LMFDB - Embedded newform 546.2.bz.a.31.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

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([0, 2, 9]))

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

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

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.10
Character	$\chi$	$=$	546.31
Dual form			546.2.bz.a.229.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.819823 - 3.05962i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.925986 - 2.47842i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.819823 - 3.05962i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.925986 - 2.47842i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.58378 - 2.74318i) q^{10} +(0.128238 - 0.0343612i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.467804 + 3.57507i) q^{13} +(-0.252972 - 2.63363i) q^{14} +(2.23980 - 2.23980i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.61860 - 2.80350i) q^{17} +(0.258819 + 0.965926i) q^{18} +(0.864122 - 3.22495i) q^{19} +(2.23980 - 2.23980i) q^{20} +(0.437281 - 2.60936i) q^{21} +0.132761 q^{22} +(-1.82480 + 1.05355i) q^{23} +(0.258819 + 0.965926i) q^{24} +(-4.35904 - 2.51669i) q^{25} +(-0.473433 + 3.57433i) q^{26} +1.00000i q^{27} +(0.437281 - 2.60936i) q^{28} +2.41342 q^{29} +(2.74318 - 1.58378i) q^{30} +(-1.84373 + 0.494026i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.128238 + 0.0343612i) q^{33} +(2.28905 - 2.28905i) q^{34} +(-8.34216 + 0.801303i) q^{35} +1.00000i q^{36} +(-1.69070 + 6.30977i) q^{37} +(1.66935 - 2.89141i) q^{38} +(-1.38241 + 3.33001i) q^{39} +(2.74318 - 1.58378i) q^{40} +(4.28763 + 4.28763i) q^{41} +(1.09773 - 2.40728i) q^{42} +6.94294i q^{43} +(0.128238 + 0.0343612i) q^{44} +(3.05962 - 0.819823i) q^{45} +(-2.03530 + 0.545357i) q^{46} +(7.68863 + 2.06016i) q^{47} +1.00000i q^{48} +(-5.28510 + 4.58996i) q^{49} +(-3.55914 - 3.55914i) q^{50} +(2.80350 - 1.61860i) q^{51} +(-1.38241 + 3.33001i) q^{52} +(-4.30897 + 7.46335i) q^{53} +(-0.258819 + 0.965926i) q^{54} -0.420528i q^{55} +(1.09773 - 2.40728i) q^{56} +(2.36082 - 2.36082i) q^{57} +(2.33118 + 0.624639i) q^{58} +(-1.76347 - 6.58136i) q^{59} +(3.05962 - 0.819823i) q^{60} +(-9.51563 + 5.49385i) q^{61} -1.90877 q^{62} +(1.68338 - 2.04114i) q^{63} +1.00000i q^{64} +(11.3219 + 1.49962i) q^{65} +(0.114975 + 0.0663807i) q^{66} +(-3.29118 - 12.2828i) q^{67} +(2.80350 - 1.61860i) q^{68} -2.10710 q^{69} +(-8.26530 - 1.38511i) q^{70} +(-7.99048 + 7.99048i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(1.62996 + 6.08308i) q^{73} +(-3.26618 + 5.65719i) q^{74} +(-2.51669 - 4.35904i) q^{75} +(2.36082 - 2.36082i) q^{76} +(-0.203908 - 0.286008i) q^{77} +(-2.19717 + 2.85875i) q^{78} +(-6.51047 - 11.2765i) q^{79} +(3.05962 - 0.819823i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.03181 + 5.25125i) q^{82} +(0.334721 + 0.334721i) q^{83} +(1.68338 - 2.04114i) q^{84} +(-7.25067 - 7.25067i) q^{85} +(-1.79696 + 6.70636i) q^{86} +(2.09008 + 1.20671i) q^{87} +(0.114975 + 0.0663807i) q^{88} +(16.6648 + 4.46531i) q^{89} +3.16755 q^{90} +(8.42735 - 4.46988i) q^{91} -2.10710 q^{92} +(-1.84373 - 0.494026i) q^{93} +(6.89344 + 3.97993i) q^{94} +(-9.15868 - 5.28777i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(-4.12633 - 4.12633i) q^{97} +(-6.29298 + 3.06568i) q^{98} +(0.0938764 + 0.0938764i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 + 20 * q^9	$ 40 q - 4 q^{7} + 20 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * q^19 + 4 * q^21 + 8 * q^22 - 24 * q^23 - 48 * q^25 - 8 * q^26 + 4 * q^28 + 24 * q^29 - 4 * q^33 - 16 * q^34 - 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * q^46 + 20 * q^47 + 16 * q^49 + 32 * q^50 - 12 * q^51 - 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 - 24 * q^59 - 12 * q^61 + 16 * q^62 - 8 * q^63 + 8 * q^65 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * q^73 - 40 * q^74 - 36 * q^75 - 16 * q^76 + 48 * q^77 - 8 * q^78 - 20 * q^81 + 24 * q^83 - 8 * q^84 - 40 * q^85 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.819823	−	3.05962i	0.366636	−	1.36830i	−0.498554	−	0.866859i	$-0.666135\pi$
$5$	0.819823	−	3.05962i	0.366636	−	1.36830i	0.865190	−	0.501445i	$-0.167198\pi$
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	−0.925986	−	2.47842i	−0.349990	−	0.936754i
$7$	−0.925986	−	2.47842i	−0.349990	−	0.936754i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.58378	−	2.74318i	0.500834	−	0.867470i
$11$	0.128238	−	0.0343612i	0.0386651	−	0.0103603i	−0.239435	−	0.970912i	$-0.576962\pi$
$11$	0.128238	−	0.0343612i	0.0386651	−	0.0103603i	0.278100	+	0.960552i	$0.410295\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.467804	+	3.57507i	0.129746	+	0.991547i
$13$	0.467804	+	3.57507i	0.129746	+	0.991547i
$14$	−0.252972	−	2.63363i	−0.0676097	−	0.703867i
$15$	2.23980	−	2.23980i	0.578313	−	0.578313i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.61860	−	2.80350i	0.392568	−	0.679948i	−0.600219	−	0.799835i	$-0.704920\pi$
$17$	1.61860	−	2.80350i	0.392568	−	0.679948i	0.992787	+	0.119887i	$0.0382534\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	0.864122	−	3.22495i	0.198243	−	0.739853i	−0.793160	−	0.609013i	$-0.791566\pi$
$19$	0.864122	−	3.22495i	0.198243	−	0.739853i	0.991403	−	0.130840i	$-0.0417676\pi$
$20$	2.23980	−	2.23980i	0.500834	−	0.500834i
$21$	0.437281	−	2.60936i	0.0954225	−	0.569410i
$22$	0.132761			0.0283048
$23$	−1.82480	+	1.05355i	−0.380497	+	0.219680i	−0.678035	−	0.735030i	$-0.737168\pi$
$23$	−1.82480	+	1.05355i	−0.380497	+	0.219680i	0.297537	+	0.954710i	$0.403835\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$	−4.35904	−	2.51669i	−0.871807	−	0.503338i
$26$	−0.473433	+	3.57433i	−0.0928479	+	0.700984i
$27$			1.00000i			0.192450i
$28$	0.437281	−	2.60936i	0.0826383	−	0.493124i
$29$	2.41342			0.448161			0.224080	−	0.974571i	$-0.428062\pi$
$29$	2.41342			0.448161			0.224080	+	0.974571i	$0.428062\pi$
$30$	2.74318	−	1.58378i	0.500834	−	0.289157i
$31$	−1.84373	+	0.494026i	−0.331144	+	0.0887297i	−0.420560	−	0.907265i	$-0.638166\pi$
$31$	−1.84373	+	0.494026i	−0.331144	+	0.0887297i	0.0894164	+	0.995994i	$0.471500\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	0.128238	+	0.0343612i	0.0223233	+	0.00598151i
$34$	2.28905	−	2.28905i	0.392568	−	0.392568i
$35$	−8.34216	+	0.801303i	−1.41008	+	0.135445i
$36$			1.00000i			0.166667i
$37$	−1.69070	+	6.30977i	−0.277949	+	1.03732i	0.675890	+	0.737003i	$0.263759\pi$
$37$	−1.69070	+	6.30977i	−0.277949	+	1.03732i	−0.953839	+	0.300318i	$0.902907\pi$
$38$	1.66935	−	2.89141i	0.270805	−	0.469048i
$39$	−1.38241	+	3.33001i	−0.221362	+	0.533228i
$40$	2.74318	−	1.58378i	0.433735	−	0.250417i
$41$	4.28763	+	4.28763i	0.669615	+	0.669615i	0.957627	−	0.288012i	$-0.0929942\pi$
$41$	4.28763	+	4.28763i	0.669615	+	0.669615i	−0.288012	+	0.957627i	$0.592994\pi$
$42$	1.09773	−	2.40728i	0.169384	−	0.371451i
$43$			6.94294i			1.05879i	0.848376	+	0.529394i	$0.177581\pi$
$43$			6.94294i			1.05879i	−0.848376	+	0.529394i	$0.822419\pi$
$44$	0.128238	+	0.0343612i	0.0193325	+	0.00518014i
$45$	3.05962	−	0.819823i	0.456101	−	0.122212i
$46$	−2.03530	+	0.545357i	−0.300089	+	0.0804086i
$47$	7.68863	+	2.06016i	1.12150	+	0.300506i	0.771491	−	0.636240i	$-0.219511\pi$
$47$	7.68863	+	2.06016i	1.12150	+	0.300506i	0.350011	+	0.936746i	$0.386178\pi$
$48$			1.00000i			0.144338i
$49$	−5.28510	+	4.58996i	−0.755014	+	0.655708i
$50$	−3.55914	−	3.55914i	−0.503338	−	0.503338i
$51$	2.80350	−	1.61860i	0.392568	−	0.226649i
$52$	−1.38241	+	3.33001i	−0.191705	+	0.461789i
$53$	−4.30897	+	7.46335i	−0.591882	+	1.02517i	0.402097	+	0.915597i	$0.368282\pi$
$53$	−4.30897	+	7.46335i	−0.591882	+	1.02517i	−0.993979	+	0.109573i	$0.965052\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$		−	0.420528i		−	0.0567040i
$56$	1.09773	−	2.40728i	0.146691	−	0.321686i
$57$	2.36082	−	2.36082i	0.312699	−	0.312699i
$58$	2.33118	+	0.624639i	0.306099	+	0.0820191i
$59$	−1.76347	−	6.58136i	−0.229584	−	0.856820i	−0.980516	−	0.196440i	$-0.937062\pi$
$59$	−1.76347	−	6.58136i	−0.229584	−	0.856820i	0.750932	−	0.660380i	$-0.229605\pi$
$60$	3.05962	−	0.819823i	0.394995	−	0.105839i
$61$	−9.51563	+	5.49385i	−1.21835	+	0.703416i	−0.964565	−	0.263844i	$-0.915009\pi$
$61$	−9.51563	+	5.49385i	−1.21835	+	0.703416i	−0.253787	+	0.967260i	$0.581676\pi$
$62$	−1.90877			−0.242414
$63$	1.68338	−	2.04114i	0.212086	−	0.257159i
$64$			1.00000i			0.125000i
$65$	11.3219	+	1.49962i	1.40431	+	0.186006i
$66$	0.114975	+	0.0663807i	0.0141524	+	0.00817090i
$67$	−3.29118	−	12.2828i	−0.402081	−	1.50059i	−0.809376	−	0.587291i	$-0.800195\pi$
$67$	−3.29118	−	12.2828i	−0.402081	−	1.50059i	0.407295	−	0.913297i	$-0.366472\pi$
$68$	2.80350	−	1.61860i	0.339974	−	0.196284i
$69$	−2.10710			−0.253665
$70$	−8.26530	−	1.38511i	−0.987892	−	0.165552i
$71$	−7.99048	+	7.99048i	−0.948296	+	0.948296i	−0.998728	−	0.0504317i	$-0.983940\pi$
$71$	−7.99048	+	7.99048i	−0.948296	+	0.948296i	0.0504317	+	0.998728i	$0.483940\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	1.62996	+	6.08308i	0.190772	+	0.711970i	0.993321	+	0.115384i	$0.0368099\pi$
$73$	1.62996	+	6.08308i	0.190772	+	0.711970i	−0.802549	+	0.596586i	$0.796523\pi$
$74$	−3.26618	+	5.65719i	−0.379686	+	0.657635i
