i
$679$	1.51651	+	2.62668i	0.0581985	+	0.100803i
$680$	1.52022	−	2.63310i	0.0582977	−	0.100975i
$681$	−9.17777	−	4.04680i	−0.351693	−	0.155074i
$682$	1.57341	+	5.87203i	0.0602489	+	0.224852i
$683$	10.8450	+	40.4741i	0.414972	+	1.54870i	0.784891	+	0.619633i	$0.212719\pi$
$683$	10.8450	+	40.4741i	0.414972	+	1.54870i	−0.369919	+	0.929064i	$0.620615\pi$
$684$	8.61975	+	0.389729i	0.329584	+	0.0149016i
$685$	−5.16258	+	8.94184i	−0.197252	+	0.341650i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	−0.381478	−	3.50837i	−0.0145543	−	0.133852i
$688$			10.7996i			0.411730i
$689$	24.5284	−	14.3714i	0.934459	−	0.547507i
$690$	2.18652	+	5.63556i	0.0832395	+	0.214542i
$691$	16.2923	+	4.36550i	0.619788	+	0.166072i	0.555031	−	0.831829i	$-0.312706\pi$
$691$	16.2923	+	4.36550i	0.619788	+	0.166072i	0.0647564	+	0.997901i	$0.479373\pi$
$692$	−7.26366	+	4.19368i	−0.276123	+	0.159420i
$693$	−0.967179	−	4.39488i	−0.0367401	−	0.166948i
$694$	9.03343	−	9.03343i	0.342904	−	0.342904i
$695$	−3.93169	+	1.05349i	−0.149137	+	0.0399612i
$696$	−8.93544	+	6.54109i	−0.338697	+	0.247940i
$697$	−13.3058	−	13.3058i	−0.503994	−	0.503994i
$698$	−25.5773	−	14.7670i	−0.968114	−	0.558941i
$699$	17.1906	+	13.8188i	0.650207	+	0.522675i
$700$	1.19857	−	4.47313i	0.0453017	−	0.169068i
$701$	29.1790			1.10208			0.551038	−	0.834480i	$-0.314232\pi$
$701$	29.1790			1.10208			0.551038	+	0.834480i	$0.314232\pi$
$702$	3.58020	−	18.3897i	0.135126	−	0.694076i
$703$	25.5036			0.961886
$704$	0.388232	−	1.44890i	0.0146321	−	0.0546076i
$705$	−8.24062	−	6.62430i	−0.310360	−	0.249486i
$706$	18.4719	+	10.6647i	0.695198	+	0.401372i
$707$	−3.61003	−	3.61003i	−0.135769	−	0.135769i
$708$	−18.0927	+	13.2446i	−0.679967	+	0.497763i
$709$	12.3313	−	3.30417i	0.463112	−	0.124091i	−0.0197161	−	0.999806i	$-0.506276\pi$
$709$	12.3313	−	3.30417i	0.463112	−	0.124091i	0.482828	+	0.875715i	$0.339610\pi$
$710$	2.46745	−	2.46745i	0.0926018	−	0.0926018i
$711$	2.37561	+	10.7948i	0.0890924	+	0.404837i
$712$	5.89081	−	3.40106i	0.220768	−	0.127460i
$713$	22.4885	+	6.02577i	0.842200	+	0.225667i
$714$	3.13549	+	8.08143i	0.117343	+	0.302440i
$715$	1.62461	−	2.85593i	0.0607571	−	0.106806i
$716$			16.6458i			0.622083i
$717$	−3.50622	−	32.2458i	−0.130942	−	1.20424i
$718$	4.68874	+	8.12113i	0.174982	+	0.303078i
$719$	−18.6879	+	32.3684i	−0.696942	+	1.20714i	0.272580	+	0.962133i	$0.412123\pi$
$719$	−18.6879	+	32.3684i	−0.696942	+	1.20714i	−0.969522	+	0.245006i	$0.921210\pi$
$720$	−1.82069	−	0.0823199i	−0.0678533	−	0.00306788i
$721$	1.52523	+	5.69223i	0.0568025	+	0.211990i
$722$	2.77650	+	10.3620i	0.103331	+	0.385635i
$723$	25.7288	+	11.3447i	0.956863	+	0.421915i
$724$	2.49636	−	4.32383i	0.0927766	−	0.160694i
$725$	−14.8037	−	25.6408i	−0.549797	−	0.952277i
$726$	−15.0666	+	1.63825i	−0.559173	+	0.0608010i
$727$		−	5.06432i		−	0.187825i	−0.995580	−	0.0939126i	$-0.970063\pi$
$727$		−	5.06432i		−	0.187825i	0.995580	−	0.0939126i	$-0.0299374\pi$
$728$	3.60548	−	0.0230552i	0.133628	−	0.000854481i
