LMFDB - Embedded newform 546.2.bu.a.197.6

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			197.6
Character	$\chi$	$=$	546.197
Dual form			546.2.bu.a.449.6

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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
$3$	1.63803	+	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	0.923118	−	0.384516i	$-0.125632\pi$
$5$	1.20435	+	1.20435i	0.538603	+	0.538603i	−0.384516	+	0.923118i	$0.625632\pi$
$6$	−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	0.607394	−	0.794401i	$-0.292215\pi$
$11$	2.44174	+	0.654262i	0.736211	+	0.197267i	0.128818	+	0.991668i	$0.458882\pi$
$12$	−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	−0.680732	−	0.732533i	$-0.738338\pi$
$17$	1.21230	−	2.09977i	0.294026	−	0.509269i	0.974758	+	0.223264i	$0.0716713\pi$
$18$	−2.39370	+	1.80838i	−0.564199	+	0.426238i
$19$	−1.04216	−	3.88941i	−0.239089	−	0.892291i	−0.976263	−	0.216589i	$-0.930507\pi$
$19$	−1.04216	−	3.88941i	−0.239089	−	0.892291i	0.737174	−	0.675703i	$-0.236160\pi$
$20$	−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	0.989462	+	0.144795i	$0.0462523\pi$
$23$	2.97403	+	5.15116i	0.620127	+	1.07409i	−0.369334	+	0.929297i	$0.620414\pi$
$24$	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	−0.496111	−	0.868259i	$-0.665239\pi$
$29$	0.0418274	−	0.0241491i	0.00776715	−	0.00448437i	0.503879	+	0.863775i	$0.331906\pi$
$30$	−2.89550	+	0.564668i	−0.528644	+	0.103094i
$31$	−5.46051	+	5.46051i	−0.980737	+	0.980737i	−0.999818	−	0.0190810i	$-0.993926\pi$
$31$	−5.46051	+	5.46051i	−0.980737	+	0.980737i	0.0190810	+	0.999818i	$0.493926\pi$
$32$	−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	−0.997302	−	0.0734107i	$-0.976612\pi$
$37$	−0.589467	+	2.19992i	−0.0969077	+	0.361665i	0.900394	+	0.435075i	$0.143278\pi$
$38$	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	−0.929696	−	0.368327i	$-0.879931\pi$
$41$	0.381675	−	1.42443i	0.0596076	−	0.222458i	0.989304	+	0.145868i	$0.0465975\pi$
$42$	−0.562898	+	1.63803i	−0.0868571	+	0.252754i
$43$	−8.13197	−	4.69500i	−1.24011	−	0.715980i	−0.270997	−	0.962580i	$-0.587353\pi$
$43$	−8.13197	−	4.69500i	−1.24011	−	0.715980i	−0.969117	+	0.246600i	$0.920687\pi$
$44$	−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	−0.367631	−	0.929972i	$-0.619831\pi$
$47$	3.85521	−	3.85521i	0.562340	−	0.562340i	0.929972	+	0.367631i	$0.119831\pi$
$48$	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	$0.0330160\pi$
$53$			1.50752i			0.207074i	−0.994626	+	0.103537i	$0.966984\pi$
$54$	−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	0.955212	−	0.295922i	$-0.0956269\pi$
$59$	−0.153522	−	0.572954i	−0.0199869	−	0.0745922i	−0.975199	+	0.221330i	$0.928960\pi$
$60$	0.203984	−	2.94299i	0.0263343	−	0.379938i
$61$	4.34749	−	7.53008i	0.556639	−	0.964127i	−0.441135	−	0.897441i	$-0.645424\pi$
$61$	4.34749	−	7.53008i	0.556639	−	0.964127i	0.997774	−	0.0666865i	$-0.0212427\pi$
$62$	−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	−0.151869	−	0.988401i	$-0.548529\pi$
$67$	−6.36486	−	1.70546i	−0.777591	−	0.208355i	−0.625722	+	0.780046i	$0.715196\pi$
$68$	−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	−0.670225	−	0.742158i	$-0.733802\pi$
$71$	−7.41146	+	1.98589i	−0.879578	+	0.235682i	−0.209353	+	0.977840i	$0.567136\pi$
$72$	2.97719	−	0.369252i	0.350865	−	0.0435167i
$73$	5.96741	+	5.96741i	0.698432	+	0.698432i	0.964072	−	0.265640i	$-0.0855832\pi$
$73$	5.96741	+	5.96741i	0.698432	+	0.698432i	−0.265640	+	0.964072i	$0.585583\pi$
$74$	−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	−0.999964	−	0.00853620i	$-0.997283\pi$
