LMFDB - Embedded newform 546.2.bu.a.449.6

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			449.6
Character	$\chi$	$=$	546.449
Dual form			546.2.bu.a.197.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(1.63803 - 0.562898i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.20435 - 1.20435i) q^{5} +(-0.967672 - 1.43653i) q^{6} +(0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.36629 - 1.84409i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(1.63803 - 0.562898i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.20435 - 1.20435i) q^{5} +(-0.967672 - 1.43653i) q^{6} +(0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.36629 - 1.84409i) q^{9} +(-1.47502 - 0.851606i) q^{10} +(2.44174 - 0.654262i) q^{11} +(-1.13713 + 1.30650i) q^{12} +(-3.45328 - 1.03675i) q^{13} -1.00000i q^{14} +(1.29484 - 2.65069i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.21230 + 2.09977i) q^{17} +(-2.39370 - 1.80838i) q^{18} +(-1.04216 + 3.88941i) q^{19} +(-0.440824 + 1.64518i) q^{20} +(1.72791 - 0.119765i) q^{21} +(-1.26394 - 2.18920i) q^{22} +(2.97403 - 5.15116i) q^{23} +(1.55629 + 0.760233i) q^{24} +2.09907i q^{25} +(-0.107646 + 3.60394i) q^{26} +(2.83802 - 4.35266i) q^{27} +(-0.965926 + 0.258819i) q^{28} +(0.0418274 + 0.0241491i) q^{29} +(-2.89550 - 0.564668i) q^{30} +(-5.46051 - 5.46051i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.63136 - 2.44615i) q^{33} +(1.71445 - 1.71445i) q^{34} +(1.47502 - 0.851606i) q^{35} +(-1.12722 + 2.78017i) q^{36} +(-0.589467 - 2.19992i) q^{37} +4.02661 q^{38} +(-6.24017 + 0.245623i) q^{39} +1.70321 q^{40} +(0.381675 + 1.42443i) q^{41} +(-0.562898 - 1.63803i) q^{42} +(-8.13197 + 4.69500i) q^{43} +(-1.78748 + 1.78748i) q^{44} +(0.628914 - 5.07078i) q^{45} +(-5.74538 - 1.53947i) q^{46} +(3.85521 + 3.85521i) q^{47} +(0.331531 - 1.70003i) q^{48} +(0.866025 + 0.500000i) q^{49} +(2.02755 - 0.543279i) q^{50} +(3.16774 + 2.75708i) q^{51} +(3.50900 - 0.828792i) q^{52} -1.50752i q^{53} +(-4.93888 - 1.61477i) q^{54} +(2.15275 - 3.72867i) q^{55} +(0.500000 + 0.866025i) q^{56} +(0.482245 + 6.95760i) q^{57} +(0.0125005 - 0.0466524i) q^{58} +(-0.153522 + 0.572954i) q^{59} +(0.203984 + 2.94299i) q^{60} +(4.34749 + 7.53008i) q^{61} +(-3.86117 + 6.68773i) q^{62} +(2.76295 - 1.16881i) q^{63} +1.00000i q^{64} +(-5.40758 + 2.91036i) q^{65} +(-3.30266 - 2.87451i) q^{66} +(-6.36486 + 1.70546i) q^{67} +(-2.09977 - 1.21230i) q^{68} +(1.97196 - 10.1118i) q^{69} +(-1.20435 - 1.20435i) q^{70} +(-7.41146 - 1.98589i) q^{71} +(2.97719 + 0.369252i) q^{72} +(5.96741 - 5.96741i) q^{73} +(-1.97239 + 1.13876i) q^{74} +(1.18156 + 3.43834i) q^{75} +(-1.04216 - 3.88941i) q^{76} +2.52787 q^{77} +(1.85233 + 5.96397i) q^{78} +6.92286 q^{79} +(-0.440824 - 1.64518i) q^{80} +(2.19866 - 8.72731i) q^{81} +(1.27711 - 0.737339i) q^{82} +(-9.18787 + 9.18787i) q^{83} +(-1.43653 + 0.967672i) q^{84} +(3.98890 + 1.06882i) q^{85} +(6.63973 + 6.63973i) q^{86} +(0.0821080 + 0.0160123i) q^{87} +(2.18920 + 1.26394i) q^{88} +(-14.5458 + 3.89754i) q^{89} +(-5.06078 + 0.704931i) q^{90} +(-3.06728 - 1.89520i) q^{91} +5.94805i q^{92} +(-12.0182 - 5.87077i) q^{93} +(2.72604 - 4.72165i) q^{94} +(3.42909 + 5.93935i) q^{95} +(-1.72791 + 0.119765i) q^{96} +(1.26639 - 4.72622i) q^{97} +(0.258819 - 0.965926i) q^{98} +(4.57134 - 6.05096i) 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^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 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} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 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^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 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 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{12}\right)$

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
$3$	1.63803	−	0.562898i	0.945718	−	0.324990i
$3$	1.63803	−	0.562898i	0.945718	−	0.324990i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.20435	−	1.20435i	0.538603	−	0.538603i	−0.384516	−	0.923118i	$-0.625632\pi$
$5$	1.20435	−	1.20435i	0.538603	−	0.538603i	0.923118	+	0.384516i	$0.125632\pi$
$6$	−0.967672	−	1.43653i	−0.395050	−	0.586460i
$7$	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
$9$	2.36629	−	1.84409i	0.788764	−	0.614697i
$10$	−1.47502	−	0.851606i	−0.466444	−	0.269301i
$11$	2.44174	−	0.654262i	0.736211	−	0.197267i	0.128818	−	0.991668i	$-0.458882\pi$
$11$	2.44174	−	0.654262i	0.736211	−	0.197267i	0.607394	+	0.794401i	$0.292215\pi$
$12$	−1.13713	+	1.30650i	−0.328260	+	0.377154i
$13$	−3.45328	−	1.03675i	−0.957768	−	0.287542i
$13$	−3.45328	−	1.03675i	−0.957768	−	0.287542i
$14$		−	1.00000i		−	0.267261i
$15$	1.29484	−	2.65069i	0.334326	−	0.684406i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.21230	+	2.09977i	0.294026	+	0.509269i	0.974758	−	0.223264i	$-0.0716713\pi$
$17$	1.21230	+	2.09977i	0.294026	+	0.509269i	−0.680732	+	0.732533i	$0.738338\pi$
$18$	−2.39370	−	1.80838i	−0.564199	−	0.426238i
$19$	−1.04216	+	3.88941i	−0.239089	+	0.892291i	0.737174	+	0.675703i	$0.236160\pi$
$19$	−1.04216	+	3.88941i	−0.239089	+	0.892291i	−0.976263	+	0.216589i	$0.930507\pi$
$20$	−0.440824	+	1.64518i	−0.0985712	+	0.367873i
$21$	1.72791	−	0.119765i	0.377060	−	0.0261348i
$22$	−1.26394	−	2.18920i	−0.269472	−	0.466739i
$23$	2.97403	−	5.15116i	0.620127	−	1.07409i	−0.369334	−	0.929297i	$-0.620414\pi$
$23$	2.97403	−	5.15116i	0.620127	−	1.07409i	0.989462	−	0.144795i	$-0.0462523\pi$
$24$	1.55629	+	0.760233i	0.317677	+	0.155182i
$25$			2.09907i			0.419814i
$26$	−0.107646	+	3.60394i	−0.0211110	+	0.706792i
$27$	2.83802	−	4.35266i	0.546178	−	0.837669i
$28$	−0.965926	+	0.258819i	−0.182543	+	0.0489122i
$29$	0.0418274	+	0.0241491i	0.00776715	+	0.00448437i	0.503879	−	0.863775i	$-0.331906\pi$
$29$	0.0418274	+	0.0241491i	0.00776715	+	0.00448437i	−0.496111	+	0.868259i	$0.665239\pi$
$30$	−2.89550	−	0.564668i	−0.528644	−	0.103094i
$31$	−5.46051	−	5.46051i	−0.980737	−	0.980737i	0.0190810	−	0.999818i	$-0.493926\pi$
$31$	−5.46051	−	5.46051i	−0.980737	−	0.980737i	−0.999818	+	0.0190810i	$0.993926\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	3.63136	−	2.44615i	0.632138	−	0.425820i
$34$	1.71445	−	1.71445i	0.294026	−	0.294026i
$35$	1.47502	−	0.851606i	0.249325	−	0.143948i
$36$	−1.12722	+	2.78017i	−0.187870	+	0.463362i
$37$	−0.589467	−	2.19992i	−0.0969077	−	0.361665i	0.900394	−	0.435075i	$-0.143278\pi$
$37$	−0.589467	−	2.19992i	−0.0969077	−	0.361665i	−0.997302	+	0.0734107i	$0.976612\pi$
$38$	4.02661			0.653203
$39$	−6.24017	+	0.245623i	−0.999226	+	0.0393312i
$40$	1.70321			0.269301
$41$	0.381675	+	1.42443i	0.0596076	+	0.222458i	0.989304	−	0.145868i	$-0.0465975\pi$
$41$	0.381675	+	1.42443i	0.0596076	+	0.222458i	−0.929696	+	0.368327i	$0.879931\pi$
$42$	−0.562898	−	1.63803i	−0.0868571	−	0.252754i
$43$	−8.13197	+	4.69500i	−1.24011	+	0.715980i	−0.969117	−	0.246600i	$-0.920687\pi$
$43$	−8.13197	+	4.69500i	−1.24011	+	0.715980i	−0.270997	+	0.962580i	$0.587353\pi$
$44$	−1.78748	+	1.78748i	−0.269472	+	0.269472i
$45$	0.628914	−	5.07078i	0.0937529	−	0.755908i
$46$	−5.74538	−	1.53947i	−0.847109	−	0.226982i
$47$	3.85521	+	3.85521i	0.562340	+	0.562340i	0.929972	−	0.367631i	$-0.119831\pi$
$47$	3.85521	+	3.85521i	0.562340	+	0.562340i	−0.367631	+	0.929972i	$0.619831\pi$
$48$	0.331531	−	1.70003i	0.0478524	−	0.245378i
$49$	0.866025	+	0.500000i	0.123718	+	0.0714286i
$50$	2.02755	−	0.543279i	0.286738	−	0.0768313i
$51$	3.16774	+	2.75708i	0.443573	+	0.386069i
$52$	3.50900	−	0.828792i	0.486611	−	0.114933i
$53$		−	1.50752i		−	0.207074i	−0.994626	−	0.103537i	$-0.966984\pi$
$53$		−	1.50752i		−	0.207074i	0.994626	−	0.103537i	$-0.0330160\pi$
$54$	−4.93888	−	1.61477i	−0.672096	−	0.219742i
$55$	2.15275	−	3.72867i	0.290277	−	0.502774i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	0.482245	+	6.95760i	0.0638749	+	0.921557i
$58$	0.0125005	−	0.0466524i	0.00164139	−	0.00612576i
$59$	−0.153522	+	0.572954i	−0.0199869	+	0.0745922i	−0.975199	−	0.221330i	$-0.928960\pi$
$59$	−0.153522	+	0.572954i	−0.0199869	+	0.0745922i	0.955212	+	0.295922i	$0.0956269\pi$
$60$	0.203984	+	2.94299i	0.0263343	+	0.379938i
$61$	4.34749	+	7.53008i	0.556639	+	0.964127i	0.997774	+	0.0666865i	$0.0212427\pi$
$61$	4.34749	+	7.53008i	0.556639	+	0.964127i	−0.441135	+	0.897441i	$0.645424\pi$
$62$	−3.86117	+	6.68773i	−0.490368	+	0.849343i
$63$	2.76295	−	1.16881i	0.348099	−	0.147257i
$64$			1.00000i			0.125000i
$65$	−5.40758	+	2.91036i	−0.670727	+	0.360986i
$66$	−3.30266	−	2.87451i	−0.406530	−	0.353828i
$67$	−6.36486	+	1.70546i	−0.777591	+	0.208355i	−0.625722	−	0.780046i	$-0.715196\pi$
$67$	−6.36486	+	1.70546i	−0.777591	+	0.208355i	−0.151869	+	0.988401i	$0.548529\pi$
$68$	−2.09977	−	1.21230i	−0.254634	−	0.147013i
$69$	1.97196	−	10.1118i	0.237397	−	1.21732i
$70$	−1.20435	−	1.20435i	−0.143948	−	0.143948i
$71$	−7.41146	−	1.98589i	−0.879578	−	0.235682i	−0.209353	−	0.977840i	$-0.567136\pi$
$71$	−7.41146	−	1.98589i	−0.879578	−	0.235682i	−0.670225	+	0.742158i	$0.733802\pi$
$72$	2.97719	+	0.369252i	0.350865	+	0.0435167i
$73$	5.96741	−	5.96741i	0.698432	−	0.698432i	−0.265640	−	0.964072i	$-0.585583\pi$
$73$	5.96741	−	5.96741i	0.698432	−	0.698432i	0.964072	+	0.265640i	$0.0855832\pi$