$75$	−2.51669	−	4.35904i	−0.290602	−	0.503338i
$76$	2.36082	−	2.36082i	0.270805	−	0.270805i
$77$	−0.203908	−	0.286008i	−0.0232374	−	0.0325937i
$78$	−2.19717	+	2.85875i	−0.248781	+	0.323689i
$79$	−6.51047	−	11.2765i	−0.732485	−	1.26870i	−0.955818	−	0.293959i	$-0.905027\pi$
$79$	−6.51047	−	11.2765i	−0.732485	−	1.26870i	0.223333	−	0.974742i	$-0.428306\pi$
$80$	3.05962	−	0.819823i	0.342076	−	0.0916590i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.03181	+	5.25125i	0.334808	+	0.579904i
$83$	0.334721	+	0.334721i	0.0367404	+	0.0367404i	0.725238	−	0.688498i	$-0.241730\pi$
$83$	0.334721	+	0.334721i	0.0367404	+	0.0367404i	−0.688498	+	0.725238i	$0.741730\pi$
$84$	1.68338	−	2.04114i	0.183672	−	0.222706i
$85$	−7.25067	−	7.25067i	−0.786446	−	0.786446i
$86$	−1.79696	+	6.70636i	−0.193772	+	0.723166i
$87$	2.09008	+	1.20671i	0.224080	+	0.129373i
$88$	0.114975	+	0.0663807i	0.0122563	+	0.00707620i
$89$	16.6648	+	4.46531i	1.76646	+	0.473322i	0.988011	−	0.154386i	$-0.0493399\pi$
$89$	16.6648	+	4.46531i	1.76646	+	0.473322i	0.778449	+	0.627707i	$0.216007\pi$
$90$	3.16755			0.333889
$91$	8.42735	−	4.46988i	0.883426	−	0.468571i
$92$	−2.10710			−0.219680
$93$	−1.84373	−	0.494026i	−0.191186	−	0.0512281i
$94$	6.89344	+	3.97993i	0.711004	+	0.410498i
$95$	−9.15868	−	5.28777i	−0.939661	−	0.542513i
$96$	−0.258819	+	0.965926i	−0.0264156	+	0.0985844i
$97$	−4.12633	−	4.12633i	−0.418965	−	0.418965i	0.465882	−	0.884847i	$-0.345737\pi$
$97$	−4.12633	−	4.12633i	−0.418965	−	0.418965i	−0.884847	+	0.465882i	$0.845737\pi$
$98$	−6.29298	+	3.06568i	−0.635687	+	0.309680i
$99$	0.0938764	+	0.0938764i	0.00943494	+	0.00943494i
$100$	−2.51669	−	4.35904i	−0.251669	−	0.435904i
$101$	−3.22882	+	5.59248i	−0.321279	+	0.556472i	−0.980752	−	0.195256i	$-0.937446\pi$
$101$	−3.22882	+	5.59248i	−0.321279	+	0.556472i	0.659473	+	0.751728i	$0.270779\pi$
$102$	3.12690	−	0.837849i	0.309609	−	0.0829594i
$103$	−6.04770	−	10.4749i	−0.595897	−	1.03212i	−0.993420	−	0.114532i	$-0.963463\pi$
$103$	−6.04770	−	10.4749i	−0.595897	−	1.03212i	0.397522	−	0.917593i	$-0.369870\pi$
$104$	−2.19717	+	2.85875i	−0.215450	+	0.280323i
$105$	−7.62517	−	3.47713i	−0.744141	−	0.339333i
$106$	−6.09380	+	6.09380i	−0.591882	+	0.591882i
$107$	2.05254	+	3.55510i	0.198426	+	0.343684i	0.948018	−	0.318216i	$-0.103084\pi$
$107$	2.05254	+	3.55510i	0.198426	+	0.343684i	−0.749592	+	0.661900i	$0.769750\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−3.87315	−	14.4548i	−0.370980	−	1.38452i	−0.859130	−	0.511758i	$-0.828995\pi$
$109$	−3.87315	−	14.4548i	−0.370980	−	1.38452i	0.488149	−	0.872760i	$-0.337672\pi$
$110$	0.108841	−	0.406199i	0.0103776	−	0.0387296i
$111$	−4.61908	+	4.61908i	−0.438423	+	0.438423i
$112$	1.68338	−	2.04114i	0.159064	−	0.192869i
$113$	−8.11684			−0.763568			−0.381784	−	0.924252i	$-0.624690\pi$
$113$	−8.11684			−0.763568			−0.381784	+	0.924252i	$0.624690\pi$
$114$	2.89141	−	1.66935i	0.270805	−	0.156349i
$115$	1.72745	+	6.44692i	0.161085	+	0.601179i
$116$	2.09008	+	1.20671i	0.194059	+	0.112040i
$117$	−2.86220	+	2.19267i	−0.264611	+	0.202712i
$118$		−	6.81352i		−	0.627236i
$119$	−8.44704	−	1.41557i	−0.774339	−	0.129765i
$120$	3.16755			0.289157
$121$	−9.51102	+	5.49119i	−0.864638	+	0.499199i
$122$	−10.6133	+	2.84383i	−0.960884	+	0.257468i
$123$	1.56938	+	5.85701i	0.141506	+	0.528109i
$124$	−1.84373	−	0.494026i	−0.165572	−	0.0443649i
$125$	−0.0747675	+	0.0747675i	−0.00668741	+	0.00668741i
$126$	2.15430	−	1.53590i	0.191921	−	0.136828i
$127$			2.15596i			0.191311i	0.995415	+	0.0956554i	$0.0304947\pi$
$127$			2.15596i			0.191311i	−0.995415	+	0.0956554i	$0.969505\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−3.47147	+	6.01276i	−0.305646	+	0.529394i
$130$	10.5480	+	4.37885i	0.925118	+	0.384050i
$131$	16.9467	−	9.78416i	1.48064	−	0.854846i	0.480878	−	0.876788i	$-0.340318\pi$
$131$	16.9467	−	9.78416i	1.48064	−	0.854846i	0.999759	+	0.0219414i	$0.00698473\pi$
$132$	0.0938764	+	0.0938764i	0.00817090	+	0.00817090i
$133$	−8.79292	+	0.844601i	−0.762443	+	0.0732362i
$134$		−	12.7161i		−	1.09851i
$135$	3.05962	+	0.819823i	0.263330	+	0.0705591i
$136$	3.12690	−	0.837849i	0.268129	−	0.0718450i
$137$	18.3364	−	4.91322i	1.56658	−	0.419764i	0.631842	−	0.775097i	$-0.282299\pi$
$137$	18.3364	−	4.91322i	1.56658	−	0.419764i	0.934740	+	0.355333i	$0.115633\pi$
$138$	−2.03530	−	0.545357i	−0.173256	−	0.0464239i
$139$			12.5387i			1.06351i	0.846897	+	0.531757i	$0.178468\pi$
$139$			12.5387i			1.06351i	−0.846897	+	0.531757i	$0.821532\pi$
$140$	−7.62517	−	3.47713i	−0.644445	−	0.293871i
$141$	5.62847	+	5.62847i	0.474003	+	0.474003i
$142$	−9.78630	+	5.65012i	−0.821248	+	0.474148i
$143$	0.182834	+	0.442385i	0.0152893	+	0.0369941i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.97857	−	7.38414i	0.164312	−	0.613220i
$146$			6.29766i			0.521198i
$147$	−6.87201	+	1.33247i	−0.566794	+	0.109900i
$148$	−4.61908	+	4.61908i	−0.379686	+	0.379686i
$149$	5.51281	+	1.47715i	0.451627	+	0.121013i	0.477461	−	0.878653i	$-0.341557\pi$
$149$	5.51281	+	1.47715i	0.451627	+	0.121013i	−0.0258335	+	0.999666i	$0.508224\pi$
$150$	−1.30273	−	4.86187i	−0.106368	−	0.396970i
$151$	−9.20838	+	2.46738i	−0.749367	+	0.200792i	−0.613237	−	0.789899i	$-0.710133\pi$
$151$	−9.20838	+	2.46738i	−0.749367	+	0.200792i	−0.136130	+	0.990691i	$0.543466\pi$
$152$	2.89141	−	1.66935i	0.234524	−	0.135403i
$153$	3.23720			0.261712
$154$	−0.122935	−	0.329038i	−0.00990640	−	0.0265146i
$155$			6.04613i			0.485637i
$156$	−2.86220	+	2.19267i	−0.229160	+	0.175554i
$157$	18.6519	+	10.7687i	1.48859	+	0.859436i	0.999915	−	0.0130320i	$-0.00414833\pi$
$157$	18.6519	+	10.7687i	1.48859	+	0.859436i	0.488672	+	0.872468i	$0.337482\pi$
$158$	−3.37007	−	12.5773i	−0.268108	−	1.00059i
$159$	−7.46335	+	4.30897i	−0.591882	+	0.341723i
$160$	3.16755			0.250417
$161$	4.30088	+	3.54705i	0.338956	+	0.279546i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	0.0542293	−	0.202387i	0.00424757	−	0.0158521i	−0.963770	−	0.266736i	$-0.914055\pi$
$163$	0.0542293	−	0.202387i	0.00424757	−	0.0158521i	0.968017	+	0.250884i	$0.0807214\pi$
$164$	1.56938	+	5.85701i	0.122548	+	0.457356i
$165$	0.210264	−	0.364188i	0.0163690	−	0.0283520i
$166$	0.236683	+	0.409947i	0.0183702	+	0.0318181i
$167$	2.04064	−	2.04064i	0.157909	−	0.157909i	−0.623730	−	0.781640i	$-0.714384\pi$
$167$	2.04064	−	2.04064i	0.157909	−	0.157909i	0.781640	+	0.623730i	$0.214384\pi$
$168$	2.15430	−	1.53590i	0.166208	−	0.118497i
$169$	−12.5623	+	3.34487i	−0.966332	+	0.257298i
$170$	−5.12700	−	8.88022i	−0.393223	−	0.681082i
$171$	3.22495	−	0.864122i	0.246618	−	0.0660810i
$172$	−3.47147	+	6.01276i	−0.264697	+	0.458469i
$173$	−6.64527	−	11.5099i	−0.505230	−	0.875085i	−0.999982	−	0.00605019i	$-0.998074\pi$
$173$	−6.64527	−	11.5099i	−0.505230	−	0.875085i	0.494751	−	0.869035i	$-0.335259\pi$
$174$	1.70654	+	1.70654i	0.129373	+	0.129373i
$175$	−2.20100	+	13.1339i	−0.166380	+	0.992832i
$176$	0.0938764	+	0.0938764i	0.00707620	+	0.00707620i
$177$	1.76347	−	6.58136i	0.132551	−	0.494685i
$178$	14.9412	+	8.62631i	1.11989	+	0.646569i
$179$	−0.516941	−	0.298456i	−0.0386380	−	0.0223077i	0.480557	−	0.876964i	$-0.340435\pi$
$179$	−0.516941	−	0.298456i	−0.0386380	−	0.0223077i	−0.519195	+	0.854656i	$0.673768\pi$
$180$	3.05962	+	0.819823i	0.228051	+	0.0611060i
$181$	8.83889			0.656989			0.328495	−	0.944506i	$-0.393459\pi$
$181$	8.83889			0.656989			0.328495	+	0.944506i	$0.393459\pi$
$182$	9.29708	−	2.13642i	0.689146	−	0.158362i
$183$	−10.9877			−0.812235
$184$	−2.03530	−	0.545357i	−0.150044	−	0.0402043i
$185$	17.9194	+	10.3458i	1.31746	+	0.760638i
$186$	−1.65304	−	0.954385i	−0.121207	−	0.0699789i
$187$	0.111234	−	0.415131i	0.00813423	−	0.0303574i
$188$	5.62847	+	5.62847i	0.410498	+	0.410498i
$189$	2.47842	−	0.925986i	0.180278	−	0.0673556i
$190$	−7.47803	−	7.47803i	−0.542513	−	0.542513i
$191$	−7.84119	−	13.5813i	−0.567369	−	0.982711i	−0.996825	−	0.0796236i	$-0.974628\pi$
$191$	−7.84119	−	13.5813i	−0.567369	−	0.982711i	0.429456	−	0.903088i	$-0.358705\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	17.0638	−	4.57224i	1.22828	−	0.329117i	0.414372	−	0.910108i	$-0.364001\pi$
$193$	17.0638	−	4.57224i	1.22828	−	0.329117i	0.813910	+	0.580990i	$0.197335\pi$
$194$	−2.91776	−	5.05370i	−0.209483	−	0.362835i
$195$	9.05523	+	6.95966i	0.648458	+	0.498391i
$196$	−6.87201	+	1.33247i	−0.490858	+	0.0951765i
$197$	−5.05240	+	5.05240i	−0.359969	+	0.359969i	−0.863801	−	0.503833i	$-0.831923\pi$
$197$	−5.05240	+	5.05240i	−0.359969	+	0.359969i	0.503833	+	0.863801i	$0.331923\pi$
$198$	0.0663807	+	0.114975i	0.00471747	+	0.00817090i
$199$	−7.81296	+	13.5324i	−0.553846	+	0.959289i	0.444147	+	0.895954i	$0.353507\pi$
$199$	−7.81296	+	13.5324i	−0.553846	+	0.959289i	−0.997992	+	0.0633348i	$0.979826\pi$
$200$	−1.30273	−	4.86187i	−0.0921173	−	0.343786i
$201$	3.29118	−	12.2828i	0.232142	−	0.866365i
$202$	−4.56624	+	4.56624i	−0.321279	+	0.321279i
$203$	−2.23479	−	5.98146i	−0.156852	−	0.419816i
$204$	3.23720			0.226649
$205$	16.6336	−	9.60342i	1.16174	−	0.670732i
$206$	−3.13052	−	11.6833i	−0.218114	−	0.814011i
$207$	−1.82480	−	1.05355i	−0.126832	−	0.0732268i
$208$	−2.86220	+	2.19267i	−0.198458	+	0.152034i
$209$		−	0.443252i		−	0.0306604i
$210$	−6.46540	−	5.33219i	−0.446155	−	0.367956i
$211$	−23.0121			−1.58422			−0.792110	−	0.610379i	$-0.791017\pi$