$729$	−16.3368	−	21.4967i	−0.605067	−	0.796175i
$730$	9.01186	+	2.41472i	0.333544	+	0.0893728i
$731$	46.8074	−	27.0243i	1.73123	−	0.999529i
$732$	−3.00972	−	0.465628i	−0.111243	−	0.0172101i
$733$	−31.5628	+	31.5628i	−1.16580	+	1.16580i	−0.182613	+	0.983185i	$0.558455\pi$
$733$	−31.5628	+	31.5628i	−1.16580	+	1.16580i	−0.983185	+	0.182613i	$0.941545\pi$
$734$	−4.27524	+	1.14555i	−0.157802	+	0.0422829i
$735$	−0.621549	−	0.849065i	−0.0229262	−	0.0313182i
$736$	−4.06211	−	4.06211i	−0.149731	−	0.149731i
$737$	−14.4127	−	8.32118i	−0.530899	−	0.306515i
$738$	−3.40856	+	10.7525i	−0.125471	+	0.395803i
$739$	−6.71344	+	25.0549i	−0.246958	+	0.921659i	0.725431	+	0.688294i	$0.241640\pi$
$739$	−6.71344	+	25.0549i	−0.246958	+	0.921659i	−0.972389	+	0.233365i	$0.925026\pi$
$740$	−5.38696			−0.198029
$741$	−17.8437	+	2.05575i	−0.655506	+	0.0755198i
$742$	7.88465			0.289455
$743$	1.54626	−	5.77071i	0.0567267	−	0.211707i	−0.931745	−	0.363114i	$-0.881714\pi$
$743$	1.54626	−	5.77071i	0.0567267	−	0.211707i	0.988472	+	0.151407i	$0.0483803\pi$
$744$	−4.39795	+	5.47104i	−0.161237	+	0.200578i
$745$	−10.9567	−	6.32586i	−0.401423	−	0.231761i
$746$	13.2070	+	13.2070i	0.483541	+	0.483541i
$747$	11.7819	−	18.4308i	0.431077	−	0.674347i
$748$	−7.25131	+	1.94298i	−0.265134	+	0.0710424i
$749$	7.53214	−	7.53214i	0.275218	−	0.275218i
$750$	1.54940	−	10.0150i	0.0565762	−	0.365697i
$751$	7.90712	−	4.56518i	0.288535	−	0.166586i	−0.348746	−	0.937217i	$-0.613392\pi$
$751$	7.90712	−	4.56518i	0.288535	−	0.166586i	0.637281	+	0.770632i	$0.280059\pi$
$752$	9.70563	+	2.60062i	0.353928	+	0.0948347i
$753$	−1.73573	+	0.673440i	−0.0632534	+	0.0245415i
$754$	16.1956	−	16.4040i	0.589807	−	0.597399i
$755$			1.57956i			0.0574862i
$756$	3.43513	−	3.89870i	0.124935	−	0.141794i
$757$	18.4318	+	31.9247i	0.669913	+	1.16032i	0.977928	+	0.208942i	$0.0670021\pi$
$757$	18.4318	+	31.9247i	0.669913	+	1.16032i	−0.308015	+	0.951382i	$0.599665\pi$
$758$	14.6209	−	25.3242i	0.531055	−	0.919815i
$759$	6.02169	−	13.6566i	0.218574	−	0.495704i
$760$	0.452243	+	1.68779i	0.0164046	+	0.0612227i
$761$	5.30708	+	19.8063i	0.192382	+	0.717978i	0.992929	+	0.118708i	$0.0378754\pi$
$761$	5.30708	+	19.8063i	0.192382	+	0.717978i	−0.800548	+	0.599269i	$0.795458\pi$
$762$	7.37713	−	16.7306i	0.267245	−	0.606087i
$763$	0.256756	−	0.444715i	0.00929519	−	0.0160997i
$764$	−0.125258	−	0.216953i	−0.00453166	−	0.00784907i
$765$	4.19921	+	8.09722i	0.151823	+	0.292756i
$766$		−	22.8846i		−	0.826853i
$767$	32.7932	−	33.2153i	1.18410	−	1.19934i
$768$	1.61477	−	0.626510i	0.0582680	−	0.0226072i
$769$	−35.5339	−	9.52129i	−1.28139	−	0.343347i	−0.447004	−	0.894532i	$-0.647509\pi$
$769$	−35.5339	−	9.52129i	−1.28139	−	0.343347i	−0.834383	+	0.551185i	$0.814176\pi$
$770$	0.789196	−	0.455643i	0.0284407	−	0.0164202i
$771$	−5.76950	+	37.2929i	−0.207783	+	1.34307i
$772$	−7.32531	+	7.32531i	−0.263644	+	0.263644i
$773$	38.5539	−	10.3305i	1.38669	−	0.371561i	0.513141	−	0.858304i	$-0.328482\pi$