$74$	−1.97239	+	1.13876i	−0.229286	+	0.132378i
$75$	1.18156	+	3.43834i	0.136435	+	0.397025i
$76$	−1.04216	−	3.88941i	−0.119544	−	0.446146i
$77$	2.52787			0.288078
$78$	1.85233	+	5.96397i	0.209735	+	0.675286i
$79$	6.92286			0.778883			0.389441	−	0.921051i	$-0.372668\pi$
$79$	6.92286			0.778883			0.389441	+	0.921051i	$0.372668\pi$
$80$	−0.440824	−	1.64518i	−0.0492856	−	0.183936i
$81$	2.19866	−	8.72731i	0.244296	−	0.969701i
$82$	1.27711	−	0.737339i	0.141033	−	0.0814254i
$83$	−9.18787	+	9.18787i	−1.00850	+	1.00850i	−0.00853620	+	0.999964i	$0.502717\pi$
$83$	−9.18787	+	9.18787i	−1.00850	+	1.00850i	−0.999964	+	0.00853620i	$0.997283\pi$
$84$	−1.43653	+	0.967672i	−0.156738	+	0.105582i
$85$	3.98890	+	1.06882i	0.432657	+	0.115930i
$86$	6.63973	+	6.63973i	0.715980	+	0.715980i
$87$	0.0821080	+	0.0160123i	0.00880290	+	0.00171670i
$88$	2.18920	+	1.26394i	0.233370	+	0.134736i
$89$	−14.5458	+	3.89754i	−1.54186	+	0.413139i	−0.926865	−	0.375396i	$-0.877507\pi$
$89$	−14.5458	+	3.89754i	−1.54186	+	0.413139i	−0.614991	+	0.788534i	$0.710840\pi$
$90$	−5.06078	+	0.704931i	−0.533453	+	0.0743063i
$91$	−3.06728	−	1.89520i	−0.321539	−	0.198670i
$92$			5.94805i			0.620127i
$93$	−12.0182	−	5.87077i	−1.24623	−	0.608771i
$94$	2.72604	−	4.72165i	0.281170	−	0.487001i
$95$	3.42909	+	5.93935i	0.351817	+	0.609364i
$96$	−1.72791	+	0.119765i	−0.176354	+	0.0122234i
$97$	1.26639	−	4.72622i	0.128582	−	0.479875i	−0.871360	−	0.490644i	$-0.836761\pi$
$97$	1.26639	−	4.72622i	0.128582	−	0.479875i	0.999942	+	0.0107693i	$0.00342805\pi$
$98$	0.258819	−	0.965926i	0.0261447	−	0.0975732i
$99$	4.57134	−	6.05096i	0.459437	−	0.608144i
$100$	−1.04953	−	1.81785i	−0.104953	−	0.181785i
$101$	3.20791	−	5.55626i	0.319199	−	0.552869i	−0.661122	−	0.750278i	$-0.729919\pi$
$101$	3.20791	−	5.55626i	0.319199	−	0.552869i	0.980321	+	0.197409i	$0.0632528\pi$
$102$	1.84326	−	3.77339i	0.182510	−	0.373621i
$103$			12.8116i			1.26237i	0.775634	+	0.631183i	$0.217430\pi$
$103$			12.8116i			1.26237i	−0.775634	+	0.631183i	$0.782570\pi$
$104$	−1.70875	−	3.17493i	−0.167557	−	0.311327i
$105$	1.93677	−	2.22525i	0.189009	−	0.217162i
$106$	−1.45615	+	0.390174i	−0.141434	+	0.0378971i
$107$	14.6203	+	8.44101i	1.41339	+	0.816023i	0.995706	−	0.0925673i	$-0.0295073\pi$
$107$	14.6203	+	8.44101i	1.41339	+	0.816023i	0.417688	+	0.908591i	$0.362841\pi$
$108$	−0.281470	+	5.18852i	−0.0270845	+	0.499266i
$109$	4.94720	+	4.94720i	0.473856	+	0.473856i	0.903160	−	0.429304i	$-0.141241\pi$
$109$	4.94720	+	4.94720i	0.473856	+	0.473856i	−0.429304	+	0.903160i	$0.641241\pi$
$110$	−4.15880	−	1.11435i	−0.396526	−	0.106249i
$111$	−2.20390	−	3.27173i	−0.209185	−	0.310539i
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	2.00294	−	1.15640i	0.188421	−	0.108785i	−0.402822	−	0.915278i	$-0.631971\pi$
$113$	2.00294	−	1.15640i	0.188421	−	0.108785i	0.591243	+	0.806494i	$0.298637\pi$
$114$	6.59571	−	2.26657i	0.617745	−	0.212284i
$115$	−2.62204	−	9.78559i	−0.244507	−	0.912511i
$116$	−0.0482981			−0.00448437
$117$	−10.0833	+	3.91492i	−0.932204	+	0.361934i
$118$	0.593165			0.0546053
$119$	0.627533	+	2.34199i	0.0575259	+	0.214690i
$120$	2.78991	−	0.958735i	0.254683	−	0.0875202i
$121$	−3.99226	+	2.30493i	−0.362932	+	0.209539i
$122$	6.14828	−	6.14828i	0.556639	−	0.556639i
$123$	1.42700	+	2.11841i	0.128669	+	0.191011i
$124$	7.45920	+	1.99869i	0.669856	+	0.179487i
$125$	8.54978	+	8.54978i	0.764716	+	0.764716i
$126$	−1.84409	−	2.36629i	−0.164285	−	0.210806i
$127$	7.37771	+	4.25953i	0.654666	+	0.377972i	0.790242	−	0.612795i	$-0.209955\pi$
$127$	7.37771	+	4.25953i	0.654666	+	0.377972i	−0.135575	+	0.990767i	$0.543288\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−10.6776	+	12.2680i	−0.940112	+	1.08014i
$130$	4.21078	+	4.47006i	0.369309	+	0.392050i
$131$			20.7862i			1.81609i	0.418868	+	0.908047i	$0.362427\pi$
$131$			20.7862i			1.81609i	−0.418868	+	0.908047i	$0.637573\pi$
$132$	−1.92177	+	3.93411i	−0.167269	+	0.342420i
$133$	−2.01331	+	3.48715i	−0.174576	+	0.302374i
$134$	3.29469	+	5.70657i	0.284618	+	0.492973i
$135$	−1.82416	−	8.66011i	−0.156998	−	0.745344i
$136$	−0.627533	+	2.34199i	−0.0538106	+	0.200824i
$137$	0.292252	−	1.09070i	0.0249688	−	0.0931848i	−0.952317	−	0.305110i	$-0.901307\pi$
$137$	0.292252	−	1.09070i	0.0249688	−	0.0931848i	0.977286	+	0.211925i	$0.0679734\pi$
$138$	−10.2777	+	0.712366i	−0.874893	+	0.0606406i
$139$	4.33495	+	7.50836i	0.367686	+	0.636851i	0.989203	−	0.146550i	$-0.0468169\pi$
$139$	4.33495	+	7.50836i	0.367686	+	0.636851i	−0.621517	+	0.783400i	$0.713484\pi$
$140$	−0.851606	+	1.47502i	−0.0719738	+	0.124662i
$141$	8.48504	+	4.14486i	0.714570	+	0.349060i
$142$			7.67291i			0.643896i
$143$	−9.11031	−	0.272114i	−0.761842	−	0.0227553i
$144$	−0.413884	−	2.97131i	−0.0344903	−	0.247609i
$145$	0.0794589	−	0.0212909i	0.00659870	−	0.00176812i
$146$	−7.30855	−	4.21960i	−0.604860	−	0.349216i
$147$	1.70003	+	0.331531i	0.140216	+	0.0273442i
$148$	1.61045	+	1.61045i	0.132378	+	0.132378i
$149$	12.7416	+	3.41409i	1.04383	+	0.279693i	0.739700	−	0.672937i	$-0.234968\pi$
$149$	12.7416	+	3.41409i	1.04383	+	0.279693i	0.304130	+	0.952631i	$0.401634\pi$
$150$	3.01537	−	2.03121i	0.246204	−	0.165848i
$151$	0.353814	−	0.353814i	0.0287930	−	0.0287930i	−0.692564	−	0.721357i	$-0.743519\pi$
$151$	0.353814	−	0.353814i	0.0287930	−	0.0287930i	0.721357	+	0.692564i	$0.243519\pi$
$152$	−3.48715	+	2.01331i	−0.282845	+	0.163301i
$153$	6.74082	+	2.73307i	0.544963	+	0.220955i
$154$	−0.654262	−	2.44174i	−0.0527219	−	0.196761i
$155$	−13.1528			−1.05646
$156$	5.28133	−	3.33280i	0.422845	−	0.266837i
$157$	4.53573			0.361991			0.180995	−	0.983484i	$-0.442068\pi$
$157$	4.53573			0.361991			0.180995	+	0.983484i	$0.442068\pi$
$158$	−1.79177	−	6.68697i	−0.142545	−	0.531987i
$159$	−0.848580	−	2.46936i	−0.0672967	−	0.195833i
$160$	−1.47502	+	0.851606i	−0.116611	+	0.0673254i
$161$	4.20591	−	4.20591i	0.331472	−	0.331472i
$162$	−8.99899	+	0.135047i	−0.707027	+	0.0106103i
$163$	−14.2337	−	3.81390i	−1.11487	−	0.298727i	−0.346062	−	0.938212i	$-0.612481\pi$
$163$	−14.2337	−	3.81390i	−1.11487	−	0.298727i	−0.768804	+	0.639484i	$0.779148\pi$
$164$	−1.04275	−	1.04275i	−0.0814254	−	0.0814254i
$165$	1.42741	−	7.31946i	0.111124	−	0.569819i
$166$	11.2528	+	6.49681i	0.873386	+	0.504250i
$167$	2.78438	−	0.746072i	0.215462	−	0.0577328i	−0.149473	−	0.988766i	$-0.547758\pi$
$167$	2.78438	−	0.746072i	0.215462	−	0.0577328i	0.364935	+	0.931033i	$0.381091\pi$
$168$	1.30650	+	1.13713i	0.100799	+	0.0877313i
$169$	10.8503	+	7.16036i	0.834639	+	0.550797i
$170$		−	4.12961i		−	0.316727i
$171$	4.70636	+	11.1253i	0.359904	+	0.850774i
$172$	4.69500	−	8.13197i	0.357990	−	0.620057i
$173$	−0.785049	−	1.35974i	−0.0596862	−	0.103379i	0.834638	−	0.550798i	$-0.185677\pi$
$173$	−0.785049	−	1.35974i	−0.0596862	−	0.103379i	−0.894325	+	0.447419i	$0.852343\pi$
$174$	−0.00578440	−	0.0834545i	−0.000438514	−	0.00632667i
$175$	−0.543279	+	2.02755i	−0.0410680	+	0.153268i
$176$	0.654262	−	2.44174i	0.0493168	−	0.184053i
$177$	0.0710402	+	1.02493i	0.00533970	+	0.0770387i
$178$	7.52948	+	13.0414i	0.564358	+	0.977497i
$179$	13.3091	−	23.0520i	0.994767	−	1.72299i	0.408900	−	0.912579i	$-0.365912\pi$
$179$	13.3091	−	23.0520i	0.994767	−	1.72299i	0.585867	−	0.810408i	$-0.300754\pi$
$180$	1.99074	+	4.70588i	0.148381	+	0.350756i
$181$			8.15383i			0.606069i	0.952980	+	0.303035i	$0.0979998\pi$
$181$			8.15383i			0.606069i	−0.952980	+	0.303035i	$0.902000\pi$
$182$	−1.03675	+	3.45328i	−0.0768488	+	0.255974i
$183$	11.3600	+	9.88730i	0.839755	+	0.730890i
$184$	5.74538	−	1.53947i	0.423555	−	0.113491i
$185$	−3.35941	−	1.93955i	−0.246988	−	0.142599i
$186$	−2.56019	+	13.1282i	−0.187722	+	0.962603i
$187$	4.33392	+	4.33392i	0.316928	+	0.316928i
$188$	−5.26631	−	1.41110i	−0.384085	−	0.102915i
$189$	3.86787	−	3.46981i	0.281346	−	0.252392i
$190$	4.84946	−	4.84946i	0.351817	−	0.351817i
$191$	−8.73595	+	5.04370i	−0.632111	+	0.364949i	−0.781569	−	0.623819i	$-0.785580\pi$
$191$	−8.73595	+	5.04370i	−0.632111	+	0.364949i	0.149458	+	0.988768i	$0.452247\pi$
$192$	0.562898	+	1.63803i	0.0406237	+	0.118215i
$193$	−4.57467	−	17.0729i	−0.329292	−	1.22893i	−0.909927	−	0.414769i	$-0.863862\pi$
$193$	−4.57467	−	17.0729i	−0.329292	−	1.22893i	0.580635	−	0.814164i	$-0.302804\pi$
$194$	−4.89295			−0.351293
$195$	−7.21954	+	7.81118i	−0.517002	+	0.559370i
$196$	−1.00000			−0.0714286
$197$	−5.91152	−	22.0621i	−0.421178	−	1.57186i	−0.772130	−	0.635465i	$-0.780808\pi$
$197$	−5.91152	−	22.0621i	−0.421178	−	1.57186i	0.350951	−	0.936394i	$-0.385858\pi$
$198$	−7.02793	−	2.84948i	−0.499453	−	0.202503i
$199$	−14.3928	+	8.30966i	−1.02028	+	0.589056i	−0.914184	−	0.405300i	$-0.867167\pi$
$199$	−14.3928	+	8.30966i	−1.02028	+	0.589056i	−0.106091	+	0.994356i	$0.533834\pi$
$200$	−1.48427	+	1.48427i	−0.104953	+	0.104953i
$201$	−9.46583	+	6.37636i	−0.667668	+	0.449754i
$202$	−6.19721	−	1.66054i	−0.436034	−	0.116835i
$203$	0.0341519	+	0.0341519i	0.00239699	+	0.00239699i
$204$	−4.12189	−	0.803831i	−0.288590	−	0.0562795i
$205$	2.17519	+	1.25584i	0.151922	+	0.0877119i
$206$	12.3751	−	3.31589i	0.862213	−	0.231029i
$207$	−2.46180	−	17.6735i	−0.171107	−	1.22839i
$208$	−2.62449	+	2.47226i	−0.181976	+	0.171420i
$209$			10.1788i			0.704079i