$83$	−9.18787	−	9.18787i	−1.00850	−	1.00850i	−0.00853620	−	0.999964i	$-0.502717\pi$
$84$	−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	−0.614991	−	0.788534i	$-0.710840\pi$
$89$	−14.5458	−	3.89754i	−1.54186	−	0.413139i	−0.926865	+	0.375396i	$0.877507\pi$
$90$	−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	0.999942	−	0.0107693i	$-0.00342805\pi$
$97$	1.26639	+	4.72622i	0.128582	+	0.479875i	−0.871360	+	0.490644i	$0.836761\pi$
$98$	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	0.980321	−	0.197409i	$-0.0632528\pi$
$101$	3.20791	+	5.55626i	0.319199	+	0.552869i	−0.661122	+	0.750278i	$0.729919\pi$
$102$	1.84326	+	3.77339i	0.182510	+	0.373621i
$103$		−	12.8116i		−	1.26237i	−0.775634	−	0.631183i	$-0.782570\pi$
$103$		−	12.8116i		−	1.26237i	0.775634	−	0.631183i	$-0.217430\pi$
$104$	−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	0.417688	−	0.908591i	$-0.362841\pi$
$107$	14.6203	−	8.44101i	1.41339	−	0.816023i	0.995706	+	0.0925673i	$0.0295073\pi$
$108$	−0.281470	−	5.18852i	−0.0270845	−	0.499266i
$109$	4.94720	−	4.94720i	0.473856	−	0.473856i	−0.429304	−	0.903160i	$-0.641241\pi$
$109$	4.94720	−	4.94720i	0.473856	−	0.473856i	0.903160	+	0.429304i	$0.141241\pi$
$110$	−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	0.591243	−	0.806494i	$-0.298637\pi$
$113$	2.00294	+	1.15640i	0.188421	+	0.108785i	−0.402822	+	0.915278i	$0.631971\pi$
$114$	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	−0.135575	−	0.990767i	$-0.543288\pi$
$127$	7.37771	−	4.25953i	0.654666	−	0.377972i	0.790242	+	0.612795i	$0.209955\pi$
$128$	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	$-0.637573\pi$
$131$		−	20.7862i		−	1.81609i	0.418868	−	0.908047i	$-0.362427\pi$
$132$	−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	0.977286	−	0.211925i	$-0.0679734\pi$
$137$	0.292252	+	1.09070i	0.0249688	+	0.0931848i	−0.952317	+	0.305110i	$0.901307\pi$
$138$	−10.2777	−	0.712366i	−0.874893	−	0.0606406i
$139$	4.33495	−	7.50836i	0.367686	−	0.636851i	−0.621517	−	0.783400i	$-0.713484\pi$
$139$	4.33495	−	7.50836i	0.367686	−	0.636851i	0.989203	+	0.146550i	$0.0468169\pi$
$140$	−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	0.304130	−	0.952631i	$-0.401634\pi$
$149$	12.7416	−	3.41409i	1.04383	−	0.279693i	0.739700	+	0.672937i	$0.234968\pi$
$150$	3.01537	+	2.03121i	0.246204	+	0.165848i
$151$	0.353814	+	0.353814i	0.0287930	+	0.0287930i	0.721357	−	0.692564i	$-0.243519\pi$
$151$	0.353814	+	0.353814i	0.0287930	+	0.0287930i	−0.692564	+	0.721357i	$0.743519\pi$
$152$	−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	−0.768804	−	0.639484i	$-0.779148\pi$
$163$	−14.2337	+	3.81390i	−1.11487	+	0.298727i	−0.346062	+	0.938212i	$0.612481\pi$
$164$	−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	0.364935	−	0.931033i	$-0.381091\pi$
$167$	2.78438	+	0.746072i	0.215462	+	0.0577328i	−0.149473	+	0.988766i	$0.547758\pi$
$168$	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	−0.894325	−	0.447419i	$-0.852343\pi$
$173$	−0.785049	+	1.35974i	−0.0596862	+	0.103379i	0.834638	+	0.550798i	$0.185677\pi$
$174$	−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	0.585867	+	0.810408i	$0.300754\pi$
$179$	13.3091	+	23.0520i	0.994767	+	1.72299i	0.408900	+	0.912579i	$0.365912\pi$
$180$	1.99074	−	4.70588i	0.148381	−	0.350756i
$181$		−	8.15383i		−	0.606069i	−0.952980	−	0.303035i	$-0.902000\pi$
$181$		−	8.15383i		−	0.606069i	0.952980	−	0.303035i	$-0.0979998\pi$
$182$	−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	0.149458	−	0.988768i	$-0.452247\pi$
$191$	−8.73595	−	5.04370i	−0.632111	−	0.364949i	−0.781569	+	0.623819i	$0.785580\pi$
$192$	0.562898	−	1.63803i	0.0406237	−	0.118215i