$773$	38.5539	−	10.3305i	1.38669	−	0.371561i	0.873545	+	0.486743i	$0.161815\pi$
$774$	−27.2978	−	17.4501i	−0.981200	−	0.627233i
$775$	−13.2709	−	13.2709i	−0.476706	−	0.476706i
$776$	−2.62668	−	1.51651i	−0.0942923	−	0.0544397i
$777$	9.62244	−	11.9703i	0.345203	−	0.429432i
$778$	−1.72280	+	6.42959i	−0.0617655	+	0.230512i
$779$	10.8142			0.387460
$780$	3.76902	−	0.434223i	0.134952	−	0.0155477i
$781$	−8.61588			−0.308301
$782$	−7.44115	+	27.7707i	−0.266095	+	0.993080i
$783$	−2.09572	−	33.1551i	−0.0748949	−	1.18487i
$784$	0.866025	+	0.500000i	0.0309295	+	0.0178571i
$785$	8.83244	+	8.83244i	0.315243	+	0.315243i
$786$	−12.5118	−	17.0917i	−0.446282	−	0.609641i
$787$	−24.9567	+	6.68713i	−0.889611	+	0.238370i	−0.674549	−	0.738230i	$-0.735662\pi$
$787$	−24.9567	+	6.68713i	−0.889611	+	0.238370i	−0.215062	+	0.976600i	$0.568995\pi$
$788$	7.35951	−	7.35951i	0.262172	−	0.262172i
$789$	−14.6115	−	2.26052i	−0.520184	−	0.0804766i
$790$	−1.93845	+	1.11916i	−0.0689668	+	0.0398180i
$791$	−14.8368	−	3.97550i	−0.527535	−	0.141353i
$792$	3.03504	+	3.32249i	0.107845	+	0.118059i
$793$	6.33964	−	0.0405387i	0.225127	−	0.00143957i
$794$		−	20.7059i		−	0.734826i
$795$	8.24803	−	0.896840i	0.292527	−	0.0318076i
$796$	1.25541	+	2.17443i	0.0444968	+	0.0770707i
$797$	9.60039	−	16.6284i	0.340063	−	0.589007i	−0.644381	−	0.764705i	$-0.722885\pi$
$797$	9.60039	−	16.6284i	0.340063	−	0.589007i	0.984444	+	0.175698i	$0.0562182\pi$
$798$	−4.55825	−	2.00989i	−0.161360	−	0.0711495i
$799$	−13.0153	−	48.5737i	−0.460447	−	1.71841i
$800$	1.19857	+	4.47313i	0.0423759	+	0.158149i
$801$	−0.921701	+	20.3855i	−0.0325667	+	0.720288i
$802$	−11.5404	+	19.9885i	−0.407505	+	0.705820i
$803$	−11.5180	−	19.9497i	−0.406461	−	0.704011i
$804$	−2.07727	−	19.1042i	−0.0732596	−	0.673752i
$805$		−	3.49000i		−	0.123006i
$806$	7.22512	−	12.7012i	0.254494	−	0.447379i
$807$	−10.0472	−	25.8957i	−0.353678	−	0.911572i
$808$	4.93139	+	1.32136i	0.173486	+	0.0464853i
$809$	1.90278	−	1.09857i	0.0668981	−	0.0386237i	−0.466178	−	0.884691i	$-0.654369\pi$
$809$	1.90278	−	1.09857i	0.0668981	−	0.0386237i	0.533076	+	0.846067i	$0.321036\pi$
$810$	3.14999	−	4.46911i	0.110679	−	0.157028i
$811$	3.94069	−	3.94069i	0.138376	−	0.138376i	−0.634526	−	0.772902i	$-0.718804\pi$
$811$	3.94069	−	3.94069i	0.138376	−	0.138376i	0.772902	+	0.634526i	$0.218804\pi$
$812$	6.17558	−	1.65474i	0.216720	−	0.0580701i
$813$	10.9891	−	8.04448i	0.385406	−	0.282132i
$814$	9.40513	+	9.40513i	0.329650	+	0.329650i
$815$	−3.53458	−	2.04069i	−0.123811	−	0.0714823i
$816$	−6.75613	−	5.43098i	−0.236512	−	0.190122i
$817$	−8.03933	+	30.0032i	−0.281261	+	1.04968i
$818$	26.2112			0.916454
$819$	−5.76752	+	9.15072i	−0.201533	+	0.319752i
$820$	−2.28422			−0.0797685
$821$	11.0328	−	41.1750i	0.385047	−	1.43702i	−0.453045	−	0.891488i	$-0.649662\pi$
$821$	11.0328	−	41.1750i	0.385047	−	1.43702i	0.838092	−	0.545528i	$-0.183671\pi$
$822$	22.9434	+	18.4433i	0.800243	+	0.643283i
$823$	−2.04810	−	1.18247i	−0.0713923	−	0.0412184i	0.463879	−	0.885899i	$-0.346457\pi$