$210$	−2.65069	−	1.29484i	−0.182915	−	0.0893524i
$211$	−13.4706	+	23.3318i	−0.927357	+	1.60623i	−0.139631	+	0.990204i	$0.544592\pi$
$211$	−13.4706	+	23.3318i	−0.927357	+	1.60623i	−0.787726	+	0.616026i	$0.788742\pi$
$212$	0.753759	+	1.30555i	0.0517684	+	0.0896655i
$213$	−13.2581	+	0.918942i	−0.908427	+	0.0629649i
$214$	4.36939	−	16.3068i	0.298685	−	1.11471i
$215$	−4.13933	+	15.4482i	−0.282300	+	1.05356i
$216$	5.08458	−	1.07101i	0.345962	−	0.0728730i
$217$	−3.86117	−	6.68773i	−0.262113	−	0.453993i
$218$	3.49820	−	6.05906i	0.236928	−	0.410371i
$219$	6.41576	−	13.1338i	0.433537	−	0.887503i
$220$			4.30550i			0.290277i
$221$	−2.00949	−	8.50794i	−0.135173	−	0.572306i
$222$	−2.58984	+	2.97559i	−0.173818	+	0.199708i
$223$	−25.7832	+	6.90858i	−1.72657	+	0.462632i	−0.979388	−	0.201989i	$-0.935259\pi$
$223$	−25.7832	+	6.90858i	−1.72657	+	0.462632i	−0.747180	+	0.664622i	$0.768593\pi$
$224$	−0.866025	−	0.500000i	−0.0578638	−	0.0334077i
$225$	3.87087	+	4.96701i	0.258058	+	0.331134i
$226$	−1.63539	−	1.63539i	−0.108785	−	0.108785i
$227$	−9.06914	−	2.43007i	−0.601940	−	0.161289i	−0.0550355	−	0.998484i	$-0.517527\pi$
$227$	−9.06914	−	2.43007i	−0.601940	−	0.161289i	−0.546904	+	0.837195i	$0.684194\pi$
$228$	−3.89644	−	5.78434i	−0.258048	−	0.383077i
$229$	3.49552	−	3.49552i	0.230990	−	0.230990i	−0.582116	−	0.813106i	$-0.697775\pi$
$229$	3.49552	−	3.49552i	0.230990	−	0.230990i	0.813106	+	0.582116i	$0.197775\pi$
$230$	−8.77352	+	5.06539i	−0.578509	+	0.334002i
$231$	4.14073	−	1.42294i	0.272440	−	0.0936223i
$232$	0.0125005	+	0.0466524i	0.000820696	+	0.00306288i
$233$	−19.8275			−1.29894			−0.649472	−	0.760386i	$-0.725010\pi$
$233$	−19.8275			−1.29894			−0.649472	+	0.760386i	$0.725010\pi$
$234$	6.39128	+	8.72649i	0.417811	+	0.570468i
$235$	9.28606			0.605756
$236$	−0.153522	−	0.572954i	−0.00999346	−	0.0372961i
$237$	11.3399	−	3.89687i	0.736603	−	0.253129i
$238$	2.09977	−	1.21230i	0.136108	−	0.0785818i
$239$	14.9255	−	14.9255i	0.965451	−	0.965451i	−0.0339722	−	0.999423i	$-0.510816\pi$
$239$	14.9255	−	14.9255i	0.965451	−	0.965451i	0.999423	+	0.0339722i	$0.0108158\pi$
$240$	−1.64815	−	2.44671i	−0.106388	−	0.157934i
$241$	−27.0678	−	7.25281i	−1.74359	−	0.467194i	−0.760353	−	0.649510i	$-0.774974\pi$
$241$	−27.0678	−	7.25281i	−1.74359	−	0.467194i	−0.983240	+	0.182316i	$0.941641\pi$
$242$	3.25966	+	3.25966i	0.209539	+	0.209539i
$243$	−1.31111	−	15.5332i	−0.0841077	−	0.996457i
$244$	−7.53008	−	4.34749i	−0.482064	−	0.278320i
$245$	1.64518	−	0.440824i	0.105106	−	0.0281632i
$246$	1.67690	−	1.92667i	0.106915	−	0.122840i
$247$	7.63122	−	12.3508i	0.485563	−	0.785860i
$248$		−	7.72233i		−	0.490368i
$249$	−9.87818	+	20.2219i	−0.626004	+	1.28151i
$250$	6.04561	−	10.4713i	0.382358	−	0.662263i
$251$	4.42232	+	7.65968i	0.279134	+	0.483474i	0.971170	−	0.238389i	$-0.0766193\pi$
$251$	4.42232	+	7.65968i	0.279134	+	0.483474i	−0.692036	+	0.721863i	$0.743286\pi$
$252$	−1.80838	+	2.39370i	−0.113917	+	0.150789i
$253$	3.89158	−	14.5236i	0.244662	−	0.913089i
$254$	2.20489	−	8.22877i	0.138347	−	0.516319i
$255$	7.13558	−	0.494581i	0.446847	−	0.0309719i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.05002	−	12.2110i	0.439768	−	0.761701i	−0.557903	−	0.829906i	$-0.688394\pi$
$257$	7.05002	−	12.2110i	0.439768	−	0.761701i	0.997671	+	0.0682054i	$0.0217273\pi$
$258$	14.6136	+	7.13859i	0.909801	+	0.444429i
$259$		−	2.27752i		−	0.141519i
$260$	3.22792	−	5.22423i	0.200187	−	0.323993i
$261$	0.143509	−	0.0199898i	0.00888297	−	0.00123734i
$262$	20.0779	−	5.37985i	1.24042	−	0.332368i
$263$	2.32601	+	1.34293i	0.143428	+	0.0828083i	0.569997	−	0.821647i	$-0.306944\pi$
$263$	2.32601	+	1.34293i	0.143428	+	0.0828083i	−0.426569	+	0.904455i	$0.640278\pi$
$264$	4.29745	+	0.838068i	0.264490	+	0.0515795i
$265$	−1.81558	−	1.81558i	−0.111530	−	0.111530i
$266$	3.88941	+	1.04216i	0.238475	+	0.0638991i
$267$	−21.6326	+	14.5721i	−1.32389	+	0.891800i
$268$	4.65940	−	4.65940i	0.284618	−	0.284618i
$269$	21.1279	−	12.1982i	1.28819	−	0.743736i	0.309858	−	0.950783i	$-0.399719\pi$
$269$	21.1279	−	12.1982i	1.28819	−	0.743736i	0.978331	+	0.207047i	$0.0663853\pi$
$270$	−7.89290	+	4.00340i	−0.480347	+	0.243639i
$271$	−5.12304	−	19.1194i	−0.311202	−	1.16142i	−0.927474	−	0.373889i	$-0.878024\pi$
$271$	−5.12304	−	19.1194i	−0.311202	−	1.16142i	0.616271	−	0.787534i	$-0.288643\pi$
$272$	2.42460			0.147013
$273$	−6.09111	−	1.37782i	−0.368651	−	0.0833894i
$274$	−1.12918			−0.0682160
$275$	1.37334	+	5.12538i	0.0828156	+	0.309072i
$276$	3.34815	+	9.74309i	0.201535	+	0.586465i
$277$	19.5143	−	11.2666i	1.17250	−	0.676943i	0.218233	−	0.975897i	$-0.429971\pi$
$277$	19.5143	−	11.2666i	1.17250	−	0.676943i	0.954268	+	0.298953i	$0.0966375\pi$
$278$	6.13055	−	6.13055i	0.367686	−	0.367686i
$279$	−22.9908	−	2.85148i	−1.37643	−	0.170714i
$280$	1.64518	+	0.440824i	0.0983181	+	0.0263443i
$281$	0.262594	+	0.262594i	0.0156650	+	0.0156650i	0.714896	−	0.699231i	$-0.246474\pi$
$281$	0.262594	+	0.262594i	0.0156650	+	0.0156650i	−0.699231	+	0.714896i	$0.746474\pi$
$282$	1.80754	−	9.26869i	0.107637	−	0.551943i
$283$	−25.0610	−	14.4690i	−1.48972	−	0.860090i	−0.489788	−	0.871841i	$-0.662926\pi$
$283$	−25.0610	−	14.4690i	−1.48972	−	0.860090i	−0.999931	+	0.0117514i	$0.996259\pi$
$284$	7.41146	−	1.98589i	0.439789	−	0.117841i
$285$	8.96020	+	7.79861i	0.530756	+	0.461950i
$286$	2.09508	+	8.87031i	0.123885	+	0.524513i
$287$			1.47468i			0.0870475i
$288$	−2.76295	+	1.16881i	−0.162808	+	0.0688730i
$289$	5.56065	−	9.63133i	0.327097	−	0.566549i
$290$	−0.0411309	−	0.0712409i	−0.00241529	−	0.00418341i
$291$	−0.586001	−	8.45455i	−0.0343520	−	0.495614i
$292$	−2.18422	+	8.15163i	−0.127822	+	0.477038i
$293$	7.64906	−	28.5467i	0.446863	−	1.66771i	−0.264108	−	0.964493i	$-0.585078\pi$
$293$	7.64906	−	28.5467i	0.446863	−	1.66771i	0.710971	−	0.703222i	$-0.248256\pi$
$294$	−0.119765	−	1.72791i	−0.00698481	−	0.100773i
$295$	0.505143	+	0.874933i	0.0294106	+	0.0509406i
$296$	1.13876	−	1.97239i	0.0661892	−	0.114643i
$297$	4.08193	−	12.4849i	0.236857	−	0.724445i
$298$		−	13.1910i		−	0.764136i
$299$	−15.6106	+	14.7051i	−0.902784	+	0.850418i
$300$	−2.74243	−	2.38691i	−0.158335	−	0.137808i
$301$	−9.07004	+	2.43031i	−0.522788	+	0.140081i
$302$	−0.433332	−	0.250184i	−0.0249355	−	0.0143965i
$303$	2.12704	−	10.9071i	0.122196	−	0.626594i
$304$	2.84724	+	2.84724i	0.163301	+	0.163301i
$305$	14.3048	+	3.83295i	0.819089	+	0.219474i
$306$	0.895289	−	7.21850i	0.0511802	−	0.412654i
$307$	3.04668	−	3.04668i	0.173883	−	0.173883i	−0.614800	−	0.788683i	$-0.710763\pi$
$307$	3.04668	−	3.04668i	0.173883	−	0.173883i	0.788683	+	0.614800i	$0.210763\pi$
$308$	−2.18920	+	1.26394i	−0.124741	+	0.0720194i
$309$	7.21164	+	20.9858i	0.410256	+	1.19384i
$310$	3.40419	+	12.7046i	0.193345	+	0.721572i
$311$	−25.5871			−1.45091			−0.725455	−	0.688269i	$-0.758371\pi$
$311$	−25.5871			−1.45091			−0.725455	+	0.688269i	$0.758371\pi$
$312$	−4.58615	−	4.23878i	−0.259639	−	0.239974i
$313$	17.7604			1.00388			0.501938	−	0.864903i	$-0.332620\pi$
$313$	17.7604			1.00388			0.501938	+	0.864903i	$0.332620\pi$
$314$	−1.17393	−	4.38118i	−0.0662489	−	0.247244i
$315$	1.91990	−	4.73523i	0.108174	−	0.266800i
$316$	−5.99537	+	3.46143i	−0.337266	+	0.194721i
$317$	0.122626	−	0.122626i	0.00688738	−	0.00688738i	−0.703655	−	0.710542i	$-0.748450\pi$
$317$	0.122626	−	0.122626i	0.00688738	−	0.00688738i	0.710542	+	0.703655i	$0.248450\pi$
$318$	−2.16559	+	1.45878i	−0.121440	+	0.0818045i
$319$	0.117931	+	0.0315996i	0.00660288	+	0.00176924i
$320$	1.20435	+	1.20435i	0.0673254	+	0.0673254i
$321$	28.6999	+	5.59692i	1.60187	+	0.312389i
$322$	−5.15116	−	2.97403i	−0.287063	−	0.165736i
$323$	−9.43027	+	2.52683i	−0.524714	+	0.140597i
$324$	2.45955	+	8.65740i	0.136642	+	0.480967i
$325$	2.17620	−	7.24868i	0.120714	−	0.402084i
$326$			14.7358i			0.816138i
$327$	10.8884	+	5.31890i	0.602132	+	0.294136i
$328$	−0.737339	+	1.27711i	−0.0407127	+	0.0705165i
$329$	2.72604	+	4.72165i	0.150292	+	0.260313i
$330$	−7.43950	+	0.515646i	−0.409531	+	0.0283854i
$331$	1.92841	−	7.19693i	0.105995	−	0.395579i	−0.892461	−	0.451124i	$-0.851023\pi$
$331$	1.92841	−	7.19693i	0.105995	−	0.395579i	0.998456	+	0.0555454i	$0.0176897\pi$
$332$	3.36299	−	12.5509i	0.184568	−	0.688818i
$333$	−5.45170	−	4.11862i	−0.298751	−	0.225699i
$334$	−1.44130	−	2.49641i	−0.0788645	−	0.136597i
$335$	−5.61156	+	9.71951i	−0.306592	+	0.531033i
$336$	0.760233	−	1.55629i	0.0414741	−	0.0849027i
$337$		−	19.7859i		−	1.07781i	−0.842368	−	0.538903i	$-0.818839\pi$
$337$		−	19.7859i		−	1.07781i	0.842368	−	0.538903i	$-0.181161\pi$
$338$	4.10811	−	12.3338i	0.223452	−	0.670872i
$339$	2.62994	−	3.02166i	0.142839	−	0.164114i
$340$	−3.98890	+	1.06882i	−0.216328	+	0.0579650i
$341$	−16.9057	−	9.76053i	−0.915497	−	0.528563i
$342$	9.52813	−	7.42543i	0.515222	−	0.401521i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−9.07004	−	2.43031i	−0.489024	−	0.131034i
$345$	−9.80328	−	14.5532i	−0.527791	−	0.783516i
$346$	−1.11023	+	1.11023i	−0.0596862	+	0.0596862i
$347$	28.5337	−	16.4739i	1.53177	−	0.884367i	0.532488	−	0.846437i	$-0.321257\pi$
$347$	28.5337	−	16.4739i	1.53177	−	0.884367i	0.999280	−	0.0379296i	$-0.0120763\pi$
$348$	−0.0791138	+	0.0271869i	−0.00424094	+	0.00145737i