$211$	−23.0121			−1.58422			−0.792110	+	0.610379i	$0.791017\pi$
$212$	−7.46335	+	4.30897i	−0.512585	+	0.295941i
$213$	−10.9152	+	2.92472i	−0.747897	+	0.200398i
$214$	1.06247	+	3.96520i	0.0726291	+	0.271055i
$215$	21.2427	+	5.69198i	1.44874	+	0.388190i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	2.93167	+	4.11207i	0.199015	+	0.279146i
$218$		−	14.9647i		−	1.01354i
$219$	−1.62996	+	6.08308i	−0.110142	+	0.411056i
$220$	0.210264	−	0.364188i	0.0141760	−	0.0245536i
$221$	10.7799	+	4.47513i	0.725135	+	0.301030i
$222$	−5.65719	+	3.26618i	−0.379686	+	0.219212i
$223$	−4.37796	−	4.37796i	−0.293170	−	0.293170i	0.545161	−	0.838331i	$-0.316468\pi$
$223$	−4.37796	−	4.37796i	−0.293170	−	0.293170i	−0.838331	+	0.545161i	$0.816468\pi$
$224$	2.15430	−	1.53590i	0.143940	−	0.102621i
$225$		−	5.03338i		−	0.335559i
$226$	−7.84026	−	2.10079i	−0.521527	−	0.139743i
$227$	−7.30201	+	1.95657i	−0.484651	+	0.129862i	−0.492868	−	0.870104i	$-0.664051\pi$
$227$	−7.30201	+	1.95657i	−0.484651	+	0.129862i	0.00821638	+	0.999966i	$0.497385\pi$
$228$	3.22495	−	0.864122i	0.213577	−	0.0572279i
$229$	−14.8351	−	3.97504i	−0.980328	−	0.262678i	−0.267145	−	0.963656i	$-0.586080\pi$
$229$	−14.8351	−	3.97504i	−0.980328	−	0.262678i	−0.713183	+	0.700978i	$0.752747\pi$
$230$			6.67435i			0.440093i
$231$	−0.0335849	−	0.349644i	−0.00220973	−	0.0230049i
$232$	1.70654	+	1.70654i	0.112040	+	0.112040i
$233$	20.1700	−	11.6452i	1.32138	−	0.762900i	0.337432	−	0.941350i	$-0.390442\pi$
$233$	20.1700	−	11.6452i	1.32138	−	0.762900i	0.983949	+	0.178450i	$0.0571084\pi$
$234$	−3.33218	+	1.37716i	−0.217831	+	0.0900279i
$235$	12.6066	−	21.8353i	0.822366	−	1.42438i
$236$	1.76347	−	6.58136i	0.114792	−	0.428410i
$237$		−	13.0209i		−	0.845800i
$238$	−7.79284	−	3.55359i	−0.505134	−	0.230345i
$239$	−9.93729	+	9.93729i	−0.642790	+	0.642790i	−0.951240	−	0.308450i	$-0.900190\pi$
$239$	−9.93729	+	9.93729i	−0.642790	+	0.642790i	0.308450	+	0.951240i	$0.400190\pi$
$240$	3.05962	+	0.819823i	0.197498	+	0.0529193i
$241$	−0.955972	−	3.56773i	−0.0615795	−	0.229818i	0.928277	−	0.371890i	$-0.121290\pi$
$241$	−0.955972	−	3.56773i	−0.0615795	−	0.229818i	−0.989856	+	0.142072i	$0.954624\pi$
$242$	−10.6082	+	2.84245i	−0.681918	+	0.182719i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−10.9877			−0.703416
$245$	9.71068	+	19.9333i	0.620393	+	1.27349i
$246$			6.06362i			0.386603i
$247$	11.9337	+	1.58066i	0.759321	+	0.100575i
$248$	−1.65304	−	0.954385i	−0.104968	−	0.0606035i
$249$	0.122516	+	0.457237i	0.00776415	+	0.0289762i
$250$	−0.0915711	+	0.0528686i	−0.00579147	+	0.00334371i
$251$	11.9846			0.756463			0.378231	−	0.925711i	$-0.376532\pi$
$251$	11.9846			0.756463			0.378231	+	0.925711i	$0.376532\pi$
$252$	2.47842	−	0.925986i	0.156126	−	0.0583316i
$253$	−0.197807	+	0.197807i	−0.0124360	+	0.0124360i
$254$	−0.558004	+	2.08250i	−0.0350123	+	0.130668i
$255$	−2.65393	−	9.90460i	−0.166196	−	0.620250i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.1709	−	26.2767i	−0.946334	−	1.63910i	−0.753059	−	0.657953i	$-0.771423\pi$
$257$	−15.1709	−	26.2767i	−0.946334	−	1.63910i	−0.193275	−	0.981145i	$-0.561911\pi$
$258$	−4.90940	+	4.90940i	−0.305646	+	0.305646i
$259$	17.2038	−	1.65251i	1.06899	−	0.102682i
$260$	9.05523	+	6.95966i	0.561581	+	0.431620i
$261$	1.20671	+	2.09008i	0.0746934	+	0.129373i
$262$	18.9015	−	5.06466i	1.16774	−	0.312895i
$263$	−12.5802	+	21.7895i	−0.775727	+	1.34360i	0.158659	+	0.987333i	$0.449283\pi$
$263$	−12.5802	+	21.7895i	−0.775727	+	1.34360i	−0.934385	+	0.356264i	$0.884050\pi$
$264$	0.0663807	+	0.114975i	0.00408545	+	0.00707620i
$265$	19.3024	+	19.3024i	1.18574	+	1.18574i
$266$	−8.71191	−	1.45995i	−0.534162	−	0.0895155i
$267$	12.1994	+	12.1994i	0.746594	+	0.746594i
$268$	3.29118	−	12.2828i	0.201041	−	0.750294i
$269$	−3.86820	−	2.23331i	−0.235848	−	0.136167i	0.377419	−	0.926043i	$-0.376812\pi$
$269$	−3.86820	−	2.23331i	−0.235848	−	0.136167i	−0.613267	+	0.789876i	$0.710145\pi$
$270$	2.74318	+	1.58378i	0.166945	+	0.0963855i
$271$	5.04576	+	1.35201i	0.306508	+	0.0821287i	0.408795	−	0.912626i	$-0.365949\pi$
$271$	5.04576	+	1.35201i	0.306508	+	0.0821287i	−0.102286	+	0.994755i	$0.532616\pi$
$272$	3.23720			0.196284
$273$	9.53324	+	0.342640i	0.576978	+	0.0207375i
$274$	18.9832			1.14682
$275$	−0.645469	−	0.172953i	−0.0389232	−	0.0104294i
$276$	−1.82480	−	1.05355i	−0.109840	−	0.0634162i
$277$	−2.68824	−	1.55206i	−0.161521	−	0.0932541i	0.417061	−	0.908879i	$-0.363060\pi$
$277$	−2.68824	−	1.55206i	−0.161521	−	0.0932541i	−0.578582	+	0.815625i	$0.696394\pi$
$278$	−3.24524	+	12.1114i	−0.194637	+	0.726394i
$279$	−1.34970	−	1.34970i	−0.0808047	−	0.0808047i
$280$	−6.46540	−	5.33219i	−0.386382	−	0.318659i
$281$	7.08699	+	7.08699i	0.422774	+	0.422774i	0.886158	−	0.463384i	$-0.153365\pi$
$281$	7.08699	+	7.08699i	0.422774	+	0.422774i	−0.463384	+	0.886158i	$0.653365\pi$
$282$	3.97993	+	6.89344i	0.237001	+	0.410498i
$283$	15.5041	−	26.8539i	0.921622	−	1.59630i	0.124717	−	0.992192i	$-0.460198\pi$
$283$	15.5041	−	26.8539i	0.921622	−	1.59630i	0.796905	−	0.604104i	$-0.206469\pi$
$284$	−10.9152	+	2.92472i	−0.647698	+	0.173550i
$285$	−5.28777	−	9.15868i	−0.313220	−	0.542513i
$286$	0.0621063	+	0.474632i	0.00367242	+	0.0280656i
$287$	6.65625	−	14.5968i	0.392906	−	0.861623i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	3.26027	+	5.64695i	0.191780	+	0.332173i
$290$	3.82231	−	6.62044i	0.224454	−	0.388766i
$291$	−1.51034	−	5.63667i	−0.0885378	−	0.330427i
$292$	−1.62996	+	6.08308i	−0.0953859	+	0.355985i
$293$	−8.56363	+	8.56363i	−0.500293	+	0.500293i	−0.911529	−	0.411236i	$-0.865097\pi$
$293$	−8.56363	+	8.56363i	−0.500293	+	0.500293i	0.411236	+	0.911529i	$0.365097\pi$
$294$	−6.98272	−	0.491539i	−0.407241	−	0.0286671i
$295$	−21.5822			−1.25656
$296$	−5.65719	+	3.26618i	−0.328817	+	0.189843i
$297$	0.0343612	+	0.128238i	0.00199384	+	0.00744110i
$298$	4.94265	+	2.85364i	0.286320	+	0.165307i
$299$	−4.62017	−	6.03095i	−0.267191	−	0.348779i
$300$		−	5.03338i		−	0.290602i
$301$	17.2075	−	6.42906i	0.991823	−	0.370565i
$302$	−9.53321			−0.548575
$303$	−5.59248	+	3.22882i	−0.321279	+	0.185491i
$304$	3.22495	−	0.864122i	0.184963	−	0.0495608i
$305$	9.00797	+	33.6182i	0.515795	+	1.92497i
$306$	3.12690	+	0.837849i	0.178753	+	0.0478966i
$307$	−6.97645	+	6.97645i	−0.398167	+	0.398167i	−0.877586	−	0.479419i	$-0.840847\pi$
$307$	−6.97645	+	6.97645i	−0.398167	+	0.398167i	0.479419	+	0.877586i	$0.340847\pi$
$308$	−0.0335849	−	0.349644i	−0.00191368	−	0.0199228i
$309$		−	12.0954i		−	0.688083i
$310$	−1.56485	+	5.84011i	−0.0888777	+	0.331696i
$311$	11.2510	−	19.4873i	0.637986	−	1.10502i	−0.347888	−	0.937536i	$-0.613101\pi$
$311$	11.2510	−	19.4873i	0.637986	−	1.10502i	0.985874	−	0.167489i	$-0.0535657\pi$
$312$	−3.33218	+	1.37716i	−0.188648	+	0.0779664i
$313$	22.7282	−	13.1221i	1.28467	−	0.741706i	0.306973	−	0.951718i	$-0.400684\pi$
$313$	22.7282	−	13.1221i	1.28467	−	0.741706i	0.977699	+	0.210012i	$0.0673504\pi$
$314$	15.2292	+	15.2292i	0.859436	+	0.859436i
$315$	−4.86503	−	6.82387i	−0.274113	−	0.384481i
$316$		−	13.0209i		−	0.732485i
$317$	25.6668	+	6.87739i	1.44159	+	0.386272i	0.893090	−	0.449879i	$-0.148533\pi$
$317$	25.6668	+	6.87739i	1.44159	+	0.386272i	0.548499	+	0.836151i	$0.315200\pi$
$318$	−8.32429	+	2.23049i	−0.466803	+	0.125079i
$319$	0.309491	−	0.0829279i	0.0173282	−	0.00464307i
$320$	3.05962	+	0.819823i	0.171038	+	0.0458295i
$321$			4.10507i			0.229123i
$322$	3.23628	+	4.53933i	0.180351	+	0.252967i
$323$	−7.64246	−	7.64246i	−0.425238	−	0.425238i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	6.95818	−	16.7612i	0.385970	−	0.929744i
$326$	0.104763	−	0.181455i	0.00580228	−	0.0100499i
$327$	3.87315	−	14.4548i	0.214186	−	0.799352i
$328$			6.06362i			0.334808i
$329$	−2.01362	−	20.9633i	−0.111015	−	1.15575i
$330$	0.297358	−	0.297358i	0.0163690	−	0.0163690i
$331$	8.27289	+	2.21671i	0.454719	+	0.121842i	0.478907	−	0.877866i	$-0.341033\pi$
$331$	8.27289	+	2.21671i	0.454719	+	0.121842i	−0.0241875	+	0.999707i	$0.507700\pi$
$332$	0.122516	+	0.457237i	0.00672395	+	0.0250941i
$333$	−6.30977	+	1.69070i	−0.345774	+	0.0926497i
$334$	2.49926	−	1.44295i	0.136754	−	0.0789547i
$335$	−40.2790			−2.20068
$336$	2.47842	−	0.925986i	0.135209	−	0.0505167i
$337$			7.59201i			0.413563i	0.978387	+	0.206782i	$0.0662990\pi$
$337$			7.59201i			0.413563i	−0.978387	+	0.206782i	$0.933701\pi$
$338$	−13.0000	−	0.0204713i	−0.707106	−	0.00111349i
$339$	−7.02939	−	4.05842i	−0.381784	−	0.220423i
$340$	−2.65393	−	9.90460i	−0.143930	−	0.537152i
$341$	−0.219460	+	0.126705i	−0.0118844	+	0.00686149i
$342$	3.33871			0.180537
$343$	16.2698	+	8.84844i	0.878484	+	0.477771i
$344$	−4.90940	+	4.90940i	−0.264697	+	0.264697i
$345$	−1.72745	+	6.44692i	−0.0930027	+	0.347091i
$346$	−3.43984	−	12.8377i	−0.184927	−	0.690158i
$347$	−2.00675	+	3.47579i	−0.107728	+	0.186590i	−0.914849	−	0.403795i	$-0.867691\pi$
$347$	−2.00675	+	3.47579i	−0.107728	+	0.186590i	0.807122	+	0.590385i	$0.201024\pi$
$348$	1.20671	+	2.09008i	0.0646864	+	0.112040i
$349$	14.9823	−	14.9823i	0.801986	−	0.801986i	−0.181420	−	0.983406i	$-0.558069\pi$
$349$	14.9823	−	14.9823i	0.801986	−	0.801986i	0.983406	+	0.181420i	$0.0580693\pi$
$350$	−5.52532	+	12.1167i	−0.295341	+	0.647667i
$351$	−3.57507	+	0.467804i	−0.190823	+	0.0249695i