$193$	−4.57467	+	17.0729i	−0.329292	+	1.22893i	0.580635	+	0.814164i	$0.302804\pi$
$193$	−4.57467	+	17.0729i	−0.329292	+	1.22893i	−0.909927	+	0.414769i	$0.863862\pi$
$194$	−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	0.350951	+	0.936394i	$0.385858\pi$
$197$	−5.91152	+	22.0621i	−0.421178	+	1.57186i	−0.772130	+	0.635465i	$0.780808\pi$
$198$	−7.02793	+	2.84948i	−0.499453	+	0.202503i
$199$	−14.3928	−	8.30966i	−1.02028	−	0.589056i	−0.106091	−	0.994356i	$-0.533834\pi$
$199$	−14.3928	−	8.30966i	−1.02028	−	0.589056i	−0.914184	+	0.405300i	$0.867167\pi$
$200$	−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	−0.787726	−	0.616026i	$-0.788742\pi$
$211$	−13.4706	−	23.3318i	−0.927357	−	1.60623i	−0.139631	−	0.990204i	$-0.544592\pi$
$212$	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	−0.747180	−	0.664622i	$-0.768593\pi$
$223$	−25.7832	−	6.90858i	−1.72657	−	0.462632i	−0.979388	+	0.201989i	$0.935259\pi$
$224$	−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	−0.546904	−	0.837195i	$-0.684194\pi$
$227$	−9.06914	+	2.43007i	−0.601940	+	0.161289i	−0.0550355	+	0.998484i	$0.517527\pi$
$228$	−3.89644	+	5.78434i	−0.258048	+	0.383077i
$229$	3.49552	+	3.49552i	0.230990	+	0.230990i	0.813106	−	0.582116i	$-0.197775\pi$
$229$	3.49552	+	3.49552i	0.230990	+	0.230990i	−0.582116	+	0.813106i	$0.697775\pi$
$230$	−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	0.999423	−	0.0339722i	$-0.0108158\pi$
$239$	14.9255	+	14.9255i	0.965451	+	0.965451i	−0.0339722	+	0.999423i	$0.510816\pi$
$240$	−1.64815	+	2.44671i	−0.106388	+	0.157934i
$241$	−27.0678	+	7.25281i	−1.74359	+	0.467194i	−0.983240	−	0.182316i	$-0.941641\pi$
$241$	−27.0678	+	7.25281i	−1.74359	+	0.467194i	−0.760353	+	0.649510i	$0.774974\pi$
$242$	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	−0.692036	−	0.721863i	$-0.743286\pi$
$251$	4.42232	−	7.65968i	0.279134	−	0.483474i	0.971170	+	0.238389i	$0.0766193\pi$
$252$	−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	0.997671	−	0.0682054i	$-0.0217273\pi$
$257$	7.05002	+	12.2110i	0.439768	+	0.761701i	−0.557903	+	0.829906i	$0.688394\pi$
$258$	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	−0.426569	−	0.904455i	$-0.640278\pi$
$263$	2.32601	−	1.34293i	0.143428	−	0.0828083i	0.569997	+	0.821647i	$0.306944\pi$
$264$	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	0.978331	−	0.207047i	$-0.0663853\pi$
$269$	21.1279	+	12.1982i	1.28819	+	0.743736i	0.309858	+	0.950783i	$0.399719\pi$
$270$	−7.89290	−	4.00340i	−0.480347	−	0.243639i
$271$	−5.12304	+	19.1194i	−0.311202	+	1.16142i	0.616271	+	0.787534i	$0.288643\pi$
$271$	−5.12304	+	19.1194i	−0.311202	+	1.16142i	−0.927474	+	0.373889i	$0.878024\pi$
$272$	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	0.954268	−	0.298953i	$-0.0966375\pi$
$277$	19.5143	+	11.2666i	1.17250	+	0.676943i	0.218233	+	0.975897i	$0.429971\pi$
$278$	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	−0.699231	−	0.714896i	$-0.746474\pi$
$281$	0.262594	−	0.262594i	0.0156650	−	0.0156650i	0.714896	+	0.699231i	$0.246474\pi$
$282$	1.80754	+	9.26869i	0.107637	+	0.551943i
$283$	−25.0610	+	14.4690i	−1.48972	+	0.860090i	−0.999931	−	0.0117514i	$-0.996259\pi$
$283$	−25.0610	+	14.4690i	−1.48972	+	0.860090i	−0.489788	+	0.871841i	$0.662926\pi$
$284$	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	0.710971	+	0.703222i	$0.248256\pi$
$293$	7.64906	+	28.5467i	0.446863	+	1.66771i	−0.264108	+	0.964493i	$0.585078\pi$
$294$	−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	0.788683	−	0.614800i	$-0.210763\pi$
$307$	3.04668	+	3.04668i	0.173883	+	0.173883i	−0.614800	+	0.788683i	$0.710763\pi$