$823$	−2.04810	−	1.18247i	−0.0713923	−	0.0412184i	−0.535271	+	0.844680i	$0.679791\pi$
$824$	−4.16700	−	4.16700i	−0.145164	−	0.145164i
$825$	−9.70833	+	7.10688i	−0.338001	+	0.247430i
$826$	12.5045	−	3.35057i	0.435087	−	0.116581i
$827$	−24.7966	+	24.7966i	−0.862263	+	0.862263i	−0.991601	−	0.129338i	$-0.958715\pi$
$827$	−24.7966	+	24.7966i	−0.862263	+	0.862263i	0.129338	+	0.991601i	$0.458715\pi$
$828$	16.8313	−	3.70406i	0.584929	−	0.128725i
$829$	−9.04046	+	5.21951i	−0.313988	+	0.181281i	−0.648710	−	0.761036i	$-0.724691\pi$
$829$	−9.04046	+	5.21951i	−0.313988	+	0.181281i	0.334722	+	0.942317i	$0.391358\pi$
$830$	4.27883	+	1.14651i	0.148521	+	0.0397960i
$831$	−12.0831	−	31.1430i	−0.419157	−	1.08034i
$832$	−3.11091	+	1.82271i	−0.107851	+	0.0631909i
$833$		−	5.00469i		−	0.173402i
$834$	1.25444	+	11.5368i	0.0434376	+	0.399486i
$835$	−2.12402	−	3.67891i	−0.0735046	−	0.127314i
$836$	2.15716	−	3.73631i	0.0746069	−	0.129223i
$837$	−6.72273	−	19.9568i	−0.232371	−	0.689807i
$838$	−4.97878	−	18.5810i	−0.171989	−	0.641872i
$839$	−2.38140	−	8.88750i	−0.0822150	−	0.306831i	0.912557	−	0.408949i	$-0.134105\pi$
$839$	−2.38140	−	8.88750i	−0.0822150	−	0.306831i	−0.994772	+	0.102118i	$0.967438\pi$
$840$	0.962810	+	0.424537i	0.0332201	+	0.0146479i
$841$	5.93799	−	10.2849i	0.204758	−	0.354652i
$842$	4.38788	+	7.60003i	0.151216	+	0.261914i
$843$	−39.1326	+	4.25503i	−1.34780	+	0.146551i
$844$		−	22.1402i		−	0.762097i
$845$	−7.60186	+	2.14148i	−0.261512	+	0.0736690i
$846$	−22.2560	+	20.3305i	−0.765178	+	0.698979i
$847$	8.45181	+	2.26466i	0.290408	+	0.0778145i
$848$	−6.82831	+	3.94233i	−0.234485	+	0.135380i
$849$	25.0046	+	3.86841i	0.858156	+	0.132763i
$850$	16.3881	−	16.3881i	0.562108	−	0.562108i
$851$	49.2034	−	13.1840i	1.68667	−	0.451942i
$852$	−5.87653	−	8.02761i	−0.201327	−	0.275021i
$853$	1.15798	+	1.15798i	0.0396485	+	0.0396485i	0.726653	−	0.687005i	$-0.241075\pi$
$853$	1.15798	+	1.15798i	0.0396485	+	0.0396485i	−0.687005	+	0.726653i	$0.741075\pi$
$854$	1.52276	+	0.879168i	0.0521079	+	0.0300845i
$855$	−4.99694	−	1.58404i	−0.170892	−	0.0541732i
$856$	−2.75695	+	10.2891i	−0.0942308	+	0.351674i
$857$	29.9765			1.02398			0.511988	−	0.858993i	$-0.328909\pi$
$857$	29.9765			1.02398			0.511988	+	0.858993i	$0.328909\pi$
$858$	−7.33847	−	5.82224i	−0.250531	−	0.198768i
$859$	−27.9021			−0.952008			−0.476004	−	0.879443i	$-0.657915\pi$
$859$	−27.9021			−0.952008			−0.476004	+	0.879443i	$0.657915\pi$
$860$	1.69810	−	6.33738i	0.0579046	−	0.216103i
$861$	4.08019	−	5.07575i	0.139052	−	0.172981i
$862$	−6.56149	−	3.78828i	−0.223485	−	0.129029i
$863$	35.5898	+	35.5898i	1.21149	+	1.21149i	0.970537	+	0.240954i	$0.0774603\pi$
$863$	35.5898	+	35.5898i	1.21149	+	1.21149i	0.240954	+	0.970537i	$0.422540\pi$
$864$	−1.02556	+	5.09394i	−0.0348903	+	0.173299i
$865$	4.92184	−	1.31880i	0.167348	−	0.0448407i
$866$	−2.68763	+	2.68763i	−0.0913295	+	0.0913295i
$867$	−2.13091	+	13.7738i	−0.0723697	+	0.467783i
$868$	3.50978	−	2.02637i	0.119130	−	0.0687796i