$352$	0.0663807	+	0.114975i	0.00353810	+	0.00612817i
$353$	−23.4575	+	6.28543i	−1.24852	+	0.334540i	−0.821764	−	0.569828i	$-0.807010\pi$
$353$	−23.4575	+	6.28543i	−1.24852	+	0.334540i	−0.426755	+	0.904367i	$0.640343\pi$
$354$	3.40676	−	5.90069i	0.181067	−	0.313618i
$355$	17.8971	+	30.9986i	0.949877	+	1.64524i
$356$	12.1994	+	12.1994i	0.646569	+	0.646569i
$357$	−6.60757	−	5.44943i	−0.349709	−	0.288415i
$358$	−0.422081	−	0.422081i	−0.0223077	−	0.0223077i
$359$	2.77948	−	10.3732i	0.146695	−	0.547475i	−0.852979	−	0.521946i	$-0.825206\pi$
$359$	2.77948	−	10.3732i	0.146695	−	0.547475i	0.999674	−	0.0255289i	$-0.00812699\pi$
$360$	2.74318	+	1.58378i	0.144578	+	0.0834723i
$361$	6.80091	+	3.92651i	0.357943	+	0.206658i
$362$	8.53771	+	2.28767i	0.448732	+	0.120237i
$363$	−10.9824			−0.576425
$364$	9.53324	+	0.342640i	0.499677	+	0.0179592i
$365$	19.9482			1.04414
$366$	−10.6133	−	2.84383i	−0.554767	−	0.148649i
$367$	0.979626	+	0.565587i	0.0511361	+	0.0295234i	0.525350	−	0.850886i	$-0.323934\pi$
$367$	0.979626	+	0.565587i	0.0511361	+	0.0295234i	−0.474214	+	0.880410i	$0.657268\pi$
$368$	−1.82480	−	1.05355i	−0.0951244	−	0.0549201i
$369$	−1.56938	+	5.85701i	−0.0816987	+	0.304904i
$370$	14.6312	+	14.6312i	0.760638	+	0.760638i
$371$	22.4873	+	3.76846i	1.16748	+	0.195649i
$372$	−1.34970	−	1.34970i	−0.0699789	−	0.0699789i
$373$	14.6335	+	25.3460i	0.757693	+	1.31236i	0.944024	+	0.329877i	$0.107007\pi$
$373$	14.6335	+	25.3460i	0.757693	+	1.31236i	−0.186331	+	0.982487i	$0.559660\pi$
$374$	0.214888	−	0.372196i	0.0111116	−	0.0192458i
$375$	−0.102134	+	0.0273668i	−0.00527419	+	0.00141322i
$376$	3.97993	+	6.89344i	0.205249	+	0.355502i
$377$	1.12901	+	8.62815i	0.0581468	+	0.444372i
$378$	2.63363	−	0.252972i	0.135459	−	0.0130115i
$379$	−9.42782	+	9.42782i	−0.484275	+	0.484275i	−0.906494	−	0.422219i	$-0.861251\pi$
$379$	−9.42782	+	9.42782i	−0.484275	+	0.484275i	0.422219	+	0.906494i	$0.361251\pi$
$380$	−5.28777	−	9.15868i	−0.271257	−	0.469830i
$381$	−1.07798	+	1.86712i	−0.0552267	+	0.0956554i
$382$	−4.05890	−	15.1480i	−0.207671	−	0.775040i
$383$	3.97371	−	14.8301i	0.203047	−	0.757782i	−0.786989	−	0.616967i	$-0.788361\pi$
$383$	3.97371	−	14.8301i	0.203047	−	0.757782i	0.990036	−	0.140815i	$-0.0449723\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−1.04224	+	0.389403i	−0.0531177	+	0.0198458i
$386$	17.6658			0.899165
$387$	−6.01276	+	3.47147i	−0.305646	+	0.176465i
$388$	−1.51034	−	5.63667i	−0.0766760	−	0.286159i
$389$	−18.9577	−	10.9452i	−0.961192	−	0.554944i	−0.0646522	−	0.997908i	$-0.520594\pi$
$389$	−18.9577	−	10.9452i	−0.961192	−	0.554944i	−0.896540	+	0.442963i	$0.853927\pi$
$390$	6.94539	+	9.06618i	0.351693	+	0.459084i
$391$			6.82110i			0.344958i
$392$	−6.98272	−	0.491539i	−0.352681	−	0.0248265i
$393$	19.5683			0.987091
$394$	−6.18790	+	3.57259i	−0.311742	+	0.179984i
$395$	−39.8391	+	10.6749i	−2.00452	+	0.537110i
$396$	0.0343612	+	0.128238i	0.00172671	+	0.00644418i
$397$	10.6875	+	2.86371i	0.536391	+	0.143726i	0.516838	−	0.856083i	$-0.327109\pi$
$397$	10.6875	+	2.86371i	0.536391	+	0.143726i	0.0195531	+	0.999809i	$0.493776\pi$
$398$	−11.0492	+	11.0492i	−0.553846	+	0.553846i
$399$	−8.03720	−	3.66502i	−0.402363	−	0.183480i
$400$		−	5.03338i		−	0.251669i
$401$	2.15409	−	8.03917i	0.107570	−	0.401457i	−0.891054	−	0.453897i	$-0.850033\pi$
$401$	2.15409	−	8.03917i	0.107570	−	0.401457i	0.998624	+	0.0524404i	$0.0167000\pi$
$402$	6.35806	−	11.0125i	0.317111	−	0.549253i
$403$	−2.62869	−	6.36037i	−0.130944	−	0.316833i
$404$	−5.59248	+	3.22882i	−0.278236	+	0.160640i
$405$	2.23980	+	2.23980i	0.111296	+	0.111296i
$406$	−0.610528	−	6.35605i	−0.0303000	−	0.315445i
$407$			0.867245i			0.0429877i
$408$	3.12690	+	0.837849i	0.154804	+	0.0414797i
$409$	−24.7662	+	6.63609i	−1.22461	+	0.328134i	−0.812479	−	0.582990i	$-0.801883\pi$
$409$	−24.7662	+	6.63609i	−1.22461	+	0.328134i	−0.412132	+	0.911124i	$0.635216\pi$
$410$	18.5524	−	4.97110i	0.916237	−	0.245505i
$411$	18.3364	+	4.91322i	0.904466	+	0.242351i
$412$		−	12.0954i		−	0.595897i
$413$	−14.6784	+	10.4649i	−0.722277	+	0.514942i
$414$	−1.48994	−	1.48994i	−0.0732268	−	0.0732268i
$415$	1.29853	−	0.749706i	0.0637423	−	0.0368016i
$416$	−3.33218	+	1.37716i	−0.163374	+	0.0675209i
$417$	−6.26933	+	10.8588i	−0.307010	+	0.531757i
$418$	0.114722	−	0.428148i	0.00561123	−	0.0209414i
$419$		−	17.9834i		−	0.878545i	−0.898354	−	0.439273i	$-0.855236\pi$
$419$		−	17.9834i		−	0.878545i	0.898354	−	0.439273i	$-0.144764\pi$
$420$	−4.86503	−	6.82387i	−0.237389	−	0.332971i
$421$	7.80826	−	7.80826i	0.380552	−	0.380552i	−0.490749	−	0.871301i	$-0.663277\pi$
$421$	7.80826	−	7.80826i	0.380552	−	0.380552i	0.871301	+	0.490749i	$0.163277\pi$
$422$	−22.2280	−	5.95597i	−1.08204	−	0.289932i
$423$	2.06016	+	7.68863i	0.100169	+	0.373834i
$424$	−8.32429	+	2.23049i	−0.404263	+	0.108322i
$425$	−14.1111	+	8.14703i	−0.684488	+	0.395189i
$426$	−11.3002			−0.547499
$427$	22.4274	+	18.4965i	1.08534	+	0.895107i
$428$			4.10507i			0.198426i
$429$	−0.0628536	+	0.474533i	−0.00303460	+	0.0229107i
$430$	19.0457	+	10.9961i	0.918466	+	0.530277i
$431$	−0.877111	−	3.27342i	−0.0422489	−	0.157675i	0.941579	−	0.336793i	$-0.109342\pi$
$431$	−0.877111	−	3.27342i	−0.0422489	−	0.157675i	−0.983828	+	0.179118i	$0.942676\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	3.14209			0.150999			0.0754996	−	0.997146i	$-0.475945\pi$
$433$	3.14209			0.150999			0.0754996	+	0.997146i	$0.475945\pi$
$434$	1.76749	+	4.73073i	0.0848425	+	0.227082i
$435$	5.40557	−	5.40557i	0.259177	−	0.259177i
$436$	3.87315	−	14.4548i	0.185490	−	0.692259i
$437$	1.82079	+	6.79528i	0.0871002	+	0.325062i
$438$	−3.14883	+	5.45394i	−0.150457	+	0.260599i
$439$	−19.5705	−	33.8970i	−0.934047	−	1.61782i	−0.776324	−	0.630334i	$-0.782918\pi$
$439$	−19.5705	−	33.8970i	−0.934047	−	1.61782i	−0.157723	−	0.987483i	$-0.550415\pi$
$440$	0.297358	−	0.297358i	0.0141760	−	0.0141760i
$441$	−6.61757	−	2.28205i	−0.315122	−	0.108669i
$442$	9.25434	+	7.11269i	0.440184	+	0.338316i
$443$	−14.2259	−	24.6399i	−0.675892	−	1.17068i	−0.976207	−	0.216839i	$-0.930425\pi$
$443$	−14.2259	−	24.6399i	−0.675892	−	1.17068i	0.300316	−	0.953840i	$-0.402908\pi$
$444$	−6.30977	+	1.69070i	−0.299449	+	0.0802370i
$445$	27.3243	−	47.3270i	1.29530	−	2.24352i
$446$	−3.09569	−	5.36189i	−0.146585	−	0.253893i
$447$	4.03566	+	4.03566i	0.190880	+	0.190880i
$448$	2.47842	−	0.925986i	0.117094	−	0.0437487i
$449$	−2.60464	−	2.60464i	−0.122921	−	0.122921i	0.642970	−	0.765891i	$-0.277702\pi$
$449$	−2.60464	−	2.60464i	−0.122921	−	0.122921i	−0.765891	+	0.642970i	$0.777702\pi$
$450$	1.30273	−	4.86187i	0.0614115	−	0.229191i
$451$	0.697163	+	0.402507i	0.0328281	+	0.0189533i
$452$	−7.02939	−	4.05842i	−0.330635	−	0.190892i
$453$	−9.20838	−	2.46738i	−0.432647	−	0.115927i
$454$	−7.55959			−0.354789
$455$	−6.76721	−	29.4490i	−0.317252	−	1.38059i
$456$	3.33871			0.156349
$457$	−25.6138	−	6.86319i	−1.19816	−	0.321046i	−0.396054	−	0.918227i	$-0.629621\pi$
$457$	−25.6138	−	6.86319i	−1.19816	−	0.321046i	−0.802107	+	0.597181i	$0.796288\pi$
$458$	−13.3007	−	7.67919i	−0.621503	−	0.358825i
$459$	2.80350	+	1.61860i	0.130856	+	0.0755498i
$460$	−1.72745	+	6.44692i	−0.0805427	+	0.300589i
$461$	−11.5349	−	11.5349i	−0.537233	−	0.537233i	0.385482	−	0.922715i	$-0.374035\pi$
$461$	−11.5349	−	11.5349i	−0.537233	−	0.537233i	−0.922715	+	0.385482i	$0.874035\pi$
$462$	0.0580540	−	0.346423i	0.00270092	−	0.0161170i
$463$	−1.46395	−	1.46395i	−0.0680358	−	0.0680358i	0.672270	−	0.740306i	$-0.265319\pi$
$463$	−1.46395	−	1.46395i	−0.0680358	−	0.0680358i	−0.740306	+	0.672270i	$0.765319\pi$
$464$	1.20671	+	2.09008i	0.0560201	+	0.0970296i
$465$	−3.02306	+	5.23610i	−0.140191	+	0.242818i
$466$	22.4967	−	6.02798i	1.04214	−	0.279241i
$467$	14.4242	+	24.9834i	0.667471	+	1.15609i	0.978609	+	0.205729i	$0.0659565\pi$
$467$	14.4242	+	24.9834i	0.667471	+	1.15609i	−0.311138	+	0.950365i	$0.600710\pi$
$468$	−3.57507	+	0.467804i	−0.165258	+	0.0216243i
$469$	−27.3944	+	19.5306i	−1.26496	+	0.901841i
$470$	17.8285	−	17.8285i	0.822366	−	0.822366i
$471$	10.7687	+	18.6519i	0.496196	+	0.859436i
$472$	3.40676	−	5.90069i	0.156809	−	0.271601i
$473$	0.238567	+	0.890346i	0.0109693	+	0.0409381i
$474$	3.37007	−	12.5773i	0.154792	−	0.577692i
$475$	−11.8829	+	11.8829i	−0.545226	+	0.545226i
$476$	−6.60757	−	5.44943i	−0.302857	−	0.249774i
$477$	−8.61793			−0.394588
$478$	−12.1706	+	7.02673i	−0.556673	+	0.321395i
$479$	−8.31070	−	31.0160i	−0.379726	−	1.41716i	−0.846316	−	0.532682i	$-0.821184\pi$
$479$	−8.31070	−	31.0160i	−0.379726	−	1.41716i	0.466590	−	0.884474i	$-0.345482\pi$
$480$	2.74318	+	1.58378i	0.125208	+	0.0722891i
$481$	−23.3488	−	3.09264i	−1.06462	−	0.141012i
$482$		−	3.69359i		−	0.168238i
$483$	1.95114	+	5.22227i	0.0887801	+	0.237622i
$484$	−10.9824			−0.499199
$485$	−16.0079	+	9.24214i	−0.726879	+	0.419664i
$486$	−0.965926	+	0.258819i	−0.0438153	+	0.0117403i
$487$	3.84333	+	14.3435i	0.174158	+	0.649967i	0.996694	+	0.0812528i	$0.0258921\pi$
$487$	3.84333	+	14.3435i	0.174158	+	0.649967i	−0.822536	+	0.568714i	$0.807441\pi$
$488$	−10.6133	−	2.84383i	−0.480442	−	0.128734i
$489$	0.148157	−	0.148157i	0.00669990	−	0.00669990i
$490$	4.22067	+	21.7674i	0.190670	+	0.983353i
$491$		−	9.86395i		−	0.445154i	−0.974915	−	0.222577i	$-0.928553\pi$