$308$	−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	0.710542	−	0.703655i	$-0.248450\pi$
$317$	0.122626	+	0.122626i	0.00688738	+	0.00688738i	−0.703655	+	0.710542i	$0.748450\pi$
$318$	−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	0.998456	−	0.0555454i	$-0.0176897\pi$
$331$	1.92841	+	7.19693i	0.105995	+	0.395579i	−0.892461	+	0.451124i	$0.851023\pi$
$332$	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	$0.181161\pi$
$337$			19.7859i			1.07781i	−0.842368	+	0.538903i	$0.818839\pi$
$338$	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	0.999280	+	0.0379296i	$0.0120763\pi$
$347$	28.5337	+	16.4739i	1.53177	+	0.884367i	0.532488	+	0.846437i	$0.321257\pi$
$348$	−0.0791138	−	0.0271869i	−0.00424094	−	0.00145737i
$349$	7.05811	−	26.3412i	0.377812	−	1.41001i	−0.471380	−	0.881930i	$-0.656244\pi$
$349$	7.05811	−	26.3412i	0.377812	−	1.41001i	0.849192	−	0.528084i	$-0.177089\pi$
$350$	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	−0.860677	−	0.509152i	$-0.829959\pi$
$353$	2.61659	−	9.76525i	0.139267	−	0.519752i	0.999944	−	0.0105999i	$-0.00337411\pi$
$354$	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	−0.878012	−	0.478638i	$-0.841131\pi$
$359$	−7.56706	+	7.56706i	−0.399374	+	0.399374i	0.478638	+	0.878012i	$0.341131\pi$
$360$	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	−0.973898	−	0.226986i	$-0.927113\pi$
$367$	−13.0944	−	22.6802i	−0.683524	−	1.18390i	0.290374	−	0.956913i	$-0.406220\pi$
$368$	−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	0.200897	+	0.979612i	$0.435614\pi$
$373$	−14.4447	+	25.0190i	−0.747920	+	1.29544i	−0.948818	+	0.315824i	$0.897719\pi$
$374$	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	−0.321678	−	0.946849i	$-0.604247\pi$
$379$	−20.9024	−	5.60078i	−1.07368	−	0.287693i	−0.752006	+	0.659156i	$0.770914\pi$
$380$	−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	−0.614322	−	0.789056i	$-0.710570\pi$
$383$	−14.7133	+	3.94240i	−0.751812	+	0.201447i	−0.137490	+	0.990503i	$0.543904\pi$
$384$	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	−0.193766	−	0.981048i	$-0.562070\pi$
$397$	2.56934	−	0.688451i	0.128951	−	0.0345524i	0.322717	+	0.946495i	$0.395404\pi$
$398$	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	0.156951	−	0.987606i	$-0.449834\pi$
$401$	−4.02361	−	1.07812i	−0.200930	−	0.0538389i	−0.357880	+	0.933768i	$0.616500\pi$
$402$	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	−0.960105	−	0.279639i	$-0.909785\pi$
$409$	−5.42905	−	20.2615i	−0.268449	−	1.00187i	0.691656	−	0.722227i	$-0.256881\pi$
$410$	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	−0.775622	−	0.631198i	$-0.782564\pi$
$419$	−12.6256	+	7.28938i	−0.616800	+	0.356109i	0.158822	+	0.987307i	$0.449230\pi$
$420$	−0.564668	−	2.89550i	−0.0275530	−	0.141286i
$421$	13.7352	−	13.7352i	0.669413	−	0.669413i	−0.288167	−	0.957580i	$-0.593046\pi$
$421$	13.7352	−	13.7352i	0.669413	−	0.669413i	0.957580	+	0.288167i	$0.0930459\pi$
$422$	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	0.821842	+	0.569715i	$0.192946\pi$
$431$	−3.62793	+	13.5396i	−0.174751	+	0.652181i	−0.996594	+	0.0824664i	$0.973720\pi$
$432$	−2.35050	+	4.63413i	−0.113089	+	0.222960i
$433$	13.5616	+	7.82982i	0.651731	+	0.376277i	0.789119	−	0.614240i	$-0.210537\pi$
$433$	13.5616	+	7.82982i	0.651731	+	0.376277i	−0.137388	+	0.990517i	$0.543871\pi$
$434$	−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	−0.989623	−	0.143688i	$-0.954104\pi$
$439$	−28.4951	+	16.4517i	−1.36000	+	0.785195i	−0.370374	+	0.928883i	$0.620771\pi$
$440$	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	$-0.868920\pi$