$869$	5.33830	+	1.43039i	0.181089	+	0.0485228i
$870$	6.27197	−	2.43344i	0.212640	−	0.0825015i
$871$	10.6004	+	38.5728i	0.359180	+	1.30699i
$872$			0.513512i			0.0173897i
$873$	8.07749	−	4.18898i	0.273382	−	0.141775i
$874$	−8.26139	−	14.3092i	−0.279446	−	0.484014i
$875$	−2.92548	+	5.06708i	−0.0988992	+	0.171299i
$876$	10.7317	−	24.3384i	0.362590	−	0.822320i
$877$	−7.29271	−	27.2167i	−0.246257	−	0.919044i	−0.972747	−	0.231867i	$-0.925516\pi$
$877$	−7.29271	−	27.2167i	−0.246257	−	0.919044i	0.726490	−	0.687177i	$-0.241150\pi$
$878$	1.14555	+	4.27526i	0.0386606	+	0.144283i
$879$	5.91494	−	13.4145i	0.199506	−	0.452460i
$880$	−0.455643	+	0.789196i	−0.0153597	+	0.0266038i
$881$	11.9196	+	20.6454i	0.401582	+	0.695560i	0.993917	−	0.110131i	$-0.0351271\pi$
$881$	11.9196	+	20.6454i	0.401582	+	0.695560i	−0.592335	+	0.805692i	$0.701794\pi$
$882$	−2.66318	+	1.38112i	−0.0896738	+	0.0465048i
$883$			55.7346i			1.87562i	0.347152	+	0.937809i	$0.387149\pi$
$883$			55.7346i			1.87562i	−0.347152	+	0.937809i	$0.612851\pi$
$884$	15.6845	+	8.92222i	0.527527	+	0.300087i
$885$	12.6997	−	4.92731i	0.426895	−	0.165630i
$886$	0.719002	+	0.192656i	0.0241554	+	0.00647241i
$887$	14.0025	−	8.08433i	0.470157	−	0.271445i	−0.246148	−	0.969232i	$-0.579165\pi$
$887$	14.0025	−	8.08433i	0.470157	−	0.271445i	0.716305	+	0.697787i	$0.245832\pi$
$888$	−2.34813	+	15.1778i	−0.0787980	+	0.509334i
$889$	−7.46476	+	7.46476i	−0.250360	+	0.250360i
$890$	−3.99160	+	1.06955i	−0.133799	+	0.0358513i
$891$	−13.3022	+	2.30306i	−0.445641	+	0.0771554i
$892$	−6.95113	−	6.95113i	−0.232741	−	0.232741i
$893$	25.0281	+	14.4500i	0.837532	+	0.483550i
$894$	−22.5991	+	28.1132i	−0.755827	+	0.940247i
$895$	2.61734	−	9.76804i	0.0874880	−	0.326510i
$896$	−1.00000			−0.0334077
$897$	−33.3627	+	13.1904i	−1.11395	+	0.440414i
$898$	−13.7394			−0.458491
$899$	6.70625	−	25.0281i	0.223666	−	0.834733i
$900$	−13.2433	−	4.19816i	−0.441443	−	0.139939i
$901$	34.1736	+	19.7301i	1.13849	+	0.657306i
$902$	3.98804	+	3.98804i	0.132787	+	0.132787i
$903$	11.0490	+	15.0935i	0.367688	+	0.502279i
$904$	14.8368	−	3.97550i	0.493464	−	0.132223i
$905$	−2.14478	+	2.14478i	−0.0712948	+	0.0712948i
$906$	4.45043	+	0.688517i	0.147856	+	0.0228744i
$907$	−13.6200	+	7.86351i	−0.452244	+	0.261103i	−0.708778	−	0.705432i	$-0.750753\pi$
$907$	−13.6200	+	7.86351i	−0.452244	+	0.261103i	0.256533	+	0.966535i	$0.417420\pi$
$908$	−5.59370	−	1.49883i	−0.185634	−	0.0497404i
$909$	−11.3082	+	10.3299i	−0.375069	+	0.342620i
$910$	−2.11938	−	0.553386i	−0.0702568	−	0.0183446i
$911$			47.4021i			1.57050i	0.619179	+	0.785250i	$0.287466\pi$
$911$			47.4021i			1.57050i	−0.619179	+	0.785250i	$0.712534\pi$
$912$	4.95251	−	0.538505i	0.163994	−	0.0178317i
$913$	−5.46875	−	9.47215i	−0.180989	−	0.313482i
$914$	−6.82546	+	11.8220i	−0.225766	+	0.391039i
$915$	1.69294	+	0.746479i	0.0559670	+	0.0246778i
$916$	−0.527342	−	1.96807i	−0.0174239	−	0.0650268i
$917$	3.16519	+	11.8127i	0.104524	+	0.390088i
$918$	24.6444	−	8.30182i	0.813386	−	0.274001i