$491$		−	9.86395i		−	0.445154i	0.974915	−	0.222577i	$-0.0714469\pi$
$492$	−1.56938	+	5.85701i	−0.0707532	+	0.264054i
$493$	3.90636	−	6.76601i	0.175934	−	0.304726i
$494$	11.1179	+	4.61546i	0.500219	+	0.207659i
$495$	0.364188	−	0.210264i	0.0163690	−	0.00945067i
$496$	−1.34970	−	1.34970i	−0.0606035	−	0.0606035i
$497$	27.2028	+	12.4047i	1.22021	+	0.556426i
$498$			0.473366i			0.0212121i
$499$	6.11829	+	1.63939i	0.273892	+	0.0733892i	0.393151	−	0.919474i	$-0.371385\pi$
$499$	6.11829	+	1.63939i	0.273892	+	0.0733892i	−0.119258	+	0.992863i	$0.538052\pi$
$500$	−0.102134	+	0.0273668i	−0.00456759	+	0.00122388i
$501$	2.78756	−	0.746926i	0.124539	−	0.0333702i
$502$	11.5763	+	3.10185i	0.516674	+	0.138442i
$503$			9.84473i			0.438955i	0.975618	+	0.219477i	$0.0704352\pi$
$503$			9.84473i			0.438955i	−0.975618	+	0.219477i	$0.929565\pi$
$504$	2.63363	−	0.252972i	0.117311	−	0.0112683i
$505$	14.4638	+	14.4638i	0.643630	+	0.643630i
$506$	−0.242263	+	0.139871i	−0.0107699	+	0.00621801i
$507$	−12.5517	−	3.38442i	−0.557442	−	0.150307i
$508$	−1.07798	+	1.86712i	−0.0478277	+	0.0828400i
$509$	−5.24046	+	19.5576i	−0.232279	+	0.866877i	0.747077	+	0.664737i	$0.231456\pi$
$509$	−5.24046	+	19.5576i	−0.232279	+	0.866877i	−0.979357	+	0.202140i	$0.935210\pi$
$510$		−	10.2540i		−	0.454055i
$511$	13.5671	−	9.67255i	0.600172	−	0.427889i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	3.22495	+	0.864122i	0.142385	+	0.0381519i
$514$	−7.85303	−	29.3079i	−0.346382	−	1.29272i
$515$	−37.0073	+	9.91608i	−1.63074	+	0.436955i
$516$	−6.01276	+	3.47147i	−0.264697	+	0.152823i
$517$	1.05676			0.0464763
$518$	17.0453	+	2.85648i	0.748928	+	0.125506i
$519$		−	13.2905i		−	0.583390i
$520$	6.94539	+	9.06618i	0.304575	+	0.397578i
$521$	2.42079	+	1.39765i	0.106057	+	0.0612319i	0.552090	−	0.833784i	$-0.313830\pi$
$521$	2.42079	+	1.39765i	0.106057	+	0.0612319i	−0.446033	+	0.895016i	$0.647164\pi$
$522$	0.624639	+	2.33118i	0.0273397	+	0.102033i
$523$	−28.8220	+	16.6404i	−1.26030	+	0.727633i	−0.973132	−	0.230248i	$-0.926046\pi$
$523$	−28.8220	+	16.6404i	−1.26030	+	0.727633i	−0.287165	+	0.957881i	$0.592713\pi$
$524$	19.5683			0.854846
$525$	−8.47309	+	10.2738i	−0.369796	+	0.448386i
$526$	−17.7910	+	17.7910i	−0.775727	+	0.775727i
$527$	−1.59926	+	5.96853i	−0.0696649	+	0.259993i
$528$	0.0343612	+	0.128238i	0.00149538	+	0.00558083i
$529$	−9.28007	+	16.0735i	−0.403481	+	0.698850i
$530$	13.6489	+	23.6405i	0.592869	+	1.02688i
$531$	4.81789	−	4.81789i	0.209079	−	0.209079i
$532$	−8.03720	−	3.66502i	−0.348457	−	0.158899i
$533$	−13.3228	+	17.3344i	−0.577076	+	0.750835i
$534$	8.62631	+	14.9412i	0.373297	+	0.646569i
$535$	12.5600	−	3.36543i	0.543015	−	0.145500i
$536$	6.35806	−	11.0125i	0.274627	−	0.475667i
$537$	−0.298456	−	0.516941i	−0.0128793	−	0.0223077i
$538$	−3.15837	−	3.15837i	−0.136167	−	0.136167i
$539$	−0.520032	+	0.770207i	−0.0223994	+	0.0331752i
$540$	2.23980	+	2.23980i	0.0963855	+	0.0963855i
$541$	−5.05346	+	18.8598i	−0.217265	+	0.810845i	0.768092	+	0.640340i	$0.221207\pi$
$541$	−5.05346	+	18.8598i	−0.217265	+	0.810845i	−0.985357	+	0.170505i	$0.945460\pi$
$542$	4.52391	+	2.61188i	0.194319	+	0.112190i
$543$	7.65470	+	4.41944i	0.328495	+	0.189656i
$544$	3.12690	+	0.837849i	0.134065	+	0.0359225i
$545$	−47.4015			−2.03046
$546$	9.11972	+	2.79835i	0.390288	+	0.119758i
$547$	26.5031			1.13319			0.566594	−	0.823997i	$-0.308261\pi$
$547$	26.5031			1.13319			0.566594	+	0.823997i	$0.308261\pi$
$548$	18.3364	+	4.91322i	0.783291	+	0.209882i
$549$	−9.51563	−	5.49385i	−0.406117	−	0.234472i
$550$	−0.578711	−	0.334119i	−0.0246763	−	0.0142469i
$551$	2.08549	−	7.78314i	0.0888447	−	0.331573i
$552$	−1.48994	−	1.48994i	−0.0634162	−	0.0634162i
$553$	−21.9192	+	26.5775i	−0.932098	+	1.13019i
$554$	−2.19494	−	2.19494i	−0.0932541	−	0.0932541i
$555$	10.3458	+	17.9194i	0.439154	+	0.760638i
$556$	−6.26933	+	10.8588i	−0.265879	+	0.460515i
$557$	3.72224	−	0.997371i	0.157716	−	0.0422600i	−0.179097	−	0.983831i	$-0.557318\pi$
$557$	3.72224	−	0.997371i	0.157716	−	0.0422600i	0.336813	+	0.941571i	$0.390651\pi$
$558$	−0.954385	−	1.65304i	−0.0404024	−	0.0699789i
$559$	−24.8215	+	3.24794i	−1.04984	+	0.137373i
$560$	−4.86503	−	6.82387i	−0.205585	−	0.288361i
$561$	0.303897	−	0.303897i	0.0128305	−	0.0128305i
$562$	5.01126	+	8.67975i	0.211387	+	0.366133i
$563$	−14.9206	+	25.8432i	−0.628826	+	1.08916i	0.358961	+	0.933352i	$0.383131\pi$
$563$	−14.9206	+	25.8432i	−0.628826	+	1.08916i	−0.987788	+	0.155807i	$0.950202\pi$
$564$	2.06016	+	7.68863i	0.0867485	+	0.323750i
$565$	−6.65437	+	24.8344i	−0.279951	+	1.04479i
$566$	21.9261	−	21.9261i	0.921622	−	0.921622i
$567$	2.60936	+	0.437281i	0.109583	+	0.0183641i
$568$	−11.3002			−0.474148
$569$	5.44783	−	3.14531i	0.228385	−	0.131858i	−0.381442	−	0.924393i	$-0.624572\pi$
$569$	5.44783	−	3.14531i	0.228385	−	0.131858i	0.609827	+	0.792535i	$0.291239\pi$
$570$	−2.73715	−	10.2152i	−0.114647	−	0.427867i
$571$	5.12924	+	2.96137i	0.214652	+	0.123929i	0.603472	−	0.797385i	$-0.293784\pi$
$571$	5.12924	+	2.96137i	0.214652	+	0.123929i	−0.388820	+	0.921314i	$0.627117\pi$
$572$	−0.0628536	+	0.474533i	−0.00262804	+	0.0198412i
$573$		−	15.6824i		−	0.655141i
$574$	10.2074	−	12.3767i	0.426048	−	0.516593i
$575$	10.6058			0.442294
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	−4.97088	+	1.33194i	−0.206941	+	0.0554496i	−0.360800	−	0.932643i	$-0.617496\pi$
$577$	−4.97088	+	1.33194i	−0.206941	+	0.0554496i	0.153859	+	0.988093i	$0.450830\pi$
$578$	1.68764	+	6.29835i	0.0701965	+	0.261977i
$579$	17.0638	+	4.57224i	0.709149	+	0.190016i
$580$	5.40557	−	5.40557i	0.224454	−	0.224454i
$581$	0.519630	−	1.13952i	0.0215579	−	0.0472754i
$582$		−	5.83551i		−	0.241890i
$583$	−0.296122	+	1.10514i	−0.0122641	+	0.0457704i
$584$	−3.14883	+	5.45394i	−0.130300	+	0.225686i
$585$	4.36223	+	10.5549i	0.180356	+	0.436389i
$586$	−10.4883	+	6.05540i	−0.433266	+	0.250146i
$587$	−21.2729	−	21.2729i	−0.878027	−	0.878027i	0.115304	−	0.993330i	$-0.463216\pi$
$587$	−21.2729	−	21.2729i	−0.878027	−	0.878027i	−0.993330	+	0.115304i	$0.963216\pi$
$588$	−6.61757	−	2.28205i	−0.272904	−	0.0941102i
$589$			6.37283i			0.262588i
$590$	−20.8468	−	5.58588i	−0.858249	−	0.229967i
$591$	−6.90171	+	1.84931i	−0.283898	+	0.0760704i
$592$	−6.30977	+	1.69070i	−0.259330	+	0.0694873i
$593$	−42.1148	−	11.2846i	−1.72945	−	0.463404i	−0.749393	−	0.662126i	$-0.769655\pi$
$593$	−42.1148	−	11.2846i	−1.72945	−	0.463404i	−0.980056	+	0.198721i	$0.936321\pi$
$594$			0.132761i			0.00544726i
$595$	−11.2562	+	24.6842i	−0.461458	+	1.01195i
$596$	4.03566	+	4.03566i	0.165307	+	0.165307i
$597$	−13.5324	+	7.81296i	−0.553846	+	0.319763i
$598$	−2.90182	−	7.02123i	−0.118664	−	0.287120i
$599$	−5.94701	+	10.3005i	−0.242988	+	0.420868i	−0.961564	−	0.274581i	$-0.911461\pi$
$599$	−5.94701	+	10.3005i	−0.242988	+	0.420868i	0.718576	+	0.695449i	$0.244794\pi$
$600$	1.30273	−	4.86187i	0.0531839	−	0.198485i
$601$		−	35.7070i		−	1.45652i	−0.685301	−	0.728260i	$-0.740329\pi$
$601$		−	35.7070i		−	1.45652i	0.685301	−	0.728260i	$-0.259671\pi$
$602$	18.2851	−	1.75637i	0.745246	−	0.0715843i
$603$	8.99166	−	8.99166i	0.366169	−	0.366169i
$604$	−9.20838	−	2.46738i	−0.374683	−	0.100396i
$605$	9.00360	+	33.6019i	0.366048	+	1.36611i
$606$	−6.23760	+	1.67136i	−0.253385	+	0.0678943i
$607$	−12.4957	+	7.21439i	−0.507185	+	0.292823i	−0.731676	−	0.681653i	$-0.761261\pi$
$607$	−12.4957	+	7.21439i	−0.507185	+	0.292823i	0.224491	+	0.974476i	$0.427928\pi$
$608$	3.33871			0.135403
$609$	1.05534	−	6.29749i	0.0427646	−	0.255187i
$610$			34.8041i			1.40918i
$611$	−3.76846	+	28.4512i	−0.152456	+	1.15101i
$612$	2.80350	+	1.61860i	0.113325	+	0.0654280i
$613$	−1.71583	−	6.40358i	−0.0693019	−	0.258638i	0.922579	−	0.385808i	$-0.126077\pi$
$613$	−1.71583	−	6.40358i	−0.0693019	−	0.258638i	−0.991881	+	0.127170i	$0.959411\pi$
$614$	−8.54437	+	4.93310i	−0.344823	+	0.199084i
$615$	19.2068			0.774495
$616$	0.0580540	−	0.346423i	0.00233906	−	0.0139578i
$617$	27.5574	−	27.5574i	1.10942	−	1.10942i	0.116192	−	0.993227i	$-0.462931\pi$
$617$	27.5574	−	27.5574i	1.10942	−	1.10942i	0.993227	−	0.116192i	$-0.0370687\pi$
$618$	3.13052	−	11.6833i	0.125928	−	0.469969i
$619$	11.8751	+	44.3183i	0.477299	+	1.78130i	0.612483	+	0.790484i	$0.290171\pi$
$619$	11.8751	+	44.3183i	0.477299	+	1.78130i	−0.135184	+	0.990821i	$0.543162\pi$
$620$	−3.02306	+	5.23610i	−0.121409	+	0.210287i
$621$	−1.05355	−	1.82480i	−0.0422775	−	0.0732268i
$622$	15.9113	−	15.9113i	0.637986	−	0.637986i
$623$	−4.36444	−	45.4370i	−0.174857	−	1.82040i
$624$	−3.57507	+	0.467804i	−0.143118	+	0.0187272i
$625$	−12.4160	−	21.5051i	−0.496640	−	0.860205i
$626$	25.3500	−	6.79251i	1.01319	−	0.271483i
$627$	0.221626	−	0.383867i	0.00885088	−	0.0153302i
$628$	10.7687	+	18.6519i	0.429718	+	0.744293i
$629$	14.9529	+	14.9529i	0.596210	+	0.596210i
$630$	−2.93311	−	7.85051i	−0.116858	−	0.312772i
$631$	−30.4681	−	30.4681i	−1.21291	−	1.21291i	−0.970064	−	0.242850i	$-0.921918\pi$
$631$	−30.4681	−	30.4681i	−1.21291	−	1.21291i	−0.242850	−	0.970064i	$-0.578082\pi$
$632$	3.37007	−	12.5773i	0.134054	−	0.500296i
$633$	−19.9291	−	11.5061i	−0.792110	−	0.457325i
$634$	23.0122	+	13.2861i	0.913930	+	0.527658i
$635$	6.59643	+	1.76751i	0.261771	+	0.0701414i
$636$	−8.61793			−0.341723
$637$	−18.8818	−	16.7474i	−0.748126	−	0.663557i