$443$		−	16.8490i		−	0.800518i	0.916402	−	0.400259i	$-0.131080\pi$
$444$	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	0.976956	+	0.213441i	$0.0684673\pi$
$449$	5.03482	+	18.7902i	0.237608	+	0.886765i	−0.739348	+	0.673324i	$0.764866\pi$
$450$	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	0.916343	−	0.400395i	$-0.131127\pi$
$457$	32.2742	+	8.64783i	1.50972	+	0.404529i	0.593379	+	0.804924i	$0.297794\pi$
$458$	−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	0.0485337	−	0.998822i	$-0.484545\pi$
$461$	12.6673	−	3.39420i	0.589976	−	0.158084i	0.541442	+	0.840738i	$0.317879\pi$
$462$	−2.44615	+	3.63136i	−0.113805	+	0.168946i
$463$	14.6471	+	14.6471i	0.680707	+	0.680707i	0.960160	−	0.279452i	$-0.0901528\pi$
$463$	14.6471	+	14.6471i	0.680707	+	0.680707i	−0.279452	+	0.960160i	$0.590153\pi$
$464$	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	−0.142206	−	0.989837i	$-0.545420\pi$
$479$	−16.6395	−	4.45855i	−0.760279	−	0.203716i	−0.618073	+	0.786121i	$0.712086\pi$
$480$	−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	0.949338	−	0.314255i	$-0.101755\pi$
$487$	−0.660728	−	2.46587i	−0.0299404	−	0.111739i	−0.979279	+	0.202516i	$0.935088\pi$
$488$	−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	0.999994	+	0.00346360i	$0.00110250\pi$
$491$	11.1457	+	19.3048i	0.502997	+	0.871216i	−0.496997	+	0.867752i	$0.665564\pi$
$492$	−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	−0.299058	−	0.954235i	$-0.596672\pi$
$499$	14.6355	−	14.6355i	0.655177	−	0.655177i	0.954235	+	0.299058i	$0.0966724\pi$
$500$	−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	0.711857	−	0.702324i	$-0.247854\pi$
$503$	10.3067	+	5.95060i	0.459555	+	0.265324i	−0.252302	+	0.967648i	$0.581188\pi$
$504$	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	−0.981466	−	0.191637i	$-0.938620\pi$
$509$	−0.804816	+	3.00361i	−0.0356728	+	0.133133i	0.945793	+	0.324770i	$0.105287\pi$
$510$	−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	$0.132515\pi$
$521$			18.4606i			0.808774i	−0.914588	+	0.404387i	$0.867485\pi$
$522$	−0.0564515	+	0.133445i	−0.00247081	+	0.00584073i
$523$	−4.75204	−	8.23078i	−0.207792	−	0.359907i	0.743227	−	0.669040i	$-0.233294\pi$
$523$	−4.75204	−	8.23078i	−0.207792	−	0.359907i	−0.951019	+	0.309133i	$0.899961\pi$
$524$	−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	0.479506	−	0.877539i	$-0.340816\pi$
$541$	−9.25800	−	9.25800i	−0.398032	−	0.398032i	−0.877539	+	0.479506i	$0.840816\pi$
$542$	−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	−0.503097	−	0.864230i	$-0.667806\pi$
$557$	−32.3546	−	8.66938i	−1.37091	−	0.367333i	−0.867810	+	0.496896i	$0.834473\pi$
$558$	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	−0.697761	−	0.716331i	$-0.745820\pi$
$563$	6.44159	−	11.1572i	0.271480	−	0.470218i	0.969241	+	0.246113i	$0.0791534\pi$
$564$	−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	−0.915891	−	0.401428i	$-0.868514\pi$
$569$	−19.2164	−	33.2837i	−0.805592	−	1.39533i	0.110298	−	0.993899i	$-0.464819\pi$
$570$	5.21381	+	10.6733i	0.218383	+	0.447056i
$571$		−	6.25069i		−	0.261583i	−0.991410	−	0.130792i	$-0.958248\pi$
$571$		−	6.25069i		−	0.261583i	0.991410	−	0.130792i	$-0.0417519\pi$
$572$	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	−0.935726	−	0.352726i	$-0.885255\pi$
$577$	−14.0041	+	14.0041i	−0.583000	+	0.583000i	0.352726	+	0.935726i	$0.385255\pi$
$578$	−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	−0.528712	−	0.848801i	$-0.677325\pi$
$587$	8.56624	−	31.9696i	0.353566	−	1.31953i	0.882279	−	0.470727i	$-0.156008\pi$
$588$	−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	−0.475046	−	0.879961i	$-0.657569\pi$