$349$	7.05811	+	26.3412i	0.377812	+	1.41001i	0.849192	+	0.528084i	$0.177089\pi$
$349$	7.05811	+	26.3412i	0.377812	+	1.41001i	−0.471380	+	0.881930i	$0.656244\pi$
$350$	2.09907			0.112200
$351$	−14.3131	+	12.0886i	−0.763976	+	0.645244i
$352$	−2.52787			−0.134736
$353$	2.61659	+	9.76525i	0.139267	+	0.519752i	0.999944	+	0.0105999i	$0.00337411\pi$
$353$	2.61659	+	9.76525i	0.139267	+	0.519752i	−0.860677	+	0.509152i	$0.829959\pi$
$354$	0.971623	−	0.333892i	0.0516412	−	0.0177461i
$355$	−11.3177	+	6.53429i	−0.600683	+	0.346804i
$356$	10.6483	−	10.6483i	0.564358	−	0.564358i
$357$	2.34622	+	3.48301i	0.124175	+	0.184340i
$358$	−25.7112	−	6.88928i	−1.35888	−	0.364110i
$359$	−7.56706	−	7.56706i	−0.399374	−	0.399374i	0.478638	−	0.878012i	$-0.341131\pi$
$359$	−7.56706	−	7.56706i	−0.399374	−	0.399374i	−0.878012	+	0.478638i	$0.841131\pi$
$360$	4.03029	−	3.14088i	0.212415	−	0.165539i
$361$	2.41310	+	1.39320i	0.127005	+	0.0733265i
$362$	7.87600	−	2.11037i	0.413953	−	0.110918i
$363$	−5.24200	+	6.02278i	−0.275134	+	0.316114i
$364$	3.60394	+	0.107646i	0.188898	+	0.00564216i
$365$		−	14.3737i		−	0.752355i
$366$	6.61022	−	13.5319i	0.345522	−	0.707325i
$367$	−13.0944	+	22.6802i	−0.683524	+	1.18390i	0.290374	+	0.956913i	$0.406220\pi$
$367$	−13.0944	+	22.6802i	−0.683524	+	1.18390i	−0.973898	+	0.226986i	$0.927113\pi$
$368$	−2.97403	−	5.15116i	−0.155032	−	0.268523i
$369$	3.52993	+	2.66677i	0.183761	+	0.138827i
$370$	−1.00399	+	3.74693i	−0.0521948	+	0.194794i
$371$	0.390174	−	1.45615i	0.0202568	−	0.0755996i
$372$	13.3435	−	0.924861i	0.691826	−	0.0479518i
$373$	−14.4447	−	25.0190i	−0.747920	−	1.29544i	−0.948818	−	0.315824i	$-0.897719\pi$
$373$	−14.4447	−	25.0190i	−0.747920	−	1.29544i	0.200897	−	0.979612i	$-0.435614\pi$
$374$	3.06454	−	5.30795i	0.158464	−	0.274467i
$375$	18.8175	+	9.19215i	0.971730	+	0.474681i
$376$			5.45209i			0.281170i
$377$	−0.119405	−	0.126758i	−0.00614969	−	0.00652836i
$378$	−4.35266	−	2.83802i	−0.223877	−	0.145972i
$379$	−20.9024	+	5.60078i	−1.07368	+	0.287693i	−0.752006	−	0.659156i	$-0.770914\pi$
$379$	−20.9024	+	5.60078i	−1.07368	+	0.287693i	−0.321678	+	0.946849i	$0.604247\pi$
$380$	−5.93935	−	3.42909i	−0.304682	−	0.175908i
$381$	14.4826	+	2.82433i	0.741966	+	0.144695i
$382$	7.13287	+	7.13287i	0.364949	+	0.364949i
$383$	−14.7133	−	3.94240i	−0.751812	−	0.201447i	−0.137490	−	0.990503i	$-0.543904\pi$
$383$	−14.7133	−	3.94240i	−0.751812	−	0.201447i	−0.614322	+	0.789056i	$0.710570\pi$
$384$	1.43653	−	0.967672i	0.0733075	−	0.0493813i
$385$	3.04445	−	3.04445i	0.155160	−	0.155160i
$386$	−15.3071	+	8.83758i	−0.779113	+	0.449821i
$387$	−10.5846	+	26.1058i	−0.538046	+	1.32703i
$388$	1.26639	+	4.72622i	0.0642911	+	0.239938i
$389$	−20.6777			−1.04840			−0.524200	−	0.851595i	$-0.675636\pi$
$389$	−20.6777			−1.04840			−0.524200	+	0.851595i	$0.675636\pi$
$390$	9.41357	+	4.95186i	0.476675	+	0.250747i
$391$	14.4217			0.729335
$392$	0.258819	+	0.965926i	0.0130723	+	0.0487866i
$393$	11.7005	+	34.0484i	0.590212	+	1.71751i
$394$	−19.7803	+	11.4202i	−0.996518	+	0.575340i
$395$	8.33757	−	8.33757i	0.419509	−	0.419509i
$396$	−0.933421	+	7.52595i	−0.0469062	+	0.378193i
$397$	2.56934	+	0.688451i	0.128951	+	0.0345524i	0.322717	−	0.946495i	$-0.395404\pi$
$397$	2.56934	+	0.688451i	0.128951	+	0.0345524i	−0.193766	+	0.981048i	$0.562070\pi$
$398$	11.7516	+	11.7516i	0.589056	+	0.589056i
$399$	−1.33495	+	6.84534i	−0.0668309	+	0.342696i
$400$	1.81785	+	1.04953i	0.0908924	+	0.0524767i
$401$	−4.02361	+	1.07812i	−0.200930	+	0.0538389i	−0.357880	−	0.933768i	$-0.616500\pi$
$401$	−4.02361	+	1.07812i	−0.200930	+	0.0538389i	0.156951	+	0.987606i	$0.449834\pi$
$402$	8.60903	+	7.49297i	0.429379	+	0.373715i
$403$	13.1955	+	24.5179i	0.657316	+	1.22132i
$404$			6.41582i			0.319199i
$405$	−7.86279	−	13.1587i	−0.390705	−	0.653862i
$406$	0.0241491	−	0.0418274i	0.00119850	−	0.00207586i
$407$	−2.87865	−	4.98596i	−0.142689	−	0.247145i
$408$	0.290381	+	4.18948i	0.0143760	+	0.207410i
$409$	−5.42905	+	20.2615i	−0.268449	+	1.00187i	0.691656	+	0.722227i	$0.256881\pi$
$409$	−5.42905	+	20.2615i	−0.268449	+	1.00187i	−0.960105	+	0.279639i	$0.909785\pi$
$410$	0.650073	−	2.42610i	0.0321048	−	0.119817i
$411$	−0.135235	−	1.95111i	−0.00667066	−	0.0962411i
$412$	−6.40581	−	11.0952i	−0.315592	−	0.546621i
$413$	−0.296583	+	0.513696i	−0.0145939	+	0.0252773i
$414$	−16.4341	+	6.95216i	−0.807694	+	0.341680i
$415$			22.1309i			1.08636i
$416$	3.06728	+	1.89520i	0.150386	+	0.0929196i
$417$	11.3272	+	9.85878i	0.554697	+	0.482787i
$418$	9.83193	−	2.63446i	0.480895	−	0.128855i
$419$	−12.6256	−	7.28938i	−0.616800	−	0.356109i	0.158822	−	0.987307i	$-0.449230\pi$
$419$	−12.6256	−	7.28938i	−0.616800	−	0.356109i	−0.775622	+	0.631198i	$0.782564\pi$
$420$	−0.564668	+	2.89550i	−0.0275530	+	0.141286i
$421$	13.7352	+	13.7352i	0.669413	+	0.669413i	0.957580	−	0.288167i	$-0.0930459\pi$
$421$	13.7352	+	13.7352i	0.669413	+	0.669413i	−0.288167	+	0.957580i	$0.593046\pi$
$422$	26.0233	+	6.97292i	1.26679	+	0.339436i
$423$	16.2319	+	2.01319i	0.789222	+	0.0978848i
$424$	1.06598	−	1.06598i	0.0517684	−	0.0517684i
$425$	−4.40756	+	2.54471i	−0.213798	+	0.123436i
$426$	4.31907	+	12.5685i	0.209259	+	0.608944i
$427$	2.25043	+	8.39871i	0.108906	+	0.406442i
$428$	−16.8820			−0.816023
$429$	−15.0761	+	4.68245i	−0.727883	+	0.226071i
$430$	15.9932			0.771258
$431$	−3.62793	−	13.5396i	−0.174751	−	0.652181i	−0.996594	−	0.0824664i	$-0.973720\pi$
$431$	−3.62793	−	13.5396i	−0.174751	−	0.652181i	0.821842	−	0.569715i	$-0.192946\pi$
$432$	−2.35050	−	4.63413i	−0.113089	−	0.222960i
$433$	13.5616	−	7.82982i	0.651731	−	0.376277i	−0.137388	−	0.990517i	$-0.543871\pi$
$433$	13.5616	−	7.82982i	0.651731	−	0.376277i	0.789119	+	0.614240i	$0.210537\pi$
$434$	−5.46051	+	5.46051i	−0.262113	+	0.262113i
$435$	0.118171	−	0.0796025i	0.00566589	−	0.00381665i
$436$	−6.75800	−	1.81080i	−0.323650	−	0.0867216i
$437$	16.9355	+	16.9355i	0.810137	+	0.810137i
$438$	−14.3468	−	2.79785i	−0.685519	−	0.133687i
$439$	−28.4951	−	16.4517i	−1.36000	−	0.785195i	−0.370374	−	0.928883i	$-0.620771\pi$
$439$	−28.4951	−	16.4517i	−1.36000	−	0.785195i	−0.989623	+	0.143688i	$0.954104\pi$
$440$	4.15880	−	1.11435i	0.198263	−	0.0531244i
$441$	2.97131	−	0.413884i	0.141491	−	0.0197087i
$442$	−7.69795	+	4.14304i	−0.366154	+	0.197064i
$443$			16.8490i			0.800518i	0.916402	+	0.400259i	$0.131080\pi$
$443$			16.8490i			0.800518i	−0.916402	+	0.400259i	$0.868920\pi$
$444$	3.54449	+	1.73145i	0.168214	+	0.0821710i
$445$	−12.8243	+	22.2123i	−0.607930	+	1.05297i
$446$	13.3463	+	23.1165i	0.631968	+	1.09460i
$447$	22.7929	−	1.57982i	1.07807	−	0.0747228i
$448$	−0.258819	+	0.965926i	−0.0122281	+	0.0456357i
$449$	5.03482	−	18.7902i	0.237608	−	0.886765i	−0.739348	−	0.673324i	$-0.764866\pi$
$449$	5.03482	−	18.7902i	0.237608	−	0.886765i	0.976956	−	0.213441i	$-0.0684673\pi$
$450$	3.79591	−	5.02453i	0.178941	−	0.236859i
$451$	1.86390	+	3.22837i	0.0877675	+	0.152018i
$452$	−1.15640	+	2.00294i	−0.0543923	+	0.0942103i
$453$	0.380397	−	0.778720i	0.0178726	−	0.0365875i
$454$			9.38906i			0.440651i
$455$	−5.97658	+	1.41161i	−0.280186	+	0.0661772i
$456$	−4.57877	+	5.26077i	−0.214420	+	0.246358i
$457$	32.2742	−	8.64783i	1.50972	−	0.404529i	0.593379	−	0.804924i	$-0.297794\pi$
$457$	32.2742	−	8.64783i	1.50972	−	0.404529i	0.916343	+	0.400395i	$0.131127\pi$
$458$	−4.28112	−	2.47170i	−0.200044	−	0.115495i
$459$	12.5801	+	0.682453i	0.587189	+	0.0318542i
$460$	7.16355	+	7.16355i	0.334002	+	0.334002i
$461$	12.6673	+	3.39420i	0.589976	+	0.158084i	0.541442	−	0.840738i	$-0.317879\pi$
$461$	12.6673	+	3.39420i	0.589976	+	0.158084i	0.0485337	+	0.998822i	$0.484545\pi$
$462$	−2.44615	−	3.63136i	−0.113805	−	0.168946i
$463$	14.6471	−	14.6471i	0.680707	−	0.680707i	−0.279452	−	0.960160i	$-0.590153\pi$
$463$	14.6471	−	14.6471i	0.680707	−	0.680707i	0.960160	+	0.279452i	$0.0901528\pi$
$464$	0.0418274	−	0.0241491i	0.00194179	−	0.00112109i
$465$	−21.5446	+	7.40367i	−0.999109	+	0.343337i
$466$	5.13174	+	19.1519i	0.237723	+	0.887195i
$467$	15.2948			0.707759			0.353880	−	0.935291i	$-0.384862\pi$
$467$	15.2948			0.707759			0.353880	+	0.935291i	$0.384862\pi$
$468$	6.77496	−	8.43208i	0.313172	−	0.389773i
$469$	−6.58939			−0.304270
$470$	−2.40341	−	8.96965i	−0.110861	−	0.413739i
$471$	7.42967	−	2.55316i	0.342341	−	0.117643i
$472$	−0.513696	+	0.296583i	−0.0236448	+	0.0136513i
$473$	−16.7844	+	16.7844i	−0.771747	+	0.771747i
$474$	−6.69906	−	9.94488i	−0.307698	−	0.456784i
$475$	−8.16414	−	2.18757i	−0.374596	−	0.100373i
$476$	−1.71445	−	1.71445i	−0.0785818	−	0.0785818i
$477$	−2.78000	−	3.56723i	−0.127287	−	0.163332i
$478$	−18.2799	−	10.5539i	−0.836105	−	0.482725i
$479$	−16.6395	+	4.45855i	−0.760279	+	0.203716i	−0.618073	−	0.786121i	$-0.712086\pi$
$479$	−16.6395	+	4.45855i	−0.760279	+	0.203716i	−0.142206	+	0.989837i	$0.545420\pi$
$480$	−1.93677	+	2.22525i	−0.0884010	+	0.101568i
$481$	−0.245165	+	8.20807i	−0.0111786	+	0.374256i
$482$			28.0227i			1.27640i
$483$	4.52191	−	9.25690i	0.205754	−	0.421204i
$484$	2.30493	−	3.99226i	0.104770	−	0.181466i
$485$	−4.16686	−	7.21721i	−0.189207	−	0.327717i
$486$	−14.6646	+	5.28673i	−0.665200	+	0.239811i
$487$	−0.660728	+	2.46587i	−0.0299404	+	0.111739i	−0.979279	−	0.202516i	$-0.935088\pi$