$638$	0.320409			0.0126851
$639$	−10.9152	−	2.92472i	−0.431799	−	0.115700i
$640$	2.74318	+	1.58378i	0.108434	+	0.0626042i
$641$	3.02599	+	1.74706i	0.119519	+	0.0690045i	0.558568	−	0.829459i	$-0.311351\pi$
$641$	3.02599	+	1.74706i	0.119519	+	0.0690045i	−0.439048	+	0.898463i	$0.644684\pi$
$642$	−1.06247	+	3.96520i	−0.0419324	+	0.156494i
$643$	10.5150	+	10.5150i	0.414670	+	0.414670i	0.883362	−	0.468692i	$-0.155275\pi$
$643$	10.5150	+	10.5150i	0.414670	+	0.414670i	−0.468692	+	0.883362i	$0.655275\pi$
$644$	1.95114	+	5.22227i	0.0768859	+	0.205786i
$645$	15.5508	+	15.5508i	0.612311	+	0.612311i
$646$	−5.40404	−	9.36006i	−0.212619	−	0.368267i
$647$	2.59053	−	4.48692i	0.101844	−	0.176399i	−0.810600	−	0.585600i	$-0.800859\pi$
$647$	2.59053	−	4.48692i	0.101844	−	0.176399i	0.912444	+	0.409201i	$0.134192\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−0.452286	−	0.783383i	−0.0177538	−	0.0307505i
$650$	11.0592	−	14.3892i	0.433778	−	0.564389i
$651$	0.482866	+	5.02700i	0.0189250	+	0.197023i
$652$	0.148157	−	0.148157i	0.00580228	−	0.00580228i
$653$	−0.687303	−	1.19044i	−0.0268962	−	0.0465857i	0.852264	−	0.523112i	$-0.175229\pi$
$653$	−0.687303	−	1.19044i	−0.0268962	−	0.0465857i	−0.879160	+	0.476526i	$0.841896\pi$
$654$	7.48235	−	12.9598i	0.292583	−	0.506769i
$655$	−16.0426	−	59.8716i	−0.626834	−	2.33938i
$656$	−1.56938	+	5.85701i	−0.0612741	+	0.228678i
$657$	−4.45312	+	4.45312i	−0.173733	+	0.173733i
$658$	3.48070	−	20.7702i	0.135692	−	0.809706i
$659$	−41.5643			−1.61911			−0.809557	−	0.587042i	$-0.800293\pi$
$659$	−41.5643			−1.61911			−0.809557	+	0.587042i	$0.800293\pi$
$660$	0.364188	−	0.210264i	0.0141760	−	0.00818452i
$661$	−6.83007	−	25.4902i	−0.265659	−	0.991453i	−0.961846	−	0.273592i	$-0.911788\pi$
$661$	−6.83007	−	25.4902i	−0.265659	−	0.991453i	0.696187	−	0.717861i	$-0.254879\pi$
$662$	7.41727	+	4.28236i	0.288280	+	0.166439i
$663$	7.09810	+	9.26553i	0.275668	+	0.359843i
$664$			0.473366i			0.0183702i
$665$	−4.62448	+	27.5954i	−0.179330	+	1.07010i
$666$	−6.53236			−0.253124
$667$	−4.40401	+	2.54266i	−0.170524	+	0.0984520i
$668$	2.78756	−	0.746926i	0.107854	−	0.0288994i
$669$	−1.60245	−	5.98041i	−0.0619541	−	0.231216i
$670$	−38.9065	−	10.4250i	−1.50309	−	0.402752i
$671$	−1.03149	+	1.03149i	−0.0398201	+	0.0398201i
$672$	2.63363	−	0.252972i	0.101594	−	0.00975862i
$673$			14.1537i			0.545587i	0.962073	+	0.272793i	$0.0879476\pi$
$673$			14.1537i			0.545587i	−0.962073	+	0.272793i	$0.912052\pi$
$674$	−1.96496	+	7.33332i	−0.0756873	+	0.282469i
$675$	2.51669	−	4.35904i	0.0968675	−	0.167779i
$676$	−12.5517	−	3.38442i	−0.482759	−	0.130170i
$677$	−32.5882	+	18.8148i	−1.25247	+	0.723113i	−0.971599	−	0.236634i	$-0.923956\pi$
$677$	−32.5882	+	18.8148i	−1.25247	+	0.723113i	−0.280869	+	0.959746i	$0.590623\pi$
$678$	−5.73947	−	5.73947i	−0.220423	−	0.220423i
$679$	−6.40584	+	14.0477i	−0.245834	+	0.539101i
$680$		−	10.2540i		−	0.393223i
$681$	−7.30201	−	1.95657i	−0.279813	−	0.0749758i
$682$	−0.244776	+	0.0655876i	−0.00937296	+	0.00251148i
$683$	41.6157	−	11.1509i	1.59238	−	0.426677i	0.649651	−	0.760233i	$-0.274915\pi$
$683$	41.6157	−	11.1509i	1.59238	−	0.426677i	0.942731	+	0.333555i	$0.108248\pi$
$684$	3.22495	+	0.864122i	0.123309	+	0.0330405i
$685$		−	60.1303i		−	2.29746i
$686$	13.4252	+	12.7579i	0.512578	+	0.487097i
$687$	−10.8600	−	10.8600i	−0.414335	−	0.414335i
$688$	−6.01276	+	3.47147i	−0.229234	+	0.132349i
$689$	−28.6978	−	11.9135i	−1.09330	−	0.453868i
$690$	−3.33717	+	5.78015i	−0.127044	+	0.220047i
$691$	9.17273	−	34.2331i	0.348947	−	1.30229i	−0.538985	−	0.842315i	$-0.681192\pi$
$691$	9.17273	−	34.2331i	0.348947	−	1.30229i	0.887933	−	0.459974i	$-0.152141\pi$
$692$		−	13.2905i		−	0.505230i
$693$	0.145737	−	0.319593i	0.00553608	−	0.0121403i
$694$	−2.83797	+	2.83797i	−0.107728	+	0.107728i
$695$	38.3635	+	10.2795i	1.45521	+	0.389923i
$696$	0.624639	+	2.33118i	0.0236769	+	0.0883633i
$697$	18.9603	−	5.08040i	0.718173	−	0.192434i
$698$	18.3495	−	10.5941i	0.694540	−	0.400993i
$699$	23.2903			0.880921
$700$	−8.47309	+	10.2738i	−0.320253	+	0.388314i
$701$			22.0570i			0.833081i	0.909117	+	0.416540i	$0.136758\pi$
$701$			22.0570i			0.833081i	−0.909117	+	0.416540i	$0.863242\pi$
$702$	−3.57433	−	0.473433i	−0.134905	−	0.0178686i
$703$	18.8877	+	10.9048i	0.712364	+	0.411283i
$704$	0.0343612	+	0.128238i	0.00129504	+	0.00483314i
$705$	21.8353	−	12.6066i	0.822366	−	0.474793i
$706$	−24.2850			−0.913979
$707$	16.8503	+	2.82380i	0.633722	+	0.106200i
$708$	4.81789	−	4.81789i	0.181067	−	0.181067i
$709$	8.07082	−	30.1207i	0.303106	−	1.13121i	−0.631458	−	0.775410i	$-0.717543\pi$
$709$	8.07082	−	30.1207i	0.303106	−	1.13121i	0.934564	−	0.355796i	$-0.115790\pi$
$710$	9.26420	+	34.5745i	0.347679	+	1.29756i
$711$	6.51047	−	11.2765i	0.244162	−	0.422900i
$712$	8.62631	+	14.9412i	0.323285	+	0.559945i
$713$	2.84396	−	2.84396i	0.106507	−	0.106507i
$714$	−4.97200	−	6.97391i	−0.186072	−	0.260992i
$715$	1.50342	−	0.196725i	0.0562247	−	0.00735709i
$716$	−0.298456	−	0.516941i	−0.0111538	−	0.0193190i
$717$	−13.5746	+	3.63730i	−0.506953	+	0.135838i
$718$	5.36954	−	9.30032i	0.200390	−	0.347085i
$719$	−12.7941	−	22.1601i	−0.477141	−	0.826433i	0.522516	−	0.852630i	$-0.324994\pi$
$719$	−12.7941	−	22.1601i	−0.477141	−	0.826433i	−0.999657	+	0.0261969i	$0.991660\pi$
$720$	2.23980	+	2.23980i	0.0834723	+	0.0834723i
$721$	−20.3611	+	24.6883i	−0.758288	+	0.919442i
$722$	5.55292	+	5.55292i	0.206658	+	0.206658i
$723$	0.955972	−	3.56773i	0.0355530	−	0.132685i
$724$	7.65470	+	4.41944i	0.284485	+	0.164247i
$725$	−10.5202	−	6.07383i	−0.390710	−	0.225576i
$726$	−10.6082	−	2.84245i	−0.393706	−	0.105493i
$727$	−4.02875			−0.149418			−0.0747090	−	0.997205i	$-0.523803\pi$
$727$	−4.02875			−0.149418			−0.0747090	+	0.997205i	$0.523803\pi$
$728$	9.11972	+	2.79835i	0.337999	+	0.103714i
$729$	−1.00000			−0.0370370
$730$	19.2685	+	5.16297i	0.713158	+	0.191090i
$731$	19.4645	+	11.2378i	0.719921	+	0.415646i
$732$	−9.51563	−	5.49385i	−0.351708	−	0.203059i
$733$	−1.16395	+	4.34392i	−0.0429914	+	0.160446i	−0.984084	−	0.177702i	$-0.943134\pi$
$733$	−1.16395	+	4.34392i	−0.0429914	+	0.160446i	0.941093	+	0.338148i	$0.109800\pi$
$734$	0.799861	+	0.799861i	0.0295234	+	0.0295234i
$735$	−1.55698	+	22.1181i	−0.0574299	+	0.815839i
$736$	−1.48994	−	1.48994i	−0.0549201	−	0.0549201i
$737$	−0.844105	−	1.46203i	−0.0310930	−	0.0538547i
$738$	−3.03181	+	5.25125i	−0.111603	+	0.193301i
$739$	−13.9113	+	3.72751i	−0.511734	+	0.137119i	−0.505441	−	0.862861i	$-0.668670\pi$
$739$	−13.9113	+	3.72751i	−0.511734	+	0.137119i	−0.00629360	+	0.999980i	$0.502003\pi$
$740$	10.3458	+	17.9194i	0.380319	+	0.658732i
$741$	9.54453	+	7.33572i	0.350627	+	0.269484i
$742$	20.7457	+	9.46020i	0.761600	+	0.347295i
$743$	28.8005	−	28.8005i	1.05659	−	1.05659i	0.0582865	−	0.998300i	$-0.481436\pi$
$743$	28.8005	−	28.8005i	1.05659	−	1.05659i	0.998300	−	0.0582865i	$-0.0185637\pi$
$744$	−0.954385	−	1.65304i	−0.0349895	−	0.0606035i
$745$	9.03905	−	15.6561i	0.331165	−	0.573595i
$746$	7.57485	+	28.2697i	0.277335	+	1.03503i
$747$	−0.122516	+	0.457237i	−0.00448263	+	0.0167294i
$748$	0.303897	−	0.303897i	0.0111116	−	0.0111116i
$749$	6.91040	−	8.37901i	0.252500	−	0.306163i
$750$	−0.105737			−0.00386098
$751$	22.0684	−	12.7412i	0.805286	−	0.464932i	−0.0400304	−	0.999198i	$-0.512745\pi$
$751$	22.0684	−	12.7412i	0.805286	−	0.464932i	0.845316	+	0.534267i	$0.179412\pi$
$752$	2.06016	+	7.68863i	0.0751264	+	0.280376i
$753$	10.3790	+	5.99231i	0.378231	+	0.218372i
$754$	−1.14259	+	8.62636i	−0.0416108	+	0.314154i
$755$			30.1969i			1.09898i
$756$	2.60936	+	0.437281i	0.0949017	+	0.0159038i
$757$	31.4162			1.14184			0.570921	−	0.821005i	$-0.306586\pi$
$757$	31.4162			1.14184			0.570921	+	0.821005i	$0.306586\pi$
$758$	−11.5467	+	6.66648i	−0.419394	+	0.242137i
$759$	−0.270209	+	0.0724024i	−0.00980798	+	0.00262804i
$760$	−2.73715	−	10.2152i	−0.0992869	−	0.370544i
$761$	−26.8440	−	7.19283i	−0.973095	−	0.260740i	−0.262961	−	0.964807i	$-0.584699\pi$
$761$	−26.8440	−	7.19283i	−0.973095	−	0.260740i	−0.710134	+	0.704067i	$0.751366\pi$
$762$	−1.52450	+	1.52450i	−0.0552267	+	0.0552267i
$763$	−32.2385	+	22.9842i	−1.16711	+	0.832084i
$764$		−	15.6824i		−	0.567369i
$765$	2.65393	−	9.90460i	0.0959530	−	0.358102i
$766$	7.67662	−	13.2963i	0.277368	−	0.480415i
$767$	22.7039	−	9.38332i	0.819790	−	0.338812i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−35.0151	−	35.0151i	−1.26268	−	1.26268i	−0.949790	−	0.312889i	$-0.898703\pi$
$769$	−35.0151	−	35.0151i	−1.26268	−	1.26268i	−0.312889	−	0.949790i	$-0.601297\pi$
$770$	−1.10752	+	0.106382i	−0.0399121	+	0.00383374i
$771$		−	30.3418i		−	1.09273i
$772$	17.0638	+	4.57224i	0.614141	+	0.164559i
$773$	36.6470	−	9.81954i	1.31810	−	0.353184i	0.469835	−	0.882754i	$-0.344313\pi$
$773$	36.6470	−	9.81954i	1.31810	−	0.353184i	0.848266	+	0.529570i	$0.177647\pi$
$774$	−6.70636	+	1.79696i	−0.241055	+	0.0645906i
$775$	9.28020	+	2.48662i	0.333355	+	0.0893221i
$776$		−	5.83551i		−	0.209483i
$777$	15.7252	+	7.17080i	0.564138	+	0.257251i
$778$	−15.4789	−	15.4789i	−0.554944	−	0.554944i
$779$	17.5324	−	10.1223i	0.628164	−	0.362671i
$780$	4.36223	+	10.5549i	0.156193	+	0.377924i
$781$	−0.750118	+	1.29924i	−0.0268413	+	0.0464906i
$782$	−1.76543	+	6.58868i	−0.0631317	+	0.235611i