$593$	9.86033	−	9.86033i	0.404915	−	0.404915i	0.879961	+	0.475046i	$0.157569\pi$
$594$	−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	$0.247267\pi$
$599$			34.3137i			1.40202i	−0.713152	+	0.701009i	$0.752733\pi$
$600$	−1.59578	−	3.26677i	−0.0651476	−	0.133365i
$601$	6.93693	+	12.0151i	0.282963	+	0.490107i	0.972113	−	0.234512i	$-0.0753492\pi$
$601$	6.93693	+	12.0151i	0.282963	+	0.490107i	−0.689150	+	0.724619i	$0.742016\pi$
$602$	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	−0.936244	−	0.351351i	$-0.885722\pi$
$607$	−4.03666	+	6.99170i	−0.163843	+	0.283784i	0.772401	+	0.635135i	$0.219056\pi$
$608$	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	0.0663532	−	0.997796i	$-0.478864\pi$
$613$	−9.28658	−	2.48833i	−0.375081	−	0.100503i	−0.441435	+	0.897293i	$0.645530\pi$
$614$	−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	0.298901	−	0.954284i	$-0.403380\pi$
$617$	25.7063	−	6.88799i	1.03490	−	0.277300i	0.735998	+	0.676984i	$0.236713\pi$
$618$	18.4042	+	12.3974i	0.740327	+	0.498698i
$619$	−23.2210	−	23.2210i	−0.933331	−	0.933331i	0.0645819	−	0.997912i	$-0.479429\pi$
$619$	−23.2210	−	23.2210i	−0.933331	−	0.933331i	−0.997912	+	0.0645819i	$0.979429\pi$
$620$	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	−0.419711	−	0.907658i	$-0.637869\pi$
$631$	−8.27351	+	2.21688i	−0.329363	+	0.0882526i	0.0903481	+	0.995910i	$0.471202\pi$
$632$	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	−0.936330	−	0.351120i	$-0.885801\pi$
$641$	−4.15434	+	7.19552i	−0.164086	+	0.284206i	0.772244	+	0.635326i	$0.219134\pi$
$642$	−2.02187	+	29.1705i	−0.0797967	+	1.15127i
$643$	3.88101	+	14.4841i	0.153052	+	0.571198i	0.999264	+	0.0383522i	$0.0122109\pi$
$643$	3.88101	+	14.4841i	0.153052	+	0.571198i	−0.846212	+	0.532846i	$0.821122\pi$
$644$	−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	0.972940	+	0.231058i	$0.0742188\pi$
$647$	17.4638	+	30.2482i	0.686572	+	1.18918i	−0.286368	+	0.958120i	$0.592448\pi$
$648$	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	−0.214363	−	0.976754i	$-0.568767\pi$
$653$	13.3992	−	7.73602i	0.524350	−	0.302734i	0.738713	+	0.674020i	$0.235434\pi$
$654$	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	0.864046	−	0.503413i	$-0.167922\pi$
$659$	22.0796	+	12.7477i	0.860101	+	0.496579i	−0.00394522	+	0.999992i	$0.501256\pi$
$660$	2.42356	−	7.05255i	0.0943370	−	0.274520i
$661$	−9.89796	+	36.9397i	−0.384986	+	1.43679i	0.453202	+	0.891408i	$0.350281\pi$
$661$	−9.89796	+	36.9397i	−0.384986	+	1.43679i	−0.838189	+	0.545380i	$0.816385\pi$
$662$	−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	0.472233	−	0.881474i	$-0.343448\pi$
$673$	38.1799	−	22.0432i	1.47173	−	0.849703i	0.999495	+	0.0317707i	$0.0101146\pi$
$674$	−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	$-0.869977\pi$
$677$		−	20.6704i		−	0.794430i	0.917726	−	0.397215i	$-0.130023\pi$
$678$	−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	−0.973942	−	0.226796i	$-0.927175\pi$
$683$	−6.37367	−	23.7869i	−0.243882	−	0.910179i	0.730061	−	0.683382i	$-0.239492\pi$
$684$	−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	0.147433	−	0.989072i	$-0.452899\pi$
$691$	−5.76792	−	1.54551i	−0.219422	−	0.0587939i	−0.366855	+	0.930278i	$0.619566\pi$
$692$	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	−0.261813	−	0.965119i	$-0.584320\pi$
$709$	−0.159505	+	0.0427392i	−0.00599032	+	0.00160510i	0.255823	+	0.966724i	$0.417654\pi$
$710$	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	−0.542279	−	0.840198i	$-0.682438\pi$
$719$	12.2405	−	21.2012i	0.456494	−	0.790670i	0.998773	+	0.0495281i	$0.0157717\pi$