$487$	−0.660728	+	2.46587i	−0.0299404	+	0.111739i	0.949338	+	0.314255i	$0.101755\pi$
$488$	−2.25043	+	8.39871i	−0.101872	+	0.380192i
$489$	−25.4620	+	1.76482i	−1.15143	+	0.0798080i
$490$	−0.851606	−	1.47502i	−0.0384716	−	0.0666348i
$491$	11.1457	−	19.3048i	0.502997	−	0.871216i	−0.496997	−	0.867752i	$-0.665564\pi$
$491$	11.1457	−	19.3048i	0.502997	−	0.871216i	0.999994	−	0.00346360i	$-0.00110250\pi$
$492$	−2.29503	−	1.12110i	−0.103468	−	0.0505430i
$493$			0.117104i			0.00527409i
$494$	−13.9050	−	4.17458i	−0.625617	−	0.187823i
$495$	−1.78198	−	12.7930i	−0.0800939	−	0.575002i
$496$	−7.45920	+	1.99869i	−0.334928	+	0.0897437i
$497$	−6.64493	−	3.83645i	−0.298066	−	0.172088i
$498$	22.0895	+	4.30779i	0.989853	+	0.193037i
$499$	14.6355	+	14.6355i	0.655177	+	0.655177i	0.954235	−	0.299058i	$-0.0966724\pi$
$499$	14.6355	+	14.6355i	0.655177	+	0.655177i	−0.299058	+	0.954235i	$0.596672\pi$
$500$	−11.6792	−	3.12944i	−0.522311	−	0.139953i
$501$	4.14094	−	2.78941i	0.185003	−	0.124622i
$502$	6.25410	−	6.25410i	0.279134	−	0.279134i
$503$	10.3067	−	5.95060i	0.459555	−	0.265324i	−0.252302	−	0.967648i	$-0.581188\pi$
$503$	10.3067	−	5.95060i	0.459555	−	0.265324i	0.711857	+	0.702324i	$0.247854\pi$
$504$	2.78017	+	1.12722i	0.123839	+	0.0502105i
$505$	−2.82825	−	10.5552i	−0.125855	−	0.469698i
$506$	−15.0359			−0.668428
$507$	21.8037	+	5.62127i	0.968336	+	0.249649i
$508$	−8.51905			−0.377972
$509$	−0.804816	−	3.00361i	−0.0356728	−	0.133133i	0.945793	−	0.324770i	$-0.105287\pi$
$509$	−0.804816	−	3.00361i	−0.0356728	−	0.133133i	−0.981466	+	0.191637i	$0.938620\pi$
$510$	−2.32455	−	6.76443i	−0.102933	−	0.299534i
$511$	7.30855	−	4.21960i	0.323311	−	0.186664i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	13.9716	+	15.5744i	0.616860	+	0.687627i
$514$	−13.6196	−	3.64936i	−0.600734	−	0.160966i
$515$	15.4297	+	15.4297i	0.679914	+	0.679914i
$516$	3.11308	−	15.9632i	0.137046	−	0.702742i
$517$	11.9357	+	6.89109i	0.524933	+	0.303070i
$518$	−2.19992	+	0.589467i	−0.0966589	+	0.0258997i
$519$	−2.05133	−	1.78540i	−0.0900435	−	0.0783704i
$520$	−5.88167	−	1.76580i	−0.257928	−	0.0774354i
$521$		−	18.4606i		−	0.808774i	−0.914588	−	0.404387i	$-0.867485\pi$
$521$		−	18.4606i		−	0.808774i	0.914588	−	0.404387i	$-0.132515\pi$
$522$	−0.0564515	−	0.133445i	−0.00247081	−	0.00584073i
$523$	−4.75204	+	8.23078i	−0.207792	+	0.359907i	−0.951019	−	0.309133i	$-0.899961\pi$
$523$	−4.75204	+	8.23078i	−0.207792	+	0.359907i	0.743227	+	0.669040i	$0.233294\pi$
$524$	−10.3931	−	18.0013i	−0.454024	−	0.786392i
$525$	0.251394	+	3.62699i	0.0109717	+	0.158295i
$526$	0.695149	−	2.59433i	0.0303099	−	0.113118i
$527$	4.84602	−	18.0856i	0.211096	−	0.787821i
$528$	−0.302749	−	4.36792i	−0.0131755	−	0.190089i
$529$	−6.18965	−	10.7208i	−0.269115	−	0.466122i
$530$	−1.28381	+	2.22363i	−0.0557652	+	0.0965882i
$531$	0.693299	+	1.63888i	0.0300866	+	0.0711215i
$532$		−	4.02661i		−	0.174576i
$533$	0.158742	−	5.31465i	0.00687590	−	0.230203i
$534$	19.6745	+	17.1239i	0.851400	+	0.741026i
$535$	27.7739	−	7.44199i	1.20077	−	0.321745i
$536$	−5.70657	−	3.29469i	−0.246486	−	0.142309i
$537$	8.82474	−	45.2515i	0.380816	−	1.95275i
$538$	−17.2508	−	17.2508i	−0.743736	−	0.743736i
$539$	2.44174	+	0.654262i	0.105173	+	0.0281810i
$540$	5.90982	+	6.58780i	0.254318	+	0.283494i
$541$	−9.25800	+	9.25800i	−0.398032	+	0.398032i	−0.877539	−	0.479506i	$-0.840816\pi$
$541$	−9.25800	+	9.25800i	−0.398032	+	0.398032i	0.479506	+	0.877539i	$0.340816\pi$
$542$	−17.1420	+	9.89695i	−0.736313	+	0.425110i
$543$	4.58978	+	13.3562i	0.196966	+	0.573171i
$544$	−0.627533	−	2.34199i	−0.0269053	−	0.100412i
$545$	11.9163			0.510440
$546$	0.245623	+	6.24017i	0.0105117	+	0.267054i
$547$	7.20907			0.308238			0.154119	−	0.988052i	$-0.450746\pi$
$547$	7.20907			0.308238			0.154119	+	0.988052i	$0.450746\pi$
$548$	0.292252	+	1.09070i	0.0124844	+	0.0465924i
$549$	24.1736	+	9.80118i	1.03170	+	0.418304i
$550$	4.59529	−	2.65309i	0.195944	−	0.113128i
$551$	−0.137516	+	0.137516i	−0.00585840	+	0.00585840i
$552$	8.54454	−	5.75576i	0.363680	−	0.244981i
$553$	6.68697	+	1.79177i	0.284359	+	0.0761938i
$554$	−15.9334	−	15.9334i	−0.676943	−	0.676943i
$555$	−6.59458	−	1.28604i	−0.279924	−	0.0545896i
$556$	−7.50836	−	4.33495i	−0.318425	−	0.183843i
$557$	−32.3546	+	8.66938i	−1.37091	+	0.367333i	−0.867810	−	0.496896i	$-0.834473\pi$
$557$	−32.3546	+	8.66938i	−1.37091	+	0.367333i	−0.503097	+	0.864230i	$0.667806\pi$
$558$	3.19615	+	22.9455i	0.135304	+	0.971359i
$559$	32.9495	−	7.78235i	1.39362	−	0.329158i
$560$		−	1.70321i		−	0.0719738i
$561$	9.53865	+	4.65954i	0.402722	+	0.196726i
$562$	0.185682	−	0.321610i	0.00783252	−	0.0135663i
$563$	6.44159	+	11.1572i	0.271480	+	0.470218i	0.969241	−	0.246113i	$-0.0791534\pi$
$563$	6.44159	+	11.1572i	0.271480	+	0.470218i	−0.697761	+	0.716331i	$0.745820\pi$
$564$	−9.42069	+	0.652967i	−0.396683	+	0.0274949i
$565$	1.01953	−	3.80495i	0.0428921	−	0.160076i
$566$	−7.48968	+	27.9519i	−0.314815	+	1.17490i
$567$	4.38254	−	7.86087i	0.184049	−	0.330126i
$568$	−3.83645	−	6.64493i	−0.160974	−	0.278815i
$569$	−19.2164	+	33.2837i	−0.805592	+	1.39533i	0.110298	+	0.993899i	$0.464819\pi$
$569$	−19.2164	+	33.2837i	−0.805592	+	1.39533i	−0.915891	+	0.401428i	$0.868514\pi$
$570$	5.21381	−	10.6733i	0.218383	−	0.447056i
$571$			6.25069i			0.261583i	0.991410	+	0.130792i	$0.0417519\pi$
$571$			6.25069i			0.261583i	−0.991410	+	0.130792i	$0.958248\pi$
$572$	8.02582	−	4.31950i	0.335576	−	0.180607i
$573$	−11.4707	+	13.1792i	−0.479194	+	0.550569i
$574$	1.42443	−	0.381675i	0.0594545	−	0.0159308i
$575$	10.8127	+	6.24269i	0.450919	+	0.260338i
$576$	1.84409	+	2.36629i	0.0768371	+	0.0985954i
$577$	−14.0041	−	14.0041i	−0.583000	−	0.583000i	0.352726	−	0.935726i	$-0.385255\pi$
$577$	−14.0041	−	14.0041i	−0.583000	−	0.583000i	−0.935726	+	0.352726i	$0.885255\pi$
$578$	−10.7423	−	2.87840i	−0.446823	−	0.119726i
$579$	−17.1038	−	25.3909i	−0.710808	−	1.05521i
$580$	−0.0581679	+	0.0581679i	−0.00241529	+	0.00241529i
$581$	−11.2528	+	6.49681i	−0.466845	+	0.269533i
$582$	−8.01480	+	2.75423i	−0.332224	+	0.114167i
$583$	−0.986311	−	3.68096i	−0.0408488	−	0.152450i
$584$	8.43919			0.349216
$585$	−7.42893	+	16.8588i	−0.307149	+	0.697026i
$586$	−29.5537			−1.22085
$587$	8.56624	+	31.9696i	0.353566	+	1.31953i	0.882279	+	0.470727i	$0.156008\pi$
$587$	8.56624	+	31.9696i	0.353566	+	1.31953i	−0.528712	+	0.848801i	$0.677325\pi$
$588$	−1.63803	+	0.562898i	−0.0675513	+	0.0232135i
$589$	26.9289	−	15.5474i	1.10959	−	0.640620i
$590$	0.714380	−	0.714380i	0.0294106	−	0.0294106i
$591$	−22.1020	−	32.8108i	−0.909153	−	1.34966i
$592$	−2.19992	−	0.589467i	−0.0904162	−	0.0242269i
$593$	9.86033	+	9.86033i	0.404915	+	0.404915i	0.879961	−	0.475046i	$-0.157569\pi$
$593$	9.86033	+	9.86033i	0.404915	+	0.404915i	−0.475046	+	0.879961i	$0.657569\pi$
$594$	−13.1159	−	0.711521i	−0.538153	−	0.0291940i
$595$	3.57635	+	2.06481i	0.146616	+	0.0846488i
$596$	−12.7416	+	3.41409i	−0.521915	+	0.139847i
$597$	−18.8983	+	21.7131i	−0.773455	+	0.888659i
$598$	18.2444	+	11.2727i	0.746067	+	0.460976i
$599$		−	34.3137i		−	1.40202i	−0.713152	−	0.701009i	$-0.752733\pi$
$599$		−	34.3137i		−	1.40202i	0.713152	−	0.701009i	$-0.247267\pi$
$600$	−1.59578	+	3.26677i	−0.0651476	+	0.133365i
$601$	6.93693	−	12.0151i	0.282963	−	0.490107i	−0.689150	−	0.724619i	$-0.742016\pi$
$601$	6.93693	−	12.0151i	0.282963	−	0.490107i	0.972113	+	0.234512i	$0.0753492\pi$
$602$	4.69500	+	8.13197i	0.191354	+	0.331435i
$603$	−11.9161	+	15.7730i	−0.485260	+	0.642325i
$604$	−0.129505	+	0.483319i	−0.00526948	+	0.0196660i
$605$	−2.03214	+	7.58403i	−0.0826181	+	0.308335i
$606$	−11.0859	+	0.768388i	−0.450335	+	0.0312136i
$607$	−4.03666	−	6.99170i	−0.163843	−	0.283784i	0.772401	−	0.635135i	$-0.219056\pi$
$607$	−4.03666	−	6.99170i	−0.163843	−	0.283784i	−0.936244	+	0.351351i	$0.885722\pi$
$608$	2.01331	−	3.48715i	0.0816503	−	0.141422i
$609$	0.0751660	+	0.0367178i	0.00304588	+	0.00148788i
$610$		−	14.8094i		−	0.599615i
$611$	−9.31625	−	17.3100i	−0.376895	−	0.700288i
$612$	−7.20425	+	1.00350i	−0.291215	+	0.0405642i
$613$	−9.28658	+	2.48833i	−0.375081	+	0.100503i	−0.441435	−	0.897293i	$-0.645530\pi$
$613$	−9.28658	+	2.48833i	−0.375081	+	0.100503i	0.0663532	+	0.997796i	$0.478864\pi$
$614$	−3.73140	−	2.15433i	−0.150587	−	0.0869416i
$615$	4.26993	+	0.832703i	0.172180	+	0.0335778i
$616$	1.78748	+	1.78748i	0.0720194	+	0.0720194i
$617$	25.7063	+	6.88799i	1.03490	+	0.277300i	0.735998	−	0.676984i	$-0.236713\pi$
$617$	25.7063	+	6.88799i	1.03490	+	0.277300i	0.298901	+	0.954284i	$0.403380\pi$
$618$	18.4042	−	12.3974i	0.740327	−	0.498698i
$619$	−23.2210	+	23.2210i	−0.933331	+	0.933331i	−0.997912	−	0.0645819i	$-0.979429\pi$
$619$	−23.2210	+	23.2210i	−0.933331	+	0.933331i	0.0645819	+	0.997912i	$0.479429\pi$
$620$	11.3906	−	6.57638i	0.457459	−	0.264114i
$621$	−13.9809	−	27.5640i	−0.561034	−	1.10611i
$622$	6.62243	+	24.7152i	0.265535	+	0.990990i
$623$	−15.0590			−0.603324
$624$	−2.90737	+	5.52695i	−0.116388	+	0.221255i
$625$	10.0986			0.403942
$626$	−4.59673	−	17.1552i	−0.183722	−	0.685660i
$627$	5.72961	+	16.6731i	0.228818	+	0.665860i
$628$	−3.92806	+	2.26786i	−0.156747	+	0.0904977i
$629$	3.90471	−	3.90471i	0.155691	−	0.155691i