$783$			2.41342i			0.0862485i
$784$	−6.61757	−	2.28205i	−0.236342	−	0.0815018i
$785$	48.2394	−	48.2394i	1.72174	−	1.72174i
$786$	18.9015	+	5.06466i	0.674196	+	0.180650i
$787$	13.8492	+	51.6860i	0.493671	+	1.84241i	0.537347	+	0.843361i	$0.319427\pi$
$787$	13.8492	+	51.6860i	0.493671	+	1.84241i	−0.0436756	+	0.999046i	$0.513907\pi$
$788$	−6.90171	+	1.84931i	−0.245863	+	0.0658789i
$789$	−21.7895	+	12.5802i	−0.775727	+	0.447866i
$790$	−41.2445			−1.46741
$791$	7.51608	+	20.1169i	0.267241	+	0.715275i
$792$			0.132761i			0.00471747i
$793$	−24.0924	−	31.4491i	−0.855546	−	1.11679i
$794$	9.58216	+	5.53227i	0.340058	+	0.196333i
$795$	7.06518	+	26.3676i	0.250576	+	0.935162i
$796$	−13.5324	+	7.81296i	−0.479644	+	0.276923i
$797$	19.8240			0.702201			0.351100	−	0.936338i	$-0.385808\pi$
$797$	19.8240			0.702201			0.351100	+	0.936338i	$0.385808\pi$
$798$	−6.81476	−	5.62031i	−0.241240	−	0.198957i
$799$	18.2205	−	18.2205i	0.644594	−	0.644594i
$800$	1.30273	−	4.86187i	0.0460586	−	0.171893i
$801$	4.46531	+	16.6648i	0.157774	+	0.588820i
$802$	4.16138	−	7.20772i	0.146943	−	0.254513i
$803$	0.418043	+	0.724072i	0.0147524	+	0.0255519i
$804$	8.99166	−	8.99166i	0.317111	−	0.317111i
$805$	14.3786	−	10.2511i	0.506778	−	0.361304i
$806$	−0.892931	−	6.82400i	−0.0314521	−	0.240365i
$807$	−2.23331	−	3.86820i	−0.0786162	−	0.136167i
$808$	−6.23760	+	1.67136i	−0.219438	+	0.0587982i
$809$	−20.8295	+	36.0777i	−0.732326	+	1.26843i	0.223561	+	0.974690i	$0.428232\pi$
$809$	−20.8295	+	36.0777i	−0.732326	+	1.26843i	−0.955887	+	0.293736i	$0.905101\pi$
$810$	1.58378	+	2.74318i	0.0556482	+	0.0963855i
$811$	23.1115	+	23.1115i	0.811556	+	0.811556i	0.984867	−	0.173311i	$-0.0554467\pi$
$811$	23.1115	+	23.1115i	0.811556	+	0.811556i	−0.173311	+	0.984867i	$0.555447\pi$
$812$	1.05534	−	6.29749i	0.0370352	−	0.220999i
$813$	3.69376	+	3.69376i	0.129546	+	0.129546i
$814$	−0.224459	+	0.837694i	−0.00786730	+	0.0293612i
$815$	−0.574767	−	0.331842i	−0.0201332	−	0.0116239i
$816$	2.80350	+	1.61860i	0.0981420	+	0.0566623i
$817$	22.3906	+	5.99954i	0.783348	+	0.209897i
$818$	−25.6399			−0.896478
$819$	8.08470	+	5.06335i	0.282502	+	0.176928i
$820$	19.2068			0.670732
$821$	33.3532	+	8.93697i	1.16404	+	0.311902i	0.788576	−	0.614937i	$-0.210819\pi$
$821$	33.3532	+	8.93697i	1.16404	+	0.311902i	0.375459	+	0.926839i	$0.377485\pi$
$822$	16.4399	+	9.49160i	0.573409	+	0.331058i
$823$	10.3596	+	5.98112i	0.361113	+	0.208489i	0.669569	−	0.742750i	$-0.266479\pi$
$823$	10.3596	+	5.98112i	0.361113	+	0.208489i	−0.308456	+	0.951239i	$0.599812\pi$
$824$	3.13052	−	11.6833i	0.109057	−	0.407006i
$825$	−0.472516	−	0.472516i	−0.0164509	−	0.0164509i
$826$	−16.8868	+	6.30923i	−0.587565	+	0.219526i
$827$	21.4792	+	21.4792i	0.746906	+	0.746906i	0.973897	−	0.226991i	$-0.0728887\pi$
$827$	21.4792	+	21.4792i	0.746906	+	0.746906i	−0.226991	+	0.973897i	$0.572889\pi$
$828$	−1.05355	−	1.82480i	−0.0366134	−	0.0634162i
$829$	−8.11868	+	14.0620i	−0.281974	+	0.488392i	−0.971871	−	0.235515i	$-0.924322\pi$
$829$	−8.11868	+	14.0620i	−0.281974	+	0.488392i	0.689897	+	0.723907i	$0.257656\pi$
$830$	1.44832	−	0.388076i	0.0502720	−	0.0134703i
$831$	−1.55206	−	2.68824i	−0.0538403	−	0.0932541i
$832$	−3.57507	+	0.467804i	−0.123943	+	0.0162182i
$833$	4.31347	+	22.2461i	0.149453	+	0.770781i
$834$	−8.86617	+	8.86617i	−0.307010	+	0.307010i
$835$	−4.57062	−	7.91654i	−0.158173	−	0.273963i
$836$	0.221626	−	0.383867i	0.00766509	−	0.0132763i
$837$	−0.494026	−	1.84373i	−0.0170760	−	0.0637287i
$838$	4.65444	−	17.3706i	0.160785	−	0.600058i
$839$	−2.56377	+	2.56377i	−0.0885113	+	0.0885113i	−0.749976	−	0.661465i	$-0.769935\pi$
$839$	−2.56377	+	2.56377i	−0.0885113	+	0.0885113i	0.661465	+	0.749976i	$0.269935\pi$
$840$	−2.93311	−	7.85051i	−0.101202	−	0.270868i
$841$	−23.1754			−0.799152
$842$	9.56313	−	5.52128i	0.329567	−	0.190276i
$843$	2.59402	+	9.68100i	0.0893427	+	0.333431i
$844$	−19.9291	−	11.5061i	−0.685987	−	0.396055i
$845$	−0.0648439	+	41.1781i	−0.00223070	+	1.41657i
$846$			7.95986i			0.273666i
$847$	22.4165	+	18.4875i	0.770241	+	0.635238i
$848$	−8.61793			−0.295941
$849$	26.8539	−	15.5041i	0.921622	−	0.532099i
$850$	−15.7389	+	4.21721i	−0.539838	+	0.144649i
$851$	−3.56247	−	13.2953i	−0.122120	−	0.455758i
$852$	−10.9152	−	2.92472i	−0.373949	−	0.100199i
$853$	17.6718	−	17.6718i	0.605071	−	0.605071i	−0.336583	−	0.941654i	$-0.609271\pi$
$853$	17.6718	−	17.6718i	0.605071	−	0.605071i	0.941654	+	0.336583i	$0.109271\pi$
$854$	16.8760	+	23.6709i	0.577484	+	0.810000i
$855$		−	10.5755i		−	0.361676i
$856$	−1.06247	+	3.96520i	−0.0363145	+	0.135528i
$857$	18.3964	−	31.8635i	0.628410	−	1.08844i	−0.359461	−	0.933160i	$-0.617039\pi$
$857$	18.3964	−	31.8635i	0.628410	−	1.08844i	0.987871	−	0.155278i	$-0.0496272\pi$
$858$	−0.183530	+	0.442096i	−0.00626562	+	0.0150929i
$859$	0.678380	−	0.391663i	0.0231460	−	0.0133634i	−0.488382	−	0.872630i	$-0.662413\pi$
$859$	0.678380	−	0.391663i	0.0231460	−	0.0133634i	0.511528	+	0.859266i	$0.329080\pi$
$860$	15.5508	+	15.5508i	0.530277	+	0.530277i
$861$	13.0629	−	9.31309i	0.445182	−	0.317389i
$862$		−	3.38889i		−	0.115426i
$863$	22.3491	+	5.98844i	0.760774	+	0.203849i	0.618292	−	0.785949i	$-0.287825\pi$
$863$	22.3491	+	5.98844i	0.760774	+	0.203849i	0.142482	+	0.989797i	$0.454492\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	−40.6640	+	10.8959i	−1.38262	+	0.370471i
$866$	3.03502	+	0.813232i	0.103134	+	0.0276348i
$867$			6.52054i			0.221449i
$868$	0.482866	+	5.02700i	0.0163895	+	0.170627i
$869$	−1.22236	−	1.22236i	−0.0414657	−	0.0414657i
$870$	6.62044	−	3.82231i	0.224454	−	0.129589i
$871$	42.3724	−	17.5122i	1.43574	−	0.593377i
$872$	7.48235	−	12.9598i	0.253384	−	0.438875i
$873$	1.51034	−	5.63667i	0.0511173	−	0.190772i
$874$			7.03499i			0.237962i
$875$	0.254539	+	0.116071i	0.00860498	+	0.00392393i
$876$	−4.45312	+	4.45312i	−0.150457	+	0.150457i
$877$	−54.9809	−	14.7321i	−1.85657	−	0.497467i	−0.856739	−	0.515750i	$-0.827513\pi$
$877$	−54.9809	−	14.7321i	−1.85657	−	0.497467i	−0.999833	+	0.0182827i	$0.994180\pi$
$878$	−10.1304	−	37.8072i	−0.341885	−	1.27593i
$879$	−11.6981	+	3.13451i	−0.394568	+	0.105724i
$880$	0.364188	−	0.210264i	0.0122768	−	0.00708800i
$881$	36.3094			1.22329			0.611647	−	0.791131i	$-0.290507\pi$
$881$	36.3094			1.22329			0.611647	+	0.791131i	$0.290507\pi$
$882$	−5.80144	−	3.91705i	−0.195345	−	0.131894i
$883$			48.4701i			1.63115i	0.578653	+	0.815574i	$0.303579\pi$
$883$			48.4701i			1.63115i	−0.578653	+	0.815574i	$0.696421\pi$
$884$	7.09810	+	9.26553i	0.238735	+	0.311633i
$885$	−18.6907	−	10.7911i	−0.628282	−	0.362739i
$886$	−7.36386	−	27.4823i	−0.247394	−	0.923285i
$887$	7.20573	−	4.16023i	0.241945	−	0.139687i	−0.374125	−	0.927378i	$-0.622057\pi$
$887$	7.20573	−	4.16023i	0.241945	−	0.139687i	0.616070	+	0.787691i	$0.288724\pi$
$888$	−6.53236			−0.219212
$889$	5.34338	−	1.99639i	0.179211	−	0.0669568i
$890$	38.6424	−	38.6424i	1.29530	−	1.29530i
$891$	−0.0343612	+	0.128238i	−0.00115114	+	0.00429612i
$892$	−1.60245	−	5.98041i	−0.0536539	−	0.200239i
$893$	13.2878	−	23.0152i	0.444660	−	0.770174i
$894$	2.85364	+	4.94265i	0.0954400	+	0.165307i
$895$	−1.33696	+	1.33696i	−0.0446897	+	0.0446897i
$896$	2.63363	−	0.252972i	0.0879834	−	0.00845121i
$897$	−0.985710	−	7.53304i	−0.0329119	−	0.251521i
$898$	−1.84176	−	3.19002i	−0.0614604	−	0.106452i
$899$	−4.44969	+	1.19229i	−0.148406	+	0.0397652i
$900$	2.51669	−	4.35904i	0.0838897	−	0.145301i
$901$	13.9490	+	24.1604i	0.464708	+	0.804898i
$902$	0.569232	+	0.569232i	0.0189533	+	0.0189533i
$903$	18.1167	+	3.03601i	0.602885	+	0.101032i
$904$	−5.73947	−	5.73947i	−0.190892	−	0.190892i
$905$	7.24632	−	27.0436i	0.240876	−	0.898961i
$906$	−8.25600	−	4.76661i	−0.274287	−	0.158360i
$907$	37.1412	+	21.4435i	1.23325	+	0.712019i	0.967706	−	0.252080i	$-0.0811145\pi$
$907$	37.1412	+	21.4435i	1.23325	+	0.712019i	0.265546	+	0.964098i	$0.414448\pi$
$908$	−7.30201	−	1.95657i	−0.242326	−	0.0649309i
$909$	−6.45763			−0.214186
$910$	1.08533	−	30.1970i	0.0359784	−	1.00102i
$911$	−13.3641			−0.442774			−0.221387	−	0.975186i	$-0.571058\pi$
$911$	−13.3641			−0.442774			−0.221387	+	0.975186i	$0.571058\pi$
$912$	3.22495	+	0.864122i	0.106789	+	0.0286139i
$913$	0.0544251	+	0.0314224i	0.00180121	+	0.00103993i
$914$	−22.9647	−	13.2587i	−0.759604	−	0.438557i
$915$	−9.00797	+	33.6182i	−0.297794	+	1.11138i
$916$	−10.8600	−	10.8600i	−0.358825	−	0.358825i
$917$	−39.9416	−	32.9409i	−1.31899	−	1.08780i
$918$	2.28905	+	2.28905i	0.0755498	+	0.0755498i
$919$	−4.12875	−	7.15121i	−0.136195	−	0.235897i	0.789858	−	0.613289i	$-0.210154\pi$
$919$	−4.12875	−	7.15121i	−0.136195	−	0.235897i	−0.926053	+	0.377393i	$0.876821\pi$
$920$	−3.33717	+	5.78015i	−0.110023	+	0.190566i
$921$	−9.53001	+	2.55356i	−0.314025	+	0.0841426i
$922$	−8.15640	−	14.1273i	−0.268617	−	0.465258i
$923$	−32.3046	−	24.8286i	−1.06332	−	0.817243i
$924$	0.145737	−	0.319593i	0.00479438	−	0.0105138i
$925$	23.2496	−	23.2496i	0.764441	−	0.764441i
$926$	−1.03517	−	1.79297i	−0.0340179	−	0.0589207i
$927$	6.04770	−	10.4749i	0.198632	−	0.344042i
$928$	0.624639	+	2.33118i	0.0205048	+	0.0765248i
$929$	11.4545	−	42.7488i	0.375810	−	1.40254i	−0.476347	−	0.879257i	$-0.658039\pi$
$929$	11.4545	−	42.7488i	0.375810	−	1.40254i	0.852157	−	0.523286i	$-0.175294\pi$