$720$	−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	$0.215061\pi$
$727$			33.7248i			1.25078i	−0.780311	+	0.625392i	$0.784939\pi$
$728$	−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	−0.503620	−	0.863925i	$-0.667999\pi$
$733$	9.75491	−	9.75491i	0.360306	−	0.360306i	0.863925	+	0.503620i	$0.167999\pi$
$734$	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	−0.791436	−	0.611253i	$-0.790666\pi$
$739$	5.42588	−	20.2496i	0.199594	−	0.744895i	0.991030	−	0.133643i	$-0.0426674\pi$
$740$	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	0.204371	+	0.978893i	$0.434485\pi$
$743$	−12.5950	+	47.0052i	−0.462066	+	1.72445i	−0.666437	+	0.745561i	$0.732182\pi$
$744$	−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	0.00282713	−	0.999996i	$-0.499100\pi$
$751$	23.8490	−	13.7692i	0.870263	−	0.502446i	0.867436	+	0.497550i	$0.165767\pi$
$752$	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	0.876618	−	0.481187i	$-0.159794\pi$
$757$	0.593994	+	1.02883i	0.0215891	+	0.0373934i	−0.855029	+	0.518580i	$0.826461\pi$
$758$	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	0.922731	−	0.385444i	$-0.125952\pi$
$761$	−1.90620	−	7.11402i	−0.0690996	−	0.257883i	−0.991831	+	0.127561i	$0.959285\pi$
$762$	−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	−0.995333	−	0.0964985i	$-0.969236\pi$
$769$	−52.8430	−	14.1592i	−1.90557	−	0.510595i	−0.910233	−	0.414096i	$-0.864098\pi$
$770$	−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	−0.00543129	−	0.999985i	$-0.501729\pi$
$773$	13.6195	−	3.64932i	0.489858	−	0.131257i	0.495289	+	0.868728i	$0.335062\pi$
$774$	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	0.502517	−	0.864567i	$-0.332408\pi$
$787$	38.4331	−	10.2981i	1.36999	−	0.367088i	0.867476	+	0.497479i	$0.165741\pi$
$788$	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	−0.999386	−	0.0350373i	$-0.988845\pi$
$797$	−13.2503	+	22.9502i	−0.469350	+	0.812938i	0.530036	+	0.847975i	$0.322178\pi$
$798$	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	−0.433502	−	0.901152i	$-0.642722\pi$
$809$	3.70234	−	2.13755i	0.130167	−	0.0751521i	0.563670	+	0.826000i	$0.309389\pi$
$810$	−10.6753	−	11.0006i	−0.375092	−	0.386522i
$811$	16.0439	−	16.0439i	0.563379	−	0.563379i	−0.366887	−	0.930266i	$-0.619576\pi$
$811$	16.0439	−	16.0439i	0.563379	−	0.563379i	0.930266	+	0.366887i	$0.119576\pi$
$812$	−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	−0.947504	−	0.319743i	$-0.896403\pi$
$821$	0.943552	−	3.52138i	0.0329302	−	0.122897i	0.980434	+	0.196846i	$0.0630700\pi$
$822$	−1.84962	−	0.635611i	−0.0645131	−	0.0221695i
$823$	24.9791	+	14.4217i	0.870718	+	0.502709i	0.867587	−	0.497286i	$-0.165670\pi$
$823$	24.9791	+	14.4217i	0.870718	+	0.502709i	0.00313111	+	0.999995i	$0.499003\pi$
$824$	−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	0.0332208	−	0.999448i	$-0.489424\pi$
$827$	29.6971	−	29.6971i	1.03267	−	1.03267i	0.999448	−	0.0332208i	$-0.0105765\pi$
$828$	10.9687	−	14.0748i	0.381190	−	0.489134i
$829$	−14.5577	+	8.40491i	−0.505611	+	0.291915i	−0.731028	−	0.682348i	$-0.760959\pi$
$829$	−14.5577	+	8.40491i	−0.505611	+	0.291915i	0.225417	+	0.974262i	$0.427626\pi$
$830$	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	0.909296	+	0.416150i	$0.136621\pi$
$839$	9.55565	+	35.6622i	0.329898	+	1.23119i	−0.579398	+	0.815044i	$0.696712\pi$
$840$	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	0.994657	+	0.103238i	$0.0329205\pi$
$853$	32.0653	+	32.0653i	1.09790	+	1.09790i	0.103238	+	0.994657i	$0.467080\pi$
$854$	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	0.999877	+	0.0156867i	$0.00499343\pi$