$630$	−5.07078	−	0.628914i	−0.202025	−	0.0250565i
$631$	−8.27351	−	2.21688i	−0.329363	−	0.0882526i	0.0903481	−	0.995910i	$-0.471202\pi$
$631$	−8.27351	−	2.21688i	−0.329363	−	0.0882526i	−0.419711	+	0.907658i	$0.637869\pi$
$632$	4.89520	+	4.89520i	0.194721	+	0.194721i
$633$	−8.93187	+	45.8009i	−0.355010	+	1.82042i
$634$	−0.150186	−	0.0867099i	−0.00596465	−	0.00344369i
$635$	14.0153	−	3.75540i	0.556182	−	0.149028i
$636$	1.96957	+	1.71424i	0.0780986	+	0.0679740i
$637$	−2.47226	−	2.62449i	−0.0979544	−	0.103986i
$638$		−	0.122091i		−	0.00483365i
$639$	−21.1998	+	8.96819i	−0.838652	+	0.354776i
$640$	0.851606	−	1.47502i	0.0336627	−	0.0583055i
$641$	−4.15434	−	7.19552i	−0.164086	−	0.284206i	0.772244	−	0.635326i	$-0.219134\pi$
$641$	−4.15434	−	7.19552i	−0.164086	−	0.284206i	−0.936330	+	0.351120i	$0.885801\pi$
$642$	−2.02187	−	29.1705i	−0.0797967	−	1.15127i
$643$	3.88101	−	14.4841i	0.153052	−	0.571198i	−0.846212	−	0.532846i	$-0.821122\pi$
$643$	3.88101	−	14.4841i	0.153052	−	0.571198i	0.999264	−	0.0383522i	$-0.0122109\pi$
$644$	−1.53947	+	5.74538i	−0.0606636	+	0.226400i
$645$	1.91541	+	27.6346i	0.0754193	+	1.08811i
$646$	4.88147	+	8.45495i	0.192059	+	0.332655i
$647$	17.4638	−	30.2482i	0.686572	−	1.18918i	−0.286368	−	0.958120i	$-0.592448\pi$
$647$	17.4638	−	30.2482i	0.686572	−	1.18918i	0.972940	−	0.231058i	$-0.0742188\pi$
$648$	7.72583	−	4.61645i	0.303499	−	0.181351i
$649$			1.49945i			0.0588584i
$650$	−7.56493	−	0.225955i	−0.296721	−	0.00886270i
$651$	−10.0892	−	8.78127i	−0.395428	−	0.344165i
$652$	14.2337	−	3.81390i	0.557433	−	0.149364i
$653$	13.3992	+	7.73602i	0.524350	+	0.302734i	0.738713	−	0.674020i	$-0.235434\pi$
$653$	13.3992	+	7.73602i	0.524350	+	0.302734i	−0.214363	+	0.976754i	$0.568767\pi$
$654$	2.31952	−	11.8941i	0.0907006	−	0.465094i
$655$	25.0339	+	25.0339i	0.978154	+	0.978154i
$656$	1.42443	+	0.381675i	0.0556146	+	0.0149019i
$657$	3.11618	−	25.1251i	0.121574	−	0.980222i
$658$	3.85521	−	3.85521i	0.150292	−	0.150292i
$659$	22.0796	−	12.7477i	0.860101	−	0.496579i	−0.00394522	−	0.999992i	$-0.501256\pi$
$659$	22.0796	−	12.7477i	0.860101	−	0.496579i	0.864046	+	0.503413i	$0.167922\pi$
$660$	2.42356	+	7.05255i	0.0943370	+	0.274520i
$661$	−9.89796	−	36.9397i	−0.384986	−	1.43679i	−0.838189	−	0.545380i	$-0.816385\pi$
$661$	−9.89796	−	36.9397i	−0.384986	−	1.43679i	0.453202	−	0.891408i	$-0.350281\pi$
$662$	−7.45081			−0.289584
$663$	−8.08072	−	12.8051i	−0.313829	−	0.497310i
$664$	−12.9936			−0.504250
$665$	1.77503	+	6.62448i	0.0688325	+	0.256886i
$666$	−2.56728	+	6.33192i	−0.0994800	+	0.245357i
$667$	0.248791	−	0.143640i	0.00963324	−	0.00556175i
$668$	−2.03831	+	2.03831i	−0.0788645	+	0.0788645i
$669$	−38.3448	+	25.8298i	−1.48249	+	0.998636i
$670$	10.8407	+	2.90476i	0.418813	+	0.112221i
$671$	15.5421	+	15.5421i	0.599995	+	0.599995i
$672$	−1.70003	−	0.331531i	−0.0655799	−	0.0127891i
$673$	38.1799	+	22.0432i	1.47173	+	0.849703i	0.999495	−	0.0317707i	$-0.0101146\pi$
$673$	38.1799	+	22.0432i	1.47173	+	0.849703i	0.472233	+	0.881474i	$0.343448\pi$
$674$	−19.1117	+	5.12096i	−0.736155	+	0.197252i
$675$	9.13653	+	5.95721i	0.351665	+	0.229293i
$676$	−12.9768	−	0.775897i	−0.499109	−	0.0298422i
$677$			20.6704i			0.794430i	0.917726	+	0.397215i	$0.130023\pi$
$677$			20.6704i			0.794430i	−0.917726	+	0.397215i	$0.869977\pi$
$678$	−3.59938	−	1.75826i	−0.138233	−	0.0675257i
$679$	2.44647	−	4.23741i	0.0938870	−	0.162617i
$680$	2.06481	+	3.57635i	0.0791817	+	0.137147i
$681$	−16.2234	+	1.12448i	−0.621683	+	0.0430900i
$682$	−5.05242	+	18.8559i	−0.193467	+	0.722030i
$683$	−6.37367	+	23.7869i	−0.243882	+	0.910179i	0.730061	+	0.683382i	$0.239492\pi$
$683$	−6.37367	+	23.7869i	−0.243882	+	0.910179i	−0.973942	+	0.226796i	$0.927175\pi$
$684$	−9.63848	−	7.28162i	−0.368536	−	0.278420i
$685$	−0.961613	−	1.66556i	−0.0367413	−	0.0636378i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	3.75815	−	7.69339i	0.143382	−	0.293521i
$688$			9.39000i			0.357990i
$689$	−1.56292	+	5.20589i	−0.0595423	+	0.198328i
$690$	−11.5200	+	13.2359i	−0.438559	+	0.503881i
$691$	−5.76792	+	1.54551i	−0.219422	+	0.0587939i	−0.366855	−	0.930278i	$-0.619566\pi$
$691$	−5.76792	+	1.54551i	−0.219422	+	0.0587939i	0.147433	+	0.989072i	$0.452899\pi$
$692$	1.35974	+	0.785049i	0.0516897	+	0.0298431i
$693$	5.98168	−	4.66162i	0.227225	−	0.177080i
$694$	−23.2977	−	23.2977i	−0.884367	−	0.884367i
$695$	14.2635	+	3.82190i	0.541046	+	0.144973i
$696$	0.0467367	+	0.0693816i	0.00177155	+	0.00262990i
$697$	−2.52827	+	2.52827i	−0.0957649	+	0.0957649i
$698$	23.6169	−	13.6352i	0.893913	−	0.516101i
$699$	−32.4781	+	11.1609i	−1.22843	+	0.422143i
$700$	−0.543279	−	2.02755i	−0.0205340	−	0.0766340i
$701$	12.3400			0.466076			0.233038	−	0.972468i	$-0.425133\pi$
$701$	12.3400			0.466076			0.233038	+	0.972468i	$0.425133\pi$
$702$	15.3812	+	10.6966i	0.580527	+	0.403718i
$703$	9.17071			0.345880
$704$	0.654262	+	2.44174i	0.0246584	+	0.0920264i
$705$	15.2109	−	5.22711i	0.572874	−	0.196864i
$706$	8.75528	−	5.05486i	0.329509	−	0.190242i
$707$	4.53667	−	4.53667i	0.170619	−	0.170619i
$708$	−0.573989	−	0.852098i	−0.0215718	−	0.0320238i
$709$	−0.159505	−	0.0427392i	−0.00599032	−	0.00160510i	0.255823	−	0.966724i	$-0.417654\pi$
$709$	−0.159505	−	0.0427392i	−0.00599032	−	0.00160510i	−0.261813	+	0.965119i	$0.584320\pi$
$710$	9.24088	+	9.24088i	0.346804	+	0.346804i
$711$	16.3815	−	12.7664i	0.614354	−	0.478777i
$712$	−13.0414	−	7.52948i	−0.488749	−	0.282179i
$713$	−44.3677	+	11.8883i	−1.66158	+	0.445220i
$714$	2.75708	−	3.16774i	0.103181	−	0.118550i
$715$	−11.2997	+	10.6443i	−0.422587	+	0.398074i
$716$			26.6181i			0.994767i
$717$	16.0469	−	32.8500i	0.599282	−	1.22680i
$718$	−5.35072	+	9.26772i	−0.199687	+	0.345868i
$719$	12.2405	+	21.2012i	0.456494	+	0.790670i	0.998773	−	0.0495281i	$-0.0157717\pi$
$719$	12.2405	+	21.2012i	0.456494	+	0.790670i	−0.542279	+	0.840198i	$0.682438\pi$
$720$	−4.07697	−	3.08005i	−0.151940	−	0.114787i
$721$	−3.31589	+	12.3751i	−0.123490	+	0.460872i
$722$	0.721175	−	2.69146i	0.0268394	−	0.100166i
$723$	−48.4206	+	3.35612i	−1.80078	+	0.124816i
$724$	−4.07692	−	7.06142i	−0.151517	−	0.262436i
$725$	−0.0506905	+	0.0877986i	−0.00188260	+	0.00326076i
$726$	7.17429	+	3.50457i	0.266263	+	0.130067i
$727$		−	33.7248i		−	1.25078i	−0.780311	−	0.625392i	$-0.784939\pi$
$727$		−	33.7248i		−	1.25078i	0.780311	−	0.625392i	$-0.215061\pi$
$728$	−0.828792	−	3.50900i	−0.0307171	−	0.130052i
$729$	−10.8913	−	24.7059i	−0.403380	−	0.915033i
$730$	−13.8840	+	3.72020i	−0.513868	+	0.137691i
$731$	−19.7168	−	11.3835i	−0.729253	−	0.421034i
$732$	−14.7817	−	2.88266i	−0.546347	−	0.106546i
$733$	9.75491	+	9.75491i	0.360306	+	0.360306i	0.863925	−	0.503620i	$-0.167999\pi$
$733$	9.75491	+	9.75491i	0.360306	+	0.360306i	−0.503620	+	0.863925i	$0.667999\pi$
$734$	25.2965	+	6.77818i	0.933712	+	0.250187i
$735$	2.44671	−	1.64815i	0.0902483	−	0.0607929i
$736$	−4.20591	+	4.20591i	−0.155032	+	0.155032i
$737$	−14.4255	+	8.32856i	−0.531370	+	0.306787i
$738$	1.66229	−	4.09986i	0.0611897	−	0.150918i
$739$	5.42588	+	20.2496i	0.199594	+	0.744895i	0.991030	+	0.133643i	$0.0426674\pi$
$739$	5.42588	+	20.2496i	0.199594	+	0.744895i	−0.791436	+	0.611253i	$0.790666\pi$
$740$	3.87911			0.142599
$741$	5.54794	−	24.5265i	0.203809	−	0.901004i
$742$	−1.50752			−0.0553427
$743$	−12.5950	−	47.0052i	−0.462066	−	1.72445i	−0.666437	−	0.745561i	$-0.732182\pi$
$743$	−12.5950	−	47.0052i	−0.462066	−	1.72445i	0.204371	−	0.978893i	$-0.434485\pi$
$744$	−4.34689	−	12.6494i	−0.159365	−	0.463750i
$745$	19.4571	−	11.2336i	0.712853	−	0.411566i
$746$	−20.4279	+	20.4279i	−0.747920	+	0.747920i
$747$	−4.79791	+	38.6844i	−0.175546	+	1.41539i
$748$	−5.92024	−	1.58632i	−0.216466	−	0.0580018i
$749$	11.9374	+	11.9374i	0.436183	+	0.436183i
$750$	4.00862	−	20.5554i	0.146374	−	0.750576i
$751$	23.8490	+	13.7692i	0.870263	+	0.502446i	0.867436	−	0.497550i	$-0.165767\pi$
$751$	23.8490	+	13.7692i	0.870263	+	0.502446i	0.00282713	+	0.999996i	$0.499100\pi$
$752$	5.26631	−	1.41110i	0.192043	−	0.0514577i
$753$	11.5555	+	10.0575i	0.421106	+	0.366515i
$754$	−0.0915344	+	0.148144i	−0.00333348	+	0.00539509i
$755$		−	0.852234i		−	0.0310160i
$756$	−1.61477	+	4.93888i	−0.0587285	+	0.179625i
$757$	0.593994	−	1.02883i	0.0215891	−	0.0373934i	−0.855029	−	0.518580i	$-0.826461\pi$
$757$	0.593994	−	1.02883i	0.0215891	−	0.0373934i	0.876618	+	0.481187i	$0.159794\pi$
$758$	10.8199	+	18.7406i	0.392996	+	0.680688i
$759$	−1.80077	−	25.9806i	−0.0653638	−	0.943037i
$760$	−1.77503	+	6.62448i	−0.0643869	+	0.240295i
$761$	−1.90620	+	7.11402i	−0.0690996	+	0.257883i	−0.991831	−	0.127561i	$-0.959285\pi$
$761$	−1.90620	+	7.11402i	−0.0690996	+	0.257883i	0.922731	+	0.385444i	$0.125952\pi$
$762$	−1.02028	−	14.7201i	−0.0369609	−	0.533253i
$763$	3.49820	+	6.05906i	0.126643	+	0.219353i
$764$	5.04370	−	8.73595i	0.182475	−	0.316055i
$765$	11.4099	−	4.82675i	0.412526	−	0.174511i
$766$			15.2323i			0.550365i
$767$	1.12416	−	1.81941i	0.0405912	−	0.0656950i
$768$	−1.30650	−	1.13713i	−0.0471443	−	0.0410325i
$769$	−52.8430	+	14.1592i	−1.90557	+	0.510595i	−0.910233	+	0.414096i	$0.864098\pi$
$769$	−52.8430	+	14.1592i	−1.90557	+	0.510595i	−0.995333	+	0.0964985i	$0.969236\pi$
$770$	−3.72867	−	2.15275i	−0.134372	−	0.0775798i