$930$	−4.27526	+	4.27526i	−0.140191	+	0.140191i
$931$	10.2354	+	21.0104i	0.335452	+	0.688589i
$932$	23.2903			0.762900
$933$	19.4873	−	11.2510i	0.637986	−	0.368342i
$934$	7.46650	+	27.8654i	0.244311	+	0.911782i
$935$	−1.17895	−	0.680667i	−0.0385558	−	0.0222602i
$936$	−3.57433	−	0.473433i	−0.116831	−	0.0154747i
$937$		−	9.36599i		−	0.305973i	−0.988228	−	0.152987i	$-0.951111\pi$
$937$		−	9.36599i		−	0.305973i	0.988228	−	0.152987i	$-0.0488892\pi$
$938$	−31.5159	+	11.7750i	−1.02903	+	0.384466i
$939$	26.2442			0.856448
$940$	21.8353	−	12.6066i	0.712190	−	0.411183i
$941$	−22.1054	+	5.92312i	−0.720615	+	0.193088i	−0.600446	−	0.799665i	$-0.705010\pi$
$941$	−22.1054	+	5.92312i	−0.720615	+	0.193088i	−0.120169	+	0.992753i	$0.538344\pi$
$942$	5.57429	+	20.8035i	0.181620	+	0.677816i
$943$	−12.3413	−	3.30684i	−0.401888	−	0.107686i
$944$	4.81789	−	4.81789i	0.156809	−	0.156809i
$945$	−0.801303	−	8.34216i	−0.0260664	−	0.271370i
$946$			0.921754i			0.0299688i
$947$	0.200663	−	0.748885i	0.00652068	−	0.0243355i	−0.962589	−	0.270966i	$-0.912657\pi$
$947$	0.200663	−	0.748885i	0.00652068	−	0.0243355i	0.969110	+	0.246631i	$0.0793235\pi$
$948$	6.51047	−	11.2765i	0.211450	−	0.366242i
$949$	−20.9850	+	8.67290i	−0.681200	+	0.281534i
$950$	−14.5536	+	8.40250i	−0.472180	+	0.272613i
$951$	18.7894	+	18.7894i	0.609287	+	0.609287i
$952$	−4.97200	−	6.97391i	−0.161143	−	0.226026i
$953$			26.2222i			0.849421i	0.905329	+	0.424711i	$0.139624\pi$
$953$			26.2222i			0.849421i	−0.905329	+	0.424711i	$0.860376\pi$
$954$	−8.32429	−	2.23049i	−0.269509	−	0.0722146i
$955$	−47.9821	+	12.8568i	−1.55266	+	0.416035i
$956$	−13.5746	+	3.63730i	−0.439034	+	0.117639i
$957$	0.309491	+	0.0829279i	0.0100044	+	0.00268068i
$958$		−	32.1101i		−	1.03743i
$959$	−29.1562	−	40.8956i	−0.941503	−	1.32059i
$960$	2.23980	+	2.23980i	0.0722891	+	0.0722891i
$961$	−23.6915	+	13.6783i	−0.764242	+	0.441235i
$962$	−21.7528	−	9.03038i	−0.701339	−	0.291151i
$963$	−2.05254	+	3.55510i	−0.0661421	+	0.114561i
$964$	0.955972	−	3.56773i	0.0307898	−	0.114909i
$965$		−	55.9573i		−	1.80133i
$966$	0.533038	+	5.54932i	0.0171502	+	0.178546i
$967$	36.6449	−	36.6449i	1.17842	−	1.17842i	0.198273	−	0.980147i	$-0.436467\pi$
$967$	36.6449	−	36.6449i	1.17842	−	1.17842i	0.980147	−	0.198273i	$-0.0635331\pi$
$968$	−10.6082	−	2.84245i	−0.340959	−	0.0913597i
$969$	−2.79733	−	10.4398i	−0.0898633	−	0.335375i
$970$	−17.8544	+	4.78408i	−0.573272	+	0.153608i
$971$	39.7725	−	22.9627i	1.27636	−	0.736907i	0.300184	−	0.953881i	$-0.402952\pi$
$971$	39.7725	−	22.9627i	1.27636	−	0.736907i	0.976177	+	0.216974i	$0.0696186\pi$
$972$	−1.00000			−0.0320750
$973$	31.0760	−	11.6106i	0.996251	−	0.372219i
$974$			14.8495i			0.475809i
$975$	14.4066	−	11.0365i	0.461379	−	0.353452i
$976$	−9.51563	−	5.49385i	−0.304588	−	0.175854i
$977$	−4.45814	−	16.6380i	−0.142629	−	0.532297i	−0.999850	−	0.0173484i	$-0.994478\pi$
$977$	−4.45814	−	16.6380i	−0.142629	−	0.532297i	0.857221	−	0.514949i	$-0.172189\pi$
$978$	0.181455	−	0.104763i	0.00580228	−	0.00334995i
$979$	2.29048			0.0732041
$980$	−1.55698	+	22.1181i	−0.0497358	+	0.706538i
$981$	10.5816	−	10.5816i	0.337846	−	0.337846i
$982$	2.55298	−	9.52785i	0.0814688	−	0.304046i
$983$	−10.8690	−	40.5638i	−0.346668	−	1.29378i	−0.890651	−	0.454687i	$-0.849751\pi$
$983$	−10.8690	−	40.5638i	−0.346668	−	1.29378i	0.543983	−	0.839096i	$-0.316916\pi$
$984$	−3.03181	+	5.25125i	−0.0966506	+	0.167404i
$985$	11.3164	+	19.6005i	0.360569	+	0.624524i
$986$	5.52443	−	5.52443i	0.175934	−	0.175934i
$987$	8.73781	−	19.1616i	0.278128	−	0.609920i
$988$	9.54453	+	7.33572i	0.303652	+	0.233380i
$989$	−7.31473	−	12.6695i	−0.232595	−	0.402866i
$990$	0.406199	−	0.108841i	0.0129099	−	0.00345919i
$991$	−28.1761	+	48.8024i	−0.895043	+	1.55026i	−0.0612922	+	0.998120i	$0.519522\pi$
$991$	−28.1761	+	48.8024i	−0.895043	+	1.55026i	−0.833751	+	0.552141i	$0.813811\pi$
$992$	−0.954385	−	1.65304i	−0.0303018	−	0.0524842i
$993$	6.05618	+	6.05618i	0.192187	+	0.192187i
$994$	23.0653	+	19.0226i	0.731588	+	0.603360i
$995$	34.9989	+	34.9989i	1.10954	+	1.10954i
$996$	−0.122516	+	0.457237i	−0.00388208	+	0.0144881i
$997$	4.99140	+	2.88179i	0.158079	+	0.0912671i	0.576953	−	0.816777i	$-0.304242\pi$
$997$	4.99140	+	2.88179i	0.158079	+	0.0912671i	−0.418874	+	0.908045i	$0.637575\pi$
$998$	5.48551	+	3.16706i	0.173641	+	0.100252i
$999$	−6.30977	−	1.69070i	−0.199632	−	0.0534913i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.a.31.10	✓	40
7.5	odd	6		546.2.bz.b.187.5	yes	40
13.8	odd	4		546.2.bz.b.73.5	yes	40
91.47	even	12	inner	546.2.bz.a.229.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.31.10	✓	40	1.1	even	1	trivial
546.2.bz.a.229.10	yes	40	91.47	even	12	inner
546.2.bz.b.73.5	yes	40	13.8	odd	4
546.2.bz.b.187.5	yes	40	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.819823 - 3.05962i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.925986 - 2.47842i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.819823 - 3.05962i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.925986 - 2.47842i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.58378 - 2.74318i) q^{10} +(0.128238 - 0.0343612i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.467804 + 3.57507i) q^{13} +(-0.252972 - 2.63363i) q^{14} +(2.23980 - 2.23980i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.61860 - 2.80350i) q^{17} +(0.258819 + 0.965926i) q^{18} +(0.864122 - 3.22495i) q^{19} +(2.23980 - 2.23980i) q^{20} +(0.437281 - 2.60936i) q^{21} +0.132761 q^{22} +(-1.82480 + 1.05355i) q^{23} +(0.258819 + 0.965926i) q^{24} +(-4.35904 - 2.51669i) q^{25} +(-0.473433 + 3.57433i) q^{26} +1.00000i q^{27} +(0.437281 - 2.60936i) q^{28} +2.41342 q^{29} +(2.74318 - 1.58378i) q^{30} +(-1.84373 + 0.494026i) q^{31} +(0.258819 + 0.965926i) q^{32} +(0.128238 + 0.0343612i) q^{33} +(2.28905 - 2.28905i) q^{34} +(-8.34216 + 0.801303i) q^{35} +1.00000i q^{36} +(-1.69070 + 6.30977i) q^{37} +(1.66935 - 2.89141i) q^{38} +(-1.38241 + 3.33001i) q^{39} +(2.74318 - 1.58378i) q^{40} +(4.28763 + 4.28763i) q^{41} +(1.09773 - 2.40728i) q^{42} +6.94294i q^{43} +(0.128238 + 0.0343612i) q^{44} +(3.05962 - 0.819823i) q^{45} +(-2.03530 + 0.545357i) q^{46} +(7.68863 + 2.06016i) q^{47} +1.00000i q^{48} +(-5.28510 + 4.58996i) q^{49} +(-3.55914 - 3.55914i) q^{50} +(2.80350 - 1.61860i) q^{51} +(-1.38241 + 3.33001i) q^{52} +(-4.30897 + 7.46335i) q^{53} +(-0.258819 + 0.965926i) q^{54} -0.420528i q^{55} +(1.09773 - 2.40728i) q^{56} +(2.36082 - 2.36082i) q^{57} +(2.33118 + 0.624639i) q^{58} +(-1.76347 - 6.58136i) q^{59} +(3.05962 - 0.819823i) q^{60} +(-9.51563 + 5.49385i) q^{61} -1.90877 q^{62} +(1.68338 - 2.04114i) q^{63} +1.00000i q^{64} +(11.3219 + 1.49962i) q^{65} +(0.114975 + 0.0663807i) q^{66} +(-3.29118 - 12.2828i) q^{67} +(2.80350 - 1.61860i) q^{68} -2.10710 q^{69} +(-8.26530 - 1.38511i) q^{70} +(-7.99048 + 7.99048i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(1.62996 + 6.08308i) q^{73} +(-3.26618 + 5.65719i) q^{74} +(-2.51669 - 4.35904i) q^{75} +(2.36082 - 2.36082i) q^{76} +(-0.203908 - 0.286008i) q^{77} +(-2.19717 + 2.85875i) q^{78} +(-6.51047 - 11.2765i) q^{79} +(3.05962 - 0.819823i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.03181 + 5.25125i) q^{82} +(0.334721 + 0.334721i) q^{83} +(1.68338 - 2.04114i) q^{84} +(-7.25067 - 7.25067i) q^{85} +(-1.79696 + 6.70636i) q^{86} +(2.09008 + 1.20671i) q^{87} +(0.114975 + 0.0663807i) q^{88} +(16.6648 + 4.46531i) q^{89} +3.16755 q^{90} +(8.42735 - 4.46988i) q^{91} -2.10710 q^{92} +(-1.84373 - 0.494026i) q^{93} +(6.89344 + 3.97993i) q^{94} +(-9.15868 - 5.28777i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(-4.12633 - 4.12633i) q^{97} +(-6.29298 + 3.06568i) q^{98} +(0.0938764 + 0.0938764i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 + 20 * q^9	\( 40 q - 4 q^{7} + 20 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 32 q^{19} + 4 q^{21} + 8 q^{22} - 24 q^{23} - 48 q^{25} - 8 q^{26} + 4 q^{28} + 24 q^{29} - 4 q^{33} - 16 q^{34} - 8 q^{35} - 8 q^{37} + 16 q^{38} - 4 q^{39} - 8 q^{41} - 4 q^{44} + 44 q^{46} + 20 q^{47} + 16 q^{49} + 32 q^{50} - 12 q^{51} - 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} - 24 q^{59} - 12 q^{61} + 16 q^{62} - 8 q^{63} + 8 q^{65} - 12 q^{68} - 16 q^{69} + 4 q^{70} + 8 q^{71} + 12 q^{73} - 40 q^{74} - 36 q^{75} - 16 q^{76} + 48 q^{77} - 8 q^{78} - 20 q^{81} + 24 q^{83} - 8 q^{84} - 40 q^{85} + 16 q^{86} - 72 q^{87} - 24 q^{89} + 8 q^{91} - 16 q^{92} - 36 q^{94} - 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 + 20 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 32 * q^19 + 4 * q^21 + 8 * q^22 - 24 * q^23 - 48 * q^25 - 8 * q^26 + 4 * q^28 + 24 * q^29 - 4 * q^33 - 16 * q^34 - 8 * q^35 - 8 * q^37 + 16 * q^38 - 4 * q^39 - 8 * q^41 - 4 * q^44 + 44 * q^46 + 20 * q^47 + 16 * q^49 + 32 * q^50 - 12 * q^51 - 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 - 24 * q^59 - 12 * q^61 + 16 * q^62 - 8 * q^63 + 8 * q^65 - 12 * q^68 - 16 * q^69 + 4 * q^70 + 8 * q^71 + 12 * q^73 - 40 * q^74 - 36 * q^75 - 16 * q^76 + 48 * q^77 - 8 * q^78 - 20 * q^81 + 24 * q^83 - 8 * q^84 - 40 * q^85 + 16 * q^86 - 72 * q^87 - 24 * q^89 + 8 * q^91 - 16 * q^92 - 36 * q^94 - 32 * q^98 - 8 * q^99

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