$919$	0.751314	−	1.30131i	0.0247836	−	0.0429264i	−0.853368	−	0.521310i	$-0.825444\pi$
$919$	0.751314	−	1.30131i	0.0247836	−	0.0429264i	0.878151	+	0.478383i	$0.158777\pi$
$920$	1.74500	+	3.02243i	0.0575310	+	0.0996466i
$921$	−1.52225	−	13.9998i	−0.0501599	−	0.461309i
$922$		−	19.5691i		−	0.644476i
$923$	14.7374	+	14.5501i	0.485087	+	0.478923i
$924$	−0.939774	−	2.42218i	−0.0309163	−	0.0796838i
$925$	−39.6639	−	10.6279i	−1.30414	−	0.349444i
$926$	−1.37646	+	0.794697i	−0.0452332	+	0.0261154i
$927$	17.2659	−	3.79971i	0.567088	−	0.124799i
$928$	−4.52084	+	4.52084i	−0.148404	+	0.148404i
$929$	−10.8527	+	2.90796i	−0.356065	+	0.0954072i	−0.432417	−	0.901674i	$-0.642339\pi$
$929$	−10.8527	+	2.90796i	−0.356065	+	0.0954072i	0.0763525	+	0.997081i	$0.475673\pi$
$930$	3.44104	−	2.51898i	0.112836	−	0.0826006i
$931$	2.03377	+	2.03377i	0.0666541	+	0.0666541i
$932$	11.0281	+	6.36707i	0.361237	+	0.208560i
$933$	36.0853	+	29.0075i	1.18138	+	0.949664i
$934$	7.14814	−	26.6772i	0.233894	−	0.872905i
$935$	4.56070			0.149151
$936$	0.419454	−	10.8085i	0.0137103	−	0.353287i
$937$	−6.05112			−0.197682			−0.0988408	−	0.995103i	$-0.531513\pi$
$937$	−6.05112			−0.197682			−0.0988408	+	0.995103i	$0.531513\pi$
$938$	−2.87155	+	10.7168i	−0.0937593	+	0.349914i
$939$	−22.8512	−	18.3692i	−0.745721	−	0.599455i
$940$	−5.28652	−	3.05217i	−0.172427	−	0.0995509i
$941$	−12.4785	−	12.4785i	−0.406787	−	0.406787i	0.473830	−	0.880616i	$-0.342871\pi$
$941$	−12.4785	−	12.4785i	−0.406787	−	0.406787i	−0.880616	+	0.473830i	$0.842871\pi$
$942$	28.7355	−	21.0355i	0.936252	−	0.685374i
$943$	20.8636	−	5.59039i	0.679413	−	0.182048i
$944$	−9.15393	+	9.15393i	−0.297935	+	0.297935i
$945$	−2.62882	+	1.74769i	−0.0855154	+	0.0568525i
$946$	−14.0292	+	8.09976i	−0.456129	+	0.263346i
$947$	−13.7924	−	3.69567i	−0.448193	−	0.120093i	0.0276607	−	0.999617i	$-0.491194\pi$
$947$	−13.7924	−	3.69567i	−0.448193	−	0.120093i	−0.475854	+	0.879524i	$0.657861\pi$
$948$	2.30830	+	5.94942i	0.0749701	+	0.193228i
$949$	−13.9888	+	53.5749i	−0.454096	+	1.73911i
$950$			13.3194i			0.432138i
$951$	1.48170	+	13.6268i	0.0480474	+	0.441881i
$952$	2.50234	+	4.33419i	0.0811014	+	0.140472i
$953$	−4.47592	+	7.75252i	−0.144989	+	0.251129i	−0.929369	−	0.369152i	$-0.879648\pi$
$953$	−4.47592	+	7.75252i	−0.144989	+	0.251129i	0.784380	+	0.620281i	$0.212981\pi$
$954$	1.06839	−	23.6298i	0.0345903	−	0.765044i
$955$	0.0393903	+	0.147007i	0.00127464	+	0.00475703i
$956$	−4.84687	−	18.0888i	−0.156759	−	0.585033i
$957$	−15.1989	−	6.70171i	−0.491309	−	0.216636i
$958$	−20.4118	+	35.3543i	−0.659475	+	1.14225i
$959$	−8.49782	−	14.7186i	−0.274409	−	0.475290i
$960$	−1.04609	+	0.113745i	−0.0337623	+	0.00367110i
$961$			14.5752i			0.470169i
$962$	−0.204434	−	31.9703i	−0.00659121	−	1.03077i
$963$	−21.5527	−	23.5940i	−0.694527	−	0.760305i
$964$	15.6813	+	4.20178i	0.505060	+	0.135330i
$965$	5.45043	−	3.14681i	0.175456	−	0.101299i
$966$	−9.83312	−	1.52126i	−0.316375	−	0.0489458i
$967$	37.1103	−	37.1103i	1.19339	−	1.19339i	0.217277	−	0.976110i	$-0.430282\pi$