$771$	4.67460	−	23.9704i	0.168352	−	0.863274i
$772$	12.4982	+	12.4982i	0.449821	+	0.449821i
$773$	13.6195	+	3.64932i	0.489858	+	0.131257i	0.495289	−	0.868728i	$-0.335062\pi$
$773$	13.6195	+	3.64932i	0.489858	+	0.131257i	−0.00543129	+	0.999985i	$0.501729\pi$
$774$	27.9558	+	3.46727i	1.00485	+	0.124628i
$775$	11.4620	−	11.4620i	0.411727	−	0.411727i
$776$	4.23741	−	2.44647i	0.152114	−	0.0878232i
$777$	−1.28202	−	3.73066i	−0.0459920	−	0.133837i
$778$	5.35178	+	19.9731i	0.191871	+	0.716071i
$779$	−5.93795			−0.212749
$780$	2.34672	−	10.3744i	0.0840260	−	0.371465i
$781$	−19.3961			−0.694048
$782$	−3.73260	−	13.9303i	−0.133478	−	0.498145i
$783$	0.223820	−	0.113525i	0.00799866	−	0.00405704i
$784$	0.866025	−	0.500000i	0.0309295	−	0.0178571i
$785$	5.46262	−	5.46262i	0.194969	−	0.194969i
$786$	29.8599	−	20.1142i	1.06507	−	0.717449i
$787$	38.4331	+	10.2981i	1.36999	+	0.367088i	0.867476	−	0.497479i	$-0.165741\pi$
$787$	38.4331	+	10.2981i	1.36999	+	0.367088i	0.502517	+	0.864567i	$0.332408\pi$
$788$	16.1506	+	16.1506i	0.575340	+	0.575340i
$789$	4.56601	+	0.890443i	0.162554	+	0.0317006i
$790$	−10.2114	−	5.89555i	−0.363305	−	0.209754i
$791$	2.23399	−	0.598595i	0.0794314	−	0.0212836i
$792$	7.51110	−	1.04624i	0.266895	−	0.0371767i
$793$	−7.20633	−	30.5107i	−0.255904	−	1.08347i
$794$		−	2.65997i		−	0.0943989i
$795$	−3.99597	−	1.95199i	−0.141722	−	0.0692301i
$796$	8.30966	−	14.3928i	0.294528	−	0.510138i
$797$	−13.2503	−	22.9502i	−0.469350	−	0.812938i	0.530036	−	0.847975i	$-0.322178\pi$
$797$	−13.2503	−	22.9502i	−0.469350	−	0.812938i	−0.999386	+	0.0350373i	$0.988845\pi$
$798$	6.95760	−	0.482245i	0.246296	−	0.0170713i
$799$	−3.42137	+	12.7687i	−0.121039	+	0.451725i
$800$	0.543279	−	2.02755i	0.0192078	−	0.0716846i
$801$	−27.2322	+	36.0466i	−0.962204	+	1.27364i
$802$	2.08277	+	3.60747i	0.0735453	+	0.127384i
$803$	10.6666	−	18.4751i	0.376416	−	0.651972i
$804$	5.00947	−	10.2550i	0.176670	−	0.361666i
$805$		−	10.1308i		−	0.357063i
$806$	20.2672	−	19.0916i	0.713881	−	0.672472i
$807$	27.7418	−	31.8738i	0.976556	−	1.12201i
$808$	6.19721	−	1.66054i	0.218017	−	0.0584175i
$809$	3.70234	+	2.13755i	0.130167	+	0.0751521i	0.563670	−	0.826000i	$-0.309389\pi$
$809$	3.70234	+	2.13755i	0.130167	+	0.0751521i	−0.433502	+	0.901152i	$0.642722\pi$
$810$	−10.6753	+	11.0006i	−0.375092	+	0.386522i
$811$	16.0439	+	16.0439i	0.563379	+	0.563379i	0.930266	−	0.366887i	$-0.119576\pi$
$811$	16.0439	+	16.0439i	0.563379	+	0.563379i	−0.366887	+	0.930266i	$0.619576\pi$
$812$	−0.0466524	−	0.0125005i	−0.00163718	−	0.000438680i
$813$	−19.1540	−	28.4345i	−0.671760	−	0.997240i
$814$	−4.07102	+	4.07102i	−0.142689	+	0.142689i
$815$	−21.7356	+	12.5491i	−0.761365	+	0.439574i
$816$	3.97158	−	1.36481i	0.139033	−	0.0477777i
$817$	−9.78591	−	36.5215i	−0.342366	−	1.27773i
$818$	20.9762			0.733416
$819$	−10.7530	+	1.17176i	−0.375740	+	0.0409448i
$820$	−2.51169			−0.0877119
$821$	0.943552	+	3.52138i	0.0329302	+	0.122897i	0.980434	−	0.196846i	$-0.0630700\pi$
$821$	0.943552	+	3.52138i	0.0329302	+	0.122897i	−0.947504	+	0.319743i	$0.896403\pi$
$822$	−1.84962	+	0.635611i	−0.0645131	+	0.0221695i
$823$	24.9791	−	14.4217i	0.870718	−	0.502709i	0.00313111	−	0.999995i	$-0.499003\pi$
$823$	24.9791	−	14.4217i	0.870718	−	0.502709i	0.867587	+	0.497286i	$0.165670\pi$
$824$	−9.05919	+	9.05919i	−0.315592	+	0.315592i
$825$	5.13464	+	7.62247i	0.178765	+	0.265380i
$826$	0.572954	+	0.153522i	0.0199356	+	0.00534173i
$827$	29.6971	+	29.6971i	1.03267	+	1.03267i	0.999448	+	0.0332208i	$0.0105765\pi$
$827$	29.6971	+	29.6971i	1.03267	+	1.03267i	0.0332208	+	0.999448i	$0.489424\pi$
$828$	10.9687	+	14.0748i	0.381190	+	0.489134i
$829$	−14.5577	−	8.40491i	−0.505611	−	0.291915i	0.225417	−	0.974262i	$-0.427626\pi$
$829$	−14.5577	−	8.40491i	−0.505611	−	0.291915i	−0.731028	+	0.682348i	$0.760959\pi$
$830$	21.3768	−	5.72789i	0.741999	−	0.198818i
$831$	25.6231	−	29.4396i	0.888855	−	1.02125i
$832$	1.03675	−	3.45328i	0.0359427	−	0.119721i
$833$			2.42460i			0.0840075i
$834$	6.59115	−	13.4929i	0.228233	−	0.467221i
$835$	2.45484	−	4.25191i	0.0849533	−	0.147143i
$836$	−5.08938	−	8.81506i	−0.176020	−	0.304875i
$837$	−39.2648	+	8.27069i	−1.35719	+	0.285877i
$838$	−3.77326	+	14.0820i	−0.130345	+	0.486455i
$839$	9.55565	−	35.6622i	0.329898	−	1.23119i	−0.579398	−	0.815044i	$-0.696712\pi$
$839$	9.55565	−	35.6622i	0.329898	−	1.23119i	0.909296	−	0.416150i	$-0.136621\pi$
$840$	2.94299	−	0.203984i	0.101543	−	0.00703813i
$841$	−14.4988	−	25.1127i	−0.499960	−	0.865956i
$842$	9.71226	−	16.8221i	0.334706	−	0.579729i
$843$	0.577950	+	0.282323i	0.0199057	+	0.00972373i
$844$		−	26.9413i		−	0.927357i
$845$	21.6912	−	4.44400i	0.746200	−	0.152878i
$846$	−2.25653	−	16.1999i	−0.0775811	−	0.556963i
$847$	−4.45278	+	1.19312i	−0.152999	+	0.0409961i
$848$	−1.30555	−	0.753759i	−0.0448327	−	0.0258842i
$849$	−49.1952	−	9.59382i	−1.68837	−	0.329259i
$850$	3.59876	+	3.59876i	0.123436	+	0.123436i
$851$	−13.0852	−	3.50618i	−0.448556	−	0.120190i
$852$	11.0223	−	7.42485i	0.377619	−	0.254371i
$853$	32.0653	−	32.0653i	1.09790	−	1.09790i	0.103238	−	0.994657i	$-0.467080\pi$
$853$	32.0653	−	32.0653i	1.09790	−	1.09790i	0.994657	−	0.103238i	$-0.0329205\pi$
$854$	7.53008	−	4.34749i	0.257674	−	0.148768i
$855$	19.0669	+	7.73069i	0.652075	+	0.264384i
$856$	4.36939	+	16.3068i	0.149343	+	0.557354i
$857$	−16.9899			−0.580363			−0.290181	−	0.956972i	$-0.593716\pi$
$857$	−16.9899			−0.580363			−0.290181	+	0.956972i	$0.593716\pi$
$858$	8.42489	+	13.3505i	0.287621	+	0.455780i
$859$	−42.5204			−1.45078			−0.725388	−	0.688340i	$-0.758340\pi$
$859$	−42.5204			−1.45078			−0.725388	+	0.688340i	$0.758340\pi$
$860$	−4.13933	−	15.4482i	−0.141150	−	0.526779i
$861$	0.830094	+	2.41557i	0.0282895	+	0.0823223i
$862$	−12.1393	+	7.00863i	−0.413466	+	0.238715i
$863$	29.8341	−	29.8341i	1.01556	−	1.01556i	0.0156867	−	0.999877i	$-0.495007\pi$
$863$	29.8341	−	29.8341i	1.01556	−	1.01556i	0.999877	−	0.0156867i	$-0.00499343\pi$
$864$	−3.86787	+	3.46981i	−0.131588	+	0.118045i
$865$	−2.58309	−	0.692136i	−0.0878276	−	0.0235333i
$866$	−11.0730	−	11.0730i	−0.376277	−	0.376277i
$867$	3.68706	−	18.9065i	0.125219	−	0.642098i
$868$	6.68773	+	3.86117i	0.226997	+	0.131056i
$869$	16.9038	−	4.52936i	0.573423	−	0.153648i
$870$	−0.107475	−	0.0935422i	−0.00364375	−	0.00317138i
$871$	23.7478	+	0.709318i	0.804663	+	0.0240343i
$872$			6.99640i			0.236928i
$873$	−5.71894	−	13.5189i	−0.193557	−	0.457547i
$874$	11.9752	−	20.7417i	0.405069	−	0.701599i
$875$	6.04561	+	10.4713i	0.204379	+	0.353995i
$876$	1.01072	+	14.5821i	0.0341489	+	0.492684i
$877$	1.17343	−	4.37929i	0.0396238	−	0.147878i	−0.943280	−	0.331999i	$-0.892277\pi$
$877$	1.17343	−	4.37929i	0.0396238	−	0.147878i	0.982904	+	0.184121i	$0.0589437\pi$
$878$	−8.51601	+	31.7822i	−0.287401	+	1.07260i
$879$	−3.53948	−	51.0660i	−0.119384	−	1.72241i
$880$	−2.15275	−	3.72867i	−0.0725692	−	0.125694i
$881$	−6.80234	+	11.7820i	−0.229177	+	0.396946i	−0.957564	−	0.288219i	$-0.906937\pi$
$881$	−6.80234	+	11.7820i	−0.229177	+	0.396946i	0.728388	+	0.685165i	$0.240270\pi$
$882$	−1.16881	−	2.76295i	−0.0393560	−	0.0930333i
$883$		−	49.1232i		−	1.65313i	−0.562843	−	0.826564i	$-0.690292\pi$
$883$		−	49.1232i		−	1.65313i	0.562843	−	0.826564i	$-0.309708\pi$
$884$	5.99424	+	6.36335i	0.201608	+	0.214023i
$885$	1.31994	+	1.14882i	0.0443692	+	0.0386173i
$886$	16.2748	−	4.36083i	0.546764	−	0.146505i
$887$	6.59110	+	3.80538i	0.221308	+	0.127772i	0.606556	−	0.795041i	$-0.292551\pi$
$887$	6.59110	+	3.80538i	0.221308	+	0.127772i	−0.385248	+	0.922813i	$0.625884\pi$
$888$	0.755070	−	3.87185i	0.0253385	−	0.129931i
$889$	6.02388	+	6.02388i	0.202034	+	0.202034i
$890$	24.7746	+	6.63834i	0.830448	+	0.222518i
$891$	−0.341383	−	22.7483i	−0.0114367	−	0.762096i
$892$	18.8746	−	18.8746i	0.631968	−	0.631968i
$893$	−19.0122	+	10.9767i	−0.636220	+	0.367322i
$894$	−7.42521	−	21.6073i	−0.248336	−	0.722657i
$895$	−11.7339	−	43.7915i	−0.392221	−	1.46379i
$896$	1.00000			0.0334077
$897$	−17.2932	+	32.8746i	−0.577402	+	1.09765i
$898$	−19.4531			−0.649157
$899$	−0.0965328	−	0.360265i	−0.00321955	−	0.0120155i
$900$	−5.83578	−	2.36612i	−0.194526	−	0.0788706i
$901$	3.16544	−	1.82757i	0.105456	−	0.0608851i
$902$	2.63595	−	2.63595i	0.0877675	−	0.0877675i
$903$	−13.4890	+	9.08643i	−0.448885	+	0.302378i
$904$	2.23399	+	0.598595i	0.0743013	+	0.0199090i
$905$	9.82009	+	9.82009i	0.326431	+	0.326431i
$906$	−0.850640	−	0.165888i	−0.0282606	−	0.00551125i
$907$	−15.7227	−	9.07753i	−0.522065	−	0.301415i	0.215714	−	0.976457i	$-0.430792\pi$
$907$	−15.7227	−	9.07753i	−0.522065	−	0.301415i	−0.737779	+	0.675042i	$0.764125\pi$
$908$	9.06914	−	2.43007i	0.300970	−	0.0806447i
$909$	−2.65540	−	19.0634i	−0.0880742	−	0.632294i
$910$	2.91036	+	5.40758i	0.0964775	+	0.179259i
$911$			21.8135i			0.722715i	0.932427	+	0.361357i	$0.117687\pi$
$911$			21.8135i			0.722715i	−0.932427	+	0.361357i	$0.882313\pi$
$912$	6.26658	+	3.06116i	0.207507	+	0.101365i
$913$	−16.4231	+	28.4456i	−0.543525	+	0.941413i
$914$	−16.7063	−	28.9362i	−0.552596	−	0.957125i
$915$	25.5892	−	1.77364i	0.845954	−	0.0586347i
$916$	−1.27945	+	4.77497i	−0.0422742	+	0.157769i
$917$	−5.37985	+	20.0779i	−0.177658	+	0.663030i