$863$	29.8341	+	29.8341i	1.01556	+	1.01556i	0.0156867	+	0.999877i	$0.495007\pi$
$864$	−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	0.982904	−	0.184121i	$-0.0589437\pi$
$877$	1.17343	+	4.37929i	0.0396238	+	0.147878i	−0.943280	+	0.331999i	$0.892277\pi$
$878$	−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	0.728388	−	0.685165i	$-0.240270\pi$
$881$	−6.80234	−	11.7820i	−0.229177	−	0.396946i	−0.957564	+	0.288219i	$0.906937\pi$
$882$	−1.16881	+	2.76295i	−0.0393560	+	0.0930333i
$883$			49.1232i			1.65313i	0.562843	+	0.826564i	$0.309708\pi$
$883$			49.1232i			1.65313i	−0.562843	+	0.826564i	$0.690292\pi$
$884$	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	−0.385248	−	0.922813i	$-0.625884\pi$
$887$	6.59110	−	3.80538i	0.221308	−	0.127772i	0.606556	+	0.795041i	$0.292551\pi$
$888$	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	−0.737779	−	0.675042i	$-0.764125\pi$
$907$	−15.7227	+	9.07753i	−0.522065	+	0.301415i	0.215714	+	0.976457i	$0.430792\pi$
$908$	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	$-0.882313\pi$
$911$		−	21.8135i		−	0.722715i	0.932427	−	0.361357i	$-0.117687\pi$
$912$	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	0.0924821	−	0.995714i	$-0.470520\pi$
$919$	27.5429	−	47.7056i	0.908555	−	1.57366i	0.816073	−	0.577949i	$-0.196147\pi$
$920$	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	0.472085	−	0.881553i	$-0.343502\pi$
$929$	40.2847	−	10.7943i	1.32170	−	0.354148i	0.849614	+	0.527405i	$0.176835\pi$
$930$	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	−0.971069	−	0.238798i	$-0.923247\pi$
$941$	−37.1136	−	37.1136i	−1.20987	−	1.20987i	−0.238798	−	0.971069i	$-0.576753\pi$
$942$	−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	−0.472939	−	0.881095i	$-0.656807\pi$
$947$	−40.7151	−	10.9096i	−1.32306	−	0.354514i	−0.850125	+	0.526581i	$0.823474\pi$
$948$	−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	0.0650548	+	0.997882i	$0.479278\pi$
$953$	−25.6740	+	44.4687i	−0.831663	+	1.44048i	−0.896718	+	0.442602i	$0.854056\pi$
$954$	−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	−0.185992	+	0.982551i	$0.559550\pi$
$967$	−36.3377	+	36.3377i	−1.16854	+	1.16854i	−0.982551	+	0.185992i	$0.940450\pi$
$968$	−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	0.238585	−	0.971122i	$-0.423316\pi$
$971$	−15.0550	−	8.69202i	−0.483139	−	0.278940i	−0.721724	+	0.692181i	$0.756650\pi$
$972$	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	0.0209430	−	0.999781i	$-0.493333\pi$
$977$	15.7128	−	58.6409i	0.502696	−	1.87609i	0.481753	−	0.876307i	$-0.340000\pi$
$978$	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	−0.653136	−	0.757241i	$-0.726547\pi$
$983$	3.26400	−	3.26400i	0.104105	−	0.104105i	0.757241	+	0.653136i	$0.226547\pi$
$984$	−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	0.951344	−	0.308130i	$-0.0997033\pi$
$991$	6.57379	+	11.3861i	0.208823	+	0.361693i	−0.742521	+	0.669823i	$0.766370\pi$
$992$	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	−0.856665	−	0.515874i	$-0.827467\pi$
$997$	0.581853	−	1.00780i	0.0184275	−	0.0319173i	0.875092	+	0.483956i	$0.160801\pi$
$998$	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.197.6	✓	56
3.2	odd	2		546.2.bu.b.197.10	yes	56
13.7	odd	12		546.2.bu.b.449.10	yes	56
39.20	even	12	inner	546.2.bu.a.449.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.197.6	✓	56	1.1	even	1	trivial
546.2.bu.a.449.6	yes	56	39.20	even	12	inner
546.2.bu.b.197.10	yes	56	3.2	odd	2
546.2.bu.b.449.10	yes	56	13.7	odd	12

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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