$967$	37.1103	−	37.1103i	1.19339	−	1.19339i	0.976110	−	0.217277i	$-0.0697176\pi$
$968$	−8.45181	+	2.26466i	−0.271651	+	0.0727888i
$969$	−14.7269	−	20.1176i	−0.473095	−	0.646269i
$970$	1.30293	+	1.30293i	0.0418345	+	0.0418345i
$971$	35.3036	+	20.3825i	1.13295	+	0.654106i	0.944674	−	0.328011i	$-0.106378\pi$
$971$	35.3036	+	20.3825i	1.13295	+	0.654106i	0.188271	+	0.982117i	$0.439712\pi$
$972$	−11.2187	−	10.8232i	−0.359840	−	0.347153i
$973$	1.73409	−	6.47172i	0.0555924	−	0.207474i
$974$	3.64826			0.116898
$975$	28.6078	+	4.23872i	0.916182	+	0.135748i
$976$	−1.75834			−0.0562830
$977$	−9.78097	+	36.5031i	−0.312921	+	1.16784i	0.612988	+	0.790092i	$0.289967\pi$
$977$	−9.78097	+	36.5031i	−0.312921	+	1.16784i	−0.925909	+	0.377746i	$0.876699\pi$
$978$	−7.29036	+	9.06920i	−0.233120	+	0.290001i
$979$	8.83630	+	5.10164i	0.282409	+	0.163049i
$980$	−0.429580	−	0.429580i	−0.0137224	−	0.0137224i
$981$	−1.29799	−	0.829742i	−0.0414417	−	0.0264916i
$982$	23.4608	−	6.28631i	0.748665	−	0.200604i
$983$	−26.7287	+	26.7287i	−0.852513	+	0.852513i	−0.990442	−	0.137929i	$-0.955955\pi$
$983$	−26.7287	+	26.7287i	−0.852513	+	0.852513i	0.137929	+	0.990442i	$0.455955\pi$
$984$	−0.995672	+	6.43582i	−0.0317409	+	0.205166i
$985$	−5.47588	+	3.16150i	−0.174476	+	0.100734i
$986$	30.9069	+	8.28147i	0.984275	+	0.263736i
$987$	16.2252	−	6.29518i	0.516455	−	0.200378i
$988$	−9.99951	+	2.74801i	−0.318127	+	0.0874258i
$989$			62.0402i			1.97277i
$990$	−1.25860	−	2.42691i	−0.0400008	−	0.0771324i
$991$	10.0610	+	17.4262i	0.319598	+	0.553560i	0.980404	−	0.196996i	$-0.0631187\pi$
$991$	10.0610	+	17.4262i	0.319598	+	0.553560i	−0.660806	+	0.750557i	$0.729785\pi$
$992$	−2.02637	+	3.50978i	−0.0643374	+	0.111436i
$993$	−15.0740	+	34.1864i	−0.478359	+	1.08487i
$994$	1.48662	+	5.54815i	0.0471528	+	0.175977i
$995$	−0.394794	−	1.47339i	−0.0125158	−	0.0467096i
$996$	5.09541	−	11.5559i	0.161454	−	0.366163i
$997$	1.24765	−	2.16100i	0.0395135	−	0.0684395i	−0.845592	−	0.533829i	$-0.820753\pi$
$997$	1.24765	−	2.16100i	0.0395135	−	0.0684395i	0.885106	+	0.465390i	$0.154086\pi$
$998$	−4.27223	−	7.39971i	−0.135235	−	0.234234i
$999$	−34.5704	−	30.4599i	−1.09376	−	0.963707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.b.197.2	yes	56
3.2	odd	2		546.2.bu.a.197.11	✓	56
13.7	odd	12		546.2.bu.a.449.11	yes	56
39.20	even	12	inner	546.2.bu.b.449.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.197.11	✓	56	3.2	odd	2
546.2.bu.a.449.11	yes	56	13.7	odd	12
546.2.bu.b.197.2	yes	56	1.1	even	1	trivial
546.2.bu.b.449.2	yes	56	39.20	even	12	inner