$918$	−2.59677	−	12.3281i	−0.0857063	−	0.406887i
$919$	27.5429	+	47.7056i	0.908555	+	1.57366i	0.816073	+	0.577949i	$0.196147\pi$
$919$	27.5429	+	47.7056i	0.908555	+	1.57366i	0.0924821	+	0.995714i	$0.470520\pi$
$920$	5.06539	−	8.77352i	0.167001	−	0.289254i
$921$	3.27558	−	6.70552i	0.107934	−	0.220955i
$922$		−	13.1142i		−	0.431892i
$923$	23.5350	+	14.5417i	0.774664	+	0.478645i
$924$	−2.87451	+	3.30266i	−0.0945645	+	0.108650i
$925$	4.61779	−	1.23733i	0.151832	−	0.0406832i
$926$	−17.9389	−	10.3570i	−0.589510	−	0.340354i
$927$	23.6258	+	30.3160i	0.775973	+	0.995709i
$928$	−0.0341519	−	0.0341519i	−0.00112109	−	0.00112109i
$929$	40.2847	+	10.7943i	1.32170	+	0.354148i	0.849614	−	0.527405i	$-0.176835\pi$
$929$	40.2847	+	10.7943i	1.32170	+	0.354148i	0.472085	+	0.881553i	$0.343502\pi$
$930$	12.7276	+	18.8943i	0.417353	+	0.619569i
$931$	−2.84724	+	2.84724i	−0.0933146	+	0.0933146i
$932$	17.1711	−	9.91376i	0.562459	−	0.324736i
$933$	−41.9124	+	14.4029i	−1.37215	+	0.471531i
$934$	−3.95859	−	14.7736i	−0.129529	−	0.483408i
$935$	10.4391			0.341396
$936$	−9.89825	−	4.36172i	−0.323534	−	0.142567i
$937$	−9.82405			−0.320938			−0.160469	−	0.987041i	$-0.551301\pi$
$937$	−9.82405			−0.320938			−0.160469	+	0.987041i	$0.551301\pi$
$938$	1.70546	+	6.36486i	0.0556852	+	0.207820i
$939$	29.0921	−	9.99730i	0.949384	−	0.326249i
$940$	−8.04197	+	4.64303i	−0.262300	+	0.151439i
$941$	−37.1136	+	37.1136i	−1.20987	+	1.20987i	−0.238798	+	0.971069i	$0.576753\pi$
$941$	−37.1136	+	37.1136i	−1.20987	+	1.20987i	−0.971069	+	0.238798i	$0.923247\pi$
$942$	−4.38910	−	6.51570i	−0.143005	−	0.212293i
$943$	8.47258	+	2.27022i	0.275905	+	0.0739285i
$944$	0.419431	+	0.419431i	0.0136513	+	0.0136513i
$945$	0.479403	−	8.83715i	0.0155950	−	0.287473i
$946$	20.5566	+	11.8684i	0.668352	+	0.385873i
$947$	−40.7151	+	10.9096i	−1.32306	+	0.354514i	−0.850125	−	0.526581i	$-0.823474\pi$
$947$	−40.7151	+	10.9096i	−1.32306	+	0.354514i	−0.472939	+	0.881095i	$0.656807\pi$
$948$	−7.87218	+	9.04472i	−0.255676	+	0.293759i
$949$	−26.7938	+	14.4205i	−0.869765	+	0.468108i
$950$			8.45214i			0.274224i
$951$	0.131840	−	0.269892i	0.00427519	−	0.00875185i
$952$	−1.21230	+	2.09977i	−0.0392909	+	0.0680539i
$953$	−25.6740	−	44.4687i	−0.831663	−	1.44048i	−0.896718	−	0.442602i	$-0.854056\pi$
$953$	−25.6740	−	44.4687i	−0.831663	−	1.44048i	0.0650548	−	0.997882i	$-0.479278\pi$
$954$	−2.72616	+	3.60854i	−0.0882627	+	0.116831i
$955$	−4.44677	+	16.5956i	−0.143894	+	0.537020i
$956$	−5.46311	+	20.3886i	−0.176690	+	0.659415i
$957$	0.210962	−	0.0146222i	0.00681945	−	0.000472669i
$958$	8.61325	+	14.9186i	0.278282	+	0.481998i
$959$	0.564588	−	0.977895i	0.0182315	−	0.0315779i
$960$	2.65069	+	1.29484i	0.0855508	+	0.0417907i
$961$			28.6344i			0.923690i
$962$	7.99184	−	1.88759i	0.257667	−	0.0608585i
$963$	50.1618	−	6.98719i	1.61644	−	0.225159i
$964$	27.0678	−	7.25281i	0.871797	−	0.233597i
$965$	−26.0713	−	15.0523i	−0.839265	−	0.484550i
$966$	−10.1118	−	1.97196i	−0.325343	−	0.0634469i
$967$	−36.3377	−	36.3377i	−1.16854	−	1.16854i	−0.982551	−	0.185992i	$-0.940450\pi$
$967$	−36.3377	−	36.3377i	−1.16854	−	1.16854i	−0.185992	−	0.982551i	$-0.559550\pi$
$968$	−4.45278	−	1.19312i	−0.143118	−	0.0383483i
$969$	−14.0247	+	9.44731i	−0.450539	+	0.303491i
$970$	−5.89283	+	5.89283i	−0.189207	+	0.189207i
$971$	−15.0550	+	8.69202i	−0.483139	+	0.278940i	−0.721724	−	0.692181i	$-0.756650\pi$
$971$	−15.0550	+	8.69202i	−0.483139	+	0.278940i	0.238585	+	0.971122i	$0.423316\pi$
$972$	8.90206	+	12.7966i	0.285534	+	0.410451i
$973$	2.24394	+	8.37448i	0.0719373	+	0.268474i
$974$	2.55286			0.0817988
$975$	−0.515581	−	13.0985i	−0.0165118	−	0.419489i
$976$	8.69498			0.278320
$977$	15.7128	+	58.6409i	0.502696	+	1.87609i	0.481753	+	0.876307i	$0.340000\pi$
$977$	15.7128	+	58.6409i	0.502696	+	1.87609i	0.0209430	+	0.999781i	$0.493333\pi$
$978$	8.29474	+	24.1376i	0.265236	+	0.771836i
$979$	−32.9671	+	19.0336i	−1.05363	+	0.608315i
$980$	−1.20435	+	1.20435i	−0.0384716	+	0.0384716i
$981$	20.8296	+	2.58343i	0.665038	+	0.0824826i
$982$	−21.5318	−	5.76942i	−0.687106	−	0.184110i
$983$	3.26400	+	3.26400i	0.104105	+	0.104105i	0.757241	−	0.653136i	$-0.226547\pi$
$983$	3.26400	+	3.26400i	0.104105	+	0.104105i	−0.653136	+	0.757241i	$0.726547\pi$
$984$	−0.488901	+	2.50699i	−0.0155856	+	0.0799199i
$985$	−33.6901	−	19.4510i	−1.07346	−	0.619760i
$986$	0.113114	−	0.0303087i	0.00360227	−	0.000965225i
$987$	7.12315	+	6.19972i	0.226733	+	0.197339i
$988$	−0.433447	+	14.5117i	−0.0137898	+	0.461678i
$989$			55.8522i			1.77600i
$990$	−11.8959	+	5.03233i	−0.378076	+	0.159938i
$991$	6.57379	−	11.3861i	0.208823	−	0.361693i	−0.742521	−	0.669823i	$-0.766370\pi$
$991$	6.57379	−	11.3861i	0.208823	−	0.361693i	0.951344	+	0.308130i	$0.0997033\pi$
$992$	3.86117	+	6.68773i	0.122592	+	0.212336i
$993$	−0.892343	−	12.8743i	−0.0283176	−	0.408553i
$994$	−1.98589	+	7.41146i	−0.0629887	+	0.235077i
$995$	−7.32619	+	27.3417i	−0.232256	+	0.866790i
$996$	−1.55617	−	22.4517i	−0.0493093	−	0.711410i
$997$	0.581853	+	1.00780i	0.0184275	+	0.0319173i	0.875092	−	0.483956i	$-0.160801\pi$
$997$	0.581853	+	1.00780i	0.0184275	+	0.0319173i	−0.856665	+	0.515874i	$0.827467\pi$
$998$	10.3489	−	17.9248i	0.327588	−	0.567400i
$999$	−11.2484	−	3.67767i	−0.355884	−	0.116356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.449.6	yes	56
3.2	odd	2		546.2.bu.b.449.10	yes	56
13.2	odd	12		546.2.bu.b.197.10	yes	56
39.2	even	12	inner	546.2.bu.a.197.6	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.197.6	✓	56	39.2	even	12	inner
546.2.bu.a.449.6	yes	56	1.1	even	1	trivial
546.2.bu.b.197.10	yes	56	13.2	odd	12
546.2.bu.b.449.10	yes	56	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.63803 - 0.562898i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.20435 - 1.20435i) q^{5} +(-0.967672 - 1.43653i) q^{6} +(0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.36629 - 1.84409i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.63803 - 0.562898i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.20435 - 1.20435i) q^{5} +(-0.967672 - 1.43653i) q^{6} +(0.965926 + 0.258819i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.36629 - 1.84409i) q^{9} +(-1.47502 - 0.851606i) q^{10} +(2.44174 - 0.654262i) q^{11} +(-1.13713 + 1.30650i) q^{12} +(-3.45328 - 1.03675i) q^{13} -1.00000i q^{14} +(1.29484 - 2.65069i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.21230 + 2.09977i) q^{17} +(-2.39370 - 1.80838i) q^{18} +(-1.04216 + 3.88941i) q^{19} +(-0.440824 + 1.64518i) q^{20} +(1.72791 - 0.119765i) q^{21} +(-1.26394 - 2.18920i) q^{22} +(2.97403 - 5.15116i) q^{23} +(1.55629 + 0.760233i) q^{24} +2.09907i q^{25} +(-0.107646 + 3.60394i) q^{26} +(2.83802 - 4.35266i) q^{27} +(-0.965926 + 0.258819i) q^{28} +(0.0418274 + 0.0241491i) q^{29} +(-2.89550 - 0.564668i) q^{30} +(-5.46051 - 5.46051i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.63136 - 2.44615i) q^{33} +(1.71445 - 1.71445i) q^{34} +(1.47502 - 0.851606i) q^{35} +(-1.12722 + 2.78017i) q^{36} +(-0.589467 - 2.19992i) q^{37} +4.02661 q^{38} +(-6.24017 + 0.245623i) q^{39} +1.70321 q^{40} +(0.381675 + 1.42443i) q^{41} +(-0.562898 - 1.63803i) q^{42} +(-8.13197 + 4.69500i) q^{43} +(-1.78748 + 1.78748i) q^{44} +(0.628914 - 5.07078i) q^{45} +(-5.74538 - 1.53947i) q^{46} +(3.85521 + 3.85521i) q^{47} +(0.331531 - 1.70003i) q^{48} +(0.866025 + 0.500000i) q^{49} +(2.02755 - 0.543279i) q^{50} +(3.16774 + 2.75708i) q^{51} +(3.50900 - 0.828792i) q^{52} -1.50752i q^{53} +(-4.93888 - 1.61477i) q^{54} +(2.15275 - 3.72867i) q^{55} +(0.500000 + 0.866025i) q^{56} +(0.482245 + 6.95760i) q^{57} +(0.0125005 - 0.0466524i) q^{58} +(-0.153522 + 0.572954i) q^{59} +(0.203984 + 2.94299i) q^{60} +(4.34749 + 7.53008i) q^{61} +(-3.86117 + 6.68773i) q^{62} +(2.76295 - 1.16881i) q^{63} +1.00000i q^{64} +(-5.40758 + 2.91036i) q^{65} +(-3.30266 - 2.87451i) q^{66} +(-6.36486 + 1.70546i) q^{67} +(-2.09977 - 1.21230i) q^{68} +(1.97196 - 10.1118i) q^{69} +(-1.20435 - 1.20435i) q^{70} +(-7.41146 - 1.98589i) q^{71} +(2.97719 + 0.369252i) q^{72} +(5.96741 - 5.96741i) q^{73} +(-1.97239 + 1.13876i) q^{74} +(1.18156 + 3.43834i) q^{75} +(-1.04216 - 3.88941i) q^{76} +2.52787 q^{77} +(1.85233 + 5.96397i) q^{78} +6.92286 q^{79} +(-0.440824 - 1.64518i) q^{80} +(2.19866 - 8.72731i) q^{81} +(1.27711 - 0.737339i) q^{82} +(-9.18787 + 9.18787i) q^{83} +(-1.43653 + 0.967672i) q^{84} +(3.98890 + 1.06882i) q^{85} +(6.63973 + 6.63973i) q^{86} +(0.0821080 + 0.0160123i) q^{87} +(2.18920 + 1.26394i) q^{88} +(-14.5458 + 3.89754i) q^{89} +(-5.06078 + 0.704931i) q^{90} +(-3.06728 - 1.89520i) q^{91} +5.94805i q^{92} +(-12.0182 - 5.87077i) q^{93} +(2.72604 - 4.72165i) q^{94} +(3.42909 + 5.93935i) q^{95} +(-1.72791 + 0.119765i) q^{96} +(1.26639 - 4.72622i) q^{97} +(0.258819 - 0.965926i) q^{98} +(4.57134 - 6.05096i) 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	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 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^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 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 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Introduction

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