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.34996 - 1.08518i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.429580 + 0.429580i) q^{5} +(1.39760 - 1.02310i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.644780 + 2.92989i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.34996 - 1.08518i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.429580 + 0.429580i) q^{5} +(1.39760 - 1.02310i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.644780 + 2.92989i) q^{9} +(-0.526126 + 0.303759i) q^{10} +(1.44890 + 0.388232i) q^{11} +(0.626510 + 1.61477i) q^{12} +(-1.82271 - 3.11091i) q^{13} -1.00000i q^{14} +(-0.113745 - 1.04609i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.50234 - 4.33419i) q^{17} +(-2.99694 - 0.135502i) q^{18} +(0.744411 + 2.77818i) q^{19} +(-0.157237 - 0.586817i) q^{20} +(1.58483 + 0.698806i) q^{21} +(-0.750007 + 1.29905i) q^{22} +(2.87235 + 4.97505i) q^{23} +(-1.72190 + 0.187229i) q^{24} -4.63092i q^{25} +(3.47666 - 0.955436i) q^{26} +(2.30902 - 4.65493i) q^{27} +(0.965926 + 0.258819i) q^{28} +(5.53687 - 3.19672i) q^{29} +(1.03988 + 0.160878i) q^{30} +(2.86572 - 2.86572i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.53466 - 2.09641i) q^{33} +(3.53885 + 3.53885i) q^{34} +(-0.526126 - 0.303759i) q^{35} +(0.906550 - 2.85975i) q^{36} +(2.29499 - 8.56502i) q^{37} -2.87618 q^{38} +(-0.915309 + 6.17756i) q^{39} +0.607518 q^{40} +(0.973141 - 3.63181i) q^{41} +(-1.08518 + 1.34996i) q^{42} +(9.35271 + 5.39979i) q^{43} +(-1.06067 - 1.06067i) q^{44} +(-0.981638 + 1.53561i) q^{45} +(-5.54895 + 1.48684i) q^{46} +(7.10501 - 7.10501i) q^{47} +(0.264812 - 1.71169i) q^{48} +(0.866025 - 0.500000i) q^{49} +(4.47313 + 1.19857i) q^{50} +(-8.08143 + 3.13549i) q^{51} +(0.0230552 + 3.60548i) q^{52} +7.88465i q^{53} +(3.89870 + 3.43513i) q^{54} +(0.455643 + 0.789196i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(2.00989 - 4.55825i) q^{57} +(1.65474 + 6.17558i) q^{58} +(3.35057 + 12.5045i) q^{59} +(-0.424537 + 0.962810i) q^{60} +(-0.879168 + 1.52276i) q^{61} +(2.02637 + 3.50978i) q^{62} +(-1.38112 - 2.66318i) q^{63} -1.00000i q^{64} +(0.553386 - 2.11938i) q^{65} +(2.42218 - 0.939774i) q^{66} +(-10.7168 - 2.87155i) q^{67} +(-4.33419 + 2.50234i) q^{68} +(1.52126 - 9.83312i) q^{69} +(0.429580 - 0.429580i) q^{70} +(-5.54815 + 1.48662i) q^{71} +(2.52767 + 1.61582i) q^{72} +(-10.8592 - 10.8592i) q^{73} +(7.67919 + 4.43358i) q^{74} +(-5.02537 + 6.25156i) q^{75} +(0.744411 - 2.77818i) q^{76} -1.50001 q^{77} +(-5.73016 - 2.48299i) q^{78} +3.68438 q^{79} +(-0.157237 + 0.586817i) q^{80} +(-8.16852 + 3.77827i) q^{81} +(3.25619 + 1.87996i) q^{82} +(-5.15594 - 5.15594i) q^{83} +(-1.02310 - 1.39760i) q^{84} +(2.93684 - 0.786923i) q^{85} +(-7.63646 + 7.63646i) q^{86} +(-10.9436 - 1.69306i) q^{87} +(1.29905 - 0.750007i) q^{88} +(6.57035 + 1.76052i) q^{89} +(-1.22922 - 1.34563i) q^{90} +(2.56576 + 2.53316i) q^{91} -5.74469i q^{92} +(-6.97843 + 0.758792i) q^{93} +(5.02400 + 8.70183i) q^{94} +(-0.873667 + 1.51324i) q^{95} +(1.58483 + 0.698806i) q^{96} +(-0.785006 - 2.92968i) q^{97} +(0.258819 + 0.965926i) q^{98} +(-0.203255 + 4.49545i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 56 * q + 8 * q^6 - 24 * q^9	\( 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) \) 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Introduction

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